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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2205.1447', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.9308737486442042, 0.36534102436639504], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.7330518718298263, -0.6801727377709194], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.4338837391175581, 0.9009688679024191], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 10.239976950235675, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]], [7, [1]]], 'bad_primes': [3, 5, 7], 'central_character': '2205.1447', 'coeff_info': ['x^84 - 1', '0.997203797181180 + 0.0747300935864243*I', '\\\\zeta_{84}'], 'conductor': 2205, 'conductor_radical': 105, 'conjugate': 'dirichlet_L_2205.2173', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^37', 0, 'a^74', 0, 0, 0, 'a^27', 0, 0, 'a^72', 0, 'a^37', 0, 0, 'a^64', 'a^31', 0, 'a^56', 0, 0, 'a^25', 'a^39', 0, 0, 'a^74', 0, 0, 'a^38', 0, 'a^14', 'a^17', 0, 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'193.816245261238854548141581458385', '194.60362149662671170889222482507', '195.02247068015778022680375225662', '195.71754915356870412021373930918', '196.395160025717856880588451105039', '196.68538909757001969773212066075', '197.40599900110167591975901283896', '198.012718853751719880547292715173', '198.214086812690473930345049757613', '199.04311332008843138050575890277', '199.57067852053706390993667964529', '199.89700220933082733477282464215'], 'prelabel': '1-2205-2205.1447-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.239976950235675, 'root_angle': -0.09273490668018201, 'root_number': '0.834996114347236926192235666118-0.550255839610099945247070224672*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0927349066802', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(84)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.650639074729240785613430359136+0.0356197776098949925006957504513*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.451826174834', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.68388769664', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.38945433098', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 10.239976950235675, 'bad_primes': [3, 5, 7], 'central_character': '2205.1447', 'conductor': 2205, 'conductor_radical': 105, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2205/1447'], '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': '1-2205-2205.1447-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': '1-2205-2205.1447-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.239976950235675, 'root_angle': -0.09273490668018201, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.451826174834', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2205.1447', 'Lhash_array': ['dirichlet_L_2205.1447'], 'factors': ['1-2205-2205.1447-r0-0-0'], 'label': '1-2205-2205.1447-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2205/1447'}
Lfunction data - 1-2205-2205.1447-r0-0-0