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lfunc_lfunctions • Show schema
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{'Lhash': '1514530083621030636971800233956', 'a10': [-3.0, 5.196152422706632], 'a2': [0.3007674663608706, 1.7057370639048863], 'a3': [0.0, 0.0], 'a4': [-0.9396926207859084, 0.3420201433256687], 'a5': [2.6536557926757536, 2.2266815969056775], 'a6': [0.0, 0.0], 'a7': [0.9396926207859084, 0.3420201433256687], 'a8': [0.8660254037844386, 1.5], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.82', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '2564003792979012281854071883097', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.3007674663608706, -1.7057370639048863], [-1.8793852415718169, 0.6840402866513374]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.6536557926757536, -2.2266815969056775], [0.8682408883346517, 4.924038765061041]], [[1.0, 0], 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'positive_zeros': ['1.19475357274974093344576100748208', '2.04163807764496035973278188876927', '3.24614602853304289953305633150675', '4.55973426849479449646016263256819', '5.25060921636549554577470820489271', '6.37868333126960020429288477545049', '7.51873973536084641363063118434090', '8.876465974020775582839104507821073', '9.277425558064261322990905750510096', '10.18700722054856216514550724546626'], 'prelabel': '2-3e6-27.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.7407407407407407, 'root_number': '-0.6862416378687335 - 0.7273736415730488*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.37037037037', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.19475357274974093344576100748', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.04163807764496035973278188877', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.24614602853304289953305633151', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '27.13', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/e/n/82/2'], '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': '2-3e6-27.13-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': '2-3e6-27.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.37037037037037035, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.19475357274974093344576100748', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1514530083621030636971800233956', 'Lhash_array': ['1514530083621030636971800233956'], 'label': '2-3e6-27.13-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/e/n/82/2'}