# Evaluate polynomial with imaginary number as input?

I am trying to evaluate the polynomial (`19v^2 + 49v + 8`

) raised to the 67th power where `v^3 + 2 = 0`

.
All computations are done mod 67.

Here's my first attempt:

```
R.<v> = PolynomialRing(GF(67))
poly = (19 * (v^2) + 49*v + 8)
after_frobenius = poly^67
after_frobenius(sqrt(-2))
```

But this gives the error: "positive characteristic not allowed in symbolic computation".

I suspect, I need to define the `PolynomialRing`

over an extension field where `v^3 + 2 = 0`

. But, I'm not sure how to do that.
Any ideas?