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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_837.209', 'a10': [0.9135454576426009, -0.4067366430758002], 'a2': [0.9975640502598242, -0.0697564737441253], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9902680687415704, -0.13917310096006544], 'a5': [0.9396926207859084, -0.3420201433256687], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.882947592858927, 0.46947156278589075], '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': '837.209', 'coeff_info': ['x^90 - 1', '0.997564050259824 + 0.0697564737441253*I', '\\\\zeta_{90}'], 'conductor': 837, 'conductor_radical': 93, 'conjugate': 'dirichlet_L_837.833', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^89', 0, 'a^88', 'a^85', 0, 'a^38', 'a^87', 0, 'a^84', 'a^68', 0, 'a^1', 'a^37', 0, 'a^86', 'a^12', 0, 'a^24', 'a^83', 0, 'a^67', 'a^52', 0, 'a^80', 'a^0', 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'192.24129674101164638744627630470', '192.51392010168044295223881001011', '193.47436898533481131490289297268', '193.82874287797263120023968165090', '194.34242628155749792074961235857', '194.97434380537525952717756569983', '195.83726320068469375128180736125', '196.38089590251688652938492760613', '196.8257692353031919486055434089', '197.424652089928965888520589092782', '197.67879799949170467584228453317', '198.761445145319688557538549376732', '199.62721663777892198690270841927'], 'prelabel': '1-837-837.209-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': -0.05095686139378686, 'root_number': '0.949181486546705938120748060557-0.314729257611975906684847420712*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0509568613938', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(90)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.18818027009798295275162516585-0.213004519282158667551298105916*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.27012449779', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.26752556239', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.3523351643', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'bad_primes': [3, 31], 'central_character': '837.209', 'conductor': 837, 'conductor_radical': 93, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/837/209'], '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': '1-837-837.209-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': '1-837-837.209-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': -0.05095686139378686, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.27012449779', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_837.209', 'Lhash_array': ['dirichlet_L_837.209'], 'factors': ['1-837-837.209-r0-0-0'], 'label': '1-837-837.209-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/837/209'}
Lfunction data - 1-837-837.209-r0-0-0