The exact solutions of two rigid spheres in Stokes flows


Programs

The following results are obtained by the C programs using GMP library (GNU Multiple Precision Arithmetic Library). That is, the following numbers are exact!

The code is available at https://github.com/kichiki/twobody. (Apr 15, 2018)


Resistance functions

Equal rigid spheres

The case of equal spheres is a special case of unequal situations with $\lambda = a_1 / a_2 \equiv 1$.

Jump to: summary, XA, YA, YB, XC, YC, XG, YG, YH, XM, YM, ZM, XP, XQ. TQ.

Summary

Expressions for equal spheres upto 11st order.

XAf [0] = 1
XAf [1] = 3
XAf [2] = 9
XAf [3] = 19
XAf [4] = 93
XAf [5] = 387
XAf [6] = 1197
XAf [7] = 5331
XAf [8] = 19821
XAf [9] = 76115
XAf [10] = 320173
XAf [11] = 1178451
YAf [0] = 1
YAf [1] = 3/2
YAf [2] = 9/4
YAf [3] = 59/8
YAf [4] = 465/16
YAf [5] = 2259/32
YAf [6] = 14745/64
YAf [7] = 89643/128
YAf [8] = 570017/256
YAf [9] = 4451395/512
YAf [10] = 33678825/1024
YAf [11] = 266862875/2048
YBf [0] = 0
YBf [1] = 0
YBf [2] = -6
YBf [3] = -9
YBf [4] = -27/2
YBf [5] = -273/4
YBf [6] = -1683/8
YBf [7] = -17625/16
YBf [8] = -129003/32
YBf [9] = -1017825/64
YBf [10] = -7087107/128
YBf [11] = -47478057/256
XCf [0] = 1
XCf [1] = 0
XCf [2] = 0
XCf [3] = 8
XCf [4] = 0
XCf [5] = 0
XCf [6] = 64
XCf [7] = 0
XCf [8] = 768
XCf [9] = 512
XCf [10] = 6144
XCf [11] = 12288
YCf [0] = 1
YCf [1] = 0
YCf [2] = 0
YCf [3] = 4
YCf [4] = 12
YCf [5] = 18
YCf [6] = 283
YCf [7] = 369/2
YCf [8] = 11955/4
YCf [9] = 5945/8
YCf [10] = 511755/16
YCf [11] = 448833/32
XGf [0] = 0
XGf [1] = 0
XGf [2] = 15
XGf [3] = 45
XGf [4] = 39
XGf [5] = 597
XGf [6] = 2331
XGf [7] = 6021
XGf [8] = 34347
XGf [9] = 101205
XGf [10] = 458859
XGf [11] = 1886037
YGf [0] = 0
YGf [1] = 0
YGf [2] = 0
YGf [3] = 0
YGf [4] = 32
YGf [5] = 108
YGf [6] = 162
YGf [7] = 531
YGf [8] = 1305/2
YGf [9] = 2475/4
YGf [10] = 81697/8
YGf [11] = 936387/16
YHf [0] = 0
YHf [1] = 0
YHf [2] = 0
YHf [3] = 10
YHf [4] = 0
YHf [5] = 0
YHf [6] = -96
YHf [7] = 216
YHf [8] = 324
YHf [9] = 7078
YHf [10] = 14969
YHf [11] = 196299/2
XMf [0] = 1
XMf [1] = 0
XMf [2] = 0
XMf [3] = 40
XMf [4] = 60
XMf [5] = -204
XMf [6] = 1372
XMf [7] = 3636
XMf [8] = 48828/5
XMf [9] = 328004/5
XMf [10] = 468732/5
XMf [11] = 4368132/5
YMf [0] = 1
YMf [1] = 0
YMf [2] = 0
YMf [3] = -20
YMf [4] = 0
YMf [5] = 256
YMf [6] = 640
YMf [7] = 0
YMf [8] = 10496/5
YMf [9] = -61696/5
YMf [10] = -168384/5
YMf [11] = -640672/5
ZMf [0] = 1
ZMf [1] = 0
ZMf [2] = 0
ZMf [3] = 0
ZMf [4] = 0
ZMf [5] = 64
ZMf [6] = 0
ZMf [7] = 0
ZMf [8] = 800
ZMf [9] = 0
ZMf [10] = 3072
ZMf [11] = 0
XPf [0] = 0
XPf [1] = 0
XPf [2] = 6
XPf [3] = 18
XPf [4] = 54
XPf [5] = 354
XPf [6] = 1278
XPf [7] = 4962
XPf [8] = 22782
XPf [9] = 82050
XPf [10] = 358398
XPf [11] = 1420674
XQf [0] = 0
XQf [1] = 0
XQf [2] = 0
XQf [3] = 20
XQf [4] = 30
XQf [5] = 90
XQf [6] = 878
XQf [7] = 2394
XQf [8] = 10662
XQf [9] = 49562
XQf [10] = 148614
XQf [11] = 800250
TQf [0] = 0
TQf [1] = 0
TQf [2] = 0
TQf [3] = 0
TQf [4] = 12
TQf [5] = 36
TQf [6] = 428
TQf [7] = 1188
TQf [8] = 7356
TQf [9] = 28004
TQf [10] = 608844/5
TQf [11] = 521508

XA

(text file)

XAf [0] = 1
XAf [1] = 3
XAf [2] = 9
XAf [3] = 19
XAf [4] = 93
XAf [5] = 387
XAf [6] = 1197
XAf [7] = 5331
XAf [8] = 19821
XAf [9] = 76115
XAf [10] = 320173
XAf [11] = 1178451
XAf [12] = 4918189
XAf [13] = 18925651
XAf [14] = 75342765
XAf [15] = 303110227
XAf [16] = 1177065389
XAf [17] = 4801620051
XAf [18] = 18682136493
XAf [19] = 75670042707
XAf [20] = 298279372717
XAf [21] = 1193632839763
XAf [22] = 4762291161005
XAf [23] = 18896904108115
XAf [24] = 75903359862701
XAf [25] = 300271222569043
XAf [26] = 1208070767986605
XAf [27] = 4784126072633427
XAf [28] = 19216523754293165
XAf [29] = 76340897818523731
XAf [30] = 305730485359822765
XAf [31] = 1218932811820349523
XAf [32] = 4867469839287011245
XAf [33] = 19463380614107805779
XAf [34] = 77565461675743725485
XAf [35] = 310711477349136644179
XAf [36] = 1237184909044491569069
XAf [37] = 4958880116354020456531
XAf [38] = 19748591466148681303981
XAf [39] = 79130568130020882954323
XAf [40] = 315410850698332335065005
XAf [41] = 1262724654781155271161939
XAf [42] = 5039172641609210497419181
XAf [43] = 20153064176269115168569427
XAf [44] = 80520325257821884013168557
XAf [45] = 321725945044064497234262099
XAf [46] = 1286659301993200951461234605
XAf [47] = 5137644273107735617990473811
XAf [48] = 20559265224192220496304097197
XAf [49] = 82068015370298973130741168211
XAf [50] = 328497895983216340958395320237
XAf [51] = 1311293010421040609487793076307
XAf [52] = 5248643525527674351741183281069
XAf [53] = 20956439527794169283363949426771
XAf [54] = 83862161551690733570514055415725
XAf [55] = 334966525704599176211188854732883
XAf [56] = 1340002156424151625799915400153005
XAf [57] = 5354614868469744904430104440911955
XAf [58] = 21413060715379161164743629630162861
XAf [59] = 85601173857988243580395704412977235
XAf [60] = 342211568500117916889405000930903981
XAf [61] = 1368495420381429183267871757875198035
XAf [62] = 5469622544754308246596865794408269741
XAf [63] = 21878222916713123041868415795871004755
XAf [64] = 87431218077237807614249184931033991085
XAf [65] = 349770464706314927469738768878188542035
XAf [66] = 1397715413114521885811899137742619101101
XAf [67] = 5591870324642803139648045937291337578579
XAf [68] = 22346451139320802434710902925939565479853
XAf [69] = 89399744887307950472560911443571723122771
XAf [70] = 357297157144471416515444931247061948516269
XAf [71] = 1429301663749190283417498964726516727855187
XAf [72] = 5713145922125865936283420857864273373775789
XAf [73] = 22851946415504596810617410990800286049548371
XAf [74] = 91356609245093804390751071702842749766158253
XAf [75] = 365373411193023873161642212091914780210542675
XAf [76] = 1460893673620776768392002877890035574844245933
XAf [77] = 5842074995342178594391472831635569659785164883
XAf [78] = 23361859208286660141770765306203657217738098605
XAf [79] = 93414628583271363396263397855268451842122496083
XAf [80] = 373597211338782670227714494083052058565677238189
XAf [81] = 1493758952972942215035049505378952894204249815123
XAf [82] = 5974554712444785701464464932361561904779041523629
XAf [83] = 23887108387031064406143759941862812477155761371219
XAf [84] = 95545941615389576185423773958884430893644590958509
XAf [85] = 381999732650993214678017434823053905159630199109715
XAf [86] = 1528000393142363320152828610838523349567563238557613
XAf [87] = 6109104405524549880531772590580477938964207541074003
XAf [88] = 24436521938888703537217818960081034844614499233777581
XAf [89] = 97702437407600929130411293352708433026569861869779027
XAf [90] = 390805342518474188249624276815805778921494377490630573
XAf [91] = 1562589400828922641117999259306821073703954291995097171
XAf [92] = 6250105746521616708723590647698788873126704595670747053
XAf [93] = 24991611830464434261774571478613451272752152462663530579
XAf [94] = 99958706767284549014040682116696468866351038843582498733
XAf [95] = 399716420722824370416875996099472610604118031828265121875
XAf [96] = 1598677369131060837354128127010217057360636898424991598509
XAf [97] = 6393175728834286014348092550857599788079991203013932791891
XAf [98] = 25568683930697961991386448479189950292695651229117599270829
XAf [99] = 102255586649670507687575058696022423836075533262776568821843
XAf [100] = 408943699658645811693936913019502634486874239971822726629293

YA

(text file)

YAf [0] = 1
YAf [1] = 3/2
YAf [2] = 9/4
YAf [3] = 59/8
YAf [4] = 465/16
YAf [5] = 2259/32
YAf [6] = 14745/64
YAf [7] = 89643/128
YAf [8] = 570017/256
YAf [9] = 4451395/512
YAf [10] = 33678825/1024
YAf [11] = 266862875/2048
YAf [12] = 2034611569/4096
YAf [13] = 15334900403/8192
YAf [14] = 112694825785/16384
YAf [15] = 4153619817271/163840
YAf [16] = 30265822807621/327680
YAf [17] = 223394574902447/655360
YAf [18] = 1652619698132909/1310720
YAf [19] = 12317836564455399/2621440
YAf [20] = 92978794161339989/5242880
YAf [21] = 701692898326155999/10485760
YAf [22] = 26912651578571408689/104857600
YAf [23] = 1440613711182651569573/1468006400
YAf [24] = 2232494180605775288259/587202560
YAf [25] = 86278996837935963806221/5872025600
YAf [26] = 134287866171663614306459/2348810240
YAf [27] = 5219845264316548009929653/23488102400
YAf [28] = 40628539931987687033118463/46976204800
YAf [29] = 1581001608458552211116701457/469762048000
YAf [30] = 1754574611259785033270396181/134217728000
YAf [31] = 95439029258688280196422945241/1879048192000
YAf [32] = 147953536150638004889956380207/751619276800
YAf [33] = 1147274114241215316049723737133/1503238553600
YAf [34] = 310806025964675886097077159669013/105226698752000
YAf [35] = 7221289845077540303832849182553437/631360192512000
YAf [36] = 13306857453590272717878730750852423/300647710720000
YAf [37] = 2164722601595650850848362172696226713/12627203850240000
YAf [38] = 16774664550817524161673512215584486443/25254407700480000
YAf [39] = 477262113535399194435026105269975711993/185198989803520000
YAf [40] = 11120590341143686154571438477327402330337/1111193938821120000
YAf [41] = 28839166931491529382428983749486577700097/740795959214080000
YAf [42] = 32090635982834134960773481913456909620933/211655988346880000
YAf [43] = 8764340440607734599435779413111102282291309/14815919184281600000
YAf [44] = 205400432775147542509623329152462427851128437/88895515105689600000
YAf [45] = 11250774754375618577033813002374564960827235001/1244537211479654400000
YAf [46] = 88116413168842675045091136211659390838957190539/2489074422959308800000
YAf [47] = 2994554650932865603884259946512890710545308879343/21571978332314009600000
YAf [48] = 23499904525123937142668715270141798603852576423789/43143956664628019200000
YAf [49] = 553751576177200297479764888496168218769419965775221/258863739987768115200000
YAf [50] = 65271209887096158858080442974343353026546682308773809/7765912199633043456000000
YAf [51] = 171051428871812802439422031220623029155352893366207953/5177274799755362304000000
YAf [52] = 4035520579884705844422054030731038945017749246641850233/31063648798532173824000000
YAf [53] = 31740442718875201046786660170327892978099812837068585931/62127297597064347648000000
YAf [54] = 5095911393747660757726554578504326193105058223499860049/2535808065186299904000000
YAf [55] = 1964195535899704057774935823745878049620862642258278670051/248509190388257390592000000
YAf [56] = 36058462351784387976108648263165236400041186105230000948949/1159709555145201156096000000
YAf [57] = 4254576158544538941454740883315096799648709833819512177453457/34791286654356034682880000000
YAf [58] = 3147023248250891270697338838408154285252570900972823378102381/6541951336716519342080000000
YAf [59] = 579238759099834681040807897968270273777292795757293345361069047/306163322558333105209344000000
YAf [60] = 22785290616384647131944282321315146900287185014888496293454066329/3061633225583331052093440000000
YAf [61] = 11948637858034284683214144870819030401723690541500355752682645797/408217763411110806945792000000
YAf [62] = 1410126472141323078367821544171288461814742600456225699726788866977/12246532902333324208373760000000
YAf [63] = 188592373989288711589044718377217164144502455398454802297245103375219/416382118679333023084707840000000
YAf [64] = 1060021528786312584736198288862282071113935549871146832062037544693883/594831598113332890121011200000000
YAf [65] = 15924852899890609669575580070096570568869823083844455534744457726378703/2271175192796361944098406400000000
YAf [66] = 153203411130398360172415917316751695156356186948096614266588946336975831/5551761582391106974462771200000000
YAf [67] = 1688493365915022256518138536393001372553378564264838943335466924142118759/15544932430695099528495759360000000
YAf [68] = 119662877789117253560281398269252859831832540390464355880470254652379966333/279808783752511791512923668480000000
YAf [69] = 40277077511295674890242285246727669354296885563193840541381004163649162631/23915280662607845428455014400000000
YAf [70] = 14625364224456917325731313995973983736588417337916584164673246056818670191941/2204554053807668660404853145600000000
YAf [71] = 32847927640632385729390709511801478485309761092276627050182920845240186794958803/1256595810670371136430766292992000000000
YAf [72] = 949417697928988165149120942717952538069722371064278243341821830590393831331407921/9215035944916055000492286148608000000000
YAf [73] = 82268162409146108396193035774746957480985227932212778610633342027927620167281481/202528262525627582428401893376000000000
YAf [74] = 177146132441466909527918618803440441205743243254399224798818076259409503154943452139/110580431338992660005907433783296000000000
YAf [75] = 1397692284506847204530339004468349837548362554912601873917688939143664065259290323937/221160862677985320011814867566592000000000
YAf [76] = 11030870485535393288662694838168237230199274687669865451760243956071063255356013416451/442321725355970640023629735133184000000000
YAf [77] = 957942869355273751053821371472349922162123639433155382222987166093238225382304803550403/9731077957831354080519854172930048000000000
YAf [78] = 264762839628453525434193328329612705293494090112055883625311672456128018493203998155438939/681175457048194785636389792105103360000000000
YAf [79] = 9463310702393604563207546051014783918608157927399750686128536763743236196209662459472229/6164483774191808014808957394616320000000000
YAf [80] = 4506564675329191113586792990490200751765272174248372897041434482250347941882696623807279403/743100498598030675239697955023749120000000000
YAf [81] = 130591160298162119628481701957077872108419151681030597139202751850822940719778960302028701689/5449403656385558285091118336840826880000000000
YAf [82] = 442410963058224758035588479086587676492474677279112196600180095822849610498205352381663524567/4670917419759049958649530003006423040000000000
YAf [83] = 24485677311202917527861498437171069703585463008156649390691607744079663715684317054451003771907/65392843876626699421093420042089922560000000000
YAf [84] = 7171600503721372131776554600365921661171487526838787875205532467957000452281022551556362273803/4843914361231607364525438521636290560000000000
YAf [85] = 7657746291952206875833063833905649025147753144747804063835945818199994980200853485943251212995143/1307856877532533988421868400841798451200000000000
YAf [86] = 60578503863503404601183994993999557393809434548500621431611708644875017940843167018688090894623093/2615713755065067976843736801683596902400000000000
YAf [87] = 408289994458893957849021354046211799370809206101770671681545947803918903410079025619352128145644939/4456401212333078775363403439905387315200000000000
YAf [88] = 87231331736948641178930769020588067158636107311203282927308669216115307729981829260220813756803010651/240645665465986253869623785754890915020800000000000
YAf [89] = 284261005560514819930952624298646755037027705868373621095889909374499804235418578526688743018231463911/198178783324929856127925470621674871193600000000000
YAf [90] = 1662940413079470966541631229805825586253582879890367171031164492757343629862039636395753160019599823779/292959940567287613406498521788562853068800000000000
YAf [91] = 100917565803230097769311394737985016922338467150924631226818542791012774368521843680160514544225693409349/4492052422031743405566310667424630413721600000000000
YAf [92] = 11188849699343714022215044643190501238539425711678329908835713940433780136924582885408958270898249137807/125827798936463400716143155950269759488000000000000
YAf [93] = 411103472004673409236460932690496475846642233612058884116073251421873963651967814106876235624438478369664237/1167933629728253285447240773530403907567616000000000000
YAf [94] = 33199529232758008724021019750519815926360481096571296722545913302570940156344615465621282870165101627237937473/23825846046456367023123711780020239714379366400000000000
YAf [95] = 3943079804784244732248102765348789682361530362496915528014993065691338316747215424847296428886661978292250729997/714775381393691010693711353400607191431380992000000000000
YAf [96] = 7632206983825809469546747156333371327196817794541637264689963877111145772433125507345758659775958267788724454817/349445742014693383005814439440296849144230707200000000000
YAf [97] = 2719728447166810027338207061948982417062686767362377860832475681385544121129097571076572941867305364166352945523911/31450116781322404470523299549626716422980763648000000000000
YAf [98] = 3076878224088375912859170560574378930751713622323288404183424024168269304034261172911446613207096232735461567367203/8985747651806401277292371299893347549423075328000000000000
YAf [99] = 121840073751932579073875563240240062006854855745284464331812303297287076938997925738301089302379661961221899206517677/89857476518064012772923712998933475494230753280000000000000
YAf [100] = 47284188427117305168945959367040548200504493925497526958985351503853915318495933436671766234786323791979880607442878263/8806032698770273251746523873895480598434613821440000000000000

YB

(text file)

YBf [0] = 0
YBf [1] = 0
YBf [2] = -6
YBf [3] = -9
YBf [4] = -27/2
YBf [5] = -273/4
YBf [6] = -1683/8
YBf [7] = -17625/16
YBf [8] = -129003/32
YBf [9] = -1017825/64
YBf [10] = -7087107/128
YBf [11] = -47478057/256
YBf [12] = -336619227/512
YBf [13] = -2254376625/1024
YBf [14] = -17059513971/2048
YBf [15] = -123488732793/4096
YBf [16] = -4838427982839/40960
YBf [17] = -7380064525953/16384
YBf [18] = -57770883900387/32768
YBf [19] = -2239670688173037/327680
YBf [20] = -3473248410754491/131072
YBf [21] = -134813431242794133/1310720
YBf [22] = -1036985484225404319/2621440
YBf [23] = -40092319525548379761/26214400
YBf [24] = -429145553255286580833/73400320
YBf [25] = -2359136161406040585273/104857600
YBf [26] = -125827754487348700317261/1468006400
YBf [27] = -193168239674263201459803/587202560
YBf [28] = -7361490748640084134005237/5872025600
YBf [29] = -56544743811283283147428287/11744051200
YBf [30] = -2163698419060924396307454033/117440512000
YBf [31] = -3335872075296684389214345591/46976204800
YBf [32] = -128484994139609817607852229913/469762048000
YBf [33] = -142209174301830260814024325437/134217728000
YBf [34] = -7722614431836718373890423274017/1879048192000
YBf [35] = -84181041143654004000431700715281/5261334937600
YBf [36] = -469251443432093744149423424244073/7516192768000
YBf [37] = -128362807993228142240675734661506609/526133493760000
YBf [38] = -40229277595019982884507228198041323/42090679500800
YBf [39] = -7878044761530659996840165808269900281/2104533975040000
YBf [40] = -680291610913451005410723100840323916857/46299747450880000
YBf [41] = -69264103298835126180445176871574925239/1202590842880000
YBf [42] = -41883260360576270163920968676470865353281/185198989803520000
YBf [43] = -29847744368800253262550576794616325878857/33672543600640000
YBf [44] = -12884620666151297289925614151363511572118701/3703979796070400000
YBf [45] = -20190049483484207071732337172881396362076923/1481591918428160000
YBf [46] = -5541396199427294105376899231814035447320317779/103711434289971200000
YBf [47] = -6199030559764577960374488565610827452720667103/29631838368563200000
YBf [48] = -4420264584141841435303201458068747931919447681199/5392994583078502400000
YBf [49] = -7985660566143710795338123072586346747373107183203/2489074422959308800000
YBf [50] = -271050118633480613941074412933597941457096950498279/21571978332314009600000
YBf [51] = -31833149773027569888895913867285035895125229582547707/647159349969420288000000
YBf [52] = -9974558903850159525912346744436878618586626395278777/51772747997553623040000
YBf [53] = -390690789763718468967823085829194089253851173963923639/517727479975536230400000
YBf [54] = -15310362840087686005323103150585049413452749743055464921/5177274799755362304000000
YBf [55] = -1600552835786288711906369751852942788885192691061665761/138060661326809661440000
YBf [56] = -44840287867471232337171316268639182330373103063627221149/986147580905783296000000
YBf [57] = -1326597355796229341424330797652160707803159633521777152611/7434035609905135616000000
YBf [58] = -290197900914118836538693105602694453275565869669479571747533/414181983980428984320000000
YBf [59] = -35119406317329981013495888692399218507995350602193684250723039/12756805106597212717056000000
YBf [60] = -9653691595418667491879403208150392705819910073151478996971071/892084273188616273920000000
YBf [61] = -3620334308182788162201580241793722203608367887733073122382857041/85045367377314751447040000000
YBf [62] = -222024282039971167407640693136122184194294211044856771233737593/1325382348737372749824000000
YBf [63] = -673237111052040946213133052633597569168919929219473811058201122891/1020544408527777017364480000000
YBf [64] = -270496399301172837303676632030166026703454424233843527936843921667891/104095529669833255771176960000000
YBf [65] = -29865653299989522072085151185883157961859126514240018060785195618777/2915841167222220049612800000000
YBf [66] = -1868176101586737107380800917314471972518059717641869282904995203317747/46264679853259224787189760000000
YBf [67] = -663233416092363161152519969244699939918563132959440359437075589678171589/4163821186793330230847078400000000
YBf [68] = -12210365782574384906388049802577572333629931594024390448445617690038340803/19431165538368874410619699200000000
YBf [69] = -1967076680519382072516012049485989569782169729726626960833427825033778361/793108797484443853494681600000000
YBf [70] = -65220274937253767286431819671987181498523238098922213373469478764798427259/6662113898869328369355325440000000
YBf [71] = -234351385717859755436588409357791967005378200132880732046519090649621782708919/6062523647971088816113346150400000000
YBf [72] = -58548252863923041748285284241599095756439651462405338307174000031884707960353/383576254783385572781064192000000000
YBf [73] = -2924000080255687332995922799076538064276683902690146108580467558107336583821731/4850018918376871052890676920320000000
YBf [74] = -10971509378414442056070431718179599746714801747845672420564491097332712428614989491/4607517972458027500246143074304000000000
YBf [75] = -86686812656545713932931411863428144756230540633233762096306415251167011213781937977/9215035944916055000492286148608000000000
YBf [76] = -684903978196782719642416045560883225958498136346285589148640870682714403965644397323/18430071889832110000984572297216000000000
YBf [77] = -1804057921130456029034596147931164311560829984963052648871268884969151047025875440747/12286714593221406667323048198144000000000
YBf [78] = -470434372995291379854931782551658904688067650719204909554334433870601003626375540119937/810923163152612840043321181077504000000000
YBf [79] = -35487584816566619736798262309265646789056845093753406995491320889343358578161110112890161/15481260387458972400827040729661440000000000
YBf [80] = -9793533892936579711046005183978777413738929436484879546985046821485794201620889651652931/1081230884203483786724428241436672000000000
YBf [81] = -2216518829652779969889238335215983917205821307337971519215749185270539345536370497218705657/61925041549835889603308162918645760000000000
YBf [82] = -192703313721443418585791590742193983149152152026955141595117064371311174675901388820387996473/1362350914096389571272779584210206720000000000
YBf [83] = -72530559302942916251232366345591674808455913606169099636685424780620609400917151656917926559/129747706104418054406931388972400640000000000
YBf [84] = -12039686230992217369414457729681467497967342653244086476677751555570823200613702208301081301313/5449403656385558285091118336840826880000000000
YBf [85] = -786553446900257381806982458442441840740340945976645264502437719881104342195348253370999937659/90072787708852203059357327881666560000000000
YBf [86] = -3762002099815055744667611972564323664510704484408996702866131682573250821784380792964463485724589/108988073127711165701822366736816537600000000000
YBf [87] = -1189704718706360854250972939251239300250157124067559488259229447074596412199008625038489443389439/8719045850216893256145789338945323008000000000
YBf [88] = -216359893416634002387363029746500194275485473751539167326606226543146652918027264802237834288930587/401076109109977089782706309591484858368000000000
YBf [89] = -11003739611243478760110390953288143311430673069419202373414576851328393785545599204357711847928903/5159198727938990092393958188725043200000000000
YBf [90] = -14350518626875509277809795826840483552622496339141949913287596749245281321846238020770143106046270809/1701535008345357350593299495236602429440000000000
YBf [91] = -2675379729040623691936552665270298658929370026016709669689491824493568847488606971428125695377363679889/80215221821995417956541261918296971673600000000000
YBf [92] = -148144224161249909800877018549554111967504600203386268947882079160820548829795027801273157364086144037509/1123013105507935851391577666856157603430400000000000
YBf [93] = -5859958521981203581543966251656985618427265642874810578181014529568995017172004609741044811398778499467051/11230131055079358513915776668561576034304000000000000
YBf [94] = -361663258261174523359370251672660186638818457523828614257464724177509988148081718071979037298934234276116251/175190044459237992817086116029560586135142400000000000
YBf [95] = -6237597676329500478935276783608416303257188072156464809340050120763177593837581665919809905218597878868767091/763648911745396378946272813462187170332672000000000000
YBf [96] = -113258417478591196966803431196980413176837644572318115305505872842637448489159095196307537818707717487743732607/3503800889184759856341722320591211722702848000000000000
YBf [97] = -33529476210739697911626495062337852220529141686358818354667195026432830523105213077839794982985189686073098490019/262084306511020037254360829580222636858173030400000000000
YBf [98] = -120661376367430791268092744759112678786772343187398186503199824007216527627053885911321965052663347317929060934823/238258460464563670231237117800202397143793664000000000000
YBf [99] = -10509325883320045111268976978484166085821657940083435695248795531515136311252418074619352117494775242962426618995303/5241686130220400745087216591604452737163460608000000000000
YBf [100] = -37830661266732973859439443448433608755821914049152939334512243739702065763391447156494843072647704543127406190617627/4765169209291273404624742356004047942875873280000000000000

XC

(text file)

XCf [0] = 1
XCf [1] = 0
XCf [2] = 0
XCf [3] = 8
XCf [4] = 0
XCf [5] = 0
XCf [6] = 64
XCf [7] = 0
XCf [8] = 768
XCf [9] = 512
XCf [10] = 6144
XCf [11] = 12288
XCf [12] = 45056
XCf [13] = 196608
XCf [14] = 393216
XCf [15] = 2654208
XCf [16] = 4718592
XCf [17] = 33030144
XCf [18] = 68943872
XCf [19] = 397934592
XCf [20] = 1050673152
XCf [21] = 4800380928
XCf [22] = 15728640000
XCf [23] = 59391344640
XCf [24] = 229109661696
XCf [25] = 764034416640
XCf [26] = 3263906709504
XCf [27] = 10247657750528
XCf [28] = 45825153564672
XCf [29] = 142455475273728
XCf [30] = 638592917438464
XCf [31] = 2032206725775360
XCf [32] = 8884642362949632
XCf [33] = 29462109850959872
XCf [34] = 123969454995406848
XCf [35] = 430859780421058560
XCf [36] = 1740392422753435648
XCf [37] = 6325582203816247296
XCf [38] = 24632380712420376576
XCf [39] = 92984237659818819584
XCf [40] = 351796434191744237568
XCf [41] = 1366971760887069671424
XCf [42] = 5070136306468869111808
XCf [43] = 20093052157837159956480
XCf [44] = 73694178674538190995456
XCf [45] = 295381181823610804764672
XCf [46] = 1079214921365269518483456
XCf [47] = 4344968576587287993778176
XCf [48] = 15905543723433036380897280
XCf [49] = 63988537367512878522826752
XCf [50] = 235645944330266741682733056
XCf [51] = 943972266918029222349897728
XCf [52] = 3505854392336302509303791616
XCf [53] = 13955613911692356226507603968
XCf [54] = 52332568717187721004496977920
XCf [55] = 206829923641845604960161497088
XCf [56] = 783237739876338399742720475136
XCf [57] = 3073573398136819298824666218496
XCf [58] = 11747116664641511871564214173696
XCf [59] = 45801873273284899340685636796416
XCf [60] = 176490788895853585718134651748352
XCf [61] = 684439804200209110307524508123136
XCf [62] = 2655555206234060350712697090736128
XCf [63] = 10255812975334527669737890592587776
XCf [64] = 40009323969452309685273570519810048
XCf [65] = 154075738079537167713231407004254208
XCf [66] = 603531000976199393709662176840515584
XCf [67] = 2320375920358602936004609023091408896
XCf [68] = 9114881526148994399544557338714177536
XCf [69] = 35023862880016151596201674582779756544
XCf [70] = 137819102394535915886844079425498120192
XCf [71] = 529748563264876359928399866957498679296
XCf [72] = 2086297217172119396054416255424252608512
XCf [73] = 8027774523361197746591557746415940665344
XCf [74] = 31619577575823480553786489347265020297216
XCf [75] = 121860792454858651848397307457452183126016
XCf [76] = 479793274990604622966558992903027696861184
XCf [77] = 1852705247244455337154759738498282728456192
XCf [78] = 7289099981190681227544159037034135212261376
XCf [79] = 28207171270962826049433361652814114755444736
XCf [80] = 110870489290645824595002380936480822151610368
XCf [81] = 430000235680586284613507862415535303041220608
XCf [82] = 1688408823693645182820524317643456590576091136
XCf [83] = 6562759475386142196034565518416379978708942848
XCf [84] = 25742615135481963726841890904379042788137762816
XCf [85] = 100270397183082262060541826141537641701337726976
XCf [86] = 392944887483656152664818907068719803600411295744
XCf [87] = 1533535072512998880366227808352564203885137231872
XCf [88] = 6004850286972572008389122236530787024311246913536
XCf [89] = 23475852363399809563642909442077001290401611513856
XCf [90] = 91864884497419073920491728956846290488148755480576
XCf [91] = 359693430059721023726523381963795113732265750822912
XCf [92] = 1406880127750115624707991171841842208562047224905728
XCf [93] = 5515793119155493948370942443848710345053208003477504
XCf [94] = 21567856264514744401003826365063041924238807935221760
XCf [95] = 84650964189953709303828090966913241892913171126026240
XCf [96] = 330963818043911544968125790468121923119060263299448832
XCf [97] = 1300142944541493783934299637016229237362700031528796160
XCf [98] = 5083451804107116594661724844989173898000342860865470464
XCf [99] = 19983629466395869453425379799005391316529543574802399232
XCf [100] = 78148855922121215697930627405727346898274787824030973952

YC

(text file)
YCf [0] = 1
YCf [1] = 0
YCf [2] = 0
YCf [3] = 4
YCf [4] = 12
YCf [5] = 18
YCf [6] = 283
YCf [7] = 369/2
YCf [8] = 11955/4
YCf [9] = 5945/8
YCf [10] = 511755/16
YCf [11] = 448833/32
YCf [12] = 28793891/64
YCf [13] = 54503817/128
YCf [14] = 1747429371/256
YCf [15] = 4022353425/512
YCf [16] = 102118840467/1024
YCf [17] = 1157453474877/10240
YCf [18] = 29083242124183/20480
YCf [19] = 60802336406373/40960
YCf [20] = 331148023590915/16384
YCf [21] = 3156038859210189/163840
YCf [22] = 95283216052051527/327680
YCf [23] = 33753550324241073/131072
YCf [24] = 27830890448144944443/6553600
YCf [25] = 334091660518914164919/91750400
YCf [26] = 11566366155102571579077/183500800
YCf [27] = 20085331436991480829487/367001600
YCf [28] = 696190225467708422175789/734003200
YCf [29] = 1258445562621870786461031/1468006400
YCf [30] = 42264036327290426130278101/2936012800
YCf [31] = 399527405451392390108786139/29360128000
YCf [32] = 1838616360630111137958494343/8388608000
YCf [33] = 5038121649743269838467744023/23488102400
YCf [34] = 783563577446501532147686040441/234881024000
YCf [35] = 312574207445598775207398664591/93952409600
YCf [36] = 333310123109708893331197938088071/6576668672000
YCf [37] = 667344836657152302324718037287989/13153337344000
YCf [38] = 101106314543024039322076951122573947/131533373440000
YCf [39] = 200923681613987669532988031620457873/263066746880000
YCf [40] = 6131295280119546828810420327773953811/526133493760000
YCf [41] = 18884992720121111327923980213152952021/1653562408960000
YCf [42] = 818921256694060963939612424057408478341/4629974745088000
YCf [43] = 7905429983317287609473989510232562433323/46299747450880000
YCf [44] = 249215714284075844133601865606532800720801/92599494901760000
YCf [45] = 2376172754800076240804515465674538421899343/925994949017600000
YCf [46] = 76102067709755311675970432531606145563342477/1851989898035200000
YCf [47] = 1008520146452179559907449543544798522542945201/25927858572492800000
YCf [48] = 97970005461729247384492063181785883850171269209/155567151434956800000
YCf [49] = 114656230468129532025586704854465831824895735411/192606949395660800000
YCf [50] = 78353318272540704479853197023110245870751097362413/8089491874617753600000
YCf [51] = 148669161082783776480864371400536752780882110167207/16178983749235507200000
YCf [52] = 24174689542291054214953532216843213038328654983009001/161789837492355072000000
YCf [53] = 46194665297243246962973065691160476349025337423194139/323579674984710144000000
YCf [54] = 498412620394286354201292275059237183701131530330735483/215719783323140096000000
YCf [55] = 576398951519425190763755775918675432293430611118383191/258863739987768115200000
YCf [56] = 30878771159974689442331649309963048512178656942198190099/862879133292560384000000
YCf [57] = 60032223736167950652105509964013629645662285046622510937/1725758266585120768000000
YCf [58] = 2681222252449861981321339463291156876964242463462787629257/4832123146438338150400000
YCf [59] = 393869788148285501276237133327218355157440511090772665732553/724818471965750722560000000
YCf [60] = 137285294433515741435298480382830756516710713971534480345607177/15946006383246515896320000000
YCf [61] = 12876704232769034972966792059162238371279883055342007772640591/1518667274594906275840000000
YCf [62] = 8523949201190239150980270032529714334702465160028678087971009681/63784025532986063585280000000
YCf [63] = 50548256122755716216833534309434377993173136576805167324431238201/382704153197916381511680000000
YCf [64] = 529399743232069213677530876325822323398017597688545216751719469913/255136102131944254341120000000
YCf [65] = 5939261469009810639888008468074872045969224175047161496454019624457/2891542490828701549199360000000
YCf [66] = 8386577740049966517702001604385404334720994412952452624939683716617887/260238824174583139427942400000000
YCf [67] = 790526040142498127505884638557798044192220912690571312621215624035273/24784649921388870421708800000000
YCf [68] = 2316348782697689854353501752268441976422616336363277862663860923378999/4626467985325922478718976000000
YCf [69] = 7210887797434316305826256536352750325225746774854938243453516756600120451/14573374153776655807964774400000000
YCf [70] = 9072513026431530124431500260125979125063104844528365884239888017255148817/1165869932302132464637181952000000
YCf [71] = 149080531473877607519446573061703938306138398021802916649876236106332947401/19431165538368874410619699200000000
YCf [72] = 183410038011571327688779882489900999193913775428448477942768462356472624283261/1515630911992772204028336537600000000
YCf [73] = 11420348551327809035394417820030663142858762869892215970862296622232793758127299/95989957759542239588461314048000000000
YCf [74] = 98592027332774055553180994712920509744620213008109946040819754656737258447976593/52358158777932130684615262208000000000
YCf [75] = 6199508310895343817512619866746149229407864023439807422708028672590322472011287/3358249251062702259654623232000000000
YCf [76] = 67551924177565105781613654161326363745969722650229992409389535029100251538008826067/2303758986229013750123071537152000000000
YCf [77] = 2935851038215751204937362378169112957521917388443795302516635771419423011670759069/102389288276845055561025401651200000000
YCf [78] = 12633017874392377535683511171029596664303239978808969531345491257002199866064464960129/27645107834748165001476858445824000000000
YCf [79] = 90410021834044420527686687763652647881390822199194945516934251076774444954398975487211/202730790788153210010830295269376000000000
YCf [80] = 303443623444661860265146874483430070311188786130759893484405536380677354719665087469498953/42573466065512174102274362006568960000000000
YCf [81] = 591494330739036195245713930091677078080769530457921200296950427558430020019134129901931067/85146932131024348204548724013137920000000000
YCf [82] = 574170411502911312262674313974871001940991242956720642590921055477614236637725560520533681/5160420129152990800275680243220480000000000
YCf [83] = 36914359643409969866511317019386708763399053895900181248200783567170580746414278507886763219/340587728524097392818194896052551680000000000
YCf [84] = 1184106469767570779789489497424632546873578888509531071742412317212999598918817708783335206297/681175457048194785636389792105103360000000000
YCf [85] = 2307412317926271647540122573655733620233972802866788726661314027156884492423795026996358937131/1362350914096389571272779584210206720000000000
YCf [86] = 74057443486968429451242394196351702333844992611131949711346685759915559019079209407986943559329/2724701828192779142545559168420413440000000000
YCf [87] = 26748065965630706520526895777387212502186733118304808845113904752104277536682242035760387847901/1009148825256584867609466358674227200000000000
YCf [88] = 7725247564018095444566386737154453863198142705632379855564675655174402230947758219416578869160751/18164678854618527616970394456136089600000000000
YCf [89] = 347034237158207002648296721925077000924834005101315709194985392516100837853586329500697312951955723/835575227312452270380638144982260121600000000000
YCf [90] = 1335375595089690975504223950649944076255702125469596907620708111727181124459700944628780414259902523/200538054554988544891353154795742429184000000000
YCf [91] = 457246731665320431676295098861926499099256011782064545950926551067233122284539072282455477053263292639/70188319094245990711973604178509850214400000000000
YCf [92] = 14644621081126054243160628773417718661291810800369652326128768495896889953915055653824627446219395626557/140376638188491981423947208357019700428800000000000
YCf [93] = 17226822140945658314856536587496446875776935376644286284890333739804508049843392924655472029009046674881/168451965826190377708736650028423640514560000000000
YCf [94] = 4591000156008093573923854945576929020249257894350744984046020092306311869592380259666123341052199680305913/2807532763769839628478944167140394008576000000000000
YCf [95] = 351750479681756851509996447246340766630884084996007660069250631967523984036538274718267784303114348204295533/218987555574047491021357645036950732668928000000000000
YCf [96] = 27275603909867011249336990037281621264594392440476753261901307655897786525001820723680604253649734456975145969/1063653841359659242103737133036617844391936000000000000
YCf [97] = 53688844565166824629585924977136903992524141533685824166911981630162903584890440309201694201409094652167095859/2127307682719318484207474266073235688783872000000000000
YCf [98] = 18827148872382947365655764748664940340159152788293638434797561947278981889772217380431838840520793825048408471283/46800769019825006652564433853611185153245184000000000000
YCf [99] = 259866818930810132000513803425976963858960781070900701178231317505259768708930071511735489030591674727513147373519/655210766277550093135902073950556592145432576000000000000
YCf [100] = 8272638558558583386363970682335956456266723003763318854442080075780419449633976033213202580044090509091522214558989/1310421532555100186271804147901113184290865152000000000000

XG

(text file)
XGf [0] = 0
XGf [1] = 0
XGf [2] = 15
XGf [3] = 45
XGf [4] = 39
XGf [5] = 597
XGf [6] = 2331
XGf [7] = 6021
XGf [8] = 34347
XGf [9] = 101205
XGf [10] = 458859
XGf [11] = 1886037
XGf [12] = 6614187
XGf [13] = 30753621
XGf [14] = 105935787
XGf [15] = 465035349
XGf [16] = 1756681131
XGf [17] = 7021144149
XGf [18] = 28722620331
XGf [19] = 109097498709
XGf [20] = 459407325099
XGf [21] = 1737335736405
XGf [22] = 7249656297387
XGf [23] = 27964620769365
XGf [24] = 113967784818603
XGf [25] = 450517520844885
XGf [26] = 1795874432972715
XGf [27] = 7233402454968405
XGf [28] = 28439597977139115
XGf [29] = 115653721282611285
XGf [30] = 452650204566353835
XGf [31] = 1843010845444966485
XGf [32] = 7231729701251676075
XGf [33] = 29313268799550556245
XGf [34] = 115776403558136510379
XGf [35] = 466000022205966092373
XGf [36] = 1854526530861500692395
XGf [37] = 7412606176702429694037
XGf [38] = 29691330340839432877995
XGf [39] = 118058780841920369297493
XGf [40] = 474890725546388898150315
XGf [41] = 1883010136648817179658325
XGf [42] = 7587543283636375100815275
XGf [43] = 30072589722204445138258005
XGf [44] = 121129827906746480718739371
XGf [45] = 480734298684635551815993429
XGf [46] = 1932846597869436407625250731
XGf [47] = 7689218761923982707015059541
XGf [48] = 30838727570006300470619895723
XGf [49] = 123011578995373895137833814101
XGf [50] = 492123832638540792538559641515
XGf [51] = 1967799345180651764042067642453
XGf [52] = 7856199938002678949336796067755
XGf [53] = 31471573746292060954882830534741
XGf [54] = 125471967258891739656017162500011
XGf [55] = 503191957555151527575018564257877
XGf [56] = 2004820063936089818734625571174315
XGf [57] = 8043290794190200218832042536765525
XGf [58] = 32045831898968825780624043165054891
XGf [59] = 128542360136207377998514958261848149
XGf [60] = 512382983290031012813543545052821419
XGf [61] = 2054035231831381171982210665182955605
XGf [62] = 8194096872513045611632775973677529003
XGf [63] = 32821299355657785660300653287136331861
XGf [64] = 131054169543528992556428564743759820715
XGf [65] = 524471343266733871193313865617696131157
XGf [66] = 2096100131756900033695943210813200758699
XGf [67] = 8381648112100149343596285827272853719125
XGf [68] = 33524498478595845663921420616780967016363
XGf [69] = 133965569032639808306403207994367096686677
XGf [70] = 536152850172146615237102609440684667533227
XGf [71] = 2141504979961521944590457387209431822927957
XGf [72] = 8574049480560229225663383385155327185876907
XGf [73] = 34237832262721487118626568610948182811117653
XGf [74] = 137105689428109484159901065486218055672362923
XGf [75] = 547455597324177437377657977962162480685811797
XGf [76] = 2192311822533841903223072464633919228163880875
XGf [77] = 8754637080310080141121984061548807402446424149
XGf [78] = 35053719673664548853552539439160515034506819499
XGf [79] = 140011511272932940201293784453058288138548447317
XGf [80] = 560478893111223173902115965655644946249006675883
XGf [81] = 2239315850340922104053824563682992990715547519061
XGf [82] = 8961608293196896344901153846470830480807652456363
XGf [83] = 35816530304330715479493665805554166200035258173525
XGf [84] = 143291799970532998643667955163653133324057902544811
XGf [85] = 572875449735522962090249792938295174121935771568213
XGf [86] = 2291242570692559749994871306127692004695720201254827
XGf [87] = 9163032210400931665894964681284754726732251285981269
XGf [88] = 36638623071677044282015121942847239127814881293596587
XGf [89] = 146560221678565895636277781673634641665805235257378901
XGf [90] = 585905915438392700072013021553761195735842347550734251
XGf [91] = 2344165349122002549996866621057404543922034889197652053
XGf [92] = 9369967458667177720681089104948361553473489476331206571
XGf [93] = 37493367858864185871093976079931341607895570133781874773
XGf [94] = 149854313369788113480217193760914067127581058706519848875
XGf [95] = 599673479471567561768122220048070475149916761573390583893
XGf [96] = 2396734207762113625448765363281422182553835867062193321899
XGf [97] = 9591144752363406257290336055677555643217331280516334258261
XGf [98] = 38334318304451386756568809762679501973434340284498934986667
XGf [99] = 153399141598860267687768381500776625269418927474933197998165
XGf [100] = 613154916679890080195752167336036456452827674648770766665643

YG

(text file)
YGf [0] = 0
YGf [1] = 0
YGf [2] = 0
YGf [3] = 0
YGf [4] = 32
YGf [5] = 108
YGf [6] = 162
YGf [7] = 531
YGf [8] = 1305/2
YGf [9] = 2475/4
YGf [10] = 81697/8
YGf [11] = 936387/16
YGf [12] = 10661481/32
YGf [13] = 99781275/64
YGf [14] = 787046897/128
YGf [15] = 6051117107/256
YGf [16] = 43421057977/512
YGf [17] = 299806705803/1024
YGf [18] = 10650782280901/10240
YGf [19] = 71434718218287/20480
YGf [20] = 512399400653357/40960
YGf [21] = 711399106009467/16384
YGf [22] = 25984470524554453/163840
YGf [23] = 193843182694747743/327680
YGf [24] = 293464365531640153/131072
YGf [25] = 58503384714877890419/6553600
YGf [26] = 3224766407204240517711/91750400
YGf [27] = 5297076639130818265321/36700160
YGf [28] = 213194267151245578664583/367001600
YGf [29] = 1744710855338599499385397/734003200
YGf [30] = 14060977874575839984609919/1468006400
YGf [31] = 113001271021881031746606877/2936012800
YGf [32] = 4501934108481439129501387027/29360128000
YGf [33] = 35464515712560127111151209049/58720256000
YGf [34] = 39739773497628062405305058173/16777216000
YGf [35] = 307989766651037091468302946647/33554432000
YGf [36] = 50002274202699141086272670652809/1409286144000
YGf [37] = 894526886984390665194717606085279/6576668672000
YGf [38] = 20540066156529455734102567395230327/39460012032000
YGf [39] = 783633509452981627524489814455733273/394600120320000
YGf [40] = 1991600593937742997093680833867339577/263066746880000
YGf [41] = 45629750745420362712593456864539736353/1578400481280000
YGf [42] = 548033582433420644026663791798512180567/4960687226880000
YGf [43] = 1402804827451729369285379861489269899319/3307124817920000
YGf [44] = 20619086861982565499204653198185943187611/12627203850240000
YGf [45] = 159650671786991267438457008316495756903409/25254407700480000
YGf [46] = 68264684634228194643307411752974541184105717/2777984847052800000
YGf [47] = 177751118045543721296057835835839415961912213/1851989898035200000
YGf [48] = 9764500708939927911860237500302788925046798937/25927858572492800000
YGf [49] = 230555969823941172334980370385137758311666514241/155567151434956800000
YGf [50] = 23689450064276668431214434424514238900141145132487/4044745937308876800000
YGf [51] = 562248044284238214933229175960409112592634729739231/24268475623853260800000
YGf [52] = 1487410551898400214304316748900694071295380804265919/16178983749235507200000
YGf [53] = 176981287664051701787426554292197221564083817831671539/485369512477065216000000
YGf [54] = 1406481426634589840119561134957016903785419837668300793/970739024954130432000000
YGf [55] = 11162928971318099367768401990674081409841109112346729803/1941478049908260864000000
YGf [56] = 1611821181690097720188331504475984661849040461410580871/70599201814845849600000
YGf [57] = 63904665068835074002850351300246263451030312069452776457/705992018148458496000000
YGf [58] = 5571788316030849504858769012879234565135012677675541000777/15531824399266086912000000
YGf [59] = 12349117714470427154998903928069597247261554969075803628581/8697821663589008670720000
YGf [60] = 12205754178461065360433358185166365122588438427641816903782547/2174455415897252167680000000
YGf [61] = 151509570320325822194011281801634091759986544857607641541390677/6834002735677078241280000000
YGf [62] = 66927137403039060451200721827492128870468220010659920030374861/765408306395832763023360000
YGf [63] = 65950036511504399648041480141657114975638913778903093506017983147/191352076598958190755840000000
YGf [64] = 10594977978229451753016146811025418328765631753051346355283995377/7810288840773803704320000000
YGf [65] = 4085607323333065116641397983132859594642489757115192048672369315011/765408306395832763023360000000
YGf [66] = 1637750727477587206650061987736878400976947510368689348378329043618283/78071647252374941828382720000000
YGf [67] = 21454500238874901210483237420687494835902579319480365908052843820751991/260238824174583139427942400000000
YGf [68] = 1392390832863684218466810146397058933969808353336855433234302091184877/4301468168174927924428800000000
YGf [69] = 567139649934901976938628659931585753922195584922618953433770100389198987/446123698584999667590758400000000
YGf [70] = 6611119813511968828708408380927173699349314982506254776002983952957377489/1324852195797877800724070400000000
YGf [71] = 571122021785300787055647689474962432885186960549094284076722201035037838353/29146748307553311615929548800000000
YGf [72] = 13454632788580131727866291117986058340769947638230290475300758019412766820281/174880489845319869695577292800000000
YGf [73] = 458058694219328881971952974265287184240016976012253018307978361356648865782021/1515630911992772204028336537600000000
YGf [74] = 37996754690913363882676564786456489133691639047966034483056010283461438995622249/31996652586514079862820438016000000000
YGf [75] = 8066642903871083713954028073375795223088729150318249546564722226962215801905064281/1727819239671760312592303652864000000000
YGf [76] = 3340095188106759135176903816545150556720125812536803564400108352953563850247942217/181875709439132664483400384512000000000
YGf [77] = 26292834141961976741659622123064830270830377511720489497958677722001690714527450171/363751418878265328966800769024000000000
YGf [78] = 1311780408134964556844581921231614581387602715523871832856401002838378392978202420353/4607517972458027500246143074304000000000
YGf [79] = 31019991127290297529335049403523806298018776608856939898437342476608286260403569893801/27645107834748165001476858445824000000000
YGf [80] = 897256278583586370700677391330871590219525185157838621854018343576339227891033333240483/202730790788153210010830295269376000000000
YGf [81] = 2230977446407719843545848333869153041631702524264556372368672994769715329933573022783052307/127720398196536522306823086019706880000000000
YGf [82] = 34354396788692969463407724549081181150211143715681870426643769012483457525485564918164313/497935275620025428096776163819520000000000
YGf [83] = 139300784554332904244877067679849454849285374795858687090004487080968076454771711886163865963/510881592786146089227292344078827520000000000
YGf [84] = 8284277163119781021126865918120785680355437701663496217723184490286843011232743830838077741/7682429966708963747778832241786880000000000
YGf [85] = 322937087870531473021280276858448219895561224598122327209375021774682834212462642743106986681/75686161894243865070709976900567040000000000
YGf [86] = 69039778328956197881869045954604464041017426261482376778253150016526394593192155864415853172137/4087052742289168713818338752630620160000000000
YGf [87] = 546895086699632352281953662854111911179225843841070879757611525777662867754191536535649133672539/8174105484578337427636677505261240320000000000
YGf [88] = 218887385707945424320414313213183561862737885019464049758491225269870509313049445878245043311047/825667220664478528044108838915276800000000000
YGf [89] = 15616732994364261008456385756256340257866136839788678782774519283160645629835978573384275301631901/14862009971960613504793959100474982400000000000
YGf [90] = 31329276687413244538106910033938846628810152365239490718504579323522331375238599113694128375389288923/7520177045812070433425743304840341094400000000000
YGf [91] = 49695907028102673408311158205195958334263748889035011764286316132933519523277858446843828237819024573/3008070818324828173370297321936136437760000000000
YGf [92] = 811587130926530348050625440967162186275148804911775606595146180051840861904924649595077170373620092117/12386173957808116007995341913854679449600000000000
YGf [93] = 109455255035079034665378687603954285079194292756127905605828816924680651482922179092083229429895888819279/421129914565475944271841625071059101286400000000000
YGf [94] = 173671163032666996422807030953309094996031800049427024575548844996511142824010066823536292004723638445801/168451965826190377708736650028423640514560000000000
YGf [95] = 3827401837562463436731467679007290977424098006764566633177727455252557147319647324228920275964210276000843/935844254589946542826314722380131336192000000000000
YGf [96] = 50993922589581899229897297151365284248491987871959820479921721031135928717938085512941382259279490793933359/3143362041732739105569726962252881330176000000000000
YGf [97] = 31940333838456399559265488098248763818771632569532482508730353199618063104239461934064028046065461739540940257/496371792634507646315077328750421660716236800000000000
YGf [98] = 11401022370461778183606811366622692951354872201587654613368570867170146966558507900596072961951531388806658213511/44673461337105688168356959587537949464461312000000000000
YGf [99] = 994690948563893176110765752482498594030203441094031869050728570157341674629319403628954348396871417349063279213639/982816149416325139703853110925834888218148864000000000000
YGf [100] = 7888303594336695469640120839338751286654241351541262627447250407145351748834179401965744533359809769196381357176693/1965632298832650279407706221851669776436297728000000000000

YH

(text file)
YHf [0] = 0
YHf [1] = 0
YHf [2] = 0
YHf [3] = 10
YHf [4] = 0
YHf [5] = 0
YHf [6] = -96
YHf [7] = 216
YHf [8] = 324
YHf [9] = 7078
YHf [10] = 14969
YHf [11] = 196299/2
YHf [12] = 467073/4
YHf [13] = 7965155/8
YHf [14] = 2300617/16
YHf [15] = 343897019/32
YHf [16] = -270726831/64
YHf [17] = 19161182803/128
YHf [18] = -1671643623/256
YHf [19] = 6172066351703/2560
YHf [20] = 6568584505253/5120
YHf [21] = 405484533959887/10240
YHf [22] = 751445308824589/20480
YHf [23] = 5183507988231835/8192
YHf [24] = 57736806168001973/81920
YHf [25] = 1589232587791750399/163840
YHf [26] = 18152427038719975697/1638400
YHf [27] = 3276060404306224737029/22937600
YHf [28] = 6966976335779511376623/45875200
YHf [29] = 187601950959488572265069/91750400
YHf [30] = 49593275805779010871009/26214400
YHf [31] = 425599802712284785780317/14680064
YHf [32] = 2358773204406962237178921/104857600
YHf [33] = 3046063016610753929442301681/7340032000
YHf [34] = 4033563168790314425048282931/14680064000
YHf [35] = 107122421814314090627766198383/17616076800
YHf [36] = 220286893705818594522196279179/58720256000
YHf [37] = 32287022961134738756688199667779/352321536000
YHf [38] = 291679372212811469370956129631583/4932501504000
YHf [39] = 4650114860036643443059822286987583/3288334336000
YHf [40] = 101068468960689888017026061506998899/98650030080000
YHf [41] = 4367390837154079500712468909652167289/197300060160000
YHf [42] = 1024787184669235592976723859024837661/56371445760000
YHf [43] = 431720949859808442429966106362866573149/1240171806720000
YHf [44] = 5491498250436227513897508126036487089857/17362405294080000
YHf [45] = 37927765461036200331246070575124614242951/6944962117632000
YHf [46] = 17551697618672318951828920749890708858917/3307124817920000
YHf [47] = 19709253466447593682483103711823658906862797/231498737254400000
YHf [48] = 119062967078400307778736117267033805498857941/1388992423526400000
YHf [49] = 25619524172970682145105224645780894119953077657/19445893929369600000
YHf [50] = 2839320155861098764920563573728345875732550407/2121370246840320000
YHf [51] = 20479718932755216219932857343320987305804732964397/1011186484327219200000
YHf [52] = 123435722537824602400103055491208108910836273605173/6067118905963315200000
YHf [53] = 3760065934752996897331216449569522626955038463117951/12134237811926630400000
YHf [54] = 36827471370052056403651043230275076341717646775047057/121342378119266304000000
YHf [55] = 1147789331962664152364665820525698416492528225294231827/242684756238532608000000
YHf [56] = 2174917022150594559536674120281841553722051149417572953/485369512477065216000000
YHf [57] = 70064536150180739498224065968362063337487293661181753451/970739024954130432000000
YHf [58] = 25635727161821509323132617543826151747276695844987641517/388295609981652172800000
YHf [59] = 1428208480756949942636731059442437341080075160748986994049/1294318699938840576000000
YHf [60] = 53162438043024112547192412971972033222458514974472491033247/54361385397431304192000000
YHf [61] = 9199806870352585060905026992451201290185589195765737051093361/543613853974313041920000000
YHf [62] = 1924985492739024517406444375968486453082284202081432193500131/131423129532251504640000000
YHf [63] = 6232970023680741138083686266484558877433209864286703900865732467/23919009574869773844480000000
YHf [64] = 10647624822904734611991261511003177849164016135657834991196156281/47838019149739547688960000000
YHf [65] = 1156545272305236882650422797213339160022549858608165785824508751201/287028114898437286133760000000
YHf [66] = 14603236243042185827000191918721322728443418965446489573054310181/4252268368865737572352000000
YHf [67] = 3363343178727376467650038107524692033750670350127210807768241212651/53768352102186599055360000000
YHf [68] = 10485399127037088896651877215219342356848712839150902092202331248657719/195179118130937354570956800000000
YHf [69] = 126785892830822635119972167955856273863014029763065716434352173326771223/130119412087291569713971200000000
YHf [70] = 44211539224698030776904087692263546065803051003990661990843236793245537/52047764834916627885588480000000
YHf [71] = 12795297163258841136540240629064527198785414871008728662178112757240972519/840771585794807065844121600000000
YHf [72] = 26880497411075563652834628348799494040252190918971282073448091806863021459/1987278293696816701086105600000000
YHf [73] = 3470503196104587945106049073262481896565980288083493343406453875662460133233/14573374153776655807964774400000000
YHf [74] = 22335287958393612418508714862995381102707860233439432921597018637311669654511/103338471272234468456477491200000000
YHf [75] = 805733981769285134754727593682282099434329237021826966445132629125289556776164849/215977404958970039074037956608000000000
YHf [76] = 1492462220875482402995612433405283780011762291439734976439902288354680779342015539/431954809917940078148075913216000000000
YHf [77] = 16838045753205602426793140304843971548591246677288777126480036771676958975574559379/287969873278626718765383942144000000000
YHf [78] = 31751292394015917149281019584872683832947563675186124118543374241516500703206792921/575939746557253437530767884288000000000
YHf [79] = 351869131003908140475589905123032723868098755810932577404267627761714242981101355513/383959831038168958353845256192000000000
YHf [80] = 519309198363116422021124579749472695266763304710355813315068511018591007235318998403/592395167887460678603075538124800000000
YHf [81] = 16413835132805656816008607557508575956737670771348440563461278409504348431952901595079/1143218745045976748181373845504000000000
YHf [82] = 443177070730747875436948736289197444149510573910889573622134605701596646115802214163902961/31930099549134130576705771504926720000000000
YHf [83] = 14356241220196457272289733301541315084770944198303426127426011837667339098511617526373673011/63860199098268261153411543009853440000000000
YHf [84] = 282204798014492886408763077393441315560103172954374101937008304711904132767752235874828339/1290105032288247700068920060805120000000000
YHf [85] = 179710389679150103617944240317886343792074687308291902339298855034077646070646044413607988047/51088159278614608922729234407882752000000000
YHf [86] = 1753415396071962237696328147947412677305324287119326135067633272068375641045685982798448616897/510881592786146089227292344078827520000000000
YHf [87] = 56205118072875751766613118957760870976312412442566310645376837293736887667277722571164475011491/1021763185572292178454584688157655040000000000
YHf [88] = 109608732312153732552135959828853774163256954483277711227689568585792129396209824567920651811337/2043526371144584356909169376315310080000000000
YHf [89] = 836652552648357963683836618844467773649708279068307801678792861377404396376751146776161255429259/973107795783135408051985417293004800000000000
YHf [90] = 1797282781099898405912499603503288008216619682261527566277484148112165121281082284014370994486391/2151080390678509849378073027700326400000000000
YHf [91] = 25256824214465846817813502952608049720718893377285056539021062536099614801843994428520668603795053193/1880044261453017608356435826210085273600000000000
YHf [92] = 4438571157533026178786204306472540591934432565497268691637471346775182201404725502296376142282634961/341826229355094110610261059310924595200000000000
YHf [93] = 1660274373739128871009005597297634977203831905616699512342098180335102531254567997468260479936604297/7910028447886475286849016248517263360000000000
YHf [94] = 7072233958959938443908283368256629158197710113542045017017571950711027759789569493964074393986138597463/35094159547122995355986802089254925107200000000000
YHf [95] = 2071885920459979433081404922295059892049202083773331790089873181943802098978870371976170629524654718537421/631694871848213916407762437606588651929600000000000
YHf [96] = 387233600057740447284816062817653304102442776311695782277852840104907486331741602114929347034438787563793/123861739578081160079953419138546794496000000000000
YHf [97] = 1202981836457846210997841849339649840163427591358907754629195860800935466600137073699346206854152883665823587/23462952382933659752288319111101864214528000000000000
YHf [98] = 11781688622062780518658414937429792649159764794551947739862992646091088681021519683250763417535970212954300137/242790550745139609610635649932271464480768000000000000
YHf [99] = 8956298679364057120759248158519343611533299440384618123201543757365001697957552901521466763468091631216410023533/11168365334276422042089239896884487366115328000000000000
YHf [100] = 14254498086343600977014455891291955342586608291527388546577420100867001778511138431781793563266382304945406639137/18900310565698560378920252133189132465733632000000000000

XM

(text file)
XMf [0] = 1
XMf [1] = 0
XMf [2] = 0
XMf [3] = 40
XMf [4] = 60
XMf [5] = -204
XMf [6] = 1372
XMf [7] = 3636
XMf [8] = 48828/5
XMf [9] = 328004/5
XMf [10] = 468732/5
XMf [11] = 4368132/5
XMf [12] = 12182524/5
XMf [13] = 53377284/5
XMf [14] = 51503052
XMf [15] = 148527156
XMf [16] = 842681292
XMf [17] = 12240631044/5
XMf [18] = 61553875708/5
XMf [19] = 213496444164/5
XMf [20] = 178040249292
XMf [21] = 3642572010756/5
XMf [22] = 2681861364684
XMf [23] = 59770549286148/5
XMf [24] = 42272172792780
XMf [25] = 190182905160756
XMf [26] = 3425457937206012/5
XMf [27] = 14866444660356356/5
XMf [28] = 56041325367544572/5
XMf [29] = 46245534451967028
XMf [30] = 914833757385935612/5
XMf [31] = 3610457558890427652/5
XMf [32] = 14822254221674826492/5
XMf [33] = 56869548117751084292/5
XMf [34] = 47618362060374203340
XMf [35] = 904385525031929230596/5
XMf [36] = 3796711019817307884284/5
XMf [37] = 14491449994092017726724/5
XMf [38] = 60253361299532117592828/5
XMf [39] = 233210961006569730979076/5
XMf [40] = 954225193658976226921212/5
XMf [41] = 3757587138986748399957252/5
XMf [42] = 15116017244269991213550332/5
XMf [43] = 60479236013230829320385796/5
XMf [44] = 239907024351820572683291388/5
XMf [45] = 194239156692882351682036788
XMf [46] = 3817740634257114578390764284/5
XMf [47] = 3110980570628636438846317620
XMf [48] = 60918229382479693196765317884/5
XMf [49] = 248551807108627397096998810884/5
XMf [50] = 194846585580408320185617537996
XMf [51] = 3964921203150828795661797405956/5
XMf [52] = 3120821698445987419778882132940
XMf [53] = 63189846041043776043444771337476/5
XMf [54] = 250118175684525015732090639371004/5
XMf [55] = 1006834798988616141620990830032132/5
XMf [56] = 4009579779822969821924494425869052/5
XMf [57] = 16047369143262810266714381170095364/5
XMf [58] = 64253467748438125612944892613774076/5
XMf [59] = 255939347171956421860247272684107012/5
XMf [60] = 1029013635438041848255315727107902204/5
XMf [61] = 4085349297819079217159696386833888516/5
XMf [62] = 3293526137319115889111906927262751692
XMf [63] = 65265585203656594804471905874717816068/5
XMf [64] = 263355703664860680185623432519201737468/5
XMf [65] = 1043418672166973549561729257735715403012/5
XMf [66] = 4209296250761244381186781641591414475516/5
XMf [67] = 16690963325594846702780176641437081384196/5
XMf [68] = 13450356425843411531498207588638767373260
XMf [69] = 267098723551325344744421092308372133885188/5
XMf [70] = 1074241908273933883560220580611028355009276/5
XMf [71] = 855031359622030750521885989942147587318836
XMf [72] = 17158305676124107320919975582444133360749308/5
XMf [73] = 13686286809042509363664119640783437530735668
XMf [74] = 54816077058954498267861354722066768744602572
XMf [75] = 1095296333798396071188591971413901485036647684/5
XMf [76] = 4378791579682019899226847145057785956323969788/5
XMf [77] = 17528535344486493913225622262722716003283350788/5
XMf [78] = 69972738286023394686366144350247970288786885372/5
XMf [79] = 280465022870012873430941165642408719973891028228/5
XMf [80] = 1118440180884634707493832998856280291017479310076/5
XMf [81] = 4486680002083410254812714352721011078183707587844/5
XMf [82] = 17881544471314286526704201812736274274309834689276/5
XMf [83] = 71761126321763357715399840283007449074067994948868/5
XMf [84] = 285953765158464754195891687172957109867294034905852/5
XMf [85] = 1147579605670897489036024817267750436944033012626692/5
XMf [86] = 4573718067526861443185237118606978874047734773861116/5
XMf [87] = 18349400484347301307028805430818590828473522552681732/5
XMf [88] = 73165584964721907009766406540322738818418992362179324/5
XMf [89] = 293375904614359041875148337669216180529422613755835652/5
XMf [90] = 1170545963701821743865777661917146463750876164554902268/5
XMf [91] = 4690385351021511751683385806221286235425614231883068676/5
XMf [92] = 18728176612326164537037552598968638845511635510953921276/5
XMf [93] = 74987808122693015717037145955827883227403333929752179972/5
XMf [94] = 299648007686083250309853871076528820149036227414275279612/5
XMf [95] = 1198905298905851292505992556620566275736780690799639246084/5
XMf [96] = 4794271893647251022005356086701565458887733242546292673276/5
XMf [97] = 19169118233722137018447794696519739335528597177131627820292/5
XMf [98] = 76704205908200206543930340412825358077500376557373705571068/5
XMf [99] = 61302765826080375458423778172723874316630891576347684316212
XMf [100] = 1227140398755622124574475023886986052264067703947580371520252/5

YM

(text file)
YMf [0] = 1
YMf [1] = 0
YMf [2] = 0
YMf [3] = -20
YMf [4] = 0
YMf [5] = 256
YMf [6] = 640
YMf [7] = 0
YMf [8] = 10496/5
YMf [9] = -61696/5
YMf [10] = -168384/5
YMf [11] = -640672/5
YMf [12] = -70960
YMf [13] = 244248/5
YMf [14] = 7070292
YMf [15] = 82081846/5
YMf [16] = 690605681/5
YMf [17] = 524270679/2
YMf [18] = 33943663673/20
YMf [19] = 104683588107/40
YMf [20] = 1349441284673/80
YMf [21] = 11015452470191/800
YMf [22] = 236139299835053/1600
YMf [23] = -358352104923417/3200
YMf [24] = 1679027382853393/1280
YMf [25] = -53093209771062817/12800
YMf [26] = 430844881181686077/25600
YMf [27] = -3068287776837723497/51200
YMf [28] = 171684977676450853369/512000
YMf [29] = -3050171068452283732211/7168000
YMf [30] = 104379399003066171173383/14336000
YMf [31] = 99157545178663840393397/28672000
YMf [32] = 8300427031904878122890751/57344000
YMf [33] = 21425322042015650564917661/114688000
YMf [34] = 592442329501996395890929591/229376000
YMf [35] = 9453405900958198211128855257/2293760000
YMf [36] = 192609850995151364063408343531/4587520000
YMf [37] = 269009742521557872851263896197/3932160000
YMf [38] = 11621929487634854699252164535811/18350080000
YMf [39] = 2986745080877829057647343301321/3145728000
YMf [40] = 4638701958191600154914484513754621/513802240000
YMf [41] = 11649116525766943437648544557965527/1027604480000
YMf [42] = 1274143916555329009161078167563732921/10276044800000
YMf [43] = 2380606318341039471488142092725228683/20552089600000
YMf [44] = 68970612922523893425933847498160355777/41104179200000
YMf [45] = 125797415580446746391227083228448999351/129184563200000
YMf [46] = 124525530487535621370758712801752657227561/5425751654400000
YMf [47] = 66003270223557134572220332080576443356379/10851503308800000
YMf [48] = 7052731047303234588230516161984246305708209/21703006617600000
YMf [49] = 5149393846025017688638038147715217039373887/217030066176000000
YMf [50] = 42799232756334763246845689884279237328537069/8858370048000000
YMf [51] = 333561468966211788950454671192418969048584077/1215368370585600000
YMf [52] = 2747351668389482594223036112969695200729060424937/36461051117568000000
YMf [53] = 4693522291127259922365465465870343495080123267701/315995776352256000000
YMf [54] = 209630300077371116869653741374692209806164189307479/172361332555776000000
YMf [55] = 30849101314826535761488390513288157635362394455593/60189671686144000000
YMf [56] = 68834565247787878857807443269701938722156406473914379/3447226651115520000000
YMf [57] = 110403373242838958615899869712945575880700472711812403/8426554036060160000000
YMf [58] = 5539026067246631643698832965070801196743999432424831673/16853108072120320000000
YMf [59] = 5694455691264309116395614903632708864654056328826361069/20223729686544384000000
YMf [60] = 1086533742107075784592569158231144471403302405287096438339/202237296865443840000000
YMf [61] = 6560657689790375436347469551640752476885687191693408658363/1213423781192663040000000
YMf [62] = 1474499748586547893738707141411258714013142638093195158909239/16987932936697282560000000
YMf [63] = 5427401121553524067862982295215324099693448305805937793552499/56626443122324275200000000
YMf [64] = 1723504286563104760377909630300193654671260966731940534541127987/1245781748691134054400000000
YMf [65] = 3985293299154451395254961292855592200767529399268685360427544249/2491563497382268108800000000
YMf [66] = 325317436188975786667551184545140870267833024140894803373036567713/14949380984293608652800000000
YMf [67] = 2282905100149116102239225204513092940646962267569525724957535674057/89696285905761651916800000000
YMf [68] = 20227348717803083645423454658486321988514698539574615837483866488809/59797523937174434611200000000
YMf [69] = 792215560039802399887983175192088017445245024292641102470550208348363/2033115813863930776780800000000
YMf [70] = 11762886574353469999982491053706813047602742876371678257840850394436509/2259017570959923085312000000000
YMf [71] = 235065780117154617379852216225577983923570671531308144670543396414471023/40662316277278615535616000000000
YMf [72] = 719057486059747793695392935984278179677149617426094545376770710614504901/9036070283839692341248000000000
YMf [73] = 21977857687987875913664309120050374036428539988687048488102430885914890431/262741120560877208076288000000000
YMf [74] = 551331495472833798726276337138742987036574974259982457713077892644957862711/455417942305520493998899200000000
YMf [75] = 492008449466945396732501906097958008553156283871294981957246180580671291563/414016311186836812726272000000000
YMf [76] = 6530653118931040091668445741678390666485166700413768122549038040025725384063309/355225994998305985319141376000000000
YMf [77] = 161057448155507595868217154631526147144183022873862950422615726639989065776041759/9641848435668305315805265920000000000
YMf [78] = 37719985372950054230386392954158278096445304574421034549635823686610281036068325099/134985878099356274421273722880000000000
YMf [79] = 9041929094392629448432524628030966864699454173220476417661022676942058378296809943/38567393742673221263221063680000000000
YMf [80] = 6554767917485246620101395368656564108574468615120695045915440455606647650054087901/1538300605120869224174059520000000000
YMf [81] = 3585937619029389656288225768538225272556231935192462214320527476425993614656263375401/1079887024794850195370189783040000000000
YMf [82] = 423141600357386246995767096964197972026936727013588770532966194809500484514569913061777/6479322148769101172221138698240000000000
YMf [83] = 2280076558896541815700962738458279809978057775993709422742356129284983226971596168413339/47515029090973408596288350453760000000000
YMf [84] = 10050297596679517860769533003372558089169217390369013211059534279658950124622448973303471577/9978156109104415805220553595289600000000000
YMf [85] = 4748876302988402852942912878061795133551011672950473827638272471390948453769522754104762617/6652104072736277203480369063526400000000000
YMf [86] = 41616434476664821203932053381891290879160653937356410638496057993961071060421640031385810959/2660841629094510881392147625410560000000000
YMf [87] = 292232524965796965481928653504670812441268069900661335911401485275958489977104467026818133249/26608416290945108813921476254105600000000000
YMf [88] = 2295826945576856147360826627832654283684566175319374413898072748454168088770001669171967964313/9391205749745332522560521030860800000000000
YMf [89] = 241173511376264856289096120914700354490413110230564277620527001833829593255054793611423978733/1382255391737408250073842922291200000000000
YMf [90] = 31874530355354467472474914805862455412860513829378711140538418451171810804957807987293359681269/8293532350424449500443057533747200000000000
YMf [91] = 1397127048303609177214711380844818928851379755405834934703179332874750531911782302359455925968251/491232300755909701180088792383488000000000000
YMf [92] = 775272861747361260742979003109969959469570518381262453914416343781820819506260929729809443587579229/12772039819653652230682308601970688000000000000
YMf [93] = 27700923680342740665824936399102757723435962429668614471544787211367296354661708017275220831538295857/587513831704068002611386195690651648000000000000
YMf [94] = 226033181522193030037460000649173291231290279827102278868028081673126414108076734473428138204534912151/235005532681627201044554478276260659200000000000
YMf [95] = 12961933302203978297074148838629396379804184909649826171272697895774512690083061532633248516964569581519/16450387287713904073118813479338246144000000000000
YMf [96] = 502355853815112091818818937971626706538825272430742375916784253473689048775713596150297621159495359409421/32900774575427808146237626958676492288000000000000
YMf [97] = 371642147707156634706142002432459029452780985294520637800891216613925066653947815449422567688066921919491/28200663921795264125346537393151279104000000000000
YMf [98] = 30038671080596635550942006702851757701898843544378105807494796683619888960426480241306849484458422773449/123850083099671779206616325837291520000000000000
YMf [99] = 11263710226259407456597983439389431044657556548727819597241441689661736628953677915794166195714286452803927869/51325208337667380708130698055535327969280000000000000
YMf [100] = 2240100437950447772612444542360924969609962437902360875865696843495539684618775793656760293715064663065079512237/581685694493563648025481244629400383651840000000000000

ZM

(text file)
ZMf [0] = 1
ZMf [1] = 0
ZMf [2] = 0
ZMf [3] = 0
ZMf [4] = 0
ZMf [5] = 64
ZMf [6] = 0
ZMf [7] = 0
ZMf [8] = 800
ZMf [9] = 0
ZMf [10] = 3072
ZMf [11] = 0
ZMf [12] = -21504
ZMf [13] = -44800
ZMf [14] = -442368/5
ZMf [15] = -268288
ZMf [16] = 5350400
ZMf [17] = 14417920
ZMf [18] = 130926592
ZMf [19] = 453509120
ZMf [20] = 1958543360
ZMf [21] = 194260844544/25
ZMf [22] = 22642032640
ZMf [23] = 2340958519296/25
ZMf [24] = 1012408942592/5
ZMf [25] = 5501913006080/7
ZMf [26] = 5593300926464/5
ZMf [27] = 20998291193856/7
ZMf [28] = -415890849267712/125
ZMf [29] = -1287364183588864/35
ZMf [30] = -155542593095073792/875
ZMf [31] = -6066958113964032/7
ZMf [32] = -1855885374934482944/875
ZMf [33] = -1192808955123859456/175
ZMf [34] = 83851850289250304/35
ZMf [35] = 1032072741556999684096/13125
ZMf [36] = 881052856293129191424/1225
ZMf [37] = 53801579833226776543232/13125
ZMf [38] = 125619973293950734696448/6125
ZMf [39] = 1264620908186079286263808/13125
ZMf [40] = 2530063210258853456248832/6125
ZMf [41] = 587272526428739021125451776/336875
ZMf [42] = 1063220119048122473589506048/153125
ZMf [43] = 5466544490760437422341750784/202125
ZMf [44] = 15754515143592002105175441408/153125
ZMf [45] = 378272095988567906162820775936/1010625
ZMf [46] = 6941521039707682730189850148864/5053125
ZMf [47] = 33186019031090630065944625414144/7074375
ZMf [48] = 84004125607284043229361543839744/5053125
ZMf [49] = 40837587308866204708901342408605696/766390625
ZMf [50] = 27736063252507886875688826830848/153125
ZMf [51] = 49841961117203647719904682832822272/91966875
ZMf [52] = 184454254225316122751034681215418368/106115625
ZMf [53] = 734922702010473865250078444048351232/153278125
ZMf [54] = 19330046618116600946565671885278806016/1379503125
ZMf [55] = 16134245084122638799860434565181997056/459834375
ZMf [56] = 2995404844242051588741016622484452016128/34487578125
ZMf [57] = 97067987043800084009046548362588848128/459834375
ZMf [58] = 34797985850632723048367298034602531094528/80471015625
ZMf [59] = 190838879030806807640639091833281970176/91966875
ZMf [60] = 4149420311426342402941329376724918686711808/531108703125
ZMf [61] = 3793310591880423459493575033896329805824/58953125
ZMf [62] = 15654692206679741828060050917269830815973376/48282609375
ZMf [63] = 2493609543871983215415157434420813354124705792/1207065234375
ZMf [64] = 1072935635071345811497126340428981691406614528/106221740625
ZMf [65] = 12138930824954043783781186844191758915213493010432/225721198828125
ZMf [66] = 20110053733200740738677190978421163044370382848/80471015625
ZMf [67] = 5298729687256809316578771874855742929016868306944/4425905859375
ZMf [68] = 14161081041431662524922552795883537187663945662464/2655543515625
ZMf [69] = 22632212983379367608212359211515974929405050955497472/948029035078125
ZMf [70] = 12882651093849852103310840682723733823985482740006912/125400666015625
ZMf [71] = 415857412175496145956854676535324905946558762368106496/948029035078125
ZMf [72] = 2989221677634675712687464830880017587689958045250486272/1630208658203125
ZMf [73] = 680673045895539727409587907063944966498844270658257420288/90062758332421875
ZMf [74] = 351498354735050320554275320275810703491998823390763810816/11411460607421875
ZMf [75] = 218039735151763407314481098298846289212990609478289195008/1765936437890625
ZMf [76] = 2971619102150101948216492463458480398242544294148635099136/6041361498046875
ZMf [77] = 56398716117278333235661010060912560361370732022529002141908992/29270396458037109375
ZMf [78] = 2933683784989920576643670036179375624772676432328949573353472/390271952773828125
ZMf [79] = 9295325078764925464936406445260940325581903134635896254278664192/321974361038408203125
ZMf [80] = 4526055060226625348860182568618763800789097969550997691180253184/40978555041251953125
ZMf [81] = 134208549201674604766664833792649595259101791937856052134424870912/321974361038408203125
ZMf [82] = 9165742439454522386418252144151031549575931931593811525625708544/5854079291607421875
ZMf [83] = 6859686866499466232600418079783475969793161849671038492930473984/1179393263876953125
ZMf [84] = 80673165681980881319492759595249514484629098754069754794011478982656/3756367545448095703125
ZMf [85] = 177268573993345767061084586563803760324963901656011956804845236649984/2253820527268857421875
ZMf [86] = 1933502368337174130857825133092970042792381323234562678864092516581376/6761461581806572265625
ZMf [87] = 111016270652620543800468196154508989542895374784779528888088394727424/107324787012802734375
ZMf [88] = 25103442396524036059834487955934584127076784087218195997917160109244416/6761461581806572265625
ZMf [89] = 2135094248116994248117176145057446799700011081470294887936436897579008/160488768195615234375
ZMf [90] = 64036037225280082473987551819414249236242886192244286067135589933645824/1352292316361314453125
ZMf [91] = 1532431087446935703391855626580601947132540214232149560758804098197640708096/9071627622257151123046875
ZMf [92] = 64487048058131763502995879282049513372744402982873456023345018789953536/107324787012802734375
ZMf [93] = 6506227605553986974716180763488230369955530399512562638742340253420112314368/3023875874085717041015625
ZMf [94] = 6017000667725686589625029488000249964303836711595208923282723059591804878848/777568081907755810546875
ZMf [95] = 663965116930874933115552123812309160563924594361830162620129900696428397723648/23586231817868592919921875
ZMf [96] = 9613528740911894954401830770606202026159839495685145511826309287391240961130496/92530601747022941455078125
ZMf [97] = 3933220237481416558329446986540467740659528779040303206431475047534844553723904/10108385064800825537109375
ZMf [98] = 37978037576762584354129751057697009116946088527565616827673491326442879526121766912/25445915480431308900146484375
ZMf [99] = 410631095256812927058687262858980414165732054432733750087672045709303577661407232/70758695453605778759765625
ZMf [100] = 2558849797318395073832000539523616215784459667994331652573854562757968884337481875456/110265633748535671900634765625

XP

(text file)
XPf [0] = 0
XPf [1] = 0
XPf [2] = 6
XPf [3] = 18
XPf [4] = 54
XPf [5] = 354
XPf [6] = 1278
XPf [7] = 4962
XPf [8] = 22782
XPf [9] = 82050
XPf [10] = 358398
XPf [11] = 1420674
XPf [12] = 5617278
XPf [13] = 23582082
XPf [14] = 90728574
XPf [15] = 378550146
XPf [16] = 1485594750
XPf [17] = 6025402242
XPf [18] = 24231831678
XPf [19] = 96316790658
XPf [20] = 391827867774
XPf [21] = 1548261832578
XPf [22] = 6295103981694
XPf [23] = 24955168339842
XPf [24] = 100836398352510
XPf [25] = 402238902613890
XPf [26] = 1614310064670846
XPf [27] = 6474603196692354
XPf [28] = 25858853901846654
XPf [29] = 104037704797894530
XPf [30] = 414575582119348350
XPf [31] = 1669188892168402818
XPf [32] = 6651001788074182782
XPf [33] = 26751562904745129858
XPf [34] = 106732965730437187710
XPf [35] = 428478378300199778178
XPf [36] = 1712692726890429302910
XPf [37] = 6861455725273024149378
XPf [38] = 27473574152378417301630
XPf [39] = 109881408051318235969410
XPf [40] = 440502853036640947292286
XPf [41] = 1759972044910731636356994
XPf [42] = 7059508669230525828188286
XPf [43] = 28194616163006921450305410
XPf [44] = 113089455963920952742791294
XPf [45] = 451732037733988694903863170
XPf [46] = 1811085317310314568367884414
XPf [47] = 7237903515404742888548579202
XPf [48] = 28998452645033883613287303294
XPf [49] = 115964590378896335609712457602
XPf [50] = 464272114691670138304648857726
XPf [51] = 1857764790810800522125054162818
XPf [52] = 7432978049871393477209195169918
XPf [53] = 29757221918973377723625564125058
XPf [54] = 119004446349191181455247525955710
XPf [55] = 476568380282541579266967773755266
XPf [56] = 1905372867514710709052076944935038
XPf [57] = 7631202939892733237542036772075394
XPf [58] = 30507834831080818544988682426140798
XPf [59] = 122181441058346284716851377785649026
XPf [60] = 488484415544534255759405472666765438
XPf [61] = 1956024070522934543503049520536205186
XPf [62] = 7821486119394291814512651878699255934
XPf [63] = 31312113569961037208448885419723569026
XPf [64] = 125232947664947299648656601185018857598
XPf [65] = 501222927726974709437980512227834836866
XPf [66] = 2005080222728199155293872196027838515326
XPf [67] = 8023033812703758125608437390697410705282
XPf [68] = 32101401454190589804209167956054947285118
XPf [69] = 128422649117829440171334304610248914745218
XPf [70] = 513916876489681642088567788827346842568830
XPf [71] = 2055623626582254295251656047348643907876738
XPf [72] = 8226934035893762114945220954274715249559678
XPf [73] = 32903805103896526452341535135216816208066434
XPf [74] = 131692366852349533548571695730533694980900990
XPf [75] = 526682866804395306728026344377431968750090114
XPf [76] = 2107962830312284644936177438420264593167632510
XPf [77] = 8430469248985005465937235632036052780621346690
XPf [78] = 33740225417721670145371608824936917727648827518
XPf [79] = 134943561830918411793104685425548040778748114818
XPf [80] = 540031187733716883118277758648373815813872175230
XPf [81] = 2159974535153976329136981914559215554276141676418
XPf [82] = 8643280066140665593809484032550814535578749913214
XPf [83] = 34573186000375353677829703086665272363072181876610
XPf [84] = 138334323502282634522345940010983366877728007932030
XPf [85] = 553379452105632735592933348538959617668426709448578
XPf [86] = 2213987859336111868390856251852477699423485894740094
XPf [87] = 8857240505224170333615872989326828878578509107804034
XPf [88] = 35433678270407580469519241991197849463586338053179518
XPf [89] = 141763679194812314661422612273976038036451848059729794
XPf [90] = 567092958580289314196401518901939508534457223071811710
XPf [91] = 2268936819987863757889549497797566542490020039351711618
XPf [92] = 9075908713054555624316530889315868640471625435695171710
XPf [93] = 36313728521579278406087800452585840310861327988434777986
XPf [94] = 145252715902000462137176764495801856631340512514790541438
XPf [95] = 581180079572601763244101682460487679530717695670826416002
XPf [96] = 2324645801358462969476099151269216627952643245183993268350
XPf [97] = 9301279318091198652865058471174308473627551273359905503106
XPf [98] = 37203823281777696416340008498512053330688277530412864391294
XPf [99] = 148856410276282327755118751827054092360624717523760694540162
XPf [100] = 595410262993541295689774092847387937604605686439212740921470

XQ

(text file)
XQf [0] = 0
XQf [1] = 0
XQf [2] = 0
XQf [3] = 20
XQf [4] = 30
XQf [5] = 90
XQf [6] = 878
XQf [7] = 2394
XQf [8] = 10662
XQf [9] = 49562
XQf [10] = 148614
XQf [11] = 800250
XQf [12] = 2654854
XQf [13] = 11845626
XQf [14] = 47399430
XQf [15] = 180395514
XQf [16] = 786816006
XQf [17] = 2899338234
XQf [18] = 12481057798
XQf [19] = 47785571322
XQf [20] = 195781266438
XQf [21] = 786032636922
XQf [22] = 3092771367942
XQf [23] = 12779388048378
XQf [24] = 49392850824198
XQf [25] = 205524063261690
XQf [26] = 795056348163078
XQf [27] = 3283219337876474
XQf [28] = 12841964007287814
XQf [29] = 52311443914134522
XQf [30] = 207430129052773382
XQf [31] = 833717923412481018
XQf [32] = 3343962946209278982
XQf [33] = 13312080366410961914
XQf [34] = 53763802360396606470
XQf [35] = 213037043908874376186
XQf [36] = 862242003154190167046
XQf [37] = 3415743755741617492986
XQf [38] = 13802695066419453717510
XQf [39] = 54829188925665065341946
XQf [40] = 220723580960710894513158
XQf [41] = 880423529897200738931706
XQf [42] = 3528627665714908508417030
XQf [43] = 14133599292910451617207290
XQf [44] = 56424536897791874333371398
XQf [45] = 226741105058712265995359226
XQf [46] = 902738171264777408248507398
XQf [47] = 3634654967495762477632754682
XQf [48] = 14451707534110785614538304518
XQf [49] = 58219792648278950139360482298
XQf [50] = 231475058301662555040051588102
XQf [51] = 932010417540311872533025559546
XQf [52] = 3708889618894364885660936924166
XQf [53] = 14914267160356153392109526750202
XQf [54] = 59436714743849086122115458886662
XQf [55] = 238616692556369315262116466299898
XQf [56] = 952492973306866345503990961105926
XQf [57] = 3817584923857955147835495375999994
XQf [58] = 15261901105006607194521937125534726
XQf [59] = 61082246334604713112746990139118586
XQf [60] = 244490157840719059383303397930134534
XQf [61] = 977477493491055080460888479256056826
XQf [62] = 3915675930811200280986061046523325446
XQf [63] = 15644867084397228800244361405468283898
XQf [64] = 62697155521000184126553898217302354950
XQf [65] = 250440186795777474739089573480841122810
XQf [66] = 1003688334013856621353631652341677517830
XQf [67] = 4009480185091248109244947842847301735418
XQf [68] = 16064974169495484947491377043169911729158
XQf [69] = 64195548724187726338148236173330178151418
XQf [70] = 257106591921805059737741883903017268243462
XQf [71] = 1027862828833612368717933064153086166078458
XQf [72] = 4114518094347822791442912045581357912386566
XQf [73] = 16457417006266494467901930600703560859554810
XQf [74] = 65843758315177148540979947121631434542902278
XQf [75] = 263494161412033485402586759515173427636900858
XQf [76] = 1053690814654606884226086894825708088232733702
XQf [77] = 4218459423163344903606615184341819553463964666
XQf [78] = 16862556336319816834630901930302188260088048646
XQf [79] = 67531306794863483307781085216920903003047760890
XQf [80] = 269867087465173211872663832945535418724956204038
XQf [81] = 1080993917097857181152058647047391268082041263098
XQf [82] = 4319107220676546936433470759141954509217665608710
XQf [83] = 17302523088744340063467267687808524436885439812602
XQf [84] = 69128045584359471335058636158915392211460384844806
XQf [85] = 276928112215983153611390072686463619059356635534330
XQf [86] = 1106439558028871011443305719407092788206549807885318
XQf [87] = 4432009617950418530290726196555955155410425709892602
XQf [88] = 17709654637247472829447548614795177371301349292993542
XQf [89] = 70927658214923341684544867562330685846783319003403258
XQf [90] = 283463359352473329696181303472712524201935074051976198
XQf [91] = 1135055569847157741631551869122336416315250539518530554
XQf [92] = 4537156603408667303418006610255021813190239882181569542
XQf [93] = 18163943414382600207739833936718694437902964792880043002
XQf [94] = 72621738605844395707141844395873544237189138444229504006
XQf [95] = 290669158641837370968973507340842707903481713544210191354
XQf [96] = 1162364356133663645360329007084964322366519567872952331270
XQf [97] = 4651435687305103786039946850912020341394296895839869637626
XQf [98] = 18604082782997520280776953708894916977859243170754086267910
XQf [99] = 74434949559656492430456134383568591119461780539525579183098
XQf [100] = 297757706684600881112280296121135081530086697880843936820230

TQ

(text file)
TQf [0] = 0
TQf [1] = 0
TQf [2] = 0
TQf [3] = 0
TQf [4] = 12
TQf [5] = 36
TQf [6] = 428
TQf [7] = 1188
TQf [8] = 7356
TQf [9] = 28004
TQf [10] = 608844/5
TQf [11] = 521508
TQf [12] = 2126300
TQf [13] = 8797476
TQf [14] = 258942468/7
TQf [15] = 145426212
TQf [16] = 624094428
TQf [17] = 12066242484/5
TQf [18] = 30825543316/3
TQf [19] = 200467333044/5
TQf [20] = 836125294668/5
TQf [21] = 662677238564
TQf [22] = 29839639612788/11
TQf [23] = 10870781768484
TQf [24] = 219997955637324/5
TQf [25] = 1239931101750780/7
TQf [26] = 46395342284473308/65
TQf [27] = 100533242794622444/35
TQf [28] = 405057525599683092/35
TQf [29] = 232190550654435252/5
TQf [30] = 937105365128593484/5
TQf [31] = 3747567600867327924/5
TQf [32] = 3030398067674320092
TQf [33] = 181304284218877099804/15
TQf [34] = 4157888064622385054988/85
TQf [35] = 974171337135536586676/5
TQf [36] = 82781395210714773669436/105
TQf [37] = 3139624094631248917284


Unequal rigid spheres

The letter "l" denotes $\lambda = a_2 / a_1$.

Jump to: XA, YA, YB, XC, YC, XG, YG, YH, XM, YM, ZM, XP, XQ. TQ.

XA

This corresponds to [JO-1984] p.268. (text file)

XAf_0 = 1 l^0 
XAf_1 = 3 l^1 
XAf_2 = 9 l^1 
XAf_3 = -4 l^1 27 l^2 -4 l^3 
XAf_4 = -24 l^1 81 l^2 36 l^3 
XAf_5 = 72 l^2 243 l^3 72 l^4 
XAf_6 = 16 l^1 108 l^2 281 l^3 648 l^4 144 l^5 
XAf_7 = 288 l^2 1620 l^3 1515 l^4 1620 l^5 288 l^6 
XAf_8 = 576 l^2 4848 l^3 5409 l^4 4524 l^5 3888 l^6 576 l^7 
XAf_9 = 1152 l^2 9072 l^3 14752 l^4 26163 l^5 14752 l^6 9072 l^7 1152 l^8 
XAf_10 = 2304 l^2 20736 l^3 42804 l^4 115849 l^5 76176 l^6 39264 l^7 20736 l^8 2304 l^9 
XAf_11 = 4608 l^2 46656 l^3 108912 l^4 269100 l^5 319899 l^6 269100 l^7 108912 l^8 46656 l^9 4608 l^10 
XAf_12 = 9216 l^2 103680 l^3 286160 l^4 847800 l^5 1007697 l^6 1551540 l^7 727200 l^8 272000 l^9 103680 l^10 9216 l^11 
XAf_13 = 18432 l^2 228096 l^3 695808 l^4 2208672 l^5 4094456 l^6 4434723 l^7 4094456 l^8 2208672 l^9 695808 l^10 228096 l^11 18432 l^12 
XAf_14 = 36864 l^2 497664 l^3 1725504 l^4 6296112 l^5 11277948 l^6 17399673 l^7 14649048 l^8 15577200 l^9 5679360 l^10 1668864 l^11 497664 l^12 36864 l^13 
XAf_15 = 73728 l^2 1078272 l^3 4066048 l^4 15788160 l^5 39777920 l^6 53394756 l^7 74752459 l^8 53394756 l^9 39777920 l^10 15788160 l^11 4066048 l^12 1078272 l^13 73728 l^14 
XAf_16 = 147456 l^2 2322432 l^3 9709824 l^4 42179328 l^5 103226272 l^6 181857600 l^7 244156673 l^8 248778684 l^9 162307152 l^10 131251904 l^11 39174912 l^12 9483264 l^13 2322432 l^14 147456 l^15 
XAf_17 = 294912 l^2 4976640 l^3 22364160 l^4 102769920 l^5 326593152 l^6 526752144 l^7 962606160 l^8 908905875 l^9 962606160 l^10 526752144 l^11 326593152 l^12 102769920 l^13 22364160 l^14 4976640 l^15 294912 l^16 
XAf_18 = 589824 l^2 10616832 l^3 52007936 l^4 262409472 l^5 817599872 l^6 1634586528 l^7 3031504324 l^8 3493704937 l^9 3744802592 l^10 2832790464 l^11 1508623872 l^12 982349312 l^13 248242176 l^14 51101696 l^15 10616832 l^16 589824 l^17 
XAf_19 = 1179648 l^2 22560768 l^3 117731328 l^4 625185792 l^5 2393483008 l^6 4526149824 l^7 10056648784 l^8 12193017436 l^9 15798129531 l^10 12193017436 l^11 10056648784 l^12 4526149824 l^13 2393483008 l^14 625185792 l^15 117731328 l^16 22560768 l^17 1179648 l^18 
XAf_20 = 2359296 l^2 47775744 l^3 268455936 l^4 1544103936 l^5 5841832704 l^6 13153655808 l^7 30661148592 l^8 41094691272 l^9 59771519281 l^10 51526996164 l^11 45875792448 l^12 27553381632 l^13 12395109888 l^14 6748747776 l^15 1478836224 l^16 264830976 l^17 47775744 l^18 2359296 l^19 
XAf_21 = 4718592 l^2 100859904 l^3 599523328 l^4 3613409280 l^5 16159297536 l^6 35139224064 l^7 91218692096 l^8 137449570880 l^9 205638658728 l^10 213784930947 l^11 205638658728 l^12 137449570880 l^13 91218692096 l^14 35139224064 l^15 16159297536 l^16 3613409280 l^17 599523328 l^18 100859904 l^19 4718592 l^20 

YA

This corresponds to [JO-1984] p.272. (text file)

YAf_0 = 1 l^0 
YAf_1 = 3/2 l^1 
YAf_2 = 9/4 l^1 
YAf_3 = 2 l^1 27/8 l^2 2 l^3 
YAf_4 = 6 l^1 81/16 l^2 18 l^3 
YAf_5 = 63/2 l^2 243/32 l^3 63/2 l^4 
YAf_6 = 4 l^1 54 l^2 1241/64 l^3 81 l^4 72 l^5 
YAf_7 = 144 l^2 1053/8 l^3 19083/128 l^4 1053/8 l^5 144 l^6 
YAf_8 = 279 l^2 4261/8 l^3 126369/256 l^4 -117/8 l^5 648 l^6 288 l^7 
YAf_9 = 576 l^2 1134 l^3 60443/32 l^4 766179/512 l^5 60443/32 l^6 1134 l^7 576 l^8 
YAf_10 = 1152 l^2 7857/4 l^3 98487/16 l^4 10548393/1024 l^5 67617/8 l^6 -351/2 l^7 3888 l^8 1152 l^9 
YAf_11 = 2304 l^2 7128 l^3 22071/2 l^4 2744505/128 l^5 95203835/2048 l^6 2744505/128 l^7 22071/2 l^8 7128 l^9 2304 l^10 
YAf_12 = 4608 l^2 12960 l^3 657071/16 l^4 6158727/128 l^5 551881713/4096 l^6 18459213/128 l^7 85122 l^8 566 l^9 20736 l^10 4608 l^11 
YAf_13 = 9216 l^2 38880 l^3 61170 l^4 872109/4 l^5 227130487/512 l^6 2704352211/8192 l^7 227130487/512 l^8 872109/4 l^9 61170 l^10 38880 l^11 9216 l^12 
YAf_14 = 18432 l^2 72576 l^3 227490 l^4 31720689/64 l^5 43288187/32 l^6 13612266873/16384 l^7 374418387/256 l^8 51215745/32 l^9 681174 l^10 14280 l^11 103680 l^12 18432 l^13 
YAf_15 = 36864 l^2 196992 l^3 326680 l^4 1724229 l^5 15250397/4 l^6 8427155925/2048 l^7 807290551831/163840 l^8 8427155925/2048 l^9 15250397/4 l^10 1724229 l^11 326680 l^12 196992 l^13 36864 l^14 
YAf_16 = 73728 l^2 373248 l^3 1189896 l^4 3967614 l^5 2729745239/256 l^6 21412319913/2048 l^7 6545699868741/327680 l^8 27895077711/2048 l^9 382847865/32 l^10 116842269/8 l^11 4771008 l^12 132960 l^13 497664 l^14 73728 l^15 
YAf_17 = 147456 l^2 953856 l^3 1690272 l^4 11878092 l^5 60694011/2 l^6 4923356841/128 l^7 422692016979/8192 l^8 46344413358287/655360 l^9 422692016979/8192 l^10 4923356841/128 l^11 60694011/2 l^12 11878092 l^13 1690272 l^14 953856 l^15 147456 l^16 
YAf_18 = 294912 l^2 1824768 l^3 5990432 l^4 27368892 l^5 309171435/4 l^6 106801734081/1024 l^7 4138414180093/20480 l^8 268528742954093/1310720 l^9 1179055732229/5120 l^10 88253102889/512 l^11 1345341369/16 l^12 231928201/2 l^13 30570912 l^14 946304 l^15 2322432 l^16 294912 l^17 
YAf_19 = 589824 l^2 4478976 l^3 8517504 l^4 74862576 l^5 224202158 l^6 9751407645/32 l^7 1360319378553/2560 l^8 144264498430261/163840 l^9 1678576024744263/2621440 l^10 144264498430261/163840 l^11 1360319378553/2560 l^12 9751407645/32 l^13 224202158 l^14 74862576 l^15 8517504 l^16 4478976 l^17 589824 l^18 
YAf_20 = 1179648 l^2 8626176 l^3 29329536 l^4 171964800 l^5 527916608 l^6 870429420 l^7 37944812826187/20480 l^8 421235543611959/163840 l^9 15672425839243733/5242880 l^10 477209069308629/163840 l^11 390628115581/160 l^12 228752154927/128 l^13 536418729 l^14 832766842 l^15 183707136 l^16 5887488 l^17 10616832 l^18 1179648 l^19 
YAf_21 = 2359296 l^2 20570112 l^3 41984512 l^4 443092032 l^5 1549634496 l^6 17335240101/8 l^7 3252043928903/640 l^8 23345108631549/2560 l^9 5308335864584043/655360 l^10 145424905669117311/10485760 l^11 5308335864584043/655360 l^12 23345108631549/2560 l^13 3252043928903/640 l^14 17335240101/8 l^15 1549634496 l^16 443092032 l^17 41984512 l^18 20570112 l^19 2359296 l^20 

YB

This corresponds to [JO-1984] p.274. (text file)

YBf_0 = 
YBf_1 = 
YBf_2 = -6 l^1 
YBf_3 = -9 l^1 
YBf_4 = -27/2 l^2 
YBf_5 = -12 l^1 -81/4 l^2 -36 l^3 
YBf_6 = -108 l^2 -243/8 l^3 -72 l^4 
YBf_7 = -189 l^2 -8409/16 l^3 -243 l^4 -144 l^5 
YBf_8 = -432 l^2 -486 l^3 -77451/32 l^4 -405 l^5 -288 l^6 
YBf_9 = -864 l^2 -3159/4 l^3 -283041/64 l^4 -30525/4 l^5 -1620 l^6 -576 l^7 
YBf_10 = -1728 l^2 -3888 l^3 -59553/4 l^4 -1125603/128 l^5 -22002 l^6 -2916 l^7 -1152 l^8 
YBf_11 = -3456 l^2 -6804 l^3 -614481/16 l^4 -4579497/256 l^5 -536679/16 l^6 -73989 l^7 -9072 l^8 -2304 l^9 
YBf_12 = -6912 l^2 -23328 l^3 -81891 l^4 -513891/4 l^5 -69486075/512 l^6 -1330155/16 l^7 -176550 l^8 -16848 l^9 -4608 l^10 
YBf_13 = -13824 l^2 -42768 l^3 -220581 l^4 -16444971/64 l^5 -631898097/1024 l^6 -16394481/64 l^7 -634041/4 l^8 -579780 l^9 -46656 l^10 -9216 l^11 
YBf_14 = -27648 l^2 -124416 l^3 -427332 l^4 -1143180 l^5 -50958567/64 l^6 -5042884563/2048 l^7 -47085087/32 l^8 -2010825/4 l^9 -1268016 l^10 -88128 l^11 -18432 l^12 
YBf_15 = -55296 l^2 -233280 l^3 -1168812 l^4 -4824711/2 l^5 -1257376101/256 l^6 -21328703865/4096 l^7 -2340531291/256 l^8 -38833425/16 l^9 -332703 l^10 -3992592 l^11 -228096 l^12 -36864 l^13 
YBf_16 = -110592 l^2 -622080 l^3 -2150064 l^4 -8317188 l^5 -93982851/16 l^6 -3935734137/128 l^7 -606411198999/40960 l^8 -7649857281/256 l^9 -116859465/8 l^10 -2153547 l^11 -8346528 l^12 -435456 l^13 -73728 l^14 
YBf_17 = -221184 l^2 -1181952 l^3 -5904528 l^4 -17955486 l^5 -69407031/2 l^6 -70819907967/1024 l^7 -1739587389249/16384 l^8 -56588369445/1024 l^9 -7567907949/64 l^10 -71712297/4 l^11 2733948 l^12 -25210176 l^13 -1078272 l^14 -147456 l^15 
YBf_18 = -442368 l^2 -2985984 l^3 -10529856 l^4 -54006912 l^5 -193874775/4 l^6 -4543398891/16 l^7 -1072001125281/5120 l^8 -74324497462479/163840 l^9 -271080176913/1280 l^10 -19481493585/64 l^11 -250072611/2 l^12 -4651524 l^13 -51379200 l^14 -2073600 l^15 -294912 l^16 
YBf_19 = -884736 l^2 -5723136 l^3 -28868544 l^4 -117800136 l^5 -232861233 l^6 -42739872507/64 l^7 -4132645103097/4096 l^8 -345896767139949/327680 l^9 -37577696864523/20480 l^10 -92007279405/256 l^11 -20817999735/16 l^12 -110815209 l^13 44870544 l^14 -149556480 l^15 -4976640 l^16 -589824 l^17 
YBf_20 = -1769472 l^2 -13934592 l^3 -50504448 l^4 -325425600 l^5 -390566043 l^6 -17811395883/8 l^7 -3340412605287/1280 l^8 -12021550538127/2560 l^9 -2904406309451079/655360 l^10 -113582561046579/20480 l^11 -1394147381463/640 l^12 -44788497897/16 l^13 -945358194 l^14 27265104 l^15 -300215808 l^16 -9621504 l^17 -1179648 l^18 
YBf_21 = -3538944 l^2 -26873856 l^3 -137809152 l^4 -712937376 l^5 -1511146260 l^6 -86456287575/16 l^7 -2267589302703/256 l^8 -1070851060903839/81920 l^9 -27879227453281749/1310720 l^10 -1034686280377917/81920 l^11 -127158422355573/5120 l^12 -56816024625/64 l^13 -49851951129/4 l^14 -586269252 l^15 415594944 l^16 -846406656 l^17 -22560768 l^18 -2359296 l^19 

XC

This corresponds to [JO-1984] p.275. (text file)

XCf_0 = 1 l^0 
XCf_1 = 
XCf_2 = 
XCf_3 = 8 l^3 
XCf_4 = 
XCf_5 = 
XCf_6 = 64 l^3 
XCf_7 = 
XCf_8 = 768 l^5 
XCf_9 = 512 l^6 
XCf_10 = 6144 l^7 
XCf_11 = 6144 l^6 6144 l^8 
XCf_12 = 4096 l^6 40960 l^9 
XCf_13 = 49152 l^6 98304 l^8 49152 l^10 
XCf_14 = 49152 l^6 98304 l^8 245760 l^11 
XCf_15 = 327680 l^6 983040 l^8 32768 l^9 983040 l^10 327680 l^12 
XCf_16 = 393216 l^6 1572864 l^8 1376256 l^10 1376256 l^13 
XCf_17 = 1966080 l^6 7864320 l^8 786432 l^9 11796480 l^10 786432 l^11 7864320 l^12 1966080 l^14 
XCf_18 = 2621440 l^6 15728640 l^8 262144 l^9 28311552 l^10 14680064 l^12 7340032 l^15 
XCf_19 = 11010048 l^6 55050240 l^8 11010048 l^9 110100480 l^10 23592960 l^11 110100480 l^12 11010048 l^13 55050240 l^14 11010048 l^16 
XCf_20 = 15728640 l^6 125829120 l^8 6291456 l^9 346030080 l^10 9437184 l^11 377487360 l^12 132120576 l^14 37748736 l^17 
XCf_21 = 58720256 l^6 352321536 l^8 117440512 l^9 880803840 l^10 402653184 l^11 1176502272 l^12 402653184 l^13 880803840 l^14 117440512 l^15 352321536 l^16 58720256 l^18 

YC

This corresponds to [JO-1984] p.277. (text file)

YCf_0 = 1 l^0 
YCf_1 = 
YCf_2 = 
YCf_3 = 4 l^3 
YCf_4 = 12 l^1 
YCf_5 = 18 l^4 
YCf_6 = 27 l^2 256 l^3 
YCf_7 = 72 l^4 81/2 l^5 72 l^6 
YCf_8 = 216 l^2 243/4 l^3 216 l^4 2496 l^5 
YCf_9 = 288 l^4 486 l^5 -6439/8 l^6 486 l^7 288 l^8 
YCf_10 = 864 l^2 972 l^3 151179/16 l^4 972 l^5 1296 l^6 18432 l^7 
YCf_11 = 1152 l^4 3240 l^5 -10947/2 l^6 518049/32 l^7 -10947/2 l^8 3240 l^9 1152 l^10 
YCf_12 = 3456 l^2 7776 l^3 119457/2 l^4 1872099/64 l^5 432545/2 l^6 8748 l^7 6912 l^8 117760 l^9 
YCf_13 = 4608 l^4 18144 l^5 -8694 l^6 1131111/8 l^7 14709417/128 l^8 1131111/8 l^9 -8694 l^10 18144 l^11 4608 l^12 
YCf_14 = 13824 l^2 46656 l^3 329670 l^4 824931/2 l^5 467512827/256 l^6 627939/2 l^7 3098193 l^8 62208 l^9 34560 l^10 688128 l^11 
YCf_15 = 18432 l^4 93312 l^5 156040 l^6 1726137/2 l^7 91202289/32 l^8 -54112783/512 l^9 91202289/32 l^10 1726137/2 l^11 156040 l^12 93312 l^13 18432 l^14 
YCf_16 = 55296 l^2 248832 l^3 1702536 l^4 3551256 l^5 390210279/32 l^6 10610113491/1024 l^7 1001617383/32 l^8 8778051/4 l^9 33777552 l^10 388800 l^11 165888 l^12 3784704 l^13 
YCf_17 = 73728 l^4 456192 l^5 2136096 l^6 4121406 l^7 274211601/8 l^8 -2357762469/128 l^9 693707368797/10240 l^10 -2357762469/128 l^11 274211601/8 l^12 4121406 l^13 2136096 l^14 456192 l^15 73728 l^16 
YCf_18 = 221184 l^2 1244160 l^3 8428896 l^4 25094664 l^5 593995907/8 l^6 8347815801/64 l^7 4618762355223/20480 l^8 14197915513/64 l^9 6246248193/16 l^10 10709280 l^11 309002864 l^12 2239488 l^13 774144 l^14 19922944 l^15 
YCf_19 = 294912 l^4 2156544 l^5 18373248 l^6 14549256 l^7 621091881/2 l^8 -8319506835/32 l^9 2250674065593/2560 l^10 -18259054443963/40960 l^11 2250674065593/2560 l^12 -8319506835/32 l^13 621091881/2 l^14 14549256 l^15 18373248 l^16 2156544 l^17 294912 l^18 
YCf_20 = 884736 l^2 5971968 l^3 40523904 l^4 158775552 l^5 865335639/2 l^6 9636947307/8 l^7 3851746114977/2560 l^8 60613228458435/16384 l^9 7059401393313/2560 l^10 241042827051/64 l^11 3995435679 l^12 25787916 l^13 2501824896 l^14 12192768 l^15 3538944 l^16 101449728 l^17 
YCf_21 = 1179648 l^4 9953280 l^5 131078656 l^6 19523808 l^7 2395497426 l^8 -19601631881/8 l^9 1090733170989/128 l^10 -47686799248629/10240 l^11 1854668309477997/163840 l^12 -47686799248629/10240 l^13 1090733170989/128 l^14 -19601631881/8 l^15 2395497426 l^16 19523808 l^17 131078656 l^18 9953280 l^19 1179648 l^20 

XG

This corresponds to [J-1992] p.19. (text file)

XGf_0 = 
XGf_1 = 
XGf_2 = 15 l^1 
XGf_3 = 45 l^1 
XGf_4 = -36 l^1 135 l^2 -60 l^3 
XGf_5 = -168 l^1 405 l^2 360 l^3 
XGf_6 = 216 l^2 1215 l^3 900 l^4 
XGf_7 = 144 l^1 108 l^2 -1251 l^3 4860 l^4 2160 l^5 
XGf_8 = 864 l^2 6804 l^3 8679 l^4 12960 l^5 5040 l^6 
XGf_9 = 1728 l^2 27072 l^3 25893 l^4 -3888 l^5 38880 l^6 11520 l^7 
XGf_10 = 3456 l^2 34992 l^3 66384 l^4 155007 l^5 75900 l^6 97200 l^7 25920 l^8 
XGf_11 = 6912 l^2 77760 l^3 178260 l^4 790845 l^5 500580 l^6 14880 l^7 259200 l^8 57600 l^9 
XGf_12 = 13824 l^2 171072 l^3 437616 l^4 1336716 l^5 1353399 l^6 2020248 l^7 532512 l^8 622080 l^9 126720 l^10 
XGf_13 = 27648 l^2 373248 l^3 1102608 l^4 3949992 l^5 4529205 l^6 12667320 l^7 5937840 l^8 334080 l^9 1555200 l^10 276480 l^11 
XGf_14 = 55296 l^2 808704 l^3 2620416 l^4 9824544 l^5 16613832 l^6 26682255 l^7 21744180 l^8 19958400 l^9 3400320 l^10 3628800 l^11 599040 l^12 
XGf_15 = 110592 l^2 1741824 l^3 6331968 l^4 26863920 l^5 45761916 l^6 96781581 l^7 70793100 l^8 148312080 l^9 55097280 l^10 3241728 l^11 8709120 l^12 1290240 l^13 
XGf_16 = 221184 l^2 3732480 l^3 14688000 l^4 65232000 l^5 157857600 l^6 278464068 l^7 398382855 l^8 360077520 l^9 268437840 l^10 166423680 l^11 20492544 l^12 19906560 l^13 2764800 l^14 
XGf_17 = 442368 l^2 7962624 l^3 34467072 l^4 169337088 l^5 404795040 l^6 900398736 l^7 1108701381 l^8 1606106016 l^9 844213440 l^10 1428542976 l^11 439229952 l^12 24600576 l^13 46448640 l^14 5898240 l^15 
XGf_18 = 884736 l^2 16920576 l^3 78483456 l^4 403073280 l^5 1273123200 l^6 2492065872 l^7 4973366592 l^8 5036362527 l^9 6433609644 l^10 3836048400 l^11 2706649536 l^12 1236646656 l^13 118342656 l^14 104509440 l^15 12533760 l^16 
XGf_19 = 1769472 l^2 35831808 l^3 180237312 l^4 1008011520 l^5 3145484160 l^6 7453054944 l^7 13783697316 l^8 19375178589 l^9 19259053236 l^10 20800556352 l^11 8436863232 l^12 12033197568 l^13 3155023872 l^14 164118528 l^15 238878720 l^16 26542080 l^17 
XGf_20 = 3538944 l^2 75644928 l^3 404484096 l^4 2359784448 l^5 9183471360 l^6 19970935488 l^7 49890664656 l^8 59629793532 l^9 98853000663 l^10 70749476616 l^11 80046586176 l^12 34967052288 l^13 23574329856 l^14 8451330048 l^15 660357120 l^16 530841600 l^17 56033280 l^18 
XGf_21 = 7077888 l^2 159252480 l^3 913674240 l^4 5737789440 l^5 22145314560 l^6 56462282496 l^7 138255865200 l^8 203306039160 l^9 315134929365 l^10 312969146760 l^11 266056071696 l^12 226622707200 l^13 74355079680 l^14 91891445760 l^15 20998103040 l^16 1008599040 l^17 1194393600 l^18 117964800 l^19 

YG

This corresponds to [J-1992] p.21. (text file)

YGf_0 = 
YGf_1 = 
YGf_2 = 
YGf_3 = 
YGf_4 = 12 l^1 20 l^3 
YGf_5 = 18 l^1 90 l^3 
YGf_6 = 27 l^2 135 l^4 
YGf_7 = 24 l^1 81/2 l^2 -336 l^3 405/2 l^4 600 l^5 
YGf_8 = 216 l^2 243/4 l^3 -1008 l^4 1215/4 l^5 1080 l^6 
YGf_9 = 378 l^2 21209/8 l^3 -972 l^4 -62147/8 l^5 2970 l^6 3360 l^7 
YGf_10 = 864 l^2 972 l^3 42123/16 l^4 648 l^5 -96073/16 l^6 4860 l^7 6240 l^8 
YGf_11 = 1728 l^2 3159/2 l^3 103329/32 l^4 69387 l^5 763173/32 l^6 -166737/2 l^7 24840 l^8 17280 l^9 
YGf_12 = 3456 l^2 7776 l^3 41889/2 l^4 102627/64 l^5 223571 l^6 3651183/64 l^7 -114139/2 l^8 43200 l^9 32640 l^10 
YGf_13 = 6912 l^2 13608 l^3 473169/8 l^4 1469097/128 l^5 1093161/4 l^6 144173133/128 l^7 3933297/8 l^8 -676326 l^9 168480 l^10 84480 l^11 
YGf_14 = 13824 l^2 46656 l^3 128454 l^4 306531/2 l^5 540398587/256 l^6 -244827 l^7 735757799/256 l^8 2188143/2 l^9 -491306 l^10 302400 l^11 161280 l^12 
YGf_15 = 27648 l^2 85536 l^3 370506 l^4 10445355/32 l^5 1966761457/512 l^6 1227879/16 l^7 1154007221/512 l^8 458849427/32 l^9 11254797/2 l^10 -4730248 l^11 1019520 l^12 399360 l^13 
YGf_16 = 55296 l^2 248832 l^3 713352 l^4 1712664 l^5 493695463/32 l^6 -1232575533/1024 l^7 443763493/16 l^8 685421855/1024 l^9 904580483/32 l^10 12318822 l^11 -3773464 l^12 1866240 l^13 768000 l^14 
YGf_17 = 110592 l^2 466560 l^3 2055000 l^4 3756807 l^5 3898039653/128 l^6 -1361516679/2048 l^7 3201749061/64 l^8 72344279133/2048 l^9 -750370155/128 l^10 1194924801/8 l^11 50277522 l^12 -30110304 l^13 5736960 l^14 1843200 l^15 
YGf_18 = 221184 l^2 1244160 l^3 3734880 l^4 13703688 l^5 815609731/8 l^6 262496889/64 l^7 3539484278807/20480 l^8 2903561699/32 l^9 1179375190551/4096 l^10 1356226397/64 l^11 1964643915/8 l^12 108985320 l^13 -26302112 l^14 10644480 l^15 3563520 l^16 
YGf_19 = 442368 l^2 2363904 l^3 10678560 l^4 30367548 l^5 210145943 l^6 14966081919/512 l^7 20631131645509/40960 l^8 80717093955/256 l^9 2393826011461/8192 l^10 441985526775/512 l^11 -11448810295/32 l^12 2680606215/2 l^13 388220712 l^14 -179458176 l^15 30689280 l^16 8355840 l^17 
YGf_20 = 884736 l^2 5971968 l^3 18798720 l^4 93747456 l^5 1272292439/2 l^6 1009480299/8 l^7 2326508129953/2560 l^8 165186336815311/81920 l^9 1126045351443/1280 l^10 31414510656207/16384 l^11 1567319156385/512 l^12 546786335/4 l^13 3937295627/2 l^14 835180512 l^15 -169745792 l^16 57507840 l^17 16220160 l^18 
YGf_21 = 1769472 l^2 11446272 l^3 53215104 l^4 208339344 l^5 1337878754 l^6 15387042555/32 l^7 8509841729017/2048 l^8 139035555583305/32768 l^9 5297338913505/1024 l^10 252774261063021/32768 l^11 16670060089/2048 l^12 1634740119621/128 l^13 -43140428783/8 l^14 10760806730 l^15 2716639776 l^16 -1018545664 l^17 158146560 l^18 37355520 l^19 

YH

This corresponds to [J-1992] p.22. (text file)

YHf_0 = 
YHf_1 = 
YHf_2 = 
YHf_3 = 10 l^3 
YHf_4 = 
YHf_5 = 
YHf_6 = 24 l^1 -120 l^3 
YHf_7 = 36 l^4 180 l^6 
YHf_8 = 54 l^2 1280 l^3 270 l^4 -1280 l^5 
YHf_9 = 144 l^4 81 l^5 5248 l^6 405 l^7 1200 l^8 
YHf_10 = 432 l^2 243/2 l^3 -1872 l^4 46015/2 l^5 2880 l^6 -9600 l^7 
YHf_11 = 576 l^4 972 l^5 153049/4 l^6 -864 l^7 186173/4 l^8 5940 l^9 6720 l^10 
YHf_12 = 1728 l^2 1944 l^3 115851/8 l^4 1620 l^5 -1060425/8 l^6 269388 l^7 21600 l^8 -61440 l^9 
YHf_13 = 2304 l^4 6480 l^5 246845 l^6 294561/16 l^7 206484 l^8 1984293/16 l^9 306863 l^10 49680 l^11 34560 l^12 
YHf_14 = 6912 l^2 15552 l^3 101793 l^4 849123/32 l^5 -68993 l^6 6713199/32 l^7 -2412958 l^8 2485320 l^9 138240 l^10 -358400 l^11 
YHf_15 = 9216 l^4 36288 l^5 1488916 l^6 801639/4 l^7 33682857/64 l^8 4846768 l^9 -33941939/64 l^10 7734897/4 l^11 1729588 l^12 336960 l^13 168960 l^14 
YHf_16 = 27648 l^2 93312 l^3 588684 l^4 617571 l^5 253180923/128 l^6 -1726263/4 l^7 -32956697/128 l^8 14573025/4 l^9 -29058090 l^10 19728256 l^11 806400 l^12 -1966080 l^13 
YHf_17 = 36864 l^4 186624 l^5 8565520 l^6 1290681 l^7 5649905/16 l^8 17181331697/256 l^9 -106191573/4 l^10 22036167349/256 l^11 -296194413/16 l^12 19526157 l^13 8766704 l^14 2039040 l^15 798720 l^16 
YHf_18 = 110592 l^2 497664 l^3 3122448 l^4 5955120 l^5 357549031/16 l^6 2378797011/512 l^7 1745559539/16 l^8 -48158413281/512 l^9 46635469 l^10 80236521/2 l^11 -280285504 l^12 141183360 l^13 4423680 l^14 -10321920 l^15 
YHf_19 = 147456 l^4 912384 l^5 47509568 l^6 6077052 l^7 -7296495/4 l^8 42830540635/64 l^9 -1270187738019/5120 l^10 10075936939/8 l^11 -326548578723/1024 l^12 62579465365/64 l^13 -793410303/4 l^14 160919844 l^15 40868672 l^16 11473920 l^17 3686400 l^18 
YHf_20 = 442368 l^2 2488320 l^3 15727296 l^4 44327952 l^5 696962947/4 l^6 3682494585/32 l^7 13433135689751/10240 l^8 -68750937219/64 l^9 6669159963415/2048 l^10 -167443324305/64 l^11 9124775587/8 l^12 349114248 l^13 -2344098848 l^14 936494080 l^15 23224320 l^16 -52428800 l^17 
YHf_21 = 589824 l^4 4313088 l^5 255833344 l^6 18739728 l^7 28605225 l^8 89856088429/16 l^9 -1823444336711/1280 l^10 259981224181061/20480 l^11 273436411701/320 l^12 58231405935429/4096 l^13 -361781287433/256 l^14 141813078729/16 l^15 -1543662585 l^16 1171992144 l^17 176512768 l^18 61378560 l^19 16711680 l^20 

XM

This corresponds to [J-1992] p.24. (text file)

XMf_0 = 1 l^0 
XMf_1 = 
XMf_2 = 
XMf_3 = 40 l^3 
XMf_4 = 60 l^1 
XMf_5 = -192 l^3 180 l^4 -192 l^5 
XMf_6 = -288 l^1 540 l^2 1120 l^3 
XMf_7 = 1008 l^4 1620 l^5 1008 l^6 
XMf_8 = 1728/5 l^1 -432 l^2 -9348 l^3 8640 l^4 10560 l^5 
XMf_9 = 5184 l^4 15552 l^5 120644/5 l^6 15552 l^7 5184 l^8 
XMf_10 = 6912/5 l^2 52416 l^3 28380 l^4 -151632 l^5 86400 l^6 76800 l^7 
XMf_11 = 25344 l^4 108864 l^5 846288/5 l^6 1333476/5 l^7 846288/5 l^8 108864 l^9 25344 l^10 
XMf_12 = 27648/5 l^2 373248/5 l^3 911088/5 l^4 1772988 l^5 944800 l^6 -1721280 l^7 691200 l^8 486400 l^9 
XMf_13 = 119808 l^4 663552 l^5 4785024/5 l^6 14643936/5 l^7 6685764/5 l^8 14643936/5 l^9 4785024/5 l^10 663552 l^11 119808 l^12 
XMf_14 = 110592/5 l^2 1741824/5 l^3 5381568/5 l^4 23337504/5 l^5 26497932/5 l^6 32892048 l^7 15311040 l^8 -15778560 l^9 4838400 l^10 2826240 l^11 
XMf_15 = 552960 l^4 3732480 l^5 4982272 l^6 25857792 l^7 14160432 l^8 49955284 l^9 14160432 l^10 25857792 l^11 4982272 l^12 3732480 l^13 552960 l^14 
XMf_16 = 442368/5 l^2 7962624/5 l^3 29928192/5 l^4 146843712/5 l^5 232832592/5 l^6 677990124/5 l^7 421531008/5 l^8 439568640 l^9 178698240 l^10 -125540352 l^11 30965760 l^12 15482880 l^13 
XMf_17 = 2506752 l^4 19906560 l^5 24996864 l^6 199328256 l^7 177928128 l^8 608904192 l^9 1904923524/5 l^10 608904192 l^11 177928128 l^12 199328256 l^13 24996864 l^14 19906560 l^15 2506752 l^16 
XMf_18 = 1769472/5 l^2 35831808/5 l^3 159132672/5 l^4 877851648/5 l^5 2015939456/5 l^6 5681121408/5 l^7 5525964492/5 l^8 13291823408/5 l^9 4759395072/5 l^10 23827356672/5 l^11 1711818752 l^12 -903340032 l^13 185794560 l^14 81264640 l^15 
XMf_19 = 11206656 l^4 102187008 l^5 616574976/5 l^6 1398297600 l^7 1965228288 l^8 5972283840 l^9 35612769552/5 l^10 46545721188/5 l^11 35612769552/5 l^12 5972283840 l^13 1965228288 l^14 1398297600 l^15 616574976/5 l^16 102187008 l^17 11206656 l^18 
XMf_20 = 7077888/5 l^2 31850496 l^3 163491840 l^4 1005972480 l^5 3119909376 l^6 43666563456/5 l^7 14646195696 l^8 28285877820 l^9 18838563168 l^10 40281253056 l^11 42493003776/5 l^12 44647593984 l^13 14342307840 l^14 -6030655488 l^15 1061683200 l^16 412876800 l^17 
XMf_21 = 49545216 l^4 509607936 l^5 3019046912/5 l^6 45733330944/5 l^7 92360497152/5 l^8 50631053312 l^9 477126826752/5 l^10 556070704416/5 l^11 782049133764/5 l^12 556070704416/5 l^13 477126826752/5 l^14 50631053312 l^15 92360497152/5 l^16 45733330944/5 l^17 3019046912/5 l^18 509607936 l^19 49545216 l^20 

YM

This corresponds to [J-1992] p.26. (text file)

YMf_0 = 1 l^0 
YMf_1 = 
YMf_2 = 
YMf_3 = -20 l^3 
YMf_4 = 
YMf_5 = 128 l^3 128 l^5 
YMf_6 = 640 l^3 
YMf_7 = 
YMf_8 = 576/5 l^1 -4736 l^3 6720 l^5 
YMf_9 = 864 l^4 -70336/5 l^6 864 l^8 
YMf_10 = 1296/5 l^2 16384 l^3 2592 l^4 -110592 l^5 6480 l^6 51200 l^7 
YMf_11 = 5760 l^4 1944 l^5 -384128/5 l^6 50544/5 l^7 -384128/5 l^8 1944 l^9 5760 l^10 
YMf_12 = 10368/5 l^2 2916/5 l^3 -100224/5 l^4 543432 l^5 413056 l^6 -1429260 l^7 86400 l^8 332800 l^9 
YMf_13 = 32256 l^4 28512 l^5 -2075282/5 l^6 -111456/5 l^7 4010044/5 l^8 -111456/5 l^9 -2075282/5 l^10 28512 l^11 32256 l^12 
YMf_14 = 41472/5 l^2 46656/5 l^3 241569/5 l^4 31104/5 l^5 2198858/5 l^6 48845376/5 l^7 7961637 l^8 -13910272 l^9 771840 l^10 1966080 l^11 
YMf_15 = 165888 l^4 238464 l^5 -10504088/5 l^6 2462319/10 l^7 77326776/5 l^8 -58069369/5 l^9 77326776/5 l^10 2462319/10 l^11 -10504088/5 l^12 238464 l^13 165888 l^14 
YMf_16 = 165888/5 l^2 373248/5 l^3 2019096/5 l^4 -521559/20 l^5 35748024/5 l^6 25147341/10 l^7 -36148952/5 l^8 538157901/4 l^9 98422504 l^10 -114370240 l^11 5713920 l^12 10895360 l^13 
YMf_17 = 811008 l^4 1617408 l^5 -52329248/5 l^6 31778982/5 l^7 6314768359/40 l^8 -792143918/5 l^9 5332355263/20 l^10 -792143918/5 l^11 6314768359/40 l^12 31778982/5 l^13 -52329248/5 l^14 1617408 l^15 811008 l^16 
YMf_18 = 663552/5 l^2 2239488/5 l^3 12432672/5 l^4 9845064/5 l^5 839861757/16 l^6 -24975324/5 l^7 -3989117387/40 l^8 1906530512/5 l^9 -30632471927/80 l^10 7614311604/5 l^11 967334768 l^12 -839675904 l^13 37785600 l^14 57671680 l^15 
YMf_19 = 3833856 l^4 9787392 l^5 -262277504/5 l^6 371030328/5 l^7 12670455481/10 l^8 -243000162017/160 l^9 4968589311/2 l^10 -153506584393/80 l^11 4968589311/2 l^12 -243000162017/160 l^13 12670455481/10 l^14 371030328/5 l^15 -262277504/5 l^16 9787392 l^17 3833856 l^18 
YMf_20 = 2654208/5 l^2 11943936/5 l^3 68155776/5 l^4 115385472/5 l^5 3538235061/10 l^6 -2708407323/64 l^7 -6635737347/10 l^8 522084860893/160 l^9 -69469988197/10 l^10 3261850805457/320 l^11 -72588024909/10 l^12 14868149364 l^13 8216024320 l^14 -5680647168 l^15 231505920 l^16 294912000 l^17 
YMf_21 = 17694720 l^4 55074816 l^5 -1330606592/5 l^6 3281468256/5 l^7 44538542086/5 l^8 -97723581709/8 l^9 2213421857387/128 l^10 -493166032147/40 l^11 15251992845867/1600 l^12 -493166032147/40 l^13 2213421857387/128 l^14 -97723581709/8 l^15 44538542086/5 l^16 3281468256/5 l^17 -1330606592/5 l^18 55074816 l^19 17694720 l^20 

ZM

This corresponds to [J-1992] p.27. (text file)

ZMf_0 = 1 l^0 
ZMf_1 = 
ZMf_2 = 
ZMf_3 = 
ZMf_4 = 
ZMf_5 = 32 l^3 32 l^5 
ZMf_6 = 
ZMf_7 = 
ZMf_8 = 800 l^5 
ZMf_9 = 
ZMf_10 = 1024 l^3 -6912 l^5 8960 l^7 
ZMf_11 = 
ZMf_12 = 53760 l^5 -144384 l^7 69120 l^9 
ZMf_13 = 25600 l^6 -96000 l^8 25600 l^10 
ZMf_14 = 6193152/5 l^7 -1777664 l^9 450560 l^11 
ZMf_15 = 286720 l^6 -420864 l^8 -420864 l^10 286720 l^12 
ZMf_16 = 18923520 l^9 640000 l^10 -16875520 l^11 2662400 l^13 
ZMf_17 = 2211840 l^6 -954368 l^8 11902976 l^10 -954368 l^12 2211840 l^14 
ZMf_18 = 819200 l^6 -6144000 l^8 18892800 l^10 224919552 l^11 14336000 l^12 -136642560 l^13 14745600 l^15 
ZMf_19 = 14417920 l^6 -1916928 l^8 214253568 l^10 214253568 l^12 -1916928 l^14 14417920 l^16 
ZMf_20 = 9175040 l^6 -19857408 l^8 -56655872 l^10 495452160 l^12 2254307328 l^13 190873600 l^14 -992739328 l^15 77987840 l^17 
ZMf_21 = 85196800 l^6 -38993920 l^8 20480000 l^9 10703863808/5 l^10 -76800000 l^11 87728062464/25 l^12 -76800000 l^13 10703863808/5 l^14 20480000 l^15 -38993920 l^16 85196800 l^18 

XP

This corresponds to [JMB-1993] p.2319. (text file)

XPf_0 = 
XPf_1 = 
XPf_2 = 6 l^1 
XPf_3 = 18 l^1 
XPf_4 = 54 l^2 
XPf_5 = -24 l^1 162 l^2 216 l^3 
XPf_6 = 216 l^2 486 l^3 576 l^4 
XPf_7 = 432 l^2 498 l^3 2592 l^4 1440 l^5 
XPf_8 = 864 l^2 3888 l^3 7446 l^4 7128 l^5 3456 l^6 
XPf_9 = 1728 l^2 9720 l^3 23490 l^4 15720 l^5 23328 l^6 8064 l^7 
XPf_10 = 3456 l^2 23328 l^3 61704 l^4 110214 l^5 81648 l^6 59616 l^7 18432 l^8 
XPf_11 = 6912 l^2 54432 l^3 169152 l^4 364338 l^5 420912 l^6 197568 l^7 165888 l^8 41472 l^9 
XPf_12 = 13824 l^2 124416 l^3 419904 l^4 1079136 l^5 1213494 l^6 1542024 l^7 727968 l^8 404352 l^9 92160 l^10 
XPf_13 = 27648 l^2 279936 l^3 1068192 l^4 3169800 l^5 4585314 l^6 6489720 l^7 4936320 l^8 1785600 l^9 1036800 l^10 202752 l^11 
XPf_14 = 55296 l^2 622080 l^3 2553600 l^4 8510400 l^5 13418040 l^6 22764582 l^7 18567840 l^8 15779520 l^9 5568000 l^10 2446848 l^11 442368 l^12 
XPf_15 = 110592 l^2 1368576 l^3 6202368 l^4 23205312 l^5 42376656 l^6 81576018 l^7 76665408 l^8 80753760 l^9 45861120 l^10 13499904 l^11 5971968 l^12 958464 l^13 
XPf_16 = 221184 l^2 2985984 l^3 14436864 l^4 58959360 l^5 122032800 l^6 252572688 l^7 306683478 l^8 322093368 l^9 217150272 l^10 134426880 l^11 38198784 l^12 13768704 l^13 2064384 l^14 
XPf_17 = 442368 l^2 6469632 l^3 33980928 l^4 152789760 l^5 347262720 l^6 813885336 l^7 1008696834 l^8 1387664136 l^9 969383520 l^10 809585280 l^11 367170048 l^12 91133952 l^13 32514048 l^14 4423680 l^15 
XPf_18 = 884736 l^2 13934592 l^3 77543424 l^4 374395392 l^5 969435264 l^6 2343110112 l^7 3813840744 l^8 4738621638 l^9 4855162320 l^10 3607691808 l^11 2098392576 l^12 1013617152 l^13 242110464 l^14 73654272 l^15 9437184 l^16 
XPf_19 = 1769472 l^2 29859840 l^3 178421760 l^4 935124480 l^5 2584710912 l^6 7007732064 l^7 11320516320 l^8 18024585330 l^9 17388498000 l^10 18244338048 l^11 10175821824 l^12 7016647680 l^13 2650152960 l^14 568688640 l^15 169869312 l^16 20054016 l^17 
XPf_20 = 3538944 l^2 63700992 l^3 400982016 l^4 2232631296 l^5 6981338112 l^6 19200771072 l^7 39207622272 l^8 56645875392 l^9 77126061942 l^10 68618207976 l^11 60182814816 l^12 34580385408 l^13 17714182656 l^14 7002003456 l^15 1445732352 l^16 379551744 l^17 42467328 l^18 
XPf_21 = 7077888 l^2 135364608 l^3 906928128 l^4 5423265792 l^5 17815054848 l^6 54356448384 l^7 110190210528 l^8 195783216936 l^9 254871462306 l^10 298506547608 l^11 239229667008 l^12 200832265728 l^13 93444148224 l^14 54742044672 l^15 17719492608 l^16 3349020672 l^17 859963392 l^18 89653248 l^19 

XQ

This corresponds to [JMB-1993] p.2321. (text file)

XQf [0] = 
XQf [1] = 
XQf [2] = 
XQf [3] =  20 l^3
XQf [4] =  30 l
XQf [5] =  90 l^4
XQf [6] =  -72 l +270 l^2 +680 l^3
XQf [7] =  720 l^4 +810 l^5 +864 l^6
XQf [8] =  432 l^2 -1410 l^3 +5400 l^4 +6240 l^5
XQf [9] =  4320 l^4 +9720 l^5 +19898 l^6 +11016 l^7 +4608 l^8
XQf [10] =  1728 l^2 +13608 l^3 +37518 l^4 -8880 l^5 +60480 l^6 +44160 l^7
XQf [11] =  23040 l^4 +77760 l^5 +203424 l^6 +224586 l^7 +162864 l^8 +85536 l^9 +23040 l^10
XQf [12] =  6912 l^2 +69984 l^3 +236448 l^4 +621054 l^5 +924680 l^6 +3456 l^7 +518400 l^8 +273920 l^9
XQf [13] =  115200 l^4 +518400 l^5 +1565760 l^6 +2729160 l^7 +2312250 l^8 +2738520 l^9 +1206240 l^10 +549504 l^11 +110592 l^12
XQf [14] =  27648 l^2 +342144 l^3 +1382112 l^4 +4850712 l^5 +8124078 l^6 +13075776 l^7 +13548960 l^8 +679680 l^9 +3801600 l^10 +1566720 l^11
XQf [15] =  552960 l^4 +3110400 l^5 +10396160 l^6 +25699680 l^7 +25315440 l^8 +49727210 l^9 +28241664 l^10 +25436736 l^11 +8205824 l^12 +3193344 l^13 +516096 l^14
XQf [16] =  110592 l^2 +1617408 l^3 +7636992 l^4 +32920128 l^5 +64754064 l^6 +145034910 l^7 +154469496 l^8 +187929504 l^9 +149616000 l^10 +9088512 l^11 +25159680 l^12 +8478720 l^13
XQf [17] =  2580480 l^4 +17418240 l^5 +63008256 l^6 +206962560 l^7 +243401760 l^8 +651019800 l^9 +508638042 l^10 +629017512 l^11 +303555648 l^12 +201864960 l^13 +52093440 l^14 +17418240 l^15 +2359296 l^16
XQf [18] =  442368 l^2 +7464960 l^3 +40435200 l^4 +205113600 l^5 +485033600 l^6 +1317939336 l^7 +1644392910 l^8 +2842892720 l^9 +2134277760 l^10 +2137798656 l^11 +1381209088 l^12 +85155840 l^13 +154828800 l^14 +44072960 l^15
XQf [19] =  11796480 l^4 +92897280 l^5 +358858752 l^6 +1497775104 l^7 +2128530432 l^8 +6888094080 l^9 +7346678592 l^10 +10542284682 l^11 +7810442448 l^12 +6433500384 l^13 +2817792000 l^14 +1442557440 l^15 +312840192 l^16 +90906624 l^17 +10616832 l^18
XQf [20] =  1769472 l^2 +33841152 l^3 +207101952 l^4 +1204277760 l^5 +3417772800 l^6 +10573174944 l^7 +16674309504 l^8 +33326943294 l^9 +29933012328 l^10 +42547253568 l^11 +24073191936 l^12 +20731769856 l^13 +11261816832 l^14 +670433280 l^15 +902430720 l^16 +222167040 l^17
XQf [21] =  53084160 l^4 +477757440 l^5 +1953529856 l^6 +10025938944 l^7 +17174793216 l^8 +62815158784 l^9 +88147380864 l^10 +137779541352 l^11 +146743042938 l^12 +134017937400 l^13 +94529034528 l^14 +57248498560 l^15 +23207271936 l^16 +9556936704 l^17 +1796366336 l^18 +459177984 l^19 +47185920 l^20

TQ

This corresponds to [KSB-2006]. (text file)

TQf_0 = 
TQf_1 = 
TQf_2 = 
TQf_3 = 
TQf_4 = 12 l^1 
TQf_5 = 36 l^4 
TQf_6 = 108 l^2 320 l^3 
TQf_7 = 432 l^4 324 l^5 432 l^6 
TQf_8 = 432 l^2 972 l^3 2592 l^4 3360 l^5 
TQf_9 = 2880 l^4 5184 l^5 11876 l^6 5184 l^7 2880 l^8 
TQf_10 = 1728 l^2 7776 l^3 26412 l^4 27216 l^5 32832 l^6 129024/5 l^7 
TQf_11 = 16128 l^4 46656 l^5 131280 l^6 133380 l^7 131280 l^8 46656 l^9 16128 l^10 
TQf_12 = 6912 l^2 46656 l^3 192528 l^4 375948 l^5 626816 l^6 404352 l^7 304128 l^8 168960 l^9 
TQf_13 = 82944 l^4 331776 l^5 1101696 l^6 1809504 l^7 2145636 l^8 1809504 l^9 1101696 l^10 331776 l^11 82944 l^12 
TQf_14 = 27648 l^2 248832 l^3 1208448 l^4 3402432 l^5 6842988 l^6 8419248 l^7 9133440 l^8 4354560 l^9 2350080 l^10 7028736/7 l^11 
TQf_15 = 405504 l^4 2073600 l^5 7953920 l^6 18167040 l^7 26324208 l^8 35577668 l^9 26324208 l^10 18167040 l^11 7953920 l^12 2073600 l^13 405504 l^14 
TQf_16 = 110592 l^2 1244160 l^3 6950400 l^4 25315200 l^5 59629680 l^6 106613964 l^7 135997920 l^8 126826560 l^9 101099520 l^10 38568960 l^11 16146432 l^12 5591040 l^13 
TQf_17 = 1916928 l^4 11943936 l^5 52067328 l^6 152547840 l^7 268720320 l^8 486235776 l^9 2331921204/5 l^10 486235776 l^11 268720320 l^12 152547840 l^13 52067328 l^14 11943936 l^15 1916928 l^16 
TQf_18 = 442368 l^2 5971968 l^3 37721088 l^4 167685120 l^5 456852800 l^6 1055686176 l^7 1568133036 l^8 2152103696 l^9 1966448064 l^10 1494726912 l^11 937919488 l^12 299593728 l^13 102187008 l^14 89128960/3 l^15 
TQf_19 = 8847360 l^4 65028096 l^5 317927424 l^6 1136894976 l^7 2394912000 l^8 5308044480 l^9 32639537232/5 l^10 8574343044 l^11 32639537232/5 l^12 5308044480 l^13 2394912000 l^14 1136894976 l^15 317927424 l^16 65028096 l^17 8847360 l^18 
TQf_20 = 1769472 l^2 27869184 l^3 196374528 l^4 1027482624 l^5 3207115008 l^6 8973042624 l^7 15616041168 l^8 27426948876 l^9 29343312960 l^10 32792752128 l^11 23146199040 l^12 14896465920 l^13 7690518528 l^14 2118057984 l^15 608698368 l^16 762052608/5 l^17 
TQf_21 = 40108032 l^4 339738624 l^5 1842544640 l^6 7777566720 l^7 19235543040 l^8 49734135808 l^9 76029297408 l^10 116927873184 l^11 118823623652 l^12 116927873184 l^13 76029297408 l^14 49734135808 l^15 19235543040 l^16 7777566720 l^17 1842544640 l^18 339738624 l^19 40108032 l^20 


Appendix

Here, we study two sheres of radii $a_1$ and $a_2$ at $\mathbf{x}_1$ and $\mathbf{x}_2$. Following Jeffrey and Onishi (1984), we use two non-dimensional parameters
$\displaystyle{ s = \frac{2r}{a_1 + a_2},\quad \lambda = \frac{a_2}{a_1}, }$
where $\mathbf{r} = \mathbf{x}_2 - \mathbf{x}_1$. Resistance problem is given by the resistance matrix
$\displaystyle{ \left[\begin{array}{c} \mathbf{F}\\ \mathbf{T}\\ \mathbf{S} \end{array}\right] = \mu \left[\begin{array}{ccc} \mathbf{A} & \tilde{\mathbf{B}} & \tilde{\mathbf{G}}\\ \mathbf{B} & \mathbf{C} & \tilde{\mathbf{H}}\\ \mathbf{G} & \mathbf{H} & \mathbf{M} \end{array}\right] \cdot \left[\begin{array}{c} \mathbf{U}\\ \mathbf{\Omega}\\ \mathbf{E} \end{array}\right] , }$
where each vector on both sides has elements for two particles and each sub-matrix has four sub-components of all particle-particle pairs, 11, 12, 21, and 22. From the symmetry, those resistance matrices are given by
$ \begin{eqnarray} A_{ij}^{\alpha\beta} &=& X_{\alpha\beta}^A e_i e_j + Y_{\alpha\beta}^A (\delta_{ij} + e_i e_j),\\ B_{ij}^{\alpha\beta} &=& Y_{\alpha\beta}^B \varepsilon_{ijk} e_k,\\ C_{ij}^{\alpha\beta} &=& X_{\alpha\beta}^C e_i e_j + Y_{\alpha\beta}^C (\delta_{ij} + e_i e_j), \end{eqnarray} }$
where $\mathbf{e} = \mathbf{r} / r$.
$ \begin{eqnarray} X_{11}^{A}(s,\lambda) & = & \sum_{k=0}^{\infty} f_{2k}(\lambda) (1+\lambda)^{-2k} s^{-2k},\\ X_{12}^{A}(s,\lambda) &=& \frac{-2}{1+\lambda} \sum_{k=0}^\infty f_{2k+1}(\lambda) (1+\lambda)^{-2k-1} s^{-2k-1}, \end{eqnarray} }$
where
$\displaystyle{ f_k(\lambda) = 2^k \sum_{q=0}^k P_{1,k-q,q} \lambda^q. }$

References