Derousseau's Generalization of the Malfatti circles

The Smallest Pythagorean Triangle

\(C=90\degree\).   \(a:b:c=3:4:5\).


[Top] > The Smallest Pythagorean Triangle

Reference Triangle

reference triangle

Triangle Centers and their Extraversions

Approximately,
\[ \begin{alignedat}{4} I&{}\approx{}&0.250000000000&{}:{}&0.333333333333&{}:{}&0.416666666667&,\\ I_{\mathbf{a}}&{}\approx{}&-0.500000000000&{}:{}&0.666666666667&{}:{}&0.833333333333&,\\ I_{\mathbf{b}}&{}\approx{}&0.750000000000&{}:{}&-1.000000000000&{}:{}&1.250000000000&,\\ I_{\mathbf{c}}&{}\approx{}&1.500000000000&{}:{}&2.000000000000&{}:{}&-2.500000000000&. \end{alignedat} \] \[ \begin{alignedat}{4} P&{}\approx{}&0.218219101089&{}:{}&0.307863489535&{}:{}&0.473917409375&,\\ P_{\mathbf{1}}&{}\approx{}&0.013125705415&{}:{}&0.018517744099&{}:{}&0.968356550486&,\\ P_{\mathbf{2}}&{}\approx{}&0.002186055432&{}:{}&0.993066377918&{}:{}&0.004747566651&,\\ P_{\mathbf{3}}&{}\approx{}&0.001890184895&{}:{}&0.858660325171&{}:{}&0.139449489934&,\\ P_{\mathbf{4}}&{}\approx{}&0.997521724384&{}:{}&0.000975939141&{}:{}&0.001502336475&,\\ P_{\mathbf{5}}&{}\approx{}&0.950443520472&{}:{}&0.000929879531&{}:{}&0.048626599997&,\\ P_{\mathbf{6}}&{}\approx{}&0.759568951087&{}:{}&0.239287085717&{}:{}&0.001143963197&,\\ P_{\mathbf{7}}&{}\approx{}&0.731961479201&{}:{}&0.230589900975&{}:{}&0.037448619824&,\\ P_{\mathbf{a}}&{}\approx{}&-0.278614241899&{}:{}&0.673533664275&{}:{}&0.605080577624&,\\ P_{\mathbf{1a}}&{}\approx{}&-0.056366158180&{}:{}&0.933952934371&{}:{}&0.122413223809&,\\ P_{\mathbf{2a}}&{}\approx{}&-0.013299106188&{}:{}&0.032149812806&{}:{}&0.981149293381&,\\ P_{\mathbf{3a}}&{}\approx{}&-0.011192571526&{}:{}&0.185454097941&{}:{}&0.825738473585&,\\ P_{\mathbf{4a}}&{}\approx{}&1.066840293917&{}:{}&-0.012258601144&{}:{}&-0.054581692773&,\\ P_{\mathbf{5a}}&{}\approx{}&1.055786112658&{}:{}&-0.001769974007&{}:{}&-0.054016138651&,\\ P_{\mathbf{6a}}&{}\approx{}&1.013167773897&{}:{}&-0.011641873393&{}:{}&-0.001525900504&,\\ P_{\mathbf{7a}}&{}\approx{}&1.003192681006&{}:{}&-0.001681803680&{}:{}&-0.001510877327&,\\ P_{\mathbf{b}}&{}\approx{}&0.742299567528&{}:{}&-0.477775860227&{}:{}&0.735476292698&,\\ P_{\mathbf{1b}}&{}\approx{}&0.914335235943&{}:{}&-0.158822226047&{}:{}&0.244486990104&,\\ P_{\mathbf{2b}}&{}\approx{}&-0.021811136794&{}:{}&1.219932514912&{}:{}&-0.198121378118&,\\ P_{\mathbf{3b}}&{}\approx{}&-0.005793987199&{}:{}&1.200809762299&{}:{}&-0.195015775099&,\\ P_{\mathbf{4b}}&{}\approx{}&0.029399088684&{}:{}&-0.018922515249&{}:{}&0.989523426565&,\\ P_{\mathbf{5b}}&{}\approx{}&0.100910273272&{}:{}&-0.017528356780&{}:{}&0.916618083508&,\\ P_{\mathbf{6b}}&{}\approx{}&-0.018293494781&{}:{}&1.023185050200&{}:{}&-0.004891555418&,\\ P_{\mathbf{7b}}&{}\approx{}&-0.004871864768&{}:{}&1.009698946980&{}:{}&-0.004827082212&,\\ P_{\mathbf{c}}&{}\approx{}&0.899207291927&{}:{}&0.991734417275&{}:{}&-0.890941709201&,\\ P_{\mathbf{1c}}&{}\approx{}&-0.165469293634&{}:{}&-0.337570405823&{}:{}&1.503039699457&,\\ P_{\mathbf{2c}}&{}\approx{}&0.970637883464&{}:{}&0.288904049605&{}:{}&-0.259541933069&,\\ P_{\mathbf{3c}}&{}\approx{}&-0.039842346058&{}:{}&-0.301183398540&{}:{}&1.341025744598&,\\ P_{\mathbf{4c}}&{}\approx{}&0.132125334504&{}:{}&0.998785493743&{}:{}&-0.130910828247&,\\ P_{\mathbf{5c}}&{}\approx{}&-0.128438083528&{}:{}&-0.038228759754&{}:{}&1.166666843281&,\\ P_{\mathbf{6c}}&{}\approx{}&0.360661147201&{}:{}&0.735777177453&{}:{}&-0.096438324654&,\\ P_{\mathbf{7c}}&{}\approx{}&-0.031690292878&{}:{}&-0.034951178024&{}:{}&1.066641470902&. \end{alignedat} \] \[ \begin{alignedat}{4} P^-&{}\approx{}&0.206879095206&{}:{}&0.298775383522&{}:{}&0.494345521272&,\\ P^-_{\mathbf{1}}&{}\approx{}&-0.010930768419&{}:{}&-0.013454289835&{}:{}&1.024385058254&,\\ P^-_{\mathbf{2}}&{}\approx{}&-0.010110323950&{}:{}&1.025801936124&{}:{}&-0.015691612174&,\\ P^-_{\mathbf{3}}&{}\approx{}&-0.075705892763&{}:{}&1.022955776511&{}:{}&0.052750116252&,\\ P^-_{\mathbf{4}}&{}\approx{}&1.021959809881&{}:{}&-0.009889535600&{}:{}&-0.012070274281&,\\ P^-_{\mathbf{5}}&{}\approx{}&1.099850274582&{}:{}&-0.069972798038&{}:{}&-0.029877476544&,\\ P^-_{\mathbf{6}}&{}\approx{}&1.148008781039&{}:{}&0.167596476715&{}:{}&-0.315605257754&,\\ P^-_{\mathbf{7}}&{}\approx{}&-0.087155651310&{}:{}&0.405207394538&{}:{}&0.681948256772&,\\ P^-_{\mathbf{a}}&{}\approx{}&-0.216258929939&{}:{}&0.675467816597&{}:{}&0.540791113342&,\\ P^-_{\mathbf{1a}}&{}\approx{}&0.002073696390&{}:{}&0.969162535490&{}:{}&0.028763768120&,\\ P^-_{\mathbf{2a}}&{}\approx{}&0.018395315697&{}:{}&-0.009170524006&{}:{}&0.990775208309&,\\ P^-_{\mathbf{3a}}&{}\approx{}&0.064906841236&{}:{}&0.110537082036&{}:{}&0.824556076729&,\\ P^-_{\mathbf{4a}}&{}\approx{}&0.670912547922&{}:{}&0.159300269295&{}:{}&0.169787182783&,\\ P^-_{\mathbf{5a}}&{}\approx{}&0.879465324005&{}:{}&0.073985475081&{}:{}&0.046549200915&,\\ P^-_{\mathbf{6a}}&{}\approx{}&0.934151405280&{}:{}&0.023778837094&{}:{}&0.042069757626&,\\ P^-_{\mathbf{7a}}&{}\approx{}&0.972508981335&{}:{}&0.011960761241&{}:{}&0.015530257423&,\\ P^-_{\mathbf{b}}&{}\approx{}&0.740357468020&{}:{}&-0.346067511513&{}:{}&0.605710043493&,\\ P^-_{\mathbf{1b}}&{}\approx{}&0.938648316351&{}:{}&-0.034371600845&{}:{}&0.095723284494&,\\ P^-_{\mathbf{2b}}&{}\approx{}&0.165976642650&{}:{}&0.679805302934&{}:{}&0.154218054416&,\\ P^-_{\mathbf{3b}}&{}\approx{}&0.100926923260&{}:{}&0.890047272047&{}:{}&0.009025804694&,\\ P^-_{\mathbf{4b}}&{}\approx{}&-0.005737313314&{}:{}&0.028914688887&{}:{}&0.976822624427&,\\ P^-_{\mathbf{5b}}&{}\approx{}&0.042234659609&{}:{}&0.071283904759&{}:{}&0.886481435632&,\\ P^-_{\mathbf{6b}}&{}\approx{}&0.015683682597&{}:{}&0.933711277759&{}:{}&0.050605039644&,\\ P^-_{\mathbf{7b}}&{}\approx{}&0.012619114489&{}:{}&0.963132629919&{}:{}&0.024248255592&,\\ P^-_{\mathbf{c}}&{}\approx{}&0.785034888947&{}:{}&0.800127390635&{}:{}&-0.585162279583&,\\ P^-_{\mathbf{1c}}&{}\approx{}&0.149186857990&{}:{}&0.104065420702&{}:{}&0.746747721308&,\\ P^-_{\mathbf{2c}}&{}\approx{}&0.918572418286&{}:{}&0.120609032192&{}:{}&-0.039181450478&,\\ P^-_{\mathbf{3c}}&{}\approx{}&0.110208259647&{}:{}&-0.076943583553&{}:{}&0.966735323906&,\\ P^-_{\mathbf{4c}}&{}\approx{}&0.042597657552&{}:{}&0.933255799293&{}:{}&0.024146543155&,\\ P^-_{\mathbf{5c}}&{}\approx{}&-0.023239415330&{}:{}&0.093442780710&{}:{}&0.929796634620&,\\ P^-_{\mathbf{6c}}&{}\approx{}&0.251941929525&{}:{}&0.615141147269&{}:{}&0.132916923205&,\\ P^-_{\mathbf{7c}}&{}\approx{}&0.016955824486&{}:{}&0.029678384686&{}:{}&0.953365790828&. \end{alignedat} \] \[ \begin{alignedat}{4} P^+&{}\approx{}&0.224836610348&{}:{}&0.313166892929&{}:{}&0.461996496723&,\\ P^+_{\mathbf{1}}&{}\approx{}&0.033120847037&{}:{}&0.045092102042&{}:{}&0.921787050921&,\\ P^+_{\mathbf{2}}&{}\approx{}&0.013372323027&{}:{}&0.963286171677&{}:{}&0.023341505296&,\\ P^+_{\mathbf{3}}&{}\approx{}&0.049626992282&{}:{}&0.757586397830&{}:{}&0.192786609888&,\\ P^+_{\mathbf{4}}&{}\approx{}&0.974583442003&{}:{}&0.011174582887&{}:{}&0.014241975110&,\\ P^+_{\mathbf{5}}&{}\approx{}&0.845714717145&{}:{}&0.050630126476&{}:{}&0.103655156379&,\\ P^+_{\mathbf{6}}&{}\approx{}&0.605705924598&{}:{}&0.267684106880&{}:{}&0.126609968522&,\\ P^+_{\mathbf{7}}&{}\approx{}&0.390534343609&{}:{}&0.303374547311&{}:{}&0.306091109080&,\\ P^+_{\mathbf{a}}&{}\approx{}&-0.318500755387&{}:{}&0.672296454641&{}:{}&0.646204300746&,\\ P^+_{\mathbf{1a}}&{}\approx{}&-0.102619985859&{}:{}&0.906085328697&{}:{}&0.196534657163&,\\ P^+_{\mathbf{2a}}&{}\approx{}&-0.041341264414&{}:{}&0.068708656728&{}:{}&0.972632607686&,\\ P^+_{\mathbf{3a}}&{}\approx{}&-0.069223141475&{}:{}&0.242583016208&{}:{}&0.826640125267&,\\ P^+_{\mathbf{4a}}&{}\approx{}&1.867314760466&{}:{}&-0.359111017238&{}:{}&-0.508203743228&,\\ P^+_{\mathbf{5a}}&{}\approx{}&1.283786511862&{}:{}&-0.099729339807&{}:{}&-0.184057172055&,\\ P^+_{\mathbf{6a}}&{}\approx{}&1.101398850039&{}:{}&-0.051193265829&{}:{}&-0.050205584211&,\\ P^+_{\mathbf{7a}}&{}\approx{}&1.035182349490&{}:{}&-0.015905027534&{}:{}&-0.019277321956&,\\ P^+_{\mathbf{b}}&{}\approx{}&0.743590502517&{}:{}&-0.565323853981&{}:{}&0.821733351463&,\\ P^+_{\mathbf{1b}}&{}\approx{}&0.895573639399&{}:{}&-0.254856639641&{}:{}&0.359283000241&,\\ P^+_{\mathbf{2b}}&{}\approx{}&-0.387595300582&{}:{}&2.272024302558&{}:{}&-0.884429001976&,\\ P^+_{\mathbf{3b}}&{}\approx{}&-0.154514739965&{}:{}&1.633872329725&{}:{}&-0.479357589761&,\\ P^+_{\mathbf{4b}}&{}\approx{}&0.061413458122&{}:{}&-0.062509161547&{}:{}&1.001095703425&,\\ P^+_{\mathbf{5b}}&{}\approx{}&0.150601952502&{}:{}&-0.092742404604&{}:{}&0.942140452101&,\\ P^+_{\mathbf{6b}}&{}\approx{}&-0.055567499415&{}:{}&1.121340520015&{}:{}&-0.065773020600&,\\ P^+_{\mathbf{7b}}&{}\approx{}&-0.023212791643&{}:{}&1.058528083615&{}:{}&-0.035315291972&,\\ P^+_{\mathbf{c}}&{}\approx{}&0.981936569052&{}:{}&1.130572791456&{}:{}&-1.112509360508&,\\ P^+_{\mathbf{1c}}&{}\approx{}&-0.671232574146&{}:{}&-1.047434755406&{}:{}&2.718667329552&,\\ P^+_{\mathbf{2c}}&{}\approx{}&1.014145045823&{}:{}&0.429535437838&{}:{}&-0.443680483662&,\\ P^+_{\mathbf{3c}}&{}\approx{}&-0.226215347855&{}:{}&-0.579704416467&{}:{}&1.805919764322&,\\ P^+_{\mathbf{4c}}&{}\approx{}&0.211290286782&{}:{}&1.056730202134&{}:{}&-0.268020488916&,\\ P^+_{\mathbf{5c}}&{}\approx{}&-0.249245273290&{}:{}&-0.189436650952&{}:{}&1.438681924242&,\\ P^+_{\mathbf{6c}}&{}\approx{}&0.451956918310&{}:{}&0.837079961216&{}:{}&-0.289036879526&,\\ P^+_{\mathbf{7c}}&{}\approx{}&-0.083635975130&{}:{}&-0.103964429452&{}:{}&1.187600404583&. \end{alignedat} \] \[ \begin{alignedat}{4} Q&{}\approx{}&0.199711799657&{}:{}&0.290524035034&{}:{}&0.509764165309&,\\ Q_{\mathbf{1}}&{}\approx{}&-0.080500144965&{}:{}&-0.117104883017&{}:{}&1.197605027981&,\\ Q_{\mathbf{2}}&{}\approx{}&-0.044343286406&{}:{}&1.157529479812&{}:{}&-0.113186193407&,\\ Q_{\mathbf{3}}&{}\approx{}&-0.025011954860&{}:{}&0.652907744206&{}:{}&0.372104210653&,\\ Q_{\mathbf{4}}&{}\approx{}&1.117975688967&{}:{}&-0.042828037674&{}:{}&-0.075147651292&,\\ Q_{\mathbf{5}}&{}\approx{}&0.738844717962&{}:{}&-0.028304076492&{}:{}&0.289459358529&,\\ Q_{\mathbf{6}}&{}\approx{}&0.617207145668&{}:{}&0.424280042126&{}:{}&-0.041487187795&,\\ Q_{\mathbf{7}}&{}\approx{}&0.480956034150&{}:{}&0.330618412088&{}:{}&0.188425553762&,\\ Q_{\mathbf{a}}&{}\approx{}&-0.186532501706&{}:{}&0.710408481001&{}:{}&0.476124020704&,\\ Q_{\mathbf{1a}}&{}\approx{}&0.118789171705&{}:{}&1.184420068139&{}:{}&-0.303209239844&,\\ Q_{\mathbf{2a}}&{}\approx{}&0.082859945762&{}:{}&-0.315571858341&{}:{}&1.232711912580&,\\ Q_{\mathbf{3a}}&{}\approx{}&0.038687968720&{}:{}&0.385749019792&{}:{}&0.575563011488&,\\ Q_{\mathbf{4a}}&{}\approx{}&2.893047208112&{}:{}&-0.759629632407&{}:{}&-1.133417575705&,\\ Q_{\mathbf{5a}}&{}\approx{}&1.411392400725&{}:{}&0.141552932733&{}:{}&-0.552945333458&,\\ Q_{\mathbf{6a}}&{}\approx{}&1.242781246185&{}:{}&-0.326318028463&{}:{}&0.083536782278&,\\ Q_{\mathbf{7a}}&{}\approx{}&0.856523186617&{}:{}&0.085903373829&{}:{}&0.057573439554&,\\ Q_{\mathbf{b}}&{}\approx{}&0.801819298444&{}:{}&-0.262617327447&{}:{}&0.460798029003&,\\ Q_{\mathbf{1b}}&{}\approx{}&1.147315378081&{}:{}&0.195213613534&{}:{}&-0.342528991616&,\\ Q_{\mathbf{2b}}&{}\approx{}&-3.193680423844&{}:{}&9.750897329564&{}:{}&-5.557216905720&,\\ Q_{\mathbf{3b}}&{}\approx{}&0.283471782768&{}:{}&1.666028970695&{}:{}&-0.949500753464&,\\ Q_{\mathbf{4b}}&{}\approx{}&-0.373542825939&{}:{}&0.122345295038&{}:{}&1.251197530901&,\\ Q_{\mathbf{5b}}&{}\approx{}&0.343617241206&{}:{}&0.058465845233&{}:{}&0.597916913561&,\\ Q_{\mathbf{6b}}&{}\approx{}&-0.425218285517&{}:{}&1.298270112994&{}:{}&0.126948172523&,\\ Q_{\mathbf{7b}}&{}\approx{}&0.134193585987&{}:{}&0.788686619007&{}:{}&0.077119795006&,\\ Q_{\mathbf{c}}&{}\approx{}&0.779553414178&{}:{}&0.668448620013&{}:{}&-0.448002034191&,\\ Q_{\mathbf{1c}}&{}\approx{}&2.346612327186&{}:{}&2.736649604236&{}:{}&-4.083261931422&,\\ Q_{\mathbf{2c}}&{}\approx{}&1.172203012917&{}:{}&-0.522162164214&{}:{}&0.349959151297&,\\ Q_{\mathbf{3c}}&{}\approx{}&0.475140607557&{}:{}&-1.066644214975&{}:{}&1.591503607418&,\\ Q_{\mathbf{4c}}&{}\approx{}&-0.549573490654&{}:{}&1.233738761087&{}:{}&0.315834729567&,\\ Q_{\mathbf{5c}}&{}\approx{}&-0.843511437593&{}:{}&0.375745287241&{}:{}&1.467766150353&,\\ Q_{\mathbf{6c}}&{}\approx{}&0.405718824309&{}:{}&0.473154533074&{}:{}&0.121126642617&,\\ Q_{\mathbf{7c}}&{}\approx{}&0.192048473131&{}:{}&0.164677024698&{}:{}&0.643274502171&. \end{alignedat} \] \[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.233970657965&{}:{}&0.320895389436&{}:{}&0.445133952599&,\\ I^\prime_{\mathbf{1}}&{}\approx{}&0.074292983178&{}:{}&0.101894297245&{}:{}&0.823812719577&,\\ I^\prime_{\mathbf{2}}&{}\approx{}&0.036345867083&{}:{}&0.894505378899&{}:{}&0.069148754018&,\\ I^\prime_{\mathbf{3}}&{}\approx{}&0.027248234267&{}:{}&0.670604227497&{}:{}&0.302147538235&,\\ I^\prime_{\mathbf{4}}&{}\approx{}&0.920624914364&{}:{}&0.033250813799&{}:{}&0.046124271837&,\\ I^\prime_{\mathbf{5}}&{}\approx{}&0.752939500973&{}:{}&0.027194409752&{}:{}&0.219866089275&,\\ I^\prime_{\mathbf{6}}&{}\approx{}&0.588856682171&{}:{}&0.381640981690&{}:{}&0.029502336139&,\\ I^\prime_{\mathbf{7}}&{}\approx{}&0.515433274099&{}:{}&0.334054901097&{}:{}&0.150511824804&,\\ I^\prime_{\mathbf{a}}&{}\approx{}&-0.370663725296&{}:{}&0.665468421915&{}:{}&0.705195303382&,\\ I^\prime_{\mathbf{1a}}&{}\approx{}&-0.178482548008&{}:{}&0.838915857229&{}:{}&0.339566690779&,\\ I^\prime_{\mathbf{2a}}&{}\approx{}&-0.084146438277&{}:{}&0.151071695632&{}:{}&0.933074742645&,\\ I^\prime_{\mathbf{3a}}&{}\approx{}&-0.067617961931&{}:{}&0.317822560974&{}:{}&0.749795400956&,\\ I^\prime_{\mathbf{4a}}&{}\approx{}&1.711705482154&{}:{}&-0.211869851448&{}:{}&-0.499835630705&,\\ I^\prime_{\mathbf{5a}}&{}\approx{}&1.513520868154&{}:{}&-0.071557185962&{}:{}&-0.441963682191&,\\ I^\prime_{\mathbf{6a}}&{}\approx{}&1.210475104788&{}:{}&-0.149829035022&{}:{}&-0.060646069766&,\\ I^\prime_{\mathbf{7a}}&{}\approx{}&1.107885529448&{}:{}&-0.052379304788&{}:{}&-0.055506224660&,\\ I^\prime_{\mathbf{b}}&{}\approx{}&0.736018478900&{}:{}&-0.681837030797&{}:{}&0.945818551897&,\\ I^\prime_{\mathbf{1b}}&{}\approx{}&0.842941130372&{}:{}&-0.405666854564&{}:{}&0.562725724193&,\\ I^\prime_{\mathbf{2b}}&{}\approx{}&-0.267036670875&{}:{}&2.306051627355&{}:{}&-1.039014956480&,\\ I^\prime_{\mathbf{3b}}&{}\approx{}&-0.122948098990&{}:{}&2.043805322007&{}:{}&-0.920857223017&,\\ I^\prime_{\mathbf{4b}}&{}\approx{}&0.132215342733&{}:{}&-0.122482409476&{}:{}&0.990267066744&,\\ I^\prime_{\mathbf{5b}}&{}\approx{}&0.226775075125&{}:{}&-0.109135891114&{}:{}&0.882360815989&,\\ I^\prime_{\mathbf{6b}}&{}\approx{}&-0.143510376500&{}:{}&1.239314196762&{}:{}&-0.095803820262&,\\ I^\prime_{\mathbf{7b}}&{}\approx{}&-0.069743418466&{}:{}&1.159367009379&{}:{}&-0.089623590914&,\\ I^\prime_{\mathbf{c}}&{}\approx{}&1.078042283606&{}:{}&1.307293031736&{}:{}&-1.385335315343&,\\ I^\prime_{\mathbf{1c}}&{}\approx{}&-0.805390790266&{}:{}&-1.328310188544&{}:{}&3.133700978809&,\\ I^\prime_{\mathbf{2c}}&{}\approx{}&1.039077103195&{}:{}&0.654583929966&{}:{}&-0.693661033161&,\\ I^\prime_{\mathbf{3c}}&{}\approx{}&-0.301656096168&{}:{}&-0.957689085290&{}:{}&2.259345181458&,\\ I^\prime_{\mathbf{4c}}&{}\approx{}&0.346053821241&{}:{}&1.098641704032&{}:{}&-0.444695525273&,\\ I^\prime_{\mathbf{5c}}&{}\approx{}&-0.442293769655&{}:{}&-0.278630327865&{}:{}&1.720924097520&,\\ I^\prime_{\mathbf{6c}}&{}\approx{}&0.504617259636&{}:{}&0.832252187871&{}:{}&-0.336869447506&,\\ I^\prime_{\mathbf{7c}}&{}\approx{}&-0.189496231731&{}:{}&-0.229793494234&{}:{}&1.419289725966&. \end{alignedat} \]

Central Triangles and their Extraversions

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.436000484963&{}:{}&0.250666451128&{}:{}&0.313333063909&,\\B^\prime&{}\approx{}&0.166223547185&{}:{}&0.556737207507&{}:{}&0.277039245308&,\\C^\prime&{}\approx{}&0.126983490588&{}:{}&0.169311320784&{}:{}&0.703705188628&,\\[.5em] A^\prime_{\mathbf{1}}&{}\approx{}&-0.167552905630&{}:{}&0.518912402502&{}:{}&0.648640503128&,\\B^\prime_{\mathbf{1}}&{}\approx{}&0.468000242482&{}:{}&-0.248000646617&{}:{}&0.780000404136&,\\C^\prime_{\mathbf{1}}&{}\approx{}&0.023430099995&{}:{}&0.031240133326&{}:{}&0.945329766679&,\\[.5em] A^\prime_{\mathbf{2}}&{}\approx{}&-0.373016509412&{}:{}&0.610229559739&{}:{}&0.762786949673&,\\B^\prime_{\mathbf{2}}&{}\approx{}&0.011715049997&{}:{}&0.968759866674&{}:{}&0.019525083329&,\\C^\prime_{\mathbf{2}}&{}\approx{}&0.936000484963&{}:{}&1.248000646617&{}:{}&-1.184001131580&,\\[.5em] A^\prime_{\mathbf{3}}&{}\approx{}&-0.476569900005&{}:{}&0.656253288891&{}:{}&0.820316611114&,\\B^\prime_{\mathbf{3}}&{}\approx{}&0.063491745294&{}:{}&0.830688679216&{}:{}&0.105819575490&,\\C^\prime_{\mathbf{3}}&{}\approx{}&0.332447094370&{}:{}&0.443262792493&{}:{}&0.224290113137&,\\[.5em] A^\prime_{\mathbf{4}}&{}\approx{}&0.976569900005&{}:{}&0.010413377775&{}:{}&0.013016722219&,\\B^\prime_{\mathbf{4}}&{}\approx{}&0.686508254706&{}:{}&-0.830688679216&{}:{}&1.144180424510&,\\C^\prime_{\mathbf{4}}&{}\approx{}&1.167552905630&{}:{}&1.556737207507&{}:{}&-1.724290113137&,\\[.5em] A^\prime_{\mathbf{5}}&{}\approx{}&0.873016509412&{}:{}&0.056437106928&{}:{}&0.070546383660&,\\B^\prime_{\mathbf{5}}&{}\approx{}&0.738284950003&{}:{}&-0.968759866674&{}:{}&1.230474916671&,\\C^\prime_{\mathbf{5}}&{}\approx{}&0.563999515037&{}:{}&0.751999353383&{}:{}&-0.315998868420&,\\[.5em] A^\prime_{\mathbf{6}}&{}\approx{}&0.667552905630&{}:{}&0.147754264164&{}:{}&0.184692830205&,\\B^\prime_{\mathbf{6}}&{}\approx{}&0.281999757518&{}:{}&0.248000646617&{}:{}&0.469999595864&,\\C^\prime_{\mathbf{6}}&{}\approx{}&1.476569900005&{}:{}&1.968759866674&{}:{}&-2.445329766679&,\\[.5em] A^\prime_{\mathbf{7}}&{}\approx{}&0.063999515037&{}:{}&0.416000215539&{}:{}&0.520000269424&,\\B^\prime_{\mathbf{7}}&{}\approx{}&0.583776452815&{}:{}&-0.556737207507&{}:{}&0.972960754692&,\\C^\prime_{\mathbf{7}}&{}\approx{}&1.373016509412&{}:{}&1.830688679216&{}:{}&-2.203705188628&,\\[.5em] A^\prime_{\mathbf{a}}&{}\approx{}&-1.048631302823&{}:{}&0.910502801255&{}:{}&1.138128501568&,\\B^\prime_{\mathbf{a}}&{}\approx{}&-0.183049043273&{}:{}&0.877967304485&{}:{}&0.305081738788&,\\C^\prime_{\mathbf{a}}&{}\approx{}&-0.239614308448&{}:{}&0.319485744597&{}:{}&0.920128563851&,\\[.5em] A^\prime_{\mathbf{1a}}&{}\approx{}&0.010385691552&{}:{}&0.439828581532&{}:{}&0.549785726915&,\\B^\prime_{\mathbf{1a}}&{}\approx{}&-0.065015054523&{}:{}&0.956656630318&{}:{}&0.108358424204&,\\C^\prime_{\mathbf{1a}}&{}\approx{}&-1.298631302823&{}:{}&1.731508403764&{}:{}&0.567122899059&,\\[.5em] A^\prime_{\mathbf{2a}}&{}\approx{}&0.158475478364&{}:{}&0.374010898505&{}:{}&0.467513623131&,\\B^\prime_{\mathbf{2a}}&{}\approx{}&-2.597262605646&{}:{}&-0.731508403764&{}:{}&4.328771009409&,\\C^\prime_{\mathbf{2a}}&{}\approx{}&-0.032507527261&{}:{}&0.043343369682&{}:{}&0.989164157580&,\\[.5em] A^\prime_{\mathbf{3a}}&{}\approx{}&0.217492472739&{}:{}&0.347781123227&{}:{}&0.434726404034&,\\B^\prime_{\mathbf{3a}}&{}\approx{}&-0.479228616896&{}:{}&0.680514255403&{}:{}&0.798714361493&,\\C^\prime_{\mathbf{3a}}&{}\approx{}&-0.091524521636&{}:{}&0.122032695515&{}:{}&0.969491826121&,\\[.5em] A^\prime_{\mathbf{4a}}&{}\approx{}&2.298631302823&{}:{}&-0.577169467921&{}:{}&-0.721461834902&,\\B^\prime_{\mathbf{4a}}&{}\approx{}&1.683049043273&{}:{}&2.122032695515&{}:{}&-2.805081738788&,\\C^\prime_{\mathbf{4a}}&{}\approx{}&0.989614308448&{}:{}&-1.319485744597&{}:{}&1.329871436149&,\\[.5em] A^\prime_{\mathbf{5a}}&{}\approx{}&1.239614308448&{}:{}&-0.106495248199&{}:{}&-0.133119060249&,\\B^\prime_{\mathbf{5a}}&{}\approx{}&1.565015054523&{}:{}&2.043343369682&{}:{}&-2.608358424204&,\\C^\prime_{\mathbf{5a}}&{}\approx{}&2.048631302823&{}:{}&-2.731508403764&{}:{}&1.682877100941&,\\[.5em] A^\prime_{\mathbf{6a}}&{}\approx{}&1.091524521636&{}:{}&-0.040677565172&{}:{}&-0.050846956465&,\\B^\prime_{\mathbf{6a}}&{}\approx{}&4.097262605646&{}:{}&3.731508403764&{}:{}&-6.828771009409&,\\C^\prime_{\mathbf{6a}}&{}\approx{}&0.782507527261&{}:{}&-1.043343369682&{}:{}&1.260835842420&,\\[.5em] A^\prime_{\mathbf{7a}}&{}\approx{}&1.032507527261&{}:{}&-0.014447789894&{}:{}&-0.018059737367&,\\B^\prime_{\mathbf{7a}}&{}\approx{}&1.979228616896&{}:{}&2.319485744597&{}:{}&-3.298714361493&,\\C^\prime_{\mathbf{7a}}&{}\approx{}&0.841524521636&{}:{}&-1.122032695515&{}:{}&1.280508173879&,\\[.5em] A^\prime_{\mathbf{b}}&{}\approx{}&0.921519886806&{}:{}&-0.313920452774&{}:{}&0.392400565968&,\\B^\prime_{\mathbf{b}}&{}\approx{}&1.194570142487&{}:{}&-2.185520379965&{}:{}&1.990950237478&,\\C^\prime_{\mathbf{b}}&{}\approx{}&0.348570869931&{}:{}&-0.464761159908&{}:{}&1.116190289977&,\\[.5em] A^\prime_{\mathbf{1b}}&{}\approx{}&0.962089301849&{}:{}&-0.151642792606&{}:{}&0.189553490757&,\\B^\prime_{\mathbf{1b}}&{}\approx{}&0.424285434966&{}:{}&-0.131427826575&{}:{}&0.707142391609&,\\C^\prime_{\mathbf{1b}}&{}\approx{}&1.889140284973&{}:{}&-2.518853713298&{}:{}&1.629713428324&,\\[.5em] A^\prime_{\mathbf{2b}}&{}\approx{}&1.578480113194&{}:{}&2.313920452774&{}:{}&-2.892400565968&,\\B^\prime_{\mathbf{2b}}&{}\approx{}&-0.944570142487&{}:{}&3.518853713298&{}:{}&-1.574283570811&,\\C^\prime_{\mathbf{2b}}&{}\approx{}&-0.848570869931&{}:{}&1.131427826575&{}:{}&0.717143043356&,\\[.5em] A^\prime_{\mathbf{3b}}&{}\approx{}&1.537910698151&{}:{}&2.151642792606&{}:{}&-2.689553490757&,\\B^\prime_{\mathbf{3b}}&{}\approx{}&-0.174285434966&{}:{}&1.464761159908&{}:{}&-0.290475724943&,\\C^\prime_{\mathbf{3b}}&{}\approx{}&-2.389140284973&{}:{}&3.185520379965&{}:{}&0.203619905009&,\\[.5em] A^\prime_{\mathbf{4b}}&{}\approx{}&-0.889140284973&{}:{}&-7.556561139894&{}:{}&9.445701424867&,\\B^\prime_{\mathbf{4b}}&{}\approx{}&0.289240056597&{}:{}&0.228693182409&{}:{}&0.482066760995&,\\C^\prime_{\mathbf{4b}}&{}\approx{}&0.037910698151&{}:{}&-0.050547597535&{}:{}&1.012636899384&,\\[.5em] A^\prime_{\mathbf{5b}}&{}\approx{}&0.651429130069&{}:{}&-1.394283479725&{}:{}&1.742854349656&,\\B^\prime_{\mathbf{5b}}&{}\approx{}&0.268955349076&{}:{}&0.282785735798&{}:{}&0.448258915126&,\\C^\prime_{\mathbf{5b}}&{}\approx{}&0.078480113194&{}:{}&-0.104640150925&{}:{}&1.026160037731&,\\[.5em] A^\prime_{\mathbf{6b}}&{}\approx{}&3.389140284973&{}:{}&9.556561139893&{}:{}&-11.945701424867&,\\B^\prime_{\mathbf{6b}}&{}\approx{}&-0.039240056597&{}:{}&1.104640150925&{}:{}&-0.065400094328&,\\C^\prime_{\mathbf{6b}}&{}\approx{}&-0.537910698151&{}:{}&0.717214264202&{}:{}&0.820696433950&,\\[.5em] A^\prime_{\mathbf{7b}}&{}\approx{}&1.848570869931&{}:{}&3.394283479725&{}:{}&-4.242854349656&,\\B^\prime_{\mathbf{7b}}&{}\approx{}&-0.018955349076&{}:{}&1.050547597535&{}:{}&-0.031592248460&,\\C^\prime_{\mathbf{7b}}&{}\approx{}&-0.578480113194&{}:{}&0.771306817591&{}:{}&0.807173295602&,\\[.5em] A^\prime_{\mathbf{c}}&{}\approx{}&1.137704095259&{}:{}&0.550816381038&{}:{}&-0.688520476297&,\\B^\prime_{\mathbf{c}}&{}\approx{}&0.467232496600&{}:{}&1.311488331067&{}:{}&-0.778720827667&,\\C^\prime_{\mathbf{c}}&{}\approx{}&3.564755078384&{}:{}&4.753006771179&{}:{}&-7.317761849563&,\\[.5em] A^\prime_{\mathbf{1c}}&{}\approx{}&0.612295904741&{}:{}&-1.550816381038&{}:{}&1.938520476297&,\\B^\prime_{\mathbf{1c}}&{}\approx{}&-0.967232496600&{}:{}&0.355178335600&{}:{}&1.612054161000&,\\C^\prime_{\mathbf{1c}}&{}\approx{}&-3.314755078384&{}:{}&-4.419673437846&{}:{}&8.734428516230&,\\[.5em] A^\prime_{\mathbf{2c}}&{}\approx{}&1.056565265175&{}:{}&0.226261060701&{}:{}&-0.282826325877&,\\B^\prime_{\mathbf{2c}}&{}\approx{}&6.629510156769&{}:{}&5.419673437846&{}:{}&-11.049183594614&,\\C^\prime_{\mathbf{2c}}&{}\approx{}&0.483616248300&{}:{}&0.644821664400&{}:{}&-0.128437912700&,\\[.5em] A^\prime_{\mathbf{3c}}&{}\approx{}&0.693434734825&{}:{}&-1.226261060701&{}:{}&1.532826325877&,\\B^\prime_{\mathbf{3c}}&{}\approx{}&-7.129510156769&{}:{}&-3.753006771179&{}:{}&11.882516927948&,\\C^\prime_{\mathbf{3c}}&{}\approx{}&-0.233616248300&{}:{}&-0.311488331067&{}:{}&1.545104579367&,\\[.5em] A^\prime_{\mathbf{4c}}&{}\approx{}&4.314755078384&{}:{}&13.259020313537&{}:{}&-16.573775391922&,\\B^\prime_{\mathbf{4c}}&{}\approx{}&0.113130530351&{}:{}&1.075420353567&{}:{}&-0.188550883918&,\\C^\prime_{\mathbf{4c}}&{}\approx{}&0.387704095259&{}:{}&0.516938793679&{}:{}&0.095357111061&,\\[.5em] A^\prime_{\mathbf{5c}}&{}\approx{}&-2.564755078384&{}:{}&-14.259020313537&{}:{}&17.823775391922&,\\B^\prime_{\mathbf{5c}}&{}\approx{}&-0.613130530351&{}:{}&0.591246313100&{}:{}&1.021884217251&,\\C^\prime_{\mathbf{5c}}&{}\approx{}&-0.137704095259&{}:{}&-0.183605460346&{}:{}&1.321309555605&,\\[.5em] A^\prime_{\mathbf{6c}}&{}\approx{}&1.233616248300&{}:{}&0.934464993201&{}:{}&-1.168081241501&,\\B^\prime_{\mathbf{6c}}&{}\approx{}&0.275408190519&{}:{}&1.183605460346&{}:{}&-0.459013650865&,\\C^\prime_{\mathbf{6c}}&{}\approx{}&0.306565265175&{}:{}&0.408753686900&{}:{}&0.284681047924&,\\[.5em] A^\prime_{\mathbf{7c}}&{}\approx{}&0.516383751700&{}:{}&-1.934464993201&{}:{}&2.418081241501&,\\B^\prime_{\mathbf{7c}}&{}\approx{}&-0.775408190519&{}:{}&0.483061206321&{}:{}&1.292346984198&,\\C^\prime_{\mathbf{7c}}&{}\approx{}&-0.056565265175&{}:{}&-0.075420353567&{}:{}&1.131985618742&. \end{alignedat} \] \[ \begin{alignedat}{4} A^{\prime\prime}&{}\approx{}&0.143977759878&{}:{}&0.337099556066&{}:{}&0.518922684056&,\\B^{\prime\prime}&{}\approx{}&0.251561692011&{}:{}&0.202109115078&{}:{}&0.546329192911&,\\C^{\prime\prime}&{}\approx{}&0.292819591879&{}:{}&0.413109855691&{}:{}&0.294070552430&,\\[.5em] A^{\prime\prime}_{\mathbf{1}}&{}\approx{}&0.044626029495&{}:{}&0.017926670906&{}:{}&0.937447299599&,\\B^{\prime\prime}_{\mathbf{1}}&{}\approx{}&0.012585226673&{}:{}&0.058932356331&{}:{}&0.928482416996&,\\C^{\prime\prime}_{\mathbf{1}}&{}\approx{}&0.121004919965&{}:{}&0.170713730949&{}:{}&0.708281349087&,\\[.5em] A^{\prime\prime}_{\mathbf{2}}&{}\approx{}&0.023140472166&{}:{}&0.972211661624&{}:{}&0.004647866210&,\\B^{\prime\prime}_{\mathbf{2}}&{}\approx{}&0.056855344697&{}:{}&0.819669040503&{}:{}&0.123475614800&,\\C^{\prime\prime}_{\mathbf{2}}&{}\approx{}&0.002112851079&{}:{}&0.959811603291&{}:{}&0.038075545630&,\\[.5em] A^{\prime\prime}_{\mathbf{3}}&{}\approx{}&0.106620741008&{}:{}&0.768562049403&{}:{}&0.124817209588&,\\B^{\prime\prime}_{\mathbf{3}}&{}\approx{}&0.006297128787&{}:{}&0.529128532709&{}:{}&0.464574338503&,\\C^{\prime\prime}_{\mathbf{3}}&{}\approx{}&0.001784736249&{}:{}&0.810757831872&{}:{}&0.187457431879&,\\[.5em] A^{\prime\prime}_{\mathbf{4}}&{}\approx{}&0.864625962367&{}:{}&0.053309979403&{}:{}&0.082064058231&,\\B^{\prime\prime}_{\mathbf{4}}&{}\approx{}&0.977838940903&{}:{}&0.020688366250&{}:{}&0.001472692846&,\\C^{\prime\prime}_{\mathbf{4}}&{}\approx{}&0.973307144066&{}:{}&0.000952248473&{}:{}&0.025740607461&,\\[.5em] A^{\prime\prime}_{\mathbf{5}}&{}\approx{}&0.639479875463&{}:{}&0.006764812343&{}:{}&0.353755312194&,\\B^{\prime\prime}_{\mathbf{5}}&{}\approx{}&0.851443972781&{}:{}&0.104994442978&{}:{}&0.043561584241&,\\C^{\prime\prime}_{\mathbf{5}}&{}\approx{}&0.865710845562&{}:{}&0.000846980150&{}:{}&0.133442174288&,\\[.5em] A^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.473557987287&{}:{}&0.523937218551&{}:{}&0.002504794162&,\\B^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.724030539754&{}:{}&0.274879020346&{}:{}&0.001090439899&,\\C^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.558785949906&{}:{}&0.176034395957&{}:{}&0.265179654137&,\\[.5em] A^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.819233023619&{}:{}&0.155511375973&{}:{}&0.025255600408&,\\B^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.306379024312&{}:{}&0.677946009273&{}:{}&0.015674966415&,\\C^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.245038499524&{}:{}&0.077194504009&{}:{}&0.677766996467&,\\[.5em] A^{\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.207546595830&{}:{}&0.636097469292&{}:{}&0.571449126538&,\\B^{\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.449753986343&{}:{}&0.473000608660&{}:{}&0.976753377682&,\\C^{\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.366025392403&{}:{}&0.884845017551&{}:{}&0.481180374852&,\\[.5em] A^{\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.123830617085&{}:{}&0.993599515126&{}:{}&0.130231101959&,\\B^{\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.254770335235&{}:{}&0.701472770276&{}:{}&0.553297564960&,\\C^{\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.052600895687&{}:{}&0.871564826561&{}:{}&0.181036069127&,\\[.5em] A^{\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.064211380228&{}:{}&0.033765150341&{}:{}&1.030446229887&,\\B^{\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.012673425524&{}:{}&0.077684086996&{}:{}&0.934989338528&,\\C^{\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.110137665926&{}:{}&0.266251377534&{}:{}&0.843886288393&,\\[.5em] A^{\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.153695764262&{}:{}&0.211589378012&{}:{}&0.942106386250&,\\B^{\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.011258307065&{}:{}&0.180670155809&{}:{}&0.830588151256&,\\C^{\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.028066991791&{}:{}&0.465052971294&{}:{}&0.563014020497&,\\[.5em] A^{\prime\prime}_{\mathbf{4a}}&{}\approx{}&1.246374268551&{}:{}&-0.045185377164&{}:{}&-0.201188891387&,\\B^{\prime\prime}_{\mathbf{4a}}&{}\approx{}&1.900285500615&{}:{}&-0.803063076633&{}:{}&-0.097222423981&,\\C^{\prime\prime}_{\mathbf{4a}}&{}\approx{}&2.172695213497&{}:{}&-0.024965502505&{}:{}&-1.147729710992&,\\[.5em] A^{\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.774461866512&{}:{}&-0.024572018155&{}:{}&-0.749889848356&,\\B^{\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.269972432037&{}:{}&-0.204998090975&{}:{}&-0.064974341062&,\\C^{\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.255414927555&{}:{}&-0.002104641994&{}:{}&-0.253310285560&,\\[.5em] A^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.314053220853&{}:{}&-0.277660283693&{}:{}&-0.036392937160&,\\B^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.079928750260&{}:{}&-0.078302303124&{}:{}&-0.001626447136&,\\C^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.113739800778&{}:{}&-0.012797503126&{}:{}&-0.100942297652&,\\[.5em] A^{\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.180939510296&{}:{}&-0.095313228485&{}:{}&-0.085626281811&,\\B^{\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.030079608459&{}:{}&-0.028528237567&{}:{}&-0.001551370893&,\\C^{\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.037662395736&{}:{}&-0.001739590478&{}:{}&-0.035922805258&,\\[.5em] A^{\prime\prime}_{\mathbf{b}}&{}\approx{}&0.539668572619&{}:{}&-0.853453141685&{}:{}&1.313784569066&,\\B^{\prime\prime}_{\mathbf{b}}&{}\approx{}&0.690539198596&{}:{}&-0.374730907662&{}:{}&0.684191709066&,\\C^{\prime\prime}_{\mathbf{b}}&{}\approx{}&0.966475532745&{}:{}&-0.622065132791&{}:{}&0.655589600046&,\\[.5em] A^{\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.692941814049&{}:{}&-0.569284993142&{}:{}&0.876343179093&,\\B^{\prime\prime}_{\mathbf{1b}}&{}\approx{}&1.014731422764&{}:{}&-0.286063666742&{}:{}&0.271332243978&,\\C^{\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.848402373744&{}:{}&-0.147369529561&{}:{}&0.298967155817&,\\[.5em] A^{\prime\prime}_{\mathbf{2b}}&{}\approx{}&-0.894000752836&{}:{}&2.261233038526&{}:{}&-0.367232285690&,\\B^{\prime\prime}_{\mathbf{2b}}&{}\approx{}&-0.051544619992&{}:{}&1.519749979671&{}:{}&-0.468205359679&,\\C^{\prime\prime}_{\mathbf{2b}}&{}\approx{}&-0.055320658033&{}:{}&3.094174784169&{}:{}&-2.038854126136&,\\[.5em] A^{\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.324871792088&{}:{}&1.581754317465&{}:{}&-0.256882525377&,\\B^{\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.045254491075&{}:{}&2.568443851024&{}:{}&-1.523189359949&,\\C^{\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.007390623871&{}:{}&1.531714342500&{}:{}&-0.524323718629&,\\[.5em] A^{\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.067035104274&{}:{}&-0.018188775902&{}:{}&0.951153671628&,\\B^{\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.031750644233&{}:{}&-0.100423439295&{}:{}&1.068672795062&,\\C^{\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.232020953184&{}:{}&-0.149338643517&{}:{}&0.917317690333&,\\[.5em] A^{\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.121505422052&{}:{}&-0.017126840552&{}:{}&0.895621418500&,\\B^{\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.118477795779&{}:{}&-0.194670403171&{}:{}&1.076192607392&,\\C^{\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.347202003362&{}:{}&-0.060309821709&{}:{}&0.713107818347&,\\[.5em] A^{\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.073144307846&{}:{}&1.078299348982&{}:{}&-0.005155041136&,\\B^{\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.263762503300&{}:{}&1.334290793143&{}:{}&-0.070528289843&,\\C^{\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.020572626522&{}:{}&1.150660612000&{}:{}&-0.130087985478&,\\[.5em] A^{\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.036707872805&{}:{}&1.041687884990&{}:{}&-0.004980012186&,\\B^{\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.129083788468&{}:{}&1.256981028805&{}:{}&-0.127897240337&,\\C^{\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.005152544207&{}:{}&1.067870047264&{}:{}&-0.062717503057&,\\[.5em] A^{\prime\prime}_{\mathbf{c}}&{}\approx{}&0.826177851031&{}:{}&1.710296418385&{}:{}&-1.536474269416&,\\B^{\prime\prime}_{\mathbf{c}}&{}\approx{}&1.389759904956&{}:{}&0.987225219851&{}:{}&-1.376985124807&,\\C^{\prime\prime}_{\mathbf{c}}&{}\approx{}&0.823077303330&{}:{}&0.907770763337&{}:{}&-0.730848066667&,\\[.5em] A^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-1.497500295804&{}:{}&-0.723384299357&{}:{}&3.220884595161&,\\B^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.407743518916&{}:{}&-2.295993184536&{}:{}&3.703736703452&,\\C^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.250085107259&{}:{}&-0.510193337347&{}:{}&1.760278444606&,\\[.5em] A^{\prime\prime}_{\mathbf{2c}}&{}\approx{}&0.901471068418&{}:{}&0.969460335128&{}:{}&-0.870931403546&,\\B^{\prime\prime}_{\mathbf{2c}}&{}\approx{}&0.907743518916&{}:{}&0.334980891128&{}:{}&-0.242724410044&,\\C^{\prime\prime}_{\mathbf{2c}}&{}\approx{}&1.195655818313&{}:{}&0.355879173613&{}:{}&-0.551534991926&,\\[.5em] A^{\prime\prime}_{\mathbf{3c}}&{}\approx{}&-0.452408209071&{}:{}&-0.420680348452&{}:{}&1.873088557524&,\\B^{\prime\prime}_{\mathbf{3c}}&{}\approx{}&-0.045831707403&{}:{}&-0.496785774450&{}:{}&1.542617481854&,\\C^{\prime\prime}_{\mathbf{3c}}&{}\approx{}&-0.200408653961&{}:{}&-1.514964992501&{}:{}&2.715373646461&,\\[.5em] A^{\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.175152306462&{}:{}&0.949268302909&{}:{}&-0.124420609371&,\\B^{\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.535065522666&{}:{}&0.995081636481&{}:{}&-0.530147159147&,\\C^{\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.160392468186&{}:{}&1.212467473636&{}:{}&-0.372859941821&,\\[.5em] A^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.224897952433&{}:{}&-0.041496587389&{}:{}&1.266394539822&,\\B^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.168558582526&{}:{}&-0.362542660834&{}:{}&1.531101243361&,\\C^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.718955126836&{}:{}&-0.213992314916&{}:{}&1.932947441751&,\\[.5em] A^{\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.290152700718&{}:{}&0.816921167863&{}:{}&-0.107073868581&,\\B^{\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.588675328794&{}:{}&0.568732428917&{}:{}&-0.157407757711&,\\C^{\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.545724679713&{}:{}&1.113321375540&{}:{}&-0.659046055253&,\\[.5em] A^{\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.105438868549&{}:{}&-0.037449601839&{}:{}&1.142888470388&,\\B^{\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.035065522666&{}:{}&-0.145180454184&{}:{}&1.180245976850&,\\C^{\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.325475374362&{}:{}&-0.358966318031&{}:{}&1.684441692393&. \end{alignedat} \] \[ \begin{alignedat}{4} A^{\prime\prime\prime}&{}\approx{}&0.101101661394&{}:{}&0.338622641568&{}:{}&0.560275697038&,\\B^{\prime\prime\prime}&{}\approx{}&0.252241117390&{}:{}&0.145019072008&{}:{}&0.602739810602&,\\C^{\prime\prime\prime}&{}\approx{}&0.316169953677&{}:{}&0.456613555245&{}:{}&0.227216491078&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1}}&{}\approx{}&0.024499659832&{}:{}&-0.012982752846&{}:{}&0.988483093015&,\\B^{\prime\prime\prime}_{\mathbf{1}}&{}\approx{}&-0.010437024633&{}:{}&0.032323530929&{}:{}&0.978113493704&,\\C^{\prime\prime\prime}_{\mathbf{1}}&{}\approx{}&-0.609609710931&{}:{}&-0.750346674921&{}:{}&2.359956385852&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2}}&{}\approx{}&0.012131702742&{}:{}&1.003214389493&{}:{}&-0.015346092236&,\\B^{\prime\prime\prime}_{\mathbf{2}}&{}\approx{}&1.091575854718&{}:{}&-1.785743623776&{}:{}&1.694167769059&,\\C^{\prime\prime\prime}_{\mathbf{2}}&{}\approx{}&-0.009755550080&{}:{}&0.989806282152&{}:{}&0.019949267928&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3}}&{}\approx{}&0.067759508522&{}:{}&0.886525584986&{}:{}&0.045714906492&,\\B^{\prime\prime\prime}_{\mathbf{3}}&{}\approx{}&-0.931262069901&{}:{}&1.282380184282&{}:{}&0.648881885619&,\\C^{\prime\prime\prime}_{\mathbf{3}}&{}\approx{}&-0.070256650945&{}:{}&0.949324343195&{}:{}&0.120932307750&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4}}&{}\approx{}&-0.592817058853&{}:{}&0.717320463752&{}:{}&0.875496595101&,\\B^{\prime\prime\prime}_{\mathbf{4}}&{}\approx{}&1.001149009633&{}:{}&0.010675470181&{}:{}&-0.011824479814&,\\C^{\prime\prime\prime}_{\mathbf{4}}&{}\approx{}&0.996361295834&{}:{}&-0.009641818015&{}:{}&0.013280522181&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5}}&{}\approx{}&-1.146186633268&{}:{}&1.503998706765&{}:{}&0.642187926503&,\\B^{\prime\prime\prime}_{\mathbf{5}}&{}\approx{}&0.963873023464&{}:{}&0.062310625634&{}:{}&-0.026183649098&,\\C^{\prime\prime\prime}_{\mathbf{5}}&{}\approx{}&0.983103089917&{}:{}&-0.062545307803&{}:{}&0.079442217886&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&4.477325463352&{}:{}&3.937519733347&{}:{}&-7.414845196699&,\\B^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&1.056611343681&{}:{}&0.233867353848&{}:{}&-0.290478697529&,\\C^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&0.702908489980&{}:{}&0.102616799035&{}:{}&0.194474710985&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&-0.641563499862&{}:{}&0.611847685239&{}:{}&1.029715814624&,\\B^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&-3.082287839717&{}:{}&-20.035033155111&{}:{}&24.117320994828&,\\C^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&0.223422375219&{}:{}&-1.038743870108&{}:{}&1.815321494890&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.130951923948&{}:{}&0.628091278872&{}:{}&0.502860645075&,\\B^{\prime\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.422129330949&{}:{}&0.366525333820&{}:{}&1.055603997129&,\\C^{\prime\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.311646061027&{}:{}&0.973402043800&{}:{}&0.338244017226&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.070665912037&{}:{}&1.039805530948&{}:{}&0.030860381089&,\\B^{\prime\prime\prime}_{\mathbf{1a}}&{}\approx{}&0.017476331757&{}:{}&0.740113469424&{}:{}&0.242410198819&,\\C^{\prime\prime\prime}_{\mathbf{1a}}&{}\approx{}&0.001918293208&{}:{}&0.896533319738&{}:{}&0.101548387054&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.034308699033&{}:{}&-0.009662904941&{}:{}&1.043971603973&,\\B^{\prime\prime\prime}_{\mathbf{2a}}&{}\approx{}&0.017476331757&{}:{}&0.041245110035&{}:{}&0.941278558208&,\\C^{\prime\prime\prime}_{\mathbf{2a}}&{}\approx{}&0.289725392033&{}:{}&-0.144435339219&{}:{}&0.854709947186&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.090804085441&{}:{}&0.128943624009&{}:{}&0.961860461432&,\\B^{\prime\prime\prime}_{\mathbf{3a}}&{}\approx{}&0.065347799154&{}:{}&0.104494333547&{}:{}&0.830157867299&,\\C^{\prime\prime\prime}_{\mathbf{3a}}&{}\approx{}&0.212683484620&{}:{}&0.362202370959&{}:{}&0.425114144421&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4a}}&{}\approx{}&0.277419102863&{}:{}&0.349777333577&{}:{}&0.372803563560&,\\B^{\prime\prime\prime}_{\mathbf{4a}}&{}\approx{}&0.998027544212&{}:{}&-0.250597399399&{}:{}&0.252569855186&,\\C^{\prime\prime\prime}_{\mathbf{4a}}&{}\approx{}&1.082752187239&{}:{}&0.257086732900&{}:{}&-0.339838920139&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5a}}&{}\approx{}&0.319784872146&{}:{}&0.417523330741&{}:{}&0.262691797113&,\\B^{\prime\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.034105853540&{}:{}&-0.088840019663&{}:{}&0.054734166123&,\\C^{\prime\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.023815972130&{}:{}&0.086129047986&{}:{}&-0.109945020115&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6a}}&{}\approx{}&0.283928910755&{}:{}&0.258583161132&{}:{}&0.457487928113&,\\B^{\prime\prime\prime}_{\mathbf{6a}}&{}\approx{}&0.992291362309&{}:{}&-0.036979468404&{}:{}&0.044688106094&,\\C^{\prime\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.021584461791&{}:{}&0.026004446771&{}:{}&-0.047588908562&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7a}}&{}\approx{}&0.270741005131&{}:{}&0.317285176921&{}:{}&0.411973817947&,\\B^{\prime\prime\prime}_{\mathbf{7a}}&{}\approx{}&0.998027544212&{}:{}&-0.013965314428&{}:{}&0.015937770216&,\\C^{\prime\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.005219374265&{}:{}&0.012363062102&{}:{}&-0.017582436366&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{b}}&{}\approx{}&0.421470565186&{}:{}&-0.771099558751&{}:{}&1.349628993565&,\\B^{\prime\prime\prime}_{\mathbf{b}}&{}\approx{}&0.676829591870&{}:{}&-0.230565454932&{}:{}&0.553735863062&,\\C^{\prime\prime\prime}_{\mathbf{b}}&{}\approx{}&1.043421047656&{}:{}&-0.487729429390&{}:{}&0.444308381734&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.643951538543&{}:{}&-0.199472204690&{}:{}&0.555520666147&,\\B^{\prime\prime\prime}_{\mathbf{1b}}&{}\approx{}&1.058916285427&{}:{}&-0.166904488335&{}:{}&0.107988202908&,\\C^{\prime\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.861768406823&{}:{}&-0.031556397838&{}:{}&0.169787991015&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2b}}&{}\approx{}&-0.280075335746&{}:{}&1.043378454244&{}:{}&0.236696881502&,\\B^{\prime\prime\prime}_{\mathbf{2b}}&{}\approx{}&0.294544570142&{}:{}&0.431777821848&{}:{}&0.273677608011&,\\C^{\prime\prime\prime}_{\mathbf{2b}}&{}\approx{}&0.306429532844&{}:{}&1.255070701983&{}:{}&-0.561500234827&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.133518335437&{}:{}&1.122138932164&{}:{}&0.011379403273&,\\B^{\prime\prime\prime}_{\mathbf{3b}}&{}\approx{}&0.401848849627&{}:{}&0.562214166307&{}:{}&0.035936984066&,\\C^{\prime\prime\prime}_{\mathbf{3b}}&{}\approx{}&0.123917366050&{}:{}&1.092793776428&{}:{}&-0.216711142478&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.035085526767&{}:{}&0.027741042743&{}:{}&0.937173430490&,\\B^{\prime\prime\prime}_{\mathbf{4b}}&{}\approx{}&-0.006220486844&{}:{}&-0.052866223648&{}:{}&1.059086710492&,\\C^{\prime\prime\prime}_{\mathbf{4b}}&{}\approx{}&-0.068198073694&{}:{}&0.343702004007&{}:{}&0.724496069687&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.066107671366&{}:{}&0.069507100541&{}:{}&0.864385228093&,\\B^{\prime\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.050380157362&{}:{}&-0.107830948716&{}:{}&1.057450791353&,\\C^{\prime\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.186454531542&{}:{}&0.314699045554&{}:{}&0.498846422904&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.034871709233&{}:{}&0.981667548186&{}:{}&0.053204161047&,\\B^{\prime\prime\prime}_{\mathbf{6b}}&{}\approx{}&0.141917162483&{}:{}&0.400172293277&{}:{}&0.457910544240&,\\C^{\prime\prime\prime}_{\mathbf{6b}}&{}\approx{}&0.017541018802&{}:{}&1.044285803246&{}:{}&-0.061826822047&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.017915509571&{}:{}&0.992917379863&{}:{}&0.024998129708&,\\B^{\prime\prime\prime}_{\mathbf{7b}}&{}\approx{}&0.210184888586&{}:{}&0.385934402960&{}:{}&0.403880708453&,\\C^{\prime\prime\prime}_{\mathbf{7b}}&{}\approx{}&0.013328338662&{}:{}&1.017262968701&{}:{}&-0.030591307363&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{c}}&{}\approx{}&0.570086553371&{}:{}&1.600192340823&{}:{}&-1.170278894194&,\\B^{\prime\prime\prime}_{\mathbf{c}}&{}\approx{}&1.353636460621&{}:{}&0.655359455580&{}:{}&-1.008995916200&,\\C^{\prime\prime\prime}_{\mathbf{c}}&{}\approx{}&0.707193012522&{}:{}&0.720788983715&{}:{}&-0.427981996237&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.499444201438&{}:{}&0.183401365044&{}:{}&1.316042836394&,\\B^{\prime\prime\prime}_{\mathbf{1c}}&{}\approx{}&0.287963415461&{}:{}&-0.729350594018&{}:{}&1.441387178556&,\\C^{\prime\prime\prime}_{\mathbf{1c}}&{}\approx{}&0.205611668514&{}:{}&0.143424595662&{}:{}&0.650963735825&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2c}}&{}\approx{}&0.644359285343&{}:{}&0.526768467145&{}:{}&-0.171127752489&,\\B^{\prime\prime\prime}_{\mathbf{2c}}&{}\approx{}&0.853611576376&{}:{}&0.182798987496&{}:{}&-0.036410563872&,\\C^{\prime\prime\prime}_{\mathbf{2c}}&{}\approx{}&1.157922248310&{}:{}&0.152035788297&{}:{}&-0.309958036606&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3c}}&{}\approx{}&-0.196562014835&{}:{}&-0.103471144077&{}:{}&1.300033158912&,\\B^{\prime\prime\prime}_{\mathbf{3c}}&{}\approx{}&0.124945207587&{}:{}&-0.220951497077&{}:{}&1.096006289491&,\\C^{\prime\prime\prime}_{\mathbf{3c}}&{}\approx{}&0.398038687510&{}:{}&-0.277896802906&{}:{}&0.879858115396&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.093006238989&{}:{}&0.884118567354&{}:{}&0.022875193657&,\\B^{\prime\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.215526532702&{}:{}&0.662301943747&{}:{}&0.122171523550&,\\C^{\prime\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.052445446895&{}:{}&1.149007252360&{}:{}&-0.201452699256&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.104607008850&{}:{}&0.100873313667&{}:{}&1.003733695183&,\\B^{\prime\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.029895487332&{}:{}&-0.166207044387&{}:{}&1.196102531719&,\\C^{\prime\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.100297092599&{}:{}&0.403282057511&{}:{}&0.697015035088&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.160610175781&{}:{}&0.690244835068&{}:{}&0.149144989151&,\\B^{\prime\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.437623309955&{}:{}&0.331499900334&{}:{}&0.230876789710&,\\C^{\prime\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.400846066979&{}:{}&0.978705330964&{}:{}&-0.379551397943&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.050929452976&{}:{}&0.031727860619&{}:{}&1.019201592357&,\\B^{\prime\prime\prime}_{\mathbf{7c}}&{}\approx{}&0.018698484051&{}:{}&-0.070047833038&{}:{}&1.051349348987&,\\C^{\prime\prime\prime}_{\mathbf{7c}}&{}\approx{}&0.134534147826&{}:{}&0.235479919949&{}:{}&0.629985932225&. \end{alignedat} \] \[ \begin{alignedat}{4} A^*&{}\approx{}&0.000000000000&{}:{}&0.363024264146&{}:{}&0.636975735854&,\\B^*&{}\approx{}&0.281491987776&{}:{}&0.000000000000&{}:{}&0.718508012224&,\\C^*&{}\approx{}&0.407379031733&{}:{}&0.592620968267&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1}}&{}\approx{}&0.000000000000&{}:{}&-0.108380256645&{}:{}&1.108380256645&,\\B^*_{\mathbf{1}}&{}\approx{}&-0.072061402818&{}:{}&0.000000000000&{}:{}&1.072061402818&,\\C^*_{\mathbf{1}}&{}\approx{}&0.407379031733&{}:{}&0.592620968267&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2}}&{}\approx{}&0.000000000000&{}:{}&1.108380256645&{}:{}&-0.108380256645&,\\B^*_{\mathbf{2}}&{}\approx{}&0.281491987776&{}:{}&0.000000000000&{}:{}&0.718508012224&,\\C^*_{\mathbf{2}}&{}\approx{}&-0.039834563767&{}:{}&1.039834563767&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3}}&{}\approx{}&0.000000000000&{}:{}&0.636975735854&{}:{}&0.363024264146&,\\B^*_{\mathbf{3}}&{}\approx{}&-0.072061402818&{}:{}&0.000000000000&{}:{}&1.072061402818&,\\C^*_{\mathbf{3}}&{}\approx{}&-0.039834563767&{}:{}&1.039834563767&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4}}&{}\approx{}&0.000000000000&{}:{}&0.363024264146&{}:{}&0.636975735854&,\\B^*_{\mathbf{4}}&{}\approx{}&1.072061402818&{}:{}&0.000000000000&{}:{}&-0.072061402818&,\\C^*_{\mathbf{4}}&{}\approx{}&1.039834563767&{}:{}&-0.039834563767&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5}}&{}\approx{}&0.000000000000&{}:{}&-0.108380256645&{}:{}&1.108380256645&,\\B^*_{\mathbf{5}}&{}\approx{}&0.718508012224&{}:{}&0.000000000000&{}:{}&0.281491987776&,\\C^*_{\mathbf{5}}&{}\approx{}&1.039834563767&{}:{}&-0.039834563767&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6}}&{}\approx{}&0.000000000000&{}:{}&1.108380256645&{}:{}&-0.108380256645&,\\B^*_{\mathbf{6}}&{}\approx{}&1.072061402818&{}:{}&0.000000000000&{}:{}&-0.072061402818&,\\C^*_{\mathbf{6}}&{}\approx{}&0.592620968267&{}:{}&0.407379031733&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7}}&{}\approx{}&0.000000000000&{}:{}&0.636975735854&{}:{}&0.363024264146&,\\B^*_{\mathbf{7}}&{}\approx{}&0.718508012224&{}:{}&0.000000000000&{}:{}&0.281491987776&,\\C^*_{\mathbf{7}}&{}\approx{}&0.592620968267&{}:{}&0.407379031733&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{a}}&{}\approx{}&0.000000000000&{}:{}&0.598726524541&{}:{}&0.401273475459&,\\B^*_{\mathbf{a}}&{}\approx{}&-0.644122805635&{}:{}&0.000000000000&{}:{}&1.644122805635&,\\C^*_{\mathbf{a}}&{}\approx{}&-0.356062329784&{}:{}&1.356062329784&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1a}}&{}\approx{}&0.000000000000&{}:{}&1.344082517041&{}:{}&-0.344082517041&,\\B^*_{\mathbf{1a}}&{}\approx{}&-0.644122805635&{}:{}&0.000000000000&{}:{}&1.644122805635&,\\C^*_{\mathbf{1a}}&{}\approx{}&0.091151265716&{}:{}&0.908848734284&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2a}}&{}\approx{}&0.000000000000&{}:{}&-0.344082517041&{}:{}&1.344082517041&,\\B^*_{\mathbf{2a}}&{}\approx{}&0.062983975551&{}:{}&0.000000000000&{}:{}&0.937016024449&,\\C^*_{\mathbf{2a}}&{}\approx{}&-0.356062329784&{}:{}&1.356062329784&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3a}}&{}\approx{}&0.000000000000&{}:{}&0.401273475459&{}:{}&0.598726524541&,\\B^*_{\mathbf{3a}}&{}\approx{}&0.062983975551&{}:{}&0.000000000000&{}:{}&0.937016024449&,\\C^*_{\mathbf{3a}}&{}\approx{}&0.091151265716&{}:{}&0.908848734284&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4a}}&{}\approx{}&0.000000000000&{}:{}&0.401273475459&{}:{}&0.598726524541&,\\B^*_{\mathbf{4a}}&{}\approx{}&1.644122805635&{}:{}&0.000000000000&{}:{}&-0.644122805635&,\\C^*_{\mathbf{4a}}&{}\approx{}&1.356062329784&{}:{}&-0.356062329784&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5a}}&{}\approx{}&0.000000000000&{}:{}&-0.344082517041&{}:{}&1.344082517041&,\\B^*_{\mathbf{5a}}&{}\approx{}&1.644122805635&{}:{}&0.000000000000&{}:{}&-0.644122805635&,\\C^*_{\mathbf{5a}}&{}\approx{}&0.908848734284&{}:{}&0.091151265716&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6a}}&{}\approx{}&0.000000000000&{}:{}&1.344082517041&{}:{}&-0.344082517041&,\\B^*_{\mathbf{6a}}&{}\approx{}&0.937016024449&{}:{}&0.000000000000&{}:{}&0.062983975551&,\\C^*_{\mathbf{6a}}&{}\approx{}&1.356062329784&{}:{}&-0.356062329784&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7a}}&{}\approx{}&0.000000000000&{}:{}&0.598726524541&{}:{}&0.401273475459&,\\B^*_{\mathbf{7a}}&{}\approx{}&0.937016024449&{}:{}&0.000000000000&{}:{}&0.062983975551&,\\C^*_{\mathbf{7a}}&{}\approx{}&0.908848734284&{}:{}&0.091151265716&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{b}}&{}\approx{}&0.000000000000&{}:{}&-1.325140769936&{}:{}&2.325140769936&,\\B^*_{\mathbf{b}}&{}\approx{}&0.635045378369&{}:{}&0.000000000000&{}:{}&0.364954621631&,\\C^*_{\mathbf{b}}&{}\approx{}&1.487048159267&{}:{}&-0.487048159267&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1b}}&{}\approx{}&0.000000000000&{}:{}&-1.325140769936&{}:{}&2.325140769936&,\\B^*_{\mathbf{1b}}&{}\approx{}&1.425614793411&{}:{}&0.000000000000&{}:{}&-0.425614793411&,\\C^*_{\mathbf{1b}}&{}\approx{}&0.854592627233&{}:{}&0.145407372767&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2b}}&{}\approx{}&0.000000000000&{}:{}&2.325140769936&{}:{}&-1.325140769936&,\\B^*_{\mathbf{2b}}&{}\approx{}&0.364954621631&{}:{}&0.000000000000&{}:{}&0.635045378369&,\\C^*_{\mathbf{2b}}&{}\approx{}&-0.487048159267&{}:{}&1.487048159267&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3b}}&{}\approx{}&0.000000000000&{}:{}&2.325140769936&{}:{}&-1.325140769936&,\\B^*_{\mathbf{3b}}&{}\approx{}&-0.425614793411&{}:{}&0.000000000000&{}:{}&1.425614793411&,\\C^*_{\mathbf{3b}}&{}\approx{}&0.145407372767&{}:{}&0.854592627233&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4b}}&{}\approx{}&0.000000000000&{}:{}&0.089072792437&{}:{}&0.910927207563&,\\B^*_{\mathbf{4b}}&{}\approx{}&-0.425614793411&{}:{}&0.000000000000&{}:{}&1.425614793411&,\\C^*_{\mathbf{4b}}&{}\approx{}&1.487048159267&{}:{}&-0.487048159267&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5b}}&{}\approx{}&0.000000000000&{}:{}&0.089072792437&{}:{}&0.910927207563&,\\B^*_{\mathbf{5b}}&{}\approx{}&0.364954621631&{}:{}&0.000000000000&{}:{}&0.635045378369&,\\C^*_{\mathbf{5b}}&{}\approx{}&0.854592627233&{}:{}&0.145407372767&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6b}}&{}\approx{}&0.000000000000&{}:{}&0.910927207563&{}:{}&0.089072792437&,\\B^*_{\mathbf{6b}}&{}\approx{}&1.425614793411&{}:{}&0.000000000000&{}:{}&-0.425614793411&,\\C^*_{\mathbf{6b}}&{}\approx{}&-0.487048159267&{}:{}&1.487048159267&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7b}}&{}\approx{}&0.000000000000&{}:{}&0.910927207563&{}:{}&0.089072792437&,\\B^*_{\mathbf{7b}}&{}\approx{}&0.635045378369&{}:{}&0.000000000000&{}:{}&0.364954621631&,\\C^*_{\mathbf{7b}}&{}\approx{}&0.145407372767&{}:{}&0.854592627233&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{c}}&{}\approx{}&0.000000000000&{}:{}&3.032247551123&{}:{}&-2.032247551123&,\\B^*_{\mathbf{c}}&{}\approx{}&2.351229586822&{}:{}&0.000000000000&{}:{}&-1.351229586822&,\\C^*_{\mathbf{c}}&{}\approx{}&0.538364861216&{}:{}&0.461635138784&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1c}}&{}\approx{}&0.000000000000&{}:{}&-2.032247551123&{}:{}&3.032247551123&,\\B^*_{\mathbf{1c}}&{}\approx{}&-1.351229586822&{}:{}&0.000000000000&{}:{}&2.351229586822&,\\C^*_{\mathbf{1c}}&{}\approx{}&0.461635138784&{}:{}&0.538364861216&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2c}}&{}\approx{}&0.000000000000&{}:{}&3.032247551123&{}:{}&-2.032247551123&,\\B^*_{\mathbf{2c}}&{}\approx{}&0.770090756738&{}:{}&0.000000000000&{}:{}&0.229909243262&,\\C^*_{\mathbf{2c}}&{}\approx{}&1.803275925284&{}:{}&-0.803275925284&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3c}}&{}\approx{}&0.000000000000&{}:{}&-2.032247551123&{}:{}&3.032247551123&,\\B^*_{\mathbf{3c}}&{}\approx{}&0.229909243262&{}:{}&0.000000000000&{}:{}&0.770090756738&,\\C^*_{\mathbf{3c}}&{}\approx{}&-0.803275925284&{}:{}&1.803275925284&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4c}}&{}\approx{}&0.000000000000&{}:{}&0.796179573623&{}:{}&0.203820426377&,\\B^*_{\mathbf{4c}}&{}\approx{}&2.351229586822&{}:{}&0.000000000000&{}:{}&-1.351229586822&,\\C^*_{\mathbf{4c}}&{}\approx{}&-0.803275925284&{}:{}&1.803275925284&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5c}}&{}\approx{}&0.000000000000&{}:{}&0.203820426377&{}:{}&0.796179573623&,\\B^*_{\mathbf{5c}}&{}\approx{}&-1.351229586822&{}:{}&0.000000000000&{}:{}&2.351229586822&,\\C^*_{\mathbf{5c}}&{}\approx{}&1.803275925284&{}:{}&-0.803275925284&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6c}}&{}\approx{}&0.000000000000&{}:{}&0.796179573623&{}:{}&0.203820426377&,\\B^*_{\mathbf{6c}}&{}\approx{}&0.770090756738&{}:{}&0.000000000000&{}:{}&0.229909243262&,\\C^*_{\mathbf{6c}}&{}\approx{}&0.461635138784&{}:{}&0.538364861216&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7c}}&{}\approx{}&0.000000000000&{}:{}&0.203820426377&{}:{}&0.796179573623&,\\B^*_{\mathbf{7c}}&{}\approx{}&0.229909243262&{}:{}&0.000000000000&{}:{}&0.770090756738&,\\C^*_{\mathbf{7c}}&{}\approx{}&0.538364861216&{}:{}&0.461635138784&{}:{}&0.000000000000&. \end{alignedat} \]