Structure of relative genus fields of cubic Kummer extensions

Let N=K( 3 D) be a cubic Kummer extension of the cyclotomic field K=ℚ(ζ _3), containing a primitive cube root of unity ζ _3, with cube free integer radicand D>1. Denote by f the 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 D and conductors f such that the genus group Gal( N^*/N) ≅ℤ/3ℤ×ℤ/3ℤ is elementary bicyclic.