$$U_{580}(x, y) = \frac{1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- x}}{2} \right)}}{3} \right)}}{3}}{\sqrt{1 - 4 y}}$$

$$T_{580}(n, m, k) = \begin{cases}4^{m} {\binom{\frac{k}{2} + m - 1}{m}}&\text{if n==0} ,\ \\\frac{\left(-1\right)^{n - 1} \cdot 4^{m} k {\binom{- k + 3 n - 1}{n - 1}} {\binom{\frac{k}{2} + m - 1}{m}}}{n}&\text{if n>0} \end{cases} $$