  Electric and color neutral solutions, and the critical conditions for the
formation of gapless color superconductors, are investigated in $K^0$ condensed
color-flavor locked quark matter for nonzero strange quark mass. We show that
as the strange quark mass increases, gapless modes for up-strange quark pairing
occur first, followed by down-strange quark pairing. The behavior of the gaps,
the dispersion relations, and the thermodynamic potential are all found as
functions of the strange quark mass on the basis of a Nambu Jona-Lasinio type
model. To a high degree of accuracy, they are presented as relatively simple
elementary functions. This allows for easy computation for any reasonable range
of baryon chemical potential and strange quark mass.
