I checked the ratio of your real and imaginary part and it appears to be
about -15.  If your eigenvalues are real and x_r is the real eigenvector
then x_r + (i * c x_r)  is also an eigenvector corresponding to the same
real eigenvalue.  You may just discard the imaginary part.

A(x_r +  (i *c*x_r) ) =   w(x_r + ic_r)

-Nachiket
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