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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_37.9', 'a10': [-0.5, -0.8660254037844386], 'a2': [-0.9396926207859084, 0.3420201433256687], 'a3': [-0.9396926207859084, -0.3420201433256687], 'a4': [0.766044443118978, -0.6427876096865394], 'a5': [0.17364817766693036, 0.984807753012208], 'a6': [1.0, 0.0], 'a7': [0.17364817766693036, 0.984807753012208], 'a8': [-0.5, 0.8660254037844386], 'a9': [0.766044443118978, 0.6427876096865394], 'algebraic': True, 'analytic_conductor': 0.17182727762300226, 'analytic_normalization': 0, 'bad_lfactors': [[37, [1]]], 'bad_primes': [37], 'central_character': '37.9', 'coeff_info': ['x^9 - 1', '0.766044443118978 + 0.642787609686539*I', '\\\\zeta_{9}'], 'conductor': 37, 'conductor_radical': 37, 'conjugate': 'dirichlet_L_37.33', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^4', 'a^5', 'a^8', 'a^2', 'a^0', 'a^2', 'a^3', 'a^1', 'a^6', 'a^3', 'a^4', 'a^8', 'a^6', 'a^7', 'a^7', 'a^1', 'a^5', 'a^5', 'a^1', 'a^7', 'a^7', 'a^6', 'a^8', 'a^4', 'a^3', 'a^6', 'a^1', 'a^3', 'a^2', 'a^0', 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'186.45273811380154446064098253762', '187.349406942371955613501608572551', '188.19135392530164881151175452717', '189.17281403463830598732617958060', '189.951661236200838083492164407875', '190.16719064201857755827437192349', '191.30267678200920222805672906188', '192.5140727862493054352322932830', '193.36439153559906060548080673279', '194.2357505922348318372712475005', '195.20891186551332054435801146481', '196.41850962562953280752472557599', '196.67037187511976402097530324108', '198.20252362524686228090501088230', '198.94619427803562938364123799395', '199.306814794395772885359590453689'], 'prelabel': '1-37-37.9-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.17182727762300226, 'root_angle': 0.40025610996241534, 'root_number': '0.308251680849906875713625273202+0.951304841390606586622285683497*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.200128054981', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(9)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.514113567962511462983881523967+0.189025261133763789224245278289*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.16828332359', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '5.585658775', 'prec': 37}, 'z3': {'__RealLiteral__': 0, 'data': '6.65682600505', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.17182727762300226, 'bad_primes': [37], 'central_character': '37.9', 'conductor': 37, 'conductor_radical': 37, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/37/9'], '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': '1-37-37.9-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': '1-37-37.9-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.17182727762300226, 'root_angle': 0.20012805498120767, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.16828332359', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_37.9', 'Lhash_array': ['dirichlet_L_37.9'], 'label': '1-37-37.9-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/37/9'}
Lfunction data - 1-37-37.9-r0-0-0