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lfunc_lfunctions • Show schema
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{'Lhash': '3835819448407117806631286663382,5814321663509808594736599976178', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -4, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 5, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.0781070621112613, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1, 4, 5]], [7, [1, 0, 1]]], 'bad_primes': [5, 7], 'central_character': '35.1', 'coefficient_field': '1.1.1.1', 'conductor': 1225, 'conductor_radical': 35, 'degree': 4, 'euler_factors': [[1, 0, 0, 0, 4], [1, 0, -5, 0, 9], [1, 4, 5], [1, 0, 1], [1, 6, 31, 66, 121], [1, 0, -25, 0, 169], [1, 0, 15, 0, 289], [1, 0, 38, 0, 361], [1, 0, -10, 0, 529], [1, -10, 83, -290, 841], [1, -4, 66, -124, 961], [1, 0, -70, 0, 1369], [1, -4, 86, -164, 1681], [1, 0, -70, 0, 1849], [1, 0, -85, 0, 2209], [1, 0, -70, 0, 2809], [1, 20, 218, 1180, 3481], [1, 16, 186, 976, 3721], [1, 0, -130, 0, 4489], [1, 16, 206, 1136, 5041], [1, 0, -110, 0, 5329], [1, -10, 183, -790, 6241], [1, 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['3.02592800233480114290664971805765', '4.58669105072248681251752024316752', '4.60140633504418596338695192636418', '6.41057499424661595037771355876511', '7.35689965275207777678389254869020', '7.69057201102210773213766625761004', '8.382229318624263597580461235223452', '9.316604718406395525588995501969644', '10.42068121271810089671381063106814', '10.57199601674620508871050040716133', '11.42621865015752539898361587726808', '12.36148837795374284937339794164077', '12.39216276691738128396285050554669', '13.34283107156104634236933164891015', '13.73908249804327735744761172915587', '14.84551408076473918952506948409371', '15.51459514519935734353166136015426', '15.70323106477834300119154299757688', '15.98210910707013386448206162216525', '16.58448451363154192517734140834941'], 'prelabel': '4-35e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.5286552818940539, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 2208748744610669746, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.02592800233480114290664971806', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.58669105072248681251752024317', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.60140633504418596338695192636', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.0781070621112613, 'bad_primes': [5, 7], 'central_character': '1.1', 'conductor': 1225, 'conductor_radical': 35, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -4, 0, 0, 0, 5, 0, -6, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 10, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -20, 0, 0, 0, -1, 0, 0, 0, 0, 0, 24, 0, 0, 0, -20, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 10, 16, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30, 0], 'euler11': [1, 6, 31, 66, 121], 'euler13': [1, 0, -25, 0, 169], 'euler17': [1, 0, 15, 0, 289], 'euler19': [1, 0, 38, 0, 361], 'euler2': [1, 0, 0, 0, 4], 'euler23': [1, 0, -10, 0, 529], 'euler29': [1, -10, 83, -290, 841], 'euler3': [1, 0, -5, 0, 9], 'euler31': [1, -4, 66, -124, 961], 'euler37': [1, 0, -70, 0, 1369], 'euler41': [1, -4, 86, -164, 1681], 'euler43': [1, 0, -70, 0, 1849], 'euler47': [1, 0, -85, 0, 2209], 'euler5': [1, 4, 5, 0, 0], 'euler53': [1, 0, -70, 0, 2809], 'euler59': [1, 20, 218, 1180, 3481], 'euler61': [1, 16, 186, 976, 3721], 'euler67': [1, 0, -130, 0, 4489], 'euler7': [1, 0, 1, 0, 0], 'euler71': [1, 16, 206, 1136, 5041], 'euler73': [1, 0, -110, 0, 5329], 'euler79': [1, -10, 183, -790, 6241], 'euler83': [1, 0, -150, 0, 6889], 'euler89': [1, 0, 178, 0, 7921], 'euler97': [1, 0, -145, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 4], [1, 0, -5, 0, 9], [1, 4, 5, 0, 0], [1, 0, 1, 0, 0], [1, 6, 31, 66, 121], [1, 0, -25, 0, 169], [1, 0, 15, 0, 289], [1, 0, 38, 0, 361], [1, 0, -10, 0, 529], [1, -10, 83, -290, 841], [1, -4, 66, -124, 961], [1, 0, -70, 0, 1369], [1, -4, 86, -164, 1681], [1, 0, -70, 0, 1849], [1, 0, -85, 0, 2209], [1, 0, -70, 0, 2809], [1, 20, 218, 1180, 3481], [1, 16, 186, 976, 3721], [1, 0, -130, 0, 4489], [1, 16, 206, 1136, 5041], [1, 0, -110, 0, 5329], [1, -10, 183, -790, 6241], [1, 0, -150, 0, 6889], [1, 0, 178, 0, 7921], [1, 0, -145, 0, 9409]], 'index': 1, 'instance_types': ['ECNF', 'HMF', 'CMF'], 'instance_urls': ['EllipticCurve/2.2.5.1/49.1/a', 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-49.1-a', 'ModularForm/GL2/Q/holomorphic/35/2/b/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, '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': '4-35e2-1.1-c1e2-0-1', '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': '4-35e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.5286552818940539, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2208748744610669746, 'z1': {'__RealLiteral__': 0, 'data': '3.02592800233480114290664971806', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9955765
{'Lhash': '3835819448407117806631286663382,5814321663509808594736599976178', 'Lhash_array': ['3835819448407117806631286663382', '5814321663509808594736599976178'], 'label': '4-35e2-1.1-c1e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/35/2/b/a'}
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id: 9531682
{'Lhash': '_3835819448407117806631286663382', 'Lhash_array': ['_3835819448407117806631286663382'], 'label': '4-35e2-1.1-c1e2-0-1', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-49.1-a'}
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id: 9531126
{'Lhash': '_3835819448407117806631286663382', 'Lhash_array': ['_3835819448407117806631286663382'], 'label': '4-35e2-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.5.1/49.1/a'}