Consider the fermionic field operators $\psi_a(x), \psi^{\dagger}_b(y)$ with the canonical anti-commutation relations $\{\psi_a(x),\psi_b(y)\} = 0 $ amd$$\{\psi_a(x),\psi_b(y)\} = 0 $$ and $\{\psi^{\dagger}_b(t,\vec{x}),\psi_a(t,\vec{y})\} = \delta_{ab} \delta(\vec{x}-\vec{y})$.$$\{\psi^{\dagger}_b(t,\vec{x}),\psi_a(t,\vec{y})\} = \delta_{ab} \delta(\vec{x}-\vec{y}).$$
What can we say about their eigenvalues? Are they real or Grassmann-numbers?
I'm a bit confused about this at first I would guess they are Grassmann-numbers since $\psi_a(x)\psi_a(x) = -\psi_a(x)\psi_a(x) = 0$$$\psi_a(x)\psi_a(x) = -\psi_a(x)\psi_a(x) = 0$$ but I'm not sure if this conclusion is true.
