# Stored data for newform 784.4.a.g, downloaded from the LMFDB on 19 April 2024.
{"label": "784.4.a.g", "space_label": "784.4.a", "level": 784, "weight": 4, "hecke_orbit": 7, "hecke_orbit_code": 27021597831332624, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1326351757347429666, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [2, 1]], [5, [16, 1]]], "qexp_display": "q-2q^{3}-2^{4}q^{5}-23q^{9}+8q^{11}-28q^{13}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 12544, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 46.25749744450064, "hecke_ring_index": 1, "level_radical": 14, "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": [784, 1, [687, 197, 689], [1, 1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 7], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.013", "prec": 17}, {"__RealLiteral__": 0, "data": "0.998", "prec": 17}, {"__RealLiteral__": 0, "data": "0.011", "prec": 17}, {"__RealLiteral__": 0, "data": "1.989", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.951", "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], [7, -1]], "trace_display": [0, -2, -16, 0], "traces": [0, 1, 0, -2, 0, -16, 0, 0, 0, -23, 0, 8, 0, -28, 0, 32, 0, -54, 0, -110, 0, 0, 0, -48, 0, 131, 0, 100, 0, -110, 0, 12, 0, -16, 0, 0, 0, -246, 0, 56, 0, -182, 0, -128, 0, 368, 0, 324, 0, 0, 0, 108, 0, -162, 0, -128, 0, 220, 0, 810, 0, 488, 0, 0, 0, 448, 0, -244, 0, 96, 0, 768, 0, 702, 0, -262, 0, 0, 0, -440, 0, 421, 0, -1302, 0, 864, 0, 220, 0, -730, 0, 0, 0, -24, 0, 1760, 0, -294, 0, -184, 0, 688, 0, 1388, 0, 0, 0, -244, 0, 90, 0, 492, 0, 1318, 0, 768, 0, 644, 0, 0, 0, -1267, 0, 364, 0, -96, 0, 1776, 0, 256, 0, -1118, 0, 0, 0, -1600, 0, 2274, 0, -210, 0, -648, 0, -224, 0, 1760, 0, 0, 0, -2010, 0, -1112, 0, 1242, 0, -192, 0, -124, 0, 324, 0, 0, 0, -2008, 0, 256, 0, 2884, 0, -1413, 0, 2530, 0, -2228, 0, 0, 0, -1620, 0, 820, 0, -3892, 0, -976, 0, 3936, 0, -432, 0, 0, 0, 5048, 0, -2962, 0, -896, 0, 3334, 0, 1860, 0, 488, 0, 0, 0, 2912, 0, 1104, 0, -880, 0, 4268, 0, -1536, 0, 2048, 0, 0, 0, -1404, 0, 1512, 0, -5432, 0, -3013, 0, -2046, 0, 2980, 0, 0, 0, 4458, 0, -5184, 0, 880, 0, -4440, 0, -3302, 0, -3542, 0, 0, 0, 3080, 0, 2604, 0, 1582, 0, -384, 0, -1728, 0, -2354, 0, 0, 0, 2530, 0, 3872, 0, 2592, 0, 1460, 0, -180, 0, 2032, 0, 0, 0, 1048, 0, -5426, 0, -276, 0, 842, 0, -3782, 0, -3520, 0, 0, 0, -1997, 0, 588, 0, 4312, 0, -12960, 0, 800, 0, 1344, 0, 0, 0, -1376, 0, -7808, 0, 2674, 0, -2776, 0, -3768, 0, -2438, 0, 0, 0, -3186, 0, -880, 0, 488, 0, 5940, 0, -3668, 0, -180, 0, 0, 0, -8672, 0, 5658, 0, 3904, 0, 814, 0, -2636, 0, 96, 0, 0, 0, -1536, 0, -9344, 0, 5180, 0, -2800, 0, -12178, 0, -12288, 0, 0, 0, -440, 0, 5241, 0, 2534, 0, -11232, 0, -9816, 0, 4186, 0, 0, 0, -442, 0, 192, 0, 3080, 0, 3960, 0, -3552, 0, 6708, 0, 0, 0, 2944, 0, -13350, 0, 2592, 0, 2236, 0, 7040, 0, 1356, 0, 0, 0, 6222, 0, -336, 0, -6736, 0, -1968, 0, -5150, 0, -4548, 0, 0, 0, 20832, 0, 420, 0, 2310, 0, 1262, 0, -7452, 0, -7074, 0, 0, 0, 448, 0, 4488, 0, -17038, 0, -3520, 0, 5280, 0, 16200, 0, 0, 0, 8772, 0, 11680, 0, 4020, 0, 2130, 0, -1456, 0, 2224, 0, 0, 0, 10534, 0, -5400, 0, 9268, 0, 9392, 0, 384, 0, -10806, 0, 0, 0, 248, 0, -1024, 0, -14410, 0, 3726, 0, 4940, 0, 6888, 0, 0, 0, 4704, 0, 5216, 0, 4016, 0, -4412, 0, 5940, 0, 2944, 0, 0, 0, -19060, 0, -5768, 0, 12768, 0, -11008, 0, 2826, 0, 5500, 0, 0, 0, -11000, 0, -22208, 0, 2592, 0, 4456, 0, 7338, 0, -17582, 0, 0, 0, -648, 0, -9863, 0, -18630, 0, 5096, 0, 3904, 0, -1640, 0, 0, 0, -1618, 0, 7784, 0, -1440, 0, -16144, 0, -11224, 0, 12100, 0, 0, 0, -7872, 0, 4654, 0, 3584, 0, 864, 0, 10078, 0, -21088, 0, 0, 0, -5930, 0, 19048, 0, -10096, 0, -6288, 0, 14366, 0, 5924, 0, 0, 0, -1296, 0, -10304, 0, -3626, 0, -1320, 0, -6668, 0, 1062, 0, 0, 0, -3720, 0, 10200, 0, 25158, 0, 5612, 0, 20272, 0, 25664, 0, 0, 0, -9072, 0, 19018, 0, -5824, 0, 17334, 0, 18730, 0, -4800, 0, 0, 0, -14839, 0, 1760, 0, 13284, 0, 6928, 0, -8536, 0, -28416, 0, 0, 0, -17664, 0, 16302, 0, 4718, 0, -4096, 0, -21436, 0, 6480, 0, 0, 0, 4458, 0, 17888, 0, -16146, 0, 26640, 0, -7432, 0, -3024, 0, 0, 0, 5280, 0, 10864, 0, 3904, 0, 58, 0, 13100, 0, 21516, 0, 0, 0, 4092, 0, -18108, 0, -36384, 0, -5960, 0, 4536, 0, -10078, 0, 0, 0, 3360, 0, 9828, 0, -8916, 0, 18762, 0, 27060, 0, 10368, 0, 0, 0, 6810, 0, 10120, 0, -576, 0, 3584, 0, 8880, 0, 4860, 0, 0, 0, 6604, 0, -14410, 0, -13636, 0, -4283, 0, 6912, 0, -2088, 0, 0, 0, -1952, 0, 5160, 0, -6160, 0, 28152, 0, 32160, 0, 29946, 0, 0, 0, 16808, 0, -3164, 0, 17792, 0, 21674, 0, 768, 0, -7422, 0, 0, 0, -19872, 0, -22680, 0, -13790, 0, 4708, 0, 6232, 0, 1572, 0, 0, 0, 20020, 0, 6144, 0, -11000, 0, 1984, 0, -1766, 0, -7744, 0, 0, 0, -13664, 0, -5184, 0, -1204, 0, -17496, 0, 16790, 0, 5616, 0, 0, 0, 360, 0, -7050, 0, 23282, 0, -4064, 0, 32128, 0, 14080, 0, 0, 0, 10142, 0, 9192, 0, -2096, 0, 46716, 0, -11240, 0, 10852, 0, 0, 0, -46144, 0, 1200, 0, 700, 0, -12289, 0, -1684, 0, 22608, 0, 0, 0, 7564, 0, 11808, 0, 37492, 0, -40480, 0, -28894, 0, -2770, 0, 0, 0, -17688, 0, 35648, 0, 3994, 0, -3520, 0, 6832, 0, 6762, 0, 0, 0, -33566, 0, -8624, 0, 16758, 0, -11468, 0, 25920, 0, -50356, 0, 0, 0, 3368, 0, -35640, 0, -13120, 0, -2688, 0, -1320, 0, 8748, 0, 0, 0, 62272, 0, 8716, 0, -15824, 0, -7632, 0, -10416, 0, 15616, 0, 0, 0, 23080, 0, -5348, 0, -21504, 0, -32226, 0, -31924, 0, -45110, 0, 0, 0, 7536, 0, 6912, 0, -16674, 0, 4876, 0, -43832, 0, 8736, 0, 0, 0, 736, 0, -19656, 0, 6372, 0, 38138, 0, -80768, 0, 1760, 0, 0, 0, -29647, 0, 5612, 0, 47392, 0, -26224, 0, -11880, 0, 18762, 0, 0, 0, 7336, 0, 38394, 0, -5840, 0, -2070, 0, 5388, 0, -53344, 0, 0, 0, 6144, 0, -25472, 0, 17344, 0, -29760, 0, 17096, 0, -24600, 0, 0, 0, -43740, 0, -7808, 0, 17820, 0, -8930, 0, -1628, 0, -53468, 0, 0, 0, -30314, 0, 33300, 0, -50652, 0, -192, 0, -23842, 0, 12320, 0, 0, 0, 7008, 0, -63862, 0, -17664, 0, -26352, 0, -8500, 0, 18688, 0, 0, 0, 14080, 0, -10360, 0, 39550, 0, -15892, 0, -11788, 0, -68288, 0, 0, 0, 24356, 0, 30442, 0, -29232, 0, 24576, 0, -2352, 0, 44840, 0, 0, 0, 27060, 0, -16768, 0, 880, 0, 36456, 0, -15552, 0, -10482, 0, 0, 0, 6616, 0, 29141, 0, 65982, 0, 338, 0, 22464, 0, 40486, 0, 0, 0, 19632, 0, -53808, 0, -24192, 0, -18200, 0, 16060, 0, 5504, 0, 0, 0, 86912, 0, -39866, 0, 884, 0, -89100, 0, -6302, 0, 2208, 0, 0, 0, 55810, 0, -6160, 0, 11104, 0, 32736, 0, -7920, 0, 13176, 0, 0, 0, -40848, 0, -47680, 0, -2952, 0, -13416, 0, -13148, 0, -7618, 0, 0, 0, 20440, 0, -53680, 0, -12800, 0, -73068, 0, -71328, 0, 26700, 0, 0, 0, 47188, 0, -5184, 0, 42444, 0, -1952, 0, 25714, 0, -2172, 0, 0, 0, -14080, 0, -22924, 0, 20020, 0, -2712, 0, 74622, 0, 71040, 0, 0, 0, 720, 0, 5102, 0, -12444, 0, 52832, 0, -41472, 0, 672, 0, 0, 0, -48462, 0, 56672, 0, -19194, 0, 7776, 0, 3936, 0, 2088, 0, 0, 0, 10300, 0, 230, 0, 5012, 0, -52302, 0, -49280, 0, 5976, 0, 0, 0, -37908, 0, 10544, 0, -41664, 0, 14080, 0, -74170, 0, 4830, 0, 0, 0, -25312, 0, -4620, 0, 57890, 0, 8232, 0, -2524, 0, 6144, 0, 0, 0, 32400, 0, -2184, 0, 26840, 0, 14148, 0, -19304, 0, -64860, 0, 0, 0, 41112, 0, 37664, 0, 5152, 0, 48750, 0, 29062, 0, -8976, 0, 0, 0, 8574, 0, 34076, 0, 49728, 0, 42152, 0, -40480, 0, -28166, 0, 0, 0, -10560, 0, -19264, 0, -61952, 0, -32400, 0, -12280, 0, 60338, 0, 0, 0, -21222, 0, -21104, 0, -17544, 0, -20784, 0, -1536, 0, -23360, 0, 0, 0, -38864, 0, 46230, 0, 23760, 0, 2880, 0, -4260, 0, -84480, 0, 0, 0, 2912, 0, -32512, 0, -38880, 0, 25576, 0, 72578, 0, -35640, 0, 0, 0, -56104, 0, 9863, 0, -21068, 0, 32538, 0, -768, 0, -22734, 0, 0, 0, 66002, 0, -18536, 0, 86816, 0, -77220, 0, -18784, 0, 6832, 0, 0, 0, 4416, 0, 14208, 0, -73640, 0, 21612, 0, -23424, 0, -13472, 0, 0, 0, -65710, 0, 70308, 0, 2852, 0, 60512, 0, -2520, 0, 2048, 0, 0, 0, -56888, 0, 28820, 0, 20594, 0, 6050, 0, -16200, 0, -52138, 0, 0, 0, -9880, 0, 46600, 0, -8944, 0, -13776, 0, 31952, 0, 12224, 0, 0, 0, 12888, 0, -21302, 0, -9408, 0, 3888, 0, -45530, 0, -10432, 0, 0, 0, -68992, 0, 46184, 0, -36904, 0, -13232, 0, 8824, 0, 106110, 0, 0, 0, -11880, 0, -107318, 0, 58338, 0, -12800, 0, 86784, 0, 26570, 0, 0, 0, -12202, 0, -21504, 0, 38120, 0, -55260, 0, 48400, 0, -66332, 0, 0, 0, 18192, 0, -25536, 0, -7168, 0, 39420, 0, 22016, 0, 44772, 0, 0, 0, 32499, 0, -21888, 0, 63928, 0, -11000, 0, -1680, 0, 90162, 0, 0, 0, -42784, 0, 17820, 0, -46310, 0, 11712, 0, 94848, 0, 44416, 0, 0, 0, -17690, 0, -5184, 0, -92778, 0, 60288, 0, 51244, 0, 40420, 0, 0, 0, -14676, 0, 39008, 0, -69776, 0, 35164, 0, 68402, 0, 35476, 0, 0, 0, 143220, 0, 31760, 0, 1296, 0, 84432, 0, 50976, 0, 19726, 0, 0, 0, 31488, 0, 81000, 0, 14080, 0, -78706, 0, -10192, 0, 55998, 0, 0, 0, -7808, 0, -23344, 0, -92890, 0, -18860, 0, 34232, 0, -95040, 0, 0, 0, 49540, 0, 52562, 0, 3236, 0, 2688, 0, 67254, 0, 89516, 0, 0, 0, -36864, 0, 2880, 0, 84336, 0, -16080, 0, 32288, 0, -1944, 0, 0, 0, 48800, 0, 15876, 0, -49728, 0, -24200, 0, 138752, 0, -92654, 0, 0, 0, -8896, 0, -72008, 0, -90528, 0, 25576, 0, 85360, 0, -9308, 0, 0, 0, -31964, 0, -7168, 0, -33696, 0, -35797, 0, 9936, 0, -13024, 0, 0, 0, -20156, 0, 80300, 0, -120008, 0, 42176, 0, -34214, 0, 24950, 0, 0, 0, 31304, 0, -1536, 0, 11860, 0, 47070, 0, -89100, 0, -38096, 0, 0, 0, -37152, 0, -116104, 0, 77798, 0, 87932, 0, 12576, 0, -992, 0, 0, 0, -28732, 0, -99422, 0, 149504, 0, 68126, 0, -79704, 0, -22612, 0, 0, 0, -82880, 0, 128416, 0, 2592, 0, -74952, 0, 21422, 0, 44800, 0, 0, 0, 5440, 0, 7252, 0, 23296, 0, 194848, 0, 2640, 0, -53680, 0, 0, 0, -76682, 0, 100608, 0, -73234, 0, -2124, 0, -63672, 0, -122512, 0, 0, 0, 8576, 0, 128190, 0, -42780, 0, -16064, 0, 7040, 0, -20400, 0, 0, 0, 108142, 0, -50316, 0, -83856, 0, 5880, 0, -24400, 0, 56282, 0, 0, 0, -40544, 0, 21120, 0, 13176, 0, -51328, 0, 74408, 0, 91962, 0, 0, 0, 9720, 0, 48168, 0, 18144, 0, 157056, 0, 23072, 0, -38036, 0, 0, 0, 32340, 0, -66976, 0, -74116, 0, -63123, 0, -34668, 0, -4860, 0, 0, 0, -37460, 0, -11304, 0, 89768, 0, -20208, 0, 7072, 0, 51074, 0, 0, 0, -75312, 0, 82018, 0, 29678, 0, -34746, 0, 53660, 0, 20240, 0, 0, 0, -49280, 0, -26568, 0, -17010, 0, 5856, 0, -13856, 0, -63360, 0, 0, 0, -98164, 0, 122422, 0, -17824, 0, 56832, 0, -75686, 0, 62496, 0, 0, 0, -63162, 0, -107328, 0, 76800, 0, -75680, 0, -71172, 0, -32604, 0, 0, 0, -58968, 0, -9436, 0, -5838, 0, -143162, 0, -47104, 0, 56280, 0, 0, 0, 42872, 0, 26840, 0, 213600, 0, -12960, 0, 79340, 0, 33952, 0, 0, 0, -41472, 0, -152680, 0, -8916, 0, 39852, 0, 31136, 0, -35776, 0, 0, 0, 6560, 0, 70200, 0, -49028, 0, -57640, 0, -53280, 0, 22430, 0, 0, 0, 14864, 0, -21696, 0, 63854, 0, -34776, 0, -31136, 0, -130398, 0, 0, 0, 46794, 0, 40160, 0, -10560, 0, -92248, 0, -99552, 0, 124936, 0, 0, 0, 42288, 0, -7808, 0, 5376, 0, 24474, 0, -116, 0, -41472, 0, 0, 0, 55151, 0, 4656, 0, 42000, 0, -43032, 0, 26840, 0, 31488, 0, 0, 0, 119120, 0, 3472, 0, 47058, 0, 82400, 0, 35040, 0, 36216, 0, 0, 0, -2402, 0, 72768, 0, 68418, 0, -84480, 0, -68540, 0, 23928, 0, 0, 0, -9072, 0, -113590, 0, -9900, 0, 20156, 0, -170562, 0, -2928, 0, 0, 0, -84918, 0, -12648, 0, -6720, 0, 115456, 0, 173350, 0, -19656, 0, 0, 0, -36960, 0, -102534, 0, -11970, 0, 40384, 0, -37524, 0, -20192, 0, 0, 0, -54120, 0, -167712, 0, -82138, 0, 119232, 0, -77220, 0, 56224, 0, 0, 0, -23696, 0, 5184, 0, -13620, 0, -86910, 0, 122582, 0, -44000, 0, 0, 0, 154594, 0, 1152, 0, -145992, 0, -91688, 0, -7168, 0, -144980, 0, 0, 0, 102120, 0, -59802, 0, -71808, 0, -9720, 0, -95904, 0, 120818, 0, 0, 0, 272608, 0, 26672, 0, 75946, 0, -80752, 0, 29484, 0, 28820, 0, 0, 0, 142640, 0, 27272, 0, -199260, 0, -84480, 0, 104200, 0, 14880, 0, 0, 0, -13824, 0, -259200, 0, 101080, 0, 4176, 0, 9216, 0, -189502, 0, 0, 0, 83056, 0, 1153, 0, 3904, 0, 176178, 0, -140352, 0, -10320, 0, 0, 0, 72862, 0, -70840, 0, -95630, 0, 60372, 0, -56304, 0, 14112, 0, 0, 0, -64320, 0, 177834, 0, 162260, 0, -130200, 0, -79242, 0, -34080, 0, 0, 0, 62384, 0, 22268, 0, -33616, 0, 23296, 0, -120048, 0, -36386, 0, 0, 0, 8424, 0, -35584, 0, 14434, 0, -85510, 0, -43348, 0, -72018, 0, 0, 0, 8832, 0, 20736, 0, 41398, 0, 14844, 0, -168544, 0, 82084, 0, 0, 0, 48400, 0, -82202, 0, 86400, 0, -150106, 0, 139370, 0, 45360, 0, 0, 0, -148288, 0, 27580, 0, -116340, 0, -13792, 0, 54142, 0, -150272, 0, 0, 0, -12464, 0, 34144, 0, -33024, 0, -3144, 0, -22960, 0, -122796, 0, 0, 0, -109222, 0, 172896, 0, -40040, 0, -197920, 0, -75892, 0, -12288, 0, 0, 0, 202616, 0, -46310, 0, 172872, 0, 108976, 0, -3968, 0, 129736, 0, 0, 0, 3532, 0, 11340, 0, 16384, 0, -89056, 0, -66624, 0, 40462, 0, 0, 0, 10560, 0, 53514, 0, 27328, 0, -188858, 0, -198732, 0, -59616, 0, 0, 0, -41210, 0, 2408, 0, 119182, 0, -79040, 0, 34992, 0, 154380, 0, 0, 0, -73000, 0, -110208, 0, 143220, 0, -11232, 0, -184998, 0, -195360, 0, 0, 0, -13966, 0, -147420, 0, 4140, 0, 123072, 0, -38514, 0, 14100, 0, 0, 0, 12096, 0, -46564, 0, -83456, 0, -33066, 0, -46736, 0, 155678, 0, 0, 0, -64256, 0, 95376, 0, -5280, 0, -28160, 0, -43456, 0, 70592, 0, 0, 0, -85700, 0, 11712, 0, -20284, 0, -95040, 0, 42194, 0, -18384, 0, 0, 0, 132838, 0, -24104, 0, 11116, 0, 60024, 0, -93432, 0, -141344, 0, 0, 0, 22480, 0, 122980, 0, -52488, 0, 124798, 0, 304960, 0, -16368, 0, 0, 0, -88816, 0, -147328, 0, 92288, 0, -4320, 0, 82936, 0, 5052, 0, 0, 0, -204288, 0, -1400, 0, 23840, 0, 53622, 0, 24578, 0, 90128, 0, 0, 0, -19366, 0, -126972, 0, 108540, 0, -45216, 0, -103680, 0, -174690, 0, 0, 0, -164688, 0, -88000, 0, 86986, 0, -115050, 0, -241768, 0, -23616, 0, 0, 0, 4654, 0, -74984, 0, -93352, 0, 35664, 0, 176000, 0, 60048, 0, 0, 0, 57788, 0, -15624, 0, 181828, 0, 5540, 0, 118690, 0, 80300, 0, 0, 0, -41472, 0, -52080, 0, 35376, 0, 55928, 0, 63142, 0, -71296, 0, 0, 0, -63264, 0, 45931, 0, -250140, 0, -117408, 0, 7040, 0, 103290, 0, 0, 0, -13664, 0, 281312, 0, -22974, 0, -29400, 0, -41732, 0, -62464, 0, 0, 0, -188928, 0, -35520, 0, 67132, 0, 159798, 0, 10368, 0, -99176, 0, 0, 0, 23100, 0, -33516, 0, 157808, 0, -60664, 0, 22936, 0, -26416, 0, 0, 0, 298080, 0, 49874, 0, -101010, 0, 100712, 0, 18968, 0, -81536, 0, 0, 0, 6696, 0, 190408, 0, -28336, 0, -31964, 0, -19024, 0, 71280, 0, 0, 0, -6908, 0, 26240, 0, -129276, 0, 148990, 0, -30912, 0, -196128, 0, 0, 0, 2640, 0, 155100, 0, -172692, 0, -17496, 0, 25888, 0, 164054, 0, 0, 0, 114808, 0, -134702, 0, -124544, 0, 24640, 0, -209540, 0, -17432, 0, 0, 0, 11790, 0, 68800, 0, 54810, 0, 245628, 0, 15264, 0, 258304, 0, 0, 0, 20832, 0, 12522, 0, -119504, 0, 179584, 0, 44408, 0, 146200, 0, 0, 0, 155378, 0, -193600, 0, -46160, 0, -8760, 0, 12656, 0, -61502, 0, 0, 0, 67376, 0, 43008, 0, 108432, 0, 262440, 0, 64452, 0, -8094, 0, 0, 0, 138800, 0, 60816, 0, -74464, 0, 90220, 0, 230820, 0, 199852, 0, 0, 0, -57344, 0, -57786, 0, 86664, 0, -94498, 0, 275798, 0, -13824, 0, 0, 0, -122633, 0, 33348, 0, 32340, 0, -161248, 0, 56074, 0, -53730, 0, 0, 0, 87664, 0, 172658, 0, -18832, 0, -17472, 0, 221100, 0, -17978, 0, 0, 0, 33074, 0, -155736, 0, -1472, 0, 209032, 0, 94880, 0, 39312, 0, 0, 0, 119708, 0, 73278, 0, -304768, 0, -2406, 0, -76276, 0, 295188, 0, 0, 0, 161536, 0, 158112, 0, 122320, 0, 20240, 0, 76302, 0, 4608, 0, 0, 0, -125880, 0, 31232, 0, 59294, 0, -229856, 0, 1244, 0, -24400, 0, 0, 0, 30976, 0, -94784, 0, -225414, 0, 152096, 0, 52448, 0, -89472, 0, 0, 0, -136620, 0, 159690, 0, -139776, 0, -37524, 0, 20736, 0, 189656, 0, 0, 0, -85248, 0, 108240, 0, 84364, 0, -128144, 0, -75680, 0, -76788, 0, 0, 0, 58016, 0, 11680, 0, 269990, 0, 120312, 0, 9000, 0, 21120, 0, 0, 0, -10776, 0, 57288, 0, -129878, 0, 106688, 0, -145584, 0, -1440, 0, 0, 0, -254848, 0, -16992, 0, -12288, 0, 197850, 0, 122022, 0, 50944, 0, 0, 0, -83440, 0, 199456, 0, 16256, 0, 13640, 0, 59520, 0, -152680, 0, 0, 0, -34192, 0, -127764, 0, -163200, 0, -103566, 0, 205140, 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": "7.4.a.a", "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], [-2], [0], [-16], [0], [0], [0], [-23], [0], [8], [0], [-28], [0], [32], [0], [-54], [0], [-110], [0], [0], [0], [-48], [0], [131], [0], [100], [0], [-110], [0], [12], [0], [-16], [0], [0], [0], [-246], [0], [56], [0], [-182], [0], [-128], [0], [368], [0], [324], [0], [0], [0], [108], [0], [-162], [0], [-128], [0], [220], [0], [810], [0], [488], [0], [0], [0], [448], [0], [-244], [0], [96], [0], [768], [0], [702], [0], [-262], [0], [0], [0], [-440], [0], [421], [0], [-1302], [0], [864], [0], [220], [0], [-730], [0], [0], [0], [-24], [0], [1760], [0], [-294], [0], [-184], [0]]}