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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_693.389', 'a10': [-0.5, -0.8660254037844386], 'a2': [-0.30901699437494745, -0.9510565162951535], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.8090169943749475, 0.5877852522924731], 'a5': [0.9781476007338057, -0.20791169081775934], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.8090169943749475, 0.5877852522924731], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 74.47319288267514, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [11, [1]]], 'bad_primes': [3, 7, 11], 'central_character': '693.389', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 693, 'conductor_radical': 231, 'conjugate': 'dirichlet_L_693.212', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^21', 0, 'a^12', 'a^29', 0, 0, 'a^3', 0, 'a^20', 0, 0, 'a^16', 0, 0, 'a^24', 'a^29', 0, 'a^28', 'a^11', 0, 0, 'a^5', 0, 'a^28', 'a^7', 0, 0, 'a^17', 0, 'a^6', 'a^15', 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'197.92648712825365444712101741401', '198.55786069551289971442059842195', '199.27533330129422023908024420851', '199.8518941548082067839340923275'], 'prelabel': '1-693-693.389-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 74.47319288267514, 'root_angle': -0.4985056322615085, 'root_number': '0.00469467746372315454392985276359-0.999988979941034955167943097477*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.250747183869', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.951499169213272372583129664866-0.496904072123685549024302375045*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.667843279654', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.68227661258', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.67146772118', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 74.47319288267514, 'bad_primes': [3, 7, 11], 'central_character': '693.389', 'conductor': 693, 'conductor_radical': 231, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/693/389'], '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': '1-693-693.389-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': '1-693-693.389-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 74.47319288267514, 'root_angle': -0.24925281613075426, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.667843279654', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_693.389', 'Lhash_array': ['dirichlet_L_693.389'], 'label': '1-693-693.389-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/693/389'}
Lfunction data - 1-693-693.389-r1-0-0