There are many fundamental d=4m with class number 8, though only seven are prime namely p=41,113,137,313,337,457,577. Their Ramanujan G-functions are
G41=(x+√x2−42)1/2=√x−24+√x+24G113=(y+√y2−42)1/2=√y−24+√y+24 where x=(5+√414)(1+√−5+√418)y=(9+√1134)(1+√−7+√1132) and similarly for the other p, though the quartic roots get more complicated.
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