when Dynare gives me the eigenvalues of my forward looking variables, it just prints out the values, but does not tell me which eigenvalue belongs to which forward looking variable. How can I get this information?

You canâ€™t. Your system of equations is not decoupled. The eigenvalues belong to an interdependent system. Only if all equations were completely independent of each other could you say that a particular eigenvalue belongs to a particular equation and variable. This can be seen in Klein/Gomme (2011).