# Stored data for newform 1800.4.a.r, downloaded from the LMFDB on 23 April 2024.
{"label": "1800.4.a.r", "space_label": "1800.4.a", "level": 1800, "weight": 4, "hecke_orbit": 18, "hecke_orbit_code": 76561193732409096, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1724445344085496658, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [2, 1]], [11, [-34, 1]], [17, [38, 1]]], "qexp_display": "q-2q^{7}+34q^{11}+68q^{13}-38q^{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": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.997", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.982", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.957", "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, -2], "traces": [0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 34, 0, 68, 0, 0, 0, -38, 0, 4, 0, 0, 0, 152, 0, 0, 0, 0, 0, 46, 0, -260, 0, 0, 0, 0, 0, 312, 0, 0, 0, -48, 0, 200, 0, 0, 0, 104, 0, -339, 0, 0, 0, -414, 0, 0, 0, 0, 0, 2, 0, -38, 0, 0, 0, 0, 0, 244, 0, 0, 0, -708, 0, 378, 0, 0, 0, -68, 0, -852, 0, 0, 0, 844, 0, 0, 0, 0, 0, 1380, 0, -136, 0, 0, 0, 0, 0, -514, 0, 0, 0, 702, 0, -898, 0, 0, 0, 876, 0, 602, 0, 0, 0, 1350, 0, 0, 0, 0, 0, 76, 0, -175, 0, 0, 0, 0, 0, 366, 0, 0, 0, -498, 0, -8, 0, 0, 0, -2026, 0, 2460, 0, 0, 0, 2312, 0, 0, 0, 0, 0, 3362, 0, 2096, 0, 0, 0, 0, 0, -2092, 0, 0, 0, -304, 0, -244, 0, 0, 0, 2064, 0, 2427, 0, 0, 0, 1258, 0, 0, 0, 0, 0, 3986, 0, 2570, 0, 0, 0, 0, 0, -1292, 0, 0, 0, -4684, 0, -214, 0, 0, 0, 3014, 0, -1792, 0, 0, 0, -92, 0, 0, 0, 0, 0, 136, 0, -4540, 0, 0, 0, 0, 0, 520, 0, 0, 0, -2584, 0, -6506, 0, 0, 0, -3696, 0, -3386, 0, 0, 0, 3306, 0, 0, 0, 0, 0, 4188, 0, 5462, 0, 0, 0, 0, 0, 272, 0, 0, 0, 3366, 0, 5168, 0, 0, 0, 1158, 0, -624, 0, 0, 0, 8304, 0, 0, 0, 0, 0, 7478, 0, -6792, 0, 0, 0, 0, 0, 2296, 0, 0, 0, -3980, 0, 1972, 0, 0, 0, 96, 0, -3469, 0, 0, 0, 9254, 0, 0, 0, 0, 0, 10336, 0, -400, 0, 0, 0, 0, 0, 5888, 0, 0, 0, 4604, 0, 8026, 0, 0, 0, 2838, 0, 1564, 0, 0, 0, -152, 0, 0, 0, 0, 0, -208, 0, -1020, 0, 0, 0, 0, 0, -814, 0, 0, 0, -8840, 0, 1364, 0, 0, 0, -4544, 0, 6978, 0, 0, 0, 2818, 0, 0, 0, 0, 0, -744, 0, -6843, 0, 0, 0, 0, 0, 6454, 0, 0, 0, 828, 0, 5900, 0, 0, 0, 3128, 0, -11876, 0, 0, 0, -552, 0, 0, 0, 0, 0, 1722, 0, -5776, 0, 0, 0, 0, 0, -4576, 0, 0, 0, -2892, 0, -17680, 0, 0, 0, 10608, 0, -230, 0, 0, 0, -4, 0, 0, 0, 0, 0, 15438, 0, 12294, 0, 0, 0, 0, 0, 76, 0, 0, 0, -17488, 0, 8698, 0, 0, 0, 608, 0, 8536, 0, 0, 0, -8712, 0, 0, 0, 0, 0, 5484, 0, -1632, 0, 0, 0, 0, 0, -19402, 0, 0, 0, 13578, 0, -6222, 0, 0, 0, -15260, 0, -488, 0, 0, 0, 6800, 0, 0, 0, 0, 0, -9812, 0, 21216, 0, 0, 0, 0, 0, 7226, 0, 0, 0, 6750, 0, -1748, 0, 0, 0, 1416, 0, -4156, 0, 0, 0, 14088, 0, 0, 0, 0, 0, -16970, 0, -756, 0, 0, 0, 0, 0, 3536, 0, 0, 0, 8500, 0, -20620, 0, 0, 0, 9880, 0, 10937, 0, 0, 0, -3264, 0, 0, 0, 0, 0, -11526, 0, 5314, 0, 0, 0, 0, 0, -24104, 0, 0, 0, 184, 0, 1704, 0, 0, 0, -23582, 0, 13600, 0, 0, 0, -2680, 0, 0, 0, 0, 0, 25004, 0, -11180, 0, 0, 0, 0, 0, 15862, 0, 0, 0, -1688, 0, -14076, 0, 0, 0, 15036, 0, -1040, 0, 0, 0, -12786, 0, 0, 0, 0, 0, -13464, 0, 8518, 0, 0, 0, 0, 0, 11082, 0, 0, 0, 7072, 0, 26568, 0, 0, 0, 3282, 0, -2308, 0, 0, 0, -2760, 0, 0, 0, 0, 0, -11856, 0, -24572, 0, 0, 0, 0, 0, -23052, 0, 0, 0, -2136, 0, 5508, 0, 0, 0, -4536, 0, 68, 0, 0, 0, -27914, 0, 0, 0, 0, 0, -22842, 0, 16458, 0, 0, 0, 0, 0, 6992, 0, 0, 0, -1292, 0, 16050, 0, 0, 0, -5314, 0, 1028, 0, 0, 0, -15876, 0, 0, 0, 0, 0, -28152, 0, -13372, 0, 0, 0, 0, 0, 1824, 0, 0, 0, 3230, 0, 1248, 0, 0, 0, -1404, 0, -6154, 0, 0, 0, -39520, 0, 0, 0, 0, 0, -20264, 0, 1796, 0, 0, 0, 0, 0, 25354, 0, 0, 0, -7600, 0, 13344, 0, 0, 0, 8296, 0, -28452, 0, 0, 0, -5784, 0, 0, 0, 0, 0, -1752, 0, 852, 0, 0, 0, 0, 0, 5704, 0, 0, 0, 24828, 0, -1204, 0, 0, 0, 136, 0, -13298, 0, 0, 0, -642, 0, 0, 0, 0, 0, -192, 0, -24072, 0, 0, 0, 0, 0, 20236, 0, 0, 0, -2700, 0, -2584, 0, 0, 0, 11562, 0, -3952, 0, 0, 0, 12852, 0, 0, 0, 0, 0, -18984, 0, -2332, 0, 0, 0, 0, 0, 800, 0, 0, 0, 19126, 0, -37102, 0, 0, 0, -11304, 0, -974, 0, 0, 0, 12882, 0, 0, 0, 0, 0, -16480, 0, -22273, 0, 0, 0, 0, 0, 350, 0, 0, 0, 47424, 0, -11192, 0, 0, 0, -34278, 0, -14020, 0, 0, 0, -30528, 0, 0, 0, 0, 0, -28968, 0, 16592, 0, 0, 0, 0, 0, -2932, 0, 0, 0, -7116, 0, 35140, 0, 0, 0, -20296, 0, -732, 0, 0, 0, 416, 0, 0, 0, 0, 0, -11960, 0, 15732, 0, 0, 0, 0, 0, -19512, 0, 0, 0, 16720, 0, 28696, 0, 0, 0, 996, 0, 7340, 0, 0, 0, -48144, 0, 0, 0, 0, 0, -48932, 0, -1356, 0, 0, 0, 0, 0, -30298, 0, 0, 0, -8414, 0, -7296, 0, 0, 0, 23912, 0, 25704, 0, 0, 0, -22866, 0, 0, 0, 0, 0, 4052, 0, 37809, 0, 0, 0, 0, 0, -738, 0, 0, 0, -44098, 0, -4920, 0, 0, 0, 34426, 0, 46920, 0, 0, 0, -30216, 0, 0, 0, 0, 0, 30400, 0, 4592, 0, 0, 0, 0, 0, 24276, 0, 0, 0, -4624, 0, -76, 0, 0, 0, -1656, 0, 11750, 0, 0, 0, 27490, 0, 0, 0, 0, 0, -47326, 0, 9070, 0, 0, 0, 0, 0, -57936, 0, 0, 0, 46472, 0, -20654, 0, 0, 0, 1444, 0, 14732, 0, 0, 0, -6724, 0, 0, 0, 0, 0, -19404, 0, -40124, 0, 0, 0, 0, 0, -4192, 0, 0, 0, -47014, 0, -45310, 0, 0, 0, -17476, 0, -6242, 0, 0, 0, 14352, 0, 0, 0, 0, 0, 57392, 0, 15808, 0, 0, 0, 0, 0, 52282, 0, 0, 0, -7530, 0, -28712, 0, 0, 0, -28714, 0, 4184, 0, 0, 0, -52592, 0, 0, 0, 0, 0, -25774, 0, 23868, 0, 0, 0, 0, 0, 316, 0, 0, 0, 8, 0, 30460, 0, 0, 0, -51528, 0, 23846, 0, 0, 0, -30532, 0, 0, 0, 0, 0, -9272, 0, 488, 0, 0, 0, 0, 0, -81120, 0, 0, 0, 13564, 0, -46862, 0, 0, 0, 93840, 0, -152, 0, 0, 0, 70152, 0, 0, 0, 0, 0, -4128, 0, 43940, 0, 0, 0, 0, 0, 29784, 0, 0, 0, 71354, 0, -4854, 0, 0, 0, 3644, 0, -2208, 0, 0, 0, 40942, 0, 0, 0, 0, 0, 20468, 0, -38622, 0, 0, 0, 0, 0, 26904, 0, 0, 0, -2516, 0, 16164, 0, 0, 0, -15458, 0, -62928, 0, 0, 0, 35824, 0, 0, 0, 0, 0, 25866, 0, 34396, 0, 0, 0, 0, 0, -23924, 0, 0, 0, -14364, 0, 45900, 0, 0, 0, 9200, 0, -83634, 0, 0, 0, -7972, 0, 0, 0, 0, 0, 64290, 0, -34952, 0, 0, 0, 0, 0, -5140, 0, 0, 0, 12480, 0, 976, 0, 0, 0, -64130, 0, 36556, 0, 0, 0, 64472, 0, 0, 0, 0, 0, 60276, 0, 35012, 0, 0, 0, 0, 0, 29090, 0, 0, 0, -45358, 0, 88870, 0, 0, 0, 38616, 0, 2584, 0, 0, 0, 47736, 0, 0, 0, 0, 0, -5252, 0, -68286, 0, 0, 0, 0, 0, 34118, 0, 0, 0, -51204, 0, -52000, 0, 0, 0, 9368, 0, -61064, 0, 0, 0, 32376, 0, 0, 0, 0, 0, -2832, 0, 428, 0, 0, 0, 0, 0, 304, 0, 0, 0, -65548, 0, 4784, 0, 0, 0, 2904, 0, 46691, 0, 0, 0, -44302, 0, 0, 0, 0, 0, -6028, 0, -83602, 0, 0, 0, 0, 0, 1512, 0, 0, 0, 59568, 0, 3584, 0, 0, 0, 12444, 0, 65800, 0, 0, 0, -5776, 0, 0, 0, 0, 0, 58792, 0, -32072, 0, 0, 0, 0, 0, 40936, 0, 0, 0, -15594, 0, 20850, 0, 0, 0, 64572, 0, -72530, 0, 0, 0, -65522, 0, 0, 0, 0, 0, 37064, 0, -16932, 0, 0, 0, 0, 0, 107626, 0, 0, 0, -92134, 0, 15092, 0, 0, 0, -27040, 0, -64188, 0, 0, 0, -272, 0, 0, 0, 0, 0, 91800, 0, -25144, 0, 0, 0, 0, 0, 9080, 0, 0, 0, 89308, 0, 73452, 0, 0, 0, 12960, 0, 67938, 0, 0, 0, 61662, 0, 0, 0, 0, 0, -43262, 0, -3408, 0, 0, 0, 0, 0, -68884, 0, 0, 0, -115812, 0, -52440, 0, 0, 0, -14976, 0, 88140, 0, 0, 0, 54512, 0, 0, 0, 0, 0, 83640, 0, 101788, 0, 0, 0, 0, 0, -19044, 0, 0, 0, 37088, 0, 83330, 0, 0, 0, 5168, 0, 28450, 0, 0, 0, 104242, 0, 0, 0, 0, 0, 92444, 0, 13012, 0, 0, 0, 0, 0, -66874, 0, 0, 0, -23782, 0, -11900, 0, 0, 0, 3376, 0, -95180, 0, 0, 0, 44824, 0, 0, 0, 0, 0, 7392, 0, 62400, 0, 0, 0, 0, 0, 82032, 0, 0, 0, -67328, 0, 6772, 0, 0, 0, -21672, 0, -91294, 0, 0, 0, 96106, 0, 0, 0, 0, 0, -8922, 0, -14182, 0, 0, 0, 0, 0, -103716, 0, 0, 0, -6612, 0, -107616, 0, 0, 0, -60654, 0, 114308, 0, 0, 0, 107640, 0, 0, 0, 0, 0, 19532, 0, 24888, 0, 0, 0, 0, 0, 21738, 0, 0, 0, 71264, 0, -42514, 0, 0, 0, 39136, 0, -17154, 0, 0, 0, -8376, 0, 0, 0, 0, 0, 57456, 0, -66617, 0, 0, 0, 0, 0, -10924, 0, 0, 0, 5520, 0, -120512, 0, 0, 0, 88342, 0, -55604, 0, 0, 0, -33864, 0, 0, 0, 0, 0, 89650, 0, 92, 0, 0, 0, 0, 0, -26676, 0, 0, 0, 87624, 0, 33972, 0, 0, 0, -71128, 0, -544, 0, 0, 0, 39710, 0, 0, 0, 0, 0, 32448, 0, 106046, 0, 0, 0, 0, 0, -140848, 0, 0, 0, 34124, 0, -11262, 0, 0, 0, -6732, 0, 124436, 0, 0, 0, -9600, 0, 0, 0, 0, 0, -1748, 0, -10336, 0, 0, 0, 0, 0, -82190, 0, 0, 0, -137768, 0, -57578, 0, 0, 0, 65168, 0, 27914, 0, 0, 0, -8296, 0, 0, 0, 0, 0, -2316, 0, 63386, 0, 0, 0, 0, 0, 167280, 0, 0, 0, -2634, 0, -105768, 0, 0, 0, -129504, 0, -33288, 0, 0, 0, 65304, 0, 0, 0, 0, 0, -520, 0, 70968, 0, 0, 0, 0, 0, 70176, 0, 0, 0, -16608, 0, -2056, 0, 0, 0, 101992, 0, -39507, 0, 0, 0, -22876, 0, 0, 0, 0, 0, 82518, 0, -103946, 0, 0, 0, 0, 0, -81088, 0, 0, 0, -113636, 0, 87766, 0, 0, 0, 53070, 0, 43536, 0, 0, 0, -14956, 0, 0, 0, 0, 0, -23232, 0, 9880, 0, 0, 0, 0, 0, 13584, 0, 0, 0, -94166, 0, 42772, 0, 0, 0, -142908, 0, 128288, 0, 0, 0, -97662, 0, 0, 0, 0, 0, 2808, 0, -51300, 0, 0, 0, 0, 0, -4992, 0, 0, 0, 143298, 0, 66200, 0, 0, 0, 228616, 0, -4592, 0, 0, 0, 11224, 0, 0, 0, 0, 0, -49854, 0, 118124, 0, 0, 0, 0, 0, -3592, 0, 0, 0, -129168, 0, 142528, 0, 0, 0, 7960, 0, 135524, 0, 0, 0, 66066, 0, 0, 0, 0, 0, 65194, 0, -3944, 0, 0, 0, 0, 0, -56112, 0, 0, 0, 87380, 0, -71598, 0, 0, 0, -61290, 0, -69064, 0, 0, 0, -89804, 0, 0, 0, 0, 0, 16272, 0, 25236, 0, 0, 0, 0, 0, -19234, 0, 0, 0, 20800, 0, 6938, 0, 0, 0, -31428, 0, -87746, 0, 0, 0, 3504, 0, 0, 0, 0, 0, -69924, 0, -142256, 0, 0, 0, 0, 0, 209760, 0, 0, 0, -18508, 0, -2036, 0, 0, 0, 6650, 0, -32568, 0, 0, 0, -38464, 0, 0, 0, 0, 0, -79074, 0, 2408, 0, 0, 0, 0, 0, -63440, 0, 0, 0, 1860, 0, 122648, 0, 0, 0, -53048, 0, -105002, 0, 0, 0, -20672, 0, 0, 0, 0, 0, 3802, 0, -159256, 0, 0, 0, 0, 0, -67800, 0, 0, 0, 36420, 0, -80830, 0, 0, 0, 17388, 0, -16592, 0, 0, 0, -7276, 0, 0, 0, 0, 0, -100904, 0, -71404, 0, 0, 0, 0, 0, 121066, 0, 0, 0, 48774, 0, 15026, 0, 0, 0, 5400, 0, -11776, 0, 0, 0, 47594, 0, 0, 0, 0, 0, -13908, 0, -49578, 0, 0, 0, 0, 0, 102476, 0, 0, 0, 140352, 0, 19872, 0, 0, 0, -9208, 0, -98132, 0, 0, 0, 624, 0, 0, 0, 0, 0, -60928, 0, -16052, 0, 0, 0, 0, 0, 15640, 0, 0, 0, 184080, 0, -51536, 0, 0, 0, -142784, 0, -93007, 0, 0, 0, 66642, 0, 0, 0, 0, 0, -5676, 0, 119750, 0, 0, 0, 0, 0, 18924, 0, 0, 0, -78128, 0, -3128, 0, 0, 0, 12770, 0, 31708, 0, 0, 0, -100348, 0, 0, 0, 0, 0, 85544, 0, -42716, 0, 0, 0, 0, 0, -11856, 0, 0, 0, 304, 0, -98280, 0, 0, 0, -187764, 0, -142858, 0, 0, 0, 75354, 0, 0, 0, 0, 0, -82800, 0, 158074, 0, 0, 0, 0, 0, -38610, 0, 0, 0, -39192, 0, 129412, 0, 0, 0, -1494, 0, -700, 0, 0, 0, -35256, 0, 0, 0, 0, 0, -175754, 0, -55336, 0, 0, 0, 0, 0, 2040, 0, 0, 0, -154360, 0, 106704, 0, 0, 0, 271048, 0, 76988, 0, 0, 0, -131494, 0, 0, 0, 0, 0, 19546, 0, -75050, 0, 0, 0, 0, 0, -92080, 0, 0, 0, 65316, 0, 174760, 0, 0, 0, 100338, 0, 1628, 0, 0, 0, -93480, 0, 0, 0, 0, 0, -136496, 0, 3988, 0, 0, 0, 0, 0, 168150, 0, 0, 0, 127846, 0, -183626, 0, 0, 0, 17680, 0, -28678, 0, 0, 0, -77998, 0, 0, 0, 0, 0, -170736, 0, 113549, 0, 0, 0, 0, 0, 38824, 0, 0, 0, 48274, 0, 1464, 0, 0, 0, -150418, 0, -96, 0, 0, 0, -133136, 0, 0, 0, 0, 0, 9088, 0, -87856, 0, 0, 0, 0, 0, -38780, 0, 0, 0, -63680, 0, -13956, 0, 0, 0, 103408, 0, 221520, 0, 0, 0, -221204, 0, 0, 0, 0, 0, -201246, 0, 133152, 0, 0, 0, 0, 0, -64764, 0, 0, 0, -5636, 0, -88594, 0, 0, 0, -194646, 0, 76128, 0, 0, 0, -318512, 0, 0, 0, 0, 0, -1992, 0, -43056, 0, 0, 0, 0, 0, -125664, 0, 0, 0, 1824, 0, -105626, 0, 0, 0, 91504, 0, -14552, 0, 0, 0, 1488, 0, 0, 0, 0, 0, -115124, 0, -31690, 0, 0, 0, 0, 0, 13686, 0, 0, 0, -74262, 0, -127756, 0, 0, 0, 400, 0, -61348, 0, 0, 0, 220600, 0, 0, 0, 0, 0, -81042, 0, -63960, 0, 0, 0, 0, 0, 48784, 0, 0, 0, 204952, 0, 112404, 0, 0, 0, -79648, 0, -12908, 0, 0, 0, -219440, 0, 0, 0, 0, 0, -53670, 0, 63480, 0, 0, 0, 0, 0, -121856, 0, 0, 0, -179992, 0, 61078, 0, 0, 0, 140346, 0, 205200, 0, 0, 0, -8104, 0, 0, 0, 0, 0, -41076, 0, -11800, 0, 0, 0, 0, 0, -211346, 0, 0, 0, 49466, 0, -7600, 0, 0, 0, -220896, 0, 142392, 0, 0, 0, -34834, 0, 0, 0, 0, 0, -6256, 0, 9840, 0, 0, 0, 0, 0, 245574, 0, 0, 0, 185708, 0, 23752, 0, 0, 0, -86166, 0, 93996, 0, 0, 0, 106928, 0, 0, 0, 0, 0, 79496, 0, 171940, 0, 0, 0, 0, 0, -32808, 0, 0, 0, 1104, 0, -35256, 0, 0, 0, 248096, 0, -231122, 0, 0, 0, 126858, 0, 0, 0, 0, 0, 186330, 0, 117936, 0, 0, 0, 0, 0, -194236, 0, 0, 0, 59408, 0, 35710, 0, 0, 0, 9248, 0, -5080, 0, 0, 0, -3444, 0, 0, 0, 0, 0, -238392, 0, -139540, 0, 0, 0, 0, 0, 11552, 0, 0, 0, 118506, 0, -308720, 0, 0, 0, -11712, 0, 234510, 0, 0, 0, -229458, 0, 0, 0, 0, 0, -358800, 0, 114444, 0, 0, 0, 0, 0, -442, 0, 0, 0, 9272, 0, 208, 0, 0, 0, -83946, 0, 9152, 0, 0, 0, -26600, 0, 0, 0, 0, 0, 75270, 0, 16452, 0, 0, 0, 0, 0, -241144, 0, 0, 0, 153540, 0, -91732, 0, 0, 0, 5784, 0, 22519, 0, 0, 0, -23644, 0, 0, 0, 0, 0, -14562, 0, 35360, 0, 0, 0, 0, 0, 39372, 0, 0, 0, 13448, 0, 232742, 0, 0, 0, -48066, 0, -78432, 0, 0, 0, 124660, 0, 0, 0, 0, 0, -21216, 0, 105148, 0, 0, 0, 0, 0, 36338, 0, 0, 0, 65406, 0, 460, 0, 0, 0, -3952, 0, 8384, 0, 0, 0, -92226, 0, 0, 0, 0, 0, -262328, 0, 48800, 0, 0, 0, 0, 0, 252158, 0, 0, 0, -678, 0, 282336, 0, 0, 0, -37338, 0, -442408, 0, 0, 0, -140256, 0, 0, 0, 0, 0, -54606, 0, 33984, 0, 0, 0, 0, 0, 145700, 0, 0, 0, 55632, 0, -265824, 0, 0, 0, -105856, 0, 32292, 0, 0, 0, -30876, 0, 0, 0, 0, 0, -127826, 0, -47804, 0, 0, 0, 0, 0, -24588, 0, 0, 0, -251328, 0, -78798, 0, 0, 0, 64110, 0, 254252, 0, 0, 0, 197052, 0, 0, 0, 0, 0, 105360, 0, -268228, 0, 0, 0, 0, 0, -230248, 0, 0, 0, -230928, 0, -8368, 0, 0, 0, -41308, 0, 12882, 0, 0, 0, -18144, 0, 0, 0, 0, 0, 282992, 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": "360.4.a.d", "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], [-2], [0], [0], [0], [34], [0], [68], [0], [0], [0], [-38], [0], [4], [0], [0], [0], [152], [0], [0], [0], [0], [0], [46], [0], [-260], [0], [0], [0], [0], [0], [312], [0], [0], [0], [-48], [0], [200], [0], [0], [0], [104], [0], [-339], [0], [0], [0], [-414], [0], [0], [0], [0], [0], [2], [0], [-38], [0], [0], [0], [0], [0], [244], [0], [0], [0], [-708], [0], [378], [0], [0], [0], [-68], [0], [-852], [0], [0], [0], [844], [0], [0], [0], [0], [0], [1380], [0], [-136], [0], [0], [0], [0], [0], [-514], [0], [0], [0]]}