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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_200.189', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.8090169943749475, -0.5877852522924731], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-1.0, -1.4081532572346456e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.30901699437494745, 0.9510565162951535], 'algebraic': True, 'analytic_conductor': 0.9287960952594716, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '200.189', 'coeff_info': ['x^10 - 1', '0.809016994374947 + 0.587785252292473*I', '\\\\zeta_{10}'], 'conductor': 200, 'conductor_radical': 10, 'conjugate': 'dirichlet_L_200.109', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^6', 0, 0, 0, 'a^5', 0, 'a^2', 0, 'a^13', 0, 'a^12', 0, 0, 0, 'a^9', 0, 'a^9', 0, 'a^11', 0, 'a^3', 0, 0, 0, 'a^8', 0, 'a^11', 0, 'a^4', 0, 'a^9', 0, 0, 0, 'a^12', 0, 'a^8', 0, 'a^2', 0, 'a^0', 0, 0, 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'193.31877111969017951427999735102', '194.14663567106222611038706253830', '194.72284590797551395736192802565', '195.78212624004413646658930588164', '195.918526558972148580413872346651', '196.92122927054238253456166517539', '197.56495985951929020920488192846', '198.46510322523287895470687767963', '199.360260761745940849571616918870', '199.90141422850109160595197495341'], 'prelabel': '1-200-200.189-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9287960952594716, 'root_angle': 0.12000000000000001, 'root_number': '0.728968627421411523146730319055+0.684547105928688673732283357621*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.12', 'prec': 14}, 'spectral_label': 'r0-0', 'st_group': 'mu(10)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.744901445570671008445975241469+0.0366310054323870593602548076372*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.37562245065', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.94053655997', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.58035631975', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.9287960952594716, 'bad_primes': [2, 5], 'central_character': '200.189', 'conductor': 200, 'conductor_radical': 10, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/200/189'], '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': '1-200-200.189-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': '1-200-200.189-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9287960952594716, 'root_angle': 0.12000000000000001, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.37562245065', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_200.189', 'Lhash_array': ['dirichlet_L_200.189'], 'factors': ['1-200-200.189-r0-0-0'], 'label': '1-200-200.189-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/200/189'}
Lfunction data - 1-200-200.189-r0-0-0