  $$\begin{split}  C_{\tau}^{\mathrm{point \ basis}}(\alpha, \tilde{\beta})_{j,k}=& \mu \partial_{\tau} W^{(N,l)}(p_{0};\tau) e^{\frac{0\pi i l k}{N}} \delta_{j,k}, \\ \\   C_{\mu}^{\mathrm{point \ basis}}(\alpha, \tilde{\beta})_{j,k}=& 