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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_668.155', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.9821451197042027, 0.18812486236863377], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.9545040627715552, -0.29819791104666543], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.3870502972022171, 0.9220586030376136], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.9292180723175653, 0.3695318309407569], 'algebraic': True, 'analytic_conductor': 3.1021789581666352, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [167, [1]]], 'bad_primes': [2, 167], 'central_character': '668.155', 'coeff_info': ['x^166 - 1', '0.999283754816331 + 0.0378414767176703*I', '\\\\zeta_{166}'], 'conductor': 668, 'conductor_radical': 334, 'conjugate': 'dirichlet_L_668.487', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^171', 0, 'a^91', 0, 'a^197', 0, 'a^10', 0, 'a^141', 0, 'a^77', 0, 'a^96', 0, 'a^9', 0, 'a^215', 0, 'a^36', 0, 'a^128', 0, 'a^16', 0, 'a^181', 0, 'a^38', 0, 'a^139', 0, 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'199.56540992974241525546255245363'], 'prelabel': '1-668-668.155-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1021789581666352, 'root_angle': 0.23134429571775278, 'root_number': '0.747311516764418522001893471609+0.664473849682035428665201891932*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.115672147859', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(166)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.34238890117947450315917994632+0.222342111894801742597868154140*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.30914556018', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.5530113585', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.4757029765', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.1021789581666352, 'bad_primes': [2, 167], 'central_character': '668.155', 'conductor': 668, 'conductor_radical': 334, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/668/155'], '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': '1-668-668.155-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': '1-668-668.155-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1021789581666352, 'root_angle': 0.11567214785887639, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.30914556018', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_668.155', 'Lhash_array': ['dirichlet_L_668.155'], 'label': '1-668-668.155-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/668/155'}
Lfunction data - 1-668-668.155-r0-0-0