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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_837.230', 'a10': [0.30901699437494745, -0.9510565162951535], 'a2': [-0.03489949670250097, -0.9993908270190958], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.9975640502598242, 0.0697564737441253], 'a5': [0.9396926207859084, 0.3420201433256687], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.7193398003386512, 0.6946583704589973], 'a8': [0.10452846326765347, 0.9945218953682733], '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': '837.230', 'coeff_info': ['x^90 - 1', '0.997564050259824 + 0.0697564737441253*I', '\\\\zeta_{90}'], 'conductor': 837, 'conductor_radical': 93, 'conjugate': 'dirichlet_L_837.353', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^67', 0, 'a^44', 'a^5', 0, 'a^34', 'a^21', 0, 'a^72', 'a^64', 0, 'a^53', 'a^11', 0, 'a^88', 'a^66', 0, 'a^72', 'a^49', 0, 'a^41', 'a^26', 0, 'a^10', 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'192.349257800435570235633471422935', '193.241948082827836957650532038', '193.61892866176928512170190206523', '193.950679138800323869012269641611', '194.62910050843067701195118047353', '195.433915230278214692246955525761', '196.16559722302288163538207845180', '196.6133738816479515162172244606', '197.479527924477552420033204160896', '197.86847454082175446396955233637', '198.88987402601017064595810278109', '199.32158846149651993555851953026', '199.91016859946584448842253152439'], 'prelabel': '1-837-837.230-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': -0.36888990411166284, 'root_number': '-0.679445984587831731047060438610-0.733725530445460188362692256681*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.368889904112', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(90)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.789780976865727738738462930354-0.484572187905998789858678333399*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.508024700352', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.01856753504', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.8434995755', 'prec': 40}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'bad_primes': [3, 31], 'central_character': '837.230', 'conductor': 837, 'conductor_radical': 93, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/837/230'], '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': '1-837-837.230-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': '1-837-837.230-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': -0.36888990411166284, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.508024700352', 'prec': 47}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_837.230', 'Lhash_array': ['dirichlet_L_837.230'], 'factors': ['1-837-837.230-r0-0-0'], 'label': '1-837-837.230-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/837/230'}