# Stored data for newform 8330.2.a.x, downloaded from the LMFDB on 11 September 2025.
{"Nk2": 33320, "analytic_conductor": 66.51538488372655, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [5, 1], [7, 1], [17, 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": [8330, 1, [1667, 2551, 2451], [1, 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": [[3, [-1, 1]], [11, [-3, 1]], [13, [-5, 1]], [19, [-2, 1]]], "hecke_orbit": 24, "hecke_orbit_code": 103582791463084170, "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": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "8330.2.a.x", "level": 8330, "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, 5, 7, 17], "level_radical": 1190, "minimal_twist": "1190.2.i.b", "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/8330/x"], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "8330.2.a", "trace_display": [1, 1, -1, 0], "trace_hash": 564566845499662389, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.015", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.015", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.978", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.016", "prec": 17}, "traces": [0, 1, 1, 1, 1, -1, 1, 0, 1, -2, -1, 3, 1, 5, 0, -1, 1, -1, -2, 2, -1, 0, 3, 0, 1, 1, 5, -5, 0, 0, -1, 8, 1, 3, -1, 0, -2, 2, 2, 5, -1, -6, 0, 2, 3, 2, 0, -6, 1, 0, 1, -1, 5, -3, -5, -3, 0, 2, 0, 6, -1, 8, 8, 0, 1, -5, 3, 2, -1, 0, 0, -15, -2, 8, 2, 1, 2, 0, 5, 5, -1, 1, -6, 6, 0, 1, 2, 0, 3, -3, 2, 0, 0, 8, -6, -2, 1, 8, 0, -6, 1, 6, -1, 8, 5, 0, -3, -15, -5, 14, -3, 2, 0, -6, 2, 0, 0, -10, 6, 0, -1, -2, 8, -6, 8, -1, 0, -4, 1, 2, -5, 12, 3, 0, 2, 5, -1, 3, 0, 17, 0, -6, -15, 15, -2, 0, 8, 0, 2, -3, 1, 8, 2, 2, 0, -8, 5, -13, 5, -3, -1, 0, 1, 20, -6, -3, 6, 21, 0, 12, 1, -4, 2, -6, 0, 0, 3, 6, -3, 18, 2, 8, 0, 8, 0, -2, 8, -3, -6, 0, -2, 0, 1, -10, 8, -5, 0, -18, -6, -25, 1, 2, 6, 0, -1, 6, 8, 0, 5, 6, 0, -4, -3, -15, -15, -2, -5, 0, 14, 8, -3, -5, 2, 26, 0, -2, -6, 9, 2, -10, 0, 0, 0, 6, -10, 6, 6, 5, 0, -6, -1, 8, -2, 16, 8, 0, -6, 10, 8, 6, -1, -6, 0, 0, -4, 1, 1, 9, 2, 0, -5, 0, 12, -6, 3, 3, 0, -3, 2, 30, 5, -16, -1, 0, 3, 3, 0, -22, 17, -16, 0, -15, -6, 11, -15, -2, 15, 0, -2, 1, 0, 8, 8, 27, 0, -6, 2, -15, -3, 0, 1, 0, 8, 6, 2, -8, 2, 2, 0, 8, -8, -27, 5, -22, -13, 0, 5, 18, -3, 0, -1, -15, 0, -2, 1, 5, 20, 14, -6, 0, -3, 20, 6, -4, 21, -2, 0, 14, 12, -6, 1, 24, -4, 0, 2, 0, -6, -12, 0, 26, 0, -25, 3, 9, 6, 15, -3, 0, 18, -24, 2, -15, 8, -2, 0, -8, 8, 23, 0, 12, -2, 0, 8, -19, -3, -1, -6, 0, 0, 35, -2, -4, 0, -18, 1, 0, -10, -4, 8, 33, -5, 0, 0, 12, -18, -5, -6, -16, -25, 0, 1, 6, 2, 40, 6, -1, 0, 6, -1, -25, 6, 3, 8, 0, 0, -6, 5, 17, 6, -21, 0, 2, -4, 12, -3, -1, -15, 0, -15, 15, -2, 15, -5, 26, 0, 0, 14, 0, 8, -19, -3, 0, -5, -18, 2, 3, 26, -3, 0, 6, -2, -18, -6, 8, 9, 0, 2, -22, -10, 5, 0, 27, 0, -40, 0, -8, 6, 18, -10, 0, 6, -13, 6, 6, 5, 2, 0, 6, -6, 12, -1, 10, 8, 0, -2, -8, 16, -13, 8, 20, 0, -18, -6, 0, 10, 6, 8, 0, 6, -7, -1, 21, -6, 21, 0, -6, 0, 12, -4, -30, 1, 0, 1, -10, 9, -8, 2, -18, 0, -6, -5, -36, 0, -34, 12, 0, -6, -8, 3, -23, 3, -12, 0, -30, -3, 15, 2, 18, 30, 0, 5, -40, -16, 8, -1, -14, 0, 35, 3, -16, 3, 0, 0, 0, -22, -2, 17, 9, -16, 10, 0, -3, -15, 18, -6, 6, 11, 0, -15, -15, -2, -4, 15, 0, 0, 0, -2, -13, 1, -10, 0, 0, 8, -9, 8, 10, 27, -30, 0, 16, -6, -18, 2, -21, -15, 0, -3, -25, 0, -6, 1, -28, 0, -4, 8, 2, 6, 5, 2, 0, -8, -30, 2, 11, 2, 6, 0, -42, 8, 17, -8, 0, -27, 0, 5, 1, -22, 6, -13, -2, 0, 20, 5, -4, 18, 4, -3, 0, 0, 30, -1, 36, -15, -1, 0, -2, -2, 18, 1, 18, 5, 0, 20, -12, 14, -12, -6, -16, 0, 0, -3, 26, 20, -5, 6, 0, -4, 0, 21, 26, -2, 24, 0, -34, 14, -5, 12, -18, -6, 0, 1, 9, 24, 27, -4, -3, 0, -10, 2, -15, 0, -28, -6, 0, -12, -17, 0, 6, 26, 6, 0, -33, -25, 4, 3, 6, 9, 0, 6, -46, 15, -10, -3, 0, 0, -15, 18, -6, -24, -45, 2, 0, -15, 8, 8, 0, -2, -40, 0, 13, -8, -2, 8, 5, 23, 0, 0, 6, 12, -16, -2, 10, 0, -27, 8, 3, -19, -12, -3, 0, -1, 17, -6, -6, 0, -8, 0, 11, 35, 0, -2, 21, -4, 0, 0, -2, -18, 30, 1, -31, 0, 9, -10, -21, -4, 8, 8, 0, 33, -12, -5, -45, 0, 0, 0, 13, 12, -40, -18, -6, -5, 0, -6, 40, -16, 3, -25, 9, 0, 6, 1, 6, 6, 24, 2, 0, 40, 30, 6, -24, -1, 11, 0, -16, 6, -20, -1, 4, -25, 0, 6, -36, 3, 5, 8, 3, 0, 33, 0, -7, -6, -22, 5, 0, 17, -21, 6, -40, -21, 24, 0, -29, 2, -15, -4, -12, 12, 0, -3, 11, -1, 0, -15, 20, 0, 4, -15, 0, 15, 14, -2, 0, 15, 24, -5, 6, 26, 1, 0, 15, 0, 10, 14, -16, 0, 0, 8, 50, -19, 27, -3, 12, 0, -40, -5, -6, -18, -15, 2, 0, 3, 3, 26, -12, -3, -18, 0, 0, 6, 0, -2, 3, -18, 0, -6, -8, 8, -16, 9, -12, 0, 48, 2, 18, -22, -8, -10, 0, 5, 56, 0, 2, 27, -75, 0, 2, -40, -16, 0, 42, -8, 0, 6, -27, 18, 3, -10, -58, 0, -22, 6, 0, -13, 0, 6, 0, 6, -15, 5, 40, 2, 18, 0, -9, 6, 0, -6, 0, 12, 0, -1, 33, 10, 30, 8, 10, 0, -16, -2, -2, -8, -30, 16, 0, -13, 5, 8, -42, 20, -9, 0, -28, -18, -9, -6, 18, 0, 0, 10, 0, 6, -61, 8, 20, 0, 25, 6, 20, -7, -10, -1, 0, 21, -6, -6, -2, 21, -6, 0, 50, -6, 14, 0, 24, 12, 0, -4, 12, -30, 54, 1, 23, 0, 24, 1, -6, -10, 25, 9, 0, -8, -27, 2, -49, -18, 0, 0, -8, -6, -16, -5, -12, -36, 0, 0, -6, -34, 26, 12, 54, 0, 23, -6, 5, -8, 4, 3, 0, -23, 9, 3, 30, -12, 2, 0, 15, -30, 24, -3, 29, 15, 0, 2, 0, 18, 2, 30, -24, 0, 30, 5, 0, -40, -15, -16, 0, 8, -10, -1, 4, -14, -12, 0, 56, 35, -8, 3, 3, -16, 0, 3, 23, 0, -48, 0, 5, 0, 30, -22, -9, -2, 18, 17, 0, 9, -26, -16, 38, 10, -19, 0, 12, -3, -28, -15, 2, 18, 0, -6, 20, 6, 0, 11, 24, 0, -9, -15, 35, -15, -2, -2, 0, -4, 8, 15, 10, 0, 16, 0, -18, 0, -63, -2, -52, -13, 0, 1, -15, -10, 16, 0, -10, 0, 39, 8, -6, -9, 33, 8, 0, 10, 38, 27, 0, -30, -6, 0, -45, 16, -24, -6, -15, -18, 0, 2, -5, -21, -3, -15, 0, 0, -16, -3, -48, -25, 6, 0, 0, -6, 42, 1, 8, -28, 6, 0, -8, -4, 15, 8, 40, 2, 0, 6, -64, 5, -16, 2, -18, 0, 0, -8, 6, -30, -48, 2, 0, 11, -25, 2, 30, 6, 23, 0, -6, -42, -10, 8, 23, 17, 0, -8, -8, 0, -18, -27, -6, 0, 0, 5, -46, 1, -34, -22, 0, 6, 6, -13, -21, -2, 36, 0, 40, 20, 2, 5, 0, -4, 0, 18, 30, 4, -48, -3, 4, 0, -1, 0, 30, 30, -34, -1, 0, 36, 48, -15, -9, -1, -30, 0, -6, -2, 32, -2, 15, 18, 0, 1, -52, 18, 26, 5, -54, 0, 8, 20, 0, -12, 6, 14, 0, -12, 0, -6, 30, -16, 6, 0, -19, 0, -69, -3, 20, 26, 0, 20, -3, -5, -22, 6, -18, 0, -39, -4, 16, 0, 3, 21, 0, 26, 40, -2, 6, 24, -5, 0, -30, -34, 6, 14, -30, -5, 0, 12, -18, -18, 16, -6, 0, 0, -16, 1, -45, 9, 0, 24, 0, 27, -3, -4, -33, -3, -22, 0, 9, -10, -3, 2, -1, -15, 0, 0, -55, -28, 27, -6, 22, 0, 16, -12, -40, -17, -75, 0, 0, 6, 16, 26, -12, 6, -55, 0, 18, -33, 0, -25, 15, 4, 0, 3, 18, 6, -6, 9, 26, 0, -11, 6, 70, -46, 6, 15, 0, -10, 65, -3, 2, 0, -54, 0, -46, -15, 15, 18, 66, -6, 0, -24, 12, -45, 72, 2, 36, 0, 10, -15, -1, 8, 56, 8, 0, 0, 63, -2, 41, -40, -8, 0, -48, 13, -43, -8, -13, -2, 0, 8, -27, 5, -40, 23, -30, 0, 2, 0, -18, 6, 6, 12, 0, -16, 0, -2, 39, 10, -28, 0, 15, -27, -24, 8, -16, 3, 0, -19, 6, -12, 0, -3, -7, 0, -12, -1, 10, 17, -42, -6, 0, -6, 9, 0, 21, -8, 42, 0, 3, 11, -6, 35, -12, 0, 0, -2, -24, 21, -36, -4, 8, 0, -30, 0, 51, -2, 32, -18, 0, 30, -2, 1, 0, -31, 2, 0, 0, 9, -10, -10, -8, -21, 0, -4, 29, 8, -18, 8, 18, 0, 27, 33, 12, -12, -15, -5, 0, -45, -36, 0, 22, 0, -13, 0, -34, 13, -36, 12, -10, -40, 0, -18, 12, -6, -40, -5, -8, 0, -6, -6, -18, 40, -23, -16, 0, 3, 4, -25, -30, 9, 0, 0, -13, 6, -30, 1, -18, 6, 0, 6, 15, 24, -12, 2, -58, 0, -36, 40, 51, 30, 2, 6, 0, -24, 18, -1, -10, 11, -40, 0, -5, -16, 56, 6, -16, -20, 0, -1, 0, 4, -14, -25, 0, 0, -9, 6, 35, -36, -24, 3, 0, 5, -40, 8, -8, 3, -20, 0, 0, 33, -20, 0, 2, -7, 0, -6, 24, -22, -16, 5, 4, 0, 48, 17, 68, -21, 9, 6, 0, -40, 2, -21, 10, 24, 0, 0, -5, -29, 6, 2, -14, -15, 0, -4, 18, -12, -6, 12, -4, 0, 6, -3, 12, 11, -40, -1, 0, 0, 60, -15, -24, 20, -15, 0, 75, 4, 0, -15, -4, 0, 0, 15, -6, 14, 0, -2, -9, 0, -31, 15, 0, 24, -39, -5, 0, 6, -13, 26, -42, 1, 12, 0, 20, 15, -12, 0, -10, 10, 0, 14, -26, -16, 2, 0, -9, 0, -8, 8, -37, 50, 25, -19, 0, 27, 20, -3, -30, 12, -12, 0, -9, -40, 16, -5, 0, -6, 0, -18, 36, -15, -15, 2, -49, 0, -21, 3, 15, 3, 56, 26, 0, -12, -54, -3, 59, -18, 50, 0, 60, 0, 24, 6, -6, 0, 0, -2, 65, 3, -28, -18, 15, 0, 85, -6, -10, -8, -24, 8, 0, -16, 2, 9, 0, -12, 15, 0, 5, 48, 12, 2, 8, 18, 0, -22, 48, -8, 20, -10, -30, 0, -23, 5, 63, 56, 11, 0, 0, 2, 16, 27, -12, -75, -63, 0, -39, 2, -42, -40, -14, -16, 0, 0, 17, 42, 36, -8, -13, 0, 0, 6, 19, -27, -4, 18, 0, 3, 48, -10, 50, -58, 1, 0, 12, -22, 62, 6, -12, 0, 0, -13, 0, 0, -2, 6, 30, 0, 64, 6, 20, -15, -35, 5, 0, 40, 8, 2, 36, 18, -18, 0, 4, -9, -69, 6, 0, 0, 0, -6, 45, 0, 18, 12, 75, 0, 12, -1, 6, 33, 36, 10, 0, 30, 36, 8, -1, 10, -12, 0, 74, -16, 4, -2, -15, -2, 0, -8, 18, -30, 0, 16, -33, 0, 18, -13, 72, 5, -64, 8, 0, -42, 0, 20, 16, -9, -12, 0, -6, -28, 40, -18, -12, -9, 0, -6, 54, 18, -40, 0, 69, 0, 5, 10, 0, 0, -60, 6, 0, -61, 26, 8, 16, 20, -64, 0, 10, 25, 24, 6, 14, 20, 0, -7, -81, -10, -61, -1, 0, 0, -51, 21, -6, -6, -52, -6, 0, -2, 5, 21, 24, -6, -40, 0, -40, 50, -34, -6, -12, 14, 0, 0, 1, 24, -48, 12, 56, 0, -18, -4, -30, 12, -6, -30, 0, 54, -6, 1, -65, 23, -18, 0, 25, 24, 0, 1, 27, -6, 0, -10, -25, 25, -3, 9, 2, 0, 0, -8, 20, -27, 24, 2, 0, -49, -15, -18, 60, 0, 28, 0, -28, -8, 6, -6, 16, -16, 0, -5, -24, -12, 32, -36, -17, 0, -30, 0, 41, -6, 6, -34, 0, 26, 21, 12, -12, 54, 0, 0, 0, 23, -33, -6, -2, 5, 0, -8, 4, 4, -39, 3, -10, 0, -12, -23, 0, 9, 100, 3, 0, 30, -30, -12, 1, 2, -46, 0, -30, 15, 20, -30, -25, 24, 0, -3, -40, 29, 0, 15, -66, 0, 44, 2, -15, 0, -12, 18, 0, 2, 12, 30, 54, -24, -15, 0, -45, 30, 4, 5, 26, 0, 0, -40, -26, -15, -54, -16, -16, 0, 105, 8, 18, -10, 0, -1, 0, 4, 20, -14, -40, -12, 12, 0, 0, 56, -35, 35, -75, -8, 0, 3, -2, 3, 19, -16, -5, 0, 5, 3, -120, 23, 11, 0, 0, -48, -72, 0, -11, 5, 6, 0, 30, 30, 18, -22, -16, -9, 0, -2, -46, 18, -20, 17, -3, 0, -12, 9, -27, -26, 0, -16, 0, 38, 3, 10, -84, -19, 8, 0, -30, 12, -78, -3, -6, -28, 0, -15, -30, 2, -31, 18, 17, 0, 18, -6, 16, 20, 12, 6, 0, 0, 64, 11, -8, 24, 9, 0, 47, -9, 11, -15, -54, 35, 0, -15, 0, -2, -6, -2, 74, 0, 21, -4, 22, 8, -82, 15, 0, 10, 0, 0, -19, 16, -5, 0, -57, -18, -4, 0, 30, -63, 0, -2, -27, -52, -31, -13, 66, 0, -16, 1, -18, -15, 40, -10, 0, 16, -21, 0, -12, -10, 0, 0, 8, 39, 90, 8, -3, -6, 0, -9, -51, 33, -18, 8, -12, 0, 81, 10, 32, 38, -45, 27, 0, 0, -28, -30, 0, -6, 21, 0, 40, -45, 13, 16, 42, -24, 0, -6, -40, -15, -17, -18, -6, 0, 12, 2, 0, -5, -4, -21, 0, -3, -2, -15, -52, 0, 40, 0, -15, -16, 44, -3, -6, -48, 0, -25, 77, 6, 9, 0, 51, 0, -12, -6, 6, 42, 84, 1, 0, 8, 15, -28, -10, 6, 0, 0, 24, -8, 27, -4, -8, 15, 0, 8, 48, 40, -36, 2, -60, 0, -30, 6, 8, -64, -24, 5, 0, -16, -15, 2, 11, -18, 13, 0, 62, 0, 32, -8, 24, 6, 0, -30, -20, -48, -78, 2, 40, 0, 4, 11, 78, -25, 18, 2, 0, 30, -48, 6, 0, 23, -36, 0, 0, -6, -28, -42, 5, -10, 0, 8, -73, 23, -6, 17, -48, 0, 4, -8, 33, -8, 0, 0, 0, -18, -7, -27, 24, -6, 18, 0, 44, 0, 7, 5, 27, -46, 0, 1, -48, -34, -64, -22, -21, 0, 0, 6, -50, 6, 8, -13, 0, -21, -21, -2, 24, 36, -30, 0, -88, 40, -29, 20, 6, 2, 0, 5, 30, 0, 12, -4, 3, 0, -12, 18, 12, 30, -4, 4, 0, -48, -63, -3, 30, 4, -22, 0, -45, -1, 20, 0, 0, 30, 0, 30, 68, -34, 20, -1, -90, 0, 18, 36, 10, 48, -8, -15, 0, -9, 0, -1, 48, -30, 8, 0, 14, -6, -99, -2, 0, 32, 0, -2, 18, 15, -125, 18, 24, 0, 27, 1, -79, -52, 6, 18, 0, 26, 0, 5, -2, -54, 6, 0, 36, 8, 15, 20, -3, 0, 0, -12, 10, 6, 34, 14, 77, 0, -40, -12, 0, 0, 16, -6, 0, 30, -30, -16, -18, 6, 50, 0, -93, -19, 8, 0, -54, -69, 0, -3, 34, 20, 12, 26, 23, 0, -52, 20, -40, -3, 24, -5, 0, -22, 12, 6, 42, -18, -76, 0, -15, -39, 24, -4, 30, 16, 0, 0, 13, 3, -40, 21, 48, 0, -15, 26, -58, 40, -12, -2, 0, 6, 53, 24, -18, -5, 72, 0, 8, -30, 0, -34, 24, 6, 0, 14, 0, -30, -72, -5, 16, 0, 3, 12, 40, -18, 20, -18, 0, 16, 18, -6, -22, 0, -8, 0, 30, -16, 20, 1, -16, -45, 0, 9, 14, 0, -30, 24, -51, 0, 11, 27, 48, -3, -35, -4, 0, -33, 18, -3, 63, -22, -20, 0, 16, 9, -12, -10, 50, -3, 0, 2, 75, -1, 0, -15, 56, 0, -24, 0, -18, -55, -4, -28, 0, 27, -94, -6, -75, 22, -20, 0, -36, 16, 2, -12, -6, -40, 0, -17, -40, -75, 0, 0, -9, 0, 42, 6, -15, 16, -31, 26, 0, -12, -10, 6, 98, -55, 54, 0, -99, 18, 26, -33, 3, 0, 0, -25, -44, 15, -58, 4, 0, 0, -18, 3, 44, 18, 60, 6, 0, -6, 0, 9, -6, 26, 27, 0, 0, -11, -6, 6, -10, 70, 0, -46, -81, 6, -21, 15, -15, 0, -54, -10, 15, 65, 40, -3, 0, 2, -1, 0, -36, -54, 4, 0, -43, -46, -9, -15, 102, 15, 0, 18, 0, 66, -48, -6, 16, 0, 0, -24, -12, 12, 0, -45, 0, 72, 45, 2, 4, 36, 33, 0, 13, 10, -73, -15, 75, -1, 0, 8, -18, 56, 10, 8, 96, 0, 130, 0, -16, 63, -84, -2, 0, 41, 4, -40, 63, -8, 90, 0, -30, -48, 9, 13, -100, -43, 0, -8, 0, -13, 10, -2, -10, 0, 69, 8, 0, -27, -42, 5, 0, -40, 30, 23, -9, -30, 0, 0, 6, 2, -70, 0, -16, -18, 0, 6, -9, 6, 45, 12, 56, 0, 18, -16, -57, 0, 90, -2, 0, 39, 24, 10, 21, -28, 0, 0, 36, 15, -52, -27, -61, -24, 0, 8, -50, -16, -40, 3, -48, 0, -26, -19, 25, 6, 0, -12, 0, 0, 20, -3, -48, -7, 6, 0, 2, -12, -39, -1, 71, 10, 0, 17, 28, -42, 64, -6, -6, 0, 42, -6, 0, 9, 4, 0, 0, 21, -13, -8, -6, 42, 0, 0, -2], "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, -2, -1, 3, 1, 5, 0, -1, 1, -1, -2, 2, -1, 0, 3, 0, 1, 1, 5, -5, 0, 0, -1, 8, 1, 3, -1, 0, -2, 2, 2, 5, -1, -6, 0, 2, 3, 2, 0, -6, 1, 0, 1, -1, 5, -3, -5, -3, 0, 2, 0, 6, -1, 8, 8, 0, 1, -5, 3, 2, -1, 0, 0, -15, -2, 8, 2, 1, 2, 0, 5, 5, -1, 1, -6, 6, 0, 1, 2, 0, 3, -3, 2, 0, 0, 8, -6, -2, 1, 8, 0, -6, 1, 6, -1, 8, 5, 0, -3, -15, -5, 14, -3, 2, 0, -6, 2, 0, 0, -10, 6, 0, -1, -2, 8, -6, 8, -1, 0, -4, 1, 2, -5, 12, 3, 0, 2, 5, -1, 3, 0, 17, 0, -6, -15, 15, -2, 0, 8, 0, 2, -3, 1, 8, 2, 2, 0, -8, 5, -13, 5, -3, -1, 0, 1, 20, -6, -3, 6, 21, 0, 12, 1, -4, 2, -6, 0, 0, 3, 6, -3, 18, 2, 8, 0, 8, 0, -2, 8, -3, -6, 0, -2, 0, 1, -10, 8, -5, 0, -18, -6, -25, 1, 2, 6, 0, -1, 6, 8, 0, 5, 6, 0, -4, -3, -15, -15, -2, -5, 0, 14, 8, -3, -5, 2, 26, 0, -2, -6, 9, 2, -10, 0, 0, 0, 6, -10, 6, 6, 5, 0, -6, -1, 8, -2, 16, 8, 0, -6, 10, 8, 6, -1, -6, 0, 0, -4, 1, 1, 9, 2, 0, -5, 0, 12, -6, 3, 3, 0, -3, 2, 30, 5, -16, -1, 0, 3, 3, 0, -22, 17, -16, 0, -15, -6, 11, -15, -2, 15, 0, -2, 1, 0, 8, 8, 27, 0, -6, 2, -15, -3, 0, 1, 0, 8, 6, 2, -8, 2, 2, 0, 8, -8, -27, 5, -22, -13, 0, 5, 18, -3, 0, -1, -15, 0, -2, 1, 5, 20, 14, -6, 0, -3, 20, 6, -4, 21, -2, 0, 14, 12, -6, 1, 24, -4, 0, 2, 0, -6, -12, 0, 26, 0, -25, 3, 9, 6, 15, -3, 0, 18, -24, 2, -15, 8, -2, 0, -8, 8, 23, 0, 12, -2, 0, 8, -19, -3, -1, -6, 0, 0, 35, -2, -4, 0, -18, 1, 0, -10, -4, 8, 33, -5, 0, 0, 12, -18, -5, -6, -16, -25, 0, 1, 6, 2, 40, 6, -1, 0, 6, -1, -25, 6, 3, 8, 0, 0, -6, 5, 17, 6, -21, 0, 2, -4, 12, -3, -1, -15, 0, -15, 15, -2, 15, -5, 26, 0, 0, 14, 0, 8, -19, -3, 0, -5, -18, 2, 3, 26, -3, 0, 6, -2, -18, -6, 8, 9, 0, 2, -22, -10, 5, 0, 27, 0, -40, 0, -8, 6, 18, -10, 0, 6, -13, 6, 6, 5, 2, 0, 6, -6, 12, -1, 10, 8, 0, -2, -8, 16, -13, 8, 20, 0, -18, -6, 0, 10, 6, 8, 0, 6, -7, -1, 21, -6, 21, 0, -6, 0, 12, -4, -30, 1, 0, 1, -10, 9, -8, 2, -18, 0, -6, -5, -36, 0, -34, 12, 0, -6, -8, 3, -23, 3, -12, 0, -30, -3, 15, 2, 18, 30, 0, 5, -40, -16, 8, -1, -14, 0, 35, 3, -16, 3, 0, 0, 0, -22, -2, 17, 9, -16, 10, 0, -3, -15, 18, -6, 6, 11, 0, -15, -15, -2, -4, 15, 0, 0, 0, -2, -13, 1, -10, 0, 0, 8, -9, 8, 10, 27, -30, 0, 16, -6, -18, 2, -21, -15, 0, -3, -25, 0, -6, 1, -28, 0, -4, 8, 2, 6, 5, 2, 0, -8, -30, 2, 11, 2, 6, 0, -42, 8, 17, -8, 0, -27, 0, 5, 1, -22, 6, -13, -2, 0, 20, 5, -4, 18, 4, -3, 0, 0, 30, -1, 36, -15, -1, 0, -2, -2, 18, 1, 18, 5, 0, 20, -12, 14, -12, -6, -16, 0, 0, -3, 26, 20, -5, 6, 0, -4, 0, 21, 26, -2, 24, 0, -34, 14, -5, 12, -18, -6, 0, 1, 9, 24, 27, -4, -3, 0, -10, 2, -15, 0, -28, -6, 0, -12, -17, 0, 6, 26, 6, 0, -33, -25, 4, 3, 6, 9, 0, 6, -46, 15, -10, -3, 0, 0, -15, 18, -6, -24, -45, 2, 0, -15, 8, 8, 0, -2, -40, 0, 13, -8, -2, 8, 5, 23, 0, 0, 6, 12, -16, -2, 10, 0, -27, 8, 3, -19, -12, -3, 0, -1, 17, -6, -6, 0, -8, 0, 11, 35, 0, -2, 21, -4, 0, 0, -2, -18, 30, 1, -31, 0, 9, -10, -21, -4, 8, 8, 0, 33, -12, -5, -45, 0, 0, 0, 13, 12, -40, -18, -6, -5, 0, -6, 40, -16, 3, -25, 9, 0, 6, 1, 6, 6, 24, 2, 0, 40, 30, 6, -24, -1, 11, 0, -16, 6, -20, -1, 4, -25, 0, 6, -36, 3, 5, 8, 3, 0, 33, 0, -7, -6, -22, 5, 0, 17, -21, 6, -40, -21, 24, 0, -29, 2, -15, -4, -12, 12, 0, -3, 11, -1, 0, -15, 20, 0, 4, -15, 0, 15, 14, -2, 0, 15, 24, -5, 6, 26, 1, 0, 15, 0, 10, 14, -16, 0, 0, 8, 50, -19, 27, -3, 12, 0, -40, -5, -6, -18, -15, 2, 0, 3, 3, 26, -12, -3, -18, 0, 0, 6, 0, -2, 3, -18, 0, -6, -8, 8, -16, 9, -12, 0, 48, 2, 18, -22, -8, -10, 0, 5, 56, 0, 2, 27, -75, 0, 2, -40, -16, 0, 42, -8, 0, 6, -27, 18, 3, -10, -58, 0, -22, 6, 0, -13, 0, 6, 0, 6, -15, 5, 40, 2, 18, 0, -9, 6, 0, -6, 0, 12, 0, -1, 33, 10, 30, 8, 10, 0, -16, -2, -2, -8, -30, 16, 0, -13, 5, 8, -42, 20, -9, 0, -28, -18, -9, -6, 18, 0, 0, 10, 0, 6, -61, 8, 20, 0, 25, 6, 20, -7, -10, -1, 0, 21, -6, -6, -2, 21, -6, 0, 50, -6, 14, 0, 24, 12, 0, -4, 12, -30, 54, 1, 23, 0, 24, 1, -6, -10, 25, 9, 0, -8, -27, 2, -49, -18, 0, 0, -8, -6, -16, -5, -12, -36, 0, 0, -6, -34, 26, 12, 54, 0, 23, -6, 5, -8, 4, 3, 0, -23, 9, 3, 30, -12, 2, 0, 15, -30, 24, -3, 29, 15, 0, 2, 0, 18, 2, 30, -24, 0, 30, 5, 0, -40, -15, -16, 0, 8, -10, -1, 4, -14, -12, 0, 56, 35, -8, 3, 3, -16, 0, 3, 23, 0, -48, 0, 5, 0, 30, -22, -9, -2, 18, 17, 0, 9, -26, -16, 38, 10, -19, 0, 12, -3, -28, -15, 2, 18, 0, -6, 20, 6, 0, 11, 24, 0, -9, -15, 35, -15, -2, -2, 0, -4, 8, 15, 10, 0, 16, 0, -18, 0, -63, -2, -52, -13, 0, 1, -15, -10, 16, 0, -10, 0, 39, 8, -6, -9, 33, 8, 0, 10, 38, 27, 0, -30, -6, 0, -45, 16, -24, -6, -15, -18, 0, 2, -5, -21, -3, -15, 0, 0, -16, -3, -48, -25, 6, 0, 0, -6, 42, 1, 8, -28, 6, 0, -8, -4, 15, 8, 40, 2, 0, 6, -64, 5, -16, 2, -18, 0, 0, -8, 6, -30, -48, 2, 0, 11, -25, 2, 30, 6, 23, 0, -6, -42, -10, 8, 23, 17, 0, -8, -8, 0, -18, -27, -6, 0, 0, 5, -46, 1, -34, -22, 0, 6, 6, -13, -21, -2, 36, 0, 40, 20, 2, 5, 0, -4, 0, 18, 30, 4, -48, -3, 4, 0, -1, 0, 30, 30, -34, -1, 0, 36, 48, -15, -9, -1, -30, 0, -6, -2, 32, -2, 15, 18, 0, 1, -52, 18, 26, 5, -54, 0, 8, 20, 0, -12, 6, 14, 0, -12, 0, -6, 30, -16, 6, 0, -19, 0, -69, -3, 20, 26, 0, 20, -3, -5, -22, 6, -18, 0, -39, -4, 16, 0, 3, 21, 0, 26, 40, -2, 6, 24, -5, 0, -30, -34, 6, 14, -30, -5, 0, 12, -18, -18, 16, -6, 0, 0, -16, 1, -45, 9, 0, 24, 0, 27, -3, -4, -33, -3, -22, 0, 9, -10, -3, 2, -1, -15, 0, 0, -55, -28, 27, -6, 22, 0, 16, -12, -40, -17, -75, 0, 0, 6, 16, 26, -12, 6, -55, 0, 18, -33, 0, -25, 15, 4, 0, 3, 18, 6, -6, 9, 26, 0, -11, 6, 70, -46, 6, 15, 0, -10, 65, -3, 2, 0, -54, 0, -46, -15, 15, 18, 66, -6, 0, -24, 12, -45, 72, 2, 36, 0, 10, -15, -1, 8, 56, 8, 0, 0, 63, -2, 41, -40, -8, 0, -48, 13, -43, -8, -13, -2, 0, 8, -27, 5, -40, 23, -30, 0, 2, 0, -18, 6, 6, 12, 0, -16, 0, -2, 39, 10, -28, 0, 15, -27, -24, 8, -16, 3, 0, -19, 6, -12, 0, -3, -7, 0, -12, -1, 10, 17, -42, -6, 0, -6, 9, 0, 21, -8, 42, 0, 3, 11, -6, 35, -12, 0, 0, -2, -24, 21, -36, -4, 8, 0, -30, 0, 51, -2, 32, -18, 0, 30, -2, 1, 0, -31, 2, 0, 0, 9, -10, -10, -8, -21, 0, -4, 29, 8, -18, 8, 18, 0, 27, 33, 12, -12, -15, -5, 0, -45, -36, 0, 22, 0, -13, 0, -34, 13, -36, 12, -10, -40, 0, -18, 12, -6, -40, -5, -8, 0, -6, -6, -18, 40, -23, -16, 0, 3, 4, -25, -30, 9, 0, 0, -13, 6, -30, 1, -18, 6, 0, 6, 15, 24, -12, 2, -58, 0, -36, 40, 51, 30, 2, 6, 0, -24, 18, -1, -10, 11, -40, 0, -5, -16, 56, 6, -16, -20, 0, -1, 0, 4, -14, -25, 0, 0, -9, 6, 35, -36, -24, 3, 0, 5, -40, 8, -8, 3, -20, 0, 0, 33, -20, 0, 2, -7, 0, -6, 24, -22, -16, 5, 4, 0, 48, 17, 68, -21, 9, 6, 0, -40, 2, -21, 10, 24, 0, 0, -5, -29, 6, 2, -14, -15, 0, -4, 18, -12, -6, 12, -4, 0, 6, -3, 12, 11, -40, -1, 0, 0, 60, -15, -24, 20, -15, 0, 75, 4, 0, -15, -4, 0, 0, 15, -6, 14, 0, -2, -9, 0, -31, 15, 0, 24, -39, -5, 0, 6, -13, 26, -42, 1, 12, 0, 20, 15, -12, 0, -10, 10, 0, 14, -26, -16, 2, 0, -9, 0, -8, 8, -37, 50, 25, -19, 0, 27, 20, -3, -30, 12, -12, 0, -9, -40, 16, -5, 0, -6, 0, -18, 36, -15, -15, 2, -49, 0, -21, 3, 15, 3, 56, 26, 0, -12, -54, -3, 59, -18, 50, 0, 60, 0, 24, 6, -6, 0, 0, -2, 65, 3, -28, -18, 15, 0, 85, -6, -10, -8, -24, 8, 0, -16, 2, 9, 0, -12, 15, 0, 5, 48, 12, 2, 8, 18, 0, -22, 48, -8, 20, -10, -30, 0, -23, 5, 63, 56, 11, 0, 0, 2, 16, 27, -12, -75, -63, 0, -39, 2, -42, -40, -14, -16, 0, 0, 17, 42, 36, -8, -13, 0, 0, 6, 19, -27, -4, 18, 0, 3, 48, -10, 50, -58, 1, 0, 12, -22, 62, 6, -12, 0, 0, -13, 0, 0, -2, 6, 30, 0, 64, 6, 20, -15, -35, 5, 0, 40, 8, 2, 36, 18, -18, 0, 4, -9, -69, 6, 0, 0, 0, -6, 45, 0, 18, 12, 75, 0, 12, -1, 6, 33, 36, 10, 0, 30, 36, 8, -1, 10, -12, 0, 74, -16, 4, -2, -15, -2, 0, -8, 18, -30, 0, 16, -33, 0, 18, -13, 72, 5, -64, 8, 0, -42, 0, 20, 16, -9, -12, 0, -6, -28, 40, -18, -12, -9, 0, -6, 54, 18, -40, 0, 69, 0, 5, 10, 0, 0, -60, 6, 0, -61, 26, 8, 16, 20, -64, 0, 10, 25, 24, 6, 14, 20, 0, -7, -81, -10, -61, -1, 0, 0, -51, 21, -6, -6, -52, -6, 0, -2, 5, 21, 24, -6, -40, 0, -40, 50, -34, -6, -12, 14, 0, 0, 1, 24, -48, 12, 56, 0, -18, -4, -30, 12, -6, -30, 0, 54, -6, 1, -65, 23, -18, 0, 25, 24, 0, 1, 27, -6, 0, -10, -25, 25, -3, 9, 2, 0, 0, -8, 20, -27, 24, 2, 0, -49, -15, -18, 60, 0, 28, 0, -28, -8, 6, -6, 16, -16, 0, -5, -24, -12, 32, -36, -17, 0, -30, 0, 41, -6, 6, -34, 0, 26, 21, 12, -12, 54, 0, 0, 0, 23, -33, -6, -2, 5, 0, -8, 4, 4, -39, 3, -10, 0, -12, -23, 0, 9, 100, 3, 0, 30, -30, -12, 1, 2, -46, 0, -30, 15, 20, -30, -25, 24, 0, -3, -40, 29, 0, 15, -66, 0, 44, 2, -15, 0, -12, 18, 0, 2, 12, 30, 54, -24, -15, 0, -45, 30, 4, 5, 26, 0, 0, -40, -26, -15, -54, -16, -16, 0, 105, 8, 18, -10, 0, -1, 0, 4, 20, -14, -40, -12, 12, 0, 0, 56, -35, 35, -75, -8, 0, 3, -2, 3, 19, -16, -5, 0, 5, 3, -120, 23, 11, 0, 0, -48, -72, 0, -11, 5, 6, 0, 30, 30, 18, -22, -16, -9, 0, -2, -46, 18, -20, 17, -3, 0, -12, 9, -27, -26, 0, -16, 0, 38, 3, 10, -84, -19, 8, 0, -30, 12, -78, -3, -6, -28, 0, -15, -30, 2, -31, 18, 17, 0, 18, -6, 16, 20, 12, 6, 0, 0, 64, 11, -8, 24, 9, 0, 47, -9, 11, -15, -54, 35, 0, -15, 0, -2, -6, -2, 74, 0, 21, -4, 22, 8, -82, 15, 0, 10, 0, 0, -19, 16, -5, 0, -57, -18, -4, 0, 30, -63, 0, -2, -27, -52, -31, -13, 66, 0, -16, 1, -18, -15, 40, -10, 0, 16, -21, 0, -12, -10, 0, 0, 8, 39, 90, 8, -3, -6, 0, -9, -51, 33, -18, 8, -12, 0, 81, 10, 32, 38, -45, 27, 0, 0, -28, -30, 0, -6, 21, 0, 40, -45, 13, 16, 42, -24, 0, -6, -40, -15, -17, -18, -6, 0, 12, 2, 0, -5, -4, -21, 0, -3, -2, -15, -52, 0, 40, 0, -15, -16, 44, -3, -6, -48, 0, -25, 77, 6, 9, 0, 51, 0, -12, -6, 6, 42, 84, 1, 0, 8, 15, -28, -10, 6, 0, 0, 24, -8, 27, -4, -8, 15, 0, 8, 48, 40, -36, 2, -60, 0, -30, 6, 8, -64, -24, 5, 0, -16, -15, 2, 11, -18, 13, 0, 62, 0, 32, -8, 24, 6, 0, -30, -20, -48, -78, 2, 40, 0, 4, 11, 78, -25, 18, 2, 0, 30, -48, 6, 0, 23, -36, 0, 0, -6, -28, -42, 5, -10, 0, 8, -73, 23, -6, 17, -48, 0, 4, -8, 33, -8, 0, 0, 0, -18, -7, -27, 24, -6, 18, 0, 44, 0, 7, 5, 27, -46, 0, 1, -48, -34, -64, -22, -21, 0, 0, 6, -50, 6, 8, -13, 0, -21, -21, -2, 24, 36, -30, 0, -88, 40, -29, 20, 6, 2, 0, 5, 30, 0, 12, -4, 3, 0, -12, 18, 12, 30, -4, 4, 0, -48, -63, -3, 30, 4, -22, 0, -45, -1, 20, 0, 0, 30, 0, 30, 68, -34, 20, -1, -90, 0, 18, 36, 10, 48, -8, -15, 0, -9, 0, -1, 48, -30, 8, 0, 14, -6, -99, -2, 0, 32, 0, -2, 18, 15, -125, 18, 24, 0, 27, 1, -79, -52, 6, 18, 0, 26, 0, 5, -2, -54, 6, 0, 36, 8, 15, 20, -3, 0, 0, -12, 10, 6, 34, 14, 77, 0, -40, -12, 0, 0, 16, -6, 0, 30, -30, -16, -18, 6, 50, 0, -93, -19, 8, 0, -54, -69, 0, -3, 34, 20, 12, 26, 23, 0, -52, 20, -40, -3, 24, -5, 0, -22, 12, 6, 42, -18, -76, 0, -15, -39, 24, -4, 30, 16, 0, 0, 13, 3, -40, 21, 48, 0, -15, 26, -58, 40, -12, -2, 0, 6, 53, 24, -18, -5, 72, 0, 8, -30, 0, -34, 24, 6, 0, 14, 0, -30, -72, -5, 16, 0, 3, 12, 40, -18, 20, -18, 0, 16, 18, -6, -22, 0, -8, 0, 30, -16, 20, 1, -16, -45, 0, 9, 14, 0, -30, 24, -51, 0, 11, 27, 48, -3, -35, -4, 0, -33, 18, -3, 63, -22, -20, 0, 16, 9, -12, -10, 50, -3, 0, 2, 75, -1, 0, -15, 56, 0, -24, 0, -18, -55, -4, -28, 0, 27, -94, -6, -75, 22, -20, 0, -36, 16, 2, -12, -6, -40, 0, -17, -40, -75, 0, 0, -9, 0, 42, 6, -15, 16, -31, 26, 0, -12, -10, 6, 98, -55, 54, 0, -99, 18, 26, -33, 3, 0, 0, -25, -44, 15, -58, 4, 0, 0, -18, 3, 44, 18, 60, 6, 0, -6, 0, 9, -6, 26, 27, 0, 0, -11, -6, 6, -10, 70, 0, -46, -81, 6, -21, 15, -15, 0, -54, -10, 15, 65, 40, -3, 0, 2, -1, 0, -36, -54, 4, 0, -43, -46, -9, -15, 102, 15, 0, 18, 0, 66, -48, -6, 16, 0, 0, -24, -12, 12, 0, -45, 0, 72, 45, 2, 4, 36, 33, 0, 13, 10, -73, -15, 75, -1, 0, 8, -18, 56, 10, 8, 96, 0, 130, 0, -16, 63, -84, -2, 0, 41, 4, -40, 63, -8, 90, 0, -30, -48, 9, 13, -100, -43, 0, -8, 0, -13, 10, -2, -10, 0, 69, 8, 0, -27, -42, 5, 0, -40, 30, 23, -9, -30, 0, 0, 6, 2, -70, 0, -16, -18, 0, 6, -9, 6, 45, 12, 56, 0, 18, -16, -57, 0, 90, -2, 0, 39, 24, 10, 21, -28, 0, 0, 36, 15, -52, -27, -61, -24, 0, 8, -50, -16, -40, 3, -48, 0, -26, -19, 25, 6, 0, -12, 0, 0, 20, -3, -48, -7, 6, 0, 2, -12, -39, -1, 71, 10, 0, 17, 28, -42, 64, -6, -6, 0, 42, -6, 0, 9, 4, 0, 0, 21, -13, -8, -6, 42, 0, 0, -2]}