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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1984.451', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.2840153447039226, 0.958819734868193], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.6087614290087207, -0.7933533402912352], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.838670567945424, -0.5446390350150271], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.838670567945424, -0.5446390350150271], 'algebraic': True, 'analytic_conductor': 9.213657264973959, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [31, [1]]], 'bad_primes': [2, 31], 'central_character': '1984.451', 'coeff_info': ['x^240 - 1', '0.999657324975557 + 0.0261769483078731*I', '\\\\zeta_{240}'], 'conductor': 1984, 'conductor_radical': 62, 'conjugate': 'dirichlet_L_1984.1003', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^71', 0, 'a^205', 0, 'a^218', 0, 'a^142', 0, 'a^193', 0, 'a^331', 0, 'a^276', 0, 'a^212', 0, 'a^419', 0, 'a^289', 0, 'a^102', 0, 'a^170', 0, 'a^213', 0, 'a^39', 0, 0, 0, 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'193.48696861128426373633265158570', '193.73138679147110844990412109769', '194.660847280049914206310270139331', '195.01982756019743693990500453131', '195.57220348844220681063115144473', '196.30373327608856829323303057408', '197.00547403503874815425009976645', '197.39844191247189201103597854565', '198.153439761374984820937803759159', '198.45174825010394187317507708058', '199.01077685764891933129716814487', '199.85528557099293812526468806486'], 'prelabel': '1-1984-1984.451-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.213657264973959, 'root_angle': -0.17911156782788365, 'root_number': '0.430823542611795203302666159463-0.902436188952671978723438152086*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.179111567828', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(240)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.10893517121066127768909849104-0.0986437537259080724762980677840*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.557729785886', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.56374008544', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.74718552502', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 9.213657264973959, 'bad_primes': [2, 31], 'central_character': '1984.451', 'conductor': 1984, 'conductor_radical': 62, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1984/451'], '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': '1-1984-1984.451-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': '1-1984-1984.451-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.213657264973959, 'root_angle': -0.17911156782788365, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.557729785886', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1984.451', 'Lhash_array': ['dirichlet_L_1984.451'], 'factors': ['1-1984-1984.451-r0-0-0'], 'label': '1-1984-1984.451-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1984/451'}
Lfunction data - 1-1984-1984.451-r0-0-0