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lfunc_lfunctions • Show schema
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{'Lhash': '2033063052117076916551401685787', 'a10': [-4.269064167331899, -0.0534610124732631], 'a2': [-1.1326634314723638, 0.8468019550079287], 'a3': [0.09861441930256495, 0.12851681336310422], 'a4': [0.5658528979894999, -1.9182832162735732], 'a5': [2.395070989533398, 1.83780260839445], 'a6': [-0.22052523536716345, -0.062059411768363326], 'a7': [0.13436865305734982, -2.6423370460778757], 'a8': [0.9834850926539908, 2.6519345905446783], 'a9': [0.7696653676849374, -2.872430257026368], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7886490052766815, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.1326634314723638, -0.8468019550079287]]], [7, [[1.0, 0], [-0.13436865305734982, 2.6423370460778757]]]], 'bad_primes': [2, 7], 'central_character': '224.109', 'coefficient_field': 'CDF', 'conductor': 224, 'conductor_radical': 14, 'conjugate': '1918054417663469792744825098043', 'degree': 2, 'euler_factors': [[[1.0, 0], 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['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.60380395966447039800962258710', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.78123400814658041449448351126', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.85064890769338820818774014285', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.7886490052766815, 'bad_primes': [2, 7], 'central_character': '224.109', 'conductor': 224, 'conductor_radical': 14, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/224/2/bd/a/109/7'], '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': '2-224-224.109-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': '2-224-224.109-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3374038302908666, 'root_angle': -0.0864455665271871, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.60380395966447039800962258710', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2033063052117076916551401685787', 'Lhash_array': ['2033063052117076916551401685787'], 'label': '2-224-224.109-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/224/2/bd/a/109/7'}