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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_4033.1031', 'a10': [-0.23061587074244017, -0.9730448705798238], 'a2': [-0.9396926207859084, 0.3420201433256687], 'a3': [0.05814482891047583, 0.9983081582712682], 'a4': [0.766044443118978, -0.6427876096865394], 'a5': [-0.11609291412523023, 0.993238357741943], 'a6': [-0.39607976603915684, -0.918216106880274], 'a7': [0.5971585917027862, -0.8021231927550437], 'a8': [-0.5, 0.8660254037844386], 'a9': [-0.993238357741943, 0.11609291412523023], 'algebraic': True, 'analytic_conductor': 18.729173260907245, 'analytic_normalization': 0, 'bad_lfactors': [[37, [1]], [109, [1]]], 'bad_primes': [37, 109], 'central_character': '4033.1031', 'coeff_info': ['x^108 - 1', '0.998308158271268 + 0.0581448289104758*I', '\\\\zeta_{108}'], 'conductor': 4033, 'conductor_radical': 4033, 'conjugate': 'dirichlet_L_4033.133', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^48', 'a^26', 'a^96', 'a^29', 'a^74', 'a^92', 'a^36', 'a^52', 'a^77', 'a^85', 'a^14', 'a^20', 'a^32', 'a^55', 'a^84', 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[1, 'a^27']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-4033-4033.1031-r0-0-0', 'leading_term': '1.02476840077923359668198305918+0.780095792566566947765121099293*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/4033/1031', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.2879051676329618, 1.2714391000298828, 0.46488164372230223, -1.1685168764142029, -2.229778979554604, -1.157642735160179, 1.7627663874663957, 4.109041606530846, 3.648185471739774, 0.9985215008937253, -0.7366472961645378, 0.4708004068079155, 2.89007763121504, 2.9106025667974724, -0.3558367787314212, -3.566519321826793, -3.1148331434223815, 0.2474864614508196, 2.3003170955855485, 0.8156947442604711, -1.6852157093278883, -1.628625081731172, 0.6788294493539471, 1.8286558594114983, 0.46023443071412773, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.729173260907245, 'bad_primes': [37, 109], 'central_character': '4033.1031', 'conductor': 4033, 'conductor_radical': 4033, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4033/1031'], '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': '1-4033-4033.1031-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': '1-4033-4033.1031-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.729173260907245, 'root_angle': 0.20711044760001773, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.723103098928', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_4033.1031', 'Lhash_array': ['dirichlet_L_4033.1031'], 'label': '1-4033-4033.1031-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4033/1031'}