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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_261.185', 'a10': [-0.9749279121818236, -0.2225209339563144], 'a2': [-0.14904226617617444, -0.9888308262251285], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.9555728057861407, 0.2947551744109042], 'a5': [0.36534102436639504, -0.9308737486442042], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.9555728057861407, 0.2947551744109042], 'a8': [0.4338837391175581, 0.9009688679024191], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 1.2120789043136104, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [29, [1]]], 'bad_primes': [3, 29], 'central_character': '261.185', 'coeff_info': ['x^84 - 1', '0.997203797181180 + 0.0747300935864243*I', '\\\\zeta_{84}'], 'conductor': 261, 'conductor_radical': 87, 'conjugate': 'dirichlet_L_261.182', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^61', 0, 'a^38', 'a^68', 0, 'a^4', 'a^15', 0, 'a^45', 'a^13', 0, 'a^62', 'a^65', 0, 'a^76', 'a^21', 0, 'a^3', 'a^22', 0, 'a^74', 'a^2', 0, 'a^52', 'a^39', 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'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2120789043136104, 'root_angle': -0.4782903412954076, 'root_number': '0.0681500407456394662994269833783-0.997675083354479531193522273460*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.239145170648', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(84)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.937494436589225523233403795713-0.563523420022201028072273537308*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.20837014936', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.07014497195', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.66915725637', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.2120789043136104, 'bad_primes': [3, 29], 'central_character': '261.185', 'conductor': 261, 'conductor_radical': 87, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/261/185'], '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': '1-261-261.185-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': '1-261-261.185-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2120789043136104, 'root_angle': -0.2391451706477038, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.20837014936', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_261.185', 'Lhash_array': ['dirichlet_L_261.185'], 'label': '1-261-261.185-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/261/185'}
Lfunction data - 1-261-261.185-r0-0-0