When I run the eig command (see help here: eig) I don't get any complex eigenvectors. Maybe the problem is data entry? Assuming your matrix is in a, then
[v,d] = eig(a)
v =
-0.7059 -0.6622 0.4830 0.3203 -0.0000 0.4644
0.0294 -0.1076 0.4654 -0.4804 0.5774 0.4425
0.0294 0.2235 0.2239 0.3203 -0.0000 -0.2974
0.0294 -0.2235 -0.2239 -0.4804 0.5774 -0.2974
0.0294 0.1076 -0.4654 0.3203 -0.0000 0.4425
-0.7059 0.6622 -0.4830 -0.4804 0.5774 0.4644
d =
-40.0000 0 0 0 0 0
0 -31.1332 0 0 0 0
0 0 -2.4668 0 0 0
0 0 0 0.0000 0 0
0 0 0 0 -0.0000 0
0 0 0 0 0 -9.6000
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