# Stored data for newform 1421.2.a.f, downloaded from the LMFDB on 24 May 2026.
{"Nk2": 5684, "analytic_conductor": 11.346742127223942, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[7, -1], [29, 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": [1421, 1, [1277, 785], [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, [0, 1]], [3, [-2, 1]], [5, [-3, 1]]], "hecke_orbit": 6, "hecke_orbit_code": 22517998170408333, "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": "1421.2.a.f", "level": 1421, "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": [7, 29], "level_radical": 203, "minimal_twist": "203.2.e.b", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q+2q^{3}-2q^{4}+3q^{5}+q^{9}+6q^{11}+\\cdots", "related_objects": ["EllipticCurve/Q/1421/f"], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1421.2.a", "trace_display": [0, 2, 3, 0], "trace_hash": 1089146049749348678, "trace_moments": [{"__RealLiteral__": 0, "data": "0.007", "prec": 17}, {"__RealLiteral__": 0, "data": "0.971", "prec": 17}, {"__RealLiteral__": 0, "data": "0.035", "prec": 17}, {"__RealLiteral__": 0, "data": "1.897", "prec": 17}, {"__RealLiteral__": 0, "data": "0.100", "prec": 17}, {"__RealLiteral__": 0, "data": "4.678", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.014", "prec": 17}, "traces": [0, 1, 0, 2, -2, 3, 0, 0, 0, 1, 0, 6, -4, 1, 0, 6, 4, 0, 0, -2, -6, 0, 0, 0, 0, 4, 0, -4, 0, -1, 0, -2, 0, 12, 0, 0, -2, -10, 0, 2, 0, 12, 0, 8, -12, 3, 0, -6, 8, 0, 0, 0, -2, 9, 0, 18, 0, -4, 0, 12, -12, -2, 0, 0, -8, 3, 0, -4, 0, 0, 0, 9, 0, -2, 0, 8, 4, 0, 0, -10, 12, -11, 0, 3, 0, 0, 0, -2, 0, 6, 0, 0, 0, -4, 0, -6, 0, -8, 0, 6, -8, 12, 0, -17, 0, 0, 0, 3, 8, -7, 0, -20, 0, -12, 0, 0, 2, 1, 0, 0, 0, 25, 0, 24, 4, -3, 0, -4, 0, 16, 0, -6, -24, 0, 0, -12, 0, 12, 0, 19, 0, -12, 0, 6, 4, -3, 0, 0, 20, 3, 0, -13, 0, 0, 0, -6, -4, 4, 0, 18, 0, 0, 0, -22, -24, 36, 0, 0, 0, -12, 0, -2, -16, -15, 0, 0, 24, 24, 0, 0, -6, -2, 0, -4, 0, -30, 0, 0, 12, 0, 0, 6, -16, -16, 0, 6, 0, 3, 0, 7, 0, -8, 0, 0, 0, 36, 0, 0, 4, -12, 0, -28, -18, 18, 0, 24, 0, 0, 0, -4, -36, 0, 0, -17, 0, 4, 0, -15, 8, 28, 0, 0, 0, -21, 0, -18, -24, -20, 0, 15, 24, -17, 0, -10, 4, 0, 0, -2, 0, 6, 0, 18, 0, 0, 0, 0, 16, 3, 0, 0, -6, -1, 0, 6, 0, 27, 0, 12, 8, 6, 0, -8, 0, 0, 0, 24, 0, -7, 0, -2, 0, -21, 0, 25, -18, -12, 0, 0, 0, -17, 0, -16, 4, -24, 0, 36, 0, -24, 0, 0, -16, 0, 0, 24, -8, -6, 0, 16, 0, -34, 0, 0, 0, 19, 0, 0, 20, -18, 0, -6, -24, 6, 0, 0, 22, 4, 0, -14, 0, 0, 0, 8, -6, -10, 0, -12, 0, 14, 0, -24, 0, -12, 0, 0, 0, 0, 0, -21, 4, -29, 0, -4, 0, 21, 0, 27, -12, 0, 0, -6, 0, -15, 0, 50, 0, -6, 0, -8, 0, 12, 0, 0, 8, -22, 0, -6, 0, -1, 0, -10, 12, -8, 0, 9, 0, 0, 0, 8, 16, -18, 0, 0, 0, -12, 0, -30, -12, -2, 0, 0, 16, 27, 0, -2, -24, -33, 0, -60, 0, -14, 0, 24, 34, 0, 0, 9, 0, 38, 0, -15, 0, -10, 0, -6, 0, 0, 0, 0, -6, 12, 0, 33, -16, 4, 0, -6, 14, 0, 0, 19, 0, 0, 0, 0, 40, 18, 0, 6, 0, 0, 0, 72, 24, -26, 0, 0, 0, -1, 0, 0, 0, -12, 0, 23, -4, -12, 0, 18, -2, 0, 0, 8, 0, 48, 0, -8, 0, 9, 0, -6, 0, -10, 0, 0, -50, -24, 0, 29, 0, -44, 0, -18, -48, 0, 0, 18, -8, 0, 0, -28, 6, 0, 0, -12, 0, 36, 0, -24, 8, 15, 0, 0, 0, 8, 0, -51, -32, -36, 0, -30, 0, -30, 0, -20, 12, 0, 0, 0, 48, -23, 0, 12, 0, 12, 0, 9, 0, 0, 0, 0, 24, -16, 0, -4, 0, -21, 0, 5, -24, -2, 0, 2, 0, 0, 0, -60, -38, -30, 0, 8, 0, 0, 0, -30, 24, -36, 0, 0, 0, 30, 0, -31, -12, 12, 0, 0, -8, 10, 0, -32, 6, 0, 0, 54, 0, 3, 0, 39, 0, 4, 0, 6, -40, 21, 0, 0, -6, 14, 0, 18, 0, 28, 0, -4, 26, 75, 0, 4, 0, 0, 0, -6, 0, 29, 0, 72, 0, 30, 0, 22, 12, 0, 0, 0, 8, -29, 0, -24, -8, 0, 0, -40, 0, -56, 0, -12, -36, 0, 0, 9, 0, 24, 0, 40, 0, 48, 0, 39, 0, 72, 0, 0, 44, -24, 0, -18, 48, -2, 0, -24, -72, -5, 0, 0, 0, 0, 0, 0, 0, -34, 0, -12, 0, 26, 0, -16, 24, -30, 0, 0, 0, -30, 0, 21, 4, 36, 0, 56, 32, 9, 0, 19, 30, 0, 0, 57, 0, 0, 0, -42, 0, 27, 0, 20, -48, -36, 0, 0, -48, 11, 0, -10, 0, 0, 0, 18, 0, 30, 0, 15, 12, 0, 0, -34, 4, -4, 0, 46, 0, 13, 0, 0, 8, 16, 0, 0, 0, -24, 0, 20, 60, -4, 0, -6, 0, 9, 0, 3, 0, 0, 0, 32, -24, 36, 0, -39, 0, 8, 0, 0, 0, 6, 0, 0, -12, 0, 0, 12, 32, 4, 0, 6, 32, 12, 0, -8, 0, 0, 0, -24, -12, 54, 0, 4, 0, 12, 0, 28, -6, 12, 0, 0, 0, -2, 0, 54, -14, -24, 0, 0, 0, 6, 0, -12, 16, 0, 0, 12, 0, 18, 0, 43, 0, -16, 0, -66, 0, -16, 0, 0, -72, -9, 0, -34, 0, 48, 0, 48, 0, -20, 0, -14, -8, 0, 0, 0, 24, 8, 0, 0, 0, 1, 0, -42, 56, -36, 0, 0, 36, 50, 0, 0, -36, 46, 0, -6, 0, 6, 0, 22, -48, 0, 0, -9, 0, -45, 0, -34, 0, -60, 0, -4, 0, -8, 0, 0, 8, 2, 0, -48, 72, 6, 0, 20, 0, 72, 0, -36, 0, 0, 0, -66, 34, 12, 0, 0, 0, 0, 0, 2, -8, 0, 0, 0, 0, -6, 0, -34, 30, 12, 0, 42, -16, 18, 0, -12, -56, 0, 0, -1, 0, 32, 0, 9, 0, -40, 0, -17, 0, 18, 0, 0, 42, 0, 0, 0, 0, -38, 0, 38, 36, 27, 0, 0, 48, 0, 0, 30, 40, -2, 0, -36, 0, -21, 0, 18, -30, -12, 0, 0, -48, -27, 0, 3, 34, -48, 0, -16, 0, 0, 0, -6, 20, 0, 0, 8, -8, -3, 0, 36, 0, -7, 0, 48, 0, 9, 0, 0, 4, 0, 0, 17, 0, 16, 0, 21, -12, -2, 0, 40, 0, 0, 0, 0, -36, -24, 0, -18, 0, -31, 0, 28, 0, -48, 0, 0, 0, -12, 0, -27, 0, -14, 0, -24, -32, 48, 0, -10, -6, 0, 0, -27, 0, -10, 0, 0, 0, 0, 0, -32, 12, -42, 0, 0, 2, -36, 0, -58, 0, 33, 0, -25, -12, -11, 0, -84, 0, 0, 0, 42, -54, -24, 0, -56, 0, 54, 0, -48, -24, -50, 0, 0, -16, 10, 0, 32, -12, -12, 0, 3, 0, 0, 0, -30, 16, 0, 0, 8, 0, 25, 0, 12, 0, -1, 0, -12, 0, -18, 0, 0, -48, -16, 0, 27, 0, 0, 0, -48, 14, 6, 0, 72, 0, 0, 0, -51, 4, -4, 0, -44, 0, -24, 0, 46, 42, -3, 0, 0, 0, 14, 0, -2, -50, -102, 0, -45, 36, -20, 0, 0, 24, 0, 0, -4, 0, 84, 0, 20, 0, 18, 0, -51, 0, -29, 0, 0, 34, 6, 0, 4, 0, -32, 0, 12, 32, -63, 0, -36, -8, 0, 0, 32, 48, 0, 0, -24, 0, 18, 0, -6, -72, 36, 0, 0, 0, -60, 0, 12, 48, -12, 0, -4, 0, -21, 0, 45, 0, 0, 0, -42, 32, 32, 0, 54, 0, -51, 0, 0, 0, -4, 0, 0, -48, 11, 0, -30, 16, 15, 0, 0, 12, -120, 0, 36, 0, 0, 0, -28, -32, -18, 0, 37, 0, 12, 0, -6, 68, -8, 0, 0, 0, 0, 0, -72, 0, 18, 0, -8, 0, -2, 0, 19, -38, 0, 0, 54, 0, -30, 0, -36, 0, -8, 0, -20, -40, 0, 0, 0, 36, 24, 0, -24, 0, 8, 0, 0, 12, -42, 0, -32, 48, 0, 0, 24, -12, 9, 0, 6, 0, -18, 0, 40, 0, 66, 0, 0, -44, -52, 0, 8, -8, 63, 0, 26, 0, -3, 0, -12, 28, 0, 0, 0, 0, 12, 0, 18, 0, 38, 0, 12, 0, -26, 0, 0, -16, 36, 0, 41, 12, 0, 0, 84, 20, -16, 0, 36, 0, 0, 0, -17, 24, 3, 0, 0, 0, 18, 0, 0, -28, -18, 0, 0, 0, 144, 0, -24, 48, 0, 0, -13, 0, -66, 0, 6, 24, 0, 0, 45, 0, 63, 0, -2, 0, -18, 0, -18, 0, 0, 0, 0, 0, 2, 0, -24, 0, -21, 0, 4, 42, 46, 0, 3, -8, 0, 0, -6, 58, -24, 0, 31, 0, 36, 0, 0, 8, -63, 0, 0, 0, 60, 0, 0, -42, 4, 0, 75, 0, -7, 0, 96, -54, 0, 0, 56, 24, -16, 0, -60, 0, 8, 0, -36, 0, -42, 0, 0, 12, -12, 0, -12, 0, -36, 0, -20, 30, -51, 0, 28, 0, 0, 0, 45, -100, -4, 0, -48, 0, 12, 0, 52, 12, 58, 0, 0, 0, -72, 0, -22, 16, -12, 0, 44, 0, -36, 0, 48, -24, 0, 0, 0, 0, -18, 0, -53, 0, -72, 0, -72, -16, -14, 0, 0, 44, -24, 0, 0, 0, -56, 0, 51, 12, 20, 0, 0, 0, 0, 0, 72, 2, -24, 0, 48, 0, 0, 0, 72, 20, -120, 0, 0, -24, -12, 0, 60, 16, -8, 0, 30, 0, 114, 0, -29, -18, 0, 0, 48, 0, -9, 0, 22, 0, 0, 0, -32, 0, -102, 0, 0, -16, -40, 0, -72, -32, 42, 0, 0, 36, -15, 0, 39, 0, 0, 0, -60, 0, 57, 0, 25, 0, -40, 0, -27, 24, 25, 0, 0, 0, -6, 0, 41, 60, 0, 0, -48, 24, -54, 0, -46, 4, 0, 0, -80, 0, -48, 0, -18, 0, -46, 0, 24, -32, 45, 0, 0, -54, 18, 0, -24, 0, -2, 0, 0, 4, 42, 0, 0, 48, 0, 0, 45, 66, -58, 0, -32, 0, -3, 0, -50, 120, -2, 0, 0, 0, 0, 0, -42, 28, 39, 0, 18, 0, 10, 0, -18, -48, 0, 0, 8, -68, 0, 0, -4, 0, 4, 0, 24, 0, 43, 0, 0, -18, -78, 0, 8, 0, -30, 0, -30, -76, -38, 0, -60, 0, 0, 0, -16, 30, 16, 0, 0, 0, 103, 0, 0, 20, 42, 0, 0, 0, -60, 0, -12, 12, -50, 0, -72, 0, 0, 0, -50, 0, 0, 0, -6, 0, -36, 0, 60, 0, 30, 0, -12, 12, -62, 0, 0, -24, 0, 0, 6, 0, 72, 0, -22, -66, 0, 0, 24, 32, 0, 0, 20, -8, -51, 0, -63, 0, -16, 0, 60, 12, 31, 0, 0, -28, -87, 0, 11, 0, 108, 0, 0, 0, -38, 0, -12, -38, 0, 0, -64, 0, 78, 0, 96, 0, 63, 0, 8, 0, 2, 0, 0, 0, 3, 0, 36, -80, -14, 0, 42, -36, 12, 0, -44, 0, 0, 0, -6, -12, 11, 0, 7, 0, -132, 0, -18, 0, 36, 0, 0, 0, -10, 0, 56, -144, -45, 0, 19, -48, 16, 0, 75, 52, 0, 0, 150, 0, 0, 0, 0, 0, 8, 0, 51, 0, -8, 0, 0, 2, -24, 0, -43, 0, -12, 0, -24, 0, 0, 0, 58, 0, 0, 0, 16, 24, 36, 0, 15, 0, 21, 0, 60, -46, 0, 0, 0, 8, 44, 0, -72, 24, 49, 0, 0, 0, -66, 0, 64, -36, 0, 0, 54, 4, -64, 0, -58, 0, -54, 0, 43, 0, -12, 0, 0, -16, -3, 0, 0, 0, 39, 0, 4, -96, -80, 0, -30, 0, 0, 0, -28, 16, -45, 0, -90, 0, -24, 0, 3, -18, 0, 0, 0, 0, 54, 0, 27, 12, -36, 0, -24, 0, 0, 0, 48, 20, 0, 0, -72, 0, 80, 0, 12, 0, -46, 0, 24, 100, 3, 0, 0, 48, 78, 0, 4, 0, -54, 0, 144, -58, 45, 0, 16, 0, 0, 0, 0, 88, 34, 0, -48, 0, -90, 0, -13, 36, -36, 0, 0, 96, 0, 0, 8, 0, 42, 0, -40, 0, -48, 0, 9, -36, 0, 0, -10, 16, -6, 0, 40, 0, 0, 0, -12, 0, 70, 0, 0, 56, -27, 0, 56, -12, 0, 0, -36, 0, 81, 0, -17, 0, 0, 0, -40, 24, -24, 0, -6, 0, 53, 0, 52, -72, -48, 0, 0, 0, -44, 0, -48, 48, -50, 0, -60, -16, -6, 0, -180, -30, 0, 0, 15, 0, 4, 0, -15, 0, -42, 0, 0, 0, 42, 0, 0, -16, -25, 0, 72, 0, 0, 0, -9, 102, 28, 0, 51, 64, 0, 0, 18, 72, -60, 0, 14, 0, 38, 0, 12, 60, 8, 0, 0, 0, -6, 0, -1, 60, 114, 0, 3, 0, -59, 0, 0, 40, 0, 0, -45, -24, -21, 0, 72, 0, 36, 0, 54, 0, -30, 0, 0, 0, 40, 0, 0, -96, -26, 0, -18, 46, 2, 0, -22, 0, 0, 0, -96, -24, 0, 0, 22, 0, 72, 0, 28, -24, 40, 0, 0, 0, 41, 0, 0, -18, 9, 0, -40, 0, 36, 0, 24, 0, 0, 0, 15, 0, -66, 0, 99, 0, 30, 0, 0, -48, 28, 0, 0, 32, 12, 0, 18, 0, -17, 0, 0, 8, 108, 0, -8, 0, 0, 0, 32, 42, 92, 0, -120, 0, 0, 0, 56, -10, 42, 0, 0, 48, 0, 0, 57, 4, -25, 0, 32, 0, -18, 0, 16, -4, 0, 0, 12, 0, -11, 0, -48, 0, 69, 0, 0, 0, 40, 0, 0, 120, -88, 0, -2, 76, 24, 0, 0, 60, -12, 0, 0, 0, 0, 0, 18, -16, -66, 0, 1, 0, -12, 0, -66, 0, 0, 0, 0, 0, -15, 0, -4, 60, 64, 0, 216, -48, 20, 0, 18, 72, 0, 0, 4, 0, -78, 0, -33, 0, -85, 0, 16, 0, -36, 0, 0, -60, 0, 0, 72, 0, 16, 0, 12, 62, -3, 0, 16, 24, 0, 0, 10, -24, 56, 0, 0, 0, 57, 0, -50, 0, 24, 0, 0, 16, -36, 0, 8, -20, -42, 0, -19, 0, 3, 0, 69, 64, 0, 0, 24, -12, -168, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, -108, 63, 0, 54, 0, -48, 0, 24, -6, -62, 0, 108, 0, 0, 0, -10, -78, 11, 0, 6, 0, -2, 0, 24, -8, -18, 0, 0, 0, 56, 0, 0, -12, 144, 0, 6, 80, 0, 0, -29, -42, 0, 0, 6, 0, -13, 0, -4, 0, -72, 0, 91, 12, 27, 0, 0, -28, -16, 0, -48, 0, 18, 0, -18, -36, 0, 0, -24, 0, 0, 0, -24, -56, -30, 0, -3, 0, -24, 0, -12, 8, 8, 0, 0, -52, -12, 0, 144, -150, 6, 0, -48, 0, -32, 0, 36, -8, 0, 0, 0, 0, 86, 0, 87, 0, 83, 0, -8, 0, 63, 0, 0, 12, -132, 0, 12, 0, 20, 0, -32, -58, -102, 0, -54, 0, 0, 0, 60, -144, 0, 0, -18, 0, 0, 0, 70, -60, -68, 0, 0, 0, 74, 0, 24, -44, -12, 0, 40, -24, 96, 0, 6, 0, 0, 0, -40, 0, 12, 0, -54, 0, -7, 0, -84, -16, -90, 0, 0, 58, -24, 0, 17, 0, 0, 0, 0, 48, -16, 0, 22, 16, 0, 0, -36, 0, 0, 0, 168, 0, 62, 0, 2, 80, 48, 0, 0, 0, -21, 0, 30, 112, 0, 0, -72, 0, 96, 0, 31, 24, 0, 0, -72, 72, 45, 0, 25, 0, 24, 0, 40, 0, 0, 0, 0, -18, 29, 0, 92, 0, 3, 0, -126, -48, 24, 0, 0, 0, 0, 0, 12, -80, -6, 0, -68, 0, 44, 0, -66, -96, -6, 0, 0, 0, -108, 0, 7, -78, -18, 0, 78, 0, -68, 0, -90, -144, 0, 0, 0, 0, -17, 0, -24, 0, -90, 0, -120, -88, -3, 0, 0, 48, -8, 0, -60, 0, -17, 0, 32, 36, 78, 0, -16, -96, 0, 0, -90, 4, 90, 0, 4, 0, -39, 0, 0, 48, -24, 0, 0, 144, -38, 0, 12, 10, -69, 0, 8, 0, 40, 0, -102, 0, 0, 0, 36, 0, -36, 0, -20, 0, -72, 0, -3, 0, 36, 0, 0, 0, 0, 0, 20, 0, -60, 0, 12, 68, 73, 0, 24, 0, 0, 0, -34, 24, 0, 0, 48, 0, -64, 0, 0, -52, 39, 0, 0, 0, 4, 0, -12, 32, 20, 0, 0, -48, -48, 0, -92, 60, 0, 0, -24, 0, 41, 0, -12, 0, -12, 0, -47, 0, -68, 0, 0, 60, -28, 0, -48, 0, -54, 0, -31, -42, 84, 0, 15, -8, 0, 0, 36, -72, -90, 0, -28, 0, -6, 0, -48, -112, -41, 0, 0, -64, 54, 0, 6, -18, -2, 0, -12, 0, 108, 0, 16, -38, 0, 0, 14, -60, 18, 0, 0, 0, -72, 0, -80, 0, 63, 0, 0, -114, 68, 0, 0, 0, -90, 0, 36, 0, 30, 0, -5, 0, 0, 0, 24, 84, 50, 0, 0, 0, -36, 0, -26, -54, 0, 0, 0, 0, 28, 0, -76, -40, 8, 0, -90, 96, 19, 0, 57, 72, 0, 0, 54, 0, -48, 0, 18, 0, 0, 0, -6, 96, 91, 0, 0, -22, 9, 0, 0, 0, 60, 0, -15, 20, 90, 0, -4, 0, 0, 0, -4, 0, -18, 0, -93, 0, 26, 0, -42, -36, 42, 0, 0, 0, 36, 0, 12, -60, 26, 0, -6, 0, 0, 0, 0, -30, 0, 0, 102, -24, -32, 0, -54, 0, 30, 0, 37, 0, -12, 0, 0, 68, 36, 0, -96, -8, -72, 0, -17, 8, -32, 0, -90, 0, 0, 0, 0, -92, 81, 0, 108, 0, -12, 0, 162, -26, 52, 0, 0, 0, 0, 0, 100, 0, 4, 0, -96, -16, -12, 0, -6, -32, 0, 0, 117, 0, 72, 0, 0, 0, 0, 0, 28, 0, 12, 0, 0, 48, 96, 0, -15, 0, -47, 0, 18, -40, -57, 0, 36, -120, 0, 0, -75, 8, 63, 0, 0, 0, 24, 0, 52, 12, 34, 0, 0, 0, 28, 0, 8, -18, -48, 0, -8, 0, 42, 0, 17, -6, 0, 0, -4, 0, -24, 0, 54, 0, 110, 0, -24, 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, 0, 2, -2, 3, 0, 0, 0, 1, 0, 6, -4, 1, 0, 6, 4, 0, 0, -2, -6, 0, 0, 0, 0, 4, 0, -4, 0, -1, 0, -2, 0, 12, 0, 0, -2, -10, 0, 2, 0, 12, 0, 8, -12, 3, 0, -6, 8, 0, 0, 0, -2, 9, 0, 18, 0, -4, 0, 12, -12, -2, 0, 0, -8, 3, 0, -4, 0, 0, 0, 9, 0, -2, 0, 8, 4, 0, 0, -10, 12, -11, 0, 3, 0, 0, 0, -2, 0, 6, 0, 0, 0, -4, 0, -6, 0, -8, 0, 6, -8, 12, 0, -17, 0, 0, 0, 3, 8, -7, 0, -20, 0, -12, 0, 0, 2, 1, 0, 0, 0, 25, 0, 24, 4, -3, 0, -4, 0, 16, 0, -6, -24, 0, 0, -12, 0, 12, 0, 19, 0, -12, 0, 6, 4, -3, 0, 0, 20, 3, 0, -13, 0, 0, 0, -6, -4, 4, 0, 18, 0, 0, 0, -22, -24, 36, 0, 0, 0, -12, 0, -2, -16, -15, 0, 0, 24, 24, 0, 0, -6, -2, 0, -4, 0, -30, 0, 0, 12, 0, 0, 6, -16, -16, 0, 6, 0, 3, 0, 7, 0, -8, 0, 0, 0, 36, 0, 0, 4, -12, 0, -28, -18, 18, 0, 24, 0, 0, 0, -4, -36, 0, 0, -17, 0, 4, 0, -15, 8, 28, 0, 0, 0, -21, 0, -18, -24, -20, 0, 15, 24, -17, 0, -10, 4, 0, 0, -2, 0, 6, 0, 18, 0, 0, 0, 0, 16, 3, 0, 0, -6, -1, 0, 6, 0, 27, 0, 12, 8, 6, 0, -8, 0, 0, 0, 24, 0, -7, 0, -2, 0, -21, 0, 25, -18, -12, 0, 0, 0, -17, 0, -16, 4, -24, 0, 36, 0, -24, 0, 0, -16, 0, 0, 24, -8, -6, 0, 16, 0, -34, 0, 0, 0, 19, 0, 0, 20, -18, 0, -6, -24, 6, 0, 0, 22, 4, 0, -14, 0, 0, 0, 8, -6, -10, 0, -12, 0, 14, 0, -24, 0, -12, 0, 0, 0, 0, 0, -21, 4, -29, 0, -4, 0, 21, 0, 27, -12, 0, 0, -6, 0, -15, 0, 50, 0, -6, 0, -8, 0, 12, 0, 0, 8, -22, 0, -6, 0, -1, 0, -10, 12, -8, 0, 9, 0, 0, 0, 8, 16, -18, 0, 0, 0, -12, 0, -30, -12, -2, 0, 0, 16, 27, 0, -2, -24, -33, 0, -60, 0, -14, 0, 24, 34, 0, 0, 9, 0, 38, 0, -15, 0, -10, 0, -6, 0, 0, 0, 0, -6, 12, 0, 33, -16, 4, 0, -6, 14, 0, 0, 19, 0, 0, 0, 0, 40, 18, 0, 6, 0, 0, 0, 72, 24, -26, 0, 0, 0, -1, 0, 0, 0, -12, 0, 23, -4, -12, 0, 18, -2, 0, 0, 8, 0, 48, 0, -8, 0, 9, 0, -6, 0, -10, 0, 0, -50, -24, 0, 29, 0, -44, 0, -18, -48, 0, 0, 18, -8, 0, 0, -28, 6, 0, 0, -12, 0, 36, 0, -24, 8, 15, 0, 0, 0, 8, 0, -51, -32, -36, 0, -30, 0, -30, 0, -20, 12, 0, 0, 0, 48, -23, 0, 12, 0, 12, 0, 9, 0, 0, 0, 0, 24, -16, 0, -4, 0, -21, 0, 5, -24, -2, 0, 2, 0, 0, 0, -60, -38, -30, 0, 8, 0, 0, 0, -30, 24, -36, 0, 0, 0, 30, 0, -31, -12, 12, 0, 0, -8, 10, 0, -32, 6, 0, 0, 54, 0, 3, 0, 39, 0, 4, 0, 6, -40, 21, 0, 0, -6, 14, 0, 18, 0, 28, 0, -4, 26, 75, 0, 4, 0, 0, 0, -6, 0, 29, 0, 72, 0, 30, 0, 22, 12, 0, 0, 0, 8, -29, 0, -24, -8, 0, 0, -40, 0, -56, 0, -12, -36, 0, 0, 9, 0, 24, 0, 40, 0, 48, 0, 39, 0, 72, 0, 0, 44, -24, 0, -18, 48, -2, 0, -24, -72, -5, 0, 0, 0, 0, 0, 0, 0, -34, 0, -12, 0, 26, 0, -16, 24, -30, 0, 0, 0, -30, 0, 21, 4, 36, 0, 56, 32, 9, 0, 19, 30, 0, 0, 57, 0, 0, 0, -42, 0, 27, 0, 20, -48, -36, 0, 0, -48, 11, 0, -10, 0, 0, 0, 18, 0, 30, 0, 15, 12, 0, 0, -34, 4, -4, 0, 46, 0, 13, 0, 0, 8, 16, 0, 0, 0, -24, 0, 20, 60, -4, 0, -6, 0, 9, 0, 3, 0, 0, 0, 32, -24, 36, 0, -39, 0, 8, 0, 0, 0, 6, 0, 0, -12, 0, 0, 12, 32, 4, 0, 6, 32, 12, 0, -8, 0, 0, 0, -24, -12, 54, 0, 4, 0, 12, 0, 28, -6, 12, 0, 0, 0, -2, 0, 54, -14, -24, 0, 0, 0, 6, 0, -12, 16, 0, 0, 12, 0, 18, 0, 43, 0, -16, 0, -66, 0, -16, 0, 0, -72, -9, 0, -34, 0, 48, 0, 48, 0, -20, 0, -14, -8, 0, 0, 0, 24, 8, 0, 0, 0, 1, 0, -42, 56, -36, 0, 0, 36, 50, 0, 0, -36, 46, 0, -6, 0, 6, 0, 22, -48, 0, 0, -9, 0, -45, 0, -34, 0, -60, 0, -4, 0, -8, 0, 0, 8, 2, 0, -48, 72, 6, 0, 20, 0, 72, 0, -36, 0, 0, 0, -66, 34, 12, 0, 0, 0, 0, 0, 2, -8, 0, 0, 0, 0, -6, 0, -34, 30, 12, 0, 42, -16, 18, 0, -12, -56, 0, 0, -1, 0, 32, 0, 9, 0, -40, 0, -17, 0, 18, 0, 0, 42, 0, 0, 0, 0, -38, 0, 38, 36, 27, 0, 0, 48, 0, 0, 30, 40, -2, 0, -36, 0, -21, 0, 18, -30, -12, 0, 0, -48, -27, 0, 3, 34, -48, 0, -16, 0, 0, 0, -6, 20, 0, 0, 8, -8, -3, 0, 36, 0, -7, 0, 48, 0, 9, 0, 0, 4, 0, 0, 17, 0, 16, 0, 21, -12, -2, 0, 40, 0, 0, 0, 0, -36, -24, 0, -18, 0, -31, 0, 28, 0, -48, 0, 0, 0, -12, 0, -27, 0, -14, 0, -24, -32, 48, 0, -10, -6, 0, 0, -27, 0, -10, 0, 0, 0, 0, 0, -32, 12, -42, 0, 0, 2, -36, 0, -58, 0, 33, 0, -25, -12, -11, 0, -84, 0, 0, 0, 42, -54, -24, 0, -56, 0, 54, 0, -48, -24, -50, 0, 0, -16, 10, 0, 32, -12, -12, 0, 3, 0, 0, 0, -30, 16, 0, 0, 8, 0, 25, 0, 12, 0, -1, 0, -12, 0, -18, 0, 0, -48, -16, 0, 27, 0, 0, 0, -48, 14, 6, 0, 72, 0, 0, 0, -51, 4, -4, 0, -44, 0, -24, 0, 46, 42, -3, 0, 0, 0, 14, 0, -2, -50, -102, 0, -45, 36, -20, 0, 0, 24, 0, 0, -4, 0, 84, 0, 20, 0, 18, 0, -51, 0, -29, 0, 0, 34, 6, 0, 4, 0, -32, 0, 12, 32, -63, 0, -36, -8, 0, 0, 32, 48, 0, 0, -24, 0, 18, 0, -6, -72, 36, 0, 0, 0, -60, 0, 12, 48, -12, 0, -4, 0, -21, 0, 45, 0, 0, 0, -42, 32, 32, 0, 54, 0, -51, 0, 0, 0, -4, 0, 0, -48, 11, 0, -30, 16, 15, 0, 0, 12, -120, 0, 36, 0, 0, 0, -28, -32, -18, 0, 37, 0, 12, 0, -6, 68, -8, 0, 0, 0, 0, 0, -72, 0, 18, 0, -8, 0, -2, 0, 19, -38, 0, 0, 54, 0, -30, 0, -36, 0, -8, 0, -20, -40, 0, 0, 0, 36, 24, 0, -24, 0, 8, 0, 0, 12, -42, 0, -32, 48, 0, 0, 24, -12, 9, 0, 6, 0, -18, 0, 40, 0, 66, 0, 0, -44, -52, 0, 8, -8, 63, 0, 26, 0, -3, 0, -12, 28, 0, 0, 0, 0, 12, 0, 18, 0, 38, 0, 12, 0, -26, 0, 0, -16, 36, 0, 41, 12, 0, 0, 84, 20, -16, 0, 36, 0, 0, 0, -17, 24, 3, 0, 0, 0, 18, 0, 0, -28, -18, 0, 0, 0, 144, 0, -24, 48, 0, 0, -13, 0, -66, 0, 6, 24, 0, 0, 45, 0, 63, 0, -2, 0, -18, 0, -18, 0, 0, 0, 0, 0, 2, 0, -24, 0, -21, 0, 4, 42, 46, 0, 3, -8, 0, 0, -6, 58, -24, 0, 31, 0, 36, 0, 0, 8, -63, 0, 0, 0, 60, 0, 0, -42, 4, 0, 75, 0, -7, 0, 96, -54, 0, 0, 56, 24, -16, 0, -60, 0, 8, 0, -36, 0, -42, 0, 0, 12, -12, 0, -12, 0, -36, 0, -20, 30, -51, 0, 28, 0, 0, 0, 45, -100, -4, 0, -48, 0, 12, 0, 52, 12, 58, 0, 0, 0, -72, 0, -22, 16, -12, 0, 44, 0, -36, 0, 48, -24, 0, 0, 0, 0, -18, 0, -53, 0, -72, 0, -72, -16, -14, 0, 0, 44, -24, 0, 0, 0, -56, 0, 51, 12, 20, 0, 0, 0, 0, 0, 72, 2, -24, 0, 48, 0, 0, 0, 72, 20, -120, 0, 0, -24, -12, 0, 60, 16, -8, 0, 30, 0, 114, 0, -29, -18, 0, 0, 48, 0, -9, 0, 22, 0, 0, 0, -32, 0, -102, 0, 0, -16, -40, 0, -72, -32, 42, 0, 0, 36, -15, 0, 39, 0, 0, 0, -60, 0, 57, 0, 25, 0, -40, 0, -27, 24, 25, 0, 0, 0, -6, 0, 41, 60, 0, 0, -48, 24, -54, 0, -46, 4, 0, 0, -80, 0, -48, 0, -18, 0, -46, 0, 24, -32, 45, 0, 0, -54, 18, 0, -24, 0, -2, 0, 0, 4, 42, 0, 0, 48, 0, 0, 45, 66, -58, 0, -32, 0, -3, 0, -50, 120, -2, 0, 0, 0, 0, 0, -42, 28, 39, 0, 18, 0, 10, 0, -18, -48, 0, 0, 8, -68, 0, 0, -4, 0, 4, 0, 24, 0, 43, 0, 0, -18, -78, 0, 8, 0, -30, 0, -30, -76, -38, 0, -60, 0, 0, 0, -16, 30, 16, 0, 0, 0, 103, 0, 0, 20, 42, 0, 0, 0, -60, 0, -12, 12, -50, 0, -72, 0, 0, 0, -50, 0, 0, 0, -6, 0, -36, 0, 60, 0, 30, 0, -12, 12, -62, 0, 0, -24, 0, 0, 6, 0, 72, 0, -22, -66, 0, 0, 24, 32, 0, 0, 20, -8, -51, 0, -63, 0, -16, 0, 60, 12, 31, 0, 0, -28, -87, 0, 11, 0, 108, 0, 0, 0, -38, 0, -12, -38, 0, 0, -64, 0, 78, 0, 96, 0, 63, 0, 8, 0, 2, 0, 0, 0, 3, 0, 36, -80, -14, 0, 42, -36, 12, 0, -44, 0, 0, 0, -6, -12, 11, 0, 7, 0, -132, 0, -18, 0, 36, 0, 0, 0, -10, 0, 56, -144, -45, 0, 19, -48, 16, 0, 75, 52, 0, 0, 150, 0, 0, 0, 0, 0, 8, 0, 51, 0, -8, 0, 0, 2, -24, 0, -43, 0, -12, 0, -24, 0, 0, 0, 58, 0, 0, 0, 16, 24, 36, 0, 15, 0, 21, 0, 60, -46, 0, 0, 0, 8, 44, 0, -72, 24, 49, 0, 0, 0, -66, 0, 64, -36, 0, 0, 54, 4, -64, 0, -58, 0, -54, 0, 43, 0, -12, 0, 0, -16, -3, 0, 0, 0, 39, 0, 4, -96, -80, 0, -30, 0, 0, 0, -28, 16, -45, 0, -90, 0, -24, 0, 3, -18, 0, 0, 0, 0, 54, 0, 27, 12, -36, 0, -24, 0, 0, 0, 48, 20, 0, 0, -72, 0, 80, 0, 12, 0, -46, 0, 24, 100, 3, 0, 0, 48, 78, 0, 4, 0, -54, 0, 144, -58, 45, 0, 16, 0, 0, 0, 0, 88, 34, 0, -48, 0, -90, 0, -13, 36, -36, 0, 0, 96, 0, 0, 8, 0, 42, 0, -40, 0, -48, 0, 9, -36, 0, 0, -10, 16, -6, 0, 40, 0, 0, 0, -12, 0, 70, 0, 0, 56, -27, 0, 56, -12, 0, 0, -36, 0, 81, 0, -17, 0, 0, 0, -40, 24, -24, 0, -6, 0, 53, 0, 52, -72, -48, 0, 0, 0, -44, 0, -48, 48, -50, 0, -60, -16, -6, 0, -180, -30, 0, 0, 15, 0, 4, 0, -15, 0, -42, 0, 0, 0, 42, 0, 0, -16, -25, 0, 72, 0, 0, 0, -9, 102, 28, 0, 51, 64, 0, 0, 18, 72, -60, 0, 14, 0, 38, 0, 12, 60, 8, 0, 0, 0, -6, 0, -1, 60, 114, 0, 3, 0, -59, 0, 0, 40, 0, 0, -45, -24, -21, 0, 72, 0, 36, 0, 54, 0, -30, 0, 0, 0, 40, 0, 0, -96, -26, 0, -18, 46, 2, 0, -22, 0, 0, 0, -96, -24, 0, 0, 22, 0, 72, 0, 28, -24, 40, 0, 0, 0, 41, 0, 0, -18, 9, 0, -40, 0, 36, 0, 24, 0, 0, 0, 15, 0, -66, 0, 99, 0, 30, 0, 0, -48, 28, 0, 0, 32, 12, 0, 18, 0, -17, 0, 0, 8, 108, 0, -8, 0, 0, 0, 32, 42, 92, 0, -120, 0, 0, 0, 56, -10, 42, 0, 0, 48, 0, 0, 57, 4, -25, 0, 32, 0, -18, 0, 16, -4, 0, 0, 12, 0, -11, 0, -48, 0, 69, 0, 0, 0, 40, 0, 0, 120, -88, 0, -2, 76, 24, 0, 0, 60, -12, 0, 0, 0, 0, 0, 18, -16, -66, 0, 1, 0, -12, 0, -66, 0, 0, 0, 0, 0, -15, 0, -4, 60, 64, 0, 216, -48, 20, 0, 18, 72, 0, 0, 4, 0, -78, 0, -33, 0, -85, 0, 16, 0, -36, 0, 0, -60, 0, 0, 72, 0, 16, 0, 12, 62, -3, 0, 16, 24, 0, 0, 10, -24, 56, 0, 0, 0, 57, 0, -50, 0, 24, 0, 0, 16, -36, 0, 8, -20, -42, 0, -19, 0, 3, 0, 69, 64, 0, 0, 24, -12, -168, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, -108, 63, 0, 54, 0, -48, 0, 24, -6, -62, 0, 108, 0, 0, 0, -10, -78, 11, 0, 6, 0, -2, 0, 24, -8, -18, 0, 0, 0, 56, 0, 0, -12, 144, 0, 6, 80, 0, 0, -29, -42, 0, 0, 6, 0, -13, 0, -4, 0, -72, 0, 91, 12, 27, 0, 0, -28, -16, 0, -48, 0, 18, 0, -18, -36, 0, 0, -24, 0, 0, 0, -24, -56, -30, 0, -3, 0, -24, 0, -12, 8, 8, 0, 0, -52, -12, 0, 144, -150, 6, 0, -48, 0, -32, 0, 36, -8, 0, 0, 0, 0, 86, 0, 87, 0, 83, 0, -8, 0, 63, 0, 0, 12, -132, 0, 12, 0, 20, 0, -32, -58, -102, 0, -54, 0, 0, 0, 60, -144, 0, 0, -18, 0, 0, 0, 70, -60, -68, 0, 0, 0, 74, 0, 24, -44, -12, 0, 40, -24, 96, 0, 6, 0, 0, 0, -40, 0, 12, 0, -54, 0, -7, 0, -84, -16, -90, 0, 0, 58, -24, 0, 17, 0, 0, 0, 0, 48, -16, 0, 22, 16, 0, 0, -36, 0, 0, 0, 168, 0, 62, 0, 2, 80, 48, 0, 0, 0, -21, 0, 30, 112, 0, 0, -72, 0, 96, 0, 31, 24, 0, 0, -72, 72, 45, 0, 25, 0, 24, 0, 40, 0, 0, 0, 0, -18, 29, 0, 92, 0, 3, 0, -126, -48, 24, 0, 0, 0, 0, 0, 12, -80, -6, 0, -68, 0, 44, 0, -66, -96, -6, 0, 0, 0, -108, 0, 7, -78, -18, 0, 78, 0, -68, 0, -90, -144, 0, 0, 0, 0, -17, 0, -24, 0, -90, 0, -120, -88, -3, 0, 0, 48, -8, 0, -60, 0, -17, 0, 32, 36, 78, 0, -16, -96, 0, 0, -90, 4, 90, 0, 4, 0, -39, 0, 0, 48, -24, 0, 0, 144, -38, 0, 12, 10, -69, 0, 8, 0, 40, 0, -102, 0, 0, 0, 36, 0, -36, 0, -20, 0, -72, 0, -3, 0, 36, 0, 0, 0, 0, 0, 20, 0, -60, 0, 12, 68, 73, 0, 24, 0, 0, 0, -34, 24, 0, 0, 48, 0, -64, 0, 0, -52, 39, 0, 0, 0, 4, 0, -12, 32, 20, 0, 0, -48, -48, 0, -92, 60, 0, 0, -24, 0, 41, 0, -12, 0, -12, 0, -47, 0, -68, 0, 0, 60, -28, 0, -48, 0, -54, 0, -31, -42, 84, 0, 15, -8, 0, 0, 36, -72, -90, 0, -28, 0, -6, 0, -48, -112, -41, 0, 0, -64, 54, 0, 6, -18, -2, 0, -12, 0, 108, 0, 16, -38, 0, 0, 14, -60, 18, 0, 0, 0, -72, 0, -80, 0, 63, 0, 0, -114, 68, 0, 0, 0, -90, 0, 36, 0, 30, 0, -5, 0, 0, 0, 24, 84, 50, 0, 0, 0, -36, 0, -26, -54, 0, 0, 0, 0, 28, 0, -76, -40, 8, 0, -90, 96, 19, 0, 57, 72, 0, 0, 54, 0, -48, 0, 18, 0, 0, 0, -6, 96, 91, 0, 0, -22, 9, 0, 0, 0, 60, 0, -15, 20, 90, 0, -4, 0, 0, 0, -4, 0, -18, 0, -93, 0, 26, 0, -42, -36, 42, 0, 0, 0, 36, 0, 12, -60, 26, 0, -6, 0, 0, 0, 0, -30, 0, 0, 102, -24, -32, 0, -54, 0, 30, 0, 37, 0, -12, 0, 0, 68, 36, 0, -96, -8, -72, 0, -17, 8, -32, 0, -90, 0, 0, 0, 0, -92, 81, 0, 108, 0, -12, 0, 162, -26, 52, 0, 0, 0, 0, 0, 100, 0, 4, 0, -96, -16, -12, 0, -6, -32, 0, 0, 117, 0, 72, 0, 0, 0, 0, 0, 28, 0, 12, 0, 0, 48, 96, 0, -15, 0, -47, 0, 18, -40, -57, 0, 36, -120, 0, 0, -75, 8, 63, 0, 0, 0, 24, 0, 52, 12, 34, 0, 0, 0, 28, 0, 8, -18, -48, 0, -8, 0, 42, 0, 17, -6, 0, 0, -4, 0, -24, 0, 54, 0, 110, 0, -24, 0]}