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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1521.241', 'a10': [0.8451900855437947, 0.5344658261278011], 'a2': [-0.16041128085776024, 0.9870502626379128], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.9485364419471455, -0.3166679938014725], 'a5': [0.3919666098600751, -0.9199794436588242], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.46472317204376856, -0.8854560256532099], 'a8': [0.46472317204376856, -0.8854560256532099], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 163.45415061262466, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [13, [1]]], 'bad_primes': [3, 13], 'central_character': '1521.241', 'coeff_info': ['x^156 - 1', '0.999188998171570 + 0.0402659401094151*I', '\\\\zeta_{156}'], 'conductor': 1521, 'conductor_radical': 39, 'conjugate': 'dirichlet_L_1521.1237', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^43', 0, 'a^86', 'a^127', 0, 'a^129', 'a^129', 0, 'a^14', 'a^61', 0, 0, 'a^16', 0, 'a^16', 'a^142', 0, 'a^91', 'a^57', 0, 'a^104', 'a^78', 0, 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'196.96116208096518450636479927576', '197.30398435868983077201047786253', '198.19749681066634130704446429125', '198.612836164273549210474819927133', '198.95385887136547887316604909766', '199.80523419546842031240042106816'], 'prelabel': '1-39e2-1521.241-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 163.45415061262466, 'root_angle': -0.13823142669296515, 'root_number': '0.645946612680402533598995974317-0.763382586627907063885925398205*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.138231426693', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(156)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.00843108564072698112005940394+0.0874217798563502618159951827654*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.467093607922', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.17181363259', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.43714693326', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 163.45415061262466, 'bad_primes': [3, 13], 'central_character': '1521.241', 'conductor': 1521, 'conductor_radical': 39, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1521/241'], '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': '1-39e2-1521.241-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': '1-39e2-1521.241-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 163.45415061262466, 'root_angle': -0.13823142669296515, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.467093607922', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1521.241', 'Lhash_array': ['dirichlet_L_1521.241'], 'factors': ['1-39e2-1521.241-r1-0-0'], 'label': '1-39e2-1521.241-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1521/241'}
Lfunction data - 1-39e2-1521.241-r1-0-0