Derousseau's Generalization of the Malfatti circles

Martin's solution

Problem 4331 (proposed by A. Martin) I. Solution by the Proposer, Mathematical Questions with their Solutions, from the “Educational Times”.

\(a:b:c=231:250:289\).


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Reference Triangle

reference triangle

Triangle Centers and their Extraversions

Approximately,
\[ \begin{alignedat}{4} I&{}\approx{}&0.300000000000&{}:{}&0.324675324675&{}:{}&0.375324675325&,\\ I_{\mathbf{a}}&{}\approx{}&-0.750000000000&{}:{}&0.811688311688&{}:{}&0.938311688312&,\\ I_{\mathbf{b}}&{}\approx{}&0.855555555556&{}:{}&-0.925925925926&{}:{}&1.070370370370&,\\ I_{\mathbf{c}}&{}\approx{}&1.203125000000&{}:{}&1.302083333333&{}:{}&-1.505208333333&. \end{alignedat} \] \[ \begin{alignedat}{4} P&{}\approx{}&0.284732052578&{}:{}&0.315903510039&{}:{}&0.399364437383&,\\ P_{\mathbf{1}}&{}\approx{}&0.008641558567&{}:{}&0.009587605817&{}:{}&0.981770835617&,\\ P_{\mathbf{2}}&{}\approx{}&0.003491271820&{}:{}&0.991611879392&{}:{}&0.004896848787&,\\ P_{\mathbf{3}}&{}\approx{}&0.002508551881&{}:{}&0.712493891513&{}:{}&0.284997556605&,\\ P_{\mathbf{4}}&{}\approx{}&0.993911224727&{}:{}&0.002689153747&{}:{}&0.003399621527&,\\ P_{\mathbf{5}}&{}\approx{}&0.781395348837&{}:{}&0.002114164905&{}:{}&0.216490486258&,\\ P_{\mathbf{6}}&{}\approx{}&0.589601386482&{}:{}&0.408381912715&{}:{}&0.002016700804&,\\ P_{\mathbf{7}}&{}\approx{}&0.507692307692&{}:{}&0.351648351648&{}:{}&0.140659340659&,\\ P_{\mathbf{a}}&{}\approx{}&-0.385664306768&{}:{}&0.701047554412&{}:{}&0.684616752356&,\\ P_{\mathbf{1a}}&{}\approx{}&-0.067562380038&{}:{}&0.947628187551&{}:{}&0.119934192487&,\\ P_{\mathbf{2a}}&{}\approx{}&-0.034222708945&{}:{}&0.062208884749&{}:{}&0.972013824197&,\\ P_{\mathbf{3a}}&{}\approx{}&-0.024137931034&{}:{}&0.338557993730&{}:{}&0.685579937304&,\\ P_{\mathbf{4a}}&{}\approx{}&1.115409836066&{}:{}&-0.038152011923&{}:{}&-0.077257824143&,\\ P_{\mathbf{5a}}&{}\approx{}&1.079560324522&{}:{}&-0.004785583430&{}:{}&-0.074774741092&,\\ P_{\mathbf{6a}}&{}\approx{}&1.040077821012&{}:{}&-0.035575319622&{}:{}&-0.004502501390&,\\ P_{\mathbf{7a}}&{}\approx{}&1.008839354343&{}:{}&-0.004472084411&{}:{}&-0.004367269932&,\\ P_{\mathbf{b}}&{}\approx{}&0.729196337742&{}:{}&-0.451339437097&{}:{}&0.722143099356&,\\ P_{\mathbf{1b}}&{}\approx{}&0.942594142259&{}:{}&-0.095676429568&{}:{}&0.153082287308&,\\ P_{\mathbf{2b}}&{}\approx{}&-0.044670050761&{}:{}&1.160744500846&{}:{}&-0.116074450085&,\\ P_{\mathbf{3b}}&{}\approx{}&-0.007061790668&{}:{}&1.118957545187&{}:{}&-0.111895754519&,\\ P_{\mathbf{4b}}&{}\approx{}&0.061628406844&{}:{}&-0.038145186714&{}:{}&0.976516779870&,\\ P_{\mathbf{5b}}&{}\approx{}&0.285960903783&{}:{}&-0.029025979521&{}:{}&0.743065075738&,\\ P_{\mathbf{6b}}&{}\approx{}&-0.040286123033&{}:{}&1.046828803052&{}:{}&-0.006542680019&,\\ P_{\mathbf{7b}}&{}\approx{}&-0.006391326057&{}:{}&1.012720831253&{}:{}&-0.006329505195&,\\ P_{\mathbf{c}}&{}\approx{}&0.811942475713&{}:{}&0.823386998228&{}:{}&-0.635329473941&,\\ P_{\mathbf{1c}}&{}\approx{}&-0.123293357934&{}:{}&-0.158210332103&{}:{}&1.281503690037&,\\ P_{\mathbf{2c}}&{}\approx{}&0.963407109245&{}:{}&0.160217521683&{}:{}&-0.123624630928&,\\ P_{\mathbf{3c}}&{}\approx{}&-0.018329741379&{}:{}&-0.143426724138&{}:{}&1.161756465517&,\\ P_{\mathbf{4c}}&{}\approx{}&0.124342105263&{}:{}&0.972953216374&{}:{}&-0.097295321637&,\\ P_{\mathbf{5c}}&{}\approx{}&-0.108370113493&{}:{}&-0.018022278268&{}:{}&1.126392391761&,\\ P_{\mathbf{6c}}&{}\approx{}&0.464062500000&{}:{}&0.595486111111&{}:{}&-0.059548611111&,\\ P_{\mathbf{7c}}&{}\approx{}&-0.016295441001&{}:{}&-0.016525129122&{}:{}&1.032820570123&. \end{alignedat} \] \[ \begin{alignedat}{4} P^-&{}\approx{}&0.279172413793&{}:{}&0.312709359606&{}:{}&0.408118226601&,\\ P^-_{\mathbf{1}}&{}\approx{}&-0.014273081925&{}:{}&-0.015193285258&{}:{}&1.029466367183&,\\ P^-_{\mathbf{2}}&{}\approx{}&-0.012894736842&{}:{}&1.028468899522&{}:{}&-0.015574162679&,\\ P^-_{\mathbf{3}}&{}\approx{}&-0.149827586207&{}:{}&0.911083743842&{}:{}&0.238743842365&,\\ P^-_{\mathbf{4}}&{}\approx{}&1.027381242387&{}:{}&-0.012841482513&{}:{}&-0.014539759875&,\\ P^-_{\mathbf{5}}&{}\approx{}&1.013793103448&{}:{}&-0.153605015674&{}:{}&0.139811912226&,\\ P^-_{\mathbf{6}}&{}\approx{}&0.814153846154&{}:{}&0.473286713287&{}:{}&-0.287440559441&,\\ P^-_{\mathbf{7}}&{}\approx{}&0.212903225806&{}:{}&0.313364055300&{}:{}&0.473732718894&,\\ P^-_{\mathbf{a}}&{}\approx{}&-0.289829859782&{}:{}&0.671944735269&{}:{}&0.617885124513&,\\ P^-_{\mathbf{1a}}&{}\approx{}&0.009397693293&{}:{}&0.962958442668&{}:{}&0.027643864039&,\\ P^-_{\mathbf{2a}}&{}\approx{}&0.022911739411&{}:{}&0.002384279878&{}:{}&0.974703980711&,\\ P^-_{\mathbf{3a}}&{}\approx{}&0.098790322581&{}:{}&0.258431085044&{}:{}&0.642778592375&,\\ P^-_{\mathbf{4a}}&{}\approx{}&0.652045342533&{}:{}&0.172946816614&{}:{}&0.175007840853&,\\ P^-_{\mathbf{5a}}&{}\approx{}&0.890636000939&{}:{}&0.079525262346&{}:{}&0.029838736715&,\\ P^-_{\mathbf{6a}}&{}\approx{}&0.912030346821&{}:{}&0.025030966144&{}:{}&0.062938687036&,\\ P^-_{\mathbf{7a}}&{}\approx{}&0.962761976048&{}:{}&0.016909363092&{}:{}&0.020328660860&,\\ P^-_{\mathbf{b}}&{}\approx{}&0.697324840764&{}:{}&-0.331634819533&{}:{}&0.634309978769&,\\ P^-_{\mathbf{1b}}&{}\approx{}&0.952853133770&{}:{}&0.002182725288&{}:{}&0.044964140942&,\\ P^-_{\mathbf{2b}}&{}\approx{}&0.173461538462&{}:{}&0.655128205128&{}:{}&0.171410256410&,\\ P^-_{\mathbf{3b}}&{}\approx{}&0.088677130045&{}:{}&0.892002989537&{}:{}&0.019319880419&,\\ P^-_{\mathbf{4b}}&{}\approx{}&0.003616569794&{}:{}&0.026724482578&{}:{}&0.969658947627&,\\ P^-_{\mathbf{5b}}&{}\approx{}&0.202387190684&{}:{}&0.102571567200&{}:{}&0.695041242115&,\\ P^-_{\mathbf{6b}}&{}\approx{}&0.019962636776&{}:{}&0.914153545058&{}:{}&0.065883818166&,\\ P^-_{\mathbf{7b}}&{}\approx{}&0.017287547693&{}:{}&0.959463521794&{}:{}&0.023248930512&,\\ P^-_{\mathbf{c}}&{}\approx{}&0.725220665074&{}:{}&0.717264126297&{}:{}&-0.442484791371&,\\ P^-_{\mathbf{1c}}&{}\approx{}&0.166023514137&{}:{}&0.160307270629&{}:{}&0.673669215234&,\\ P^-_{\mathbf{2c}}&{}\approx{}&0.940508756191&{}:{}&0.051144117052&{}:{}&0.008347126756&,\\ P^-_{\mathbf{3c}}&{}\approx{}&0.095142907413&{}:{}&-0.009139427588&{}:{}&0.913996520175&,\\ P^-_{\mathbf{4c}}&{}\approx{}&0.034101711027&{}:{}&0.945421419518&{}:{}&0.020476869455&,\\ P^-_{\mathbf{5c}}&{}\approx{}&-0.001991599073&{}:{}&0.089054654307&{}:{}&0.912936944766&,\\ P^-_{\mathbf{6c}}&{}\approx{}&0.366450471698&{}:{}&0.502161949686&{}:{}&0.131387578616&,\\ P^-_{\mathbf{7c}}&{}\approx{}&0.022405150029&{}:{}&0.025323379496&{}:{}&0.952271470475&. \end{alignedat} \] \[ \begin{alignedat}{4} P^+&{}\approx{}&0.287948922586&{}:{}&0.317751681678&{}:{}&0.394299395736&,\\ P^+_{\mathbf{1}}&{}\approx{}&0.028441727718&{}:{}&0.031000371825&{}:{}&0.940557900457&,\\ P^+_{\mathbf{2}}&{}\approx{}&0.018246445498&{}:{}&0.958423093494&{}:{}&0.023330461008&,\\ P^+_{\mathbf{3}}&{}\approx{}&0.077768313458&{}:{}&0.614383061572&{}:{}&0.307848624970&,\\ P^+_{\mathbf{4}}&{}\approx{}&0.963385914241&{}:{}&0.016853397658&{}:{}&0.019760688101&,\\ P^+_{\mathbf{5}}&{}\approx{}&0.663157894737&{}:{}&0.081339712919&{}:{}&0.255502392344&,\\ P^+_{\mathbf{6}}&{}\approx{}&0.501568154403&{}:{}&0.382936725518&{}:{}&0.115495120079&,\\ P^+_{\mathbf{7}}&{}\approx{}&0.347368421053&{}:{}&0.330827067669&{}:{}&0.321804511278&,\\ P^+_{\mathbf{a}}&{}\approx{}&-0.448462187365&{}:{}&0.720117893096&{}:{}&0.728344294268&,\\ P^+_{\mathbf{1a}}&{}\approx{}&-0.130359010108&{}:{}&0.935119255091&{}:{}&0.195239755017&,\\ P^+_{\mathbf{2a}}&{}\approx{}&-0.083491702976&{}:{}&0.113797692990&{}:{}&0.969694009986&,\\ P^+_{\mathbf{3a}}&{}\approx{}&-0.115963855422&{}:{}&0.398411829135&{}:{}&0.717552026287&,\\ P^+_{\mathbf{4a}}&{}\approx{}&2.036238981391&{}:{}&-0.457661828867&{}:{}&-0.578577152524&,\\ P^+_{\mathbf{5a}}&{}\approx{}&1.317657497782&{}:{}&-0.111040689568&{}:{}&-0.206616808214&,\\ P^+_{\mathbf{6a}}&{}\approx{}&1.189502529511&{}:{}&-0.106299686822&{}:{}&-0.083202842689&,\\ P^+_{\mathbf{7a}}&{}\approx{}&1.057464454976&{}:{}&-0.027035760448&{}:{}&-0.030428694528&,\\ P^+_{\mathbf{b}}&{}\approx{}&0.750381033023&{}:{}&-0.530906011854&{}:{}&0.780524978831&,\\ P^+_{\mathbf{1b}}&{}\approx{}&0.934292202877&{}:{}&-0.174867524603&{}:{}&0.240575321726&,\\ P^+_{\mathbf{2b}}&{}\approx{}&-0.467910447761&{}:{}&2.141791044776&{}:{}&-0.673880597015&,\\ P^+_{\mathbf{3b}}&{}\approx{}&-0.130115273775&{}:{}&1.410662824207&{}:{}&-0.280547550432&,\\ P^+_{\mathbf{4b}}&{}\approx{}&0.112243419464&{}:{}&-0.094743620704&{}:{}&0.982500201240&,\\ P^+_{\mathbf{5b}}&{}\approx{}&0.350573936529&{}:{}&-0.130767499437&{}:{}&0.780193562908&,\\ P^+_{\mathbf{6b}}&{}\approx{}&-0.109898242368&{}:{}&1.200123342584&{}:{}&-0.090225100216&,\\ P^+_{\mathbf{7b}}&{}\approx{}&-0.031446817882&{}:{}&1.069074359539&{}:{}&-0.037627541657&,\\ P^+_{\mathbf{c}}&{}\approx{}&0.872024809950&{}:{}&0.896910715209&{}:{}&-0.768935525159&,\\ P^+_{\mathbf{1c}}&{}\approx{}&-0.636482855681&{}:{}&-0.723196008188&{}:{}&2.359678863869&,\\ P^+_{\mathbf{2c}}&{}\approx{}&0.982632553255&{}:{}&0.251795489264&{}:{}&-0.234428042519&,\\ P^+_{\mathbf{3c}}&{}\approx{}&-0.157696648098&{}:{}&-0.308358144449&{}:{}&1.466054792547&,\\ P^+_{\mathbf{4c}}&{}\approx{}&0.201649022801&{}:{}&0.996539087948&{}:{}&-0.198188110749&,\\ P^+_{\mathbf{5c}}&{}\approx{}&-0.235347510373&{}:{}&-0.145833333333&{}:{}&1.381180843707&,\\ P^+_{\mathbf{6c}}&{}\approx{}&0.541277985075&{}:{}&0.669309701493&{}:{}&-0.210587686567&,\\ P^+_{\mathbf{7c}}&{}\approx{}&-0.057618992606&{}:{}&-0.061209950709&{}:{}&1.118828943315&. \end{alignedat} \] \[ \begin{alignedat}{4} Q&{}\approx{}&0.275862068966&{}:{}&0.310344827586&{}:{}&0.413793103448&,\\ Q_{\mathbf{1}}&{}\approx{}&-0.087912087912&{}:{}&-0.098901098901&{}:{}&1.186813186813&,\\ Q_{\mathbf{2}}&{}\approx{}&-0.064516129032&{}:{}&1.161290322581&{}:{}&-0.096774193548&,\\ Q_{\mathbf{3}}&{}\approx{}&-0.032786885246&{}:{}&0.590163934426&{}:{}&0.442622950820&,\\ Q_{\mathbf{4}}&{}\approx{}&1.148936170213&{}:{}&-0.063829787234&{}:{}&-0.085106382979&,\\ Q_{\mathbf{5}}&{}\approx{}&0.620689655172&{}:{}&-0.034482758621&{}:{}&0.413793103448&,\\ Q_{\mathbf{6}}&{}\approx{}&0.551020408163&{}:{}&0.489795918367&{}:{}&-0.040816326531&,\\ Q_{\mathbf{7}}&{}\approx{}&0.391304347826&{}:{}&0.347826086957&{}:{}&0.260869565217&,\\ Q_{\mathbf{a}}&{}\approx{}&-0.253164556962&{}:{}&0.683544303797&{}:{}&0.569620253165&,\\ Q_{\mathbf{1a}}&{}\approx{}&0.160000000000&{}:{}&1.200000000000&{}:{}&-0.360000000000&,\\ Q_{\mathbf{2a}}&{}\approx{}&0.136986301370&{}:{}&-0.369863013699&{}:{}&1.232876712329&,\\ Q_{\mathbf{3a}}&{}\approx{}&0.057142857143&{}:{}&0.428571428571&{}:{}&0.514285714286&,\\ Q_{\mathbf{4a}}&{}\approx{}&5.400000000000&{}:{}&-2.000000000000&{}:{}&-2.400000000000&,\\ Q_{\mathbf{5a}}&{}\approx{}&1.451612903226&{}:{}&0.193548387097&{}:{}&-0.645161290323&,\\ Q_{\mathbf{6a}}&{}\approx{}&1.350000000000&{}:{}&-0.500000000000&{}:{}&0.150000000000&,\\ Q_{\mathbf{7a}}&{}\approx{}&0.803571428571&{}:{}&0.107142857143&{}:{}&0.089285714286&,\\ Q_{\mathbf{b}}&{}\approx{}&0.717948717949&{}:{}&-0.282051282051&{}:{}&0.564102564103&,\\ Q_{\mathbf{1b}}&{}\approx{}&1.189189189189&{}:{}&0.189189189189&{}:{}&-0.378378378378&,\\ Q_{\mathbf{2b}}&{}\approx{}&-3.666666666667&{}:{}&9.333333333333&{}:{}&-4.666666666667&,\\ Q_{\mathbf{3b}}&{}\approx{}&0.241379310345&{}:{}&1.517241379310&{}:{}&-0.758620689655&,\\ Q_{\mathbf{4b}}&{}\approx{}&-0.394366197183&{}:{}&0.154929577465&{}:{}&1.239436619718&,\\ Q_{\mathbf{5b}}&{}\approx{}&0.411214953271&{}:{}&0.065420560748&{}:{}&0.523364485981&,\\ Q_{\mathbf{6b}}&{}\approx{}&-0.536585365854&{}:{}&1.365853658537&{}:{}&0.170731707317&,\\ Q_{\mathbf{7b}}&{}\approx{}&0.123893805310&{}:{}&0.778761061947&{}:{}&0.097345132743&,\\ Q_{\mathbf{c}}&{}\approx{}&0.704697986577&{}:{}&0.664429530201&{}:{}&-0.369127516779&,\\ Q_{\mathbf{1c}}&{}\approx{}&6.600000000000&{}:{}&7.000000000000&{}:{}&-12.600000000000&,\\ Q_{\mathbf{2c}}&{}\approx{}&1.204379562044&{}:{}&-0.459854014599&{}:{}&0.255474452555&,\\ Q_{\mathbf{3c}}&{}\approx{}&0.323076923077&{}:{}&-0.846153846154&{}:{}&1.523076923077&,\\ Q_{\mathbf{4c}}&{}\approx{}&-0.466666666667&{}:{}&1.222222222222&{}:{}&0.244444444444&,\\ Q_{\mathbf{5c}}&{}\approx{}&-0.774647887324&{}:{}&0.295774647887&{}:{}&1.478873239437&,\\ Q_{\mathbf{6c}}&{}\approx{}&0.440000000000&{}:{}&0.466666666667&{}:{}&0.093333333333&,\\ Q_{\mathbf{7c}}&{}\approx{}&0.150214592275&{}:{}&0.141630901288&{}:{}&0.708154506438&. \end{alignedat} \] \[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.292358803987&{}:{}&0.320360702421&{}:{}&0.387280493593&,\\ I^\prime_{\mathbf{1}}&{}\approx{}&0.071337579618&{}:{}&0.078170237406&{}:{}&0.850492182976&,\\ I^\prime_{\mathbf{2}}&{}\approx{}&0.050359712230&{}:{}&0.882930019621&{}:{}&0.066710268149&,\\ I^\prime_{\mathbf{3}}&{}\approx{}&0.032835820896&{}:{}&0.575692963753&{}:{}&0.391471215352&,\\ I^\prime_{\mathbf{4}}&{}\approx{}&0.893233082707&{}:{}&0.048335123523&{}:{}&0.058431793770&,\\ I^\prime_{\mathbf{5}}&{}\approx{}&0.608695652174&{}:{}&0.032938076416&{}:{}&0.358366271410&,\\ I^\prime_{\mathbf{6}}&{}\approx{}&0.517808219178&{}:{}&0.448318804483&{}:{}&0.033872976339&,\\ I^\prime_{\mathbf{7}}&{}\approx{}&0.407407407407&{}:{}&0.352733686067&{}:{}&0.239858906526&,\\ I^\prime_{\mathbf{a}}&{}\approx{}&-0.528301886792&{}:{}&0.740994854202&{}:{}&0.787307032590&,\\ I^\prime_{\mathbf{1a}}&{}\approx{}&-0.227979274611&{}:{}&0.888230940044&{}:{}&0.339748334567&,\\ I^\prime_{\mathbf{2a}}&{}\approx{}&-0.157142857143&{}:{}&0.220408163265&{}:{}&0.936734693878&,\\ I^\prime_{\mathbf{3a}}&{}\approx{}&-0.112903225806&{}:{}&0.439882697947&{}:{}&0.673020527859&,\\ I^\prime_{\mathbf{4a}}&{}\approx{}&1.948453608247&{}:{}&-0.374882849110&{}:{}&-0.573570759138&,\\ I^\prime_{\mathbf{5a}}&{}\approx{}&1.571428571429&{}:{}&-0.108843537415&{}:{}&-0.462585034014&,\\ I^\prime_{\mathbf{6a}}&{}\approx{}&1.362385321101&{}:{}&-0.262123197903&{}:{}&-0.100262123198&,\\ I^\prime_{\mathbf{7a}}&{}\approx{}&1.166666666667&{}:{}&-0.080808080808&{}:{}&-0.085858585859&,\\ I^\prime_{\mathbf{b}}&{}\approx{}&0.772413793103&{}:{}&-0.632183908046&{}:{}&0.859770114943&,\\ I^\prime_{\mathbf{1b}}&{}\approx{}&0.893401015228&{}:{}&-0.296108291032&{}:{}&0.402707275804&,\\ I^\prime_{\mathbf{2b}}&{}\approx{}&-0.400000000000&{}:{}&2.121212121212&{}:{}&-0.721212121212&,\\ I^\prime_{\mathbf{3b}}&{}\approx{}&-0.130841121495&{}:{}&1.713395638629&{}:{}&-0.582554517134&,\\ I^\prime_{\mathbf{4b}}&{}\approx{}&0.215799614644&{}:{}&-0.176621708414&{}:{}&0.960822093770&,\\ I^\prime_{\mathbf{5b}}&{}\approx{}&0.404597701149&{}:{}&-0.134099616858&{}:{}&0.729501915709&,\\ I^\prime_{\mathbf{6b}}&{}\approx{}&-0.259587020649&{}:{}&1.376597836775&{}:{}&-0.117010816126&,\\ I^\prime_{\mathbf{7b}}&{}\approx{}&-0.091056910569&{}:{}&1.192411924119&{}:{}&-0.101355013550&,\\ I^\prime_{\mathbf{c}}&{}\approx{}&0.945000000000&{}:{}&0.990000000000&{}:{}&-0.935000000000&,\\ I^\prime_{\mathbf{1c}}&{}\approx{}&-0.700471698113&{}:{}&-0.825471698113&{}:{}&2.525943396226&,\\ I^\prime_{\mathbf{2c}}&{}\approx{}&0.976973684211&{}:{}&0.414473684211&{}:{}&-0.391447368421&,\\ I^\prime_{\mathbf{3c}}&{}\approx{}&-0.200211864407&{}:{}&-0.582627118644&{}:{}&1.782838983051&,\\ I^\prime_{\mathbf{4c}}&{}\approx{}&0.342391304348&{}:{}&0.996376811594&{}:{}&-0.338768115942&,\\ I^\prime_{\mathbf{5c}}&{}\approx{}&-0.458333333333&{}:{}&-0.194444444444&{}:{}&1.652777777778&,\\ I^\prime_{\mathbf{6c}}&{}\approx{}&0.562500000000&{}:{}&0.662878787879&{}:{}&-0.225378787879&,\\ I^\prime_{\mathbf{7c}}&{}\approx{}&-0.145833333333&{}:{}&-0.152777777778&{}:{}&1.298611111111&. \end{alignedat} \]

Central Triangles and their Extraversions

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.522727272727&{}:{}&0.221369539551&{}:{}&0.255903187721&,\\B^\prime&{}\approx{}&0.195555555556&{}:{}&0.559788359788&{}:{}&0.244656084656&,\\C^\prime&{}\approx{}&0.171875000000&{}:{}&0.186011904762&{}:{}&0.642113095238&,\\[.5em] A^\prime_{\mathbf{1}}&{}\approx{}&-0.350000000000&{}:{}&0.626159554731&{}:{}&0.723840445269&,\\B^\prime_{\mathbf{1}}&{}\approx{}&0.622222222222&{}:{}&-0.400673400673&{}:{}&0.778451178451&,\\C^\prime_{\mathbf{1}}&{}\approx{}&0.021875000000&{}:{}&0.023674242424&{}:{}&0.954450757576&,\\[.5em] A^\prime_{\mathbf{2}}&{}\approx{}&-0.500000000000&{}:{}&0.695732838590&{}:{}&0.804267161410&,\\B^\prime_{\mathbf{2}}&{}\approx{}&0.015555555556&{}:{}&0.964983164983&{}:{}&0.019461279461&,\\C^\prime_{\mathbf{2}}&{}\approx{}&0.875000000000&{}:{}&0.946969696970&{}:{}&-0.821969696970&,\\[.5em] A^\prime_{\mathbf{3}}&{}\approx{}&-0.718181818182&{}:{}&0.796930342385&{}:{}&0.921251475797&,\\B^\prime_{\mathbf{3}}&{}\approx{}&0.122222222222&{}:{}&0.724867724868&{}:{}&0.152910052910&,\\C^\prime_{\mathbf{3}}&{}\approx{}&0.275000000000&{}:{}&0.297619047619&{}:{}&0.427380952381&,\\[.5em] A^\prime_{\mathbf{4}}&{}\approx{}&0.968181818182&{}:{}&0.014757969303&{}:{}&0.017060212515&,\\B^\prime_{\mathbf{4}}&{}\approx{}&0.733333333333&{}:{}&-0.650793650794&{}:{}&0.917460317460&,\\C^\prime_{\mathbf{4}}&{}\approx{}&0.928125000000&{}:{}&1.004464285714&{}:{}&-0.932589285714&,\\[.5em] A^\prime_{\mathbf{5}}&{}\approx{}&0.750000000000&{}:{}&0.115955473098&{}:{}&0.134044526902&,\\B^\prime_{\mathbf{5}}&{}\approx{}&0.840000000000&{}:{}&-0.890909090909&{}:{}&1.050909090909&,\\C^\prime_{\mathbf{5}}&{}\approx{}&0.328125000000&{}:{}&0.355113636364&{}:{}&0.316761363636&,\\[.5em] A^\prime_{\mathbf{6}}&{}\approx{}&0.600000000000&{}:{}&0.185528756957&{}:{}&0.214471243043&,\\B^\prime_{\mathbf{6}}&{}\approx{}&0.233333333333&{}:{}&0.474747474747&{}:{}&0.291919191919&,\\C^\prime_{\mathbf{6}}&{}\approx{}&1.181250000000&{}:{}&1.278409090909&{}:{}&-1.459659090909&,\\[.5em] A^\prime_{\mathbf{7}}&{}\approx{}&-0.272727272727&{}:{}&0.590318772137&{}:{}&0.682408500590&,\\B^\prime_{\mathbf{7}}&{}\approx{}&0.660000000000&{}:{}&-0.485714285714&{}:{}&0.825714285714&,\\C^\prime_{\mathbf{7}}&{}\approx{}&1.031250000000&{}:{}&1.116071428571&{}:{}&-1.147321428571&,\\[.5em] A^\prime_{\mathbf{a}}&{}\approx{}&-1.700000000000&{}:{}&1.252319109462&{}:{}&1.447680890538&,\\B^\prime_{\mathbf{a}}&{}\approx{}&-0.273437500000&{}:{}&0.931344696970&{}:{}&0.342092803030&,\\C^\prime_{\mathbf{a}}&{}\approx{}&-0.311111111111&{}:{}&0.336700336700&{}:{}&0.974410774411&,\\[.5em] A^\prime_{\mathbf{1a}}&{}\approx{}&0.045454545455&{}:{}&0.442739079103&{}:{}&0.511806375443&,\\B^\prime_{\mathbf{1a}}&{}\approx{}&-0.085937500000&{}:{}&0.978422619048&{}:{}&0.107514880952&,\\C^\prime_{\mathbf{1a}}&{}\approx{}&-2.444444444444&{}:{}&2.645502645503&{}:{}&0.798941798942&,\\[.5em] A^\prime_{\mathbf{2a}}&{}\approx{}&0.140909090909&{}:{}&0.398465171192&{}:{}&0.460625737898&,\\B^\prime_{\mathbf{2a}}&{}\approx{}&-3.437500000000&{}:{}&0.136904761905&{}:{}&4.300595238095&,\\C^\prime_{\mathbf{2a}}&{}\approx{}&-0.061111111111&{}:{}&0.066137566138&{}:{}&0.994973544974&,\\[.5em] A^\prime_{\mathbf{3a}}&{}\approx{}&0.250000000000&{}:{}&0.347866419295&{}:{}&0.402133580705&,\\B^\prime_{\mathbf{3a}}&{}\approx{}&-0.437500000000&{}:{}&0.890151515152&{}:{}&0.547348484848&,\\C^\prime_{\mathbf{3a}}&{}\approx{}&-0.194444444444&{}:{}&0.210437710438&{}:{}&0.984006734007&,\\[.5em] A^\prime_{\mathbf{4a}}&{}\approx{}&3.000000000000&{}:{}&-0.927643784787&{}:{}&-1.072356215213&,\\B^\prime_{\mathbf{4a}}&{}\approx{}&1.476562500000&{}:{}&1.370738636364&{}:{}&-1.847301136364&,\\C^\prime_{\mathbf{4a}}&{}\approx{}&1.166666666667&{}:{}&-1.262626262626&{}:{}&1.095959595960&,\\[.5em] A^\prime_{\mathbf{5a}}&{}\approx{}&1.254545454545&{}:{}&-0.118063754427&{}:{}&-0.136481700118&,\\B^\prime_{\mathbf{5a}}&{}\approx{}&1.289062500000&{}:{}&1.323660714286&{}:{}&-1.612723214286&,\\C^\prime_{\mathbf{5a}}&{}\approx{}&3.300000000000&{}:{}&-3.571428571429&{}:{}&1.271428571429&,\\[.5em] A^\prime_{\mathbf{6a}}&{}\approx{}&1.159090909091&{}:{}&-0.073789846517&{}:{}&-0.085301062574&,\\B^\prime_{\mathbf{6a}}&{}\approx{}&4.640625000000&{}:{}&2.165178571429&{}:{}&-5.805803571429&,\\C^\prime_{\mathbf{6a}}&{}\approx{}&0.916666666667&{}:{}&-0.992063492063&{}:{}&1.075396825397&,\\[.5em] A^\prime_{\mathbf{7a}}&{}\approx{}&1.050000000000&{}:{}&-0.023191094620&{}:{}&-0.026808905380&,\\B^\prime_{\mathbf{7a}}&{}\approx{}&1.640625000000&{}:{}&1.411931818182&{}:{}&-2.052556818182&,\\C^\prime_{\mathbf{7a}}&{}\approx{}&1.050000000000&{}:{}&-1.136363636364&{}:{}&1.086363636364&,\\[.5em] A^\prime_{\mathbf{b}}&{}\approx{}&0.950347222222&{}:{}&-0.318287037037&{}:{}&0.367939814815&,\\B^\prime_{\mathbf{b}}&{}\approx{}&1.400000000000&{}:{}&-2.151515151515&{}:{}&1.751515151515&,\\C^\prime_{\mathbf{b}}&{}\approx{}&0.350000000000&{}:{}&-0.378787878788&{}:{}&1.028787878788&,\\[.5em] A^\prime_{\mathbf{1b}}&{}\approx{}&0.982445987654&{}:{}&-0.112525720165&{}:{}&0.130079732510&,\\B^\prime_{\mathbf{1b}}&{}\approx{}&0.440000000000&{}:{}&0.009523809524&{}:{}&0.550476190476&,\\C^\prime_{\mathbf{1b}}&{}\approx{}&2.750000000000&{}:{}&-2.976190476190&{}:{}&1.226190476190&,\\[.5em] A^\prime_{\mathbf{2b}}&{}\approx{}&1.252777777778&{}:{}&1.620370370370&{}:{}&-1.873148148148&,\\B^\prime_{\mathbf{2b}}&{}\approx{}&-1.100000000000&{}:{}&3.476190476190&{}:{}&-1.376190476190&,\\C^\prime_{\mathbf{2b}}&{}\approx{}&-1.100000000000&{}:{}&1.190476190476&{}:{}&0.909523809524&,\\[.5em] A^\prime_{\mathbf{3b}}&{}\approx{}&1.220679012346&{}:{}&1.414609053498&{}:{}&-1.635288065844&,\\B^\prime_{\mathbf{3b}}&{}\approx{}&-0.140000000000&{}:{}&1.315151515152&{}:{}&-0.175151515152&,\\C^\prime_{\mathbf{3b}}&{}\approx{}&-3.500000000000&{}:{}&3.787878787879&{}:{}&0.712121212121&,\\[.5em] A^\prime_{\mathbf{4b}}&{}\approx{}&0.255208333333&{}:{}&-4.774305555556&{}:{}&5.519097222222&,\\B^\prime_{\mathbf{4b}}&{}\approx{}&0.373333333333&{}:{}&0.159595959596&{}:{}&0.467070707071&,\\C^\prime_{\mathbf{4b}}&{}\approx{}&0.064814814815&{}:{}&-0.070145903479&{}:{}&1.005331088664&,\\[.5em] A^\prime_{\mathbf{5b}}&{}\approx{}&0.905208333333&{}:{}&-0.607638888889&{}:{}&0.702430555556&,\\B^\prime_{\mathbf{5b}}&{}\approx{}&0.325925925926&{}:{}&0.266313932981&{}:{}&0.407760141093&,\\C^\prime_{\mathbf{5b}}&{}\approx{}&0.183333333333&{}:{}&-0.198412698413&{}:{}&1.015079365079&,\\[.5em] A^\prime_{\mathbf{6b}}&{}\approx{}&1.947916666667&{}:{}&6.076388888889&{}:{}&-7.024305555556&,\\B^\prime_{\mathbf{6b}}&{}\approx{}&-0.073333333333&{}:{}&1.165079365079&{}:{}&-0.091746031746&,\\C^\prime_{\mathbf{6b}}&{}\approx{}&-0.814814814815&{}:{}&0.881834215168&{}:{}&0.932980599647&,\\[.5em] A^\prime_{\mathbf{7b}}&{}\approx{}&1.297916666667&{}:{}&1.909722222222&{}:{}&-2.207638888889&,\\B^\prime_{\mathbf{7b}}&{}\approx{}&-0.025925925926&{}:{}&1.058361391695&{}:{}&-0.032435465769&,\\C^\prime_{\mathbf{7b}}&{}\approx{}&-0.933333333333&{}:{}&1.010101010101&{}:{}&0.923232323232&,\\[.5em] A^\prime_{\mathbf{c}}&{}\approx{}&1.066203703704&{}:{}&0.424382716049&{}:{}&-0.490586419753&,\\B^\prime_{\mathbf{c}}&{}\approx{}&0.410156250000&{}:{}&1.102982954545&{}:{}&-0.513139204545&,\\C^\prime_{\mathbf{c}}&{}\approx{}&2.362500000000&{}:{}&2.556818181818&{}:{}&-3.919318181818&,\\[.5em] A^\prime_{\mathbf{1c}}&{}\approx{}&0.789351851852&{}:{}&-1.350308641975&{}:{}&1.560956790123&,\\B^\prime_{\mathbf{1c}}&{}\approx{}&-1.160156250000&{}:{}&0.708705357143&{}:{}&1.451450892857&,\\C^\prime_{\mathbf{1c}}&{}\approx{}&-2.062500000000&{}:{}&-2.232142857143&{}:{}&5.294642857143&,\\[.5em] A^\prime_{\mathbf{2c}}&{}\approx{}&1.021064814815&{}:{}&0.135030864198&{}:{}&-0.156095679012&,\\B^\prime_{\mathbf{2c}}&{}\approx{}&5.156250000000&{}:{}&2.294642857143&{}:{}&-6.450892857143&,\\C^\prime_{\mathbf{2c}}&{}\approx{}&0.464062500000&{}:{}&0.502232142857&{}:{}&0.033705357143&,\\[.5em] A^\prime_{\mathbf{3c}}&{}\approx{}&0.834490740741&{}:{}&-1.060956790123&{}:{}&1.226466049383&,\\B^\prime_{\mathbf{3c}}&{}\approx{}&-5.906250000000&{}:{}&-0.482954545455&{}:{}&7.389204545455&,\\C^\prime_{\mathbf{3c}}&{}\approx{}&-0.164062500000&{}:{}&-0.177556818182&{}:{}&1.341619318182&,\\[.5em] A^\prime_{\mathbf{4c}}&{}\approx{}&1.993055555556&{}:{}&6.365740740741&{}:{}&-7.358796296296&,\\B^\prime_{\mathbf{4c}}&{}\approx{}&0.109375000000&{}:{}&1.027462121212&{}:{}&-0.136837121212&,\\C^\prime_{\mathbf{4c}}&{}\approx{}&0.437500000000&{}:{}&0.473484848485&{}:{}&0.089015151515&,\\[.5em] A^\prime_{\mathbf{5c}}&{}\approx{}&-0.137500000000&{}:{}&-7.291666666667&{}:{}&8.429166666667&,\\B^\prime_{\mathbf{5c}}&{}\approx{}&-0.859375000000&{}:{}&0.784226190476&{}:{}&1.075148809524&,\\C^\prime_{\mathbf{5c}}&{}\approx{}&-0.137500000000&{}:{}&-0.148809523810&{}:{}&1.286309523810&,\\[.5em] A^\prime_{\mathbf{6c}}&{}\approx{}&1.078993055556&{}:{}&0.506365740741&{}:{}&-0.585358796296&,\\B^\prime_{\mathbf{6c}}&{}\approx{}&0.343750000000&{}:{}&1.086309523810&{}:{}&-0.430059523810&,\\C^\prime_{\mathbf{6c}}&{}\approx{}&0.343750000000&{}:{}&0.372023809524&{}:{}&0.284226190476&,\\[.5em] A^\prime_{\mathbf{7c}}&{}\approx{}&0.776562500000&{}:{}&-1.432291666667&{}:{}&1.655729166667&,\\B^\prime_{\mathbf{7c}}&{}\approx{}&-1.093750000000&{}:{}&0.725378787879&{}:{}&1.368371212121&,\\C^\prime_{\mathbf{7c}}&{}\approx{}&-0.043750000000&{}:{}&-0.047348484848&{}:{}&1.091098484848&. \end{alignedat} \] \[ \begin{alignedat}{4} A^{\prime\prime}&{}\approx{}&0.182952182952&{}:{}&0.360855360855&{}:{}&0.456192456192&,\\B^{\prime\prime}&{}\approx{}&0.332075471698&{}:{}&0.202156334232&{}:{}&0.465768194070&,\\C^{\prime\prime}&{}\approx{}&0.355465791467&{}:{}&0.394380928337&{}:{}&0.250153280196&,\\[.5em] A^{\prime\prime}_{\mathbf{1}}&{}\approx{}&0.042264150943&{}:{}&0.009262435678&{}:{}&0.948473413379&,\\B^{\prime\prime}_{\mathbf{1}}&{}\approx{}&0.008327137546&{}:{}&0.045623521460&{}:{}&0.946049340994&,\\C^{\prime\prime}_{\mathbf{1}}&{}\approx{}&0.118440185063&{}:{}&0.131406597368&{}:{}&0.750153217569&,\\[.5em] A^{\prime\prime}_{\mathbf{2}}&{}\approx{}&0.030567685590&{}:{}&0.964668519254&{}:{}&0.004763795157&,\\B^{\prime\prime}_{\mathbf{2}}&{}\approx{}&0.082352941176&{}:{}&0.802139037433&{}:{}&0.115508021390&,\\C^{\prime\prime}_{\mathbf{2}}&{}\approx{}&0.003375120540&{}:{}&0.958621898834&{}:{}&0.038002980626&,\\[.5em] A^{\prime\prime}_{\mathbf{3}}&{}\approx{}&0.169230769231&{}:{}&0.593406593407&{}:{}&0.237362637363&,\\B^{\prime\prime}_{\mathbf{3}}&{}\approx{}&0.004943820225&{}:{}&0.433386837881&{}:{}&0.561669341894&,\\C^{\prime\prime}_{\mathbf{3}}&{}\approx{}&0.002588235294&{}:{}&0.735126050420&{}:{}&0.262285714286&,\\[.5em] A^{\prime\prime}_{\mathbf{4}}&{}\approx{}&0.819310344828&{}:{}&0.079802955665&{}:{}&0.100886699507&,\\B^{\prime\prime}_{\mathbf{4}}&{}\approx{}&0.967601809955&{}:{}&0.029088558500&{}:{}&0.003309631545&,\\C^{\prime\prime}_{\mathbf{4}}&{}\approx{}&0.963894523327&{}:{}&0.002607939728&{}:{}&0.033497536946&,\\[.5em] A^{\prime\prime}_{\mathbf{5}}&{}\approx{}&0.471910112360&{}:{}&0.005107252298&{}:{}&0.522982635342&,\\B^{\prime\prime}_{\mathbf{5}}&{}\approx{}&0.646153846154&{}:{}&0.174825174825&{}:{}&0.179020979021&,\\C^{\prime\prime}_{\mathbf{5}}&{}\approx{}&0.760180995475&{}:{}&0.002056766763&{}:{}&0.237762237762&,\\[.5em] A^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.389690721649&{}:{}&0.607310215558&{}:{}&0.002999062793&,\\B^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.673663366337&{}:{}&0.324032403240&{}:{}&0.002304230423&,\\C^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.444705882353&{}:{}&0.308021390374&{}:{}&0.247272727273&,\\[.5em] A^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.804878048780&{}:{}&0.139372822300&{}:{}&0.055749128920&,\\B^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.178378378378&{}:{}&0.772200772201&{}:{}&0.049420849421&,\\C^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.149321266968&{}:{}&0.103425985779&{}:{}&0.747252747253&,\\[.5em] A^{\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.291060291060&{}:{}&0.653184653185&{}:{}&0.637875637876&,\\B^{\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.605405405405&{}:{}&0.530712530713&{}:{}&1.074692874693&,\\C^{\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.546107036979&{}:{}&0.992694931843&{}:{}&0.553412105136&,\\[.5em] A^{\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.166037735849&{}:{}&1.035040431267&{}:{}&0.130997304582&,\\B^{\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.311504424779&{}:{}&0.758533501896&{}:{}&0.552970922882&,\\C^{\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.063127690100&{}:{}&0.885427341668&{}:{}&0.177700348432&,\\[.5em] A^{\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.120087336245&{}:{}&0.067373674361&{}:{}&1.052713661884&,\\B^{\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.032352941176&{}:{}&0.113445378151&{}:{}&0.918907563025&,\\C^{\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.205285159749&{}:{}&0.373160431685&{}:{}&0.832124728064&,\\[.5em] A^{\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.269230769231&{}:{}&0.419580419580&{}:{}&0.849650349650&,\\B^{\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.026923076923&{}:{}&0.262237762238&{}:{}&0.764685314685&,\\C^{\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.041176470588&{}:{}&0.577540106952&{}:{}&0.463636363636&,\\[.5em] A^{\prime\prime}_{\mathbf{4a}}&{}\approx{}&1.303448275862&{}:{}&-0.100313479624&{}:{}&-0.203134796238&,\\B^{\prime\prime}_{\mathbf{4a}}&{}\approx{}&2.223529411765&{}:{}&-1.069518716578&{}:{}&-0.154010695187&,\\C^{\prime\prime}_{\mathbf{4a}}&{}\approx{}&2.440459110473&{}:{}&-0.083474631538&{}:{}&-1.356984478936&,\\[.5em] A^{\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.853932584270&{}:{}&-0.051364365971&{}:{}&-0.802568218299&,\\B^{\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.320000000000&{}:{}&-0.228571428571&{}:{}&-0.091428571429&,\\C^{\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.257238646754&{}:{}&-0.005573213741&{}:{}&-0.251665433013&,\\[.5em] A^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.530927835052&{}:{}&-0.471281296024&{}:{}&-0.059646539028&,\\B^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.142307692308&{}:{}&-0.137362637363&{}:{}&-0.004945054945&,\\C^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.209502262443&{}:{}&-0.041370394312&{}:{}&-0.168131868132&,\\[.5em] A^{\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.280487804878&{}:{}&-0.141906873614&{}:{}&-0.138580931264&,\\B^{\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.050000000000&{}:{}&-0.045454545455&{}:{}&-0.004545454545&,\\C^{\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.057614826753&{}:{}&-0.004688301223&{}:{}&-0.052926525529&,\\[.5em] A^{\prime\prime}_{\mathbf{b}}&{}\approx{}&0.560000000000&{}:{}&-0.733333333333&{}:{}&1.173333333333&,\\B^{\prime\prime}_{\mathbf{b}}&{}\approx{}&0.676226415094&{}:{}&-0.345911949686&{}:{}&0.669685534591&,\\C^{\prime\prime}_{\mathbf{b}}&{}\approx{}&1.028407460545&{}:{}&-0.636537541846&{}:{}&0.608130081301&,\\[.5em] A^{\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.758620689655&{}:{}&-0.402298850575&{}:{}&0.643678160920&,\\B^{\prime\prime}_{\mathbf{1b}}&{}\approx{}&1.046840148699&{}:{}&-0.216852540273&{}:{}&0.170012391574&,\\C^{\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.878764237791&{}:{}&-0.089197482707&{}:{}&0.210433244916&,\\[.5em] A^{\prime\prime}_{\mathbf{2b}}&{}\approx{}&-1.100000000000&{}:{}&2.333333333333&{}:{}&-0.233333333333&,\\B^{\prime\prime}_{\mathbf{2b}}&{}\approx{}&-0.103529411765&{}:{}&1.372549019608&{}:{}&-0.269019607843&,\\C^{\prime\prime}_{\mathbf{2b}}&{}\approx{}&-0.103529411765&{}:{}&2.690196078431&{}:{}&-1.586666666667&,\\[.5em] A^{\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.269230769231&{}:{}&1.410256410256&{}:{}&-0.141025641026&,\\B^{\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.062921348315&{}:{}&2.059925093633&{}:{}&-0.997003745318&,\\C^{\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.008360704688&{}:{}&1.324773564248&{}:{}&-0.316412859560&,\\[.5em] A^{\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.110453648915&{}:{}&-0.036160420776&{}:{}&0.925706771861&,\\B^{\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.067571644042&{}:{}&-0.138260432378&{}:{}&1.070688788336&,\\C^{\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.364116631108&{}:{}&-0.225371668529&{}:{}&0.861255037421&,\\[.5em] A^{\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.234666666667&{}:{}&-0.031111111111&{}:{}&0.796444444444&,\\B^{\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.361025641026&{}:{}&-0.299145299145&{}:{}&0.938119658120&,\\C^{\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.538689622190&{}:{}&-0.054678782082&{}:{}&0.515989159892&,\\[.5em] A^{\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.134556574924&{}:{}&1.141692150866&{}:{}&-0.007135575943&,\\B^{\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.464686468647&{}:{}&1.540154015402&{}:{}&-0.075467546755&,\\C^{\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.047273704002&{}:{}&1.228400035813&{}:{}&-0.181126331811&,\\[.5em] A^{\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.050450450450&{}:{}&1.057057057057&{}:{}&-0.006606606607&,\\B^{\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.161441441441&{}:{}&1.321321321321&{}:{}&-0.159879879880&,\\C^{\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.006757164404&{}:{}&1.070688788336&{}:{}&-0.063931623932&,\\[.5em] A^{\prime\prime}_{\mathbf{c}}&{}\approx{}&0.698964497041&{}:{}&1.318047337278&{}:{}&-1.017011834320&,\\B^{\prime\prime}_{\mathbf{c}}&{}\approx{}&1.250735294118&{}:{}&0.727941176471&{}:{}&-0.978676470588&,\\C^{\prime\prime}_{\mathbf{c}}&{}\approx{}&0.745550366069&{}:{}&0.756059075991&{}:{}&-0.501609442060&,\\[.5em] A^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-1.485000000000&{}:{}&-0.350000000000&{}:{}&2.835000000000&,\\B^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.285576923077&{}:{}&-1.682692307692&{}:{}&2.968269230769&,\\C^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.220836087244&{}:{}&-0.283377395902&{}:{}&1.504213483146&,\\[.5em] A^{\prime\prime}_{\mathbf{2c}}&{}\approx{}&0.851490825688&{}:{}&0.650229357798&{}:{}&-0.501720183486&,\\B^{\prime\prime}_{\mathbf{2c}}&{}\approx{}&0.903040540541&{}:{}&0.212837837838&{}:{}&-0.115878378378&,\\C^{\prime\prime}_{\mathbf{2c}}&{}\approx{}&1.118762054002&{}:{}&0.186053519769&{}:{}&-0.304815573770&,\\[.5em] A^{\prime\prime}_{\mathbf{3c}}&{}\approx{}&-0.319256756757&{}:{}&-0.185810810811&{}:{}&1.505067567568&,\\B^{\prime\prime}_{\mathbf{3c}}&{}\approx{}&-0.020907079646&{}:{}&-0.304203539823&{}:{}&1.325110619469&,\\C^{\prime\prime}_{\mathbf{3c}}&{}\approx{}&-0.125073529412&{}:{}&-0.978676470588&{}:{}&2.103750000000&,\\[.5em] A^{\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.175000000000&{}:{}&0.916666666667&{}:{}&-0.091666666667&,\\B^{\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.545192307692&{}:{}&0.881410256410&{}:{}&-0.426602564103&,\\C^{\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.143762677485&{}:{}&1.124915483435&{}:{}&-0.268678160920&,\\[.5em] A^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.237068965517&{}:{}&-0.020114942529&{}:{}&1.257183908046&,\\B^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.137500000000&{}:{}&-0.291666666667&{}:{}&1.429166666667&,\\C^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.777714932127&{}:{}&-0.129336349925&{}:{}&1.907051282051&,\\[.5em] A^{\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.343750000000&{}:{}&0.729166666667&{}:{}&-0.072916666667&,\\B^{\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.655147058824&{}:{}&0.428921568627&{}:{}&-0.084068627451&,\\C^{\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.655147058824&{}:{}&0.840686274510&{}:{}&-0.495833333333&,\\[.5em] A^{\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.084134615385&{}:{}&-0.017628205128&{}:{}&1.101762820513&,\\B^{\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.017500000000&{}:{}&-0.091666666667&{}:{}&1.109166666667&,\\C^{\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.247454751131&{}:{}&-0.250942684766&{}:{}&1.498397435897&. \end{alignedat} \] \[ \begin{alignedat}{4} A^{\prime\prime\prime}&{}\approx{}&0.131605184447&{}:{}&0.376726961971&{}:{}&0.491667853582&,\\B^{\prime\prime\prime}&{}\approx{}&0.346575342466&{}:{}&0.146771037182&{}:{}&0.506653620352&,\\C^{\prime\prime\prime}&{}\approx{}&0.383188186293&{}:{}&0.429220533348&{}:{}&0.187591280359&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1}}&{}\approx{}&0.022733423545&{}:{}&-0.014638946980&{}:{}&0.991905523435&,\\B^{\prime\prime\prime}_{\mathbf{1}}&{}\approx{}&-0.013714514194&{}:{}&0.024535640289&{}:{}&0.989178873905&,\\C^{\prime\prime\prime}_{\mathbf{1}}&{}\approx{}&-274.400000000094&{}:{}&-292.090909091008&{}:{}&567.490909091102&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2}}&{}\approx{}&0.016104294479&{}:{}&0.999023982153&{}:{}&-0.015128276631&,\\B^{\prime\prime\prime}_{\mathbf{2}}&{}\approx{}&1.225000000000&{}:{}&-1.704545454545&{}:{}&1.479545454545&,\\C^{\prime\prime\prime}_{\mathbf{2}}&{}\approx{}&-0.012442864398&{}:{}&0.992428089940&{}:{}&0.020014774459&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3}}&{}\approx{}&0.117857142857&{}:{}&0.698979591837&{}:{}&0.183163265306&,\\B^{\prime\prime\prime}_{\mathbf{3}}&{}\approx{}&-0.587162162162&{}:{}&0.651544401544&{}:{}&0.935617760618&,\\C^{\prime\prime\prime}_{\mathbf{3}}&{}\approx{}&-0.157142857143&{}:{}&0.955567036941&{}:{}&0.201575820201&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4}}&{}\approx{}&-1.120754716981&{}:{}&0.994609164420&{}:{}&1.126145552561&,\\B^{\prime\prime\prime}_{\mathbf{4}}&{}\approx{}&0.998910468972&{}:{}&0.015226365297&{}:{}&-0.014136834269&,\\C^{\prime\prime\prime}_{\mathbf{4}}&{}\approx{}&0.994904458599&{}:{}&-0.012435547467&{}:{}&0.017531088869&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5}}&{}\approx{}&1.105263157895&{}:{}&-1.172248803828&{}:{}&1.066985645933&,\\B^{\prime\prime\prime}_{\mathbf{5}}&{}\approx{}&0.773684210526&{}:{}&0.119617224880&{}:{}&0.106698564593&,\\C^{\prime\prime\prime}_{\mathbf{5}}&{}\approx{}&0.973509933775&{}:{}&-0.147501505117&{}:{}&0.173991571343&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&0.555882352941&{}:{}&1.131016042781&{}:{}&-0.686898395722&,\\B^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&1.045849802372&{}:{}&0.323392022997&{}:{}&-0.369241825368&,\\C^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&0.515789473684&{}:{}&0.299840510367&{}:{}&0.184370015949&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&-1.178571428571&{}:{}&0.867346938776&{}:{}&1.311224489796&,\\B^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&0.942857142857&{}:{}&-2.040816326531&{}:{}&2.097959183673&,\\C^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&-33.000000000002&{}:{}&-48.571428571431&{}:{}&82.571428571433&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.180567497850&{}:{}&0.615023841163&{}:{}&0.565543656687&,\\B^{\prime\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.535175072278&{}:{}&0.394241158777&{}:{}&1.140933913501&,\\C^{\prime\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.460832042487&{}:{}&1.068398076807&{}:{}&0.392433965680&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.093352192362&{}:{}&1.062840977975&{}:{}&0.030511214387&,\\B^{\prime\prime\prime}_{\mathbf{1a}}&{}\approx{}&0.073089700997&{}:{}&0.711912672046&{}:{}&0.214997626958&,\\C^{\prime\prime\prime}_{\mathbf{1a}}&{}\approx{}&0.008716323296&{}:{}&0.893140140367&{}:{}&0.098143536337&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.065268987342&{}:{}&0.002599457505&{}:{}&1.062669529837&,\\B^{\prime\prime\prime}_{\mathbf{2a}}&{}\approx{}&0.021565899317&{}:{}&0.060984424126&{}:{}&0.917449676557&,\\C^{\prime\prime\prime}_{\mathbf{2a}}&{}\approx{}&0.228674892704&{}:{}&0.023796750460&{}:{}&0.747528356836&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.164062500000&{}:{}&0.333806818182&{}:{}&0.830255681818&,\\B^{\prime\prime\prime}_{\mathbf{3a}}&{}\approx{}&0.112385321101&{}:{}&0.156380316931&{}:{}&0.731234361968&,\\C^{\prime\prime\prime}_{\mathbf{3a}}&{}\approx{}&0.191406250000&{}:{}&0.500710227273&{}:{}&0.307883522727&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4a}}&{}\approx{}&0.348708487085&{}:{}&0.323716873532&{}:{}&0.327574639383&,\\B^{\prime\prime\prime}_{\mathbf{4a}}&{}\approx{}&1.042553191489&{}:{}&-0.322372662798&{}:{}&0.279819471309&,\\C^{\prime\prime\prime}_{\mathbf{4a}}&{}\approx{}&1.101582014988&{}:{}&0.292180758459&{}:{}&-0.393762773446&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5a}}&{}\approx{}&0.414572864322&{}:{}&0.425699928212&{}:{}&0.159727207466&,\\B^{\prime\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.064516129032&{}:{}&-0.100180324584&{}:{}&0.035664195552&,\\C^{\prime\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.019887127116&{}:{}&0.091066149653&{}:{}&-0.110953276769&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6a}}&{}\approx{}&0.378826530612&{}:{}&0.176749271137&{}:{}&0.444424198251&,\\B^{\prime\prime\prime}_{\mathbf{6a}}&{}\approx{}&0.994680851064&{}:{}&-0.063323201621&{}:{}&0.068642350557&,\\C^{\prime\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.048380398671&{}:{}&0.028773137162&{}:{}&-0.077153535833&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7a}}&{}\approx{}&0.345394736842&{}:{}&0.297248803828&{}:{}&0.357356459330&,\\B^{\prime\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.000972762646&{}:{}&-0.022108241953&{}:{}&0.021135479307&,\\C^{\prime\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.008032915361&{}:{}&0.017704474209&{}:{}&-0.025737389570&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{b}}&{}\approx{}&0.416216216216&{}:{}&-0.639639639640&{}:{}&1.223423423423&,\\B^{\prime\prime\prime}_{\mathbf{b}}&{}\approx{}&0.635034802784&{}:{}&-0.212683681361&{}:{}&0.577648878577&,\\C^{\prime\prime\prime}_{\mathbf{b}}&{}\approx{}&1.096993987976&{}:{}&-0.521710086840&{}:{}&0.424716098864&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.681415929204&{}:{}&0.014749262537&{}:{}&0.303834808260&,\\B^{\prime\prime\prime}_{\mathbf{1b}}&{}\approx{}&1.072210526316&{}:{}&-0.122807017544&{}:{}&0.050596491228&,\\C^{\prime\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.881294341582&{}:{}&0.002018803715&{}:{}&0.116686854704&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2b}}&{}\approx{}&-0.334782608696&{}:{}&1.057971014493&{}:{}&0.276811594203&,\\B^{\prime\prime\prime}_{\mathbf{2b}}&{}\approx{}&0.304729729730&{}:{}&0.394144144144&{}:{}&0.301126126126&,\\C^{\prime\prime\prime}_{\mathbf{2b}}&{}\approx{}&0.304729729730&{}:{}&1.150900900901&{}:{}&-0.455630630631&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.116314199396&{}:{}&1.092648539778&{}:{}&0.023665659617&,\\B^{\prime\prime\prime}_{\mathbf{3b}}&{}\approx{}&0.420744680851&{}:{}&0.487588652482&{}:{}&0.091666666667&,\\C^{\prime\prime\prime}_{\mathbf{3b}}&{}\approx{}&0.102887617066&{}:{}&1.034946236559&{}:{}&-0.137833853625&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.059037761165&{}:{}&0.025238003961&{}:{}&0.915724234873&,\\B^{\prime\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.003993480033&{}:{}&-0.074707959794&{}:{}&1.070714479761&,\\C^{\prime\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.033316335203&{}:{}&0.246189585812&{}:{}&0.720494078985&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.135982339956&{}:{}&0.111111111111&{}:{}&0.752906548933&,\\B^{\prime\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.265749235474&{}:{}&-0.178389398573&{}:{}&0.912640163099&,\\C^{\prime\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.438059231254&{}:{}&0.222012182315&{}:{}&0.339928586431&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.062373430539&{}:{}&0.990954502498&{}:{}&0.071418928041&,\\B^{\prime\prime\prime}_{\mathbf{6b}}&{}\approx{}&0.134774774775&{}:{}&0.420420420420&{}:{}&0.444804804805&,\\C^{\prime\prime\prime}_{\mathbf{6b}}&{}\approx{}&0.023155027241&{}:{}&1.060343404326&{}:{}&-0.083498431567&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.024502784407&{}:{}&1.000265181649&{}:{}&0.024237602758&,\\B^{\prime\prime\prime}_{\mathbf{7b}}&{}\approx{}&0.262039957939&{}:{}&0.385559060638&{}:{}&0.352400981423&,\\C^{\prime\prime\prime}_{\mathbf{7b}}&{}\approx{}&0.018248388987&{}:{}&1.012790470611&{}:{}&-0.031038859598&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{c}}&{}\approx{}&0.492560652009&{}:{}&1.324583017437&{}:{}&-0.817143669447&,\\B^{\prime\prime\prime}_{\mathbf{c}}&{}\approx{}&1.269207217505&{}:{}&0.505184519922&{}:{}&-0.774391737427&,\\C^{\prime\prime\prime}_{\mathbf{c}}&{}\approx{}&0.654063162678&{}:{}&0.646887306877&{}:{}&-0.300950469555&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.459143109541&{}:{}&0.280477031802&{}:{}&1.178666077739&,\\B^{\prime\prime\prime}_{\mathbf{1c}}&{}\approx{}&0.298773364486&{}:{}&-0.511098130841&{}:{}&1.212324766355&,\\C^{\prime\prime\prime}_{\mathbf{1c}}&{}\approx{}&0.253608417805&{}:{}&0.244876597620&{}:{}&0.501514984575&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2c}}&{}\approx{}&0.658912271805&{}:{}&0.293230223124&{}:{}&0.047857505071&,\\B^{\prime\prime\prime}_{\mathbf{2c}}&{}\approx{}&0.876331822463&{}:{}&0.115890628679&{}:{}&0.007777548858&,\\C^{\prime\prime\prime}_{\mathbf{2c}}&{}\approx{}&1.109257644850&{}:{}&0.060320547210&{}:{}&-0.169578192060&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3c}}&{}\approx{}&-0.140930043384&{}:{}&-0.011523861171&{}:{}&1.152453904555&,\\B^{\prime\prime\prime}_{\mathbf{3c}}&{}\approx{}&0.107121632330&{}:{}&-0.136192551506&{}:{}&1.029070919176&,\\C^{\prime\prime\prime}_{\mathbf{3c}}&{}\approx{}&0.421290685596&{}:{}&-0.040469182825&{}:{}&0.619178497230&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.094362745098&{}:{}&0.886437908497&{}:{}&0.019199346405&,\\B^{\prime\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.208575581395&{}:{}&0.666182170543&{}:{}&0.125242248062&,\\C^{\prime\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.039949888641&{}:{}&1.107553823311&{}:{}&-0.147503711952&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.107903587444&{}:{}&0.098467862481&{}:{}&1.009435724963&,\\B^{\prime\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.002473021583&{}:{}&-0.131145083933&{}:{}&1.133618105516&,\\C^{\prime\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.009522160665&{}:{}&0.425784856879&{}:{}&0.583737303786&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.200520833333&{}:{}&0.633680555556&{}:{}&0.165798611111&,\\B^{\prime\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.547095070423&{}:{}&0.256748826291&{}:{}&0.196156103286&,\\C^{\prime\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.547095070423&{}:{}&0.749706572770&{}:{}&-0.296801643192&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.040646114865&{}:{}&0.026956644144&{}:{}&1.013689470721&,\\B^{\prime\prime\prime}_{\mathbf{7c}}&{}\approx{}&0.024005023184&{}:{}&-0.044274858320&{}:{}&1.020269835137&,\\C^{\prime\prime\prime}_{\mathbf{7c}}&{}\approx{}&0.234611027190&{}:{}&0.265168680765&{}:{}&0.500220292044&. \end{alignedat} \] \[ \begin{alignedat}{4} A^*&{}\approx{}&0.000000000000&{}:{}&0.428571428571&{}:{}&0.571428571429&,\\B^*&{}\approx{}&0.400000000000&{}:{}&0.000000000000&{}:{}&0.600000000000&,\\C^*&{}\approx{}&0.470588235294&{}:{}&0.529411764706&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1}}&{}\approx{}&0.000000000000&{}:{}&-0.090909090909&{}:{}&1.090909090909&,\\B^*_{\mathbf{1}}&{}\approx{}&-0.080000000000&{}:{}&0.000000000000&{}:{}&1.080000000000&,\\C^*_{\mathbf{1}}&{}\approx{}&0.470588235294&{}:{}&0.529411764706&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2}}&{}\approx{}&0.000000000000&{}:{}&1.090909090909&{}:{}&-0.090909090909&,\\B^*_{\mathbf{2}}&{}\approx{}&0.400000000000&{}:{}&0.000000000000&{}:{}&0.600000000000&,\\C^*_{\mathbf{2}}&{}\approx{}&-0.058823529412&{}:{}&1.058823529412&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3}}&{}\approx{}&0.000000000000&{}:{}&0.571428571429&{}:{}&0.428571428571&,\\B^*_{\mathbf{3}}&{}\approx{}&-0.080000000000&{}:{}&0.000000000000&{}:{}&1.080000000000&,\\C^*_{\mathbf{3}}&{}\approx{}&-0.058823529412&{}:{}&1.058823529412&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4}}&{}\approx{}&0.000000000000&{}:{}&0.428571428571&{}:{}&0.571428571429&,\\B^*_{\mathbf{4}}&{}\approx{}&1.080000000000&{}:{}&0.000000000000&{}:{}&-0.080000000000&,\\C^*_{\mathbf{4}}&{}\approx{}&1.058823529412&{}:{}&-0.058823529412&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5}}&{}\approx{}&0.000000000000&{}:{}&-0.090909090909&{}:{}&1.090909090909&,\\B^*_{\mathbf{5}}&{}\approx{}&0.600000000000&{}:{}&0.000000000000&{}:{}&0.400000000000&,\\C^*_{\mathbf{5}}&{}\approx{}&1.058823529412&{}:{}&-0.058823529412&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6}}&{}\approx{}&0.000000000000&{}:{}&1.090909090909&{}:{}&-0.090909090909&,\\B^*_{\mathbf{6}}&{}\approx{}&1.080000000000&{}:{}&0.000000000000&{}:{}&-0.080000000000&,\\C^*_{\mathbf{6}}&{}\approx{}&0.529411764706&{}:{}&0.470588235294&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7}}&{}\approx{}&0.000000000000&{}:{}&0.571428571429&{}:{}&0.428571428571&,\\B^*_{\mathbf{7}}&{}\approx{}&0.600000000000&{}:{}&0.000000000000&{}:{}&0.400000000000&,\\C^*_{\mathbf{7}}&{}\approx{}&0.529411764706&{}:{}&0.470588235294&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{a}}&{}\approx{}&0.000000000000&{}:{}&0.545454545455&{}:{}&0.454545454545&,\\B^*_{\mathbf{a}}&{}\approx{}&-0.800000000000&{}:{}&0.000000000000&{}:{}&1.800000000000&,\\C^*_{\mathbf{a}}&{}\approx{}&-0.588235294118&{}:{}&1.588235294118&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1a}}&{}\approx{}&0.000000000000&{}:{}&1.428571428571&{}:{}&-0.428571428571&,\\B^*_{\mathbf{1a}}&{}\approx{}&-0.800000000000&{}:{}&0.000000000000&{}:{}&1.800000000000&,\\C^*_{\mathbf{1a}}&{}\approx{}&0.117647058824&{}:{}&0.882352941176&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2a}}&{}\approx{}&0.000000000000&{}:{}&-0.428571428571&{}:{}&1.428571428571&,\\B^*_{\mathbf{2a}}&{}\approx{}&0.100000000000&{}:{}&0.000000000000&{}:{}&0.900000000000&,\\C^*_{\mathbf{2a}}&{}\approx{}&-0.588235294118&{}:{}&1.588235294118&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3a}}&{}\approx{}&0.000000000000&{}:{}&0.454545454545&{}:{}&0.545454545455&,\\B^*_{\mathbf{3a}}&{}\approx{}&0.100000000000&{}:{}&0.000000000000&{}:{}&0.900000000000&,\\C^*_{\mathbf{3a}}&{}\approx{}&0.117647058824&{}:{}&0.882352941176&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4a}}&{}\approx{}&0.000000000000&{}:{}&0.454545454545&{}:{}&0.545454545455&,\\B^*_{\mathbf{4a}}&{}\approx{}&1.800000000000&{}:{}&0.000000000000&{}:{}&-0.800000000000&,\\C^*_{\mathbf{4a}}&{}\approx{}&1.588235294118&{}:{}&-0.588235294118&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5a}}&{}\approx{}&0.000000000000&{}:{}&-0.428571428571&{}:{}&1.428571428571&,\\B^*_{\mathbf{5a}}&{}\approx{}&1.800000000000&{}:{}&0.000000000000&{}:{}&-0.800000000000&,\\C^*_{\mathbf{5a}}&{}\approx{}&0.882352941176&{}:{}&0.117647058824&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6a}}&{}\approx{}&0.000000000000&{}:{}&1.428571428571&{}:{}&-0.428571428571&,\\B^*_{\mathbf{6a}}&{}\approx{}&0.900000000000&{}:{}&0.000000000000&{}:{}&0.100000000000&,\\C^*_{\mathbf{6a}}&{}\approx{}&1.588235294118&{}:{}&-0.588235294118&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7a}}&{}\approx{}&0.000000000000&{}:{}&0.545454545455&{}:{}&0.454545454545&,\\B^*_{\mathbf{7a}}&{}\approx{}&0.900000000000&{}:{}&0.000000000000&{}:{}&0.100000000000&,\\C^*_{\mathbf{7a}}&{}\approx{}&0.882352941176&{}:{}&0.117647058824&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{b}}&{}\approx{}&0.000000000000&{}:{}&-1.000000000000&{}:{}&2.000000000000&,\\B^*_{\mathbf{b}}&{}\approx{}&0.560000000000&{}:{}&0.000000000000&{}:{}&0.440000000000&,\\C^*_{\mathbf{b}}&{}\approx{}&1.647058823529&{}:{}&-0.647058823529&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1b}}&{}\approx{}&0.000000000000&{}:{}&-1.000000000000&{}:{}&2.000000000000&,\\B^*_{\mathbf{1b}}&{}\approx{}&1.466666666667&{}:{}&0.000000000000&{}:{}&-0.466666666667&,\\C^*_{\mathbf{1b}}&{}\approx{}&0.862745098039&{}:{}&0.137254901961&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2b}}&{}\approx{}&0.000000000000&{}:{}&2.000000000000&{}:{}&-1.000000000000&,\\B^*_{\mathbf{2b}}&{}\approx{}&0.440000000000&{}:{}&0.000000000000&{}:{}&0.560000000000&,\\C^*_{\mathbf{2b}}&{}\approx{}&-0.647058823529&{}:{}&1.647058823529&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3b}}&{}\approx{}&0.000000000000&{}:{}&2.000000000000&{}:{}&-1.000000000000&,\\B^*_{\mathbf{3b}}&{}\approx{}&-0.466666666667&{}:{}&0.000000000000&{}:{}&1.466666666667&,\\C^*_{\mathbf{3b}}&{}\approx{}&0.137254901961&{}:{}&0.862745098039&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4b}}&{}\approx{}&0.000000000000&{}:{}&0.111111111111&{}:{}&0.888888888889&,\\B^*_{\mathbf{4b}}&{}\approx{}&-0.466666666667&{}:{}&0.000000000000&{}:{}&1.466666666667&,\\C^*_{\mathbf{4b}}&{}\approx{}&1.647058823529&{}:{}&-0.647058823529&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5b}}&{}\approx{}&0.000000000000&{}:{}&0.111111111111&{}:{}&0.888888888889&,\\B^*_{\mathbf{5b}}&{}\approx{}&0.440000000000&{}:{}&0.000000000000&{}:{}&0.560000000000&,\\C^*_{\mathbf{5b}}&{}\approx{}&0.862745098039&{}:{}&0.137254901961&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6b}}&{}\approx{}&0.000000000000&{}:{}&0.888888888889&{}:{}&0.111111111111&,\\B^*_{\mathbf{6b}}&{}\approx{}&1.466666666667&{}:{}&0.000000000000&{}:{}&-0.466666666667&,\\C^*_{\mathbf{6b}}&{}\approx{}&-0.647058823529&{}:{}&1.647058823529&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7b}}&{}\approx{}&0.000000000000&{}:{}&0.888888888889&{}:{}&0.111111111111&,\\B^*_{\mathbf{7b}}&{}\approx{}&0.560000000000&{}:{}&0.000000000000&{}:{}&0.440000000000&,\\C^*_{\mathbf{7b}}&{}\approx{}&0.137254901961&{}:{}&0.862745098039&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{c}}&{}\approx{}&0.000000000000&{}:{}&2.250000000000&{}:{}&-1.250000000000&,\\B^*_{\mathbf{c}}&{}\approx{}&2.100000000000&{}:{}&0.000000000000&{}:{}&-1.100000000000&,\\C^*_{\mathbf{c}}&{}\approx{}&0.514705882353&{}:{}&0.485294117647&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1c}}&{}\approx{}&0.000000000000&{}:{}&-1.250000000000&{}:{}&2.250000000000&,\\B^*_{\mathbf{1c}}&{}\approx{}&-1.100000000000&{}:{}&0.000000000000&{}:{}&2.100000000000&,\\C^*_{\mathbf{1c}}&{}\approx{}&0.485294117647&{}:{}&0.514705882353&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2c}}&{}\approx{}&0.000000000000&{}:{}&2.250000000000&{}:{}&-1.250000000000&,\\B^*_{\mathbf{2c}}&{}\approx{}&0.825000000000&{}:{}&0.000000000000&{}:{}&0.175000000000&,\\C^*_{\mathbf{2c}}&{}\approx{}&1.617647058824&{}:{}&-0.617647058824&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3c}}&{}\approx{}&0.000000000000&{}:{}&-1.250000000000&{}:{}&2.250000000000&,\\B^*_{\mathbf{3c}}&{}\approx{}&0.175000000000&{}:{}&0.000000000000&{}:{}&0.825000000000&,\\C^*_{\mathbf{3c}}&{}\approx{}&-0.617647058824&{}:{}&1.617647058824&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4c}}&{}\approx{}&0.000000000000&{}:{}&0.833333333333&{}:{}&0.166666666667&,\\B^*_{\mathbf{4c}}&{}\approx{}&2.100000000000&{}:{}&0.000000000000&{}:{}&-1.100000000000&,\\C^*_{\mathbf{4c}}&{}\approx{}&-0.617647058824&{}:{}&1.617647058824&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5c}}&{}\approx{}&0.000000000000&{}:{}&0.166666666667&{}:{}&0.833333333333&,\\B^*_{\mathbf{5c}}&{}\approx{}&-1.100000000000&{}:{}&0.000000000000&{}:{}&2.100000000000&,\\C^*_{\mathbf{5c}}&{}\approx{}&1.617647058824&{}:{}&-0.617647058824&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6c}}&{}\approx{}&0.000000000000&{}:{}&0.833333333333&{}:{}&0.166666666667&,\\B^*_{\mathbf{6c}}&{}\approx{}&0.825000000000&{}:{}&0.000000000000&{}:{}&0.175000000000&,\\C^*_{\mathbf{6c}}&{}\approx{}&0.485294117647&{}:{}&0.514705882353&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7c}}&{}\approx{}&0.000000000000&{}:{}&0.166666666667&{}:{}&0.833333333333&,\\B^*_{\mathbf{7c}}&{}\approx{}&0.175000000000&{}:{}&0.000000000000&{}:{}&0.825000000000&,\\C^*_{\mathbf{7c}}&{}\approx{}&0.514705882353&{}:{}&0.485294117647&{}:{}&0.000000000000&. \end{alignedat} \]