Numerical inequalities for self-conjugate 9-core partitions

Let $sc_9(n)$ denote the number of self-conjugate $9$-core partitions of $n$, and let $n$ be a non-negative integer. Numerical inequalities for self-conjugate 9-core partitions. The following inequalities are conjectured:

1. If $n\geq 49$, then $sc_9(4n)>3\,sc_9(n)$.
2. If $n\geq 1$, then $sc_9(4n+1)>1.9\,sc_9(n)$.
3. If $n\geq 17$, then $sc_9(4n+3)>1.9\,sc_9(n)$.
4. If $n\geq 1$, then $sc_9(4n+4)>2.6\,sc_9(n)$. These claims are based on experimental data, and the source gives no proof.