Derousseau's Generalization of the Malfatti circles

Pythagorean Triangle U

\(C=90\degree\).   \(a:b:c=5:12:13\).


[Top] > Pythagorean Triangle U

Reference Triangle

reference triangle

Triangle Centers and their Extraversions

Approximately,
\[ \begin{alignedat}{4} I&{}\approx{}&0.166666666667&{}:{}&0.400000000000&{}:{}&0.433333333333&,\\ I_{\mathbf{a}}&{}\approx{}&-0.250000000000&{}:{}&0.600000000000&{}:{}&0.650000000000&,\\ I_{\mathbf{b}}&{}\approx{}&0.833333333333&{}:{}&-2.000000000000&{}:{}&2.166666666667&,\\ I_{\mathbf{c}}&{}\approx{}&1.250000000000&{}:{}&3.000000000000&{}:{}&-3.250000000000&. \end{alignedat} \] \[ \begin{alignedat}{4} P&{}\approx{}&0.136898592336&{}:{}&0.383990531012&{}:{}&0.479110876652&,\\ P_{\mathbf{1}}&{}\approx{}&0.008150396943&{}:{}&0.022861266845&{}:{}&0.968988336212&,\\ P_{\mathbf{2}}&{}\approx{}&0.002956284236&{}:{}&0.986697459400&{}:{}&0.010346256364&,\\ P_{\mathbf{3}}&{}\approx{}&0.002204336719&{}:{}&0.735725412682&{}:{}&0.262070250599&,\\ P_{\mathbf{4}}&{}\approx{}&0.999394264747&{}:{}&0.000269489308&{}:{}&0.000336245945&,\\ P_{\mathbf{5}}&{}\approx{}&0.988436245040&{}:{}&0.000266534449&{}:{}&0.011297220510&,\\ P_{\mathbf{6}}&{}\approx{}&0.968595378743&{}:{}&0.031078737590&{}:{}&0.000325883667&,\\ P_{\mathbf{7}}&{}\approx{}&0.958298871449&{}:{}&0.030748359751&{}:{}&0.010952768800&,\\ P_{\mathbf{a}}&{}\approx{}&-0.156379250510&{}:{}&0.609090936413&{}:{}&0.547288314097&,\\ P_{\mathbf{1a}}&{}\approx{}&-0.020008952338&{}:{}&0.949982617282&{}:{}&0.070026335057&,\\ P_{\mathbf{2a}}&{}\approx{}&-0.008211296765&{}:{}&0.031982673018&{}:{}&0.976228623747&,\\ P_{\mathbf{3a}}&{}\approx{}&-0.006047179017&{}:{}&0.287107233441&{}:{}&0.718939945576&,\\ P_{\mathbf{4a}}&{}\approx{}&1.016253645879&{}:{}&-0.004638489525&{}:{}&-0.011615156354&,\\ P_{\mathbf{5a}}&{}\approx{}&1.011944825222&{}:{}&-0.000378916047&{}:{}&-0.011565909174&,\\ P_{\mathbf{6a}}&{}\approx{}&1.004924888365&{}:{}&-0.004586781644&{}:{}&-0.000338106721&,\\ P_{\mathbf{7a}}&{}\approx{}&1.000711398859&{}:{}&-0.000374709765&{}:{}&-0.000336689094&,\\ P_{\mathbf{b}}&{}\approx{}&0.797818964807&{}:{}&-0.816182936917&{}:{}&1.018363972109&,\\ P_{\mathbf{1b}}&{}\approx{}&0.897290830879&{}:{}&-0.414625789317&{}:{}&0.517334958438&,\\ P_{\mathbf{2b}}&{}\approx{}&-0.029070964164&{}:{}&1.598449083631&{}:{}&-0.569378119468&,\\ P_{\mathbf{3b}}&{}\approx{}&-0.012925023376&{}:{}&1.573369701203&{}:{}&-0.560444677827&,\\ P_{\mathbf{4b}}&{}\approx{}&0.023074334733&{}:{}&-0.023605453268&{}:{}&1.000531118535&,\\ P_{\mathbf{5b}}&{}\approx{}&0.049692614584&{}:{}&-0.022962275815&{}:{}&0.973269661231&,\\ P_{\mathbf{6b}}&{}\approx{}&-0.018723845326&{}:{}&1.029519118620&{}:{}&-0.010795273294&,\\ P_{\mathbf{7b}}&{}\approx{}&-0.008371417971&{}:{}&1.019056988049&{}:{}&-0.010685570077&,\\ P_{\mathbf{c}}&{}\approx{}&0.874017676303&{}:{}&1.241608990642&{}:{}&-1.115626666945&,\\ P_{\mathbf{1c}}&{}\approx{}&-0.092900105345&{}:{}&-0.726622872365&{}:{}&1.819522977710&,\\ P_{\mathbf{2c}}&{}\approx{}&0.938872591365&{}:{}&0.602436420515&{}:{}&-0.541309011880&,\\ P_{\mathbf{3c}}&{}\approx{}&-0.039928131880&{}:{}&-0.691404056550&{}:{}&1.731332188429&,\\ P_{\mathbf{4c}}&{}\approx{}&0.058686208501&{}:{}&1.016222916292&{}:{}&-0.074909124793&,\\ P_{\mathbf{5c}}&{}\approx{}&-0.055728494635&{}:{}&-0.035758712244&{}:{}&1.091487206880&,\\ P_{\mathbf{6c}}&{}\approx{}&0.121285650836&{}:{}&0.948641852015&{}:{}&-0.069927502851&,\\ P_{\mathbf{7c}}&{}\approx{}&-0.024425610155&{}:{}&-0.034698448318&{}:{}&1.059124058474&. \end{alignedat} \] \[ \begin{alignedat}{4} P^-&{}\approx{}&0.126434937858&{}:{}&0.378363107821&{}:{}&0.495201954321&,\\ P^-_{\mathbf{1}}&{}\approx{}&-0.007574850487&{}:{}&-0.014551926795&{}:{}&1.022126777282&,\\ P^-_{\mathbf{2}}&{}\approx{}&-0.007728204711&{}:{}&1.024988021230&{}:{}&-0.017259816519&,\\ P^-_{\mathbf{3}}&{}\approx{}&-0.057475331931&{}:{}&0.857552589716&{}:{}&0.199922742215&,\\ P^-_{\mathbf{4}}&{}\approx{}&1.015190670300&{}:{}&-0.007313188717&{}:{}&-0.007877481583&,\\ P^-_{\mathbf{5}}&{}\approx{}&1.087225286554&{}:{}&-0.047787429778&{}:{}&-0.039437856776&,\\ P^-_{\mathbf{6}}&{}\approx{}&1.165102327170&{}:{}&-0.059322803588&{}:{}&-0.105779523583&,\\ P^-_{\mathbf{7}}&{}\approx{}&-5.700464752738&{}:{}&3.136684898725&{}:{}&3.563779854013&,\\ P^-_{\mathbf{a}}&{}\approx{}&-0.127875918644&{}:{}&0.611858720039&{}:{}&0.516017198604&,\\ P^-_{\mathbf{1a}}&{}\approx{}&0.006762042702&{}:{}&0.990720650378&{}:{}&0.002517306919&,\\ P^-_{\mathbf{2a}}&{}\approx{}&0.010388126972&{}:{}&-0.011711655184&{}:{}&1.001323528212&,\\ P^-_{\mathbf{3a}}&{}\approx{}&0.048837113559&{}:{}&0.216712892127&{}:{}&0.734449994314&,\\ P^-_{\mathbf{4a}}&{}\approx{}&0.722078621358&{}:{}&0.135830636120&{}:{}&0.142090742521&,\\ P^-_{\mathbf{5a}}&{}\approx{}&0.911679386795&{}:{}&0.047323054781&{}:{}&0.040997558424&,\\ P^-_{\mathbf{6a}}&{}\approx{}&0.943639397878&{}:{}&0.024938808133&{}:{}&0.031421793988&,\\ P^-_{\mathbf{7a}}&{}\approx{}&0.982660079590&{}:{}&0.008290403207&{}:{}&0.009049517202&,\\ P^-_{\mathbf{b}}&{}\approx{}&0.789860062090&{}:{}&-0.550885108697&{}:{}&0.761025046607&,\\ P^-_{\mathbf{1b}}&{}\approx{}&0.907562864444&{}:{}&-0.160003302040&{}:{}&0.252440437596&,\\ P^-_{\mathbf{2b}}&{}\approx{}&0.162225773979&{}:{}&0.800248548144&{}:{}&0.037525677878&,\\ P^-_{\mathbf{3b}}&{}\approx{}&0.121334904069&{}:{}&1.006450210230&{}:{}&-0.127785114299&,\\ P^-_{\mathbf{4b}}&{}\approx{}&-0.002727154777&{}:{}&0.039329883771&{}:{}&0.963397271006&,\\ P^-_{\mathbf{5b}}&{}\approx{}&0.013052902521&{}:{}&0.069475612134&{}:{}&0.917471485345&,\\ P^-_{\mathbf{6b}}&{}\approx{}&0.007295688553&{}:{}&0.937005755293&{}:{}&0.055698556154&,\\ P^-_{\mathbf{7b}}&{}\approx{}&0.008904333621&{}:{}&0.957091698573&{}:{}&0.034003967806&,\\ P^-_{\mathbf{c}}&{}\approx{}&0.803698348760&{}:{}&0.912740143513&{}:{}&-0.716438492273&,\\ P^-_{\mathbf{1c}}&{}\approx{}&0.157356793669&{}:{}&-0.032145986020&{}:{}&0.874789192351&,\\ P^-_{\mathbf{2c}}&{}\approx{}&0.898939327946&{}:{}&0.294708668716&{}:{}&-0.193647996661&,\\ P^-_{\mathbf{3c}}&{}\approx{}&0.124870308247&{}:{}&-0.219798224130&{}:{}&1.094927915883&,\\ P^-_{\mathbf{4c}}&{}\approx{}&0.012995544980&{}:{}&0.940138771310&{}:{}&0.046865683709&,\\ P^-_{\mathbf{5c}}&{}\approx{}&-0.006290075653&{}:{}&0.079183338695&{}:{}&0.927106736958&,\\ P^-_{\mathbf{6c}}&{}\approx{}&0.060246789953&{}:{}&0.837708058440&{}:{}&0.102045151607&,\\ P^-_{\mathbf{7c}}&{}\approx{}&0.007462751586&{}:{}&0.041235024083&{}:{}&0.951302224331&. \end{alignedat} \] \[ \begin{alignedat}{4} P^+&{}\approx{}&0.143042797667&{}:{}&0.387294925634&{}:{}&0.469662276699&,\\ P^+_{\mathbf{1}}&{}\approx{}&0.021272205742&{}:{}&0.054080411453&{}:{}&0.924647382804&,\\ P^+_{\mathbf{2}}&{}\approx{}&0.012407158546&{}:{}&0.952827866866&{}:{}&0.034764974588&,\\ P^+_{\mathbf{3}}&{}\approx{}&0.036786112845&{}:{}&0.665131854479&{}:{}&0.298082032676&,\\ P^+_{\mathbf{4}}&{}\approx{}&0.984175252544&{}:{}&0.007575003782&{}:{}&0.008249743674&,\\ P^+_{\mathbf{5}}&{}\approx{}&0.908795282426&{}:{}&0.039006296572&{}:{}&0.052198421002&,\\ P^+_{\mathbf{6}}&{}\approx{}&0.836719117164&{}:{}&0.091747418198&{}:{}&0.071533464638&,\\ P^+_{\mathbf{7}}&{}\approx{}&0.537467329224&{}:{}&0.227042467414&{}:{}&0.235490203362&,\\ P^+_{\mathbf{a}}&{}\approx{}&-0.174095171106&{}:{}&0.607370652090&{}:{}&0.566724519016&,\\ P^+_{\mathbf{1a}}&{}\approx{}&-0.041724549383&{}:{}&0.916937498497&{}:{}&0.124787050886&,\\ P^+_{\mathbf{2a}}&{}\approx{}&-0.024330763512&{}:{}&0.069851011329&{}:{}&0.954479752183&,\\ P^+_{\mathbf{3a}}&{}\approx{}&-0.043899505083&{}:{}&0.335656452818&{}:{}&0.708243052266&,\\ P^+_{\mathbf{4a}}&{}\approx{}&1.565742096837&{}:{}&-0.267020254885&{}:{}&-0.298721841952&,\\ P^+_{\mathbf{5a}}&{}\approx{}&1.131153218295&{}:{}&-0.057093127625&{}:{}&-0.074060090670&,\\ P^+_{\mathbf{6a}}&{}\approx{}&1.072844190630&{}:{}&-0.037308351475&{}:{}&-0.035535839155&,\\ P^+_{\mathbf{7a}}&{}\approx{}&1.019299269712&{}:{}&-0.009297381757&{}:{}&-0.010001887955&,\\ P^+_{\mathbf{b}}&{}\approx{}&0.803314657142&{}:{}&-0.999373420905&{}:{}&1.196058763763&,\\ P^+_{\mathbf{1b}}&{}\approx{}&0.889516139794&{}:{}&-0.607344316691&{}:{}&0.717828176896&,\\ P^+_{\mathbf{2b}}&{}\approx{}&-0.372904662315&{}:{}&3.033121962265&{}:{}&-1.660217299950&,\\ P^+_{\mathbf{3b}}&{}\approx{}&-0.209585943868&{}:{}&2.403780614283&{}:{}&-1.194194670415&,\\ P^+_{\mathbf{4b}}&{}\approx{}&0.047330990203&{}:{}&-0.082772610528&{}:{}&1.035441620325&,\\ P^+_{\mathbf{5b}}&{}\approx{}&0.083199086026&{}:{}&-0.107495348767&{}:{}&1.024296262741&,\\ P^+_{\mathbf{6b}}&{}\approx{}&-0.046435881247&{}:{}&1.128050232191&{}:{}&-0.081614350944&,\\ P^+_{\mathbf{7b}}&{}\approx{}&-0.026386686114&{}:{}&1.083674802186&{}:{}&-0.057288116072&,\\ P^+_{\mathbf{c}}&{}\approx{}&0.925194119490&{}:{}&1.480950555180&{}:{}&-1.406144674671&,\\ P^+_{\mathbf{1c}}&{}\approx{}&-0.491850103855&{}:{}&-1.833731423075&{}:{}&3.325581526930&,\\ P^+_{\mathbf{2c}}&{}\approx{}&0.970648871349&{}:{}&0.847306044559&{}:{}&-0.817954915908&,\\ P^+_{\mathbf{3c}}&{}\approx{}&-0.261287317733&{}:{}&-1.324870508220&{}:{}&2.586157825953&,\\ P^+_{\mathbf{4c}}&{}\approx{}&0.101121793394&{}:{}&1.086886700633&{}:{}&-0.188008494026&,\\ P^+_{\mathbf{5c}}&{}\approx{}&-0.109217382054&{}:{}&-0.160117916057&{}:{}&1.269335298110&,\\ P^+_{\mathbf{6c}}&{}\approx{}&0.176367098613&{}:{}&1.048748470474&{}:{}&-0.225115569087&,\\ P^+_{\mathbf{7c}}&{}\approx{}&-0.057993843948&{}:{}&-0.114632079747&{}:{}&1.172625923695&. \end{alignedat} \] \[ \begin{alignedat}{4} Q&{}\approx{}&0.121346147327&{}:{}&0.371044613433&{}:{}&0.507609239240&,\\ Q_{\mathbf{1}}&{}\approx{}&-0.049204237573&{}:{}&-0.150453621409&{}:{}&1.199657858981&,\\ Q_{\mathbf{2}}&{}\approx{}&-0.035496684994&{}:{}&1.183984672971&{}:{}&-0.148487987977&,\\ Q_{\mathbf{3}}&{}\approx{}&-0.017625498021&{}:{}&0.587894884100&{}:{}&0.429730613921&,\\ Q_{\mathbf{4}}&{}\approx{}&1.076421539491&{}:{}&-0.032271867348&{}:{}&-0.044149672143&,\\ Q_{\mathbf{5}}&{}\approx{}&0.827079539377&{}:{}&-0.024796420549&{}:{}&0.197716881172&,\\ Q_{\mathbf{6}}&{}\approx{}&0.777590457810&{}:{}&0.254302590141&{}:{}&-0.031893047950&,\\ Q_{\mathbf{7}}&{}\approx{}&0.638531483916&{}:{}&0.208824849399&{}:{}&0.152643666685&,\\ Q_{\mathbf{a}}&{}\approx{}&-0.116441789457&{}:{}&0.629348219008&{}:{}&0.487093570449&,\\ Q_{\mathbf{1a}}&{}\approx{}&0.063746890279&{}:{}&1.202915967926&{}:{}&-0.266662858205&,\\ Q_{\mathbf{2a}}&{}\approx{}&0.050059173307&{}:{}&-0.270561382752&{}:{}&1.220502209445&,\\ Q_{\mathbf{3a}}&{}\approx{}&0.022598165071&{}:{}&0.426431681468&{}:{}&0.550970153461&,\\ Q_{\mathbf{4a}}&{}\approx{}&1.736333899111&{}:{}&-0.321255896499&{}:{}&-0.415078002612&,\\ Q_{\mathbf{5a}}&{}\approx{}&1.228592719729&{}:{}&0.065107594704&{}:{}&-0.293700314433&,\\ Q_{\mathbf{6a}}&{}\approx{}&1.168230342340&{}:{}&-0.216145573232&{}:{}&0.047915230892&,\\ Q_{\mathbf{7a}}&{}\approx{}&0.914069378891&{}:{}&0.048439859439&{}:{}&0.037490761670&,\\ Q_{\mathbf{b}}&{}\approx{}&0.880334064292&{}:{}&-0.325131054938&{}:{}&0.444796990646&,\\ Q_{\mathbf{1b}}&{}\approx{}&1.100542534547&{}:{}&0.273172980514&{}:{}&-0.373715515061&,\\ Q_{\mathbf{2b}}&{}\approx{}&3.682517731657&{}:{}&-9.970889437661&{}:{}&7.288371706004&,\\ Q_{\mathbf{3b}}&{}\approx{}&0.479876041339&{}:{}&1.933295137058&{}:{}&-1.413171178397&,\\ Q_{\mathbf{4b}}&{}\approx{}&-0.432115884436&{}:{}&0.159592022007&{}:{}&1.272523862429&,\\ Q_{\mathbf{5b}}&{}\approx{}&0.309847094033&{}:{}&0.076909207526&{}:{}&0.613243698441&,\\ Q_{\mathbf{6b}}&{}\approx{}&-0.488471521915&{}:{}&1.322599344626&{}:{}&0.165872177290&,\\ Q_{\mathbf{7b}}&{}\approx{}&0.180701187852&{}:{}&0.727997852861&{}:{}&0.091300959287&,\\ Q_{\mathbf{c}}&{}\approx{}&0.871414193625&{}:{}&0.568875949233&{}:{}&-0.440290142859&,\\ Q_{\mathbf{1c}}&{}\approx{}&1.809509648629&{}:{}&2.771838734689&{}:{}&-3.581348383318&,\\ Q_{\mathbf{2c}}&{}\approx{}&1.110089629930&{}:{}&-0.487047089356&{}:{}&0.376957459426&,\\ Q_{\mathbf{3c}}&{}\approx{}&0.600368860211&{}:{}&-1.368375379749&{}:{}&1.768006519538&,\\ Q_{\mathbf{4c}}&{}\approx{}&-0.560386158700&{}:{}&1.277245829250&{}:{}&0.283140329449&,\\ Q_{\mathbf{5c}}&{}\approx{}&-0.705254708953&{}:{}&0.309427494852&{}:{}&1.395827214101&,\\ Q_{\mathbf{6c}}&{}\approx{}&0.348263202803&{}:{}&0.533475704939&{}:{}&0.118261092258&,\\ Q_{\mathbf{7c}}&{}\approx{}&0.217500699509&{}:{}&0.141988640760&{}:{}&0.640510659731&. \end{alignedat} \] \[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.151261011934&{}:{}&0.392458182810&{}:{}&0.456280805256&,\\ I^\prime_{\mathbf{1}}&{}\approx{}&0.047223044176&{}:{}&0.122523774417&{}:{}&0.830253181407&,\\ I^\prime_{\mathbf{2}}&{}\approx{}&0.030941555648&{}:{}&0.875722840244&{}:{}&0.093335604108&,\\ I^\prime_{\mathbf{3}}&{}\approx{}&0.021329234185&{}:{}&0.603670279334&{}:{}&0.375000486481&,\\ I^\prime_{\mathbf{4}}&{}\approx{}&0.947852955761&{}:{}&0.024112871576&{}:{}&0.028034172663&,\\ I^\prime_{\mathbf{5}}&{}\approx{}&0.834847233084&{}:{}&0.021238066511&{}:{}&0.143914700405&,\\ I^\prime_{\mathbf{6}}&{}\approx{}&0.765064993596&{}:{}&0.212307061849&{}:{}&0.022627944554&,\\ I^\prime_{\mathbf{7}}&{}\approx{}&0.689709175272&{}:{}&0.191395671947&{}:{}&0.118895152781&,\\ I^\prime_{\mathbf{a}}&{}\approx{}&-0.197085219125&{}:{}&0.602575098265&{}:{}&0.594510120861&,\\ I^\prime_{\mathbf{1a}}&{}\approx{}&-0.078795346806&{}:{}&0.841108160721&{}:{}&0.237687186085&,\\ I^\prime_{\mathbf{2a}}&{}\approx{}&-0.050919192507&{}:{}&0.155682082933&{}:{}&0.895237109575&,\\ I^\prime_{\mathbf{3a}}&{}\approx{}&-0.036689010756&{}:{}&0.391640212356&{}:{}&0.645048798400&,\\ I^\prime_{\mathbf{4a}}&{}\approx{}&1.383216537776&{}:{}&-0.144771483710&{}:{}&-0.238445054066&,\\ I^\prime_{\mathbf{5a}}&{}\approx{}&1.253701868665&{}:{}&-0.037583132594&{}:{}&-0.216118736071&,\\ I^\prime_{\mathbf{6a}}&{}\approx{}&1.155053746175&{}:{}&-0.120891299397&{}:{}&-0.034162446779&,\\ I^\prime_{\mathbf{7a}}&{}\approx{}&1.063325529863&{}:{}&-0.031876082646&{}:{}&-0.031449447216&,\\ I^\prime_{\mathbf{b}}&{}\approx{}&0.796928933401&{}:{}&-1.248724961858&{}:{}&1.451796028457&,\\ I^\prime_{\mathbf{1b}}&{}\approx{}&0.853783559874&{}:{}&-0.899114392204&{}:{}&1.045330832330&,\\ I^\prime_{\mathbf{2b}}&{}\approx{}&-0.298378035089&{}:{}&3.427615958124&{}:{}&-2.129237923035&,\\ I^\prime_{\mathbf{3b}}&{}\approx{}&-0.182661048441&{}:{}&3.122132208906&{}:{}&-1.939471160465&,\\ I^\prime_{\mathbf{4b}}&{}\approx{}&0.099493101869&{}:{}&-0.155897865706&{}:{}&1.056404763837&,\\ I^\prime_{\mathbf{5b}}&{}\approx{}&0.141184169980&{}:{}&-0.148680210238&{}:{}&1.007496040259&,\\ I^\prime_{\mathbf{6b}}&{}\approx{}&-0.107954717346&{}:{}&1.240129193221&{}:{}&-0.132174475875&,\\ I^\prime_{\mathbf{7b}}&{}\approx{}&-0.070073392212&{}:{}&1.197728780605&{}:{}&-0.127655388392&,\\ I^\prime_{\mathbf{c}}&{}\approx{}&0.975882762576&{}:{}&1.801920325713&{}:{}&-1.777803088289&,\\ I^\prime_{\mathbf{1c}}&{}\approx{}&-0.554506108829&{}:{}&-2.402472276392&{}:{}&3.956978385220&,\\ I^\prime_{\mathbf{2c}}&{}\approx{}&0.983662115547&{}:{}&1.220685668015&{}:{}&-1.204347783562&,\\ I^\prime_{\mathbf{3c}}&{}\approx{}&-0.315333151301&{}:{}&-2.032833073008&{}:{}&3.348166224310&,\\ I^\prime_{\mathbf{4c}}&{}\approx{}&0.177781512088&{}:{}&1.146089892707&{}:{}&-0.323871404795&,\\ I^\prime_{\mathbf{5c}}&{}\approx{}&-0.204286721104&{}:{}&-0.253511717770&{}:{}&1.457798438875&,\\ I^\prime_{\mathbf{6c}}&{}\approx{}&0.243410668045&{}:{}&1.054609448743&{}:{}&-0.298020116789&,\\ I^\prime_{\mathbf{7c}}&{}\approx{}&-0.128676649241&{}:{}&-0.237595209797&{}:{}&1.366271859037&. \end{alignedat} \]

Central Triangles and their Extraversions

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.301497473876&{}:{}&0.335281212540&{}:{}&0.363221313584&,\\B^\prime&{}\approx{}&0.099419031209&{}:{}&0.642091487647&{}:{}&0.258489481144&,\\C^\prime&{}\approx{}&0.084368200921&{}:{}&0.202483682210&{}:{}&0.713148116870&,\\[.5em] A^\prime_{\mathbf{1}}&{}\approx{}&-0.100871453186&{}:{}&0.528418297529&{}:{}&0.572453155657&,\\B^\prime_{\mathbf{1}}&{}\approx{}&0.367664982584&{}:{}&-0.323593937302&{}:{}&0.955928954718&,\\C^\prime_{\mathbf{1}}&{}\approx{}&0.015332607192&{}:{}&0.036798257260&{}:{}&0.947869135548&,\\[.5em] A^\prime_{\mathbf{2}}&{}\approx{}&-0.165631799079&{}:{}&0.559503263558&{}:{}&0.606128535521&,\\B^\prime_{\mathbf{2}}&{}\approx{}&0.010221738128&{}:{}&0.963201742740&{}:{}&0.026576519133&,\\C^\prime_{\mathbf{2}}&{}\approx{}&0.551497473876&{}:{}&1.323593937302&{}:{}&-0.875091411178&,\\[.5em] A^\prime_{\mathbf{3}}&{}\approx{}&-0.234667392808&{}:{}&0.592640348548&{}:{}&0.642027044260&,\\B^\prime_{\mathbf{3}}&{}\approx{}&0.056245467280&{}:{}&0.797516317790&{}:{}&0.146238214929&,\\C^\prime_{\mathbf{3}}&{}\approx{}&0.149128546814&{}:{}&0.357908512353&{}:{}&0.492962940833&,\\[.5em] A^\prime_{\mathbf{4}}&{}\approx{}&0.984667392808&{}:{}&0.007359651452&{}:{}&0.007972955740&,\\B^\prime_{\mathbf{4}}&{}\approx{}&0.777087866053&{}:{}&-1.797516317790&{}:{}&2.020428451737&,\\C^\prime_{\mathbf{4}}&{}\approx{}&1.100871453186&{}:{}&2.642091487647&{}:{}&-2.742962940833&,\\[.5em] A^\prime_{\mathbf{5}}&{}\approx{}&0.915631799079&{}:{}&0.040496736442&{}:{}&0.043871464479&,\\B^\prime_{\mathbf{5}}&{}\approx{}&0.823111595205&{}:{}&-1.963201742740&{}:{}&2.140090147534&,\\C^\prime_{\mathbf{5}}&{}\approx{}&0.698502526124&{}:{}&1.676406062698&{}:{}&-1.374908588822&,\\[.5em] A^\prime_{\mathbf{6}}&{}\approx{}&0.850871453186&{}:{}&0.071581702471&{}:{}&0.077546844343&,\\B^\prime_{\mathbf{6}}&{}\approx{}&0.465668350749&{}:{}&-0.676406062698&{}:{}&1.210737711948&,\\C^\prime_{\mathbf{6}}&{}\approx{}&1.234667392808&{}:{}&2.963201742740&{}:{}&-3.197869135548&,\\[.5em] A^\prime_{\mathbf{7}}&{}\approx{}&0.448502526124&{}:{}&0.264718787460&{}:{}&0.286778686416&,\\B^\prime_{\mathbf{7}}&{}\approx{}&0.733914302124&{}:{}&-1.642091487647&{}:{}&1.908177185523&,\\C^\prime_{\mathbf{7}}&{}\approx{}&1.165631799079&{}:{}&2.797516317790&{}:{}&-2.963148116870&,\\[.5em] A^\prime_{\mathbf{a}}&{}\approx{}&-0.506052104307&{}:{}&0.722905010067&{}:{}&0.783147094240&,\\B^\prime_{\mathbf{a}}&{}\approx{}&-0.103748070570&{}:{}&0.834003087088&{}:{}&0.269744983482&,\\C^\prime_{\mathbf{a}}&{}\approx{}&-0.122256164685&{}:{}&0.293414795243&{}:{}&0.828841369441&,\\[.5em] A^\prime_{\mathbf{1a}}&{}\approx{}&0.044410501982&{}:{}&0.458682959049&{}:{}&0.496906538969&,\\B^\prime_{\mathbf{1a}}&{}\approx{}&-0.028054161137&{}:{}&0.955113342180&{}:{}&0.072940818957&,\\C^\prime_{\mathbf{1a}}&{}\approx{}&-0.672718770973&{}:{}&1.614525050336&{}:{}&0.058193720637&,\\[.5em] A^\prime_{\mathbf{2a}}&{}\approx{}&0.097501286287&{}:{}&0.433199382582&{}:{}&0.469299331131&,\\B^\prime_{\mathbf{2a}}&{}\approx{}&-1.009078156460&{}:{}&-0.614525050336&{}:{}&2.623603206796&,\\C^\prime_{\mathbf{2a}}&{}\approx{}&-0.018702774091&{}:{}&0.044886657820&{}:{}&0.973816116272&,\\[.5em] A^\prime_{\mathbf{3a}}&{}\approx{}&0.147963892575&{}:{}&0.408977331564&{}:{}&0.443058775861&,\\B^\prime_{\mathbf{3a}}&{}\approx{}&-0.183384247027&{}:{}&0.706585204757&{}:{}&0.476799042270&,\\C^\prime_{\mathbf{3a}}&{}\approx{}&-0.069165380380&{}:{}&0.165996912912&{}:{}&0.903168467468&,\\[.5em] A^\prime_{\mathbf{4a}}&{}\approx{}&1.672718770973&{}:{}&-0.322905010067&{}:{}&-0.349813760906&,\\B^\prime_{\mathbf{4a}}&{}\approx{}&1.353748070570&{}:{}&3.165996912912&{}:{}&-3.519744983482&,\\C^\prime_{\mathbf{4a}}&{}\approx{}&0.955589498018&{}:{}&-2.293414795243&{}:{}&2.337825297225&,\\[.5em] A^\prime_{\mathbf{5a}}&{}\approx{}&1.122256164685&{}:{}&-0.058682959049&{}:{}&-0.063573205636&,\\B^\prime_{\mathbf{5a}}&{}\approx{}&1.278054161137&{}:{}&3.044886657820&{}:{}&-3.322940818957&,\\C^\prime_{\mathbf{5a}}&{}\approx{}&1.506052104307&{}:{}&-3.614525050336&{}:{}&3.108472946029&,\\[.5em] A^\prime_{\mathbf{6a}}&{}\approx{}&1.069165380380&{}:{}&-0.033199382582&{}:{}&-0.035965997798&,\\B^\prime_{\mathbf{6a}}&{}\approx{}&2.259078156460&{}:{}&4.614525050336&{}:{}&-5.873603206796&,\\C^\prime_{\mathbf{6a}}&{}\approx{}&0.852036107425&{}:{}&-2.044886657820&{}:{}&2.192850550395&,\\[.5em] A^\prime_{\mathbf{7a}}&{}\approx{}&1.018702774091&{}:{}&-0.008977331564&{}:{}&-0.009725442528&,\\B^\prime_{\mathbf{7a}}&{}\approx{}&1.433384247027&{}:{}&3.293414795243&{}:{}&-3.726799042270&,\\C^\prime_{\mathbf{7a}}&{}\approx{}&0.902498713713&{}:{}&-2.165996912912&{}:{}&2.263498199199&,\\[.5em] A^\prime_{\mathbf{b}}&{}\approx{}&0.954847509134&{}:{}&-0.541829890387&{}:{}&0.586982381253&,\\B^\prime_{\mathbf{b}}&{}\approx{}&1.537998084118&{}:{}&-4.536793102824&{}:{}&3.998795018706&,\\C^\prime_{\mathbf{b}}&{}\approx{}&0.373827207244&{}:{}&-0.897185297387&{}:{}&1.523358090142&,\\[.5em] A^\prime_{\mathbf{1b}}&{}\approx{}&0.971350761400&{}:{}&-0.343790863202&{}:{}&0.372440101802&,\\B^\prime_{\mathbf{1b}}&{}\approx{}&0.415884804830&{}:{}&-0.497185297387&{}:{}&1.081300492557&,\\C^\prime_{\mathbf{1b}}&{}\approx{}&2.056997126177&{}:{}&-4.936793102824&{}:{}&3.879795976647&,\\[.5em] A^\prime_{\mathbf{2b}}&{}\approx{}&1.295152490866&{}:{}&3.541829890387&{}:{}&-3.836982381253&,\\B^\prime_{\mathbf{2b}}&{}\approx{}&-1.371331417451&{}:{}&5.936793102824&{}:{}&-3.565461685373&,\\C^\prime_{\mathbf{2b}}&{}\approx{}&-0.623827207244&{}:{}&1.497185297387&{}:{}&0.126641909858&,\\[.5em] A^\prime_{\mathbf{3b}}&{}\approx{}&1.278649238600&{}:{}&3.343790863202&{}:{}&-3.622440101802&,\\B^\prime_{\mathbf{3b}}&{}\approx{}&-0.249218138163&{}:{}&1.897185297387&{}:{}&-0.647967159224&,\\C^\prime_{\mathbf{3b}}&{}\approx{}&-2.306997126177&{}:{}&5.536793102824&{}:{}&-2.229795976647&,\\[.5em] A^\prime_{\mathbf{4b}}&{}\approx{}&-1.056997126177&{}:{}&-24.683965514118&{}:{}&26.740962640295&,\\B^\prime_{\mathbf{4b}}&{}\approx{}&0.196768327244&{}:{}&0.291634021923&{}:{}&0.511597650834&,\\C^\prime_{\mathbf{4b}}&{}\approx{}&0.028649238600&{}:{}&-0.068758172640&{}:{}&1.040108934040&,\\[.5em] A^\prime_{\mathbf{5b}}&{}\approx{}&0.626172792756&{}:{}&-4.485926486933&{}:{}&4.859753694177&,\\B^\prime_{\mathbf{5b}}&{}\approx{}&0.185766159067&{}:{}&0.331241827360&{}:{}&0.482992013574&,\\C^\prime_{\mathbf{5b}}&{}\approx{}&0.045152490866&{}:{}&-0.108365978077&{}:{}&1.063213487212&,\\[.5em] A^\prime_{\mathbf{6b}}&{}\approx{}&3.306997126177&{}:{}&27.683965514118&{}:{}&-29.990962640295&,\\B^\prime_{\mathbf{6b}}&{}\approx{}&-0.030101660577&{}:{}&1.108365978077&{}:{}&-0.078264317500&,\\C^\prime_{\mathbf{6b}}&{}\approx{}&-0.278649238600&{}:{}&0.668758172640&{}:{}&0.609891065960&,\\[.5em] A^\prime_{\mathbf{7b}}&{}\approx{}&1.623827207244&{}:{}&7.485926486933&{}:{}&-8.109753694177&,\\B^\prime_{\mathbf{7b}}&{}\approx{}&-0.019099492400&{}:{}&1.068758172640&{}:{}&-0.049658680240&,\\C^\prime_{\mathbf{7b}}&{}\approx{}&-0.295152490866&{}:{}&0.708365978077&{}:{}&0.586786512788&,\\[.5em] A^\prime_{\mathbf{c}}&{}\approx{}&1.061771066627&{}:{}&0.741252799527&{}:{}&-0.803023866155&,\\B^\prime_{\mathbf{c}}&{}\approx{}&0.433993829509&{}:{}&1.694390127214&{}:{}&-1.128383956722&,\\C^\prime_{\mathbf{c}}&{}\approx{}&2.980750764737&{}:{}&7.153801835369&{}:{}&-9.134552600107&,\\[.5em] A^\prime_{\mathbf{1c}}&{}\approx{}&0.771562266706&{}:{}&-2.741252799527&{}:{}&2.969690532821&,\\B^\prime_{\mathbf{1c}}&{}\approx{}&-0.683993829509&{}:{}&-0.094390127214&{}:{}&1.778383956722&,\\C^\prime_{\mathbf{1c}}&{}\approx{}&-2.814084098071&{}:{}&-6.753801835369&{}:{}&10.567885933440&,\\[.5em] A^\prime_{\mathbf{2c}}&{}\approx{}&1.037016188229&{}:{}&0.444194258749&{}:{}&-0.481210446978&,\\B^\prime_{\mathbf{2c}}&{}\approx{}&4.221126147106&{}:{}&7.753801835369&{}:{}&-10.974927982475&,\\C^\prime_{\mathbf{2c}}&{}\approx{}&0.455995886339&{}:{}&1.094390127214&{}:{}&-0.550386013553&,\\[.5em] A^\prime_{\mathbf{3c}}&{}\approx{}&0.796317145104&{}:{}&-2.444194258749&{}:{}&2.647877113645&,\\B^\prime_{\mathbf{3c}}&{}\approx{}&-4.471126147106&{}:{}&-6.153801835369&{}:{}&11.624927982475&,\\C^\prime_{\mathbf{3c}}&{}\approx{}&-0.289329219672&{}:{}&-0.694390127214&{}:{}&1.983719346886&,\\[.5em] A^\prime_{\mathbf{4c}}&{}\approx{}&3.814084098071&{}:{}&33.769009176847&{}:{}&-36.583093274918&,\\B^\prime_{\mathbf{4c}}&{}\approx{}&0.055524282344&{}:{}&1.088838851750&{}:{}&-0.144363134093&,\\C^\prime_{\mathbf{4c}}&{}\approx{}&0.228437733294&{}:{}&0.548250559905&{}:{}&0.223311706801&,\\[.5em] A^\prime_{\mathbf{5c}}&{}\approx{}&-1.980750764737&{}:{}&-35.769009176847&{}:{}&38.749759941585&,\\B^\prime_{\mathbf{5c}}&{}\approx{}&-0.305524282344&{}:{}&0.511161148250&{}:{}&0.794363134093&,\\C^\prime_{\mathbf{5c}}&{}\approx{}&-0.061771066627&{}:{}&-0.148250559905&{}:{}&1.210021626533&,\\[.5em] A^\prime_{\mathbf{6c}}&{}\approx{}&1.289329219672&{}:{}&3.471950636069&{}:{}&-3.761279855741&,\\B^\prime_{\mathbf{6c}}&{}\approx{}&0.092656599941&{}:{}&1.148250559905&{}:{}&-0.240907159846&,\\C^\prime_{\mathbf{6c}}&{}\approx{}&0.203682854896&{}:{}&0.488838851750&{}:{}&0.307478293354&,\\[.5em] A^\prime_{\mathbf{7c}}&{}\approx{}&0.544004113661&{}:{}&-5.471950636069&{}:{}&5.927946522408&,\\B^\prime_{\mathbf{7c}}&{}\approx{}&-0.342656599941&{}:{}&0.451749440095&{}:{}&0.890907159846&,\\C^\prime_{\mathbf{7c}}&{}\approx{}&-0.037016188229&{}:{}&-0.088838851750&{}:{}&1.125855039979&. \end{alignedat} \] \[ \begin{alignedat}{4} A^{\prime\prime}&{}\approx{}&0.091277339597&{}:{}&0.404287252706&{}:{}&0.504435407697&,\\B^{\prime\prime}&{}\approx{}&0.166123509110&{}:{}&0.252485705756&{}:{}&0.581390785134&,\\C^{\prime\prime}&{}\approx{}&0.183437440152&{}:{}&0.514528592657&{}:{}&0.302033967192&,\\[.5em] A^{\prime\prime}_{\mathbf{1}}&{}\approx{}&0.029437588678&{}:{}&0.022370615673&{}:{}&0.948191795650&,\\B^{\prime\prime}_{\mathbf{1}}&{}\approx{}&0.007767176080&{}:{}&0.068805035128&{}:{}&0.923427788792&,\\C^{\prime\prime}_{\mathbf{1}}&{}\approx{}&0.074618144197&{}:{}&0.209298432689&{}:{}&0.716083423115&,\\[.5em] A^{\prime\prime}_{\mathbf{2}}&{}\approx{}&0.020071461455&{}:{}&0.969759885238&{}:{}&0.010168653307&,\\B^{\prime\prime}_{\mathbf{2}}&{}\approx{}&0.047440669208&{}:{}&0.786528838987&{}:{}&0.166030491805&,\\C^{\prime\prime}_{\mathbf{2}}&{}\approx{}&0.002835081641&{}:{}&0.946244551902&{}:{}&0.050920366457&,\\[.5em] A^{\prime\prime}_{\mathbf{3}}&{}\approx{}&0.081683214280&{}:{}&0.677121600153&{}:{}&0.241195185567&,\\B^{\prime\prime}_{\mathbf{3}}&{}\approx{}&0.004618527974&{}:{}&0.446291683119&{}:{}&0.549089788907&,\\C^{\prime\prime}_{\mathbf{3}}&{}\approx{}&0.002275592466&{}:{}&0.759507924455&{}:{}&0.238216483079&,\\[.5em] A^{\prime\prime}_{\mathbf{4}}&{}\approx{}&0.911067497140&{}:{}&0.039565732015&{}:{}&0.049366770845&,\\B^{\prime\prime}_{\mathbf{4}}&{}\approx{}&0.984990184714&{}:{}&0.014678415591&{}:{}&0.000331399696&,\\C^{\prime\prime}_{\mathbf{4}}&{}\approx{}&0.983851468320&{}:{}&0.000265298152&{}:{}&0.015883233527&,\\[.5em] A^{\prime\prime}_{\mathbf{5}}&{}\approx{}&0.755704774914&{}:{}&0.005630791516&{}:{}&0.238664433570&,\\B^{\prime\prime}_{\mathbf{5}}&{}\approx{}&0.910510351933&{}:{}&0.079083072757&{}:{}&0.010406575310&,\\C^{\prime\prime}_{\mathbf{5}}&{}\approx{}&0.913773251376&{}:{}&0.000246401376&{}:{}&0.085980347248&,\\[.5em] A^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.676272942813&{}:{}&0.320367763033&{}:{}&0.003359294154&,\\B^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.859924081571&{}:{}&0.139786597191&{}:{}&0.000289321237&,\\C^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.827684584354&{}:{}&0.026557417647&{}:{}&0.145757997999&,\\[.5em] A^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.900713962997&{}:{}&0.073208637035&{}:{}&0.026077399969&,\\B^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.510495673307&{}:{}&0.483669674008&{}:{}&0.005834652685&,\\C^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.485792576122&{}:{}&0.015587334327&{}:{}&0.498620089550&,\\[.5em] A^{\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.112244278848&{}:{}&0.585844055075&{}:{}&0.526400223773&,\\B^{\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.233059286351&{}:{}&0.417410001066&{}:{}&0.815649285284&,\\C^{\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.206816084122&{}:{}&0.805540389357&{}:{}&0.401275694765&,\\[.5em] A^{\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.053862128333&{}:{}&0.981511682454&{}:{}&0.072350445879&,\\B^{\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.114249398737&{}:{}&0.714405042035&{}:{}&0.399844356702&,\\C^{\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.018778638842&{}:{}&0.891569942010&{}:{}&0.127208696832&,\\[.5em] A^{\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.036724870524&{}:{}&0.032887186099&{}:{}&1.003837684425&,\\B^{\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.007792579159&{}:{}&0.081344656862&{}:{}&0.926447922296&,\\C^{\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.070404745655&{}:{}&0.274223673019&{}:{}&0.796181072636&,\\[.5em] A^{\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.100446326780&{}:{}&0.314047001991&{}:{}&0.786399324789&,\\B^{\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.006479461211&{}:{}&0.236146140955&{}:{}&0.770333320256&,\\C^{\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.011633273663&{}:{}&0.552323158913&{}:{}&0.459310114750&,\\[.5em] A^{\prime\prime}_{\mathbf{4a}}&{}\approx{}&1.120345034693&{}:{}&-0.034344244176&{}:{}&-0.086000790517&,\\B^{\prime\prime}_{\mathbf{4a}}&{}\approx{}&1.584210999625&{}:{}&-0.566104438795&{}:{}&-0.018106560830&,\\C^{\prime\prime}_{\mathbf{4a}}&{}\approx{}&1.643883353889&{}:{}&-0.007503181660&{}:{}&-0.636380172229&,\\[.5em] A^{\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.382717450616&{}:{}&-0.012140636710&{}:{}&-0.370576813905&,\\B^{\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.128387666454&{}:{}&-0.115490886967&{}:{}&-0.012896779487&,\\C^{\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.125180876643&{}:{}&-0.000421316538&{}:{}&-0.124759560106&,\\[.5em] A^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.237380562420&{}:{}&-0.221083753689&{}:{}&-0.016296808731&,\\B^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.065696535654&{}:{}&-0.065337982327&{}:{}&-0.000358553327&,\\C^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.076407261946&{}:{}&-0.004913048853&{}:{}&-0.071494213093&,\\[.5em] A^{\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.107613233147&{}:{}&-0.056682308091&{}:{}&-0.050930925055&,\\B^{\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.018223135134&{}:{}&-0.017880554221&{}:{}&-0.000342580913&,\\C^{\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.019782108871&{}:{}&-0.000381850666&{}:{}&-0.019400258205&,\\[.5em] A^{\prime\prime}_{\mathbf{b}}&{}\approx{}&0.601462415139&{}:{}&-1.608853056736&{}:{}&2.007390641597&,\\B^{\prime\prime}_{\mathbf{b}}&{}\approx{}&0.736076943569&{}:{}&-0.675631244854&{}:{}&0.939554301285&,\\C^{\prime\prime}_{\mathbf{b}}&{}\approx{}&1.029491148212&{}:{}&-1.053187685355&{}:{}&1.023696537143&,\\[.5em] A^{\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.691884103021&{}:{}&-1.243830498087&{}:{}&1.551946395066&,\\B^{\prime\prime}_{\mathbf{1b}}&{}\approx{}&1.042031448097&{}:{}&-0.642816920700&{}:{}&0.600785472603&,\\C^{\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.829043531200&{}:{}&-0.383089647940&{}:{}&0.554046116741&,\\[.5em] A^{\prime\prime}_{\mathbf{2b}}&{}\approx{}&-0.857549708345&{}:{}&2.885319606231&{}:{}&-1.027769897886&,\\B^{\prime\prime}_{\mathbf{2b}}&{}\approx{}&-0.053662585204&{}:{}&2.104687301042&{}:{}&-1.051024715838&,\\C^{\prime\prime}_{\mathbf{2b}}&{}\approx{}&-0.086992606621&{}:{}&4.783234967840&{}:{}&-3.696242361219&,\\[.5em] A^{\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.449841245026&{}:{}&2.252028762085&{}:{}&-0.802187517059&,\\B^{\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.071447962111&{}:{}&4.169518189229&{}:{}&-3.098070227118&,\\C^{\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.017388286049&{}:{}&2.116684947350&{}:{}&-1.099296661302&,\\[.5em] A^{\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.050016179840&{}:{}&-0.022954457508&{}:{}&0.972938277668&,\\B^{\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.025633527638&{}:{}&-0.137134352061&{}:{}&1.111500824424&,\\C^{\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.173232062988&{}:{}&-0.177219469797&{}:{}&1.003987406810&,\\[.5em] A^{\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.072647270395&{}:{}&-0.022407622504&{}:{}&0.949760352109&,\\B^{\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.058857067528&{}:{}&-0.211619880555&{}:{}&1.152762813027&,\\C^{\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.225579561844&{}:{}&-0.104237222386&{}:{}&0.878657660542&,\\[.5em] A^{\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.054333799984&{}:{}&1.065506426959&{}:{}&-0.011172626974&,\\B^{\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.194074284281&{}:{}&1.305968230298&{}:{}&-0.111893946017&,\\C^{\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.021415845031&{}:{}&1.177537066605&{}:{}&-0.156121221574&,\\[.5em] A^{\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.035877340837&{}:{}&1.046854387310&{}:{}&-0.010977046473&,\\B^{\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.129263863316&{}:{}&1.294260770012&{}:{}&-0.164996906696&,\\C^{\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.009100540528&{}:{}&1.107813449509&{}:{}&-0.098712908981&,\\[.5em] A^{\prime\prime}_{\mathbf{c}}&{}\approx{}&0.757671564297&{}:{}&2.388249046583&{}:{}&-2.145920610881&,\\B^{\prime\prime}_{\mathbf{c}}&{}\approx{}&1.241940696762&{}:{}&1.343315754724&{}:{}&-1.585256451486&,\\C^{\prime\prime}_{\mathbf{c}}&{}\approx{}&0.800759333081&{}:{}&1.137539908231&{}:{}&-0.938299241311&,\\[.5em] A^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-1.100499301987&{}:{}&-1.396532792654&{}:{}&3.497032094641&,\\B^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.263625366595&{}:{}&-3.899688606449&{}:{}&5.163313973044&,\\C^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.138817544824&{}:{}&-1.085768447511&{}:{}&2.224585992335&,\\[.5em] A^{\prime\prime}_{\mathbf{2c}}&{}\approx{}&0.823077159430&{}:{}&1.743649291855&{}:{}&-1.566726451285&,\\B^{\prime\prime}_{\mathbf{2c}}&{}\approx{}&0.869273759103&{}:{}&0.631907896343&{}:{}&-0.501181655446&,\\C^{\prime\prime}_{\mathbf{2c}}&{}\approx{}&1.170763435259&{}:{}&0.751231359500&{}:{}&-0.921994794759&,\\[.5em] A^{\prime\prime}_{\mathbf{3c}}&{}\approx{}&-0.543488947812&{}:{}&-1.026200260424&{}:{}&2.569689208236&,\\B^{\prime\prime}_{\mathbf{3c}}&{}\approx{}&-0.049137456558&{}:{}&-1.081522211006&{}:{}&2.130659667565&,\\C^{\prime\prime}_{\mathbf{3c}}&{}\approx{}&-0.180893882927&{}:{}&-3.132397098807&{}:{}&4.313290981733&,\\[.5em] A^{\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.089334773687&{}:{}&0.983135358694&{}:{}&-0.072470132381&,\\B^{\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.285721812565&{}:{}&1.078983481238&{}:{}&-0.364705293803&,\\C^{\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.070297902075&{}:{}&1.217293481395&{}:{}&-0.287591383470&,\\[.5em] A^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.102765041016&{}:{}&-0.037351893006&{}:{}&1.140116934021&,\\B^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.069691765945&{}:{}&-0.295277294348&{}:{}&1.364969060293&,\\C^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.339176265378&{}:{}&-0.217635637804&{}:{}&1.556811903183&,\\[.5em] A^{\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.127371232503&{}:{}&0.942071983811&{}:{}&-0.069443216314&,\\B^{\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.337672839467&{}:{}&0.857013162395&{}:{}&-0.194686001862&,\\C^{\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.164688966485&{}:{}&1.288123080481&{}:{}&-0.452812046966&,\\[.5em] A^{\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.066814591915&{}:{}&-0.036134210836&{}:{}&1.102948802750&,\\B^{\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.027733841437&{}:{}&-0.174839134769&{}:{}&1.202572976206&,\\C^{\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.226811266559&{}:{}&-0.322202760166&{}:{}&1.549014026725&. \end{alignedat} \] \[ \begin{alignedat}{4} A^{\prime\prime\prime}&{}\approx{}&0.062848639681&{}:{}&0.405903940709&{}:{}&0.531247419610&,\\B^{\prime\prime\prime}&{}\approx{}&0.165873032509&{}:{}&0.184459626651&{}:{}&0.649667340840&,\\C^{\prime\prime\prime}&{}\approx{}&0.192408481420&{}:{}&0.575792357984&{}:{}&0.231799160596&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1}}&{}\approx{}&0.016144565582&{}:{}&-0.014209358492&{}:{}&0.998064792911&,\\B^{\prime\prime\prime}_{\mathbf{1}}&{}\approx{}&-0.007185176653&{}:{}&0.037639775126&{}:{}&0.969545401527&,\\C^{\prime\prime\prime}_{\mathbf{1}}&{}\approx{}&-0.363109318090&{}:{}&-0.697563631723&{}:{}&2.060672949813&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2}}&{}\approx{}&0.010678744770&{}:{}&1.006265807604&{}:{}&-0.016944552374&,\\B^{\prime\prime\prime}_{\mathbf{2}}&{}\approx{}&-6.913702863200&{}:{}&23.354448461788&{}:{}&-15.440745598588&,\\C^{\prime\prime\prime}_{\mathbf{2}}&{}\approx{}&-0.007391583616&{}:{}&0.980342129483&{}:{}&0.027049454133&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3}}&{}\approx{}&0.054098400978&{}:{}&0.767072612821&{}:{}&0.178828986201&,\\B^{\prime\prime\prime}_{\mathbf{3}}&{}\approx{}&-0.199845809199&{}:{}&0.504700242341&{}:{}&0.695145566859&,\\C^{\prime\prime\prime}_{\mathbf{3}}&{}\approx{}&-0.060037482729&{}:{}&0.895780799600&{}:{}&0.164256683129&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4}}&{}\approx{}&-0.262827771611&{}:{}&0.607958544815&{}:{}&0.654869226796&,\\B^{\prime\prime\prime}_{\mathbf{4}}&{}\approx{}&1.000285438179&{}:{}&0.007476384647&{}:{}&-0.007761822826&,\\C^{\prime\prime\prime}_{\mathbf{4}}&{}\approx{}&0.999107450670&{}:{}&-0.007197329082&{}:{}&0.008089878411&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5}}&{}\approx{}&-0.298199128586&{}:{}&0.711234117383&{}:{}&0.586965011203&,\\B^{\prime\prime\prime}_{\mathbf{5}}&{}\approx{}&0.992108441892&{}:{}&0.043879159869&{}:{}&-0.035987601761&,\\C^{\prime\prime\prime}_{\mathbf{5}}&{}\approx{}&0.996055317793&{}:{}&-0.043780184423&{}:{}&0.047724866630&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&-0.328664738688&{}:{}&0.477401613156&{}:{}&0.851263125532&,\\B^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&1.006707068095&{}:{}&0.084691765782&{}:{}&-0.091398833877&,\\C^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&0.961333481241&{}:{}&-0.048947629715&{}:{}&0.087614148474&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&-0.264582514778&{}:{}&0.591988320762&{}:{}&0.672594194016&,\\B^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&1.036210882669&{}:{}&0.611600765739&{}:{}&-0.647811648408&,\\C^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&0.918136196316&{}:{}&-0.505205113421&{}:{}&0.587068917104&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.072367906342&{}:{}&0.581746310689&{}:{}&0.490621595653&,\\B^{\prime\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.224023618489&{}:{}&0.320021979557&{}:{}&0.904001638932&,\\C^{\prime\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.187534691880&{}:{}&0.897313096584&{}:{}&0.290221595296&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.030182445693&{}:{}&1.027571505002&{}:{}&0.002610940691&,\\B^{\prime\prime\prime}_{\mathbf{1a}}&{}\approx{}&0.085466254011&{}:{}&0.882717207399&{}:{}&0.031816538590&,\\C^{\prime\prime\prime}_{\mathbf{1a}}&{}\approx{}&0.006301158351&{}:{}&0.923195545183&{}:{}&0.070503296466&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.019818067163&{}:{}&-0.012069133241&{}:{}&1.031887200405&,\\B^{\prime\prime\prime}_{\mathbf{2a}}&{}\approx{}&0.009819887146&{}:{}&0.043629876187&{}:{}&0.946550236666&,\\C^{\prime\prime\prime}_{\mathbf{2a}}&{}\approx{}&0.213408216659&{}:{}&-0.240598084100&{}:{}&1.027189867441&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.062849082309&{}:{}&0.242159467958&{}:{}&0.820689614351&,\\B^{\prime\prime\prime}_{\mathbf{3a}}&{}\approx{}&0.053183562326&{}:{}&0.147001211069&{}:{}&0.799815226606&,\\C^{\prime\prime\prime}_{\mathbf{3a}}&{}\approx{}&0.118598159291&{}:{}&0.526274962384&{}:{}&0.355126878325&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4a}}&{}\approx{}&0.172855936653&{}:{}&0.404256429774&{}:{}&0.422887633572&,\\B^{\prime\prime\prime}_{\mathbf{4a}}&{}\approx{}&0.996275787094&{}:{}&-0.192323090195&{}:{}&0.196047303101&,\\C^{\prime\prime\prime}_{\mathbf{4a}}&{}\approx{}&1.021469515834&{}:{}&0.192149234182&{}:{}&-0.213618750017&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5a}}&{}\approx{}&0.183606606791&{}:{}&0.437431624031&{}:{}&0.378961769178&,\\B^{\prime\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.007374882739&{}:{}&-0.052675797960&{}:{}&0.045300915221&,\\C^{\prime\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.004762690979&{}:{}&0.052154782214&{}:{}&-0.056917473193&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6a}}&{}\approx{}&0.178052608217&{}:{}&0.363700661948&{}:{}&0.458246729835&,\\B^{\prime\prime\prime}_{\mathbf{6a}}&{}\approx{}&0.997758199656&{}:{}&-0.030982069568&{}:{}&0.033223869913&,\\C^{\prime\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.007263373092&{}:{}&0.026620283191&{}:{}&-0.033883656283&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7a}}&{}\approx{}&0.172244979437&{}:{}&0.395758614525&{}:{}&0.431996406037&,\\B^{\prime\prime\prime}_{\mathbf{7a}}&{}\approx{}&0.999603466355&{}:{}&-0.008809018664&{}:{}&0.009205552309&,\\C^{\prime\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.001111428293&{}:{}&0.008446071605&{}:{}&-0.009557499898&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{b}}&{}\approx{}&0.470537625590&{}:{}&-1.387993832008&{}:{}&1.917456206418&,\\B^{\prime\prime\prime}_{\mathbf{b}}&{}\approx{}&0.716310948722&{}:{}&-0.406471901656&{}:{}&0.690160952934&,\\C^{\prime\prime\prime}_{\mathbf{b}}&{}\approx{}&1.090164293995&{}:{}&-0.760331233873&{}:{}&0.670166939877&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.591485842436&{}:{}&-0.707114232250&{}:{}&1.115628389814&,\\B^{\prime\prime\prime}_{\mathbf{1b}}&{}\approx{}&1.081991937685&{}:{}&-0.382950173116&{}:{}&0.300958235430&,\\C^{\prime\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.828414643244&{}:{}&-0.146049473343&{}:{}&0.317634830099&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2b}}&{}\approx{}&-0.283107567176&{}:{}&1.225634467917&{}:{}&0.057473099259&,\\B^{\prime\prime\prime}_{\mathbf{2b}}&{}\approx{}&0.252143257710&{}:{}&0.689531567221&{}:{}&0.058325175069&,\\C^{\prime\prime\prime}_{\mathbf{2b}}&{}\approx{}&0.336659632898&{}:{}&1.660718736846&{}:{}&-0.997378369745&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.177116136499&{}:{}&1.348305274138&{}:{}&-0.171189137639&,\\B^{\prime\prime\prime}_{\mathbf{3b}}&{}\approx{}&0.390329829583&{}:{}&1.020750084069&{}:{}&-0.411079913652&,\\C^{\prime\prime\prime}_{\mathbf{3b}}&{}\approx{}&0.154755857176&{}:{}&1.283670730899&{}:{}&-0.438426588075&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.025781794028&{}:{}&0.038211679644&{}:{}&0.936006526328&,\\B^{\prime\prime\prime}_{\mathbf{4b}}&{}\approx{}&-0.003040363615&{}:{}&-0.071001357313&{}:{}&1.074041720929&,\\C^{\prime\prime\prime}_{\mathbf{4b}}&{}\approx{}&-0.025826063525&{}:{}&0.372452669442&{}:{}&0.653373394083&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.037979081144&{}:{}&0.067720947145&{}:{}&0.894299971712&,\\B^{\prime\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.015594625615&{}:{}&-0.111720510552&{}:{}&1.096125884937&,\\C^{\prime\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.071004268062&{}:{}&0.377928585606&{}:{}&0.551067146332&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.026309212305&{}:{}&0.968725155669&{}:{}&0.057584056636&,\\B^{\prime\prime\prime}_{\mathbf{6b}}&{}\approx{}&0.058803541204&{}:{}&0.492263871028&{}:{}&0.448932587768&,\\C^{\prime\prime\prime}_{\mathbf{6b}}&{}\approx{}&0.008308141310&{}:{}&1.067037904097&{}:{}&-0.075346045406&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.017560652705&{}:{}&0.982648685224&{}:{}&0.034911967481&,\\B^{\prime\prime\prime}_{\mathbf{7b}}&{}\approx{}&0.106057335066&{}:{}&0.488929739669&{}:{}&0.405012925264&,\\C^{\prime\prime\prime}_{\mathbf{7b}}&{}\approx{}&0.009662598159&{}:{}&1.038594562927&{}:{}&-0.048257161087&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{c}}&{}\approx{}&0.543576880205&{}:{}&2.122222106807&{}:{}&-1.665798987012&,\\B^{\prime\prime\prime}_{\mathbf{c}}&{}\approx{}&1.239615826008&{}:{}&0.865411320997&{}:{}&-1.105027147005&,\\C^{\prime\prime\prime}_{\mathbf{c}}&{}\approx{}&0.724969175496&{}:{}&0.823329387582&{}:{}&-0.548298563079&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.382064822711&{}:{}&-0.052724375080&{}:{}&1.434789197791&,\\B^{\prime\prime\prime}_{\mathbf{1c}}&{}\approx{}&0.332622437876&{}:{}&-1.181760991121&{}:{}&1.849138553245&,\\C^{\prime\prime\prime}_{\mathbf{1c}}&{}\approx{}&0.215301729012&{}:{}&-0.043983397282&{}:{}&0.828681668269&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2c}}&{}\approx{}&0.613532372747&{}:{}&1.126999827078&{}:{}&-0.740532199825&,\\B^{\prime\prime\prime}_{\mathbf{2c}}&{}\approx{}&0.824456361540&{}:{}&0.353146639890&{}:{}&-0.177603001430&,\\C^{\prime\prime\prime}_{\mathbf{2c}}&{}\approx{}&1.157666333777&{}:{}&0.379529845272&{}:{}&-0.537196179049&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3c}}&{}\approx{}&-0.223217891182&{}:{}&-0.307224315138&{}:{}&1.530442206320&,\\B^{\prime\prime\prime}_{\mathbf{3c}}&{}\approx{}&0.149272711842&{}:{}&-0.458173615268&{}:{}&1.308900903426&,\\C^{\prime\prime\prime}_{\mathbf{3c}}&{}\approx{}&0.389872379765&{}:{}&-0.686258069775&{}:{}&1.296385690010&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.046322677197&{}:{}&0.908394102911&{}:{}&0.045283219892&,\\B^{\prime\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.074293902986&{}:{}&0.657780853077&{}:{}&0.267925243937&,\\C^{\prime\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.015685886129&{}:{}&1.134766547696&{}:{}&-0.150452433826&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.049353783090&{}:{}&0.082571952191&{}:{}&0.966781830899&,\\B^{\prime\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.007792186975&{}:{}&-0.140713719448&{}:{}&1.148505906423&,\\C^{\prime\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.032100891654&{}:{}&0.404105755843&{}:{}&0.627995135811&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.067104488831&{}:{}&0.831595017749&{}:{}&0.101300493420&,\\B^{\prime\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.185645154063&{}:{}&0.499911737745&{}:{}&0.314443108193&,\\C^{\prime\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.083421125218&{}:{}&1.159938129376&{}:{}&-0.243359254594&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.032537698732&{}:{}&0.042896845375&{}:{}&0.989640853358&,\\B^{\prime\prime\prime}_{\mathbf{7c}}&{}\approx{}&0.008444895276&{}:{}&-0.084944302654&{}:{}&1.076499407379&,\\C^{\prime\prime\prime}_{\mathbf{7c}}&{}\approx{}&0.057397626497&{}:{}&0.317147433291&{}:{}&0.625454940213&. \end{alignedat} \] \[ \begin{alignedat}{4} A^*&{}\approx{}&0.000000000000&{}:{}&0.422287584928&{}:{}&0.577712415072&,\\B^*&{}\approx{}&0.192932837398&{}:{}&0.000000000000&{}:{}&0.807067162602&,\\C^*&{}\approx{}&0.246442778780&{}:{}&0.753557221220&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1}}&{}\approx{}&0.000000000000&{}:{}&-0.143397840021&{}:{}&1.143397840021&,\\B^*_{\mathbf{1}}&{}\approx{}&-0.042769422997&{}:{}&0.000000000000&{}:{}&1.042769422997&,\\C^*_{\mathbf{1}}&{}\approx{}&0.246442778780&{}:{}&0.753557221220&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2}}&{}\approx{}&0.000000000000&{}:{}&1.143397840021&{}:{}&-0.143397840021&,\\B^*_{\mathbf{2}}&{}\approx{}&0.192932837398&{}:{}&0.000000000000&{}:{}&0.807067162602&,\\C^*_{\mathbf{2}}&{}\approx{}&-0.030907319333&{}:{}&1.030907319333&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3}}&{}\approx{}&0.000000000000&{}:{}&0.577712415072&{}:{}&0.422287584928&,\\B^*_{\mathbf{3}}&{}\approx{}&-0.042769422997&{}:{}&0.000000000000&{}:{}&1.042769422997&,\\C^*_{\mathbf{3}}&{}\approx{}&-0.030907319333&{}:{}&1.030907319333&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4}}&{}\approx{}&0.000000000000&{}:{}&0.422287584928&{}:{}&0.577712415072&,\\B^*_{\mathbf{4}}&{}\approx{}&1.042769422997&{}:{}&0.000000000000&{}:{}&-0.042769422997&,\\C^*_{\mathbf{4}}&{}\approx{}&1.030907319333&{}:{}&-0.030907319333&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5}}&{}\approx{}&0.000000000000&{}:{}&-0.143397840021&{}:{}&1.143397840021&,\\B^*_{\mathbf{5}}&{}\approx{}&0.807067162602&{}:{}&0.000000000000&{}:{}&0.192932837398&,\\C^*_{\mathbf{5}}&{}\approx{}&1.030907319333&{}:{}&-0.030907319333&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6}}&{}\approx{}&0.000000000000&{}:{}&1.143397840021&{}:{}&-0.143397840021&,\\B^*_{\mathbf{6}}&{}\approx{}&1.042769422997&{}:{}&0.000000000000&{}:{}&-0.042769422997&,\\C^*_{\mathbf{6}}&{}\approx{}&0.753557221220&{}:{}&0.246442778780&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7}}&{}\approx{}&0.000000000000&{}:{}&0.577712415072&{}:{}&0.422287584928&,\\B^*_{\mathbf{7}}&{}\approx{}&0.807067162602&{}:{}&0.000000000000&{}:{}&0.192932837398&,\\C^*_{\mathbf{7}}&{}\approx{}&0.753557221220&{}:{}&0.246442778780&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{a}}&{}\approx{}&0.000000000000&{}:{}&0.563708941166&{}:{}&0.436291058834&,\\B^*_{\mathbf{a}}&{}\approx{}&-0.314154134496&{}:{}&0.000000000000&{}:{}&1.314154134496&,\\C^*_{\mathbf{a}}&{}\approx{}&-0.227023454471&{}:{}&1.227023454471&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1a}}&{}\approx{}&0.000000000000&{}:{}&1.284819196258&{}:{}&-0.284819196258&,\\B^*_{\mathbf{1a}}&{}\approx{}&-0.314154134496&{}:{}&0.000000000000&{}:{}&1.314154134496&,\\C^*_{\mathbf{1a}}&{}\approx{}&0.050326643642&{}:{}&0.949673356358&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2a}}&{}\approx{}&0.000000000000&{}:{}&-0.284819196258&{}:{}&1.284819196258&,\\B^*_{\mathbf{2a}}&{}\approx{}&0.039399256098&{}:{}&0.000000000000&{}:{}&0.960600743902&,\\C^*_{\mathbf{2a}}&{}\approx{}&-0.227023454471&{}:{}&1.227023454471&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3a}}&{}\approx{}&0.000000000000&{}:{}&0.436291058834&{}:{}&0.563708941166&,\\B^*_{\mathbf{3a}}&{}\approx{}&0.039399256098&{}:{}&0.000000000000&{}:{}&0.960600743902&,\\C^*_{\mathbf{3a}}&{}\approx{}&0.050326643642&{}:{}&0.949673356358&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4a}}&{}\approx{}&0.000000000000&{}:{}&0.436291058834&{}:{}&0.563708941166&,\\B^*_{\mathbf{4a}}&{}\approx{}&1.314154134496&{}:{}&0.000000000000&{}:{}&-0.314154134496&,\\C^*_{\mathbf{4a}}&{}\approx{}&1.227023454471&{}:{}&-0.227023454471&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5a}}&{}\approx{}&0.000000000000&{}:{}&-0.284819196258&{}:{}&1.284819196258&,\\B^*_{\mathbf{5a}}&{}\approx{}&1.314154134496&{}:{}&0.000000000000&{}:{}&-0.314154134496&,\\C^*_{\mathbf{5a}}&{}\approx{}&0.949673356358&{}:{}&0.050326643642&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6a}}&{}\approx{}&0.000000000000&{}:{}&1.284819196258&{}:{}&-0.284819196258&,\\B^*_{\mathbf{6a}}&{}\approx{}&0.960600743902&{}:{}&0.000000000000&{}:{}&0.039399256098&,\\C^*_{\mathbf{6a}}&{}\approx{}&1.227023454471&{}:{}&-0.227023454471&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7a}}&{}\approx{}&0.000000000000&{}:{}&0.563708941166&{}:{}&0.436291058834&,\\B^*_{\mathbf{7a}}&{}\approx{}&0.960600743902&{}:{}&0.000000000000&{}:{}&0.039399256098&,\\C^*_{\mathbf{7a}}&{}\approx{}&0.949673356358&{}:{}&0.050326643642&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{b}}&{}\approx{}&0.000000000000&{}:{}&-2.716989200105&{}:{}&3.716989200105&,\\B^*_{\mathbf{b}}&{}\approx{}&0.664337358189&{}:{}&0.000000000000&{}:{}&0.335662641811&,\\C^*_{\mathbf{b}}&{}\approx{}&1.585607515558&{}:{}&-0.585607515558&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1b}}&{}\approx{}&0.000000000000&{}:{}&-2.716989200105&{}:{}&3.716989200105&,\\B^*_{\mathbf{1b}}&{}\approx{}&1.514173943788&{}:{}&0.000000000000&{}:{}&-0.514173943788&,\\C^*_{\mathbf{1b}}&{}\approx{}&0.801142975005&{}:{}&0.198857024995&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2b}}&{}\approx{}&0.000000000000&{}:{}&3.716989200105&{}:{}&-2.716989200105&,\\B^*_{\mathbf{2b}}&{}\approx{}&0.335662641811&{}:{}&0.000000000000&{}:{}&0.664337358189&,\\C^*_{\mathbf{2b}}&{}\approx{}&-0.585607515558&{}:{}&1.585607515558&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3b}}&{}\approx{}&0.000000000000&{}:{}&3.716989200105&{}:{}&-2.716989200105&,\\B^*_{\mathbf{3b}}&{}\approx{}&-0.514173943788&{}:{}&0.000000000000&{}:{}&1.514173943788&,\\C^*_{\mathbf{3b}}&{}\approx{}&0.198857024995&{}:{}&0.801142975005&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4b}}&{}\approx{}&0.000000000000&{}:{}&0.111437924641&{}:{}&0.888562075359&,\\B^*_{\mathbf{4b}}&{}\approx{}&-0.514173943788&{}:{}&0.000000000000&{}:{}&1.514173943788&,\\C^*_{\mathbf{4b}}&{}\approx{}&1.585607515558&{}:{}&-0.585607515558&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5b}}&{}\approx{}&0.000000000000&{}:{}&0.111437924641&{}:{}&0.888562075359&,\\B^*_{\mathbf{5b}}&{}\approx{}&0.335662641811&{}:{}&0.000000000000&{}:{}&0.664337358189&,\\C^*_{\mathbf{5b}}&{}\approx{}&0.801142975005&{}:{}&0.198857024995&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6b}}&{}\approx{}&0.000000000000&{}:{}&0.888562075359&{}:{}&0.111437924641&,\\B^*_{\mathbf{6b}}&{}\approx{}&1.514173943788&{}:{}&0.000000000000&{}:{}&-0.514173943788&,\\C^*_{\mathbf{6b}}&{}\approx{}&-0.585607515558&{}:{}&1.585607515558&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7b}}&{}\approx{}&0.000000000000&{}:{}&0.888562075359&{}:{}&0.111437924641&,\\B^*_{\mathbf{7b}}&{}\approx{}&0.664337358189&{}:{}&0.000000000000&{}:{}&0.335662641811&,\\C^*_{\mathbf{7b}}&{}\approx{}&0.198857024995&{}:{}&0.801142975005&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{c}}&{}\approx{}&0.000000000000&{}:{}&4.424095981292&{}:{}&-3.424095981292&,\\B^*_{\mathbf{c}}&{}\approx{}&2.021260915682&{}:{}&0.000000000000&{}:{}&-1.021260915682&,\\C^*_{\mathbf{c}}&{}\approx{}&0.605026839867&{}:{}&0.394973160133&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1c}}&{}\approx{}&0.000000000000&{}:{}&-3.424095981292&{}:{}&4.424095981292&,\\B^*_{\mathbf{1c}}&{}\approx{}&-1.021260915682&{}:{}&0.000000000000&{}:{}&2.021260915682&,\\C^*_{\mathbf{1c}}&{}\approx{}&0.394973160133&{}:{}&0.605026839867&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2c}}&{}\approx{}&0.000000000000&{}:{}&4.424095981292&{}:{}&-3.424095981292&,\\B^*_{\mathbf{2c}}&{}\approx{}&0.746506037284&{}:{}&0.000000000000&{}:{}&0.253493962716&,\\C^*_{\mathbf{2c}}&{}\approx{}&1.781723650696&{}:{}&-0.781723650696&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3c}}&{}\approx{}&0.000000000000&{}:{}&-3.424095981292&{}:{}&4.424095981292&,\\B^*_{\mathbf{3c}}&{}\approx{}&0.253493962716&{}:{}&0.000000000000&{}:{}&0.746506037284&,\\C^*_{\mathbf{3c}}&{}\approx{}&-0.781723650696&{}:{}&1.781723650696&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4c}}&{}\approx{}&0.000000000000&{}:{}&0.818544705828&{}:{}&0.181455294172&,\\B^*_{\mathbf{4c}}&{}\approx{}&2.021260915682&{}:{}&0.000000000000&{}:{}&-1.021260915682&,\\C^*_{\mathbf{4c}}&{}\approx{}&-0.781723650696&{}:{}&1.781723650696&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5c}}&{}\approx{}&0.000000000000&{}:{}&0.181455294172&{}:{}&0.818544705828&,\\B^*_{\mathbf{5c}}&{}\approx{}&-1.021260915682&{}:{}&0.000000000000&{}:{}&2.021260915682&,\\C^*_{\mathbf{5c}}&{}\approx{}&1.781723650696&{}:{}&-0.781723650696&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6c}}&{}\approx{}&0.000000000000&{}:{}&0.818544705828&{}:{}&0.181455294172&,\\B^*_{\mathbf{6c}}&{}\approx{}&0.746506037284&{}:{}&0.000000000000&{}:{}&0.253493962716&,\\C^*_{\mathbf{6c}}&{}\approx{}&0.394973160133&{}:{}&0.605026839867&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7c}}&{}\approx{}&0.000000000000&{}:{}&0.181455294172&{}:{}&0.818544705828&,\\B^*_{\mathbf{7c}}&{}\approx{}&0.253493962716&{}:{}&0.000000000000&{}:{}&0.746506037284&,\\C^*_{\mathbf{7c}}&{}\approx{}&0.605026839867&{}:{}&0.394973160133&{}:{}&0.000000000000&. \end{alignedat} \]