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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_837.202', 'a10': [-0.9781476007338057, 0.20791169081775934], 'a2': [0.03489949670250097, 0.9993908270190958], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.9975640502598242, 0.0697564737441253], 'a5': [0.17364817766693036, 0.984807753012208], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.24192189559966773, -0.9702957262759965], 'a8': [-0.10452846326765347, -0.9945218953682733], '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': '837.202', 'coeff_info': ['x^45 - 1', '0.990268068741570 + 0.139173100960065*I', '\\\\zeta_{45}'], 'conductor': 837, 'conductor_radical': 93, 'conjugate': 'dirichlet_L_837.808', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^11', 0, 'a^22', 'a^10', 0, 'a^32', 'a^33', 0, 'a^21', 'a^17', 0, 'a^34', 'a^43', 0, 'a^44', 'a^3', 0, 'a^6', 'a^32', 0, 'a^28', 'a^13', 0, 'a^20', 'a^0', 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'194.27834559084539943142939501702', '194.6930954159156665292878492526', '195.61990119172635171371898999681', '195.98865035436213776298412535609', '196.94528982565454740345424083751', '197.20441515633186161141658091934', '197.88996617656464751432731970769', '198.49583148013883784109539241492', '198.84642151364260170286688860258', '199.504359722887893034446077505416'], 'prelabel': '1-837-837.202-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': -0.9767644831036458, 'root_number': '-0.997336936188465367598883926650-0.0729317195341297258660329692256*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.488382241552', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(45)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.646949973470325154056451071018+0.560985777595410366055128343994*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.38748078147', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.161448271', 'prec': 37}, 'z3': {'__RealLiteral__': 0, 'data': '3.69037717499', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'bad_primes': [3, 31], 'central_character': '837.202', 'conductor': 837, 'conductor_radical': 93, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/837/202'], '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': '1-837-837.202-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': '1-837-837.202-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': -0.4883822415518229, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.38748078147', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_837.202', 'Lhash_array': ['dirichlet_L_837.202'], 'label': '1-837-837.202-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/837/202'}
Lfunction data - 1-837-837.202-r0-0-0