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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_47.14', 'a10': [-0.5766803221148672, -0.816969893010442], 'a2': [-0.917211301505453, -0.39840108984624145], 'a3': [-0.06824241336467098, -0.9976687691905392], 'a4': [0.6825531432186541, 0.7308359642781241], 'a5': [0.8544194045464886, 0.5195839500354336], 'a6': [-0.33487961217098616, 0.9422609221188205], 'a7': [0.20345601305263378, -0.9790840876823229], 'a8': [-0.33487961217098616, -0.9422609221188205], 'a9': [-0.9906859460363308, 0.1361666490962466], 'algebraic': True, 'analytic_conductor': 0.21826708238597584, 'analytic_normalization': 0, 'bad_lfactors': [[47, [1]]], 'bad_primes': [47], 'central_character': '47.14', 'coeff_info': ['x^23 - 1', '0.962917287347799 + 0.269796771157024*I', '\\\\zeta_{23}'], 'conductor': 47, 'conductor_radical': 47, 'conjugate': 'dirichlet_L_47.37', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^13', 'a^17', 'a^3', 'a^2', 'a^7', 'a^18', 'a^16', 'a^11', 'a^15', 'a^14', 'a^20', 'a^22', 'a^8', 'a^19', 'a^6', 'a^9', 'a^1', 'a^21', 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'198.84943449240832329451537891222', '199.76101472908079201225486220774'], 'prelabel': '1-47-47.14-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.21826708238597584, 'root_angle': -0.44467425880061523, 'root_number': '0.172937117923249104379345297596-0.984932867379498222306353439164*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2223371294', 'prec': 44}, 'spectral_label': 'r0-0', 'st_group': 'mu(23)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.659511008788432574552845660570-0.338431576227255992830204276058*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.40416399807', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.02875171509', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '6.11614896735', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.21826708238597584, 'bad_primes': [47], 'central_character': '47.14', 'conductor': 47, 'conductor_radical': 47, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/47/14'], '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': '1-47-47.14-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': '1-47-47.14-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.21826708238597584, 'root_angle': -0.22233712940030761, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.40416399807', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_47.14', 'Lhash_array': ['dirichlet_L_47.14'], 'label': '1-47-47.14-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/47/14'}