Cannot convert elements of cyclotomic fields to algebraic numbers

[rbeezer]

sage: C.<z> = CyclotomicField(7)
sage: a = 2*z^2 + 5*z^4
sage: E = C.algebraic_closure()
sage: E(a)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<snip>
TypeError: Illegal initializer for algebraic number

[arminstraub]

Unfortunately, at the moment, elements of number fields don't coerce/convert to the algebraic closure QQbar. This is an instance of #12715 (Number field embeddings should go via AA and QQbar).

Note that you can coerce elements to numerical complex numbers though:

sage: C.<z> = CyclotomicField(7)
sage: CC(z)
0.623489801858734 + 0.781831482468030*I
sage: QQbar(z)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<your snip>
TypeError: Illegal initializer for algebraic number

I would therefore suggest to mark this ticket as a duplicate. (I don't immediately see a way to do that myself, so please let me know if I could and should have done so myself.)