there are partially filled ${\mib k}$-points in the electronic state in the $U = 0$ limit, as is shown in Fig. \[fig:kpoints\] for $N_s = 10 \times 10$ and $N_e = 84$ with $t' = 0$. While the other cases with $\rho = 0.72, 0.80$ and $0.88$ have a closed shell. The curve has almost no dependence on the shell state in the region of $0.76 \leq \rho \leq 0.92$, making a definite contrast with the case with $t'=0$ described later. This suggests that the curve is already close to the bulk limit one in this region. For $t' = - 0.15$ with open diamonds, the cases of $\rho = 0.68$, $0.76$ and $0.88$ have an open shell while others have a closed shell. Here we observe a weak dependence on the shell structure. However the deviation from the rough average between the open-shell and closed-shell curves are only of the order of $1/10$ of the average energy gain per site in the region of $0.76 \leq \rho \leq 0.92$, which is small enough to judge that the points are already close to the bulk limit. The smooth dependence on $\rho$ is also observed in the SC gap amplitude $\Delta$ 