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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_571.509', 'a10': [0.13735355781840816, -0.9905220846375032], 'a2': [-0.59223525266498, -0.8057651056609781], 'a3': [-0.7541066097768963, -0.6567520240477344], 'a4': [-0.2985148110016945, 0.9544050018795074], 'a5': [0.7167825131684512, 0.6972968010939954], 'a6': [-0.08257934547233232, 0.9965844930066698], 'a7': [0.5469481581224269, -0.8371664782625285], 'a8': [0.9458172417006346, -0.3246994692046835], 'a9': [0.13735355781840816, 0.9905220846375032], 'algebraic': True, 'analytic_conductor': 2.6517128519657915, 'analytic_normalization': 0, 'bad_lfactors': [[571, [1]]], 'bad_primes': [571], 'central_character': '571.509', 'coeff_info': ['x^57 - 1', '0.993930677317949 + 0.110008220994079*I', '\\\\zeta_{57}'], 'conductor': 571, 'conductor_radical': 571, 'conjugate': 'dirichlet_L_571.396', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^37', 'a^35', 'a^17', 'a^7', 'a^15', 'a^48', 'a^54', 'a^13', 'a^44', 'a^32', 'a^52', 'a^8', 'a^28', 'a^42', 'a^34', 'a^34', 'a^50', 'a^35', 'a^24', 'a^26', 'a^12', 'a^3', 'a^32', 'a^14', 'a^45', 'a^48', 'a^8', 'a^46', 'a^22', 'a^15', 'a^14', 'a^10', 'a^14', 'a^55', 'a^30', 'a^49', 'a^15', 'a^43', 'a^4', 'a^7', 'a^6', 'a^44', 'a^49', 'a^20', 'a^40', 'a^53', 'a^12', 'a^39', 'a^51', 'a^12', 'a^25', 'a^20', 'a^28', 'a^39', 'a^45', 'a^13', 'a^26', 'a^48', 'a^2', 'a^56', 'a^52', 'a^4', 'a^51', 'a^15', 'a^47', 'a^1', 'a^51', 'a^38', 'a^35', 'a^38', 'a^10', 'a^11', 'a^29', 'a^49', 'a^52', 'a^23', 'a^23', 'a^2', 'a^41', 'a^26', 'a^44', 'a^53', 'a^43', 'a^41', 'a^24', 'a^24', 'a^29', 'a^34', 'a^0', 'a^56', 'a^20', 'a^50', 'a^33', 'a^42', 'a^49', 'a^17', 'a^19', 'a^45', 'a^31'], 'euler_factors': [[1, 'a^37'], [1, 'a^35'], [1, 'a^7'], [1, 'a^48'], [1, 'a^32'], [1, 'a^8'], [1, 'a^34'], [1, 'a^35'], [1, 'a^3'], [1, 'a^46'], [1, 'a^15'], [1, 'a^49'], [1, 'a^7'], [1, 'a^44'], [1, 'a^53'], [1, 'a^20'], [1, 'a^48'], [1, 'a^56'], [1, 'a^1'], [1, 'a^38'], [1, 'a^11'], [1, 'a^2'], [1, 'a^53'], [1, 'a^34'], [1, 'a^17'], [1, 'a^40']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-571-571.509-r0-0-0', 'leading_term': '0.555496676036543733358264677019-0.627748063305479051448963239154*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/571/509', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.8382387416908313, 0.6278555161984105, 0.20744304369387176, -0.4199201087889486, -0.8749566308692436, -0.7701000424160347, -0.10401182408931653, 0.6014353966746635, 0.5911570835706118, -0.5280486284720263, -2.315429928578688, -3.604356474954747, -3.2702271827979192, -1.1722475429257946, 1.5023881387293032, 2.925701753105708, 1.9706333385083132, -0.8188740497041449, -3.50990627405241, -4.230859186606737, -2.665917999899759, -0.3049572515506963, 0.848122261714599, 0.03470613188434584, -1.606840481544907, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.6517128519657915, 'bad_primes': [571], 'central_character': '571.509', 'conductor': 571, 'conductor_radical': 571, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/571/509'], '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': '1-571-571.509-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': '1-571-571.509-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6517128519657915, 'root_angle': -0.26941256122382207, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.732942076368', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_571.509', 'Lhash_array': ['dirichlet_L_571.509'], 'label': '1-571-571.509-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/571/509'}