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lfunc_lfunctions • Show schema
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{'Lhash': '1497124831113039574555970156992', 'a10': [-3.8407778420336927, -3.2227952706843412], 'a2': [1.6226604506499687, 1.9338114216226399], 'a3': [0.17364817766693036, 0.984807753012208], 'a4': [-0.7593033209607553, 4.306223119740082], 'a5': [-1.9559444908327643, 0.3448857865018972], 'a6': [-1.6226604506499687, 1.9338114216226399], 'a7': [2.6250808603924907, 0.3300764705352696], 'a8': [-5.187105899768839, 2.994776987546635], 'a9': [-0.9396926207859084, 0.3420201433256687], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.186031040649089, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.17364817766693036, -0.984807753012208]]], [7, [[1.0, 0], [-2.6250808603924907, -0.3300764705352696]]], [19, [[1.0, 0], [-4.17515300228022, 1.2522369614216242]]]], 'bad_primes': [3, 7, 19], 'central_character': '399.10', 'coefficient_field': 'CDF', 'conductor': 399, 'conductor_radical': 399, 'conjugate': 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'sign_arg': {'__RealLiteral__': 0, 'data': '-0.466995215994', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.18102324950068681793605968537', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.47026070743060438052848674391', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.76635610751951446792094620602', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.186031040649089, 'bad_primes': [3, 7, 19], 'central_character': '133.10', 'conductor': 399, 'conductor_radical': 399, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/399/2/ck/b/10/13'], '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': '2-399-133.10-c1-0-9', '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': '2-399-133.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7849456688227485, 'root_angle': -0.46699521599391713, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.18102324950068681793605968537', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1497124831113039574555970156992', 'Lhash_array': ['1497124831113039574555970156992'], 'factors': ['2-399-133.10-c1-0-9'], 'label': '2-399-133.10-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/399/2/ck/b/10/13'}