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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_196.123', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.7330518718298263, -0.6801727377709194], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.9555728057861407, 0.2947551744109042], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.07473009358642425, -0.9972037971811801], 'algebraic': True, 'analytic_conductor': 21.063125259746503, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '196.123', 'coeff_info': ['x^42 - 1', '0.988830826225129 + 0.149042266176174*I', '\\\\zeta_{42}'], 'conductor': 196, 'conductor_radical': 14, 'conjugate': 'dirichlet_L_196.51', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^37', 0, 'a^2', 0, 0, 0, 'a^32', 0, 'a^31', 0, 'a^24', 0, 'a^39', 0, 'a^22', 0, 'a^35', 0, 0, 0, 'a^41', 0, 'a^4', 0, 'a^27', 0, 'a^36', 0, 'a^49', 0, 'a^26', 0, 0, 0, 'a^8', 0, 'a^61', 0, 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'190.671378219930865382002722068297', '191.01533791057006203696529953157', '191.86721486722563324041615105029', '192.70170272731018003753610461135', '193.20393899808551371406970669042', '194.135851030765382837500651479302', '194.90993923460919999315074312271', '195.54935948965832676340959450384', '196.54718619551617654357651895005', '196.96039899122361271270221739545', '197.49272608493844558488824478168', '198.20525503942390365848077431759', '199.057669341554344804158335827730', '199.99320516124826830838292786557'], 'prelabel': '1-14e2-196.123-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.063125259746503, 'root_angle': -0.489795918367347, 'root_number': '0.0320515775716551742335505253458-0.999486216200687867697489397011*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.244897959184', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(42)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.43666154045384770182535381699-0.567007669374287186871419306544*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.813139909285', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.35800454253', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.11170054401', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.063125259746503, 'bad_primes': [2, 7], 'central_character': '196.123', 'conductor': 196, 'conductor_radical': 14, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/196/123'], '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': '1-14e2-196.123-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': '1-14e2-196.123-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.063125259746503, 'root_angle': -0.2448979591836735, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.813139909285', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_196.123', 'Lhash_array': ['dirichlet_L_196.123'], 'label': '1-14e2-196.123-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/196/123'}
Lfunction data - 1-14e2-196.123-r1-0-0