I purchased a used Spinner Sport spin bike several years ago. It has always been missing one crank arm nut. I was able to cinch it down with the nut from the other crank arm, but then removed it and put it back onto the original crank arm bolt. The cinched down nutless arm has held even without a nut (surprisingly) but never seemed safe to use. Unfortunately a standard nut from Home Depot that has the correct thread doesn't work because the metal around the nut is too big and you can't fit a socket wrench socket in the hole so you can't tighten it. You need a special nut that avoids the problem. I finally dug deep and found the correct nut to replace it with and figured I would share in case someone else is looking for the same, because I couldn't find the information anywhere. It requires the following:
M10-1.25 flange nut (14mm socket wrench tool size)
I ended up buying a nut described as, "14mm Crank Arm Nut". Sugino was the brand. It worked perfectly.
Here are some pictures of the old spin bike: