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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_4033.2127', 'a10': [0.44879918020046217, 0.8936326403234123], 'a2': [0.5, -0.8660254037844386], 'a3': [0.6862416378687336, -0.7273736415730487], 'a4': [-0.5, -0.8660254037844386], 'a5': [-0.549508978070806, 0.8354878114129364], 'a6': [-0.28680323271109026, -0.9579895123154889], 'a7': [-0.05814482891047583, 0.9983081582712682], 'a8': [-1.0, -1.4081532572346456e-30], 'a9': [-0.05814482891047583, -0.9983081582712682], 'algebraic': True, 'analytic_conductor': 18.729173260907245, 'analytic_normalization': 0, 'bad_lfactors': [[37, [1]], [109, [1]]], 'bad_primes': [37, 109], 'central_character': '4033.2127', 'coeff_info': ['x^108 - 1', '0.998308158271268 + 0.0581448289104758*I', '\\\\zeta_{108}'], 'conductor': 4033, 'conductor_radical': 4033, 'conjugate': 'dirichlet_L_4033.146', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^90', 'a^94', 'a^72', 'a^37', 'a^76', 'a^28', 'a^54', 'a^80', 'a^19', 'a^35', 'a^58', 'a^10', 'a^10', 'a^23', 'a^36', 'a^0', 'a^62', 'a^6', 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[[0], []], 'index': 0, 'label': '1-4033-4033.2127-r0-0-0', 'leading_term': '1.07124579945656696233722313822+0.582443264289067970153977051333*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/4033/2127', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.2193472511836179, 2.4226126707725095, 2.9798686656365088, 2.0889302420170286, 0.316848157552901, -0.7777694208572272, -0.4415072155509279, 0.4054603000677063, 0.397344116600847, -0.4461321053083015, -0.7896574713077573, -0.06327367889674092, 0.3378810072983909, -1.1461272687401314, -3.5520190375436647, -3.88807121167963, -0.9637546681055329, 2.4186220042510866, 2.5639232504456517, -0.2326371642426073, -1.7954016203874092, 0.3549371455159541, 3.4272848335657913, 3.1276595863202044, -0.19406235133678704, -1.8767821466445773, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.729173260907245, 'bad_primes': [37, 109], 'central_character': '4033.2127', 'conductor': 4033, 'conductor_radical': 4033, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4033/2127'], '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': '1-4033-4033.2127-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': '1-4033-4033.2127-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.729173260907245, 'root_angle': 0.1585178405142496, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.3118095051', 'prec': 40}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_4033.2127', 'Lhash_array': ['dirichlet_L_4033.2127'], 'label': '1-4033-4033.2127-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4033/2127'}