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With Sage, you can have a look at the norms of the eigenvalues:

sage: [e.norm() for e in M.eigenvalues()]
[1, 0.50000000000000000?, 0.50000000000000000?]

You can have a look at the (right) eigenvectors:

sage: M.eigenvectors_right()
[(1, [
  (1, 1/10, 1/20)
  ], 1),
 (-0.50000000000000000? - 0.50000000000000000?*I,
  [(1, -0.10000000000000000? + 0.10000000000000000?*I, 0.?e-20 - 0.10000000000000000?*I)],
  1),
 (-0.50000000000000000? + 0.50000000000000000?*I,
  [(1, -0.10000000000000000? - 0.10000000000000000?*I, 0.?e-20 + 0.10000000000000000?*I)],
  1)]

This should be enough to conclude.