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lfunc_lfunctions • Show schema
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{'Lhash': '1791294185908350755048794087558', 'a10': [-1.4624173878090105, -0.8114818977455003], 'a2': [0.38920527244244796, 1.3596026095528795], 'a3': [1.5740815347913464, 1.5740815347913464], 'a4': [-1.6970385118059996, 1.0583290081289833], 'a5': [-0.8362367318132421, 0.8362367318132421], 'a6': [-1.5274845297562238, 2.752766194946409], 'a7': [0.0, -0.22632871197520718], 'a8': [-2.099403217550457, -1.8953907592205859], 'a9': [0.0, 1.9554653563421613], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6608883620426327, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.38920527244244796, -1.3596026095528795]]], [13, [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]]]], 'bad_primes': [2, 13], 'central_character': '208.157', 'coefficient_field': 'CDF', 'conductor': 208, 'conductor_radical': 26, 'conjugate': '4178482636845477583509313621883', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.38920527244244796, 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'-0.6612862335796694 - 0.7501336662742281*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.364994561662', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.41308195301279698573636217318', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.80829290911209313876192510116', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.07415435451463160025971554005', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6608883620426327, 'bad_primes': [2, 13], 'central_character': '16.13', 'conductor': 208, 'conductor_radical': 26, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/208/2/n/a/157/14'], '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': '2-208-16.13-c1-0-6', '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': '2-208-16.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2887545778939575, 'root_angle': -0.3649945616622984, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.41308195301279698573636217318', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1791294185908350755048794087558', 'Lhash_array': ['1791294185908350755048794087558'], 'label': '2-208-16.13-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/208/2/n/a/157/14'}