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lfunc_lfunctions • Show schema
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{'Lhash': '1928626184717838637871237212724', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.2928932188134525, -0.7071067811865476], 'a4': [0.0, 1.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.7071067811865476, -0.2928932188134525], 'a8': [0.0, 0.0], 'a9': [0.2928932188134525, 0.2928932188134525], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.39875294509376896, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[17, [[1.0, 0], [1.0, 0]]], [47, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [17, 47], 'central_character': '799.93', 'coefficient_field': 'CDF', 'conductor': 799, 'conductor_radical': 799, 'conjugate': '2208924279111807453715438730257', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [-0.2928932188134525, 0.7071067811865476], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, 0], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [-0.7071067811865476, 0.2928932188134525], 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'data': '-0.012089257049555817', 'prec': 70}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.52141779790946051256389488615', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.90150301558418022506540329796', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.46965917503732683491478775816', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.39875294509376896, 'bad_primes': [17, 47], 'central_character': '799.93', 'conductor': 799, 'conductor_radical': 799, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/799/1/h/a/93/1'], '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': '2-799-799.93-c0-0-2', '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': '2-799-799.93-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6314688789590259, 'root_angle': -0.012089257049555817, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.52141779790946051256389488615', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1928626184717838637871237212724', 'Lhash_array': ['1928626184717838637871237212724'], 'label': '2-799-799.93-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/799/1/h/a/93/1'}