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lfunc_lfunctions • Show schema
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{'Lhash': '2861099632109882220437893843216', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.1033577239371046, -1.3351410910567962], 'a4': [0.0, 0.0], 'a5': [0.2667802378930476, -0.46207692648607035], 'a6': [0.0, 0.0], 'a7': [2.547158411914426, -0.715530589572226], 'a8': [0.0, 0.0], 'a9': [-0.5652034660566639, -2.946276470726658], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.0122301309362665, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.1033577239371046, 1.3351410910567962]]], [7, [[1.0, 0], [-2.547158411914426, 0.715530589572226]]]], 'bad_primes': [2, 3, 7], 'central_character': '252.41', 'coefficient_field': 'CDF', 'conductor': 252, 'conductor_radical': 42, 'conjugate': '1900626501344562259549513853332', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.1033577239371046, 1.3351410910567962]], [[1.0, 0], [-0.2667802378930476, 0.46207692648607035], [-2.5, 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'12.07880798573799389176800945531587'], 'prelabel': '2-252-63.41-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4185309763753016, 'root_angle': 0.2969430596970134, 'root_number': '0.5955275523805199 + 0.803334883069114*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.148471529849', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.25700964571370554301348390799', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.57381425979581670628485448677', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.93417646689399348285905001466', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.0122301309362665, 'bad_primes': [2, 3, 7], 'central_character': '63.41', 'conductor': 252, 'conductor_radical': 42, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/252/2/x/a/41/6'], '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': '2-252-63.41-c1-0-6', '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': '2-252-63.41-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4185309763753016, 'root_angle': 0.1484715298485067, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.25700964571370554301348390799', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2861099632109882220437893843216', 'Lhash_array': ['2861099632109882220437893843216'], 'label': '2-252-63.41-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/252/2/x/a/41/6'}