@Preben Alsholm 

how did you conduct your experiments and what do you mean by n-2 real eigenvalues outside the intervals?

@nm 

I am sorry, the code I used was at the following website, http://www.mapleprimes.com/questions/203613-How-Do-I-Find-A-Condition-For-Eigenvalues. But the equation is wrong in that post. The top element needs to be -i*x. Does this help at all?

The only issue is that the top and bottom elements of the matrix need to be opposite. That is the first entry in the first row and first column must be -I*x and the bottom entry must be I*x. Sorry I did not type this correctly in the question. Can I just replace the matrix entries and run this? Thanks again!

@Kitonum