31" aluminum window balance

A quick learner from Chicago, IL says:
Looking for a replacement window balance, 31". There is a spring and rope inside, but no nylon fittings on either end.
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Bob from SWISCO responded:

I believe we can help, but I'd like to clarify a few points. Is there a pivot shoe in the window that the balance attaches to? Can you confirm the clip or hook at the bottom of the balance that attaches to the shoe? Does the shoe resemble something like our 15-129? And does this balance attach to the top of the window jamb with a screw?

A quick learner from Chicago, IL says:
Hi Bob, thank you for your assistance.
Yes, there is a pivot shoe. It looks exactly like the photo you sent.
Picture of the clip attached. It is an L shaped clip.
Yes, this balance attaches to the top of the window with the screw.
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Paul from SWISCO responded:

This appears to me to be an S770-31, with an older style of the clip that attaches to the pivot shoe. Your balance uses an older rating system, but for a stamp of 30-7, I'd suggest a stamp option of 31F, which would support a window sash that weighs 33 through 37 lbs. See if this looks correct to you. 

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