  We compute partition functions describing multiplicities and charges of
massless and first massive string states of pure-spinor superstrings in
3,4,6,10 dimensions. At the massless level we find a spin-one gauge multiplet
of minimal supersymmetry in d dimensions. At the first massive string level we
find a massive spin-two multiplet. The result is confirmed by a direct analysis
of the BRST cohomology at ghost number one. The central charges of the pure
spinor systems are derived in a manifestly SO(d) covariant way confirming that
the resulting string theories are critical. A critical string model with
N=(2,0) supersymmetry in d=2 is also described.
