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lfunc_lfunctions • Show schema
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{'Lhash': '1240872353568039121388278915284,1534510367803690841670953582870', 'a10': -4, 'a2': -2, 'a3': 0, 'a4': 3, 'a5': 2, 'a6': 0, 'a7': 0, 'a8': -4, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.614594053632576, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1, 2, 1]], [3, [1]], [5, [1, -2, 1]]], 'bad_primes': [2, 3, 5], 'central_character': '3240.1', 'coefficient_field': '1.1.1.1', 'conductor': 10497600, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1, 2, 1], [1], [1, -2, 1], [1, 0, -1, 0, 1], [1, 0, 2, 0, 1], [1, 0, -1, 0, 1], [1, 0, -2, 0, 1], [1, -2, 3, -2, 1], [1, 2, 3, 2, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -1, 0, 1], [1, 0, -2, 0, 1], [1, -2, 3, -2, 1], [1, -2, 3, -2, 1], [1, 0, -1, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -1, 0, 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'6.01154955992664242009573294742740', '6.61138011113362149162249830832571', '6.83242225115492755852226526121876', '7.21853567200084208870066654996293', '7.67849326775452767797140083067996', '7.890029286948739667792957851102441', '8.397375180912137666304748937216456', '8.897890477540212442963696653360033', '9.023133435735267180074635152506960'], 'prelabel': '4-3240e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.2716016046431082, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0e2-0', 'trace_hash': 1701014032889380412, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.978875688099410759521335671866', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.21051523781664732651206950632', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.11926612017279930212291372171', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.614594053632576, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 10497600, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, -2, 0, 3, 2, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, 5, 0, 0, 2, 6, 0, 0, -2, 0, 3, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, -4, 0, -8, 0, 0, 0, 0, 0, 4, 2, 0, 1, -6, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, -4, 4, 0, 0, -2, 0, 9], 'euler11': [1, 0, 2, 0, 1], 'euler13': [1, 0, -1, 0, 1], 'euler17': [1, 0, -2, 0, 1], 'euler19': [1, -2, 3, -2, 1], 'euler2': [1, 2, 1, 0, 0], 'euler23': [1, 2, 3, 2, 1], 'euler29': [1, 0, -2, 0, 1], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, -2, 0, 1], 'euler37': [1, 0, 2, 0, 1], 'euler41': [1, 0, -1, 0, 1], 'euler43': [1, 0, -2, 0, 1], 'euler47': [1, -2, 3, -2, 1], 'euler5': [1, -2, 1, 0, 0], 'euler53': [1, -2, 3, -2, 1], 'euler59': [1, 0, -1, 0, 1], 'euler61': [1, 0, -2, 0, 1], 'euler67': [1, 0, -2, 0, 1], 'euler7': [1, 0, -1, 0, 1], 'euler71': [1, 0, -2, 0, 1], 'euler73': [1, 0, -2, 0, 1], 'euler79': [1, 0, -2, 0, 1], 'euler83': [1, 0, -2, 0, 1], 'euler89': [1, 0, 2, 0, 1], 'euler97': [1, 0, -2, 0, 1], 'euler_factors': [[1, 2, 1, 0, 0], [1, 0, 0, 0, 0], [1, -2, 1, 0, 0], [1, 0, -1, 0, 1], [1, 0, 2, 0, 1], [1, 0, -1, 0, 1], [1, 0, -2, 0, 1], [1, -2, 3, -2, 1], [1, 2, 3, 2, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -1, 0, 1], [1, 0, -2, 0, 1], [1, -2, 3, -2, 1], [1, -2, 3, -2, 1], [1, 0, -1, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1]], 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3240/1/p/e'], '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': '4-3240e2-1.1-c0e2-0-13', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0], 'order_of_vanishing': 0, 'prelabel': '4-3240e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.2716016046431082, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 1701014032889380412, 'z1': {'__RealLiteral__': 0, 'data': '0.978875688099410759521335671866', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1240872353568039121388278915284,1534510367803690841670953582870', 'Lhash_array': ['1240872353568039121388278915284', '1534510367803690841670953582870'], 'label': '4-3240e2-1.1-c0e2-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3240/1/p/e'}