# Stored data for newform 799.1.c.d, downloaded from the LMFDB on 23 April 2024. {"label": "799.1.c.d", "space_label": "799.1.c", "level": 799, "weight": 1, "hecke_orbit": 4, "hecke_orbit_code": 13510936337842975, "dim": 4, "is_polredabs": true, "nf_label": "4.0.125.1", "trace_hash": 390328943958019476, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [-1, -1, 1]]], "qexp_display": "q+(-\\zeta_{10}^{2}+\\zeta_{10}^{3})q^{2}+(\\zeta_{10}+\\zeta_{10}^{4}+\\cdots)q^{3}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 799, "char_orbit_label": "c", "char_is_real": true, "Nk2": 799, "analytic_conductor": 0.3987529450937689, "hecke_ring_index": 1, "level_radical": 799, "projective_image": "D10", "projective_image_type": "Dn", "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 10, "field_poly_is_real_cyclotomic": false, "projective_field_label": "10.2.6928449225617.1", "hecke_ring_index_proved": true, "self_twist_type": 1, "is_self_dual": false, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.768", "prec": 17}, "analytic_rank_proved": true, "char_values": [799, 2, [377, 52], [1, 1]], "hecke_ring_generator_nbound": 17, "inner_twist_count": 4, "level_primes": [17, 47], "conrey_indexes": [798], "field_disc": 125, "field_disc_factorization": [[5, 3]], "field_poly": [1, -1, 1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "-0.007", "prec": 20}, {"__RealLiteral__": 0, "data": "3.040", "prec": 17}, {"__RealLiteral__": 0, "data": "-0.911", "prec": 20}, {"__RealLiteral__": 0, "data": "146.818", "prec": 24}, {"__RealLiteral__": 0, "data": "-62.662", "prec": 24}, {"__RealLiteral__": 0, "data": "9196.639", "prec": 27}], "related_objects": [], "self_twist_discs": [-47], "cm_discs": [-47], "rm_discs": [], "relative_dim": 4, "trace_display": [2, 0, 0, 0], "traces": [0, 4, 2, 0, 2, 0, 0, 0, 4, -6, 0, 0, 0, 0, 0, 0, 0, -1, -8, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -4, 0, 2, 0, -8, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 4, 0, -6, -2, 5, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 8, 10, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, -2, 2, 5, 2, 0, 0, -6, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 6, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 12, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -10, 0, -8, 0, 0, 0, 0, 2, 0, 0, 0, -4, 0, -4, 0, 5, 0, -4, 0, 0, 0, 0, 0, -6, 10, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -10, -5, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -1, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -3, 2, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -6, 5, 0, 0, 0, 4, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -10, 0, 0, 0, -4, -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, 5, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -2, 1, 10, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -10, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, -2, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -10, 0, -5, 8, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 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, 10, 0, 0, 0, 0, 8, 0, 0, 6, 0, 0, -4, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 1, 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, 0, 0, 0, 0, 8, 0, -3, 0, 0, 0, 10, 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, -3, -2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 6, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 6, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -10, 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, 6, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -10, 0, 0, 0, 0, 0, -6, 0, 0, -10, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, -8, 0, 0, -4, 0, 4, 0, 0, -2, 0, 0, 0, 2, 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, -1, 4, 8, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 10, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -8, 0, 0, 0, -2, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, -10, -10, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 14, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, -4, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 10, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 4, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 10, 0, -10, 0, 0, 10, 0, 0, 0, 0, 4, 0, 0, 0, -10, 0, 6, 0, 0, 0, 0, 0, -2, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -2, -2, 6, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 2, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 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, 0, 8, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, -5, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, 6, -6, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 2, 0, 5, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, -8, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, 6, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 5, -10, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 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, 0, 0, -2, 6, -8, 0, 0, 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, 0, 0, 0, 2, 0, -10, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, -6, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, -10, -2, 0, 0, 0, 0, 0, 0, 0, -6, -4, 0, 0, 0, 0, 0, -8, 0, 0, 2, 4, 0, 0, 0, 0, 0, 4, 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, 6, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 14, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 10, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 2, 0, 10, -2, -2, 10, 0, 0, 10, 0, 0, 0, 0, 8, 0, 0, 0, -10, 0, 0, 0, -3, 0, 12, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -3, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 10, 0, 0, 6, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, -2, 0, 0, 0, 0, -10, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, 10, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0], "projective_field": [-1024, 0, 576, 416, 328, 69, -8, 3, 2, -2, 1], "weight_parity": -1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 47, 2, -1, 2, -47], [1, 1, 17, 2, 1, 2, 0], [1, 1, 799, 3, -1, 2, 0]], "char_orbit_index": 3, "prim_orbit_index": 3, "minimal_twist": "799.1.c.d", "char_is_minimal": true, "conrey_index": 798, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "sato_tate_group": null, "atkin_lehner_eigenvals": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[], [[1, 0]], [[-1, 2], [1, 3]], [[1, 1], [1, 4]], [[1, 0], [-1, 1], [1, 4]], [], [[1, 1], [-1, 2], [-1, 3], [1, 4]], [[1, 2], [1, 3]], [[1, 1], [-1, 2], [1, 3], [-1, 4]], [[-1, 0], [1, 2], [-1, 3]], [], [], [[1, 1], [-1, 2], [-1, 3], [1, 4]], [], [[-1, 1], [-1, 4]], [], [[1, 0], [-1, 1], [1, 2], [-1, 3], [1, 4]], [[-1, 1]], [[-2, 0], [1, 1], [1, 2], [-1, 3], [-1, 4]], [], [], [[-1, 1], [-1, 2], [1, 3], [1, 4]], [], [], [[1, 1], [1, 2], [-1, 2], [-1, 3], [1, 3], [1, 4]], [[-1, 0]], [], [[-1, 1], [1, 2], [1, 3], [-1, 4]], [[-1, 1], [1, 2], [-1, 2], [-1, 4]], [], [], [], [[-2, 0], [1, 1], [-1, 2], [1, 3], [-1, 4]], [], [[1, 3], [-1, 4]], [], [[-1, 0], [1, 1], [-1, 1], [1, 2], [1, 2], [-2, 3]], [[1, 1], [1, 4]], [], [], [], [], [[2, 0], [-1, 2], [1, 3]], [], [], [], [], [[1, 0]], [[1, 1], [-1, 1], [-1, 2], [1, 2], [1, 3], [-1, 3]], [[-1, 0], [-1, 1], [1, 4]], [[1, 2], [-1, 3]], [[1, 0], [-1, 2]], [], [[1, 2], [-1, 3]], [[-2, 1], [1, 2], [1, 3], [-2, 4]], [], [[1, 2], [1, 3]], [], [], [[-1, 2], [1, 3]], [], [[-1, 2], [-1, 3]], [], [[1, 1], [-1, 2], [-1, 3], [1, 4]], [[1, 0], [-1, 1], [2, 2], [-2, 3], [1, 4]], [], [], [], [[1, 0], [-1, 1], [1, 2]], [], [], [[-1, 1], [-1, 4]], [[-2, 0], [-1, 1], [2, 1], [1, 2], [-1, 2], [-1, 4]], [], [[1, 1], [-1, 2], [-1, 3], [1, 4]], [[-1, 1], [-1, 4]], [], [], [], [[1, 1], [1, 4]], [], [[1, 0], [-1, 1], [-1, 2], [1, 3], [1, 4]], [], [[1, 0], [1, 0]], [[2, 0], [-1, 2], [1, 3]], [], [], [], [], [[1, 2], [-1, 3]], [], [], [], [], [[-1, 2], [1, 3]], [], [[-2, 1], [1, 1], [1, 2], [-1, 2], [-1, 3], [1, 3], [-1, 4]], [[1, 2], [1, 3]], [[1, 1], [1, 2], [-1, 2], [-1, 4]], [], [[-1, 0], [1, 1], [-1, 4]]]}