Aligned spin coefficients

Spin term	Exact correction
SO3	\(4 \cdot \chi_{1} \cdot \left(- \frac{25 \cdot \delta^{2}}{16} + \frac{113 \cdot \left(\frac{\delta}{2} + \frac{1}{2}\right)^{2}}{12} + \frac{25}{16}\right) + 4 \cdot \chi_{2} \cdot \left(- \frac{25 \cdot \delta^{2}}{16} + \frac{113 \cdot \left(\frac{1}{2} - \frac{\delta}{2}\right)^{2}}{12} + \frac{25}{16}\right)\)
SS4	\(- \frac{405 \cdot \chi_{1}^{2} \cdot \left(\frac{\delta}{2} + \frac{1}{2}\right)^{2}}{8} - 10 \cdot \chi_{1} \cdot \chi_{2} \cdot \left(\frac{79}{32} - \frac{79 \cdot \delta^{2}}{32}\right) - \frac{405 \cdot \chi_{2}^{2} \cdot \left(\frac{1}{2} - \frac{\delta}{2}\right)^{2}}{8}\)
SO5	\(- \chi_{1} \cdot \left(\left(\frac{1}{4} - \frac{\delta^{2}}{4}\right) \cdot \left(\frac{5 \cdot \delta^{2}}{6} + \frac{4615}{28}\right) + \left(\frac{741805}{2268} - \frac{35 \cdot \delta^{2}}{9}\right) \cdot \left(\frac{\delta}{2} + \frac{1}{2}\right)^{2}\right) - \chi_{2} \cdot \left(\left(\frac{1}{4} - \frac{\delta^{2}}{4}\right) \cdot \left(\frac{5 \cdot \delta^{2}}{6} + \frac{4615}{28}\right) + \left(\frac{1}{2} - \frac{\delta}{2}\right)^{2} \cdot \left(\frac{741805}{2268} - \frac{35 \cdot \delta^{2}}{9}\right)\right)\)
SO6	\(\pi \cdot \left(\frac{2270 \cdot \delta \cdot \left(\frac{\chi_{1}}{2} - \frac{\chi_{2}}{2}\right)}{3} + \left(\frac{\chi_{1}}{2} + \frac{\chi_{2}}{2}\right) \cdot \left(130 \cdot \delta^{2} + \frac{1880}{3}\right)\right)\)
SS6	\(\delta \cdot \left(\frac{\chi_{1}}{2} - \frac{\chi_{2}}{2}\right) \cdot \left(\frac{\chi_{1}}{2} + \frac{\chi_{2}}{2}\right) \cdot \left(\frac{8225 \cdot \delta^{2}}{72} + \frac{59065}{144}\right) + \left(\frac{\chi_{1}}{2} - \frac{\chi_{2}}{2}\right)^{2} \cdot \left(\frac{263245 \cdot \delta^{2}}{1008} - 480 \cdot \left(\frac{1}{4} - \frac{\delta^{2}}{4}\right)^{2} + \frac{235}{224}\right) + \left(\frac{\chi_{1}}{2} + \frac{\chi_{2}}{2}\right)^{2} \cdot \left(\frac{232415 \cdot \delta^{2}}{2016} + \frac{1255 \cdot \left(\frac{1}{4} - \frac{\delta^{2}}{4}\right)^{2}}{9} + \frac{16455}{112}\right)\)
SO7	\(\delta \cdot \left(\frac{\chi_{1}}{2} - \frac{\chi_{2}}{2}\right) \cdot \left(- \frac{26804935 \cdot \delta^{2}}{24192} - \frac{1985 \cdot \left(\frac{1}{4} - \frac{\delta^{2}}{4}\right)^{2}}{48} - \frac{21772661965}{3048192}\right) + \left(\frac{\chi_{1}}{2} + \frac{\chi_{2}}{2}\right) \cdot \left(- \frac{10566655595 \cdot \delta^{2}}{3048192} + \frac{5345 \cdot \left(\frac{1}{4} - \frac{\delta^{2}}{4}\right)^{3}}{36} - \frac{1042165 \cdot \left(\frac{1}{4} - \frac{\delta^{2}}{4}\right)^{2}}{3024} - \frac{3645857045}{762048}\right)\)
SS7	\(- \pi \cdot \left(\frac{815 \cdot \chi_{1}^{2} \cdot \left(\frac{\delta}{2} + \frac{1}{2}\right)^{2}}{2} + 785 \cdot \chi_{1} \cdot \chi_{2} \cdot \left(\frac{1}{2} - \frac{\delta}{2}\right) \cdot \left(\frac{\delta}{2} + \frac{1}{2}\right) + \frac{815 \cdot \chi_{2}^{2} \cdot \left(\frac{1}{2} - \frac{\delta}{2}\right)^{2}}{2}\right)\)
SSS7	\(\delta \cdot \left(\frac{\chi_{1}}{2} - \frac{\chi_{2}}{2}\right)^{3} \cdot \left(595 \cdot \delta^{2} + \frac{305}{24}\right) + \delta \cdot \left(\frac{\chi_{1}}{2} - \frac{\chi_{2}}{2}\right) \cdot \left(\frac{\chi_{1}}{2} + \frac{\chi_{2}}{2}\right)^{2} \cdot \left(\frac{215 \cdot \delta^{2}}{8} + \frac{7185}{4}\right) + \left(\frac{\chi_{1}}{2} - \frac{\chi_{2}}{2}\right)^{2} \cdot \left(\frac{\chi_{1}}{2} + \frac{\chi_{2}}{2}\right) \cdot \left(\frac{3635 \cdot \delta^{2}}{2} + 80 \cdot \left(\frac{1}{4} - \frac{\delta^{2}}{4}\right)^{2} + \frac{45}{8}\right) + \left(\frac{\chi_{1}}{2} + \frac{\chi_{2}}{2}\right)^{3} \cdot \left(\frac{475 \cdot \delta^{2}}{24} + \frac{100 \cdot \left(\frac{1}{4} - \frac{\delta^{2}}{4}\right)^{2}}{3} + \frac{7055}{12}\right)\)
SO5_log	\(- 3 \cdot \chi_{1} \cdot \left(\left(\frac{1}{4} - \frac{\delta^{2}}{4}\right) \cdot \left(\frac{5 \cdot \delta^{2}}{6} + \frac{4615}{28}\right) + \left(\frac{741805}{2268} - \frac{35 \cdot \delta^{2}}{9}\right) \cdot \left(\frac{\delta}{2} + \frac{1}{2}\right)^{2}\right) - 3 \cdot \chi_{2} \cdot \left(\left(\frac{1}{4} - \frac{\delta^{2}}{4}\right) \cdot \left(\frac{5 \cdot \delta^{2}}{6} + \frac{4615}{28}\right) + \left(\frac{1}{2} - \frac{\delta}{2}\right)^{2} \cdot \left(\frac{741805}{2268} - \frac{35 \cdot \delta^{2}}{9}\right)\right)\)