# Stored data for newform 294.2.a.e, downloaded from the LMFDB on 04 September 2025.
{"Nk2": 1176, "analytic_conductor": 2.3476018194256434, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [3, 1], [7, 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": [294, 1, [197, 199], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 1, "field_disc": 1, "field_disc_factorization": [], "field_poly": [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": [[5, [-1, 1]]], "hecke_orbit": 5, "hecke_orbit_code": 18014398543036710, "hecke_ring_generator_nbound": 1, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": true, "is_maximal": true, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "294.2.a.e", "level": 294, "level_is_powerful": false, "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, 7], "level_radical": 42, "minimal_twist": "42.2.e.a", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\\cdots", "related_objects": ["EllipticCurve/Q/294/e"], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "294.2.a", "trace_display": [1, -1, 1, 0], "trace_hash": 1910170857327021813, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.987", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.913", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.646", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.016", "prec": 17}, "traces": [0, 1, 1, -1, 1, 1, -1, 0, 1, 1, 1, 5, -1, 0, 0, -1, 1, -4, 1, 8, 1, 0, 5, -4, -1, -4, 0, -1, 0, -5, -1, 3, 1, -5, -4, 0, 1, -4, 8, 0, 1, 0, 0, 2, 5, 1, -4, -6, -1, 0, -4, 4, 0, -9, -1, 5, 0, -8, -5, -11, -1, -6, 3, 0, 1, 0, -5, -2, -4, 4, 0, 2, 1, 10, -4, 4, 8, 0, 0, 3, 1, 1, 0, -7, 0, -4, 2, 5, 5, -6, 1, 0, -4, -3, -6, 8, -1, 7, 0, 5, -4, 10, 4, 8, 0, 0, -9, 3, -1, -2, 5, 4, 0, 16, -8, -4, -5, 0, -11, 0, -1, 14, -6, 0, 3, -9, 0, 9, 1, -2, 0, 1, -5, 0, -2, -1, -4, -2, 4, -14, 0, 6, 2, 0, 1, -5, 10, 0, -4, -18, 4, 19, 8, -4, 0, 3, 0, -4, 3, 9, 1, 0, 1, -4, 0, -5, -7, -14, 0, -13, -4, 8, 2, 22, 5, 0, 5, 11, -6, 12, 1, 0, 0, 6, -4, -4, -3, -20, -6, 0, 8, 24, -1, 5, 7, 0, 0, 2, 5, -4, -4, 2, 10, 0, 4, 0, 8, -4, 0, 40, 0, 2, -9, -2, 3, 2, -1, 0, -2, -10, 5, 0, 4, -7, 0, -4, 16, 3, -8, -20, -4, 0, -5, -4, 0, -6, -11, -3, 0, -12, -1, -25, 14, -1, -6, 0, 0, 0, 3, 7, -9, 21, 0, -20, 9, 4, 1, -6, -2, 0, 0, -5, 1, -30, -5, -9, 0, 6, -2, 31, -1, 15, -4, 0, -2, -20, 4, -16, -14, 3, 0, 2, 6, 10, 2, -8, 0, 0, 1, -1, -5, -7, 10, -21, 0, -11, -4, -5, -18, 0, 4, 0, 19, -10, 8, -6, -4, 28, 0, -8, 3, -32, 0, 1, -4, 0, 3, 3, 9, -25, 1, -3, 0, -32, 1, 0, -4, 2, 0, 0, -5, -4, -7, -4, -14, -2, 0, 9, -13, -16, -4, 15, 8, 0, 2, 4, 22, 12, 5, -14, 0, 0, 5, 24, 11, 2, -6, 0, 12, 10, 1, 45, 0, -14, 0, 10, 6, 17, -4, 0, -4, 0, -3, -32, -20, 9, -6, 0, 0, 16, 8, -9, 24, -34, -1, 0, 5, 2, 7, -2, 0, 16, 0, -1, 2, 3, 5, 36, -4, 0, -4, 24, 2, 0, 10, 1, 0, -20, 4, -25, 0, 2, 8, 0, -4, -7, 0, 14, 40, 0, 0, 30, 2, -6, -9, 16, -2, 0, 3, 0, 2, 12, -1, 14, 0, 5, -2, -32, -10, 15, 5, 0, 0, 17, 4, -6, -7, 18, 0, 16, -4, 0, 16, -19, 3, 0, -8, 31, -20, 4, -4, -14, 0, 16, -5, -3, -4, -20, 0, 0, -6, 4, -11, 10, -3, -32, 0, -9, -12, 38, -1, 0, -25, 0, 14, 7, -1, 5, -6, 4, 0, 9, 0, 20, 0, 5, 3, 0, 7, 10, -9, 14, 21, 0, 0, 10, -20, 13, 9, 15, 4, 0, 1, -8, -6, 8, -2, -30, 0, -22, 0, -18, -5, 8, 1, 0, -30, -12, -5, -7, -9, -11, 0, 0, 6, 3, -2, -12, 31, 0, -1, -18, 15, 0, -4, -2, 0, -12, -2, -6, -20, -40, 4, 0, -16, 4, -14, -23, 3, 0, 0, 20, 2, 17, 6, 16, 10, 0, 2, 24, -8, -30, 0, -24, 0, 16, 1, 31, -1, -5, -5, 0, -7, -45, 10, 0, -21, 35, 0, 24, -11, -2, -4, 36, -5, 0, -18, 4, 0, -30, 4, 35, 0, -2, 19, 14, -10, -27, 8, 0, -6, 0, -4, 12, 28, 0, 0, 2, -8, 10, 3, 4, -32, 0, 0, 11, 1, -40, -4, 16, 0, -19, 3, -2, 3, 9, 9, 0, -25, 2, 1, 26, -3, 14, 0, -2, -32, -18, 1, -55, 0, 0, -4, -39, 2, 1, 0, 10, 0, -40, -5, 10, -4, 0, -7, 0, -4, 20, -14, 7, -2, -30, 0, -19, 9, 4, -13, -27, -16, 0, -4, -3, 15, -9, 8, -2, 0, 20, 2, 0, 4, 8, 22, 0, 12, -14, 5, 0, -14, 4, 0, -5, 0, -32, 5, 6, 24, 0, 11, 38, 2, 3, -6, -12, 0, 0, 12, 12, 10, -6, 1, 0, 45, 25, 0, 20, -14, 7, 0, 1, 10, -8, 6, -6, 17, 0, -4, -10, 0, -30, -4, 0, 0, 30, -3, -18, -32, -7, -20, 0, 9, 45, -6, -21, 0, 19, 0, -54, 16, 20, 8, 8, -9, 0, 24, -4, -34, 0, -1, -35, 0, 6, 5, 10, 2, -12, 7, 0, -2, 0, 0, 10, 16, 5, 0, -4, -1, -18, 2, 30, 3, 0, 5, 0, 36, 9, -4, 21, 0, 24, -4, -6, 24, 50, 2, 0, 0, -31, 10, 40, 1, -14, 0, -15, -20, -4, 4, 16, -25, 0, 0, -25, 2, 40, 8, 20, 0, 9, -4, -32, -7, 16, 0, 0, 14, -14, 40, -3, 0, -28, 0, -4, 30, -2, 2, -13, -6, 0, -9, -10, 16, 16, -2, 14, 0, 8, 3, -18, 0, -34, 2, 0, 12, 10, -1, 22, 14, 1, 0, 15, 5, 0, -2, 7, -32, 0, -10, -32, 15, 21, 5, -42, 0, -40, 0, 11, 17, 36, 4, 0, -6, 5, -7, -48, 18, 12, 0, 0, 16, -15, -4, 36, 0, 0, 16, 0, -19, 12, 3, 10, 0, 30, -8, -35, 31, 6, -20, 0, 4, -32, -4, -28, -14, 0, 0, 16, 16, 8, -5, -6, -3, 0, -4, 32, -20, -20, 0, 35, 0, -1, -6, -11, 4, 0, -11, 0, 10, -32, -3, 0, -32, -3, 0, 2, -9, 24, -12, 25, 38, 0, -1, -22, 0, 3, -25, 5, 0, -61, 14, 32, 7, 15, -1, 0, 5, 0, -6, -30, 4, -30, 0, -2, 9, -60, 0, 2, 20, 0, 0, -8, 5, 47, 3, 4, 0, -4, 7, 38, 10, 4, -9], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0], 1, 1, -1, 1, 1, -1, 0, 1, 1, 1, 5, -1, 0, 0, -1, 1, -4, 1, 8, 1, 0, 5, -4, -1, -4, 0, -1, 0, -5, -1, 3, 1, -5, -4, 0, 1, -4, 8, 0, 1, 0, 0, 2, 5, 1, -4, -6, -1, 0, -4, 4, 0, -9, -1, 5, 0, -8, -5, -11, -1, -6, 3, 0, 1, 0, -5, -2, -4, 4, 0, 2, 1, 10, -4, 4, 8, 0, 0, 3, 1, 1, 0, -7, 0, -4, 2, 5, 5, -6, 1, 0, -4, -3, -6, 8, -1, 7, 0, 5, -4, 10, 4, 8, 0, 0, -9, 3, -1, -2, 5, 4, 0, 16, -8, -4, -5, 0, -11, 0, -1, 14, -6, 0, 3, -9, 0, 9, 1, -2, 0, 1, -5, 0, -2, -1, -4, -2, 4, -14, 0, 6, 2, 0, 1, -5, 10, 0, -4, -18, 4, 19, 8, -4, 0, 3, 0, -4, 3, 9, 1, 0, 1, -4, 0, -5, -7, -14, 0, -13, -4, 8, 2, 22, 5, 0, 5, 11, -6, 12, 1, 0, 0, 6, -4, -4, -3, -20, -6, 0, 8, 24, -1, 5, 7, 0, 0, 2, 5, -4, -4, 2, 10, 0, 4, 0, 8, -4, 0, 40, 0, 2, -9, -2, 3, 2, -1, 0, -2, -10, 5, 0, 4, -7, 0, -4, 16, 3, -8, -20, -4, 0, -5, -4, 0, -6, -11, -3, 0, -12, -1, -25, 14, -1, -6, 0, 0, 0, 3, 7, -9, 21, 0, -20, 9, 4, 1, -6, -2, 0, 0, -5, 1, -30, -5, -9, 0, 6, -2, 31, -1, 15, -4, 0, -2, -20, 4, -16, -14, 3, 0, 2, 6, 10, 2, -8, 0, 0, 1, -1, -5, -7, 10, -21, 0, -11, -4, -5, -18, 0, 4, 0, 19, -10, 8, -6, -4, 28, 0, -8, 3, -32, 0, 1, -4, 0, 3, 3, 9, -25, 1, -3, 0, -32, 1, 0, -4, 2, 0, 0, -5, -4, -7, -4, -14, -2, 0, 9, -13, -16, -4, 15, 8, 0, 2, 4, 22, 12, 5, -14, 0, 0, 5, 24, 11, 2, -6, 0, 12, 10, 1, 45, 0, -14, 0, 10, 6, 17, -4, 0, -4, 0, -3, -32, -20, 9, -6, 0, 0, 16, 8, -9, 24, -34, -1, 0, 5, 2, 7, -2, 0, 16, 0, -1, 2, 3, 5, 36, -4, 0, -4, 24, 2, 0, 10, 1, 0, -20, 4, -25, 0, 2, 8, 0, -4, -7, 0, 14, 40, 0, 0, 30, 2, -6, -9, 16, -2, 0, 3, 0, 2, 12, -1, 14, 0, 5, -2, -32, -10, 15, 5, 0, 0, 17, 4, -6, -7, 18, 0, 16, -4, 0, 16, -19, 3, 0, -8, 31, -20, 4, -4, -14, 0, 16, -5, -3, -4, -20, 0, 0, -6, 4, -11, 10, -3, -32, 0, -9, -12, 38, -1, 0, -25, 0, 14, 7, -1, 5, -6, 4, 0, 9, 0, 20, 0, 5, 3, 0, 7, 10, -9, 14, 21, 0, 0, 10, -20, 13, 9, 15, 4, 0, 1, -8, -6, 8, -2, -30, 0, -22, 0, -18, -5, 8, 1, 0, -30, -12, -5, -7, -9, -11, 0, 0, 6, 3, -2, -12, 31, 0, -1, -18, 15, 0, -4, -2, 0, -12, -2, -6, -20, -40, 4, 0, -16, 4, -14, -23, 3, 0, 0, 20, 2, 17, 6, 16, 10, 0, 2, 24, -8, -30, 0, -24, 0, 16, 1, 31, -1, -5, -5, 0, -7, -45, 10, 0, -21, 35, 0, 24, -11, -2, -4, 36, -5, 0, -18, 4, 0, -30, 4, 35, 0, -2, 19, 14, -10, -27, 8, 0, -6, 0, -4, 12, 28, 0, 0, 2, -8, 10, 3, 4, -32, 0, 0, 11, 1, -40, -4, 16, 0, -19, 3, -2, 3, 9, 9, 0, -25, 2, 1, 26, -3, 14, 0, -2, -32, -18, 1, -55, 0, 0, -4, -39, 2, 1, 0, 10, 0, -40, -5, 10, -4, 0, -7, 0, -4, 20, -14, 7, -2, -30, 0, -19, 9, 4, -13, -27, -16, 0, -4, -3, 15, -9, 8, -2, 0, 20, 2, 0, 4, 8, 22, 0, 12, -14, 5, 0, -14, 4, 0, -5, 0, -32, 5, 6, 24, 0, 11, 38, 2, 3, -6, -12, 0, 0, 12, 12, 10, -6, 1, 0, 45, 25, 0, 20, -14, 7, 0, 1, 10, -8, 6, -6, 17, 0, -4, -10, 0, -30, -4, 0, 0, 30, -3, -18, -32, -7, -20, 0, 9, 45, -6, -21, 0, 19, 0, -54, 16, 20, 8, 8, -9, 0, 24, -4, -34, 0, -1, -35, 0, 6, 5, 10, 2, -12, 7, 0, -2, 0, 0, 10, 16, 5, 0, -4, -1, -18, 2, 30, 3, 0, 5, 0, 36, 9, -4, 21, 0, 24, -4, -6, 24, 50, 2, 0, 0, -31, 10, 40, 1, -14, 0, -15, -20, -4, 4, 16, -25, 0, 0, -25, 2, 40, 8, 20, 0, 9, -4, -32, -7, 16, 0, 0, 14, -14, 40, -3, 0, -28, 0, -4, 30, -2, 2, -13, -6, 0, -9, -10, 16, 16, -2, 14, 0, 8, 3, -18, 0, -34, 2, 0, 12, 10, -1, 22, 14, 1, 0, 15, 5, 0, -2, 7, -32, 0, -10, -32, 15, 21, 5, -42, 0, -40, 0, 11, 17, 36, 4, 0, -6, 5, -7, -48, 18, 12, 0, 0, 16, -15, -4, 36, 0, 0, 16, 0, -19, 12, 3, 10, 0, 30, -8, -35, 31, 6, -20, 0, 4, -32, -4, -28, -14, 0, 0, 16, 16, 8, -5, -6, -3, 0, -4, 32, -20, -20, 0, 35, 0, -1, -6, -11, 4, 0, -11, 0, 10, -32, -3, 0, -32, -3, 0, 2, -9, 24, -12, 25, 38, 0, -1, -22, 0, 3, -25, 5, 0, -61, 14, 32, 7, 15, -1, 0, 5, 0, -6, -30, 4, -30, 0, -2, 9, -60, 0, 2, 20, 0, 0, -8, 5, 47, 3, 4, 0, -4, 7, 38, 10, 4, -9]}