# Stored data for newform 675.2.e.c, downloaded from the LMFDB on 30 March 2023.
{"level_primes": [3, 5], "is_polredabs": true, "sato_tate_group": "1.2.3.c3", "rm_discs": [], "conrey_indexes": [226, 451], "cm_discs": [], "trace_hash": 2131598115599500012, "level_radical": 15, "hecke_ring_index_proved": true, "self_twist_type": 0, "related_objects": [], "prim_orbit_index": 3, "is_cm": false, "hecke_orbit": 3, "analytic_conductor": 5.389902136436426, "inner_twist_count": 2, "field_disc_factorization": [[3, 4], [13, 4], [23, 2]], "is_rm": false, "char_order": 3, "level_is_square": false, "weight_parity": 1, "label": "675.2.e.c", "field_poly_is_real_cyclotomic": false, "is_self_twist": false, "is_twist_minimal": false, "minimal_twist": "225.2.e.c", "field_poly_is_cyclotomic": false, "dim": 8, "trace_zratio": {"__RealLiteral__": 0, "data": "0.006", "prec": 17}, "traces": [0, 8, -2, 0, -4, 0, 0, -1, 18, 0, 0, -1, 0, 2, 3, 0, -4, 22, 0, 4, 0, 0, 3, -15, 0, 0, 20, 0, 8, 1, 0, 4, -10, 0, -9, 0, 0, 2, -23, 0, 0, -5, 0, -10, -44, 0, 0, -20, 0, 3, 0, 0, 17, 40, 0, 0, -30, 0, -18, 17, 0, 13, -12, 0, 38, 0, 0, 17, -34, 0, 0, 16, 0, -4, 40, 0, -11, -12, 0, 7, 0, 0, -24, -30, 0, 0, -34, 0, 9, 18, 0, -34, 12, 0, -3, 0, 0, -19, 26, 0, 0, 0, 0, -7, 36, 0, -21, 30, 0, -44, 0, 0, -40, -5, 0, 0, 74, 0, -18, 9, 0, -7, 25, 0, -5, 0, 0, -16, -15, 0, 0, -15, 0, 13, -90, 0, 72, -12, 0, -14, 0, 0, -15, 70, 0, 0, -25, 0, 59, -23, 0, 1, 0, 0, -24, 0, 0, 2, 0, 0, 0, -48, 0, 32, -10, 0, 18, -39, 0, -12, 0, 0, 104, -3, 0, 0, -14, 0, -27, -16, 0, -32, 30, 0, 21, 0, 0, 48, 26, 0, 0, 16, 0, -16, 16, 0, 21, 42, 0, 46, 0, 0, 48, -24, 0, 0, 58, 0, -4, -13, 0, 4, 8, 0, 51, 0, 0, -68, 29, 0, 0, 41, 0, 14, 30, 0, -120, -43, 0, 19, 0, 0, -60, -36, 0, 0, 37, 0, -3, -43, 0, -14, -94, 0, -128, 0, 0, -47, 33, 0, 0, 0, 0, 30, 8, 0, -10, -27, 0, 17, 0, 0, -30, -22, 0, 0, 6, 0, 47, 92, 0, 64, 2, 0, -9, 0, 0, -7, -118, 0, 0, 27, 0, -1, 20, 0, 30, 72, 0, 26, 0, 0, 2, 18, 0, 0, -150, 0, -72, -24, 0, 41, 52, 0, -41, 0, 0, 134, 45, 0, 0, 66, 0, -43, 94, 0, 58, -7, 0, 15, 0, 0, 66, -14, 0, 0, -59, 0, -51, -48, 0, 28, -6, 0, 156, 0, 0, 35, 57, 0, 0, -120, 0, -98, -21, 0, -39, -8, 0, 25, 0, 0, -126, 54, 0, 0, -51, 0, -18, 0, 0, -36, 56, 0, 32, 0, 0, -28, -126, 0, 0, 18, 0, 2, -16, 0, -81, -40, 0, -86, 0, 0, -102, -18, 0, 0, -14, 0, 26, -69, 0, -30, 66, 0, -69, 0, 0, -10, 28, 0, 0, 45, 0, 28, -18, 0, 126, -22, 0, -65, 0, 0, -52, -150, 0, 0, 61, 0, 45, 46, 0, -11, -130, 0, -12, 0, 0, 34, 63, 0, 0, 66, 0, 2, 21, 0, 40, -12, 0, -14, 0, 0, 120, 6, 0, 0, 73, 0, 14, 128, 0, -6, 77, 0, -18, 0, 0, 77, -48, 0, 0, 60, 0, 5, -103, 0, 27, 44, 0, 62, 0, 0, 129, 67, 0, 0, 114, 0, 144, -24, 0, 2, 70, 0, 89, 0, 0, -100, 111, 0, 0, -20, 0, -12, -94, 0, -164, 21, 0, 40, 0, 0, -21, 110, 0, 0, -12, 0, -1, -34, 0, -19, -146, 0, 6, 0, 0, -48, 78, 0, 0, -152, 0, 140, 27, 0, -39, -48, 0, -19, 0, 0, 40, 56, 0, 0, 33, 0, -30, 46, 0, 52, -5, 0, -93, 0, 0, -40, -48, 0, 0, -17, 0, 7, 48, 0, 91, -42, 0, -4, 0, 0, 54, -54, 0, 0, -48, 0, -66, -51, 0, 73, -7, 0, -36, 0, 0, 104, 23, 0, 0, -18, 0, -60, 30, 0, 78, 9, 0, 23, 0, 0, 155, -58, 0, 0, 5, 0, -96, -23, 0, -8, -18, 0, 64, 0, 0, 8, -10, 0, 0, -34, 0, -46, -67, 0, 3, 30, 0, -5, 0, 0, -294, -66, 0, 0, -50, 0, -46, -38, 0, -56, -15, 0, 27, 0, 0, -81, -82, 0, 0, 66, 0, 59, 39, 0, -114, 232, 0, -72, 0, 0, -145, 71, 0, 0, 62, 0, 42, 74, 0, -98, -9, 0, -45, 0, 0, -132, -78, 0, 0, -31, 0, 113, 38, 0, -24, -15, 0, -43, 0, 0, -57, 18, 0, 0, 36, 0, -10, -79, 0, 10, 42, 0, -66, 0, 0, -18, -29, 0, 0, -86, 0, -122, 53, 0, 45, 6, 0, -53, 0, 0, 252, -9, 0, 0, 64, 0, 63, -30, 0, -34, 39, 0, 25, 0, 0, 32, 36, 0, 0, -97, 0, 44, 48, 0, 36, 36, 0, 82, 0, 0, 66, -47, 0, 0, -4, 0, -42, -33, 0, -68, -85, 0, 87, 0, 0, -46, -26, 0, 0, 36, 0, -41, 188, 0, -60, -47, 0, 106, 0, 0, -1, 12, 0, 0, -75, 0, 6, 46, 0, -57, -24, 0, -84, 0, 0, -46, -99, 0, 0, -18, 0, 106, 38, 0, -29, 20, 0, -12, 0, 0, 60, -71, 0, 0, -81, 0, 15, -44, 0, 166, -75, 0, -78, 0, 0, -50, 140, 0, 0, 48, 0, -79, -42, 0, 78, -62, 0, 94, 0, 0, 23, 32, 0, 0, -38, 0, -162, 1, 0, 35, -86, 0, 106, 0, 0, 194, -7, 0, 0, -81, 0, -4, -144, 0, -30, -80, 0, -14, 0, 0, 57, 200, 0, 0, 29, 0, -14, 72, 0, 41, -42, 0, 150, 0, 0, 53, -110, 0, 0, 188, 0, -124, 58, 0, 51, -36, 0, 35, 0, 0, -238, 4, 0, 0, 18, 0, -33, -54, 0, 0, -10, 0, 81, 0, 0, -37, 118, 0, 0, -25, 0, -18, -31, 0, -38, -120, 0, -56, 0, 0, -75, -85, 0, 0, 246, 0, 186, -35, 0, -60, 36, 0, -114, 0, 0, 74, -18, 0, 0, 91, 0, 21, -320, 0, -18, 63, 0, -79, 0, 0, -93, -38, 0, 0, -152, 0, 156, 99, 0, 24, 278, 0, -230, 0, 0, 71, -15, 0, 0, 210, 0, 10, -20, 0, 130, 37, 0, -27, 0, 0, 246, -105, 0, 0, -95, 0, 4, 78, 0, -44, -21, 0, 57, 0, 0, 161, 172, 0, 0], "hecke_ring_index_factorization": [[3, 1]], "nf_label": "8.0.1223810289.2", "field_poly": [9, 15, 37, -8, 23, -2, 8, -2, 1], "has_non_self_twist": 1, "char_values": [675, 3, [326, 352], [1, 3]], "Nk2": 2700, "field_poly_root_of_unity": 0, "analytic_rank": 0, "char_orbit_label": "e", "weight": 2, "trace_display": [-2, 0, 0, -1], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": false, "hecke_ring_index": 3, "level_is_prime": false, "char_is_minimal": false, "qexp_display": "q-\\beta _{1}q^{2}+(\\beta _{1}-\\beta _{2}-\\beta _{3}+\\beta _{6})q^{4}+\\cdots", "self_twist_discs": [], "char_is_real": false, "field_disc": 1223810289, "level_is_prime_power": false, "relative_dim": 4, "hecke_cutters": [[2, [9, -15, 37, 8, 23, 2, 8, 2, 1]]], "space_label": "675.2.e", "level": 675, "is_self_dual": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 9, 3, 1, 3, 0]], "char_degree": 2, "char_conductor": 9, "char_orbit_index": 5, "hecke_ring_generator_nbound": 4, "hecke_orbit_code": 9007474166203043, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.668", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "221.934", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "10887.708", "prec": 30}], "id": null, "projective_field": null, "embedded_related_objects": null, "projective_image_type": null, "artin_image": null, "atkin_lehner_string": null, "atkin_lehner_eigenvals": null, "artin_field": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "fricke_eigenval": null, "artin_degree": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, -1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0, 0], [1, 0, 1, 1, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, -1, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, 2, 0, 0, -2, 0], [2, 1, -1, -1, 1, -2, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, -3, 0, 0, -2, 1, 0, 0], [2, 0, 0, 2, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 2, -1, -1, 0, 1, 1], [-5, -1, 1, 1, -1, 5, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [4, 0, -3, 1, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 2, 2, 0, 0, 0, 0], [0, -2, 0, 0, -1, 2, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 1, -2, -2, -1, 2, 2], [0, 2, -2, -3, 0, 0, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -5, 0, 0, -1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, 0, -4, -1, 0, 0, 0, -1], [0, 0, 0, 0, 1, -5, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 1, -1, 1, 1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, 2, -1, -2, 0], [-5, 0, -1, 1, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, -2, 0, 0, 0, -2], [0, 0, 0, 0, -2, -5, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, 2, -1, 0, -2, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 3, 1, 0], [6, 0, 1, -3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -3, 0, 0, 0, -6, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 3, -3, -3, 2, 1, 3, -2], [3, -1, 1, 0, -3, -3, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 1, 1, 2, 0], [0, 0, 0, -3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 2, 2, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, -3, 3, 0, 1, -3, 0, -1], [-5, 4, -4, -2, 2, 5, 2, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 1, -3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 3, -3, 0, 0, 0, 2], [0, 4, 0, 0, 2, 5, 5, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 4, -4, -1, 1, 0, 1, -1], [-5, -1, 1, 4, 2, 5, -4, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 3, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, 3, 0, 0, 0, 0, 2], [0, 3, 0, 0, 0, -9, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-6, 5, -5, 0, 0, 6, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, -1, -1, 5, 0], [0, 0, 3, 0, 0, 0, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, -1, -1, 0, 0, 0, 3], [0, 2, 0, 0, 2, 2, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, 5, -5, -2, 1, -3, 2, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, -1, -5, -1, 0], [6, 0, -4, 0, 0, 0, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0]]}