# Stored data for newform 1050.2.a.b, downloaded from the LMFDB on 18 April 2024.
{"label": "1050.2.a.b", "space_label": "1050.2.a", "level": 1050, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503599660925978, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1005077644766038273, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[11, [-2, 1]], [13, [-1, 1]], [17, [3, 1]], [19, [0, 1]]], "qexp_display": "q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 4200, "fricke_eigenval": -1, "atkin_lehner_string": "++-+", "analytic_conductor": 8.38429221223444, "hecke_ring_index": 1, "level_radical": 210, "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": [1050, 1, [701, 127, 451], [1, 1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 3, 5, 7], "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": "1.033", "prec": 17}, {"__RealLiteral__": 0, "data": "0.034", "prec": 17}, {"__RealLiteral__": 0, "data": "2.110", "prec": 17}, {"__RealLiteral__": 0, "data": "0.195", "prec": 17}, {"__RealLiteral__": 0, "data": "5.331", "prec": 17}], "related_objects": ["EllipticCurve/Q/1050/b"], "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], [7, 1]], "trace_display": [-1, -1, 0, -1], "traces": [0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 2, -1, 1, 1, 0, 1, -3, -1, 0, 0, 1, -2, 1, 1, 0, -1, -1, -1, -5, 0, 7, -1, -2, 3, 0, 1, 2, 0, -1, 0, 7, -1, 11, 2, 0, -1, -8, -1, 1, 0, 3, 1, 1, 1, 0, 1, 0, 5, -5, 0, -3, -7, -1, 1, 0, 2, 12, -3, -1, 0, 12, -1, 6, -2, 0, 0, -2, 1, 10, 0, 1, -7, 11, 1, 0, -11, 5, -2, -10, 0, -1, 1, -7, 8, 0, 1, 2, -1, 2, 0, 12, -3, 11, -1, 0, -1, 2, -1, 0, 0, -2, -1, 6, 0, 0, -5, 1, 5, 3, 0, -7, 3, -7, 7, 0, 1, 22, -1, -11, 0, -8, -2, 0, -12, 0, 3, 12, 1, 20, 0, 8, -12, 2, 1, 0, -6, -1, 2, 15, 0, -18, 0, -3, 2, 0, -1, 2, -10, -1, 0, -1, -1, 1, 7, 0, -11, -18, -1, -12, 0, 0, 11, -24, -5, 0, 2, 5, 10, -10, 0, -18, 1, 3, -1, 0, 7, -6, -8, 1, 0, -3, -1, -14, -2, 0, 1, 17, -2, 0, 0, -12, -12, 5, 3, 0, -11, 1, 1, 0, 0, -13, 1, -12, -2, 0, 1, -7, 0, -6, 0, -3, 2, -9, 1, 0, -6, 17, 0, -10, 0, 2, 5, -24, -1, 0, -5, -10, -3, 0, 0, 22, 7, -1, -3, 0, 7, 0, -7, -11, 0, 7, -1, 2, -22, 0, 1, -23, 11, -2, 0, -5, 8, 21, 2, 0, 0, 10, 12, -10, 0, -28, -3, 1, -12, 0, -1, 2, -20, 7, 0, 32, -8, 16, 12, 0, -2, -7, -1, -8, 0, -2, 6, -24, 1, 0, -2, -2, -15, 1, 0, -11, 18, -12, 0, 0, 3, 2, -2, -11, 0, -18, 1, 6, -2, 0, 10, -3, 1, -10, 0, -2, 1, 0, 1, 0, -1, 0, -7, 8, 0, 17, 11, 2, 18, 0, 1, 27, 12, -6, 0, 14, 0, -1, -11, 0, 24, 2, 5, 15, 0, -1, -2, 6, -5, 0, -10, -3, 10, 25, 0, -19, 18, 7, -1, 0, -3, -23, 1, 7, 0, -1, -7, -24, 6, 0, 8, -5, -1, -25, 0, -22, 3, -4, 1, 0, 14, 11, 2, 10, 0, -3, -1, 8, -17, 0, 2, -13, 0, 0, 0, -8, 12, 7, 12, 0, -5, 4, -3, -10, 0, -12, 11, 5, -1, 0, -1, -20, 0, 25, 0, 22, 13, -8, -1, 0, 12, 3, 2, -2, 0, -3, -1, -14, 7, 0, 0, 0, 6, 35, 0, 1, 3, 16, -2, 0, 9, -15, -1, 20, 0, 14, 6, 18, -17, 0, 0, -33, 10, 3, 0, 12, -2, -4, -5, 0, 24, -33, 1, -12, 0, -2, 5, 22, 10, 0, 3, 1, 0, -20, 0, 2, -22, 1, -7, 0, 1, 2, 3, -1, 0, 2, -7, 15, 0, 0, 7, -12, 11, 25, 0, 18, -7, 6, 1, 0, -2, 12, 22, 20, 0, -6, -1, 0, 23, 0, -11, -16, 2, 24, 0, -3, 5, -4, -8, 0, -21, -21, -2, -22, 0, -5, 0, 7, -10, 0, -12, 10, 10, 2, 0, 32, 28, 18, 3, 0, -1, 37, 12, -3, 0, 0, 1, -10, -2, 0, 20, -18, -7, 11, 0, 6, -32, 31, 8, 0, -16, -1, -12, 30, 0, 7, 2, 3, 7, 0, 1, -38, 8, 14, 0, -11, 2, 2, -6, 0, 24, 27, -1, 0, 0, -17, 2, -14, 2, 0, 15, 0, -1, 5, 0, -8, 11, 12, -18, 0, 12, -28, 0, -5, 0, -8, -3, -14, -2, 0, 2, -38, 11, -10, 0, -1, 18, 10, -1, 0, -6, 0, 2, -6, 0, -38, -10, 13, 3, 0, -1, 1, 10, 12, 0, 42, 2, -34, -1, 0, 0, 22, -1, -10, 0, 7, 1, -14, 0, 0, 7, 6, -8, -30, 0, 42, -17, 3, -11, 0, -2, -5, -18, 9, 0, -6, -1, -29, -27, 0, -12, 32, 6, -2, 0, -17, -14, 46, 0, 0, 1, 10, 11, 1, 0, 42, -24, -2, -2, 0, -5, -21, -15, 24, 0, 27, 1, 0, 2, 0, -6, -12, 5, 20, 0, 10, 10, 7, 3, 0, -10, 0, -25, -10, 0, -11, 19, -22, -18, 0, -7, -13, 1, 1, 0, -33, 3, 11, 23, 0, -1, 24, -7, -25, 0, 0, 1, -29, 7, 0, 24, 11, -6, -2, 0, 32, -8, -7, 5, 0, 1, 2, 25, -2, 0, -18, 22, 0, -3, 0, 4, -5, -1, -20, 0, 23, -14, -24, -11, 0, -2, 2, -10, 0, 0, 24, 3, 5, 1, 0, -8, 22, 17, -21, 0, -6, -2, -3, 13, 0, 0, 42, 0, 24, 0, -10, 8, 12, -12, 0, -7, 10, -12, 0, 0, -18, 5, 28, -4, 0, 3, 0, 10, -1, 0, -18, 12, -54, -11, 0, -5, 2, 1, -5, 0, -2, 1, -3, 20, 0, 0, -7, -25, -40, 0, -4, -22, -32, -13, 0, 8, 7, 1, -16, 0, 2, -12, -29, -3, 0, -2, 22, 2, 0, 0, 7, 3, 16, 1, 0, 14, 8, -7, 20, 0, 12, 0, 2, 0, 0, -6, 32, -35, 24, 0, 7, -1, -39, -3, 0, -16, -58, 2, -22, 0, 2, -9, 0, 15, 0, 1, -1, -20, -35, 0, -3, -14, 11, -6, 0, -18, 17, 17, 12, 0, -53, 0, 22, 33, 0, -10, 8, -3, 0, 0, -2, -12, 12, 2, 0, 4, 11, 5, -45, 0, 0, -24, 18, 33, 0, -1, 42, 12, -6, 0, -48, 2, 7, -5, 0, -22, 52, -10, 6, 0, 3, -3, 16, -1, 0, 0, 10, 20, -12, 0, 18, -2, 2, 22, 0, -1, -8, 7, 0, 0, 12, -1, -20, -2, 0, -3, -18, 1, -20, 0, 0, -2, 16, 7, 0, -15, -8, 0, 11, 0, -8, -7, -17, 12, 0, -11, -58, -25, -2, 0, -2, -18, 15, 7, 0, -6, 0, -1, -25, 0, -27, 2, -24, -12, 0, -22, 6, -20, -30, 0, -53, 6, -14, 1, 0, 0, 10, -23, 1, 0, -43, 11, 31, 16, 0, -2, 9, -24, 20, 0, -2, 3, -15, -5, 0, 4, -15, 8, 35, 0, -28, 21, 1, 21, 0, 2, 18, 22, -6, 0, -23, 5, 11, 0, 0, -7, 4, 10, -35, 0, 3, 12, -10, -10, 0, -10, -25, -2, 11, 0, -8, -32, 19, -28, 0, -18, 42, -3, -7, 0, 47, 1, 6, -37, 0, -12, 47, 3, -2, 0, 23, 0, -24, -1, 0, 10, -7, 2, -30, 0, 24, -20, 1, 18, 0, 7, -8, -11, 24, 0, 0, -6, 6, 32, 0, -31, 1, -8, 25, 0, 5, 16, 22, 1, 0, 12, 25, -30, -36, 0, -1, -7, 22, -2, 0, -3, 14, -7, 4, 0, -48, -1, 36, 38, 0, -8, -10, -14, 0, 0, -11, 11, -24, -2, 0, -2, -10, 6, 18, 0, 32, -24, 3, -27, 0, 1, 4, 0, -8, 0, -38, 17, 12, -2, 0, 14, 32, -2, -35, 0, 13, -15, -49, 0, 0, 1, 0, -5, 0, 0, -43, 8, 8, -11, 0, -12, -36, 18, -7, 0, 24, -12, 46, 28, 0, 0, 62, 5, 1, 0, -4, 8, 16, 3, 0, 14, 10, 2, 50, 0, 17, -2, 12, 38, 0, -11, 47, 10, -5, 0, -18, 1, 12, -18, 0, -10, -55, 1, 70, 0, 20, 6, 10, 0, 0, -2, -25, 6, -65, 0, 2, 38, -22, 10, 0, -13, 18, -3, 8, 0, 49, 1, 0, -1, 0, -10, 12, -12, -5, 0, -3, -42, -34, -2, 0, 34, 2, 1, 30, 0, 62, 0, 3, -22, 0, 1, 22, 10, 14, 0, 22, -7, -34, -1, 0, 14, 27, 0, 6, 0, 0, -7, 12, -6, 0, 8, -35, 30, 50, 0, -8, -42, -1, 17, 0, -3, -8, 11, -16, 0, -36, 2, 77, 5, 0, 18, 3, -9, 11, 0, 15, 6, -30, 1, 0, 29, -20, 27, 0, 0, 14, 12, -14, -32, 0, -6, -5, 2, -18, 0, 42, 17, 40, 14, 0, -46, -33, 0, -33, 0, 33, -1, 1, -10, 0, -11, -3, -1, -17, 0, 32, -42, -12, 24, 0, 2, 0, 2, 4, 0, 2, 5, 0, 21, 0, 15, 44, -24, 35, 0, 33, -27, -3, -1, 0, 0, 12, -2, 10, 0, -33, 6, 2, 12, 0, -5, 0, -20, -22, 0, -5, -10, -4, -10, 0, -7, 12, -3, 10, 0, -1, 10, 26, 0, 0, 25, 20, 10, -40, 0, -16, 11, -2, -19, 0, 22, -28, 18, -1, 0, 62, 7, -4, 13, 0, -1, -56, -1, -20, 0, -2, 33, 0, -3, 0, -11, 1, -23, 6, 0, -68, 1, -2, -24, 0, 7, 13, 25, -15, 0, 22, 0, 56, -1, 0, 29, -8, -7, -10, 0, 12, -24, -54, -11, 0, 6, -25, 2, -10, 0, 0, -32, -18, 8, 0, 7, 24, -5, -6, 0, 62, -1, 30, -2, 0, -25, 14, 2, 7, 0, -12, 18, -24, -22, 0, 0, -20, 3, 40, 0, 62, -4, 6, 5, 0, 1, -5, 20, 0, 0, 12, -23, 1, 14, 0, 24, 3, 11, -10, 0, 16, 2, -39, -2, 0, 10, -24, 0, 0, 0, 9, -24, 3, -3, 0, -5, -53, -1, 4, 0, -28, 8, -7, -22, 0, -17, 0, 21, 60, 0, 21, 6, -24, 2, 0, 3, 22, -13, -17, 0, 22, 0, 5, -42, 0, 0, -68, -24, -7, 0, 27, 10, 10, -8, 0, -12, -33, 12, 10, 0, -10, 7, -24, -10, 0, 12, -2, 0, -10, 0, -58, 18, -32, -5, 0, -28, -38, 4, -18, 0, 24, -3, 12, 0, 0, -10, 62, 1, 30, 0, -37, 18, 7, -12, 0, 54, 3, 11, -6, 0, 22, 5, 0, -2, 0, -1, 2, 5, 10, 0, -36, 2, -24, -1, 0, 3, -48, -20, 35, 0, 18, 0, 0, 7, 0, 25, -11, 40, 6, 0, 8, 4, -6, 22, 0, 32, -22, 13, -31, 0, 0, -8, 66, -7, 0, -1, -23, 16, 10, 0, 1, -2, -8, 12, 0, 29, -30, 3, 75, 0, 25, 2, -7, -22, 0, -2, -36, 0, -3, 0, 7, -7, -49, -3, 0, -16, 4, -1, 0, 0, 38, -14, -59, -8, 0, 7, -14, -20, -16, 0, 7, -12, 11, 0, 0, -2, -3, 0, -2, 0, -33, 6, 56, -32, 0, 35, -7, -24, 0, 0, -27, -7, 77, 1, 0, 39, 0, 3, 15, 0, -2, 16, 17, 58, 0, -2, 12, 22, 14, 0, 12, -2, 36, 9, 0, 0, -48, -15, 50, 0, 0, -1, 2, 1, 0, 20, -5, 35, 23, 0, -73, 3, 8, 14, 0, -11, 20, 6, -12, 0, -33, 18, 2, -17, 0, -17, 10, -12, -6, 0, 28, 53, -44, 0, 0, -22, 5, -33, -35, 0, -28, 10, 8, -8, 0, 3, -36, 0, 14, 0, -21, 2, 0, 12, 0, -12, 12, -2, 78, 0, 38, -4, 0, -11, 0, -5, 10, 45, -24, 0, 37, 0, 1, 24, 0, -18, 32, -33, -10, 0, -3, 1, 11, -42, 0, -12, -78, 6, 25, 0, 0, 48, 10, -2, 0, -7, 6, 5, -50, 0, -21, 22, 38, -52, 0, 10, 28, -6, -13, 0, -38, -3, -48, 3, 0, -16, 12, 1, 11, 0, -1, 0, 36, -10, 0, -20, -12, 12, 0, 0, -18, -18, -42, 2, 0, -2, -56, -22, 34, 0, 32, 1, 46, 8, 0, -7, 15, 0, -2, 0, -22, -12, -60, 1, 0, 20, 10, 2, 0, 0, -23, 3, -7, 18, 0, -1, 0, 20, 14, 0, 2, 0, -18, 2, 0, -16, -32, -7, -20, 0, -6, 15, 66, 8, 0, 0, 30, -11, 75, 0, -16, 8, -42, 7, 0, 17, 42, -12, -3, 0, -36, 11, -44, 58, 0, 25, 57, 2, -10, 0, 5, 2, -24, 18, 0, -15, -9, -7, 7, 0, 52, 6, 6, 0, 0, 1, -43, 25, 29, 0, -88, 27, 8, -2, 0, 24, 22, 12, -25, 0, -32, 22, 0, -6, 0, 20, 2, 30, -45, 0, 2, 53, 17, -6, 0, 14, -10, -1, -46, 0, 24, 0, 26, -10, 0, 23, 21, -1, -60, 0, -10, 43, 6, -11, 0, -31, -1, -16, -25, 0, 0, 2, -42, -9, 0, 24, 84, -20, 2, 0, 42, 2, 16, -3, 0, 15, -3, 5, 50, 0, 21, -4, -1, 15, 0, -8, -24, -35, -20, 0, -6, 28, -27, -21, 0, -1, 11, -21, 0, 0, -63, -2, -44, -18, 0, -22, -30, 6, 1, 0, 12, 23, -28, -5, 0, -11, -20, 0, 80, 0, -78, 7, -10, -4, 0, -10, 62, 35, -7, 0, -78, -3, 16, -12, 0, 10, 0, 10, -2, 0, 0, 10, 66, 25, 0, 2, 10, -11, -66, 0, -28, 8, 11, 32, 0, -19, 34, 28, 22, 0, -18, 18, 7, -42, 0, 3, 18, 7, -45, 0, 13, -47, -10, -1, 0, -6, -1, 37, 0, 0, -6, 12, 33, -47, 0, -3, -25, 2, -11, 0, 84, -23, -74, 0, 0, 24, -48, 1, 17, 0, -24, -10, 21, 7, 0, -2, 25, 30, 3, 0, -78, -24, 0, 20, 0, -1, 24, -18, 29, 0, 2, -7, 10, 8, 0, 11, 37, -24, -15, 0, -11, 0, 21, 6, 0, -6, 2, -32, -24, 0, -33, 31, -32, -1, 0, 8, -6, -25, 7, 0, 0, -5, 42, -16, 0, -22, -28, -1, -20, 0, -2, -12, 21, -25, 0, 30, 2, 36, 11, 0, -38, 1, 18, 7, 0, -22, 7, 2, 0, 0, -50, 3, -34, -14, 0, 7, 42, -4, 0, 0, 5, 48, -8, 1, 0, -36, 20, -38, -60, 0, -8, 8, -23, 10, 0, 14, -17, 0, 24, 0, -26, 11, 12, -11, 0, 24, -10, 2, -36, 0, -2, 2, -49, 10, 0, -6, 0, -18, 0, 0, 22, -32, -24, 24, 0, -3, 17, 27, -5, 0, 12, -1, -18, -4, 0, 0, 2, 8, -27, 0, -22, 38, -60, -17, 0, -12, 21, 2, 11, 0, 52, -14, 6, -32, 0, 2, -13, 35, 3, 0, -63, -13, -79, 15, 0, 49, -14, 0, -30, 0, -42, -1, 51, 0, 0, 5, -24, 0, 30, 0, 1, 43, 10, -8, 0, -8, -55, 11, -12, 0, -3, 12, 0, 36, 0, -18, -78, 7, -35, 0, -10, -24, -19, 12, 0, -46, 0, -28, -2, 0, -6, 0, 18, -62, 0, -5, -28, -1, -28, 0, 2, 4, -15, -8, 0, -16, -48, -3, 70, 0, 0, -14, -18, -10, 0, -2, 1, -50, -40, 0, 2, -17, 18, 2, 0, -12, 42, -38, 54, 0, -6, 11, 1, -47, 0, -10, 22, 5, 24, 0, -2, 18, -3, -1, 0, -12, 5, 18, 0, 0, -8, 10, 2, 55, 0, -1, 34, -70, 3, 0, -21, -20, -24, -6, 0, -10, 0, 0, -14, 0, 7, 2, -25, 25, 0, -6, 40, 65, -20, 0, 57, -2, 4, -38, 0, 22, 19, -10, 32, 0, 72, 13, -45, -18, 0, 3, -55, -8, -60, 0, -7, -49, 81, -1, 0, 0, 16, 1, -15, 0, 47, 10, -2, -12, 0, 12, -28, 5, 29, 0, 17, 3, -48, 42, 0, 34, 54, 2, 23, 0, -22, -34, 77, -2, 0, -1, 0, -30, 15, 0, 50, -62, -7, 0, 0, -3, 0, 22, -16, 0, -8, -1, -84, -22, 0, -10, 1, -14, 6, 0, -8, -22, 0, 7, 0, 34, -20, 1, 85, 0, 24, -14, -12, -27, 0, 0, 32, -6, -2, 0, 42, 0, -33, 7, 0, -12, 24, 6, 0, 0, -32, -8, 96, 35, 0, -30, -24, -50, 5, 0, 0, 8, -7, 42, 0, 1, 12, -17, 39, 0, 44, 3, 25, 8, 0, -11, -48, 16, 40, 0, 58, 36, -24, -2, 0, -77, 22, -5, -6, 0, -58, -18, -2, -3, 0, 9, 42, -11, 0, 0, 4, -15, -4, -6, 0, 30, 22, -1, -65, 0, 1, -29, -84, 20, 0, -27, 35, 0, -90, 0, 12, -14, 3, -12, 0, 14, -38, 32, -11, 0, -43, 6, -14, 5, 0, -2, 0, 18, -35, 0, -17, -42, -10, -17, 0, -40, -12, -14, 45, 0, 12, 46, 53, 33, 0, 0, 3, 33, -22, 0, 102, -33, -13, 1, 0, -1, 84, 10, 85, 0, -8, 11, -54, 3, 0, 1, 0, 17, -70, 0, 14, -32, 2, 42, 0, 12, -48, -24, -12, 0, -3, -2, 40, 0, 0, -2, -33, -4, 13, 0, -11, -2, -7, -5, 0, 0, 45, -21, -60, 0, 57, -15, 0, -44, 0, 24, 22, -35, -18, 0, 42, -33, -54, 27, 0, 3, 8, 1, -52, 0, -42, 0, -10, -12, 0, 2, 6, -10, 0, 0, -7, 33, 48, -6, 0, -2, -46, -12, -7, 0, 0, 5, -84, 0, 0, 20, -58, 22, 54, 0, -52, 5, -24, 10, 0, 4, -6, 10, -4, 0, -13, 7, -3, -12, 0, 3, 27, -10, -16, 0, -8, 1, 10, -10, 0, -26, 24, 0, 0, 0, -10, -25, 36, -20, 0, -10, 12, 40, 85, 0, 132, 16, -18, -11, 0, 2, -3, 19, -2, 0, -5, -22, 42, 28, 0, -18, -23, 1, -9, 0, 8, -62, 106, -7, 0, 4, 0, -13, 85, 0, 84, 1, -12, 56, 0, 1, -43, 20, 20, 0, 22, 2, 20, -33, 0, 0, 27, 3, -60, 0, 18, 11, -25, -1, 0, 23, 20, -6, 105, 0, 72, 68, 0, -1, 0, 2, -22, 24, -16, 0, 17, -7, -44, -13, 0, -25, 52, 15, -20, 0, 8, -22, 86, 0, 0, -56, -11, 1, 90, 0, -68, -29, 8, 8, 0, 7, -10, 10, 17, 0, -56, -12, 0, 24, 0, 54, -55, 11, -3, 0, 58, -6, 42, 25, 0, -2, 2, 10, 90, 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": "1050.2.a.b", "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], [-1], [-1], [1], [0], [2], [-1], [1], [1], [0], [1], [-3], [-1], [0], [0], [1], [-2], [1], [1], [0], [-1], [-1], [-1], [-5], [0], [7], [-1], [-2], [3], [0], [1], [2], [0], [-1], [0], [7], [-1], [11], [2], [0], [-1], [-8], [-1], [1], [0], [3], [1], [1], [1], [0], [1], [0], [5], [-5], [0], [-3], [-7], [-1], [1], [0], [2], [12], [-3], [-1], [0], [12], [-1], [6], [-2], [0], [0], [-2], [1], [10], [0], [1], [-7], [11], [1], [0], [-11], [5], [-2], [-10], [0], [-1], [1], [-7], [8], [0], [1], [2], [-1], [2], [0]]}