Primes in arithmetic progressions under the presence of Landau-Siegel zeroes

Let $x\geqslant 2$ and assume that $a$ and $q$ are coprime positive integers. As usual, $ψ(x;q,a):=\sum_{n\leqslant x,n\equiv a(\!\!\!\mod{\!\!q})}Λ(n)$, where $Λ$ is the von Mangoldt function. In 2003, Friedlander and Iwaniec assumed the existence of exceptional characters corresponding to "extreme