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lfunc_lfunctions • Show schema
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{'Lhash': '2462531249694293116496439467440', 'a10': [50.62826400180563, -29.23024185004592], 'a2': [6.758444316651647, 3.9019896455219247], 'a3': [18.12990424112357, 0.0], 'a4': [14.451046387520632, 25.029946565720415], 'a5': [3.7455560503077816, -6.487493381730087], 'a6': [122.52994827986016, 70.74269862316818], 'a7': [84.2020614074161, 48.61408281989308], 'a8': [0.0, -24.176003829153103], 'a9': [85.6934277923103, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.78341300859182, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[61, [[1.0, 0], [28220.733432217057, 6941.650059441665]]]], 'bad_primes': [61], 'central_character': '61.48', 'coefficient_field': 'CDF', 'conductor': 61, 'conductor_radical': 61, 'conjugate': '2915595306586548406498174678730', 'degree': 2, 'euler_factors': [[[1.0, 0], [-6.758444316651647, -3.9019896455219247], [16.0, 27.712812921102035]], [[1.0, 0], [-18.12990424112357, 0], [243.0, 0]], [[1.0, 0], 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'3.32431068368545937386700565137290', '4.38093231333626694310569892334486', '6.17797358404781963823295433821453', '8.162598201746858881642477870443298', '9.024849091487495378207453005854235', '11.03837300911337290518215041664723', '11.51846740781485783552405725949056', '13.27489484717269370129690328293973', '13.95783926261683955090597627718699'], 'prelabel': '2-61-61.48-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1278447865250314, 'root_angle': -0.27015501790597307, 'root_number': '0.6609464804885626 - 0.750433041603168*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.135077508953', 'prec': 50}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.94259463076886951859238754584', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.32431068368545937386700565137', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.38093231333626694310569892334', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.78341300859182, 'bad_primes': [61], 'central_character': '61.48', 'conductor': 61, 'conductor_radical': 61, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/61/6/f/a/48/22'], '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': '2-61-61.48-c5-0-15', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-61-61.48-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1278447865250314, 'root_angle': -0.13507750895298654, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.94259463076886951859238754584', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2462531249694293116496439467440', 'Lhash_array': ['2462531249694293116496439467440'], 'label': '2-61-61.48-c5-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/61/6/f/a/48/22'}