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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_571.117', 'a10': [-0.9345644645994609, -0.3557938469225165], 'a2': [-0.9863613034027223, 0.1645945902807339], 'a3': [-0.724425204791089, -0.6893534091185659], 'a4': [0.9458172417006346, -0.3246994692046835], 'a5': [0.8632564809575739, 0.5047655377348437], 'a6': [0.82800883114802, 0.5607150573516727], 'a7': [-0.9733265972480059, 0.22942392004675158], 'a8': [-0.8794737512064891, 0.47594739303707356], 'a9': [0.049583754673222305, 0.9987699691483047], 'algebraic': True, 'analytic_conductor': 2.6517128519657915, 'analytic_normalization': 0, 'bad_lfactors': [[571, [1]]], 'bad_primes': [571], 'central_character': '571.117', 'coeff_info': ['x^95 - 1', '0.997813627218775 + 0.0660905843256994*I', '\\\\zeta_{95}'], 'conductor': 571, 'conductor_radical': 571, 'conjugate': 'dirichlet_L_571.449', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^45', 'a^59', 'a^90', 'a^8', 'a^9', 'a^44', 'a^40', 'a^23', 'a^53', 'a^42', 'a^54', 'a^58', 'a^89', 'a^67', 'a^85', 'a^47', 'a^68', 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'gamma_factors': [[0], []], 'index': 0, 'label': '1-571-571.117-r0-0-0', 'leading_term': '0.551149661663688839846244777665+0.00565616934991077475656802650321*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/571/117', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.5511786840977377, 0.5222805895264935, 0.2027911120054168, -0.544112237099144, -1.4350655637135739, -1.9131696282320507, -1.580385790951305, -0.639603347029554, 0.011692415338906794, -0.7536630935605084, -3.456951769066861, -7.377822157408919, -10.700612227044505, -11.534651196477567, -9.198826238927568, -4.8147565568982715, -0.6507059813378802, 1.399239437893442, 1.0650734260112908, -0.3194452787015925, -1.087975156297785, -0.6656418182649689, 0.10694692220617501, 0.011086800252579337, -1.173746018160076, 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'198.95336249950780680989639978967', '199.65891300825495875790111325111'], 'prelabel': '1-571-571.117-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6517128519657915, 'root_angle': 0.006533076387116266, 'root_number': '0.999789384671107873772433937269+0.0205228238546133830191690168576*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.00326653819356', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(95)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.537424924226188356902039326880+0.0165770062318949421081047712566*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.727471327948', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.47743603513', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.56672970415', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.6517128519657915, 'bad_primes': [571], 'central_character': '571.117', 'conductor': 571, 'conductor_radical': 571, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/571/117'], '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': '1-571-571.117-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': '1-571-571.117-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6517128519657915, 'root_angle': 0.003266538193558133, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.727471327948', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_571.117', 'Lhash_array': ['dirichlet_L_571.117'], 'label': '1-571-571.117-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/571/117'}
Lfunction data - 1-571-571.117-r0-0-0