# simple script gives "ValueError: element is not in the prime field"

I have a very simple script that does not work. It is the following.

```
for a in range(1,r):
for b in range(1,r):
g=a+b*x^2+x^4
if g.is_irreducible():
K.<a>=FiniteField(r^4, name='a', modulus = g)
if a^l != 1:
print("hooray")
```

Here l is defined somewhere else, but that is not what gives the error I think. I think the error occurs when sage goes over the line "K.=FiniteField(r^4, name='a', modulus = g)", because maybe the line "g=a+b*x^2+x^4" does not work? If I do this script manually without the for loops, by just assigning some values to a and b, then it works fine.

The error depends on the information you've omitted, such as the definition of

`r`

,`l`

, and`x`

. As a general rule, please give an unambiguous self-contained example that produces the error. Probably the problem is that`l`

cannot be lifted to an integer.