I do not know how efficiently relative extensions of Q[i] are implemented.
I would not mind an absolute field. 
I need things like computing resultants and factoring univariate polynomials to 
work not too slowly.

I did some Groebner basis computation that gave me what I suspect is an 
superfield of what I need, and it is of degree 32 over Q, with really huge 
coefs....

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