Couldn't find any window part #

Hello there. This looks like the 15-087 Pivot Shoe, which uses Series 180 Coil Balances. Let me know if you have any other questions about this system.

Series 180 coil balance diagram

The only other way is to remove your sash and weigh it on a scale, then divide that weight by how many springs support it. So, for example, if your sash weighs 12 pounds and it has 2 springs on either side, then you'd want four 3 pound springs. 

Otherwise, there is no other way. You will need to either weigh your sash or remove the coils. Removing the balance assembly to properly identify before purchase is routine for this kind of job.