Primes in arithmetic progressions and Siegel zeroes

Let $χ$ be a Dirichlet character mod $D$ with $L(s,χ)$ its associated $L$-function, and let $ψ(x,q,a)$ be, as usual, Chebyshev's prime-counting function for the primes of the arithmetic progression $a$ (mod $q$) with $(a,q)=1$. Let $χ$ be a primitive character modulo $D$, and let $ν>0$ be small. We