Question 13
Let $\omega \neq 1$ be a $13$th root of unity. Find the remainder when $$
\prod_{k=0}^{12} \left(2 - 2\omega^k + \omega^{2k}\right)
$$ is divided by $1000.$
\prod_{k=0}^{12} \left(2 - 2\omega^k + \omega^{2k}\right)
$$ is divided by $1000.$