# Stored data for newform 900.4.a.j, downloaded from the LMFDB on 25 April 2024.
{"label": "900.4.a.j", "space_label": "900.4.a", "level": 900, "weight": 4, "hecke_orbit": 10, "hecke_orbit_code": 40532396713444228, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 613193374975462894, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[7, [2, 1]], [11, [-30, 1]]], "qexp_display": "q-2q^{7}+30q^{11}+4q^{13}-90q^{17}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 14400, "fricke_eigenval": -1, "atkin_lehner_string": "-++", "analytic_conductor": 53.10171900516655, "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": [900, 1, [451, 101, 577], [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": "1.009", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.004", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.981", "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, 30, 0, 4, 0, 0, 0, -90, 0, -28, 0, 0, 0, -120, 0, 0, 0, 0, 0, 210, 0, -4, 0, 0, 0, 0, 0, -200, 0, 0, 0, 240, 0, 136, 0, 0, 0, 120, 0, -339, 0, 0, 0, 30, 0, 0, 0, 0, 0, -450, 0, -166, 0, 0, 0, 0, 0, -908, 0, 0, 0, -1020, 0, 250, 0, 0, 0, -60, 0, -916, 0, 0, 0, 1140, 0, 0, 0, 0, 0, -420, 0, -8, 0, 0, 0, 0, 0, -1538, 0, 0, 0, 450, 0, 1150, 0, 0, 0, 1620, 0, -1702, 0, 0, 0, -1350, 0, 0, 0, 0, 0, 180, 0, -431, 0, 0, 0, 0, 0, -2450, 0, 0, 0, 690, 0, 56, 0, 0, 0, -2070, 0, -1924, 0, 0, 0, 120, 0, 0, 0, 0, 0, 2910, 0, 176, 0, 0, 0, 0, 0, -2348, 0, 0, 0, 240, 0, 1996, 0, 0, 0, -3120, 0, -2181, 0, 0, 0, -1770, 0, 0, 0, 0, 0, -2130, 0, -1654, 0, 0, 0, 0, 0, -2700, 0, 0, 0, 1740, 0, -86, 0, 0, 0, 2490, 0, -832, 0, 0, 0, -420, 0, 0, 0, 0, 0, -840, 0, 2084, 0, 0, 0, 0, 0, 8, 0, 0, 0, -360, 0, 1174, 0, 0, 0, 3120, 0, -58, 0, 0, 0, 5910, 0, 0, 0, 0, 0, 3300, 0, -2986, 0, 0, 0, 0, 0, -112, 0, 0, 0, -6630, 0, -3600, 0, 0, 0, 1530, 0, 400, 0, 0, 0, -2640, 0, 0, 0, 0, 0, -7350, 0, 3512, 0, 0, 0, 0, 0, 5368, 0, 0, 0, -3060, 0, 5044, 0, 0, 0, -480, 0, 3187, 0, 0, 0, 2010, 0, 0, 0, 0, 0, -480, 0, -272, 0, 0, 0, 0, 0, 2752, 0, 0, 0, 9540, 0, -9254, 0, 0, 0, -150, 0, 6300, 0, 0, 0, 2520, 0, 0, 0, 0, 0, -240, 0, 1892, 0, 0, 0, 0, 0, 7378, 0, 0, 0, -120, 0, 1364, 0, 0, 0, -6720, 0, 5186, 0, 0, 0, -3330, 0, 0, 0, 0, 0, 9000, 0, -6075, 0, 0, 0, 0, 0, 8758, 0, 0, 0, -60, 0, -4724, 0, 0, 0, 840, 0, 7292, 0, 0, 0, -14520, 0, 0, 0, 0, 0, 7110, 0, 10800, 0, 0, 0, 0, 0, 11488, 0, 0, 0, 780, 0, -16, 0, 0, 0, -6000, 0, 5402, 0, 0, 0, 900, 0, 0, 0, 0, 0, -2190, 0, -7162, 0, 0, 0, 0, 0, 332, 0, 0, 0, 9360, 0, -12806, 0, 0, 0, 3360, 0, 11288, 0, 0, 0, 8520, 0, 0, 0, 0, 0, -1260, 0, 7200, 0, 0, 0, 0, 0, 13750, 0, 0, 0, -3210, 0, 12850, 0, 0, 0, 8220, 0, 1816, 0, 0, 0, 4080, 0, 0, 0, 0, 0, -7020, 0, -800, 0, 0, 0, 0, 0, 8122, 0, 0, 0, -13470, 0, -18900, 0, 0, 0, 2040, 0, 2468, 0, 0, 0, 4440, 0, 0, 0, 0, 0, -11190, 0, -500, 0, 0, 0, 0, 0, 3600, 0, 0, 0, -4020, 0, 9076, 0, 0, 0, 360, 0, 2233, 0, 0, 0, 960, 0, 0, 0, 0, 0, -10170, 0, -7486, 0, 0, 0, 0, 0, -7400, 0, 0, 0, -5880, 0, 1832, 0, 0, 0, -11490, 0, 544, 0, 0, 0, 19320, 0, 0, 0, 0, 0, 8340, 0, 21044, 0, 0, 0, 0, 0, -1418, 0, 0, 0, -2280, 0, 900, 0, 0, 0, 22020, 0, 112, 0, 0, 0, -25230, 0, 0, 0, 0, 0, 8280, 0, -18874, 0, 0, 0, 0, 0, -10550, 0, 0, 0, 480, 0, -11000, 0, 0, 0, 11310, 0, -17572, 0, 0, 0, 840, 0, 0, 0, 0, 0, 18000, 0, 1604, 0, 0, 0, 0, 0, -1356, 0, 0, 0, 31320, 0, 31300, 0, 0, 0, -10920, 0, -13500, 0, 0, 0, 3210, 0, 0, 0, 0, 0, -11910, 0, -3382, 0, 0, 0, 0, 0, -25200, 0, 0, 0, -4980, 0, -15950, 0, 0, 0, -32190, 0, 3076, 0, 0, 0, -22140, 0, 0, 0, 0, 0, 120, 0, -6172, 0, 0, 0, 0, 0, -21600, 0, 0, 0, 19170, 0, 5600, 0, 0, 0, -900, 0, -21898, 0, 0, 0, 480, 0, 0, 0, 0, 0, 16680, 0, -2300, 0, 0, 0, 0, 0, -6518, 0, 0, 0, -12240, 0, 23200, 0, 0, 0, -27240, 0, -16324, 0, 0, 0, 120, 0, 0, 0, 0, 0, -3240, 0, 30548, 0, 0, 0, 0, 0, -16952, 0, 0, 0, -20220, 0, 3404, 0, 0, 0, -1800, 0, -20722, 0, 0, 0, -4350, 0, 0, 0, 0, 0, -6720, 0, -30600, 0, 0, 0, 0, 0, -41972, 0, 0, 0, 2700, 0, -664, 0, 0, 0, 39510, 0, -10800, 0, 0, 0, 7500, 0, 0, 0, 0, 0, 16680, 0, -15484, 0, 0, 0, 0, 0, -3808, 0, 0, 0, 4170, 0, 30226, 0, 0, 0, 14760, 0, -9934, 0, 0, 0, 30510, 0, 0, 0, 0, 0, -23520, 0, 19711, 0, 0, 0, 0, 0, 862, 0, 0, 0, 24000, 0, -29816, 0, 0, 0, 35430, 0, -36196, 0, 0, 0, -480, 0, 0, 0, 0, 0, -27480, 0, -3632, 0, 0, 0, 0, 0, -28532, 0, 0, 0, -20340, 0, 10756, 0, 0, 0, -600, 0, 4900, 0, 0, 0, -3360, 0, 0, 0, 0, 0, -840, 0, -2700, 0, 0, 0, 0, 0, -25400, 0, 0, 0, -36240, 0, 34200, 0, 0, 0, -1380, 0, 6572, 0, 0, 0, -4080, 0, 0, 0, 0, 0, 2340, 0, 9492, 0, 0, 0, 0, 0, -2522, 0, 0, 0, -52770, 0, -28800, 0, 0, 0, -28200, 0, 1000, 0, 0, 0, 15570, 0, 0, 0, 0, 0, 4140, 0, -29775, 0, 0, 0, 0, 0, 8350, 0, 0, 0, 43650, 0, 3848, 0, 0, 0, -18810, 0, -12600, 0, 0, 0, 25320, 0, 0, 0, 0, 0, -16320, 0, -6736, 0, 0, 0, 0, 0, 20500, 0, 0, 0, -240, 0, 40500, 0, 0, 0, -840, 0, -18202, 0, 0, 0, -23010, 0, 0, 0, 0, 0, 59550, 0, 48494, 0, 0, 0, 0, 0, -3664, 0, 0, 0, 48120, 0, -41006, 0, 0, 0, 14940, 0, 56012, 0, 0, 0, -5820, 0, 0, 0, 0, 0, -52980, 0, -16924, 0, 0, 0, 0, 0, -352, 0, 0, 0, 38310, 0, -43646, 0, 0, 0, -46140, 0, 2078, 0, 0, 0, -42000, 0, 0, 0, 0, 0, 4560, 0, -14400, 0, 0, 0, 0, 0, 59578, 0, 0, 0, 810, 0, 42136, 0, 0, 0, 4650, 0, 4696, 0, 0, 0, -54000, 0, 0, 0, 0, 0, 36270, 0, 13500, 0, 0, 0, 0, 0, 15292, 0, 0, 0, 12600, 0, -43076, 0, 0, 0, 40680, 0, 40742, 0, 0, 0, 34500, 0, 0, 0, 0, 0, 81720, 0, -3992, 0, 0, 0, 0, 0, 800, 0, 0, 0, -41340, 0, 8434, 0, 0, 0, -1680, 0, 4648, 0, 0, 0, -43080, 0, 0, 0, 0, 0, 6240, 0, 17156, 0, 0, 0, 0, 0, 48600, 0, 0, 0, -570, 0, 4362, 0, 0, 0, -49980, 0, 50400, 0, 0, 0, 54930, 0, 0, 0, 0, 0, -51060, 0, 64802, 0, 0, 0, 0, 0, 91800, 0, 0, 0, 3540, 0, -19100, 0, 0, 0, -34590, 0, -3600, 0, 0, 0, 44400, 0, 0, 0, 0, 0, 31350, 0, -77092, 0, 0, 0, 0, 0, 4300, 0, 0, 0, -22500, 0, -40500, 0, 0, 0, 28560, 0, 36686, 0, 0, 0, 4260, 0, 0, 0, 0, 0, -84450, 0, -6152, 0, 0, 0, 0, 0, 3308, 0, 0, 0, -960, 0, 25424, 0, 0, 0, 78210, 0, 87308, 0, 0, 0, -46680, 0, 0, 0, 0, 0, -55860, 0, 12836, 0, 0, 0, 0, 0, 16162, 0, 0, 0, 7470, 0, -76634, 0, 0, 0, 1320, 0, 5400, 0, 0, 0, 1800, 0, 0, 0, 0, 0, -50940, 0, 35138, 0, 0, 0, 0, 0, 75718, 0, 0, 0, -52860, 0, -544, 0, 0, 0, -3480, 0, 4600, 0, 0, 0, 82440, 0, 0, 0, 0, 0, 28560, 0, 172, 0, 0, 0, 0, 0, 54000, 0, 0, 0, 15180, 0, 25200, 0, 0, 0, 75720, 0, -10653, 0, 0, 0, 40590, 0, 0, 0, 0, 0, -4980, 0, 35054, 0, 0, 0, 0, 0, -7000, 0, 0, 0, 6480, 0, 1664, 0, 0, 0, -73500, 0, 47432, 0, 0, 0, 19920, 0, 0, 0, 0, 0, 70680, 0, -102600, 0, 0, 0, 0, 0, -6808, 0, 0, 0, -71190, 0, -59150, 0, 0, 0, 3780, 0, 61358, 0, 0, 0, -50190, 0, 0, 0, 0, 0, 1080, 0, 20700, 0, 0, 0, 0, 0, 61162, 0, 0, 0, 17190, 0, 76084, 0, 0, 0, -480, 0, -77596, 0, 0, 0, 1680, 0, 0, 0, 0, 0, -5400, 0, 78344, 0, 0, 0, 0, 0, -4168, 0, 0, 0, 40740, 0, -74900, 0, 0, 0, 38400, 0, 63074, 0, 0, 0, -102750, 0, 0, 0, 0, 0, 87870, 0, 25648, 0, 0, 0, 0, 0, -62100, 0, 0, 0, -47580, 0, 37800, 0, 0, 0, -48000, 0, 1356, 0, 0, 0, -21360, 0, 0, 0, 0, 0, -57720, 0, -67204, 0, 0, 0, 0, 0, 6300, 0, 0, 0, 108960, 0, -25214, 0, 0, 0, 720, 0, -31582, 0, 0, 0, -65970, 0, 0, 0, 0, 0, 9060, 0, -2348, 0, 0, 0, 0, 0, 89542, 0, 0, 0, 42150, 0, -1724, 0, 0, 0, -31920, 0, -30892, 0, 0, 0, 73800, 0, 0, 0, 0, 0, -6240, 0, -27200, 0, 0, 0, 0, 0, -59600, 0, 0, 0, 65280, 0, 116, 0, 0, 0, -94200, 0, -57502, 0, 0, 0, 30870, 0, 0, 0, 0, 0, -14310, 0, 55706, 0, 0, 0, 0, 0, -64100, 0, 0, 0, -11820, 0, 122400, 0, 0, 0, 8430, 0, 87300, 0, 0, 0, -120, 0, 0, 0, 0, 0, 138420, 0, -9800, 0, 0, 0, 0, 0, -89750, 0, 0, 0, 5280, 0, -71954, 0, 0, 0, 6240, 0, -84994, 0, 0, 0, -6600, 0, 0, 0, 0, 0, -30000, 0, -11321, 0, 0, 0, 0, 0, 5972, 0, 0, 0, 11760, 0, 22336, 0, 0, 0, 13290, 0, -113236, 0, 0, 0, 2760, 0, 0, 0, 0, 0, -52530, 0, -94500, 0, 0, 0, 0, 0, -40500, 0, 0, 0, -124680, 0, 56500, 0, 0, 0, -70440, 0, 224, 0, 0, 0, -103710, 0, 0, 0, 0, 0, -24000, 0, 90686, 0, 0, 0, 0, 0, -66800, 0, 0, 0, -103500, 0, 2050, 0, 0, 0, 13260, 0, -43948, 0, 0, 0, 32640, 0, 0, 0, 0, 0, -34860, 0, 7200, 0, 0, 0, 0, 0, -88718, 0, 0, 0, -8280, 0, -44906, 0, 0, 0, 73200, 0, 55562, 0, 0, 0, 59880, 0, 0, 0, 0, 0, -3060, 0, 37274, 0, 0, 0, 0, 0, -7696, 0, 0, 0, 103050, 0, 67800, 0, 0, 0, 109920, 0, -145800, 0, 0, 0, -29880, 0, 0, 0, 0, 0, 1800, 0, -85192, 0, 0, 0, 0, 0, -93600, 0, 0, 0, 5280, 0, 43064, 0, 0, 0, 93240, 0, -61011, 0, 0, 0, 153180, 0, 0, 0, 0, 0, -65430, 0, -129034, 0, 0, 0, 0, 0, -118592, 0, 0, 0, 20580, 0, 45526, 0, 0, 0, -20430, 0, 21584, 0, 0, 0, 14700, 0, 0, 0, 0, 0, 84480, 0, 664, 0, 0, 0, 0, 0, -7024, 0, 0, 0, -98730, 0, -53100, 0, 0, 0, 69180, 0, -136800, 0, 0, 0, 132990, 0, 0, 0, 0, 0, -12600, 0, 121500, 0, 0, 0, 0, 0, 28800, 0, 0, 0, -3330, 0, 75544, 0, 0, 0, 11640, 0, -10736, 0, 0, 0, -190680, 0, 0, 0, 0, 0, -129090, 0, 31724, 0, 0, 0, 0, 0, -32200, 0, 0, 0, -6000, 0, 704, 0, 0, 0, 6120, 0, -63900, 0, 0, 0, 31470, 0, 0, 0, 0, 0, 21270, 0, -10088, 0, 0, 0, 0, 0, -153200, 0, 0, 0, -49620, 0, 48850, 0, 0, 0, -107670, 0, 53432, 0, 0, 0, 37260, 0, 0, 0, 0, 0, -81360, 0, -57868, 0, 0, 0, 0, 0, -97442, 0, 0, 0, 16320, 0, -6374, 0, 0, 0, -156540, 0, 36158, 0, 0, 0, -45360, 0, 0, 0, 0, 0, 86820, 0, -9392, 0, 0, 0, 0, 0, 50400, 0, 0, 0, -4020, 0, 47500, 0, 0, 0, 38790, 0, -214200, 0, 0, 0, -81120, 0, 0, 0, 0, 0, 17250, 0, 47656, 0, 0, 0, 0, 0, 3632, 0, 0, 0, 22140, 0, -20456, 0, 0, 0, -174120, 0, 34262, 0, 0, 0, 960, 0, 0, 0, 0, 0, 33510, 0, 52200, 0, 0, 0, 0, 0, -46104, 0, 0, 0, 103740, 0, -62654, 0, 0, 0, 52500, 0, 7984, 0, 0, 0, -2580, 0, 0, 0, 0, 0, 15720, 0, -124108, 0, 0, 0, 0, 0, 18922, 0, 0, 0, 74490, 0, 1714, 0, 0, 0, 37800, 0, -5504, 0, 0, 0, -70890, 0, 0, 0, 0, 0, 220500, 0, -79018, 0, 0, 0, 0, 0, 74700, 0, 0, 0, -12480, 0, 7200, 0, 0, 0, -19080, 0, 63308, 0, 0, 0, 90000, 0, 0, 0, 0, 0, -24960, 0, 18508, 0, 0, 0, 0, 0, -17512, 0, 0, 0, 4080, 0, 79216, 0, 0, 0, -13920, 0, -89423, 0, 0, 0, -69330, 0, 0, 0, 0, 0, 300, 0, 200006, 0, 0, 0, 0, 0, -62100, 0, 0, 0, 184560, 0, -12600, 0, 0, 0, 161310, 0, 141212, 0, 0, 0, -109380, 0, 0, 0, 0, 0, -7080, 0, 41924, 0, 0, 0, 0, 0, 33200, 0, 0, 0, -5040, 0, -1000, 0, 0, 0, -30540, 0, -29578, 0, 0, 0, -57690, 0, 0, 0, 0, 0, 4080, 0, -197254, 0, 0, 0, 0, 0, 184750, 0, 0, 0, -192360, 0, -99836, 0, 0, 0, 70230, 0, 12068, 0, 0, 0, -40680, 0, 0, 0, 0, 0, 91530, 0, -5416, 0, 0, 0, 0, 0, -3784, 0, 0, 0, 62520, 0, -54000, 0, 0, 0, -8520, 0, 186300, 0, 0, 0, 49830, 0, 0, 0, 0, 0, -60570, 0, -31786, 0, 0, 0, 0, 0, -126512, 0, 0, 0, 132060, 0, -6616, 0, 0, 0, -159090, 0, -14756, 0, 0, 0, 173160, 0, 0, 0, 0, 0, -138000, 0, 128756, 0, 0, 0, 0, 0, 78550, 0, 0, 0, -171750, 0, -18506, 0, 0, 0, 240, 0, 157562, 0, 0, 0, 93870, 0, 0, 0, 0, 0, -134160, 0, 113549, 0, 0, 0, 0, 0, 239400, 0, 0, 0, -103890, 0, 68600, 0, 0, 0, -146670, 0, -108000, 0, 0, 0, 10800, 0, 0, 0, 0, 0, 13440, 0, -10800, 0, 0, 0, 0, 0, 181828, 0, 0, 0, -167040, 0, -10372, 0, 0, 0, 65520, 0, 3664, 0, 0, 0, 35220, 0, 0, 0, 0, 0, -25890, 0, -194400, 0, 0, 0, 0, 0, 45700, 0, 0, 0, 6660, 0, -45074, 0, 0, 0, 179670, 0, 181600, 0, 0, 0, 6960, 0, 0, 0, 0, 0, -19320, 0, 3600, 0, 0, 0, 0, 0, 93600, 0, 0, 0, -39840, 0, -119450, 0, 0, 0, 204240, 0, -344, 0, 0, 0, -18000, 0, 0, 0, 0, 0, -1740, 0, 119606, 0, 0, 0, 0, 0, 12150, 0, 0, 0, -87210, 0, -261900, 0, 0, 0, -61200, 0, 206012, 0, 0, 0, 144360, 0, 0, 0, 0, 0, 45330, 0, 78248, 0, 0, 0, 0, 0, 25552, 0, 0, 0, 9960, 0, 177300, 0, 0, 0, -15840, 0, -17516, 0, 0, 0, -4560, 0, 0, 0, 0, 0, -183450, 0, -88200, 0, 0, 0, 0, 0, -3328, 0, 0, 0, 225240, 0, -20714, 0, 0, 0, -10170, 0, 162000, 0, 0, 0, 57960, 0, 0, 0, 0, 0, -64140, 0, 9448, 0, 0, 0, 0, 0, 242158, 0, 0, 0, 176070, 0, -22576, 0, 0, 0, 204000, 0, 99000, 0, 0, 0, -60270, 0, 0, 0, 0, 0, -1680, 0, 53872, 0, 0, 0, 0, 0, 161350, 0, 0, 0, -89580, 0, -14584, 0, 0, 0, -13290, 0, -198196, 0, 0, 0, -201360, 0, 0, 0, 0, 0, 211320, 0, 219044, 0, 0, 0, 0, 0, 151000, 0, 0, 0, 29040, 0, 161800, 0, 0, 0, -119040, 0, 251438, 0, 0, 0, 85110, 0, 0, 0, 0, 0, -22170, 0, -50000, 0, 0, 0, 0, 0, -82748, 0, 0, 0, -159120, 0, -250754, 0, 0, 0, -3360, 0, 124328, 0, 0, 0, -14220, 0, 0, 0, 0, 0, 181560, 0, -130996, 0, 0, 0, 0, 0, -21600, 0, 0, 0, 115350, 0, 8336, 0, 0, 0, -217920, 0, -6514, 0, 0, 0, -176430, 0, 0, 0, 0, 0, 1680, 0, -198900, 0, 0, 0, 0, 0, 108742, 0, 0, 0, -179640, 0, -54000, 0, 0, 0, 17130, 0, -22976, 0, 0, 0, 51720, 0, 0, 0, 0, 0, 114810, 0, 112772, 0, 0, 0, 0, 0, 102088, 0, 0, 0, 198780, 0, -64916, 0, 0, 0, -1560, 0, -147977, 0, 0, 0, -322980, 0, 0, 0, 0, 0, 167970, 0, 32, 0, 0, 0, 0, 0, 45900, 0, 0, 0, -81480, 0, 80806, 0, 0, 0, -110910, 0, 280800, 0, 0, 0, 133260, 0, 0, 0, 0, 0, 12000, 0, 229724, 0, 0, 0, 0, 0, -398, 0, 0, 0, -31230, 0, -10804, 0, 0, 0, -19920, 0, -4928, 0, 0, 0, 196290, 0, 0, 0, 0, 0, 93240, 0, -123488, 0, 0, 0, 0, 0, -49922, 0, 0, 0, 152550, 0, -79200, 0, 0, 0, -191910, 0, 4696, 0, 0, 0, -149760, 0, 0, 0, 0, 0, -277170, 0, -244800, 0, 0, 0, 0, 0, -62108, 0, 0, 0, 294000, 0, 183200, 0, 0, 0, -3360, 0, 94500, 0, 0, 0, 4380, 0, 0, 0, 0, 0, -261870, 0, 159300, 0, 0, 0, 0, 0, 14324, 0, 0, 0, 12480, 0, -217550, 0, 0, 0, -129390, 0, -220500, 0, 0, 0, 75780, 0, 0, 0, 0, 0, 7920, 0, 224156, 0, 0, 0, 0, 0, -232, 0, 0, 0, 105360, 0, 65744, 0, 0, 0, 241500, 0, 56274, 0, 0, 0, 60000, 0, 0, 0, 0, 0, 150480, 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": "180.4.a.b", "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], [30], [0], [4], [0], [0], [0], [-90], [0], [-28], [0], [0], [0], [-120], [0], [0], [0], [0], [0], [210], [0], [-4], [0], [0], [0], [0], [0], [-200], [0], [0], [0], [240], [0], [136], [0], [0], [0], [120], [0], [-339], [0], [0], [0], [30], [0], [0], [0], [0], [0], [-450], [0], [-166], [0], [0], [0], [0], [0], [-908], [0], [0], [0], [-1020], [0], [250], [0], [0], [0], [-60], [0], [-916], [0], [0], [0], [1140], [0], [0], [0], [0], [0], [-420], [0], [-8], [0], [0], [0], [0], [0], [-1538], [0], [0], [0]]}