# Stored data for newform 429.1.v.c, downloaded from the LMFDB on 08 March 2021. {"level_primes": [3, 11, 13], "is_polredabs": true, "rm_discs": [], "conrey_indexes": [38, 311, 350, 389], "cm_discs": [-39], "trace_hash": 884855438440953724, "projective_field": [219, 96, -62, 35, -56, -2, 20, -14, 10, -4, 1], "level_radical": 429, "hecke_ring_index_proved": true, "self_twist_type": 1, "related_objects": [], "prim_orbit_index": 22, "is_cm": true, "hecke_orbit": 3, "analytic_conductor": 0.21409889041955804, "inner_twist_count": 8, "field_disc_factorization": [[2, 8], [5, 6]], "is_rm": false, "char_order": 10, "level_is_square": false, "weight_parity": -1, "label": "429.1.v.c", "field_poly_is_real_cyclotomic": false, "is_self_twist": true, "is_twist_minimal": true, "minimal_twist": "429.1.v.c", "projective_image_type": "Dn", "field_poly_is_cyclotomic": true, "dim": 8, "trace_zratio": {"__RealLiteral__": 0, "data": "0.761", "prec": 17}, "traces": [0, 8, 0, 2, -8, 0, 0, 0, 0, -2, 0, 0, -12, 2, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 10, 0, 0, 0, 0, 0, -8, 0, 0, -2, -10, 0, 0, -4, 0, 0, 0, 0, 12, -2, 0, 0, 8, 0, 0, -10, 0, 0, 0, 0, 0, -6, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, -6, 0, -2, 0, 0, 0, 0, 0, 0, 10, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 6, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -10, 0, -20, 2, 0, 0, 0, 0, 0, 4, 0, -6, -10, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 8, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 10, 4, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 6, 0, 0, 0, 0, 0, -8, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 20, 0, 0, -4, 0, 0, 0, 0, -10, 4, 0, 0, -10, 0, 0, -2, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 2, 8, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -10, 0, 0, 0, 0, 0, 0, 0, -10, -2, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, -10, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -4, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 12, -6, 0, 0, 0, 0, 0, -4, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -6, 20, 0, 0, 0, 0, 0, -10, 0, 10, 0, 0, 0, -12, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, -8, 6, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 10, 0, 0, -4, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, -4, 0, 4, 10, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, -2, 0, 0, 0, 0, 0, 10, 0, 0, -4, 0, 0, 0, -6, 0, 0, 0, 0, 0, -4, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -12, 0, 0, 4, 0, 0, 0, 0, -4, 10, 0, 0, -8, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 4, 0, -2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 6, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 10, 0, -10, -4, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 6, 0, 0, 0, 0, 0, 4, 0, 4, 8, 0, 0, 20, 0, 0, 0, 0, 0, -2, 0, 0, -14, 0, -20, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, -10, 4, 0, 0, 10, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 10, 0, -2, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 6, -10, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, -8, 0, 0, -4, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -10, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, -10, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -6, 0, 0, -20, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 10, 0, 0, 6, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, -4, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 4, 10, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 12, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 10, 6, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, -4, 0, -4, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 4, 0, 0, 0, 0, 8, 4, 0, -4, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 2, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 10, 0, 0, 10, 0, 0, 0, 0, 6, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 20, 0, 0, 0, -8, 0, 0, -6, 0, 0, 0, 0, -8, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 10, 0, 0, 4, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -10, 20, 0, 0, 0, 0, 0, -14, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -10, 0, -6, 6, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -2, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, -6, -10, 0, 0, 0, 0, -4, -4, 0, -10, -4, 0, 0, 10, 0, 0, 0, 0, 0, -20, 0, 0, 4, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, 0, -10, 0, 0, 0, -10, 0, 0, -4, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 20, 0, -12, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 10, -4, 0, 0, 0, 0, -8, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 4, 0, 12, 0, 0, 0, 0, 0, 0, 20, 0, 6, 0, 0, 0, -20, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 20, 6, 0, 0, 0, 0, 0, 6, 0], "hecke_ring_index_factorization": [], "nf_label": "8.0.4000000.1", "field_poly": [1, 0, -1, 0, 1, 0, -1, 0, 1], "has_non_self_twist": 1, "char_values": [429, 10, [287, 79, 67], [5, 4, 5]], "Nk2": 429, "field_poly_root_of_unity": 20, "analytic_rank": 0, "char_orbit_label": "v", "weight": 1, "trace_display": [0, 2, 0, 0], "analytic_rank_proved": true, "char_parity": -1, "level_is_squarefree": true, "hecke_ring_index": 1, "level_is_prime": false, "char_is_minimal": true, "qexp_display": "q+(-\\zeta_{20}+\\zeta_{20}^{5})q^{2}-\\zeta_{20}^{4}q^{3}+(-1+\\cdots)q^{4}+\\cdots", "self_twist_discs": [-39], "char_is_real": false, "field_disc": 4000000, "level_is_prime_power": false, "relative_dim": 2, "hecke_cutters": [[2, [25, 0, 0, 0, 10, 0, 5, 0, 1]]], "space_label": "429.1.v", "level": 429, "is_self_dual": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 39, 4, -1, 2, -39], [1, 1, 3, 2, -1, 2, 0], [1, 1, 11, 3, 1, 5, 0], [1, 1, 13, 2, 1, 2, 0], [1, 1, 33, 8, -1, 10, 0], [1, 1, 143, 14, 1, 10, 0], [1, 1, 429, 22, -1, 10, 0]], "char_degree": 4, "char_conductor": 429, "char_orbit_index": 22, "hecke_ring_generator_nbound": 11, "projective_image": "D10", "hecke_orbit_code": 9008642380530093, "projective_field_label": "10.0.1487719872058563.1", "trace_moments": [{"__RealLiteral__": 0, "data": "0.082", "prec": 17}, {"__RealLiteral__": 0, "data": "7.074", "prec": 17}, {"__RealLiteral__": 0, "data": "5.230", "prec": 17}, {"__RealLiteral__": 0, "data": "590.288", "prec": 24}, {"__RealLiteral__": 0, "data": "1048.156", "prec": 27}, {"__RealLiteral__": 0, "data": "118663.844", "prec": 34}], "id": null, "sato_tate_group": null, "embedded_related_objects": null, "artin_image": null, "atkin_lehner_string": null, "atkin_lehner_eigenvals": null, "artin_field": null, "artin_field_label": null, "fricke_eigenval": null, "artin_degree": null, "qexp": [[], [[1, 0]], [[-1, 1], [1, 5]], [[-1, 4]], [[-1, 0], [1, 2], [-1, 6]], [[1, 1], [1, 3]], [[1, 5], [-1, 9]], [], [[2, 1], [-1, 1], [-1, 3], [-1, 5], [1, 7]], [[1, 8]], [[-1, 2], [-1, 4], [1, 6], [1, 8]], [[1, 7]], [[-1, 0], [1, 4], [-1, 6]], [[-1, 8]], [], [[-1, 5], [-1, 7]], [[1, 0], [-2, 2], [1, 2], [1, 4], [1, 6], [-1, 8]], [], [[-1, 3], [-1, 9]], [], [[-1, 1], [1, 5], [-1, 7], [-1, 9]], [], [[-1, 2], [-1, 8]], [], [[1, 1], [-1, 5], [1, 7], [1, 9]], [[1, 2], [1, 4], [1, 6]], [[1, 3], [1, 9]], [[1, 2]], [], [], [[1, 0], [1, 2], [1, 6], [1, 8]], [], [[-2, 1], [1, 1], [2, 3], [-1, 3], [-1, 7], [1, 9]], [[1, 1]], [], [], [[-1, 0], [1, 4], [-1, 8]], [], [], [[-1, 2]], [[-1, 0], [1, 2], [-2, 6]], [], [], [[1, 4], [-1, 6]], [[1, 3], [-1, 7], [1, 9]], [[-1, 1], [1, 9]], [], [[-1, 1], [-1, 7]], [[1, 0], [-1, 2], [-1, 4], [1, 6], [-1, 8]], [[-1, 2]], [[-1, 1], [-1, 3], [-1, 5], [1, 9]], [], [[1, 0], [-1, 4], [1, 8]], [], [[-1, 3], [1, 7]], [[-1, 0], [1, 8]], [], [], [], [[-1, 3], [-1, 9]], [[-1, 1], [-1, 3], [1, 5], [-1, 9]], [[-1, 0], [-1, 4]], [], [], [[1, 0], [-1, 0], [2, 2], [-1, 2], [-2, 4], [1, 4], [1, 8]], [[1, 1], [-1, 9]], [[-1, 2], [1, 6]], [], [], [], [], [], [[1, 1], [1, 3], [-1, 5], [1, 9]], [], [], [[1, 0], [-1, 6], [-1, 8]], [], [], [[1, 3], [-1, 7]], [[-1, 0], [1, 6]], [[1, 1], [1, 1], [2, 7]], [[-1, 6]], [], [[-1, 1], [-1, 3]], [], [], [[1, 1], [-1, 5], [1, 7], [1, 9]], [], [[1, 0], [1, 2], [-1, 4], [1, 8]], [], [[1, 0], [1, 2], [-1, 4], [-1, 6]], [], [], [], [[1, 2], [1, 2], [-1, 6], [1, 8]], [], [[-1, 1], [1, 3], [1, 5], [-1, 7]], [], [[1, 3], [-1, 7]], [[-1, 5]], [[1, 0], [-1, 2], [1, 2]]]}