You're right - thanks. I have a question about the output of this though.
F5 has 4 distinct eigenvalues (one of them has multiplicity 2).
F5.eigenspaces() correctly returns the eigenspaces defined over
QQ(zeta5). There are two eigenvalues not in QQ(zeta5)
but the output simply indicates "(a2,[ ])". What does this means?

didier deshommes wrote:
>
> This seems to have been corrected as of 2.0, so I would suggest you upgrade 
> :) :
>
> sage: F5.eigenspaces()
> [
> (2*zeta5^3 + 2*zeta5^2 + 1, [
> (1, 1/2*zeta5^3 + 1/2*zeta5^2, 1/2*zeta5^3 + 1/2*zeta5^2, 1/2*zeta5^3
> + 1/2*zeta5^2, 1/2*zeta5^3 + 1/2*zeta5^2)
> ]),
> (-2*zeta5^3 - 2*zeta5^2 - 1, [
> (1, 0, -zeta5^3 - zeta5^2 - 1, -zeta5^3 - zeta5^2 - 1, 0),
> (0, 1, -1, -1, 1)
> ]),
> (a2, [
>
> ])
> ]
>
> >
>
>   


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