It's been a while since algebraic number theory, so I apologize if this is too simple.
Let $F=\Bbb{Q}(\sqrt{s})$ and $E=F(i\sqrt{t})$, where $s,t > 0$ are square-free integers. I would like to find a positive integer representative for the nontrivial class in $F^{\times} / N_{E/F}(E^{\times})$ (I think there are only two classes anyway). When $s$ is a square, I seem to recall that any prime $p$ not dividing $t$ suffices, but I can't find a source for that.
Any help is appreciated.
In fact, even just working a relatively simple case of $s=3$, $t=1$ would be nice.