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lfunc_lfunctions • Show schema
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{'Lhash': '1914754338717823639299274566175', 'a10': [-0.31286893008046174, -2.238846510780214e-80], 'a2': [0.09668181640676986, -0.2975560346993159], 'a3': [-1.4416788403346845, 1.0474409892285987], 'a4': [0.7298247742126793, 0.5302487364574218], 'a5': [-0.30901699437494745, -0.9510565162951535], 'a6': [0.17228825837762787, 0.5302487364574218], 'a7': [0.0, 0.0], 'a8': [0.48145577770113623, -0.3497980978537706], 'a9': [0.6722882583776278, -2.0690905050450485], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5215229382014875, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0.30901699437494745, 0.9510565162951535]]], [11, [[1.0, 0], [0.9510565162951535, 0.30901699437494745]]], [19, [[1.0, 0], [-0.8090169943749475, 0.5877852522924731]]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.284', 'coefficient_field': 'CDF', 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': '1078240598510560027605380857374', 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['1.51047484091680220904798594505877', '2.49537051034919396804455674666520', '4.29623414056635024986549847590960', '5.49617670156035972805251495084697', '6.04978187364051797597068320118541', '6.90730714384291636260161384033030', '7.19651142471171418179539945297964', '8.034002820146800907149286370065476', '9.673299755069104978606101227983414', '10.65542476454483898268835327364682'], 'prelabel': '2-1045-1045.284-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7221654507115994, 'root_angle': 0.18543426013921355, 'root_number': '0.83505756927040604738043798542082 + 0.55016257234039558553812043975620*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.09271713006960679', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.51047484091680220904798594506', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.49537051034919396804455674667', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.29623414056635024986549847591', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5215229382014875, 'bad_primes': [5, 11, 19], 'central_character': '1045.284', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1045/1/w/f/284/3'], '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': '2-1045-1045.284-c0-0-4', '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': '2-1045-1045.284-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7221654507115994, 'root_angle': 0.09271713006960677, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.51047484091680220904798594506', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1914754338717823639299274566175', 'Lhash_array': ['1914754338717823639299274566175'], 'label': '2-1045-1045.284-c0-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1045/1/w/f/284/3'}