Let $k$ be an algebraically closed field of characteristic 0. Consider the $n$-th dimensional affine space $\mathbb{A}_k^n$. When $n=1$, I know that the etale fundamental group $\pi_1^{et}(\mathbb{A}_k^1 - \{0\}) = \hat{\mathbb{Z}}$, since $\mathbb{A}_k^1 - \{0\} = \mathbb{G}_{m,k}$ and the only possible etale covers are of the form $\mathbb{G}_{m,k} \to \mathbb{G}_{m,k}$ given by $x \mapsto x^r$ for $r \in \mathbb{Z}$. My question is, do we have a similar nice characterization in higher dimensions, i.e.
What is $\pi_1^{et}(\mathbb{A}_k^n - \{0\})$ for $n > 1$?