Is there a way to tell GAP to do calculations in a field smaller than Q(E(n)) ?

For example, if I have matrices over Q( sqrt(-7), sqrt(5) ), GAP translates all
the entries to E(35) and that results in expressions that are much more
complicated than they have to be; ER(-7) + ER(5) for example becomes

 2*E(35)-2*E(35)^3+2*E(35)^4+2*E(35)^9+2*E(35)^11-2*E(35)^12-2*E(35)^13
+2*E(35)^16-2*E(35)^17-2*E(35)^27+2*E(35)^29-2*E(35)^33

I looked at "NumberField" which seems to set up such subfields, but I couldn't
find anything that goes beyond this. Is what I am trying to do possible in
3.3? how about 3.4? Thanks.

Jacob Hirbawi
JcbHrb@CERF.net