Let \( \omega (\ne 1) \) be a cube root of unity. Then the minimum value of the set
\[
\left\{ |a + b\omega + c\omega^2|^2 : a,b,c \text{ are distinct non-zero integers} \right\}
\]
equals:
Show Hint
For cube roots of unity:
\begin{itemize}
\item Use \( 1+\omega+\omega^2=0 \).
\item Modulus simplifies to symmetric quadratic form.
\end{itemize}