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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_161.44', 'a10': [0.7860530947427875, 0.6181589862206052], 'a2': [0.5800569095711982, -0.8145759520503357], 'a3': [0.23575893550942723, -0.9718115683235417], 'a4': [-0.32706796331742166, -0.9450008187146685], 'a5': [-0.0475819158237423, 0.998867339183008], 'a6': [-0.6548607339452851, -0.7557495743542583], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.9594929736144974, -0.28173255684142967], 'a9': [-0.8888354486549235, -0.4582265217274104], 'algebraic': True, 'analytic_conductor': 17.30185289193463, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [23, [1]]], 'bad_primes': [7, 23], 'central_character': '161.44', 'coeff_info': ['x^66 - 1', '0.995471922573085 + 0.0950560433041827*I', '\\\\zeta_{66}'], 'conductor': 161, 'conductor_radical': 161, 'conjugate': 'dirichlet_L_161.11', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^56', 'a^52', 'a^46', 'a^17', 'a^42', 0, 'a^36', 'a^38', 'a^7', 'a^43', 'a^32', 'a^18', 0, 'a^3', 'a^26', 'a^31', 'a^28', 'a^35', 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'189.684529285842576058422761995838', '190.41584538326103198910166386722', '190.85081399387095340947217646736', '191.49266873114810590128309057562', '192.38660059559864581049680111392', '193.04673857898618517223311120011', '194.22760147682444158198646420531', '194.40715777361971815256407515672', '195.14138984326514678731709195835', '195.90174303482097014776183375251', '196.58958036155105895713157853389', '197.399164458121069274060730061958', '198.022431813877231714665657852533', '199.22791508697628745093611186801', '199.934596238594464385860852598979'], 'prelabel': '1-161-161.44-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.30185289193463, 'root_angle': 0.3102609493650968, 'root_number': '-0.369648512412725298060243612727+0.929171661896260841429667352316*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.310260949365', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(66)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.735270627386005196194785375694-0.700162304466718384291819261935*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.167692476172', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.01598718695', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.81216726902', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 17.30185289193463, 'bad_primes': [7, 23], 'central_character': '161.44', 'conductor': 161, 'conductor_radical': 161, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/161/44'], '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': '1-161-161.44-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-161-161.44-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.30185289193463, 'root_angle': 0.3102609493650968, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.167692476172', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_161.44', 'Lhash_array': ['dirichlet_L_161.44'], 'factors': ['1-161-161.44-r1-0-0'], 'label': '1-161-161.44-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/161/44'}
Lfunction data - 1-161-161.44-r1-0-0