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lfunc_lfunctions • Show schema
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{'Lhash': '2908356501411006626776040238460', 'a10': [-0.5, -0.8660254037844386], 'a2': [0.8660254037844386, -0.5], 'a3': [0.5, 0.8660254037844386], 'a4': [0.5, -0.8660254037844386], 'a5': [0.0, -1.0], 'a6': [0.8660254037844386, 0.5], 'a7': [-0.8660254037844386, -0.5], 'a8': [3.9689140359382235e-80, -1.0], 'a9': [-4.582907174201562e-80, 2.6459426906140066e-80], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6747358970798193, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, 0.5]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 13], 'central_character': '1352.315', 'coefficient_field': 'CDF', 'conductor': 1352, 'conductor_radical': 26, 'conjugate': '1643848351482194292263147690250', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, 0.5]], [[1.0, 0], [-0.5, -0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 1.0], [-1.0, 0]], [[1.0, 0], [0.8660254037844386, 0.5], [0.5, 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['2.29428874240850158571732940593552', '2.75626672508052850615022171515022', '3.75559546066981199487332866594801', '4.98053795137731331921032491751542', '6.10944561910638960081987133091070', '6.65520050365649572652023475849897', '7.30157786417098438273091637499623', '7.971085016617006416533514411199842', '8.924852405632046828378905518650005', '9.878223563661038460325055686557383'], 'prelabel': '2-1352-104.3-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8214230926141651, 'root_angle': 0.33741523611846674, 'root_number': '0.48885356426140289006372607505883 + 0.87236585943566271307206279130642*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.16870761805923337', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.29428874240850158571732940594', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.75626672508052850615022171515', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.75559546066981199487332866595', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6747358970798193, 'bad_primes': [2, 13], 'central_character': '104.3', 'conductor': 1352, 'conductor_radical': 26, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1352/1/n/a/315/2'], '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': '2-1352-104.3-c0-0-7', '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': '2-1352-104.3-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8214230926141651, 'root_angle': 0.16870761805923337, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.29428874240850158571732940594', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2908356501411006626776040238460', 'Lhash_array': ['2908356501411006626776040238460'], 'label': '2-1352-104.3-c0-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1352/1/n/a/315/2'}