$$U_{620}(x, y) = x + \frac{\sqrt{4 x \left(1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- y}}{2} \right)}}{3} \right)}}{3}\right) + \left(1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- y}}{2} \right)}}{3} \right)}}{3}\right)^{2}}}{2} - \frac{2 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- y}}{2} \right)}}{3} \right)}}{3} + \frac{1}{2}$$

$$T_{620}(n, m, k) = \begin{cases}0&\text{if n = 0,m = 0} ,\ \\\frac{2 \left(-1\right)^{n - 1} k {\binom{- 2 k + 2 n - 1}{n - 1}}}{n}&\text{if m = 0, n > 0} ,\ \\\frac{\left(-1\right)^{m - 1} k {\binom{2 k - n - 1}{n}} {\binom{- k + 3 m + n - 1}{m - 1}}}{m} \end{cases} $$