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lfunc_lfunctions • Show schema
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{'Lhash': '913274306529997818302759162769', 'a10': [-14.262009154863232, 0.0], 'a2': [-4.737129681435949, 0.0], 'a3': [3.0, 0.0], 'a4': [14.440397618741454, 0.0], 'a5': [3.010685819042227, 0.0], 'a6': [-14.211389044307847, 0.0], 'a7': [21.82872347346299, 0.0], 'a8': [-30.508998719989545, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 118.77084484155591, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-3.0, 0]]], [11, [[1.0, 0], [11.0, 0]]], [61, [[1.0, 0], [-61.0, 0]]]], 'bad_primes': [3, 11, 61], 'central_character': '2013.1', 'coefficient_field': 'CDF', 'conductor': 2013, 'conductor_radical': 2013, 'degree': 2, 'euler_factors': [[[1.0, 0], [4.737129681435949, 0], [8.0, 0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [-3.010685819042227, 0], [125.0, 0]], [[1.0, 0], [-21.82872347346299, 0], [343.0, 0]], [[1.0, 0], [11.0, 0]], [[1.0, 0], [-4.7880055654040685, 0], [2197.0, 0]], [[1.0, 0], 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 118.77084484155591, 'bad_primes': [3, 11, 61], 'central_character': '1.1', 'conductor': 2013, 'conductor_radical': 2013, 'degree': 2, 'index': 99, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2013/4/a/h/1/4'], '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': '2-2013-1.1-c3-0-99', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-2013-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.898203743808239, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.72044639616434589191667938155', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '913274306529997818302759162769', 'Lhash_array': ['913274306529997818302759162769'], 'label': '2-2013-1.1-c3-0-99', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2013/4/a/h/1/4'}