# Stored data for newform 320.4.a.e, downloaded from the LMFDB on 28 March 2024. {"label": "320.4.a.e", "space_label": "320.4.a", "level": 320, "weight": 4, "hecke_orbit": 5, "hecke_orbit_code": 18014398576591168, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 2168045340703437088, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [4, 1]], [7, [-16, 1]]], "qexp_display": "q-4q^{3}-5q^{5}+2^{4}q^{7}-11q^{9}-6^{2}q^{11}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 5120, "fricke_eigenval": 1, "atkin_lehner_string": "++", "analytic_conductor": 18.880611201836995, "hecke_ring_index": 1, "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": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [320, 1, [191, 261, 257], [1, 1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 5], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.996", "prec": 17}, {"__RealLiteral__": 0, "data": "0.002", "prec": 17}, {"__RealLiteral__": 0, "data": "1.935", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.677", "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]], "trace_display": [0, -4, -5, 16], "traces": [0, 1, 0, -4, 0, -5, 0, 16, 0, -11, 0, -36, 0, 42, 0, 20, 0, -110, 0, 116, 0, -64, 0, 16, 0, 25, 0, 152, 0, -198, 0, 240, 0, 144, 0, -80, 0, 258, 0, -168, 0, 442, 0, 292, 0, 55, 0, 392, 0, -87, 0, 440, 0, -142, 0, 180, 0, -464, 0, 348, 0, 570, 0, -176, 0, -210, 0, -692, 0, -64, 0, 168, 0, -134, 0, -100, 0, -576, 0, 784, 0, -311, 0, -564, 0, 550, 0, 792, 0, 1034, 0, 672, 0, -960, 0, -580, 0, -382, 0, 396, 0, 674, 0, -992, 0, 320, 0, 500, 0, -1046, 0, -1032, 0, -558, 0, -80, 0, -462, 0, -1760, 0, -35, 0, -1768, 0, -125, 0, -328, 0, -1168, 0, 212, 0, 1856, 0, -760, 0, 1434, 0, -2196, 0, -1568, 0, -1512, 0, 990, 0, 348, 0, 2418, 0, 3672, 0, 1210, 0, -1200, 0, -358, 0, 568, 0, 256, 0, -2564, 0, -720, 0, -3056, 0, -433, 0, -1276, 0, 234, 0, 400, 0, -1392, 0, -524, 0, 1138, 0, -2280, 0, -1290, 0, 3960, 0, 2432, 0, 1520, 0, -2142, 0, 840, 0, 2306, 0, 3288, 0, 2768, 0, -3168, 0, -2210, 0, -176, 0, -4176, 0, 3876, 0, -672, 0, -1460, 0, 3840, 0, 536, 0, -4620, 0, -5688, 0, -275, 0, 2796, 0, -4446, 0, 2304, 0, 2522, 0, -1960, 0, -3136, 0, 816, 0, -5422, 0, -2860, 0, 435, 0, 4872, 0, 2256, 0, 5900, 0, -576, 0, -2200, 0, 5250, 0, 4128, 0, 2178, 0, 6240, 0, 710, 0, -4136, 0, 714, 0, 2144, 0, -2688, 0, -900, 0, 4466, 0, -2640, 0, -5302, 0, 6932, 0, 2320, 0, 7072, 0, 7187, 0, 1528, 0, 4034, 0, -1740, 0, -5472, 0, 672, 0, 4672, 0, -2696, 0, -2850, 0, 3836, 0, 3968, 0, 664, 0, 2986, 0, 880, 0, -2726, 0, 7128, 0, -2000, 0, -12760, 0, 1050, 0, 4184, 0, 6272, 0, 9212, 0, -2838, 0, 3460, 0, -3278, 0, 2232, 0, -8640, 0, -6880, 0, 320, 0, -4956, 0, -4678, 0, 6384, 0, 1890, 0, -840, 0, 7040, 0, -6472, 0, 6597, 0, 140, 0, 670, 0, 1960, 0, -4862, 0, -2272, 0, -8750, 0, 500, 0, -8316, 0, 380, 0, 1312, 0, -9688, 0, 2880, 0, -3212, 0, -3870, 0, -1760, 0, -848, 0, -3920, 0, -1622, 0, -7424, 0, 9906, 0, 10080, 0, 1555, 0, -9288, 0, -4214, 0, -5736, 0, 5568, 0, 2820, 0, 8784, 0, 7012, 0, 1602, 0, -4312, 0, -2750, 0, 9120, 0, 6048, 0, -3584, 0, -3470, 0, -3960, 0, 1856, 0, -3416, 0, 957, 0, -9708, 0, -5170, 0, -9672, 0, -10366, 0, -15912, 0, -14688, 0, -3360, 0, -16742, 0, -16720, 0, 1258, 0, 13528, 0, 4800, 0, -6916, 0, -11072, 0, 1432, 0, -10512, 0, 2900, 0, 1562, 0, 1728, 0, 10836, 0, -1024, 0, 1910, 0, 16656, 0, 10256, 0, 1084, 0, 21780, 0, -1980, 0, 2688, 0, -5804, 0, 12224, 0, 10512, 0, -3370, 0, 1732, 0, 4314, 0, -2144, 0, 17632, 0, 4960, 0, -14112, 0, -936, 0, -1190, 0, 3780, 0, -1600, 0, -26400, 0, -11911, 0, -3828, 0, 18564, 0, -2500, 0, 2096, 0, 3132, 0, 11002, 0, -4552, 0, 5230, 0, -5908, 0, -6270, 0, -22968, 0, 12544, 0, 5160, 0, -14806, 0, 12264, 0, -15840, 0, 684, 0, 2790, 0, -4976, 0, -2582, 0, 2540, 0, -6080, 0, 400, 0, 22786, 0, 8568, 0, -9024, 0, 5112, 0, 2310, 0, -7884, 0, 27840, 0, -9224, 0, -21902, 0, 8800, 0, -13152, 0, 15080, 0, -19702, 0, 7612, 0, 175, 0, 7320, 0, 12672, 0, 16464, 0, -24350, 0, 8840, 0, 19546, 0, -3476, 0, 2432, 0, 16544, 0, 625, 0, 16704, 0, -28380, 0, 21880, 0, -15504, 0, 1640, 0, -3654, 0, -1848, 0, 20994, 0, 18204, 0, 5840, 0, -2064, 0, -12528, 0, -15360, 0, -9942, 0, -1060, 0, 1474, 0, -24236, 0, -17614, 0, 18480, 0, -9280, 0, -3168, 0, 22752, 0, -20520, 0, 13058, 0, 3800, 0, 33186, 0, -6112, 0, -11184, 0, 31716, 0, -7170, 0, 17784, 0, -5964, 0, 2084, 0, 6336, 0, 10980, 0, -48620, 0, -10088, 0, 7418, 0, 29928, 0, 7840, 0, 10784, 0, 18242, 0, -8624, 0, 3840, 0, 7560, 0, -3264, 0, 3024, 0, -15872, 0, 21688, 0, -4950, 0, -26176, 0, 19837, 0, -32120, 0, 17818, 0, -1740, 0, 24912, 0, 22052, 0, -19488, 0, 15840, 0, -12090, 0, 6204, 0, 8000, 0, 21024, 0, -23600, 0, -18360, 0, 38034, 0, 2304, 0, 37802, 0, -16736, 0, -6050, 0, 14616, 0, 15042, 0, -21000, 0, -5950, 0, 6000, 0, -16512, 0, 51272, 0, -6048, 0, -30096, 0, 1790, 0, -23364, 0, -24960, 0, -8928, 0, 23940, 0, -2840, 0, -19846, 0, -43120, 0, -11374, 0, 4824, 0, -1280, 0, -2856, 0, 24762, 0, -16644, 0, -8576, 0, 12820, 0, 33872, 0, -7392, 0, -3182, 0, -7504, 0, 3600, 0, -12604, 0, -12230, 0, -17864, 0, 9570, 0, 15280, 0, 36480, 0, 9656, 0, 14815, 0, 21208, 0, 2165, 0, -560, 0, -27728, 0, 4128, 0, -5806, 0, 6380, 0, -39094, 0, 18876, 0, -28288, 0, 32296, 0, -1170, 0, -28748, 0, -28224, 0, -29064, 0, 4202, 0, -2000, 0, 9578, 0, -16136, 0, -41710, 0, -2260, 0, 6960, 0, -33696, 0, -5248, 0, 11196, 0, 45472, 0, 2620, 0, -2688, 0, -47520, 0, 15620, 0, -18688, 0, -5690, 0, -7756, 0, -7414, 0, -5312, 0, 20304, 0, 11400, 0, 3392, 0, -23576, 0, -15344, 0, 7056, 0, 6450, 0, 10912, 0, -19038, 0, -10092, 0, -2656, 0, -19800, 0, 20570, 0, -11944, 0, 21386, 0, 7072, 0, -12160, 0, -38020, 0, -5628, 0, 10904, 0, 20202, 0, -7600, 0, -28512, 0, 22944, 0, 27809, 0, -5500, 0, 10710, 0, 29840, 0, 51040, 0, 12476, 0, -35136, 0, -4200, 0, -36974, 0, -37224, 0, 11506, 0, -16368, 0, -11530, 0, -25088, 0, 4672, 0, -49552, 0, -36848, 0, -16440, 0, -24414, 0, 39216, 0, -24192, 0, -38280, 0, -13840, 0, -16472, 0, -63214, 0, 13112, 0, -5838, 0, 15840, 0, 6138, 0, 8060, 0, 13210, 0, 34560, 0, 11050, 0, 32928, 0, 27520, 0, 10376, 0, 4090, 0, 880, 0, -62700, 0, -39184, 0, 19824, 0, 38688, 0, 20880, 0, 18712, 0, 30666, 0, -27252, 0, -13062, 0, -19380, 0, 58752, 0, -7560, 0, 59298, 0, -48192, 0, 3360, 0, 13752, 0, 18154, 0, 19360, 0, -51084, 0, 7300, 0, 25888, 0, -23688, 0, 6272, 0, -26388, 0, -19200, 0, -17384, 0, 385, 0, 27412, 0, -18814, 0, -2680, 0, -6918, 0, -5728, 0, -7840, 0, -17928, 0, 23100, 0, 67184, 0, 24850, 0, -24264, 0, 9088, 0, 28440, 0, -20198, 0, 35000, 0, 40368, 0, -7172, 0, 1375, 0, -1392, 0, 41722, 0, 33264, 0, 35712, 0, -13980, 0, -1520, 0, 76120, 0, -41024, 0, 3608, 0, 22230, 0, 61920, 0, 38752, 0, 75600, 0, -27326, 0, -11520, 0, 43428, 0, 66120, 0, 44384, 0, -46812, 0, -12610, 0, 15480, 0, -48896, 0, -40444, 0, 7040, 0, 9800, 0, -18000, 0, -2332, 0, -26214, 0, -6928, 0, 15680, 0, 844, 0, -87516, 0, 6488, 0, 48986, 0, -4080, 0, -20416, 0, 37656, 0, -29870, 0, -39624, 0, 27110, 0, -18480, 0, -40320, 0, 3744, 0, 7898, 0, 14300, 0, -14142, 0, -2272, 0, 37152, 0, 63040, 0, -2175, 0, 16856, 0, -28502, 0, 76256, 0, -15774, 0, -24360, 0, 9554, 0, -22272, 0, 14740, 0, 20088, 0, -11280, 0, -57816, 0, -33118, 0, 24156, 0, -8384, 0, -29500, 0, -28048, 0, -25076, 0, -16044, 0, -6408, 0, 2880, 0, 18208, 0, 59584, 0, 106080, 0, -80272, 0, 11000, 0, -67398, 0, -45568, 0, -36480, 0, 44060, 0, -26250, 0, 16632, 0, -10470, 0, 30332, 0, 14336, 0, -20640, 0, -21166, 0, 13880, 0, -6542, 0, -28208, 0, -10890, 0, -26876, 0, 63360, 0, -7424, 0, 28308, 0, -31200, 0, 13664, 0, 28760, 0, 15418, 0, -13224, 0, -3550, 0, 22024, 0, 38832, 0, 49176, 0, 70080, 0, 20680, 0, 24320, 0, -41664, 0, -26598, 0, -86240, 0, -3570, 0, 41464, 0, 19488, 0, -34272, 0, 63648, 0, -10720, 0, 5568, 0, -40392, 0, -41870, 0, -77616, 0, 13440, 0, 67552, 0, 15911, 0, 66968, 0, -77190, 0, 4500, 0, 34210, 0, 36896, 0, 22594, 0, -5032, 0, -22330, 0, -15544, 0, -54112, 0, 21000, 0, 52608, 0, 13200, 0, 11808, 0, 32840, 0, 27664, 0, 9120, 0, 26510, 0, 44288, 0, -36030, 0, 62040, 0, 3938, 0, -34660, 0, -43932, 0, 42048, 0, 17226, 0, -72712, 0, -11600, 0, -57604, 0, -105550, 0, -21584, 0, 72618, 0, -35360, 0, -6912, 0, 101664, 0, -7632, 0, -43344, 0, -35935, 0, 64432, 0, -2816, 0, -58020, 0, 35722, 0, -7640, 0, 94080, 0, -44780, 0, -66624, 0, -66816, 0, -20170, 0, 28204, 0, -23436, 0, -67600, 0, -4336, 0, 8700, 0, 62016, 0, -87120, 0, 5722, 0, -64092, 0, 27360, 0, -53784, 0, 72370, 0, -10752, 0, -76590, 0, -3360, 0, 23216, 0, 82460, 0, 90944, 0, 33616, 0, -23360, 0, -51624, 0, -42048, 0, -101528, 0, -113740, 0, 13480, 0, 114036, 0, -20880, 0, 4763, 0, -1044, 0, 14250, 0, -17256, 0, 79056, 0, 49036, 0, 8576, 0, -19180, 0, 28116, 0, -36076, 0, -11072, 0, -65088, 0, -19840, 0, -73920, 0, 76714, 0, 56448, 0, -62606, 0, -3320, 0, -2574, 0, -12024, 0, -91008, 0, 4760, 0, -14930, 0, 50776, 0, -15120, 0, -63468, 0, -1470, 0, -4400, 0, -65424, 0, -70260, 0, 105600, 0, 22328, 0, 13630, 0, 47644, 0, 44736, 0, 75336, 0, 52896, 0, -35640, 0, -28006, 0, -74256, 0, -107070, 0, -71136, 0, 10000, 0, 26800, 0, 9242, 0, 5764, 0, -90934, 0, 63800, 0, -12528, 0, 97140, 0, -98350, 0, -44008, 0, -5250, 0, -38620, 0, -12518, 0, 40352, 0, 2688, 0, -20920, 0, 52098, 0, -87048, 0, 23632, 0, -34080, 0, -31360, 0, 86640, 0, 42020, 0, -13776, 0, 91872, 0, -46060, 0, -46678, 0, -50176, 0, -132192, 0, -57848, 0, 14190, 0, -40436, 0, -33598, 0, 59224, 0, 13056, 0, -17300, 0, -49056, 0, -2144, 0, 126443, 0, -43560, 0, 16390, 0, -86752, 0, -2736, 0, 119944, 0, 128026, 0, -11160, 0, -69886, 0, -110908, 0, -45760, 0, 8904, 0, 43200, 0, 10328, 0, 89290, 0, -68904, 0, -10160, 0, 34400, 0, -74140, 0, -16720, 0, -45590, 0, 29972, 0, -1600, 0, 12888, 0, 77952, 0, -91144, 0, -125918, 0, 24780, 0, 23562, 0, 101136, 0, -90326, 0, 36096, 0, 23390, 0, 73596, 0, -20448, 0, 109120, 0, -38486, 0, -31920, 0, 94400, 0, 32416, 0, 31536, 0, 129064, 0, -9450, 0, -111360, 0, -112860, 0, -9216, 0, -25366, 0, 4200, 0, -1134, 0, 87608, 0, 60228, 0, 128592, 0, -35200, 0, 96036, 0, 1050, 0, -36168, 0, 92304, 0, 32360, 0, -60320, 0, 84000, 0, -66534, 0, 78808, 0, -32985, 0, -92232, 0, -105184, 0, 6948, 0, -22446, 0, -700, 0, 12544, 0, -55000, 0, -29280, 0, -86040, 0, -3350, 0, 34848, 0, 83520, 0, 20200, 0, -65856, 0, -9800, 0, 110016, 0, 97400, 0, 99840, 0, -44312, 0, 24310, 0, -145376, 0, 5757, 0, -78184, 0, 115060, 0, 11360, 0, 13904, 0, 15588, 0, 53186, 0, -4976, 0, 43750, 0, 89780, 0, -66176, 0, -44928, 0, 117714, 0, -2500, 0, -93038, 0, 12520, 0, 45936, 0, 11424, 0, 41580, 0, 113520, 0, 17250, 0, 136800, 0, -87520, 0, -1900, 0, 34304, 0, -42636, 0, 94826, 0, -8424, 0, -6560, 0, -138084, 0, -9024, 0, 14616, 0, -75318, 0, 48440, 0, 25536, 0, 78184, 0, 61380, 0, -83976, 0, -14400, 0, 173264, 0, -72816, 0, -142564, 0, -33526, 0, 16060, 0, 101556, 0, 71456, 0, 8256, 0, 137016, 0, 19350, 0, 50112, 0, 21082, 0, 11632, 0, -42240, 0, 8800, 0, -115072, 0, 39768, 0, -36636, 0, 154224, 0, 4240, 0, -84832, 0, 18864, 0, -20368, 0, 146706, 0, 19600, 0, 96944, 0, -34116, 0, 110912, 0, 70456, 0, 8110, 0, 77356, 0, 50820, 0, -40968, 0, -63398, 0, 37120, 0, -100982, 0, 70096, 0, 12672, 0, -17940, 0, -49530, 0, 62568, 0, -38454, 0, -79188, 0, 82080, 0, -50400, 0, -113086, 0, -52232, 0, 114464, 0, 114992, 0, -7775, 0, -77804, 0, 55626, 0, -132744, 0, 58000, 0, 46440, 0, 24448, 0, -22616, 0, -15036, 0, -30756, 0, 21070, 0, 16544, 0, -126864, 0, 64544, 0, -144926, 0, 28680, 0, 3850, 0, -33264, 0, 48906, 0, 118808, 0, -27840, 0, 23856, 0, -129774, 0, -121336, 0, -8336, 0, -14100, 0, -166080, 0, -87552, 0, -103966, 0, 122396, 0, -43920, 0, 44048, 0, -36614, 0, 194480, 0, 10752, 0, -35060, 0, -27742, 0, -85036, 0, -54720, 0, -29672, 0, -8010, 0, -25404, 0, -119712, 0, 78672, 0, -147390, 0, 21560, 0, 26532, 0, -107688, 0, -43136, 0, 77112, 0, 13750, 0, -72968, 0, 145074, 0, 60676, 0, 119168, 0, -45600, 0, -32886, 0, -15360, 0, -22566, 0, 10056, 0, -30240, 0, -64728, 0, 61376, 0, -8976, 0, 81274, 0, 17920, 0, -12096, 0, 36080, 0, 171858, 0, 63488, 0, 17350, 0, -83016, 0, 59642, 0, -128352, 0, -62764, 0, 19800, 0, 10624, 0, 117860, 0, 104704, 0, 89784, 0, -9280, 0, -2128, 0, -118368, 0, 47776, 0, 128480, 0, 17080, 0, -110460, 0, -71272, 0, 40320, 0, 12340, 0, -4785, 0, -110760, 0, 49841, 0, -99648, 0, -115358, 0, 48540, 0, -88208, 0, -43616, 0, 86186, 0, -53592, 0, 25850, 0, -23320, 0, -63360, 0, -6112, 0, 114048, 0, 48360, 0, 171514, 0, -3104, 0, -85728, 0, -3332, 0, 51830, 0, -32000, 0, 9828, 0, -129124, 0, -84096, 0, 79560, 0, 147060, 0, -64900, 0, -204160, 0, -32160, 0, 73440, 0, -169052, 0, 10650, 0, -152136, 0, -177438, 0, 16800, 0, 6336, 0, -41464, 0, 51130, 0, -151208, 0, 83710, 0, 40680, 0, 66944, 0, -155232, 0, 168914, 0, 83600, 0, 14250, 0, -4060, 0, -58464, 0, -34104, 0, -6290, 0, -60168, 0, 177698, 0, -167320, 0, -57750, 0, -67640, 0, 147392, 0, 23800, 0, -139536, 0, 10784, 0, -24000, 0, -22008, 0, -157740, 0, -45408, 0, -100390, 0, 34580, 0, -205088, 0, 90692, 0, -88958, 0, 24192, 0, 55360, 0, 123572, 0, 61578, 0, -197792, 0, 47796, 0, -7160, 0, -16974, 0, -52448, 0, 93456, 0, 241560, 0, 52560, 0, -68640, 0, -15872, 0, -112556, 0, 35712, 0, -14500, 0, 8794, 0, -95760, 0, -207990, 0, 60536, 0, -7810, 0, -138240, 0, 162514, 0, 79384, 0, 65194, 0, -8640, 0, 172480, 0, -46464, 0, -80239, 0, 157168, 0, -54180, 0, 111672, 0, -19296, 0, 21724, 0, -38048, 0, 5120, 0, -202382, 0, 153816, 0, -7854, 0, -118832, 0, -9550, 0, -99048, 0, -79296, 0, 166320, 0, 66576, 0, -83280, 0, 161602, 0, -23584, 0, 89562, 0, -74848, 0, -51280, 0, -57528, 0, 188160, 0, -135488, 0, 204768, 0, -5420, 0, 102144, 0, 5308, 0, 8000, 0, 12728, 0, -108900, 0, -18292, 0, 30016, 0, 30240, 0, -5542, 0, 9900, 0, -72822, 0, -178536, 0, 50416, 0, 63840, 0, -13440, 0, 48920, 0, 24592, 0, -55664, 0, -49126, 0, 29020, 0, -100656, 0, -38280, 0, 251940, 0, 50912, 0, -61120, 0, -16736, 0, -89964, 0, -74640, 0, -103552, 0, -52560, 0, -38624, 0, 160056, 0, 43850, 0, -59260, 0, 16850, 0, 105552, 0, 58322, 0, -7308, 0, -265980, 0, -8660, 0, 101616, 0, 193900, 0, 2240, 0, 187192, 0, -21570, 0, -76252, 0, 3794, 0, -5512, 0, -16512, 0, 10720, 0, 135002, 0, 23224, 0, 96852, 0, -90792, 0, -88160, 0, -403920, 0, 31360, 0, 156376, 0, -135360, 0, -24800, 0, -75504, 0, -210444, 0, -204732, 0, -77792, 0, 70560, 0, 138096, 0, -129184, 0, -69456, 0, 101346, 0, 4680, 0, 12354, 0, -8928, 0, -79057, 0, 166344, 0, 5950, 0, 112896, 0, 166098, 0, -140000, 0, 116256, 0, -18900, 0, 220394, 0, -58064, 0, -155430, 0, 166440, 0, 8000, 0, 43344, 0, -29376, 0, -38312, 0, -100070, 0, 132000, 0, -44374, 0, -133056, 0, -254736, 0, 166840, 0, 59555, 0, 259776, 0, 9040, 0, 195192, 0, 6080, 0, 19140, 0, -51294, 0, -28412, 0, 134784, 0, -44224, 0, -92820, 0, 20992, 0, 39380, 0, 193088, 0, 102960, 0, 12500, 0, -102510, 0, -181888, 0, -155008, 0, -20332, 0, -10480, 0, -190792, 0, -222270, 0, -7392, 0, 114722, 0, -15660, 0, 190080, 0, 236204, 0, -34572, 0, -62480, 0, -55010, 0, 176828, 0, -51392, 0, -272360, 0, -112566, 0, 22760, 0, -175392, 0, 71872, 0, 31024, 0, -61920, 0, -26150, 0, 102448, 0, -6598, 0, 57916, 0, 21248, 0, 29540, 0, -28160, 0, -81216, 0, 216530, 0, 162792, 0, 31350, 0, -305864, 0, -158854, 0, -13568, 0, -71070, 0, 114840, 0, 94304, 0, 248160, 0, -212400, 0, -42196, 0, -62720, 0, 182856, 0, -28224, 0, 282040, 0, 136416, 0, -25800, 0, 114698, 0, -25952, 0, -150784, 0, -560, 0, 74030, 0, 76152, 0, -11454, 0, 49672, 0, 40368, 0, -61320, 0, 261386, 0, -7304, 0, 186834, 0, 5612, 0, 79200, 0, 158496, 0, -128713, 0, -82280, 0, 75636, 0, -3420, 0, -32846, 0, 138756, 0, 161280, 0, -85544, 0, -13950, 0, -189000, 0, -28288, 0, 280488, 0, 143730, 0, 24880, 0, -199374, 0, 336160, 0, 152080, 0, -281068, 0, 12910, 0, 22512, 0, -148608, 0, 132980, 0, 29986, 0, -12700, 0, 250778, 0, -80808, 0, 203210, 0, -67424, 0, 30400, 0, 223440, 0, 425952, 0, -78408, 0, 47630, 0, -2000, 0, -91776, 0, 111936, 0, -202064, 0, -111236, 0, -113930, 0, -158800, 0, 76000, 0, -30276, 0, -224640, 0, -42840, 0, -25902, 0, -238896, 0, -119360, 0, 140976, 0, 45120, 0, 140360, 0, -41126, 0, 74256, 0, -49904, 0, -25560, 0, -224926, 0, 140544, 0, -5248, 0, 202272, 0, -11550, 0, -43896, 0, -133452, 0, 147896, 0, 112192, 0, 39420, 0, 148896, 0, 168028, 0, -25740, 0, -158992, 0, -139200, 0, 25632, 0, 65472, 0, 117432, 0, 168538, 0, 46120, 0, 34122, 0, -25704, 0, -68992, 0, -93268, 0, 109510, 0, -18688, 0, 144522, 0, -143668, 0, 198208, 0, -44000, 0, -186732, 0, -101332, 0, -77184, 0, -41528, 0, 65760, 0, 196416, 0, -49590, 0, 97656, 0, -59228, 0, -75400, 0, -80238, 0, 6312, 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": "40.4.a.b", "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], [-4], [0], [-5], [0], [16], [0], [-11], [0], [-36], [0], [42], [0], [20], [0], [-110], [0], [116], [0], [-64], [0], [16], [0], [25], [0], [152], [0], [-198], [0], [240], [0], [144], [0], [-80], [0], [258], [0], [-168], [0], [442], [0], [292], [0], [55], [0], [392], [0], [-87], [0], [440], [0], [-142], [0], [180], [0], [-464], [0], [348], [0], [570], [0], [-176], [0], [-210], [0], [-692], [0], [-64], [0], [168], [0], [-134], [0], [-100], [0], [-576], [0], [784], [0], [-311], [0], [-564], [0], [550], [0], [792], [0], [1034], [0], [672], [0], [-960], [0], [-580], [0], [-382], [0], [396], [0]]}