Computing the Mertens and Meissel-Mertens constants for sums over arithmetic progressions

We give explicit numerical values with 100 decimal digits for the Mertens constant involved in the asymptotic formula for $\sum\limits_{\substack{p\leq x p\equiv a \bmod{q}}}1/p$ and, as a by-product, for the Meissel-Mertens constant defined as ${\sum }_{p\equiv aq}(\log (1-1\mathrm{/}p)+1\mathrm{/}p)$, for $q\in \{3$, …, $100\}$ and $(q,a)=1$.