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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_260.203', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [2.9010907910729803e-30, -1.0], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, 0.0], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-1.0, -1.4081532572346456e-30], 'algebraic': True, 'analytic_conductor': 27.940880446602506, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [13, [1]]], 'bad_primes': [2, 5, 13], 'central_character': '260.203', 'coeff_info': ['x^4 - 1', '6.12323399573677e-17 + 1.00000000000000*I', '\\\\zeta_{4}'], 'conductor': 260, 'conductor_radical': 130, 'conjugate': 'dirichlet_L_260.187', 'degree': 1, 'dirichlet_coefficients': [1, 0, '-I', 0, 0, 0, 1, 0, -1, 0, 'I', 0, 0, 0, 0, 0, 'I', 0, 'I', 0, '-I', 0, 'I', 0, 0, 0, 'I', 0, -1, 0, '-I', 0, 1, 0, 0, 0, -1, 0, 0, 0, 'I', 0, 'I', 0, 0, 0, 1, 0, 1, 0, 1, 0, 'I', 0, 0, 0, 1, 0, '-I', 0, 1, 0, -1, 0, 0, 0, -1, 0, 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'z1': {'__RealLiteral__': 0, 'data': '1.38458254153', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.12809383581', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.82346322632', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 27.940880446602506, 'bad_primes': [2, 5, 13], 'central_character': '260.203', 'conductor': 260, 'conductor_radical': 130, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/260/203'], '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': '1-260-260.203-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-260-260.203-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.940880446602506, 'root_angle': 0.11510414395985862, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.38458254153', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_260.203', 'Lhash_array': ['dirichlet_L_260.203'], 'factors': ['1-260-260.203-r1-0-0'], 'label': '1-260-260.203-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/260/203'}