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lfunc_lfunctions • Show schema
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{'Lhash': '2340122322083803552362944021948', 'a10': [0.006670415318065419, 0.4189923290791242], 'a2': [-0.7265128256550372, -1.2133338840396461], 'a3': [0.0, 0.0], 'a4': [-0.944358228317467, 1.7630052571132893], 'a5': [-0.25661186615270587, -0.14815493000051694], 'a6': [0.0, 0.0], 'a7': [-0.8660254037844386, 0.5], 'a8': [2.82520238108109, -0.13502409390082995], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.0366903928088, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7265128256550372, 1.2133338840396461]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.8660254037844386, -0.5]]]], 'bad_primes': [2, 3, 7], 'central_character': '756.71', 'coefficient_field': 'CDF', 'conductor': 756, 'conductor_radical': 42, 'conjugate': '117358805386969825808243450626', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7265128256550372, 1.2133338840396461]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.25661186615270587, 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'9.604480310219266530920038458996653', '10.62071190967607327611752187848720'], 'prelabel': '2-756-36.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4569677231923093, 'root_angle': -0.8141953219600202, 'root_number': '-0.8344167786248824 - 0.5511339578988705*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.40709766098', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.84603101332692541544727490025', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.51631535381383255303854391594', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.92815236415348164050180043168', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.0366903928088, 'bad_primes': [2, 3, 7], 'central_character': '36.23', 'conductor': 756, 'conductor_radical': 42, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/756/2/ba/a/71/13'], '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': '2-756-36.23-c1-0-29', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-756-36.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4569677231923093, 'root_angle': -0.4070976609800101, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.84603101332692541544727490025', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2340122322083803552362944021948', 'Lhash_array': ['2340122322083803552362944021948'], 'label': '2-756-36.23-c1-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/756/2/ba/a/71/13'}