  The quark number density at finite imaginary chemical potential is
investigated in the lattice QCD using the Dirac-mode expansion. We find the
analytical formula of the quark number density in terms of the Polyakov loop in
the large quark mass regime. On the other hand, in the small quark mass region,
the quark number density is investigated by using the quenched lattice QCD
simulation. The quark number density is found to strongly depend on the
low-lying Dirac modes while its sign does not change. This result leads to that
the quark number holonomy is not sensitive to the low-lying Dirac modes. We
discuss the confinement-deconfinement transition from the property of the quark
number density and the quark number holonomy.
