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Matrix elements above the diagonal get the phase factor e—imt because their energy difference is opposite in sign (downward transition). The factor eimt is 1, i, —1, —i, and 1 for mT = 0, n/2, n, 3n/2, and 2n. It can be represented as a vector in the complex plane of unit length rotating with angular velocity m. The phase factor e—imt rotates in the opposite direction with values of 1, —i, — 1, i, and 1 for mT = 0, n/2, n, 3n/2, and 2n. Thus the final matrix would be

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