# Stored data for newform 7569.2.a.r, downloaded from the LMFDB on 05 May 2024.
{"label": "7569.2.a.r", "space_label": "7569.2.a", "level": 7569, "weight": 2, "hecke_orbit": 18, "hecke_orbit_code": 76561193698860433, "dim": 3, "is_polredabs": true, "nf_label": "3.3.49.1", "trace_hash": 917536337839734506, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [1, -2, -1, 1]], [5, [-1, -4, -3, 1]], [7, [1, -4, 3, 1]], [19, [-13, -4, 3, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+\\beta _{2}q^{4}+(2-2\\beta _{1}+\\beta _{2})q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 30276, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 60.43876928990712, "hecke_ring_index": 1, "level_radical": 87, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 14, "field_poly_is_real_cyclotomic": true, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [7569, 1, [5888, 1684], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [3, 29], "conrey_indexes": [1], "field_disc": 49, "field_disc_factorization": [[7, 2]], "field_poly": [1, -2, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.922", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "22.898", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "268.325", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [29, 1]], "trace_display": [1, 0, 3, -3], "traces": [0, 3, 1, 0, -1, 3, 0, -3, 0, 0, -6, -5, 0, 1, -8, 0, -5, -4, 0, -3, -1, 0, -11, 7, 0, 2, 5, 0, -6, 0, 0, -15, -4, 0, -6, 4, 0, -5, 6, 0, 14, -10, 0, 3, 4, 0, 0, 19, 0, -4, -25, 0, 16, 9, 0, 16, 7, 0, 0, 28, 0, -9, -12, 0, 4, 8, 0, 13, 6, 0, -1, 21, 0, 5, -11, 0, 8, 12, 0, -15, -12, 0, 6, 9, 0, 10, 8, 0, 21, -7, 0, -22, 7, 0, 11, -10, 0, 11, 22, 0, -3, 11, 0, -23, 7, 0, 10, -3, 0, 13, -11, 0, 19, 11, 0, 21, 0, 0, 14, 4, 0, 8, -10, 0, 5, 36, 0, 25, -7, 0, -9, -21, 0, -11, -19, 0, 14, 13, 0, -7, 1, 0, 21, 17, 0, 0, -24, 0, 4, -3, 0, -29, -7, 0, 18, -1, 0, -12, 9, 0, -11, -14, 0, 1, 8, 0, 10, 1, 0, 22, -6, 0, 13, 22, 0, 26, -8, 0, 14, 3, 0, 17, -40, 0, 14, 16, 0, 30, -4, 0, 13, 30, 0, 35, 34, 0, 27, 15, 0, -27, 49, 0, 34, 0, 0, -24, -3, 0, -46, -2, 0, -47, -3, 0, -1, 3, 0, 22, -12, 0, -10, 22, 0, -1, 25, 0, -22, 25, 0, 1, -28, 0, 0, -12, 0, 12, -14, 0, 6, 55, 0, 37, 5, 0, -4, -25, 0, 20, 14, 0, -23, -29, 0, 14, -1, 0, 13, -45, 0, 12, -12, 0, 14, -41, 0, -5, -13, 0, -2, -31, 0, -5, -12, 0, -5, 69, 0, 33, -28, 0, 7, 35, 0, -11, 0, 0, -20, -4, 0, -27, 0, 0, -25, -19, 0, 14, 21, 0, -36, 42, 0, -24, 16, 0, -9, -2, 0, 42, 17, 0, 16, -37, 0, 31, 38, 0, 12, -11, 0, 0, 39, 0, -35, 4, 0, 17, 5, 0, -14, -26, 0, 48, 18, 0, -44, 62, 0, -1, 47, 0, -8, 46, 0, -24, 0, 0, -44, 2, 0, -30, 25, 0, -12, -13, 0, 0, -7, 0, 8, -15, 0, -40, -20, 0, -23, 33, 0, -93, -42, 0, -11, -16, 0, -1, 10, 0, -7, 0, 0, 5, 1, 0, 38, 41, 0, 5, 28, 0, 22, -42, 0, 14, -21, 0, 40, -36, 0, -15, 12, 0, -22, -11, 0, 2, 29, 0, 0, 41, 0, 53, 34, 0, 24, -28, 0, 16, -62, 0, 4, 73, 0, -47, 3, 0, -14, 44, 0, 23, 36, 0, -6, 57, 0, -43, 47, 0, -16, 0, 0, -33, 28, 0, -2, 35, 0, -49, 65, 0, 10, -61, 0, -2, -34, 0, 48, 13, 0, 1, 26, 0, -14, -7, 0, -36, 0, 0, 24, 57, 0, 8, -31, 0, -14, 2, 0, -30, 8, 0, 2, -5, 0, 17, 31, 0, -26, -24, 0, 19, 7, 0, 29, -25, 0, 0, 30, 0, 18, -42, 0, 45, -19, 0, -26, -1, 0, -17, -35, 0, 8, -1, 0, 44, 65, 0, -8, -16, 0, -41, 18, 0, 14, -24, 0, -20, 21, 0, 12, 34, 0, -20, -4, 0, -8, 6, 0, 32, 49, 0, -1, -12, 0, 7, -46, 0, -18, 34, 0, 83, 40, 0, -5, 0, 0, -6, -3, 0, 21, -47, 0, 50, -16, 0, 77, -42, 0, 32, -6, 0, -21, 59, 0, 49, -71, 0, 8, 49, 0, -37, -9, 0, 0, -37, 0, -36, 28, 0, -88, 65, 0, 8, -42, 0, -8, -21, 0, 4, 22, 0, 35, -37, 0, -85, -43, 0, 19, -20, 0, 61, -17, 0, 11, 11, 0, 57, 0, 0, -7, -73, 0, 9, -2, 0, 11, 0, 0, 89, 64, 0, 60, 30, 0, 7, -21, 0, -34, 60, 0, 78, 0, 0, -21, -57, 0, 25, -21, 0, 6, 25, 0, -70, -55, 0, -26, -21, 0, -49, 12, 0, -60, 5, 0, -41, -12, 0, 7, -4, 0, 0, -26, 0, -75, 22, 0, 35, -33, 0, -12, 73, 0, -67, 14, 0, 55, -51, 0, 76, -8, 0, -40, -4, 0, 39, -40, 0, 24, 63, 0, 4, -10, 0, 24, -17, 0, -2, 47, 0, -2, -74, 0, 67, -21, 0, -42, -21, 0, 3, 13, 0, -19, 89, 0, 2, -18, 0, -36, 0, 0, 115, 35, 0, -38, 10, 0, 69, -38, 0, -49, 53, 0, -5, -10, 0, -31, 31, 0, 88, 44, 0, -38, -32, 0, -51, -34, 0, 0, -71, 0, -19, 18, 0, -35, -25, 0, 15, 4, 0, -54, -14, 0, -3, -17, 0, -28, -37, 0, 39, -35, 0, 42, 24, 0, -63, -14, 0, -47, -40, 0, 1, -19, 0, 51, 45, 0, -24, 37, 0, 2, 47, 0, -30, -19, 0, -20, 22, 0, 21, -39, 0, -28, -33, 0, 62, 0, 0, 16, -34, 0, 18, -8, 0, 8, -33, 0, -45, 7, 0, -70, 43, 0, -30, -25, 0, 27, 10, 0, 64, -25, 0, -13, 125, 0, 0, -32, 0, 32, -62, 0, 13, -8, 0, -4, 14, 0, -22, 45, 0, 35, -25, 0, -25, -8, 0, 68, -47, 0, 92, 2, 0, 37, -3, 0, 37, 21, 0, 35, 6, 0, 21, -18, 0, -29, 63, 0, -65, -54, 0, 7, -18, 0, -32, 56, 0, 40, -12, 0, 3, -49, 0, -4, 0, 0, -26, 32, 0, 21, 38, 0, 47, 1, 0, 9, 24, 0, 6, -16, 0, 44, -14, 0, -17, 63, 0, 56, 21, 0, 69, -68, 0, 0, 20, 0, 53, -10, 0, 12, 2, 0, -41, -16, 0, -4, 9, 0, -28, -28, 0, -25, 37, 0, -66, 25, 0, 0, -35, 0, -12, -44, 0, -88, -48, 0, -4, -20, 0, 4, -14, 0, -3, -28, 0, 13, 43, 0, 14, -38, 0, 29, -93, 0, -56, -1, 0, 78, -67, 0, -69, 0, 0, -9, 35, 0, 23, 13, 0, -84, -76, 0, 37, -6, 0, 63, 74, 0, -56, -44, 0, -12, -2, 0, -11, 6, 0, -42, 35, 0, 0, 35, 0, 65, 51, 0, 45, 59, 0, -16, -58, 0, 9, 22, 0, 39, 49, 0, 25, -72, 0, 17, 12, 0, -49, 3, 0, -36, 17, 0, -37, 54, 0, -28, 13, 0, 15, 51, 0, 30, -68, 0, -6, -23, 0, 4, -6, 0, 19, 7, 0, 16, -58, 0, -55, -29, 0, -52, 0, 0, -5, 50, 0, -11, 80, 0, 42, -70, 0, -24, -13, 0, -73, 32, 0, -47, -63, 0, -95, 16, 0, 63, 9, 0, -86, -37, 0, 0, 8, 0, -6, 12, 0, -18, 5, 0, -44, 70, 0, -4, -92, 0, 15, 61, 0, -17, -28, 0, 7, 14, 0, -84, 21, 0, 15, -43, 0, 6, 57, 0, -45, -42, 0, -41, 34, 0, 20, -21, 0, -14, -6, 0, 46, 6, 0, -105, 47, 0, -1, 4, 0, -19, -56, 0, -5, 0, 0, -73, -45, 0, -82, -33, 0, 36, 69, 0, 47, -38, 0, 38, -13, 0, 75, -23, 0, 0, -101, 0, -57, -12, 0, -63, -131, 0, 0, -8, 0, 91, 21, 0, 62, 0, 0, -66, 4, 0, 102, -33, 0, -27, 16, 0, -42, -42, 0, 12, 62, 0, 39, -52, 0, -18, -64, 0, 7, 3, 0, 48, 89, 0, -89, -16, 0, 0, -39, 0, -61, -69, 0, -15, -29, 0, 27, -102, 0, -35, -2, 0, -2, -32, 0, 21, 0, 0, 75, -10, 0, -1, -24, 0, -50, -28, 0, 10, -10, 0, 76, 70, 0, 18, 56, 0, 39, -15, 0, -85, 36, 0, -34, 117, 0, 0, -22, 0, -53, -50, 0, -96, 39, 0, -52, 62, 0, 35, -49, 0, -99, -20, 0, -15, 5, 0, 51, -98, 0, -85, 85, 0, -27, -35, 0, 28, 91, 0, -2, 70, 0, 4, 104, 0, -55, -45, 0, -31, -27, 0, -75, -30, 0, -2, -43, 0, -1, -71, 0, 15, -12, 0, -15, 0, 0, 63, -72, 0, 53, -30, 0, 40, 6, 0, -10, 42, 0, -30, 0, 0, -35, -84, 0, -20, 58, 0, 42, -111, 0, -12, -3, 0, 0, -34, 0, -31, -13, 0, -70, -89, 0, 1, 3, 0, 31, -53, 0, 29, -36, 0, 31, 62, 0, 70, 54, 0, -54, 60, 0, -56, 139, 0, 13, 20, 0, -60, 19, 0, -9, 0, 0, 118, -28, 0, -70, 4, 0, 7, 98, 0, 16, 37, 0, -125, -4, 0, -26, 69, 0, 0, 0, 0, -117, 56, 0, -28, -17, 0, -73, -20, 0, 0, 102, 0, -18, 40, 0, 88, -21, 0, 0, 24, 0, 11, -55, 0, 147, 21, 0, 0, 20, 0, -3, 36, 0, 95, -102, 0, -33, -4, 0, -6, 23, 0, 100, -19, 0, 24, -92, 0, -25, 49, 0, -50, -28, 0, 12, 10, 0, 28, -57, 0, 53, -25, 0, 43, 23, 0, -19, -85, 0, 82, -57, 0, 14, -28, 0, -62, 27, 0, 36, 4, 0, -30, 11, 0, 95, 0, 0, 100, -21, 0, -42, 38, 0, 73, -2, 0, -1, 40, 0, -20, -39, 0, 22, 5, 0, -42, 126, 0, -23, -65, 0, 42, 84, 0, 0, 20, 0, -11, 84, 0, -107, -49, 0, -10, 34, 0, 34, 97, 0, -65, 31, 0, -128, 70, 0, -20, 31, 0, -104, -84, 0, -28, -67, 0, -80, -74, 0, 52, -75, 0, -93, 12, 0, -84, 19, 0, -9, 12, 0, 57, 32, 0, 31, -50, 0, 26, -74, 0, 2, -49, 0, 18, 0, 0, -91, -38, 0, 124, 7, 0, -71, -71, 0, 5, 12, 0, -133, -7, 0, -108, 67, 0, -24, -86, 0, 10, -155, 0, -69, 2, 0, 0, 19, 0, -55, -37, 0, 33, -2, 0, 42, 27, 0, 8, -33, 0, 152, -84, 0, -25, -59, 0, 23, -43, 0, -6, -24, 0, 83, -56, 0, 110, 118, 0, 27, -80, 0, -17, -10, 0, 145, 105, 0, 8, 105, 0, -41, -65, 0, -35, -13, 0, 179, -50, 0, 16, -7, 0, -71, 0, 0, 11, 34, 0, -72, -21, 0, 40, 14, 0, -111, 23, 0, -5, -19, 0, 108, -38, 0, -35, 28, 0, -52, 30, 0, 32, -89, 0, 0, -100, 0, 1, -31, 0, -10, -55, 0, 7, -27, 0, 74, -12, 0, 24, 6, 0, -41, -114, 0, -23, -113, 0, 16, -35, 0, 48, -41, 0, -4, -18, 0, -3, -100, 0, 59, 7, 0, -47, 54, 0, 53, 56, 0, 18, 99, 0, -61, -19, 0, 35, 4, 0, 15, -45, 0, -28, 0, 0, 63, 28, 0, -48, -63, 0, -57, -90, 0, 28, 191, 0, 117, -91, 0, 38, -15, 0, 47, -6, 0, -90, -67, 0, 48, 11, 0, 0, 31, 0, 1, -18, 0, -18, -33, 0, 98, 47, 0, -55, 5, 0, -12, 25, 0, -70, -42, 0, 74, 5, 0, 64, 119, 0, 113, -54, 0, -40, -154, 0, -13, -7, 0, 7, -86, 0, 80, -29, 0, -49, -22, 0, 45, 56, 0, 84, 71, 0, -84, -5, 0, -30, -8, 0, 5, 0, 0, 58, -165, 0, -53, 20, 0, -70, -8, 0, -25, 16, 0, -32, -93, 0, -42, -37, 0, -5, 17, 0, 121, 70, 0, -53, -18, 0, 0, 42, 0, -14, 15, 0, 52, -52, 0, 80, 47, 0, 75, -113, 0, -18, -93, 0, 52, -30, 0, -98, 81, 0, 70, -18, 0, 7, -10, 0, 125, -59, 0, -114, 52, 0, -24, 57, 0, -71, -27, 0, -54, -21, 0, -21, 64, 0, -23, -106, 0, 59, 118, 0, -12, 1, 0, 26, 0, 0, -98, 7, 0, -39, 55, 0, 77, 33, 0, -17, 28, 0, 44, 35, 0, -84, -36, 0, 2, 55, 0, -6, -126, 0, 2, 54, 0, 0, -56, 0, -87, -49, 0, 42, 81, 0, 11, 66, 0, 15, -78, 0, -167, -63, 0, 103, -12, 0, 103, -53, 0, 55, 83, 0, -43, -74, 0, 111, -23, 0, -53, -56, 0, -21, 60, 0, 73, 12, 0, 11, -26, 0, -151, 50, 0, -6, 26, 0, 55, 42, 0, 70, -27, 0, -138, 0, 0, -100, 38, 0, 13, 54, 0, 150, 45, 0, 178, 8, 0, 39, 130, 0, -77, -133, 0, 102, 145, 0, -77, 24, 0, -7, -62, 0, 0, -4, 0, 105, -37, 0, 28, 55, 0, 23, -71, 0, -41, -7, 0, 18, 20, 0, -16, 42, 0, 15, 69, 0, 19, -34, 0, 1, 10, 0, 52, 39, 0, 2, -77, 0, 122, 14, 0, 44, 41, 0, -106, -30, 0, -14, -19, 0, 73, -44, 0, 115, 77, 0, 109, 33, 0, 23, 0, 0, -107, 7, 0, -128, -140, 0, 8, 46, 0, 44, -164, 0, 3, -30, 0, -66, -12, 0, 19, 54, 0, -34, 133, 0, -55, -50, 0, 0, -67, 0, -42, -53, 0, 21, -35, 0, -34, -87, 0, 92, 18, 0, 21, 21, 0, -56, -113, 0, -158, 63, 0, -9, -58, 0, -16, 48, 0, 28, 58, 0, -97, -9, 0, -119, -70, 0, -63, 29, 0, -30, -32, 0, -94, -164, 0, -4, -12, 0, -64, -122, 0, 42, -126, 0, 74, 0, 0, -2, 3, 0, -16, -16, 0, 9, 107, 0, 84, 21, 0, 46, 60, 0, 62, -73, 0, -70, -147, 0, 14, 39, 0, 93, 42, 0, 0, 12, 0, 2, 77, 0, -77, 24, 0, 42, 151, 0, -103, -105, 0, -105, -72, 0, 1, 42, 0, 119, -86, 0, 22, 82, 0, 1, 10, 0, 3, 7, 0, 68, 13, 0, 95, 20, 0, -42, -57, 0, 123, -64, 0, -26, 9, 0, -85, 44, 0, -42, -6, 0, -35, 142, 0, 5, 0, 0, 75, 55, 0, -14, 103, 0, -29, -70, 0, -45, -2, 0, -70, -54, 0, 80, 107, 0, -19, -28, 0, -7, 34, 0, -34, -25, 0, 0, 55, 0, 63, -46, 0, 90, 50, 0, 90, 94, 0, 26, 19, 0, 106, 61, 0, 93, 39, 0, 5, 123, 0, 119, 43, 0, 3, 4, 0, -149, 61, 0, -90, -24, 0, -47, 73, 0, 64, 98, 0, -15, 98, 0, 2, -89, 0, 47, -14, 0, -83, -70, 0, -74, -78, 0, -84, 0, 0, -6, 63, 0, 89, -93, 0, -126, -67, 0, 137, -117, 0, -28, 105, 0, 107, -18, 0, -36, -7, 0, 59, 20, 0, 12, 3, 0, 0, 35, 0, -53, 119, 0, -18, -42, 0, 46, -135, 0, -84, 23, 0, 58, 15, 0, -128, 146, 0, -109, -86, 0, -102, 63, 0, -12, 75, 0, -74, 28, 0, -21, 207, 0, 100, 113, 0, 116, 71, 0, 54, 24, 0, -54, -115, 0, -151, 42, 0, -153, 9, 0, 98, 31, 0, -86, 0, 0, -13, -6, 0, 9, -22, 0, -75, -12, 0, -122, -6, 0, 53, 25, 0, -10, 38, 0, 21, -10, 0, -91, 56, 0, 64, 7, 0, 0, 157, 0, -142, -80, 0, -25, 16, 0, -31, -98, 0, -43, 28, 0, -70, 79, 0, -106, -6, 0, 34, -38, 0, -176, 10, 0, -45, 156, 0, -14, -107, 0, 47, 6, 0, -70, -73, 0, 116, 41, 0, 42, 14, 0, -39, -34, 0, -2, -37, 0, -78, 54, 0, -5, 57, 0, 98, 0, 0, 2, 9, 0, 61, 50, 0, 79, -86, 0, -92, -2, 0, 34, 6, 0, 107, 97, 0, 85, -38, 0, 1, 70, 0, -21, 79, 0, 0, 72, 0, -28, 85, 0, -58, 50, 0, -17, -37, 0, -78, 59, 0, 70, 9, 0, -14, 42, 0, 82, 22, 0, -10, -100, 0, 80, -102, 0, -125, 63, 0, 70, -146, 0, -85, -24, 0, 14, -115, 0, -30, -46, 0, 177, -63, 0, -94, 96, 0, 49, -117, 0, -36, -60, 0, -2, 0, 0, 0, -11, 0, -19, 29, 0, -15, 70, 0, -47, -85, 0, -96, 58, 0, -89, -57, 0, -21, 6, 0, 115, -1, 0, -50, -54, 0, 0, 44, 0, -79, 31, 0, -136, 103, 0, -41, 20, 0, 182, 78, 0, 13, 9, 0, 30, 33, 0, 41, 41, 0, 21, -131, 0, -89, 35, 0, 42, 87, 0, 22, -77, 0, 17, 98, 0, -163, -92, 0, -53, 29, 0, -49, 14, 0, -78, -108, 0, -77, -4, 0, -78, -70, 0, 88, 0, 0, -98, 29, 0, 59, 24, 0, -30, 104, 0, 28, -21, 0, -58, 187, 0, 31, -7, 0, -76, -90, 0, -3, -125, 0, 11, 193, 0, 0, 76, 0, -47, -7, 0, -10, -97, 0, -55, -27, 0, 44, 10, 0, -87, -62, 0, 182, -11, 0, 14, 5, 0, -48, -42, 0, 100, -56, 0, -47, 65, 0, -20, 7, 0, 81, -70, 0, -108, -20, 0, 75, -66, 0, -125, 36, 0, -13, 71, 0, -35, 102, 0, -118, 35, 0, -25, 0, 0, 126, -101, 0, 14, -77, 0, 145, -18, 0, 28, 96, 0, 68, -85, 0, 15, -11, 0, 15, -46, 0, 22, 51, 0, 36, 42, 0, 0, -152, 0, 136, 10, 0, 63, -20, 0, 97, -56, 0, -64, 98, 0, 53, 55, 0, 34, -11, 0, -53, -40, 0, 48, -64, 0, 64, 22, 0, 63, -118, 0, 133, 17, 0, -91, -223, 0, 20, 63, 0, 25, -2, 0, 55, 7, 0, 82, -42, 0, 66, 70, 0, 37, 121, 0, 93, 0, 0, 142, 35, 0, 26, -8, 0, -71, -33, 0, -42, 118, 0, -97, 20, 0, 26, 171, 0, 105, 126, 0, -3, -36, 0, 52, 19, 0, 0, -81, 0, -72, -10, 0, 58, 7, 0, -124, 177, 0, 8, 85, 0, 35, 15, 0, 68, -41, 0, -196, 6, 0, -43, 74, 0, -87, 190, 0, 103, -29, 0, -138, 121, 0, 14, 48, 0, 21, -65, 0, 83, 48, 0, 115, -2, 0, 152, -46, 0, -55, 90, 0, 110, -7, 0, 44, 0, 0, -37, -56, 0, 34, -68, 0, 40, -29, 0, 9, 46, 0], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "29.2.d.a", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0], [1, 0, 0], [0, 1, 0], [0, 0, 0], [0, 0, 1], [2, -2, 1], [0, 0, 0], [-1, -1, -1], [1, -2, 1], [0, 0, 0], [-3, 2, -1], [0, -3, 2], [0, 0, 0], [2, -1, 4], [-3, -1, -2], [0, 0, 0], [-3, 1, -3], [0, -2, 2], [0, 0, 0], [-1, 1, 1], [-1, 1, -1], [0, 0, 0], [-4, 0, -1], [4, -2, 3], [0, 0, 0], [4, -7, 3], [2, 2, 3], [0, 0, 0], [-2, -1, -1], [0, 0, 0], [0, 0, 0], [-4, -2, 1], [-3, 1, -4], [0, 0, 0], [-2, 0, 0], [2, -1, 1], [0, 0, 0], [0, -3, 2], [3, -1, 2], [0, 0, 0], [7, -5, 2], [-4, 2, 0], [0, 0, 0], [2, 0, 3], [-1, 2, -5], [0, 0, 0], [-1, 4, 1], [6, 1, 0], [0, 0, 0], [-1, 3, 4], [-11, 4, -4], [0, 0, 0], [3, 4, -3], [2, 2, -1], [0, 0, 0], [7, -4, 1], [3, 0, 2], [0, 0, 0], [0, 0, 0], [8, 2, -2], [0, 0, 0], [-3, -1, -1], [-3, -4, -1], [0, 0, 0], [4, -5, 3], [3, -2, -1], [0, 0, 0], [8, -7, 4], [0, 2, -4], [0, 0, 0], [-1, 2, 0], [6, 3, 0], [0, 0, 0], [2, -4, -3], [-4, 0, -1], [0, 0, 0], [2, 1, -1], [5, 1, 4], [0, 0, 0], [-6, 3, 0], [-6, 5, -1], [0, 0, 0], [4, -4, 2], [5, -1, 5], [0, 0, 0], [4, -2, 0], [3, 2, 3], [0, 0, 0], [7, -1, -1], [-6, 6, -5], [0, 0, 0], [-7, -5, -4], [1, 3, -1], [0, 0, 0], [2, 6, 1], [-6, 5, -3], [0, 0, 0], [3, 5, 3], [10, -1, 7], [0, 0, 0], [-4, 3, -6]]}