f_{33}&=t^3 y+\textstyle\frac{769}{6451200}t^{10}+\textstyle\frac{1961}{2150400}t^8 s+\textstyle\frac{271}{44800} t^7 v-\textstyle\frac{1}{307200}t^6 s^2+\textstyle\frac{9061}{268800}t^6 u_1-\textstyle\frac{1}{134400}t^5 s v+\textstyle\frac{423}{2800}t^5 w_1 \\
&\quad+\textstyle\frac{1}{6451200}t^4 s^3-\textstyle\frac{1}{89600}t^4 s u_1+\textstyle\frac{281}{560}t^4 x_1,
\\
f_{34}&=s^5+\textstyle\frac{4699}{28}t^{10}+\textstyle\frac{19701}{28}t^8 s-\textstyle\frac{468}{7} t^7 v-\textstyle\frac{593}{4}t^6 s^2-\textstyle\frac{20718}{7} t^6 u_1-\textstyle\frac{10940}{7}t^5 s v-\textstyle\frac{13696}{7}t^5 w_1-\textstyle\frac{13373}{28} t^4 s^3\\
&\quad-\textstyle\frac{2606}{7}t^4 s u_1-\textstyle\frac{1920}{7} t^4 x_1,
\\
f_{35}&=s^3  u_1+\textstyle\frac{14219}{4032}t^{10}+\textstyle\frac{1109}{2240}t^8 s-\textstyle\frac{5077}{140}t^7 v-\textstyle\frac{13757}{320}t^6 s^2-\textstyle\frac{150531}{280}t^6 u_1-\textstyle\frac{4435}{28}t^5 s v-\textstyle\frac{73704}{35}t^5 w_1+\textstyle\frac{5837}{6720}t^4 s^3\\
&\quad-\textstyle\frac{98571}{280}t^4 s u_1-\textstyle\frac{5808}{7}t^4 x_1,
\\
f_{36}&=s^3  u_2+\textstyle\frac{605559}{11200} t^{10}+\textstyle\frac{2365561}{11200}t^8 s+\textstyle\frac{903953}{4200}t^7 v+\textstyle\frac{89257}{4800}t^6 s^2-\textstyle\frac{1275297}{700}t^6 u_1+\textstyle\frac{24121}{40}t^6 u_2+\textstyle\frac{32163}{1400}t^5 s v\\
&\quad-\textstyle\frac{1903824}{175}t^5 w_1+\textstyle\frac{1548}{5}t^5 w_2+4788t^5 w_3-\textstyle\frac{165853}{11200}t^4 s^3+\textstyle\frac{146421}{700}t^4 s u_1-\textstyle\frac{2667}{40}t^4 s u_2-\textstyle\frac{835284}{35}t^4 x_1+\textstyle\frac{3483}{5}t^4 x_2,
\\
f_{37}&=s^2  x_1-\textstyle\frac{214609}{2419200} t^{10}-\textstyle\frac{55729}{89600}t^8 s-\textstyle\frac{64511}{16800}t^7 v+\textstyle\frac{2107}{38400}t^6 s^2-\textstyle\frac{640487}{33600}t^6 u_1+\textstyle\frac{3547}{16800}t^5 s v-\textstyle\frac{25271}{350}t^5 w_1-\textstyle\frac{187}{806400}t^4 s^3\\
&\quad+\textstyle\frac{5787}{11200}t^4 s u_1-\textstyle\frac{11667}{70}t^4 x_1,
\\
f_{38}&=sv  w_2-\textstyle\frac{6926111}{9676800}t^{10}-\textstyle\frac{3964277}{1075200} t^8 s-\textstyle\frac{615323}{33600} t^7 v+\textstyle\frac{73879}{51200}t^6 s^2-\textstyle\frac{9098347}{134400}t^6 u_1-\textstyle\frac{679}{640}t^6 u_2+\textstyle\frac{25661}{5600}t^5 s v\\
&\quad-\textstyle\frac{861193}{4200}t^5 w_1+\textstyle\frac{17}{4}t^5 w_2-\textstyle\frac{243}{20}t^5 w_3-\textstyle\frac{87677}{3225600}t^4 s^3+\textstyle\frac{1113461}{134400}t^4 s u_1-\textstyle\frac{19}{640} t^4 s u_2-\textstyle\frac{122803}{280} t^4 x_1-\textstyle\frac{99}{80}t^4 x_2,
\\
%f_{39}&=sv  w_3+\textstyle\frac{661805}{774144}t^{10}+\textstyle\frac{860953}{307200}t^8 s+\textstyle\frac{3863}{134400}t^7 v-\textstyle\frac{9917}{102400}t^6 s^2-\textstyle\frac{13609109}{268800}t^6 u_1+\textstyle\frac{3201}{320} t^6 u_2-\textstyle\frac{28457}{44800}t^5 s v\\
%&\quad-\textstyle\frac{2085701}{8400}t^5 w_1+\textstyle\frac{11}{2}t^5 w_2+\textstyle\frac{349}{5}t^5 w_3-\textstyle\frac{169}{6451200}t^4 s^3-\textstyle\frac{217613}{268800}t^4 s u_1-\textstyle\frac{11}{320} t^4 s u_2-\textstyle\frac{51733}{112}t^4 x_1+\textstyle\frac{429}{40}t^4 x_2,
f_{39}&=sz+\textstyle\frac{1987}{19353600} t^{10}+\textstyle\frac{547}{716800}t^8 s+\textstyle\frac{653}{134400}t^7 v-\textstyle\frac{1}{307200} t^6 s^2+\textstyle\frac{6821}{268800}t^6 u_1-\textstyle\frac{1}{134400} t^5 s v+\textstyle\frac{283}{2800}t^5 w_1\\
&\quad+\textstyle\frac{1}{6451200} t^4 s^3-\textstyle\frac{1}{89600}t^4 s u_1+\textstyle\frac{141}{560}t^4 x_1,
\\
f_{40}&=vy+\textstyle\frac{1987}{3225600} t^{10}+\textstyle\frac{1641}{358400}t^8s+\textstyle\frac{653}{22400}t^7v-\textstyle\frac{1}{51200}t^6s^2+\textstyle\frac{6821}{44800}t^6u_1-\textstyle\frac{1}{22400}t^5sv+\textstyle\frac{849}{1400}t^5w_1+\textstyle\frac{1}{1075200}t^4s^3\\
\\
\\
\\
\\
&\quad-\textstyle\frac{1075106}{525}t^5w_1+\textstyle\frac{667}{15}t^5w_2+635 t^5w_3+\textstyle\frac{68219}{604800}t^4s^3-\textstyle\frac{131573}{16800}t^4su_1-\textstyle\frac{2141}{1440}t^4su_2-\textstyle\frac{131847}{35}t^4x_1+\textstyle\frac{1961}{20}t^4x_2,
\\
\\
\\
\\
\\
\\
\end{align*}

Degree $11$.

\begin{align*}
%f_{52}&=t^5 s^3-\textstyle\frac{53}{147}t^{11}-\textstyle\frac{73}{49}t^9 s+\textstyle\frac{24}{49}t^8 v+\textstyle\frac{15}{49} t^7 s^2+\textstyle\frac{48}{7} t^7 u_1+\textstyle\frac{24}{7} t^6 s v,
%f_{53}&=t^5 s u_1-\textstyle\frac{17}{1617} t^{11}+\textstyle\frac{13}{1078} t^9 s+\textstyle\frac{95}{539} t^8 v+\textstyle\frac{159} {1078}t^7 s^2+\textstyle\frac{135}{77} t^7 u_1+\textstyle\frac{39}{77} t^6 s v+\textstyle\frac{64}{11} t^6 w_1,
f_{51}&=t^5 s u_2+\textstyle\frac{7439}{48510} t^{11} +\textstyle\frac{10789}{16170} t^9 s+\textstyle\frac{3376}{2695} t^8 v+\textstyle\frac{18}{49} t^7 s^2-\textstyle\frac{34}{77} t^7 u_1+\textstyle\frac37  t^7 u_2 +\textstyle\frac{82}{105} t^6 s v-\textstyle\frac{96}{11} t^6 w_1-\textstyle\frac{96}{11} t^6 w_3,
\\
%f_{55}&=t^5 x_1+\textstyle\frac{1759}{2457840} t^{11}+\textstyle\frac{4149}{819280} t^9 s+\textstyle\frac{9281}{307230} t^8 v-\textstyle\frac{1}{61446}t^7 s^2+\textstyle\frac{211}{1463} t^7 u_1-\textstyle\frac{1}{43890}t^6 s v+\textstyle\frac{105}{209} t^6 w_1,
%f_{56}&=t^5 x_2+\textstyle\frac{103727}{921690} t^{11}+\textstyle\frac{76261}{153615} t^9 s+\textstyle\frac{1939876}{1382535}t^8 v-\textstyle\frac{761}{553014} t^7 s^2+\textstyle\frac{25519}{13167} t^7 u_1+\textstyle\frac{19}{21} t^7 u_2-\textstyle\frac{5501}{197505} t^6 s v-\textstyle\frac{96}{209} t^6 w_1\\
%&\quad+\textstyle\frac49  t^6 w_2+\textstyle\frac{200}{33} t^6 w_3,
\\
\\
f_{54}&=u_2y+\textstyle\frac{4979}{110602800} t^{11}+\textstyle\frac{52627}{13825350} t^9 s+\textstyle\frac{25226}{768075} t^8 v-\textstyle\frac{29}{614460} t^7 s^2+\textstyle\frac{13933}{87780} t^7 u_1-\textstyle\frac{29}{438900} t^6 s v+\textstyle\frac{2447}{6270} t^6 w_1+\textstyle\frac16 t^6 w_3,
\\
\\
f_{56}&=w_1x_2-\textstyle\frac{15581}{9216900} t^{11}-\textstyle\frac{1757219}{27650700} t^9 s-\textstyle\frac{1294471}{2513700} t^8 v-\textstyle\frac{6035}{1106028} t^7 s^2-\textstyle\frac{318643}{131670} t^7 u_1+\textstyle\frac{4}{105} t^7 u_2-\textstyle\frac{41879}{3950100} t^6 s v\\
&\quad-\textstyle\frac{17912}{3135} t^6 w_1+\textstyle\frac 1{45}t^6 w_2-\textstyle\frac{262}{165} t^6 w_3,
\\
f_{57}&=w_2x_1+\textstyle\frac{138679}{126403200} t^{11}-\textstyle\frac{82583}{126403200} t^9 s-\textstyle\frac{648539}{15800400} t^8 v-\textstyle\frac{367}{790020} t^7 s^2-\textstyle\frac{137509}{526680} t^7 u_1+\textstyle\frac 1{30}t^7 u_2+\textstyle\frac{5633}{4514400} t^6 s v\\
&\quad-\textstyle\frac{8137}{12540} t^6 w_1-\textstyle\frac{37}{360} t^6 w_2+\textstyle\frac{98}{165} t^6 w_3,
\\
f_{58}&=w_2x_2+\textstyle\frac{361001}{13825350} t^{11}+\textstyle\frac{881611}{4608450} t^9 s+\textstyle\frac{617984}{768075} t^8 v+\textstyle\frac{4376}{51205} t^7 s^2+\textstyle\frac{659159}{263340} t^7 u_1+\textstyle\frac{31}{252} t^7 u_2+\textstyle\frac{693521}{3950100} t^6 s v\\
&\quad+\textstyle\frac{11612}{3135} t^6 w_1+\textstyle\frac{17}{45} t^6 w_2+\textstyle\frac{22}{15} t^6 w_3,
\\
f_{59}&=w_3x_1-\textstyle\frac{19129}{80438400} t^{11}-\textstyle\frac{27149}{8937600} t^9 s-\textstyle\frac{1331623}{60328800} t^8 v-\textstyle\frac{124}{377055} t^7 s^2-\textstyle\frac{13759}{143640} t^7 u_1+\textstyle\frac{11}{630} t^7 u_2+\textstyle\frac{737}{2154600} t^6 s v\\
&\quad-\textstyle\frac{71}{380} t^6 w_1+\textstyle\frac{11}{540} t^6 w_2+\textstyle\frac{91}{360} t^6 w_3,
\\
f_{60}&=w_3x_2+\textstyle\frac{746203}{15800400} t^{11}+\textstyle\frac{4453159}{15800400} t^9 s+\textstyle\frac{3331721}{2633400} t^8 v+\textstyle\frac{1493}{87780} t^7 s^2+\textstyle\frac{143107}{35112} t^7 u_1+\textstyle\frac1{40}t^7 u_2+\textstyle\frac{2971}{94050} t^6 s v\\
&\quad+\textstyle\frac{2023}{285} t^6 w_1+\textstyle\frac{21}{55} t^6 w_3.
\end{align*}

Degree $12$.

\begin{align*}
%f_{66}&=t^7 s v+\textstyle\frac{3}{224} t^{12}+\textstyle\frac{41}{112} t^{10} s+\textstyle\frac{59}{42} t^9 v +\textstyle\frac{115}{224} t^8 s^2+\textstyle\frac{15}{4} t^8 u_1,
%f_{67}&=t^7 w_1+\textstyle\frac{221}{48384} t^{12}+\textstyle\frac{229}{8064}t^{10} s+\textstyle\frac{71}{504} t^9 v-\textstyle\frac{1}{16128}t^8 s^2+\textstyle\frac{145}{288} t^8 u_1,
%f_{68}&=t^7 w_2-\textstyle\frac{29}{2880} t^{12}-\textstyle\frac{5}{96} t^{10} s-\textstyle\frac{13}{72} t^9 v-\textstyle\frac{1}{576}t^8 s^2-\textstyle\frac13 t^8 u_1+ \textstyle\frac{1}{12}t^8 u_2,
%f_{69}&=t^7 w_3+\textstyle\frac{1313}{241920} t^{12}+\textstyle\frac{169}{8064} t^{10} s+\textstyle\frac{151}{3024} t^9 v-\textstyle\frac{107}{48384} t^8 s^2+\textstyle\frac{11}{288} t^8 u_1+\textstyle\frac{11}{144} t^8 u_2,
\\
f_{62}&=u_2z+\textstyle\frac{15671}{55883520} t^{12}+\textstyle\frac{863}{846720} t^{10} s+\textstyle\frac{1493}{635040} t^9 v-\textstyle\frac{263}{5080320} t^8 s^2+\textstyle\frac{31}{15120} t^8 u_1+\textstyle\frac{11}{6048} t^8 u_2,
\\
\\
f_{64}&=w_2y+\textstyle\frac{31403}{111767040} t^{12}+\textstyle\frac{10663}{8467200} t^{10} s+\textstyle\frac{1033}{254016} t^9 v-\textstyle\frac{299}{10160640} t^8 s^2+\textstyle\frac{31}{4320} t^8 u_1+\textstyle\frac{11}{12096} t^8 u_2,
\\
f_{65}&=w_3y+\textstyle\frac{40631}{243855360} t^{12}+\textstyle\frac{136279}{203212800} t^{10} s+\textstyle\frac{5687}{3048192} t^9 v-\textstyle\frac{6017}{243855360} t^8 s^2+\textstyle\frac{3817}{1451520} t^8 u_1+\textstyle\frac{121}{145152} t^8 u_2,
\\
\\
f_{67}&=x_1x_2-\textstyle\frac{15671}{2794176} t^{12}-\textstyle\frac{863}{42336} t^{10} s-\textstyle\frac{1493}{31752} t^9 v+\textstyle\frac{263}{254016} t^8 s^2-\textstyle\frac{31}{756} t^8 u_1-\textstyle\frac{55}{1512} t^8 u_2,
\\
f_{68}&=x_2^2+\textstyle\frac{815827}{3492720} t^{12}+\textstyle\frac{11353}{10584} t^{10} s+\textstyle\frac{13688}{3969} t^9 v-\textstyle\frac{1943}{317520} t^8 s^2+\textstyle\frac{1609}{270} t^8 u_1+\textstyle\frac{356}{945} t^8 u_2.
\end{align*}

Degree $13$.

\begin{align*}
%f_{78}&=t^9 s^2+\textstyle\frac{9}{65} t^{13}+\textstyle\frac 65t^{11} s+\textstyle\frac85 t^{10} v,
%f_{79}&=t^9 u_1+\textstyle\frac{1007}{36465} t^{13}+\textstyle\frac{131}{935} t^{11} s+\textstyle\frac{43}{85} t^{10} v,
%f_{80}&=t^9 u_2+\textstyle\frac{229}{1870} t^{13}+\textstyle\frac{783}{1870} t^{11} s+\textstyle\frac{62}{85} t^{10} v,
\\
f_{70}&=w_2z-\textstyle\frac{101}{61261200} t^{13}-\textstyle\frac{23}{3534300} t^{11} s-\textstyle\frac1{71400}t^{10} v,
\\
f_{71}&=w_3z-\textstyle\frac{101}{267321600} t^{13}-\textstyle\frac{23}{15422400} t^{11} s-\textstyle\frac{11}{3427200} t^{10} v,
\\
\\
\end{align*}

Degree $14$.

\begin{align*}
%f_{86}&=t^{11} v+\textstyle\frac9{64}t^{14}+\textstyle\frac{33}{64}t^{12} s,
\\
\\
\end{align*}

Degree $15$.

\begin{align*}
%f_{90}&=t^{13} s+\textstyle\frac7{15}t^{15},
\end{align*}

Degree $16$.

\begin{align*}
\end{align*}

§ THE PRINCIPAL KINEMATIC FORMULA

Keeping the notation from Section <ref> and denoting $\mu\odot\nu=\frac12\left(\mu\otimes\nu+\nu\otimes \mu\right)$, we have

\begin{align*}
&51609600\, \pi^8\sum_{i,j=1}^{27}(M_{8}^{-1})_{i,j}\psi^{(i)}_{8}\otimes\psi^{(j)}_{8}
\\
&=\textstyle\frac{101042723}{8448} \hat t^8 \odot  \hat t^8 + \textstyle\frac{41912485}{528} \hat t^8 \odot  \hat t^6 \hat s + \textstyle\frac{131398835}{3168} \hat t^8 \odot  \hat t^5 \hat v  -\textstyle\frac{10178935}{792} \hat t^8 \odot  \hat t^4 \hat s^2  -\textstyle\frac{600048805}{528} \hat t^8 \odot  \hat t^4 \hat u_1
\\
&+ \textstyle\frac{4538995}{16} \hat t^8 \odot  \hat t^4 \hat u_2  -\textstyle\frac{37975765}{792} \hat t^8 \odot  \hat t^3 \hat s \hat v -\textstyle\frac{189207035}{33} \hat t^8 \odot  \hat t^3 \hat w_1 + \textstyle\frac{5826055}{24} \hat t^8 \odot  \hat t^3 \hat w_2 + \textstyle\frac{7976745}{4} \hat t^8 \odot  \hat t^3 \hat w_3
\\
&+ \textstyle\frac{133415}{352} \hat t^8 \odot  \hat t^2 \hat s^3 -\textstyle\frac{10151365}{132} \hat t^8 \odot  \hat t^2 \hat s \hat u_1+ \textstyle\frac{8215}{8} \hat t^8 \odot  \hat t^2 \hat s \hat u_2  -\textstyle\frac{112512535}{11} \hat t^8 \odot  \hat t^2 \hat x_1+\textstyle\frac{2265005}{8} \hat t^8 \odot  \hat t^2 \hat x_2
\\
&  + \textstyle\frac{2835155}{3168} \hat t^8 \odot \hat t \hat s^2 \hat v -\textstyle\frac{79005}{44} \hat t^8 \odot \hat t \hat s \hat w_1 + \textstyle\frac{397455}{8} \hat t^8 \odot  \hat t \hat s \hat w_2 -\textstyle\frac{360555}{11} \hat t^8 \odot \hat  t \hat s \hat w_3  +\textstyle\frac{5465925}{22} \hat t^8 \odot  \hat t \hat y  -\textstyle\frac{190945}{12672} \hat t^8 \odot  \hat s^4
\\
& + \textstyle\frac{163545}{176} \hat t^8 \odot  \hat s^2  \hat u_1 + \textstyle\frac{25135}{48} \hat t^8 \odot  \hat s^2  \hat u_2 +\textstyle\frac{882875}{11} \hat t^8 \odot \hat s  \hat x_1 -9900 \hat t^8 \odot  \hat v  \hat w_2  -\textstyle\frac{661775}{22} \hat t^8 \odot \hat v  \hat w_3 + \textstyle\frac{20210400}{11} \hat t^8 \odot  \hat z
\\
&+\textstyle\frac{17385985}{132} \hat t^6 \hat s \odot  \hat t^6 \hat s + \textstyle\frac{436979155}{3168} \hat t^6 \hat s \odot  \hat t^5 \hat v  -\textstyle\frac{270203215}{6336} \hat t^6 \hat s \odot  \hat t^4 \hat s^2  -\textstyle\frac{662726705}{176} \hat t^6 \hat s \odot  \hat t^4 \hat u_1 + \textstyle\frac{45172565}{48} \hat t^6 \hat s \odot  \hat t^4 \hat u_2
\\
& -\textstyle\frac{31560245}{198} \hat t^6 \hat s \odot  \hat t^3 \hat s \hat v -\textstyle\frac{7507001455}{396} \hat t^6 \hat s \odot  \hat t^3 \hat w_1 + \textstyle\frac{6451745}{8} \hat t^6 \hat s \odot  \hat t^3 \hat w_2 + \textstyle\frac{72690555}{11} \hat t^6 \hat s \odot  \hat t^3 \hat w_3 + \textstyle\frac{999775}{792} \hat t^6 \hat s \odot  \hat t^2 \hat s^3
\\
& -\textstyle\frac{101244185}{396} \hat t^6 \hat s \odot  \hat t^2 \hat s \hat u_1 + \textstyle\frac{27955}{8} \hat t^6 \hat s \odot  \hat t^2 \hat s \hat u_2 -\textstyle\frac{2196730045}{66} \hat t^6 \hat s \odot  \hat t^2 \hat x_1 + \textstyle\frac{7511925}{8} \hat t^6 \hat s \odot  \hat t^2 \hat x_2 + \textstyle\frac{9489955}{3168} \hat t^6 \hat s \odot \hat  t \hat s^2 \hat v
\\
&+ \textstyle\frac{37990}{9} \hat t^6 \hat s \odot\hat   t \hat s \hat w_1 + \textstyle\frac{4010285}{24} \hat t^6 \hat s \odot \hat  t \hat s \hat w_2  -\textstyle\frac{5102905}{44} \hat t^6 \hat s \odot \hat  t \hat s \hat w_3 + \textstyle\frac{113103315}{22} \hat t^6 \hat s \odot\hat   t \hat y  -\textstyle\frac{315575}{6336} \hat t^6 \hat s \odot  \hat s^4
\\
&+ \textstyle\frac{5247175}{1584} \hat t^6 \hat s \odot  \hat s^2  \hat u_1 + \textstyle\frac{83515}{48} \hat t^6 \hat s \odot  \hat s^2  \hat u_2 + \textstyle\frac{3741990}{11} \hat t^6 \hat s \odot \hat s  \hat x_1 -\textstyle\frac{93575}{3} \hat t^6 \hat s \odot  \hat v  \hat w_2  -\textstyle\frac{2197925}{22} \hat t^6 \hat s \odot \hat v  \hat w_3
\\
&+ \textstyle\frac{228977280}{11} \hat t^6 \hat s \odot  \hat z +\textstyle\frac{372273293}{9504} \hat t^5 \hat v \odot  \hat t^5 \hat v  -\textstyle\frac{19067905}{864} \hat t^5 \hat v \odot  \hat t^4 \hat s^2 -\textstyle\frac{493836119}{264} \hat t^5 \hat v \odot  \hat t^4 \hat u_1 + \textstyle\frac{35130295}{72} \hat t^5 \hat v \odot  \hat t^4 \hat u_2
\\
&-\textstyle\frac{66023681}{792} \hat t^5 \hat v \odot  \hat t^3 \hat s \hat v -\textstyle\frac{10474501303}{1188} \hat t^5 \hat v \odot  \hat t^3 \hat w_1 + \textstyle\frac{5095775}{12} \hat t^5 \hat v \odot  \hat t^3 \hat w_2 + \textstyle\frac{148030505}{44} \hat t^5 \hat v \odot  \hat t^3 \hat w_3 + \textstyle\frac{26071}{36} \hat t^5 \hat v \odot  \hat t^2 \hat s^3
\\
& -\textstyle\frac{139961069}{1188} \hat t^5 \hat v \odot  \hat t^2 \hat s \hat u_1 +\textstyle\frac{24175}{12} \hat t^5 \hat v \odot  \hat t^2 \hat s \hat u_2  -\textstyle\frac{1569950995}{198} \hat t^5 \hat v \odot  \hat t^2 \hat x_1 + \textstyle\frac{1943975}{4} \hat t^5 \hat v \odot  \hat t^2 \hat x_2 + \textstyle\frac{358893}{176} \hat t^5 \hat v \odot \hat  t \hat s^2 \hat v
\\
&+ \textstyle\frac{236431805}{1188} \hat t^5 \hat v \odot \hat  t \hat s \hat w_1 + \textstyle\frac{416265}{4} \hat t^5 \hat v \odot \hat  t \hat s \hat w_2  -\textstyle\frac{5516905}{44} \hat t^5 \hat v \odot \hat  t \hat s \hat w_3 + \textstyle\frac{646168905}{11} \hat t^5 \hat v \odot \hat  t \hat y  -\textstyle\frac{195559}{9504} \hat t^5 \hat v \odot  \hat s^4
\\
&+ \textstyle\frac{11259665}{2376} \hat t^5 \hat v \odot  \hat s^2  \hat u_1 + \textstyle\frac{65105}{72} \hat t^5 \hat v \odot  \hat s^2  \hat u_2 + \textstyle\frac{12228860}{11} \hat t^5 \hat v \odot \hat s  \hat x_1 -\textstyle\frac{9665}{9} \hat t^5 \hat v \odot  \hat v  \hat w_2 -\textstyle\frac{1898395}{33} \hat t^5 \hat v \odot \hat v  \hat w_3
\\
&+ \textstyle\frac{2034789120}{11} \hat t^5 \hat v \odot  \hat z +\textstyle\frac{132412835}{38016} \hat t^4 \hat s^2 \odot  \hat t^4 \hat s^2 + \textstyle\frac{108459275}{176} \hat t^4 \hat s^2 \odot  \hat t^4 \hat u_1-\textstyle\frac{21953365}{144} \hat t^4 \hat s^2 \odot  \hat t^4 \hat u_2+ \textstyle\frac{40775785}{1584} \hat t^4 \hat s^2 \odot  \hat t^3 \hat s \hat v
\\
&  +\textstyle\frac{7474927855}{2376} \hat t^4 \hat s^2 \odot  \hat t^3 \hat w_1 -\textstyle\frac{1031415}{8} \hat t^4 \hat s^2 \odot  \hat t^3 \hat w_2  -\textstyle\frac{94810205}{88} \hat t^4 \hat s^2 \odot  \hat t^3 \hat w_3 -\textstyle\frac{313285}{1584} \hat t^4 \hat s^2 \odot  \hat t^2 \hat s^3+ \textstyle\frac{98639645}{2376} \hat t^4 \hat s^2 \odot  \hat t^2 \hat s \hat u_1
\\
&  -\textstyle\frac{6265}{24} \hat t^4 \hat s^2 \odot  \hat t^2 \hat s \hat u_2+\textstyle\frac{2395429675}{396} \hat t^4 \hat s^2 \odot  \hat t^2 \hat x_1 -\textstyle\frac{1223425}{8} \hat t^4 \hat s^2 \odot  \hat t^2 \hat x_2   -\textstyle\frac{1392715}{3168} \hat t^4 \hat s^2 \odot \hat  t \hat s^2 \hat v  +\textstyle\frac{2469905}{216} \hat t^4 \hat s^2 \odot \hat  t \hat s \hat w_1
\\
& -\textstyle\frac{194775}{8} \hat t^4 \hat s^2 \odot \hat  t \hat s \hat w_2  +\textstyle\frac{1053325}{88} \hat t^4 \hat s^2 \odot  \hat t \hat s \hat w_3 + \textstyle\frac{69259275}{22} \hat t^4 \hat s^2 \odot \hat  t \hat y + \textstyle\frac{76115}{9504} \hat t^4 \hat s^2 \odot  \hat s^4  -\textstyle\frac{1319135}{4752} \hat t^4 \hat s^2 \odot  \hat s^2  \hat u_1
\\
& -\textstyle\frac{38675}{144} \hat t^4 \hat s^2 \odot  \hat s^2  \hat u_2+ \textstyle\frac{172200}{11} \hat t^4 \hat s^2 \odot \hat s  \hat x_1 + \textstyle\frac{106925}{18} \hat t^4 \hat s^2 \odot  \hat v  \hat w_2 + \textstyle\frac{1117375}{66} \hat t^4 \hat s^2 \odot \hat v  \hat w_3+ \textstyle\frac{97070400}{11} \hat t^4 \hat s^2 \odot  \hat z
\\
&+\textstyle\frac{7302883913}{264} \hat t^4 \hat u_1 \odot  \hat t^4 \hat u_1  -\textstyle\frac{162129715}{12} \hat t^4 \hat u_1 \odot  \hat t^4 \hat u_2 + \textstyle\frac{305659649}{132} \hat t^4 \hat u_1 \odot  \hat t^3 \hat s \hat v+ \textstyle\frac{56608773187}{198} \hat t^4 \hat u_1 \odot  \hat t^3 \hat w_1
\\
&-\textstyle\frac{69294665}{6} \hat t^4 \hat u_1 \odot  \hat t^3 \hat w_2  -\textstyle\frac{190666245}{2} \hat t^4 \hat u_1 \odot  \hat t^3 \hat w_3  -\textstyle\frac{3367217}{198} \hat t^4 \hat u_1 \odot  \hat t^2 \hat s^3 + \textstyle\frac{796349201}{198} \hat t^4 \hat u_1 \odot  \hat t^2 \hat s \hat u_1
\\
&-\textstyle\frac{295565}{6} \hat t^4 \hat u_1 \odot  \hat t^2 \hat s \hat u_2 + \textstyle\frac{19501574935}{33} \hat t^4 \hat u_1 \odot  \hat t^2 \hat x_1 -\textstyle\frac{26975625}{2} \hat t^4 \hat u_1 \odot  \hat t^2 \hat x_2  -\textstyle\frac{28250459}{792} \hat t^4 \hat u_1 \odot \hat t \hat s^2 \hat v
\\
& + \textstyle\frac{518106715}{198} \hat t^4 \hat u_1 \odot \hat  t \hat s \hat w_1 -\textstyle\frac{4543815}{2} \hat t^4 \hat u_1 \odot \hat  t \hat s \hat w_2 + \textstyle\frac{2273065}{2} \hat t^4 \hat u_1 \odot \hat  t \hat s \hat w_3 + \textstyle\frac{6008331870}{11} \hat t^4 \hat u_1 \odot \hat  t \hat y + \textstyle\frac{413467}{528} \hat t^4 \hat u_1 \odot  \hat s^4
\\
&-\textstyle\frac{5377685}{396} \hat t^4 \hat u_1 \odot  \hat s^2  \hat u_1  -\textstyle\frac{99455}{4} \hat t^4 \hat u_1 \odot  \hat s^2  \hat u_2  +\textstyle\frac{57302840}{11} \hat t^4 \hat u_1 \odot \hat s  \hat x_1+ \textstyle\frac{1667170}{3} \hat t^4 \hat u_1 \odot  \hat v  \hat w_2+ \textstyle\frac{15188410}{11} \hat t^4 \hat u_1 \odot \hat v  \hat w_3
\\
&+ \textstyle\frac{16174529280}{11} \hat t^4 \hat u_1 \odot  \hat z +\textstyle\frac{40431875}{24} \hat t^4 \hat u_2 \odot  \hat t^4 \hat u_2 -\textstyle\frac{6793615}{12} \hat t^4 \hat u_2 \odot  \hat t^3 \hat s \hat v -\textstyle\frac{1226983165}{18} \hat t^4 \hat u_2 \odot  \hat t^3 \hat w_1
\\
&+ \textstyle\frac{17297225}{6} \hat t^4 \hat u_2 \odot  \hat t^3 \hat w_2 + \textstyle\frac{47471025}{2} \hat t^4 \hat u_2 \odot  \hat t^3 \hat w_3+ \textstyle\frac{40190}{9} \hat t^4 \hat u_2 \odot  \hat t^2 \hat s^3  -\textstyle\frac{16143095}{18} \hat t^4 \hat u_2 \odot  \hat t^2 \hat s \hat u_1 + \textstyle\frac{74525}{6} \hat t^4 \hat u_2 \odot  \hat t^2 \hat s \hat u_2
\\
&  -\textstyle\frac{366421225}{3} \hat t^4 \hat u_2 \odot  \hat t^2 \hat x_1 + \textstyle\frac{6726225}{2} \hat t^4 \hat u_2 \odot  \hat t^2 \hat x_2 + \textstyle\frac{761065}{72} \hat t^4 \hat u_2 \odot \hat  t \hat s^2 \hat v + \textstyle\frac{307835}{18} \hat t^4 \hat u_2 \odot\hat   t \hat s \hat w_1 + \textstyle\frac{1149775}{2} \hat t^4 \hat u_2 \odot \hat  t \hat s \hat w_2
\\
&-\textstyle\frac{655525}{2} \hat t^4 \hat u_2 \odot \hat  t \hat s \hat w_3 -2063250 \hat t^4 \hat u_2 \odot \hat  t \hat y -\textstyle\frac{25745}{144} \hat t^4 \hat u_2 \odot  \hat s^4 + \textstyle\frac{388055}{36} \hat t^4 \hat u_2 \odot  \hat s^2  \hat u_1 + \textstyle\frac{74525}{12} \hat t^4 \hat u_2 \odot  \hat s^2  \hat u_2
\\
&+ 917000 \hat t^4 \hat u_2 \odot \hat s  \hat x_1 -\textstyle\frac{395450}{3} \hat t^4 \hat u_2 \odot  \hat v  \hat w_2  -355350 \hat t^4 \hat u_2 \odot \hat v  \hat w_3+\textstyle\frac{14256331}{297} \hat t^3 \hat s \hat v \odot  \hat t^3 \hat s \hat v+ \textstyle\frac{108352963}{9} \hat t^3 \hat s \hat v \odot  \hat t^3 \hat w_1
\\
& -\textstyle\frac{2819225}{6} \hat t^3 \hat s \hat v \odot  \hat t^3 \hat w_2  -\textstyle\frac{132191920}{33} \hat t^3 \hat s \hat v \odot  \hat t^3 \hat w_3 -\textstyle\frac{222529}{297} \hat t^3 \hat s \hat v \odot  \hat t^2 \hat s^3 + \textstyle\frac{16188959}{99} \hat t^3 \hat s \hat v \odot  \hat t^2 \hat s \hat u_1  -\textstyle\frac{1675}{6} \hat t^3 \hat s \hat v \odot  \hat t^2 \hat s \hat u_2
\\
&+\textstyle\frac{275442210}{11} \hat t^3 \hat s \hat v \odot  \hat t^2 \hat x_1  -\textstyle\frac{3412525}{6} \hat t^3 \hat s \hat v \odot  \hat t^2 \hat x_2  -\textstyle\frac{3443051}{2376} \hat t^3 \hat s \hat v \odot \hat  t \hat s^2 \hat v  +\textstyle\frac{10790080}{99} \hat t^3 \hat s \hat v \odot \hat  t \hat s \hat w_1  -\textstyle\frac{1582885}{18} \hat t^3 \hat s \hat v \odot \hat  t \hat s \hat w_2
\\
&+ \textstyle\frac{1764145}{33} \hat t^3 \hat s \hat v \odot\hat   t \hat s \hat w_3 + \textstyle\frac{254846310}{11} \hat t^3 \hat s \hat v \odot \hat  t \hat y + \textstyle\frac{52823}{1584} \hat t^3 \hat s \hat v \odot  \hat s^4  -\textstyle\frac{127885}{396} \hat t^3 \hat s \hat v \odot  \hat s^2  \hat u_1  -\textstyle\frac{12385}{12} \hat t^3 \hat s \hat v \odot  \hat s^2  \hat u_2
\\
&+\textstyle\frac{7738360}{33} \hat t^3 \hat s \hat v \odot  \hat s  \hat x_1+ \textstyle\frac{68660}{3} \hat t^3 \hat s \hat v \odot  \hat v  \hat w_2 + \textstyle\frac{2074690}{33} \hat t^3 \hat s \hat v \odot \hat v  \hat w_3+ \textstyle\frac{629475840}{11} \hat t^3 \hat s \hat v \odot  \hat z +\textstyle\frac{222457237834}{297} \hat t^3 \hat w_1 \odot  \hat t^3 \hat w_1
\\
&-\textstyle\frac{525452755}{9} \hat t^3 \hat w_1 \odot  \hat t^3 \hat w_2  -\textstyle\frac{5283356470}{11} \hat t^3 \hat w_1 \odot  \hat t^3 \hat w_3 -\textstyle\frac{23603398}{297} \hat t^3 \hat w_1 \odot  \hat t^2 \hat s^3+ \textstyle\frac{6703353544}{297} \hat t^3 \hat w_1 \odot  \hat t^2 \hat s \hat u_1
\\
&-\textstyle\frac{763135}{3} \hat t^3 \hat w_1 \odot  \hat t^2 \hat s \hat u_2 + \textstyle\frac{327601805680}{99} \hat t^3 \hat w_1 \odot  \hat t^2 \hat x_1  -\textstyle\frac{204106025}{3} \hat t^3 \hat w_1 \odot  \hat t^2 \hat x_2   -\textstyle\frac{58823117}{396} \hat t^3 \hat w_1 \odot \hat  t \hat s^2 \hat v
\\
&+ \textstyle\frac{6633686990}{297} \hat t^3 \hat w_1 \odot \hat  t \hat s \hat w_1 -\textstyle\frac{105045545}{9} \hat t^3 \hat w_1 \odot\hat   t \hat s \hat w_2 + \textstyle\frac{210155900}{33} \hat t^3 \hat w_1 \odot \hat  t \hat s \hat w_3 + \textstyle\frac{43860881220}{11} \hat t^3 \hat w_1 \odot \hat  t \hat y
\\
&+ \textstyle\frac{9913909}{2376} \hat t^3 \hat w_1 \odot  \hat s^4  -\textstyle\frac{1418575}{594} \hat t^3 \hat w_1 \odot  \hat s^2  \hat u_1  -\textstyle\frac{2256995}{18} \hat t^3 \hat w_1 \odot  \hat s^2  \hat u_2 + \textstyle\frac{1412144720}{33} \hat t^3 \hat w_1 \odot \hat s  \hat x_1+ \textstyle\frac{23670160}{9} \hat t^3 \hat w_1 \odot  \hat v  \hat w_2
\\
&+\textstyle\frac{230312380}{33} \hat t^3 \hat w_1 \odot \hat v  \hat w_3+\textstyle\frac{104970055680}{11} \hat t^3 \hat w_1 \odot  \hat z +\textstyle\frac{7244875}{6} \hat t^3 \hat w_2 \odot   \hat t^3 \hat w_2 + 20489175 \hat t^3 \hat w_2 \odot   \hat t^3 \hat w_3 + \textstyle\frac{34565}{9} \hat t^3 \hat w_2 \odot   \hat t^2 \hat s^3
\\
& -\textstyle\frac{6291365}{9} \hat t^3 \hat w_2 \odot   \hat t^2 \hat s \hat u_1 + \textstyle\frac{24475}{3} \hat t^3 \hat w_2 \odot   \hat t^2 \hat s \hat u_2  -\textstyle\frac{314478350}{3} \hat t^3 \hat w_2 \odot   \hat t^2 \hat x_1 + 2880075 \hat t^3 \hat w_2 \odot   \hat t^2 \hat x_2   +\textstyle\frac{323075}{36} \hat t^3 \hat w_2 \odot  \hat  t \hat s^2 \hat v
\\
&+ \textstyle\frac{1721765}{9} \hat t^3 \hat w_2 \odot   \hat t \hat s \hat w_1 + 437525 \hat t^3 \hat w_2 \odot \hat   t \hat s \hat w_2  -149075 \hat t^3 \hat w_2 \odot \hat   t \hat s \hat w_3  -2223900 \hat t^3 \hat w_2 \odot \hat   t \hat y  -\textstyle\frac{1235}{8} \hat t^3 \hat w_2 \odot   \hat s^4
\\
&+ \textstyle\frac{165245}{18} \hat t^3 \hat w_2 \odot   \hat s^2  \hat u_1 + \textstyle\frac{10725}{2} \hat t^3 \hat w_2 \odot   \hat s^2  \hat u_2 + 988400 \hat t^3 \hat w_2 \odot  \hat s  \hat x_1 -\textstyle\frac{467500}{3} \hat t^3 \hat w_2 \odot   \hat v  \hat w_2  -300500 \hat t^3 \hat w_2 \odot  \hat v  \hat w_3
\\
&+\textstyle\frac{918940050}{11} \hat t^3 \hat w_3 \odot   \hat t^3 \hat w_3 + \textstyle\frac{93100}{3} \hat t^3 \hat w_3 \odot   \hat t^2 \hat s^3 -\textstyle\frac{70189910}{11} \hat t^3 \hat w_3 \odot   \hat t^2 \hat s \hat u_1 + 98525 \hat t^3 \hat w_3 \odot   \hat t^2 \hat s \hat u_2
\\
& -860220900 \hat t^3 \hat w_3 \odot   \hat t^2 \hat x_1 + 23687475 \hat t^3 \hat w_3 \odot   \hat t^2 \hat x_2  + \textstyle\frac{9783655}{132} \hat t^3 \hat w_3 \odot  \hat  t \hat s^2 \hat v + \textstyle\frac{103320}{11} \hat t^3 \hat w_3 \odot  \hat  t \hat s \hat w_1
\\
& + 4089225 \hat t^3 \hat w_3 \odot  \hat  t \hat s \hat w_2  -\textstyle\frac{23682750}{11} \hat t^3 \hat w_3 \odot  \hat  t \hat s \hat w_3  -\textstyle\frac{158703300}{11} \hat t^3 \hat w_3 \odot   \hat t \hat y  -\textstyle\frac{330505}{264} \hat t^3 \hat w_3 \odot   \hat s^4 + \textstyle\frac{1660785}{22} \hat t^3 \hat w_3 \odot   \hat s^2  \hat u_1
\\
& + \textstyle\frac{86975}{2} \hat t^3 \hat w_3 \odot   \hat s^2  \hat u_2 + \textstyle\frac{70534800}{11} \hat t^3 \hat w_3 \odot  \hat s  \hat x_1 -919800 \hat t^3 \hat w_3 \odot   \hat v  \hat w_2  -\textstyle\frac{27461700}{11} \hat t^3 \hat w_3 \odot  \hat v  \hat w_3+\textstyle\frac{26489}{4752} \hat t^2 \hat s^3 \odot    \hat t^2 \hat s^3
\\
& -\textstyle\frac{296414}{297} \hat t^2 \hat s^3 \odot    \hat t^2 \hat s \hat u_1 + \textstyle\frac{200}{9} \hat t^2 \hat s^3 \odot    \hat t^2 \hat s \hat u_2  -\textstyle\frac{7172180}{99} \hat t^2 \hat s^3 \odot    \hat t^2 \hat x_1 + \textstyle\frac{13375}{3} \hat t^2 \hat s^3 \odot    \hat t^2 \hat x_2+ \textstyle\frac{36571}{1188} \hat t^2 \hat s^3 \odot \hat   t \hat s^2 \hat v
\\
&+ \textstyle\frac{657680}{297} \hat t^2 \hat s^3 \odot   \hat t \hat s \hat w_1 + \textstyle\frac{8395}{9} \hat t^2 \hat s^3 \odot  \hat  t \hat s \hat w_2  -\textstyle\frac{34750}{33} \hat t^2 \hat s^3 \odot  \hat  t \hat s \hat w_3 + \textstyle\frac{4812180}{11} \hat t^2 \hat s^3 \odot   \hat t \hat y  -\textstyle\frac{359}{1056} \hat t^2 \hat s^3 \odot    \hat s^4
\\
&+\textstyle\frac{37385}{594} \hat t^2 \hat s^3 \odot    \hat s^2  \hat u_1 + 15 \hat t^2 \hat s^3 \odot    \hat s^2  \hat u_2 + 8260 \hat t^2 \hat s^3 \odot   \hat s  \hat x_1+ \textstyle\frac{40}{9} \hat t^2 \hat s^3 \odot    \hat v  \hat w_2  -\textstyle\frac{19780}{33} \hat t^2 \hat s^3 \odot   \hat v  \hat w_3+ \textstyle\frac{10926720}{11} \hat t^2 \hat s^3 \odot    \hat z
\\
&+\textstyle\frac{54046126}{297} \hat t^2 \hat s \hat u_1 \odot    \hat t^2 \hat s \hat u_1 +3905 \hat t^2 \hat s \hat u_1 \odot    \hat t^2 \hat s \hat u_2 +\textstyle\frac{6185875640}{99} \hat t^2 \hat s \hat u_1 \odot    \hat t^2 \hat x_1  -\textstyle\frac{2724175}{3} \hat t^2 \hat s \hat u_1 \odot    \hat t^2 \hat x_2
\\
&-\textstyle\frac{94211}{396} \hat t^2 \hat s \hat u_1 \odot  \hat  t \hat s^2 \hat v + \textstyle\frac{222580090}{297} \hat t^2 \hat s \hat u_1 \odot   \hat t \hat s \hat w_1  -\textstyle\frac{1083055}{9} \hat t^2 \hat s \hat u_1 \odot   \hat t \hat s \hat w_2 + \textstyle\frac{3730420}{33} \hat t^2 \hat s \hat u_1 \odot  \hat  t \hat s \hat w_3
\\
&+ \textstyle\frac{1463127060}{11} \hat t^2 \hat s \hat u_1 \odot  \hat  t \hat y + \textstyle\frac{178397}{2376} \hat t^2 \hat s \hat u_1 \odot    \hat s^4 + \textstyle\frac{3233635}{594} \hat t^2 \hat s \hat u_1 \odot    \hat s^2  \hat u_1  -\textstyle\frac{30865}{18} \hat t^2 \hat s \hat u_1 \odot    \hat s^2  \hat u_2 + \textstyle\frac{59595760}{33} \hat t^2 \hat s \hat u_1 \odot   \hat s  \hat x_1
\\
&+ \textstyle\frac{374480}{9} \hat t^2 \hat s \hat u_1 \odot    \hat v  \hat w_2 + \textstyle\frac{3496940}{33} \hat t^2 \hat s \hat u_1 \odot   \hat v  \hat w_3+ \textstyle\frac{3213181440}{11} \hat t^2 \hat s \hat u_1 \odot    \hat z+\textstyle\frac{275}{6} \hat t^2 \hat s \hat u_2 \odot   \hat t^2 \hat s \hat u_2  -473750 \hat t^2 \hat s \hat u_2 \odot   \hat t^2 \hat x_1
\\
&+ 12375 \hat t^2 \hat s \hat u_2 \odot   \hat t^2 \hat x_2  + \textstyle\frac{725}{12} \hat t^2 \hat s \hat u_2 \odot  \hat t \hat s^2 \hat v + \textstyle\frac{54365}{3} \hat t^2 \hat s \hat u_2 \odot \hat  t \hat s \hat w_1  -\textstyle\frac{8525}{3} \hat t^2 \hat s \hat u_2 \odot  \hat t \hat s \hat w_2 +11275 \hat t^2 \hat s \hat u_2 \odot \hat  t \hat s \hat w_3
\\
&-56700 \hat t^2 \hat s \hat u_2 \odot  \hat t \hat y  -\textstyle\frac{95}{72} \hat t^2 \hat s \hat u_2 \odot   \hat s^4 + \textstyle\frac{395}{6} \hat t^2 \hat s \hat u_2 \odot   \hat s^2  \hat u_1 + \textstyle\frac{275}{6} \hat t^2 \hat s \hat u_2 \odot   \hat s^2  \hat u_2 + 25200 \hat t^2 \hat s \hat u_2 \odot  \hat s  \hat x_1 -5500 \hat t^2 \hat s \hat u_2 \odot   \hat v  \hat w_2
\\
&+ 1500 \hat t^2 \hat s \hat u_2 \odot  \hat v  \hat w_3+\textstyle\frac{14477882600}{3} \hat t^2 \hat x_1 \odot   \hat t^2 \hat x_1  -121877050 \hat t^2 \hat x_1 \odot   \hat t^2 \hat x_2 +\textstyle\frac{3463615}{66} \hat t^2 \hat x_1 \odot  \hat t \hat s^2 \hat v
\\
&+ \textstyle\frac{13225952500}{99} \hat t^2 \hat x_1 \odot \hat  t \hat s \hat w_1 -\textstyle\frac{63199450}{3} \hat t^2 \hat x_1 \odot \hat  t \hat s \hat w_2 + 11526800 \hat t^2 \hat x_1 \odot \hat  t \hat s \hat w_3 + \textstyle\frac{242526403800}{11} \hat t^2 \hat x_1 \odot \hat  t \hat y
\\
&+ \textstyle\frac{3826345}{396} \hat t^2 \hat x_1 \odot   \hat s^4 + \textstyle\frac{6844375}{9} \hat t^2 \hat x_1 \odot   \hat s^2  \hat u_1  -\textstyle\frac{673175}{3} \hat t^2 \hat x_1 \odot   \hat s^2  \hat u_2 + \textstyle\frac{3086557600}{11} \hat t^2 \hat x_1 \odot  \hat s  \hat x_1+ \textstyle\frac{13851200}{3} \hat t^2 \hat x_1 \odot   \hat v  \hat w_2
\\
&+12442600 \hat t^2 \hat x_1 \odot  \hat v  \hat w_3+ \textstyle\frac{522924595200}{11} \hat t^2 \hat x_1 \odot   \hat z  +\textstyle\frac{3356925}{2} \hat t^2 \hat x_2 \odot    \hat t^2 \hat x_2  + \textstyle\frac{126575}{12} \hat t^2 \hat x_2 \odot  \hat  t \hat s^2 \hat v -\textstyle\frac{37325}{3} \hat t^2 \hat x_2 \odot \hat   t \hat s \hat w_1
\\
&+ 578875 \hat t^2 \hat x_2 \odot \hat   t \hat s \hat w_2 -325875 \hat t^2 \hat x_2 \odot  \hat  t \hat s \hat w_3 -1984500 \hat t^2 \hat x_2 \odot \hat   t \hat y -\textstyle\frac{1425}{8} \hat t^2 \hat x_2 \odot    \hat s^4+ \textstyle\frac{64525}{6} \hat t^2 \hat x_2 \odot    \hat s^2  \hat u_1
\\
&+ \textstyle\frac{12375}{2} \hat t^2 \hat x_2 \odot    \hat s^2  \hat u_2 + 882000 \hat t^2 \hat x_2 \odot   \hat s  \hat x_1 -126500 \hat t^2 \hat x_2 \odot    \hat v  \hat w_2  -343500 \hat t^2 \hat x_2 \odot   \hat v  \hat w_3+\textstyle\frac{532517}{9504}\hat t \hat s^2 \hat v \odot   \hat t \hat s^2 \hat v
\\
&+\textstyle\frac{5089175}{396}\hat t \hat s^2 \hat v \odot \hat   t \hat s \hat w_1 +\textstyle\frac{68795}{36}\hat t \hat s^2 \hat v \odot \hat   t \hat s \hat w_2  -\textstyle\frac{217055}{132}\hat t \hat s^2 \hat v \odot  \hat  t \hat s \hat w_3 + \textstyle\frac{19873065}{11}\hat t \hat s^2 \hat v \odot \hat  t \hat y  -\textstyle\frac{4633}{9504}\hat t \hat s^2 \hat v \odot    \hat s^4
\\
&+ \textstyle\frac{166205}{792}\hat t \hat s^2 \hat v \odot    \hat s^2  \hat u_1 + \textstyle\frac{2735}{72}\hat t \hat s^2 \hat v \odot    \hat s^2  \hat u_2 +\textstyle\frac{1034740}{33}\hat t \hat s^2 \hat v \odot   \hat s  \hat x_1-\textstyle\frac{935}{3}\hat t \hat s^2 \hat v \odot    \hat v  \hat w_2 -\textstyle\frac{38915}{33}\hat t \hat s^2 \hat v \odot   \hat v  \hat w_3
\\
&+ \textstyle\frac{39432960}{11}\hat t \hat s^2 \hat v \odot    \hat z +\textstyle\frac{502001260}{297}\hat t \hat s \hat w_1 \odot  \hat  t \hat s \hat w_1 + \textstyle\frac{590395}{9}\hat t \hat s \hat w_1 \odot \hat   t \hat s \hat w_2 + \textstyle\frac{4781930}{33}\hat t \hat s \hat w_1 \odot \hat   t \hat s \hat w_3 + \textstyle\frac{5760977100}{11}\hat t \hat s \hat w_1 \odot  \hat  t \hat y
\\
&+ \textstyle\frac{254365}{2376}\hat t \hat s \hat w_1 \odot    \hat s^4 + \textstyle\frac{1659235}{54}\hat t \hat s \hat w_1 \odot    \hat s^2  \hat u_1 -\textstyle\frac{3995}{18}\hat t \hat s \hat w_1 \odot    \hat s^2  \hat u_2 + \textstyle\frac{245058800}{33}\hat t \hat s \hat w_1 \odot   \hat s  \hat x_1+ \textstyle\frac{59800}{9}\hat t \hat s \hat w_1 \odot    \hat v  \hat w_2
\\
&+ \textstyle\frac{876100}{33}\hat t \hat s \hat w_1 \odot   \hat v  \hat w_3+ \textstyle\frac{11292825600}{11}\hat t \hat s \hat w_1 \odot    \hat z +\textstyle\frac{241175}{6}\hat t \hat s \hat w_2 \odot \hat   t \hat s \hat w_2  -129025\hat t \hat s \hat w_2 \odot\hat    t \hat s \hat w_3 -434700\hat t \hat s \hat w_2 \odot \hat   t \hat y
\\
&-\textstyle\frac{2375}{72}\hat t \hat s \hat w_2 \odot    \hat s^4+ \textstyle\frac{35785}{18}\hat t \hat s \hat w_2 \odot    \hat s^2  \hat u_1 +\textstyle\frac{6875}{6}\hat t \hat s \hat w_2 \odot    \hat s^2  \hat u_2+193200\hat t \hat s \hat w_2 \odot   \hat s  \hat x_1 -\textstyle\frac{73700}{3}\hat t \hat s \hat w_2 \odot    \hat v  \hat w_2
\\
& -94100\hat t \hat s \hat w_2 \odot   \hat v  \hat w_3+\textstyle\frac{3656700}{11}\hat t \hat s \hat w_3 \odot \hat   t \hat s \hat w_3  -\textstyle\frac{4932900}{11}\hat t \hat s \hat w_3 \odot  \hat  t \hat y + \textstyle\frac{6365}{264}\hat t \hat s \hat w_3 \odot    \hat s^4  -\textstyle\frac{114535}{66}\hat t \hat s \hat w_3 \odot    \hat s^2  \hat u_1
\\
&-\textstyle\frac{1675}{2}\hat t \hat s \hat w_3 \odot    \hat s^2  \hat u_2 +\textstyle\frac{2192400}{11}\hat t \hat s \hat w_3 \odot   \hat s  \hat x_1 -75200\hat t \hat s \hat w_3 \odot    \hat v  \hat w_2 + \textstyle\frac{2222700}{11}\hat t \hat s \hat w_3 \odot   \hat v  \hat w_3+\textstyle\frac{457398003600}{11}\hat t \hat y \odot \hat   t \hat y
\\
&+ \textstyle\frac{252315}{22}\hat t \hat y \odot    \hat s^4 + \textstyle\frac{44199750}{11}\hat t \hat y \odot    \hat s^2  \hat u_1  -3150\hat t \hat y \odot    \hat s^2  \hat u_2 + \textstyle\frac{11863958400}{11}\hat t \hat y \odot   \hat s  \hat x_1+ 126000\hat t \hat y \odot    \hat v  \hat w_2 + \textstyle\frac{1512000}{11}\hat t \hat y \odot   \hat v  \hat w_3
\\
&+ \textstyle\frac{1784556748800}{11}\hat t \hat y \odot    \hat z +\textstyle\frac{1109}{76032} \hat s^4 \odot    \hat s^4 -\textstyle\frac{365}{4752} \hat s^4 \odot    \hat s^2  \hat u_1  -\textstyle\frac{95}{144} \hat s^4 \odot    \hat s^2  \hat u_2 + \textstyle\frac{4445}{33} \hat s^4 \odot   \hat s  \hat x_1+ \textstyle\frac{95}{18} \hat s^4 \odot    \hat v  \hat w_2
\\
&+\textstyle\frac{1235}{66} \hat s^4 \odot   \hat v  \hat w_3+ \textstyle\frac{211680}{11} \hat s^4 \odot    \hat z +\textstyle\frac{408305}{2376} \hat s^2  \hat u_1 \odot    \hat s^2  \hat u_1 + \textstyle\frac{1465}{36} \hat s^2  \hat u_1 \odot    \hat s^2  \hat u_2 +\textstyle\frac{1913800}{33} \hat s^2  \hat u_1 \odot   \hat s  \hat x_1-\textstyle\frac{2650}{9} \hat s^2  \hat u_1 \odot    \hat v  \hat w_2
\\
&-\textstyle\frac{38650}{33} \hat s^2  \hat u_1 \odot   \hat v  \hat w_3+ \textstyle\frac{76204800}{11} \hat s^2  \hat u_1 \odot    \hat z +\textstyle\frac{275}{24} \hat s^2  \hat u_2 \odot    \hat s^2  \hat u_2 +1400 \hat s^2  \hat u_2 \odot   \hat s  \hat x_1 -\textstyle\frac{550}{3} \hat s^2  \hat u_2 \odot    \hat v  \hat w_2 -650 \hat s^2  \hat u_2 \odot   \hat v  \hat w_3
\\
&+\textstyle\frac{76574400}{11}\hat s  \hat x_1 \odot   \hat s  \hat x_1 -56000\hat s  \hat x_1 \odot    \hat v  \hat w_2  -\textstyle\frac{672000}{11}\hat s  \hat x_1 \odot   \hat v  \hat w_3+ \textstyle\frac{20727705600}{11}\hat s  \hat x_1 \odot    \hat z +\textstyle\frac{17600}{3}\hat v  \hat w_2 \odot     \hat v  \hat w_2
\\
&-400\hat v  \hat w_2 \odot    \hat v  \hat w_3+\textstyle\frac{433200}{11}\hat v  \hat w_3 \odot    \hat v  \hat w_3+\textstyle\frac{1575305625600}{11}\hat z \odot     \hat z.
\end{align*}