The tables require some explanation. Let *S* be a finite set of primes. We are
interested in the fields which are unramified outside of the set *S*, and this
is what we mean by "prescribed ramification". A classical result from number theory
tells us that the number of such fields is finite. Unless stated otherwise, the tables
presented below are complete in the sense that every field is listed.

The field data is partitioned by Galois group. Each row in a table gives the numbers of each type of field and the total number of fields. The last two columns give links to the actual field data in two different formats: text and gp.

In some cases, to reduce the width of the tables, we partition the results into new
and old fields. A field is said to be *old* if it's Galois closure is the compositum
of smaller degree fields; otherwise, it is said to be *new*. Note that this definition
differs slightly from that in the literature. The key point here is that old fields can be
easily generated from tables of smaller degree fields by forming compositums and then
computing the subfields of the compositums.

- Tables of Cubics
- Tables of Quartics
- Tables of Quintics
- Tables of Sextics:
- Tables of Septics
- Tables of Octics:
- Imprimitive Nonics
- Tables of Decics: