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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_571.96', 'a10': [-0.6608983362288612, -0.7504754420831657], 'a2': [-0.9264940672148018, 0.3763093719478355], 'a3': [0.20251743509939205, -0.9792786572170168], 'a4': [0.7167825131684512, -0.6972968010939954], 'a5': [0.3299074452755829, 0.9440132825081108], 'a6': [0.18088053433210985, 0.9835050748723824], 'a7': [-0.01653394476635846, -0.999863304992469], 'a8': [-0.4016954246529695, 0.9157733266550574], 'a9': [-0.917973376961527, -0.396642003814334], 'algebraic': True, 'analytic_conductor': 2.6517128519657915, 'analytic_normalization': 0, 'bad_lfactors': [[571, [1]]], 'bad_primes': [571], 'central_character': '571.96', 'coeff_info': ['x^285 - 1', '0.999756990959495 + 0.0220444783929454*I', '\\\\zeta_{285}'], 'conductor': 571, 'conductor_radical': 571, 'conjugate': 'dirichlet_L_571.458', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^125', 'a^223', 'a^250', 'a^56', 'a^63', 'a^213', 'a^90', 'a^161', 'a^181', 'a^199', 'a^188', 'a^121', 'a^53', 'a^279', 'a^215', 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'1.60371999542', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.46832384714', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.6517128519657915, 'bad_primes': [571], 'central_character': '571.96', 'conductor': 571, 'conductor_radical': 571, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/571/96'], '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': '1-571-571.96-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': '1-571-571.96-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6517128519657915, 'root_angle': 0.47157642777557146, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0928098581195', 'prec': 50}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_571.96', 'Lhash_array': ['dirichlet_L_571.96'], 'label': '1-571-571.96-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/571/96'}