Let $K$ be an abelian number field. Let $p$, $q$ be rational primes. Is there some condition like $p\equiv q$ modulo some integer which depends on conductor of $K$ or $\operatorname{disc}(K)$ that implies $\genfrac(){}{}{L/\Bbb Q}{p}=\genfrac(){}{}{L/\Bbb Q}{q}$?