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lfunc_lfunctions • Show schema
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{'Lhash': '2541348793483044312031346616627', 'a10': [-2.75510701765842, 1.5522194823056847], 'a2': [-1.362526166135379, 0.37884356480798986], 'a3': [0.8910065241883679, -0.4539904997395468], 'a4': [1.7129551068071487, -1.0323685398457807], 'a5': [2.1709768820519515, -0.535592548114691], 'a6': [-1.042028324093696, 0.9561260229627072], 'a7': [2.2110125384414077, -2.2110125384414077], 'a8': [-1.9428399766091682, 2.055571167653722], 'a9': [0.5877852522924731, -0.8090169943749475], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.3955120606384126, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.362526166135379, -0.37884356480798986]]], [3, [[1.0, 0], [-0.8910065241883679, 0.4539904997395468]]], [5, [[1.0, 0], [-2.1709768820519515, 0.535592548114691]]]], 'bad_primes': [2, 3, 5], 'central_character': '300.127', 'coefficient_field': 'CDF', 'conductor': 300, 'conductor_radical': 30, 'conjugate': 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0.18336903198550492, 'root_number': '0.8386094810639447 + 0.5447330890166865*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0916845159928', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.00477070970936052317275623328', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.71206241776597526632087085162', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.71720234401629671146507539811', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.3955120606384126, 'bad_primes': [2, 3, 5], 'central_character': '100.27', 'conductor': 300, 'conductor_radical': 30, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/300/2/w/a/127/3'], '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': '2-300-100.27-c1-0-20', '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': '2-300-100.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5477441844951034, 'root_angle': 0.09168451599275246, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.00477070970936052317275623328', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2541348793483044312031346616627', 'Lhash_array': ['2541348793483044312031346616627'], 'label': '2-300-100.27-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/300/2/w/a/127/3'}