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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_201.152', 'a10': [0.5800569095711982, 0.8145759520503357], 'a2': [-0.32706796331742166, -0.9450008187146685], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.7860530947427875, 0.6181589862206052], 'a5': [-0.9594929736144974, 0.28173255684142967], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.9819286972627067, -0.18925124436041021], 'a8': [0.8412535328311812, 0.5406408174555976], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.933440075735769, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [67, [1]]], 'bad_primes': [3, 67], 'central_character': '201.152', 'coeff_info': ['x^66 - 1', '0.995471922573085 + 0.0950560433041827*I', '\\\\zeta_{66}'], 'conductor': 201, 'conductor_radical': 201, 'conjugate': 'dirichlet_L_201.41', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^46', 0, 'a^26', 'a^30', 0, 'a^35', 'a^6', 0, 'a^10', 'a^8', 0, 'a^49', 'a^15', 0, 'a^52', 'a^7', 0, 'a^64', 'a^56', 0, 'a^54', 'a^1', 0, 'a^60', 'a^29', 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'186.58005616577447877128143554999', '187.41797706254230271819126374329', '187.80496631636014410160308969935', '189.01395809303940598766529917765', '189.84294336544505874433426823011', '190.338337655331401723647744558949', '191.12290023250403310463239802990', '191.48838426140321291398340841346', '192.301750401090051104101682283871', '193.172925908333684094665851117639', '193.811678683839162821937106377469', '194.34146095433006780369409226013', '195.19501243422269106257408032267', '195.637850624027376884571501857686', '196.787049932477081575695511824367', '197.56291390113124233335005567466', '198.41910114536387863972993106967', '199.04266746848924588514404818770', '199.5280222889613050652409574184'], 'prelabel': '1-201-201.152-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.933440075735769, 'root_angle': -0.1701690953501689, 'root_number': '0.860471488149721076358313965194-0.509498594778635695953765453057*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0850845476751', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(66)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.689084533056739864613376524709-0.211792233514115574259056451888*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.06390317541', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.04891333452', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.60651736422', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.933440075735769, 'bad_primes': [3, 67], 'central_character': '201.152', 'conductor': 201, 'conductor_radical': 201, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/201/152'], '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': '1-201-201.152-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': '1-201-201.152-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.933440075735769, 'root_angle': -0.08508454767508444, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.06390317541', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_201.152', 'Lhash_array': ['dirichlet_L_201.152'], 'label': '1-201-201.152-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/201/152'}
Lfunction data - 1-201-201.152-r0-0-0