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What is the most useful basefield for finite matrix groups?

Hi everyone, I am trying to write a notebook that does some elementary computations in a finite matrix group like conjugacy classes and character tables. It is meant to be used in cases where the group is realized explicitly as some subgroup of GL(3,R) or GL(2,R). My problem now is that if I want to implement rotations like

for t in [1/3,2/3]:

the base ring will be the symbolic ring SR because there is a sqrt(2) in some denominators. If I then try to compute the characters via


I will get an error message. My assumption is that because of the base ring SR, Sage doesn't realize that this is in fact a finite group. What would a suitable base field be to make this computation possible?

Thanks in advance.