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 $\genfrac(){}{}{L/\Bbb Q}{p}=\genfrac(){}{}{L/\Bbb Q}{q}$?

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 $\genfrac(){}{}{K/\Bbb Q}{p}=\genfrac(){}{}{K/\Bbb Q}{q}$?

Let $K$ be a abelian number field. Let p,q are rations primes. There there condition like $p\cong q$ modulo some integer which depend on conductor of K or disc(K) implies $(\frac{L/\Bbb Q}{p})=(\frac{L/\Bbb Q}{p}) .$

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 $\genfrac(){}{}{L/\Bbb Q}{p}=\genfrac(){}{}{L/\Bbb Q}{q}$?