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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_76.15', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.9396926207859084, 0.3420201433256687], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.17364817766693036, -0.984807753012208], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.5, 0.8660254037844386], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.766044443118978, -0.6427876096865394], 'algebraic': True, 'analytic_conductor': 0.35294251619859923, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [19, [1]]], 'bad_primes': [2, 19], 'central_character': '76.15', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 76, 'conductor_radical': 38, 'conjugate': 'dirichlet_L_76.71', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^26', 0, 'a^14', 0, 'a^21', 0, 'a^16', 0, 'a^15', 0, 'a^1', 0, 'a^22', 0, 'a^2', 0, 0, 0, 'a^11', 0, 'a^13', 0, 'a^10', 0, 'a^24', 0, 'a^7', 0, 'a^12', 0, 'a^5', 0, 'a^17', 0, 'a^9', 0, 'a^9', 0, 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'192.02116646672390308189710091989', '192.230009964275172194622296360094', '192.9757457273240758426958471217', '193.82840641106225324180135406772', '194.93304309785232873065660933169', '195.254823497241332734084541804719', '196.29879065192710925621199739077', '196.93196616419287889335809640346', '198.07474432866254548885638006309', '199.025004415880569197453775983340', '199.64149683671968230941548444589'], 'prelabel': '1-76-76.15-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.35294251619859923, 'root_angle': -0.019163368314845542, 'root_number': '0.992759831450808727819719377972-0.120116264751122884346980219288*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0191633683148', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(18)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.889053561819422050317307985967+0.0183537808416836338423537107732*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.39845297492', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.96460373979', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.36491213542', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.35294251619859923, 'bad_primes': [2, 19], 'central_character': '76.15', 'conductor': 76, 'conductor_radical': 38, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/76/15'], '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': '1-76-76.15-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': '1-76-76.15-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.35294251619859923, 'root_angle': -0.019163368314845542, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.39845297492', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_76.15', 'Lhash_array': ['dirichlet_L_76.15'], 'factors': ['1-76-76.15-r0-0-0'], 'label': '1-76-76.15-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/76/15'}
Lfunction data - 1-76-76.15-r0-0-0