# Stored data for newform 225.6.a.i, downloaded from the LMFDB on 25 April 2024.
{"label": "225.6.a.i", "space_label": "225.6.a", "level": 225, "weight": 6, "hecke_orbit": 9, "hecke_orbit_code": 36028797119627489, "dim": 2, "is_polredabs": true, "nf_label": "2.2.89.1", "trace_hash": 1320218606345047095, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [-2, 9, 1]], [7, [-9900, -108, 1]]], "qexp_display": "q+(-4-\\beta )q^{2}+(6+9\\beta )q^{4}+(42+24\\beta )q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 8100, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 36.08635945792064, "hecke_ring_index": 1, "level_radical": 15, "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": {"__RealLiteral__": 0, "data": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [225, 1, [101, 127], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [3, 5], "conrey_indexes": [1], "field_disc": 89, "field_disc_factorization": [[89, 1]], "field_poly": [-22, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.924", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.291", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "62.527", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "5.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [5, -1]], "trace_display": [-9, 0, 0, 108], "traces": [0, 2, -9, 0, 21, 0, 0, 108, -207, 0, 0, -168, 0, 1296, -1554, 0, 1105, -576, 0, -1336, 0, 0, 5562, -5904, 0, 0, -2094, 0, 10746, 3552, 0, -11648, 6057, 0, -3638, 0, 0, 14688, 9216, 0, 0, -1812, 0, -7560, -45018, 0, 22652, -3240, 0, -2150, 0, 0, -20034, 22176, 0, 0, -31470, 0, -54432, -57336, 0, -30140, 58824, 0, -84911, 0, 0, -5184, 50022, 0, 0, -17424, 0, -3456, -48474, 0, -42864, -124416, 0, -57520, 0, 0, -126414, -133992, 0, 0, -25788, 0, 108702, -136764, 0, -19728, -26748, 0, 71896, 0, 0, 85536, -105669, 0, 0, -226608, 0, -3780, -63114, 0, -10258, -106920, 0, 90644, 0, 0, -46062, -106272, 0, 0, 383328, 0, 109026, 118416, 0, 211058, 276606, 0, -179976, 0, 0, 168156, 282393, 0, 0, 93480, 0, -149040, 226248, 0, -58754, -15264, 0, -280744, 0, 0, 222588, 294840, 0, 0, -19692, 0, -4374, 339528, 0, -69056, 199152, 0, 909108, 0, 0, -197856, 675360, 0, 0, -224832, 0, -769392, 1192086, 0, 298940, 454752, 0, 411214, 0, 0, 458892, -839232, 0, 0, 382974, 0, 403974, -390600, 0, -791708, -401436, 0, 536660, 0, 0, -624456, -549864, 0, 0, 211152, 0, 801792, 309288, 0, 1015521, -531072, 0, -350608, 0, 0, 712152, 1114560, 0, 0, 1137342, 0, 1086102, 458256, 0, 523672, -572958, 0, -769844, 0, 0, -782784, -2086794, 0, 0, -896568, 0, -980964, 862146, 0, 700190, 436392, 0, 520076, 0, 0, -1098144, -1477440, 0, 0, 738846, 0, -561708, -188304, 0, -2277332, -1757169, 0, -1585254, 0, 0, -596592, 1327320, 0, 0, -2573064, 0, 73008, -3335922, 0, -152991, 1683360, 0, 370224, 0, 0, 151254, 2199312, 0, 0, 1557120, 0, -1880712, -1115424, 0, -1017392, -935010, 0, 1780870, 0, 0, 1194912, 2301444, 0, 0, -2232636, 0, -331344, -1480572, 0, 1473516, 3131784, 0, -1801626, 0, 0, 280908, 1749312, 0, 0, -1185390, 0, -335988, -4154736, 0, 1027152, 2905992, 0, -420944, 0, 0, -798120, -4449492, 0, 0, -3124848, 0, 3349728, 2869890, 0, -4352640, -4187520, 0, -4450752, 0, 0, 3953016, -63792, 0, 0, 5096304, 0, -2369250, -1550544, 0, 1647784, 1329300, 0, -3490676, 0, 0, 3160512, 2993985, 0, 0, 1670496, 0, 837000, -353892, 0, 4089290, -3866616, 0, 1429748, 0, 0, -2916594, -5321376, 0, 0, 467154, 0, 6011010, -2644416, 0, -3829062, 3280734, 0, 4204764, 0, 0, 1208412, -3649644, 0, 0, -951312, 0, 6436800, 1949244, 0, 1424344, -927936, 0, 2469560, 0, 0, -5535108, 2035512, 0, 0, -5249580, 0, -5349672, 3828984, 0, 2248592, -1969011, 0, 4245118, 0, 0, 8586000, -2401632, 0, 0, -2679420, 0, -7009632, 388872, 0, -8988480, 669384, 0, 2983916, 0, 0, -10122678, 479520, 0, 0, 2052198, 0, -5541696, 5294136, 0, 1736236, -3215196, 0, -594070, 0, 0, -5010984, 10136196, 0, 0, 6464448, 0, 6805728, 10088592, 0, 16061826, 3661920, 0, -2987920, 0, 0, -1079028, 3115944, 0, 0, 11239926, 0, -6844014, 5061348, 0, -14381136, -3113550, 0, -2377436, 0, 0, -8849952, -1750806, 0, 0, 1526376, 0, -10102860, -1843872, 0, 5043098, -3981240, 0, -5150016, 0, 0, 3103542, -5824224, 0, 0, 1502892, 0, -3641436, 4229520, 0, 10998072, 13887738, 0, 9482781, 0, 0, 3830436, 5798034, 0, 0, -5691720, 0, 4359744, 2263872, 0, -5801128, -4401216, 0, 13624904, 0, 0, 17898678, 9278424, 0, 0, -14186904, 0, 24978618, 5206944, 0, 659232, 2120553, 0, -2821274, 0, 0, 6462288, -8557812, 0, 0, 12878388, 0, 1699920, -4165686, 0, -745924, 2457504, 0, 4900530, 0, 0, -9542880, -12477888, 0, 0, 4392024, 0, 9133344, -12276552, 0, 725332, -3124152, 0, 1376814, 0, 0, 4307688, -15569910, 0, 0, -5140992, 0, -13102560, -3556698, 0, -12290676, 2519424, 0, -9922752, 0, 0, 20081790, 5463288, 0, 0, -7131984, 0, 4542804, -704604, 0, 3632488, -22106844, 0, -20392092, 0, 0, -15734304, 11695797, 0, 0, 61008, 0, 7806888, -311940, 0, -26566354, 18523800, 0, 8242240, 0, 0, 9859698, -2201760, 0, 0, -7161948, 0, 5124168, -8241792, 0, 19938628, -3814776, 0, -24082248, 0, 0, -18875484, -5651280, 0, 0, 2715024, 0, -10212048, -13274316, 0, 19512540, 395136, 0, -4298824, 0, 0, 15244092, -2310120, 0, 0, -15719916, 0, -19893330, -6697224, 0, -8300336, 13867200, 0, 12997786, 0, 0, -11082096, 31793472, 0, 0, 5780028, 0, -10588320, -28832184, 0, 3525952, 9210744, 0, -11274264, 0, 0, -22784976, 4678272, 0, 0, -14323362, 0, 11802672, -5675880, 0, 6922564, -11596248, 0, 8091716, 0, 0, -7102080, 17773524, 0, 0, 17757168, 0, -30170016, -25909428, 0, -39282285, -18626112, 0, -12041856, 0, 0, -36045648, -12067128, 0, 0, 9102900, 0, -10097892, 21890904, 0, -4315112, -11626650, 0, 20610892, 0, 0, 19361376, -39909258, 0, 0, 8834400, 0, -8542800, 17297214, 0, 40355834, -4854816, 0, 967004, 0, 0, 10137258, 33820992, 0, 0, -42381090, 0, 14129856, -6273792, 0, -27092088, 12950235, 0, -5775366, 0, 0, 9763524, -7272180, 0, 0, 10550400, 0, 38603520, 5858382, 0, -15918348, 22350816, 0, 7351016, 0, 0, -2726244, -42473160, 0, 0, -22919118, 0, 1190484, 24249936, 0, 36148768, 3884184, 0, -14099904, 0, 0, -2975616, 261180, 0, 0, 41071524, 0, 45188280, 43481412, 0, -34494544, -49668552, 0, 8339492, 0, 0, 23192460, 13318272, 0, 0, 4336824, 0, -13270284, -8478480, 0, 17035056, 9400104, 0, -12606931, 0, 0, 23200560, -22273902, 0, 0, -11065872, 0, -7688736, -47853306, 0, 32132928, -5306400, 0, -7091120, 0, 0, 42066054, -3516048, 0, 0, 13925616, 0, 17609832, 53080380, 0, -4787096, 47459520, 0, 30802788, 0, 0, 743904, 8692794, 0, 0, 42421584, 0, 19783332, 21677538, 0, 20414340, 15902424, 0, 36816260, 0, 0, -47116458, 16767360, 0, 0, 36127584, 0, -7526466, -36727680, 0, -1494874, -15284790, 0, 13226604, 0, 0, 30774924, 21116106, 0, 0, -44909712, 0, -7063632, 46256892, 0, -12702476, 21633120, 0, 10855640, 0, 0, -13557024, -5249520, 0, 0, -23753196, 0, -67313808, 49815840, 0, 13686048, -41280678, 0, -23320960, 0, 0, 25053408, 22897440, 0, 0, -25495596, 0, 17115840, 36608292, 0, -12646876, -12227040, 0, 70981704, 0, 0, -71730414, 6291072, 0, 0, 53634210, 0, -58494258, -26223360, 0, -18921448, 71664588, 0, 15216506, 0, 0, 45304920, 8305164, 0, 0, -4249824, 0, -21579264, 37052256, 0, 154974, -8678016, 0, -63624640, 0, 0, -4561812, 820368, 0, 0, 22136682, 0, 30019680, 29257476, 0, -6868568, -1064682, 0, -8358644, 0, 0, -54978048, 36901008, 0, 0, -12413352, 0, 17191008, -46427754, 0, 13066200, -47223144, 0, -5199984, 0, 0, -12803940, 28452384, 0, 0, 38422044, 0, 37341540, -41916624, 0, 11502402, -10620396, 0, -56669682, 0, 0, -48466404, -37185255, 0, 0, -973512, 0, -40074480, -29588382, 0, -2695726, 22192704, 0, -11349936, 0, 0, -12743946, -23095224, 0, 0, -19610304, 0, -2477088, 27580224, 0, -7815056, -38486376, 0, 36895608, 0, 0, 8681904, -85915584, 0, 0, -51285744, 0, 37370808, -83896182, 0, -17346616, -8367120, 0, 18198860, 0, 0, 125491896, -36872352, 0, 0, -66409326, 0, -21393504, -27751224, 0, 2892220, -3024216, 0, -3979855, 0, 0, -2285280, -25109334, 0, 0, 8589984, 0, 831168, -41680560, 0, 65913588, -11056320, 0, -92478832, 0, 0, -74908314, -10270800, 0, 0, -34441488, 0, 1191186, -88878444, 0, -48080888, -59266044, 0, 23379248, 0, 0, -66014784, 1067679, 0, 0, 25646472, 0, 93974580, 32268000, 0, -34436196, 67788576, 0, -3080980, 0, 0, 17224920, 10860480, 0, 0, -48737376, 0, 59766930, -112364832, 0, 4520672, -106842906, 0, 58639128, 0, 0, 21154068, 11277918, 0, 0, -10923288, 0, -12713328, 78704796, 0, 34111282, 117624960, 0, -58193136, 0, 0, 54508032, 42446520, 0, 0, 112169280, 0, -3837078, 81317400, 0, -14184000, 48780828, 0, -60829418, 0, 0, 107925696, -8232840, 0, 0, 27573456, 0, -91189584, -113757030, 0, -54632620, 16497072, 0, -66541372, 0, 0, 74128176, 121313376, 0, 0, 4647060, 0, 43906374, -26915808, 0, -80764128, 15024168, 0, 22689684, 0, 0, -83005344, 89575308, 0, 0, -92753136, 0, -81406080, 64973088, 0, -51213393, -106386048, 0, 30283792, 0, 0, 54859896, -98254152, 0, 0, 10637076, 0, -5398596, 59219616, 0, -8185640, 186617826, 0, -39196724, 0, 0, -126124992, -60030720, 0, 0, -118809528, 0, -94061196, 35653986, 0, 145449758, 22095144, 0, 113048640, 0, 0, -12495276, 67891968, 0, 0, 78524568, 0, -77640768, -188934864, 0, 35482588, -58401522, 0, 3518424, 0, 0, -15167088, 56456856, 0, 0, -52824432, 0, 14074992, 25692378, 0, 63497008, 52164000, 0, -73342544, 0, 0, 18867600, -4400568, 0, 0, 85534830, 0, 143412444, -15799992, 0, -912320, -34165476, 0, 41004010, 0, 0, 110410992, 101411964, 0, 0, 5929488, 0, 32899176, -43451388, 0, 72008460, 38247552, 0, 62990684, 0, 0, 40987404, -123171840, 0, 0, 58089318, 0, -20690748, 129100968, 0, 113740128, -102054528, 0, 9455680, 0, 0, -35985384, 8645526, 0, 0, -8824704, 0, 18073152, -28891830, 0, -152618688, -65121408, 0, 102109424, 0, 0, -106212654, 40174632, 0, 0, 55736472, 0, 79154280, 167855028, 0, -218694584, -29819808, 0, -163999568, 0, 0, -120496896, -74529396, 0, 0, 5865576, 0, -29620836, 110678832, 0, 82726226, -192330936, 0, -13061232, 0, 0, 61930926, -172679040, 0, 0, -59707728, 0, -57530250, 38848944, 0, 16072300, 80155422, 0, 54932712, 0, 0, 67935564, -104128956, 0, 0, -77872368, 0, 35417088, 138503040, 0, -74508380, 121440384, 0, 91658448, 0, 0, -164175660, -41747040, 0, 0, 198987468, 0, 138369492, 22020192, 0, 82693152, 49483863, 0, 130875898, 0, 0, 182366640, 45998928, 0, 0, 90931620, 0, -55275264, 274295952, 0, -41419204, 65581128, 0, -23840930, 0, 0, -107036100, -37556640, 0, 0, 7068348, 0, 955908, -73204944, 0, -68411684, 51268968, 0, 92802686, 0, 0, -228960, -69499548, 0, 0, -174366816, 0, 76572000, -42726228, 0, 316290882, -292680864, 0, -82483792, 0, 0, -73089216, 76567392, 0, 0, 50201280, 0, -196453458, 52917420, 0, 81153056, -203561226, 0, 126245808, 0, 0, -82289952, 157822146, 0, 0, 95838816, 0, -75852828, -96497046, 0, -148304096, 17821800, 0, -75538180, 0, 0, 121239990, 86360832, 0, 0, -47836224, 0, 38170872, -56892384, 0, 53914392, 184430844, 0, -1680255, 0, 0, -31067820, 76584690, 0, 0, 112954584, 0, 140588784, -187014750, 0, -59430708, 27123264, 0, -7053016, 0, 0, -6702696, 108254880, 0, 0, -192836778, 0, -88977798, -50219112, 0, -125265872, 242374932, 0, -130081104, 0, 0, 48886416, -126831816, 0, 0, 196010340, 0, -91659168, 53075556, 0, 156124808, 14294304, 0, 27051068, 0, 0, 13168062, -171975168, 0, 0, 48275844, 0, -119582568, -94789464, 0, 68412800, -60026112, 0, -38527656, 0, 0, 186197832, 154737216, 0, 0, -61579440, 0, 68992992, 106208550, 0, -76437420, -66596256, 0, -4087936, 0, 0, -184591170, 187758648, 0, 0, -342411540, 0, -108967788, 135696864, 0, 145967656, 249385536, 0, 19804572, 0, 0, -37972800, -12062322, 0, 0, -2553792, 0, -53136972, -114174276, 0, -269227294, 74311344, 0, 11236532, 0, 0, 115984440, 36808992, 0, 0, 4563036, 0, 125141760, 6610704, 0, -216786168, -130638744, 0, -152058696, 0, 0, 134495532, 51276069, 0, 0, 131096328, 0, 68943312, -161499936, 0, 90216538, 67616928, 0, -168675784, 0, 0, 118531836, 140460192, 0, 0, 69620100, 0, 173099754, 33493296, 0, -79204608, -39320064, 0, 13782106, 0, 0, 116682768, 25495632, 0, 0, -256006404, 0, 13935240, -298211886, 0, 10477944, 2882592, 0, 109485836, 0, 0, 84958416, -334459008, 0, 0, -155651736, 0, -183112110, -189484488, 0, 232909204, -119754468, 0, -190843200, 0, 0, -255066624, -297306612, 0, 0, -41252592, 0, 38747808, 24493056, 0, -167752626, -20774592, 0, 100203552, 0, 0, -41872680, -116260128, 0, 0, 63862410, 0, 108824418, -121822368, 0, -107689392, -198114660, 0, 20251492, 0, 0, 107492832, -87815970, 0, 0, 286086624, 0, 201459420, 48643206, 0, -35536798, 97148232, 0, -112606612, 0, 0, -113540832, 97562880, 0, 0, -91085886, 0, 278215560, 13303584, 0, 176862902, -129840363, 0, 85476030, 0, 0, -210329784, -70514820, 0, 0, 76132944, 0, 230025312, -294792162, 0, 22303482, 111101184, 0, -25750648, 0, 0, 121314456, 108615816, 0, 0, -295403466, 0, -265982508, 82420056, 0, 26895168, -182920716, 0, 125858866, 0, 0, 108324864, 74599740, 0, 0, 67526220, 0, -38669616, -71920224, 0, 73834148, 230410008, 0, -22116960, 0, 0, 9606924, -120232512, 0, 0, 205773360, 0, -397379520, -1097424, 0, -122731364, 60216048, 0, -116129894, 0, 0, -91099080, 100031040, 0, 0, -155757840, 0, -69891552, 36289986, 0, -116439360, -290622816, 0, -161394352, 0, 0, 19705950, 187708752, 0, 0, -373846248, 0, -4363308, -175331904, 0, 336543264, 20343564, 0, -75120884, 0, 0, -220177440, -548490852, 0, 0, 133932216, 0, -313703172, 231215946, 0, -71787392, -84450312, 0, 92328020, 0, 0, -259509582, 241105248, 0, 0, 374607882, 0, 353306880, -23190864, 0, 38950348, -9717516, 0, -213547212, 0, 0, -94722048, -36740646, 0, 0, 219870408, 0, -61465824, -70705356, 0, -53026340, 133145280, 0, 205930720, 0, 0, -76611312, 89153136, 0, 0, -199338072, 0, -67971744, 312470880, 0, -93462464, -42626682, 0, 20016108, 0, 0, -194182704, 445485600, 0, 0, -100860672, 0, -7155648, -4734972, 0, 57171528, 156574152, 0, -185058134, 0, 0, 103855662, 208939968, 0, 0, -232119456, 0, -319207986, 488658408, 0, -60800372, 104514048, 0, 122412782, 0, 0, 129158280, 194664996, 0, 0, 394468848, 0, -274918752, 195349032, 0, -177608592, 56085696, 0, 268813808, 0, 0, 239603076, -158967360, 0, 0, 323433096, 0, -99000090, -13229460, 0, 195835904, 57130920, 0, 368368780, 0, 0, 129918816, -5897448, 0, 0, -225219048, 0, 104272056, 62570076, 0, -203746426, -42805080, 0, 422298496, 0, 0, -65797812, -134846208, 0, 0, -462959460, 0, 289233612, 129228096, 0, -468904, -126401193, 0, -234358596, 0, 0, -170388144, 304858998, 0, 0, -24425256, 0, 74893248, 145234518, 0, 36676153, 320132736, 0, 20835504, 0, 0, 354964086, -184529664, 0, 0, 386309640, 0, 151382358, -18413880, 0, -355927616, -161907966, 0, -405673838, 0, 0, 83188944, -259806204, 0, 0, 198316008, 0, 173251872, 285447114, 0, 309664112, -361400616, 0, 492167880, 0, 0, 45700416, -144006336, 0, 0, 53752224, 0, 67244688, -208252440, 0, 189060192, 348390792, 0, 508074584, 0, 0, -24812136, -200023992, 0, 0, 36052656, 0, 198454752, -203077590, 0, 364493136, -27140544, 0, -280361632, 0, 0, 224557272, -3531672, 0, 0, 53340972, 0, 386390034, 350748156, 0, 423112840, -122233176, 0, 13369280, 0, 0, 179352576, 46457370, 0, 0, -64785504, 0, -183411324, -270865320, 0, 150463970, 109184760, 0, -261212596, 0, 0, -162436590, -18648288, 0, 0, 36333216, 0, -295255206, 292972656, 0, 38070504, 215699346, 0, 7440984, 0, 0, 422336160, -340764615, 0, 0, 543129648, 0, 77544000, 172683840, 0, -83904686, 52252416, 0, -155516544, 0, 0, -134736480, -139778640, 0, 0, -49915236, 0, 181256400, -135915264, 0, -181430704, -169262460, 0, 103038452, 0, 0, 59412096, 576072792, 0, 0, -45651372, 0, -29284632, 287823186, 0, -70727400, -427866120, 0, -316760116, 0, 0, 258975792, 101375712, 0, 0, 108267186, 0, 405700974, -181295688, 0, -512908560, -100537236, 0, -53760172, 0, 0, 163149336, -284138352, 0, 0, -121173744, 0, 24905664, 474085392, 0, -156625011, 24312960, 0, -361306656, 0, 0, -483471828, -244634256, 0, 0, -391284558, 0, 5412960, -180276468, 0, 98822872, 684262404, 0, -157818384, 0, 0, -550383552, -228934710, 0, 0, -251404848, 0, 211202100, -117362664, 0, -299937600, 86971248, 0, 361682064, 0, 0, 193611168, 563502240, 0, 0, -169605810, 0, 58203144, 312661872, 0, -291984692, -183195936, 0, 939826194, 0, 0, 244981800, -41045832, 0, 0, 173358768, 0, -290842272, -418061454, 0, 142583246, -197116416, 0, 203037800, 0, 0, -513478818, -480074040, 0, 0, -231886410, 0, -837573804, -400320672, 0, 196392672, 161072658, 0, -642743354, 0, 0, 192204576, 474419268, 0, 0, 122239296, 0, -593260632, -336342528, 0, -185226832, -501087384, 0, -379618206, 0, 0, -616446720, -78145632, 0, 0, -89085678, 0, -150042780, -85820784, 0, 465317164, -454873968, 0, -52339556, 0, 0, -106990200, 471882042, 0, 0, -313591872, 0, -522702720, -586871982, 0, 371778120, 95857344, 0, 381327920, 0, 0, -116410176, 150486984, 0, 0, 287240496, 0, 421741458, -517551672, 0, 125444200, 327794940, 0, 270468364, 0, 0, -165521664, 435708702, 0, 0, -81178080, 0, 15052608, -129543504, 0, -649101420, -293202504, 0, -508338148, 0, 0, -125002764, -45486432, 0, 0, -374019246, 0, 78828336, -204158976, 0, 174561460, 862532064, 0, -244192152, 0, 0, -533386404, 440128404, 0, 0, -462028800, 0, 92689920, 317953872, 0, -443821860, -377709408, 0, -199120120, 0, 0, 447849540, -145080072, 0, 0, 680585292, 0, -112728672, -497365296, 0, -96350336, 254649411, 0, 86096628, 0, 0, 189329616, -278733312, 0, 0, -136725024, 0, 696014208, -495569304, 0, 733852220, 104169240, 0, -235309448, 0, 0, -329940324, -217147392, 0, 0, 7190748, 0, -587317608, 317868120, 0, -821096420, 323894556, 0, -536248342, 0, 0, 416095272, -202943484, 0, 0, -514094352, 0, -536710752, 415716360, 0, 293009280, 25894368, 0, 451158624, 0, 0, 568361772, -64479168, 0, 0, 465287298, 0, -586315854, -87430656, 0, 235139128, -1242995022, 0, -687824948, 0, 0, -432217728, -712877760, 0, 0, -151767552, 0, 887604156, 305586132, 0, 87326270, 774888768, 0, -547993276, 0, 0, 172144440, -177553152, 0, 0, 946020672, 0, 1209051684, 86166336, 0, -227532550, -462077982, 0, -72545142, 0, 0, 24706944, -90969480, 0, 0, 182398104, 0, -298032048, 81003816, 0, 218775320, -149729472, 0, 502480080, 0, 0, 702748116, 154345968, 0, 0, 382889490, 0, 335033118, -285864144, 0, -476955360, -303793488, 0, 308116966, 0, 0, 190383696, 22316472, 0, 0, -724986996, 0, 880615800, -251259120, 0, 136202096, 699775848, 0, 394975360, 0, 0, -463452030, 819564480, 0, 0, -237845844, 0, 347387292, 5534664, 0, 425714432, 45513936, 0, -551761092, 0, 0, 706389120, -380890170, 0, 0, -681185712, 0, -452977056, -472147158, 0, -783742956, 128618784, 0, 42285024, 0, 0, -5766984, -248307120, 0, 0, -422063052, 0, 345885012, -21266832, 0, 79394672, -578772540, 0, -132999552, 0, 0, -81333504, 122219586, 0, 0, -399004584, 0, -345013668, -358973508, 0, 992532420, -119838240, 0, 381673872, 0, 0, 86658822, -196318080, 0, 0, 387133452, 0, -338092758, 19983504, 0, -627648332, 97877808, 0, 1167500832, 0, 0, -104036292, -382875840, 0, 0, 1106919624, 0, -264648384, 569480892, 0, 322333294, 416967264, 0, -308599816, 0, 0, 817629552, -336124584, 0, 0, -225184512, 0, 592489350, 151790496, 0, -460754624, 684189504, 0, 771163414, 0, 0, 26252208, -850104864, 0, 0, -188289960, 0, -49276296, 782513046, 0, -801087364, -343445472, 0, -205855416, 0, 0, -183978648, 736589952, 0, 0, 166966248, 0, -630257058, 626618136, 0, -60187968, 1016047080, 0, 68141344, 0, 0, -561460896, 1199673792, 0, 0, -835885440, 0, 548889696, 912000060, 0, 1008992484, -255911328, 0, 294181936, 0, 0, -1019412, 133473456, 0, 0, 315192318, 0, -263319120, -479024892, 0, 202471632, -884884194, 0, 732551692, 0, 0, 143868960, 345751416, 0, 0, 146492616, 0, -75542544, -207681954, 0, 154210896, -70866576, 0, -468973296, 0, 0, 252160560, -53843040, 0, 0, 688048650, 0, -516555684, 388506240, 0, 262279904, -435325734, 0, -929075718, 0, 0, 86938812, -249988824, 0, 0, 584388240, 0, -139624560, 173993910, 0, -253478748, 976945824, 0, 93211688, 0, 0, 151409196, 476500320, 0, 0, 164722656, 0, -1033464960, -220152792, 0, -46320704, 108265572, 0, -906822792, 0, 0, -615180960, 306447300, 0, 0, 717951408, 0, 211491000, 944865900, 0, 247078720, 521465040, 0, -50160124, 0, 0, -885786732, 896355648, 0, 0, -549168348, 0, -223316352, 962009352, 0, -39337488, -888917976, 0, 706796087, 0, 0, -1010644992, -619099722, 0, 0, 103032480, 0, 412129728, -268579320, 0, -52734672, 4668192, 0, 373920800, 0, 0, 57393414, 111721680, 0, 0, 412817664, 0, -714936240, -523328916, 0, -553413368, 734786676, 0, 110211928, 0, 0, -347026464, 366116121, 0, 0, 919220424, 0, 267211008, 157889100, 0, 935553158, -608933376, 0, -1003414948, 0, 0, 194469660, 100497024, 0, 0, -665330292, 0, 713200572, 766062720, 0, 898685496, -461145870, 0, -331967352, 0, 0, 435952908, -432713826, 0, 0, -7180704, 0, -99009648, 19036800, 0, 461206036, -58861728, 0, 684835344, 0, 0, -225820440, -551991312, 0, 0, -372235200, 0, -196305228, -37270944, 0, -245941808, -784011366, 0, 1937797236, 0, 0, -585687024, -179616168, 0, 0, -1023179388, 0, -961472592, 392770944, 0, -701700296, -864896616, 0, -410361090, 0, 0, -195527520, -447876864, 0, 0, 1143467550, 0, 94158450, 384852984, 0, 44305344, 139755240, 0, 862545614, 0, 0, 372013128, -990567792, 0, 0, -140988768, 0, 451706976, -548206188, 0, -1449409434, 854205120, 0, 71232304, 0, 0, -594794016, -778587624, 0, 0, -124648830, 0, -308246310, -775413648, 0, 608498488, 320107104, 0, 214077196, 0, 0, 1293122880, 489035970, 0, 0, -999530496, 0, -369758520, 205271190, 0, 249832886, 230403888, 0, 232986688, 0, 0, 316066752, -796652352, 0, 0, -155324088, 0, 1059751944, -207851904, 0, -253128960, -66023100, 0, -847114956, 0, 0, 741405420, 314977581, 0, 0, 447807912, 0, 803563632, 254661114, 0, -465331918, -1299627648, 0, -62315280, 0, 0, -954133830, 1281837024, 0, 0, -86293302, 0, 1390227030, -881670072, 0, -420214176, 185849964, 0, -466244032, 0, 0, 37040112, -55775484, 0, 0, -269425152, 0, -257484960, -256187736, 0, -919751040, 1014756408, 0, -136703232, 0, 0, 577425402, -105248160, 0, 0, 89557842, 0, 171197604, 421822344, 0, 197914376, 1111984128, 0, -692879180, 0, 0, 273078216, 500205456, 0, 0, 248033568, 0, 939422016, -545998008, 0, 920955864, -206432640, 0, 538000704, 0, 0, -325011906, -685832904, 0, 0, -447169080, 0, -34675020, -331462260, 0, 33630088, -130928472, 0, -715204508, 0, 0, 386530272, -959537358, 0, 0, -746400000, 0, 274694544, -551325642, 0, 622537526, -974680128, 0, -333009292, 0, 0, -430231932, 109708992, 0, 0, 348745032, 0, -64135206, -59415456, 0], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "15.6.b.a", "char_is_minimal": true, "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, 0], [1, 0], [-4, -1], [0, 0], [6, 9], [0, 0], [0, 0], [42, 24], [-94, -19], [0, 0], [0, 0], [-30, -108], [0, 0], [690, -84], [-696, -162], [0, 0], [602, -99], [-358, 140], [0, 0], [-632, -72], [0, 0], [0, 0], [2496, 570], [-2996, 88], [0, 0], [0, 0], [-912, -270], [0, 0], [5004, 738], [1344, 864], [0, 0], [-5752, -144], [2778, 501], [0, 0], [-1648, -342], [0, 0], [0, 0], [7542, -396], [4112, 992], [0, 0], [0, 0], [-2418, 3024], [0, 0], [-4452, 1344], [-21564, -1890], [0, 0], [10048, 2556], [-976, -1288], [0, 0], [-2371, 2592], [0, 0], [0, 0], [-12492, 4950], [12094, -2012], [0, 0], [0, 0], [-13980, -3510], [0, 0], [-24384, -5664], [-30342, 3348], [0, 0], [-13486, -3168], [26176, 6472], [0, 0], [-41398, -2115], [0, 0], [0, 0], [-312, -4560], [25572, -1122], [0, 0], [0, 0], [-7092, -3240], [0, 0], [-2124, 792], [-21456, -5562], [0, 0], [-18048, -6768], [-58284, -7848], [0, 0], [-24080, -9360], [0, 0], [0, 0], [-56856, -12702], [-70412, 6832], [0, 0], [0, 0], [-11760, -2268], [0, 0], [47964, 12774], [-70758, 4752], [0, 0], [-15372, 11016], [-552, -25644], [0, 0], [32240, 7416], [0, 0], [0, 0], [50568, -15600], [-47540, -10589], [0, 0], [0, 0]]}