Moduli $n$ for which $\mathbb Z_n[x]/(x^2+x+1)$ is a field

Let \(I=(x^2+x+1)\subset\mathbb Z_n[x]\).

1. For which \(n\), \(1\le n\le10\), is \(\mathbb Z_n[x]/I\) a field?
2. Give the multiplication table for the resulting quotient when \(n=2\).