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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1832.13', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.08257934547233232, 0.9965844930066698], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.24548548714079915, -0.9694002659393304], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.8371664782625285, -0.5469481581224269], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.9863613034027223, 0.1645945902807339], 'algebraic': True, 'analytic_conductor': 196.87574222375304, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [229, [1]]], 'bad_primes': [2, 229], 'central_character': '1832.13', 'coeff_info': ['x^76 - 1', '0.996584493006670 + 0.0825793454723323*I', '\\\\zeta_{76}'], 'conductor': 1832, 'conductor_radical': 458, 'conjugate': 'dirichlet_L_1832.141', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^94', 0, 'a^60', 0, 'a^69', 0, 'a^36', 0, 'a^48', 0, 'a^41', 0, 'a^2', 0, 'a^60', 0, 'a^54', 0, 'a^87', 0, 'a^71', 0, 'a^44', 0, 'a^54', 0, 'a^69', 0, 'a^67', 0, 'a^66', 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'194.601693523680618273122583451860', '194.91941785362896255081188150164', '195.74897522202563851373998356358', '196.31754362736593822632882195272', '196.90521717689277664338482028732', '197.35913855294936079578738028573', '198.12973713519875810747431144605', '198.552601696385425494369207554620', '199.08246211691822709268489940846', '199.61487372957116603037694065440'], 'prelabel': '1-1832-1832.13-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 196.87574222375304, 'root_angle': -0.4428720807499202, 'root_number': '-0.936267845695494530968553957521-0.351286949824096999684898540530*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.44287208075', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(76)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.01647437809972785313443543250-0.178771304931220267045002739324*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.226016208602', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '0.951142686051', 'prec': 47}, 'z3': {'__RealLiteral__': 0, 'data': '2.42333645998', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 196.87574222375304, 'bad_primes': [2, 229], 'central_character': '1832.13', 'conductor': 1832, 'conductor_radical': 458, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1832/13'], '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': '1-1832-1832.13-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-1832-1832.13-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 196.87574222375304, 'root_angle': -0.4428720807499202, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.226016208602', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1832.13', 'Lhash_array': ['dirichlet_L_1832.13'], 'factors': ['1-1832-1832.13-r1-0-0'], 'label': '1-1832-1832.13-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1832/13'}
Lfunction data - 1-1832-1832.13-r1-0-0