Low-dimensional complex characters of the symplectic and orthogonal groups

We classify the irreducible complex characters of the symplectic groups $Sp_{2n}(q)$ and the orthogonal groups $Spin_{2n}^\pm(q)$, $Spin_{2n+1}(q)$ of degrees up to the bound D, where $D=(q^n-1)q^{4n-10}/2$ for symplectic groups, $D=q^{4n-8}$ for orthogonal groups in odd dimension, and $D=q^{4n-10}$ for orthogonal groups in even dimension.