# Stored data for newform 256.12.a.d, downloaded from the LMFDB on 10 February 2025.
{"Nk2": 36864, "analytic_conductor": 196.69585422325474, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, 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": [256, 1, [255, 5], [1, 1]], "cm_discs": [-8], "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, [-394, 1]], [5, [0, 1]], [7, [0, 1]]], "hecke_orbit": 4, "hecke_orbit_code": 13510799083438336, "hecke_ring_generator_nbound": 1, "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, 8, 4, -1, 2, -8]], "is_cm": true, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": true, "is_twist_minimal": false, "label": "256.12.a.d", "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": "64.12.b.a", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q+394q^{3}-21911q^{9}-141906q^{11}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "11.2.1.d1", "self_twist_discs": [-8], "self_twist_type": 1, "space_label": "256.12.a", "trace_display": [0, 394, 0, 0], "trace_hash": 553675452833609727, "trace_moments": [{"__RealLiteral__": 0, "data": "0.002", "prec": 17}, {"__RealLiteral__": 0, "data": "1.011", "prec": 17}, {"__RealLiteral__": 0, "data": "0.006", "prec": 17}, {"__RealLiteral__": 0, "data": "3.024", "prec": 17}, {"__RealLiteral__": 0, "data": "0.090", "prec": 17}, {"__RealLiteral__": 0, "data": "10.010", "prec": 20}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.507", "prec": 17}, "traces": [0, 1, 0, 394, 0, 0, 0, 0, 0, -21911, 0, -141906, 0, 0, 0, 0, 0, 5215578, 0, 12105322, 0, 0, 0, 0, 0, -48828125, 0, -78428852, 0, 0, 0, 0, 0, -55910964, 0, 0, 0, 0, 0, 0, 0, 1179887286, 0, 219226270, 0, 0, 0, 0, 0, -1977326743, 0, 2054937732, 0, 0, 0, 0, 0, 4769496868, 0, -10496647794, 0, 0, 0, 0, 0, 0, 0, 21183162938, 0, 0, 0, 0, 0, 34041283054, 0, -19238281250, 0, 0, 0, 0, 0, -27019499771, 0, 10275997626, 0, 0, 0, 0, 0, 103091787198, 0, 0, 0, 0, 0, 0, 0, 69880926730, 0, 3109302366, 0, 0, 0, 0, 0, 0, 0, -27565359762, 0, 0, 0, 0, 0, 389312025714, 0, 0, 0, 0, 0, 0, 0, -265174357775, 0, 464875590684, 0, 0, 0, 0, 0, 86375150380, 0, -445376279718, 0, 0, 0, 0, 0, -323488341258, 0, 753191582462, 0, 0, 0, 0, 0, 0, 0, -779066736742, 0, 0, 0, 0, 0, -114278529558, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2231320640074, 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