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lfunc_lfunctions • Show schema
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{'Lhash': '2021527412243564047058008116042', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.6791809906501929, 2.3111943567298], 'a4': [0.0, 0.0], 'a5': [-2.480265375640166, -0.805887072429998], 'a6': [0.0, 0.0], 'a7': [0.1588601030095914, -0.11541862083978058], 'a8': [0.0, 0.0], 'a9': [-1.5949195720938691, -4.908657710151901], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.810734151149071, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [2.89042333806855, 1.626484837540351]]]], 'bad_primes': [2, 11], 'central_character': '352.49', 'coefficient_field': 'CDF', 'conductor': 352, 'conductor_radical': 22, 'conjugate': '338694672949737705189185390564', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.6791809906501929, -2.3111943567298], [-0.9270509831248422, -2.853169548885461]], [[1.0, 0], [2.480265375640166, 0.805887072429998], [4.045084971874737, 2.9389262614623655]], [[1.0, 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-1.512227965204245], 'positive_zeros': ['1.59470394435154743765689264071450', '3.40566530257385580711219363771622', '4.95227721350620216895642054682349', '6.06279672572496198544392325879596', '7.00503120662548153972290036566440', '7.70421920871280066103733149449702', '8.461793631548944650963175391424053', '10.21097384720534865901851766634800', '11.04366957846045593182646715208088', '11.94886573337401307118172179127806'], 'prelabel': '2-352-88.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6765244260520247, 'root_angle': 0.4559243144211701, 'root_number': '0.13802579202789647 + 0.9904286348521391*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.227962157211', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.59470394435154743765689264071', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.40566530257385580711219363772', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.95227721350620216895642054682', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.810734151149071, 'bad_primes': [2, 11], 'central_character': '88.5', 'conductor': 352, 'conductor_radical': 22, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/352/2/w/a/49/1'], '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': '2-352-88.5-c1-0-5', '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': '2-352-88.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6765244260520247, 'root_angle': 0.22796215721058505, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.59470394435154743765689264071', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2021527412243564047058008116042', 'Lhash_array': ['2021527412243564047058008116042'], 'label': '2-352-88.5-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/352/2/w/a/49/1'}