Solved
Actually "genvecs" generates the necessary vectors. But on contrary to "eigenvec" there is no "genvec" which would return an eigenvector associated with a certain eigenvalue.
And "genvecs" returns the vectors in the same order as the values in "genvals" and also differently scaled.
Scaling could easily be fixed but I don't know if the order after sorted eigenvals could be automated.

But of course we could automate what you did manually

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