  We present a hardware-accelerated computation of Hasse-Weil invariants of all
hyperelliptic curves of given genus over a fixed finite field. Our main
motivation is the determination of traces of Frobenius on cohomology
corresponding moduli stacks \`a la Bergstr\"om-Faber-van-der-Geer. This paper
also constitutes a case study of the performance of lookup table based Zech
arithmetic on Graphics Processing Units (GPUs). GPUs are by now ubiquitous in
numerics, to an extend that their development itself is propelled by scientific
computing. Algebraic computing has profited very little from the advancement of
hardware design. We suggest that specific computations can be benificially
adjusted to GPUs with comparatively little effort.
