spiral balance - non-tilt - 1/2" diameter - 29" long

It's hard to believe, but it looks like the window manufacturer used an S400-29 non tilt balance, which is 3/8" in diameter. I see you ordered an S500-29, which is 5/8" in diameter, but I don't know if you can squeeze in a 5/8" tube in the window sash. I would triple check the diameter of the outer tube. It should be either 5/8" or 3/8". There is only one type of spiral balance that is 1/2", and it's a very unique style that you do not have.