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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_608.307', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.9961946980917455, -0.08715574274765818], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.9063077870366499, 0.42261826174069944], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.8660254037844386, -0.5], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.984807753012208, 0.17364817766693036], 'algebraic': True, 'analytic_conductor': 2.823540129588794, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [19, [1]]], 'bad_primes': [2, 19], 'central_character': '608.307', 'coeff_info': ['x^72 - 1', '0.996194698091746 + 0.0871557427476582*I', '\\\\zeta_{72}'], 'conductor': 608, 'conductor_radical': 38, 'conjugate': 'dirichlet_L_608.507', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^37', 0, 'a^103', 0, 'a^42', 0, 'a^74', 0, 'a^111', 0, 'a^53', 0, 'a^68', 0, 'a^52', 0, 0, 0, 'a^79', 0, 'a^86', 0, 'a^62', 0, 'a^39', 0, 'a^65', 0, 'a^96', 0, 'a^4', 0, 'a^73', 0, 'a^99', 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'1-608-608.307-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.823540129588794, 'root_angle': 0.21885388095900352, 'root_number': '0.194450118701113181964785641765+0.980912407576294751794034849718*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.218853880959', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(72)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.504077643888667755751804087509+0.0119476819724437147421210821662*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.832754613486', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.79489834264', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.62786142491', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.823540129588794, 'bad_primes': [2, 19], 'central_character': '608.307', 'conductor': 608, 'conductor_radical': 38, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/608/307'], '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': '1-608-608.307-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': '1-608-608.307-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.823540129588794, 'root_angle': 0.21885388095900352, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.832754613486', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_608.307', 'Lhash_array': ['dirichlet_L_608.307'], 'factors': ['1-608-608.307-r0-0-0'], 'label': '1-608-608.307-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/608/307'}
Lfunction data - 1-608-608.307-r0-0-0