# Stored data for newform 4998.2.a.be, downloaded from the LMFDB on 24 April 2024.
{"label": "4998.2.a.be", "space_label": "4998.2.a", "level": 4998, "weight": 2, "hecke_orbit": 31, "hecke_orbit_code": 135107988854674310, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1447946057586152553, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[5, [-2, 1]], [11, [4, 1]], [13, [-2, 1]], [23, [0, 1]]], "qexp_display": "q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 19992, "fricke_eigenval": 1, "atkin_lehner_string": "-+-+", "analytic_conductor": 39.909230930235935, "hecke_ring_index": 1, "level_radical": 714, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.016", "prec": 17}, "analytic_rank_proved": true, "char_values": [4998, 1, [1667, 2551, 4117], [1, 1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 3, 7, 17], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.958", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.854", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.490", "prec": 17}], "related_objects": ["EllipticCurve/Q/4998/be"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [3, 1], [7, -1], [17, 1]], "trace_display": [1, -1, 2, 0], "traces": [0, 1, 1, -1, 1, 2, -1, 0, 1, 1, 2, -4, -1, 2, 0, -2, 1, -1, 1, -4, 2, 0, -4, 0, -1, -1, 2, -1, 0, -10, -2, -8, 1, 4, -1, 0, 1, -2, -4, -2, 2, -10, 0, 12, -4, 2, 0, 0, -1, 0, -1, 1, 2, 6, -1, -8, 0, 4, -10, -12, -2, 10, -8, 0, 1, 4, 4, -12, -1, 0, 0, 0, 1, -10, -2, 1, -4, 0, -2, -8, 2, 1, -10, -4, 0, -2, 12, 10, -4, 6, 2, 0, 0, 8, 0, -8, -1, 14, 0, -4, -1, 10, 1, 8, 2, 0, 6, -4, -1, -10, -8, 2, 0, 2, 4, 0, -10, 2, -12, 0, -2, 5, 10, 10, -8, -12, 0, 0, 1, -12, 4, 12, 4, 0, -12, -2, -1, 10, 0, 4, 0, 0, 0, -8, 1, -20, -10, 0, -2, -10, 1, 24, -4, -1, 0, -16, -2, 2, -8, -6, 2, 0, 1, 4, -10, 8, -4, -16, 0, -9, -2, -4, 12, -6, 10, 0, -4, 12, 6, -12, 2, -14, 0, -10, 0, -4, 8, 4, 0, 0, -8, -16, -1, 18, 14, -4, 0, 14, -4, 0, -1, 12, 10, 0, 1, -20, 8, 0, 2, 16, 0, -28, 6, 0, -4, 24, -1, 0, -10, 10, -8, -2, 2, -16, 0, -1, 2, -4, 4, 26, 0, 0, -10, 26, 2, 0, -12, 8, 0, 0, -2, -2, 5, -1, 10, 0, 10, -8, -8, 4, -12, -28, 0, 0, 0, 2, 1, -2, -12, 0, 4, -10, 12, -8, 4, 12, 0, -6, -12, -6, -2, -16, -1, 0, 10, 4, 0, 30, 4, -8, 0, -6, 0, -12, 0, 8, -8, 0, 1, 1, -20, -14, -10, 26, 0, -24, -2, 4, -10, 0, 1, 0, 24, -10, -4, 20, -1, 12, 0, -8, -16, 0, -2, -10, 2, 0, -8, 6, -6, 40, 2, 4, 0, 4, 1, -2, 4, 10, -10, 0, 8, -20, -4, -2, -16, -24, 0, -14, -9, -2, -2, 32, -4, 0, 12, 0, -6, 28, 10, -14, 0, -2, -4, 30, 12, 0, 6, 0, -12, -24, 2, -3, -14, -5, 0, -20, -10, -24, 0, -10, -4, 0, 8, 6, 4, 12, 0, -20, 0, -4, -8, 0, -16, 16, -1, 0, 18, 12, 14, -26, -4, 0, 0, -12, 14, -16, -4, 26, 0, 0, -1, -14, 12, -16, 10, 2, 0, 8, 1, -26, -20, -10, 8, 0, 0, -8, 2, -4, 16, -4, 0, 22, -28, 0, 6, 1, 0, 0, -4, 8, 24, -8, -1, 14, 0, 20, -10, 0, 10, -16, -8, 0, -2, -4, 2, 12, -16, 10, 0, 2, -1, 40, 2, -24, -4, 0, 4, 10, 26, 1, 0, -30, 0, 32, -10, 16, 26, 12, 2, 0, 0, -2, -12, -48, 8, 4, 0, 6, 0, -24, -2, -4, -2, 0, 5, 28, -1, -16, 10, -4, 0, 12, 10, 10, -8, -8, -8, 0, 4, 4, -12, 16, -28, 0, 0, 20, 0, 9, 0, -30, 2, 0, 1, 4, -2, 16, -12, 0, 0, 6, 4, 22, -10, 4, 12, 0, -8, 8, 4, -23, 12, -12, 0, -20, -6, -8, -12, 12, -6, 0, -2, -10, -16, 14, -1, -20, 0, -12, 10, 10, 4, 40, 0, 0, 30, 4, 4, -34, -8, 24, 0, -4, -6, -36, 0, 4, -12, 0, 0, -6, 8, 28, -8, 16, 0, 0, 1, -2, 1, -18, -20, 0, -14, -24, -10, 4, 26, 20, 0, 32, -24, -14, -2, 14, 4, 0, -10, 0, 0, -8, 1, 6, 0, -12, 24, 10, -10, 24, -4, 0, 20, 0, -1, 38, 12, 20, 0, -6, -8, 20, -16, 0, 0, 0, -2, -19, -10, -16, 2, 2, 0, -24, -8, 28, 6, 0, -6, 0, 40, 0, 2, 2, 4, 28, 0, -24, 4, 40, 1, 48, -2, 0, 4, 6, 10, 24, -10, -10, 0, 36, 8, -6, -20, 2, -4, 0, -2, 0, -16, 16, -24, -40, 0, -46, -14, 1, -9, -46, -2, 0, -2, 4, 32, -20, -4, 20, 0, -26, 12, 12, 0, 28, -6, 0, 28, 8, 10, 10, -14, -26, 0, 46, -2, 8, -4, 0, 30, 0, 12, 46, 0, -8, 6, 0, 0, -16, -12, 0, -24, -40, 2, 0, -3, 2, -14, 10, -5, 8, 0, 1, -20, -12, -10, -46, -24, 0, 0, 48, -10, 52, -4, 8, 0, -16, 8, -20, 6, -4, 4, 0, 12, 8, 0, 28, -20, 48, 0, -10, -4, 0, -8, 6, 0, 0, -16, -2, 16, -24, -1, 30, 0, 2, 18, -38, 12, 8, 14, 0, -26, 40, -4, 0, 0, 10, 0, 4, -12, -4, 14, 8, -16, 0, -4, 20, 26, -12, 0, -14, 0, 0, -1, 6, -14, 40, 12, 0, -16, 6, 10, -22, 2, 20, 0, 16, 8, 8, 1, -48, -26, 0, -20, -34, -10, 32, 8, -4, 0, -20, 0, 34, -8, -30, 2, 0, -4, -32, 16, 8, -4, 0, 0, 71, 22, 6, -28, -18, 0, 0, 6, 12, 1, 0, 0, 2, 0, -8, -4, 6, 8, 36, 24, 0, -8, -32, -1, -12, 14, -1, 0, 32, 20, -24, -10, 14, 0, 0, 10, 22, -16, -26, -8, -2, 0, 36, -2, 24, -4, 48, 2, 0, 12, -4, -16, 0, 10, -24, 0, 0, 2, 80, -1, -6, 40, 0, 2, -28, -24, 28, -4, 10, 0, 8, 4, 16, 10, -20, 26, 0, 1, 24, 0, -12, -30, 0, 0, 2, 32, 8, -10, -2, 16, 0, 26, 0, 12, 8, 2, 22, 0, 10, 0, 10, -2, 0, -12, 0, -48, -28, 8, -20, 4, -6, 0, -6, 6, -32, 0, -40, -24, 0, -2, 33, -4, -4, -2, 36, 0, -8, 5, -4, 28, 4, -1, 0, -16, 2, 10, -46, -4, -24, 0, -10, 12, -48, 10, 28, 10, 0, -8, 0, -8, -40, -8, 20, 0, 0, 4, 2, 4, 2, -12, 0, 16, 12, -28, 24, 0, -24, 0, 34, 20, 14, 0, 34, 9, 0, 0, 2, -30, 12, 2, 50, 0, -32, 1, 10, 4, -16, -2, 0, 16, 32, -12, -54, 0, 0, 0, -10, 6, 16, 4, -28, 22, 0, -10, 32, 4, 14, 12, 54, 0, 28, -8, 2, 8, -56, 4, 0, -23, -30, 12, -50, -12, -24, 0, 0, -20, -56, -6, 18, -8, 0, -12, 20, 12, -12, -6, 24, 0, -8, -2, 0, -10, 3, -16, 0, 14, 16, -1, 5, -20, 12, 0, -2, -12, 20, 10, -42, 10, 0, 4, 24, 40, 32, 0, -4, 0, 10, 30, -38, 4, -40, 4, 0, -34, -32, -8, 22, 24, -6, 0, 48, -4, -4, -6, -12, -36, 0, 0, 26, 4, 20, -12, -32, 0, -8, 0, 4, -6, 12, 8, 0, 28, 0, -8, 52, 16, 16, 0, -16, 0, -8, 1, 62, -2, 0, 1, 12, -18, -40, -20, -12, 0, 44, -14, 52, -24, 26, -10, 0, 4, 36, 26, 0, 20, 0, 0, 16, 32, 12, -24, 2, -14, 0, -2, 16, 14, 4, 4, 100, 0, -26, -10, 6, 0, 0, 0, 0, -8, 40, 1, -46, 6, 14, 0, -4, -12, 0, 24, 16, 10, 0, -10, -42, 24, -2, -4, -18, 0, 0, 20, -8, 0, 56, -1, 0, 38, 26, 12, -42, 20, -24, 0, 10, -6, -16, -8, -22, 20, 0, -16, 10, 0, -8, 0, 8, 0, -120, -2, 30, -19, 4, -10, 0, -16, -56, 2, 4, 2, 36, 0, 28, -24, -22, -8, 0, 28, 0, 6, 0, 0, 80, -6, 48, 0, -1, 40, -30, 0, -16, 2, 0, 2, 36, 4, -4, 28, -8, 0, -6, -24, -12, 4, 8, 40, 0, 1, 2, 48, -14, -2, 42, 0, 16, 4, -20, 6, -28, 10, 0, 24, 0, -10, 20, -10, -16, 0, 16, 36, -32, 8, -26, -6, 0, -20, -6, 2, 64, -4, 4, 0, 24, -2, -96, 0, -12, -16, 0, 16, 16, -24, -10, -40, 8, 0, -12, -46, -2, -14, 0, 1, 0, -9, -40, -46, -32, -2, 0, 0, 24, -2, -18, 4, 0, 32, 0, -20, -16, -4, -33, 20, -10, 0, 14, -26, 48, 12, -1, 12, 0, 0, -26, 28, 30, -6, 60, 0, 40, 28, -32, 8, -8, 10, 0, 10, -16, -14, 0, -26, 0, 0, -12, 46, 0, -2, -12, 8, 0, -4, 66, 0, 4, 30, 2, 0, -24, 12, -20, 46, 48, 0, 0, -8, 56, 6, -4, 0, 12, 0, -58, -16, -6, -12, -42, 0, 0, -24, 24, -40, -56, 2, -48, 0, 4, -3, 2, 2, -8, -14, 0, 10, -52, -5, -34, 8, -28, 0, 0, 1, -20, -20, 16, -12, 0, -10, 52, -46, 4, -24, 4, 0, -16, 0, -12, 48, 12, -10, 0, 52, -10, -4, -54, 8, 4, 0, 8, -16, 16, 8, 30, -20, 0, 6, -66, -4, 0, 4, -4, 0, 12, 12, 32, 8, -16, 0, 0, 28, -40, -20, 0, 48, -40, 0, -6, -10, -20, -4, 20, 0, 0, -8, -9, 6, -76, 0, -10, 0, 30, -16, -16, -2, -28, 16, 0, -24, 24, -1, -60, 30, -4, 0, 0, 2, 56, 18, -16, -38, 0, 12, -50, 8, 0, 14, -2, 0, 0, -26, -6, 40, 0, -4, 0, 0, -22, 0, -20, 10, -40, 0, -4, 4, -68, -12, 10, -4, 0, 14, 16, 8, 12, -16, -8, 0, -16, -4, 12, 20, 23, 26, 0, -12, -24, 0, 12, -14, 80, 0, -2, 0, 20, -1, -50, 6, 0, -14, 8, 40, -72, 12, -10, 0, -12, -16, -14, 6, 8, 10, 0, -22, -12, 2, 14, 20, 10, 0, -24, 16, -28, 8, -14, 8, 0, 1, 0, -48, 20, -26, 18, 0, 40, -20, 12, -34, -48, -10, 0, 32, -10, 8, -14, -4, 0, 0, -40, -20, -40, 0, 6, 34, 0, -8, -96, -30, -24, 2, -4, 0, -44, -4, -30, -32, 34, 16, 0, 8, 12, -4, -24, 0, 0, 0, 59, 71, 4, 22, -28, 6, 0, -28, 36, -18, -24, 0, -70, 0, -4, 6, -2, 12, -52, 1, 0, 0, 24, 0, 64, 2, 6, 0, 30, -8, 120, -4, -28, 6, 0, 8, -10, 36, -16, 24, 6, 0, 60, -8, 0, -32, -8, -1, 0, -12, 2, 14, 6, -1, 56, 0, 18, 32, 0, 20, 10, -24, 0, -10, -28, 14, -12, 0, 24, 0, -8, 10, -26, 22, -4, -16, 0, -26, -48, -8, -20, -2, -120, 0, 60, 36, -32, -2, -100, 24, 0, -4, 14, 48, 0, 2, 14, 0, -14, 12, 20, -4, -40, -16, 0, 0, -20, 10, -18, -24, 0, 0, -16, 0, -48, 2, 8, 80, 0, -1, 74, -6, -6, 40, -6, 0, 8, 2, 12, -28, -36, -24, 0, 28, -10, -4, 0, 10, 4, 0, -24, 8, 48, 4, 10, 16, 0, 10, 96, -20, -16, 26, 0, 0, -48, 1, 64, 24, -38, 0, 0, -12, -56, -30, -20, 0, -80, 0, 101, 2, 6, 32, 10, 8, 0, -10, -20, -2, 36, 16, -54, 0, 0, 26, 12, 0, -28, 12, 0, 8, -48, 2, 2, 22, 19, 0, 30, 10, -24, 0, 16, 10, 0, -2, -40, 0, -2, -12, -34, 0, -80, -48, 24, -28, -8, 8, 0, -20, -28, 4, -26, -6, 24, 0, 0, -6, 44, 6, 0, -32, 0, 0, 58, -40, 32, -24, 0, 0, -40, -2, -2, 33, -2, -4, 0, -4, 0, -2, -28, 36, -28, 0, -26, -8, 24, 5, -20, -4, 0, 28, -40, 4, 120, -1, -52, 0, -48, -16, 42, 2, -48, 10, 0, -46, 0, -4, -32, -24, -6, 0, -12, -10, 48, 12, -24, -48, 0, 10, 48, 28, 10, 10, 26, 0, 8, -8, -36, 0, 4, -8, 0, -40, 6, -8, 52, 20, -68, 0, -2, 0, 56, 4, 22, 2, 0, 4, -18, 2, -56, -12, 0, 0, -12, 16, -28, 12, -16, -28, 0, 24, -68, 0, 40, -24, -32, 0, -14, 34, 46, 20, 0, 14, 0, 0, -1, 34, 60, 9, 58, 0, 46, 0, 16, 2, 16, -30, 0, 12, -40, 2, 4, 50, -4, 0, -52, -32, 0, 1, 20, 10, 0, 4, -58, -16, -20, -2, -5, 0, 0, 16, 26, 32, -24, -12, 0, -54, -12, 0, 78, 0, 40, 0, -28, -10, 4, 6, 96, 16, 0, 4, -30, -28, 84, 22, -8, 0, -88, -10, -42, 32, -10, 4, 0, 14, -8, 12, 26, 54, -84, 0, 64, 28, -46, -8, 44, 2, 0, 8, -8, -56, 8, 4, -34, 0, 0, -23, 100, -30, 8, 12, 0, -50, -72, -12, 12, -24, -46, 0, 18, 0, 12, -20, 8, -56, 0, -6, -22, 18, 0, -8, 66, 0, -16, -12, 16, 20, -8, 12, 0, -12, 0, -6, -54, 24, -16, 0, 40, -8, 0, -2, 46, 0, 0, -10, 28, 3, -56, -16, -2, 0, -32, 14, -60, 16, -10, -1, 0, 5, 20, -20, -8, 12, 24, 0, 0, -2, -1, -12, 0, 20, 0, 10, 12, -42, -32, 10, -44, 0, 46, 4, 0, 24, 84, 40, 0, 32, 24, 0, -47, -4, -48, 0, 78, 10, -8, 30, -52, -38, 0, 4, 22, -40, -8, 4, -6, 0, -12, -34, 16, -32, 0, -8, 0, 22, 20, 24, 38, -6, 40, 0, 4, 48, 76, -4, 4, -4, 0, -6, -12, -12, -20, -36, -8, 0, 80, 0, -20, 26, -28, 4, 0, 20, 80, -12, -48, -32, -12, 0, 78, -8, 10, 0, 78, 4, 0, -6, 0, 12, 72, 8, -10, 0, -6, 28, 20, 0, 0, -8, 0, 52, 80, 16, 6, 16, 2, 0, -70, -16, -20, 0, 24, -8, 0, 1, -60, 62, -30, -2, -14, 0, 56, 1, -2, 12, 64, -18, 0, -40, 38, -20, 112, -12, 0, 0, -8, 44, -24, -14, -10, 52, 0, -24, 46, 26, 24, -10, -40, 0, 36, 4, 66, 36, 0, 26, 0, 0, 60, 20, -10, 0, 40, 0, -28, 16, -4, 32, 34, 12, 0, -24, 4, 2, -4, -14, -96, 0, -8, -2, 0, 16, -4, 14, 0, 4, 48, 4, 26, 100, -20, 0, 14, -26, 8, -10, 12, 6, 0, 0, 22, 0, 14, 0, 70, 0, -48, -8, 0, 40, -32, 1, 0, -46, -6, 6, -8, 14, 40, 0, -40, -4, 20, -12, 0, 0, 0, 24, -78, 16, 120, 10, -6, 0, 40, -10, -14, -42, 22, 24, 0, -2, 8, -4, -20, -18, -32, 0, -66, 0, -16, 20, -58, -8, 0, 0, -8, 56, -32, -1, 64, 0, 48, 38, 64, 26, 24, 12, 0, -42, -36, 20, 0, -24, 34, 0, 20, 10, -84, -6, -32, -16, 0, -8, -86, -22, 4, 20, -6, 0, 24, -16, 20, 10, -32, 0, 0, -8, -34, 0, -48, 8, 0, 0, 30, -120, 8, -2, 16, 30, 0, -19, -100, 4, -24, -10, 32, 0, 0, -16, 36, -56, -8, 2, 0, 4, 0, 2, 0, 36, -104, 0, -22, 28, -71, -24, -10, -22, 0, -8, -6, 0, -12, 28, 10, 0, 18, 6, -144, 0, -28, 0, 0, 80, -72, -6, -60, 48, -12, 0, 6, -1, 72, 40, 0, -30, 0, 0, -58, -16, -2, 2, 28, 0, -104, 2, 8, 36, -24, 4, 0, -4, -6, 28, 32, -8, -8, 0, -36, -6, 12, -24, -60, -12, 0, 4, 0, 8, 0, 40, 32, 0, 24, 1, -34, 2, 12, 48, 0, -14, 0, -2, 1, 42, -40, 0, 44, 16, -32, 4, 14, -20, 0, 6, 24, -28, 8, 10, -58, 0, -14, 24, 10, 0, 120, -10, 0, 20, 0, -10, 0, -16, -22, 0, -54, 16, 16, 36, 26, -32, 0, 8, -16, -26, 2, -6, -46, 0, -48, -20, -36, -6, 8, 2, 0, 64, -24, -4, 18, 4, -4, 0, -48, 24, -64, -2, -40, -96, 0, 0, -2, -12, 80, -16, 4, 0, 4, 16, -86, 16, 0, -24, 0, -10, -36, -40, 24, 8, -64, 0, -62, -12, 0, -46, -78, -2, 0, -14, -80, 0, -36, 1, 20, 0, 6, -9, -20, -40, -20, -46, 0, -32, 72, -2, -54, 0, 28, 0, 32, 24, 32, -2, -28, -18, 0, 4, 10, 0, -10, 32, 22, 0, 92, -20, -8, -16, -24, -4, 0, -33, -16, 20, 38, -10, -56, 0, 20, 14, 120, -26, -54, 48, 0, 12, 66, -1, 80, 12, -24, 0, -48, 0, 112, -26, 12, 28, 0, 30, 32, -6, 0, 60, -4, 0, 0, 40, -2, 28, -58, -32, 0, 8, -8, -8, 0, 10, -68, 0, 2, 10, 90, -16, 80, -14, 0, 0, 48, -26, -50, 0, 0, 0, -14, -12, -20, 46, -8, 0, 0, -2, -17, -12, -22, 8, -140, 0, -72, -4, -10, 66, 92, 0, 0, 4, -10, 30, -2, 2, 8, 0, 0, -24, 40, 12, 46, -20, 0, 46, -10, 48, 16, 0, 28, 0, 76, -8, -12, 56, 20, 6, 0, -4, -44, 0, 6, 12, 56, 0, 42, -58, 6, -16, -22, -6, 0, -12, 32, -42, 0, 0, -96, 0, 40, -24, 9, 24, 0, -40, 0, -56, -24, 2, -144, -48, -33, 0, -4, 4, -80, -3, 4, 2, 0, 2, 32, -8, -36, -14, 78, 0, -32, 10, 8, -52, 56, -5, 0, -34, 4, 8, 14, -28, 0, 0, -4, 0, -48, 1, -14, -20, 0, -20, 0, 16, 16, -12, -2, 0, 40, -10, -100, 52, 46, -46, 0, 4, 40, -24, 24, 4, 4, 0, 6, -16, 10, 0, 64, -12, 0, 48, 48, 12, -8, -10, -26, 0, -28, 52, 18, -10, 24, -4, 0, -54, 36, 8, 28, 4, 0, 0, -54, 8, 52, -16, 40, 16, 0, 8, 52, 30, -20, -20, 64, 0, -8, 6, 0, -66, -80, -4, 0, 0, -2, 4, 100, -4, -16, 0, -2, 12, -16, 12], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "102.2.a.c", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0], [1], [1], [-1], [1], [2], [-1], [0], [1], [1], [2], [-4], [-1], [2], [0], [-2], [1], [-1], [1], [-4], [2], [0], [-4], [0], [-1], [-1], [2], [-1], [0], [-10], [-2], [-8], [1], [4], [-1], [0], [1], [-2], [-4], [-2], [2], [-10], [0], [12], [-4], [2], [0], [0], [-1], [0], [-1], [1], [2], [6], [-1], [-8], [0], [4], [-10], [-12], [-2], [10], [-8], [0], [1], [4], [4], [-12], [-1], [0], [0], [0], [1], [-10], [-2], [1], [-4], [0], [-2], [-8], [2], [1], [-10], [-4], [0], [-2], [12], [10], [-4], [6], [2], [0], [0], [8], [0], [-8], [-1], [14], [0], [-4], [-1]]}