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lfunc_lfunctions • Show schema
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{'Lhash': '1439898905870744265681384205658', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -5, 'a6': 0, 'a7': -14, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 127.44412561239979, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 5]]], 'bad_primes': [2, 3, 5], 'central_character': '2160.1', 'coefficient_field': '1.1.1.1', 'conductor': 2160, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1], [1, 5], [1, 14, 343], [1, -3, 1331], [1, -47, 2197], [1, -39, 4913], [1, 32, 6859], [1, 99, 12167], [1, 51, 24389], [1, 83, 29791], [1, -314, 50653], [1, -108, 68921], [1, 299, 79507], [1, -531, 103823], [1, 564, 148877], [1, -12, 205379], [1, -230, 226981], [1, -268, 300763], [1, -120, 357911], [1, -1106, 389017], [1, -739, 493039], [1, -1086, 571787], [1, -120, 704969], [1, 1642, 912673], [1, 33, 1030301], [1, -1198, 1092727], [1, 1542, 1225043], [1, 556, 1295029], [1, 1605, 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True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 766857968168822749, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.13587995431193979124584298365', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.41384144506462781980835384211', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.53443410936500912091243470426', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 127.44412561239979, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 2160, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -5, 0, -14, 0, 0, 0, 3, 0, 47, 0, 0, 0, 39, 0, -32, 0, 0, 0, -99, 0, 25, 0, 0, 0, -51, 0, -83, 0, 0, 0, 70, 0, 314, 0, 0, 0, 108, 0, -299, 0, 0, 0, 531, 0, -147, 0, 0, 0, -564, 0, -15, 0, 0, 0, 12, 0, 230, 0, 0, 0, -235, 0, 268, 0, 0, 0, 120, 0, 1106, 0, 0, 0, -42, 0, 739, 0, 0, 0, 1086, 0, -195, 0, 0, 0, 120, 0, -658, 0, 0, 0, 160, 0, -1642, 0, 0, 0], 'euler11': [1, -3, 1331], 'euler13': [1, -47, 2197], 'euler17': [1, -39, 4913], 'euler19': [1, 32, 6859], 'euler2': [1, 0, 0], 'euler23': [1, 99, 12167], 'euler29': [1, 51, 24389], 'euler3': [1, 0, 0], 'euler31': [1, 83, 29791], 'euler37': [1, -314, 50653], 'euler41': [1, -108, 68921], 'euler43': [1, 299, 79507], 'euler47': [1, -531, 103823], 'euler5': [1, 5, 0], 'euler53': [1, 564, 148877], 'euler59': [1, -12, 205379], 'euler61': [1, -230, 226981], 'euler67': [1, -268, 300763], 'euler7': [1, 14, 343], 'euler71': [1, -120, 357911], 'euler73': [1, -1106, 389017], 'euler79': [1, -739, 493039], 'euler83': [1, -1086, 571787], 'euler89': [1, -120, 704969], 'euler97': [1, 1642, 912673], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 5, 0], [1, 14, 343], [1, -3, 1331], [1, -47, 2197], [1, -39, 4913], [1, 32, 6859], [1, 99, 12167], [1, 51, 24389], [1, 83, 29791], [1, -314, 50653], [1, -108, 68921], [1, 299, 79507], [1, -531, 103823], [1, 564, 148877], [1, -12, 205379], [1, -230, 226981], [1, -268, 300763], [1, -120, 357911], [1, -1106, 389017], [1, -739, 493039], [1, -1086, 571787], [1, -120, 704969], [1, 1642, 912673]], 'index': 57, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2160/4/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/2160/4/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': '2-2160-1.1-c3-0-57', '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': '2-2160-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 11.289115360044816, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 766857968168822749, 'z1': {'__RealLiteral__': 0, 'data': '1.13587995431193979124584298365', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21282554
{'Lhash': '1439898905870744265681384205658', 'Lhash_array': ['1439898905870744265681384205658'], 'label': '2-2160-1.1-c3-0-57', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2160/4/a/b'}
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id: 24593009
{'Lhash': '1439898905870744265681384205658', 'Lhash_array': ['1439898905870744265681384205658'], 'label': '2-2160-1.1-c3-0-57', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2160/4/a/b/1/1'}