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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_37.16', 'a10': [-0.5, -0.8660254037844386], 'a2': [0.766044443118978, 0.6427876096865394], 'a3': [0.766044443118978, -0.6427876096865394], 'a4': [0.17364817766693036, 0.984807753012208], 'a5': [-0.9396926207859084, -0.3420201433256687], 'a6': [1.0, 0.0], 'a7': [-0.9396926207859084, -0.3420201433256687], 'a8': [-0.5, 0.8660254037844386], 'a9': [0.17364817766693036, -0.984807753012208], 'algebraic': True, 'analytic_conductor': 0.17182727762300226, 'analytic_normalization': 0, 'bad_lfactors': [[37, [1]]], 'bad_primes': [37], 'central_character': '37.16', 'coeff_info': ['x^9 - 1', '0.766044443118978 + 0.642787609686539*I', '\\\\zeta_{9}'], 'conductor': 37, 'conductor_radical': 37, 'conjugate': 'dirichlet_L_37.7', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 'a^8', 'a^2', 'a^5', 'a^0', 'a^5', 'a^3', 'a^7', 'a^6', 'a^3', 'a^1', 'a^2', 'a^6', 'a^4', 'a^4', 'a^7', 'a^8', 'a^8', 'a^7', 'a^4', 'a^4', 'a^6', 'a^2', 'a^1', 'a^3', 'a^6', 'a^7', 'a^3', 'a^5', 'a^0', 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'186.218036454094809910804118132433', '186.902299118454634595955785378414', '187.80600916346019363279709595834', '188.46385282003358280200708974320', '189.72056522902983669798567853939', '190.84196658845080406722714830433', '191.0176136834180946676438938843', '192.51132994760079566149045701068', '193.290779678304115866152808977190', '194.48144305425646673145181490326', '195.2887715899064669081145907175', '195.94608712913901298960649352434', '196.67772147181937232033004424915', '197.53845801400080484658144108483', '198.270513449421663381155721279655', '199.266824962093351579444972270083'], 'prelabel': '1-37-37.16-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.17182727762300226, 'root_angle': 0.06474618605770664, 'root_number': '0.918386813954814531228921396113+0.395683787833068643916271526019*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0647461860577', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(9)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.34742023934805778281315745095+0.228750720767339498308280964907*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.98263622148', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.44608025964', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '6.76586612623', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.17182727762300226, 'bad_primes': [37], 'central_character': '37.16', 'conductor': 37, 'conductor_radical': 37, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/37/16'], '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': '1-37-37.16-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': '1-37-37.16-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.17182727762300226, 'root_angle': 0.06474618605770664, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.98263622148', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_37.16', 'Lhash_array': ['dirichlet_L_37.16'], 'factors': ['1-37-37.16-r0-0-0'], 'label': '1-37-37.16-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/37/16'}
Lfunction data - 1-37-37.16-r0-0-0