Let $n$ be a positive integer and let $Q_n^d$ be the set of algebraic integers $\zeta$ which live in a degree $d$ extension of the rationals and such that any Galois-conjugate $\zeta^\sigma$ of $\zeta$ has complex norm $n$. The set $Q_n^d$ is finite since the coefficients of the minimal polynomial of any such $\zeta$ are bounded. Moreover it is not difficult to show that if $n = 1$ the set $S$ contains only roots of unity.
What is known about $Q_n^d$ ? For example, is it possible to list all its elements for small values of $n$ ?