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lfunc_lfunctions • Show schema
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{'Lhash': '1769276373627068346008017840745', 'a10': [0.2178500376263925, -2.0050022999045902], 'a2': [-0.764889820286288, -0.4779562062843348], 'a3': [-1.9771663259344234, 0.5669433208393913], 'a4': [-0.5201279915262784, -1.0664204191392523], 'a5': [0.9731695219609874, 2.0131917647174657], 'a6': [1.7832884745267195, 0.5113497415474003], 'a7': [-2.1504042748253394, 3.724609460810795], 'a8': [-0.3004187816993546, 2.8582937779811934], 'a9': [1.0436176628953522, -0.6521246926545458], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.79289409601082, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-0.9731695219609874, -2.0131917647174657]]], [19, [[1.0, 0], [4.353186470295158, -0.22308642907891177]]]], 'bad_primes': [5, 19], 'central_character': '475.6', 'coefficient_field': 'CDF', 'conductor': 475, 'conductor_radical': 95, 'conjugate': '100499623425489790625996905887', 'degree': 2, 'euler_factors': [[[1.0, 0], 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10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/475/2/bc/a/6/18', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.08972942587614793, 0.223606093612426, 0.34904185524194464, 0.465048965456272, 0.5678128463498663, 0.6504181121119985, 0.7030165057970095, 0.7133654730069677, 0.6676759107723507, 0.5517297286482142, 0.3522333478589494, 0.058355971228220234, -0.3366320155219117, -0.833744806913104, -1.4268518073405148, -2.101618870827712, -2.8350127510876937, -3.5955447115320442, -4.344385837784586, -5.037416020493369, -5.628173974000027, -6.071564148000356, -6.3280590323952, -6.368026491789363, -6.175727707274941, -5.7524884016860565, -5.118558289147996, -4.313250219362009, -3.3930930909220636, -2.427934034413867, -1.4951685578015965, -0.672536063757223, -0.03015914858623196, 0.37730816255030447, 0.5174604886465566, 0.38490588175008517, 0.0032225045250102034, -0.5764056834716395, -1.280000167744589, 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1.9475353901818626, 'root_angle': 0.8263146671786834, 'root_number': '-0.8547908828005568 + 0.5189725876007757*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.413157333589', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.39571296168559823353637248602', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.00717313439490927898064714902', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.50081879801746599900027151798', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.79289409601082, 'bad_primes': [5, 19], 'central_character': '475.6', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/2/bc/a/6/18'], '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': '2-475-475.6-c1-0-23', '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': '2-475-475.6-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.4131573335893417, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.39571296168559823353637248602', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1769276373627068346008017840745', 'Lhash_array': ['1769276373627068346008017840745'], 'label': '2-475-475.6-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/bc/a/6/18'}