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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_47.11', 'a10': [0.7757112907044198, -0.6310879443260528], 'a2': [-0.06824241336467098, -0.9976687691905392], 'a3': [0.9629172873477992, 0.2697967711570243], 'a4': [-0.9906859460363308, 0.1361666490962466], 'a5': [0.5766803221148672, 0.816969893010442], 'a6': [0.20345601305263378, -0.9790840876823229], 'a7': [0.6825531432186541, -0.7308359642781241], 'a8': [0.20345601305263378, 0.9790840876823229], 'a9': [0.8544194045464886, 0.5195839500354336], 'algebraic': True, 'analytic_conductor': 5.050851465347376, 'analytic_normalization': 0, 'bad_lfactors': [[47, [1]]], 'bad_primes': [47], 'central_character': '47.11', 'coeff_info': ['x^46 - 1', '0.990685946036331 + 0.136166649096247*I', '\\\\zeta_{46}'], 'conductor': 47, 'conductor_radical': 47, 'conjugate': 'dirichlet_L_47.30', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^34', 'a^2', 'a^22', 'a^7', 'a^36', 'a^40', 'a^10', 'a^4', 'a^41', 'a^3', 'a^24', 'a^31', 'a^28', 'a^9', 'a^44', 'a^20', 'a^38', 'a^39', 'a^29', 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.050851465347376, 'bad_primes': [47], 'central_character': '47.11', 'conductor': 47, 'conductor_radical': 47, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/47/11'], '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': '1-47-47.11-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': '1-47-47.11-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.050851465347376, 'root_angle': -0.11358166338375096, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.77377697737', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_47.11', 'Lhash_array': ['dirichlet_L_47.11'], 'label': '1-47-47.11-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/47/11'}