Uniform lower bound in the Landau Prime Ideal Theorem

Question

Are there positive constants $\alpha,\beta,C$ such that for every number field $K$, the number of prime ideals of $\mathcal{O}_K$ of norm at most $x$ is at least $\alpha x^{\beta}$ for all $x\geq C$?

Crucially, $\alpha$, $\beta$ and $C$ must not depend on $K$ (and neither on $x$).

We can assume the Generalized Riemann Hypothesis if it helps.