# Stored data for newform 1694.2.a.e, downloaded from the LMFDB on 15 November 2024.
{"Nk2": 6776, "analytic_conductor": 13.526658102404896, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [7, 1], [11, -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": [1694, 1, [969, 365], [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": [[3, [2, 1]], [5, [0, 1]], [13, [-4, 1]]], "hecke_orbit": 5, "hecke_orbit_code": 18014398543038110, "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": "1694.2.a.e", "level": 1694, "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, 7, 11], "level_radical": 154, "minimal_twist": "14.2.a.a", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q+q^{2}-2q^{3}+q^{4}-2q^{6}-q^{7}+q^{8}+\\cdots", "related_objects": ["EllipticCurve/Q/1694/e"], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1694.2.a", "trace_display": [1, -2, 0, -1], "trace_hash": 2247578083762146412, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.976", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.943", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.854", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.022", "prec": 17}, "traces": [0, 1, 1, -2, 1, 0, -2, -1, 1, 1, 0, 0, -2, 4, -1, 0, 1, -6, 1, -2, 0, 2, 0, 0, -2, -5, 4, 4, -1, 6, 0, -4, 1, 0, -6, 0, 1, 2, -2, -8, 0, -6, 2, -8, 0, 0, 0, -12, -2, 1, -5, 12, 4, 6, 4, 0, -1, 4, 6, -6, 0, -8, -4, -1, 1, 0, 0, -4, -6, 0, 0, 0, 1, -2, 2, 10, -2, 0, -8, -8, 0, -11, -6, 6, 2, 0, -8, -12, 0, -6, 0, -4, 0, 8, -12, 0, -2, -10, 1, 0, -5, 0, 12, -4, 4, 0, 6, -12, 4, -2, 0, -4, -1, 6, 4, 0, 6, 4, -6, 6, 0, 0, -8, 12, -4, 0, -1, 16, 1, 16, 0, -18, 0, 2, -4, 0, -6, 18, 0, -14, 0, 24, 0, 0, 1, 0, -2, -2, 2, 18, 10, -8, -2, -6, 0, 0, -8, -4, -8, -12, 0, 0, -11, -16, -6, 0, 6, 12, 2, 3, 0, -2, -8, 12, -12, 5, 0, 12, -6, -12, 0, 20, -4, 16, 0, 0, 8, 0, -12, -4, 0, 24, -2, -14, -10, 0, 1, 18, 0, 20, -5, 8, 0, -6, 12, 0, -4, 0, 4, 0, 0, 4, 6, 0, -12, 0, 4, 4, -2, 4, 0, -24, -4, 8, -1, -5, 6, -18, 4, -4, 0, 0, 6, 6, 4, 0, -6, 16, 6, -24, 0, 10, 0, 10, -8, 0, 12, -8, -4, -12, 0, -18, -1, 0, 16, 0, 1, 18, 16, -2, 0, 6, -18, 0, 0, 0, 2, 12, -4, -12, 0, 16, -6, 8, 18, 0, 0, 10, -14, -4, 0, 6, 24, 22, 0, 0, 0, 6, 1, 19, 0, 20, -2, -24, -2, 0, 2, 0, 18, 0, 10, 8, -8, 0, -2, 0, -6, -2, 0, 8, 0, -24, -8, -10, -4, 0, -8, 6, -12, 0, 0, 24, 0, 12, -11, -20, -16, 4, -6, 12, 0, 8, 6, 2, 12, 0, 2, -14, 3, -12, 0, 0, -2, -1, -8, 0, 12, 24, -12, 28, 5, 16, 0, 18, 12, 0, -6, -12, -12, 24, 0, -15, 20, 0, -4, 0, 16, 8, 0, -6, 0, -6, 8, -14, 0, 0, -12, 24, -4, -16, 0, -32, 24, 36, -2, 0, -14, -8, -10, 18, 0, 0, 1, 36, 18, 0, 0, 20, 20, -4, -5, -18, 8, -16, 0, 0, -6, 0, 12, -14, 0, -36, -4, 6, 0, 0, 4, 28, 0, 6, 0, -10, 4, -12, 6, 30, 0, 8, -12, 0, 0, -24, 4, -34, 4, 0, -2, 0, 4, -8, 0, 1, -24, -12, -4, 0, 8, -36, -1, 18, -5, 0, 6, 16, -18, 0, 4, 10, -4, -24, 0, -12, 0, 32, 6, 0, 6, -6, 4, 4, 0, 8, -6, 0, 16, 10, 6, 6, -24, 36, 0, 8, 10, 0, 0, 0, 10, -16, -8, 32, 0, 12, 12, -36, -8, 0, -4, 0, -12, -4, 0, -24, -18, 0, -1, 0, 0, -6, 16, 36, 0, 2, 1, -8, 18, 0, 16, 0, -2, -24, 0, 6, 6, -2, -18, -10, 0, 24, 0, -23, 0, -6, 2, -24, 12, 0, -4, 24, -12, 0, 0, -38, 16, -40, -6, 0, 8, -8, 18, -8, 0, -12, 0, 8, 10, 0, -14, -6, -4, -32, 0, 0, 6, -30, 24, 0, 22, 11, 0, -6, 0, -32, 0, -48, 6, 0, 1, 2, 19, 28, 0, -6, 20, 0, -2, 0, -24, -42, -2, 8, 0, -36, 2, 6, 0, 0, 18, -40, 0, -24, 10, -26, 8, -4, -8, 0, 0, -32, -2, 12, 0, -48, -6, -2, -2, 0, 0, 6, 8, 26, 0, 0, -24, 6, -8, 25, -10, 0, -4, -12, 0, -16, -8, -8, 6, 0, -12, 4, 0, 0, 0, -18, 24, 14, 0, 0, 12, -12, -11, 0, -20, -8, -16, 18, 4, 0, -6, -2, 12, 24, 0, -40, 8, 48, 6, 0, 2, 0, 12, -16, 0, 0, 2, -26, -14, -20, 3, 12, -12, 10, 0, 36, 0, -12, -2, 0, -1, 8, -8, 24, 0, -46, 12, 0, 24, 0, -12, 36, 28, -12, 5, -18, 16, -4, 0, 0, 18, 0, 12, -46, 0, -8, -6, 0, -12, 0, -12, 48, 24, 12, 0, 4, -15, -20, 20, -30, 0, 44, -4, 13, 0, 48, 16, 40, 8, 0, 0, 0, -6, 16, 0, 16, -6, -24, 8, 0, -14, 6, 0, 12, 0, -40, -12, 36, 24, 0, -4, 2, -16, 0, 0, 18, -32, 2, 24, 0, 36, -24, -2, -14, 0, -36, -14, 24, -8, 20, -10, 4, 18, 12, 0, 0, 0, 24, 1, 0, 36, 22, 18, 0, 0, -6, 0, -32, 20, 0, 20, -12, -4, 72, -5, -6, -18, 0, 8, 0, -16, 24, 0, -6, 0, -2, -6, -32, 0, 0, 12, 16, -14, -4, 0, -6, -36, -40, -4, 0, 6, 36, 0, 56, 0, -20, 4, -6, 28, 0, 0, -16, 6, 12, 0, 7, -10, -12, 4, 0, -12, 0, 6, -44, 30, 0, 0, -44, 8, 0, -12, 18, 0, 14, 0, -12, -24, -24, 4, 0, -34, -38, 4, 0, 0, -16, -2, -10, 0, 0, 4, 22, -8, 48, 0, -54, 1, 20, -24, 0, -12, 36, -4, -16, 0, 0, 8, 24, -36, 0, -1, 0, 18, -24, -5, -36, 0, -16, 6, 0, 16, 44, -18, 0, 0, 48, 4, 0, 10, 0, -4, 18, -24, -56, 0, 4, -12, 0, 0, -10, 32, -4, 6, 6, 0, -2, 6, 48, -6, 0, 4, -2, 4, 20, 0, 24, 8, 0, -6, 0, 0, 24, 16, -8, 10, -12, 6, 54, 6, 0, -24, 0, 36, -18, 0, -15, 8, -12, 10, 0, 0, -32, 0, -24, 0, -6, 10, 14, -16, 40, -8, -6, 32, 0, 0, -2, 12, -36, 12, 0, -36, -24, -8, 0, 0, -16, -4, -16, 0, 0, -12, -8, -4, 8, 0, 0, -24, 36, -18, 0, 0, -12, -1, 34, 0, 28, 0, -36, -6, 0, 16, 6, 36, -36, 0, -4, 2, 0, 1, 30, -8, -32, 18, 2, 0, 0, 16, -26, 0, 0, -2, 48, -24, -4, 0, -48, 6, -18, 6, 0, -2, -56, -18, -30, -10, -44, 0, -44, 24, 0, 0, 8, -23, -36, 0, -30, -6, 16, 2, 0, -24, 0, 12, -8, 0, 6, -4, 12, 24, 40, -12, -48, 0, 24, 0, 0, -38, 30, 16, 0, -40, 8, -6, 0, 0, -30, 8, -22, -8, 0, 18, 6, -8, 4, 0, -16, -12, 48, 0, 0, 8, -24, 10, 36, 0, 0, -14, 12, -6, 0, -4, 34, -32, 28, 0, 12, 0, -46, 6, 0, -30, 0, 24, -50, 0, -48, 22, 0, 11, 0, 0, 32, -6, 24, 0, 16, -32, 16, 0, 0, -48, -8, 6, -72, 0, 12, 1, 2, 2, 0, 19, -24, 28, 16, 0, -32, -6, 60, 20, 0, 0, -36, -2, -12, 0, 20, -24, 0, -42, 60, -2, 0, 8, -18, 0, 60, -36, -3, 2, 0, 6, 12, 0, -36, 0, -40, 18, 66, -40, 0, 0, 2, -24, 0, 10, -14, -26, 36, 8, 0, -4, 0, -8, 32, 0, -12, 0, 26, -32, 0, -2, 6, 12, 0, 0, 0, -48, 24, -6, -5, -2, 28, -2, -30, 0, 28, 0, 18, 6, 0, 8, -40, 26, -12, 0, 12, 0, 0, -24, 0, 6, -48, -8, -26, 25, -14, -10, 12, 0, 0, -4, -12, -12, 18, 0, -40, -16, 20, -8, 0, -8, -20, 6, -48, 0, 24, -12, 8, 4, -60, 0, 24, 0, 20, 0, -16, -18, 0, 24, 0, 14, 0, 0, -30, 0, -58, 12, 48, -12, 0, -11, 34, 0, 68, -20, -48, -8, 8, -16, 0, 18, 42, 4, 0, 0, 0, -6, 0, -2, 0, 12, 16, 24, 24, 0, 62, -40, 4, 8, -30, 48, -32, 6, 24, 0, 0, 2, 32, 0, 0, 12, -24, -16, -16, 0, 18, 0, 48, 2, 0, -26, -36, -14, 0, -20, 14, 3, 0, 12, 0, -12, 0, 10, -8, 0, 18, 36, -72, 0, 0, -12, -24, -2, -33, 0, -20, -1, -30, 8, 0, -8, 66, 24, -18, 0, 22, -46, 24, 12, 0, 0, 4, 24, -64, 0, -48, -12, -20, 36, 0, 28, 0, -12, 40, 5, 12, -18, 0, 16, 0, -4, -8, 0, 18, 0, -36, 18, -4, 0, 0, 12, -8, -46, 0, 0, 6, -8, 56, -6, -20, 0, 30, -12, -26, 0, 24, -12, 42, 48, 0, 24, -72, 12, 24, 0, 0, 4, -16, -15, 0, -20, 64, 20, 0, -30, 48, 0, 50, 44, 0, -4, 48, 13, -38, 0, 32, 48, 0, 16, 0, 40, -16, 8, 24, 0, -32, 0, -24, 0, 30, -6, -4, 16, 72, 0, 6, 16, -46, -6, 0, -24, 0, 8, -58, 0, 0, -14, -30, 6, 0, 0, 8, 12, -12, 0, 16, -40, 12, -12, 0, 36, 0, 24, 0, 0, 0, -4, 36, 2, 0, -16, -12, 0, -4, 0, 3, 18, -72, -32, 40, 2, -72, 24, 0, 0, -2, 36, -4, -24, 0, -2, 36, -14, 22, 0, 0, -36, 32, -14, 0, 24, 24, -8, -34, 20, 0, -10, -42, 4, 0, 18, 12, 12, 12, 0, -8, 0, -12, 0, 0, 24, -16, 1, 4, 0, 66, 36, 0, 22, 5, 18, -12, 0, 40, 0, -48, -6, 0, 0, 0, -32, 46, 20, 18, 0, -16, 20, -24, -12, 0, -4, 58, 72, 48, -5, -66, -6, 4, -18, 0, 0, 48, 8, 26, 0, -12, -16, 72, 24, 0, 0, 0, -6, 60, 0, 74, -2, 76, -6, 0, -32, 10, 0, 20, 0, -6, 12, 0, 16, 0, -14, 0, -4, 0, 0, 16, -6, -24, -36, 0, -40, -32, -4, 60, 0, 64, 6, 24, 36, 0, 0, 34, 56, -16, 0, 0, -20, -8, 4, 0, -6, -48, 28, -32, 0, 12, 0, 24, -16, 20, 6, 64, 12, 0, 0, -5, 7, 0, -10, 0, -12, -10, 4, 60, 0, 12, -12, -56, 0, 0, 6, -42, -44, -10, 30, -10, 0, -72, 0, 0, -44, 12, 8, 54, 0, -36, -12, 64, 18, 0, 0, 0, 14, 24, 0, -6, -12, 4, -24, 0, -24, 0, 4, 8, 0, -4, -34, 6, -38, 0, 4, -14, 0, -24, 0, -76, -16, 12, -2, 0, -10, 56, 0, 0, 0, 24, 4, -46, 22, 0, -8, 18, 48, -32, 0, 84, -54, 48, 1, 0, 20, -16, -24, -48, 0, 0, -12, 18, 36, 0, -4, -50, -16, -12, 0, 72, 0, -16, 8, 0, 24, 72, -36, 10, 0, 20, -1, 0, 0, 0, 18, 48, -24, -18, -5, 34, -36, 52, 0, 0, -16, -56, 6, -16, 0, -42, 16, 2, 44, 0, -18, 0, 0, 72, 0, 64, 48, 24, 4, 10, 0, -6, 10, 24, 0, -40, -4, 96, 18, 0, -24, 0, -56, 4, 0, 0, 4, 20, -12, 0, 0, -12, 0, 21, -10, -12, 32, 12, -4, 0, 6, -52, 6, 0, 0, -8, -2, 0, 6, 0, 48, -50, -6, -12, 0, 48, 4, 2, -2, -50, 4, -78, 20, 44, 0, 0, 24, 12, 8, 0, 0, 24, -6, -18, 0, 32, 0, 32, 24, 0, 16, -16, -8, 4, 10, -18, -12, 0, 6, 0, 54, 42, 6, 0, 0, -8, -24, -54, 0, 0, 36, 0, -18, 0, 0, -36, -15, 36, 8, 0, -12, 72, 10, -28, 0, 30, 0, -62, -32, 0, 0, 72, -24, -10, 0, 24, -6, -24, 10, 0, 14, 0, -16, -84, 40, -64, -8, 4, -6, 0, 32, 8, 0, -36, 0, 12, -2, -32, 12, 0, -36, -6, 12, 0, 0, -8, -36, -60, -24, 40, -8, -48, 0, -30, 0, -22, -16, 80, -4, 0, -16, 82, 0, -24, 0, 0, -12, -14, -8, 0, -4, 78, 8, 16, 0, 0, 0, -48, -24, 0, 36, 8, -18, -6, 0, -40, 0, 0, -12, 0, -1, -70, 34, 52, 0, 96, 28, -19, 0, 55, -36, -72, -6, 32, 0, -24, 16, 24, 6, 0, 36, -20, -36, 0, 0, -16, -4, -18, 2, 0, 0, 0, 1, 24, 30, 24, -8, -38, -32, 0, 18, 0, 2, 0, 0, -4, 0, -24, 16, 0, -26, -48, 0, -30, 0, 4, -2, 92, 48, -30, -24, 16, -4, 0, 0, -42, -48, 32, 6, 0, -18, 0, 6, 70, 0, -72, -2, 0, -56, 0, -18, 6, -30, 30, -10, 0, -44, 36, 0, 0, -44, -8, 24, 8, 0, -48, 0, 26, 8, 0, -23, -12, -36, -64, 0, 0, -30, 0, -6, 0, 16, 92, 2, 30, 0, 10, -24, -32, 0, 0, 12, 50, -8, 0, 0, 72, 6, 56, -4, 0, 12, -12, 24, 2, 40, -24, -12, -54, -48, 0, 0, -24, 24, -96, 0, -34, 0, -8, -38, 0, 30, 0, 16, 10, 0, 48, -40, -36, 8, 60, -6, 24, 0, -88, 0, -88, -30, -12, 8, 0, -22, -56, -8, 0, 0, 10, 18, -96, 6, 0, -8, -40, 4, -80, 0, 0, -16, -46, -12, 0, 48, 48, 0, 97, 0, 0, 8, 54, -24, 0, 10, -32, 36, -6, 0, 10, 0, -8, -14, 30, 12, 108, -6, 48, 0, 0, -4, 0, 34, 0, -32, -78, 28, 28, 0, 24, 12, -54, 0, 0, -46, -24, 6, 48, 0, -92, -30, 80, 0, 0, 24, -16, -50, -18, 0, -12, -48, 8, 22, 0, 0, 18, 11, 2, 0, -4, 0, -18, 32, 20, -6, 0, 24, -48, 0, -22, 16, -36, -32, 0, 16, -20, 0, -4, 0, -48, -48, -82, -8, 0, 6, -42, -72, 0, 0, 48, 12, -12, 1, 0, 2, 28, 2, 12, 0, -64, 19, 18, -24, 0, 28, -8, 16, -48, 0, 0, -32, 0, -6, -40, 60, -48, 20, -108, 0, -2, 0, -30, -36, 0, -2, -24, -12, 72, 0, 20, 20, 0, -24, 0, 0, 80, -42, -66, 60, 24, -2, 80, 0, 0, 8, -24, -18, 14, 0, -44, 60, 84, -36, 0, -3, 0, 2, 0, 0, -14, 6, 12, 12, 0, 0, -70, -36, 64, 0, -66, -40, 28, 18, 0, 66, 0, -40, -14, 0, 24, 0, -18, 2, 0, -24, -144, 0, -36, 10, 1, -14, -24, -26, 0, 36, 36, 8, 0, 0, -42, -4, -32, 0, 0, -8, -18, 32, 36, 0, -12, -12, 48, 0, 50, 26, 12, -32, -24, 0, 0, -2, 4, 6, 0, 12, -62, 0, 16, 0, 30, 0, -28, -48, 0, 24, -48, -6, 32, -5, -32, -2, 0, 28, 0, -2, -16, -30, -60, 0, 0, 28, 12, 0, 0, 18, 2, 6, 80, 0, -18, 8, -10, -40, 0, 26, -84, -12, -8, 0, -72, 12, 96, 0, 0, 0, -112, -24, 36, 0, -72, 6, 10, -48, 0, -8, 0, -26, 12, 25, 48, -14, 16, -10, 0, 12, 0, 0, -56, 0, 44, -4, -24, -12, 0, -12, -24, 18, 0, 0, -38, -40, -14, -16, 0, 20, 15, -8, 6, 0, 36, -8, -108, -20, 0, 6, 48, -48, -34, 0, 0, 24, 0, -12, 0, 8, 22, 4, -30, -60, 40, 0, 0, 24, 0, 0, 38, 20, 88, 0, 72, -16, 0, -18, 0, 0, 48, 24, -8, 0, -36, 14, -24, 0, 20, 0, -28, -30, -78, 0, -36, -58, 6, 12, 0, 48, 80, -12, 48, 0, -72, -11, 70, 34, 0, 0, 6, 68, 0, -20, 19, -48, -36, -8, 0, 8, 0, -16, 42, 0, 14, 18, 32, 42, 0, 4, 82, 0, -40, 0, 36, 0, 64, -6, 0, 0, 0, -2, 0, 0, -44, 12, 6, 16, 0, 24, -24, 24, -24, 0, 28, 62, 108, -40, 0, 4, -56, 8, -40, -30, 0, 48, 16, -32, 0, 6, -18, 24, -14, 0, -72, 0, 24, 2, 0, 32, 32, 0, 24, 0, 8, 12, 0, -24, 60, -16, 32, -16, -48, 0, -36, 18, -20, 0, 0, 48, -12, 2, 62, 0, 0, -26, -48, -36, 0, -14, 48, 0, 60, -20, -4, 14, 72, 3, 0, 0, -10, 12, 8, 0, 24, -12, 94, 0, 0, 10, 0, -8, 52, 0, -88, 18, -18, 36, 10, -72, 0, 0, -42, 0, -4, -12, -96, -24, 0, -2, 0, -33, 0, 0, -66, -20, 16, -1, 0, -30, 24, 8, 40, 0, -36, -8, -78, 66, 0, 24, 112, -18, 24, 0, 0, 22, -2, -46, 0, 24, -32, 12, 0, 0, 96, 0, 72, 4, 20, 24, -18, -64, -20, 0, -16, -48, 0, -12, 0, -20, -12, 36, -60, 0, -92, 28, 4, 0, 0, -12, 62, 40, -24, 5, -30, 12, 86, -18, 0, 0, 18, 16, -17, 0, 4, -4, -60, -8, 0, 0, -10, 18, -66, 0, 16, -36, -48, 18, -30, -4, 0, 0, 0, 0, -36, 12, -26, -8, 0, -46, -42, 0, -72, 0, -48, 6, 0, -8, 0, 56, 16, -6, 0, -20, -44, 0, 6, 30, 0, -12, 22, -26, -108, 0, 12, 24, 14, -12, 0, 42, 96, 48, 16, 0, 0, 24, -18, -72, 0, 12, 36, 24, 24, 0, 32, 0, 30, 4, 0, -16, 44, -15, -48, 0, -6, -20, 0, 64, 0, 20, 54, 0, 32, -30, 64, 48, 0, 0, 0, 50, 12, 44, 18, 0, 0, -4, 12, 48, 0, 13, -56, -38, -28, 0, 0, 32, -16, 48, -20, 0, -96, 16, 0, 0, 12, 40, -6, -16, 0, 8, 0, 24, -6, 0, -72, -32, -8, 0, 0, -24, 10, 0, 72, 30, -72, -6, 38, -4, 0, 16, -96, 72, 0, 0, 12, 6, 24, 16, 0, -46, 0, -6, 54, 0, 38, -24, 32, 0, -30, 8, -16, -58, 8, 0, 0, 0, 8, -14, 0, -30, -24, 6, -8, 0, 16, 0, 12, 8, 0, 12, -22, -12, -36, 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, -2, 1, 0, -2, -1, 1, 1, 0, 0, -2, 4, -1, 0, 1, -6, 1, -2, 0, 2, 0, 0, -2, -5, 4, 4, -1, 6, 0, -4, 1, 0, -6, 0, 1, 2, -2, -8, 0, -6, 2, -8, 0, 0, 0, -12, -2, 1, -5, 12, 4, 6, 4, 0, -1, 4, 6, -6, 0, -8, -4, -1, 1, 0, 0, -4, -6, 0, 0, 0, 1, -2, 2, 10, -2, 0, -8, -8, 0, -11, -6, 6, 2, 0, -8, -12, 0, -6, 0, -4, 0, 8, -12, 0, -2, -10, 1, 0, -5, 0, 12, -4, 4, 0, 6, -12, 4, -2, 0, -4, -1, 6, 4, 0, 6, 4, -6, 6, 0, 0, -8, 12, -4, 0, -1, 16, 1, 16, 0, -18, 0, 2, -4, 0, -6, 18, 0, -14, 0, 24, 0, 0, 1, 0, -2, -2, 2, 18, 10, -8, -2, -6, 0, 0, -8, -4, -8, -12, 0, 0, -11, -16, -6, 0, 6, 12, 2, 3, 0, -2, -8, 12, -12, 5, 0, 12, -6, -12, 0, 20, -4, 16, 0, 0, 8, 0, -12, -4, 0, 24, -2, -14, -10, 0, 1, 18, 0, 20, -5, 8, 0, -6, 12, 0, -4, 0, 4, 0, 0, 4, 6, 0, -12, 0, 4, 4, -2, 4, 0, -24, -4, 8, -1, -5, 6, -18, 4, -4, 0, 0, 6, 6, 4, 0, -6, 16, 6, -24, 0, 10, 0, 10, -8, 0, 12, -8, -4, -12, 0, -18, -1, 0, 16, 0, 1, 18, 16, -2, 0, 6, -18, 0, 0, 0, 2, 12, -4, -12, 0, 16, -6, 8, 18, 0, 0, 10, -14, -4, 0, 6, 24, 22, 0, 0, 0, 6, 1, 19, 0, 20, -2, -24, -2, 0, 2, 0, 18, 0, 10, 8, -8, 0, -2, 0, -6, -2, 0, 8, 0, -24, -8, -10, -4, 0, -8, 6, -12, 0, 0, 24, 0, 12, -11, -20, -16, 4, -6, 12, 0, 8, 6, 2, 12, 0, 2, -14, 3, -12, 0, 0, -2, -1, -8, 0, 12, 24, -12, 28, 5, 16, 0, 18, 12, 0, -6, -12, -12, 24, 0, -15, 20, 0, -4, 0, 16, 8, 0, -6, 0, -6, 8, -14, 0, 0, -12, 24, -4, -16, 0, -32, 24, 36, -2, 0, -14, -8, -10, 18, 0, 0, 1, 36, 18, 0, 0, 20, 20, -4, -5, -18, 8, -16, 0, 0, -6, 0, 12, -14, 0, -36, -4, 6, 0, 0, 4, 28, 0, 6, 0, -10, 4, -12, 6, 30, 0, 8, -12, 0, 0, -24, 4, -34, 4, 0, -2, 0, 4, -8, 0, 1, -24, -12, -4, 0, 8, -36, -1, 18, -5, 0, 6, 16, -18, 0, 4, 10, -4, -24, 0, -12, 0, 32, 6, 0, 6, -6, 4, 4, 0, 8, -6, 0, 16, 10, 6, 6, -24, 36, 0, 8, 10, 0, 0, 0, 10, -16, -8, 32, 0, 12, 12, -36, -8, 0, -4, 0, -12, -4, 0, -24, -18, 0, -1, 0, 0, -6, 16, 36, 0, 2, 1, -8, 18, 0, 16, 0, -2, -24, 0, 6, 6, -2, -18, -10, 0, 24, 0, -23, 0, -6, 2, -24, 12, 0, -4, 24, -12, 0, 0, -38, 16, -40, -6, 0, 8, -8, 18, -8, 0, -12, 0, 8, 10, 0, -14, -6, -4, -32, 0, 0, 6, -30, 24, 0, 22, 11, 0, -6, 0, -32, 0, -48, 6, 0, 1, 2, 19, 28, 0, -6, 20, 0, -2, 0, -24, -42, -2, 8, 0, -36, 2, 6, 0, 0, 18, -40, 0, -24, 10, -26, 8, -4, -8, 0, 0, -32, -2, 12, 0, -48, -6, -2, -2, 0, 0, 6, 8, 26, 0, 0, -24, 6, -8, 25, -10, 0, -4, -12, 0, -16, -8, -8, 6, 0, -12, 4, 0, 0, 0, -18, 24, 14, 0, 0, 12, -12, -11, 0, -20, -8, -16, 18, 4, 0, -6, -2, 12, 24, 0, -40, 8, 48, 6, 0, 2, 0, 12, -16, 0, 0, 2, -26, -14, -20, 3, 12, -12, 10, 0, 36, 0, -12, -2, 0, -1, 8, -8, 24, 0, -46, 12, 0, 24, 0, -12, 36, 28, -12, 5, -18, 16, -4, 0, 0, 18, 0, 12, -46, 0, -8, -6, 0, -12, 0, -12, 48, 24, 12, 0, 4, -15, -20, 20, -30, 0, 44, -4, 13, 0, 48, 16, 40, 8, 0, 0, 0, -6, 16, 0, 16, -6, -24, 8, 0, -14, 6, 0, 12, 0, -40, -12, 36, 24, 0, -4, 2, -16, 0, 0, 18, -32, 2, 24, 0, 36, -24, -2, -14, 0, -36, -14, 24, -8, 20, -10, 4, 18, 12, 0, 0, 0, 24, 1, 0, 36, 22, 18, 0, 0, -6, 0, -32, 20, 0, 20, -12, -4, 72, -5, -6, -18, 0, 8, 0, -16, 24, 0, -6, 0, -2, -6, -32, 0, 0, 12, 16, -14, -4, 0, -6, -36, -40, -4, 0, 6, 36, 0, 56, 0, -20, 4, -6, 28, 0, 0, -16, 6, 12, 0, 7, -10, -12, 4, 0, -12, 0, 6, -44, 30, 0, 0, -44, 8, 0, -12, 18, 0, 14, 0, -12, -24, -24, 4, 0, -34, -38, 4, 0, 0, -16, -2, -10, 0, 0, 4, 22, -8, 48, 0, -54, 1, 20, -24, 0, -12, 36, -4, -16, 0, 0, 8, 24, -36, 0, -1, 0, 18, -24, -5, -36, 0, -16, 6, 0, 16, 44, -18, 0, 0, 48, 4, 0, 10, 0, -4, 18, -24, -56, 0, 4, -12, 0, 0, -10, 32, -4, 6, 6, 0, -2, 6, 48, -6, 0, 4, -2, 4, 20, 0, 24, 8, 0, -6, 0, 0, 24, 16, -8, 10, -12, 6, 54, 6, 0, -24, 0, 36, -18, 0, -15, 8, -12, 10, 0, 0, -32, 0, -24, 0, -6, 10, 14, -16, 40, -8, -6, 32, 0, 0, -2, 12, -36, 12, 0, -36, -24, -8, 0, 0, -16, -4, -16, 0, 0, -12, -8, -4, 8, 0, 0, -24, 36, -18, 0, 0, -12, -1, 34, 0, 28, 0, -36, -6, 0, 16, 6, 36, -36, 0, -4, 2, 0, 1, 30, -8, -32, 18, 2, 0, 0, 16, -26, 0, 0, -2, 48, -24, -4, 0, -48, 6, -18, 6, 0, -2, -56, -18, -30, -10, -44, 0, -44, 24, 0, 0, 8, -23, -36, 0, -30, -6, 16, 2, 0, -24, 0, 12, -8, 0, 6, -4, 12, 24, 40, -12, -48, 0, 24, 0, 0, -38, 30, 16, 0, -40, 8, -6, 0, 0, -30, 8, -22, -8, 0, 18, 6, -8, 4, 0, -16, -12, 48, 0, 0, 8, -24, 10, 36, 0, 0, -14, 12, -6, 0, -4, 34, -32, 28, 0, 12, 0, -46, 6, 0, -30, 0, 24, -50, 0, -48, 22, 0, 11, 0, 0, 32, -6, 24, 0, 16, -32, 16, 0, 0, -48, -8, 6, -72, 0, 12, 1, 2, 2, 0, 19, -24, 28, 16, 0, -32, -6, 60, 20, 0, 0, -36, -2, -12, 0, 20, -24, 0, -42, 60, -2, 0, 8, -18, 0, 60, -36, -3, 2, 0, 6, 12, 0, -36, 0, -40, 18, 66, -40, 0, 0, 2, -24, 0, 10, -14, -26, 36, 8, 0, -4, 0, -8, 32, 0, -12, 0, 26, -32, 0, -2, 6, 12, 0, 0, 0, -48, 24, -6, -5, -2, 28, -2, -30, 0, 28, 0, 18, 6, 0, 8, -40, 26, -12, 0, 12, 0, 0, -24, 0, 6, -48, -8, -26, 25, -14, -10, 12, 0, 0, -4, -12, -12, 18, 0, -40, -16, 20, -8, 0, -8, -20, 6, -48, 0, 24, -12, 8, 4, -60, 0, 24, 0, 20, 0, -16, -18, 0, 24, 0, 14, 0, 0, -30, 0, -58, 12, 48, -12, 0, -11, 34, 0, 68, -20, -48, -8, 8, -16, 0, 18, 42, 4, 0, 0, 0, -6, 0, -2, 0, 12, 16, 24, 24, 0, 62, -40, 4, 8, -30, 48, -32, 6, 24, 0, 0, 2, 32, 0, 0, 12, -24, -16, -16, 0, 18, 0, 48, 2, 0, -26, -36, -14, 0, -20, 14, 3, 0, 12, 0, -12, 0, 10, -8, 0, 18, 36, -72, 0, 0, -12, -24, -2, -33, 0, -20, -1, -30, 8, 0, -8, 66, 24, -18, 0, 22, -46, 24, 12, 0, 0, 4, 24, -64, 0, -48, -12, -20, 36, 0, 28, 0, -12, 40, 5, 12, -18, 0, 16, 0, -4, -8, 0, 18, 0, -36, 18, -4, 0, 0, 12, -8, -46, 0, 0, 6, -8, 56, -6, -20, 0, 30, -12, -26, 0, 24, -12, 42, 48, 0, 24, -72, 12, 24, 0, 0, 4, -16, -15, 0, -20, 64, 20, 0, -30, 48, 0, 50, 44, 0, -4, 48, 13, -38, 0, 32, 48, 0, 16, 0, 40, -16, 8, 24, 0, -32, 0, -24, 0, 30, -6, -4, 16, 72, 0, 6, 16, -46, -6, 0, -24, 0, 8, -58, 0, 0, -14, -30, 6, 0, 0, 8, 12, -12, 0, 16, -40, 12, -12, 0, 36, 0, 24, 0, 0, 0, -4, 36, 2, 0, -16, -12, 0, -4, 0, 3, 18, -72, -32, 40, 2, -72, 24, 0, 0, -2, 36, -4, -24, 0, -2, 36, -14, 22, 0, 0, -36, 32, -14, 0, 24, 24, -8, -34, 20, 0, -10, -42, 4, 0, 18, 12, 12, 12, 0, -8, 0, -12, 0, 0, 24, -16, 1, 4, 0, 66, 36, 0, 22, 5, 18, -12, 0, 40, 0, -48, -6, 0, 0, 0, -32, 46, 20, 18, 0, -16, 20, -24, -12, 0, -4, 58, 72, 48, -5, -66, -6, 4, -18, 0, 0, 48, 8, 26, 0, -12, -16, 72, 24, 0, 0, 0, -6, 60, 0, 74, -2, 76, -6, 0, -32, 10, 0, 20, 0, -6, 12, 0, 16, 0, -14, 0, -4, 0, 0, 16, -6, -24, -36, 0, -40, -32, -4, 60, 0, 64, 6, 24, 36, 0, 0, 34, 56, -16, 0, 0, -20, -8, 4, 0, -6, -48, 28, -32, 0, 12, 0, 24, -16, 20, 6, 64, 12, 0, 0, -5, 7, 0, -10, 0, -12, -10, 4, 60, 0, 12, -12, -56, 0, 0, 6, -42, -44, -10, 30, -10, 0, -72, 0, 0, -44, 12, 8, 54, 0, -36, -12, 64, 18, 0, 0, 0, 14, 24, 0, -6, -12, 4, -24, 0, -24, 0, 4, 8, 0, -4, -34, 6, -38, 0, 4, -14, 0, -24, 0, -76, -16, 12, -2, 0, -10, 56, 0, 0, 0, 24, 4, -46, 22, 0, -8, 18, 48, -32, 0, 84, -54, 48, 1, 0, 20, -16, -24, -48, 0, 0, -12, 18, 36, 0, -4, -50, -16, -12, 0, 72, 0, -16, 8, 0, 24, 72, -36, 10, 0, 20, -1, 0, 0, 0, 18, 48, -24, -18, -5, 34, -36, 52, 0, 0, -16, -56, 6, -16, 0, -42, 16, 2, 44, 0, -18, 0, 0, 72, 0, 64, 48, 24, 4, 10, 0, -6, 10, 24, 0, -40, -4, 96, 18, 0, -24, 0, -56, 4, 0, 0, 4, 20, -12, 0, 0, -12, 0, 21, -10, -12, 32, 12, -4, 0, 6, -52, 6, 0, 0, -8, -2, 0, 6, 0, 48, -50, -6, -12, 0, 48, 4, 2, -2, -50, 4, -78, 20, 44, 0, 0, 24, 12, 8, 0, 0, 24, -6, -18, 0, 32, 0, 32, 24, 0, 16, -16, -8, 4, 10, -18, -12, 0, 6, 0, 54, 42, 6, 0, 0, -8, -24, -54, 0, 0, 36, 0, -18, 0, 0, -36, -15, 36, 8, 0, -12, 72, 10, -28, 0, 30, 0, -62, -32, 0, 0, 72, -24, -10, 0, 24, -6, -24, 10, 0, 14, 0, -16, -84, 40, -64, -8, 4, -6, 0, 32, 8, 0, -36, 0, 12, -2, -32, 12, 0, -36, -6, 12, 0, 0, -8, -36, -60, -24, 40, -8, -48, 0, -30, 0, -22, -16, 80, -4, 0, -16, 82, 0, -24, 0, 0, -12, -14, -8, 0, -4, 78, 8, 16, 0, 0, 0, -48, -24, 0, 36, 8, -18, -6, 0, -40, 0, 0, -12, 0, -1, -70, 34, 52, 0, 96, 28, -19, 0, 55, -36, -72, -6, 32, 0, -24, 16, 24, 6, 0, 36, -20, -36, 0, 0, -16, -4, -18, 2, 0, 0, 0, 1, 24, 30, 24, -8, -38, -32, 0, 18, 0, 2, 0, 0, -4, 0, -24, 16, 0, -26, -48, 0, -30, 0, 4, -2, 92, 48, -30, -24, 16, -4, 0, 0, -42, -48, 32, 6, 0, -18, 0, 6, 70, 0, -72, -2, 0, -56, 0, -18, 6, -30, 30, -10, 0, -44, 36, 0, 0, -44, -8, 24, 8, 0, -48, 0, 26, 8, 0, -23, -12, -36, -64, 0, 0, -30, 0, -6, 0, 16, 92, 2, 30, 0, 10, -24, -32, 0, 0, 12, 50, -8, 0, 0, 72, 6, 56, -4, 0, 12, -12, 24, 2, 40, -24, -12, -54, -48, 0, 0, -24, 24, -96, 0, -34, 0, -8, -38, 0, 30, 0, 16, 10, 0, 48, -40, -36, 8, 60, -6, 24, 0, -88, 0, -88, -30, -12, 8, 0, -22, -56, -8, 0, 0, 10, 18, -96, 6, 0, -8, -40, 4, -80, 0, 0, -16, -46, -12, 0, 48, 48, 0, 97, 0, 0, 8, 54, -24, 0, 10, -32, 36, -6, 0, 10, 0, -8, -14, 30, 12, 108, -6, 48, 0, 0, -4, 0, 34, 0, -32, -78, 28, 28, 0, 24, 12, -54, 0, 0, -46, -24, 6, 48, 0, -92, -30, 80, 0, 0, 24, -16, -50, -18, 0, -12, -48, 8, 22, 0, 0, 18, 11, 2, 0, -4, 0, -18, 32, 20, -6, 0, 24, -48, 0, -22, 16, -36, -32, 0, 16, -20, 0, -4, 0, -48, -48, -82, -8, 0, 6, -42, -72, 0, 0, 48, 12, -12, 1, 0, 2, 28, 2, 12, 0, -64, 19, 18, -24, 0, 28, -8, 16, -48, 0, 0, -32, 0, -6, -40, 60, -48, 20, -108, 0, -2, 0, -30, -36, 0, -2, -24, -12, 72, 0, 20, 20, 0, -24, 0, 0, 80, -42, -66, 60, 24, -2, 80, 0, 0, 8, -24, -18, 14, 0, -44, 60, 84, -36, 0, -3, 0, 2, 0, 0, -14, 6, 12, 12, 0, 0, -70, -36, 64, 0, -66, -40, 28, 18, 0, 66, 0, -40, -14, 0, 24, 0, -18, 2, 0, -24, -144, 0, -36, 10, 1, -14, -24, -26, 0, 36, 36, 8, 0, 0, -42, -4, -32, 0, 0, -8, -18, 32, 36, 0, -12, -12, 48, 0, 50, 26, 12, -32, -24, 0, 0, -2, 4, 6, 0, 12, -62, 0, 16, 0, 30, 0, -28, -48, 0, 24, -48, -6, 32, -5, -32, -2, 0, 28, 0, -2, -16, -30, -60, 0, 0, 28, 12, 0, 0, 18, 2, 6, 80, 0, -18, 8, -10, -40, 0, 26, -84, -12, -8, 0, -72, 12, 96, 0, 0, 0, -112, -24, 36, 0, -72, 6, 10, -48, 0, -8, 0, -26, 12, 25, 48, -14, 16, -10, 0, 12, 0, 0, -56, 0, 44, -4, -24, -12, 0, -12, -24, 18, 0, 0, -38, -40, -14, -16, 0, 20, 15, -8, 6, 0, 36, -8, -108, -20, 0, 6, 48, -48, -34, 0, 0, 24, 0, -12, 0, 8, 22, 4, -30, -60, 40, 0, 0, 24, 0, 0, 38, 20, 88, 0, 72, -16, 0, -18, 0, 0, 48, 24, -8, 0, -36, 14, -24, 0, 20, 0, -28, -30, -78, 0, -36, -58, 6, 12, 0, 48, 80, -12, 48, 0, -72, -11, 70, 34, 0, 0, 6, 68, 0, -20, 19, -48, -36, -8, 0, 8, 0, -16, 42, 0, 14, 18, 32, 42, 0, 4, 82, 0, -40, 0, 36, 0, 64, -6, 0, 0, 0, -2, 0, 0, -44, 12, 6, 16, 0, 24, -24, 24, -24, 0, 28, 62, 108, -40, 0, 4, -56, 8, -40, -30, 0, 48, 16, -32, 0, 6, -18, 24, -14, 0, -72, 0, 24, 2, 0, 32, 32, 0, 24, 0, 8, 12, 0, -24, 60, -16, 32, -16, -48, 0, -36, 18, -20, 0, 0, 48, -12, 2, 62, 0, 0, -26, -48, -36, 0, -14, 48, 0, 60, -20, -4, 14, 72, 3, 0, 0, -10, 12, 8, 0, 24, -12, 94, 0, 0, 10, 0, -8, 52, 0, -88, 18, -18, 36, 10, -72, 0, 0, -42, 0, -4, -12, -96, -24, 0, -2, 0, -33, 0, 0, -66, -20, 16, -1, 0, -30, 24, 8, 40, 0, -36, -8, -78, 66, 0, 24, 112, -18, 24, 0, 0, 22, -2, -46, 0, 24, -32, 12, 0, 0, 96, 0, 72, 4, 20, 24, -18, -64, -20, 0, -16, -48, 0, -12, 0, -20, -12, 36, -60, 0, -92, 28, 4, 0, 0, -12, 62, 40, -24, 5, -30, 12, 86, -18, 0, 0, 18, 16, -17, 0, 4, -4, -60, -8, 0, 0, -10, 18, -66, 0, 16, -36, -48, 18, -30, -4, 0, 0, 0, 0, -36, 12, -26, -8, 0, -46, -42, 0, -72, 0, -48, 6, 0, -8, 0, 56, 16, -6, 0, -20, -44, 0, 6, 30, 0, -12, 22, -26, -108, 0, 12, 24, 14, -12, 0, 42, 96, 48, 16, 0, 0, 24, -18, -72, 0, 12, 36, 24, 24, 0, 32, 0, 30, 4, 0, -16, 44, -15, -48, 0, -6, -20, 0, 64, 0, 20, 54, 0, 32, -30, 64, 48, 0, 0, 0, 50, 12, 44, 18, 0, 0, -4, 12, 48, 0, 13, -56, -38, -28, 0, 0, 32, -16, 48, -20, 0, -96, 16, 0, 0, 12, 40, -6, -16, 0, 8, 0, 24, -6, 0, -72, -32, -8, 0, 0, -24, 10, 0, 72, 30, -72, -6, 38, -4, 0, 16, -96, 72, 0, 0, 12, 6, 24, 16, 0, -46, 0, -6, 54, 0, 38, -24, 32, 0, -30, 8, -16, -58, 8, 0, 0, 0, 8, -14, 0, -30, -24, 6, -8, 0, 16, 0, 12, 8, 0, 12, -22, -12, -36, 0]}