Wadge degrees of ${\mathrm{\Delta }}_2^0$ omega-powers

We provide, for each natural number $n$ and each class among $D_n({\mathrm{\Sigma }}_1^0)$, ${\bar{D}}_n({\mathrm{\Sigma }}_1^0)$ and $D_{2n+1}({\mathrm{\Sigma }}_1^0)\oplus {\bar{D}}_{2n+1}({\mathrm{\Sigma }}_1^0)$, a regular language whose associated omega-power is complete for this class.