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lfunc_lfunctions • Show schema
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{'Lhash': '1407594104228956093680267871752', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.9396926207859084, 0.3420201433256687], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.9396926207859084, 0.3420201433256687], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.3638183942094588, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.647', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '2146345452431518188420607157419', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0.9396926207859084, -0.3420201433256687]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.17364817766693036, -0.984807753012208]], [[1.0, 0], [-0.9396926207859084, -0.3420201433256687], [0.766044443118978, 0.6427876096865394]], [[1.0, 0], [0, 0], [-0.17364817766693036, 0.984807753012208]], [[1.0, 0], 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'root_angle': -0.24074074074074073, 'root_number': '0.72737364157304869598717641766404 - 0.68624163786873358572960499961778*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.12037037037037036', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.11039595924581354552842731452', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.89788122762755178437030296667', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.31598678520314317107371364768', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.3638183942094588, 'bad_primes': [3], 'central_character': '27.14', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 0, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/1/f/a/647/1', 'ArtinRepresentation/2.729.18t16.a.b'], 'is_instance_Artin': True, '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': '2-3e6-27.14-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3e6-27.14-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6031736020495747, 'root_angle': -0.12037037037037036, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.11039595924581354552842731452', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24603599
{'Lhash': '1407594104228956093680267871752', 'Lhash_array': ['1407594104228956093680267871752'], 'label': '2-3e6-27.14-c0-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/2.729.18t16.a.b'}
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id: 19812438
{'Lhash': '1407594104228956093680267871752', 'Lhash_array': ['1407594104228956093680267871752'], 'label': '2-3e6-27.14-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/1/f/a/647/1'}