  We calculate the classical Iwasawa invariants of the Iwasawa modules
associated to the $p$-adic topological $K$-theory of finite spectra. We show
that the graded average of the orders of $n$ consecutive $K(1)$-local homotopy
groups of a finite spectrum $X$ grows asymptotically like
$\frac{-\log_p(n)}{2}$ times the total Iwasawa $\lambda$-invariant of $X$. We
show that the Iwasawa $\mu$-invariants of finite spectra are all zero. Finally,
we prove a spectral analogue of a weak form of the Iwasawa Main Conjecture,
describing the orders of the $K(1)$-local homotopy groups of a certain
``torsion-free replacement'' of $X$ in terms of the characteristic polynomials
of the Iwasawa modules associated to $X$.
