# Stored data for newform 6422.2.a.bm, downloaded from the LMFDB on 25 April 2024.
{"label": "6422.2.a.bm", "space_label": "6422.2.a", "level": 6422, "weight": 2, "hecke_orbit": 39, "hecke_orbit_code": 171136785873639702, "dim": 14, "is_polredabs": true, "trace_hash": 1395596826901689901, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [358, -922, -4327, 6430, 4418, -8194, -817, 3996, -374, -912, 164, 98, -22, -4, 1]], [5, [-276992, -110848, 577856, 129888, -347888, -58424, 97813, 13004, -14806, -1516, 1245, 88, -55, -2, 1]], [7, [-48128, 26432, 179785, -97736, -186813, 87970, 71809, -24912, -13845, 2842, 1357, -130, -61, 2, 1]]], "qexp_display": "q-q^{2}+\\beta _{1}q^{3}+q^{4}+\\beta _{4}q^{5}-\\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": 25688, "fricke_eigenval": -1, "atkin_lehner_string": "+-+", "analytic_conductor": 51.279928178066264, "hecke_ring_index": 1, "level_radical": 494, "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": "0.007", "prec": 17}, "analytic_rank_proved": true, "char_values": [6422, 1, [4903, 4733], [1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 1, "level_primes": [2, 13, 19], "conrey_indexes": [1], "field_disc": 29809656188423305422166867968, "field_disc_factorization": [[2, 14], [3, 7], [13, 1], [251, 1], [491, 1], [1021, 1], [508585456297, 1]], "field_poly": [358, -922, -4327, 6430, 4418, -8194, -817, 3996, -374, -912, 164, 98, -22, -4, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.249", "prec": 17}, {"__RealLiteral__": 0, "data": "12.166", "prec": 20}, {"__RealLiteral__": 0, "data": "4.076", "prec": 17}, {"__RealLiteral__": 0, "data": "391.773", "prec": 24}, {"__RealLiteral__": 0, "data": "15.027", "prec": 20}, {"__RealLiteral__": 0, "data": "19506.304", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 14, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [13, -1], [19, 1]], "trace_display": [-14, 4, 2, -2], "traces": [0, 14, -14, 4, 14, 2, -4, -2, -14, 18, -2, -10, 4, 0, 2, 4, 14, 2, -18, -14, 2, 18, 10, 12, -4, 44, 0, 10, -2, 4, -4, -4, -14, -12, -2, 14, 18, -18, 14, 0, -2, -6, -18, 28, -10, -8, -12, 20, 4, 28, -44, 10, 0, 12, -10, -2, 2, -4, -4, -16, 4, 30, 4, -28, 14, 0, 12, -2, 2, -42, -14, -44, -18, 36, 18, 46, -14, 68, 0, 34, 2, -6, 6, -2, 18, 30, -28, 52, 10, -42, 8, 0, 12, 12, -20, -2, -4, -40, -28, -12, 44, 18, -10, 34, 0, 8, -12, -22, 10, 8, 2, 26, -2, 46, 4, 8, 4, 0, 16, -44, -4, 86, -30, -12, -4, 54, 28, 60, -14, 64, 0, -8, -12, 2, 2, -28, -2, 28, 42, 56, 14, 32, 44, 0, 18, 8, -36, 28, -18, 32, -46, 14, 14, 20, -68, 32, 0, 12, -34, -32, -2, 44, 6, -26, -6, 154, 2, -12, -18, 0, -30, -18, 28, 10, -52, -12, -10, 88, 42, -18, -8, 26, 0, 24, -12, -96, -12, -18, 20, -4, 2, 36, 4, -12, 40, 0, 28, 22, 12, 14, -44, -88, -18, -24, 10, 40, -34, -12, 0, 10, -8, -6, 12, 98, 22, 36, -10, 96, -8, 58, -2, 0, -26, -28, 2, 94, -46, -44, -4, 50, -8, -14, -4, -8, 0, 16, -16, -28, 44, 4, 4, -60, -86, 104, 30, 36, 12, 0, 4, 30, -54, 32, -28, 58, -60, 74, 14, 30, -64, 52, 0, 96, 8, -90, 12, 114, -2, -10, -2, -52, 28, 16, 2, 0, -28, -94, -42, 104, -56, -26, -14, -36, -32, -16, -44, -4, 0, 26, -18, -8, -8, 48, 36, 54, -28, 92, 18, -86, -32, 0, 46, 102, -14, 34, -14, -112, -20, -4, 68, 50, -32, 20, 0, 44, -12, -186, 34, 34, 32, -24, 2, -24, -44, -2, -6, 0, 26, 124, 6, -28, -154, -68, -2, 38, 12, -14, 18, 116, 0, 76, 30, -86, 18, 44, -28, 22, -10, 74, 52, 76, 12, 0, 10, -68, -88, 96, -42, 48, 18, -100, 8, 14, -26, 44, 0, 0, -24, 50, 12, 64, 96, -4, 12, 90, 18, 68, -20, 0, 4, -74, -2, 70, -36, -18, -4, 212, 12, 176, -40, 0, 0, -102, -28, 10, -22, 86, -12, 28, -14, -18, 44, -42, 88, 0, 18, 12, 24, -38, -10, -18, -40, -18, 34, 22, 12, 50, 0, 136, -10, -46, 8, -18, 6, 188, -12, 88, -98, 146, -22, 0, -36, -114, 10, 94, -96, -42, 8, -12, -58, -12, 2, -62, 0, 68, 26, -62, 28, 32, -2, 32, -94, 26, 46, 0, 44, 0, 4, 128, -50, -44, 8, 104, 14, -10, 4, 60, 8, -92, 0, -64, -16, -94, 16, 56, 28, -44, -44, -46, -4, 36, -4, 0, 60, 104, 86, -20, -104, -88, -30, -92, -36, 34, -12, 86, 0, 38, -4, -26, -30, 60, 54, 52, -32, -62, 28, 24, -58, 0, 60, 164, -74, 4, -14, -10, -30, -102, 64, -10, -52, 64, 0, -126, -96, 72, -8, 160, 90, -84, -12, 38, -114, 86, 2, 0, 10, 116, 2, -90, 52, -12, -28, 0, -16, -34, -2, -90, 0, 102, 28, -84, 94, -4, 42, 38, -104, 34, 56, 60, 26, 0, 14, 72, 36, -78, 32, -58, 16, 130, 44, 60, 4, 72, 0, 0, -26, -80, 18, 4, 8, -162, 8, 118, -48, 148, -36, 0, -54, -80, 28, 4, -92, -30, -18, -28, 86, -60, 32, -26, 0, 0, -46, 40, -102, -32, 14, 370, -34, 52, 14, 76, 112, 0, 20, 220, 4, -18, -68, 0, -50, -62, 32, -164, -20, -40, 0, -98, -44, 12, 12, 84, 186, 56, -34, -20, -34, 148, -32, 0, 24, -82, -2, 16, 24, 104, 44, 18, 2, -14, 6, -10, 0, -112, -26, 16, -124, 68, -6, 88, 28, -12, 154, 4, 68, 0, 2, -14, -38, 94, -12, 106, 14, -60, -18, -66, -116, 34, 0, -106, -76, 220, -30, 92, 86, -52, -18, 16, -44, 230, 28, 0, -22, 182, 10, 82, -74, -4, -52, -10, -76, 142, -12, -16, 0, 18, -10, -174, 68, 28, 88, 174, -96, 86, 42, -10, -48, 0, -18, 2, 100, -90, -8, -4, -14, -32, 26, -30, -44, 10, 0, 54, 0, 8, 24, 118, -50, -106, -12, -132, -64, 90, -96, 0, 4, -54, -12, -60, -90, 96, -18, 48, -68, -64, 20, -2, 0, 100, -4, 232, 74, 238, 2, 172, -70, 98, 36, 270, 18, 0, 4, -120, -212, -176, -12, 4, -176, 58, 40, -78, 0, 6, 0, -42, 102, 66, 28, 160, -10, 38, 22, -102, -86, 82, 12, 0, -28, 456, 14, -92, 18, -34, -44, 118, 42, -54, -88, 2, 0, 216, -18, 48, -12, 74, -24, 286, 38, -136, 10, -28, 18, 0, 40, 84, 18, 206, -34, 104, -22, -24, -12, -2, -50, -24, 0, 208, -136, 266, 10, 46, 46, 8, -8, 44, 18, 146, -6, 0, -188, 60, 12, -130, -88, -48, 98, 98, -146, 8, 22, 32, 0, -136, 36, 10, 114, -122, -10, 80, -94, -106, 96, 50, 42, 0, -8, -236, 12, -36, 58, 98, 12, -8, -2, 42, 62, 180, 0, -96, -68, 8, -26, 172, 62, -270, -28, -20, -32, 56, 2, 0, -32, -182, 94, -2, -26, -122, -46, -146, 0, 108, -44, -14, 0, -10, -4, 118, -128, -100, 50, 260, 44, -22, -8, -128, -104, 0, -14, -106, 10, -90, -4, -100, -60, -28, -8, -114, 92, -242, 0, 62, 64, -250, 16, -4, 94, -214, -16, -204, -56, 44, -28, 0, 44, 90, 44, -58, 46, 204, 4, 154, -36, 130, 4, -32, 0, -74, -60, 50, -104, 4, -86, -10, 20, -110, 104, -250, 88, 0, 30, 90, 92, -24, 36, 8, -34, -132, 12, 150, -86, 26, 0, -10, -38, 50, 4, 24, 26, 72, 30, -130, -60, 116, -54, 0, -52, 12, 32, -276, 62, -12, -28, -44, -24, -50, 58, 12, 0, -496, -60, 180, -164, 48, 74, -180, -4, -292, 14, -76, 10, 0, 30, 156, 102, -54, -64, -28, 10, -32, 52, -72, -64, -76, 0, 92, 126, -50, 96, 2, -72, -94, 8, -170, -160, -54, -90, 0, 84, -72, 12, -62, -38, -308, 114, 196, -86, 8, -2, 78, 0, 36, -10, 126, -116, -284, -2, -48, 90, 66, -52, -62, 12, 0, 28, -52, 0, 4, 16, 58, 34, 80, 2, 148, 90, -172, 0, 90, -102, -30, -28, -58, 84, 148, -94, -64, 4, 32, -42, 0, -38, 270, 104, -236, -34, -198, -56, -128, -60, -244, -26, 92, 0, -134, -14, 16, -72, 54, -36, 188, 78, -98, -32, 54, 58, 0, -16, -168, -130, 292, -44, 40, -60, -160, -4, -8, -72, 88, 0, -42, 0, 260, 26, 150, 80, -150, -18, 94, -4, 38, -8, 0, 162, -30, -8, 50, -118, -112, 48, -4, -148, -360, 36, -82, 0, -296, 54, 32, 80, -64, -28, -86, -4, -246, 92, 144, 30, 0, 18, 276, 28, 84, -86, 60, 60, -78, -32, -216, 26, -144, 0, 28, 0, 30, 46, -76, -40, -112, 102, -104, 32, 10, -14, 0, -370, -252, 34, 296, -52, -322, -14, -68, -76, 82, -112, -464, 0, 48, -20, 352, -220, -244, -4, 96, 18, 20, 68, -316, 0, 0, 50, 22, 62, -158, -32, 92, 164, -104, 20, -210, 40, 42, 0, 44, 98, 244, 44, 210, -12, -164, -12, -192, -84, -6, -186, 0, -56, -206, 34, -46, 20, -106, 34, 252, -148, -12, 32, 2, 0, 4, -24, -234, 82, 156, 2, -124, -16, 2, -24, -314, -104, 0, -44, 156, -18, -24, -2, 18, 14, 108, -6, 60, 10, -152, 0, 66, 112, 128, 26, 262, -16, -14, 124, -68, -68, 42, 6, 0, -88, -118, -28, 90, 12, 0, -154, -38, -4, -352, -68, -84, 0, 152, -2, -88, 14, -114, 38, 104, -94, -324, 12, 56, -106, 0, -14, 114, 60, 46, 18, -130, 66, 114, 116, 44, -34, -140, 0, -362, 106, 18, 76, -116, -220, -236, 30, 86, -92, 12, -86, 0, 52, -186, 18, 102, -16, 70, 44, 78, -230, 58, -28, -194, 0, -176, 22, 176, -182, -78, -10, 60, -82, -36, 74, -256, 4, 0, 52, -28, 10, -310, 76, 40, -142, 12, 12, -94, 16, -10, 0, -54, -18, -2, 10, -136, 174, -70, -68, -166, -28, -48, -88, 0, -174, -288, 96, -30, -86, 54, -42, -46, 10, -74, 48, 10, 0, 94, 18, -234, -2, -258, -100, 60, 90, -136, 8, 152, 4, 0, 14, 60, 32, 198, -26, 112, 30, 128, 44, 198, -10, -216, 0, -102, -54, 6, 0, -26, -8, -68, -24, -54, -118, -156, 50, 0, 106, -6, 12, -58, 132, -102, 64, 184, -90, 68, 96, -194, 0, 68, -4, 114, 54, -196, 12, -48, 60, -298, 90, -162, -96, 0, 18, 64, -48, -388, 68, -34, 64, 16, -20, -378, 2, 160, 0, -196, -100, -108, 4, 140, -232, -334, -74, -44, -238, -138, -2, 0, -172, -34, 70, -228, -98, 296, -36, -172, -270, -162, -18, -200, 0, -122, -4, 108, 120, 6, 212, 214, 176, 60, 12, -360, -4, 0, 176, 68, -58, -266, -40, 54, 78, 56, 0, 134, -6, -368, 0, -102, 42, -40, -102, -246, -66, -148, -28, -130, -160, -96, 10, 0, -38, -338, -22, 2, 102, -212, 86, 252, -82, -78, -12, -86, 0, 74, 28, -218, -456, 0, -14, 216, 92, -236, -18, -78, 34, 0, 44, 148, -118, 108, -42, -160, 54, -114, 88, -96, -2, -146, 0, -68, -216, -30, 18, 234, -48, 50, 12, 4, -74, 192, 24, 0, -286, -136, -38, 44, 136, 224, -10, -304, 28, 74, -18, -118, 0, -318, -40, -116, -84, -36, -18, -106, -206, 128, 34, -228, -104, 0, 22, -52, 24, -76, 12, 16, 2, -60, 50, -304, 24, 30, 0, -492, -208, 154, 136, -140, -266, -364, -10, -310, -46, -36, -46, 0, -8, 40, 8, 110, -44, -174, -18, 38, -146, 218, 6, -174, 0, 42, 188, 156, -60, -140, -12, 140, 130, -182, 88, 46, 48, 0, -98, -82, -98, 160, 146, 122, -8, 190, -22, -62, -32, 86, 0, -128, 136, -74, -36, -4, -10, -294, -114, -242, 122, -182, 10, 0, -80, -126, 94, -220, 106, -146, -96, 250, -50, -34, -42, -82, 0, 370, 8, 100, 236, -4, -12, 98, 36, -136, -58, 24, -98, 0, -12, 4, 8, 14, 2, -338, -42, -4, -62, 192, -180, -12, 0, 56, 96, 20, 68, -16, -8, 68, 26, 8, -172, -6, -62, 0, 270, 192, 28, -216, 20, 126, 32, 30, -56, -332, -2, 124, 0, 100, 32, -122, 182, -14, -94, 86, 2, 34, 26, 2, 122, 0, 46, -280, 146, 80, 0, -162, -108, -146, 44, 18, 14, 32, 0, 168, 10, -14, 4, -28, -118, 10, 128, -10, 100, 140, -50, 0, -260, -480, -44, 26, 22, -32, 8, -100, 128, 40, 104, -130, 0, -170, 14, 272, 106, -114, -10, 146, 90, 104, 4, -128, 100, 0, 60, -182, 28, -146, 8, 134, 114, 34, -92, 96, 242, 94, 0, -222, -62, -150, -64, -36, 250, -224, -16, 12, 4, -104, -94, 0, 214, 10, 16, -146, 204, 218, 56, -138, -44, -38, 28, 200, 0, -48, -44, 12, -90, -590, -44, 320, 58, -126, -46, -264, -204, 0, -4, -288, -154, -50, 36, 14, -130, -18, -4, 4, 32, -82, 0, 560, 74, 220, 60, 46, -50, -154, 104, 100, -4, 268, 86, 0, 10, -38, -20, 108, 110, -82, -104, 208, 250, 54, -88, 30, 0, -174, -30, 42, -90, -248, -92, -34, 24, 114, -36, -128, -8, 0, 34, 542, 132, 154, -12, -20, -150, -158, 86, 56, -26, 318, 0, 400, 10, 8, 38, -230, -50, 104, -4, -220, -24, 252, -26, 0, -72, -154, -30, 92, 130, -8, 60, 38, -116, 62, 54, 130, 0, -130, 52, 148, -12, 46, -32, -28, 276, -34, -62, -580, 12, 0, 28, 194, 44, -180, 24, 308, 50, -306, -58, -62, -12, -96, 0, -362, 496, 4, 60, 22, -180, 2, 164, -36, -48, -236, -74, 0, 180, 0, 4, -252, 292, 76, -14, 176, 76, 124, -10, 262, 0, 324, -30, -218, -156, -278, -102, -72, 54, 228, 64, -376, 28, 0, -10, -74, 32, -8, -52, 22, 72, 228, 64, 84, 76, -304, 0, -104, -92, 106, -126, -182, 50, 224, -96, -154, -2, 46, 72, 0, 94, 498, -8, -130, 170, -54, 160, 46, 54, -374, 90, -176, 0, -48, -84, -26, 72, 116, -12, 92, 62, -122, 38, 252, 308, 0, -114, -258, -196, 308, 86, 314, -8, -120, 2, -80, -78, 92, 0, -70, -36, -112, 10, 192, -126, -462, 116, 140, 284, -40, 2, 0, 48, -46, -90, -20, -66, -66, 52, -188, 62, -130, -12, 100, 0, 82, -28, 140, 52, -152, 0, -44, -4, 124, -16, -168, -58, 0, -34, 260, -80, -10, -2, 144, -148, -190, -90, -290, 172, -50, 0, -8, -90, 176, 102, 230, 30, -320, 28, 392, 58, -12, -84, 0, -148, -210, 94, 170, 64, -280, -4, 220, -32, 192, 42, -78, 0, 132, 38, 280, -270, 180, -104, -254, 236, -264, 34, 138, 198, 0, 56, -332, 128, 36, 60, 132, 244, -108, 26, -118, -92, -478, 0, 320, 134, 24, 14, 308, -16, 24, 72, -34, -54, 286, 36, 0, -188, -180, -78, 72, 98, -108, 32, 306, -54, 366, -58, 44, 0, 82, 16, -328, 168, -226, 130, 384, -292, 218, 44, -76, -40, 0, 60, 860, 160, -170, 4, 56, 8, 144, 72, 150, -88, 230, 0, 250, 42, -348, 0, 14, -260, 216, -26, 56, -150, -86, -80, 0, 150, -102, 18, 188, -94, 270, 4, 202, -38, 96, 8, 338, 0, 246, -162, 198, 30, -292, 8, 156, -50, 118, 118, 310, 112, 0, -48, -64, 4, 236, 148, 208, 360, -316, -36, 12, 82, 198, 0, -126, 296, -64, -54, -180, -32, 70, -80, 36, 64, 90, 28, 0, 86, -692, 4, 198, 246, -14, -92, 52, -144, -90, -30, 94, 0, -82, -18, -272, -276, -28, -28, -38, -84, -54, 86, -156, -60, 0, -60, -70, 78, -58, 32, 216, 216, -188, -26, 196, 144, 178, 0, 194, -28, 448, 0, -236, -30, -8, -46, 6, 76, 26, 40, 0, 112, -248, -102, -422, 104, 40, -32, -60, -10, 360, 14, -90, 0, 60, 370, -94, 252, -108, -34, -292, -296, 82, 52, 246, 322, 0, 14, -20, 68, -196, 76, 140, -82, -172, 112, 76, 464, -38, 0, -230, -48, 8, 20, 308, -352, -64, 220, 102, 244, 10, 4, 0, -96, -18, -18, 152, -20, 14, -68, -122, 316, -48, 0, -62, 0, 40, -50, 84, -22, -646, -62, 242, 158, -126, 32, -388, -92, 0, -164, 392, 104, -40, -20, 8, 210, -114, -40, 104, -42, 358, 0, -100, -44, -238, -98, 224, -244, -250, -44, 168, -210, -72, 12, 0, 164, 412, 12, 22, 192, -38, 84, -146, 6, -40, 186, 292, 0, 410, 56, -240, 206, -2, -34, -458, 46, 322, -20, -50, 106, 0, -34, 334, -252, -422, 148, 272, 12, 280, -32, 342, -2, -14, 0, 58, -4, -164, 24, -392, 234, -348, -82, 248, -156, -174, -2, 0, 124, -134, 16, 28, -2, 46, 24, -136, 314, 6, 104, -116, 0, -72, 44, -164, -156, -80, 18, 396, 24, -18, 2, 180, -18, 0, -14, 530, -108, -30, 6, -116, -60, -294, -10, -288, 152, 140, 0, -64, -66, -28, -112, -154, -128, 0, -26, 48, -262, 96, 16, 0, 14, -242, -124, 316, 68, 124, 68, 136, -42, 140, -6, 190, 0, 50, 88, -288, 118, -84, 28, 96, -90, 372, -12, -2, 0, 0, 154, -56, 38, 274, 4, 348, 352, -62, 68, 76, 84, 224, 0, -86, -152, 226, 2, -220, 88, -494, -14, 462, 114, 122, -38, 0, -104, 420, 94, 92, 324, -178, -12, -404, -56, 122, 106, -12, 0, -32, 14, 74, -114, 70, -60, -110, -46, 80, -18, 46, 130, 0, -66, -238, -114, 126, -116, -132, -44, -136, 34, 174, 140, 380, 0, -56, 362, -64, -106, -84, -18, -288, -76, 56, 116, -62, 220, 0, 236, -298, -30, 42, -86, -182, 92, 188, -12, -148, 86, -98, 0, 52, -52, 94, 186, 298, -18, 300, -102, 114, 16, 126, -70, 0, -44, -588, -78, -246, 230, -8, -58, -74, 28, 14, 194, -8, 0, 194, 176, -140, -22, 256, -176, -346, 182, 344, 78, -32, 10, 0, -60, 304, 82, 194, 36, 264, -74, 166, 256, 220, -4, 94, 0, 392, -52, 168, 28, -88, -10, 386, 310, 174, -76, -28, -40, 0, 142, 364, -12, 242, -12, 328, 94, -330, -16, -304, 10, 140, 0, 38, 54, -88, 18, 204, 2, -22, -10, -120, 136, -118, -174, 0, 70, -142, 68, -12, 166, -26, 28, -414, 48, -32, 88, 182, 0, -298, 174, 116, 288, -124, -96, 84, 30, 416, 86, 8, -54, 0, 42, -824, 46, 318, -10, 90, 74, 52, -48, 226, -10, 338, 0, 16, -94, -62, -18, 362, 234, -78, 2, -14, 258, -28, 100, 0, -60, -262, -90, -230, 136, 48, -8, -24, -152, -144, -4, 386, 0, -100, -14, -202, -60, -298, -32, 108, -198, 110, 26, 84, -112, 0, -30, -136, -128, 172, -44, 240, -198, -20, 10, 112, 216, -58, 0, 384, 102, -220, 54, -312, -6, -166, 0, 48, 26, 150, 8, 0, 68, 134, 24, -118, 54, -44, 118, 54, 156, 206, -50, -32, 0, -192, -106, 212, 6, 94, -12, -32, 58, 266, -132, 258, 102, 0, -64, 22, -184, 306, 90, 360, -68, -140, -96, 148, 194, -264, 0, -116, -68, -322, 4, 200, -114, 192, -54, -292, 196, -256, -12, 0, 48, -34, -60, -50, 298, -12, -90, 74, 162, -128, 96, -170, 0, -178, -18, 138, -64, -18, 48, 446, 388, 116, -68], "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": "494.2.m.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, 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, 0, 0], [0, 1, 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, 1, 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, 0, 0, 0, -1, 0], [-1, 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], [0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -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, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [-1, 1, 0, 0, 1, 0, 0, -1, 0, 1, 0, -1, 0, 1], [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], [-1, 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, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -2, 1, 0, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0], [1, -1, 0, 0, 0, 0, 0, -1, 1, 0, -1, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 1, 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, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0], [0, 1, 0, 1, 0, -1, -1, -1, 1, 0, -1, 0, 0, 0], [1, -1, 0, 0, -1, 0, 0, 1, 0, -1, 0, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 0, 0, 1, 0, 1, 1, 0, -1, -1, -1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -1, -1, 0, 1, 2, 1, 0, 0, 1, -1, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, -1, -1, 0, 0, 1, 1, 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, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, -1, -1, 0, 0, 1, 0, -1, 0], [-2, 2, -1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 1, 0], [1, 1, 1, -1, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0], [-2, 1, 0, 0, 1, -1, -1, -1, -1, 0, -1, -1, 1, 0], [-1, 1, 0, 0, 0, 0, 0, 1, -1, 0, 1, 0, 0, 0], [1, 0, 1, -1, 1, 1, 0, 0, 0, -1, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, -1, 0, 0, -1, -1, 1, -1, -1, -1, 0, 0, -1, -1], [-3, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0], [0, 2, -1, 1, 0, -1, -2, -1, 0, 2, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, 1, 2, 0, -1, -1, 1, 1, 0, -1, 0, 1], [0, -1, -1, 0, -1, -1, 0, -1, 0, 0, -1, 0, 0, -1], [-1, 2, 1, -1, -1, 2, 2, 1, -1, -1, 1, -2, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, -1, 0, 1, 1, 1, -1, 0, 1, 0, 0, 0], [-2, 2, 0, 0, 1, 0, -1, 2, 0, 0, 0, 0, 0, 0], [-1, 1, 0, 0, 1, 0, 0, -1, 0, 1, 0, -1, 0, 1], [3, 1, -2, 1, -1, -1, -2, 0, 1, 1, 0, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0], [-2, 1, 0, 0, -1, 1, 0, 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, 0, 0, 0], [1, 1, 0, 0, -1, 0, -1, -1, 0, 1, 1, 1, 0, 0], [1, -2, 0, 0, -1, 0, 0, 0, 0, 0, -1, 1, 1, -1], [0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 1, -1, -1, 1, 1, 1, 2, 0, -2, 0, -2, -1, 1], [-1, 0, 1, 1, 0, -1, -2, -1, 0, 0, -1, 1, 0, 0], [-4, 2, 0, -1, 1, 1, 1, 1, -1, 0, 1, 0, 1, 0], [-1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 1, -1, 1, -1, -2, -2, -2, 1, 1, -1, 1, 0, -1], [1, 0, 0, 0, 1, 1, 0, 0, -1, -1, 0, -1, 0, 0], [2, 4, 0, 0, 1, 0, -1, -3, 0, 1, 1, 0, -1, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, -1, 1, 0, 1, 1, 1, -1, -2, -1, 0, -1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -1, 1, -1, 0, 0, 1, 2, -1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 0, 0], [0, 0, 0, -1, -1, 0, 1, 1, 0, 0, -1, 0, 1, 0], [0, -1, 2, -1, 1, 2, 2, 2, -2, -2, 2, -1, -2, 0], [2, -2, 1, 0, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0], [1, 1, 2, -1, 0, 0, 0, 2, -2, 1, 0, 1, 1, 0], [-1, -1, -1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0], [2, 3, 0, 1, 0, -1, -2, 0, 1, 1, -1, -1, -1, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0], [-2, -1, 0, 1, -1, -2, -1, 0, 2, 0, -1, 1, 0, -1], [2, -1, 0, 0, -1, 1, 1, 1, 1, 0, 1, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 0, 0, 0, 0, 0, -1, 1, 0, -1, 0, 0, 0], [2, -2, 1, 0, 1, 0, 1, 0, -1, -1, 2, 1, 0, 0], [-1, 0, -1, 1, -1, -1, 0, 0, 0, 1, -1, 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, 0, 0, 0, 0], [-2, 2, -2, 2, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0], [-3, 1, 0, 0, 1, 1, -1, 1, 1, 1, 0, 0, 1, 1], [-2, 0, -3, -1, 1, 0, -1, -3, 3, 1, -2, -1, 1, 1], [3, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0]]}