For odd class number h(−d), the kind that is d≡7mod8 seems more well-behaved than d≡3mod8. For class number 3, there are only two of the first kind: d=23,31. Hence, K(k23)=√2π2√23x4/3(23∏m=1[Γ(m23)](−23m))1/6K(k31)=√2π2√31y4/3(31∏m=1[Γ(m31)](−31m))1/6 where (x,y) are the real roots of the cubics x3−x−1=0y3−y2−1=0 or the plastic ratio and supergolden ratio, respectively. But for d=59 which is of the second kind, then the radical involved will be an algebraic number of degree 3×3=9.
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