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lfunc_lfunctions • Show schema
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{'Lhash': '1472320945943743544671310944691', 'a10': [1.0833504408394037, 0.9090389553440874], 'a2': [-1.0833504408394037, 0.9090389553440874], 'a3': [-1.3289260487773493, -0.48368952529595055], 'a4': [0.17364817766693036, -0.984807753012208], 'a5': [-0.17364817766693036, -0.984807753012208], 'a6': [1.8793852415718169, -0.6840402866513374], 'a7': [0.0, 0.0], 'a8': [2.3847109579533255e-79, -1.90842961336666e-78], 'a9': [0.766044443118978, 0.6427876096865394], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9008123478025694, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0.17364817766693036, 0.984807753012208]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 19], 'central_character': '1805.849', 'coefficient_field': 'CDF', 'conductor': 1805, 'conductor_radical': 95, 'conjugate': '691405196414052879002286874403', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0833504408394037, -0.9090389553440874], 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'7.31530723543424235123443459575730', '8.207416724356486193959675098829564', '9.115742684208134934491106542606392', '9.834456604049416608099916883478292'], 'prelabel': '2-1805-95.89-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9491113463669947, 'root_angle': 0.3381566578344696, 'root_number': '0.48682028616020860649050220597363 + 0.87350215167616651081057072959226*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1690783289172348', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.16145643419303792214584905934', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.52610247492520836734286134394', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.59357063301225749018263706735', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9008123478025694, 'bad_primes': [5, 19], 'central_character': '95.89', 'conductor': 1805, 'conductor_radical': 95, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1805/1/o/b/849/1'], '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': '2-1805-95.89-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1805-95.89-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9491113463669947, 'root_angle': 0.1690783289172348, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.16145643419303792214584905934', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1472320945943743544671310944691', 'Lhash_array': ['1472320945943743544671310944691'], 'label': '2-1805-95.89-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1805/1/o/b/849/1'}