# Stored data for newform 448.8.a.n, downloaded from the LMFDB on 05 February 2025.
{"Nk2": 28672, "analytic_conductor": 139.94849141688655, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [7, 1]], "atkin_lehner_string": "-+", "char_conductor": 1, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [448, 1, [127, 197, 129], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 3529, "field_disc_factorization": [[3529, 1]], "field_poly": [-882, -1, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": -1, "has_non_self_twist": 0, "hecke_cutters": [[3, [-3480, 14, 1]]], "hecke_orbit": 14, "hecke_orbit_code": 58546795290034624, "hecke_ring_generator_nbound": 3, "hecke_ring_index": 2, "hecke_ring_index_factorization": [[2, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "448.8.a.n", "level": 448, "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, 7], "level_radical": 14, "minimal_twist": "28.8.a.a", "nf_label": "2.2.3529.1", "prim_orbit_index": 1, "qexp_display": "q+(-7-\\beta )q^{3}+(-21+3\\beta )q^{5}-7^{3}q^{7}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "7.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "448.8.a", "trace_display": [0, -14, -42, -686], "trace_hash": 1918605220844778843, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.952", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.376", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "62.763", "prec": 20}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "traces": [0, 2, 0, -14, 0, -42, 0, -686, 0, 2782, 0, 7428, 0, -11830, 0, -20880, 0, 15792, 0, 26614, 0, 4802, 0, -32640, 0, -91846, 0, -87668, 0, 158016, 0, 180740, 0, -348432, 0, 14406, 0, 45824, 0, 19288, 0, -321720, 0, 1023868, 0, 238014, 0, -1665972, 0, 235298, 0, 2133900, 0, 410628, 0, 733320, 0, 4268, 0, 1702134, 0, 547526, 0, -954226, 0, 438996, 0, -2590616, 0, 10900176, 0, -4129272, 0, -8008868, 0, 1532230, 0, -2547804, 0, -2470456, 0, -10397042, 0, -9900786, 0, -7064964, 0, 2154684, 0, 15423492, 0, 4057690, 0, -19940648, 0, -1130592, 0, -17377472, 0, 14482452, 0, -13373850, 0, -2042404, 0, 7161840, 0, 34078368, 0, 10727432, 0, 53927020, 0, 32168568, 0, -31329648, 0, -15566222, 0, -5416656, 0, 1063562, 0, -55214196, 0, 2542092, 0, 10494440, 0, -50743168, 0, 2755158, 0, 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