Minkowski bound of $229$-th cyclotomic field

Question

If $K = \mathbb{Q}\zeta_{229}$, the $229$-th cyclotomic field, Wwat is a good approximation for the bound $n$ such that every class in the ideal class group of $K$ contains an integral ideal of norm $p < n$. Without any calculation necessary, prove that $n < 2^{(229-1)/2}$.