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lfunc_lfunctions • Show schema
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{'Lhash': '1019626136980468375532368423113,1096511665502829897710267042810,2068239804243262696558781185494', 'a10': 0, 'a2': 1, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 3, 'a8': 2, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1989.1750139616286, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]], [7, [1, -3, 3, -1]]], 'bad_primes': [3, 5, 7], 'central_character': '1575.1', 'coefficient_field': '1.1.1.1', 'conductor': 3906984375, 'conductor_radical': 105, 'degree': 6, 'euler_factors': [[1, -1, 1, -3, 2, -4, 8], [1], [1], [1, -3, 3, -1], [1, 6, 45, 140, 495, 726, 1331], [1, -6, 35, -148, 455, -1014, 2197], [1, 0, 35, -16, 595, 0, 4913], [1, -6, 53, -188, 1007, -2166, 6859], [1, -4, 61, -168, 1403, -2116, 12167], [1, 2, 35, 76, 1015, 1682, 24389], [1, -2, 41, 60, 1271, -1922, 29791], [1, -4, 31, -232, 1147, -5476, 50653], [1, 2, 63, -36, 2583, 3362, 68921], [1, 4, -15, -488, -645, 7396, 79507], [1, -8, 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{'__RealLiteral__': 0, 'data': '0.864995185033961696016580530337', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.63155352418946846412030406660', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 1989.1750139616286, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 3906984375, 'conductor_radical': 105, 'degree': 6, 'dirichlet_coefficients': [1, 1, 0, 0, 0, 0, 3, 2, 0, 0, -6, 0, 6, 3, 0, 3, 0, 0, 6, 0, 0, -6, 4, 0, 0, 6, 0, 0, -2, 0, 2, 3, 0, 0, 0, 0, 4, 6, 0, 0, -2, 0, -4, 0, 0, 4, 8, 0, 6, 0, 0, 0, 14, 0, 0, 6, 0, -2, -16, 0, -6, 2, 0, 2, 0, 0, -8, 0, 0, 0, -6, 0, 18, 4, 0, 0, -18, 0, 12, 0, 0, -2, 8, 0, 0, -4, 0, -12, -14, 0, 18, 0, 0, 8, 0, 0, 22, 6, 0, 0], 'euler11': [1, 6, 45, 140, 495, 726, 1331], 'euler13': [1, -6, 35, -148, 455, -1014, 2197], 'euler17': [1, 0, 35, -16, 595, 0, 4913], 'euler19': [1, -6, 53, -188, 1007, -2166, 6859], 'euler2': [1, -1, 1, -3, 2, -4, 8], 'euler23': [1, -4, 61, -168, 1403, -2116, 12167], 'euler29': [1, 2, 35, 76, 1015, 1682, 24389], 'euler3': [1, 0, 0, 0, 0, 0, 0], 'euler31': [1, -2, 41, 60, 1271, -1922, 29791], 'euler37': [1, -4, 31, -232, 1147, -5476, 50653], 'euler41': [1, 2, 63, -36, 2583, 3362, 68921], 'euler43': [1, 4, -15, -488, -645, 7396, 79507], 'euler47': [1, -8, 109, -624, 5123, -17672, 103823], 'euler5': [1, 0, 0, 0, 0, 0, 0], 'euler53': [1, -14, 171, -1188, 9063, -39326, 148877], 'euler59': [1, 16, 113, 608, 6667, 55696, 205379], 'euler61': [1, 6, 131, 484, 7991, 22326, 226981], 'euler67': [1, 8, 169, 944, 11323, 35912, 300763], 'euler7': [1, -3, 3, -1, 0, 0, 0], 'euler71': [1, 6, 225, 860, 15975, 30246, 357911], 'euler73': [1, -18, 311, -2732, 22703, -95922, 389017], 'euler79': [1, -12, 221, -1576, 17459, -74892, 493039], 'euler83': [1, -8, 185, -1072, 15355, -55112, 571787], 'euler89': [1, 14, 319, 2532, 28391, 110894, 704969], 'euler97': [1, -22, 255, -2404, 24735, -206998, 912673], 'euler_factors': [[1, -1, 1, -3, 2, -4, 8], [1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, -3, 3, -1, 0, 0, 0], [1, 6, 45, 140, 495, 726, 1331], [1, -6, 35, -148, 455, -1014, 2197], [1, 0, 35, -16, 595, 0, 4913], [1, -6, 53, -188, 1007, -2166, 6859], [1, -4, 61, -168, 1403, -2116, 12167], [1, 2, 35, 76, 1015, 1682, 24389], [1, -2, 41, 60, 1271, -1922, 29791], [1, -4, 31, -232, 1147, -5476, 50653], [1, 2, 63, -36, 2583, 3362, 68921], [1, 4, -15, -488, -645, 7396, 79507], [1, -8, 109, -624, 5123, -17672, 103823], [1, -14, 171, -1188, 9063, -39326, 148877], [1, 16, 113, 608, 6667, 55696, 205379], [1, 6, 131, 484, 7991, 22326, 226981], [1, 8, 169, 944, 11323, 35912, 300763], [1, 6, 225, 860, 15975, 30246, 357911], [1, -18, 311, -2732, 22703, -95922, 389017], [1, -12, 221, -1576, 17459, -74892, 493039], [1, -8, 185, -1072, 15355, -55112, 571787], [1, 14, 319, 2532, 28391, 110894, 704969], [1, -22, 255, -2404, 24735, -206998, 912673]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1575/2/a/x'], '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': '6-1575e3-1.1-c1e3-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '6-1575e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.546327440938254, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 2052912766121416553, 'z1': {'__RealLiteral__': 0, 'data': '0.804343197405415663425383782976', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1019626136980468375532368423113,1096511665502829897710267042810,2068239804243262696558781185494', 'Lhash_array': ['1019626136980468375532368423113', '1096511665502829897710267042810', '2068239804243262696558781185494'], 'label': '6-1575e3-1.1-c1e3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1575/2/a/x'}