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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1089.391', 'a10': [0.6548607339452851, 0.7557495743542583], 'a2': [-0.8612262431802006, 0.5082217607085691], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.48342128388456385, -0.8753878353549357], 'a5': [-0.17989487036885388, -0.983685841930732], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.8308078967080545, -0.5565592859413437], 'a8': [0.028556050793696254, 0.9995921928281892], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 117.02930310134664, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [11, [1]]], 'bad_primes': [3, 11], 'central_character': '1089.391', 'coeff_info': ['x^330 - 1', '0.999818745523526 + 0.0190388051033467*I', '\\\\zeta_{330}'], 'conductor': 1089, 'conductor_radical': 33, 'conjugate': 'dirichlet_L_1089.376', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^137', 0, 'a^274', 'a^238', 0, 'a^299', 'a^81', 0, 'a^45', 0, 0, 'a^307', 'a^106', 0, 'a^218', 'a^3', 0, 'a^261', 'a^182', 0, 0, 'a^130', 0, 'a^146', 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'187.042718496883115211453716495362', '187.52661392734966795649370199905', '188.07444054458442373634488066150', '188.597256969044816361067583642664', '189.12228031406998701360794436022', '189.58342683399175757167581355106', '190.413678168677103658137821100323', '190.926561085184637608248010840895', '191.76922475783856418402090147067', '192.000011018140071132308952218305', '192.47594455993594156731398795317', '193.03698247712347614871662876144', '194.17084702077724724082081457839', '194.74427615274160877287999549561', '195.303379241378855404471272235589', '195.9780527059170724866120415687', '196.63748362057450488256051645730', '196.77565870797355657214261476802', '197.78299790207910739439765479932', '198.27620339781520541379712727589', '198.75170267963058532727860319706', '199.46087227271375363216511627947', '199.91029941096096724248218327987'], 'prelabel': '1-33e2-1089.391-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 117.02930310134664, 'root_angle': -0.8832874196510561, 'root_number': '-0.933528725044511271387858920892-0.358502607405816888494283058214*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.441643709826', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(330)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.724731676296364310037674869330-0.166089686507358306194884135834*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.245746660052', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.1324370721', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '1.86535437104', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 117.02930310134664, 'bad_primes': [3, 11], 'central_character': '1089.391', 'conductor': 1089, 'conductor_radical': 33, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1089/391'], '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': '1-33e2-1089.391-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': '1-33e2-1089.391-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 117.02930310134664, 'root_angle': -0.44164370982552803, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.245746660052', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1089.391', 'Lhash_array': ['dirichlet_L_1089.391'], 'label': '1-33e2-1089.391-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1089/391'}
Lfunction data - 1-33e2-1089.391-r1-0-0