# Stored data for newform 1800.4.a.j, downloaded from the LMFDB on 23 April 2024.
{"label": "1800.4.a.j", "space_label": "1800.4.a", "level": 1800, "weight": 4, "hecke_orbit": 10, "hecke_orbit_code": 40532396713445128, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1382777613778073748, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [10, 1]], [11, [-46, 1]], [17, [-66, 1]]], "qexp_display": "q-10q^{7}+46q^{11}+34q^{13}+66q^{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": "0.979", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.946", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.813", "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, -10], "traces": [0, 1, 0, 0, 0, 0, 0, -10, 0, 0, 0, 46, 0, 34, 0, 0, 0, 66, 0, 104, 0, 0, 0, 164, 0, 0, 0, 0, 0, -224, 0, -72, 0, 0, 0, 0, 0, 22, 0, 0, 0, -194, 0, -108, 0, 0, 0, -480, 0, -243, 0, 0, 0, 286, 0, 0, 0, 0, 0, -426, 0, 698, 0, 0, 0, 0, 0, -328, 0, 0, 0, -188, 0, 740, 0, 0, 0, -460, 0, 1168, 0, 0, 0, 412, 0, 0, 0, 0, 0, -1206, 0, -340, 0, 0, 0, 0, 0, 1384, 0, 0, 0, 1128, 0, 758, 0, 0, 0, 1324, 0, 1602, 0, 0, 0, -2074, 0, 0, 0, 0, 0, -660, 0, 785, 0, 0, 0, 0, 0, 534, 0, 0, 0, -1806, 0, -1040, 0, 0, 0, 1822, 0, 532, 0, 0, 0, 1564, 0, 0, 0, 0, 0, 1284, 0, 184, 0, 0, 0, 0, 0, 3746, 0, 0, 0, -1640, 0, -1504, 0, 0, 0, 3012, 0, -1041, 0, 0, 0, -438, 0, 0, 0, 0, 0, 1462, 0, 586, 0, 0, 0, 0, 0, 3036, 0, 0, 0, -60, 0, 4676, 0, 0, 0, 2286, 0, -3536, 0, 0, 0, 2240, 0, 0, 0, 0, 0, 4784, 0, -3500, 0, 0, 0, 0, 0, 720, 0, 0, 0, 2244, 0, -5874, 0, 0, 0, -124, 0, -1362, 0, 0, 0, -3870, 0, 0, 0, 0, 0, -6116, 0, -5962, 0, 0, 0, 0, 0, 3536, 0, 0, 0, 1490, 0, 7544, 0, 0, 0, -5394, 0, -220, 0, 0, 0, -636, 0, 0, 0, 0, 0, 3360, 0, 5768, 0, 0, 0, 0, 0, 1398, 0, 0, 0, 4194, 0, 8256, 0, 0, 0, 1940, 0, -557, 0, 0, 0, 5534, 0, 0, 0, 0, 0, 5576, 0, 1080, 0, 0, 0, 0, 0, 484, 0, 0, 0, 2724, 0, -5308, 0, 0, 0, 4218, 0, -10304, 0, 0, 0, 6864, 0, 0, 0, 0, 0, 4800, 0, -4640, 0, 0, 0, 0, 0, 8156, 0, 0, 0, -3312, 0, 5860, 0, 0, 0, 4124, 0, 3650, 0, 0, 0, 6834, 0, 0, 0, 0, 0, -3904, 0, 3957, 0, 0, 0, 0, 0, 13174, 0, 0, 0, -2860, 0, 1090, 0, 0, 0, -7616, 0, -9220, 0, 0, 0, -3960, 0, 0, 0, 0, 0, 1788, 0, 10824, 0, 0, 0, 0, 0, -9642, 0, 0, 0, 410, 0, -2448, 0, 0, 0, 1012, 0, 13766, 0, 0, 0, 4260, 0, 0, 0, 0, 0, -16998, 0, -2450, 0, 0, 0, 0, 0, -6980, 0, 0, 0, 9248, 0, 5028, 0, 0, 0, 17056, 0, 3120, 0, 0, 0, -8220, 0, 0, 0, 0, 0, 5826, 0, -8924, 0, 0, 0, 0, 0, 16896, 0, 0, 0, 996, 0, -10046, 0, 0, 0, -8388, 0, 3280, 0, 0, 0, -4968, 0, 0, 0, 0, 0, -11396, 0, 748, 0, 0, 0, 0, 0, -6454, 0, 0, 0, -18638, 0, -14784, 0, 0, 0, 1880, 0, 17768, 0, 0, 0, -7952, 0, 0, 0, 0, 0, 12896, 0, -7400, 0, 0, 0, 0, 0, -22080, 0, 0, 0, 2714, 0, 13792, 0, 0, 0, -4752, 0, 14729, 0, 0, 0, -6596, 0, 0, 0, 0, 0, -11178, 0, 6802, 0, 0, 0, 0, 0, 18188, 0, 0, 0, -23296, 0, -11680, 0, 0, 0, 21462, 0, -3672, 0, 0, 0, -17244, 0, 0, 0, 0, 0, -8790, 0, -5984, 0, 0, 0, 0, 0, 9344, 0, 0, 0, -4120, 0, 13156, 0, 0, 0, -6932, 0, -7488, 0, 0, 0, 9382, 0, 0, 0, 0, 0, -4096, 0, 22962, 0, 0, 0, 0, 0, 3490, 0, 0, 0, -16320, 0, -6386, 0, 0, 0, -19534, 0, 8764, 0, 0, 0, 12060, 0, 0, 0, 0, 0, 1452, 0, 7856, 0, 0, 0, 0, 0, -8262, 0, 0, 0, 22974, 0, 6216, 0, 0, 0, 13384, 0, -19596, 0, 0, 0, 12882, 0, 0, 0, 0, 0, 2082, 0, -9430, 0, 0, 0, 0, 0, -36736, 0, 0, 0, 32108, 0, -3268, 0, 0, 0, -15606, 0, -13840, 0, 0, 0, 428, 0, 0, 0, 0, 0, 9724, 0, -6384, 0, 0, 0, 0, 0, -12804, 0, 0, 0, 12224, 0, 2288, 0, 0, 0, -11280, 0, 19510, 0, 0, 0, -11808, 0, 0, 0, 0, 0, 3368, 0, -7580, 0, 0, 0, 0, 0, -22134, 0, 0, 0, -7128, 0, -32298, 0, 0, 0, -15088, 0, 25104, 0, 0, 0, -27696, 0, 0, 0, 0, 0, -13240, 0, -2176, 0, 0, 0, 0, 0, -25514, 0, 0, 0, -18238, 0, -16020, 0, 0, 0, -14484, 0, -14462, 0, 0, 0, 34034, 0, 0, 0, 0, 0, -20176, 0, -8648, 0, 0, 0, 0, 0, -22064, 0, 0, 0, 20740, 0, 23732, 0, 0, 0, -23334, 0, -31680, 0, 0, 0, 34040, 0, 0, 0, 0, 0, 7566, 0, 5964, 0, 0, 0, 0, 0, -11232, 0, 0, 0, 11880, 0, 1762, 0, 0, 0, -14124, 0, -21350, 0, 0, 0, -16038, 0, 0, 0, 0, 0, 26136, 0, 25787, 0, 0, 0, 0, 0, -7850, 0, 0, 0, 3608, 0, 7030, 0, 0, 0, -9574, 0, -43748, 0, 0, 0, 41436, 0, 0, 0, 0, 0, 53728, 0, -11152, 0, 0, 0, 0, 0, -4606, 0, 0, 0, 4610, 0, -23512, 0, 0, 0, -30396, 0, -5340, 0, 0, 0, -49920, 0, 0, 0, 0, 0, 16128, 0, 18876, 0, 0, 0, 0, 0, -3452, 0, 0, 0, -14256, 0, 18952, 0, 0, 0, 18060, 0, 8064, 0, 0, 0, -6392, 0, 0, 0, 0, 0, 40930, 0, -25272, 0, 0, 0, 0, 0, -9016, 0, 0, 0, 10444, 0, -31816, 0, 0, 0, 21516, 0, 25160, 0, 0, 0, -28098, 0, 0, 0, 0, 0, -18220, 0, -24607, 0, 0, 0, 0, 0, 14558, 0, 0, 0, -24846, 0, -5320, 0, 0, 0, -12950, 0, -55476, 0, 0, 0, -26728, 0, 0, 0, 0, 0, -17712, 0, 3880, 0, 0, 0, 0, 0, -18582, 0, 0, 0, -15640, 0, -28116, 0, 0, 0, 29744, 0, 50486, 0, 0, 0, -13710, 0, 0, 0, 0, 0, -25634, 0, -27690, 0, 0, 0, 0, 0, 39712, 0, 0, 0, 55680, 0, 26380, 0, 0, 0, 46068, 0, 35960, 0, 0, 0, -12840, 0, 0, 0, 0, 0, 9026, 0, -4068, 0, 0, 0, 0, 0, -1840, 0, 0, 0, -37340, 0, -32182, 0, 0, 0, 63664, 0, -14274, 0, 0, 0, -4928, 0, 0, 0, 0, 0, 14008, 0, -78720, 0, 0, 0, 0, 0, -59174, 0, 0, 0, 42, 0, 21942, 0, 0, 0, -10242, 0, -37460, 0, 0, 0, -17784, 0, 0, 0, 0, 0, -66868, 0, 51888, 0, 0, 0, 0, 0, 17810, 0, 0, 0, -44304, 0, 27712, 0, 0, 0, -39852, 0, -12830, 0, 0, 0, 34868, 0, 0, 0, 0, 0, -21648, 0, 15040, 0, 0, 0, 0, 0, -1584, 0, 0, 0, -44580, 0, 9884, 0, 0, 0, -41004, 0, 72592, 0, 0, 0, 156, 0, 0, 0, 0, 0, -30120, 0, 68380, 0, 0, 0, 0, 0, 60904, 0, 0, 0, 37188, 0, 10410, 0, 0, 0, -16548, 0, 43456, 0, 0, 0, 2326, 0, 0, 0, 0, 0, 73692, 0, 10126, 0, 0, 0, 0, 0, -12408, 0, 0, 0, 4380, 0, -5342, 0, 0, 0, -16274, 0, 46904, 0, 0, 0, 49688, 0, 0, 0, 0, 0, 33588, 0, 7888, 0, 0, 0, 0, 0, -5494, 0, 0, 0, 48840, 0, -95404, 0, 0, 0, 24192, 0, -8114, 0, 0, 0, -14620, 0, 0, 0, 0, 0, -21490, 0, 47056, 0, 0, 0, 0, 0, -5860, 0, 0, 0, 13968, 0, -34112, 0, 0, 0, 14518, 0, 40624, 0, 0, 0, -24596, 0, 0, 0, 0, 0, -89102, 0, 6784, 0, 0, 0, 0, 0, 46156, 0, 0, 0, -73212, 0, 25654, 0, 0, 0, -39844, 0, -30360, 0, 0, 0, 38352, 0, 0, 0, 0, 0, 15268, 0, 70918, 0, 0, 0, 0, 0, 8030, 0, 0, 0, -25116, 0, 7776, 0, 0, 0, 600, 0, 25772, 0, 0, 0, 77088, 0, 0, 0, 0, 0, -19552, 0, -46760, 0, 0, 0, 0, 0, -69864, 0, 0, 0, 24442, 0, 107520, 0, 0, 0, 848, 0, -50169, 0, 0, 0, -89402, 0, 0, 0, 0, 0, -22860, 0, -35290, 0, 0, 0, 0, 0, 76960, 0, 0, 0, 45016, 0, 35360, 0, 0, 0, 24564, 0, 47320, 0, 0, 0, 114472, 0, 0, 0, 0, 0, -82962, 0, 27192, 0, 0, 0, 0, 0, 54468, 0, 0, 0, 54432, 0, 63354, 0, 0, 0, 43100, 0, -32650, 0, 0, 0, 69198, 0, 0, 0, 0, 0, -61832, 0, -83076, 0, 0, 0, 0, 0, -574, 0, 0, 0, -25362, 0, 68602, 0, 0, 0, 34560, 0, -34428, 0, 0, 0, -47840, 0, 0, 0, 0, 0, -70516, 0, -63600, 0, 0, 0, 0, 0, 35000, 0, 0, 0, -48350, 0, 34520, 0, 0, 0, 18348, 0, 51710, 0, 0, 0, 49350, 0, 0, 0, 0, 0, 72190, 0, 121472, 0, 0, 0, 0, 0, 83812, 0, 0, 0, 71460, 0, -79596, 0, 0, 0, -4268, 0, 17496, 0, 0, 0, -115052, 0, 0, 0, 0, 0, 24472, 0, -103768, 0, 0, 0, 0, 0, -64064, 0, 0, 0, -53792, 0, 28682, 0, 0, 0, -22440, 0, -50206, 0, 0, 0, -29574, 0, 0, 0, 0, 0, 86900, 0, 58740, 0, 0, 0, 0, 0, 101038, 0, 0, 0, 25350, 0, 26690, 0, 0, 0, 42848, 0, -35952, 0, 0, 0, 4148, 0, 0, 0, 0, 0, 1240, 0, -2376, 0, 0, 0, 0, 0, 105966, 0, 0, 0, -39810, 0, 13620, 0, 0, 0, -45036, 0, -66890, 0, 0, 0, 35798, 0, 0, 0, 0, 0, 115122, 0, -78142, 0, 0, 0, 0, 0, -44872, 0, 0, 0, 38700, 0, -30832, 0, 0, 0, 35054, 0, 59064, 0, 0, 0, -20592, 0, 0, 0, 0, 0, 91344, 0, 18156, 0, 0, 0, 0, 0, 46596, 0, 0, 0, 8464, 0, -1154, 0, 0, 0, 41380, 0, -22082, 0, 0, 0, 61160, 0, 0, 0, 0, 0, 121360, 0, -31285, 0, 0, 0, 0, 0, 59620, 0, 0, 0, -125424, 0, -104458, 0, 0, 0, -32562, 0, -94176, 0, 0, 0, -61404, 0, 0, 0, 0, 0, 36268, 0, 95424, 0, 0, 0, 0, 0, 74448, 0, 0, 0, 40894, 0, -125808, 0, 0, 0, 172316, 0, -35360, 0, 0, 0, 26634, 0, 0, 0, 0, 0, -10560, 0, -16250, 0, 0, 0, 0, 0, -101644, 0, 0, 0, 50028, 0, -32204, 0, 0, 0, -14900, 0, -21320, 0, 0, 0, 20952, 0, 0, 0, 0, 0, -156352, 0, -75440, 0, 0, 0, 0, 0, -94788, 0, 0, 0, 61948, 0, 133078, 0, 0, 0, -115676, 0, -28302, 0, 0, 0, -69184, 0, 0, 0, 0, 0, 53940, 0, 96630, 0, 0, 0, 0, 0, 18088, 0, 0, 0, -89486, 0, -5346, 0, 0, 0, 191552, 0, 87384, 0, 0, 0, -118340, 0, 0, 0, 0, 0, 30672, 0, 20896, 0, 0, 0, 0, 0, 138552, 0, 0, 0, 6360, 0, 143936, 0, 0, 0, -46384, 0, -67843, 0, 0, 0, 105732, 0, 0, 0, 0, 0, -47886, 0, -146738, 0, 0, 0, 0, 0, 57244, 0, 0, 0, 144204, 0, -77320, 0, 0, 0, 18426, 0, -46904, 0, 0, 0, -33600, 0, 0, 0, 0, 0, 24062, 0, -50256, 0, 0, 0, 0, 0, -57680, 0, 0, 0, -107764, 0, -20148, 0, 0, 0, 114716, 0, 67568, 0, 0, 0, -48806, 0, 0, 0, 0, 0, 117312, 0, -136884, 0, 0, 0, 0, 0, 93120, 0, 0, 0, 48102, 0, 70446, 0, 0, 0, 43656, 0, -13980, 0, 0, 0, 73472, 0, 0, 0, 0, 0, 19956, 0, 107600, 0, 0, 0, 0, 0, 78832, 0, 0, 0, 6292, 0, 6256, 0, 0, 0, -41940, 0, 67252, 0, 0, 0, 23058, 0, 0, 0, 0, 0, -1682, 0, -82560, 0, 0, 0, 0, 0, 110308, 0, 0, 0, 26956, 0, 23732, 0, 0, 0, -116894, 0, 62840, 0, 0, 0, -140220, 0, 0, 0, 0, 0, 47142, 0, 97544, 0, 0, 0, 0, 0, -148896, 0, 0, 0, 51840, 0, 5570, 0, 0, 0, 83868, 0, -80546, 0, 0, 0, 137696, 0, 0, 0, 0, 0, -122844, 0, 127364, 0, 0, 0, 0, 0, -197784, 0, 0, 0, -55340, 0, 71266, 0, 0, 0, 51810, 0, 42112, 0, 0, 0, 95676, 0, 0, 0, 0, 0, -142080, 0, 166608, 0, 0, 0, 0, 0, 23616, 0, 0, 0, -18334, 0, -121780, 0, 0, 0, -59464, 0, -22458, 0, 0, 0, -55760, 0, 0, 0, 0, 0, -81354, 0, -2760, 0, 0, 0, 0, 0, 26244, 0, 0, 0, -102188, 0, 148356, 0, 0, 0, -165760, 0, -51136, 0, 0, 0, 215096, 0, 0, 0, 0, 0, 71662, 0, -171200, 0, 0, 0, 0, 0, -182876, 0, 0, 0, -69512, 0, -170958, 0, 0, 0, -215696, 0, -4840, 0, 0, 0, -140134, 0, 0, 0, 0, 0, 35244, 0, 92198, 0, 0, 0, 0, 0, 105156, 0, 0, 0, 102408, 0, -55484, 0, 0, 0, -27240, 0, -15212, 0, 0, 0, -9372, 0, 0, 0, 0, 0, -162656, 0, 53080, 0, 0, 0, 0, 0, -110092, 0, 0, 0, 13536, 0, 6252, 0, 0, 0, -62296, 0, 126577, 0, 0, 0, -61790, 0, 0, 0, 0, 0, -42180, 0, 58078, 0, 0, 0, 0, 0, -119196, 0, 0, 0, 226976, 0, 103040, 0, 0, 0, -65146, 0, -16184, 0, 0, 0, -38092, 0, 0, 0, 0, 0, -14892, 0, 151428, 0, 0, 0, 0, 0, 15356, 0, 0, 0, -68640, 0, -53280, 0, 0, 0, -49588, 0, 73942, 0, 0, 0, -43838, 0, 0, 0, 0, 0, -30888, 0, -67542, 0, 0, 0, 0, 0, -142986, 0, 0, 0, -261632, 0, -97534, 0, 0, 0, -28982, 0, 81640, 0, 0, 0, 116640, 0, 0, 0, 0, 0, -50872, 0, -139808, 0, 0, 0, 0, 0, 46400, 0, 0, 0, -161000, 0, 184992, 0, 0, 0, 49708, 0, 120252, 0, 0, 0, 115878, 0, 0, 0, 0, 0, -96450, 0, -137882, 0, 0, 0, 0, 0, -99396, 0, 0, 0, 183540, 0, 19924, 0, 0, 0, -114862, 0, -81560, 0, 0, 0, 35112, 0, 0, 0, 0, 0, 124312, 0, -145364, 0, 0, 0, 0, 0, 5936, 0, 0, 0, 155088, 0, -152322, 0, 0, 0, 33120, 0, 152570, 0, 0, 0, 151322, 0, 0, 0, 0, 0, -31936, 0, 24749, 0, 0, 0, 0, 0, -92288, 0, 0, 0, -175514, 0, 55536, 0, 0, 0, 62662, 0, 82644, 0, 0, 0, -157148, 0, 0, 0, 0, 0, -41240, 0, 103224, 0, 0, 0, 0, 0, -90374, 0, 0, 0, 99918, 0, -36500, 0, 0, 0, 27064, 0, -84096, 0, 0, 0, -270204, 0, 0, 0, 0, 0, -224370, 0, 217136, 0, 0, 0, 0, 0, -20536, 0, 0, 0, -68340, 0, -227744, 0, 0, 0, -84426, 0, -7216, 0, 0, 0, -2040, 0, 0, 0, 0, 0, -187824, 0, -137280, 0, 0, 0, 0, 0, -5704, 0, 0, 0, -135412, 0, 35174, 0, 0, 0, 262728, 0, 158984, 0, 0, 0, 39040, 0, 0, 0, 0, 0, -62652, 0, -228358, 0, 0, 0, 0, 0, -39570, 0, 0, 0, -47298, 0, 84744, 0, 0, 0, 46008, 0, 128764, 0, 0, 0, -41160, 0, 0, 0, 0, 0, 193888, 0, 111496, 0, 0, 0, 0, 0, -131354, 0, 0, 0, 77724, 0, -178020, 0, 0, 0, 12144, 0, -131740, 0, 0, 0, -29664, 0, 0, 0, 0, 0, 190030, 0, 270144, 0, 0, 0, 0, 0, -120224, 0, 0, 0, 231816, 0, -146888, 0, 0, 0, -69498, 0, -340136, 0, 0, 0, 189488, 0, 0, 0, 0, 0, -38014, 0, -10900, 0, 0, 0, 0, 0, 127912, 0, 0, 0, 62532, 0, -75384, 0, 0, 0, -4136, 0, -281336, 0, 0, 0, -163610, 0, 0, 0, 0, 0, 76160, 0, 55328, 0, 0, 0, 0, 0, -48994, 0, 0, 0, -274252, 0, 92200, 0, 0, 0, -24110, 0, 60860, 0, 0, 0, -188532, 0, 0, 0, 0, 0, 247236, 0, 12744, 0, 0, 0, 0, 0, 195134, 0, 0, 0, 39600, 0, -60988, 0, 0, 0, -108924, 0, 226962, 0, 0, 0, -229026, 0, 0, 0, 0, 0, 264638, 0, 16280, 0, 0, 0, 0, 0, -98440, 0, 0, 0, -109592, 0, 20864, 0, 0, 0, 162656, 0, 5176, 0, 0, 0, -17880, 0, 0, 0, 0, 0, 71334, 0, -191568, 0, 0, 0, 0, 0, -108240, 0, 0, 0, 121124, 0, -119000, 0, 0, 0, 63632, 0, -57642, 0, 0, 0, 131326, 0, 0, 0, 0, 0, 86832, 0, 68540, 0, 0, 0, 0, 0, 160350, 0, 0, 0, -99264, 0, 204480, 0, 0, 0, -147586, 0, 96420, 0, 0, 0, 128740, 0, 0, 0, 0, 0, 221856, 0, 8624, 0, 0, 0, 0, 0, 73486, 0, 0, 0, -97046, 0, 136000, 0, 0, 0, -4100, 0, -67081, 0, 0, 0, -310016, 0, 0, 0, 0, 0, -219478, 0, 24480, 0, 0, 0, 0, 0, -248124, 0, 0, 0, 133536, 0, -134008, 0, 0, 0, -11322, 0, 198792, 0, 0, 0, 202068, 0, 0, 0, 0, 0, -10120, 0, -211024, 0, 0, 0, 0, 0, -71356, 0, 0, 0, -36832, 0, -137660, 0, 0, 0, -335040, 0, 19136, 0, 0, 0, -68706, 0, 0, 0, 0, 0, -161880, 0, 35424, 0, 0, 0, 0, 0, 125414, 0, 0, 0, 103518, 0, -29256, 0, 0, 0, 94150, 0, -199716, 0, 0, 0, 27340, 0, 0, 0, 0, 0, 99700, 0, 36472, 0, 0, 0, 0, 0, -215966, 0, 0, 0, 87576, 0, 25696, 0, 0, 0, 25872, 0, -252672, 0, 0, 0, 169980, 0, 0, 0, 0, 0, 20274, 0, -28908, 0, 0, 0, 0, 0, 24500, 0, 0, 0, -4216, 0, 200460, 0, 0, 0, 30870, 0, 154560, 0, 0, 0, -291604, 0, 0, 0, 0, 0, -8666, 0, -116872, 0, 0, 0, 0, 0, -46308, 0, 0, 0, 265328, 0, 389584, 0, 0, 0, -169792, 0, -169614, 0, 0, 0, -143560, 0, 0, 0, 0, 0, 38728, 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": "120.4.f.a", "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], [-10], [0], [0], [0], [46], [0], [34], [0], [0], [0], [66], [0], [104], [0], [0], [0], [164], [0], [0], [0], [0], [0], [-224], [0], [-72], [0], [0], [0], [0], [0], [22], [0], [0], [0], [-194], [0], [-108], [0], [0], [0], [-480], [0], [-243], [0], [0], [0], [286], [0], [0], [0], [0], [0], [-426], [0], [698], [0], [0], [0], [0], [0], [-328], [0], [0], [0], [-188], [0], [740], [0], [0], [0], [-460], [0], [1168], [0], [0], [0], [412], [0], [0], [0], [0], [0], [-1206], [0], [-340], [0], [0], [0], [0], [0], [1384], [0], [0], [0]]}