# Stored data for newform 1800.4.a.c, downloaded from the LMFDB on 18 April 2024.
{"label": "1800.4.a.c", "space_label": "1800.4.a", "level": 1800, "weight": 4, "hecke_orbit": 3, "hecke_orbit_code": 9007199321851656, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1450120317933936805, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [26, 1]], [11, [-59, 1]], [17, [-5, 1]]], "qexp_display": "q-26q^{7}+59q^{11}-28q^{13}+5q^{17}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 28800, "fricke_eigenval": 1, "atkin_lehner_string": "--+", "analytic_conductor": 106.2034380103331, "hecke_ring_index": 1, "level_radical": 30, "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": "0.003", "prec": 17}, "analytic_rank_proved": true, "char_values": [1800, 1, [1351, 901, 1001, 577], [1, 1, 1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 3, 5], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.032", "prec": 17}, {"__RealLiteral__": 0, "data": "0.970", "prec": 17}, {"__RealLiteral__": 0, "data": "0.022", "prec": 17}, {"__RealLiteral__": 0, "data": "1.872", "prec": 17}, {"__RealLiteral__": 0, "data": "0.017", "prec": 17}, {"__RealLiteral__": 0, "data": "4.512", "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], [3, -1], [5, 1]], "trace_display": [0, 0, 0, -26], "traces": [0, 1, 0, 0, 0, 0, 0, -26, 0, 0, 0, 59, 0, -28, 0, 0, 0, 5, 0, 109, 0, 0, 0, -194, 0, 0, 0, 0, 0, 32, 0, 10, 0, 0, 0, 0, 0, 198, 0, 0, 0, -117, 0, -388, 0, 0, 0, -68, 0, 333, 0, 0, 0, -18, 0, 0, 0, 0, 0, -392, 0, -710, 0, 0, 0, 0, 0, 253, 0, 0, 0, 612, 0, 549, 0, 0, 0, -1534, 0, 414, 0, 0, 0, -121, 0, 0, 0, 0, 0, 81, 0, 728, 0, 0, 0, 0, 0, 1502, 0, 0, 0, 234, 0, 1172, 0, 0, 0, 1125, 0, -1234, 0, 0, 0, 567, 0, 0, 0, 0, 0, -130, 0, 2150, 0, 0, 0, 0, 0, 2358, 0, 0, 0, 1692, 0, -2834, 0, 0, 0, 229, 0, 2781, 0, 0, 0, -1652, 0, 0, 0, 0, 0, -1472, 0, 1322, 0, 0, 0, 0, 0, -298, 0, 0, 0, 5044, 0, 341, 0, 0, 0, 684, 0, -1413, 0, 0, 0, -2344, 0, 0, 0, 0, 0, 1111, 0, 2042, 0, 0, 0, 0, 0, 295, 0, 0, 0, -5270, 0, -613, 0, 0, 0, 1174, 0, 3428, 0, 0, 0, -832, 0, 0, 0, 0, 0, 6431, 0, 2339, 0, 0, 0, 0, 0, -260, 0, 0, 0, -140, 0, -3932, 0, 0, 0, 6084, 0, 4996, 0, 0, 0, 3222, 0, 0, 0, 0, 0, -2736, 0, 1673, 0, 0, 0, 0, 0, -3052, 0, 0, 0, -5355, 0, -11446, 0, 0, 0, -5490, 0, -5148, 0, 0, 0, 3150, 0, 0, 0, 0, 0, -176, 0, 2394, 0, 0, 0, 0, 0, 6256, 0, 0, 0, 4802, 0, -2123, 0, 0, 0, 3042, 0, -4888, 0, 0, 0, -8834, 0, 0, 0, 0, 0, 5432, 0, 10088, 0, 0, 0, 0, 0, -1369, 0, 0, 0, 10426, 0, 3574, 0, 0, 0, 9036, 0, 1888, 0, 0, 0, 545, 0, 0, 0, 0, 0, 1768, 0, 10233, 0, 0, 0, 0, 0, -4627, 0, 0, 0, 590, 0, 260, 0, 0, 0, 4901, 0, -4482, 0, 0, 0, -1210, 0, 0, 0, 0, 0, 9882, 0, 5022, 0, 0, 0, 0, 0, 11260, 0, 0, 0, 468, 0, 3230, 0, 0, 0, -896, 0, 11575, 0, 0, 0, -18, 0, 0, 0, 0, 0, -10710, 0, -970, 0, 0, 0, 0, 0, 3788, 0, 0, 0, 10539, 0, -280, 0, 0, 0, 11682, 0, 5581, 0, 0, 0, 10192, 0, 0, 0, 0, 0, -5193, 0, 4788, 0, 0, 0, 0, 0, 18460, 0, 0, 0, -8006, 0, 2395, 0, 0, 0, -21146, 0, 1864, 0, 0, 0, 5463, 0, 0, 0, 0, 0, -12969, 0, -6903, 0, 0, 0, 0, 0, -18313, 0, 0, 0, -12492, 0, -4428, 0, 0, 0, -1084, 0, -6578, 0, 0, 0, -22892, 0, 0, 0, 0, 0, 13082, 0, -5544, 0, 0, 0, 0, 0, 3014, 0, 0, 0, 3564, 0, 160, 0, 0, 0, -15912, 0, -15796, 0, 0, 0, -10908, 0, 0, 0, 0, 0, -21946, 0, -14274, 0, 0, 0, 0, 0, -4012, 0, 0, 0, 6395, 0, 5615, 0, 0, 0, 50, 0, 25469, 0, 0, 0, 3276, 0, 0, 0, 0, 0, 19647, 0, -4112, 0, 0, 0, 0, 0, 2167, 0, 0, 0, 3488, 0, -10764, 0, 0, 0, -19444, 0, 10864, 0, 0, 0, 20416, 0, 0, 0, 0, 0, 3127, 0, -22580, 0, 0, 0, 0, 0, 829, 0, 0, 0, 3146, 0, -1062, 0, 0, 0, 7119, 0, 1090, 0, 0, 0, -8217, 0, 0, 0, 0, 0, 90, 0, -17117, 0, 0, 0, 0, 0, 15120, 0, 0, 0, 1904, 0, 6570, 0, 0, 0, 18846, 0, 16316, 0, 0, 0, -2106, 0, 0, 0, 0, 0, 990, 0, 20170, 0, 0, 0, 0, 0, -9324, 0, 0, 0, 12726, 0, -2196, 0, 0, 0, -16884, 0, -23128, 0, 0, 0, -4018, 0, 0, 0, 0, 0, -19071, 0, 17424, 0, 0, 0, 0, 0, -6208, 0, 0, 0, -41890, 0, 5382, 0, 0, 0, -4496, 0, -39052, 0, 0, 0, 3249, 0, 0, 0, 0, 0, 504, 0, -13399, 0, 0, 0, 0, 0, -585, 0, 0, 0, 18148, 0, 21582, 0, 0, 0, -6084, 0, 4868, 0, 0, 0, -1940, 0, 0, 0, 0, 0, 17366, 0, -30472, 0, 0, 0, 0, 0, -21824, 0, 0, 0, -1940, 0, 31428, 0, 0, 0, 14927, 0, -14292, 0, 0, 0, 13950, 0, 0, 0, 0, 0, -29250, 0, -38736, 0, 0, 0, 0, 0, 3664, 0, 0, 0, -19557, 0, 32084, 0, 0, 0, 10976, 0, -13283, 0, 0, 0, 24840, 0, 0, 0, 0, 0, -12753, 0, 36108, 0, 0, 0, 0, 0, -18044, 0, 0, 0, -14742, 0, 19880, 0, 0, 0, -6174, 0, -340, 0, 0, 0, 32391, 0, 0, 0, 0, 0, 1998, 0, -7156, 0, 0, 0, 0, 0, -42292, 0, 0, 0, -27922, 0, -22636, 0, 0, 0, 26559, 0, 12580, 0, 0, 0, 1665, 0, 0, 0, 0, 0, 11344, 0, -23365, 0, 0, 0, 0, 0, -55900, 0, 0, 0, -38412, 0, -14786, 0, 0, 0, -29259, 0, -13651, 0, 0, 0, 29016, 0, 0, 0, 0, 0, 24426, 0, -7084, 0, 0, 0, 0, 0, -21412, 0, 0, 0, 1170, 0, 12655, 0, 0, 0, 32764, 0, -61308, 0, 0, 0, -7412, 0, 0, 0, 0, 0, 320, 0, -90, 0, 0, 0, 0, 0, 29844, 0, 0, 0, -15628, 0, -7139, 0, 0, 0, -43992, 0, 42974, 0, 0, 0, -17136, 0, 0, 0, 0, 0, -13342, 0, 36297, 0, 0, 0, 0, 0, 3005, 0, 0, 0, -16204, 0, 22698, 0, 0, 0, -30200, 0, -15372, 0, 0, 0, -29583, 0, 0, 0, 0, 0, -5954, 0, -29691, 0, 0, 0, 0, 0, 6480, 0, 0, 0, 40171, 0, -72306, 0, 0, 0, 50801, 0, 4779, 0, 0, 0, -58338, 0, 0, 0, 0, 0, 75272, 0, -51202, 0, 0, 0, 0, 0, -1764, 0, 0, 0, 42952, 0, -1960, 0, 0, 0, -1962, 0, -52579, 0, 0, 0, 41288, 0, 0, 0, 0, 0, -13775, 0, -49670, 0, 0, 0, 0, 0, -11592, 0, 0, 0, 2074, 0, 14005, 0, 0, 0, -3550, 0, 47096, 0, 0, 0, 38272, 0, 0, 0, 0, 0, -42111, 0, -7613, 0, 0, 0, 0, 0, -34372, 0, 0, 0, -22982, 0, -49528, 0, 0, 0, 88618, 0, 30106, 0, 0, 0, 6336, 0, 0, 0, 0, 0, 3388, 0, 13192, 0, 0, 0, 0, 0, 12844, 0, 0, 0, -513, 0, 25786, 0, 0, 0, -30353, 0, 7748, 0, 0, 0, -62428, 0, 0, 0, 0, 0, 43420, 0, 13806, 0, 0, 0, 0, 0, 18982, 0, 0, 0, -42728, 0, 30763, 0, 0, 0, -64602, 0, 74177, 0, 0, 0, 69148, 0, 0, 0, 0, 0, 1265, 0, -8866, 0, 0, 0, 0, 0, 1980, 0, 0, 0, -2560, 0, 55441, 0, 0, 0, -2268, 0, -77390, 0, 0, 0, -50733, 0, 0, 0, 0, 0, -17784, 0, 23219, 0, 0, 0, 0, 0, 66375, 0, 0, 0, -9734, 0, 36738, 0, 0, 0, -73499, 0, -3744, 0, 0, 0, 41306, 0, 0, 0, 0, 0, -72806, 0, 43875, 0, 0, 0, 0, 0, 3060, 0, 0, 0, 60944, 0, -15282, 0, 0, 0, -35077, 0, 3492, 0, 0, 0, 590, 0, 0, 0, 0, 0, -59562, 0, 52036, 0, 0, 0, 0, 0, 27664, 0, 0, 0, 2745, 0, 33453, 0, 0, 0, -12416, 0, -4653, 0, 0, 0, -28886, 0, 0, 0, 0, 0, -62316, 0, -42056, 0, 0, 0, 0, 0, -53092, 0, 0, 0, -1170, 0, 27577, 0, 0, 0, -39262, 0, 36442, 0, 0, 0, -5540, 0, 0, 0, 0, 0, -16110, 0, 40328, 0, 0, 0, 0, 0, 81566, 0, 0, 0, 26158, 0, -58832, 0, 0, 0, 31761, 0, -7670, 0, 0, 0, -6552, 0, 0, 0, 0, 0, 47750, 0, -44487, 0, 0, 0, 0, 0, -23194, 0, 0, 0, 48321, 0, -3880, 0, 0, 0, 137020, 0, -32816, 0, 0, 0, 2070, 0, 0, 0, 0, 0, 66708, 0, 15938, 0, 0, 0, 0, 0, 76048, 0, 0, 0, 87115, 0, -2176, 0, 0, 0, -63738, 0, -11449, 0, 0, 0, -67190, 0, 0, 0, 0, 0, -30524, 0, -4474, 0, 0, 0, 0, 0, 59841, 0, 0, 0, -31500, 0, -89128, 0, 0, 0, 139122, 0, 84340, 0, 0, 0, 137740, 0, 0, 0, 0, 0, 75335, 0, -605, 0, 0, 0, 0, 0, 34552, 0, 0, 0, 10656, 0, 12762, 0, 0, 0, -26271, 0, 81550, 0, 0, 0, -41737, 0, 0, 0, 0, 0, 62896, 0, 99828, 0, 0, 0, 0, 0, 76348, 0, 0, 0, 74785, 0, 19502, 0, 0, 0, -680, 0, -38745, 0, 0, 0, -167206, 0, 0, 0, 0, 0, -15876, 0, 35450, 0, 0, 0, 0, 0, -60814, 0, 0, 0, -53887, 0, -69192, 0, 0, 0, -85914, 0, 36045, 0, 0, 0, -91800, 0, 0, 0, 0, 0, -98995, 0, 45126, 0, 0, 0, 0, 0, 13511, 0, 0, 0, 106308, 0, 405, 0, 0, 0, -23166, 0, 3330, 0, 0, 0, 82129, 0, 0, 0, 0, 0, 164079, 0, 32239, 0, 0, 0, 0, 0, -576, 0, 0, 0, -49082, 0, -51922, 0, 0, 0, 3640, 0, 38116, 0, 0, 0, 42899, 0, 0, 0, 0, 0, 82624, 0, 102232, 0, 0, 0, 0, 0, 8594, 0, 0, 0, -49028, 0, -60200, 0, 0, 0, -13189, 0, 23815, 0, 0, 0, -50152, 0, 0, 0, 0, 0, -158184, 0, -76824, 0, 0, 0, 0, 0, -32976, 0, 0, 0, 4325, 0, -129896, 0, 0, 0, 8550, 0, 67427, 0, 0, 0, 48344, 0, 0, 0, 0, 0, 77985, 0, 105200, 0, 0, 0, 0, 0, -67815, 0, 0, 0, -83772, 0, -118728, 0, 0, 0, 114282, 0, -86848, 0, 0, 0, -180, 0, 0, 0, 0, 0, 7510, 0, -66024, 0, 0, 0, 0, 0, -59517, 0, 0, 0, 77998, 0, -39142, 0, 0, 0, 50171, 0, -86472, 0, 0, 0, 71136, 0, 0, 0, 0, 0, -106506, 0, -55232, 0, 0, 0, 0, 0, -43498, 0, 0, 0, 8829, 0, 89236, 0, 0, 0, 73589, 0, -49727, 0, 0, 0, -47376, 0, 0, 0, 0, 0, 67370, 0, -12544, 0, 0, 0, 0, 0, 1170, 0, 0, 0, -104670, 0, 76527, 0, 0, 0, -17582, 0, 79352, 0, 0, 0, -67262, 0, 0, 0, 0, 0, -13464, 0, 15956, 0, 0, 0, 0, 0, 86321, 0, 0, 0, 5860, 0, 52281, 0, 0, 0, 139230, 0, -24184, 0, 0, 0, 45396, 0, 0, 0, 0, 0, -22720, 0, 297596, 0, 0, 0, 0, 0, 81694, 0, 0, 0, -6412, 0, -114812, 0, 0, 0, -76271, 0, -52120, 0, 0, 0, 20119, 0, 0, 0, 0, 0, 142740, 0, -30034, 0, 0, 0, 0, 0, -77868, 0, 0, 0, 50103, 0, 65934, 0, 0, 0, -80316, 0, 5625, 0, 0, 0, 8820, 0, 0, 0, 0, 0, -3920, 0, 85230, 0, 0, 0, 0, 0, 40356, 0, 0, 0, -81900, 0, 163718, 0, 0, 0, 107384, 0, 71037, 0, 0, 0, -6170, 0, 0, 0, 0, 0, -83367, 0, 1684, 0, 0, 0, 0, 0, -23635, 0, 0, 0, 52808, 0, 76546, 0, 0, 0, 43488, 0, 43200, 0, 0, 0, 4576, 0, 0, 0, 0, 0, 70110, 0, -7100, 0, 0, 0, 0, 0, -62244, 0, 0, 0, -8914, 0, -138296, 0, 0, 0, -11196, 0, 23474, 0, 0, 0, -26613, 0, 0, 0, 0, 0, 25506, 0, 2835, 0, 0, 0, 0, 0, 7956, 0, 0, 0, 94581, 0, -52156, 0, 0, 0, 41216, 0, -162656, 0, 0, 0, 8096, 0, 0, 0, 0, 0, -89478, 0, 117962, 0, 0, 0, 0, 0, 127748, 0, 0, 0, -3564, 0, -37016, 0, 0, 0, -124852, 0, 65549, 0, 0, 0, 94104, 0, 0, 0, 0, 0, 67964, 0, 55198, 0, 0, 0, 0, 0, 117081, 0, 0, 0, 120478, 0, -125937, 0, 0, 0, 114102, 0, 25856, 0, 0, 0, 20525, 0, 0, 0, 0, 0, -38961, 0, 40563, 0, 0, 0, 0, 0, -97849, 0, 0, 0, 26384, 0, 127088, 0, 0, 0, 42804, 0, -148706, 0, 0, 0, 122625, 0, 0, 0, 0, 0, -5994, 0, 8344, 0, 0, 0, 0, 0, -15714, 0, 0, 0, 229684, 0, 64474, 0, 0, 0, 10750, 0, 19584, 0, 0, 0, -150962, 0, 0, 0, 0, 0, 73206, 0, -134506, 0, 0, 0, 0, 0, 2530, 0, 0, 0, -182169, 0, 16136, 0, 0, 0, -136372, 0, 88966, 0, 0, 0, -141232, 0, 0, 0, 0, 0, -40621, 0, -310930, 0, 0, 0, 0, 0, -129204, 0, 0, 0, -133272, 0, 63665, 0, 0, 0, 17568, 0, -9548, 0, 0, 0, -36167, 0, 0, 0, 0, 0, -116419, 0, -112516, 0, 0, 0, 0, 0, 134731, 0, 0, 0, 28404, 0, -119746, 0, 0, 0, 61803, 0, 35594, 0, 0, 0, 29434, 0, 0, 0, 0, 0, 11790, 0, 3618, 0, 0, 0, 0, 0, 69266, 0, 0, 0, -19152, 0, 2106, 0, 0, 0, -271076, 0, -95165, 0, 0, 0, -77616, 0, 0, 0, 0, 0, 202252, 0, -92924, 0, 0, 0, 0, 0, 101080, 0, 0, 0, 6120, 0, 136540, 0, 0, 0, 43250, 0, -99199, 0, 0, 0, 171828, 0, 0, 0, 0, 0, -234936, 0, -58636, 0, 0, 0, 0, 0, 8460, 0, 0, 0, -291388, 0, -49088, 0, 0, 0, -88574, 0, 56206, 0, 0, 0, 93037, 0, 0, 0, 0, 0, 65632, 0, -110231, 0, 0, 0, 0, 0, -140580, 0, 0, 0, -14170, 0, 5490, 0, 0, 0, -154728, 0, 29240, 0, 0, 0, -182718, 0, 0, 0, 0, 0, 6984, 0, 151615, 0, 0, 0, 0, 0, -166410, 0, 0, 0, 13248, 0, 45784, 0, 0, 0, -68535, 0, 234350, 0, 0, 0, -22644, 0, 0, 0, 0, 0, -88582, 0, -94420, 0, 0, 0, 0, 0, -266058, 0, 0, 0, 138001, 0, -45396, 0, 0, 0, -31108, 0, 1145, 0, 0, 0, 10750, 0, 0, 0, 0, 0, 90572, 0, -117692, 0, 0, 0, 0, 0, 9917, 0, 0, 0, -146448, 0, -57176, 0, 0, 0, -148266, 0, 120302, 0, 0, 0, 13905, 0, 0, 0, 0, 0, -227368, 0, -45449, 0, 0, 0, 0, 0, 77166, 0, 0, 0, 22010, 0, 1684, 0, 0, 0, -15340, 0, -81334, 0, 0, 0, 225859, 0, 0, 0, 0, 0, -180036, 0, -120979, 0, 0, 0, 0, 0, -3872, 0, 0, 0, -100921, 0, 257022, 0, 0, 0, -44402, 0, 45864, 0, 0, 0, 146588, 0, 0, 0, 0, 0, -127426, 0, -8260, 0, 0, 0, 0, 0, -83978, 0, 0, 0, 110813, 0, 116532, 0, 0, 0, -37498, 0, 4140, 0, 0, 0, -231988, 0, 0, 0, 0, 0, -111492, 0, -218250, 0, 0, 0, 0, 0, 208593, 0, 0, 0, 31460, 0, -144523, 0, 0, 0, 6552, 0, 50094, 0, 0, 0, 147560, 0, 0, 0, 0, 0, 184428, 0, 1224, 0, 0, 0, 0, 0, 358956, 0, 0, 0, 83070, 0, 128248, 0, 0, 0, 239396, 0, 17164, 0, 0, 0, -256932, 0, 0, 0, 0, 0, 294764, 0, 65645, 0, 0, 0, 0, 0, -130572, 0, 0, 0, -76068, 0, -7360, 0, 0, 0, 152096, 0, -78355, 0, 0, 0, -177988, 0, 0, 0, 0, 0, 138564, 0, -207072, 0, 0, 0, 0, 0, -76238, 0, 0, 0, -32872, 0, 190098, 0, 0, 0, 6610, 0, -292760, 0, 0, 0, -1210, 0, 0, 0, 0, 0, -233829, 0, 2592, 0, 0, 0, 0, 0, -95984, 0, 0, 0, -1634, 0, 139429, 0, 0, 0, -5994, 0, -109998, 0, 0, 0, 24961, 0, 0, 0, 0, 0, 144567, 0, -83980, 0, 0, 0, 0, 0, -94994, 0, 0, 0, 4270, 0, 275480, 0, 0, 0, 121176, 0, -161424, 0, 0, 0, 191785, 0, 0, 0, 0, 0, 23296, 0, 303129, 0, 0, 0, 0, 0, -25416, 0, 0, 0, 98707, 0, -300950, 0, 0, 0, -141849, 0, 16272, 0, 0, 0, 98986, 0, 0, 0, 0, 0, -1490, 0, -9872, 0, 0, 0, 0, 0, -177120, 0, 0, 0, 468, 0, 52128, 0, 0, 0, 189058, 0, -141605, 0, 0, 0, 53748, 0, 0, 0, 0, 0, -140931, 0, 108702, 0, 0, 0, 0, 0, 108953, 0, 0, 0, -128210, 0, 126091, 0, 0, 0, -180068, 0, -134668, 0, 0, 0, 278460, 0, 0, 0, 0, 0, -137817, 0, 16109, 0, 0, 0, 0, 0, 25220, 0, 0, 0, -10890, 0, -65492, 0, 0, 0, -29601, 0, 212904, 0, 0, 0, 220005, 0, 0, 0, 0, 0, 810, 0, -315945, 0, 0, 0, 0, 0, -151516, 0, 0, 0, 1705, 0, 26656, 0, 0, 0, 73233, 0, -98488, 0, 0, 0, -417100, 0, 0, 0, 0, 0, 129456, 0, 97992, 0, 0, 0, 0, 0, -51994, 0, 0, 0, 17046, 0, -156628, 0, 0, 0, -274014, 0, -148553, 0, 0, 0, 48064, 0, 0, 0, 0, 0, 10341, 0, 7280, 0, 0, 0, 0, 0, -323910, 0, 0, 0, -160448, 0, 31265, 0, 0, 0, -37296, 0, 3420, 0, 0, 0, 254183, 0, 0, 0, 0, 0, -303732, 0, 97660, 0, 0, 0, 0, 0, -101143, 0, 0, 0, 74610, 0, -145106, 0, 0, 0, 48280, 0, 144098, 0, 0, 0, -7065, 0, 0, 0, 0, 0, 133754, 0, -98164, 0, 0, 0, 0, 0, 221030, 0, 0, 0, -130536, 0, 185850, 0, 0, 0, -133407, 0, 110096, 0, 0, 0, 39006, 0, 0, 0, 0, 0, 124704, 0, -71604, 0, 0, 0, 0, 0, -78886, 0, 0, 0, -457452, 0, 81972, 0, 0, 0, 84874, 0, 7488, 0, 0, 0, 135018, 0, 0, 0, 0, 0, 212513, 0, -11720, 0, 0, 0, 0, 0, -124488, 0, 0, 0, -170352, 0, 105507, 0, 0, 0, -34272, 0, -10384, 0, 0, 0, 211608, 0, 0, 0, 0, 0, -69867, 0, -71767, 0, 0, 0, 0, 0, -139888, 0, 0, 0, 141246, 0, -32482, 0, 0, 0, 37504, 0, -236430, 0, 0, 0, -64233, 0, 0, 0, 0, 0, 67018, 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": "200.4.a.b", "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], [0], [0], [0], [0], [0], [-26], [0], [0], [0], [59], [0], [-28], [0], [0], [0], [5], [0], [109], [0], [0], [0], [-194], [0], [0], [0], [0], [0], [32], [0], [10], [0], [0], [0], [0], [0], [198], [0], [0], [0], [-117], [0], [-388], [0], [0], [0], [-68], [0], [333], [0], [0], [0], [-18], [0], [0], [0], [0], [0], [-392], [0], [-710], [0], [0], [0], [0], [0], [253], [0], [0], [0], [612], [0], [549], [0], [0], [0], [-1534], [0], [414], [0], [0], [0], [-121], [0], [0], [0], [0], [0], [81], [0], [728], [0], [0], [0], [0], [0], [1502], [0], [0], [0]]}