Question: Possible bug in Eingenvalues

I am using maple 13 to found Eingenvalues of an hermitian matrix :

M1:=Matrix([
> [lambda3+lambda4,0,0,0,0,0,lambda4/sqrt(2),0,0,I*lambda4/sqrt(2)],
> [0,lambda3/4,0,0,0,0,0,0,0,0],
> [0,0,lambda3/4,0,0,0,0,0,0,0],
> [0,0,0,lambda3/4,0,0,0,0,0,0],
> [0,0,0,0,lambda3/4,0,0,0,0,0],
> [0,0,0,0,0,lambda3,0,0,0,0],
> [lambda4/sqrt(2),0,0,0,0,0,lambda3/2,0,0,0],
> [0,0,0,0,0,0,0,lambda2,0,0],
> [0,0,0,0,0,0,0,0,lambda2,0],
> [-I*lambda4/sqrt(2),0,0,0,0,0,0,0,0,lambda4/2]
> ]);

>Eigenvalues(M1);

my surprise is that maple gives me 8 correct solutions an 2 complex eigenvalues which are not acceptable (we now that the eigenvalues for an hermitian matrix are all real) .

To understand the output of maple, first,  I suspect that the complex part of the roots was null but without success I haven't found how to do it zero...

is it a bug? Thanks a lot to cooperation

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