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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_69.11', 'a10': [0.14231483827328514, 0.9898214418809327], 'a2': [-0.41541501300188644, 0.9096319953545183], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.6548607339452851, -0.7557495743542583], 'a5': [0.8412535328311812, -0.5406408174555976], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.14231483827328514, -0.9898214418809327], 'a8': [0.9594929736144974, -0.28173255684142967], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.3204346528645177, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [23, [1]]], 'bad_primes': [3, 23], 'central_character': '69.11', 'coeff_info': ['x^22 - 1', '0.959492973614497 + 0.281732556841430*I', '\\\\zeta_{22}'], 'conductor': 69, 'conductor_radical': 69, 'conjugate': 'dirichlet_L_69.44', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^7', 0, 'a^14', 'a^20', 0, 'a^17', 'a^21', 0, 'a^5', 'a^4', 0, 'a^16', 'a^2', 0, 'a^6', 'a^8', 0, 'a^3', 'a^12', 0, 'a^11', 0, 0, 'a^18', 'a^1', 0, 'a^9', 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'193.04681193301640089609353295159', '194.0702440688667370424562143622', '194.93821680305362406195125719291', '195.77866098760627389385647787939', '196.51624438878359932610906242104', '197.30523803120451478107821267119', '197.87954813715892797025826731502', '198.706626645397920959741651110199', '199.601805886779929824323822921504'], 'prelabel': '1-69-69.11-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.3204346528645177, 'root_angle': 0.1117722664449647, 'root_number': '0.938980190803941658736628133188+0.343971221583715221736654910934*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0558861332225', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(22)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.889998788207046340670301629678+0.178370074023786560809131349625*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.44832072438', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.31714857277', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.62556278685', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.3204346528645177, 'bad_primes': [3, 23], 'central_character': '69.11', 'conductor': 69, 'conductor_radical': 69, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/69/11'], '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': '1-69-69.11-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': '1-69-69.11-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.3204346528645177, 'root_angle': 0.05588613322248235, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.44832072438', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_69.11', 'Lhash_array': ['dirichlet_L_69.11'], 'label': '1-69-69.11-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/69/11'}
Lfunction data - 1-69-69.11-r0-0-0