# Stored data for newform 1805.2.a.b, downloaded from the LMFDB on 25 April 2024.
{"label": "1805.2.a.b", "space_label": "1805.2.a", "level": 1805, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503599660926733, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 855407089274774607, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [0, 1]], [3, [-2, 1]]], "qexp_display": "q+2q^{3}-2q^{4}-q^{5}-4q^{7}+q^{9}+3q^{11}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 7220, "fricke_eigenval": -1, "atkin_lehner_string": "+-", "analytic_conductor": 14.41299756484111, "hecke_ring_index": 1, "level_radical": 95, "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": "0.015", "prec": 17}, "analytic_rank_proved": true, "char_values": [1805, 1, [362, 1446], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [5, 19], "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": "1.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.006", "prec": 17}, {"__RealLiteral__": 0, "data": "0.006", "prec": 17}, {"__RealLiteral__": 0, "data": "5.013", "prec": 17}], "related_objects": ["EllipticCurve/Q/1805/b"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[5, 1], [19, -1]], "trace_display": [0, 2, -1, -4], "traces": [0, 1, 0, 2, -2, -1, 0, -4, 0, 1, 0, 3, -4, -2, 0, -2, 4, 6, 0, 0, 2, -8, 0, 0, 0, 1, 0, -4, 8, 3, 0, 7, 0, 6, 0, 4, -2, -8, 0, -4, 0, 6, 0, -4, -6, -1, 0, 6, 8, 9, 0, 12, 4, 6, 0, -3, 0, 0, 0, 15, 4, 5, 0, -4, -8, 2, 0, -2, -12, 0, 0, 3, 0, 8, 0, 2, 0, -12, 0, -5, -4, -11, 0, 12, 16, -6, 0, 6, 0, 15, 0, 8, 0, 14, 0, 0, 0, -8, 0, 3, -2, 15, 0, 16, 0, 8, 0, 0, 8, -11, 0, -16, -16, -6, 0, 0, -6, -2, 0, -24, 0, -2, 0, 12, -14, -1, 0, -2, 0, -8, 0, 12, -12, 0, 0, 4, 0, -12, 0, -16, -8, 12, 0, -6, 4, -3, 0, 18, 16, 3, 0, -17, 0, 6, 0, -7, 8, 2, 0, 12, 0, 0, 0, -10, -12, -6, 0, 0, 0, -9, 0, 0, 8, 0, 0, -4, 12, 30, 0, 9, 2, -2, 0, 10, 0, 8, 0, 18, -12, 16, 0, -15, -16, 16, 0, 4, -18, -18, 0, -19, 0, -4, 0, -12, -24, -6, 0, 0, -8, 0, 0, 7, -12, 6, 0, 4, 0, -28, 0, 16, 6, -12, 0, 4, 0, 1, 0, 24, 0, -7, 0, -24, 0, 6, 0, -6, -30, -10, 0, -3, -8, -5, 0, -10, -10, -9, 0, 0, 0, 24, 0, -15, 8, 0, 0, -12, 16, 18, 0, 32, -4, 3, 0, -18, 0, -6, 0, 30, 4, 21, 0, 11, 24, 16, 0, 3, 0, 8, 0, 7, 0, -6, 0, 14, -6, 0, 0, -24, 0, 19, 0, -16, -16, -24, 0, -15, 0, -12, 0, 0, -4, 16, 0, 30, 0, -5, 0, 34, 24, 32, 0, 24, 0, -10, 0, 4, 10, -24, 0, 9, 8, 0, 0, 0, 22, -2, 0, -22, 0, -24, 0, 4, -24, -8, 0, 2, -32, 16, 0, -12, 12, 21, 0, -8, 0, 0, 0, 12, -12, 14, 0, 8, 0, 12, 0, -3, -30, -48, 0, 24, 0, 0, 0, -4, -16, -8, 0, -4, 0, 6, 0, -24, -28, 4, 0, -2, 0, -6, 0, 37, 0, -4, 0, -30, 0, 12, 0, -4, 16, 15, 0, 0, 0, 24, 0, 5, -6, 8, 0, 0, 4, 33, 0, -14, -30, 11, 0, -24, 0, -23, 0, -24, -32, -60, 0, -12, 0, -32, 0, -3, -16, 19, 0, 6, 0, 6, 0, -20, 0, -12, 0, 15, -16, -8, 0, -6, 22, 0, 0, 13, 0, 9, 0, -12, 32, -15, 0, 6, 32, 9, 0, 18, 12, -34, 0, -8, 0, -22, 0, -24, 0, -9, 0, -16, 12, -14, 0, 0, 4, 8, 0, 4, 0, -12, 0, 0, 48, 6, 0, 15, 0, 16, 0, 0, 4, 8, 0, -2, 0, -20, 0, -15, -24, 18, 0, -3, 28, -12, 0, 20, 2, 0, 0, -42, 0, -15, 0, -18, 4, 18, 0, -32, 0, 0, 0, -16, 16, 18, 0, 0, 0, 45, 0, -26, -24, -8, 0, 42, 24, -23, 0, 15, 0, -12, 0, 0, 0, 18, 0, 27, -8, -37, 0, -4, 0, 11, 0, 4, 24, 5, 0, 0, 0, 20, 0, 16, 32, 12, 0, 8, 16, 36, 0, -6, -24, 6, 0, 44, 0, -39, 0, -7, 12, -30, 0, 0, -8, -16, 0, 32, 6, -48, 0, 18, 0, 2, 0, -36, -36, 0, 0, -36, -32, 12, 0, 24, -6, -38, 0, 0, 0, 31, 0, -2, 34, 2, 0, -2, 0, -24, 0, -12, -12, 2, 0, -12, 0, 36, 0, -4, 14, 0, 0, -60, -16, 1, 0, 0, -4, -48, 0, -19, 0, 14, 0, 2, -24, -18, 0, 3, 0, -9, 0, -34, 0, 8, 0, 18, 0, 45, 0, -56, 20, 24, 0, -12, 24, 8, 0, 12, 12, -5, 0, -24, 0, 0, 0, 0, 0, 8, 0, 15, 0, 4, 0, -4, 18, -48, 0, 32, 0, 48, 0, 18, 0, 12, 0, -14, -16, -12, 0, -37, 0, -12, 0, 16, 0, 36, 0, 12, 8, 6, 0, 0, -24, -12, 0, -60, -60, -31, 0, -5, 0, 0, 0, 6, -18, -6, 0, 15, -4, -64, 0, -10, 4, 3, 0, 14, 0, 13, 0, -24, -20, 32, 0, -18, 0, -6, 0, 35, -16, 0, 0, 24, 0, -3, 0, 12, -36, 0, 0, 7, 24, -30, 0, 17, -32, -10, 0, 0, 0, 6, 0, 44, 30, -6, 0, -30, 32, 29, 0, 36, -32, -30, 0, 7, 0, 64, 0, 0, -8, 9, 0, -12, 36, -2, 0, 34, 36, -36, 0, 24, 0, -10, 0, -12, 38, 30, 0, 36, 0, 15, 0, 24, 8, 0, 0, 42, 0, -27, 0, 43, 24, 22, 0, 10, 48, 0, 0, 8, 12, -3, 0, -22, 0, 6, 0, 42, 0, -26, 0, 16, 16, 54, 0, 0, 0, -28, 0, 0, 0, -20, 0, -12, -14, 9, 0, 8, 24, 28, 0, 0, -12, 14, 0, 0, 0, -36, 0, -7, -8, -48, 0, -18, 0, 0, 0, 38, 56, -15, 0, 4, 0, -8, 0, 4, -32, 52, 0, -48, -12, 9, 0, 8, 24, -30, 0, -36, 0, 8, 0, -33, -8, 0, 0, -9, 0, 0, 0, 21, -2, 36, 0, 32, 0, 2, 0, -8, -48, 15, 0, -21, 0, 36, 0, -10, 14, -48, 0, 8, 0, 68, 0, -6, 48, -8, 0, 16, 0, 27, 0, 0, -12, 48, 0, -18, 0, -46, 0, -20, 12, 9, 0, 0, 60, -16, 0, -18, 20, -16, 0, -48, 0, 12, 0, 15, 6, 18, 0, 48, 16, 18, 0, 0, 10, -16, 0, -16, 0, 0, 0, 12, 20, 64, 0, -4, 20, 12, 0, 45, 18, -11, 0, 36, 0, 18, 0, -48, 0, 0, 0, -8, 0, 8, 0, 19, -48, -22, 0, 32, 0, 24, 0, 90, 30, 4, 0, 0, -16, 7, 0, 32, 0, -54, 0, 12, 0, -6, 0, -3, 24, -2, 0, 42, -32, 6, 0, 10, -36, -16, 0, 21, 0, -22, 0, 0, -64, 30, 0, -56, 8, 24, 0, -12, -6, 0, 0, 28, 0, 18, 0, 23, 36, 22, 0, -7, 0, 68, 0, 24, 12, -30, 0, 28, 0, -6, 0, -24, -60, -22, 0, -24, -8, -24, 0, -4, -42, 48, 0, -24, 0, 0, 0, 0, -22, 28, 0, 62, -48, -2, 0, -3, -32, 34, 0, -16, 0, -24, 0, -8, -6, -8, 0, 6, 0, 12, 0, -24, -16, -51, 0, 45, 0, -48, 0, -4, -14, -20, 0, 8, 0, 0, 0, -14, 12, -1, 0, 0, 0, 58, 0, -12, -28, 48, 0, -24, 12, 74, 0, -12, 0, 40, 0, -2, 0, 7, 0, -56, 48, -60, 0, 27, 0, -62, 0, 24, -38, -30, 0, 0, 0, 16, 0, -48, 32, -6, 0, 30, 32, 0, 0, -17, 48, 0, 0, 6, 0, 0, 0, 12, 30, -9, 0, 36, 0, 10, 0, 12, 24, 18, 0, 16, 0, -18, 0, 3, 0, 0, 0, -33, 8, -22, 0, 66, -32, 5, 0, 18, 0, -28, 0, 0, -60, -40, 0, 10, 0, 12, 0, 0, 10, -48, 0, 54, 0, 9, 0, -46, -68, -18, 0, 37, -48, -12, 0, 0, -64, -56, 0, -120, 0, 48, 0, -18, -48, -24, 0, -12, 0, -14, 0, -16, 20, -36, 0, 15, 0, -6, 0, -12, -8, 16, 0, 38, -20, 0, 0, 8, 48, -24, 0, 42, 0, 0, 0, 12, -18, 66, 0, 47, -16, -40, 0, -18, 0, -18, 0, -6, 0, -27, 0, -20, 0, 30, 0, -32, -44, -28, 0, -16, 4, 9, 0, -40, 0, -3, 0, 66, 44, -72, 0, 0, 0, -30, 0, 18, 48, 26, 0, 12, 0, -50, 0, -36, -8, 6, 0, -22, 48, -24, 0, -39, 16, -28, 0, -30, 0, 60, 0, -32, -4, 3, 0, -30, 64, -21, 0, 18, -32, 0, 0, -64, 0, 36, 0, -11, 24, 0, 0, -17, -24, -30, 0, 18, -42, -16, 0, 18, 0, 27, 0, -44, 16, -24, 0, -3, 0, -66, 0, 72, 0, -29, 0, -18, 0, -8, 0, 0, -24, -32, 0, 0, 24, 76, 0, -7, -28, -6, 0, 16, 0, 0, 0, 0, -16, 6, 0, 16, 0, -21, 0, 72, -24, 2, 0, -14, 0, 22, 0, -24, 6, 27, 0, -64, 60, 0, 0, 42, 96, -22, 0, -24, 0, -48, 0, 24, -48, 30, 0, -60, 0, 36, 0, 32, 0, -19, 0, -8, 0, 0, 0, -33, 8, -34, 0, 16, 32, 42, 0, 1, 16, -4, 0, 0, 0, 24, 0, -10, 8, 12, 0, 13, 0, -30, 0, 15, -12, -28, 0, 36, 0, -42, 0, 26, 48, 12, 0, 18, 56, -61, 0, -24, -8, -36, 0, 0, 0, 40, 0, -33, 4, 0, 0, 0, 0, -16, 0, -36, 12, -84, 0, 33, 0, 90, 0, -30, -74, -48, 0, 63, 0, -9, 0, -54, 8, 5, 0, 36, 0, -48, 0, 20, 60, -64, 0, -34, 0, 18, 0, 0, -24, 0, 0, -16, 0, -32, 0, 48, 8, 46, 0, 36, -32, 6, 0, -24, -30, 0, 0, -24, 0, -16, 0, 90, 0, 10, 0, 38, 0, -52, 0, 0, -48, 4, 0, -4, 0, 0, 0, 25, -10, 84, 0, -60, 12, 24, 0, -46, -16, -96, 0, 32, 0, -60, 0, -9, 0, 2, 0, -24, -8, 15, 0, 28, -66, 0, 0, -12, 0, 10, 0, 9, 28, 0, 0, 0, 60, 54, 0, 57, -22, -73, 0, -74, 0, 2, 0, -68, 48, -2, 0, -24, 0, 0, 0, 22, 46, 30, 0, 9, 0, 8, 0, 42, 48, 24, 0, -20, 64, -48, 0, 4, 120, 0, 0, -4, 0, -46, 0, 40, 24, -51, 0, 22, 0, 8, 0, -72, 64, 65, 0, 24, 0, 12, 0, -2, 6, 16, 0, 0, 32, -5, 0, 18, -38, -16, 0, 20, 0, -12, 0, 0, -12, -26, 0, 12, 0, -18, 0, -5, -12, 40, 0, -24, 0, -21, 0, -78, 40, -9, 0, 45, 0, -14, 0, 8, 24, 90, 0, -15, 0, -33, 0, 16, -30, 0, 0, 6, 32, 0, 0, -32, 16, 36, 0, -12, 0, 16, 0, -48, 12, 34, 0, -96, -44, -14, 0, 34, 0, 36, 0, 96, 0, 44, 0, -8, -26, 60, 0, 59, 0, -72, 0, -24, -18, -12, 0, 0, 0, 15, 0, 0, 24, -18, 0, 3, -64, -74, 0, 24, 30, 24, 0, 8, 0, 48, 0, -30, -12, -14, 0, -19, -64, -30, 0, -24, -18, 0, 0, -72, 0, -26, 0, 62, -36, 0, 0, 32, -24, 8, 0, 69, 68, -72, 0, 4, 0, 0, 0, 0, 16, -4, 0, -60, 0, 8, 0, -12, 44, 105, 0, 23, 0, -24, 0, 4, 48, 0, 0, 4, 0, 72, 0, 0, 18, -6, 0, 6, 0, -27, 0, 72, 32, -66, 0, 24, -24, -8, 0, -27, 28, 22, 0, 0, 0, -4, 0, -22, 0, -120, 0, 48, -8, -28, 0, 2, -16, 54, 0, 23, 0, 0, 0, -84, -8, 6, 0, -96, 0, -27, 0, 35, 24, -38, 0, -37, 0, -44, 0, 7, 0, 57, 0, 0, -96, 4, 0, -18, -12, 0, 0, -36, 0, -36, 0, 30, -30, -12, 0, 0, 0, -36, 0, -18, -32, -12, 0, 36, 0, -68, 0, -15, 0, -50, 0, 4, -8, -6, 0, -32, -16, 36, 0, -6, 0, -15, 0, 90, 4, -57, 0, -8, 0, -28, 0, 0, 40, 0, 0, 48, 0, -48, 0, 34, 30, -24, 0, 24, 48, 27, 0, -32, -36, 72, 0, -5, 0, 24, 0, 48, 6, -56, 0, -10, -56, -8, 0, 14, 24, -12, 0, -6, 0, -4, 0, 0, -40, 66, 0, -19, -4, 0, 0, 30, 0, -33, 0, 4, 0, 54, 0, 83, 84, 30, 0, 14, 0, -62, 0, 8, 30, -24, 0, -76, 0, -11, 0, -24, 36, -65, 0, -96, -8, 0, 0, 24, -36, 64, 0, 0, 0, -4, 0, 24, 64, 23, 0, 0, 0, 36, 0, 96, 0, -46, 0, 24, 0, -12, 0, 9, 32, -7, 0, 66, -32, 60, 0, -24, -36, -75, 0, 0, 0, -74, 0, 12, 0, -14, 0, 48, 0, 57, 0, -38, -90, 32, 0, 60, 0, -65, 0, 72, 52, 0, 0, 3, 48, 6, 0, -57, 16, -45, 0, 12, 0, -19, 0, -36, -84, 0, 0, 51, -48, -76, 0, -6, 46, 24, 0, 20, 0, -120, 0, 48, -30, -6, 0, -62, 0, 78, 0, 76, 24, 20, 0, 20, 0, -88, 0, 0, 0, 87, 0, -26, 0, 12, 0, 0, -36, -136, 0, -3, 0, 60, 0, -15, -54, 30, 0, -12, 16, -17, 0, -128, 74, 8, 0, -54, 0, -5, 0, 0, 8, 36, 0, 6, 0, -96, 0, 28, -22, 28, 0, -120, 0, 0, 0, 56, -8, -57, 0, 40, -48, -48, 0, -13, -10, 44, 0, 64, 0, 21, 0, 76, 0, -9, 0, -72, 0, -11, 0, -12, -40, 30, 0, 12, 0, 70, 0, 96, -32, 5, 0, 0, -64, 15, 0, 72, -24, 48, 0, 0, 0, -36, 0, -6, -16, 42, 0, 17, -32, -48, 0, -42, -72, -9, 0, 0, 0, 0, 0, 20, 12, 14, 0, -18, 48, -40, 0, -15, -12, 0, 0, 56, 0, 34, 0, -42, -88, -26, 0, -20, 0, 12, 0, 8, 78, 0, 0, -24, 0, -7, 0, 12, 14, 22, 0, 62, -24, 88, 0, -15, 60, -26, 0, 24, 0, 36, 0, 0, 0, -60, 0, 54, 16, 9, 0, 58, 32, 81, 0, 64, 0, 18, 0, 16, -64, -16, 0, -60, -12, 21, 0, 0, 96, 14, 0, -18, 0, -72, 0, 32, -36, 30, 0, 0, 0, 0, 0, 39, -4, -79, 0, 18, 0, -8, 0, 82, 72, -33, 0, 27, 72, 4, 0, -4, 0, -18, 0, -64, 0, 68, 0, -96, 72, 12, 0, -18, 64, 0, 0, -83, -24, 48, 0, 0, 0, 10, 0, -20, -48, -63, 0, 46, 12, -6, 0, -84, 76, 67, 0, 60, 0, -90, 0, -15, 0, 72, 0, 12, 0, -31, 0, -60, -62, -16, 0, 36, 0, 48, 0, 51, 4, 0, 0, 0, -68, -36, 0, 90, -4, 21, 0, -60, 0, -8, 0, -54, 4, -48, 0, -36, 0, 86, 0, 2, 48, -82, 0, 11, 0, 15, 0, -56, 24, 20, 0, 60, 24, -35, 0, 0, -4, 12, 0, 15, 0, -32, 0, -84, 24, 0, 0, -6, 0, -18, 0, 20, -72, -44, 0, -48, 0, -8, 0, 3, 8, -42, 0, 16, -28, 84, 0, 30, 0, 12, 0, -52, 0, 0, 0, 36, 120, 8, 0, -20, 32, 72, 0, 108, -2, 30, 0, 46, 0, 0, 0, 0, 0, -32, 0, -77, 8, -96, 0, 42, 96, 0, 0, -21, 0, -89, 0, -40, 38, 15, 0, 0, 0, -6, 0, -48, -28, 18, 0, 18, 0, -60, 0, 1, -4, 16, 0, 66, 48, -18, 0, 14, 36, 9, 0, -88, 0, 0, 0, 32, -6, -28, 0, 28, 0, 36, 0, 18, 18, 0, 0, -102, 0, 16, 0, -72, 68, 84, 0, 16, 0, -14, 0, 51, -16, 45, 0, -24, 0, -18, 0, 38, -36, -36, 0, -9, 0, -16, 0, 0, -90, 54, 0, 0, 0, 19, 0, 0, 112, -45, 0, -30, -40, -69, 0, -16, -48, 8, 0, 26, 0, 22, 0, 32, 24, -3, 0, -20, -48, 8, 0, -24, -16, -9, 0, 104, 0, 78, 0, -42, -24, -24, 0, 24, -24, 0, 0, 18, 10, 23, 0, 38, 0, 16, 0, -15, 48, -148, 0, -15, 0, -36, 0, -29, 0, -72, 0, -24, 0, 12, 0, 16, 0, 12, 0, 41, 0, -30, 0, 0, -16, 32, 0, 0, 0, 120, 0, -34, -30, -18, 0, 84, 0, -14, 0, 0, -8, -54, 0, -27, 0, 42, 0, 9, 8, -64, 0, 72, -36, 37, 0, 68, 96, 16, 0, 75, 0, -32, 0, 4, -64, 0, 0, -71, 0, -16, 0, -60, -96, -11, 0, -60, 0, 15, 0, -20, -36, -42, 0, -4, 0, 0, 0, 72, -24, -87, 0, -14, 0, -5, 0, -12, 28, 70, 0, -96, 32, 6, 0, 0, 24, 16, 0, 105, 0, -45, 0, 34, 74, -20, 0, 94, 0, -12, 0, -60, 24, 90, 0, -16, 0, 60, 0, -32, -32, -64, 0, 0, 0, -12, 0, 54, -72, 42, 0, 8, 0, 0, 0, -8, -24, -40, 0, 24, -16, -39, 0, 40, -12, -36, 0, -132, 0, -17, 0, -92, 0, -24, 0, 6, 48, -10, 0, 12, 24, 56, 0, 18, 0, -6, 0, 54, 120, 0, 0, 0, 120, -14, 0, -44, 62, 60, 0, 0, 0, -36, 0, 54, 10, 39, 0, -32, 0, 96, 0, -31, 0, -24, 0, 7, 0, -58, 0, 24, -12, 63, 0, 92, 36, 30, 0, 30, 12, 0, 0, 9, 0, -54, 0, 0, -30, 96, 0, -39, 8, 8, 0, 36, 128, 16, 0, 28, 0, 0, 0, 135, 20, -54, 0, -32, -8, -42, 0, -8, -6, -32, 0, -36, 0, 48, 0, 0, -28, -27, 0, 18, 0, 24, 0, -18, -26, 46, 0, 128, 0, 0, 0, 40, 48, -2, 0, 48, 40, 45, 0, 24, -64, 12, 0, 36, 0, 90, 0, -9, 36, 0, 0, 44, 0, 0, 0, -76, 12, 72, 0, -48, 0, -26, 0, 36, -70, 66, 0, 63, 32, -24, 0, 6, 0, -12, 0, 0, 0, 87, 0, -19, -48, -16, 0, -24, 0, 14, 0, 4, 6, 33, 0, 0, 0, 38, 0, 48, -24, 45, 0, -44, 72, 48, 0, 0, 0, 88, 0, 9, 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": "95.2.e.a", "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], [0], [2], [-2], [-1], [0], [-4], [0], [1], [0], [3], [-4], [-2], [0], [-2], [4], [6], [0], [0], [2], [-8], [0], [0], [0], [1], [0], [-4], [8], [3], [0], [7], [0], [6], [0], [4], [-2], [-8], [0], [-4], [0], [6], [0], [-4], [-6], [-1], [0], [6], [8], [9], [0], [12], [4], [6], [0], [-3], [0], [0], [0], [15], [4], [5], [0], [-4], [-8], [2], [0], [-2], [-12], [0], [0], [3], [0], [8], [0], [2], [0], [-12], [0], [-5], [-4], [-11], [0], [12], [16], [-6], [0], [6], [0], [15], [0], [8], [0], [14], [0], [0], [0], [-8], [0], [3], [-2]]}