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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_147.71', 'a10': [-0.9009688679024191, 0.4338837391175581], 'a2': [-0.6234898018587335, 0.7818314824680298], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.2225209339563144, -0.9749279121818236], 'a5': [0.9009688679024191, 0.4338837391175581], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.9009688679024191, 0.4338837391175581], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 15.797343944809878, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '147.71', 'coeff_info': ['x^14 - 1', '0.900968867902419 + 0.433883739117558*I', '\\\\zeta_{14}'], 'conductor': 147, 'conductor_radical': 21, 'conjugate': 'dirichlet_L_147.29', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^5', 0, 'a^10', 'a^1', 0, 0, 'a^1', 0, 'a^6', 'a^5', 0, 'a^12', 0, 0, 'a^6', 'a^11', 0, 'a^0', 'a^11', 0, 'a^10', 'a^3', 0, 'a^2', 'a^3', 0, 0, 'a^11', 0, 'a^0', 'a^11', 0, 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'196.732485105819619302834202181272', '197.3425228791819433835556161373', '198.08251645966159055150294385428', '198.65547207639945503357727326372', '199.4904442249392700043228415799'], 'prelabel': '1-147-147.71-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.797343944809878, 'root_angle': 0.40816326530612246, 'root_number': '0.284527586631032441870502993463+0.958667853036660622150983388310*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.204081632653', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(14)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.903864462627770131455143515158+0.392597581834809345735131373730*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.16479338495', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.77081184286', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.96465728302', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 15.797343944809878, 'bad_primes': [3, 7], 'central_character': '147.71', 'conductor': 147, 'conductor_radical': 21, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/147/71'], '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': '1-147-147.71-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-147-147.71-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.797343944809878, 'root_angle': 0.20408163265306123, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.16479338495', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_147.71', 'Lhash_array': ['dirichlet_L_147.71'], 'label': '1-147-147.71-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/147/71'}
Lfunction data - 1-147-147.71-r1-0-0