# Stored data for newform 48.12.a.f, downloaded from the LMFDB on 24 April 2024.
{"label": "48.12.a.f", "space_label": "48.12.a", "level": 48, "weight": 12, "hecke_orbit": 6, "hecke_orbit_code": 22517998338179120, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 292529548846418997, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [5370, 1]]], "qexp_display": "q+3^{5}q^{3}-5370q^{5}+27760q^{7}+3^{10}q^{9}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 6912, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 36.880472666860264, "hecke_ring_index": 1, "level_radical": 6, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": 0, "analytic_rank_proved": true, "char_values": [48, 1, [31, 37, 17], [1, 1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 3], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.027", "prec": 17}, {"__RealLiteral__": 0, "data": "0.974", "prec": 17}, {"__RealLiteral__": 0, "data": "0.068", "prec": 17}, {"__RealLiteral__": 0, "data": "1.907", "prec": 17}, {"__RealLiteral__": 0, "data": "0.191", "prec": 17}, {"__RealLiteral__": 0, "data": "4.720", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "11.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [3, -1]], "trace_display": [0, 243, -5370, 27760], "traces": [0, 1, 0, 243, 0, -5370, 0, 27760, 0, 59049, 0, -637836, 0, 766214, 0, -1304910, 0, 3084354, 0, 19511404, 0, 6745680, 0, -15312360, 0, -19991225, 0, 14348907, 0, 10751262, 0, 50937400, 0, -154994148, 0, -149071200, 0, 664740830, 0, 186190002, 0, 898833450, 0, 957947188, 0, -317093130, 0, 1555741344, 0, -1206709143, 0, 749498022, 0, 3792417030, 0, 3425179320, 0, 4741271172, 0, -555306924, 0, 4950420998, 0, 1639200240, 0, -4114569180, 0, -5292399284, 0, -3720903480, 0, 14831086248, 0, 13971005210, 0, -4857867675, 0, -17706327360, 0, -3720542360, 0, 3486784401, 0, -8768454036, 0, -16562980980, 0, 2612556666, 0, -25472769174, 0, 21270100640, 0, 12377788200, 0, -104776239480, 0, -39092494846, 0, -37663577964, 0, 9310781526, 0, -48575052512, 0, -36224301600, 0, -225595713276, 0, -69451179514, 0, 161532021690, 0, -359664575694, 0, 82227373200, 0, 45244170486, 0, 85621667040, 0, 121523092285, 0, 218416528350, 0, 369559909500, 0, -250273055864, 0, 232781166684, 0, 97891780812, 0, 541636575040, 0, -77053630590, 0, -155014706262, 0, 1126265370436, 0, 378045146592, 0, -488718872904, 0, -57734276940, 0, -293230321749, 0, -1384580812362, 0, 698601450208, 0, 182128019346, 0, -273533838000, 0, 2131269853958, 0, 921557338290, 0, -425071113600, 0, 163564486972, 0, 832318574760, 0, 8809425240, 0, -1205076500241, 0, 1152128894796, 0, -730851575394, 0, -554956406000, 0, -134939582532, 0, -3923714421540, 0, 2279308973150, 0, 1202952302514, 0, -3569658257100, 0, -1967312017944, 0, 398325658320, 0, -3387088726656, 0, -4929207776254, 0, -999840310740, 0, 6357850272342, 0, 3785535410272, 0, -1286053026012, 0, 298455033120, 0, -4826735626500, 0, -904179545640, 0, -12445075881744, 0, -179493837380, 0, 3603953958264, 0, -5144176399560, 0, 1414022224000, 0, 3394954266030, 0, 2363275215756, 0, -2225684379704, 0, -1180461845025, 0, 415847834940, 0, 18124772488334, 0, -4302637548480, 0, -18764059878, 0, -8354331017280, 0, -904091793480, 0, 17625242631984, 0, -890116982734, 0, 847288609443, 0, 6480028097910, 0, 14949910904456, 0, -2130734330748, 0, 24228041356548, 0, 9766774452960, 0, -4024804378140, 0, 7804917351426, 0, 18453205440800, 0, 634851269838, 0, -16595574775368, 0, -20365279451100, 0, -6189882909282, 0, 28523590257006, 0, -23379994087976, 0, 5168634455520, 0, 12751122989100, 0, -30364120269058, 0, 3007802532600, 0, 15974859435594, 0, -28704507156044, 0, -25460626193640, 0, 24951616572000, 0, -24758656710317, 0, -9499476247578, 0, 48175396168278, 0, 2981998181880, 0, -9152249445252, 0, -11732544605040, 0, 26592613938880, 0, 2262519910818, 0, -26583760759260, 0, -25735029040676, 0, -11803737760416, 0, -34604265524376, 0, 12606588910058, 0, -8802505288800, 0, -81824296913634, 0, -6857541949032, 0, -54819758326068, 0, 60180076973016, 0, -15317556472150, 0, -16876636621902, 0, 43187379709440, 0, 34011469184548, 0, 39252281270670, 0, 28420184155080, 0, -59943948292558, 0, -87398491893642, 0, -32489707466400, 0, -88388836195360, 0, 19981251687600, 0, -97868505351324, 0, -142789606547098, 0, 10994333428098, 0, 144245920772994, 0, -79642933151760, 0, 20806065090720, 0, 124349284943496, 0, 264204627152997, 0, 29530111425255, 0, -75024297977700, 0, 160109534089768, 0, 53075216389050, 0, 105277496752800, 0, -34725822875218, 0, 89803058008500, 0, 8237767462068, 0, 146500203674500, 0, -60816352574952, 0, -64341851639808, 0, 95082977923200, 0, 56565823504212, 0, -39890033609466, 0, -47228738815440, 0, 23787702737316, 0, 19979312473200, 0, 106551979242806, 0, 131617687734720, 0, 34144491481698, 0, 39028949003600, 0, -18724032233370, 0, -423995632043880, 0, 53334901088234, 0, -37668573621666, 0, -15415320210240, 0, 47086598173320, 0, 273682485015948, 0, 101287654153404, 0, -157928472303826, 0, 91864970621856, 0, -61660014793650, 0, 137423686904480, 0, -118758686115672, 0, -513171359936640, 0, -74924767954222, 0, -14029429296420, 0, -298765642153440, 0, 368335241090320, 0, -71254968185007, 0, 111247830230916, 0, 136788770464380, 0, -336453137403966, 0, -88331413841262, 0, -573308332414200, 0, 169760152400544, 0, -114220440436800, 0, -9420937722310, 0, 44257108701078, 0, -697133548616898, 0, 187941271733848, 0, -66468722634000, 0, -320006635626996, 0, -146917004123840, 0, 517898574511794, 0, -611013202605168, 0, -390056867429900, 0, 223938433204470, 0, 150382370364240, 0, 509333730317620, 0, -103292280604800, 0, 209926697323020, 0, -176546273555504, 0, 39746170334196, 0, 860958181676292, 0, 33160697954748, 0, 202253413666680, 0, 411710954244480, 0, -601209457412516, 0, 2140690333320, 0, -1092030351829704, 0, -49998896794620, 0, -292833589558563, 0, 876371101334814, 0, 387835104629600, 0, 279967321435428, 0, 260848031989440, 0, -992307835891584, 0, -177596932820742, 0, -371989239852150, 0, 973507481712628, 0, -134854406658000, 0, 157108973439600, 0, -718341389144327, 0, -32790318555276, 0, 688698773058300, 0, 1211448980292120, 0, -953462604434220, 0, 769682532934548, 0, 1746062781765590, 0, 553872080475450, 0, 372952833990180, 0, -174624425985380, 0, 292317409510902, 0, 209772216391848, 0, -103282255913600, 0, -867426956475300, 0, 1583649005842494, 0, 733992546706232, 0, -478056820360392, 0, 975797917848204, 0, 1931398771476780, 0, 96793134971760, 0, 1924274391870426, 0, -1611320399461196, 0, -823062560577408, 0, 306112834041000, 0, -2532503285394046, 0, -1197797489629722, 0, -243412284039360, 0, -2418940108747080, 0, -242961195509820, 0, 3115075841122404, 0, 993860190109600, 0, 1544957616179106, 0, -2207230435400238, 0, -459788352004800, 0, 919885104696096, 0, -3411585709398408, 0, -1575452477398774, 0, -312510885320916, 0, -652579005570450, 0, 505592119502056, 0, 72524573048160, 0, 1192030798151616, 0, -1983747166907074, 0, -1172896757239500, 0, -1930986428345862, 0, -947688701475164, 0, -219715629590520, 0, -707124072270240, 0, -1008402680811875, 0, -3024153439263792, 0, 2050296037973820, 0, -1005926522765312, 0, -43617002483340, 0, 1343966309989680, 0, -924597439294602, 0, 875760811858152, 0, 1131443807632530, 0, 868305558659068, 0, -1250034865093080, 0, 1376364875369256, 0, 354194747176464, 0, 343607400432000, 0, 2552758540391838, 0, -525678862960440, 0, 824973886645290, 0, -926792107209060, 0, -1903318977724498, 0, 574275877428708, 0, -2908588407964800, 0, -164627194198320, 0, -540841304268072, 0, -3157556727680328, 0, 4929900506581730, 0, -286852228341075, 0, 430293314013702, 0, -1085207656924960, 0, 101051023890420, 0, 3812440532297652, 0, 832428972626940, 0, 4404319714665162, 0, 2905803022224420, 0, -4037287750902356, 0, -1045540924280640, 0, -6048045039241320, 0, 2772320546841300, 0, -4559666550354, 0, -4712672943685602, 0, 12970026889425320, 0, -2030102437199040, 0, 258467295161760, 0, 866706096098606, 0, -219694305815640, 0, -779971806264000, 0, 2624420347494480, 0, 4282933959572112, 0, -26266614058368, 0, -1348443457733120, 0, -216298426804362, 0, -214930897675950, 0, 5680181884175392, 0, 205891132094649, 0, 2954648241096552, 0, -1623115878038218, 0, 1574646827792130, 0, 3375682789709424, 0, -3647940323190644, 0, 3632828349782808, 0, -6760448268703752, 0, 7435198962383940, 0, -517768442371764, 0, -6262537000541760, 0, -26483336560376, 0, 5887414049641164, 0, -3751489787616960, 0, 7373643624794558, 0, 2373326192069280, 0, 6209832596186874, 0, -1927964743308640, 0, -978027463888020, 0, -425483939465736, 0, -8861954082034942, 0, 1896594916396518, 0, -2950474409673642, 0, -1018301024315000, 0, 4484128922114400, 0, 17537502571663800, 0, -9459800728079328, 0, 154268858570634, 0, -11444919115754460, 0, -13554522166415156, 0, -4032724670414424, 0, -9984288621265440, 0, 3793081874561572, 0, -4948762906617300, 0, -15992249482082994, 0, 4798457037331776, 0, -1504141546955526, 0, -8911210079125560, 0, 2282631880032000, 0, 6931232432452458, 0, 9458590804847370, 0, 10799627434960948, 0, -5681338563378168, 0, -878341295039640, 0, 18690894595731952, 0, 1255978172691360, 0, -11041089876780186, 0, -12610352980858976, 0, 3098522886351300, 0, 786172343593716, 0, -5925892982962570, 0, -7378481225381094, 0, -3721918172048622, 0, -47306613538800, 0, 730896015421800, 0, -21020885793462840, 0, -12084920131113185, 0, 3881890842849342, 0, 6471260806294170, 0, 3373481041831600, 0, -6975195238918692, 0, -10178750895658800, 0, -19837829468018002, 0, -6186932165054520, 0, 7966388437568826, 0, 15974892909578980, 0, 6063242826996000, 0, 4029257485765728, 0, 3924672959865780, 0, -6016353580607031, 0, 2373095856732960, 0, -4055110424990776, 0, -2308372728161454, 0, 10258983087720000, 0, 9769575093688790, 0, 11706621268891554, 0, 16258292298256914, 0, -16606117429647572, 0, 724625558196840, 0, 19131414356441544, 0, -6947580030784640, 0, -2223996615196236, 0, 30354697882286976, 0, 21070346443669800, 0, -2851008339024720, 0, 547641332998800, 0, 11697156636148620, 0, 6462005187147840, 0, -12239889185815500, 0, 10725166653853684, 0, 549792338328774, 0, 28224866626031568, 0, 5592835648506096, 0, -6459853864500180, 0, 2717475835341120, 0, -18355082826013760, 0, -6253612056884268, 0, 11363785918425072, 0, -13288983499216750, 0, -2868308275781088, 0, -11012509124864814, 0, -23544589599566772, 0, -8408836522423368, 0, 10564465536359280, 0, 8363567050915322, 0, 3063401105144094, 0, 22294170304617630, 0, -13763261366442000, 0, -2139008785178400, 0, 37803832630940892, 0, 10704779785974940, 0, -19883304150013062, 0, 4795681030490394, 0, 18188666462142720, 0, -1666382693614776, 0, -4303208245833120, 0, -22813858177644831, 0, -13321201273234524, 0, 26469845758483980, 0, -33741958118885504, 0, 14623758704442888, 0, -35858687142537900, 0, 31265126683303360, 0, -3722166222732450, 0, -12002334917621406, 0, 16247449198867464, 0, -4101022699122186, 0, 4426868496055080, 0, -34141655962476540, 0, 10494533269393920, 0, -14668432203643680, 0, 37916708594080408, 0, 8264787011845164, 0, -20328325153160640, 0, 57600280458878, 0, 9538304348772810, 0, -13566835911815040, 0, -1712763132267096, 0, 6906104749684440, 0, 73995380808810120, 0, 7035218914614770, 0, -14566379435091594, 0, 13683066346126326, 0, -1602703527854400, 0, -21237833530155006, 0, -20867877644988876, 0, -43321549659971482, 0, -7894998914335200, 0, -17968781736476250, 0, -2850731643825040, 0, -21478487195472480, 0, -61898855996524584, 0, -59456551648533862, 0, 4855444160086800, 0, 15268850806865292, 0, -26121771539998712, 0, -23782046800371732, 0, -38435963351169120, 0, 66830057484965280, 0, -34697874390944814, 0, 40972592810939466, 0, -29050978742193740, 0, 2671623023027814, 0, 963881906730600, 0, 19393176257774080, 0, 35051758747837542, 0, -73950101045550234, 0, -12851211568257632, 0, -19353232755877680, 0, 24934600542593256, 0, 30770326113449270, 0, 5055873817044960, 0, 7146802825427460, 0, -19150537773425300, 0, 30216876241269528, 0, -6718512240739704, 0, -23822071526211840, 0, 64201724398178271, 0, -7593299342880000, 0, -4867276861531400, 0, 7175817076336965, 0, -66250008587571396, 0, -46992779590122514, 0, -18230904408581100, 0, -43718422033413414, 0, 59164051145874080, 0, 38906616783813624, 0, 37173650350909488, 0, -12690787908609720, 0, 12897277582539150, 0, 63283189582399830, 0, -5938751645417736, 0, 25582431710930400, 0, 11951925119010480, 0, 25131310316782454, 0, -8438374958677974, 0, -10834817738161296, 0, 71766794335592236, 0, 21822143096065500, 0, 18477564812907480, 0, 43501961665276442, 0, 2001777493282524, 0, 30982917194044032, 0, -2233102873627800, 0, 35599549492903500, 0, -16323632901202536, 0, 4540550158342720, 0, -14778373675713336, 0, -97330028262353580, 0, 33860169554042000, 0, -15635069948473344, 0, 31575190205097216, 0, 78153256556596802, 0, 23105163635337600, 0, -19517592359887236, 0, 96589664062061192, 0, 13745495111523516, 0, 584867308546884, 0, 100763001544860, 0, -9693278167100238, 0, 244549644662400, 0, 29326799954985532, 0, -11476583532151920, 0, -31101175249706400, 0, 143893067373110736, 0, 5780411765167788, 0, -114725429284591794, 0, -33452923646690160, 0, 4854972930987600, 0, -124749906820108884, 0, 9663593915313900, 0, 25892130956001858, 0, 44364383610990906, 0, -94647552933754080, 0, 31983098119536960, 0, 44298462536491704, 0, -38701375524845614, 0, 8297111430052614, 0, 4779928197281580, 0, 45744320193363792, 0, 9484034607874800, 0, -20288439732937440, 0, 25280358000068246, 0, -4549939832708910, 0, 92946264072139266, 0, -58070854833490800, 0, -103030938586662840, 0, 118510164885612312, 0, 24123593987270175, 0, 12960380964440862, 0, -80704789081784322, 0, -155137596983924648, 0, -9153463390064838, 0, -80281021556928720, 0, -189425889091716418, 0, -3745922811088320, 0, 43091525803484340, 0, 229407014302358184, 0, 11442043356116760, 0, 10299141200351256, 0, -80404666215468574, 0, 66504843858875364, 0, -108922312341950400, 0, -130104582084662760, 0, 24612899959277172, 0, -194512569561303948, 0, -29953216845933044, 0, -38376618769829718, 0, -52447578812395200, 0, 63273617094644000, 0, 22323187861111008, 0, 45784238976030000, 0, -103262140559434736, 0, -14983383594856950, 0, 36267602202286110, 0, 147601141337531464, 0, 33393955917788640, 0, -17983370202913668, 0, -41912406177157620, 0, -28858360726108296, 0, 245216661611093178, 0, -189066286410006284, 0, -124700640464603520, 0, -99093713217096000, 0, 149090803733447858, 0, -18206718612875946, 0, -24634054221738, 0, -128663175680808080, 0, -3409151319030060, 0, -22947146672884044, 0, -54612581618125440, 0, -72600051043285920, 0, 7134051156162564, 0, 89118236543726160, 0, 89505463584947760, 0, 199039501350243816, 0, 8463690470903738, 0, -17314957268956701, 0, -75815062140561750, 0, -25357162960188728, 0, 27033222746112588, 0, 104470251645142536, 0, 48795339094031200, 0, 33239671222844340, 0, -94025583051970560, 0, -37218885285429568, 0, -81758112389163738, 0, -11475469710235440, 0, -153171679680122220, 0, -21464533563426666, 0, 289375315543572192, 0, -136834807868811040, 0, -139313924776650600, 0, 125550568252431120, 0, 8503059530780640, 0, 41251717033332192, 0, -226534485261064062, 0, 16726182793576128, 0, -27755567026142400, 0, 350720195537631528, 0, 263962749289628487, 0, -2289287866521330, 0, -57480967603440978, 0, -235718614435842000, 0, 10754477414361954, 0, 176493923560213920, 0, -37215526806612946, 0, -169403452313906214, 0, 163055325844841460, 0, 272593926938414840, 0, 45669729031325064, 0, -172854593852057064, 0, 105086462989150720, 0, -16151899600062000, 0, 159633164860070304, 0, 53927729950346128, 0, -77761612457360028, 0, -75802628472935280, 0, -85784995169139780, 0, -35700832002093120, 0, 218169256596366450, 0, -27045016279752744, 0, 125849353606365942, 0, 154143203427956280, 0, -53214466060139996, 0, -148476208233055824, 0, -12973646154188466, 0, 380914090762375384, 0, -94783818785465700, 0, 335419764117401004, 0, 71900245276829870, 0, 54417039268686210, 0, 280193116514043498, 0, -133990180991640000, 0, 36542915998510320, 0, 63535374862583184, 0, -62438901906002832, 0, 123768096467181660, 0, 132953986534402290, 0, 281865445173238144, 0, -25100024186966400, 0, -267789482952372924, 0, 254329240197940550, 0, 51012187449493860, 0, 79245419135865600, 0, -54456755233215476, 0, -42900744473987472, 0, -345475306477213440, 0, -258701877423652860, 0, 9658319391209628, 0, -275580033200802516, 0, -268673600398308056, 0, 209212838147338956, 0, 11101265661741900, 0, -4982748925668800, 0, 8058049603003764, 0, -187405619635787622, 0, -415049744220705356, 0, 49147579521003240, 0, -302640903260506464, 0, -459073914578361838, 0, 100045761881408640, 0, -142133133768388362, 0, 63003764529064800, 0, -146093898151241388, 0, -62210982507069756, 0, -72593005085073440, 0, 520187750996760, 0, -142802336851785600, 0, 98873960183329032, 0, -265363375494618072, 0, 111331068305310792, 0, -78567037492903596, 0, -12149731921092660, 0, 597491293584763500, 0, -61466626300648200, 0, -71158562262730809, 0, 230876385326482764, 0, -98964980015742550, 0, 212958177624359802, 0, -718372598817416496, 0, -368696070337116044, 0, 94243930424992800, 0, 138197105948430120, 0, 40773269102791860, 0, 68032059108809004, 0, 81039123100350240, 0, -36748174434530768, 0, 63386071773433920, 0, 65604519989386560, 0, 645797444078571158, 0, -241130804121654912, 0, -216615264931402062, 0, 185824905865899120, 0, -43156054675440306, 0, -449669039276902344, 0, -61784998380583040, 0, -90393385284072450, 0, -67697382447011460, 0, 223622334716320888, 0, 236562318056168604, 0, -576501882331083060, 0, 93112694632058990, 0, -32769620817894000, 0, -171084849151826544, 0, -279213123169530044, 0, 38177480545822800, 0, -440915544388523088, 0, 439396474426214580, 0, -174556957562071461, 0, 11543935897934400, 0, 636786608847286040, 0, -7968047408932068, 0, 36825000266301840, 0, 26130638692028150, 0, 167353801853166900, 0, -699551742161992158, 0, 503143684276151840, 0, 294382102210985160, 0, -90538933214884440, 0, -481549578192124006, 0, -231691412877515460, 0, -184621303294521042, 0, -323167013345095920, 0, 187032855503095164, 0, 630979763091050268, 0, 233560259699929022, 0, 424293255969038370, 0, 283161976497633000, 0, -126809206771191404, 0, 134590915555534350, 0, -520890302213280, 0, -227098931820425280, 0, 90627538659613740, 0, 194852937743039862, 0, 883135487033728632, 0, -42433735514447340, 0, 193175863223922000, 0, -231916229039692800, 0, 71033130511149186, 0, -120575092848239484, 0, -191762719225778896, 0, 50974648583219064, 0, -182641589521022760, 0, 876370806945939242, 0, -25097588187004800, 0, -445593154594869888, 0, -812045213668716152, 0, -210784750423497900, 0, 299055303522626700, 0, -371241649241849458, 0, 384826708419726042, 0, 489276735463875840, 0, 105801544876282900, 0, 178360188849614376, 0, -213929061337395600, 0, 257572539122654059, 0, -116167807347575256, 0, 321899002331036460, 0, -24709647440695840, 0, 237118894037113572, 0, -497009490352660296, 0, 854647847257328966, 0, 469329901468857540, 0, -123060392681316846, 0, 685014984276002572, 0, 23520731798137680, 0, 75006052943085768, 0, 174469729094568000, 0, 467598677224513518, 0, -362759879734162434, 0, -5970250230338088, 0, -391550857069070628, 0, 474648050369083200, 0, 28717746242844204, 0, -200004202220310144, 0, 664563856092363978, 0, -166105057993741340, 0, 74385418671963000, 0, -1359400638569154888, 0, 415009526707698560, 0, -615398298350753178, 0, -321635282269051194, 0, 525553873736609880, 0, -291064789980022446, 0, 1034164792275875520, 0, -1112347718563418506, 0, -59149185021564480, 0, 766780187157916260, 0, -155642185797887396, 0, -587802446425540440, 0, -149822657515597248, 0, -1122061776605762422, 0, -59039570508886260, 0, 672570428057772480, 0, -509412722850571112, 0, 756963429392744172, 0, 861034975907838600, 0, -774600594550977780, 0, 241508026196632800, 0, 53223273159799476, 0, 271125658814169600, 0, 375424700731522758, 0, -296491582178173800, 0, 1007928184524089426, 0, -536356995802257834, 0, -118774438143832068, 0, -71968517875692848, 0, -111728569537166400, 0, -483983942729063772, 0, 464151471669900230, 0, 223532080441151328, 0, -104327318112272592, 0, -667755660146573520, 0, -829015327383813144, 0, 216664505675585760, 0, -631889005114786534, 0, -382834952007902082, 0, -1418778847811593890, 0, 862960294543249304, 0, -75940145132982588, 0, -623432360264613540, 0, -802148837286408690, 0, -158576698353619350, 0, 56970284011569600, 0, -695817040625683704, 0, 122858885038999608, 0, 619213031856076560, 0, -279297508629282250, 0, 17623471250702880, 0, -28285890910557600, 0, 285228416860651936, 0, 289663483950842688, 0, -859788198062054160, 0, -5618968557380640, 0, -482050561558418982, 0, -460693155764215680, 0, -762749460308223784, 0, -285013912009198500, 0, 859932402046570200, 0, -11630924474115363, 0, -469229702088044466, 0, -214212023338723956, 0, -565340157562536000, 0, -230288354458464852, 0, 768641174607718476, 0, 897173543059521566, 0, -53390897990496360, 0, 186477668839920660, 0, -717291166408466156, 0, -171831149561668320, 0, -161133481125336240, 0, 1219101007190464658, 0, -245041851437285625, 0, 357365189670860118, 0, -1868170331611036832, 0, -734869285741101456, 0, 791814865534486560, 0, -44236811271305160, 0, 498221937227638260, 0, 1286527030720736130, 0, 252161574543525200, 0, -244440145031970816, 0, -786706093732065000, 0, -649028635882213760, 0, -10598931603451620, 0, -807836208443388354, 0, 466163445443007384, 0, 326583813327492240, 0, 1636639912799383644, 0, 134265724842684960, 0, -224677177748588286, 0, 1870216084915228938, 0, 345515743305768960, 0, 212809877281530936, 0, 181666419909522504, 0, -1109332872700091676, 0, 274940845254704790, 0, 353971174177416000, 0, 1398352359535156800, 0, 210998250754153524, 0, 1813863775239094596, 0, -1851809960115681322, 0, -303758472217618440, 0, -1060885202563137468, 0, -842907978669050080, 0, 334456664714729208, 0, -56899971310896408, 0, 214209480482832420, 0, 86069323563880752, 0, 981408548734770990, 0, 2082672779361104488, 0, 83496598304976000, 0, 253618327438912800, 0, -947767473882846848, 0, 620320325315216634, 0, 2520974444228334900, 0, 535278211569672512, 0, -127739963699386920, 0, 443462097932089440, 0, 2502686311777387440, 0, 200468654454805470, 0, 1720703724609572934, 0, 74378199440791000, 0, -225210482051801580, 0, -612994190716256220, 0, -796837118651781440, 0, -462506511587053014, 0, -572184128533868220, 0, -1572627238676851748, 0, 139549038215176044, 0, -1453825318198103400, 0, 510281865590253146, 0, -706786983135446400, 0, 120453934861278, 0, -15192882075744632, 0, -40004408190191760, 0, -890730891203861316, 0, -183355919256718260, 0, -131424436937141496, 0, -1084630542149233350, 0, 677529054481947652, 0, -767286284826319704, 0, -209585456149332000, 0, -593243114021244286, 0, 1197965823099360390, 0, 1490318045740140672, 0, -687300310278399920, 0, -69705091486881225, 0, -1520060577011916396, 0, 1589562447562958246, 0, 104561275305329586, 0, -4401689102396199504, 0, 2276856544075635600, 0, -263705460632765280, 0, 69971709179496984, 0, 1633008799880575012, 0, 24555398805372060, 0, -286408418843816580, 0, 390048211789190640, 0, 926423049348329436, 0, 1337348997631397280, 0, 1860853308387437342, 0, 202280240348346420, 0, 374820235781608890, 0, 159452893996844976, 0, 1070249690663634366, 0, -134853070780172112, 0, 82780269528988800, 0, 706110134400534060, 0, -1426832561006316954, 0, -1355090021774177656, 0, -981060923469272508, 0, 175292137535834100, 0, -269581059288821600, 0, -254066444600195520, 0, -720171956971750350, 0, 432876052703726812, 0, -1469674944535640760, 0, 221064294312858744, 0, -2761918686836314054, 0, 673673892882435900, 0, -325695438235910400, 0, -543914702803779480, 0, -1107998971736022, 0, -2812980248190936132, 0, 2160407125055356416, 0, -1145179525315601286, 0, 848075896271545620, 0, -1155963630270739884, 0, 3151716534130352760, 0, 1829226412520424528, 0, -1550889483928340350, 0, -493314892239366720, 0, 150205937416075020, 0, 125325399820764008, 0, 62807552724307680, 0, 3144026171174746344, 0, 1139853585105963000, 0, 210609581351961258, 0, -1964252535605949678, 0, -1457452719826739780, 0, -53385716313200520, 0, -737965198677057600, 0, -3080081533851666550, 0, -189533148922152000, 0, -2441687998652935074, 0, 162290519201227768, 0, 637734144441158640, 0, -7017560840854214376, 0, -714404406169165760, 0, 1040752952176023216, 0, -1124564690107172118, 0, 2755730202859756800, 0, -6382787216183424, 0, -771930700946351856, 0, -2941966959933316174, 0, -327671760229148160, 0, 402346003914172140, 0, -4055265786309531912, 0, -52560517713459966, 0, 6749904950841360, 0, 3408751282913653500, 0, -52228208135255850, 0, -960614410956677760, 0, 1228749955233837820, 0, 1380284197854620256, 0, -369135185564506920, 0, 1604371498363972800, 0, 50031545098999707, 0, -2414550763946251392, 0, 349958908143210080, 0, 717979522586462136, 0, -1977960244655018400, 0, -2296524869712323492, 0, -394417158363286974, 0, 755456972648875200, 0, 1591134529495886212, 0, 382639179153487590, 0, 1814500159041446112, 0, -51828085653085967, 0, 820290917899390032, 0, 4239858752715888486, 0, -597400848340018920, 0, -886449498535326492, 0, -2271442482322479840, 0, 3762437926461675782, 0, 882777288997222344, 0, 509231859930498150, 0, 301932905714615448, 0, -1642788929295011736, 0, 598598354380096560, 0, -190365364505128320, 0, 1806753347859297420, 0, -2425319243974409586, 0, 3234177293591528680, 0, -125817731496338652, 0, -140151952575007764, 0, 474339692327576940, 0, -1521796491131647680, 0, -559988708988938316, 0, -238936035732896828, 0, -6435450784171368, 0, 3078665745064254000, 0, 3290746963059948340, 0, 1430641614062802852, 0, 1670598936770924160, 0, 711646680783854000, 0, -911612018390921280, 0, -32764594960319868, 0, -1294049121957741562, 0, 1791795400825077594, 0, -1251988642476310974, 0, -425215367666884000, 0, 576718264672835040, 0, 3632935229611811640, 0, 1153428863684137658, 0, 1508989320873410382, 0, 50590435568804700, 0, -1953959796094914344, 0, -468495432623999520, 0, -40000525694458320, 0, -5079435715408269298, 0, -237660673724788860, 0, 1174119799525195290, 0, 2371086148901918140, 0, -103392597290173848, 0, -1877327303947908192, 0, 3743607156072742260, 0, -2153454841934490906, 0, 3471572618165179254, 0, 653932658656941088, 0, 460872564684353874, 0, -1009244629210763760, 0, 944158384563052480, 0, -716965281550695006, 0, 114487631259109680, 0, -142570038607461360, 0, -247447148908545000, 0, -3006404921785849560, 0, -478120229318024748, 0, 1089643328073799200, 0, 3287974529946603966, 0, 1718435633316968520, 0, 4261613124914303400, 0, -2067288790032226980, 0, 1580714990270326478, 0, -2298731576923276704, 0, 788944312145020800, 0, 5889941608844545348, 0, 37487332632664062, 0, 3258492283761670560, 0, 1746438445553154100, 0, -2781115345128333780, 0, 2441047836708018342, 0, -1664044004601410080, 0, -3293748886438882908, 0, 3473801100365758344, 0, 3281140897989752160, 0, -979952094910705032, 0, 743798691082648320, 0, -3585646333015498916, 0, -2426182134967501920, 0, 7210632696457938000, 0, -6631429266836880838, 0, 921718895518461996, 0, -4059348713022707250, 0, -4613335128978493064, 0, -1202549386308003900, 0, -901914279267264000, 0, -4988294911703665234, 0, -3886116624146167542, 0, 2273623873498051146, 0, -807553328855968800, 0, 1166025060071621568, 0, 6049895375043677184, 0, -67615833306682351, 0, -365506395910192818, 0, -2735122131805619400, 0, -94271946675993432, 0, -2165424049227511080, 0, -3283436125656096444, 0, -4883178703277073056, 0, 554679546847776000, 0, -3360155163277965918, 0, -499128438307807800, 0, 1684289481085947294, 0, -3714403848276287256, 0, 781506860277726350, 0, 2298437565577910910, 0, -2716829708552754240, 0, -1507382010516944016, 0, 2624309466695510364, 0, 948053488993056480, 0, -2203788239432237506, 0, -1380565270900894824, 0, 5760823127043089274, 0, -3963839477747440480, 0, -213436934694632520, 0, -2927511105787413072, 0, -189514754408264000, 0, 4541887386762864336, 0, 1419621622012880544, 0, -4623345435601688040, 0, 305202695964000480, 0, 5202701106207670596, 0, 3454402776138891360, 0, -2682984840057585198, 0, -178072948016996760, 0, -4180611401373403316, 0, -3064315774348731168, 0, 4004266760658313440, 0, 3132797379588730490, 0, 752941061383365900, 0, -6683114760508033266, 0, -3518073892737565720, 0, 191039879493272988, 0, -2595234801606000384, 0, -2210887824292857600, 0, -1439991994859904510, 0, 1910006083702380048, 0, 5900019967260688320, 0, -1792970937767605842, 0, 3228494786305210920, 0, -265242719646789840, 0, -904426115807815146, 0, 4449603984584783100, 0, -5113200035210844656, 0, -11495507089928400, 0, 1063461463142993040, 0, -3776828007074682356, 0, 177607731747497400, 0, 3451936150031448960, 0, 5864202989325510480, 0, -5108075247811470120, 0, -11560632384869005224, 0, 3228162282877252106, 0, -2936635591860503955, 0, -186133928412109350, 0, 7334320449767196720, 0, 943299474812390106, 0, -1323844645625851524, 0, -4270537366931984148, 0, 1572516375929483310, 0, -531954706322729712, 0, -9359349974945579756, 0, 819755893165078800, 0, 6460049525503315920, 0, -4706112814167951180, 0, -1694972443057242156, 0, 2710417144331600646, 0, 8110065773214896896, 0, -2473436467645088400, 0, -2082674511860952000, 0, 3630956106089678870, 0, -4820592560728374486, 0, 4871473888572253188, 0, 11968392896344008, 0, -1503424516108248360, 0, 2154734177354845632, 0, 4444640666331959680, 0, 1935832390329224718, 0, -446642250613346400, 0, 971074804154207200, 0, 3881898977027692140, 0, -8153377180322153556, 0, -273864415255197588, 0, 1473368006960028000, 0, 5328693078737806080, 0, 2900530228846150208, 0, 979109569041071904, 0, 6304326448519379232, 0, -4948624225973923486, 0, 953695529247384540, 0, -4576344304169905290, 0, 5507313462273777840, 0, -1461973920087508533, 0, -3024554559819211848, 0, 1997582218006045500, 0, 576662293186109280, 0, -3924698535405340542, 0, -963988843016051680, 0, -985391833272758568, 0, -5227735176796812360, 0, -4465293981413555254, 0, -560934572943233322, 0, -7907445325225780338, 0, 4742241874450253624, 0, 2492932890315960000, 0, 9858828582297105840, 0, -11242014259414146624, 0, 2374006747766375970, 0, 8155850330320705002, 0, -843675187370652000, 0, 2844708968340647622, 0, 228680424747007680, 0, 21975018653786452144, 0, 3950765028476430102, 0, 3857493259705035990, 0, -10682375842877588192, 0, -4035286535404359996, 0, 567748655799123624, 0, 4066845654004120000, 0, 176084010641832120, 0, -3919789660791249246, 0, 4588826428695804508, 0, 4648933688615295192, 0, 8502787672725203928, 0, -3698312411323071000, 0, -1688261947480667520, 0, 6573590699134773132, 0, 939395724091248136, 0, -540431177492685348, 0, 4509934663136003100, 0, 9362180583347524766, 0, 7376191585395735168, 0, -1786129801521070080, 0, -717452170483577132, 0, 5120094185811761400, 0, -3671876128256864976, 0, 5757292136871561794, 0, -692795026383006960, 0, -534375151926608154, 0, -4133195201858522760, 0, 133076843918708400, 0, -2258678401923775932, 0, 9287097599229724300, 0, 2842409062584114660, 0, -9376357138081218300, 0, -4116845892096177620, 0, 1570267260476925120, 0, -9871593505575901368, 0, -1943940422796578902, 0, -2974293072153166500, 0, -9535591371654597216, 0, -499507381328478680, 0, 2606215496886445212, 0, -1107347332998776160, 0, 1388414156179764650, 0, 133599538213892082, 0, 3848447736693211434, 0, 15140856358861714900, 0, 6858642590125671024, 0, 937733167541490600, 0, -1311069789516614400, 0, 1359059062586981328, 0, -1827016601541499626, 0, -137530691114279320, 0, -1569744489073543740, 0, -4756985507215249800, 0, -5630777033064670522, 0, 660346627987892160, 0, -12644755342370430606, 0, -1126476802024223760, 0, -4460285126721343680, 0, -1297516632523707600, 0, -15453516986695150128, 0, -1519627729822877124, 0, 554625714256032000, 0, -1811154401922382280, 0, 2761399978177292496, 0, 504490779650036088, 0, -863913940276265856, 0, -3229222990309670250, 0, -3620513072172553350, 0, 2957882943780294560, 0, -696998911014804384, 0, -1860805337381142600, 0, -8504195161374192780, 0, -2676039717342149802, 0, 3434452585385782806, 0, 6252381255078271600, 0, -5721335272694725596, 0, -3941539975812465840, 0, 4399176367863243014, 0, -2043347274948878424, 0, -14857306465435362174, 0, -5424066481289070068, 0, 2567165125335305040, 0, 947851083531936480, 0, 5113391000061829303, 0, 2032346793372423246, 0, -420293654322995652, 0, -5240034818844855480, 0, 744406468550014842, 0, -4373078750563583364, 0, 1083443624339936000, 0, 5417483384022084090, 0, 7190135457228285150, 0, -4978257263764154136, 0, -3344472512045406000, 0, -27015115600643176248, 0, -4217610023906544526, 0, -519779134798351200, 0, 17464418679207309846, 0, 27171385976694960, 0, 9186331329318636756, 0, -6092328969411307740, 0, -10333353484344187620, 0, 2601261487991910420, 0, -11770118745538108800, 0, 3992189947850532604, 0, -4831642908453174066, 0, 8652790545106622520, 0, 6715645306316154746, 0, 1165350490409165742, 0, -8537397336078716466, 0, 1480576854209375840, 0, 4419845950300680960, 0, 7701574616794341312, 0, 13630695129994172032, 0, -404930994548390568, 0, -3716882523824329314, 0, -5658834375831420000, 0, -1045679603737448160, 0, -8506088532993142656, 0, -5069839011881013392, 0, -5543767537167693933, 0, 13599542642566027020, 0, 10003457796462437584, 0, -3237051909395989332, 0, 670093942362006132, 0, 10585255032421623648, 0, 6432172519311607140, 0, 352731723000101730, 0, -1705350531310520656, 0, -8199295822889177472, 0, -3807561697580393544, 0, 1307123965291363200, 0, 3553573365179621784, 0, -9605809694571481362, 0, 13330676419537395600, 0, -8713660975636709700, 0, 12989708383971819600, 0, -1155880902462658018, 0, 7597425784042716480, 0, 3832271129689679040, 0, -2473196416436558800, 0, -904486392123985350, 0, -15408566150204655312, 0, 100102651610785812, 0, -2916567384982001658, 0, 2811745279298495040, 0, -16727957266827309480, 0, 3948130155324793752, 0, 17410405260649145316, 0, -2254204979972785476, 0, -996548515886691198, 0, -5337029220888552000, 0, -4384094391154209760, 0, 1075729044541384440, 0, 318628433000717160, 0, -16802974031724281446, 0, -8296422398881799220, 0, -12082689563400779154, 0, -18193372715167679016, 0, 2550171584462722560, 0, 13064328531515147340, 0, 11852827438099278060, 0, -3564429025485414240, 0, 14414036895378228330, 0, -5290193597767838876, 0, 9213760188361539144, 0, -1711682010671724000, 0, 13887454427376347476, 0, 2008343243878374852, 0, 14912601909098259936, 0, 41584067153595537032, 0, -4939783012218035520, 0, -522243116220270144, 0, -5973718279985784714, 0, 13996868151507354, 0, 12557606812872274500, 0, 18320215259469450960, 0, 2317807956751792830, 0, -567534879035334024, 0], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "3.12.a.a", "char_is_minimal": false, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0], [1], [0], [243], [0], [-5370], [0], [27760], [0], [59049], [0], [-637836], [0], [766214], [0], [-1304910], [0], [3084354], [0], [19511404], [0], [6745680], [0], [-15312360], [0], [-19991225], [0], [14348907], [0], [10751262], [0], [50937400], [0], [-154994148], [0], [-149071200], [0], [664740830], [0], [186190002], [0], [898833450], [0], [957947188], [0], [-317093130], [0], [1555741344], [0], [-1206709143], [0], [749498022], [0], [3792417030], [0], [3425179320], [0], [4741271172], [0], [-555306924], [0], [4950420998], [0], [1639200240], [0], [-4114569180], [0], [-5292399284], [0], [-3720903480], [0], [14831086248], [0], [13971005210], [0], [-4857867675], [0], [-17706327360], [0], [-3720542360], [0], [3486784401], [0], [-8768454036], [0], [-16562980980], [0], [2612556666], [0], [-25472769174], [0], [21270100640], [0], [12377788200], [0], [-104776239480], [0], [-39092494846], [0], [-37663577964], [0]]}