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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_109.61', 'a10': [-0.39607976603915684, 0.918216106880274], 'a2': [-0.17364817766693036, 0.984807753012208], 'a3': [0.39607976603915684, -0.918216106880274], 'a4': [-0.9396926207859084, -0.3420201433256687], 'a5': [0.9730448705798238, 0.23061587074244017], 'a6': [0.8354878114129364, 0.549508978070806], 'a7': [-0.28680323271109026, -0.9579895123154889], 'a8': [0.5, -0.8660254037844386], 'a9': [-0.6862416378687336, -0.7273736415730487], 'algebraic': True, 'analytic_conductor': 0.5061938719164121, 'analytic_normalization': 0, 'bad_lfactors': [[109, [1]]], 'bad_primes': [109], 'central_character': '109.61', 'coeff_info': ['x^54 - 1', '0.993238357741943 + 0.116092914125230*I', '\\\\zeta_{54}'], 'conductor': 109, 'conductor_radical': 109, 'conjugate': 'dirichlet_L_109.84', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^15', 'a^44', 'a^30', 'a^2', 'a^5', 'a^38', 'a^45', 'a^34', 'a^17', 'a^37', 'a^20', 'a^11', 'a^53', 'a^46', 'a^6', 'a^33', 'a^49', 'a^51', 'a^32', 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5061938719164121, 'bad_primes': [109], 'central_character': '109.61', 'conductor': 109, 'conductor_radical': 109, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/109/61'], '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': '1-109-109.61-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': '1-109-109.61-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5061938719164121, 'root_angle': -0.03675282839343336, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.22799255562', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_109.61', 'Lhash_array': ['dirichlet_L_109.61'], 'label': '1-109-109.61-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/109/61'}