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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_247.220', 'a10': [-0.5, 0.8660254037844386], 'a2': [0.5, 0.8660254037844386], 'a3': [-0.5, -0.8660254037844386], 'a4': [-0.5, 0.8660254037844386], 'a5': [0.5, 0.8660254037844386], 'a6': [0.5, -0.8660254037844386], 'a7': [-1.0, -1.4081532572346456e-30], 'a8': [-1.0, -1.4081532572346456e-30], 'a9': [-0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 1.1470631776454474, 'analytic_normalization': 0, 'bad_lfactors': [[13, [1]], [19, [1]]], 'bad_primes': [13, 19], 'central_character': '247.220', 'coeff_info': ['x^6 - 1', '0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{6}'], 'conductor': 247, 'conductor_radical': 247, 'conjugate': 'dirichlet_L_247.64', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 'a^4', 'a^2', 'a^1', 'a^5', 'a^3', 'a^3', 'a^2', 'a^2', 'a^3', 'a^0', 0, 'a^4', 'a^5', 'a^4', 'a^4', 'a^3', 0, 'a^3', 'a^1', 'a^4', 'a^2', 'a^1', 'a^2', 0, 'a^0', 'a^5', 'a^2', 'a^0', 'a^3', 'a^5', 'a^1', 'a^5', 'a^4', 'a^4', 'a^3', 0, 0, 'a^4', 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'184.28809211645979146007476534806', '184.8381201392996654113278560307', '185.717894143961865606556189878937', '186.27989043092522404514720100612', '186.82172897212018230270640902449', '187.8261716060445930799339411574', '188.38533423759315038738434617259', '189.14664048519023582968773414304', '189.66347772256283061348522976126', '190.45681398691898417952223299683', '190.68224745254775551711218985359', '191.6092713094802059712166590755', '193.1407619682246637464238608073', '193.67895802798302964996396434685', '194.13730597944057990453011537694', '194.5932941363297015908717227789', '195.62471326812655900997546027190', '196.05756654796121852807934772037', '196.85426539466475694700564417619', '197.34808867809474223539229439639', '197.902055767177498923107758254121', '198.909301274940903879696115305569', '199.625268134696526424487332018614'], 'prelabel': '1-247-247.220-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1470631776454474, 'root_angle': -0.4661233559688616, 'root_number': '-0.977432150027937166462765683932-0.211249596666512314167367531935*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.466123355969', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(6)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.642550455512597244357651462969+0.390661250816928347129446275367*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.36462281215', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.39307432028', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.24536772304', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.1470631776454474, 'bad_primes': [13, 19], 'central_character': '247.220', 'conductor': 247, 'conductor_radical': 247, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/247/220'], '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': '1-247-247.220-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': '1-247-247.220-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1470631776454474, 'root_angle': -0.4661233559688616, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.36462281215', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_247.220', 'Lhash_array': ['dirichlet_L_247.220'], 'factors': ['1-247-247.220-r0-0-0'], 'label': '1-247-247.220-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/247/220'}
Lfunction data - 1-247-247.220-r0-0-0