Derousseau's Generalization of the Malfatti circles

Test Case in ETC

The test case used in “Encyclopedis of Triangle Centers” to search for triangle centers.

\(a:b:c=6:9:13\).


[Top] > Test Case in ETC

Reference Triangle

reference triangle

Triangle Centers and their Extraversions

Approximately,
\[ \begin{alignedat}{4} I&{}\approx{}&0.214285714286&{}:{}&0.321428571429&{}:{}&0.464285714286&,\\ I_{\mathbf{a}}&{}\approx{}&-0.375000000000&{}:{}&0.562500000000&{}:{}&0.812500000000&,\\ I_{\mathbf{b}}&{}\approx{}&0.600000000000&{}:{}&-0.900000000000&{}:{}&1.300000000000&,\\ I_{\mathbf{c}}&{}\approx{}&3.000000000000&{}:{}&4.500000000000&{}:{}&-6.500000000000&. \end{alignedat} \] \[ \begin{alignedat}{4} P&{}\approx{}&0.159447590766&{}:{}&0.246863875275&{}:{}&0.593688533959&,\\ P_{\mathbf{1}}&{}\approx{}&0.026489928890&{}:{}&0.041012890004&{}:{}&0.932497181107&,\\ P_{\mathbf{2}}&{}\approx{}&0.000471437338&{}:{}&0.997773208815&{}:{}&0.001755353847&,\\ P_{\mathbf{3}}&{}\approx{}&0.000464543439&{}:{}&0.983182621155&{}:{}&0.016352835406&,\\ P_{\mathbf{4}}&{}\approx{}&0.999371961038&{}:{}&0.000184450286&{}:{}&0.000443588676&,\\ P_{\mathbf{5}}&{}\approx{}&0.995638119502&{}:{}&0.000183761145&{}:{}&0.004178119353&,\\ P_{\mathbf{6}}&{}\approx{}&0.798246585324&{}:{}&0.201399099006&{}:{}&0.000354315670&,\\ P_{\mathbf{7}}&{}\approx{}&0.795862606597&{}:{}&0.200797616737&{}:{}&0.003339776666&,\\ P_{\mathbf{a}}&{}\approx{}&-0.207564625291&{}:{}&0.699126789355&{}:{}&0.508437835935&,\\ P_{\mathbf{1a}}&{}\approx{}&-0.070640817164&{}:{}&0.897603315436&{}:{}&0.173037501728&,\\ P_{\mathbf{2a}}&{}\approx{}&-0.002277009832&{}:{}&0.007669508093&{}:{}&0.994607501739&,\\ P_{\mathbf{3a}}&{}\approx{}&-0.002229600710&{}:{}&0.028330603607&{}:{}&0.973898997103&,\\ P_{\mathbf{4a}}&{}\approx{}&1.056620232005&{}:{}&-0.001600516836&{}:{}&-0.055019715170&,\\ P_{\mathbf{5a}}&{}\approx{}&1.055378837526&{}:{}&-0.000423763529&{}:{}&-0.054955073997&,\\ P_{\mathbf{6a}}&{}\approx{}&1.001810031150&{}:{}&-0.001517493014&{}:{}&-0.000292538135&,\\ P_{\mathbf{7a}}&{}\approx{}&1.000694018324&{}:{}&-0.000401806075&{}:{}&-0.000292212249&,\\ P_{\mathbf{b}}&{}\approx{}&0.748885850337&{}:{}&-0.431363764551&{}:{}&0.682477914214&,\\ P_{\mathbf{1b}}&{}\approx{}&0.873433919452&{}:{}&-0.217415151806&{}:{}&0.343981232354&,\\ P_{\mathbf{2b}}&{}\approx{}&-0.003716837056&{}:{}&1.264740884515&{}:{}&-0.261024047459&,\\ P_{\mathbf{3b}}&{}\approx{}&-0.001602837804&{}:{}&1.262077123995&{}:{}&-0.260474286191&,\\ P_{\mathbf{4b}}&{}\approx{}&0.006137522517&{}:{}&-0.003535258166&{}:{}&0.997397735649&,\\ P_{\mathbf{5b}}&{}\approx{}&0.014088764253&{}:{}&-0.003506974885&{}:{}&0.989418210631&,\\ P_{\mathbf{6b}}&{}\approx{}&-0.002950900545&{}:{}&1.004113042733&{}:{}&-0.001162142188&,\\ P_{\mathbf{7b}}&{}\approx{}&-0.001273090162&{}:{}&1.002433288233&{}:{}&-0.001160198070&,\\ P_{\mathbf{c}}&{}\approx{}&1.152256660770&{}:{}&1.443910539004&{}:{}&-1.596167199774&,\\ P_{\mathbf{1c}}&{}\approx{}&-0.382159745195&{}:{}&-0.780717375460&{}:{}&2.162877120655&,\\ P_{\mathbf{2c}}&{}\approx{}&1.060561207988&{}:{}&0.574326049362&{}:{}&-0.634887257350&,\\ P_{\mathbf{3c}}&{}\approx{}&-0.135700778741&{}:{}&-0.641504235939&{}:{}&1.777205014680&,\\ P_{\mathbf{4c}}&{}\approx{}&0.230303806447&{}:{}&1.088725273053&{}:{}&-0.319029079500&,\\ P_{\mathbf{5c}}&{}\approx{}&-0.242831320268&{}:{}&-0.131500522347&{}:{}&1.374331842615&,\\ P_{\mathbf{6c}}&{}\approx{}&0.409119242429&{}:{}&0.835793160362&{}:{}&-0.244912402791&,\\ P_{\mathbf{7c}}&{}\approx{}&-0.092222142236&{}:{}&-0.115564984468&{}:{}&1.207787126704&. \end{alignedat} \] \[ \begin{alignedat}{4} P^-&{}\approx{}&0.141123855203&{}:{}&0.221948657777&{}:{}&0.636927487020&,\\ P^-_{\mathbf{1}}&{}\approx{}&-0.001061519089&{}:{}&-0.000126787561&{}:{}&1.001188306649&,\\ P^-_{\mathbf{2}}&{}\approx{}&-0.005547399205&{}:{}&1.016812198527&{}:{}&-0.011264799322&,\\ P^-_{\mathbf{3}}&{}\approx{}&-0.018877135280&{}:{}&1.043043083848&{}:{}&-0.024165948568&,\\ P^-_{\mathbf{4}}&{}\approx{}&1.013062489312&{}:{}&-0.005417484204&{}:{}&-0.007645005107&,\\ P^-_{\mathbf{5}}&{}\approx{}&1.038934456102&{}:{}&-0.017617071545&{}:{}&-0.021317384557&,\\ P^-_{\mathbf{6}}&{}\approx{}&1.396778541197&{}:{}&0.078374632035&{}:{}&-0.475153173232&,\\ P^-_{\mathbf{7}}&{}\approx{}&-0.839901868399&{}:{}&0.540088659552&{}:{}&1.299813208847&,\\ P^-_{\mathbf{a}}&{}\approx{}&-0.159542460854&{}:{}&0.738312738897&{}:{}&0.421229721957&,\\ P^-_{\mathbf{1a}}&{}\approx{}&-0.018051002358&{}:{}&0.955505367660&{}:{}&0.062545634699&,\\ P^-_{\mathbf{2a}}&{}\approx{}&0.010303424101&{}:{}&-0.011057558742&{}:{}&1.000754134641&,\\ P^-_{\mathbf{3a}}&{}\approx{}&0.022450749985&{}:{}&-0.007035638076&{}:{}&0.984584888091&,\\ P^-_{\mathbf{4a}}&{}\approx{}&0.708490426358&{}:{}&0.135572875173&{}:{}&0.155936698470&,\\ P^-_{\mathbf{5a}}&{}\approx{}&0.852549193227&{}:{}&0.079399583775&{}:{}&0.068051222998&,\\ P^-_{\mathbf{6a}}&{}\approx{}&0.971101486441&{}:{}&0.011062424337&{}:{}&0.017836089222&,\\ P^-_{\mathbf{7a}}&{}\approx{}&0.984741086278&{}:{}&0.006125760478&{}:{}&0.009133153245&,\\ P^-_{\mathbf{b}}&{}\approx{}&0.787949887418&{}:{}&-0.308404979429&{}:{}&0.520455092011&,\\ P^-_{\mathbf{1b}}&{}\approx{}&0.925266762137&{}:{}&-0.088022598289&{}:{}&0.162755836152&,\\ P^-_{\mathbf{2b}}&{}\approx{}&0.147712151652&{}:{}&0.721763609679&{}:{}&0.130524238668&,\\ P^-_{\mathbf{3b}}&{}\approx{}&0.106733861837&{}:{}&0.872730057686&{}:{}&0.020536080478&,\\ P^-_{\mathbf{4b}}&{}\approx{}&-0.007685159222&{}:{}&0.017330762649&{}:{}&0.990354396573&,\\ P^-_{\mathbf{5b}}&{}\approx{}&-0.006737440621&{}:{}&0.028358854392&{}:{}&0.978378586229&,\\ P^-_{\mathbf{6b}}&{}\approx{}&0.008816918941&{}:{}&0.966950383971&{}:{}&0.024232697089&,\\ P^-_{\mathbf{7b}}&{}\approx{}&0.006480409818&{}:{}&0.977901146842&{}:{}&0.015618443340&,\\ P^-_{\mathbf{c}}&{}\approx{}&0.909064932799&{}:{}&1.041681689858&{}:{}&-0.950746622657&,\\ P^-_{\mathbf{1c}}&{}\approx{}&0.062674292678&{}:{}&-0.086178084012&{}:{}&1.023503791335&,\\ P^-_{\mathbf{2c}}&{}\approx{}&0.913743541908&{}:{}&0.277148180383&{}:{}&-0.190891722290&,\\ P^-_{\mathbf{3c}}&{}\approx{}&0.101411483793&{}:{}&-0.252719148256&{}:{}&1.151307664463&,\\ P^-_{\mathbf{4c}}&{}\approx{}&0.099334080693&{}:{}&0.927417431241&{}:{}&-0.026751511934&,\\ P^-_{\mathbf{5c}}&{}\approx{}&-0.089752100890&{}:{}&0.087131412062&{}:{}&1.002620688828&,\\ P^-_{\mathbf{6c}}&{}\approx{}&0.264904257589&{}:{}&0.631834127402&{}:{}&0.103261615009&,\\ P^-_{\mathbf{7c}}&{}\approx{}&-0.006177878347&{}:{}&0.012867861963&{}:{}&0.993310016384&. \end{alignedat} \] \[ \begin{alignedat}{4} P^+&{}\approx{}&0.170431169963&{}:{}&0.261798508208&{}:{}&0.567770321829&,\\ P^+_{\mathbf{1}}&{}\approx{}&0.047791180025&{}:{}&0.072819806435&{}:{}&0.879389013540&,\\ P^+_{\mathbf{2}}&{}\approx{}&0.006169476178&{}:{}&0.979748977372&{}:{}&0.014081546449&,\\ P^+_{\mathbf{3}}&{}\approx{}&0.016843102738&{}:{}&0.932492701622&{}:{}&0.050664195641&,\\ P^+_{\mathbf{4}}&{}\approx{}&0.986142818874&{}:{}&0.005597593320&{}:{}&0.008259587806&,\\ P^+_{\mathbf{5}}&{}\approx{}&0.956661348297&{}:{}&0.016208650026&{}:{}&0.027130001676&,\\ P^+_{\mathbf{6}}&{}\approx{}&0.602000443398&{}:{}&0.241736255224&{}:{}&0.156263301378&,\\ P^+_{\mathbf{7}}&{}\approx{}&0.442204697637&{}:{}&0.274153507860&{}:{}&0.283641794503&,\\ P^+_{\mathbf{a}}&{}\approx{}&-0.238081621429&{}:{}&0.674225007337&{}:{}&0.563856614092&,\\ P^+_{\mathbf{1a}}&{}\approx{}&-0.109724275369&{}:{}&0.854571932906&{}:{}&0.255152342463&,\\ P^+_{\mathbf{2a}}&{}\approx{}&-0.014061898459&{}:{}&0.025212336752&{}:{}&0.988849561707&,\\ P^+_{\mathbf{3a}}&{}\approx{}&-0.024024024690&{}:{}&0.059561394260&{}:{}&0.964462630430&,\\ P^+_{\mathbf{4a}}&{}\approx{}&1.734368889050&{}:{}&-0.268653439934&{}:{}&-0.465715449116&,\\ P^+_{\mathbf{5a}}&{}\approx{}&1.338503357919&{}:{}&-0.111847056705&{}:{}&-0.226656301214&,\\ P^+_{\mathbf{6a}}&{}\approx{}&1.033952390331&{}:{}&-0.014684780029&{}:{}&-0.019267610302&,\\ P^+_{\mathbf{7a}}&{}\approx{}&1.017025724421&{}:{}&-0.007084358108&{}:{}&-0.009941366313&,\\ P^+_{\mathbf{b}}&{}\approx{}&0.723265913625&{}:{}&-0.512005616453&{}:{}&0.788739702828&,\\ P^+_{\mathbf{1b}}&{}\approx{}&0.835850063223&{}:{}&-0.311237347861&{}:{}&0.475387284638&,\\ P^+_{\mathbf{2b}}&{}\approx{}&-0.307581015132&{}:{}&2.354303356929&{}:{}&-1.046722341797&,\\ P^+_{\mathbf{3b}}&{}\approx{}&-0.170921313919&{}:{}&1.870584233458&{}:{}&-0.699662919539&,\\ P^+_{\mathbf{4b}}&{}\approx{}&0.019345355921&{}:{}&-0.023473135052&{}:{}&1.004127779130&,\\ P^+_{\mathbf{5b}}&{}\approx{}&0.033532700373&{}:{}&-0.033257817757&{}:{}&0.999725117384&,\\ P^+_{\mathbf{6b}}&{}\approx{}&-0.015196724615&{}:{}&1.042785235292&{}:{}&-0.027588510678&,\\ P^+_{\mathbf{7b}}&{}\approx{}&-0.009231848736&{}:{}&1.027614869600&{}:{}&-0.018383020864&,\\ P^+_{\mathbf{c}}&{}\approx{}&1.344772292931&{}:{}&1.762323265507&{}:{}&-2.107095558438&,\\ P^+_{\mathbf{1c}}&{}\approx{}&-0.985772505320&{}:{}&-1.723164991949&{}:{}&3.708937497269&,\\ P^+_{\mathbf{2c}}&{}\approx{}&1.188073265858&{}:{}&0.832426880403&{}:{}&-1.020500146262&,\\ P^+_{\mathbf{3c}}&{}\approx{}&-0.415061943527&{}:{}&-1.099563442940&{}:{}&2.514625386466&,\\ P^+_{\mathbf{4c}}&{}\approx{}&0.349957482996&{}:{}&1.236095791072&{}:{}&-0.586053274068&,\\ P^+_{\mathbf{5c}}&{}\approx{}&-0.411869584696&{}:{}&-0.372925602060&{}:{}&1.784795186756&,\\ P^+_{\mathbf{6c}}&{}\approx{}&0.538887740715&{}:{}&1.019320950130&{}:{}&-0.558208690846&,\\ P^+_{\mathbf{7c}}&{}\approx{}&-0.183337143514&{}:{}&-0.251566600817&{}:{}&1.434903744331&. \end{alignedat} \] \[ \begin{alignedat}{4} Q&{}\approx{}&0.124506936676&{}:{}&0.195962661716&{}:{}&0.679530401609&,\\ Q_{\mathbf{1}}&{}\approx{}&-0.070385374478&{}:{}&-0.110780215921&{}:{}&1.181165590399&,\\ Q_{\mathbf{2}}&{}\approx{}&-0.019329530417&{}:{}&1.124825689246&{}:{}&-0.105496158829&,\\ Q_{\mathbf{3}}&{}\approx{}&-0.013518355959&{}:{}&0.786661327558&{}:{}&0.226857028401&,\\ Q_{\mathbf{4}}&{}\approx{}&1.083158670498&{}:{}&-0.018613504890&{}:{}&-0.064545165608&,\\ Q_{\mathbf{5}}&{}\approx{}&0.857603143946&{}:{}&-0.014737453291&{}:{}&0.157134309346&,\\ Q_{\mathbf{6}}&{}\approx{}&0.634610079081&{}:{}&0.403206183454&{}:{}&-0.037816262535&,\\ Q_{\mathbf{7}}&{}\approx{}&0.549877919767&{}:{}&0.349370715505&{}:{}&0.100751364728&,\\ Q_{\mathbf{a}}&{}\approx{}&-0.117842720415&{}:{}&0.809222742208&{}:{}&0.308619978206&,\\ Q_{\mathbf{1a}}&{}\approx{}&0.085333645441&{}:{}&1.138147853490&{}:{}&-0.223481498931&,\\ Q_{\mathbf{2a}}&{}\approx{}&0.034358139274&{}:{}&-0.235936403903&{}:{}&1.201578264628&,\\ Q_{\mathbf{3a}}&{}\approx{}&0.020279952962&{}:{}&0.270486334118&{}:{}&0.709233712920&,\\ Q_{\mathbf{4a}}&{}\approx{}&2.116232844801&{}:{}&-0.308175515164&{}:{}&-0.808057329637&,\\ Q_{\mathbf{5a}}&{}\approx{}&1.442713608994&{}:{}&0.108168733268&{}:{}&-0.550882342262&,\\ Q_{\mathbf{6a}}&{}\approx{}&1.132541826361&{}:{}&-0.164925925633&{}:{}&0.032384099271&,\\ Q_{\mathbf{7a}}&{}\approx{}&0.906149988922&{}:{}&0.067939399643&{}:{}&0.025910611434&,\\ Q_{\mathbf{b}}&{}\approx{}&0.881309275532&{}:{}&-0.178763290848&{}:{}&0.297454015316&,\\ Q_{\mathbf{1b}}&{}\approx{}&1.097132208512&{}:{}&0.146293430416&{}:{}&-0.243425638928&,\\ Q_{\mathbf{2b}}&{}\approx{}&-1.033919930423&{}:{}&5.097261414898&{}:{}&-3.063341484475&,\\ Q_{\mathbf{3b}}&{}\approx{}&0.250470958986&{}:{}&1.878414879051&{}:{}&-1.128885838037&,\\ Q_{\mathbf{4b}}&{}\approx{}&-0.269549689511&{}:{}&0.054675005565&{}:{}&1.214874683946&,\\ Q_{\mathbf{5b}}&{}\approx{}&0.244129673288&{}:{}&0.032552656001&{}:{}&0.723317670710&,\\ Q_{\mathbf{6b}}&{}\approx{}&-0.240853036775&{}:{}&1.187413894337&{}:{}&0.053439142439&,\\ Q_{\mathbf{7b}}&{}\approx{}&0.113159993522&{}:{}&0.848646950554&{}:{}&0.038193055924&,\\ Q_{\mathbf{c}}&{}\approx{}&0.846301882882&{}:{}&0.748963831077&{}:{}&-0.595265713959&,\\ Q_{\mathbf{1c}}&{}\approx{}&1.411945916145&{}:{}&1.595447520668&{}:{}&-2.007393436813&,\\ Q_{\mathbf{2c}}&{}\approx{}&1.135573336979&{}:{}&-0.660642613977&{}:{}&0.525069276997&,\\ Q_{\mathbf{3c}}&{}\approx{}&0.692607399846&{}:{}&-1.190517353287&{}:{}&1.497909953441&,\\ Q_{\mathbf{4c}}&{}\approx{}&-0.703103932619&{}:{}&1.208559760021&{}:{}&0.494544172598&,\\ Q_{\mathbf{5c}}&{}\approx{}&-0.996520850439&{}:{}&0.579746034956&{}:{}&1.416774815482&,\\ Q_{\mathbf{6c}}&{}\approx{}&0.385750953027&{}:{}&0.435884543852&{}:{}&0.178364503120&,\\ Q_{\mathbf{7c}}&{}\approx{}&0.247054145389&{}:{}&0.218639025809&{}:{}&0.534306828802&. \end{alignedat} \] \[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.186419499351&{}:{}&0.284090530142&{}:{}&0.529489970507&,\\ I^\prime_{\mathbf{1}}&{}\approx{}&0.088831623580&{}:{}&0.135373301206&{}:{}&0.775795075214&,\\ I^\prime_{\mathbf{2}}&{}\approx{}&0.016615557506&{}:{}&0.936191036845&{}:{}&0.047193405649&,\\ I^\prime_{\mathbf{3}}&{}\approx{}&0.015133729456&{}:{}&0.852698554716&{}:{}&0.132167715827&,\\ I^\prime_{\mathbf{4}}&{}\approx{}&0.954516994553&{}:{}&0.015882006906&{}:{}&0.029600998541&,\\ I^\prime_{\mathbf{5}}&{}\approx{}&0.899286975663&{}:{}&0.014963046273&{}:{}&0.085749978064&,\\ I^\prime_{\mathbf{6}}&{}\approx{}&0.607460835328&{}:{}&0.373700896310&{}:{}&0.018838268363&,\\ I^\prime_{\mathbf{7}}&{}\approx{}&0.584611232197&{}:{}&0.359644159359&{}:{}&0.055744608444&,\\ I^\prime_{\mathbf{a}}&{}\approx{}&-0.281570361744&{}:{}&0.632898214354&{}:{}&0.648672147390&,\\ I^\prime_{\mathbf{1a}}&{}\approx{}&-0.176381553416&{}:{}&0.770039776868&{}:{}&0.406341776547&,\\ I^\prime_{\mathbf{2a}}&{}\approx{}&-0.031238765872&{}:{}&0.070216762222&{}:{}&0.961022003651&,\\ I^\prime_{\mathbf{3a}}&{}\approx{}&-0.029300144219&{}:{}&0.127917438528&{}:{}&0.901382705691&,\\ I^\prime_{\mathbf{4a}}&{}\approx{}&1.622206882543&{}:{}&-0.077325463419&{}:{}&-0.544881419124&,\\ I^\prime_{\mathbf{5a}}&{}\approx{}&1.563551983312&{}:{}&-0.038372098607&{}:{}&-0.525179884705&,\\ I^\prime_{\mathbf{6a}}&{}\approx{}&1.078539355889&{}:{}&-0.051410554602&{}:{}&-0.027128801287&,\\ I^\prime_{\mathbf{7a}}&{}\approx{}&1.052293625377&{}:{}&-0.025824990271&{}:{}&-0.026468635106&,\\ I^\prime_{\mathbf{b}}&{}\approx{}&0.677662908379&{}:{}&-0.629902544536&{}:{}&0.952239636157&,\\ I^\prime_{\mathbf{1b}}&{}\approx{}&0.761795137361&{}:{}&-0.465493587296&{}:{}&0.703698449936&,\\ I^\prime_{\mathbf{2b}}&{}\approx{}&-0.108026788254&{}:{}&2.440569118297&{}:{}&-1.332542330043&,\\ I^\prime_{\mathbf{3b}}&{}\approx{}&-0.068479950910&{}:{}&2.353462208093&{}:{}&-1.284982257183&,\\ I^\prime_{\mathbf{4b}}&{}\approx{}&0.053093111173&{}:{}&-0.049351211954&{}:{}&0.996258100782&,\\ I^\prime_{\mathbf{5b}}&{}\approx{}&0.078590112147&{}:{}&-0.048022350675&{}:{}&0.969432238529&,\\ I^\prime_{\mathbf{6b}}&{}\approx{}&-0.048382754863&{}:{}&1.093075701734&{}:{}&-0.044692946871&,\\ I^\prime_{\mathbf{7b}}&{}\approx{}&-0.031287163781&{}:{}&1.075251319245&{}:{}&-0.043964155463&,\\ I^\prime_{\mathbf{c}}&{}\approx{}&1.566018606833&{}:{}&2.147029822589&{}:{}&-2.713048429421&,\\ I^\prime_{\mathbf{1c}}&{}\approx{}&-1.331109313533&{}:{}&-2.330149601974&{}:{}&4.661258915508&,\\ I^\prime_{\mathbf{2c}}&{}\approx{}&1.311650453174&{}:{}&1.182156927546&{}:{}&-1.493807380720&,\\ I^\prime_{\mathbf{3c}}&{}\approx{}&-0.600964112749&{}:{}&-1.600305000045&{}:{}&3.201269112794&,\\ I^\prime_{\mathbf{4c}}&{}\approx{}&0.518014890839&{}:{}&1.379419839423&{}:{}&-0.897434730262&,\\ I^\prime_{\mathbf{5c}}&{}\approx{}&-0.624800511857&{}:{}&-0.563116683747&{}:{}&2.187917195604&,\\ I^\prime_{\mathbf{6c}}&{}\approx{}&0.620479807063&{}:{}&1.086169829001&{}:{}&-0.706649636064&,\\ I^\prime_{\mathbf{7c}}&{}\approx{}&-0.338309036996&{}:{}&-0.463825645820&{}:{}&1.802134682816&. \end{alignedat} \]

Central Triangles and their Extraversions

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.349607047620&{}:{}&0.266069844155&{}:{}&0.384323108224&,\\B^\prime&{}\approx{}&0.159580615309&{}:{}&0.494661384854&{}:{}&0.345757999837&,\\C^\prime&{}\approx{}&0.087754730048&{}:{}&0.131632095073&{}:{}&0.780613174879&,\\[.5em] A^\prime_{\mathbf{1}}&{}\approx{}&-0.009294423249&{}:{}&0.412893173147&{}:{}&0.596401250102&,\\B^\prime_{\mathbf{1}}&{}\approx{}&0.316192166234&{}:{}&-0.001275193075&{}:{}&0.685083026841&,\\C^\prime_{\mathbf{1}}&{}\approx{}&0.029114908048&{}:{}&0.043672362073&{}:{}&0.927212729879&,\\[.5em] A^\prime_{\mathbf{2}}&{}\approx{}&-0.334779082061&{}:{}&0.546045988116&{}:{}&0.788733093945&,\\B^\prime_{\mathbf{2}}&{}\approx{}&0.005822981610&{}:{}&0.981560558236&{}:{}&0.012616460154&,\\C^\prime_{\mathbf{2}}&{}\approx{}&1.580960831172&{}:{}&2.371441246757&{}:{}&-2.952402077929&,\\[.5em] A^\prime_{\mathbf{3}}&{}\approx{}&-0.361655667145&{}:{}&0.557040954741&{}:{}&0.804614712404&,\\B^\prime_{\mathbf{3}}&{}\approx{}&0.017550946010&{}:{}&0.944422004303&{}:{}&0.038027049688&,\\C^\prime_{\mathbf{3}}&{}\approx{}&0.797903076547&{}:{}&1.196854614821&{}:{}&-0.994757691368&,\\[.5em] A^\prime_{\mathbf{4}}&{}\approx{}&0.986655667145&{}:{}&0.005459045259&{}:{}&0.007885287596&,\\B^\prime_{\mathbf{4}}&{}\approx{}&0.582449053990&{}:{}&-0.844422004303&{}:{}&1.261972950312&,\\C^\prime_{\mathbf{4}}&{}\approx{}&2.202096923453&{}:{}&3.303145385179&{}:{}&-4.505242308632&,\\[.5em] A^\prime_{\mathbf{5}}&{}\approx{}&0.959779082061&{}:{}&0.016454011884&{}:{}&0.023766906055&,\\B^\prime_{\mathbf{5}}&{}\approx{}&0.594177018390&{}:{}&-0.881560558236&{}:{}&1.287383539846&,\\C^\prime_{\mathbf{5}}&{}\approx{}&1.419039168828&{}:{}&2.128558753243&{}:{}&-2.547597922071&,\\[.5em] A^\prime_{\mathbf{6}}&{}\approx{}&0.634294423249&{}:{}&0.149606826853&{}:{}&0.216098749898&,\\B^\prime_{\mathbf{6}}&{}\approx{}&0.283807833766&{}:{}&0.101275193075&{}:{}&0.614916973159&,\\C^\prime_{\mathbf{6}}&{}\approx{}&2.970885091952&{}:{}&4.456327637927&{}:{}&-6.427212729879&,\\[.5em] A^\prime_{\mathbf{7}}&{}\approx{}&0.275392952380&{}:{}&0.296430155845&{}:{}&0.428176891776&,\\B^\prime_{\mathbf{7}}&{}\approx{}&0.440419384691&{}:{}&-0.394661384854&{}:{}&0.954242000163&,\\C^\prime_{\mathbf{7}}&{}\approx{}&2.912245269952&{}:{}&4.368367904927&{}:{}&-6.280613174879&,\\[.5em] A^\prime_{\mathbf{a}}&{}\approx{}&-0.679420184127&{}:{}&0.687035529870&{}:{}&0.992384654257&,\\B^\prime_{\mathbf{a}}&{}\approx{}&-0.124513520549&{}:{}&0.854734226027&{}:{}&0.269779294522&,\\C^\prime_{\mathbf{a}}&{}\approx{}&-0.226425905618&{}:{}&0.339638858427&{}:{}&0.886787047191&,\\[.5em] A^\prime_{\mathbf{1a}}&{}\approx{}&-0.082224400214&{}:{}&0.442728163724&{}:{}&0.639496236490&,\\B^\prime_{\mathbf{1a}}&{}\approx{}&-0.062841355180&{}:{}&0.926685085623&{}:{}&0.136156269557&,\\C^\prime_{\mathbf{1a}}&{}\approx{}&-0.682466322424&{}:{}&1.023699483636&{}:{}&0.658766838788&,\\[.5em] A^\prime_{\mathbf{2a}}&{}\approx{}&0.181675030333&{}:{}&0.334769305773&{}:{}&0.483555663894&,\\B^\prime_{\mathbf{2a}}&{}\approx{}&-3.412331612121&{}:{}&-2.981053547475&{}:{}&7.393385159596&,\\C^\prime_{\mathbf{2a}}&{}\approx{}&-0.012568271036&{}:{}&0.018852406554&{}:{}&0.993715864482&,\\[.5em] A^\prime_{\mathbf{3a}}&{}\approx{}&0.197827264120&{}:{}&0.328161573769&{}:{}&0.474011162111&,\\B^\prime_{\mathbf{3a}}&{}\approx{}&-1.132129528091&{}:{}&-0.320817782772&{}:{}&2.452947310863&,\\C^\prime_{\mathbf{3a}}&{}\approx{}&-0.024902704110&{}:{}&0.037354056165&{}:{}&0.987548647945&,\\[.5em] A^\prime_{\mathbf{4a}}&{}\approx{}&1.893705898413&{}:{}&-0.365606958442&{}:{}&-0.528098939971&,\\B^\prime_{\mathbf{4a}}&{}\approx{}&3.124513520549&{}:{}&4.645265773973&{}:{}&-6.769779294522&,\\C^\prime_{\mathbf{4a}}&{}\approx{}&0.826425905618&{}:{}&-1.239638858427&{}:{}&1.413212952809&,\\[.5em] A^\prime_{\mathbf{5a}}&{}\approx{}&1.296510114500&{}:{}&-0.121299592295&{}:{}&-0.175210522204&,\\B^\prime_{\mathbf{5a}}&{}\approx{}&3.062841355180&{}:{}&4.573314914377&{}:{}&-6.636156269557&,\\C^\prime_{\mathbf{5a}}&{}\approx{}&1.282466322424&{}:{}&-1.923699483636&{}:{}&1.641233161212&,\\[.5em] A^\prime_{\mathbf{6a}}&{}\approx{}&1.032610683953&{}:{}&-0.013340734344&{}:{}&-0.019269949609&,\\B^\prime_{\mathbf{6a}}&{}\approx{}&6.412331612121&{}:{}&8.481053547475&{}:{}&-13.893385159596&,\\C^\prime_{\mathbf{6a}}&{}\approx{}&0.612568271036&{}:{}&-0.918852406554&{}:{}&1.306284135518&,\\[.5em] A^\prime_{\mathbf{7a}}&{}\approx{}&1.016458450166&{}:{}&-0.006733002341&{}:{}&-0.009725447825&,\\B^\prime_{\mathbf{7a}}&{}\approx{}&4.132129528091&{}:{}&5.820817782772&{}:{}&-8.952947310863&,\\C^\prime_{\mathbf{7a}}&{}\approx{}&0.624902704110&{}:{}&-0.937354056165&{}:{}&1.312451352055&,\\[.5em] A^\prime_{\mathbf{b}}&{}\approx{}&0.882461329374&{}:{}&-0.264462008909&{}:{}&0.382000679535&,\\B^\prime_{\mathbf{b}}&{}\approx{}&0.828080165740&{}:{}&-1.622253858178&{}:{}&1.794173692438&,\\C^\prime_{\mathbf{b}}&{}\approx{}&0.356373904386&{}:{}&-0.534560856579&{}:{}&1.178186952193&,\\[.5em] A^\prime_{\mathbf{1b}}&{}\approx{}&0.924257658374&{}:{}&-0.170420268659&{}:{}&0.246162610286&,\\B^\prime_{\mathbf{1b}}&{}\approx{}&0.417927945364&{}:{}&-0.323438493651&{}:{}&0.905510548288&,\\C^\prime_{\mathbf{1b}}&{}\approx{}&1.074140290046&{}:{}&-1.611210435069&{}:{}&1.537070145023&,\\[.5em] A^\prime_{\mathbf{2b}}&{}\approx{}&3.117538670626&{}:{}&4.764462008909&{}:{}&-6.882000679535&,\\B^\prime_{\mathbf{2b}}&{}\approx{}&-0.613794451455&{}:{}&2.943682429607&{}:{}&-1.329887978152&,\\C^\prime_{\mathbf{2b}}&{}\approx{}&-0.731373904386&{}:{}&1.097060856579&{}:{}&0.634313047807&,\\[.5em] A^\prime_{\mathbf{3b}}&{}\approx{}&3.075742341626&{}:{}&4.670420268659&{}:{}&-6.746162610286&,\\B^\prime_{\mathbf{3b}}&{}\approx{}&-0.203642231078&{}:{}&1.644867065080&{}:{}&-0.441224834002&,\\C^\prime_{\mathbf{3b}}&{}\approx{}&-1.449140290046&{}:{}&2.173710435069&{}:{}&0.275429854977&,\\[.5em] A^\prime_{\mathbf{4b}}&{}\approx{}&-4.728748213577&{}:{}&-12.889683480548&{}:{}&18.618431694126&,\\B^\prime_{\mathbf{4b}}&{}\approx{}&0.226879143281&{}:{}&0.281549379609&{}:{}&0.491571477110&,\\C^\prime_{\mathbf{4b}}&{}\approx{}&0.014201689055&{}:{}&-0.021302533582&{}:{}&1.007100844527&,\\[.5em] A^\prime_{\mathbf{5b}}&{}\approx{}&-0.900660823394&{}:{}&-4.276486852636&{}:{}&6.177147676029&,\\B^\prime_{\mathbf{5b}}&{}\approx{}&0.222400965174&{}:{}&0.295730276948&{}:{}&0.481868757878&,\\C^\prime_{\mathbf{5b}}&{}\approx{}&0.022038500742&{}:{}&-0.033057751114&{}:{}&1.011019250371&,\\[.5em] A^\prime_{\mathbf{6b}}&{}\approx{}&8.728748213577&{}:{}&17.389683480548&{}:{}&-25.118431694126&,\\B^\prime_{\mathbf{6b}}&{}\approx{}&-0.012593428996&{}:{}&1.039879191820&{}:{}&-0.027285762824&,\\C^\prime_{\mathbf{6b}}&{}\approx{}&-0.389201689055&{}:{}&0.583802533582&{}:{}&0.805399155473&,\\[.5em] A^\prime_{\mathbf{7b}}&{}\approx{}&4.900660823394&{}:{}&8.776486852636&{}:{}&-12.677147676029&,\\B^\prime_{\mathbf{7b}}&{}\approx{}&-0.008115250889&{}:{}&1.025698294480&{}:{}&-0.017583043592&,\\C^\prime_{\mathbf{7b}}&{}\approx{}&-0.397038500742&{}:{}&0.595557751114&{}:{}&0.801480749629&,\\[.5em] A^\prime_{\mathbf{c}}&{}\approx{}&1.407583257728&{}:{}&0.917062329887&{}:{}&-1.324645587615&,\\B^\prime_{\mathbf{c}}&{}\approx{}&0.679566334881&{}:{}&1.792827390695&{}:{}&-1.472393725577&,\\C^\prime_{\mathbf{c}}&{}\approx{}&10.856414843638&{}:{}&16.284622265457&{}:{}&-26.141037109095&,\\[.5em] A^\prime_{\mathbf{1c}}&{}\approx{}&0.192416742272&{}:{}&-1.817062329887&{}:{}&2.624645587615&,\\B^\prime_{\mathbf{1c}}&{}\approx{}&-1.054566334881&{}:{}&-0.230327390695&{}:{}&2.284893725577&,\\C^\prime_{\mathbf{1c}}&{}\approx{}&-10.642129129352&{}:{}&-15.963193694029&{}:{}&27.605322823381&,\\[.5em] A^\prime_{\mathbf{2c}}&{}\approx{}&1.198601612729&{}:{}&0.446853628640&{}:{}&-0.645455241369&,\\B^\prime_{\mathbf{2c}}&{}\approx{}&18.623725976367&{}:{}&22.727680305761&{}:{}&-40.351406282128&,\\C^\prime_{\mathbf{2c}}&{}\approx{}&0.602609334218&{}:{}&0.903914001327&{}:{}&-0.506523335545&,\\[.5em] A^\prime_{\mathbf{3c}}&{}\approx{}&0.401398387271&{}:{}&-1.346853628640&{}:{}&1.945455241369&,\\B^\prime_{\mathbf{3c}}&{}\approx{}&-18.998725976367&{}:{}&-21.165180305761&{}:{}&41.163906282128&,\\C^\prime_{\mathbf{3c}}&{}\approx{}&-0.388323619932&{}:{}&-0.582485429898&{}:{}&1.970809049831&,\\[.5em] A^\prime_{\mathbf{4c}}&{}\approx{}&20.865307708125&{}:{}&44.696942343280&{}:{}&-64.562250051405&,\\B^\prime_{\mathbf{4c}}&{}\approx{}&0.186189011933&{}:{}&1.217220513922&{}:{}&-0.403409525855&,\\C^\prime_{\mathbf{4c}}&{}\approx{}&0.432633888068&{}:{}&0.648950832103&{}:{}&-0.081584720171&,\\[.5em] A^\prime_{\mathbf{5c}}&{}\approx{}&-19.265307708125&{}:{}&-45.596942343280&{}:{}&65.862250051405&,\\B^\prime_{\mathbf{5c}}&{}\approx{}&-0.561189011933&{}:{}&0.345279486078&{}:{}&1.215909525855&,\\C^\prime_{\mathbf{5c}}&{}\approx{}&-0.218348173783&{}:{}&-0.327522260674&{}:{}&1.545870434457&,\\[.5em] A^\prime_{\mathbf{6c}}&{}\approx{}&1.724870757207&{}:{}&1.630959203716&{}:{}&-2.355829960922&,\\B^\prime_{\mathbf{6c}}&{}\approx{}&0.382109304120&{}:{}&1.445794188140&{}:{}&-0.827903492259&,\\C^\prime_{\mathbf{6c}}&{}\approx{}&0.320679435390&{}:{}&0.481019153086&{}:{}&0.198301411524&,\\[.5em] A^\prime_{\mathbf{7c}}&{}\approx{}&-0.124870757207&{}:{}&-2.530959203716&{}:{}&3.655829960922&,\\B^\prime_{\mathbf{7c}}&{}\approx{}&-0.757109304120&{}:{}&0.116705811860&{}:{}&1.640403492259&,\\C^\prime_{\mathbf{7c}}&{}\approx{}&-0.106393721105&{}:{}&-0.159590581657&{}:{}&1.265984302762&. \end{alignedat} \] \[ \begin{alignedat}{4} A^{\prime\prime}&{}\approx{}&0.113238597558&{}:{}&0.260435106540&{}:{}&0.626326295902&,\\B^{\prime\prime}&{}\approx{}&0.174423075766&{}:{}&0.176128540332&{}:{}&0.649448383901&,\\C^{\prime\prime}&{}\approx{}&0.249574943921&{}:{}&0.386403065307&{}:{}&0.364021990772&,\\[.5em] A^{\prime\prime}_{\mathbf{1}}&{}\approx{}&0.053320111467&{}:{}&0.039882564433&{}:{}&0.906797324100&,\\B^{\prime\prime}_{\mathbf{1}}&{}\approx{}&0.025440898308&{}:{}&0.078989843797&{}:{}&0.895569257895&,\\C^{\prime\prime}_{\mathbf{1}}&{}\approx{}&0.142186646282&{}:{}&0.220139710766&{}:{}&0.637673642951&,\\[.5em] A^{\prime\prime}_{\mathbf{2}}&{}\approx{}&0.011603226314&{}:{}&0.986660969284&{}:{}&0.001735804402&,\\B^{\prime\prime}_{\mathbf{2}}&{}\approx{}&0.023776760580&{}:{}&0.887692644112&{}:{}&0.088530595308&,\\C^{\prime\prime}_{\mathbf{2}}&{}\approx{}&0.000460537290&{}:{}&0.974703809901&{}:{}&0.024835652809&,\\[.5em] A^{\prime\prime}_{\mathbf{3}}&{}\approx{}&0.034346397050&{}:{}&0.949855089425&{}:{}&0.015798513524&,\\B^{\prime\prime}_{\mathbf{3}}&{}\approx{}&0.006622650490&{}:{}&0.760247130897&{}:{}&0.233130218614&,\\C^{\prime\prime}_{\mathbf{3}}&{}\approx{}&0.000437969453&{}:{}&0.926940128751&{}:{}&0.072621901796&,\\[.5em] A^{\prime\prime}_{\mathbf{4}}&{}\approx{}&0.921234039768&{}:{}&0.023132965856&{}:{}&0.055632994376&,\\B^{\prime\prime}_{\mathbf{4}}&{}\approx{}&0.988661089360&{}:{}&0.010900076171&{}:{}&0.000438834469&,\\C^{\prime\prime}_{\mathbf{4}}&{}\approx{}&0.984145713436&{}:{}&0.000181640035&{}:{}&0.015672646529&,\\[.5em] A^{\prime\prime}_{\mathbf{5}}&{}\approx{}&0.837625355554&{}:{}&0.006840662084&{}:{}&0.155533982361&,\\B^{\prime\prime}_{\mathbf{5}}&{}\approx{}&0.963301984604&{}:{}&0.032655592164&{}:{}&0.004042423232&,\\C^{\prime\prime}_{\mathbf{5}}&{}\approx{}&0.953151902146&{}:{}&0.000175919625&{}:{}&0.046672178229&,\\[.5em] A^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.518119823625&{}:{}&0.481033907190&{}:{}&0.000846269184&,\\B^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.710189970238&{}:{}&0.289494799556&{}:{}&0.000315230206&,\\C^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.543153291088&{}:{}&0.137038586144&{}:{}&0.319808122768&,\\[.5em] A^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.765128279731&{}:{}&0.231029116630&{}:{}&0.003842603639&,\\B^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.442954877516&{}:{}&0.555186296159&{}:{}&0.001858826325&,\\C^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.326506623684&{}:{}&0.082378228781&{}:{}&0.591115147535&,\\[.5em] A^{\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.160672096378&{}:{}&0.671978078225&{}:{}&0.488694018153&,\\B^{\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.376283018429&{}:{}&0.454562743015&{}:{}&0.921720275413&,\\C^{\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.243121193007&{}:{}&0.818889725805&{}:{}&0.424231467202&,\\[.5em] A^{\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.115085648128&{}:{}&0.934864950700&{}:{}&0.180220697428&,\\B^{\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.263443026642&{}:{}&0.618128815849&{}:{}&0.645314210793&,\\C^{\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.066243810640&{}:{}&0.841732392764&{}:{}&0.224511417877&,\\[.5em] A^{\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.025044299121&{}:{}&0.007843725308&{}:{}&1.017200573812&,\\B^{\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.002212703037&{}:{}&0.035694680695&{}:{}&0.966518022342&,\\C^{\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.038956596460&{}:{}&0.131215038058&{}:{}&0.907741558401&,\\[.5em] A^{\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.048733450750&{}:{}&0.029645154824&{}:{}&1.019088295925&,\\B^{\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.002140701444&{}:{}&0.067073278699&{}:{}&0.935067422746&,\\C^{\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.017554802437&{}:{}&0.223061531585&{}:{}&0.794493270851&,\\[.5em] A^{\prime\prime}_{\mathbf{4a}}&{}\approx{}&1.307121490516&{}:{}&-0.008681580748&{}:{}&-0.298439909768&,\\B^{\prime\prime}_{\mathbf{4a}}&{}\approx{}&1.650624752914&{}:{}&-0.564674379254&{}:{}&-0.085950373660&,\\C^{\prime\prime}_{\mathbf{4a}}&{}\approx{}&1.982771265040&{}:{}&-0.003003405287&{}:{}&-0.979767859754&,\\[.5em] A^{\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.807923019671&{}:{}&-0.006182294991&{}:{}&-0.801740724680&,\\B^{\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.295677103731&{}:{}&-0.228209357951&{}:{}&-0.067467745780&,\\C^{\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.341945902724&{}:{}&-0.000538828060&{}:{}&-0.341407074664&,\\[.5em] A^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.118305158587&{}:{}&-0.099184619976&{}:{}&-0.019120538611&,\\B^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.026599403674&{}:{}&-0.026299626804&{}:{}&-0.000299776870&,\\C^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.040061954065&{}:{}&-0.001575435163&{}:{}&-0.038486518902&,\\[.5em] A^{\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.085625991078&{}:{}&-0.049573681585&{}:{}&-0.036052309493&,\\B^{\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.013665968550&{}:{}&-0.013369968368&{}:{}&-0.000296000183&,\\C^{\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.019839282796&{}:{}&-0.000409493424&{}:{}&-0.019429789372&,\\[.5em] A^{\prime\prime}_{\mathbf{b}}&{}\approx{}&0.498299037933&{}:{}&-0.861821669413&{}:{}&1.363522631480&,\\B^{\prime\prime}_{\mathbf{b}}&{}\approx{}&0.708335977919&{}:{}&-0.353859805823&{}:{}&0.645523827905&,\\C^{\prime\prime}_{\mathbf{b}}&{}\approx{}&0.872915384100&{}:{}&-0.502805689345&{}:{}&0.629890305246&,\\[.5em] A^{\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.601732861538&{}:{}&-0.684143097369&{}:{}&1.082410235832&,\\B^{\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.938594545532&{}:{}&-0.308237744934&{}:{}&0.369643199402&,\\C^{\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.816032991599&{}:{}&-0.203126914121&{}:{}&0.387093922522&,\\[.5em] A^{\prime\prime}_{\mathbf{2b}}&{}\approx{}&-0.667445442798&{}:{}&2.101077063119&{}:{}&-0.433631620321&,\\B^{\prime\prime}_{\mathbf{2b}}&{}\approx{}&-0.010999451647&{}:{}&1.783463066709&{}:{}&-0.772463615061&,\\C^{\prime\prime}_{\mathbf{2b}}&{}\approx{}&-0.009517497835&{}:{}&3.238551609440&{}:{}&-2.229034111606&,\\[.5em] A^{\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.357102229771&{}:{}&1.710026783542&{}:{}&-0.352924553771&,\\B^{\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.012027964215&{}:{}&2.966670776352&{}:{}&-1.954642812137&,\\C^{\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.002324864380&{}:{}&1.830602037678&{}:{}&-0.828277173298&,\\[.5em] A^{\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.026730180203&{}:{}&-0.003462008232&{}:{}&0.976731828029&,\\B^{\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.006376039684&{}:{}&-0.042534770762&{}:{}&1.036158731078&,\\C^{\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.099404279045&{}:{}&-0.057257596738&{}:{}&0.957853317693&,\\[.5em] A^{\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.040103048153&{}:{}&-0.003414439738&{}:{}&0.963311391585&,\\B^{\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.014960638134&{}:{}&-0.065608341954&{}:{}&1.050647703820&,\\C^{\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.141132448352&{}:{}&-0.035130685905&{}:{}&0.893998237553&,\\[.5em] A^{\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.024397428520&{}:{}&1.025584421291&{}:{}&-0.001186992771&,\\B^{\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.093038649228&{}:{}&1.129679714459&{}:{}&-0.036641065231&,\\C^{\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.003108148839&{}:{}&1.057620458610&{}:{}&-0.054512309771&,\\[.5em] A^{\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.015905403975&{}:{}&1.017082556843&{}:{}&-0.001177152868&,\\B^{\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.060389879342&{}:{}&1.115424647156&{}:{}&-0.055034767814&,\\C^{\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.001316270618&{}:{}&1.036433650440&{}:{}&-0.035117379822&,\\[.5em] A^{\prime\prime}_{\mathbf{c}}&{}\approx{}&1.279068322161&{}:{}&2.646516017306&{}:{}&-2.925584339466&,\\B^{\prime\prime}_{\mathbf{c}}&{}\approx{}&1.911322729339&{}:{}&1.736343153291&{}:{}&-2.647665882630&,\\C^{\prime\prime}_{\mathbf{c}}&{}\approx{}&1.062802832222&{}:{}&1.331814570986&{}:{}&-1.394617403208&,\\[.5em] A^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-1.918974661791&{}:{}&-1.648792221674&{}:{}&4.567766883465&,\\B^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.914825197230&{}:{}&-3.262733437258&{}:{}&5.177558634487&,\\C^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.474221901905&{}:{}&-0.968791933992&{}:{}&2.443013835897&,\\[.5em] A^{\prime\prime}_{\mathbf{2c}}&{}\approx{}&1.167443605865&{}:{}&1.587934386408&{}:{}&-1.755377992273&,\\B^{\prime\prime}_{\mathbf{2c}}&{}\approx{}&1.001438676347&{}:{}&0.598055864696&{}:{}&-0.599494541043&,\\C^{\prime\prime}_{\mathbf{2c}}&{}\approx{}&1.472943048489&{}:{}&0.797643319030&{}:{}&-1.270586367519&,\\[.5em] A^{\prime\prime}_{\mathbf{3c}}&{}\approx{}&-0.761090954928&{}:{}&-0.994757887471&{}:{}&2.755848842400&,\\B^{\prime\prime}_{\mathbf{3c}}&{}\approx{}&-0.149899191198&{}:{}&-0.813255307735&{}:{}&1.963154498933&,\\C^{\prime\prime}_{\mathbf{3c}}&{}\approx{}&-0.474097613890&{}:{}&-2.241222418773&{}:{}&3.715320032663&,\\[.5em] A^{\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.260338381621&{}:{}&1.046241756398&{}:{}&-0.306580138020&,\\B^{\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.725048476228&{}:{}&1.279327228771&{}:{}&-1.004375704999&,\\C^{\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.314597674643&{}:{}&1.487211368808&{}:{}&-0.801809043451&,\\[.5em] A^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.314377808135&{}:{}&-0.139070657065&{}:{}&1.453448465200&,\\B^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.354186518322&{}:{}&-0.650372901018&{}:{}&2.004559419340&,\\C^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.900234034020&{}:{}&-0.487504023687&{}:{}&2.387738057707&,\\[.5em] A^{\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.348709616457&{}:{}&0.921241792019&{}:{}&-0.269951408477&,\\B^{\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.640494701591&{}:{}&0.742926756197&{}:{}&-0.383421457788&,\\C^{\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.731283288886&{}:{}&1.493944815475&{}:{}&-1.225228104361&,\\[.5em] A^{\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.186569528526&{}:{}&-0.125547618778&{}:{}&1.312117147303&,\\B^{\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.107489690767&{}:{}&-0.300248858926&{}:{}&1.407738549693&,\\C^{\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.561285927098&{}:{}&-0.703356025722&{}:{}&2.264641952821&. \end{alignedat} \] \[ \begin{alignedat}{4} A^{\prime\prime\prime}&{}\approx{}&0.076951751851&{}:{}&0.238531854658&{}:{}&0.684516393491&,\\B^{\prime\prime\prime}&{}\approx{}&0.159380182962&{}:{}&0.121296926738&{}:{}&0.719322890300&,\\C^{\prime\prime\prime}&{}\approx{}&0.272329471274&{}:{}&0.428298678033&{}:{}&0.299371850692&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1}}&{}\approx{}&0.030448229362&{}:{}&-0.000122796753&{}:{}&0.969674567391&,\\B^{\prime\prime\prime}_{\mathbf{1}}&{}\approx{}&-0.001013592918&{}:{}&0.045027602578&{}:{}&0.955985990340&,\\C^{\prime\prime\prime}_{\mathbf{1}}&{}\approx{}&-0.015860879755&{}:{}&-0.001894419302&{}:{}&1.017755299057&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2}}&{}\approx{}&0.005963058155&{}:{}&1.005172793499&{}:{}&-0.011135851654&,\\B^{\prime\prime\prime}_{\mathbf{2}}&{}\approx{}&0.714499290504&{}:{}&-1.165393813405&{}:{}&1.450894522901&,\\C^{\prime\prime\prime}_{\mathbf{2}}&{}\approx{}&-0.005415613683&{}:{}&0.992656531755&{}:{}&0.012759081928&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3}}&{}\approx{}&0.018669393459&{}:{}&1.004606018408&{}:{}&-0.023275411867&,\\B^{\prime\prime\prime}_{\mathbf{3}}&{}\approx{}&1.351500958093&{}:{}&-2.081652390445&{}:{}&1.730151432352&,\\C^{\prime\prime\prime}_{\mathbf{3}}&{}\approx{}&-0.017705658692&{}:{}&0.978313953348&{}:{}&0.039391705344&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4}}&{}\approx{}&-0.400694693995&{}:{}&0.580918475699&{}:{}&0.819776218296&,\\B^{\prime\prime\prime}_{\mathbf{4}}&{}\approx{}&1.002017614697&{}:{}&0.005544041038&{}:{}&-0.007561655735&,\\C^{\prime\prime\prime}_{\mathbf{4}}&{}\approx{}&0.997362670103&{}:{}&-0.005333527367&{}:{}&0.007970857264&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5}}&{}\approx{}&-0.438795806075&{}:{}&0.651026653308&{}:{}&0.787769152767&,\\B^{\prime\prime\prime}_{\mathbf{5}}&{}\approx{}&1.003386395763&{}:{}&0.017201595647&{}:{}&-0.020587991410&,\\C^{\prime\prime\prime}_{\mathbf{5}}&{}\approx{}&0.992254434996&{}:{}&-0.016825524719&{}:{}&0.024571089722&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&-1.239839937101&{}:{}&-0.442429750252&{}:{}&2.682269687353&,\\B^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&1.116463320802&{}:{}&0.263332812965&{}:{}&-0.379796133767&,\\C^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&0.715920804132&{}:{}&0.040171027786&{}:{}&0.243908168081&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&-0.487157101029&{}:{}&0.436543219524&{}:{}&1.050613881506&,\\B^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&1.891030156368&{}:{}&2.035485509397&{}:{}&-2.926515665765&,\\C^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&0.523081656194&{}:{}&-0.336361283574&{}:{}&0.813279627379&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.102238559843&{}:{}&0.701825761030&{}:{}&0.400412798813&,\\B^{\prime\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.377152916947&{}:{}&0.381380271282&{}:{}&0.995772645665&,\\C^{\prime\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.196528416585&{}:{}&0.909472204096&{}:{}&0.287056212489&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.067973133574&{}:{}&1.002360450786&{}:{}&0.065612682789&,\\B^{\prime\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.127399428194&{}:{}&0.685968091671&{}:{}&0.441431336523&,\\C^{\prime\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.016747305823&{}:{}&0.886495956863&{}:{}&0.130251348960&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.012954739385&{}:{}&-0.011317414656&{}:{}&1.024272154041&,\\B^{\prime\prime\prime}_{\mathbf{2a}}&{}\approx{}&0.010002901988&{}:{}&0.018432167305&{}:{}&0.971564930708&,\\C^{\prime\prime\prime}_{\mathbf{2a}}&{}\approx{}&0.386330225039&{}:{}&-0.414606747734&{}:{}&1.028276522696&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.026060053842&{}:{}&-0.007384781057&{}:{}&1.033444834899&,\\B^{\prime\prime\prime}_{\mathbf{3a}}&{}\approx{}&0.021498833453&{}:{}&0.035662885253&{}:{}&0.942838281294&,\\C^{\prime\prime\prime}_{\mathbf{3a}}&{}\approx{}&0.324390415097&{}:{}&-0.101657786824&{}:{}&0.777267371727&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4a}}&{}\approx{}&0.238279829948&{}:{}&0.354254552399&{}:{}&0.407465617652&,\\B^{\prime\prime\prime}_{\mathbf{4a}}&{}\approx{}&0.973678701061&{}:{}&-0.187982573584&{}:{}&0.214303872523&,\\C^{\prime\prime\prime}_{\mathbf{4a}}&{}\approx{}&1.095909697900&{}:{}&0.209707320165&{}:{}&-0.305617018065&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5a}}&{}\approx{}&0.265047512049&{}:{}&0.395758578165&{}:{}&0.339193909786&,\\B^{\prime\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.013929015791&{}:{}&-0.094861717511&{}:{}&0.080932701720&,\\C^{\prime\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.043850210556&{}:{}&0.097215823908&{}:{}&-0.141066034464&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6a}}&{}\approx{}&0.224462493476&{}:{}&0.296877725876&{}:{}&0.478659780648&,\\B^{\prime\prime\prime}_{\mathbf{6a}}&{}\approx{}&0.994582072662&{}:{}&-0.012849426625&{}:{}&0.018267353963&,\\C^{\prime\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.007323000053&{}:{}&0.011475046251&{}:{}&-0.018798046304&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7a}}&{}\approx{}&0.221782513776&{}:{}&0.312418957663&{}:{}&0.465798528560&,\\B^{\prime\prime\prime}_{\mathbf{7a}}&{}\approx{}&0.997356314757&{}:{}&-0.006606470142&{}:{}&0.009250155385&,\\C^{\prime\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.003358534485&{}:{}&0.006241573690&{}:{}&-0.009600108175&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{b}}&{}\approx{}&0.426078114356&{}:{}&-0.834710084236&{}:{}&1.408631969880&,\\B^{\prime\prime\prime}_{\mathbf{b}}&{}\approx{}&0.734844990160&{}:{}&-0.220223341086&{}:{}&0.485378350926&,\\C^{\prime\prime\prime}_{\mathbf{b}}&{}\approx{}&0.960172837354&{}:{}&-0.375813346611&{}:{}&0.415640509257&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.603475761431&{}:{}&-0.467035749577&{}:{}&0.863559988147&,\\B^{\prime\prime\prime}_{\mathbf{1b}}&{}\approx{}&1.008557181205&{}:{}&-0.185963929238&{}:{}&0.177406748033&,\\C^{\prime\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.853822692194&{}:{}&-0.081225971710&{}:{}&0.227403279516&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2b}}&{}\approx{}&-0.214446567756&{}:{}&1.028459270193&{}:{}&0.185987297563&,\\B^{\prime\prime\prime}_{\mathbf{2b}}&{}\approx{}&0.293090456776&{}:{}&0.447923344027&{}:{}&0.258986199197&,\\C^{\prime\prime\prime}_{\mathbf{2b}}&{}\approx{}&0.271829716307&{}:{}&1.328237352618&{}:{}&-0.600067068924&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.137602614501&{}:{}&1.111449267985&{}:{}&0.026153346517&,\\B^{\prime\prime\prime}_{\mathbf{3b}}&{}\approx{}&0.368884744243&{}:{}&0.560140153157&{}:{}&0.070975102600&,\\C^{\prime\prime\prime}_{\mathbf{3b}}&{}\approx{}&0.143197773043&{}:{}&1.170884277753&{}:{}&-0.314082050796&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.013669582095&{}:{}&0.016963491235&{}:{}&0.969366926669&,\\B^{\prime\prime\prime}_{\mathbf{4b}}&{}\approx{}&-0.007991049150&{}:{}&-0.021782105870&{}:{}&1.029773155020&,\\C^{\prime\prime\prime}_{\mathbf{4b}}&{}\approx{}&-0.192589899859&{}:{}&0.434308482969&{}:{}&0.758281416890&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.020744798798&{}:{}&0.027584705349&{}:{}&0.951670495854&,\\B^{\prime\prime\prime}_{\mathbf{5b}}&{}\approx{}&-0.007170154719&{}:{}&-0.034045082888&{}:{}&1.041215237607&,\\C^{\prime\prime\prime}_{\mathbf{5b}}&{}\approx{}&-0.099328488719&{}:{}&0.418087862595&{}:{}&0.681240626124&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.011955641829&{}:{}&0.987215091870&{}:{}&0.024740549959&,\\B^{\prime\prime\prime}_{\mathbf{6b}}&{}\approx{}&0.174195922355&{}:{}&0.347038530524&{}:{}&0.478765547120&,\\C^{\prime\prime\prime}_{\mathbf{6b}}&{}\approx{}&0.009277108564&{}:{}&1.017419321678&{}:{}&-0.026696430241&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.007848671742&{}:{}&0.992004970691&{}:{}&0.015843701051&,\\B^{\prime\prime\prime}_{\mathbf{7b}}&{}\approx{}&0.192271477853&{}:{}&0.344334806739&{}:{}&0.463393715408&,\\C^{\prime\prime\prime}_{\mathbf{7b}}&{}\approx{}&0.006697282034&{}:{}&1.010627408744&{}:{}&-0.017324690778&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{c}}&{}\approx{}&0.812806714508&{}:{}&2.144341275183&{}:{}&-1.957147989691&,\\B^{\prime\prime\prime}_{\mathbf{c}}&{}\approx{}&1.651079526095&{}:{}&1.075703926370&{}:{}&-1.726783452465&,\\C^{\prime\prime\prime}_{\mathbf{c}}&{}\approx{}&0.830010086176&{}:{}&0.951094116572&{}:{}&-0.781104202748&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.726978457596&{}:{}&-0.158779059876&{}:{}&1.885757517473&,\\B^{\prime\prime\prime}_{\mathbf{1c}}&{}\approx{}&0.126788496599&{}:{}&-1.197310578655&{}:{}&2.070522082056&,\\C^{\prime\prime\prime}_{\mathbf{1c}}&{}\approx{}&0.075384040660&{}:{}&-0.103654176404&{}:{}&1.028270135744&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2c}}&{}\approx{}&0.724736667707&{}:{}&0.884440810095&{}:{}&-0.609177477802&,\\B^{\prime\prime\prime}_{\mathbf{2c}}&{}\approx{}&0.859179777535&{}:{}&0.320312935648&{}:{}&-0.179492713183&,\\C^{\prime\prime\prime}_{\mathbf{2c}}&{}\approx{}&1.307524912015&{}:{}&0.396586277823&{}:{}&-0.704111189838&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3c}}&{}\approx{}&-0.337707757521&{}:{}&-0.376217099372&{}:{}&1.713924856893&,\\B^{\prime\prime\prime}_{\mathbf{3c}}&{}\approx{}&0.111142854050&{}:{}&-0.372929142272&{}:{}&1.261786288222&,\\C^{\prime\prime\prime}_{\mathbf{3c}}&{}\approx{}&0.298091278401&{}:{}&-0.742848552872&{}:{}&1.444757274472&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.136073377978&{}:{}&0.889586906089&{}:{}&-0.025660284068&,\\B^{\prime\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.348085546347&{}:{}&0.745656848834&{}:{}&-0.093742395181&,\\C^{\prime\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.138081347144&{}:{}&1.289175350263&{}:{}&-0.427256697407&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.149362843508&{}:{}&0.091897604459&{}:{}&1.057465239049&,\\B^{\prime\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.128135977182&{}:{}&-0.303270980780&{}:{}&1.431406957962&,\\C^{\prime\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.295028954361&{}:{}&0.286414347270&{}:{}&1.008614607091&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.185113271195&{}:{}&0.700416579120&{}:{}&0.114470149684&,\\B^{\prime\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.428199186483&{}:{}&0.404885642185&{}:{}&0.166915171332&,\\C^{\prime\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.495211159428&{}:{}&1.181148667237&{}:{}&-0.676359826665&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.090471558268&{}:{}&0.013945881527&{}:{}&1.076525676741&,\\B^{\prime\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.007167618967&{}:{}&-0.145277818439&{}:{}&1.152445437407&,\\C^{\prime\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.032938289373&{}:{}&0.068606945157&{}:{}&0.964331344216&. \end{alignedat} \] \[ \begin{alignedat}{4} A^*&{}\approx{}&0.000000000000&{}:{}&0.223831198584&{}:{}&0.776168801416&,\\B^*&{}\approx{}&0.154852182538&{}:{}&0.000000000000&{}:{}&0.845147817462&,\\C^*&{}\approx{}&0.388514034719&{}:{}&0.611485965281&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1}}&{}\approx{}&0.000000000000&{}:{}&-0.103495636770&{}:{}&1.103495636770&,\\B^*_{\mathbf{1}}&{}\approx{}&-0.063365707697&{}:{}&0.000000000000&{}:{}&1.063365707697&,\\C^*_{\mathbf{1}}&{}\approx{}&0.388514034719&{}:{}&0.611485965281&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2}}&{}\approx{}&0.000000000000&{}:{}&1.103495636770&{}:{}&-0.103495636770&,\\B^*_{\mathbf{2}}&{}\approx{}&0.154852182538&{}:{}&0.000000000000&{}:{}&0.845147817462&,\\C^*_{\mathbf{2}}&{}\approx{}&-0.017484936752&{}:{}&1.017484936752&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3}}&{}\approx{}&0.000000000000&{}:{}&0.776168801416&{}:{}&0.223831198584&,\\B^*_{\mathbf{3}}&{}\approx{}&-0.063365707697&{}:{}&0.000000000000&{}:{}&1.063365707697&,\\C^*_{\mathbf{3}}&{}\approx{}&-0.017484936752&{}:{}&1.017484936752&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4}}&{}\approx{}&0.000000000000&{}:{}&0.223831198584&{}:{}&0.776168801416&,\\B^*_{\mathbf{4}}&{}\approx{}&1.063365707697&{}:{}&0.000000000000&{}:{}&-0.063365707697&,\\C^*_{\mathbf{4}}&{}\approx{}&1.017484936752&{}:{}&-0.017484936752&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5}}&{}\approx{}&0.000000000000&{}:{}&-0.103495636770&{}:{}&1.103495636770&,\\B^*_{\mathbf{5}}&{}\approx{}&0.845147817462&{}:{}&0.000000000000&{}:{}&0.154852182538&,\\C^*_{\mathbf{5}}&{}\approx{}&1.017484936752&{}:{}&-0.017484936752&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6}}&{}\approx{}&0.000000000000&{}:{}&1.103495636770&{}:{}&-0.103495636770&,\\B^*_{\mathbf{6}}&{}\approx{}&1.063365707697&{}:{}&0.000000000000&{}:{}&-0.063365707697&,\\C^*_{\mathbf{6}}&{}\approx{}&0.611485965281&{}:{}&0.388514034719&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7}}&{}\approx{}&0.000000000000&{}:{}&0.776168801416&{}:{}&0.223831198584&,\\B^*_{\mathbf{7}}&{}\approx{}&0.845147817461&{}:{}&0.000000000000&{}:{}&0.154852182539&,\\C^*_{\mathbf{7}}&{}\approx{}&0.611485965281&{}:{}&0.388514034719&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{a}}&{}\approx{}&0.000000000000&{}:{}&0.723914668343&{}:{}&0.276085331657&,\\B^*_{\mathbf{a}}&{}\approx{}&-0.617697946698&{}:{}&0.000000000000&{}:{}&1.617697946698&,\\C^*_{\mathbf{a}}&{}\approx{}&-0.170445654633&{}:{}&1.170445654633&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1a}}&{}\approx{}&0.000000000000&{}:{}&1.244331168209&{}:{}&-0.244331168209&,\\B^*_{\mathbf{1a}}&{}\approx{}&-0.617697946698&{}:{}&0.000000000000&{}:{}&1.617697946698&,\\C^*_{\mathbf{1a}}&{}\approx{}&0.069746576075&{}:{}&0.930253423925&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2a}}&{}\approx{}&0.000000000000&{}:{}&-0.244331168209&{}:{}&1.244331168209&,\\B^*_{\mathbf{2a}}&{}\approx{}&0.027799277670&{}:{}&0.000000000000&{}:{}&0.972200722330&,\\C^*_{\mathbf{2a}}&{}\approx{}&-0.170445654633&{}:{}&1.170445654633&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3a}}&{}\approx{}&0.000000000000&{}:{}&0.276085331657&{}:{}&0.723914668343&,\\B^*_{\mathbf{3a}}&{}\approx{}&0.027799277670&{}:{}&0.000000000000&{}:{}&0.972200722330&,\\C^*_{\mathbf{3a}}&{}\approx{}&0.069746576075&{}:{}&0.930253423925&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4a}}&{}\approx{}&0.000000000000&{}:{}&0.276085331657&{}:{}&0.723914668343&,\\B^*_{\mathbf{4a}}&{}\approx{}&1.617697946698&{}:{}&0.000000000000&{}:{}&-0.617697946698&,\\C^*_{\mathbf{4a}}&{}\approx{}&1.170445654633&{}:{}&-0.170445654633&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5a}}&{}\approx{}&0.000000000000&{}:{}&-0.244331168209&{}:{}&1.244331168209&,\\B^*_{\mathbf{5a}}&{}\approx{}&1.617697946698&{}:{}&0.000000000000&{}:{}&-0.617697946698&,\\C^*_{\mathbf{5a}}&{}\approx{}&0.930253423925&{}:{}&0.069746576075&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6a}}&{}\approx{}&0.000000000000&{}:{}&1.244331168209&{}:{}&-0.244331168209&,\\B^*_{\mathbf{6a}}&{}\approx{}&0.972200722330&{}:{}&0.000000000000&{}:{}&0.027799277670&,\\C^*_{\mathbf{6a}}&{}\approx{}&1.170445654633&{}:{}&-0.170445654633&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7a}}&{}\approx{}&0.000000000000&{}:{}&0.723914668343&{}:{}&0.276085331657&,\\B^*_{\mathbf{7a}}&{}\approx{}&0.972200722330&{}:{}&0.000000000000&{}:{}&0.027799277670&,\\C^*_{\mathbf{7a}}&{}\approx{}&0.930253423925&{}:{}&0.069746576075&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{b}}&{}\approx{}&0.000000000000&{}:{}&-1.506126882702&{}:{}&2.506126882702&,\\B^*_{\mathbf{b}}&{}\approx{}&0.747655854551&{}:{}&0.000000000000&{}:{}&0.252344145449&,\\C^*_{\mathbf{b}}&{}\approx{}&1.254450661943&{}:{}&-0.254450661943&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1b}}&{}\approx{}&0.000000000000&{}:{}&-1.506126882702&{}:{}&2.506126882702&,\\B^*_{\mathbf{1b}}&{}\approx{}&1.285139704438&{}:{}&0.000000000000&{}:{}&-0.285139704438&,\\C^*_{\mathbf{1b}}&{}\approx{}&0.882346458175&{}:{}&0.117653541825&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2b}}&{}\approx{}&0.000000000000&{}:{}&2.506126882702&{}:{}&-1.506126882702&,\\B^*_{\mathbf{2b}}&{}\approx{}&0.252344145449&{}:{}&0.000000000000&{}:{}&0.747655854551&,\\C^*_{\mathbf{2b}}&{}\approx{}&-0.254450661943&{}:{}&1.254450661943&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3b}}&{}\approx{}&0.000000000000&{}:{}&2.506126882702&{}:{}&-1.506126882702&,\\B^*_{\mathbf{3b}}&{}\approx{}&-0.285139704438&{}:{}&0.000000000000&{}:{}&1.285139704438&,\\C^*_{\mathbf{3b}}&{}\approx{}&0.117653541825&{}:{}&0.882346458175&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4b}}&{}\approx{}&0.000000000000&{}:{}&0.043066455781&{}:{}&0.956933544219&,\\B^*_{\mathbf{4b}}&{}\approx{}&-0.285139704438&{}:{}&0.000000000000&{}:{}&1.285139704438&,\\C^*_{\mathbf{4b}}&{}\approx{}&1.254450661943&{}:{}&-0.254450661943&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5b}}&{}\approx{}&0.000000000000&{}:{}&0.043066455781&{}:{}&0.956933544219&,\\B^*_{\mathbf{5b}}&{}\approx{}&0.252344145449&{}:{}&0.000000000000&{}:{}&0.747655854551&,\\C^*_{\mathbf{5b}}&{}\approx{}&0.882346458175&{}:{}&0.117653541825&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6b}}&{}\approx{}&0.000000000000&{}:{}&0.956933544219&{}:{}&0.043066455781&,\\B^*_{\mathbf{6b}}&{}\approx{}&1.285139704438&{}:{}&0.000000000000&{}:{}&-0.285139704438&,\\C^*_{\mathbf{6b}}&{}\approx{}&-0.254450661943&{}:{}&1.254450661943&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7b}}&{}\approx{}&0.000000000000&{}:{}&0.956933544219&{}:{}&0.043066455781&,\\B^*_{\mathbf{7b}}&{}\approx{}&0.747655854551&{}:{}&0.000000000000&{}:{}&0.252344145449&,\\C^*_{\mathbf{7b}}&{}\approx{}&0.117653541825&{}:{}&0.882346458175&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{c}}&{}\approx{}&0.000000000000&{}:{}&4.872953846944&{}:{}&-3.872953846944&,\\B^*_{\mathbf{c}}&{}\approx{}&3.371234856368&{}:{}&0.000000000000&{}:{}&-2.371234856368&,\\C^*_{\mathbf{c}}&{}\approx{}&0.530508413411&{}:{}&0.469491586589&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1c}}&{}\approx{}&0.000000000000&{}:{}&-3.872953846944&{}:{}&4.872953846944&,\\B^*_{\mathbf{1c}}&{}\approx{}&-2.371234856368&{}:{}&0.000000000000&{}:{}&3.371234856368&,\\C^*_{\mathbf{1c}}&{}\approx{}&0.469491586589&{}:{}&0.530508413411&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2c}}&{}\approx{}&0.000000000000&{}:{}&4.872953846944&{}:{}&-3.872953846944&,\\B^*_{\mathbf{2c}}&{}\approx{}&0.683815606936&{}:{}&0.000000000000&{}:{}&0.316184393064&,\\C^*_{\mathbf{2c}}&{}\approx{}&2.391029432250&{}:{}&-1.391029432250&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3c}}&{}\approx{}&0.000000000000&{}:{}&-3.872953846944&{}:{}&4.872953846944&,\\B^*_{\mathbf{3c}}&{}\approx{}&0.316184393064&{}:{}&0.000000000000&{}:{}&0.683815606936&,\\C^*_{\mathbf{3c}}&{}\approx{}&-1.391029432250&{}:{}&2.391029432250&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4c}}&{}\approx{}&0.000000000000&{}:{}&0.709621848012&{}:{}&0.290378151988&,\\B^*_{\mathbf{4c}}&{}\approx{}&3.371234856368&{}:{}&0.000000000000&{}:{}&-2.371234856368&,\\C^*_{\mathbf{4c}}&{}\approx{}&-1.391029432250&{}:{}&2.391029432250&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5c}}&{}\approx{}&0.000000000000&{}:{}&0.290378151988&{}:{}&0.709621848012&,\\B^*_{\mathbf{5c}}&{}\approx{}&-2.371234856368&{}:{}&0.000000000000&{}:{}&3.371234856368&,\\C^*_{\mathbf{5c}}&{}\approx{}&2.391029432250&{}:{}&-1.391029432250&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6c}}&{}\approx{}&0.000000000000&{}:{}&0.709621848012&{}:{}&0.290378151988&,\\B^*_{\mathbf{6c}}&{}\approx{}&0.683815606936&{}:{}&0.000000000000&{}:{}&0.316184393064&,\\C^*_{\mathbf{6c}}&{}\approx{}&0.469491586589&{}:{}&0.530508413411&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7c}}&{}\approx{}&0.000000000000&{}:{}&0.290378151988&{}:{}&0.709621848012&,\\B^*_{\mathbf{7c}}&{}\approx{}&0.316184393064&{}:{}&0.000000000000&{}:{}&0.683815606936&,\\C^*_{\mathbf{7c}}&{}\approx{}&0.530508413411&{}:{}&0.469491586589&{}:{}&0.000000000000&. \end{alignedat} \]