%0 Journal Article %T Tables of Pure Quintic Fields %A Daniel C. Mayer %J Advances in Pure Mathematics %P 347-403 %@ 2160-0384 %D 2019 %I Scientific Research Publishing %R 10.4236/apm.2019.94017 %X By making use of our generalization of Barrucand and Cohn¡¯s theory of principal factorizations in pure cubic fields \"\" and their Galois closures \"\" with 3 possible types to pure quintic fields \"\" and their pure metacyclic normal fields \"\" with 13 possible types, we compile an extensive database with arithmetical invariants of the 900 pairwise non-isomorphic fields N having normalized radicands in the range 2¡ÜD<103. Our classification is based on the Galois cohomology of the unit group UN, viewed as a module over the automorphism group Gal(N/K) of N over the cyclotomic field K=Q(¦Î5), by employing theorems of Hasse and Iwasawa on the Herbrand quotient of the unit norm index (Uk:NN/K(UN)) by the number #(PN/K/PK) of primitive ambiguous principal ideals, which can be interpreted as principal factors of the different DN/K. The precise structure of the F5-vector space of differential principal factors is expressed in terms of norm kernels and central orthogonal idempotents. A connection with integral representation theory is established via class number relations by Parry and Walter involving the index of subfield units (U<SUB>N</SUB>:U<SUB>0</SUB>)