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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_185.123', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.984807753012208, -0.17364817766693036], 'a3': [-0.984807753012208, 0.17364817766693036], 'a4': [0.9396926207859084, 0.3420201433256687], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, 0.0], 'a7': [-0.6427876096865394, -0.766044443118978], 'a8': [-0.8660254037844386, -0.5], 'a9': [0.9396926207859084, -0.3420201433256687], 'algebraic': True, 'analytic_conductor': 19.88101108700563, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [37, [1]]], 'bad_primes': [5, 37], 'central_character': '185.123', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 185, 'conductor_radical': 185, 'conjugate': 'dirichlet_L_185.182', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^19', 'a^17', 'a^2', 0, 'a^0', 'a^23', 'a^21', 'a^34', 0, 'a^12', 'a^19', 'a^29', 'a^6', 0, 'a^4', 'a^7', 'a^17', 'a^26', 0, 'a^4', 'a^31', 'a^33', 'a^2', 0, 'a^12', 'a^15', 'a^25', 'a^30', 0, 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'187.5146858118329553778538041772', '188.07398710716565191347543944348', '188.53361081152182474412459348503', '189.50369135545064149541457702510', '189.89136658290340622154781473511', '190.91358055619014238245649781818', '191.19982217680462246334965180443', '192.31716173261794576691157834998', '192.97449368016555401261408886299', '193.61763423417717978769213591217', '194.40839006353264695625289352166', '194.75893588883984203082552260298', '196.10235200630465681244926599903', '196.71487931905039600350194008900', '197.37415516402372731990928225178', '198.49879872813384925698151344720', '198.82343463700054010173547425301', '199.43189830153791249669545072659'], 'prelabel': '1-185-185.123-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.88101108700563, 'root_angle': 0.8583303711065514, 'root_number': '-0.902581277927198588657530305627+0.430519496347500037086965817198*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.429165185553', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.423170339577914842367847583195-0.0467298174951979870410012514641*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.16893889787', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.01354609048', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.54233310095', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 19.88101108700563, 'bad_primes': [5, 37], 'central_character': '185.123', 'conductor': 185, 'conductor_radical': 185, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/185/123'], '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': '1-185-185.123-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-185-185.123-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.88101108700563, 'root_angle': 0.4291651855532757, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.16893889787', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_185.123', 'Lhash_array': ['dirichlet_L_185.123'], 'label': '1-185-185.123-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/185/123'}
Lfunction data - 1-185-185.123-r1-0-0