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{'Lhash': 'dirichlet_L_2001.1211', 'a10': [-0.45217190728268575, -0.8919308080026939], 'a2': [0.9867124733912889, -0.1624761362602058], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9472030102919101, -0.3206344605527355], 'a5': [-0.30124618953723425, -0.9535463980789276], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.45217190728268575, -0.8919308080026939], 'a8': [0.8825215767863213, -0.4702719069927368], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 9.292604933071013, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [23, [1]], [29, [1]]], 'bad_primes': [3, 23, 29], 'central_character': '2001.1211', 'coeff_info': ['x^154 - 1', '0.999167799344583 + 0.0407885860615856*I', '\\\\zeta_{154}'], 'conductor': 2001, 'conductor_radical': 2001, 'conjugate': 'dirichlet_L_2001.1193', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^150', 0, 'a^146', 'a^108', 0, 'a^127', 'a^142', 0, 'a^104', 'a^103', 0, 'a^82', 'a^123', 0, 'a^138', 'a^63', 0, 'a^146', 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'0.541919275723', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.51626030904', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.56287441617', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.292604933071013, 'bad_primes': [3, 23, 29], 'central_character': '2001.1211', 'conductor': 2001, 'conductor_radical': 2001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2001/1211'], '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': '1-2001-2001.1211-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': '1-2001-2001.1211-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.292604933071013, 'root_angle': -0.422614457663817, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.541919275723', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_2001.1211', 'Lhash_array': ['dirichlet_L_2001.1211'], 'label': '1-2001-2001.1211-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2001/1211'}