  Using a definition of Euler characteristic for fractionally-graded complexes
based on roots of unity, we show that the Euler characteristics of Dowlin's
"$\mathfrak{sl}(n)$-like" Heegaard Floer knot invariants $HFK_n$ recover both
Alexander polynomial evaluations and $\mathfrak{sl}(n)$ polynomial evaluations
at certain roots of unity for links in $S^3$. We show that the equality of
these evaluations can be viewed as the decategorified content of the
conjectured spectral sequences relating $\mathfrak{sl}(n)$ homology and
$HFK_n$.
