Let 0,1≠m∈Z and α=m8. According to the results of Gaál and El Fadil, α generates a power integral basis in K=Q(α), if and only if m is square-free and m≢1(mod4). In the present paper, we consider totally complex pure octic fields, as in the case mm>−5000, which yields 2024 fields.
István Gaál (Thu,) studied this question.