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lfunc_lfunctions • Show schema
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{'Lhash': '3345780792400665525884005827786', 'a10': [-1.902113032590307, 0.0], 'a2': [1.902113032590307, 0.0], 'a3': [1.902113032590307, 0.0], 'a4': [1.618033988749895, 0.0], 'a5': [-1.0, 0.0], 'a6': [3.618033988749895, 0.0], 'a7': [-4.23606797749979, 0.0], 'a8': [-0.7265425280053609, 0.0], 'a9': [0.6180339887498949, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.412997564841117, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 19], 'central_character': '1805.1', 'coefficient_field': 'CDF', 'conductor': 1805, 'conductor_radical': 95, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.902113032590307, 0], [2.0, 0]], [[1.0, 0], [-1.902113032590307, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [4.23606797749979, 0], [7.0, 0]], [[1.0, 0], [5.854101966249685, 0], [11.0, 0]], [[1.0, 0], [3.0776835371752536, 0], [13.0, 0]], [[1.0, 0], [-5.23606797749979, 0], 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'7.39043228338248023518536147351562', '7.84386276238155230548400732359994', '8.946466158605900879370401918340479'], 'prelabel': '2-1805-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7964453854679796, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.63935566456426318279151265882', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.94670681704639266892164841900', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.56377211486846548284762013262', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.412997564841117, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 1805, 'conductor_radical': 95, 'degree': 2, 'index': 112, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1805/2/a/l/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': '2-1805-1.1-c1-0-112', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-1805-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7964453854679796, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.63935566456426318279151265882', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3345780792400665525884005827786', 'Lhash_array': ['3345780792400665525884005827786'], 'label': '2-1805-1.1-c1-0-112', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1805/2/a/l/1/4'}