# Stored data for newform 4225.2.a.d, downloaded from the LMFDB on 04 December 2025.
{"Nk2": 16900, "analytic_conductor": 33.736794853990965, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[5, -1], [13, -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": [4225, 1, [677, 3551], [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": [[2, [1, 1]], [3, [2, 1]], [7, [5, 1]], [11, [3, 1]]], "hecke_orbit": 4, "hecke_orbit_code": 13510798915670145, "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": "4225.2.a.d", "level": 4225, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": true, "level_is_squarefree": false, "level_primes": [5, 13], "level_radical": 65, "minimal_twist": "325.2.c.a", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q-q^{2}-2q^{3}-q^{4}+2q^{6}-5q^{7}+3q^{8}+\\cdots", "related_objects": ["EllipticCurve/Q/4225/d"], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "4225.2.a", "trace_display": [-1, -2, 0, -5], "trace_hash": 2188686772563645126, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.989", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.985", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.967", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.013", "prec": 17}, "traces": [0, 1, -1, -2, -1, 0, 2, -5, 3, 1, 0, -3, 2, 0, 5, 0, -1, -5, -1, 4, 0, 10, 3, -4, -6, 0, 0, 4, 5, -1, 0, -1, -5, 6, 5, 0, -1, 4, -4, 0, 0, 8, -10, 4, 3, 0, 4, -7, 2, 18, 0, 10, 0, -3, -4, 0, -15, -8, 1, 3, 0, 1, 1, -5, 7, 0, -6, -3, 5, 8, 0, -8, 3, 4, -4, 0, -4, 15, 0, 10, 0, -11, -8, 9, -10, 0, -4, 2, -9, 18, 0, 0, 4, 2, 7, 0, 10, 14, -18, -3, 0, -1, -10, -4, 0, 0, 3, -16, -4, 2, 0, -8, 5, 10, 8, 0, 1, 0, -3, 25, 0, -2, -1, -16, 1, 0, 5, -18, 3, -8, 0, 18, -6, -20, 3, 0, -15, 18, -8, 4, 0, 14, 8, 0, -1, 0, -4, -36, -4, -10, 0, -13, 12, -5, -15, 0, 0, -13, -10, 6, 0, 20, 11, 12, -8, 0, -9, 16, 30, 0, 0, 4, -4, -13, -2, 0, 3, -6, -18, -12, 0, -3, 0, -2, -12, 0, -2, 15, 7, -20, 0, 10, -14, 4, -14, 0, -18, 8, 3, 6, 0, 6, 1, 5, -10, 0, 4, -4, 0, -12, 0, -12, 3, 16, 16, 0, 12, 5, -2, -8, 0, 0, 8, 16, 25, 0, -10, -9, 8, 2, 0, -30, -3, -14, 0, 0, -3, -20, -25, -5, 0, 0, 2, 10, -1, 0, 16, 0, -3, -18, 0, -12, 5, 12, 18, 0, -17, -15, 8, -20, 0, -1, -18, -6, 18, 0, 20, -36, 3, -17, 0, -29, 5, 0, -18, 0, -8, 2, -4, -1, 0, 18, -14, 28, 8, 0, 0, -40, -5, 8, 0, -28, -4, -6, 36, 0, 12, -12, 10, 0, 0, -20, 13, 2, -4, 0, 5, 8, -15, 8, 0, -4, 0, 17, 13, 0, -10, -22, -6, 3, 0, 32, -20, -20, 11, 0, -12, -4, 24, 35, 0, 20, -9, 4, -16, 0, -10, 3, 0, -20, 0, 3, -4, -55, 12, 0, 13, 4, -2, -2, 0, 0, 15, -6, 6, 0, -18, -50, 12, -23, 0, -3, 3, 4, 0, 0, 2, -18, 4, 8, 0, 15, -2, 31, -15, 0, -21, 0, 20, -27, 0, 36, -10, 32, -6, 0, -4, 4, -14, -34, 0, 20, 54, -36, -8, 0, 3, 8, -6, 40, 0, 26, -6, 0, 1, 0, -5, -12, 30, 6, 0, -36, 4, -15, 4, 0, 0, -8, 12, -18, 0, 4, 12, -7, -9, 0, -16, -5, 16, 0, 0, 0, -4, -14, -5, 0, -2, -16, 8, -22, 0, 18, 0, -24, 8, 0, -16, 20, -35, 6, 0, -24, -10, 26, 9, 0, -24, 10, -2, -20, 0, -26, 30, -19, 1, 0, 14, -18, 0, 15, 0, 26, 9, -12, 20, 0, -25, -3, 5, 3, 0, 0, 0, -40, 2, 0, -10, 15, 3, -24, 0, 28, 16, 5, 0, 0, 1, 40, 18, 19, 0, -32, 12, -16, -15, 0, -12, 0, 18, 0, 0, -20, 11, 16, 15, 0, 8, 21, 20, 26, 0, 10, 1, -22, -18, 0, 6, 5, -6, -7, 0, 3, 20, 0, 36, 0, -9, 24, 17, -54, 0, -38, 29, 6, 25, 0, 0, 38, -18, 1, 0, -4, 24, -50, -2, 0, -4, -24, 1, 0, 0, -30, -18, 30, -14, 0, -28, 55, -24, 33, 0, -2, 0, -20, 40, 0, 7, 38, -8, -8, 0, -45, 28, 9, 12, 0, 6, -25, 36, -4, 0, -16, -4, 8, 12, 0, 10, -12, 0, -14, 0, 29, 20, -3, 13, 0, -2, -8, -20, -10, 0, 0, 5, -10, -8, 0, 45, 4, -8, -28, 0, -16, 4, -90, 0, 0, -17, 24, 13, -20, 0, 20, 30, 24, 22, 0, -6, 0, -3, -8, 0, 15, -32, -4, -20, 0, 20, 14, -33, -9, 0, -10, -12, 31, 4, 0, -8, 4, -35, -6, 0, 38, -20, 0, 27, 0, -4, 4, -16, -32, 0, -3, -50, 23, -3, 0, 0, 6, 20, -70, 0, 18, -3, 41, -4, 0, 55, -4, -4, 0, 0, -17, 13, 15, -4, 0, 6, -40, 2, 28, 0, 45, 0, 16, -21, 0, 6, 5, 6, -8, 0, 10, 54, 4, 50, 0, 12, 10, 23, -30, 0, 20, 3, 0, 3, 0, -4, 16, 0, 13, 0, -20, 2, 42, 18, 0, 20, 9, -8, -9, 0, 0, -15, 41, 6, 0, -31, 9, -15, 80, 0, 32, 7, 24, 0, 0, 20, 5, 27, -24, 0, 10, -36, -10, -10, 0, -32, 0, 34, -40, 0, 30, -4, -18, -4, 0, 42, 40, 34, 32, 0, 24, -20, -4, -18, 0, 36, 43, -8, 12, 0, -50, -9, 0, -8, 0, -6, 53, -40, 35, 0, 18, -26, -12, -6, 0, 0, 34, -3, -30, 0, -25, -5, 58, 12, 0, -10, 16, -6, 0, 0, 30, 36, -12, -12, 0, 15, -19, 4, 11, 0, -4, 0, -90, 8, 0, 12, -4, 18, -36, 0, -28, -4, -36, 12, 0, 7, 10, 3, -56, 0, -16, -16, 54, 5, 0, -48, -14, 0, -4, 0, 80, 0, 33, -20, 0, 14, -16, -5, -30, 0, 0, 6, 14, 16, 0, 8, -14, 22, 12, 0, 33, -18, -28, 0, 0, 24, -22, -24, 90, 0, 33, -16, -28, -20, 0, -15, 0, -6, 1, 0, 15, 24, 40, 30, 0, -26, 20, 9, -1, 0, 2, 8, -27, -10, 0, -2, -90, 20, 46, 0, -16, 26, 0, 30, 0, 19, -4, 5, 56, 0, 72, 14, 8, 18, 0, 0, -1, -15, -34, 0, -8, -26, -32, -3, 0, 12, -3, 20, 0, 0, 44, 75, 9, 3, 0, 5, -6, -3, -90, 0, -30, 0, -16, 0, 0, 40, -37, -6, 40, 0, -48, -10, -20, -15, 0, -1, -46, 24, -54, 0, 2, -28, 11, -48, 0, -5, -70, 0, -16, 0, 4, 5, -40, -40, 0, 18, 45, -19, 16, 0, 0, 32, -15, 12, 0, 16, -12, 5, -38, 0, -6, -12, 3, 0, 0, -54, 10, 0, -16, 0, -28, 20, -6, 23, 0, -16, 0, 15, 110, 0, -56, -24, -34, -21, 0, 20, -5, -26, 48, 0, -8, -10, 50, 1, 0, 22, 4, 54, -9, 0, 35, 6, 0, -5, 0, -30, 65, 7, 12, 0, 36, -3, 48, -60, 0, 0, -42, 36, 43, 0, 25, 3, -4, -24, 0, 17, 46, 54, 0, 0, 28, 38, 6, 29, 0, -6, -36, -35, -2, 0, -6, 0, 26, -38, 0, 54, -48, -1, 65, 0, 36, 4, 5, -8, 0, 50, 32, -2, 30, 0, 3, 12, -30, 24, 0, 1, -47, 0, -62, 0, 12, 30, -9, -18, 0, -30, -72, 42, 56, 0, 0, -28, 12, -55, 0, 8, 54, -33, 15, 0, -60, 2, -18, 0, 0, 20, -4, 40, -64, 0, -33, 3, 2, -38, 0, -8, 0, 8, 4, 0, 16, 45, -51, 28, 0, -9, 68, -4, -80, 0, -50, 6, -40, 25, 0, -108, 48, 4, 18, 0, -32, 16, 0, -20, 0, -8, 2, 12, -8, 0, -16, -30, -39, 12, 0, 0, -20, 14, -6, 0, 40, -29, -52, 20, 0, 3, 40, -39, 0, 0, 65, -2, -11, 8, 0, 28, 56, 10, 12, 0, 24, 0, -14, -15, 0, 10, -12, -8, -52, 0, -14, -15, 18, -4, 0, -8, 22, 28, 30, 0, -20, 16, -30, 4, 0, 90, -4, 0, -11, 0, 4, -17, 60, -24, 0, -39, 36, 20, 13, 0, 0, -20, -8, -10, 0, -24, 15, 22, -28, 0, -8, 18, -12, 0, 0, -3, 30, 8, 1, 0, 10, -15, 60, -32, 0, 4, 0, 60, -12, 0, 18, 20, 0, -14, 0, 11, -39, 9, 28, 0, 14, 10, 26, 36, 0, -31, 3, 4, -75, 0, 32, -40, 0, -4, 0, -35, 44, 6, -7, 0, -26, -38, 72, -20, 0, 0, 14, -9, 48, 0, 39, -4, -4, -4, 0, 48, -50, 32, 0, 0, -10, 3, -50, 70, 0, -23, -12, -3, -32, 0, -20, 0, 48, -6, 0, 20, -12, 70, -13, 0, 23, -18, 7, -3, 0, -41, -37, 12, -21, 0, -20, 55, -58, 4, 0, -20, 55, 0, -40, 0, 70, 17, 52, -39, 0, -15, 16, -4, 38, 0, 0, -2, -30, 40, 0, 2, 54, -28, 40, 0, 36, -45, -4, 0, 0, -16, -30, -9, 4, 0, -45, 6, -13, -5, 0, -18, 0, 8, 24, 0, -18, -10, -51, -18, 0, -4, -38, 50, -33, 0, -12, -36, -54, -10, 0, 23, -6, 30, 2, 0, -54, -20, 0, 3, 0, 0, -10, -9, 20, 0, -1, -4, -26, -16, 0, 0, 7, -13, -42, 0, -30, 20, 60, -6, 0, -42, 12, 18, 0, 0, -73, -28, -56, -9, 0, -8, 60, 9, -10, 0, -2, 0, -32, -15, 0, -41, -36, -2, 20, 0, -80, -31, -50, -9, 0, 45, -38, -80, 34, 0, 40, -32, 16, 35, 0, -24, -54, 0, 32, 0, 54, -60, -90, -5, 0, 27, 32, 24, -18, 0, 0, -10, 56, -36, 0, 10, 0, 30, -12, 0, -54, -32, 40, 0, 0, -22, 3, 40, -44, 0, 12, -30, -32, 12, 0, 18, 0, -4, 24, 0, -42, -14, -40, -40, 0, 34, -13, -32, -44, 0, -80, -24, -20, -20, 0, 4, 8, -90, 44, 0, 20, 36, 0, -43, 0, 24, 36, -12, 41, 0, -10, 50, -38, 3, 0, 0, 14, -8, 45, 0, 16, 18, 12, -53, 0, -40, -60, -35, 0, 0, -2, -18, -10, -26, 0, 12, -36, 18, -9, 0, -12, 0, -54, -34, 0, 1, 108, 30, -37, 0, -10, 25, 76, 15, 0, -58, 53, 12, -3, 0, 70, -50, 32, -16, 0, -6, -3, 0, 30, 0, -76, -30, 3, 36, 0, 12, 4, 4, -70, 0, 0, 15, 8, 19, 0, -12, 12, -11, 100, 0, 39, 4, 46, 0, 0, 90, -40, 8, -52, 0, 48, -36, 25, 4, 0, 18, 0, 36, -16, 0, 23, 28, 15, -4, 0, 36, 0, -36, -60, 0, 72, 7, 46, -10, 0, 15, 24, 56, 0, 0, -50, 16, 0, 48, 0, -54, -66, 5, -24, 0, -3, 16, 4, 14, 0, 0, 5, 4, 10, 0, -70, -80, 33, 0, 0, -33, 39, 28, 0, 0, -76, 14, 51, 16, 0, 15, 4, 30, -28, 0, 58, 0, 90, -2, 0, -14, 19, 16, -18, 0, 20, -24, -42, 14, 0, 22, 60, -12, 48, 0, 50, -33, 32, -18, 0, 28, 8, 0, -1, 0, -60, 24, 8, 22, 0, 8, -23, -90, -16, 0, 0, -33, -5, 48, 0, 28, -68, -20, -2, 0, 6, 85, -36, 0, 0, -6, 28, -1, 75, 0, 74, -15, -58, 24, 0, -40, 0, -10, -12, 0, -66, -26, 72, -20, 0, -27, -40, 1, 80, 0, 16, -2, -18, 40, 0, 27, 5, -10, -3, 0, 72, 6, 0, 90, 0, 20, -48, -46, 20, 0, 30, 16, 56, 26, 0, 0, 6, -90, -27, 0, -8, 19, -10, 4, 0, -7, 56, -56, 0, 0, -28, -72, 44, -42, 0, -8, 9, 18, 180, 0, 60, 0, -69, 1, 0, -15, -6, 34, 77, 0, -12, 8, 85, -26, 0, 32, 40, -15, 49, 0, -1, 12, -40, 3, 0, -60, 145, 0, -12, 0, -31, -44, 39, -25, 0, -9, -40, 3, -36, 0, 0, -15, -4, 6, 0, -3, -32, 90, -4, 0, -50, 30, -30, 0, 0, 16, -56, 0, 8, 0, -27, 40, 71, 37, 0, 2, 0, -40, -10, 0, -28, 48, 3, 30, 0, 20, 18, -15, 5, 0, 14, -5, 5, 46, 0, 24, -16, 54, -62, 0, -12, -2, 0, -28, 0, -11, -90, 16, 36, 0, 16, -5, -54, 70, 0, 0, 12, 16, 0, 0, -140, -4, -76, -7, 0, 40, -67, -40, 0, 0, 9, -54, 1, -45, 0, -19, 30, -16, 26, 0, -8, 0, -12, 32, 0, 15, 16, -36, 144, 0, 56, 16, 6, 12, 0, 25, -58, 38, -46, 0, -28, 6, -40, 36, 0, -3, 24, 0, -14, 0, -12, 18, -64, -10, 0, 0, 140, 16, 48, 0, 0, 28, -9, 20, 0, 6, -72, -45, -82, 0, 30, -16, 77, 0, 0, -45, 10, -110, 8, 0, 2, 56, -62, 8, 0, 34, 0, -21, -12, 0, 8, -60, 34, 5, 0, -26, 3, -48, 60, 0, -71, 8, 10, -10, 0, -50, -9, -3, -70, 0, 80, 22, 0, -4, 0, -18, -14, 9, -15, 0, -30, -35, -90, -18, 0, 0, 72, -5, -32, 0, 24, 42, -32, -65, 0, 7, -4, -12, 0, 0, -10, -36, -12, -3, 0, -48, 16, 20, 27, 0, -2, 0, 40, 42, 0, -108, -24, -43, -8, 0, 30, -25, -77, 15, 0, 4, 40, -24, -40, 0, -5, -51, -24, -46, 0, 54, 60, 0, 90, 0, -53, -28, -40, 38, 0, -6, -24, -87, 0, 0, 0, -6, -24, 36, 0, -15, 20, 2, -7, 0, -32, 6, 12, 0, 0, -26, -56, -38, -18, 0, -85, -18, 40, 48, 0, -1, 0, -65, -84, 0, 8, -36, 19, 4, 0, -5, -84, -40, 2, 0, -18, 50, 27, -32, 0, 6, 18, -30, 110, 0, -78, -3, 0, -4, 0, 30, -90, 24, -82, 0, -56, -3, -15, 47, 0, 0, -78, 62, 30, 0, 36, -12, -73, 30, 0, 9, -160, 54, 0, 0, -23, -30, -64, 72, 0, -14, 4, -56, -12, 0, 100, 0, -4, 84, 0, -12, 33, -55, -80, 0, -10, 40, 68, -54, 0, -33, 12, -15, -12, 0, -58, 60, -20, 2, 0, 18, -42, 0, 20, 0, -10, 20, -28, 4, 0, -120, -38, 64, -8, 0, 0, 33, -126, -17, 0, -2, 80, -38, 16, 0, 38, 24, -15, 0, 0, 8, -100, -4, 36, 0, 36, -16, 4, 45, 0, 51, 0, -84, -90, 0, -20, -9, -6, -68, 0, -20, -64, 80, -2, 0, 71, 50, -48, -18, 0, 40, 25, 25, 11, 0, 35, 36, 0, -48, 0, 4, -75, -18, -15, 0, -86, 32, -20, 16, 0, 0, -6, 28, 16, 0, 41, -8, 100, -2, 0, -36, 64, 8, 0, 0, 50, 16, -4, 10, 0, 39, -15, 12, -22, 0, -106, 0, -91, 20, 0, 14, -70, 6, -27, 0, 149, -40, 72, -29, 0, 52, -9, -60, 24, 0, -83, 3, -72, -40, 0, 13, -3, 0, 24, 0, -17, -65, 31, 6, 0, 11, 60, 8, -20, 0, 0, 12, 50, -56, 0, 10, -50, -12, -29, 0, -66, -24, 10, 0, 0, 14, 52, 5, -10, 0, -32, 10, -48, 12, 0, 24, 0, 52, 36, 0, 64, 14, -60, -75, 0, -18, 82, -4, 24, 0, 30, 24, -14, -22, 0, 28, 30, -30, -12, 0, 38, 20, 0, 16, 0, 30, -22, -12, 72, 0, 21, 90, 2, 4, 0, 0, 27, 11, 180, 0, 8, -4, 7, 51, 0, -60, -8, -24, 0, 0, 11, 13, 115, -36, 0, 20, 72, -13, -6, 0, -57, 0, 56, -20, 0, 8, 15, -50, 18, 0, -60, -24, 50, -15, 0, -66, 12, 28, 88, 0, -20, 8, 48, -6, 0, 12, 28, 0, 45, 0, -44, 9, 32, -30, 0, 8, -55, -1, -108, 0, 0, -10, 42, -15, 0, -60, 65, 96, 90, 0, 28, 4, -9, 0, 0, -20, 8, 12, 43, 0, -18, -18, -40, -60, 0, 0, 0, -14, -66, 0, -42, 55, 6, 39, 0, 9, -54, -28, -40, 0, 8, -14, 72, 10, 0, -26, 60, -12, -77, 0, -155, -31, 0, -3, 0, -12, 14, 75, 56, 0, -20, -32, 4, 56, 0, 0, -32, -4, 15, 0, 28, 105, -60, -44, 0, 6, -6, 7, 0, 0, 16, 26, -66, -38, 0, -72, 25, 60, 56, 0, 0, 0, 135, -14, 0, -45, 96, -48, -88, 0, 44, -39, -48, 12, 0, 4, -180, -4, 65, 0, 31, -16, -30, 50, 0, 32, 71, 0, 56, 0, -160, 10, 4, 3, 0, 50, -72, 30, -58, 0, 0, -23, -54, 12, 0, 9, -2, 32, -85, 0, 16, 20, -30, 0, 0, -48, 18, -6, -20, 0, 49, -60, 55, 12, 0, 70, 0, 13, 51, 0, -40, -23, 170, -18, 0, -7, -4, 9, -29, 0, 80, -41, -4, 37, 0, -4, -100, 21, 54, 0, 30, 20, 0, -165, 0, 58, -24, 4, -96, 0, 180, 28, 27, -55, 0, 0, -92, 40, -18, 0, 36, -70, 8, 17, 0, -52, -19, 13, 0, 0, -60, -15, -21, -16, 0, 12, -50, -38, -40, 0, -16, 0, 8, -10, 0, 30, -112, 40, 96, 0, -42, -6, -144, -54, 0, -28, -88, -40, -4, 0, 60, -36, 85, -45, 0, 4, -130, 0, -44, 0, 2, -16, -14, 30, 0, 51, 17, -4, 92, 0, 0, 45, 16, -18, 0, 13, 45, -5, 64, 0, -40, 6, 37, 0, 0, 8, -71, -24, -80, 0, 6, 18, 68, -10, 0, 51, 0, -90, 60, 0, -6, -4, -22, 38, 0, -150, 34, 33, -18, 0, -63, 12, -30, 12, 0, 54, -7, -10, -52, 0, 3, -69, 0, 6, 0, 30, 180, -2, -72, 0, -12, 54, 60, -20, 0, 0, -40, -9, -64, 0, 54, 0, 18, 10, 0, 3, 42, -20, 0, 0, 74, 1, 24, 12, 0, 26, -20, -16, -105, 0, -64, 0, 96, -7, 0, -13, 100, 42, 40, 0, 72, 30, 40, 20, 0, -60, 3, 2, 1, 0, 92, -42, 90, -12, 0, -54, 108, 0, -80, 0, 65, 73, 8, -12, 0, 56, -20, -9, -22, 0, 0, 24, 60, -60, 0, 9, -24, 10, 51, 0, 35, 2, 70, 0, 0, 32, 32, 45, 14, 0, 65, -41, -8, 36, 0, -10, 0, -20, 20, 0, 87, 80, -52, 93, 0, 50, 4, -9, 18, 0, -90, -15, 32, 38, 0, -80, -44, -34, 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, -5, 3, 1, 0, -3, 2, 0, 5, 0, -1, -5, -1, 4, 0, 10, 3, -4, -6, 0, 0, 4, 5, -1, 0, -1, -5, 6, 5, 0, -1, 4, -4, 0, 0, 8, -10, 4, 3, 0, 4, -7, 2, 18, 0, 10, 0, -3, -4, 0, -15, -8, 1, 3, 0, 1, 1, -5, 7, 0, -6, -3, 5, 8, 0, -8, 3, 4, -4, 0, -4, 15, 0, 10, 0, -11, -8, 9, -10, 0, -4, 2, -9, 18, 0, 0, 4, 2, 7, 0, 10, 14, -18, -3, 0, -1, -10, -4, 0, 0, 3, -16, -4, 2, 0, -8, 5, 10, 8, 0, 1, 0, -3, 25, 0, -2, -1, -16, 1, 0, 5, -18, 3, -8, 0, 18, -6, -20, 3, 0, -15, 18, -8, 4, 0, 14, 8, 0, -1, 0, -4, -36, -4, -10, 0, -13, 12, -5, -15, 0, 0, -13, -10, 6, 0, 20, 11, 12, -8, 0, -9, 16, 30, 0, 0, 4, -4, -13, -2, 0, 3, -6, -18, -12, 0, -3, 0, -2, -12, 0, -2, 15, 7, -20, 0, 10, -14, 4, -14, 0, -18, 8, 3, 6, 0, 6, 1, 5, -10, 0, 4, -4, 0, -12, 0, -12, 3, 16, 16, 0, 12, 5, -2, -8, 0, 0, 8, 16, 25, 0, -10, -9, 8, 2, 0, -30, -3, -14, 0, 0, -3, -20, -25, -5, 0, 0, 2, 10, -1, 0, 16, 0, -3, -18, 0, -12, 5, 12, 18, 0, -17, -15, 8, -20, 0, -1, -18, -6, 18, 0, 20, -36, 3, -17, 0, -29, 5, 0, -18, 0, -8, 2, -4, -1, 0, 18, -14, 28, 8, 0, 0, -40, -5, 8, 0, -28, -4, -6, 36, 0, 12, -12, 10, 0, 0, -20, 13, 2, -4, 0, 5, 8, -15, 8, 0, -4, 0, 17, 13, 0, -10, -22, -6, 3, 0, 32, -20, -20, 11, 0, -12, -4, 24, 35, 0, 20, -9, 4, -16, 0, -10, 3, 0, -20, 0, 3, -4, -55, 12, 0, 13, 4, -2, -2, 0, 0, 15, -6, 6, 0, -18, -50, 12, -23, 0, -3, 3, 4, 0, 0, 2, -18, 4, 8, 0, 15, -2, 31, -15, 0, -21, 0, 20, -27, 0, 36, -10, 32, -6, 0, -4, 4, -14, -34, 0, 20, 54, -36, -8, 0, 3, 8, -6, 40, 0, 26, -6, 0, 1, 0, -5, -12, 30, 6, 0, -36, 4, -15, 4, 0, 0, -8, 12, -18, 0, 4, 12, -7, -9, 0, -16, -5, 16, 0, 0, 0, -4, -14, -5, 0, -2, -16, 8, -22, 0, 18, 0, -24, 8, 0, -16, 20, -35, 6, 0, -24, -10, 26, 9, 0, -24, 10, -2, -20, 0, -26, 30, -19, 1, 0, 14, -18, 0, 15, 0, 26, 9, -12, 20, 0, -25, -3, 5, 3, 0, 0, 0, -40, 2, 0, -10, 15, 3, -24, 0, 28, 16, 5, 0, 0, 1, 40, 18, 19, 0, -32, 12, -16, -15, 0, -12, 0, 18, 0, 0, -20, 11, 16, 15, 0, 8, 21, 20, 26, 0, 10, 1, -22, -18, 0, 6, 5, -6, -7, 0, 3, 20, 0, 36, 0, -9, 24, 17, -54, 0, -38, 29, 6, 25, 0, 0, 38, -18, 1, 0, -4, 24, -50, -2, 0, -4, -24, 1, 0, 0, -30, -18, 30, -14, 0, -28, 55, -24, 33, 0, -2, 0, -20, 40, 0, 7, 38, -8, -8, 0, -45, 28, 9, 12, 0, 6, -25, 36, -4, 0, -16, -4, 8, 12, 0, 10, -12, 0, -14, 0, 29, 20, -3, 13, 0, -2, -8, -20, -10, 0, 0, 5, -10, -8, 0, 45, 4, -8, -28, 0, -16, 4, -90, 0, 0, -17, 24, 13, -20, 0, 20, 30, 24, 22, 0, -6, 0, -3, -8, 0, 15, -32, -4, -20, 0, 20, 14, -33, -9, 0, -10, -12, 31, 4, 0, -8, 4, -35, -6, 0, 38, -20, 0, 27, 0, -4, 4, -16, -32, 0, -3, -50, 23, -3, 0, 0, 6, 20, -70, 0, 18, -3, 41, -4, 0, 55, -4, -4, 0, 0, -17, 13, 15, -4, 0, 6, -40, 2, 28, 0, 45, 0, 16, -21, 0, 6, 5, 6, -8, 0, 10, 54, 4, 50, 0, 12, 10, 23, -30, 0, 20, 3, 0, 3, 0, -4, 16, 0, 13, 0, -20, 2, 42, 18, 0, 20, 9, -8, -9, 0, 0, -15, 41, 6, 0, -31, 9, -15, 80, 0, 32, 7, 24, 0, 0, 20, 5, 27, -24, 0, 10, -36, -10, -10, 0, -32, 0, 34, -40, 0, 30, -4, -18, -4, 0, 42, 40, 34, 32, 0, 24, -20, -4, -18, 0, 36, 43, -8, 12, 0, -50, -9, 0, -8, 0, -6, 53, -40, 35, 0, 18, -26, -12, -6, 0, 0, 34, -3, -30, 0, -25, -5, 58, 12, 0, -10, 16, -6, 0, 0, 30, 36, -12, -12, 0, 15, -19, 4, 11, 0, -4, 0, -90, 8, 0, 12, -4, 18, -36, 0, -28, -4, -36, 12, 0, 7, 10, 3, -56, 0, -16, -16, 54, 5, 0, -48, -14, 0, -4, 0, 80, 0, 33, -20, 0, 14, -16, -5, -30, 0, 0, 6, 14, 16, 0, 8, -14, 22, 12, 0, 33, -18, -28, 0, 0, 24, -22, -24, 90, 0, 33, -16, -28, -20, 0, -15, 0, -6, 1, 0, 15, 24, 40, 30, 0, -26, 20, 9, -1, 0, 2, 8, -27, -10, 0, -2, -90, 20, 46, 0, -16, 26, 0, 30, 0, 19, -4, 5, 56, 0, 72, 14, 8, 18, 0, 0, -1, -15, -34, 0, -8, -26, -32, -3, 0, 12, -3, 20, 0, 0, 44, 75, 9, 3, 0, 5, -6, -3, -90, 0, -30, 0, -16, 0, 0, 40, -37, -6, 40, 0, -48, -10, -20, -15, 0, -1, -46, 24, -54, 0, 2, -28, 11, -48, 0, -5, -70, 0, -16, 0, 4, 5, -40, -40, 0, 18, 45, -19, 16, 0, 0, 32, -15, 12, 0, 16, -12, 5, -38, 0, -6, -12, 3, 0, 0, -54, 10, 0, -16, 0, -28, 20, -6, 23, 0, -16, 0, 15, 110, 0, -56, -24, -34, -21, 0, 20, -5, -26, 48, 0, -8, -10, 50, 1, 0, 22, 4, 54, -9, 0, 35, 6, 0, -5, 0, -30, 65, 7, 12, 0, 36, -3, 48, -60, 0, 0, -42, 36, 43, 0, 25, 3, -4, -24, 0, 17, 46, 54, 0, 0, 28, 38, 6, 29, 0, -6, -36, -35, -2, 0, -6, 0, 26, -38, 0, 54, -48, -1, 65, 0, 36, 4, 5, -8, 0, 50, 32, -2, 30, 0, 3, 12, -30, 24, 0, 1, -47, 0, -62, 0, 12, 30, -9, -18, 0, -30, -72, 42, 56, 0, 0, -28, 12, -55, 0, 8, 54, -33, 15, 0, -60, 2, -18, 0, 0, 20, -4, 40, -64, 0, -33, 3, 2, -38, 0, -8, 0, 8, 4, 0, 16, 45, -51, 28, 0, -9, 68, -4, -80, 0, -50, 6, -40, 25, 0, -108, 48, 4, 18, 0, -32, 16, 0, -20, 0, -8, 2, 12, -8, 0, -16, -30, -39, 12, 0, 0, -20, 14, -6, 0, 40, -29, -52, 20, 0, 3, 40, -39, 0, 0, 65, -2, -11, 8, 0, 28, 56, 10, 12, 0, 24, 0, -14, -15, 0, 10, -12, -8, -52, 0, -14, -15, 18, -4, 0, -8, 22, 28, 30, 0, -20, 16, -30, 4, 0, 90, -4, 0, -11, 0, 4, -17, 60, -24, 0, -39, 36, 20, 13, 0, 0, -20, -8, -10, 0, -24, 15, 22, -28, 0, -8, 18, -12, 0, 0, -3, 30, 8, 1, 0, 10, -15, 60, -32, 0, 4, 0, 60, -12, 0, 18, 20, 0, -14, 0, 11, -39, 9, 28, 0, 14, 10, 26, 36, 0, -31, 3, 4, -75, 0, 32, -40, 0, -4, 0, -35, 44, 6, -7, 0, -26, -38, 72, -20, 0, 0, 14, -9, 48, 0, 39, -4, -4, -4, 0, 48, -50, 32, 0, 0, -10, 3, -50, 70, 0, -23, -12, -3, -32, 0, -20, 0, 48, -6, 0, 20, -12, 70, -13, 0, 23, -18, 7, -3, 0, -41, -37, 12, -21, 0, -20, 55, -58, 4, 0, -20, 55, 0, -40, 0, 70, 17, 52, -39, 0, -15, 16, -4, 38, 0, 0, -2, -30, 40, 0, 2, 54, -28, 40, 0, 36, -45, -4, 0, 0, -16, -30, -9, 4, 0, -45, 6, -13, -5, 0, -18, 0, 8, 24, 0, -18, -10, -51, -18, 0, -4, -38, 50, -33, 0, -12, -36, -54, -10, 0, 23, -6, 30, 2, 0, -54, -20, 0, 3, 0, 0, -10, -9, 20, 0, -1, -4, -26, -16, 0, 0, 7, -13, -42, 0, -30, 20, 60, -6, 0, -42, 12, 18, 0, 0, -73, -28, -56, -9, 0, -8, 60, 9, -10, 0, -2, 0, -32, -15, 0, -41, -36, -2, 20, 0, -80, -31, -50, -9, 0, 45, -38, -80, 34, 0, 40, -32, 16, 35, 0, -24, -54, 0, 32, 0, 54, -60, -90, -5, 0, 27, 32, 24, -18, 0, 0, -10, 56, -36, 0, 10, 0, 30, -12, 0, -54, -32, 40, 0, 0, -22, 3, 40, -44, 0, 12, -30, -32, 12, 0, 18, 0, -4, 24, 0, -42, -14, -40, -40, 0, 34, -13, -32, -44, 0, -80, -24, -20, -20, 0, 4, 8, -90, 44, 0, 20, 36, 0, -43, 0, 24, 36, -12, 41, 0, -10, 50, -38, 3, 0, 0, 14, -8, 45, 0, 16, 18, 12, -53, 0, -40, -60, -35, 0, 0, -2, -18, -10, -26, 0, 12, -36, 18, -9, 0, -12, 0, -54, -34, 0, 1, 108, 30, -37, 0, -10, 25, 76, 15, 0, -58, 53, 12, -3, 0, 70, -50, 32, -16, 0, -6, -3, 0, 30, 0, -76, -30, 3, 36, 0, 12, 4, 4, -70, 0, 0, 15, 8, 19, 0, -12, 12, -11, 100, 0, 39, 4, 46, 0, 0, 90, -40, 8, -52, 0, 48, -36, 25, 4, 0, 18, 0, 36, -16, 0, 23, 28, 15, -4, 0, 36, 0, -36, -60, 0, 72, 7, 46, -10, 0, 15, 24, 56, 0, 0, -50, 16, 0, 48, 0, -54, -66, 5, -24, 0, -3, 16, 4, 14, 0, 0, 5, 4, 10, 0, -70, -80, 33, 0, 0, -33, 39, 28, 0, 0, -76, 14, 51, 16, 0, 15, 4, 30, -28, 0, 58, 0, 90, -2, 0, -14, 19, 16, -18, 0, 20, -24, -42, 14, 0, 22, 60, -12, 48, 0, 50, -33, 32, -18, 0, 28, 8, 0, -1, 0, -60, 24, 8, 22, 0, 8, -23, -90, -16, 0, 0, -33, -5, 48, 0, 28, -68, -20, -2, 0, 6, 85, -36, 0, 0, -6, 28, -1, 75, 0, 74, -15, -58, 24, 0, -40, 0, -10, -12, 0, -66, -26, 72, -20, 0, -27, -40, 1, 80, 0, 16, -2, -18, 40, 0, 27, 5, -10, -3, 0, 72, 6, 0, 90, 0, 20, -48, -46, 20, 0, 30, 16, 56, 26, 0, 0, 6, -90, -27, 0, -8, 19, -10, 4, 0, -7, 56, -56, 0, 0, -28, -72, 44, -42, 0, -8, 9, 18, 180, 0, 60, 0, -69, 1, 0, -15, -6, 34, 77, 0, -12, 8, 85, -26, 0, 32, 40, -15, 49, 0, -1, 12, -40, 3, 0, -60, 145, 0, -12, 0, -31, -44, 39, -25, 0, -9, -40, 3, -36, 0, 0, -15, -4, 6, 0, -3, -32, 90, -4, 0, -50, 30, -30, 0, 0, 16, -56, 0, 8, 0, -27, 40, 71, 37, 0, 2, 0, -40, -10, 0, -28, 48, 3, 30, 0, 20, 18, -15, 5, 0, 14, -5, 5, 46, 0, 24, -16, 54, -62, 0, -12, -2, 0, -28, 0, -11, -90, 16, 36, 0, 16, -5, -54, 70, 0, 0, 12, 16, 0, 0, -140, -4, -76, -7, 0, 40, -67, -40, 0, 0, 9, -54, 1, -45, 0, -19, 30, -16, 26, 0, -8, 0, -12, 32, 0, 15, 16, -36, 144, 0, 56, 16, 6, 12, 0, 25, -58, 38, -46, 0, -28, 6, -40, 36, 0, -3, 24, 0, -14, 0, -12, 18, -64, -10, 0, 0, 140, 16, 48, 0, 0, 28, -9, 20, 0, 6, -72, -45, -82, 0, 30, -16, 77, 0, 0, -45, 10, -110, 8, 0, 2, 56, -62, 8, 0, 34, 0, -21, -12, 0, 8, -60, 34, 5, 0, -26, 3, -48, 60, 0, -71, 8, 10, -10, 0, -50, -9, -3, -70, 0, 80, 22, 0, -4, 0, -18, -14, 9, -15, 0, -30, -35, -90, -18, 0, 0, 72, -5, -32, 0, 24, 42, -32, -65, 0, 7, -4, -12, 0, 0, -10, -36, -12, -3, 0, -48, 16, 20, 27, 0, -2, 0, 40, 42, 0, -108, -24, -43, -8, 0, 30, -25, -77, 15, 0, 4, 40, -24, -40, 0, -5, -51, -24, -46, 0, 54, 60, 0, 90, 0, -53, -28, -40, 38, 0, -6, -24, -87, 0, 0, 0, -6, -24, 36, 0, -15, 20, 2, -7, 0, -32, 6, 12, 0, 0, -26, -56, -38, -18, 0, -85, -18, 40, 48, 0, -1, 0, -65, -84, 0, 8, -36, 19, 4, 0, -5, -84, -40, 2, 0, -18, 50, 27, -32, 0, 6, 18, -30, 110, 0, -78, -3, 0, -4, 0, 30, -90, 24, -82, 0, -56, -3, -15, 47, 0, 0, -78, 62, 30, 0, 36, -12, -73, 30, 0, 9, -160, 54, 0, 0, -23, -30, -64, 72, 0, -14, 4, -56, -12, 0, 100, 0, -4, 84, 0, -12, 33, -55, -80, 0, -10, 40, 68, -54, 0, -33, 12, -15, -12, 0, -58, 60, -20, 2, 0, 18, -42, 0, 20, 0, -10, 20, -28, 4, 0, -120, -38, 64, -8, 0, 0, 33, -126, -17, 0, -2, 80, -38, 16, 0, 38, 24, -15, 0, 0, 8, -100, -4, 36, 0, 36, -16, 4, 45, 0, 51, 0, -84, -90, 0, -20, -9, -6, -68, 0, -20, -64, 80, -2, 0, 71, 50, -48, -18, 0, 40, 25, 25, 11, 0, 35, 36, 0, -48, 0, 4, -75, -18, -15, 0, -86, 32, -20, 16, 0, 0, -6, 28, 16, 0, 41, -8, 100, -2, 0, -36, 64, 8, 0, 0, 50, 16, -4, 10, 0, 39, -15, 12, -22, 0, -106, 0, -91, 20, 0, 14, -70, 6, -27, 0, 149, -40, 72, -29, 0, 52, -9, -60, 24, 0, -83, 3, -72, -40, 0, 13, -3, 0, 24, 0, -17, -65, 31, 6, 0, 11, 60, 8, -20, 0, 0, 12, 50, -56, 0, 10, -50, -12, -29, 0, -66, -24, 10, 0, 0, 14, 52, 5, -10, 0, -32, 10, -48, 12, 0, 24, 0, 52, 36, 0, 64, 14, -60, -75, 0, -18, 82, -4, 24, 0, 30, 24, -14, -22, 0, 28, 30, -30, -12, 0, 38, 20, 0, 16, 0, 30, -22, -12, 72, 0, 21, 90, 2, 4, 0, 0, 27, 11, 180, 0, 8, -4, 7, 51, 0, -60, -8, -24, 0, 0, 11, 13, 115, -36, 0, 20, 72, -13, -6, 0, -57, 0, 56, -20, 0, 8, 15, -50, 18, 0, -60, -24, 50, -15, 0, -66, 12, 28, 88, 0, -20, 8, 48, -6, 0, 12, 28, 0, 45, 0, -44, 9, 32, -30, 0, 8, -55, -1, -108, 0, 0, -10, 42, -15, 0, -60, 65, 96, 90, 0, 28, 4, -9, 0, 0, -20, 8, 12, 43, 0, -18, -18, -40, -60, 0, 0, 0, -14, -66, 0, -42, 55, 6, 39, 0, 9, -54, -28, -40, 0, 8, -14, 72, 10, 0, -26, 60, -12, -77, 0, -155, -31, 0, -3, 0, -12, 14, 75, 56, 0, -20, -32, 4, 56, 0, 0, -32, -4, 15, 0, 28, 105, -60, -44, 0, 6, -6, 7, 0, 0, 16, 26, -66, -38, 0, -72, 25, 60, 56, 0, 0, 0, 135, -14, 0, -45, 96, -48, -88, 0, 44, -39, -48, 12, 0, 4, -180, -4, 65, 0, 31, -16, -30, 50, 0, 32, 71, 0, 56, 0, -160, 10, 4, 3, 0, 50, -72, 30, -58, 0, 0, -23, -54, 12, 0, 9, -2, 32, -85, 0, 16, 20, -30, 0, 0, -48, 18, -6, -20, 0, 49, -60, 55, 12, 0, 70, 0, 13, 51, 0, -40, -23, 170, -18, 0, -7, -4, 9, -29, 0, 80, -41, -4, 37, 0, -4, -100, 21, 54, 0, 30, 20, 0, -165, 0, 58, -24, 4, -96, 0, 180, 28, 27, -55, 0, 0, -92, 40, -18, 0, 36, -70, 8, 17, 0, -52, -19, 13, 0, 0, -60, -15, -21, -16, 0, 12, -50, -38, -40, 0, -16, 0, 8, -10, 0, 30, -112, 40, 96, 0, -42, -6, -144, -54, 0, -28, -88, -40, -4, 0, 60, -36, 85, -45, 0, 4, -130, 0, -44, 0, 2, -16, -14, 30, 0, 51, 17, -4, 92, 0, 0, 45, 16, -18, 0, 13, 45, -5, 64, 0, -40, 6, 37, 0, 0, 8, -71, -24, -80, 0, 6, 18, 68, -10, 0, 51, 0, -90, 60, 0, -6, -4, -22, 38, 0, -150, 34, 33, -18, 0, -63, 12, -30, 12, 0, 54, -7, -10, -52, 0, 3, -69, 0, 6, 0, 30, 180, -2, -72, 0, -12, 54, 60, -20, 0, 0, -40, -9, -64, 0, 54, 0, 18, 10, 0, 3, 42, -20, 0, 0, 74, 1, 24, 12, 0, 26, -20, -16, -105, 0, -64, 0, 96, -7, 0, -13, 100, 42, 40, 0, 72, 30, 40, 20, 0, -60, 3, 2, 1, 0, 92, -42, 90, -12, 0, -54, 108, 0, -80, 0, 65, 73, 8, -12, 0, 56, -20, -9, -22, 0, 0, 24, 60, -60, 0, 9, -24, 10, 51, 0, 35, 2, 70, 0, 0, 32, 32, 45, 14, 0, 65, -41, -8, 36, 0, -10, 0, -20, 20, 0, 87, 80, -52, 93, 0, 50, 4, -9, 18, 0, -90, -15, 32, 38, 0, -80, -44, -34, 36, 0]}