Prime number theorem in an arithmetic progression with an exceptional zero

Uniformly for $x\ge 2$ and $(a,q)=1$,where the second term occurs only when a real character ${\chi }_1$ has an exceptional zero $\beta$.

If some $ϵ>0$ satisfiesuniformly for sufficiently large $q$, then every exceptional zero modulo $q$ satisfiesChoose ${\chi }_1(a)=-1$ and $x=\exp (A(\log q{)}^2)$ in the exceptional-zero asymptotic, with $A$ large in terms of $ϵ$.