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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_4235.2979', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.9911314021003612, -0.13288545357025405], 'a3': [0.9781476007338057, -0.20791169081775934], 'a4': [0.9646829124588557, -0.2634138918316567], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.9418443636395247, -0.33604939321543015], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.9211236531148501, -0.3892701063173915], 'a9': [0.9135454576426009, -0.4067366430758002], 'algebraic': True, 'analytic_conductor': 19.66725731711931, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [7, [1]], [11, [1]]], 'bad_primes': [5, 7, 11], 'central_character': '4235.2979', 'coeff_info': ['x^330 - 1', '0.999818745523526 + 0.0190388051033467*I', '\\\\zeta_{330}'], 'conductor': 4235, 'conductor_radical': 385, 'conjugate': 'dirichlet_L_4235.2249', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^323', 'a^319', 'a^316', 0, 'a^312', 0, 'a^309', 'a^308', 0, 0, 'a^305', 'a^63', 0, 0, 'a^302', 'a^97', 'a^301', 'a^134', 0, 0, 0, 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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': '4235.2979', 'conductor': 4235, 'conductor_radical': 385, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4235/2979'], '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': '1-4235-4235.2979-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': '1-4235-4235.2979-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.66725731711931, 'root_angle': 0.013467242481291402, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.35457376784', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_4235.2979', 'Lhash_array': ['dirichlet_L_4235.2979'], 'label': '1-4235-4235.2979-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4235/2979'}