# Stored data for newform 8.20.b.a, downloaded from the LMFDB on 25 April 2024. {"label": "8.20.b.a", "space_label": "8.20.b", "level": 8, "weight": 20, "hecke_orbit": 1, "hecke_orbit_code": 69055021064, "dim": 18, "is_polredabs": false, "trace_hash": 2033808297437661148, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q+(-5^{2}+\\beta _{1})q^{2}+(2+5\\beta _{1}-\\beta _{2})q^{3}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 8, "char_orbit_label": "b", "char_is_real": true, "Nk2": 3200, "analytic_conductor": 18.30533572451046, "hecke_ring_index": 2150341662903251651298822730278742925435376509795696640000, "level_radical": 2, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": false, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.506", "prec": 17}, "analytic_rank_proved": true, "char_values": [8, 2, [7, 5], [2, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2], "conrey_indexes": [5], "field_poly": [1155804113673024778339834102840085457131269774629483366903990104576, -27738358516840927193180104500114450400133860395870028292288768, 27738447216461514660719783835924541644179956872586393406592768, -177399249018514584235839520819873862547126510378177038080, 88699644118206331836031766951870758907094189945148981184, -23530739624732277774733733894667178736900394654048, 7843581170028346695466748185748667347430921666496, -1110100819550071174104182779845774739997744, 277525242785226225995541366728053703523138, -25265139517319958838954290038554593, 5053028465804290954773516593713297, -306731077539161966630890980, 51121850635988052944521232, -2021289743039984830, 288755694526787238, -6779858660, 847482358, -9, 1], "hecke_ring_index_factorization": [[2, 153], [3, 16], [5, 4], [7, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "14.990", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1341.368", "prec": 27}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "171987.228", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 18, "sato_tate_group": "19.2.3.c2", "trace_display": [-458, 0, 0, -80707216], "traces": [0, 18, -458, 0, -412108, 0, -47240948, -80707216, -173313752, -6198727826, 758800104, 0, -9351642296, 0, -122453668784, 156097960432, -696212072432, 14121426692, 1813497117770, 0, 6517087595632, 0, -11074654117412, 2177121583952, -36473014189168, -44414474211734, 26782030269304, 0, -97002327802784, 0, 327847200544208, 428505770260416, 122449430282912, -185380269683736, -478448330325748, 0, -1053851053424436, 0, -486194587539796, 942830575043152, -1697818250610976, 1200260021141524, 4964410757677984, 0, 7031781193616424, 0, -14917443628457488, -1134160959992928, -3197964747991392, 31570092936329058, -34734151321861826, 0, -26877456911772208, 0, 32102189624395064, -51757047863478736, 52858270161183424, -7740744140670520, -20470056808312424, 0, -25825294995349152, 0, 93766686763697984, 430168668665078416, -253721318369185216, -184007586011668640, 479551889901302712, 0, 201388986348307752, 0, -340698473416023872, -1599477989199799056, -115475454880420648, -93004298989809068, -93558253821761240, 0, -1090379619519933176, 0, 2029949680340770544, 1813975801025264480, 3057120301750869696, 1801762045144484330, -2418785089528546244, 0, 141493317659087296, 0, 1332333723895598620, -13124960835754102512, -3097741184498130608, 4470509771045743540, -288100905697646824, 0, -2965990502259463392, 0, -3533635112749329696, 23809730986995679856, -2990158800543707584, 8246429789464117220, 8841667592735478822, 0, -16638956151225401436, 0, 34422083247958274392, -6812642063468704592, 11682126024736085408, -24189294951381827456, -45942722546844915896, 0, -94931217028447848112, 0, 72074156406301051536, -59304217061251036304, 114030517449119872896, 50243681471783050692, -113980880562689311400, 0, -25543933313651169648, 0, 68929302383856021692, 84532221388425702368, 118453538027239021760, 47494122816128453726, -128044743315734328360, 0, -151992864520182397568, 0, 344345447454616919984, -340001757518382769408, 447104862244909364864, -134158772041676699288, -437239999145864008160, 0, -614830238357509658352, 0, 832243163267417075340, 510659702528519154272, 890483019709075564496, -260291582789150273964, -1570087789428093831968, 0, -2037851092305284905856, 0, 1639745924905900908240, 244226190309637301520, 2848890023002659959792, -202721151947764878880, -2403636138330904118532, 0, -2476743996291494063632, 0, 3990668320452066508444, 641434662665409798736, 2838919699940419403536, 179169088090470465532, -4211915180129840886496, 0, -5147804475729684946656, 0, 3974307582886700532256, 377682949430479587888, 6186238744630306069376, 508859578561386927488, -9619445662365179921474, 0, -8119891054908627294264, 0, 10911800027287988964908, -4578934067982652952528, 17753213390132713986944, 1613274187000449690650, -15399607321109890560176, 0, -16077272333745667920472, 0, 23496991058770157341488, 6398372513484261172912, 19394597621147373712416, -2349731378480426398936, -20673315065947820988644, 0, -36568610306666580203632, 0, 29934690716947780217920, -7000256859920642243952, 29275999660247528043584, -5845516036779743906528, -41167030981334688277888, 0, -32538052369859007477696, 0, 39286993797191384780624, 1034551112219826590336, 46688096386250400652928, 19333794577440649252, -32343866540115417611348, 0, -46300110735177362785452, 0, 64625679892162843432740, 7088125746369975859184, 58348360602419739299080, 22363091836841536962312, -61897926071766201287256, 0, -78817387858131406394864, 0, 67784768134589133966864, -28264462375292471252816, 68630058967811038000704, 10786457568063767003304, -128698785631410325700224, 0, -101893665845661605600592, 0, 96915527703640251954076, 30799146328047253609264, 126434689207797213127840, -22366002568458379755008, -96804154314034883304904, 0, -93065519206305059167264, 0, 90933799862508401011280, -38906252569797710674368, 90113729854651548932864, 34872750234386275821334, -42123639188617930173108, 0, -64362540439152999527472, 0, 56045546402562038926912, 36458207963137424591040, 24206659401355032661792, -32260114861700215386092, -42126908630310109047160, 0, -29945985558384654170776, 0, 11474453819171104412576, 55857656829766134902304, -29637129111034738205824, -95442276269600158753212, 78689708198860434239258, 0, 83185163659754390457360, 0, -85556378100773589478216, 13321452421494865156048, -104244036289311284432128, -69464256933543831347512, 77784251954032315008272, 0, 205061740934481635527584, 0, -153086292926499479531264, 2516836685643512665312, -100970207768514582224640, 1060825279235883985956, 202250153728737706134584, 0, 377447074749609903000000, 0, -416702327205401185671412, -272793668634502482480272, -504454386723640196677344, 340383916188276687300512, 626131293867406374745760, 0, 550595559985611786783816, 0, -1089373430497690454028512, 364398035569805180192224, -903243031477995728462048, 19779814239516356205952, 898277082980856738596604, 0, 1576945455063484650352960, 0, -1284573535602552189176356, -429715431822849164404672, -1634542888668413410551552, -598907599680550878945228, 1853669476532051389781952, 0, 1085854504273996754378592, 0, -1290343836309137413757136, 569042269464544683619168, -1991686240016837580524192, 221308693936064992825942, 1763518414114939087873440, 0, 1541236993245945685674568, 0, -2338383925358221240764948, 546162981423835322918832, -1657659945843511722446368, 1386775202736141433020816, 2026851969443167495333384, 0, 2728776870904143392395432, 0, -1321282293550518507176208, -1271099645567043519041936, -2292053274562944713829984, -963425615312792546513184, 2498750648342114382679028, 0, 1843208624000747796847296, 0, -2029410831946140319290624, 119676651291944500122896, -2359338708863674989805504, -2233765547771339405412492, 1935385300053583795272856, 0, 2336275141502594785754560, 0, -3502655741564389557041520, -1399036954329728878450480, -3156076623228623684373760, 2300908279594362791789160, 2841849245434795000184960, 0, 3016642824128653811883684, 0, -2351434013979070599936692, 494842971629514894108368, -1049263653655605143887088, 3357063184989620153451264, 2309043339543844950498336, 0, 2694638920812479221701128, 0, -1269472866620549559584624, -210706704674250313177104, -606071405021944048452864, -1922276159052160757047036, 282169761729630509812302, 0, -1578087235943672656764448, 0, 1377499428115733540068948, 101135813267666449912288, 4042960266343671618475088, -4947469486537566187009664, -4072753493071043030577992, 0, -6167882058296605241365344, 0, 6006697250940245791153168, 4618130052463014082188320, 2814866352510971621147968, -281104632167564444352924, -10531189503297629097553544, 0, -6261990555220753061900280, 0, 8844983040264705761354732, -1499675501760543616722256, 9386122626013498407498016, 4779393504228563776782158, -5971748096819097148089784, 0, -12722318816969024147125888, 0, 12184387555025539040657328, 8492489765947326652647712, 12359001143013389256515200, -276652496953233771947284, -12007113933999732492071072, 0, -13893481774481166231515392, 0, 14331509984154335763846648, -9326761276806246213622944, 16467151603907101434784896, -8330790645092915253113184, -24572412686774084308758976, 0, -14264709853395589078374816, 0, 10373670854685899293800320, 961341472291584568073472, 28158564877246631167832320, 6244207879773816592555648, -19801429569738689646209940, 0, -16457475153298789334477336, 0, 31188334432053497152846400, -14128652427617904052989536, 23121535389626916518652264, 6301779835633490211666440, -29034735053311256205302680, 0, -43005749749132981002391080, 0, 35483479354746710459822032, 18008031677421167862741440, 34431595067766845256525008, -8073952587189118948452348, -28212939361097912268681960, 0, -33909045434291537339638544, 0, 36015559282255140625242944, -14460750457464878056586832, 40480238986712926491852320, 4387303999816793546892212, -38826879523067426680950640, 0, -30070040791743198815570720, 0, 48202797704249534606631440, 5089723467651235314808944, 24042204982988875425339008, -7663297686295024563002392, -23606635253831625773075976, 0, -30821861193203045583354624, 0, 10229858166760339459809580, 9721170523645165433982048, 14553656351207418635119456, 2904093712762677532808756, -3832827817241839962947424, 0, -13940166352627539412486488, 0, -5299445081264526147569264, -9650193557213745130537824, -24398960655917219211633600, 7235213368507236298067652, -12304415432339862773725696, 0, 9432738213627885852030544, 0, 1936362367163105101989432, -12497129729590141242117104, -13561023782522515234244160, 2000621603892726930579486, 15220071734492338877210480, 0, -963057211364494711873440, 0, -27804946265334154063760704, 35491244916399108791967408, -12532837367824367446438400, 17057031795957586753731108, 52443020859986951575689026, 0, 70226781011855447953038504, 0, -30996927702979758081525300, -54536282981011520027237120, -39818308134762310482568544, 4407659480363897389979604, 68468495371135674779540648, 0, 73039104987380512047814016, 0, -117678308040121970914854336, 82317310458478037979994208, -32766328777193824391496384, 17693909563930463325843968, 42703413144405502860768316, 0, 91573964815815497633744432, 0, -130634335859239254828498816, -147890023866246316087074032, -146064890059401052964250672, 19622800055079218059585992, 97479081430810464737641024, 0, 158514254998959029060326080, 0, -110403785966234682321470880, 148113576545400703062045760, -274810801390229408250920192, -59376988175041179176702368, 240298129210515759723003596, 0, 139168725161267292518055468, 0, -242038591608383174657406332, -169077485868288853081807440, -152524266415248304444044768, -170361050101412652236979320, 320605399171406093495938344, 0, 394053202107657091993861712, 0, -148293661195579042813485200, 346627188389815922457951696, -249322047811571045694673408, 12266359014790224240928896, 287844431623965661428255832, 0, 236076705339880817363205216, 0, -332799167054449730962586564, -284284412271165932057925744, -252508609542483293357478592, 125037350858918532932824864, 153093219069755873478060384, 0, 175386750799160857654775296, 0, -336333076969585941922099552, 326418838241776827212652896, -247305890404556481094923776, -16839043457202432292300208, 41281751501623099608883308, 0, 200068289935486757130911760, 0, -133351754986785097669177664, -458800685590061363656266288, -158648308000890811631880320, -91896479803952730147449004, 341504959964427408164817000, 0, 42764682672175107248344904, 0, -155189221350288716272360880, 364801484250170330554069888, -78947398849132449126996672, 118119339389593128027347458, 163643769257041399907198688, 0, 282533136065109284458554304, 0, 22956387442574006049004664, -487382985151307853169104592, -141945188770800606114220656, 423980360129404629389323592, -54812751382409047878323336, 0, 114303552887455051625731008, 0, -197182884431819206912433760, 695021175696895333086325808, 157650344873596278905912128, -170455047638874550179400096, -52412753253301074051016576, 0, -156378230932479673117198776, 0, 10283429427640140427558188, -646784110246768016188084080, -122377446177777901585675648, -392540447957076001277786880, -95191978926670791043507960, 0, -267481274134229126024844248, 0, 368032162691653950553680064, 679221581685890750344293392, 159672935648439756915190272, 207930102417268922127243600, -45556596775361955755375460, 0, -550254989083930276388407680, 0, 442158164667356599780161148, -1284604669872250997636298064, 307279714156143188590147776, 82780121193334808690173812, -872113428047037029784757856, 0, -483590527679249213746809696, 0, 1138610466135469555751430688, 1307905310898679749135116048, 1246702065839278514826411456, -184383154241089274788196444, -770854068403203785837547262, 0, -848097194763473536094059840, 0, 1022044111484026412834229400, -1243176298219701454099884688, 1134247133660018956349923344, -36544533407852947284162400, -950941181927429094005072600, 0, -1651776458154136519538993016, 0, 1269004099187675303713496848, 1970431860539316441610433264, 1227132878889072447295208640, -44039784717611930228602620, -1646481339385360486697605968, 0, -1307968125631239212584070352, 0, 1320451477008148228893747392, -2372675065393893272968289584, 1780301991935178039401593424, -5323413963784758708374604, -1183202094759136051240965344, 0, -1163739596335674652931882720, 0, 1092833644655209854700180304, 2913341714767658409800566592, 939245772453055597771717696, 255225324643222658388469632, -1275636954256757763845088096, 0, -1180394172010481578809329448, 0, 1397399162500435677697352172, -5148117383450438358049816480, 1355472679216889713931832704, 755222402188263566779019540, -1777599231052787867863733472, 0, -781493475430877549892992512, 0, 301413800727856164601165616, 5064491773477894477850474080, 1956037101883143454548334208, -537922816032380029067556222, -1533189333743516277019098532, 0, -1784310042235484407752263536, 0, 1735071263277514405144407872, -4367508122377642155377678704, 638488569282975461658525568, -1057490281619004529024466744, -1398763196301136757755738152, 0, -812732645806788744179897376, 0, 1176556817207657350068621936, 7014373592350135114806847248, 335003581646656147759529472, 876021681029861775476350628, -858081881605839319740786888, 0, -1440544632643082505541953792, 0, 1114313964500399717871538840, -5677041266075049405718527888, 1131032819059814248041839368, 100002803727628628615246984, -388030258390076491433464040, 0, -502158063254982115265614648, 0, 957596894138649613495471216, 7373825467398579831245189616, 763250724110241045491151776, -735814724463575250002741076, 422246478945056069286103296, 0, -304080201252859795088599872, 0, -713742934995217021339411364, -9150422200668001821634224224, -332850652191072249189668592, -1951260356998882789220238208, 1097597530102533637137517784, 0, 821471006489783050317178848, 0, -1041923117728329287809548336, 6871283728566540729707484240, -2545166566947267777913524736, 180933263798594223927455076, 1667206986009400832624402188, 0, 3120464693527615037842844804, 0, -3689731498387237744137701928, -9848939379872855954809453344, -2913847071026168310152650816, 3002553786996113988108658312, 2606489658756626439461720192, 0, 5130612374370444690175004920, 0, -4404300467337143419074345568, 12441244039245744992454006896, -2994290860675162620714335712, 454431928085237503454220768, 5527203551284920117817875584, 0, 5180225664636467096872228176, 0, -5253937226014865855027773956, -11099509375288909925838092752, -6356566107496772754643476672, -1109025857217025891207004440, 6629457866749635317850677272, 0, 4858095708308440114736257248, 0, -4667144489733062749668316064, 12404105274265933251400509424, -6924706920087829407681723264, -322415063879664836701279488, 4932326825076475875613767468, 0, 5161303132639584623728910736, 0, -5842585841523195151238207808, -20300968884512237188080816992, -2607133213149612013851504752, 1738131670318012753634764288, 7058982128782527012706897216, 0, 4661531853125881161584352392, 0, -4757057117337069399333816304, 13991413243254250313773157984, -9245777392638069127547702976, -226828834512489793580225920, 2957704380257488787042228202, 0, 8789797211992453832758240432, 0, -7467643077751687420940665708, -18259152302563947942816980528, -8629535933666035158237084928, -1450066017792096231062162042, 6380354843098392652381687184, 0, 4581568968672338372728826784, 0, -8437213289008848370879345824, 32822958615204309001115329392, -4667751952794637688218582784, 2924808277167123375635751144, 12160906893667274000868639940, 0, 6048783574474298059373183808, 0, -4527765792809872369067917888, -20979444488140151120339168336, -10359155569883805588631880192, 2871052167582631308467822240, 5956583188966929615361160648, 0, 7200433093149138981894163920, 0, -5859821717171684211333006816, 26792728807500060618976502304, -3322497495698458505962937088, -6145183541710043158217205720, 5977869953305576226786057184, 0, 7518818816267639782513913216, 0, -5729262156278363675861330116, -38803443792013405925882771904, -7234757623535767948581939520, -573824525444053630257256972, 8220209750087192470804337152, 0, 4730940306882282704953567488, 0, -9276700031115952442997942528, 31909205451819220091594165648, -5768467346045611992463676928, -427287235746123081084015196, 2042422645869637317090237312, 0, 574732433168567699814115432, 0, -4619891833576681124726924572, -39762330494207525006359272256, 1277190169789866642010258768, -593181391759564697313774464, -5706914202022135560671460376, 0, -3564016228430896826123920000, 0, 6145897876662027128091321568, 53190050490153948316222780320, 4722509963361391776777150096, 5475297273531040900873735648, -10658948940136971604383105512, 0, -185210083801992181095907984, 0, 7033149590082030132307725184, -52601472973524277854270016032, 19144277257682049204575197872, -4546072387132466796568699488, -2607761466338229303731249032, 0, -8994752151619344114295526048, 0, 19845198583805537457444113728, 48017051544434730611018227008, 16083541470316975585087805984, 3093205025137290470377637708, -22424059921751474038597014516, 0, -9533557595509019687876046768, 0, 14964203851394005395316320512, -60306771513208066962904845744, 15206636979645969558797019104, -4846032451901053348378856940, -28117519550542473158615038520, 0, -21751880411255739462889299072, 0, 14447460207377717585965985040, 53723871731279178325957312240, 19419438487011938570642137920, -2646065699313027433545444824, 1783028334251669017965217564, 0, -31627938244908576237526904480, 0, 29582371613131901237211758136, -34360808351756021726779645680, 11800169350929934378539830208, 3850427990816729826568014024, -18617232531395102705864313312, 0, -30379427466037624808407798560, 0, 16810306111304949319878553936, 57057624950707622751586222256, 15665626613873312183606870272, -12727735638382096180501194588, -29937767624570529759222391880, 0, -15539597465479298803093505904, 0, 28064474549028513422898167884, -45507350135826099076592416016, 44657587211892948004390484480, -11181394000319987530417682566, -36643669717296714459820969432, 0, -16469810935123234507356103672, 0, 25570006150696955863437260064, 49861609495972455582079732496, 17580734575018600027870888896, 14312908548641458477683038632, -28239652844860435961487657316, 0, -54336745698405109656831205440, 0, 24277725841904766078834166080, -72358199285551147440451608176, 39988237273321127987418302032, 28690674787075344518816156724, -28550580844430729602935280800, 0, -20019051396920182104718469664, 0, 37739478200719754450884666848, 47738681562863592659305449792, 26449091502327037543374951040, -7566707452846626832783759264, -31074617505753431435962953652, 0, -37201619000853565911084559360, 0, 51223060183807443910529659200, -50633266234718791652395418544, 28907293833361328521265014432, -8221343704023534633146833124, -20416787587528576451577512480, 0, -37734950873498504603124514992, 0, 24330748047034285912777184304, 62657037684407811781923701616, 41503382786406922781547220352, 10881828380036982931036112836, -53882294945688007614545597862, 0, -21149683681841749686752297312, 0, 13834049742249009329209412284, -73084443781954107995483596656, 7731995774221135060799466176, 18246560490371429201291520000, -19636251521080995661201993456, 0, -19797380869409599359598352768, 0, 13311820103954700280695047184, 65257657183172795457716026224, 4764979175463550232225057792, 14475835725361523271133835392, -3367496074011821017277025684, 0, 3398915436284842708073139036, 0, -21700825901856755479730269224, -83687992466046916592426672960, -2750507510091963663597781296, -50173122238991342750189083744, 10981789599164780497315798752, 0, 15242866885221892926437603272, 0, -2709672181798075248243134720, 61394876575341994121182566624, 3935518576913207637567347776, -6030596318221872733632622168, 69925105097984154580994130812, 0, 68551166100464262509382764272, 0, -23234240443791769186540316944, -59008561000516822003478354864, -68766633412233365335527417088, 53192495617030898956187132232, 15786600975282084187759078648, 0, 43917657767572582199071330176, 0, -27242969784172714240616720096, 74561295743665860108215600976, -42655676959619233329711072128, -42465703298729432482738180252, 85336973478879913839636239872, 0, 43668723223435653524547593160, 0, -49095069242518332019434814932, -48317107707336846549377332896, -52889108691410576057246506400, -15557171512532420410964140908, 77841926723272659809368135584, 0, 4749608889008913406958568192, 0, -97245528554158348138665844432, 79627475369367734721636900896, -87550463239841072855190555360, -11745290142380895191387681536, 17546943885589667940673850712, 0, 56773560275595522708749821312, 0, -75043424631649376014164961348, -46593708943231185172755846512, -68203892909891634083194513024, -39770442811921010039786835852, 59858094856582122963657950904, 0, 109025004828487253134718734656, 0, -101098131486039008140958532416, 7885475441410358976749551968, -84401922323944031916365750784, 7251163456586142264406881618, 94692429202546979578135173920, 0, 65359860294644796304861597096, 0, -111627845601267291002423445248, 20301444092986765187558660592, -115358828806512474051756273256, 11263601754738130411653551888, 118359939539284733653805549776, 0, 198642364538345575841147743768, 0, -85852310476685849175431177968, -28472528917212143502459495920, -57771038075987233686852216000, 80326660331740350631166203268, 60759573842601839247282633368, 0, 184809839693219421289111157232, 0, -98528925519178989994785458788, 46238017551280257145133590480, -97491977730349988081498927456, 27074412164571686958228768288, 186711157594183911148425726384, 0, 86060952731604753874615945248, 0, -174558420247515806313240325776, -77327104148366930646312321984, -158304372128705381453970535424, -323737610153614681659968792, 68234599044151026055213382016, 0, 64327243196433960919070387664, 0, -197207524190846115445881294228, 119533713113223961193332044128, -187681430550140478791070407488], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": true, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 2, 1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 2, "minimal_twist": "8.20.b.a", "char_is_minimal": true, "conrey_index": 5, "id": null, "nf_label": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "field_disc": null, "field_disc_factorization": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-25, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 5, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-22907, -27, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-34, -80, 5, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2624536, -129, 89, 5, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4489606, -13201, -31, -21, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-9639250, -23397, -1410, -29, 0, 1, -4, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [-344295579, 175766, 217, -232, -2, 5, 4, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [42159278, 2214, 12169, -30, 1, -6, -64, 9, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0], [521436, 1175468, -5387, -1355, 0, -30, -123, -18, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0], [-520720591, -2653173, -26134, -257, 3, -88, -85, -62, -2, -4, 0, 0, 0, -1, 1, 0, 0, 0], [-1256856, -2843219, 32134, 5521, -6, -154, -591, 38, 1, 3, 0, 0, 2, -1, 0, 0, -1, 0], [-6805080756, -4812309, 170799, -13360, -5, -37, -613, -189, 10, 22, 0, 0, 2, 0, 5, 0, 2, -1], [8687769868, 35206087, 60824, -2384, 72, 22, 64, 540, 9, -63, 0, 0, 22, 6, -2, -1, -2, 2], [-38683597078, -11510054, -148659, -29478, -463, 987, 8508, 263, 80, 32, -1, -1, 4, -2, -16, -2, 4, 2], [761950163, -50740950, -74125, 38875, -250, 2486, -115, -640, -3, -326, -2, -1, -84, 12, -12, -2, -4, -4], [100599334942, -339948555, 2714475, 189404, -1316, -1154, -3124, -1659, -388, 272, 2, 0, -20, -8, -54, -4, 4, -10], [22817372, 51492172, -101913, 206279, -116, 6288, 59707, -474, -16, 1139, 4, 6, -208, -8, -11, -16, -8, 16], [362086807608, 59776074, -848524, 36290, 8880, -7710, -22418, -4240, -1036, 28, -22, -26, 88, 30, 78, -28, 8, 20], [-229811086, -526447145, 18552341, -9116, -1706, -40634, -65476, 5330, 19, 6729, -40, -12, 518, 29, 0, -32, 29, -32], [-615268084350, -30145597, 18263791, 1112201, 17036, 2597, 184553, 5790, 2320, 512, 44, -8, 56, -16, -64, -56, -64, -16], [120249994008, -1576487219, -3013342, -719706, -642, -112610, -4616, -27324, -439, -11679, 80, 136, 598, -186, 126, -97, 62, 2], [-2026552502748, -617387634, 1073558, -2956194, -75570, -17096, 332352, 6712, 4208, 994, -214, -318, 344, 60, 392, -140, -136, 28], [-2469162919030, -3803721900, -8189246, -3749747, -10912, 292011, 123991, -52633, 96, -20858, -350, 17, 1236, -396, 268, -190, 132, 4], [1487940760982, 74221122, 74528207, -2256538, -128445, -64530, -1140792, -22489, -2720, -3237, 424, -208, 875, 288, 1280, -272, -128, 160], [-1443723986, -3410259991, 336894814, 19641175, 2204, 735528, 1269627, 44310, -1872, 46283, 692, 1422, 4720, 280, -3, -208, 280, -304], [-5392161296068, -7071759928, -10133448, -3638424, 219732, 828, -5205768, 24112, 9536, 13912, -1188, -2444, -880, -392, -2448, -168, -272, -360], [855679410, 2165100600, -482639729, 4047421, -42040, -1664244, -1130907, -21040, 3448, 11032, -1720, 1276, -9328, -360, -512, -352, -360, 672], [18217969309604, 9553593987, -10542049, 32970864, 547555, -72205, 12462147, -114941, -36966, -10970, 2288, -2496, 1106, 576, -787, -224, 914, 631], [23810824158910, 11118380364, 8776717, -29137233, 15987, -2919326, -64968, 108332, -6849, 26791, 3280, 9160, -16038, 2538, -2318, 473, -846, -626], [6785639689668, -38391277436, -180616066, -16902268, -332434, -345678, 16350248, -336526, -66112, 37160, -3966, -13326, -4616, -780, -3376, 1092, 2104, -1316], [-10276473607056, 50425710550, 39449105, -121696602, -65082, 5822371, 3039230, 895985, 19981, 208772, -4916, 12198, 5432, 5880, -2680, 1324, -1960, 1240], [-26580378020847, -474416916, 1253851709, -37777468, -56476, 682482, -39207564, 190739, 85732, -26704, 7086, -18304, -7436, -4792, -12282, 2724, 1820, -582], [15779735964, 35963972226, -671822414, 411881524, 87436, 8856354, 15358968, -125980, -8848, -659174, 8452, 41222, -31184, -4488, 462, 3568, -4488, 2064], [-58504291409885, 98128810235, -3106749776, -323362337, -832312, -598248, -92394000, 53088, 102912, -57232, -6952, -55224, 12448, 2800, 29856, 4592, 4192, 1904], [3822411560, 9697995671, -1994223350, 504642155, -293394, -6576254, -26014357, 72914, 18195, -701959, -6368, 66544, 67750, 2349, 14848, 7808, 2349, -5504], [-27012387376534, -1367738617, -4210089645, 7137557, -2633220, -2447359, 100101653, -912778, 42576, -156288, 9372, -91560, -23016, -9552, 24256, 9576, -7488, -6480], [52476623584118, 218340010285, -20577973, -1034089071, -80299, -3970040, 16284264, 2999576, 52680, 857000, 6256, 140376, 147952, -19344, 20464, 5912, 6448, 7568], [-94163062475128, 357973983684, 5081971812, 13719204, 6751684, -1045520, 165844096, 3296576, 413920, -371268, 1644, -181604, 35408, 5480, 3792, 3864, -19312, 15624], [66568733400233, -252706323652, -1093537050, -1668025761, -1654880, -4788615, 26792973, -4209043, -94832, 540674, 8790, 249771, -198244, -50820, 16260, 8982, 16940, -17620], [275810850270188, 13777722776, 17892956952, -366101896, 12402204, -9666600, -322021096, -3818720, -723424, -66332, -17032, -330096, 532, 48480, 50944, 2000, -14720, -5152], [-64664913650, -142720418289, -3952827725, 3231711102, -2185704, -21627648, 18771046, 3336428, 16736, 1288630, -33784, 383372, -22176, 43120, -1126, -7712, 43120, -3040], [390383793946941, -597320270433, -23971904510, 26397891, -7536729, -10144936, -257949857, -1647782, -1273594, -266196, 45584, -485264, -206912, -10461, -197443, -15712, -38080, 6176], [14732742244, 27664626131, 15269420536, 7384079185, -1926370, 84988326, 295667961, 3128250, -150705, 3116381, 63080, 694764, -206402, -6911, -196608, -31456, -6911, 17696], [-828723870990884, 80872912801, -58939478875, -1827729008, -11352415, 2019697, 150670913, 427921, 1402398, 1960930, -107536, -881088, 109574, 95808, -247249, -50912, 36678, 28829], [-63175867098778, -375344708070, -3275092543, -6625770189, -7160705, 145388590, 139697632, -2440660, -683331, -5781163, -135232, 865888, -670002, 82302, -92202, -45973, -27434, -37334], [-178539980974268, -2035668968572, 132355134346, -363624316, 3572354, -26050522, -18827336, -17513618, -285088, 1472880, 134398, -1055778, -369656, -19364, 153792, -51076, 113800, -90172], [1754351212205625, 1027135753328, -1783782904, -9276527552, 4152976, -148606168, 133001728, 9479064, 62664, -10388832, 155328, 1468960, 1454016, 271296, -69696, -108960, -90432, 111168], [-1930781276540327, -2561003267983, 142546546978, -3798745816, -22124920, -43647020, 275317672, -38907202, 1758760, 2914080, -226804, -1738880, 225224, -328752, 45916, -103960, 69720, 57252], [-1626143395270, -3658303083181, 5862033548, 15835312175, -14757264, -256353650, -312810385, 54630170, 670144, 13467077, -233264, 1593912, 1220544, -271008, -8613, -67392, -271008, -33984], [-1492605286348792, 1415193387790, -189063795140, -755155018, 52888688, -50876490, 936699034, 18581776, 3908668, 3935412, 202510, -1810718, 1926088, 5546, 723706, -57652, 219224, -125732], [2166926432380, 4865957044273, 30947461904, 20836129235, -5999926, 197305986, 569510347, -61623618, -446459, 4709471, 195896, 2266564, -306838, -10005, 1559040, -64672, -10005, 28512], [1783395851906594, 82859280230, -438184278884, -3344017542, 112732764, -154520990, -2970056554, -149111706, -8030512, -10487936, -176132, -2360808, 50648, -638416, 1354944, -4184, -89920, -25040], [-2872048484926254, 7514700263643, 5826789289, -18725966821, -24827465, 183140768, 337062536, 121134248, 8330364, 3500860, -108752, 2176056, 906408, -118296, 122824, 16772, 39432, 43960], [2934386144525616, -5243253629464, 648468665648, -4174089048, -93581376, -34177352, -3989165280, 155074408, -8931968, -1689336, 44416, -2146240, 3435008, 192, -1342784, 50176, -422144, 243328], [-435427383568004, -12108377004898, -26679236147, -13877299254, -58723010, 122391683, 237533562, -181542119, -1065663, 22354780, -59596, 1922586, -4099576, -817080, 219320, 263668, 272360, -325400], [-1137053081430062, -45946704582, 876294163815, 2420184638, -150025201, 177771430, 4924986880, -68841433, 8914176, -17201841, 360640, -1269632, -784177, 1539840, -1617920, 316544, -150528, -185600], [-3275130494102, -7316811550223, -97973748303, 5350014558, 21440300, 793030038, 1503395746, 134929376, -1969808, -57251352, 566756, 1357270, -5623888, 1120056, 36416, 283760, 1120056, 176016], [-1427033963734628, 18145264889480, -1606821429768, 4066984744, 122877684, 229212444, 7009346232, 310992816, 4334400, -24988392, -643524, -501228, -10714864, 136248, -970768, 371224, -768400, 633688], [5988426517648, 13588989422461, -243320952850, -16216818495, -1549678, -771836702, -2519425399, -204600410, 2328129, -55670669, -902200, -1844292, 4788002, 158415, -8115712, 682144, 158415, -404320], [5219626830927672, 24066270187292, -1486695359116, 10425995552, 33457676, 388251612, -6102025780, -122295980, 11739016, 58652248, 1543568, 3949504, -1756696, 2888640, -3949148, 719840, -73560, -298644], [23915020213513932, 37677940141313, 84279435412, 45534593444, 182956684, -2156338366, -1160258384, 537157764, -52541693, 77671851, 1889184, -3313008, 6201906, -677502, 835242, 645141, 225834, 383574], [-14092499439084440, 6161196620456, 1732246708444, -33499372888, 30587676, 51893828, -6979112752, 576173988, 33940224, -23368528, -1884924, 5779876, -20395024, 310440, 4954464, 695688, 766320, 55608], [-10243517093242509, -46917952946244, -54086238090, 73902363011, 296312720, 2213459837, -728687527, -748317999, 5546232, 85914874, -2180546, -11672545, -2907348, 432012, -332172, 668350, -144004, -44164], [26638403263557345, -9005998052822, 2891045694555, 56425654172, 508661468, -575776354, 6267659212, -1296331499, -56849476, 87086736, 2765602, 15525120, -994772, -4830344, 8341290, 650684, -284732, -147562], [-39067722461876, -88242846262612, 631350551565, -114296482243, 114154152, 2276930590, 2396740549, 1246664070, -2656352, -63791237, 2900024, -15103276, 4853152, -2700016, 87989, 443680, -2700016, -21280], [11176016374244370, -26102485685158, -2980619779376, -4082064686, -739301000, -857616984, -5622639216, 1802480544, -56117760, 77923088, -2773528, 19533304, 40215648, -601968, -3390368, 161168, 1098400, -1090544], [73909569684878, 166696541159513, -977076282589, -312747973276, 51821562, -4065216878, -9193579300, -2581708786, 5356477, 7250567, -2763848, -28420476, -12715302, -456141, 28196352, -627360, -456141, 930144], [-18929201530171284, -985733371408, -4775875437572, 17316766496, -1249832280, 655027648, 19341895672, -2697696668, 44758240, -315220096, 2036200, 32871312, 3028368, -8393440, 2582656, -1251856, 1354880, 1128736], [-88784463557539056, 169564424882135, 385397914522, 224235510910, -372920762, -819176334, -4118794632, 2801228556, 214621303, -194440417, 1345104, -35690616, -34187350, 4190394, -4560894, -1235103, -1396798, -1767298], [-6440118874429678, -58900617620443, 6223142410306, 104856561885, 947609472, 1934775103, 26287495940, 3997155585, 20185856, 151095361, -1362176, 40975488, 77456384, -1198720, -4220544, -1703936, 1035776, -2349824], [-5280517882275952, -255391467194362, -330562763551, 298301598872, -1214882034, -846291347, -5417823676, -3753871653, 11402313, -346056288, -566208, -47874592, 49944000, 7381440, -1350720, -3791520, -2460480, 3570240], [-5197022958440046, -224398186986, 3384236473765, 25805457314, 813407745, 2550278266, -29944096296, -4429879763, 44922400, -501746999, -2861192, 49903760, 10073081, 8336736, -18956544, -4613168, 2995840, 2706400], [-187483565700586, -423125331585069, 2245434923501, -563144663284, 48382844, -5648181862, -21914017376, 5702371300, 4396208, 662270586, -4480172, -59959554, 38418160, 937816, -614898, -3626320, 937816, -2065072], [-60590522710258311, -30017944651853, -2457680098086, 3400533511, -1318065253, 5393996792, -37693536909, 5159397970, 95760782, -48879172, 4383312, 63099440, -112421184, 528871, 17883513, -3842784, 3569728, -2873184], [199151621355090, 447026123662391, 2006822894765, -354082108036, 275885798, 7942883886, 23481657156, -6736768558, -18066029, 651650793, 6541448, -57267620, -18623290, -384771, -60453376, -5367904, -384771, 1883040], [112800067863136164, 57810007389601, -2524077607379, 194741304432, 254279505, -2166924943, 76420506161, -8114955927, -202305954, 1172275458, -11334528, 53733888, 11012422, 10993152, 22109743, -4337920, -4112570, 28253], [100966074343363236, 426348762871142, 946397835382, 513427949994, 1385183306, 7865755184, -6769222968, 7040098696, -689894796, -396040588, -13694800, -71121928, 40188792, -7185096, 5893976, -4078004, 2395032, 1103912], [169801330844123512, -86335263308936, -1089126240212, 334978708856, -1264115780, -6874609676, 118290638736, 10734232292, -319401664, -307710688, 14526532, 67170692, -194150672, 415944, -37189760, -4266104, -10669584, 5419512], [99645957533391597, -1015955338497530, -1561768945399, 556961467114, 6056681990, -19664691953, -10289689750, -17754968979, -87716899, -239805348, 17561652, -35868006, -105205752, -31025592, 10347192, 936180, 10341864, -10336536], [-134350800085025392, 60298882190822, -3197697219514, -246236885768, -4751068648, -515735236, -102450857096, -12407303334, 341387768, 2123006304, -19099292, 24269440, -10042152, 3786352, -1222316, 2295608, -7582328, -5848148], [-515440294382238, -1157474904209219, -4856026453999, -622554906406, -114059468, -18860701974, 21798793014, 16879464528, 23628944, -291482576, -21325508, -39830182, -111232304, 19058184, -410520, 36112, 19058184, 4565232], [7986462657680960, 276657302152232, 12311144060240, 71368292360, 5976097888, -15169819032, -77278286216, 26538615936, 275499728, -261859024, 23383304, 22183224, 237374432, 4077496, -23015624, 1706320, -23308384, 17990416], [726711259382122, 1633670224887605, 3124907535225, 408534911410, 475226138, 22740371214, 1485133154, -23776970250, -42477959, -911045045, 24326096, 37535064, 171663154, 5657639, 43281920, 11831872, 5657639, -12915136], [74021867204752684, 3723340241427, 7481724244809, -122941380847, 6686110776, 6368910845, -5364772635, -27999774324, 49629088, -3111712000, -18184328, -60629200, -36773200, 23702112, -66694784, 12428368, 1448320, -8125856], [-728071074094731396, 2458003151187049, 3850255790480, -1163604691104, -3215476080, 26494847314, 21494435816, 39578900348, 1734895855, 1726781591, -15504656, 70030488, 190133498, -16616310, 22355090, 11769961, 5538770, 11277550], [-171930604469601516, 382810748025558, -18357468162498, -622547031450, -6357157610, 28221207896, -28513736384, 34805790936, 321351856, -56550438, 18504194, -105824198, 303504888, 10563404, 152064104, 16796836, 27774872, 2681516], [247391611883429836, -2180743776917306, -4361714902095, -1392015064940, -19409879586, -5327114519, 15963255256, -31255422665, 39936257, 2200665960, 14384024, 175698700, -78341456, 38794800, -23574960, 18681848, -12931600, 2288240], [-16018388773799914, -1401341298982, -54720823536581, -116866021554, -4348598601, -7026248138, 23738211896, -54553995165, -643622752, -5852030177, 3189976, -210347568, -44545009, -68235040, 127918848, 24969232, -3274624, -8048288], [-1413075544157100, -3176971424977434, -3921726093810, 2486754549812, -587245420, 8431747166, -176424853424, 48285220908, 68843664, -4050214674, 13864284, 277787146, -62094000, -71106744, 6938730, 25465488, -71106744, 9586032], [-165136706070576460, -837170131723560, 57283138397608, 149612929464, 6399047292, 50346221108, 228157779432, 43269784720, -1176806464, 239490056, -10733932, -330789668, -273964112, -14672280, -42935472, 25867016, 47566544, -26554168], [1934458780575280, 4366072392280504, -25653387262880, 2965015228152, -1452726528, -22410968424, -29897829336, -61473548208, 72842808, -3467155896, -21885456, 368171208, -202046160, -10436952, 195134976, 18634944, -10436952, 11603136], [-196329551283081312, -71727485912478, 68682968773138, -174806078080, -1217166638, -11639068158, -320525641134, -59410127366, 1215230780, 7158001060, 45891504, -410381504, -29631220, -155377856, -4555458, 17720736, 25558348, 10439322], [1324646163598321346, 4233592849547839, 6437528881981, -2555822476737, 3467838115, -51892038664, 32390283200, 66047721584, -2790970060, 1141496468, 57792640, 550885184, -693523784, 99559800, -95045928, 17820268, -33186600, -28672728], [-166220014364944472, -186011065113944, -80688497444148, -2003248231256, 6439918956, -100802207340, -732919271408, 77196750932, 1173209728, 650365520, -64976780, -615605676, -84378064, -29902392, -137849440, 12671848, -14117200, -26467112], [456618998462816655, -3407985652362470, -7385236399317, -3499114493945, 50067284838, 97513683562, 97441243633, -64578106172, 380504061, 371100482, -84938890, 558977019, 621278748, 106461180, -20249980, -11307434, -35487060, 50724140], [491975385040712455, 1778624569316313, -83400399386056, 615753304160, 25608927328, -2189964624, 797305978336, -73296526520, -1117556384, 11469701760, 88719696, -608704512, 100631264, 195476160, -325860208, -34529952, 66130592, 53834096], [-3038488710517962, -6859303937670513, 50992886283831, 8296352080554, -1471514028, 124675136634, 828126948966, 102896224080, -315985776, 5098282992, 100913820, 792673002, 634232400, 97141704, -1871640, -17016432, 97141704, -49655184], [-925242219240326031, -1974640004471519, 97151197003552, -2586583770227, -25797482704, -183783366128, 341286322848, 87378246208, -186723328, 961605024, -128403312, -844038096, -391055936, 4411552, 140528064, -20646240, 19906624, -40796256]]}