# Stored data for newform 576.4.a.r, downloaded from the LMFDB on 29 March 2024. {"label": "576.4.a.r", "space_label": "576.4.a", "level": 576, "weight": 4, "hecke_orbit": 18, "hecke_orbit_code": 76561193732407872, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 97011510668797004, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [-6, 1]], [7, [-16, 1]], [11, [12, 1]]], "qexp_display": "q+6q^{5}+2^{4}q^{7}-12q^{11}-38q^{13}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 9216, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 33.98510016330659, "hecke_ring_index": 1, "level_radical": 6, "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": [576, 1, [127, 325, 65], [1, 1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 3], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.002", "prec": 17}, {"__RealLiteral__": 0, "data": "0.990", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.964", "prec": 17}, {"__RealLiteral__": 0, "data": "0.003", "prec": 17}, {"__RealLiteral__": 0, "data": "4.908", "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]], "trace_display": [0, 0, 6, 16], "traces": [0, 1, 0, 0, 0, 6, 0, 16, 0, 0, 0, -12, 0, -38, 0, 0, 0, 126, 0, 20, 0, 0, 0, 168, 0, -89, 0, 0, 0, 30, 0, 88, 0, 0, 0, 96, 0, -254, 0, 0, 0, -42, 0, -52, 0, 0, 0, -96, 0, -87, 0, 0, 0, 198, 0, -72, 0, 0, 0, 660, 0, 538, 0, 0, 0, -228, 0, 884, 0, 0, 0, 792, 0, 218, 0, 0, 0, -192, 0, 520, 0, 0, 0, 492, 0, 756, 0, 0, 0, -810, 0, -608, 0, 0, 0, 120, 0, 1154, 0, 0, 0, -618, 0, -128, 0, 0, 0, 1476, 0, -1190, 0, 0, 0, 462, 0, 1008, 0, 0, 0, 2016, 0, -1187, 0, 0, 0, -1284, 0, 2536, 0, 0, 0, -2292, 0, 320, 0, 0, 0, 726, 0, 380, 0, 0, 0, 456, 0, 180, 0, 0, 0, 1590, 0, -2432, 0, 0, 0, 528, 0, -614, 0, 0, 0, 2688, 0, -1852, 0, 0, 0, -2136, 0, -753, 0, 0, 0, 1758, 0, -1424, 0, 0, 0, 540, 0, -1982, 0, 0, 0, -1524, 0, -1512, 0, 0, 0, -2688, 0, -2302, 0, 0, 0, 4374, 0, 1600, 0, 0, 0, 480, 0, -252, 0, 0, 0, -240, 0, 3332, 0, 0, 0, -312, 0, 1408, 0, 0, 0, -4788, 0, -2648, 0, 0, 0, -2244, 0, 5650, 0, 0, 0, -4698, 0, -576, 0, 0, 0, -1200, 0, -718, 0, 0, 0, -522, 0, -760, 0, 0, 0, -6012, 0, -2016, 0, 0, 0, 2046, 0, -4064, 0, 0, 0, -6072, 0, 1188, 0, 0, 0, -6930, 0, -1352, 0, 0, 0, 1068, 0, 1186, 0, 0, 0, -2442, 0, 2828, 0, 0, 0, -672, 0, 10963, 0, 0, 0, 4758, 0, 3960, 0, 0, 0, -6384, 0, -832, 0, 0, 0, 3228, 0, -8476, 0, 0, 0, 4632, 0, -4822, 0, 0, 0, -3426, 0, -360, 0, 0, 0, 2520, 0, 3382, 0, 0, 0, -1536, 0, -2788, 0, 0, 0, 5304, 0, 434, 0, 0, 0, -1056, 0, -6880, 0, 0, 0, -6684, 0, -2630, 0, 0, 0, 7422, 0, 4752, 0, 0, 0, -10440, 0, -6459, 0, 0, 0, 1308, 0, -10424, 0, 0, 0, 3168, 0, -3278, 0, 0, 0, -1140, 0, 6140, 0, 0, 0, -3072, 0, -1152, 0, 0, 0, 6150, 0, 21168, 0, 0, 0, 3120, 0, 106, 0, 0, 0, 1758, 0, -3344, 0, 0, 0, 3048, 0, -3670, 0, 0, 0, 10560, 0, 2952, 0, 0, 0, 9660, 0, -8462, 0, 0, 0, -11214, 0, 8608, 0, 0, 0, 9792, 0, -7342, 0, 0, 0, 3360, 0, -10640, 0, 0, 0, 17412, 0, -4860, 0, 0, 0, 1710, 0, 504, 0, 0, 0, -3648, 0, -646, 0, 0, 0, -6018, 0, 6712, 0, 0, 0, -5364, 0, 14144, 0, 0, 0, 624, 0, -1780, 0, 0, 0, 9840, 0, 9652, 0, 0, 0, 6924, 0, -1424, 0, 0, 0, 4548, 0, 3780, 0, 0, 0, 12672, 0, 6500, 0, 0, 0, 12168, 0, -3708, 0, 0, 0, -21090, 0, 3488, 0, 0, 0, -768, 0, 1152, 0, 0, 0, 5238, 0, 8588, 0, 0, 0, 11088, 0, 16057, 0, 0, 0, 1596, 0, 8856, 0, 0, 0, 1044, 0, -3062, 0, 0, 0, -7140, 0, -8476, 0, 0, 0, 600, 0, 8320, 0, 0, 0, -12546, 0, 1976, 0, 0, 0, 12, 0, 2772, 0, 0, 0, -19290, 0, -12148, 0, 0, 0, -14952, 0, -10366, 0, 0, 0, 7872, 0, -2376, 0, 0, 0, -7644, 0, 1760, 0, 0, 0, -8658, 0, 12096, 0, 0, 0, 25800, 0, 16202, 0, 0, 0, -7122, 0, 24136, 0, 0, 0, 3648, 0, 4642, 0, 0, 0, 6726, 0, -21220, 0, 0, 0, -12960, 0, 3421, 0, 0, 0, -32004, 0, -29792, 0, 0, 0, 15216, 0, 3306, 0, 0, 0, 10158, 0, 29828, 0, 0, 0, 1944, 0, -7920, 0, 0, 0, 26718, 0, -13752, 0, 0, 0, -4260, 0, -22862, 0, 0, 0, 1920, 0, 5040, 0, 0, 0, -6456, 0, -32542, 0, 0, 0, 14214, 0, 18464, 0, 0, 0, 7092, 0, 4356, 0, 0, 0, -7524, 0, -13228, 0, 0, 0, 2280, 0, -5292, 0, 0, 0, 28062, 0, -5080, 0, 0, 0, -9888, 0, 27250, 0, 0, 0, 14784, 0, 2736, 0, 0, 0, -14400, 0, -2048, 0, 0, 0, -2670, 0, -17984, 0, 0, 0, -6552, 0, -16598, 0, 0, 0, -10608, 0, 1460, 0, 0, 0, -30072, 0, 9540, 0, 0, 0, 23616, 0, 18088, 0, 0, 0, -14592, 0, -24734, 0, 0, 0, 22278, 0, -19040, 0, 0, 0, -25080, 0, 16130, 0, 0, 0, 29718, 0, -7832, 0, 0, 0, -840, 0, -9504, 0, 0, 0, -3684, 0, 9524, 0, 0, 0, 7392, 0, -20444, 0, 0, 0, -33906, 0, -12096, 0, 0, 0, -2616, 0, 16128, 0, 0, 0, 630, 0, -20788, 0, 0, 0, -11112, 0, -1040, 0, 0, 0, -43098, 0, 14272, 0, 0, 0, -13644, 0, 2410, 0, 0, 0, -10962, 0, -12816, 0, 0, 0, 23160, 0, -23489, 0, 0, 0, -4518, 0, -18992, 0, 0, 0, -42672, 0, -32078, 0, 0, 0, 14406, 0, 30620, 0, 0, 0, 17568, 0, 10548, 0, 0, 0, -6240, 0, -33592, 0, 0, 0, -20544, 0, 21706, 0, 0, 0, 14958, 0, -32812, 0, 0, 0, -38856, 0, 40576, 0, 0, 0, -1920, 0, 3240, 0, 0, 0, 2640, 0, 24948, 0, 0, 0, -11892, 0, -28276, 0, 0, 0, 8112, 0, -5904, 0, 0, 0, -36672, 0, 26080, 0, 0, 0, -30096, 0, 22606, 0, 0, 0, -49170, 0, -1740, 0, 0, 0, -9072, 0, 48314, 0, 0, 0, 34782, 0, -7056, 0, 0, 0, 25116, 0, -8284, 0, 0, 0, 15462, 0, -16128, 0, 0, 0, 11616, 0, -22047, 0, 0, 0, -13812, 0, 736, 0, 0, 0, 29268, 0, 6080, 0, 0, 0, -16674, 0, 9720, 0, 0, 0, -31272, 0, 26244, 0, 0, 0, -8736, 0, 15928, 0, 0, 0, 9600, 0, -42014, 0, 0, 0, 7296, 0, 83160, 0, 0, 0, 3960, 0, 12530, 0, 0, 0, -19722, 0, 2880, 0, 0, 0, 18420, 0, 53818, 0, 0, 0, 3738, 0, -19760, 0, 0, 0, 13992, 0, -28582, 0, 0, 0, 67788, 0, 19240, 0, 0, 0, 25440, 0, -1440, 0, 0, 0, 8310, 0, 39692, 0, 0, 0, 19992, 0, -38912, 0, 0, 0, 26982, 0, 17152, 0, 0, 0, -13848, 0, 31210, 0, 0, 0, -7620, 0, 4628, 0, 0, 0, -18696, 0, -16128, 0, 0, 0, 8448, 0, -61544, 0, 0, 0, -24132, 0, -9038, 0, 0, 0, -28314, 0, -9824, 0, 0, 0, 32208, 0, -28728, 0, 0, 0, -44970, 0, 7416, 0, 0, 0, -15888, 0, -51734, 0, 0, 0, 13200, 0, -47212, 0, 0, 0, -14616, 0, -21670, 0, 0, 0, 1536, 0, -13464, 0, 0, 0, 111384, 0, -29632, 0, 0, 0, 33900, 0, -22352, 0, 0, 0, 29952, 0, 58178, 0, 0, 0, 30780, 0, 10760, 0, 0, 0, 23172, 0, -28188, 0, 0, 0, -34176, 0, 55172, 0, 0, 0, 8544, 0, -17712, 0, 0, 0, 9102, 0, -12048, 0, 0, 0, -1044, 0, -1260, 0, 0, 0, 59142, 0, -7200, 0, 0, 0, 14280, 0, -5038, 0, 0, 0, -4308, 0, 99792, 0, 0, 0, 28128, 0, -3638, 0, 0, 0, -1794, 0, 33264, 0, 0, 0, 74088, 0, 7743, 0, 0, 0, 14910, 0, 38968, 0, 0, 0, -4560, 0, 38626, 0, 0, 0, 27468, 0, -5544, 0, 0, 0, -1560, 0, -37150, 0, 0, 0, 8640, 0, -36072, 0, 0, 0, -37260, 0, -43852, 0, 0, 0, -12096, 0, -31712, 0, 0, 0, -3696, 0, 17680, 0, 0, 0, 11934, 0, -21080, 0, 0, 0, -15108, 0, 12276, 0, 0, 0, 59910, 0, 56972, 0, 0, 0, -24384, 0, 6194, 0, 0, 0, -87978, 0, 17872, 0, 0, 0, -64524, 0, -24192, 0, 0, 0, 23484, 0, -36432, 0, 0, 0, 92760, 0, 61562, 0, 0, 0, -17622, 0, 8296, 0, 0, 0, 30216, 0, -4576, 0, 0, 0, -43008, 0, 4864, 0, 0, 0, 65520, 0, -41580, 0, 0, 0, 15840, 0, -36832, 0, 0, 0, -8112, 0, 110880, 0, 0, 0, -49602, 0, -2880, 0, 0, 0, -75816, 0, 13863, 0, 0, 0, -15762, 0, 15408, 0, 0, 0, 69984, 0, 60658, 0, 0, 0, 7116, 0, 4360, 0, 0, 0, -56088, 0, 25600, 0, 0, 0, -30432, 0, 29680, 0, 0, 0, 90384, 0, -14652, 0, 0, 0, -46770, 0, 61992, 0, 0, 0, 16968, 0, 45220, 0, 0, 0, -2610, 0, 47032, 0, 0, 0, -59604, 0, -85070, 0, 0, 0, -59178, 0, -4032, 0, 0, 0, -12240, 0, 27504, 0, 0, 0, 65778, 0, -62624, 0, 0, 0, 95748, 0, 14362, 0, 0, 0, -8448, 0, 10100, 0, 0, 0, -3840, 0, 28548, 0, 0, 0, -17556, 0, 28168, 0, 0, 0, -58740, 0, 53312, 0, 0, 0, -68442, 0, -46132, 0, 0, 0, -40416, 0, -37870, 0, 0, 0, -75402, 0, -38304, 0, 0, 0, -60, 0, 10400, 0, 0, 0, -4992, 0, -8712, 0, 0, 0, -12168, 0, -102060, 0, 0, 0, 10668, 0, -7656, 0, 0, 0, -64308, 0, -47882, 0, 0, 0, -4560, 0, -89908, 0, 0, 0, -50856, 0, 5940, 0, 0, 0, 148512, 0, -62768, 0, 0, 0, -76608, 0, 44170, 0, 0, 0, 69582, 0, 27792, 0, 0, 0, -13560, 0, -42368, 0, 0, 0, -28932, 0, -84584, 0, 0, 0, -8052, 0, 45106, 0, 0, 0, 9840, 0, -39940, 0, 0, 0, -6192, 0, -20556, 0, 0, 0, -35904, 0, 13208, 0, 0, 0, -2160, 0, -63254, 0, 0, 0, -23202, 0, 90400, 0, 0, 0, -69096, 0, 58970, 0, 0, 0, -55122, 0, 15120, 0, 0, 0, -71460, 0, -542, 0, 0, 0, 48792, 0, 94124, 0, 0, 0, -75168, 0, 133056, 0, 0, 0, 46134, 0, -19080, 0, 0, 0, 17424, 0, -9216, 0, 0, 0, 145404, 0, -96368, 0, 0, 0, -16728, 0, -119446, 0, 0, 0, 29184, 0, 80872, 0, 0, 0, -62004, 0, -11630, 0, 0, 0, -19200, 0, -78676, 0, 0, 0, 36624, 0, -67157, 0, 0, 0, 2604, 0, -11488, 0, 0, 0, -16200, 0, -86438, 0, 0, 0, 122286, 0, -15820, 0, 0, 0, 87096, 0, -6336, 0, 0, 0, 132030, 0, 19800, 0, 0, 0, -41280, 0, -77868, 0, 0, 0, -106122, 0, -120292, 0, 0, 0, 7368, 0, -12160, 0, 0, 0, 27078, 0, -40104, 0, 0, 0, 24384, 0, -53462, 0, 0, 0, -15780, 0, 14564, 0, 0, 0, -16128, 0, 54218, 0, 0, 0, -96192, 0, 11320, 0, 0, 0, 2184, 0, 44532, 0, 0, 0, 16140, 0, -32256, 0, 0, 0, -70488, 0, 42194, 0, 0, 0, -27588, 0, -29648, 0, 0, 0, 24996, 0, 33370, 0, 0, 0, 22224, 0, -62640, 0, 0, 0, 32736, 0, -20518, 0, 0, 0, -38754, 0, -14440, 0, 0, 0, -83172, 0, 22098, 0, 0, 0, 87360, 0, 185976, 0, 0, 0, 82608, 0, -19402, 0, 0, 0, 58080, 0, -65792, 0, 0, 0, -62544, 0, 25632, 0, 0, 0, -97152, 0, 23080, 0, 0, 0, -70296, 0, -76803, 0, 0, 0, -149940, 0, 19008, 0, 0, 0, 9036, 0, -13502, 0, 0, 0, -19668, 0, -6676, 0, 0, 0, -97488, 0, 30098, 0, 0, 0, -23466, 0, 125440, 0, 0, 0, -110880, 0, -6840, 0, 0, 0, 19710, 0, 47344, 0, 0, 0, 36840, 0, -21632, 0, 0, 0, -57858, 0, -21096, 0, 0, 0, 107676, 0, 82656, 0, 0, 0, -114378, 0, -18432, 0, 0, 0, -12360, 0, 58212, 0, 0, 0, 17088, 0, 4032, 0, 0, 0, 70788, 0, 25162, 0, 0, 0, -60420, 0, 18976, 0, 0, 0, 26520, 0, 36900, 0, 0, 0, 66030, 0, 2248, 0, 0, 0, 127008, 0, -2560, 0, 0, 0, -50292, 0, 92416, 0, 0, 0, -39072, 0, -6480, 0, 0, 0, 45318, 0, -46280, 0, 0, 0, 106020, 0, 45248, 0, 0, 0, 636, 0, -40156, 0, 0, 0, 23784, 0, 49178, 0, 0, 0, 81054, 0, -78680, 0, 0, 0, -26628, 0, 10548, 0, 0, 0, 3654, 0, -148228, 0, 0, 0, -20064, 0, 110594, 0, 0, 0, 4992, 0, 175408, 0, 0, 0, -91884, 0, -42950, 0, 0, 0, 29520, 0, 18288, 0, 0, 0, 35880, 0, 23332, 0, 0, 0, -22020, 0, -136080, 0, 0, 0, 76128, 0, 161602, 0, 0, 0, -149562, 0, 23760, 0, 0, 0, 76368, 0, 63360, 0, 0, 0, 120870, 0, -23800, 0, 0, 0, -43788, 0, 77792, 0, 0, 0, 31758, 0, -66652, 0, 0, 0, -99576, 0, -169990, 0, 0, 0, -102144, 0, 57960, 0, 0, 0, 164220, 0, 32256, 0, 0, 0, -50772, 0, 4524, 0, 0, 0, 18672, 0, -100222, 0, 0, 0, 6540, 0, 70376, 0, 0, 0, 27624, 0, -161784, 0, 0, 0, 150510, 0, 187652, 0, 0, 0, 51648, 0, 28874, 0, 0, 0, -147618, 0, -488, 0, 0, 0, 9240, 0, -135616, 0, 0, 0, -21738, 0, 58752, 0, 0, 0, 319536, 0, 120242, 0, 0, 0, -44052, 0, -52488, 0, 0, 0, 81168, 0, -8316, 0, 0, 0, 74112, 0, -9340, 0, 0, 0, -167640, 0, 20160, 0, 0, 0, -19200, 0, -77152, 0, 0, 0, -63840, 0, 112100, 0, 0, 0, 69696, 0, 200828, 0, 0, 0, 86304, 0, -94607, 0, 0, 0, 13158, 0, 104472, 0, 0, 0, -54816, 0, -42662, 0, 0, 0, 72090, 0, -288792, 0, 0, 0, 193872, 0, -5760, 0, 0, 0, 9294, 0, 135880, 0, 0, 0, 43692, 0, 10260, 0, 0, 0, -66804, 0, 24572, 0, 0, 0, 3024, 0, -136652, 0, 0, 0, 40320, 0, 19184, 0, 0, 0, -93564, 0, -148070, 0, 0, 0, 83262, 0, 54112, 0, 0, 0, -10296, 0, -30598, 0, 0, 0, -3876, 0, 112696, 0, 0, 0, 15600, 0, -99758, 0, 0, 0, -1434, 0, -23740, 0, 0, 0, 8352, 0, -36108, 0, 0, 0, 145590, 0, 60928, 0, 0, 0, 40272, 0, -44608, 0, 0, 0, -39984, 0, -103824, 0, 0, 0, -20520, 0, 91476, 0, 0, 0, 34878, 0, -32184, 0, 0, 0, 78300, 0, 18898, 0, 0, 0, 84864, 0, 66044, 0, 0, 0, 62112, 0, 75316, 0, 0, 0, 5094, 0, 6944, 0, 0, 0, 47880, 0, 3744, 0, 0, 0, -21504, 0, 200612, 0, 0, 0, -25680, 0, -23686, 0, 0, 0, -26418, 0, -26408, 0, 0, 0, -16896, 0, -154190, 0, 0, 0, -15498, 0, 59040, 0, 0, 0, 9600, 0, -80239, 0, 0, 0, 57912, 0, 14760, 0, 0, 0, 91908, 0, 50720, 0, 0, 0, 20766, 0, -27720, 0, 0, 0, -22632, 0, -102706, 0, 0, 0, -106944, 0, 57456, 0, 0, 0, -8544, 0, -44894, 0, 0, 0, 194118, 0, -42080, 0, 0, 0, -71856, 0, 45760, 0, 0, 0, 31776, 0, 27288, 0, 0, 0, 47940, 0, 247968, 0, 0, 0, 22680, 0, -189196, 0, 0, 0, 118752, 0, 217658, 0, 0, 0, 85134, 0, -224536, 0, 0, 0, 102144, 0, 76032, 0, 0, 0, -45840, 0, -19008, 0, 0, 0, 39000, 0, 26928, 0, 0, 0, -22596, 0, -6608, 0, 0, 0, -199920, 0, 87476, 0, 0, 0, -167040, 0, 73008, 0, 0, 0, -67800, 0, -41398, 0, 0, 0, 55002, 0, -103344, 0, 0, 0, -188292, 0, 200340, 0, 0, 0, -34320, 0, 8300, 0, 0, 0, 42288, 0, -126540, 0, 0, 0, -123450, 0, -202592, 0, 0, 0, 20928, 0, -249014, 0, 0, 0, -166212, 0, 56376, 0, 0, 0, -306432, 0, -166784, 0, 0, 0, 43296, 0, 11392, 0, 0, 0, 184620, 0, -24300, 0, 0, 0, 6912, 0, -60800, 0, 0, 0, -196128, 0, 122978, 0, 0, 0, -17226, 0, 77616, 0, 0, 0, 14520, 0, 31428, 0, 0, 0, 143550, 0, -52448, 0, 0, 0, 51528, 0, 49034, 0, 0, 0, 17742, 0, -27976, 0, 0, 0, -201168, 0, 14400, 0, 0, 0, -242538, 0, 66528, 0, 0, 0, -18240, 0, 7600, 0, 0, 0, 96342, 0, -75584, 0, 0, 0, 8616, 0, 98240, 0, 0, 0, -245154, 0, -77020, 0, 0, 0, -67032, 0, 9576, 0, 0, 0, -77364, 0, 190888, 0, 0, 0, -131364, 0, 57346, 0, 0, 0, -49152, 0, -61972, 0, 0, 0, -122736, 0, 122690, 0, 0, 0, -198042, 0, 6264, 0, 0, 0, 139140, 0, -55372, 0, 0, 0, -18372, 0, 85844, 0, 0, 0, 199992, 0, -24982, 0, 0, 0, 9120, 0, 248200, 0, 0, 0, 98400, 0, 105910, 0, 0, 0, 37590, 0, -177748, 0, 0, 0, -50856, 0, 338688, 0, 0, 0, -165738, 0, -126616, 0, 0, 0, -37128, 0, -150950, 0, 0, 0, 56142, 0, 3600, 0, 0, 0, -71280, 0, 72144, 0, 0, 0, 49920, 0, -188264, 0, 0, 0, -233352, 0, -63360, 0, 0, 0, 72966, 0, 1696, 0, 0, 0, -199416, 0, -75276, 0, 0, 0, -29610, 0, 47248, 0, 0, 0, 11856, 0, 249946, 0, 0, 0, 267198, 0, 187508, 0, 0, 0, 28128, 0, -109673, 0, 0, 0, 34620, 0, 72, 0, 0, 0, -164100, 0, -53504, 0, 0, 0, -41118, 0, -24552, 0, 0, 0, 31800, 0, -201742, 0, 0, 0, -149226, 0, -269136, 0, 0, 0, -272988, 0, -115740, 0, 0, 0, 48768, 0, -54268, 0, 0, 0, -72888, 0, 7994, 0, 0, 0, 44622, 0, -58720, 0, 0, 0, -51648, 0, -48640, 0, 0, 0, -94878, 0, -215712, 0, 0, 0, 120960, 0, -45968, 0, 0, 0, -62196, 0, 223216, 0, 0, 0, -57420, 0, 72864, 0, 0, 0, -139554, 0, 100624, 0, 0, 0, 200328, 0, 47232, 0, 0, 0, 182190, 0, -33264, 0, 0, 0, -14256, 0, -245054, 0, 0, 0, 426048, 0, -132080, 0, 0, 0, -18096, 0, -18540, 0, 0, 0, 154560, 0, -45864, 0, 0, 0, -61980, 0, 221508, 0, 0, 0, 10560, 0, -135392, 0, 0, 0, 85272, 0, -155302, 0, 0, 0, -35346, 0, 83160, 0, 0, 0, 194892, 0, -51948, 0, 0, 0, 206550, 0, -83428, 0, 0, 0, -179424, 0, -214700, 0, 0, 0, 16224, 0, -12280, 0, 0, 0, -3840, 0, -46806, 0, 0, 0, -9156, 0, 154800, 0, 0, 0, 196680, 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": "6.4.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], [0], [0], [6], [0], [16], [0], [0], [0], [-12], [0], [-38], [0], [0], [0], [126], [0], [20], [0], [0], [0], [168], [0], [-89], [0], [0], [0], [30], [0], [88], [0], [0], [0], [96], [0], [-254], [0], [0], [0], [-42], [0], [-52], [0], [0], [0], [-96], [0], [-87], [0], [0], [0], [198], [0], [-72], [0], [0], [0], [660], [0], [538], [0], [0], [0], [-228], [0], [884], [0], [0], [0], [792], [0], [218], [0], [0], [0], [-192], [0], [520], [0], [0], [0], [492], [0], [756], [0], [0], [0], [-810], [0], [-608], [0], [0], [0], [120], [0], [1154], [0], [0], [0]]}