nostr:npub1t76as6gjr7pzg0taz40e55smjjegmj89ud7g056aqed90hs7cynspe4l63 - Neat!  Among other things, you're finding an element of order n in SL(2,F) where the field F is the rationals with cos(π/n) adjoined.   I guess this is a subfield of the 2nth cyclotomic field: the rationals with a primitive 2nth root of unity adjoined.  I'm a bit confused about why we need the factor of 2 here, but the nth cyclotomic field would only have cos(2π/n) in it.