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lfunc_lfunctions • Show schema
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{'Lhash': '2411071240552962430405138267675', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.7182192504625178, -0.21845504649703962], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, -3.644264152356288], 'a8': [0.0, 0.0], 'a9': [2.9045547853199527, -0.7507073325037957], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.8328192970214605, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.7182192504625178, 0.21845504649703962]]], [5, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '480.431', 'coefficient_field': 'CDF', 'conductor': 480, 'conductor_radical': 30, 'conjugate': '1817229639117376664554957307894', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.7182192504625178, 0.21845504649703962]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 3.644264152356288], [-7.0, 0]], [[1.0, 0], [0, -5.074027394851169], [-11.0, 0]], [[1.0, 0], [0, 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['1.90199984137495785113130321799672', '2.93221897186327431717375345158590', '4.07118420215339861950875112193420', '5.60345162431722067458840274973810', '6.21981201889557157432271763674478', '7.70337577639865026138749595408151', '8.646116403123228488759414707233195', '9.006709577209535693668191047512852', '9.996491547975187987607031676487735', '10.99783949195867194706530651122963'], 'prelabel': '2-480-24.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9577587433137569, 'root_angle': 0.1627521223349573, 'root_number': '0.8721087133116104 + 0.48931216229107494*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0813760611675', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.90199984137495785113130321800', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.93221897186327431717375345159', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.07118420215339861950875112193', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.8328192970214605, 'bad_primes': [2, 3, 5], 'central_character': '24.11', 'conductor': 480, 'conductor_radical': 30, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/480/2/b/b/431/7'], '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': '2-480-24.11-c1-0-11', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-480-24.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9577587433137569, 'root_angle': 0.08137606116747866, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.90199984137495785113130321800', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2411071240552962430405138267675', 'Lhash_array': ['2411071240552962430405138267675'], 'label': '2-480-24.11-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/480/2/b/b/431/7'}