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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_287.87', 'a10': [-0.9135454576426009, -0.4067366430758002], 'a2': [-0.6691306063588582, -0.7431448254773942], 'a3': [-0.8660254037844386, 0.5], 'a4': [-0.10452846326765347, 0.9945218953682733], 'a5': [0.9135454576426009, -0.4067366430758002], 'a6': [0.9510565162951535, 0.30901699437494745], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.8090169943749475, -0.5877852522924731], 'a9': [0.5, -0.8660254037844386], 'algebraic': True, 'analytic_conductor': 30.842433416057382, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [41, [1]]], 'bad_primes': [7, 41], 'central_character': '287.87', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 287, 'conductor_radical': 287, 'conjugate': 'dirichlet_L_287.33', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^38', 'a^25', 'a^16', 'a^56', 'a^3', 0, 'a^54', 'a^50', 'a^34', 'a^19', 'a^41', 'a^33', 0, 'a^21', 'a^32', 'a^19', 'a^28', 'a^47', 'a^12', 0, 'a^57', 'a^8', 'a^19', 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'196.120129270409497122818017397299', '196.93931092058649031264063002088', '197.805208544532373943148483824997', '198.40728248470450292270903534328', '199.16750634468510705689267287394', '199.50729438831506415006504046404'], 'prelabel': '1-287-287.87-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 30.842433416057382, 'root_angle': 0.49940008811350484, 'root_number': '-0.999992895980238203880517558521+0.00376934862496101081656877064649*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.499400088114', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.542459576899657840136977754853-0.118993345841413514687138400702*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.0868368114568', 'prec': 50}, 'z2': {'__RealLiteral__': 0, 'data': '1.4949970809', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.71389149982', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 30.842433416057382, 'bad_primes': [7, 41], 'central_character': '287.87', 'conductor': 287, 'conductor_radical': 287, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/287/87'], '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': '1-287-287.87-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': '1-287-287.87-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 30.842433416057382, 'root_angle': 0.49940008811350484, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0868368114568', 'prec': 50}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_287.87', 'Lhash_array': ['dirichlet_L_287.87'], 'factors': ['1-287-287.87-r1-0-0'], 'label': '1-287-287.87-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/287/87'}
Lfunction data - 1-287-287.87-r1-0-0