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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_45.29', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.5, -0.8660254037844386], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.5, 0.8660254037844386], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.5, 0.8660254037844386], 'a8': [1.0, 0.0], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 4.835921615758126, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '45.29', 'coeff_info': ['x^6 - 1', '0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{6}'], 'conductor': 45, 'conductor_radical': 15, 'conjugate': 'dirichlet_L_45.14', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^4', 0, 'a^2', 0, 0, 'a^1', 'a^0', 0, 0, 'a^1', 0, 'a^5', 'a^5', 0, 'a^4', 'a^0', 0, 'a^0', 0, 0, 'a^5', 'a^2', 0, 0, 'a^3', 0, 'a^3', 'a^1', 0, 'a^2', 'a^2', 0, 'a^4', 0, 0, 'a^3', 'a^4', 0, 0, 'a^5', 0, 'a^1', 'a^3', 0, 'a^0', 'a^4', 0, 'a^2', 0, 0, 'a^1', 'a^0', 0, 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'184.868698037994083851691338363731', '185.838948524750566650427721986861', '186.61448430055883861448475629616', '187.82885887965241602171069802400', '188.874602687373229755357946435123', '189.81729139480349946744130380760', '190.105825834170064843591868890', '191.49412705636684902165123677581', '191.941114387191423736343089376798', '193.00166529463441165649136648192', '193.46909706908816044763608437119', '194.556957397820574026690452277984', '195.42729322597078979818175189968', '196.292766311607094002274964847292', '197.493202934015407045129967984715', '198.517928026542597692270218177709', '199.0320146382982114769334676545', '199.89544344073242353493882392306'], 'prelabel': '1-45-45.29-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.835921615758126, 'root_angle': -0.055555555555555566, 'root_number': '0.984807753012208059366743024589-0.173648177666930348851716626769*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0277777777778', 'prec': 54}, 'spectral_label': 'r1-0', 'st_group': 'mu(6)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.922412268080436862134538668114-0.162646170199070612015874572624*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.54474594652', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.33029895743', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.24499814264', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.835921615758126, 'bad_primes': [3, 5], 'central_character': '45.29', 'conductor': 45, 'conductor_radical': 15, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/45/29'], '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': '1-45-45.29-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': '1-45-45.29-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.835921615758126, 'root_angle': -0.027777777777777783, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.54474594652', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_45.29', 'Lhash_array': ['dirichlet_L_45.29'], 'label': '1-45-45.29-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/45/29'}
Lfunction data - 1-45-45.29-r1-0-0