  It is known that the first two-variable Links--Gould quantum link invariant
$LG\equiv LG^{2,1}$ is more powerful than the HOMFLYPT and Kauffman
polynomials, in that it distinguishes all prime knots (including reflections)
of up to 10 crossings. Here we report investigations which greatly expand the
set of evaluations of $LG$ for prime knots. Through them, we show that the
invariant is complete, modulo mutation, for all prime knots (including
reflections) of up to 11 crossings, but fails to distinguish some nonmutant
pairs of 12-crossing prime knots. As a byproduct, we classify the mutants
within the prime knots of 11 and 12 crossings. In parallel, we learn that $LG$
distinguishes the chirality of all chiral prime knots of at most 12 crossings.
We then demonstrate that every mutation-insensitive link invariant fails to
distinguish the chirality of a number of 14-crossing prime knots. This provides
14-crossing examples of chiral prime knots whose chirality is undistinguished
by $LG$.
