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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_161.10', 'a10': [-0.8888354486549235, -0.4582265217274104], 'a2': [-0.7860530947427875, -0.6181589862206052], 'a3': [-0.5800569095711982, 0.8145759520503357], 'a4': [0.23575893550942723, 0.9718115683235417], 'a5': [0.9819286972627067, -0.18925124436041021], 'a6': [0.9594929736144974, -0.28173255684142967], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.41541501300188644, -0.9096319953545183], 'a9': [-0.32706796331742166, -0.9450008187146685], 'algebraic': True, 'analytic_conductor': 0.7476808566838746, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [23, [1]]], 'bad_primes': [7, 23], 'central_character': '161.10', 'coeff_info': ['x^66 - 1', '0.995471922573085 + 0.0950560433041827*I', '\\\\zeta_{66}'], 'conductor': 161, 'conductor_radical': 161, 'conjugate': 'dirichlet_L_161.145', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^40', 'a^23', 'a^14', 'a^64', 'a^63', 0, 'a^54', 'a^46', 'a^38', 'a^59', 'a^37', 'a^27', 0, 'a^21', 'a^28', 'a^8', 'a^20', 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'190.0036383278370038561023711274', '190.73947607866013797510201623597', '191.84274634105248521638632516142', '192.49175847944118721220232145390', '192.86977475690850004104046702326', '193.58921459033922273599931326879', '194.25684811067982812175490328902', '194.89532850401841856358625046486', '196.00944202055897780752987051564', '197.16197733073528953110718235943', '197.63161456946776653881095221855', '198.3130425551109092856780891396', '199.04327194639692286086695399398', '199.83742939909563379880329779300'], 'prelabel': '1-161-161.10-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7476808566838746, 'root_angle': 0.0014245432291719385, 'root_number': '0.999959943028877411746149619742+0.00895054957442508062172015319114*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.00142454322917', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(66)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.755773607260633776857629381287+0.0214722265651718021659963386308*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.23642693605', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.90373393226', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.27977124006', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.7476808566838746, 'bad_primes': [7, 23], 'central_character': '161.10', 'conductor': 161, 'conductor_radical': 161, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/161/10'], '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': '1-161-161.10-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': '1-161-161.10-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7476808566838746, 'root_angle': 0.0014245432291719385, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.23642693605', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_161.10', 'Lhash_array': ['dirichlet_L_161.10'], 'factors': ['1-161-161.10-r0-0-0'], 'label': '1-161-161.10-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/161/10'}
Lfunction data - 1-161-161.10-r0-0-0