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lfunc_lfunctions • Show schema
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{'Lhash': '1245446351703697723220020222910', 'a10': [0, 0], 'a2': [0, 4.459382791946336], 'a3': [0, 0], 'a4': [-11.886094885107095, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, -5.081234416107328], 'a8': [0, -17.329584658517255], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 39.82628925387493, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '675.649', 'coefficient_field': 'CDF', 'conductor': 675, 'conductor_radical': 15, 'conjugate': '423038992441214336543587752590', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -4.459382791946336], [-8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 5.081234416107328], [-343.0, 0]], [[1.0, 0], [58.300676292106395, 0], [1331.0, 0]], [[1.0, 0], [0, -21.21191721124963], [-2197.0, 0]], [[1.0, 0], [0, 68.84505583253478], [-4913.0, 0]], [[1.0, 0], [-40.813269795462425, 0], [6859.0, 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['0.982483936409185624519269565669975', '2.37800815811876254332999011334093', '2.99436100914583143567323470228049', '4.23986839540833921490792650258678', '5.17662748439117658362962948428012', '6.29613099818038788599820377925714', '7.76948005825038946831702015513693', '8.460753148221496131511489503825908', '9.544791872155365912946285047456365', '10.32095619040348418012261483950779'], 'prelabel': '2-675-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.310807337724305, 'root_angle': -0.14758361765043326, 'root_number': '0.89442719099991587856366946749251049417624734384461028971 - 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.07379180882521663', 'prec': 67}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.982483936409185624519269565670', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.37800815811876254332999011334', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.99436100914583143567323470228', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 39.82628925387493, 'bad_primes': [3, 5], 'central_character': '5.4', 'conductor': 675, 'conductor_radical': 15, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/675/4/b/k/649/5'], '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': '2-675-5.4-c3-0-38', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-675-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.310807337724305, 'root_angle': -0.07379180882521663, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.982483936409185624519269565670', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1245446351703697723220020222910', 'Lhash_array': ['1245446351703697723220020222910'], 'label': '2-675-5.4-c3-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/675/4/b/k/649/5'}