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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_287.184', 'a10': [0.6691306063588582, 0.7431448254773942], 'a2': [0.10452846326765347, -0.9945218953682733], 'a3': [0.8660254037844386, 0.5], 'a4': [-0.9781476007338057, -0.20791169081775934], 'a5': [-0.6691306063588582, 0.7431448254773942], 'a6': [0.5877852522924731, -0.8090169943749475], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.30901699437494745, 0.9510565162951535], 'a9': [0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [41, [1]]], 'bad_primes': [7, 41], 'central_character': '287.184', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 287, 'conductor_radical': 287, 'conjugate': 'dirichlet_L_287.39', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^46', 'a^5', 'a^32', 'a^22', 'a^51', 0, 'a^18', 'a^10', 'a^8', 'a^53', 'a^37', 'a^21', 0, 'a^27', 'a^4', 'a^23', 'a^56', 'a^19', 'a^54', 0, 'a^39', 'a^16', 'a^23', 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'197.733772502450604104920833879247', '198.07628579687401529857609316325', '198.87484283034847704910202815457', '199.43061175690675632637315144492'], 'prelabel': '1-287-287.184-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': 0.08545907622106032, 'root_number': '0.859270138211815425806022255621+0.511522071447017441041728405849*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0854590762211', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.14994834744644743615117859848-0.0418934464808158989317489476676*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.76617959879', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.9249204', 'prec': 30}, 'z3': {'__RealLiteral__': 0, 'data': '3.83815362591', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'bad_primes': [7, 41], 'central_character': '287.184', 'conductor': 287, 'conductor_radical': 287, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/287/184'], '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': '1-287-287.184-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': '1-287-287.184-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': 0.08545907622106032, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.76617959879', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_287.184', 'Lhash_array': ['dirichlet_L_287.184'], 'factors': ['1-287-287.184-r0-0-0'], 'label': '1-287-287.184-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/287/184'}
Lfunction data - 1-287-287.184-r0-0-0