# Stored data for newform 4025.2.a.ba, downloaded from the LMFDB on 16 April 2024.
{"label": "4025.2.a.ba", "space_label": "4025.2.a", "level": 4025, "weight": 2, "hecke_orbit": 27, "hecke_orbit_code": 117093590345191353, "dim": 14, "is_polredabs": true, "trace_hash": 1610106877048597048, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [-5, 3, 386, -193, -1429, 443, 1581, -346, -772, 118, 187, -18, -22, 1, 1]], [3, [405, 135, -3258, -2694, 5298, 4860, -3000, -3128, 632, 909, -8, -121, -12, 6, 1]], [11, [-30528, 1189152, -1593248, -4537424, -1262144, 1283456, 483981, -150514, -61324, 8946, 3589, -265, -98, 3, 1]]], "qexp_display": "q-\\beta _{1}q^{2}-\\beta _{4}q^{3}+(1+\\beta _{2})q^{4}+(\\beta _{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": 27, "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": "0.007", "prec": 17}, "analytic_rank_proved": true, "char_values": [4025, 1, [2577, 1151, 3501], [1, 1, 1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 1, "level_primes": [5, 7, 23], "conrey_indexes": [1], "field_disc": 3134391703906299112657305, "field_disc_factorization": [[3, 3], [5, 1], [108278801, 1], [214425317890543, 1]], "field_poly": [-5, -3, 386, 193, -1429, -443, 1581, 346, -772, -118, 187, 18, -22, -1, 1], "hecke_ring_index_factorization": [[3, 3]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11.355", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "374.773", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "19999.315", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 14, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[5, -1], [7, 1], [23, -1]], "trace_display": [-1, -6, 0, -14], "traces": [0, 14, -1, -6, 17, 0, -4, -14, -9, 18, 0, -3, -11, -15, 1, 0, 23, -9, -17, -4, 0, 6, -9, 14, 10, 0, -5, -33, -17, 11, 0, -1, -24, -26, -6, 0, 13, -18, 6, 6, 0, -7, 4, -18, -16, 0, -1, -10, -40, 14, 0, 28, -46, -5, -24, 0, 9, 26, -2, -24, 0, -6, 16, -18, 29, 0, 27, -61, -35, -6, 0, 11, -12, -28, -49, 0, -27, 3, -38, 6, 0, 26, 14, -16, 11, 0, 46, -61, -58, -39, 0, 15, 17, -21, -74, 0, 41, -19, -1, -9, 0, -3, 29, -69, -73, 0, 3, -7, -10, 22, 0, 4, -23, -29, -97, 0, 87, 22, -43, 9, 0, 51, -27, -17, -86, 0, 17, -45, -42, -89, 0, 6, 14, 4, 9, 0, 28, -21, -4, -23, 0, 22, -76, -26, -58, 0, 73, -6, -87, -7, 0, 23, 81, -36, 9, 0, 133, -19, -2, -10, 0, -14, 74, -40, -78, 0, -20, -61, -10, 51, 0, 5, 12, -50, -66, 0, -4, -1, 23, 7, 0, -6, 5, -65, -9, 0, 89, -50, -11, 33, 0, 16, -108, -16, -71, 0, 17, 54, 35, -13, 0, -27, -5, -11, -89, 0, 28, 18, -106, -2, 0, 46, 12, -12, 6, 0, 35, 1, -102, 3, 0, -25, 199, -123, 24, 0, 49, -6, 47, 2, 0, 26, -27, 7, 32, 0, -51, -49, 6, 45, 0, -56, 56, -135, -91, 0, -15, -129, 82, 24, 0, -10, -13, -3, -34, 0, 111, 39, 0, 18, 0, 62, -80, 2, -158, 0, -6, -10, -81, 40, 0, -33, 141, -6, -84, 0, -11, 6, -6, -32, 0, -53, 17, 17, 82, 0, 57, 7, -131, 21, 0, 18, 9, 35, -4, 0, -11, -80, -85, -15, 0, 18, 94, -7, -106, 0, -110, -67, 16, 96, 0, -10, 57, 26, 37, 0, 20, 2, 21, -22, 0, -57, 1, -80, -131, 0, 187, 41, -87, 10, 0, 13, -59, 62, -138, 0, 40, 4, 57, -37, 0, -103, 182, -14, -105, 0, 102, -48, -110, 59, 0, -106, -201, 15, -2, 0, 20, -28, -118, -5, 0, 120, 60, 38, 46, 0, 131, -128, 23, 37, 0, 5, 163, -16, -86, 0, -123, 37, 24, -8, 0, -91, -22, -178, 239, 0, 91, -27, 41, 36, 0, -9, -9, 64, -62, 0, 175, -47, -18, -26, 0, -96, 12, 67, -22, 0, 2, 27, 135, 15, 0, -156, -155, 24, -17, 0, 86, 0, 66, 17, 0, -43, -21, -61, 117, 0, 4, 6, 10, 144, 0, 3, 211, -49, -16, 0, 76, -4, 11, -60, 0, 18, 44, 49, -92, 0, -40, -29, -29, 36, 0, -35, 30, -73, 96, 0, -245, -56, 192, 76, 0, 57, -27, -136, 67, 0, 39, -16, 31, 61, 0, -125, -133, 10, -267, 0, 35, 6, 106, -33, 0, -122, 14, 6, 108, 0, 109, -177, -31, -8, 0, -73, -28, -34, -78, 0, -285, -11, -42, 57, 0, 120, 63, 12, 12, 0, -9, 19, 113, 54, 0, 28, -109, 119, -16, 0, -188, 27, 49, -21, 0, -140, 98, -99, 131, 0, -144, -83, 134, 14, 0, -143, 27, 109, 104, 0, 115, 55, -18, -3, 0, -81, 146, 112, 6, 0, 38, -3, 76, 112, 0, -166, 10, -6, -249, 0, 95, -51, -10, 4, 0, -27, -108, 94, -86, 0, -95, -26, -52, 53, 0, -87, 149, 134, -14, 0, 187, -107, 72, 59, 0, 16, 11, -62, 246, 0, -259, -68, -11, 24, 0, 55, -18, 46, 147, 0, 93, 57, -5, -24, 0, -102, -46, -143, -43, 0, 298, -41, 96, 61, 0, 28, -66, -154, -118, 0, 58, -58, 190, 22, 0, -33, 83, 39, 45, 0, 66, -112, 178, 88, 0, -60, -81, 64, 254, 0, -55, -15, 14, 76, 0, 49, 113, -140, -17, 0, -36, -74, 211, -3, 0, 21, -56, 85, 191, 0, -253, -107, 74, 75, 0, -22, 96, -159, 49, 0, -164, 11, 114, 118, 0, 6, -41, 126, -118, 0, -50, 188, 17, 19, 0, 57, -20, 71, 4, 0, 1, 14, 312, 58, 0, -111, 31, 9, -8, 0, 149, -189, 65, -34, 0, -199, -62, -48, -127, 0, -3, 3, 105, 149, 0, 134, -52, -1, -29, 0, 10, -76, 88, -34, 0, 69, 72, 6, -103, 0, -300, -113, 73, 141, 0, 118, 112, -25, 89, 0, -24, 117, 274, 95, 0, -44, -3, 2, -147, 0, 93, 116, -139, 7, 0, 15, 143, 238, 19, 0, 10, -66, 109, -26, 0, 35, 328, -22, 79, 0, -138, 41, -147, 40, 0, -148, -51, 29, 269, 0, 11, -4, -10, -15, 0, 58, -6, -78, 23, 0, 275, 3, 271, -78, 0, 29, 291, 97, -12, 0, -211, 23, 97, 97, 0, -106, 153, -29, 96, 0, 46, 13, -128, 168, 0, -76, -87, 100, 52, 0, -65, -100, -158, -22, 0, 16, 231, -142, -23, 0, 43, 36, 13, 88, 0, -50, 49, -9, -79, 0, 275, -50, 140, -182, 0, -67, -91, 14, 305, 0, -11, -51, 31, 129, 0, -18, 226, 18, 27, 0, 203, -24, 273, 102, 0, 17, -88, 44, 126, 0, -83, 193, 86, 6, 0, -54, -64, -11, 6, 0, -142, 3, 60, -133, 0, -180, -17, -174, 72, 0, -155, 117, 321, 45, 0, 82, -135, 180, 34, 0, 42, 6, 259, -71, 0, -108, 446, 89, -61, 0, 376, -79, -130, 1, 0, -10, 379, 152, -56, 0, -246, -6, 157, 133, 0, 20, 91, 63, -14, 0, 180, -222, 72, 46, 0, -4, 235, 63, -33, 0, -108, -24, -9, -55, 0, -98, 143, -7, 88, 0, -261, 18, 40, -59, 0, -166, -28, 147, -223, 0, 317, 116, -125, 21, 0, 199, 256, 58, -107, 0, 4, -88, 428, 282, 0, -91, 151, 23, -173, 0, -65, -102, -68, -107, 0, -143, 17, -24, 394, 0, 85, -22, -13, -18, 0, -84, 490, 249, 76, 0, 61, -79, 376, 25, 0, 26, 282, 65, 136, 0, -159, -126, 58, 112, 0, 239, -16, 36, -309, 0, -232, -87, 114, -176, 0, -80, -73, -8, 86, 0, -1, 240, -72, 6, 0, 68, 359, 76, 189, 0, 87, 37, -209, 58, 0, -268, 151, 7, 40, 0, -2, -174, -105, -243, 0, 49, -38, 153, 204, 0, 150, -23, -1, 78, 0, 82, 235, -123, -81, 0, 177, 75, 135, -60, 0, 36, -127, -134, 294, 0, -118, 87, -9, -117, 0, -10, 148, -116, 262, 0, 49, -319, 314, 33, 0, -36, -133, -116, 86, 0, -237, -7, -110, 19, 0, -211, -30, -29, -40, 0, 2, 92, 47, 165, 0, -114, -110, 10, 118, 0, -153, -64, 4, -15, 0, -85, 182, -176, -307, 0, -197, 14, 22, 74, 0, 140, -6, 359, -74, 0, 229, 93, 160, -101, 0, 40, 256, -13, 221, 0, -228, -34, 78, 76, 0, 87, -274, -159, -79, 0, -237, -5, -127, 5, 0, 19, 20, -76, -294, 0, 218, -107, -132, 61, 0, -18, 133, 28, -29, 0, 10, -49, -78, -301, 0, -257, 236, -51, -370, 0, -126, -149, -307, 89, 0, 96, -188, 204, -3, 0, -46, -5, 277, 249, 0, -43, -61, 159, -12, 0, 196, -202, 37, 59, 0, 50, 49, 41, 203, 0, -653, -145, 66, -5, 0, -202, 60, 3, -60, 0, -193, 101, 7, 22, 0, -125, 4, 319, 254, 0, 445, 83, -19, 1, 0, 42, -24, -22, -475, 0, -23, 166, 68, -8, 0, -99, 223, -7, -564, 0, 172, -54, -211, -80, 0, -54, 97, 149, 98, 0, 100, 6, -125, 260, 0, 82, 124, 120, -5, 0, -179, 7, -293, -87, 0, 65, -182, -10, 378, 0, 86, -345, 9, 44, 0, 136, -341, -152, 87, 0, -308, -73, -173, -421, 0, -18, -89, -249, 308, 0, 116, 122, -184, 50, 0, 26, -120, 182, -60, 0, 11, -130, 35, -74, 0, -225, 24, -33, -150, 0, 177, -75, -398, -31, 0, -48, -58, -43, -2, 0, -547, -16, -66, 112, 0, -62, -220, -98, 108, 0, -157, -18, 62, 26, 0, 16, 319, 39, -2, 0, -5, -24, 71, -181, 0, 69, -188, -187, -412, 0, -29, -119, 386, 150, 0, -46, -17, -188, -99, 0, -185, 59, -158, -54, 0, -73, -197, 128, 131, 0, -35, -49, -124, 36, 0, -61, -65, 13, -276, 0, 98, 17, -231, -195, 0, -126, -260, -6, -23, 0, 190, 27, -110, 67, 0, -88, -38, 171, 5, 0, 214, -345, -63, 341, 0, 11, 234, -243, 222, 0, 16, 4, 89, 305, 0, 217, -145, 215, 148, 0, 104, 5, 136, -63, 0, -313, -28, -280, 365, 0, 201, -47, 66, -18, 0, 102, 150, 71, 22, 0, 106, -19, -129, -65, 0, -49, -105, 2, -84, 0, -34, -146, -127, -64, 0, -65, 29, -168, -3, 0, 175, -46, 9, -22, 0, 169, 396, 58, -12, 0, -138, 33, 228, -56, 0, 12, -61, 144, 173, 0, -238, -319, -6, -47, 0, -196, -263, -295, -138, 0, -109, 39, -249, -90, 0, 206, -35, -63, -214, 0, -35, 154, 27, -1, 0, 195, -139, -116, -443, 0, 102, 71, 9, 100, 0, 25, -161, -3, 523, 0, 392, 21, -82, -389, 0, -61, -171, -69, 306, 0, 60, 25, 156, 7, 0, -110, -244, 139, -199, 0, 414, 168, 149, 130, 0, 123, -306, 43, -35, 0, -247, -13, -24, 194, 0, 286, -251, -175, 78, 0, -281, 334, -154, 154, 0, -123, -49, -70, 220, 0, 445, -6, -200, 6, 0, -8, 142, 198, -201, 0, -47, 124, 82, -118, 0, -126, 53, -2, -486, 0, 182, -212, -283, -66, 0, 174, -132, -129, 2, 0, 186, -26, 131, 330, 0, 123, 275, -224, 27, 0, 105, -132, -90, -42, 0, -7, 88, 11, 347, 0, -15, -95, -32, -16, 0, 38, 166, -160, -389, 0, 2, -305, -358, 65, 0, -17, 51, -40, 4, 0, -12, -109, 119, 49, 0, -38, 21, -121, -68, 0, -6, 176, -42, 18, 0, 196, 129, -45, -86, 0, 202, -259, 34, -28, 0, 99, 213, -28, 211, 0, 165, 56, -102, 275, 0, -29, 302, 329, -56, 0, -7, 12, -134, 186, 0, 135, -49, -86, -205, 0, 112, 214, 91, -114, 0, 198, -260, 198, -49, 0, -197, 62, -199, -96, 0, -104, 15, -198, -328, 0, 17, 36, -243, 129, 0, 351, -199, 94, -92, 0, -82, -43, 129, -190, 0, -5, 187, -24, 351, 0, 31, -124, -27, -184, 0, -40, -220, -54, -97, 0, -66, 10, 30, -29, 0, 171, -82, 36, 13, 0, 58, -131, -219, -189, 0, 3, -10, -5, -24, 0, -251, -7, 34, -256, 0, -4, -411, -331, 272, 0, 285, 292, -279, 108, 0, -70, -111, -80, -38, 0, 21, 431, -290, -39, 0, 69, -72, 55, 132, 0, 0, -99, -112, 256, 0, 128, -100, -18, -203, 0, -107, 6, -446, -240, 0, -62, -413, -173, -606, 0, 248, -62, -188, -28, 0, -19, 478, 222, 80, 0, 242, 111, -223, 79, 0, -2, -24, -43, 205, 0, -343, -159, 158, 194, 0, 241, -74, 167, -166, 0, 226, 152, -93, -357, 0, -136, 6, 26, -30, 0, 40, 82, -320, 10, 0, 28, -62, 130, -573, 0, 81, -14, -141, 50, 0, 190, 219, -40, -479, 0, 14, 33, 255, 50, 0, 55, -163, 49, -1, 0, 268, 33, -26, 40, 0, -43, 17, -331, -141, 0, -24, 61, -44, -16, 0, 6, 4, 27, 144, 0, -361, -69, 84, -143, 0, -154, -274, -85, 500, 0, -155, -172, -291, -236, 0, 52, 11, -145, -172, 0, 107, 124, -51, -6, 0, -30, -151, 31, -416, 0, 6, 692, -119, -19, 0, -53, 39, 32, -67, 0, 416, -191, -595, -160, 0, 93, -351, -111, 70, 0, -20, 53, -281, -138, 0, 184, 67, 85, -17, 0, -11, 204, 46, 191, 0, -17, 6, -370, -437, 0, -91, 266, -82, -261, 0, 275, -416, -152, 167, 0, 0, 24, 95, -118, 0, -61, -57, -5, -138, 0, 320, -300, 312, -7, 0, 218, 212, 284, 41, 0, 131, -59, -43, 250, 0, -102, -445, -21, -58, 0, -465, 45, -204, -221, 0, -22, 42, -11, 421, 0, 263, -18, 329, -21, 0, -14, 258, 30, -9, 0, 305, -39, -362, -175, 0, -35, -367, 95, -217, 0, 279, -20, 4, -126, 0, 273, -79, -295, -258, 0, -258, 285, 503, -72, 0, -73, 11, 115, 66, 0, 189, -9, -136, 80, 0, -41, 217, -147, -463, 0, 85, 46, -443, -241, 0, 62, -162, 15, -321, 0, 413, -43, 368, -230, 0, -110, -528, 2, -243, 0, 245, -18, -14, 577, 0, 36, 139, 5, -94, 0, 17, 70, 206, 116, 0, 7, 20, 0, -274, 0, 271, -83, 106, -52, 0, 156, 266, -82, 703, 0, 205, -58, 54, -21, 0, -355, 110, -474, 342, 0, -228, 293, 62, 67, 0, 147, -66, 242, -51, 0, -16, 198, -139, 100, 0, -78, -74, -96, -249, 0, 134, -71, 123, -470, 0, -31, -42, 222, -210, 0, -219, 10, -248, -17, 0, 221, -142, 44, -57, 0, 248, -194, -207, -133, 0, -26, -183, -26, 46, 0, -350, -84, -37, -163, 0, 27, -8, -158, -45, 0, 327, 200, 41, 48, 0, 315, -20, -58, -792, 0, 121, 12, -211, -2, 0, 125, -320, -482, 438, 0, -21, 192, 3, -233, 0, -19, 220, 22, 217, 0, -248, -158, 212, -36, 0, -216, -723, 106, 265, 0, 126, 57, -42, 398, 0, 45, -80, 7, -1, 0, -147, 96, -169, -227, 0, 80, -232, -184, -141, 0, -179, 0, 131, 218, 0, 223, -178, 224, -164, 0, -53, -9, 168, -357, 0, 111, -187, 134, -206, 0, 54, 43, 400, -41, 0, 379, 56, -6, 230, 0, 87, -126, 318, -130, 0, -431, -117, -10, 1, 0, 429, 66, -117, -245, 0, 87, 81, 159, 56, 0, 359, -13, -450, 218, 0, -351, -329, -3, 59, 0, -295, -31, 8, -307, 0, -62, -261, -44, 173, 0, 333, -230, 138, -36, 0, 31, 230, -177, -172, 0, 29, -99, 257, 287, 0, -82, -40, 33, -614, 0, 441, 103, -357, -4, 0, 92, 377, -29, -49, 0, -57, 238, 396, -69, 0, 34, 19, 37, 211, 0, -433, 179, -170, -488, 0, 128, 114, -210, 612, 0, 127, 103, -200, -3, 0, 160, -73, -139, -182, 0, -75, 134, -24, 11, 0, 14, -152, 107, -493, 0, -232, -147, 105, 33, 0, 379, -229, -108, 131, 0, 128, -52, -674, 123, 0, -153, -102, -56, 210, 0, 62, 49, -562, 48, 0, 412, 554, 115, 326, 0, 110, 267, 3, -248, 0, -79, 413, -59, -33, 0, -48, 140, 72, -202, 0, 333, -542, -350, 455, 0, -461, 106, -114, -362, 0, -7, -102, 38, 201, 0, 168, -305, 33, 62, 0, -15, -628, 192, 511, 0, 266, 39, 2, 63, 0, -226, 30, -40, -10, 0, -140, -236, 205, -372, 0, -75, -20, 120, 172, 0, -260, 155, -363, 28, 0, -180, 167, -414, -62, 0, 118, 22, -75, -372, 0, 378, 431, 5, -764, 0, 278, 225, 25, -6, 0, 263, 138, -121, 452, 0, 11, -120, -18, 117, 0, 50, -245, 171, -60, 0, -91, 280, 196, -155, 0, -38, -320, -70, -528, 0, -434, 259, -46, 199, 0, -178, -121, 4, 407, 0, 127, 91, -397, -362, 0, -76, -131, -412, -80, 0, 1, -67, -526, 128, 0, 287, -418, 255, -443, 0, -23, -63, 470, -65, 0, -35, -7, -37, 314, 0, 267, -109, -106, 173, 0, 230, 501, 298, 137, 0, -53, -5, -20, -29, 0, -203, -314, 77, -163, 0, -419, 28, -48, 74, 0, 16, 230, 53, 114, 0, -16, 6, 86, 194, 0, -135, -97, -245, -254, 0, -39, 10, -306, -343, 0, 233, 123, 180, 20, 0, -324, 559, -393, -37, 0, 216, -82, 9, 46, 0, -24, 130, -283, 169, 0, 367, -63, 8, -98, 0, -53, 31, 87, -33, 0, 315, -173, 57, 124, 0, 507, 91, 87, 358, 0, 35, 358, 265, 22, 0, 254, -65, 4, -242, 0, 178, -216, -79, 381, 0, -32, -6, -239, -138, 0, 22, 297, -97, 416, 0, -40, 129, 378, -181, 0, -123, -91, -49, -173, 0, 178, -176, 54, 27, 0, 54, -122, 108, -43, 0, -41, 171, -259, -14, 0, -17, -150, -36, 61, 0, -267, -138, 446, 130, 0, 256, 234, -110, 221, 0, -29, 9, -26, -531, 0, -28, -212, -59, 9, 0, -424, 73, -146, 159, 0, -64, 531, -30, 105, 0, 28, 55, 62, 73, 0, -54, -468, -111, 399, 0, -751, -335, -362, 324, 0, -154, -175, -143, -462, 0, -96, -67, -745, 47, 0, -230, 76, 51, 388, 0, 18, 392, 45, -120, 0, -46, 572, 26, 87, 0, -488, -256, 421, 165, 0, 75, -205, 189, -400, 0, -27, 96, 347, 121, 0, 218, -671, 249, -12, 0, -85, 18, -111, 288, 0, -67, -141, 59, 266, 0, -532, 158, 22, -17, 0, -66, 411, 168, 376, 0, -101, 522, -320, -104, 0, 198, -2, 74, 351, 0, 148, 226, -12, -27, 0, 315, -86, 14, -102, 0, -135, -32, -59, -165, 0, 23, 141, -15, -452, 0, -331, 159, -693, -278, 0, -190, -273, 186, -86, 0, 208, 156, 298, 324, 0, -10, -72, 230, 155, 0, -178, -431, -538, -366, 0, -24, -182, 322, -40, 0, -403, -71, 17, 178, 0, 152, 133, -193, -434, 0, -102, 167, -167, 112, 0, -190, -86, 265, 163, 0, -99, 12, 76, 0, 0, -45, 57, -201, 369, 0, -66, -91, 564, -446, 0, 63, -38, -17, -8, 0, 378, 628, 124, -191, 0, -39, -280, 275, -42, 0, -288, 43, 5, 132, 0, -122, -210, -176, 21, 0, -14, 124, 391, 91, 0, 61, -45, -224, 283, 0, -220, -89, -117, -106, 0, 18, 108, 143, 365, 0, -609, 102, 340, -427, 0, 45, -4, -434, 321, 0, -166, -278, 323, -6, 0, -124, -380, -58, -258, 0, -10, 82, 361, -143, 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": "4025.2.a.ba", "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], [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], [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, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 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, 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, 0, 0, 0, -1], [0, 2, -1, -1, -1, -1, 1, 1, 0, -2, 0, 0, 1, -1], [-1, 1, -1, 0, 0, 0, 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, 0, 1, 1, 1, 0, 0, -1, 0, 2, 1, 0, 0, 1], [-1, -1, 0, 1, 0, 0, 0, -1, 0, 2, 0, 0, -1, 1], [-1, -2, 0, 1, 1, 0, -1, -1, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, -1, 0, 1, 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, 0, 0, 0, 0, 0, 0], [0, -1, -1, 0, -1, 2, -1, -1, 0, 0, 0, 0, -1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 1, 1, -1, -1, -1, 2, 0, 0, -1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, -1, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0], [-3, 0, 0, 0, -1, 1, -1, -1, 0, 1, 2, 0, 0, 1], [-1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, -1, -1, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, -1, -1, 1, -1, 0, 2, 0, -2, 0, -1, 1, 0], [-2, 1, -1, -2, 0, -1, 1, 0, 0, -2, 1, 0, 0, 0], [-1, 1, 0, 1, 0, -1, 1, 0, 0, -1, 1, 1, 0, 0], [-1, 3, 0, -1, 0, -1, 1, 0, 0, -1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 1, 1, 1, -1, -1, 0, 1, 0, -1, 0, 0], [-1, 1, 0, 0, 0, 0, -1, 1, -1, 1, -1, 0, 0, 0], [-2, -2, 1, 1, 3, 1, -2, 0, 0, 2, -1, -2, 1, 1], [-1, 1, 1, -2, 0, 1, 0, 0, 0, -1, 1, -1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 1, -1, 0, -1, -1, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [-3, -2, 1, 2, 3, -1, -1, -1, -1, 2, 0, -1, 0, 1], [1, -1, -1, 2, -1, 1, 0, -1, 2, 0, -1, 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, 0, 0, 0], [-1, 0, -1, 1, 0, 1, 0, -1, 2, 1, 1, 0, 0, 1], [-1, 0, -1, -1, 0, -2, 1, 0, 1, -2, -1, 1, 0, -2], [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], [2, -3, -1, 1, 1, 1, -1, -2, 1, 2, 0, 1, -1, 1], [-2, 2, -2, 0, -2, 0, 0, 0, -1, 0, -1, 0, 0, -1], [-1, 1, -1, -2, -1, 2, 1, 0, 0, -1, 1, 1, 0, 0], [-3, 3, 0, -2, 0, -1, 2, 1, 1, 0, 0, 0, 1, -1], [0, 0, 0, 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], [2, 2, 1, 2, 1, -2, 0, 1, -1, 2, -2, 0, 0, 1], [-1, -3, 0, 0, 1, 0, 1, -2, 0, 1, 0, 1, -1, 0], [-1, 2, 0, 1, 0, -1, 0, -1, -1, 0, 1, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, -2, 0, 0, 0, 2, 1, 2, -1, 0, 2, 0, 0], [1, 1, 1, 3, 0, -2, 0, 1, 0, 2, -1, -1, 2, 1], [-1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 2, 2, 2, 0, 1, 0, -1, 3, -1, 0, -1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 4, -2, -2, 0, 0, 2, 1, -2, -1, -1, 0, -1, 1], [-4, 1, 0, -1, 0, 0, 0, 0, 0, -1, 1, 1, 0, -1], [-5, 2, 0, -1, 2, 0, 1, 1, -1, 0, 1, 0, 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, 0, 0, 0], [-1, 4, 0, -2, 1, -1, 1, 2, 0, -2, 0, -1, 3, -1], [1, 0, -2, -2, -2, 1, 0, 1, 2, -1, -1, 0, 0, -2], [-1, -2, 0, -1, -2, 2, 1, -1, 1, 0, 1, 2, -2, 0], [-1, 6, -1, -1, -3, -2, 1, 2, 0, -4, 0, 0, 2, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, -1, 0, -2, -1, 0, 1, -3, -1, -1, 1, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [-3, -8, 1, 1, -1, 2, -1, -3, 2, 4, 1, 1, -1, 0], [-2, 0, 0, 0, 2, 0, 0, -2, -2, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, -1, -1, 4, -2, 2, 1, -1, -1, -2, 0, -1, -1], [4, 2, -1, 1, -1, -1, 1, 1, 1, -2, -2, 1, 1, -3], [-1, -1, 1, 0, 1, -1, -2, 1, 0, 0, -2, -2, 1, -1], [0, -2, 1, 1, 1, 1, -1, -1, 0, 2, 0, 0, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 0, -2, 2, -2, 0, 0, 0, -2, -1, -1, 1, 0], [-5, 4, -2, -3, -2, 1, 2, 1, 1, -2, 2, 0, 1, -1], [-3, 0, -3, 1, 3, 1, -2, 1, 0, -1, -2, -1, 0, -1], [-3, 2, 1, 0, 1, -2, 0, 2, -1, -1, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, -4, 2, 1, 2, 1, -2, 0, -1, 1, 0, -3, 1, 1], [-6, -1, -2, 0, 1, 1, -1, -1, 1, 1, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 2, 2, 4, 3, -1, -2, -1, 4, 0, -2, -1, 2], [-1, -1, 1, 0, -1, 2, -1, -2, 0, 1, 0, 0, -3, 0], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -1, 2, -2, 2, 0, 1, 2, 3, 0, 0, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}