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[Lapack] Possible bug in the computation of complex left eigenvectors

Dear lapack team,
I tried to compute the left-eigenvector of the matrix A=[[0,1]; [-1,0]] 
using the function zgeev and I got some results that seem wrong.

I get the eigenvalue eig=I and the associated left-eigenvector vect = 
[-0.7071 * I, 0.7071].
However, this is not a left eigenvector:
vect * A = [-0.701, -0.701]
eig * vect = [0.701, 0.701*I]

The correct left-eigenvector for I should be [0.701, -0.701*I]

Also the other eigenvalue, eigenvector pair that is returned by zgeev 
seems wrong (eig= -I, vect=[0.707*I, 0.707])

I bumped into this problem using the lapacke c interface, but I 
reproduced it also with fortran (I used the example code provided online 
for zgeev).
I also tried the examples using the svn version of the library, but I 
get the same results.
I attach a tar.gz archive with the source code and the test case to 
reproduce the issue.


As I am new to lapack I could have missed some details and I could have 
misused the library.

Thank you,
Sergio Mover
mover@Domain.Removed

PS: I also tried to use the forum, but I cannot post the bug report 
since the website always mark it as spam.


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