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lfunc_lfunctions • Show schema
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{'Lhash': '1543048932283842999716486024023', 'a10': [-0.31975520069890345, -0.5538322535948842], 'a2': [-0.9396926207859084, 0.3420201433256687], 'a3': [-1.7300451080663821, -0.08333021094164986], 'a4': [0.766044443118978, -0.6427876096865394], 'a5': [0.11104981580177631, 0.6297948014285094], 'a6': [1.65421123236636, -0.5134054915103345], 'a7': [-0.766044443118978, -0.6427876096865394], 'a8': [-0.5, 0.8660254037844386], 'a9': [2.9861121518888405, 0.2883300475874821], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.0183451964044, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9396926207859084, -0.3420201433256687]]], [3, [[1.0, 0], [1.7300451080663821, 0.08333021094164986]]], [7, [[1.0, 0], [0.766044443118978, 0.6427876096865394]]]], 'bad_primes': [2, 3, 7], 'central_character': '378.169', 'coefficient_field': 'CDF', 'conductor': 378, 'conductor_radical': 42, 'conjugate': '929728156590682628975360786167', 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'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.21725097752174813599695414508', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.04422688392116672675078863323', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.73446554000394037466465366683', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.0183451964044, 'bad_primes': [2, 3, 7], 'central_character': '27.7', 'conductor': 378, 'conductor_radical': 42, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/378/2/u/d/169/1'], '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': '2-378-27.7-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': '2-378-27.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.737338538225754, 'root_angle': 0.08779486230716575, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.21725097752174813599695414508', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1543048932283842999716486024023', 'Lhash_array': ['1543048932283842999716486024023'], 'label': '2-378-27.7-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/378/2/u/d/169/1'}