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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': -2, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1527147363677563021682049952023', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896257, 0], 'a4': [-1.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 39.77453894000138, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 2]], [3, [1, -1]], [19, [1, 2, 1]]], 'bad_primes': [2, 3, 19], 'central_character': '623808.1', 'coefficient_field': '1.1.1.1', 'conductor': 623808, 'conductor_radical': 114, 'degree': 4, 'euler_factors': [[1, 0, 2], [1, -1], [1, 0, 8, 0, 25], [1, 0, -6, 0, 49], [1, 0, 6, 0, 121], [1, 0, -8, 0, 169], [1, 0, 30, 0, 289], [1, 2, 1], [1, 0, 44, 0, 529], [1, 0, 26, 0, 841], [1, 0, -44, 0, 961], [1, 0, -24, 0, 1369], [1, 0, 82, 0, 1681], [1, -8, 102, -344, 1849], [1, 0, 76, 0, 2209], [1, 0, 74, 0, 2809], [1, 0, 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3.2050100900306298, 3.772879352374687], 'positive_zeros': ['1.20470685171656408945477638185363', '2.00669945433898559128893684071467', '2.72447220511300502563204735740713', '3.34783349995921635939576352452467', '3.93246989003627989923612947569651', '4.33386863833412742892715424471081', '4.68218539424631870153596716604284', '5.45724855145797667979830685447627', '5.86419362513548861116095541244339', '6.17193319541139457653871321098144', '6.95342660923974710678587001034877', '7.46948111262134750676001885535952', '7.75874489116368219190333094072284', '8.146218163409257504246896511696051'], 'prelabel': '4-623808-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.511315565741991, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 348137607623578402, 'z1': {'__RealLiteral__': 0, 'data': '1.20470685171656408945477638185363', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.00669945433898559128893684071467', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.72447220511300502563204735740713', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 39.77453894000138, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 623808, 'conductor_radical': 114, 'degree': 4, 'dirichlet_coefficients': [1, 0, 1, -2, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 4, 0, 0, -2, 0, 0, 0, 0, 0, -8, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 4, 6, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -8, 0, 0, -16, 0, 0, 0, 0, 0, -24, 0, -8, 4, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 16], 'euler11': [1, 0, 6, 0, 121], 'euler13': [1, 0, -8, 0, 169], 'euler17': [1, 0, 30, 0, 289], 'euler19': [1, 2, 1, 0, 0], 'euler2': [1, 0, 2, 0, 0], 'euler23': [1, 0, 44, 0, 529], 'euler29': [1, 0, 26, 0, 841], 'euler3': [1, -1, 0, 0, 0], 'euler31': [1, 0, -44, 0, 961], 'euler37': [1, 0, -24, 0, 1369], 'euler41': [1, 0, 82, 0, 1681], 'euler43': [1, -8, 102, -344, 1849], 'euler47': [1, 0, 76, 0, 2209], 'euler5': [1, 0, 8, 0, 25], 'euler53': [1, 0, 74, 0, 2809], 'euler59': [1, 0, 82, 0, 3481], 'euler61': [1, 0, -122, 0, 3721], 'euler67': [1, 16, 198, 1072, 4489], 'euler7': [1, 0, -6, 0, 49], 'euler71': [1, 0, 14, 0, 5041], 'euler73': [1, 24, 290, 1752, 5329], 'euler79': [1, 0, -60, 0, 6241], 'euler83': [1, 0, 150, 0, 6889], 'euler89': [1, 0, 78, 0, 7921], 'euler97': [1, -12, 230, -1164, 9409], 'euler_factors': [[1, 0, 2, 0, 0], [1, -1, 0, 0, 0], [1, 0, 8, 0, 25], [1, 0, -6, 0, 49], [1, 0, 6, 0, 121], [1, 0, -8, 0, 169], [1, 0, 30, 0, 289], [1, 2, 1, 0, 0], [1, 0, 44, 0, 529], [1, 0, 26, 0, 841], [1, 0, -44, 0, 961], [1, 0, -24, 0, 1369], [1, 0, 82, 0, 1681], [1, -8, 102, -344, 1849], [1, 0, 76, 0, 2209], [1, 0, 74, 0, 2809], [1, 0, 82, 0, 3481], [1, 0, -122, 0, 3721], [1, 16, 198, 1072, 4489], [1, 0, 14, 0, 5041], [1, 24, 290, 1752, 5329], [1, 0, -60, 0, 6241], [1, 0, 150, 0, 6889], [1, 0, 78, 0, 7921], [1, -12, 230, -1164, 9409]], 'index': 53, 'instance_types': ['ECNF', 'BMF', 'ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.8.1/9747.5/c', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/9747.8/e', 'EllipticCurve/2.0.8.1/9747.8/e', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/9747.5/c'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-623808-1.1-c1e2-0-53', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'prelabel': '4-623808-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.511315565741991, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 348137607623578402, 'z1': {'__RealLiteral__': 0, 'data': '1.20470685171656408945477638185363', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9888055
{'Lhash': '1527147363677563021682049952023', 'Lhash_array': ['1527147363677563021682049952023'], 'label': '4-623808-1.1-c1e2-0-53', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/9747.5/c'}
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id: 9887969
{'Lhash': '1527147363677563021682049952023', 'Lhash_array': ['1527147363677563021682049952023'], 'label': '4-623808-1.1-c1e2-0-53', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/9747.8/e'}
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id: 9887596
{'Lhash': '1527147363677563021682049952023', 'Lhash_array': ['1527147363677563021682049952023'], 'label': '4-623808-1.1-c1e2-0-53', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/9747.8/e'}
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id: 9887400
{'Lhash': '1527147363677563021682049952023', 'Lhash_array': ['1527147363677563021682049952023'], 'label': '4-623808-1.1-c1e2-0-53', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/9747.5/c'}