# Stored data for newform 6615.2.a.h, downloaded from the LMFDB on 19 June 2024. {"Nk2": 26460, "analytic_conductor": 52.82104093707697, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, -1], [5, -1], [7, 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": [6615, 1, [3431, 2647, 1081], [1, 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]], [11, [3, 1]], [13, [-6, 1]], [17, [1, 1]]], "hecke_orbit": 8, "hecke_orbit_code": 31525197425154519, "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": "6615.2.a.h", "level": 6615, "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": [3, 5, 7], "level_radical": 105, "minimal_twist": "945.2.j.a", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q+q^{2}-q^{4}+q^{5}-3q^{8}+q^{10}-3q^{11}+\\cdots", "related_objects": ["EllipticCurve/Q/6615/h"], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "6615.2.a", "trace_display": [1, 0, 1, 0], "trace_hash": 661253611178992813, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.953", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.842", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.538", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.013", "prec": 17}, "traces": [0, 1, 1, 0, -1, 1, 0, 0, -3, 0, 1, -3, 0, 6, 0, 0, -1, -1, 0, 4, -1, 0, -3, -4, 0, 1, 6, 0, 0, -8, 0, -2, 5, 0, -1, 0, 0, -2, 4, 0, -3, -12, 0, 4, 3, 0, -4, -4, 0, 0, 1, 0, -6, -11, 0, -3, 0, 0, -8, 1, 0, 10, -2, 0, 7, 6, 0, 7, 1, 0, 0, 15, 0, 4, -2, 0, -4, 0, 0, -4, -1, 0, -12, -4, 0, -1, 4, 0, 9, 6, 0, 0, 4, 0, -4, 4, 0, -6, 0, 0, -1, 2, 0, -13, -18, 0, -11, 12, 0, -6, -3, 0, 0, 9, 0, -4, 8, 0, 1, 0, 0, -2, 10, 0, 2, 1, 0, -19, -3, 0, 6, -19, 0, 0, 7, 0, 3, -22, 0, -6, 0, 0, 15, -18, 0, -8, 4, 0, 2, -4, 0, -10, -12, 0, 0, -2, 0, -20, -4, 0, 5, 0, 0, -21, 12, 0, -4, 14, 0, 23, -1, 0, -4, -9, 0, 0, 3, 0, 6, -21, 0, -17, 0, 0, 12, -2, 0, 3, 4, 0, 4, 1, 0, 0, -6, 0, 0, 15, 0, -4, -3, 0, 2, 0, 0, -12, -13, 0, -6, -12, 0, 10, 11, 0, 12, 4, 0, 0, -6, 0, 3, -6, 0, -9, 0, 0, 9, -22, 0, 13, -4, 0, 24, -9, 0, -4, -1, 0, 0, 8, 0, -18, -2, 0, -10, 0, 0, 24, 6, 0, 1, -9, 0, 12, -19, 0, -17, -15, 0, 0, -6, 0, -19, -8, 0, -11, 0, 0, -7, -10, 0, 24, 1, 0, -22, -3, 0, 8, -6, 0, 0, 6, 0, 5, -15, 0, -18, 0, 0, -16, -8, 0, -4, -13, 0, 1, 6, 0, -4, -24, 0, 0, -10, 0, -4, 10, 0, 15, 0, 0, -2, 9, 0, -22, -20, 0, 4, 5, 0, 24, 7, 0, 0, -4, 0, 6, -21, 0, 36, 0, 0, -18, 4, 0, 14, 7, 0, 10, 23, 0, 1, 6, 0, 0, -12, 0, -9, 16, 0, 35, 0, 0, -15, -33, 0, 15, -6, 0, -21, 12, 0, -3, -17, 0, 0, 4, 0, 37, 4, 0, -2, 0, 0, -4, 3, 0, 12, -48, 0, -4, -4, 0, 1, 22, 0, 0, 0, 0, 6, -12, 0, 4, 0, 0, 15, -4, 0, 32, -4, 0, -1, 30, 0, -12, -2, 0, 0, 6, 0, 5, -12, 0, 13, 0, 0, -4, 30, 0, -12, 3, 0, -35, 10, 0, 33, -1, 0, 0, -12, 0, 4, 28, 0, -32, 0, 0, 6, -16, 0, -26, 9, 0, -6, -24, 0, 6, -9, 0, 0, 24, 0, 36, -9, 0, -22, 0, 0, 18, 13, 0, 4, -32, 0, 33, 8, 0, -9, 10, 0, 0, -4, 0, -3, -12, 0, 4, 0, 0, 8, 11, 0, -12, -18, 0, 2, -6, 0, -4, -30, 0, 0, 24, 0, 8, 24, 0, 2, 0, 0, 38, -1, 0, -9, -44, 0, 2, 12, 0, 19, -8, 0, 0, -11, 0, -15, -13, 0, 12, 0, 0, -18, 28, 0, -7, 19, 0, -8, 2, 0, -7, -11, 0, 0, -72, 0, 12, -21, 0, -10, 0, 0, -45, 24, 0, -5, -6, 0, 3, 22, 0, -3, -32, 0, 0, 8, 0, 6, 17, 0, 24, 0, 0, 6, 10, 0, 9, 5, 0, -45, 42, 0, -6, 18, 0, 0, -4, 0, -2, -16, 0, 8, 0, 0, 33, -12, 0, -13, 12, 0, -8, 1, 0, 2, 30, 0, 0, 4, 0, -24, 32, 0, -3, 0, 0, 10, -2, 0, -1, 20, 0, 10, -24, 0, -18, 15, 0, 0, 27, 0, -36, 2, 0, 9, 0, 0, 1, -22, 0, 20, 2, 0, 0, 12, 0, 5, -19, 0, 0, 24, 0, -3, -24, 0, 40, 0, 0, -4, 18, 0, -3, 6, 0, 21, -34, 0, -19, 12, 0, 0, 12, 0, 26, -18, 0, 12, 0, 0, 32, -14, 0, 7, -30, 0, -28, 10, 0, -23, 22, 0, 0, 3, 0, 6, 30, 0, -22, 0, 0, -4, -66, 0, 6, 9, 0, 16, -6, 0, 12, 35, 0, 0, -26, 0, -8, -21, 0, -33, 0, 0, 1, 15, 0, -18, 8, 0, -18, 21, 0, 12, -13, 0, 0, -3, 0, 17, -8, 0, 16, 0, 0, 4, -4, 0, -4, 37, 0, -20, -21, 0, -34, 2, 0, 0, -12, 0, -4, -4, 0, -3, 0, 0, -28, 4, 0, -48, -10, 0, 2, -4, 0, -12, -18, 0, 0, -1, 0, 22, 6, 0, 5, 0, 0, 0, -39, 0, -2, 18, 0, -12, -48, 0, -45, 4, 0, 0, -20, 0, 28, -15, 0, -4, 0, 0, 60, 32, 0, 4, -21, 0, 4, 5, 0, 30, -12, 0, 0, -12, 0, -6, 30, 0, -18, 0, 0, 6, -21, 0, 16, 5, 0, 12, -18, 0, -40, 39, 0, 0, 48, 0, 15, -4, 0, 42, 0, 0, 14, 12, 0, 3, 36, 0, 35, -35, 0, -10, 23, 0, 0, 11, 0, -1, 8, 0, 6, 0, 0, -36, 39, 0, 20, -4, 0, 28, -24, 0, -9, -32, 0, 0, 12, 0, 42, 18, 0, -16, 0, 0, 2, -26, 0, 3, 36, 0, 43, 6, 0, -24, 22, 0, 0, 6, 0, 9, -16, 0, -21, 0, 0, 24, 16, 0, 11, 36, 0, -27, -17, 0, 7, 22, 0, 0, 27, 0, 12, 18, 0, -13, 0, 0, -6, 12, 0, -32, 90, 0, -2, 33, 0, -40, -26, 0, 0, 9, 0, 10, 3, 0, 4, 0, 0, 4, 6, 0, 48, -1, 0, -12, -46, 0, 24, 4, 0, 0, -14, 0, 1, -8, 0, 11, 0, 0, -27, -12, 0, 18, 0, 0, -17, 6, 0, -6, 8, 0, 0, -4, 0, -10, 11, 0, -18, 0, 0, 24, 14, 0, 15, 8, 0, -24, -16, 0, 60, -10, 0, 0, -4, 0, -34, 38, 0, -3, 0, 0, -1, 9, 0, -44, -44, 0, -9, 2, 0, -12, -37, 0, 0, 57, 0, -8, -52, 0, 5, 0, 0, 23, -12, 0, -24, 15, 0, -13, -5, 0, 46, 12, 0, 0, -10, 0, -18, -6, 0, 28, 0, 0, -12, -7, 0, 57, -40, 0, 26, 8, 0, 2, 10, 0, 0, -7, 0, 11, 30, 0, -16, 0, 0, -72, 18, 0, -14, 12, 0, -7, 16, 0, 4, 10, 0, 0, -24, 0, 16, -45, 0, -24, 0, 0, 32, -7, 0, -6, 25, 0, -12, 3, 0, 66, -14, 0, 0, 3, 0, -32, 14, 0, -6, 0, 0, -8, 22, 0, -6, 18, 0, 17, -9, 0, 56, 24, 0, 0, 4, 0, -13, -6, 0, 10, 0, 0, 26, 9, 0, -5, 39, 0, -22, -15, 0, 42, -7, 0, 0, -6, 0, 54, 13, 0, 4, 0, 0, -4, 25, 0, 20, -2, 0, 16, 36, 0, 40, 24, 0, 0, 56, 0, -9, 33, 0, -4, 0, 0, -64, 13, 0, 12, -4, 0, -36, -8, 0, -1, 20, 0, 0, -10, 0, 30, -18, 0, 96, 0, 0, 12, 21, 0, 8, 24, 0, 32, 18, 0, -63, -3, 0, 0, -18, 0, -15, 30, 0, -2, 0, 0, 4, -1, 0, 28, -31, 0, 44, -10, 0, -24, 14, 0, 0, -18, 0, -15, 60, 0, -44, 0, 0, 27, 24, 0, -56, -36, 0, 6, -4, 0, -27, -9, 0, 0, -32, 0, -17, 1, 0, 22, 0, 0, -9, 60, 0, 2, -25, 0, -36, 0, 0, 4, 12, 0, 0, -5, 0, -19, 24, 0, 28, 0, 0, -24, -70, 0, -30, -17, 0, -24, 14, 0, -15, 40, 0, 0, -56, 0, 42, 4, 0, 18, 0, 0, 22, -3, 0, -6, 46, 0, -8, 63, 0, -34, -38, 0, 0, -19, 0, -60, 12, 0, -8, 0, 0, 12, -3, 0, 41, 26, 0, 18, -11, 0, 32, 4, 0, 0, 39, 0, -8, 32, 0, -42, 0, 0, -78, -7, 0, -30, 4, 0, -10, -28, 0, -10, 60, 0, 0, -69, 0, 22, 24, 0, -4, 0, 0, 1, -42, 0, 32, -6, 0, 30, -8, 0, -33, -22, 0, 0, -67, 0, -3, 20, 0, -66, 0, 0, 49, 6, 0, 27, 8, 0, 16, -16, 0, -6, 72, 0, 0, 12, 0, -35, 57, 0, 20, 0, 0, -26, -40, 0, 6, -8, 0, 9, 18, 0, 4, 33, 0, 0, 5, 0, -36, 1, 0, -15, 0, 0, 31, -6, 0, 8, 48, 0, -10, -18, 0, 63, -23, 0, 0, -12, 0, -13, 31, 0, 57, 0, 0, 3, -16, 0, -16, 51, 0, -8, -21, 0, 32, 16, 0, 0, 8, 0, -52, -4, 0, -4, 0, 0, -13, -4, 0, -37, 54, 0, -32, -28, 0, -21, 1, 0, 0, -34, 0, 6, 22, 0, -12, 0, 0, -12, 2, 0, 33, -4, 0, 4, -13, 0, -24, -9, 0, 0, -9, 0, -16, -28, 0, -20, 0, 0, 66, 48, 0, -10, -72, 0, -6, 2, 0, 4, 24, 0, 0, -4, 0, -18, -52, 0, 10, 0, 0, -3, 18, 0, 0, -22, 0, 6, 15, 0, 88, 5, 0, 0, -28, 0, -11, 0, 0, -39, 0, 0, -29, -2, 0, 6, -10, 0, 9, 12, 0, -48, 23, 0, 0, -45, 0, -4, -22, 0, 40, 0, 0, -20, 9, 0, -12, 28, 0, -45, -16, 0, -12, 4, 0, 0, -22, 0, 5, 60, 0, -32, 0, 0, -8, 12, 0, -21, 24, 0, 56, 4, 0, 7, -42, 0, 0, -30, 0, -12, 48, 0, 22, 0, 0, 12, -42, 0, -4, -2, 0, 30, -65, 0, -9, -18, 0, 0, 6, 0, 19, -6, 0, -21, 0, 0, -60, 16, 0, -5, 65, 0, 12, 36, 0, -18, 22, 0, 0, -40, 0, 13, 6, 0, -114, 0, 0, 48, -18, 0, -26, 15, 0, 4, 30, 0, -8, -18, 0, 0, -4, 0, -11, 14, 0, 36, 0, 0, 7, -3, 0, 36, -16, 0, 103, 35, 0, 35, 10, 0, 0, -30, 0, 23, 24, 0, -40, 0, 0, -55, 13, 0, 28, 1, 0, 8, -114, 0, 6, 6, 0, 0, 36, 0, -8, -12, 0, 39, 0, 0, -2, 20, 0, -12, -10, 0, 49, -28, 0, -24, 60, 0, 0, -9, 0, 32, 26, 0, 16, 0, 0, 12, 8, 0, -66, 42, 0, 6, 35, 0, 23, 16, 0, 0, 13, 0, 16, 2, 0, 26, 0, 0, -70, -15, 0, 36, -48, 0, -33, 43, 0, 18, -80, 0, 0, 24, 0, 22, 15, 0, -72, 0, 0, -6, -132, 0, -35, 27, 0, -16, -14, 0, -13, -21, 0, 0, 63, 0, 12, -24, 0, 16, 0, 0, -47, 11, 0, -36, -3, 0, -36, -9, 0, -17, 20, 0, 0, 7, 0, 66, 16, 0, -12, 0, 0, 27, -6, 0, 4, 12, 0, -18, -2, 0, -50, -39, 0, 0, 37, 0, -42, -6, 0, 4, 0, 0, -24, 32, 0, 90, 0, 0, -27, -2, 0, -33, 6, 0, 0, -56, 0, -26, -69, 0, -82, 0, 0, 27, -4, 0, -23, -10, 0, 3, 29, 0, 48, 4, 0, 0, 45, 0, -32, 12, 0, 6, 0, 0, -48, 48, 0, 5, 38, 0, -20, 12, 0, -46, -4, 0, 0, 24, 0, -4, -36, 0, 27, 0, 0, -14, 30, 0, 16, 1, 0, -24, 59, 0, 22, -11, 0, 0, 8, 0, -9, -27, 0, 12, 0, 0, 48, 54, 0, 0, 33, 0, 44, -17, 0, 2, -24, 0, 0, 6, 0, 8, -56, 0, -12, 0, 0, 4, -66, 0, -32, 50, 0, 11, 4, 0, -52, -18, 0, 0, 22, 0, -60, -24, 0, 14, 0, 0, 63, 15, 0, -8, 7, 0, -4, -72, 0, -16, 39, 0, 0, 60, 0, -14, 32, 0, -25, 0, 0, -4, 51, 0, -40, -34, 0, -38, -18, 0, 52, -1, 0, 0, -6, 0, 30, -1, 0, 27, 0, 0, -36, 44, 0, -44, -12, 0, 72, -9, 0, -2, -16, 0, 0, -36, 0, -37, 52, 0, -67, 0, 0, 19, 48, 0, 6, 8, 0, -52, -79, 0, -120, 5, 0, 0, 5, 0, -24, 45, 0, -12, 0, 0, 0, -24, 0, 45, 2, 0, -120, 13, 0, -5, 48, 0, 0, 46, 0, -12, 6, 0, -24, 0, 0, -10, -4, 0, -14, -18, 0, 30, -18, 0, 69, -28, 0, 0, 2, 0, 7, -12, 0, 7, 0, 0, 3, 19, 0, -40, 35, 0, -3, 26, 0, 24, -35, 0, 0, -2, 0, 10, -48, 0, 58, 0, 0, 7, -32, 0, -126, 33, 0, 30, 0, 0, -1, -16, 0, 0, 54, 0, -46, 72, 0, 18, 0, 0, -38, -14, 0, -12, -42, 0, 85, 35, 0, 16, 36, 0, 0, 4, 0, 30, 71, 0, 28, 0, 0, -24, 19, 0, 83, 16, 0, 45, -32, 0, -45, -72, 0, 0, 84, 0, 132, 32, 0, 3, 0, 0, 66, 6, 0, 25, -2, 0, -16, -12, 0, -3, 12, 0, 0, 22, 0, -14, -26, 0, 60, 0, 0, 9, -30, 0, -44, 32, 0, 14, 54, 0, -31, -6, 0, 0, 3, 0, -24, -24, 0, 22, 0, 0, 22, -6, 0, 6, 6, 0, 19, -17, 0, -9, 24, 0, 0, 56, 0, -24, 2, 0, -2, 0, 0, 4, -42, 0, 24, -13, 0, -18, -54, 0, 74, -10, 0, 0, 36, 0, -20, 26, 0, -9, 0, 0, -8, -15, 0, 39, 6, 0, -7, -22, 0, 75, 3, 0, 0, -42, 0, -7, -44, 0, -73, 0, 0, 6, 18, 0, 52, 18, 0, 13, 32, 0, 38, 4, 0, 0, -57, 0, -8, 4, 0, 25, 0, 0, -32, 20, 0, 2, -8, 0, -44, 48, 0, 36, 33, 0, 0, 40, 0, 8, -30, 0, -8, 0, 0, 56, -126, 0, 22, -9, 0, -33, 21, 0, 10, 20, 0, 0, -59, 0, 13, -64, 0, 39, 0, 0, -53, -12, 0, -4, 49, 0, -102, -36, 0, 8, -54, 0, 0, -3, 0, 20, 6, 0, -12, 0, 0, -14, 52, 0, 40, -30, 0, -18, 4, 0, -26, 96, 0, 0, -60, 0, -52, 4, 0, 21, 0, 0, 55, 8, 0, 72, -21, 0, 11, -32, 0, 18, 87, 0, 0, -63, 0, 3, -12, 0, 32, 0, 0, -18, 21, 0, -76, -15, 0, 10, 74, 0, -12, 2, 0, 0, -26, 0, -6, 4, 0, 1, 0, 0, 18, -12, 0, -31, -4, 0, 6, 44, 0, -30, -48, 0, 0, 24, 0, 14, -12, 0, 8, 0, 0, 18, 27, 0, 24, -45, 0, 60, -60, 0, -48, -44, 0, 0, 8, 0, 32, -27, 0, 24, 0, 0, -38, -56, 0, 36, 33, 0, -14, 2, 0, -4, 6, 0, 0, -27, 0, -27, -76, 0, 44, 0, 0, -32, 38, 0, 66, -17, 0, -1, -120, 0, 40, 66, 0, 0, 24, 0, 0, -9, 0, 20, 0, 0, -44, -2, 0, -25, -39, 0, -71, -36, 0, 0, 2, 0, 0, -20, 0, 12, -12, 0, 4, 0, 0, -15, 4, 0, -50, 19, 0, 24, 90, 0, -8, 28, 0, 0, -58, 0, 30, -72, 0, -70, 0, 0, 74, -30, 0, -11, 90, 0, 27, 24, 0, 14, 10, 0, 0, -15, 0, -40, 8, 0, -13, 0, 0, -56, -33, 0, -48, 42, 0, 12, 12, 0, -24, -18, 0, 0, -36, 0, 34, 22, 0, 3, 0, 0, -36, -18, 0, 46, -88, 0, 28, -8, 0, 21, -94, 0, 0, 34, 0, -38, -7, 0, 38, 0, 0, 19, -24, 0, 40, -84, 0, 12, -30, 0, -24, -8, 0, 0, 82, 0, 2, -12, 0, -3, 0, 0, -24, 41, 0, -26, -7, 0, -32, 54, 0, -11, 54, 0, 0, 32, 0, -20, 75, 0, 88, 0, 0, 39, 96, 0, -72, -8, 0, -32, 20, 0, -34, -14, 0, 0, 12, 0, -62, -78, 0, -21, 0, 0, 81, 30, 0, 4, -102, 0, -55, -10, 0, 28, -71, 0, 0, -30, 0, 60, -57, 0, -8, 0, 0, -23, -45, 0, 13, -22, 0, 24, 56, 0, 94, -4, 0, 0, -72, 0, -78, -5, 0, -42, 0, 0, -6, 32, 0, -18, -70, 0, -18, -30, 0, -8, 3, 0, 0, -33, 0, 22, 68, 0, 60, 0, 0, -67, -84, 0, 62, -3, 0, 28, -27, 0, -32, 66, 0, 0, -12, 0, 27, 49, 0, -6, 0, 0, 67, 9, 0, 8, 21, 0, -4, 16, 0, -48, -7, 0, 0, 6, 0, 72, 8, 0, 17, 0, 0, -12, 84, 0, -20, -105, 0, 57, 24, 0, -30, 20, 0, 0, -82, 0, 35, 26, 0, -40, 0, 0, 68, 6, 0, 8, 48, 0, 10, 51, 0, 18, -57, 0, 0, 4, 0, 99, 9, 0, 45, 0, 0, 5, -16, 0, -26, -36, 0, -1, 35, 0, -14, -45, 0, 0, 54, 0, 42, 31, 0, 30, 0, 0, 52, -8, 0, 48, -6, 0, 32, -10, 0, 18, -70, 0, 0, 21, 0, -23, -40, 0, -40, 0, 0, -36, -23, 0, -4, 13, 0, 31, 49, 0, 28, 57, 0, 0, -2, 0, 88, 9, 0, -16, 0, 0, 24, -16, 0, 17, -86, 0, -54, 8, 0, -21, -54, 0, 0, 32, 0, -16, -30, 0, -180, 0, 0, 8, 33, 0, -16, -52, 0, -12, 76, 0, 8, 4, 0, 0, 98, 0, -16, -13, 0, 4, 0, 0, 12, -111, 0, 54, 19, 0, 9, -32, 0, 12, -8, 0, 0, 21, 0, 1, -132, 0, -68, 0, 0, 34, 39, 0, 30, 2, 0, 22, 20, 0, 30, -12, 0, 0, -48, 0, 88, 12, 0, 2, 0, 0, 78, 33, 0, 4, -72, 0, -80, 12, 0, -13, 104, 0, 0, -24, 0, -3, -48, 0, 32, 0, 0, -9, 9, 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, 1, 0, 0, -3, 0, 1, -3, 0, 6, 0, 0, -1, -1, 0, 4, -1, 0, -3, -4, 0, 1, 6, 0, 0, -8, 0, -2, 5, 0, -1, 0, 0, -2, 4, 0, -3, -12, 0, 4, 3, 0, -4, -4, 0, 0, 1, 0, -6, -11, 0, -3, 0, 0, -8, 1, 0, 10, -2, 0, 7, 6, 0, 7, 1, 0, 0, 15, 0, 4, -2, 0, -4, 0, 0, -4, -1, 0, -12, -4, 0, -1, 4, 0, 9, 6, 0, 0, 4, 0, -4, 4, 0, -6, 0, 0, -1, 2, 0, -13, -18, 0, -11, 12, 0, -6, -3, 0, 0, 9, 0, -4, 8, 0, 1, 0, 0, -2, 10, 0, 2, 1, 0, -19, -3, 0, 6, -19, 0, 0, 7, 0, 3, -22, 0, -6, 0, 0, 15, -18, 0, -8, 4, 0, 2, -4, 0, -10, -12, 0, 0, -2, 0, -20, -4, 0, 5, 0, 0, -21, 12, 0, -4, 14, 0, 23, -1, 0, -4, -9, 0, 0, 3, 0, 6, -21, 0, -17, 0, 0, 12, -2, 0, 3, 4, 0, 4, 1, 0, 0, -6, 0, 0, 15, 0, -4, -3, 0, 2, 0, 0, -12, -13, 0, -6, -12, 0, 10, 11, 0, 12, 4, 0, 0, -6, 0, 3, -6, 0, -9, 0, 0, 9, -22, 0, 13, -4, 0, 24, -9, 0, -4, -1, 0, 0, 8, 0, -18, -2, 0, -10, 0, 0, 24, 6, 0, 1, -9, 0, 12, -19, 0, -17, -15, 0, 0, -6, 0, -19, -8, 0, -11, 0, 0, -7, -10, 0, 24, 1, 0, -22, -3, 0, 8, -6, 0, 0, 6, 0, 5, -15, 0, -18, 0, 0, -16, -8, 0, -4, -13, 0, 1, 6, 0, -4, -24, 0, 0, -10, 0, -4, 10, 0, 15, 0, 0, -2, 9, 0, -22, -20, 0, 4, 5, 0, 24, 7, 0, 0, -4, 0, 6, -21, 0, 36, 0, 0, -18, 4, 0, 14, 7, 0, 10, 23, 0, 1, 6, 0, 0, -12, 0, -9, 16, 0, 35, 0, 0, -15, -33, 0, 15, -6, 0, -21, 12, 0, -3, -17, 0, 0, 4, 0, 37, 4, 0, -2, 0, 0, -4, 3, 0, 12, -48, 0, -4, -4, 0, 1, 22, 0, 0, 0, 0, 6, -12, 0, 4, 0, 0, 15, -4, 0, 32, -4, 0, -1, 30, 0, -12, -2, 0, 0, 6, 0, 5, -12, 0, 13, 0, 0, -4, 30, 0, -12, 3, 0, -35, 10, 0, 33, -1, 0, 0, -12, 0, 4, 28, 0, -32, 0, 0, 6, -16, 0, -26, 9, 0, -6, -24, 0, 6, -9, 0, 0, 24, 0, 36, -9, 0, -22, 0, 0, 18, 13, 0, 4, -32, 0, 33, 8, 0, -9, 10, 0, 0, -4, 0, -3, -12, 0, 4, 0, 0, 8, 11, 0, -12, -18, 0, 2, -6, 0, -4, -30, 0, 0, 24, 0, 8, 24, 0, 2, 0, 0, 38, -1, 0, -9, -44, 0, 2, 12, 0, 19, -8, 0, 0, -11, 0, -15, -13, 0, 12, 0, 0, -18, 28, 0, -7, 19, 0, -8, 2, 0, -7, -11, 0, 0, -72, 0, 12, -21, 0, -10, 0, 0, -45, 24, 0, -5, -6, 0, 3, 22, 0, -3, -32, 0, 0, 8, 0, 6, 17, 0, 24, 0, 0, 6, 10, 0, 9, 5, 0, -45, 42, 0, -6, 18, 0, 0, -4, 0, -2, -16, 0, 8, 0, 0, 33, -12, 0, -13, 12, 0, -8, 1, 0, 2, 30, 0, 0, 4, 0, -24, 32, 0, -3, 0, 0, 10, -2, 0, -1, 20, 0, 10, -24, 0, -18, 15, 0, 0, 27, 0, -36, 2, 0, 9, 0, 0, 1, -22, 0, 20, 2, 0, 0, 12, 0, 5, -19, 0, 0, 24, 0, -3, -24, 0, 40, 0, 0, -4, 18, 0, -3, 6, 0, 21, -34, 0, -19, 12, 0, 0, 12, 0, 26, -18, 0, 12, 0, 0, 32, -14, 0, 7, -30, 0, -28, 10, 0, -23, 22, 0, 0, 3, 0, 6, 30, 0, -22, 0, 0, -4, -66, 0, 6, 9, 0, 16, -6, 0, 12, 35, 0, 0, -26, 0, -8, -21, 0, -33, 0, 0, 1, 15, 0, -18, 8, 0, -18, 21, 0, 12, -13, 0, 0, -3, 0, 17, -8, 0, 16, 0, 0, 4, -4, 0, -4, 37, 0, -20, -21, 0, -34, 2, 0, 0, -12, 0, -4, -4, 0, -3, 0, 0, -28, 4, 0, -48, -10, 0, 2, -4, 0, -12, -18, 0, 0, -1, 0, 22, 6, 0, 5, 0, 0, 0, -39, 0, -2, 18, 0, -12, -48, 0, -45, 4, 0, 0, -20, 0, 28, -15, 0, -4, 0, 0, 60, 32, 0, 4, -21, 0, 4, 5, 0, 30, -12, 0, 0, -12, 0, -6, 30, 0, -18, 0, 0, 6, -21, 0, 16, 5, 0, 12, -18, 0, -40, 39, 0, 0, 48, 0, 15, -4, 0, 42, 0, 0, 14, 12, 0, 3, 36, 0, 35, -35, 0, -10, 23, 0, 0, 11, 0, -1, 8, 0, 6, 0, 0, -36, 39, 0, 20, -4, 0, 28, -24, 0, -9, -32, 0, 0, 12, 0, 42, 18, 0, -16, 0, 0, 2, -26, 0, 3, 36, 0, 43, 6, 0, -24, 22, 0, 0, 6, 0, 9, -16, 0, -21, 0, 0, 24, 16, 0, 11, 36, 0, -27, -17, 0, 7, 22, 0, 0, 27, 0, 12, 18, 0, -13, 0, 0, -6, 12, 0, -32, 90, 0, -2, 33, 0, -40, -26, 0, 0, 9, 0, 10, 3, 0, 4, 0, 0, 4, 6, 0, 48, -1, 0, -12, -46, 0, 24, 4, 0, 0, -14, 0, 1, -8, 0, 11, 0, 0, -27, -12, 0, 18, 0, 0, -17, 6, 0, -6, 8, 0, 0, -4, 0, -10, 11, 0, -18, 0, 0, 24, 14, 0, 15, 8, 0, -24, -16, 0, 60, -10, 0, 0, -4, 0, -34, 38, 0, -3, 0, 0, -1, 9, 0, -44, -44, 0, -9, 2, 0, -12, -37, 0, 0, 57, 0, -8, -52, 0, 5, 0, 0, 23, -12, 0, -24, 15, 0, -13, -5, 0, 46, 12, 0, 0, -10, 0, -18, -6, 0, 28, 0, 0, -12, -7, 0, 57, -40, 0, 26, 8, 0, 2, 10, 0, 0, -7, 0, 11, 30, 0, -16, 0, 0, -72, 18, 0, -14, 12, 0, -7, 16, 0, 4, 10, 0, 0, -24, 0, 16, -45, 0, -24, 0, 0, 32, -7, 0, -6, 25, 0, -12, 3, 0, 66, -14, 0, 0, 3, 0, -32, 14, 0, -6, 0, 0, -8, 22, 0, -6, 18, 0, 17, -9, 0, 56, 24, 0, 0, 4, 0, -13, -6, 0, 10, 0, 0, 26, 9, 0, -5, 39, 0, -22, -15, 0, 42, -7, 0, 0, -6, 0, 54, 13, 0, 4, 0, 0, -4, 25, 0, 20, -2, 0, 16, 36, 0, 40, 24, 0, 0, 56, 0, -9, 33, 0, -4, 0, 0, -64, 13, 0, 12, -4, 0, -36, -8, 0, -1, 20, 0, 0, -10, 0, 30, -18, 0, 96, 0, 0, 12, 21, 0, 8, 24, 0, 32, 18, 0, -63, -3, 0, 0, -18, 0, -15, 30, 0, -2, 0, 0, 4, -1, 0, 28, -31, 0, 44, -10, 0, -24, 14, 0, 0, -18, 0, -15, 60, 0, -44, 0, 0, 27, 24, 0, -56, -36, 0, 6, -4, 0, -27, -9, 0, 0, -32, 0, -17, 1, 0, 22, 0, 0, -9, 60, 0, 2, -25, 0, -36, 0, 0, 4, 12, 0, 0, -5, 0, -19, 24, 0, 28, 0, 0, -24, -70, 0, -30, -17, 0, -24, 14, 0, -15, 40, 0, 0, -56, 0, 42, 4, 0, 18, 0, 0, 22, -3, 0, -6, 46, 0, -8, 63, 0, -34, -38, 0, 0, -19, 0, -60, 12, 0, -8, 0, 0, 12, -3, 0, 41, 26, 0, 18, -11, 0, 32, 4, 0, 0, 39, 0, -8, 32, 0, -42, 0, 0, -78, -7, 0, -30, 4, 0, -10, -28, 0, -10, 60, 0, 0, -69, 0, 22, 24, 0, -4, 0, 0, 1, -42, 0, 32, -6, 0, 30, -8, 0, -33, -22, 0, 0, -67, 0, -3, 20, 0, -66, 0, 0, 49, 6, 0, 27, 8, 0, 16, -16, 0, -6, 72, 0, 0, 12, 0, -35, 57, 0, 20, 0, 0, -26, -40, 0, 6, -8, 0, 9, 18, 0, 4, 33, 0, 0, 5, 0, -36, 1, 0, -15, 0, 0, 31, -6, 0, 8, 48, 0, -10, -18, 0, 63, -23, 0, 0, -12, 0, -13, 31, 0, 57, 0, 0, 3, -16, 0, -16, 51, 0, -8, -21, 0, 32, 16, 0, 0, 8, 0, -52, -4, 0, -4, 0, 0, -13, -4, 0, -37, 54, 0, -32, -28, 0, -21, 1, 0, 0, -34, 0, 6, 22, 0, -12, 0, 0, -12, 2, 0, 33, -4, 0, 4, -13, 0, -24, -9, 0, 0, -9, 0, -16, -28, 0, -20, 0, 0, 66, 48, 0, -10, -72, 0, -6, 2, 0, 4, 24, 0, 0, -4, 0, -18, -52, 0, 10, 0, 0, -3, 18, 0, 0, -22, 0, 6, 15, 0, 88, 5, 0, 0, -28, 0, -11, 0, 0, -39, 0, 0, -29, -2, 0, 6, -10, 0, 9, 12, 0, -48, 23, 0, 0, -45, 0, -4, -22, 0, 40, 0, 0, -20, 9, 0, -12, 28, 0, -45, -16, 0, -12, 4, 0, 0, -22, 0, 5, 60, 0, -32, 0, 0, -8, 12, 0, -21, 24, 0, 56, 4, 0, 7, -42, 0, 0, -30, 0, -12, 48, 0, 22, 0, 0, 12, -42, 0, -4, -2, 0, 30, -65, 0, -9, -18, 0, 0, 6, 0, 19, -6, 0, -21, 0, 0, -60, 16, 0, -5, 65, 0, 12, 36, 0, -18, 22, 0, 0, -40, 0, 13, 6, 0, -114, 0, 0, 48, -18, 0, -26, 15, 0, 4, 30, 0, -8, -18, 0, 0, -4, 0, -11, 14, 0, 36, 0, 0, 7, -3, 0, 36, -16, 0, 103, 35, 0, 35, 10, 0, 0, -30, 0, 23, 24, 0, -40, 0, 0, -55, 13, 0, 28, 1, 0, 8, -114, 0, 6, 6, 0, 0, 36, 0, -8, -12, 0, 39, 0, 0, -2, 20, 0, -12, -10, 0, 49, -28, 0, -24, 60, 0, 0, -9, 0, 32, 26, 0, 16, 0, 0, 12, 8, 0, -66, 42, 0, 6, 35, 0, 23, 16, 0, 0, 13, 0, 16, 2, 0, 26, 0, 0, -70, -15, 0, 36, -48, 0, -33, 43, 0, 18, -80, 0, 0, 24, 0, 22, 15, 0, -72, 0, 0, -6, -132, 0, -35, 27, 0, -16, -14, 0, -13, -21, 0, 0, 63, 0, 12, -24, 0, 16, 0, 0, -47, 11, 0, -36, -3, 0, -36, -9, 0, -17, 20, 0, 0, 7, 0, 66, 16, 0, -12, 0, 0, 27, -6, 0, 4, 12, 0, -18, -2, 0, -50, -39, 0, 0, 37, 0, -42, -6, 0, 4, 0, 0, -24, 32, 0, 90, 0, 0, -27, -2, 0, -33, 6, 0, 0, -56, 0, -26, -69, 0, -82, 0, 0, 27, -4, 0, -23, -10, 0, 3, 29, 0, 48, 4, 0, 0, 45, 0, -32, 12, 0, 6, 0, 0, -48, 48, 0, 5, 38, 0, -20, 12, 0, -46, -4, 0, 0, 24, 0, -4, -36, 0, 27, 0, 0, -14, 30, 0, 16, 1, 0, -24, 59, 0, 22, -11, 0, 0, 8, 0, -9, -27, 0, 12, 0, 0, 48, 54, 0, 0, 33, 0, 44, -17, 0, 2, -24, 0, 0, 6, 0, 8, -56, 0, -12, 0, 0, 4, -66, 0, -32, 50, 0, 11, 4, 0, -52, -18, 0, 0, 22, 0, -60, -24, 0, 14, 0, 0, 63, 15, 0, -8, 7, 0, -4, -72, 0, -16, 39, 0, 0, 60, 0, -14, 32, 0, -25, 0, 0, -4, 51, 0, -40, -34, 0, -38, -18, 0, 52, -1, 0, 0, -6, 0, 30, -1, 0, 27, 0, 0, -36, 44, 0, -44, -12, 0, 72, -9, 0, -2, -16, 0, 0, -36, 0, -37, 52, 0, -67, 0, 0, 19, 48, 0, 6, 8, 0, -52, -79, 0, -120, 5, 0, 0, 5, 0, -24, 45, 0, -12, 0, 0, 0, -24, 0, 45, 2, 0, -120, 13, 0, -5, 48, 0, 0, 46, 0, -12, 6, 0, -24, 0, 0, -10, -4, 0, -14, -18, 0, 30, -18, 0, 69, -28, 0, 0, 2, 0, 7, -12, 0, 7, 0, 0, 3, 19, 0, -40, 35, 0, -3, 26, 0, 24, -35, 0, 0, -2, 0, 10, -48, 0, 58, 0, 0, 7, -32, 0, -126, 33, 0, 30, 0, 0, -1, -16, 0, 0, 54, 0, -46, 72, 0, 18, 0, 0, -38, -14, 0, -12, -42, 0, 85, 35, 0, 16, 36, 0, 0, 4, 0, 30, 71, 0, 28, 0, 0, -24, 19, 0, 83, 16, 0, 45, -32, 0, -45, -72, 0, 0, 84, 0, 132, 32, 0, 3, 0, 0, 66, 6, 0, 25, -2, 0, -16, -12, 0, -3, 12, 0, 0, 22, 0, -14, -26, 0, 60, 0, 0, 9, -30, 0, -44, 32, 0, 14, 54, 0, -31, -6, 0, 0, 3, 0, -24, -24, 0, 22, 0, 0, 22, -6, 0, 6, 6, 0, 19, -17, 0, -9, 24, 0, 0, 56, 0, -24, 2, 0, -2, 0, 0, 4, -42, 0, 24, -13, 0, -18, -54, 0, 74, -10, 0, 0, 36, 0, -20, 26, 0, -9, 0, 0, -8, -15, 0, 39, 6, 0, -7, -22, 0, 75, 3, 0, 0, -42, 0, -7, -44, 0, -73, 0, 0, 6, 18, 0, 52, 18, 0, 13, 32, 0, 38, 4, 0, 0, -57, 0, -8, 4, 0, 25, 0, 0, -32, 20, 0, 2, -8, 0, -44, 48, 0, 36, 33, 0, 0, 40, 0, 8, -30, 0, -8, 0, 0, 56, -126, 0, 22, -9, 0, -33, 21, 0, 10, 20, 0, 0, -59, 0, 13, -64, 0, 39, 0, 0, -53, -12, 0, -4, 49, 0, -102, -36, 0, 8, -54, 0, 0, -3, 0, 20, 6, 0, -12, 0, 0, -14, 52, 0, 40, -30, 0, -18, 4, 0, -26, 96, 0, 0, -60, 0, -52, 4, 0, 21, 0, 0, 55, 8, 0, 72, -21, 0, 11, -32, 0, 18, 87, 0, 0, -63, 0, 3, -12, 0, 32, 0, 0, -18, 21, 0, -76, -15, 0, 10, 74, 0, -12, 2, 0, 0, -26, 0, -6, 4, 0, 1, 0, 0, 18, -12, 0, -31, -4, 0, 6, 44, 0, -30, -48, 0, 0, 24, 0, 14, -12, 0, 8, 0, 0, 18, 27, 0, 24, -45, 0, 60, -60, 0, -48, -44, 0, 0, 8, 0, 32, -27, 0, 24, 0, 0, -38, -56, 0, 36, 33, 0, -14, 2, 0, -4, 6, 0, 0, -27, 0, -27, -76, 0, 44, 0, 0, -32, 38, 0, 66, -17, 0, -1, -120, 0, 40, 66, 0, 0, 24, 0, 0, -9, 0, 20, 0, 0, -44, -2, 0, -25, -39, 0, -71, -36, 0, 0, 2, 0, 0, -20, 0, 12, -12, 0, 4, 0, 0, -15, 4, 0, -50, 19, 0, 24, 90, 0, -8, 28, 0, 0, -58, 0, 30, -72, 0, -70, 0, 0, 74, -30, 0, -11, 90, 0, 27, 24, 0, 14, 10, 0, 0, -15, 0, -40, 8, 0, -13, 0, 0, -56, -33, 0, -48, 42, 0, 12, 12, 0, -24, -18, 0, 0, -36, 0, 34, 22, 0, 3, 0, 0, -36, -18, 0, 46, -88, 0, 28, -8, 0, 21, -94, 0, 0, 34, 0, -38, -7, 0, 38, 0, 0, 19, -24, 0, 40, -84, 0, 12, -30, 0, -24, -8, 0, 0, 82, 0, 2, -12, 0, -3, 0, 0, -24, 41, 0, -26, -7, 0, -32, 54, 0, -11, 54, 0, 0, 32, 0, -20, 75, 0, 88, 0, 0, 39, 96, 0, -72, -8, 0, -32, 20, 0, -34, -14, 0, 0, 12, 0, -62, -78, 0, -21, 0, 0, 81, 30, 0, 4, -102, 0, -55, -10, 0, 28, -71, 0, 0, -30, 0, 60, -57, 0, -8, 0, 0, -23, -45, 0, 13, -22, 0, 24, 56, 0, 94, -4, 0, 0, -72, 0, -78, -5, 0, -42, 0, 0, -6, 32, 0, -18, -70, 0, -18, -30, 0, -8, 3, 0, 0, -33, 0, 22, 68, 0, 60, 0, 0, -67, -84, 0, 62, -3, 0, 28, -27, 0, -32, 66, 0, 0, -12, 0, 27, 49, 0, -6, 0, 0, 67, 9, 0, 8, 21, 0, -4, 16, 0, -48, -7, 0, 0, 6, 0, 72, 8, 0, 17, 0, 0, -12, 84, 0, -20, -105, 0, 57, 24, 0, -30, 20, 0, 0, -82, 0, 35, 26, 0, -40, 0, 0, 68, 6, 0, 8, 48, 0, 10, 51, 0, 18, -57, 0, 0, 4, 0, 99, 9, 0, 45, 0, 0, 5, -16, 0, -26, -36, 0, -1, 35, 0, -14, -45, 0, 0, 54, 0, 42, 31, 0, 30, 0, 0, 52, -8, 0, 48, -6, 0, 32, -10, 0, 18, -70, 0, 0, 21, 0, -23, -40, 0, -40, 0, 0, -36, -23, 0, -4, 13, 0, 31, 49, 0, 28, 57, 0, 0, -2, 0, 88, 9, 0, -16, 0, 0, 24, -16, 0, 17, -86, 0, -54, 8, 0, -21, -54, 0, 0, 32, 0, -16, -30, 0, -180, 0, 0, 8, 33, 0, -16, -52, 0, -12, 76, 0, 8, 4, 0, 0, 98, 0, -16, -13, 0, 4, 0, 0, 12, -111, 0, 54, 19, 0, 9, -32, 0, 12, -8, 0, 0, 21, 0, 1, -132, 0, -68, 0, 0, 34, 39, 0, 30, 2, 0, 22, 20, 0, 30, -12, 0, 0, -48, 0, 88, 12, 0, 2, 0, 0, 78, 33, 0, 4, -72, 0, -80, 12, 0, -13, 104, 0, 0, -24, 0, -3, -48, 0, 32, 0, 0, -9, 9, 0]}