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lfunc_lfunctions • Show schema
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{'Lhash': '2431867395883846987723506054824', 'a10': [0.0, 0.0], 'a2': [1.0, 0.0], 'a3': [0.0, 0.0], 'a4': [1.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.6180339887498949, 0.0], 'a8': [1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.4990650126330024, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '1000.499', 'coefficient_field': 'CDF', 'conductor': 1000, 'conductor_radical': 10, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.6180339887498949, 0], [1.0, 0]], [[1.0, 0], [1.618033988749895, 0], [1.0, 0]], [[1.0, 0], [1.618033988749895, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.6180339887498949, 0], [1.0, 0]], [[1.0, 0], [1.618033988749895, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], 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'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.91840511529439621330329674315', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.80912449030115518576986234228', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.19102068368152253136825469476', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.4990650126330024, 'bad_primes': [2, 5], 'central_character': '40.19', 'conductor': 1000, 'conductor_radical': 10, 'degree': 2, 'index': 3, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1000/1/e/b/499/2', 'ArtinRepresentation/2.1000.5t2.a.a'], 'is_instance_Artin': True, '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': '2-10e3-40.19-c0-0-3', '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': '2-10e3-40.19-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7064453359128379, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.91840511529439621330329674315', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24597588
{'Lhash': '2431867395883846987723506054824', 'Lhash_array': ['2431867395883846987723506054824'], 'label': '2-10e3-40.19-c0-0-3', 'type': 'Artin', 'url': 'ArtinRepresentation/2.1000.5t2.a.a'}
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id: 19808601
{'Lhash': '2431867395883846987723506054824', 'Lhash_array': ['2431867395883846987723506054824'], 'label': '2-10e3-40.19-c0-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1000/1/e/b/499/2'}