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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_5328.4045', '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': [-0.3420201433256687, 0.9396926207859084], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.17364817766693036, -0.984807753012208], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 24.743127977712323, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [37, [1]]], 'bad_primes': [2, 3, 37], 'central_character': '5328.4045', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 5328, 'conductor_radical': 222, 'conjugate': 'dirichlet_L_5328.5029', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^47', 0, 'a^26', 0, 0, 0, 'a^51', 0, 'a^17', 0, 0, 0, 'a^16', 0, 'a^17', 0, 0, 0, 'a^30', 0, 'a^22', 0, 0, 0, 'a^33', 0, 'a^24', 0, 0, 0, 'a^37', 0, 0, 0, 0, 0, 'a^26', 0, 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'194.53228644466020819614164102408', '194.92312263666476562277790213656', '195.24431996235493613722548669570', '196.117778427912477071341703992745', '196.53106073511234127467866144026', '197.052886425013925497799195449367', '197.753440516940226010854275060456', '198.139397037690966675404161505021', '198.549823031388035482808345663499', '198.97141758534032503332298594453', '199.64415796814252292262627701219'], 'prelabel': '1-5328-5328.4045-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 24.743127977712323, 'root_angle': 0.19088039225177852, 'root_number': '0.362975732224469446432621945125+0.931798592945981139556015594838*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.745904893424078234004736113402+0.0560097078172788782246927645077*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.587549752205', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.19698203464', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.40903309305', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 24.743127977712323, 'bad_primes': [2, 3, 37], 'central_character': '5328.4045', 'conductor': 5328, 'conductor_radical': 222, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/5328/4045'], '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': '1-5328-5328.4045-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': '1-5328-5328.4045-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 24.743127977712323, 'root_angle': 0.19088039225177852, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.587549752205', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_5328.4045', 'Lhash_array': ['dirichlet_L_5328.4045'], 'factors': ['1-5328-5328.4045-r0-0-0'], 'label': '1-5328-5328.4045-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/5328/4045'}
Lfunction data - 1-5328-5328.4045-r0-0-0