# Stored data for newform 200.6.a.i, downloaded from the LMFDB on 24 April 2024.
{"label": "200.6.a.i", "space_label": "200.6.a", "level": 200, "weight": 6, "hecke_orbit": 9, "hecke_orbit_code": 36028797119627464, "dim": 3, "is_polredabs": true, "nf_label": "3.3.47217.1", "trace_hash": 1484118002730258235, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [-1095, -441, -1, 1]]], "qexp_display": "q+\\beta _{1}q^{3}+(-24+\\beta _{1}+\\beta _{2})q^{7}+(50+\\cdots)q^{9}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 7200, "fricke_eigenval": -1, "atkin_lehner_string": "+-", "analytic_conductor": 32.076763962596125, "hecke_ring_index": 80, "level_radical": 10, "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": [200, 1, [151, 101, 177], [1, 1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [2, 5], "conrey_indexes": [1], "field_disc": 47217, "field_disc_factorization": [[3, 1], [15739, 1]], "field_poly": [-24, -38, -1, 1], "hecke_ring_index_factorization": [[2, 4], [5, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.073", "prec": 17}, {"__RealLiteral__": 0, "data": "2.893", "prec": 17}, {"__RealLiteral__": 0, "data": "0.472", "prec": 17}, {"__RealLiteral__": 0, "data": "22.248", "prec": 20}, {"__RealLiteral__": 0, "data": "7.491", "prec": 17}, {"__RealLiteral__": 0, "data": "239.720", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "5.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [5, -1]], "trace_display": [0, 1, 0, -70], "traces": [0, 3, 0, 1, 0, 0, 0, -70, 0, 154, 0, -19, 0, -196, 0, 0, 0, 1223, 0, 1221, 0, 958, 0, -2490, 0, 0, 0, 4123, 0, 11912, 0, 7442, 0, -6969, 0, 0, 0, 14766, 0, 27396, 0, 3223, 0, -41060, 0, 0, 0, 29188, 0, 66423, 0, 43165, 0, -12878, 0, 0, 0, 77791, 0, 64912, 0, 22478, 0, -112916, 0, 0, 0, 26499, 0, 178642, 0, 86676, 0, 8305, 0, 0, 0, 106822, 0, 21982, 0, -71453, 0, -213353, 0, 0, 0, 14952, 0, 182381, 0, 149224, 0, 196470, 0, 0, 0, 76342, 0, -149130, 0, -156302, 0, -217212, 0, 0, 0, -192515, 0, 38442, 0, 186186, 0, 485685, 0, 0, 0, 10056, 0, -551598, 0, -313990, 0, -252323, 0, 0, 0, -403486, 0, -222364, 0, -111332, 0, 742262, 0, 0, 0, -179881, 0, -689595, 0, -640324, 0, -101260, 0, 0, 0, -754563, 0, -326504, 0, 390538, 0, 842386, 0, 0, 0, -266250, 0, -1307546, 0, -427084, 0, 196315, 0, 0, 0, -57788, 0, -132583, 0, -243770, 0, 505960, 0, 0, 0, -108192, 0, -399183, 0, -167706, 0, 8970, 0, 0, 0, -915623, 0, -249686, 0, -50082, 0, 409271, 0, 0, 0, 245082, 0, 347092, 0, -123799, 0, -836336, 0, 0, 0, 1434196, 0, 66563, 0, 241939, 0, -1104372, 0, 0, 0, -186212, 0, 2113867, 0, 679756, 0, 1128412, 0, 0, 0, -70212, 0, 1365452, 0, 450738, 0, -2259886, 0, 0, 0, 1060906, 0, 1285848, 0, 2615283, 0, -908240, 0, 0, 0, 3012500, 0, 1080933, 0, -2028437, 0, -2084662, 0, 0, 0, 1622010, 0, 4307652, 0, 1235760, 0, 1015542, 0, 0, 0, 1063871, 0, 629632, 0, 2785202, 0, -4685352, 0, 0, 0, -1725496, 0, 1558524, 0, 668506, 0, 1218059, 0, 0, 0, 4664338, 0, 1163208, 0, -4260046, 0, -3633270, 0, 0, 0, 139053, 0, 5061656, 0, 5404968, 0, 3097846, 0, 0, 0, -4523583, 0, -1827044, 0, -954490, 0, -378082, 0, 0, 0, 1211444, 0, -732664, 0, -573545, 0, 822737, 0, 0, 0, 6436574, 0, -4941480, 0, -762431, 0, -2806620, 0, 0, 0, -4477239, 0, 1279719, 0, -1805602, 0, 6979708, 0, 0, 0, -5695283, 0, -3014726, 0, -1485012, 0, -630302, 0, 0, 0, -3065690, 0, -6836170, 0, 3961266, 0, 1534030, 0, 0, 0, 1907540, 0, -6094478, 0, -9821540, 0, 5866798, 0, 0, 0, -1007200, 0, 1468455, 0, -5664634, 0, 2887454, 0, 0, 0, -7806712, 0, -6653814, 0, 11102318, 0, 1324708, 0, 0, 0, -9431156, 0, -14452382, 0, -4319865, 0, 5320904, 0, 0, 0, 2927298, 0, 1723263, 0, -10391043, 0, 2335232, 0, 0, 0, 6159, 0, -1326415, 0, 3382332, 0, 1858424, 0, 0, 0, -18211388, 0, -3799284, 0, 623942, 0, 9193943, 0, 0, 0, 10612698, 0, -8361456, 0, -8603598, 0, -14488377, 0, 0, 0, 13216248, 0, -4049245, 0, 6999705, 0, 4752942, 0, 0, 0, -6101277, 0, 536335, 0, -6631564, 0, 8524300, 0, 0, 0, -11439412, 0, 11216794, 0, 8141554, 0, 6585044, 0, 0, 0, 1641436, 0, -4965250, 0, 9125400, 0, -23854244, 0, 0, 0, 9076706, 0, 11887313, 0, -9199972, 0, 8241064, 0, 0, 0, 12123768, 0, 14005284, 0, -12243428, 0, -11380860, 0, 0, 0, -7608397, 0, 7633526, 0, 31482046, 0, -2110667, 0, 0, 0, 1405196, 0, -9824328, 0, -6154905, 0, -8276647, 0, 0, 0, 13572106, 0, 23357895, 0, -1296672, 0, -3072948, 0, 0, 0, 18595331, 0, 13922745, 0, 12652144, 0, -18858718, 0, 0, 0, -14449375, 0, 18849636, 0, 2387336, 0, 13553956, 0, 0, 0, 19349372, 0, 869168, 0, -12458565, 0, -21547432, 0, 0, 0, 34550170, 0, 5706467, 0, 19215684, 0, -8820550, 0, 0, 0, -14408791, 0, 11664621, 0, 1351922, 0, 1688814, 0, 0, 0, -15875073, 0, 18666638, 0, 13482622, 0, -11216171, 0, 0, 0, 8909052, 0, -3697114, 0, 14493241, 0, -11270614, 0, 0, 0, 4512432, 0, 5036496, 0, -25668976, 0, 24237962, 0, 0, 0, 32023402, 0, 13315044, 0, -9936314, 0, -7819258, 0, 0, 0, -13372959, 0, -7453098, 0, 29316546, 0, -12046311, 0, 0, 0, -20287668, 0, -16496424, 0, -464754, 0, 8165052, 0, 0, 0, 526764, 0, 4607200, 0, -25107180, 0, -2714198, 0, 0, 0, -18582914, 0, 9520271, 0, 6818296, 0, 28876980, 0, 0, 0, -4230544, 0, -22214796, 0, -17842558, 0, -1487986, 0, 0, 0, -963328, 0, -15903660, 0, -23827068, 0, -6357303, 0, 0, 0, 33523044, 0, -48378264, 0, 9195281, 0, -8121612, 0, 0, 0, -36067253, 0, -16428346, 0, 12083660, 0, 48605298, 0, 0, 0, -29939780, 0, -12391828, 0, -6616988, 0, 34636292, 0, 0, 0, -15450216, 0, -5191510, 0, 22631960, 0, 33779393, 0, 0, 0, -25594440, 0, -27576521, 0, -50241876, 0, -31049092, 0, 0, 0, 12860965, 0, -1295180, 0, -16909524, 0, 7704774, 0, 0, 0, -413502, 0, -48226970, 0, -1229256, 0, -23100335, 0, 0, 0, -43166864, 0, -27743538, 0, 2460503, 0, 64103500, 0, 0, 0, -4285952, 0, -18769825, 0, -30357090, 0, 10984192, 0, 0, 0, -44285172, 0, 9223825, 0, 23796636, 0, 16501176, 0, 0, 0, 16156756, 0, -18630750, 0, -52542378, 0, -19111144, 0, 0, 0, 17129614, 0, -1901772, 0, 18944390, 0, 12623343, 0, 0, 0, 9801504, 0, -23901162, 0, 27315460, 0, -23014666, 0, 0, 0, -6932876, 0, -650448, 0, 8905726, 0, 36233740, 0, 0, 0, -41445089, 0, -16796732, 0, -18231608, 0, -51629013, 0, 0, 0, 2674770, 0, 60127968, 0, -11245255, 0, 2932478, 0, 0, 0, 22956780, 0, 4182961, 0, -2103492, 0, 15517166, 0, 0, 0, 19633607, 0, -1379867, 0, 13313926, 0, 16494352, 0, 0, 0, 87229688, 0, 4445442, 0, 6124876, 0, -7671724, 0, 0, 0, -44176644, 0, 44393662, 0, 70441850, 0, -27843079, 0, 0, 0, -7329556, 0, 53022524, 0, 32278269, 0, -66337364, 0, 0, 0, -8269848, 0, 33104336, 0, -25015478, 0, -5714152, 0, 0, 0, 51651268, 0, 44463004, 0, -24632004, 0, -12643535, 0, 0, 0, 110128936, 0, 40098710, 0, -7268813, 0, -25514544, 0, 0, 0, -39241736, 0, -21262918, 0, 8239665, 0, -47005886, 0, 0, 0, 36908473, 0, 11321962, 0, 52560924, 0, -84325778, 0, 0, 0, -8176992, 0, 94466196, 0, 36466748, 0, 55573179, 0, 0, 0, -31837848, 0, 76018642, 0, -24335569, 0, 39780310, 0, 0, 0, 58745456, 0, 96357235, 0, 25632893, 0, -29180778, 0, 0, 0, 20470619, 0, -13746477, 0, -24484564, 0, -105270018, 0, 0, 0, 122930408, 0, -36423848, 0, 15397806, 0, -59078717, 0, 0, 0, 24937836, 0, 8571918, 0, 21570808, 0, 202448, 0, 0, 0, -171537026, 0, 18349887, 0, 115259011, 0, 143762704, 0, 0, 0, 72848502, 0, 6386879, 0, 5394958, 0, -51480150, 0, 0, 0, 44238072, 0, 78636500, 0, -43252554, 0, -10071871, 0, 0, 0, 97677814, 0, -28752768, 0, -27398457, 0, -61901392, 0, 0, 0, -83785778, 0, 53553357, 0, -9316957, 0, 41075196, 0, 0, 0, -52702132, 0, -125608170, 0, -15408158, 0, -13738264, 0, 0, 0, 23963594, 0, -28737626, 0, -1661636, 0, 38632656, 0, 0, 0, -126489358, 0, 44874268, 0, -135174680, 0, -44451498, 0, 0, 0, 28591604, 0, -21916340, 0, 99823913, 0, 887666, 0, 0, 0, 62938829, 0, -149654188, 0, -10008260, 0, 4201132, 0, 0, 0, 9572431, 0, 16452780, 0, -60946434, 0, 231559732, 0, 0, 0, 8333406, 0, -38085670, 0, 39002080, 0, 17478429, 0, 0, 0, -262357458, 0, -31035733, 0, 128170272, 0, 34731116, 0, 0, 0, -57555035, 0, -55534889, 0, -194227926, 0, -97500964, 0, 0, 0, 67565748, 0, -43026166, 0, -84411928, 0, -13123411, 0, 0, 0, 14613060, 0, -96853198, 0, -52738612, 0, 77489907, 0, 0, 0, -54896850, 0, -128758376, 0, -27934909, 0, 212813290, 0, 0, 0, -46915365, 0, -105075320, 0, 94147594, 0, -145911538, 0, 0, 0, -26996291, 0, -15461400, 0, 3157316, 0, 113171358, 0, 0, 0, -96176492, 0, 6943174, 0, -33627335, 0, 181882941, 0, 0, 0, -96592380, 0, 65684280, 0, 49207856, 0, -35666354, 0, 0, 0, 69931201, 0, -202262300, 0, -47595114, 0, 16988798, 0, 0, 0, -9025931, 0, -125564842, 0, -77325356, 0, -143041806, 0, 0, 0, 147925424, 0, 19915104, 0, -40994147, 0, -54346149, 0, 0, 0, -189026272, 0, -55812199, 0, 11288262, 0, 194468446, 0, 0, 0, -144397213, 0, -50143660, 0, -147674824, 0, 155838708, 0, 0, 0, 274698292, 0, 69726548, 0, -57738102, 0, 71052525, 0, 0, 0, -156864674, 0, 40551010, 0, 95402700, 0, -134547756, 0, 0, 0, -46999272, 0, 5561562, 0, 39434096, 0, -233024414, 0, 0, 0, -30207290, 0, -45987155, 0, 195780534, 0, -34738984, 0, 0, 0, -53718919, 0, -14514802, 0, 16927582, 0, 71123304, 0, 0, 0, 115013056, 0, 235438162, 0, -162971885, 0, 114225711, 0, 0, 0, -74997390, 0, -19104699, 0, 5930679, 0, -157076344, 0, 0, 0, 191318212, 0, -20884336, 0, 132709776, 0, -4479770, 0, 0, 0, 154267601, 0, 28359996, 0, -189024398, 0, 56069067, 0, 0, 0, -104240192, 0, 91373772, 0, 237010679, 0, 125496992, 0, 0, 0, 89636758, 0, 75446637, 0, 201787969, 0, -187321186, 0, 0, 0, -187200473, 0, 176936204, 0, -187778790, 0, -67451908, 0, 0, 0, 364434103, 0, 16268356, 0, -55422540, 0, -445215016, 0, 0, 0, 95934510, 0, 99049564, 0, 62785108, 0, 87774908, 0, 0, 0, -31879762, 0, 41645939, 0, -6634597, 0, 191581012, 0, 0, 0, 255201736, 0, 149897196, 0, 212997480, 0, -104557162, 0, 0, 0, -197991527, 0, -6938118, 0, 43250242, 0, -90418331, 0, 0, 0, 47116602, 0, 270744088, 0, 95979924, 0, -30521304, 0, 0, 0, 126450236, 0, 149977240, 0, -101142545, 0, -269895146, 0, 0, 0, -63385288, 0, 74738951, 0, -15993402, 0, 173677690, 0, 0, 0, 270655994, 0, -39406428, 0, -205801062, 0, -258707644, 0, 0, 0, -56901382, 0, 201939720, 0, 202983597, 0, 592176, 0, 0, 0, 50100630, 0, -121964225, 0, 117870984, 0, -9896736, 0, 0, 0, -98411524, 0, 100378275, 0, 178687762, 0, 53795320, 0, 0, 0, 165940409, 0, 268865964, 0, 99135292, 0, 146335337, 0, 0, 0, 159655350, 0, -22361142, 0, 96813998, 0, 106013225, 0, 0, 0, -115322286, 0, -43028109, 0, -234184625, 0, -455503094, 0, 0, 0, -23982672, 0, 177731029, 0, -120857514, 0, -109573126, 0, 0, 0, -94361656, 0, -77954612, 0, 29563956, 0, -88013719, 0, 0, 0, -94998864, 0, -44936816, 0, -308671480, 0, 312006925, 0, 0, 0, 173767374, 0, -191290485, 0, 31016812, 0, 85305160, 0, 0, 0, -15276455, 0, 63307175, 0, 360986430, 0, -41830896, 0, 0, 0, 125017901, 0, -7365912, 0, -62473896, 0, 90424224, 0, 0, 0, -24212576, 0, -132903948, 0, 195445553, 0, 92319400, 0, 0, 0, -131800202, 0, 166615401, 0, -93275218, 0, 63800432, 0, 0, 0, 11811627, 0, -188828529, 0, -89780200, 0, 256595408, 0, 0, 0, -228005513, 0, -392210956, 0, -53253412, 0, -394803768, 0, 0, 0, -46365714, 0, -187377704, 0, -231246701, 0, -301024212, 0, 0, 0, 48521550, 0, -129682818, 0, -95935224, 0, 372554472, 0, 0, 0, -5960017, 0, -212922932, 0, -87667850, 0, 295334598, 0, 0, 0, -7961877, 0, 38827120, 0, -50075612, 0, 358038384, 0, 0, 0, -527679984, 0, 246382594, 0, -50424704, 0, -84042786, 0, 0, 0, 99154426, 0, -92249448, 0, 134096123, 0, -32264340, 0, 0, 0, -170719401, 0, -125761095, 0, -143238560, 0, 155659440, 0, 0, 0, -505773983, 0, -283793654, 0, 236157760, 0, 171868060, 0, 0, 0, 274312138, 0, -245543644, 0, 42386074, 0, -53800487, 0, 0, 0, -228253174, 0, -443408072, 0, -299707037, 0, 217872838, 0, 0, 0, 269653170, 0, -127801944, 0, -124097964, 0, -213590346, 0, 0, 0, -239328865, 0, 218800074, 0, -271119052, 0, 479301829, 0, 0, 0, -136911638, 0, -525534160, 0, 593997, 0, 221667116, 0, 0, 0, 224242650, 0, 177713744, 0, -98060372, 0, -89668340, 0, 0, 0, -430729274, 0, -15848729, 0, -226358836, 0, -272427812, 0, 0, 0, -3635575, 0, -180782024, 0, 507693720, 0, -297287443, 0, 0, 0, 206017250, 0, -471388980, 0, -248025158, 0, 67681763, 0, 0, 0, 6862932, 0, 29756003, 0, 66591633, 0, 487878390, 0, 0, 0, 118605244, 0, 157606825, 0, -75810480, 0, 191190708, 0, 0, 0, -404728224, 0, 124503232, 0, 340140502, 0, 424760496, 0, 0, 0, -19723284, 0, -211350610, 0, -190630572, 0, -400787846, 0, 0, 0, 94542680, 0, 362119167, 0, -159916082, 0, 37552162, 0, 0, 0, -11482276, 0, -80087625, 0, 12134988, 0, -113323610, 0, 0, 0, -173853261, 0, -66378142, 0, -110967256, 0, 15190714, 0, 0, 0, 213440072, 0, 22782256, 0, -252184806, 0, -611828800, 0, 0, 0, 314456610, 0, -159397338, 0, 91462196, 0, 265642630, 0, 0, 0, 88245020, 0, -9086070, 0, 325918278, 0, 147746008, 0, 0, 0, -406049412, 0, 440771518, 0, 360090612, 0, 262165137, 0, 0, 0, 149172804, 0, -9990194, 0, 464408721, 0, -444127686, 0, 0, 0, 62316788, 0, 377772132, 0, 306275419, 0, -428830236, 0, 0, 0, 351564256, 0, 479506512, 0, -691800732, 0, 43655800, 0, 0, 0, -112541232, 0, 355843898, 0, 63676730, 0, -258201144, 0, 0, 0, -125149044, 0, -219381666, 0, -669271596, 0, 69578152, 0, 0, 0, 828475788, 0, 19126807, 0, -102594839, 0, 379744512, 0, 0, 0, 90174029, 0, 114490268, 0, 355567914, 0, -689022536, 0, 0, 0, -372398089, 0, 285297192, 0, 441072634, 0, 243444667, 0, 0, 0, -14875630, 0, -114068800, 0, 821609904, 0, -660271691, 0, 0, 0, 204721416, 0, 655868859, 0, 16790259, 0, -123224010, 0, 0, 0, 418126147, 0, 491761946, 0, -390848880, 0, -61373264, 0, 0, 0, -121482388, 0, -32987398, 0, -79764768, 0, -435926765, 0, 0, 0, 703530332, 0, 230493826, 0, 108437432, 0, -137422008, 0, 0, 0, 80652218, 0, 30192123, 0, -258576244, 0, 358599666, 0, 0, 0, -117665550, 0, 253031712, 0, 144320616, 0, 153125566, 0, 0, 0, 254914584, 0, 160283670, 0, 925973334, 0, 89558371, 0, 0, 0, 12620674, 0, 114523014, 0, -130551757, 0, 60035568, 0, 0, 0, 677957820, 0, 302460018, 0, -422263415, 0, -997625840, 0, 0, 0, -104073700, 0, 137908677, 0, 269701522, 0, 32456212, 0, 0, 0, -388602324, 0, -105591354, 0, 663323448, 0, 220083581, 0, 0, 0, -87402984, 0, 152183084, 0, -329270732, 0, -285820567, 0, 0, 0, -63871868, 0, -239614519, 0, -220010508, 0, -24945842, 0, 0, 0, 215425783, 0, 653369580, 0, 205373052, 0, -182697238, 0, 0, 0, 40959171, 0, 593511614, 0, -417307632, 0, 178444686, 0, 0, 0, 77773806, 0, -681154534, 0, 308516022, 0, 91977448, 0, 0, 0, 60494246, 0, 171519290, 0, -493056240, 0, -21311318, 0, 0, 0, -549221868, 0, 393349971, 0, 3223832, 0, 448608480, 0, 0, 0, -172769987, 0, -518454644, 0, 474604548, 0, -992486380, 0, 0, 0, -294495704, 0, -557056636, 0, -64862760, 0, 413331180, 0, 0, 0, 912592786, 0, 184355427, 0, 9126471, 0, 159658484, 0, 0, 0, 637177612, 0, -154787560, 0, 442665092, 0, 420275928, 0, 0, 0, -509504084, 0, -510417390, 0, -878583380, 0, 351147280, 0, 0, 0, -237270362, 0, 380476398, 0, -334521801, 0, 2330725, 0, 0, 0, 274449490, 0, -271831904, 0, -79346943, 0, -220162056, 0, 0, 0, -578913108, 0, -54429734, 0, -721596162, 0, 425914182, 0, 0, 0, -594419296, 0, -632736848, 0, -203167152, 0, -816254202, 0, 0, 0, -122602068, 0, 128771240, 0, 1084967757, 0, -47436643, 0, 0, 0, -275295558, 0, -1224900508, 0, 35913264, 0, 674551784, 0, 0, 0, 26478771, 0, 98722310, 0, 459849408, 0, 963551988, 0, 0, 0, -581580507, 0, 754045530, 0, 102645396, 0, 331418700, 0, 0, 0, -394876130, 0, -486630320, 0, 56354197, 0, 992740420, 0, 0, 0, 773085892, 0, -990317045, 0, -889762632, 0, -797128398, 0, 0, 0, -481538813, 0, -568837860, 0, -54983420, 0, 54690948, 0, 0, 0, -154708941, 0, -446016312, 0, -216058808, 0, -282342536, 0, 0, 0, -41360382, 0, -346369618, 0, -1062101748, 0, -42022959, 0, 0, 0, 105250164, 0, -293570520, 0, -482243513, 0, 202413042, 0, 0, 0, -540370538, 0, 824289960, 0, -50716270, 0, 549255588, 0, 0, 0, 324956932, 0, -725922186, 0, 323586778, 0, 691683321, 0, 0, 0, -306100660, 0, -294194484, 0, 781932711, 0, 215095973, 0, 0, 0, -808285160, 0, -264142563, 0, 207580369, 0, -350512930, 0, 0, 0, -402759606, 0, 282752976, 0, 687008256, 0, 369156572, 0, 0, 0, -199953582, 0, -969212218, 0, -340659356, 0, -385983396, 0, 0, 0, -79523682, 0, -153917764, 0, -993635911, 0, 568421932, 0, 0, 0, 259135702, 0, 260290740, 0, -1590441844, 0, -86170076, 0, 0, 0, 409852104, 0, -1058397460, 0, 369132970, 0, 443739722, 0, 0, 0, -433227857, 0, -409504828, 0, -383303428, 0, -7167695, 0, 0, 0, -1016235312, 0, 570510750, 0, 595564717, 0, -70694024, 0, 0, 0, 237518780, 0, 710182324, 0, 1103372312, 0, -633759056, 0, 0, 0, 205673460, 0, -272675415, 0, -754571178, 0, 195547368, 0, 0, 0, 927079860, 0, 139632140, 0, -216939342, 0, -737137804, 0, 0, 0, 375785024, 0, -182078956, 0, 107983743, 0, 86188435, 0, 0, 0, -438773700, 0, -793499764, 0, 738090588, 0, 934048760, 0, 0, 0, -693973376, 0, 816482901, 0, -411113660, 0, 247090124, 0, 0, 0, -298800614, 0, 320215876, 0, 333266768, 0, 236196372, 0, 0, 0, 298126730, 0, -96182438, 0, 568670600, 0, 49403982, 0, 0, 0, 626786402, 0, 259083480, 0, -898952467, 0, -266249798, 0, 0, 0, 861560751, 0, 395912397, 0, 760048056, 0, -508881476, 0, 0, 0, -195992240, 0, 56900512, 0, -501589742, 0, 178493953, 0, 0, 0, 237205482, 0, 78882858, 0, 614994800, 0, -479100751, 0, 0, 0, -180226554, 0, -168424365, 0, 351529572, 0, -170382924, 0, 0, 0, -24833562, 0, 286175942, 0, 98832622, 0, -1033228456, 0, 0, 0, 794732616, 0, 522807288, 0, 589966996, 0, -476843229, 0, 0, 0, 430473196, 0, 607786816, 0, -533175189, 0, 108800030, 0, 0, 0, -401951040, 0, 1202024155, 0, -152554451, 0, -451426510, 0, 0, 0, -611790219, 0, 106610120, 0, -1147196028, 0, 469753642, 0, 0, 0, 438393908, 0, 1115228606, 0, 794098384, 0, 243053040, 0, 0, 0, 1058778432, 0, 1129653716, 0, -772810012, 0, -132890840, 0, 0, 0, 193279786, 0, -318175903, 0, 1079609808, 0, -274856228, 0, 0, 0, 942157200, 0, -1336427981, 0, 1618232538, 0, -1595106290, 0, 0, 0, 159385623, 0, 1184942000, 0, -19708150, 0, 430326535, 0, 0, 0, -230972356, 0, 64406660, 0, 287213788, 0, -1072809876, 0, 0, 0, -304072142, 0, 615467603, 0, -382854219, 0, 66951028, 0, 0, 0, 116311332, 0, 278352843, 0, -234431066, 0, -430871540, 0, 0, 0, 593777687, 0, 73382992, 0, -766586216, 0, -503889273, 0, 0, 0, 277409506, 0, 682237038, 0, 30422637, 0, -754737650, 0, 0, 0, -219846556, 0, 312273648, 0, 1666648527, 0, 603345472, 0, 0, 0, 1268024603, 0, 977059944, 0, -247654412, 0, 510955220, 0, 0, 0, 462296958, 0, 424586352, 0, 61097920, 0, 786565347, 0, 0, 0, -331366794, 0, 242369812, 0, 21383310, 0, -271439124, 0, 0, 0, 322072338, 0, 1384097149, 0, 1582363715, 0, 296601488, 0, 0, 0, -416502908, 0, -257620197, 0, -640815824, 0, -1749514556, 0, 0, 0, -165734970, 0, -932838326, 0, 529325656, 0, 163749629, 0, 0, 0, 127770960, 0, -33129356, 0, 445765360, 0, -125759161, 0, 0, 0, -1062368148, 0, 1220770140, 0, -1067369100, 0, 405085592, 0, 0, 0, 1032117781, 0, -862451991, 0, -1480348022, 0, -1727756926, 0, 0, 0, 765952808, 0, 271855270, 0, -561223632, 0, 282509093, 0, 0, 0, 1050464646, 0, -549906418, 0, 159958508, 0, 1232712869, 0, 0, 0, -946165166, 0, -191995235, 0, 1839041616, 0, -2642982, 0, 0, 0, -1111610037, 0, -1033792784, 0, 738546320, 0, -609365970, 0, 0, 0, 1321130734, 0, 1257623528, 0, 1096328772, 0, -505262921, 0, 0, 0, 260869794, 0, -27369438, 0, -1088082844, 0, 827483052, 0, 0, 0, 8356946, 0, -395989968, 0, -644171687, 0, 1138772126, 0, 0, 0, -614467479, 0, -243269921, 0, -638425912, 0, -262694998, 0, 0, 0, 508707912, 0, 226611114, 0, -718526928, 0, 1234919311, 0, 0, 0, -260463864, 0, -687449696, 0, -845010736, 0, -1593999728, 0, 0, 0, -3469157848, 0, -1170092943, 0, -164174767, 0, 478421498, 0, 0, 0, 1027007216, 0, 20580622, 0, 351081054, 0, -376909254, 0, 0, 0, -981878368, 0, -777189738, 0, -374518908, 0, 693329677, 0, 0, 0, 949772334, 0, 284190382, 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": "200.6.a.h", "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, 0], [1, 0, 0], [0, 0, 0], [0, 1, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-24, 1, 1], [0, 0, 0], [50, 5, -1], [0, 0, 0], [-4, -8, 1], [0, 0, 0], [-76, 31, 1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [393, 49, -5], [0, 0, 0], [376, 87, 6], [0, 0, 0], [370, -147, -5], [0, 0, 0], [-896, 204, -6], [0, 0, 0], [0, 0, 0], [0, 0, 0], [1388, -40, -1], [0, 0, 0], [3968, 13, -5], [0, 0, 0], [2408, 220, -2], [0, 0, 0], [-2267, -172, 4], [0, 0, 0], [0, 0, 0], [0, 0, 0], [4842, 201, 39], [0, 0, 0], [9160, -49, -35], [0, 0, 0], [1157, -292, 44], [0, 0, 0], [-13620, -241, 41], [0, 0, 0], [0, 0, 0], [0, 0, 0], [9984, -733, -31], [0, 0, 0], [22413, -888, 72], [0, 0, 0], [13972, 1278, -29], [0, 0, 0], [-3778, -1468, -76], [0, 0, 0], [0, 0, 0], [0, 0, 0], [25953, 43, -111], [0, 0, 0], [21676, -151, 35], [0, 0, 0], [7538, 19, -155], [0, 0, 0], [-37624, 32, -76], [0, 0, 0], [0, 0, 0], [0, 0, 0], [8852, -162, 105], [0, 0, 0], [59310, 892, -180], [0, 0, 0], [29280, -1299, 135], [0, 0, 0], [1895, 2363, 257], [0, 0, 0], [0, 0, 0], [0, 0, 0], [35410, 455, 137], [0, 0, 0], [6896, 1181, 113], [0, 0, 0], [-23947, 101, 287], [0, 0, 0], [-71540, 1310, -43], [0, 0, 0], [0, 0, 0], [0, 0, 0], [3424, 4673, 7], [0, 0, 0], [60427, 1141, -41], [0, 0, 0], [51568, -5350, -130], [0, 0, 0], [64306, 3764, -212], [0, 0, 0], [0, 0, 0], [0, 0, 0], [27090, -4846, -82], [0, 0, 0], [-49116, -1695, -87], [0, 0, 0]]}