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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_4017.1025', 'a10': [0.15339165487868536, -0.9881654720812594], 'a2': [-0.9957341762950345, -0.092268359463302], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9829730996839018, 0.18374951781657034], 'a5': [-0.061560906133942835, 0.9981033287370441], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.961825643172819, 0.2736629900720829], 'a8': [-0.961825643172819, -0.2736629900720829], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 18.654869573286486, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [13, [1]], [103, [1]]], 'bad_primes': [3, 13, 103], 'central_character': '4017.1025', 'coeff_info': ['x^204 - 1', '0.999525719713366 + 0.0307950585561704*I', '\\\\zeta_{204}'], 'conductor': 4017, 'conductor_radical': 4017, 'conjugate': 'dirichlet_L_4017.968', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^105', 0, 'a^6', 'a^53', 0, 'a^93', 'a^111', 0, 'a^158', 'a^139', 0, 0, 'a^198', 0, 'a^12', 'a^72', 0, 'a^143', 'a^59', 0, 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'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.654869573286486, 'bad_primes': [3, 13, 103], 'central_character': '4017.1025', 'conductor': 4017, 'conductor_radical': 4017, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4017/1025'], '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': '1-4017-4017.1025-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': '1-4017-4017.1025-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.654869573286486, 'root_angle': 0.08136012917040567, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.400286649859', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_4017.1025', 'Lhash_array': ['dirichlet_L_4017.1025'], 'label': '1-4017-4017.1025-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4017/1025'}