# Stored data for newform 3525.2.a.bh, downloaded from the LMFDB on 19 April 2024.
{"label": "3525.2.a.bh", "space_label": "3525.2.a", "level": 3525, "weight": 2, "hecke_orbit": 34, "hecke_orbit_code": 148618787736784325, "dim": 13, "is_polredabs": true, "trace_hash": 470771603684215487, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [2, 12, -293, -107, 923, 309, -852, -288, 316, 106, -51, -17, 3, 1]], [7, [24064, 56192, -1792, -72464, -22104, 33677, 12580, -7272, -2388, 842, 172, -48, -4, 1]], [11, [-2451456, -6953472, -505856, 4668608, -98752, -1014460, 104072, 94552, -15976, -3548, 892, 17, -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": 8, "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": "0.004", "prec": 17}, "analytic_rank_proved": true, "char_values": [3525, 1, [2351, 1552, 2026], [1, 1, 1]], "hecke_ring_generator_nbound": 29, "inner_twist_count": 1, "level_primes": [3, 5, 47], "conrey_indexes": [1], "field_disc": 554216731101493391605760, "field_disc_factorization": [[2, 14], [5, 1], [6765340955828776753, 1]], "field_poly": [-2, 12, 293, -107, -923, 309, 852, -288, -316, 106, 51, -17, -3, 1], "hecke_ring_index_factorization": [[2, 3]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.224", "prec": 17}, {"__RealLiteral__": 0, "data": "10.712", "prec": 20}, {"__RealLiteral__": 0, "data": "7.347", "prec": 17}, {"__RealLiteral__": 0, "data": "360.639", "prec": 24}, {"__RealLiteral__": 0, "data": "347.793", "prec": 24}, {"__RealLiteral__": 0, "data": "19219.326", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 13, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[3, 1], [5, -1], [47, 1]], "trace_display": [-3, -13, 0, 4], "traces": [0, 13, -3, -13, 17, 0, 3, 4, -15, 13, 0, 16, -17, 8, -4, 0, 29, -12, -3, 28, 0, -4, 0, -6, 15, 0, 4, -13, 20, 12, 0, 26, -53, -16, 8, 0, 17, 4, -2, -8, 0, 24, 4, 6, 4, 0, 16, -13, -29, 21, 0, 12, 32, -6, 3, 0, 0, -28, 4, 34, 0, 24, -30, 4, 13, 0, 0, 24, -44, 6, 0, 20, -15, 6, 20, 0, 66, 2, -4, 6, 0, 13, -20, -14, -20, 0, 48, -12, 22, 36, 0, 4, -4, -26, 3, 0, 53, 32, 39, 16, 0, 4, -8, 28, -48, 0, 4, 2, -17, 22, 0, -4, 20, -16, 2, 0, 44, 8, 46, 0, 0, 79, -14, -24, 52, 0, -4, 40, -95, -6, 0, 52, -4, 16, -60, 0, 76, -52, -16, 50, 0, 13, 42, -12, 29, 0, 58, -21, 48, 38, 0, 16, -10, -12, -136, 0, -32, 8, -16, 6, 0, 50, -3, 16, 8, 0, -8, 46, 0, 25, 0, 28, 8, -40, -4, 0, 28, -34, 50, -4, 0, -14, 24, -24, 16, 0, 30, 20, -17, -4, 0, 18, -13, 58, -2, 0, 83, -40, 0, 26, 0, -24, 70, -50, 44, 0, 6, -6, 94, 10, 0, 44, 30, -20, -18, 0, 15, 12, 30, -6, 0, -46, -20, 30, 10, 0, -14, 6, -66, -4, 0, -2, 36, -22, 4, 0, 62, -6, 196, -8, 0, 10, 3, -13, -20, 0, 20, 152, -34, 14, 0, 52, 20, 28, -116, 0, -11, -30, -48, 78, 0, 12, 86, -48, -22, 0, 22, -36, 202, 62, 0, 42, -98, -4, -8, 0, 4, -8, -30, 26, 0, 28, -3, 52, -38, 0, 4, 20, -53, 21, 0, -32, 64, -34, -39, 0, 58, -16, -42, 76, 0, -54, 14, -4, 56, 0, 8, 20, 68, -28, 0, 52, 48, 44, 62, 0, -32, -50, -4, 22, 0, -2, 82, -40, 17, 0, 40, -22, 22, -4, 0, 36, 52, 4, -78, 0, -20, -28, -51, 16, 0, 18, -2, 68, -28, 0, -32, 26, -44, 4, 0, -8, -66, -60, -46, 0, 44, 0, 122, 76, 0, 47, 58, -79, -96, 0, 14, 82, 100, 24, 0, 74, -52, 36, -8, 0, 15, 14, 4, 34, 0, -40, -22, -32, 95, 0, -130, 6, 216, -4, 0, -16, -21, -52, -28, 0, 4, 20, -74, -16, 0, -24, 60, 4, -152, 0, 32, -14, -76, 30, 0, 52, 36, -54, 16, 0, -148, -50, 192, 164, 0, 6, 54, -13, 12, 0, -42, 92, -44, 12, 0, 38, -29, 40, -88, 0, -104, 40, -58, 26, 0, 21, -50, 28, -48, 0, -20, -38, -52, -4, 0, 80, 16, -16, -32, 0, 10, -84, 26, 12, 0, -70, 136, 24, -44, 0, -90, -34, 32, 0, 0, -8, 14, -30, 16, 0, -96, -6, -142, 32, 0, -32, 44, -50, 105, 0, 3, 32, -28, -16, 0, -2, -8, 46, -28, 0, -16, -60, 8, 8, 0, -46, -234, -2, 0, 0, 0, -25, 124, 100, 0, -8, 71, -28, -40, 0, -8, -16, -112, 40, 0, -62, 4, -8, 88, 0, -88, -16, -28, -23, 0, 34, -202, 10, -50, 0, -216, 4, -142, 168, 0, -88, -78, 14, 136, 0, -24, 58, -32, 24, 0, 82, -16, -36, -262, 0, 64, 22, -30, 136, 0, -20, -112, 28, 17, 0, -162, 4, 154, 82, 0, 136, -110, -18, 0, 0, 13, -18, -95, -58, 0, -150, 2, -8, -86, 0, 2, -60, -83, -16, 0, 40, -112, -4, 0, 0, 6, -26, -120, -20, 0, -14, 112, 24, -286, 0, -70, 40, -214, 50, 0, -8, -44, 188, 46, 0, -318, -70, -6, 190, 0, 6, -144, 102, -94, 0, -28, -10, 4, -96, 0, -56, -146, -44, -126, 0, -30, 126, 168, 20, 0, -114, 18, -8, -6, 0, -52, 80, -15, 56, 0, -12, -52, -58, -30, 0, 16, 6, 4, 168, 0, -48, 160, 46, -124, 0, 20, -28, 200, -30, 0, 128, -10, 130, -96, 0, -79, -120, 14, -90, 0, -6, -216, 24, 66, 0, -292, 4, -56, -10, 0, 92, -52, 2, -204, 0, -36, 38, -130, 22, 0, -52, -4, 34, -200, 0, -50, 2, -62, 32, 0, 6, 118, -124, -196, 0, -304, 8, 98, 88, 0, -180, -69, -10, -168, 0, -3, 80, -32, 13, 0, 112, 20, 12, -156, 0, -190, -174, -20, -58, 0, -152, -92, 40, 34, 0, -230, -14, -174, -176, 0, 2, -29, -52, -134, 0, -20, -2, -40, -28, 0, -36, 116, 96, -136, 0, -156, -100, 11, 14, 0, 30, -28, -38, 48, 0, -96, -78, 114, 112, 0, -166, 160, -12, 35, 0, -86, -66, -128, 48, 0, -108, 22, 24, -12, 0, 34, 22, -22, 12, 0, 36, -82, 122, -202, 0, 62, -62, 46, 30, 0, 6, -36, -42, -162, 0, 98, 88, -62, 4, 0, -4, 8, -16, 50, 0, -26, -30, -4, -106, 0, 8, 76, -226, 30, 0, -278, -26, -86, -8, 0, -185, -154, -28, 16, 0, 3, 292, -16, -52, 0, 20, 38, 124, -290, 0, -60, 2, -4, 24, 0, -20, -78, 10, 53, 0, 8, -21, 210, -72, 0, 48, 262, 32, -22, 0, -64, 82, -156, 34, 0, -32, 39, 84, -250, 0, -224, 24, -58, 56, 0, 16, -70, -28, 42, 0, -12, -76, -136, 60, 0, -94, -78, 54, -290, 0, -14, 168, -8, 4, 0, -22, -56, 130, -98, 0, -112, -42, -8, 100, 0, -20, 28, 8, -68, 0, 64, 28, -130, -76, 0, 134, 184, -52, 16, 0, -48, 132, 240, -44, 0, -62, -62, 136, -32, 0, 8, 36, 32, -28, 0, 50, 188, -238, 4, 0, 12, -22, -162, -72, 0, -151, 408, 2, 100, 0, -82, 112, -131, 40, 0, 200, -17, 190, 60, 0, -44, -148, -40, 136, 0, 22, 18, -24, -22, 0, -26, 4, 220, -78, 0, -26, -50, -36, 50, 0, -52, 206, 98, -4, 0, 76, 78, -32, 112, 0, 124, 20, 20, 60, 0, 28, -160, 172, 51, 0, -168, -16, 94, 64, 0, -50, -340, -18, -51, 0, 2, 144, -196, -68, 0, -16, 28, 20, 0, 0, 32, -100, 32, -132, 0, -26, -102, 64, 44, 0, -64, -4, -54, 72, 0, 110, 14, 8, -26, 0, 66, 16, -225, 60, 0, 4, 46, 30, 186, 0, -94, 82, -44, -10, 0, 0, 350, -114, -122, 0, 238, -76, -256, -100, 0, 6, -180, -47, 184, 0, -58, 16, -36, 79, 0, 124, 96, 140, -48, 0, -60, 104, -14, 194, 0, -82, -140, 76, -100, 0, 32, -24, 60, 42, 0, 84, 6, -74, 18, 0, 52, 104, 72, -36, 0, 2, 8, -16, 276, 0, 120, -28, -15, -70, 0, -14, 172, 22, -4, 0, -240, -34, 112, -32, 0, -172, 142, 40, 132, 0, 22, 70, 36, 32, 0, 132, -95, 36, 56, 0, 157, -144, 130, 2, 0, -6, -328, 32, -216, 0, -96, 4, 52, 38, 0, 94, 4, 16, -140, 0, 21, 160, 66, 52, 0, -66, 28, -80, -26, 0, -226, 132, -4, 94, 0, -20, -230, -52, 74, 0, 224, 16, -154, -58, 0, 52, 170, 24, -312, 0, -60, -92, 210, -4, 0, 48, 152, 164, 232, 0, 86, -320, -32, -18, 0, 14, -4, 288, 76, 0, -168, -30, -184, -8, 0, 188, 556, -52, -226, 0, -36, 104, -18, 54, 0, -248, -16, -32, 288, 0, 340, -2, 148, 74, 0, 50, -134, -46, -192, 0, 280, -164, -124, 146, 0, 58, 146, -6, 64, 0, -54, 28, 156, 13, 0, 26, -12, 68, 266, 0, 44, 56, 42, -60, 0, -92, 160, 52, 44, 0, 86, -12, -58, 142, 0, -46, -320, -38, 92, 0, 29, 152, 176, -40, 0, 58, 88, -236, -12, 0, 32, 70, 104, -24, 0, -40, -200, -76, 58, 0, -20, -26, -194, 8, 0, -112, 196, -21, 184, 0, 50, 100, 64, -28, 0, 252, 48, 40, -24, 0, -326, -92, 20, -110, 0, 38, -74, 52, 52, 0, 168, 4, -320, 110, 0, -44, 83, -80, 124, 0, -16, 22, 146, 16, 0, -88, 32, -12, 368, 0, -44, -48, -10, 29, 0, 84, 228, 214, -26, 0, 44, -12, -64, -124, 0, 12, -218, 70, -80, 0, -136, -80, -88, -24, 0, -46, 44, -34, 86, 0, 200, -272, 90, 60, 0, 34, -34, -4, -32, 0, 412, 0, 86, -38, 0, -116, 4, 8, -100, 0, -14, -12, -316, 30, 0, -114, -16, -108, 132, 0, 204, 70, 96, -28, 0, 6, 324, 20, 142, 0, 228, -32, -58, -260, 0, -40, -180, 32, 135, 0, -44, -80, 318, 50, 0, 216, -105, 28, -180, 0, 162, -26, -3, 212, 0, -32, -428, -86, 28, 0, -108, 16, 180, 42, 0, 138, 32, 2, 140, 0, 8, -70, -66, -46, 0, -2, 28, -22, 402, 0, -192, -102, 16, 96, 0, 60, -180, -156, -8, 0, 296, -8, -434, 178, 0, 22, 266, 46, 53, 0, 234, -104, 142, 2, 0, 94, 0, 140, -274, 0, 40, 32, 0, 46, 0, 25, -222, 90, -124, 0, 196, -100, -162, 6, 0, 262, -254, 8, 56, 0, -71, 28, 82, 28, 0, -176, 40, 20, -158, 0, 274, 212, 8, -126, 0, 16, 260, -166, 112, 0, 200, -40, -172, 86, 0, -78, 244, 62, -220, 0, -4, 140, -45, 8, 0, 280, -88, 94, 164, 0, 372, -128, 88, 190, 0, 16, 2, -128, 28, 0, 134, 23, -132, -186, 0, 38, -114, -34, 212, 0, 202, 6, -8, -10, 0, 198, 50, -178, -122, 0, 192, 2, 216, -40, 0, -4, -72, 218, 142, 0, -188, -168, -4, -88, 0, -84, -370, 88, 104, 0, 78, 46, 208, -14, 0, 16, -136, -160, 188, 0, -48, 94, 24, -120, 0, -58, -116, -16, 32, 0, 386, -24, -248, 34, 0, 300, -26, -82, -92, 0, 16, 164, 186, 36, 0, -166, 262, -184, -316, 0, 26, -86, -64, 2, 0, -22, 356, 174, 30, 0, 396, -136, 106, 112, 0, -115, 53, 20, 362, 0, 112, -360, 90, -28, 0, -100, -17, 36, -366, 0, 48, -170, 162, 106, 0, -4, 212, 180, -154, 0, 136, -82, -36, -22, 0, 112, -200, -136, 200, 0, 110, 52, 250, 18, 0, -172, 0, -200, 214, 0, 16, -122, -13, -126, 0, 18, 60, 46, 95, 0, -320, 58, -58, -4, 0, -50, -206, 150, -124, 0, -2, 256, 198, 8, 0, 6, 86, 20, -340, 0, 288, -184, -2, -214, 0, 60, -524, -68, 83, 0, -124, 16, 308, -82, 0, 274, 492, -40, 160, 0, 112, 188, -60, 4, 0, 128, 0, -134, 180, 0, 2, 82, -6, -146, 0, 26, -132, -232, 120, 0, -4, 20, -12, 212, 0, -32, 316, 14, -224, 0, -112, -76, 380, -24, 0, -86, 286, 268, 214, 0, -56, -122, 70, 2, 0, -40, 194, 86, 214, 0, 288, -50, -112, 36, 0, -6, 186, 8, 140, 0, 44, 24, -190, -188, 0, -148, -46, 152, -82, 0, -32, 74, 318, -103, 0, 70, -194, -52, 6, 0, 116, -190, -214, 156, 0, 124, 566, -6, -48, 0, 144, -224, -332, -102, 0, 180, 94, 22, 162, 0, 226, 22, 28, -172, 0, 10, -194, -64, -4, 0, -272, 96, -222, -60, 0, 170, -116, 56, 272, 0, 146, 88, -66, 44, 0, 26, 126, -256, -186, 0, 30, 86, 30, -54, 0, -126, -422, -78, -168, 0, 176, -20, 76, -12, 0, -90, -215, 114, -2, 0, -18, -24, -112, 8, 0, 316, 6, -160, 18, 0, 185, -8, 52, -32, 0, -80, -430, 88, 15, 0, 198, -56, -280, 4, 0, 92, 74, 12, -88, 0, 52, 62, 20, 58, 0, -52, 30, -116, -18, 0, -28, 186, -16, -126, 0, -6, -38, -130, -4, 0, -346, -168, 112, 108, 0, 34, -278, 48, 92, 0, -160, 72, 86, -46, 0, -214, 124, -48, 252, 0, 240, -46, -20, 168, 0, 28, -420, 68, -200, 0, -32, 30, -522, -10, 0, 18, 500, -128, -58, 0, 10, -72, 94, -130, 0, -6, 96, -208, 266, 0, 166, -140, 79, 72, 0, 120, 56, -204, -14, 0, -132, 90, -106, -396, 0, -350, -48, 6, 90, 0, 216, 30, 425, -24, 0, 272, -66, -212, 44, 0, 374, -74, 292, 214, 0, -4, -228, -58, 56, 0, -84, 10, -4, -52, 0, 88, -230, -92, 126, 0, 52, 48, 378, -2, 0, -20, 204, -182, -182, 0, -136, -188, 36, -126, 0, -38, -556, 118, 130, 0, 156, -22, 44, 316, 0, -102, -350, 52, -200, 0, 4, 68, -116, -34, 0, 160, 200, 46, -138, 0, -13, 12, 50, -88, 0, -2, 182, 174, 62, 0, 52, -32, -48, -58, 0, 176, 444, -6, 262, 0, -118, 236, -122, 124, 0, -198, 196, -116, -336, 0, 136, -34, 304, -24, 0, -8, -486, 58, -98, 0, 472, -88, -324, -144, 0, -10, -16, 180, -84, 0, 69, -40, 128, 10, 0, 26, 168, 60, 318, 0, 196, 54, 3, -94, 0, -80, -194, 112, 32, 0, -352, -13, 76, 36, 0, 120, 96, -112, -76, 0, -20, -122, -34, -12, 0, 96, 156, -184, 356, 0, 84, -32, 190, 13, 0, 174, -388, -4, 20, 0, -414, 58, -58, 16, 0, -78, 456, 152, 102, 0, 92, -140, -160, -40, 0, -16, -34, -228, -12, 0, -104, 58, 230, 94, 0, 14, 130, -146, 174, 0, -230, 176, -380, -126, 0, 112, -280, -2, -4, 0, 29, 196, 368, 52, 0, 290, 134, -28, -88, 0, 92, 128, 20, -392, 0, 2, 178, -112, 40, 0, 294, 28, 190, -180, 0, -114, 428, 36, 384, 0, -116, -160, -338, -96, 0, -124, 136, 24, -28, 0, -118, -122, 156, 172, 0, 100, -154, -21, -11, 0, 254, -14, -242, 8, 0, 242, -49, -30, 282, 0, 28, -108, 212, 38, 0, -100, -48, -258, 8, 0, -22, -194, 96, -4, 0, 78, 110, -40, -114, 0, -202, -112, -304, -98, 0, -104, 86, 166, 84, 0, -160, -196, 396, 12, 0, 228, -35, -140, -414, 0, -108, 282, 86, -82, 0, 66, 98, 76, 128, 0, 64, -48, -280, -326, 0, 98, 248, 108, 176, 0, -22, 396, -214, -24, 0, -98, 12, -42, 286, 0, 278, -46, -34, -16, 0, -22, -556, -78, 22, 0, -156, -12, -148, -94, 0, 101, 238, -36, -4, 0, 82, 178, 156, -122, 0, 490, 202, 368, -4, 0, -520, -38, -62, 152, 0, 62, -296, 18, -46, 0, 316, -30, 88, -46, 0, -24, -678, -6, 264, 0, 36, 148, -136, 42, 0, -192, 162, -254, -32, 0, -120, -66, -98, 82, 0, -88, 300, 220, 62, 0, 294, -4, -130, 160, 0, -226, 258, 4, -270, 0, -8, -170, -28, 16, 0, 82, -50, -106, 260, 0, 324, 94, 26, -254, 0, 30, 326, 100, 4, 0, 156, 106, -358, 56, 0, 6, 286, -8, -24, 0, -76, 244, 334, 226, 0, -138, -30, -104, -148, 0, 34, 208, 278, -48, 0, 26, -372, 42, 86, 0, -250, 8, 414, 124, 0, -110, -276, 185, 212, 0, 154, -20, 122, 28, 0, 24, -16, -308, 640, 0, -8, 4, -3, -64, 0, -292, 24, -70, 16, 0, -342, 52, 114, -226, 0, -58, 410, -20, -82, 0, -38, -16, 78, -124, 0, -138, 290, 12, -378, 0, 188, -24, 60, -142, 0, -2, -304, -24, 4, 0, 146, -24, -452, 16, 0, -126, 470, 20, 202, 0, 78, -272, 148, -10, 0, -106, -53, -12, 20, 0, 170, 286, -8, 112, 0, 21, -186, -172, -210, 0, -12, 72, -40, -78, 0, -74, 368, -48, 10, 0, -262, -148, 928, -32, 0, -242, 22, 0, 372, 0, -30, -186, 64, -92, 0, -82, 0, 92, 156, 0, -100, -34, -162, -296, 0, -182, 562, 32, -160, 0, -39, 2, 96, -84, 0, 12, 250, 220, 20, 0, -180, -422, 224, 378, 0, -24, -410, -98, 58, 0, 116, -56, 284, -134, 0, -156, 576, -16, 512, 0, 70, 190, 280, 28, 0, -348, -42, -88, 768, 0, -312, 82, 12, -278, 0, 76, 532, 10, 136, 0, 122, -60, -274, 20, 0, 86, -572, 94, 149, 0, 78, 20, 328, -54, 0, -78, 290, -136, -94, 0, 128, 448, 14, -158, 0, -168, -166, 172, 8, 0, -4, -4, -272, 68, 0, -146, 352, 22, 668, 0, 56, 162, 225, -130, 0, -196, 98, -272, -520, 0, -240, -258, 112, -116, 0, 42, -100, -28, 8, 0, 218, -100, -356, -88, 0, -148, 520, 20, 478, 0, -28, 22, 18, -8, 0, 192, 68, -34, 282, 0, 60, 150, -64, -112, 0, -28, 124, 308, 130, 0, -234, 76, -532, -144, 0, -142, -618, -134, -84, 0, -184, 104, 156, 52, 0, -44, -16, 222, 216, 0, 258, -314, 48, -319, 0, -132, -110, 270, -240, 0, -292, 44, 250, -64, 0, -192, 240, 62, 94, 0, 62, 120, -250, -136, 0, -208, 32, -30, 438, 0, 150, 22, -8, -498, 0, -36, 174, -218, -32, 0, -32, 28, -38, -180, 0, 82, -234, -50, -432, 0, -188, -104, -2, 238, 0, -42, -4, 48, -516, 0, -266, -24, -12, -118, 0, 22, -124, 14, 162, 0, -138, 72, -84, -246, 0, -16, -356, 151, -222, 0, -408, -162, -175, -2, 0, -58, -100, 86, 134, 0, -320, -126, 82, 36, 0, -112, -398, 80, 131, 0, 236, -40, -316, -4, 0, -20, 272, -200, 30, 0, 17, -288, -206, -190, 0, -216, -60, -12, 188, 0, -128, -142, 44, -50, 0, 148, -280, 82, 40, 0, -568, -136, -196, 68, 0, -418, 36, -22, -148, 0, -18, 484, -256, 24, 0, -92, 22, 28, 432, 0, -292, -24, 26, -96, 0, -4, -130, -234, -220, 0, 356, 78, -100, -358, 0, 200, -180, 26, 66, 0, 50, 444, -108, 36, 0, 148, -50, -324, -330, 0, -100, 174, 52, 42, 0, -206, -158, -90, -98, 0, -16, 4, -206, -8, 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.c", "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, 0, 0, 0], [1, 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], [-1, 0, 0, 0, 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, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0], [-1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 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, -1], [-1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, -1, 1, -1, 1, 0, -1, 0, -1, 0, 2, -2, 0], [0, -1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, -1, 0, 2, 0, 0, 0, -1, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -1, 0, 0, 1, -1, 1, 1, -1, -2, 2, 0], [1, 0, 0, -1, 0, 0, -1, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0], [-4, 0, -2, 0, -1, 0, 0, 0, 0, -1, -1, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 1, 1, -2, 1, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 1, 0, -1, 0, 2, 0, 0, 1, -1, 0, 0], [0, -3, 1, 1, -1, 0, 2, 0, 0, 0, -1, 1, -1], [-1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, -1, -1, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, -1], [1, -1, 1, 1, -1, -1, 1, -1, 0, 0, 0, 0, 0], [0, 0, 2, 1, -2, 1, -1, 1, -1, 0, 0, 2, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, -1, 0, 1, -1, -1, -1, -1, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 0, 0, -1, -1, 1, 1, 1, -1, -2, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [3, -1, 0, -1, 1, 0, 0, 1, 2, 1, 1, 0, 1], [-1, 0, -1, -1, 0, 0, -1, 1, 1, -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, 0, 0, 0, 0, 0], [0, -2, 0, -1, 2, 0, 0, -1, 0, -1, 1, -2, 2], [-2, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0], [0, -2, 2, 1, 0, 1, 0, 0, -1, 0, 0, 0, -1], [3, -2, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 1, 1, 1, -1, 0, 0, 0, -2, 1, 0, 0, -1], [-1, -3, 0, 0, 1, 0, 0, 0, 0, 1, 1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0], [1, 4, 0, 0, 0, 0, -1, 0, 1, 1, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, 1, -1, 0, 1, 0, 1, 0, -2, 2, 0], [1, 1, 1, 0, 1, 0, -1, 0, 0, -2, 0, 0, 1], [-3, -1, 0, 1, 1, 1, 0, -2, -2, -1, 1, 0, 1], [0, 1, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, -2, -2, 0, 0, -2, 1, 0, -1, 1, 0, 1], [-1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -2, 2, 1, 0, 1, -1, 1, -1, 1, 1, 0, -1], [3, -2, 0, -1, 0, -2, 1, 0, 1, 1, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, -2, 1, -2, 2, 0, -1, 1, 1, 1, 3, -1, 2], [-1, 3, 1, 2, 1, 0, -1, 0, -1, 0, -2, 0, -2], [0, 1, 0, 0, 1, 0, -2, 0, 0, 0, 1, 0, 0], [1, 1, 1, 2, -1, -1, 1, -1, -1, 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], [-2, -1, 2, 2, -1, 0, 2, -1, -1, -1, -1, 0, 0], [-1, 0, 1, 0, 0, 1, -2, 1, 0, 0, 2, 0, -1], [-1, 0, 1, 0, 0, -1, 1, -1, -1, 1, 2, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -1, -1, -1, -1, 0, 0, 2, 1, 1, -1, 0, 0], [-1, 0, 0, 1, 0, 0, 1, 0, 0, 0, -1, 0, 0], [4, -2, 1, -1, 2, 0, -1, -2, -1, 3, 5, -2, 2], [2, -2, 1, 1, 2, 1, 1, -1, -1, -1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, -1, 2, 1, 0, 1, -1, 1, -1, -3, 0, 0], [1, -2, -2, -2, 2, 0, -4, 2, 2, 0, 1, 0, 1], [-2, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 2, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0], [2, -1, 1, -1, 1, 0, -1, 0, 1, -1, 1, 0, 0], [4, -4, 0, -2, 1, -2, 3, -1, 1, 0, 2, -2, 2], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}