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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_57.47', 'a10': [-0.9396926207859084, -0.3420201433256687], 'a2': [0.9396926207859084, -0.3420201433256687], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.766044443118978, -0.6427876096865394], 'a5': [-0.766044443118978, -0.6427876096865394], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5, -0.8660254037844386], 'a8': [0.5, -0.8660254037844386], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 6.1255007132936266, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [19, [1]]], 'bad_primes': [3, 19], 'central_character': '57.47', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 57, 'conductor_radical': 57, 'conjugate': 'dirichlet_L_57.17', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^17', 0, 'a^16', 'a^11', 0, 'a^12', 'a^15', 0, 'a^10', 'a^15', 0, 'a^4', 'a^11', 0, 'a^14', 'a^17', 0, 0, 'a^9', 0, 'a^14', 'a^7', 0, 'a^4', 'a^3', 0, 'a^10', 'a^1', 0, 'a^12', 'a^13', 0, 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'198.07269149923024659075937269941', '199.52792490083270524218125042581'], 'prelabel': '1-57-57.47-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.1255007132936266, 'root_angle': -0.5505244691364124, 'root_number': '-0.158061634812934700902630978367-0.987429247895899865530597529653*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.275262234568', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(18)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.43233872591763080290683684540-0.797046298886815550838801891474*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.02652290763', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.43586172547', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.42903168577', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.1255007132936266, 'bad_primes': [3, 19], 'central_character': '57.47', 'conductor': 57, 'conductor_radical': 57, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/57/47'], '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': '1-57-57.47-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': '1-57-57.47-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.1255007132936266, 'root_angle': -0.2752622345682062, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.02652290763', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_57.47', 'Lhash_array': ['dirichlet_L_57.47'], 'label': '1-57-57.47-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/57/47'}