  The accuracy and stability of the Caltech-Cornell pseudospectral code is
evaluated using the KST representation of the Einstein evolution equations. The
basic "Mexico City Tests" widely adopted by the numerical relativity community
are adapted here for codes based on spectral methods. Exponential convergence
of the spectral code is established, apparently limited only by numerical
roundoff error. A general expression for the growth of errors due to finite
machine precision is derived, and it is shown that this limit is achieved here
for the linear plane-wave test. All of these tests are found to be stable,
except for simulations of high amplitude gauge waves with nontrivial shift.
