Given $c$, a positive integer, we set $$M(f,c) :={2overphi (f)}sum_{chiin X_f^-}chi (c)ert L(1,chi)ert^2,$$ where $X_f^-$ is the set of the $phi (f)/2$ odd Dirichlet characters mod $f>2$, with $gcd (f,c)=1$. We point out several mistakes in recently published papers and we give explicit closed formulas for the $f$'s such that their prime divisors are all equal to $pm 1$ modulo $c$. As a Corollary, we obtain closed formulas for $M(f,c)$ for $cin{1,2,3,4,5, 6,8,10}$. We also discuss the case of twisted quadratic moments for primitive characters.
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机译：给定$ c $，一个正整数，我们设置$$ M（f，c）：= {2 over phi（f）} sum _ { chi in X_f ^-} chi（c） vert L （1， chi） vert ^ 2，$$其中$ X_f ^-$是$ phi（f）/ 2 $ Dirichlet奇数字符mod $ f> 2 $的集合，其中$ gcd（f， c）= 1 $。我们指出了最近发表的论文中的一些错误，并给出了$ f $的显式封闭公式，使得它们的主要除数都等于$ pm 1 $模$ c $。作为推论，我们为$ c in {1,2,3,4,5，6,8,10 } $获得$ M（f，c）$的封闭式。我们还讨论了原始字符扭曲二次矩的情况。
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