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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_231.38', 'a10': [0.5, 0.8660254037844386], 'a2': [0.10452846326765347, 0.9945218953682733], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.9781476007338057, 0.20791169081775934], 'a5': [0.9135454576426009, -0.4067366430758002], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.30901699437494745, -0.9510565162951535], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 1.0727594900246897, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [11, [1]]], 'bad_primes': [3, 7, 11], 'central_character': '231.38', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 231, 'conductor_radical': 231, 'conjugate': 'dirichlet_L_231.152', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^7', 0, 'a^14', 'a^28', 0, 0, 'a^21', 0, 'a^5', 0, 0, 'a^27', 0, 0, 'a^28', 'a^8', 0, 'a^1', 'a^12', 0, 0, 'a^25', 0, 'a^26', 'a^4', 0, 0, 'a^9', 0, 'a^17', 'a^5', 0, 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'186.71795827188503523475730411392', '187.48016948117878341643239403113', '188.1794656847486214146950333733', '188.87570710666135963943823410959', '189.39050047043838621071713579006', '190.01289879491617628058704147309', '190.74684879667188317701669622345', '191.59120627798823581329151879524', '192.50722441393054816896586272859', '193.07038379063265837530261239645', '194.11626223059232164549274989215', '194.42159356075469472884162084593', '195.47238874072895381108180412632', '195.948290404736688212580583061459', '196.87663620565015695868778792192', '197.22356864744775204954450391034', '197.723291501904813801722591738690', '198.7559860551903977437229902913', '199.52797115426626980859280092822', '199.75177332659088313198100158836'], 'prelabel': '1-231-231.38-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0727594900246897, 'root_angle': 0.1628900831235529, 'root_number': '0.520407206608087001691325054461+0.853918227531400016150284568846*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.162890083124', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.10049863738419360269726975594+0.477364209096858065537886382346*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.3102394123', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '3.25213522657', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.66055043332', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.0727594900246897, 'bad_primes': [3, 7, 11], 'central_character': '231.38', 'conductor': 231, 'conductor_radical': 231, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/231/38'], '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': '1-231-231.38-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': '1-231-231.38-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0727594900246897, 'root_angle': 0.1628900831235529, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.3102394123', 'prec': 40}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_231.38', 'Lhash_array': ['dirichlet_L_231.38'], 'factors': ['1-231-231.38-r0-0-0'], 'label': '1-231-231.38-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/231/38'}
Lfunction data - 1-231-231.38-r0-0-0