Here is the CIS spin-adapted singlet matrix for the H2O STO-3G test case. Note that the row/column ordering follows i and a combinations with a as the faster-running index (i.e., a indexes the inner loop). Thus the first row/column corresponds to i=0 and a=0 and the second row/column to i=0 and a=1. Notice that the matrix is diagonally dominant --- that is, the largest element on any row/column combination is the diagonal entry --- and that all the diagonal elements are positive.
1 2 3 4 5 6 7 8 9 10
1 19.9585039 0.0000000 0.0074145 -0.0000000 -0.0000000 -0.0076611 0.0180084 -0.0000000 -0.0000000 0.0000000
2 0.0000000 20.0113341 -0.0000000 0.0089205 -0.0076611 -0.0000000 -0.0000000 0.0037402 0.0000000 -0.0000000
3 0.0074145 -0.0000000 1.0931793 0.0000000 -0.0000000 -0.0867137 0.0485372 -0.0000000 0.0000000 0.0000000
4 -0.0000000 0.0089205 0.0000000 1.1888405 -0.0867137 0.0000000 -0.0000000 -0.0183287 0.0000000 0.0000000
5 -0.0000000 -0.0076611 -0.0000000 -0.0867137 0.4757743 0.0000000 0.0000000 0.0615255 -0.0000000 0.0000000
6 -0.0076611 -0.0000000 -0.0867137 0.0000000 0.0000000 0.5527668 0.0615255 -0.0000000 0.0000000 -0.0000000
7 0.0180084 -0.0000000 0.0485372 -0.0000000 0.0000000 0.0615255 0.3703281 -0.0000000 0.0000000 -0.0000000
8 -0.0000000 0.0037402 -0.0000000 -0.0183287 0.0615255 -0.0000000 -0.0000000 0.4442931 -0.0000000 0.0000000
9 -0.0000000 0.0000000 0.0000000 0.0000000 -0.0000000 0.0000000 0.0000000 -0.0000000 0.2872555 0.0000000
10 0.0000000 -0.0000000 0.0000000 0.0000000 0.0000000 -0.0000000 -0.0000000 0.0000000 0.0000000 0.3659890