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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1792.101', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.8492021815265789, 0.528067850650368], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.986643332084879, -0.16289547339458874], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.4422886902190013, 0.8968727415326883], 'algebraic': True, 'analytic_conductor': 192.57714523196805, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '1792.101', 'coeff_info': ['x^192 - 1', '0.999464587476366 + 0.0327190828217761*I', '\\\\zeta_{192}'], 'conductor': 1792, 'conductor_radical': 14, 'conjugate': 'dirichlet_L_1792.621', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^209', 0, 'a^187', 0, 0, 0, 'a^226', 0, 'a^311', 0, 'a^213', 0, 'a^12', 0, 'a^212', 0, 'a^205', 0, 0, 0, 'a^250', 0, 'a^182', 0, 'a^243', 0, 'a^57', 0, 'a^56', 0, 'a^328', 0, 0, 0, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 192.57714523196805, 'bad_primes': [2, 7], 'central_character': '1792.101', 'conductor': 1792, 'conductor_radical': 14, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1792/101'], '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': '1-1792-1792.101-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': '1-1792-1792.101-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 192.57714523196805, 'root_angle': 0.2636625363872795, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.27278263054', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1792.101', 'Lhash_array': ['dirichlet_L_1792.101'], 'label': '1-1792-1792.101-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1792/101'}