Confirm the first few coefficients in the low-temperature series for the two-dimensional Ising model in equation (13.4.53). Write a program to calculate the energies of all \(2^{16}\) states for a \(4 \times 4\) periodic lattice. Show that the coefficients here are

\[
g_{q}=\{2,0,32,64,424,1728,6688,13568,20524,13568,6688,1728,424,64,32,0,2\}
\]

Extend your code to calculate the partition function for a \(6 \times 6\) lattice, which has \(2^{36}\) states.