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lfunc_lfunctions • Show schema
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{'Lhash': '1605001034434137912802561339928', 'a10': [2.086481576182694, -3.6138920990048193], 'a2': [0.0, 2.588600645839141], 'a3': [-0.2592329192139507, 0.44900458707296087], 'a4': [-4.700853303638818, 0.0], 'a5': [-1.396079424152856, -0.8060268313447492], 'a6': [-1.1622935640818033, -0.6710505020999987], 'a7': [1.061525925073549, 2.4234608951655785], 'a8': [0.0, -6.991430606116222], 'a9': [1.3655965871916267, 2.3652826716585595], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-1.061525925073549, -2.4234608951655785]]], [13, [[1.0, 0], [-2.3684010822135573, 2.7185798339886307]]]], 'bad_primes': [7, 13], 'central_character': '91.23', 'coefficient_field': 'CDF', 'conductor': 91, 'conductor_radical': 91, 'conjugate': '5507965638642577995651505961128', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -2.588600645839141], [-2.0, 0]], [[1.0, 0], 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'8.360790708578977239248235477625053', '9.603173921960597174735709023613238', '10.63864451778223732063958098317497', '11.66814975298971300007850876850214', '11.98949995808972793448462448609579', '13.53429236003749609406744102316491'], 'prelabel': '2-91-91.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': -0.91938182348861, 'root_number': '-0.9680983645018303 - 0.2505704624429651*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.459690911744', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.26612256890437437309622037185', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.52586268377497243789815218450', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.33935097469234951997144780227', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'bad_primes': [7, 13], 'central_character': '91.23', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/91/2/k/b/23/6'], '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': '2-91-91.23-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': '2-91-91.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': -0.459690911744305, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.26612256890437437309622037185', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1605001034434137912802561339928', 'Lhash_array': ['1605001034434137912802561339928'], 'label': '2-91-91.23-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/2/k/b/23/6'}