Recorded data and provenance for the associated calculation.
| created_utc | 20261014T173243Z |
|---|
View complete data
{
"created_utc": "20261014T173243Z",
"certificates": [
{
"label": "W",
"depth": 2,
"N": 75,
"dimension": 39,
"precision_bits": 768,
"root_ball_euclidean_radius": "[1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8 +/- 1.68e-239]",
"inverse_frobenius_bound": "[12.736005831130994622564336378031522320185315998712832526489492346558397443982323842847107269615187783643931912262054520192524298579662892742776524374240073498839822181254382665692262884061037053152510699169745261151510439900178729 +/- 1.49e-231]",
"residual_norm_bound": "[1.3914453039183169339738235011952616680250563753516975992436395087906870154901352731577401170909437088508801225292823557195418673623740630622865542152497760892919003848195677004114852814034989664455675322576982472938258329519891805e-12 +/- 8.6e-245]",
"contraction_bound": "[1.1462405286225913152236099799297920699754820245713555178424275189019469692982828857002623079124274405433080039256549339881515492980335716938910365068548907537344517982202052811727950376705000735839025008450223261502527322268553347e-6 +/- 1.72e-237]",
"self_mapping_bound": "[1.7732917909689749384354592461071319732436769139102548662399392734411047577867922425977446480856787373134904393394118146025554225924929990112709777402686121313530416577330594980331786074067356768987819954014042503191578443809473451e-11 +/- 7.37e-242]",
"F_over_D_center": "0.4848243701841249",
"certified_unique_stationary_root_in_ball": true,
"full_angular_hessian_certificate": [
{
"l": 0,
"radial_rank": 38,
"known_eigenvalue_over_F": "1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"remaining_trace_over_D_upper": "[0.028310853333355813683377916280887672680692891716308054689752260011112032738798038479303302331913814933873027343372286875545919878862202805962180500126657025193434943435581477478061375048929491826118599098649775713000140322726731526 +/- 2.07e-232]",
"strict_gap_below_F_third_over_D": "[0.13329726672801915298328875038577899398597377495035861197691440665555463392786862818736336433475285173279363932329437979112074678780446386070448616654000964147323172323108518918860529161773717484054806756801689095366652634393993514 +/- 2.44e-232]"
},
{
"l": 1,
"radial_rank": 38,
"known_eigenvalue_over_F": "[0.33333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333 +/- 3.45e-231]",
"remaining_trace_over_D_upper": "[0.0078929215326828879648008204180010823599426810247327289089494856940002168260673349438498331823650166562962065090213468136590939803005011777900179602889574593691384672204878530024896115926765057765094778600229431913792648830664144436 +/- 2.19e-233]",
"strict_gap_below_F_third_over_D": "[0.15371519852869207870186584624866558430672398564193393775771718097266644984059933172281683348430165001037046015764531985300757268636616548887664870637770920729752819944617881366417705507399016089015718880664372347528740178360025222 +/- 2.42e-231]"
},
{
"l": 2,
"radial_rank": 37,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.042379987817279000054948909599093219843813822634902543188331259867083151960214740843358664069033755927521610947754129665410516188467094911230199815082661696170384309167848387451338315026317031355974133103375319980399205107935240394 +/- 7.07e-233]",
"strict_gap_below_F_third_over_D": "[0.11922813224409596661171775706757344682285284403176412347833540679958351470645192582330800259763291073914505571891253700125615047819957175543646685158400497049628235749881827921532835164034963531069253356329134668626746155873142627 +/- 2.19e-231]"
},
{
"l": 3,
"radial_rank": 37,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.011477522687191130301973428822244936461261895745440740380601284529922510868006602240694991366010489157491461571855565670509844170855365783709159945595316424827060947074539214884869357310726360483224009424363112229363866143313265865 +/- 3.77e-232]",
"strict_gap_below_F_third_over_D": "[0.15013059737418383636469323784442173020540477092122592628606538213674415579866006442597167530065617750917520509481110099615682249581130088295750672107135024183960571959212745178179730935594030618344265724230355443730280052335340080 +/- 1.21e-231]"
},
{
"l": 4,
"radial_rank": 36,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.0049956734048287526686019026919712182584592726436635257560557569558324755143728025771121565448364561900555230418963172706666672505102421090923688149130439180853331525203360749870278216829780952320617216163133295457484108030328157815 +/- 3.55e-234]",
"strict_gap_below_F_third_over_D": "[0.15661244665654621399806476397469544840820739402300314091061090971083419115229386408955451012183021047661114362477034939599999941615642455757429785175362274858133351414633059167963884498368857143460494505035333712091825586363385088 +/- 4.24e-231]"
},
{
"l": 5,
"radial_rank": 36,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.0029545651414224183348249845142190766253009213462403413301882317818304206746943802397198701721266072111655378113536710304285226328296685644265207675918704098845521543040932939850109718250940005257438795228821436313270301799003744542 +/- 1.38e-233]",
"strict_gap_below_F_third_over_D": "[0.15865355491995254833184168215244759004136574532042632533647843488483624599197228642694679649454005945550112885531299563623814403383699810224014589907479625678211451236257337268165569484157266614092278714378452303533963648676629221 +/- 1.67e-231]"
},
{
"l": 6,
"radial_rank": 35,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.0020097385182715218845170325456693729046037553080022062835600540840270895950557201573552311895510762152115417605629170124125784574648253664342020795340456851552097454504990294550222678896479792994377769498053594188465038929840841255 +/- 6.65e-234]",
"strict_gap_below_F_third_over_D": "[0.15959838154310344478214963412099729376206291135866446038310661258263957707161094650931143547711559045145512490610374965425408820920184130023246458713262098151145692121616763721164439877701868736722888971686130724782016277368258254 +/- 2.32e-232]"
},
{
"l": 7,
"radial_rank": 35,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.0014640474355950906418867822332557238113924356731993956911101927823784384197633987197456481856386731650577919264445186881313670658923263027907796503922342034317517229443455313728519594143197692963497686487563469333092768934176638470 +/- 1.83e-233]",
"strict_gap_below_F_third_over_D": "[0.16014407262577987602477988443341094285527423099346727097555647388428822824690326794692101848102799350160887474022214797853529960077434036387588701627443246323491494372232113529381470725234689737031689801791031973335738977324900282 +/- 1.24e-231]"
},
{
"l": 8,
"radial_rank": 34,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.0011187645958417064167339777750876193905240666839151591479273045250919334586984420185037803159676616897597255377782292122849077973599861350542572965124770106888967915555044169253286419329326391695341878027183727696420276813379956267 +/- 1.29e-233]",
"strict_gap_below_F_third_over_D": "[0.16048935546553326024993268889157904727614259998275150751873936214157473320796822464816288635069900497690694112888843745438175886930668053161240937015418965597776987511116224974133802473373402749713247886394829389702463898532867104 +/- 9.16e-232]"
},
{
"l": 9,
"radial_rank": 34,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00088539778207638387975235499068774598551407574473693748202103294809763428784213802483842522970058966734332218872411039568492132527608345525152004787153956562627376056665000759862390962460871379893312823643916195498784370765235265803 +/- 2.75e-234]",
"strict_gap_below_F_third_over_D": "[0.16072272227929858278691431167597892068115259092192972918464563371856903237882452864182824143696607699932334447794255627098174534139058321141514661879512710104039290610001665906804275704205795286773353843022750471167882295901431401 +/- 2.21e-231]"
},
{
"l": 10,
"radial_rank": 33,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00071885739346605209377317692291195885629050744271816155746116763914327616676618682812736422394919115623841376701615070292445589300725460751199220250527617252334699899398437749568717669664357483311729443196566616193752534989279891632 +/- 1.81e-235]",
"strict_gap_below_F_third_over_D": "[0.16088926266790891457289348974375470781037615922394850510920549902752339049990047983853930244271747551042825289965051596374221077365941205915467446416139049414331966767268228917097948997002309183354937223470100050472914131677386775 +/- 5.23e-232]"
},
{
"l": 11,
"radial_rank": 33,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00059722122375441625793398945252815004490436764702653541785195989714686686296061806977608733487124894903286604570176355085517551687182219873006342466873673180163607401022256192449953048286062252035441513275602062638449264708720382432 +/- 1.02e-234]",
"strict_gap_below_F_third_over_D": "[0.16101089883762055040873267721413851662176229901964013124881470676951979980370604859689057933179541771763380062096490311581149114979484446793660324199792993486503059265644410474216713618380604414631225153391064604028217401957946284 +/- 1.49e-231]"
},
{
"l": 12,
"radial_rank": 32,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00050370965199641216884657469210305825023359925093572848053943287471506669078048898488654191642120456975532619162189066342628053942901349064507940514839515538578421728089831093853897318087698225098607802233013379501501670193314313418 +/- 2.77e-234]",
"strict_gap_below_F_third_over_D": "[0.16110441040937855449782009197456360841643306741573093818612723379195159997588617768178012475024546209691134047504477600324038612723765317602158726151827151128088244938576835572812769348578968441568058864433653287165164996473352353 +/- 1.69e-231]"
},
{
"l": 13,
"radial_rank": 32,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00043220991105457057327297376954476413387108933788904658928393456263917667228194512841725367936962712143160123870522143357921471664916355126919479977852794492741718008899776288458806957542534271544195138083723277909779865544564075859 +/- 2.44e-234]",
"strict_gap_below_F_third_over_D": "[0.16117591015032039609339369289712190253279557732877762007738273210402748999438472153824941298729703954523506542796144523308745195001750311539747186688813872173924948657766890378207859709124132395122471528582943388756886801122102591 +/- 2.75e-231]"
},
{
"l": 14,
"radial_rank": 31,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00037416392731487448519109985060619480371502734718690971376686908834238423050445556340162939716193301553321274475670675803713233025975871083685105217116453809127661436906080112968657207544773166333478693796982674296470291477927572891 +/- 3.96e-234]",
"strict_gap_below_F_third_over_D": "[0.16123395613406009218147556681606047186295163931947975695289979757832428243616221110326503726950473365113345392190995990862953433640690795582981561449550212857539005229760586553698009459121893500333187972869683992370196375188739094 +/- 3.18e-231]"
},
{
"l": 15,
"radial_rank": 31,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00032855286032736657046205139169977950421445977693951616059947256469606616261426062983138537499948452796521823527570697371580808294200313120919256393551012059454027892117599225036621573156046284701311119033086939877577663733961603984 +/- 3.37e-235]",
"strict_gap_below_F_third_over_D": "[0.16127956720104760009620461527496688716245220688972715050606719410197060050405240603683528129166718213870144843139095969295085858372466353545747410273115654607212638774549067441630045093510620381965355547633579726789089002932705063 +/- 4.11e-231]"
},
{
"l": 16,
"radial_rank": 30,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00028982617145183631212145009028906483218966218405409688558438128875860570258296661807175364211419065433724732037424291495478190912221572005506803857204050762258854517412094470243570645105650001225853630720660055557339969058925865218 +/- 4.42e-234]",
"strict_gap_below_F_third_over_D": "[0.16131829388992313035454521657637760183447700448261256978108228537790806096408370004859491302455247601232941934629242375171188475754445094661159862809462615904407812149254572196423096021561016665440813035946006611109326697607740801 +/- 3.65e-231]"
},
{
"l": 17,
"radial_rank": 30,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00025895014522764224683141063096900870586928154404434024571044139142288880442893598038799894475830280143083283946466065409660647415632385426044372262103340183118532263487866313335260769819650381489534267214815867880726467583278558576 +/- 3.93e-234]",
"strict_gap_below_F_third_over_D": "[0.16134916991614732441983525603569765796079738512262232642095622527524377786223773068627866772190836386523583382720200601257006019251034281240622294404563326483548134403178800353331405896847016285177132399451850798785940199083388108 +/- 2.65e-233]"
},
{
"l": 18,
"radial_rank": 29,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00023165480077509919892414439527521250301692642422282673313668746354668695863272220018711039275681148989958151005621178615093374570756169907397098661602405598086367199846215274075884634187831871819066349647140252033180097025895249940 +/- 2.83e-234]",
"strict_gap_below_F_third_over_D": "[0.16137646526059986746774252227139145416364974024244383993352997920311997970803394446647955627390985517676708515661045488051573292095910496759269568005064261068580299466820451392590782032478834794847600317019526414633486569640771417 +/- 3.57e-231]"
},
{
"l": 19,
"radial_rank": 29,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00020979116534630035354309031760561011791172928661574812745416729858638489212140355305048018395556595797661394388890824716866500797190712068327946404134709242165854407065801676584649502852453989815524398526783946383427189185099412067 +/- 1.58e-234]",
"strict_gap_below_F_third_over_D": "[0.16139832889602866631312357634906105654875493738005091853921249936808028177454526311361618648271110070869005272277775841949800165869475954598338720262531957424500812259600864990082017163814212676851142268139882720283239477481567255 +/- 4.82e-231]"
},
{
"l": 20,
"radial_rank": 28,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00018969750239858175076921150838862134039309429491560700683160730979923887737557809665098244808418509609500081446546673279829190542596162353115463313394899414433636195906498762227277894250756618130094326709430719563111344441445704281 +/- 4.37e-234]",
"strict_gap_below_F_third_over_D": "[0.16141842255897638491589745515827804532627357237175105965983505935686742778929108857001568421858248157057166585220119993386837476124070504313551203353271767252233030470760167904439388772415910048536572339957235947103555322225220962 +/- 3.05e-231]"
},
{
"l": 21,
"radial_rank": 28,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00017366079208780596012271860185306022591714103614444207785137411623829696683069250748220733585058282637040127606786303567737766132584811797651590752474823702602522831951822366737965343860689648030374516310368371112834743195043869495 +/- 1.86e-234]",
"strict_gap_below_F_third_over_D": "[0.16143445926928716070654394806481360644074952563052222458881529255042836969983597415918445933081608384029626539059880363098928900534081854869015075914191842964064143834714844299928701322805977018636292150356298295553831923471622797 +/- 8.53e-232]"
},
{
"l": 22,
"radial_rank": 27,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00015833335500516078243462882717544419035298336980570791451532337355727133441874669944582280599163927770440074268758340564581056590439288670970422840680010884360741660159752916873577976482768061704112066311385988105584583499605477093 +/- 1.74e-234]",
"strict_gap_below_F_third_over_D": "[0.16144978670636980588423203783949122247631368329686095875215134329310939533224791996722084386067502738896226592397908326102085610076227377995696243825986655782305925006506913749793088690183898604962554600355280678561082083167061189 +/- 4.94e-231]"
},
{
"l": 23,
"radial_rank": 27,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00014623436963264650616297766923608214199418740799047015991316532820672353668497117047526436666619065826662196779354890891516643348356994254327088500694550475667861670180188409200199627204229945852377445323669981811414497436133130278 +/- 1.37e-234]",
"strict_gap_below_F_third_over_D": "[0.16146188569174232016050368899743058452467247925867619650675350133845994312998169549619140230000047600840004469887311775775150023318309672412339578165972116190998804996486478257466467039462436720814289221342996684855252169230533536 +/- 2.99e-231]"
},
{
"l": 24,
"radial_rank": 26,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00013418944263640484025040199522823637987907143725982345745917657363759289009135416590644254122024995779283647503996841409446625908695155855604147578079402378481170118442490223122225334397130733829434185162540868338980533891944055739 +/- 3.80e-234]",
"strict_gap_below_F_third_over_D": "[0.16147393061873856182641626467143843028678759522940684320920749009302907377657531250076022412544641670887383019162669825257220040757971510811062519088587264288185496548224176443544441332269535932837232481504125798327686132774722611 +/- 1.65e-231]"
},
{
"l": 25,
"radial_rank": 26,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00012484933584634900297526960236918199773628930238051983360833117749979545788783461923627011718689056096372833150712224555546119139945518690660086344597641431418460634534680870285743109251780552402693412173234756761046466153490072425 +/- 3.18e-234]",
"strict_gap_below_F_third_over_D": "[0.16148327072552861766369139706429748466893037736428614683305833548916687120877883204743039654947977610570293833515954442111120547526721147976006580322069025235248206032131985796380923557414886114263973254493431909905620200513176594 +/- 1.53e-231]"
},
{
"l": 26,
"radial_rank": 25,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00011514060366245810209996888235153777676157108157149309273193061569204438463123806617427053727672370316281080434142385686973086453746890726736961312442152812356652337533139820738210368562244229154995560910908118394467939086957319960 +/- 4.99e-234]",
"strict_gap_below_F_third_over_D": "[0.16149297945771250856456669778431512888990509558509517357393473605097462228203542860049239612938994296350385586232524280979693580212919775939929705354224513854310014329133526845928456298104422437511671105755758548272198727579709347 +/- 3.75e-231]"
},
{
"l": 27,
"radial_rank": 25,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00010779244000018917220070573749601410907554935843956848638301936759040747371679234893393247782291706480284562808640279730852558601824379282293688235625940148584364695172803842435391158574628585014368973133209866661472636244100111040 +/- 1.20e-234]",
"strict_gap_below_F_third_over_D": "[0.16150032762137477749446596092917065255759111730822709818028364729907625919294987431773273418884374960186382103858026386935814108064842287384372978431040726518082301971493862824231275508092038081652297693533456800005194030422566556 +/- 4.60e-231]"
},
{
"l": 28,
"radial_rank": 24,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[9.9792931299630302941401428119644370395860676853728771457687031476979677384568756648459926182899328043541472484241398891186617523745165140524942865494567851537039655883819700958684321936229068490992943511861165184948812850047426463e-5 +/- 3.28e-235]",
"strict_gap_below_F_third_over_D": "[0.16150832713007533636372526523854702229627080598981293789520897963518968698928209791001820674048376733862312519418242526777548004914292150152614172380117209881512962701078284696570798234473043759817567372315480550148171785381661924 +/- 6.56e-232]"
},
{
"l": 29,
"radial_rank": 24,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[9.3920030464982365481458477201100005650199651271996124274329673202697388467976203343310929167335256033335350280943732017751652118477821374500445944106471216603377673621157865368498382733847845986080038916193686476352361887633840861e-5 +/- 4.65e-235]",
"strict_gap_below_F_third_over_D": "[0.16151420003090998430118520818946556666101646701539467054239233699346396927819869046332335573749933141063333131638572293464891501454818884529216622072256019545006328899304550880129816828393281882068058662775047298019031430477903282 +/- 4.93e-231]"
},
{
"l": 30,
"radial_rank": 23,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[8.7200796829336164974597822853686247968024399317932732616508337264933837381448227012220457834581398800039578213165446195450268325308192874976930764994163219557414736678408379329590088663217561666510651369838977220611185891788811038e-5 +/- 2.75e-235]",
"strict_gap_below_F_third_over_D": "[0.16152091926454563050169206884381298041869864226734873393405015832940173282928521843965444620883208526786662708845350122047121639834135847379168973590167250344710925192998825828733707657800344910500015601529682768944605548077487785 +/- 4.77e-231]"
},
{
"l": 31,
"radial_rank": 23,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[8.2444594647630720434138444787483559592818286010168436167390854589473039959337807537664362943438733882621550189968997098040641753062364627447615596145760539336986898255385440763382476715720275781667146772973507571653839963655488199e-5 +/- 3.22e-235]",
"strict_gap_below_F_third_over_D": "[0.16152567546672733594623252822187918310707384838065649823049927581207719362670732885912900230372322793278404511647669766956862602491360430203921905107052090612732967976841128122590328418995094639088499951989369315909501282670301118 +/- 2.43e-231]"
},
{
"l": 32,
"radial_rank": 22,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[7.6703992582549980610580444705662186182230693907861384472816795823807560537248796678122902624170547131929030481432935199814053631941300952622638098520714205229022729647804476919446187978265020985031540207654245160855529816517292847e-5 +/- 3.88e-236]",
"strict_gap_below_F_third_over_D": "[0.16153141606879241668605608622196100448048443597275880528219384987084285910612941786998854376404249611953473763618523373146685261303472536571404402856814595246143764393701886218974722047868840164568163512645901242150581113685014937 +/- 2.90e-231]"
},
{
"l": 33,
"radial_rank": 22,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[7.2809219526097950285566578928416601842671389521179366286502125097903389408764715135858225659609889628832978532108118858022531795621057350460940317005841375795513760258310136998278617413776673617959215644976137739207274761347298054e-5 +/- 3.72e-235]",
"strict_gap_below_F_third_over_D": "[0.16153531084184886871638110008773825006482399527714548730038016454156876327725790195153080844100705677703783368813455854780864413487104560931620572634966082529087115290640835652966838804925288999304870745102169052892745939190531937 +/- 2.19e-231]"
},
{
"l": 34,
"radial_rank": 21,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[6.7830023223059349851303467717126484560071913927577347836407311203652265179532094162942380526002538458483534644317843477761452102727882939576931902042097362722339575608127102125036705469375149174535871752180483068778614679188778145e-5 +/- 8.46e-236]",
"strict_gap_below_F_third_over_D": "[0.16154029003815190731681536319894954018210659475273908931883025935546301440148713457250372428614066412820818313202234882318890521456393878372708973476462456930394432709105853956454162996119729151749213079491448618359788805198747789 +/- 2.36e-231]"
},
{
"l": 35,
"radial_rank": 21,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[6.4610865383195411976841622834075284160595934593244641245045715175303498850698182392654740381689081214341318399327041700551232123742012911607730234143417127994338103611966521977078282745286706075593729732060842945344560063143285526e-5 +/- 1.10e-235]",
"strict_gap_below_F_third_over_D": "[0.16154350919599177125468982504383259138250607073207342202542162095149136316781596848427401192628497758545232534826733962496611543454292465375505893643252324953867232856305470014468958838392137996059107293693460582372132210660352338 +/- 1.95e-232]"
},
{
"l": 36,
"radial_rank": 20,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[6.0233354521340567689659986311934975300720127867642442958282283821765067877598711090058364169210381834514995262348437736789635550179415272984017792501993952852334459176743240020028188729349547481253578108699332738680932916701626668e-5 +/- 3.08e-235]",
"strict_gap_below_F_third_over_D": "[0.16154788670685362609897700668035473169136594653879902422370838438284490159878906795557660830249745628483215167140431822892987703111648725139368264887416467271381433220748992342664663847793731711918541308855796733392798573374996504 +/- 7.99e-232]"
},
{
"l": 37,
"radial_rank": 20,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[5.7551890736338626099087436184291029287927932275924713510019554176441011974413642523165713177219012884418979272032547258754173292824160351213604231665084813032872758917459038748875582552021219414303223895087425035459783103538426370e-5 +/- 1.74e-235]",
"strict_gap_below_F_third_over_D": "[0.16155056817063862804056757923048237563737873873439074195315664711249022565469225302414350095348944765378224768739463411940791249337384250631545306243500158185363379390774920762791779108411464544725236344277157924163120688356312824 +/- 6.06e-232]"
},
{
"l": 38,
"radial_rank": 19,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[5.3656453230744166275427103660639448953192940198539125969886517681311588315238770049299486175163125590109729500755790506426420014153787037245760488538084495731063939013281988582345546462900004492348643602268407105030700789243683568e-5 +/- 3.73e-235]",
"strict_gap_below_F_third_over_D": "[0.16155446360814422250039123956300602721771347372646812754069678014898535507835142789661736718049150354107655693716591087616024024665251287962942090617812858217093560272765338467808432112020376666217431802306439825956163596587742298 +/- 2.29e-231]"
},
{
"l": 39,
"radial_rank": 19,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[5.1408526814066750070238059729053079844135338167524788724343441390837979231313586521989103348184016881722237351084986954314817462475907235310026547050298727980053371692407861556521900914282963815862403532313995757850970439990490221e-5 +/- 2.27e-235]",
"strict_gap_below_F_third_over_D": "[0.16155671153456089991659642860693761358682253132849914187794232322527582868743535308014467756331848264978494442931558167971235184920419075943135664011961636793868661329497425880511014476575238370285080426313435267090881569622667618 +/- 4.42e-231]"
},
{
"l": 40,
"radial_rank": 18,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.7904114658804988211816588412908488370615304268177825218588405048981099440667505109514485399694144745937261431625370001141132438236877598534793434897943967447797660206421817349683769637331720298357378357767972112203254608031419192e-5 +/- 4.24e-235]",
"strict_gap_below_F_third_over_D": "[0.16156021594671616167845485007825375817829605136239848884144807826161768556722599916155715218126697252192072940523504129666552553422842978906813187323176872269921886900646024484931698289702933494636830928830889869455446341205863525 +/- 3.38e-231]"
},
{
"l": 41,
"radial_rank": 18,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.6009845996328878506395785698806025154372287895918769599141332457378152820013288622708870856443271786807623733887625120903147110876460557085307991952679059767892075832778969410214435085905078309036076012590954880183065214017915227e-5 +/- 3.22e-235]",
"strict_gap_below_F_third_over_D": "[0.16156211021537863778816027088096786064151229437877074789706752533420928851384665337804395779581022339487985904293277904154576351955579020610958135867471398760689877459083388769725645223158076158835763059065407571178648360145264875 +/- 5.35e-232]"
},
{
"l": 42,
"radial_rank": 17,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.2826135487784067988637469085541274327141034329273955395967916410982936495625900862745364503898420557662934232198190319770721526748125276331786100015158829365667910914089726291106949593129102266923575263756303447832232567590050634e-5 +/- 4.72e-236]",
"strict_gap_below_F_third_over_D": "[0.16156529392588718259867802919758112539233952563233739271127069875025568373017104076580392130216276824610900373243446847634689594513991854139033488056665150783730099875575257694037555971707353756439974309140291036321883443409907662 +/- 4.84e-231]"
},
{
"l": 43,
"radial_rank": 17,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.1223410214653720634077178455875245044167883817900808716911905826583015488050551642063377638141463093654353326033543151387892447177777341460377152961890655108978988314177467510876021337464637183643742190758893719593142677429780333e-5 +/- 3.93e-235]",
"strict_gap_below_F_third_over_D": "[0.16156689665116031294603258948821079142162249878284876585794975476084008365117861611502460328902852520357301231334063312351527877421948888932520628951370477601155768767835248919915579064532920202948302292447590777294707352398923689 +/- 4.58e-231]"
},
{
"l": 44,
"radial_rank": 16,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.8305366626264011852502407147403562407470321375099702480046810472932841363244440640886759339556371451810511628020140665443831179306925698764627706618070956967722611993019279605022437000619282177215800707929631384706287306892010475e-5 +/- 2.93e-235]",
"strict_gap_below_F_third_over_D": "[0.16156981469474870265481416425951926310425919634529156696418661985619373382530342222602577990732711029521485615503864652600122283548735974096790203896004859570969894405467364738706164422966604738448945086595873703528196037935977466 +/- 4.63e-231]"
},
{
"l": 45,
"radial_rank": 16,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.6945277742249638065188783942272954776630802645671860683978144263194049462373924275592519010366415558752232409483595996693511788354697176750366577842451796856505232834525171939348252194695684358494058169845985774389814185405178403e-5 +/- 2.07e-236]",
"strict_gap_below_F_third_over_D": "[0.16157117478363271702860147788272439371189003586402099480598268852240347261720429274239107414765630025110791443425718307066997315487831196948991630008882421486981016143383214149472731841447197098230817260849682068089227685248126149 +/- 2.64e-231]"
},
{
"l": 46,
"radial_rank": 15,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.4249316351471190242363904218408467564339625904232879328524654739308094566461357168381352933818927019449118137733377308005361086989224201954652264154267612025424961341557110372977159556375762928102833239658091526461232267501729452e-5 +/- 4.54e-235]",
"strict_gap_below_F_third_over_D": "[0.16157387074502349547642430276244825819910232704076243378733814201192735857210020530949828531373284773964721754852893328935866130557967744246471201440251239905464124170532510955629368950711029090373856383342700857514020543439916494 +/- 3.65e-231]"
},
{
"l": 47,
"radial_rank": 15,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.3092917183380966612812150889880101186199522048184673620369428056356692626280739178849898522028305238241932427651229043748147971980555660849764602045293897925883736613212615187444521203069276930221395971171922765350809531686552213e-5 +/- 3.34e-235]",
"strict_gap_below_F_third_over_D": "[0.16157502714419158570005385451577678656548046714461848199304629723861030997404038592748781676814463836142842473423901543762291851869468611100581690206462137276874078293005345405147922214546359738973644527069549474390131585713498011 +/- 3.56e-231]"
},
{
"l": 48,
"radial_rank": 14,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.0584145912027787769663541588563475277095043093950413510382582731631642594819310447571337822116467815406289222217467969285639961065953496906545106693139923784012834163402036798878489978557178394259295549425719752828860017799798055e-5 +/- 4.05e-235]",
"strict_gap_below_F_third_over_D": "[0.16157753591546293887889700312507810319138957162357271625315628408393503502407184735621909532884455019885126037744444919869738102670560071316976012155997352674288265383250326462986778817668810948827240737111724094691383780664886687 +/- 2.31e-231]"
},
{
"l": 49,
"radial_rank": 14,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.9600099654043715448120077363017769084284569032764625338313819690052994842024105379254903862013405667388334604606147525234945880440910616943876839317131519292147009931337544618414421825807350266463295957123626116338970438928148455e-5 +/- 4.70e-235]",
"strict_gap_below_F_third_over_D": "[0.16157851996172092295121854658930364889758238209763390204132835284697661367182464256128741176280465326099927833206206051914143172078622575604972278982734953514737451965673532912204825224484085931640020337070954304055032769622773852 +/- 2.65e-231]"
},
{
"l": 50,
"radial_rank": 13,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.7250308168396618236190952201062291009408386557956057795499735515391250283865980133015448252958903149300360892432493826216500966171357716435317337110957060542018293289074127441699442121687571226868801339449035382161918314820160452e-5 +/- 2.30e-236]",
"strict_gap_below_F_third_over_D": "[0.16158086975320657004843047571446560437565725828010871060887116693115127541638280068653365121841370776351736630577423417284045016570049530895023134932955570960612464837337759253922496722454497909543979786532721763128450474835184651 +/- 4.74e-231]"
},
{
"l": 51,
"radial_rank": 13,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.6413161502127580290875153866853590906830335711375577138981132883746878948184757602651694190318436015502978949629601715821091105412893671541488920818921433403653224481331283555041347330507575810338872733464547918634611240763418426e-5 +/- 3.91e-235]",
"strict_gap_below_F_third_over_D": "[0.16158170689987283908637579151279981307575983633095529108952768553378291978771848190906401497247634823065116368771703706495084557556125377299512517774584774523326301344218533538311162531933615909085632779393320211874803205542590325 +/- 2.66e-231]"
},
{
"l": 52,
"radial_rank": 12,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.4199334164146170834032584652443070116670410496872576644225574655440346995979499991778363029435113879155468037333288518944493250907102461699661146187330611240385086876282798132243843079516884864163857416414906513374415418984075966e-5 +/- 2.85e-235]",
"strict_gap_below_F_third_over_D": "[0.16158392072721082049583263408201422359654999625616979409002244109201122631967068716667488830363723155278751119862933337814772217341575956420496700552047933605542628157979038386853442282358714978180250280925025176015329225124768259 +/- 1.36e-232]"
},
{
"l": 53,
"radial_rank": 12,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.3488232280391089676858952953155913732547623750594449464095817313509496346566316370387741007995188842111792871802618521323198044134240147031856915004006503673405405796336159357366661438661839660349128600047580545569154233074950579e-5 +/- 3.54e-236]",
"strict_gap_below_F_third_over_D": "[0.16158463182909457557698980771371351075293411904291607221720257084935315717032010035029627892565867147782455487379486404814534346862253242651963480975166266016299326126087033050730930000522800482700631753806661908612109751243359172 +/- 4.76e-231]"
},
{
"l": 54,
"radial_rank": 11,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.1391434390037449894823251538360102414613200987262653943313313665509318811161989325809457828053808885487441159590422216526990390918365683464434663565006575996433031176431787765739276802154740868504609680356442226363210429902462454e-5 +/- 4.89e-235]",
"strict_gap_below_F_third_over_D": "[0.16158672862698492921677184341512830656425205346567940401272335335300115734785550467734085720883861285778117922550707624445013967627574830098320223200310166009067023363549023487890092738986451192579816205698631022444030345623676420 +/- 3.28e-231]"
},
{
"l": 55,
"radial_rank": 11,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.0789152808530083960472396952139500835521248346601594878637003915333500081876503307947229566245931583714078491179573478852937983235174347726496994294777455811898931550086098384309965789357683350212847055264508839741422515972635352e-5 +/- 3.61e-235]",
"strict_gap_below_F_third_over_D": "[0.16158733090856643658270619426971452716583114541832006507178802966275133316658479016335871943710042073508295258817548709318781372868343149231894016967237188921085476773511658056828235670087730898331645381961140215782692524415069403 +/- 4.52e-232]"
},
{
"l": 56,
"radial_rank": 10,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.8793686605147122992591055088554605976694963166835641544102881011156233508457654582525643220061954887246794351700152738048769782353442297112634937220827240366735004957274516179382888078945778695756958753884741713755674539340909200e-5 +/- 1.60e-235]",
"strict_gap_below_F_third_over_D": "[0.16158932637476981954367407561157811206068997170349983102512256378565551043315820901208414102344660471177941987231496651392861789688431322436955403172944583942629993166170939215048728377858772088797090970791278192495291099212732576 +/- 3.41e-231]"
},
{
"l": 57,
"radial_rank": 10,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.8285893440768758350410775254641506393802422303090782967900278568293851213423126396277011528586551667079325228393127692336761436178316967799513465353224733943449022715805724830973629817138568769823134069240752226153589968630909129e-5 +/- 2.77e-235]",
"strict_gap_below_F_third_over_D": "[0.16158983416793419790831625589141202516027286424436357588369876638809837281545324354027038965513808011499958734143827353897432990523048834969886715320131344193272321764395086094183569303684952809789684353259742591444051307669803576 +/- 3.30e-231]"
},
{
"l": 58,
"radial_rank": 9,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.6378651578262546316733149664375133017506587002343750932555375352196463899922596865325697523391842899675582333997506263928246964524249776579624315217212110345174313923965959766817738980282248186499015398990693231025175654992891591e-5 +/- 2.73e-235]",
"strict_gap_below_F_third_over_D": "[0.16159174140979670412034993351700229153364916007966432291573411129131447020276674406980134096914327482376699108433266916040273841970214241689008704235144945455632149235274270070689984892768638441848016765126767597343564149101167377 +/- 4.22e-231]"
},
{
"l": 59,
"radial_rank": 9,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.5953339530980704720722009249429911278219748457710766982759174908776073299901335244945719849549919256157445984460788576462197691671177842537612904363178262348111935364604541206939381347805639696634778572557818999843005684841448250e-5 +/- 4.73e-235]",
"strict_gap_below_F_third_over_D": "[0.16159216672184398596194594465741723675538844691820895589968390749175789059336676533142172094681711674741050922068220587809020446897499548882412905376230348840431855473130206212545972728531886102697003188809410884766682366098182522 +/- 2.53e-231]"
},
{
"l": 60,
"radial_rank": 8,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.4123304844953050753191662192959652490119152201636969493154553428598695976801647986306669175265771169433812981454822264232036806349741915333229792996575413225090622310058745658904579120635724255685486718364559813925551216882256364e-5 +/- 3.60e-235]",
"strict_gap_below_F_third_over_D": "[0.16159399675653001361591347500447370701417654751446502969717351211323806797068986501868035999749140089549723285368521184440243462986031692475133343687367009125344157604435660792100776208754603094241098117994830210685274111544978441 +/- 5.95e-232]"
},
{
"l": 61,
"radial_rank": 8,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.3770349633410146457526664960932466330629162334187851521913092179679394225917165077654383700036028635053261571993009933689632294759206754706960388763874033389872509092199687964220315051711990736832883084406296455001569894693833793e-5 +/- 4.74e-235]",
"strict_gap_below_F_third_over_D": "[0.16159434971174155652020914000170573420033603750433247881514475357448698727244074950158901228296663063803161340509467365673297703437190745991195970627790279263327679415757446697870244635161495467592983378358226037021166509677197283 +/- 2.07e-231]"
},
{
"l": 62,
"radial_rank": 7,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.2008204487658868480213480268081845346925158076149576578809437478755753268169360356493282547329828426273564014270074681205796617079103713530865435135465686945133199277400100466347535170730344816683402637157459824809851651229396415e-5 +/- 1.35e-235]",
"strict_gap_below_F_third_over_D": "[0.16159611185688730779818645318639858482131974150859051709008785722918791091339849730631017338411933683824039310265239659198546087004958756295313580123153120097972153346738926656620031913149593632184998326402950920684185681501543727 +/- 5.57e-232]"
},
{
"l": 63,
"radial_rank": 7,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.1719018490999185514549328510165527108481856036973600786017183647237061264478458323089984815774448667682354042609744913876641270010743177078778379206816719819750075136550092025015211926258265749402946228717029864891506232870000487e-5 +/- 1.90e-235]",
"strict_gap_below_F_third_over_D": "[0.16159640104288396748115211733815650113955818481062969306588064948301942960540218820834357668185089221799898431262405692175279002539665592348958788828745984994684691659153011657464165145474040840091726372043794963680177516043379667 +/- 4.62e-231]"
},
{
"l": 64,
"radial_rank": 6,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.0016837050879262122642470774891691000816332675080426750148046225433627055955315689507902294475164639074125609092059584317502054612984577291740664255025205931679481361825688708469592459093786138259215234428524987270721449479890998e-5 +/- 2.58e-235]",
"strict_gap_below_F_third_over_D": "[0.16159810322432408740454402419589177497566585033399158623991651862044123303961071135097715876437219150202759254105757460708234916461205368208937492600241164146073498718530484097795819707420757288052840745143223814167939594521718677 +/- 4.80e-231]"
},
{
"l": 65,
"radial_rank": 6,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[9.7840953531315100908219845058418024939637167610935423978571678672273860126570882505745767832507548338652679609517241367833952473276177590287121368322478328022765916974458742247941566341788435135714689510911362870276034625623558742e-6 +/- 1.93e-236]",
"strict_gap_below_F_third_over_D": "[0.16159833596602183515657584468216082486417270294990557312426880949879943928065400957841609208988341591183280139870571494252988327141933904890763795452983441883386439007496922079244187251003248782315309519771557553037963906320410431 +/- 5.92e-233]"
},
{
"l": 66,
"radial_rank": 5,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[8.1350992189566083284987981892958304286882970119637840267425588153477422134726779252215451655947956202837276128324178800117004923514056596938057703564896250102875890275294462368939975646751327474570921234790730188011509905224311362e-6 +/- 4.16e-236]",
"strict_gap_below_F_third_over_D": "[0.16159998496215601005833816786847737083623797836965470288263992410785131892445319398874144512150107187104638293905383424878665496617431526100697286089631017704165637907763913722042977266910199153391920957454318759364786551567614423 +/- 4.64e-231]"
},
{
"l": 67,
"radial_rank": 5,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[7.9525212242031759525273902903034957078368046713256680070281893064030500052073469112767567766295232599476095831742162214716319320640401609300085766091682075141871665850703026070848016166101634049882179957298903962359465604828148010e-6 +/- 2.69e-236]",
"strict_gap_below_F_third_over_D": "[0.16160016754015076349071413927637636317095882986199534099865963847736026361666145931975538990989003714340671905708349245044519503473460262650573665809005749845915247950008159636405958186505005650326167844867093677627043072010618385 +/- 1.03e-231]"
},
{
"l": 68,
"radial_rank": 4,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[6.3508839091296487014753397110827032590125761374310371013560946365561933163406315301230163702583553113437135798535445476277513192468187197253275134888712823037675120157289167731554900922444806571514851857434050128381761010494556162e-6 +/- 2.15e-236]",
"strict_gap_below_F_third_over_D": "[0.16160176917746583701796519132695558396340765409052923562956531057203011047335032603513654365029640831135532295308681312211903891534741984794694133915317779538436289915465093774989351117657442218600951518148092326165382849056561721 +/- 2.12e-232]"
},
{
"l": 69,
"radial_rank": 4,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[6.2130579788352645016106163301593651387981151480062423642022197306801015816497426689578903523694678478003547868674519672644436526325785143496004966252379890467740349166724303041266636536008929458275453712054089673161612602548448399e-6 +/- 1.36e-237]",
"strict_gap_below_F_third_over_D": "[0.16160190700339613140216505605033650730152786855151866042430246444693598656508501692399770877631429719881886631187979921469940222301403408815231706617004142867761989263174999423636254000301306577372083912129546125769935050540641182 +/- 1.02e-231]"
},
{
"l": 70,
"radial_rank": 3,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.6537473573864398721726833645937973081797339736961516298141737351670710216185290161619646656552703346126131481409112074514623702917523245149220757325000155440507347576915570981269018335827356680577432888808944224133406255020795688e-6 +/- 1.58e-236]",
"strict_gap_below_F_third_over_D": "[0.16160346631401758022679449398330207286935848693269297051503685249293149959564504813765050470200101139633205405351852575545921520429637491434215174459093416665112261593190897510956853976483308393099860892337778577224425332604116459 +/- 3.79e-231]"
},
{
"l": 71,
"radial_rank": 3,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.5559890257640349183055226306927724947276104747718644169528240974271188795950024917562391126341480791812728843699916751966379126279263137118451817901585663303560368827921972507514357538976352910088451562460442202360224594918797828e-6 +/- 3.09e-236]",
"strict_gap_below_F_third_over_D": "[0.16160356407234920263174836114403597389417193905619189480224971384256923954778707166417491042755403251858748539378229667499147002875403874035295482148487650810033631062978387446941591523091276903137565782151042062244643064420717479 +/- 4.01e-231]"
},
{
"l": 72,
"radial_rank": 2,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.0346395324438368259395064326670535121916888041121408064588288400465353946751785275814478303794772298293667644195398419176071080990352800406630381435880588881474343521663186607726860371003846499551579042682917800845929577193815890e-6 +/- 2.76e-236]",
"strict_gap_below_F_third_over_D": "[0.16160508542184252282984072716023399961315447497786255452586020783782662013127199148813908521883628718943683729990224712682474905955856763138662600362852307860777851923231450034800589398062956628201671150876239837488658207370894728 +/- 4.23e-231]"
},
{
"l": 73,
"radial_rank": 2,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.9728761289944040800749988400158233504323900132953852542245535320864263450488579696571098267522716826181037868470631893986119280064888286819050900579129383130700106843755793121366328157224295799393187226507682254596829607653547171e-6 +/- 1.65e-236]",
"strict_gap_below_F_third_over_D": "[0.16160514718524597226258659166782665084331623427665337128141244211313458024032161780869700955683991439498404856287981960347726805473866017783798476157660875372835359665598229108735453003385094423708672734794401589844120698370590131 +/- 1.06e-231]"
},
{
"l": 74,
"radial_rank": 1,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.4856844387604090105004841213679075926971423451517969057429312637575771099400151400675640244954724506025804392844691736538220918183446586578877319863338822731453471647328599412511816434664004756578935963437310214875759859090295120e-6 +/- 1.78e-237]",
"strict_gap_below_F_third_over_D": "[0.16160663437693620625765616618254529875907396952432151486976092373540290908955672665152659910264217119421606408622738219749301284457484832200800877893468033278439352131950193380672541548502320026619100877307032293564517909068075764 +/- 3.65e-231]"
},
{
"l": 75,
"radial_rank": 1,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.4563606277079142991431439530065681120432935358492857419775590211230916449352812294095180341612562632475719582372132583873059265227723825243614866797684155984501561314470670530145427944686891223420965575672696302484066346324943694e-6 +/- 6.11e-237]",
"strict_gap_below_F_third_over_D": "[0.16160666370074725875236752352271366009855462337313081738092468910764554357502173138543725714863250541040341909470842945340827936074014389428414230517998689825106821651053521959961365212387219797754432457010909939703641826003203417 +/- 1.38e-231]"
}
],
"strict_local_maximum_modulo_phase_and_rotations": true
},
{
"label": "Z",
"depth": 2,
"N": 80,
"dimension": 42,
"precision_bits": 768,
"root_ball_euclidean_radius": "[1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8 +/- 1.68e-239]",
"inverse_frobenius_bound": "[13.227884127199610560558365464910912986341089094153269467799410424770413822779192598018217132974515146846099152731387575622828367211309632890139373448801499995218681475989155408394182011173891255087838534252220816772629767018593488 +/- 4.57e-229]",
"residual_norm_bound": "[1.6994133575789529603922159631335673727106913350114322947927386692412400082618750150153550267124338955203140493762726981224032570517974791579013260471650800977776433475724566339665629766862161833900965619075276239365170412192494163e-11 +/- 7.00e-242]",
"contraction_bound": "[1.1905095754163301865834031769914451481306409792203124738826215194286841936314266641071640988104028808986210806956759656571180957323269463785472419480317970351347703015887335541962913169743364265468721672592350958715223635180523303e-6 +/- 4.26e-236]",
"self_mapping_bound": "[2.2480833487845044197165145410385460206498762675514160437456578815560561658267102185012898313971573357253801651520013611407934673586696930838629761767560347181026466863677471207253789271408699642258090377282327398503394105124219595e-10 +/- 4.24e-241]",
"F_over_D_center": "0.48481263940715513",
"certified_unique_stationary_root_in_ball": true,
"full_angular_hessian_certificate": [
{
"l": 0,
"radial_rank": 41,
"known_eigenvalue_over_F": "1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"remaining_trace_over_D_upper": "[0.028306417777107102464308556846108544862427425273525656039924227282657942415402904089789705598576443194006888647155711747999600517638627002130682526812724129485650551341096478687633263217823151442623085652806284691413393524903440499 +/- 2.77e-232]",
"strict_gap_below_F_third_over_D": "[0.13329779202527794086902477648722478847090590805980767729340910605067539091793042924354362773475689013932644468617762158533373281569470633120265080652060920384768278199223685464570007011551018189071024768052704864191993980842989283 +/- 3.65e-231]"
},
{
"l": 1,
"radial_rank": 40,
"known_eigenvalue_over_F": "[0.33333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333 +/- 3.45e-231]",
"remaining_trace_over_D_upper": "[0.0078868534289668399057884120815053993688778680992967235314873453121625714648608259029848794980393535282552876558745988579146485041670014860470065695924512932770044013562282205178744568057188033482694006312930935473245344114056144908 +/- 4.66e-233]",
"strict_gap_below_F_third_over_D": "[0.15371735637341820342754492125182793396445546523403660980184598802117076186847250743034845383529397980507804567745873447541868482916633184728632676374088204005632893197710511281545887652761452998506393270204023978600879892192771884 +/- 2.17e-231]"
},
{
"l": 2,
"radial_rank": 40,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.042376649820592752297072137278701267803597312777746112813871440614985793275464685459981450237663731731394905694909542938924789107026686639868518057845685949754008927055439283876994152796590405320223246582763168302166748231558482026 +/- 8.05e-233]",
"strict_gap_below_F_third_over_D": "[0.11922755998179229103626119605463206552973602055558722051946189271834754005786864787335188309566960160193842763842379039440854422630664669346481527548764738357932440627789404945633918053674292801311008675057016503116658510177485131 +/- 2.92e-231]"
},
{
"l": 3,
"radial_rank": 39,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.011472396404829660160481407496516168082128441544618537238211732745143731547640847752048128899170226954443517053718078571147407709412218237523216216244992127479996247432288062008895163359287737054569601184067541161288538051759328812 +/- 3.38e-232]",
"strict_gap_below_F_third_over_D": "[0.15013181339755538317285192583681716525120489178871479609512160058818960178569248558128520443416310637888981627961525476218592562392111509581011711708834120585333708590104527132443816997404559627876373214926579217204479528157400452 +/- 3.83e-232]"
},
{
"l": 4,
"radial_rank": 39,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.0049919399228229434517851215316665590652014915116648455439500196435796652777975865278645207800388012780413222958134185814600465709909518273509876528094103794397032231177053167649314684029824490922282103301355703553653706203532211159 +/- 1.33e-233]",
"strict_gap_below_F_third_over_D": "[0.15661226987956209988154821180166677426813184182166848778938331368975366805553574680546881255329453205529201103751991475187328676234238150598234568052392295389363011021562801656840186493035088424110512300319776297796796271298011222 +/- 3.20e-231]"
},
{
"l": 5,
"radial_rank": 38,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.0029496858106421894920189616505798463512718782805675689390458675731756871695062294594137048082585871573069800837439468802358477797120472347297792521105185245565235165046275803905275232175626848249108326359046813295403661184594931670 +/- 1.60e-233]",
"strict_gap_below_F_third_over_D": "[0.15865452399174285384131437168275348698206145505276576439428746576015764616382710387391962852507474617602635324958938645309748555362128609860355408122281480877680981682870575294280581011577064850842250069742865200379296721487384017 +/- 4.33e-231]"
},
{
"l": 6,
"radial_rank": 38,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.0020065561033054384925115170950470721374287553292421527531634939258578132152428596340258840054817472630209373113561936667333299783398020349933928656202587682012291955828494926631709363881837803963438211527946514029272437540111336128 +/- 8.81e-234]",
"strict_gap_below_F_third_over_D": "[0.15959765369907960484082181623828626119590457800409118058016983940747552011809047369930744932785158607031239602197713966660000335499353129833994046771307456513210413775048384067016239694514955293698951218053868193040608957932219972 +/- 9.91e-233]"
},
{
"l": 7,
"radial_rank": 37,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.0014598110631536290374941224697460678428838459363765386068423642571405285571879669571432837496728660431932561333097366910285076097855217243289037438469881499591264448993900454388149524435616310696177197958580507389563203577476936242 +/- 2.67e-233]",
"strict_gap_below_F_third_over_D": "[0.16014439873923141429583921086358726549044948739695679472649096907619280477614536637619004958366046729014007720002359664230482572354781160900442958948634518337420688843394328789451838088977170226371561353747528259437701297558563971 +/- 1.55e-231]"
},
{
"l": 8,
"radial_rank": 37,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.0011161364014812377337338226678128761679821640396890568399132005614499626822689380608333699058944368368055410418615190021463692472247580801489912954138284593814679824287087134865317879704831827276014953247560025433339932979553066507 +/- 2.62e-233]",
"strict_gap_below_F_third_over_D": "[0.16048807340090380559959951066552045716535116929364427649342013277188337065106439527249996342743889649652779229147181433118696408610857525318434203791950487395186535090462461984680154536285015060573183800857733078999934003537802668 +/- 2.08e-231]"
},
{
"l": 9,
"radial_rank": 36,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00088168134505752316952279323593810709056228599448041377763320878409848345320464371500832986089945717708887316951040819111765460375707518778315640827575767571736245707880017855384656607570643470834731096744188271424047988189083418157 +/- 3.36e-234]",
"strict_gap_below_F_third_over_D": "[0.16072252845732752016381054009739522624277104733885291955570012454923484988012868961832500347243387615624446016382292514221567872957625814555017692505757565761597087625453315477948676725762689862498602236589145061909285345144249915 +/- 1.04e-231]"
},
{
"l": 10,
"radial_rank": 36,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00071668950878399339238894884587641829550501045707755810164724405167931025072236485254962738406887103218902153542152418830382904067576797313232160795510107935247035847927166722095333083055423647593988812600743637048373121585450989074 +/- 1.93e-234]",
"strict_gap_below_F_third_over_D": "[0.16088752029360104994094438448745691503782832287625577523168608928165402308261096848078370594926446230114431179791180914502950429265756536020101172537823225398086297485406166611238000250277909685739344520732589696284960211747882344 +/- 2.00e-231]"
},
{
"l": 11,
"radial_rank": 35,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00059393380784631622635966737233319801036219385824234074920260149203271399323169861914116128265161781186163420182718686789309386156847946014045839100755530285867882984138943741797004171646772878012212347463582390484090110021857327400 +/- 2.12e-234]",
"strict_gap_below_F_third_over_D": "[0.16101027599453872710697366596100013532297113947509099258413073184130061934010163471419217205068171552147169913150614646544023947176485387319287494232577803047465450349194389591536329161686560455321120985869750942849243223311476006 +/- 1.38e-231]"
},
{
"l": 12,
"radial_rank": 35,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00050193333546013549863517134445964706044233402477934221815824879530399656280937952087416398217072711152959226207664715229193163324154801590918068002258169876998729204773206154377935098634758502871533974493484063348865424669592739619 +/- 5.10e-235]",
"strict_gap_below_F_third_over_D": "[0.16110227646692490783469816198887368627289099930855399111517508453802933677052395381245916935116260622180374107125668618104140170009178531742415265331075163456334604128560127178955398234698574830461799358839849269984467908663740594 +/- 3.47e-231]"
},
{
"l": 13,
"radial_rank": 34,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00042928947696854045539895740194503955747577295651938654165617613442357852394488251906816624827487114531338628292408063286091240102662459800250449940730273248708009762924691205819958801114375053623636339806015650442480320080087224167 +/- 1.36e-234]",
"strict_gap_below_F_third_over_D": "[0.16117492032541650287793437593138829377585756037681394679167715719890975480938845081426516708505846218801994705040925270047242093230670873533082883392603060084625323570408642127513374532218958279709696993527317682890853013253246109 +/- 9.86e-232]"
},
{
"l": 14,
"radial_rank": 34,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00037272933118928131999658144256943529503090291124705247937430623269255435808286228785036799576167094521341208416093556463451394320777773455555740738411267616632466402080513193217295383728695854360608938503839766683888113248740120590 +/- 4.91e-234]",
"strict_gap_below_F_third_over_D": "[0.16123148047119576201333675189076389803830243042208628085395902710064077897525047104548296533757166238811992124917239776869881939012555559877777592594922065716700866931252820140116037949604637478972724394829493566649445220084593213 +/- 3.22e-231]"
},
{
"l": 15,
"radial_rank": 33,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00032595508059015122368345285736785702082206646865438107659195427478808262075531280523535943127300546614810197331252725215149375714541224768632113671999221516930473414511605135779741952576219047344650010724239739360012085528644647737 +/- 4.30e-235]",
"strict_gap_below_F_third_over_D": "[0.16127825472179489210964988047596547631251126686467895225674137905854525071257802052809797390206032786718523136002080608118183957618792108564701219661334111816402859918821728197553591380757114285988683322609093593973321247804688686 +/- 4.66e-231]"
},
{
"l": 16,
"radial_rank": 33,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00028869608832498894259579656032416175375910681881119799071194548270254590023071576115960466078187839816959163463975555508531714429937055261129753100865043328275735002900852932266747083143892707484154058647686240756456293718608805959 +/- 6.01e-235]",
"strict_gap_below_F_third_over_D": "[0.16131551371406005439073753677300917157957422651452213534262138785063078743310261757217372867255145493516374169869357777824801618903396278072203580232468290005057598330432480401066586250189440625849179274685647092576877039614724527 +/- 3.11e-231]"
},
{
"l": 17,
"radial_rank": 32,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00025664198564567119028000273066135404634353880518987230832694719119474927673679228482036578997551887873292101884072118264924318004621153209353133101044849365310765514423916893895065964998477959441630906466112718437607498606525669752 +/- 2.99e-234]",
"strict_gap_below_F_third_over_D": "[0.16134756781673937214305333060267197928698979452814346102500638614213858405659654104851296754335781445460041231449261215068409015328712180123980200232288483968022567818909416439438267368334855373891702426867220614895725834726807664 +/- 4.89e-231]"
},
{
"l": 18,
"radial_rank": 32,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00023080066009612280043495613630410170252669448757151261235243507652513595154375870920099983747855064228816829027085062608325628430254688819868842760219580333236826585983076905692619157161745798863481717382192843664036799861350284857 +/- 1.29e-235]",
"strict_gap_below_F_third_over_D": "[0.16137340914228892053289837719702923163080663884576182072098089825680819738178957462413233349585478269104516504306248270725007704903078644513464490573113753000096506747350256427640714176171587534469851615951140489669296533471983048 +/- 4.08e-231]"
},
{
"l": 19,
"radial_rank": 31,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00020774716009464643917875834775129708038899363786561975201483325780429720010744366795641679216605358948641434299868596474472739352121559478182681774454547742726094321363671700181704044784154478420379167107365926711677770248475787588 +/- 3.64e-235]",
"strict_gap_below_F_third_over_D": "[0.16139646264229039689415457498558203625294433969546771358131850007552903613322588966537691654116727974384691899033464736858860593981211773855150651558878785590607239011969661633151629288549178854912954166225967406621655563084857546 +/- 3.14e-231]"
},
{
"l": 20,
"radial_rank": 31,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00018909682346611360133700851786959293207118948030915272841353656418385658751051382892936421384082233186180573963637742765986823399593022229063476764285361454109824233475748012225557777514870767016214369219338997060364977278009995850 +/- 4.24e-234]",
"strict_gap_below_F_third_over_D": "[0.16141511297891892973199632481546374040126214385302418060491979676914947674582281950440396911949251100147152759369695590567346509933740311104269856569047971879223509099857585321107775555818462566317118964113994336272968356055323337 +/- 4.21e-231]"
},
{
"l": 21,
"radial_rank": 30,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00017186077465134299162357514750118984033089703703820677211458560165727762913692705481534426428260334646047112590375685938496440638914385917409889058506383736246152294792746176830544882432606678612669564961389705971784577045874265668 +/- 3.03e-234]",
"strict_gap_below_F_third_over_D": "[0.16143234902773370034170975818583214349300243629629512656121874773167605570419640627851798906905072998687286220742957647394836892694418947415923444274826949597087181038540587156502788450900726654720663768371943627361548756287459068 +/- 4.06e-231]"
},
{
"l": 22,
"radial_rank": 30,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00015796807804359824292567880075128489878933323368402332577552434313960266232213646566327484494175223721627456969824249060183649100498734843650182249974974596371397947392036102470104994259926922553828111128634988756098365258942318458 +/- 1.02e-234]",
"strict_gap_below_F_third_over_D": "[0.16144624172434144509040765453258204843454400009964931000755780899019373067101119686767005848839158109611705876363509084273149684232834598489683151083358358736961935385941297230863228339073406410779505222204698344577234968074391015 +/- 1.96e-231]"
},
{
"l": 23,
"radial_rank": 29,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00014466202219631787714904741092649628342743732816122648799731885873295709984277283552635924858152685011728476884551348387237692410453267308484191401736503719915903787697569081493583209493125902687183499977160558534024136122466073987 +/- 2.11e-234]",
"strict_gap_below_F_third_over_D": "[0.16145954778018872545618428592240683704990589600517210684533601447460037623349056049780697408475180648321604856448781984946095640922880066024849141931596829613417429545635764251839750123840207430646149833356172774799309197210867259 +/- 2.86e-231]"
},
{
"l": 24,
"radial_rank": 29,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00013404480030009494246594846517534028777070978892395602594452373846292739993888372251864686629493362111764500219884673641320359723937076619949611885849265267621797609569282429493056407497316160565136962298804505647889281404474509335 +/- 2.86e-234]",
"strict_gap_below_F_third_over_D": "[0.16147016500208494839086738486815799304556262354440937730738880959487040593339444961081468646703839971221568833113448659692012973609396256713383721447484068065711535723764050903840276925836017172768196371034528827685444051928858824 +/- 7.15e-232]"
},
{
"l": 25,
"radial_rank": 28,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00012349122090792588511470913891542968054937912007164862972582457185913594849874883946702705036152152504773345116201565042384976137235736307449518949994625464705236415838072879238833105837353660832563474956969069531213112402380759043 +/- 8.76e-235]",
"strict_gap_below_F_third_over_D": "[0.16148071858147711744821862419441790365278395421326168470360750876147419738483458449386630628297181180828559988217131768290948357196097597025883814383338707868628096917495260454094500227495979672500769858376364263802120220930952574 +/- 2.30e-231]"
},
{
"l": 26,
"radial_rank": 28,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00011520433615713196816826100950906912387426786337289868998069512677256490908628594680271443121947721942762363404912929852539219690986318422253261535895964566242220865123378654077960099818752821028407690033687378661486529632379032862 +/- 2.75e-234]",
"strict_gap_below_F_third_over_D": "[0.16148900546622791136516507232382426420945906546996043464335263820656076842424704738653061890211385611390570969928420403480794113642347014911080071797437368767091112468209954679255373233514580512304925643299645954671846803700954300 +/- 4.15e-231]"
},
{
"l": 27,
"radial_rank": 27,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00010663732930856732233971056028922218669130106139477737721097698875106050268404669522517192846534117481044479836186432730515394681531525620062028034019590087992513180775961086873180759306128825793801561724841102646109549060550467330 +/- 1.93e-234]",
"strict_gap_below_F_third_over_D": "[0.16149757247307647601099362277304411114664203227193855595612235634458227283064928663810816140486799215852288853497146900602817938651801807713271305299313743245340820152557372246460152574027204507539531771608492230687223784272782866 +/- 5.58e-232]"
},
{
"l": 28,
"radial_rank": 27,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00010005472667903781548683648921461643043398310297949737320028159039581086225729807087800700165246372023044270792987397000909434586518237825277570271850723335065384645975620733777418949605825772655804151328707164896610216753390736898 +/- 4.95e-234]",
"strict_gap_below_F_third_over_D": "[0.16150415507570600551784649684411871690289935023035383596013305174293752247107603526245532633168086961310289062540345936332423898746815095508055763061482609998267948687357712599555914383727507560677529182004626168436723116579942596 +/- 3.71e-231]"
},
{
"l": 29,
"radial_rank": 26,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[9.2958425156062161087862764087430877195686709666626124851312917116685299372026315913082675946324106289965058698052509145491218398205328812242924974407863401911467745805816521481304508131262317011035312865081371033033667521401594413e-5 +/- 4.99e-235]",
"strict_gap_below_F_third_over_D": "[0.16151125137722898117224547056924590245613764662366670720848202041621664803396130701742025065738700922704336827463528082418784211493512800452109040835892546993142186558752751681185202882520207101632229802046825196230029966581193174 +/- 1.79e-231]"
},
{
"l": 30,
"radial_rank": 26,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[8.7651882776290394208499056108021290090901219654825066802456916087525425385406632105432254473873350369020391708993720157783757341311580189812114578992906160746057472862701664062077846759216941580441725423220655749242113718759470545e-5 +/- 8.71e-236]",
"strict_gap_below_F_third_over_D": "[0.16151655791960875293912483427722531204324243211367850826653087641724580790794792670122790107885945998296431294162433961317554957599202175314352121875434042717258727586047063166927125548657411639175289160791011267758409121961457386 +/- 2.13e-231]"
},
{
"l": 31,
"radial_rank": 25,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[8.1668373012912203646599194100578604851909372110168618528567615050642149829167329903000014338743384576785386630019212813697304199535932758842569995566991929388933316010407598265658404411007045111064056230407992505928608944003726790e-5 +/- 8.03e-236]",
"strict_gap_below_F_third_over_D": "[0.16152254142937213112968673413923275472848142396122316471480476571828269118350416600343033331899458994875654794670331412051963602913379740057449076333776634140394440001732292573506767492892232628822226927710292534082740472438932961 +/- 4.07e-231]"
},
{
"l": 32,
"radial_rank": 25,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[7.7336832526632049259099730738378249473328018476321944381859578883220954218265046389959252156108489296572598574724961518813351213189345660672493261920560569436530206041946833381261499801808307695025095220233028048925977260218340586e-5 +/- 1.45e-235]",
"strict_gap_below_F_third_over_D": "[0.16152687296985841128407423360259495508386000531485701138895147375445011237911506828694337408117722484403676073475860837181451998212014398767266084007141277276389680312729138649995207183353152502563830823811310030528440735607311499 +/- 2.09e-231]"
},
{
"l": 33,
"radial_rank": 24,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[7.2211372748741117139780614622888162235391698392018626980153678754379862549658932783269033541558645142083941760635297605958136736331329104158598432272653080997050657436009681683722707163087490282676539797356308656784435644558842007e-5 +/- 1.12e-235]",
"strict_gap_below_F_third_over_D": "[0.16153199842963630221619355271871044517109794163494131470635317965457895347078367440055006429979177468819124939157269803572737519659700200422917473490106068025233628267589732365164961062617024584305065679353597702467654889768877449 +/- 7.19e-232]"
},
{
"l": 34,
"radial_rank": 24,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[6.8638085907581728283918170291601856207069813931021563754147989346176076494160808470867051766983053056554289743214129498978235162980682150839527212820317486710191923005632537797642683991348834694872086104086430915889213431753342718e-5 +/- 4.85e-235]",
"strict_gap_below_F_third_over_D": "[0.16153557171647746160504941516304173147712626351940231176957918534398715725683917252486246628156635028027677904359011920383435509817035265118249380612051301584662314141032770079553569064934198449863846124722924690241744411990157999 +/- 4e-235]"
},
{
"l": 35,
"radial_rank": 23,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[6.4185295550435667756579146633680366284462643139280696743178783716201463775114290580967321372097446636711326545519602729451366900952199479624889294814777213311185071788620067999859539495707194077008546179231328144031671810949716840e-5 +/- 2.57e-235]",
"strict_gap_below_F_third_over_D": "[0.16154002450683460766557675418669965296704887069019405263659015454961713186955821904275236601196123588669662200678781373060388196643238113385370844403851855612002214826154471326533347379383762613925632478715410200518930166152238362 +/- 4.12e-231]"
},
{
"l": 36,
"radial_rank": 23,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[6.1210936342362867309706125405121663849535453157146631763464616851342847854772967426511986435896894149251419174093020273749461446878343955057703291690617158551840154165279916208664706429842762127703788983427826613413194241605810204e-5 +/- 1.45e-235]",
"strict_gap_below_F_third_over_D": "[0.16154299886604268046602362720792821166948379788017618670156986871648199048547856036590682134689743643918408191415924031305958387188645498937827563004164271617478149317916805341712466862690349057120562954434990550671992013909172752 +/- 2.56e-231]"
},
{
"l": 37,
"radial_rank": 22,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[5.7293253945883499887666548203619315388000577840359829361246452148872976035332919076225522745464158258664370994406239528688043528729901342497238751429282889084221580755626799201272884594025337771999495491728010417435152024688975207e-5 +/- 2.31e-235]",
"strict_gap_below_F_third_over_D": "[0.16154691654843915983344566678512971401794533275549297350397208688118446035729800041425710781058786917507466896233892709380464528980460343199083609458190405044424911175257770653413206044873930799556133383784160532291589818130864436 +/- 2.49e-231]"
},
{
"l": 38,
"radial_rank": 22,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[5.4798539215102711280397519859374148900639842126407544471830787523570532911364768645757332534064981561650887852538886923887286113063425329073132278359504671183283649621618730826144408773031058689868843875651225157393968611963928184e-5 +/- 4.40e-235]",
"strict_gap_below_F_third_over_D": "[0.16154941126316994062205293581347395918443269349120692578886150254580976280042196856468757600079926835177168244548079444640944604722026990800426020105497382866215004968371171460250718892456030227464346448945768210817593936472136940 +/- 4.51e-231]"
},
{
"l": 39,
"radial_rank": 21,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[5.1312109569459445477424619146409727261500035841549691439812384407750110057538636017424346564024318793589967876573097818433045019324407092932486648317506314483334021559580495873673070037313217605556892665712008816837798082370560201e-5 +/- 2.42e-235]",
"strict_gap_below_F_third_over_D": "[0.16155289769281558388785590871418692360607183329749178364189352094892558322327579469731590898676930901453974336545676023551490028831400892624040084668501582701884999931177375283745966026329602011572777644066762132451649553525096277 +/- 2.44e-231]"
},
{
"l": 40,
"radial_rank": 21,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.9206268225375842469907640884243877482196521480941798678826171410185449005715868879250422613416467927315625486170833818448211075037537235522668749194728677139009215909324385369361753751767549739905952553364055163326328896660990335e-5 +/- 6.51e-236]",
"strict_gap_below_F_third_over_D": "[0.16155500353415966749086342569244908945585113681185239153465450716192314788432761746445408291071991686540601770784716249951488512225829579609781066458413860465619432411742400894796397157958156578359342738077996927817000700443667234 +/- 2.35e-231]"
},
{
"l": 41,
"radial_rank": 20,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.6071466594755662954889218888640073543530421105486605914449286459382856347897312939498224569172302058472817764418321905087027367126271310142271729409825470223743965423252887146711078363692380892812923992295014558621486010548365802e-5 +/- 2.92e-235]",
"strict_gap_below_F_third_over_D": "[0.16155813833579028767037844411444469325978980291222784672741888404687395047698543602039383510876416103127486051556891501142824630596620706202319106160392350786310958936791008044618662225496964095244052040934103831877471184732278497 +/- 3.17e-231]"
},
{
"l": 42,
"radial_rank": 20,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.4284409987529389758358108257678643280519387230423425564076097109037815085793026108671969694830248490703886088821330132671117663645072720657100954931285275051450223752952231963573152635581158222233455171055847102706476262593791136e-5 +/- 4.06e-235]",
"strict_gap_below_F_third_over_D": "[0.16155992539239751394357497522507565469005281394610290990776925723622429551824754030722466136363850308484262944724451200320066221566968826061267623237840204805828188310958038110136976018069775217511109987816227748623062685707073954 +/- 1.52e-231]"
},
{
"l": 43,
"radial_rank": 19,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.1439339181467895036768829988832082292420959222126130411057132067129830333961238588013023944299000323804178864015754729512391550927647050030715724236872188808813675431551066774303240171873205326381475540882632854079273963461574576e-5 +/- 4.69e-236]",
"strict_gap_below_F_third_over_D": "[0.16156277046320357543829656450334450125104091237411120720292227620126620350299937209474532030938903433300952915446931757860382094178240568628330261760909646114452451965790178226655903009316146012800695185779245070047925405936987176 +/- 1.91e-231]"
},
{
"l": 44,
"radial_rank": 19,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.9916233595034956992600973163345482569829329310212006165579503566424490059469025394022898060136322040016195995305619447947651394131403908486180243932722205641381659787448106476635832977363089275436675664581074659097299972693291816e-5 +/- 3.52e-235]",
"strict_gap_below_F_third_over_D": "[0.16156429356879000837634073236016998785076350400402312132716775382976690884327386430793931043527319701129331713733802771388538568193920192942484715308940061112769195167354588522685669750035597024405789665766875225867423603336064004 +/- 8.11e-232]"
},
{
"l": 45,
"radial_rank": 18,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.7312172977264850348871946629100503320340036631045099519777511876369081602320402259608808451719969619017700392608077382549705277465157450641969880864382819224964445990112493781759218922316445760150421519065544693621218222413468162e-5 +/- 3.41e-236]",
"strict_gap_below_F_third_over_D": "[0.16156689762940777848298446138670423283001299329670228823381355582145696425173101293107372452488161336371431563294072525595078362805586817588269136345246895051410836888734322083955157411441101688757318291181426778863971211511091986 +/- 4.52e-231]"
},
{
"l": 46,
"radial_rank": 18,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.6009606752387881589297010174474603320645586138727863236446093279061499081363562724633526846204690547095038478858583941458911639503571285799489207706913207732538673333116235239215383164960526214687562473929519173002668123577868276e-5 +/- 3.87e-235]",
"strict_gap_below_F_third_over_D": "[0.16156820019563265545174403632315885873001268774719460547009688724005427183425196977060869980648712864278623829485447474939187442169382976204753384412562642012560079466000021709809411795016837280711864577085940381416033066520975546 +/- 4.40e-231]"
},
{
"l": 47,
"radial_rank": 17,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.3607770609335133691092646112151508995926571521562557524275711059456088417369303668987907475413651901115959883095451993020471351116199127096005313686219472061857165305355990019636324291455658154404815120374924913990031708370515806e-5 +/- 1.17e-235]",
"strict_gap_below_F_third_over_D": "[0.16157060203177570819964224068722118182433740676181177077580905762227387724491596402966434542585791968143221737345023788134031286198221713420623732801964711386127147616802797734331369700904187767517892851821295840841934330162496282 +/- 3.08e-231]"
},
{
"l": 48,
"radial_rank": 17,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.2491001591008794038919658926524593805257790112043129606267949733329514884508867296590585354104116276267456668821607248076765981117977231212202649975629769857798657554096909535016850808553575317694612323828696877832263049318111448e-5 +/- 3.66e-236]",
"strict_gap_below_F_third_over_D": "[0.16157171880079403453929441367440680873952807554322129020372706538360000381844882446603674274797922921705706587666451172608525656735221535610212113068335770356347553467577923642379831648252477975801563872100950463645550107028401522 +/- 1.24e-231]"
},
{
"l": 49,
"radial_rank": 16,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.0260192957516300413221318227130581697739200153541112095915602287850638818948513737989285616808063643422217538005063025404655541427613586325923177468904498415022961650972664451451864115881225140190512452421000331666981467021091217e-5 +/- 4.57e-235]",
"strict_gap_below_F_third_over_D": "[0.16157394960942752703292011201510620275163559413317979222123741773104548269451438481959534404771652526968991111579532827030792867779190571974700741015586442883491831037168236066888188146921745210819314282088091233300166635186631224 +/- 1.46e-231]"
},
{
"l": 50,
"radial_rank": 16,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.9301141424774701726359143646020267902238375637274920562934148673652640292329648433118925280892252855189873267428465281904611051160792309618798782950554757051936708508303200572227759776347022421655766820904933181163696635578733348e-5 +/- 1.81e-235]",
"strict_gap_below_F_third_over_D": "[0.16157490866096026863160697418968731306543109495769605841277039918465968069304100368490021440805244108047814346006590486805142872228217254102371453455038277857628139662482503013276110557355698631091167756651242840015216963669775460 +/- 6.96e-232]"
},
{
"l": 51,
"radial_rank": 15,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.7216029134656991746845660647206092656393384209301075102465748937744128566748999104201516461229270882727371174818748495758641319827514287581573556867413289563891831008156032361703387367317339267597956144067571451694730698280613251e-5 +/- 2.08e-236]",
"strict_gap_below_F_third_over_D": "[0.16157699377325038634158648767268612724067693994912403225823086758439558920476658433422913181687210406245060596215851458483757469201350581904575175977646592004376944150232517730097162994596601599406573537718926576188163860263505272 +/- 5.06e-232]"
},
{
"l": 52,
"radial_rank": 15,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.6391793831613685047002879731251368005049126583166258653412561033668637735836704789086984776782902136556730995741027929534306420228931708617676879961245201168773143482737546074419673378146873517397203351123332905442565882881675576e-5 +/- 4.60e-235]",
"strict_gap_below_F_third_over_D": "[0.16157781800855342964828633045360208196532828420675016707467992077229966469559749662854424634855655043119677660233759230540379902691310440162471565645337208813216456018985059578725891365995518645981593612998221000042789076745045166 +/- 2.98e-231]"
},
{
"l": 53,
"radial_rank": 14,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.4431630310384212075923831641148823972831181536993637996967637770502077738974559851860503732911698845323782204777133801348704240501522567129504412545668086746815907044391062335319122615620057266033517094880343109802706256522225584e-5 +/- 4.63e-235]",
"strict_gap_below_F_third_over_D": "[0.16157977817207465912125740950169218450936050215179633969533636569556283125559435877348147282960042163448800955112855619953198462909283181076620382892078766524658651742628894227099801421071771327606729981623845299022353062707681111 +/- 2.91e-231]"
},
{
"l": 54,
"radial_rank": 14,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.3723377186790406302789032861028631216300841511737101455026048942353640775487559590299563894168646816305465425666429640007827887318736539618993632963647994360630073797972843267065857259560813117709894589638008588925651953376330420e-5 +/- 4.35e-235]",
"strict_gap_below_F_third_over_D": "[0.16158048642519825292703054430047230470211703249182159623187830728439097969255784577374303376943916468651702786790766690369332550544601459679371433970036968533897270325953536049006626747607377252021562343874369532474440768137995700 +/- 2.31e-231]"
},
{
"l": 55,
"radial_rank": 13,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.1871032528230782290886377345957442722104930589025709142028001945724954938056028701759562145079350508184724954053251287316980964418540507059951882429883856563087968990512764613180057220630420482776158706990889009823592722511597605e-5 +/- 1.22e-235]",
"strict_gap_below_F_third_over_D": "[0.16158233876985681255104244695598737589061122840274430762419130533138760837839527730463157377118825398282514860837928008204601635236891479282627338145090344947677024536434282056872015327611270291285055717462634244432350974061082174 +/- 4.92e-231]"
},
{
"l": 56,
"radial_rank": 13,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.1263152783490263633829238660382562212261472103544711965818544859759627789023464815646733953566200346554037248835388284848505890642943333550484226252582348360307133190394762857681845442765764386108080093352706254681941205127459253e-5 +/- 4.09e-235]",
"strict_gap_below_F_third_over_D": "[0.16158294664960155306969950409467295077112107186122978862136751478847357370554430986851768659937976713298677929608449794504848482744269038999978284910708075098497302620014293857047565148789056756894722525323998062707865139212820587 +/- 3.44e-231]"
},
{
"l": 57,
"radial_rank": 12,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.9504378868036238574366951489621694030236274057217579949572531454542789329790828856179755731810849600268482039600127897295830690393020502111668628814261116562675754719229076372689069109151361742646199702363087662701815397753928228e-5 +/- 2.39e-235]",
"strict_gap_below_F_third_over_D": "[0.16158470542351700709475896638184371163930309705927611575338376080187879054400354250447715357760152248373306485129373320543603750264294031283122166470451907221677065757861410425696064426422418197159068713363097024567063151793557940 +/- 4.39e-231]"
},
{
"l": 58,
"radial_rank": 12,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.8983844108827294362020805191022116464208803377416620924637820484681973381654866336791373785305251672426408203756375411690928435044403944337984097125147023339608878796288298102847377185298521322307450521769330330041383006186974940e-5 +/- 2.04e-236]",
"strict_gap_below_F_third_over_D": "[0.16158522595827621603897131252814231121686912452995591671240869551284865135995167846699654195954802808166090692512957695792164240489828892938899534923620818630999372445453704503523048595614803481201102588281156400300329195032714636 +/- 2.23e-231]"
},
{
"l": 59,
"radial_rank": 11,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.7306708124371112117829529325265150341967411887891928429617318662851429344849849331818737562939823342635073208680885026431171015824296454655898404216370788291365858529520655027018749491514522072257761923620163099270641408886887649e-5 +/- 4.52e-235]",
"strict_gap_below_F_third_over_D": "[0.16158690309426067222121550380400806818299136592144544140490371601467048190398848348400151459577039350999069826012465244830690216231750903687867743492911696254504196747480381267830631458384181881126107557140971317023406269192444644 +/- 4.98e-231]"
},
{
"l": 60,
"radial_rank": 11,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.6862571527009835630655055962165973127656144560214304961378582128960114015573527434169440904658761645871987155053558103218880861634353554434527321719151718458807462521281325457465327368032522517482447782603987934868105636378257334e-5 +/- 1.79e-235]",
"strict_gap_below_F_third_over_D": "[0.16158734723085803349770267827737116736020567718877311902837195475120437321931775980589916389242867457168746134617827977523011445247169897977889880601161418161487452587081205200787586800596530081081585088555072934539846522769695508 +/- 4.60e-231]"
},
{
"l": 61,
"radial_rank": 10,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.5257015676117360595269410674733734761720225586236888587411420569466020593446366152967946525222762268929584336371118720291720483237474442747992815311598083987329339032681239851815684780451954691921904337165549971315211611734733349e-5 +/- 4.16e-235]",
"strict_gap_below_F_third_over_D": "[0.16158895278670892597273806392265859959857161310774709644474592191276386731273988696718036538680811057106440374899696221461304161285009585889058534051802173524934600399430065209348151764855288137864141142899616778336201812172159860 +/- 6.73e-232]"
},
{
"l": 62,
"radial_rank": 10,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.4880022497459427411814015916628794294554291552157279492811765974583130391804388358753990777985513460299687160447755045343740365832714941439861269125760951230232579490175252503239142818081536654291453595486918780752554055599104484e-5 +/- 3.44e-235]",
"strict_gap_below_F_third_over_D": "[0.16158932977988758390592151931741670453903877904178117605384052156735875020294152894497457934255534781987303364617288557828798959296750061839189347206420757238210310075384315808083009419051525179667904187973784641455258077927773423 +/- 1.87e-231]"
},
{
"l": 63,
"radial_rank": 9,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.3337518705310371356735416759666600953901952402803896753892065648987258873690714339278193400745727286998036419912116422490278348521201174703079322968541211317367426262736877125231855715208682918808150515685177460214126496687925984e-5 +/- 2.34e-235]",
"strict_gap_below_F_third_over_D": "[0.16159087228367973296197659791657366673237943138093052943657944126768434607445964261899405513993258760604633529691342121691084305498481213215863025401036479212201596590707059645620810147761812465041452518281764815587311920683664541 +/- 3.30e-231]"
},
{
"l": 64,
"radial_rank": 9,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.3019799533626076973249545778072696216835785799913477875827281627172356215874736907011698404573200803124497420462778265466809859154703470288503685025028102213839711842373696380693359690915084716346302449086014652045735807344474458e-5 +/- 1.14e-236]",
"strict_gap_below_F_third_over_D": "[0.16159119000285141725636008378755526063711649754753341985545750605170616097711745859642632163492876013253020883591287055506786652347417862986304482964830830523111949362149095963695263997364241824861698703088424731868128759752598886 +/- 1.80e-231]"
},
{
"l": 65,
"radial_rank": 8,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.1533076389910149208155879241737850663309178798213717497770676270364485319570893078791162126303320807142157479240490978239845528848984962047546427182973804659333129980838973141798058706896391548436811948594618348403346015439736854e-5 +/- 1.32e-235]",
"strict_gap_below_F_third_over_D": "[0.16159267672599513318412517745409159548267002415453511961583556265706296884801376244025454217120703001252619117585409284235509348780448434837128578690615035952867400020335249436019153527462643694178489652138473871498492998731789360 +/- 4.14e-231]"
},
{
"l": 66,
"radial_rank": 8,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.1267903603445936181383327584011216381979261068867144229613736379927655654898674388997375574331724398671092653475786036991485076396062607756171219113984035341204726148910780915106301816084142705249443889548999779378880523185726435e-5 +/- 2.59e-235]",
"strict_gap_below_F_third_over_D": "[0.16159294189878159739715195000574932211695135407226446618910371959695340567767843465894433595775900160893466224067985754729634184825693727072557716211421934929799212860718442255241822703151724919062808388944378433355395445281014761 +/- 3.74e-231]"
},
{
"l": 67,
"radial_rank": 7,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[9.8307287371510689077535104529112533193505223122474757084426138385208611032761920888986090475264154951799306414627932017640880153247725932360530773415892212146147987959041313119187176285481099750750346559096756163295685684359127541e-6 +/- 3.07e-237]",
"strict_gap_below_F_third_over_D": "[0.16159437907364789226442557982288042208001398281102108585762489071949481247223005714124443472428580691783815340269187054013156924531800856074009728025599174411211871853453742920202141461570478522335825829867742365771700376476489742 +/- 6.3e-234]"
},
{
"l": 68,
"radial_rank": 7,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[9.6123216821717955005391133196747459651816863813042580697614901125357437999266218461067863587704997434828960209158713186725319686041971459823530396845231952858709036662546402803564771108483103115740933554923202035966552596800631977e-6 +/- 4.13e-236]",
"strict_gap_below_F_third_over_D": "[0.16159459748070287153783279422001365858736815164695202907526357184322079758953340671148722654697456283358985043731241746201466080136472913618735098029364881013804746242966707869305297685622248502302175923997784101312973667807365327 +/- 5.30e-232]"
},
{
"l": 69,
"radial_rank": 6,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[8.2193270450467593574759990030662826539990409072916133926961524195879114037326093391601882595409800603582776683750552933804873847983220605709349286741353716219552237582663642368155309956560767479680235598672972952350630318861557327e-6 +/- 3.94e-236]",
"strict_gap_below_F_third_over_D": "[0.16159599047533999657397585733433026705067933429242604171994063718091374542192960072399417314507379235327297505566495827803995284594853501127276239840465919796171137810957506696909651780233767725658536530977346603603809827030144718 +/- 3.06e-231]"
},
{
"l": 70,
"radial_rank": 6,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[8.0426950813386504224708960516000545989003356403748296822637097805265575912481404929580862106076104069438353155360887420549605463280069830527913649370634470296645531003072180226413313323736309534338421186773388999362305762570952284e-6 +/- 2.52e-236]",
"strict_gap_below_F_third_over_D": "[0.16159616710730370468291086243728173327873443299769295850365106962355280677574208519284037524712272572292638949801779724459127837278700532635028054196839626988630366878023302611531069200200095970237989949121465599443339710275707624 +/- 2.57e-231]"
},
{
"l": 71,
"radial_rank": 5,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[6.6892357154502550433385445759833322056896186963581613566810107095952853441323453613855931071696524464137698220381589716142751708441480036652784677610385538392611246903707509582406227118063007377701033133030320072210370703290318377e-6 +/- 3.41e-236]",
"strict_gap_below_F_third_over_D": "[0.16159752056666959307828999478875735000112764371463697517197665232262373804798920098797194774022616368088691956351129517436171905816248918532966805486557229477949407220864296258237509271062152703259556323002003030132611229626300430 +/- 8.86e-232]"
},
{
"l": 72,
"radial_rank": 5,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[6.5500509262633321568801542616675667149340915100298982809205451987075061224076267041228382036583347602488054172904130357579998560166325191652874242458180125807851931205911024157693158933298856973837103696067678133956272406052955122e-6 +/- 2.68e-236]",
"strict_gap_below_F_third_over_D": "[0.16159765975145878000117645317907166576661839924182330343505241278813462582721092570662921049512967499857308452791604292029757533347731670081416804590908751532075254814021274223091756401744000344763594962296372656551993770609272804 +/- 2.85e-231]"
},
{
"l": 73,
"radial_rank": 4,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[5.2320900605346838001456646393145146611042559938768714481380631754988304014325188481960905370847865819911637603263974334311316972434339651243595858722006334711158325828873653859688330880526143270354524252651202342481077965153095040e-6 +/- 2.65e-236]",
"strict_gap_below_F_third_over_D": "[0.16159897771232450864953318766869401881867222907733945646188519527015783450293190081448513724279624854675134216957300693589990220163608989936820897374746113269986221750075044596794736450024528071900629788090806821309908522553681802 +/- 3.25e-231]"
},
{
"l": 74,
"radial_rank": 4,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[5.1265833729071820326285116744568998233084438839518551040216932533116567865003231069422024649721154363018951933156739877723767042644298195137277153432785371239682859845669926450080209515856185536401028695171969074608494159737109341e-6 +/- 4.50e-236]",
"strict_gap_below_F_third_over_D": "[0.16159908321901213615130070482165887643351002488944938147822931164008002167654683301022639113086836121789703143814001765934556095662906890351381960561799005479620936504734876634068832531238174771477969323046381613642587248391735962 +/- 1.69e-231]"
},
{
"l": 75,
"radial_rank": 3,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.8405983711301827631848319658228532808228479906772893688414472103078892661382997239184198918817410731278300345202376958546313529312173364199024784016625530770849066176322919147166118265044495928888627757428243481560462028328347428e-6 +/- 2.21e-236]",
"strict_gap_below_F_third_over_D": "[0.16160036920401391315057014850136751048005251048534265604396449188612302544406719503360941491344145159226020550329881309563747870198040211599691343085493167078025624842671570104141861672150682888374044447055759050898517728713050050 +/- 2.02e-231]"
},
{
"l": 76,
"radial_rank": 3,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.7654742798183061886685570024425808554126974895359795849113778332510803511972778715584981892288940845955048999065059112857313823692386168086728838109943927298485232187202663921159507214729237907810170837333988339604867490707445922e-6 +/- 5.68e-237]",
"strict_gap_below_F_third_over_D": "[0.16160044432810522502714466477633089075247792063584379735374842195550008225298213605546177483514410443924873782843342682742204760195096409471652466044952233894060348481011461306694121738261186040954255231624959993449937284658426259 +/- 1.96e-231]"
},
{
"l": 77,
"radial_rank": 2,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.5083792139378540373591756899429608840879075720572512747584802719833499015983230895581570523456184833932044972039430988801680975412880678828737444654442863179124234620509135398966364726829391360051173043024667715931238866783317487e-6 +/- 7.37e-237]",
"strict_gap_below_F_third_over_D": "[0.16160170142317110547929597415764339037244924542576127608205857485306134998343173501024377517628098771484994012883612939023445316523579204526545045958886788904701542090987128241979343669686065039419732821602903086656174020944665500 +/- 9.30e-232]"
},
{
"l": 78,
"radial_rank": 2,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.4607453863326936185909021463997082450523263258015508175428841235049877453968512329572645607575583624152632327050792972618604171060043490055363281972266402331507236169777389474947758065182695157483185773748045130158446649084227894e-6 +/- 1.48e-236]",
"strict_gap_below_F_third_over_D": "[0.16160174905699871063971474243118693362508828100700753178251579044920982834558793648210037606877257577497091807010062825403607147291622732898432779700513610669310018260971635559438583855752681506381758501475595852882031748866842491 +/- 1.33e-232]"
},
{
"l": 79,
"radial_rank": 1,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.2298269500740134098911726316330313140083563454762111076712309211343304500719501390031540518694813065716256834734884825265098328483062950733487698885929280733181447185743458022222828173076961024276430153775757130732595374234889166e-6 +/- 9.66e-237]",
"strict_gap_below_F_third_over_D": "[0.16160297997543496931992344216070170030201932497698785712222566210241219900288326138319433017928146385202676170764985984485080682350048502703825998456344474040526001518861475898753111105051602563723090569031795575762026007379590984 +/- 3.83e-231]"
},
{
"l": 80,
"radial_rank": 1,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.2071358083438297388854457377841692462660160891035967848254583983374947040922488606503002329839303680152209935000209202951671762012942904420252071005472711050229369643764586973006251942930712143074123294740052429937900954569642317e-6 +/- 1.46e-237]",
"strict_gap_below_F_third_over_D": "[0.16160300266657669950359444788759554916408706731724422973654850787493499583862924108447268303310034940296531811233983331241303816615713203904289130812623278606222831039636895687463603270813904026211902592100385932809033954323787637 +/- 1.56e-231]"
}
],
"strict_local_maximum_modulo_phase_and_rotations": true
},
{
"label": "Higgs",
"depth": 2,
"N": 94,
"dimension": 49,
"precision_bits": 768,
"root_ball_euclidean_radius": "[1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8 +/- 1.68e-239]",
"inverse_frobenius_bound": "14.310057400443504501801447521380761356346810855682947420991796548766125430131595131332869827123524511918695229840817026543279410301938480074096281156718303210769170696946370885394017591352167073637247085571289062500000000000000000",
"residual_norm_bound": "2.5597270062634127013321449749923523536055382061485815263728195724632494862673007508764132788935886580913504973525374759942901256554180495079640522155372005357182944995071769821864959837398600939195603132247924804687500000000000000e-11",
"contraction_bound": "[1.2879051703329327420827106153562661396524076341519185653756039164264793135147054095598614321443355424355429446007690921573977705455229727983979216108241920092900831089664494731865934363147020923603484994897526458544345696244449645e-6 +/- 1.77e-237]",
"self_mapping_bound": "[3.6631128294265178659354699357120066708918621419439428048854258239524554902754065151258261332274228832304350003466047804058617391775737392683587842144800937012643431725890608723963360143398828594371171524883658456911485718837060661e-10 +/- 2.32e-240]",
"F_over_D_center": "0.4847890310041417",
"certified_unique_stationary_root_in_ball": true,
"full_angular_hessian_certificate": [
{
"l": 0,
"radial_rank": 48,
"known_eigenvalue_over_F": "1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"remaining_trace_over_D_upper": "[0.028295649365475208989620649633355482508262666641812807577768961566841271069364971241438174719339233435434756846170089151397893690045742401353065952953928221664920108565292435060619254604011899235808877323361455486484150400278265809 +/- 4.27e-232]",
"strict_gap_below_F_third_over_D": "[0.13330069096923869101037935036664451749173733335818719242223103843315872893063502875856182528066076656456524315382991084860210630995425759864693404704607177833507989143470756493938074539598810076419112267663854451351584959972173419 +/- 7.50e-232]"
},
{
"l": 1,
"radial_rank": 47,
"known_eigenvalue_over_F": "[0.33333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333 +/- 3.45e-231]",
"remaining_trace_over_D_upper": "[0.0078756650418916345203642154473283920560734918617338594455018173603902572809363844633606641434486599851715442908044271598209924337953985872373880703672194729970360747760802661459704125964956118958923956461462180205079910793068088354 +/- 4.36e-234]",
"strict_gap_below_F_third_over_D": "[0.15372067529282226547963578455267160794392650813826614055449818263960974271906361553663933585655134001482845570919557284017900756620460141276261192963278052700296392522391973385402958740350438810410760435385378197949200892069319116 +/- 3.92e-231]"
},
{
"l": 2,
"radial_rank": 47,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.042368089231736452004905344610929137526176518203339199182279159342939182859827708134773461632407961168660990864503352787477765339141358364438959912959168982119521534341246389145358287312179250427544077100757282071291758115468401673 +/- 3.39e-232]",
"strict_gap_below_F_third_over_D": "[0.11922825110297744799509465538907086247382348179666080081772084065706081714017229186522653836759203883133900913549664721252223466085864163556104008704083101788047846565875361085464171268782074957245592289924271792870824188453159833 +/- 4.06e-231]"
},
{
"l": 3,
"radial_rank": 46,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.011463103182520324753520428652331389500781530970577149193782938035164143603012075528744336573030262176699484284611088814098090939770342258509830294704188255026071254601796137875093146917958677034269538690515878551915965261854846124 +/- 2.24e-232]",
"strict_gap_below_F_third_over_D": "[0.15013323715219357524647957134766861049921846902942285080621706196483585639698792447125566342696973782330051571538891118590190906022965774149016970529581174497392874539820386212490685308204132296573046130948412144808403473814515387 +/- 4.93e-231]"
},
{
"l": 4,
"radial_rank": 46,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.0049825791976113400372267620261606355558217729153472957425724065741520949684693128776738204987708534651404567873544117636939311324470239988326730012725399052096801965899339330560204210344637407029103674502577591162232432802120652034 +/- 1.61e-233]",
"strict_gap_below_F_third_over_D": "[0.15661376113710255996277323797383936444417822708465270425742759342584790503153068712232617950122914653485954321264558823630606886755297600116732699872746009479031980341006606694397957896553625929708963254974224088377675671978793480 +/- 4.25e-231]"
},
{
"l": 5,
"radial_rank": 45,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.0029408863185046391855383880338158677431684278136690142232742138203367213395920332141973640169564466476113937877851008949208398988401410485592244671231181584830819693185956921325967708398267506137076616392155920387120989554575380290 +/- 4.59e-233]",
"strict_gap_below_F_third_over_D": "[0.15865545401620926081446161196618413225683157218633098577672578617966327866040796678580263598304355335238860621221489910507916010115985895144077553287688184151691803068140430786740322916017324938629233836078440796128790104454246197 +/- 3.53e-233]"
},
{
"l": 6,
"radial_rank": 45,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.0019982977788187092822454098094647123706602522166197704145627610110872156067642015187894026077140647892610302298881834249747480963383699678490032312018269510631312474407299237924272315513759822019343532892863840348198082944874498451 +/- 1.98e-234]",
"strict_gap_below_F_third_over_D": "[0.15959804255589519071775459019053528762933974778338022958543723898891278439323579848121059739228593521073896977011181657502525190366163003215099676879817304893686875255927007620757276844862401779806564671071361596518019170551255015 +/- 4.05e-231]"
},
{
"l": 7,
"radial_rank": 44,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.0014523006699393111007574155660663854299121764865735099182322484363574634541945808153914912716628743739706776946250582575375534126853217869944298593711429485400114753673764724233503784125406209897252614148233102045717392482721029462 +/- 3.23e-233]",
"strict_gap_below_F_third_over_D": "[0.16014403966477458889924258443393361457008782351342649008176775156364253654580541918460850872833712562602932230537494174246244658731467821300557014062885705145998852463262352757664962158745937901027473858517668979542826075172789705 +/- 2.87e-231]"
},
{
"l": 8,
"radial_rank": 44,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.0011089857797476277201880324597273231717919092599504921761613776404886423167977556503872743493972686358172774697197853932276710764632382023349070911331305000263335654137667593572533669443888567786012346288493797225203674904929134920 +/- 1.87e-233]",
"strict_gap_below_F_third_over_D": "[0.16048735455496627227981196754027267682820809074004950782383862235951135768320224434961272565060273136418272253028021460677232892353676179766509290886686949997366643458623324064274663305561114322139876537115062027747963250950708651 +/- 2.83e-231]"
},
{
"l": 9,
"radial_rank": 43,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00087521097274484791118683577453416261329621612459099129832600405269792014232373469421085912995257292744571822006668425254257626479413384043241627879616994947865241057997975248109592997667851426585800813635561845378605366173818310746 +/- 4.75e-235]",
"strict_gap_below_F_third_over_D": "[0.16072112936196905208881316422546583738670378387540900870167399594730207985767626530578914087004742707255428177993331574745742373520586615956758372120383005052134758942002024751890407002332148573414199186364438154621394633826181689 +/- 1.69e-231]"
},
{
"l": 10,
"radial_rank": 43,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00071045674048384475955090151417225673451374101771469059953015553062058060886007945311431704823423677640125804571302152689397943228836774136299774909643769132941135160381995584820705930302139328578940214857553888624480112680469835011 +/- 8.10e-235]",
"strict_gap_below_F_third_over_D": "[0.16088588359423005524044909848582774326548625898228530940046984446937941939113992054688568295176576322359874195428697847310602056771163225863700225090356230867058864839618004415179294069697860671421059785142446111375519887319530165 +/- 1.10e-231]"
},
{
"l": 11,
"radial_rank": 42,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00058831914448404300913811186133297711487154909335463765459642191029772838730532268593812308697919419634246834480986425021311386614244353651802061886905136669924158218068411239540368973279477587398937814628756513970550374747440495754 +/- 4.10e-234]",
"strict_gap_below_F_third_over_D": "[0.16100802119022985699086188813866702288512845090664536234540357808970227161269467731406187691302080580365753165519013574978688613385755646348197938113094863330075841781931588760459631026720522412601062185371243486029449625252559504 +/- 1.47e-231]"
},
{
"l": 12,
"radial_rank": 42,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00049647935585531303921718015142167584389964200197427336047961117002062645450019186026933839308348108081158510979685502707296305172103701274523277929469620409184300120666836342764539695548462849849629613585258385785763352223801389904 +/- 1.52e-234]",
"strict_gap_below_F_third_over_D": "[0.16109986097885858696078281984857832415610035799802572663952038882997937354549980813973066160691651891918841489020314497292703694827896298725476722070530379590815699879333163657235460304451537150150370386414741614214236647776198610 +/- 6.51e-233]"
},
{
"l": 13,
"radial_rank": 41,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00042440451189851845496503982821463142513661974435945365399482779750956656233427014329820006122381494994818272592005311447051097843333844785793509000919556251667607243943947986278103965943407495691273549695726608683922629030059929717 +/- 1.98e-234]",
"strict_gap_below_F_third_over_D": "[0.16117193582281538154503496017178536857486338025564054634600517220249043343766572985670179993877618505005181727407994688552948902156666155214206490999080443748332392756056052013721896034056592504308726450304273391316077370969940070 +/- 1.93e-231]"
},
{
"l": 14,
"radial_rank": 41,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00036795315839230791455584671166331471025988300847663592330082981634485179759749101617138128736014507265400911088352703399264670813510176220268421223748210557133428885306233890835189877364858042429689223683576096411265208680056998184 +/- 3.85e-234]",
"strict_gap_below_F_third_over_D": "[0.16122838717632159208544415328833668528974011699152336407669917018365514820240250898382861871263985492734599088911647296600735329186489823779731578776251789442866571114693766109164810122635141957570310776316423903588734791319943002 +/- 2.75e-231]"
},
{
"l": 15,
"radial_rank": 40,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00032170962970077320052370409394059819972428451858955684042970730884130044732181866647476967800149563102175177403631287056196909714164550605747704293394227831539881004030288060820160908916932409370709804412555585503976199750868671295 +/- 5.84e-236]",
"strict_gap_below_F_third_over_D": "[0.16127463070501312679947629590605940180027571548141044315957029269115869955267818133352523032199850436897824822596368712943803090285835449394252295706605772168460118995969711939179839091083067590629290195587444414496023800249131329 +/- 3.89e-231]"
},
{
"l": 16,
"radial_rank": 40,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00028452220916912356032942668632839435719528924358924089685953848989729897151849611891793880225985518544625755907546923778781579286890612202239541528925116904337075147237389492184193152193863534235093117507857210945927676152364059430 +/- 3.76e-234]",
"strict_gap_below_F_third_over_D": "[0.16131181812554477643967057331367160564280471075641075910314046151010270102848150388108206119774014481455374244092453076221218420713109387797760458471074883095662924852762610507815806847806136465764906882492142789054072323847635940 +/- 4.86e-231]"
},
{
"l": 17,
"radial_rank": 39,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00025296874654293430510424818905199200512887759648887866451346929635579396076870467441084622174422518505993340538989476039004524442484206865063396920502607263346923476535485562165498257626805116315953540456048611852012770604354296481 +/- 2.73e-234]",
"strict_gap_below_F_third_over_D": "[0.16134337158817096569489575181094800799487112240351112133548653070364420603923129532558915377825577481494006659461010523960995475557515793134936603079497392736653076523464514437834501742373194883684046459543951388147987229395645703 +/- 4.29e-231]"
},
{
"l": 18,
"radial_rank": 39,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00022717096957860641737546982877444919507142758098405097734332366360121093128140877462543172199475331173746468675519229884129864001982104430382928497504777427718319055162315299341640931746562476013445258760418799305618053580003047151 +/- 3.45e-234]",
"strict_gap_below_F_third_over_D": "[0.16136916936513529358262453017122555080492857241901594902265667633639878906871859122537456827800524668826253531324480770115870135998017895569617071502495222572281680944837684700658359068253437523986554741239581200694381946419996953 +/- 2.51e-231]"
},
{
"l": 19,
"radial_rank": 38,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00020459418265734182234846612969969822143369861904966737287519554331054383435003656569329210794819566734930534749342598118518987454713499419658846819376699381720617084540602852958911685894449013248764683016865487786646184155400809921 +/- 2.99e-234]",
"strict_gap_below_F_third_over_D": "[0.16139174615205655817765153387030030177856630138095033262712480445668945616564996343430670789205180433265069465250657401881481012545286500580341153180623300618279382915459397147041088314105550986751235316983134512213353815844599190 +/- 1.98e-232]"
},
{
"l": 20,
"radial_rank": 38,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00018596550451863655304469306252277094138371080257368439013086490980970299407901526830377582336105041597207112812859409389060434957541706156767564098717350194814621043402033733562995612257261196996352525859042488179421006702009192363 +/- 1.71e-234]",
"strict_gap_below_F_third_over_D": "[0.16141037483019526344695530693747722905861628919742631560986913509019029700592098473169622417663894958402792887187140590610939565042458293843232435901282649805185378956597966266437004387742738803003647474140957511820578993297990808 +/- 4.53e-231]"
},
{
"l": 21,
"radial_rank": 37,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00016918686501428884016125786315346121915597370634005209110507256502229884876110993572338333825391339184168752362028364603390275831565120565680344467960295242927740256876887554719365837769318627269603351662350579243404947952913358113 +/- 1.30e-234]",
"strict_gap_below_F_third_over_D": "[0.16142715346969961115983874213684653878084402629365994790889492743497770115123889006427661666174608660815831247637971635396609724168434879434319655532039704757072259743123112445280634162230681372730396648337649420756595052047086642 +/- 2.04e-231]"
},
{
"l": 22,
"radial_rank": 37,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00015529824844256070497318456553089853465437990494821773992662915196722510300242110058612568228562616722404273133782619119579442265782224827045200057300625349510884762052508224868188561799491264252006945927283211444239621645642783649 +/- 3.62e-235]",
"strict_gap_below_F_third_over_D": "[0.16144104208627133929502681543446910146534562009505178226007337084803277489699757889941387431771437383277595726866217380880420557734217775172954799942699374650489115237947491775131811438200508735747993054072716788555760378354357216 +/- 2.52e-231]"
},
{
"l": 23,
"radial_rank": 36,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00014243380111067290596274186185951417235072218791575489589488106211570955056160266392089411245281980212222922773047554680441808615008592363248892398170814203691794925766054140498033020812070360743735480321770894146647170823530862758 +/- 4.60e-234]",
"strict_gap_below_F_third_over_D": "[0.16145390653360322709403725813814048582764927781208424510410511893788429044943839733607910588754718019787777077226952445319558191384991407636751107601829185796308205074233945859501966979187929639256264519678229105853352829176469137 +/- 1.49e-231]"
},
{
"l": 24,
"radial_rank": 36,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00013180624391890658609013367336676418797356193823036428115802642619169003885459913759545105823219222292724873732689888098125594406443596858842289004304565825322882655620250776616123352108651984953231155962944471239157965463337676910 +/- 3.02e-234]",
"strict_gap_below_F_third_over_D": "[0.16146453409079499341390986632663323581202643806176963571884197357380830996114540086240454894176780777707275126267310111901874405593556403141157710995695434174677117344379749223383876647891348015046768844037055528760842034536662323 +/- 6.0e-234]"
},
{
"l": 25,
"radial_rank": 35,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00012168115963643848580341091427595490849577766772701456428887575721542319116630237095421783733885318659763353514788913774220831590980634806286596798374811783851749801900185685648016518449956945339299564645403511451474207803276569767 +/- 4.68e-234]",
"strict_gap_below_F_third_over_D": "[0.16147465917507746151419658908572404509150422233227298543571112424278457680883369762904578216266114681340236646485211086225779168409019365193713403201625188216148250198099814314351983481550043054660700435354596488548525792196723430 +/- 1.46e-231]"
},
{
"l": 26,
"radial_rank": 35,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00011337192261951399920340949232613690327093528655532275638190577864361827903441244434397725594302414960699034939004770515231279501053665888789906419653358152119179408370491887526620583085745323190118991967098568516793629398425677130 +/- 2.92e-234]",
"strict_gap_below_F_third_over_D": "[0.16148296841209438600079659050767386309672906471344467724361809422135638172096558755565602274405697585039300965060995229484768720498946334111210093580346641847880820591629508112473379416914254676809881008032901431483206370601574323 +/- 2.26e-231]"
},
{
"l": 27,
"radial_rank": 34,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00010522238909836485057372251366746254262910137380892270429780144410222892335947047873762845744527847070393610611459094140263623989738600539492727212952995741626311991093812917675394375431563703261566391726000057760133238071051697116 +/- 1.10e-234]",
"strict_gap_below_F_third_over_D": "[0.16149111794561553514942627748633253745737089862619107729570219855589777107664052952126237154255472152929606389388540905859736376010261399460507272787047004258373688008906187082324605624568436296738433608273999942239866761928948303 +/- 2.05e-231]"
},
{
"l": 28,
"radial_rank": 34,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[9.8607282311692237765149741331105677122821390909229037728666413133296914450044638843377309636523938665263258238081356363206869039673492013502018552578998784991192979190501770541098600481188305985907151552270151440363164794860984473e-5 +/- 3.89e-235]",
"strict_gap_below_F_third_over_D": "[0.16149773305240220776223485025866889432287717860909077096227133358686670308554995536115662269036347606133473674176191864363679313096032650798649798144742100121500880702080949822945890139951881169401409284844772984855963683520513901 +/- 4.65e-231]"
},
{
"l": 29,
"radial_rank": 33,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[9.1919084773398773981923864327765354193305815652047028118815239039023936548454534561511611623091627278435857009939557692442136490848858122418142507771696599090575379026842104968991412850759827588009638421590992758834232032888020256e-5 +/- 4.39e-235]",
"strict_gap_below_F_third_over_D": "[0.16150442124994050122601807613567223464580669418434795297188118476096097606345154546543848838837690837272156414299006044230755786350915114187758185749222830340090942462097315789503100858714924017241199036157840900724116576796711198 +/- 1.11e-231]"
},
{
"l": 30,
"radial_rank": 33,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[8.6571365711997146980004491852747747292925120508730464280191153467588802298723637190783322288571966384834707992176873700140012873648021467745632160236719164215173607537974399124402618621617236585127096898305365898504155365339770375e-5 +/- 1.33e-235]",
"strict_gap_below_F_third_over_D": "[0.16150976896900190285301999550814725225270707487949126953571980884653241119770127636280921667771142803361516529200782312629985998712635197853225436783976328083578482639246202560087559738137838276341487290310169463410149584463466023 +/- 1.35e-231]"
},
{
"l": 31,
"radial_rank": 32,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[8.0987915035679573171266249718651858617715226796522318830691075919258955806439794668825450399385558053506364034726515972751582446758323202481821954478612959917350580705985979823251578466771974970214982994618565485297470338894984730e-5 +/- 4.25e-235]",
"strict_gap_below_F_third_over_D": "[0.16151535241967822042682873375028134814138228477320347768116930892408074104419356020533117454960061444194649363596527348402724841755324167679751817804552138704008264941929401402017674842153322802502978501700538143451470252966110501 +/- 4.37e-231]"
},
{
"l": 32,
"radial_rank": 32,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[7.6607717763373273170605171758615638766010471999625625245841379967652328054541064794749642760923803489155535589727816034195129895874452753527610974613709212837560388928388536137443574986367082991348150869874913290547627715032709126e-5 +/- 8.00e-236]",
"strict_gap_below_F_third_over_D": "[0.16151973261695052672682939482824138436123398952800037437475415862003234767194545893520525035723907619651084446441027218396580487010412554724647238902538629078716243961107161146386255642501363291700865184913012508670945237228496729 +/- 3.5e-234]"
},
{
"l": 33,
"radial_rank": 31,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[7.1875347986808409933558289071281027608230837693457884745646003845038705330611300471586165487316063366554912185976596913719787527883124488884920003591095777272111352630726052402673024615959431918468333035657273553908215710289094202e-5 +/- 4.47e-235]",
"strict_gap_below_F_third_over_D": "[0.16152446498672709159006644171092871897239176916230654211525435399615496129466938869952841383451268393663344508781402340308628021247211687551111507999640890422272788864736927394759732697538404056808153166696434272644609178428971090 +/- 4.86e-231]"
},
{
"l": 34,
"radial_rank": 31,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[6.8246898463763798148639116618111227525071174924587147195289545397595293246108042826712237681624657983656042976758368832682806994940669858882108200981941873129124131895298882544220450537126741527396629953116991766610060164626817344e-5 +/- 1.92e-235]",
"strict_gap_below_F_third_over_D": "[0.16152809343625013620185136088338188877247492882507541285280471045460240470675389195717328776231837534201634395702324163116731719300505933014111789179901805812687087586810470111745577954946287325847260337004688300823338993983537318 +/- 1.68e-231]"
},
{
"l": 35,
"radial_rank": 30,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[6.4181113474444449360783415966758647662858376420580356596374307661943870599090088592857653781621248002595892953811540952177018787972365889192502077092563963779502013223198228308736737645970331686382956257711537722447874381227059366e-5 +/- 2.92e-235]",
"strict_gap_below_F_third_over_D": "[0.16153215922123945555063921658403324135233714162357941964340362569233805612940090991140714234621837875199740410704618845904782298121202763411080749792290743603622049798677680177169126326235402966831361704374228846227755212561877294 +/- 2.27e-232]"
},
{
"l": 36,
"radial_rank": 30,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[6.1145890975685972999157108228659968031875446767219164670297436587997686657313502635676750794169851044304708874376330841733559530940795807159120661552072096051033633488068890638603663084854391152164562645556800055639959668319899286e-5 +/- 2.01e-235]",
"strict_gap_below_F_third_over_D": "[0.16153519444373821402700084289177134003196812455323278083532970256341200231334268649736432324920583014895569529112562366915826644046905920419284087933844792790394896636651193110936139633691514560884783543735444319994436004033168010 +/- 2.74e-232]"
},
{
"l": 37,
"radial_rank": 29,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[5.7609864336590453577576207796914895294713926473610469282869465654346216046255879897968328683707049119253921066734325638281712795522162526351397921369039300734171438581558114985176461734718991762015341275706773441335996988093695816e-5 +/- 3.68e-235]",
"strict_gap_below_F_third_over_D": "[0.16153873047037730954642242379220308510470528607352638953071713053434565378395374412010203167131629295088074607893326567436171828720447783747364860207863096069926582856141844188501482353826528100823798465872429322655866400301190630 +/- 3.27e-231]"
},
{
"l": 38,
"radial_rank": 29,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[5.5049258248526532775066034882665948446073705330200988452268664338636661222881097082220592917021522995044096548441599669793031424310702350066269217857954929381701936078755559958898708908567939239441662471152588932653408926336631203e-5 +/- 4.12e-235]",
"strict_gap_below_F_third_over_D": "[0.16154129107646537346722493396511733405155392629466979901154773133566136333877711890291777940708297847700495590345155840033020696857568929764993373078214204507061829806392124444004110129109143206076055833752884741106734659107366337 +/- 2.20e-231]"
},
{
"l": 39,
"radial_rank": 28,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[5.1939751518557558884699298584234553932201619249375719021482452155378006680422462015332664916898303235928983504985164783167595712095684770753176443210482613764152294820013696830624226919016598654033705149037196947030964866268748256e-5 +/- 1.10e-235]",
"strict_gap_below_F_third_over_D": "[0.16154440058319534244111530070141576544606779838075062428097851754784462199331957753798466733508310169676407101649501483521683240428790431522924682355678951738623584770517998630316937577308098340134596629485096280305296903513373125 +/- 7.79e-232]"
},
{
"l": 40,
"radial_rank": 28,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.9763557603055375889602684494637250330994208235627662551040997165310418618774184354488710794139599291476912058255194764389702073704343623880804428463013538576236861945177681300916778360322075698707349278243398092340556365260871711e-5 +/- 3.51e-235]",
"strict_gap_below_F_third_over_D": "[0.16154657677711084462411039731550536274966900579176437233744895900283468958138122581564551128920586040070852308794174480523561029792629565637611919557153698646142376313805482231869908322163967792430129265072175660190765944363473913 +/- 2.62e-231]"
},
{
"l": 41,
"radial_rank": 27,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.7001468091827311851862998680539741622525608164704132231408893980039038174251177566092936611891345204844225026098267883551429568043324651493100147965170162937418969804659442184724853143886546301832275476676139431400286797361213522e-5 +/- 6.18e-236]",
"strict_gap_below_F_third_over_D": "[0.16154933886662207268814813700131946025837747439183529586776859110601996096182574882243390706338810865479515577497390173211644857043195667534850689985203482983706258103019534055781527514685611345369816772452332386056859971320263879 +/- 4.46e-231]"
},
{
"l": 42,
"radial_rank": 27,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.5140079419577597023387651550492827831733671345128044124180193568641470413557765319273316690988474852072860283111128267144577013734818581368627509384625579512375614586552728432006412352850691454792166667546951954156522611541527193e-5 +/- 4.93e-235]",
"strict_gap_below_F_third_over_D": "[0.16155120025529432240297661234844950717216826632865487195587581980643135852958644223468072668330901152514792713971688887173285542298626518141863137249061537442048762438541344727156799358764714930854520783333245304804584347738845847 +/- 1.90e-231]"
},
{
"l": 43,
"radial_rank": 26,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.2663955272839114535646131519908406676342393074078337884067029237510474039815277585964461226445805556949227729266131658316846271319024763881783548988301335113155888881130155395702543248490515758097690947766243117881248609939719370e-5 +/- 1.12e-235]",
"strict_gap_below_F_third_over_D": "[0.16155367637944106088546435386848009159332365760692592166211593297076248952596018472241403553877355419444305077227073386834168315372868097523611821645101169866488684411111886984460429745675150948424190230905223375688211875139006028 +/- 2.78e-232]"
},
{
"l": 44,
"radial_rank": 26,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.1062950556528567989322648271841941520955120620102683566826057035545600342510906784665768174470536071530777797499425398099256879895923537684984294130334653110648862243616743101854047358968090480574405763037693346954496997194752575e-5 +/- 1.10e-235]",
"strict_gap_below_F_third_over_D": "[0.16155527738415737143201067735172815805847904487937989731643317394296445439965748909321533423182552946392846922220250057460190074312010407646231501570586966534688935113775638325689814595264103190951942559423696230665304550300280525 +/- 3.47e-231]"
},
{
"l": 45,
"radial_rank": 25,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.8824453735357300376951879830291308525338669174717928785764755492745859937444884339224850866990681146606286552145270643681349982662390426297654371050372651578770491271447998591875008568693914017788960944815064847356087345130743463e-5 +/- 2.47e-235]",
"strict_gap_below_F_third_over_D": "[0.16155751588097854269962304812016970869147466133082528207121423524450725414006255511566077514913300931885339371344785472935631865001733760957370234562894962734842122950872855200140812499143130608598221103905518493515264391265486926 +/- 4.44e-231]"
},
{
"l": 46,
"radial_rank": 25,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.7440776811041964484806405181378730778952519249774272433828864969854208048079874514098522070752665350647068662215809717956377253844416668314616872611398890091783422664891437340341025462851126948384798254376422337891051375490455612e-5 +/- 1.03e-235]",
"strict_gap_below_F_third_over_D": "[0.16155889955790285803551519359481862126922104748075022572756617113503014579195192012548590147792924733464935293133778419028204362274615558333168538312738860110990821657733510856265965897453714887305161520174562357766210894862450954 +/- 3.46e-231]"
},
{
"l": 47,
"radial_rank": 24,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.5401452423221049430078640943881949580980949113308977916616561921781222841034537088737678969238503754458596597142590621202422312591271870208415003774910152485589662835277919921371833127304055981482285719268353040823731113469805479e-5 +/- 3.47e-235]",
"strict_gap_below_F_third_over_D": "[0.16156093888229067895056992135905611805041901905088669102208338343807821877715896546291126232103076149624554140340285740937879757768740872812979158499622508984751441033716472208007862816687269594401851771428073164695917626888653019 +/- 3.67e-231]"
},
{
"l": 48,
"radial_rank": 24,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.4200669449002473504674769526611196590010555470442925058072157634942155551288886554607098202954452809741068713043016415370767392125543301923076202283772103199551086187875904055974368084561741423548462152353878127403362535189312256e-5 +/- 3.93e-235]",
"strict_gap_below_F_third_over_D": "[0.16156213966526489752649532523047338880340998944452955707494192784236505784444871111344539290179704554719025893128695698358462923260787445669807692379771622789680044891381212409594402563191543825857645153784764612187259663746481069 +/- 3.10e-231]"
},
{
"l": 49,
"radial_rank": 23,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.2329608270563605350383629195509158814681172391344687909081906249298228968917122931886361388871702831604725199825351913583604375128869542377839641472731674910882809298675824914412202595312088490695940393169603380356821270143456228e-5 +/- 1.46e-236]",
"strict_gap_below_F_third_over_D": "[0.16156401072644333639464961637080449084118531882760865531209091809375070177103108287706811363861112829716839527480017464808641639562487113045762216035852726832508911719070132417508558779740468791150930405960683039661964317872985654 +/- 2.84e-231]"
},
{
"l": 50,
"radial_rank": 23,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.1283908430073131052053019623862664294499390648864509071712817381792530231347440127552075216990718388157032670844349838100868672498170410836894312985927148044682937005957286471908219166056850451071128606735915583689600027981538009e-5 +/- 1.87e-235]",
"strict_gap_below_F_third_over_D": "[0.16156505642628382686894794698037613733570550060935113549092828718261820746976865255987244792478300928161184296732915565016189913132750182958916310568701407285195531706299404271352809178083394314954892887139326408441631039997201846 +/- 1.06e-231]"
},
{
"l": 51,
"radial_rank": 22,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.9556030921510850482826313798519607748608668649971796593361399214612985214971908367067501991251333879621489697002690897156254549756788382927203899370030328045847576301071755778120332264475775530987799197888200221654562927826531639e-5 +/- 3.81e-235]",
"strict_gap_below_F_third_over_D": "[0.16156678430379238914951717368620148039225139133135002820340663860078538701478502809163293249800874866612037851030299730910284374545024321161707279610062996967195415242369892824422187966773552422446901220080211179977834543707217347 +/- 2.57e-231]"
},
{
"l": 52,
"radial_rank": 22,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.8642748710642034870722375721475035043991676314266727176092676174749920861393647921491595299181186838000928391684769027635008783249985023614398990699284104438103911041631586182867032226753107632361123882199332981568018595547469186e-5 +/- 2.72e-235]",
"strict_gap_below_F_third_over_D": "[0.16156769758600325796512927762427852496495600832368573327282390732382525007913860635207850840470081881316199907160831523097236499121675001497638560100930071589556189608895836841381713296777324689236763887611780066701843198140445253 +/- 1.60e-232]"
},
{
"l": 53,
"radial_rank": 21,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.7037528439861744724713144451965767721499441064644954363899729722654022277210223893748909341755780418812328739496751530541291070911047045081433654275574777094765407222428576083444835142817174243556825646134254729123360488103051348e-5 +/- 1.10e-235]",
"strict_gap_below_F_third_over_D": "[0.16156930280627403825527528685554803423227850055893535504563610027027734597772278977610625109065824421958118767126050324846945870892908895295491856634572442522290523459277757142391655516485718282575644317435386574527087663951189695 +/- 2.26e-231]"
},
{
"l": 54,
"radial_rank": 21,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.6238037485116451180048333020278649585130830658964967862194756162669931637507421330691715992919144812079628432853535273387758275933334430593070940922410669285497644360599254253869652294922805398298232849654585502488429158844289958e-5 +/- 4.20e-235]",
"strict_gap_below_F_third_over_D": "[0.16157010229722878354881995166697972135041486916934103503213780524383733006836249257866930828400708085518792037156714646472661224172406666556940692905907758933071450235563940074574613034770507719460170176715034541449751157084115571 +/- 8.65e-232]"
},
{
"l": 55,
"radial_rank": 20,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.4738539792677064402812633062960220686546844706575866570336632634487486305625619758008003222090725137702190443902537427861766611372996536960529808902024799107577938692287800685667360286597547031225797721960066632302728410763102856e-5 +/- 3.87e-235]",
"strict_gap_below_F_third_over_D": "[0.16157160179492122293559718736693703977931345315529342413342966336736551251369437438024199199677790927486229780955609746257213823338862700346303947019109797520089242206130771219931433263971340245296877420227803993336769727158923690 +/- 3.73e-231]"
},
{
"l": 56,
"radial_rank": 20,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.4037415049784475898499067028230166478660578402167984470920024331232705984468631611775748530510629065845760433699245434789658183356238547547809616321416537114210028882681510212604629747292612479020603463037814207211940583369179626e-5 +/- 1.57e-235]",
"strict_gap_below_F_third_over_D": "[0.16157230291966411552410150093297176983352133942159783201552907997566876729401553136838822425146948937093415423956630075456521034181664376145245219038367858346288578997111731848978739537025270738752097939653696218579278805941663082 +/- 5.89e-232]"
},
{
"l": 57,
"radial_rank": 19,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.2629564935800327482060000981073383885514671113085542424537881652279809337001136883031688442712571328463929425452220975041720268754711193971266405141873109533877053423089221538838275636074132214205012945571616198595514965093968763e-5 +/- 2.09e-235]",
"strict_gap_below_F_third_over_D": "[0.16157371076977809967251793999901892661611448532888691445757546211834772019066299886311696831155728742867153607057454777902495827973124528880602873359485812689046612294657691077846116172436392586778579498705442838380140448503490603 +/- 3.27e-232]"
},
{
"l": 58,
"radial_rank": 19,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.2013941271698622902968782806973636893166000311809328879536159309597298831535125771497308174200598110135838465834698090768599639591106870414477721720451251986754263521035523233325195569881141153775150082474838747984458450679547059e-5 +/- 1.14e-235]",
"strict_gap_below_F_third_over_D": "[0.16157432639344220137709703121719302636310683399968819067112046384069040270116846487422850269182579940188986416153416530190923140036040889312958552227827954874801324573647896447676667480443011885884622484991752516125201554154932045 +/- 2.00e-231]"
},
{
"l": 59,
"radial_rank": 18,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.0685960033581873792965002719082556857678091917847222233373446222867042204749167352021756145714125634797384846307964595276694963256513935600450137341113752962093647669228400053819227221696527053538260060745278862446513279384994490e-5 +/- 1.49e-235]",
"strict_gap_below_F_third_over_D": "[0.16157565437468031812620703499728091744314232190808215277776662655377713295779525083264797824385428587436520261515369203540472330503674348606439954986265888624703790635233077159994618077277830347294646173993925472113755348672061500 +/- 4.65e-231]"
},
{
"l": 60,
"radial_rank": 18,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.0145036230563877709627272463199175901223176492054457826209422241953494578713456321083120378620204146197783477890004021657677659640562060173210554404299220021323733099063434497594021408639609943681581033937211840344254363308404917e-5 +/- 1.50e-235]",
"strict_gap_below_F_third_over_D": "[0.16157619529848333612229037272753680082409877682350794554217379057775804650542128654367891687962137979585380221652210999597834232234035943793982678944559570077997867626690093656550240597859136039005631841896606278815965574563669159 +/- 4.19e-231]"
},
{
"l": 61,
"radial_rank": 17,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.8887003765264472112491326129916793351122280303780980945601087649308062887796861617697916545019277230874348748534362225020153125864712347340803728112611467980687609443656704255079592888198244955616720741567720187556226424593987751e-5 +/- 2.04e-235]",
"strict_gap_below_F_third_over_D": "[0.16157745333094863552788750867387008320664887771969621901905439891235069193711220313838230208345498072276912565125146563777497984687413528765265919627188738853201931239055634329574492040711180175504438327925843227981244377357540601 +/- 1.30e-231]"
},
{
"l": 62,
"radial_rank": 17,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.8411655405195312674775645881209514493059129666162739844551553900262603590371860576470643179289744704689586251839647504085836903072775177145431977374502044792474795981517120409888284799873488828584950213223099001572345296460413541e-5 +/- 6.37e-236]",
"strict_gap_below_F_third_over_D": "[0.16157792867930870468732522435411879048550694087033383726015544844609973739640962813942352935682071025529531041374816035249591416309692722482285456802262549795520752520401848287959011171520012651117141504978677690099842765470353959 +/- 4.46e-231]"
},
{
"l": 63,
"radial_rank": 16,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.7215167090898808147246639273678473517964331415925234160312932440841297819448414439881462186918831786614147948833854387934807947015644096594692079820045799499582035754641726309959347417508095251535421757415489909720390194495623429e-5 +/- 3.39e-235]",
"strict_gap_below_F_third_over_D": "[0.16157912516762300119185275336072632152648203566858407476583968706755915870218055158556011853781308116821338585205116614561206519205298435590340530792017995420050041796424535827369004065258249190474846457824258451009027960980550438 +/- 4.34e-231]"
},
{
"l": 64,
"radial_rank": 16,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.6797641799912482792087404365788357396992162911824471898393601885605833657293832090516651267539113780253769905602926036559293985794763489562400039247446638559367492541238871427565729939992028898252322764411473151754583204393858390e-5 +/- 3.51e-235]",
"strict_gap_below_F_third_over_D": "[0.16157954269291398751720791259563421164260300783708817552810160639811439416634270616790948334873246088621974623009439707396344070601420523651043759996075255336144063250745876112857243427006000797110174767723558852684824541679560614 +/- 6.36e-232]"
},
{
"l": 65,
"radial_rank": 15,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.5655537269240383969640046337490175362676600081937643564422022401154663066104166538772568529679163492286071741872061962828149739977891937489082105805831365004532717611002319303995838933995401557885009174538150353389131531923670180e-5 +/- 2.79e-235]",
"strict_gap_below_F_third_over_D": "[0.16158068479744465961603035995366250982463732339991806235643557797759884533693389583346122743147032083650771392825812793803717185026002210806251091789419416863499546728238899768069600416106600459844211499082546184964661086846807633 +/- 1.18e-231]"
},
{
"l": 66,
"radial_rank": 15,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.5289212860580828865048668698225392740992943258274353454997637519673237184593264234061328386688720603323407931516547607212664816762962355171631304512014111175605544778280143717130617269408806362584490602641765858937764596413451980e-5 +/- 4.49e-235]",
"strict_gap_below_F_third_over_D": "[0.16158105112185331917113495133130177460725900705674172564654500236248032676281540673576593867161331127939667659206848345239278733518323703764482836869548798588882439445522171985628286938273059119363741550939735823414106223540358655 +/- 2.93e-231]"
},
{
"l": 67,
"radial_rank": 14,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.4195359926439343966781183558509795229200120785031552496581407114825893156211522736453434461116969080334284808484990176924660173423155705220539226347962910808439697857340310537430117825096286641668528642447391304933589080805262093e-5 +/- 2.57e-235]",
"strict_gap_below_F_third_over_D": "[0.16158214497478746065603321881644149020477079987921496844750341859288517410684378847726354656553888303091966571519151500982307533982657684429477946077365203708919156030214265968946256988217490371335833147135755260869506641091919474 +/- 3.09e-231]"
},
{
"l": 68,
"radial_rank": 14,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.3874551008668902651971346347212966734588673909520585173228886764376054461532514891432047372259117814995692323187522796167214995209735040784369038568460386582515562190990280052937098005102019528840101976138736490501035142544893949e-5 +/- 2.97e-235]",
"strict_gap_below_F_third_over_D": "[0.16158246578370523109734802865365278703326541132609047941482677111323562394553846748510856795262774088218500430767681247720383278500479026495921563096143153961341748443780900971994706290199489798047115989802386126350949896485745511 +/- 4.81e-231]"
},
{
"l": 69,
"radial_rank": 13,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.2823672268005255722682163617172250356685098297029544883856365593643872387802386973705796594968604210994973116211539418360751423041987943739081645146022191619728135988895554531219300692766247635616719946058199777378336010425079480e-5 +/- 2.60e-235]",
"strict_gap_below_F_third_over_D": "[0.16158351666244589474427731783638282774964331490170297045511614363440635612761219761302629420340503139578900502688378846058163924857695801205626091835485397780838027186401110444546878069930723375236438328005394180022262166398957492 +/- 3.47e-232]"
},
{
"l": 70,
"radial_rank": 13,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.2543474510802318865736449632858092929020511956283805527462491572797007833587161642608280587532053859235871964401986781053620505885749772147893908603566416147618229849109411112241301365865704469569761735449758079964411287152347636e-5 +/- 8.98e-236]",
"strict_gap_below_F_third_over_D": "[0.16158379686020309768113426355036714190707097948804371619447253750842720299216641283835739171941246794614076412803559801321894637949411425022785210609139643358385238177015089058888775869863413429553043023826455024192003558871284765 +/- 1.37e-231]"
},
{
"l": 71,
"radial_rank": 12,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.1531007241317237341377533217590913222328884907559985362277491320547773120225845901137647533662535185325275138089101364668668866500429432940563835330671005094448075539511207903621130826320041944143100428986610741299928299510331180e-5 +/- 2.89e-235]",
"strict_gap_below_F_third_over_D": "[0.16158480932747258276265862246678240908677767111509244001463772250867945222687977415409886235246633746481467472486191089863533133113349957056705943616466932899490555192446048879209637886917367995805585689957101338925870007170048967 +/- 2.16e-231]"
},
{
"l": 72,
"radial_rank": 12,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.1287171131397024646969620916311646281236529421735565136768141264605596730253616937967378181098177311816656883061557403543961692534071632153690118852597132208550146749644219253933723157501263938427084102609745309507097577742067839e-5 +/- 7.4e-238]",
"strict_gap_below_F_third_over_D": "[0.16158505316358250297535303037908368835371876347057826443486323185873539440326974638306203262181890182268818334311693844259645603830746592836784630988114740286779144985325035578074606627684249873606157291589739025469049290242225793 +/- 1.28e-231]"
},
{
"l": 73,
"radial_rank": 11,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.0309153358051631119139842059884743333215086882379851560710402797027112712312109345640844853803984817833061121743553360465358447961423689035617832264916353752301663244330027050345129146897753737933041172879280168442379201850879423e-5 +/- 1.28e-235]",
"strict_gap_below_F_third_over_D": "[0.16158603118135584836888086015794011525666678491311762014843928959720297288728768789065435915514619601518216693887825644663953464155203857631096438216773508364624769833675566997294965487085310224626206695882712071983155762079814912 +/- 3.58e-232]"
},
{
"l": 74,
"radial_rank": 11,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.0097981219910905594639282492941022744840591594750930919496759419379858502152534733107341927377038409071025951121576685515490360248539564522035253749141306211314201215858937085691961503745759870842853948746210113242997825898757966e-5 +/- 4.58e-235]",
"strict_gap_below_F_third_over_D": "[0.16158624235349398909440536071750705897725515940840524906908050324058062014149784746526689265807262296159092897404887842331448450963975146043547796474625085869378868579878414106291430803849625424012915714605125378988675700217410124 +/- 1.08e-231]"
},
{
"l": 75,
"radial_rank": 10,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[9.1509584996446905856277421852994270145347640603386079779755822636192131288603261341813022644250936865314364992538542236579928352012858633646642727473572675896802886500813108005197678228893250633186565873811360231072542300069745487e-6 +/- 2.60e-236]",
"strict_gap_below_F_third_over_D": "[0.16158718937621425530941437225781470057298546523593966139202202441773638078687113967386581869773557490631346856350074614577634200716479871413663533572725264273241031971134991868919948023217711067493668134341261886397689274576999302 +/- 4.56e-231]"
},
{
"l": 76,
"radial_rank": 10,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[8.9692199977561287266037115836399276468654283437719765341620490770192352797698520550498918304363278825715364366011130206526497860281252699974444339992790517363052339814045603546027104248887635029071791198024514534441707217842273788e-6 +/- 2.63e-236]",
"strict_gap_below_F_third_over_D": "[0.16158737111471614387127339628841636007235313457165622802346583795092298076472023014794495010816956367211742846356339888697934735021397187473000255556600072094826369476601859543964539728957511123649709282088019754854655582927821577 +/- 1.64e-231]"
},
{
"l": 77,
"radial_rank": 9,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[8.0501687173697777464160305906276444240503626080782809234356233608990690987490998370120178140650563551173947541508416206781445802616171405163889965105094980719282122491243952919578254209930740919955031638114386325540576783029246973e-6 +/- 1.85e-237]",
"strict_gap_below_F_third_over_D": "[0.16158829016599653022225358396940937235557594963739192171907656437663910093090125090016298798218593494364488260524584915837932185541973838285948361100348949050192807178775087560470804217457900692590800449683618856136744594232169707 +/- 4.40e-231]"
},
{
"l": 78,
"radial_rank": 9,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[7.8950311363604125674069946583419832471935479395711485143394617362027565712017731096275955711986061016769900302864523071205785842845602840412196011039701527084998052206185469057706041921373853568234009531610004493576240471511193290e-6 +/- 4.00e-237]",
"strict_gap_below_F_third_over_D": "[0.16158844530357753958743259300534165801675280645206042885148566053826379724342879822689037240442880139389832300996971354769287942141571543971595878039889602984729150019477938145309422939580786261464317659904683899955064237595284888 +/- 2.25e-232]"
},
{
"l": 79,
"radial_rank": 8,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[7.0012950559971305988881839041716374229758718278648303685905862513499285330357686663742468028082516285266251615380960362070487062529423938333844028527316276335022354343715385765287576885236429079351973239840264311338410126586948179e-6 +/- 4.68e-236]",
"strict_gap_below_F_third_over_D": "[0.16158933903965790286940111181609582836257702412817213516963140941374865007146696423133362575319719174837147337483846190396379295129374705760616661559714726837236649776456562846142347124231147635709206480267601597356886615898734130 +/- 4.20e-231]"
},
{
"l": 80,
"radial_rank": 8,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[6.8702654708087535625986761835841777161368702592135325909665371436140288729780309369062651982710170529294191648755106866648302980152311225500453367251422653145107876921879617302102817532702237052295574575612588515548582626597014226e-6 +/- 1.82e-237]",
"strict_gap_below_F_third_over_D": "[0.16158947006924309124643740132381641582228386312974078646740903346285638597112702196906309373480172898294707058083512448931333516970198476887744995466327485773468548921230781203826978971824672977629477044254243874114844514173734030 +/- 2.31e-231]"
},
{
"l": 81,
"radial_rank": 7,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[5.9995029561744310936225712181455185164560713045844969023990483922101016385265424552470805575825357996763593147277434675803255477697671303298722365485986759162722038973675273924906322315817424093815466022617606207762969196580862782e-6 +/- 8.63e-237]",
"strict_gap_below_F_third_over_D": "[0.16159034083175772556890637742878185448148354392869541550309760095160778989836147345754475291944241746420032364068527225653241967445223023286967012776345140132408372779610263247260750936776841825759061845339773823937922370308034191 +/- 2.75e-231]"
},
{
"l": 82,
"radial_rank": 7,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[5.8903800247821275947782166341367439527022538057281124972386065724879863534920650066620903676910213483459544977410050074715282906896017034019698115921574604214705487072403761227506059766116873979922131479792852591988990706464770234e-6 +/- 2.37e-236]",
"strict_gap_below_F_third_over_D": "[0.16159044995468911787240522178336586325604729774619427188750276139342751201364650793499333790963230897865165404550225899499252847170931039829659803018840784253957852945129275962387724939402338831260200778685202071474080110092935352 +/- 2.12e-231]"
},
{
"l": 83,
"radial_rank": 6,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[5.0405199541210391134010719568247906167451077210013216977672963797711022509497444748084527443611700105861986925507438007841163176037371461507974997168555217475673711813529668595554356216487292094187235441621809988156782920065096785e-6 +/- 1.43e-236]",
"strict_gap_below_F_third_over_D": "[0.16159129981475977896088659892804317520938325489227899867830223270362022889774905025552519154725563882998941380130744925619921588368239626285384920250028314447825243262881864703314044456437835127079058127645583781900118432170799349 +/- 5.21e-232]"
},
{
"l": 84,
"radial_rank": 6,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.9513535411397563956698823634146170221627987577621641763256049071215947258029347443404766608495518377197951885337852945307038686532866723260403051875152136151885421008092365405200764030857219147190440658690989810825270529765743832e-6 +/- 3.44e-236]",
"strict_gap_below_F_third_over_D": "[0.16159138898117276024360433011763658538297783720124223783582367439509287840527419706525565952333915044816228020481146621470546929613134671332767395969481248478638481145789919076345947992359691427808528095593413090101891747294702342 +/- 4.74e-231]"
},
{
"l": 85,
"radial_rank": 5,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.1205582906393831649397327126916995600376996982328622855871571915100743917068028589520086027114062837178754983767739406531016222501493164348802824958412105783982024434728369756790711270327029328027837964306004932410489928842520214e-6 +/- 2.38e-236]",
"strict_gap_below_F_third_over_D": "[0.16159221977642326061683506026728730830043996230030176713771441284280848992560829319714104799139728859371628212450162322605934689837774985068356511971750415878942160179755652716302432092887296729706719721620356939950675895100711575 +/- 2.88e-231]"
},
{
"l": 86,
"radial_rank": 5,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.0496154974253102621970746601957090369360095577415722569129066445846846297769738435703805316144340668826360491251516495747188900011408711397061043324820297552725546840732389270565602335201868496486644828001834443638220414306778404e-6 +/- 1.22e-236]",
"strict_gap_below_F_third_over_D": "[0.16159229071921647468973780292533980429096306399044225842774308709335541531537022302615642961946838556593311736395087484835042528110999885912886029389566751797024472744531592676107294343976647981315035133551719981655563617795856932 +/- 1.32e-231]"
},
{
"l": 87,
"radial_rank": 4,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.2362497322322708670158474538421330232174587345991922211224861130855126862568560304700324303145807255744986758312434368476212885351212324893800190399810299165842891125455783401631406167904081507019046229693616880249696712735944935e-6 +/- 9.61e-238]",
"strict_gap_below_F_third_over_D": "[0.16159310408498166772913298415254615786697678254126540080777887751388691448731374314396952996756968541927442550132416875656315237871146487876751061998096001897008341571088745442165983685938320959184929809537703063831197503032872640 +/- 4.60e-231]"
},
{
"l": 88,
"radial_rank": 4,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.1819861945009751901976841645798537127557805127259557607012448534708548586782299908331372281376448697275866066358832467356137199629213921258038785499353638241637668673001782104457692534856192722877258922395674329466083391539781867e-6 +/- 1.01e-236]",
"strict_gap_below_F_third_over_D": "[0.16159315834851939902480980231583542014628724421948727404423929875514652914514132177000916686277186235513027241339336411675326438628003707860787419612145006463617583623313269982178955423074651438072771227410776043256705339166084602 +/- 9.49e-232]"
},
{
"l": 89,
"radial_rank": 3,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.3845904447329786549406030335223506240833516681914200444642227204060065452641787645765402091672755133130256008318820885447669860836965115050663742738064745767366950291832594699266280602429262114761445203502594912491082046000639600e-6 +/- 3.21e-236]",
"strict_gap_below_F_third_over_D": "[0.16159395574426916702134505939696647764937591664833180857995553577727959399345473582123542345979083272448668697439916811791145523301391630348849493362572619352542326330497081674053007337193975707378852385547964974050875089179539994 +/- 4.83e-231]"
},
{
"l": 90,
"radial_rank": 3,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.3456259819133884176866924720006451019397143647234818270480304644404935161571552579421830087093891202924615253470166105719163537767945364327109603346917020574807682340472681628240908299974262071638860238246737374912048873553504110e-6 +/- 1.98e-236]",
"strict_gap_below_F_third_over_D": "[0.16159399470873198661158231330752799935489806028563527651817295196953555950648384284474205781699129061087970753847465298338942808364622320546356728903966530829794251923176595273183717590917000257379283611397617532626250879511264465 +/- 1.39e-231]"
},
{
"l": 91,
"radial_rank": 2,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.5628941808749711768622958301954996904978771345331664061262308743563483130720342400945041680059679212806281861206540720573501447807651669187065558193668458455645353879302525798266927576907125718343109157890151817694130873562369987e-6 +/- 1.85e-236]",
"strict_gap_below_F_third_over_D": "[0.16159477744053302502882313770416980450030950212286546683359387376912564365168692796575990549583199403207871937181387934592794264985521923483308129344418063315415443546461206974742017330724230928742816568908421098481823058691264376 +/- 2.12e-231]"
},
{
"l": 92,
"radial_rank": 2,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.5379920570072978512057893270330148953332451152615622259910982063307608746866541008916825073370529561843699516893126076339014102776669751994201387396783813919172788241976242545358005454687452622063739215070481996287192002570583347e-6 +/- 4.36e-236]",
"strict_gap_below_F_third_over_D": "[0.16159480234265689270214879421067296698510466675488473843777400890179366923912531334589910831749266294704381563004831068739236609858972233302480057986126032161860808272117580237574546419945453125473779362607849295180037128079974294 +/- 7.19e-232]"
},
{
"l": 93,
"radial_rank": 1,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[7.6875237489321648701231828091130611489921031599605080988277311215501760291486959256361625598788065807853399339460689338490759703701834779741288048291660528853602948489353835913922334464625077561201265636052080850097745619936480286e-7 +/- 7.45e-238]",
"strict_gap_below_F_third_over_D": "[0.16159557158233900678351298768171908869388510078968400394919011722688784498239708513040743638374401211934192146600660539310661509240296298165220258711951708339471146397051510646164086077665535374922438798734363947919149902254380063 +/- 4.21e-231]"
},
{
"l": 94,
"radial_rank": 1,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[7.5680156980366266605556113033179416411795937641236002458711373874263546665269264947790807134964679782081367929508649541483059146372915935118347020495303797437602209800455427423954746229080109669724411479540269097853127677232181967e-7 +/- 4.55e-237]",
"strict_gap_below_F_third_over_D": "[0.16159558353314409633733394443886966820583588204062358763997541288626125736453334730735052209192865035320217918632070491350458516940853627084064881652979504696202562397790199544572576045253770919890330275588520459730902146872322768 +/- 2.78e-231]"
}
],
"strict_local_maximum_modulo_phase_and_rotations": true
},
{
"label": "down",
"depth": 3,
"N": 0,
"dimension": 2,
"precision_bits": 768,
"root_ball_euclidean_radius": "[1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8 +/- 1.68e-239]",
"inverse_frobenius_bound": "[2.4494897427831780981972840747058913919659474806566701284326925672509603774573150265398594331046402348185946012266141891248588654598377573416257839512372785528289127475276765712476301052709117702234813106789866908536324433525456040 +/- 3.53e-230]",
"residual_norm_bound": "0",
"contraction_bound": "[2.2045407758533295167270899618271544768870269084888455575594336958239420414644646562578185694137545106506558455597365738922155462884305779869764775809909025512578571312616471567058968084867109090138684902815319538052292715781883737e-7 +/- 6.94e-238]",
"self_mapping_bound": "[2.2045407758533295167270899618271544768870269084888455575594336958239420414644646562578185694137545106506558455597365738922155462884305779869764775809909025512578571312616471567058968084867109090138684902815319538052292715781883737e-15 +/- 4.67e-246]",
"F_over_D_center": "1.0",
"certified_unique_stationary_root_in_ball": true,
"full_angular_hessian_certificate": [
{
"l": 0,
"radial_rank": 1,
"known_eigenvalue_over_F": "1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"remaining_trace_over_D_upper": "[3.0000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001438681e-8 +/- 5.00e-238]",
"strict_gap_below_F_third_over_D": "[0.33333329999999990000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 +/- 3.13e-231]"
}
],
"strict_local_maximum_modulo_phase_and_rotations": true
},
{
"label": "strange",
"depth": 3,
"N": 3,
"dimension": 3,
"precision_bits": 768,
"root_ball_euclidean_radius": "[1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8 +/- 1.68e-239]",
"inverse_frobenius_bound": "[3.3685916261978883582985177906289535376207902628083346721275419735099015770582073010650796701338660166191795924102887175276878954100264723803589025992476146697137849325147434566665535791005833673622897564452561494412953149240776002 +/- 3.73e-230]",
"residual_norm_bound": "[3.1787926629041064912110522847720850199701210678243642508878524158254836998709155756472903972093585425422748491424599994842752407073919113609884981236642035178381775726090018739394089208947465836465725965842453793090947181185261661e-14 +/- 2.74e-244]",
"contraction_bound": "[3.0317324736838745773433892546499878671088239329955281365357283560074823372569791826912169389683510684134208226442077849236766505632113256663151504608070473971204059311784881965018601263864879655296959236803358380248975650858821094e-7 +/- 2.77e-237]",
"self_mapping_bound": "[1.1011227593046447486473599558196970014005499055131079231478882964841835408347445260905064071435285018510414624524417688209656212315205000466991324471715401537216681012085391774840656568812492296766915779221365007724008896388396463e-13 +/- 2.12e-243]",
"F_over_D_center": "0.3906508437755871",
"certified_unique_stationary_root_in_ball": true,
"full_angular_hessian_certificate": [
{
"l": 0,
"radial_rank": 2,
"known_eigenvalue_over_F": "1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"remaining_trace_over_D_upper": "[0.017445813018702349695790940846000560632047860472529710270066700718318167800320904617551268241284231398150148574786532003545417480446318924650965821632310775238537157980583227829721331075589135651435066906558836794743974309780248844 +/- 1.21e-232]",
"strict_gap_below_F_third_over_D": "[0.11277113157316001697087572582066610603461880619413695639659996594834849886634576204911539842538243526851651809188013466312124918622034774201570084503435589142812950868608343883694533559107753101523159976010782987192269235688641782 +/- 2.38e-231]"
},
{
"l": 1,
"radial_rank": 2,
"known_eigenvalue_over_F": "[0.33333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333 +/- 3.45e-231]",
"remaining_trace_over_D_upper": "[0.0053590271819600257173059006673798939653811938058630436034000340516515011336542379508846015746175647314834819081198653368787508137796522579842991549656441085718704913139165611630546644089224689847684002398921701280773076431135805009 +/- 2.60e-233]",
"strict_gap_below_F_third_over_D": "[0.12485791740990234094936076599928677270128547286080362306326663261501516553301242871578206509204910193518318475854680132978791585288701440868236751170102255809479617535275010550361200225774419768189826642677449653858935902355308617 +/- 4.80e-231]"
},
{
"l": 2,
"radial_rank": 1,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.027913240829922269906669366496631180316023930236264855135033350359159083900160452308775634120642115699075074287393266001772708740223159462325482910816155387619268578990291613914860665537794567825717533453279418397371987154890123550 +/- 3.98e-232]",
"strict_gap_below_F_third_over_D": "[0.10230370376194009675999730017003548635064273643040181153163331630750758276650621435789103254602455096759159237927340066489395792644350720434118375585051127904739808767637505275180600112887209884094913321338724826929467951177654312 +/- 3.50e-231]"
},
{
"l": 3,
"radial_rank": 1,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.0065156619620905997221347556990127803160239302362648551350333503591590839001604523087756341206421156990750742873932660017727087402231594623254829108161553876192685789902916139148606655377945678257175334532794183973719871548901235426 +/- 1.25e-233]",
"strict_gap_below_F_third_over_D": "[0.12370128262977176694453191096765388635064273643040181153163331630750758276650621435789103254602455096759159237927340066489395792644350720434118375585051127904739808767637505275180600112887209884094913321338724826929467951177654312 +/- 3.55e-231]"
}
],
"strict_local_maximum_modulo_phase_and_rotations": true
},
{
"label": "up",
"depth": 4,
"N": 2,
"dimension": 3,
"precision_bits": 768,
"root_ball_euclidean_radius": "[1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8 +/- 1.68e-239]",
"inverse_frobenius_bound": "[3.7473588270533881323959781475130205080809349372079234443801169063729290914187713882501443712980814236330509777844677110606764487860100625692203700346859103599658731383735070841268773852137737621131304319861642487559147347030206489 +/- 3.73e-230]",
"residual_norm_bound": "[2.0402611738601661541652498383911584205332463789573204565285444991681876115353391655917789927931981276731181701923649417672799714083066764639420810279547742477163453187158493715827010616681672190327482480469089846181992619593350298e-14 +/- 3.04e-244]",
"contraction_bound": "[3.3726229555901258919548711810550973860389693321502783165030597832808077494716429528653471369272247010934079695744120421724281377798222075114735165165717121227278697863145538378428101582674385673176048044929405569747553658115000128e-7 +/- 4.56e-238]",
"self_mapping_bound": "[7.9828530149182136243656992569093366875995607659214500545439871503384016694323341750974559481837360261567037652307341728142130704471764422770993872435077335388355786629522177848574799163668829973354770129097030086231942750632850354e-14 +/- 4.22e-244]",
"F_over_D_center": "0.3374971531721895",
"certified_unique_stationary_root_in_ball": true,
"full_angular_hessian_certificate": [
{
"l": 0,
"radial_rank": 2,
"known_eigenvalue_over_F": "1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"remaining_trace_over_D_upper": "[0.014574519069767065965489177692328731069756970816756134535839153983622405588455027428030721772675659669961432319917767286443108411929318201281191547904102181015289133996688922315942718689698862798695419688324587482505494520407000584 +/- 1.96e-232]",
"strict_gap_below_F_third_over_D": "[0.097924528654296100701177488974337935596909695849910532130827512683044261078211639238635944893991006996705234346748899380223558254737348465385475118762564485651377532669977744350723947976967803867971246978342079184161172146259666082 +/- 2.23e-232]"
},
{
"l": 1,
"radial_rank": 1,
"known_eigenvalue_over_F": "[0.33333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333 +/- 3.45e-231]",
"remaining_trace_over_D_upper": "[2.3333330391389865038444678759474272424802317461207313516385750596733621453107954754825731769228920110099352823037160948145358598494579989713345990484447038506392283855097365298738788825338741649238101687680646686654142894214768120e-8 +/- 4.50e-238]",
"strict_gap_below_F_third_over_D": "[0.11249902439073277527680162822198790719239424186434920545935315028091606993304521355871191184093489743774655656731384362950571852130806817208667695332067618221962816027438281156930136792787784132792501742856497898601998001252377245 +/- 1.26e-231]"
},
{
"l": 2,
"radial_rank": 1,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.021992483725385642591344172192557176299474721686216015207427168919139707844128433244719245834310086788258247881077988852116604628871033581815442550046124956449974817823437838716194176020707263424439072330966367259870285886972771507 +/- 1.94e-232]",
"strict_gap_below_F_third_over_D": "[0.090506563998677524075322494474109490367191944980450651459239497747526958822538233421947420832356579878408418785588677814550062037795633084851224116620541710216691848843228827950472490645959403242227594335700299406796380779693895159 +/- 2.07e-232]"
}
],
"strict_local_maximum_modulo_phase_and_rotations": true
},
{
"label": "charm",
"depth": 4,
"N": 19,
"dimension": 11,
"precision_bits": 768,
"root_ball_euclidean_radius": "[1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8 +/- 1.68e-239]",
"inverse_frobenius_bound": "[12.066988403707311911534803753042146035937626900392924203937947443195511335502394438617952922438855739961514840511366030560898613033211793025383776959732017318289277384884078642323388660567746363379100589398815097868579279814213793 +/- 3.47e-229]",
"residual_norm_bound": "[3.0062061366786343547368393457427309411397612512274719838803957272591251892026622535587645246443487774137583246800955283781481969416933305167534829312036561666112394381876812326359501938634515688688451909844826253192275267117470559e-14 +/- 3.58e-244]",
"contraction_bound": "[1.0860289599537546341094515468434801015811921468473048232696547404108165310165344520827986510395751111294296739629649333997888288250982325976322138829377652428981558663243784362461414375111337530057597526832849125672497815766545324e-6 +/- 1.49e-236]",
"self_mapping_bound": "[3.7361883550408593739598102431428351809301614762538765522490291700962680120476462999661388772047152605112314345462642327033724741017517150380775058896718261021726228879277382237243520769798690223262291737791158878847883380373986980e-13 +/- 4.27e-243]",
"F_over_D_center": "0.25479297094717784",
"certified_unique_stationary_root_in_ball": true,
"full_angular_hessian_certificate": [
{
"l": 0,
"radial_rank": 10,
"known_eigenvalue_over_F": "1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"remaining_trace_over_D_upper": "[0.010830121820289875614160242553820266306727057989442878641595111281607355865390555984327233479668207243962644557055232080146075212730089915385581901330212814465088883279289891347716669021302836262378236169931338734904763509919135761 +/- 2.25e-232]",
"strict_gap_below_F_third_over_D": "[0.074100865162102737719173090779513067026606275343890454691738222051725977467942777349006099853665126089370688776278101253187258120603243417947751432003120518868244450054043441985616664312030497070955097163401994598428569823414197572 +/- 1.86e-232]"
},
{
"l": 1,
"radial_rank": 10,
"known_eigenvalue_over_F": "[0.33333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333 +/- 3.45e-231]",
"remaining_trace_over_D_upper": "[0.0021502374731249566112132056642240719175182383264444692279466637472864079045124001430912184604197832697896157235271246809308787972808144442847227666748058616480822305419020833429326945436789996849742742469628153179171105095830087280 +/- 3.75e-233]",
"strict_gap_below_F_third_over_D": "[0.082780749509267656722120127669109261415815095006888864105386669586046925428820933190242114872913550063543717609806208652402454536052518889048610566658527471685251102791431249990400638789654333648359059086370518015416222823750324605 +/- 7.69e-233]"
},
{
"l": 2,
"radial_rank": 9,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.022072626708251284226021303255471209098259438985543133256370881606063984517510588627424231212430152331486003464995982793917051391047641806106199826426623883511944027216674583561731187403102423453948567861140728308234293425518867653 +/- 2.88e-232]",
"strict_gap_below_F_third_over_D": "[0.062858360274141329107312030077862124235073894347790200076962451727269348815822744705909102120903181001847329868337350539416281942285691527227133506906709449821389306116658749771602145930230909879384765472192605025099039907814465680 +/- 3.27e-232]"
},
{
"l": 3,
"radial_rank": 9,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.0048241562843413035771523007499641362872127249391369530239176088204418061032934466303838206363969470913485814580830110054037010696681670330216772107894974439164958326813389661015395179791588902075407031348910586278239152536814454790 +/- 3.07e-233]",
"strict_gap_below_F_third_over_D": "[0.080106830698051309756181032583369197046120608394196380309415724512891527230039886702949512696936386241984751875250322327929632263665166300311656122543835889416837500651994367231793815354174443125792630198442274705509418079651887854 +/- 1.55e-232]"
},
{
"l": 4,
"radial_rank": 8,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.0012485928746031381532654633398735703019464417242766631279114201172734798900044629981193341730758706695349897768999641462307497192085809849686078657711405500316174200750016751809401049168268684545000265562070917685573445062340261233 +/- 4.47e-233]",
"strict_gap_below_F_third_over_D": "[0.083682394107789475180067869993459763031386891609056670205421913216059853443328870335213999160257462663798343556433369187102583614124752348364725467562192783301715913258331658152393228416506464878833306777126241564775988827099307210 +/- 4.46e-232]"
},
{
"l": 5,
"radial_rank": 8,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00047878153222000239606572682459401341685608421070191588547493602587224552233374309254394368287359397616475704723366041967904967516761856255410847129346393625651504991238641031395283364554932039429847866258038614259049251362891200474 +/- 3.07e-234]",
"strict_gap_below_F_third_over_D": "[0.084452205450172610937267606508739319916477249122631417447858397307461087810999590240789389650459739357168576286099672913654283658165714770779224862039869397076818283420946923019380499687784012939034854670752947190742840819704421328 +/- 1.15e-232]"
},
{
"l": 6,
"radial_rank": 7,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00024083115514028822891381573080252101679447327511378549147469737269316013151851333186998817412159311148501223590659828232724335780785950142908345838236441932363810562953820306744092885649019887074797783943344577181162812006748794298 +/- 4.44e-234]",
"strict_gap_below_F_third_over_D": "[0.084690155827252325104419517602530812316538860058219547841858635960640173201814820001463345159211740221848321097426735051006089975525473831904249874950968914009695227703795130265892404476843134462585355493899887561521705213265845390 +/- 1.70e-232]"
},
{
"l": 7,
"radial_rank": 7,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00014125146487187763915478877706480247059178628763674732334947415774533554106750159320753001803307676334015438683080865421989445137224599676676771616913264857811974149445897030996678893816614155309357851264886842373599239046758587399 +/- 2.83e-234]",
"strict_gap_below_F_third_over_D": "[0.084789735517520735694178544556268530862741547045696586009983859175587997792265831740125803315300256569993178946502524679113438881961087336566565617164200684755213591838874363023366544395167191780239754820684464909597340942865747459 +/- 1.36e-232]"
},
{
"l": 8,
"radial_rank": 6,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[8.8738692876069387097301855516883879957151480617673075404718516704958460088112753573619615367027272942919330730952631254081585085687381822671273391315767768218694047220937627328401007518467634721398900174169268777535369425251163101e-5 +/- 3.46e-235]",
"strict_gap_below_F_third_over_D": "[0.084842248289516543946236031477816449453376181852715660257928614816628374873245220579759713717966306060390414002602380702079251748247645951510662059942017565565114639286112395706004932325814865698611934433159164064555797963908082170 +/- 2.22e-232]"
},
{
"l": 9,
"radial_rank": 6,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[6.0722542803771800357918826652955088308318619803723375515029460556339805841422478041438221164676977004803919471134263532600474495276489376441822961626703339723457899628574937078347945810488543138970435391234012880117830518565230532e-5 +/- 4.44e-235]",
"strict_gap_below_F_third_over_D": "[0.084870264439588841532975414506680378245025014713529609957818303872776993527491910855291895112168656356328529413862199069800732858838056843956891510371706629993609875433704758396254985387522844790194362897942099320453215502814768102 +/- 2.92e-232]"
},
{
"l": 10,
"radial_rank": 5,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.1753767245932379810194816897685873499999046350578329983851485793452565726288227943471197651603465164131884676135538028930606218068795731440844493309693044500505309729672906816884534330752263364479988921488367601622381863403103088e-5 +/- 2.48e-235]",
"strict_gap_below_F_third_over_D": "[0.084889233215146680953523138516435647459833334286982755003349481847539880767607045105389862135681729868169201448657197795304402727115264537601892488840023640288832828023603660426516448799002581069968853344411844965731710951469930230 +/- 2.11e-232]"
},
{
"l": 11,
"radial_rank": 5,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.1279246020092940413947779555732542311462973479660743745572616336488093981815242467675231943240317791591190077578165570655982711582041882098955065839237835005056425991965144377367619521622106878180392610839462486199681597070702328e-5 +/- 1.47e-235]",
"strict_gap_below_F_third_over_D": "[0.084899707736372520392919385553777600791021870359853672589587760716996845239351518090865658101390093015541742143255755167762677350621751291451234378267494095498328276907341368188955965713811711226455152940722493870847133651736262630 +/- 4.86e-232]"
},
{
"l": 12,
"radial_rank": 4,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.2214714131113418892770267018608689748512330585016208715930240706133637510818565833869628044453073608413607180237707218973107306573012565950798691801923896851668393868461452850289699599470392231041530714185959786496452658539638623e-5 +/- 3.98e-236]",
"strict_gap_below_F_third_over_D": "[0.084908772268261499914440563066314724643584821002748317124617403092627199695822514767499463705288880259724919726153095626114360226026760320767382534641531409436481664939464871880483043633733862941102291802619147373546836880674793694 +/- 1.87e-232]"
},
{
"l": 13,
"radial_rank": 4,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.7673243980609201577828398840040012121485553409092482173224014547593682523959114326474137441188940233020687549308775422760022514848898068896353335640921330079782868316722328715744731297039049196435225766140983393829264122490169417e-5 +/- 3.74e-235]",
"strict_gap_below_F_third_over_D": "[0.084913313738412004131755504934493293321211847779924240851160109318785739650809374219006859195892144393100312645784024557910573310818484435264436979997692412003253550465016611004617588602036294284136898107567192349939504069210843163 +/- 4.52e-232]"
},
{
"l": 14,
"radial_rank": 3,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.2338200583676713749524832812870371069547501738408591361098002803825478040051745265431113794745347975198350180839825267473425893775157703290764112576424702007830820980623996977566756840914822483792892623676777102385607531393755415e-5 +/- 2.89e-235]",
"strict_gap_below_F_third_over_D": "[0.084918648781808936619583808500520462962263785831594924741972235330529507855293281588067902219538587985358134983152493508065859907439558175630042569220756908631325502512352709336355766576492418510849540440709656556230947725801939577 +/- 4.28e-232]"
},
{
"l": 15,
"radial_rank": 3,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.0237233020423866799462550301664296763367402217417932372856738426973630345790751806569035622039672753277441963139945520254429438983907890203208726096633729655282536428773868877427132247795857290769293086370365846771763547747931468e-5 +/- 8.24e-236]",
"strict_gap_below_F_third_over_D": "[0.084920749749372189466533870783031669036569965931115915400960476594906359702987542581526764297711293660580055891370193387813078903894349425443130124607236699603678050796904559464455906201085537476042564040246962967486561569785585401 +/- 3.48e-232]"
},
{
"l": 16,
"radial_rank": 2,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[6.5548362772719988840540696397466516124981919284715190227129683049983155180505359184523258538131259993091889692768823974186469864115705678808183865304883295685027608509530387240545024392671709581805623842843712978578319412958777720e-6 +/- 3.92e-236]",
"strict_gap_below_F_third_over_D": "[0.084924432146115341334449279263693586681720835141404861814310620365028335017815282797414881007479520207334024144364056450935914686346921762765452514946802845003764830572482380294609278830894066162375152770949048962035475501392037455 +/- 7.76e-233]"
},
{
"l": 17,
"radial_rank": 2,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[5.6066212965542951053335999865337886974472825867590928116716182281554742383009423501649475068322938063441689847338283740754077538626785528447551684506336842889830217927292641291939001379948425285078437613391024667842295589959012130e-6 +/- 3.04e-236]",
"strict_gap_below_F_third_over_D": "[0.084925380361096059038227999733346799544635886050746574240521661715105177859095032390983168385826501039526989164348599504959257925579470654780488578164882699649044350311540604069204139433195338490804825489571994230866549103774337432 +/- 4.00e-232]"
},
{
"l": 18,
"radial_rank": 1,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.7493872857935094066697881248066421225837778053280623975391185628723728387589872043774192591537713858735436238401984486585420838962035683348453824403793848086097310052954266093888803613357850207331225337075103155301024699299082974e-6 +/- 3.50e-237]",
"strict_gap_below_F_third_over_D": "[0.084928237595106819823926663545208526691210749555528005270935794214770460960494574346128955914074179561947459789709493134884674791249437129764998487950892953948524723602328037906723944452971997548312600210799625823017803230863403425 +/- 4.80e-232]"
},
{
"l": 19,
"radial_rank": 1,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.4055108866559263222897948661569037964391618260148130062571721164060062851345442935111698848927720257674672854241789279304806356738920496013577496998808257513791943742634857769450014664161571894711676619664385928588912456028578473e-6 +/- 3.30e-236]",
"strict_gap_below_F_third_over_D": "[0.084928581471505957407011043538467176429536894171507318520327076161216927327048198789039822163448440561307565866047909154405402852697659441283731975583633452507581954138959069847556388331866917176143862165671366894740474442087730475 +/- 2.7e-234]"
}
],
"strict_local_maximum_modulo_phase_and_rotations": true
},
{
"label": "top",
"depth": 4,
"N": 71,
"dimension": 37,
"precision_bits": 768,
"root_ball_euclidean_radius": "[1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8 +/- 1.68e-239]",
"inverse_frobenius_bound": "[23.609955294544239076531156265265490843263349581725647374608760969644108512427349898645479351458842233390439743753793967977778927860512202655252999524252008023983606575738120136525184511128502337006868674570305875423554108502312578 +/- 2.75e-229]",
"residual_norm_bound": "[1.2229863757828992638578855423197686651680718846884171805213798252954838948346100182011171143615359569785359576887473577732893455415036560006774883807293040411463702674354976940501155613966281386007567760081179591178479441730087001e-12 +/- 2.04e-242]",
"contraction_bound": "[2.1248959835919681270651062870465245303372340585500314906422302834807965516696740683395791633335312184336677764338596377234995602305277027179818059046908713049944461173073743099596880627309625392694470316714614949109313461861839796e-6 +/- 1.59e-236]",
"self_mapping_bound": "[2.8895902617906852526427109434203667213277667965642547039416153539511268940426585196712539199624125655535988830709232770395716079753986480729327797264757233526372159343415097503753227633529997538152545061184899502280607403050690801e-11 +/- 3.78e-241]",
"F_over_D_center": "0.2521803567756858",
"certified_unique_stationary_root_in_ball": true,
"full_angular_hessian_certificate": [
{
"l": 0,
"radial_rank": 36,
"known_eigenvalue_over_F": "1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"remaining_trace_over_D_upper": "[0.010704796984908442747236643850469441367163766084642021070511334986259935771041605537148374931944070897821355874523348017642107653150812471484301842004189447532705814049041088798762005213266411418817322372795453255797764394085680225 +/- 8.53e-233]",
"strict_gap_below_F_third_over_D": "[0.073355318606986823919430022816197225299502900582024645596155331680406730895625061129518291734722595768845310792143318649024559013515854195182364824662477219133960852617625577867904661453400255247849344293871213410868902272580986441 +/- 8.52e-233]"
},
{
"l": 1,
"radial_rank": 36,
"known_eigenvalue_over_F": "[0.33333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333 +/- 3.45e-231]",
"remaining_trace_over_D_upper": "[0.0020857538168517568756630727171446551851149040004331130998486717367488440294194067484764469750533310213464325547450667133310271119076189330064593784379049933856534493685056707472924629663004064586731408671843487505110567495183581115 +/- 5.08e-234]",
"strict_gap_below_F_third_over_D": "[0.081974361775043509791003593949522011481551762666233553566817994929917822637247259918190219691613335645320234111921599953335639554759047733660207288228761673281013217298160995919374203700366260207993525799482317916155609917148308555 +/- 3.35e-232]"
},
{
"l": 2,
"radial_rank": 35,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.021997675911237605570182204426086242601108818141246008994952013684598679413872627341934734129276895237014500961635882054823827985270349090108642606994632311742603360012448235432681547320041054569992580742782629125272718115151243894 +/- 1.55e-232]",
"strict_gap_below_F_third_over_D": "[0.062062439680657661096484462240580424065557848525420657671714652982067987252794039324731932537389771429652165705030784611842838681396317576558024059672034354924063306654218431233985119346625612096674085923884037541393948551515422772 +/- 1.61e-233]"
},
{
"l": 3,
"radial_rank": 35,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.0048389820300662217731118495475608753055181495099893593678050862254364143201563839012250155611483486652790717849688883787475956260302764253436829421255586914166853180239100071606165710519763026225039920080185462491555165283952130738 +/- 1.50e-233]",
"strict_gap_below_F_third_over_D": "[0.079221133561829044893554817119105791361148517156677307298861580441230252346510282765441651105518318001387594881697778287919071040636390241322983724541107975249981348642756659506050095614690364044162674658648120417511150138271453592 +/- 2.30e-232]"
},
{
"l": 4,
"radial_rank": 34,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.0012297320717583578888032062821362197950868555300200395697905433823005500480877163824336275555983118877038903046720670112372604873424995844030786847973097079806685159335384549893086656096889183660414282892426577814832616985137137676 +/- 3.55e-233]",
"strict_gap_below_F_third_over_D": "[0.082830383520136908777863460384530446871579811136646627096876123284366116618578950284233039111068354778962776361994599655429406179324167082263587981869356958685998150733128211677358001056977748300625238377424008885183404968152952898 +/- 4.75e-232]"
},
{
"l": 5,
"radial_rank": 34,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00045188433644705417540097968536294051621691021052254146724467932848988692007983890276479591625866460890457916236346703305480195195908824058406353944901145848932769050623859205634730703073257922155897542027625750605475964352772250635 +/- 3.42e-234]",
"strict_gap_below_F_third_over_D": "[0.083608231255448212491265686981303726150449756456144125199421987338176779746586827763901870750408002057762087504303199633611864714707578426082603127217655208177338976160428074610319359635934087445107691246390409160611907023138944160 +/- 2.69e-232]"
},
{
"l": 6,
"radial_rank": 33,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00021842704290873607178924404845676233914403928699537627112649783199769228396192732343132683281257230114934077573959793845871855965227201885263639145141303629490664885864888365277115730962956592883696995243420845252662087961785389004 +/- 4.21e-234]",
"strict_gap_below_F_third_over_D": "[0.083841688548986530594877422618209904327522627379671290395540168834668974382704739343235339833854094365517325890927068728207948107014394647814030275215253630371760017808017783013895509357037100737829696714232458214140045787048812776 +/- 1.27e-233]"
},
{
"l": 7,
"radial_rank": 33,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00012224848676946235145497856737493731364978873767782532590386985412922876607542237254840134282704689611890775910899602960087145149495214271192874667135522331105560716447573772382957252889980757205224888949408740380213227870978740103 +/- 4.20e-234]",
"strict_gap_below_F_third_over_D": "[0.083937867105125804315211688099291729353016877928988841340762796812537437900591244294118265323839619770547758907557670637065795215171714523954737919995311443355611059502190928942837094137766859094614417777172579262864534387956879265 +/- 5.96e-233]"
},
{
"l": 8,
"radial_rank": 32,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[7.4555848900489717827750126774915533036420903152033351360423715905556020067474723164705067240029834883332739483577575410201778087443203943920514088189080187937152842573365938949378084558320483538067870607553826088386452950173644551e-5 +/- 1.92e-235]",
"strict_gap_below_F_third_over_D": "[0.083985559742994776948838916539891751133630245763514633315306242950761110646599191943501961599426636831783333927183089091256464888579223462722746152578477586478729513824093300727717288582108346183128598796059112840578280213716493021 +/- 4.90e-232]"
},
{
"l": 9,
"radial_rank": 32,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.8394278987822278578999120377073547318527513400186603299119605186819436403326339679299315179385407813606445228075780036020997929902460417638994086456604147437595728802053478218623859477086006726516710854692321955553290441879048859e-5 +/- 2.99e-235]",
"strict_gap_below_F_third_over_D": "[0.084011721312907444388087667546289593119348139153266480063367547061479847230263340326987367351487281258853060221438590886630645668736764206249027672580210062519229070937864613188448042807189580659940149955811974344711113376224787617 +/- 2.05e-232]"
},
{
"l": 10,
"radial_rank": 31,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.2939610380107236357795262023015384463971872033815020287180496701708080439465434606355158271385298940013992037797790087722130747694571925663033802912941041418728188515776589389427090912992421125302442693341911926477014786442099498e-5 +/- 1.61e-236]",
"strict_gap_below_F_third_over_D": "[0.084027175981515159430308871404643651282202694794632851646379486169964958586227201232060311508395281367726652674628868876578944535918972094741003632863753725625247938478150890077277239575753674245541364223973324754740189651880224567 +/- 4.12e-232]"
},
{
"l": 11,
"radial_rank": 31,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.3334517070834785531404108827710508042667855157924796709815914293450646769482232961240781764380288054892084350328462446836002802552132279261297551637634970227899939517239122171547528272546093819918822399724018152269538119315956821e-5 +/- 1.35e-235]",
"strict_gap_below_F_third_over_D": "[0.084036781074824431881135262557838956158623998811508741869956850752373216019897184433705425884902286378611774582316338204219830663864114534387405369115029031696438766727149427544495119138394120572846747844266942648514397128547350709 +/- 2.47e-232]"
},
{
"l": 12,
"radial_rank": 30,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.7062083708005412706674775977086658400960755286890866671251154405903857725710206410752781514938608083635486858189567304974338497777569227991731023739749163067781342163997533971620564023937297500520219760913272791696964717981074646e-5 +/- 3.30e-235]",
"strict_gap_below_F_third_over_D": "[0.084043053508187261253959991890689580008265705911379775799995415512260762808940956460255913885151728058583031179808477099361692328168889097438674935642926917503598885324502669132695046102642729369166146446905753393874969701948685591 +/- 3.71e-232]"
},
{
"l": 13,
"radial_rank": 30,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.2849686972171337448496782424786800704022793094141596620916532745246823217719773194893398679484411600171819416397243155464918810142384577864227080467117714890153406556316486975640797293180651344747029235358584635220797155388525525e-5 +/- 3.21e-235]",
"strict_gap_below_F_third_over_D": "[0.084047265904923095329218169884241879865962643873572525070045750133921419843448946893471773267987182255066494847250269423511201747856524282088802439586199548951776513260110350179691025869373486015321919637431308082031445869511278141 +/- 4.91e-232]"
},
{
"l": 14,
"radial_rank": 29,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[9.8970285383368796904998502326093817062921785978198493873259614149267434307156501492728760237191186234267844686161248151256302411318986032826632349372201306244975809728603811639817825686389244387421684058673769859658821484824440193e-6 +/- 3.14e-236]",
"strict_gap_below_F_third_over_D": "[0.084050218563356929786976166816434057284960374488068846817279340705251739923235951016517393790642947548043239882198050541851541036425534768063384003431729446536042169085693806285502684884098027742227924498260799289680700784518184222 +/- 2.35e-233]"
},
{
"l": 15,
"radial_rank": 29,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[7.8084981545982696974828622656015061698818795400792434800056699992596142914199252661625279900929739788911265657880878747618987439966239055493323342461296904481635584331817545735815474247815016904673855264353012289801302804696320569e-6 +/- 9.35e-237]",
"strict_gap_below_F_third_over_D": "[0.084052307093740668396969183804401065160496784787126587423186660996667407052375246741400504138676573692687775540100878578791904767922670042761117334332420536976218503108233484912093085119241885164976199281140231365437686536386197034 +/- 1.48e-233]"
},
{
"l": 16,
"radial_rank": 28,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[6.2600408596666048046567425713923207485671420007262339883971063733551984970714383931599185530703473683080405753146987032712037290478690677267096270235962601172442880543593809560650492148023475077222477518126503288642557257800695852e-6 +/- 3.11e-236]",
"strict_gap_below_F_third_over_D": "[0.084053855551035600061862009924095274345918099524665940432678269560293311468169595228273506748113596319298358626091351967963395462937618797598939957039643070406549422378612307285710601617451864319158944418914854016337802410940886597 +/- 4.98e-232]"
},
{
"l": 17,
"radial_rank": 28,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[5.1263274871860923343524196890708282926966218222207049429511477732414161656448662070642910006123843469509508384612819070090731626845432806780013291517998979159990147914829755061902572358849266917971010716077734746705190080577177106e-6 +/- 2.71e-236]",
"strict_gap_below_F_third_over_D": "[0.084054989264408080574332314246977595838373970044844445961723715518893425250501021800459602375666054282319715715828205384759657593503982123385988665337514866768750667651875183691160476409430781739974869565595058893191996147658608948 +/- 3.43e-232]"
},
{
"l": 18,
"radial_rank": 27,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.2432396847527409242896398670338083639571684072347244008783876959045322934922450603626082450279177126544764644371267398958980480929005794536147446584869328448681320567533740019714680943013475323980985997567960429372086061112266685e-6 +/- 1.72e-236]",
"strict_gap_below_F_third_over_D": "[0.084055872352210513925742377026799632858302709498259431942265788278970762134373174421606304058421638748954012190202229539926770768618573766087213051922008179733821798534609913292664695198572365319134268568066909870623729458060555439 +/- 3.42e-232]"
},
{
"l": 19,
"radial_rank": 27,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.5832663402613329958609799377813823400711471214223251626677470321758789113015527995744940069898083266008598297079584644061121775740023380750258874546056106964055335887033765808507556284721509097959426333398122967003104175534879151e-6 +/- 2.49e-236]",
"strict_gap_below_F_third_over_D": "[0.084056532325555005333670805686728885284326595519545244341503998919634490787755365113867092172659676858340065806836958708202260554489092664328591640779212061055970261133077963290085815911038194515756870724033326854369966356249113178 +/- 1.73e-232]"
},
{
"l": 20,
"radial_rank": 26,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.0439820208474136189035885816613049307924567200148315056707981111005259765763249155955408368244860251238436753174417559932698142994190127197855075231919365461642527570634450910076683339821889210684794111553695350000844742058399788e-6 +/- 3.67e-236]",
"strict_gap_below_F_third_over_D": "[0.084057071609874419253047763078085005361735874209946651835160995868555566140690090341751071125829842180641542822991349224910673396852367247653946881159143474730120502413909603221575658998332684477745598187255511297131666582192460826 +/- 6.61e-233]"
},
{
"l": 21,
"radial_rank": 26,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.6378024444795300163054858220175090560323981707029757755003098959303321658101644411281917723053307870235129234812835406339797856967978256731505267134015397461403230629824117540568574897137662500337679610430398725905545258510668859e-6 +/- 2.40e-236]",
"strict_gap_below_F_third_over_D": "[0.084057477789450787136650361180844649157610634268495963690891166356770736334500856502225538474894361335879643153743185383126032686880969868840993516139953265126920526343603684254912609809176952900416632898705623626794076112140815599 +/- 1.65e-232]"
},
{
"l": 22,
"radial_rank": 25,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.2887628318563699527673672580787517282342001325099954141596332591493674869457079980158282448287298172756467615851966524894403330639412771535455319633308781441886925642386452904834627732842127015451112065334177894535872259600699775e-6 +/- 5.62e-237]",
"strict_gap_below_F_third_over_D": "[0.084057826829063410296713899299408587914938432466534156671252507033407517299179720958668650838421837936849391019905081470014177226333602725389513121134703335788522477974102428021376183203893382453965121555460133248877213079440706596 +/- 5.60e-233]"
},
{
"l": 23,
"radial_rank": 25,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.0271830379617322947575357553145596428379853104125185329423287238225901255833237198213406493171532855302415917847574346665922492458847076166752267257021316337470652726051340640970171985146384174618563748756014806526916040849264931e-6 +/- 3.71e-236]",
"strict_gap_below_F_third_over_D": "[0.084058088408857304934371909130911352107023828681356254148133724337942844076541083342946845326017349513381136425074881909232000074417420781959049991439940964535032919601394061532602569649468152028249204810291791065186013975062581740 +/- 4.58e-232]"
},
{
"l": 24,
"radial_rank": 24,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.7894451670359565492219684025327468577364488566838726027920773351867761404870767568545448661625866522556259940470070317327935059264424611007689260003244764336565719924704733324298663085088113992441504040392574714773997388324428687e-6 +/- 2.55e-236]",
"strict_gap_below_F_third_over_D": "[0.084058326146728230710117444698264133919808930217809982794063874589331479890526179589909812121800504080014411040672619659634933873160740224205565897740666342190233010094674196193334236800358157855267422516262627409195189266927834223 +/- 1.97e-232]"
},
{
"l": 25,
"radial_rank": 24,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.6145300238030658757477245784780235347467820251077087085954570483367754260717579323289978716999549288305219953528320682547760541041073063438337645078776384909137410933718593293804074244749649051144142299613091324811273823373654936e-6 +/- 7.23e-237]",
"strict_gap_below_F_third_over_D": "[0.084058501061871463600790918942088188643131919884641558957958071209618329891240594908734337668794966711737836144671313834598411890612562559360322832902158789028175752925573294807337286259242191701761552252436705357534185539284329301 +/- 4.46e-232]"
},
{
"l": 26,
"radial_rank": 23,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.4449907699857573684615323147874723811348393547760212627122102227462133483229987635750391330203068378308584929292779750004488935958771773238540490053225491843553241076636994728799645638189292138352945598434750217213114691329328034e-6 +/- 2.00e-236]",
"strict_gap_below_F_third_over_D": "[0.084058670601125280909298205134351879194285531827311890645403954456443920453318343667903091627533646359828835808173737388691666217773070789489342812617661344117482311342559002967193786702102847737452831372106823191644945355197533733 +/- 2.65e-232]"
},
{
"l": 27,
"radial_rank": 23,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.3242682596933635198665326034120813196185117487492000046823626057293986047314279751594916027661915276284257272213057717142993329784057037908011922999408917539165633411190257885691536646888572506902927567485845892595962176761737990e-6 +/- 4.41e-236]",
"strict_gap_below_F_third_over_D": "[0.084058791323635573303146800134063254585347048154917917466661984304060937268061935238691507175063900475139038240939445360894952367333688260962875865474366725774912750103325547640878097513001977809415976373909918082077407070448990492 +/- 2.31e-232]"
},
{
"l": 28,
"radial_rank": 22,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.1981816497549593770678038271077201235418700916974819407395742166001869313199180998063864847166891846430969442595326475682861308832114206761062951590371221742175572797964649827570879351626299091135815712513069069340871762253896421e-6 +/- 4.62e-236]",
"strict_gap_below_F_third_over_D": "[0.084058917410245511707289598862839558946543124796574969184725927092450066479735346748566860280181949977482023569722407134019098380535783455245990560371507629544492449109386870201683909578731504036757553085095415359759732579490441276 +/- 4.39e-232]"
},
{
"l": 29,
"radial_rank": 22,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.1125924741940726753844336769449103855876501231930488059699071096993260058322393533832097099025821400189465997809615413537704259726849323407861721550396689455185588772359523732379407372806113760361546231680543302380357442201103100e-6 +/- 1.96e-236]",
"strict_gap_below_F_third_over_D": "[0.084059002999421072593991282232989721756281079016543473617860696759556967340660834427313283456956764084526647720066885705125312896240693981734325880494511626997721148107789430714293428725929386055290630512043498612336428630922446556 +/- 2.23e-232]"
},
{
"l": 30,
"radial_rank": 21,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.0151342210363554812110064946959993941122509007549518841995913713238968297779761768537098634029134516553252298933751627595496623418852659810840474344588934928726663599532573664833281234480411178317837926557131729711128593707398095e-6 +/- 1.10e-236]",
"strict_gap_below_F_third_over_D": "[0.084059100457674230311185455660171970667272554415765911714782467075295342769836888690489812956803263753215011341436773291503907117004324781400685582619232207773173794000306713409300183338543218625548834882874010953493695553807295926 +/- 2.23e-232]"
},
{
"l": 31,
"radial_rank": 21,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[9.5304247458869665967019717399033655335368984594011647213869807996707991898864451967130737942074702718393040011420629071512098095386424355984249751166866143578903720262786962318599017691134437549641106820136656400248641330269311846e-7 +/- 1.58e-237]",
"strict_gap_below_F_third_over_D": "[0.084059162549420677970006996469492676330113312976820726550194527968586699586747678022146995359287245919639482736266552460375951545685712802423106824169154998005230877629464038797043480676489755322291170255598465300102664180253363973 +/- 3.64e-233]"
},
{
"l": 32,
"radial_rank": 20,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[8.7500143702482007399743700254723371690728108798024385160529557864717214180052036362303218539870038589475345198438995390701698864553343966607125741726094717788459815108860260156806054246429626457219689643124133735312722908261454353e-7 +/- 4.57e-237]",
"strict_gap_below_F_third_over_D": "[0.084059240590458241846592669229664119432949759385578686422815061371088019494524866146303043634481267966280771913214682276712759649678021133227000595409249405719488782068515578064065098606124202370402094469770235425329313539437584052 +/- 4.58e-232]"
},
{
"l": 33,
"radial_rank": 20,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[8.2905743373253833877782121985882997525347181590684610780939692959363775788381580966319809443506805043601777213611208711664260275321198861486696654648511512913327320500238892572797952942152185961402976452898256305265364602827885088e-7 +/- 9.84e-238]",
"strict_gap_below_F_third_over_D": "[0.084059286534461534128327888845446807836691413194850759820558857269737073028908782850857003468572231598616230648894530554579550024063913454678051799700120181551537533393461664277740938687137245144807052636902137684103614013020638387 +/- 2.28e-232]"
},
{
"l": 34,
"radial_rank": 19,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[7.6452554193623382042470261984380452420007452570073047428847774060494564972432797592257989513543940836045378298909723459914770569044299945172688881639710555079312791072942003032009091268787909171752520443945982739619799568831634946e-7 +/- 3.95e-237]",
"strict_gap_below_F_third_over_D": "[0.084059351066353330432846241964046822862142466592140965936192378188926061721016942338690744086771531227258306212883677569432067518960976223667214939777850269561115873538755937246636346575753978787574949141462227206839270468670978350 +/- 2.98e-232]"
},
{
"l": 35,
"radial_rank": 19,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[7.2994689860271652277046218906495487615135829051282699852534975331803501593239178774995687004256120668909642686661563891884812442208091088610704140790567085895584328230068952368444047287381868096685897107781684818998427982757048236e-7 +/- 4.09e-237]",
"strict_gap_below_F_third_over_D": "[0.084059385644996663950143896204477601711790515308376153839668141316913348631650734274878916709796624105459977570239800051027747818542244585755780559625258760995807710823384365977142982226193792847985699807695588849818476682386839096 +/- 4.16e-232]"
},
{
"l": 36,
"radial_rank": 18,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[6.7502757001930219458649515572727817006827432279030365736939082107396952374779353721124967720885237579298316756347854237809671500119442092904447107089393186604723942887410286292964357944578999155770767002138289277432605933519852980e-7 +/- 1.68e-237]",
"strict_gap_below_F_third_over_D": "[0.084059440564325247364472080171510939388496598392343876363009297275845592697142918873129455416989457814290873683499103188124288569951665472245737622195595772734800619427237792563803737023087220876675108958996645283773892340607331467 +/- 4.89e-232]"
},
{
"l": 37,
"radial_rank": 18,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[6.4861981393606622491329729386230817249468705845766132698683563264987416424235603261257641537357175985396411640166610063687219219846384622283577706977108980524289412870524245153421510904392147186563720654557127490937045763239472024e-7 +/- 3.59e-237]",
"strict_gap_below_F_third_over_D": "[0.084059466972081330600441753369372804358494171979608209005339679831034016792502424310634054090251293094906812702550265000566029794474468202820443830889596895576861423772537961424215132451557622745194801029460121095391757296209034271 +/- 3.47e-232]"
},
{
"l": 38,
"radial_rank": 17,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[6.0067890400692319627071870021994500636317228695813224521758261799860640132207790032465226984826589716224228084096332041324036096744121823125759448862935843153292011363597824308238338234704646920722105932087597886717253973275492463e-7 +/- 1.83e-237]",
"strict_gap_below_F_third_over_D": "[0.084059514912991259743470395947966446721660303494379708534421449084048668060265344588766342014396818400769504424385825703346253426305699225448435409072178037308235133746553030688423584283284319620197459445607345790687799494126933911 +/- 1.25e-232]"
},
{
"l": 39,
"radial_rank": 17,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[5.8025796213523447404207858761355964922330316589507975986610050304662192172920806224029666377277427778065003327154386595231784026251155730178710067397813894210212402017431116386734529187727595542575664726049707881227574247744698275e-7 +/- 3.41e-237]",
"strict_gap_below_F_third_over_D": "[0.084059535333933131432192624588079053107017443363500771586906800566163620044744937458604426370002893892388886016633395122800714348826404155109364879565992688527724564542646492355502799321374789390711240910019406169587854390924189219 +/- 6.74e-233]"
},
{
"l": 40,
"radial_rank": 16,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[5.3747511989615493534739159899189887508549222790328310190980285331024781836120845529857468956829174813677007890159355604954520849413643189198477720850637502063137833196837153304260108848242783204440315447876177231027221612904117725e-7 +/- 3.85e-238]",
"strict_gap_below_F_third_over_D": "[0.084059578116775370511731319275067674767791581174438763383564756863813356418848305458211368091977098374918529896587765073110617121458172530234774681889458160291646035288334698295133624065578184238834622263512187904894356394450537625 +/- 8.81e-233]"
},
{
"l": 41,
"radial_rank": 16,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[5.2151628355072560693650509925991957794855167236267725728223990024311354355605838573915705581073593066930093229974588031439425889520880217054284493623621916917077576309382464152896146846734087216609709310409404707342262383802140624e-7 +/- 7.49e-238]",
"strict_gap_below_F_third_over_D": "[0.084059594075611715941059730161567406747088718114994303989409384426766423553123110608280927509610855930735997365734366920786352272407771457864496123821730430447497495890903572842025137705198199325794500569573562572619593244042828645 +/- 3.49e-232]"
},
{
"l": 42,
"radial_rank": 15,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.8260842592977959318139719763682664857420703160278468870304779323219327414366993246725131357439739481464488775933571834062537022348953273100779463070236432539993468414873949548700433171830953652556383622025315311497162526831895431e-7 +/- 1.39e-237]",
"strict_gap_below_F_third_over_D": "[0.084059632983469336887073485269469029840018092459635063881977963618873434473392522996734199415353092269271852021778907330948326041296443177133935658872035964302341266731982517927171179662334948357130141102830446413513551695041398347 +/- 1.12e-232]"
},
{
"l": 43,
"radial_rank": 15,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.7002712079274067401287331127489112939009651100790547407531671366295533063517978331763356697517068053567682260178989482177016613517124334060337978630120608041179992221469959567632575712106715012464991117413212836110853652120043412e-7 +/- 5.71e-238]",
"strict_gap_below_F_third_over_D": "[0.084059645564774473925992653793355391775537276570155658761192591349953003711336031486883349033099691495986130989844064876771844896500531495423326063286880365460586254866744451967070990340909545599516542016755492534538305558130145466 +/- 3.91e-232]"
},
{
"l": 44,
"radial_rank": 14,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.3407356868532079252473613326828076225583972045757089073907552137271059920485687374032181796641381470816265608519872268459737953732070001318147073200803929219538453687771133154247247130504120047364107785512332616381640877820756690e-7 +/- 3.98e-237]",
"strict_gap_below_F_third_over_D": "[0.084059681518326581345874141930533398385904410826946209095775927591145293956067461809792926344848700252851958504010581467943982069287129345966653485195934658627374471282129788955335124194195361625466193025588811543340502850257888458 +/- 4.84e-232]"
},
{
"l": 45,
"radial_rank": 14,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.2408507231119537387560669544314278026899047064205561853391377171251396520266662075527166881241114607227543615045861049900945287362065486594595644513070521761213824698733534899264975412035460711176856885886747110659412282251359167e-7 +/- 4.46e-237]",
"strict_gap_below_F_third_over_D": "[0.084059691506822955471292791059971223523886397676196024611048132752894954152701464000045911394997854255520594391230516208056167657213793046011800720710221535961449054528419679331317674016912546312059554898097807799195560072543844152 +/- 4.93e-232]"
},
{
"l": 46,
"radial_rank": 13,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.9041439215135823235118915127941764477269957089949245981500627089142258807716983392221615270772154745793664659196740169538413075154677921509255440404790765128195888919389934372614382992421812241181777174921896585984413524459671388e-7 +/- 4.27e-237]",
"strict_gap_below_F_third_over_D": "[0.084059725177503115308434315477515387249021893967095767174206851660395775244078589496832744450513958945119208730020074699264971282535915119887451574112262618759015384707777472767322940522836742448544254848894917447700806822531422069 +/- 3.56e-232]"
},
{
"l": 47,
"radial_rank": 13,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.8244207750066944698887121123308809851044434699115287648214914049194964939539085424353629765961844302051766544731285595418712464921235853863223258804635168103519111585276612197792796555092754274852447149063030062167393688401892595e-7 +/- 2.73e-237]",
"strict_gap_below_F_third_over_D": "[0.084059733149817765997219677795455433578568156222319675513790184517526174717017271275812423130369007048223646149001219353810712479542017454308128034434078620314985631475550813900544688738701115739123918142195176036366044992729782647 +/- 1.00e-232]"
},
{
"l": 48,
"radial_rank": 12,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.5055730786420244198069566762331080581380728139732964822968227844377253181515156165186930138529063166060811638641740107896134891751044541244272504915847244183714284104516862425837127984693273561995374496154423852954573258181274948e-7 +/- 1.78e-237]",
"strict_gap_below_F_third_over_D": "[0.084059765034587402464224685970999043355860852859385269337018436984388222894134851515105014797365281376035006058550280249265587705317749156221254223941617508194224829523825621498042408295386819733931046712921705122428137120934084853 +/- 2.74e-232]"
},
{
"l": 49,
"radial_rank": 12,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.4417141955970774682792831735941179524146907077343722041365608467329390725154193177201726659840664603342576021258758908827563593749989887877387298194424098935396779959552057273299609614517904535921648585440169688066166946378823762e-7 +/- 2.09e-237]",
"strict_gap_below_F_third_over_D": "[0.084059771420475706958919838738349307254871425197595893229446253010581993372759415124734894649400068260020633240906454079077578391030729166767787892793684722425677312698867071146093933670570521487621307450180812264969786004997202878 +/- 2.28e-232]"
},
{
"l": 50,
"radial_rank": 11,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.1369971375587261573020902942486743670595588576888129199888140524361777303752130837987536449265741849055901796417756089372383851055647057739891440264567539320614407759443880263922661561345792420805720101437888735143393797969492972e-7 +/- 4.08e-237]",
"strict_gap_below_F_third_over_D": "[0.084059801892181510794050936457637241799229960710780897785374667785261423048893629145358286791302174009248176107648702489105772942828156110196089267752264020991273460522589072227864027440051053208742458609465652287779315232728686971 +/- 1.57e-232]"
},
{
"l": 51,
"radial_rank": 11,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.0857576820615960306973887550618422231033620562997164144927540344082208706232216287989140540367523602706185880420161336771877450855860346826895768224374097435681778723215291689796535298051137823176621411821372873020676476376137795e-7 +/- 1.76e-237]",
"strict_gap_below_F_third_over_D": "[0.084059807016127060507063596927791160482444356330461036695025217391263225844579604344503786775261262991430639604807862465053298947892158108063198397708984422925692309848879434513749768701313686155288434900452548452937936459901902905 +/- 3.35e-232]"
},
{
"l": 52,
"radial_rank": 10,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.7923388579068886145417387200558908065172703259157039643053087584244007183400700989074651977580818772177285517011866754113358550777714930931557384022716071952468031204350812940378533101017176578362252561687868201847808721716983592e-7 +/- 8.41e-238]",
"strict_gap_below_F_third_over_D": "[0.084059836358009475977805212492794661077586014939634075096270236135790824226594832659656775920146890858478944893811496547999125533081158889517357351092826439505947141986354623158537262881335656494900883044141049787984648188579449496 +/- 1.96e-232]"
},
{
"l": 53,
"radial_rank": 10,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.7512393096859144008073105712522584439250165349948679614100235027735671398549510704259722804613078534283808219381756286762932336557005501832293296039408682783702549208746082451211276324227011798116689023508589317700752985299609077e-7 +/- 1.71e-237]",
"strict_gap_below_F_third_over_D": "[0.084059840467964298075226585935609541440822274165013167179870525664316389309952681171559624069438620535881323828584472849103799037343301096611648343733706272579838829641174579205842154553903424396548685499776431580773489659136813670 +/- 5.52e-233]"
},
{
"l": 54,
"radial_rank": 9,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.4669420992280770991120579716288351043654810058213853815656345421450699108922156343550877234336103769335807733761817455544574296745129457282295596260228083230113650823930162772987089298337025290279235757235579575231917003616396245e-7 +/- 3.07e-237]",
"strict_gap_below_F_third_over_D": "[0.084059868897685343858956755460869503783156230118566084528128510103212452159675577445103231157894323305628973308589329048492111220923699215372093843710704064385834365530158427365038936795773683296413763874309094310870914347496630502 +/- 4.80e-233]"
},
{
"l": 55,
"radial_rank": 9,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.4340666340404134995488886551080361241187140315761081793042577511627436126724400721887241693650330156853579226572706059550101306427651564729209521598199245065369314733492032526295325377065948370288960449760621462214792129041612879e-7 +/- 2.06e-237]",
"strict_gap_below_F_third_over_D": "[0.084059872185231862625316711777801155863054254795263509055848736240891550392305399422659447794249730163365098130874400939606071165653602390151019374571450684674216012973519331746341403713412896007182963777062169060452044518745376250 +/- 1.06e-232]"
},
{
"l": 56,
"radial_rank": 8,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.1572004226266050904166422360659234236154784543121285093837421236291999487306968868366578801797505340358302510827724196757731861618186235113903833539213104861387021952974025445183650958762887627682555057799775829626452287452689155e-7 +/- 1.43e-237]",
"strict_gap_below_F_third_over_D": "[0.084059899871853004006157625002443060074324305118821235453815728292454303746671793596977983000878648691613263083641558389424699089348050484804315527628331274535618052796447136926412214830157079037790389841116088668908370402143792139 +/- 1.45e-232]"
},
{
"l": 57,
"radial_rank": 8,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.1310534599884005336149440949249139155542988852168541615081037453357390312083538009810871050681188348495413629920541490949269569051635464566375177337786767294879733105835464867060813608881523932339788817212041236578696994332071104e-7 +/- 2.74e-237]",
"strict_gap_below_F_third_over_D": "[0.084059902486549267826613305172257174175275111236778144981250515856292133092763545831286568557956159854783181712530367461251757173970976150312021002914893288798993717869335608312017996058530577851427343268778494546254300879696723345 +/- 3.66e-232]"
},
{
"l": 58,
"radial_rank": 7,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.8602920338425574045993426290614770595070824612009279798626127977620044560553750130713334466657225880349437994033862037076106379657156122621176503877872257840078749191037290034577011904754694302850185752507897011070899133080568967e-7 +/- 3.36e-237]",
"strict_gap_below_F_third_over_D": "[0.084059929562691882410926206732403760518960715958420546573868680405386890466221061129165359533322000094407863172286726328046295905602870095105440454901627887944088265879174756293766320896547619119723638164809141587696555957675335860 +/- 3.21e-232]"
},
{
"l": 59,
"radial_rank": 7,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.8396948277197715231677505764007284898951890473583691270455358648433305257866462109391789191077442905170811326707706406513211946998000208462804301010190220162302122605673251448316851416917074384374054145317359436673581446386571949e-7 +/- 2.86e-237]",
"strict_gap_below_F_third_over_D": "[0.084059931622412494689514349891609026593817677147761930829753962113080182333614088002045572748774755892237614958553399589602601534547196686664582038623656564764465043645440609934152183498152497495922822926125213493072299930852202800 +/- 3.33e-232]"
},
{
"l": 60,
"radial_rank": 6,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.5739881702837651700914779326323178077866021560018551738736717919160636005825410981852846869543200957568006232074242175972966139775077425082208447764027773483683300708241863894144219397258741150659890643240802909477066954403815726e-7 +/- 3.84e-237]",
"strict_gap_below_F_third_over_D": "[0.084059958193078238290149657518873403434885888006451066481149279299487475060306608412556848138197971234657090986604345924244906937005268915892415844582189026388931829833659584248027725224472694079255160067760234258637571895997122628 +/- 1.38e-232]"
},
{
"l": 61,
"radial_rank": 6,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.5580033546797071655654003380224431808105031799357804666130141131649535682535649087565058445270719323668324652118439174508697273108615281118342584804898620635446671305529657097041526195046637736902457823404172440928595824765895424e-7 +/- 1.88e-237]",
"strict_gap_below_F_third_over_D": "[0.084059959791559798695950110126632864422348585616348673088620005365255350171309841310175791016082213959473429983420145482274921579693935580513855483240818617680460312199953611370095696251404716200289297642088432624942257380708419007 +/- 6.85e-233]"
},
{
"l": 62,
"radial_rank": 5,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.2965129159934396390847498992317816447037654800030363346177465997758878008134018086667262841996264834091602476444103218024191792143252892849925325928392834908074384960080663052271006736872116865039659254093544773538517129129786389e-7 +/- 1.04e-237]",
"strict_gap_below_F_third_over_D": "[0.084059985940603667322702758191676743488502196290118666363033204892006689077886585326485799994038246704018325750641902225634486424748745234137738167413407382738317585922817065860036143956599297945498016270074125731218931281495375368 +/- 1.74e-232]"
},
{
"l": 63,
"radial_rank": 5,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.2843888222505396147451272227695625355934318597426597928872222770235479277493268005300849599844561295113744682492598737990899840021683524177159094872532854564509478384867417488179368799143461064439692089307765297054706787947812271e-7 +/- 4.25e-238]",
"strict_gap_below_F_third_over_D": "[0.084059987153013041612705192153944389710413107323480692400687377944438964311873891733986613658170668221053715529219841740679286757668266449831424895075717941338121021571882817992491784872978675232056022269745773589013696119598787188 +/- 3.86e-233]"
},
{
"l": 64,
"radial_rank": 4,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.0264394929327323923637968311376620280693297838103161593494205559200052839366318944569776500826713638536402930541406933154451064369810218126675436592970552388083362374620898386062889204543470837725216192767371045929707856033075191e-7 +/- 4.35e-237]",
"strict_gap_below_F_third_over_D": "[0.084060012947945973393427430286983552900463859733688285635050731724611074666138273003477220968901658399530281302637361252597335122156022968564485399912300736961142785833042920457682806037774621231958289414504738992956207369588106335 +/- 3.06e-232]"
},
{
"l": 65,
"radial_rank": 4,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.0175686217204625059658568612890179326115597409375609739352722108664762443684106392294160263502952615844675435516577699123277702097724024696244165896876983798317224014016390528453000265890951828968390319547238175262502614847729441e-7 +/- 9.26e-238]",
"strict_gap_below_F_third_over_D": "[0.084060013835033094620416070080980537764873405510692572910569273139445580019042229825602743725064031637140508219912311500889675433889645689426419704225007697896828683494426526502761382136664007757148376982763471194284914041640518189 +/- 2.44e-232]"
},
{
"l": 66,
"radial_rank": 3,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[7.6261273498252584947290000022204633001039268211539192971665197634139519816416081086069360128634759961956325619239047984901362057477512780983144628919763274726447010419324802618860544718129021976988062946360634859652661262560247256e-8 +/- 1.56e-238]",
"strict_gap_below_F_third_over_D": "[0.084060039330621768414081719376666644462033665627398455127473695001469032527146850250585580597306538031906704710341047427618681765304609189153885683522037746903391940219656247341864047806121948537644689678603720306031807014005404106 +/- 2.37e-232]"
},
{
"l": 67,
"radial_rank": 3,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[7.5650047723022337497087961370346060828546345994077236297611953246252300622789374298818411149231511085328511519847388435502243084037126691259428466986231458537129622388369894444799542219507352134274717561588117330351156584459777007e-8 +/- 2.33e-238]",
"strict_gap_below_F_third_over_D": "[0.084060039941847543644329169578705296320605838120320672589430369054713420414366043877292367848255517435155581338155146819278231164423582629539975407238199680435208129537044278296772221867124447159314532391949105078549336315510082206 +/- 2.88e-232]"
},
{
"l": 68,
"radial_rank": 2,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[5.0409056709246661967628592006043347176781028601037709894723285840176032418542267919473802569363567745513684491839921235745771240195906002482390677337190472715700778775802343070668375861836957322904751006908102067680853365784471333e-8 +/- 4.28e-238]",
"strict_gap_below_F_third_over_D": "[0.084060065182838557420004699038074660623319489885638065628956771943380826490634248124398747192864097303098921152982174826745430920895426470760664184275989329476193950965887890864323595998290804829709343761915659758564598985813300882 +/- 4.39e-232]"
},
{
"l": 69,
"radial_rank": 2,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[5.0033142504280430476101172587070111553748382286028098070627168420556225340658238015947902363308107623706603067621134101766908027696194863612729947903039435874865330017231234906674334803840494286378259395290478973064924278058055238e-8 +/- 2.30e-238]",
"strict_gap_below_F_third_over_D": "[0.084060065558752762386236190565494079596555112918284380638568596039498246110441326008428650718764303358559042960063599045532564899758638970471803053936718763627230791801336649435431759992331862826172380288407271376187693601742388608 +/- 4e-235]"
},
{
"l": 70,
"radial_rank": 1,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.5009942478989622053405157719693582002580253951277890036169025757726432882116516607029362916813804491870985858161876692632515278257326876528705410237411893390979893388706887519375426311005789501150218896527667316946232997979193267e-8 +/- 3.02e-238]",
"strict_gap_below_F_third_over_D": "[0.084060090581952787677044613261508946973084664086412715388776630497640908940233784550150059637303749852862174795680808504789974034151388409339790137961256429254773275686773277959779147291240355660877165516447770138999349720433668687 +/- 1.29e-232]"
},
{
"l": 71,
"radial_rank": 1,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.4835877655314677816803015835797204891392521393890000600059145542373528168403798262364708860238875514982450433592217221459747316077467429594862980180940418867476671046181544715911874041751061210650247062837154714951279467090677097e-8 +/- 3.70e-239]",
"strict_gap_below_F_third_over_D": "[0.084060090756017611351988849863650830869461775274145272776666066607521124293138498262868404301957806427791151684216233074449445206919350589199237071803686485726247799189995620485121950754792624915605456016419603829511951715387199575 +/- 4.06e-232]"
}
],
"strict_local_maximum_modulo_phase_and_rotations": true
},
{
"label": "nu1",
"depth": 5,
"N": 9,
"dimension": 6,
"precision_bits": 768,
"root_ball_euclidean_radius": "[1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8 +/- 1.68e-239]",
"inverse_frobenius_bound": "[10.658397104062442083957810774431189082128481294520662639340354061126321658838807516021905337132922337435180523554301073051539780331395742284480050848158300462708134814917926488875441012609662165206347245355131278276408315272691227 +/- 4.96e-229]",
"residual_norm_bound": "[1.8776685600228500624536917524049409307315710369092043137419456947411565725890020784587648233046775302756602266475329722463820253713444918073642731730441218191137574237797965821604069781406161388341908595521042765943015578733037550e-14 +/- 4.29e-244]",
"contraction_bound": "[9.5925574256313896038543254080481458330022714210841600608774090950136591796258300896242926337312427630675785597516403380704551311175758626984463308127825251517300424741122532807144194178373478618905190122404518602774552765559767110e-7 +/- 4.68e-237]",
"self_mapping_bound": "[2.0972192885099779777737968311843192297703231995732521546404957383260326894475695080019540574642819286149138046384835310220003446603748578584900335454685449923783186538050603857899869236558366834647957603083072818561095743714425047e-13 +/- 4.71e-243]",
"F_over_D_center": "0.19582488413327068",
"certified_unique_stationary_root_in_ball": true,
"full_angular_hessian_certificate": [
{
"l": 0,
"radial_rank": 5,
"known_eigenvalue_over_F": "1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"remaining_trace_over_D_upper": "[0.0075567998271932530969107317619542684546151304041686715539190380730955571250754679014750060146870119155284911791597141055174766176341168381765201664782578462098584559006641291584137583276483135718664698276297274648883954787763093271 +/- 1.90e-233]",
"strict_gap_below_F_third_over_D": "[0.057718158217230306903089268238045731545384869595831328446080961926904442874924532098524993985312988084471508820840285894482523382365883161823479833521742153790141544099335870841586241672351686428133530172370272535111604521223690673 +/- 2.77e-232]"
},
{
"l": 1,
"radial_rank": 5,
"known_eigenvalue_over_F": "[0.33333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333 +/- 3.45e-231]",
"remaining_trace_over_D_upper": "[0.0014680927370059481020844099747747912653975985476309487301060958904738830434852916316053158620403141293874743025523511807053147798819573731814112004424814099915182251643092145305318629594764255991607758867084046520161677037474003523 +/- 4.32e-233]",
"strict_gap_below_F_third_over_D": "[0.063806865307417611897915590025225208734602401452369051269893904109526116956514708368394684137959685870612525697447648819294685220118042626818588799557518590008481774835690785469468137040523574400839224113291595347983832296252599648 +/- 4.55e-232]"
},
{
"l": 2,
"radial_rank": 4,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.016790148505442854679078931112155804906917613644206823623256127005550219583921145467868659125111453580320569930335804122767067045665242210206412623105813012897125418429715852233166739376099758053014188151522965419970082073639825035 +/- 4.14e-233]",
"strict_gap_below_F_third_over_D": "[0.048484809538980705320921068887844195093082386355793176376743872994449780416078854532131340874888546419679430069664195877232932954334757789793587376894186987102874581570284147766833260623900241946985811848477034580029917926360174965 +/- 1.17e-232]"
},
{
"l": 3,
"radial_rank": 4,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.0035085913212888560913479765757887947917119371640890970033852564041419803961795179594136000764293801810221297590356014189676767841427441452218353743596713840976637814815107909208632629320911139070355693193998624023611711306893889949 +/- 4.84e-233]",
"strict_gap_below_F_third_over_D": "[0.061766366723134703908652023424211205208288062835910902996614743595858019603820482040586399923570619818977870240964398581032323215857255854778164625640328615902336218518489209079136737067908886092964430680600137597638828869310611005 +/- 1.52e-232]"
},
{
"l": 4,
"radial_rank": 3,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00081114122735736917327599191441801797513265034485831033136802767137251315045704745037469304684460390605210065298027987205564798569172732159521869705158361106237579500138961332564632780383269327615298092091519277124843779716535084959 +/- 8.81e-235]",
"strict_gap_below_F_third_over_D": "[0.064463816817066190826724008085581982024867349655141689668631972328627486849542952549625306953155396093947899347019720127944352014308272678404781302948416388937624204998610386674353672196167306723847019079084807228751562202834649150 +/- 1.06e-232]"
},
{
"l": 5,
"radial_rank": 3,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00028796426372569472904891792299547286129229021784260920780955939055162235239703327389562033889246085102930160820323840358793125157686658269610744468088668279779661962746316388165965520216513852835610425370972297969996538523034957710 +/- 2.52e-234]",
"strict_gap_below_F_third_over_D": "[0.064986993780697865270951082077004527138707709782157390792190440609448377647602966726104379661107539148970698391796761596412068748423133417303892555319113317202203380372536836118340344797834861471643895746290277020300034614769650423 +/- 3.79e-232]"
},
{
"l": 6,
"radial_rank": 2,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00012803382922751207873045872057034188912819685596453891819004797235914081141752306265359312656596131058369073079797170297929936500961619151446589776013983613277097562914828189884212282099166103103352938775533723352520055953919653062 +/- 3.47e-235]",
"strict_gap_below_F_third_over_D": "[0.065146924215196047921269541279429658110871803144035461081809952027640859188582476937346406873434038689416309269202028297020700634990383808485534102239860163867229024370851718101157877179008338968966470612244662766474799440460803469 +/- 8.16e-233]"
},
{
"l": 7,
"radial_rank": 2,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[7.5697061408681437171074366875465468394954578071811083996238377188440551031383765355329962047663655106349851132402378009218291164396375802008563213686737419335000576466804001268280265178645119862113483383858303784888061347254346801e-5 +/- 9.29e-236]",
"strict_gap_below_F_third_over_D": "[0.065199260983014878562828925633124534531605045421928188916003761622811559448968616234644670037952336344893650148867597621990781708835603624197991436786313262580664999423533195998731719734821354880137886516616141696215111938652745653 +/- 1.28e-232]"
},
{
"l": 8,
"radial_rank": 1,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.3168171651429926287040195966779378477065026730148080576655022205791754427495276954036848610699595717196273176550314856344990058401923414736698773715468202112644678485158714806399518305546336593203334522791459372994580232807649647e-5 +/- 4.32e-235]",
"strict_gap_below_F_third_over_D": "[0.065241789872772130073712959804033220621522934973269851919423344977794208245572504723045963151389300404282803726823449685143655009941598076585263301226284531797887355321514841285193600481694453663406796665477208540627005419767192350 +/- 4.46e-233]"
},
{
"l": 9,
"radial_rank": 1,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.3340032140647922625504223183658697869910657199782926429885076842803474959993665638702028941041777052355007912435419239107903835384829838695777700061989859086374817474563880815755435097606429308359137875577758284955439372651187889e-5 +/- 9.89e-236]",
"strict_gap_below_F_third_over_D": "[0.065251618012282912077374495776816341302130089342800217073570114923157196525040006334361297971058958222947644992087564580760892096164615170161304222299938010140913625182525436119184244564902393570691640862124422241715044560627348812 +/- 1.87e-232]"
}
],
"strict_local_maximum_modulo_phase_and_rotations": true
},
{
"label": "nu2",
"depth": 5,
"N": 14,
"dimension": 9,
"precision_bits": 768,
"root_ball_euclidean_radius": "[1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8 +/- 1.68e-239]",
"inverse_frobenius_bound": "[14.289211612796066789951401489414754301884172828649149509754395616227938390895933652514477506514004982991905994787679650244567538598254362233055656910280821246476405525425559220841072982910904912843818151285104335282362852581539536 +/- 3.16e-229]",
"residual_norm_bound": "[2.5104865308536024055490670552722855332986470639459634416605873264968549074385358462173856067614231433328143365757411459713866821309968016893887430486344793555337442877566879151036138640994928511418823030324240367838433401726554137e-14 +/- 1.04e-244]",
"contraction_bound": "[1.2860290494384095702844280904488049034444191583032610411796894920911616483594956605414875165870457831615536099179514902342641907350147345717772999749104336341707235321015188551612779000760321631575385336212722051321915807275711508e-6 +/- 4.09e-236]",
"self_mapping_bound": "[3.7158902339879816289520147613090111618418522348776574516699007213423916492356098982349925801182465186858292365687515796971204629702559042263672973425696268631437874944851700393048245843526382901041289751292501291078831930918618775e-13 +/- 1.41e-243]",
"F_over_D_center": "0.189741366141274",
"certified_unique_stationary_root_in_ball": true,
"full_angular_hessian_certificate": [
{
"l": 0,
"radial_rank": 8,
"known_eigenvalue_over_F": "1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"remaining_trace_over_D_upper": "[0.0073070030785173395512564128482042557649115940444151708852348592642757267397593079982256423949200702270138152573209194206922581205294792046502811677178828908122822863116918814070960036301343341573191339254973728453211386351156749508 +/- 4.44e-233]",
"strict_gap_below_F_third_over_D": "[0.055940115635240660448743587151795744235088405955584829114765140735724273260240692001774357605079929772986184742679080579307741879470520795349718832282117109187717713688308118592903996369865665842680866074502627154678861364884325049 +/- 4.79e-234]"
},
{
"l": 1,
"radial_rank": 7,
"known_eigenvalue_over_F": "[0.33333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333 +/- 3.45e-231]",
"remaining_trace_over_D_upper": "[0.0013724525686054976093209250718587874674849336466781619850165149941231852884826405333950947983493381687090286918275017940675302042691240250203492886934684873929525097330008470032687796708660223320848216016474788294375938264472360026 +/- 3.69e-233]",
"strict_gap_below_F_third_over_D": "[0.061874666145152502390679074928141212532515066353321838014983485005876814711517359466604905201650661831290971308172498205932469795730875974979650711306531512607047490266999152996731220329133977667915178398352521170562406173552763997 +/- 1.15e-232]"
},
{
"l": 2,
"radial_rank": 7,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.016568495283402778763065538792183137822517161003160580317032796246843704025943488481710582633391563747597098126073911096855964775370849613282415837972665876895555123205549762502578598288754674544004316651256020244274028353038375868 +/- 4.75e-232]",
"strict_gap_below_F_third_over_D": "[0.046678623430355221236934461207816862177482838996839419682967203753156295974056511518289417366608436252402901873926088903144035224629150386717584162027334123104444876794450237497421401711245325455995683348743979755725971646961624132 +/- 2.26e-232]"
},
{
"l": 3,
"radial_rank": 6,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.0035430779075630012573504252412669656369531579558888957121619318966966783312261410298484693183933937662157609114829555609659094100120376918295930497227844784555154330113773902285626304775998105954809157634769554574544579221130479208 +/- 4.00e-233]",
"strict_gap_below_F_third_over_D": "[0.059704040806194998742649574758733034363046842044111104287838068103303321668773858970151530681606606233784239088517044439034090589987962308170406950277215521544484566988622609771437369522400189404519084236523044542545542077886952079 +/- 1.32e-232]"
},
{
"l": 4,
"radial_rank": 6,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00080738727096604885994318531410940907516562486672940461752885498338809291855049513845793781829245414800236359860688675320965806376849410686597668956030991337025983247836491802978667385100402321539874073002612327777295472119782216857 +/- 3.63e-234]",
"strict_gap_below_F_third_over_D": "[0.062439731442791951140056814685890590924834375133270595382471145016611907081449504861542062181707545851997636401393113246790341936231505893134023310439690086629740167521635081970213326148995976784601259269973876722227045278802177831 +/- 1.09e-232]"
},
{
"l": 5,
"radial_rank": 5,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00025876780382640198711307920930847258174658077646007868515449424287336822324479691510093805840332754127230302517997913900530898582079895088940407094657207752651987873986386957341242444495526014239591434008275217755082633877194945568 +/- 4.60e-234]",
"strict_gap_below_F_third_over_D": "[0.062988350909931598012886920790691527418253419223539921314845505757126631776755203084899061941596672458727696974820020860994691014179201049110595929053427922473480121260136130426587575555044739857604085659917247822449173661228050544 +/- 6.95e-233]"
},
{
"l": 6,
"radial_rank": 5,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00011602218238505187095445169696049954243434757917622201541563798347712517278479052777318356962946350973458474596640072157103995445317607383686608236486080297339325592391396921907715441622554288628482745993873004468950062922316591618 +/- 4.61e-234]",
"strict_gap_below_F_third_over_D": "[0.063131096531372948129045548303039500457565652420823777984584362016522874827215209472226816430370536490265415254033599278428960045546823926163133917635139197026606744076086030780922845583774457113715172540061269955310499370776834083 +/- 3.87e-232]"
},
{
"l": 7,
"radial_rank": 4,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[6.0902519863189069002677234044041649958502197289766266318716896861554783201808109523885063259482496115208093319250951355929252192462614829027145472014701275195472119822232086104787373065273800720248827251405685343037314745836437140e-5 +/- 1.03e-235]",
"strict_gap_below_F_third_over_D": "[0.063186216193894810930997322765955958350041497802710233733681283103138445216798191890476114936740517503884791906680749048644070747807537385170972854527985298724804527880177767913895212626934726199279751172748594314656962685254163562 +/- 4.45e-232]"
},
{
"l": 8,
"radial_rank": 4,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.6851605896864111950240308561739275810895462613326355653747593744866273929915259236462772976030355274112940055113783651592556674089159611496851948434736100129944888955239804714280661863686557216557967712161203109762231036821005349e-5 +/- 1.79e-235]",
"strict_gap_below_F_third_over_D": "[0.063210267107861135888049759691438260724189104537386673644346252406255133726070084740763537227023969644725887059944886216348407443325910840388503148051565263899870055111044760195285719338136313442783442032287838796890237768963178994 +/- 2.68e-232]"
},
{
"l": 9,
"radial_rank": 3,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.2149562874774797989356875437056342134693266242423997627931958763532416591484539123335078114953438632471819147863179279822653978481629087988064156203505883783633425163420420806416889589408571907415689568658327609855567849019548143e-5 +/- 1.39e-235]",
"strict_gap_below_F_third_over_D": "[0.063224969150883225202010643124562943657865306733757576002372068041236467583408515460876664921885046561367528180852136820720177346021518370912011935843796494116216366574836579579193583110410591428092584310431341672390144432150980451 +/- 4.57e-232]"
},
{
"l": 10,
"radial_rank": 3,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.5426732665141399656893573943150790073443670883215826971853056362919176399923936649768316240842737096319215238917771737112781058926564618141207031813007451111969851255486296074525505651147041166091894447798024728311974788275499925e-5 +/- 3.75e-235]",
"strict_gap_below_F_third_over_D": "[0.063231691981092858600343106426056849209926556329116784173028146943637080823600076063350231683759157262903680784761082228262887218941073435381858792968186992548888030148744513703925474494348852958833908105552201975271688025211724500 +/- 3.63e-232]"
},
{
"l": 11,
"radial_rank": 2,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[9.1886167453232537683459257388166520938618328172195341442207786576651775434888286415722213741833232682932877576645809180727071823980604154527593753946958984169029280325976290816191224275407341306266757123060887286221850136854460244e-6 +/- 2.44e-236]",
"strict_gap_below_F_third_over_D": "[0.063237930097012676746231654074261183347906138167182780465855779221342334822456511171358427778625816676731706712242335419081927292817601939584547240624605304101583097071967402370918380877572459265869373324287693911271377814986314554 +/- 4.73e-232]"
},
{
"l": 12,
"radial_rank": 2,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[6.9814750616778274976623813081492310952493343698332730094119365723800341077538088036860969695559049213980801889851392895973810665014596421180033254502008830245619491138057083624259389079438723949190539463054572408193978390632152897e-6 +/- 5.17e-237]",
"strict_gap_below_F_third_over_D": "[0.063240137238696322172502337618691850768904750665630166726990588063427619965892246191196313903030444095078601919811014860710402618933498540357881996674549799116975438050886194291637574061092056127605080946053694542759180602160936784 +/- 3.31e-232]"
},
{
"l": 13,
"radial_rank": 1,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.3225947533801979405159275500296299308160308305700955025172156607573300119199612148963899083349452870941799092445167213084171789596667138582034381801991843578802467237227155026722302415699548321103955105355950679770608642024328789e-6 +/- 4.52e-236]",
"strict_gap_below_F_third_over_D": "[0.063243796119004619802059484072449970370069183969169429904497482784339242669988080038785103610091665054712905820090755483278691582821040333286141796561819800815642119753276277284497327769758430045167889604489464404932022939135797567 +/- 2.81e-232]"
},
{
"l": 14,
"radial_rank": 1,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.6730683766780917102117868517635794865363475144729970610370264594690605717814518397032633713954549943290923000799559960518366290808241806378875894175830513613360778210569643352318657444843362648598851193319151188379108788304777431e-6 +/- 3.47e-236]",
"strict_gap_below_F_third_over_D": "[0.063244445645381321908289788213148236420513463652485527002938962973540530939428218548160296736628604545005670907699920044003948163370919175819362112410582416948638663922178943035664768134255515663735140114880668084881162089121169522 +/- 1.16e-232]"
}
],
"strict_local_maximum_modulo_phase_and_rotations": true
},
{
"label": "nu3",
"depth": 5,
"N": 21,
"dimension": 12,
"precision_bits": 768,
"root_ball_euclidean_radius": "[1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8 +/- 1.68e-239]",
"inverse_frobenius_bound": "[17.215850002477583240741275387621661637328394689684237555451624569016143668166571514391720916100249249895502125610912251434090708571958382667392350948910722536345418488917563485089744552158640025087556390908693924340570345711981134 +/- 3.03e-229]",
"residual_norm_bound": "[2.6891467427578318067417398668487177087950885751773013471400817193143891010324055471300180621796024404670683702739702451762453703655924118465747747906921864059593827974198669869877191896747077864633563934542229967908298172929374661e-14 +/- 5.44e-245]",
"contraction_bound": "[1.5494265053877375666784193928658620074938536587779895227201960715490201485061371564169365060024580419954511031578813609662054791884717289010747210994724023781961027589119702443467361273274763502305309647336153779535257775607369855e-6 +/- 2.24e-236]",
"self_mapping_bound": "[4.7845373463357741178523995436784953063940539471050730671955281552733669883167871548383860604747209771014720837896914119056721860467250707858672669880095387998347078645808565025030491045459198658868474709343088579387561020882998548e-13 +/- 1.10e-244]",
"F_over_D_center": "0.18685740335254017",
"certified_unique_stationary_root_in_ball": true,
"full_angular_hessian_certificate": [
{
"l": 0,
"radial_rank": 11,
"known_eigenvalue_over_F": "1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"remaining_trace_over_D_upper": "[0.0071907247848786428961916356137140248571057687320278638849394735862056209966855639082440482559662759899445886054494333638174793073753968704673613138957500525408061968645839842471755168352188519880343779817565955248635981585303250659 +/- 2.63e-233]",
"strict_gap_below_F_third_over_D": "[0.055095072999301413770475031052952641809560897934638802781727193080461045669981102758422618410700390676722078061217233302849187359291269796199305352770916614125860469802082682419491149831447814678632288684910071141803068508136341601 +/- 3.58e-232]"
},
{
"l": 1,
"radial_rank": 11,
"known_eigenvalue_over_F": "[0.33333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333 +/- 3.45e-231]",
"remaining_trace_over_D_upper": "[0.0013369088760547475811356887586787611425934660915421146388292230731293345164305027673635500071762010841142271086457025296111553447575838491858562079697174448655545811503954355131742660771832227360210008757721811508392214790379111524 +/- 1.84e-233]",
"strict_gap_below_F_third_over_D": "[0.060948888908125309085530977907987905524073200575124552027837443593537332150236163899303116659490465582552439558020964137055511321909082817480810458696949221801112085516271231153492400589483443930645665790894485515827445187628755514 +/- 1.35e-232]"
},
{
"l": 2,
"radial_rank": 10,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.016457513824325352690316261262466499763748999852293169752987660919901214322082598378546233529502604060576827907875028537361119493028099174141714565766913462881675460159006402040690356605418780544380486822029431121926007215313348959 +/- 2.93e-232]",
"strict_gap_below_F_third_over_D": "[0.045828283959854703976350405404200166902917666814373496913679005746765452344584068288120433137164062606089838758791638129305547173638567492524952100899753203784991206507660264625976310061247886122286179844637235544740659451353317708 +/- 2.52e-232]"
},
{
"l": 3,
"radial_rank": 10,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.0035661660818036920827424188753623754309879115728151614311758052071115502511493862542775982742329288630831610638857114337109275844080961428387394693087632284070306571220606684404878489309905429255818332327072334202320823267529448100 +/- 2.93e-233]",
"strict_gap_below_F_third_over_D": "[0.058719631702376364583924247791304291235678755093851505235490861459555116415517280412389068392433737803583505602780955232955739082258570523827927197357903438259636009544605998226178817735676123741084833433959433246434584339913721856 +/- 4.76e-232]"
},
{
"l": 4,
"radial_rank": 9,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00080583605262683820787213062472653065608571931597439326469360744344481866499620550871381404820369498761258175950129427726617306893198900478859163440102331172920577228883334210040205943731025331351394881236373523686576004360494389443 +/- 8.49e-235]",
"strict_gap_below_F_third_over_D": "[0.061479961731553218458794536041940136010580947350692273401973059223221848001670461157952852618462971679054084907165372389400493597734677661878075032265643354937460894377833324566264607229356413353152717854302931429800906623061722772 +/- 3.59e-233]"
},
{
"l": 5,
"radial_rank": 9,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00024937060463638055286468822590579177098278960710385081291256145587915234254038637335666736328436070876518168220155391624742895512178761601822906367591769797139947659464712286111417853310889965978010475073112081677068660425919106778 +/- 1.10e-234]",
"strict_gap_below_F_third_over_D": "[0.062036427179543676113801978440760874895683877059562815853754105210787514324126280293309999303382305957901484984465112750419237711544879050648437602990748968695267190072019543805552488133557767006886561915935545849895980062407475599 +/- 3.21e-232]"
},
{
"l": 6,
"radial_rank": 8,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00010598560985260530999492846015321106492490736980861557416658181433777241869934309483299031900134730076606442360740337817328910317321545140475862083920491285596094747079209754581328138049726108644649789117737638958753574596595926709 +/- 2.02e-234]",
"strict_gap_below_F_third_over_D": "[0.062179812174327451356671738206513455601741759296858051092500084852328894247967323571833676347665319365900602243059263288493377563493451215261908045827461753810705719195874569120853385286169405580220168775489290277079130920700707399 +/- 3.66e-232]"
},
{
"l": 7,
"radial_rank": 8,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[5.4483513245431633362587698257107848947916041526753385703911695122020284166840286978331190945380780008371708275597493376480553839211721402244058164519618230268897625944420487650396169145541325263827931897443319984574865832826375836e-5 +/- 1.26e-235]",
"strict_gap_below_F_third_over_D": "[0.062231314270934625033304078968409558817718750625139913280962754971544646382499826379688335475721285886658294958391069173290186112827454945264422608502147048436397769040722246179016270497521125341402838734769223346682091800833840291 +/- 3.84e-232]"
},
{
"l": 8,
"radial_rank": 7,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.1039201638911523117630713450266707143626239672370894185028104802472169689026153793308714106368149158092766779369376828267281569138067845803249476926815144680165760827857048418321045605143379036331028759838325608698942909358112762e-5 +/- 4.38e-235]",
"strict_gap_below_F_third_over_D": "[0.062254758582541145143549035953216399959523040426994295772481638561864194496977640512873357952560298517508573899887297289838399385097528598820863417189739851521986500905838809618248345621061523287630335637906828341057967723757308554 +/- 2.91e-232]"
},
{
"l": 9,
"radial_rank": 7,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.9277985230720926625136226293177813683609170425217123361305626453730558213293495907828145631289370277574191221946417602457060469833625147368453308765966765138004214532539806923017774603338229006836327930762670206639276947442920755e-5 +/- 1.37e-235]",
"strict_gap_below_F_third_over_D": "[0.062266519798949335740041530440373488852983057496241449543305361040212936108453373170758838521035377296389092475444720249064209606196833041519298213357900699901528662452134126859743648892063328437659830338735903996460027389719223746 +/- 3.12e-232]"
},
{
"l": 10,
"radial_rank": 6,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.2466392047170627254283952328105596541513440105973912099238679480775089963842318571278790830709245139410746972274606092544210446761765354706074245966297471744341956661397862347876705138174545474391749170973713563781919724257725072e-5 +/- 3.34e-235]",
"strict_gap_below_F_third_over_D": "[0.062273331392132886039412382714338561070125153226560692754567427987185891576702824348095387875835957421527255919694392060574122456219904901311960592420700369194922324710005268804318789961528492121192274917495692953102884746942408941 +/- 3.64e-232]"
},
{
"l": 11,
"radial_rank": 6,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[8.6553958282791140242127096254609319107862722057825173209970591804039136826895740239047541450476751380690457729664241665460799407176160472484403763261890271932059404165660846547059870354437340788040403419272956034565183749958232799e-6 +/- 2.70e-236]",
"strict_gap_below_F_third_over_D": "[0.062277142388351777552642453957041205734755880394460884149345669607486262752983977092642761912521618991528597620893700242500120586725949050619418226290340477639473460726250100582011960679631222932587862626324739371063210148291670843 +/- 1.71e-232]"
},
{
"l": 12,
"radial_rank": 5,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[5.9917794853776877967888109780145685531424921367222724965300051088578840391491455966386262747028979237479145533192783620693718741116106864925061344203160835321767918768838496225559512712969840277787322757091852707541949218482542287e-6 +/- 1.11e-236]",
"strict_gap_below_F_third_over_D": "[0.062279806004694678978869877855688652098113524174529944394170136661557808782627517521070028040391963768742918752113347388304597294792555055980174160532246350583134489874789782817044110715395369682638887934390957481395912471744818412 +/- 2.34e-232]"
},
{
"l": 13,
"radial_rank": 5,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.4937511375908225474410487925830989017054297820642501006469884298219338783150997435423332943710092188799663743844311483341000484482806612273289825810791085190857411536705129493319914797265597328889049983462993415681534095168770431e-6 +/- 1.89e-236]",
"strict_gap_below_F_third_over_D": "[0.062281304033042465844119225617874083567764961236884602416566019678236844732788351566923124333372295657447786700292282235518332566618218386005439337684085587558147580925512996153717334675186940106933777761668320367325098513257149789 +/- 4.08e-232]"
},
{
"l": 14,
"radial_rank": 4,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.1911506553246985906686478230446460309749269937245929252831213002301040518926030347222891615342469505759866088985870370405084211786432276118294006932836060032210379223583159403456527067222681028829256640214046360370212875267948749e-6 +/- 1.68e-236]",
"strict_gap_below_F_third_over_D": "[0.062282606633524731968075998018843622020635691739672942073741383545366436562614774063631944377505132419716090680057768079629626158245488023439054837265973383060663445628744308350726321013959944398563783741002645262030629645379139872 +/- 4.32e-232]"
},
{
"l": 15,
"radial_rank": 4,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.5307985194413688000388360267887604773484369319741353916425995893325114998422950195489115834189873935285213388074342446387806741350531379533333423120143960285051294777866200091782933920165738473095198909614815143389745817966035632e-6 +/- 4.98e-237]",
"strict_gap_below_F_third_over_D": "[0.062283266985660615297866627830639877906189318229734692531275024067077334155166824371647117755083247679273138145327859232422027885992531613528713333324354652270638161537188880046657488373274650092819357146775705185152327692084870063 +/- 1.19e-232]"
},
{
"l": 16,
"radial_rank": 3,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.7639351631520456186678155035649708009928881262258268905101013501182461776178784863123573696767981145730252878784706268226225034946707406803849259815051658552861323099045578004388575184503598302779027309742901646207847969559880633e-6 +/- 4.06e-236]",
"strict_gap_below_F_third_over_D": "[0.062284033849016904621047998851163101695865673778540440839776156565316548420489048788180354309296989868552093641378788196039844044163171995925986281740685161500811380534356762108866227809148216306836388763935692376502045881869710678 +/- 3.80e-232]"
},
{
"l": 17,
"radial_rank": 3,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.4578099930082633872211809262599622139140018430472046714226485919865006051856792547269417315852284831734479968473024956389407553659177561591965460991086794926265306220371468596030339951466574047753793369290574124973081093738501469e-6 +/- 3.72e-236]",
"strict_gap_below_F_third_over_D": "[0.062284339974187048403279445485740406704452752664823619461995244018074680166061480987411939724935081438183493218669819364171027725911300748910507470120567557987174040136044629519807063632671520009261891287329737609254169358557292816 +/- 3.18e-232]"
},
{
"l": 18,
"radial_rank": 2,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[9.3210984847203454531969171830609776777154218927729302109348968824020015754763832040854017793566217511169894614916913673372287019482434207723939182148668032132366133418141319386014857594238077169026166982779249882289886226352527312e-7 +/- 1.75e-237]",
"strict_gap_below_F_third_over_D": "[0.062284865674331584632121346974948360568898895124477389373645573176978426466509119028346258126488731004491554967720517497529932943796471842324589427274845179986345343005332485253472806518090724285894976404996838874167843767804403141 +/- 1.86e-232]"
},
{
"l": 19,
"radial_rank": 2,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[7.9449048585067264223778050206883548023524766966855057516932048519662864292664757141713747346808096026680026133070686520540666973615459195465189040648412848470999668367296927549104926606269221410218197815669266979519187241149814970e-7 +/- 3.87e-237]",
"strict_gap_below_F_third_over_D": "[0.062285003293694205994024428886164597831186431418996998116091497346181470038023740019095249529193198585706399866405335959801461259996930512074712014776260182538181956669982993697391175617400603974452564484688509973996871474794255168 +/- 2.96e-232]"
},
{
"l": 20,
"radial_rank": 1,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.8929790246769442122912815232406061080813774964350312739711934835502459882861805644385059214413701076073390373854613890611834661931205080626739743179591194463386246441680729315208147165831113446922223143064499291618595446372778227e-7 +/- 4.99e-237]",
"strict_gap_below_F_third_over_D": "[0.062285408486277588972245437538514342606055858528917023163539269547318311642067838048610222816074522529655905932762928120527760548320047354615860399269234870754722032804202249859373514585195008355532197444435236021673750480712202939 +/- 3.11e-232]"
},
{
"l": 21,
"radial_rank": 1,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.3968590587571351683456980781703408873479709487533790391504581419019815856367920787806931052813462463111682316868463279002242743216446458945205552385009630183444261403723708201168229349735333090889419685591176360009693634087601208e-7 +/- 3.94e-237]",
"strict_gap_below_F_third_over_D": "[0.062285458098274180953149832096858849632577931869571791328762751620852476468508102987458788597356138532042035549843497982033876644239234502202077214611142816570364832224052629429584654984373169313335757772469810754903066569730325790 +/- 4.54e-232]"
}
],
"strict_local_maximum_modulo_phase_and_rotations": true
},
{
"label": "electron",
"depth": 6,
"N": 12,
"dimension": 8,
"precision_bits": 768,
"root_ball_euclidean_radius": "[1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8 +/- 1.68e-239]",
"inverse_frobenius_bound": "[17.513554700723585951318840915395802145113433538585337659504983172814292805038198381617592137120989656068220390382144549750140114419859754583419107784559670002254444404616460449248118318519107765060738373122015508242174281198064799 +/- 2.01e-229]",
"residual_norm_bound": "[1.0979534019835260135879321852425761824629676509695568455488319722014514497574307756169353210917557696016420915706432620703640348630550986185904938742760153646010759867603755143610693272646264378697344482516477888223645338072936239e-14 +/- 4.43e-244]",
"contraction_bound": "[1.5762199283191892717917534435289124328947139867204113410081261647099611141715501687406615219060470173220467012936131905092716684709241752140638603970710859778484249882661355802411299522582078359150760145807889929546352028911276267e-6 +/- 1.08e-236]",
"self_mapping_bound": "[2.0805286892803224266514954454290928566597686640314565400302224138670447153696372756858000218728113848977988826392188324312783550327214039360757523466815339972245391600141964372870648373714787052987012978789013649384007320896443130e-13 +/- 1.05e-243]",
"F_over_D_center": "0.14322889019247556",
"certified_unique_stationary_root_in_ball": true,
"full_angular_hessian_certificate": [
{
"l": 0,
"radial_rank": 7,
"known_eigenvalue_over_F": "1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"remaining_trace_over_D_upper": "[0.0050870826539253180243377425315631667414968868869417663107852663301251247312032405407578953992425790482932613111539770547568597191521606125178739258998077085189024911385882548723194618742217258887844087294919647820810592837286783320 +/- 3.00e-233]",
"strict_gap_below_F_third_over_D": "[0.042655877410233201975662257468436833258503113113058233689214733669874875268796759459242104600757420951706738688846022945243140280847839387482126074100192291481097508861411745127680538125778274111215591270508035217918940716271321668 +/- 1.26e-232]"
},
{
"l": 1,
"radial_rank": 6,
"known_eigenvalue_over_F": "[0.33333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333 +/- 3.45e-231]",
"remaining_trace_over_D_upper": "[0.00092704083091111951449659358666021418571323307841529258972230798029233766932154697220554937673954935276390874625586039218710299179592954856825624982739350188712829046550452045497572069260898247360580137575879777430142672975277710361 +/- 4.39e-234]",
"strict_gap_below_F_third_over_D": "[0.046815919233247400485503406413339785814286766921584707410277692019707662330678453027794450623260450647236091253744139607812897008204070451431743750172606498112871709534495479545024279307391017526394198624241202225698573270247222896 +/- 2.30e-232]"
},
{
"l": 2,
"radial_rank": 6,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.012607629039891481076339160377552440672354721891314804350894813284925621061630410164331968131505042424719752992983918612339814258061539591031044584209507418113606156253494691862011632092363403062096442840948344612024167623675876709 +/- 2.64e-232]",
"strict_gap_below_F_third_over_D": "[0.035135331024267038923660839622447559327645278108685195649105186715074378938369589835668031868494957575280247007016081387660185741938460408968955415790492581886393843746505308137988367907636596937903557159051655387975832376324123291 +/- 4.19e-232]"
},
{
"l": 3,
"radial_rank": 5,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.0026769899550531069997707902831488134145773990133223741808612472182908000337004058000021075947411332513649849219650564686952718818787915957873147263364130784565199075573142862886815998235061616483700557244034282411485116658740516029 +/- 2.88e-233]",
"strict_gap_below_F_third_over_D": "[0.045065970109105413000229209716851186585422600986677625819138752781709199966299594199997892405258866748635015078034943531304728118121208404212685273663586921543480092442685713711318400176493838351629944275596571758851488334125948397 +/- 8.99e-233]"
},
{
"l": 4,
"radial_rank": 5,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00056081043602363484635301765224146340152279793969676785365390949387063702316974938239917738689022868160503436221632913051834508832215537325674354258800002097247285699513182625151186080468415975185200780623154255921990800304154766248 +/- 3.94e-234]",
"strict_gap_below_F_third_over_D": "[0.047182149628134885153646982347758536598477202060303232146346090506129362976830250617600822613109771318394965637783670869481654911677844626743256457411999979027527143004868173748488139195315840248147992193768457440780091996958452337 +/- 3.13e-232]"
},
{
"l": 5,
"radial_rank": 4,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00015444364712539423177859223564108304016351366039903387251352930058428297843691957908342626306050174515879410345556640386464364455280268489342734521250791633747788172057346872839656963243557513367755583525404832794551297603193793203 +/- 3.89e-234]",
"strict_gap_below_F_third_over_D": "[0.047588516417033125768221407764358916959836486339600966127486470699415717021563080420916573736939498254841205896544433596135356355447197315106572654787492083662522118279426531271603430367564424866322444164745951672054487023968062068 +/- 2.39e-232]"
},
{
"l": 6,
"radial_rank": 4,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[6.1326380400987381928944707426383170104174558993921628611675508632967006275037730180562840863867194089503018579742767284325828599737567451778944438453187621839503828559827378835090672476884043213915814090634708853619954228380678836e-5 +/- 3.32e-235]",
"strict_gap_below_F_third_over_D": "[0.047681633683757532618071055292573616829895825441006078371388324491367032993724962269819437159136132805910496981420257232715674171400262432548221055561546812378160496171440172621164909327523115956786084185909365291146380045771619321 +/- 7.05e-233]"
},
{
"l": 7,
"radial_rank": 3,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.9259624894888712908757790638845524698661701942547341273520882012551412973763767298212701054080712022105750545943765422442929112748269753937269050840094055348666452735082858616513369390822070376901995372690982895560474239822458973e-5 +/- 3.25e-235]",
"strict_gap_below_F_third_over_D": "[0.047713700439263631287091242209361154475301338298057452658726479117987448587026236232701787298945919287977894249454056234577557070887251730246062730949159905944651333547264917141383486630609177929623098004627309017104439525760177541 +/- 1.98e-232]"
},
{
"l": 8,
"radial_rank": 3,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.6734582816518788650490414140710224803252387341981203292749951230912910585188641528554849000283196113774389292914654873535847990443535454808249099777888062787485448496232486059957976252853644665914274994337472753651238910390674790e-5 +/- 4.63e-235]",
"strict_gap_below_F_third_over_D": "[0.047726225481342001211349509585859289775196747612658018796707250048769087089414811358471445150999716803886225610707085345126464152009556464545191750900222111937212514551503767513940042023747146355334085725005662527246348761089609325 +/- 2.18e-233]"
},
{
"l": 9,
"radial_rank": 2,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[9.0372788769398790858829563311208744864171337509140164029162649160758861189395362842059968220861416231923587297872709707575370332456446940819633479481433735742468802981707878147299270472334893702167741273929170398235072840421007922e-6 +/- 1.80e-236]",
"strict_gap_below_F_third_over_D": "[0.047733922785281580120914117043668879125513582866249085983597083735083924113881060463715794003177913858376807641270212729029242462966754355305918036652051856626425753119701829212185270072952766510629783225872607082960176492715957899 +/- 2.10e-233]"
},
{
"l": 10,
"radial_rank": 2,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[6.1009795072149834082712035304018911417518341794421405777568180146288782596758206778328328272316235138928020153106289901284360849224947046818597489590131910093650723422192239317851605629595003084423964250641406430662371095547773600e-6 +/- 2.75e-236]",
"strict_gap_below_F_third_over_D": "[0.047736859084651305016591728796469598108858248165820557859422243181985371121740324179322167167172768376486107197984689371009871563915077505295318140251040986808990634927657780776068214839437040499691557603574935859356933762890445222 +/- 4.14e-232]"
},
{
"l": 11,
"radial_rank": 1,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.7967193501053356268492008528392179240829515753386541893009392883392485791686066560757762931482695709422947363106139032789420131244248307195064849039091858785836606308503198882015436246226845292441859830960709062798138391247626026e-6 +/- 4.58e-236]",
"strict_gap_below_F_third_over_D": "[0.047740163344808414664373150799147160782075917048424661345810699060711660751420831393343924223706851730429057705263689386096721057986875575169280493515096090814121416339369149680111798456375377315470755814016903929093720186160875237 +/- 1.87e-232]"
},
{
"l": 12,
"radial_rank": 1,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.0859856439770705185300739057046491509976090020310814690089559162911056539337851973125384156051629967441231511830574671113185208962467063086570921608519725041900709744690341724624524174544850376032650287827172946524088821532682311e-6 +/- 1.32e-236]",
"strict_gap_below_F_third_over_D": "[0.047740874078514542929481469926094295350849002390997968918530991044083708894346066214802687461584394837003255876848816942532888681479103753293691342907839148027495809929025530965827537547582545514962396734971217282705347591117846732 +/- 4.51e-232]"
}
],
"strict_local_maximum_modulo_phase_and_rotations": true
},
{
"label": "muon",
"depth": 6,
"N": 34,
"dimension": 19,
"precision_bits": 768,
"root_ball_euclidean_radius": "[1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8 +/- 1.68e-239]",
"inverse_frobenius_bound": "[30.453725649044670372671286891479397302661595895521651475214593170265708102977313404923790618572118084046537526881727136554247163546835754526924748399931468405820113870708772228662667836367338736399293265529381135788456258595112073 +/- 1.62e-229]",
"residual_norm_bound": "[2.7062379075416894053006951540006479605522782408558600912932924982753872633734518891082472406276515990861697506844543267239759753478072539093724425720899846486384701733286794149064494597218288845163905221721549009454065935626951785e-14 +/- 2.86e-244]",
"contraction_bound": "[2.7408353175501380654380571038818233362199094813346263638553563827491938277598425041793287551533987648236107412683564741270441604335998748480412012487328958215006226163147759551927197189390040718253220038278391271441751407825986110e-6 +/- 1.32e-236]",
"self_mapping_bound": "[8.5155862094869463900302444576601971206506161598335927318135638458480121992109866176293893941343078516052914432225543479896355994649570211410036300645018574521885898298069921751466997037142523803503015680480441044697403359616194441e-13 +/- 1.66e-243]",
"F_over_D_center": "0.13653323589754152",
"certified_unique_stationary_root_in_ball": true,
"full_angular_hessian_certificate": [
{
"l": 0,
"radial_rank": 18,
"known_eigenvalue_over_F": "1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"remaining_trace_over_D_upper": "[0.0048461178891458710314890424221669986393163496026805877904635089427170859188063580339399074000120709759357582916745886745721634381918331498091421443847737715524458005187137571796386674898459825749596770110974007481510360605821091393 +/- 2.84e-233]",
"strict_gap_below_F_third_over_D": "[0.040664957410034635635177624244499668027350317063986078876203157723949580747860308632726759266654595690730908374992077992094503228474833516857524522281892895114220866147952909487027999176820684091706989655569265918515630606084557527 +/- 1.82e-232]"
},
{
"l": 1,
"radial_rank": 17,
"known_eigenvalue_over_F": "[0.33333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333 +/- 3.45e-231]",
"remaining_trace_over_D_upper": "[0.00087852508544301819433157446345544785560937453891063515565705427609937595472975228008654295281659062691862289818407339669266903451101668748210802208090209891818716129013561212321773426685811711565624839197240301909895589376667604454 +/- 9.40e-235]",
"strict_gap_below_F_third_over_D": "[0.044632550213737488472335092203211218811057292127756031511009612390567290711936914386580123713850076039748043768482593269973997632155649979184558644585764567748479505376531054543448932399808549551010418274694263647567710772899990622 +/- 2.92e-233]"
},
{
"l": 2,
"radial_rank": 17,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.012287967931291606619433814894564077365762535977249563154215272635000711400235544567957967443569709621990126422205547841515189914777417469941619338713533171940045440121527740889000716943586619533895283164417932447243415672101731766 +/- 1.42e-232]",
"strict_gap_below_F_third_over_D": "[0.033223107367888900047232851772102589300904130689417103512451394031665955266431122098708699223096957044676540244461118825151476751889249196725047327953133494726621226545138925777665949723080047132771383502248734219423250994564934901 +/- 3.49e-232]"
},
{
"l": 3,
"radial_rank": 16,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.0027162064091266775312034893463769322603350343889652068177529515627110208166735473722283899401675107352301505964885621801511021037738664207267874746625766180653739346719696060386232270574431390437461045760612441121561400213714575808 +/- 1.16e-233]",
"strict_gap_below_F_third_over_D": "[0.042794868890053829135463177320289734406331632277701459848913715103955645849993119294438276726499155931436516070178104486515564562892800245939879192004090048601292731994697060628043439609223527622920562090605422554510526645295209086 +/- 3.22e-232]"
},
{
"l": 4,
"radial_rank": 16,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00057549720156652026292680019553483492890822255866726665552279490000308102075382276433417863925796712801852620596207410259149978994478950413439848269497673534459689005322700426787285457641625268615871532602246486500989273831575003049 +/- 6.11e-235]",
"strict_gap_below_F_third_over_D": "[0.044935578097613986403739866471131831737758444107999400011143871766663585645912843902332488027408699538648140460704592564075166876721877162532268183971689931322069776613439662398793812090250413980507951340644201801656773928350916636 +/- 2.55e-233]"
},
{
"l": 5,
"radial_rank": 15,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00014899039022282598008838871819693993644340038749593320742515278202644540294688427662659495917439029280590261903671496590495396009513661117554915284362313734077497631539221473352707214930444601238011452194124654784888869209853469566 +/- 7.23e-235]",
"strict_gap_below_F_third_over_D": "[0.045362084908957680686578277948469726730223266279170733459241513884640221263719782390040071707492276373860764047629951700761712706571530055491117513823043529325891690351274451933139594517362220654286552144725420118817777974568131971 +/- 1.92e-232]"
},
{
"l": 6,
"radial_rank": 15,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[5.2799691864465016683054259780862235914521184061374386470533948938268009927701444284355678776191833595410184136783513880946756966578536813049951105196137345832588894640850451096610628063665559839009052009173876144459345656694397049e-5 +/- 1.34e-235]",
"strict_gap_below_F_third_over_D": "[0.045458275607316041649983612406885804430752145482605292280196132717728398656738965222382310987890474833071256482529883152785719909700088129853616715561470529320834077772025816215570056038603001106827657614657492790522207321009972269 +/- 4.20e-232]"
},
{
"l": 7,
"radial_rank": 14,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.3478028275568551847504991125808334274836885271334510173338355215247378981917416371905503647089133874913878794943434260634838478039761418382336001360244977890111885447788754154650367829736653173331401444274250618319714451383713352e-5 +/- 4.90e-235]",
"strict_gap_below_F_third_over_D": "[0.045487597270904938114819161675540858332391829781395332156493328311451419287684749250294761163019577532791752787871723232406031828188626905248284330665306421688776554781218877912512016298836930013493335265222392416048346952215282953 +/- 9.05e-233]"
},
{
"l": 8,
"radial_rank": 14,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.1969714266958594086100168340479512021071300893274402508082666079685055562992530647644084082454527000333780695149057488282511392233134586537609991914327605234336605492038453387380785831538198848553414794508216763062313004505394366e-5 +/- 3.55e-235]",
"strict_gap_below_F_third_over_D": "[0.045499105584913548072580566498326187154645595365773392264158584000586981611103674136019022582584212139666332885971517609178384155274433532080129056674752339061432330061174628213279285880835128467818113251872158449903604353662161272 +/- 1.02e-232]"
},
{
"l": 9,
"radial_rank": 13,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[6.6772042552376138249880927520661928496074955665018234222362196928473593332913395901269659081589694530586751138665351526043228240518428483137038263342326135586223850564773584897746059751977202528119033987702572626655741049270863036e-6 +/- 2.20e-236]",
"strict_gap_below_F_third_over_D": "[0.045504398094925269052841678573914600473817059171100164843244430446973819307333375327076539700758507697213607991552800131514062343842614823818352962840332434053108044281610189308176892060691468946413854763267896409404001092561739580 +/- 1.50e-232]"
},
{
"l": 10,
"radial_rank": 13,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.0205389611381994340112030671425655730391411487057460054440883444238747873298692635938464246657120188849025345549843098736356492923726809559429574881116149758158902924811569623141138878678285389109638811348766150090077636341573460e-6 +/- 2.96e-236]",
"strict_gap_below_F_third_over_D": "[0.045507054760219368467232655463599524101093627525517960920661222578322242791879336797403072820242000954647781764132111682356793031017374293985710723709178555051690850776374185509704352552778798838127755702785531790051657658903032509 +/- 9.46e-233]"
},
{
"l": 11,
"radial_rank": 12,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.5592190902282432838140743673550646259515474626155001864436645934002887122765765720211133031767847223993997155698254593381093739494076725341747712444861958744935619559140172411813465306552268634790148295785076917857100978234793455e-6 +/- 4.38e-236]",
"strict_gap_below_F_third_over_D": "[0.045508516080090278423382852592299311602040715119204051166480223002073266377954390090094645553363489881944267266951096841207328557292717258994132491895422180470792173104710752649425485320136011439803187651837088158974880956568843187 +/- 1.03e-232]"
},
{
"l": 12,
"radial_rank": 12,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.7361229156965562755739485066620507179890194151160934540737877882096577006046453777666548472535568639515519274188475202751098532643573443128202333524337518085300834005620881033156962713376208347990276383910062246693791217270384509e-6 +/- 4.46e-236]",
"strict_gap_below_F_third_over_D": "[0.045509339176264810110391092718160004615948677647251550573212592878878457008966062021288900011819413109802715114739247819146391556813402309322353846433314232914858136583266104578563350970395329045831867639028275660441997287544939628 +/- 7.82e-234]"
},
{
"l": 13,
"radial_rank": 11,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.2189787744839971781772958956174856023849285096887303680572813854742687082625587603170047874261272322309530642482845527082132765012718604775672092964632813711694841594334302990047148328861598108800814119397742332507183683300823806e-6 +/- 6.21e-237]",
"strict_gap_below_F_third_over_D": "[0.045509856320406022669488489370771049181064281738156977936298609385281192397958404107906349661879240539434435713602418382113958453390165394806189099457370203385295497182507233236367661951833780506855786585254726892433415948298336584 +/- 6.07e-233]"
},
{
"l": 14,
"radial_rank": 11,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[9.1115104605502947251244111146229108148523687812454094248283466392640660493188956711861277374801753250141619076539062067798601106088079664307858115587316060034196114576360314960847486087681752967659975768683369475981680639812896556e-7 +/- 1.14e-237]",
"strict_gap_below_F_third_over_D": "[0.045510164148134451637194154225555204375585181429788542125724183832002740260061734777099548053892918649134165250475901276045988680655605785870023588085510793506066324705520903063517058191805789849136990066908979832971906849860268537 +/- 5.00e-232]"
},
{
"l": 15,
"radial_rank": 10,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[6.8907415907837549298344141318626558151004429877199084448519030315592131252492257785828125502932994746067781818891166059877546729824725187000565938535645717519849770892294196178004924345675466751070766788426279299586692421815682952e-7 +/- 3.85e-237]",
"strict_gap_below_F_third_over_D": "[0.045510386225021428291173683225253480401085156622367894675822181476363510745354141744088808385411637336719205988848477755006067891199368419414796661007281310209491468168957743724704886617423209911999155958998782403873670799742448510 +/- 3.97e-232]"
},
{
"l": 16,
"radial_rank": 10,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[5.5725840894038017094767055163638031545645701236192235117102486206982437922230058259023806161869067770018169861660118419264558798960293110028595322927530588339489360319229725368655789070470347695752098255045119466637889799262192106e-7 +/- 4.12e-237]",
"strict_gap_below_F_third_over_D": "[0.045510518040771566286495718996115030286351210209654304744315495641804596842287444366084076428605047975988966484968050065482474021078677063735566380713437391360783271773063474369412980108775961963189709145684116215472000287768674045 +/- 4.79e-232]"
},
{
"l": 17,
"radial_rank": 9,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.4394217148529950364815197392368146974200524448569911564432022487693315846972771176936030870564628404144654394791119710640153133486172773442156928451997796488673383445166172813856559597214626725189116080744648052413717071615428030e-7 +/- 3.87e-237]",
"strict_gap_below_F_third_over_D": "[0.045510631357009021367163018514692742985196924661422180967551022346441789733508196938954897306357961020382625220122718755469560265135331804938932245097382146688701779932832215004938528101070694520399414775505859220186142529495950512 +/- 1.79e-232]"
},
{
"l": 18,
"radial_rank": 9,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.8143575718769458225801535846706762744519610928669749849579039185550611441216525564451325058838194991994411730285288474469841879908637953549235804993948325437883472352351862917964598915303774094625327780947434214353205813309716387e-7 +/- 2.73e-237]",
"strict_gap_below_F_third_over_D": "[0.045510693863423318972084408651308199599039221470557379969168170876274811160552254501411022153416078284716746722549363813781921968247867580287131174308616727183412287831943143148037487020677513628925720413388857192324523134608533569 +/- 2.78e-232]"
},
{
"l": 19,
"radial_rank": 8,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.1350893074155378309983854661027765187967292682891557785229121921620751360361545947012967974167129096721427099412514037325499201792256760235077366958604738084652977620668591668859218344097894161925413575152985451656379579540732915e-7 +/- 7.26e-238]",
"strict_gap_below_F_third_over_D": "[0.045510761790249765112883566828120056389014786993739837751088814375447450459153063051207196536986924995375699452395672541526293411674648744099064315892997080619285820136890459980749978074483225687725047412530915136812150102870871259 +/- 1.04e-232]"
},
{
"l": 20,
"radial_rank": 8,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.8145963428367852792727181490859351304987209178791617197856356069812577745368191299651559571406017486082950309337073481663296795456320822823247815751689432439168631178844012912469894643397474123010779825349243307313751971913476642e-7 +/- 3.41e-237]",
"strict_gap_below_F_third_over_D": "[0.045510793839546222988138739394851758073153616794574878750494688103105968540889212984753670151070952606491805837163573295931850033698712103458438434188509149772342274980354878226537541967720232691925436558868413174233593529146947532 +/- 3.10e-232]"
},
{
"l": 21,
"radial_rank": 7,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.3442265942968383249218767165562845377107436498831205547223521429182577569059890508935399182199357879038882020064050289779323769935684849523404137017405260987178581484737320129458156956444086023024277673884857550238758065628975669e-7 +/- 4.28e-237]",
"strict_gap_below_F_third_over_D": "[0.045510840876521076982834174478995011038212895592301678354611194431452374840890976067761577312674844673087876277846466026163768873428967309818171432625296492614056794880851819293465372085097102225806436423889927818091164279086010377 +/- 2.95e-232]"
},
{
"l": 22,
"radial_rank": 7,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.1698844097185483376745904904136281204408033276757471077159525330697536626946097525775120248066736101831037736359065966428030576037543265857164042795052195035144594966044111381159017935162565255235937300609697331555535788590770010e-7 +/- 4.99e-237]",
"strict_gap_below_F_third_over_D": "[0.045510858310739534811832899207617625303854622586333899091955895071413359691300397205691408915464185999305648356289303076007002386360906291234008095026238716144716315220717006225552855076487315041014114307293660569693351111308780759 +/- 2.39e-232]"
},
{
"l": 23,
"radial_rank": 6,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.8036325482099036896422300692831307587513761534297724905836781454993396104201108639911212258991326317198021641077144506853136423000186860120950622894838580980493385588228275940129919083871836150954112119500594158570144566161431323e-7 +/- 1.38e-237]",
"strict_gap_below_F_third_over_D": "[0.045510894935925685676297702443659738353590791529051323689417608298852116732705624655580267554544076753403494686450255895221598135302436664798065457160437718280856861732810784383907265367475827948305157125545471660725080965221005052 +/- 1.45e-232]"
},
{
"l": 24,
"radial_rank": 6,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.7047046995837005612431072936596135592846214826448909944410885403346290620692945171392760237706431867515527286560068646187565462534423544879212346145508461351770455503699259342472264059336079357896256138791651245213925935344623035e-7 +/- 1.77e-237]",
"strict_gap_below_F_third_over_D": "[0.045510904828710548296610542355937300705310738204518402177567222557812633203760459737214952739064289602347991511393801065980204791012041322431217874543205211582053148962111629674073241944026073305873087704105278750154214527407313220 +/- 2.29e-232]"
},
{
"l": 25,
"radial_rank": 5,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.3939179547646335362475417688000768786036121145398339774007459683979361575235848435381537534094564464352709724562470981111949447686548785127963863123287282974549090145945509531958431825347311235428830534078766195425646014914459294e-7 +/- 4.59e-237]",
"strict_gap_below_F_third_over_D": "[0.045510935907385030203313041912489786658978806305455212683268926592069826873050914308182312851291325721022023139569421041956855547172189801178815387028035433793836921175765207211571347082348413193554312378361325879004712410206517522 +/- 1.44e-232]"
},
{
"l": 26,
"radial_rank": 5,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.3363641905432449397055558549704218016526180303176356524766950851000703813983510642068910846810364127496956531159321158707162269614554977943286953327245310583873843777065267218498606846796022456587611300204210279449272620835473150e-7 +/- 3.01e-237]",
"strict_gap_below_F_third_over_D": "[0.045510941662761452342172696111081169624486501404863634903101418997158156659628526831560245977558198563025391697101355073455079595043970521116887233797133394213560827928228896013994481680598198706442100790553664624563872173940458312 +/- 2.95e-232]"
},
{
"l": 27,
"radial_rank": 4,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.0568486139180110177303375622592936340655780375603183684226258409116431544148751984691352503891623541235022783167315693289816721668418451463475890550211393172139679043919406536688134442160565424082676563539284517539161639894894736e-7 +/- 2.49e-237]",
"strict_gap_below_F_third_over_D": "[0.045510969614319114865564893632910440737303260108862910634829824404082575502351225179146819753141627750431254316438834993509733768499449982482152031907761164552734945269876227472601299785322245061012425839901031273821491275050267717 +/- 4.93e-232]"
},
{
"l": 28,
"radial_rank": 4,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.0232215043575731950124803368315612901150964868162773760025086539087215404316436401112012745658990147130883874965298152473407590367276323944181938407057368880401343117886984495286995671170753904706408991067728071489168919753291408e-7 +/- 4.29e-237]",
"strict_gap_below_F_third_over_D": "[0.045510972977030070909347165418632983510537655157017985038929066415801275794512623502302655546539210076765195357827917013685141932590762993903427224847282596092977862653235487796821713796709954959127619602576755989385951774977469134 +/- 4.74e-232]"
},
{
"l": 29,
"radial_rank": 3,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[7.6222414708831682266772516257196415634794765767365884955050162320968978234679401500948037747576231679264329914534733877272880139011562127006874665935835463932624771034002264773461271114923392551624267196472126114817055685783232413e-8 +/- 4.40e-238]",
"strict_gap_below_F_third_over_D": "[0.045510999076765797834984399894150409470251031871900899300781711616504345697688431987265165718628919090434987402336752131932789393786527655104539659792000730831202734041895632664401893205395551743274115042399470194540551849610980883 +/- 2.23e-232]"
},
{
"l": 30,
"radial_rank": 3,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[7.4308438564392329716511586742769346394965301051614044660330936409871361863667784380857153948628616208008342156627626160068292365817056569731999224106719337144222926250460311945258315116444847728780546486408501573031004493944301372e-8 +/- 2.80e-238]",
"strict_gap_below_F_third_over_D": "[0.045511000990741942274336950155079923897320271701365615052622006335730256795304802998882285809512718038050458658324510039040506598374300849610096934667442559947329522443740416206354721408351550221818937886120180258165093635662172722 +/- 1.55e-232]"
},
{
"l": 31,
"radial_rank": 2,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.9353621485075300732236217997301546328610416837042255598342589568881435257576558167225898026930299520125218565466615631879789327243142143004963581413937164071253207359399710179142831013988335810197086312971819376172694314514951152e-8 +/- 2.19e-238]",
"strict_gap_below_F_third_over_D": "[0.045511025945559021591365934430448669365120338056249829624411068324077097785231409090108499440768639736367146541448101200051034786877339423524523661703085252729502595413459307266956487523835652678330856469580353694847290493972352151 +/- 4.87e-232]"
},
{
"l": 32,
"radial_rank": 2,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.8353140461282262259197786665769331429666740011447469851972821446631080145420542462346078648928231438278705993578992394185967440511141234802265051783805006529612625107421204625785408957317041236541835857175015083929752136203343230e-8 +/- 1.59e-238]",
"strict_gap_below_F_third_over_D": "[0.045511026946040045384404407468880000897335236999926655219196814693845220035586521246124204320588017738435228387960673087674272480699226155525431864401614882861660137054041559245462040881257709349625430124830809491651582736914530463 +/- 1.03e-232]"
},
{
"l": 33,
"radial_rank": 1,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.4133778236929812200624340299189307684678868959352336418972614946848532614809035182016408363084073320564378119391126890652250563856408634798564004604144971153097362730068828792835179453149071817505063392325420979858991872216695186e-8 +/- 2.98e-238]",
"strict_gap_below_F_third_over_D": "[0.045511051165402269736854466042326367477358981987797707314330247694051719818134051857631484650258303582593346102288547275539776014416102810258031868102662062521695513569303936597837873831487213517594849161603274341245686807674794450 +/- 2.41e-232]"
},
{
"l": 34,
"radial_rank": 1,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.3730491616400944463354460462395721200890463890620314322760486704582747750342263507910725502486137898452187667389323131030026307476742991912464543889811608154710019761350579652611362578731197650880080968646267810900341551332347208e-8 +/- 3.39e-239]",
"strict_gap_below_F_third_over_D": "[0.045511051568688890265722203312206204270945465776202776046352343906179962083918916324403158755941164180528768214478999277343535636640359189923674754202122776855058511956646905316087014055304087935469015786585698020398855766325115334 +/- 1.01e-232]"
}
],
"strict_local_maximum_modulo_phase_and_rotations": true
},
{
"label": "tau",
"depth": 10,
"N": 22,
"dimension": 13,
"precision_bits": 768,
"root_ball_euclidean_radius": "[1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8 +/- 1.68e-239]",
"inverse_frobenius_bound": "[76.448196701770978738255707694016499839153841662885549112094772982850807308445565771370748378249900430574157285181685111270388096604573995890211840901930472235435489396532537770203545165319762121296608905726992009299397511750938613 +/- 2.73e-229]",
"residual_norm_bound": "[5.7146713926950835039966499434923280022317147131595515965974450123950273799993018554034104153774785397412764284403254945339824752287499980062846760404416941969943455243973722811231400200893992321889549422719819137878474710605516695e-15 +/- 2.92e-246]",
"contraction_bound": "[6.8803377260938473150550494634367208691526755082486809658719125955391980079823648923739768716424044179750910297928427188756987350198796650447221624239473988727699212777532506264143939687442624569847883625379797700240569641559838162e-6 +/- 3.09e-236]",
"self_mapping_bound": "[5.0567969997567572151959275250211330922694968715504651446943442799969595281550217387128201857176216584317934864486157711703241026010703445901168466770425606729630020381272778969106246932793592605312590044500655168556386888775497352e-13 +/- 1.82e-243]",
"F_over_D_center": "0.043767774370488",
"certified_unique_stationary_root_in_ball": true,
"full_angular_hessian_certificate": [
{
"l": 0,
"radial_rank": 12,
"known_eigenvalue_over_F": "1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"remaining_trace_over_D_upper": "[0.0012298851709701639745572124306749272779562012429598994968592934874382951233848502672983117713497651466546074420182689112001717421658029111373346403118076944177779238342970627236541458476656633720455954155236150672378225889999512420 +/- 4.27e-233]",
"strict_gap_below_F_third_over_D": "[0.013359369619192502692109454235991739388710465423706767169807373179228371543281816399368354895316901520012059224648397755466494924500863755529332026354858972248888742832369603943012520819001003294621071251143051599428844077666715425 +/- 3.55e-232]"
},
{
"l": 1,
"radial_rank": 11,
"known_eigenvalue_over_F": "[0.33333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333 +/- 3.45e-231]",
"remaining_trace_over_D_upper": "[0.00022889353581084268256730511770220267317933644693388536540918949467037326707098149545005876157372675542726153568820944208702669621961796373854420951467168285039924567952901050495863119441062635108634896463900615238817331950339955368 +/- 2.54e-234]",
"strict_gap_below_F_third_over_D": "[0.014360361254351823984099361548964463993487330219732781301257477171996293399595685171216607905092939911239405130978457224579639970447048702928122457151994983816267420987137656161708035472256040315580317702027660514278493347163267113 +/- 7.47e-233]"
},
{
"l": 2,
"radial_rank": 11,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.0041127955810362516245540557550989582994504901581911378705455771861254788436513496794076458738049695945972707421740144788137644032521979659205413443590637468583835294734240549335582946564605768287015080391445049378385731368157066791 +/- 4.58e-233]",
"strict_gap_below_F_third_over_D": "[0.010476459209126415042112610911567708367216176508475528796121089480541187823015316987259020792861697072069395924492652187852902263414468700746125322307602919808283137193242611733108372010206089837965158627522161728828093529850959988 +/- 4.52e-232]"
},
{
"l": 3,
"radial_rank": 10,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00096314464778048972659064108577374507507075923715802025715479222531554854470915555502150621173057939093453265815490947560046116598246785373549561769273055481287621008843340354167303437913602790047465697482547514973182294889234153375 +/- 4.00e-234]",
"strict_gap_below_F_third_over_D": "[0.013626110142382176940076025580892921591595907429508646409511874441351118121957511111645160454936087275732134008511757191066205500684198812931171048973936111853790456578233263124993632287530638766192009691841191516934843717774325133 +/- 1.59e-232]"
},
{
"l": 4,
"radial_rank": 10,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[0.00019687263742867992585899179222913088643325667020508763711327589787198501331028138348011576467199223968113636664626016021282793220132052101869463504934376299970454505633171169880449558123315019427630250381474081487196578622681190538 +/- 4.16e-234]",
"strict_gap_below_F_third_over_D": "[0.014392382152733986740807674874437535780233409996461579029553390768794681653356385283186550901994674426985530300020406506453838734465346145647972031617322903666962121610334954967862171085433516472390364162851925851794700880439854761 +/- 2.12e-232]"
},
{
"l": 5,
"radial_rank": 9,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.8865075056555803216189815532995546343661816147982249617726179635084734392955201422820782891228732530951491914063060736728966631154181482963895077301047749207400269088301687994555182981602703052371218988405510260338218482744532092e-5 +/- 2.08e-235]",
"strict_gap_below_F_third_over_D": "[0.014550389715106110863450476851133671120323004850518684417048940487031581932273711465243845883775437934135715174752603605929937700035512485183702771589365618917459266397578364978672111483685063963614295447678261156406328448183922134 +/- 4.97e-232]"
},
{
"l": 6,
"radial_rank": 9,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[8.8383007867165877834585628240990924035573276265430774147004988685439600885334956373862288635495445642901807367943084903551077446562339188298578484750568187099792470884127979048857815162793001007054839174500204109565518967966090152e-6 +/- 1.21e-236]",
"strict_gap_below_F_third_over_D": "[0.014580416489375950078883208103842567574263109339040123589251966167798122706578133171029280437803117122102376485929872358176311558922010432747836808818191609847956687419578253868761780885150387366565961182749216646255710114769870058 +/- 4.23e-232]"
},
{
"l": 7,
"radial_rank": 8,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.6393672107668932145427313472535663071829857939232357411489458480707723551313924321295390279815526969417173550925455477715621917315875497722295379821902071035367475314992724195114001597693301507591994950176512001921696116865672455e-6 +/- 4.89e-236]",
"strict_gap_below_F_third_over_D": "[0.014586615422951899773452123935319413100359483680872743430925517720818595894311535274234537127638685113969724949311574121118895104474935079116894437128684476459563129919135167394247155266506897336515907467171649015466474497054980099 +/- 3.39e-232]"
},
{
"l": 8,
"radial_rank": 8,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.0455294207007730064282076572239813413178433283714366344384142823298625029591500517354699874177373436245132205195401709523037923769405388103306389934431345718988456532436835714714295212464502180883379084186982844708759469310195058e-6 +/- 3.11e-236]",
"strict_gap_below_F_third_over_D": "[0.014588209260741965893660238459009442685325348823338295230032228252384336804163707516614931196679248929323042153446147126495714362874289726127856336027673223532094767821013422983095195237145420216448578328758247968382195790719735647 +/- 7.81e-233]"
},
{
"l": 9,
"radial_rank": 7,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[5.0624701868811628407228142495257839997105490447764162704910280700166372769910430922477243610163695185859669319802327332447601350489149985142839282445404972267767689747855825216720188218986963787906724868484062754208567043967360898e-7 +/- 2.59e-237]",
"strict_gap_below_F_third_over_D": "[0.014588748543143978550382594385241714088266695611762189025039617563859665002938967562357441894230565029714808069973468643393342190653161775166815238273842212616943988989769188108414499464784476797028787599417981826039124580996226993 +/- 2.45e-233]"
},
{
"l": 10,
"radial_rank": 7,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[3.0778303170490202011958280123067485939135710710182584099389936835888586032124933321506369157431148428085891875252911129093071419524712847537255979416909215772572998206508075100879335628354539911450753756557986093959748921633578193e-7 +/- 2.23e-237]",
"strict_gap_below_F_third_over_D": "[0.014588947007130961764646547083865435991807275309559564840825672767298307780806345417333451602975092355182385807747914137555375735952471419538191294106872497574508940936684601585915657873310383121267552159129101086805727069177450331 +/- 1.93e-232]"
},
{
"l": 11,
"radial_rank": 6,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.0291873168968262095000427981522106789297738272426495202746233070020515957747751704916908308999993650015413399431927325961540418329082028293530941866757598297346682024397863362263828815427566936803697923362278998594285111050323746e-7 +/- 3.28e-237]",
"strict_gap_below_F_third_over_D": "[0.014589051871430976984045716662386851445598773689283942401714639204335966461507089189149617497583576666730166512532672347393407051262483375846383731357247999090683693199846422688033044028378512390997298629687433043876680723815556163 +/- 3.54e-232]"
},
{
"l": 12,
"radial_rank": 6,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.6396008607699693878353845440600166979195957058406688111654687609474443946369485969275364884761578575729459351607522114190762526382601949238437599134455110700705578280187282270995221977384619776727291295344972092831804427886280411e-7 +/- 1.84e-237]",
"strict_gap_below_F_third_over_D": "[0.014589090830076589669727883128212260664996874707096082599785550119790571922227202971806973913017819050880909372073150591445524759041402840647174282290675322115559659610883864793843956714446892820468899393753713216945738348622387804 +/- 2.19e-232]"
},
{
"l": 13,
"radial_rank": 5,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.2443156197873509251321066687803831593410942884730131757356628373369108453028899449836543659115080696561275031196035156133178067933493047912662974048509654703360599638911934645335816503001306632369420245484658907167191708025537124e-7 +/- 3.21e-238]",
"strict_gap_below_F_third_over_D": "[0.014589130358600687931574153455999788628350732557237819365349093100382932975582136377672168301230075515859701053916354706315105334885987331736187540036926181570119633060670277547320213308501636653600342972464211820077594994749586411 +/- 2.21e-232]"
},
{
"l": 14,
"radial_rank": 5,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[1.1448897441629528393614667318189334421167413382452342829651447931870825486949367116709033881570264450705990556068383566115948985997817504887211306066160090673607932427204932345324274099878256052143685890109498397084026248162243318e-7 +/- 2.63e-237]",
"strict_gap_below_F_third_over_D": "[0.014589140301188250371382730519993484773322454992532842143238370152187347958411797172995499576327850964022159606761105982831005507176806688491617794553606005065759930587342394617343213423925667884106145229807765571682695826404185044 +/- 1.52e-232]"
},
{
"l": 15,
"radial_rank": 4,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[8.8719487059009671293163927137590829874839651692144197126506050319862004773555733336911277330736046553236318613402988274529584429017601748945522853707215652250444968868615515084560067498946669624590732103062059443175327700981182949e-8 +/- 2.71e-238]",
"strict_gap_below_F_third_over_D": "[0.014589166070675607656995373502739529075836791827014974522469540160616346804661893110933329755389335930620113430348053263678392137082237649064917721143812959451014416221697798051151582106599167719997042075934563604607223491338965685 +/- 4.04e-232]"
},
{
"l": 16,
"radial_rank": 4,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[8.5674981460016017271650869156635105281629510669324841151439547524355389800831187627173792044957002757024097965285908152817902800191357363464936397863220063474562516344202226553818504786368688668830248021106125674596965298198736418e-8 +/- 1.28e-238]",
"strict_gap_below_F_third_over_D": "[0.014589169115181206650649395015797510031561385037155997341825515227119142311276865835479039492874621709663909642568701380758513848763866475309303201730268803446603192104150322464440112848161880297977997836418645560540992069701368468 +/- 1.51e-232]"
},
{
"l": 17,
"radial_rank": 3,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[6.3536127273885575426855547620815334964097014838357043186411750669004382727736423968858630822027667289739306201110955174846738759495886933677778725091294295790946308710376201085855721318786454410123527271692059123720973453505975557e-8 +/- 2.33e-238]",
"strict_gap_below_F_third_over_D": "[0.014589191254035392781091239811119045851331702569651828309623480254915997662283938930242697808035844638999376927360465555711491819927907170779732988887941575372370875720357956290465580810945347880212256543139394974607542945693213161 +/- 3.86e-232]"
},
{
"l": 18,
"radial_rank": 3,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[6.2486940146102718399886146169257440130810409017578249486661589292056093768151290693407097312424136872332533358204912517685673924170468888894877009852541202131202923374151337607364158179835634865946547879018829080871670933607270627e-8 +/- 3.74e-238]",
"strict_gap_below_F_third_over_D": "[0.014589192303222520563948266780520497409226535856257649088417180005077374610572898515375973259569354242529794334133308461754148980992742496197777771789656814125464535463743292515329059302508486831031800720118787647837585794995733059 +/- 3.14e-232]"
},
{
"l": 19,
"radial_rank": 2,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.1488310613597317054024890505062912829391404767245277068249041326340011775445530187206759932414755877826975478849285586200152139164567397273100122654727105538353738115334057483463925952601310772046003275339649244328395465215417646e-8 +/- 2.69e-238]",
"strict_gap_below_F_third_over_D": "[0.014589213301852053069349612641776161603753837275261899421389598417625340326654891221136479459906734251910788839691187817381080466514527502099269393566544011939561128312928551332609183202740714065355894620663391327017422338271201451 +/- 1.66e-232]"
},
{
"l": 20,
"radial_rank": 2,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[4.1114367383361998638022244130906160925266108405701496158948921200680124965279533864939490505078934589639149088901857816117241601174217883632978618798999752184711997783205047350822673477265862494402598281398638878753681387194584261e-8 +/- 5.80e-239]",
"strict_gap_below_F_third_over_D": "[0.014589213675795283304668028644422535760505741400558260965170507717745465986541701387132801727176161587732077027517577764808850549425065492448783033688047867666914481954668883461619315843993189400804172264068385268027787912985279472 +/- 6.77e-234]"
},
{
"l": 21,
"radial_rank": 1,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.0529016993987409203204842797594794959586837681997072882327310064448782245546807314047626068897152080567965941677326073483460771264965855164336516297077474833655215356756489589997217870202414492601416219651495484298355076387747757e-8 +/- 1.39e-238]",
"strict_gap_below_F_third_over_D": "[0.014589234261145672679257463461823869071871707079828984669593784339356602217884421119859352619040597769514586098700724989340593183205895401700811502330150369589191833011451309910177076669448796464252174065250447015171182368311590279 +/- 1.58e-232]"
},
{
"l": 22,
"radial_rank": 1,
"known_eigenvalue_over_F": "0",
"remaining_trace_over_D_upper": "[2.0415909835026393902777406960104294547837703922840920484860376237770889164888627319712793191454479893519623979850375522951847012364362297383909836550799700716719762683977212487252396053610408164068272837788843858296361592834120920e-8 +/- 2.86e-239]",
"strict_gap_below_F_third_over_D": "[0.014589234374252831640272763889259706562372118828962743825746181806290428895777501778039346953873475212186773147042686816291143714819654302304369282756830115866965949946903982689454179414270613056258502598393828877822808370305073832 +/- 4.64e-232]"
}
],
"strict_local_maximum_modulo_phase_and_rotations": true
}
],
"sources": {},
"scope": [
"Certified real stationary root; optional trace bounds certify local constrained Hessians, not global maximality.",
"Euclidean ball in orthonormal real zonal coefficients and f=F/D.",
"Uniform derivative bound uses ||u||_infinity <= sqrt(D)||u||_2.",
"Finite shape-band canonical action; no spatial localization or physical mass selection."
],
"publication": {
"originalReportSHA256": "2e9bc7ca57868efc5dce1b70ca672e7ea96fd4ed9fc1fc0084e11b5d8147615e",
"omittedPrivateSourceLocations": 2,
"archivedSourceSHA256": [
"4d4d5f938614fedd224ee176c896591028de3b168f6078bb16d026c0f7c1c619",
"595646d9e8942f353918de4b049de3c354ba5c25ba28b12ba2ad20f202782052"
]
}
}