Derousseau's Generalization of the Malfatti circles

The Smallest Eisenstein Triangle

\(C=120\degree\).   \(a:b:c=3:5:7\).


[Top] > The Smallest Eisenstein Triangle

Reference Triangle

reference triangle

Triangle Centers and their Extraversions

Approximately,
\[ \begin{alignedat}{4} I&{}\approx{}&0.200000000000&{}:{}&0.333333333333&{}:{}&0.466666666667&,\\ I_{\mathbf{a}}&{}\approx{}&-0.333333333333&{}:{}&0.555555555556&{}:{}&0.777777777778&,\\ I_{\mathbf{b}}&{}\approx{}&0.600000000000&{}:{}&-1.000000000000&{}:{}&1.400000000000&,\\ I_{\mathbf{c}}&{}\approx{}&3.000000000000&{}:{}&5.000000000000&{}:{}&-7.000000000000&. \end{alignedat} \] \[ \begin{alignedat}{4} P&{}\approx{}&0.146960670558&{}:{}&0.254360157408&{}:{}&0.598679172034&,\\ P_{\mathbf{1}}&{}\approx{}&0.025384292556&{}:{}&0.043935242169&{}:{}&0.930680465275&,\\ P_{\mathbf{2}}&{}\approx{}&0.000462444057&{}:{}&0.997653680320&{}:{}&0.001883875624&,\\ P_{\mathbf{3}}&{}\approx{}&0.000455578038&{}:{}&0.982841274568&{}:{}&0.016703147394&,\\ P_{\mathbf{4}}&{}\approx{}&0.999520436600&{}:{}&0.000142996715&{}:{}&0.000336566685&,\\ P_{\mathbf{5}}&{}\approx{}&0.996836421159&{}:{}&0.000142612726&{}:{}&0.003020966115&,\\ P_{\mathbf{6}}&{}\approx{}&0.848421382210&{}:{}&0.151292930412&{}:{}&0.000285687378&,\\ P_{\mathbf{7}}&{}\approx{}&0.846486737601&{}:{}&0.150947939045&{}:{}&0.002565323354&,\\ P_{\mathbf{a}}&{}\approx{}&-0.186969427939&{}:{}&0.694804074166&{}:{}&0.492165353773&,\\ P_{\mathbf{1a}}&{}\approx{}&-0.062106567306&{}:{}&0.898621547287&{}:{}&0.163485020019&,\\ P_{\mathbf{2a}}&{}\approx{}&-0.001947894931&{}:{}&0.007238645105&{}:{}&0.994709249826&,\\ P_{\mathbf{3a}}&{}\approx{}&-0.001907932339&{}:{}&0.027605922934&{}:{}&0.974302009405&,\\ P_{\mathbf{4a}}&{}\approx{}&1.045375736184&{}:{}&-0.001250253677&{}:{}&-0.044125482507&,\\ P_{\mathbf{5a}}&{}\approx{}&1.044405331076&{}:{}&-0.000320809529&{}:{}&-0.044084521547&,\\ P_{\mathbf{6a}}&{}\approx{}&1.001415569936&{}:{}&-0.001197677978&{}:{}&-0.000217891958&,\\ P_{\mathbf{7a}}&{}\approx{}&1.000525029026&{}:{}&-0.000307330836&{}:{}&-0.000217698190&,\\ P_{\mathbf{b}}&{}\approx{}&0.755037788899&{}:{}&-0.470293118044&{}:{}&0.715255329145&,\\ P_{\mathbf{1b}}&{}\approx{}&0.868845561449&{}:{}&-0.251798142965&{}:{}&0.382952581516&,\\ P_{\mathbf{2b}}&{}\approx{}&-0.003640020030&{}:{}&1.314880716372&{}:{}&-0.311240696342&,\\ P_{\mathbf{3b}}&{}\approx{}&-0.001690321366&{}:{}&1.312326392984&{}:{}&-0.310636071618&,\\ P_{\mathbf{4b}}&{}\approx{}&0.005430340741&{}:{}&-0.003382415975&{}:{}&0.997952075234&,\\ P_{\mathbf{5b}}&{}\approx{}&0.011598854870&{}:{}&-0.003361437575&{}:{}&0.991762582705&,\\ P_{\mathbf{6b}}&{}\approx{}&-0.002779412860&{}:{}&1.004004467550&{}:{}&-0.001225054690&,\\ P_{\mathbf{7b}}&{}\approx{}&-0.001291273044&{}:{}&1.002514509734&{}:{}&-0.001223236690&,\\ P_{\mathbf{c}}&{}\approx{}&1.147698972970&{}:{}&1.534870451693&{}:{}&-1.682569424663&,\\ P_{\mathbf{1c}}&{}\approx{}&-0.368149323909&{}:{}&-0.891918732013&{}:{}&2.260068055923&,\\ P_{\mathbf{2c}}&{}\approx{}&1.063690516406&{}:{}&0.661864397016&{}:{}&-0.725554913421&,\\ P_{\mathbf{3c}}&{}\approx{}&-0.143116987592&{}:{}&-0.745216502540&{}:{}&1.888333490132&,\\ P_{\mathbf{4c}}&{}\approx{}&0.210925647993&{}:{}&1.098299204994&{}:{}&-0.309224852988&,\\ P_{\mathbf{5c}}&{}\approx{}&-0.221397430242&{}:{}&-0.137761006992&{}:{}&1.359158437234&,\\ P_{\mathbf{6c}}&{}\approx{}&0.364883838671&{}:{}&0.884007411079&{}:{}&-0.248891249750&,\\ P_{\mathbf{7c}}&{}\approx{}&-0.092106566391&{}:{}&-0.123178333770&{}:{}&1.215284900161&. \end{alignedat} \] \[ \begin{alignedat}{4} P^-&{}\approx{}&0.129318325634&{}:{}&0.228091499336&{}:{}&0.642590175029&,\\ P^-_{\mathbf{1}}&{}\approx{}&-0.000555688782&{}:{}&0.000943800024&{}:{}&0.999611888757&,\\ P^-_{\mathbf{2}}&{}\approx{}&-0.005228462733&{}:{}&1.016600415211&{}:{}&-0.011371952478&,\\ P^-_{\mathbf{3}}&{}\approx{}&-0.017357695346&{}:{}&1.040822662412&{}:{}&-0.023464967066&,\\ P^-_{\mathbf{4}}&{}\approx{}&1.012053812179&{}:{}&-0.005080133848&{}:{}&-0.006973678331&,\\ P^-_{\mathbf{5}}&{}\approx{}&1.035414325931&{}:{}&-0.015988426907&{}:{}&-0.019425899024&,\\ P^-_{\mathbf{6}}&{}\approx{}&1.406431713679&{}:{}&-0.005365113819&{}:{}&-0.401066599860&,\\ P^-_{\mathbf{7}}&{}\approx{}&-1.481699780813&{}:{}&0.807770718910&{}:{}&1.673929061903&,\\ P^-_{\mathbf{a}}&{}\approx{}&-0.144617378745&{}:{}&0.735097205827&{}:{}&0.409520172919&,\\ P^-_{\mathbf{1a}}&{}\approx{}&-0.015328758158&{}:{}&0.957789289916&{}:{}&0.057539468242&,\\ P^-_{\mathbf{2a}}&{}\approx{}&0.009207054840&{}:{}&-0.011218555743&{}:{}&1.002011500903&,\\ P^-_{\mathbf{3a}}&{}\approx{}&0.020353108133&{}:{}&-0.007855173601&{}:{}&0.987502065469&,\\ P^-_{\mathbf{4a}}&{}\approx{}&0.716287621340&{}:{}&0.131655359368&{}:{}&0.152057019292&,\\ P^-_{\mathbf{5a}}&{}\approx{}&0.855657824819&{}:{}&0.075833166843&{}:{}&0.068509008337&,\\ P^-_{\mathbf{6a}}&{}\approx{}&0.973240786545&{}:{}&0.010554646162&{}:{}&0.016204567293&,\\ P^-_{\mathbf{7a}}&{}\approx{}&0.986118481558&{}:{}&0.005696353877&{}:{}&0.008185164566&,\\ P^-_{\mathbf{b}}&{}\approx{}&0.795294173629&{}:{}&-0.332751914798&{}:{}&0.537457741169&,\\ P^-_{\mathbf{1b}}&{}\approx{}&0.920740953615&{}:{}&-0.107372367136&{}:{}&0.186631413522&,\\ P^-_{\mathbf{2b}}&{}\approx{}&0.147266920696&{}:{}&0.736172288398&{}:{}&0.116560790906&,\\ P^-_{\mathbf{3b}}&{}\approx{}&0.109593851268&{}:{}&0.884655678720&{}:{}&0.005750470012&,\\ P^-_{\mathbf{4b}}&{}\approx{}&-0.007105785090&{}:{}&0.017630636481&{}:{}&0.989475148609&,\\ P^-_{\mathbf{5b}}&{}\approx{}&-0.006651931837&{}:{}&0.027551890820&{}:{}&0.979100041017&,\\ P^-_{\mathbf{6b}}&{}\approx{}&0.008037794643&{}:{}&0.968041507137&{}:{}&0.023920698220&,\\ P^-_{\mathbf{7b}}&{}\approx{}&0.006100425007&{}:{}&0.977897517502&{}:{}&0.016002057491&,\\ P^-_{\mathbf{c}}&{}\approx{}&0.908822192989&{}:{}&1.087999788320&{}:{}&-0.996821981309&,\\ P^-_{\mathbf{1c}}&{}\approx{}&0.065956458802&{}:{}&-0.132535537606&{}:{}&1.066579078804&,\\ P^-_{\mathbf{2c}}&{}\approx{}&0.912976887089&{}:{}&0.324203415270&{}:{}&-0.237180302359&,\\ P^-_{\mathbf{3c}}&{}\approx{}&0.101306788342&{}:{}&-0.298441051084&{}:{}&1.197134262742&,\\ P^-_{\mathbf{4c}}&{}\approx{}&0.090396537568&{}:{}&0.929688237120&{}:{}&-0.020084774688&,\\ P^-_{\mathbf{5c}}&{}\approx{}&-0.082404275863&{}:{}&0.083917200764&{}:{}&0.998487075099&,\\ P^-_{\mathbf{6c}}&{}\approx{}&0.229457479615&{}:{}&0.672474462969&{}:{}&0.098068057416&,\\ P^-_{\mathbf{7c}}&{}\approx{}&-0.009343125490&{}:{}&0.013948850609&{}:{}&0.995394274881&. \end{alignedat} \] \[ \begin{alignedat}{4} P^+&{}\approx{}&0.157555049665&{}:{}&0.270134711381&{}:{}&0.572310238954&,\\ P^+_{\mathbf{1}}&{}\approx{}&0.045382591818&{}:{}&0.077079280111&{}:{}&0.877538128072&,\\ P^+_{\mathbf{2}}&{}\approx{}&0.005846253208&{}:{}&0.979729365536&{}:{}&0.014424381255&,\\ P^+_{\mathbf{3}}&{}\approx{}&0.015570281012&{}:{}&0.933643609634&{}:{}&0.050786109354&,\\ P^+_{\mathbf{4}}&{}\approx{}&0.987368065008&{}:{}&0.005207348539&{}:{}&0.007424586453&,\\ P^+_{\mathbf{5}}&{}\approx{}&0.961664163908&{}:{}&0.014849608325&{}:{}&0.023486227768&,\\ P^+_{\mathbf{6}}&{}\approx{}&0.643356086122&{}:{}&0.208863778859&{}:{}&0.147780135019&,\\ P^+_{\mathbf{7}}&{}\approx{}&0.471129035537&{}:{}&0.256843015477&{}:{}&0.272027948987&,\\ P^+_{\mathbf{a}}&{}\approx{}&-0.213796211484&{}:{}&0.669281457387&{}:{}&0.544514754096&,\\ P^+_{\mathbf{1a}}&{}\approx{}&-0.096887287105&{}:{}&0.854628536176&{}:{}&0.242258750929&,\\ P^+_{\mathbf{2a}}&{}\approx{}&-0.012399228392&{}:{}&0.024531628469&{}:{}&0.987867599923&,\\ P^+_{\mathbf{3a}}&{}\approx{}&-0.021532679463&{}:{}&0.058867491912&{}:{}&0.962665187551&,\\ P^+_{\mathbf{4a}}&{}\approx{}&1.675071904802&{}:{}&-0.255559514775&{}:{}&-0.419512390027&,\\ P^+_{\mathbf{5a}}&{}\approx{}&1.304386723298&{}:{}&-0.105215529429&{}:{}&-0.199171193870&,\\ P^+_{\mathbf{6a}}&{}\approx{}&1.030832247618&{}:{}&-0.013468023643&{}:{}&-0.017364223975&,\\ P^+_{\mathbf{7a}}&{}\approx{}&1.015249647623&{}:{}&-0.006443566305&{}:{}&-0.008806081318&,\\ P^+_{\mathbf{b}}&{}\approx{}&0.728541307969&{}:{}&-0.560821810409&{}:{}&0.832280502439&,\\ P^+_{\mathbf{1b}}&{}\approx{}&0.831404646193&{}:{}&-0.355996859032&{}:{}&0.524592212839&,\\ P^+_{\mathbf{2b}}&{}\approx{}&-0.305447773169&{}:{}&2.472274071036&{}:{}&-1.166826297867&,\\ P^+_{\mathbf{3b}}&{}\approx{}&-0.178305273327&{}:{}&1.991066602544&{}:{}&-0.812761329217&,\\ P^+_{\mathbf{4b}}&{}\approx{}&0.017459223766&{}:{}&-0.023545228107&{}:{}&1.006086004341&,\\ P^+_{\mathbf{5b}}&{}\approx{}&0.028783583756&{}:{}&-0.032469068711&{}:{}&1.003685484955&,\\ P^+_{\mathbf{6b}}&{}\approx{}&-0.013999314970&{}:{}&1.041306229146&{}:{}&-0.027306914176&,\\ P^+_{\mathbf{7b}}&{}\approx{}&-0.008869284705&{}:{}&1.027751992775&{}:{}&-0.018882708070&,\\ P^+_{\mathbf{c}}&{}\approx{}&1.337596543337&{}:{}&1.890114913920&{}:{}&-2.227711457257&,\\ P^+_{\mathbf{1c}}&{}\approx{}&-0.953017124550&{}:{}&-1.915030601159&{}:{}&3.868047725708&,\\ P^+_{\mathbf{2c}}&{}\approx{}&1.194102742404&{}:{}&0.954041822919&{}:{}&-1.148144565324&,\\ P^+_{\mathbf{3c}}&{}\approx{}&-0.432557280265&{}:{}&-1.274276398347&{}:{}&2.706833678612&,\\ P^+_{\mathbf{4c}}&{}\approx{}&0.321866223190&{}:{}&1.253496548562&{}:{}&-0.575362771752&,\\ P^+_{\mathbf{5c}}&{}\approx{}&-0.373517596898&{}:{}&-0.380375300182&{}:{}&1.753892897080&,\\ P^+_{\mathbf{6c}}&{}\approx{}&0.487687695912&{}:{}&1.075824293278&{}:{}&-0.563511989190&,\\ P^+_{\mathbf{7c}}&{}\approx{}&-0.179551094354&{}:{}&-0.268061409903&{}:{}&1.447612504257&. \end{alignedat} \] \[ \begin{alignedat}{4} Q&{}\approx{}&0.113377225166&{}:{}&0.200117955067&{}:{}&0.686504819768&,\\ Q_{\mathbf{1}}&{}\approx{}&-0.064934692603&{}:{}&-0.114613828991&{}:{}&1.179548521594&,\\ Q_{\mathbf{2}}&{}\approx{}&-0.018096102781&{}:{}&1.127668918308&{}:{}&-0.109572815527&,\\ Q_{\mathbf{3}}&{}\approx{}&-0.012581667745&{}:{}&0.784033768415&{}:{}&0.228547899331&,\\ Q_{\mathbf{4}}&{}\approx{}&1.076539617477&{}:{}&-0.017275612770&{}:{}&-0.059264004707&,\\ Q_{\mathbf{5}}&{}\approx{}&0.870243223501&{}:{}&-0.013965101424&{}:{}&0.143721877922&,\\ Q_{\mathbf{6}}&{}\approx{}&0.661593775481&{}:{}&0.374827268378&{}:{}&-0.036421043859&,\\ Q_{\mathbf{7}}&{}\approx{}&0.577466102496&{}:{}&0.327164568049&{}:{}&0.095369329454&,\\ Q_{\mathbf{a}}&{}\approx{}&-0.107802540284&{}:{}&0.804860293848&{}:{}&0.302942246436&,\\ Q_{\mathbf{1a}}&{}\approx{}&0.077387626438&{}:{}&1.140083885251&{}:{}&-0.217471511689&,\\ Q_{\mathbf{2a}}&{}\approx{}&0.030604998768&{}:{}&-0.228498774114&{}:{}&1.197893775347&,\\ Q_{\mathbf{3a}}&{}\approx{}&0.018224037448&{}:{}&0.268478726828&{}:{}&0.713297235724&,\\ Q_{\mathbf{4a}}&{}\approx{}&1.959982000059&{}:{}&-0.262518899407&{}:{}&-0.697463100652&,\\ Q_{\mathbf{5a}}&{}\approx{}&1.404440927829&{}:{}&0.095331888542&{}:{}&-0.499772816371&,\\ Q_{\mathbf{6a}}&{}\approx{}&1.121567151553&{}:{}&-0.150222080727&{}:{}&0.028654929174&,\\ Q_{\mathbf{7a}}&{}\approx{}&0.914555045413&{}:{}&0.062078979562&{}:{}&0.023365975025&,\\ Q_{\mathbf{b}}&{}\approx{}&0.892334222867&{}:{}&-0.181836845053&{}:{}&0.289502622186&,\\ Q_{\mathbf{1b}}&{}\approx{}&1.089681915053&{}:{}&0.151463881335&{}:{}&-0.241145796388&,\\ Q_{\mathbf{2b}}&{}\approx{}&-1.212072001599&{}:{}&5.948042748385&{}:{}&-3.735970746785&,\\ Q_{\mathbf{3b}}&{}\approx{}&0.272066863629&{}:{}&1.957340181499&{}:{}&-1.229407045128&,\\ Q_{\mathbf{4b}}&{}\approx{}&-0.268633447366&{}:{}&0.054741213878&{}:{}&1.213892233488&,\\ Q_{\mathbf{5b}}&{}\approx{}&0.236893889655&{}:{}&0.032927836551&{}:{}&0.730178273794&,\\ Q_{\mathbf{6b}}&{}\approx{}&-0.242210876421&{}:{}&1.188609789827&{}:{}&0.053601086594&,\\ Q_{\mathbf{7b}}&{}\approx{}&0.117387866014&{}:{}&0.844527642600&{}:{}&0.038084491386&,\\ Q_{\mathbf{c}}&{}\approx{}&0.859918296271&{}:{}&0.741212616596&{}:{}&-0.601130912867&,\\ Q_{\mathbf{1c}}&{}\approx{}&1.370520539954&{}:{}&1.590010290344&{}:{}&-1.960530830298&,\\ Q_{\mathbf{2c}}&{}\approx{}&1.125007038184&{}:{}&-0.661448221993&{}:{}&0.536441183809&,\\ Q_{\mathbf{3c}}&{}\approx{}&0.716156161129&{}:{}&-1.218055616328&{}:{}&1.501899455199&,\\ Q_{\mathbf{4c}}&{}\approx{}&-0.714347000962&{}:{}&1.214978553222&{}:{}&0.499368447741&,\\ Q_{\mathbf{5c}}&{}\approx{}&-0.981883107052&{}:{}&0.577298464206&{}:{}&1.404584642846&,\\ Q_{\mathbf{6c}}&{}\approx{}&0.379221071192&{}:{}&0.439953570876&{}:{}&0.180825357932&,\\ Q_{\mathbf{7c}}&{}\approx{}&0.252581090427&{}:{}&0.217714045334&{}:{}&0.529704864240&. \end{alignedat} \] \[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.172965088465&{}:{}&0.293769570429&{}:{}&0.533265341105&,\\ I^\prime_{\mathbf{1}}&{}\approx{}&0.083698291999&{}:{}&0.142155920044&{}:{}&0.774145787956&,\\ I^\prime_{\mathbf{2}}&{}\approx{}&0.015613713290&{}:{}&0.936247947250&{}:{}&0.048138339461&,\\ I^\prime_{\mathbf{3}}&{}\approx{}&0.014242493332&{}:{}&0.854025234005&{}:{}&0.131732272663&,\\ I^\prime_{\mathbf{4}}&{}\approx{}&0.958339177159&{}:{}&0.014798265296&{}:{}&0.026862557545&,\\ I^\prime_{\mathbf{5}}&{}\approx{}&0.909477399214&{}:{}&0.014043762537&{}:{}&0.076478838249&,\\ I^\prime_{\mathbf{6}}&{}\approx{}&0.635649016855&{}:{}&0.346533535314&{}:{}&0.017817447831&,\\ I^\prime_{\mathbf{7}}&{}\approx{}&0.613777132768&{}:{}&0.334609751724&{}:{}&0.051613115508&,\\ I^\prime_{\mathbf{a}}&{}\approx{}&-0.252078775602&{}:{}&0.627345134507&{}:{}&0.624733641096&,\\ I^\prime_{\mathbf{1a}}&{}\approx{}&-0.156518182688&{}:{}&0.768614941193&{}:{}&0.387903241495&,\\ I^\prime_{\mathbf{2a}}&{}\approx{}&-0.027772123623&{}:{}&0.069116118911&{}:{}&0.958656004711&,\\ I^\prime_{\mathbf{3a}}&{}\approx{}&-0.026021777990&{}:{}&0.127785328297&{}:{}&0.898236449692&,\\ I^\prime_{\mathbf{4a}}&{}\approx{}&1.558793627719&{}:{}&-0.069594650621&{}:{}&-0.489198977098&,\\ I^\prime_{\mathbf{5a}}&{}\approx{}&1.507063777257&{}:{}&-0.034099271151&{}:{}&-0.472964506106&,\\ I^\prime_{\mathbf{6a}}&{}\approx{}&1.072016560229&{}:{}&-0.047861767358&{}:{}&-0.024154792871&,\\ I^\prime_{\mathbf{7a}}&{}\approx{}&1.047294131480&{}:{}&-0.023696387043&{}:{}&-0.023597744437&,\\ I^\prime_{\mathbf{b}}&{}\approx{}&0.681265979294&{}:{}&-0.694130366975&{}:{}&1.012864387681&,\\ I^\prime_{\mathbf{1b}}&{}\approx{}&0.758075783567&{}:{}&-0.526856043671&{}:{}&0.768780260103&,\\ I^\prime_{\mathbf{2b}}&{}\approx{}&-0.106249659921&{}:{}&2.607013108030&{}:{}&-1.500763448109&,\\ I^\prime_{\mathbf{3b}}&{}\approx{}&-0.070106174355&{}:{}&2.521836547934&{}:{}&-1.451730373579&,\\ I^\prime_{\mathbf{4b}}&{}\approx{}&0.048335533334&{}:{}&-0.049248256203&{}:{}&1.000912722870&,\\ I^\prime_{\mathbf{5b}}&{}\approx{}&0.069300614852&{}:{}&-0.048163321605&{}:{}&0.978862706753&,\\ I^\prime_{\mathbf{6b}}&{}\approx{}&-0.044399942077&{}:{}&1.089426837486&{}:{}&-0.045026895409&,\\ I^\prime_{\mathbf{7b}}&{}\approx{}&-0.029864174568&{}:{}&1.074264393877&{}:{}&-0.044400219308&,\\ I^\prime_{\mathbf{c}}&{}\approx{}&1.554181635732&{}:{}&2.320320697670&{}:{}&-2.874502333401&,\\ I^\prime_{\mathbf{1c}}&{}\approx{}&-1.289807158786&{}:{}&-2.591789921755&{}:{}&4.881597080540&,\\ I^\prime_{\mathbf{2c}}&{}\approx{}&1.321393924846&{}:{}&1.345654435015&{}:{}&-1.667048359862&,\\ I^\prime_{\mathbf{3c}}&{}\approx{}&-0.623958723754&{}:{}&-1.838128524240&{}:{}&3.462087247994&,\\ I^\prime_{\mathbf{4c}}&{}\approx{}&0.477011451243&{}:{}&1.405234547637&{}:{}&-0.882245998880&,\\ I^\prime_{\mathbf{5c}}&{}\approx{}&-0.566126464975&{}:{}&-0.576520425929&{}:{}&2.142646890904&,\\ I^\prime_{\mathbf{6c}}&{}\approx{}&0.572129290421&{}:{}&1.149659403542&{}:{}&-0.721788693962&,\\ I^\prime_{\mathbf{7c}}&{}\approx{}&-0.327264710139&{}:{}&-0.488590949150&{}:{}&1.815855659289&. \end{alignedat} \]

Central Triangles and their Extraversions

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.327040090657&{}:{}&0.280399962226&{}:{}&0.392559947117&,\\B^\prime&{}\approx{}&0.147886008493&{}:{}&0.507046638357&{}:{}&0.345067353150&,\\C^\prime&{}\approx{}&0.081129518039&{}:{}&0.135215863398&{}:{}&0.783654618563&,\\[.5em] A^\prime_{\mathbf{1}}&{}\approx{}&-0.004697758905&{}:{}&0.418624066210&{}:{}&0.586073692694&,\\B^\prime_{\mathbf{1}}&{}\approx{}&0.297168040796&{}:{}&0.009439864014&{}:{}&0.693392095190&,\\C^\prime_{\mathbf{1}}&{}\approx{}&0.027539679553&{}:{}&0.045899465921&{}:{}&0.926560854526&,\\[.5em] A^\prime_{\mathbf{2}}&{}\approx{}&-0.297275769760&{}:{}&0.540531570734&{}:{}&0.756744199027&,\\B^\prime_{\mathbf{2}}&{}\approx{}&0.005507935911&{}:{}&0.981640213631&{}:{}&0.012851850458&,\\C^\prime_{\mathbf{2}}&{}\approx{}&1.485840203979&{}:{}&2.476400339964&{}:{}&-2.962240543943&,\\[.5em] A^\prime_{\mathbf{3}}&{}\approx{}&-0.321093475754&{}:{}&0.550455614898&{}:{}&0.770637860857&,\\B^\prime_{\mathbf{3}}&{}\approx{}&0.016225903608&{}:{}&0.945913654641&{}:{}&0.037860441752&,\\C^\prime_{\mathbf{3}}&{}\approx{}&0.739430042465&{}:{}&1.232383404108&{}:{}&-0.971813446573&,\\[.5em] A^\prime_{\mathbf{4}}&{}\approx{}&0.987760142421&{}:{}&0.005099940658&{}:{}&0.007139916921&,\\B^\prime_{\mathbf{4}}&{}\approx{}&0.583774096392&{}:{}&-0.945913654641&{}:{}&1.362139558248&,\\C^\prime_{\mathbf{4}}&{}\approx{}&2.260569957535&{}:{}&3.767616595892&{}:{}&-5.028186553427&,\\[.5em] A^\prime_{\mathbf{5}}&{}\approx{}&0.963942436427&{}:{}&0.015023984822&{}:{}&0.021033578751&,\\B^\prime_{\mathbf{5}}&{}\approx{}&0.594492064089&{}:{}&-0.981640213631&{}:{}&1.387148149542&,\\C^\prime_{\mathbf{5}}&{}\approx{}&1.514159796021&{}:{}&2.523599660036&{}:{}&-3.037759456057&,\\[.5em] A^\prime_{\mathbf{6}}&{}\approx{}&0.671364425571&{}:{}&0.136931489345&{}:{}&0.191704085083&,\\B^\prime_{\mathbf{6}}&{}\approx{}&0.302831959204&{}:{}&-0.009439864014&{}:{}&0.706607904810&,\\C^\prime_{\mathbf{6}}&{}\approx{}&2.972460320447&{}:{}&4.954100534079&{}:{}&-6.926560854526&,\\[.5em] A^\prime_{\mathbf{7}}&{}\approx{}&0.339626576009&{}:{}&0.275155593329&{}:{}&0.385217830661&,\\B^\prime_{\mathbf{7}}&{}\approx{}&0.452113991507&{}:{}&-0.507046638357&{}:{}&1.054932646850&,\\C^\prime_{\mathbf{7}}&{}\approx{}&2.918870481961&{}:{}&4.864784136602&{}:{}&-6.783654618563&,\\[.5em] A^\prime_{\mathbf{a}}&{}\approx{}&-0.599580303007&{}:{}&0.666491792920&{}:{}&0.933088510088&,\\B^\prime_{\mathbf{a}}&{}\approx{}&-0.111674790330&{}:{}&0.851100279560&{}:{}&0.260574510770&,\\C^\prime_{\mathbf{a}}&{}\approx{}&-0.203565106639&{}:{}&0.339275177731&{}:{}&0.864289928907&,\\[.5em] A^\prime_{\mathbf{1a}}&{}\approx{}&-0.071420142185&{}:{}&0.446425059244&{}:{}&0.624995082941&,\\B^\prime_{\mathbf{1a}}&{}\approx{}&-0.055575084545&{}:{}&0.925899887274&{}:{}&0.129675197271&,\\C^\prime_{\mathbf{1a}}&{}\approx{}&-0.599685227256&{}:{}&0.999475378759&{}:{}&0.600209848496&,\\[.5em] A^\prime_{\mathbf{2a}}&{}\approx{}&0.170220055912&{}:{}&0.345741643370&{}:{}&0.484038300718&,\\B^\prime_{\mathbf{2a}}&{}\approx{}&-2.998426136278&{}:{}&-2.997901515037&{}:{}&6.996327651315&,\\C^\prime_{\mathbf{2a}}&{}\approx{}&-0.011115016909&{}:{}&0.018525028182&{}:{}&0.992589988727&,\\[.5em] A^\prime_{\mathbf{3a}}&{}\approx{}&0.185179977455&{}:{}&0.339508342727&{}:{}&0.475311679818&,\\B^\prime_{\mathbf{3a}}&{}\approx{}&-1.017825533194&{}:{}&-0.357100710925&{}:{}&2.374926244119&,\\C^\prime_{\mathbf{3a}}&{}\approx{}&-0.022334958066&{}:{}&0.037224930110&{}:{}&0.985110027956&,\\[.5em] A^\prime_{\mathbf{4a}}&{}\approx{}&1.799580303007&{}:{}&-0.333158459586&{}:{}&-0.466421843421&,\\B^\prime_{\mathbf{4a}}&{}\approx{}&3.111674790330&{}:{}&5.148899720440&{}:{}&-7.260574510770&,\\C^\prime_{\mathbf{4a}}&{}\approx{}&0.803565106639&{}:{}&-1.339275177731&{}:{}&1.535710071093&,\\[.5em] A^\prime_{\mathbf{5a}}&{}\approx{}&1.271420142185&{}:{}&-0.113091725910&{}:{}&-0.158328416275&,\\B^\prime_{\mathbf{5a}}&{}\approx{}&3.055575084545&{}:{}&5.074100112726&{}:{}&-7.129675197271&,\\C^\prime_{\mathbf{5a}}&{}\approx{}&1.199685227256&{}:{}&-1.999475378759&{}:{}&1.799790151504&,\\[.5em] A^\prime_{\mathbf{6a}}&{}\approx{}&1.029779944088&{}:{}&-0.012408310037&{}:{}&-0.017371634051&,\\B^\prime_{\mathbf{6a}}&{}\approx{}&5.998426136278&{}:{}&8.997901515037&{}:{}&-13.996327651315&,\\C^\prime_{\mathbf{6a}}&{}\approx{}&0.611115016909&{}:{}&-1.018525028182&{}:{}&1.407410011273&,\\[.5em] A^\prime_{\mathbf{7a}}&{}\approx{}&1.014820022545&{}:{}&-0.006175009394&{}:{}&-0.008645013151&,\\B^\prime_{\mathbf{7a}}&{}\approx{}&4.017825533194&{}:{}&6.357100710925&{}:{}&-9.374926244119&,\\C^\prime_{\mathbf{7a}}&{}\approx{}&0.622334958066&{}:{}&-1.037224930110&{}:{}&1.414889972044&,\\[.5em] A^\prime_{\mathbf{b}}&{}\approx{}&0.884489355921&{}:{}&-0.288776610198&{}:{}&0.404287254278&,\\B^\prime_{\mathbf{b}}&{}\approx{}&0.835089355133&{}:{}&-1.783631183776&{}:{}&1.948541828643&,\\C^\prime_{\mathbf{b}}&{}\approx{}&0.359305255565&{}:{}&-0.598842092609&{}:{}&1.239536837044&,\\[.5em] A^\prime_{\mathbf{1b}}&{}\approx{}&0.922629435690&{}:{}&-0.193426410776&{}:{}&0.270796975086&,\\B^\prime_{\mathbf{1b}}&{}\approx{}&0.415583153339&{}:{}&-0.385277177798&{}:{}&0.969694024458&,\\C^\prime_{\mathbf{1b}}&{}\approx{}&1.058482258555&{}:{}&-1.764137097591&{}:{}&1.705654839036&,\\[.5em] A^\prime_{\mathbf{2b}}&{}\approx{}&3.115510644079&{}:{}&5.288776610198&{}:{}&-7.404287254278&,\\B^\prime_{\mathbf{2b}}&{}\approx{}&-0.635089355133&{}:{}&3.116964517109&{}:{}&-1.481875161976&,\\C^\prime_{\mathbf{2b}}&{}\approx{}&-0.692638588899&{}:{}&1.154397648165&{}:{}&0.538240940734&,\\[.5em] A^\prime_{\mathbf{3b}}&{}\approx{}&3.077370564310&{}:{}&5.193426410776&{}:{}&-7.270796975086&,\\B^\prime_{\mathbf{3b}}&{}\approx{}&-0.215583153339&{}:{}&1.718610511131&{}:{}&-0.503027357792&,\\C^\prime_{\mathbf{3b}}&{}\approx{}&-1.391815591888&{}:{}&2.319692653146&{}:{}&0.072122938741&,\\[.5em] A^\prime_{\mathbf{4b}}&{}\approx{}&-5.350893551327&{}:{}&-15.877233878318&{}:{}&22.228127429646&,\\B^\prime_{\mathbf{4b}}&{}\approx{}&0.211551064408&{}:{}&0.294829785307&{}:{}&0.493619150285&,\\C^\prime_{\mathbf{4b}}&{}\approx{}&0.012895094052&{}:{}&-0.021491823420&{}:{}&1.008596729368&,\\[.5em] A^\prime_{\mathbf{5b}}&{}\approx{}&-1.155831533393&{}:{}&-5.389578833482&{}:{}&7.545410366875&,\\B^\prime_{\mathbf{5b}}&{}\approx{}&0.207737056431&{}:{}&0.307543145230&{}:{}&0.484719798339&,\\C^\prime_{\mathbf{5b}}&{}\approx{}&0.019251774013&{}:{}&-0.032086290022&{}:{}&1.012834516009&,\\[.5em] A^\prime_{\mathbf{6b}}&{}\approx{}&9.350893551327&{}:{}&20.877233878318&{}:{}&-29.228127429646&,\\B^\prime_{\mathbf{6b}}&{}\approx{}&-0.011551064408&{}:{}&1.038503548026&{}:{}&-0.026952483619&,\\C^\prime_{\mathbf{6b}}&{}\approx{}&-0.346228427385&{}:{}&0.577047378975&{}:{}&0.769181048410&,\\[.5em] A^\prime_{\mathbf{7b}}&{}\approx{}&5.155831533393&{}:{}&10.389578833482&{}:{}&-14.545410366875&,\\B^\prime_{\mathbf{7b}}&{}\approx{}&-0.007737056431&{}:{}&1.025790188103&{}:{}&-0.018053131672&,\\C^\prime_{\mathbf{7b}}&{}\approx{}&-0.352585107347&{}:{}&0.587641845578&{}:{}&0.764943261769&,\\[.5em] A^\prime_{\mathbf{c}}&{}\approx{}&1.396259365476&{}:{}&0.990648413689&{}:{}&-1.386907779164&,\\B^\prime_{\mathbf{c}}&{}\approx{}&0.676196490926&{}:{}&1.901595321235&{}:{}&-1.577791812161&,\\C^\prime_{\mathbf{c}}&{}\approx{}&11.093372939391&{}:{}&18.488954898986&{}:{}&-28.582327838377&,\\[.5em] A^\prime_{\mathbf{1c}}&{}\approx{}&0.203740634524&{}:{}&-1.990648413689&{}:{}&2.786907779164&,\\B^\prime_{\mathbf{1c}}&{}\approx{}&-1.009529824259&{}:{}&-0.346039765679&{}:{}&2.355569589938&,\\C^\prime_{\mathbf{1c}}&{}\approx{}&-10.893372939391&{}:{}&-18.155621565652&{}:{}&30.048994505044&,\\[.5em] A^\prime_{\mathbf{2c}}&{}\approx{}&1.205558966630&{}:{}&0.513897416576&{}:{}&-0.719456383207&,\\B^\prime_{\mathbf{2c}}&{}\approx{}&18.155621565652&{}:{}&25.207495420870&{}:{}&-42.363116986522&,\\C^\prime_{\mathbf{2c}}&{}\approx{}&0.605717894556&{}:{}&1.009529824259&{}:{}&-0.615247718815&,\\[.5em] A^\prime_{\mathbf{3c}}&{}\approx{}&0.394441033370&{}:{}&-1.513897416576&{}:{}&2.119456383207&,\\B^\prime_{\mathbf{3c}}&{}\approx{}&-18.488954898986&{}:{}&-23.651939865314&{}:{}&43.140894764300&,\\C^\prime_{\mathbf{3c}}&{}\approx{}&-0.405717894556&{}:{}&-0.676196490926&{}:{}&2.081914385482&,\\[.5em] A^\prime_{\mathbf{4c}}&{}\approx{}&22.786745878783&{}:{}&54.466864696957&{}:{}&-76.253610575740&,\\B^\prime_{\mathbf{4c}}&{}\approx{}&0.171299138859&{}:{}&1.228398851812&{}:{}&-0.399697990670&,\\C^\prime_{\mathbf{4c}}&{}\approx{}&0.398129682738&{}:{}&0.663549471230&{}:{}&-0.061679153967&,\\[.5em] A^\prime_{\mathbf{5c}}&{}\approx{}&-21.186745878783&{}:{}&-55.466864696957&{}:{}&77.653610575740&,\\B^\prime_{\mathbf{5c}}&{}\approx{}&-0.504632472192&{}:{}&0.327156703744&{}:{}&1.177475768448&,\\C^\prime_{\mathbf{5c}}&{}\approx{}&-0.198129682738&{}:{}&-0.330216137896&{}:{}&1.528345820634&,\\[.5em] A^\prime_{\mathbf{6c}}&{}\approx{}&1.811435789111&{}:{}&2.028589472778&{}:{}&-2.840025261889&,\\B^\prime_{\mathbf{6c}}&{}\approx{}&0.330216137896&{}:{}&1.440288183862&{}:{}&-0.770504321758&,\\C^\prime_{\mathbf{6c}}&{}\approx{}&0.302779483315&{}:{}&0.504632472192&{}:{}&0.192588044493&,\\[.5em] A^\prime_{\mathbf{7c}}&{}\approx{}&-0.211435789111&{}:{}&-3.028589472778&{}:{}&4.240025261889&,\\B^\prime_{\mathbf{7c}}&{}\approx{}&-0.663549471230&{}:{}&0.115267371694&{}:{}&1.548282099536&,\\C^\prime_{\mathbf{7c}}&{}\approx{}&-0.102779483315&{}:{}&-0.171299138859&{}:{}&1.274078622174&. \end{alignedat} \] \[ \begin{alignedat}{4} A^{\prime\prime}&{}\approx{}&0.104778228581&{}:{}&0.266938161975&{}:{}&0.628283609445&,\\B^{\prime\prime}&{}\approx{}&0.161133715053&{}:{}&0.182449852251&{}:{}&0.656416432696&,\\C^{\prime\prime}&{}\approx{}&0.231695575894&{}:{}&0.401019694120&{}:{}&0.367284729986&,\\[.5em] A^{\prime\prime}_{\mathbf{1}}&{}\approx{}&0.050407872089&{}:{}&0.042807190345&{}:{}&0.906784937566&,\\B^{\prime\prime}_{\mathbf{1}}&{}\approx{}&0.024354305496&{}:{}&0.082728299997&{}:{}&0.892917394507&,\\C^{\prime\prime}_{\mathbf{1}}&{}\approx{}&0.133575265356&{}:{}&0.231192640811&{}:{}&0.635232093834&,\\[.5em] A^{\prime\prime}_{\mathbf{2}}&{}\approx{}&0.010975187346&{}:{}&0.987160750894&{}:{}&0.001864061760&,\\B^{\prime\prime}_{\mathbf{2}}&{}\approx{}&0.022197956069&{}:{}&0.887373401289&{}:{}&0.090428642642&,\\C^{\prime\prime}_{\mathbf{2}}&{}\approx{}&0.000451606803&{}:{}&0.974273930608&{}:{}&0.025274462589&,\\[.5em] A^{\prime\prime}_{\mathbf{3}}&{}\approx{}&0.031754982293&{}:{}&0.952064907159&{}:{}&0.016180110547&,\\B^{\prime\prime}_{\mathbf{3}}&{}\approx{}&0.006345580218&{}:{}&0.761002375724&{}:{}&0.232652044058&,\\C^{\prime\prime}_{\mathbf{3}}&{}\approx{}&0.000429876983&{}:{}&0.927395104842&{}:{}&0.072175018175&,\\[.5em] A^{\prime\prime}_{\mathbf{4}}&{}\approx{}&0.927920222920&{}:{}&0.021492823146&{}:{}&0.050586953934&,\\B^{\prime\prime}_{\mathbf{4}}&{}\approx{}&0.989480720806&{}:{}&0.010186093164&{}:{}&0.000333186030&,\\C^{\prime\prime}_{\mathbf{4}}&{}\approx{}&0.985653613507&{}:{}&0.000141012854&{}:{}&0.014205373639&,\\[.5em] A^{\prime\prime}_{\mathbf{5}}&{}\approx{}&0.853773920225&{}:{}&0.006591806573&{}:{}&0.139634273202&,\\B^{\prime\prime}_{\mathbf{5}}&{}\approx{}&0.967198711644&{}:{}&0.029870140906&{}:{}&0.002931147450&,\\C^{\prime\prime}_{\mathbf{5}}&{}\approx{}&0.958424069483&{}:{}&0.000137117250&{}:{}&0.041438813267&,\\[.5em] A^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.549664521906&{}:{}&0.449486709557&{}:{}&0.000848768538&,\\B^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.733256098333&{}:{}&0.266496993685&{}:{}&0.000246907983&,\\C^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.592717830532&{}:{}&0.105695140845&{}:{}&0.301587028623&,\\[.5em] A^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.782953582064&{}:{}&0.213419407240&{}:{}&0.003627010697&,\\B^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.477700838466&{}:{}&0.520851463581&{}:{}&0.001447697953&,\\C^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.369715208310&{}:{}&0.065928674661&{}:{}&0.564356117029&,\\[.5em] A^{\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.144227242941&{}:{}&0.669784521365&{}:{}&0.474442721576&,\\B^{\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.337152836255&{}:{}&0.449655095261&{}:{}&0.887497740994&,\\C^{\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.218183694473&{}:{}&0.810800575833&{}:{}&0.407383118640&,\\[.5em] A^{\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.101723106389&{}:{}&0.932140100646&{}:{}&0.169583005743&,\\B^{\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.234523192506&{}:{}&0.617180607251&{}:{}&0.617342585256&,\\C^{\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.058297745062&{}:{}&0.843511598585&{}:{}&0.214786146477&,\\[.5em] A^{\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.022147932531&{}:{}&0.007384581739&{}:{}&1.014763350791&,\\B^{\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.001893099021&{}:{}&0.035165850665&{}:{}&0.966727248356&,\\C^{\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.034816185400&{}:{}&0.129381726893&{}:{}&0.905434458508&,\\[.5em] A^{\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.043710736551&{}:{}&0.028757730355&{}:{}&1.014953006197&,\\B^{\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.001830453876&{}:{}&0.067093486246&{}:{}&0.934736967630&,\\C^{\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.015435755462&{}:{}&0.223340349632&{}:{}&0.792095405830&,\\[.5em] A^{\prime\prime}_{\mathbf{4a}}&{}\approx{}&1.277282286918&{}:{}&-0.007640056732&{}:{}&-0.269642230186&,\\B^{\prime\prime}_{\mathbf{4a}}&{}\approx{}&1.601168311558&{}:{}&-0.533582732635&{}:{}&-0.067585578923&,\\C^{\prime\prime}_{\mathbf{4a}}&{}\approx{}&1.878781780718&{}:{}&-0.002246994786&{}:{}&-0.876534785932&,\\[.5em] A^{\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.722916118449&{}:{}&-0.005222759835&{}:{}&-0.717693358614&,\\B^{\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.267579968152&{}:{}&-0.214075208309&{}:{}&-0.053504759844&,\\C^{\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.310180060729&{}:{}&-0.000402447437&{}:{}&-0.309777613293&,\\[.5em] A^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.109223228887&{}:{}&-0.092411015959&{}:{}&-0.016812212927&,\\B^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.024740894495&{}:{}&-0.024517927321&{}:{}&-0.000222967174&,\\C^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.035939167404&{}:{}&-0.001238967682&{}:{}&-0.034700199722&,\\[.5em] A^{\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.077735690145&{}:{}&-0.045503340650&{}:{}&-0.032232349495&,\\B^{\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.012497232531&{}:{}&-0.012276929381&{}:{}&-0.000220303150&,\\C^{\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.017586668785&{}:{}&-0.000312571652&{}:{}&-0.017274097132&,\\[.5em] A^{\prime\prime}_{\mathbf{b}}&{}\approx{}&0.502433603565&{}:{}&-0.955257755724&{}:{}&1.452824152159&,\\B^{\prime\prime}_{\mathbf{b}}&{}\approx{}&0.713626705381&{}:{}&-0.389652874598&{}:{}&0.676026169217&,\\C^{\prime\prime}_{\mathbf{b}}&{}\approx{}&0.876000940496&{}:{}&-0.545637873723&{}:{}&0.669636933227&,\\[.5em] A^{\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.596835650867&{}:{}&-0.774019053740&{}:{}&1.177183402873&,\\B^{\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.936053022617&{}:{}&-0.348627981105&{}:{}&0.412574958488&,\\C^{\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.811942135629&{}:{}&-0.235307091407&{}:{}&0.423364955778&,\\[.5em] A^{\prime\prime}_{\mathbf{2b}}&{}\approx{}&-0.662616760822&{}:{}&2.178213975023&{}:{}&-0.515597214200&,\\B^{\prime\prime}_{\mathbf{2b}}&{}\approx{}&-0.010347789033&{}:{}&1.895137718045&{}:{}&-0.884789929012&,\\C^{\prime\prime}_{\mathbf{2b}}&{}\approx{}&-0.009631399157&{}:{}&3.479140476367&{}:{}&-2.469509077210&,\\[.5em] A^{\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.373338594492&{}:{}&1.799227211857&{}:{}&-0.425888617365&,\\B^{\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.011944169131&{}:{}&3.206964507613&{}:{}&-2.195020338482&,\\C^{\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.002503240932&{}:{}&1.943458331967&{}:{}&-0.940955091035&,\\[.5em] A^{\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.024308465701&{}:{}&-0.003318213663&{}:{}&0.979009747963&,\\B^{\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.005644349521&{}:{}&-0.042925541745&{}:{}&1.037281192224&,\\C^{\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.090709597619&{}:{}&-0.056500615106&{}:{}&0.965791017487&,\\[.5em] A^{\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.035237917714&{}:{}&-0.003281043866&{}:{}&0.968043126152&,\\B^{\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.012297441176&{}:{}&-0.063792796349&{}:{}&1.051495355173&,\\C^{\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.125428466373&{}:{}&-0.036350136674&{}:{}&0.910921670301&,\\[.5em] A^{\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.022356266674&{}:{}&1.023605237608&{}:{}&-0.001248970933&,\\B^{\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.085408745089&{}:{}&1.123053524400&{}:{}&-0.037644779311&,\\C^{\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.002925515071&{}:{}&1.056780820070&{}:{}&-0.053855304999&,\\[.5em] A^{\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.015141843309&{}:{}&1.016382000675&{}:{}&-0.001240157367&,\\B^{\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.057703896919&{}:{}&1.112367412296&{}:{}&-0.054663515377&,\\C^{\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.001336203800&{}:{}&1.037397709170&{}:{}&-0.036061505370&,\\[.5em] A^{\prime\prime}_{\mathbf{c}}&{}\approx{}&1.274694014690&{}:{}&2.854588071446&{}:{}&-3.129282086136&,\\B^{\prime\prime}_{\mathbf{c}}&{}\approx{}&1.889412640990&{}:{}&1.880536635931&{}:{}&-2.769949276921&,\\C^{\prime\prime}_{\mathbf{c}}&{}\approx{}&1.059408776929&{}:{}&1.416795924950&{}:{}&-1.476204701880&,\\[.5em] A^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-1.847815627408&{}:{}&-1.856537191531&{}:{}&4.704352818939&,\\B^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.892762666339&{}:{}&-3.587905781692&{}:{}&5.480668448031&,\\C^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.453777646476&{}:{}&-1.099371251760&{}:{}&2.553148898235&,\\[.5em] A^{\prime\prime}_{\mathbf{2c}}&{}\approx{}&1.172324064859&{}:{}&1.790771526367&{}:{}&-1.963095591226&,\\B^{\prime\prime}_{\mathbf{2c}}&{}\approx{}&1.003214693775&{}:{}&0.681089000823&{}:{}&-0.684303694597&,\\C^{\prime\prime}_{\mathbf{2c}}&{}\approx{}&1.488616123592&{}:{}&0.926267554174&{}:{}&-1.414883677765&,\\[.5em] A^{\prime\prime}_{\mathbf{3c}}&{}\approx{}&-0.794012146822&{}:{}&-1.169545612637&{}:{}&2.963557759459&,\\B^{\prime\prime}_{\mathbf{3c}}&{}\approx{}&-0.158666999892&{}:{}&-0.934838563044&{}:{}&2.093505562936&,\\C^{\prime\prime}_{\mathbf{3c}}&{}\approx{}&-0.489832575446&{}:{}&-2.550579947535&{}:{}&4.040412522980&,\\[.5em] A^{\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.239535721483&{}:{}&1.058477329035&{}:{}&-0.298013050518&,\\B^{\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.667598988612&{}:{}&1.311125984251&{}:{}&-0.978724972862&,\\C^{\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.289224232884&{}:{}&1.506003409562&{}:{}&-0.795227642446&,\\[.5em] A^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.284541991663&{}:{}&-0.144883060921&{}:{}&1.429425052585&,\\B^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.322343703908&{}:{}&-0.656523730898&{}:{}&1.978867434805&,\\C^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.813554859361&{}:{}&-0.506221488417&{}:{}&2.319776347778&,\\[.5em] A^{\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.315903201426&{}:{}&0.952182729172&{}:{}&-0.268085930598&,\\B^{\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.603312550619&{}:{}&0.808213526449&{}:{}&-0.411526077067&,\\C^{\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.646315512321&{}:{}&1.565834499189&{}:{}&-1.212150011510&,\\[.5em] A^{\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.177989547185&{}:{}&-0.132865046404&{}:{}&1.310854593588&,\\B^{\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.108596164417&{}:{}&-0.324258017455&{}:{}&1.432854181872&,\\C^{\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.542616100337&{}:{}&-0.725665386687&{}:{}&2.268281487024&. \end{alignedat} \] \[ \begin{alignedat}{4} A^{\prime\prime\prime}&{}\approx{}&0.070982724666&{}:{}&0.243373611136&{}:{}&0.685643664198&,\\B^{\prime\prime\prime}&{}\approx{}&0.146489143169&{}:{}&0.125597904919&{}:{}&0.727912951912&,\\C^{\prime\prime\prime}&{}\approx{}&0.252261479537&{}:{}&0.444938478830&{}:{}&0.302800041633&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1}}&{}\approx{}&0.028838104788&{}:{}&0.000916073569&{}:{}&0.970245821643&,\\B^{\prime\prime\prime}_{\mathbf{1}}&{}\approx{}&-0.000529946914&{}:{}&0.047224333205&{}:{}&0.953305613708&,\\C^{\prime\prime\prime}_{\mathbf{1}}&{}\approx{}&-0.007971020534&{}:{}&0.013538242306&{}:{}&0.994432778228&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2}}&{}\approx{}&0.005642409938&{}:{}&1.005606562488&{}:{}&-0.011248972427&,\\B^{\prime\prime\prime}_{\mathbf{2}}&{}\approx{}&0.737068776614&{}:{}&-1.340199855114&{}:{}&1.603131078500&,\\C^{\prime\prime\prime}_{\mathbf{2}}&{}\approx{}&-0.005102524720&{}:{}&0.992113554965&{}:{}&0.012988969756&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3}}&{}\approx{}&0.017246659570&{}:{}&1.005420171254&{}:{}&-0.022666830824&,\\B^{\prime\prime\prime}_{\mathbf{3}}&{}\approx{}&1.568548005965&{}:{}&-2.688986610804&{}:{}&2.120438604839&,\\C^{\prime\prime\prime}_{\mathbf{3}}&{}\approx{}&-0.016296405516&{}:{}&0.977184346148&{}:{}&0.039112059369&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4}}&{}\approx{}&-0.351538047846&{}:{}&0.569611844100&{}:{}&0.781926203747&,\\B^{\prime\prime\prime}_{\mathbf{4}}&{}\approx{}&1.001730472737&{}:{}&0.005172071383&{}:{}&-0.006902544121&,\\C^{\prime\prime\prime}_{\mathbf{4}}&{}\approx{}&0.997796104673&{}:{}&-0.005008565457&{}:{}&0.007212460784&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5}}&{}\approx{}&-0.376299246022&{}:{}&0.621354757393&{}:{}&0.754944488629&,\\B^{\prime\prime\prime}_{\mathbf{5}}&{}\approx{}&1.003185612785&{}:{}&0.015635628073&{}:{}&-0.018821240858&,\\C^{\prime\prime\prime}_{\mathbf{5}}&{}\approx{}&0.993661637026&{}:{}&-0.015343699673&{}:{}&0.021682062646&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&-0.734528818062&{}:{}&0.022896698800&{}:{}&1.711632119261&,\\B^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&1.088383327267&{}:{}&0.221986665222&{}:{}&-0.310369992490&,\\C^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&0.780195941150&{}:{}&-0.002976212769&{}:{}&0.222780271619&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&-0.408902602683&{}:{}&0.458584989628&{}:{}&0.950317613055&,\\B^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&1.469647391994&{}:{}&1.190665656617&{}:{}&-1.660313048611&,\\C^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&0.629297132966&{}:{}&-0.343070711143&{}:{}&0.713773578177&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.092021668855&{}:{}&0.701319141561&{}:{}&0.390702527294&,\\B^{\prime\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.339749318725&{}:{}&0.377664395319&{}:{}&0.962084923406&,\\C^{\prime\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.177327445463&{}:{}&0.901364073993&{}:{}&0.275963371470&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.060019627647&{}:{}&0.999947493168&{}:{}&0.060072134479&,\\B^{\prime\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.111057032304&{}:{}&0.694182911279&{}:{}&0.416874121026&,\\C^{\prime\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.014238092635&{}:{}&0.889641058594&{}:{}&0.124597034041&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.011454506729&{}:{}&-0.011452502585&{}:{}&1.022907009314&,\\B^{\prime\prime\prime}_{\mathbf{2a}}&{}\approx{}&0.008939587559&{}:{}&0.018157600039&{}:{}&0.972902812402&,\\C^{\prime\prime\prime}_{\mathbf{2a}}&{}\approx{}&0.380933608633&{}:{}&-0.464157648368&{}:{}&1.083224039735&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.023388886457&{}:{}&-0.008205913203&{}:{}&1.031594799660&,\\B^{\prime\prime\prime}_{\mathbf{3a}}&{}\approx{}&0.019473481378&{}:{}&0.035702614724&{}:{}&0.944823903898&,\\C^{\prime\prime\prime}_{\mathbf{3a}}&{}\approx{}&0.314385271932&{}:{}&-0.121335320020&{}:{}&0.806950048088&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4a}}&{}\approx{}&0.219018488896&{}:{}&0.362410699137&{}:{}&0.418570811967&,\\B^{\prime\prime\prime}_{\mathbf{4a}}&{}\approx{}&0.973564166329&{}:{}&-0.180237101629&{}:{}&0.206672935300&,\\C^{\prime\prime\prime}_{\mathbf{4a}}&{}\approx{}&1.081526919385&{}:{}&0.198787206417&{}:{}&-0.280314125803&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5a}}&{}\approx{}&0.240337089970&{}:{}&0.399104725482&{}:{}&0.360558184548&,\\B^{\prime\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.008962863918&{}:{}&-0.089746377200&{}:{}&0.080783513282&,\\C^{\prime\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.037240263631&{}:{}&0.091926014917&{}:{}&-0.129166278548&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6a}}&{}\approx{}&0.208200450502&{}:{}&0.312309780339&{}:{}&0.479489769159&,\\B^{\prime\prime\prime}_{\mathbf{6a}}&{}\approx{}&0.995420435007&{}:{}&-0.011994295913&{}:{}&0.016573860905&,\\C^{\prime\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.006060936125&{}:{}&0.010910575620&{}:{}&-0.016971511745&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7a}}&{}\approx{}&0.205941724766&{}:{}&0.325845976662&{}:{}&0.468212298571&,\\B^{\prime\prime\prime}_{\mathbf{7a}}&{}\approx{}&0.997789343342&{}:{}&-0.006071380571&{}:{}&0.008282037230&,\\C^{\prime\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.002749764296&{}:{}&0.005792425164&{}:{}&-0.008542189460&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{b}}&{}\approx{}&0.432159811138&{}:{}&-0.923031422664&{}:{}&1.490871611526&,\\B^{\prime\prime\prime}_{\mathbf{b}}&{}\approx{}&0.741120760348&{}:{}&-0.241968249237&{}:{}&0.500847488889&,\\C^{\prime\prime\prime}_{\mathbf{b}}&{}\approx{}&0.962756304520&{}:{}&-0.402818245670&{}:{}&0.440061941150&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.593704503647&{}:{}&-0.550409211184&{}:{}&0.956704707537&,\\B^{\prime\prime\prime}_{\mathbf{1b}}&{}\approx{}&1.006998566976&{}:{}&-0.211114138496&{}:{}&0.204115571520&,\\C^{\prime\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.849696721928&{}:{}&-0.099087531648&{}:{}&0.249390809721&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2b}}&{}\approx{}&-0.213447051941&{}:{}&1.047579969346&{}:{}&0.165867082595&,\\B^{\prime\prime\prime}_{\mathbf{2b}}&{}\approx{}&0.286610418828&{}:{}&0.486539335764&{}:{}&0.226850245409&,\\C^{\prime\prime\prime}_{\mathbf{2b}}&{}\approx{}&0.276066993599&{}:{}&1.380030691676&{}:{}&-0.656097685275&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.142374411636&{}:{}&1.134996666317&{}:{}&0.007377745320&,\\B^{\prime\prime\prime}_{\mathbf{3b}}&{}\approx{}&0.364951664934&{}:{}&0.615899052687&{}:{}&0.019149282379&,\\C^{\prime\prime\prime}_{\mathbf{3b}}&{}\approx{}&0.149043216623&{}:{}&1.203096035357&{}:{}&-0.352139251980&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.012405532399&{}:{}&0.017289066657&{}:{}&0.970305400944&,\\B^{\prime\prime\prime}_{\mathbf{4b}}&{}\approx{}&-0.007391965055&{}:{}&-0.021933525096&{}:{}&1.029325490151&,\\C^{\prime\prime\prime}_{\mathbf{4b}}&{}\approx{}&-0.177454008928&{}:{}&0.440292956195&{}:{}&0.737161052733&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.018151990823&{}:{}&0.026873011709&{}:{}&0.954974997469&,\\B^{\prime\prime\prime}_{\mathbf{5b}}&{}\approx{}&-0.007065770353&{}:{}&-0.032947298320&{}:{}&1.040013068674&,\\C^{\prime\prime\prime}_{\mathbf{5b}}&{}\approx{}&-0.103411961942&{}:{}&0.428325959222&{}:{}&0.675086002720&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.010973691035&{}:{}&0.986594539852&{}:{}&0.024379151183&,\\B^{\prime\prime\prime}_{\mathbf{6b}}&{}\approx{}&0.161065002739&{}:{}&0.359601113342&{}:{}&0.479333883919&,\\C^{\prime\prime\prime}_{\mathbf{6b}}&{}\approx{}&0.008452334902&{}:{}&1.017967163966&{}:{}&-0.026419498867&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.007476580644&{}:{}&0.991255929614&{}:{}&0.016220651030&,\\B^{\prime\prime\prime}_{\mathbf{7b}}&{}\approx{}&0.177361018291&{}:{}&0.357402345205&{}:{}&0.465236636504&,\\C^{\prime\prime\prime}_{\mathbf{7b}}&{}\approx{}&0.006309994529&{}:{}&1.011491490884&{}:{}&-0.017801485413&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{c}}&{}\approx{}&0.809277125324&{}:{}&2.275843805387&{}:{}&-2.085120930712&,\\B^{\prime\prime\prime}_{\mathbf{c}}&{}\approx{}&1.632191181593&{}:{}&1.158042441729&{}:{}&-1.790233623322&,\\C^{\prime\prime\prime}_{\mathbf{c}}&{}\approx{}&0.830667423392&{}:{}&0.994436522112&{}:{}&-0.825103945504&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.706368134193&{}:{}&-0.242124063862&{}:{}&1.948492198055&,\\B^{\prime\prime\prime}_{\mathbf{1c}}&{}\approx{}&0.135126833464&{}:{}&-1.320257087198&{}:{}&2.185130253734&,\\C^{\prime\prime\prime}_{\mathbf{1c}}&{}\approx{}&0.078931184156&{}:{}&-0.158607467957&{}:{}&1.079676283801&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2c}}&{}\approx{}&0.728502128525&{}:{}&1.011461601712&{}:{}&-0.739963730237&,\\B^{\prime\prime\prime}_{\mathbf{2c}}&{}\approx{}&0.857276127649&{}:{}&0.365433794186&{}:{}&-0.222709921835&,\\C^{\prime\prime\prime}_{\mathbf{2c}}&{}\approx{}&1.318698554074&{}:{}&0.468277544578&{}:{}&-0.786976098652&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3c}}&{}\approx{}&-0.350608210434&{}:{}&-0.448514497157&{}:{}&1.799122707591&,\\B^{\prime\prime\prime}_{\mathbf{3c}}&{}\approx{}&0.111372992221&{}:{}&-0.427458785813&{}:{}&1.316085793593&,\\C^{\prime\prime\prime}_{\mathbf{3c}}&{}\approx{}&0.291766139272&{}:{}&-0.859517853643&{}:{}&1.567751714371&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.124748133085&{}:{}&0.894578130797&{}:{}&-0.019326263882&,\\B^{\prime\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.315646414989&{}:{}&0.754485553522&{}:{}&-0.070131968511&,\\C^{\prime\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.125973874293&{}:{}&1.295585342814&{}:{}&-0.421559217107&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.135829464760&{}:{}&0.088059176551&{}:{}&1.047770288209&,\\B^{\prime\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.117661807738&{}:{}&-0.308038412655&{}:{}&1.425700220394&,\\C^{\prime\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.271476697554&{}:{}&0.276460951725&{}:{}&0.995015745829&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.166730025519&{}:{}&0.727218503552&{}:{}&0.106051470930&,\\B^{\prime\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.392577105356&{}:{}&0.439638980287&{}:{}&0.167783914357&,\\C^{\prime\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.423211653471&{}:{}&1.240312714441&{}:{}&-0.663524367912&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.086430810133&{}:{}&0.015014181684&{}:{}&1.071416628449&,\\B^{\prime\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.010963266475&{}:{}&-0.157036959415&{}:{}&1.168000225890&,\\C^{\prime\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.048670226433&{}:{}&0.072662378165&{}:{}&0.976007848268&. \end{alignedat} \] \[ \begin{alignedat}{4} A^*&{}\approx{}&0.000000000000&{}:{}&0.225708114823&{}:{}&0.774291885177&,\\B^*&{}\approx{}&0.141742430504&{}:{}&0.000000000000&{}:{}&0.858257569496&,\\C^*&{}\approx{}&0.361655401151&{}:{}&0.638344598849&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1}}&{}\approx{}&0.000000000000&{}:{}&-0.107625218511&{}:{}&1.107625218511&,\\B^*_{\mathbf{1}}&{}\approx{}&-0.058257569496&{}:{}&0.000000000000&{}:{}&1.058257569496&,\\C^*_{\mathbf{1}}&{}\approx{}&0.361655401151&{}:{}&0.638344598849&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2}}&{}\approx{}&0.000000000000&{}:{}&1.107625218511&{}:{}&-0.107625218511&,\\B^*_{\mathbf{2}}&{}\approx{}&0.141742430504&{}:{}&0.000000000000&{}:{}&0.858257569496&,\\C^*_{\mathbf{2}}&{}\approx{}&-0.016309071859&{}:{}&1.016309071859&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3}}&{}\approx{}&0.000000000000&{}:{}&0.774291885177&{}:{}&0.225708114823&,\\B^*_{\mathbf{3}}&{}\approx{}&-0.058257569496&{}:{}&0.000000000000&{}:{}&1.058257569496&,\\C^*_{\mathbf{3}}&{}\approx{}&-0.016309071859&{}:{}&1.016309071859&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4}}&{}\approx{}&0.000000000000&{}:{}&0.225708114823&{}:{}&0.774291885177&,\\B^*_{\mathbf{4}}&{}\approx{}&1.058257569496&{}:{}&0.000000000000&{}:{}&-0.058257569496&,\\C^*_{\mathbf{4}}&{}\approx{}&1.016309071859&{}:{}&-0.016309071859&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5}}&{}\approx{}&0.000000000000&{}:{}&-0.107625218511&{}:{}&1.107625218511&,\\B^*_{\mathbf{5}}&{}\approx{}&0.858257569496&{}:{}&0.000000000000&{}:{}&0.141742430504&,\\C^*_{\mathbf{5}}&{}\approx{}&1.016309071859&{}:{}&-0.016309071859&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6}}&{}\approx{}&0.000000000000&{}:{}&1.107625218511&{}:{}&-0.107625218511&,\\B^*_{\mathbf{6}}&{}\approx{}&1.058257569496&{}:{}&0.000000000000&{}:{}&-0.058257569496&,\\C^*_{\mathbf{6}}&{}\approx{}&0.638344598849&{}:{}&0.361655401151&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7}}&{}\approx{}&0.000000000000&{}:{}&0.774291885177&{}:{}&0.225708114823&,\\B^*_{\mathbf{7}}&{}\approx{}&0.858257569496&{}:{}&0.000000000000&{}:{}&0.141742430504&,\\C^*_{\mathbf{7}}&{}\approx{}&0.638344598849&{}:{}&0.361655401151&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{a}}&{}\approx{}&0.000000000000&{}:{}&0.726537685716&{}:{}&0.273462314284&,\\B^*_{\mathbf{a}}&{}\approx{}&-0.552437750421&{}:{}&0.000000000000&{}:{}&1.552437750421&,\\C^*_{\mathbf{a}}&{}\approx{}&-0.154653670708&{}:{}&1.154653670708&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1a}}&{}\approx{}&0.000000000000&{}:{}&1.235712762933&{}:{}&-0.235712762933&,\\B^*_{\mathbf{1a}}&{}\approx{}&-0.552437750421&{}:{}&0.000000000000&{}:{}&1.552437750421&,\\C^*_{\mathbf{1a}}&{}\approx{}&0.063564219528&{}:{}&0.936435780472&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2a}}&{}\approx{}&0.000000000000&{}:{}&-0.235712762933&{}:{}&1.235712762933&,\\B^*_{\mathbf{2a}}&{}\approx{}&0.024912518769&{}:{}&0.000000000000&{}:{}&0.975087481231&,\\C^*_{\mathbf{2a}}&{}\approx{}&-0.154653670708&{}:{}&1.154653670708&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3a}}&{}\approx{}&0.000000000000&{}:{}&0.273462314284&{}:{}&0.726537685716&,\\B^*_{\mathbf{3a}}&{}\approx{}&0.024912518769&{}:{}&0.000000000000&{}:{}&0.975087481231&,\\C^*_{\mathbf{3a}}&{}\approx{}&0.063564219528&{}:{}&0.936435780472&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4a}}&{}\approx{}&0.000000000000&{}:{}&0.273462314284&{}:{}&0.726537685716&,\\B^*_{\mathbf{4a}}&{}\approx{}&1.552437750421&{}:{}&0.000000000000&{}:{}&-0.552437750421&,\\C^*_{\mathbf{4a}}&{}\approx{}&1.154653670708&{}:{}&-0.154653670708&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5a}}&{}\approx{}&0.000000000000&{}:{}&-0.235712762933&{}:{}&1.235712762933&,\\B^*_{\mathbf{5a}}&{}\approx{}&1.552437750421&{}:{}&0.000000000000&{}:{}&-0.552437750421&,\\C^*_{\mathbf{5a}}&{}\approx{}&0.936435780472&{}:{}&0.063564219528&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6a}}&{}\approx{}&0.000000000000&{}:{}&1.235712762933&{}:{}&-0.235712762933&,\\B^*_{\mathbf{6a}}&{}\approx{}&0.975087481231&{}:{}&0.000000000000&{}:{}&0.024912518769&,\\C^*_{\mathbf{6a}}&{}\approx{}&1.154653670708&{}:{}&-0.154653670708&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7a}}&{}\approx{}&0.000000000000&{}:{}&0.726537685716&{}:{}&0.273462314284&,\\B^*_{\mathbf{7a}}&{}\approx{}&0.975087481231&{}:{}&0.000000000000&{}:{}&0.024912518769&,\\C^*_{\mathbf{7a}}&{}\approx{}&0.936435780472&{}:{}&0.063564219528&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{b}}&{}\approx{}&0.000000000000&{}:{}&-1.688901059317&{}:{}&2.688901059317&,\\B^*_{\mathbf{b}}&{}\approx{}&0.755040111164&{}:{}&0.000000000000&{}:{}&0.244959888836&,\\C^*_{\mathbf{b}}&{}\approx{}&1.255928946018&{}:{}&-0.255928946018&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1b}}&{}\approx{}&0.000000000000&{}:{}&-1.688901059317&{}:{}&2.688901059317&,\\B^*_{\mathbf{1b}}&{}\approx{}&1.284190373377&{}:{}&0.000000000000&{}:{}&-0.284190373377&,\\C^*_{\mathbf{1b}}&{}\approx{}&0.877964473009&{}:{}&0.122035526991&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2b}}&{}\approx{}&0.000000000000&{}:{}&2.688901059317&{}:{}&-1.688901059317&,\\B^*_{\mathbf{2b}}&{}\approx{}&0.244959888836&{}:{}&0.000000000000&{}:{}&0.755040111164&,\\C^*_{\mathbf{2b}}&{}\approx{}&-0.255928946018&{}:{}&1.255928946018&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3b}}&{}\approx{}&0.000000000000&{}:{}&2.688901059317&{}:{}&-1.688901059317&,\\B^*_{\mathbf{3b}}&{}\approx{}&-0.284190373377&{}:{}&0.000000000000&{}:{}&1.284190373377&,\\C^*_{\mathbf{3b}}&{}\approx{}&0.122035526991&{}:{}&0.877964473009&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4b}}&{}\approx{}&0.000000000000&{}:{}&0.043149748252&{}:{}&0.956850251748&,\\B^*_{\mathbf{4b}}&{}\approx{}&-0.284190373377&{}:{}&0.000000000000&{}:{}&1.284190373377&,\\C^*_{\mathbf{4b}}&{}\approx{}&1.255928946018&{}:{}&-0.255928946018&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5b}}&{}\approx{}&0.000000000000&{}:{}&0.043149748252&{}:{}&0.956850251748&,\\B^*_{\mathbf{5b}}&{}\approx{}&0.244959888836&{}:{}&0.000000000000&{}:{}&0.755040111164&,\\C^*_{\mathbf{5b}}&{}\approx{}&0.877964473009&{}:{}&0.122035526991&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6b}}&{}\approx{}&0.000000000000&{}:{}&0.956850251748&{}:{}&0.043149748252&,\\B^*_{\mathbf{6b}}&{}\approx{}&1.284190373377&{}:{}&0.000000000000&{}:{}&-0.284190373377&,\\C^*_{\mathbf{6b}}&{}\approx{}&-0.255928946018&{}:{}&1.255928946018&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7b}}&{}\approx{}&0.000000000000&{}:{}&0.956850251748&{}:{}&0.043149748252&,\\B^*_{\mathbf{7b}}&{}\approx{}&0.755040111164&{}:{}&0.000000000000&{}:{}&0.244959888836&,\\C^*_{\mathbf{7b}}&{}\approx{}&0.122035526991&{}:{}&0.877964473009&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{c}}&{}\approx{}&0.000000000000&{}:{}&5.291287847478&{}:{}&-4.291287847478&,\\B^*_{\mathbf{c}}&{}\approx{}&3.322875655532&{}:{}&0.000000000000&{}:{}&-2.322875655532&,\\C^*_{\mathbf{c}}&{}\approx{}&0.537069323539&{}:{}&0.462930676461&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1c}}&{}\approx{}&0.000000000000&{}:{}&-4.291287847478&{}:{}&5.291287847478&,\\B^*_{\mathbf{1c}}&{}\approx{}&-2.322875655532&{}:{}&0.000000000000&{}:{}&3.322875655532&,\\C^*_{\mathbf{1c}}&{}\approx{}&0.462930676461&{}:{}&0.537069323539&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2c}}&{}\approx{}&0.000000000000&{}:{}&5.291287847478&{}:{}&-4.291287847478&,\\B^*_{\mathbf{2c}}&{}\approx{}&0.677124344468&{}:{}&0.000000000000&{}:{}&0.322875655532&,\\C^*_{\mathbf{2c}}&{}\approx{}&2.426891688585&{}:{}&-1.426891688585&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3c}}&{}\approx{}&0.000000000000&{}:{}&-4.291287847478&{}:{}&5.291287847478&,\\B^*_{\mathbf{3c}}&{}\approx{}&0.322875655532&{}:{}&0.000000000000&{}:{}&0.677124344468&,\\C^*_{\mathbf{3c}}&{}\approx{}&-1.426891688585&{}:{}&2.426891688585&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4c}}&{}\approx{}&0.000000000000&{}:{}&0.708712152522&{}:{}&0.291287847478&,\\B^*_{\mathbf{4c}}&{}\approx{}&3.322875655532&{}:{}&0.000000000000&{}:{}&-2.322875655532&,\\C^*_{\mathbf{4c}}&{}\approx{}&-1.426891688585&{}:{}&2.426891688585&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5c}}&{}\approx{}&0.000000000000&{}:{}&0.291287847478&{}:{}&0.708712152522&,\\B^*_{\mathbf{5c}}&{}\approx{}&-2.322875655532&{}:{}&0.000000000000&{}:{}&3.322875655532&,\\C^*_{\mathbf{5c}}&{}\approx{}&2.426891688585&{}:{}&-1.426891688585&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6c}}&{}\approx{}&0.000000000000&{}:{}&0.708712152522&{}:{}&0.291287847478&,\\B^*_{\mathbf{6c}}&{}\approx{}&0.677124344468&{}:{}&0.000000000000&{}:{}&0.322875655532&,\\C^*_{\mathbf{6c}}&{}\approx{}&0.462930676461&{}:{}&0.537069323539&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7c}}&{}\approx{}&0.000000000000&{}:{}&0.291287847478&{}:{}&0.708712152522&,\\B^*_{\mathbf{7c}}&{}\approx{}&0.322875655532&{}:{}&0.000000000000&{}:{}&0.677124344468&,\\C^*_{\mathbf{7c}}&{}\approx{}&0.537069323539&{}:{}&0.462930676461&{}:{}&0.000000000000&. \end{alignedat} \]