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lfunc_lfunctions • Show schema
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{'Lhash': '2441318311634025616512955833081', 'a10': [-0.20952735087015806, 0.3629120172824248], 'a2': [0.03711479974055464, 0.1385143183444941], 'a3': [0.4077387941560106, 0.10925328061694281], 'a4': [1.714242099542219, -0.9897181376268893], 'a5': [2.066354493146654, 2.066354493146654], 'a6': [8.417524616033747e-62, 0.06053257476622226], 'a7': [0.8589155791843355, -0.6590691043037203], 'a8': [0.4035129226257871, 0.4035129226257871], 'a9': [-2.4437615664190826, -1.410906398207319], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.9243946887128582, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[241, [[1.0, 0], [6.883541135326206, 13.91462760688449]]]], 'bad_primes': [241], 'central_character': '241.2', 'coefficient_field': 'CDF', 'conductor': 241, 'conductor_radical': 241, 'conjugate': '2636675892781390955591470581425', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.03711479974055464, -0.1385143183444941], [-1.7320508075688772, 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['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.92586057324824964427454226948', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.02228177589033747067890083658', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.99987429352215177970177768118', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.9243946887128582, 'bad_primes': [241], 'central_character': '241.2', 'conductor': 241, 'conductor_radical': 241, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/241/2/m/a/2/11'], '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': '2-241-241.2-c1-0-8', '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': '2-241-241.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3872255363540775, 'root_angle': -0.03180556828454852, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.92586057324824964427454226948', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2441318311634025616512955833081', 'Lhash_array': ['2441318311634025616512955833081'], 'label': '2-241-241.2-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/241/2/m/a/2/11'}