# Stored data for newform 4719.2.a.bq, downloaded from the LMFDB on 11 September 2025.
{"Nk2": 18876, "analytic_conductor": 37.68140471384221, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, -1], [11, 1], [13, 1]], "atkin_lehner_string": "-++", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [4719, 1, [1574, 3511, 4357], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 18, "field_disc": 131190698033316560210868505000000000000, "field_disc_factorization": [[2, 12], [5, 13], [11, 1], [389, 1], [14083961, 1], [435377456870779, 1]], "field_poly": [55, -630, 151, 11016, -12506, -21589, 26541, 18293, -22969, -8392, 10427, 2242, -2689, -348, 396, 29, -31, -1, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": -1, "has_non_self_twist": 0, "hecke_cutters": [[2, [55, 630, 151, -11016, -12506, 21589, 26541, -18293, -22969, 8392, 10427, -2242, -2689, 348, 396, -29, -31, 1, 1]], [5, [-42944, 225056, 177072, -1909436, 1599855, 2286223, -2976127, -335670, 1370062, -196875, -262602, 70738, 22386, -8923, -590, 494, -21, -10, 1]], [7, [-11501824, 31615744, 5248128, -59460800, 10284736, 38445072, -6678188, -12956016, 1370817, 2536215, -65522, -288683, -12146, 18070, 1618, -569, -69, 7, 1]]], "hecke_orbit": 43, "hecke_orbit_code": 189151184383119983, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": true, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "4719.2.a.bq", "level": 4719, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [3, 11, 13], "level_radical": 429, "minimal_twist": "429.2.n.d", "prim_orbit_index": 1, "qexp_display": "q-\\beta _{1}q^{2}+q^{3}+(2+\\beta _{2})q^{4}+(1-\\beta _{7}+\\cdots)q^{5}+\\cdots", "related_objects": [], "relative_dim": 18, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "4719.2.a", "trace_display": [-1, 18, 10, -7], "trace_hash": 876149990952786330, "trace_moments": [{"__RealLiteral__": 0, "data": "0.157", "prec": 17}, {"__RealLiteral__": 0, "data": "14.519", "prec": 20}, {"__RealLiteral__": 0, "data": "15.007", "prec": 20}, {"__RealLiteral__": 0, "data": "637.521", "prec": 24}, {"__RealLiteral__": 0, "data": "1760.496", "prec": 27}, {"__RealLiteral__": 0, "data": "46733.566", "prec": 30}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.007", "prec": 17}, "traces": [0, 18, -1, 18, 27, 10, -1, -7, -3, 18, 3, 0, 27, -18, 10, 10, 41, 5, -1, -10, 16, -7, 0, 9, -3, 52, 1, 18, -4, 0, 3, 36, -37, 0, 20, 23, 27, 37, 6, -18, 54, -12, 10, 2, 0, 10, -6, 0, 41, 61, 48, 5, -27, 18, -1, 0, 36, -10, 40, 10, 16, 12, 25, -7, 67, -10, 0, 52, 18, 9, -13, 1, -3, -29, 2, 52, -26, 0, 1, 18, 48, 18, -6, 26, -4, -15, 9, 0, 0, 59, 3, 7, 4, 36, 53, 5, -37, 70, -93, 0, 50, 50, 20, 37, 3, 23, 25, 11, 27, -20, 0, 37, -80, 35, 6, 69, 19, -18, -2, -49, 54, 0, -44, -12, 90, 48, 10, 24, -40, 2, -3, -5, 0, 54, 64, 10, 54, 4, -6, 14, 44, 0, -31, 0, 41, -22, 74, 61, 81, -28, 48, -47, -101, 5, 0, -11, -27, 61, -39, 18, 176, 13, -1, 54, -176, 0, 9, -16, 36, 18, -89, -10, 153, 76, 40, -88, 0, 10, -73, -14, 16, 35, -10, 12, 19, 35, 25, 0, -153, -7, -12, 12, 67, 26, 0, -10, 91, -79, 0, 47, 53, 52, 21, -30, 18, -13, 40, 9, -41, 0, -13, 34, -47, 1, 26, 26, -3, -15, -146, -29, 0, -5, 2, 66, 18, 52, -72, -38, -26, 70, -243, 0, -38, 8, 1, 67, -29, 18, 176, 104, 48, 2, 0, 18, -30, 10, -6, 10, -19, 26, 43, -17, -4, 0, -155, -15, 129, 79, 9, 77, -16, 0, -60, -54, 0, 44, -56, 59, -8, -6, 3, -50, 37, 7, -28, 0, 4, 129, -93, 36, -166, -62, 53, 33, -171, 5, 0, -70, -37, 95, -98, 70, -32, 12, -93, 43, -41, 0, -74, -9, 50, 25, -216, 50, -71, 51, 20, -38, 0, 37, -159, 12, 3, 68, 149, 23, 24, -8, 25, 0, -138, 11, -78, -107, 27, -52, 114, -20, 3, 65, 0, 58, 41, 37, -4, 19, -80, 75, -1, 35, 10, 0, 6, 13, -31, 69, 27, 11, 19, -109, -234, -18, 0, 102, -2, 51, 31, -49, -93, -71, 54, 76, -150, 0, 4, 150, -44, 56, -194, -12, 165, 93, 90, -24, 0, 48, 27, 0, 10, 86, -12, 24, -166, -115, -40, 0, -216, 2, 51, -8, -3, 2, 53, -5, -118, 24, 0, 15, -135, 54, 63, 89, 64, -36, 67, 10, 151, 0, 54, -22, -2, 4, 22, -18, -6, 117, 37, 14, 0, 6, 44, -61, -144, 0, -63, -145, -31, 48, -79, 0, 9, -34, 41, 125, 47, -22, 34, -25, 74, 16, 0, 61, -20, -60, 81, -33, 98, -28, -133, 147, 48, 0, -98, -47, 5, -23, -101, 23, 88, 5, 146, -26, 0, 45, -304, -11, -31, 17, -27, 48, 155, 61, 54, 0, -39, -50, -44, 18, 28, 41, 176, -37, 38, 13, 0, 14, -1, 92, -101, 54, -50, -147, -176, 5, -6, 0, 67, 220, 9, 51, 178, -16, -12, 21, 36, -74, 0, 18, -13, 106, -89, 49, -108, -10, -66, -72, 153, 0, -195, 76, -54, 55, 40, 181, 234, -88, 6, 16, 0, 119, -119, 10, 61, 12, -73, -84, 171, -14, 36, 0, 16, 77, 93, 35, 97, 34, -10, -80, -209, 12, 0, 57, 19, 85, 40, 35, 1, -192, 25, -2, -72, 0, 23, 16, -153, 13, -68, -7, 106, -9, -12, 146, 0, 12, -14, -63, 67, 4, 36, 26, -211, -21, 0, 0, 243, -10, -173, -139, 91, 97, -64, -79, 234, -13, 0, 116, -102, 47, 6, 73, 53, 83, 190, 52, 156, 0, 21, 24, -190, -30, -154, 0, 18, -14, 0, -13, 0, -79, 40, 44, -27, 9, -286, -128, -41, 202, 173, 0, 231, 67, -13, -6, -173, 34, 22, -22, -47, -61, 0, 1, 355, 56, 26, 50, 81, 26, -92, -146, -3, 0, -48, -15, 11, -39, -146, -27, -166, -29, 54, 30, 0, 107, -16, -5, 17, -7, 2, 23, 36, 66, 48, 0, 18, 66, 88, 52, 27, -51, -72, 54, -268, -38, 0, -95, -26, -10, 98, 70, 313, -18, -243, 32, 91, 0, -80, -165, -38, 7, -87, 8, -335, 40, 1, -40, 0, 67, 84, -213, -29, 27, -290, 18, -54, -8, 176, 0, -175, 104, 30, -4, 48, -113, 149, 2, 6, -68, 0, 107, -36, 18, 25, -89, -30, -116, 139, 10, 174, 0, -6, -114, 123, 10, -342, 94, -19, 72, 39, 26, 0, 73, 43, -109, -183, -17, -40, -144, -4, 44, 301, 0, -185, 223, -155, -98, 170, -15, 224, -10, 129, 6, 0, 79, 29, -47, 9, 54, -122, 77, -4, -201, -16, 0, 11, 0, -23, 28, -60, -33, -100, -54, -71, 129, 0, -12, -130, 44, -184, -99, -56, -133, 133, 59, 15, 0, -8, 160, -25, -6, 78, 86, 3, -204, -5, -50, 0, 25, 37, 24, -35, 7, -418, -181, -28, -182, -7, 0, -47, -28, 4, 97, 11, 129, -67, 74, -93, 213, 0, 36, 62, 33, -166, 56, -34, -62, 232, 10, 53, 0, -232, 33, -480, -216, -171, -39, -222, 5, 21, -32, 0, -41, 308, -70, 64, -41, -37, 20, 18, 95, 79, 0, -98, -52, -280, 70, -69, 157, -32, -91, 54, 12, 0, 131, -93, 82, -18, 43, 185, 86, -41, 141, -70, 0, -102, 6, -74, -231, -17, -9, -108, 243, 50, 65, 0, 25, -158, -194, -216, 154, -187, 50, 13, 9, -71, 0, 164, 51, 31, -185, 20, 88, -389, -38, -268, -1, 0, 171, -68, 37, -4, 244, -159, -142, 16, 12, 65, 0, 3, 85, -36, 68, -200, -123, 149, -10, -62, 23, 0, -74, 24, 29, -3, -8, 181, -112, 25, -76, 245, 0, -325, -242, -138, 100, -2, 11, 92, 188, -78, -63, 0, -107, -182, -145, 27, 15, 59, -52, -428, -162, 114, 0, -286, -20, -156, 13, 3, -18, 47, 65, 26, 41, 0, 10, 308, 58, -354, -191, 41, -136, 136, 37, 473, 0, -4, -1, 219, 19, 44, 75, -80, 3, -251, 75, 0, 96, -1, -182, -290, 35, -38, -128, 10, 118, -412, 0, 109, 35, 6, -18, -173, 13, -47, 58, -31, -114, 0, 69, -106, -321, 27, -96, -48, 11, 11, -280, 19, 0, -92, -109, -318, 123, -234, 39, -117, -18, 189, 299, 0, -31, -46, 102, 18, -81, -2, -166, 60, 51, 6, 0, 31, 204, -163, -49, -156, -3, -93, -52, -56, -71, 0, -26, 54, 103, 47, 76, -377, -380, -150, -5, -296, 0, -284, -113, 4, -32, 4, 150, 56, 1, -44, -172, 0, 56, 185, -162, -194, 15, -315, -12, 379, -36, 165, 0, -74, 93, 31, -302, 90, 22, -9, -24, -962, 241, 0, 129, -230, 48, -282, -128, 27, 36, -17, 0, 28, 0, 10, -45, -410, 86, -261, -83, -12, -54, -75, 24, 0, -81, -166, -69, -217, -115, -148, -84, -40, 12, -201, 0, -75, -59, -216, -109, -391, 2, 82, -181, 51, -3, 0, -8, -99, 122, -3, -9, 556, 2, 257, -102, 53, 0, -406, -5, -207, -21, -118, -7, -122, 24, -36, 203, 0, -48, -9, 15, -297, 50, -135, 42, -4, 54, 146, 0, 63, -98, 45, 89, 64, -227, 64, -3, -536, -36, 0, -123, 67, 75, 150, 10, -540, -3, 151, 22, 8, 0, -53, -26, 54, 134, -18, -22, -162, 145, -2, 96, 0, 4, 132, -5, 22, -72, -47, -18, -95, -44, -6, 0, -16, 117, -378, -218, 37, 116, 691, 14, 85, -39, 0, -275, 87, 6, 18, -55, 44, -70, -241, -61, 105, 0, -144, -71, -159, 0, -125, -110, -63, 239, 93, -145, 0, -22, -31, -30, -173, 48, -130, -144, -79, 7, -138, 0, -345, -2, 9, -42, -18, -34, -105, -48, 41, 31, 0, 125, -50, -194, 47, 164, 750, -22, 67, 63, 34, 0, -23, -25, 71, -50, 74, 238, 446, 16, -60, 49, 0, 164, -182, 61, 296, -111, -20, 32, 698, -60, 368, 0, 81, 30, 217, -33, -361, -160, 98, -37, 308, -28, 0, -120, -133, 54, -121, 147, -196, -246, 48, -124, -3, 0, 10, -51, -98, 73, -23, -47, -147, 50, 5, 103, 0, -23, 55, 8, -101, 77, -200, 23, -404, -2, 88, 0, -31, 5, -25, -169, 146, 121, 474, -26, 268, 238, 0, 202, 3, 45, -377, -11, -304, -56, 61, -11, -94, 0, -31, -203, -26, 17, 217, 210, -27, 110, -70, 48, 0, 63, 155, 77, 350, 61, -306, 3, 54, 20, -173, 0, 46, 213, -39, -53, 223, -50, -48, -328, -44, -12, 0, 18, -200, -2, 28, -13, -488, 41, 5, -160, 176, 0, 96, -37, -309, -160, 38, 284, -177, 13, 48, 117, 0, -12, 38, 14, 80, -79, -1, 238, 668, 92, -26, 0, -101, 82, -37, 54, 65, -35, -50, 0, -339, -147, 0, -38, -176, -92, 128, 5, 214, -71, -6, 90, 754, 0, 175, 74, 67, 113, -232, 220, 359, -189, 9, -69, 0, 51, -301, 23, 178, -101, -46, -16, 0, -45, -12, 0, -19, 21, 205, -58, 36, -407, -95, -74, 209, -56, 0, -28, -144, 18, 89, -217, -13, 125, -210, 106, -385, 0, -89, -100, -50, 49, 2, -178, -108, 61, -169, -10, 0, -54, -66, -16, -39, -72, 406, 49, 153, -49, -177, 0, -66, -16, -195, 77, -102, 76, 62, 129, -54, 118, 0, 55, 327, -271, 40, -47, -430, 181, 194, 124, 234, 0, 85, -88, -20, -157, 6, 121, -51, 16, 230, -61, 0, 133, 44, 119, -244, -125, -119, -195, -440, 10, -16, 0, 61, 51, 64, 12, 245, 3, -73, 52, 652, -84, 0, -97, 171, 228, 325, -14, -90, -99, 36, -206, 186, 0, -25, -103, 16, 115, 325, 77, 412, -48, 93, -26, 0, 35, 4, -327, 97, 207, -112, 34, -72, -148, -10, 0, 149, -80, -129, -119, -209, -206, 133, 12, 137, -45, 0, -24, -37, 57, -173, 154, 19, 31, -252, 85, 6, 0, 40, 49, 40, 35, 130, 207, 1, -260, 76, -192, 0, -14, 25, 233, 266, -2, -341, 464, -72, -138, -61, 0, 158, 279, 23, -254, -313, 16, 3, -333, -153, -14, 0, 13, -204, 12, -68, 142, -277, -7, 258, 5, 106, 0, 346, -9, 13, 10, -12, 69, -131, 146, -215, 209, 0, -86, 647, 12, 508, 101, -14, -165, -459, -63, 516, 0, 67, -54, 157, 4, 98, 375, 36, -117, 456, 26, 0, 44, -211, 144, -64, -21, 263, 81, 0, 337, -230, 0, -387, 32, 243, 127, 326, -10, -186, -89, -173, -47, 0, -139, -22, -258, 91, -314, 93, 97, -54, 376, -64, 0, 141, -79, 107, -58, 234, 137, -12, -13, -406, -4, 0, 44, 121, 116, -11, -29, -102, -43, -243, 47, -521, 0, 6, -291, 512, 73, -135, -63, 53, -7, 455, 83, 0, 109, 190, -14, -198, 52, -63, 133, 156, 93, -150, 0, 61, -74, 21, -25, -44, 24, 73, 112, -190, -102, 0, -30, -59, -56, -154, 21, 224, 0, -174, -53, 18, 0, -253, -14, -107, 350, 0, 251, 232, -13, 31, 137, 0, 20, 582, -79, 214, 82, 40, 113, -578, 44, -176, 0, -27, 3, 553, 9, 89, -192, -286, -29, -201, -128, 0, 90, -41, 87, 508, 202, 315, -102, 173, -19, -418, 0, -156, -136, 231, 22, 244, 67, -239, 70, -13, -110, 0, -6, -397, -94, -173, 115, -74, 34, 262, 94, 22, 0, 274, -22, 122, -2, -47, -232, -112, -61, 195, 14, 0, 156, 22, 1, 239, -280, 355, 161, -58, 56, -81, 0, 26, 206, 274, 50, -252, -114, 81, 282, 134, 26, 0, 28, -92, 215, 159, -146, 131, -70, -3, 308, -534, 0, 20, 243, -48, 11, -45, -15, -38, -321, 11, -276, 0, -39, 302, 121, -146, 47, -265, -27, -322, -127, -166, 0, 343, -29, 555, 52, 54, 548, 101, 30, -536, -89, 0, -31, -177, 107, -342, 137, -16, 77, 307, -5, -426, 0, 17, -183, 99, -7, 111, -57, 2, -42, 742, 23, 0, -248, 36, -86, 131, 66, 26, 36, 48, 15, -209, 0, 430, 11, 18, 331, -123, 66, -8, -242, 88, -99, 0, 52, 131, -41, 27, 216, 1229, -51, 351, 221, -72, 0, 187, 54, 6, -146, -268, -61, 3, -38, 61, 254, 0, -60, -360, -95, -225, -19, -26, 389, 39, -10, 453, 0, 98, -42, -158, 70, 401, -178, 313, 127, -82, -18, 0, 192, -243, 223, -1, 32, -71, 157, 91, 230, -119, 0, -176, 42, -80, 14, 423, -165, -8, -109, -38, 128, 0, 7, 471, -13, -87, 92, 446, 8, 81, -53, -335, 0, 263, 40, -3, 475, 1, -303, 832, -40, -394, 1, 0, -153, -322, 67, 271, -223, 84, -54, -690, -213, -227, 0, -29, 40, 137, 27, -151, -138, -290, -177, 176, 18, 0, -115, -54, 152, 137, -8, -279, 94, 176, -221, 205, 0, -217, 82, -175, 140, 220, 104, -232, 70, 30, -188, 0, -4, -9, -116, 48, 344, 489, -113, -11, 294, 149, 0, 60, 2, 424, 16, 6, 47, 95, -68, 272, -182, 0, 42, -298, 107, 259, -28, -36, 115, 594, 18, 36, 0, 25, -577, 263, -89, 98, 24, -30, -18, -12, -116, 0, 267, 139, 226, 246, 10, -78, -213, 174, -70, 89, 0, 537, 580, -6, -270, 581, -114, -144, -280, 123, -116, 0, 10, -117, 539, -342, 135, -174, 94, -484, 189, -19, 0, 263, 72, -153, -82, 39, 226, 377, 26, 310, -142, 0, 45, -158, 73, 34, -76, 43, 51, -203, -109, -101, 0, -183, 202, 418, -17, -32, 137, -40, 30, 21, -144, 0, -121, -4, -36, 113, 44, 840, -122, 301, 88, -380, 0, -31, -288, -185, 319, 207, 223, -111, -89, -155, 308, 0, -98, 578, -102, 170, -105, -19, -15, 271, -39, 224, 0, 75, -10, -93, -357, 129, -276, 110, 6, -269, 63, 0, 166, 277, 79, 73, 25, 29, -96, 440, -47, -192, 0, 9, 238, 202, 54, -87, 14, -122, 13, 333, 77, 0, -38, -4, -484, 886, -201, 334, 274, -16, 189, 110, 0, -306, -43, 11, 82, -301, 0, 23, 108, -23, -35, 0, 28, -398, 305, -60, -131, -181, -33, -33, -248, -100, 0, 10, -54, 455, 374, -71, -167, -13, 129, 158, -46, 0, 105, -61, -12, -202, -193, -130, -341, -406, 44, -208, 0, -184, 127, 658, -99, -19, -214, -56, 274, 227, -133, 0, -268, 133, -2, 272, 59, 551, -35, 15, -376, -178, 0, 12, -170, -8, 321, 240, 160, 392, 107, -25, -36, 0, -6, 46, -142, 78, 322, -300, 86, 675, 231, 3, 0, 58, -204, 142, -217, -5, -312, -463, -50, -183, -87, 0, -50, 153, 25, -103, -306, 37, -17, -341, 24, -51, 0, -35, 196, 271, 7, 27, 595, -418, 31, 790, -181, 0, 242, -28, 287, -204, -182, 12, -126, -7, -126, 363, 0, 469, 14, -47, -74, 528, -28, 22, -12, 4, -377, 0, 97, -313, 142, 11, 84, 51, 129, 64, -467, -67, 0, 350, 74, 479, 114, -93, -47, -61, 213, -2, 179, 0, -26, -353, 36, 498, 201, 62, 190, -566, 33, -128, 0, -166, 99, 0, 56, -248, -78, -34, -241, -341, -62, 0, -82, 232, 93, 356, 10, -6, -36, 53, 132, -654, 0, 158, 110, -232, 121, 90, 33, -91, -44, -480, -8, 0, -216, 406, -279, -171, -42, 215, -39, 749, 79, -222, 0, 560, 5, 2, -165, 21, -121, -9, -32, 44, 190, 0, -184, 1086, -41, -479, -164, 308, -113, -548, -70, -350, 0, 64, -47, -94, -41, 24, -171, -37, 255, 399, 20, 0, 21, 18, 57, -53, 95, -66, 104, 79, 141, -115, 0, -511, -85, -98, 67, 586, -52, -662, 392, -280, -272, 0, 70, 194, 31, -69, -180, 213, 157, -21, 197, -32, 0, 682, -91, -134, -153, 54, 634, -47, 12, -406, 30, 0, 271, -324, 131, 345, 347, -93, 142, -236, 82, -10, 0, -18, 79, 297, 43, 163, -139, 185, -25, 663, 86, 0, -193, -41, 13, 267, 141, 171, 236, -70, 26, -30, 0, 226, -366, -102, 72, -40, 6, -31, 389, -74, -561, 0, -231, -117, -279, -17, 38, 108, -9, -122, 94, -108, 0, 23, 243, -509, -61, 50, -289, 841, 65, 41, -105, 0, 116, 379, 25, 323, 188, -158, 101, -40, -194, -15, 0, -216, -78, 434, 154, -250, -56, -187, -355, 81, 50, 0, 175, 13, 118, 163, 9, 476, 106, -71, 265, -572, 0, -569, -12, 164, -34, 702, 51, -418, -164, 31, -82, 0, -185, 367, 3, 20, 16, 47, 88, 694, -82, -389, 0, 173, -38, 170, 427, -268, 301, -173, -1, 549, 725, 0, -69, -382, 171, -510, 210, -68, 441, 500, 37, -26, 0, -4, -411, 355, 244, -204, -91, -159, 268, -120, -142, 0, -26, 16, 76, 414, 12, -1008, -250, 65, 6, -119, 0, -114, -110, 3, 360, -81, 85, 14, -216, -36, -452, 0, 68, 266, 162, -200, 15, 27, -123, -360, -38, 149, 0, 227, -10, 65, 57, -62, -15, 146, 23, 154, 246, 0, -249, -581, -74, -36, -247, 24, -87, -375, 29, -481, 0, -3, -226, 336, -8, 316, -191, 181, 75, 126, -112, 0, 156, 25, -113, -222, -76, 157, 184, 245, -26, -270, 0, 460, 5, -325, -243, -29, -242, -206, -193, -138, 106, 0, 100, 43, -99, -2, -4, 1002, 11, 5, 257, 92, 0, 128, 188, 274, 149, -78, -66, -624, -63, -677, -39, 0, -380, 3, -107, 64, 213, -182, 447, -18, -145, 154, 0, 27, 190, -454, 15, -41, -145, 59, 216, 84, -52, 0, -370, -428, 308, 325, -162, -503, -106, 114, -106, 1059, 0, 72, -381, -286, -80, 426, -20, 711, 159, -156, 331, 0, 13, -61, 38, 3, -234, 32, -18, -523, -83, 47, 0, 477, 65, 400, -335, 26, -94, 865, 41, -1069, 233, 0, -62, -393, 10, -125, -335, 308, -70, -308, 58, -280, 0, -354, -161, -209, -191, 56, -29, 41, 296, 243, -136, 0, -69, 136, -284, 436, 37, -399, 209, 473], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "nf_label": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[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, -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, 0, 0, 0, 0, 0, 0], [2, 0, 1, 0, 0, 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, 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, 0, 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], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 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], [2, 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, 0, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, -1, 1, 0, 0, 1, 1], [1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 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, -1, 1, -1, 0, -1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [2, -1, 2, -1, 0, 1, 2, -1, -1, 0, -1, -1, 0, 0, 0, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, -1, 0, 0, -1, 1, -1, 0], [0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, -1, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 1, 0, 1, -1], [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, 0, 0, 0, 0, 0, 0], [1, -1, -1, 0, -1, -1, -2, -1, 0, 0, -1, 1, 1, 0, -1, 1, -2, 0], [1, -1, 0, 1, 0, -1, -1, -1, 0, -1, 0, 0, -1, 0, 0, 0, 1, 0], [0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, 1], [2, 0, -1, 1, -1, 0, -2, 0, -1, 0, 1, 1, 0, 0, -1, 1, 0, -1], [-2, -2, 0, -1, 0, 1, 0, -1, -1, 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], [1, 0, 0, 0, 0, 0, -2, 1, 1, 0, 1, 1, 1, 0, -1, 1, -2, 0], [2, -1, 0, -1, 0, -1, 0, 1, 1, 0, -1, -1, 0, 0, 1, 1, -1, 0], [2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 1, -1, 2, 1, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0], [1, 0, 0, 0, 0, 0, 1, -1, 1, -1, -1, -1, -1, 0, 1, -1, 1, 1], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, -1, 1, 3, 5, 2, 1, 1, 1, 0, 0, -1, 1, -1, 1, 0], [-2, 1, -1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, -1, 1, 0, 0, 1, 1], [1, 0, 1, 0, -1, 1, 0, 0, 0, 1, 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], [1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 1, 2, -1, -1, 2, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1], [0, 0, -1, 1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [3, 0, 0, -1, 0, -1, 1, 0, 1, -1, 0, 0, -1, 0, 1, 0, 1, 0], [2, -2, 3, -1, 1, 1, 4, 1, 0, 0, -1, -1, 0, -2, 1, -3, 2, 0], [0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [-2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, -1, 1, -1, -1, 0, 1, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 1, -2, 2, 0, -1, -3, 1, 0, 0, 2, 1, -2, 1, 1, 1, 1, 0], [0, 0, -1, 1, -1, 0, -1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [5, -1, -1, 0, -1, -1, -5, 0, 1, 0, -1, 0, 1, 0, 0, 2, -2, 0], [2, -1, -1, 0, -1, -1, -3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [2, -1, 2, -1, 0, 1, 2, -1, -1, 0, -1, -1, 0, 0, 0, -1, 0, 0], [1, 1, 1, 0, 1, 0, 2, -1, 1, -1, -1, -1, -1, -1, 0, -1, 0, 0], [-1, -3, 0, -1, 0, -1, 2, 2, 2, 1, 0, 1, 1, 0, -1, 1, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0], [0, 4, 4, -1, 3, 3, 6, 3, 2, 1, 0, 0, 1, -1, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -1, -1, 0, -1, 1, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -3, -2, 1, -2, -2, -3, -1, -1, 0, 2, 1, -1, 1, -2, 3, 0, -1], [2, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, -1, 0, 0, -1, 1, -1, 0], [2, -3, -1, 2, -1, -3, -3, -1, -1, -2, 0, -1, -2, 0, -1, -1, 1, 0], [-1, 2, -1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, -1], [0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 2, 0, -1, -1, 0, 1, -1, 1, 0, -1, 1, -1, 0], [3, -2, 0, -1, 0, 3, -4, -2, 0, 0, -1, -1, 0, 0, 0, 1, 1, 0], [3, -1, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 1, 0, 1, -1], [0, 1, 0, 0, 0, 0, 0, -2, 1, -2, -3, -1, -1, 0, 2, -1, 1, 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], [2, 0, 0, -1, 0, -2, -2, 0, 0, 0, -2, 1, 1, -1, 1, 1, 0, -1], [-1, -4, 1, -3, -1, 1, 5, 1, -1, 0, 0, 1, 2, -2, -1, -1, 0, -3], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 4, 0, 1, 0, -1, 2, 0, -1, 0, 0, 0, 1, 0, -1, 0, -1, -1], [-1, 0, -1, 0, -1, -1, 1, 1, 0, 2, 1, 2, 1, 0, -1, 0, -1, -1], [1, -1, -1, 0, -1, -1, -2, -1, 0, 0, -1, 1, 1, 0, -1, 1, -2, 0], [-3, 3, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, -1, 0, -1, -1, -1, -2], [-1, -3, 0, -1, 0, 0, 3, 1, -1, 0, 0, 1, -1, 0, 1, -1, 1, 0], [1, -1, 0, 1, 0, -1, -1, -1, 0, -1, 0, 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], [2, 1, 0, -2, 0, 0, 0, 1, 2, 0, -1, 1, 1, -2, 0, 1, 0, -1], [0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [5, -2, -1, -1, -1, -4, -8, -2, -1, 0, -2, 0, 1, 0, -2, 2, -2, -2], [2, 0, -1, 1, -1, 0, -2, 0, -1, 0, 1, 1, 0, 0, -1, 1, 0, -1], [7, 3, 0, 2, 1, 0, -4, -3, -1, 0, -1, -1, -1, 1, 0, 1, 0, 1], [2, 0, -1, 1, -1, 0, -1, -1, -2, 0, -1, 0, 0, 0, 0, 2, 1, 1], [-2, -2, 0, -1, 0, 1, 0, -1, -1, 0, 0, 0, 0, 0, -1, 0, 0, -1], [3, 0, -1, 0, -1, 1, 3, 0, 0, 0, 0, -1, 0, 0, 0, 1, -1, 0], [-4, -4, -1, 0, -3, -1, -3, 0, 0, 0, 0, 1, 2, 0, -1, 1, -2, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, -1, 4, -2, 1, 6, 1, 0, -2, 0, 0, -3, 0, -1, 2, -2, 3, 0]]}