# Stored data for newform 1690.4.a.a, downloaded from the LMFDB on 16 April 2024. {"label": "1690.4.a.a", "space_label": "1690.4.a", "level": 1690, "weight": 4, "hecke_orbit": 1, "hecke_orbit_code": 67110554, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 2214693918050563640, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [8, 1]], [7, [-4, 1]]], "qexp_display": "q-2q^{2}-8q^{3}+4q^{4}-5q^{5}+2^{4}q^{6}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 27040, "fricke_eigenval": 1, "atkin_lehner_string": "+++", "analytic_conductor": 99.71322790970164, "hecke_ring_index": 1, "level_radical": 130, "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": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [1690, 1, [677, 171], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 5, 13], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.039", "prec": 17}, {"__RealLiteral__": 0, "data": "0.983", "prec": 17}, {"__RealLiteral__": 0, "data": "0.097", "prec": 17}, {"__RealLiteral__": 0, "data": "1.924", "prec": 17}, {"__RealLiteral__": 0, "data": "0.307", "prec": 17}, {"__RealLiteral__": 0, "data": "4.709", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [5, 1], [13, 1]], "trace_display": [-2, -8, -5, 4], "traces": [0, 1, -2, -8, 4, -5, 16, 4, -8, 37, 10, -12, -32, 0, -8, 40, 16, 66, -74, 100, -20, -32, 24, 132, 64, 25, 0, -80, 16, -90, -80, -152, -32, 96, -132, -20, 148, 34, -200, 0, 40, 438, 64, 32, -48, -185, -264, 204, -128, -327, -50, -528, 0, 222, 160, 60, -32, -800, 180, -420, 160, 902, 304, 148, 64, 0, -192, 1024, 264, -1056, 40, -432, -296, -362, -68, -200, 400, -48, 0, -160, -80, -359, -876, -72, -128, -330, -64, 720, 96, -810, 370, 0, 528, 1216, -408, -500, 256, -1106, 654, -444, 100, -258, 1056, -988, 0, 160, -444, -24, -320, -950, -120, -272, 64, -1038, 1600, -660, -360, 0, 840, 264, -320, -1187, -1804, -3504, -608, -125, -296, -124, -128, -256, 0, 132, 384, 400, -2048, 400, -528, 1254, 2112, -2860, -80, -1632, 864, 0, 592, 450, 724, 2616, 136, -750, 400, 448, -800, 2442, 96, 760, 0, 2246, 320, -1776, 160, 528, 718, 568, 1752, -480, 144, 1524, 256, 0, 660, 3700, 128, 3702, -1440, 100, -192, 3360, 1620, 3180, -740, -2098, 0, -7216, -1056, -170, -2432, -792, 816, -320, 1000, 4392, -512, 2158, 2212, 0, -1308, 1074, 888, 2840, -200, -8192, 516, -360, -2112, -2190, 1976, 4884, 0, -1200, -320, -2668, 888, 3456, 48, -160, 640, -608, 1900, 2896, 240, 0, 544, -1772, -128, 925, 2076, 2784, -3200, -350, 1320, 384, 720, 1962, 0, -1020, -1680, 1280, -528, 4320, 640, 478, 2374, 5032, 3608, 1635, 7008, 0, 1216, 576, 250, 2652, 592, -1584, 248, 2640, 256, -2334, 512, 136, 0, -3330, -264, -3948, -768, -1110, -800, 6480, 4096, 1590, -800, -4952, 1056, 0, -2508, -300, -4224, 1646, 5720, -5624, 160, 1158, 3264, 6992, -1728, 4000, 0, 1752, -1184, -557, -900, 8848, -1448, 258, -5232, 2100, -272, 960, 1500, 0, -800, 128, -896, 2064, 1600, -4510, -4884, 8944, -192, 7904, -1520, 1392, 0, -5878, -4492, -740, -640, -10326, 3552, 1080, -320, 192, -1056, 6600, -1436, 0, -1136, 7600, -3504, 816, 960, 4228, -288, 1258, -3048, -5120, -512, 1106, 0, 8304, -1320, 1824, -7400, -2680, -256, 5280, -7404, 9336, 2880, 11770, -200, 0, 384, -8322, -6720, 2160, -3240, -2112, -6360, -10680, 1480, 3141, 4196, 9496, 0, 1810, 14432, -5884, 2112, 16206, 340, 888, 4864, -2098, 1584, 1000, -1632, 0, 640, -3860, -2000, 992, -8784, 9588, 1024, 240, -4316, 1184, -4424, -13410, 0, 8712, 2616, -1056, -2148, 800, -1776, 13114, -5680, -3200, 400, 5838, 16384, 0, -1032, 1795, 720, -408, 4224, -9530, 4380, -10032, -3952, -1680, -9768, 360, 0, 22880, 2400, 7260, 640, -12062, 5336, 7548, -1776, 1650, -6912, 3608, -96, 0, 320, 13608, -1280, -3838, 1216, -3600, -3800, 13200, -5792, 7400, -480, -12099, 0, 8352, -1088, 4050, 3544, 6000, 256, -10770, -1850, -5256, -4152, -3584, -5568, 0, 6400, 6694, 700, -5280, -2640, 3018, -768, -14492, -1440, -6080, -3924, 7776, 0, 4096, 2040, -17968, 3360, -384, -2560, 2500, 1056, 8214, -8640, 13680, -1280, 0, -956, -4224, -4748, 5530, -10064, -7916, -7216, -4544, -3270, 13932, -14016, -5940, 0, 2220, -2432, -1728, -1152, 8260, -500, -12192, -5304, -11148, -1184, 1290, 3168, 0, -496, 9690, -5280, -1448, -512, -8000, 4668, 4940, -1024, -2448, -272, -29616, 0, -16038, 6660, 992, 528, -800, 7896, -10032, 1536, 5257, 2220, -15540, 1600, 0, -12960, 120, -8192, -25440, -3180, 3924, 1600, -7142, 9904, 16784, -2112, 4750, 0, 7616, 5016, 33374, 600, -9000, 8448, -640, -3292, 1360, -11440, 10314, 11248, 0, -320, 6336, -2316, -7128, -6528, 5190, -13984, -1436, 3456, 2010, -8000, -23188, 0, -35136, -3504, 3300, 2368, -22466, 1114, -17264, 1800, -288, -17696, -2664, 2896, 0, -516, -22776, 10464, -15200, -4200, -8592, 544, 21198, -1920, -1320, -3000, -22720, 0, 15960, 1600, 5882, -256, 37888, 1792, 5935, -4128, 8516, -3200, 2880, 9020, 0, 9768, -8462, -17888, 17520, 384, 11094, -15808, -2180, 3040, -10560, -2784, -3240, 0, 625, 11756, 9600, 8984, 2244, 1480, 26848, 1280, 21344, 20652, 620, -7104, 0, -2160, -15984, 640, 26322, -384, 10168, 2112, 1280, -13200, -23604, 2872, 5040, 0, 4864, 2272, 16422, -15200, -660, 7008, -13394, -1632, -26100, -1920, 3058, -8456, 0, 576, -2000, -2516, -11880, 6096, 14176, 10240, -10824, 1024, 10802, -2212, -2000, 0, -10674, -16608, -4424, 2640, -22272, -3648, 28608, 14800, -6270, 5360, 2800, 512, 0, -10560, 2428, 14808, -1776, -18672, 14300, -5760, 28908, -23540, -15696, 400, -6618, 0, 3400, -768, 8160, 16644, -1032, 13440, -20510, -4320, -5920, 6480, -20064, 4224, 0, 12720, -34560, 21360, 31680, -2960, -3952, -6282, -3824, -8392, -2250, -18992, 13196, 0, -30563, -3620, 2112, -28864, -8102, 11768, -13080, -4224, -12288, -32412, 12580, -680, 0, -1776, -29892, -9728, 3750, 4196, -2664, -3168, -96, -2000, -40408, 3264, -21216, 0, -2240, -1280, 32366, 7720, 12672, 4000, 17238, -1984, -3800, 17568, -12210, -19176, 0, -2048, -10850, -480, 18672, 8632, -9102, -2368, -3800, 8848, -1088, 26820, 43800, 0, 5184, -17424, 7200, -5232, -11230, 2112, 25504, 4296, 31584, -1600, -4152, 3552, 0, -26228, 8880, 11360, 14166, 6400, 13464, -800, -29970, -11676, 4344, -32768, -2640, 0, -12720, 2064, 33210, -3590, -39212, -1440, 39616, 816, -2840, -8448, 3200, 19060, 0, -8760, -6222, 20064, 31172, 7904, 2400, 3360, 264, 19536, -29050, -720, -13168, 0, -21582, -45760, -7620, -4800, 12160, -14520, 21720, -1280, -16289, 24124, -9264, -10672, 0, -15096, -4748, 3552, -55936, -3300, 4488, 13824, 6658, -7216, -18500, 192, -13974, 0, 23780, -640, -14016, -27216, 12228, 2560, -18510, 7676, 4456, -2432, 1920, 7200, 0, 7600, -40922, -26400, -500, 11584, -11606, -14800, -2064, 960, -32958, 24198, 8072, 0, -16800, -16704, 15756, 2176, -496, -8100, 4308, -7088, 20400, -12000, -15900, -512, 0, 21540, 13680, 3700, 14652, 10512, -1024, 8304, 10490, 7168, 18776, 11136, -9546, 0, -20568, -12800, 864, -13388, 36080, -1400, 528, 10560, -6280, 5280, -71552, -6036, 0, 1536, 850, 28984, -36556, 2880, 20430, 12160, -32700, 7848, -11136, -15552, 3960, 0, 8906, -8192, 47024, -4080, 17418, 35936, 57816, -6720, 1600, 768, 2544, 5120, 0, -5000, 82608, -2112, 15402, -16428, -21960, 17280, -8640, -27360, 5016, 2560, -6687, 0, -888, 1912, -10790, 8448, 49444, 9496, -52800, -11060, -25188, 20128, -11440, 15832, 0, 14432, -2946, 9088, 9720, 6540, -35150, -27864, -15012, 28032, -5370, 11880, -6528, 0, 4224, -4440, -5128, 4864, -33824, 3456, -14200, 2304, -49714, -16520, -2720, 1000, 0, 24384, -27720, 10608, 40960, 22296, 22200, 2368, 16270, -2580, -8848, -6336, -21378, 0, 1800, 992, -38406, -19380, -1620, 10560, 6298, 2896, -14592, 1024, 10950, 16000, 0, -9336, 21440, -9880, 45792, 2048, 27958, 4896, -24420, 544, 59532, 59232, 35600, 0, -74688, 32076, -3000, -13320, 6000, -1984, -94160, -1056, 50730, 1600, 6868, -15792, 0, 20064, 13340, -3072, 1792, -10514, 66576, -4440, -21342, 31080, -12748, -3200, -17280, 0, 13272, 25920, -12010, -240, 9768, 16384, -3060, 50880, 800, 6360, 85440, -7848, 0, -3200, 26928, 14284, -25128, -19808, 3040, -33568, -2996, 4224, -43919, -9500, 25092, 0, 67502, -15232, -14480, -10032, -52266, -66748, 8984, -1200, 47072, 18000, -56652, -16896, 0, 1280, -35040, 6584, 17550, -2720, 3096, 22880, -7104, -20628, 8860, -22496, -51514, 0, 16784, 640, -42000, -12672, -49832, 4632, -4625, 14256, -43164, 13056, -3050, -10380, 0, 27968, 11856, 2872, -13920, -6912, 30880, -4020, 67584, 16000, 2272, 46376, -4588, 0, 1750, 70272, -5168, 7008, -76704, -6600, -30552, -4736, -10558, 44932, -1920, -2228, 0, 34528, 90200, -3600, -2560, 576, 55728, 35392, -9810, 5328, 107280, -5792, 6096, 0, 15332, 1032, -69696, 45552, 5100, -20928, 288, 30400, 4884, 8400, -56742, 17184, 0, -1088, -6400, -42396, 8496, 3840, -39420, 2640, -104912, 6000, -22518, 45440, -21600, 0, 14800, -31920, 11400, -3200, -2882, -11764, -46704, 512, -2390, -75776, -28512, -3584, 0, -11870, 14808, 8256, -55978, -17032, -25160, 6400, -35586, -5760, 29304, -18040, 3264, 0, -14268, -19536, -8175, 16924, 76240, 35776, 64650, -35040, 3512, -768, 46398, -22188, 0, 31616, -25886, 4360, 13440, -6080, -23892, 21120, 12456, 5568, -2880, 6480, -2880, 0, 75170, -1250, -105820, -23512, 12720, -19200, -13260, -17968, -58080, -4488, 81900, -2960, 0, -53696, 96496, -2560, 7920, -42688, -8392, -41304, -16320, -1240, -66576, 14208, 102400, 0, -13200, 4320, -1914, 31968, -13760, -1280, -28864, -52644, 25992, 768, 11670, -20336, 0, -4224, -2490, -2560, -33508, 26400, -108864, 47208, -680, -5744, 76706, -10080, 30704, 0, -5778, -9728, -49948, -4544, 16650, -32844, -20616, 30400, -3168, 1320, -105600, -14016, 0, 26788, 19740, 3264, -59200, 52200, -19080, 3840, 1078, -6116, 26160, 16912, 5550, 0, 58676, -1152, -66816, 4000, 30216, 5032, -4864, 23760, -32400, -12192, 17568, -28352, 0, -20480, -27750, 21648, -10560, -2048, -7950, -21604, 86160, 4424, -43200, 4000, 8632, 0, 42048, 21348, 24760, 33216, -55440, 8848, 16576, -5280, 18162, 44544, -18360, 7296, 0, -57216, -50556, -29600, -49497, 12540, -53552, -10720, 38058, -5600, 1500, -1024, -23694, 0, 4296, 21120, -31618, -4856, -24144, -29616, -8230, 3552, -36200, 37344, 115936, -28600, 0, 11520, 11360, -57816, 28120, 47080, 1488, 31392, 23560, -800, -62208, 13236, 119064, 0, -5790, -6800, -32768, 1536, 55710, -16320, -4752, -33288, 83102, 2064, -34960, -26880, 0, 41020, 3072, 8640, 29430, 11840, 10708, -12960, -20000, 40128, 31296, -8448, 29390, 0, -17760, -25440, -36678, 69120, -8760, -42720, -109440, -63360, 103680, 5920, -1584, 7904, 0, 12564, 2785, 7648, -58564, 16784, 19536, 4500, 81828, 37984, -57658, -26392, -44240, 0, -31008, 61126, 81020, 7240, 63328, -4224, -4800, 57728, -1290, 16204, 21016, -23536, 0, 26160, 44248, 8448, -111456, 24576, -10500, 64824, -10672, -25160, 47520, 1360, 96522, 0, -9808, 3552, -4800, 59784, 61164, 19456, 6910, -7500, 13824, -8392, 15138, 5328, 0, 6336, -66080, 192, -13740, 4000, -16000, 80816, 56388, -6528, -640, 42432, -15048, 0, 89184, 4480, 59232, 2560, -53460, -64732, -10320, -15440, 14892, -25344, 49704, -8000, 0, -34476, 22488, 3968, 22550, 7600, -77520, -35136, 34320, 24420, 26012, 38352, 11584, 0, -44720, 4096, -19980, 21700, -35900, 960, 135168, -37344, -101788, -17264, -39520, 18204, 0, 4736, -26390, 7600, 19584, -17696, 101358, 2176, -6960, -53640, 136974, -87600, 73320, 0, -7088, -10368, 128304, 34848, 29390, -14400, 36604, 10464, -7936, 22460, -1332, -4224, 0, -51008, 3700, -8592, -7200, -63168, 32140, 3200, 80256, 8304, 91932, -7104, 51630, 0, -42056, 52456, 11136, -17760, 1088, -22720, 33600, -28332, -5400, -12800, 68074, -26928, 0, 1600, -97602, 59940, -1400, 23352, -960, -8688, 117684, 65536, -19510, 5280, 117660, 0, -90378, 25440, -33000, -4128, -31392, -66420, 99780, 7180, 97742, 78424, 57136, 2880, 0, -79232, -97976, -1632, -77626, 5680, 7848, 16896, -57024, -6400, -38000, -38120, 66846, 0, 9000, 17520, -60928, 12444, -33744, -40128, -4080, -62344, -72160, -15808, -72996, -4800, 0, -6720, 72000, -528, -21140, -39072, 69334, 58100, 5120, 1440, -5376, 26336, 21212, 0, -6290, 43164, 59136, 91520, 39490, 15240, -82512, 9600, 17280, -24320, 25600, 29040, 0, -43440, -47784, 2560, 122923, 32578, -29304, -48248, -5530, 18528, 1912, 21344, 57024, 0, -81000, 30192, -13018, 9496, -41520, -7104, -63186, 111872, 9740, 6600, 20128, -8976, 0, -27648, -9120, -13316, -16080, 14432, -34230, 37000, 37800, -384, 185504, 27948, 13400, 0, -17028, -47560, 162504, 1280, -42, 28032, -44192, 54432, -26400, -24456, -26952, -5120, 0, 37020, 179728, -15352, 34302, -8912, -46680, 4864, 79846, -3840, 6936, -14400, -85738, 0, 2304, -15200, -58850, 81844, 132064, 52800, 21312, 1000, -65208, -23168, 96838, 23212, 0, 29600, 10608, 4128, -115360, -1920, 182208, 65916, 14016, -48396, 41610, -16144, 121600, 0, -81180, 33600, -6336, 33408, 39738, -31512, -10800, -4352, 41426, 992, -169584, 16200, 0, -8616, 39148, 14176, 10560, -40800, -32136, 24000, 33850, 31800, 105080, 1024, -6816, 0, 53400, -43080, -127680, -27360, -9336, -7400, -28682, -29304, -47056, -21024, -15705, 2048, 0, -16608, -81920, -20980, 34932, -14336, -11118, -37552, -47480, -22272, -21120, 19092, -1584, 0, -68128, 41136, 58812, 25600, -9050, -1728, -13320, 26776, 63840, -72160, -25472, 2800, 0, -1056, 29420, -21120, -18288, 12560, 67696, -10560, -15792, 143104, -110600, 12072, -81030, 0, -86964, -3072, -78483, -1700, -88752, -57968, -62700, 73112, -4440, -5760, 17440, -40860, 0, -24320, -76862, 65400, -47388, -15696, 10490, 22272, 46024, 31104, 25920, -7920, -108888, 0, 114242, -17812, -5000, 16384, 50274, -94048, -44120, 8160, -44400, -34836, 6360, -71872, 0, -115632, -17952, 13440, -111630, -3200, -137104, -1536, -214784, -5088, 19300, -10240, -19808, 0, -98716, 10000, 120822, -165216, -44424, 4224, -4960, -30804, 11136, 32856, -9504, 43920, 0, -34560, -93402, 17280, -47940, 54720, 34560, -10032, -25800, -5120, -68508, 13374, -210576, 0, -1200, 1776, 89352, -3824, -81344, 21580, 94548, -16896, 98102, -98888, -5920, -18992, 0, 105600, 6584, 22120, 188832, 50376, -92160, -40256, 67050, 22880, -40320, -31664, 45510, 0, 100952, -28864, -22496, 5892, -43560, -18176, -98800, -19440, -131376, -13080, 7548, 70300, 0, 55728, 5280, 30024, 4632, -56064, -38160, 10740, 28960, -23760, -151698, 13056, -4000, 0, 208800, -8448, -151020, 8880, 27968, 10256, -24464, -9728, -65570, 67648, -32816, -6912, 0, 28400, 25176, -4608, -152998, 99428, 16000, 33040, 128874, 5440, 37760, -2000, 95040, 0, -26088, -48768, -29190, 55440, -65564, -21216, -143226, -81920, -48868, -44592, 86592, -44400, 0, -4736, 45454, -32540, -86416, 5160, 6528, 17696, -2228, 12672, -8975, 42756, 60216, 0, 55190, -3600, 85392, -1984, -2400, 76812, 2040, 38760, 35392, 3240, -32520, -21120, 0, -12596, 103008, -5792, 47650, 29184, -106920, -2048, -228864, -21900, 1032, -32000, -142018, 0, 50160, 18672, -78342, -42880, 38880, 19760, -12950, -91584, 41052, -4096, 8400, -55916, 0, -9792, -51630, 48840, -95000, -1088, -19424, -119064, -1800, -118464, -155648, -71200, 3840, 0, -84318, 149376, 80792, -64152, -114400, 6000, 181044, 26640, -13990, -12000, -231264, 3968, 0, 188320, -36300, 2112, 72594, -101460, -97500, -3200, -52704, -13736, 52944, 31584, 60310, 0, -10464, -40128, -27200, -26680, -62712, 6144, -85922, -3584, -37740, 21028, 32580, -133152, 0, 8880, 8256, 42684, -25896, -62160, -8250, 25496, 164080, 6400, 69570, 34560, -80188, 0, 12800, -26544, -18040, -51840, -72266, 24020, 160512, 480, 55782, -19536, -68012, -32768, 0, 6120, -103800, -101760, 35776, -1600, 159840, -12720, 20838, -170880, -68040, 15696, -253440, 0, -8184, 6400, -93598, -53856, 31616, -28568, 19190, 50256, -12888, 39616, 17686, -6080, 0, 67136, 97236, 5992, 18000, -8448, 5568, 87838, -133580, 19000, -105568, -50184, -14280, 0, -66000, -135004, 108640, 30464, -34080, 28960, -23512, 20064, -16896, 104532, -37000, 133496, 0, -17968, 64816, 2400, 65664, -94144, 117088, -36000, 60495, 113304, -82044, 33792, -62207, 0, 98304, -2560, -55218, 70080, -41760, -13168, -100640, -35100, -41304, 5440, 184138, -6192, 0, -45760, -20250, 14208, 8712, 41256, 239136, -17720, -145992, 44992, 4320, 103028, -30000, 0, 179526, -33568, 24560, -1280, 5760, 84000, -47832, 25344, 53850, 99664, 768, -9264, 0, 9250, 87028, -28512, 323264, 86328, 26280, -26112, 30668, 6100, 98124, 20760, 26400, 0, 55024, -55936, 17920, -23712, -33336, -5744, 95290, 27840, -258928, 13824, -79842, -61760, 0, 8040, -58608, -135168, 7104, -32000, 66838, -4544, -137904, -92752, -33470, 9176, 15716, 0, 30400, -3500, 14400, -140544, 15058, 10336, 26400, -14016, 88746, 153408, -118700, 13200, 0, 61104, -66708, 9472, -15090, 21116, 86800, -89864, -93630, 3840, -16528, 4456, -86358, 0, 72460, -69056, 16912, -180400, 72816, 7200, 32016, 5120, -34056, -1152, 30400, -111456, 0, -70784, 82764, 19620, 5032, -10656, 102138, -214560, -38880, 11584, -350400, -12192, -6900, 0, -38338, -30664, -41472, -2064, -20480, 139392, -38696, -91104, 32310, -10200, 143448, 41856, 0, -576, 89840, -60800, 164766, -9768, 4424, -16800, -204032, 113484, -188760, -34368, 1920, 0, -146076, 2176, -130416, 12800, -170852, 84792, 33216, -16992, -12500, -7680, -170426, 78840, 0, -5280, -93942, 209824, -141748, -12000, -41070, 45036, 7296, -90880, 227630, 43200, -113328, 0, 17562, -29600, -68400, 63840, -107712, -22800, 87120, 6400, 101441, 5764, 64800, 23528, 0, 93408, 6480, -1024, -34752, 4780, -123132, 151552, -12400, 57024, 21120, 7168, 155106, 0, -183960, 23740, 58830, -29616, 163308, -16512, -27650, 111956, -265680, 34064, 37344, 50320, 0, -12800, 313696, 71172, 39580, 11520, -27566, -58608, -183224, 36080, -104358, -6528, 47080, 0, 22720, 28536, 30276, 39072, 24320, 16350, -25600, -33848, 21264, -152480, -69660, -71552, 0, -129300, -115140, 70080, -3168, -7024, 49776, 1536, 29700, -92796, -190384, 44376, -249376, 0, -33288, -63232, 156362, 51772, -11100, -8720, 86394, -26880, 34816, 12160, -2112, 47784, 0, -42240, 8640, -24912, 232400, -11136, 13200, 5760, 45288, -12960, 60902, 5760, -41300, 0, -33408, -150340, 172656, 2500, 395076, 211640, -181172, 47024, 60960, -25440, -125400, 38400, 0, 26520, 54568, 35936, -42720, 116160, 55740, 8976, -173760, -163800, 4200, 5920, 162842, 0, 130312, 107392, -6450, -192992, 12564, 5120, 42846, -15840, 148932, 85376, -49500, 16784, 0, 82608, -13440, 32640, -30460, 2480, 37984, 133152, -86652, -28416, -48450, -204800, 258704, 0, -172530, 26400, 173792, -8640, -35904, 3828, 7240, -63936, 203606, 27520, -53264, 2560, 0, 57728, -23544, 105288, 40000, -51984, 29568, -1536, -23536, -23340, 111792, 40672, 10944, 0, -24700, 8448, -190240, 4980, 238500, 5120, 72900, 67016, 64824, -52800, 12240, 217728, 0, -94416, -97824, 1360, -8328, 11488, 235678, -153412, 148080, 20160, -72594, -61408, -137016, 0, -20609, 11556, 125400, 19456, 80190, 99896, -15360, 9088, 179490, -33300, -8392, 65688, 0, 41232, -4960, -60800, -108214, 6336, 88480, -2640, 60378, 211200, 28864, 28032, 4000, 0, -14688, -53576, -51840, -39480, 92848, -6528, -192762, 118400, 50160, -104400, 9546, 38160, 0, -7680, -286000, -2156, 263664, 12232, -26285, -52320, 130804, -33824, -64576, -11100, -5736, 0, -15440, -117352, 77700, 2304, 72414, 133632, 163060, -8000, -126048, -60432, -261012, -10064, 0, 9728, 3968, -47520, 148236, 64800, -85592, 24384, -60384, -35136, -600, 56704, -130354, 0, -163200, 40960, 38352, 55500, 52288, -43296, 127200, 21120, 20676, 4096, -32210, 15900, 0, 43208, -257022, -172320, -19620, -8848, -109440, 86400, 6540, -8000, -12308, -17264, -117216, 0, 35710, -84096, -145504, -42696, 4736, -49520, -173472, -66432, -70198, 110880, -83920, -17696, 0, -33152, -122480, 10560, -150208, -36324, -53640, -89088, -23750, 36720, 20640, -14592, -89670, 0, -85108, 114432, 164544, 101112, -38080, 59200, 34848, 98994, -6912, -25080, 160338, 107104, 0, 21440, -166870, -76116, 448512, 11200, -119270, -3000, -4224, 2048, -12558, 47388, 45000, 0, 50240, -8592, 123120, -42240, -31824, 63236, 330928, 9712, 3200, 48288, 187804, 59232, 0, 16460, 37488, -7104, -85680, 72400, -6800, -74688, -23946, -231872, 52456, 57200, 79040, 0, -156684, -23040, -51570, -22720, -163440, 115632, 151170, -56240, 164432, -94160, 261600, -2976, 0, -62784, 217594, -47120, 51504, 1600, 84078, 124416, 201688, -26472, -31680, -238128, 23352, 0, -99593, 11580, -71248, 13600, 99540, 65536, 35640, -3072, -217486, -111420, -10140, 32640, 0, 9504, -139344, 66576, -25950, -166204, 28008, -4128, -462528, 69920, -75000, 53760, 188882, 0, 7180, -82040, 9966, -6144, 100584, -17280, -20352, -58860, -201648, -23680, -10050, -21416, 0, 25920, -1632, 40000, -87388, -80256, -382062, -62592, 115940, 16896, 132746, -58780, -123216, 0, -157098, 35520, -38120, 50880, 175680, 73356, 184008, -138240, 44800, 17520, 39960, 85440, 0, 218880, -16500, 126720, -40128, -207360, -179520, -11840, 32768, 3168, 53496, -15808, 112330, 0, 235916, -25128, 1920, -5570, 137340, -15296, 47376, 117128, 86320, -33568, 116574, -39072, 0, -9000, -395552, -163656, -155628, -75968, 1440, 115316, 244200, 52784, -37530, 88480, -189216, 0, 201504, 62016, 13320, -122252, -165326, -162040, 91520, -14480, -16368, -126656, -5440, 8448, 0, 9600, -89556, -115456, 23220, 2580, 23568, -32408, 29040, -42032, 113880, 47072, -77760, 0, -170940, -52320, 244332, -88496, 76000, -16896, 76000, 222912, -48248, -49152, 120096, 21000, 0, -129648, -57242, 21344, 42960, 50320, -7446, -95040, -19080, -2720, 30192, -193044, 255192, 0, -105990, 19616, -33792, -7104, -74490, 9600, 29428, -119568, 41024, -122328, 6600, -38912, 0, -13820, 156436, 15000, 59424, -27648, 224600, 16784, 113600, -30276, 88920, -10656, -294954, 0, 397712, -12672, -158556, 132160, -79800, -384, -12206, 27480, -100440, -8000], "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": "10.4.a.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], [1], [-2], [-8], [4], [-5], [16], [4], [-8], [37], [10], [-12], [-32], [0], [-8], [40], [16], [66], [-74], [100], [-20], [-32], [24], [132], [64], [25], [0], [-80], [16], [-90], [-80], [-152], [-32], [96], [-132], [-20], [148], [34], [-200], [0], [40], [438], [64], [32], [-48], [-185], [-264], [204], [-128], [-327], [-50], [-528], [0], [222], [160], [60], [-32], [-800], [180], [-420], [160], [902], [304], [148], [64], [0], [-192], [1024], [264], [-1056], [40], [-432], [-296], [-362], [-68], [-200], [400], [-48], [0], [-160], [-80], [-359], [-876], [-72], [-128], [-330], [-64], [720], [96], [-810], [370], [0], [528], [1216], [-408], [-500], [256], [-1106], [654], [-444], [100]]}