Pairs of orthogonal cyclotomic orthomorphisms, one quadratic the other quartic, for the cases where near-linear examples do not exist. There are only 5 such fields and all of them have prime order. Hence we give field elements as numbers, rather than powers of a primitive element. The 5 fields are listed below, followed by a line that gives the multipliers for the quadratic orthomorphism, followed by a line that gives the multipliers for the quartic orthomorphism. GF(13) 2 5 3 6 7 3 GF(17) 2 9 3 5 15 13 GF(29) 2 8 5 6 5 5 GF(37) 2 5 3 4 11 30 GF(41) 2 5 3 3 12 7