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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_644.107', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.32706796331742166, 0.9450008187146685], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.9283679330160726, 0.3716624556603275], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.7860530947427875, 0.6181589862206052], 'algebraic': True, 'analytic_conductor': 2.9907234267354985, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [7, [1]], [23, [1]]], 'bad_primes': [2, 7, 23], 'central_character': '644.107', 'coeff_info': ['x^66 - 1', '0.995471922573085 + 0.0950560433041827*I', '\\\\zeta_{66}'], 'conductor': 644, 'conductor_radical': 322, 'conjugate': 'dirichlet_L_644.319', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^79', 0, 'a^29', 0, 0, 0, 'a^26', 0, 'a^52', 0, 'a^54', 0, 'a^42', 0, 'a^49', 0, 'a^50', 0, 0, 0, 0, 0, 'a^58', 0, 'a^39', 0, 'a^60', 0, 'a^97', 0, 'a^65', 0, 0, 0, 'a^59', 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'198.902398722349601508872458812801', '199.48559191650189697915306371136', '199.99677801465675392503391363112'], 'prelabel': '1-644-644.107-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9907234267354985, 'root_angle': -0.05270089994330668, 'root_number': '0.945675726972463133747679555184-0.325111395394106976577753013220*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0527008999433', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(66)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.967138814101334608440059446530+0.121367805519979946619973111818*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.593247407897', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.74867667526', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.28124098151', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.9907234267354985, 'bad_primes': [2, 7, 23], 'central_character': '644.107', 'conductor': 644, 'conductor_radical': 322, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/644/107'], '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': '1-644-644.107-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': '1-644-644.107-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9907234267354985, 'root_angle': -0.05270089994330668, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.593247407897', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_644.107', 'Lhash_array': ['dirichlet_L_644.107'], 'factors': ['1-644-644.107-r0-0-0'], 'label': '1-644-644.107-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/644/107'}
Lfunction data - 1-644-644.107-r0-0-0