# Stored data for newform 3525.2.a.bf, downloaded from the LMFDB on 29 March 2024. {"label": "3525.2.a.bf", "space_label": "3525.2.a", "level": 3525, "weight": 2, "hecke_orbit": 32, "hecke_orbit_code": 139611588482043333, "dim": 10, "is_polredabs": true, "trace_hash": 1802999721034023429, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [-4, 30, 6, -101, -21, 91, 25, -29, -9, 3, 1]], [7, [-32, 812, 745, -1084, -980, 388, 382, -20, -36, 0, 1]], [11, [8192, -9888, -11148, 10088, 6776, -1832, -1652, -172, 65, 16, 1]]], "qexp_display": "q-\\beta _{1}q^{2}+q^{3}+(1+\\beta _{2})q^{4}-\\beta _{1}q^{6}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 14100, "fricke_eigenval": 1, "atkin_lehner_string": "--+", "analytic_conductor": 28.147266712501334, "hecke_ring_index": 1, "level_radical": 705, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "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": "0.005", "prec": 17}, "analytic_rank_proved": true, "char_values": [3525, 1, [2351, 1552, 2026], [1, 1, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 1, "level_primes": [3, 5, 47], "conrey_indexes": [1], "field_disc": 2344712986440704, "field_disc_factorization": [[2, 10], [11, 1], [311, 1], [669324401, 1]], "field_poly": [-4, -30, 6, 101, -21, -91, 25, 29, -9, -3, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "8.319", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "220.598", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "10155.046", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 10, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [5, -1], [47, 1]], "trace_display": [-3, 10, 0, 0], "traces": [0, 10, -3, 10, 7, 0, -3, 0, -9, 10, 0, -16, 7, -1, -12, 0, -3, -14, -3, -26, 0, 0, 0, -7, -9, 0, -10, 10, 24, -14, 0, -22, -11, -16, -12, 0, 7, -2, 2, -1, 0, -22, -12, 11, -36, 0, -14, -10, -3, 2, 0, -14, -14, -22, -3, 0, -48, -26, 20, -37, 0, -25, 2, 0, -7, 0, 0, 4, -8, -7, 0, -27, -9, -1, 4, 0, -42, -34, -10, 5, 0, 10, 32, -2, 24, 0, -6, -14, 58, 9, 0, -64, -34, -22, 3, 0, -11, 40, -29, -16, 0, -39, -12, 16, 40, 0, -20, -7, 7, -26, 0, -2, 36, -59, 2, 0, -28, -1, 108, -20, 0, 16, 48, -22, 4, 0, -12, -4, 3, 11, 0, -69, -36, 4, 0, 0, -20, -47, -14, -74, 0, -10, 0, 20, -3, 0, -12, 2, 32, -25, 0, -36, 34, -14, 68, 0, -14, 12, -14, -22, 0, 18, -3, -9, -48, 0, 8, -17, -48, 17, 0, -26, 70, 22, 20, 0, -52, -37, 16, -28, 0, -42, 44, -25, 16, 0, 2, 28, -7, 0, 0, -7, -7, 32, 18, 0, 25, 8, 0, -58, 0, 4, 4, -34, -8, 0, -34, -7, -2, -26, 0, -66, 66, -27, 12, 0, -9, -4, 70, -1, 0, 12, 4, 19, -10, 0, -52, -38, -42, 2, 0, -34, 36, -56, -10, 0, -56, 5, 64, -60, 0, 25, -5, 10, -78, 0, 32, 78, 22, -2, 0, -72, 24, 80, 80, 0, -23, -43, -6, 6, 0, -14, -16, -12, 58, 0, 34, 9, 74, 13, 0, -54, 42, -64, 86, 0, -34, 50, 38, -22, 0, 42, 3, 28, -48, 0, -52, 48, -11, -4, 0, 40, -18, -33, -29, 0, -30, -16, 96, -91, 0, -34, 6, -39, 72, 0, -12, 74, -104, 16, 0, -34, 40, 42, 10, 0, 38, -17, -20, -42, 0, -7, -22, -16, 7, 0, -18, -26, -2, 0, 0, -9, 0, -2, 76, 0, 36, 50, -61, -59, 0, 70, 2, 60, -32, 0, -36, 44, -28, -76, 0, -1, 94, -12, 108, 0, 34, -20, -42, -10, 0, 84, -14, 16, -40, 0, 48, -50, 32, -22, 0, -10, 4, 47, 48, 0, 9, -60, -12, -34, 0, -4, -76, -50, 3, 0, 54, 11, 40, -12, 0, 10, -95, -69, 12, 0, -36, 20, -98, 4, 0, -1, 0, -24, 106, 0, 20, -70, -20, -26, 0, -47, -84, -70, -14, 0, 52, -74, 44, -20, 0, 38, 18, -10, 20, 0, 0, -32, -38, 20, 0, -34, -3, -22, -64, 0, 40, -50, -12, -51, 0, 2, -14, -76, 32, 0, 30, -25, 64, -2, 0, -24, -138, -36, 60, 0, 34, 76, -10, -14, 0, 36, 68, 67, 32, 0, 110, 41, -14, -8, 0, 12, 66, -82, -14, 0, 4, -22, 58, -45, 0, -34, -46, 18, 135, 0, -3, 42, 104, -9, 0, 10, -48, 138, -20, 0, 12, -92, 8, -92, 0, -17, -14, -38, -48, 0, 100, 17, -88, -4, 0, 32, 165, -26, -98, 0, 70, 16, -112, 22, 0, -15, 20, 50, 14, 0, -32, -68, -52, -25, 0, -37, -58, -8, 16, 0, 92, -28, -8, -56, 0, 103, 58, -42, 120, 0, 44, 82, -134, -25, 0, -2, 16, 116, 174, 0, 12, -99, 2, 15, 0, 28, -212, 13, -7, 0, -14, 0, 6, 26, 0, -25, 82, -7, 60, 0, -7, 7, 9, 32, 0, -26, 18, 4, -26, 0, 120, 73, 25, 8, 0, 8, 68, -78, 0, 0, -28, -58, 130, -30, 0, 47, -168, 4, 30, 0, 4, -9, 10, -34, 0, 1, -8, 174, 142, 0, 222, -110, -34, -35, 0, -7, -8, 10, -2, 0, -72, -26, -36, -80, 0, -26, -90, -66, 4, 0, 66, -75, -96, -27, 0, 210, 12, 84, 62, 0, 108, 86, -9, 60, 0, -4, -22, -20, 70, 0, 28, -1, 12, 17, 0, -31, -26, 12, 68, 0, 4, 58, -70, 19, 0, 48, -10, -27, -20, 0, 53, -45, -52, -10, 0, -38, 112, 54, -42, 0, 92, 2, 56, 70, 0, -38, 196, -34, -32, 0, 36, 14, 30, -56, 0, 78, -10, 6, 72, 0, 110, 42, -56, -31, 0, 5, -90, 84, 64, 0, -64, -60, 162, 40, 0, -4, -101, 25, -156, 0, -5, -63, 184, 10, 0, -6, -78, 20, -168, 0, 34, 58, 32, -17, 0, 78, 4, -92, 22, 0, 64, -2, -10, -116, 0, 2, 3, -72, 206, 0, 24, 88, -108, 80, 0, 7, 80, -52, 38, 0, 80, -33, -23, -35, 0, -43, -100, 58, -6, 0, 4, 6, -222, 172, 0, 34, 144, -14, 91, 0, -16, 157, -48, -12, 0, 80, 58, -15, 160, 0, 6, 28, 34, 14, 0, 9, 44, -70, 74, 0, 150, 13, -2, 32, 0, -50, -40, -54, 134, 0, 42, 14, 146, -64, 0, -56, 86, 76, 78, 0, 158, -8, -34, -44, 0, 50, -140, 100, 38, 0, 178, -22, -50, 130, 0, 234, 42, 42, 68, 0, 3, 152, -44, 28, 0, -2, -48, 82, 334, 0, 100, -87, -52, -88, 0, 48, -150, 56, -11, 0, 156, -4, 62, -32, 0, -32, 46, 40, 134, 0, -18, 36, 42, -33, 0, -50, -29, 22, 94, 0, 128, 27, -30, 84, 0, -16, -120, 26, 96, 0, 136, -91, 8, -152, 0, 10, -94, -34, 158, 0, 6, -10, 44, -39, 0, 58, 72, 130, -10, 0, 8, 158, -12, 48, 0, 74, 4, 95, -104, 0, 118, 16, -26, -61, 0, -104, -108, -34, -106, 0, 40, -23, -140, 42, 0, 80, 10, -34, -144, 0, 120, -136, 38, -93, 0, -17, -52, -105, -20, 0, -108, -42, -100, -60, 0, -2, 264, -7, 170, 0, -22, -18, -65, -16, 0, 32, 7, -102, 68, 0, -184, -84, -18, 4, 0, -26, 162, 27, -2, 0, 18, 0, 136, -51, 0, 139, -98, -9, 98, 0, 0, -48, 190, -2, 0, 224, 76, -26, 28, 0, -144, 92, 36, 42, 0, 50, 92, 27, -61, 0, 60, -59, 118, -136, 0, 8, 184, 70, -79, 0, 2, 41, 38, 60, 0, -94, -32, -2, 0, 0, 200, 150, -36, 174, 0, 44, -80, 48, -28, 0, -116, -76, 50, -66, 0, -135, 154, -1, -6, 0, 94, 152, 41, -12, 0, 54, 108, -9, 230, 0, -66, -94, 34, -44, 0, -20, -166, -82, -42, 0, 160, -10, 136, 120, 0, 7, -142, 84, -248, 0, -14, 150, 8, 16, 0, -98, -40, 110, -92, 0, 52, -38, 48, -198, 0, -50, 88, -27, 32, 0, -132, -22, -284, 24, 0, -96, 174, -10, 16, 0, 4, 30, 38, 47, 0, 52, 48, 56, 188, 0, 18, 19, 9, 77, 0, -60, 92, 82, -12, 0, 100, -34, -24, -192, 0, 128, -16, -4, -180, 0, -76, 266, -140, -50, 0, -84, 3, 78, -18, 0, -97, -89, 54, -44, 0, 11, 152, 75, 40, 0, 88, -12, 0, 62, 0, -28, -58, 10, -138, 0, -95, 152, 66, -69, 0, -15, 12, 68, -206, 0, 210, 56, -36, 90, 0, 20, -98, 6, -98, 0, -198, 4, 34, 50, 0, -46, -196, -1, 100, 0, 0, 138, -90, -24, 0, -88, 106, 59, 86, 0, -70, 6, 20, -134, 0, -70, 10, 156, -20, 0, -120, -26, -60, -90, 0, -59, -160, -47, -226, 0, -84, 1, -112, -70, 0, 154, -14, 160, 4, 0, -116, 160, 52, -21, 0, -74, -54, 2, 44, 0, 52, -20, -104, -106, 0, 26, -154, 38, 68, 0, 18, 116, 38, -10, 0, -134, 20, -128, 200, 0, -108, 74, 0, -18, 0, -32, -76, -72, -38, 0, -38, 20, 2, 70, 0, -22, 176, -34, -72, 0, -3, 208, -140, -22, 0, 16, -64, 58, 40, 0, -60, -227, 40, -76, 0, -50, 92, 39, -12, 0, -24, -51, -252, 31, 0, -120, 66, 2, 142, 0, -14, -12, -204, -76, 0, -108, 32, -48, -240, 0, -6, 32, 30, -26, 0, -25, -378, -62, 64, 0, 18, -2, 128, 80, 0, -72, -303, -24, 122, 0, -138, -59, 58, -36, 0, 32, 60, 14, 68, 0, -96, -26, 34, 64, 0, 76, 72, -75, -10, 0, -184, -14, -120, -112, 0, 42, 202, 36, -160, 0, 68, -22, -28, 67, 0, -37, 32, 6, 138, 0, -220, 40, 110, -179, 0, 41, -218, -67, -14, 0, 108, -8, -206, -6, 0, -36, 56, 12, -28, 0, 66, 16, 26, -82, 0, -24, -14, -69, 48, 0, -68, 52, 4, -44, 0, -22, 8, -77, 58, 0, -24, -45, 222, 14, 0, 84, 112, -34, 13, 0, -46, 108, -26, 18, 0, -102, 135, 17, 94, 0, -198, 22, -3, -41, 0, 42, -108, 190, 104, 0, -144, -9, 64, -59, 0, -51, 188, 10, -132, 0, -48, 154, -8, 138, 0, 11, -20, -153, -78, 0, 104, -89, 12, 3, 0, -92, 70, 16, 8, 0, -8, -92, -74, 91, 0, 8, -78, -17, 11, 0, -14, 128, -18, -38, 0, 3, -48, -22, -26, 0, -88, -176, 100, 82, 0, 17, -80, 59, -88, 0, -44, -4, -98, 30, 0, -110, 10, 32, -110, 0, 165, -136, 392, -26, 0, 24, -98, -21, 38, 0, -286, 40, 70, -52, 0, 16, -148, -118, -112, 0, 156, 22, -212, -49, 0, 70, 152, -15, -28, 0, 20, -234, 41, 50, 0, -138, 14, -139, -382, 0, 116, -120, -32, -87, 0, -68, 50, 102, -52, 0, -88, -25, -188, 170, 0, -8, 146, -37, 20, 0, -58, 68, 12, -8, 0, -79, 16, -98, 116, 0, 80, -10, 92, -58, 0, -28, -372, 131, -8, 0, -44, -56, -140, -181, 0, -84, 106, 103, 12, 0, 58, -19, -152, -42, 0, -104, 120, -9, -156, 0, -8, 5, 44, 128, 0, 82, -196, 108, -134, 0, 62, -25, -28, -74, 0, -124, -346, -2, 144, 0, 16, 0, 82, 116, 0, 78, 174, 120, -12, 0, -66, -434, 12, 64, 0, -99, -352, 74, 2, 0, -100, 15, -258, -5, 0, -108, 233, 28, 6, 0, -212, 52, 18, 13, 0, -94, -7, -34, -274, 0, -88, 168, -14, -63, 0, 0, -256, -251, 6, 0, -84, 26, -376, 11, 0, -98, -28, -25, -22, 0, 82, 42, 98, -7, 0, -120, 60, -145, -42, 0, -316, 286, -7, 178, 0, 7, -304, 31, 9, 0, 32, 32, -158, 2, 0, 213, 78, -26, -136, 0, 18, 138, -50, 4, 0, -54, -26, -100, -40, 0, -122, -156, 120, 16, 0, 73, 96, -50, 25, 0, -180, 8, -4, 208, 0, -78, -116, 8, 70, 0, 68, -55, 92, -78, 0, 47, 0, -51, -112, 0, -2, -170, -28, 103, 0, -58, -332, -48, 130, 0, -316, -30, -424, -48, 0, 60, -160, 47, 136, 0, -168, 156, 100, 4, 0, -247, 30, 258, 46, 0, -12, -85, 4, -52, 0, -9, -270, 104, 10, 0, -328, -34, -16, 236, 0, -96, 82, 1, -68, 0, -8, -84, -6, 174, 0, 12, 142, -252, -126, 0, 110, -158, 222, -13, 0, -110, 236, 0, -34, 0, 32, -35, -80, -164, 0, 55, 382, -7, 8, 0, -8, 244, 238, 10, 0, 102, -2, -43, -4, 0, -78, -204, -72, 20, 0, -26, -202, -136, -36, 0, 56, -80, -86, -1, 0, -126, -308, -26, 40, 0, -90, -80, 16, -66, 0, 80, 4, -112, 102, 0, -36, -138, 66, -130, 0, -75, 130, -277, -96, 0, -18, -27, -8, 186, 0, 8, 181, 210, -618, 0, 12, 22, 16, 84, 0, -181, 62, 126, -70, 0, 41, -157, 108, -152, 0, 86, 74, -60, -9, 0, 162, 60, -52, 32, 0, -79, 170, -4, 280, 0, -22, 30, 212, -20, 0, 76, 70, -148, -142, 0, -14, 66, 28, 250, 0, -1, -74, 179, 12, 0, -386, 17, 18, 50, 0, 18, -200, -31, 44, 0, -26, -191, 90, 12, 0, -50, 68, 82, -352, 0, -48, 131, 4, 72, 0, 58, -176, 187, -70, 0, -296, 19, -82, -124, 0, -39, 8, 48, -66, 0, -10, 55, -2, -27, 0, -11, -20, -136, 42, 0, 4, -14, 53, 150, 0, -45, -148, -82, -52, 0, -200, -10, 118, 185, 0, 278, 352, -38, -10, 0, 112, 69, 63, 54, 0, 28, -42, 108, 2, 0, -174, -164, 92, -36, 0, 2, 112, 90, 56, 0, -96, 70, 36, 73, 0, -24, -278, -38, -102, 0, 196, 168, 74, -34, 0, -216, -32, -219, -144, 0, 144, 87, 36, 87, 0, 14, 212, 14, 30, 0, 4, -56, -144, -20, 0, -30, 228, 78, -184, 0, -10, -243, -8, 6, 0, -134, 72, 35, -6, 0, 187, 102, 110, 97, 0, 42, -130, 158, -56, 0, -466, -31, -352, 163, 0, -140, 304, 5, -366, 0, -90, -19, 110, 84, 0, 378, 64, -202, -244, 0, -444, 384, -64, -136, 0, -60, 38, -285, 162, 0, -192, 40, -248, -184, 0, 186, 14, -4, 10, 0, -101, -16, 236, 25, 0, -75, -156, -72, -262, 0, -84, 218, -5, 2, 0, -63, 70, 214, 184, 0, 288, 10, 40, 280, 0, -88, 84, -6, -40, 0, -78, 163, 134, 20, 0, 224, -168, -53, 44, 0, -282, -191, 34, 10, 0, 58, 112, -212, 32, 0, 158, -17, -46, 4, 0, -111, -24, 78, -146, 0, 4, 14, 22, -92, 0, -184, 22, 72, -156, 0, 46, 186, 64, 132, 0, -2, -394, 190, -10, 0, -74, -116, -376, 32, 0, -321, 50, 2, -130, 0, 3, -94, 130, -72, 0, 222, 206, -52, -36, 0, 92, -49, 24, 74, 0, 88, 50, -128, -108, 0, -2, 80, -2, 120, 0, -43, -44, 7, -10, 0, 80, 85, 146, -52, 0, -78, 38, 56, -100, 0, 230, -224, 80, -6, 0, -33, -46, -2, -23, 0, 318, -35, 40, -42, 0, 146, 341, -43, -4, 0, -100, -112, 124, 58, 0, -16, -6, -259, -236, 0, -128, 118, 4, 10, 0, 6, -26, -137, -222, 0, 58, 172, 196, 85, 0, 206, -74, 34, -184, 0, 144, -43, 262, -14, 0, 36, 91, 136, 130, 0, -244, 104, -16, 110, 0, 157, -280, 100, -48, 0, -208, -12, -4, 190, 0, -122, -368, 80, 160, 0, 58, 208, 234, -15, 0, 258, 160, -118, -114, 0, -102, 10, 6, 322, 0, 28, 284, -84, 34, 0, 16, 14, -252, -169, 0, 42, 242, 9, 190, 0, 44, -306, -4, -70, 0, 53, 74, 112, -168, 0, -4, 85, 150, 2, 0, 13, -84, 2, -2, 0, -298, 32, 82, 242, 0, 8, 246, -50, 68, 0, -40, -315, 208, -54, 0, -108, 134, -46, 14, 0, 136, 164, 42, -190, 0, 14, 172, 24, 146, 0, -90, -64, -126, -138, 0, 247, 108, -56, 34, 0, 86, 118, 188, 76, 0, 78, 78, -125, -38, 0, -54, -207, 158, 58, 0, -8, -154, -107, -34, 0, 128, -44, -78, 2, 0, 22, 122, 50, 236, 0, -140, 216, -88, 100, 0, 100, 38, -46, 68, 0, -6, -108, 178, 10, 0, -22, -148, 58, -50, 0, 22, 130, -202, 136, 0, -48, 100, 234, 0, 0, 42, -180, 142, 42, 0, 56, 68, 126, 168, 0, 112, -83, 3, 124, 0, 152, -140, 17, -44, 0, 22, 28, -480, -102, 0, -258, -246, -2, 66, 0, -48, 154, 158, 82, 0, 262, 334, 36, 174, 0, 52, -44, 100, 42, 0, -87, 148, 16, -52, 0, 70, -88, -88, -102, 0, -128, 30, 48, -110, 0, -150, 60, 324, 56, 0, -59, -11, 110, -540, 0, 414, -50, 156, 359, 0, -4, -86, 126, 62, 0, 20, -32, 20, -89, 0, -54, -160, -32, -48, 0, 46, 258, 68, 40, 0, -28, 134, -333, -16, 0, -112, 336, -18, 32, 0, 36, 48, -206, 42, 0, 314, -33, -40, 124, 0, 266, -130, -50, -246, 0, -29, 27, -132, 22, 0, -100, 94, 24, 408, 0, 164, 6, 128, -281, 0, 27, -122, 99, -30, 0, 100, 84, -36, 126, 0, 4, -56, -16, -48, 0, -120, -39, -80, 26, 0, 4, 96, -190, 328, 0, 300, 144, 136, 74, 0, -91, 70, -12, 8, 0, -418, -152, 158, -136, 0, 124, 336, 10, 433, 0, -94, 50, -34, -34, 0, -13, 158, 312, -24, 0, 24, -236, 6, -86, 0, -10, 62, 332, 44, 0, -20, -39, 32, 171, 0, -56, 64, 58, -96, 0, 72, -106, -247, 130, 0, 352, -10, -266, -248, 0, 14, -166, 8, -144, 0, 158, -280, 62, -12, 0, 214, 48, 96, 128, 0, 164, -100, 74, -318, 0, 4, -133, 18, 95, 0, -370, -104, 37, 198, 0, -140, -176, 118, -24, 0, 16, 138, -137, -26, 0, 186, -61, 32, -58, 0, 66, 262, -104, -260, 0, -108, 434, 106, -34, 0, 69, -106, -106, -48, 0, -156, 246, 40, -112, 0, -23, -530, -74, -140, 0, 284, 42, -70, -256, 0, -32, -36, 80, -18, 0, 10, -224, -178, -34, 0, -58, -144, -32, -134, 0, 264, -58, 120, 72, 0, -136, -350, -102, 38, 0, 110, -93, -78, -196, 0, 20, 486, -17, 108, 0, -52, 2, 194, -105, 0, 104, -20, 60, 84, 0, -84, 25, -108, 194, 0, -42, 160, 70, -100, 0, -438, -60, 180, 43, 0, 176, 12, -2, -38, 0, 264, -45, 219, -7, 0, 7, 170, -118, 150, 0, 248, 51, -22, -1, 0, -18, 442, 16, -65, 0, 114, -16, 38, 133, 0, -158, 60, 32, -2, 0, 7, 210, 68, -102, 0, 68, 68, -258, -104, 0, -344, -134, -184, 104, 0, -84, -156, 2, -18, 0, 124, 4, 82, -96, 0, 450, 466, -26, -192, 0, 162, -72, -140, 27, 0, -228, -2, 3, -64, 0, -74, 126, 18, -16, 0, 0, -92, 44, 136, 0, 398, -51, 24, -73, 0, 62, -276, 139, -384, 0, -98, -54, 198, -9, 0, 404, 98, -216, -142, 0, 164, -118, 0, 241, 0, -48, 58, -52, 190, 0, 0, -2, -12, -22, 0], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "705.2.c.b", "char_is_minimal": true, "conrey_index": 1, "id": null, "nf_label": 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, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [-1, 0, -1, -1, 0, -1, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 1, 0, -1, -1, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 0, 1, -1, 0, -1, 0, -1, -1], [-1, 0, -1, -1, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 0, 2, 0, 1, -1, 0, 0, 0], [-1, 1, 1, 0, -1, 1, -1, 0, 1, 0], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, -2, 2, 1, 0, 0, -1, -1, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 2, 0, 2, 0, 2, 0, -1, 0, 0], [-1, 1, -1, -1, 0, 0, 1, 0, 1, 2], [-1, 0, -1, -1, 0, -1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 0, 1, -1, 1, 2, 1, 2], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 1, 2, 0, 1, -1, 1, 0, 1], [0, -1, 0, -1, 0, -1, 1, 0, 3, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 0, 0, 0, 0, 1, 1, -1, 1], [-2, 2, 0, 0, -1, 1, -2, 0, 0, 0], [-2, 1, 0, -1, -1, 0, 0, 0, 0, 1], [-3, 2, -2, 0, 1, -1, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 0, 1, 1, 0, 1, 2, -1, 0], [-2, 4, 1, -2, 0, -1, 0, 3, 1, 2], [-1, 1, 0, 1, -1, 0, -1, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -1, -1, 1, 1, 0, -1, -1, 0, -1], [-1, 0, -1, -1, 0, 0, 0, 0, 0, -1], [3, -1, 1, 1, -1, 0, 1, -2, 1, 0], [-4, 0, -4, -1, 0, 0, 1, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 3, 0, 2, -2, 3, -2, -3, -1, -2], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 0, 2, 0, 1, -1, 0, 0, 0], [-1, 1, 1, 0, 1, 1, -1, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 1, 0, -1, 1, -1, 0, 1, 0], [1, 0, 0, -1, -1, 0, -1, -4, 0, -3], [-1, 0, 1, 0, 0, 0, 1, -1, -1, -2], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, -1, -2, 0, -2, -1, 0, -2, -1, 0], [-3, 0, -2, 2, 1, 0, 0, -1, -1, -2], [1, 2, 2, 1, -1, -2, -3, -1, 0, -1], [-2, -4, 0, 0, 0, 1, 1, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -1, 0, -3, 1, -1, 0, 2, 1, -1], [1, 2, 0, 1, -2, 2, 0, -3, -2, -2], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [-1, 1, -2, -3, 2, -1, 2, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 2, 0, 2, 0, -1, 0, 0], [1, -1, 1, -3, 0, -3, 3, 0, 0, 2], [-2, 2, -2, 1, 1, 0, 0, 0, -1, -2], [-1, 1, -1, -1, 0, 0, 1, 0, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 1, 0, 2, -1, 2, -1, 2, -1, -1], [-1, 0, -1, -1, 0, -1, 1, 0, 0, 0], [1, 0, -1, -1, 2, 1, 1, 1, 1, -2], [1, 0, 0, 0, -2, 0, -1, -3, -3, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 1, 0, 0, -2, 1, -3, -2, 0, -1], [-4, -1, -1, 0, -2, -2, 0, -1, -1, 0], [-2, 0, 0, 0, 1, -1, 1, 2, 1, 2], [-2, 1, 2, 1, 0, -1, -4, 1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 3, 1, -2, 1, -1, 0, 3, 2, 1], [-2, 1, 2, -2, -1, -1, -2, 2, -2, 0], [1, 2, 1, 2, 0, 1, -1, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -3, 1, -3, -2, -3, 2, 1, 1, 3], [0, -1, 0, -1, 0, -1, 1, 0, 3, 1], [4, 3, 4, 0, 1, 1, -2, 3, 0, 2], [2, -1, 1, 1, -1, 2, 0, -1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, -1, 0, -2, -2, -1, 2, -5, 1, 0], [-6, 1, -2, -1, 2, 0, 2, 4, 0, 3], [-3, 0, 0, 0, 0, 0, 1, 1, -1, 1], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 2, 0, 0, -1, 1, -2, 0, 0, 0], [2, -1, 2, -2, 1, -2, -1, 5, -1, 0], [-4, 1, -4, 1, 1, 0, -2, -3, -3, -4], [-2, 1, 0, -1, -1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}