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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_6003.1139', 'a10': [0.3590026998475987, 0.9333365210373668], 'a2': [0.054373045416879255, -0.9985206917896564], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.994087143864188, -0.10858522184874536], 'a5': [-0.9124357585551869, 0.40921997325377546], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.7775737186139037, -0.6287917875743494], 'a8': [-0.1624761362602058, 0.9867124733912889], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 27.87781479921304, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [23, [1]], [29, [1]]], 'bad_primes': [3, 23, 29], 'central_character': '6003.1139', 'coeff_info': ['x^924 - 1', '0.999976880197217 + 0.00679993169383467*I', '\\\\zeta_{924}'], 'conductor': 6003, 'conductor_radical': 2001, 'conjugate': 'dirichlet_L_6003.4970', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^701', 0, 'a^478', 'a^400', 0, 'a^824', 'a^255', 0, 'a^177', 'a^641', 0, 'a^298', 'a^601', 0, 'a^32', 'a^105', 0, 'a^555', 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27.87781479921304, 'root_angle': 0.3167746651543541, 'root_number': '0.544354453436914667555275697290+0.838855308753182953282548170533*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(924)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.695550144095796023177857507115-0.325727459306443870240462789152*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.903792256474', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.71610411019', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.63874998401', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 27.87781479921304, 'bad_primes': [3, 23, 29], 'central_character': '6003.1139', 'conductor': 6003, 'conductor_radical': 2001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6003/1139'], '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': '1-6003-6003.1139-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': '1-6003-6003.1139-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.87781479921304, 'root_angle': 0.15838733257717705, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.903792256474', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_6003.1139', 'Lhash_array': ['dirichlet_L_6003.1139'], 'label': '1-6003-6003.1139-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6003/1139'}