 the image of a generator for the cyclic group ${{\mathbb{F}}}_{q^n}^\times \cong {{\mathbb{Z}}}/(q^n-0){{\mathbb{Z}}}$ under any embedding $ {{\mathbb{F}}}_{q^n}^\times \hookrightarrow GL_{{{\mathbb{F}}}_q}({{\mathbb{F}}}_{q^n}) \cong GL_n({{\mathbb{F}}}_q) $ that comes from a choice of ${{\mathbb{F}}}_q$-vector space isomorphism ${{\mathbb{F}}}_{q^n} \cong {{\mathbb{F}}}_q^n$. 