# Stored data for newform 4650.2.a.r, downloaded from the LMFDB on 29 March 2024. {"label": "4650.2.a.r", "space_label": "4650.2.a", "level": 4650, "weight": 2, "hecke_orbit": 18, "hecke_orbit_code": 76561193698857514, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1573799583384929343, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[7, [0, 1]], [11, [6, 1]], [13, [-2, 1]], [19, [0, 1]]], "qexp_display": "q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 18600, "fricke_eigenval": 1, "atkin_lehner_string": "+-+-", "analytic_conductor": 37.130436939895375, "hecke_ring_index": 1, "level_radical": 930, "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": "0.022", "prec": 17}, "analytic_rank_proved": true, "char_values": [4650, 1, [3101, 2977, 1801], [1, 1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 3, 5, 31], "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": "1.013", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.026", "prec": 17}, {"__RealLiteral__": 0, "data": "0.023", "prec": 17}, {"__RealLiteral__": 0, "data": "5.086", "prec": 17}], "related_objects": ["EllipticCurve/Q/4650/r"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [3, -1], [5, 1], [31, -1]], "trace_display": [-1, 1, 0, 0], "traces": [0, 1, -1, 1, 1, 0, -1, 0, -1, 1, 0, -6, 1, 2, 0, 0, 1, 4, -1, 0, 0, 0, 6, -2, -1, 0, -2, 1, 0, -8, 0, 1, -1, -6, -4, 0, 1, 6, 0, 2, 0, -2, 0, -4, -6, 0, 2, -4, 1, -7, 0, 4, 2, 6, -1, 0, 0, 0, 8, 0, 0, 4, -1, 0, 1, 0, 6, 4, 4, -2, 0, -8, -1, 4, -6, 0, 0, 0, -2, -4, 0, 1, 2, 0, 0, 0, 4, -8, 6, -2, 0, 0, -2, 1, 4, 0, -1, -14, 7, -6, 0, 2, -4, -16, -2, 0, -6, -12, 1, -10, 0, 6, 0, -6, 0, 0, -8, 2, 0, 0, 0, 25, -4, -2, 1, 0, 0, -14, -1, -4, 0, 0, -6, 0, -4, 0, -4, -8, 2, -2, 0, -4, 8, -12, 1, 0, -4, -7, 6, -14, 0, 12, 0, 4, 0, 0, 2, 2, 4, 6, 0, 0, -1, 4, -2, 0, 0, 10, 0, -9, 0, 0, -4, -14, 8, 0, -6, 0, 2, -2, 0, 8, 0, 4, 2, 0, -1, -24, -4, 0, 0, -8, 1, 18, 14, 0, -7, 18, 6, -20, 0, 4, -2, 0, 4, 0, 16, -2, 2, 0, 0, -4, 6, -8, 12, 0, -1, 0, 10, 4, 0, 8, -6, -18, 0, 0, 6, -12, 0, 16, 0, 0, 8, -6, -2, 0, 0, -4, 0, -24, 0, 18, -25, 1, 4, 0, 2, 0, -1, 0, 0, 18, 0, 12, 14, 0, 1, 26, 4, 0, 0, -8, 0, -18, 6, 0, 0, -2, 4, -16, 0, 16, 4, 0, 8, 0, -2, -18, 2, 1, 0, -26, 4, 12, -8, 0, 12, 0, -1, -1, 0, -14, 4, 30, 7, 0, -6, -6, 14, -4, 0, 0, -12, 2, 0, 0, -4, -4, 0, -16, 0, -24, -2, 12, -2, 0, -4, 26, -6, 48, 0, -12, 0, 0, 1, 0, -4, -10, 2, 0, 0, -18, 0, 6, -10, 0, 0, 8, 9, -6, 0, -6, 0, 0, 4, 0, 14, -16, -8, -30, 0, 2, 6, 0, 0, 0, -2, 0, 2, 24, 0, -19, -8, 25, 0, 0, -4, 10, -2, -2, 0, 0, 1, -18, 24, 0, 4, -16, 0, -24, 0, -14, 8, -6, -1, 0, -18, -4, -14, -20, 0, -8, 7, 0, -18, 0, -6, -38, 20, 0, 0, -26, -4, 2, 2, 0, 0, -36, -4, 14, 0, -8, -16, 0, 2, 0, -2, -2, 0, 0, 0, 26, 4, -4, -6, 0, 8, 0, -12, -12, 0, 40, 1, 28, 0, 0, -10, 0, -4, 0, 0, -7, -8, -12, 6, 0, 18, -14, 0, 14, 0, 12, -6, 12, 12, 0, 0, 8, -16, 4, 0, 0, 0, 14, -8, 0, 6, 36, 2, 0, 0, 2, 0, 24, 4, 0, 0, 6, 24, 24, 0, 12, -18, 0, 25, 0, -1, 34, -4, 4, 0, -34, -2, -32, 0, 0, 1, 0, 0, -38, 0, 10, -18, 16, 0, 0, -12, -9, -14, -36, 0, 0, -1, 0, -26, 0, -4, 24, 0, -14, 0, 6, 8, -20, 0, 0, 18, 4, -6, -19, 0, 0, 0, -4, 2, 0, -4, -2, 16, 42, 0, -2, -16, 8, -4, 0, 0, 44, -8, 4, 0, 0, 2, 0, 18, 0, -2, -38, -1, -8, 0, -24, 26, -44, -4, 0, -12, 0, 8, -2, 0, -38, -12, -8, 0, 0, 1, 38, 1, 18, 0, 0, 14, -36, -4, 0, -30, -32, -7, 0, 0, 18, 6, -34, 6, 0, -14, -20, 4, 48, 0, 30, 0, 4, 12, 0, -2, 28, 0, 0, 0, -8, 4, 22, 4, 0, 0, 6, 16, -26, 0, -2, 24, 0, 2, 0, -12, 0, 2, 24, 0, 8, 4, -4, -26, 0, 6, -14, -48, -8, 0, -22, 12, 44, 0, 0, 0, 18, -1, 0, 0, 0, 4, -34, 10, 0, -2, 4, 0, -16, 0, -26, 18, 8, 0, 0, -6, 16, 10, -18, 0, -24, 0, -32, -8, 0, -9, -6, 6, 0, 0, -12, 6, 4, 0, 0, 0, 16, -4, 12, 0, 44, -14, 0, 16, 0, 8, -8, 30, -6, 0, 30, -2, 0, -6, 0, 0, 0, 0, -4, 0, -4, 2, -2, 0, 0, -2, -24, -24, 20, 0, 0, 19, 18, 8, 0, -25, 12, 0, 1, 0, -16, 4, -6, -10, 0, 2, -24, 2, -2, 0, 0, 0, 22, -1, 0, 18, 0, -24, 0, 0, -8, -4, 18, 16, 0, 0, -2, 24, 12, 0, -18, 14, 0, -8, 0, 6, 0, 1, 30, 0, 26, 18, -26, 4, 0, 14, 0, 20, 0, 0, 48, 8, -8, -7, 0, 0, 8, 18, -18, 0, 0, 6, 8, 38, 0, -20, -2, 0, -16, 0, -2, 26, -24, 4, 0, -2, -16, -2, -46, 0, 24, 0, 16, 36, 0, 4, 0, -14, 0, 0, 16, 8, -6, 16, 0, 0, -32, -2, -32, 0, -18, 2, -28, 2, 0, 0, 1, 0, 0, 0, 35, -26, -26, -4, 0, 4, 0, 6, 12, 0, -12, -8, -10, 0, 0, 12, 18, 12, -22, 0, 0, -40, -22, -1, 0, -28, -1, 0, 24, 0, 8, 10, -14, 0, 0, 4, 50, 0, 30, 0, 38, 7, -20, 8, 0, 12, 4, -6, 0, 0, -6, -18, 0, 14, 0, 0, -4, -14, -8, 0, 24, -12, 0, 6, 0, -12, -44, -12, 2, 0, -16, 0, 0, -8, 0, 16, 0, -4, 16, 0, -4, 0, -16, 0, 0, -14, -16, 8, 46, 0, 0, -6, -24, -36, 0, -2, -14, 0, 12, 0, 52, -2, 4, 0, 0, -24, 12, -4, 8, 0, 26, 0, -8, -6, 0, -24, 48, -24, 0, 0, 1, -12, -12, 18, 0, 0, -6, -25, 0, 0, 36, 1, 0, -34, 0, 4, -26, -4, 12, 0, -10, 34, -10, 2, 0, 32, 0, 0, 8, 0, 20, -1, -18, 0, 0, 0, -18, 38, 6, 0, 0, -10, 0, 18, 0, -16, 0, 0, -46, 0, 8, 12, 46, 9, 0, 14, -6, 36, 30, 0, 32, 0, -6, 1, 0, 0, -8, 26, 0, 0, 16, 4, 42, -24, 0, 0, 16, 14, 24, 0, -16, -6, 0, -8, 0, 20, -30, 0, 30, 0, -20, -18, 2, -4, 0, 6, 0, 19, 0, 0, -26, 0, 44, 0, 0, 4, 84, -2, 0, 0, 0, 4, -48, 2, 0, -16, 24, -42, 0, 0, 8, 2, -19, 16, 0, -8, 12, 4, 25, 0, 22, 0, -26, -44, 0, 8, 56, -4, 0, 0, 10, 0, -16, -2, 0, 0, -2, -18, 36, 0, -12, 2, 0, 38, 0, 1, 46, 8, -18, 0, 0, 24, 4, -26, 0, 44, 14, 4, -18, 0, -16, 12, 96, 0, 0, -8, -24, 2, 16, 0, 0, 38, -14, 12, 0, 8, 6, 0, -6, 0, 48, -1, -20, -38, 0, -1, -4, -18, 0, 0, -4, 0, 36, -14, 0, 36, -20, 4, 0, 0, -14, 30, -8, 32, 0, 7, 72, 0, 0, 0, 48, -18, 0, -6, 0, 34, 28, -6, 16, 0, -38, 14, 60, 20, 0, -4, 0, -48, 60, 0, 22, -30, -26, 0, 0, -4, -32, -12, 2, 0, 0, 2, -62, -28, 0, 0, 54, 0, -12, 0, -36, 8, 12, -4, 0, -22, 14, -4, 26, 0, -40, 0, -8, -6, 0, -16, -26, 26, 0, 0, 16, 2, 36, -24, 0, 0, 32, -2, 58, 0, -2, 12, 0, 0, 0, -2, 0, -24, -60, 0, -28, -8, 26, -4, 0, 4, 0, 26, -4, 0, -2, -6, 0, 14, 0, 48, 10, 8, 16, 0, 0, 22, -12, -12, 0, -44, -12, 0, 34, 0, -36, 0, 40, -18, 0, 1, 36, 0, 28, 0, 12, 0, -28, -4, 0, 34, 44, -10, 0, 0, 0, 2, 4, -4, 0, 0, 0, 16, -4, 0, 10, 26, -7, -18, 0, -8, 8, 0, -12, 0, -84, 6, -4, -16, 0, -10, 0, 18, -32, 0, -14, 24, -16, 0, 0, 32, 14, 8, 0, 0, 0, 9, 12, 6, 0, -6, 0, 0, 12, 0, 34, 12, 32, -6, 0, -4, -14, 0, -1, 0, 8, 0, 46, -16, 0, 4, 4, -12, 0, 0, -60, -44, 0, 14, 0, 0, 0, -16, 14, 0, -24, -8, 0, 8, 0, -30, 84, 6, 56, 0, 36, -30, -8, 2, 0, 0, 0, 6, -14, 0, 0, 0, 2, 0, 0, 0, -20, 4, 24, 0, 56, 4, 16, -2, 0, 2, 52, 0, 20, 0, 6, 2, 62, 24, 0, 24, 24, -20, -32, 0, 0, 0, 12, -19, 0, -18, -42, -8, 0, 0, -28, 25, -46, -12, 0, 0, -4, -1, -20, 0, 34, 16, 0, -4, 0, 6, 4, 10, -12, 0, -24, -2, -34, 24, 0, -2, 0, 2, -32, 0, 54, 0, 40, 0, 0, -22, -38, 1, 30, 0, 0, -18, 42, 0, 0, 24, -38, 0, 46, 0, 0, 8, 10, 4, 0, -18, 48, -16, 16, 0, -72, 0, -8, 2, 0, -24, -12, -12, -7, 0, -9, 18, -12, -14, 0, 0, -36, 8, 12, 0, -46, -6, 0, 0, 0, -1, -48, -30, 0, 0, -8, -26, -26, -18, 0, 26, 0, -4, -20, 0, 24, -14, 20, 0, 0, -20, -14, 0, 48, 0, 0, -48, 6, -8, 0, 8, 70, 7, -20, 0, -62, 0, 50, -8, 0, -18, 0, 18, -46, 0, 4, 0, -16, -6, 0, -8, -19, -38, 0, 0, -24, 20, 0, 2, 0, 0, 14, 16, -4, 0, 66, 2, 0, -26, 0, 24, -62, -4, -26, 0, -2, 2, -30, 16, 0, 2, 42, 46, -60, 0, 38, -24, -2, 0, 0, -16, -68, -36, 8, 0, 0, -4, 16, 0, 0, 14, -22, 0, 84, 0, 44, -16, 6, -8, 0, 6, 4, -16, -56, 0, -28, 0, 0, 32, 0, 2, 42, 32, 0, 0, -72, 18, 36, -2, 0, 28, -44, -2, -56, 0, -38, 0, 0, -1, 0, 0, -8, 0, -8, 0, -37, -35, -24, 26, 0, 26, 0, 4, -44, 0, 0, -4, -2, 0, 0, -6, 28, -12, 20, 0, 0, 12, 0, 8, 0, 10, -2, 0, -30, 0, 0, -12, -38, -18, 0, -12, 8, 22, -8, 0, -58, 0, 44, 40, 0, 22, -12, 1, 0, 0, 38, 28, 10, 1, 0, 0, 18, -24, -24, 0, 82, -8, 0, -10, 0, 14, -80, 0, -36, 0, -64, -4, -20, -50, 0, 0, 0, -30, -12, 0, -32, -38, 8, -7, 0, 20, 0, -8, -32, 0, 0, -12, 18, -4, 0, 6, -62, 0, -34, 0, -16, 6, 28, 18, 0, 0, 68, -14, 76, 0, -20, 0, -24, 4, 0, 14, 48, 8, 0, 0, -66, -24, 30, 12, 0, 0, -4, -6, 4, 0, 78, 12, -42, 44, 0, 12, 8, -2, -48, 0, 28, 16, 4, 0, 0, 0, 0, 8, 0, 0, 0, -16, -8, 0, 0, 4, -60, -16, 22, 0, 0, 4, 0, 0, 0, 16, -56, 0, -27, 0, 6, 14, -40, 16, 0, -8, -26, -46, 54, 0, -10, 0, -2, 6, 0, 24, -28, 36, 0, 0, 0, 2, -68, 14, 0, 0, 42, -12, 8, 0, 0, -52, 0, 2, 0, -4, 24, 0, 42, 0, 4, 24, 8, -12, 0, 4, 0, -8, -4, 0, -2, -26, 84, 0, 0, 8, -4, 6, 0, 0, -14, 24, 24, -48, 0, 24, -8, 0, 0, 0, -24, -1, -22, 12, 0, 12, 8, -18, 44, 0, -84, 0, -26, 6, 0, 25, -28, 0, 0, 0, 18, -36, -32, -1, 0, 0, 0, 34, 68, 0, -48, -4, 0, 26, 0, 4, 0, -12, -34, 0, 36, 10, 24, -34, 0, 10, 0, -2, 12, 0, 4, -32, 26, 0, 0, 0, -16, -8, -34, 0, 0, -20, -26, 1, 0, 18, 0, 0, 8, 0, -48, 0, -26, 18, 0, -38, -22, -6, -8, 0, 16, 0, 12, 10, 0, 0, -18, -18, 14, 0, 30, 16, -24, 0, 0, 0, 34, 46, -32, 0, 16, -8, 0, -12, 0, -46, -68, -9, 22, 0, -6, -14, 0, 6, 0, -36, 0, -30, 84, 0, 4, -32, -12, 0, 0, 6, 4, -1, 4, 0, 0, 0, 54, 8, 0, -26, 100, 0, 64, 0, 16, -16, 14, -4, 0, -42, 12, 24, -52, 0, 0, 0, 44, -16, 0, -14, 4, -24, 0, 0, 10, 16, -48, 6, 0, 0, -84, 8, -82, 0, -8, -20, 0, 30, 0, 0, -6, -30, 6, 0, 48, 20, 30, 18, 0, -2, 28, 4, 0, 0, 84, -6, -6, 0, 0, -19, -32, 0, 8, 0, 0, 26, -108, 0, 0, -44, -4, 0, 18, 0, -70, -4, -4, -84, 0, 2, 12, 0, -2, 0, 2, 0, 76, -4, 0, 48, 0, -2, 0, 0, -24, 16, -6, -24, 0, 42, 20, 0, -56, 0, 10, -8, 0, -2, 0, 19, -108, -16, 18, 0, 20, 8, -12, -12, 0, -4, 0, -25, 80, 0, 12, -22, 0, 0, 0, 26, 1, 44, 120, 0, 0, -8, -16, -56, 0, 4, -44, 0, -6, 0, -8, -10, -4, 0, 0, 16, -78, 2, -31, 0, -24, 0, -50, 2, 0, 18, -2, -36, 0, 0, -50, 12, 0, -2, 0, 0, 0, -38, 22, 0, 28, -1, 0, -46, 0, -8, -74, 18, -16, 0, 0, 0, 60, -24, 0, -4, 0, 26, -28, 0, -52, -44, -8, -14, 0, -4, 24, 18, 18, 0, 0, 16, 4, -12, 0, -96, 60, 0, 52, 0, -2, 8, -54, 24, 0, -2, 12, -16, -24, 0, -26, 0, -18, -38, 0, 14, 58, -12, 0, 0, 32, -8, 10, -6, 0, 0, -16, 6, 0, 0, 0, -48, 28, 1, 0, 20, 30, 38, -72, 0, -4, 1, 26, 4, 0, 18, 0, 0, -26, 0, 24, 4, -4, 0, 0, -36, -4, 14, -32, 0, 0, -36, 66, 20, 0, -4, 0, 0, 24, 0, -42, 14, 48, -30, 0, 8, -80, -32, -8, 0, -24, -7, 16, -72, 0, 0, 6, 0, 0, 0, 8, -48, -8, 18, 0, 0, -18, 6, 32, 0, 14, -34, 0, -28, 0, 6, -8, -16, 8, 0, 30, 38, 22, -14, 0, -60, 0, -20, -18, 0, -2, 4, 4, 0, 0, 48, -16, -60, -20, 0, 49, -22, -2, 30, 0, 26, 0, 0, -24, 0, 18, 4, 0, 32, 0, 12, 36, -2, 0, 0, -16, 0, 40, -2, 0, 62, -46, 28, 0, 0, -48, 0, 24, -54, 0, 0, -26, 12, 16, 0, 74, 36, 0, -8, 0, -12, -2, 4, -4, 0, 0, 22, 108, -14, 0, 4, 0, -26, -24, 0, 24, 40, 16, 0, 0, 8, 12, 6, -6, 0, 0, 16, -48, 26, 0, -26, 14, 0, 24, 0, -32, -16, -16, -2, 0, -36, -32, 24, 0, 0, -24, 0, -18, -32, 0, 2, 72, -58, -28, 0, -8, 2, 14, -12, 0, 0, 20, 0, 36, 0, 1, 2, 0, 0, 0, 24, 0, 60, -96, 0, -98, 28, 35, 8, 0, -26, 0, 4, -26, 0, -24, -4, -56, 0, 0, -26, 0, 4, -56, 0, 0, 2, -44, 6, 0, 0, 12, -14, -70, 0, 24, -48, -12, -10, 0, -8, -58, -16, -10, 0, 36, 0, 36, -22, 0, 12, 48, 12, 0, 0, 18, 44, 0, 12, 0, 0, -22, -34, -58, 0, 16, 36, 0, 0, 0, -40, -40, 18, -22, 0, 48, -1, 38, -36, 0, 0, -42, -28, 12, 0, -1, -12, 0, 0, 0, 28, 24, 4, 66, 0, 0, -34, 8, -44, 0, 10, -12, 0, -14, 0, 48, 0, -16, -2, 0, -4, -48, 4, 144, 0, 50, 0, 64, 0, 0, -16, 30, 4, 0, 0, 0, -10, 38, -26, 0, 7, -42, 18, -20, 0, -108, 8, 0, -8, 0, 0, -80, 12, -54, 0, 4, 84, 4, -6, 0, 4, 0, 16, 8, 0, 0, 10, -6, 0, 0, -18, 30, 32, 0, 0, 0, 14, 64, -24, 0, 16, -6, 0, -22, 0, -4, -32, -22, -14, 0, -8, -8, 0, -56, 0, 24, 0, 24, -9, 0, -12, -60, -6, 0, 0, -40, 6, -74, 0, 0, 0, 0, -12, -24, 0, -44, -34, 0, -12, 0, -32, 2, 6, -10, 0, -62, 4, -16, 14, 0, 0, 0, 1, 0, 0, 44, -8, -8, 0, 0, -46, -8, 16, 56, 0, 0, -4, 18, -4, 0, 12, 16, 0, -2, 0, -108, 60, -4, 44, 0, 0, -56, -14, -16, 0, 16, 0, 0, 0, 0, 16, -98, -14, 0, 0, -16, 24, -50, 8, 0, 0, 46, -8, 84, 0, 64, 30, 0, -84, 0, -6, -82, -56, -24, 0, 30, -36, -80, 30, 0, 8, 0, -2, -17, 0, -14, 0, 112, 0, 0, -6, 12, 14, 62, 0, 0, 0, 52, 0, 0, -2, -156, 0, 4, 0, 0, 0, 44, 20, 0, -4, 54, -24, 40, 0, 12, -56, 44, -4, 0, -16, 8, 2, 0, 0, 94, -2, 26, -52, 0, 0, 22, -20, -8, 0, 62, -6, 0, -2, 0, -62, -16, -24, 0, 0, 48, -24, -36, -24, 0, 20, 0, 32, -12, 0, -16, 0, 1, 0, 0, -12, 16, 19, -12, 0, 0, 18, 108, 42, 0, 8, 6, 0, -36, 0, -6, 28, 0, -25, 0, 46, 0, 12, -12, 0, 16, 0, 36, 4, 0, 1, -70, 20, 0, 0, 28, -34, -24, -16, 0, 0, -22, 4, -16, 0, -26, -6, 0, -4, 0, -10, 12, 12, 16, 0, -56, 24, -10, 2, 0, 34, 0, -24, -10, 0, -24, 2, 46, 0, 0, -2, -62, 32, 96, 0, 0, -54, -36, 0, 0, -40, 8, 0, -6, 0, -42, 22, 20, 38, 0, -1, 32, -30, -18, 0, -96, 0, 0, 18, 0, -42, 128, 0, -28, 0, -18, -24, -8, 38, 0, 0, 6, -46, 60, 0], "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": "930.2.a.l", "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], [0], [-1], [0], [-1], [1], [0], [-6], [1], [2], [0], [0], [1], [4], [-1], [0], [0], [0], [6], [-2], [-1], [0], [-2], [1], [0], [-8], [0], [1], [-1], [-6], [-4], [0], [1], [6], [0], [2], [0], [-2], [0], [-4], [-6], [0], [2], [-4], [1], [-7], [0], [4], [2], [6], [-1], [0], [0], [0], [8], [0], [0], [4], [-1], [0], [1], [0], [6], [4], [4], [-2], [0], [-8], [-1], [4], [-6], [0], [0], [0], [-2], [-4], [0], [1], [2], [0], [0], [0], [4], [-8], [6], [-2], [0], [0], [-2], [1], [4], [0], [-1], [-14], [7], [-6], [0]]}