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Wigner $6j$ symbols
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Numbers
$j_1$
$j_2$
$j_3$
$j_4$
$j_5$
$j_6$ 
$\begin{Bmatrix}j_1&j_2&j_3\\j_4&j_5&j_6\end{Bmatrix}$
1/2
1/2
0
0
0
1/2:
-0.7071067811865475244008443621048490392848359376884740365883398689953662392310535194251937671638207864
1/2
1/2
0
1/2
1/2
0:
-1/2
1
1/2
1/2
0
1/2
1/2:
1/2
1
1/2
1/2
1
1/2
1/2:
1/6
1
1
0
0
0
1:
0.5773502691896257645091487805019574556476017512701268760186023264839776723029333456937153955857495252
1
1
0
1/2
1/2
1/2:
0.4082482904638630163662140124509818986609912467761116880721154278751600629095525044233099055174400391
1
1
0
1
1
0:
1/3
1
1
1
1/2
1/2
1/2:
-1/3
1
1
1
1
1
0:
-1/3
1
1
1
1
1
1:
1/6
3/2
1
1/2
0
1/2
1:
-0.4082482904638630163662140124509818986609912467761116880721154278751600629095525044233099055174400391
3/2
1
1/2
1/2
1
1/2:
-1/3
3/2
1
1/2
1
1/2
1:
-1/6
3/2
1
1/2
3/2
1
1/2:
-1/12
3/2
3/2
0
0
0
3/2:
-1/2
3/2
3/2
0
1/2
1/2
1:
-0.3535533905932737622004221810524245196424179688442370182941699344976831196155267597125968835819103932
3/2
3/2
0
1
1
1/2:
-0.2886751345948128822545743902509787278238008756350634380093011632419888361514666728468576977928747626
3/2
3/2
0
3/2
3/2
0:
-1/4
3/2
3/2
1
1/2
1/2
1:
0.2635231383473649443332411287027265444766295949437680689047920710660495365532698517786873423649416913
3/2
3/2
1
1
0
3/2:
0.2886751345948128822545743902509787278238008756350634380093011632419888361514666728468576977928747626
3/2
3/2
1
1
1
1/2:
0.2635231383473649443332411287027265444766295949437680689047920710660495365532698517786873423649416913
3/2
3/2
1
1
1
3/2:
-0.1054092553389459777332964514810906177906518379775072275619168284264198146213079407114749369459766765
3/2
3/2
1
3/2
1/2
1:
1/6
3/2
3/2
1
3/2
3/2
0:
1/4
3/2
3/2
1
3/2
3/2
1:
-11/60
2
1
1
0
1
1:
1/3
2
1
1
1
1
1:
1/6
2
1
1
2
1
1:
1/30
2
3/2
1/2
0
1/2
3/2:
0.3535533905932737622004221810524245196424179688442370182941699344976831196155267597125968835819103932
2
3/2
1/2
1/2
1
1:
0.2886751345948128822545743902509787278238008756350634380093011632419888361514666728468576977928747626
2
3/2
1/2
1
1/2
3/2:
0.1581138830084189665999446772216359266859777569662608413428752426396297219319619110672124054189650148
2
3/2
1/2
1
3/2
1/2:
1/4
2
3/2
1/2
3/2
1
1:
0.09128709291752768557616163046680035565879078249966387570448240828874887952045378896680973936064510429
2
3/2
1/2
2
3/2
1/2:
1/20
2
3/2
3/2
0
3/2
3/2:
-1/4
2
3/2
3/2
1/2
1
1:
-0.2041241452319315081831070062254909493304956233880558440360577139375800314547762522116549527587200196
2
3/2
3/2
1
3/2
1/2:
-0.2236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782275
2
3/2
3/2
1
3/2
3/2:
1/20
2
3/2
3/2
3/2
1
1:
-0.1632993161855452065464856049803927594643964987104446752288461711500640251638210017693239622069760157
2
3/2
3/2
2
3/2
1/2:
-1/10
2
3/2
3/2
2
3/2
3/2:
3/20
2
2
0
0
0
2:
0.4472135954999579392818347337462552470881236719223051448541794490821041851275609798828828816757564550
2
2
0
1/2
1/2
3/2:
0.3162277660168379331998893544432718533719555139325216826857504852792594438639238221344248108379300295
2
2
0
1
1
1:
0.2581988897471611256786176933188266407221947803527727217725049177408988727957986022346191584572449012
2
2
0
3/2
3/2
1/2:
0.2236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782275
2
2
0
3/2
3/2
3/2:
-0.2236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782275
2
2
0
2
2
0:
1/5
2
2
1
1/2
1/2
3/2:
-0.2236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782275
2
2
1
1
0
2:
-0.2581988897471611256786176933188266407221947803527727217725049177408988727957986022346191584572449012
2
2
1
1
1
1:
-0.2236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782275
2
2
1
1
1
2:
0.07453559924999298988030578895770920784802061198705085747569657484701736418792682998048048027929274250
2
2
1
3/2
1/2
3/2:
-0.1581138830084189665999446772216359266859777569662608413428752426396297219319619110672124054189650148
2
2
1
3/2
3/2
1/2:
-0.2121320343559642573202533086314547117854507813065422109765019606986098717693160558275581301491462359
2
2
1
3/2
3/2
3/2:
0.1414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641573
2
2
1
2
1
1:
-1/10
2
2
1
2
2
0:
-1/5
2
2
1
2
2
1:
1/6
2
2
2
1
1
1:
0.1527525231651946668862682397909336162994818858922657300869080707968956141849256962201453853164481678
2
2
2
3/2
3/2
1/2:
0.1870828693386970692791874366158274650878009903889363473151872733660017578153469513988404947597189786
2
2
2
2
1
1:
0.1527525231651946668862682397909336162994818858922657300869080707968956141849256962201453853164481678
2
2
2
2
2
0:
1/5
2
2
2
2
2
1:
-1/10
2
2
2
2
2
2:
-3/70
5/2
3/2
1
0
1
3/2:
-0.2886751345948128822545743902509787278238008756350634380093011632419888361514666728468576977928747626
5/2
3/2
1
1/2
3/2
1:
-1/4
5/2
3/2
1
1
1
3/2:
-0.1581138830084189665999446772216359266859777569662608413428752426396297219319619110672124054189650148
5/2
3/2
1
3/2
3/2
1:
-1/10
5/2
3/2
1
2
1
3/2:
-0.04082482904638630163662140124509818986609912467761116880721154278751600629095525044233099055174400391
5/2
3/2
1
5/2
3/2
1:
-1/60
5/2
2
1/2
0
1/2
2:
-0.3162277660168379331998893544432718533719555139325216826857504852792594438639238221344248108379300295
5/2
2
1/2
1/2
1
3/2:
-0.2581988897471611256786176933188266407221947803527727217725049177408988727957986022346191584572449012
5/2
2
1/2
1
1/2
2:
-0.1490711984999859797606115779154184156960412239741017149513931496940347283758536599609609605585854850
5/2
2
1/2
1
3/2
1:
-0.2236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782275
5/2
2
1/2
3/2
1
3/2:
-0.09128709291752768557616163046680035565879078249966387570448240828874887952045378896680973936064510429
5/2
2
1/2
3/2
2
1/2:
-1/5
5/2
2
1/2
2
3/2
1:
-0.05773502691896257645091487805019574556476017512701268760186023264839776723029333456937153955857495252
5/2
2
1/2
5/2
2
1/2:
-1/30
5/2
2
3/2
0
3/2
2:
0.2236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782275
5/2
2
3/2
1/2
1
3/2:
0.1707825127659933063870173113420175331789172110575805488256996416648391330950892345487871938063091123
5/2
2
3/2
1/2
2
3/2:
3/20
5/2
2
3/2
1
1/2
2:
0.1972026594366538680855776097187205682805167076931446774293239889714274153035217678921917509061036393
5/2
2
3/2
1
3/2
1:
0.1870828693386970692791874366158274650878009903889363473151872733660017578153469513988404947597189786
5/2
2
3/2
1
3/2
2:
-0.02357022603955158414669481207016163464282786458961580121961132896651220797436845064750645890546069288
5/2
2
3/2
3/2
1
3/2:
0.1527525231651946668862682397909336162994818858922657300869080707968956141849256962201453853164481678
5/2
2
3/2
3/2
2
1/2:
0.1870828693386970692791874366158274650878009903889363473151872733660017578153469513988404947597189786
5/2
2
3/2
3/2
2
3/2:
-1/10
5/2
2
3/2
2
1/2
2:
1/10
5/2
2
3/2
2
3/2
1:
0.1080123449734643371827661239347999442950867384509724424951892399634936229640674061900060151100935039
5/2
2
3/2
2
3/2
2:
-0.1336306209562121923422767404398767607770007074206688195108480524042869698681049652848860676855135561
5/2
2
3/2
5/2
1
3/2:
1/20
5/2
2
3/2
5/2
2
1/2:
1/15
5/2
2
3/2
5/2
2
3/2:
-47/420
5/2
5/2
0
0
0
5/2:
-0.4082482904638630163662140124509818986609912467761116880721154278751600629095525044233099055174400391
5/2
5/2
0
1/2
1/2
2:
-0.2886751345948128822545743902509787278238008756350634380093011632419888361514666728468576977928747626
5/2
5/2
0
1
1
3/2:
-0.2357022603955158414669481207016163464282786458961580121961132896651220797436845064750645890546069288
5/2
5/2
0
3/2
3/2
1:
-0.2041241452319315081831070062254909493304956233880558440360577139375800314547762522116549527587200196
5/2
5/2
0
3/2
3/2
2:
0.2041241452319315081831070062254909493304956233880558440360577139375800314547762522116549527587200196
5/2
5/2
0
2
2
1/2:
-0.1825741858350553711523232609336007113175815649993277514089648165774977590409075779336194787212902086
5/2
5/2
0
2
2
3/2:
0.1825741858350553711523232609336007113175815649993277514089648165774977590409075779336194787212902086
5/2
5/2
0
5/2
5/2
0:
-1/6
5/2
5/2
1
1/2
1/2
2:
0.1972026594366538680855776097187205682805167076931446774293239889714274153035217678921917509061036393
5/2
5/2
1
1
0
5/2:
0.2357022603955158414669481207016163464282786458961580121961132896651220797436845064750645890546069288
5/2
5/2
1
1
1
3/2:
0.1972026594366538680855776097187205682805167076931446774293239889714274153035217678921917509061036393
5/2
5/2
1
1
1
5/2:
-0.05634361698190110516730788849106301950871905934089847926552113970612211865814907654062621454460103979
5/2
5/2
1
3/2
1/2
2:
0.1490711984999859797606115779154184156960412239741017149513931496940347283758536599609609605585854850
5/2
5/2
1
3/2
3/2
1:
0.1870828693386970692791874366158274650878009903889363473151872733660017578153469513988404947597189786
5/2
5/2
1
3/2
3/2
2:
-0.1158132048287172333633065083812265260067339464312463102427349787503820405523576365802345919941117486
5/2
5/2
1
2
1
3/2:
1/10
5/2
5/2
1
2
2
1/2:
0.1763834207376393727001077169092840283806839455388300120245556306134045882153522418506928590983029074
5/2
5/2
1
2
2
3/2:
-0.1385869734367166499786560632858660222991088143519378665907222811962464621692053328826872464343808558
5/2
5/2
1
5/2
3/2
1:
1/15
5/2
5/2
1
5/2
5/2
0:
1/6
5/2
5/2
1
5/2
5/2
1:
-31/210
5/2
5/2
2
1
1
3/2:
-0.1247219128924647128527916244105516433918673269259575648767915155773345052102313009325603298398126524
5/2
5/2
2
1
1
5/2:
-0.1425393290199596718317618564692018781621340879153800741449045892312394345259786296372118055312144599
5/2
5/2
2
3/2
1/2
2:
-0.1632993161855452065464856049803927594643964987104446752288461711500640251638210017693239622069760157
5/2
5/2
2
3/2
3/2
1:
-0.1527525231651946668862682397909336162994818858922657300869080707968956141849256962201453853164481678
5/2
5/2
2
3/2
3/2
2:
-0.02182178902359923812660974854156194518564026941318081858384401011384223059784652803144934075949259539
5/2
5/2
2
2
0
5/2:
-0.1825741858350553711523232609336007113175815649993277514089648165774977590409075779336194787212902086
5/2
5/2
2
2
1
3/2:
-0.1414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641573
5/2
5/2
2
2
1
5/2:
0.07559289460184544544290330724683601216315026237378429086766669883431625209229381793601122532784410316
5/2
5/2
2
2
2
1/2:
-0.1632993161855452065464856049803927594643964987104446752288461711500640251638210017693239622069760157
5/2
5/2
2
2
2
3/2:
0.05832118435198043090945914463585455695157017811087309829601648969645143755850750063190141507392000559
5/2
5/2
2
2
2
5/2:
0.05832118435198043090945914463585455695157017811087309829601648969645143755850750063190141507392000559
5/2
5/2
2
5/2
1/2
2:
-1/10
5/2
5/2
2
5/2
3/2
1:
-0.1069044967649697538738213923519014086216005659365350556086784419234295758944839722279088541484108449
5/2
5/2
2
5/2
3/2
2:
4/35
5/2
5/2
2
5/2
5/2
0:
-1/6
5/2
5/2
2
5/2
5/2
1:
23/210
5/2
5/2
2
5/2
5/2
2:
-1/60
3
3/2
3/2
0
3/2
3/2:
1/4
3
3/2
3/2
1
3/2
3/2:
3/20
3
3/2
3/2
2
3/2
3/2:
1/20
3
3/2
3/2
3
3/2
3/2:
1/140
3
2
1
0
1
2:
0.2581988897471611256786176933188266407221947803527727217725049177408988727957986022346191584572449012
3
2
1
1/2
3/2
3/2:
0.2236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782275
3
2
1
1
1
2:
0.1490711984999859797606115779154184156960412239741017149513931496940347283758536599609609605585854850
3
2
1
1
2
1:
1/5
3
2
1
3/2
3/2
3/2:
1/10
3
2
1
2
1
2:
0.04364357804719847625321949708312389037128053882636163716768802022768446119569305606289868151898519079
3
2
1
2
2
1:
1/15
3
2
1
5/2
3/2
3/2:
0.02182178902359923812660974854156194518564026941318081858384401011384223059784652803144934075949259539
3
2
1
3
2
1:
1/105
3
2
2
0
2
2:
-1/5
3
2
2
1/2
3/2
3/2:
-0.1414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641573
3
2
2
1
2
1:
-0.1632993161855452065464856049803927594643964987104446752288461711500640251638210017693239622069760157
3
2
2
3/2
3/2
3/2:
-0.1414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641573
3
2
2
2
2
1:
-0.1069044967649697538738213923519014086216005659365350556086784419234295758944839722279088541484108449
3
2
2
2
2
2:
4/35
3
2
2
5/2
3/2
3/2:
-0.06060915267313264494864380246612991765298593751615491742185770305674567764837601595073089432832749597
3
2
2
3
2
1:
-1/35
3
2
2
3
2
2:
1/14
3
5/2
1/2
0
1/2
5/2:
0.2886751345948128822545743902509787278238008756350634380093011632419888361514666728468576977928747626
3
5/2
1/2
1/2
1
2:
0.2357022603955158414669481207016163464282786458961580121961132896651220797436845064750645890546069288
3
5/2
1/2
1
1/2
5/2:
0.1408590424547527629182697212276575487717976483522461981638028492653052966453726913515655363615025995
3
5/2
1/2
1
3/2
3/2:
0.2041241452319315081831070062254909493304956233880558440360577139375800314547762522116549527587200196
3
5/2
1/2
3/2
1
2:
0.08908708063747479489485116029325117385133380494711254634056536826952464657873664352325737845700903742
3
5/2
1/2
3/2
2
1:
0.1825741858350553711523232609336007113175815649993277514089648165774977590409075779336194787212902086
3
5/2
1/2
3/2
2
2:
-0.1690308509457033155019236654731890585261571780226954377965634191183663559744472296218786436338031194
3
5/2
1/2
2
3/2
3/2:
0.05976143046671968199844085898465624924234395494990515712937082450574419804245121498791533656892510973
3
5/2
1/2
2
5/2
1/2:
1/6
3
5/2
1/2
5/2
2
1:
0.03984095364447978799896057265643749949489596996660343808624721633716279869496747665861022437928340648
3
5/2
1/2
5/2
2
2:
-0.06900655593423542177961268646271319868161968035599510994617107051008640177454133534148839615239817856
3
5/2
1/2
3
5/2
1/2:
1/42
3
5/2
3/2
0
3/2
5/2:
-0.2041241452319315081831070062254909493304956233880558440360577139375800314547762522116549527587200196
3
5/2
3/2
1/2
1
2:
-0.1490711984999859797606115779154184156960412239741017149513931496940347283758536599609609605585854850
3
5/2
3/2
1/2
2
2:
-0.1414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641573
3
5/2
3/2
1
1/2
5/2:
-0.1781741612749495897897023205865023477026676098942250926811307365390492931574732870465147569140180748
3
5/2
3/2
1
3/2
3/2:
-0.1632993161855452065464856049803927594643964987104446752288461711500640251638210017693239622069760157
3
5/2
3/2
1
3/2
5/2:
0.008908708063747479489485116029325117385133380494711254634056536826952464657873664352325737845700903742
3
5/2
3/2
1
5/2
3/2:
-1/10
3
5/2
3/2
3/2
1
2:
-0.1425393290199596718317618564692018781621340879153800741449045892312394345259786296372118055312144599
3
5/2
3/2
3/2
2
1:
-0.1632993161855452065464856049803927594643964987104446752288461711500640251638210017693239622069760157
3
5/2
3/2
3/2
2
2:
0.07559289460184544544290330724683601216315026237378429086766669883431625209229381793601122532784410316
3
5/2
3/2
2
1/2
5/2:
-0.09759000729485331793543846362401001895938126346147459932897122380847950462576527688502125360360520702
3
5/2
3/2
2
3/2
3/2:
-0.1069044967649697538738213923519014086216005659365350556086784419234295758944839722279088541484108449
3
5/2
3/2
2
3/2
5/2:
0.1200198396297958096963536169785906985210214817724945022111420556261322682881559041729713741772092747
3
5/2
3/2
2
5/2
1/2:
-0.1593638145779191519958422906257499979795838798664137523449888653486511947798699066344408975171336259
3
5/2
3/2
2
5/2
3/2:
23/210
3
5/2
3/2
5/2
1
2:
-0.05345224838248487693691069617595070431080028296826752780433922096171478794724198611395442707420542245
3
5/2
3/2
5/2
2
1:
-8/105
3
5/2
3/2
5/2
2
2:
0.1072221928495019276945562020932206703345546109501664198320261463470244248562590499145471448944963404
3
5/2
3/2
3
3/2
3/2:
-1/35
3
5/2
3/2
3
5/2
1/2:
-1/21
3
5/2
3/2
3
5/2
3/2:
71/840
3
5/2
5/2
0
5/2
5/2:
1/6
3
5/2
5/2
1/2
2
2:
0.1414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641573
3
5/2
5/2
1
3/2
3/2:
1/10
3
5/2
5/2
1
5/2
3/2:
0.1309307341415954287596584912493716711138416164790849115030640606830533835870791681886960445569555724
3
5/2
5/2
1
5/2
5/2:
-11/210
3
5/2
5/2
3/2
2
1:
0.1309307341415954287596584912493716711138416164790849115030640606830533835870791681886960445569555724
3
5/2
5/2
3/2
2
2:
0.04040610178208842996576253497741994510199062501076994494790513537116378509891734396715392955221833065
3
5/2
5/2
2
3/2
3/2:
9/70
3
5/2
5/2
2
5/2
1/2:
0.1463850109422799769031576954360150284390718951922118989934568357127192569386479153275318804054078105
3
5/2
5/2
2
5/2
3/2:
-0.03499271061118825854567548678151273417094210686652385897760989381787086253510450037914084904435200335
3
5/2
5/2
2
5/2
5/2:
-29/420
3
5/2
5/2
5/2
2
1:
0.1049781318335647756370264603445382025128263205995715769328296814536125876053135011374225471330560101
3
5/2
5/2
5/2
2
2:
-0.09091372900969896742296570369919487647947890627423237613278655458511851647256402392609634149249124396
3
5/2
5/2
3
3/2
3/2:
9/140
3
5/2
5/2
3
5/2
1/2:
1/14
3
5/2
5/2
3
5/2
3/2:
-1/10
3
5/2
5/2
3
5/2
5/2:
79/1260
3
3
0
0
0
3:
0.3779644730092272272145165362341800608157513118689214543383334941715812604614690896800561266392205158
3
3
0
1/2
1/2
5/2:
0.2672612419124243846845534808797535215540014148413376390216961048085739397362099305697721353710271123
3
3
0
1
1
2:
0.2182178902359923812660974854156194518564026941318081858384401011384223059784652803144934075949259539
3
3
0
3/2
3/2
3/2:
0.1889822365046136136072582681170900304078756559344607271691667470857906302307345448400280633196102579
3
3
0
3/2
3/2
5/2:
-0.1889822365046136136072582681170900304078756559344607271691667470857906302307345448400280633196102579
3
3
0
2
2
1:
0.1690308509457033155019236654731890585261571780226954377965634191183663559744472296218786436338031194
3
3
0
2
2
2:
-0.1690308509457033155019236654731890585261571780226954377965634191183663559744472296218786436338031194
3
3
0
5/2
5/2
1/2:
0.1543033499620919102610944627639999204215524835013892035645560570907051756629534374142943073001335770
3
3
0
5/2
5/2
3/2:
-0.1543033499620919102610944627639999204215524835013892035645560570907051756629534374142943073001335770
3
3
0
5/2
5/2
5/2:
0.1543033499620919102610944627639999204215524835013892035645560570907051756629534374142943073001335770
3
3
0
3
3
0:
1/7
3
3
1
1/2
1/2
5/2:
-0.1781741612749495897897023205865023477026676098942250926811307365390492931574732870465147569140180748
3
3
1
1
0
3:
-0.2182178902359923812660974854156194518564026941318081858384401011384223059784652803144934075949259539
3
3
1
1
1
2:
-0.1781741612749495897897023205865023477026676098942250926811307365390492931574732870465147569140180748
3
3
1
1
1
3:
0.04454354031873739744742558014662558692566690247355627317028268413476232328936832176162868922850451871
3
3
1
3/2
1/2
5/2:
-0.1408590424547527629182697212276575487717976483522461981638028492653052966453726913515655363615025995
3
3
1
3/2
3/2
3/2:
-0.1690308509457033155019236654731890585261571780226954377965634191183663559744472296218786436338031194
3
3
1
3/2
3/2
5/2:
0.09860132971832693404278880485936028414025835384657233871466199448571370765176088394609587545305181963
3
3
1
2
1
2:
-0.09759000729485331793543846362401001895938126346147459932897122380847950462576527688502125360360520702
3
3
1
2
2
1:
-0.1593638145779191519958422906257499979795838798664137523449888653486511947798699066344408975171336259
3
3
1
2
2
2:
0.1195228609334393639968817179693124984846879098998103142587416490114883960849024299758306731378502195
3
3
1
5/2
3/2
3/2:
-0.06900655593423542177961268646271319868161968035599510994617107051008640177454133534148839615239817856
3
3
1
5/2
3/2
5/2:
0.1035098339013531326694190296940697980224295205339926649192566057651296026618120030122325942285972678
3
3
1
5/2
5/2
1/2:
-0.1505846504842085396189949306872723111295026256821531822313097548948854494590113438735356242085381093
3
3
1
5/2
5/2
3/2:
0.1279969529115772586761456910841814644600772318298302048966132916606526320401596422925052805772573929
3
3
1
5/2
5/2
5/2:
-0.09035079029052512377139695841236338667770157540929190933878585293693126967540680632412137452512286558
3
3
1
3
2
1:
-1/21
3
3
1
3
3
0:
-1/7
3
3
1
3
3
1:
11/84
3
3
2
1
1
2:
0.1069044967649697538738213923519014086216005659365350556086784419234295758944839722279088541484108449
3
3
2
1
1
3:
0.1336306209562121923422767404398767607770007074206688195108480524042869698681049652848860676855135561
3
3
2
3/2
1/2
5/2:
0.1463850109422799769031576954360150284390718951922118989934568357127192569386479153275318804054078105
3
3
2
3/2
3/2
3/2:
0.1309307341415954287596584912493716711138416164790849115030640606830533835870791681886960445569555724
3
3
2
3/2
3/2
5/2:
0.03273268353539885718991462281234291777846040411977122787576601517076334589676979204717401113923889309
3
3
2
2
0
3:
0.1690308509457033155019236654731890585261571780226954377965634191183663559744472296218786436338031194
3
3
2
2
1
2:
0.1309307341415954287596584912493716711138416164790849115030640606830533835870791681886960445569555724
3
3
2
2
1
3:
-0.05976143046671968199844085898465624924234395494990515712937082450574419804245121498791533656892510973
3
3
2
2
2
1:
0.1399708424447530341827019471260509366837684274660954359104395752714834501404180015165633961774080134
3
3
2
2
2
2:
-0.03499271061118825854567548678151273417094210686652385897760989381787086253510450037914084904435200335
3
3
2
2
2
3:
-0.06415330278717847400040505909944001264672719592196040812561813866609658131435825069509155658131200615
3
3
2
5/2
1/2
5/2:
0.09759000729485331793543846362401001895938126346147459932897122380847950462576527688502125360360520702
3
3
2
5/2
3/2
3/2:
0.1049781318335647756370264603445382025128263205995715769328296814536125876053135011374225471330560101
3
3
2
5/2
3/2
5/2:
-0.09914601339836673254608054588095274681766930278848426710322803248396744384946275107423240562566400950
3
3
2
5/2
5/2
1/2:
1/7
3
3
2
5/2
5/2
3/2:
-11/140
3
3
2
5/2
5/2
5/2:
-1/210
3
3
2
3
1
2:
2/35
3
3
2
3
2
1:
0.07824607964359515906528139754297173342182067071399760774669920710464189673181753340012263373769580368
3
3
2
3
2
2:
-1/10
3
3
2
3
3
0:
1/7
3
3
2
3
3
1:
-3/28
3
3
2
3
3
2:
19/420
3
3
3
3/2
3/2
3/2:
-0.07824607964359515906528139754297173342182067071399760774669920710464189673181753340012263373769580368
3
3
3
2
2
1:
-0.1106566670344976252908361542794971317380834772940454521882163933175280883410565438148367821959621005
3
3
3
2
2
2:
-0.05532833351724881264541807713974856586904173864702272609410819665876404417052827190741839109798105026
3
3
3
5/2
3/2
3/2:
-0.1173691194653927385979220963144576001327310060709964116200488106569628450977263001001839506065437055
3
3
3
5/2
5/2
1/2:
-0.1304101327393252651088023292382862223697011178566626795778320118410698278863625556668710562294930061
3
3
3
5/2
5/2
3/2:
0.01304101327393252651088023292382862223697011178566626795778320118410698278863625556668710562294930061
3
3
3
5/2
5/2
5/2:
0.07389907521895098356165465323502885934283063345210885176077147337660623580227211487789359853004603681
3
3
3
3
2
1:
-0.1010152544552210749144063374435498627549765625269248623697628384279094627472933599178848238805458266
3
3
3
3
2
2:
0.07377111135633175019389076951966475449205565152936363479214426221168539222737102920989118813064140034
3
3
3
3
3
0:
-1/7
3
3
3
3
3
1:
1/14
3
3
3
3
3
2:
1/42
3
3
3
3
3
3:
-1/14
7/2
2
3/2
0
3/2
2:
-0.2236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782275
7/2
2
3/2
1/2
2
3/2:
-1/5
7/2
2
3/2
1
3/2
2:
-0.1414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641573
7/2
2
3/2
3/2
2
3/2:
-1/10
7/2
2
3/2
2
3/2
2:
-0.05345224838248487693691069617595070431080028296826752780433922096171478794724198611395442707420542245
7/2
2
3/2
5/2
2
3/2:
-1/35
7/2
2
3/2
3
3/2
2:
-0.01010152544552210749144063374435498627549765625269248623697628384279094627472933599178848238805458266
7/2
2
3/2
7/2
2
3/2:
-1/280
7/2
5/2
1
0
1
5/2:
-0.2357022603955158414669481207016163464282786458961580121961132896651220797436845064750645890546069288
7/2
5/2
1
1/2
3/2
2:
-0.2041241452319315081831070062254909493304956233880558440360577139375800314547762522116549527587200196
7/2
5/2
1
1
1
5/2:
-0.1408590424547527629182697212276575487717976483522461981638028492653052966453726913515655363615025995
7/2
5/2
1
1
2
3/2:
-0.1825741858350553711523232609336007113175815649993277514089648165774977590409075779336194787212902086
7/2
5/2
1
3/2
3/2
2:
-0.09759000729485331793543846362401001895938126346147459932897122380847950462576527688502125360360520702
7/2
5/2
1
3/2
5/2
1:
-1/6
7/2
5/2
1
2
1
5/2:
-0.04454354031873739744742558014662558692566690247355627317028268413476232328936832176162868922850451871
7/2
5/2
1
2
2
3/2:
-0.06900655593423542177961268646271319868161968035599510994617107051008640177454133534148839615239817856
7/2
5/2
1
5/2
3/2
2:
-0.02439750182371332948385961590600250473984531586536864983224280595211987615644131922125531340090130175
7/2
5/2
1
5/2
5/2
1:
-1/21
7/2
5/2
1
3
2
3/2:
-0.01304101327393252651088023292382862223697011178566626795778320118410698278863625556668710562294930061
7/2
5/2
1
7/2
5/2
1:
-1/168
7/2
5/2
2
0
2
5/2:
0.1825741858350553711523232609336007113175815649993277514089648165774977590409075779336194787212902086
7/2
5/2
2
1/2
3/2
2:
0.1224744871391589049098642037352945695982973740328335064216346283625480188728657513269929716552320117
7/2
5/2
2
1/2
5/2
2:
2/15
7/2
5/2
2
1
1
5/2:
0.1463850109422799769031576954360150284390718951922118989934568357127192569386479153275318804054078105
7/2
5/2
2
1
2
3/2:
0.1414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641573
7/2
5/2
2
1
2
5/2:
0.01259881576697424090715055120780600202719171039563071514461111647238604201538230298933520422130735053
7/2
5/2
2
3/2
3/2
2:
0.1309307341415954287596584912493716711138416164790849115030640606830533835870791681886960445569555724
7/2
5/2
2
3/2
5/2
1:
0.1463850109422799769031576954360150284390718951922118989934568357127192569386479153275318804054078105
7/2
5/2
2
3/2
5/2
2:
-11/210
7/2
5/2
2
2
1
5/2:
0.1035098339013531326694190296940697980224295205339926649192566057651296026618120030122325942285972678
7/2
5/2
2
2
2
3/2:
0.1049781318335647756370264603445382025128263205995715769328296814536125876053135011374225471330560101
7/2
5/2
2
2
2
5/2:
-0.09914601339836673254608054588095274681766930278848426710322803248396744384946275107423240562566400950
7/2
5/2
2
5/2
3/2
2:
9/140
7/2
5/2
2
5/2
5/2
1:
0.07824607964359515906528139754297173342182067071399760774669920710464189673181753340012263373769580368
7/2
5/2
2
5/2
5/2
2:
-1/10
7/2
5/2
2
3
1
5/2:
0.03194382824999699566298819526758966050629454799445036748958424636300744179482578427734877726255403250
7/2
5/2
2
3
2
3/2:
0.03711537444790451343273099303226869357734582686736529917262443527396999321947428650888170400194104091
7/2
5/2
2
3
2
5/2:
-0.07407785326716212160389798079193656602031614585307823240449274818046693934801513060644887084573360619
7/2
5/2
2
7/2
3/2
2:
1/70
7/2
5/2
2
7/2
5/2
1:
1/56
7/2
5/2
2
7/2
5/2
2:
-17/360
7/2
3
1/2
0
1/2
3:
-0.2672612419124243846845534808797535215540014148413376390216961048085739397362099305697721353710271123
7/2
3
1/2
1/2
1
5/2:
-0.2182178902359923812660974854156194518564026941318081858384401011384223059784652803144934075949259539
7/2
3
1/2
1
1/2
3:
-0.1336306209562121923422767404398767607770007074206688195108480524042869698681049652848860676855135561
7/2
3
1/2
1
3/2
2:
-0.1889822365046136136072582681170900304078756559344607271691667470857906302307345448400280633196102579
7/2
3
1/2
3/2
1
5/2:
-0.08625819491779427722451585807839149835202460044499388743271383813760800221817666917686049519049772320
7/2
3
1/2
3/2
2
3/2:
-0.1690308509457033155019236654731890585261571780226954377965634191183663559744472296218786436338031194
7/2
3
1/2
3/2
2
5/2:
0.1552647508520296990041285445411046970336442808009889973788849086476944039927180045183488913428959018
7/2
3
1/2
2
3/2
2:
-0.05976143046671968199844085898465624924234395494990515712937082450574419804245121498791533656892510973
7/2
3
1/2
2
5/2
1:
-0.1543033499620919102610944627639999204215524835013892035645560570907051756629534374142943073001335770
7/2
3
1/2
2
5/2
2:
0.1463850109422799769031576954360150284390718951922118989934568357127192569386479153275318804054078105
7/2
3
1/2
5/2
2
3/2:
-0.04225771273642582887548091636829726463153929450567385944914085477959158899361180740546966090845077984
7/2
3
1/2
5/2
2
5/2:
0.06900655593423542177961268646271319868161968035599510994617107051008640177454133534148839615239817856
7/2
3
1/2
5/2
3
1/2:
-1/7
7/2
3
1/2
3
5/2
1:
-0.02916059217599021545472957231792727847578508905543654914800824484822571877925375031595070753696000280
7/2
3
1/2
3
5/2
2:
0.05050762722761053745720316872177493137748828126346243118488141921395473137364667995894241194027291331
7/2
3
1/2
7/2
3
1/2:
-1/56
7/2
3
3/2
0
3/2
3:
0.1889822365046136136072582681170900304078756559344607271691667470857906302307345448400280633196102579
7/2
3
3/2
1/2
1
5/2:
0.1336306209562121923422767404398767607770007074206688195108480524042869698681049652848860676855135561
7/2
3
3/2
1/2
2
5/2:
0.1336306209562121923422767404398767607770007074206688195108480524042869698681049652848860676855135561
7/2
3
3/2
1
1/2
3:
0.1636634176769942859495731140617145888923020205988561393788300758538167294838489602358700556961944655
7/2
3
3/2
1
3/2
2:
0.1463850109422799769031576954360150284390718951922118989934568357127192569386479153275318804054078105
7/2
3
3/2
1
5/2
2:
0.09759000729485331793543846362401001895938126346147459932897122380847950462576527688502125360360520702
7/2
3
3/2
3/2
1
5/2:
0.1336306209562121923422767404398767607770007074206688195108480524042869698681049652848860676855135561
7/2
3
3/2
3/2
2
3/2:
0.1463850109422799769031576954360150284390718951922118989934568357127192569386479153275318804054078105
7/2
3
3/2
3/2
2
5/2:
-0.05976143046671968199844085898465624924234395494990515712937082450574419804245121498791533656892510973
7/2
3
3/2
3/2
3
3/2:
1/14
7/2
3
3/2
2
1/2
3:
0.09449111825230680680362913405854501520393782796723036358458337354289531511536727242001403165980512895
7/2
3
3/2
2
3/2
2:
0.1035098339013531326694190296940697980224295205339926649192566057651296026618120030122325942285972678
7/2
3
3/2
2
3/2
3:
-0.1091089451179961906330487427078097259282013470659040929192200505692111529892326401572467037974629770
7/2
3
3/2
2
5/2
1:
1/7
7/2
3
3/2
2
5/2
2:
-0.09035079029052512377139695841236338667770157540929190933878585293693126967540680632412137452512286558
7/2
3
3/2
5/2
1
5/2:
0.05455447255899809531652437135390486296410067353295204645961002528460557649461632007862335189873148848
7/2
3
3/2
5/2
2
3/2:
0.07824607964359515906528139754297173342182067071399760774669920710464189673181753340012263373769580368
7/2
3
3/2
5/2
2
5/2:
-0.1011554561249904862661292850140339249365994019824261637170167801495235656836149835449377946647544362
7/2
3
3/2
5/2
3
1/2:
0.1383208337931220316135451928493714146726043466175568152352704916469101104263206797685459777449526256
7/2
3
3/2
5/2
3
3/2:
-3/28
7/2
3
3/2
3
3/2
2:
0.03194382824999699566298819526758966050629454799445036748958424636300744179482578427734877726255403250
7/2
3
3/2
3
3/2
3:
-0.06520506636966263255440116461914311118485055892833133978891600592053491394318127783343552811474650307
7/2
3
3/2
3
5/2
1:
0.05646924393157820235712309900772711667356348463080744333674115808558204354712925395257585907820179099
7/2
3
3/2
3
5/2
2:
-0.08476658628056142232072151400488604454030572660683074172559080769669538812613566118346618654917045399
7/2
3
3/2
7/2
2
3/2:
1/56
7/2
3
3/2
7/2
3
1/2:
1/28
7/2
3
3/2
7/2
3
3/2:
-11/168
7/2
3
5/2
0
5/2
3:
-0.1543033499620919102610944627639999204215524835013892035645560570907051756629534374142943073001335770
7/2
3
5/2
1/2
2
5/2:
-0.1259881576697424090715055120780600202719171039563071514461111647238604201538230298933520422130735053
7/2
3
5/2
1/2
3
5/2:
-2/21
7/2
3
5/2
1
3/2
2:
-0.08451542547285165775096183273659452926307858901134771889828170955918317798722361481093932181690155969
7/2
3
5/2
1
3/2
3:
-0.1219875091185666474192980795300125236992265793268432491612140297605993807822065961062765670045065088
7/2
3
5/2
1
5/2
2:
-0.1204677203873668316951959445498178489036021005457225457850478039159083595672090750988284993668304874
7/2
3
5/2
1
5/2
3:
0.03764616262105213490474873267181807778237565642053829555782743872372136236475283596838390605213452732
7/2
3
5/2
3/2
1
5/2:
-0.1157275124715689326958208470729999403161643626260419026734170428180288817472150780607207304751001828
7/2
3
5/2
3/2
2
3/2:
-0.1106566670344976252908361542794971317380834772940454521882163933175280883410565438148367821959621005
7/2
3
5/2
3/2
2
5/2:
-0.04894001140736777537617335247336350111708835334669978422517567034083777107417868675889907786777488552
7/2
3
5/2
3/2
3
3/2:
-0.1010152544552210749144063374435498627549765625269248623697628384279094627472933599178848238805458266
7/2
3
5/2
3/2
3
5/2:
1/12
7/2
3
5/2
2
1/2
3:
-0.1336306209562121923422767404398767607770007074206688195108480524042869698681049652848860676855135561
7/2
3
5/2
2
3/2
2:
-0.1173691194653927385979220963144576001327310060709964116200488106569628450977263001001839506065437055
7/2
3
5/2
2
3/2
3:
0.02061965247105806301818388501792705198741434825964738842923579737442777401081904806048983555663391162
7/2
3
5/2
2
5/2
1:
-0.1237179148263483781091033101075623119244860895578843305754147842465666440649142883629390133398034697
7/2
3
5/2
2
5/2
2:
0.01304101327393252651088023292382862223697011178566626795778320118410698278863625556668710562294930061
7/2
3
5/2
2
5/2
3:
1/14
7/2
3
5/2
5/2
1
5/2:
-0.1010152544552210749144063374435498627549765625269248623697628384279094627472933599178848238805458266
7/2
3
5/2
5/2
2
3/2:
-0.1016446390768407642428215782139088100124142723354533980061340845540476783848326571146365463407632238
7/2
3
5/2
5/2
2
5/2:
0.07377111135633175019389076951966475449205565152936363479214426221168539222737102920989118813064140034
7/2
3
5/2
5/2
3
1/2:
-0.1304101327393252651088023292382862223697011178566626795778320118410698278863625556668710562294930061
7/2
3
5/2
5/2
3
3/2:
0.05892556509887896036673703017540408660706966147403950304902832241628051993592112661876614726365173220
7/2
3
5/2
5/2
3
5/2:
1/42
7/2
3
5/2
3
1/2
3:
-1/14
7/2
3
5/2
3
3/2
2:
-0.06776309271789384282854771880927254000827618155696893200408938970269845225655510474309103089384214918
7/2
3
5/2
3
3/2
3:
0.09221388919541468774236346189958094311506956441170454349018032776460674028421378651236398516330175043
7/2
3
5/2
3
5/2
1:
-0.07985957062499248915747048816897415126573636998612591872396061590751860448706446069337194315638508125
7/2
3
5/2
3
5/2
2:
0.08914009288890086481761801316959491167790057893131439204050765017245318227473999362861851899119169208
7/2
3
5/2
3
5/2
3:
-0.04347004424644175503626744307942874078990037261888755985927733728035660929545418522229035207649766871
7/2
3
5/2
7/2
1
5/2:
-1/28
7/2
3
5/2
7/2
2
3/2:
-0.04123930494211612603636777003585410397482869651929477685847159474885554802163809612097967111326782323
7/2
3
5/2
7/2
2
5/2:
19/252
7/2
3
5/2
7/2
3
1/2:
-3/56
7/2
3
5/2
7/2
3
3/2:
1/12
7/2
3
5/2
7/2
3
5/2:
-37/504
7/2
7/2
0
0
0
7/2:
-0.3535533905932737622004221810524245196424179688442370182941699344976831196155267597125968835819103932
7/2
7/2
0
1/2
1/2
3:
-1/4
7/2
7/2
0
1
1
5/2:
-0.2041241452319315081831070062254909493304956233880558440360577139375800314547762522116549527587200196
7/2
7/2
0
3/2
3/2
2:
-0.1767766952966368811002110905262122598212089844221185091470849672488415598077633798562984417909551966
7/2
7/2
0
3/2
3/2
3:
0.1767766952966368811002110905262122598212089844221185091470849672488415598077633798562984417909551966
7/2
7/2
0
2
2
3/2:
-0.1581138830084189665999446772216359266859777569662608413428752426396297219319619110672124054189650148
7/2
7/2
0
2
2
5/2:
0.1581138830084189665999446772216359266859777569662608413428752426396297219319619110672124054189650148
7/2
7/2
0
5/2
5/2
1:
-0.1443375672974064411272871951254893639119004378175317190046505816209944180757333364234288488964373813
7/2
7/2
0
5/2
5/2
2:
0.1443375672974064411272871951254893639119004378175317190046505816209944180757333364234288488964373813
7/2
7/2
0
5/2
5/2
3:
-0.1443375672974064411272871951254893639119004378175317190046505816209944180757333364234288488964373813
7/2
7/2
0
3
3
1/2:
-0.1336306209562121923422767404398767607770007074206688195108480524042869698681049652848860676855135561
7/2
7/2
0
3
3
3/2:
0.1336306209562121923422767404398767607770007074206688195108480524042869698681049652848860676855135561
7/2
7/2
0
3
3
5/2:
-0.1336306209562121923422767404398767607770007074206688195108480524042869698681049652848860676855135561
7/2
7/2
0
7/2
7/2
0:
-1/8
7/2
7/2
1
1/2
1/2
3:
0.1636634176769942859495731140617145888923020205988561393788300758538167294838489602358700556961944655
7/2
7/2
1
1
0
7/2:
0.2041241452319315081831070062254909493304956233880558440360577139375800314547762522116549527587200196
7/2
7/2
1
1
1
5/2:
0.1636634176769942859495731140617145888923020205988561393788300758538167294838489602358700556961944655
7/2
7/2
1
1
1
7/2:
-0.03636964837266539687768291423593657530940044902196803097307335018973705099641088005241556793248765899
7/2
7/2
1
3/2
1/2
3:
0.1336306209562121923422767404398767607770007074206688195108480524042869698681049652848860676855135561
7/2
7/2
1
3/2
3/2
2:
0.1552647508520296990041285445411046970336442808009889973788849086476944039927180045183488913428959018
7/2
7/2
1
3/2
3/2
3:
-0.08625819491779427722451585807839149835202460044499388743271383813760800221817666917686049519049772320
7/2
7/2
1
2
1
5/2:
0.09449111825230680680362913405854501520393782796723036358458337354289531511536727242001403165980512895
7/2
7/2
1
2
2
3/2:
0.1463850109422799769031576954360150284390718951922118989934568357127192569386479153275318804054078105
7/2
7/2
1
2
2
5/2:
-0.1057225079027577610967250022593441872059963687499308159397188257925194633445790499587730247372389743
7/2
7/2
1
5/2
3/2
2:
0.06900655593423542177961268646271319868161968035599510994617107051008640177454133534148839615239817856
7/2
7/2
1
5/2
3/2
3:
-0.09960238411119946999740143164109374873723992491650859521561804084290699673741869164652556094820851621
7/2
7/2
1
5/2
5/2
1:
0.1383208337931220316135451928493714146726043466175568152352704916469101104263206797685459777449526256
7/2
7/2
1
5/2
5/2
2:
-0.1137304633410114482155816030094831631752524627744356036378890709096816463505303366985822483680721589
7/2
7/2
1
5/2
5/2
3:
0.07684490766284557311863621824965078592922463700975378624181693980383895023684482209363665430275145869
7/2
7/2
1
3
2
3/2:
0.05050762722761053745720316872177493137748828126346243118488141921395473137364667995894241194027291331
7/2
7/2
1
3
2
5/2:
-0.07776157913597390787927885951447274260209357081449746439468865292860191674467666750920188676522667412
7/2
7/2
1
3
3
1/2:
0.1312226647919559695462830754306727531410329007494644711660371018170157345066418764217781839163200126
7/2
7/2
1
3
3
3/2:
-0.1166423687039608618189182892717091139031403562217461965920329793929028751170150012638028301478400112
7/2
7/2
1
3
3
5/2:
0.09234187522396901560664364567343638183998611534221573896869277535271477613430354266717724053370667552
7/2
7/2
1
7/2
5/2
1:
1/28
7/2
7/2
1
7/2
7/2
0:
1/8
7/2
7/2
1
7/2
7/2
1:
-59/504
7/2
7/2
2
1
1
5/2:
-0.09449111825230680680362913405854501520393782796723036358458337354289531511536727242001403165980512895
7/2
7/2
2
1
1
7/2:
-0.1259881576697424090715055120780600202719171039563071514461111647238604201538230298933520422130735053
7/2
7/2
2
3/2
1/2
3:
-0.1336306209562121923422767404398767607770007074206688195108480524042869698681049652848860676855135561
7/2
7/2
2
3/2
3/2
2:
-0.1157275124715689326958208470729999403161643626260419026734170428180288817472150780607207304751001828
7/2
7/2
2
3/2
3/2
3:
-0.03857583749052297756527361569099998010538812087534730089113901427267629391573835935357357682503339426
7/2
7/2
2
2
0
7/2:
-0.1581138830084189665999446772216359266859777569662608413428752426396297219319619110672124054189650148
7/2
7/2
2
2
1
5/2:
-0.1219875091185666474192980795300125236992265793268432491612140297605993807822065961062765670045065088
7/2
7/2
2
2
1
7/2:
0.04879500364742665896771923181200500947969063173073729966448561190423975231288263844251062680180260351
7/2
7/2
2
2
2
3/2:
-0.1237179148263483781091033101075623119244860895578843305754147842465666440649142883629390133398034697
7/2
7/2
2
2
2
5/2:
0.02061965247105806301818388501792705198741434825964738842923579737442777401081904806048983555663391162
7/2
7/2
2
2
2
7/2:
0.06598288790738580165818843205736656635972591443087164297355455159816887683462095379356747378122851717
7/2
7/2
2
5/2
1/2
3:
-0.09449111825230680680362913405854501520393782796723036358458337354289531511536727242001403165980512895
7/2
7/2
2
5/2
3/2
2:
-0.1010152544552210749144063374435498627549765625269248623697628384279094627472933599178848238805458266
7/2
7/2
2
5/2
3/2
3:
0.08748177652797064636418871695378183542735526716630964744402473454467715633776125094785212261088000839
7/2
7/2
2
5/2
5/2
1:
-0.1262690680690263436430079218044373284437207031586560779622035480348868284341166998973560298506822833
7/2
7/2
2
5/2
5/2
2:
0.05892556509887896036673703017540408660706966147403950304902832241628051993592112661876614726365173220
7/2
7/2
2
5/2
5/2
3:
0.01683587574253684581906772290725831045916276042115414372829380640465157712454889331964747064675763777
7/2
7/2
2
3
1
5/2:
-0.05832118435198043090945914463585455695157017811087309829601648969645143755850750063190141507392000559
7/2
7/2
2
3
2
3/2:
-0.07985957062499248915747048816897415126573636998612591872396061590751860448706446069337194315638508125
7/2
7/2
2
3
2
5/2:
0.09221388919541468774236346189958094311506956441170454349018032776460674028421378651236398516330175043
7/2
7/2
2
3
3
1/2:
-0.1262690680690263436430079218044373284437207031586560779622035480348868284341166998973560298506822833
7/2
7/2
2
3
3
3/2:
0.08417937871268422909533861453629155229581380210577071864146903202325788562274446659823735323378818885
7/2
7/2
2
3
3
5/2:
-0.02525381361380526872860158436088746568874414063173121559244070960697736568682333997947120597013645666
7/2
7/2
2
7/2
3/2
2:
-1/28
7/2
7/2
2
7/2
5/2
1:
-5/84
7/2
7/2
2
7/2
5/2
2:
1/12
7/2
7/2
2
7/2
7/2
0:
-1/8
7/2
7/2
2
7/2
7/2
1:
17/168
7/2
7/2
2
7/2
7/2
2:
-7/120
7/2
7/2
3
3/2
3/2
2:
0.06487822187351767854476856020824700783988719643164313212083322008084301643246767048480281512529444791
7/2
7/2
3
3/2
3/2
3:
0.1081303697891961309079476003470783463998119940527385535347220334680716940541127841413380252088240798
7/2
7/2
3
2
1
5/2:
0.09671474291233286143404623295554809938695481055625372413870923326824900955762705589284711432080877235
7/2
7/2
3
2
1
7/2:
0.09671474291233286143404623295554809938695481055625372413870923326824900955762705589284711432080877235
7/2
7/2
3
2
2
3/2:
0.09175166127617949300083498912599957442476680365400188478776050881613228360555588150729883103127226612
7/2
7/2
3
2
2
5/2:
0.06116777418411966200055665941733304961651120243600125652517367254408818907037058767153255402084817741
7/2
7/2
3
2
2
7/2:
-0.06116777418411966200055665941733304961651120243600125652517367254408818907037058767153255402084817741
7/2
7/2
3
5/2
1/2
3:
0.1184508853698357088969618834525245244259674480567626284663815052184458800931801373824586928260103804
7/2
7/2
3
5/2
3/2
2:
0.1059456926727951849815913920114387580139986331299643085533231894906261454901978606107572744742260706
7/2
7/2
3
5/2
5/2
1:
0.1081303697891961309079476003470783463998119940527385535347220334680716940541127841413380252088240798
7/2
7/2
3
5/2
5/2
2:
0.007208691319279742060529840023138556426654132936849236902314802231204779603607518942755868347254938656
7/2
7/2
3
5/2
5/2
3:
-0.07208691319279742060529840023138556426654132936849236902314802231204779603607518942755868347254938656
7/2
7/2
3
3
0
7/2:
0.1336306209562121923422767404398767607770007074206688195108480524042869698681049652848860676855135561
7/2
7/2
3
3
1
5/2:
0.09671474291233286143404623295554809938695481055625372413870923326824900955762705589284711432080877235
7/2
7/2
3
3
1
7/2:
-0.05832118435198043090945914463585455695157017811087309829601648969645143755850750063190141507392000559
7/2
7/2
3
3
2
3/2:
0.09671474291233286143404623295554809938695481055625372413870923326824900955762705589284711432080877235
7/2
7/2
3
3
2
5/2:
-0.05583828285504082803054321563743412238795509944537782325721073679782172181849094906526328090549456114
7/2
7/2
3
3
2
7/2:
-0.03367175148507369163813544581451662091832552084230828745658761280930315424909778663929494129351527554
7/2
7/2
3
3
3
1/2:
0.1184508853698357088969618834525245244259674480567626284663815052184458800931801373824586928260103804
7/2
7/2
3
3
3
3/2:
-0.03948362845661190296565396115084150814198914935225420948879383507281529336439337912748623094200346013
7/2
7/2
3
3
3
5/2:
-0.03948362845661190296565396115084150814198914935225420948879383507281529336439337912748623094200346013
7/2
7/2
3
3
3
7/2:
0.06460957383809220485288830006501337695961860803096143370893536648278866186900734766315928699600566203
7/2
7/2
3
7/2
1/2
3:
1/14
7/2
7/2
3
7/2
3/2
2:
0.06838765055402415071250727938355868235976505307122371866309377941149881811258815032175149244758081098
7/2
7/2
3
7/2
3/2
3:
-1/12
7/2
7/2
3
7/2
5/2
1:
0.07896725691322380593130792230168301628397829870450841897758767014563058672878675825497246188400692026
7/2
7/2
3
7/2
5/2
2:
-0.07896725691322380593130792230168301628397829870450841897758767014563058672878675825497246188400692026
7/2
7/2
3
7/2
5/2
3:
1/42
7/2
7/2
3
7/2
7/2
0:
1/8
7/2
7/2
3
7/2
7/2
1:
-13/168
7/2
7/2
3
7/2
7/2
2:
1/168
7/2
7/2
3
7/2
7/2
3:
31/616
Definition
Wigner $6j$ symbols are the Wigner-convention recoupling coefficients $\begin{Bmatrix}j_1&j_2&j_3\\j_4&j_5&j_6\end{Bmatrix}$ for three angular momenta [1].
Parameters
$j_1$
—   first angular momentum ($j_1$ is a nonnegative integer or half-integer)
$j_2$
—   second angular momentum ($j_2$ is a nonnegative integer or half-integer)
$j_3$
—   third angular momentum ($j_3$ is a nonnegative integer or half-integer)
$j_4$
—   fourth angular momentum ($j_4$ is a nonnegative integer or half-integer)
$j_5$
—   fifth angular momentum ($j_5$ is a nonnegative integer or half-integer)
$j_6$
—   sixth angular momentum ($j_6$ is a nonnegative integer or half-integer)
Formulas
(1)
Put $x_1=j_1+j_2+j_3$, $x_2=j_1+j_5+j_6$, $x_3=j_4+j_2+j_6$, $x_4=j_4+j_5+j_3$, $y_1=j_1+j_2+j_4+j_5$, $y_2=j_2+j_3+j_5+j_6$ and $y_3=j_3+j_1+j_6+j_4$. With $\Delta(a,b,c)=\sqrt{(a+b-c)!(a-b+c)!(-a+b+c)!/(a+b+c+1)!}$, Racah's finite sum is $\begin{aligned}\begin{Bmatrix}j_1&j_2&j_3\\j_4&j_5&j_6\end{Bmatrix}&=\Delta(j_1,j_2,j_3)\Delta(j_1,j_5,j_6)\Delta(j_4,j_2,j_6)\Delta(j_4,j_5,j_3)\\&\quad\times\sum_s \frac{(-1)^s(s+1)!}{\prod_{i=1}^4(s-x_i)!\prod_{r=1}^3(y_r-s)!}.\end{aligned}$ The sum is over the integers $s$ for which every factorial argument is nonnegative [1].
(2)
If a Wigner $6j$ symbol has an entry $0$, tetrahedral symmetry may put that entry in the lower-right position. The value is then zero unless the first two columns are a transposed pair, and in the nonzero case $\begin{Bmatrix}j_1&j_2&j_3\\j_2&j_1&0\end{Bmatrix}=(-1)^{j_1+j_2+j_3}/\sqrt{(2j_1+1)(2j_2+1)}$ [2].
(3)
Equivalently, $\begin{aligned}\begin{Bmatrix}j_1&j_2&j_3\\j_4&j_5&j_6\end{Bmatrix}&=\sum_{m_1,m_2,m_3,\mu_1,\mu_2,\mu_3}(-1)^{j_4+\mu_1+j_5+\mu_2+j_6+\mu_3}\\&\quad\times\begin{pmatrix}j_1&j_2&j_3\\m_1&m_2&m_3\end{pmatrix}\begin{pmatrix}j_1&j_5&j_6\\m_1&\mu_2&-\mu_3\end{pmatrix}\\&\quad\times\begin{pmatrix}j_4&j_2&j_6\\-\mu_1&m_2&\mu_3\end{pmatrix}\begin{pmatrix}j_4&j_5&j_3\\\mu_1&-\mu_2&m_3\end{pmatrix}.\end{aligned}$ The sum is over magnetic quantum numbers admissible for all four Wigner $3j$ symbols [1].
Comments
(4)
A Wigner $6j$ symbol is unchanged by the 24 tetrahedral symmetries: a permutation of the three columns, followed by either no swap or by swaps of the upper and lower entries in two columns. Each class is stored once, under the lexicographically largest $(j_1,j_2,j_3,j_4,j_5,j_6)$, so a symbol in another arrangement is found by applying those symmetries first.
(5)
A Wigner $6j$ symbol is zero unless each of the four triads $(j_1,j_2,j_3)$, $(j_1,j_5,j_6)$, $(j_4,j_2,j_6)$ and $(j_4,j_5,j_3)$ satisfies the triangle inequalities and has an integer sum. This condition is necessary but not sufficient: of the 490 canonical classes with all $j_i\leq 7/2$, four nontrivial admissible classes vanish, including $\begin{Bmatrix}2&2&2\\3/2&3/2&3/2\end{Bmatrix}$.
(6)
Rows whose value is zero are omitted, as is the trivial all-zero symbol $\begin{Bmatrix}0&0&0\\0&0&0\end{Bmatrix}$, whose value is $1$.
(7)
Every nonzero Wigner $6j$ symbol is a rational number or a rational multiple of the square root of a rational number.
Programs
(P1)
Sage
from sage.functions.wigner import wigner_6j

wigner_6j(1, 1, 1, 1, 1, 1)    # 1/6
Links
Similar tables
Clebsch-Gordan coefficients and Wigner $3j$ symbols —   Wigner $6j$ symbols are finite signed sums of products of Wigner $3j$ symbols
Algebraic numbers of degree 2 —   the non-rational Wigner $6j$ symbols are quadratic algebraic numbers
Data properties
Entries are of type: real number
How well the digits are known: proven
Table is complete: no (it holds every canonical tetrahedral class with all $j_i\leq 7/2$ whose value is not zero, other than the symbol with every $j_i=0$; this cutoff covers the small angular momenta through $7/2$ and gives 485 rows)
How they were obtained:

The generator evaluates Racah's finite sum (1) with exact rational arithmetic, using integer-scaled angular momenta so every factorial argument is checked before it is used. The exact result is a sign times the square root of a rational number, converted to an arb ball for the stored real value; rational results are written exactly.

more

Before any entry is returned, the generator recomputes every row at all 24 tetrahedral images and requires the results to agree. It checks the zero-entry formula (2) wherever that formula applies, and it checks every row against the finite sum of Wigner $3j$ symbols in (3). All 485 stored rows were also compared with SageMath's exact wigner_6j function [3].



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