only the states with a fixed total electron number $N_e$. Coefficients $u_{\mib k}$ and $v_{\mib k}$ appear in our calculation only in the ratio defined by $$\begin{aligned}
& & v_{\mib k}/u_{\mib k} =  \Delta_{\mib k}/( \xi_{\mib k}
       + \sqrt{ \xi_{\mib k}^2 + \Delta_{\mib k}^2 } ), \label{eq:vu} \\
\xi_{\mib k} &=& - 2t (\cos k_x + \cos k_y) 
- 4t' \cos k_x \cos k_y - \mu , \label{eq:ek}\end{aligned}$$ where $\Delta_{\mib k}$ is a ${\mib k}$-dependent gap function defined later; $\mu$ is a variational parameter working like the chemical potential in the trial wave function; $c_{{\mib k}\sigma}$ is the Fourier transform of $c_{j\sigma}$. Neglecting constant factors, $\Psi_{\mbox{\scriptsize s}}$ can be rewritten as $$\begin{aligned}
\Psi_s 
&\sim& P_{N_e} P_{\mbox{\scriptsize G}}
        \exp [\sum_{\mib k} (v_{\mib k} / u_{\mib k})
  c_{{\mib k}\uparrow}^{\dag}c_{-{\mib k}\downarrow}^{\dag}]|0>, \label{eq:PP} \\ 
&=& P_{N_e} P_{\mbox{\scriptsize G}}
        \exp [\sum_{j,l} a(j,l) 
      c_{j\uparrow}^{\dag}c_{l\downarrow}^{\dag}]|0>, \\ 
& \sim\ & P_{\mbox{\scriptsize G}} [\sum_{j,l} a(j,l) 
      c_{j\uparrow}^{\dag}c_{l\downarrow}^{\dag}]^{N_e/2}|0>, \\ 
&=& P_{\mbox{\scriptsize G}}
      \sum_{j_1,..,j_{N_e/2},l_1,..,l_{N_e/2}}
      A(j_1, .., j_{N_e/2};l_1, .., l_{N_e/2})  \nonumber  \\
&\times& c_{j_1 \uparrow}^{\dag} c_{j_2 \uparrow}^{\dag} ...
c_{j_{N_e/2} \uparrow}^{\dag} c_{l_1 \downarrow}^{\dag} 
c_{l_2 \downarrow}^{\dag} ... c_{l_{N_e/2} \downarrow}^{\dag} |0>,\end{aligned}$$ where $a(j,l)$ is defined by $$a(j,l) = (1/N_s) \sum_{{\mib k}} (v_{\mib k} / u_{\mib k})
                     \exp [\mbox{i} {\mib k} \cdot ({\mib R}_l - 
                      {\mib R}_j 