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You are missing a couple of zeros. First of all, you must also include the reciprocal of the one located at $z=-2$, that is one at $z=-0.5$ You should also have one more zero coming from the fact that types 3 and 4 are anti-symmetric. This zero must be located at $z=1$, and is responsible for the minus sign in the anti-mirror image polynomial equation: $H(...

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