# Stored data for newform 1350.2.a.j, downloaded from the LMFDB on 07 November 2025.
{"Nk2": 5400, "analytic_conductor": 10.779804272872852, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, 1], [3, -1], [5, -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": [1350, 1, [1001, 1027], [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": [[7, [-4, 1]], [11, [5, 1]], [13, [3, 1]], [17, [1, 1]]], "hecke_orbit": 10, "hecke_orbit_code": 40532396679890246, "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": "1350.2.a.j", "level": 1350, "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, 5], "level_radical": 30, "minimal_twist": "270.2.c.a", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q-q^{2}+q^{4}+4q^{7}-q^{8}-5q^{11}-3q^{13}+\\cdots", "related_objects": ["EllipticCurve/Q/1350/j"], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1350.2.a", "trace_display": [-1, 0, 0, 4], "trace_hash": 1883703960698287780, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.003", "prec": 17}, {"__RealLiteral__": 0, "data": "0.019", "prec": 17}, {"__RealLiteral__": 0, "data": "1.997", "prec": 17}, {"__RealLiteral__": 0, "data": "0.118", "prec": 17}, {"__RealLiteral__": 0, "data": "4.953", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.013", "prec": 17}, "traces": [0, 1, -1, 0, 1, 0, 0, 4, -1, 0, 0, -5, 0, -3, -4, 0, 1, -1, 0, -6, 0, 0, 5, -1, 0, 0, 3, 0, 4, -9, 0, -5, -1, 0, 1, 0, 0, -2, 6, 0, 0, -2, 0, 1, -5, 0, 1, 13, 0, 9, 0, 0, -3, 0, 0, 0, -4, 0, 9, -4, 0, 8, 5, 0, 1, 0, 0, -4, -1, 0, 0, -6, 0, -2, 2, 0, -6, -20, 0, 9, 0, 0, 2, -4, 0, 0, -1, 0, 5, -14, 0, -12, -1, 0, -13, 0, 0, -10, -9, 0, 0, 17, 0, -10, 3, 0, 0, -6, 0, -8, 0, 0, 4, 3, 0, 0, -9, 0, 4, -4, 0, 14, -8, 0, -5, 0, 0, 4, -1, 0, 0, -3, 0, -24, 4, 0, 1, 18, 0, -8, 0, 0, 6, 15, 0, 0, 2, 0, -2, -13, 0, 13, 6, 0, 20, 0, 0, -13, -9, 0, 0, -4, 0, -19, -2, 0, 4, -12, 0, -4, 0, 0, 1, 16, 0, 0, -5, 0, 14, 20, 0, -22, 12, 0, 1, 0, 0, 5, 13, 0, 0, -6, 0, 4, 10, 0, 9, 22, 0, 3, 0, 0, -17, -36, 0, 0, 10, 0, -3, 30, 0, 0, 0, 0, 6, 0, 0, -20, 8, 0, 0, 3, 0, 22, -4, 0, -3, 2, 0, 2, 0, 0, 9, -14, 0, 0, -4, 0, 4, 16, 0, -23, -14, 0, 8, 0, 0, 18, 5, 0, 0, 15, 0, 5, -4, 0, 1, -21, 0, -8, 0, 0, 3, 8, 0, 0, 24, 0, -4, 9, 0, 16, -1, 0, -18, 0, 0, -26, 8, 0, 0, -18, 0, 20, -6, 0, -15, -8, 0, -16, 0, 0, -2, 6, 0, 0, 2, 0, 13, 3, 0, 4, -13, 0, -6, 0, 0, 21, -20, 0, 0, 18, 0, -14, 13, 0, 9, -4, 0, 45, 0, 0, 4, 6, 0, 0, 19, 0, 2, 52, 0, 10, -4, 0, 12, 0, 0, 16, 4, 0, 0, 25, 0, 8, -1, 0, -16, 6, 0, 16, 0, 0, 5, -11, 0, 0, -14, 0, -20, 6, 0, 17, 22, 0, -12, 0, 0, 22, -1, 0, 0, 0, 0, -21, -5, 0, -13, 27, 0, -28, 0, 0, 6, 19, 0, 0, -4, 0, -10, -5, 0, 1, -9, 0, -22, 0, 0, 13, -3, 0, 0, -16, 0, 15, 17, 0, 36, 10, 0, 11, 0, 0, -10, -16, 0, 0, 3, 0, -30, -23, 0, -26, 0, 0, 0, 0, 0, 32, -6, 0, 0, -8, 0, 22, 20, 0, -8, 6, 0, 0, 0, 0, -3, 30, 0, 0, -22, 0, 4, 0, 0, 10, 3, 0, -2, 0, 0, 16, -2, 0, 0, -6, 0, -6, -9, 0, 14, -6, 0, -16, 0, 0, 4, -5, 0, 0, -4, 0, -16, -2, 0, 6, 23, 0, 14, 0, 0, -12, -8, 0, 0, 24, 0, 9, -18, 0, -5, -24, 0, -12, 0, 0, -15, -9, 0, 0, -5, 0, 4, -21, 0, -8, -1, 0, 21, 0, 0, -65, 8, 0, 0, -22, 0, 23, -3, 0, -8, 5, 0, -22, 0, 0, -24, 6, 0, 0, 4, 0, -9, -45, 0, 10, -16, 0, 1, 0, 0, 25, 18, 0, 0, 54, 0, 36, 26, 0, -8, -42, 0, -3, 0, 0, 18, 4, 0, 0, -20, 0, 6, -20, 0, -32, 15, 0, 8, 0, 0, -32, 16, 0, 0, -16, 0, 0, 2, 0, -6, -36, 0, 30, 0, 0, -2, -21, 0, 0, -13, 0, -3, -42, 0, -19, -4, 0, 13, 0, 0, -10, 6, 0, 0, -39, 0, -23, -21, 0, 20, 29, 0, 26, 0, 0, -18, -56, 0, 0, 14, 0, -13, 2, 0, -4, -9, 0, 4, 0, 0, -27, -45, 0, 0, -20, 0, 21, -4, 0, -6, 0, 0, 20, 0, 0, -19, 26, 0, 0, -2, 0, -52, 20, 0, 44, -10, 0, 4, 0, 0, 9, -12, 0, 0, -40, 0, 48, -16, 0, -4, -4, 0, -40, 0, 0, -25, 44, 0, 0, -8, 0, 1, 0, 0, 22, 16, 0, -6, 0, 0, 2, -16, 0, 0, 31, 0, 12, -5, 0, 11, 68, 0, -24, 0, 0, 14, 5, 0, 0, 20, 0, -6, -20, 0, -40, -17, 0, -22, 0, 0, 0, 12, 0, 0, -1, 0, -46, -22, 0, 1, 20, 0, 10, 0, 0, 0, 9, 0, 0, 21, 0, 5, -24, 0, -7, 13, 0, -27, 0, 0, 43, 28, 0, 0, 12, 0, -32, -6, 0, -19, 12, 0, 3, 0, 0, 4, 18, 0, 0, 10, 0, 5, 12, 0, 30, -1, 0, 9, 0, 0, 13, 22, 0, 0, 12, 0, -24, -13, 0, 3, 14, 0, -13, 0, 0, 16, 10, 0, 0, -15, 0, -17, 12, 0, -26, -36, 0, -10, 0, 0, -6, -11, 0, 0, -46, 0, 24, 10, 0, 16, -22, 0, 0, 0, 0, -3, -9, 0, 0, 30, 0, 23, -34, 0, 52, 26, 0, 0, 0, 0, 56, 0, 0, 0, 2, 0, -19, -32, 0, 6, 6, 0, 2, 0, 0, 8, -39, 0, 0, -22, 0, -20, -45, 0, 12, 8, 0, -6, 0, 0, -1, 0, 0, 0, -18, 0, 36, 3, 0, -30, -51, 0, 16, 0, 0, 22, -78, 0, 0, -4, 0, 0, 45, 0, 0, -10, 0, -3, 0, 0, -3, 2, 0, 0, -36, 0, 20, -16, 0, 2, -12, 0, 33, 0, 0, 6, 18, 0, 0, 6, 0, 9, -6, 0, -54, -14, 0, 6, 0, 0, -40, 16, 0, 0, 31, 0, 2, -4, 0, 5, -48, 0, 6, 0, 0, 4, 61, 0, 0, 16, 0, 2, 72, 0, -6, -6, 0, -23, 0, 0, 2, -14, 0, 0, -9, 0, -32, 12, 0, 8, 39, 0, 70, 0, 0, -24, -29, 0, 0, -9, 0, 18, -1, 0, -17, 5, 0, 24, 0, 0, 15, 12, 0, 0, 60, 0, 4, 15, 0, 9, 0, 0, -19, 0, 0, 5, -6, 0, 0, -4, 0, 21, -27, 0, 48, 8, 0, 1, 0, 0, -27, -21, 0, 0, -62, 0, 56, 65, 0, -8, -8, 0, -41, 0, 0, 22, -52, 0, 0, -23, 0, 3, -12, 0, 62, 8, 0, -5, 0, 0, 52, 22, 0, 0, 6, 0, -2, 24, 0, -6, 50, 0, -28, 0, 0, -4, 18, 0, 0, 9, 0, 45, 12, 0, -13, -10, 0, 16, 0, 0, 4, -1, 0, 0, -4, 0, -13, -25, 0, -18, -57, 0, -52, 0, 0, -54, 16, 0, 0, -36, 0, -26, 54, 0, -85, 8, 0, 42, 0, 0, -59, 3, 0, 0, 24, 0, -19, -18, 0, -4, -9, 0, 14, 0, 0, 20, 50, 0, 0, -6, 0, 20, 4, 0, -76, 32, 0, -15, 0, 0, 10, -8, 0, 0, 38, 0, 6, 32, 0, -16, 42, 0, -48, 0, 0, 16, 20, 0, 0, 0, 0, -2, -48, 0, 52, 6, 0, 36, 0, 0, 30, -30, 0, 0, 45, 0, -16, 2, 0, 21, 60, 0, 18, 0, 0, 13, 30, 0, 0, 3, 0, 42, 40, 0, -54, 19, 0, 4, 0, 0, 6, -13, 0, 0, 64, 0, -51, 10, 0, -6, -42, 0, 0, 0, 0, 39, 16, 0, 0, 23, 0, 21, 57, 0, 48, -20, 0, -29, 0, 0, -18, -26, 0, 0, 2, 0, -15, 18, 0, 56, -9, 0, 22, 0, 0, -14, 80, 0, 0, 13, 0, -2, 1, 0, 30, 4, 0, 9, 0, 0, -88, -4, 0, 0, 10, 0, 24, 27, 0, 45, 6, 0, 15, 0, 0, 20, -46, 0, 0, -21, 0, 4, -16, 0, 28, 6, 0, 0, 0, 0, 20, -20, 0, 0, 9, 0, -58, 19, 0, -26, 18, 0, 20, 0, 0, 2, -51, 0, 0, 52, 0, -20, 26, 0, 19, -44, 0, 10, 0, 0, 26, -4, 0, 0, -15, 0, -5, -9, 0, 12, -24, 0, 30, 0, 0, 40, -9, 0, 0, -48, 0, 16, 36, 0, 16, 4, 0, 4, 0, 0, 4, 40, 0, 0, 50, 0, -117, 25, 0, -44, 37, 0, -33, 0, 0, 8, -64, 0, 0, -1, 0, 0, 88, 0, -36, -22, 0, -16, 0, 0, 12, 6, 0, 0, 18, 0, 12, -2, 0, 16, -20, 0, -41, 0, 0, -31, -8, 0, 0, -12, 0, 5, -18, 0, 4, -11, 0, -68, 0, 0, 24, 24, 0, 0, -81, 0, -10, -14, 0, -5, -48, 0, -12, 0, 0, -20, -49, 0, 0, 6, 0, 20, 38, 0, 15, 40, 0, 17, 0, 0, -46, 22, 0, 0, -53, 0, -46, 0, 0, -12, -65, 0, 64, 0, 0, 1, 120, 0, 0, 46, 0, 22, -9, 0, 5, -1, 0, -20, 0, 0, 0, -10, 0, 0, -6, 0, -20, 0, 0, -9, 8, 0, -45, 0, 0, -21, -50, 0, 0, -5, 0, 24, -36, 0, -54, 7, 0, -13, 0, 0, -90, 27, 0, 0, 54, 0, 14, -43, 0, -28, 4, 0, -45, 0, 0, -12, 30, 0, 0, 32, 0, 6, 40, 0, 8, 19, 0, -12, 0, 0, 0, -3, 0, 0, 4, 0, 70, -4, 0, -18, 12, 0, 46, 0, 0, -10, -34, 0, 0, -5, 0, -12, -6, 0, 88, -30, 0, 1, 0, 0, -18, -9, 0, 0, -63, 0, -42, -13, 0, -22, 24, 0, 62, 0, 0, -12, -73, 0, 0, 24, 0, 13, 8, 0, -2, -3, 0, -14, 0, 0, -57, 13, 0, 0, 64, 0, 8, -16, 0, -10, -8, 0, 10, 0, 0, 15, -14, 0, 0, 17, 0, -12, -45, 0, -68, 26, 0, 36, 0, 0, 59, 10, 0, 0, -56, 0, 6, 6, 0, 11, 52, 0, 65, 0, 0, 46, 0, 0, 0, -24, 0, -10, 10, 0, -12, -16, 0, 22, 0, 0, 8, 0, 0, 0, -65, 0, 36, 3, 0, 9, 14, 0, -56, 0, 0, -30, 64, 0, 0, -23, 0, 34, 2, 0, -37, -52, 0, -26, 0, 0, -92, 0, 0, 0, 84, 0, -55, -56, 0, 0, -3, 0, 32, 0, 0, -2, 9, 0, 0, 19, 0, 32, 18, 0, 36, -6, 0, -6, 0, 0, -17, -2, 0, 0, -68, 0, 61, -8, 0, 39, 65, 0, 72, 0, 0, 22, 6, 0, 0, 20, 0, 45, -26, 0, 20, -12, 0, -8, 0, 0, -49, 6, 0, 0, 10, 0, 44, 1, 0, 0, 60, 0, -29, 0, 0, 18, -2, 0, 0, -36, 0, -3, -72, 0, 20, 30, 0, 51, 0, 0, 40, -16, 0, 0, -54, 0, -52, -22, 0, 78, -44, 0, -40, 0, 0, 4, 95, 0, 0, 0, 0, -45, -84, 0, -7, 0, 0, 10, 0, 0, 24, 3, 0, 0, -15, 0, -18, 3, 0, -2, -9, 0, 6, 0, 0, 36, -51, 0, 0, -20, 0, 16, 20, 0, -1, -2, 0, 12, 0, 0, 60, -33, 0, 0, 32, 0, 60, -6, 0, -18, 43, 0, -42, 0, 0, -6, 8, 0, 0, -9, 0, 6, 20, 0, -44, 54, 0, 14, 0, 0, 29, -6, 0, 0, -80, 0, 6, 40, 0, -16, -44, 0, -37, 0, 0, -31, 36, 0, 0, -2, 0, 4, -2, 0, -40, -5, 0, 48, 0, 0, 64, -6, 0, 0, -23, 0, -80, -4, 0, -61, -54, 0, 4, 0, 0, -16, -27, 0, 0, -2, 0, -72, -102, 0, -3, 6, 0, 6, 0, 0, -26, 23, 0, 0, 24, 0, 46, -2, 0, 14, 39, 0, -104, 0, 0, 9, 36, 0, 0, 32, 0, -12, 42, 0, -48, -8, 0, -39, 0, 0, 60, -70, 0, 0, 0, 0, -39, 24, 0, 29, -72, 0, -100, 0, 0, 9, -60, 0, 0, -18, 0, 1, -17, 0, 80, 17, 0, -5, 0, 0, 72, -24, 0, 0, 110, 0, 68, -15, 0, -12, 0, 0, -25, 0, 0, -60, -78, 0, 0, -4, 0, -15, -18, 0, -52, -9, 0, 0, 0, 0, 70, 19, 0, 0, 13, 0, -64, -5, 0, 6, -80, 0, -22, 0, 0, 4, 36, 0, 0, -21, 0, 27, -76, 0, 39, -48, 0, -8, 0, 0, 14, -1, 0, 0, 24, 0, 39, 27, 0, 21, -14, 0, 54, 0, 0, 62, 51, 0, 0, -56, 0, -65, -42, 0, 48, 8, 0, 8, 0, 0, 20, 41, 0, 0, -36, 0, -39, -22, 0, 52, -37, 0, 47, 0, 0, 23, 12, 0, 0, -3, 0, 12, -43, 0, 30, -62, 0, -8, 0, 0, 9, 5, 0, 0, 44, 0, -50, -52, 0, -22, 18, 0, 57, 0, 0, -6, -20, 0, 0, 2, 0, -24, -66, 0, 38, 6, 0, -50, 0, 0, -4, 28, 0, 0, -57, 0, 40, 4, 0, -18, -18, 0, 84, 0, 0, -9, -69, 0, 0, -45, 0, -12, -4, 0, 29, 13, 0, 10, 0, 0, -110, -16, 0, 0, 36, 0, 0, -4, 0, 1, 72, 0, -24, 0, 0, 4, 8, 0, 0, 13, 0, 25, -15, 0, -56, 18, 0, 57, 0, 0, 51, 52, 0, 0, 30, 0, 36, 54, 0, -16, 59, 0, 122, 0, 0, 36, -22, 0, 0, 26, 0, -54, -16, 0, -44, 85, 0, -8, 0, 0, 3, -42, 0, 0, 10, 0, 180, 59, 0, -3, -22, 0, -19, 0, 0, -24, -14, 0, 0, 19, 0, 18, -48, 0, 66, 4, 0, 9, 0, 0, -16, -14, 0, 0, 24, 0, 10, -20, 0, -50, -42, 0, 10, 0, 0, 6, 30, 0, 0, -20, 0, -4, 0, 0, 31, 76, 0, -32, 0, 0, -74, 15, 0, 0, -81, 0, -21, -10, 0, 8, 67, 0, -84, 0, 0, -38, 117, 0, 0, -6, 0, -32, 70, 0, -61, 16, 0, -42, 0, 0, 40, 48, 0, 0, 0, 0, -17, -16, 0, -20, -60, 0, -18, 0, 0, 0, 20, 0, 0, 2, 0, 48, 33, 0, 30, -52, 0, -6, 0, 0, -76, -36, 0, 0, -4, 0, 66, -30, 0, 30, 12, 0, 64, 0, 0, -45, 8, 0, 0, 16, 0, -2, 10, 0, -70, -21, 0, -60, 0, 0, 54, -18, 0, 0, -45, 0, 42, -13, 0, -30, 100, 0, 38, 0, 0, -3, -3, 0, 0, -42, 0, -40, 48, 0, -31, 54, 0, -19, 0, 0, 36, -4, 0, 0, -27, 0, -24, -6, 0, 13, -55, 0, 8, 0, 0, -64, -13, 0, 0, 51, 0, -10, 24, 0, -15, 6, 0, 42, 0, 0, -62, 0, 0, 0, 60, 0, 64, -39, 0, -16, 24, 0, -45, 0, 0, -23, -110, 0, 0, -21, 0, -57, -35, 0, 6, -48, 0, 20, 0, 0, -63, 29, 0, 0, -44, 0, -2, 18, 0, 26, 66, 0, 8, 0, 0, -2, 18, 0, 0, 15, 0, -18, 18, 0, 0, -56, 0, 9, 0, 0, -10, -22, 0, 0, -16, 0, -54, 14, 0, -80, 8, 0, -12, 0, 0, -13, 24, 0, 0, 2, 0, -1, -10, 0, -45, -30, 0, -4, 0, 0, 68, -9, 0, 0, 17, 0, 13, 88, 0, 4, -4, 0, -70, 0, 0, -10, 53, 0, 0, -24, 0, -27, 6, 0, -12, -45, 0, -6, 0, 0, -45, -15, 0, 0, -66, 0, 70, -20, 0, 46, -13, 0, 88, 0, 0, 21, 20, 0, 0, -4, 0, 16, -35, 0, 126, -28, 0, -6, 0, 0, -9, 0, 0, 0, -82, 0, 90, -20, 0, 20, 0, 0, -3, 0, 0, -9, -108, 0, 0, 58, 0, -19, 84, 0, -84, 26, 0, -18, 0, 0, 68, -20, 0, 0, -33, 0, 8, -2, 0, 51, 12, 0, -80, 0, 0, -52, 25, 0, 0, 20, 0, -26, 108, 0, 48, -19, 0, 44, 0, 0, -100, -10, 0, 0, 115, 0, -112, -26, 0, 4, -47, 0, -30, 0, 0, 15, -63, 0, 0, 5, 0, 9, 13, 0, 48, -12, 0, 24, 0, 0, 38, -30, 0, 0, 76, 0, -39, -40, 0, 9, 5, 0, 53, 0, 0, 48, 60, 0, 0, -16, 0, -36, 60, 0, 4, -16, 0, -4, 0, 0, -43, -4, 0, 0, -10, 0, -14, -4, 0, -40, -90, 0, 80, 0, 0, -50, -20, 0, 0, 117, 0, -25, -10, 0, -40, 44, 0, -37, 0, 0, 4, 33, 0, 0, 9, 0, 0, -8, 0, 64, 8, 0, -8, 0, 0, 1, -7, 0, 0, 0, 0, -88, 70, 0, -75, 36, 0, 22, 0, 0, 8, 16, 0, 0, 19, 0, -52, -12, 0, -6, -63, 0, 52, 0, 0, -18, -14, 0, 0, -12, 0, 2, -54, 0, 44, -16, 0, 20, 0, 0, 39, 41, 0, 0, -42, 0, -76, 31, 0, 8, -64, 0, -53, 0, 0, 12, 90, 0, 0, -5, 0, 18, 39, 0, 60, -4, 0, 11, 0, 0, 105, 68, 0, 0, 78, 0, 86, -24, 0, -24, -90, 0, 12, 0, 0, 81, 6, 0, 0, 10, 0, 14, 40, 0, 76, 5, 0, 48, 0, 0, 46, 12, 0, 0, 94, 0, 44, 20, 0, 49, 104, 0, -78, 0, 0, -6, 4, 0, 0, -20, 0, -38, 88, 0, -4, -15, 0, -40, 0, 0, -6, -17, 0, 0, -36, 0, -40, 46, 0, -22, 74, 0, -66, 0, 0, 53, -81, 0, 0, 46, 0, 0, 39, 0, 12, 12, 0, 65, 0, 0, -46, -64, 0, 0, -4, 0, -18, -1, 0, -120, 47, 0, -153, 0, 0, -46, -92, 0, 0, -22, 0, 9, -45, 0, -16, -5, 0, 1, 0, 0, -104, 20, 0, 0, -6, 0, -34, 0, 0, 10, 42, 0, -45, 0, 0, 6, 22, 0, 0, 20, 0, 0, 74, 0, -90, 9, 0, -8, 0, 0, -6, 45, 0, 0, -80, 0, 78, 21, 0, 50, 90, 0, 72, 0, 0, 5, 4, 0, 0, -24, 0, 36, 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, 0, 0, 4, -1, 0, 0, -5, 0, -3, -4, 0, 1, -1, 0, -6, 0, 0, 5, -1, 0, 0, 3, 0, 4, -9, 0, -5, -1, 0, 1, 0, 0, -2, 6, 0, 0, -2, 0, 1, -5, 0, 1, 13, 0, 9, 0, 0, -3, 0, 0, 0, -4, 0, 9, -4, 0, 8, 5, 0, 1, 0, 0, -4, -1, 0, 0, -6, 0, -2, 2, 0, -6, -20, 0, 9, 0, 0, 2, -4, 0, 0, -1, 0, 5, -14, 0, -12, -1, 0, -13, 0, 0, -10, -9, 0, 0, 17, 0, -10, 3, 0, 0, -6, 0, -8, 0, 0, 4, 3, 0, 0, -9, 0, 4, -4, 0, 14, -8, 0, -5, 0, 0, 4, -1, 0, 0, -3, 0, -24, 4, 0, 1, 18, 0, -8, 0, 0, 6, 15, 0, 0, 2, 0, -2, -13, 0, 13, 6, 0, 20, 0, 0, -13, -9, 0, 0, -4, 0, -19, -2, 0, 4, -12, 0, -4, 0, 0, 1, 16, 0, 0, -5, 0, 14, 20, 0, -22, 12, 0, 1, 0, 0, 5, 13, 0, 0, -6, 0, 4, 10, 0, 9, 22, 0, 3, 0, 0, -17, -36, 0, 0, 10, 0, -3, 30, 0, 0, 0, 0, 6, 0, 0, -20, 8, 0, 0, 3, 0, 22, -4, 0, -3, 2, 0, 2, 0, 0, 9, -14, 0, 0, -4, 0, 4, 16, 0, -23, -14, 0, 8, 0, 0, 18, 5, 0, 0, 15, 0, 5, -4, 0, 1, -21, 0, -8, 0, 0, 3, 8, 0, 0, 24, 0, -4, 9, 0, 16, -1, 0, -18, 0, 0, -26, 8, 0, 0, -18, 0, 20, -6, 0, -15, -8, 0, -16, 0, 0, -2, 6, 0, 0, 2, 0, 13, 3, 0, 4, -13, 0, -6, 0, 0, 21, -20, 0, 0, 18, 0, -14, 13, 0, 9, -4, 0, 45, 0, 0, 4, 6, 0, 0, 19, 0, 2, 52, 0, 10, -4, 0, 12, 0, 0, 16, 4, 0, 0, 25, 0, 8, -1, 0, -16, 6, 0, 16, 0, 0, 5, -11, 0, 0, -14, 0, -20, 6, 0, 17, 22, 0, -12, 0, 0, 22, -1, 0, 0, 0, 0, -21, -5, 0, -13, 27, 0, -28, 0, 0, 6, 19, 0, 0, -4, 0, -10, -5, 0, 1, -9, 0, -22, 0, 0, 13, -3, 0, 0, -16, 0, 15, 17, 0, 36, 10, 0, 11, 0, 0, -10, -16, 0, 0, 3, 0, -30, -23, 0, -26, 0, 0, 0, 0, 0, 32, -6, 0, 0, -8, 0, 22, 20, 0, -8, 6, 0, 0, 0, 0, -3, 30, 0, 0, -22, 0, 4, 0, 0, 10, 3, 0, -2, 0, 0, 16, -2, 0, 0, -6, 0, -6, -9, 0, 14, -6, 0, -16, 0, 0, 4, -5, 0, 0, -4, 0, -16, -2, 0, 6, 23, 0, 14, 0, 0, -12, -8, 0, 0, 24, 0, 9, -18, 0, -5, -24, 0, -12, 0, 0, -15, -9, 0, 0, -5, 0, 4, -21, 0, -8, -1, 0, 21, 0, 0, -65, 8, 0, 0, -22, 0, 23, -3, 0, -8, 5, 0, -22, 0, 0, -24, 6, 0, 0, 4, 0, -9, -45, 0, 10, -16, 0, 1, 0, 0, 25, 18, 0, 0, 54, 0, 36, 26, 0, -8, -42, 0, -3, 0, 0, 18, 4, 0, 0, -20, 0, 6, -20, 0, -32, 15, 0, 8, 0, 0, -32, 16, 0, 0, -16, 0, 0, 2, 0, -6, -36, 0, 30, 0, 0, -2, -21, 0, 0, -13, 0, -3, -42, 0, -19, -4, 0, 13, 0, 0, -10, 6, 0, 0, -39, 0, -23, -21, 0, 20, 29, 0, 26, 0, 0, -18, -56, 0, 0, 14, 0, -13, 2, 0, -4, -9, 0, 4, 0, 0, -27, -45, 0, 0, -20, 0, 21, -4, 0, -6, 0, 0, 20, 0, 0, -19, 26, 0, 0, -2, 0, -52, 20, 0, 44, -10, 0, 4, 0, 0, 9, -12, 0, 0, -40, 0, 48, -16, 0, -4, -4, 0, -40, 0, 0, -25, 44, 0, 0, -8, 0, 1, 0, 0, 22, 16, 0, -6, 0, 0, 2, -16, 0, 0, 31, 0, 12, -5, 0, 11, 68, 0, -24, 0, 0, 14, 5, 0, 0, 20, 0, -6, -20, 0, -40, -17, 0, -22, 0, 0, 0, 12, 0, 0, -1, 0, -46, -22, 0, 1, 20, 0, 10, 0, 0, 0, 9, 0, 0, 21, 0, 5, -24, 0, -7, 13, 0, -27, 0, 0, 43, 28, 0, 0, 12, 0, -32, -6, 0, -19, 12, 0, 3, 0, 0, 4, 18, 0, 0, 10, 0, 5, 12, 0, 30, -1, 0, 9, 0, 0, 13, 22, 0, 0, 12, 0, -24, -13, 0, 3, 14, 0, -13, 0, 0, 16, 10, 0, 0, -15, 0, -17, 12, 0, -26, -36, 0, -10, 0, 0, -6, -11, 0, 0, -46, 0, 24, 10, 0, 16, -22, 0, 0, 0, 0, -3, -9, 0, 0, 30, 0, 23, -34, 0, 52, 26, 0, 0, 0, 0, 56, 0, 0, 0, 2, 0, -19, -32, 0, 6, 6, 0, 2, 0, 0, 8, -39, 0, 0, -22, 0, -20, -45, 0, 12, 8, 0, -6, 0, 0, -1, 0, 0, 0, -18, 0, 36, 3, 0, -30, -51, 0, 16, 0, 0, 22, -78, 0, 0, -4, 0, 0, 45, 0, 0, -10, 0, -3, 0, 0, -3, 2, 0, 0, -36, 0, 20, -16, 0, 2, -12, 0, 33, 0, 0, 6, 18, 0, 0, 6, 0, 9, -6, 0, -54, -14, 0, 6, 0, 0, -40, 16, 0, 0, 31, 0, 2, -4, 0, 5, -48, 0, 6, 0, 0, 4, 61, 0, 0, 16, 0, 2, 72, 0, -6, -6, 0, -23, 0, 0, 2, -14, 0, 0, -9, 0, -32, 12, 0, 8, 39, 0, 70, 0, 0, -24, -29, 0, 0, -9, 0, 18, -1, 0, -17, 5, 0, 24, 0, 0, 15, 12, 0, 0, 60, 0, 4, 15, 0, 9, 0, 0, -19, 0, 0, 5, -6, 0, 0, -4, 0, 21, -27, 0, 48, 8, 0, 1, 0, 0, -27, -21, 0, 0, -62, 0, 56, 65, 0, -8, -8, 0, -41, 0, 0, 22, -52, 0, 0, -23, 0, 3, -12, 0, 62, 8, 0, -5, 0, 0, 52, 22, 0, 0, 6, 0, -2, 24, 0, -6, 50, 0, -28, 0, 0, -4, 18, 0, 0, 9, 0, 45, 12, 0, -13, -10, 0, 16, 0, 0, 4, -1, 0, 0, -4, 0, -13, -25, 0, -18, -57, 0, -52, 0, 0, -54, 16, 0, 0, -36, 0, -26, 54, 0, -85, 8, 0, 42, 0, 0, -59, 3, 0, 0, 24, 0, -19, -18, 0, -4, -9, 0, 14, 0, 0, 20, 50, 0, 0, -6, 0, 20, 4, 0, -76, 32, 0, -15, 0, 0, 10, -8, 0, 0, 38, 0, 6, 32, 0, -16, 42, 0, -48, 0, 0, 16, 20, 0, 0, 0, 0, -2, -48, 0, 52, 6, 0, 36, 0, 0, 30, -30, 0, 0, 45, 0, -16, 2, 0, 21, 60, 0, 18, 0, 0, 13, 30, 0, 0, 3, 0, 42, 40, 0, -54, 19, 0, 4, 0, 0, 6, -13, 0, 0, 64, 0, -51, 10, 0, -6, -42, 0, 0, 0, 0, 39, 16, 0, 0, 23, 0, 21, 57, 0, 48, -20, 0, -29, 0, 0, -18, -26, 0, 0, 2, 0, -15, 18, 0, 56, -9, 0, 22, 0, 0, -14, 80, 0, 0, 13, 0, -2, 1, 0, 30, 4, 0, 9, 0, 0, -88, -4, 0, 0, 10, 0, 24, 27, 0, 45, 6, 0, 15, 0, 0, 20, -46, 0, 0, -21, 0, 4, -16, 0, 28, 6, 0, 0, 0, 0, 20, -20, 0, 0, 9, 0, -58, 19, 0, -26, 18, 0, 20, 0, 0, 2, -51, 0, 0, 52, 0, -20, 26, 0, 19, -44, 0, 10, 0, 0, 26, -4, 0, 0, -15, 0, -5, -9, 0, 12, -24, 0, 30, 0, 0, 40, -9, 0, 0, -48, 0, 16, 36, 0, 16, 4, 0, 4, 0, 0, 4, 40, 0, 0, 50, 0, -117, 25, 0, -44, 37, 0, -33, 0, 0, 8, -64, 0, 0, -1, 0, 0, 88, 0, -36, -22, 0, -16, 0, 0, 12, 6, 0, 0, 18, 0, 12, -2, 0, 16, -20, 0, -41, 0, 0, -31, -8, 0, 0, -12, 0, 5, -18, 0, 4, -11, 0, -68, 0, 0, 24, 24, 0, 0, -81, 0, -10, -14, 0, -5, -48, 0, -12, 0, 0, -20, -49, 0, 0, 6, 0, 20, 38, 0, 15, 40, 0, 17, 0, 0, -46, 22, 0, 0, -53, 0, -46, 0, 0, -12, -65, 0, 64, 0, 0, 1, 120, 0, 0, 46, 0, 22, -9, 0, 5, -1, 0, -20, 0, 0, 0, -10, 0, 0, -6, 0, -20, 0, 0, -9, 8, 0, -45, 0, 0, -21, -50, 0, 0, -5, 0, 24, -36, 0, -54, 7, 0, -13, 0, 0, -90, 27, 0, 0, 54, 0, 14, -43, 0, -28, 4, 0, -45, 0, 0, -12, 30, 0, 0, 32, 0, 6, 40, 0, 8, 19, 0, -12, 0, 0, 0, -3, 0, 0, 4, 0, 70, -4, 0, -18, 12, 0, 46, 0, 0, -10, -34, 0, 0, -5, 0, -12, -6, 0, 88, -30, 0, 1, 0, 0, -18, -9, 0, 0, -63, 0, -42, -13, 0, -22, 24, 0, 62, 0, 0, -12, -73, 0, 0, 24, 0, 13, 8, 0, -2, -3, 0, -14, 0, 0, -57, 13, 0, 0, 64, 0, 8, -16, 0, -10, -8, 0, 10, 0, 0, 15, -14, 0, 0, 17, 0, -12, -45, 0, -68, 26, 0, 36, 0, 0, 59, 10, 0, 0, -56, 0, 6, 6, 0, 11, 52, 0, 65, 0, 0, 46, 0, 0, 0, -24, 0, -10, 10, 0, -12, -16, 0, 22, 0, 0, 8, 0, 0, 0, -65, 0, 36, 3, 0, 9, 14, 0, -56, 0, 0, -30, 64, 0, 0, -23, 0, 34, 2, 0, -37, -52, 0, -26, 0, 0, -92, 0, 0, 0, 84, 0, -55, -56, 0, 0, -3, 0, 32, 0, 0, -2, 9, 0, 0, 19, 0, 32, 18, 0, 36, -6, 0, -6, 0, 0, -17, -2, 0, 0, -68, 0, 61, -8, 0, 39, 65, 0, 72, 0, 0, 22, 6, 0, 0, 20, 0, 45, -26, 0, 20, -12, 0, -8, 0, 0, -49, 6, 0, 0, 10, 0, 44, 1, 0, 0, 60, 0, -29, 0, 0, 18, -2, 0, 0, -36, 0, -3, -72, 0, 20, 30, 0, 51, 0, 0, 40, -16, 0, 0, -54, 0, -52, -22, 0, 78, -44, 0, -40, 0, 0, 4, 95, 0, 0, 0, 0, -45, -84, 0, -7, 0, 0, 10, 0, 0, 24, 3, 0, 0, -15, 0, -18, 3, 0, -2, -9, 0, 6, 0, 0, 36, -51, 0, 0, -20, 0, 16, 20, 0, -1, -2, 0, 12, 0, 0, 60, -33, 0, 0, 32, 0, 60, -6, 0, -18, 43, 0, -42, 0, 0, -6, 8, 0, 0, -9, 0, 6, 20, 0, -44, 54, 0, 14, 0, 0, 29, -6, 0, 0, -80, 0, 6, 40, 0, -16, -44, 0, -37, 0, 0, -31, 36, 0, 0, -2, 0, 4, -2, 0, -40, -5, 0, 48, 0, 0, 64, -6, 0, 0, -23, 0, -80, -4, 0, -61, -54, 0, 4, 0, 0, -16, -27, 0, 0, -2, 0, -72, -102, 0, -3, 6, 0, 6, 0, 0, -26, 23, 0, 0, 24, 0, 46, -2, 0, 14, 39, 0, -104, 0, 0, 9, 36, 0, 0, 32, 0, -12, 42, 0, -48, -8, 0, -39, 0, 0, 60, -70, 0, 0, 0, 0, -39, 24, 0, 29, -72, 0, -100, 0, 0, 9, -60, 0, 0, -18, 0, 1, -17, 0, 80, 17, 0, -5, 0, 0, 72, -24, 0, 0, 110, 0, 68, -15, 0, -12, 0, 0, -25, 0, 0, -60, -78, 0, 0, -4, 0, -15, -18, 0, -52, -9, 0, 0, 0, 0, 70, 19, 0, 0, 13, 0, -64, -5, 0, 6, -80, 0, -22, 0, 0, 4, 36, 0, 0, -21, 0, 27, -76, 0, 39, -48, 0, -8, 0, 0, 14, -1, 0, 0, 24, 0, 39, 27, 0, 21, -14, 0, 54, 0, 0, 62, 51, 0, 0, -56, 0, -65, -42, 0, 48, 8, 0, 8, 0, 0, 20, 41, 0, 0, -36, 0, -39, -22, 0, 52, -37, 0, 47, 0, 0, 23, 12, 0, 0, -3, 0, 12, -43, 0, 30, -62, 0, -8, 0, 0, 9, 5, 0, 0, 44, 0, -50, -52, 0, -22, 18, 0, 57, 0, 0, -6, -20, 0, 0, 2, 0, -24, -66, 0, 38, 6, 0, -50, 0, 0, -4, 28, 0, 0, -57, 0, 40, 4, 0, -18, -18, 0, 84, 0, 0, -9, -69, 0, 0, -45, 0, -12, -4, 0, 29, 13, 0, 10, 0, 0, -110, -16, 0, 0, 36, 0, 0, -4, 0, 1, 72, 0, -24, 0, 0, 4, 8, 0, 0, 13, 0, 25, -15, 0, -56, 18, 0, 57, 0, 0, 51, 52, 0, 0, 30, 0, 36, 54, 0, -16, 59, 0, 122, 0, 0, 36, -22, 0, 0, 26, 0, -54, -16, 0, -44, 85, 0, -8, 0, 0, 3, -42, 0, 0, 10, 0, 180, 59, 0, -3, -22, 0, -19, 0, 0, -24, -14, 0, 0, 19, 0, 18, -48, 0, 66, 4, 0, 9, 0, 0, -16, -14, 0, 0, 24, 0, 10, -20, 0, -50, -42, 0, 10, 0, 0, 6, 30, 0, 0, -20, 0, -4, 0, 0, 31, 76, 0, -32, 0, 0, -74, 15, 0, 0, -81, 0, -21, -10, 0, 8, 67, 0, -84, 0, 0, -38, 117, 0, 0, -6, 0, -32, 70, 0, -61, 16, 0, -42, 0, 0, 40, 48, 0, 0, 0, 0, -17, -16, 0, -20, -60, 0, -18, 0, 0, 0, 20, 0, 0, 2, 0, 48, 33, 0, 30, -52, 0, -6, 0, 0, -76, -36, 0, 0, -4, 0, 66, -30, 0, 30, 12, 0, 64, 0, 0, -45, 8, 0, 0, 16, 0, -2, 10, 0, -70, -21, 0, -60, 0, 0, 54, -18, 0, 0, -45, 0, 42, -13, 0, -30, 100, 0, 38, 0, 0, -3, -3, 0, 0, -42, 0, -40, 48, 0, -31, 54, 0, -19, 0, 0, 36, -4, 0, 0, -27, 0, -24, -6, 0, 13, -55, 0, 8, 0, 0, -64, -13, 0, 0, 51, 0, -10, 24, 0, -15, 6, 0, 42, 0, 0, -62, 0, 0, 0, 60, 0, 64, -39, 0, -16, 24, 0, -45, 0, 0, -23, -110, 0, 0, -21, 0, -57, -35, 0, 6, -48, 0, 20, 0, 0, -63, 29, 0, 0, -44, 0, -2, 18, 0, 26, 66, 0, 8, 0, 0, -2, 18, 0, 0, 15, 0, -18, 18, 0, 0, -56, 0, 9, 0, 0, -10, -22, 0, 0, -16, 0, -54, 14, 0, -80, 8, 0, -12, 0, 0, -13, 24, 0, 0, 2, 0, -1, -10, 0, -45, -30, 0, -4, 0, 0, 68, -9, 0, 0, 17, 0, 13, 88, 0, 4, -4, 0, -70, 0, 0, -10, 53, 0, 0, -24, 0, -27, 6, 0, -12, -45, 0, -6, 0, 0, -45, -15, 0, 0, -66, 0, 70, -20, 0, 46, -13, 0, 88, 0, 0, 21, 20, 0, 0, -4, 0, 16, -35, 0, 126, -28, 0, -6, 0, 0, -9, 0, 0, 0, -82, 0, 90, -20, 0, 20, 0, 0, -3, 0, 0, -9, -108, 0, 0, 58, 0, -19, 84, 0, -84, 26, 0, -18, 0, 0, 68, -20, 0, 0, -33, 0, 8, -2, 0, 51, 12, 0, -80, 0, 0, -52, 25, 0, 0, 20, 0, -26, 108, 0, 48, -19, 0, 44, 0, 0, -100, -10, 0, 0, 115, 0, -112, -26, 0, 4, -47, 0, -30, 0, 0, 15, -63, 0, 0, 5, 0, 9, 13, 0, 48, -12, 0, 24, 0, 0, 38, -30, 0, 0, 76, 0, -39, -40, 0, 9, 5, 0, 53, 0, 0, 48, 60, 0, 0, -16, 0, -36, 60, 0, 4, -16, 0, -4, 0, 0, -43, -4, 0, 0, -10, 0, -14, -4, 0, -40, -90, 0, 80, 0, 0, -50, -20, 0, 0, 117, 0, -25, -10, 0, -40, 44, 0, -37, 0, 0, 4, 33, 0, 0, 9, 0, 0, -8, 0, 64, 8, 0, -8, 0, 0, 1, -7, 0, 0, 0, 0, -88, 70, 0, -75, 36, 0, 22, 0, 0, 8, 16, 0, 0, 19, 0, -52, -12, 0, -6, -63, 0, 52, 0, 0, -18, -14, 0, 0, -12, 0, 2, -54, 0, 44, -16, 0, 20, 0, 0, 39, 41, 0, 0, -42, 0, -76, 31, 0, 8, -64, 0, -53, 0, 0, 12, 90, 0, 0, -5, 0, 18, 39, 0, 60, -4, 0, 11, 0, 0, 105, 68, 0, 0, 78, 0, 86, -24, 0, -24, -90, 0, 12, 0, 0, 81, 6, 0, 0, 10, 0, 14, 40, 0, 76, 5, 0, 48, 0, 0, 46, 12, 0, 0, 94, 0, 44, 20, 0, 49, 104, 0, -78, 0, 0, -6, 4, 0, 0, -20, 0, -38, 88, 0, -4, -15, 0, -40, 0, 0, -6, -17, 0, 0, -36, 0, -40, 46, 0, -22, 74, 0, -66, 0, 0, 53, -81, 0, 0, 46, 0, 0, 39, 0, 12, 12, 0, 65, 0, 0, -46, -64, 0, 0, -4, 0, -18, -1, 0, -120, 47, 0, -153, 0, 0, -46, -92, 0, 0, -22, 0, 9, -45, 0, -16, -5, 0, 1, 0, 0, -104, 20, 0, 0, -6, 0, -34, 0, 0, 10, 42, 0, -45, 0, 0, 6, 22, 0, 0, 20, 0, 0, 74, 0, -90, 9, 0, -8, 0, 0, -6, 45, 0, 0, -80, 0, 78, 21, 0, 50, 90, 0, 72, 0, 0, 5, 4, 0, 0, -24, 0, 36, 64, 0]}