  The analytic, nonlinear integral equation approach is used to calculate the
finite-size corrections to the transfer matrix eigen-spectra of the critical
dilute O(n) model on the square periodic lattice. The resulting bulk conformal
weights extend previous exact results obtained in the honeycomb limit and
include the negative spectral parameter regimes. The results give the operator
content of the 19-vertex Izergin-Korepin model along with the conformal weights
of the dilute $A_L$ face models in all four regimes.
