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lfunc_lfunctions • Show schema
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{'Lhash': '1551373284036775545437254400182', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [217.73742511576253, -217.73742511576253], 'a4': [0.0, 0.0], 'a5': [-944.9977279986331, 2978.6917084648794], 'a6': [0.0, 0.0], 'a7': [21520.508533632063, 21520.508533632063], 'a8': [0.0, 0.0], 'a9': [0.0, -35770.17259208459], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.70714505347449, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '5.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [944.9977279986331, -2978.6917084648794]]]], 'bad_primes': [2, 5], 'central_character': '20.17', 'coefficient_field': 'CDF', 'conductor': 20, 'conductor_radical': 10, 'conjugate': '2216995090017309465968874342188', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-217.73742511576253, 217.73742511576253], [0, -59049.0]], [[1.0, 0], [944.9977279986331, -2978.6917084648794]], [[1.0, 0], [-21520.508533632063, -21520.508533632063], [0, 282475249.0]], [[1.0, 0], 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'primitive': True, 'rational': False, 'root_analytic_conductor': 3.564708270458396, 'root_angle': -0.07842060141113051, 'root_number': '0.9698051891609422 - 0.24388090346828947*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0392103007056', 'prec': 54}, 'spectral_label': 'c10-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.22381773318094462042799127297', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.78376848499172644715850178804', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.82400005630219287399421328006', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.70714505347449, 'bad_primes': [2, 5], 'central_character': '5.2', 'conductor': 20, 'conductor_radical': 10, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/20/11/f/a/17/5'], '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': '2-20-5.2-c10-0-2', 'motivic_weight': 10, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [10], 'order_of_vanishing': 0, 'prelabel': '2-20-5.2-c10-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.564708270458396, 'root_angle': -0.039210300705565256, 'self_dual': False, 'spectral_label': 'c10-0', 'z1': {'__RealLiteral__': 0, 'data': '1.22381773318094462042799127297', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1551373284036775545437254400182', 'Lhash_array': ['1551373284036775545437254400182'], 'label': '2-20-5.2-c10-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/20/11/f/a/17/5'}