For distinct primes l and p, the Iwasawa invariant
λ
l
−
\lambda _l^ -
stabilizes in the cyclotomic
Z
p
{\mathbb {Z}_p}
-tower over a complex abelian base field. We calculate this stable invariant for
p
=
3
p = 3
and various l and K. Our motivation was to search for a formula of Riemann-Hurwitz type for
λ
l
−
\lambda _l^ -
that might hold in a p-extension. From our numerical results, it is clear that no formula of such a simple kind can hold. In the course of our calculations, we develop a method of computing
λ
l
−
\lambda _l^ -
for an arbitrary complex abelian field and, for
p
=
3
p = 3
, we make effective Washington’s theorem on the stabilization of the l-part of the class group in the cyclotomic
Z
p
{\mathbb {Z}_p}
-extension. A new proof of this theorem is given in the appendix.