Some complete $omega$-powers of a one-counter language, for any Borel class of finite rank

We prove that, for any natural number n $ge$ 1, we can find a finite alphabet $Sigma$ and a finitary language L over $Sigma$ accepted by a one-counter automaton, such that the $omega$-power L $infty$ := {w 0 w 1. .. $in$ $Sigma$ $omega$ | $forall$i $in$ $omega$ w i $in$ L} is $Pi$ 0 n-complete. We prove a similar result for the class $Sigma$ 0 n .