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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_4235.2897', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.3892701063173915, -0.9211236531148501], 'a3': [0.5877852522924731, -0.8090169943749475], 'a4': [-0.6969375686552934, -0.7171318047589635], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.5163974616389619, -0.8563490302515889], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.9318640292114523, 0.362807705350641], 'a9': [-0.30901699437494745, -0.9510565162951535], 'algebraic': True, 'analytic_conductor': 19.66725731711931, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [7, [1]], [11, [1]]], 'bad_primes': [5, 7, 11], 'central_character': '4235.2897', 'coeff_info': ['x^220 - 1', '0.999592192828189 + 0.0285560507936963*I', '\\\\zeta_{220}'], 'conductor': 4235, 'conductor_radical': 385, 'conjugate': 'dirichlet_L_4235.1763', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^179', 'a^187', 'a^138', 0, 'a^146', 0, 'a^97', 'a^154', 0, 0, 'a^105', 'a^39', 0, 0, 'a^56', 'a^81', 'a^113', 'a^172', 0, 0, 0, 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{'__RealLiteral__': 0, 'data': '1.52039192526', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.2236611759', 'prec': 40}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.66725731711931, 'bad_primes': [5, 7, 11], 'central_character': '4235.2897', 'conductor': 4235, 'conductor_radical': 385, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4235/2897'], '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': '1-4235-4235.2897-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': '1-4235-4235.2897-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.66725731711931, 'root_angle': -0.3825570614374017, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.698811865337', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_4235.2897', 'Lhash_array': ['dirichlet_L_4235.2897'], 'label': '1-4235-4235.2897-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4235/2897'}