sew4nin,
As Candace said the 401A and 500A are the same machine mechanically. Clean everything, if it moves, oil it. I suggest Tri-Flow due to it's superior cleaning and lubricating abilities. There are several plunger type parts that need oil. If they get stuck the ZZ won't work right. There are a couple places that need grease rather than oil.
I you have a manual follow the lube and oil chart in it. If you don't have one you can download a free .pdf manual from Singer.
{
http://www.singerco.com/accessories/instruction-manuals }
The 500 is a great machine as is the 401. We have one of each and my wife claims the 401 while I claim the 500. When I need some ZZing done I usually grab the 500.
Joe