Evaluating a multiplicative sequence at2007

Let numerical sequence $(u_{n})$, $n\in \mathbb{N}$ such that:

1. $(\forall n, m \in \mathbb{N}): u_{mn} = u_{m}.u_{n}$
2. $u_{10} = 0$
3. $u(k) = 0$ if $k \equiv 3 \mod 10$. Compute $u_{2007}$.

Source: InternLM Lean-Workbook, record lean_workbook_42477 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.