  We develop an alternative method to solve the Eilenberger equations
numerically for the vortex-lattice states of type-II superconductors. Using it,
we clarify the magnetic-field and impurity-concentration dependences of the
magnetization, the entropy, the Pauli paramagnetism, and the mixing of higher
Landau levels in the pair potential for two-dimensional $s$- and
$d_{x^2-y^2}$-wave superconductors with the cylindrical Fermi surface.
