# Stored data for newform 432.8.a.i, downloaded from the LMFDB on 13 March 2025.
{"Nk2": 27648, "analytic_conductor": 134.9503310091406, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [3, 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": [432, 1, [271, 325, 353], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 1289, "field_disc_factorization": [[1289, 1]], "field_poly": [-322, -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": [[5, [-78165, 324, 1]], [7, [-699581, -980, 1]]], "hecke_orbit": 9, "hecke_orbit_code": 36028797153182128, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 18, "hecke_ring_index_factorization": [[2, 1], [3, 2]], "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": "432.8.a.i", "level": 432, "level_is_powerful": true, "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, 3], "level_radical": 6, "minimal_twist": "108.8.a.b", "nf_label": "2.2.1289.1", "prim_orbit_index": 1, "qexp_display": "q+(-162-\\beta )q^{5}+(490+3\\beta )q^{7}+(405+\\cdots)q^{11}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "7.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "432.8.a", "trace_display": [0, 0, -324, 980], "trace_hash": 1111297835866976024, "trace_moments": [{"__RealLiteral__": 0, "data": "0.002", "prec": 17}, {"__RealLiteral__": 0, "data": "1.969", "prec": 17}, {"__RealLiteral__": 0, "data": "0.093", "prec": 17}, {"__RealLiteral__": 0, "data": "9.299", "prec": 17}, {"__RealLiteral__": 0, "data": "0.453", "prec": 17}, {"__RealLiteral__": 0, "data": "59.676", "prec": 20}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.002", "prec": 17}, "traces": [0, 2, 0, 0, 0, -324, 0, 980, 0, 0, 0, 810, 0, -7880, 0, 0, 0, 20736, 0, -10456, 0, 0, 0, -60588, 0, 105056, 0, 0, 0, -32400, 0, 145988, 0, 0, 0, -785214, 0, -10460, 0, 0, 0, 1085400, 0, 606440, 0, 0, 0, -1495908, 0, 712476, 0, 0, 0, 2079756, 0, -966492, 0, 0, 0, -3074760, 0, 601120, 0, 0, 0, 6288192, 0, 2429240, 0, 0, 0, -3201120, 0, 1097530, 0, 0, 0, 2902716, 0, 1513160, 0, 0, 0, -3760182, 0, -11711952, 0, 0, 0, -10785960, 0, -18896096, 0, 0, 0, 7958412, 0, 2988910, 0, 0, 0, -23990580, 0, 7681640, 0, 0, 0, -7771302, 0, 18394132, 0, 0, 0, -27385128, 0, 18167976, 0, 0, 0, 35218800, 0, -35305204, 0, 0, 0, -59363604, 0, -45775300, 0, 0, 0, 23328810, 0, -23917060, 0, 0, 0, -60671592, 0, 68533088, 0, 0, 0, -23237928, 0, 135133596, 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