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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_667.640', 'a10': [0.6701406618375595, -0.7422341230042699], 'a2': [-0.80661210923753, 0.5910811325286766], 'a3': [0.8521067736154565, 0.523367983696612], 'a4': [0.30124618953723425, -0.9535463980789276], 'a5': [-0.9792641587574211, 0.20258753015208097], 'a6': [-0.9966725824941932, 0.08150928354706316], 'a7': [-0.7422341230042699, 0.6701406618375595], 'a8': [0.3206344605527355, 0.9472030102919101], 'a9': [0.45217190728268575, 0.8919308080026939], 'algebraic': True, 'analytic_conductor': 3.097534977690338, 'analytic_normalization': 0, 'bad_lfactors': [[23, [1]], [29, [1]]], 'bad_primes': [23, 29], 'central_character': '667.640', 'coeff_info': ['x^308 - 1', '0.999791928189206 + 0.0203985373914054*I', '\\\\zeta_{308}'], 'conductor': 667, 'conductor_radical': 667, 'conjugate': 'dirichlet_L_667.247', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^123', 'a^27', 'a^246', 'a^144', 'a^150', 'a^118', 'a^61', 'a^54', 'a^267', 'a^9', 'a^273', 'a^58', 'a^241', 'a^171', 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'3.99340888598', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.097534977690338, 'bad_primes': [23, 29], 'central_character': '667.640', 'conductor': 667, 'conductor_radical': 667, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/667/640'], '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': '1-667-667.640-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': '1-667-667.640-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.097534977690338, 'root_angle': -0.45120718099582247, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.71386406076', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_667.640', 'Lhash_array': ['dirichlet_L_667.640'], 'label': '1-667-667.640-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/667/640'}