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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2668.695', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.14231483827328514, -0.9898214418809327], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.9594929736144974, 0.28173255684142967], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.6548607339452851, 0.7557495743542583], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.9594929736144974, 0.28173255684142967], 'algebraic': True, 'analytic_conductor': 12.390139910761352, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [23, [1]], [29, [1]]], 'bad_primes': [2, 23, 29], 'central_character': '2668.695', 'coeff_info': ['x^22 - 1', '0.959492973614497 + 0.281732556841430*I', '\\\\zeta_{22}'], 'conductor': 2668, 'conductor_radical': 1334, 'conjugate': 'dirichlet_L_2668.1739', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^16', 0, 'a^1', 0, 'a^30', 0, 'a^10', 0, 'a^31', 0, 'a^14', 0, 'a^17', 0, 'a^18', 0, 'a^15', 0, 'a^2', 0, 0, 0, 'a^2', 0, 'a^26', 0, 0, 0, 'a^28', 0, 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50}, 'spectral_label': 'r0-0', 'st_group': 'mu(22)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.960269322485421142226311540471-0.135664052750355085481670807872*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.80193852778', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.0271432771', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.67506718897', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 12.390139910761352, 'bad_primes': [2, 23, 29], 'central_character': '2668.695', 'conductor': 2668, 'conductor_radical': 1334, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2668/695'], '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': '1-2668-2668.695-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': '1-2668-2668.695-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.390139910761352, 'root_angle': 0.025498711303785147, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.80193852778', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2668.695', 'Lhash_array': ['dirichlet_L_2668.695'], 'factors': ['1-2668-2668.695-r0-0-0'], 'label': '1-2668-2668.695-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2668/695'}
Lfunction data - 1-2668-2668.695-r0-0-0