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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_67.24', 'a10': [0.41541501300188644, 0.9096319953545183], 'a2': [-0.6548607339452851, -0.7557495743542583], 'a3': [0.41541501300188644, -0.9096319953545183], 'a4': [-0.14231483827328514, 0.9898214418809327], 'a5': [-0.9594929736144974, -0.28173255684142967], 'a6': [-0.9594929736144974, 0.28173255684142967], 'a7': [-0.6548607339452851, -0.7557495743542583], 'a8': [0.8412535328311812, -0.5406408174555976], 'a9': [-0.6548607339452851, -0.7557495743542583], 'algebraic': True, 'analytic_conductor': 0.311146691911923, 'analytic_normalization': 0, 'bad_lfactors': [[67, [1]]], 'bad_primes': [67], 'central_character': '67.24', 'coeff_info': ['x^11 - 1', '0.841253532831181 + 0.540640817455598*I', '\\\\zeta_{11}'], 'conductor': 67, 'conductor_radical': 67, 'conjugate': 'dirichlet_L_67.14', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^7', 'a^9', 'a^3', 'a^6', 'a^5', 'a^7', 'a^10', 'a^7', 'a^2', 'a^6', 'a^1', 'a^1', 'a^3', 'a^4', 'a^6', 'a^8', 'a^3', 'a^4', 'a^9', 'a^5', 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'191.23576879826254094732397650680', '191.34188067674498346523873901561', '192.26890717959443684298396090378', '193.33860615373146555553182874775', '194.44479432588632621249695234917', '194.82347800717671997280182982494', '195.84019853866551209714606476870', '196.85327000781054362601933470347', '197.5937677214694562837894629640', '198.39388500288058620579153959125', '199.42547545697609796407146814652'], 'prelabel': '1-67-67.24-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.311146691911923, 'root_angle': -0.4630767145967898, 'root_number': '-0.973209448409760866416154391863-0.229920354744787662521719721546*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.463076714597', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(11)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.424593604874782956860306155726-0.467728318684110058575993462152*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.722390443976', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.7525085087', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '4.05094172844', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.311146691911923, 'bad_primes': [67], 'central_character': '67.24', 'conductor': 67, 'conductor_radical': 67, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/67/24'], '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': '1-67-67.24-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': '1-67-67.24-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.311146691911923, 'root_angle': -0.4630767145967898, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.722390443976', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_67.24', 'Lhash_array': ['dirichlet_L_67.24'], 'factors': ['1-67-67.24-r0-0-0'], 'label': '1-67-67.24-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/67/24'}
Lfunction data - 1-67-67.24-r0-0-0