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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1860.719', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5, 0.8660254037844386], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 199.88476011800253, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]], [31, [1]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '1860.719', 'coeff_info': ['x^6 - 1', '0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{6}'], 'conductor': 1860, 'conductor_radical': 930, 'conjugate': 'dirichlet_L_1860.119', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 0, 0, 'a^8', 0, 0, 0, 'a^7', 0, 'a^4', 0, 0, 0, 'a^5', 0, 'a^5', 0, 0, 0, 'a^0', 0, 0, 0, 0, 0, 'a^0', 0, 0, 0, 0, 0, 0, 0, 'a^2', 0, 0, 0, 'a^1', 0, 'a^5', 0, 0, 0, 'a^3', 0, 'a^4', 0, 0, 0, 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'197.81145316600082307954040601486', '198.60124425030217305221980730442', '199.04673052701558340831886434516', '199.4471528647414277321608924098'], 'prelabel': '1-1860-1860.719-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 199.88476011800253, 'root_angle': -0.12768199178634645, 'root_number': '0.695091172906969705906974758513-0.718921596105453729805285086817*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.127681991786', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(6)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.05056719125077842735545592044+0.00250462239810978990974806554445*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.413256954499', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.50613962473', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.84890000056', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 199.88476011800253, 'bad_primes': [2, 3, 5, 31], 'central_character': '1860.719', 'conductor': 1860, 'conductor_radical': 930, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1860/719'], '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': '1-1860-1860.719-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': '1-1860-1860.719-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 199.88476011800253, 'root_angle': -0.12768199178634645, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.413256954499', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1860.719', 'Lhash_array': ['dirichlet_L_1860.719'], 'factors': ['1-1860-1860.719-r1-0-0'], 'label': '1-1860-1860.719-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1860/719'}
Lfunction data - 1-1860-1860.719-r1-0-0