  We give a unified description of the modular and quasi-modular functions used
in Viazovska's proof of the best packing bounds in dimension 8 and the proof by
Cohn, Kumar, Miller, Radchenko, and Viazovska of the best packing bound in
dimension 24. We show that necessarily modular forms have to be used to obtain
these results. We extend these constructions to arbitrary dimensions divisible
by 4.
