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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_175.47', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.9945218953682733, -0.10452846326765347], 'a3': [0.20791169081775934, -0.9781476007338057], 'a4': [0.9781476007338057, 0.20791169081775934], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.30901699437494745, 0.9510565162951535], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.9510565162951535, -0.30901699437494745], 'a9': [-0.9135454576426009, -0.4067366430758002], 'algebraic': True, 'analytic_conductor': 0.8126965833520376, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [7, [1]]], 'bad_primes': [5, 7], 'central_character': '175.47', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 175, 'conductor_radical': 35, 'conjugate': 'dirichlet_L_175.108', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^31', 'a^47', 'a^2', 0, 'a^18', 0, 'a^33', 'a^34', 0, 'a^56', 'a^49', 'a^39', 0, 0, 'a^4', 'a^53', 'a^5', 'a^28', 0, 0, 'a^27', 'a^1', 'a^20', 0, 'a^10', 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'188.29786434969076197056622533844', '189.068761923619081656006436859090', '189.640373053849474846744712550903', '190.00829552245560717304274205965', '191.17870052902443243973965072941', '191.28970419523715647018351416692', '192.22011152017251443599367073517', '192.79965988869172202031115990590', '194.01561424826163831738488750486', '194.37807049889943797757323601519', '195.71051986856904444253273891211', '196.06729736342496395450538281132', '196.85411124703018230703271213573', '197.66201467084629133917015342706', '198.11209869057700744959493860182', '198.977714095608733830714386975575', '199.96931407896653756897458918684'], 'prelabel': '1-175-175.47-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8126965833520376, 'root_angle': -0.6270125727745589, 'root_number': '-0.388517142524689812691895555894-0.921441495681874456572311544346*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.313506286387', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.629452967321125351208856388457-0.358889378461614315487430930065*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.787136083956', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.18022532237', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.3817831193', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.8126965833520376, 'bad_primes': [5, 7], 'central_character': '175.47', 'conductor': 175, 'conductor_radical': 35, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/175/47'], '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': '1-175-175.47-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': '1-175-175.47-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8126965833520376, 'root_angle': -0.31350628638727945, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.787136083956', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_175.47', 'Lhash_array': ['dirichlet_L_175.47'], 'label': '1-175-175.47-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/175/47'}
Lfunction data - 1-175-175.47-r0-0-0