# Stored data for newform 320.4.a.r, downloaded from the LMFDB on 18 April 2024.
{"label": "320.4.a.r", "space_label": "320.4.a", "level": 320, "weight": 4, "hecke_orbit": 18, "hecke_orbit_code": 76561193732407616, "dim": 2, "is_polredabs": true, "nf_label": "2.2.13.1", "trace_hash": 1076437945406846652, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [-52, 0, 1]], [7, [-52, 0, 1]]], "qexp_display": "q-\\beta q^{3}+5q^{5}+\\beta q^{7}+5^{2}q^{9}-6\\beta 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": 4, "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": "0.505", "prec": 17}, "analytic_rank_proved": true, "char_values": [320, 1, [191, 261, 257], [1, 1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2, 5], "conrey_indexes": [1], "field_disc": 13, "field_disc_factorization": [[13, 1]], "field_poly": [-3, -1, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.003", "prec": 17}, {"__RealLiteral__": 0, "data": "1.946", "prec": 17}, {"__RealLiteral__": 0, "data": "0.075", "prec": 17}, {"__RealLiteral__": 0, "data": "15.260", "prec": 20}, {"__RealLiteral__": 0, "data": "1.295", "prec": 17}, {"__RealLiteral__": 0, "data": "149.222", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [5, -1]], "trace_display": [0, 0, 10, 0], "traces": [0, 2, 0, 0, 0, 10, 0, 0, 0, 50, 0, 0, 0, -68, 0, 0, 0, 228, 0, 0, 0, -104, 0, 0, 0, 50, 0, 0, 0, 52, 0, 0, 0, 624, 0, 0, 0, 300, 0, 0, 0, 684, 0, 0, 0, 250, 0, 0, 0, -582, 0, 0, 0, 524, 0, 0, 0, 0, 0, 0, 0, 524, 0, 0, 0, -340, 0, 0, 0, 3016, 0, 0, 0, 1364, 0, 0, 0, -624, 0, 0, 0, -1558, 0, 0, 0, 1140, 0, 0, 0, -1260, 0, 0, 0, -1456, 0, 0, 0, -1932, 0, 0, 0, -3276, 0, 0, 0, -520, 0, 0, 0, 684, 0, 0, 0, 4212, 0, 0, 0, -1700, 0, 0, 0, 1082, 0, 0, 0, 250, 0, 0, 0, -6552, 0, 0, 0, 0, 0, 0, 0, 3236, 0, 0, 0, -8424, 0, 0, 0, 260, 0, 0, 0, -2020, 0, 0, 0, 5700, 0, 0, 0, -3588, 0, 0, 0, -3016, 0, 0, 0, 3120, 0, 0, 0, -2082, 0, 0, 0, -5668, 0, 0, 0, -7072, 0, 0, 0, 2932, 0, 0, 0, 1500, 0, 0, 0, 208, 0, 0, 0, -92, 0, 0, 0, -2244, 0, 0, 0, -7176, 0, 0, 0, 3420, 0, 0, 0, 0, 0, 0, 0, 15184, 0, 0, 0, 1456, 0, 0, 0, -7752, 0, 0, 0, 1250, 0, 0, 0, 12388, 0, 0, 0, 8580, 0, 0, 0, 2912, 0, 0, 0, -6148, 0, 0, 0, -2910, 0, 0, 0, 2184, 0, 0, 0, 18096, 0, 0, 0, -7436, 0, 0, 0, 1300, 0, 0, 0, 2620, 0, 0, 0, -12116, 0, 0, 0, 3536, 0, 0, 0, 5980, 0, 0, 0, 5420, 0, 0, 0, 0, 0, 0, 0, 16166, 0, 0, 0, 7500, 0, 0, 0, -1248, 0, 0, 0, 6552, 0, 0, 0, 2620, 0, 0, 0, -9880, 0, 0, 0, 11284, 0, 0, 0, -9300, 0, 0, 0, -8840, 0, 0, 0, -1700, 0, 0, 0, 8424, 0, 0, 0, 7500, 0, 0, 0, 18532, 0, 0, 0, -8736, 0, 0, 0, 15080, 0, 0, 0, -14988, 0, 0, 0, -12540, 0, 0, 0, -11856, 0, 0, 0, -13718, 0, 0, 0, 6820, 0, 0, 0, 17100, 0, 0, 0, 5148, 0, 0, 0, -1768, 0, 0, 0, -6344, 0, 0, 0, -3120, 0, 0, 0, -10628, 0, 0, 0, -25584, 0, 0, 0, 17276, 0, 0, 0, 5604, 0, 0, 0, -7790, 0, 0, 0, -164, 0, 0, 0, 7072, 0, 0, 0, -36192, 0, 0, 0, 11484, 0, 0, 0, 5700, 0, 0, 0, -21216, 0, 0, 0, 14196, 0, 0, 0, 0, 0, 0, 0, -14550, 0, 0, 0, -6300, 0, 0, 0, -23412, 0, 0, 0, 208, 0, 0, 0, 10132, 0, 0, 0, 1188, 0, 0, 0, -7280, 0, 0, 0, 7176, 0, 0, 0, -39312, 0, 0, 0, 13100, 0, 0, 0, -10200, 0, 0, 0, -9660, 0, 0, 0, -28600, 0, 0, 0, 5928, 0, 0, 0, -15184, 0, 0, 0, -10920, 0, 0, 0, -16380, 0, 0, 0, 17428, 0, 0, 0, 0, 0, 0, 0, -50544, 0, 0, 0, -23660, 0, 0, 0, -2600, 0, 0, 0, 63130, 0, 0, 0, -23256, 0, 0, 0, 13728, 0, 0, 0, 30980, 0, 0, 0, 3420, 0, 0, 0, 13100, 0, 0, 0, -2912, 0, 0, 0, 47724, 0, 0, 0, 71136, 0, 0, 0, 21060, 0, 0, 0, -18148, 0, 0, 0, -50128, 0, 0, 0, 9524, 0, 0, 0, -2184, 0, 0, 0, -8500, 0, 0, 0, 0, 0, 0, 0, 23908, 0, 0, 0, -43264, 0, 0, 0, 35724, 0, 0, 0, 5410, 0, 0, 0, -2704, 0, 0, 0, -23044, 0, 0, 0, 16580, 0, 0, 0, -6032, 0, 0, 0, 1250, 0, 0, 0, 34200, 0, 0, 0, 6032, 0, 0, 0, 19788, 0, 0, 0, 13500, 0, 0, 0, -32760, 0, 0, 0, -42432, 0, 0, 0, -44564, 0, 0, 0, 34100, 0, 0, 0, 23516, 0, 0, 0, 0, 0, 0, 0, 36712, 0, 0, 0, 23732, 0, 0, 0, 53148, 0, 0, 0, 73112, 0, 0, 0, 16180, 0, 0, 0, -17816, 0, 0, 0, -15600, 0, 0, 0, 77976, 0, 0, 0, 14124, 0, 0, 0, -42120, 0, 0, 0, 3108, 0, 0, 0, -42224, 0, 0, 0, 76128, 0, 0, 0, 9880, 0, 0, 0, 1300, 0, 0, 0, -33334, 0, 0, 0, -30116, 0, 0, 0, -43056, 0, 0, 0, 0, 0, 0, 0, -10100, 0, 0, 0, 8840, 0, 0, 0, 29744, 0, 0, 0, -70820, 0, 0, 0, 6772, 0, 0, 0, 28500, 0, 0, 0, 23044, 0, 0, 0, 28764, 0, 0, 0, -15600, 0, 0, 0, 91104, 0, 0, 0, -17940, 0, 0, 0, 101608, 0, 0, 0, -17816, 0, 0, 0, 29100, 0, 0, 0, -31500, 0, 0, 0, -15080, 0, 0, 0, -75244, 0, 0, 0, -75088, 0, 0, 0, 0, 0, 0, 0, -37380, 0, 0, 0, 15600, 0, 0, 0, 7436, 0, 0, 0, -66348, 0, 0, 0, 2912, 0, 0, 0, -47426, 0, 0, 0, -10410, 0, 0, 0, 66248, 0, 0, 0, -53572, 0, 0, 0, 39364, 0, 0, 0, -35568, 0, 0, 0, -28340, 0, 0, 0, 17472, 0, 0, 0, -48300, 0, 0, 0, -83972, 0, 0, 0, 76284, 0, 0, 0, -35360, 0, 0, 0, 6344, 0, 0, 0, 0, 0, 0, 0, -102544, 0, 0, 0, 59736, 0, 0, 0, 14660, 0, 0, 0, -81900, 0, 0, 0, 13104, 0, 0, 0, 25584, 0, 0, 0, 63544, 0, 0, 0, 7500, 0, 0, 0, -35092, 0, 0, 0, -42640, 0, 0, 0, -22780, 0, 0, 0, -83676, 0, 0, 0, 1040, 0, 0, 0, -46376, 0, 0, 0, 57044, 0, 0, 0, 16224, 0, 0, 0, -39198, 0, 0, 0, -460, 0, 0, 0, 0, 0, 0, 0, 36192, 0, 0, 0, -4428, 0, 0, 0, 17100, 0, 0, 0, -11220, 0, 0, 0, -190008, 0, 0, 0, -79664, 0, 0, 0, -115860, 0, 0, 0, 21216, 0, 0, 0, -35880, 0, 0, 0, 57316, 0, 0, 0, 62556, 0, 0, 0, 105300, 0, 0, 0, -39196, 0, 0, 0, 17100, 0, 0, 0, 65936, 0, 0, 0, -21068, 0, 0, 0, 59736, 0, 0, 0, -11752, 0, 0, 0, 0, 0, 0, 0, 46388, 0, 0, 0, 52972, 0, 0, 0, -208, 0, 0, 0, 89844, 0, 0, 0, 75920, 0, 0, 0, -31252, 0, 0, 0, 7800, 0, 0, 0, 9984, 0, 0, 0, -244296, 0, 0, 0, 7280, 0, 0, 0, 27050, 0, 0, 0, 6028, 0, 0, 0, 136596, 0, 0, 0, -30888, 0, 0, 0, -38760, 0, 0, 0, 11940, 0, 0, 0, -27248, 0, 0, 0, 110988, 0, 0, 0, 0, 0, 0, 0, 6250, 0, 0, 0, 86748, 0, 0, 0, -59280, 0, 0, 0, -198016, 0, 0, 0, 28600, 0, 0, 0, 61940, 0, 0, 0, -60632, 0, 0, 0, -63180, 0, 0, 0, 42840, 0, 0, 0, 13104, 0, 0, 0, 42900, 0, 0, 0, 10920, 0, 0, 0, 343824, 0, 0, 0, -53040, 0, 0, 0, -43380, 0, 0, 0, 14560, 0, 0, 0, 17784, 0, 0, 0, -988, 0, 0, 0, 0, 0, 0, 0, -48004, 0, 0, 0, -30740, 0, 0, 0, 49504, 0, 0, 0, 63212, 0, 0, 0, -43068, 0, 0, 0, 93600, 0, 0, 0, -14550, 0, 0, 0, 22580, 0, 0, 0, 80900, 0, 0, 0, -99572, 0, 0, 0, 155496, 0, 0, 0, 10920, 0, 0, 0, 15652, 0, 0, 0, -13728, 0, 0, 0, 15392, 0, 0, 0, 65688, 0, 0, 0, 90480, 0, 0, 0, 16848, 0, 0, 0, 0, 0, 0, 0, 81852, 0, 0, 0, -27248, 0, 0, 0, -37180, 0, 0, 0, -27308, 0, 0, 0, 205296, 0, 0, 0, 62660, 0, 0, 0, -96516, 0, 0, 0, 6500, 0, 0, 0, -71136, 0, 0, 0, 111384, 0, 0, 0, -6656, 0, 0, 0, -108980, 0, 0, 0, 13100, 0, 0, 0, 87464, 0, 0, 0, 91728, 0, 0, 0, 50128, 0, 0, 0, -50500, 0, 0, 0, -60580, 0, 0, 0, 0, 0, 0, 0, 213408, 0, 0, 0, -205088, 0, 0, 0, -89340, 0, 0, 0, 17680, 0, 0, 0, -56306, 0, 0, 0, -70084, 0, 0, 0, -177612, 0, 0, 0, -113988, 0, 0, 0, 29900, 0, 0, 0, -6968, 0, 0, 0, 43264, 0, 0, 0, -38064, 0, 0, 0, 32760, 0, 0, 0, 27100, 0, 0, 0, 111012, 0, 0, 0, -89700, 0, 0, 0, -23256, 0, 0, 0, -15132, 0, 0, 0, 0, 0, 0, 0, -85540, 0, 0, 0, 53556, 0, 0, 0, -58656, 0, 0, 0, -153504, 0, 0, 0, 80830, 0, 0, 0, -75400, 0, 0, 0, -164548, 0, 0, 0, 117936, 0, 0, 0, -161096, 0, 0, 0, 37500, 0, 0, 0, -143208, 0, 0, 0, 66352, 0, 0, 0, -6032, 0, 0, 0, 79436, 0, 0, 0, -6240, 0, 0, 0, -820, 0, 0, 0, 142284, 0, 0, 0, 4160, 0, 0, 0, 0, 0, 0, 0, 32760, 0, 0, 0, 265512, 0, 0, 0, -143640, 0, 0, 0, 102600, 0, 0, 0, -52050, 0, 0, 0, 13100, 0, 0, 0, -217152, 0, 0, 0, -70928, 0, 0, 0, 13624, 0, 0, 0, -208104, 0, 0, 0, -49400, 0, 0, 0, 215220, 0, 0, 0, -68892, 0, 0, 0, -141700, 0, 0, 0, -36712, 0, 0, 0, 56420, 0, 0, 0, -129272, 0, 0, 0, -36788, 0, 0, 0, 0, 0, 0, 0, -165984, 0, 0, 0, -46500, 0, 0, 0, -73112, 0, 0, 0, 14144, 0, 0, 0, -33060, 0, 0, 0, -13788, 0, 0, 0, -44200, 0, 0, 0, -187428, 0, 0, 0, -52676, 0, 0, 0, -181584, 0, 0, 0, 80756, 0, 0, 0, -8500, 0, 0, 0, 73300, 0, 0, 0, 440336, 0, 0, 0, 196476, 0, 0, 0, -164840, 0, 0, 0, 42120, 0, 0, 0, -220248, 0, 0, 0, 0, 0, 0, 0, -177068, 0, 0, 0, 1248, 0, 0, 0, 37500, 0, 0, 0, -201820, 0, 0, 0, -76128, 0, 0, 0, 222768, 0, 0, 0, 96086, 0, 0, 0, 92660, 0, 0, 0, -104728, 0, 0, 0, 182828, 0, 0, 0, 98084, 0, 0, 0, 75400, 0, 0, 0, -43680, 0, 0, 0, 53204, 0, 0, 0, 113360, 0, 0, 0, -373464, 0, 0, 0, -22508, 0, 0, 0, 75400, 0, 0, 0, 0, 0, 0, 0, -192244, 0, 0, 0, -2300, 0, 0, 0, 252356, 0, 0, 0, -74940, 0, 0, 0, 163488, 0, 0, 0, -27964, 0, 0, 0, -29744, 0, 0, 0, 309816, 0, 0, 0, -62700, 0, 0, 0, 13624, 0, 0, 0, -56100, 0, 0, 0, -87308, 0, 0, 0, -110024, 0, 0, 0, -59280, 0, 0, 0, 252628, 0, 0, 0, -171600, 0, 0, 0, -155168, 0, 0, 0, -97748, 0, 0, 0, -68590, 0, 0, 0, 14352, 0, 0, 0, -87300, 0, 0, 0, 84448, 0, 0, 0, -108264, 0, 0, 0, 34100, 0, 0, 0, 99008, 0, 0, 0, 286416, 0, 0, 0, -65520, 0, 0, 0, -101608, 0, 0, 0, 85500, 0, 0, 0, 253762, 0, 0, 0, 77976, 0, 0, 0, 348608, 0, 0, 0, 29268, 0, 0, 0, 25740, 0, 0, 0, 65520, 0, 0, 0, -48988, 0, 0, 0, 286268, 0, 0, 0, 0, 0, 0, 0, -8840, 0, 0, 0, -11700, 0, 0, 0, -178672, 0, 0, 0, 75088, 0, 0, 0, -43892, 0, 0, 0, -31720, 0, 0, 0, 63336, 0, 0, 0, 32404, 0, 0, 0, -30368, 0, 0, 0, 480168, 0, 0, 0, -15600, 0, 0, 0, 337896, 0, 0, 0, -12740, 0, 0, 0, 68680, 0, 0, 0, -125320, 0, 0, 0, -53140, 0, 0, 0, 46092, 0, 0, 0, 36400, 0, 0, 0, 0, 0, 0, 0, 78600, 0, 0, 0, -127920, 0, 0, 0, 82368, 0, 0, 0, -127380, 0, 0, 0, -228384, 0, 0, 0, -66248, 0, 0, 0, 86380, 0, 0, 0, -193800, 0, 0, 0, -30940, 0, 0, 0, 265084, 0, 0, 0, 78416, 0, 0, 0, 28020, 0, 0, 0, -199044, 0, 0, 0, 163488, 0, 0, 0, 29076, 0, 0, 0, 530712, 0, 0, 0, -38950, 0, 0, 0, -159532, 0, 0, 0, 0, 0, 0, 0, 100464, 0, 0, 0, 121992, 0, 0, 0, -820, 0, 0, 0, 198120, 0, 0, 0, -169748, 0, 0, 0, 123348, 0, 0, 0, 309700, 0, 0, 0, 35360, 0, 0, 0, -31036, 0, 0, 0, -325520, 0, 0, 0, 100464, 0, 0, 0, -294684, 0, 0, 0, -180960, 0, 0, 0, -84812, 0, 0, 0, 102544, 0, 0, 0, 214500, 0, 0, 0, -300768, 0, 0, 0, 57420, 0, 0, 0, 0, 0, 0, 0, -30668, 0, 0, 0, 35464, 0, 0, 0, 170352, 0, 0, 0, 28500, 0, 0, 0, -314164, 0, 0, 0, -5824, 0, 0, 0, -51644, 0, 0, 0, 95372, 0, 0, 0, -106080, 0, 0, 0, -63544, 0, 0, 0, -109084, 0, 0, 0, -448032, 0, 0, 0, -12900, 0, 0, 0, 70980, 0, 0, 0, -153700, 0, 0, 0, 179208, 0, 0, 0, 42640, 0, 0, 0, 352664, 0, 0, 0, 0, 0, 0, 0, -259584, 0, 0, 0, -746928, 0, 0, 0, 220184, 0, 0, 0, -212576, 0, 0, 0, -72750, 0, 0, 0, 474698, 0, 0, 0, 82316, 0, 0, 0, -171808, 0, 0, 0, 174732, 0, 0, 0, -31500, 0, 0, 0, -249080, 0, 0, 0, -16224, 0, 0, 0, 125788, 0, 0, 0, -4368, 0, 0, 0, -117060, 0, 0, 0, 192712, 0, 0, 0, -257712, 0, 0, 0, 78600, 0, 0, 0, 0, 0, 0, 0, 1040, 0, 0, 0, 301900, 0, 0, 0, -327404, 0, 0, 0, 452400, 0, 0, 0, -47988, 0, 0, 0, 50660, 0, 0, 0, -35568, 0, 0, 0, 115276, 0, 0, 0, -157196, 0, 0, 0, 240448, 0, 0, 0, 5940, 0, 0, 0, -388740, 0, 0, 0, -185900, 0, 0, 0, 79664, 0, 0, 0, 36192, 0, 0, 0, -36400, 0, 0, 0, 368904, 0, 0, 0, -417204, 0, 0, 0, 0, 0, 0, 0, 124540, 0, 0, 0, 35880, 0, 0, 0, -40508, 0, 0, 0, -99688, 0, 0, 0, -103812, 0, 0, 0, -11752, 0, 0, 0, -196560, 0, 0, 0, -286520, 0, 0, 0, -219024, 0, 0, 0, -376364, 0, 0, 0, -69844, 0, 0, 0, 65500, 0, 0, 0, 128388, 0, 0, 0, -447564, 0, 0, 0, -960336, 0, 0, 0, 133690, 0, 0, 0, -51000, 0, 0, 0, 425568, 0, 0, 0, 0, 0, 0, 0, -21580, 0, 0, 0, -302900, 0, 0, 0, -48300, 0, 0, 0, 11752, 0, 0, 0, 4784, 0, 0, 0, 308300, 0, 0, 0, 308692, 0, 0, 0, -143000, 0, 0, 0, -40768, 0, 0, 0, 220272, 0, 0, 0, -7072, 0, 0, 0, -256360, 0, 0, 0, 29640, 0, 0, 0, -243256, 0, 0, 0, 119236, 0, 0, 0, 68444, 0, 0, 0, -565864, 0, 0, 0, -75920, 0, 0, 0, 0, 0, 0, 0, 149500, 0, 0, 0, 438672, 0, 0, 0, 179208, 0, 0, 0, -54600, 0, 0, 0, 3128, 0, 0, 0, -9984, 0, 0, 0, 206752, 0, 0, 0, 176780, 0, 0, 0, -81900, 0, 0, 0, 135500, 0, 0, 0, -230280, 0, 0, 0, 445536, 0, 0, 0, -56264, 0, 0, 0, 87140, 0, 0, 0, -436068, 0, 0, 0, 452400, 0, 0, 0, -84452, 0, 0, 0, 76296, 0, 0, 0, 0, 0, 0, 0, 30888, 0, 0, 0, -30576, 0, 0, 0, -478816, 0, 0, 0, -32760, 0, 0, 0, -252720, 0, 0, 0, -147160, 0, 0, 0, -165404, 0, 0, 0, -152484, 0, 0, 0, 404150, 0, 0, 0, -118300, 0, 0, 0, -140084, 0, 0, 0, 243984, 0, 0, 0, -51356, 0, 0, 0, 117924, 0, 0, 0, -13000, 0, 0, 0, 456768, 0, 0, 0, 45956, 0, 0, 0, 187500, 0, 0, 0, 0, 0, 0, 0, 315650, 0, 0, 0, 565864, 0, 0, 0, 198016, 0, 0, 0, 441124, 0, 0, 0, 598936, 0, 0, 0, -116280, 0, 0, 0, -409032, 0, 0, 0, -452400, 0, 0, 0, -48308, 0, 0, 0, 60632, 0, 0, 0, 68640, 0, 0, 0, -244724, 0, 0, 0, -263684, 0, 0, 0, -37856, 0, 0, 0, 204600, 0, 0, 0, 154900, 0, 0, 0, 163800, 0, 0, 0, 334564, 0, 0, 0, 0, 0, 0, 0, 62296, 0, 0, 0, 17100, 0, 0, 0, -82284, 0, 0, 0, -716976, 0, 0, 0, -343824, 0, 0, 0, -165348, 0, 0, 0, 65500, 0, 0, 0, 454732, 0, 0, 0, 291076, 0, 0, 0, 75296, 0, 0, 0, 178464, 0, 0, 0, -14560, 0, 0, 0, -516256, 0, 0, 0, 572832, 0, 0, 0, 298468, 0, 0, 0, 19760, 0, 0, 0, 238620, 0, 0, 0, 19772, 0, 0, 0, 0, 0, 0, 0, 269196, 0, 0, 0, -306236, 0, 0, 0, 355680, 0, 0, 0, -160466, 0, 0, 0, -50232, 0, 0, 0, 282100, 0, 0, 0, -49504, 0, 0, 0, 105300, 0, 0, 0, 1031472, 0, 0, 0, 65156, 0, 0, 0, 235980, 0, 0, 0, -508040, 0, 0, 0, -90740, 0, 0, 0, -93600, 0, 0, 0, -232500, 0, 0, 0, -118924, 0, 0, 0, -25692, 0, 0, 0, -250640, 0, 0, 0, 0, 0, 0, 0, -237348, 0, 0, 0, -168272, 0, 0, 0, 452088, 0, 0, 0, 47620, 0, 0, 0, 17680, 0, 0, 0, 609648, 0, 0, 0, 159028, 0, 0, 0, 66040, 0, 0, 0, -10920, 0, 0, 0, 19916, 0, 0, 0, 321360, 0, 0, 0, 626556, 0, 0, 0, -183976, 0, 0, 0, -42500, 0, 0, 0, -85176, 0, 0, 0, -15392, 0, 0, 0, -393120, 0, 0, 0, -646152, 0, 0, 0, 0, 0, 0, 0, 358696, 0, 0, 0, 266804, 0, 0, 0, -199204, 0, 0, 0, 210600, 0, 0, 0, 119540, 0, 0, 0, 288956, 0, 0, 0, 669968, 0, 0, 0, -421192, 0, 0, 0, -450528, 0, 0, 0, -216320, 0, 0, 0, -152484, 0, 0, 0, 466488, 0, 0, 0, -233700, 0, 0, 0], "weight_parity": 1, "has_non_self_twist": 1, "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], [1, 1, 4, 2, -1, 2, 0]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "160.4.a.e", "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, 0], [1, 0], [0, 0], [0, -1], [0, 0], [5, 0], [0, 0], [0, 1], [0, 0], [25, 0], [0, 0], [0, -6], [0, 0], [-34, 0], [0, 0], [0, -5], [0, 0], [114, 0], [0, 0], [0, 0], [0, 0], [-52, 0], [0, 0], [0, -29], [0, 0], [25, 0], [0, 0], [0, 2], [0, 0], [26, 0], [0, 0], [0, 14], [0, 0], [312, 0], [0, 0], [0, 5], [0, 0], [150, 0], [0, 0], [0, 34], [0, 0], [342, 0], [0, 0], [0, 63], [0, 0], [125, 0], [0, 0], [0, 81], [0, 0], [-291, 0], [0, 0], [0, -114], [0, 0], [262, 0], [0, 0], [0, -30], [0, 0], [0, 0], [0, 0], [0, 68], [0, 0], [262, 0], [0, 0], [0, 25], [0, 0], [-170, 0], [0, 0], [0, 69], [0, 0], [1508, 0], [0, 0], [0, -146], [0, 0], [682, 0], [0, 0], [0, -25], [0, 0], [-312, 0], [0, 0], [0, -28], [0, 0], [-779, 0], [0, 0], [0, -21], [0, 0], [570, 0], [0, 0], [0, -26], [0, 0], [-630, 0], [0, 0], [0, -34], [0, 0], [-728, 0], [0, 0], [0, 0], [0, 0], [-966, 0], [0, 0], [0, -150], [0, 0]]}