Alright, found something interesting. Since this is supposed to be a lookup for the correct x value in (e,1) or (-f,1) I assumed that the correct x value must be related to the na transform record in a fractal / golden mean ratio.
I took the (e na transform) and (-f na transform) records for c145 and c287.
For c145 (e na) the x value is 11.
11 / 1.61 (golden ratio) = 6.823 = very close to x=7, which is the correct x for the (an) and (prime) elements.
For c287 (e na) the x value is 15.
15 / 1.61 (golden ratio) = 9.31677 = very close to 9, which is the correct x for the (an) and (prime) elements.
I have only tested these two c values, so any additional help you Anons can provide to test other c values would be greatly appreciated.