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Can't construct automorphisms of p-adic fields

I'm trying to construct automorphisms of finite extensions of $\mathbb Q_p$ and getting a funny error. Here's a prototypical example:

Evaluating the cyclotomic polynomial $x^4 + x^3 + x^2 + x + 1$ at $x+1$ gives an Eisenstein polynomial for the prime $p=5$. If $\pi$ is a root of $(x+1)^4 + (x+1)^3 + (x+1)^2 + (x+1) + 1$ then $\pi+1$ will be a primitive 5th root of unity.

K.<pi> = Qp(5).ext(sum((1+x)^i for i in range(5)))

So $K=\mathbb Q_p(\zeta_5)$ with uniformizer $\pi=\zeta_5-1$. Now I want to define the automorphism $\tau:\zeta_5\mapsto\zeta_5^2$. We have $\tau(\pi)=(1+\pi)^2-1=2\pi+\pi^2$. But the following

tau = K.hom([2*pi+pi^2])

results in the error TypeError: images do not define a valid homomorphism. What's going on? Are hom's of $p$-adic fields not really implemented yet or am I doing something wrong?