On the monogenity of totally complex pure octic fields

Let 0,1≠ m∈ Z and α=√[8]m. According to the results of I. Ga\'al and L. El Fadil, α generates a power integral basis in K=Q(α), if and only if m is square-free and m≡ 1\;(\; 4). In the present paper we consider totally complex pure octic fields, that is the case $m<0$, with m satisfiying the above property. In this case (1,α,α²,…,α⁷) is an integral basis. Our purpose is to investigate whether K admits any other generators of power integral bases, inequivalent to α. We present an efficient method to calculate generators of power integral bases in this type of fields with coefficients <10²⁰⁰ in the above integral basis. We report on the results of our calculation for this type of fields with $0>m>-5000$, which yields 2024 fields.