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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_5600.5221', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.8910065241883679, 0.4539904997395468], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.5877852522924731, 0.8090169943749475], 'algebraic': True, 'analytic_conductor': 601.8035788499001, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [7, [1]]], 'bad_primes': [2, 5, 7], 'central_character': '5600.5221', 'coeff_info': ['x^40 - 1', '0.987688340595138 + 0.156434465040231*I', '\\\\zeta_{40}'], 'conductor': 5600, 'conductor_radical': 70, 'conjugate': 'dirichlet_L_5600.1581', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^43', 0, 0, 0, 0, 0, 'a^46', 0, 'a^49', 0, 'a^71', 0, 0, 0, 'a^32', 0, 'a^47', 0, 0, 0, 'a^54', 0, 0, 0, 'a^9', 0, 'a^23', 0, 'a^12', 0, 'a^12', 0, 0, 0, 'a^21', 0, 'a^34', 0, 'a^66', 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'193.97386492533592238806548751583', '194.85215760046440118916819268457', '195.55030311111810722923388080625', '195.9427723813843115132011674529', '196.32788725116348996992133328336', '196.98980694580144253502125935626', '197.39542434925709863511206317807', '198.1591201293978938166779615632', '198.288321375212237769592906563087', '198.785245621747221122552838823822', '199.46311934504628708012174302056'], 'prelabel': '1-5600-5600.5221-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 601.8035788499001, 'root_angle': -0.30375, 'root_number': '-0.331337888462570987145226672537-0.943512164028193580302205883358*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'r1-0', 'st_group': 'mu(40)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.26229829211097668147100049080+0.240963295368354895560182442089*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.0807932819698', 'prec': 50}, 'z2': {'__RealLiteral__': 0, 'data': '1.40712823889', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '1.99549012185', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 601.8035788499001, 'bad_primes': [2, 5, 7], 'central_character': '5600.5221', 'conductor': 5600, 'conductor_radical': 70, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/5600/5221'], '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': '1-5600-5600.5221-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': '1-5600-5600.5221-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 601.8035788499001, 'root_angle': -0.30375, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0807932819698', 'prec': 50}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_5600.5221', 'Lhash_array': ['dirichlet_L_5600.5221'], 'factors': ['1-5600-5600.5221-r1-0-0'], 'label': '1-5600-5600.5221-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/5600/5221'}
Lfunction data - 1-5600-5600.5221-r1-0-0