Precise Error Term in Chebotarev's Theorem

Question

Let $K/\mathbb{Q}$ be a Galois Number Field with Galois group $G$ and discriminant $\Delta_K$. Chebotarev's theorem states that the number of (unramified) rational primes with Frobenius conjugacy class in a set of conjugacy classes $D \subseteq G$ is $\pi_D(x) \sim \frac{|D|}{|G|} \pi(x)$, where $\pi(x)$ is the rational prime counting function. Serre proved assuming GRH that \begin{equation*} |\pi_D(x) - \frac{|D|}{|G|} \text{Li}(x)| \ll x^{\frac{1}{2}}|D|(\log x+ \log |G| + \log \Delta_K). \end{equation*} What is currently the best unconditional estimate on the error term?

Answer 1

The OP could be helped with this paper about of Balog and Ono.

http://www.mathcs.emory.edu/~ono/publications-cv/pdfs/062.pdf