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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_837.733', 'a10': [-0.8090169943749475, 0.5877852522924731], 'a2': [-0.9975640502598242, -0.0697564737441253], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9902680687415704, 0.13917310096006544], 'a5': [0.766044443118978, -0.6427876096865394], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.03489949670250097, 0.9993908270190958], 'a8': [-0.9781476007338057, -0.20791169081775934], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [31, [1]]], 'bad_primes': [3, 31], 'central_character': '837.733', 'coeff_info': ['x^45 - 1', '0.990268068741570 + 0.139173100960065*I', '\\\\zeta_{45}'], 'conductor': 837, 'conductor_radical': 93, 'conjugate': 'dirichlet_L_837.169', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^23', 0, 'a^1', 'a^40', 0, 'a^11', 'a^24', 0, 'a^18', 'a^26', 0, 'a^37', 'a^34', 0, 'a^2', 'a^24', 0, 'a^18', 'a^41', 0, 'a^4', 'a^19', 0, 'a^35', 'a^15', 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'193.48759039910653151096573805437', '193.88943229322810617819721702800', '194.62560759949526587507538051472', '195.92071977045060644915987730738', '196.14613574347978017220767194085', '196.73762502533835180144566949606', '197.22161968445175783172944578406', '197.9302525961317646480955402937', '198.607667885854295021866115535481', '199.42728367847757219802320739357', '199.63741452895776983449819142727'], 'prelabel': '1-837-837.733-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': 0.4958863287750054, 'root_number': '-0.999665985961465092045092900964+0.0258440807863595239698348195024*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.495886328775', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(45)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.568292533813668001178943862552-0.0628529352138253014389688206391*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.0541657054372', 'prec': 50}, 'z2': {'__RealLiteral__': 0, 'data': '1.6566007176', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.3247610019', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'bad_primes': [3, 31], 'central_character': '837.733', 'conductor': 837, 'conductor_radical': 93, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/837/733'], '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': '1-837-837.733-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': '1-837-837.733-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': 0.4958863287750054, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0541657054372', 'prec': 50}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_837.733', 'Lhash_array': ['dirichlet_L_837.733'], 'factors': ['1-837-837.733-r0-0-0'], 'label': '1-837-837.733-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/837/733'}
Lfunction data - 1-837-837.733-r0-0-0