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lfunc_lfunctions • Show schema
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{'Lhash': '855147948481765621358825792742', 'a10': [1.0, 0.0], 'a2': [-1.0, 0.0], 'a3': [1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [-1.0, 0.0], 'a7': [3.499852897391547, 0.0], 'a8': [-1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 69.23029855245012, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [17, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5, 17], 'central_character': '8670.1', 'coefficient_field': 'CDF', 'conductor': 8670, 'conductor_radical': 510, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-3.499852897391547, 0], [7.0, 0]], [[1.0, 0], [2.984916422555656, 0], [11.0, 0]], [[1.0, 0], [-0.02627901888128482, 0], [13.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.129176219844683, 0], [19.0, 0]], [[1.0, 0], [7.103703799302868, 0], [23.0, 0]], [[1.0, 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'4.85651753145285467253170168769901', '5.78312995655614778985021959975375', '6.52983725492909973450289609484131', '7.56777965945568133826717472201841', '7.902412635874880132771050771929587'], 'prelabel': '2-8670-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.320474659083466, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.67459278473721679605110151210', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.87300909472022850040694005863', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.34596946137657135581941115256', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 69.23029855245012, 'bad_primes': [2, 3, 5, 17], 'central_character': '1.1', 'conductor': 8670, 'conductor_radical': 510, 'degree': 2, 'index': 32, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8670/2/a/cd/1/6'], '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': '2-8670-1.1-c1-0-32', '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': '2-8670-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.320474659083466, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.67459278473721679605110151210', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '855147948481765621358825792742', 'Lhash_array': ['855147948481765621358825792742'], 'label': '2-8670-1.1-c1-0-32', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8670/2/a/cd/1/6'}