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Motivated by the representation theory of quantized Gieseker varieties, for every pair $m$ and $n$ of coprime positive integers, we consider semistandard versions of $m/n$-parking functions. These objects naturally have area and weight statistics, and we relate them to parabolic affine Springer fibers in order to define a dinv statistic on them. Fixing a rank $r$ of the semistandard parking functions, the generating function of these statistics turns out to be a truncation to $r$ variables of a Hikita polynomial. In particular, it can be found from an element of the $\mathfrak{gl}(r)$ DAHA. This is work-in-progress, joint with Nicolle González and Monica Vazirani.