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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_837.175', 'a10': [-0.8090169943749475, 0.5877852522924731], 'a2': [0.5591929034707468, -0.8290375725550417], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.374606593415912, -0.9271838545667874], 'a5': [-0.9396926207859084, -0.3420201433256687], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.882947592858927, -0.46947156278589075], 'a8': [-0.9781476007338057, -0.20791169081775934], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [31, [1]]], 'bad_primes': [3, 31], 'central_character': '837.175', 'coeff_info': ['x^45 - 1', '0.990268068741570 + 0.139173100960065*I', '\\\\zeta_{45}'], 'conductor': 837, 'conductor_radical': 93, 'conjugate': 'dirichlet_L_837.727', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^38', 0, 'a^31', 'a^25', 0, 'a^26', 'a^24', 0, 'a^18', 'a^41', 0, 'a^22', 'a^19', 0, 'a^17', 'a^24', 0, 'a^18', 'a^11', 0, 'a^34', 'a^4', 0, 'a^5', 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'192.87552453195137752201930023837', '193.2293314533872969228572012343', '194.19223359447630743101037341716', '194.440098113790551929338151978439', '195.149413360660582920775952023955', '195.72973963381312020952028031193', '196.19829802758619267733310932375', '196.89218420975764521986546675896', '197.769824525852435100512073349776', '198.18680521965374071831177160887', '199.25602099496617599725945946404', '199.75123802180948870379555733944'], 'prelabel': '1-837-837.175-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': 0.16255299544167204, 'root_number': '0.522214623479177205430315013460+0.852814098748667020067201025451*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.162552995442', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(45)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.635860769282722684840122005646-0.454072764938715466298423266954*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.15464235846', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.5673311553', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.54629745884', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'bad_primes': [3, 31], 'central_character': '837.175', 'conductor': 837, 'conductor_radical': 93, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/837/175'], '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': '1-837-837.175-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': '1-837-837.175-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': 0.16255299544167204, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.15464235846', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_837.175', 'Lhash_array': ['dirichlet_L_837.175'], 'factors': ['1-837-837.175-r0-0-0'], 'label': '1-837-837.175-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/837/175'}
Lfunction data - 1-837-837.175-r0-0-0