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Questions about Lie algebra

I am trying to do some calculations and I don't understand what the output is.

L = lie_algebras.sp(QQ, 4)


The output is the following

(E[alpha[1]], E[alpha[2]], E[-alpha[1]], E[-alpha[2]], h1, h2)
  1. I know that the command L.gens() gives a set of genearators of the Lie algebra. So I understand that this is giving us an element from $e_\alpha\in L_\alpha$ for each $\alpha\in \Delta$ and the corresponding elements $h_\alpha \in H$, (where $\Delta$ is a base of the root system and $H$ is a Cartan Subalgebra). But I don't understand what these elements exactly are. Are these elements of a Chevalley basis?

  2. Let's say I want to figure out $\alpha_1(h_1)$. So I thought maybe alpha1(h1) will give me the answer. But I am getting an error. I also tried L.alpha[1](h1) which results in an error as well. How can I fix this?