Derousseau's Generalization of the Malfatti circles

Ajima's example

不朽算法 十四 (Fukyū Sanpō §14)

\(a=252\),  \(b=375\),  \(c=507\).  \(a:b:c=84:125:169\).


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Reference Triangle

reference triangle

Triangle Centers and their Extraversions

Approximately,
\[ \begin{alignedat}{4} I&{}\approx{}&0.222222222222&{}:{}&0.330687830688&{}:{}&0.447089947090&,\\ I_{\mathbf{a}}&{}\approx{}&-0.400000000000&{}:{}&0.595238095238&{}:{}&0.804761904762&,\\ I_{\mathbf{b}}&{}\approx{}&0.656250000000&{}:{}&-0.976562500000&{}:{}&1.320312500000&,\\ I_{\mathbf{c}}&{}\approx{}&2.100000000000&{}:{}&3.125000000000&{}:{}&-4.225000000000&. \end{alignedat} \] \[ \begin{alignedat}{4} P&{}\approx{}&0.178316690442&{}:{}&0.278241967258&{}:{}&0.543441342300&,\\ P_{\mathbf{1}}&{}\approx{}&0.019484712851&{}:{}&0.030403574795&{}:{}&0.950111712354&,\\ P_{\mathbf{2}}&{}\approx{}&0.001021152443&{}:{}&0.995866763919&{}:{}&0.003112083637&,\\ P_{\mathbf{3}}&{}\approx{}&0.000975609756&{}:{}&0.951451800232&{}:{}&0.047572590012&,\\ P_{\mathbf{4}}&{}\approx{}&0.998876264203&{}:{}&0.000380524291&{}:{}&0.000743211506&,\\ P_{\mathbf{5}}&{}\approx{}&0.987863392605&{}:{}&0.000376328911&{}:{}&0.011760278483&,\\ P_{\mathbf{6}}&{}\approx{}&0.807207207207&{}:{}&0.192192192192&{}:{}&0.000600600601&,\\ P_{\mathbf{7}}&{}\approx{}&0.800000000000&{}:{}&0.190476190476&{}:{}&0.009523809524&,\\ P_{\mathbf{a}}&{}\approx{}&-0.226347305389&{}:{}&0.681304058550&{}:{}&0.545043246840&,\\ P_{\mathbf{1a}}&{}\approx{}&-0.060074165637&{}:{}&0.915415857319&{}:{}&0.144658308317&,\\ P_{\mathbf{2a}}&{}\approx{}&-0.005074658035&{}:{}&0.015274690852&{}:{}&0.989799967183&,\\ P_{\mathbf{3a}}&{}\approx{}&-0.004778156997&{}:{}&0.072810011377&{}:{}&0.931968145620&,\\ P_{\mathbf{4a}}&{}\approx{}&1.054117647059&{}:{}&-0.003921568627&{}:{}&-0.050196078431&,\\ P_{\mathbf{5a}}&{}\approx{}&1.050810810811&{}:{}&-0.000772200772&{}:{}&-0.050038610039&,\\ P_{\mathbf{6a}}&{}\approx{}&1.004326767840&{}:{}&-0.003736334702&{}:{}&-0.000590433138&,\\ P_{\mathbf{7a}}&{}\approx{}&1.001324503311&{}:{}&-0.000735835173&{}:{}&-0.000588668138&,\\ P_{\mathbf{b}}&{}\approx{}&0.746587030717&{}:{}&-0.466510238908&{}:{}&0.719923208191&,\\ P_{\mathbf{1b}}&{}\approx{}&0.889510366639&{}:{}&-0.203401370505&{}:{}&0.313891003866&,\\ P_{\mathbf{2b}}&{}\approx{}&-0.008823529412&{}:{}&1.261029411765&{}:{}&-0.252205882353&,\\ P_{\mathbf{3b}}&{}\approx{}&-0.003211009174&{}:{}&1.254013761468&{}:{}&-0.250802752294&,\\ P_{\mathbf{4b}}&{}\approx{}&0.012741728798&{}:{}&-0.007961760252&{}:{}&0.995220031454&,\\ P_{\mathbf{5b}}&{}\approx{}&0.034066133721&{}:{}&-0.007789789244&{}:{}&0.973723655523&,\\ P_{\mathbf{6b}}&{}\approx{}&-0.007063953488&{}:{}&1.009556686047&{}:{}&-0.002492732558&,\\ P_{\mathbf{7b}}&{}\approx{}&-0.002573529412&{}:{}&1.005055147059&{}:{}&-0.002481617647&,\\ P_{\mathbf{c}}&{}\approx{}&1.015297450425&{}:{}&1.223796033994&{}:{}&-1.239093484419&,\\ P_{\mathbf{1c}}&{}\approx{}&-0.255574043261&{}:{}&-0.570715474210&{}:{}&1.826289517471&,\\ P_{\mathbf{2c}}&{}\approx{}&1.005544330397&{}:{}&0.443546431747&{}:{}&-0.449090762143&,\\ P_{\mathbf{3c}}&{}\approx{}&-0.080485066247&{}:{}&-0.491129575567&{}:{}&1.571614641815&,\\ P_{\mathbf{4c}}&{}\approx{}&0.170018975332&{}:{}&1.037476280835&{}:{}&-0.207495256167&,\\ P_{\mathbf{5c}}&{}\approx{}&-0.175293056808&{}:{}&-0.077321911632&{}:{}&1.252614968440&,\\ P_{\mathbf{6c}}&{}\approx{}&0.358878504673&{}:{}&0.801401869159&{}:{}&-0.160280373832&,\\ P_{\mathbf{7c}}&{}\approx{}&-0.057731958763&{}:{}&-0.069587628866&{}:{}&1.127319587629&. \end{alignedat} \] \[ \begin{alignedat}{4} P^-&{}\approx{}&0.163147792706&{}:{}&0.260122475094&{}:{}&0.576729732200&,\\ P^-_{\mathbf{1}}&{}\approx{}&-0.006145433567&{}:{}&-0.007558465230&{}:{}&1.013703898797&,\\ P^-_{\mathbf{2}}&{}\approx{}&-0.007420869302&{}:{}&1.021252965824&{}:{}&-0.013832096522&,\\ P^-_{\mathbf{3}}&{}\approx{}&-0.035187287174&{}:{}&1.052916058591&{}:{}&-0.017728771418&,\\ P^-_{\mathbf{4}}&{}\approx{}&1.016732660621&{}:{}&-0.007213717011&{}:{}&-0.009518943610&,\\ P^-_{\mathbf{5}}&{}\approx{}&1.062577447336&{}:{}&-0.031856670797&{}:{}&-0.030720776539&,\\ P^-_{\mathbf{6}}&{}\approx{}&1.293729372937&{}:{}&0.077007700770&{}:{}&-0.370737073707&,\\ P^-_{\mathbf{7}}&{}\approx{}&-0.500000000000&{}:{}&0.505952380952&{}:{}&0.994047619048&,\\ P^-_{\mathbf{a}}&{}\approx{}&-0.176349614396&{}:{}&0.706083976007&{}:{}&0.470265638389&,\\ P^-_{\mathbf{1a}}&{}\approx{}&-0.007703281027&{}:{}&0.964744242918&{}:{}&0.042959038109&,\\ P^-_{\mathbf{2a}}&{}\approx{}&0.013581191908&{}:{}&-0.012122158869&{}:{}&0.998540966961&,\\ P^-_{\mathbf{3a}}&{}\approx{}&0.036981132075&{}:{}&0.017610062893&{}:{}&0.945408805031&,\\ P^-_{\mathbf{4a}}&{}\approx{}&0.693805309735&{}:{}&0.144542772861&{}:{}&0.161651917404&,\\ P^-_{\mathbf{5a}}&{}\approx{}&0.866037735849&{}:{}&0.075134770889&{}:{}&0.058827493261&,\\ P^-_{\mathbf{6a}}&{}\approx{}&0.957004680187&{}:{}&0.016447515043&{}:{}&0.026547804769&,\\ P^-_{\mathbf{7a}}&{}\approx{}&0.980000000000&{}:{}&0.008333333333&{}:{}&0.011666666667&,\\ P^-_{\mathbf{b}}&{}\approx{}&0.769849785408&{}:{}&-0.335166309013&{}:{}&0.565316523605&,\\ P^-_{\mathbf{1b}}&{}\approx{}&0.929898996839&{}:{}&-0.069529854336&{}:{}&0.139630857496&,\\ P^-_{\mathbf{2b}}&{}\approx{}&0.155973451327&{}:{}&0.706581858407&{}:{}&0.137444690265&,\\ P^-_{\mathbf{3b}}&{}\approx{}&0.105857580398&{}:{}&0.885097626340&{}:{}&0.009044793262&,\\ P^-_{\mathbf{4b}}&{}\approx{}&-0.008156422901&{}:{}&0.023493880803&{}:{}&0.984662542098&,\\ P^-_{\mathbf{5b}}&{}\approx{}&0.000717840735&{}:{}&0.044135241194&{}:{}&0.955146918070&,\\ P^-_{\mathbf{6b}}&{}\approx{}&0.011819362856&{}:{}&0.953015561455&{}:{}&0.035165075689&,\\ P^-_{\mathbf{7b}}&{}\approx{}&0.008851156069&{}:{}&0.970691835260&{}:{}&0.020457008671&,\\ P^-_{\mathbf{c}}&{}\approx{}&0.844590163934&{}:{}&0.924590163934&{}:{}&-0.769180327869&,\\ P^-_{\mathbf{1c}}&{}\approx{}&0.114446002805&{}:{}&0.009817671809&{}:{}&0.875736325386&,\\ P^-_{\mathbf{2c}}&{}\approx{}&0.908473383194&{}:{}&0.205719313682&{}:{}&-0.114192696876&,\\ P^-_{\mathbf{3c}}&{}\approx{}&0.112343909928&{}:{}&-0.171340839304&{}:{}&1.058996929376&,\\ P^-_{\mathbf{4c}}&{}\approx{}&0.065800000000&{}:{}&0.924750000000&{}:{}&0.009450000000&,\\ P^-_{\mathbf{5c}}&{}\approx{}&-0.052986348123&{}:{}&0.094816552901&{}:{}&0.958169795222&,\\ P^-_{\mathbf{6c}}&{}\approx{}&0.237000000000&{}:{}&0.638750000000&{}:{}&0.124250000000&,\\ P^-_{\mathbf{7c}}&{}\approx{}&0.007000000000&{}:{}&0.026250000000&{}:{}&0.966750000000&. \end{alignedat} \] \[ \begin{alignedat}{4} P^+&{}\approx{}&0.187287173666&{}:{}&0.288957353657&{}:{}&0.523755472677&,\\ P^+_{\mathbf{1}}&{}\approx{}&0.039942338879&{}:{}&0.060704346607&{}:{}&0.899353314513&,\\ P^+_{\mathbf{2}}&{}\approx{}&0.008864499789&{}:{}&0.972280849866&{}:{}&0.018854650345&,\\ P^+_{\mathbf{3}}&{}\approx{}&0.028229255774&{}:{}&0.874984724429&{}:{}&0.096786019797&,\\ P^+_{\mathbf{4}}&{}\approx{}&0.981804860178&{}:{}&0.007640912025&{}:{}&0.010554227797&,\\ P^+_{\mathbf{5}}&{}\approx{}&0.925349922240&{}:{}&0.027345775013&{}:{}&0.047304302748&,\\ P^+_{\mathbf{6}}&{}\approx{}&0.624535315985&{}:{}&0.235439900867&{}:{}&0.140024783147&,\\ P^+_{\mathbf{7}}&{}\approx{}&0.428571428571&{}:{}&0.280612244898&{}:{}&0.290816326531&,\\ P^+_{\mathbf{a}}&{}\approx{}&-0.258075040783&{}:{}&0.665579119086&{}:{}&0.592495921697&,\\ P^+_{\mathbf{1a}}&{}\approx{}&-0.100109051254&{}:{}&0.877706807914&{}:{}&0.222402243340&,\\ P^+_{\mathbf{2a}}&{}\approx{}&-0.022120091917&{}:{}&0.040306581220&{}:{}&0.981813510698&,\\ P^+_{\mathbf{3a}}&{}\approx{}&-0.039252336449&{}:{}&0.118380062305&{}:{}&0.920872274143&,\\ P^+_{\mathbf{4a}}&{}\approx{}&1.768421052632&{}:{}&-0.298245614035&{}:{}&-0.470175438596&,\\ P^+_{\mathbf{5a}}&{}\approx{}&1.298734177215&{}:{}&-0.102622061483&{}:{}&-0.196112115732&,\\ P^+_{\mathbf{6a}}&{}\approx{}&1.055068584811&{}:{}&-0.025378769775&{}:{}&-0.029689815036&,\\ P^+_{\mathbf{7a}}&{}\approx{}&1.023318385650&{}:{}&-0.010089686099&{}:{}&-0.013228699552&,\\ P^+_{\mathbf{b}}&{}\approx{}&0.731232294618&{}:{}&-0.553204674221&{}:{}&0.821972379603&,\\ P^+_{\mathbf{1b}}&{}\approx{}&0.859510564459&{}:{}&-0.302838241298&{}:{}&0.443327676840&,\\ P^+_{\mathbf{2b}}&{}\approx{}&-0.335526315789&{}:{}&2.360197368421&{}:{}&-1.024671052632&,\\ P^+_{\mathbf{3b}}&{}\approx{}&-0.166189931350&{}:{}&1.805277459954&{}:{}&-0.639087528604&,\\ P^+_{\mathbf{4b}}&{}\approx{}&0.032365315112&{}:{}&-0.037498941157&{}:{}&1.005133626045&,\\ P^+_{\mathbf{5b}}&{}\approx{}&0.064185684647&{}:{}&-0.054687500000&{}:{}&0.990501815353&,\\ P^+_{\mathbf{6b}}&{}\approx{}&-0.027087326306&{}:{}&1.069511409919&{}:{}&-0.042424083613&,\\ P^+_{\mathbf{7b}}&{}\approx{}&-0.014408682635&{}:{}&1.040653068862&{}:{}&-0.026244386228&,\\ P^+_{\mathbf{c}}&{}\approx{}&1.145137157107&{}:{}&1.451371571072&{}:{}&-1.596508728180&,\\ P^+_{\mathbf{1c}}&{}\approx{}&-0.795092024540&{}:{}&-1.417177914110&{}:{}&3.212269938650&,\\ P^+_{\mathbf{2c}}&{}\approx{}&1.087990434198&{}:{}&0.645542186683&{}:{}&-0.733532620880&,\\ P^+_{\mathbf{3c}}&{}\approx{}&-0.314747575230&{}:{}&-0.879631932355&{}:{}&2.194379507585&,\\ P^+_{\mathbf{4c}}&{}\approx{}&0.264079422383&{}:{}&1.139214801444&{}:{}&-0.403294223827&,\\ P^+_{\mathbf{5c}}&{}\approx{}&-0.312332695985&{}:{}&-0.270195984704&{}:{}&1.582528680688&,\\ P^+_{\mathbf{6c}}&{}\approx{}&0.465789473684&{}:{}&0.944078947368&{}:{}&-0.409868421053&,\\ P^+_{\mathbf{7c}}&{}\approx{}&-0.126595744681&{}:{}&-0.171542553191&{}:{}&1.298138297872&. \end{alignedat} \] \[ \begin{alignedat}{4} Q&{}\approx{}&0.151515151515&{}:{}&0.242424242424&{}:{}&0.606060606061&,\\ Q_{\mathbf{1}}&{}\approx{}&-0.074626865672&{}:{}&-0.119402985075&{}:{}&1.194029850746&,\\ Q_{\mathbf{2}}&{}\approx{}&-0.028571428571&{}:{}&1.142857142857&{}:{}&-0.114285714286&,\\ Q_{\mathbf{3}}&{}\approx{}&-0.018181818182&{}:{}&0.727272727273&{}:{}&0.290909090909&,\\ Q_{\mathbf{4}}&{}\approx{}&1.095890410959&{}:{}&-0.027397260274&{}:{}&-0.068493150685&,\\ Q_{\mathbf{5}}&{}\approx{}&0.816326530612&{}:{}&-0.020408163265&{}:{}&0.204081632653&,\\ Q_{\mathbf{6}}&{}\approx{}&0.640000000000&{}:{}&0.400000000000&{}:{}&-0.040000000000&,\\ Q_{\mathbf{7}}&{}\approx{}&0.533333333333&{}:{}&0.333333333333&{}:{}&0.133333333333&,\\ Q_{\mathbf{a}}&{}\approx{}&-0.142857142857&{}:{}&0.761904761905&{}:{}&0.380952380952&,\\ Q_{\mathbf{1a}}&{}\approx{}&0.096774193548&{}:{}&1.161290322581&{}:{}&-0.258064516129&,\\ Q_{\mathbf{2a}}&{}\approx{}&0.050847457627&{}:{}&-0.271186440678&{}:{}&1.220338983051&,\\ Q_{\mathbf{3a}}&{}\approx{}&0.027027027027&{}:{}&0.324324324324&{}:{}&0.648648648649&,\\ Q_{\mathbf{4a}}&{}\approx{}&2.285714285714&{}:{}&-0.428571428571&{}:{}&-0.857142857143&,\\ Q_{\mathbf{5a}}&{}\approx{}&1.411764705882&{}:{}&0.117647058824&{}:{}&-0.529411764706&,\\ Q_{\mathbf{6a}}&{}\approx{}&1.170731707317&{}:{}&-0.219512195122&{}:{}&0.048780487805&,\\ Q_{\mathbf{7a}}&{}\approx{}&0.888888888889&{}:{}&0.074074074074&{}:{}&0.037037037037&,\\ Q_{\mathbf{b}}&{}\approx{}&0.853658536585&{}:{}&-0.219512195122&{}:{}&0.365853658537&,\\ Q_{\mathbf{1b}}&{}\approx{}&1.115702479339&{}:{}&0.173553719008&{}:{}&-0.289256198347&,\\ Q_{\mathbf{2b}}&{}\approx{}&-1.800000000000&{}:{}&7.000000000000&{}:{}&-4.200000000000&,\\ Q_{\mathbf{3b}}&{}\approx{}&0.280000000000&{}:{}&1.800000000000&{}:{}&-1.080000000000&,\\ Q_{\mathbf{4b}}&{}\approx{}&-0.321100917431&{}:{}&0.082568807339&{}:{}&1.238532110092&,\\ Q_{\mathbf{5b}}&{}\approx{}&0.286624203822&{}:{}&0.044585987261&{}:{}&0.668789808917&,\\ Q_{\mathbf{6b}}&{}\approx{}&-0.317647058824&{}:{}&1.235294117647&{}:{}&0.082352941176&,\\ Q_{\mathbf{7b}}&{}\approx{}&0.127272727273&{}:{}&0.818181818182&{}:{}&0.054545454545&,\\ Q_{\mathbf{c}}&{}\approx{}&0.823529411765&{}:{}&0.705882352941&{}:{}&-0.529411764706&,\\ Q_{\mathbf{1c}}&{}\approx{}&1.636363636364&{}:{}&1.909090909091&{}:{}&-2.545454545455&,\\ Q_{\mathbf{2c}}&{}\approx{}&1.148936170213&{}:{}&-0.595744680851&{}:{}&0.446808510638&,\\ Q_{\mathbf{3c}}&{}\approx{}&0.608695652174&{}:{}&-1.173913043478&{}:{}&1.565217391304&,\\ Q_{\mathbf{4c}}&{}\approx{}&-0.636363636364&{}:{}&1.227272727273&{}:{}&0.409090909091&,\\ Q_{\mathbf{5c}}&{}\approx{}&-0.931034482759&{}:{}&0.482758620690&{}:{}&1.448275862069&,\\ Q_{\mathbf{6c}}&{}\approx{}&0.391304347826&{}:{}&0.456521739130&{}:{}&0.152173913043&,\\ Q_{\mathbf{7c}}&{}\approx{}&0.225806451613&{}:{}&0.193548387097&{}:{}&0.580645161290&. \end{alignedat} \] \[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.200000000000&{}:{}&0.304761904762&{}:{}&0.495238095238&,\\ I^\prime_{\mathbf{1}}&{}\approx{}&0.080459770115&{}:{}&0.122605363985&{}:{}&0.796934865900&,\\ I^\prime_{\mathbf{2}}&{}\approx{}&0.024054982818&{}:{}&0.916380297824&{}:{}&0.059564719359&,\\ I^\prime_{\mathbf{3}}&{}\approx{}&0.020408163265&{}:{}&0.777453838678&{}:{}&0.202137998056&,\\ I^\prime_{\mathbf{4}}&{}\approx{}&0.941176470588&{}:{}&0.022408963585&{}:{}&0.036414565826&,\\ I^\prime_{\mathbf{5}}&{}\approx{}&0.848484848485&{}:{}&0.020202020202&{}:{}&0.131313131313&,\\ I^\prime_{\mathbf{6}}&{}\approx{}&0.612021857923&{}:{}&0.364298724954&{}:{}&0.023679417122&,\\ I^\prime_{\mathbf{7}}&{}\approx{}&0.571428571429&{}:{}&0.340136054422&{}:{}&0.088435374150&,\\ I^\prime_{\mathbf{a}}&{}\approx{}&-0.301435406699&{}:{}&0.637958532695&{}:{}&0.663476874003&,\\ I^\prime_{\mathbf{1a}}&{}\approx{}&-0.167701863354&{}:{}&0.798580301686&{}:{}&0.369121561668&,\\ I^\prime_{\mathbf{2a}}&{}\approx{}&-0.047787610619&{}:{}&0.101137800253&{}:{}&0.946649810367&,\\ I^\prime_{\mathbf{3a}}&{}\approx{}&-0.042424242424&{}:{}&0.202020202020&{}:{}&0.840404040404&,\\ I^\prime_{\mathbf{4a}}&{}\approx{}&1.623188405797&{}:{}&-0.120772946860&{}:{}&-0.502415458937&,\\ I^\prime_{\mathbf{5a}}&{}\approx{}&1.521126760563&{}:{}&-0.050301810865&{}:{}&-0.470824949698&,\\ I^\prime_{\mathbf{6a}}&{}\approx{}&1.122077922078&{}:{}&-0.083487940631&{}:{}&-0.038589981447&,\\ I^\prime_{\mathbf{7a}}&{}\approx{}&1.072340425532&{}:{}&-0.035460992908&{}:{}&-0.036879432624&,\\ I^\prime_{\mathbf{b}}&{}\approx{}&0.700000000000&{}:{}&-0.675000000000&{}:{}&0.975000000000&,\\ I^\prime_{\mathbf{1b}}&{}\approx{}&0.794117647059&{}:{}&-0.463235294118&{}:{}&0.669117647059&,\\ I^\prime_{\mathbf{2b}}&{}\approx{}&-0.166666666667&{}:{}&2.430555555556&{}:{}&-1.263888888889&,\\ I^\prime_{\mathbf{3b}}&{}\approx{}&-0.094594594595&{}:{}&2.280405405405&{}:{}&-1.185810810811&,\\ I^\prime_{\mathbf{4b}}&{}\approx{}&0.079545454545&{}:{}&-0.076704545455&{}:{}&0.997159090909&,\\ I^\prime_{\mathbf{5b}}&{}\approx{}&0.125000000000&{}:{}&-0.072916666667&{}:{}&0.947916666667&,\\ I^\prime_{\mathbf{6b}}&{}\approx{}&-0.078488372093&{}:{}&1.144622093023&{}:{}&-0.066133720930&,\\ I^\prime_{\mathbf{7b}}&{}\approx{}&-0.046052631579&{}:{}&1.110197368421&{}:{}&-0.064144736842&,\\ I^\prime_{\mathbf{c}}&{}\approx{}&1.294797687861&{}:{}&1.734104046243&{}:{}&-2.028901734104&,\\ I^\prime_{\mathbf{1c}}&{}\approx{}&-1.032258064516&{}:{}&-1.881720430108&{}:{}&3.913978494624&,\\ I^\prime_{\mathbf{2c}}&{}\approx{}&1.159731543624&{}:{}&0.939597315436&{}:{}&-1.099328859060&,\\ I^\prime_{\mathbf{3c}}&{}\approx{}&-0.443564356436&{}:{}&-1.336633663366&{}:{}&2.780198019802&,\\ I^\prime_{\mathbf{4c}}&{}\approx{}&0.408759124088&{}:{}&1.231751824818&{}:{}&-0.640510948905&,\\ I^\prime_{\mathbf{5c}}&{}\approx{}&-0.504672897196&{}:{}&-0.408878504673&{}:{}&1.913551401869&,\\ I^\prime_{\mathbf{6c}}&{}\approx{}&0.533333333333&{}:{}&0.972222222222&{}:{}&-0.505555555556&,\\ I^\prime_{\mathbf{7c}}&{}\approx{}&-0.254545454545&{}:{}&-0.340909090909&{}:{}&1.595454545455&. \end{alignedat} \]

Central Triangles and their Extraversions

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.377777777778&{}:{}&0.264550264550&{}:{}&0.357671957672&,\\B^\prime&{}\approx{}&0.156250000000&{}:{}&0.529389880952&{}:{}&0.314360119048&,\\C^\prime&{}\approx{}&0.100000000000&{}:{}&0.148809523810&{}:{}&0.751190476190&,\\[.5em] A^\prime_{\mathbf{1}}&{}\approx{}&-0.066666666667&{}:{}&0.453514739229&{}:{}&0.613151927438&,\\B^\prime_{\mathbf{1}}&{}\approx{}&0.364583333333&{}:{}&-0.098090277778&{}:{}&0.733506944444&,\\C^\prime_{\mathbf{1}}&{}\approx{}&0.025925925926&{}:{}&0.038580246914&{}:{}&0.935493827160&,\\[.5em] A^\prime_{\mathbf{2}}&{}\approx{}&-0.333333333333&{}:{}&0.566893424036&{}:{}&0.766439909297&,\\B^\prime_{\mathbf{2}}&{}\approx{}&0.008101851852&{}:{}&0.975597993827&{}:{}&0.016300154321&,\\C^\prime_{\mathbf{2}}&{}\approx{}&1.166666666667&{}:{}&1.736111111111&{}:{}&-1.902777777778&,\\[.5em] A^\prime_{\mathbf{3}}&{}\approx{}&-0.382716049383&{}:{}&0.587889476778&{}:{}&0.794826572604&,\\B^\prime_{\mathbf{3}}&{}\approx{}&0.031250000000&{}:{}&0.905877976190&{}:{}&0.062872023810&,\\C^\prime_{\mathbf{3}}&{}\approx{}&0.500000000000&{}:{}&0.744047619048&{}:{}&-0.244047619048&,\\[.5em] A^\prime_{\mathbf{4}}&{}\approx{}&0.982716049383&{}:{}&0.007348618460&{}:{}&0.009935332158&,\\B^\prime_{\mathbf{4}}&{}\approx{}&0.625000000000&{}:{}&-0.882440476190&{}:{}&1.257440476190&,\\C^\prime_{\mathbf{4}}&{}\approx{}&1.600000000000&{}:{}&2.380952380952&{}:{}&-2.980952380952&,\\[.5em] A^\prime_{\mathbf{5}}&{}\approx{}&0.933333333333&{}:{}&0.028344671202&{}:{}&0.038321995465&,\\B^\prime_{\mathbf{5}}&{}\approx{}&0.648148148148&{}:{}&-0.952160493827&{}:{}&1.304012345679&,\\C^\prime_{\mathbf{5}}&{}\approx{}&0.933333333333&{}:{}&1.388888888889&{}:{}&-1.322222222222&,\\[.5em] A^\prime_{\mathbf{6}}&{}\approx{}&0.666666666667&{}:{}&0.141723356009&{}:{}&0.191609977324&,\\B^\prime_{\mathbf{6}}&{}\approx{}&0.291666666667&{}:{}&0.121527777778&{}:{}&0.586805555556&,\\C^\prime_{\mathbf{6}}&{}\approx{}&2.074074074074&{}:{}&3.086419753086&{}:{}&-4.160493827160&,\\[.5em] A^\prime_{\mathbf{7}}&{}\approx{}&0.222222222222&{}:{}&0.330687830688&{}:{}&0.447089947090&,\\B^\prime_{\mathbf{7}}&{}\approx{}&0.500000000000&{}:{}&-0.505952380952&{}:{}&1.005952380952&,\\C^\prime_{\mathbf{7}}&{}\approx{}&2.000000000000&{}:{}&2.976190476190&{}:{}&-3.976190476190&,\\[.5em] A^\prime_{\mathbf{a}}&{}\approx{}&-0.777777777778&{}:{}&0.755857898715&{}:{}&1.021919879063&,\\B^\prime_{\mathbf{a}}&{}\approx{}&-0.140000000000&{}:{}&0.858333333333&{}:{}&0.281666666667&,\\C^\prime_{\mathbf{a}}&{}\approx{}&-0.218750000000&{}:{}&0.325520833333&{}:{}&0.893229166667&,\\[.5em] A^\prime_{\mathbf{1a}}&{}\approx{}&-0.037037037037&{}:{}&0.440917107584&{}:{}&0.596119929453&,\\B^\prime_{\mathbf{1a}}&{}\approx{}&-0.060000000000&{}:{}&0.939285714286&{}:{}&0.120714285714&,\\C^\prime_{\mathbf{1a}}&{}\approx{}&-0.843750000000&{}:{}&1.255580357143&{}:{}&0.588169642857&,\\[.5em] A^\prime_{\mathbf{2a}}&{}\approx{}&0.170370370370&{}:{}&0.352733686067&{}:{}&0.476895943563&,\\B^\prime_{\mathbf{2a}}&{}\approx{}&-2.700000000000&{}:{}&-1.732142857143&{}:{}&5.432142857143&,\\C^\prime_{\mathbf{2a}}&{}\approx{}&-0.018750000000&{}:{}&0.027901785714&{}:{}&0.990848214286&,\\[.5em] A^\prime_{\mathbf{3a}}&{}\approx{}&0.200000000000&{}:{}&0.340136054422&{}:{}&0.459863945578&,\\B^\prime_{\mathbf{3a}}&{}\approx{}&-0.700000000000&{}:{}&0.291666666667&{}:{}&1.408333333333&,\\C^\prime_{\mathbf{3a}}&{}\approx{}&-0.043750000000&{}:{}&0.065104166667&{}:{}&0.978645833333&,\\[.5em] A^\prime_{\mathbf{4a}}&{}\approx{}&2.000000000000&{}:{}&-0.425170068027&{}:{}&-0.574829931973&,\\B^\prime_{\mathbf{4a}}&{}\approx{}&2.240000000000&{}:{}&3.266666666667&{}:{}&-4.506666666667&,\\C^\prime_{\mathbf{4a}}&{}\approx{}&0.875000000000&{}:{}&-1.302083333333&{}:{}&1.427083333333&,\\[.5em] A^\prime_{\mathbf{5a}}&{}\approx{}&1.259259259259&{}:{}&-0.110229276896&{}:{}&-0.149029982363&,\\B^\prime_{\mathbf{5a}}&{}\approx{}&2.160000000000&{}:{}&3.185714285714&{}:{}&-4.345714285714&,\\C^\prime_{\mathbf{5a}}&{}\approx{}&1.500000000000&{}:{}&-2.232142857143&{}:{}&1.732142857143&,\\[.5em] A^\prime_{\mathbf{6a}}&{}\approx{}&1.051851851852&{}:{}&-0.022045855379&{}:{}&-0.029805996473&,\\B^\prime_{\mathbf{6a}}&{}\approx{}&4.800000000000&{}:{}&5.857142857143&{}:{}&-9.657142857143&,\\C^\prime_{\mathbf{6a}}&{}\approx{}&0.675000000000&{}:{}&-1.004464285714&{}:{}&1.329464285714&,\\[.5em] A^\prime_{\mathbf{7a}}&{}\approx{}&1.022222222222&{}:{}&-0.009448223734&{}:{}&-0.012773998488&,\\B^\prime_{\mathbf{7a}}&{}\approx{}&2.800000000000&{}:{}&3.833333333333&{}:{}&-5.633333333333&,\\C^\prime_{\mathbf{7a}}&{}\approx{}&0.700000000000&{}:{}&-1.041666666667&{}:{}&1.341666666667&,\\[.5em] A^\prime_{\mathbf{b}}&{}\approx{}&0.896875000000&{}:{}&-0.292968750000&{}:{}&0.396093750000&,\\B^\prime_{\mathbf{b}}&{}\approx{}&0.972222222222&{}:{}&-1.928240740741&{}:{}&1.956018518519&,\\C^\prime_{\mathbf{b}}&{}\approx{}&0.350000000000&{}:{}&-0.520833333333&{}:{}&1.170833333333&,\\[.5em] A^\prime_{\mathbf{1b}}&{}\approx{}&0.939843750000&{}:{}&-0.170898437500&{}:{}&0.231054687500&,\\B^\prime_{\mathbf{1b}}&{}\approx{}&0.416666666667&{}:{}&-0.254960317460&{}:{}&0.838293650794&,\\C^\prime_{\mathbf{1b}}&{}\approx{}&1.350000000000&{}:{}&-2.008928571429&{}:{}&1.658928571429&,\\[.5em] A^\prime_{\mathbf{2b}}&{}\approx{}&2.203125000000&{}:{}&3.417968750000&{}:{}&-4.621093750000&,\\B^\prime_{\mathbf{2b}}&{}\approx{}&-0.750000000000&{}:{}&3.258928571429&{}:{}&-1.508928571429&,\\C^\prime_{\mathbf{2b}}&{}\approx{}&-0.750000000000&{}:{}&1.116071428571&{}:{}&0.633928571429&,\\[.5em] A^\prime_{\mathbf{3b}}&{}\approx{}&2.160156250000&{}:{}&3.295898437500&{}:{}&-4.456054687500&,\\B^\prime_{\mathbf{3b}}&{}\approx{}&-0.194444444444&{}:{}&1.585648148148&{}:{}&-0.391203703704&,\\C^\prime_{\mathbf{3b}}&{}\approx{}&-1.750000000000&{}:{}&2.604166666667&{}:{}&0.145833333333&,\\[.5em] A^\prime_{\mathbf{4b}}&{}\approx{}&-2.712500000000&{}:{}&-10.546875000000&{}:{}&14.259375000000&,\\B^\prime_{\mathbf{4b}}&{}\approx{}&0.243055555556&{}:{}&0.267939814815&{}:{}&0.489004629630&,\\C^\prime_{\mathbf{4b}}&{}\approx{}&0.021875000000&{}:{}&-0.032552083333&{}:{}&1.010677083333&,\\[.5em] A^\prime_{\mathbf{5b}}&{}\approx{}&0.037500000000&{}:{}&-2.734375000000&{}:{}&3.696875000000&,\\B^\prime_{\mathbf{5b}}&{}\approx{}&0.234375000000&{}:{}&0.294084821429&{}:{}&0.471540178571&,\\C^\prime_{\mathbf{5b}}&{}\approx{}&0.037500000000&{}:{}&-0.055803571429&{}:{}&1.018303571429&,\\[.5em] A^\prime_{\mathbf{6b}}&{}\approx{}&5.812500000000&{}:{}&13.671875000000&{}:{}&-18.484375000000&,\\B^\prime_{\mathbf{6b}}&{}\approx{}&-0.020833333333&{}:{}&1.062748015873&{}:{}&-0.041914682540&,\\C^\prime_{\mathbf{6b}}&{}\approx{}&-0.421875000000&{}:{}&0.627790178571&{}:{}&0.794084821429&,\\[.5em] A^\prime_{\mathbf{7b}}&{}\approx{}&3.062500000000&{}:{}&5.859375000000&{}:{}&-7.921875000000&,\\B^\prime_{\mathbf{7b}}&{}\approx{}&-0.012152777778&{}:{}&1.036603009259&{}:{}&-0.024450231481&,\\C^\prime_{\mathbf{7b}}&{}\approx{}&-0.437500000000&{}:{}&0.651041666667&{}:{}&0.786458333333&,\\[.5em] A^\prime_{\mathbf{c}}&{}\approx{}&1.257812500000&{}:{}&0.732421875000&{}:{}&-0.990234375000&,\\B^\prime_{\mathbf{c}}&{}\approx{}&0.560000000000&{}:{}&1.566666666667&{}:{}&-1.126666666667&,\\C^\prime_{\mathbf{c}}&{}\approx{}&6.222222222222&{}:{}&9.259259259259&{}:{}&-14.481481481481&,\\[.5em] A^\prime_{\mathbf{1c}}&{}\approx{}&0.398437500000&{}:{}&-1.708984375000&{}:{}&2.310546875000&,\\B^\prime_{\mathbf{1c}}&{}\approx{}&-0.960000000000&{}:{}&0.028571428571&{}:{}&1.931428571429&,\\C^\prime_{\mathbf{1c}}&{}\approx{}&-6.000000000000&{}:{}&-8.928571428571&{}:{}&15.928571428571&,\\[.5em] A^\prime_{\mathbf{2c}}&{}\approx{}&1.120312500000&{}:{}&0.341796875000&{}:{}&-0.462109375000&,\\B^\prime_{\mathbf{2c}}&{}\approx{}&10.800000000000&{}:{}&11.928571428571&{}:{}&-21.728571428571&,\\C^\prime_{\mathbf{2c}}&{}\approx{}&0.533333333333&{}:{}&0.793650793651&{}:{}&-0.326984126984&,\\[.5em] A^\prime_{\mathbf{3c}}&{}\approx{}&0.535937500000&{}:{}&-1.318359375000&{}:{}&1.782421875000&,\\B^\prime_{\mathbf{3c}}&{}\approx{}&-11.200000000000&{}:{}&-10.333333333333&{}:{}&22.533333333333&,\\C^\prime_{\mathbf{3c}}&{}\approx{}&-0.311111111111&{}:{}&-0.462962962963&{}:{}&1.774074074074&,\\[.5em] A^\prime_{\mathbf{4c}}&{}\approx{}&10.281250000000&{}:{}&26.367187500000&{}:{}&-35.648437500000&,\\B^\prime_{\mathbf{4c}}&{}\approx{}&0.140000000000&{}:{}&1.141666666667&{}:{}&-0.281666666667&,\\C^\prime_{\mathbf{4c}}&{}\approx{}&0.388888888889&{}:{}&0.578703703704&{}:{}&0.032407407407&,\\[.5em] A^\prime_{\mathbf{5c}}&{}\approx{}&-8.625000000000&{}:{}&-27.343750000000&{}:{}&36.968750000000&,\\B^\prime_{\mathbf{5c}}&{}\approx{}&-0.540000000000&{}:{}&0.453571428571&{}:{}&1.086428571429&,\\C^\prime_{\mathbf{5c}}&{}\approx{}&-0.166666666667&{}:{}&-0.248015873016&{}:{}&1.414682539683&,\\[.5em] A^\prime_{\mathbf{6c}}&{}\approx{}&1.481250000000&{}:{}&1.367187500000&{}:{}&-1.848437500000&,\\B^\prime_{\mathbf{6c}}&{}\approx{}&0.300000000000&{}:{}&1.303571428571&{}:{}&-0.603571428571&,\\C^\prime_{\mathbf{6c}}&{}\approx{}&0.300000000000&{}:{}&0.446428571429&{}:{}&0.253571428571&,\\[.5em] A^\prime_{\mathbf{7c}}&{}\approx{}&0.175000000000&{}:{}&-2.343750000000&{}:{}&3.168750000000&,\\B^\prime_{\mathbf{7c}}&{}\approx{}&-0.700000000000&{}:{}&0.291666666667&{}:{}&1.408333333333&,\\C^\prime_{\mathbf{7c}}&{}\approx{}&-0.077777777778&{}:{}&-0.115740740741&{}:{}&1.193518518519&. \end{alignedat} \] \[ \begin{alignedat}{4} A^{\prime\prime}&{}\approx{}&0.121951219512&{}:{}&0.297328687573&{}:{}&0.580720092915&,\\B^{\prime\prime}&{}\approx{}&0.200000000000&{}:{}&0.190476190476&{}:{}&0.609523809524&,\\C^{\prime\prime}&{}\approx{}&0.259875259875&{}:{}&0.405504405504&{}:{}&0.334620334620&,\\[.5em] A^{\prime\prime}_{\mathbf{1}}&{}\approx{}&0.048409405256&{}:{}&0.029506685108&{}:{}&0.922083909636&,\\B^{\prime\prime}_{\mathbf{1}}&{}\approx{}&0.018666666667&{}:{}&0.071111111111&{}:{}&0.910222222222&,\\C^{\prime\prime}_{\mathbf{1}}&{}\approx{}&0.129687268416&{}:{}&0.202361543402&{}:{}&0.667951188182&,\\[.5em] A^{\prime\prime}_{\mathbf{2}}&{}\approx{}&0.016091954023&{}:{}&0.980842911877&{}:{}&0.003065134100&,\\B^{\prime\prime}_{\mathbf{2}}&{}\approx{}&0.035897435897&{}:{}&0.854700854701&{}:{}&0.109401709402&,\\C^{\prime\prime}_{\mathbf{2}}&{}\approx{}&0.000991641876&{}:{}&0.967086933938&{}:{}&0.031921424187&,\\[.5em] A^{\prime\prime}_{\mathbf{3}}&{}\approx{}&0.058823529412&{}:{}&0.896358543417&{}:{}&0.044817927171&,\\B^{\prime\prime}_{\mathbf{3}}&{}\approx{}&0.006896551724&{}:{}&0.656814449918&{}:{}&0.336288998358&,\\C^{\prime\prime}_{\mathbf{3}}&{}\approx{}&0.000904977376&{}:{}&0.882568411980&{}:{}&0.116526610644&,\\[.5em] A^{\prime\prime}_{\mathbf{4}}&{}\approx{}&0.898876404494&{}:{}&0.034242910647&{}:{}&0.066880684858&,\\B^{\prime\prime}_{\mathbf{4}}&{}\approx{}&0.984615384615&{}:{}&0.014652014652&{}:{}&0.000732600733&,\\C^{\prime\prime}_{\mathbf{4}}&{}\approx{}&0.979911807937&{}:{}&0.000373299736&{}:{}&0.019714892326&,\\[.5em] A^{\prime\prime}_{\mathbf{5}}&{}\approx{}&0.765027322404&{}:{}&0.007285974499&{}:{}&0.227686703097&,\\B^{\prime\prime}_{\mathbf{5}}&{}\approx{}&0.933333333333&{}:{}&0.055555555556&{}:{}&0.011111111111&,\\C^{\prime\prime}_{\mathbf{5}}&{}\approx{}&0.925191646841&{}:{}&0.000352453961&{}:{}&0.074455899198&,\\[.5em] A^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.511415525114&{}:{}&0.487062404871&{}:{}&0.001522070015&,\\B^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.728455284553&{}:{}&0.271002710027&{}:{}&0.000542005420&,\\C^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.574358974359&{}:{}&0.136752136752&{}:{}&0.288888888889&,\\[.5em] A^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.800000000000&{}:{}&0.190476190476&{}:{}&0.009523809524&,\\B^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.400000000000&{}:{}&0.595238095238&{}:{}&0.004761904762&,\\C^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.307692307692&{}:{}&0.073260073260&{}:{}&0.619047619048&,\\[.5em] A^{\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.170731707317&{}:{}&0.650406504065&{}:{}&0.520325203252&,\\B^{\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.387030716724&{}:{}&0.455062571104&{}:{}&0.931968145620&,\\C^{\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.277804997550&{}:{}&0.836191409440&{}:{}&0.441613588110&,\\[.5em] A^{\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.112033195021&{}:{}&0.960284528749&{}:{}&0.151748666271&,\\B^{\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.246700507614&{}:{}&0.652646845540&{}:{}&0.594053662074&,\\C^{\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.056133056133&{}:{}&0.855360855361&{}:{}&0.200772200772&,\\[.5em] A^{\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.037241379310&{}:{}&0.015763546798&{}:{}&1.021477832512&,\\B^{\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.004886877828&{}:{}&0.051712992889&{}:{}&0.953173884939&,\\C^{\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.061286254729&{}:{}&0.184471266438&{}:{}&0.876814988290&,\\[.5em] A^{\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.082352941176&{}:{}&0.078431372549&{}:{}&1.003921568627&,\\B^{\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.004590163934&{}:{}&0.109289617486&{}:{}&0.895300546448&,\\C^{\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.021538461538&{}:{}&0.328205128205&{}:{}&0.693333333333&,\\[.5em] A^{\prime\prime}_{\mathbf{4a}}&{}\approx{}&1.258426966292&{}:{}&-0.018726591760&{}:{}&-0.239700374532&,\\B^{\prime\prime}_{\mathbf{4a}}&{}\approx{}&1.723076923077&{}:{}&-0.641025641026&{}:{}&-0.082051282051&,\\C^{\prime\prime}_{\mathbf{4a}}&{}\approx{}&2.027149321267&{}:{}&-0.007541478130&{}:{}&-1.019607843137&,\\[.5em] A^{\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.770491803279&{}:{}&-0.011709601874&{}:{}&-0.758782201405&,\\B^{\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.270588235294&{}:{}&-0.210084033613&{}:{}&-0.060504201681&,\\C^{\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.289124668435&{}:{}&-0.000947328534&{}:{}&-0.288177339901&,\\[.5em] A^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.183561643836&{}:{}&-0.158512720157&{}:{}&-0.025048923679&,\\B^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.043758389262&{}:{}&-0.043144774688&{}:{}&-0.000613614573&,\\C^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.063384615385&{}:{}&-0.003956043956&{}:{}&-0.059428571429&,\\[.5em] A^{\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.120000000000&{}:{}&-0.066666666667&{}:{}&-0.053333333333&,\\B^{\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.019325842697&{}:{}&-0.018726591760&{}:{}&-0.000599250936&,\\C^{\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.026244343891&{}:{}&-0.000754147813&{}:{}&-0.025490196078&,\\[.5em] A^{\prime\prime}_{\mathbf{b}}&{}\approx{}&0.514705882353&{}:{}&-0.893382352941&{}:{}&1.378676470588&,\\B^{\prime\prime}_{\mathbf{b}}&{}\approx{}&0.700000000000&{}:{}&-0.375000000000&{}:{}&0.675000000000&,\\C^{\prime\prime}_{\mathbf{b}}&{}\approx{}&0.909563409563&{}:{}&-0.568347193347&{}:{}&0.658783783784&,\\[.5em] A^{\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.636792452830&{}:{}&-0.668632075472&{}:{}&1.031839622642&,\\B^{\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.972000000000&{}:{}&-0.315000000000&{}:{}&0.343000000000&,\\C^{\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.826800587947&{}:{}&-0.189061734444&{}:{}&0.362261146497&,\\[.5em] A^{\prime\prime}_{\mathbf{2b}}&{}\approx{}&-0.750000000000&{}:{}&2.187500000000&{}:{}&-0.437500000000&,\\B^{\prime\prime}_{\mathbf{2b}}&{}\approx{}&-0.023076923077&{}:{}&1.682692307692&{}:{}&-0.659615384615&,\\C^{\prime\prime}_{\mathbf{2b}}&{}\approx{}&-0.023076923077&{}:{}&3.298076923077&{}:{}&-2.275000000000&,\\[.5em] A^{\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.350000000000&{}:{}&1.687500000000&{}:{}&-0.337500000000&,\\B^{\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.024137931034&{}:{}&2.909482758621&{}:{}&-1.885344827586&,\\C^{\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.004413619168&{}:{}&1.723675914250&{}:{}&-0.719262295082&,\\[.5em] A^{\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.040137614679&{}:{}&-0.007740825688&{}:{}&0.967603211009&,\\B^{\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.013461538462&{}:{}&-0.064903846154&{}:{}&1.051442307692&,\\C^{\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.145059681698&{}:{}&-0.090641578249&{}:{}&0.945581896552&,\\[.5em] A^{\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.064655172414&{}:{}&-0.007543103448&{}:{}&0.942887931034&,\\B^{\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.037500000000&{}:{}&-0.109375000000&{}:{}&1.071875000000&,\\C^{\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.212104072398&{}:{}&-0.048501131222&{}:{}&0.836397058824&,\\[.5em] A^{\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.039705882353&{}:{}&1.042279411765&{}:{}&-0.002573529412&,\\B^{\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.148170731707&{}:{}&1.200457317073&{}:{}&-0.052286585366&,\\C^{\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.007635746606&{}:{}&1.091275452489&{}:{}&-0.083639705882&,\\[.5em] A^{\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.023648648649&{}:{}&1.026182432432&{}:{}&-0.002533783784&,\\B^{\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.087500000000&{}:{}&1.171875000000&{}:{}&-0.084375000000&,\\C^{\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.002692307692&{}:{}&1.051442307692&{}:{}&-0.048750000000&,\\[.5em] A^{\prime\prime}_{\mathbf{c}}&{}\approx{}&1.027522935780&{}:{}&2.201834862385&{}:{}&-2.229357798165&,\\B^{\prime\prime}_{\mathbf{c}}&{}\approx{}&1.621719457014&{}:{}&1.357466063348&{}:{}&-1.979185520362&,\\C^{\prime\prime}_{\mathbf{c}}&{}\approx{}&0.931392931393&{}:{}&1.122661122661&{}:{}&-1.054054054054&,\\[.5em] A^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-1.655172413793&{}:{}&-1.206896551724&{}:{}&3.862068965517&,\\B^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.629508196721&{}:{}&-2.868852459016&{}:{}&4.498360655738&,\\C^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.341485104491&{}:{}&-0.762561138284&{}:{}&2.104046242775&,\\[.5em] A^{\prime\prime}_{\mathbf{2c}}&{}\approx{}&1.016470588235&{}:{}&1.317647058824&{}:{}&-1.334117647059&,\\B^{\prime\prime}_{\mathbf{2c}}&{}\approx{}&0.943617747440&{}:{}&0.477815699659&{}:{}&-0.421433447099&,\\C^{\prime\prime}_{\mathbf{2c}}&{}\approx{}&1.321886952826&{}:{}&0.583085422864&{}:{}&-0.904972375691&,\\[.5em] A^{\prime\prime}_{\mathbf{3c}}&{}\approx{}&-0.605405405405&{}:{}&-0.729729729730&{}:{}&2.335135135135&,\\B^{\prime\prime}_{\mathbf{3c}}&{}\approx{}&-0.090964467005&{}:{}&-0.685279187817&{}:{}&1.776243654822&,\\C^{\prime\prime}_{\mathbf{3c}}&{}\approx{}&-0.324343891403&{}:{}&-1.979185520362&{}:{}&3.303529411765&,\\[.5em] A^{\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.205882352941&{}:{}&0.992647058824&{}:{}&-0.198529411765&,\\B^{\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.601342281879&{}:{}&1.132550335570&{}:{}&-0.733892617450&,\\C^{\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.219500244978&{}:{}&1.339416952474&{}:{}&-0.558917197452&,\\[.5em] A^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.254716981132&{}:{}&-0.082547169811&{}:{}&1.337264150943&,\\B^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.242696629213&{}:{}&-0.491573033708&{}:{}&1.734269662921&,\\C^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.770816812054&{}:{}&-0.340007930214&{}:{}&2.110824742268&,\\[.5em] A^{\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.300000000000&{}:{}&0.875000000000&{}:{}&-0.175000000000&,\\B^{\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.590769230769&{}:{}&0.673076923077&{}:{}&-0.263846153846&,\\C^{\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.590769230769&{}:{}&1.319230769231&{}:{}&-0.910000000000&,\\[.5em] A^{\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.140000000000&{}:{}&-0.075000000000&{}:{}&1.215000000000&,\\B^{\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.065882352941&{}:{}&-0.220588235294&{}:{}&1.286470588235&,\\C^{\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.430769230769&{}:{}&-0.519230769231&{}:{}&1.950000000000&. \end{alignedat} \] \[ \begin{alignedat}{4} A^{\prime\prime\prime}&{}\approx{}&0.084033613445&{}:{}&0.284713885554&{}:{}&0.631252501000&,\\B^{\prime\prime\prime}&{}\approx{}&0.191011235955&{}:{}&0.133761369716&{}:{}&0.675227394329&,\\C^{\prime\prime\prime}&{}\approx{}&0.282392026578&{}:{}&0.450245214365&{}:{}&0.267362759057&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1}}&{}\approx{}&0.027163368258&{}:{}&-0.007308239555&{}:{}&0.980144871297&,\\B^{\prime\prime\prime}_{\mathbf{1}}&{}\approx{}&-0.005856340385&{}:{}&0.039839050237&{}:{}&0.966017290148&,\\C^{\prime\prime\prime}_{\mathbf{1}}&{}\approx{}&-0.143526654950&{}:{}&-0.176528021871&{}:{}&1.320054676821&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2}}&{}\approx{}&0.008348240906&{}:{}&1.005267342477&{}:{}&-0.013615583383&,\\B^{\prime\prime\prime}_{\mathbf{2}}&{}\approx{}&0.859649122807&{}:{}&-1.461988304094&{}:{}&1.602339181287&,\\C^{\prime\prime\prime}_{\mathbf{2}}&{}\approx{}&-0.007198472161&{}:{}&0.990646883111&{}:{}&0.016551589050&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3}}&{}\approx{}&0.033898305085&{}:{}&0.982647296207&{}:{}&-0.016545601291&,\\B^{\prime\prime\prime}_{\mathbf{3}}&{}\approx{}&-31.000000000006&{}:{}&47.619047619057&{}:{}&-15.619047619051&,\\C^{\prime\prime\prime}_{\mathbf{3}}&{}\approx{}&-0.032258064516&{}:{}&0.965264357564&{}:{}&0.066993706952&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4}}&{}\approx{}&-0.439560439560&{}:{}&0.620617477760&{}:{}&0.818942961800&,\\B^{\prime\prime\prime}_{\mathbf{4}}&{}\approx{}&1.001887979862&{}:{}&0.007491983578&{}:{}&-0.009379963439&,\\C^{\prime\prime\prime}_{\mathbf{4}}&{}\approx{}&0.996993987976&{}:{}&-0.007073671152&{}:{}&0.010079683176&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5}}&{}\approx{}&-0.530303030303&{}:{}&0.779040404040&{}:{}&0.751262626263&,\\B^{\prime\prime\prime}_{\mathbf{5}}&{}\approx{}&0.998544395924&{}:{}&0.030325084910&{}:{}&-0.028869480835&,\\C^{\prime\prime\prime}_{\mathbf{5}}&{}\approx{}&0.989042675894&{}:{}&-0.029652056901&{}:{}&0.040609381007&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&-1.696969696970&{}:{}&-0.707070707071&{}:{}&3.404040404040&,\\B^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&1.079889807163&{}:{}&0.229568411387&{}:{}&-0.309458218549&,\\C^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&0.742424242424&{}:{}&0.044191919192&{}:{}&0.213383838384&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&-0.500000000000&{}:{}&0.505952380952&{}:{}&0.994047619048&,\\B^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&2.000000000000&{}:{}&2.976190476191&{}:{}&-3.976190476191&,\\C^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&0.500000000000&{}:{}&-0.505952380952&{}:{}&1.005952380952&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.108527131783&{}:{}&0.665374677003&{}:{}&0.443152454780&,\\B^{\prime\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.379005524862&{}:{}&0.368324125230&{}:{}&1.010681399632&,\\C^{\prime\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.231600270088&{}:{}&0.927301372946&{}:{}&0.304298897142&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.065138721351&{}:{}&1.019731173531&{}:{}&0.045407547820&,\\B^{\prime\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.060674157303&{}:{}&0.722311396469&{}:{}&0.338362760835&,\\C^{\prime\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.007125890736&{}:{}&0.892432982694&{}:{}&0.114692908042&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.019529837251&{}:{}&-0.012529062258&{}:{}&1.032058899509&,\\B^{\prime\prime\prime}_{\mathbf{2a}}&{}\approx{}&0.013055818354&{}:{}&0.027030679822&{}:{}&0.959913501825&,\\C^{\prime\prime\prime}_{\mathbf{2a}}&{}\approx{}&0.344044321330&{}:{}&-0.307083498219&{}:{}&0.963039176890&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.045901639344&{}:{}&0.019125683060&{}:{}&1.026775956284&,\\B^{\prime\prime\prime}_{\mathbf{3a}}&{}\approx{}&0.035379061372&{}:{}&0.060168471721&{}:{}&0.904452466907&,\\C^{\prime\prime\prime}_{\mathbf{3a}}&{}\approx{}&0.264864864865&{}:{}&0.126126126126&{}:{}&0.609009009009&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4a}}&{}\approx{}&0.244541484716&{}:{}&0.356622998544&{}:{}&0.398835516739&,\\B^{\prime\prime\prime}_{\mathbf{4a}}&{}\approx{}&0.980000000000&{}:{}&-0.208333333333&{}:{}&0.228333333333&,\\C^{\prime\prime\prime}_{\mathbf{4a}}&{}\approx{}&1.085872576177&{}:{}&0.226223453370&{}:{}&-0.312096029548&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5a}}&{}\approx{}&0.275510204082&{}:{}&0.406341107872&{}:{}&0.318148688047&,\\B^{\prime\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.020000000000&{}:{}&-0.089285714286&{}:{}&0.069285714286&,\\C^{\prime\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.032620922385&{}:{}&0.089587015909&{}:{}&-0.122207938293&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6a}}&{}\approx{}&0.238674033149&{}:{}&0.291239147593&{}:{}&0.470086819258&,\\B^{\prime\prime\prime}_{\mathbf{6a}}&{}\approx{}&0.993264248705&{}:{}&-0.020817912657&{}:{}&0.027553663953&,\\C^{\prime\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.011275964392&{}:{}&0.017380245867&{}:{}&-0.028656210259&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7a}}&{}\approx{}&0.233333333333&{}:{}&0.319444444444&{}:{}&0.447222222222&,\\B^{\prime\prime\prime}_{\mathbf{7a}}&{}\approx{}&0.997345132743&{}:{}&-0.009218289086&{}:{}&0.011873156342&,\\C^{\prime\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.004008908686&{}:{}&0.008537490720&{}:{}&-0.012546399406&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{b}}&{}\approx{}&0.423387096774&{}:{}&-0.839717741935&{}:{}&1.416330645161&,\\B^{\prime\prime\prime}_{\mathbf{b}}&{}\approx{}&0.710396039604&{}:{}&-0.232054455446&{}:{}&0.521658415842&,\\C^{\prime\prime\prime}_{\mathbf{b}}&{}\approx{}&0.993767313019&{}:{}&-0.432652354571&{}:{}&0.438885041551&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.618455497382&{}:{}&-0.378435863874&{}:{}&0.759980366492&,\\B^{\prime\prime\prime}_{\mathbf{1b}}&{}\approx{}&1.032716520412&{}:{}&-0.187786150324&{}:{}&0.155069629912&,\\C^{\prime\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.853918228279&{}:{}&-0.063848665531&{}:{}&0.209930437252&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2b}}&{}\approx{}&-0.238636363636&{}:{}&1.036931818182&{}:{}&0.201704545455&,\\B^{\prime\prime\prime}_{\mathbf{2b}}&{}\approx{}&0.291322314050&{}:{}&0.451962809917&{}:{}&0.256714876033&,\\C^{\prime\prime\prime}_{\mathbf{2b}}&{}\approx{}&0.291322314050&{}:{}&1.319731404959&{}:{}&-0.611053719008&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.138157894737&{}:{}&1.126644736842&{}:{}&0.011513157895&,\\B^{\prime\prime\prime}_{\mathbf{3b}}&{}\approx{}&0.382963988920&{}:{}&0.584314404432&{}:{}&0.032721606648&,\\C^{\prime\prime\prime}_{\mathbf{3b}}&{}\approx{}&0.137016848365&{}:{}&1.145626858276&{}:{}&-0.282643706640&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.020701892744&{}:{}&0.022821372240&{}:{}&0.956476735016&,\\B^{\prime\prime\prime}_{\mathbf{4b}}&{}\approx{}&-0.008633036283&{}:{}&-0.033567393380&{}:{}&1.042200429663&,\\C^{\prime\prime\prime}_{\mathbf{4b}}&{}\approx{}&-0.140108471074&{}:{}&0.403570506198&{}:{}&0.736537964876&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.034002590674&{}:{}&0.042665155440&{}:{}&0.923332253886&,\\B^{\prime\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.000794491525&{}:{}&-0.057931673729&{}:{}&1.057137182203&,\\C^{\prime\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.006208609272&{}:{}&0.381725993377&{}:{}&0.612065397351&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.019269983687&{}:{}&0.982998572594&{}:{}&0.036271411093&,\\B^{\prime\prime\prime}_{\mathbf{6b}}&{}\approx{}&0.158043806647&{}:{}&0.371742824773&{}:{}&0.470213368580&,\\C^{\prime\prime\prime}_{\mathbf{6b}}&{}\approx{}&0.012746710526&{}:{}&1.027789199561&{}:{}&-0.040535910088&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.011615044248&{}:{}&0.990735619469&{}:{}&0.020879424779&,\\B^{\prime\prime\prime}_{\mathbf{7b}}&{}\approx{}&0.191406250000&{}:{}&0.366210937500&{}:{}&0.442382812500&,\\C^{\prime\prime\prime}_{\mathbf{7b}}&{}\approx{}&0.009252265861&{}:{}&1.014680891239&{}:{}&-0.023933157100&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{c}}&{}\approx{}&0.680161943320&{}:{}&1.902834008097&{}:{}&-1.582995951417&,\\B^{\prime\prime\prime}_{\mathbf{c}}&{}\approx{}&1.489017341040&{}:{}&0.867052023121&{}:{}&-1.356069364162&,\\C^{\prime\prime\prime}_{\mathbf{c}}&{}\approx{}&0.764845605701&{}:{}&0.837292161520&{}:{}&-0.602137767221&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.593639575972&{}:{}&0.017667844523&{}:{}&1.575971731449&,\\B^{\prime\prime\prime}_{\mathbf{1c}}&{}\approx{}&0.229213483146&{}:{}&-0.983146067416&{}:{}&1.753932584270&,\\C^{\prime\prime\prime}_{\mathbf{1c}}&{}\approx{}&0.145247419010&{}:{}&0.012459950160&{}:{}&0.842292630829&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2c}}&{}\approx{}&0.670509977827&{}:{}&0.740576496674&{}:{}&-0.411086474501&,\\B^{\prime\prime\prime}_{\mathbf{2c}}&{}\approx{}&0.847893569845&{}:{}&0.258684405026&{}:{}&-0.106577974871&,\\C^{\prime\prime\prime}_{\mathbf{2c}}&{}\approx{}&1.228557829605&{}:{}&0.278200856735&{}:{}&-0.506758686340&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3c}}&{}\approx{}&-0.264566929134&{}:{}&-0.244094488189&{}:{}&1.508661417323&,\\B^{\prime\prime\prime}_{\mathbf{3c}}&{}\approx{}&0.125526075023&{}:{}&-0.308783165599&{}:{}&1.183257090576&,\\C^{\prime\prime\prime}_{\mathbf{3c}}&{}\approx{}&0.357059206246&{}:{}&-0.544567338972&{}:{}&1.187508132726&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.108247422680&{}:{}&0.882731958763&{}:{}&0.009020618557&,\\B^{\prime\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.269672131148&{}:{}&0.691598360656&{}:{}&0.038729508197&,\\C^{\prime\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.086306400839&{}:{}&1.212945960126&{}:{}&-0.299252360965&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.120076238882&{}:{}&0.100857687421&{}:{}&1.019218551461&,\\B^{\prime\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.071875000000&{}:{}&-0.227864583333&{}:{}&1.299739583333&,\\C^{\prime\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.197017766497&{}:{}&0.352553934010&{}:{}&0.844463832487&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.161538461538&{}:{}&0.701923076923&{}:{}&0.136538461538&,\\B^{\prime\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.408620689655&{}:{}&0.377155172414&{}:{}&0.214224137931&,\\C^{\prime\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.408620689655&{}:{}&1.101293103448&{}:{}&-0.509913793103&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.067741935484&{}:{}&0.028225806452&{}:{}&1.039516129032&,\\B^{\prime\prime\prime}_{\mathbf{7c}}&{}\approx{}&0.007954545455&{}:{}&-0.106534090909&{}:{}&1.098579545455&,\\C^{\prime\prime\prime}_{\mathbf{7c}}&{}\approx{}&0.043750000000&{}:{}&0.164062500000&{}:{}&0.792187500000&. \end{alignedat} \] \[ \begin{alignedat}{4} A^*&{}\approx{}&0.000000000000&{}:{}&0.285714285714&{}:{}&0.714285714286&,\\B^*&{}\approx{}&0.200000000000&{}:{}&0.000000000000&{}:{}&0.800000000000&,\\C^*&{}\approx{}&0.384615384615&{}:{}&0.615384615385&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1}}&{}\approx{}&0.000000000000&{}:{}&-0.111111111111&{}:{}&1.111111111111&,\\B^*_{\mathbf{1}}&{}\approx{}&-0.066666666667&{}:{}&0.000000000000&{}:{}&1.066666666667&,\\C^*_{\mathbf{1}}&{}\approx{}&0.384615384615&{}:{}&0.615384615385&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2}}&{}\approx{}&0.000000000000&{}:{}&1.111111111111&{}:{}&-0.111111111111&,\\B^*_{\mathbf{2}}&{}\approx{}&0.200000000000&{}:{}&0.000000000000&{}:{}&0.800000000000&,\\C^*_{\mathbf{2}}&{}\approx{}&-0.025641025641&{}:{}&1.025641025641&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3}}&{}\approx{}&0.000000000000&{}:{}&0.714285714286&{}:{}&0.285714285714&,\\B^*_{\mathbf{3}}&{}\approx{}&-0.066666666667&{}:{}&0.000000000000&{}:{}&1.066666666667&,\\C^*_{\mathbf{3}}&{}\approx{}&-0.025641025641&{}:{}&1.025641025641&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4}}&{}\approx{}&0.000000000000&{}:{}&0.285714285714&{}:{}&0.714285714286&,\\B^*_{\mathbf{4}}&{}\approx{}&1.066666666667&{}:{}&0.000000000000&{}:{}&-0.066666666667&,\\C^*_{\mathbf{4}}&{}\approx{}&1.025641025641&{}:{}&-0.025641025641&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5}}&{}\approx{}&0.000000000000&{}:{}&-0.111111111111&{}:{}&1.111111111111&,\\B^*_{\mathbf{5}}&{}\approx{}&0.800000000000&{}:{}&0.000000000000&{}:{}&0.200000000000&,\\C^*_{\mathbf{5}}&{}\approx{}&1.025641025641&{}:{}&-0.025641025641&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6}}&{}\approx{}&0.000000000000&{}:{}&1.111111111111&{}:{}&-0.111111111111&,\\B^*_{\mathbf{6}}&{}\approx{}&1.066666666667&{}:{}&0.000000000000&{}:{}&-0.066666666667&,\\C^*_{\mathbf{6}}&{}\approx{}&0.615384615385&{}:{}&0.384615384615&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7}}&{}\approx{}&0.000000000000&{}:{}&0.714285714286&{}:{}&0.285714285714&,\\B^*_{\mathbf{7}}&{}\approx{}&0.800000000000&{}:{}&0.000000000000&{}:{}&0.200000000000&,\\C^*_{\mathbf{7}}&{}\approx{}&0.615384615385&{}:{}&0.384615384615&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{a}}&{}\approx{}&0.000000000000&{}:{}&0.666666666667&{}:{}&0.333333333333&,\\B^*_{\mathbf{a}}&{}\approx{}&-0.600000000000&{}:{}&0.000000000000&{}:{}&1.600000000000&,\\C^*_{\mathbf{a}}&{}\approx{}&-0.230769230769&{}:{}&1.230769230769&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1a}}&{}\approx{}&0.000000000000&{}:{}&1.285714285714&{}:{}&-0.285714285714&,\\B^*_{\mathbf{1a}}&{}\approx{}&-0.600000000000&{}:{}&0.000000000000&{}:{}&1.600000000000&,\\C^*_{\mathbf{1a}}&{}\approx{}&0.076923076923&{}:{}&0.923076923077&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2a}}&{}\approx{}&0.000000000000&{}:{}&-0.285714285714&{}:{}&1.285714285714&,\\B^*_{\mathbf{2a}}&{}\approx{}&0.040000000000&{}:{}&0.000000000000&{}:{}&0.960000000000&,\\C^*_{\mathbf{2a}}&{}\approx{}&-0.230769230769&{}:{}&1.230769230769&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3a}}&{}\approx{}&0.000000000000&{}:{}&0.333333333333&{}:{}&0.666666666667&,\\B^*_{\mathbf{3a}}&{}\approx{}&0.040000000000&{}:{}&0.000000000000&{}:{}&0.960000000000&,\\C^*_{\mathbf{3a}}&{}\approx{}&0.076923076923&{}:{}&0.923076923077&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4a}}&{}\approx{}&0.000000000000&{}:{}&0.333333333333&{}:{}&0.666666666667&,\\B^*_{\mathbf{4a}}&{}\approx{}&1.600000000000&{}:{}&0.000000000000&{}:{}&-0.600000000000&,\\C^*_{\mathbf{4a}}&{}\approx{}&1.230769230769&{}:{}&-0.230769230769&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5a}}&{}\approx{}&0.000000000000&{}:{}&-0.285714285714&{}:{}&1.285714285714&,\\B^*_{\mathbf{5a}}&{}\approx{}&1.600000000000&{}:{}&0.000000000000&{}:{}&-0.600000000000&,\\C^*_{\mathbf{5a}}&{}\approx{}&0.923076923077&{}:{}&0.076923076923&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6a}}&{}\approx{}&0.000000000000&{}:{}&1.285714285714&{}:{}&-0.285714285714&,\\B^*_{\mathbf{6a}}&{}\approx{}&0.960000000000&{}:{}&0.000000000000&{}:{}&0.040000000000&,\\C^*_{\mathbf{6a}}&{}\approx{}&1.230769230769&{}:{}&-0.230769230769&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7a}}&{}\approx{}&0.000000000000&{}:{}&0.666666666667&{}:{}&0.333333333333&,\\B^*_{\mathbf{7a}}&{}\approx{}&0.960000000000&{}:{}&0.000000000000&{}:{}&0.040000000000&,\\C^*_{\mathbf{7a}}&{}\approx{}&0.923076923077&{}:{}&0.076923076923&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{b}}&{}\approx{}&0.000000000000&{}:{}&-1.500000000000&{}:{}&2.500000000000&,\\B^*_{\mathbf{b}}&{}\approx{}&0.700000000000&{}:{}&0.000000000000&{}:{}&0.300000000000&,\\C^*_{\mathbf{b}}&{}\approx{}&1.346153846154&{}:{}&-0.346153846154&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1b}}&{}\approx{}&0.000000000000&{}:{}&-1.500000000000&{}:{}&2.500000000000&,\\B^*_{\mathbf{1b}}&{}\approx{}&1.350000000000&{}:{}&0.000000000000&{}:{}&-0.350000000000&,\\C^*_{\mathbf{1b}}&{}\approx{}&0.865384615385&{}:{}&0.134615384615&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2b}}&{}\approx{}&0.000000000000&{}:{}&2.500000000000&{}:{}&-1.500000000000&,\\B^*_{\mathbf{2b}}&{}\approx{}&0.300000000000&{}:{}&0.000000000000&{}:{}&0.700000000000&,\\C^*_{\mathbf{2b}}&{}\approx{}&-0.346153846154&{}:{}&1.346153846154&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3b}}&{}\approx{}&0.000000000000&{}:{}&2.500000000000&{}:{}&-1.500000000000&,\\B^*_{\mathbf{3b}}&{}\approx{}&-0.350000000000&{}:{}&0.000000000000&{}:{}&1.350000000000&,\\C^*_{\mathbf{3b}}&{}\approx{}&0.134615384615&{}:{}&0.865384615385&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4b}}&{}\approx{}&0.000000000000&{}:{}&0.062500000000&{}:{}&0.937500000000&,\\B^*_{\mathbf{4b}}&{}\approx{}&-0.350000000000&{}:{}&0.000000000000&{}:{}&1.350000000000&,\\C^*_{\mathbf{4b}}&{}\approx{}&1.346153846154&{}:{}&-0.346153846154&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5b}}&{}\approx{}&0.000000000000&{}:{}&0.062500000000&{}:{}&0.937500000000&,\\B^*_{\mathbf{5b}}&{}\approx{}&0.300000000000&{}:{}&0.000000000000&{}:{}&0.700000000000&,\\C^*_{\mathbf{5b}}&{}\approx{}&0.865384615385&{}:{}&0.134615384615&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6b}}&{}\approx{}&0.000000000000&{}:{}&0.937500000000&{}:{}&0.062500000000&,\\B^*_{\mathbf{6b}}&{}\approx{}&1.350000000000&{}:{}&0.000000000000&{}:{}&-0.350000000000&,\\C^*_{\mathbf{6b}}&{}\approx{}&-0.346153846154&{}:{}&1.346153846154&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7b}}&{}\approx{}&0.000000000000&{}:{}&0.937500000000&{}:{}&0.062500000000&,\\B^*_{\mathbf{7b}}&{}\approx{}&0.700000000000&{}:{}&0.000000000000&{}:{}&0.300000000000&,\\C^*_{\mathbf{7b}}&{}\approx{}&0.134615384615&{}:{}&0.865384615385&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{c}}&{}\approx{}&0.000000000000&{}:{}&4.000000000000&{}:{}&-3.000000000000&,\\B^*_{\mathbf{c}}&{}\approx{}&2.800000000000&{}:{}&0.000000000000&{}:{}&-1.800000000000&,\\C^*_{\mathbf{c}}&{}\approx{}&0.538461538462&{}:{}&0.461538461538&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1c}}&{}\approx{}&0.000000000000&{}:{}&-3.000000000000&{}:{}&4.000000000000&,\\B^*_{\mathbf{1c}}&{}\approx{}&-1.800000000000&{}:{}&0.000000000000&{}:{}&2.800000000000&,\\C^*_{\mathbf{1c}}&{}\approx{}&0.461538461538&{}:{}&0.538461538462&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2c}}&{}\approx{}&0.000000000000&{}:{}&4.000000000000&{}:{}&-3.000000000000&,\\B^*_{\mathbf{2c}}&{}\approx{}&0.720000000000&{}:{}&0.000000000000&{}:{}&0.280000000000&,\\C^*_{\mathbf{2c}}&{}\approx{}&2.076923076923&{}:{}&-1.076923076923&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3c}}&{}\approx{}&0.000000000000&{}:{}&-3.000000000000&{}:{}&4.000000000000&,\\B^*_{\mathbf{3c}}&{}\approx{}&0.280000000000&{}:{}&0.000000000000&{}:{}&0.720000000000&,\\C^*_{\mathbf{3c}}&{}\approx{}&-1.076923076923&{}:{}&2.076923076923&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4c}}&{}\approx{}&0.000000000000&{}:{}&0.750000000000&{}:{}&0.250000000000&,\\B^*_{\mathbf{4c}}&{}\approx{}&2.800000000000&{}:{}&0.000000000000&{}:{}&-1.800000000000&,\\C^*_{\mathbf{4c}}&{}\approx{}&-1.076923076923&{}:{}&2.076923076923&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5c}}&{}\approx{}&0.000000000000&{}:{}&0.250000000000&{}:{}&0.750000000000&,\\B^*_{\mathbf{5c}}&{}\approx{}&-1.800000000000&{}:{}&0.000000000000&{}:{}&2.800000000000&,\\C^*_{\mathbf{5c}}&{}\approx{}&2.076923076923&{}:{}&-1.076923076923&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6c}}&{}\approx{}&0.000000000000&{}:{}&0.750000000000&{}:{}&0.250000000000&,\\B^*_{\mathbf{6c}}&{}\approx{}&0.720000000000&{}:{}&0.000000000000&{}:{}&0.280000000000&,\\C^*_{\mathbf{6c}}&{}\approx{}&0.461538461538&{}:{}&0.538461538462&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7c}}&{}\approx{}&0.000000000000&{}:{}&0.250000000000&{}:{}&0.750000000000&,\\B^*_{\mathbf{7c}}&{}\approx{}&0.280000000000&{}:{}&0.000000000000&{}:{}&0.720000000000&,\\C^*_{\mathbf{7c}}&{}\approx{}&0.538461538462&{}:{}&0.461538461538&{}:{}&0.000000000000&. \end{alignedat} \]