sage: sage: sage: 

sage: K = QQ[7^(1/3)]
sage: r = 1
sage: s = 1
sage: w = K.number_of_roots_of_unity()
sage: d = K.disc()
sage: d
-1323
sage: R = K.regulator()
sage: R
2.44105647038903
sage: h = K.class_number()
sage: h
3
sage: w
2
sage: res = 2^r * (2*pi)^s * h * R / (w * sqrt(abs(d)))
sage: n(res)
1.26502476401470
sage: Z = K.zeta_function()
sage: Z(2)
1.75167448180254
sage: eps = 10^(-10)
sage: eps*Z(1+eps)
1.26502476362426
sage: n(res)
1.26502476401470
sage: