# Stored data for newform 960.4.f.l, downloaded from the LMFDB on 07 September 2024. {"Nk2": 15360, "analytic_conductor": 56.64183360551099, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 5, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 6, "char_orbit_label": "f", "char_order": 2, "char_parity": 1, "char_values": [960, 2, [511, 901, 641, 577], [2, 2, 2, 1]], "cm_discs": [], "conrey_index": 769, "dim": 2, "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 4, "has_non_self_twist": 1, "hecke_cutters": [[7, [100, 0, 1]], [11, [-46, 1]]], "hecke_orbit": 12, "hecke_orbit_code": 49539939565568960, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 2, 1, 2, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "960.4.f.l", "level": 960, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 3, 5], "level_radical": 30, "minimal_twist": "120.4.f.a", "nf_label": "2.0.4.1", "prim_orbit_index": 2, "qexp_display": "q+3iq^{3}+(10+5i)q^{5}+10iq^{7}-9q^{9}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "3.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "960.4.f", "trace_display": [0, 0, 20, 0], "trace_hash": 1996525407569657899, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.933", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "15.569", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "154.633", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.507", "prec": 17}, "traces": [0, 2, 0, 0, 0, 20, 0, 0, 0, -18, 0, 92, 0, 0, 0, -30, 0, 0, 0, 208, 0, -60, 0, 0, 0, 150, 0, 0, 0, 448, 0, -144, 0, 0, 0, -100, 0, 0, 0, 204, 0, 388, 0, 0, 0, -180, 0, 0, 0, 486, 0, -396, 0, 0, 0, 920, 0, 0, 0, 852, 0, -1396, 0, 0, 0, 340, 0, 0, 0, 984, 0, 376, 0, 0, 0, -600, 0, 0, 0, -2336, 0, 162, 0, 0, 0, -660, 0, 0, 0, -2412, 0, 680, 0, 0, 0, 2080, 0, 0, 0, -828, 0, 2256, 0, 0, 0, -600, 0, 0, 0, 3204, 0, -132, 0, 0, 0, 1640, 0, 0, 0, -1320, 0, 1570, 0, 0, 0, 500, 0, 0, 0, -648, 0, -3612, 0, 0, 0, 270, 0, 0, 0, 1064, 0, 2880, 0, 0, 0, 4480, 0, 0, 0, -2568, 0, 368, 0, 0, 0, -1440, 0, 0, 0, -1716, 0, 3280, 0, 0, 0, -1380, 0, 0, 0, 2082, 0, -1872, 0, 0, 0, -2000, 0, 0, 0, -2924, 0, -1172, 0, 0, 0, -220, 0, 0, 0, 540, 0, 120, 0, 0, 0, 2040, 0, 0, 0, 7072, 0, 1968, 0, 0, 0, 3880, 0, 0, 0, 9568, 0, 7000, 0, 0, 0, -1080, 0, 0, 0, -4440, 0, 4488, 0, 0, 0, -1350, 0, 0, 0, -2724, 0, -2760, 0, 0, 0, 4800, 0, 0, 0, -12232, 0, -11924, 0, 0, 0, 4860, 0, 0, 0, -2472, 0, 2980, 0, 0, 0, -3960, 0, 0, 0, -440, 0, -4032, 0, 0, 0, -2860, 0, 0, 0, -6720, 0, 11536, 0, 0, 0, 6900, 0, 0, 0, 1296, 0, -8388, 0, 0, 0, -3120, 0, 0, 0, 1114, 0, 8304, 0, 0, 0, 8520, 0, 0, 0, -11152, 0, -2160, 0, 0, 0, -13960, 0, 0, 0, -4548, 0, -5448, 0, 0, 0, 900, 0, 0, 0, 20608, 0, 7944, 0, 0, 0, 6800, 0, 0, 0, 9600, 0, 9280, 0, 0, 0, 3280, 0, 0, 0, -12444, 0, -6624, 0, 0, 0, 9840, 0, 0, 0, 7300, 0, -1836, 0, 0, 0, 3760, 0, 0, 0, -7808, 0, 7914, 0, 0, 0, -7400, 0, 0, 0, -3492, 0, -5720, 0, 0, 0, -8250, 0, 0, 0, -18440, 0, 3204, 0, 0, 0, -4600, 0, 0, 0, -3576, 0, 21648, 0, 0, 0, -23360, 0, 0, 0, -6240, 0, -820, 0, 0, 0, 1620, 0, 0, 0, -27532, 0, -10932, 0, 0, 0, -4120, 0, 0, 0, 33996, 0, 4900, 0, 0, 0, -13200, 0, 0, 0, 9384, 0, -18496, 0, 0, 0, -6720, 0, 0, 0, -6240, 0, -4374, 0, 0, 0, -24120, 0, 0, 0, 11652, 0, 17848, 0, 0, 0, 6800, 0, 0, 0, 3564, 0, 1992, 0, 0, 0, 2160, 0, 0, 0, 6560, 0, -22476, 0, 0, 0, 15600, 0, 0, 0, -22792, 0, 1496, 0, 0, 0, 13840, 0, 0, 0, -9024, 0, -37276, 0, 0, 0, -8280, 0, 0, 0, 35536, 0, -18072, 0, 0, 0, 22560, 0, 0, 0, -25792, 0, -14800, 0, 0, 0, -7580, 0, 0, 0, 2628, 0, -5428, 0, 0, 0, -4500, 0, 0, 0, -29458, 0, -7668, 0, 0, 0, 13240, 0, 0, 0, 22356, 0, -13604, 0, 0, 0, 32040, 0, 0, 0, 12564, 0, 46592, 0, 0, 0, -1320, 0, 0, 0, 7344, 0, -18216, 0, 0, 0, -20740, 0, 0, 0, -17580, 0, 11968, 0, 0, 0, 32800, 0, 0, 0, -28056, 0, -8240, 0, 0, 0, -3060, 0, 0, 0, -14976, 0, 13716, 0, 0, 0, -13200, 0, 0, 0, -8192, 0, 45924, 0, 0, 0, 15700, 0, 0, 0, -13440, 0, -32640, 0, 0, 0, -5820, 0, 0, 0, 17528, 0, -8856, 0, 0, 0, -8750, 0, 0, 0, -2904, 0, 15712, 0, 0, 0, 5340, 0, 0, 0, -3384, 0, -45948, 0, 0, 0, -6480, 0, 0, 0, 39192, 0, 4320, 0, 0, 0, -36120, 0, 0, 0, -4164, 0, 18860, 0, 0, 0, -10400, 0, 0, 0, 35244, 0, -64216, 0, 0, 0, 5400, 0, 0, 0, 27680, 0, -744, 0, 0, 0, -18220, 0, 0, 0, 19448, 0, 12768, 0, 0, 0, 10640, 0, 0, 0, -23220, 0, 24448, 0, 0, 0, 28800, 0, 0, 0, 39020, 0, 21024, 0, 0, 0, 15640, 0, 0, 0, 6736, 0, -15160, 0, 0, 0, 33600, 0, 0, 0, -1458, 0, -14256, 0, 0, 0, -7290, 0, 0, 0, 50208, 0, 21216, 0, 0, 0, -25680, 0, 0, 0, 26480, 0, -4352, 0, 0, 0, 3680, 0, 0, 0, 45264, 0, 36476, 0, 0, 0, 5940, 0, 0, 0, 28924, 0, 32364, 0, 0, 0, -10800, 0, 0, 0, 40352, 0, 17296, 0, 0, 0, -37460, 0, 0, 0, -3816, 0, -41480, 0, 0, 0, -17160, 0, 0, 0, 63360, 0, 21708, 0, 0, 0, 32800, 0, 0, 0, 15132, 0, -11928, 0, 0, 0, -15040, 0, 0, 0, -6120, 0, 23760, 0, 0, 0, -27600, 0, 0, 0, -42700, 0, -8388, 0, 0, 0, -30120, 0, 0, 0, 52272, 0, 51574, 0, 0, 0, 20820, 0, 0, 0, 49536, 0, 7216, 0, 0, 0, -18720, 0, 0, 0, -87496, 0, -11640, 0, 0, 0, 4380, 0, 0, 0, -107456, 0, -22304, 0, 0, 0, -27500, 0, 0, 0, -33204, 0, -9220, 0, 0, 0, -12780, 0, 0, 0, 10680, 0, 7452, 0, 0, 0, -29240, 0, 0, 0, -32256, 0, -37752, 0, 0, 0, -11720, 0, 0, 0, -20304, 0, 28512, 0, 0, 0, 20940, 0, 0, 0, -16128, 0, -2904, 0, 0, 0, -4400, 0, 0, 0, 81860, 0, 50544, 0, 0, 0, -30360, 0, 0, 0, 31848, 0, 20888, 0, 0, 0, 5400, 0, 0, 0, 50320, 0, 25308, 0, 0, 0, 1200, 0, 0, 0, -36440, 0, -49214, 0, 0, 0, -46760, 0, 0, 0, -41184, 0, -49692, 0, 0, 0, 15300, 0, 0, 0, -110952, 0, -28836, 0, 0, 0, 22860, 0, 0, 0, 35424, 0, 7760, 0, 0, 0, 70720, 0, 0, 0, 1188, 0], "weight": 4, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0], [1, 0], [0, 0], [0, 3], [0, 0], [10, 5], [0, 0], [0, 10], [0, 0], [-9, 0], [0, 0], [46, 0], [0, 0], [0, -34], [0, 0], [-15, 30], [0, 0], [0, 66], [0, 0], [104, 0], [0, 0], [-30, 0], [0, 0], [0, -164], [0, 0], [75, 100], [0, 0], [0, -27], [0, 0], [224, 0], [0, 0], [-72, 0], [0, 0], [0, 138], [0, 0], [-50, 100], [0, 0], [0, 22], [0, 0], [102, 0], [0, 0], [194, 0], [0, 0], [0, 108], [0, 0], [-90, -45], [0, 0], [0, -480], [0, 0], [243, 0], [0, 0], [-198, 0], [0, 0], [0, 286], [0, 0], [460, 230], [0, 0], [0, 312], [0, 0], [426, 0], [0, 0], [-698, 0], [0, 0], [0, -90], [0, 0], [170, -340], [0, 0], [0, -328], [0, 0], [492, 0], [0, 0], [188, 0], [0, 0], [0, 740], [0, 0], [-300, 225], [0, 0], [0, 460], [0, 0], [-1168, 0], [0, 0], [81, 0], [0, 0], [0, 412], [0, 0], [-330, 660], [0, 0], [0, 672], [0, 0], [-1206, 0], [0, 0], [340, 0], [0, 0], [0, -216], [0, 0], [1040, 520], [0, 0], [0, -1384], [0, 0], [-414, 0], [0, 0]]}