Image of Norm map via Quadratic Residue

Question

Let $\zeta$ be one of $\{\zeta_6,\; i\sqrt2,\; i,\; \sqrt2,\; \sqrt3,\; \Phi\}$.

For each of the primes $p$ below and each of the values of $\zeta$ listed, say whether $\pm p$ is in the image of the norm map $N : Z[\zeta] \rightarrow Z$.

1. $p = 2$
2. $p = 3$
3. $p = 2659$
4. $p = 4079$

I am new in this subject. I know this problem can be solved by quadratic residue methods in number theory but I cannot figure it out. A detailed solution would be appreciated.

Thank you.