Erik Roijackers, Jasper Cramwinckel and Reinald Baart asked:
GAP must find a primitive 19th root of unity, which is an element of
GF(2^18), 18 being the multiplicative order of 2 modulo 19. But GAP limits
the size of a finite field to 2^16.
Will this limitation be removed in the near future, or is there another
way to solve the problem?
The next version of GAP will include code for arbitrary finite algebraic
extensions of fields. This should solve your problem.