$$U_{693}(x, y) = \frac{\sqrt{4 x \left(1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- y}}{2} \right)}}{3} \right)}}{3}\right) + 1}}{2} + \frac{1}{2}$$

$$T_{693}(n, m, k) = \begin{cases}1&\text{if m = 0, n = 0} ,\ \\\frac{\left(-1\right)^{m - 1} k {\binom{k - n - 1}{n - 1}} {\binom{3 m - n - 1}{m - 1}}}{m}&\text{if m > 0} ,\ \\\frac{k {\binom{k - n - 1}{n - 1}}}{n} \end{cases} $$