# Stored data for newform 4005.2.a.t, downloaded from the LMFDB on 25 April 2024.
{"label": "4005.2.a.t", "space_label": "4005.2.a", "level": 4005, "weight": 2, "hecke_orbit": 20, "hecke_orbit_code": 85568392953597861, "dim": 10, "is_polredabs": true, "trace_hash": 2045035304620068655, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [-21, -71, 344, 59, -358, -14, 128, 1, -19, 0, 1]], [7, [-2684, 9923, -10882, 1305, 4023, -1567, -358, 228, -5, -9, 1]], [11, [92160, 79168, -41344, -49648, -2552, 6832, 1148, -296, -64, 4, 1]]], "qexp_display": "q-\\beta _{1}q^{2}+(2+\\beta _{2})q^{4}+q^{5}+(1-\\beta _{4}+\\cdots)q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 16020, "fricke_eigenval": -1, "atkin_lehner_string": "---", "analytic_conductor": 31.980086009522793, "hecke_ring_index": 1, "level_radical": 1335, "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": "0.003", "prec": 17}, "analytic_rank_proved": true, "char_values": [4005, 1, [3116, 802, 181], [1, 1, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 1, "level_primes": [3, 5, 89], "conrey_indexes": [1], "field_disc": 737556713878924096, "field_disc_factorization": [[2, 6], [184351, 1], [62512943539, 1]], "field_poly": [-21, 71, 344, -59, -358, 14, 128, -1, -19, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.096", "prec": 17}, {"__RealLiteral__": 0, "data": "8.344", "prec": 17}, {"__RealLiteral__": 0, "data": "1.822", "prec": 17}, {"__RealLiteral__": 0, "data": "202.553", "prec": 24}, {"__RealLiteral__": 0, "data": "68.271", "prec": 20}, {"__RealLiteral__": 0, "data": "7802.658", "prec": 27}], "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], [89, -1]], "trace_display": [0, 0, 10, 9], "traces": [0, 10, 0, 0, 18, 10, 0, 9, -3, 0, 0, -4, 0, 15, 1, 0, 22, -11, 0, 14, 18, 0, 10, 8, 0, 10, 14, 0, 36, -5, 0, -8, -1, 0, 2, 9, 0, 23, -8, 0, -3, -13, 0, 25, 8, 0, -14, 1, 0, 21, 0, 0, 51, -9, 0, -4, -15, 0, -8, 15, 0, 8, 8, 0, 9, 15, 0, 52, 28, 0, 1, 22, 0, 34, 18, 0, 14, -4, 0, -3, 22, 0, 17, 10, 0, -11, 6, 0, 4, 10, 0, 18, 14, 0, -43, 14, 0, 34, 38, 0, 18, 37, 0, 7, 68, 0, -35, 3, 0, -19, 10, 0, 46, 16, 0, 8, -18, 0, 10, -24, 0, 34, 2, 0, -100, 10, 0, 25, -2, 0, 14, -4, 0, 24, 24, 0, -69, -20, 0, 31, 36, 0, -30, 14, 0, -5, -52, 0, 70, 28, 0, 22, -18, 0, -154, -8, 0, 10, 9, 0, -1, 40, 0, 45, 14, 0, 8, 37, 0, -7, 2, 0, 8, -73, 0, 9, -40, 0, 0, -42, 0, 4, 23, 0, -104, 23, 0, 6, 26, 0, -8, -3, 0, 75, 98, 0, 43, -50, 0, 29, -3, 0, -36, -10, 0, -13, -8, 0, 22, 0, 0, 58, -60, 0, -100, 25, 0, -44, -10, 0, 8, -28, 0, 50, 124, 0, -50, 19, 0, -62, -14, 0, -39, 1, 0, 1, -3, 0, 26, -7, 0, 16, 8, 0, -102, 21, 0, 40, -40, 0, 0, -30, 0, 40, 6, 0, 60, 19, 0, -8, 51, 0, 46, 11, 0, -9, 0, 0, 30, 8, 0, -19, 105, 0, -72, -4, 0, -40, 46, 0, -15, -35, 0, 36, 148, 0, 24, 5, 0, 5, -8, 0, -14, 48, 0, 15, -17, 0, -32, 78, 0, -52, 164, 0, -114, 8, 0, 18, -54, 0, 8, 72, 0, -9, 28, 0, 54, 45, 0, -2, 9, 0, -96, -20, 0, 15, -28, 0, -67, 1, 0, -53, 108, 0, -226, 52, 0, 47, 54, 0, 28, -16, 0, 54, -61, 0, 30, 12, 0, -54, 1, 0, -26, -52, 0, 22, 18, 0, 24, -1, 0, -30, 96, 0, 60, 34, 0, 66, -12, 0, 18, 111, 0, -16, 128, 0, -125, -18, 0, 10, 14, 0, 2, 44, 0, -4, -63, 0, -36, -1, 0, 6, 77, 0, -108, -3, 0, 9, -80, 0, 22, -24, 0, -42, 165, 0, 14, 118, 0, 33, 17, 0, 101, 38, 0, 10, 111, 0, 0, -11, 0, -50, 134, 0, -115, -11, 0, 0, 28, 0, 6, 15, 0, 81, 40, 0, 11, 52, 0, 2, 4, 0, 41, 35, 0, 10, -104, 0, 111, -8, 0, -64, 22, 0, -29, 18, 0, 22, -188, 0, 14, 76, 0, 6, -39, 0, 150, -3, 0, -90, -43, 0, 178, -94, 0, 14, -107, 0, -11, 48, 0, 6, 18, 0, -2, 34, 0, -10, -98, 0, 38, -2, 0, 53, -148, 0, -176, -26, 0, -38, 18, 0, 118, 68, 0, 37, -80, 0, 116, 18, 0, -30, 20, 0, -71, 7, 0, 36, -134, 0, 68, -17, 0, 70, -118, 0, 52, 24, 0, 106, -35, 0, 26, -44, 0, 3, -170, 0, 160, 62, 0, -44, -139, 0, -271, -19, 0, 33, -150, 0, 10, 120, 0, 105, 12, 0, 203, -108, 0, -20, 46, 0, 104, 22, 0, 16, -18, 0, 14, -75, 0, 4, 6, 0, 22, 8, 0, 29, -283, 0, -18, 24, 0, -12, -78, 0, 50, 72, 0, 20, 10, 0, 281, -56, 0, -24, -44, 0, -58, -59, 0, 1, -8, 0, -138, 34, 0, -24, -106, 0, 2, -68, 0, 12, -184, 0, -36, -126, 0, 13, -100, 0, -62, 9, 0, 10, -98, 0, 20, 33, 0, -43, 117, 0, -30, 25, 0, 96, -28, 0, -2, -90, 0, -88, -96, 0, 142, 84, 0, -126, 14, 0, 111, -6, 0, -4, -108, 0, -248, 34, 0, -170, -122, 0, 130, 24, 0, 74, 17, 0, 24, 152, 0, 48, -23, 0, -60, -12, 0, 126, -69, 0, 128, 94, 0, -20, -99, 0, -91, -132, 0, -105, -243, 0, -104, 31, 0, 60, -56, 0, 36, -46, 0, -116, -272, 0, 26, 124, 0, -40, -30, 0, -3, -28, 0, 14, -112, 0, -125, 55, 0, -80, 84, 0, 14, -5, 0, 15, 92, 0, -52, -31, 0, 44, 100, 0, -188, -128, 0, 44, 70, 0, -40, 2, 0, 28, -266, 0, -172, -76, 0, -101, 38, 0, -159, 22, 0, -40, -22, 0, -18, 8, 0, -138, 75, 0, 84, 125, 0, 27, -154, 0, 120, -48, 0, -8, 186, 0, -51, -44, 0, 108, -120, 0, -74, 10, 0, 141, -238, 0, 9, 106, 0, 50, -205, 0, 170, -55, 0, -64, -1, 0, 122, 52, 0, 40, -112, 0, -124, -164, 0, -185, -3, 0, 40, 45, 0, 116, 103, 0, 14, 78, 0, -20, 14, 0, 135, 92, 0, -14, 8, 0, 151, -223, 0, 37, 108, 0, -304, -43, 0, -79, -88, 0, 206, -7, 0, 25, -350, 0, 2, 58, 0, 55, -220, 0, -101, -168, 0, -10, 8, 0, 116, 94, 0, -73, -70, 0, -314, 32, 0, -40, -154, 0, -148, 9, 0, 18, -64, 0, -40, -80, 0, -99, -137, 0, 170, 36, 0, 108, 0, 0, -22, -152, 0, -42, 221, 0, 128, -12, 0, -90, 62, 0, -88, 4, 0, -58, 162, 0, 23, 116, 0, 120, -230, 0, -62, -148, 0, 30, -104, 0, -60, 138, 0, 23, -134, 0, -275, -80, 0, 22, 79, 0, -66, 6, 0, 62, 64, 0, 26, 165, 0, 8, -48, 0, 92, 15, 0, -34, -8, 0, 35, -110, 0, -3, -266, 0, -206, -158, 0, -70, 245, 0, 18, 75, 0, -1, -23, 0, 98, 20, 0, -64, 2, 0, -214, -213, 0, -4, 43, 0, 2, -7, 0, -50, -29, 0, -122, 106, 0, -82, -72, 0, -78, 29, 0, 104, -190, 0, -3, -78, 0, -240, -130, 0, 6, 128, 0, 100, -36, 0, 164, -109, 0, -10, -81, 0, -260, 2, 0, -217, -122, 0, 113, -13, 0, -38, 36, 0, -8, 21, 0, 130, -46, 0, 107, -88, 0, 70, 22, 0, 145, 178, 0, 0, 108, 0, 94, -36, 0, -15, 0, 0, 22, 58, 0, -30, -140, 0, -60, 161, 0, 58, -198, 0, 79, -68, 0, 85, -100, 0, 84, -61, 0, 25, 74, 0, -342, 18, 0, 72, -238, 0, -54, -44, 0, 97, 246, 0, -10, 166, 0, -60, 80, 0, 62, -162, 0, 60, 8, 0, 102, 288, 0, -28, 160, 0, -180, -1, 0, -90, 98, 0, 4, 50, 0, 60, -71, 0, 124, -88, 0, -136, -386, 0, 36, 222, 0, -12, -50, 0, 238, -22, 0, 19, 140, 0, -332, 122, 0, -4, 6, 0, -140, -62, 0, -116, -207, 0, -14, 9, 0, 110, -169, 0, 178, 15, 0, 80, -39, 0, -98, 274, 0, 1, -186, 0, -216, -82, 0, -52, 166, 0, -260, 1, 0, -62, 176, 0, -3, 141, 0, -209, -95, 0, 206, 90, 0, -82, 26, 0, -322, 4, 0, -7, -94, 0, 41, 62, 0, 25, -46, 0, -85, 16, 0, 146, 288, 0, 8, 20, 0, 146, 26, 0, -96, -58, 0, -140, -102, 0, 93, 80, 0, 21, -28, 0, -40, 76, 0, -82, -34, 0, 52, 40, 0, -50, -211, 0, -40, -44, 0, -316, 0, 0, 1, 147, 0, 76, 0, 0, -250, 68, 0, -30, 230, 0, -173, 85, 0, -26, 186, 0, 312, 40, 0, 124, 72, 0, 6, 44, 0, 40, 118, 0, 100, -34, 0, -6, 60, 0, 126, 20, 0, 19, 12, 0, -388, -71, 0, -31, 0, 0, -28, -8, 0, -35, -104, 0, 51, 112, 0, -158, 22, 0, -48, 100, 0, -192, 46, 0, -90, 89, 0, 11, -39, 0, -152, -8, 0, 102, 148, 0, -241, -9, 0, -72, 34, 0, 0, 144, 0, -28, -348, 0, -144, 102, 0, 165, 30, 0, -80, 30, 0, 8, 192, 0, 336, 172, 0, 79, 480, 0, 146, -19, 0, -58, 312, 0, 105, 127, 0, -170, -68, 0, 262, 5, 0, 57, -72, 0, -20, -18, 0, -4, -393, 0, -267, -62, 0, -76, 50, 0, -4, -40, 0, 200, 152, 0, 46, 42, 0, 342, -144, 0, -86, 126, 0, 20, -15, 0, -290, 380, 0, -35, -114, 0, -136, -61, 0, -44, 72, 0, -21, 36, 0, -15, -212, 0, 148, -51, 0, -42, 22, 0, 316, -56, 0, -83, 24, 0, 80, -85, 0, 5, 90, 0, 64, 118, 0, -236, 149, 0, -74, 5, 0, 91, 184, 0, -8, 57, 0, 139, 194, 0, 397, -96, 0, 106, -14, 0, -75, 160, 0, 48, -14, 0, -116, 58, 0, -125, 284, 0, 408, 15, 0, -44, 192, 0, -17, -114, 0, -35, -11, 0, -4, 84, 0, 2, -32, 0, 142, -17, 0, 78, 204, 0, -8, -133, 0, -128, 20, 0, -18, -52, 0, 128, -185, 0, 164, -42, 0, -11, -144, 0, 204, -136, 0, -194, -114, 0, -344, 113, 0, 8, -201, 0, 138, 38, 0, 36, 6, 0, 120, 18, 0, -16, 154, 0, -54, 80, 0, 1, -57, 0, 392, -131, 0, -59, 8, 0, -28, -123, 0, 72, 174, 0, 176, 30, 0, 6, 256, 0, 152, -9, 0, 3, 320, 0, 28, 90, 0, 131, -159, 0, -36, 88, 0, 14, 54, 0, 392, 138, 0, 45, -170, 0, -112, 31, 0, -29, -249, 0, -18, -2, 0, 104, -50, 0, 9, 22, 0, -32, -142, 0, 256, 109, 0, -60, -96, 0, -340, 165, 0, -20, 176, 0, -150, 114, 0, -2, 440, 0, -163, 15, 0, 100, 128, 0, -28, 48, 0, -16, 106, 0, 280, 4, 0, -28, -67, 0, 220, 156, 0, 1, -40, 0, 126, -172, 0, -208, 152, 0, 306, -53, 0, 12, -218, 0, 108, -16, 0, -77, 41, 0, 281, -26, 0, -299, -226, 0, -20, -183, 0, 52, 4, 0, -7, -212, 0, -39, -67, 0, -70, 47, 0, -32, 252, 0, 54, 14, 0, 84, -315, 0, 138, 168, 0, 199, 28, 0, -216, 2, 0, -16, -14, 0, -314, -64, 0, -270, 13, 0, -10, 54, 0, -20, 36, 0, -61, 87, 0, -22, -100, 0, 154, 192, 0, -144, 30, 0, 169, 75, 0, 12, -226, 0, -154, 176, 0, 17, 90, 0, -32, -54, 0, 105, 4, 0, 1, 280, 0, 191, 114, 0, -34, -8, 0, -87, -26, 0, 162, 108, 0, -52, 25, 0, -67, 88, 0, -156, 147, 0, 0, 22, 0, -105, -228, 0, 18, -24, 0, 156, -356, 0, -148, 26, 0, 39, 24, 0, 85, -282, 0, -1, -56, 0, 234, -1, 0, 51, 420, 0, -54, -30, 0, 43, 362, 0, 96, 37, 0, 93, -222, 0, 153, -348, 0, 129, 60, 0, -466, 132, 0, 34, -40, 0, 22, -22, 0, -80, -316, 0, 234, 66, 0, -2, -218, 0, -12, 8, 0, 36, 62, 0, -62, 99, 0, 89, 18, 0, 188, 202, 0, 111, 134, 0, -170, -134, 0, -145, -244, 0, 300, -16, 0, 232, -239, 0, 128, -142, 0, 58, 68, 0, -316, 37, 0, -113, -125, 0, 68, 198, 0, -18, 432, 0, 685, -10, 0, 124, 312, 0, 34, 10, 0, -119, -284, 0, 14, -152, 0, -138, 149, 0, -120, -8, 0, -216, 2, 0, -13, -140, 0, 44, -30, 0, -392, -68, 0, 48, 28, 0, 371, -4, 0, 167, -142, 0, -63, 65, 0, 104, 264, 0, -350, -114, 0, -44, -36, 0, -142, 38, 0, -1, -55, 0, 136, 24, 0, -210, -186, 0, 33, 6, 0, 64, 10, 0, 77, -338, 0, 4, -18, 0, 356, -18, 0, -8, -108, 0, 294, 116, 0, -3, -56, 0, 16, 128, 0, -68, 358, 0, -298, 9, 0, 111, 150, 0, -80, -100, 0, 281, 106, 0, -92, -339, 0, 40, 22, 0, -526, 87, 0, -24, 221, 0, 32, 33, 0, -104, 210, 0, 376, -42, 0, -69, 80, 0, 165, 48, 0, 156, 164, 0, -146, -169, 0, -101, 14, 0, 109, 60, 0, 118, 204, 0, -62, -246, 0, 296, -127, 0, -76, 33, 0, 8, -70, 0, 17, -36, 0, 161, 197, 0, -79, -287, 0, 158, 101, 0, -166, 29, 0, 38, -46, 0, 182, 58, 0, -264, 107, 0, 146, 10, 0, 168, 228, 0, 111, -236, 0, -70, 382, 0, -22, 197, 0, 21, 0, 0, 294, -198, 0, -11, 90, 0, 280, -79, 0, -106, 137, 0, 375, -50, 0, 141, 12, 0, 134, 176, 0, 259, 238, 0, 226, 28, 0, 251, -115, 0, 76, -124, 0, -11, -214, 0, -198, 121, 0, 309, -128, 0, -216, 0, 0, -246, -253, 0, 28, 94, 0, -116, -636, 0, -347, -48, 0, -220, 6, 0, 142, -7, 0, 15, 446, 0, 46, -63, 0, 67, 304, 0, -112, 81, 0, 176, -219, 0, 40, 55, 0, 177, -132, 0, -479, -146, 0, 238, 11, 0, 210, -130, 0, 52, 134, 0, -201, -174, 0, -416, -372, 0, -24, 2, 0, 36, -154, 0, 4, -92, 0, 52, 264, 0, -70, -11, 0, 21, 41, 0, 465, -126, 0, 35, 48, 0, 192, -200, 0, 69, -28, 0, 342, 10, 0, -58, -302, 0, -104, -264, 0, 196, 134, 0, 7, -252, 0, 6, 111, 0, -376, 103, 0, -8, 184, 0, 127, -99, 0, -122, 280, 0, -4, -64, 0, 128, -124, 0, 22, -84, 0, 224, 64, 0, 536, -140, 0, -169, -29, 0, -270, -196, 0, 18, 85, 0, -466, -58, 0, -54, 323, 0, 126, 22, 0, 100, -14, 0, -188, -160, 0, -24, 58, 0, -140, 55, 0, 66, 14, 0, 72, 231, 0, 76, 134, 0, 88, 210, 0, -64, -588, 0, 14, 6, 0, 76, -112, 0, -39, -212, 0, 134, 382, 0, -202, -218, 0, -278, 150, 0, 26, -162, 0, -3, -126, 0, -369, -72, 0, 30, -130, 0, 490, -90, 0, 131, 84, 0, -43, -11, 0, 76, 384, 0, 92, -100, 0, 283, 178, 0, 51, 90, 0, -94, 255, 0, 108, -90, 0, 17, 4, 0, 58, 14, 0, 1, 204, 0, -107, -48, 0, -2, -52, 0, -168, -128, 0, 14, -11, 0, -90, -113, 0, 48, -74, 0, 552, -130, 0, 34, -25, 0, -94, 6, 0, 56, -449, 0, 18, 30, 0, 40, 10, 0, -18, -100, 0, 68, -2, 0, 325, 64, 0, 34, 350, 0, -94, 304, 0, -34, -178, 0, 154, -10, 0, -76, 328, 0, -98, -25, 0, -74, 86, 0, -118, -9, 0, -52, 38, 0, -234, 20, 0, -2, -338, 0, -282, -147, 0, -146, -76, 0, 162, 53, 0, 160, -156, 0, -148, 90, 0, 94, -68, 0, 138, -200, 0, 142, -176, 0, 408, 351, 0, -26, -184, 0, -2, -164, 0, 17, 36, 0, -65, -38, 0, -240, 86, 0, 18, -136, 0, 126, 43, 0, 256, -18, 0, -54, 118, 0, -422, 191, 0, 68, 290, 0, 264, -36, 0, 4, 158, 0, -139, 37, 0, -47, 532, 0, -80, 38, 0, -6, 604, 0, -349, -92, 0, 31, 116, 0, -72, 84, 0, 18, 292, 0, 413, -136, 0, -160, -20, 0, 192, -30, 0, -53, 410, 0, 20, 22, 0, 46, 4, 0, -262, -218, 0, -204, -71, 0, -198, -208, 0, 7, -102, 0, 8, 76, 0, -5, 24, 0, 50, 36, 0, 2, 244, 0, -134, -34, 0, 145, -213, 0, -134, 9, 0, 164, 68, 0, 68, -20, 0, -17, 542, 0, 286, 105, 0, 154, 250, 0, 126, 70, 0, 34, 644, 0, -118, 138, 0, 96, -47, 0, 198, 54, 0, -160, 52, 0, -274, -226, 0, 24, 192, 0, -370, -115, 0, -68, 18, 0, -302, 106, 0, -180, -154, 0, -35, -136, 0, 218, 308, 0, 128, -106, 0, -11, 26, 0, -192, 2, 0, -44, 206, 0, 372, -252, 0, -359, 298, 0, 301, 3, 0, -513, 28, 0, -170, -344, 0, 175, 472, 0, 58, 88, 0, -8, 160, 0, -34, -88, 0, 62, 155, 0, -4, -153, 0, -116, 54, 0, 41, -44, 0, 11, 178, 0, -139, -209, 0, 101, 518, 0, 316, -188, 0, -21, -271, 0, 76, 57, 0, -19, -42, 0, 168, -161, 0, -32, 56, 0, 264, 33, 0, -324, 29, 0, -150, 66, 0, 200, 32, 0, -212, 178, 0, -227, 10, 0, 14, -102, 0, 120, -488, 0, -246, -8, 0, -64, -188, 0, -257, 105, 0, 150, -260, 0, 12, 44, 0, 128, 292, 0, -568, 17, 0, 41, 203, 0, -229, 356, 0, -108, 224, 0, 53, 231, 0, 263, 248, 0, -276, -20, 0, -230, -84, 0, 46, -112, 0, -128, -64, 0, -12, -96, 0, 297, 104, 0, -80, -104, 0, 22, -90, 0, 0, 5, 0, -244, 368, 0, -148, 16, 0, -136, 166, 0, -18, 96, 0, 21, 236, 0, -76, -53, 0, -202, 14, 0, -273, 85, 0, -75, -82, 0, -1, -24, 0, 4, -284, 0, -152, 4, 0, -46, 59, 0, 6, -103, 0, 229, 460, 0, 105, 60, 0, -128, 22, 0, -503, -196, 0, 8, 192, 0, 78, -75, 0, 494, 76, 0, -226, 29, 0, -228, 337, 0, -283, 266, 0, -70, -38, 0, 368, -121, 0, -114, -18, 0, 114, 40, 0, 24, 113, 0, -200, 31, 0, -242, 595, 0, 180, -12, 0, -42, -84, 0, -78, -182, 0, 110, 432, 0, -220, -75, 0, -234, 50, 0, 258, 54, 0, 72, 650, 0, -14, -230, 0, 74, -8, 0, -460, 20, 0, -80, 12, 0, 10, 84, 0, 80, 406, 0, 384, 1, 0, -124, 281, 0, -250, -108, 0, -56, -75, 0, -336, -8, 0, -51, -168, 0, -270, -24, 0, -320, 126, 0, -44, 36, 0, 216, -234, 0, -166, -18, 0, 282, -58, 0, -132, -158, 0, -59, -153, 0, -66, 69, 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": "1335.2.a.i", "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], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 1, 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], [1, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, -1, -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, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 0, -1, 0, 0, 0, 0], [0, -2, 0, 0, 0, 0, 0, 0, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 1, 1, 0, 0, 0, 1, 0, 1], [-1, -1, 1, 0, 1, 1, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, -1, 0, 0], [2, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 1, -1, 3, 1, 1, 0, 0, 1], [1, 1, -1, 1, -1, -1, 1, 0, 0, -1], [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, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 1, 1, 1, -2, -1, -2, 0, 0, 0], [-1, 0, 0, 1, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, -1, -1, 1, 1, 1, 0, 0, 1], [1, 0, -1, -1, -2, -2, -2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, -1, -1, -1, -2, -1, 1, -1], [1, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 0, 1, 0, 0, 0, 1, 1, 0], [-2, -3, 1, -1, 1, 3, 1, -1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, -1, -1, 0, 0, 0], [-2, -1, 1, -1, 0, 1, 1, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0, 0, -1, -1, -2], [0, 1, -1, 1, -1, -1, -1, -1, 1, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -1, -1, -3, 1, 1, 1, 1, -1, -1], [0, 2, 0, 0, -1, 0, 0, 1, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 1, -1, 1, -3, -2, -1, 0, 0, -3], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, -1, 1, 1, -1, -2, -2, 1, 0, -1], [-2, 0, 0, -2, -1, 2, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, -3, 2, 0, 0, -1, -2, 1, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -1, 1, -3, 1, 3, 0, -1, 0, 1], [2, 1, -1, -1, -1, -2, -1, 1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, -3, 1, -1, -1, 1, 0, 1, -1], [0, 3, -1, 1, -1, 1, 1, -1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 1, 3, -1, -2, 1, 1, -2, 1], [2, 0, 0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -2, 0, 0, 2, 2, 2, 0, -1, 0], [2, -1, 2, 2, 3, 3, 3, 0, -1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, 0, 0, 0, 0, -1, 1], [3, 0, 2, 0, 2, 0, 0, -1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 0, -2, 2, 2, 0, -1, 1, 2], [3, -2, 0, -2, 2, -2, -1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, -2, 1, 0], [0, 5, -1, 1, -1, -1, -3, -1, 2, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 1, -1, 0, 1, -1, 1, 1, 3], [3, 0, 1, 1, 0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, -2, 2, -2, -2, 0, -1, 0, -3], [1, 0, 2, 0, 0, 0, -2, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 1, 0, 1, 1, 1, 0, 0, 1], [-1, -2, 0, -2, 0, 2, 1, -1, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 1, -1, 1, 3, 3, 0, -1, -1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 1, -3, 0, -2, 1, 0, 0], [1, 5, -1, 5, -1, -1, 1, 0, 1, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 1, -3, 1, 1, -3, 1, 1, -1, -2], [1, 0, 0, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, -3, -1, -1, -1, 1, -1, 0, 0, 1], [4, -4, 2, -1, 3, 1, 3, 2, -3, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 1, 0, 0, 0, 0, 0, 0, 0]]}