$$U_{1127}(x, y) = 2 x \left(y + 1\right)^{6} + \left(y + 1\right)^{3} \sqrt{4 x^{2} \left(y + 1\right)^{6} + 1}$$

$$T_{1127}(n, m, k) = \begin{cases}\frac{k {\binom{3 k + 3 n}{m}} {\binom{\frac{k}{2} + \frac{3 n}{2} + \frac{1}{2}}{n}} {\binom{k + 3 n + 1}{\frac{k}{2} + \frac{3 n}{2} + \frac{1}{2}}}}{\left(k + n\right) {\binom{k + n + 1}{\frac{k}{2} + \frac{n}{2} + \frac{1}{2}}}}&\text{if (n+k)%2=1} ,\ \\\frac{k {\binom{\frac{k}{2} + \frac{3 n}{2}}{n}} {\binom{k + 3 n}{\frac{k}{2} + \frac{3 n}{2}}} {\binom{3 k + 3 n}{m}}}{\left(k + n\right) {\binom{k + n}{\frac{k}{2} + \frac{n}{2}}}}&\text{if (n+k)%2=0} \end{cases} $$