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lfunc_lfunctions • Show schema
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{'Lhash': '2664974653912984477631912109386', 'a10': [-1.032395351143315, 0.0], 'a2': [0.8290329764197399, 0.0], 'a3': [-0.26962909132790774, 0.0], 'a4': [-1.312704324008627, 0.0], 'a5': [-1.245300706374571, 0.0], 'a6': [-0.22353140811292524, 0.0], 'a7': [4.954481990054605, 0.0], 'a8': [-2.7463411257314148, 0.0], 'a9': [-2.927300153109687, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.380047121500306, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[17, [[1.0, 0], [1.0, 0]]], [47, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [17, 47], 'central_character': '799.1', 'coefficient_field': 'CDF', 'conductor': 799, 'conductor_radical': 799, 'conjugate': '2664974653912984477631912109386', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8290329764197399, 0], [2.0, 0]], [[1.0, 0], [0.26962909132790774, 0], [3.0, 0]], [[1.0, 0], [1.245300706374571, 0], [5.0, 0]], [[1.0, 0], [-4.954481990054605, 0], [7.0, 0]], [[1.0, 0], [4.147099104827784, 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'5.22530229916776403755034872293622', '5.88562742999163430846977708860323', '7.50272183586563477303340325923866', '8.313505565389215738521731719971082', '8.559710603292493548094908678234853', '9.940336499898374037877723668842696'], 'prelabel': '2-799-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.525875515836104, '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': '2.10229431787684958591346764660', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.51869776393656596291188623645', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.55735525796986178724260282014', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.380047121500306, 'bad_primes': [17, 47], 'central_character': '1.1', 'conductor': 799, 'conductor_radical': 799, 'degree': 2, 'index': 49, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/799/2/a/e/1/9'], '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': '2-799-1.1-c1-0-49', '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': '2-799-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.525875515836104, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.10229431787684958591346764660', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2664974653912984477631912109386', 'Lhash_array': ['2664974653912984477631912109386'], 'label': '2-799-1.1-c1-0-49', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/799/2/a/e/1/9'}