Structure of relative genus fields of cubic Kummer extensions

Let N=K(D3)be a cubic Kummer extension of the cyclotomic field K=Q(ζ3),containing a primitive cube root of unity ζ3,with cube free integer radicand D>1.Denote by fthe conductor of the abelian extension N/K,  and by N∗the relative genus field of N/K. The aim of the present work is to find out all positive integers Dand conductors fsuch that the genus group GalN∗/N≅Z/3Z×Z/3Zis elementary bicyclic.