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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_529.445', 'a10': [0.9987667264919349, -0.049649028717434214], 'a2': [-0.860805229884536, 0.50893453037049], 'a3': [0.10535171660114712, 0.9944350234224414], 'a4': [0.48197128759313773, -0.8761870108234959], 'a5': [-0.8850117267125738, -0.46556873131818954], 'a6': [-0.5967896302570483, -0.8023977425302589], 'a7': [-0.9358603562568415, 0.35237110208815037], 'a8': [0.031038419855822494, 0.9995181921770377], 'a9': [-0.9778020316183832, 0.2095308735317123], 'algebraic': True, 'analytic_conductor': 2.4566656719613023, 'analytic_normalization': 0, 'bad_lfactors': [[23, [1]]], 'bad_primes': [23], 'central_character': '529.445', 'coeff_info': ['x^253 - 1', '0.999691634078213 + 0.0248321717542501*I', '\\\\zeta_{253}'], 'conductor': 529, 'conductor_radical': 23, 'conjugate': 'dirichlet_L_529.233', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^105', 'a^59', 'a^210', 'a^146', 'a^164', 'a^112', 'a^62', 'a^118', 'a^251', 'a^27', 'a^16', 'a^163', 'a^217', 'a^205', 'a^167', 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.4566656719613023, 'bad_primes': [23], 'central_character': '529.445', 'conductor': 529, 'conductor_radical': 23, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/529/445'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-23e2-529.445-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-23e2-529.445-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4566656719613023, 'root_angle': 0.08592541673827117, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.564370901424', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_529.445', 'Lhash_array': ['dirichlet_L_529.445'], 'label': '1-23e2-529.445-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/529/445'}