Problem inverting complex matrix

[parisse]

det(exact(m)) returns:
(-1245591211435133830166343338512439683+51639354804136441655581854007061939*i)/44328554791945219310918948796875252340096000000000000, evalf() to -2.80990710679e-17+1.16492303993e-18*i.
The smallest singular values of m is not too small, but there are 6 very small singular values, this is the reason why the determinant is small, and that raises an error at the end of the Gauss algorithm.
As I said, approx(inv(exact(...))) does the job.