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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_441.367', 'a10': [-0.9555728057861407, 0.2947551744109042], 'a2': [-0.9009688679024191, -0.4338837391175581], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.6234898018587335, 0.7818314824680298], 'a5': [0.7330518718298263, -0.6801727377709194], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.2225209339563144, -0.9749279121818236], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 47.39203183442964, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '441.367', 'coeff_info': ['x^42 - 1', '0.988830826225129 + 0.149042266176174*I', '\\\\zeta_{42}'], 'conductor': 441, 'conductor_radical': 21, 'conjugate': 'dirichlet_L_441.292', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^24', 0, 'a^6', 'a^37', 0, 0, 'a^30', 0, 'a^19', 'a^38', 0, 'a^17', 0, 0, 'a^12', 'a^1', 0, 'a^35', 'a^1', 0, 'a^20', 'a^34', 0, 'a^32', 'a^41', 0, 0, 'a^22', 0, 'a^21', 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'191.47611063894212411899342388566', '192.076423889979238059834996122618', '192.65278336568021783991857970681', '193.08349549964447978922223637510', '193.79175807136143156758443779274', '194.51248636583287876922254192580', '195.31938919505465387561930750433', '196.24860131052982934831530667189', '196.6984382185958769602609900016', '197.58775553837603467753035560532', '197.8676297430749465862663716119', '198.66764056124735236608905004453', '199.55148172230565697631958612862', '199.89732553997728421786661507329'], 'prelabel': '1-21e2-441.367-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 47.39203183442964, 'root_angle': -0.6405895691609979, 'root_number': '-0.427454468399391482132161491557-0.904036878365807391692268002841*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.32029478458', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(42)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.791294054656251041363848281081-0.352878541087351287119204252670*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.535900955572', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.55310429377', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.64141904529', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 47.39203183442964, 'bad_primes': [3, 7], 'central_character': '441.367', 'conductor': 441, 'conductor_radical': 21, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/441/367'], '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': '1-21e2-441.367-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': '1-21e2-441.367-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 47.39203183442964, 'root_angle': -0.3202947845804989, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.535900955572', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_441.367', 'Lhash_array': ['dirichlet_L_441.367'], 'label': '1-21e2-441.367-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/441/367'}
Lfunction data - 1-21e2-441.367-r1-0-0