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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_269.190', 'a10': [0.7921624734111293, -0.6103102618497921], 'a2': [-0.762685178110382, -0.6467699120171987], 'a3': [-0.3000846350003407, -0.953912580814779], 'a4': [0.1633773618185302, 0.9865636510865465], 'a5': [-0.2094402627661444, 0.9778214439929451], 'a6': [-0.3880918526722497, 0.9216206995773374], 'a7': [-0.6987694277788417, -0.7153469695201276], 'a8': [0.5134741935148419, -0.8581050358751443], 'a9': [-0.8198984236734246, 0.5725090172720719], 'algebraic': True, 'analytic_conductor': 1.2492307481239893, 'analytic_normalization': 0, 'bad_lfactors': [[269, [1]]], 'bad_primes': [269], 'central_character': '269.190', 'coeff_info': ['x^67 - 1', '0.995605982021898 + 0.0936414895343508*I', '\\\\zeta_{67}'], 'conductor': 269, 'conductor_radical': 269, 'conjugate': 'dirichlet_L_269.143', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^41', 'a^47', 'a^15', 'a^19', 'a^21', 'a^42', 'a^56', 'a^27', 'a^60', 'a^50', 'a^62', 'a^60', 'a^16', 'a^66', 'a^30', 'a^17', 'a^1', 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'gamma_factors': [[0], []], 'index': 0, 'label': '1-269-269.190-r0-0-0', 'leading_term': '0.0299711117547543643874042568792-0.0494346868900600131796547459295*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/269/190', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-0.05781051641124017, 0.2990225698583481, 0.6804955089446256, 0.8963289581282147, 0.7106885325011071, 0.07883873964102456, -0.7598755487295731, -1.3619205752934547, -1.3242923914223654, -0.5826537995737808, 0.42591216361313183, 0.8938347607887068, 0.06900698492329876, -2.2312913179173592, -5.34578306515067, -7.978241701164386, -8.855081579140466, -7.478062781554478, -4.487738432514829, -1.345543987565966, 0.5233538659559942, 0.5898903470178085, -0.5060498224118726, -1.483568143329392, -1.390987368288152, 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'193.992340127266867913499916997769', '194.6409657893031420577205364963', '195.09007460631272308245803311568', '196.47454523646455740849458115046', '197.063976811401976787478683610218', '197.57075901745788560727918009173', '198.30027869900229828636873486521', '199.427325777587625400649548391', '199.53139464297269248625548654472'], 'prelabel': '1-269-269.190-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2492307481239893, 'root_angle': 0.3265140663588328, 'root_number': '-0.462446116107823158947721649573+0.886647387464029999240612028337*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.326514066359', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(67)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.393507477712208812905467253472-0.214257601443825049372469507286*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.0513044269116', 'prec': 50}, 'z2': {'__RealLiteral__': 0, 'data': '1.59297694798', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.98859695625', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.2492307481239893, 'bad_primes': [269], 'central_character': '269.190', 'conductor': 269, 'conductor_radical': 269, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/269/190'], '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': '1-269-269.190-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': '1-269-269.190-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2492307481239893, 'root_angle': 0.3265140663588328, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0513044269116', 'prec': 50}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_269.190', 'Lhash_array': ['dirichlet_L_269.190'], 'factors': ['1-269-269.190-r0-0-0'], 'label': '1-269-269.190-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/269/190'}
Lfunction data - 1-269-269.190-r0-0-0