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lfunc_lfunctions • Show schema
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{'Lhash': '506918151915456426795028485641', 'a10': [3.0971979099627376, 0.0], 'a2': [-0.7690906200089404, 0.0], 'a3': [-1.0, 0.0], 'a4': [-1.4084996182142637, 0.0], 'a5': [-4.027090994721447, 0.0], 'a6': [0.7690906200089404, 0.0], 'a7': [0.0, 0.0], 'a8': [2.6214450846726445, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.997420923394913, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 7, 23], 'central_character': '3381.1', 'coefficient_field': 'CDF', 'conductor': 3381, 'conductor_radical': 483, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7690906200089404, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [4.027090994721447, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-5.471133117989497, 0], [11.0, 0]], [[1.0, 0], [4.399555752736187, 0], [13.0, 0]], [[1.0, 0], [2.249651281654676, 0], [17.0, 0]], [[1.0, 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'4.67321399587649656146673200795239', '5.36986426979709998190398631783211', '6.71171986323785627472061122160035', '7.32621846913093444427197016096419', '7.72788428873372315512130154152727', '8.748965965705160338522225594027905'], 'prelabel': '2-3381-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.195904245017888, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.39988791219298933628040433637', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.58217343181722003791338663778', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.42263851918725971075452601383', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.997420923394913, 'bad_primes': [3, 7, 23], 'central_character': '1.1', 'conductor': 3381, 'conductor_radical': 483, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3381/2/a/bi/1/4'], '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': '2-3381-1.1-c1-0-5', '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': '2-3381-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.195904245017888, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.39988791219298933628040433637', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '506918151915456426795028485641', 'Lhash_array': ['506918151915456426795028485641'], 'label': '2-3381-1.1-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3381/2/a/bi/1/4'}