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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 2, 'A5': 0, 'A6': 0, 'A7': 5, 'A8': 0, 'A9': 0, 'Lhash': '1511600534824427555679696166083', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [1.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [1.8898223650461363, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.82056271920522, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, 0, 1]], [13, [1, -1, 13]]], 'bad_primes': [3, 5, 13], 'central_character': '342225.1', 'coefficient_field': '1.1.1.1', 'conductor': 342225, 'conductor_radical': 195, 'degree': 4, 'euler_factors': [[1, 0, -2, 0, 4], [1], [1, 0, 1], [1, -5, 18, -35, 49], [1, 0, 5, 0, 121], [1, -1, 13], [1, 0, -25, 0, 289], [1, -8, 45, -152, 361], [1, 0, 33, 0, 529], [1, 0, 19, 0, 841], [1, -2, -1, -62, 961], [1, -2, 71, -74, 1369], [1, 0, -57, 0, 1681], [1, -9, 86, -387, 1849], [1, 0, 46, 0, 2209], [1, 0, -102, 0, 2809], [1, 0, 85, 0, 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-2.3826581234277042, -1.0175922604936871, 0.22920269827391748], 'positive_zeros': ['1.19244256623416350094330421935773', '1.64967964403550599417243681033965', '2.46250087092456269936239218159653', '2.98555704204796575751227839603148', '3.75921844971558256451514556986944', '4.49248596832030498227268073747939', '4.86067628904138086549907576434256', '5.37536773860380432407568736450781', '6.00945780119819937833215431024821', '6.25245532873071258354239464576135', '7.18951135720813301528886215635985', '7.34477584132857413160870749950715', '7.75656422768351241565787721704949', '8.116800026552764309039415190024756', '8.764346545926302669413322149240830'], 'prelabel': '4-585e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1413025642387781187, 'z1': {'__RealLiteral__': 0, 'data': '1.19244256623416350094330421935773', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.64967964403550599417243681033965', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.46250087092456269936239218159653', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.82056271920522, 'bad_primes': [3, 5, 13], 'central_character': '1.1', 'conductor': 342225, 'conductor_radical': 195, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 2, 0, 0, 5, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -1, 0, 0, 10, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 7, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -8, 0, 0, -15, 0, 0, 0, 0, 0, -14, 0, 0, 16, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 7, 0, 0, -2], 'euler11': [1, 0, 5, 0, 121], 'euler13': [1, -1, 13, 0, 0], 'euler17': [1, 0, -25, 0, 289], 'euler19': [1, -8, 45, -152, 361], 'euler2': [1, 0, -2, 0, 4], 'euler23': [1, 0, 33, 0, 529], 'euler29': [1, 0, 19, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -2, -1, -62, 961], 'euler37': [1, -2, 71, -74, 1369], 'euler41': [1, 0, -57, 0, 1681], 'euler43': [1, -9, 86, -387, 1849], 'euler47': [1, 0, 46, 0, 2209], 'euler5': [1, 0, 1, 0, 0], 'euler53': [1, 0, -102, 0, 2809], 'euler59': [1, 0, 85, 0, 3481], 'euler61': [1, 3, 124, 183, 3721], 'euler67': [1, 15, 190, 1005, 4489], 'euler7': [1, -5, 18, -35, 49], 'euler71': [1, 0, -7, 0, 5041], 'euler73': [1, 14, 179, 1022, 5329], 'euler79': [1, -6, 103, -474, 6241], 'euler83': [1, 0, 86, 0, 6889], 'euler89': [1, 0, -121, 0, 7921], 'euler97': [1, -7, 96, -679, 9409], 'euler_factors': [[1, 0, -2, 0, 4], [1, 0, 0, 0, 0], [1, 0, 1, 0, 0], [1, -5, 18, -35, 49], [1, 0, 5, 0, 121], [1, -1, 13, 0, 0], [1, 0, -25, 0, 289], [1, -8, 45, -152, 361], [1, 0, 33, 0, 529], [1, 0, 19, 0, 841], [1, -2, -1, -62, 961], [1, -2, 71, -74, 1369], [1, 0, -57, 0, 1681], [1, -9, 86, -387, 1849], [1, 0, 46, 0, 2209], [1, 0, -102, 0, 2809], [1, 0, 85, 0, 3481], [1, 3, 124, 183, 3721], [1, 15, 190, 1005, 4489], [1, 0, -7, 0, 5041], [1, 14, 179, 1022, 5329], [1, -6, 103, -474, 6241], [1, 0, 86, 0, 6889], [1, 0, -121, 0, 7921], [1, -7, 96, -679, 9409]], 'index': 16, 'instance_types': ['BMF', 'ECNF', 'ECNF', 'BMF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/38025.1/c', 'EllipticCurve/2.0.3.1/38025.3/c', 'EllipticCurve/2.0.3.1/38025.1/c', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/38025.3/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': '4-585e2-1.1-c1e2-0-16', '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': 0, 'prelabel': '4-585e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1413025642387781187, 'z1': {'__RealLiteral__': 0, 'data': '1.19244256623416350094330421935773', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9762962
{'Lhash': '1511600534824427555679696166083', 'Lhash_array': ['1511600534824427555679696166083'], 'label': '4-585e2-1.1-c1e2-0-16', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/38025.3/c'}
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id: 9762779
{'Lhash': '1511600534824427555679696166083', 'Lhash_array': ['1511600534824427555679696166083'], 'label': '4-585e2-1.1-c1e2-0-16', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/38025.1/c'}
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id: 9762516
{'Lhash': '1511600534824427555679696166083', 'Lhash_array': ['1511600534824427555679696166083'], 'label': '4-585e2-1.1-c1e2-0-16', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/38025.3/c'}
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id: 9762393
{'Lhash': '1511600534824427555679696166083', 'Lhash_array': ['1511600534824427555679696166083'], 'label': '4-585e2-1.1-c1e2-0-16', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/38025.1/c'}