# Stored data for newform 2352.4.a.bi, downloaded from the LMFDB on 23 April 2024.
{"label": "2352.4.a.bi", "space_label": "2352.4.a", "level": 2352, "weight": 4, "hecke_orbit": 35, "hecke_orbit_code": 153122387397708080, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1372573341888315497, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[5, [-12, 1]], [11, [20, 1]]], "qexp_display": "q+3q^{3}+12q^{5}+9q^{9}-20q^{11}-84q^{13}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 37632, "fricke_eigenval": -1, "atkin_lehner_string": "---", "analytic_conductor": 138.77249233350193, "hecke_ring_index": 1, "level_radical": 42, "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": [2352, 1, [1471, 1765, 785, 2257], [1, 1, 1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 3, 7], "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": "1.003", "prec": 17}, {"__RealLiteral__": 0, "data": "0.041", "prec": 17}, {"__RealLiteral__": 0, "data": "2.011", "prec": 17}, {"__RealLiteral__": 0, "data": "0.093", "prec": 17}, {"__RealLiteral__": 0, "data": "5.030", "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], [7, -1]], "trace_display": [0, 3, 12, 0], "traces": [0, 1, 0, 3, 0, 12, 0, 0, 0, 9, 0, -20, 0, -84, 0, 36, 0, -96, 0, -12, 0, 0, 0, 176, 0, 19, 0, 27, 0, 58, 0, 264, 0, -60, 0, 0, 0, 258, 0, -252, 0, 0, 0, -156, 0, 108, 0, 408, 0, 0, 0, -288, 0, -722, 0, -240, 0, -36, 0, -492, 0, -492, 0, 0, 0, -1008, 0, -412, 0, 528, 0, -296, 0, 240, 0, 57, 0, 0, 0, -776, 0, 81, 0, -924, 0, -1152, 0, 174, 0, -744, 0, 0, 0, 792, 0, -144, 0, -168, 0, -180, 0, -1524, 0, 408, 0, 0, 0, 820, 0, -918, 0, 774, 0, -110, 0, 2112, 0, -756, 0, 0, 0, -931, 0, 0, 0, -1272, 0, -16, 0, -468, 0, -1692, 0, 0, 0, 324, 0, 1126, 0, -1092, 0, 1224, 0, 1680, 0, 696, 0, 0, 0, 1070, 0, 120, 0, -864, 0, 3168, 0, 1836, 0, -2166, 0, 0, 0, -916, 0, -720, 0, -504, 0, 4859, 0, -108, 0, -1836, 0, 0, 0, -1476, 0, -2372, 0, -1092, 0, -1476, 0, 3096, 0, 1920, 0, 0, 0, -2512, 0, -2430, 0, -3024, 0, -1762, 0, -3096, 0, -1236, 0, 0, 0, 0, 0, 1584, 0, 240, 0, -156, 0, -888, 0, -1872, 0, 0, 0, 720, 0, 8064, 0, -5040, 0, 171, 0, -2172, 0, 2700, 0, 0, 0, -3802, 0, 4896, 0, -2328, 0, 4408, 0, 3096, 0, 243, 0, 0, 0, 1008, 0, -2772, 0, 924, 0, -3520, 0, -3456, 0, -2760, 0, 0, 0, 522, 0, 2360, 0, -8664, 0, -2232, 0, 4020, 0, -4800, 0, 0, 0, -380, 0, 6446, 0, 2376, 0, -2602, 0, 6900, 0, -432, 0, 0, 0, 4303, 0, -504, 0, -4452, 0, -5904, 0, -540, 0, -14784, 0, 0, 0, -4572, 0, -5904, 0, 2436, 0, 1224, 0, 7488, 0, -1752, 0, 0, 0, -1562, 0, -1160, 0, 2460, 0, 1152, 0, -1596, 0, -2754, 0, 0, 0, 7092, 0, 2322, 0, -4944, 0, 366, 0, -330, 0, -5280, 0, 0, 0, 6336, 0, 6364, 0, -10500, 0, -2268, 0, 408, 0, -3552, 0, 0, 0, 11936, 0, -6715, 0, -2793, 0, 2880, 0, 2448, 0, 0, 0, 0, 0, 11374, 0, -3816, 0, -4872, 0, 5892, 0, -48, 0, 10488, 0, 0, 0, -1404, 0, 4514, 0, -16896, 0, -5076, 0, -9312, 0, -6036, 0, 0, 0, -6770, 0, -22176, 0, 972, 0, -5160, 0, 12504, 0, 3378, 0, 0, 0, -11088, 0, -3276, 0, -9492, 0, 5182, 0, 3672, 0, -1824, 0, 0, 0, 5040, 0, 5720, 0, 13608, 0, 2088, 0, -2112, 0, -12864, 0, 0, 0, 13252, 0, -8928, 0, 3210, 0, 226, 0, 0, 0, 360, 0, 0, 0, -11334, 0, -2592, 0, -1596, 0, -12728, 0, 9504, 0, 3012, 0, 0, 0, 5508, 0, 3120, 0, -228, 0, -6498, 0, 4296, 0, -21672, 0, 0, 0, -2016, 0, 8184, 0, -2748, 0, 12164, 0, -5568, 0, -2160, 0, 0, 0, -972, 0, -1512, 0, -7728, 0, -18288, 0, 14577, 0, 11604, 0, 0, 0, -324, 0, 4896, 0, -8160, 0, -5508, 0, -10848, 0, 18132, 0, 0, 0, -25344, 0, 18809, 0, -4428, 0, 0, 0, 9840, 0, -7116, 0, 0, 0, 6950, 0, -3276, 0, -11016, 0, -17012, 0, -4428, 0, -696, 0, 0, 0, 9288, 0, 3926, 0, 13104, 0, 5760, 0, 18828, 0, -1320, 0, 0, 0, 11990, 0, 15716, 0, -7536, 0, 3344, 0, -13872, 0, -7290, 0, 0, 0, 14440, 0, -9072, 0, -8820, 0, -3168, 0, -5286, 0, -16872, 0, 0, 0, -9288, 0, 6056, 0, 10752, 0, -3708, 0, -11172, 0, -20256, 0, 0, 0, -34272, 0, -28190, 0, 0, 0, 29318, 0, -24348, 0, 4752, 0, 0, 0, -17639, 0, 720, 0, -24768, 0, 25184, 0, -468, 0, -192, 0, 0, 0, -2664, 0, 32318, 0, 3948, 0, -5616, 0, -13848, 0, 9840, 0, 0, 0, -3158, 0, -20304, 0, 2160, 0, 24596, 0, -15468, 0, 24192, 0, 0, 0, 10208, 0, -15120, 0, 9840, 0, 13470, 0, 513, 0, -9564, 0, 0, 0, -6516, 0, -13852, 0, 13512, 0, 8100, 0, 60648, 0, 324, 0, 0, 0, -13104, 0, 0, 0, -11406, 0, 24922, 0, -3096, 0, 14688, 0, 0, 0, -17886, 0, -6984, 0, 46464, 0, 20160, 0, 13224, 0, 6792, 0, 0, 0, 9288, 0, 1102, 0, -1512, 0, 729, 0, 14976, 0, -11244, 0, 0, 0, 8240, 0, 1996, 0, 3024, 0, 656, 0, 12840, 0, -8316, 0, 0, 0, -1056, 0, 2772, 0, 1440, 0, -18702, 0, -10560, 0, 17904, 0, 0, 0, -10368, 0, 41328, 0, -7560, 0, -8280, 0, -14292, 0, 5016, 0, 0, 0, 0, 0, 5920, 0, 1566, 0, 22032, 0, -26364, 0, 7080, 0, 0, 0, 41328, 0, -25992, 0, 17220, 0, -39168, 0, -6696, 0, -4800, 0, 0, 0, 12060, 0, 16442, 0, 31332, 0, -14400, 0, -10992, 0, 1872, 0, 0, 0, -25810, 0, -12368, 0, -1140, 0, -6316, 0, -23868, 0, 19338, 0, 0, 0, -6048, 0, 7128, 0, 48216, 0, -21025, 0, -7806, 0, 58308, 0, 0, 0, 20700, 0, 45408, 0, -27300, 0, -1296, 0, 8640, 0, -24372, 0, 0, 0, -2176, 0, -22032, 0, 12909, 0, 15520, 0, 34608, 0, -1512, 0, 0, 0, -27574, 0, -13356, 0, 16968, 0, 1860, 0, -17712, 0, -2280, 0, 0, 0, -1620, 0, -4896, 0, -28464, 0, -44352, 0, 15312, 0, 69312, 0, 0, 0, -13104, 0, -36084, 0, -13716, 0, -24152, 0, 18480, 0, -17712, 0, 0, 0, -36336, 0, 7308, 0, 24864, 0, 4902, 0, 3672, 0, 432, 0, 0, 0, 22464, 0, 23040, 0, 22176, 0, -5256, 0, -43524, 0, 0, 0, 0, 0, -1868, 0, -20160, 0, -4686, 0, -9238, 0, -30144, 0, -3480, 0, 0, 0, 39905, 0, 7380, 0, -29160, 0, 30616, 0, 3456, 0, 27540, 0, 0, 0, -4788, 0, -16402, 0, 14880, 0, -8262, 0, -55176, 0, -21144, 0, 0, 0, -27456, 0, -27096, 0, 21276, 0, -37152, 0, -16812, 0, 6966, 0, 0, 0, 47232, 0, -14832, 0, 8664, 0, -37294, 0, 1098, 0, -23004, 0, 0, 0, -990, 0, 1940, 0, 12348, 0, -15840, 0, 0, 0, 65184, 0, 0, 0, 43240, 0, -29338, 0, 19008, 0, 47232, 0, -9144, 0, 19092, 0, 0, 0, 2880, 0, -31500, 0, 49560, 0, -2900, 0, -6804, 0, -1872, 0, 0, 0, 1224, 0, 17954, 0, 5712, 0, -10656, 0, 3360, 0, -21660, 0, 0, 0, 14964, 0, -2964, 0, 35808, 0, 77616, 0, 71808, 0, -20145, 0, 0, 0, 62336, 0, -8379, 0, -38052, 0, -7166, 0, 8640, 0, 1272, 0, 0, 0, 7344, 0, 14120, 0, 96768, 0, 0, 0, -23196, 0, 30480, 0, 0, 0, -60480, 0, 63174, 0, 34122, 0, 5904, 0, -7212, 0, -11448, 0, 0, 0, 25990, 0, -14616, 0, -8160, 0, -26064, 0, 17676, 0, 39552, 0, 0, 0, -144, 0, 32400, 0, 68112, 0, 31464, 0, -51144, 0, 39072, 0, 0, 0, 62496, 0, 5904, 0, -4212, 0, 56068, 0, -45624, 0, 13542, 0, 0, 0, 1044, 0, -50688, 0, 7752, 0, -16400, 0, -15228, 0, 33780, 0, 0, 0, -27936, 0, 49036, 0, 0, 0, -18108, 0, -29832, 0, 52896, 0, 0, 0, 18360, 0, -17970, 0, -20310, 0, 37152, 0, 28416, 0, -66528, 0, 0, 0, 6586, 0, 2916, 0, -29736, 0, -127072, 0, -15480, 0, -1440, 0, 0, 0, 37512, 0, 71798, 0, 5880, 0, 10134, 0, 12096, 0, 76116, 0, 0, 0, -23040, 0, 2200, 0, -33264, 0, -9048, 0, -22608, 0, -9828, 0, 0, 0, 11088, 0, -28476, 0, -31500, 0, 14112, 0, 15546, 0, -42240, 0, 0, 0, 11016, 0, 0, 0, 4944, 0, -5472, 0, -87876, 0, 28632, 0, 0, 0, -61004, 0, -33120, 0, 15120, 0, -61990, 0, 82668, 0, 17160, 0, 0, 0, -27826, 0, 40824, 0, 23772, 0, 48312, 0, 6264, 0, 42996, 0, 0, 0, -6336, 0, 128016, 0, 28320, 0, -38592, 0, 76704, 0, 16728, 0, 0, 0, -13718, 0, 47496, 0, 39756, 0, 45240, 0, -41184, 0, -26784, 0, 0, 0, -34272, 0, 9630, 0, 74496, 0, 48240, 0, 678, 0, 3552, 0, 0, 0, 0, 0, -57600, 0, -86592, 0, 1080, 0, 52320, 0, 23664, 0, 0, 0, -26984, 0, 15911, 0, -34002, 0, -46982, 0, 25440, 0, -7776, 0, 0, 0, -19902, 0, -4788, 0, 77352, 0, -2880, 0, -38184, 0, -68880, 0, 0, 0, 28512, 0, 320, 0, -59136, 0, 9036, 0, -86592, 0, -31224, 0, 0, 0, -72094, 0, 88704, 0, 16524, 0, 82800, 0, 77112, 0, 9360, 0, 0, 0, -31296, 0, -684, 0, 76692, 0, -36846, 0, -19494, 0, -14184, 0, 0, 0, 12888, 0, 67208, 0, 33840, 0, -65016, 0, 51636, 0, -2448, 0, 0, 0, -13012, 0, -35190, 0, -6048, 0, 107712, 0, 11772, 0, 24552, 0, 0, 0, -53424, 0, -8244, 0, 9240, 0, -47448, 0, 36492, 0, -9348, 0, 0, 0, -16704, 0, -53894, 0, -40572, 0, -6480, 0, 17568, 0, -35352, 0, 0, 0, -34546, 0, -177408, 0, -2916, 0, 88660, 0, 9312, 0, -4536, 0, 0, 0, -22520, 0, -23184, 0, -86352, 0, 71424, 0, -54864, 0, 0, 0, 0, 0, 43731, 0, 15044, 0, -9348, 0, 34812, 0, 21840, 0, -107532, 0, 0, 0, 29232, 0, -41876, 0, -972, 0, -72512, 0, -118512, 0, 14688, 0, 0, 0, 78294, 0, -24480, 0, 67704, 0, 89856, 0, -16524, 0, 119016, 0, 0, 0, -32544, 0, -21024, 0, -57792, 0, 54396, 0, -33420, 0, 78204, 0, 0, 0, 11088, 0, -30652, 0, -76032, 0, 1328, 0, -18744, 0, 56427, 0, 0, 0, -40248, 0, -13284, 0, -13920, 0, -13242, 0, 0, 0, 8664, 0, 0, 0, 29520, 0, 36184, 0, -1680, 0, -21348, 0, -6900, 0, 13824, 0, 0, 0, 120380, 0, 60626, 0, 20850, 0, 106848, 0, -78612, 0, -9828, 0, 0, 0, -52096, 0, -33048, 0, -128436, 0, -21400, 0, -51036, 0, -190608, 0, 0, 0, -13284, 0, 16128, 0, 1344, 0, -2088, 0, 85104, 0, -124728, 0, 0, 0, -2400, 0, 59312, 0, 27864, 0, -99388, 0, -65532, 0, 11778, 0, 0, 0, -7828, 0, 39312, 0, 42240, 0, -68921, 0, 17280, 0, 4392, 0, 0, 0, 56484, 0, 8928, 0, -101052, 0, -3960, 0, 110448, 0, -14292, 0, 0, 0, 142128, 0, -63360, 0, 35970, 0, -40682, 0, -28536, 0, 47148, 0, 0, 0, 146304, 0, -22608, 0, 1512, 0, -57220, 0, 10032, 0, -36720, 0, 0, 0, -41616, 0, 37442, 0, 76368, 0, -21870, 0, 105264, 0, 58812, 0, 0, 0, -126000, 0, -110676, 0, 43320, 0, -39168, 0, 122208, 0, -27216, 0, 0, 0, 13056, 0, -26460, 0, 0, 0, 4896, 0, -9504, 0, -28536, 0, 0, 0, -15858, 0, -5624, 0, -58128, 0, -50616, 0, -94584, 0, -75696, 0, 0, 0, -124228, 0, -112218, 0, -27864, 0, 18320, 0, 143232, 0, 18168, 0, 0, 0, 26970, 0, 32256, 0, -80580, 0, 91728, 0, -11124, 0, -75948, 0, 0, 0, -33516, 0, -136576, 0, -78720, 0, -60768, 0, -17040, 0, 4560, 0, 0, 0, -129888, 0, -46640, 0, -102816, 0, 29376, 0, 10080, 0, -84570, 0, 0, 0, 2016, 0, 0, 0, 10584, 0, -55171, 0, 87954, 0, 88128, 0, 0, 0, -73044, 0, -97180, 0, 10500, 0, 14256, 0, 136488, 0, -9756, 0, 0, 0, 25432, 0, 127602, 0, -52917, 0, -61010, 0, -3432, 0, 2160, 0, 0, 0, -58464, 0, -74304, 0, -105336, 0, -129888, 0, 75552, 0, 70704, 0, 0, 0, -1404, 0, 61046, 0, 36720, 0, -576, 0, -92556, 0, -162624, 0, 0, 0, -25642, 0, 125856, 0, -7992, 0, 18288, 0, 10560, 0, 96954, 0, 0, 0, 0, 0, 11844, 0, -28140, 0, 57206, 0, -16848, 0, -89880, 0, 0, 0, -41544, 0, -23896, 0, 54168, 0, 29520, 0, -21852, 0, -139200, 0, 0, 0, -202752, 0, -4896, 0, -9474, 0, -186276, 0, -10080, 0, -60912, 0, 0, 0, 47440, 0, 6480, 0, -81900, 0, -14744, 0, 73788, 0, 110028, 0, 0, 0, -46404, 0, -72432, 0, -105252, 0, 72576, 0, 21840, 0, -17880, 0, 0, 0, 139306, 0, 13448, 0, 30624, 0, 87652, 0, -81240, 0, -45360, 0, 0, 0, 152692, 0, 29520, 0, -266112, 0, 5406, 0, 40410, 0, -63648, 0, 0, 0, 1539, 0, -31268, 0, 104916, 0, -28692, 0, -9840, 0, -61920, 0, 0, 0, 51584, 0, -154224, 0, -19548, 0, 150048, 0, -130944, 0, -41556, 0, 0, 0, 70398, 0, 40536, 0, 89376, 0, -17168, 0, 24300, 0, -1776, 0, 0, 0, 181944, 0, 26578, 0, 11016, 0, 972, 0, -17556, 0, -108768, 0, 0, 0, 150142, 0, 133260, 0, -39312, 0, -162584, 0, 29808, 0, 0, 0, 0, 0, -113904, 0, -34218, 0, -117012, 0, 50240, 0, 74766, 0, 62184, 0, 0, 0, -9288, 0, 58192, 0, -19152, 0, 44064, 0, 13920, 0, 76944, 0, 0, 0, 48600, 0, 122112, 0, -53658, 0, -45554, 0, 48060, 0, -20952, 0, 0, 0, -126666, 0, 139392, 0, -60228, 0, 136008, 0, 60480, 0, 1320, 0, 0, 0, 39672, 0, 111866, 0, 68640, 0, 20376, 0, 1536, 0, -37032, 0, 0, 0, 163296, 0, 35240, 0, 27864, 0, 42336, 0, 0, 0, 3306, 0, 0, 0, 7036, 0, -4536, 0, -126936, 0, -25344, 0, 2187, 0, 61920, 0, 0, 0, 44928, 0, -154368, 0, -223608, 0, -33732, 0, -78144, 0, -24204, 0, 0, 0, -9512, 0, 62641, 0, 24720, 0, 106178, 0, 159024, 0, 5988, 0, 0, 0, -121290, 0, 9072, 0, -14136, 0, 162432, 0, 1968, 0, -29568, 0, 0, 0, 38520, 0, 165178, 0, 206808, 0, -24948, 0, 47052, 0, 2712, 0, 0, 0, 154224, 0, -106868, 0, -3168, 0, 0, 0, -126936, 0, 8316, 0, 0, 0, 63360, 0, 4320, 0, 141204, 0, 48890, 0, -56106, 0, -200664, 0, 0, 0, -31680, 0, 112632, 0, 147168, 0, 53712, 0, -136008, 0, -109128, 0, 0, 0, -45008, 0, -74194, 0, -31104, 0, -28586, 0, 11172, 0, 123984, 0, 0, 0, -19152, 0, -22680, 0, -31500, 0, -59712, 0, -24840, 0, -152736, 0, 0, 0, -42876, 0, 3120, 0, -268224, 0, 15048, 0, 199248, 0, -108096, 0, 0, 0, -72262, 0, 36144, 0, 0, 0, -62204, 0, -87540, 0, 17760, 0, 0, 0, 154260, 0, 4698, 0, -24528, 0, 91728, 0, 66096, 0, -137748, 0, 0, 0, -79092, 0, 104832, 0, 37440, 0, 21240, 0, 71808, 0, -5556, 0, 0, 0, 15264, 0, 160922, 0, 123984, 0, 24502, 0, 182712, 0, -77976, 0, 0, 0, -176114, 0, 51660, 0, -231336, 0, 51552, 0, -117504, 0, -16728, 0, 0, 0, -20088, 0, -260064, 0, -53592, 0, -14400, 0, -107004, 0, 192, 0, 0, 0, 52786, 0, 0, 0, 36180, 0, -62512, 0, -3192, 0, 49326, 0, 0, 0, -161280, 0, 93996, 0, 98208, 0, -154082, 0, -43200, 0, 75192, 0, 0, 0, -32976, 0, -11864, 0, -204864, 0, 5616, 0, 100800, 0, 145968, 0, 0, 0, -85756, 0, 144320, 0, -77430, 0, -66816, 0, -65004, 0, -37104, 0, 0, 0, 130374, 0, -3420, 0, 71652, 0, -106296, 0, -18948, 0, 211008, 0, 0, 0, -71604, 0, 20304, 0, -294576, 0, 58014, 0, -11664, 0, 43440, 0, 0, 0, 0, 0, -15784, 0, -18144, 0, -161568, 0, 204120, 0, 21384, 0, 0, 0, -92736, 0, 144648, 0, -54000, 0, -14166, 0, -63075, 0, -28956, 0, 0, 0, -23418, 0, -162308, 0, -102720, 0, 174924, 0, 76752, 0, -151716, 0, 0, 0, 155408, 0, 139248, 0, 62100, 0, -76466, 0, -100704, 0, 136224, 0, 0, 0, -5146, 0, -81900, 0, 148008, 0, 76040, 0, -3888, 0, -11520, 0, 0, 0, 25920, 0, -243936, 0, 7752, 0, -73116, 0, 153396, 0, -43152, 0, 0, 0, -97920, 0, 260064, 0, -6528, 0, -139400, 0, 210912, 0, -66096, 0, 0, 0, -19360, 0, 38727, 0, -13512, 0, -130176, 0, 46560, 0, 82416, 0, 0, 0, 103824, 0, 217584, 0, 28728, 0, -4536, 0, -5388, 0, 76752, 0, 0, 0, -76368, 0, -88160, 0, -82722, 0, 194714, 0, -304128, 0, -40068, 0, 0, 0, 13104, 0, 50904, 0, 225708, 0, -85920, 0, 5580, 0, -61920, 0, 0, 0, -53136, 0, -201566, 0, 160860, 0, -6840, 0, -130272, 0, 0, 0, 0, 0, -176256, 0, -182328, 0, -4860, 0, 15580, 0, -81996, 0, -14688, 0, 0, 0, -21188, 0, -85392, 0, 169176, 0, 219998, 0, -133056, 0, 31932, 0, 0, 0, 45936, 0, -155980, 0, 61920, 0, 207936, 0, 83400, 0, 156732, 0, 0, 0, 114640, 0, 9078, 0, -39312, 0, -20160, 0, -48120, 0, -108252, 0, 0, 0, -17442, 0, -41148, 0, 47040, 0, -190276, 0, -72456, 0, -204144, 0, 0, 0, 55440, 0, -257006, 0, 13104, 0, -53136, 0, 0, 0, 75780, 0, 0, 0, 176546, 0, -8352, 0, -109008, 0, -196416, 0, -18480, 0, 21924, 0, 0, 0, -61144, 0, 74592, 0, 87936, 0, -200736, 0, 14706, 0, 137856, 0, 0, 0, 11016, 0, -163856, 0, 47112, 0, 1296, 0, 243588, 0, 141528, 0, 0, 0, 157248, 0, 89494, 0, 67392, 0, 38866, 0, 196236, 0, 69120, 0, 0, 0, 372407, 0, 66528, 0, -9744, 0, 225936, 0, -15768, 0, 93900, 0, 0, 0, -130572, 0, -2090, 0, 55200, 0, 0, 0, -12840, 0, 144576, 0, 0, 0, 59954, 0, 48384, 0, -5604, 0, 48508, 0, 143880, 0, -60480, 0, 0, 0, 291348, 0, -14058, 0, 188592, 0, 19910, 0, -27714, 0, -147324, 0, 0, 0, -90432, 0, -200736, 0, -1440, 0, -10440, 0, -466464, 0, -223872, 0, 0, 0, 145552, 0, 64272, 0, 119715, 0, -166464, 0, 194136, 0, 22140, 0, 0, 0, -47200, 0, -87480, 0, 57456, 0, 423360, 0, 91848, 0, -79728, 0, 0, 0, 10368, 0, -223238, 0, 0, 0, 82620, 0, 173280, 0, 289812, 0, 0, 0, -2816, 0, -200208, 0, -14364, 0, -216736, 0, -88392, 0, -49206, 0, 0, 0, -105840, 0, 44640, 0, 204540, 0, 176256, 0, -24786, 0, -38016, 0, 0, 0, -165528, 0, 182448, 0, -59640, 0, -63432, 0, 156060, 0, -80400, 0, 0, 0, -38380, 0, -202464, 0, -82368, 0, -214954, 0, 198588, 0, -81288, 0, 0, 0, -226800, 0, 63828, 0, 96000, 0, -22032, 0, -111456, 0, 23664, 0, 0, 0, -50436, 0, 0, 0, 72672, 0, 20898, 0, -301464, 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": "147.4.a.d", "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], [3], [0], [12], [0], [0], [0], [9], [0], [-20], [0], [-84], [0], [36], [0], [-96], [0], [-12], [0], [0], [0], [176], [0], [19], [0], [27], [0], [58], [0], [264], [0], [-60], [0], [0], [0], [258], [0], [-252], [0], [0], [0], [-156], [0], [108], [0], [408], [0], [0], [0], [-288], [0], [-722], [0], [-240], [0], [-36], [0], [-492], [0], [-492], [0], [0], [0], [-1008], [0], [-412], [0], [528], [0], [-296], [0], [240], [0], [57], [0], [0], [0], [-776], [0], [81], [0], [-924], [0], [-1152], [0], [174], [0], [-744], [0], [0], [0], [792], [0], [-144], [0], [-168], [0], [-180], [0]]}