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lfunc_lfunctions • Show schema
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{'Lhash': '1439620187422970168055525350416', 'a10': [32592.40942526364, 83044.10486519826], 'a2': [7.98751621188914, 34.99559509086166], 'a3': [139.8699550197973, 129.78035237838677], 'a4': [-699.5952001623102, 336.90729183774124], 'a5': [2457.531784118238, -370.4133170111838], 'a6': [-3424.527129306533, 5931.45497985691], 'a7': [-493.3929571776116, -854.5816699282786], 'a8': [-5919.4713495727465, -7422.782292294943], 'a9': [1249.7520217202893, 16676.781759319634], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.14654095504655, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[43, [[1.0, 0], [-1788947.8843122637, -22347086.55292805]]]], 'bad_primes': [43], 'central_character': '43.10', 'coefficient_field': 'CDF', 'conductor': 43, 'conductor_radical': 43, 'conjugate': '2920320695977281657155178619094', 'degree': 2, 'euler_factors': [[[1.0, 0], [-7.98751621188914, -34.99559509086166], [-461.2960603660386, 222.14847442818976]], 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'root_angle': -0.9876186782224197, 'root_number': '-0.9992436043656354 - 0.03888726185235169*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.49380933911120983', 'prec': 67}, 'spectral_label': 'c9-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.13566008422492692128980550780251', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.42192433181962728634848098825930', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.74261106175001753937581065470080', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.14654095504655, 'bad_primes': [43], 'central_character': '43.10', 'conductor': 43, 'conductor_radical': 43, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/43/10/g/a/10/29'], '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': '2-43-43.10-c9-0-12', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'prelabel': '2-43-43.10-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.706011151181705, 'root_angle': -0.49380933911120983, 'self_dual': False, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '1.13566008422492692128980550780251', 'prec': 113}}
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lfunc_instances • Show schema
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{'Lhash': '1439620187422970168055525350416', 'Lhash_array': ['1439620187422970168055525350416'], 'label': '2-43-43.10-c9-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/43/10/g/a/10/29'}