(09:16) gp > (09:16) gp > \p2000
   realprecision = 2003 significant digits (2000 digits displayed)
(09:16) gp > (09:16) gp > for(i=1,100,a=round(zeta(1-2*i)*(6*i)!)/(6*i)!;print("zeta(1-",2*i,") = ",a,"    ",factor(denominator(a))))
zeta(1-2) = -1/12    [2, 2; 3, 1]
zeta(1-4) = 1/120    [2, 3; 3, 1; 5, 1]
zeta(1-6) = -1/252    [2, 2; 3, 2; 7, 1]
zeta(1-8) = 1/240    [2, 4; 3, 1; 5, 1]
zeta(1-10) = -1/132    [2, 2; 3, 1; 11, 1]
zeta(1-12) = 691/32760    [2, 3; 3, 2; 5, 1; 7, 1; 13, 1]
zeta(1-14) = -1/12    [2, 2; 3, 1]
zeta(1-16) = 3617/8160    [2, 5; 3, 1; 5, 1; 17, 1]
zeta(1-18) = -43867/14364    [2, 2; 3, 3; 7, 1; 19, 1]
zeta(1-20) = 174611/6600    [2, 3; 3, 1; 5, 2; 11, 1]
zeta(1-22) = -77683/276    [2, 2; 3, 1; 23, 1]
zeta(1-24) = 236364091/65520    [2, 4; 3, 2; 5, 1; 7, 1; 13, 1]
zeta(1-26) = -657931/12    [2, 2; 3, 1]
zeta(1-28) = 3392780147/3480    [2, 3; 3, 1; 5, 1; 29, 1]
zeta(1-30) = -1723168255201/85932    [2, 2; 3, 2; 7, 1; 11, 1; 31, 1]
zeta(1-32) = 7709321041217/16320    [2, 6; 3, 1; 5, 1; 17, 1]
zeta(1-34) = -151628697551/12    [2, 2; 3, 1]
zeta(1-36) = 26315271553053477373/69090840    [2, 3; 3, 3; 5, 1; 7, 1; 13, 1; 19, 1; 37, 1]
zeta(1-38) = -154210205991661/12    [2, 2; 3, 1]
zeta(1-40) = 261082718496449122051/541200    [2, 4; 3, 1; 5, 2; 11, 1; 41, 1]
zeta(1-42) = -1520097643918070802691/75852    [2, 2; 3, 2; 7, 2; 43, 1]
zeta(1-44) = 2530297234481911294093/2760    [2, 3; 3, 1; 5, 1; 23, 1]
zeta(1-46) = -25932657025822267968607/564    [2, 2; 3, 1; 47, 1]
zeta(1-48) = 5609403368997817686249127547/2227680    [2, 5; 3, 2; 5, 1; 7, 1; 13, 1; 17, 1]
zeta(1-50) = -19802288209643185928499101/132    [2, 2; 3, 1; 11, 1]
zeta(1-52) = 61628132164268458257532691681/6360    [2, 3; 3, 1; 5, 1; 53, 1]
zeta(1-54) = -29149963634884862421418123812691/43092    [2, 2; 3, 4; 7, 1; 19, 1]
zeta(1-56) = 354198989901889536240773677094747/6960    [2, 4; 3, 1; 5, 1; 29, 1]
zeta(1-58) = -2913228046513104891794716413587449/708    [2, 2; 3, 1; 59, 1]
zeta(1-60) = 1215233140483755572040304994079820246041491/3407203800    [2, 3; 3, 2; 5, 2; 7, 1; 11, 1; 13, 1; 31, 1; 61, 1]
zeta(1-62) = -396793078518930920708162576045270521/12    [2, 2; 3, 1]
zeta(1-64) = 106783830147866529886385444979142647942017/32640    [2, 7; 3, 1; 5, 1; 17, 1]
zeta(1-66) = -133872729284212332186510857141084758385627191/388332    [2, 2; 3, 2; 7, 1; 23, 1; 67, 1]
zeta(1-68) = 4633713579924631067171126424027918014373353/120    [2, 3; 3, 1; 5, 1]
zeta(1-70) = -43010895638096200108659330496510205957469661721/9372    [2, 2; 3, 1; 11, 1; 71, 1]
zeta(1-72) = 5827954961669944110438277244641067365282488301844260429/10087262640    [2, 4; 3, 3; 5, 1; 7, 1; 13, 1; 19, 1; 37, 1; 73, 1]
zeta(1-74) = -923038305114085622008920911661422572613197507651/12    [2, 2; 3, 1]
zeta(1-76) = 1297636253996598563562484002136063152861329885729779/120    [2, 3; 3, 1; 5, 1]
zeta(1-78) = -31911258890415448330398387349964774884015336567107729499/19908    [2, 2; 3, 2; 7, 1; 79, 1]
zeta(1-80) = 4603784299479457646935574969019046849794257872751288919656867/18400800    [2, 5; 3, 1; 5, 2; 11, 1; 17, 1; 41, 1]
zeta(1-82) = -40902784126466971629833036824055363419700878721225693045893/996    [2, 2; 3, 1; 83, 1]
zeta(1-84) = 2024576195935290360231131160111731009989917391198090877281083932477/285962040    [2, 3; 3, 2; 5, 1; 7, 2; 13, 1; 29, 1; 43, 1]
zeta(1-86) = -15365456265527410548229019707587476657623969457055556552604581/12    [2, 2; 3, 1]
zeta(1-88) = 119220589879456137090501038547210167576886388688366240390629080961277/491280    [2, 4; 3, 1; 5, 1; 23, 1; 89, 1]
zeta(1-90) = -235811455804216559976824670249843016755050989933929423246309043145584507/4898124    [2, 2; 3, 3; 7, 1; 11, 1; 19, 1; 31, 1]
zeta(1-92) = 56329823835110327303888166458198989115623542770410223609709405514345489/5640    [2, 3; 3, 1; 5, 1; 47, 1]
zeta(1-94) = -25974761842122222757602163391770238382095923727716949392259895857120201/12    [2, 2; 3, 1]
zeta(1-96) = 211600449597266513097597728109824233673043954389060234150638733420050668349987259/432169920    [2, 6; 3, 2; 5, 1; 7, 1; 13, 1; 17, 1; 97, 1]
zeta(1-98) = -1385882870875622359674512602987828685864126443438867092021917576530468307311/12    [2, 2; 3, 1]
zeta(1-100) = 94598037819122125295227433069493721872702841533066936133385696204311395415197247711/3333000    [2, 3; 3, 1; 5, 3; 11, 1; 101, 1]
zeta(1-102) = -188471730050641592837824751889190692675989246891336320628176617710991854755098715223/25956    [2, 2; 3, 2; 7, 1; 103, 1]
zeta(1-104) = 24579510104910000868238719445859559590091508159867133717469497704834582181965363171081/12720    [2, 4; 3, 1; 5, 1; 53, 1]
zeta(1-106) = -686300059860705932229279625501762776777949030954371510168505969401544903271437780124017/1284    [2, 2; 3, 1; 107, 1]
zeta(1-108) = 3469342247847828789552088659323852541399766785760491146870005891371501266319724897592306597338057/22592704680    [2, 3; 3, 4; 5, 1; 7, 1; 13, 1; 19, 1; 37, 1; 109, 1]
zeta(1-110) = -1529198588096948578449626849344869500105750482682461581336718774151959521253917155995586043503/33396    [2, 2; 3, 1; 11, 2; 23, 1]
zeta(1-112) = 378697086022157101907513887812166002063307357027501413778826918240138108073553645052397314793228587/26740320    [2, 5; 3, 1; 5, 1; 17, 1; 29, 1; 113, 1]
zeta(1-114) = -1144096437861534912279513741402789025037955614688991124252953163943873972854452297416009927292771/252    [2, 2; 3, 2; 7, 1]
zeta(1-116) = 10674272985235964721121153725304876443758763036701029111913932611069274397399033388668558606750163871/7080    [2, 3; 3, 1; 5, 1; 59, 1]
zeta(1-118) = -6219713897791747653134697484501440791264514594588122106797617638583296356708584099819860616178255861/12    [2, 2; 3, 1]
zeta(1-120) = 51507486535079109061843996857849983274095170353262675213092869167199297474922985358811329367077682677803282070131/279390711600    [2, 4; 3, 2; 5, 2; 7, 1; 11, 1; 13, 1; 31, 1; 41, 1; 61, 1]
zeta(1-122) = -813666657037091506762830122557225531782340824771477701152611668740175134657384120148083830788492425714171/12    [2, 2; 3, 1]
zeta(1-124) = 3092799204330552540347577519598143374857381613332172155469468152559954624336643368181675600331241054486922871/120    [2, 3; 3, 1; 5, 1]
zeta(1-126) = -5556330281949274850616324408918951380525567307126747246796782304333594286400508981287241419934529638692081513802696639/549092628    [2, 2; 3, 3; 7, 2; 19, 1; 43, 1; 127, 1]
zeta(1-128) = 267754707742548082886954405585282394779291459592551740629978686063357792734863530145362663093519862048495908453718017/65280    [2, 8; 3, 1; 5, 1; 17, 1]
zeta(1-130) = -29664848848248167933004608034947637466270938617918899365903584931208440344669293516848837102982982811374380540654806431/17292    [2, 2; 3, 1; 11, 1; 131, 1]
zeta(1-132) = 37359267804272125291729135138506539829387097988225227493951795269331824614064078528422399345623971517646073249757760937540621/50483160    [2, 3; 3, 2; 5, 1; 7, 1; 13, 1; 23, 1; 67, 1]
zeta(1-134) = -3949107042846533218412473690281776345541112322286099827043560520009966650622246876537124125242573646994995442378350510301/12    [2, 2; 3, 1]
zeta(1-136) = 4958248608433376772428681062374481979372741905738084456893482759542967190742836046268131497401044102217148099163597931590391161/32880    [2, 4; 3, 1; 5, 1; 137, 1]
zeta(1-138) = -117168110825690475480167464509744045254307760637577499298354386654803413111284619279288407638840250338943888622865528477112621223323/1646316    [2, 2; 3, 2; 7, 1; 47, 1; 139, 1]
zeta(1-140) = 469927283776556971990099935550269143840076782418732997329638155023214971853374013813408514017896391657740209689521592056267813800278007/13589400    [2, 3; 3, 1; 5, 2; 11, 1; 29, 1; 71, 1]
zeta(1-142) = -207490891280120979800987048485256538588791789070290741918237732357852761430727367698168537876221806622668781613442289529691174438721/12    [2, 2; 3, 1]
zeta(1-144) = 3050244698373607565035155836901726357405007104256566761884191852434851033744761276392695669329626855965183503295793517411526056244431024612640493/342966929760    [2, 5; 3, 3; 5, 1; 7, 1; 13, 1; 17, 1; 19, 1; 37, 1; 73, 1]
zeta(1-146) = -56446164743563217418165935834354301728295145326144399369504351781298496749089373765148082309889112853290960869608260588863524269643696231/12    [2, 2; 3, 1]
zeta(1-148) = 45722625557135648104474624192220707827234671679656794616661639889647510031855363061751932259631384756036394180198275183619944603914285348603977/17880    [2, 3; 3, 1; 5, 1; 149, 1]
zeta(1-150) = -18534623175566509657731377032472250599289349017011831994091992293015172620062892230401223790787531852335007756551508148307720408964064556169119162651/12975732    [2, 2; 3, 2; 7, 1; 11, 1; 31, 1; 151, 1]
zeta(1-152) = 196685165323953079058204888867962219254604712183628050093079322483284722701498530760876507358554217905913440769416700502780259255706888753357673979/240    [2, 4; 3, 1; 5, 1]
zeta(1-154) = -133243099766727546117244081017911486506827774707280119921984110256504952435154075434398507198995165042148777769467619682034936678296122203868187120573/276    [2, 2; 3, 1; 23, 1]
zeta(1-156) = 81718086083262628510756459753673452313595710396116467582152090596092548699138346942995509488284650803976836337164670494733866559829768848363506624334818961419869/279956050920    [2, 3; 3, 2; 5, 1; 7, 1; 13, 2; 53, 1; 79, 1; 157, 1]
zeta(1-158) = -2173071859508268481926368145646878419462201547772526128487343484370989217688082936698808454055367256832003303598349665568111043145853126268995984475417961/12    [2, 2; 3, 1]
zeta(1-160) = 4240860794203310376065563492361156949989398087086373214710625778458441940477839981850928830420029285687066701804645453159767402961229305942765784122421197736180867/36801600    [2, 6; 3, 1; 5, 2; 11, 1; 17, 1; 41, 1]
zeta(1-162) = -1584451495144416428390934243279426140836596476080786316960222380784239380974799880364363647978168634590418215854419793716549388865905348534375629928732008786233507729/21071988    [2, 2; 3, 5; 7, 1; 19, 1; 163, 1]
zeta(1-164) = 500928405101054055257853160651040166775739781052405977271545667900740120690648794907412838744900995483735934702287910367925490117768899039660780818226374033078050563/9960    [2, 3; 3, 1; 5, 1; 83, 1]
zeta(1-166) = -69084734570733264116037292908345129295243642874159138537025167606060262465688228490400069309749327627653569983268242429865472900053832321064021543671736971949588142427/2004    [2, 2; 3, 1; 167, 1]
zeta(1-168) = 13844828515176396081238346585063517228531109156984345249260453934317772754836791258987516540324983611569758649525983347408589045734176589270143058509026392246407576578281097477/571924080    [2, 4; 3, 2; 5, 1; 7, 2; 13, 1; 29, 1; 43, 1]
zeta(1-170) = -2298049501489853298999726814570143935075415733541040320178117596557023283819846097266919665133560594971003886703743258587669782087383469091564926469349401857856264235716401/132    [2, 2; 3, 1; 11, 1]
zeta(1-172) = 266132609565891359236911161464926665418791779210056319343145538341053205401510023832124789828681434924955545833526088472748860651630930161756964362167852548549062311756691616511/20760    [2, 3; 3, 1; 5, 1; 173, 1]
zeta(1-174) = -143660743264208373513274468732783355082607390282157290070626920140600269079916940373489469630821796809738860195004943376200250063891699292523323221920607159995968451491258598176839/14868    [2, 2; 3, 2; 7, 1; 59, 1]
zeta(1-176) = 124486173680609609785965578410256757474578252225144940759721701396964367689874059777948739246049449860378177088224031460932116208362699671826981890874056119786864556246405461461603534909/16703520    [2, 5; 3, 1; 5, 1; 17, 1; 23, 1; 89, 1]
zeta(1-178) = -12632042883347654944117807316924718907581128850706373879685884287852020524813435342243305288970372833072115893416690187560191218299044218120629931987112731396954697411876171151081540469/2148    [2, 2; 3, 1; 179, 1]
zeta(1-180) = 6173136454016248924640522272263470960199559328290655337530202055853397791747341312347030141906500993752700612233695954532816018207721731818225290076670213481102834647254685911917265818955932383093313/1300628499370200    [2, 3; 3, 3; 5, 2; 7, 1; 11, 1; 13, 1; 19, 1; 31, 1; 37, 1; 61, 1; 181, 1]
zeta(1-182) = -47002959113727390561948400006908014816785364129982442765513000204642325933951599018823250664134491441093922676468739125102516360145271297708170655236608084482984753252154179757464908252821/12    [2, 2; 3, 1]
zeta(1-184) = 37274840587958964353530192928171009410061013292639363435455028229812236187718000464609959970629550418897494991698335274760044349161564739527851963937258965076622548936071553196370959837957054089/11280    [2, 4; 3, 1; 5, 1; 47, 1]
zeta(1-186) = -718020841885063485504503297477947909083760255435978650643440983890310071798144761129444381883462308079830684266472134306454412497343254960348624297682499301275711015247738093235231204952712928951/252    [2, 2; 3, 2; 7, 1]
zeta(1-188) = 301239952140931038155518869583008453896017524100371873434606851696000026824423846584547054514149597907779111184134664052629899608929721660879068949677829447214288778551927380331041352784640838049383/120    [2, 3; 3, 1; 5, 1]
zeta(1-190) = -56963745710992208380335637328387234505135131438302696675254121987199892363279048512983463868604039481118941966554759701816023190597168353486766082377517931444615047157445055506251621319157374417199784141/25212    [2, 2; 3, 1; 11, 1; 191, 1]
zeta(1-192) = 346465752997582699690191405750952366871923192340955593486485715370392154894102000406980162521728492501917598012711402163530166516991115122131398542029056286959857727373568402417020319761912636411646719477318166587/166817589120    [2, 7; 3, 2; 5, 1; 7, 1; 13, 1; 17, 1; 97, 1; 193, 1]
zeta(1-194) = -23393678609912710957048093680086185230817746693789570486938007756801705301272955637764945979191874408873564472487875262438095401668424494065073287349640098298662995920944706022417797935271814085956797257951/12    [2, 2; 3, 1]
zeta(1-196) = 1280676226744105993317410340814157420472511309251263169501849777694241319188599560826216848052624002900323179366548276214943154305773990812218035973576149318606462627537698397102156555450354243743194387437525955737/685560    [2, 3; 3, 1; 5, 1; 29, 1; 197, 1]
zeta(1-198) = -8047992260122545906218234637320960474594956945485413493585440355338290577234499460843844151150315089992748841196595969684216893313623896643984917893004822552000271471295881271939699963042627828287117858429912192655120203/4404849876    [2, 2; 3, 3; 7, 1; 19, 1; 23, 1; 67, 1; 199, 1]
zeta(1-200) = 498384049428333414764928632140399662108495887457206674968055822617263669621523687568865802302210999132601412697613279391058654527145340515840099290478026350382802884371712359337984274122861159800280019110197888555893671151/273306000    [2, 4; 3, 1; 5, 3; 11, 1; 41, 1; 101, 1]
(09:17) gp > (09:17) gp > \l
   log = 0 (off)