# Stored data for newform 1098.2.a.k, downloaded from the LMFDB on 22 February 2025. {"Nk2": 4392, "analytic_conductor": 8.767574141936587, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [3, -1], [61, -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": [1098, 1, [245, 307], [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": [[5, [-2, 1]], [7, [-4, 1]], [11, [-4, 1]]], "hecke_orbit": 11, "hecke_orbit_code": 45035996307260490, "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": "1098.2.a.k", "level": 1098, "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, 3, 61], "level_radical": 366, "minimal_twist": "366.2.a.a", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q+q^{2}+q^{4}+2q^{5}+4q^{7}+q^{8}+2q^{10}+\\cdots", "related_objects": ["EllipticCurve/Q/1098/k"], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1098.2.a", "trace_display": [1, 0, 2, 4], "trace_hash": 1241639262178830234, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.952", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.880", "prec": 17}, {"__RealLiteral__": 0, "data": "0.025", "prec": 17}, {"__RealLiteral__": 0, "data": "4.677", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.022", "prec": 17}, "traces": [0, 1, 1, 0, 1, 2, 0, 4, 1, 0, 2, 4, 0, -2, 4, 0, 1, -6, 0, 4, 2, 0, 4, -8, 0, -1, -2, 0, 4, -10, 0, 4, 1, 0, -6, 8, 0, 6, 4, 0, 2, -2, 0, -8, 4, 0, -8, 8, 0, 9, -1, 0, -2, 6, 0, 8, 4, 0, -10, -12, 0, 1, 4, 0, 1, -4, 0, 0, -6, 0, 8, 0, 0, 10, 6, 0, 4, 16, 0, -12, 2, 0, -2, 12, 0, -12, -8, 0, 4, -6, 0, -8, -8, 0, 8, 8, 0, 2, 9, 0, -1, -2, 0, -16, -2, 0, 6, 12, 0, 14, 8, 0, 4, 6, 0, -16, -10, 0, -12, -24, 0, 5, 1, 0, 4, -12, 0, -16, 1, 0, -4, -4, 0, 16, 0, 0, -6, -2, 0, -8, 8, 0, 0, -8, 0, -20, 10, 0, 6, 10, 0, 20, 4, 0, 16, 8, 0, 14, -12, 0, 2, -32, 0, 20, -2, 0, 12, 0, 0, -9, -12, 0, -8, -18, 0, -4, 4, 0, -6, -20, 0, -2, -8, 0, -8, 12, 0, -24, 8, 0, 8, 0, 0, 2, 2, 0, 9, 18, 0, -24, -1, 0, -2, -40, 0, -4, -16, 0, -2, 16, 0, -16, 6, 0, 12, -16, 0, 16, 14, 0, 8, 12, 0, -4, 4, 0, 6, 4, 0, -10, -16, 0, -10, 10, 0, 16, -12, 0, -24, 8, 0, 2, 5, 0, 1, 18, 0, -8, 4, 0, -12, -12, 0, -32, -16, 0, 1, 6, 0, 24, -4, 0, -4, 24, 0, 12, 16, 0, 0, -22, 0, 24, -6, 0, -2, -4, 0, -2, -8, 0, 8, 18, 0, 4, 0, 0, -8, -8, 0, 19, -20, 0, 10, -22, 0, -24, 6, 0, 10, 16, 0, -32, 20, 0, 4, 2, 0, 8, 16, 0, 8, 0, 0, 10, 14, 0, -12, 18, 0, -40, 2, 0, -32, -24, 0, 2, 20, 0, -2, 32, 0, 8, 12, 0, 0, 0, 0, -6, -9, 0, -12, 16, 0, 8, -8, 0, -18, -4, 0, -34, -4, 0, 4, -18, 0, 0, -6, 0, -20, -8, 0, -3, -2, 0, -8, 20, 0, -8, -8, 0, 12, 24, 0, -10, -24, 0, 8, 20, 0, 28, 8, 0, 0, 16, 0, 32, 2, 0, 2, 30, 0, 48, 9, 0, 18, -24, 0, -18, -24, 0, -1, -6, 0, -8, -2, 0, -40, 24, 0, 34, -4, 0, -16, -48, 0, 24, -2, 0, 16, 4, 0, 14, -16, 0, 6, 6, 0, 4, 12, 0, -16, 0, 0, 2, 16, 0, 14, -32, 0, 24, 8, 0, 12, 12, 0, -12, -4, 0, 4, -10, 0, -8, 6, 0, 4, -16, 0, 18, -10, 0, -16, 18, 0, -32, -10, 0, 10, -4, 0, 0, 16, 0, -12, -32, 0, -4, -24, 0, 8, 40, 0, -12, 2, 0, 5, 4, 0, -16, 1, 0, 18, -12, 0, 60, -8, 0, 4, 0, 0, -16, -12, 0, -12, 0, 0, -4, -32, 0, -16, -34, 0, 40, 1, 0, 6, -32, 0, 32, 24, 0, -4, 10, 0, 16, -4, 0, 24, -24, 0, 41, 12, 0, 16, 4, 0, 24, 0, 0, -22, 36, 0, -42, 24, 0, -6, 28, 0, -8, -2, 0, -4, -40, 0, -48, -2, 0, -8, 22, 0, 16, 8, 0, 18, -28, 0, 12, 4, 0, 0, 14, 0, -12, -8, 0, -8, 8, 0, 18, 19, 0, -20, 48, 0, 24, 10, 0, -22, 12, 0, 16, -24, 0, 6, -22, 0, -48, 10, 0, 16, 24, 0, -22, -32, 0, 20, 10, 0, -48, 4, 0, 2, -16, 0, 38, 8, 0, 16, 42, 0, -12, 8, 0, 0, -24, 0, -19, 10, 0, 14, -36, 0, 12, -12, 0, 18, -32, 0, -18, -40, 0, 2, 2, 0, -16, -32, 0, -24, 8, 0, -48, 2, 0, 20, 30, 0, -8, -2, 0, 32, -44, 0, -42, 8, 0, 12, 32, 0, 80, 0, 0, 0, 4, 0, 34, -6, 0, -9, 14, 0, 8, -12, 0, 16, 44, 0, -4, 8, 0, -8, -12, 0, 28, -18, 0, -4, -16, 0, 12, -34, 0, -4, 46, 0, 24, 4, 0, -18, -8, 0, -2, 0, 0, -6, -32, 0, -16, -20, 0, -8, 0, 0, -64, -3, 0, -2, 10, 0, 32, -8, 0, 20, 48, 0, 14, -8, 0, -8, 0, 0, -40, 12, 0, 24, 24, 0, 20, -10, 0, -24, 48, 0, 8, 8, 0, 20, 40, 0, 22, 28, 0, 8, -22, 0, 56, 0, 0, 16, 24, 0, 50, 32, 0, 2, 26, 0, -4, 2, 0, 30, -8, 0, 0, 48, 0, 9, 28, 0, 16, 18, 0, -24, 24, 0, -2, -18, 0, -24, 26, 0, -48, -1, 0, -6, 40, 0, -64, -8, 0, -2, -50, 0, -40, -40, 0, 24, 40, 0, -32, 34, 0, -4, -10, 0, -4, -16, 0, -48, -12, 0, 30, 24, 0, -2, -54, 0, 0, 16, 0, 4, -40, 0, 71, 14, 0, -16, -18, 0, 20, 6, 0, 6, -48, 0, 22, 4, 0, 12, -18, 0, -44, -16, 0, 0, -24, 0, -36, 2, 0, 16, -48, 0, 0, 14, 0, -32, -48, 0, -34, 24, 0, 8, 30, 0, -48, 12, 0, 12, 40, 0, -64, -12, 0, -4, 32, 0, -40, 4, 0, -10, -40, 0, -36, -8, 0, 6, -4, 0, -24, 4, 0, -16, 56, 0, 48, 18, 0, -10, -16, 0, 32, -16, 0, 18, 0, 0, -6, -32, 0, -10, 6, 0, 36, 10, 0, -4, -48, 0, -38, 0, 0, 16, -18, 0, 16, -12, 0, -32, -36, 0, -20, -4, 0, -24, 18, 0, 0, 8, 0, 40, -8, 0, -15, -12, 0, 2, 4, 0, 32, 5, 0, 4, -28, 0, -32, -16, 0, 1, -34, 0, -24, 18, 0, -12, -16, 0, 36, 60, 0, -8, 64, 0, -8, 4, 0, 0, -48, 0, -26, -16, 0, -12, -32, 0, 72, -12, 0, 0, 24, 0, 26, -4, 0, -32, -2, 0, -80, -16, 0, -34, 12, 0, -2, 40, 0, 1, 2, 0, 24, 6, 0, -32, -32, 0, 10, 32, 0, 24, -6, 0, 36, -4, 0, 10, 40, 0, 32, 16, 0, -4, 6, 0, -60, 24, 0, -24, -32, 0, 80, 41, 0, 12, -10, 0, -52, 16, 0, 4, 8, 0, 14, 24, 0, 0, -60, 0, 8, -22, 0, 36, -24, 0, -64, -42, 0, 24, 32, 0, -4, -6, 0, 28, -60, 0, -26, -8, 0, -2, 30, 0, 56, -4, 0, -40, 16, 0, 24, -48, 0, -2, 6, 0, -8, -8, 0, 22, -8, 0, 14, 16, 0, 8, -48, 0, -44, 18, 0, -28, -72, 0, 18, 12, 0, 4, -64, 0, 8, 0, 0, 14, 0, 0, 80, -12, 0, -8, -20, 0, 24, -8, 0, 8, 32, 0, -6, 18, 0, 19, 12, 0, 4, -20, 0, 48, -12, 0, 20, 24, 0, 10, 0, 0, -36, -22, 0, 12, -8, 0, 48, 16, 0, -24, 10, 0, -36, 6, 0, -22, -60, 0, 20, -48, 0, 10, -10, 0, 16, 16, 0, 24, 56, 0, -62, -22, 0, -32, 4, 0, 0, 20, 0, 10, -72, 0, -26, -48, 0, 4, 54, 0, -48, 2, 0, -16, -16, 0, -9, 38, 0, 8, 42, 0, -28, 16, 0, 42, -16, 0, -18, -12, 0, 8, -60, 0, 24, 0, 0, -24, 80, 0, 10, -19, 0, 10, -80, 0, -24, 14, 0, -36, 12, 0, -4, 12, 0, -12, -64, 0, -8, 18, 0, -32, -8, 0, 0, -18, 0, -40, -6, 0, -44, 2, 0, 2, 60, 0, 12, -16, 0, -32, 50, 0, -40, -24, 0, 8, 48, 0, -14, -48, 0, 2, 42, 0, 16, 20, 0, 30, 36, 0, -96, -8, 0, -2, 4, 0, 48, 32, 0, -44, -32, 0, 58, -42, 0, 8, -6, 0, 56, 12, 0, 32, -24, 0, -32, 80, 0, 0, 0, 0, 32, 0, 0, 4, 72, 0, -44, 34, 0, -6, 0, 0, 8, -9, 0, 14, 48, 0, 96, 8, 0, -12, -50, 0, -80, 16, 0, 44, 32, 0, -1, -4, 0, 8, 22, 0, -48, -8, 0, -12, 72, 0, 22, 28, 0, -18, -4, 0, 40, -4, 0, -16, -24, 0, -96, 12, 0, -34, -64, 0, 64, -4, 0, 46, -8, 0, 36, 24, 0, 4, 18, 0, -72, -18, 0, -8, 8, 0, -28, -2, 0, 0, -90, 0, 56, -6, 0, -32, 20, 0, 54, -16, 0, -20, -30, 0, -16, -8, 0, 0, 24, 0, -16, -64, 0, -3, 38, 0, 44, -2, 0, 10, -60, 0, 6, 32, 0, -8, 32, 0, -52, 20, 0, 48, 64, 0, -44, 14, 0, -8, -12, 0, 44, -8, 0, 0, 12, 0, -64, -40, 0, 12, -30, 0, 20, 24, 0, 24, 8, 0, -30, 20, 0, -10, -2, 0, 32, -24, 0, 48, 20, 0, -48, 8, 0, 8, -64, 0, -8, 20, 0, 40, 24, 0, 36, 22, 0, 28, -12, 0, 36, 8, 0, -22, 12, 0, -1, 56, 0, 0, -32, 0, -24, 16, 0, 24, 16, 0, -60, 50, 0, 32, 0, 0, -52, 2, 0, 26, 48, 0, 46, -4, 0, 2, 42, 0, 0, 30, 0, -8, 40, 0, -16, 0, 0, 48, 20, 0, -16, 9, 0, 28, 28, 0, -10, 16, 0, 18, 48, 0, 40, -24, 0, 24, 24, 0, 36, -2, 0, -18, 16, 0, -48, -24, 0, 26, -80, 0, 6, -48, 0, -1, -2, 0, -40, -6, 0, 40, -16, 0, 66, -64, 0, -8, -30, 0, -48, -2, 0, -50, -20, 0, 62, -40, 0, -40, 24, 0, 68, 24, 0, 40, 40, 0, 0, -32, 0, 34, -18, 0, 40, -4, 0, -10, 24, 0, 64, -4, 0, -16, -12, 0, 32, -48, 0, -12, 16, 0, 74, 30, 0, 24, 80, 0, 80, -2, 0, -54, 60, 0, 70, 0, 0, 16, 32, 0, 0, 4, 0, -40, -80, 0, -37, 71, 0, 14, -12, 0, 8, -16, 0, -18, -24, 0, -66, 20, 0, 6, -78, 0, -28, 6, 0, -48, 8, 0, 32, 22, 0, 4, 66, 0, 120, 12, 0, -18, 16, 0, 12, -44, 0, -16, 14, 0, 68, 0, 0, -24, 56, 0, -32, -36, 0, 2, -22, 0, -8, 16, 0, -48, 48, 0, -34, 0, 0, 14, -68, 0, -4, -32, 0, -48, 96, 0, 58, -34, 0, 24, -48, 0, 20, 8, 0, 30, 16, 0, -36, -48, 0, 12, -10, 0, -128, 12, 0, 40, 0, 0, -22, -64, 0, -12, 4, 0, 32, -4, 0, 32, -4, 0, -2, -40, 0, 4, 80, 0, -16, -10, 0, -40, 24, 0, 26, -36, 0, -8, -6, 0, 16, 6, 0, -4, 44, 0, 54, -24, 0, 4, 96, 0, -72, -16, 0, 56, -56, 0, -10, 48, 0, 18, -48, 0, 24, -10, 0, -16, -16, 0, 0, 32, 0, -16, 96, 0, 8, 18, 0, 0, 64, 0, 21, -6, 0, -32, -84, 0, 48, -10, 0, 6, -36, 0, 22, 36, 0, 10, -20, 0, 72, -4, 0, -48, 24, 0, -6, -38, 0, 0, -78, 0, -8, 16, 0, -18, -88, 0, 40, 16, 0, -12, -22, 0, 4, -32, 0, -36, 56, 0, 96, -20, 0, -4, -42, 0, -72, -24, 0, 18, 4, 0, -96, 0, 0, 8, 6, 0, 32, 40, 0, -8, -8, 0, -36, -15, 0, -12, -16, 0, -16, 2, 0, 4, -36, 0, 14, 32, 0, 5, -20, 0, -8, 4, 0, -28, 0, 0, 60, -32, 0, -16, -14, 0, -16, 1, 0, -34, 96, 0, -64, -24, 0, 18, 36, 0, -40, -12, 0, -16, 72, 0, -80, 36, 0, 60, -34, 0, 12, -8, 0, 64, -76, 0, 16, -8, 0, 4, -36, 0, 8, 0, 0, -48, -8, 0, -54, -26, 0, -16, 26, 0, -56, -12, 0, -32, -28, 0, -12, 72, 0, -12, -18, 0, -32, 0, 0, 24, -16, 0, 34, 26, 0, -4, -64, 0, 76, -32, 0, -2, -76, 0, 14, -80, 0, -16, 48, 0, 48, -34, 0, 12, 64, 0, -28, -2, 0, 40, 68, 0, 48, 1, 0, 2, -88, 0, 38, 24, 0, 6, -30, 0, 0, -32, 0, -32, -72, 0, -96, 10, 0, 32, 50, 0, 56, 24, 0, -6, -12, 0, 0, 36, 0, -4, 10, 0, -4, 10, 0, 40, 88, 0, 10, 32, 0, 16, 64, 0, 8, -4, 0, 6, -44, 0, 0, -60, 0, 24, 28, 0, -72, -24, 0, -32, -56, 0, -46, 80, 0, 41, -100, 0, -40, 12, 0, -10, 8, 0, 72, -52, 0, 16, -6, 0, -28, 4, 0, 8, 8, 0, -38, 14, 0, 24, 38, 0, -36, 0, 0, -60, 24, 0, 32, 8, 0, -22, 50, 0, 0, 36, 0, -24, 96, 0, -86, -64, 0, -42, 4, 0, 72, 24, 0, 32, 0, 0, -12, -4, 0, -6, 0, 0, -24, 28, 0, -60, -72, 0, -64, -26, 0, -8, -96, 0, 40, -2, 0, 30, 48, 0, 44, 56, 0, -4, 0, 0, 56, -40, 0, 16, 32, 0, 17, 24, 0, -48, 6, 0, 24, -2, 0, 6, 72, 0, 30, -8, 0, -8, 6, 0, 24, 22, 0, -8, -16, 0, -160, 14, 0, 16, -38, 0, 4, 8, 0, -48, -4, 0, -20, -44, 0, 18, 36, 0, -64, -28, 0, -72, -16, 0, 6, 18, 0, 12, -96, 0, 40, 4, 0, -64, -36, 0, -34, 8, 0, 0, 30, 0, 8, 14, 0, 0, -48, 0, 50, 80, 0, -12, 36, 0, 60, -8, 0, -20, 120, 0, -74, 24, 0, -8, -94, 0, 20, 8, 0, 32, 72, 0, 36, -6, 0, 18, -30, 0, 36, 19, 0, 12, -64, 0, 32, 4, 0, -20, -64, 0, 16, 48, 0, -12, 40, 0, 12, 20, 0, 24, 42, 0, -8, 10, 0, 0, 36, 0, 14, -36, 0, -22, 0, 0, -24, 12, 0, -8, -48, 0, 4, 48, 0, 16, -54, 0, -24, -24, 0, 10, 48, 0, -64, -36, 0, 6, 128, 0, -16, -22, 0, -60, -48, 0, 2, 20, 0, -48, -34, 0, -32, 10, 0, -10, 64, 0, 70, 16, 0, 16, -58, 0, 80, 24, 0, 56, -64, 0, -31, -62, 0, -22, -24, 0, -120, -32, 0, 4, 20, 0, -64, 0, 0, 20, -78, 0, 24, 10, 0, -72, 0, 0, -2, -26, 0, -48, -16, 0, 48, 4, 0, 54, -32, 0, -26, -48, 0, 2, 6, 0, -136, -16, 0, -16, -24, 0, -48, -9, 0, 38, -16, 0, -24, 8, 0, 42, 20, 0, -96, -28, 0, 16, 120, 0, 4, 42, 0, -16, -72, 0, -6, -18, 0, -12, 46, 0, 0, 8, 0, -60, 0, 0, 0, 24, 0, 0, -16, 0, 48, -24, 0, 80, -32, 0, 16, 10, 0, -19, -2, 0, -4, 10, 0, -80, -112, 0, -4, -24, 0, 14, -32, 0, 0, -36, 0, 12, -40, 0, 74, -4, 0, 12, 2, 0, -12, -12, 0, -64, 68, 0, -60, -8, 0, 18, 96, 0, -80, -32, 0, -8, 56, 0, -68, 0, 0, -18, 34, 0, -28, -40, 0, -6, 80, 0, 78, -44, 0, 2, -36, 0, 40, 2, 0, 60, -120, 0, -32, 12, 0, -16, 48, 0, 16, -32, 0, 50, -92, 0, 60, -40, 0, -24, 64, 0, 48, 8, 0, 48, -40, 0, -14, -14, 0, -48, 54, 0, -48, 2, 0, 42, -8, 0, 20, 16, 0, 20, 22, 0, -40, 30, 0, 36, 32, 0, 2, -96, 0, -8, -58, 0, -8, -2, 0, 4, 0, 0, 32, 48, 0, 32, 34, 0, -48, -44, 0, -32, 80, 0, -32, 58, 0, -42, 82, 0, -28, 8, 0, -6, 8, 0, 112, 56, 0, 12, 62, 0, 52, 32, 0, -24, 24, 0, 8, -32, 0, 80, -84, 0, -72, 0, 0, 0, -12, 0, -50, 32, 0, 0, 64, 0, 84, 4, 0, 72, 0, 0, 34, -44, 0, 34, 34, 0, 72, -6, 0, 0, 28, 0, 60, 8, 0, -9, -84, 0, -48, 14, 0, 48, -48, 0, 18, 96, 0, 8, -32, 0, -20, -12, 0, -50, 120, 0, -14, -80, 0, 16, 70, 0, 52, 44, 0, 32, -16, 0, 192, -1, 0, -4, 42, 0, 32, 8, 0, 22, 0, 0, -34, -48, 0, -8, -94, 0, -80, -12, 0, 72, -24, 0, -48, 22, 0, 28, -96, 0, 32, -18, 0, -4, -120, 0, -96, 40, 0, -4, -6, 0, -72, -16, 0, -24, -40, 0, 44, -96, 0, 12, -66, 0, -8, -34, 0, -64, 32, 0, -82, 64, 0, -4, 14, 0, 4, 46, 0, -8, -24, 0, -17, 36, 0, 24, -20, 0, -56, 4, 0, 18, 60, 0, -32, -72, 0, -18, -6, 0, 24, -8, 0, 8, 40, 0, 18, -28, 0, -2, 54, 0, 0, 0, 0, -90, -60, 0, 28, 56, 0, -6, 96, 0, 76, -32, 0, 20, -24, 0, -62, 54, 0, -16, 70, 0, 136, -20, 0, -30, 8, 0, 80, -16, 0, -8, 54, 0, 96, 0, 0, 24, -96, 0, 0, -16, 0, -64, 36, 0, -72, -3, 0, 38, -108, 0, 96, 44, 0, -2, 58, 0, 8, 10, 0, -60, -24, 0, 96, 6, 0, 32, -102, 0, 0, -8, 0, 32, 48, 0, -26, -52, 0, 20, 128, 0, -72, 48, 0, 64, -32, 0, 20, -44, 0, 14, 16, 0, 24, -8, 0, -12, -36, 0, 108, 44, 0, -8, 32, 0, 56, 0, 0, 12, -8, 0, -38, -64, 0, -40, 14, 0, -88, 12, 0, -30, -60, 0, -44, 20, 0, 24, -106, 0, 0, 24, 0, 8, 24, 0, 20, -30, 0, 20, 96, 0, 56, -10, 0, -2, 160, 0, 9, 32, 0, -24, -20, 0, 48, 48, 0, 20, 64, 0], "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, 0, 1, 2, 0, 4, 1, 0, 2, 4, 0, -2, 4, 0, 1, -6, 0, 4, 2, 0, 4, -8, 0, -1, -2, 0, 4, -10, 0, 4, 1, 0, -6, 8, 0, 6, 4, 0, 2, -2, 0, -8, 4, 0, -8, 8, 0, 9, -1, 0, -2, 6, 0, 8, 4, 0, -10, -12, 0, 1, 4, 0, 1, -4, 0, 0, -6, 0, 8, 0, 0, 10, 6, 0, 4, 16, 0, -12, 2, 0, -2, 12, 0, -12, -8, 0, 4, -6, 0, -8, -8, 0, 8, 8, 0, 2, 9, 0, -1, -2, 0, -16, -2, 0, 6, 12, 0, 14, 8, 0, 4, 6, 0, -16, -10, 0, -12, -24, 0, 5, 1, 0, 4, -12, 0, -16, 1, 0, -4, -4, 0, 16, 0, 0, -6, -2, 0, -8, 8, 0, 0, -8, 0, -20, 10, 0, 6, 10, 0, 20, 4, 0, 16, 8, 0, 14, -12, 0, 2, -32, 0, 20, -2, 0, 12, 0, 0, -9, -12, 0, -8, -18, 0, -4, 4, 0, -6, -20, 0, -2, -8, 0, -8, 12, 0, -24, 8, 0, 8, 0, 0, 2, 2, 0, 9, 18, 0, -24, -1, 0, -2, -40, 0, -4, -16, 0, -2, 16, 0, -16, 6, 0, 12, -16, 0, 16, 14, 0, 8, 12, 0, -4, 4, 0, 6, 4, 0, -10, -16, 0, -10, 10, 0, 16, -12, 0, -24, 8, 0, 2, 5, 0, 1, 18, 0, -8, 4, 0, -12, -12, 0, -32, -16, 0, 1, 6, 0, 24, -4, 0, -4, 24, 0, 12, 16, 0, 0, -22, 0, 24, -6, 0, -2, -4, 0, -2, -8, 0, 8, 18, 0, 4, 0, 0, -8, -8, 0, 19, -20, 0, 10, -22, 0, -24, 6, 0, 10, 16, 0, -32, 20, 0, 4, 2, 0, 8, 16, 0, 8, 0, 0, 10, 14, 0, -12, 18, 0, -40, 2, 0, -32, -24, 0, 2, 20, 0, -2, 32, 0, 8, 12, 0, 0, 0, 0, -6, -9, 0, -12, 16, 0, 8, -8, 0, -18, -4, 0, -34, -4, 0, 4, -18, 0, 0, -6, 0, -20, -8, 0, -3, -2, 0, -8, 20, 0, -8, -8, 0, 12, 24, 0, -10, -24, 0, 8, 20, 0, 28, 8, 0, 0, 16, 0, 32, 2, 0, 2, 30, 0, 48, 9, 0, 18, -24, 0, -18, -24, 0, -1, -6, 0, -8, -2, 0, -40, 24, 0, 34, -4, 0, -16, -48, 0, 24, -2, 0, 16, 4, 0, 14, -16, 0, 6, 6, 0, 4, 12, 0, -16, 0, 0, 2, 16, 0, 14, -32, 0, 24, 8, 0, 12, 12, 0, -12, -4, 0, 4, -10, 0, -8, 6, 0, 4, -16, 0, 18, -10, 0, -16, 18, 0, -32, -10, 0, 10, -4, 0, 0, 16, 0, -12, -32, 0, -4, -24, 0, 8, 40, 0, -12, 2, 0, 5, 4, 0, -16, 1, 0, 18, -12, 0, 60, -8, 0, 4, 0, 0, -16, -12, 0, -12, 0, 0, -4, -32, 0, -16, -34, 0, 40, 1, 0, 6, -32, 0, 32, 24, 0, -4, 10, 0, 16, -4, 0, 24, -24, 0, 41, 12, 0, 16, 4, 0, 24, 0, 0, -22, 36, 0, -42, 24, 0, -6, 28, 0, -8, -2, 0, -4, -40, 0, -48, -2, 0, -8, 22, 0, 16, 8, 0, 18, -28, 0, 12, 4, 0, 0, 14, 0, -12, -8, 0, -8, 8, 0, 18, 19, 0, -20, 48, 0, 24, 10, 0, -22, 12, 0, 16, -24, 0, 6, -22, 0, -48, 10, 0, 16, 24, 0, -22, -32, 0, 20, 10, 0, -48, 4, 0, 2, -16, 0, 38, 8, 0, 16, 42, 0, -12, 8, 0, 0, -24, 0, -19, 10, 0, 14, -36, 0, 12, -12, 0, 18, -32, 0, -18, -40, 0, 2, 2, 0, -16, -32, 0, -24, 8, 0, -48, 2, 0, 20, 30, 0, -8, -2, 0, 32, -44, 0, -42, 8, 0, 12, 32, 0, 80, 0, 0, 0, 4, 0, 34, -6, 0, -9, 14, 0, 8, -12, 0, 16, 44, 0, -4, 8, 0, -8, -12, 0, 28, -18, 0, -4, -16, 0, 12, -34, 0, -4, 46, 0, 24, 4, 0, -18, -8, 0, -2, 0, 0, -6, -32, 0, -16, -20, 0, -8, 0, 0, -64, -3, 0, -2, 10, 0, 32, -8, 0, 20, 48, 0, 14, -8, 0, -8, 0, 0, -40, 12, 0, 24, 24, 0, 20, -10, 0, -24, 48, 0, 8, 8, 0, 20, 40, 0, 22, 28, 0, 8, -22, 0, 56, 0, 0, 16, 24, 0, 50, 32, 0, 2, 26, 0, -4, 2, 0, 30, -8, 0, 0, 48, 0, 9, 28, 0, 16, 18, 0, -24, 24, 0, -2, -18, 0, -24, 26, 0, -48, -1, 0, -6, 40, 0, -64, -8, 0, -2, -50, 0, -40, -40, 0, 24, 40, 0, -32, 34, 0, -4, -10, 0, -4, -16, 0, -48, -12, 0, 30, 24, 0, -2, -54, 0, 0, 16, 0, 4, -40, 0, 71, 14, 0, -16, -18, 0, 20, 6, 0, 6, -48, 0, 22, 4, 0, 12, -18, 0, -44, -16, 0, 0, -24, 0, -36, 2, 0, 16, -48, 0, 0, 14, 0, -32, -48, 0, -34, 24, 0, 8, 30, 0, -48, 12, 0, 12, 40, 0, -64, -12, 0, -4, 32, 0, -40, 4, 0, -10, -40, 0, -36, -8, 0, 6, -4, 0, -24, 4, 0, -16, 56, 0, 48, 18, 0, -10, -16, 0, 32, -16, 0, 18, 0, 0, -6, -32, 0, -10, 6, 0, 36, 10, 0, -4, -48, 0, -38, 0, 0, 16, -18, 0, 16, -12, 0, -32, -36, 0, -20, -4, 0, -24, 18, 0, 0, 8, 0, 40, -8, 0, -15, -12, 0, 2, 4, 0, 32, 5, 0, 4, -28, 0, -32, -16, 0, 1, -34, 0, -24, 18, 0, -12, -16, 0, 36, 60, 0, -8, 64, 0, -8, 4, 0, 0, -48, 0, -26, -16, 0, -12, -32, 0, 72, -12, 0, 0, 24, 0, 26, -4, 0, -32, -2, 0, -80, -16, 0, -34, 12, 0, -2, 40, 0, 1, 2, 0, 24, 6, 0, -32, -32, 0, 10, 32, 0, 24, -6, 0, 36, -4, 0, 10, 40, 0, 32, 16, 0, -4, 6, 0, -60, 24, 0, -24, -32, 0, 80, 41, 0, 12, -10, 0, -52, 16, 0, 4, 8, 0, 14, 24, 0, 0, -60, 0, 8, -22, 0, 36, -24, 0, -64, -42, 0, 24, 32, 0, -4, -6, 0, 28, -60, 0, -26, -8, 0, -2, 30, 0, 56, -4, 0, -40, 16, 0, 24, -48, 0, -2, 6, 0, -8, -8, 0, 22, -8, 0, 14, 16, 0, 8, -48, 0, -44, 18, 0, -28, -72, 0, 18, 12, 0, 4, -64, 0, 8, 0, 0, 14, 0, 0, 80, -12, 0, -8, -20, 0, 24, -8, 0, 8, 32, 0, -6, 18, 0, 19, 12, 0, 4, -20, 0, 48, -12, 0, 20, 24, 0, 10, 0, 0, -36, -22, 0, 12, -8, 0, 48, 16, 0, -24, 10, 0, -36, 6, 0, -22, -60, 0, 20, -48, 0, 10, -10, 0, 16, 16, 0, 24, 56, 0, -62, -22, 0, -32, 4, 0, 0, 20, 0, 10, -72, 0, -26, -48, 0, 4, 54, 0, -48, 2, 0, -16, -16, 0, -9, 38, 0, 8, 42, 0, -28, 16, 0, 42, -16, 0, -18, -12, 0, 8, -60, 0, 24, 0, 0, -24, 80, 0, 10, -19, 0, 10, -80, 0, -24, 14, 0, -36, 12, 0, -4, 12, 0, -12, -64, 0, -8, 18, 0, -32, -8, 0, 0, -18, 0, -40, -6, 0, -44, 2, 0, 2, 60, 0, 12, -16, 0, -32, 50, 0, -40, -24, 0, 8, 48, 0, -14, -48, 0, 2, 42, 0, 16, 20, 0, 30, 36, 0, -96, -8, 0, -2, 4, 0, 48, 32, 0, -44, -32, 0, 58, -42, 0, 8, -6, 0, 56, 12, 0, 32, -24, 0, -32, 80, 0, 0, 0, 0, 32, 0, 0, 4, 72, 0, -44, 34, 0, -6, 0, 0, 8, -9, 0, 14, 48, 0, 96, 8, 0, -12, -50, 0, -80, 16, 0, 44, 32, 0, -1, -4, 0, 8, 22, 0, -48, -8, 0, -12, 72, 0, 22, 28, 0, -18, -4, 0, 40, -4, 0, -16, -24, 0, -96, 12, 0, -34, -64, 0, 64, -4, 0, 46, -8, 0, 36, 24, 0, 4, 18, 0, -72, -18, 0, -8, 8, 0, -28, -2, 0, 0, -90, 0, 56, -6, 0, -32, 20, 0, 54, -16, 0, -20, -30, 0, -16, -8, 0, 0, 24, 0, -16, -64, 0, -3, 38, 0, 44, -2, 0, 10, -60, 0, 6, 32, 0, -8, 32, 0, -52, 20, 0, 48, 64, 0, -44, 14, 0, -8, -12, 0, 44, -8, 0, 0, 12, 0, -64, -40, 0, 12, -30, 0, 20, 24, 0, 24, 8, 0, -30, 20, 0, -10, -2, 0, 32, -24, 0, 48, 20, 0, -48, 8, 0, 8, -64, 0, -8, 20, 0, 40, 24, 0, 36, 22, 0, 28, -12, 0, 36, 8, 0, -22, 12, 0, -1, 56, 0, 0, -32, 0, -24, 16, 0, 24, 16, 0, -60, 50, 0, 32, 0, 0, -52, 2, 0, 26, 48, 0, 46, -4, 0, 2, 42, 0, 0, 30, 0, -8, 40, 0, -16, 0, 0, 48, 20, 0, -16, 9, 0, 28, 28, 0, -10, 16, 0, 18, 48, 0, 40, -24, 0, 24, 24, 0, 36, -2, 0, -18, 16, 0, -48, -24, 0, 26, -80, 0, 6, -48, 0, -1, -2, 0, -40, -6, 0, 40, -16, 0, 66, -64, 0, -8, -30, 0, -48, -2, 0, -50, -20, 0, 62, -40, 0, -40, 24, 0, 68, 24, 0, 40, 40, 0, 0, -32, 0, 34, -18, 0, 40, -4, 0, -10, 24, 0, 64, -4, 0, -16, -12, 0, 32, -48, 0, -12, 16, 0, 74, 30, 0, 24, 80, 0, 80, -2, 0, -54, 60, 0, 70, 0, 0, 16, 32, 0, 0, 4, 0, -40, -80, 0, -37, 71, 0, 14, -12, 0, 8, -16, 0, -18, -24, 0, -66, 20, 0, 6, -78, 0, -28, 6, 0, -48, 8, 0, 32, 22, 0, 4, 66, 0, 120, 12, 0, -18, 16, 0, 12, -44, 0, -16, 14, 0, 68, 0, 0, -24, 56, 0, -32, -36, 0, 2, -22, 0, -8, 16, 0, -48, 48, 0, -34, 0, 0, 14, -68, 0, -4, -32, 0, -48, 96, 0, 58, -34, 0, 24, -48, 0, 20, 8, 0, 30, 16, 0, -36, -48, 0, 12, -10, 0, -128, 12, 0, 40, 0, 0, -22, -64, 0, -12, 4, 0, 32, -4, 0, 32, -4, 0, -2, -40, 0, 4, 80, 0, -16, -10, 0, -40, 24, 0, 26, -36, 0, -8, -6, 0, 16, 6, 0, -4, 44, 0, 54, -24, 0, 4, 96, 0, -72, -16, 0, 56, -56, 0, -10, 48, 0, 18, -48, 0, 24, -10, 0, -16, -16, 0, 0, 32, 0, -16, 96, 0, 8, 18, 0, 0, 64, 0, 21, -6, 0, -32, -84, 0, 48, -10, 0, 6, -36, 0, 22, 36, 0, 10, -20, 0, 72, -4, 0, -48, 24, 0, -6, -38, 0, 0, -78, 0, -8, 16, 0, -18, -88, 0, 40, 16, 0, -12, -22, 0, 4, -32, 0, -36, 56, 0, 96, -20, 0, -4, -42, 0, -72, -24, 0, 18, 4, 0, -96, 0, 0, 8, 6, 0, 32, 40, 0, -8, -8, 0, -36, -15, 0, -12, -16, 0, -16, 2, 0, 4, -36, 0, 14, 32, 0, 5, -20, 0, -8, 4, 0, -28, 0, 0, 60, -32, 0, -16, -14, 0, -16, 1, 0, -34, 96, 0, -64, -24, 0, 18, 36, 0, -40, -12, 0, -16, 72, 0, -80, 36, 0, 60, -34, 0, 12, -8, 0, 64, -76, 0, 16, -8, 0, 4, -36, 0, 8, 0, 0, -48, -8, 0, -54, -26, 0, -16, 26, 0, -56, -12, 0, -32, -28, 0, -12, 72, 0, -12, -18, 0, -32, 0, 0, 24, -16, 0, 34, 26, 0, -4, -64, 0, 76, -32, 0, -2, -76, 0, 14, -80, 0, -16, 48, 0, 48, -34, 0, 12, 64, 0, -28, -2, 0, 40, 68, 0, 48, 1, 0, 2, -88, 0, 38, 24, 0, 6, -30, 0, 0, -32, 0, -32, -72, 0, -96, 10, 0, 32, 50, 0, 56, 24, 0, -6, -12, 0, 0, 36, 0, -4, 10, 0, -4, 10, 0, 40, 88, 0, 10, 32, 0, 16, 64, 0, 8, -4, 0, 6, -44, 0, 0, -60, 0, 24, 28, 0, -72, -24, 0, -32, -56, 0, -46, 80, 0, 41, -100, 0, -40, 12, 0, -10, 8, 0, 72, -52, 0, 16, -6, 0, -28, 4, 0, 8, 8, 0, -38, 14, 0, 24, 38, 0, -36, 0, 0, -60, 24, 0, 32, 8, 0, -22, 50, 0, 0, 36, 0, -24, 96, 0, -86, -64, 0, -42, 4, 0, 72, 24, 0, 32, 0, 0, -12, -4, 0, -6, 0, 0, -24, 28, 0, -60, -72, 0, -64, -26, 0, -8, -96, 0, 40, -2, 0, 30, 48, 0, 44, 56, 0, -4, 0, 0, 56, -40, 0, 16, 32, 0, 17, 24, 0, -48, 6, 0, 24, -2, 0, 6, 72, 0, 30, -8, 0, -8, 6, 0, 24, 22, 0, -8, -16, 0, -160, 14, 0, 16, -38, 0, 4, 8, 0, -48, -4, 0, -20, -44, 0, 18, 36, 0, -64, -28, 0, -72, -16, 0, 6, 18, 0, 12, -96, 0, 40, 4, 0, -64, -36, 0, -34, 8, 0, 0, 30, 0, 8, 14, 0, 0, -48, 0, 50, 80, 0, -12, 36, 0, 60, -8, 0, -20, 120, 0, -74, 24, 0, -8, -94, 0, 20, 8, 0, 32, 72, 0, 36, -6, 0, 18, -30, 0, 36, 19, 0, 12, -64, 0, 32, 4, 0, -20, -64, 0, 16, 48, 0, -12, 40, 0, 12, 20, 0, 24, 42, 0, -8, 10, 0, 0, 36, 0, 14, -36, 0, -22, 0, 0, -24, 12, 0, -8, -48, 0, 4, 48, 0, 16, -54, 0, -24, -24, 0, 10, 48, 0, -64, -36, 0, 6, 128, 0, -16, -22, 0, -60, -48, 0, 2, 20, 0, -48, -34, 0, -32, 10, 0, -10, 64, 0, 70, 16, 0, 16, -58, 0, 80, 24, 0, 56, -64, 0, -31, -62, 0, -22, -24, 0, -120, -32, 0, 4, 20, 0, -64, 0, 0, 20, -78, 0, 24, 10, 0, -72, 0, 0, -2, -26, 0, -48, -16, 0, 48, 4, 0, 54, -32, 0, -26, -48, 0, 2, 6, 0, -136, -16, 0, -16, -24, 0, -48, -9, 0, 38, -16, 0, -24, 8, 0, 42, 20, 0, -96, -28, 0, 16, 120, 0, 4, 42, 0, -16, -72, 0, -6, -18, 0, -12, 46, 0, 0, 8, 0, -60, 0, 0, 0, 24, 0, 0, -16, 0, 48, -24, 0, 80, -32, 0, 16, 10, 0, -19, -2, 0, -4, 10, 0, -80, -112, 0, -4, -24, 0, 14, -32, 0, 0, -36, 0, 12, -40, 0, 74, -4, 0, 12, 2, 0, -12, -12, 0, -64, 68, 0, -60, -8, 0, 18, 96, 0, -80, -32, 0, -8, 56, 0, -68, 0, 0, -18, 34, 0, -28, -40, 0, -6, 80, 0, 78, -44, 0, 2, -36, 0, 40, 2, 0, 60, -120, 0, -32, 12, 0, -16, 48, 0, 16, -32, 0, 50, -92, 0, 60, -40, 0, -24, 64, 0, 48, 8, 0, 48, -40, 0, -14, -14, 0, -48, 54, 0, -48, 2, 0, 42, -8, 0, 20, 16, 0, 20, 22, 0, -40, 30, 0, 36, 32, 0, 2, -96, 0, -8, -58, 0, -8, -2, 0, 4, 0, 0, 32, 48, 0, 32, 34, 0, -48, -44, 0, -32, 80, 0, -32, 58, 0, -42, 82, 0, -28, 8, 0, -6, 8, 0, 112, 56, 0, 12, 62, 0, 52, 32, 0, -24, 24, 0, 8, -32, 0, 80, -84, 0, -72, 0, 0, 0, -12, 0, -50, 32, 0, 0, 64, 0, 84, 4, 0, 72, 0, 0, 34, -44, 0, 34, 34, 0, 72, -6, 0, 0, 28, 0, 60, 8, 0, -9, -84, 0, -48, 14, 0, 48, -48, 0, 18, 96, 0, 8, -32, 0, -20, -12, 0, -50, 120, 0, -14, -80, 0, 16, 70, 0, 52, 44, 0, 32, -16, 0, 192, -1, 0, -4, 42, 0, 32, 8, 0, 22, 0, 0, -34, -48, 0, -8, -94, 0, -80, -12, 0, 72, -24, 0, -48, 22, 0, 28, -96, 0, 32, -18, 0, -4, -120, 0, -96, 40, 0, -4, -6, 0, -72, -16, 0, -24, -40, 0, 44, -96, 0, 12, -66, 0, -8, -34, 0, -64, 32, 0, -82, 64, 0, -4, 14, 0, 4, 46, 0, -8, -24, 0, -17, 36, 0, 24, -20, 0, -56, 4, 0, 18, 60, 0, -32, -72, 0, -18, -6, 0, 24, -8, 0, 8, 40, 0, 18, -28, 0, -2, 54, 0, 0, 0, 0, -90, -60, 0, 28, 56, 0, -6, 96, 0, 76, -32, 0, 20, -24, 0, -62, 54, 0, -16, 70, 0, 136, -20, 0, -30, 8, 0, 80, -16, 0, -8, 54, 0, 96, 0, 0, 24, -96, 0, 0, -16, 0, -64, 36, 0, -72, -3, 0, 38, -108, 0, 96, 44, 0, -2, 58, 0, 8, 10, 0, -60, -24, 0, 96, 6, 0, 32, -102, 0, 0, -8, 0, 32, 48, 0, -26, -52, 0, 20, 128, 0, -72, 48, 0, 64, -32, 0, 20, -44, 0, 14, 16, 0, 24, -8, 0, -12, -36, 0, 108, 44, 0, -8, 32, 0, 56, 0, 0, 12, -8, 0, -38, -64, 0, -40, 14, 0, -88, 12, 0, -30, -60, 0, -44, 20, 0, 24, -106, 0, 0, 24, 0, 8, 24, 0, 20, -30, 0, 20, 96, 0, 56, -10, 0, -2, 160, 0, 9, 32, 0, -24, -20, 0, 48, 48, 0, 20, 64, 0]}