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Canonical coordinates (mirror maps) of hypergeometric Calabi–Yau families

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Numbers
$A$
$z$
normalization 
$Q_A(z)$ or $q_A(z)$
2.2.2.2
1
unit:
1.607545704384156318650530093776391996150879157716323862361040340985864091887809095275040153408104995 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$.
2.2.2.2
1
integral:
0.006279475407750610619728633178814031234964371709829390087347813831976031608936754278418125599250410139 + i * [0, 0]
2.2.2.2
1/2
unit:
0.5814620307094641230365136907866994079071783003719593020385680683269605314398451758087777209736060177 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=3$ and the unit eigenvalue at $p=5$.
2.2.2.2
1/2
integral:
0.002271336057458844230611381604635544562137415235827966023588156516902189575936895218003037972553148507 + i * [0, 0]
2.2.2.2
-1
unit:
-0.8210518038695846366355611646894515331156284676114402488508608724153387995782757340030412563052230355 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=3$ and the unit eigenvalue at $p=5$.
2.2.2.2
-1
integral:
-0.003207233608865564986857660799568170051232923701607188472073675282872417185852639585949379907442277482 + i * [0, 0]
2.2.2.2
2
unit:
2.610309621725711273748213291649061955193512854905301163912466657222763770971997913458687879298823726 + i * 2.197589069970661188925386453424551694054933355093077114713371268311227537709026137909871692010859550
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=3$ and the unit eigenvalue at $p=5$.
2.2.2.2
2
integral:
0.01019652195986605966307895817050414826247465958947383267153307287977642098035936684944799952851103018 + i * 0.008584332304572895269239790833689655054902083418332332479349106516840732569175883351210436296917420115
2.2.3
1
unit:
1.602391567868480888920922584700803062714960586293762483277273740756362256421759253654838937251276942 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$.
2.2.3
1
integral:
0.003709239740436298353983617094214821904432779134939265007586281807306394112087405679756571614007585515 + i * [0, 0]
2.2.3
1/2
unit:
0.5813313504259733189586692651742407398919910173879826823435319010282355710935193332500421823021218399 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=5$ and the unit eigenvalue at $p=5$.
2.2.3
1/2
integral:
0.001345674422282345645737660336051483194194423651361071023943360882009804562716479938078801347921578333 + i * [0, 0]
2.2.3
-1
unit:
-0.8207933151249359376384550820932414010331656359015027353762830647981080792167526727719933439830168787 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=5$ and the unit eigenvalue at $p=5$.
2.2.3
-1
integral:
-0.001899984525752166522311238615956577317206401934957182257815470057403027961149890446231466074034761293 + i * [0, 0]
2.2.3
2
unit:
2.635744767864621951269598806046505153095134799487591996779903959522712815632451973981593976071810587 + i * 2.195140332204298357672194961823748636143740250053817225105038749486844402086865925121641996253137758
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=5$ and the unit eigenvalue at $p=7$.
2.2.3
2
integral:
0.006101261036723661924235182421403947113646145369184240733286814721117390776926972161994430500166228212 + i * 0.005081343361584023976093043893110529250332732060309762095150552660849176856682560011855652769104485551
2.2.4
1
unit:
1.595622865254846328739058046740183249765107210616155896822307538938705616712917940100233407502505761 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$.
2.2.4
1
integral:
0.001558225454350435867909236373769710204848737510367339742990534705994829703821208925879134187014165782 + i * [0, 0]
2.2.4
1/2
unit:
0.5811566437931660496435746991166754108530305584803244959599191217129569118901403208973132355636003464 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=3$ and the unit eigenvalue at $p=3$.
2.2.4
1/2
integral:
0.0005675357849542637203550534171061283309111626547659418905858585172978094842677151571262824566050784633 + i * [0, 0]
2.2.4
-1
unit:
-0.8204461223040783470737480087409600502981668563255812937102873585086228915163969301477712635357086421 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=3$ and the unit eigenvalue at $p=3$.
2.2.4
-1
integral:
-0.0008012169163125765108142070397860937991193035706304504821389524985435770424964813770974328745465904708 + i * [0, 0]
2.2.4
2
unit:
2.670138077009049675753927157961349516384206437423518935050223343858685237439556008118019611651635938 + i * 2.191053472053850881336994368809542632596113574236288840009568953171683477813335040749463027754966210
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=3$ and the unit eigenvalue at $p=3$.
2.2.4
2
integral:
0.002607556715829150073978444490196630387093951599046405210009983734236997302187066414177753527003550720 + i * 0.002139700656302588751305658563290568977144642162340125820321844680831722146302085000731897488041959190
2.2.6
1
unit:
1.585539481786017732516715125713980676050289958552117822928268426718301697460075611418240741305827394 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$.
2.2.6
1
integral:
0.0002293893926195048802830895725859347042896831537257114905856869830321617039149414947075001072491069725 + i * [0, 0]
2.2.6
1/2
unit:
0.5808907340233043313407898959756253086639750960654079012472415366959421981286072004006725556099939719 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=5$ and the unit eigenvalue at $p=5$.
2.2.6
1/2
integral:
0.00008404090480661231645555409374647356896180195255575924497211249084142682264592118061352322853153847973 + i * [0, 0]
2.2.6
-1
unit:
-0.8199156472451549294280416719403441075384710176364660523799492174187322203257929959798520933229579673 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=5$ and the unit eigenvalue at $p=5$.
2.2.6
-1
integral:
-0.0001186220554463476460399365844821099692619315708386090932262658011311823235425047737239369347978816504 + i * [0, 0]
2.2.6
2
unit:
2.723430428711742961525616836146690010556887150430481263506898613905914164947923822248506199988405345 + i * 2.183292911688597678427576560112728356857721009943638822312859810602159725920962554459729829959721183
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=5$ and the unit eigenvalue at $p=5$.
2.2.6
2
integral:
0.0003940148189687128127207200283777039945828829789395950902064378781692584150676973122466010127298040141 + i * 0.0003158699235660586919021378125163090794064989887071236722096151346357291270140281473466044314177837360
3.3
1
unit:
1.588671007805435910278184340583054981040594839308100211035376937785363404520674905977284938032109095 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$.
3.3
1
integral:
0.002179246924287292057994765899290884747655136953783402209925071245247412077531789994481872342979573518 + i * [0, 0]
3.3
1/2
unit:
0.5801392459848647890702224497073745937177132077082791204116552613157598618696595923682386287825066939 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=5$ and the unit eigenvalue at $p=5$.
3.3
1/2
integral:
0.0007958014348214880508507852533708842163480290915065557207292939112699037885729212515339350189060448476 + i * [0, 0]
3.3
-1
unit:
-0.8225785461863915927652850402422584833828597653957539436361864467216826499572800151390142514720348079 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=5$ and the unit eigenvalue at $p=5$.
3.3
-1
integral:
-0.001128365632628795051804231879619010265271412572559333256016716662169660699529876563976699933432146513 + i * [0, 0]
3.3
2
unit:
2.658923646408950794062295423123746060476697535837289357464712547295876386361907441218660334645173665 + i * 2.156216287806930423378601747520697371683692784280048546736463013058225160777864225369546298916298138
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=5$ and the unit eigenvalue at $p=5$.
3.3
2
integral:
0.003647357539655625231909870264915975391600408142437982657701937650611627416134303760245075904863064013 + i * 0.002957772685606214572535804866283535489278042228093345057251663941094959068282392627393067625399585923
3.4
1
unit:
1.571324608485595283252918012571046604635821080390641012691658771674435046112034957742374900100607868 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$.
3.4
1
integral:
0.0009093313706513861592898831091267630813864705326334728082706358632375202813148350449898002894100739976 + i * [0, 0]
3.4
1/2
unit:
0.5786389432907873688111918958035731174875043459248511536005423241442377644503982858099533373198247138 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=5$ and the unit eigenvalue at $p=5$.
3.4
1/2
integral:
0.0003348604995895760236175879026641048133608242742620666398151286598056931507236101191029822553934170798 + i * [0, 0]
3.4
-1
unit:
-0.8247835482133431894243876032305852628732770095580435185807656819920363373547434207097022873643145487 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=5$ and the unit eigenvalue at $p=5$.
3.4
-1
integral:
-0.0004773052941049439753613354185362183234220353064572011102897949548565025100432542943921888237062005490 + i * [0, 0]
3.4
2
unit:
2.689610554676616962936341531778840330700821587443263048748672255791356614720378389165328316069050354 + i * 2.105723523188559215656499167555439661362414948997266482435268565881573762005937643140562130578795720
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=5$ and the unit eigenvalue at $p=5$.
3.4
2
integral:
0.001556487589511931112810382830890532598785197677918555005062889036916294337222441197433639071799218955 + i * 0.001218590001845231027578992573816805359584730873262306992150039679329614445605287987928566047788654931
3.6
1
unit:
1.546695117944233189633078818752855934848563253750935670598184687616313725747047438610460367771915313 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$.
3.6
1
integral:
0.0001326041767784836410865122444061090479122567947317331679182257105295193523445685389755195788556168821 + i * [0, 0]
3.6
1/2
unit:
0.5765196547991863085932653860286204507861659790098142725933914505976079286438256811414089366541904357 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=5$ and the unit eigenvalue at $p=5$.
3.6
1/2
integral:
0.00004942726807263257103851726560602027184380709696586199182042107772613236699621276415821407207254719099 + i * [0, 0]
3.6
-1
unit:
-0.8278208454958142357623760795531655137240966212202760906169160735066167214435664009826000612858018844 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=5$ and the unit eigenvalue at $p=5$.
3.6
-1
integral:
-0.00007097229470986061692064266800009992401612625353397428760433093908664409477396831284144376382765791190 + i * [0, 0]
3.6
2
unit:
2.735718693413890318927047049404706051640961609351423970979468133883856542915232713192132942574367745 + i * 2.031338453240913590356556677246463934954300066975716681201083990736874329049797426437739836391399559
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=5$ and the unit eigenvalue at $p=5$.
3.6
2
integral:
0.0002345437837289000616364066400381263761694925933943264721347280636045830369440357264396547447337420907 + i * 0.0001741545313135213983501849003126255088266718164416766701989955410439707072230621936246347596357509910
4.4
1
unit:
1.541179995379390799813378589130027915477608312560313357118039040686828137100332296572168874078049984 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$.
4.4
1
integral:
0.0003762646473094215819856881321118232215521504669336702532026462501676826506592608145928146665229614219 + i * [0, 0]
4.4
1/2
unit:
0.5754942694061342454259955193504952391605075960749596550769155367453706129181701997265538579529168506 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=3$ and the unit eigenvalue at $p=3$.
4.4
1/2
integral:
0.0001405015306167319935122059373414295017481707998229881970402625822132252472944751464176156879767863405 + i * [0, 0]
4.4
-1
unit:
-0.8302049004421762411535825903157475296327188188610135406122336063741011150532111561579642062764435616 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=3$ and the unit eigenvalue at $p=3$.
4.4
-1
integral:
-0.0002026867432720156838753863745888055492267379928859896339385335953061770300422878799213779800479598539 + i * [0, 0]
4.4
2
unit:
2.713001145948908932197072426380213476751994991322418985201935253777249680475144008069724736403783591 + i * 1.997887313898205353849099259807647189490266276305028198657518840470150098547479581558910662895502039
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=3$ and the unit eigenvalue at $p=3$.
4.4
2
integral:
0.0006623537953976828447746758853467318058476550271783249475590662240667113477722519550951476407235799782 + i * 0.0004877654574946790414670652489764763646216470401135322750628708106616577389031932572165309235584721776
4.6
1
unit:
1.499428196608766428671256868210411562378115469790192527353924786893447759155106887354632222934052635 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$.
4.6
1
integral:
0.00005423279067595364687034349205043444597721771809136981074052100647039379915925589146971326037811243618 + i * [0, 0]
4.6
1/2
unit:
0.5710966096964102598884388379026302969289187411847617997049908357691802206053070470130896042593634554 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=5$ and the unit eigenvalue at $p=5$.
4.6
1/2
integral:
0.00002065598270024632016378902046812175553128322993289792388979278196503111330314333937402667839479757868 + i * [0, 0]
4.6
-1
unit:
-0.8377930642075599063078302283623838119146095393865489139028349118950067697564980735197693565194491259 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=5$ and the unit eigenvalue at $p=5$.
4.6
-1
integral:
-0.00003030212182463686003717557249574594227121706956693246939752730439435064994779000555265369489726016804 + i * [0, 0]
4.6
2
unit:
2.743591312903407043351837526506289637316457089062388350744310761077937097891047971526412655397387999 + i * 1.844563044265763675708116831358182227407043980018843506063459463664211440740364427471427030322264730
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=5$ and the unit eigenvalue at $p=5$.
4.6
2
integral:
0.00009923290338915679410271403090662216570155009726064772680643485102278418322811950128495416143653747101 + i * 0.00006671596658947351257624843863419351227600708839767229116259619009202153648511156060009501701107728335
6.6
1
unit:
1.435607324172525758436718605333085122201194685854027447276036531108691619474039855214851914721511263 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$.
6.6
1
integral:
0.000007692511810766706095875764131800224634565729412369402902499338408289885649616554436807977080769414777 + i * [0, 0]
6.6
1/2
unit:
0.5635801590541463871188639007947240474924883349625714322951580752140078299806863980884125509409454247 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=5$ and the unit eigenvalue at $p=5$.
6.6
1/2
integral:
0.000003019869679431082749908178480767339932122815580860829434023266435260244287876620360127382067370463739 + i * [0, 0]
6.6
-1
unit:
-0.8519242938870121806864043687972567045816064236410391036672072022571738565654614245871071393637989240 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=5$ and the unit eigenvalue at $p=5$.
6.6
-1
integral:
-0.000004564923556922004569007225055712323734255006985387941013305937083425357170382487914668569633936679763 + i * [0, 0]
6.6
2
unit:
2.740837703998161429716362015782933239729528249559811729406588745700609641244295140290496394506307413 + i * 1.589419837901907647374384422940861460871659573292173084941470719418693890338537392592973299469145935
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=5$ and the unit eigenvalue at $p=5$.
6.6
2
integral:
0.00001468641602365269970484161745425525784320091868977093905074689614251441208657136885015055081075481938 + i * 0.000008516695804944206786771178535134074185912099050991153790195637856967452687427862400296710495269343358
5
1
unit:
1.578218973200672348148153717019159614474405673833114182051817094064360116761208824444309291223489161 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$.
5
1
integral:
0.0005050300714242151514074091894461310766318098156265965382565814701005952373635868238221789731915165316 + i * [0, 0]
5
1/2
unit:
0.5797235865463785672485483907249178980319714351729970978179760617062304897562882200798497292332396619 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=3$ and the unit eigenvalue at $p=3$.
5
1/2
integral:
0.0001855115476948411415195354850319737273702308592553590713017523397459937567220122304255519133546366918 + i * [0, 0]
5
-1
unit:
-0.8224371559978493461955121757709056535389270116770549243410368695882557007309709513389658777950236412 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=3$ and the unit eigenvalue at $p=3$.
5
-1
integral:
-0.0002631798899193117907825638962466898091324566437366575757891317982682418242339107044284690808944075652 + i * [0, 0]
5
2
unit:
2.705528394101289653769872306515797423533089534627491958729821882783828164848870450858922580093091301 + i * 2.142707763474325418245949767019320767617102238527529194760838201396824786770844491619806923509085657
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=3$ and the unit eigenvalue at $p=3$.
5
2
integral:
0.0008657690861124126892063591380850551755305886510807974267935430024908250127516385442748552256297892163 + i * 0.0006856664843117841338387039254461826456374727163288093423234682244469839317666702373183382155229074103
8
1
unit:
1.552151024536763372646706794741037290251849809684623454480325208145249075705607713054696121986535452 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$.
8
1
integral:
0.00002368394507654973407969218131623897232439956374640843894165535290748976250771496144187463565042931292 + i * [0, 0]
8
1/2
unit:
0.5776195917233048288211879067724691551539159714534188755871455113573494887726172444946083515482471295 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=3$ and the unit eigenvalue at $p=3$.
8
1/2
integral:
0.000008813775508473279248370176800117022020781188529257490167040184194295493908273578559793218254825548241 + i * [0, 0]
8
-1
unit:
-0.8252164099613336728124866420943594620244085408267263824488534961035297588650081691703074608186444130 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=3$ and the unit eigenvalue at $p=3$.
8
-1
integral:
-0.00001259180313051351429462412478781676425208142915079843723219075769200942625221264906570903718290167867 + i * [0, 0]
8
2
unit:
2.763759785402847841147819365476030697431124549217893032236216784280411795373818655032411690807443811 + i * 2.067854905673484194299333214068192992912909504783068161581824181109888529113219742181708671262575624
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=3$ and the unit eigenvalue at $p=3$.
8
2
integral:
0.00004217162758488232179485808357965134731187629011868122912958094458435686943624601219226702409068975541 + i * 0.00003155296181752752982024129049786671436939864356663617189913672151351758619862701022616132616062279700
10
1
unit:
1.498823244663539768813823006706324002199181902171462126987437331897247419228556665226697595617222406 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$.
10
1
integral:
0.000001873529055829424711017278758382905002748977377714327658734296664871559274035695831533371994521528008 + i * [0, 0]
10
1/2
unit:
0.5716476350773265289806588450103158677853339156861009141909182855310885661333478904909910132907915442 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=3$ and the unit eigenvalue at $p=3$.
10
1/2
integral:
7.145595438466581612258235562628948347316673946076261427386478569138607076666848631137387666134894302e-7 + i * [0, 0]
10
-1
unit:
-0.8359260629182693617465184990210172206331117795367763475858733135603210461392818153226901481038454563 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=3$ and the unit eigenvalue at $p=3$.
10
-1
integral:
-0.000001044907578647836702183148123776271525791389724420970434482341641950401307674102269153362685129806820 + i * [0, 0]
10
2
unit:
2.782713636641698360061019491629444350597327487105319494624519185607578783473396262176256253803271741 + i * 1.857144840235118554254037304444964973378011592121346444770375432478707208180306280824268448699429994
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=3$ and the unit eigenvalue at $p=3$.
10
2
integral:
0.000003478392045802122950076274364536805438246659358881649368280648982009473479341745327720320317254089676 + i * 0.000002321431050293898192817546630556206216722514490151683055962969290598384010225382851030335560874287492
12
1
unit:
1.557042386408223516835955914895480231452948292388943456292395727761494517198688738598478284494333287 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$.
12
1
integral:
5.214503448137108292730155000480512392072255887469401899984714344623060663415104496870975479086067733e-7 + i * [0, 0]
12
1/2
unit:
0.5788162943265502185070899530337036119818553393586432117388411522824162129380921153273579168133007438 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=5$ and the unit eigenvalue at $p=5$.
12
1/2
integral:
1.938444058395993476546056352055816816104357355426697570177339035582294523139079497168631569403254484e-7 + i * [0, 0]
12
-1
unit:
-0.8222592560296430088722591007197519649492499248608597935370981333341162792238484064654829188062149854 + i * [0, 0]
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=5$ and the unit eigenvalue at $p=5$.
12
-1
integral:
-2.753729611510453535157117723068013642903813030682213278895995870487304283023112000819438144364520993e-7 + i * [0, 0]
12
2
unit:
2.802613518168013719432609385835401350849429648240102736707001994241402628337890727555550370085901865 + i * 2.108284951717092182057352763014557851260193791064165703732370296515827900454251535236260128437804272
comment: The holomorphic denominator is $F_A(z)$. Local arithmetic of this fibre includes the Frobenius polynomial at $p=5$ and the unit eigenvalue at $p=5$.
12
2
integral:
9.385895966515606645690698228240343387136132170299983980848530984229663080371129676366485453659168520e-7 + i * 7.060603645957554300550012200382044415710847047620368038584166212932915583118501422768039374751520007e-7
Definition
The canonical coordinate is $Q_A(z)=z\exp(G_A(z)/F_A(z))$ for the normalized holomorphic and first logarithmic solutions of a hypergeometric Calabi–Yau family [1]. The forms $Q_A(z)$ and $q_A(z)=Q_A(z)/C_A$ are one number in two invertible conventions.
Parameters
$A$
—   hypergeometric template ($A$ is one of the fourteen cyclotomic numerator multisets specified in (4))
$z$
—   rational fibre ($z\in\mathbb Q\setminus\{0\}$, with the boundary prescriptions in (5))
normalization
—   canonical-coordinate normalization (unit denotes $Q_A(z)$; integral denotes $q_A(z)=Q_A(z)/C_A$)
Formulas
(1)
For $|z|<1$, $F_A(z)=\sum_{n\geq0}c_nz^n$ and $G_A(z)=\sum_{n\geq1}c_nh_nz^n$, where $c_n=\prod_{j=1}^4(\alpha_j)_n/(n!)^4$ and $h_n=\sum_{j=1}^4\sum_{k=0}^{n-1}(\alpha_j+k)^{-1}-4\sum_{k=1}^n k^{-1}$. Here $(a)_n=a(a+1)\cdots(a+n-1)$ and $(a)_0=1$ [1] [5].
(2)
With $\theta=z\,d/dz$, both $F_A$ and $F_A\log z+G_A$ satisfy $[\theta^4-z\prod_{j=1}^4(\theta+\alpha_j)]y=0$ [2] [3].
(3)
$C_A=\prod_{d\in A}\left(d^{\varphi(d)}\prod_{\ell\mid d,\ \ell\text{ prime}}\ell^{\varphi(d)/(\ell-1)}\right)$ and $Q_A(z)=C_Aq_A(z)$, where $\varphi$ is Euler's totient function. In particular, $C_{(5)}=3125$ and $C_{(2,2,2,2)}=256$ [1].
Comments
(4)
The key $A=(d_1,\ldots,d_k)$ specifies all reduced fractions $a/d_j$ with $1\leq a<d_j$, counted with multiplicity, as the four upper parameters $\alpha_1,\ldots,\alpha_4$. Dots separate cyclotomic indices. The fourteen keys are $2.2.2.2$, $2.2.3$, $2.2.4$, $2.2.6$, $3.3$, $3.4$, $3.6$, $4.4$, $4.6$, $6.6$, $5$, $8$, $10$ and $12$ [2].
(5)
Continue $F_A$ and $G_A$ from their power series into the plane cut along $[1,\infty)$. At $z=1$ take the finite limit as $z\to1^-$. At rational $z>1$ take the upper-bank value, continued through the upper half-plane without winding around a singularity. For $z<1$ the functions $F_A,G_A$ and both canonical coordinates are real [1].
(6)
The coordinate $z$ is the classical hypergeometric argument, whose finite singular points are $0$ and $1$. The factorial-series variable is $x=z/C_A$; the conifold in this variable is $x=1/C_A$ [3]. The template and fibre conventions agree with the normalized holomorphic periods.
(7)
The solutions are normalized by $F_A(0)=1$ and $G_A(0)=0$, with first logarithmic solution $F_A(z)\log z+G_A(z)$. The unit normalization satisfies $Q_A(z)/z\to1$ at the origin. The integral normalization is $q_A(z)=\mathbf q_A(z/C_A)$ in the notation of [1]; as a series in $x=z/C_A$, it begins with $x$ and has integer coefficients. These two normalizations determine one another by multiplication by $C_A$.
(8)
The term mirror map is also used for the compositional inverse of the canonical coordinate, including in [1]. This table stores the forward canonical coordinate; it does not store the inverse, the holomorphic period, or an integral period vector.
(9)
The smooth fibres $z=1/2,-1,2$ are exactly the rational solutions of $z,1-z\in\mathbb Z[1/2]^\times$. They introduce no potentially bad rational prime outside $2$ beyond the template primes [4]. The Frobenius-polynomial table and the unit-root table give local arithmetic invariants of these same global fibres.
Programs
(P1)
Python
from mpmath import mp
mp.dps = 150
alpha = [mp.mpf(j)/5 for j in range(1, 5)]
z = mp.mpf(1)/2
H = lambda t: mp.hyper([1] + [a+t for a in alpha], [1+t]*4, z)
F, G = H(0), mp.diff(H, 0)
# mpmath's real-cut value is on the lower bank.
if z > 1:
    F, G = mp.conj(F), mp.conj(G)
Q = z * mp.exp(G/F)
q = Q / 3125
print(mp.nstr(Q, 100), mp.nstr(q, 100))
References
[1]
C. Krattenthaler and T. Rivoal, Analytic properties of mirror maps, Sections 1, 3 and 4, equations (1.1)–(1.4). (arXiv)
[2]
Ling Long, Fang-Ting Tu, Noriko Yui and Wadim Zudilin, Supercongruences for rigid hypergeometric Calabi–Yau threefolds, Table 1 and Section 5. (arXiv)
[3]
Kilian Bönisch, Albrecht Klemm, Emanuel Scheidegger and Don Zagier, D-brane masses at special fibres of hypergeometric families of Calabi-Yau threefolds, modular forms, and periods, Section 2 and Table 1. (arXiv)
[4]
David P. Roberts and Fernando Rodriguez Villegas, Hypergeometric Motives, Sections 10–11. (arXiv)
Links
Similar tables
Normalized_holomorphic_periods_of_hypergeometric_Calabi_Yau_families —   gives the normalized holomorphic denominators $F_A(z)$ at the same templates and fibres
Frobenius_polynomials_of_hypergeometric_Calabi_Yau_motives —   gives good-prime Frobenius polynomials of the same global families at the smooth fibres
Unit_roots_of_hypergeometric_Calabi_Yau_motives —   gives the corresponding p-adic unit eigenvalues where they exist
Complete_elliptic_integral_of_the_first_kind_K —   gives the elliptic periods whose ratio defines the rank-two analogue of the canonical coordinate
Data properties
Entries are of type: complex number
How well the digits are known: heuristic (agreement-checked)
Table is complete: no (it holds both scalar normalizations for all fourteen classified templates at the conifold $z=1$ and at $z=1/2,-1,2$, the complete rational solution set of $z,1-z\in\mathbb Z[1/2]^\times$. The allowed extra-prime set $\{2\}$ is a noncanonical reference choice that controls possible bad reduction and aligns these analytic values with the local arithmetic companions. All templates receive negative real, interior real, singular-limit and continued complex coverage before extending any one family; the attached argument-selection note records the justification)
How they were obtained:

Taylor continuation of the hypergeometric differential equation transports the holomorphic and first logarithmic solutions at 140 and 190 decimal working digits. A local Frobenius basis with exponents 0,1,1,2, including the logarithmic term, gives the finite conifold limits. Each nonzero component is recorded to 100 significant digits. Agreement intervals do not certify truncation error. Real fibres have exactly zero imaginary component by real analytic continuation.

more

Independent differentiation with respect to a parameter of a generalized hypergeometric function checks the smooth fibres. At the conifold, a gamma-ratio asymptotic tail and its parameter derivative, summed with Hurwitz zeta, check F and G. Together these methods check the canonical coordinate at all 56 underlying fibres. The checks first reproduce known rank-two elliptic canonical coordinates on the three smooth paths and the exact conifold control F=2, G=1. Exact rational coefficient checks verify the differential equation, logarithmic normalization, scale constants and the first 41 terms of the integral-coordinate series. The two computations keep the holomorphic denominator numerically separated from zero. The attached numerical evidence states the measured agreement and compares the values read back from the draft.



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