Let $K$ be a cubic Galois extension of $\mathbb{Q}$.

I wonder if we can find a congruence for prime $p$ such that $p$ does not split completely in $K$. I know that we can do this for quadratic fields, but I am not sure for cubic fields.

Question: Does there exist a congruence for prime $p$, say $p\equiv a\textrm{ (mod } b)$ such that every prime $p$ in that congruence does not split completely in $K$?

As @Felipe Voloch mentioned, $K\subset \mathbb{Q}(\zeta_n)$ for some $n$, then how can I proceed?

Edit1: Added one more assumption on $K$(Galois over $\mathbb{Q}$)