On the Iwasawa lambda invariant of an imaginary abelian field of conductor 3pn+1

Let p be an odd prime number with p≠3, and K=Q(cos(2π/p),ζ3). Let Kn be the n-th layer of the cyclotomic Zp-extension over K, and λn the Iwasawa lambda invariant of the cyclotomic Z3-extension over Kn. By a theorem of Friedman, it is known that λn is stable for sufficiently large n. We prove that when p⩽599, we have λn=λ0 for all n⩾1 with the help of computer. Further, for these p, we calculate the invariant λ0.