Efficient Computation and Congruences for Colored Partition Functions

For a positive integer $α$, let $p_α(n)$ denote the number of $α$-colored partitions of $n$. The Rademacher-type expansion of Iskander, Jain, and Talvola is valid for every real $α>0$, but when $α>24$ it involves several polar terms and a two-parameter family of exponential sums $A_k^{(α)}(n,m)$. Fo