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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_4235.537', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.7302706799479574, -0.6831579129369344], 'a3': [-0.7431448254773942, 0.6691306063588582], 'a4': [0.0665905319833038, -0.9977803871845651], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.08557500847883974, 0.9963317308626913], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.6330124538088704, -0.7741416106390825], 'a9': [0.10452846326765347, -0.9945218953682733], 'algebraic': True, 'analytic_conductor': 19.66725731711931, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [7, [1]], [11, [1]]], 'bad_primes': [5, 7, 11], 'central_character': '4235.537', 'coeff_info': ['x^660 - 1', '0.999954685354173 + 0.00951983393957664*I', '\\\\zeta_{660}'], 'conductor': 4235, 'conductor_radical': 385, 'conjugate': 'dirichlet_L_4235.3888', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^581', 'a^253', 'a^502', 0, 'a^174', 0, 'a^423', 'a^506', 0, 0, 'a^95', 'a^381', 0, 0, 'a^344', 'a^199', 'a^427', 'a^428', 0, 0, 0, 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{'__RealLiteral__': 0, 'data': '1.01397776999', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.24514243207', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.66725731711931, 'bad_primes': [5, 7, 11], 'central_character': '4235.537', 'conductor': 4235, 'conductor_radical': 385, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4235/537'], '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': '1-4235-4235.537-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': '1-4235-4235.537-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.66725731711931, 'root_angle': 0.36393665217531884, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0871158385174', 'prec': 50}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_4235.537', 'Lhash_array': ['dirichlet_L_4235.537'], 'label': '1-4235-4235.537-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4235/537'}