Evaluations of Link Polynomials and Recent Constructions in Heegaard Floer Theory

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