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lfunc_lfunctions • Show schema
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{'Lhash': '20052354101737910657008787553', 'a10': [0.5155770655119456, 0.4326205255145379], 'a2': [-0.21772685257333996, -0.23077698129241447], 'a3': [0.0, 0.0], 'a4': [0.11043662505800515, -1.8961236249761886], 'a5': [-2.1069691552981613, 0.24626937462083986], 'a6': [0.0, 0.0], 'a7': [-2.2729959951148206, -1.1415414938707664], 'a8': [-0.9477191726269893, 0.7952308082109437], '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': '729.109', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '1948369432339705090520307702458', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.21772685257333996, 0.23077698129241447], [-0.11628965782095166, 1.9966163165425364]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.1069691552981613, -0.24626937462083986], [4.865224352899119, 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'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.01581851820850923725647747300', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.49118565687535799331163023530', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.59631653429059182146132554774', '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': '81.22', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/g/d/109/4'], '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': '2-3e6-81.22-c1-0-0', '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': '2-3e6-81.22-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.34632926794124663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.01581851820850923725647747300', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '20052354101737910657008787553', 'Lhash_array': ['20052354101737910657008787553'], 'label': '2-3e6-81.22-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/g/d/109/4'}