# Stored data for newform 29.12.a.b, downloaded from the LMFDB on 23 May 2024.
{"Nk2": 4176, "analytic_conductor": 22.281952236228076, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[29, 1]], "atkin_lehner_string": "+", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [29, 1, [2], [1]], "cm_discs": [], "conrey_index": 1, "dim": 14, "field_disc": 410656064840685861073155469830881995682445279959053238762107635566612041635027163688419356070608457366528, "field_disc_factorization": [[2, 10], [7, 1], [61, 1], [103, 1], [9118285471475916559520097053425813394616720145290305551911524018508437095773316080568246001971387, 1]], "field_poly": [30797548279705794248704, -9478460460037847384064, 709645914927917694976, 15507015861824716800, -2179155305696991232, -3617975849298944, 2125122050961664, -1439668569088, -951901011680, 532863376, 214206700, -42196, -23517, 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": [[2, [30797548279705794248704, -9478460460037847384064, 709645914927917694976, 15507015861824716800, -2179155305696991232, -3617975849298944, 2125122050961664, -1439668569088, -951901011680, 532863376, 214206700, -42196, -23517, 0, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4503599828697117, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 9437184, "hecke_ring_index_factorization": [[2, 20], [3, 2]], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": true, "label": "29.12.a.b", "level": 29, "level_is_powerful": false, "level_is_prime": true, "level_is_prime_power": true, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": true, "level_primes": [29], "level_radical": 29, "minimal_twist": "29.12.a.b", "prim_orbit_index": 1, "qexp_display": "q+\\beta _{1}q^{2}+(34-\\beta _{3})q^{3}+(1312+3\\beta _{1}+\\cdots)q^{4}+\\cdots", "related_objects": [], "relative_dim": 14, "rm_discs": [], "sato_tate_group": "11.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "29.12.a", "trace_display": [0, 476, 9760, 85024], "trace_hash": 693116902882374645, "trace_moments": [{"__RealLiteral__": 0, "data": "0.150", "prec": 17}, {"__RealLiteral__": 0, "data": "11.902", "prec": 20}, {"__RealLiteral__": 0, "data": "0.719", "prec": 17}, {"__RealLiteral__": 0, "data": "421.265", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "23480.664", "prec": 30}], "trace_zratio": 0, "traces": [0, 14, 0, 476, 18362, 9760, 18454, 85024, 126588, 1372146, 713576, 398020, -4026800, 2272440, -7199712, -4763864, 19015138, 5623508, -204156, 29803300, 65161006, 51227832, 167334266, 52654304, 221514842, 194970462, 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