## Task A-4.2.

Let $S$ be the set of all natural numbers less than 1000 whose all digits in decimal notation are even. Let $\omega$ be a complex number such that $\omega^{2}+\omega+1=0$.

Calculate the sum $\sum_{k \in S} \omega^{k}$, i.e., the sum of the values $\omega^{k}$ for all $k$ in the set $S$.