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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2601.209', 'a10': [0.9997332081116372, -0.023097891653001097], 'a2': [0.9970369782714329, 0.07692375419446384], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9881654720812594, 0.15339165487868536], 'a5': [0.9949942003533065, -0.09993268365897151], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.007699905906018644, -0.9999703552851147], 'a8': [0.9734380543606929, 0.22895054995013409], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 12.078993218849428, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [17, [1]]], 'bad_primes': [3, 17], 'central_character': '2601.209', 'coeff_info': ['x^816 - 1', '0.999970355285115 + 0.00769990590601864*I', '\\\\zeta_{816}'], 'conductor': 2601, 'conductor_radical': 51, 'conjugate': 'dirichlet_L_2601.2489', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^10', 0, 'a^20', 'a^803', 0, 'a^613', 'a^30', 0, 'a^813', 'a^241', 0, 'a^812', 'a^623', 0, 'a^40', 0, 0, 'a^738', 'a^7', 0, 'a^251', 'a^137', 0, 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'187.972381650495207374532302602205', '188.12130463944223838809930484835', '188.65716066304165490591448441788', '189.25896165894302670717587060328', '190.00334322223686406287099395699', '190.36543055821550411954766007789', '191.43618123698834371599991859098', '191.62599260029528100481654922827', '192.46517248238581816366812633213', '192.84627103131850647518668616676', '193.58018853810918590834593638048', '193.72203412183093907057154621329', '194.5210305065477139192919519376', '194.8983750306948523970289835491', '195.56665177256891033418692259515', '196.04130473349848911900839295681', '196.72387746120333485546381200155', '197.22245404252381810006962413548', '197.589775937997486595703254000161', '197.99399255045143668993968001948', '198.77010692323439851856601795037', '199.40892352421158707191494075452'], 'prelabel': '1-51e2-2601.209-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.078993218849428, 'root_angle': 0.0007689350249903884, 'root_number': '0.999997082244976439481616351474+0.00241567827614247076803938736355*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.000384467512495', 'prec': 60}, 'spectral_label': 'r0-0', 'st_group': 'mu(816)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.52399522609405800583625986764+0.00363425068818133019517270439955*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.2514148802', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '1.77350272302', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.93573289359', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 12.078993218849428, 'bad_primes': [3, 17], 'central_character': '2601.209', 'conductor': 2601, 'conductor_radical': 51, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2601/209'], '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': '1-51e2-2601.209-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': '1-51e2-2601.209-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.078993218849428, 'root_angle': 0.0003844675124951942, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.2514148802', 'prec': 40}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2601.209', 'Lhash_array': ['dirichlet_L_2601.209'], 'label': '1-51e2-2601.209-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2601/209'}
Lfunction data - 1-51e2-2601.209-r0-0-0