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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_59.57', 'a10': [-0.7259954919231308, -0.6876994588534233], 'a2': [-0.9941379571543596, -0.10811901842394177], 'a3': [0.6473862847818277, -0.7621620551276365], 'a4': [0.9766205557100867, 0.21497044021102407], 'a5': [0.7960930657056438, 0.6051742151937651], 'a6': [-0.7259954919231308, 0.6876994588534233], 'a7': [-0.37013815533991434, 0.9289767198167914], 'a8': [-0.9476531711828025, -0.31930153013597995], 'a9': [-0.16178199655276473, -0.9868265225415261], 'algebraic': True, 'analytic_conductor': 0.2739948481015441, 'analytic_normalization': 0, 'bad_lfactors': [[59, [1]]], 'bad_primes': [59], 'central_character': '59.57', 'coeff_info': ['x^29 - 1', '0.976620555710087 + 0.214970440211024*I', '\\\\zeta_{29}'], 'conductor': 59, 'conductor_radical': 59, 'conjugate': 'dirichlet_L_59.29', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^15', 'a^25', 'a^1', 'a^3', 'a^11', 'a^9', 'a^16', 'a^21', 'a^18', 'a^27', 'a^26', 'a^8', 'a^24', 'a^28', 'a^2', 'a^20', 'a^7', 'a^19', 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'190.79672579712996573638902698023', '191.98914262460304685031303533158', '192.837362984774703449816021069676', '193.20291557891251391311791085488', '194.51177432757616348075296073594', '195.64441335049462655107903806402', '196.49027944727923949771491636033', '197.28237705485577292624375339687', '197.74145607548938915637700034188', '198.52680107261047800199334404251', '199.73455122614318626298460200766'], 'prelabel': '1-59-59.57-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.2739948481015441, 'root_angle': -0.10456167432963993, 'root_number': '0.946530509153948091079383978111-0.322614313446827385117829413765*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0522808371648', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(29)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.869972211261322429036056474314-0.115009160793348270462097735409*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.89646578021', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.95389588966', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '6.27407014696', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.2739948481015441, 'bad_primes': [59], 'central_character': '59.57', 'conductor': 59, 'conductor_radical': 59, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/59/57'], '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': '1-59-59.57-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': '1-59-59.57-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.2739948481015441, 'root_angle': -0.05228083716481997, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.89646578021', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_59.57', 'Lhash_array': ['dirichlet_L_59.57'], 'label': '1-59-59.57-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/59/57'}