# Stored data for newform 784.6.a.h, downloaded from the LMFDB on 07 November 2025.
{"Nk2": 28224, "analytic_conductor": 125.74091473337681, "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": [784, 1, [687, 197, 689], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 1, "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 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, [-8, 1]]], "hecke_orbit": 8, "hecke_orbit_code": 31525197492257552, "hecke_ring_generator_nbound": 1, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "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": "784.6.a.h", "level": 784, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": true, "level_is_squarefree": false, "level_primes": [2, 7], "level_radical": 14, "minimal_twist": "14.6.a.b", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q+8q^{3}-10q^{5}-179q^{9}+340q^{11}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "5.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "784.6.a", "trace_display": [0, 8, -10, 0], "trace_hash": 1403855904205814548, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.958", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.880", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.623", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.002", "prec": 17}, "traces": [0, 1, 0, 8, 0, -10, 0, 0, 0, -179, 0, 340, 0, 294, 0, -80, 0, -1226, 0, 2432, 0, 0, 0, -2000, 0, -3025, 0, -3376, 0, -6746, 0, 8856, 0, 2720, 0, 0, 0, 9182, 0, 2352, 0, 14574, 0, -8108, 0, 1790, 0, -312, 0, 0, 0, -9808, 0, -14634, 0, -3400, 0, 19456, 0, -27656, 0, -34338, 0, 0, 0, -2940, 0, -12316, 0, -16000, 0, -36920, 0, 61718, 0, -24200, 0, 0, 0, 64752, 0, 16489, 0, -77056, 0, 12260, 0, -53968, 0, 8166, 0, 0, 0, 70848, 0, -24320, 0, -20650, 0, -60860, 0, -186250, 0, -60064, 0, 0, 0, -47892, 0, 22102, 0, 73456, 0, -245054, 0, 20000, 0, -52626, 0, 0, 0, -45451, 0, 116592, 0, 61500, 0, 96696, 0, -64864, 0, 134368, 0, 0, 0, 33760, 0, -294662, 0, 314944, 0, -2496, 0, 99960, 0, 67460, 0, 0, 0, 113622, 0, -408208, 0, 219454, 0, -88560, 0, -293546, 0, -117072, 0, 0, 0, 317116, 0, -27200, 0, 141568, 0, -284857, 0, -435328, 0, 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