This data was produced by my student David Fear for his MSc thesis.

An orthomorphism of a finite field F is a permutation θ:F➞F such that the map x➞θ(x)-x is also a permutation of F. Suppose |F|=q and k divides q-1. An orthomorphism θ is cyclotomic of index k if θ(x)/x is constant on the cosets of the subgroup of index k in F*. The value of θ(x)/x is known as a multiplier. To specify a cyclotomic orthomorphism we may just list the multipliers. There will be 1 for a linear orthomorphism, 2 for a quadratic, 3 for a cubic, 4 for a quartic and so on.

David needed the following data to support claims made in his thesis. In every case q is the order of the field.

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