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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_189.101', 'a10': [-1.0, -1.4081532572346456e-30], 'a2': [-0.17364817766693036, -0.984807753012208], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.9396926207859084, 0.3420201433256687], 'a5': [0.17364817766693036, -0.984807753012208], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.5, 0.8660254037844386], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.8777123100202007, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '189.101', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 189, 'conductor_radical': 21, 'conjugate': 'dirichlet_L_189.131', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^13', 0, 'a^8', 'a^14', 0, 0, 'a^3', 0, 'a^9', 'a^13', 0, 'a^11', 0, 0, 'a^16', 'a^0', 0, 'a^9', 'a^4', 0, 'a^8', 'a^11', 0, 'a^10', 'a^6', 0, 0, 'a^7', 0, 'a^17', 'a^11', 0, 'a^13', 0, 0, 'a^12', 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'193.58526843652639407809086951942', '193.9714498939824765796939699625', '194.7618659162369649180424782074', '195.61184216368966896768178620906', '196.35105800819327620569112659061', '196.89241488836552859564953820078', '198.06128008372210028829482312982', '198.81614715395424795482273675697', '199.35705768900190022345938882077'], 'prelabel': '1-189-189.101-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8777123100202007, 'root_angle': -0.9226170568550708, 'root_number': '-0.970595061980292037926990893864-0.240718145679699554593011581058*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.461308528428', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(18)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.573710116530756381609869225850-0.582053626865334968416597963284*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.647805298781', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.15565764564', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.53083684209', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.8777123100202007, 'bad_primes': [3, 7], 'central_character': '189.101', 'conductor': 189, 'conductor_radical': 21, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/189/101'], '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': '1-189-189.101-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': '1-189-189.101-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8777123100202007, 'root_angle': -0.4613085284275354, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.647805298781', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_189.101', 'Lhash_array': ['dirichlet_L_189.101'], 'label': '1-189-189.101-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/189/101'}
Lfunction data - 1-189-189.101-r0-0-0