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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_4033.659', 'a10': [0.8936326403234123, -0.44879918020046217], 'a2': [-1.0, -1.4081532572346456e-30], 'a3': [-0.28680323271109026, -0.9579895123154889], 'a4': [1.0, 0.0], 'a5': [-0.8936326403234123, 0.44879918020046217], 'a6': [0.28680323271109026, 0.9579895123154889], 'a7': [-0.8354878114129364, -0.549508978070806], 'a8': [-1.0, -1.4081532572346456e-30], 'a9': [-0.8354878114129364, 0.549508978070806], 'algebraic': True, 'analytic_conductor': 18.729173260907245, 'analytic_normalization': 0, 'bad_lfactors': [[37, [1]], [109, [1]]], 'bad_primes': [37, 109], 'central_character': '4033.659', 'coeff_info': ['x^54 - 1', '0.993238357741943 + 0.116092914125230*I', '\\\\zeta_{54}'], 'conductor': 4033, 'conductor_radical': 4033, 'conjugate': 'dirichlet_L_4033.2093', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^27', 'a^38', 'a^0', 'a^23', 'a^11', 'a^32', 'a^27', 'a^22', 'a^50', 'a^4', 'a^38', 'a^23', 'a^5', 'a^7', 'a^0', 'a^9', 'a^49', 'a^21', 'a^23', 'a^16', 'a^31', 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{'__RealLiteral__': 0, 'data': '1.71806612632', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.7865380353', 'prec': 40}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.729173260907245, 'bad_primes': [37, 109], 'central_character': '4033.659', 'conductor': 4033, 'conductor_radical': 4033, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4033/659'], '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': '1-4033-4033.659-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': '1-4033-4033.659-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.729173260907245, 'root_angle': 0.38950071997826763, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.05001298567', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_4033.659', 'Lhash_array': ['dirichlet_L_4033.659'], 'label': '1-4033-4033.659-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4033/659'}