# sv_certificates_w19-21.txt -- single-valuedness certificates for the 26 deep Laurent coefficients c_{3-w} of the two-vertex four-edge # modular graph functions C_{a,b,c,d} of weights w = 11 and 12 (transcendental weights 2w-3 = 19 and 21): each c_{3-w} as an exact # rational combination of single-valued multiple zeta values zsv(a,b,c) = zeta_sv(a,b,c) of weight 2w-3 and of odd-zeta monomials. # Conventions as in laurent_C4_w7-12.txt and zsv_depth3_w11-21.txt: ascending indices (Eq. (8) of the paper; Brown arXiv:1309.5309), # zeta(n) single zeta, zeta(2)^j powers of zeta(2), '*' product, exact rationals. Four parts: # PART 1 the 26 certificates, one block each: a b c d w k = 3-w then one term per line; eleven terms at weight 19, fourteen at 21. # PART 2 the 49 values zsv(a,b,c) of weights 19 and 21 in the reduced basis of the Laurent file (one line each), for checking PART 1 # by substitution against the c_{3-w} lines of laurent_C4_w7-12.txt. # PART 3 the reductions to that basis of the 42 multiple-zeta-value monomials of the weight-19/21 formulas of zsv_depth3_w11-21.txt # that are not basis monomials (regularized double shuffle, depth <= 3), for checking formula -> PART 2 by substitution. # PART 4 the f-alphabet images phi(x) of the 32 depth-two and depth-three basis generators x through weight 21 (word: coefficient); # words are the reversals of Brown's (last letter = the one a derivation D_m strips, Eq. (67) of the paper); phi(zeta(n)) = f_n, # phi(zeta(2)) = f2; sv(w) = sum_{w=uv} reverse(u) shuffle v, sv(f2) = 0 (Eq. (10)); no pure f2-power word in an even-weight # generator (a free normalization on which no formula or certificate depends). # The JSON file of the same name carries the same data and the verification recipe; check_svcert_anc.py in this directory runs it. Generated 2026-09-28T16:39:13Z. # PART 1: certificates (26) 8 1 1 1 w=11 k=-8 transcendental weight 19 (11 terms: 11 zsv + 0 odd-zeta monomials) c_{-8} = + 1035353002567/2904224526773504*zsv(11,3,5) + 15632744128772707/3717407394270085120*zsv(13,3,3) + 332095881374857/1858703697135042560*zsv(3,11,5) + 3105372750663279/675892253503651840*zsv(3,13,3) + 9191194867742227/1858703697135042560*zsv(3,3,13) - 3242382217911/47966547022839808*zsv(3,5,11) + 22488039/119057776640*zsv(3,7,9) - 1831621015863949/7434814788540170240*zsv(5,11,3) - 62658272742847/135178450700730368*zsv(5,3,11) + 1022409/5411717120*zsv(5,5,9) + 3546837/23811555328*zsv(7,3,9) 7 2 1 1 w=11 k=-8 transcendental weight 19 (11 terms: 11 zsv + 0 odd-zeta monomials) c_{-8} = + 5416975452289655/11709833291950768128*zsv(11,3,5) - 7504066181200669699/234196665839015362560*zsv(13,3,3) + 36119291669959511/117098332919507681280*zsv(3,11,5) - 64395758137312183/2027676760510955520*zsv(3,13,3) - 1881067251391983437/58549166459753840640*zsv(3,3,13) + 97375842248159/335765829159878656*zsv(3,5,11) + 308908013/833404436480*zsv(3,7,9) - 24304333056127847/468393331678030725120*zsv(5,11,3) - 6266401640648549/8516242394146013184*zsv(5,3,11) + 1903909/5411717120*zsv(5,5,9) - 38564927/166680887296*zsv(7,3,9) 6 3 1 1 w=11 k=-8 transcendental weight 19 (11 terms: 11 zsv + 0 odd-zeta monomials) c_{-8} = - 2099963920988343923/234196665839015362560*zsv(11,3,5) - 177289200441333507449/468393331678030725120*zsv(13,3,3) - 2669350259932330697/234196665839015362560*zsv(3,11,5) - 1563386040872163083/4055353521021911040*zsv(3,13,3) - 89247221700916056179/234196665839015362560*zsv(3,3,13) - 41184158527313413/3357658291598786560*zsv(3,5,11) - 438545103/416702218240*zsv(3,7,9) + 167988217807705613/936786663356061450240*zsv(5,11,3) + 99827378582489339/17032484788292026368*zsv(5,3,11) - 5516533/5411717120*zsv(5,5,9) + 1367968887/166680887296*zsv(7,3,9) 6 2 2 1 w=11 k=-8 transcendental weight 19 (11 terms: 11 zsv + 0 odd-zeta monomials) c_{-8} = + 793823099519191571/117098332919507681280*zsv(11,3,5) + 116536248342310181411/234196665839015362560*zsv(13,3,3) + 1072402647173292887/117098332919507681280*zsv(3,11,5) + 1020819905334837317/2027676760510955520*zsv(3,13,3) + 58495924011599470031/117098332919507681280*zsv(3,3,13) + 17333023123982131/1678829145799393280*zsv(3,5,11) + 243415919/416702218240*zsv(3,7,9) + 128610495529980493/468393331678030725120*zsv(5,11,3) - 36960969606686429/8516242394146013184*zsv(5,3,11) + 392523/676464640*zsv(5,5,9) - 308496025/41670221824*zsv(7,3,9) 5 4 1 1 w=11 k=-8 transcendental weight 19 (11 terms: 11 zsv + 0 odd-zeta monomials) c_{-8} = + 93086429485515107/2365622887262781440*zsv(11,3,5) + 58193150559793665/946249154905112576*zsv(13,3,3) + 94162189560479157/2365622887262781440*zsv(3,11,5) + 16436075882603355/270356901401460736*zsv(3,13,3) + 23688125800093767/473124577452556288*zsv(3,3,13) + 12335113232322273/305241662872616960*zsv(3,5,11) + 4401941/3788201984*zsv(3,7,9) + 473383093958595/1892498309810225152*zsv(5,11,3) - 14192881125223837/1892498309810225152*zsv(5,3,11) + 1037179/1082343424*zsv(5,5,9) - 116183365/15152807936*zsv(7,3,9) 5 3 2 1 w=11 k=-8 transcendental weight 19 (11 terms: 11 zsv + 0 odd-zeta monomials) c_{-8} = - 4211255849429779/522760414819230720*zsv(11,3,5) + 17145862102595233501/33456666548430766080*zsv(13,3,3) - 50828598206571617/16728333274215383040*zsv(3,11,5) + 1071899417271336979/2027676760510955520*zsv(3,13,3) + 4431140512771865753/8364166637107691520*zsv(3,3,13) - 607248632347273/239832735114199040*zsv(3,5,11) + 61313643/119057776640*zsv(3,7,9) - 83847208635074587/66913333096861532160*zsv(5,11,3) - 7821569223135985/1216606056306573312*zsv(5,3,11) + 4561363/5411717120*zsv(5,5,9) - 267738711/23811555328*zsv(7,3,9) 5 2 2 2 w=11 k=-8 transcendental weight 19 (11 terms: 11 zsv + 0 odd-zeta monomials) c_{-8} = - 692860812169711169/13010925879945297920*zsv(11,3,5) - 79287464841957633521/26021851759890595840*zsv(13,3,3) - 200618130412882393/2602185175989059584*zsv(3,11,5) - 2109296608801386261/675892253503651840*zsv(3,13,3) - 40329078165465735461/13010925879945297920*zsv(3,3,13) - 138886154378273961/1678829145799393280*zsv(3,5,11) - 1946649021/416702218240*zsv(3,7,9) + 212317407721516577/52043703519781191680*zsv(5,11,3) + 44110600509824207/946249154905112576*zsv(5,3,11) - 4059807/676464640*zsv(5,5,9) + 2958640491/41670221824*zsv(7,3,9) 4 4 2 1 w=11 k=-8 transcendental weight 19 (11 terms: 11 zsv + 0 odd-zeta monomials) c_{-8} = - 853194366405271655/11709833291950768128*zsv(11,3,5) - 15975271255945164319/117098332919507681280*zsv(13,3,3) - 4398271019561522659/58549166459753840640*zsv(3,11,5) - 142281634631568193/1013838380255477760*zsv(3,13,3) - 7109120788400267449/58549166459753840640*zsv(3,3,13) - 12733780627741267/167882914579939328*zsv(3,5,11) - 511753951/208351109120*zsv(3,7,9) + 64389133352528503/234196665839015362560*zsv(5,11,3) + 71447222679934777/4258121197073006592*zsv(5,3,11) - 1561539/676464640*zsv(5,5,9) + 184773793/10417555456*zsv(7,3,9) 4 3 3 1 w=11 k=-8 transcendental weight 19 (11 terms: 11 zsv + 0 odd-zeta monomials) c_{-8} = - 22480567227597497/944341394512158720*zsv(11,3,5) - 179728162070112097/377736557804863488*zsv(13,3,3) - 27043887731412857/944341394512158720*zsv(3,11,5) - 1622482540460719/3270446387920896*zsv(3,13,3) - 46536598228390517/94434139451215872*zsv(3,3,13) - 12113200223220247/419707286449848320*zsv(3,5,11) - 58279/42006272*zsv(3,7,9) + 1485915971475289/755473115609726976*zsv(5,11,3) + 993659403136907/68679374146338816*zsv(5,3,11) - 3837/2182144*zsv(5,5,9) + 3024755/168025088*zsv(7,3,9) 4 3 2 2 w=11 k=-8 transcendental weight 19 (11 terms: 11 zsv + 0 odd-zeta monomials) c_{-8} = + 7073996200169586313/58549166459753840640*zsv(11,3,5) + 51250724176160400229/117098332919507681280*zsv(13,3,3) + 7355592590041479577/58549166459753840640*zsv(3,11,5) + 461031351721799563/1013838380255477760*zsv(3,13,3) + 24973942252581561499/58549166459753840640*zsv(3,3,13) + 106552691220400853/839414572899696640*zsv(3,5,11) + 830458561/208351109120*zsv(3,7,9) - 366643717598246173/234196665839015362560*zsv(5,11,3) - 136752958563554995/4258121197073006592*zsv(5,3,11) + 2789229/676464640*zsv(5,5,9) - 180329909/5208777728*zsv(7,3,9) 3 3 3 2 w=11 k=-8 transcendental weight 19 (11 terms: 11 zsv + 0 odd-zeta monomials) c_{-8} = - 54109927833645441/650546293997264896*zsv(11,3,5) + 214393631967119631/6505462939972648960*zsv(13,3,3) - 270486330531814869/3252731469986324480*zsv(3,11,5) + 6036958995759171/168973063375912960*zsv(3,13,3) + 185577793185527301/3252731469986324480*zsv(3,3,13) - 7058111431449861/83941457289969664*zsv(3,5,11) - 232026309/104175554560*zsv(3,7,9) - 4463916909358647/13010925879945297920*zsv(5,11,3) + 3578599250875527/236562288726278144*zsv(5,3,11) - 685611/338232320*zsv(5,5,9) + 4637277/325548608*zsv(7,3,9) 9 1 1 1 w=12 k=-9 transcendental weight 21 (14 terms: 11 zsv + 3 odd-zeta monomials) c_{-9} = + 12930720003/5433020217425920*zsv(11,5,5) - 2903399493/388072872673280*zsv(13,5,3) - 675790940955/11952644478337024*zsv(3,11,7) + 244322889123/5433020217425920*zsv(3,13,5) + 780707307521/29881611195842560*zsv(3,9,9) + 129599348047/7470402798960640*zsv(5,7,9) - 32976893779/11952644478337024*zsv(5,9,7) - 166182109815/3415041279524864*zsv(7,3,11) - 5410552904325/2988161119584256*zsv(7,7,7) + 315938706543/8537603198812160*zsv(9,7,5) - 525460624791/14940805597921280*zsv(9,9,3) + 22946366197661337611/5020110680901550080*zeta(21) + 3312608933517/9701821816832*zeta(3)^2*zeta(15) + 17420685595953/194036436336640*zeta(3)*zeta(5)*zeta(13) 8 2 1 1 w=12 k=-9 transcendental weight 21 (14 terms: 11 zsv + 3 odd-zeta monomials) c_{-9} = + 211101465439/2716510108712960*zsv(11,5,5) - 5246653427/339563763589120*zsv(13,5,3) - 382815053275/5976322239168512*zsv(3,11,7) - 49978633071/2716510108712960*zsv(3,13,5) - 1287353169343/6403202399109120*zsv(3,9,9) + 415902929999/14940805597921280*zsv(5,7,9) - 1086567321883/17928966717505536*zsv(5,9,7) + 257671370455/11952644478337024*zsv(7,3,11) + 137900306075/53360019992576*zsv(7,7,7) - 1422584368427/29881611195842560*zsv(9,7,5) + 141859861061/1067200399851520*zsv(9,9,3) + 201595723191500270417/3765083010676162560*zeta(21) - 235240618405/4850910908416*zeta(3)^2*zeta(15) + 19225734918183/679127527178240*zeta(3)*zeta(5)*zeta(13) 7 3 1 1 w=12 k=-9 transcendental weight 21 (14 terms: 11 zsv + 3 odd-zeta monomials) c_{-9} = - 505100566081/543302021742592*zsv(11,5,5) + 43062062247/543302021742592*zsv(13,5,3) - 387590630085/853760319881216*zsv(3,11,7) + 676880384783/543302021742592*zsv(3,13,5) + 91604567999057/35857933435011072*zsv(3,9,9) - 449512367/3335001249536*zsv(5,7,9) + 3576654882547/5976322239168512*zsv(5,9,7) - 35823854893455/23905288956674048*zsv(7,3,11) - 413186242270485/5976322239168512*zsv(7,7,7) + 9376239052311/5976322239168512*zsv(9,7,5) - 22250818897095/11952644478337024*zsv(9,9,3) - 1182859479296482369055/3012066408540930048*zeta(21) - 2799034046055/9701821816832*zeta(3)^2*zeta(15) - 17906129636785/67912752717824*zeta(3)*zeta(5)*zeta(13) 7 2 2 1 w=12 k=-9 transcendental weight 21 (14 terms: 11 zsv + 3 odd-zeta monomials) c_{-9} = + 1551211278193/2716510108712960*zsv(11,5,5) - 155583756273/679127527178240*zsv(13,5,3) + 34524854055/77614574534656*zsv(3,11,7) - 3280748787327/2716510108712960*zsv(3,13,5) - 5999648523203/2716510108712960*zsv(3,9,9) + 32204138779/194036436336640*zsv(5,7,9) - 225763480489/543302021742592*zsv(5,9,7) + 689941948585/543302021742592*zsv(7,3,11) + 2300815738155/33956376358912*zsv(7,7,7) - 3315111068659/2716510108712960*zsv(9,7,5) + 4245757394241/2716510108712960*zsv(9,9,3) + 24571325501939752411/85570068424458240*zeta(21) + 2022588831549/2425455454208*zeta(3)^2*zeta(15) + 278177335474071/679127527178240*zeta(3)*zeta(5)*zeta(13) 6 4 1 1 w=12 k=-9 transcendental weight 21 (14 terms: 11 zsv + 3 odd-zeta monomials) c_{-9} = + 1673476754367/2716510108712960*zsv(11,5,5) + 831819574151/1358255054356480*zsv(13,5,3) + 104353630495/853760319881216*zsv(3,11,7) + 933163734837/2716510108712960*zsv(3,13,5) - 71924433208717/29881611195842560*zsv(3,9,9) - 2054547989497/6403202399109120*zsv(5,7,9) - 4720695088451/17928966717505536*zsv(5,9,7) + 394266122755/2988161119584256*zsv(7,3,11) + 45719978591085/2988161119584256*zsv(7,7,7) - 14096885904671/29881611195842560*zsv(9,7,5) + 83554814287579/29881611195842560*zsv(9,9,3) + 1680393389539637855443/1882541505338081280*zeta(21) - 10813654463963/4850910908416*zeta(3)^2*zeta(15) - 1054679300943171/679127527178240*zeta(3)*zeta(5)*zeta(13) 6 3 2 1 w=12 k=-9 transcendental weight 21 (14 terms: 11 zsv + 3 odd-zeta monomials) c_{-9} = + 5740518774873/5433020217425920*zsv(11,5,5) - 2359211702991/2716510108712960*zsv(13,5,3) + 19479483225/19403643633664*zsv(3,11,7) - 8358892536291/2716510108712960*zsv(3,13,5) - 599457354689/169781881794560*zsv(3,9,9) + 519063767703/776145745346560*zsv(5,7,9) - 58811314701/67912752717824*zsv(5,9,7) + 6514434743505/2173208086970368*zsv(7,3,11) + 20546729096535/135825505435648*zsv(7,7,7) - 3715887558531/1358255054356480*zsv(9,7,5) + 2327453464179/1358255054356480*zsv(9,9,3) + 19667568655396767851/456373698263777280*zeta(21) + 30669752138883/9701821816832*zeta(3)^2*zeta(15) + 3451556617963311/1358255054356480*zeta(3)*zeta(5)*zeta(13) 6 2 2 2 w=12 k=-9 transcendental weight 21 (14 terms: 11 zsv + 3 odd-zeta monomials) c_{-9} = - 381538992393/135825505435648*zsv(11,5,5) + 646666252947/135825505435648*zsv(13,5,3) - 64260564975/19403643633664*zsv(3,11,7) + 818139476781/67912752717824*zsv(3,13,5) + 5105525390067/271651010871296*zsv(3,9,9) - 82312517655/19403643633664*zsv(5,7,9) + 152932281885/67912752717824*zsv(5,9,7) - 6171642151155/543302021742592*zsv(7,3,11) - 92649643814745/135825505435648*zsv(7,7,7) + 355207120281/33956376358912*zsv(9,7,5) - 3147050874195/271651010871296*zsv(9,9,3) - 8232939061774498633/7606228304396288*zeta(21) - 42033306441555/2425455454208*zeta(3)^2*zeta(15) - 47787278154759/4244547044864*zeta(3)*zeta(5)*zeta(13) 5 5 1 1 w=12 k=-9 transcendental weight 21 (14 terms: 11 zsv + 3 odd-zeta monomials) c_{-9} = - 1232971316555/543302021742592*zsv(11,5,5) + 7896054903/135825505435648*zsv(13,5,3) - 102736720435/77614574534656*zsv(3,11,7) + 1613729714311/543302021742592*zsv(3,13,5) - 4476018805285/1629906065227776*zsv(3,9,9) + 62376847055/116421861801984*zsv(5,7,9) + 2508589588913/1629906065227776*zsv(5,9,7) - 1662318594415/543302021742592*zsv(7,3,11) - 15950224371765/271651010871296*zsv(7,7,7) + 1627976464551/543302021742592*zsv(9,7,5) + 2438349517081/543302021742592*zsv(9,9,3) + 46659519775958942821/34228027369783296*zeta(21) - 513243568695/2425455454208*zeta(3)^2*zeta(15) - 225963782927641/135825505435648*zeta(3)*zeta(5)*zeta(13) 5 4 2 1 w=12 k=-9 transcendental weight 21 (14 terms: 11 zsv + 3 odd-zeta monomials) c_{-9} = + 752696540585/543302021742592*zsv(11,5,5) - 163653081691/135825505435648*zsv(13,5,3) + 85758078045/77614574534656*zsv(3,11,7) - 1975286728657/543302021742592*zsv(3,13,5) + 4885230432405/543302021742592*zsv(3,9,9) + 4788198805/58210930900992*zsv(5,7,9) - 575725739447/543302021742592*zsv(5,9,7) + 1543727860505/543302021742592*zsv(7,3,11) + 1942070362805/271651010871296*zsv(7,7,7) - 1330127496297/543302021742592*zsv(9,7,5) - 6236494526627/543302021742592*zsv(9,9,3) - 486305827012139259383/136912109479133184*zeta(21) + 10637450309915/2425455454208*zeta(3)^2*zeta(15) + 641538614963587/135825505435648*zeta(3)*zeta(5)*zeta(13) 5 3 3 1 w=12 k=-9 transcendental weight 21 (14 terms: 11 zsv + 3 odd-zeta monomials) c_{-9} = + 2611069586697/543302021742592*zsv(11,5,5) + 449244481719/67912752717824*zsv(13,5,3) + 104830607475/77614574534656*zsv(3,11,7) + 1979564498637/543302021742592*zsv(3,13,5) - 1588649566549/543302021742592*zsv(3,9,9) - 198592408833/38807287267328*zsv(5,7,9) - 1607270126685/543302021742592*zsv(5,9,7) + 6962392785/16978188179456*zsv(7,3,11) - 21167346041865/135825505435648*zsv(7,7,7) - 614102278383/543302021742592*zsv(9,7,5) + 3559619523099/543302021742592*zsv(9,9,3) + 19398958223050415113/5704671228297216*zeta(21) - 29200891311735/1212727727104*zeta(3)^2*zeta(15) - 2019281711731845/135825505435648*zeta(3)*zeta(5)*zeta(13) 5 3 2 2 w=12 k=-9 transcendental weight 21 (14 terms: 11 zsv + 3 odd-zeta monomials) c_{-9} = - 1022977887987/135825505435648*zsv(11,5,5) - 688758533133/135825505435648*zsv(13,5,3) - 265547775105/77614574534656*zsv(3,11,7) + 1334401604085/543302021742592*zsv(3,13,5) - 1100851743737/135825505435648*zsv(3,9,9) + 397551456993/77614574534656*zsv(5,7,9) + 2751130044213/543302021742592*zsv(5,9,7) - 1510458954465/271651010871296*zsv(7,3,11) + 33787978817895/271651010871296*zsv(7,7,7) + 3138343002891/543302021742592*zsv(9,7,5) + 2297137694601/271651010871296*zsv(9,9,3) + 629644435871666823/475389269024768*zeta(21) + 44769304653645/2425455454208*zeta(3)^2*zeta(15) + 554683521340047/67912752717824*zeta(3)*zeta(5)*zeta(13) 4 4 3 1 w=12 k=-9 transcendental weight 21 (14 terms: 11 zsv + 3 odd-zeta monomials) c_{-9} = - 2197325271999/271651010871296*zsv(11,5,5) - 301208313043/67912752717824*zsv(13,5,3) - 81164983155/19403643633664*zsv(3,11,7) + 647524114501/135825505435648*zsv(3,13,5) - 62304492557/271651010871296*zsv(3,9,9) + 524616495761/116421861801984*zsv(5,7,9) + 193897303637/33956376358912*zsv(5,9,7) - 1070182810565/135825505435648*zsv(7,3,11) - 12713102222255/135825505435648*zsv(7,7,7) + 528646524683/67912752717824*zsv(9,7,5) + 504598762513/271651010871296*zsv(9,9,3) - 6569047548144272705/34228027369783296*zeta(21) + 19578540347795/1212727727104*zeta(3)^2*zeta(15) + 463307025512749/67912752717824*zeta(3)*zeta(5)*zeta(13) 4 4 2 2 w=12 k=-9 transcendental weight 21 (14 terms: 11 zsv + 3 odd-zeta monomials) c_{-9} = - 138451816173/67912752717824*zsv(11,5,5) + 224512802789/16978188179456*zsv(13,5,3) - 4486036515/1212727727104*zsv(3,11,7) + 362682727451/16978188179456*zsv(3,13,5) - 3876245098639/67912752717824*zsv(3,9,9) - 200857040803/29105465450496*zsv(5,7,9) + 62684488571/33956376358912*zsv(5,9,7) - 418864220255/33956376358912*zsv(7,3,11) + 223422342595/8489094089728*zsv(7,7,7) + 409155989107/33956376358912*zsv(9,7,5) + 4962020091151/67912752717824*zsv(9,9,3) + 205862673276311000515/8557006842445824*zeta(21) - 14593332181285/303181931776*zeta(3)^2*zeta(15) - 704764845826877/16978188179456*zeta(3)*zeta(5)*zeta(13) 4 3 3 2 w=12 k=-9 transcendental weight 21 (14 terms: 11 zsv + 3 odd-zeta monomials) c_{-9} = + 3967977064095/271651010871296*zsv(11,5,5) - 140356275741/67912752717824*zsv(13,5,3) + 179505919935/19403643633664*zsv(3,11,7) - 3045103718481/135825505435648*zsv(3,13,5) + 1640601600171/38807287267328*zsv(3,9,9) - 84961443267/38807287267328*zsv(5,7,9) - 177351169797/16978188179456*zsv(5,9,7) + 2854680854085/135825505435648*zsv(7,3,11) + 1651050939015/67912752717824*zsv(7,7,7) - 1448328377925/67912752717824*zsv(9,7,5) - 2171379499191/38807287267328*zsv(9,9,3) - 32513012744171013093/1901557076099072*zeta(21) + 9123157923165/1212727727104*zeta(3)^2*zeta(15) + 1243473191940771/67912752717824*zeta(3)*zeta(5)*zeta(13) 3 3 3 3 w=12 k=-9 transcendental weight 21 (14 terms: 11 zsv + 3 odd-zeta monomials) c_{-9} = - 9652305699333/135825505435648*zsv(11,5,5) + 176034282831/33956376358912*zsv(13,5,3) - 422606970405/9701821816832*zsv(3,11,7) + 6860215909899/67912752717824*zsv(3,13,5) - 26142580969983/135825505435648*zsv(3,9,9) + 239615200593/19403643633664*zsv(5,7,9) + 425840609151/8489094089728*zsv(5,9,7) - 6593406963975/67912752717824*zsv(7,3,11) + 9433992655935/67912752717824*zsv(7,7,7) + 3427959242151/33956376358912*zsv(9,7,5) + 34365738656475/135825505435648*zsv(9,9,3) + 145912934032332974757/1901557076099072*zeta(21) - 11442228384015/606363863552*zeta(3)^2*zeta(15) - 2556178196625009/33956376358912*zeta(3)*zeta(5)*zeta(13) # PART 2: zsv(a,b,c) at weights 19 and 21 in the reduced basis (49; label extracted/derived as in zsv_depth3_w11-21.txt) extracted zsv(3,3,13) = (-56931875*zeta(3)^2*zeta(13) + 856605750*zeta(3)*zeta(5)*zeta(11) + 1396144750*zeta(3)*zeta(7)*zeta(9) + 651651000*zeta(5)^2*zeta(9) + 709458750*zeta(5)*zeta(7)^2 + 5300795500*zeta(2)*zeta(17) + 701400700*zeta(2)^2*zeta(15) + 145545400*zeta(2)^3*zeta(13) + 30270240*zeta(2)^4*zeta(11) + 4076800*zeta(2)^5*zeta(9) + 265344*zeta(2)^6*zeta(7) + 10510500*zeta(5)*zeta(3,11) + 26276250*zeta(7)*zeta(3,9) + 49049000*zeta(9)*zeta(3,7) + 78828750*zeta(11)*zeta(3,5) + 1751750*zeta(3,3,13))/875875 extracted zsv(3,5,11) = (-165165*zeta(3)^2*zeta(13) + 1007930*zeta(3)*zeta(5)*zeta(11) + 1066450*zeta(3)*zeta(7)*zeta(9) + 480480*zeta(5)^2*zeta(9) + 311850*zeta(5)*zeta(7)^2 + 7435120*zeta(2)*zeta(17) + 668668*zeta(2)^2*zeta(15) + 69696*zeta(2)^3*zeta(13) + 15048*zeta(2)^4*zeta(11) + 1600*zeta(2)^5*zeta(9) + 4620*zeta(5)*zeta(3,11) + 11550*zeta(7)*zeta(3,9) + 53900*zeta(9)*zeta(3,7) + 160930*zeta(11)*zeta(3,5) + 770*zeta(3,5,11))/385 extracted zsv(3,7,9) = (-15015*zeta(3)^2*zeta(13) + 127050*zeta(3)*zeta(5)*zeta(11) + 54810*zeta(3)*zeta(7)*zeta(9) + 40320*zeta(5)^2*zeta(9) + 28350*zeta(5)*zeta(7)^2 + 846090*zeta(2)*zeta(17) + 68796*zeta(2)^2*zeta(15) + 5192*zeta(2)^3*zeta(13) + 840*zeta(2)^4*zeta(11) + 420*zeta(5)*zeta(5,9) + 1050*zeta(7)*zeta(3,9) + 1890*zeta(9)*zeta(3,7) + 11550*zeta(11)*zeta(3,5) + 70*zeta(3,7,9))/35 derived zsv(3,9,7) = (52682081326875*zeta(3)^2*zeta(13) - 202623389718750*zeta(3)*zeta(5)*zeta(11) + 148099277576250*zeta(3)*zeta(7)*zeta(9) - 90526936500*zeta(5)^2*zeta(9) + 79330127126250*zeta(5)*zeta(7)^2 + 4108879140366000*zeta(19) - 678960253471500*zeta(2)*zeta(17) - 11268771614100*zeta(2)^2*zeta(15) + 12467499844800*zeta(2)^3*zeta(13) - 307417710600*zeta(2)^4*zeta(11) + 37929528000*zeta(2)^5*zeta(9) - 1738004017664*zeta(2)^6*zeta(7) - 30175645500*zeta(5)*zeta(3,11) - 25540515000*zeta(5)*zeta(5,9) + 5485158428750*zeta(7)*zeta(3,9) - 40524677943750*zeta(11)*zeta(3,5) + 278517739500*zeta(3,3,13) - 646395750*zeta(3,5,11) - 287157370500*zeta(3,7,9) + 282900618000*zeta(5,3,11) - 41852811000*zeta(5,5,9))/122802054375 extracted zsv(3,11,5) = (225450225*zeta(3)^2*zeta(13) - 1953901950*zeta(3)*zeta(5)*zeta(11) - 2117865750*zeta(3)*zeta(7)*zeta(9) - 933332400*zeta(5)^2*zeta(9) - 825074250*zeta(5)*zeta(7)^2 + 39212047875*zeta(19) - 19118599500*zeta(2)*zeta(17) - 1631229600*zeta(2)^2*zeta(15) - 138738600*zeta(2)^3*zeta(13) - 10954944*zeta(2)^4*zeta(11) + 524160*zeta(2)^5*zeta(9) + 7762240*zeta(2)^6*zeta(7) - 6306300*zeta(5)*zeta(5,9) - 40290250*zeta(7)*zeta(3,9) - 73573500*zeta(9)*zeta(3,7) - 173423250*zeta(11)*zeta(3,5) - 1051050*zeta(3,5,11) - 1051050*zeta(5,3,11))/525525 extracted zsv(3,13,3) = (-113863750*zeta(3)^2*zeta(13) - 1891890000*zeta(3)*zeta(5)*zeta(11) - 2942940000*zeta(3)*zeta(7)*zeta(9) - 1303302000*zeta(5)^2*zeta(9) - 1418917500*zeta(5)*zeta(7)^2 + 22917269375*zeta(19) - 10601591000*zeta(2)*zeta(17) - 1402801400*zeta(2)^2*zeta(15) - 291090800*zeta(2)^3*zeta(13) - 60540480*zeta(2)^4*zeta(11) - 8153600*zeta(2)^5*zeta(9) - 530688*zeta(2)^6*zeta(7) - 21021000*zeta(5)*zeta(3,11) - 52552500*zeta(7)*zeta(3,9) - 98098000*zeta(9)*zeta(3,7) - 157657500*zeta(11)*zeta(3,5) - 3503500*zeta(3,3,13))/875875 extracted zsv(5,3,11) = (485585100*zeta(3)*zeta(5)*zeta(11) + 662161500*zeta(3)*zeta(7)*zeta(9) + 206005800*zeta(5)^2*zeta(9) + 367867500*zeta(5)*zeta(7)^2 + 8969660700*zeta(2)*zeta(17) + 718497780*zeta(2)^2*zeta(15) + 43603560*zeta(2)^3*zeta(13) - 9585576*zeta(2)^4*zeta(11) - 2708160*zeta(2)^5*zeta(9) - 7762240*zeta(2)^6*zeta(7) - 6306300*zeta(5)*zeta(3,11) + 6306300*zeta(5)*zeta(5,9) + 24524500*zeta(7)*zeta(3,9) - 46246200*zeta(11)*zeta(3,5) + 1051050*zeta(5,3,11))/525525 extracted zsv(5,5,9) = (-208107900*zeta(3)*zeta(5)*zeta(11) + 132432300*zeta(3)*zeta(7)*zeta(9) - 7252245*zeta(5)^2*zeta(9) + 73573500*zeta(5)*zeta(7)^2 + 2304952650*zeta(2)*zeta(17) + 167747580*zeta(2)^2*zeta(15) + 5285280*zeta(2)^3*zeta(13) - 4612608*zeta(2)^4*zeta(11) - 602784*zeta(2)^5*zeta(9) - 1552448*zeta(2)^6*zeta(7) + 4904900*zeta(7)*zeta(3,9) - 34684650*zeta(11)*zeta(3,5) + 210210*zeta(5,5,9))/105105 derived zsv(5,7,7) = (990275766480000*zeta(3)*zeta(7)*zeta(9) + 214004542752000*zeta(5)^2*zeta(9) + 275076601800000*zeta(5)*zeta(7)^2 - 899118391045875*zeta(19) + 4665001172832000*zeta(2)*zeta(17) + 442974288556800*zeta(2)^2*zeta(15) + 47468130309600*zeta(2)^3*zeta(13) - 514889575200*zeta(2)^4*zeta(11) - 209270880000*zeta(2)^5*zeta(9) - 5621625177088*zeta(2)^6*zeta(7) + 600864264000*zeta(5)*zeta(3,11) - 378378000000*zeta(5)*zeta(5,9) + 18338440120000*zeta(7)*zeta(3,9) + 35366991660000*zeta(9)*zeta(3,7) + 43702659000*zeta(3,3,13) + 798188391000*zeta(3,5,11) - 804810006000*zeta(3,7,9) + 741747006000*zeta(5,3,11) + 20348328000*zeta(5,5,9))/421035615000 derived zsv(5,9,5) = (346846500*zeta(3)*zeta(5)*zeta(11) - 264864600*zeta(3)*zeta(7)*zeta(9) - 14504490*zeta(5)^2*zeta(9) - 153453300*zeta(5)*zeta(7)^2 + 8487438960*zeta(19) - 4609905300*zeta(2)*zeta(17) - 335495160*zeta(2)^2*zeta(15) - 10570560*zeta(2)^3*zeta(13) + 9225216*zeta(2)^4*zeta(11) + 1205568*zeta(2)^5*zeta(9) + 3104896*zeta(2)^6*zeta(7) - 9809800*zeta(7)*zeta(3,9) + 69369300*zeta(11)*zeta(3,5) - 420420*zeta(5,5,9))/105105 extracted zsv(5,11,3) = (-676350675*zeta(3)^2*zeta(13) - 2300748450*zeta(3)*zeta(5)*zeta(11) - 2296544250*zeta(3)*zeta(7)*zeta(9) - 861861000*zeta(5)^2*zeta(9) - 793542750*zeta(5)*zeta(7)^2 + 33610476900*zeta(19) - 19118599500*zeta(2)*zeta(17) - 1631229600*zeta(2)^2*zeta(15) - 138738600*zeta(2)^3*zeta(13) - 10954944*zeta(2)^4*zeta(11) + 524160*zeta(2)^5*zeta(9) + 7762240*zeta(2)^6*zeta(7) - 6306300*zeta(5)*zeta(5,9) - 40290250*zeta(7)*zeta(3,9) - 73573500*zeta(9)*zeta(3,7) - 173423250*zeta(11)*zeta(3,5) - 1051050*zeta(3,5,11) - 1051050*zeta(5,3,11))/525525 extracted zsv(7,3,9) = (-243148067662500*zeta(3)*zeta(5)*zeta(11) - 353669916600000*zeta(3)*zeta(7)*zeta(9) - 141377439703500*zeta(5)^2*zeta(9) - 189115163737500*zeta(5)*zeta(7)^2 + 7116579452107125*zeta(19) - 2289656608989750*zeta(2)*zeta(17) - 230110946465400*zeta(2)^2*zeta(15) - 30684307453800*zeta(2)^3*zeta(13) - 2639831594400*zeta(2)^4*zeta(11) - 37929528000*zeta(2)^5*zeta(9) + 1738004017664*zeta(2)^6*zeta(7) + 30175645500*zeta(5)*zeta(3,11) - 1448084137500*zeta(5)*zeta(5,9) - 9169220060000*zeta(7)*zeta(3,9) - 6631310936250*zeta(9)*zeta(3,7) - 278517739500*zeta(3,3,13) + 646395750*zeta(3,5,11) + 41553261750*zeta(3,7,9) - 282900618000*zeta(5,3,11) + 41852811000*zeta(5,5,9))/122802054375 extracted zsv(7,5,7) = (-1025642758140000*zeta(3)*zeta(7)*zeta(9) - 214004542752000*zeta(5)^2*zeta(9) - 286865599020000*zeta(5)*zeta(7)^2 + 9059209645360875*zeta(19) - 4665001172832000*zeta(2)*zeta(17) - 442974288556800*zeta(2)^2*zeta(15) - 47468130309600*zeta(2)^3*zeta(13) + 514889575200*zeta(2)^4*zeta(11) + 209270880000*zeta(2)^5*zeta(9) + 5621625177088*zeta(2)^6*zeta(7) - 600864264000*zeta(5)*zeta(3,11) + 378378000000*zeta(5)*zeta(5,9) - 18338440120000*zeta(7)*zeta(3,9) - 35366991660000*zeta(9)*zeta(3,7) - 43702659000*zeta(3,3,13) - 798188391000*zeta(3,5,11) + 804810006000*zeta(3,7,9) - 741747006000*zeta(5,3,11) - 20348328000*zeta(5,5,9))/210517807500 derived zsv(7,7,5) = (1061009749800000*zeta(3)*zeta(7)*zeta(9) + 214004542752000*zeta(5)^2*zeta(9) + 300338738700000*zeta(5)*zeta(7)^2 - 17218458828445875*zeta(19) + 4665001172832000*zeta(2)*zeta(17) + 442974288556800*zeta(2)^2*zeta(15) + 47468130309600*zeta(2)^3*zeta(13) - 514889575200*zeta(2)^4*zeta(11) - 209270880000*zeta(2)^5*zeta(9) - 5621625177088*zeta(2)^6*zeta(7) + 600864264000*zeta(5)*zeta(3,11) - 378378000000*zeta(5)*zeta(5,9) + 18338440120000*zeta(7)*zeta(3,9) + 35366991660000*zeta(9)*zeta(3,7) + 43702659000*zeta(3,3,13) + 798188391000*zeta(3,5,11) - 804810006000*zeta(3,7,9) + 741747006000*zeta(5,3,11) + 20348328000*zeta(5,5,9))/421035615000 extracted zsv(7,9,3) = (-158046243980625*zeta(3)^2*zeta(13) - 283672745606250*zeta(3)*zeta(5)*zeta(11) + 148099277576250*zeta(3)*zeta(7)*zeta(9) - 90526936500*zeta(5)^2*zeta(9) + 89645499693750*zeta(5)*zeta(7)^2 - 1959875584792125*zeta(19) - 678960253471500*zeta(2)*zeta(17) - 11268771614100*zeta(2)^2*zeta(15) + 12467499844800*zeta(2)^3*zeta(13) - 307417710600*zeta(2)^4*zeta(11) + 37929528000*zeta(2)^5*zeta(9) - 1738004017664*zeta(2)^6*zeta(7) - 30175645500*zeta(5)*zeta(3,11) - 25540515000*zeta(5)*zeta(5,9) + 5485158428750*zeta(7)*zeta(3,9) - 40524677943750*zeta(11)*zeta(3,5) + 278517739500*zeta(3,3,13) - 646395750*zeta(3,5,11) - 287157370500*zeta(3,7,9) + 282900618000*zeta(5,3,11) - 41852811000*zeta(5,5,9))/122802054375 extracted zsv(9,3,7) = (-243148067662500*zeta(3)*zeta(5)*zeta(11) - 347284209772500*zeta(3)*zeta(7)*zeta(9) - 144324689008500*zeta(5)^2*zeta(9) - 178799791170000*zeta(5)*zeta(7)^2 + 1960121188900875*zeta(19) - 2289656608989750*zeta(2)*zeta(17) - 230110946465400*zeta(2)^2*zeta(15) - 30684307453800*zeta(2)^3*zeta(13) - 2639831594400*zeta(2)^4*zeta(11) - 37929528000*zeta(2)^5*zeta(9) + 1738004017664*zeta(2)^6*zeta(7) + 30175645500*zeta(5)*zeta(3,11) - 1448084137500*zeta(5)*zeta(5,9) - 9169220060000*zeta(7)*zeta(3,9) - 6631310936250*zeta(9)*zeta(3,7) - 278517739500*zeta(3,3,13) + 646395750*zeta(3,5,11) + 41553261750*zeta(3,7,9) - 282900618000*zeta(5,3,11) + 41852811000*zeta(5,5,9))/122802054375 extracted zsv(9,5,5) = (-138738600*zeta(3)*zeta(5)*zeta(11) + 132432300*zeta(3)*zeta(7)*zeta(9) + 22177155*zeta(5)^2*zeta(9) + 79879800*zeta(5)*zeta(7)^2 - 8487228750*zeta(19) + 2304952650*zeta(2)*zeta(17) + 167747580*zeta(2)^2*zeta(15) + 5285280*zeta(2)^3*zeta(13) - 4612608*zeta(2)^4*zeta(11) - 602784*zeta(2)^5*zeta(9) - 1552448*zeta(2)^6*zeta(7) + 4904900*zeta(7)*zeta(3,9) - 34684650*zeta(11)*zeta(3,5) + 210210*zeta(5,5,9))/105105 extracted zsv(9,7,3) = (45045*zeta(3)^2*zeta(13) + 150150*zeta(3)*zeta(5)*zeta(11) + 60830*zeta(3)*zeta(7)*zeta(9) + 41160*zeta(5)^2*zeta(9) + 28350*zeta(5)*zeta(7)^2 - 3199315*zeta(19) + 846090*zeta(2)*zeta(17) + 68796*zeta(2)^2*zeta(15) + 5192*zeta(2)^3*zeta(13) + 840*zeta(2)^4*zeta(11) + 420*zeta(5)*zeta(5,9) + 1050*zeta(7)*zeta(3,9) + 1890*zeta(9)*zeta(3,7) + 11550*zeta(11)*zeta(3,5) + 70*zeta(3,7,9))/35 extracted zsv(11,3,5) = (567567000*zeta(3)*zeta(5)*zeta(11) + 662161500*zeta(3)*zeta(7)*zeta(9) + 277477200*zeta(5)^2*zeta(9) + 399399000*zeta(5)*zeta(7)^2 - 33609425850*zeta(19) + 8969660700*zeta(2)*zeta(17) + 718497780*zeta(2)^2*zeta(15) + 43603560*zeta(2)^3*zeta(13) - 9585576*zeta(2)^4*zeta(11) - 2708160*zeta(2)^5*zeta(9) - 7762240*zeta(2)^6*zeta(7) - 6306300*zeta(5)*zeta(3,11) + 6306300*zeta(5)*zeta(5,9) + 24524500*zeta(7)*zeta(3,9) - 46246200*zeta(11)*zeta(3,5) + 1051050*zeta(5,3,11))/525525 derived zsv(11,5,3) = (495495*zeta(3)^2*zeta(13) + 1340570*zeta(3)*zeta(5)*zeta(11) + 1197350*zeta(3)*zeta(7)*zeta(9) + 480480*zeta(5)^2*zeta(9) + 311850*zeta(5)*zeta(7)^2 - 28726005*zeta(19) + 7435120*zeta(2)*zeta(17) + 668668*zeta(2)^2*zeta(15) + 69696*zeta(2)^3*zeta(13) + 15048*zeta(2)^4*zeta(11) + 1600*zeta(2)^5*zeta(9) + 4620*zeta(5)*zeta(3,11) + 11550*zeta(7)*zeta(3,9) + 53900*zeta(9)*zeta(3,7) + 160930*zeta(11)*zeta(3,5) + 770*zeta(3,5,11))/385 extracted zsv(13,3,3) = (174299125*zeta(3)^2*zeta(13) + 1035284250*zeta(3)*zeta(5)*zeta(11) + 1546795250*zeta(3)*zeta(7)*zeta(9) + 651651000*zeta(5)^2*zeta(9) + 709458750*zeta(5)*zeta(7)^2 - 22915517625*zeta(19) + 5300795500*zeta(2)*zeta(17) + 701400700*zeta(2)^2*zeta(15) + 145545400*zeta(2)^3*zeta(13) + 30270240*zeta(2)^4*zeta(11) + 4076800*zeta(2)^5*zeta(9) + 265344*zeta(2)^6*zeta(7) + 10510500*zeta(5)*zeta(3,11) + 26276250*zeta(7)*zeta(3,9) + 49049000*zeta(9)*zeta(3,7) + 78828750*zeta(11)*zeta(3,5) + 1751750*zeta(3,3,13))/875875 derived zsv(3,3,15) = (-11261250*zeta(3)^2*zeta(15) + 180180000*zeta(3)*zeta(5)*zeta(13) + 322822500*zeta(3)*zeta(7)*zeta(11) + 189189000*zeta(3)*zeta(9)^2 + 144144000*zeta(5)^2*zeta(11) + 339339000*zeta(5)*zeta(7)*zeta(9) + 56306250*zeta(7)^3 + 1433557125*zeta(2)*zeta(19) + 218618400*zeta(2)^2*zeta(17) + 54683200*zeta(2)^3*zeta(15) + 13590720*zeta(2)^4*zeta(13) + 2620800*zeta(2)^5*zeta(11) + 353792*zeta(2)^6*zeta(9) + 23040*zeta(2)^7*zeta(7) + 1501500*zeta(5)*zeta(3,13) + 3753750*zeta(7)*zeta(3,11) + 7007000*zeta(9)*zeta(3,9) + 11261250*zeta(11)*zeta(3,7) + 16516500*zeta(13)*zeta(3,5) + 250250*zeta(3,3,15))/125125 derived zsv(3,5,13) = (-159409250*zeta(3)^2*zeta(15) + 1002001000*zeta(3)*zeta(5)*zeta(13) + 1261260000*zeta(3)*zeta(7)*zeta(11) + 662161500*zeta(3)*zeta(9)^2 + 548648100*zeta(5)^2*zeta(11) + 784083300*zeta(5)*zeta(7)*zeta(9) + 78828750*zeta(7)^3 + 8796762975*zeta(2)*zeta(19) + 920719800*zeta(2)^2*zeta(17) + 137417280*zeta(2)^3*zeta(15) + 29333304*zeta(2)^4*zeta(13) + 4149600*zeta(2)^5*zeta(11) + 442240*zeta(2)^6*zeta(9) + 2102100*zeta(5)*zeta(3,13) + 5255250*zeta(7)*zeta(3,11) + 24524500*zeta(9)*zeta(3,9) + 73573500*zeta(11)*zeta(3,7) + 173072900*zeta(13)*zeta(3,5) + 350350*zeta(3,5,13))/175175 derived zsv(3,7,11) = (-550550*zeta(3)^2*zeta(15) + 3775200*zeta(3)*zeta(5)*zeta(13) + 1972300*zeta(3)*zeta(7)*zeta(11) + 415800*zeta(3)*zeta(9)^2 + 1379400*zeta(5)^2*zeta(11) + 884400*zeta(5)*zeta(7)*zeta(9) + 123750*zeta(7)^3 + 25356925*zeta(2)*zeta(19) + 2126080*zeta(2)^2*zeta(17) + 183040*zeta(2)^3*zeta(15) + 40656*zeta(2)^4*zeta(13) + 4000*zeta(2)^5*zeta(11) + 3300*zeta(5)*zeta(5,11) + 8250*zeta(7)*zeta(3,11) + 15400*zeta(9)*zeta(3,9) + 114950*zeta(11)*zeta(3,7) + 471900*zeta(13)*zeta(3,5) + 550*zeta(3,7,11))/275 extracted zsv(3,9,9) = (1651189439908008000*zeta(3)*zeta(5)*zeta(13) + 1587682153757700000*zeta(3)*zeta(7)*zeta(11) + 467644561652268000*zeta(3)*zeta(9)^2 + 596266640093124000*zeta(5)^2*zeta(11) + 983736474929208000*zeta(5)*zeta(7)*zeta(9) + 33926401509000000*zeta(7)^3 + 22018861486018772375*zeta(21) + 14207296443770430000*zeta(2)*zeta(19) + 1103388669965181600*zeta(2)^2*zeta(17) + 2011466577120000*zeta(2)^3*zeta(15) - 61568711987983200*zeta(2)^4*zeta(13) - 22767906847795200*zeta(2)^5*zeta(11) - 17414566433504256*zeta(2)^6*zeta(9) - 222674155038720*zeta(2)^7*zeta(7) - 986199531061248*zeta(2)^8*zeta(5) - 16127948808972000*zeta(5)*zeta(3,13) + 6271422377220000*zeta(5)*zeta(5,11) - 30083148475380000*zeta(7)*zeta(3,11) + 17668137466980000*zeta(7)*zeta(5,9) + 17320168950084000*zeta(9)*zeta(3,9) - 2640289669017000*zeta(3,3,15) + 783512369640000*zeta(3,5,13) - 237447645435000*zeta(3,7,11) + 1363304447505000*zeta(5,3,13) - 185428616373000*zeta(5,5,11) - 88681713120000*zeta(7,3,11))/320743869446000 extracted zsv(3,11,7) = (2107959603750*zeta(3)^2*zeta(15) - 14454580140000*zeta(3)*zeta(5)*zeta(13) - 4957179727500*zeta(3)*zeta(7)*zeta(11) + 884458575000*zeta(3)*zeta(9)^2 - 3714726015000*zeta(5)^2*zeta(11) + 487537050000*zeta(5)*zeta(7)*zeta(9) - 47381709375*zeta(7)^3 + 369985868752500*zeta(21) - 165786495249375*zeta(2)*zeta(19) - 12722726016000*zeta(2)^2*zeta(17) - 697458762000*zeta(2)^3*zeta(15) - 63536616000*zeta(2)^4*zeta(13) + 5951088000*zeta(2)^5*zeta(11) - 26053617920*zeta(2)^6*zeta(9) + 484704000*zeta(2)^7*zeta(7) - 23418491904*zeta(2)^8*zeta(5) + 75810735000*zeta(5)*zeta(3,13) - 24121597500*zeta(5)*zeta(5,11) + 32757725000*zeta(9)*zeta(3,9) - 347465868750*zeta(11)*zeta(3,7) - 1806822517500*zeta(13)*zeta(3,5) - 2105853750*zeta(3,7,11) - 2105853750*zeta(7,3,11))/1052926875 extracted zsv(3,13,5) = (7173416250*zeta(3)^2*zeta(15) - 75423348000*zeta(3)*zeta(5)*zeta(13) - 95776931250*zeta(3)*zeta(7)*zeta(11) - 48337789500*zeta(3)*zeta(9)^2 - 40888472625*zeta(5)^2*zeta(11) - 67230413250*zeta(5)*zeta(7)*zeta(9) - 7094587500*zeta(7)^3 + 1593617775750*zeta(21) - 762502615875*zeta(2)*zeta(19) - 77453976600*zeta(2)^2*zeta(17) - 10727917200*zeta(2)^3*zeta(15) - 1571890320*zeta(2)^4*zeta(13) - 127764000*zeta(2)^5*zeta(11) + 210974464*zeta(2)^6*zeta(9) - 94594500*zeta(5)*zeta(5,11) - 236486250*zeta(7)*zeta(3,11) - 236486250*zeta(7)*zeta(5,9) - 1790288500*zeta(9)*zeta(3,9) - 3310807500*zeta(11)*zeta(3,7) - 6763506750*zeta(13)*zeta(3,5) - 15765750*zeta(3,5,13) - 15765750*zeta(5,3,13))/7882875 derived zsv(3,15,3) = (-22522500*zeta(3)^2*zeta(15) - 396396000*zeta(3)*zeta(5)*zeta(13) - 675675000*zeta(3)*zeta(7)*zeta(11) - 392392000*zeta(3)*zeta(9)^2 - 288288000*zeta(5)^2*zeta(11) - 678678000*zeta(5)*zeta(7)*zeta(9) - 112612500*zeta(7)^3 + 6623617000*zeta(21) - 2867114250*zeta(2)*zeta(19) - 437236800*zeta(2)^2*zeta(17) - 109366400*zeta(2)^3*zeta(15) - 27181440*zeta(2)^4*zeta(13) - 5241600*zeta(2)^5*zeta(11) - 707584*zeta(2)^6*zeta(9) - 46080*zeta(2)^7*zeta(7) - 3003000*zeta(5)*zeta(3,13) - 7507500*zeta(7)*zeta(3,11) - 14014000*zeta(9)*zeta(3,9) - 22522500*zeta(11)*zeta(3,7) - 33033000*zeta(13)*zeta(3,5) - 500500*zeta(3,3,15))/125125 derived zsv(5,3,13) = (28283755500*zeta(3)*zeta(5)*zeta(13) + 39020231250*zeta(3)*zeta(7)*zeta(11) + 18540522000*zeta(3)*zeta(9)^2 + 14591201625*zeta(5)^2*zeta(11) + 30590810250*zeta(5)*zeta(7)*zeta(9) + 3547293750*zeta(7)^3 + 366648282000*zeta(2)*zeta(19) + 36021585600*zeta(2)^2*zeta(17) + 4544139600*zeta(2)^3*zeta(15) + 251891640*zeta(2)^4*zeta(13) - 58968000*zeta(2)^5*zeta(11) - 230875264*zeta(2)^6*zeta(9) - 94594500*zeta(5)*zeta(3,13) + 94594500*zeta(5)*zeta(5,11) + 236486250*zeta(7)*zeta(5,9) + 686686000*zeta(9)*zeta(3,9) - 1024773750*zeta(13)*zeta(3,5) + 15765750*zeta(5,3,13))/7882875 derived zsv(5,5,11) = (-1159458300*zeta(3)*zeta(5)*zeta(13) + 1114863750*zeta(3)*zeta(7)*zeta(11) + 1324323000*zeta(3)*zeta(9)^2 - 47072025*zeta(5)^2*zeta(11) + 1201950750*zeta(5)*zeta(7)*zeta(9) + 101351250*zeta(7)^3 + 19932862950*zeta(2)*zeta(19) + 1586665080*zeta(2)^2*zeta(17) + 103062960*zeta(2)^3*zeta(15) - 19706544*zeta(2)^4*zeta(13) - 3725280*zeta(2)^5*zeta(11) - 15524480*zeta(2)^6*zeta(9) + 6756750*zeta(7)*zeta(5,9) + 49049000*zeta(9)*zeta(3,9) - 193243050*zeta(13)*zeta(3,5) + 450450*zeta(5,5,11))/225225 extracted zsv(5,7,9) = (-8805632113278000*zeta(3)*zeta(5)*zeta(13) + 8466953955075000*zeta(3)*zeta(7)*zeta(11) + 7758808715196000*zeta(3)*zeta(9)^2 - 6886590966832500*zeta(5)^2*zeta(11) + 2798918963379000*zeta(5)*zeta(7)*zeta(9) + 8081759127750000*zeta(7)^3 - 3125723556942226625*zeta(21) + 1665540593171070000*zeta(2)*zeta(19) + 155028597315160800*zeta(2)^2*zeta(17) + 22153487460104000*zeta(2)^3*zeta(15) + 5233128130581120*zeta(2)^4*zeta(13) + 1359928349472000*zeta(2)^5*zeta(11) + 1076263468256768*zeta(2)^6*zeta(9) + 8806419578880*zeta(2)^7*zeta(7) + 537251428933632*zeta(2)^8*zeta(5) - 462253714230000*zeta(5)*zeta(3,13) + 67963955598000*zeta(5)*zeta(5,11) + 1978819936170000*zeta(7)*zeta(3,11) - 489253401945000*zeta(7)*zeta(5,9) + 287363285748000*zeta(9)*zeta(3,9) - 1467605352213000*zeta(13)*zeta(3,5) + 216429055843000*zeta(3,3,15) - 48522936000000*zeta(3,5,13) + 12326302065000*zeta(3,7,11) - 44918151432000*zeta(5,3,13) + 12301257969000*zeta(5,5,11) + 48311092830000*zeta(7,3,11))/1710495748500 extracted zsv(5,9,7) = (3892089394068876000*zeta(3)*zeta(5)*zeta(13) + 3243407828390730000*zeta(3)*zeta(7)*zeta(11) + 2667306018312936000*zeta(3)*zeta(9)^2 + 6707652332890509000*zeta(5)^2*zeta(11) + 5948682114549174000*zeta(5)*zeta(7)*zeta(9) - 5646375887319667500*zeta(7)^3 + 2434596153989406532125*zeta(21) - 1185513273689459715000*zeta(2)*zeta(19) - 110332796749550575200*zeta(2)^2*zeta(17) - 16045108466851464000*zeta(2)^3*zeta(15) - 4008248072357649120*zeta(2)^4*zeta(13) - 1052119557753264000*zeta(2)^5*zeta(11) - 892133640587825152*zeta(2)^6*zeta(9) - 6880281638630400*zeta(2)^7*zeta(7) - 413131704486359040*zeta(2)^8*zeta(5) + 357919252638948000*zeta(5)*zeta(3,13) - 53173996880004000*zeta(5)*zeta(5,11) - 1517790645135765000*zeta(7)*zeta(3,11) + 413138737401390000*zeta(7)*zeta(5,9) + 98789111789368000*zeta(9)*zeta(3,9) + 249492909876210000*zeta(11)*zeta(3,7) + 648681565678146000*zeta(13)*zeta(3,5) - 167605273400565000*zeta(3,3,15) + 39846792819834000*zeta(3,5,13) - 10577475954045000*zeta(3,7,11) + 35487791800461000*zeta(5,3,13) - 7945209307035000*zeta(5,5,11) - 37149913525725000*zeta(7,3,11))/756039120837000 derived zsv(5,11,5) = (1932430500*zeta(3)*zeta(5)*zeta(13) - 2229727500*zeta(3)*zeta(7)*zeta(11) - 2648646000*zeta(3)*zeta(9)^2 - 94144050*zeta(5)^2*zeta(11) - 2480478000*zeta(5)*zeta(7)*zeta(9) - 202702500*zeta(7)^3 + 74857808025*zeta(21) - 39865725900*zeta(2)*zeta(19) - 3173330160*zeta(2)^2*zeta(17) - 206125920*zeta(2)^3*zeta(15) + 39413088*zeta(2)^4*zeta(13) + 7450560*zeta(2)^5*zeta(11) + 31048960*zeta(2)^6*zeta(9) - 13513500*zeta(7)*zeta(5,9) - 98098000*zeta(9)*zeta(3,9) + 386486100*zeta(13)*zeta(3,5) - 900900*zeta(5,5,11))/225225 derived zsv(5,13,3) = (-21520248750*zeta(3)^2*zeta(15) - 88950361500*zeta(3)*zeta(5)*zeta(13) - 102871518750*zeta(3)*zeta(7)*zeta(11) - 50544994500*zeta(3)*zeta(9)^2 - 39280366125*zeta(5)^2*zeta(11) - 65874558750*zeta(5)*zeta(7)*zeta(9) - 7094587500*zeta(7)^3 + 1443693376125*zeta(21) - 762502615875*zeta(2)*zeta(19) - 77453976600*zeta(2)^2*zeta(17) - 10727917200*zeta(2)^3*zeta(15) - 1571890320*zeta(2)^4*zeta(13) - 127764000*zeta(2)^5*zeta(11) + 210974464*zeta(2)^6*zeta(9) - 94594500*zeta(5)*zeta(5,11) - 236486250*zeta(7)*zeta(3,11) - 236486250*zeta(7)*zeta(5,9) - 1790288500*zeta(9)*zeta(3,9) - 3310807500*zeta(11)*zeta(3,7) - 6763506750*zeta(13)*zeta(3,5) - 15765750*zeta(3,5,13) - 15765750*zeta(5,3,13))/7882875 extracted zsv(7,3,11) = (-2779726950000*zeta(3)*zeta(7)*zeta(11) - 2476484010000*zeta(3)*zeta(9)^2 - 1566755190000*zeta(5)^2*zeta(11) - 4016947935000*zeta(5)*zeta(7)*zeta(9) - 489610996875*zeta(7)^3 + 68699266886250*zeta(2)*zeta(19) + 4582337760000*zeta(2)^2*zeta(17) - 3369366000*zeta(2)^3*zeta(15) - 92128093200*zeta(2)^4*zeta(13) - 21266388000*zeta(2)^5*zeta(11) + 26053617920*zeta(2)^6*zeta(9) - 484704000*zeta(2)^7*zeta(7) + 23418491904*zeta(2)^8*zeta(5) - 75810735000*zeta(5)*zeta(3,13) + 11486475000*zeta(5)*zeta(5,11) - 31587806250*zeta(7)*zeta(3,11) - 91721630000*zeta(9)*zeta(3,9) - 92657565000*zeta(11)*zeta(3,7) + 2105853750*zeta(7,3,11))/1052926875 derived zsv(7,5,9) = (-7484787296286300000*zeta(3)*zeta(7)*zeta(11) - 6096699470429568000*zeta(3)*zeta(9)^2 - 3663779125550544000*zeta(5)^2*zeta(11) - 7394471093713704000*zeta(5)*zeta(7)*zeta(9) + 2028876005603947500*zeta(7)^3 - 846186891024993392875*zeta(21) + 449344331507846775000*zeta(2)*zeta(19) + 41810156736249501600*zeta(2)^2*zeta(17) + 6253267009485496000*zeta(2)^3*zeta(15) + 1695205438640794080*zeta(2)^4*zeta(13) + 451031227286640000*zeta(2)^5*zeta(11) + 416425187618333696*zeta(2)^6*zeta(9) + 2987844184765440*zeta(2)^7*zeta(7) + 175666572897693696*zeta(2)^8*zeta(5) - 153603110949288000*zeta(5)*zeta(3,13) + 23133928505688000*zeta(5)*zeta(5,11) + 643152233348625000*zeta(7)*zeta(3,11) - 196888733741700000*zeta(7)*zeta(5,9) - 225803684089984000*zeta(9)*zeta(3,9) - 249492909876210000*zeta(11)*zeta(3,7) + 71943630717959000*zeta(3,3,15) - 18399655107834000*zeta(3,5,13) + 5129250441315000*zeta(3,7,11) - 15633968867517000*zeta(5,3,13) + 2508053284737000*zeta(5,5,11) + 15796410494865000*zeta(7,3,11))/756039120837000 extracted zsv(7,7,7) = (4*zeta(7)^3 + 2*zeta(21))/3 derived zsv(7,9,5) = (2594726262712584000*zeta(3)*zeta(5)*zeta(13) + 3742393648143150000*zeta(3)*zeta(7)*zeta(11) + 2667306018312936000*zeta(3)*zeta(9)^2 + 6208666513138089000*zeta(5)^2*zeta(11) + 6075696686849790000*zeta(5)*zeta(7)*zeta(9) - 5601013540069447500*zeta(7)^3 + 2362068565088392285125*zeta(21) - 1185513273689459715000*zeta(2)*zeta(19) - 110332796749550575200*zeta(2)^2*zeta(17) - 16045108466851464000*zeta(2)^3*zeta(15) - 4008248072357649120*zeta(2)^4*zeta(13) - 1052119557753264000*zeta(2)^5*zeta(11) - 892133640587825152*zeta(2)^6*zeta(9) - 6880281638630400*zeta(2)^7*zeta(7) - 413131704486359040*zeta(2)^8*zeta(5) + 357919252638948000*zeta(5)*zeta(3,13) - 53173996880004000*zeta(5)*zeta(5,11) - 1517790645135765000*zeta(7)*zeta(3,11) + 413138737401390000*zeta(7)*zeta(5,9) + 98789111789368000*zeta(9)*zeta(3,9) + 249492909876210000*zeta(11)*zeta(3,7) + 648681565678146000*zeta(13)*zeta(3,5) - 167605273400565000*zeta(3,3,15) + 39846792819834000*zeta(3,5,13) - 10577475954045000*zeta(3,7,11) + 35487791800461000*zeta(5,3,13) - 7945209307035000*zeta(5,5,11) - 37149913525725000*zeta(7,3,11))/756039120837000 derived zsv(7,11,3) = (-6323878811250*zeta(3)^2*zeta(15) - 18068225175000*zeta(3)*zeta(5)*zeta(13) - 5652111465000*zeta(3)*zeta(7)*zeta(11) + 766530765000*zeta(3)*zeta(9)^2 - 3714726015000*zeta(5)^2*zeta(11) + 630735105000*zeta(5)*zeta(7)*zeta(9) + 15793903125*zeta(7)^3 + 248951924471250*zeta(21) - 165786495249375*zeta(2)*zeta(19) - 12722726016000*zeta(2)^2*zeta(17) - 697458762000*zeta(2)^3*zeta(15) - 63536616000*zeta(2)^4*zeta(13) + 5951088000*zeta(2)^5*zeta(11) - 26053617920*zeta(2)^6*zeta(9) + 484704000*zeta(2)^7*zeta(7) - 23418491904*zeta(2)^8*zeta(5) + 75810735000*zeta(5)*zeta(3,13) - 24121597500*zeta(5)*zeta(5,11) + 32757725000*zeta(9)*zeta(3,9) - 347465868750*zeta(11)*zeta(3,7) - 1806822517500*zeta(13)*zeta(3,5) - 2105853750*zeta(3,7,11) - 2105853750*zeta(7,3,11))/1052926875 derived zsv(9,3,9) = (-1651189439908008000*zeta(3)*zeta(5)*zeta(13) - 1587682153757700000*zeta(3)*zeta(7)*zeta(11) - 484964730602352000*zeta(3)*zeta(9)^2 - 596266640093124000*zeta(5)^2*zeta(11) - 997207717445940000*zeta(5)*zeta(7)*zeta(9) - 33926401509000000*zeta(7)^3 + 24906287357800473625*zeta(21) - 14207296443770430000*zeta(2)*zeta(19) - 1103388669965181600*zeta(2)^2*zeta(17) - 2011466577120000*zeta(2)^3*zeta(15) + 61568711987983200*zeta(2)^4*zeta(13) + 22767906847795200*zeta(2)^5*zeta(11) + 17414566433504256*zeta(2)^6*zeta(9) + 222674155038720*zeta(2)^7*zeta(7) + 986199531061248*zeta(2)^8*zeta(5) + 16127948808972000*zeta(5)*zeta(3,13) - 6271422377220000*zeta(5)*zeta(5,11) + 30083148475380000*zeta(7)*zeta(3,11) - 17668137466980000*zeta(7)*zeta(5,9) - 17320168950084000*zeta(9)*zeta(3,9) + 2640289669017000*zeta(3,3,15) - 783512369640000*zeta(3,5,13) + 237447645435000*zeta(3,7,11) - 1363304447505000*zeta(5,3,13) + 185428616373000*zeta(5,5,11) + 88681713120000*zeta(7,3,11))/160371934723000 derived zsv(9,5,7) = (-6985801476533880000*zeta(3)*zeta(7)*zeta(11) - 6223714042730184000*zeta(3)*zeta(9)^2 - 3663779125550544000*zeta(5)^2*zeta(11) - 7228142487129564000*zeta(5)*zeta(7)*zeta(9) + 2074238352854167500*zeta(7)^3 - 980497240841686442875*zeta(21) + 449344331507846775000*zeta(2)*zeta(19) + 41810156736249501600*zeta(2)^2*zeta(17) + 6253267009485496000*zeta(2)^3*zeta(15) + 1695205438640794080*zeta(2)^4*zeta(13) + 451031227286640000*zeta(2)^5*zeta(11) + 416425187618333696*zeta(2)^6*zeta(9) + 2987844184765440*zeta(2)^7*zeta(7) + 175666572897693696*zeta(2)^8*zeta(5) - 153603110949288000*zeta(5)*zeta(3,13) + 23133928505688000*zeta(5)*zeta(5,11) + 643152233348625000*zeta(7)*zeta(3,11) - 196888733741700000*zeta(7)*zeta(5,9) - 225803684089984000*zeta(9)*zeta(3,9) - 249492909876210000*zeta(11)*zeta(3,7) + 71943630717959000*zeta(3,3,15) - 18399655107834000*zeta(3,5,13) + 5129250441315000*zeta(3,7,11) - 15633968867517000*zeta(5,3,13) + 2508053284737000*zeta(5,5,11) + 15796410494865000*zeta(7,3,11))/756039120837000 extracted zsv(9,7,5) = (-5870421408852000*zeta(3)*zeta(5)*zeta(13) + 8466953955075000*zeta(3)*zeta(7)*zeta(11) + 8046172000944000*zeta(3)*zeta(9)^2 - 5757663772822500*zeta(5)^2*zeta(11) + 3093124232121000*zeta(5)*zeta(7)*zeta(9) + 8081759127750000*zeta(7)^3 - 3593682694312605125*zeta(21) + 1665540593171070000*zeta(2)*zeta(19) + 155028597315160800*zeta(2)^2*zeta(17) + 22153487460104000*zeta(2)^3*zeta(15) + 5233128130581120*zeta(2)^4*zeta(13) + 1359928349472000*zeta(2)^5*zeta(11) + 1076263468256768*zeta(2)^6*zeta(9) + 8806419578880*zeta(2)^7*zeta(7) + 537251428933632*zeta(2)^8*zeta(5) - 462253714230000*zeta(5)*zeta(3,13) + 67963955598000*zeta(5)*zeta(5,11) + 1978819936170000*zeta(7)*zeta(3,11) - 489253401945000*zeta(7)*zeta(5,9) + 287363285748000*zeta(9)*zeta(3,9) - 1467605352213000*zeta(13)*zeta(3,5) + 216429055843000*zeta(3,3,15) - 48522936000000*zeta(3,5,13) + 12326302065000*zeta(3,7,11) - 44918151432000*zeta(5,3,13) + 12301257969000*zeta(5,5,11) + 48311092830000*zeta(7,3,11))/1710495748500 extracted zsv(9,9,3) = (1651189439908008000*zeta(3)*zeta(5)*zeta(13) + 1587682153757700000*zeta(3)*zeta(7)*zeta(11) + 503567875030220000*zeta(3)*zeta(9)^2 + 596266640093124000*zeta(5)^2*zeta(11) + 1010678959962672000*zeta(5)*zeta(7)*zeta(9) + 33926401509000000*zeta(7)^3 - 71830794713880827625*zeta(21) + 14207296443770430000*zeta(2)*zeta(19) + 1103388669965181600*zeta(2)^2*zeta(17) + 2011466577120000*zeta(2)^3*zeta(15) - 61568711987983200*zeta(2)^4*zeta(13) - 22767906847795200*zeta(2)^5*zeta(11) - 17414566433504256*zeta(2)^6*zeta(9) - 222674155038720*zeta(2)^7*zeta(7) - 986199531061248*zeta(2)^8*zeta(5) - 16127948808972000*zeta(5)*zeta(3,13) + 6271422377220000*zeta(5)*zeta(5,11) - 30083148475380000*zeta(7)*zeta(3,11) + 17668137466980000*zeta(7)*zeta(5,9) + 17320168950084000*zeta(9)*zeta(3,9) - 2640289669017000*zeta(3,3,15) + 783512369640000*zeta(3,5,13) - 237447645435000*zeta(3,7,11) + 1363304447505000*zeta(5,3,13) - 185428616373000*zeta(5,5,11) - 88681713120000*zeta(7,3,11))/320743869446000 derived zsv(11,3,7) = (-2653375725000*zeta(3)*zeta(7)*zeta(11) - 2476484010000*zeta(3)*zeta(9)^2 - 1592025435000*zeta(5)^2*zeta(11) - 3873749880000*zeta(5)*zeta(7)*zeta(9) - 426435384375*zeta(7)^3 - 248949818617500*zeta(21) + 68699266886250*zeta(2)*zeta(19) + 4582337760000*zeta(2)^2*zeta(17) - 3369366000*zeta(2)^3*zeta(15) - 92128093200*zeta(2)^4*zeta(13) - 21266388000*zeta(2)^5*zeta(11) + 26053617920*zeta(2)^6*zeta(9) - 484704000*zeta(2)^7*zeta(7) + 23418491904*zeta(2)^8*zeta(5) - 75810735000*zeta(5)*zeta(3,13) + 11486475000*zeta(5)*zeta(5,11) - 31587806250*zeta(7)*zeta(3,11) - 91721630000*zeta(9)*zeta(3,9) - 92657565000*zeta(11)*zeta(3,7) + 2105853750*zeta(7,3,11))/1052926875 extracted zsv(11,5,5) = (-772972200*zeta(3)*zeta(5)*zeta(13) + 1114863750*zeta(3)*zeta(7)*zeta(11) + 1324323000*zeta(3)*zeta(9)^2 + 142116975*zeta(5)^2*zeta(11) + 1278527250*zeta(5)*zeta(7)*zeta(9) + 101351250*zeta(7)^3 - 74857357575*zeta(21) + 19932862950*zeta(2)*zeta(19) + 1586665080*zeta(2)^2*zeta(17) + 103062960*zeta(2)^3*zeta(15) - 19706544*zeta(2)^4*zeta(13) - 3725280*zeta(2)^5*zeta(11) - 15524480*zeta(2)^6*zeta(9) + 6756750*zeta(7)*zeta(5,9) + 49049000*zeta(9)*zeta(3,9) - 193243050*zeta(13)*zeta(3,5) + 450450*zeta(5,5,11))/225225 derived zsv(11,7,3) = (1651650*zeta(3)^2*zeta(15) + 4719000*zeta(3)*zeta(5)*zeta(13) + 2219800*zeta(3)*zeta(7)*zeta(11) + 446600*zeta(3)*zeta(9)^2 + 1386000*zeta(5)^2*zeta(11) + 884400*zeta(5)*zeta(7)*zeta(9) + 123750*zeta(7)^3 - 96631150*zeta(21) + 25356925*zeta(2)*zeta(19) + 2126080*zeta(2)^2*zeta(17) + 183040*zeta(2)^3*zeta(15) + 40656*zeta(2)^4*zeta(13) + 4000*zeta(2)^5*zeta(11) + 3300*zeta(5)*zeta(5,11) + 8250*zeta(7)*zeta(3,11) + 15400*zeta(9)*zeta(3,9) + 114950*zeta(11)*zeta(3,7) + 471900*zeta(13)*zeta(3,5) + 550*zeta(3,7,11))/275 derived zsv(13,3,5) = (30175645500*zeta(3)*zeta(5)*zeta(13) + 39020231250*zeta(3)*zeta(7)*zeta(11) + 18540522000*zeta(3)*zeta(9)^2 + 16199308125*zeta(5)^2*zeta(11) + 31946664750*zeta(5)*zeta(7)*zeta(9) + 3547293750*zeta(7)^3 - 1443677610375*zeta(21) + 366648282000*zeta(2)*zeta(19) + 36021585600*zeta(2)^2*zeta(17) + 4544139600*zeta(2)^3*zeta(15) + 251891640*zeta(2)^4*zeta(13) - 58968000*zeta(2)^5*zeta(11) - 230875264*zeta(2)^6*zeta(9) - 94594500*zeta(5)*zeta(3,13) + 94594500*zeta(5)*zeta(5,11) + 236486250*zeta(7)*zeta(5,9) + 686686000*zeta(9)*zeta(3,9) - 1024773750*zeta(13)*zeta(3,5) + 15765750*zeta(5,3,13))/7882875 extracted zsv(13,5,3) = (478227750*zeta(3)^2*zeta(15) + 1353051700*zeta(3)*zeta(5)*zeta(13) + 1418917500*zeta(3)*zeta(7)*zeta(11) + 711210500*zeta(3)*zeta(9)^2 + 548648100*zeta(5)^2*zeta(11) + 784083300*zeta(5)*zeta(7)*zeta(9) + 78828750*zeta(7)^3 - 35413378000*zeta(21) + 8796762975*zeta(2)*zeta(19) + 920719800*zeta(2)^2*zeta(17) + 137417280*zeta(2)^3*zeta(15) + 29333304*zeta(2)^4*zeta(13) + 4149600*zeta(2)^5*zeta(11) + 442240*zeta(2)^6*zeta(9) + 2102100*zeta(5)*zeta(3,13) + 5255250*zeta(7)*zeta(3,11) + 24524500*zeta(9)*zeta(3,9) + 73573500*zeta(11)*zeta(3,7) + 173072900*zeta(13)*zeta(3,5) + 350350*zeta(3,5,13))/175175 derived zsv(15,3,3) = (34284250*zeta(3)^2*zeta(15) + 216216000*zeta(3)*zeta(5)*zeta(13) + 352852500*zeta(3)*zeta(7)*zeta(11) + 203203000*zeta(3)*zeta(9)^2 + 144144000*zeta(5)^2*zeta(11) + 339339000*zeta(5)*zeta(7)*zeta(9) + 56306250*zeta(7)^3 - 6623366750*zeta(21) + 1433557125*zeta(2)*zeta(19) + 218618400*zeta(2)^2*zeta(17) + 54683200*zeta(2)^3*zeta(15) + 13590720*zeta(2)^4*zeta(13) + 2620800*zeta(2)^5*zeta(11) + 353792*zeta(2)^6*zeta(9) + 23040*zeta(2)^7*zeta(7) + 1501500*zeta(5)*zeta(3,13) + 3753750*zeta(7)*zeta(3,11) + 7007000*zeta(9)*zeta(3,9) + 11261250*zeta(11)*zeta(3,7) + 16516500*zeta(13)*zeta(3,5) + 250250*zeta(3,3,15))/125125 # PART 3: reductions of the non-basis monomials (42) w=19 zeta(3,9,7) = (-15087822750*zeta(5)^2*zeta(9) - 122802054375*zeta(5)*zeta(7)^2 + 684813190061000*zeta(19) - 363676233170250*zeta(2)*zeta(17) - 28698097277850*zeta(2)^2*zeta(15) - 1992094304200*zeta(2)^3*zeta(13) - 51236285100*zeta(2)^4*zeta(11) + 6321588000*zeta(2)^5*zeta(9) + 12639569056*zeta(2)^6*zeta(7) + 3768710400*zeta(2)^7*zeta(5) - 5029274250*zeta(5)*zeta(3,11) - 4256752500*zeta(5)*zeta(5,9) + 46419623250*zeta(3,3,13) - 107732625*zeta(3,5,11) - 47859561750*zeta(3,7,9) + 47150103000*zeta(5,3,11) - 6975468500*zeta(5,5,9))/40934018125 w=19 zeta(3,11,5) = (13070682625*zeta(19) - 6765959200*zeta(2)*zeta(17) - 608487880*zeta(2)^2*zeta(15) - 63423360*zeta(2)^3*zeta(13) - 3651648*zeta(2)^4*zeta(11) + 582400*zeta(2)^5*zeta(9) + 265344*zeta(2)^6*zeta(7) + 64512*zeta(2)^7*zeta(5) + 350350*zeta(5)*zeta(3,11) - 350350*zeta(3,5,11) - 350350*zeta(5,3,11))/350350 w=19 zeta(3,13,3) = (22917269375*zeta(19) - 10601591000*zeta(2)*zeta(17) - 1402801400*zeta(2)^2*zeta(15) - 291090800*zeta(2)^3*zeta(13) - 49729680*zeta(2)^4*zeta(11) - 4076800*zeta(2)^5*zeta(9) + 796032*zeta(2)^6*zeta(7) + 322560*zeta(2)^7*zeta(5) + 1751750*zeta(3)*zeta(3,13) - 3503500*zeta(3,3,13))/1751750 w=19 zeta(5,7,7) = (85837752000*zeta(5)^2*zeta(9) - 42815161478375*zeta(19) + 21729960252000*zeta(2)*zeta(17) + 2231618188800*zeta(2)^2*zeta(15) + 239416205600*zeta(2)^3*zeta(13) - 24518551200*zeta(2)^4*zeta(11) - 9965280000*zeta(2)^5*zeta(9) + 8698447872*zeta(2)^6*zeta(7) + 28612584000*zeta(5)*zeta(3,11) - 18018000000*zeta(5)*zeta(5,9) + 2081079000*zeta(3,3,13) + 38008971000*zeta(3,5,11) - 38324286000*zeta(3,7,9) + 35321286000*zeta(5,3,11) + 968968000*zeta(5,5,9))/40098630000 w=19 zeta(5,9,5) = (7072865800*zeta(19) - 3841587750*zeta(2)*zeta(17) - 279579300*zeta(2)^2*zeta(15) - 8808800*zeta(2)^3*zeta(13) + 3723720*zeta(2)^4*zeta(11) + 1004640*zeta(2)^5*zeta(9) + 132672*zeta(2)^6*zeta(7) + 175175*zeta(5)*zeta(5,9) - 350350*zeta(5,5,9))/175175 w=19 zeta(5,11,3) = (5601746150*zeta(19) - 2989886900*zeta(2)*zeta(17) - 239499260*zeta(2)^2*zeta(15) - 14534520*zeta(2)^3*zeta(13) + 2138136*zeta(2)^4*zeta(11) + 902720*zeta(2)^5*zeta(9) + 132672*zeta(2)^6*zeta(7) + 175175*zeta(3)*zeta(5,11) - 175175*zeta(3,5,11) - 175175*zeta(5,3,11))/175175 w=19 zeta(7,3,9) = (30175645500*zeta(5)^2*zeta(9) + 245604108750*zeta(5)*zeta(7)^2 + 2372193150702375*zeta(19) - 1251725441967000*zeta(2)*zeta(17) - 103523617497300*zeta(2)^2*zeta(15) - 8160349797600*zeta(2)^3*zeta(13) - 9803593800*zeta(2)^4*zeta(11) + 171081456000*zeta(2)^5*zeta(9) + 36725121088*zeta(2)^6*zeta(7) + 7537420800*zeta(2)^7*zeta(5) + 10058548500*zeta(5)*zeta(3,11) + 8513505000*zeta(5)*zeta(5,9) + 81868036250*zeta(7)*zeta(3,9) - 92839246500*zeta(3,3,13) + 215465250*zeta(3,5,11) + 13851087250*zeta(3,7,9) - 94300206000*zeta(5,3,11) + 13950937000*zeta(5,5,9))/81868036250 w=19 zeta(7,5,7) = (-12618149544000*zeta(5)^2*zeta(9) + 27507660180000*zeta(5)*zeta(7)^2 + 63414467517526125*zeta(19) - 32655008209824000*zeta(2)*zeta(17) - 3100820019897600*zeta(2)^2*zeta(15) - 332276912167200*zeta(2)^3*zeta(13) + 3604227026400*zeta(2)^4*zeta(11) + 11753475552000*zeta(2)^5*zeta(9) - 646401873664*zeta(2)^6*zeta(7) - 4206049848000*zeta(5)*zeta(3,11) + 2648646000000*zeta(5)*zeta(5,9) + 4584610030000*zeta(7)*zeta(3,9) - 305918613000*zeta(3,3,13) - 5587318737000*zeta(3,5,11) + 5633670042000*zeta(3,7,9) - 5192229042000*zeta(5,3,11) - 142438296000*zeta(5,5,9))/2947249305000 w=19 zeta(7,7,5) = (12618149544000*zeta(5)^2*zeta(9) - 52068071055000*zeta(5)*zeta(7)^2 - 120529211799121125*zeta(19) + 62115712262604000*zeta(2)*zeta(17) + 5873592166041600*zeta(2)^2*zeta(15) + 629359642111200*zeta(2)^3*zeta(13) - 3604227026400*zeta(2)^4*zeta(11) - 22042054944000*zeta(2)^5*zeta(9) - 283488534016*zeta(2)^6*zeta(7) - 90449049600*zeta(2)^7*zeta(5) + 4206049848000*zeta(5)*zeta(3,11) - 2648646000000*zeta(5)*zeta(5,9) - 9169220060000*zeta(7)*zeta(3,9) + 305918613000*zeta(3,3,13) + 5587318737000*zeta(3,5,11) - 5633670042000*zeta(3,7,9) + 5192229042000*zeta(5,3,11) + 142438296000*zeta(5,5,9))/5894498610000 w=19 zeta(7,9,3) = (-551135620035000*zeta(3)*zeta(5)*zeta(11) - 939435715968750*zeta(3)*zeta(7)*zeta(9) - 5642845708500*zeta(5)^2*zeta(9) - 45927968336250*zeta(5)*zeta(7)^2 - 122165578118709125*zeta(19) + 51371199606226500*zeta(2)*zeta(17) + 9328248187358100*zeta(2)^2*zeta(15) + 2299324917089200*zeta(2)^3*zeta(13) + 327265733394600*zeta(2)^4*zeta(11) + 2364273912000*zeta(2)^5*zeta(9) - 6867597643456*zeta(2)^6*zeta(7) - 1409497689600*zeta(2)^7*zeta(5) + 28374972347904*zeta(2)^8*zeta(3) - 91855936672500*zeta(3)*zeta(3,13) + 29226888941250*zeta(3)*zeta(5,11) - 1880948569500*zeta(5)*zeta(3,11) - 1592025435000*zeta(5)*zeta(5,9) - 15309322778750*zeta(7)*zeta(3,9) + 17360939095500*zeta(3,3,13) - 40292001750*zeta(3,5,11) - 17899476094500*zeta(3,7,9) + 17634138522000*zeta(5,3,11) - 2608825219000*zeta(5,5,9))/15309322778750 w=19 zeta(9,3,7) = (30175645500*zeta(5)^2*zeta(9) + 245604108750*zeta(5)*zeta(7)^2 + 653373729633625*zeta(19) - 274712297359500*zeta(2)*zeta(17) - 49883680146300*zeta(2)^2*zeta(15) - 12295855171600*zeta(2)^3*zeta(13) - 1750084135800*zeta(2)^4*zeta(11) - 12643176000*zeta(2)^5*zeta(9) + 32591503808*zeta(2)^6*zeta(7) + 7537420800*zeta(2)^7*zeta(5) + 10058548500*zeta(5)*zeta(3,11) + 8513505000*zeta(5)*zeta(5,9) + 81868036250*zeta(9)*zeta(3,7) - 92839246500*zeta(3,3,13) + 215465250*zeta(3,5,11) + 13851087250*zeta(3,7,9) - 94300206000*zeta(5,3,11) + 13950937000*zeta(5,5,9))/81868036250 w=19 zeta(9,5,5) = (175175*zeta(5)^2*zeta(9) - 14145381250*zeta(19) + 7683175500*zeta(2)*zeta(17) + 559158600*zeta(2)^2*zeta(15) + 17617600*zeta(2)^3*zeta(13) - 7447440*zeta(2)^4*zeta(11) - 2023840*zeta(2)^5*zeta(9) - 265344*zeta(2)^6*zeta(7) - 10752*zeta(2)^7*zeta(5) - 350350*zeta(5)*zeta(5,9) + 350350*zeta(5,5,9))/350350 w=19 zeta(9,7,3) = (58963905000*zeta(3)*zeta(5)*zeta(11) + 102144542500*zeta(3)*zeta(7)*zeta(9) - 74858772113125*zeta(19) + 39594262207500*zeta(2)*zeta(17) + 3219429213000*zeta(2)^2*zeta(15) + 242968726000*zeta(2)^3*zeta(13) + 2246244000*zeta(2)^4*zeta(11) - 3811808000*zeta(2)^5*zeta(9) - 1240483200*zeta(2)^6*zeta(7) - 301593600*zeta(2)^7*zeta(5) - 3066286848*zeta(2)^8*zeta(3) + 9827317500*zeta(3)*zeta(3,13) - 3126873750*zeta(3)*zeta(5,11) - 1637886250*zeta(9)*zeta(3,7) + 1637886250*zeta(3,7,9))/1637886250 w=19 zeta(11,3,5) = (-5601570975*zeta(19) + 2989886900*zeta(2)*zeta(17) + 239499260*zeta(2)^2*zeta(15) + 14534520*zeta(2)^3*zeta(13) - 2138136*zeta(2)^4*zeta(11) - 902720*zeta(2)^5*zeta(9) - 132672*zeta(2)^6*zeta(7) - 5376*zeta(2)^7*zeta(5) - 175175*zeta(5)*zeta(3,11) + 175175*zeta(11)*zeta(3,5) + 175175*zeta(5,3,11))/175175 w=19 zeta(11,5,3) = (148898750*zeta(3)*zeta(5)*zeta(11) - 5554891216875*zeta(19) + 2875532660000*zeta(2)*zeta(17) + 258607349000*zeta(2)^2*zeta(15) + 26954928000*zeta(2)^3*zeta(13) + 1531530000*zeta(2)^4*zeta(11) - 247520000*zeta(2)^5*zeta(9) - 112771200*zeta(2)^6*zeta(7) - 27417600*zeta(2)^7*zeta(5) - 2777856*zeta(2)^8*zeta(3) - 148898750*zeta(3)*zeta(5,11) - 148898750*zeta(11)*zeta(3,5) + 148898750*zeta(3,5,11))/148898750 w=19 zeta(13,3,3) = (74449375*zeta(3)^2*zeta(13) - 1947818998125*zeta(19) + 901135235000*zeta(2)*zeta(17) + 119238119000*zeta(2)^2*zeta(15) + 24725701000*zeta(2)^3*zeta(13) + 4227022800*zeta(2)^4*zeta(11) + 346528000*zeta(2)^5*zeta(9) - 67662720*zeta(2)^6*zeta(7) - 27417600*zeta(2)^7*zeta(5) - 2777856*zeta(2)^8*zeta(3) - 148898750*zeta(3)*zeta(3,13) + 148898750*zeta(3,3,13))/148898750 w=21 zeta(3,9,9) = (5486532160489380000*zeta(5)^2*zeta(11) + 4858492406367600000*zeta(5)*zeta(7)*zeta(9) - 6072458685793500000*zeta(7)^3 + 1211037381731032480625*zeta(21) - 548917572226203180000*zeta(2)*zeta(19) - 60104481409800828000*zeta(2)^2*zeta(17) - 13098884857522464000*zeta(2)^3*zeta(15) - 4453201566664250400*zeta(2)^4*zeta(13) - 1252234876628736000*zeta(2)^5*zeta(11) - 957801153842734080*zeta(2)^6*zeta(9) - 12247078527129600*zeta(2)^7*zeta(7) - 446598301058187264*zeta(2)^8*zeta(5) + 383108538512700000*zeta(5)*zeta(3,13) - 59209044754860000*zeta(5)*zeta(5,11) - 1654573166145900000*zeta(7)*zeta(3,11) + 442520176098000000*zeta(7)*zeta(5,9) - 145215931795935000*zeta(3,3,15) + 43093180330200000*zeta(3,5,13) - 13059620498925000*zeta(3,7,11) + 74981744612775000*zeta(5,3,13) - 10198573900515000*zeta(5,5,11) - 4877494221600000*zeta(7,3,11))/35281825639060000 w=21 zeta(3,11,7) = (13080308491250*zeta(21) - 6864753520625*zeta(2)*zeta(19) - 575583008000*zeta(2)^2*zeta(17) - 49553504000*zeta(2)^3*zeta(15) - 2246244000*zeta(2)^4*zeta(13) + 210392000*zeta(2)^5*zeta(11) + 105253120*zeta(2)^6*zeta(9) + 34272000*zeta(2)^7*zeta(7) + 8333568*zeta(2)^8*zeta(5) + 74449375*zeta(7)*zeta(3,11) - 74449375*zeta(3,7,11) - 74449375*zeta(7,3,11))/74449375 w=21 zeta(3,13,5) = (7525417274375*zeta(21) - 3738624264375*zeta(2)*zeta(19) - 391305915000*zeta(2)^2*zeta(17) - 58402344000*zeta(2)^3*zeta(15) - 7422815400*zeta(2)^4*zeta(13) - 464100000*zeta(2)^5*zeta(11) + 75180800*zeta(2)^6*zeta(9) + 34272000*zeta(2)^7*zeta(7) + 8333568*zeta(2)^8*zeta(5) + 74449375*zeta(5)*zeta(3,13) - 74449375*zeta(3,5,13) - 74449375*zeta(5,3,13))/74449375 w=21 zeta(3,15,3) = (1970526057500*zeta(21) - 852966489375*zeta(2)*zeta(19) - 130077948000*zeta(2)^2*zeta(17) - 32536504000*zeta(2)^3*zeta(15) - 7412605200*zeta(2)^4*zeta(13) - 1280916000*zeta(2)^5*zeta(11) - 105253120*zeta(2)^6*zeta(9) + 20563200*zeta(2)^7*zeta(7) + 8333568*zeta(2)^8*zeta(5) + 74449375*zeta(3)*zeta(3,15) - 148898750*zeta(3,3,15))/74449375 w=21 zeta(5,7,9) = (-85856669188290000*zeta(5)^2*zeta(11) - 76886502933240000*zeta(5)*zeta(7)*zeta(9) + 95056468532025000*zeta(7)^3 - 40634406240248946125*zeta(21) + 20057541205378677000*zeta(2)*zeta(19) + 1878377476401426000*zeta(2)^2*zeta(17) + 275969867671097600*zeta(2)^3*zeta(15) + 69302336205342240*zeta(2)^4*zeta(13) + 17984025499440000*zeta(2)^5*zeta(11) + 14582621162388224*zeta(2)^6*zeta(9) + 114483454525440*zeta(2)^7*zeta(7) + 6984268576137216*zeta(2)^8*zeta(5) - 6009298284990000*zeta(5)*zeta(3,13) + 883531422774000*zeta(5)*zeta(5,11) + 25724659170210000*zeta(7)*zeta(3,11) - 7027387567200000*zeta(7)*zeta(5,9) + 2813577725959000*zeta(3,3,15) - 630798168000000*zeta(3,5,13) + 160241926845000*zeta(3,7,11) - 583935968616000*zeta(5,3,13) + 159916353597000*zeta(5,5,11) + 628044206790000*zeta(7,3,11))/44472889461000 w=21 zeta(5,9,7) = (1695316139565048000*zeta(5)^2*zeta(11) + 1523726278794720000*zeta(5)*zeta(7)*zeta(9) - 1870784708960667500*zeta(7)^3 + 811532051329802177375*zeta(21) - 401031906494548329000*zeta(2)*zeta(19) - 37456219631380149600*zeta(2)^2*zeta(17) - 5464497097911051200*zeta(2)^3*zeta(15) - 1365736705216884000*zeta(2)^4*zeta(13) - 354162698089200000*zeta(2)^5*zeta(11) - 286955312354315264*zeta(2)^6*zeta(9) - 2177415615513600*zeta(2)^7*zeta(7) - 137710568162119680*zeta(2)^8*zeta(5) + 119306417546316000*zeta(5)*zeta(3,13) - 17724665626668000*zeta(5)*zeta(5,11) - 505930215045255000*zeta(7)*zeta(3,11) + 138216938547688000*zeta(7)*zeta(5,9) - 55868424466855000*zeta(3,3,15) + 13282264273278000*zeta(3,5,13) - 3525825318015000*zeta(3,7,11) + 11829263933487000*zeta(5,3,13) - 2648403102345000*zeta(5,5,11) - 12383304508575000*zeta(7,3,11))/504026080558000 w=21 zeta(5,11,5) = (8317534225*zeta(21) - 4429525100*zeta(2)*zeta(19) - 352592240*zeta(2)^2*zeta(17) - 22902880*zeta(2)^3*zeta(15) + 1434576*zeta(2)^4*zeta(13) + 827840*zeta(2)^5*zeta(11) + 176896*zeta(2)^6*zeta(9) + 23040*zeta(2)^7*zeta(7) + 50050*zeta(5)*zeta(5,11) - 100100*zeta(5,5,11))/50050 w=21 zeta(5,13,3) = (160410375125*zeta(21) - 81477396000*zeta(2)*zeta(19) - 8004796800*zeta(2)^2*zeta(17) - 1009808800*zeta(2)^3*zeta(15) - 71591520*zeta(2)^4*zeta(13) + 13104000*zeta(2)^5*zeta(11) + 5483776*zeta(2)^6*zeta(9) + 806400*zeta(2)^7*zeta(7) + 1751750*zeta(3)*zeta(5,13) - 1751750*zeta(3,5,13) - 1751750*zeta(5,3,13))/1751750 w=21 zeta(7,5,9) = (-2166821666293284000*zeta(5)^2*zeta(11) - 1957037736654000000*zeta(5)*zeta(7)*zeta(9) + 2380434196793152500*zeta(7)^3 - 846186891024993392875*zeta(21) + 412714236103294125000*zeta(2)*zeta(19) + 39188213065186785600*zeta(2)^2*zeta(17) + 6192783879818536000*zeta(2)^3*zeta(15) + 1738442235905575200*zeta(2)^4*zeta(13) + 471768300315312000*zeta(2)^5*zeta(11) + 370324738447155712*zeta(2)^6*zeta(9) + 3335878976855040*zeta(2)^7*zeta(7) + 175666572897693696*zeta(2)^8*zeta(5) - 153603110949288000*zeta(5)*zeta(3,13) + 23133928505688000*zeta(5)*zeta(5,11) + 643152233348625000*zeta(7)*zeta(3,11) - 174207560116590000*zeta(7)*zeta(5,9) + 71943630717959000*zeta(3,3,15) - 18399655107834000*zeta(3,5,13) + 5129250441315000*zeta(3,7,11) - 15633968867517000*zeta(5,3,13) + 2508053284737000*zeta(5,5,11) + 15796410494865000*zeta(7,3,11))/1512078241674000 w=21 zeta(7,7,7) = (25025*zeta(7)^3 + 50050*zeta(21) - 2304*zeta(2)^7*zeta(7))/150150 w=21 zeta(7,9,5) = (8385856003324800000*zeta(5)^2*zeta(11) + 7463987028347850000*zeta(5)*zeta(7)*zeta(9) - 9353923544803337500*zeta(7)^3 + 3936780941813987141875*zeta(21) - 1946551379825457405000*zeta(2)*zeta(19) - 180494891008267836000*zeta(2)^2*zeta(17) - 26161209399949624000*zeta(2)^3*zeta(15) - 6680413453929415200*zeta(2)^4*zeta(13) - 1770813490446000000*zeta(2)^5*zeta(11) - 1440120829356774400*zeta(2)^6*zeta(9) - 12047194051200000*zeta(2)^7*zeta(7) - 683881920252862464*zeta(2)^8*zeta(5) + 581411305314840000*zeta(5)*zeta(3,13) - 83812170091650000*zeta(5)*zeta(5,11) - 2529651075226275000*zeta(7)*zeta(3,11) + 688564562335650000*zeta(7)*zeta(5,9) - 279342122334275000*zeta(3,3,15) + 66411321366390000*zeta(3,5,13) - 17629126590075000*zeta(3,7,11) + 59146319667435000*zeta(5,3,13) - 13242015511725000*zeta(5,5,11) - 61916522542875000*zeta(7,3,11))/2520130402790000 w=21 zeta(7,11,3) = (-6796572783000*zeta(3)*zeta(5)*zeta(13) - 13490450098125*zeta(3)*zeta(7)*zeta(11) - 8462049971375*zeta(3)*zeta(9)^2 + 6521786021375625*zeta(21) - 3599425225646250*zeta(2)*zeta(19) - 240086726880000*zeta(2)^2*zeta(17) + 176534358000*zeta(2)^3*zeta(15) + 4826953731600*zeta(2)^4*zeta(13) + 912476292000*zeta(2)^5*zeta(11) + 77992561920*zeta(2)^6*zeta(9) + 330648603136*zeta(2)^9*zeta(3) - 1132762130500*zeta(3)*zeta(3,15) + 233398790625*zeta(3)*zeta(5,13) - 55166986875*zeta(3,7,11) - 55166986875*zeta(7,3,11))/55166986875 w=21 zeta(9,3,9) = (-1097306432097876000*zeta(5)^2*zeta(11) - 971698481273520000*zeta(5)*zeta(7)*zeta(9) + 1214491737158700000*zeta(7)^3 + 273969160935805209875*zeta(21) - 156280260881474730000*zeta(2)*zeta(19) - 12137275369616997600*zeta(2)^2*zeta(17) - 22126132348320000*zeta(2)^3*zeta(15) + 677255831867815200*zeta(2)^4*zeta(13) + 250446975325747200*zeta(2)^5*zeta(11) + 196370071595225088*zeta(2)^6*zeta(9) + 4073578068510720*zeta(2)^7*zeta(7) + 89714590985908224*zeta(2)^8*zeta(5) - 76621707702540000*zeta(5)*zeta(3,13) + 11841808950972000*zeta(5)*zeta(5,11) + 330914633229180000*zeta(7)*zeta(3,11) - 88504035219600000*zeta(7)*zeta(5,9) + 3528182563906000*zeta(9)*zeta(3,9) + 29043186359187000*zeta(3,3,15) - 8618636066040000*zeta(3,5,13) + 2611924099785000*zeta(3,7,11) - 14996348922555000*zeta(5,3,13) + 2039714780103000*zeta(5,5,11) + 975498844320000*zeta(7,3,11))/3528182563906000 w=21 zeta(9,5,7) = (-6500464998879852000*zeta(5)^2*zeta(11) - 5828775019195128000*zeta(5)*zeta(7)*zeta(9) + 7141302590379457500*zeta(7)^3 - 2941491722525059328625*zeta(21) + 1457923280737198275000*zeta(2)*zeta(19) + 133296301221936652800*zeta(2)^2*zeta(17) + 18941250417457368000*zeta(2)^3*zeta(15) + 4955905924128038880*zeta(2)^4*zeta(13) + 1353093681859920000*zeta(2)^5*zeta(11) + 1102556726883960832*zeta(2)^6*zeta(9) + 9868423013729280*zeta(2)^7*zeta(7) + 526999718693081088*zeta(2)^8*zeta(5) - 460809332847864000*zeta(5)*zeta(3,13) + 69401785517064000*zeta(5)*zeta(5,11) + 1929456700045875000*zeta(7)*zeta(3,11) - 527158915074792000*zeta(7)*zeta(5,9) + 7056365127812000*zeta(9)*zeta(3,9) + 215830892153877000*zeta(3,3,15) - 55198965323502000*zeta(3,5,13) + 15387751323945000*zeta(3,7,11) - 46901906602551000*zeta(5,3,13) + 7524159854211000*zeta(5,5,11) + 47389231484595000*zeta(7,3,11))/4536234725022000 w=21 zeta(9,7,5) = (-1953199047069270000*zeta(5)^2*zeta(11) - 1727696681160450000*zeta(5)*zeta(7)*zeta(9) + 2203581770515125000*zeta(7)^3 - 1083005284695116908125*zeta(21) + 538896465941148315000*zeta(2)*zeta(19) + 49895758519741134000*zeta(2)^2*zeta(17) + 6955027782214512000*zeta(2)^3*zeta(15) + 1608250827098916000*zeta(2)^4*zeta(13) + 402763495876560000*zeta(2)^5*zeta(11) + 334915446182417920*zeta(2)^6*zeta(9) + 2179341729331200*zeta(2)^7*zeta(7) + 159977979486139392*zeta(2)^8*zeta(5) - 133120685617920000*zeta(5)*zeta(3,13) + 18513663783615000*zeta(5)*zeta(5,11) + 596344371673050000*zeta(7)*zeta(3,11) - 162907620876000000*zeta(7)*zeta(5,9) - 1603719347230000*zeta(9)*zeta(3,9) + 65223847283595000*zeta(3,3,15) - 14623048440000000*zeta(3,5,13) + 3714699213225000*zeta(3,7,11) - 13536697454280000*zeta(5,3,13) + 3707151833385000*zeta(5,5,11) + 14559206611950000*zeta(7,3,11))/1030962437505000 w=21 zeta(9,9,3) = (335177343571070000*zeta(3)*zeta(9)^2 + 104244111049298220000*zeta(5)^2*zeta(11) + 92311355720984400000*zeta(5)*zeta(7)*zeta(9) - 115376715030076500000*zeta(7)^3 - 75063180476005464868125*zeta(21) + 40122683439778059120000*zeta(2)*zeta(19) + 3448067467013445276000*zeta(2)^2*zeta(17) + 253082777439107616000*zeta(2)^3*zeta(15) - 44067778288264130400*zeta(2)^4*zeta(13) - 23792462655945984000*zeta(2)^5*zeta(11) - 19145938708120407040*zeta(2)^6*zeta(9) - 541285341001574400*zeta(2)^7*zeta(7) - 8560404567217004544*zeta(2)^8*zeta(5) - 3801367500677120*zeta(2)^9*zeta(3) + 7279062231741300000*zeta(5)*zeta(3,13) - 1124971850342340000*zeta(5)*zeta(5,11) - 31436890156772100000*zeta(7)*zeta(3,11) + 8407883345862000000*zeta(7)*zeta(5,9) - 670354687142140000*zeta(9)*zeta(3,9) - 2759102704122765000*zeta(3,3,15) + 818770426273800000*zeta(3,5,13) - 248132789479575000*zeta(3,7,11) + 1424653147642725000*zeta(5,3,13) - 193772904109785000*zeta(5,5,11) - 92672390210400000*zeta(7,3,11))/670354687142140000 w=21 zeta(11,3,7) = (-14792027250*zeta(21) + 8163905750*zeta(2)*zeta(19) + 544544000*zeta(2)^2*zeta(17) - 400400*zeta(2)^3*zeta(15) - 10948080*zeta(2)^4*zeta(13) - 2069600*zeta(2)^5*zeta(11) - 176896*zeta(2)^6*zeta(9) - 3840*zeta(2)^7*zeta(7) - 125125*zeta(7)*zeta(3,11) + 125125*zeta(11)*zeta(3,7) + 125125*zeta(7,3,11))/125125 w=21 zeta(11,5,5) = (74449375*zeta(5)^2*zeta(11) - 24744515420625*zeta(21) + 13177837172500*zeta(2)*zeta(19) + 1048961914000*zeta(2)^2*zeta(17) + 68136068000*zeta(2)^3*zeta(15) - 4267863600*zeta(2)^4*zeta(13) - 2469012000*zeta(2)^5*zeta(11) - 526265600*zeta(2)^6*zeta(9) - 68544000*zeta(2)^7*zeta(7) - 2777856*zeta(2)^8*zeta(5) - 148898750*zeta(5)*zeta(5,11) + 148898750*zeta(5,5,11))/148898750 w=21 zeta(11,7,3) = (47576009481000*zeta(3)*zeta(5)*zeta(13) + 94819319595000*zeta(3)*zeta(7)*zeta(11) + 59234349799625*zeta(3)*zeta(9)^2 - 67847173975205625*zeta(21) + 35607476511481875*zeta(2)*zeta(19) + 2985549062496000*zeta(2)^2*zeta(17) + 257034025248000*zeta(2)^3*zeta(15) + 11651267628000*zeta(2)^4*zeta(13) - 1123400460000*zeta(2)^5*zeta(11) - 545947933440*zeta(2)^6*zeta(9) - 177768864000*zeta(2)^7*zeta(7) - 43226217216*zeta(2)^8*zeta(5) - 2318919903232*zeta(2)^9*zeta(3) + 7929334913500*zeta(3)*zeta(3,15) - 1633791534375*zeta(3)*zeta(5,13) - 386168908125*zeta(11)*zeta(3,7) + 386168908125*zeta(3,7,11))/386168908125 w=21 zeta(13,3,5) = (-13634732986875*zeta(21) + 6925578660000*zeta(2)*zeta(19) + 680407728000*zeta(2)^2*zeta(17) + 85833748000*zeta(2)^3*zeta(15) + 6085279200*zeta(2)^4*zeta(13) - 1113840000*zeta(2)^5*zeta(11) - 466120960*zeta(2)^6*zeta(9) - 68544000*zeta(2)^7*zeta(7) - 2777856*zeta(2)^8*zeta(5) - 148898750*zeta(5)*zeta(3,13) + 148898750*zeta(13)*zeta(3,5) + 148898750*zeta(5,3,13))/148898750 w=21 zeta(13,5,3) = (9901766875*zeta(3)*zeta(5)*zeta(13) - 1000870595725000*zeta(21) + 497237027161875*zeta(2)*zeta(19) + 52043686695000*zeta(2)^2*zeta(17) + 7767511752000*zeta(2)^3*zeta(15) + 985876491600*zeta(2)^4*zeta(13) + 61725300000*zeta(2)^5*zeta(11) - 9999046400*zeta(2)^6*zeta(9) - 4558176000*zeta(2)^7*zeta(7) - 1108364544*zeta(2)^8*zeta(5) - 112299520*zeta(2)^9*zeta(3) - 9901766875*zeta(3)*zeta(5,13) - 9901766875*zeta(13)*zeta(3,5) + 9901766875*zeta(3,5,13))/9901766875 w=21 zeta(15,3,3) = (9901766875*zeta(3)^2*zeta(15) - 524140127761250*zeta(21) + 226889086173750*zeta(2)*zeta(19) + 34600734168000*zeta(2)^2*zeta(17) + 8652446803000*zeta(2)^3*zeta(15) + 1971752983200*zeta(2)^4*zeta(13) + 340723656000*zeta(2)^5*zeta(11) + 27997329920*zeta(2)^6*zeta(9) - 5469811200*zeta(2)^7*zeta(7) - 2216729088*zeta(2)^8*zeta(5) - 224599040*zeta(2)^9*zeta(3) - 19803533750*zeta(3)*zeta(3,15) + 19803533750*zeta(3,3,15))/19803533750 w=21 zeta(2)*zeta(3,9,7) = (-15087822750*zeta(2)*zeta(5)^2*zeta(9) - 122802054375*zeta(2)*zeta(5)*zeta(7)^2 + 684813190061000*zeta(2)*zeta(19) - 363676233170250*zeta(2)^2*zeta(17) - 28698097277850*zeta(2)^3*zeta(15) - 1992094304200*zeta(2)^4*zeta(13) - 51236285100*zeta(2)^5*zeta(11) + 6321588000*zeta(2)^6*zeta(9) + 12639569056*zeta(2)^7*zeta(7) + 3768710400*zeta(2)^8*zeta(5) - 5029274250*zeta(2)*zeta(5)*zeta(3,11) - 4256752500*zeta(2)*zeta(5)*zeta(5,9) + 46419623250*zeta(2)*zeta(3,3,13) - 107732625*zeta(2)*zeta(3,5,11) - 47859561750*zeta(2)*zeta(3,7,9) + 47150103000*zeta(2)*zeta(5,3,11) - 6975468500*zeta(2)*zeta(5,5,9))/40934018125 w=21 zeta(2)*zeta(3,11,5) = (13070682625*zeta(2)*zeta(19) - 6765959200*zeta(2)^2*zeta(17) - 608487880*zeta(2)^3*zeta(15) - 63423360*zeta(2)^4*zeta(13) - 3651648*zeta(2)^5*zeta(11) + 582400*zeta(2)^6*zeta(9) + 265344*zeta(2)^7*zeta(7) + 64512*zeta(2)^8*zeta(5) + 350350*zeta(2)*zeta(5)*zeta(3,11) - 350350*zeta(2)*zeta(3,5,11) - 350350*zeta(2)*zeta(5,3,11))/350350 w=21 zeta(2)*zeta(3,13,3) = (22917269375*zeta(2)*zeta(19) - 10601591000*zeta(2)^2*zeta(17) - 1402801400*zeta(2)^3*zeta(15) - 291090800*zeta(2)^4*zeta(13) - 49729680*zeta(2)^5*zeta(11) - 4076800*zeta(2)^6*zeta(9) + 796032*zeta(2)^7*zeta(7) + 322560*zeta(2)^8*zeta(5) + 1751750*zeta(2)*zeta(3)*zeta(3,13) - 3503500*zeta(2)*zeta(3,3,13))/1751750 w=21 zeta(2)*zeta(7,5,7) = (-12618149544000*zeta(2)*zeta(5)^2*zeta(9) + 27507660180000*zeta(2)*zeta(5)*zeta(7)^2 + 63414467517526125*zeta(2)*zeta(19) - 32655008209824000*zeta(2)^2*zeta(17) - 3100820019897600*zeta(2)^3*zeta(15) - 332276912167200*zeta(2)^4*zeta(13) + 3604227026400*zeta(2)^5*zeta(11) + 11753475552000*zeta(2)^6*zeta(9) - 646401873664*zeta(2)^7*zeta(7) - 4206049848000*zeta(2)*zeta(5)*zeta(3,11) + 2648646000000*zeta(2)*zeta(5)*zeta(5,9) + 4584610030000*zeta(2)*zeta(7)*zeta(3,9) - 305918613000*zeta(2)*zeta(3,3,13) - 5587318737000*zeta(2)*zeta(3,5,11) + 5633670042000*zeta(2)*zeta(3,7,9) - 5192229042000*zeta(2)*zeta(5,3,11) - 142438296000*zeta(2)*zeta(5,5,9))/2947249305000 # PART 4: phi of the basis generators (32: 12 of depth two, weights 8-20; 20 of depth three, weights 11-21) phi(zeta(3,5)) weight 8 f3 f5 -5 phi(zeta(3,7)) weight 10 f3 f7 -14 f5 f5 -6 phi(zeta(3,3,5)) weight 11 f3 f3 f5 -5 f2 f9 -45 f2^2 f7 -6/5 f2^3 f5 4/7 phi(zeta(3,9)) weight 12 f3 f9 -27 f5 f7 -15 f7 f5 -6 phi(zeta(3,5,5)) weight 13 f3 f5 f5 25 f2 f11 -275/2 f2^2 f9 -10 phi(zeta(3,3,7)) weight 13 f3 f3 f7 -14 f3 f5 f5 30 f2 f11 -407/2 f2^2 f9 -56/5 f2^3 f7 32/35 phi(zeta(5,9)) weight 14 f3 f11 -165 f5 f9 -69 f7 f7 -15 phi(zeta(3,11)) weight 14 f3 f11 -44 f5 f9 -28 f7 f7 -15 f9 f5 -6 phi(zeta(3,5,7)) weight 15 f3 f3 f9 -42 f3 f5 f7 70 f3 f7 f5 84 f5 f5 f5 36 f2 f13 -819 f2^2 f11 -57 f2^3 f9 -32/35 phi(zeta(3,3,9)) weight 15 f3 f3 f9 -27 f3 f5 f7 75 f3 f7 f5 84 f5 f5 f5 36 f2 f13 -1209/2 f2^2 f11 -252/5 f2^3 f9 -116/35 f2^4 f7 -72/175 phi(zeta(5,11)) weight 16 f3 f13 -429 f5 f11 -209 f7 f9 -70 f9 f7 -15 phi(zeta(3,13)) weight 16 f3 f13 -65 f5 f11 -45 f7 f9 -28 f9 f7 -15 f11 f5 -6 phi(zeta(3,7,7)) weight 17 f3 f7 f7 196 f3 f9 f5 252 f5 f5 f7 84 f5 f7 f5 84 f2 f15 -2450 f2^2 f13 -1078/5 f2^3 f11 -20 f2^6 f5 1552448/525525 phi(zeta(5,3,9)) weight 17 f3 f5 f9 -162 f3 f9 f5 90 f5 f3 f9 -27 f5 f5 f7 -15 f5 f7 f5 -6 f7 f5 f5 -36 f2 f15 -2535 f2^2 f13 -156 f2^3 f11 36/7 f2^4 f9 1056/175 f2^5 f7 48/77 f2^6 f5 1552448/525525 phi(zeta(3,5,9)) weight 17 f3 f3 f11 -165 f3 f5 f9 345 f3 f7 f7 210 f3 f9 f5 162 f5 f5 f7 90 f5 f7 f5 90 f7 f5 f5 36 f2 f15 -3165 f2^2 f13 -1221/5 f2^3 f11 -96/7 f2^4 f9 -24/7 phi(zeta(3,3,11)) weight 17 f3 f3 f11 -44 f3 f5 f9 140 f3 f7 f7 210 f3 f9 f5 162 f5 f5 f7 90 f5 f7 f5 90 f7 f5 f5 36 f2 f15 -1449 f2^2 f13 -792/5 f2^3 f11 -832/35 f2^4 f9 -96/25 f2^5 f7 -96/385 phi(zeta(5,13)) weight 18 f3 f15 -910 f5 f13 -494 f7 f11 -210 f9 f9 -70 f11 f7 -15 phi(zeta(3,15)) weight 18 f3 f15 -90 f5 f13 -66 f7 f11 -45 f9 f9 -28 f11 f7 -15 f13 f5 -6 phi(zeta(5,5,9)) weight 19 f3 f5 f11 -990 f3 f9 f7 630 f5 f3 f11 -165 f5 f5 f9 -69 f5 f7 f7 210 f2 f17 -10965 f2^2 f15 -798 f2^3 f13 -176/7 f2^4 f11 768/35 f2^5 f9 1104/385 f2^6 f7 776224/105105 phi(zeta(3,7,9)) weight 19 f3 f3 f13 -429 f3 f5 f11 825 f3 f7 f9 378 f3 f9 f7 405 f3 f11 f5 990 f5 f5 f9 162 f5 f7 f7 225 f5 f9 f5 414 f7 f5 f7 90 f7 f7 f5 90 f2 f17 -12087 f2^2 f15 -4914/5 f2^3 f13 -2596/35 f2^4 f11 -12 phi(zeta(5,3,11)) weight 19 f3 f5 f11 -264 f3 f9 f7 630 f3 f11 f5 726 f5 f3 f11 -44 f5 f5 f9 -28 f5 f7 f7 210 f5 f9 f5 246 f9 f5 f5 -36 f2 f17 -8534 f2^2 f15 -3418/5 f2^3 f13 -1452/35 f2^4 f11 228/25 f2^5 f9 992/385 f2^6 f7 776224/105105 phi(zeta(3,5,11)) weight 19 f3 f3 f13 -429 f3 f5 f11 1045 f3 f7 f9 980 f3 f9 f7 405 f3 f11 f5 264 f5 f5 f9 420 f5 f7 f7 225 f5 f9 f5 168 f7 f5 f7 90 f7 f7 f5 90 f9 f5 f5 36 f2 f17 -9656 f2^2 f15 -4342/5 f2^3 f13 -3168/35 f2^4 f11 -684/35 f2^5 f9 -160/77 phi(zeta(3,3,13)) weight 19 f3 f3 f13 -65 f3 f5 f11 225 f3 f7 f9 392 f3 f9 f7 405 f3 f11 f5 264 f5 f5 f9 168 f5 f7 f7 225 f5 f9 f5 168 f7 f5 f7 90 f7 f7 f5 90 f9 f5 f5 36 f2 f17 -3026 f2^2 f15 -2002/5 f2^3 f13 -2908/35 f2^4 f11 -432/25 f2^5 f9 -128/55 f2^6 f7 -132672/875875 phi(zeta(7,13)) weight 20 f3 f17 -6188 f5 f15 -2912 f7 f13 -923 f9 f11 -210 f11 f9 -28 phi(zeta(5,15)) weight 20 f3 f17 -1700 f5 f15 -1000 f7 f13 -495 f9 f11 -210 f11 f9 -70 f13 f7 -15 phi(zeta(3,17)) weight 20 f3 f17 -119 f5 f15 -91 f7 f13 -66 f9 f11 -45 f11 f9 -28 f13 f7 -15 f15 f5 -6 phi(zeta(7,3,11)) weight 21 f3 f7 f11 -660 f3 f9 f9 -1176 f3 f11 f7 -660 f5 f5 f11 -264 f5 f7 f9 -420 f5 f9 f7 -420 f5 f11 f5 -264 f7 f3 f11 -44 f7 f5 f9 -28 f7 f7 f7 -240 f7 f9 f5 -258 f9 f5 f7 -90 f9 f7 f5 -90 f2 f19 -32623 f2^2 f17 -2176 f2^3 f15 8/5 f2^4 f13 7656/175 f2^5 f11 3888/385 f2^6 f9 -13932416/1126125 f2^7 f7 1152/5005 f2^8 f5 -1301027328/116991875 phi(zeta(5,5,11)) weight 21 f3 f5 f13 -2574 f3 f9 f9 2940 f3 f11 f7 2475 f5 f3 f13 -429 f5 f5 f11 -209 f5 f7 f9 980 f5 f9 f7 1035 f7 f7 f7 225 f2 f19 -44251 f2^2 f17 -17612/5 f2^3 f15 -1144/5 f2^4 f13 7656/175 f2^5 f11 3184/385 f2^6 f9 1552448/45045 phi(zeta(3,7,11)) weight 21 f3 f3 f15 -2002 f3 f5 f13 4290 f3 f7 f11 2926 f3 f9 f9 756 f3 f11 f7 660 f3 f13 f5 2574 f5 f5 f11 1254 f5 f7 f9 420 f5 f9 f7 420 f5 f11 f5 1254 f7 f5 f9 168 f7 f7 f7 225 f7 f9 f5 420 f9 f5 f7 90 f9 f7 f5 90 f2 f19 -92207/2 f2^2 f17 -19328/5 f2^3 f15 -1664/5 f2^4 f13 -1848/25 f2^5 f11 -80/11 phi(zeta(5,3,13)) weight 21 f3 f5 f13 -390 f3 f9 f9 1176 f3 f11 f7 2475 f3 f13 f5 2184 f5 f3 f13 -65 f5 f5 f11 -45 f5 f7 f9 392 f5 f9 f7 1035 f5 f11 f5 984 f7 f7 f7 225 f7 f9 f5 252 f11 f5 f5 -36 f2 f19 -23256 f2^2 f17 -11424/5 f2^3 f15 -10088/35 f2^4 f13 -2796/175 f2^5 f11 288/77 f2^6 f9 115437632/7882875 phi(zeta(3,5,13)) weight 21 f3 f3 f15 -910 f3 f5 f13 2470 f3 f7 f11 2940 f3 f9 f9 1890 f3 f11 f7 660 f3 f13 f5 390 f5 f5 f11 1260 f5 f7 f9 1050 f5 f9 f7 420 f5 f11 f5 270 f7 f5 f9 420 f7 f7 f7 225 f7 f9 f5 168 f9 f5 f7 90 f9 f7 f5 90 f11 f5 f5 36 f2 f19 -50217/2 f2^2 f17 -2628 f2^3 f15 -13728/35 f2^4 f13 -14652/175 f2^5 f11 -912/77 f2^6 f9 -44224/35035 phi(zeta(3,3,15)) weight 21 f3 f3 f15 -90 f3 f5 f13 330 f3 f7 f11 630 f3 f9 f9 756 f3 f11 f7 660 f3 f13 f5 390 f5 f5 f11 270 f5 f7 f9 420 f5 f9 f7 420 f5 f11 f5 270 f7 f5 f9 168 f7 f7 f7 225 f7 f9 f5 168 f9 f5 f7 90 f9 f7 f5 90 f11 f5 f5 36 f2 f19 -11457/2 f2^2 f17 -4368/5 f2^3 f15 -7648/35 f2^4 f13 -9504/175 f2^5 f11 -576/55 f2^6 f9 -176896/125125 f2^7 f7 -2304/25025