Questions about the indivisible imaginary root in affine root system.

Question

I am reading the paper. On page 5, $\delta$ is defined as the indivisible imaginary root in $\widehat{\Delta_+}$. $\Lambda_0 \in \widehat{\mathfrak{h}^*}$ is the unique element satisfying $\langle K, \Lambda_0 \rangle=1$ and $\langle \mathfrak{h}, \Lambda_0 \rangle = 0$. My question is: what is the value of $\langle \Lambda_0, \delta^{\vee} \rangle$ and $\langle \omega_i, \delta^{\vee} \rangle$? Here $\omega_i$ are fundamental weights. Thank you very much.