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lfunc_lfunctions • Show schema
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{'Lhash': '2262245748850746596618270957865', 'a10': 14, 'a2': 2, 'a3': 0, 'a4': 4, 'a5': 7, 'a6': 0, 'a7': 7, 'a8': 8, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 81.77664726795653, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2]], [3, [1]], [7, [1, -7]], [11, [1, 11]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '1386.1', 'coefficient_field': '1.1.1.1', 'conductor': 1386, 'conductor_radical': 462, 'degree': 2, 'euler_factors': [[1, -2], [1], [1, -7, 125], [1, -7], [1, 11], [1, 67, 2197], [1, 30, 4913], [1, 7, 6859], [1, 28, 12167], [1, 121, 24389], [1, 310, 29791], [1, 71, 50653], [1, -180, 68921], [1, 108, 79507], [1, 71, 103823], [1, 128, 148877], [1, -429, 205379], [1, -22, 226981], [1, 803, 300763], [1, 468, 357911], [1, 117, 389017], [1, 96, 493039], [1, -1122, 571787], [1, -1146, 704969], [1, 92, 912673], [1, -202, 1030301], [1, 1798, 1092727], [1, -1431, 1225043], [1, 278, 1295029], [1, 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{'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 1262853066713137669, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.78459722927078568737247054476', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.43489982006772064109432302748', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.65563577989240869784434108319', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 81.77664726795653, 'bad_primes': [2, 3, 7, 11], 'central_character': '1.1', 'conductor': 1386, 'conductor_radical': 462, 'degree': 2, 'dirichlet_coefficients': [1, 2, 0, 4, 7, 0, 7, 8, 0, 14, -11, 0, -67, 14, 0, 16, -30, 0, -7, 28, 0, -22, -28, 0, -76, -134, 0, 28, -121, 0, -310, 32, 0, -60, 49, 0, -71, -14, 0, 56, 180, 0, -108, -44, 0, -56, -71, 0, 49, -152, 0, -268, -128, 0, -77, 56, 0, -242, 429, 0, 22, -620, 0, 64, -469, 0, -803, -120, 0, 98, -468, 0, -117, -142, 0, -28, -77, 0, -96, 112, 0, 360, 1122, 0, -210, -216, 0, -88, 1146, 0, -469, -112, 0, -142, -49, 0, -92, 98, 0, -304], 'euler11': [1, 11, 0], 'euler13': [1, 67, 2197], 'euler17': [1, 30, 4913], 'euler19': [1, 7, 6859], 'euler2': [1, -2, 0], 'euler23': [1, 28, 12167], 'euler29': [1, 121, 24389], 'euler3': [1, 0, 0], 'euler31': [1, 310, 29791], 'euler37': [1, 71, 50653], 'euler41': [1, -180, 68921], 'euler43': [1, 108, 79507], 'euler47': [1, 71, 103823], 'euler5': [1, -7, 125], 'euler53': [1, 128, 148877], 'euler59': [1, -429, 205379], 'euler61': [1, -22, 226981], 'euler67': [1, 803, 300763], 'euler7': [1, -7, 0], 'euler71': [1, 468, 357911], 'euler73': [1, 117, 389017], 'euler79': [1, 96, 493039], 'euler83': [1, -1122, 571787], 'euler89': [1, -1146, 704969], 'euler97': [1, 92, 912673], 'euler_factors': [[1, -2, 0], [1, 0, 0], [1, -7, 125], [1, -7, 0], [1, 11, 0], [1, 67, 2197], [1, 30, 4913], [1, 7, 6859], [1, 28, 12167], [1, 121, 24389], [1, 310, 29791], [1, 71, 50653], [1, -180, 68921], [1, 108, 79507], [1, 71, 103823], [1, 128, 148877], [1, -429, 205379], [1, -22, 226981], [1, 803, 300763], [1, 468, 357911], [1, 117, 389017], [1, 96, 493039], [1, -1122, 571787], [1, -1146, 704969], [1, 92, 912673]], 'index': 71, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1386/4/a/l/1/1', 'ModularForm/GL2/Q/holomorphic/1386/4/a/l'], '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': '2-1386-1.1-c3-0-71', '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': '2-1386-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.043044137233686, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1262853066713137669, 'z1': {'__RealLiteral__': 0, 'data': '1.78459722927078568737247054476', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21248788
{'Lhash': '2262245748850746596618270957865', 'Lhash_array': ['2262245748850746596618270957865'], 'label': '2-1386-1.1-c3-0-71', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1386/4/a/l'}
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id: 24591210
{'Lhash': '2262245748850746596618270957865', 'Lhash_array': ['2262245748850746596618270957865'], 'label': '2-1386-1.1-c3-0-71', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1386/4/a/l/1/1'}