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{'Lhash': 'dirichlet_L_1840.613', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.6548607339452851, 0.7557495743542583], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.9096319953545183, -0.41541501300188644], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.14231483827328514, -0.9898214418809327], 'algebraic': True, 'analytic_conductor': 8.544924076387138, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [23, [1]]], 'bad_primes': [2, 5, 23], 'central_character': '1840.613', 'coeff_info': ['x^44 - 1', '0.989821441880933 + 0.142314838273285*I', '\\\\zeta_{44}'], 'conductor': 1840, 'conductor_radical': 230, 'conjugate': 'dirichlet_L_1840.1837', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^60', 0, 0, 0, 'a^41', 0, 'a^32', 0, 'a^53', 0, 'a^36', 0, 0, 0, 'a^7', 0, 'a^37', 0, 'a^13', 0, 0, 0, 0, 0, 'a^48', 0, 'a^51', 0, 'a^28', 0, 'a^25', 0, 0, 0, 'a^54', 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.544924076387138, 'bad_primes': [2, 5, 23], 'central_character': '1840.613', 'conductor': 1840, 'conductor_radical': 230, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1840/613'], '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': '1-1840-1840.613-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': '1-1840-1840.613-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.544924076387138, 'root_angle': 0.05176004309384374, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.815774379547', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1840.613', 'Lhash_array': ['dirichlet_L_1840.613'], 'label': '1-1840-1840.613-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1840/613'}