  Let $f : \mathbf{N} \rightarrow \mathbf{C}$ be a bounded multiplicative
function. Let $a$ be a fixed integer (say $a = 1$). Then $f$ is
well-distributed on the progression $n \equiv a \pmod{q} \subset \{1,\dots,
X\}$, for almost all primes $q \in [Q,2Q]$, for $Q$ as large as $X^{\frac{1}{2}
+ \frac{1}{78} - o(1)}$.
