# Stored data for newform 256.4.e.c, downloaded from the LMFDB on 21 October 2025.
{"Nk2": 4096, "analytic_conductor": 15.104488961469597, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 16, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 5, "char_orbit_label": "e", "char_order": 4, "char_parity": 1, "char_values": [256, 4, [255, 5], [4, 3]], "cm_discs": [], "conrey_index": 65, "dim": 16, "field_disc": 990561591461923075915776, "field_disc_factorization": [[2, 32], [3, 8], [433, 4]], "field_poly": [331776, 0, 0, 0, 201600, 0, 0, 0, 13297, 0, 0, 0, 242, 0, 0, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[3, [7269949696, 0, 0, 0, 1122922240, 0, 0, 0, 4618848, 0, 0, 0, 5104, 0, 0, 0, 1]], [5, [535824, 1756800, 2880000, 654912, 73288, -1888, 128, 16, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9007474199757056, "hecke_ring_generator_nbound": 9, "hecke_ring_index": 1099511627776, "hecke_ring_index_factorization": [[2, 40]], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 16, 5, 1, 4, 0], [1, 1, 4, 2, -1, 2, 0], [1, 1, 16, 6, -1, 4, 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": true, "label": "256.4.e.c", "level": 256, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": true, "level_is_prime_square": false, "level_is_square": true, "level_is_squarefree": false, "level_primes": [2], "level_radical": 2, "minimal_twist": "256.4.e.c", "prim_orbit_index": 5, "qexp_display": "q-\\beta _{5}q^{3}+(-2-2\\beta _{1}+\\beta _{8})q^{5}+(-\\beta _{5}+\\cdots)q^{7}+\\cdots", "related_objects": [], "relative_dim": 8, "rm_discs": [], "sato_tate_group": "3.2.3.c4", "self_twist_discs": [], "self_twist_type": 0, "space_label": "256.4.e", "trace_display": [0, 0, -32, 0], "trace_hash": 2276962635859959727, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "14.254", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1562.412", "prec": 27}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "269921.131", "prec": 34}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.627", "prec": 17}, "traces": [0, 16, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, -320, 0, 0, 0, -384, 0, 0, 0, -224, 0, 0, 0, 0, 0, 0, 0, -928, 0, 0, 0, -2432, 0, 0, 0, -640, 0, 0, 0, 0, 0, 0, 0, -896, 0, 0, 0, -2832, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, -1024, 0, 0, 0, 2208, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, -1056, 0, 0, 0, 4208, 0, 0, 0, -1824, 0, 0, 0, 0, 0, 0, 0, 3776, 0, 0, 0, 4480, 0, 0, 0, 5056, 0, 0, 0, 0, 0, 0, 0, 11232, 0, 0, 0, 6240, 0, 0, 0, 7520, 0, 0, 0, 0, 0, 0, 0, 7424, 0, 0, 0, 1344, 0, 0, 0, -6432, 0, 0, 0, 0, 0, 0, 0, -4288, 0, 0, 0, 5984, 0, 0, 0, -480, 0, 0, 0, 0, 0, 0, 0, -3136, 0, 0, 0, 4608, 0, 0, 0, 4256, 0, 0, 0, 0, 0, 0, 0, 1088, 0, 0, 0, -10560, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, -7616, 0, 0, 0, -7936, 0, 0, 0, -1312, 0, 0, 0, 0, 0, 0, 0, -25792, 0, 0, 0, -13120, 0, 0, 0, -37408, 0, 0, 0, 0, 0, 0, 0, -21600, 0, 0, 0, -26224, 0, 0, 0, 4640, 0, 0, 0, 0, 0, 0, 0, 25600, 0, 0, 0, -25856, 0, 0, 0, 51040, 0, 0, 0, 0, 0, 0, 0, 11680, 0, 0, 0, -4000, 0, 0, 0, -35840, 0, 0, 0, 0, 0, 0, 0, -50592, 0, 0, 0, -11648, 0, 0, 0, -30080, 0, 0, 0, 0, 0, 0, 0, -928, 0, 0, 0, -13904, 0, 0, 0, 40160, 0, 0, 0, 0, 0, 0, 0, 58272, 0, 0, 0, 59040, 0, 0, 0, 18016, 0, 0, 0, 0, 0, 0, 0, 672, 0, 0, 0, 41728, 0, 0, 0, -33728, 0, 0, 0, 0, 0, 0, 0, -29344, 0, 0, 0, 32672, 0, 0, 0, -22464, 0, 0, 0, 0, 0, 0, 0, 17632, 0, 0, 0, 64608, 0, 0, 0, 49536, 0, 0, 0, 0, 0, 0, 0, 75040, 0, 0, 0, 7040, 0, 0, 0, 51264, 0, 0, 0, 0, 0, 0, 0, 53056, 0, 0, 0, -28800, 0, 0, 0, 1280, 0, 0, 0, 0, 0, 0, 0, -83424, 0, 0, 0, -29696, 0, 0, 0, -69952, 0, 0, 0, 0, 0, 0, 0, -2400, 0, 0, 0, 42176, 0, 0, 0, 26912, 0, 0, 0, 0, 0, 0, 0, 130272, 0, 0, 0, 18176, 0, 0, 0, 133280, 0, 0, 0, 0, 0, 0, 0, 6880, 0, 0, 0, -22144, 0, 0, 0, -119712, 0, 0, 0, 0, 0, 0, 0, -92640, 0, 0, 0, -4992, 0, 0, 0, -139040, 0, 0, 0, 0, 0, 0, 0, -87904, 0, 0, 0, -35104, 0, 0, 0, 96224, 0, 0, 0, 0, 0, 0, 0, 71136, 0, 0, 0, -13824, 0, 0, 0, 86560, 0, 0, 0, 0, 0, 0, 0, -35200, 0, 0, 0, -126016, 0, 0, 0, -27968, 0, 0, 0, 0, 0, 0, 0, -217120, 0, 0, 0, -70928, 0, 0, 0, -149952, 0, 0, 0, 0, 0, 0, 0, -38400, 0, 0, 0, -6176, 0, 0, 0, 13600, 0, 0, 0, 0, 0, 0, 0, 77696, 0, 0, 0, -36288, 0, 0, 0, 90624, 0, 0, 0, 0, 0, 0, 0, 75712, 0, 0, 0, 119840, 0, 0, 0, -120672, 0, 0, 0, 0, 0, 0, 0, -112704, 0, 0, 0, 7072, 0, 0, 0, -37728, 0, 0, 0, 0, 0, 0, 0, -34304, 0, 0, 0, -118272, 0, 0, 0, 66720, 0, 0, 0, 0, 0, 0, 0, 131392, 0, 0, 0, -147504, 0, 0, 0, 90528, 0, 0, 0, 0, 0, 0, 0, 25856, 0, 0, 0, -25344, 0, 0, 0, -10656, 0, 0, 0, 0, 0, 0, 0, -91680, 0, 0, 0, 75424, 0, 0, 0, -85216, 0, 0, 0, 0, 0, 0, 0, 26816, 0, 0, 0, -18176, 0, 0, 0, 145280, 0, 0, 0, 0, 0, 0, 0, 273664, 0, 0, 0, 158688, 0, 0, 0, 126240, 0, 0, 0, 0, 0, 0, 0, 20416, 0, 0, 0, 241280, 0, 0, 0, -174656, 0, 0, 0, 0, 0, 0, 0, -130304, 0, 0, 0, 258304, 0, 0, 0, -182304, 0, 0, 0, 0, 0, 0, 0, -36832, 0, 0, 0, 20288, 0, 0, 0, 183264, 0, 0, 0, 0, 0, 0, 0, 193632, 0, 0, 0, -40384, 0, 0, 0, 243616, 0, 0, 0, 0, 0, 0, 0, 22368, 0, 0, 0, 41984, 0, 0, 0, -132416, 0, 0, 0, 0, 0, 0, 0, -163936, 0, 0, 0, -102368, 0, 0, 0, -170144, 0, 0, 0, 0, 0, 0, 0, 120832, 0, 0, 0, 115552, 0, 0, 0, 104640, 0, 0, 0, 0, 0, 0, 0, 108224, 0, 0, 0, 71040, 0, 0, 0, 63680, 0, 0, 0, 0, 0, 0, 0, 124288, 0, 0, 0, 38400, 0, 0, 0, 104704, 0, 0, 0, 0, 0, 0, 0, -109600, 0, 0, 0, -39296, 0, 0, 0, -21824, 0, 0, 0, 0, 0, 0, 0, -54528, 0, 0, 0, 79520, 0, 0, 0, -174336, 0, 0, 0, 0, 0, 0, 0, 9120, 0, 0, 0, -172256, 0, 0, 0, 119904, 0, 0, 0, 0, 0, 0, 0, 51520, 0, 0, 0, -374016, 0, 0, 0, -54624, 0, 0, 0, 0, 0, 0, 0, -27872, 0, 0, 0, -176768, 0, 0, 0, -80928, 0, 0, 0, 0, 0, 0, 0, -271616, 0, 0, 0, -255104, 0, 0, 0, 3488, 0, 0, 0, 0, 0, 0, 0, 15328, 0, 0, 0, 233088, 0, 0, 0, -67488, 0, 0, 0, 0, 0, 0, 0, -223328, 0, 0, 0, -160752, 0, 0, 0, -32928, 0, 0, 0, 0, 0, 0, 0, -176608, 0, 0, 0, 137600, 0, 0, 0, -100608, 0, 0, 0, 0, 0, 0, 0, 13152, 0, 0, 0, 151424, 0, 0, 0, 182720, 0, 0, 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, "nf_label": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, -1, 0, 0, 0, -1, 1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, -1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, -1, 1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-20, 20, -2, 0, 1, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, -2, 0, 0, 0, -3, -2, -3, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-24, 0, 3, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, 11, 0, 0, 0, 0, 0, 0, 0, -2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-14, -14, 0, -11, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -5, -12, 0, 0, 0, -5, 12, 0, 1, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 41, 0, -11, 11, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, -9, 4, -4, -2, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-58, 58, 6, 0, 8, 0, 0, -6, 0, 5, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -12, -9, 0, 0, 0, 12, -9, -5, 0, 0, -4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-152, 0, -11, -7, -7, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -6, 32, 0, 0, 0, 0, 0, 9, 9, 6, -6], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-40, -40, 2, -21, 0, 0, 0, 2, 7, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 27, -21, 0, 0, 0, 27, 21, 0, 14, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 80, 0, -11, 11, 0, 0, 14, 16, -16, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, -16, 14, -14, 8, 8], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-56, 56, 0, 0, 9, 0, 0, 0, 0, -11, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, -3, 0, 0, 0, -8, -3, -25, 0, 0, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-177, 0, 6, 2, 2, 0, 0, 0, 20, 20, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 22, 37, 0, 0, 0, 0, 0, -7, -7, 4, -4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, -4, -12, -27, 0, 0, 0, -12, -13, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, -15, 0, 0, 0, 3, 15, 0, -12, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -40, 0, -15, 15, 0, 0, -23, -8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -17, -16, -11, 11, -2, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-64, 64, -4, 0, 15, 0, 0, 4, 0, 19, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 27, -8, 0, 0, 0, -27, -8, 23, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [138, 0, 10, -17, -17, 0, 0, 0, -24, -24, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -17, -13, 0, 0, 0, 0, 0, 13, 13, -20, 20], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -2, 24, 19, 0, 0, 0, 24, 16, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -85, -4, 0, 0, 0, -85, 4, 0, 17, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 1, -1, 0, 0, 5, -28, 28, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -39, 38, 23, -23, -26, -26], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-66, 66, -16, 0, -45, 0, 0, 16, 0, -24, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -60, -8, 0, 0, 0, 60, -8, -22, 0, 0, -8], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [263, 0, 1, 13, 13, 0, 0, 0, -24, -24, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -77, -82, 0, 0, 0, 0, 0, -31, -31, -6, 6], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-114, -114, -10, 47, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -5, 48, 0, 0, 0, -5, -48, 0, -59, -21, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 34, 0, 43, -43, 0, 0, -5, -4, 4, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -46, 54, -57, 57, 22, 22], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [236, -236, 0, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 27, 63, 0, 0, 0, -27, 63, 72, 0, 0, 29], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [280, 0, 7, 40, 40, 0, 0, 0, 44, 44, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 131, -64, 0, 0, 0, 0, 0, 25, 25, 18, -18], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}