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lfunc_lfunctions • Show schema
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{'Lhash': '2064378382735604794870993317811', 'a10': -7, 'a2': -1, 'a3': 3, 'a4': -7, 'a5': 7, 'a6': -3, 'a7': -10, 'a8': 15, 'a9': 9, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.913968372910507, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -3]], [13, [1]]], 'bad_primes': [3, 13], 'central_character': '507.1', 'coefficient_field': '1.1.1.1', 'conductor': 507, 'conductor_radical': 39, 'degree': 2, 'euler_factors': [[1, 1, 8], [1, -3], [1, -7, 125], [1, 10, 343], [1, 22, 1331], [1], [1, -37, 4913], [1, -30, 6859], [1, 162, 12167], [1, 113, 24389], [1, -196, 29791], [1, -13, 50653], [1, -285, 68921], [1, 246, 79507], [1, 462, 103823], [1, 537, 148877], [1, -576, 205379], [1, 635, 226981], [1, -202, 300763], [1, 1086, 357911], [1, 805, 389017], [1, -884, 493039], [1, -518, 571787], [1, -194, 704969], [1, 1202, 912673], [1, 429, 1030301], [1, 1302, 1092727], [1, 1338, 1225043], [1, 1034, 1295029], [1, -1077, 1442897]], 'euler_factors_factorization': [[[[1, 1, 8], 1]], [[[1, -3], 1]], [[[1, -7, 125], 1]], [[[1, 10, 343], 1]], [[[1, 22, 1331], 1]], [1], [[[1, -37, 4913], 1]], [[[1, -30, 6859], 1]], [[[1, 162, 12167], 1]], [[[1, 113, 24389], 1]], [[[1, -196, 29791], 1]], [[[1, -13, 50653], 1]], [[[1, -285, 68921], 1]], [[[1, 246, 79507], 1]], [[[1, 462, 103823], 1]], [[[1, 537, 148877], 1]], [[[1, -576, 205379], 1]], [[[1, 635, 226981], 1]], [[[1, -202, 300763], 1]], [[[1, 1086, 357911], 1]], [[[1, 805, 389017], 1]], [[[1, -884, 493039], 1]], [[[1, -518, 571787], 1]], [[[1, -194, 704969], 1]], [[[1, 1202, 912673], 1]], [[[1, 429, 1030301], 1]], [[[1, 1302, 1092727], 1]], [[[1, 1338, 1225043], 1]], [[[1, 1034, 1295029], 1]], [[[1, -1077, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 58, 'label': '2-507-1.1-c3-0-58', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/507/4/a/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-1.1692462299418786e-60, 0.17981845577064964, 0.3578760093573102, 0.5324150035217108, 0.7016847935373572, 0.8639465385153177, 1.0174794754372596, 1.1605890734311854, 1.2916173873121015, 1.4089558364193844, 1.5110605303037752, 1.5964701500629321, 1.6638262764052432, 1.7118959361391208, 1.7395960209569794, 1.746019119195288, 1.7304601956352508, 1.6924434591334205, 1.6317486755524817, 1.5484361165629683, 1.4428692857172065, 1.3157345339003916, 1.1680566687863252, 1.0012096789690283, 0.8169217344023533, 0.6172736916733262, 0.40469042601293226, 0.18192443181185097, -0.04796872087474137, -0.28166331612355267, -0.5156048579137773, -0.7460597094717426, -0.9691726160351255, -1.181031482055497, -1.3777385293651265, -1.5554867188112305, -1.7106400810724196, -1.8398163800751486, -1.9399703322050679, -2.0084754340694677, 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'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 1815607061968590062, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.62850739972349756762561155014', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.03888161998064451376328152824', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.16701869404045162900345307031', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.913968372910507, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 507, 'conductor_radical': 39, 'degree': 2, 'dirichlet_coefficients': [1, -1, 3, -7, 7, -3, -10, 15, 9, -7, -22, -21, 0, 10, 21, 41, 37, -9, 30, -49, -30, 22, -162, 45, -76, 0, 27, 70, -113, -21, 196, -161, -66, -37, -70, -63, 13, -30, 0, 105, 285, 30, -246, 154, 63, 162, -462, 123, -243, 76, 111, 0, -537, -27, -154, -150, 90, 113, 576, -147, -635, -196, -90, -167, 0, 66, 202, -259, -486, 70, -1086, 135, -805, -13, -228, -210, 220, 0, 884, 287, 81, -285, 518, 210, 259, 246, -339, -330, 194, -63, 0, 1134, 588, 462, 210, -483, -1202, 243, -198, 532], 'euler11': [1, 22, 1331], 'euler13': [1, 0, 0], 'euler17': [1, -37, 4913], 'euler19': [1, -30, 6859], 'euler2': [1, 1, 8], 'euler23': [1, 162, 12167], 'euler29': [1, 113, 24389], 'euler3': [1, -3, 0], 'euler31': [1, -196, 29791], 'euler37': [1, -13, 50653], 'euler41': [1, -285, 68921], 'euler43': [1, 246, 79507], 'euler47': [1, 462, 103823], 'euler5': [1, -7, 125], 'euler53': [1, 537, 148877], 'euler59': [1, -576, 205379], 'euler61': [1, 635, 226981], 'euler67': [1, -202, 300763], 'euler7': [1, 10, 343], 'euler71': [1, 1086, 357911], 'euler73': [1, 805, 389017], 'euler79': [1, -884, 493039], 'euler83': [1, -518, 571787], 'euler89': [1, -194, 704969], 'euler97': [1, 1202, 912673], 'euler_factors': [[1, 1, 8], [1, -3, 0], [1, -7, 125], [1, 10, 343], [1, 22, 1331], [1, 0, 0], [1, -37, 4913], [1, -30, 6859], [1, 162, 12167], [1, 113, 24389], [1, -196, 29791], [1, -13, 50653], [1, -285, 68921], [1, 246, 79507], [1, 462, 103823], [1, 537, 148877], [1, -576, 205379], [1, 635, 226981], [1, -202, 300763], [1, 1086, 357911], [1, 805, 389017], [1, -884, 493039], [1, -518, 571787], [1, -194, 704969], [1, 1202, 912673]], 'index': 58, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/507/4/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/507/4/a/b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-507-1.1-c3-0-58', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-507-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.469366359361064, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1815607061968590062, 'z1': {'__RealLiteral__': 0, 'data': '1.62850739972349756762561155014', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20647285
{'Lhash': '2064378382735604794870993317811', 'Lhash_array': ['2064378382735604794870993317811'], 'label': '2-507-1.1-c3-0-58', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/507/4/a/b'}
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id: 24562870
{'Lhash': '2064378382735604794870993317811', 'Lhash_array': ['2064378382735604794870993317811'], 'label': '2-507-1.1-c3-0-58', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/507/4/a/b/1/1'}