  The nonanalyticity and the sign problem in the Z3-symmetric heavy quark model
at low temperature are studied phenomenologically. For the free heavy quarks,
the nonanalyticity is analyzed in the relation to the zeros of the grand
canonical partition function. The Z3-symmetric effective Polyakov-line model
(EPLM) in strong coupling limit is also considered as an phenomenological model
of Z3-symmetric QCD with large quark mass at low temperature. We examine how
the Z3-symmetric EPLM approaches to the original one in the zero-temperature
limit. The effects of the Z3-symmetry affect the structure of zeros of the
microscopic probability density function at the nonanalytic point. The average
value of the Polyakov line can detect the structure, while the other
thermodynamic quantities are not sensible to the structure in the
zero-temperature limit. The effect of the imaginary quark chemical potential is
also discussed. The imaginary part of the quark number density is very
sensitive to the symmetry structure at the nonanalytical point. For a
particular value of the imaginary quark number chemical potential, large quark
number may be induced in the vicinity of the nonanalytical point.
