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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_837.137', 'a10': [-0.9781476007338057, 0.20791169081775934], 'a2': [0.6156614753256583, -0.7880107536067219], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.24192189559966773, -0.9702957262759965], 'a5': [-0.766044443118978, -0.6427876096865394], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.5591929034707468, 0.8290375725550417], 'a8': [-0.9135454576426009, -0.4067366430758002], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [31, [1]]], 'bad_primes': [3, 31], 'central_character': '837.137', 'coeff_info': ['x^90 - 1', '0.997564050259824 + 0.0697564737441253*I', '\\\\zeta_{90}'], 'conductor': 837, 'conductor_radical': 93, 'conjugate': 'dirichlet_L_837.446', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^77', 0, 'a^64', 'a^55', 0, 'a^14', 'a^51', 0, 'a^42', 'a^14', 0, 'a^43', 'a^1', 0, 'a^38', 'a^36', 0, 'a^12', 'a^29', 0, 'a^1', 'a^46', 0, 'a^20', 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'193.3528591633613154286171441667', '193.694172767500563591469075120165', '194.79956198601328976206220377497', '195.23867652337776182857095299459', '195.62855317217345736097005115930', '196.22866037674788969107042972570', '196.60579275796179144177139893612', '197.68162483857334321196281348575', '198.48058911134305002367681009919', '199.01505444936000397425599219470', '199.641817527188732831834476266082'], 'prelabel': '1-837-837.137-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': 0.22518315473963732, 'root_number': '0.760032148903869303134210518245+0.649885476551497217129804572997*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.11259157737', 'prec': 44}, 'spectral_label': 'r0-0', 'st_group': 'mu(90)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.01118749380968106846866174519-0.293300870582662904945003978216*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.48144909265', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.17198048851', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.49047896695', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'bad_primes': [3, 31], 'central_character': '837.137', 'conductor': 837, 'conductor_radical': 93, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/837/137'], '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': '1-837-837.137-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': '1-837-837.137-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': 0.11259157736981866, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.48144909265', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_837.137', 'Lhash_array': ['dirichlet_L_837.137'], 'label': '1-837-837.137-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/837/137'}
Lfunction data - 1-837-837.137-r0-0-0