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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_283.163', 'a10': [-0.5380823531633727, 0.842892271416797], 'a2': [-0.7416521056479576, 0.6707847301392235], 'a3': [0.9910774881547801, 0.13328695537377885], 'a4': [0.10009569162409834, -0.994977815088504], 'a5': [0.9644691750543766, -0.264195401871286], 'a6': [-0.8244415603417603, 0.5659470943305952], 'a7': [0.8604015792601394, -0.5096166425919174], 'a8': [0.5931797447293552, 0.805070053127563], 'a9': [0.9644691750543766, 0.264195401871286], 'algebraic': True, 'analytic_conductor': 1.3142464747921523, 'analytic_normalization': 0, 'bad_lfactors': [[283, [1]]], 'bad_primes': [283], 'central_character': '283.163', 'coeff_info': ['x^47 - 1', '0.991077488154780 + 0.133286955373779*I', '\\\\zeta_{47}'], 'conductor': 283, 'conductor_radical': 283, 'conjugate': 'dirichlet_L_283.158', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^18', 'a^1', 'a^36', 'a^45', 'a^19', 'a^43', 'a^7', 'a^2', 'a^16', 'a^11', 'a^37', 'a^19', 'a^14', 'a^46', 'a^25', 'a^33', 'a^20', 'a^19', 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{'__RealLiteral__': 0, 'data': '4.39650040685', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3142464747921523, 'bad_primes': [283], 'central_character': '283.163', 'conductor': 283, 'conductor_radical': 283, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/283/163'], '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': '1-283-283.163-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': '1-283-283.163-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3142464747921523, 'root_angle': 0.10479620993511785, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.60101903952', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_283.163', 'Lhash_array': ['dirichlet_L_283.163'], 'label': '1-283-283.163-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/283/163'}