# Stored data for newform 177.2.a.b, downloaded from the LMFDB on 23 January 2021.
{"level_primes": [3, 59], "is_polredabs": true, "sato_tate_group": "1.2.3.c1", "rm_discs": [], "conrey_indexes": [1], "cm_discs": [], "trace_hash": 1668257242820155091, "level_radical": 177, "hecke_ring_index_proved": true, "self_twist_type": 0, "related_objects": ["Genus2Curve/Q/31329/a"], "prim_orbit_index": 1, "is_cm": false, "hecke_orbit": 2, "analytic_conductor": 1.4133521157766629, "inner_twist_count": 1, "field_disc_factorization": [[5, 1]], "is_rm": false, "char_order": 1, "level_is_square": false, "weight_parity": 1, "label": "177.2.a.b", "field_poly_is_real_cyclotomic": true, "is_self_twist": false, "is_twist_minimal": true, "minimal_twist": "177.2.a.b", "field_poly_is_cyclotomic": false, "dim": 2, "trace_zratio": {"__RealLiteral__": 0, "data": "0.011", "prec": 17}, "traces": [0, 2, -1, -2, -1, 0, 1, -7, 0, 2, -5, 0, 1, -8, 6, 0, -3, -3, -1, -5, 5, 7, 5, -7, 0, 0, -1, -2, 1, 15, 5, -1, 9, 0, 9, -5, -1, -7, 15, 8, 10, 5, -6, -4, -5, 0, 1, -15, 3, 13, 0, 3, 9, 8, 1, -10, -5, 5, 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-22, 40, -1, 15, 63, -10, 37, -3, 10, 29, 2, 65, 0, 0, -3, -1, 15, 19, 0, 68, 14, -30, 31, -5, -2, 0, 20, -25, 45, -27, -65, 54, 23, 25, -17, 5, 36, 10, 0, -6, -28, 6, -31, 0, 2, -6, -72, 19, -65, 0, 1, -70, -72, 35, 57, -1, -6, -2, -80, 0, 42, 3, 13, 0, 17, -19, -37, -69, -25, 25, 14, 15, 40, -25, 5, -16, 63, -9, 5, -29, 7, -68, 0, 40, -62, -15, 6, -40, 25, 5, -68, 31, -41, 15, -18, -24, -20, 24, 0, -7, -54, 15, -29, -20, 0, 4, 0, 1, -20, 90, -33, 51, 15, 0, 3, 0, 1, 0, -75, -30, -22, 18, -6, -50, -3, -45, -5, 64, 15, 5, 0, -9, 22, -35, 16, 45, 32, -15, 0, -15, -2, 65, -84, 20, -120, 0, 1, 72, 15, 10, 14, -36, 17, -45, 18, 9, -30, 3, 5, 5, 21, -3, 5, 0, 36, 60, -8, 1, -60, 7, 5, 33, -65, -10, 141, -19, 13, 40, 0, 11, -3, 0, -45, -15, 69, 1, -103, -63, 0, 42, -6, 14, -55, 15, -15, -50, -68, 25, 70, 75, -45, 40, 29, 5, 5, -27, -18, 86, 45, -3, 55, -29, 7, -50], "hecke_ring_index_factorization": [], "nf_label": "2.2.5.1", "field_poly": [-1, -1, 1], "atkin_lehner_string": "++", "has_non_self_twist": 0, "atkin_lehner_eigenvals": [[3, 1], [59, 1]], "char_values": [177, 1, [119, 61], [1, 1]], "Nk2": 708, "field_poly_root_of_unity": 10, "analytic_rank": 1, "char_orbit_label": "a", "weight": 2, "trace_display": [-1, -2, 0, -7], "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-\\beta q^{2}-q^{3}+(-1+\\beta )q^{4}+(-1+2\\beta )q^{5}+\\cdots", "self_twist_discs": [], "char_is_real": true, "field_disc": 5, "level_is_prime_power": false, "relative_dim": 2, "hecke_cutters": [[2, [-1, 1, 1]]], "space_label": "177.2.a", "level": 177, "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": 2, "hecke_orbit_code": 4503599660925105, "fricke_eigenval": 1, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.925", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.190", "prec": 17}, {"__RealLiteral__": 0, "data": "0.127", "prec": 17}, {"__RealLiteral__": 0, "data": "62.628", "prec": 20}], "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, 0], [1, 0], [0, -1], [-1, 0], [-1, 1], [-1, 2], [0, 1], [-3, -1], [-1, 2], [1, 0], [-2, -1], [1, -2], [1, -1], [-5, 2], [1, 4], [1, -2], [0, -3], [0, -3], [0, -1], [0, -5], [3, -1], [3, 1], [2, 1], [-4, 1], [1, -2], [0, 0], [-2, 3], [-1, 0], [2, -3], [7, 1], [2, 1], [-5, 9], [5, -1], [-1, 2], [3, 3], [1, -7], [-1, 1], [-2, -3], [5, 5], [5, -2], [5, 0], [5, -5], [-1, -4], [-5, 6], [-3, 1], [-1, 2], [-1, 3], [-9, 3], [0, 3], [3, 7], [0, 0], [0, 3], [7, -5], [5, -2], [0, 1], [-5, 0], [1, -7], [0, 5], [-1, -8], [-1, 0], [-3, 1], [-5, -3], [-9, -4], [-3, -1], [1, 2], [9, -8], [-2, -1], [7, -6], [-3, 0], [4, -1], [7, 6], [-3, 8], [-1, 2], [-1, -3], [3, 5], [0, 0], [-5, 0], [-1, 7], [2, -3], [-3, 0], [-6, -3], [1, 0], [5, 0], [-1, 1], [-2, 3], [-6, -3], [-6, -1], [-7, -1], [-5, 0], [-7, 11], [-2, -1], [13, -3], [5, -4], [5, -9], [-3, 6], [-10, -5], [-5, 1], [3, 0], [-7, -10], [1, -2], [0, 0]]}