I am looking for primitive element of galois field of order $8.$ So, I can look at the field
$\mathbb{F}_8=\mathbb{Z}_2[x]/(x^3-x-1)$. I computed $\mathbb{F}_8^{\times}$ and now the primitive element is $a\in \mathbb{F}_8^{\times}$ such that $a^7=1$. Is there any easier way to find it without checking this property for all elements? Can this be generalized since the original question was for any finite field of order $8?$