# Stored data for newform 1200.4.f.e, downloaded from the LMFDB on 29 March 2024. {"label": "1200.4.f.e", "space_label": "1200.4.f", "level": 1200, "weight": 4, "hecke_orbit": 5, "hecke_orbit_code": 18014742173975728, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 1165610377149112766, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [1024, 0, 1]], [11, [36, 1]]], "qexp_display": "q+3iq^{3}+2^{5}iq^{7}-9q^{9}-6^{2}q^{11}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 5, "char_orbit_label": "f", "char_is_real": true, "Nk2": 19200, "analytic_conductor": 70.80229200688873, "hecke_ring_index": 1, "level_radical": 30, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 4, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.508", "prec": 17}, "analytic_rank_proved": true, "char_values": [1200, 2, [751, 901, 401, 577], [2, 2, 2, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [49], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.013", "prec": 17}, {"__RealLiteral__": 0, "data": "1.963", "prec": 17}, {"__RealLiteral__": 0, "data": "0.543", "prec": 17}, {"__RealLiteral__": 0, "data": "15.503", "prec": 20}, {"__RealLiteral__": 0, "data": "7.639", "prec": 17}, {"__RealLiteral__": 0, "data": "153.018", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 2, 0, 0, 0, 0, 0, 0, 0, -18, 0, -72, 0, 0, 0, 0, 0, 0, 0, 280, 0, -192, 0, 0, 0, 0, 0, 0, 0, -12, 0, 32, 0, 0, 0, 0, 0, 0, 0, 60, 0, -780, 0, 0, 0, 0, 0, 0, 0, -1362, 0, -468, 0, 0, 0, 0, 0, 0, 0, 1032, 0, -116, 0, 0, 0, 0, 0, 0, 0, -1152, 0, 240, 0, 0, 0, 0, 0, 0, 0, -2336, 0, 162, 0, 0, 0, 0, 0, 0, 0, 3180, 0, 640, 0, 0, 0, 0, 0, 0, 0, 648, 0, 1596, 0, 0, 0, 0, 0, 0, 0, -3244, 0, -204, 0, 0, 0, 0, 0, 0, 0, -4992, 0, -70, 0, 0, 0, 0, 0, 0, 0, -312, 0, -4824, 0, 0, 0, 0, 0, 0, 0, -1112, 0, -2448, 0, 0, 0, 0, 0, 0, 0, 4836, 0, -5680, 0, 0, 0, 0, 0, 0, 0, 684, 0, -12288, 0, 0, 0, 0, 0, 0, 0, 4194, 0, -2520, 0, 0, 0, 0, 0, 0, 0, -5928, 0, -740, 0, 0, 0, 0, 0, 0, 0, 1728, 0, -2208, 0, 0, 0, 0, 0, 0, 0, 8944, 0, 5352, 0, 0, 0, 0, 0, 0, 0, -10080, 0, -2680, 0, 0, 0, 0, 0, 0, 0, 3876, 0, 1560, 0, 0, 0, 0, 0, 0, 0, -3388, 0, 6912, 0, 0, 0, 0, 0, 0, 0, 4704, 0, -7004, 0, 0, 0, 0, 0, 0, 0, -4392, 0, -9576, 0, 0, 0, 0, 0, 0, 0, -2176, 0, 108, 0, 0, 0, 0, 0, 0, 0, -108, 0, 12992, 0, 0, 0, 0, 0, 0, 0, -288, 0, -9708, 0, 0, 0, 0, 0, 0, 0, -2342, 0, 1164, 0, 0, 0, 0, 0, 0, 0, 3840, 0, -3328, 0, 0, 0, 0, 0, 0, 0, 1632, 0, -4848, 0, 0, 0, 0, 0, 0, 0, 432, 0, -936, 0, 0, 0, 0, 0, 0, 0, -26112, 0, 1976, 0, 0, 0, 0, 0, 0, 0, -6444, 0, -1152, 0, 0, 0, 0, 0, 0, 0, 7412, 0, -540, 0, 0, 0, 0, 0, 0, 0, -528, 0, 25482, 0, 0, 0, 0, 0, 0, 0, 7020, 0, 7296, 0, 0, 0, 0, 0, 0, 0, -14456, 0, 9168, 0, 0, 0, 0, 0, 0, 0, 18372, 0, -29952, 0, 0, 0, 0, 0, 0, 0, -26880, 0, -3228, 0, 0, 0, 0, 0, 0, 0, -2068, 0, 12636, 0, 0, 0, 0, 0, 0, 0, 7416, 0, -9860, 0, 0, 0, 0, 0, 0, 0, -2160, 0, 5184, 0, 0, 0, 0, 0, 0, 0, 2704, 0, 12258, 0, 0, 0, 0, 0, 0, 0, 6396, 0, 28080, 0, 0, 0, 0, 0, 0, 0, 4212, 0, 32172, 0, 0, 0, 0, 0, 0, 0, 57088, 0, 12324, 0, 0, 0, 0, 0, 0, 0, 22272, 0, 680, 0, 0, 0, 0, 0, 0, 0, -2760, 0, -23688, 0, 0, 0, 0, 0, 0, 0, -22568, 0, -12096, 0, 0, 0, 0, 0, 0, 0, 35124, 0, 41344, 0, 0, 0, 0, 0, 0, 0, 3708, 0, 6324, 0, 0, 0, 0, 0, 0, 0, -49394, 0, -9288, 0, 0, 0, 0, 0, 0, 0, 49032, 0, 35596, 0, 0, 0, 0, 0, 0, 0, 1044, 0, -1680, 0, 0, 0, 0, 0, 0, 0, 1040, 0, 16848, 0, 0, 0, 0, 0, 0, 0, -15828, 0, 4760, 0, 0, 0, 0, 0, 0, 0, 14388, 0, -46848, 0, 0, 0, 0, 0, 0, 0, 4480, 0, 7668, 0, 0, 0, 0, 0, 0, 0, 5328, 0, -1004, 0, 0, 0, 0, 0, 0, 0, 1152, 0, 8160, 0, 0, 0, 0, 0, 0, 0, 45352, 0, 10368, 0, 0, 0, 0, 0, 0, 0, -5304, 0, 14096, 0, 0, 0, 0, 0, 0, 0, -2160, 0, -40572, 0, 0, 0, 0, 0, 0, 0, -37152, 0, -3072, 0, 0, 0, 0, 0, 0, 0, -32616, 0, 64156, 0, 0, 0, 0, 0, 0, 0, 14160, 0, 4176, 0, 0, 0, 0, 0, 0, 0, 12416, 0, -8280, 0, 0, 0, 0, 0, 0, 0, -2280, 0, 59144, 0, 0, 0, 0, 0, 0, 0, 31140, 0, 11532, 0, 0, 0, 0, 0, 0, 0, -6652, 0, 21024, 0, 0, 0, 0, 0, 0, 0, -15456, 0, 17408, 0, 0, 0, 0, 0, 0, 0, -1458, 0, -8112, 0, 0, 0, 0, 0, 0, 0, 20920, 0, 8400, 0, 0, 0, 0, 0, 0, 0, -9984, 0, -53824, 0, 0, 0, 0, 0, 0, 0, 41472, 0, -34476, 0, 0, 0, 0, 0, 0, 0, -43396, 0, 9036, 0, 0, 0, 0, 0, 0, 0, -109200, 0, -8640, 0, 0, 0, 0, 0, 0, 0, -2592, 0, -68736, 0, 0, 0, 0, 0, 0, 0, -63648, 0, -28620, 0, 0, 0, 0, 0, 0, 0, 23052, 0, 67640, 0, 0, 0, 0, 0, 0, 0, -5760, 0, 39132, 0, 0, 0, 0, 0, 0, 0, 48884, 0, -2796, 0, 0, 0, 0, 0, 0, 0, -63888, 0, -48706, 0, 0, 0, 0, 0, 0, 0, -27096, 0, -13056, 0, 0, 0, 0, 0, 0, 0, 21640, 0, 74880, 0, 0, 0, 0, 0, 0, 0, 84096, 0, -17840, 0, 0, 0, 0, 0, 0, 0, -51444, 0, 31140, 0, 0, 0, 0, 0, 0, 0, 97792, 0, -5832, 0, 0, 0, 0, 0, 0, 0, -192, 0, 17784, 0, 0, 0, 0, 0, 0, 0, -14364, 0, 30144, 0, 0, 0, 0, 0, 0, 0, 48784, 0, -20856, 0, 0, 0, 0, 0, 0, 0, -27204, 0, -190680, 0, 0, 0, 0, 0, 0, 0, 9348, 0, -96660, 0, 0, 0, 0, 0, 0, 0, -12920, 0, -51228, 0, 0, 0, 0, 0, 0, 0, 134784, 0, -59070, 0, 0, 0, 0, 0, 0, 0, -65520, 0, 13944, 0, 0, 0, 0, 0, 0, 0, -114480, 0, 29196, 0, 0, 0, 0, 0, 0, 0, -19968, 0, 20384, 0, 0, 0, 0, 0, 0, 0, 1836, 0, -23040, 0, 0, 0, 0, 0, 0, 0, -70948, 0, 15276, 0, 0, 0, 0, 0, 0, 0, -85176, 0, -24116, 0, 0, 0, 0, 0, 0, 0, 64896, 0, -81744, 0, 0, 0, 0, 0, 0, 0, -10208, 0, -51336, 0, 0, 0, 0, 0, 0, 0, 37356, 0, 1112, 0, 0, 0, 0, 0, 0, 0, -68364, 0, -72900, 0, 0, 0, 0, 0, 0, 0, -53932, 0, 44928, 0, 0, 0, 0, 0, 0, 0, 14640, 0, -156672, 0, 0, 0, 0, 0, 0, 0, 630, 0, 21288, 0, 0, 0, 0, 0, 0, 0, 131456, 0, -61392, 0, 0, 0, 0, 0, 0, 0, 4260, 0, -57456, 0, 0, 0, 0, 0, 0, 0, 3372, 0, 144480, 0, 0, 0, 0, 0, 0, 0, -69364, 0, -360, 0, 0, 0, 0, 0, 0, 0, 139152, 0, -29440, 0, 0, 0, 0, 0, 0, 0, -34416, 0, 44832, 0, 0, 0, 0, 0, 0, 0, -16240, 0, 2808, 0, 0, 0, 0, 0, 0, 0, -129024, 0, -129592, 0, 0, 0, 0, 0, 0, 0, 43416, 0, -5172, 0, 0, 0, 0, 0, 0, 0, 4680, 0, -2364, 0, 0, 0, 0, 0, 0, 0, 116784, 0, 82084, 0, 0, 0, 0, 0, 0, 0, 960, 0, 39552, 0, 0, 0, 0, 0, 0, 0, 43776, 0, 7344, 0, 0, 0, 0, 0, 0, 0, -85548, 0, 122432, 0, 0, 0, 0, 0, 0, 0, -99072, 0, 100776, 0, 0, 0, 0, 0, 0, 0, 40892, 0, 10008, 0, 0, 0, 0, 0, 0, 0, -163032, 0, -3880, 0, 0, 0, 0, 0, 0, 0, 22032, 0, -12480, 0, 0, 0, 0, 0, 0, 0, -139328, 0, 11136, 0, 0, 0, 0, 0, 0, 0, -160692, 0, 62264, 0, 0, 0, 0, 0, 0, 0, -12972, 0, -26340, 0, 0, 0, 0, 0, 0, 0, 179712, 0, -161280, 0, 0, 0, 0, 0, 0, 0, 80688, 0, -103820, 0, 0, 0, 0, 0, 0, 0, 33192, 0, 98352, 0, 0, 0, 0, 0, 0, 0, -5440, 0, -43524, 0, 0, 0, 0, 0, 0, 0, 33600, 0, 153472, 0, 0, 0, 0, 0, 0, 0, 51120, 0, -74268, 0, 0, 0, 0, 0, 0, 0, 98994, 0, -9060, 0, 0, 0, 0, 0, 0, 0, 81792, 0, 192124, 0, 0, 0, 0, 0, 0, 0, 32304, 0, 3120, 0, 0, 0, 0, 0, 0, 0, -133808, 0, 15624, 0, 0, 0, 0, 0, 0, 0, 143100, 0, -114192, 0, 0, 0, 0, 0, 0, 0, 11232, 0, 8172, 0, 0, 0, 0, 0, 0, 0, -75292, 0, -6156, 0, 0, 0, 0, 0, 0, 0, 6336, 0, 173664, 0, 0, 0, 0, 0, 0, 0, 110592, 0, -146760, 0, 0, 0, 0, 0, 0, 0, 22360, 0, -87744, 0, 0, 0, 0, 0, 0, 0, 21480, 0, -35680, 0, 0, 0, 0, 0, 0, 0, 2808, 0, -30924, 0, 0, 0, 0, 0, 0, 0, -65380, 0, -23040, 0, 0, 0, 0, 0, 0, 0, -117624, 0, -327040, 0, 0, 0, 0, 0, 0, 0, 24192, 0, -25104, 0, 0, 0, 0, 0, 0, 0, -21792, 0, -37746, 0, 0, 0, 0, 0, 0, 0, 40032, 0, -80296, 0, 0, 0, 0, 0, 0, 0, 22680, 0, 342528, 0, 0, 0, 0, 0, 0, 0, 110036, 0, 88128, 0, 0, 0, 0, 0, 0, 0, -182256, 0, 151040, 0, 0, 0, 0, 0, 0, 0, 40584, 0, -130392, 0, 0, 0, 0, 0, 0, 0, 158440, 0, -7488, 0, 0, 0, 0, 0, 0, 0, -88320, 0, -3536, 0, 0, 0, 0, 0, 0, 0, -23400, 0, -88956, 0, 0, 0, 0, 0, 0, 0, -53044, 0, 53352, 0, 0, 0, 0, 0, 0, 0, -180264, 0, -137636, 0, 0, 0, 0, 0, 0, 0, 6660, 0, 332160, 0, 0, 0, 0, 0, 0, 0, -174096, 0, 119976, 0, 0, 0, 0, 0, 0, 0, 30264, 0, -30560, 0, 0, 0, 0, 0, 0, 0, 224256, 0, 204480, 0, 0, 0, 0, 0, 0, 0, -85756, 0, 66564, 0, 0, 0, 0, 0, 0, 0, 248064, 0, 166358, 0, 0, 0, 0, 0, 0, 0, 5400, 0, 445200, 0, 0, 0, 0, 0, 0, 0, 210424, 0, -15552, 0, 0, 0, 0, 0, 0, 0, -18156, 0, -6192, 0, 0, 0, 0, 0, 0, 0, 19872, 0, 81876, 0, 0, 0, 0, 0, 0, 0, 89600, 0, -154356, 0, 0, 0, 0, 0, 0, 0, -27744, 0, 149932, 0, 0, 0, 0, 0, 0, 0, -24624, 0, 42432, 0, 0, 0, 0, 0, 0, 0, 158848, 0, -21672, 0, 0, 0, 0, 0, 0, 0, 696, 0, 442368, 0, 0, 0, 0, 0, 0, 0, -17388, 0, -42120, 0, 0, 0, 0, 0, 0, 0, -290380, 0, -80496, 0, 0, 0, 0, 0, 0, 0, 96384, 0, 75316, 0, 0, 0, 0, 0, 0, 0, -48168, 0, 207816, 0, 0, 0, 0, 0, 0, 0, -24336, 0, -47856, 0, 0, 0, 0, 0, 0, 0, 16512, 0, 34736, 0, 0, 0, 0, 0, 0, 0, -122484, 0, -27648, 0, 0, 0, 0, 0, 0, 0, 153606, 0, -38052, 0, 0, 0, 0, 0, 0, 0, -150984, 0, 69244, 0, 0, 0, 0, 0, 0, 0, -305280, 0, -242496, 0, 0, 0, 0, 0, 0, 0, -752, 0, 90720, 0, 0, 0, 0, 0, 0, 0, 20028, 0, -1856, 0, 0, 0, 0, 0, 0, 0, 24120, 0, 183852, 0, 0, 0, 0, 0, 0, 0, -281088, 0, -40860, 0, 0, 0, 0, 0, 0, 0, 223440, 0, -167544, 0, 0, 0, 0, 0, 0, 0, -96648, 0, 226488, 0, 0, 0, 0, 0, 0, 0, -29824, 0, -164736, 0, 0, 0, 0, 0, 0, 0, 18612, 0, 41120, 0, 0, 0, 0, 0, 0, 0, 75132, 0, 7752, 0, 0, 0, 0, 0, 0, 0, 213408, 0, -34884, 0, 0, 0, 0, 0, 0, 0, 73032, 0, -289024, 0, 0, 0, 0, 0, 0, 0, -14040, 0, 26640, 0, 0, 0, 0, 0, 0, 0, 308704, 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, 5, 2, 1, 2, 0]], "char_orbit_index": 6, "prim_orbit_index": 2, "minimal_twist": "60.4.a.b", "char_is_minimal": false, "conrey_index": 49, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [0, 0], [0, 3], [0, 0], [0, 0], [0, 0], [0, 32], [0, 0], [-9, 0], [0, 0], [-36, 0], [0, 0], [0, -10], [0, 0], [0, 0], [0, 0], [0, 78], [0, 0], [140, 0], [0, 0], [-96, 0], [0, 0], [0, 192], [0, 0], [0, 0], [0, 0], [0, -27], [0, 0], [-6, 0], [0, 0], [16, 0], [0, 0], [0, -108], [0, 0], [0, 0], [0, 0], [0, 34], [0, 0], [30, 0], [0, 0], [-390, 0], [0, 0], [0, 52], [0, 0], [0, 0], [0, 0], [0, 408], [0, 0], [-681, 0], [0, 0], [-234, 0], [0, 0], [0, -114], [0, 0], [0, 0], [0, 0], [0, 420], [0, 0], [516, 0], [0, 0], [-58, 0], [0, 0], [0, -288], [0, 0], [0, 0], [0, 0], [0, -892], [0, 0], [-576, 0], [0, 0], [120, 0], [0, 0], [0, -646], [0, 0], [0, 0], [0, 0], [0, -1152], [0, 0], [-1168, 0], [0, 0], [81, 0], [0, 0], [0, 732], [0, 0], [0, 0], [0, 0], [0, -18], [0, 0], [1590, 0], [0, 0], [320, 0], [0, 0], [0, 48], [0, 0], [0, 0], [0, 0], [0, -194], [0, 0], [324, 0], [0, 0]]}