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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '851919934628461349,1626648016933741962', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.28858135490323, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '82944.1', 'coefficient_field': '1.1.1.1', 'conductor': 82944, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1], [1, 0, -6, 0, 25], [1, 0, 14, 0, 49], [1, 0, 22, 0, 121], [1, 12, 62, 156, 169], [1, 0, -30, 0, 289], [1, 0, 38, 0, 361], [1, 0, 46, 0, 529], [1, 0, 42, 0, 841], [1, 0, 62, 0, 961], [1, 4, 78, 148, 1369], [1, 0, 18, 0, 1681], [1, 0, 86, 0, 1849], [1, 0, 94, 0, 2209], [1, 0, 90, 0, 2809], [1, 0, 118, 0, 3481], [1, 20, 222, 1220, 3721], [1, 0, 134, 0, 4489], 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['1.74502909344688296171382532979317', '2.68900975784905443020785166460403', '3.02473421793484999957631922901558', '4.15127486396668832984271170028258', '4.85517883035181554193637871803076', '5.01237677697104957198001932438398', '5.66990658847027277525585177583481', '6.69932041253260706274722644088522', '6.81411763071537323600840753230656', '7.46428835432640754113355987046078', '7.909987862286350183375095910258850', '8.338442505726918333995265218224404', '9.327959901425306425198768202784495', '9.372732192062624224981148085357381'], 'prelabel': '4-288e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.5164734017492283, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'N(U(1))', 'symmetry_type': 'symplectic', 'trace_hash': 172724942348509360, 'z1': {'__RealLiteral__': 0, 'data': '1.74502909344688296171382532979317', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.68900975784905443020785166460403', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.02473421793484999957631922901558', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.28858135490323, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 82944, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, 12, 62, 156, 169], 'euler17': [1, 0, -30, 0, 289], 'euler19': [1, 0, 38, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 0, 42, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, 62, 0, 961], 'euler37': [1, 4, 78, 148, 1369], 'euler41': [1, 0, 18, 0, 1681], 'euler43': [1, 0, 86, 0, 1849], 'euler47': [1, 0, 94, 0, 2209], 'euler5': [1, 0, -6, 0, 25], 'euler53': [1, 0, 90, 0, 2809], 'euler59': [1, 0, 118, 0, 3481], 'euler61': [1, 20, 222, 1220, 3721], 'euler67': [1, 0, 134, 0, 4489], 'euler7': [1, 0, 14, 0, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, -12, 182, -876, 5329], 'euler79': [1, 0, 158, 0, 6241], 'euler83': [1, 0, 166, 0, 6889], 'euler89': [1, 0, -78, 0, 7921], 'euler97': [1, 36, 518, 3492, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, -6, 0, 25], [1, 0, 14, 0, 49], [1, 0, 22, 0, 121], [1, 12, 62, 156, 169], [1, 0, -30, 0, 289], [1, 0, 38, 0, 361], [1, 0, 46, 0, 529], [1, 0, 42, 0, 841], [1, 0, 62, 0, 961], [1, 4, 78, 148, 1369], [1, 0, 18, 0, 1681], [1, 0, 86, 0, 1849], [1, 0, 94, 0, 2209], [1, 0, 90, 0, 2809], [1, 0, 118, 0, 3481], [1, 20, 222, 1220, 3721], [1, 0, 134, 0, 4489], [1, 0, 142, 0, 5041], [1, -12, 182, -876, 5329], [1, 0, 158, 0, 6241], [1, 0, 166, 0, 6889], [1, 0, -78, 0, 7921], [1, 36, 518, 3492, 9409]], 'index': 18, 'instance_types': ['ECNF', 'HMF', 'BMF', 'ECNF'], 'instance_urls': ['EllipticCurve/2.2.12.1/576.1/c', 'ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-576.1-c', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/9216.1/d', 'EllipticCurve/2.0.3.1/9216.1/d'], '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': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-288e2-1.1-c1e2-0-18', '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': '4-288e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.5164734017492283, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 172724942348509360, 'z1': {'__RealLiteral__': 0, 'data': '1.74502909344688296171382532979317', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9809668
{'Lhash': '851919934628461349,1626648016933741962', 'Lhash_array': ['851919934628461349', '1626648016933741962'], 'label': '4-288e2-1.1-c1e2-0-18', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/9216.1/d'}
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id: 9809402
{'Lhash': '851919934628461349,1626648016933741962', 'Lhash_array': ['851919934628461349', '1626648016933741962'], 'label': '4-288e2-1.1-c1e2-0-18', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/9216.1/d'}
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id: 9589847
{'Lhash': '851919934628461349,1626648016933741962', 'Lhash_array': ['851919934628461349', '1626648016933741962'], 'label': '4-288e2-1.1-c1e2-0-18', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-576.1-c'}
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id: 9589588
{'Lhash': '851919934628461349,1626648016933741962', 'Lhash_array': ['851919934628461349', '1626648016933741962'], 'label': '4-288e2-1.1-c1e2-0-18', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.12.1/576.1/c'}