# pascal matrix test

## 1532 days 전, jhlee2chn 작성

# Generating Pascal matrix (n=87) def pascal_matrix(n): A=matrix(n,n,0) for i in range(1, n): A[i,0]=1 A[i,i-1]=1 for j in range(1,i-1): A[i,j]=((A[i-1,j-1] % 2) + (A[i-1,j] % 2)) % 2 A=A+A.transpose() return A A=pascal_matrix(87) # size of matrices without zero eigenvalues list=[3, 7, 11, 23, 43, 87] m=len(list) for i in range(m-1): n=list[i] s=list[i+1]-list[i] print "n= ", n B=A.submatrix(0,0,n,n) D=A.submatrix(n,n,s,s) alp=A.submatrix(n,0,s,n) show(D-alp*B.inverse()*alp.transpose())
 n= 3 \newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrr} 0 & 0 & 0 & -1 \\ 0 & -\frac{3}{2} & \frac{1}{2} & 0 \\ 0 & \frac{1}{2} & \frac{1}{2} & 1 \\ -1 & 0 & 1 & 0 \end{array}\right) n= 7 \newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrr} 0 & 0 & 0 & -1 \\ 0 & -\frac{3}{2} & \frac{1}{2} & 1 \\ 0 & \frac{1}{2} & \frac{1}{2} & 2 \\ -1 & 1 & 2 & -2 \end{array}\right) n= 11 \newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrrrrrrr} 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & -4 & 0 & -2 & 0 & 0 & 0 & -2 & 0 & -4 & -1 & -4 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & -1 \\ 0 & -2 & 0 & -4 & 0 & 0 & 0 & -2 & 1 & -4 & -1 & -6 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & -1 & 0 & -1 \\ 0 & 0 & 0 & 0 & 0 & -\frac{3}{2} & \frac{1}{2} & 1 & \frac{1}{2} & 1 & \frac{1}{2} & 1 \\ 0 & 0 & 0 & 0 & 0 & \frac{1}{2} & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 \\ 0 & -2 & 0 & -2 & -1 & 1 & 2 & -2 & 2 & -2 & 0 & -4 \\ 0 & 0 & 0 & 1 & 0 & \frac{1}{2} & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 \\ 0 & -4 & -1 & -4 & -1 & 1 & 2 & -2 & 2 & -6 & 0 & -6 \\ 0 & -1 & 0 & -1 & 0 & \frac{1}{2} & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 \\ 1 & -4 & -1 & -6 & -1 & 1 & 2 & -4 & 2 & -6 & 0 & -10 \end{array}\right) n= 23 \newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrrrrrrrrrrrrrrr} 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & -4 & 0 & -2 & 0 & -2 & 0 & -2 & 0 & 0 & 0 & -2 & 0 & -2 & 0 & -2 & 0 & -4 & -1 & -6 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & -1 \\ 0 & -2 & 0 & -8 & 0 & -2 & -2 & -6 & 0 & 0 & 0 & -2 & 2 & -2 & 0 & 2 & 1 & -4 & -1 & -8 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & -2 & 0 & 0 & 0 & -2 & 0 & 0 & 0 & -1 & 0 & -1 & 0 & -3 \\ 0 & -2 & 0 & -2 & 0 & -4 & 0 & -2 & 0 & 0 & 0 & -2 & 0 & -2 & 1 & -2 & 1 & -4 & -1 & -6 \\ 0 & 0 & 0 & -2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 1 & 0 & -1 & 0 & -1 \\ 0 & -2 & 0 & -6 & -2 & -2 & 0 & -8 & 0 & 0 & 0 & -6 & 1 & -2 & -1 & -2 & 1 & -4 & -1 & -12 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -\frac{3}{2} & \frac{1}{2} & 1 & \frac{1}{2} & 1 & \frac{1}{2} & 1 & \frac{1}{2} & 1 & \frac{1}{2} & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{2} & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 \\ 0 & -2 & 0 & -2 & -2 & -2 & 0 & -6 & -1 & 1 & 2 & -6 & 2 & 0 & 0 & -4 & 2 & -2 & 0 & -10 \\ 0 & 0 & 0 & 2 & 0 & 0 & 0 & 1 & 0 & \frac{1}{2} & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 0 & \frac{1}{2} & 2 & \frac{1}{2} & 2 \\ 0 & -2 & 0 & -2 & 0 & -2 & -1 & -2 & -1 & 1 & 2 & 0 & 2 & -2 & 2 & 0 & 2 & -2 & 0 & -4 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & -1 & 0 & \frac{1}{2} & \frac{1}{2} & 0 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 0 \\ 0 & -2 & 0 & 2 & -1 & -2 & 1 & -2 & -1 & 1 & 2 & -4 & 0 & 0 & 2 & -6 & 2 & -2 & 0 & -6 \\ 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & \frac{1}{2} & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 \\ 0 & -4 & -1 & -4 & -1 & -4 & -1 & -4 & -1 & 1 & 2 & -2 & 2 & -2 & 2 & -2 & 2 & -6 & 0 & -8 \\ 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & \frac{1}{2} & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 \\ 1 & -6 & -1 & -8 & -3 & -6 & -1 & -12 & -1 & 1 & 2 & -10 & 2 & -4 & 0 & -6 & 2 & -8 & 0 & -22 \end{array}\right) n= 43 \newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr} 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ 0 & -8 & 0 & -4 & 0 & 0 & 0 & 12 & 0 & 8 & 0 & 10 & 0 & 0 & 0 & 6 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -6 & 0 & 0 & 0 & -10 & 0 & -8 & 0 & -12 & 0 & 0 & 0 & 4 & 0 & 8 & 1 & 4 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 \\ 0 & -4 & 0 & -8 & 0 & 0 & 0 & 6 & 0 & 4 & 0 & 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -6 & 0 & 0 & 0 & -6 & 0 & 0 & 0 & -6 & 0 & 0 & 0 & -8 & 0 & -4 & 0 & -6 & 0 & 0 & 0 & 0 & -1 & 6 & 1 & 6 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 & -4 & 0 & -2 & 0 & -2 & 0 & -2 & 0 & -2 & 0 & -2 & 0 & -2 & 0 & -2 & 0 & 0 & 0 & -2 & 0 & -2 & 0 & -2 & 0 & -2 & 0 & -2 & 0 & -2 & 0 & -2 & 0 & -4 & -1 & -6 & -1 & -6 & -1 & -6 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 \\ 0 & 12 & 0 & 6 & 0 & -2 & 0 & -32 & 0 & -20 & 0 & -26 & 0 & -2 & -2 & -18 & -2 & -4 & 0 & -2 & 0 & 0 & 0 & -2 & 0 & 0 & 2 & 14 & 2 & -2 & 0 & 22 & 0 & 16 & 0 & 26 & 1 & -4 & -1 & -12 & -1 & -18 & -1 & -8 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 \\ 0 & 8 & 0 & 4 & 0 & -2 & 0 & -20 & 0 & -16 & 0 & -18 & 0 & -2 & -2 & -14 & -2 & -6 & 0 & -4 & 0 & 0 & 0 & -4 & 0 & -2 & 2 & 6 & 2 & -2 & 0 & 12 & 0 & 10 & 1 & 16 & 1 & -4 & -1 & -12 & -1 & -16 & -1 & -10 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -2 & 0 & -2 & 0 & -2 & 0 & 0 & 0 & -2 & 0 & -2 & 0 & -2 & 0 & 0 & 0 & -2 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -3 & 0 & -3 & 0 & -3 \\ 0 & 10 & 0 & 2 & 0 & -2 & 0 & -26 & 0 & -18 & 0 & -28 & 0 & -2 & -2 & -22 & -2 & -8 & 0 & -12 & 0 & 0 & 0 & -12 & 0 & -4 & 2 & 4 & 2 & -2 & 0 & 12 & -1 & 12 & 1 & 22 & 1 & -4 & -1 & -18 & -1 & -20 & -1 & -12 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -2 & 0 & -2 & 0 & -2 & 0 & 0 & 0 & -2 & 0 & -2 & 0 & -2 & 0 & 0 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -3 & 0 & -3 & 0 & -3 \\ 0 & 0 & 0 & 0 & 0 & -2 & 0 & -2 & 0 & -2 & 0 & -2 & 0 & -4 & 0 & -2 & 0 & -2 & 0 & -2 & 0 & 0 & 0 & -2 & 0 & -2 & 0 & -2 & 0 & -2 & 1 & -2 & 1 & -2 & 1 & -2 & 1 & -4 & -1 & -6 & -1 & -6 & -1 & -6 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & -2 & 0 & -2 & 0 & -2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 \\ 0 & 6 & 0 & 0 & 0 & -2 & 0 & -18 & 0 & -14 & -2 & -22 & -2 & -2 & 0 & -20 & 0 & -8 & 0 & -14 & 0 & 0 & 0 & -14 & 0 & -6 & 2 & -2 & 1 & -2 & -1 & 4 & -1 & 6 & 1 & 14 & 1 & -4 & -1 & -18 & -1 & -18 & -1 & -12 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & -2 & 0 & -2 & 0 & -2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & -1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 \\ 0 & 0 & 0 & 0 & 0 & -2 & 0 & -4 & 0 & -6 & -2 & -8 & -2 & -2 & 0 & -8 & 0 & -8 & 0 & -8 & 0 & 0 & 0 & -8 & 0 & -6 & 1 & -6 & 1 & -2 & -1 & -4 & -1 & -2 & 1 & 0 & 1 & -4 & -1 & -12 & -1 & -12 & -1 & -12 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 \\ 0 & 0 & 0 & -6 & 0 & -2 & 0 & -2 & 0 & -4 & -2 & -12 & -2 & -2 & 0 & -14 & 0 & -8 & 0 & -20 & 0 & 0 & 0 & -18 & 1 & -8 & 1 & -14 & 1 & -2 & -1 & -12 & -1 & -4 & 1 & -2 & 1 & -4 & -1 & -18 & -1 & -12 & -1 & -12 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -\frac{3}{2} & \frac{1}{2} & 1 & \frac{1}{2} & 1 & \frac{1}{2} & 1 & \frac{1}{2} & 1 & \frac{1}{2} & 1 & \frac{1}{2} & 1 & \frac{1}{2} & 1 & \frac{1}{2} & 1 & \frac{1}{2} & 1 & \frac{1}{2} & 1 & \frac{1}{2} & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{2} & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 \\ 0 & 0 & 0 & -6 & 0 & -2 & 0 & -2 & 0 & -4 & -2 & -12 & -2 & -2 & 0 & -14 & 0 & -8 & 0 & -18 & -1 & 1 & 2 & -18 & 2 & -6 & 2 & -12 & 2 & 0 & 0 & -10 & 0 & -2 & 2 & 0 & 2 & -2 & 0 & -16 & 0 & -10 & 0 & -10 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & \frac{1}{2} & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 \\ 0 & 0 & 0 & 0 & 0 & -2 & 0 & 0 & 0 & -2 & -2 & -4 & -2 & -2 & 0 & -6 & 0 & -6 & -1 & -8 & -1 & 1 & 2 & -6 & 2 & -6 & 2 & -6 & 2 & 0 & 0 & -6 & 0 & -4 & 2 & -2 & 2 & -2 & 0 & -10 & 0 & -10 & 0 & -10 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 2 & 0 & 2 & 0 & 2 & 0 & 0 & 0 & 2 & 0 & 1 & 0 & 1 & 0 & \frac{1}{2} & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 \\ 0 & -6 & 0 & -6 & 0 & -2 & 0 & 14 & 0 & 6 & -2 & 4 & -2 & -2 & 0 & -2 & 1 & -6 & -1 & -14 & -1 & 1 & 2 & -12 & 2 & -6 & 2 & -18 & 2 & 0 & 0 & -20 & 0 & -12 & 2 & -16 & 2 & -2 & 0 & -10 & 0 & -4 & 0 & -10 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 2 & 0 & 2 & 0 & 2 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & \frac{1}{2} & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 \\ 0 & 0 & 0 & 0 & 0 & -2 & 0 & -2 & 0 & -2 & 0 & -2 & 0 & -2 & -1 & -2 & -1 & -2 & -1 & -2 & -1 & 1 & 2 & 0 & 2 & 0 & 2 & 0 & 2 & -2 & 2 & 0 & 2 & 0 & 2 & 0 & 2 & -2 & 0 & -4 & 0 & -4 & 0 & -4 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & \frac{1}{2} & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 \\ 0 & -10 & 0 & -8 & 0 & -2 & 0 & 22 & 0 & 12 & -2 & 12 & -1 & -2 & 1 & 4 & 1 & -4 & -1 & -12 & -1 & 1 & 2 & -10 & 2 & -6 & 0 & -20 & 0 & 0 & 2 & -26 & 2 & -16 & 2 & -24 & 2 & -2 & 0 & -6 & 0 & 2 & 0 & -6 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & \frac{1}{2} & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 \\ 0 & -8 & 0 & -4 & 0 & -2 & 0 & 16 & 0 & 10 & -1 & 12 & -1 & -2 & 1 & 6 & 1 & -2 & -1 & -4 & -1 & 1 & 2 & -2 & 2 & -4 & 0 & -12 & 0 & 0 & 2 & -16 & 2 & -14 & 2 & -18 & 2 & -2 & 0 & -2 & 0 & 2 & 0 & -4 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & \frac{1}{2} & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 \\ 0 & -12 & 0 & -6 & 0 & -2 & 0 & 26 & -1 & 16 & -1 & 22 & -1 & -2 & 1 & 14 & 1 & 0 & -1 & -2 & -1 & 1 & 2 & 0 & 2 & -2 & 0 & -16 & 0 & 0 & 2 & -24 & 2 & -18 & 2 & -30 & 2 & -2 & 0 & 2 & 0 & 8 & 0 & -2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & \frac{1}{2} & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 & \frac{1}{2} & 2 \\ 0 & 0 & 0 & 0 & 0 & -4 & -1 & -4 & -1 & -4 & -1 & -4 & -1 & -4 & -1 & -4 & -1 & -4 & -1 & -4 & -1 & 1 & 2 & -2 & 2 & -2 & 2 & -2 & 2 & -2 & 2 & -2 & 2 & -2 & 2 & -2 & 2 & -6 & 0 & -8 & 0 & -8 & 0 & -8 \\ 0 & 0 & 0 & 0 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & \frac{1}{2} & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 \\ 0 & 4 & 0 & 0 & 1 & -6 & -1 & -12 & -1 & -12 & -3 & -18 & -3 & -6 & -1 & -18 & -1 & -12 & -1 & -18 & -1 & 1 & 2 & -16 & 2 & -10 & 2 & -10 & 2 & -4 & 0 & -6 & 0 & -2 & 2 & 2 & 2 & -8 & 0 & -26 & 0 & -24 & -2 & -24 \\ 0 & 0 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & \frac{1}{2} & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 \\ 0 & 8 & 1 & 6 & 1 & -6 & -1 & -18 & -1 & -16 & -3 & -20 & -3 & -6 & -1 & -18 & -1 & -12 & -1 & -12 & -1 & 1 & 2 & -10 & 2 & -10 & 2 & -4 & 2 & -4 & 0 & 2 & 0 & 2 & 2 & 8 & 2 & -8 & 0 & -24 & 0 & -30 & -2 & -26 \\ 0 & 1 & 0 & 1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & \frac{1}{2} & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & \frac{1}{2} & -2 & \frac{1}{2} & -2 & \frac{1}{2} & -2 \\ -1 & 4 & 1 & 6 & 1 & -6 & -1 & -8 & -1 & -10 & -3 & -12 & -3 & -6 & -1 & -12 & -1 & -12 & -1 & -12 & -1 & 1 & 2 & -10 & 2 & -10 & 2 & -10 & 2 & -4 & 0 & -6 & 0 & -4 & 2 & -2 & 2 & -8 & 0 & -24 & 0 & -26 & -2 & -30 \end{array}\right) n= 3 n= 7 n= 11 n= 23 n= 43