Sewnoma - the A stands for Anderson - the plant it was made. Just as the K has always stood for Kilbowe (hope I got spelling correct).
Those made at Elizabethport did not have a letter, and Singer started with the A around the time the 301's came out - though there are early ones with no "A"
Singer most certainly jumped around in the number sequence, and who knows why they did the 101,201,301,401, and then used 500. With all of those, the x01 is the high end, and the 403, 404 and 503 are the same model with less features. And most of the time they kept the model number and gave updates a new suffix, until they got into the T&S group made after the Rocketeer.
And to confuse it more, the industrial model numbers are intermixed with the domestic -
So it's fun to learn about - but there appears no logical reason for most of the numbers. I find the 66/99 the funniest one.