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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_276.131', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.6548607339452851, -0.7557495743542583], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.8412535328311812, 0.5406408174555976], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 1.2817386114580709, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [23, [1]]], 'bad_primes': [2, 3, 23], 'central_character': '276.131', 'coeff_info': ['x^22 - 1', '0.959492973614497 + 0.281732556841430*I', '\\\\zeta_{22}'], 'conductor': 276, 'conductor_radical': 138, 'conjugate': 'dirichlet_L_276.59', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^19', 0, 'a^31', 0, 0, 0, 'a^28', 0, 'a^2', 0, 0, 0, 'a^1', 0, 'a^21', 0, 0, 0, 0, 0, 'a^16', 0, 0, 0, 'a^1', 0, 'a^15', 0, 0, 0, 'a^28', 0, 'a^14', 0, 0, 0, 'a^19', 0, 'a^29', 0, 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0, 'data': '0.0208529945861', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(22)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.15236579220286459909242551956+0.0156087250802234221443937885496*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.32738014525', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.61830034418', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.03025622487', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.2817386114580709, 'bad_primes': [2, 3, 23], 'central_character': '276.131', 'conductor': 276, 'conductor_radical': 138, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/276/131'], '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': '1-276-276.131-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': '1-276-276.131-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2817386114580709, 'root_angle': 0.020852994586112145, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.32738014525', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_276.131', 'Lhash_array': ['dirichlet_L_276.131'], 'factors': ['1-276-276.131-r0-0-0'], 'label': '1-276-276.131-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/276/131'}
Lfunction data - 1-276-276.131-r0-0-0