Complex Numbers

Let $\omega$ be a complex root of the quadratic polynomial $x^2+x+1$. The value of

\(\left(\omega+\frac{1}{\omega}\right) \cdot\left(\omega^2+\frac{1}{\omega^2}\right) \cdots\left(\omega^{100}+\frac{1}{\omega^{100}}\right)\)

is