Let ω be a complex number such that 2 ω+1=z where z=√ -3. If |1, 1, 1; 1, -ω^2-1, ω^2; 1, ω^2, ω^7| =3 k, then k is equal to:

Let $\displaystyle \omega$ be a complex number such that $\displaystyle 2 \omega+1=z$ where $\displaystyle z=\sqrt{-3}$. If $$\left|\begin{array}{rrr} 1 & 1 & 1 \\ 1 & -\omega^2-1 & \omega^2 \\ 1 & \omega^2 & \omega^7 \end{array}\right|=3 k, $$ then k is equal to :