# Stored data for newform 4025.2.a.y, downloaded from the LMFDB on 18 April 2024.
{"label": "4025.2.a.y", "space_label": "4025.2.a", "level": 4025, "weight": 2, "hecke_orbit": 25, "hecke_orbit_code": 108086391090450361, "dim": 12, "is_polredabs": true, "trace_hash": 966647708541160906, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [17, 58, -81, -210, 170, 244, -162, -120, 71, 26, -14, -2, 1]], [3, [-8, -60, 75, 672, 669, -372, -581, 68, 174, -4, -22, 0, 1]], [11, [-7392, -28480, 21040, 45752, -6026, -19422, 3, 3456, 188, -274, -25, 8, 1]]], "qexp_display": "q+\\beta _{1}q^{2}-\\beta _{6}q^{3}+(1+\\beta _{2})q^{4}+(-1+\\cdots)q^{6}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 16100, "fricke_eigenval": 1, "atkin_lehner_string": "-+-", "analytic_conductor": 32.13978681356535, "hecke_ring_index": 1, "level_radical": 805, "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": "0.006", "prec": 17}, "analytic_rank_proved": true, "char_values": [4025, 1, [2577, 1151, 3501], [1, 1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [5, 7, 23], "conrey_indexes": [1], "field_disc": 18351441299517730816, "field_disc_factorization": [[2, 12], [12277, 1], [312757, 1], [1166839, 1]], "field_poly": [17, 58, -81, -210, 170, 244, -162, -120, 71, 26, -14, -2, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "10.187", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "281.643", "prec": 24}, {"__RealLiteral__": 0, "data": "80.060", "prec": 20}, {"__RealLiteral__": 0, "data": "13092.858", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 12, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[5, -1], [7, 1], [23, -1]], "trace_display": [2, 0, 0, -12], "traces": [0, 12, 2, 0, 8, 0, -6, -12, 6, 8, 0, -8, -12, 2, -2, 0, -4, -8, 20, -26, 0, 0, 4, 12, -12, 0, -22, 12, -8, -12, 0, -50, 14, 4, -28, 0, -18, 8, -4, -26, 0, -4, 6, 26, -10, 0, 2, 16, -40, 12, 0, -32, 10, -18, -10, 0, -6, -10, -18, -18, 0, 8, -54, -8, 12, 0, -2, 38, -36, 0, 0, -24, 18, -14, 36, 0, -56, 8, -26, -44, 0, -16, -44, -14, 12, 0, -32, 16, 32, -10, 0, -2, 8, 26, 18, 0, -38, -4, 2, -56, 0, -22, -2, -20, -32, 0, -28, 0, -4, -30, 0, -84, 4, 16, 12, 0, 6, -42, -30, 8, 0, -18, 4, -38, -62, 0, -20, 16, 2, 28, 0, -28, 0, 26, 56, 0, -48, -34, -6, -20, 0, -10, 50, -22, 0, 0, -40, 0, 66, -52, 0, -94, -104, 18, -4, 0, -22, -32, -14, -10, 0, -12, -36, 2, 0, 0, 6, 12, 12, -2, 0, -62, 2, 2, 16, 0, -10, 58, -10, 6, 0, -4, 22, 18, 6, 0, 26, -16, 52, -12, 0, -24, 88, 84, 16, 0, 8, -52, -98, -104, 0, -34, 64, 12, 32, 0, 18, 8, -30, 24, 0, 2, 8, -36, -50, 0, -14, 50, -44, -34, 0, -14, -88, -40, -14, 0, -86, -20, 78, -80, 0, -4, -62, 40, 98, 0, -52, 20, 28, -38, 0, -42, 6, -44, -12, 0, -46, 84, 22, -42, 0, 0, 18, -8, 96, 0, -84, 6, 62, -8, 0, 72, -6, -6, 28, 0, 4, -54, 26, 2, 0, -84, -8, 26, -66, 0, -12, 50, -58, -18, 0, -34, 24, -90, 74, 0, -16, 4, -90, -18, 0, -64, -18, 12, -6, 0, 78, -28, -8, 2, 0, -26, -70, 84, -40, 0, 46, -76, 10, 28, 0, 32, 24, -46, -36, 0, -146, -2, 92, -108, 0, -32, -2, 26, 118, 0, -14, -82, -28, -16, 0, -78, 68, 6, 36, 0, 40, 40, 86, 0, 0, 34, -22, -12, 8, 0, 20, 54, 8, -6, 0, -8, 24, 22, 54, 0, 12, 32, 44, 2, 0, 52, -134, 56, -10, 0, 76, 16, -4, -52, 0, 18, 42, 24, 38, 0, -46, 36, 10, -68, 0, 72, 56, 2, 136, 0, 84, -14, -74, -20, 0, -8, 6, -30, -36, 0, -14, -34, 6, 10, 0, -4, -4, 6, 46, 0, 18, -30, 30, -6, 0, 60, 0, 18, 20, 0, 14, 150, -56, -8, 0, -98, 162, -52, -70, 0, -34, -8, -130, -18, 0, -18, -44, -46, 54, 0, -20, -26, 94, -48, 0, 8, 26, -80, -28, 0, -50, -62, -12, -86, 0, -62, 40, 104, -36, 0, 144, 70, -46, -34, 0, 40, 2, 40, -86, 0, -28, -102, 86, -38, 0, -4, -78, 6, 184, 0, 36, -34, 60, -18, 0, 36, -6, 0, 40, 0, -26, 124, -26, -42, 0, 6, 36, 16, 118, 0, -34, 24, 36, -90, 0, 8, -88, -24, -18, 0, 4, 60, -18, 86, 0, 14, -156, -34, -90, 0, 72, -118, -36, 0, 0, -16, 176, 28, -48, 0, -10, 48, 98, 12, 0, -48, 56, 20, 198, 0, 88, -68, 64, -8, 0, -52, 10, -78, 0, 0, 26, 106, -78, 38, 0, -2, -12, 44, 106, 0, 108, 66, -214, -180, 0, 198, 94, -46, 4, 0, 84, 16, 100, -20, 0, -30, -164, -122, 44, 0, 32, 30, 206, 18, 0, 14, -178, -18, 110, 0, 10, -32, -12, 10, 0, -52, 90, -90, 56, 0, -76, -26, -22, -44, 0, 94, 32, 14, -114, 0, 88, -116, 24, -16, 0, 118, 52, 110, -6, 0, -32, -120, 48, -78, 0, 12, 6, 10, 96, 0, 36, 30, -198, -56, 0, -104, -26, -48, -14, 0, 108, 2, -140, -56, 0, 6, -94, 36, -8, 0, 170, 36, 64, 26, 0, -26, 40, 86, -68, 0, 146, -102, -18, 128, 0, 16, -2, -54, 30, 0, 72, -12, 232, -12, 0, -78, 38, 36, 12, 0, 56, -66, -130, 4, 0, 48, 48, 34, 74, 0, -2, -66, -38, 36, 0, -104, 46, 56, 46, 0, -70, 136, 20, 114, 0, 174, -8, -28, 88, 0, 114, 22, 84, -66, 0, -20, -260, -50, 2, 0, 16, 4, 130, -98, 0, 20, 88, -26, -32, 0, 150, -12, 32, -166, 0, 106, 142, -84, 192, 0, 14, 132, -88, 62, 0, 104, 28, -100, 206, 0, -14, -212, -72, 0, 0, -78, 136, 44, 104, 0, 4, -68, -2, 4, 0, 84, -132, 30, -76, 0, 114, 20, 52, 14, 0, -12, 80, -46, -74, 0, 48, 84, 20, 72, 0, 56, -28, -4, -4, 0, 38, -32, -62, 24, 0, -16, -118, -38, 50, 0, 108, -54, -12, -144, 0, -40, -40, -2, -130, 0, 186, -28, 92, -40, 0, -30, -6, -56, -98, 0, 60, -116, 164, 42, 0, 102, 204, 26, 48, 0, 30, 100, -18, 40, 0, -18, -90, -8, 186, 0, 14, 76, -44, 62, 0, -24, -162, 160, 134, 0, 22, 18, -60, 38, 0, 8, -108, -10, -4, 0, 196, 130, -36, -160, 0, 38, -126, 52, 66, 0, 18, 64, 62, 122, 0, -44, 164, 20, -4, 0, 174, 56, 98, -12, 0, 24, 20, 46, 228, 0, 116, -56, -120, -16, 0, 48, 140, 24, 144, 0, -2, -26, 28, -6, 0, -6, 256, -28, -60, 0, 110, -124, -214, 68, 0, -42, 202, 180, 180, 0, 44, 28, -160, -60, 0, 20, -244, -56, 0, 0, -44, 108, -48, -26, 0, -26, -186, 90, -4, 0, 204, -14, -56, 50, 0, 114, 240, -4, 116, 0, 126, 112, 188, -80, 0, 70, 48, -44, 152, 0, -56, -132, 250, 34, 0, 160, 52, -66, -94, 0, 6, -138, -228, 24, 0, 2, -64, 20, 104, 0, -8, -72, -140, -188, 0, 132, 156, 58, 232, 0, 110, 10, -2, 26, 0, -182, -126, -160, -50, 0, -16, -66, 222, 26, 0, 22, -130, -30, -36, 0, 266, -44, 0, -36, 0, 208, -10, 102, 70, 0, 130, 54, -88, 156, 0, -76, 40, -110, -154, 0, 162, -92, 122, 0, 0, -48, 94, -52, 148, 0, -66, -110, -30, -204, 0, 70, -98, 52, 152, 0, 200, 6, -70, 46, 0, -140, -64, 122, 72, 0, 64, 94, 2, 118, 0, 310, -182, -22, 104, 0, -108, 152, 148, -10, 0, -18, -58, 106, 148, 0, -48, 16, 4, -34, 0, 16, 308, -168, 100, 0, 102, 90, -90, -14, 0, 106, 22, -50, 78, 0, -30, 82, -12, 32, 0, 84, 76, -16, -40, 0, 14, 38, 78, 86, 0, -66, -86, 10, -22, 0, 0, 72, -348, 12, 0, 4, 264, -6, 18, 0, -178, 12, -20, -54, 0, -40, -106, -140, 36, 0, 128, 26, -140, 16, 0, -2, -118, 368, 10, 0, -144, -184, 0, -38, 0, -30, -10, 174, -30, 0, 104, -30, -8, -80, 0, 106, -6, 64, -134, 0, -66, -32, 210, -12, 0, -84, 10, -32, -70, 0, -12, 100, 272, 6, 0, 148, -56, 2, 108, 0, 94, 46, 86, -126, 0, -46, 0, -40, -22, 0, 10, 62, -354, -44, 0, -54, -92, -260, -2, 0, 116, -38, -198, 94, 0, -2, -66, 0, -12, 0, 64, -20, -16, -18, 0, 38, -86, 204, 178, 0, 168, -24, -208, -150, 0, -108, 10, -200, 100, 0, 112, 26, 32, -58, 0, -38, -10, -66, 124, 0, 10, -92, -14, -16, 0, -150, 24, -6, -18, 0, -384, -34, -116, 22, 0, 134, 58, 48, -84, 0, -146, 4, -36, 38, 0, 84, -174, -152, -22, 0, -184, -58, 130, -170, 0, -18, -138, 76, 208, 0, 26, 2, -6, 32, 0, -144, 208, 2, -20, 0, 10, 172, 294, -34, 0, -210, -26, 76, 0, 0, 198, -148, -20, 16, 0, -10, 36, -200, -154, 0, -52, -108, -134, 20, 0, 22, -340, 12, -122, 0, -104, 118, 4, -160, 0, -114, 72, -64, -18, 0, 158, 24, -158, -182, 0, 14, -88, 64, -88, 0, -224, 236, -130, 84, 0, -84, -158, 194, 62, 0, -96, -18, -16, -82, 0, 128, 266, -96, 52, 0, 6, 124, -96, -34, 0, 58, -8, 118, -14, 0, 144, -140, -28, 52, 0, 116, 110, 170, -38, 0, 98, -80, 108, -6, 0, -88, -140, 104, 46, 0, 70, -24, 176, -208, 0, -102, -46, 8, -96, 0, -180, 34, -134, -78, 0, 24, -154, -32, -64, 0, 140, -36, 144, 116, 0, -12, -156, 86, -42, 0, -54, -16, -32, -136, 0, -74, -72, -128, 190, 0, -30, 200, -206, -142, 0, -8, -18, 86, -30, 0, -330, -62, -168, -8, 0, -84, 120, -134, -190, 0, 30, -76, -88, 12, 0, 116, -12, -24, -38, 0, 10, 168, 272, 158, 0, -178, 12, -56, -84, 0, -240, -2, -78, -172, 0, 138, 14, -178, -8, 0, -48, 230, 302, -112, 0, 36, 28, 18, -62, 0, -186, -160, 50, 76, 0, 8, 22, -20, -12, 0, -124, 208, 324, 116, 0, 52, 14, 258, -118, 0, -322, -78, -2, -50, 0, -160, -44, -28, -194, 0, 44, -80, 126, -24, 0, 50, -84, 34, -48, 0, 120, 262, -8, -36, 0, 38, 2, -128, 24, 0, 60, 14, -360, 154, 0, -174, -102, -202, 88, 0, -76, 162, 200, 158, 0, 40, -142, 158, -36, 0, -116, 12, 14, 140, 0, -112, 44, 86, -52, 0, -154, 68, 108, -262, 0, 128, 86, 38, 92, 0, -46, 0, 242, 20, 0, -100, 188, -88, 126, 0, -78, 22, -388, 118, 0, -92, 240, 80, -162, 0, 50, -46, -320, -190, 0, -108, -50, 170, -232, 0, 20, 4, -62, 66, 0, -18, -374, -268, 62, 0, -20, -58, 84, -104, 0, -40, 66, -24, 90, 0, 12, -14, -98, -90, 0, -66, 230, -84, 186, 0, -214, 76, 56, 122, 0, -316, 52, -94, 174, 0, 18, -150, 40, -20, 0, 138, -144, -88, 26, 0, -28, -56, 34, 142, 0, -16, -16, 38, -96, 0, 108, -102, 48, -14, 0, 6, 188, 272, -260, 0, -34, 42, 8, 130, 0, 62, -184, -254, -6, 0, -18, -54, 140, -182, 0, 44, 36, 266, -226, 0, 70, -52, 12, 78, 0, -128, 214, -150, -152, 0, 132, -168, 290, 18, 0, 36, 46, 108, 16, 0, -64, -104, 128, -84, 0, -70, 46, -94, 238, 0, -22, 54, -136, -32, 0, -140, -34, 42, 0, 0, 4, -34, -56, -94, 0, -70, 46, -54, 172, 0, 62, 0, 204, -104, 0, 260, -148, 154, -18, 0, -146, -20, 354, 176, 0, 8, 292, -112, -96, 0, -160, -150, -96, -24, 0, 20, 144, -172, 136, 0, -68, 150, 340, -226, 0, -216, 84, -196, -26, 0, -192, 32, 172, -6, 0, -26, 60, -120, -106, 0, -62, -112, -126, -92, 0, -102, 136, 8, -306, 0, -112, -44, -16, -22, 0, 92, -118, -176, -32, 0, 158, -72, -60, 126, 0, -166, 34, 220, 6, 0, -128, -140, 70, -110, 0, 6, -208, 258, 140, 0, -176, 88, -28, 36, 0, 70, -200, 164, -244, 0, -64, 108, 28, 282, 0, -38, -4, -16, -218, 0, -2, -76, 22, 54, 0, 24, 262, 168, -126, 0, -26, 28, 384, -252, 0, 126, 250, -2, 398, 0, -44, -92, -226, -104, 0, -126, 166, -328, -100, 0, -48, 84, -304, 176, 0, 28, -148, -88, 8, 0, 138, 156, -4, -14, 0, -26, 22, 150, -104, 0, 52, -228, 66, -60, 0, 130, 102, 86, -34, 0, -500, 196, 294, 140, 0, -52, 12, 120, 18, 0, -90, -292, -112, -50, 0, -190, 264, -214, 74, 0, 58, -56, 274, 114, 0, -314, -34, 18, -80, 0, -222, -166, 148, -20, 0, 160, 6, -108, 76, 0, -100, 34, 204, -130, 0, -52, 282, 26, -24, 0, 112, 26, -32, -186, 0, 90, -26, 166, 8, 0, -270, -208, -74, -96, 0, -46, -60, -70, -82, 0, -94, -30, 24, -98, 0, 16, 16, -300, -278, 0, -6, -100, -78, -4, 0, -62, -60, -228, -34, 0, 90, 336, -288, 256, 0, -190, 88, 18, 32, 0, -128, -138, -20, 174, 0, -226, 84, 156, 316, 0, -44, 64, -258, -90, 0, -82, -304, -54, 18, 0, -12, -10, 42, 44, 0, -12, -24, -8, 86, 0, 76, -142, 6, -48, 0, -8, 334, 212, -22, 0, 14, 86, -194, 38, 0, -260, -78, 296, -178, 0, -102, -172, -170, 28, 0, 88, -168, 94, 40, 0, 8, -178, 196, -270, 0, 74, 130, -2, -150, 0, -274, 48, 10, 86, 0, 124, -172, 34, -90, 0, -44, 26, 304, 198, 0, -114, -168, -124, 70, 0, 8, -192, -268, 66, 0, -84, 80, -54, -246, 0, -130, -82, 40, 4, 0, -108, 84, -92, -214, 0, -196, -62, 230, 26, 0, 50, -46, 44, 74, 0, -170, -20, 240, 76, 0, 12, 44, -168, -78, 0, -10, 16, -276, 62, 0, 44, 18, -28, 64, 0, -210, 56, -270, 182, 0, 14, 140, -250, -6, 0, -16, -32, 238, -146, 0, 120, 46, -282, -24, 0, 270, 92, 122, 246, 0, 46, -342, 38, -248, 0, -192, -176, 36, 32, 0, -192, -2, 184, 234, 0, 110, 108, -38, 84, 0, 182, 146, 64, -6, 0, 50, -44, 208, 2, 0, -48, -220, 14, -132, 0, -92, -120, -186, 162, 0, -4, 102, 108, 68, 0, -88, 38, -398, -174, 0, -26, 42, 244, 28, 0, -276, 32, 100, 84, 0, -72, -54, -94, 2, 0, 8, 184, 76, 52, 0, -26, -2, 42, -262, 0, -14, 220, -118, 196, 0, 10, 80, -234, -102, 0, -52, -56, -28, -142, 0, 158, 14, -160, -116, 0, 104, 96, -166, 82, 0, -126, 112, 158, -66, 0, 28, 66, -152, 144, 0, 106, 30, 16, -116, 0, -110, -126, -98, 162, 0, -348, 48, 66, -244, 0, -142, 78, -46, 98, 0, -98, -48, -22, -68, 0, -192, 172, 144, -86, 0, -6, -114, 52, 100, 0, -38, -86, -36, 74, 0, -120, 2, 152, -216, 0, -2, 68, -344, 112, 0, -74, -40, 128, -24, 0, 416, -46, 110, -40, 0, 52, 204, -128, -14, 0, -86, -248, -140, -20, 0, -144, -26, 0, -276, 0, 132, 88, -180, 138, 0, -46, 16, -222, 130, 0, 94, -34, -164, -44, 0, -174, -32, -142, 22, 0, -142, -216, -180, -78, 0, 12, 24, 46, 136, 0, 26, -244, -8, 14, 0, -76, 234, -294, 10, 0, -102, -104, 368, 170, 0, 218, -20, -6, -166, 0, -454, -36, -12, -54, 0, -88, 34, 310, -124, 0, -8, 82, -28, -286, 0, 168, 52, 6, -78, 0, -354, -178, 268, 290, 0, -312, 24, 124, -128, 0, 234, 8, -84, 158, 0, 0, 74, -368, -24, 0, -234, -92, -166, 154, 0, -22, 92, 94, 130, 0, 0, 370, -54, -44, 0, 492, -230, 102, -4, 0, 2, 300, 38, 118, 0, -80, -12, 110, -246, 0, -186, 160, -214, -32, 0, -170, -126, 164, -206, 0, -44, -30, -100, -68, 0, 116, -44, -2, -156, 0, -320, 64, -110, 22, 0, 232, 448, 252, -216, 0, 230, -52, -168, 246, 0, 34, -356, 168, 134, 0, 0, -200, 228, -90, 0, -56, 162, 208, -124, 0, -236, -70, 10, 160, 0, 46, 52, -84, -172, 0, 174, -64, 96, 122, 0, 196, -76, 102, -368, 0, -204, 216, 610, -16, 0, -198, -482, -6, -226, 0, 4, -198, -404, -36, 0, 72, 62, 52, 248, 0, -106, 20, 52, -174, 0, 120, 116, -172, -32, 0, -178, -18, -154, 16, 0, -70, 8, 104, -42, 0, -136, -40, 274, 118, 0, -24, 136, -232, -232, 0, -82, 130, -38, -68, 0, 206, 12, -28, -210, 0, -196, 122, -458, 190, 0, -254, 46, -26, -92, 0, 148, -172, 826, -36, 0, -116, 208, -536, 20, 0, -10, -116, 326, 138, 0, 56, -138, 68, -214, 0, 272, 268, -76, 32, 0, 200, -132, -36, 46, 0, -136, -72, 6, 346, 0, -200, 184, -58, -56, 0, -214, 86, -2, 180, 0, -2, -396, 284, 98, 0, 124, 76, -136, -118, 0, -42, 256, -86, 146, 0, -452, -2, -482, 146, 0, 26, -84, -48, -16, 0, 220, -132, 168, 14, 0, 4, 48, 282, -30, 0, 74, 252, -44, -300, 0, 26, 108, 20, 198, 0, -56, 2, -286, 0, 0, 242, -248, 188, 54, 0, 118, 8, 130, 192, 0, 48, 184, -260, -6, 0, -86, -288, -224, 124, 0, 30, 118, 158, -174, 0, 236, 18, 36, -32, 0, 72, 118, 272, -152, 0, 238, 76, -98, 148, 0, 228, 14, 348, -146, 0, 12, -226, 280, 34, 0, 280, -64, -18, 98, 0, -6, 192, 18, -46, 0, -328, 396, -10, -238, 0, 404, 62, 266, 118, 0, 78, -362, -68, -204, 0, 4, 4, -388, -42, 0, 122, -304, -134, 4, 0, 134, -256, 32, 168, 0, -6, -70, -60, 58, 0, -10, -148, -46, -38, 0, -88, 100, -166, 320, 0, -174, -116, 92, -214, 0, 22, -18, 96, 30, 0, -192, 552, 176, 30, 0, 54, -62, 30, -176, 0, -30, 228, 4, 212, 0, 342, 50, 6, -20, 0, -92, 82, 192, 314, 0, -140, -130, -20, 142, 0, -34, -60, 118, -56, 0, 58, -356, -68, 0, 0, 32, 184, 262, 88, 0, -18, -84, 126, -30, 0, -34, -216, -20, -24, 0, -192, -2, 272, -122, 0, 62, -30, -124, -116, 0, -36, -14, 36, -20, 0, -294, 124, 178, -150, 0, 16, -188, -264, -280, 0, 56, -282, -248, 32, 0, 170, 16, 8, 292, 0, 68, 88, 134, -192, 0, -30, 34, 70, 2, 0, -380, 98, 108, -50, 0, 20, 164, -198, -162, 0, 262, 86, -414, 78, 0, 52, 16, -56, 64, 0, 70, 28, 70, 196, 0, -262, -276, -84, 42, 0, 2, 100, -152, 206, 0, 118, 34, 378, 130, 0, 258, 170, -124, 8, 0, 44, -336, 188, 240, 0, 130, 202, -48, 100, 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": "805.2.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, 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, -1, 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], [-1, 0, 0, 0, 0, 0, -1, 0, 0, -1, -1, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0], [1, 1, 0, 0, 0, 0, 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, 1, 1, 0, 0], [-2, 0, -1, 0, -1, 0, 0, 0, 0, -1, -1, 0], [0, -1, 0, -1, 1, 0, 1, 0, 0, 0, 1, -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, 1, 1, 0, 0, 0, 1, 1], [0, 0, 0, 1, -1, -1, 0, -1, 0, 0, -1, 1], [2, 0, 2, -1, 1, -1, 0, 0, -1, -1, 0, 0], [-3, 0, -1, 0, 0, -1, 0, 0, 1, 0, 1, 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], [1, 0, 1, 1, -2, 0, -1, -2, 1, 0, -1, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -2, -2, 1, -1, 0, 0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 1, -2, -1, 1, 0, 2, 0, -1, 1, 1, -2], [1, 0, -1, 1, -1, 0, 0, 0, 0, 0, -1, -1], [-1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 1, -1, -1, -1, 0, 0, -2, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, -2, -1, 1, 1, 1, 0, 0, 0, 1, 0, -1], [1, 0, 0, 1, -1, -1, 0, 0, 1, 0, -1, 0], [1, 0, 0, 1, -1, -1, 1, -1, 1, 1, 0, 2], [-2, 0, -1, 0, -1, -2, 0, -1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 2, 0, -1, 2, -1, 1, 0, -1, 1, 1, -1], [0, 1, 0, -1, -1, 0, 3, 1, -1, 0, 0, -1], [0, -2, -2, 1, -1, -1, 0, -1, 0, 0, -1, -1], [-3, -3, 0, -1, 2, 2, 2, 2, 0, -1, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -2, 1, 2, -1, 0, 0, -1, 1, 0, 1, 2], [1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0], [3, -1, 0, 3, -2, -1, -2, 0, 1, 0, -2, 2], [-2, 0, -3, 1, 0, 1, 1, 2, 1, 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, 0], [1, -1, 2, -1, 2, 2, 0, 0, 0, -2, 2, 0], [-3, -3, -1, 1, 1, 0, 0, 0, 2, 1, 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], [-2, 1, 0, 1, -2, -1, -1, -2, 2, 2, -1, 1], [2, 0, 2, -1, -1, -2, 0, -2, -2, -1, -1, 0], [-3, 1, 1, -3, -1, 0, 1, 0, -2, -2, -2, -1], [-3, 0, -1, -1, 0, 1, 0, 1, 1, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 0, 0, -1, -1, -1, -1, 0, -1, -1, 0], [-1, -2, 2, -3, 4, 3, 4, 1, -1, -1, 1, 0], [-1, -1, 0, -1, 4, 0, 0, 1, -2, -1, 1, -1], [-2, 0, 1, -2, 0, 2, -1, -2, 0, -1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 0, -2, -1, 1, 1, 1, -2, -2, -1, -1], [-6, -4, 0, -3, -1, 0, 1, 0, 0, -1, 1, 0], [-1, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 2, -3, 1, -1, -1, -2, 0, 1, 1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 1, 0, 2, -2, -2, 1, -2, 1, 3, 0, 2], [3, 1, -1, 0, 2, 0, 0, 0, 1, 1, -1, 0], [-2, -1, 0, -1, 1, -2, -1, -2, -1, 0, 0, -1], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -1, 2, 0, 2, 0, 0, 2, 1, 0, 2, 2], [4, 1, 1, -1, -1, -1, 2, -3, -2, 2, 1, -1], [-2, -5, 1, -1, 3, 4, 2, 3, 0, -2, 2, 2], [5, -1, 2, 1, 3, 2, 2, 1, 0, 1, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-6, 0, -3, -2, -1, 0, 0, -1, -2, -1, -2, -1], [1, 0, 1, 0, 0, 0, 0, 0, -1, -1, 0, 0], [-2, -4, -1, 1, 0, 2, 1, 2, 0, 0, 1, -1], [-5, -1, -2, -1, 3, 2, 0, 1, 0, -1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 1, -1, -1, 0, 1, 0, 0, 1, 0, -2], [-5, -2, -5, 1, 0, 0, 3, 3, 2, 3, 1, 0], [-1, -1, 0, 2, 0, -1, -1, 0, 3, 1, -1, 1], [2, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 2, 0, 2, -3, 0, -3, 0, 2, -1, -1, 4], [0, 2, -1, 0, -2, 0, 0, 1, -2, -2, -3, -3], [2, -3, 3, 0, 0, 1, -1, 2, 0, -3, 1, 1], [0, 1, 3, 3, -1, -2, -3, -2, 0, -4, -4, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, -1, 0, -1, 0, 0, 0, -1, 1], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 0, -1, 1, -2, 0, 6, 0, -1, 3, 3, 0], [-1, 0, -5, -1, 2, 2, 3, 5, 0, 2, 1, -4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 2, 1, -2, -1, 0, 1, -1, -1, -1, -2, 0], [0, 0, -4, 1, 1, -2, 2, 0, 2, 4, 2, -1], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, -2, 2, 2, -2, -1, -2, -3, 2, 0, -1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}