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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_621.218', 'a10': [-0.9283679330160726, -0.3716624556603275], 'a2': [0.7014748877063213, -0.7126941713788629], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.015865963834807928, -0.9998741276738751], 'a5': [-0.3863451256931286, -0.9223542941045814], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5272254676105024, -0.8497254299495144], 'a8': [-0.7237340381050702, -0.690079011482112], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 2.8839118757806594, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [23, [1]]], 'bad_primes': [3, 23], 'central_character': '621.218', 'coeff_info': ['x^198 - 1', '0.999496542383185 + 0.0317279334980676*I', '\\\\zeta_{198}'], 'conductor': 621, 'conductor_radical': 69, 'conjugate': 'dirichlet_L_621.527', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^173', 0, 'a^148', 'a^136', 0, 'a^131', 'a^123', 0, 'a^111', 'a^80', 0, 'a^34', 'a^106', 0, 'a^98', 'a^138', 0, 'a^159', 'a^86', 0, 'a^55', 0, 0, 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'196.655165401684928629168738136851', '197.32398951289627680136021680025', '197.84509513040318888660566123725', '199.07882648991251023560273091975', '199.41718277499358007259345965832'], 'prelabel': '1-621-621.218-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8839118757806594, 'root_angle': 0.387535964872314, 'root_number': '-0.760552704529550252311754905345+0.649276199804664510328767393800*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.387535964872', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(198)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.714504703751671031171273089877-0.786015298572724715004744252729*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.360248202573', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.60397062256', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.84391390999', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.8839118757806594, 'bad_primes': [3, 23], 'central_character': '621.218', 'conductor': 621, 'conductor_radical': 69, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/621/218'], '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': '1-621-621.218-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': '1-621-621.218-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8839118757806594, 'root_angle': 0.387535964872314, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.360248202573', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_621.218', 'Lhash_array': ['dirichlet_L_621.218'], 'factors': ['1-621-621.218-r0-0-0'], 'label': '1-621-621.218-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/621/218'}
Lfunction data - 1-621-621.218-r0-0-0