$ω≠1$ and $ω^{13}=1$. If $\alpha=ω+ω^3+ω^4+ω^{−4}+ω^{−3}+ω^{−1}$ and $\beta=ω^2+ω^5+ω^6+ω^{−6}+ω^{−5}+ω^{−2}$, then quadratic equation, whose roots are $\alpha$ and $\beta$ is:

I tried finding the sum and product of roots and placing in the equation $x^2-(\alpha+\beta)x+(\alpha\cdot\beta)=0$ but I was not able to solve for it.