Derousseau's Generalization of the Malfatti circles

Isosceles Triangle with 135° Top Angle

\(A=22.5\degree\), \(B=22.5\degree\), \(C=135\degree\).


[Top] > Isosceles Triangle with 135° Top Angle

Reference Triangle

reference triangle

Triangle Centers and their Extraversions

Approximately,
\[ \begin{alignedat}{4} I&{}\approx{}&0.259891532474&{}:{}&0.259891532474&{}:{}&0.480216935052&,\\ I_{\mathbf{a}}&{}\approx{}&-0.541196100146&{}:{}&0.541196100146&{}:{}&1.000000000000&,\\ I_{\mathbf{b}}&{}\approx{}&0.541196100146&{}:{}&-0.541196100146&{}:{}&1.000000000000&,\\ I_{\mathbf{c}}&{}\approx{}&6.568535592272&{}:{}&6.568535592272&{}:{}&-12.137071184544&. \end{alignedat} \] \[ \begin{alignedat}{4} P&{}\approx{}&0.172650295333&{}:{}&0.172650295333&{}:{}&0.654699409335&,\\ P_{\mathbf{1}}&{}\approx{}&0.047564446284&{}:{}&0.047564446284&{}:{}&0.904871107431&,\\ P_{\mathbf{2}}&{}\approx{}&0.000094058383&{}:{}&0.999549267060&{}:{}&0.000356674557&,\\ P_{\mathbf{3}}&{}\approx{}&0.000093923818&{}:{}&0.998119259436&{}:{}&0.001786816746&,\\ P_{\mathbf{4}}&{}\approx{}&0.999549267060&{}:{}&0.000094058383&{}:{}&0.000356674557&,\\ P_{\mathbf{5}}&{}\approx{}&0.998119259436&{}:{}&0.000093923818&{}:{}&0.001786816746&,\\ P_{\mathbf{6}}&{}\approx{}&0.499910807065&{}:{}&0.499910807065&{}:{}&0.000178385870&,\\ P_{\mathbf{7}}&{}\approx{}&0.499552854332&{}:{}&0.499552854332&{}:{}&0.000894291336&,\\ P_{\mathbf{a}}&{}\approx{}&-0.269848945318&{}:{}&0.741300112730&{}:{}&0.528548832588&,\\ P_{\mathbf{1a}}&{}\approx{}&-0.142559615498&{}:{}&0.863330366494&{}:{}&0.279229249005&,\\ P_{\mathbf{2a}}&{}\approx{}&-0.000798135709&{}:{}&0.002192552912&{}:{}&0.998605582797&,\\ P_{\mathbf{3a}}&{}\approx{}&-0.000796033466&{}:{}&0.004820719120&{}:{}&0.995975314347&,\\ P_{\mathbf{4a}}&{}\approx{}&1.134180612673&{}:{}&-0.000646332543&{}:{}&-0.133534280131&,\\ P_{\mathbf{5a}}&{}\approx{}&1.133780226419&{}:{}&-0.000293086302&{}:{}&-0.133487140117&,\\ P_{\mathbf{6a}}&{}\approx{}&1.000754750339&{}:{}&-0.000570297495&{}:{}&-0.000184452844&,\\ P_{\mathbf{7a}}&{}\approx{}&1.000443013535&{}:{}&-0.000258618149&{}:{}&-0.000184395386&,\\ P_{\mathbf{b}}&{}\approx{}&0.741300112730&{}:{}&-0.269848945318&{}:{}&0.528548832588&,\\ P_{\mathbf{1b}}&{}\approx{}&0.863330366494&{}:{}&-0.142559615498&{}:{}&0.279229249005&,\\ P_{\mathbf{2b}}&{}\approx{}&-0.000646332543&{}:{}&1.134180612673&{}:{}&-0.133534280131&,\\ P_{\mathbf{3b}}&{}\approx{}&-0.000293086302&{}:{}&1.133780226419&{}:{}&-0.133487140117&,\\ P_{\mathbf{4b}}&{}\approx{}&0.002192552912&{}:{}&-0.000798135709&{}:{}&0.998605582797&,\\ P_{\mathbf{5b}}&{}\approx{}&0.004820719120&{}:{}&-0.000796033466&{}:{}&0.995975314347&,\\ P_{\mathbf{6b}}&{}\approx{}&-0.000570297495&{}:{}&1.000754750339&{}:{}&-0.000184452844&,\\ P_{\mathbf{7b}}&{}\approx{}&-0.000258618149&{}:{}&1.000443013535&{}:{}&-0.000184395386&,\\ P_{\mathbf{c}}&{}\approx{}&1.613914110072&{}:{}&1.613914110072&{}:{}&-2.227828220144&,\\ P_{\mathbf{1c}}&{}\approx{}&-0.876114078250&{}:{}&-0.876114078250&{}:{}&2.752228156499&,\\ P_{\mathbf{2c}}&{}\approx{}&1.208535181249&{}:{}&0.548216543556&{}:{}&-0.756751724805&,\\ P_{\mathbf{3c}}&{}\approx{}&-0.268767146754&{}:{}&-0.592493160293&{}:{}&1.861260307047&,\\ P_{\mathbf{4c}}&{}\approx{}&0.548216543556&{}:{}&1.208535181249&{}:{}&-0.756751724805&,\\ P_{\mathbf{5c}}&{}\approx{}&-0.592493160293&{}:{}&-0.268767146754&{}:{}&1.861260307047&,\\ P_{\mathbf{6c}}&{}\approx{}&0.727893522251&{}:{}&0.727893522251&{}:{}&-0.455787044502&,\\ P_{\mathbf{7c}}&{}\approx{}&-0.203038350841&{}:{}&-0.203038350841&{}:{}&1.406076701682&. \end{alignedat} \] \[ \begin{alignedat}{4} P^-&{}\approx{}&0.145066082349&{}:{}&0.145066082349&{}:{}&0.709867835302&,\\ P^-_{\mathbf{1}}&{}\approx{}&0.010612418154&{}:{}&0.010612418154&{}:{}&0.978775163693&,\\ P^-_{\mathbf{2}}&{}\approx{}&-0.003458899062&{}:{}&1.009664732823&{}:{}&-0.006205833762&,\\ P^-_{\mathbf{3}}&{}\approx{}&-0.007989416378&{}:{}&1.021088469546&{}:{}&-0.013099053168&,\\ P^-_{\mathbf{4}}&{}\approx{}&1.009664732823&{}:{}&-0.003458899062&{}:{}&-0.006205833762&,\\ P^-_{\mathbf{5}}&{}\approx{}&1.021088469546&{}:{}&-0.007989416378&{}:{}&-0.013099053168&,\\ P^-_{\mathbf{6}}&{}\approx{}&1.048341617171&{}:{}&1.048341617171&{}:{}&-1.096683234343&,\\ P^-_{\mathbf{7}}&{}\approx{}&-0.170483256580&{}:{}&-0.170483256580&{}:{}&1.340966513159&,\\ P^-_{\mathbf{a}}&{}\approx{}&-0.195627557949&{}:{}&0.796034415883&{}:{}&0.399593142066&,\\ P^-_{\mathbf{1a}}&{}\approx{}&-0.061794522698&{}:{}&0.928595852513&{}:{}&0.133198670184&,\\ P^-_{\mathbf{2a}}&{}\approx{}&0.008019871917&{}:{}&-0.006602701147&{}:{}&0.998582829229&,\\ P^-_{\mathbf{3a}}&{}\approx{}&0.012365342917&{}:{}&-0.008242636546&{}:{}&0.995877293628&,\\ P^-_{\mathbf{4a}}&{}\approx{}&0.719801913471&{}:{}&0.133370071477&{}:{}&0.146828015052&,\\ P^-_{\mathbf{5a}}&{}\approx{}&0.830334170838&{}:{}&0.097805468980&{}:{}&0.071860360183&,\\ P^-_{\mathbf{6a}}&{}\approx{}&0.983265606349&{}:{}&0.005574535548&{}:{}&0.011159858103&,\\ P^-_{\mathbf{7a}}&{}\approx{}&0.988626098647&{}:{}&0.003891720452&{}:{}&0.007482180901&,\\ P^-_{\mathbf{b}}&{}\approx{}&0.796034415883&{}:{}&-0.195627557949&{}:{}&0.399593142066&,\\ P^-_{\mathbf{1b}}&{}\approx{}&0.928595852513&{}:{}&-0.061794522698&{}:{}&0.133198670184&,\\ P^-_{\mathbf{2b}}&{}\approx{}&0.133370071477&{}:{}&0.719801913471&{}:{}&0.146828015052&,\\ P^-_{\mathbf{3b}}&{}\approx{}&0.097805468980&{}:{}&0.830334170838&{}:{}&0.071860360183&,\\ P^-_{\mathbf{4b}}&{}\approx{}&-0.006602701147&{}:{}&0.008019871917&{}:{}&0.998582829229&,\\ P^-_{\mathbf{5b}}&{}\approx{}&-0.008242636546&{}:{}&0.012365342917&{}:{}&0.995877293628&,\\ P^-_{\mathbf{6b}}&{}\approx{}&0.005574535548&{}:{}&0.983265606349&{}:{}&0.011159858103&,\\ P^-_{\mathbf{7b}}&{}\approx{}&0.003891720452&{}:{}&0.988626098647&{}:{}&0.007482180901&,\\ P^-_{\mathbf{c}}&{}\approx{}&1.130766460211&{}:{}&1.130766460211&{}:{}&-1.261532920422&,\\ P^-_{\mathbf{1c}}&{}\approx{}&-0.150265610510&{}:{}&-0.150265610510&{}:{}&1.300531221021&,\\ P^-_{\mathbf{2c}}&{}\approx{}&0.957080395984&{}:{}&0.265784096255&{}:{}&-0.222864492240&,\\ P^-_{\mathbf{3c}}&{}\approx{}&0.051894541629&{}:{}&-0.256649091659&{}:{}&1.204754550030&,\\ P^-_{\mathbf{4c}}&{}\approx{}&0.265784096255&{}:{}&0.957080395984&{}:{}&-0.222864492240&,\\ P^-_{\mathbf{5c}}&{}\approx{}&-0.256649091659&{}:{}&0.051894541629&{}:{}&1.204754550030&,\\ P^-_{\mathbf{6c}}&{}\approx{}&0.484073871176&{}:{}&0.484073871176&{}:{}&0.031852257648&,\\ P^-_{\mathbf{7c}}&{}\approx{}&-0.037643518691&{}:{}&-0.037643518691&{}:{}&1.075287037382&. \end{alignedat} \] \[ \begin{alignedat}{4} P^+&{}\approx{}&0.189548592918&{}:{}&0.189548592918&{}:{}&0.620902814163&,\\ P^+_{\mathbf{1}}&{}\approx{}&0.074975567222&{}:{}&0.074975567222&{}:{}&0.850048865556&,\\ P^+_{\mathbf{2}}&{}\approx{}&0.003552423498&{}:{}&0.989703110874&{}:{}&0.006744465628&,\\ P^+_{\mathbf{3}}&{}\approx{}&0.007703721666&{}:{}&0.976495643280&{}:{}&0.015800635054&,\\ P^+_{\mathbf{4}}&{}\approx{}&0.989703110874&{}:{}&0.003552423498&{}:{}&0.006744465628&,\\ P^+_{\mathbf{5}}&{}\approx{}&0.976495643280&{}:{}&0.007703721666&{}:{}&0.015800635054&,\\ P^+_{\mathbf{6}}&{}\approx{}&0.401447312137&{}:{}&0.401447312137&{}:{}&0.197105375726&,\\ P^+_{\mathbf{7}}&{}\approx{}&0.353623965370&{}:{}&0.353623965370&{}:{}&0.292752069260&,\\ P^+_{\mathbf{a}}&{}\approx{}&-0.317824756245&{}:{}&0.705920518352&{}:{}&0.611904237893&,\\ P^+_{\mathbf{1a}}&{}\approx{}&-0.200035210506&{}:{}&0.816884897140&{}:{}&0.383150313366&,\\ P^+_{\mathbf{2a}}&{}\approx{}&-0.009337460454&{}:{}&0.010709843190&{}:{}&0.998627617264&,\\ P^+_{\mathbf{3a}}&{}\approx{}&-0.013346099268&{}:{}&0.017277317002&{}:{}&0.996068782266&,\\ P^+_{\mathbf{4a}}&{}\approx{}&1.954195477811&{}:{}&-0.265851671716&{}:{}&-0.688343806094&,\\ P^+_{\mathbf{5a}}&{}\approx{}&1.609646222900&{}:{}&-0.154131852383&{}:{}&-0.455514370517&,\\ P^+_{\mathbf{6a}}&{}\approx{}&1.018649834244&{}:{}&-0.006857758045&{}:{}&-0.011792076199&,\\ P^+_{\mathbf{7a}}&{}\approx{}&1.012443906015&{}:{}&-0.004473573387&{}:{}&-0.007970332628&,\\ P^+_{\mathbf{b}}&{}\approx{}&0.705920518352&{}:{}&-0.317824756245&{}:{}&0.611904237893&,\\ P^+_{\mathbf{1b}}&{}\approx{}&0.816884897140&{}:{}&-0.200035210506&{}:{}&0.383150313366&,\\ P^+_{\mathbf{2b}}&{}\approx{}&-0.265851671716&{}:{}&1.954195477811&{}:{}&-0.688343806094&,\\ P^+_{\mathbf{3b}}&{}\approx{}&-0.154131852383&{}:{}&1.609646222900&{}:{}&-0.455514370517&,\\ P^+_{\mathbf{4b}}&{}\approx{}&0.010709843190&{}:{}&-0.009337460454&{}:{}&0.998627617264&,\\ P^+_{\mathbf{5b}}&{}\approx{}&0.017277317002&{}:{}&-0.013346099268&{}:{}&0.996068782266&,\\ P^+_{\mathbf{6b}}&{}\approx{}&-0.006857758045&{}:{}&1.018649834244&{}:{}&-0.011792076199&,\\ P^+_{\mathbf{7b}}&{}\approx{}&-0.004473573387&{}:{}&1.012443906015&{}:{}&-0.007970332628&,\\ P^+_{\mathbf{c}}&{}\approx{}&2.018211926313&{}:{}&2.018211926313&{}:{}&-3.036423852626&,\\ P^+_{\mathbf{1c}}&{}\approx{}&-1.777787726467&{}:{}&-1.777787726467&{}:{}&4.555575452935&,\\ P^+_{\mathbf{2c}}&{}\approx{}&1.438420640281&{}:{}&0.806422458090&{}:{}&-1.244843098371&,\\ P^+_{\mathbf{3c}}&{}\approx{}&-0.622619364797&{}:{}&-0.963099231763&{}:{}&2.585718596560&,\\ P^+_{\mathbf{4c}}&{}\approx{}&0.806422458090&{}:{}&1.438420640281&{}:{}&-1.244843098371&,\\ P^+_{\mathbf{5c}}&{}\approx{}&-0.963099231763&{}:{}&-0.622619364797&{}:{}&2.585718596560&,\\ P^+_{\mathbf{6c}}&{}\approx{}&0.952925126855&{}:{}&0.952925126855&{}:{}&-0.905850253710&,\\ P^+_{\mathbf{7c}}&{}\approx{}&-0.376927630039&{}:{}&-0.376927630039&{}:{}&1.753855260078&. \end{alignedat} \] \[ \begin{alignedat}{4} Q&{}\approx{}&0.113841646514&{}:{}&0.113841646514&{}:{}&0.772316706973&,\\ Q_{\mathbf{1}}&{}\approx{}&-0.075784598068&{}:{}&-0.075784598068&{}:{}&1.151569196137&,\\ Q_{\mathbf{2}}&{}\approx{}&-0.010492878040&{}:{}&1.081677943109&{}:{}&-0.071185065069&,\\ Q_{\mathbf{3}}&{}\approx{}&-0.008526445804&{}:{}&0.878964600913&{}:{}&0.129561844890&,\\ Q_{\mathbf{4}}&{}\approx{}&1.081677943109&{}:{}&-0.010492878040&{}:{}&-0.071185065069&,\\ Q_{\mathbf{5}}&{}\approx{}&0.878964600913&{}:{}&-0.008526445804&{}:{}&0.129561844890&,\\ Q_{\mathbf{6}}&{}\approx{}&0.517012249752&{}:{}&0.517012249752&{}:{}&-0.034024499505&,\\ Q_{\mathbf{7}}&{}\approx{}&0.465678818685&{}:{}&0.465678818685&{}:{}&0.068642362630&,\\ Q_{\mathbf{a}}&{}\approx{}&-0.106928052948&{}:{}&0.890977102650&{}:{}&0.215950950298&,\\ Q_{\mathbf{1a}}&{}\approx{}&0.088089562205&{}:{}&1.089815338754&{}:{}&-0.177904900959&,\\ Q_{\mathbf{2a}}&{}\approx{}&0.022877566451&{}:{}&-0.190627130210&{}:{}&1.167749563759&,\\ Q_{\mathbf{3a}}&{}\approx{}&0.015524308276&{}:{}&0.192061679716&{}:{}&0.792414012009&,\\ Q_{\mathbf{4a}}&{}\approx{}&2.598494936932&{}:{}&-0.311850891987&{}:{}&-1.286644044945&,\\ Q_{\mathbf{5a}}&{}\approx{}&1.707416774411&{}:{}&0.138010166320&{}:{}&-0.845426940731&,\\ Q_{\mathbf{6a}}&{}\approx{}&1.111631062982&{}:{}&-0.133409203006&{}:{}&0.021778140024&,\\ Q_{\mathbf{7a}}&{}\approx{}&0.908743138030&{}:{}&0.073453531382&{}:{}&0.017803330588&,\\ Q_{\mathbf{b}}&{}\approx{}&0.890977102650&{}:{}&-0.106928052948&{}:{}&0.215950950298&,\\ Q_{\mathbf{1b}}&{}\approx{}&1.089815338754&{}:{}&0.088089562205&{}:{}&-0.177904900959&,\\ Q_{\mathbf{2b}}&{}\approx{}&-0.311850891987&{}:{}&2.598494936932&{}:{}&-1.286644044945&,\\ Q_{\mathbf{3b}}&{}\approx{}&0.138010166320&{}:{}&1.707416774411&{}:{}&-0.845426940731&,\\ Q_{\mathbf{4b}}&{}\approx{}&-0.190627130210&{}:{}&0.022877566451&{}:{}&1.167749563759&,\\ Q_{\mathbf{5b}}&{}\approx{}&0.192061679716&{}:{}&0.015524308276&{}:{}&0.792414012009&,\\ Q_{\mathbf{6b}}&{}\approx{}&-0.133409203006&{}:{}&1.111631062982&{}:{}&0.021778140024&,\\ Q_{\mathbf{7b}}&{}\approx{}&0.073453531382&{}:{}&0.908743138030&{}:{}&0.017803330588&,\\ Q_{\mathbf{c}}&{}\approx{}&0.843296904551&{}:{}&0.843296904551&{}:{}&-0.686593809102&,\\ Q_{\mathbf{1c}}&{}\approx{}&1.295727196969&{}:{}&1.295727196969&{}:{}&-1.591454393939&,\\ Q_{\mathbf{2c}}&{}\approx{}&1.143057852177&{}:{}&-0.769865097862&{}:{}&0.626807245685&,\\ Q_{\mathbf{3c}}&{}\approx{}&0.746899309312&{}:{}&-1.108959378294&{}:{}&1.362060068982&,\\ Q_{\mathbf{4c}}&{}\approx{}&-0.769865097862&{}:{}&1.143057852177&{}:{}&0.626807245685&,\\ Q_{\mathbf{5c}}&{}\approx{}&-1.108959378294&{}:{}&0.746899309312&{}:{}&1.362060068982&,\\ Q_{\mathbf{6c}}&{}\approx{}&0.392409230104&{}:{}&0.392409230104&{}:{}&0.215181539792&,\\ Q_{\mathbf{7c}}&{}\approx{}&0.261532306397&{}:{}&0.261532306397&{}:{}&0.476935387207&. \end{alignedat} \] \[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.215190892271&{}:{}&0.215190892271&{}:{}&0.569618215458&,\\ I^\prime_{\mathbf{1}}&{}\approx{}&0.126120751079&{}:{}&0.126120751079&{}:{}&0.747758497842&,\\ I^\prime_{\mathbf{2}}&{}\approx{}&0.009369094039&{}:{}&0.965830569058&{}:{}&0.024800336903&,\\ I^\prime_{\mathbf{3}}&{}\approx{}&0.009089605290&{}:{}&0.937018949093&{}:{}&0.053891445616&,\\ I^\prime_{\mathbf{4}}&{}\approx{}&0.965830569058&{}:{}&0.009369094039&{}:{}&0.024800336903&,\\ I^\prime_{\mathbf{5}}&{}\approx{}&0.937018949093&{}:{}&0.009089605290&{}:{}&0.053891445616&,\\ I^\prime_{\mathbf{6}}&{}\approx{}&0.493661940902&{}:{}&0.493661940902&{}:{}&0.012676118196&,\\ I^\prime_{\mathbf{7}}&{}\approx{}&0.486023490490&{}:{}&0.486023490490&{}:{}&0.027953019020&,\\ I^\prime_{\mathbf{a}}&{}\approx{}&-0.390648057027&{}:{}&0.647474008384&{}:{}&0.743174048643&,\\ I^\prime_{\mathbf{1a}}&{}\approx{}&-0.297327717849&{}:{}&0.731687521071&{}:{}&0.565640196777&,\\ I^\prime_{\mathbf{2a}}&{}\approx{}&-0.020517324001&{}:{}&0.034006143825&{}:{}&0.986511180176&,\\ I^\prime_{\mathbf{3a}}&{}\approx{}&-0.020184590973&{}:{}&0.049671834969&{}:{}&0.970512756004&,\\ I^\prime_{\mathbf{4a}}&{}\approx{}&1.961910428851&{}:{}&-0.046834520438&{}:{}&-0.915075908413&,\\ I^\prime_{\mathbf{5a}}&{}\approx{}&1.932362994164&{}:{}&-0.031068625030&{}:{}&-0.901294369134&,\\ I^\prime_{\mathbf{6a}}&{}\approx{}&1.044197063812&{}:{}&-0.024926963029&{}:{}&-0.019270100783&,\\ I^\prime_{\mathbf{7a}}&{}\approx{}&1.035767662910&{}:{}&-0.016653122231&{}:{}&-0.019114540678&,\\ I^\prime_{\mathbf{b}}&{}\approx{}&0.647474008384&{}:{}&-0.390648057027&{}:{}&0.743174048643&,\\ I^\prime_{\mathbf{1b}}&{}\approx{}&0.731687521071&{}:{}&-0.297327717849&{}:{}&0.565640196777&,\\ I^\prime_{\mathbf{2b}}&{}\approx{}&-0.046834520438&{}:{}&1.961910428851&{}:{}&-0.915075908413&,\\ I^\prime_{\mathbf{3b}}&{}\approx{}&-0.031068625030&{}:{}&1.932362994164&{}:{}&-0.901294369134&,\\ I^\prime_{\mathbf{4b}}&{}\approx{}&0.034006143825&{}:{}&-0.020517324001&{}:{}&0.986511180176&,\\ I^\prime_{\mathbf{5b}}&{}\approx{}&0.049671834969&{}:{}&-0.020184590973&{}:{}&0.970512756004&,\\ I^\prime_{\mathbf{6b}}&{}\approx{}&-0.024926963029&{}:{}&1.044197063812&{}:{}&-0.019270100783&,\\ I^\prime_{\mathbf{7b}}&{}\approx{}&-0.016653122231&{}:{}&1.035767662910&{}:{}&-0.019114540678&,\\ I^\prime_{\mathbf{c}}&{}\approx{}&2.481806171257&{}:{}&2.481806171257&{}:{}&-3.963612342513&,\\ I^\prime_{\mathbf{1c}}&{}\approx{}&-2.443405087842&{}:{}&-2.443405087842&{}:{}&5.886810175683&,\\ I^\prime_{\mathbf{2c}}&{}\approx{}&1.672613439834&{}:{}&1.126528029260&{}:{}&-1.799141469094&,\\ I^\prime_{\mathbf{3c}}&{}\approx{}&-0.915409495002&{}:{}&-1.359155018361&{}:{}&3.274564513363&,\\ I^\prime_{\mathbf{4c}}&{}\approx{}&1.126528029260&{}:{}&1.672613439834&{}:{}&-1.799141469094&,\\ I^\prime_{\mathbf{5c}}&{}\approx{}&-1.359155018361&{}:{}&-0.915409495002&{}:{}&3.274564513363&,\\ I^\prime_{\mathbf{6c}}&{}\approx{}&1.081837671059&{}:{}&1.081837671059&{}:{}&-1.163675342118&,\\ I^\prime_{\mathbf{7c}}&{}\approx{}&-0.634051832675&{}:{}&-0.634051832675&{}:{}&2.268103665351&. \end{alignedat} \]

Central Triangles and their Extraversions

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.382683432365&{}:{}&0.216772751325&{}:{}&0.400543816310&,\\B^\prime&{}\approx{}&0.216772751325&{}:{}&0.382683432365&{}:{}&0.400543816310&,\\C^\prime&{}\approx{}&0.093996764303&{}:{}&0.093996764303&{}:{}&0.812006471395&,\\[.5em] A^\prime_{\mathbf{1}}&{}\approx{}&0.076120467489&{}:{}&0.324423348821&{}:{}&0.599456183690&,\\B^\prime_{\mathbf{1}}&{}\approx{}&0.324423348821&{}:{}&0.076120467489&{}:{}&0.599456183690&,\\C^\prime_{\mathbf{1}}&{}\approx{}&0.042301124316&{}:{}&0.042301124316&{}:{}&0.915397751368&,\\[.5em] A^\prime_{\mathbf{2}}&{}\approx{}&-0.519141344633&{}:{}&0.533451499915&{}:{}&0.985689844718&,\\B^\prime_{\mathbf{2}}&{}\approx{}&0.003485282707&{}:{}&0.990074754576&{}:{}&0.006439962716&,\\C^\prime_{\mathbf{2}}&{}\approx{}&3.937549278574&{}:{}&3.937549278574&{}:{}&-6.875098557148&,\\[.5em] A^\prime_{\mathbf{3}}&{}\approx{}&-0.531270854722&{}:{}&0.537710817439&{}:{}&0.993560037284&,\\B^\prime_{\mathbf{3}}&{}\approx{}&0.007744600231&{}:{}&0.977945244486&{}:{}&0.014310155282&,\\C^\prime_{\mathbf{3}}&{}\approx{}&2.630986313698&{}:{}&2.630986313698&{}:{}&-4.261972627396&,\\[.5em] A^\prime_{\mathbf{4}}&{}\approx{}&0.990074754576&{}:{}&0.003485282707&{}:{}&0.006439962716&,\\B^\prime_{\mathbf{4}}&{}\approx{}&0.533451499915&{}:{}&-0.519141344633&{}:{}&0.985689844718&,\\C^\prime_{\mathbf{4}}&{}\approx{}&3.937549278574&{}:{}&3.937549278574&{}:{}&-6.875098557148&,\\[.5em] A^\prime_{\mathbf{5}}&{}\approx{}&0.977945244486&{}:{}&0.007744600231&{}:{}&0.014310155282&,\\B^\prime_{\mathbf{5}}&{}\approx{}&0.537710817439&{}:{}&-0.531270854722&{}:{}&0.993560037284&,\\C^\prime_{\mathbf{5}}&{}\approx{}&2.630986313698&{}:{}&2.630986313698&{}:{}&-4.261972627396&,\\[.5em] A^\prime_{\mathbf{6}}&{}\approx{}&0.382683432365&{}:{}&0.216772751325&{}:{}&0.400543816310&,\\B^\prime_{\mathbf{6}}&{}\approx{}&0.216772751325&{}:{}&0.382683432365&{}:{}&0.400543816310&,\\C^\prime_{\mathbf{6}}&{}\approx{}&6.526234467956&{}:{}&6.526234467956&{}:{}&-12.052468935912&,\\[.5em] A^\prime_{\mathbf{7}}&{}\approx{}&0.076120467489&{}:{}&0.324423348821&{}:{}&0.599456183690&,\\B^\prime_{\mathbf{7}}&{}\approx{}&0.324423348821&{}:{}&0.076120467489&{}:{}&0.599456183690&,\\C^\prime_{\mathbf{7}}&{}\approx{}&6.474538827970&{}:{}&6.474538827970&{}:{}&-11.949077655939&,\\[.5em] A^\prime_{\mathbf{a}}&{}\approx{}&-0.865858935109&{}:{}&0.655202526796&{}:{}&1.210656408313&,\\B^\prime_{\mathbf{a}}&{}\approx{}&-0.160638130892&{}:{}&0.863817568348&{}:{}&0.296820562545&,\\C^\prime_{\mathbf{a}}&{}\approx{}&-0.370459237183&{}:{}&0.370459237183&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{1a}}&{}\approx{}&-0.246727081811&{}:{}&0.437792331916&{}:{}&0.808934749895&,\\B^\prime_{\mathbf{1a}}&{}\approx{}&-0.107334967498&{}:{}&0.909005808310&{}:{}&0.198329159188&,\\C^\prime_{\mathbf{1a}}&{}\approx{}&-0.823192531266&{}:{}&0.823192531266&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{2a}}&{}\approx{}&0.241791662387&{}:{}&0.266247361627&{}:{}&0.491960975985&,\\B^\prime_{\mathbf{2a}}&{}\approx{}&-9.991146350560&{}:{}&-7.470084888655&{}:{}&18.461231239215&,\\C^\prime_{\mathbf{2a}}&{}\approx{}&-0.008843564140&{}:{}&0.008843564140&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{3a}}&{}\approx{}&0.247797585933&{}:{}&0.264138361741&{}:{}&0.488064052326&,\\B^\prime_{\mathbf{3a}}&{}\approx{}&-4.496290132666&{}:{}&-2.811770718939&{}:{}&8.308060851606&,\\C^\prime_{\mathbf{3a}}&{}\approx{}&-0.013235329055&{}:{}&0.013235329055&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{4a}}&{}\approx{}&2.125750467584&{}:{}&-0.395310994322&{}:{}&-0.730439473262&,\\B^\prime_{\mathbf{4a}}&{}\approx{}&6.729173723164&{}:{}&6.704718023924&{}:{}&-12.433891747089&,\\C^\prime_{\mathbf{4a}}&{}\approx{}&0.911655337330&{}:{}&-0.911655337330&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{5a}}&{}\approx{}&1.506618614285&{}:{}&-0.177900799442&{}:{}&-0.328717814843&,\\B^\prime_{\mathbf{5a}}&{}\approx{}&6.675870559770&{}:{}&6.659529783962&{}:{}&-12.335400343732&,\\C^\prime_{\mathbf{5a}}&{}\approx{}&1.364388631412&{}:{}&-1.364388631412&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{6a}}&{}\approx{}&1.018099870087&{}:{}&-0.006355829153&{}:{}&-0.011744040934&,\\B^\prime_{\mathbf{6a}}&{}\approx{}&16.559681942832&{}:{}&15.038620480927&{}:{}&-30.598302423759&,\\C^\prime_{\mathbf{6a}}&{}\approx{}&0.550039664287&{}:{}&-0.550039664287&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{7a}}&{}\approx{}&1.012093946541&{}:{}&-0.004246829266&{}:{}&-0.007847117275&,\\B^\prime_{\mathbf{7a}}&{}\approx{}&11.064825724938&{}:{}&10.380306311212&{}:{}&-20.445132036150&,\\C^\prime_{\mathbf{7a}}&{}\approx{}&0.554431429201&{}:{}&-0.554431429201&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{b}}&{}\approx{}&0.863817568348&{}:{}&-0.160638130892&{}:{}&0.296820562545&,\\B^\prime_{\mathbf{b}}&{}\approx{}&0.655202526796&{}:{}&-0.865858935109&{}:{}&1.210656408313&,\\C^\prime_{\mathbf{b}}&{}\approx{}&0.370459237183&{}:{}&-0.370459237183&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{1b}}&{}\approx{}&0.909005808310&{}:{}&-0.107334967498&{}:{}&0.198329159188&,\\B^\prime_{\mathbf{1b}}&{}\approx{}&0.437792331916&{}:{}&-0.246727081811&{}:{}&0.808934749895&,\\C^\prime_{\mathbf{1b}}&{}\approx{}&0.823192531266&{}:{}&-0.823192531266&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{2b}}&{}\approx{}&6.704718023924&{}:{}&6.729173723164&{}:{}&-12.433891747089&,\\B^\prime_{\mathbf{2b}}&{}\approx{}&-0.395310994322&{}:{}&2.125750467584&{}:{}&-0.730439473262&,\\C^\prime_{\mathbf{2b}}&{}\approx{}&-0.911655337330&{}:{}&0.911655337330&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{3b}}&{}\approx{}&6.659529783962&{}:{}&6.675870559770&{}:{}&-12.335400343732&,\\B^\prime_{\mathbf{3b}}&{}\approx{}&-0.177900799442&{}:{}&1.506618614285&{}:{}&-0.328717814843&,\\C^\prime_{\mathbf{3b}}&{}\approx{}&-1.364388631412&{}:{}&1.364388631412&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{4b}}&{}\approx{}&-7.470084888655&{}:{}&-9.991146350560&{}:{}&18.461231239215&,\\B^\prime_{\mathbf{4b}}&{}\approx{}&0.266247361627&{}:{}&0.241791662387&{}:{}&0.491960975985&,\\C^\prime_{\mathbf{4b}}&{}\approx{}&0.008843564140&{}:{}&-0.008843564140&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{5b}}&{}\approx{}&-2.811770718939&{}:{}&-4.496290132666&{}:{}&8.308060851606&,\\B^\prime_{\mathbf{5b}}&{}\approx{}&0.264138361741&{}:{}&0.247797585933&{}:{}&0.488064052326&,\\C^\prime_{\mathbf{5b}}&{}\approx{}&0.013235329055&{}:{}&-0.013235329055&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{6b}}&{}\approx{}&15.038620480927&{}:{}&16.559681942832&{}:{}&-30.598302423759&,\\B^\prime_{\mathbf{6b}}&{}\approx{}&-0.006355829153&{}:{}&1.018099870087&{}:{}&-0.011744040934&,\\C^\prime_{\mathbf{6b}}&{}\approx{}&-0.550039664287&{}:{}&0.550039664287&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{7b}}&{}\approx{}&10.380306311212&{}:{}&11.064825724938&{}:{}&-20.445132036150&,\\B^\prime_{\mathbf{7b}}&{}\approx{}&-0.004246829266&{}:{}&1.012093946541&{}:{}&-0.007847117275&,\\C^\prime_{\mathbf{7b}}&{}\approx{}&-0.554431429201&{}:{}&0.554431429201&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{c}}&{}\approx{}&1.923879532511&{}:{}&1.089790213552&{}:{}&-2.013669746063&,\\B^\prime_{\mathbf{c}}&{}\approx{}&1.089790213552&{}:{}&1.923879532511&{}:{}&-2.013669746063&,\\C^\prime_{\mathbf{c}}&{}\approx{}&32.809596275628&{}:{}&32.809596275628&{}:{}&-64.619192551255&,\\[.5em] A^\prime_{\mathbf{1c}}&{}\approx{}&-0.382683432365&{}:{}&-1.630986313698&{}:{}&3.013669746063&,\\B^\prime_{\mathbf{1c}}&{}\approx{}&-1.630986313698&{}:{}&-0.382683432365&{}:{}&3.013669746063&,\\C^\prime_{\mathbf{1c}}&{}\approx{}&-32.549704743153&{}:{}&-32.549704743153&{}:{}&66.099409486307&,\\[.5em] A^\prime_{\mathbf{2c}}&{}\approx{}&1.375426647384&{}:{}&0.442845925067&{}:{}&-0.818272572451&,\\B^\prime_{\mathbf{2c}}&{}\approx{}&67.781251278963&{}:{}&58.462170210314&{}:{}&-125.243421489277&,\\C^\prime_{\mathbf{2c}}&{}\approx{}&0.783227248675&{}:{}&0.783227248675&{}:{}&-0.566454497351&,\\[.5em] A^\prime_{\mathbf{3c}}&{}\approx{}&0.165769452762&{}:{}&-0.984042025213&{}:{}&1.818272572451&,\\B^\prime_{\mathbf{3c}}&{}\approx{}&-68.322447379109&{}:{}&-56.920974110168&{}:{}&126.243421489277&,\\C^\prime_{\mathbf{3c}}&{}\approx{}&-0.523335716201&{}:{}&-0.523335716201&{}:{}&2.046671432402&,\\[.5em] A^\prime_{\mathbf{4c}}&{}\approx{}&58.462170210314&{}:{}&67.781251278963&{}:{}&-125.243421489277&,\\B^\prime_{\mathbf{4c}}&{}\approx{}&0.442845925067&{}:{}&1.375426647384&{}:{}&-0.818272572451&,\\C^\prime_{\mathbf{4c}}&{}\approx{}&0.783227248675&{}:{}&0.783227248675&{}:{}&-0.566454497351&,\\[.5em] A^\prime_{\mathbf{5c}}&{}\approx{}&-56.920974110168&{}:{}&-68.322447379109&{}:{}&126.243421489277&,\\B^\prime_{\mathbf{5c}}&{}\approx{}&-0.984042025213&{}:{}&0.165769452762&{}:{}&1.818272572451&,\\C^\prime_{\mathbf{5c}}&{}\approx{}&-0.523335716201&{}:{}&-0.523335716201&{}:{}&2.046671432402&,\\[.5em] A^\prime_{\mathbf{6c}}&{}\approx{}&1.923879532511&{}:{}&1.089790213552&{}:{}&-2.013669746063&,\\B^\prime_{\mathbf{6c}}&{}\approx{}&1.089790213552&{}:{}&1.923879532511&{}:{}&-2.013669746063&,\\C^\prime_{\mathbf{6c}}&{}\approx{}&0.472553645310&{}:{}&0.472553645310&{}:{}&0.054892709380&,\\[.5em] A^\prime_{\mathbf{7c}}&{}\approx{}&-0.382683432365&{}:{}&-1.630986313698&{}:{}&3.013669746063&,\\B^\prime_{\mathbf{7c}}&{}\approx{}&-1.630986313698&{}:{}&-0.382683432365&{}:{}&3.013669746063&,\\C^\prime_{\mathbf{7c}}&{}\approx{}&-0.212662112836&{}:{}&-0.212662112836&{}:{}&1.425324225672&. \end{alignedat} \] \[ \begin{alignedat}{4} A^{\prime\prime}&{}\approx{}&0.131132148997&{}:{}&0.181314249869&{}:{}&0.687553601134&,\\B^{\prime\prime}&{}\approx{}&0.181314249869&{}:{}&0.131132148997&{}:{}&0.687553601134&,\\C^{\prime\prime}&{}\approx{}&0.299728091845&{}:{}&0.299728091845&{}:{}&0.400543816310&,\\[.5em] A^{\prime\prime}_{\mathbf{1}}&{}\approx{}&0.074843504673&{}:{}&0.046202135415&{}:{}&0.878954359912&,\\B^{\prime\prime}_{\mathbf{1}}&{}\approx{}&0.046202135415&{}:{}&0.074843504673&{}:{}&0.878954359912&,\\C^{\prime\prime}_{\mathbf{1}}&{}\approx{}&0.200271908155&{}:{}&0.200271908155&{}:{}&0.599456183690&,\\[.5em] A^{\prime\prime}_{\mathbf{2}}&{}\approx{}&0.006964400944&{}:{}&0.992681375206&{}:{}&0.000354223850&,\\B^{\prime\prime}_{\mathbf{2}}&{}\approx{}&0.012602758174&{}:{}&0.939606890140&{}:{}&0.047790351686&,\\C^{\prime\prime}_{\mathbf{2}}&{}\approx{}&0.000092887912&{}:{}&0.987110790876&{}:{}&0.012796321212&,\\[.5em] A^{\prime\prime}_{\mathbf{3}}&{}\approx{}&0.015443740099&{}:{}&0.982796873040&{}:{}&0.001759386861&,\\B^{\prime\prime}_{\mathbf{3}}&{}\approx{}&0.005347135768&{}:{}&0.892928382147&{}:{}&0.101724482085&,\\C^{\prime\prime}_{\mathbf{3}}&{}\approx{}&0.000091437238&{}:{}&0.971694615132&{}:{}&0.028213947631&,\\[.5em] A^{\prime\prime}_{\mathbf{4}}&{}\approx{}&0.939606890140&{}:{}&0.012602758174&{}:{}&0.047790351686&,\\B^{\prime\prime}_{\mathbf{4}}&{}\approx{}&0.992681375206&{}:{}&0.006964400944&{}:{}&0.000354223850&,\\C^{\prime\prime}_{\mathbf{4}}&{}\approx{}&0.987110790876&{}:{}&0.000092887912&{}:{}&0.012796321212&,\\[.5em] A^{\prime\prime}_{\mathbf{5}}&{}\approx{}&0.892928382147&{}:{}&0.005347135768&{}:{}&0.101724482085&,\\B^{\prime\prime}_{\mathbf{5}}&{}\approx{}&0.982796873040&{}:{}&0.015443740099&{}:{}&0.001759386861&,\\C^{\prime\prime}_{\mathbf{5}}&{}\approx{}&0.971694615132&{}:{}&0.000091437238&{}:{}&0.028213947631&,\\[.5em] A^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.419607974722&{}:{}&0.580184994736&{}:{}&0.000207030542&,\\B^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.580184994736&{}:{}&0.419607974722&{}:{}&0.000207030542&,\\C^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.299728091845&{}:{}&0.299728091845&{}:{}&0.400543816310&,\\[.5em] A^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.617885940244&{}:{}&0.381431227821&{}:{}&0.000682831935&,\\B^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.381431227821&{}:{}&0.617885940244&{}:{}&0.000682831935&,\\C^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.200271908155&{}:{}&0.200271908155&{}:{}&0.599456183690&,\\[.5em] A^{\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.224101579146&{}:{}&0.714594158588&{}:{}&0.509507420557&,\\B^{\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.549392878506&{}:{}&0.473305794955&{}:{}&1.076087083552&,\\C^{\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.299495333936&{}:{}&0.822741495422&{}:{}&0.476753838514&,\\[.5em] A^{\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.189908076237&{}:{}&0.899107374019&{}:{}&0.290800702217&,\\B^{\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.446866005564&{}:{}&0.571596675585&{}:{}&0.875269329979&,\\C^{\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.134781121956&{}:{}&0.816224391515&{}:{}&0.318556730441&,\\[.5em] A^{\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.017671486540&{}:{}&0.002229519123&{}:{}&1.015441967417&,\\B^{\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.000786196579&{}:{}&0.017118526271&{}:{}&0.983667670309&,\\C^{\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.023820911731&{}:{}&0.065438256692&{}:{}&0.958382655039&,\\[.5em] A^{\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.026392967481&{}:{}&0.004944016600&{}:{}&1.021448950881&,\\B^{\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.000779726239&{}:{}&0.025207568343&{}:{}&0.975572157896&,\\C^{\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.015434087312&{}:{}&0.093467678127&{}:{}&0.921966409185&,\\[.5em] A^{\prime\prime}_{\mathbf{4a}}&{}\approx{}&1.605764791221&{}:{}&-0.002917899166&{}:{}&-0.602846892056&,\\B^{\prime\prime}_{\mathbf{4a}}&{}\approx{}&1.758529720179&{}:{}&-0.551486858002&{}:{}&-0.207042862176&,\\C^{\prime\prime}_{\mathbf{4a}}&{}\approx{}&2.381177196198&{}:{}&-0.001356955228&{}:{}&-1.379820240970&,\\[.5em] A^{\prime\prime}_{\mathbf{5a}}&{}\approx{}&2.265718474976&{}:{}&-0.002772941545&{}:{}&-1.262945533432&,\\B^{\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.490212596613&{}:{}&-0.314760411920&{}:{}&-0.175452184694&,\\C^{\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.640794968502&{}:{}&-0.000424151453&{}:{}&-0.640370817050&,\\[.5em] A^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.064714214022&{}:{}&-0.048898757974&{}:{}&-0.015815456048&,\\B^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.012753114521&{}:{}&-0.012566450214&{}:{}&-0.000186664307&,\\C^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.024062650191&{}:{}&-0.000583579907&{}:{}&-0.023479070284&,\\[.5em] A^{\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.055951694529&{}:{}&-0.032662938072&{}:{}&-0.023288756457&,\\B^{\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.008614995028&{}:{}&-0.008429093433&{}:{}&-0.000185901595&,\\C^{\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.015950840180&{}:{}&-0.000262626978&{}:{}&-0.015688213202&,\\[.5em] A^{\prime\prime}_{\mathbf{b}}&{}\approx{}&0.473305794955&{}:{}&-0.549392878506&{}:{}&1.076087083552&,\\B^{\prime\prime}_{\mathbf{b}}&{}\approx{}&0.714594158588&{}:{}&-0.224101579146&{}:{}&0.509507420557&,\\C^{\prime\prime}_{\mathbf{b}}&{}\approx{}&0.822741495422&{}:{}&-0.299495333936&{}:{}&0.476753838514&,\\[.5em] A^{\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.571596675585&{}:{}&-0.446866005564&{}:{}&0.875269329979&,\\B^{\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.899107374019&{}:{}&-0.189908076237&{}:{}&0.290800702217&,\\C^{\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.816224391515&{}:{}&-0.134781121956&{}:{}&0.318556730441&,\\[.5em] A^{\prime\prime}_{\mathbf{2b}}&{}\approx{}&-0.551486858002&{}:{}&1.758529720179&{}:{}&-0.207042862176&,\\B^{\prime\prime}_{\mathbf{2b}}&{}\approx{}&-0.002917899166&{}:{}&1.605764791221&{}:{}&-0.602846892056&,\\C^{\prime\prime}_{\mathbf{2b}}&{}\approx{}&-0.001356955228&{}:{}&2.381177196198&{}:{}&-1.379820240970&,\\[.5em] A^{\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.314760411920&{}:{}&1.490212596613&{}:{}&-0.175452184694&,\\B^{\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.002772941545&{}:{}&2.265718474976&{}:{}&-1.262945533432&,\\C^{\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.000424151453&{}:{}&1.640794968502&{}:{}&-0.640370817050&,\\[.5em] A^{\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.017118526271&{}:{}&-0.000786196579&{}:{}&0.983667670309&,\\B^{\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.002229519123&{}:{}&-0.017671486540&{}:{}&1.015441967417&,\\C^{\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.065438256692&{}:{}&-0.023820911731&{}:{}&0.958382655039&,\\[.5em] A^{\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.025207568343&{}:{}&-0.000779726239&{}:{}&0.975572157896&,\\B^{\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.004944016600&{}:{}&-0.026392967481&{}:{}&1.021448950881&,\\C^{\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.093467678127&{}:{}&-0.015434087312&{}:{}&0.921966409185&,\\[.5em] A^{\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.012566450214&{}:{}&1.012753114521&{}:{}&-0.000186664307&,\\B^{\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.048898757974&{}:{}&1.064714214022&{}:{}&-0.015815456048&,\\C^{\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.000583579907&{}:{}&1.024062650191&{}:{}&-0.023479070284&,\\[.5em] A^{\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.008429093433&{}:{}&1.008614995028&{}:{}&-0.000185901595&,\\B^{\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.032662938072&{}:{}&1.055951694529&{}:{}&-0.023288756457&,\\C^{\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.000262626978&{}:{}&1.015950840180&{}:{}&-0.015688213202&,\\[.5em] A^{\prime\prime}_{\mathbf{c}}&{}\approx{}&2.109511742531&{}:{}&2.916786936777&{}:{}&-4.026298679308&,\\B^{\prime\prime}_{\mathbf{c}}&{}\approx{}&2.916786936777&{}:{}&2.109511742531&{}:{}&-4.026298679308&,\\C^{\prime\prime}_{\mathbf{c}}&{}\approx{}&1.506834873031&{}:{}&1.506834873031&{}:{}&-2.013669746063&,\\[.5em] A^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-3.106322389017&{}:{}&-1.917584275156&{}:{}&6.023906664173&,\\B^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-1.917584275156&{}:{}&-3.106322389017&{}:{}&6.023906664173&,\\C^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-1.006834873031&{}:{}&-1.006834873031&{}:{}&3.013669746063&,\\[.5em] A^{\prime\prime}_{\mathbf{2c}}&{}\approx{}&1.548560540122&{}:{}&1.442106609715&{}:{}&-1.990667149838&,\\B^{\prime\prime}_{\mathbf{2c}}&{}\approx{}&1.161529878283&{}:{}&0.565788409543&{}:{}&-0.727318287826&,\\C^{\prime\prime}_{\mathbf{2c}}&{}\approx{}&1.806470076964&{}:{}&0.819452174001&{}:{}&-1.625922250965&,\\[.5em] A^{\prime\prime}_{\mathbf{3c}}&{}\approx{}&-1.038715091156&{}:{}&-0.952046047524&{}:{}&2.990761138679&,\\B^{\prime\prime}_{\mathbf{3c}}&{}\approx{}&-0.284090212417&{}:{}&-0.683285050440&{}:{}&1.967375262857&,\\C^{\prime\prime}_{\mathbf{3c}}&{}\approx{}&-0.806654402114&{}:{}&-1.778257580008&{}:{}&3.584911982122&,\\[.5em] A^{\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.565788409543&{}:{}&1.161529878283&{}:{}&-0.727318287826&,\\B^{\prime\prime}_{\mathbf{4c}}&{}\approx{}&1.442106609715&{}:{}&1.548560540122&{}:{}&-1.990667149838&,\\C^{\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.819452174001&{}:{}&1.806470076964&{}:{}&-1.625922250965&,\\[.5em] A^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.683285050440&{}:{}&-0.284090212417&{}:{}&1.967375262857&,\\B^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.952046047524&{}:{}&-1.038715091156&{}:{}&2.990761138679&,\\C^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-1.778257580008&{}:{}&-0.806654402114&{}:{}&3.584911982122&,\\[.5em] A^{\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.659245831340&{}:{}&0.911528288850&{}:{}&-0.570774120189&,\\B^{\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.911528288850&{}:{}&0.659245831340&{}:{}&-0.570774120189&,\\C^{\prime\prime}_{\mathbf{6c}}&{}\approx{}&1.506834873031&{}:{}&1.506834873031&{}:{}&-2.013669746063&,\\[.5em] A^{\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.376263706774&{}:{}&-0.232273819991&{}:{}&1.608537526765&,\\B^{\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.232273819991&{}:{}&-0.376263706774&{}:{}&1.608537526765&,\\C^{\prime\prime}_{\mathbf{7c}}&{}\approx{}&-1.006834873031&{}:{}&-1.006834873031&{}:{}&3.013669746063&. \end{alignedat} \] \[ \begin{alignedat}{4} A^{\prime\prime\prime}&{}\approx{}&0.087688292400&{}:{}&0.154802005828&{}:{}&0.757509701772&,\\B^{\prime\prime\prime}&{}\approx{}&0.154802005828&{}:{}&0.087688292400&{}:{}&0.757509701772&,\\C^{\prime\prime\prime}&{}\approx{}&0.328227057688&{}:{}&0.328227057688&{}:{}&0.343545884624&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1}}&{}\approx{}&0.043716483905&{}:{}&0.010257335682&{}:{}&0.946026180414&,\\B^{\prime\prime\prime}_{\mathbf{1}}&{}\approx{}&0.010257335682&{}:{}&0.043716483905&{}:{}&0.946026180414&,\\C^{\prime\prime\prime}_{\mathbf{1}}&{}\approx{}&0.101264812114&{}:{}&0.101264812114&{}:{}&0.797470375771&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2}}&{}\approx{}&0.003529490951&{}:{}&1.002633123515&{}:{}&-0.006162614466&,\\B^{\prime\prime\prime}_{\mathbf{2}}&{}\approx{}&0.566059285041&{}:{}&-0.581662735530&{}:{}&1.015603450489&,\\C^{\prime\prime\prime}_{\mathbf{2}}&{}\approx{}&-0.003415275003&{}:{}&0.996930717527&{}:{}&0.006484557476&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3}}&{}\approx{}&0.007958327031&{}:{}&1.004933481561&{}:{}&-0.012891808592&,\\B^{\prime\prime\prime}_{\mathbf{3}}&{}\approx{}&0.614466172935&{}:{}&-0.621914613235&{}:{}&1.007448440299&,\\C^{\prime\prime\prime}_{\mathbf{3}}&{}\approx{}&-0.007771499506&{}:{}&0.993237573411&{}:{}&0.014533926094&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4}}&{}\approx{}&-0.581662735530&{}:{}&0.566059285041&{}:{}&1.015603450489&,\\B^{\prime\prime\prime}_{\mathbf{4}}&{}\approx{}&1.002633123515&{}:{}&0.003529490951&{}:{}&-0.006162614466&,\\C^{\prime\prime\prime}_{\mathbf{4}}&{}\approx{}&0.996930717527&{}:{}&-0.003415275003&{}:{}&0.006484557476&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5}}&{}\approx{}&-0.621914613235&{}:{}&0.614466172935&{}:{}&1.007448440299&,\\B^{\prime\prime\prime}_{\mathbf{5}}&{}\approx{}&1.004933481561&{}:{}&0.007958327031&{}:{}&-0.012891808592&,\\C^{\prime\prime\prime}_{\mathbf{5}}&{}\approx{}&0.993237573411&{}:{}&-0.007771499506&{}:{}&0.014533926094&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&1.088619529491&{}:{}&1.921812845662&{}:{}&-2.010432375154&,\\B^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&1.921812845662&{}:{}&1.088619529491&{}:{}&-2.010432375154&,\\C^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&0.328227057688&{}:{}&0.328227057688&{}:{}&0.343545884624&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&-1.636887027219&{}:{}&-0.384067935279&{}:{}&3.020954962498&,\\B^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&-0.384067935279&{}:{}&-1.636887027219&{}:{}&3.020954962498&,\\C^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&0.101264812114&{}:{}&0.101264812114&{}:{}&0.797470375771&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.141307498512&{}:{}&0.759868775088&{}:{}&0.381438723424&,\\B^{\prime\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.555762389735&{}:{}&0.420549938664&{}:{}&1.135212451070&,\\C^{\prime\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.223846518284&{}:{}&0.910861099008&{}:{}&0.312985419276&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.115158922691&{}:{}&0.975265862056&{}:{}&0.139893060636&,\\B^{\prime\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.341307585682&{}:{}&0.605615900531&{}:{}&0.735691685151&,\\C^{\prime\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.057784039153&{}:{}&0.868329695847&{}:{}&0.189454343306&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.008982392730&{}:{}&-0.006715869615&{}:{}&1.015698262346&,\\B^{\prime\prime\prime}_{\mathbf{2a}}&{}\approx{}&0.007897976659&{}:{}&0.008696807106&{}:{}&0.983405216235&,\\C^{\prime\prime\prime}_{\mathbf{2a}}&{}\approx{}&0.452211298296&{}:{}&-0.372302212368&{}:{}&0.920090914073&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.013526308191&{}:{}&-0.008458724011&{}:{}&1.021985032202&,\\B^{\prime\prime\prime}_{\mathbf{3a}}&{}\approx{}&0.012105991418&{}:{}&0.012904309493&{}:{}&0.974989699089&,\\C^{\prime\prime\prime}_{\mathbf{3a}}&{}\approx{}&0.434213232761&{}:{}&-0.289442992798&{}:{}&0.855229760037&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4a}}&{}\approx{}&0.323282325216&{}:{}&0.322107426834&{}:{}&0.354610247950&,\\B^{\prime\prime\prime}_{\mathbf{4a}}&{}\approx{}&0.982298113268&{}:{}&-0.182671131818&{}:{}&0.200373018550&,\\C^{\prime\prime\prime}_{\mathbf{4a}}&{}\approx{}&1.188110838086&{}:{}&0.220141714592&{}:{}&-0.408252552678&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5a}}&{}\approx{}&0.366235803298&{}:{}&0.365339354347&{}:{}&0.268424842355&,\\B^{\prime\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.032562492694&{}:{}&-0.121924481207&{}:{}&0.089361988513&,\\C^{\prime\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.111595283972&{}:{}&0.130935353359&{}:{}&-0.242530637331&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6a}}&{}\approx{}&0.268370108047&{}:{}&0.243719427540&{}:{}&0.487910464413&,\\B^{\prime\prime\prime}_{\mathbf{6a}}&{}\approx{}&0.994918993176&{}:{}&-0.006211114771&{}:{}&0.011292121596&,\\C^{\prime\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.005900455804&{}:{}&0.005702861783&{}:{}&-0.011603317587&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7a}}&{}\approx{}&0.267252119926&{}:{}&0.250718713165&{}:{}&0.482029166909&,\\B^{\prime\prime\prime}_{\mathbf{7a}}&{}\approx{}&0.996639153889&{}:{}&-0.004181979688&{}:{}&0.007542825799&,\\C^{\prime\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.003831479147&{}:{}&0.003951576337&{}:{}&-0.007783055484&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{b}}&{}\approx{}&0.420549938664&{}:{}&-0.555762389735&{}:{}&1.135212451070&,\\B^{\prime\prime\prime}_{\mathbf{b}}&{}\approx{}&0.759868775088&{}:{}&-0.141307498512&{}:{}&0.381438723424&,\\C^{\prime\prime\prime}_{\mathbf{b}}&{}\approx{}&0.910861099008&{}:{}&-0.223846518284&{}:{}&0.312985419276&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.605615900531&{}:{}&-0.341307585682&{}:{}&0.735691685151&,\\B^{\prime\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.975265862056&{}:{}&-0.115158922691&{}:{}&0.139893060636&,\\C^{\prime\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.868329695847&{}:{}&-0.057784039153&{}:{}&0.189454343306&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2b}}&{}\approx{}&-0.182671131818&{}:{}&0.982298113268&{}:{}&0.200373018550&,\\B^{\prime\prime\prime}_{\mathbf{2b}}&{}\approx{}&0.322107426834&{}:{}&0.323282325216&{}:{}&0.354610247950&,\\C^{\prime\prime\prime}_{\mathbf{2b}}&{}\approx{}&0.220141714592&{}:{}&1.188110838086&{}:{}&-0.408252552678&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.121924481207&{}:{}&1.032562492694&{}:{}&0.089361988513&,\\B^{\prime\prime\prime}_{\mathbf{3b}}&{}\approx{}&0.365339354347&{}:{}&0.366235803298&{}:{}&0.268424842355&,\\C^{\prime\prime\prime}_{\mathbf{3b}}&{}\approx{}&0.130935353359&{}:{}&1.111595283972&{}:{}&-0.242530637331&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.008696807106&{}:{}&0.007897976659&{}:{}&0.983405216235&,\\B^{\prime\prime\prime}_{\mathbf{4b}}&{}\approx{}&-0.006715869615&{}:{}&-0.008982392730&{}:{}&1.015698262346&,\\C^{\prime\prime\prime}_{\mathbf{4b}}&{}\approx{}&-0.372302212368&{}:{}&0.452211298296&{}:{}&0.920090914073&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.012904309493&{}:{}&0.012105991418&{}:{}&0.974989699089&,\\B^{\prime\prime\prime}_{\mathbf{5b}}&{}\approx{}&-0.008458724011&{}:{}&-0.013526308191&{}:{}&1.021985032202&,\\C^{\prime\prime\prime}_{\mathbf{5b}}&{}\approx{}&-0.289442992798&{}:{}&0.434213232761&{}:{}&0.855229760037&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.006211114771&{}:{}&0.994918993176&{}:{}&0.011292121596&,\\B^{\prime\prime\prime}_{\mathbf{6b}}&{}\approx{}&0.243719427540&{}:{}&0.268370108047&{}:{}&0.487910464413&,\\C^{\prime\prime\prime}_{\mathbf{6b}}&{}\approx{}&0.005702861783&{}:{}&1.005900455804&{}:{}&-0.011603317587&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.004181979688&{}:{}&0.996639153889&{}:{}&0.007542825799&,\\B^{\prime\prime\prime}_{\mathbf{7b}}&{}\approx{}&0.250718713165&{}:{}&0.267252119926&{}:{}&0.482029166909&,\\C^{\prime\prime\prime}_{\mathbf{7b}}&{}\approx{}&0.003951576337&{}:{}&1.003831479147&{}:{}&-0.007783055484&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{c}}&{}\approx{}&1.256524894379&{}:{}&2.218227413245&{}:{}&-2.474752307623&,\\B^{\prime\prime\prime}_{\mathbf{c}}&{}\approx{}&2.218227413245&{}:{}&1.256524894379&{}:{}&-2.474752307623&,\\C^{\prime\prime\prime}_{\mathbf{c}}&{}\approx{}&1.048956292708&{}:{}&1.048956292708&{}:{}&-1.097912585416&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1c}}&{}\approx{}&-1.256140786156&{}:{}&-0.294732250996&{}:{}&2.550873037152&,\\B^{\prime\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.294732250996&{}:{}&-1.256140786156&{}:{}&2.550873037152&,\\C^{\prime\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.170209910570&{}:{}&-0.170209910570&{}:{}&1.340419821139&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2c}}&{}\approx{}&0.877746531603&{}:{}&0.757067273970&{}:{}&-0.634813805573&,\\B^{\prime\prime\prime}_{\mathbf{2c}}&{}\approx{}&0.918179918055&{}:{}&0.295626259650&{}:{}&-0.213806177705&,\\C^{\prime\prime\prime}_{\mathbf{2c}}&{}\approx{}&1.464600020884&{}:{}&0.406723818145&{}:{}&-0.871323839029&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3c}}&{}\approx{}&-0.481302194728&{}:{}&-0.400983729597&{}:{}&1.882285924325&,\\B^{\prime\prime\prime}_{\mathbf{3c}}&{}\approx{}&0.054706898814&{}:{}&-0.324751554676&{}:{}&1.270044655861&,\\C^{\prime\prime\prime}_{\mathbf{3c}}&{}\approx{}&0.142387394064&{}:{}&-0.704189577613&{}:{}&1.561802183549&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.295626259650&{}:{}&0.918179918055&{}:{}&-0.213806177705&,\\B^{\prime\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.757067273970&{}:{}&0.877746531603&{}:{}&-0.634813805573&,\\C^{\prime\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.406723818145&{}:{}&1.464600020884&{}:{}&-0.871323839029&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.324751554676&{}:{}&0.054706898814&{}:{}&1.270044655861&,\\B^{\prime\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.400983729597&{}:{}&-0.481302194728&{}:{}&1.882285924325&,\\C^{\prime\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.704189577613&{}:{}&0.142387394064&{}:{}&1.561802183549&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.347038012205&{}:{}&0.612649407548&{}:{}&0.040312580247&,\\B^{\prime\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.612649407548&{}:{}&0.347038012205&{}:{}&0.040312580247&,\\C^{\prime\prime\prime}_{\mathbf{6c}}&{}\approx{}&1.048956292708&{}:{}&1.048956292708&{}:{}&-1.097912585416&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.182893532196&{}:{}&-0.042912882880&{}:{}&1.225806415076&,\\B^{\prime\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.042912882880&{}:{}&-0.182893532196&{}:{}&1.225806415076&,\\C^{\prime\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.170209910570&{}:{}&-0.170209910570&{}:{}&1.340419821139&. \end{alignedat} \] \[ \begin{alignedat}{4} A^*&{}\approx{}&0.000000000000&{}:{}&0.128466482391&{}:{}&0.871533517609&,\\B^*&{}\approx{}&0.128466482391&{}:{}&0.000000000000&{}:{}&0.871533517609&,\\C^*&{}\approx{}&0.500000000000&{}:{}&0.500000000000&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1}}&{}\approx{}&0.000000000000&{}:{}&-0.070445884989&{}:{}&1.070445884989&,\\B^*_{\mathbf{1}}&{}\approx{}&-0.070445884989&{}:{}&0.000000000000&{}:{}&1.070445884989&,\\C^*_{\mathbf{1}}&{}\approx{}&0.500000000000&{}:{}&0.500000000000&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2}}&{}\approx{}&0.000000000000&{}:{}&1.070445884989&{}:{}&-0.070445884989&,\\B^*_{\mathbf{2}}&{}\approx{}&0.128466482391&{}:{}&0.000000000000&{}:{}&0.871533517609&,\\C^*_{\mathbf{2}}&{}\approx{}&-0.009795579104&{}:{}&1.009795579104&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3}}&{}\approx{}&0.000000000000&{}:{}&0.871533517609&{}:{}&0.128466482391&,\\B^*_{\mathbf{3}}&{}\approx{}&-0.070445884989&{}:{}&0.000000000000&{}:{}&1.070445884989&,\\C^*_{\mathbf{3}}&{}\approx{}&-0.009795579104&{}:{}&1.009795579104&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4}}&{}\approx{}&0.000000000000&{}:{}&0.128466482391&{}:{}&0.871533517609&,\\B^*_{\mathbf{4}}&{}\approx{}&1.070445884989&{}:{}&0.000000000000&{}:{}&-0.070445884989&,\\C^*_{\mathbf{4}}&{}\approx{}&1.009795579104&{}:{}&-0.009795579104&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5}}&{}\approx{}&0.000000000000&{}:{}&-0.070445884989&{}:{}&1.070445884989&,\\B^*_{\mathbf{5}}&{}\approx{}&0.871533517609&{}:{}&0.000000000000&{}:{}&0.128466482391&,\\C^*_{\mathbf{5}}&{}\approx{}&1.009795579104&{}:{}&-0.009795579104&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6}}&{}\approx{}&0.000000000000&{}:{}&1.070445884989&{}:{}&-0.070445884989&,\\B^*_{\mathbf{6}}&{}\approx{}&1.070445884989&{}:{}&0.000000000000&{}:{}&-0.070445884989&,\\C^*_{\mathbf{6}}&{}\approx{}&0.500000000000&{}:{}&0.500000000000&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7}}&{}\approx{}&0.000000000000&{}:{}&0.871533517609&{}:{}&0.128466482391&,\\B^*_{\mathbf{7}}&{}\approx{}&0.871533517609&{}:{}&0.000000000000&{}:{}&0.128466482391&,\\C^*_{\mathbf{7}}&{}\approx{}&0.500000000000&{}:{}&0.500000000000&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{a}}&{}\approx{}&0.000000000000&{}:{}&0.804909677984&{}:{}&0.195090322016&,\\B^*_{\mathbf{a}}&{}\approx{}&-0.980785280403&{}:{}&0.000000000000&{}:{}&1.980785280403&,\\C^*_{\mathbf{a}}&{}\approx{}&-0.136379290286&{}:{}&1.136379290286&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1a}}&{}\approx{}&0.000000000000&{}:{}&1.195090322016&{}:{}&-0.195090322016&,\\B^*_{\mathbf{1a}}&{}\approx{}&-0.980785280403&{}:{}&0.000000000000&{}:{}&1.980785280403&,\\C^*_{\mathbf{1a}}&{}\approx{}&0.074784952616&{}:{}&0.925215047384&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2a}}&{}\approx{}&0.000000000000&{}:{}&-0.195090322016&{}:{}&1.195090322016&,\\B^*_{\mathbf{2a}}&{}\approx{}&0.019214719597&{}:{}&0.000000000000&{}:{}&0.980785280403&,\\C^*_{\mathbf{2a}}&{}\approx{}&-0.136379290286&{}:{}&1.136379290286&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3a}}&{}\approx{}&0.000000000000&{}:{}&0.195090322016&{}:{}&0.804909677984&,\\B^*_{\mathbf{3a}}&{}\approx{}&0.019214719597&{}:{}&0.000000000000&{}:{}&0.980785280403&,\\C^*_{\mathbf{3a}}&{}\approx{}&0.074784952616&{}:{}&0.925215047384&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4a}}&{}\approx{}&0.000000000000&{}:{}&0.195090322016&{}:{}&0.804909677984&,\\B^*_{\mathbf{4a}}&{}\approx{}&1.980785280403&{}:{}&0.000000000000&{}:{}&-0.980785280403&,\\C^*_{\mathbf{4a}}&{}\approx{}&1.136379290286&{}:{}&-0.136379290286&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5a}}&{}\approx{}&0.000000000000&{}:{}&-0.195090322016&{}:{}&1.195090322016&,\\B^*_{\mathbf{5a}}&{}\approx{}&1.980785280403&{}:{}&0.000000000000&{}:{}&-0.980785280403&,\\C^*_{\mathbf{5a}}&{}\approx{}&0.925215047384&{}:{}&0.074784952616&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6a}}&{}\approx{}&0.000000000000&{}:{}&1.195090322016&{}:{}&-0.195090322016&,\\B^*_{\mathbf{6a}}&{}\approx{}&0.980785280403&{}:{}&0.000000000000&{}:{}&0.019214719597&,\\C^*_{\mathbf{6a}}&{}\approx{}&1.136379290286&{}:{}&-0.136379290286&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7a}}&{}\approx{}&0.000000000000&{}:{}&0.804909677984&{}:{}&0.195090322016&,\\B^*_{\mathbf{7a}}&{}\approx{}&0.980785280403&{}:{}&0.000000000000&{}:{}&0.019214719597&,\\C^*_{\mathbf{7a}}&{}\approx{}&0.925215047384&{}:{}&0.074784952616&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{b}}&{}\approx{}&0.000000000000&{}:{}&-0.980785280403&{}:{}&1.980785280403&,\\B^*_{\mathbf{b}}&{}\approx{}&0.804909677984&{}:{}&0.000000000000&{}:{}&0.195090322016&,\\C^*_{\mathbf{b}}&{}\approx{}&1.136379290286&{}:{}&-0.136379290286&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1b}}&{}\approx{}&0.000000000000&{}:{}&-0.980785280403&{}:{}&1.980785280403&,\\B^*_{\mathbf{1b}}&{}\approx{}&1.195090322016&{}:{}&0.000000000000&{}:{}&-0.195090322016&,\\C^*_{\mathbf{1b}}&{}\approx{}&0.925215047384&{}:{}&0.074784952616&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2b}}&{}\approx{}&0.000000000000&{}:{}&1.980785280403&{}:{}&-0.980785280403&,\\B^*_{\mathbf{2b}}&{}\approx{}&0.195090322016&{}:{}&0.000000000000&{}:{}&0.804909677984&,\\C^*_{\mathbf{2b}}&{}\approx{}&-0.136379290286&{}:{}&1.136379290286&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3b}}&{}\approx{}&0.000000000000&{}:{}&1.980785280403&{}:{}&-0.980785280403&,\\B^*_{\mathbf{3b}}&{}\approx{}&-0.195090322016&{}:{}&0.000000000000&{}:{}&1.195090322016&,\\C^*_{\mathbf{3b}}&{}\approx{}&0.074784952616&{}:{}&0.925215047384&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4b}}&{}\approx{}&0.000000000000&{}:{}&0.019214719597&{}:{}&0.980785280403&,\\B^*_{\mathbf{4b}}&{}\approx{}&-0.195090322016&{}:{}&0.000000000000&{}:{}&1.195090322016&,\\C^*_{\mathbf{4b}}&{}\approx{}&1.136379290286&{}:{}&-0.136379290286&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5b}}&{}\approx{}&0.000000000000&{}:{}&0.019214719597&{}:{}&0.980785280403&,\\B^*_{\mathbf{5b}}&{}\approx{}&0.195090322016&{}:{}&0.000000000000&{}:{}&0.804909677984&,\\C^*_{\mathbf{5b}}&{}\approx{}&0.925215047384&{}:{}&0.074784952616&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6b}}&{}\approx{}&0.000000000000&{}:{}&0.980785280403&{}:{}&0.019214719597&,\\B^*_{\mathbf{6b}}&{}\approx{}&1.195090322016&{}:{}&0.000000000000&{}:{}&-0.195090322016&,\\C^*_{\mathbf{6b}}&{}\approx{}&-0.136379290286&{}:{}&1.136379290286&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7b}}&{}\approx{}&0.000000000000&{}:{}&0.980785280403&{}:{}&0.019214719597&,\\B^*_{\mathbf{7b}}&{}\approx{}&0.804909677984&{}:{}&0.000000000000&{}:{}&0.195090322016&,\\C^*_{\mathbf{7b}}&{}\approx{}&0.074784952616&{}:{}&0.925215047384&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{c}}&{}\approx{}&0.000000000000&{}:{}&5.381494871788&{}:{}&-4.381494871788&,\\B^*_{\mathbf{c}}&{}\approx{}&5.381494871788&{}:{}&0.000000000000&{}:{}&-4.381494871788&,\\C^*_{\mathbf{c}}&{}\approx{}&0.500000000000&{}:{}&0.500000000000&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1c}}&{}\approx{}&0.000000000000&{}:{}&-4.381494871788&{}:{}&5.381494871788&,\\B^*_{\mathbf{1c}}&{}\approx{}&-4.381494871788&{}:{}&0.000000000000&{}:{}&5.381494871788&,\\C^*_{\mathbf{1c}}&{}\approx{}&0.500000000000&{}:{}&0.500000000000&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2c}}&{}\approx{}&0.000000000000&{}:{}&5.381494871788&{}:{}&-4.381494871788&,\\B^*_{\mathbf{2c}}&{}\approx{}&0.645844620338&{}:{}&0.000000000000&{}:{}&0.354155379662&,\\C^*_{\mathbf{2c}}&{}\approx{}&3.062915447742&{}:{}&-2.062915447742&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3c}}&{}\approx{}&0.000000000000&{}:{}&-4.381494871788&{}:{}&5.381494871788&,\\B^*_{\mathbf{3c}}&{}\approx{}&0.354155379662&{}:{}&0.000000000000&{}:{}&0.645844620338&,\\C^*_{\mathbf{3c}}&{}\approx{}&-2.062915447742&{}:{}&3.062915447742&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4c}}&{}\approx{}&0.000000000000&{}:{}&0.645844620338&{}:{}&0.354155379662&,\\B^*_{\mathbf{4c}}&{}\approx{}&5.381494871788&{}:{}&0.000000000000&{}:{}&-4.381494871788&,\\C^*_{\mathbf{4c}}&{}\approx{}&-2.062915447742&{}:{}&3.062915447742&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5c}}&{}\approx{}&0.000000000000&{}:{}&0.354155379662&{}:{}&0.645844620338&,\\B^*_{\mathbf{5c}}&{}\approx{}&-4.381494871788&{}:{}&0.000000000000&{}:{}&5.381494871788&,\\C^*_{\mathbf{5c}}&{}\approx{}&3.062915447742&{}:{}&-2.062915447742&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6c}}&{}\approx{}&0.000000000000&{}:{}&0.645844620338&{}:{}&0.354155379662&,\\B^*_{\mathbf{6c}}&{}\approx{}&0.645844620338&{}:{}&0.000000000000&{}:{}&0.354155379662&,\\C^*_{\mathbf{6c}}&{}\approx{}&0.500000000000&{}:{}&0.500000000000&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7c}}&{}\approx{}&0.000000000000&{}:{}&0.354155379662&{}:{}&0.645844620338&,\\B^*_{\mathbf{7c}}&{}\approx{}&0.354155379662&{}:{}&0.000000000000&{}:{}&0.645844620338&,\\C^*_{\mathbf{7c}}&{}\approx{}&0.500000000000&{}:{}&0.500000000000&{}:{}&0.000000000000&. \end{alignedat} \]