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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_169.12', 'a10': [0.8854560256532099, 0.46472317204376856], 'a2': [0.3546048870425356, -0.9350162426854148], 'a3': [0.5680647467311558, 0.8229838658936564], 'a4': [-0.7485107481711011, -0.6631226582407952], 'a5': [-0.12053668025532305, 0.992708874098054], 'a6': [0.970941817426052, -0.23931566428755777], 'a7': [-0.8854560256532099, 0.46472317204376856], 'a8': [-0.8854560256532099, 0.46472317204376856], 'a9': [-0.3546048870425356, 0.9350162426854148], 'algebraic': True, 'analytic_conductor': 0.7848327004942536, 'analytic_normalization': 0, 'bad_lfactors': [[13, [1]]], 'bad_primes': [13], 'central_character': '169.12', 'coeff_info': ['x^26 - 1', '0.970941817426052 + 0.239315664287558*I', '\\\\zeta_{26}'], 'conductor': 169, 'conductor_radical': 13, 'conjugate': 'dirichlet_L_169.155', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^21', 'a^4', 'a^16', 'a^7', 'a^25', 'a^11', 'a^11', 'a^8', 'a^2', 'a^5', 'a^20', 0, 'a^6', 'a^11', 'a^6', 'a^24', 'a^3', 'a^13', 'a^23', 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'st_group': 'mu(26)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.17353306350730102103286851559+0.118898407633445280338004755368*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.28364497545', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.1499366274', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '4.11559400731', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.7848327004942536, 'bad_primes': [13], 'central_character': '169.12', 'conductor': 169, 'conductor_radical': 13, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/169/12'], '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': '1-13e2-169.12-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': '1-13e2-169.12-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7848327004942536, 'root_angle': 0.13609467455621305, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.28364497545', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_169.12', 'Lhash_array': ['dirichlet_L_169.12'], 'factors': ['1-13e2-169.12-r0-0-0'], 'label': '1-13e2-169.12-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/169/12'}
Lfunction data - 1-13e2-169.12-r0-0-0