(11:47) gp > (11:47) gp > \p180
   realprecision = 183 significant digits (180 digits displayed)
(11:47) gp > (11:47) gp > \rread1
? L=[8,12,13,17,21,24,28,29,33,37,40,41,44];for(i=1,13,k=zetakinit(x^2-L[i]);print("k=zetakinit(x^2-",L[i],")");for(j=12,16,a=round(zetak(k,1-2*j)*32!)/32!;print("z(1-",2*j,")=",a,"  ",factor(denominator(a)))))
k=zetakinit(x^2-8)
z(1-24)=109511675519893842297200129361077/5040  [2, 4; 3, 2; 5, 1; 7, 1]
z(1-26)=3854553830778219905574569395190491/12  [2, 2; 3, 1]
z(1-28)=22620741302181663024236570255435200710817/3480  [2, 3; 3, 1; 5, 1; 29, 1]
z(1-30)=487857934646005911764739665381199198181718311/2772  [2, 2; 3, 2; 7, 1; 11, 1]
z(1-32)=102010928071772976385504537152795193127593261481587/16320  [2, 6; 3, 1; 5, 1; 17, 1]
k=zetakinit(x^2-12)
z(1-24)=9784043347352101537435984662493577693/32760  [2, 3; 3, 2; 5, 1; 7, 1; 13, 1]
z(1-26)=59603426243912408678663547473670548011/6  [2, 1; 3, 1]
z(1-28)=787021254910761302606269484108127241457524021/1740  [2, 2; 3, 1; 5, 1; 29, 1]
z(1-30)=1183905977142282240924625045967870444850942156438481/42966  [2, 1; 3, 2; 7, 1; 11, 1; 31, 1]
z(1-32)=17967653479516058193170206595247961216400601193448372071/8160  [2, 5; 3, 1; 5, 1; 17, 1]
k=zetakinit(x^2-13)
z(1-24)=64184156678679131455067913889018026839/32760  [2, 3; 3, 2; 5, 1; 7, 1; 13, 1]
z(1-26)=458886127252695004415215453937104183681/6  [2, 1; 3, 1]
z(1-28)=7111224376757111074805747134193347871898539743/1740  [2, 2; 3, 1; 5, 1; 29, 1]
z(1-30)=163208472336761293665410529395434958347731151528481623/558558  [2, 1; 3, 2; 7, 1; 11, 1; 13, 1; 31, 1]
z(1-32)=223613340952997516543979434097249313411112078292443739253/8160  [2, 5; 3, 1; 5, 1; 17, 1]
k=zetakinit(x^2-17)
z(1-24)=298351132018971004567540400687875435236427/278460  [2, 2; 3, 2; 5, 1; 7, 1; 13, 1; 17, 1]
z(1-26)=214568990123121934081140751114385756495221/3  Mat([3, 1])
z(1-28)=5686139876816447516702858747211275127486402350227/870  [2, 1; 3, 1; 5, 1; 29, 1]
z(1-30)=17166574403140221832916979783252769628368689264870342751/21483  [3, 2; 7, 1; 11, 1; 31, 1]
z(1-32)=522869296910136361444008056083241178880315792311858750499297/4080  [2, 4; 3, 1; 5, 1; 17, 1]
k=zetakinit(x^2-21)
z(1-24)=2516995799150646956921735521465227682859207/16380  [2, 2; 3, 2; 5, 1; 7, 1; 13, 1]
z(1-26)=46958202553101671949745551053973392661384001/3  Mat([3, 1])
z(1-28)=1898903097880229637752971691810662177381309130557999/870  [2, 1; 3, 1; 5, 1; 29, 1]
z(1-30)=8748017705410806049483908729513978270817352992906979405971/21483  [3, 2; 7, 1; 11, 1; 31, 1]
z(1-32)=406593003450625001304111375054300637821213252779485306067512069/4080  [2, 4; 3, 1; 5, 1; 17, 1]
k=zetakinit(x^2-24)
z(1-24)=5527184623827320720804884942579502766150331/1560  [2, 3; 3, 1; 5, 1; 13, 1]
z(1-26)=942789767203372848785249600906315045590165291/2  Mat([2, 1])
z(1-28)=49795498846995002717120976487518848181828208151855349/580  [2, 2; 5, 1; 29, 1]
z(1-30)=42803845767925533625901559679513737511976953587525759879143/2046  [2, 1; 3, 1; 11, 1; 31, 1]
z(1-32)=18189257533562225887976804252771500706059403491007010114263580199/2720  [2, 5; 5, 1; 17, 1]
k=zetakinit(x^2-28)
z(1-24)=1086207585206051133826593793036434968608347383/8190  [2, 1; 3, 2; 5, 1; 7, 1; 13, 1]
z(1-26)=72052533297687250070851590149268259458553914182/3  Mat([3, 1])
z(1-28)=2589930235278901379476484409573188441973232999360487851/435  [3, 1; 5, 1; 29, 1]
z(1-30)=42423098338052835761554482182300426383623392308824498015155882/21483  [3, 2; 7, 1; 11, 1; 31, 1]
z(1-32)=1752669821286918828603663357134083205160911340722781263609653854301/2040  [2, 3; 3, 1; 5, 1; 17, 1]
k=zetakinit(x^2-29)
z(1-24)=1101208363970191358787380920063859644073436829/3640  [2, 3; 5, 1; 7, 1; 13, 1]
z(1-26)=117537686023780342476773135374150296667814279041/2  Mat([2, 1])
z(1-28)=9064124893476564976878775908967259889632319629943934559/580  [2, 2; 5, 1; 29, 1]
z(1-30)=2413104879248463465849126200146051798954986110646114972249747/434  [2, 1; 7, 1; 31, 1]
z(1-32)=7058262269962997044431002162780496658702197178741230844188729661429/2720  [2, 5; 5, 1; 17, 1]
k=zetakinit(x^2-33)
z(1-24)=34410061486343846835304341132900205543844899231/5460  [2, 2; 3, 1; 5, 1; 7, 1; 13, 1]
z(1-26)=1585271581234277858085177035004723218759816049061  matrix(0,2,j,k,0)
z(1-28)=5458663149172524227621559855410344257948095544186286203/10  [2, 1; 5, 1]
z(1-30)=1800861987827503536068944731868661152166622715228596656141065031/7161  [3, 1; 7, 1; 11, 1; 31, 1]
z(1-32)=206690239576900618793811606277709087256072191888957128715911192664317/1360  [2, 4; 5, 1; 17, 1]
k=zetakinit(x^2-37)
z(1-24)=433911874930178370627361990523141469876914594077/4680  [2, 3; 3, 2; 5, 1; 13, 1]
z(1-26)=175911166485334350140633936023221162252822595543205/6  [2, 1; 3, 1]
z(1-28)=22082569468039048855099345948162953549100473737499786154883/1740  [2, 2; 3, 1; 5, 1; 29, 1]
z(1-30)=45115240238382314357179807313418320850080812921254585950553043865/6138  [2, 1; 3, 2; 11, 1; 31, 1]
z(1-32)=45565529434948529023674033156713910264466057785696102264822266218754033/8160  [2, 5; 3, 1; 5, 1; 17, 1]
k=zetakinit(x^2-40)
z(1-24)=18974436285039855244365922390662114802894020172307/32760  [2, 3; 3, 2; 5, 1; 7, 1; 13, 1]
z(1-26)=1284337697708472979372679882122257485773034425490317/6  [2, 1; 3, 1]
z(1-28)=188430828053950266672225355211898845875545322299932105450539/1740  [2, 2; 3, 1; 5, 1; 29, 1]
z(1-30)=3149489747561981724204704081586571990837347499024599495197940316807/42966  [2, 1; 3, 2; 7, 1; 11, 1; 31, 1]
z(1-32)=531094543673857504216340861327958747347181609388965009640737833983210249/8160  [2, 5; 3, 1; 5, 1; 17, 1]
k=zetakinit(x^2-41)
z(1-24)=4237305315191737531693797080486099851545364991834/4095  [3, 2; 5, 1; 7, 1; 13, 1]
z(1-26)=1205335113210720999099053080674507703268775833425444/3  Mat([3, 1])
z(1-28)=3203319572341859771873441135349548114989623635687280592504/15  [3, 1; 5, 1]
z(1-30)=3262603011651575071608873923836328530577245128911004709237729463764/21483  [3, 2; 7, 1; 11, 1; 31, 1]
z(1-32)=72252622819452126528953616703345956974563213860732415492125070382882909/510  [2, 1; 3, 1; 5, 1; 17, 1]
k=zetakinit(x^2-44)
z(1-24)=178195602951418769387248613782238554963197881783123/32760  [2, 3; 3, 2; 5, 1; 7, 1; 13, 1]
z(1-26)=14594616971473493215520156507649856776365301930628237/6  [2, 1; 3, 1]
z(1-28)=2590900879751548185461971322384417102931821687710198139310571/1740  [2, 2; 3, 1; 5, 1; 29, 1]
z(1-30)=52399170394895627715682952998769642135319661333469727999989000524807/42966  [2, 1; 3, 2; 7, 1; 11, 1; 31, 1]
z(1-32)=10691568483016382137593722574105500990769954492520571787854701471842530761/8160  [2, 5; 3, 1; 5, 1; 17, 1]
? 
(12:09) gp > (12:09) gp > \rread1
? L=[8,12,13,17,21,24,28,29,33,37,40,41,44];for(i=1,13,k=zetakinit(x^2-L[i]);print("k=zetakinit(x^2-",L[i],")");for(j=16,18,a=round(zetak(k,1-2*j)*32!)/32!;print("z(1-",2*j,")=",a,"  ",factor(denominator(a)))))
k=zetakinit(x^2-8)
z(1-32)=102010928071772976385504537152795193127593261481587/16320  [2, 6; 3, 1; 5, 1; 17, 1]
z(1-34)=3434757869192636734100930146655497570361814688585871/12  [2, 2; 3, 1]
z(1-36)=625666657487685236486584126530978138626472600098248697402520902893093761166070768723027027/37590119561956218595316858880000000  [2, 31; 3, 14; 5, 7; 7, 3; 11, 2; 13, 2; 17, 1; 19, 1; 23, 1; 29, 1; 31, 1]
k=zetakinit(x^2-12)
z(1-32)=17967653479516058193170206595247961216400601193448372071/8160  [2, 5; 3, 1; 5, 1; 17, 1]
z(1-34)=1361204292314783105732805341719017219109085563241077649231/6  [2, 1; 3, 1]
z(1-36)=433918576297976571807102372136101517844735658778230624909440370290566325107175471113313196972973/14618379829649640564845445120000000  [2, 30; 3, 12; 5, 7; 7, 4; 11, 2; 13, 2; 17, 1; 19, 1; 23, 1; 29, 1; 31, 1]
k=zetakinit(x^2-13)
z(1-32)=223613340952997516543979434097249313411112078292443739253/8160  [2, 5; 3, 1; 5, 1; 17, 1]
z(1-34)=19881716170300177604943960879958666096944395349276789711341/6  [2, 1; 3, 1]
z(1-36)=19126586997609540316815082181043789504569826077370246639855055755895429375562996140653929555027027/37590119561956218595316858880000000  [2, 31; 3, 14; 5, 7; 7, 3; 11, 2; 13, 2; 17, 1; 19, 1; 23, 1; 29, 1; 31, 1]
k=zetakinit(x^2-17)
z(1-32)=522869296910136361444008056083241178880315792311858750499297/4080  [2, 4; 3, 1; 5, 1; 17, 1]
z(1-34)=79498775217502075049340852422591674555579426424731546331341361/3  Mat([3, 1])
z(1-36)=107704612085438846347884912655506082321454596953782307449239161236430848473981510223046248752211027027/15478284525511384127483412480000000  [2, 31; 3, 14; 5, 7; 7, 4; 11, 2; 13, 2; 19, 1; 23, 1; 29, 1; 31, 1]
k=zetakinit(x^2-21)
z(1-32)=406593003450625001304111375054300637821213252779485306067512069/4080  [2, 4; 3, 1; 5, 1; 17, 1]
z(1-34)=94333933790513857496373692004699532219053678069457887430121091821/3  Mat([3, 1])
z(1-36)=255028152101695839651110522028512462776124799875496598264435373369933451016811185354417631967568979027027/20240833610284117705170616320000000  [2, 31; 3, 14; 5, 7; 7, 4; 11, 2; 13, 1; 17, 1; 19, 1; 23, 1; 29, 1; 31, 1]
k=zetakinit(x^2-24)
z(1-32)=18189257533562225887976804252771500706059403491007010114263580199/2720  [2, 5; 5, 1; 17, 1]
z(1-34)=5511970821772721584086223746242599677014403850712665374289138080591/2  Mat([2, 1])
z(1-36)=63254924791960824682227063287124953021796146774276894074522446526180600888312289880170009955923125331027027/43855139488948921694536335360000000  [2, 30; 3, 13; 5, 7; 7, 4; 11, 2; 13, 2; 17, 1; 19, 1; 23, 1; 29, 1; 31, 1]
k=zetakinit(x^2-28)
z(1-32)=1752669821286918828603663357134083205160911340722781263609653854301/2040  [2, 3; 3, 1; 5, 1; 17, 1]
z(1-34)=1445824639345407102078655514302126651407845294397400121460513555550942/3  Mat([3, 1])
z(1-36)=11291890004514633144709886294658851664217000134762957210967500877788175193173167389321391332354203837523027027/32891354616711691270902251520000000  [2, 28; 3, 14; 5, 7; 7, 4; 11, 2; 13, 2; 17, 1; 19, 1; 23, 1; 29, 1; 31, 1]
k=zetakinit(x^2-29)
z(1-32)=7058262269962997044431002162780496658702197178741230844188729661429/2720  [2, 5; 5, 1; 17, 1]
z(1-34)=3122937136716884564413847046368240042882993613722423698681579915266541/2  Mat([2, 1])
z(1-36)=44851544065823183408503901044454637146624057481567433263063549919920911820172720044633670934413798284204972973/37590119561956218595316858880000000  [2, 31; 3, 14; 5, 7; 7, 3; 11, 2; 13, 2; 17, 1; 19, 1; 23, 1; 29, 1; 31, 1]
k=zetakinit(x^2-33)
z(1-32)=206690239576900618793811606277709087256072191888957128715911192664317/1360  [2, 4; 5, 1; 17, 1]
z(1-34)=118417885747975332507614037219192571018901177632722691326682556680538481  matrix(0,2,j,k,0)
z(1-36)=18232958128859558110496836530968864978289169318681687569421369706537523391693241149/155610  [2, 1; 3, 2; 5, 1; 7, 1; 13, 1; 19, 1]
k=zetakinit(x^2-37)
z(1-32)=45565529434948529023674033156713910264466057785696102264822266218754033/8160  [2, 5; 3, 1; 5, 1; 17, 1]
z(1-34)=32817789385672302405698899493694670283958202718161570082249370089698415905/6  [2, 1; 3, 1]
z(1-36)=99456967360091327771047406794082635181395673279752875735537787665096934366315374312726481208133014567248979027027/14618379829649640564845445120000000  [2, 30; 3, 12; 5, 7; 7, 4; 11, 2; 13, 2; 17, 1; 19, 1; 23, 1; 29, 1; 31, 1]
k=zetakinit(x^2-40)
z(1-32)=531094543673857504216340861327958747347181609388965009640737833983210249/8160  [2, 5; 3, 1; 5, 1; 17, 1]
z(1-34)=447055329671540958752211046354104758009806750016023773935137726413340895657/6  [2, 1; 3, 1]
z(1-36)=4750342846471076082395132307567437687101504485210419439755416786573288901596583985212442743051265447501241260972973/43855139488948921694536335360000000  [2, 30; 3, 13; 5, 7; 7, 4; 11, 2; 13, 2; 17, 1; 19, 1; 23, 1; 29, 1; 31, 1]
k=zetakinit(x^2-41)
z(1-32)=72252622819452126528953616703345956974563213860732415492125070382882909/510  [2, 1; 3, 1; 5, 1; 17, 1]
z(1-34)=511188142951485403129238972414935140271972584689043096443896209790071318404/3  Mat([3, 1])
z(1-36)=5267809662720256640732157767670018492513966607151456968946204516539739646887232877196238657181860598511311788972973/20240833610284117705170616320000000  [2, 31; 3, 14; 5, 7; 7, 4; 11, 2; 13, 1; 17, 1; 19, 1; 23, 1; 29, 1; 31, 1]
k=zetakinit(x^2-44)
z(1-32)=10691568483016382137593722574105500990769954492520571787854701471842530761/8160  [2, 5; 3, 1; 5, 1; 17, 1]
z(1-34)=10889707874192178568357333572044524510856826605968841320249856684620427584937/6  [2, 1; 3, 1]
z(1-36)=84007203652468403269975073950974070788522629787185203851241264264205519049630606300626674838011615122257039072172973/26313083693369353016721801216000000  [2, 30; 3, 14; 5, 6; 7, 4; 11, 2; 13, 2; 17, 1; 19, 1; 23, 1; 29, 1; 31, 1]
? 
(12:46) gp > (12:46) gp > \l
   log = 0 (off)