# Stored data for newform 847.2.a.b, downloaded from the LMFDB on 24 May 2022.
{"level_primes": [7, 11], "is_polredabs": true, "sato_tate_group": "1.2.3.c1", "rm_discs": [], "conrey_indexes": [1], "cm_discs": [], "trace_hash": 583392718229927299, "level_radical": 77, "hecke_ring_index_proved": true, "self_twist_type": 0, "related_objects": ["EllipticCurve/Q/847/b"], "prim_orbit_index": 1, "is_cm": false, "hecke_orbit": 2, "analytic_conductor": 6.763329051202448, "inner_twist_count": 1, "field_disc_factorization": [], "is_rm": false, "char_order": 1, "level_is_square": false, "weight_parity": 1, "label": "847.2.a.b", "field_poly_is_real_cyclotomic": false, "is_self_twist": false, "is_twist_minimal": false, "minimal_twist": "77.2.a.a", "field_poly_is_cyclotomic": false, "dim": 1, "trace_zratio": {"__RealLiteral__": 0, "data": "0.015", "prec": 17}, "traces": [0, 1, 0, -3, -2, -1, 0, 1, 0, 6, 0, 0, 6, 4, 0, 3, 4, -2, 0, 6, 2, -3, 0, -5, 0, -4, 0, -9, -2, -10, 0, 1, 0, 0, 0, -1, -12, -5, 0, -12, 0, 2, 0, 8, 0, -6, 0, 8, -12, 1, 0, 6, -8, -6, 0, 0, 0, -18, 0, 3, -6, 2, 0, 6, -8, -4, 0, -3, 4, 15, 0, 1, 0, -10, 0, 12, -12, 0, 0, -6, -4, 9, 0, -12, 6, 2, 0, 30, 0, -15, 0, 4, 10, -3, 0, -6, 0, -5, 0, 0, 8, 12, 0, -12, 0, 3, 0, 10, 18, -4, 0, 15, 4, -19, 0, 5, 20, 24, 0, -2, 0, 0, 0, -6, -2, 9, 0, -2, 0, -24, 0, -18, 0, 6, 0, 9, 0, -3, 0, 10, 2, -24, 0, 0, 24, 10, 0, -3, 10, 22, 0, -6, 0, -12, 0, -1, 24, 7, 0, 18, 0, -5, 0, 4, -4, 0, 0, 2, 0, 3, 0, 36, -16, -16, 0, -4, 0, -9, 0, 1, 12, 5, 0, -6, 0, 5, 0, 0, -16, -9, 0, 5, 24, -14, 0, 12, -2, -18, 0, -8, 0, 9, 0, -10, -12, -2, 0, -30, 16, 0, 0, 2, 12, -3, 0, -8, 0, 1, 0, 30, 0, -8, 0, 1, 0, -24, 0, -4, 36, -7, 0, 0, 0, -6, 0, -8, -6, 18, 0, -4, 12, 12, 0, 0, -4, -1, 0, 24, 0, 36, 0, -21, -12, 0, 0, -6, 16, -6, 0, -5, 8, -60, 0, -18, 0, 6, 0, 45, 6, -18, 0, -16, -8, -12, 0, 0, -30, -24, 0, 6, 0, 4, 0, 0, -2, 18, 0, 2, 0, -13, 0, 15, 20, 6, 0, -3, 0, 0, 0, -20, -24, 8, 0, -36, 24, -2, 0, 28, 0, 36, 0, 8, 0, -23, 0, -6, 12, 9, 0, 0, 8, -30, 0, -12, -18, -16, 0, 12, 0, 8, 0, -17, 24, -30, 0, 3, -12, 18, 0, 57, -4, 0, 0, 1, 0, -15, 0, -14, -60, 34, 0, -36, 0, 9, 0, -1, 30, 6, 0, -8, 0, 17, 0, 0, -8, 10, 0, -11, -20, 12, 0, -6, 6, 4, 0, -27, 0, -40, 0, -29, 12, 6, 0, 17, 0, 0, 0, 48, 10, 9, 0, 10, 0, 54, 0, 6, 0, 18, 0, -18, -16, -6, 0, 4, -24, -9, 0, 0, 0, 26, 0, 9, 24, 3, 0, 12, 0, -30, 0, 16, -6, 22, 0, 48, 0, 8, 0, 2, -20, 0, 0, 20, -36, -25, 0, -30, 8, -30, 0, 14, 0, 6, 0, -39, -30, 15, 0, -66, -8, 15, 0, 0, 38, 18, 0, -4, 0, -8, 0, 18, -10, -18, 0, 13, -40, 3, 0, 3, -48, -3, 0, -21, 0, 0, 0, -24, 4, -36, 0, 28, 0, -20, 0, 15, 0, 5, 0, -13, 0, -12, 0, 30, 12, 20, 0, 0, 4, 1, 0, 44, -18, -6, 0, 0, 0, -12, 0, -9, 4, -31, 0, -10, 0, -54, 0, 12, 48, 0, 0, 48, 0, 7, 0, -32, 36, 12, 0, -2, 0, 2, 0, 18, -12, 8, 0, -10, 0, -3, 0, 0, -18, -32, 0, -15, 0, 4, 0, 24, 6, 12, 0, -60, 0, -6, 0, -15, -20, -14, 0, 32, -4, 0, 0, -20, 48, 19, 0, 9, 0, 18, 0, 20, 0, -15, 0, 20, -48, -25, 0, 42, -20, -12, 0, 0, 0, -24, 0, 36, 6, 6, 0, 54, -20, -30, 0, 2, -44, 24, 0, -48, 0, -8, 0, -18, 12, 0, 0, 10, 0, 30, 0, 32, 24, -16, 0, 6, 0, -30, 0, 17, 2, 45, 0, -15, -48, 11, 0, 0, -14, 10, 0, 27, 0, -6, 0, 2, -36, 4, 0, 6, 0, 15, 0, -29, 10, 24, 0, -21, 0, 0, 0, -3, -8, -17, 0, 18, 8, -60, 0, 2, 0, 35, 0, 24, 0, -6, 0, 50, -4, -3, 0, 0, 0, -4, 0, 36, -6, -38, 0, -5, 0, 12, 0, 12, -72, 3, 0, 21, 32, -24, 0, 15, 32, 0, 0, -10, 0, -4, 0, 18, 8, 0, 0, -30, 0, 24, 0, 12, 18, 39, 0, -36, 0, -5, 0, 0, -2, 12, 0, -11, -24, -12, 0, -36, -10, 40, 0, -19, 0, -27, 0, -16, 12, 4, 0, 3, 0, 0, 0, 18, -10, -72, 0, 24, 0, -22, 0, -72, 0, 10, 0, -23, 32, 63, 0, 6, 18, 38, 0, 0, 0, 48, 0, -4, -10, 12, 0, 12, -48, -40, 0, 18, 28, -6, 0, -4, 0, 15, 0, 12, -24, 0, 0, 90, 4, -7, 0, 22, 36, 54, 0, -19, 0, 8, 0, -18, 16, 23, 0, -16, 0, -90, 0, 0, -18, 5, 0, 54, 0, -30, 0, 22, 20, 48, 0, -4, 24, 48, 0, 24, 4, -18, 0, -25, 0, 0, 0, -20, 60, -29, 0, 72, -32, -2, 0, -2, 0, -9, 0, 45, 0, 71, 0, -12, -4, -3, 0, 0, -24, 0, 0, 25, 6, 34, 0, -36, 0, 28, 0, 55, 16, -6, 0, 52, 0, 16, 0, 39, -2, 0, 0, -12, 0, -30, 0, 9, -60, 38, 0, -18, 0, 27, 0, -44, 16, 9, 0, 2, 0, -2, 0, 0, -2, 48, 0, -1, 0, 60, 0, -10, 48, 12, 0, -24, 0, -5, 0, -40, 8, 72, 0, 0, -72, 0, 0, 6, 14, -18, 0, -48, 0, -84, 0, 4, 0, 20, 0, -72, 0, -30, 0, 6, 12, -24, 0, 0, 0, -36, 0, 69, 16, -58, 0, -10, 12, 9, 0, 5, -36, -40, 0, -27, 0, -44, 0, -5, 8, 0, 0, -3, -24, -30, 0, 60, -24, 14, 0, 34, 0, 36, 0, 29, 0, 10, 0, 48, 8, -31, 0, 0, 2, -24, 0, -27, 0, 18, 0, -24, -48, -40, 0, -32, 0, 51, 0, 8, -72, 12, 0, 45, 0], "hecke_ring_index_factorization": [], "nf_label": "1.1.1.1", "field_poly": [0, 1], "atkin_lehner_string": "--", "has_non_self_twist": 0, "atkin_lehner_eigenvals": [[7, -1], [11, -1]], "char_values": [847, 1, [122, 365], [1, 1]], "Nk2": 3388, "field_poly_root_of_unity": 0, "analytic_rank": 1, "char_orbit_label": "a", "weight": 2, "trace_display": [0, -3, -1, 1], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": false, "hecke_ring_index": 1, "level_is_prime": false, "char_is_minimal": true, "qexp_display": "q-3q^{3}-2q^{4}-q^{5}+q^{7}+6q^{9}+6q^{12}+\\cdots", "self_twist_discs": [], "char_is_real": true, "field_disc": 1, "level_is_prime_power": false, "relative_dim": 1, "hecke_cutters": [[2, [0, 1]], [3, [3, 1]]], "space_label": "847.2.a", "level": 847, "is_self_dual": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_degree": 1, "char_conductor": 1, "char_orbit_index": 1, "hecke_ring_generator_nbound": 1, "hecke_orbit_code": 4503599660925775, "fricke_eigenval": 1, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.960", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.816", "prec": 17}], "id": null, "projective_field": null, "embedded_related_objects": null, "projective_image_type": null, "artin_image": null, "artin_field": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "artin_degree": null, "qexp": [[0], [1], [0], [-3], [-2], [-1], [0], [1], [0], [6], [0], [0], [6], [4], [0], [3], [4], [-2], [0], [6], [2], [-3], [0], [-5], [0], [-4], [0], [-9], [-2], [-10], [0], [1], [0], [0], [0], [-1], [-12], [-5], [0], [-12], [0], [2], [0], [8], [0], [-6], [0], [8], [-12], [1], [0], [6], [-8], [-6], [0], [0], [0], [-18], [0], [3], [-6], [2], [0], [6], [-8], [-4], [0], [-3], [4], [15], [0], [1], [0], [-10], [0], [12], [-12], [0], [0], [-6], [-4], [9], [0], [-12], [6], [2], [0], [30], [0], [-15], [0], [4], [10], [-3], [0], [-6], [0], [-5], [0], [0], [8]]}