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Lee–Yang zeros of the Ising model on finite rectangles at critical coupling
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Numbers
$m$
$n$
$j$ 
$z_{m,n,j}$
2
2
1:
-0.7573593128807148535949338273709057642909843738691557804699607860278025646136788834488373970170752818 + i * -0.6529983699771780165776990250095222876035555286318348872805829440961291104038345154446481618143822719
comment: Multiplicity 1.
2
2
2:
-0.7573593128807148535949338273709057642909843738691557804699607860278025646136788834488373970170752818 + i * 0.6529983699771780165776990250095222876035555286318348872805829440961291104038345154446481618143822719
comment: Multiplicity 1.
2
2
3:
0.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727 + i * -0.9101797211244546826087155156449371392403807569663001851765191389816004064668965831828036395220416980
comment: Multiplicity 1.
2
2
4:
0.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727 + i * 0.9101797211244546826087155156449371392403807569663001851765191389816004064668965831828036395220416980
comment: Multiplicity 1.
2
3
1:
-0.8803836287182499875429238518983297577900237911525761931484662863883715503855645197148967110671375312 + i * -0.4742622336691870258498081449645026431410109103335429710238089623978652768032782992604826114632742356
comment: Multiplicity 1.
2
3
2:
-0.8803836287182499875429238518983297577900237911525761931484662863883715503855645197148967110671375312 + i * 0.4742622336691870258498081449645026431410109103335429710238089623978652768032782992604826114632742356
comment: Multiplicity 1.
2
3
3:
-0.2005922839245654051091942567683982522320621026466884715358609730787851940704470349961941070688602081 + i * -0.9796748111643610791636542173074755551104013171112955981245682375574001649298315788649681584454494000
comment: Multiplicity 1.
2
3
4:
-0.2005922839245654051091942567683982522320621026466884715358609730787851940704470349961941070688602081 + i * 0.9796748111643610791636542173074755551104013171112955981245682375574001649298315788649681584454494000
comment: Multiplicity 1.
2
3
5:
0.6667623502697203438504293844570299314524140184223165915076475214764242659939045158607032838083561665 + i * -0.7452703994274821319768191096333305774903571538358321801755099382895049377368480857105561040754055104
comment: Multiplicity 1.
2
3
6:
0.6667623502697203438504293844570299314524140184223165915076475214764242659939045158607032838083561665 + i * 0.7452703994274821319768191096333305774903571538358321801755099382895049377368480857105561040754055104
comment: Multiplicity 1.
2
4
1:
-0.9234431748605609859914816703200317901219883137305113410438816927895302749383630844824086383017976256 + i * -0.3837351988069994428281504000293976136079189958400670545045096387587645899323027375504395023182303271
comment: Multiplicity 1.
2
4
2:
-0.9234431748605609859914816703200317901219883137305113410438816927895302749383630844824086383017976256 + i * 0.3837351988069994428281504000293976136079189958400670545045096387587645899323027375504395023182303271
comment: Multiplicity 1.
2
4
3:
-0.5005038911116499308439629084064733140552908240281058014337011703716519080507227764727266607423650062 + i * -0.8657342865926575218263462975122133232838201164723269223901542976686426099743573435952044396320286777
comment: Multiplicity 1.
2
4
4:
-0.5005038911116499308439629084064733140552908240281058014337011703716519080507227764727266607423650062 + i * 0.8657342865926575218263462975122133232838201164723269223901542976686426099743573435952044396320286777
comment: Multiplicity 1.
2
4
5:
0.1676443163604433019716336221283964044998425080872231427728004902609006795441205061189003658310198236 + i * -0.9858475456134379412904774126512895896395215818393785995272453738106266316840044172847266098801216249
comment: Multiplicity 1.
2
4
6:
0.1676443163604433019716336221283964044998425080872231427728004902609006795441205061189003658310198236 + i * 0.9858475456134379412904774126512895896395215818393785995272453738106266316840044172847266098801216249
comment: Multiplicity 1.
2
4
7:
0.7710213753731973220536786113399202282594053774097055606447039449558866326723231217339097272472933718 + i * -0.6368092640011003719226926436067070658418101130917760590790932981432805264089167981668096587366968124
comment: Multiplicity 1.
2
4
8:
0.7710213753731973220536786113399202282594053774097055606447039449558866326723231217339097272472933718 + i * 0.6368092640011003719226926436067070658418101130917760590790932981432805264089167981668096587366968124
comment: Multiplicity 1.
2
5
1:
-0.9467075847137523579724261428308544039104003602879453082695535397262244924976802487393023161889455730 + i * -0.3220943170027273280170800849227878652620849434616709481653427676376113909324945519987010257707566954
comment: Multiplicity 1.
2
5
2:
-0.9467075847137523579724261428308544039104003602879453082695535397262244924976802487393023161889455730 + i * 0.3220943170027273280170800849227878652620849434616709481653427676376113909324945519987010257707566954
comment: Multiplicity 1.
2
5
3:
-0.6585992850607210222636786452934501862821590140466548206363059484828651183976547724464012799787503643 + i * -0.7524938416475626754547216714648876690503524521057960139057091181396818190860113404524560293459391554
comment: Multiplicity 1.
2
5
4:
-0.6585992850607210222636786452934501862821590140466548206363059484828651183976547724464012799787503643 + i * 0.7524938416475626754547216714648876690503524521057960139057091181396818190860113404524560293459391554
comment: Multiplicity 1.
2
5
5:
-0.1677760884222529857607413395179430608166224949874270658067179049227350038691991842282235123892627980 + i * -0.9858251285870777333657741675833219170835066100854575376758230448179980961349841508552566584077577834
comment: Multiplicity 1.
2
5
6:
-0.1677760884222529857607413395179430608166224949874270658067179049227350038691991842282235123892627980 + i * 0.9858251285870777333657741675833219170835066100854575376758230448179980961349841508552566584077577834
comment: Multiplicity 1.
2
5
7:
0.3922676153066601838487524113054128678925563595376272292995378635775500915521348004243445299205691810 + i * -0.9198511390337167251348043696184882027094672142419465812919430957488440974890819738028677662476709710
comment: Multiplicity 1.
2
5
8:
0.3922676153066601838487524113054128678925563595376272292995378635775500915521348004243445299205691810 + i * 0.9198511390337167251348043696184882027094672142419465812919430957488440974890819738028677662476709710
comment: Multiplicity 1.
2
5
9:
0.8244661567860206453295177500301559188502348806379711604695624116562172601292219776353197010323322543 + i * -0.5659112618728212086571475535912524362318226893620857029710759024282448914972060895449716579647270147
comment: Multiplicity 1.
2
5
10:
0.8244661567860206453295177500301559188502348806379711604695624116562172601292219776353197010323322543 + i * 0.5659112618728212086571475535912524362318226893620857029710759024282448914972060895449716579647270147
comment: Multiplicity 1.
2
6
1:
-0.9598707515809939475522264593244873924196819273571205406497720341778972011157489980878729754025366438 + i * -0.2804427575448112818239164822454809345860512876541388334717922877352021850024947689141346194278202103
comment: Multiplicity 1.
2
6
2:
-0.9598707515809939475522264593244873924196819273571205406497720341778972011157489980878729754025366438 + i * 0.2804427575448112818239164822454809345860512876541388334717922877352021850024947689141346194278202103
comment: Multiplicity 1.
2
6
3:
-0.7524245901485985545172794154835703064302368170376107889974955650968166337575378881146145149101016282 + i * -0.6586784011486284397241946546530197326813371337259939036396732414079221208018893772532274502673510448
comment: Multiplicity 1.
2
6
4:
-0.7524245901485985545172794154835703064302368170376107889974955650968166337575378881146145149101016282 + i * 0.6586784011486284397241946546530197326813371337259939036396732414079221208018893772532274502673510448
comment: Multiplicity 1.
2
6
5:
-0.3824871026110921923781830963948669657491674308848205100515906102858794770728340882090572809325706412 + i * -0.9239608305205214878646469417727812340647516849399732322928531314801053691769937258374320714969178126
comment: Multiplicity 1.
2
6
6:
-0.3824871026110921923781830963948669657491674308848205100515906102858794770728340882090572809325706412 + i * 0.9239608305205214878646469417727812340647516849399732322928531314801053691769937258374320714969178126
comment: Multiplicity 1.
2
6
7:
0.07720623897248404314231361590795808971299526594650205391250827634303135212135249528892352664215119049 + i * -0.9970151436481412272100727108130487116199152079830942079103725749674345803509223048569551341771277522
comment: Multiplicity 1.
2
6
8:
0.07720623897248404314231361590795808971299526594650205391250827634303135212135249528892352664215119049 + i * 0.9970151436481412272100727108130487116199152079830942079103725749674345803509223048569551341771277522
comment: Multiplicity 1.
2
6
9:
0.5343038597096382775381292013424418184326842164484887389822433208212377503759542601104453686786654141 + i * -0.8452924851785819455729877333124369791355446796169316388136308089661209530687451663543432917720238612
comment: Multiplicity 1.
2
6
10:
0.5343038597096382775381292013424418184326842164484887389822433208212377503759542601104453686786654141 + i * 0.8452924851785819455729877333124369791355446796169316388136308089661209530687451663543432917720238612
comment: Multiplicity 1.
2
6
11:
0.8558553476890415929402265665973554993386566868533918759772308045446045540551015974059753266821271450 + i * -0.5172152586999630730042119743510145365627722262461089501719506297835835493026230735938679261067566385
comment: Multiplicity 1.
2
6
12:
0.8558553476890415929402265665973554993386566868533918759772308045446045540551015974059753266821271450 + i * 0.5172152586999630730042119743510145365627722262461089501719506297835835493026230735938679261067566385
comment: Multiplicity 1.
3
3
1:
-1
comment: Multiplicity 1. The root is exactly $-1$; spin reversal makes every odd-degree field polynomial divisible by $z+1$.
3
3
2:
-0.8125761921267911449548091802666904309271459444468269415600042090696452875446050737669170478217062338 + i * -0.5828549836698011836692941753066931459200113338249093553632425711593026764736536780650085497822090246
comment: Multiplicity 1.
3
3
3:
-0.8125761921267911449548091802666904309271459444468269415600042090696452875446050737669170478217062338 + i * 0.5828549836698011836692941753066931459200113338249093553632425711593026764736536780650085497822090246
comment: Multiplicity 1.
3
3
4:
-0.3085645924954505134918269011196592628223103116117698498468695685354628616388841807625176496635587373 + i * -0.9512033916350995458381335971286804866567790619588873607838151529004286253331621154806707570924280293
comment: Multiplicity 1.
3
3
5:
-0.3085645924954505134918269011196592628223103116117698498468695685354628616388841807625176496635587373 + i * 0.9512033916350995458381335971286804866567790619588873607838151529004286253331621154806707570924280293
comment: Multiplicity 1.
3
3
6:
0.2912810772525742618660795400948298150913306120474186447690373869822324711031303475878342739369559489 + i * -0.9566375144403338027075577489965197336451618260919996137008584600630122449905048583132211151670387774
comment: Multiplicity 1.
3
3
7:
0.2912810772525742618660795400948298150913306120474186447690373869822324711031303475878342739369559489 + i * 0.9566375144403338027075577489965197336451618260919996137008584600630122449905048583132211151670387774
comment: Multiplicity 1.
3
3
8:
0.8298597073696673965805565412915198786581256440111781466378363906228756780803589069416004235483090222 + i * -0.5579721015286785788204292939151239823376452433322076700860237342381262156570347147329567360355030878
comment: Multiplicity 1.
3
3
9:
0.8298597073696673965805565412915198786581256440111781466378363906228756780803589069416004235483090222 + i * 0.5579721015286785788204292939151239823376452433322076700860237342381262156570347147329567360355030878
comment: Multiplicity 1.
3
4
1:
-0.9694699401072330790497673236811817864562768455253361532998915304494181359287038424657911704919846787 + i * -0.2452101858171432212246641675136253760885786537981265454401519065555745711184873232516454545639885081
comment: Multiplicity 1.
3
4
2:
-0.9694699401072330790497673236811817864562768455253361532998915304494181359287038424657911704919846787 + i * 0.2452101858171432212246641675136253760885786537981265454401519065555745711184873232516454545639885081
comment: Multiplicity 1.
3
4
3:
-0.7583581364572799791913848474447174153305852620855585621519322304454809107907919326245873174634772011 + i * -0.6518381216751913156637987635808082564207570163197131278670989346998827044100934426008211192486692833
comment: Multiplicity 1.
3
4
4:
-0.7583581364572799791913848474447174153305852620855585621519322304454809107907919326245873174634772011 + i * 0.6518381216751913156637987635808082564207570163197131278670989346998827044100934426008211192486692833
comment: Multiplicity 1.
3
4
5:
-0.3714051648235922190686759890580846027149280114332887098787760331598372071923106406336592515140475227 + i * -0.9284708953663331158069552837166434132594391439771352125884306610665586696616107893928329181134788357
comment: Multiplicity 1.
3
4
6:
-0.3714051648235922190686759890580846027149280114332887098787760331598372071923106406336592515140475227 + i * 0.9284708953663331158069552837166434132594391439771352125884306610665586696616107893928329181134788357
comment: Multiplicity 1.
3
4
7:
0.08282297469778869735164115136153885771058055953501640663080238544028726476262954209626147287472443650 + i * -0.9965642753290976029259567897532727788318068398348313610397950572588725819460666311920405455458983263
comment: Multiplicity 1.
3
4
8:
0.08282297469778869735164115136153885771058055953501640663080238544028726476262954209626147287472443650 + i * 0.9965642753290976029259567897532727788318068398348313610397950572588725819460666311920405455458983263
comment: Multiplicity 1.
3
4
9:
0.5391823252784818035566080609769834211566905749334972921450433905434435275496888868091567815207607129 + i * -0.8421890643479582977449363443976527340738457040290773239530513062390574062083967932327446809860054018
comment: Multiplicity 1.
3
4
10:
0.5391823252784818035566080609769834211566905749334972921450433905434435275496888868091567815207607129 + i * 0.8421890643479582977449363443976527340738457040290773239530513062390574062083967932327446809860054018
comment: Multiplicity 1.
3
4
11:
0.8914415037849298252032676720551596042041908599526177997314337560617379400615950256690070194016658258 + i * -0.4531357912697505559141138102177290431491410925297273523677194610897039258909499329072526921270887741
comment: Multiplicity 1.
3
4
12:
0.8914415037849298252032676720551596042041908599526177997314337560617379400615950256690070194016658258 + i * 0.4531357912697505559141138102177290431491410925297273523677194610897039258909499329072526921270887741
comment: Multiplicity 1.
3
5
1:
-1
comment: Multiplicity 1. The root is exactly $-1$; spin reversal makes every odd-degree field polynomial divisible by $z+1$.
3
5
2:
-0.9249540742897915722768276040317289310058008287479704054748591413706292507878456084740175871825016598 + i * -0.3800788871467536976315260318303155755047333845310102507602692542962711706370935524362757256652396250
comment: Multiplicity 1.
3
5
3:
-0.9249540742897915722768276040317289310058008287479704054748591413706292507878456084740175871825016598 + i * 0.3800788871467536976315260318303155755047333845310102507602692542962711706370935524362757256652396250
comment: Multiplicity 1.
3
5
4:
-0.7238551651573286154025972756954116987832434268672031115707616086653723628519338478270564546240627065 + i * -0.6899519547584864356199858294059453253994634101544754735104945787159948788998248856372574340852160405
comment: Multiplicity 1.
3
5
5:
-0.7238551651573286154025972756954116987832434268672031115707616086653723628519338478270564546240627065 + i * 0.6899519547584864356199858294059453253994634101544754735104945787159948788998248856372574340852160405
comment: Multiplicity 1.
3
5
6:
-0.4044535519337205874235086891040799630776466516105824296591813670036693441298505432855737019648764552 + i * -0.9145585406786146151000678471708789334349263605328675938214601979092443864225465971602574123329142539
comment: Multiplicity 1.
3
5
7:
-0.4044535519337205874235086891040799630776466516105824296591813670036693441298505432855737019648764552 + i * 0.9145585406786146151000678471708789334349263605328675938214601979092443864225465971602574123329142539
comment: Multiplicity 1.
3
5
8:
-0.04711762160136867835712081388767961339913752089613130603214819798343157419762605222800810539967667439 + i * -0.9988893480934863967001741237924808644148326220642160932624753476532352373731717623570960622325221701
comment: Multiplicity 1.
3
5
9:
-0.04711762160136867835712081388767961339913752089613130603214819798343157419762605222800810539967667439 + i * 0.9988893480934863967001741237924808644148326220642160932624753476532352373731717623570960622325221701
comment: Multiplicity 1.
3
5
10:
0.3310688098661869543027805403331790859082296800512711817238929434982795085139663565658040947505303608 + i * -0.9436066146089622190875016578501506143562389162095719880200900850696302290220960475621531745659330671
comment: Multiplicity 1.
3
5
11:
0.3310688098661869543027805403331790859082296800512711817238929434982795085139663565658040947505303608 + i * 0.9436066146089622190875016578501506143562389162095719880200900850696302290220960475621531745659330671
comment: Multiplicity 1.
3
5
12:
0.6763380031317745982691846730561911756535052320454876443982661757157155434850398840911112668864463858 + i * -0.7365914101587960099062274199361025821811723820323178589908887605997000929410298405898997915865433619
comment: Multiplicity 1.
3
5
13:
0.6763380031317745982691846730561911756535052320454876443982661757157155434850398840911112668864463858 + i * 0.7365914101587960099062274199361025821811723820323178589908887605997000929410298405898997915865433619
comment: Multiplicity 1.
3
5
14:
0.9214007247304379984914666177489261018434372667790245729681506717905724368924638888585155561894238947 + i * -0.3886138243375081248502524928043515326198168532186094921351801443039242316348861284069914634422343807
comment: Multiplicity 1.
3
5
15:
0.9214007247304379984914666177489261018434372667790245729681506717905724368924638888585155561894238947 + i * 0.3886138243375081248502524928043515326198168532186094921351801443039242316348861284069914634422343807
comment: Multiplicity 1.
3
6
1:
-0.9863099509465668006506738858031984720498879670661022817680906639462842508774994791169586978236756618 + i * -0.1649020335344018474762336670955988222385405788065733143146974988096276859864388603352380404606746121
comment: Multiplicity 1.
3
6
2:
-0.9863099509465668006506738858031984720498879670661022817680906639462842508774994791169586978236756618 + i * 0.1649020335344018474762336670955988222385405788065733143146974988096276859864388603352380404606746121
comment: Multiplicity 1.
3
6
3:
-0.8841865776692687389911433635670603218964178994784333426235113813583108695934121765211339075528043908 + i * -0.4671339164195918237851210620774424585050384051349743093059607087157979324832345428402817543057181484
comment: Multiplicity 1.
3
6
4:
-0.8841865776692687389911433635670603218964178994784333426235113813583108695934121765211339075528043908 + i * 0.4671339164195918237851210620774424585050384051349743093059607087157979324832345428402817543057181484
comment: Multiplicity 1.
3
6
5:
-0.6999533545846108568346870478338631623200130432598658612073112349327826224651192278708998918604191520 + i * -0.7141885615198202147734420553401748671522137097068861878325498165119248659148963195843540588461890321
comment: Multiplicity 1.
3
6
6:
-0.6999533545846108568346870478338631623200130432598658612073112349327826224651192278708998918604191520 + i * 0.7141885615198202147734420553401748671522137097068861878325498165119248659148963195843540588461890321
comment: Multiplicity 1.
3
6
7:
-0.4273970020237758992559396112718196569720870573025154384939883737735716538293610911499687109731053798 + i * -0.9040640478755299446772473972116630722079868991122725552673209601977567169576905092755613050526046734
comment: Multiplicity 1.
3
6
8:
-0.4273970020237758992559396112718196569720870573025154384939883737735716538293610911499687109731053798 + i * 0.9040640478755299446772473972116630722079868991122725552673209601977567169576905092755613050526046734
comment: Multiplicity 1.
3
6
9:
-0.1329558292759831645568294398345222765023514075661468881351014759106113049520262072771049078105146933 + i * -0.9911219639688829023142663739531482370082731064646187157655316207306776611097571174578333949247965262
comment: Multiplicity 1.
3
6
10:
-0.1329558292759831645568294398345222765023514075661468881351014759106113049520262072771049078105146933 + i * 0.9911219639688829023142663739531482370082731064646187157655316207306776611097571174578333949247965262
comment: Multiplicity 1.
3
6
11:
0.1841633212916989830871940276474650702509555850829211513354513782185122713446423845664260597013018735 + i * -0.9828956562579826825142849493796036158831248225367000328363721877769142656232813501823547852215355193
comment: Multiplicity 1.
3
6
12:
0.1841633212916989830871940276474650702509555850829211513354513782185122713446423845664260597013018735 + i * 0.9828956562579826825142849493796036158831248225367000328363721877769142656232813501823547852215355193
comment: Multiplicity 1.
3
6
13:
0.4917268480936742170960003312820532943539885586491691276509905468413359911333357782547069245298449444 + i * -0.8707495086785066001483666769927110480313623055417706645508822524781495553119150509938621835348493232
comment: Multiplicity 1.
3
6
14:
0.4917268480936742170960003312820532943539885586491691276509905468413359911333357782547069245298449444 + i * 0.8707495086785066001483666769927110480313623055417706645508822524781495553119150509938621835348493232
comment: Multiplicity 1.
3
6
15:
0.7591613863944849605076802237802653441223856475466653820197304899182279364859086209684444215025411471 + i * -0.6509024423119055289984339867124267398455150840309816111515890962503385454147957907777250291373685477
comment: Multiplicity 1.
3
6
16:
0.7591613863944849605076802237802653441223856475466653820197304899182279364859086209684444215025411471 + i * 0.6509024423119055289984339867124267398455150840309816111515890962503385454147957907777250291373685477
comment: Multiplicity 1.
3
6
17:
0.9383918458396324460034649382297744167224432095251523707518699289156819381398525146976513132697560308 + i * -0.3455730655906034208599218740185934876000650837543238685882543583010504374310646323396016314144811346
comment: Multiplicity 1.
3
6
18:
0.9383918458396324460034649382297744167224432095251523707518699289156819381398525146976513132697560308 + i * 0.3455730655906034208599218740185934876000650837543238685882543583010504374310646323396016314144811346
comment: Multiplicity 1.
4
4
1:
-0.9816273497352462093203103400070870651774573126727732548964818871730595807324292814502209854090012638 + i * -0.1908081398991055198547678671346167868800632579993330841616511299620060651218236329066657237630247838
comment: Multiplicity 1.
4
4
2:
-0.9816273497352462093203103400070870651774573126727732548964818871730595807324292814502209854090012638 + i * 0.1908081398991055198547678671346167868800632579993330841616511299620060651218236329066657237630247838
comment: Multiplicity 1.
4
4
3:
-0.8541469284245303144312502794101497777916080866402276231247469171813236101723853892202959286926765136 + i * -0.5200317535140909912157147432544426840020187711840766412078875044678928620388830256634858932536422836
comment: Multiplicity 1.
4
4
4:
-0.8541469284245303144312502794101497777916080866402276231247469171813236101723853892202959286926765136 + i * 0.5200317535140909912157147432544426840020187711840766412078875044678928620388830256634858932536422836
comment: Multiplicity 1.
4
4
5:
-0.6210432950914609269825074619602516059315613280861416057539127139497526311828580922158965008026585540 + i * -0.7837762599249485969835706064030328621177428901783671989682898066826861740989176838991568593551073903
comment: Multiplicity 1.
4
4
6:
-0.6210432950914609269825074619602516059315613280861416057539127139497526311828580922158965008026585540 + i * 0.7837762599249485969835706064030328621177428901783671989682898066826861740989176838991568593551073903
comment: Multiplicity 1.
4
4
7:
-0.3115531865925516205070862842650874577797436704976289881595800754305469973130942425779000659698215272 + i * -0.9502287155858986737886120323188677018164430788468785837767946152035402389101024355125152441501089155
comment: Multiplicity 1.
4
4
8:
-0.3115531865925516205070862842650874577797436704976289881595800754305469973130942425779000659698215272 + i * 0.9502287155858986737886120323188677018164430788468785837767946152035402389101024355125152441501089155
comment: Multiplicity 1.
4
4
9:
0.04571729086164276109835522321609214552053829344847956140511336252296574227306904340025796841222363204 + i * -0.9989544180373156321958980751587474170614993475079341906753628696896391287055312423567654971102847670
comment: Multiplicity 1.
4
4
10:
0.04571729086164276109835522321609214552053829344847956140511336252296574227306904340025796841222363204 + i * 0.9989544180373156321958980751587474170614993475079341906753628696896391287055312423567654971102847670
comment: Multiplicity 1.
4
4
11:
0.3942345023293815260768470847293584902979154717862905107300741702005079054165740690871250207487501398 + i * -0.9190098787135559796347118403062328710509617747263651270203532535147556702967008118211183542181587441
comment: Multiplicity 1.
4
4
12:
0.3942345023293815260768470847293584902979154717862905107300741702005079054165740690871250207487501398 + i * 0.9190098787135559796347118403062328710509617747263651270203532535147556702967008118211183542181587441
comment: Multiplicity 1.
4
4
13:
0.7078405537092570126403996603999870074678568560452721603025087373255187657579114675500305081870118908 + i * -0.7063722464285898303967680772835796846183888269849814635452848098314860958035651566619422156017007950
comment: Multiplicity 1.
4
4
14:
0.7078405537092570126403996603999870074678568560452721603025087373255187657579114675500305081870118908 + i * 0.7063722464285898303967680772835796846183888269849814635452848098314860958035651566619422156017007950
comment: Multiplicity 1.
4
4
15:
0.9342869119282681618390621909747228919514347796323138249104632276115502336500687362300002581473047779 + i * -0.3565220416742006866207195683460522301334493116224824411523014485532311668141063286072762826464028511
comment: Multiplicity 1.
4
4
16:
0.9342869119282681618390621909747228919514347796323138249104632276115502336500687362300002581473047779 + i * 0.3565220416742006866207195683460522301334493116224824411523014485532311668141063286072762826464028511
comment: Multiplicity 1.
4
5
1:
-0.9882915727564124540109916848681086828163827770278608611513981702101254863823384364797308198888678991 + i * -0.1525770861520716973678244295551519583985906990392299568026188681593845010288994817784575747337062795
comment: Multiplicity 1.
4
5
2:
-0.9882915727564124540109916848681086828163827770278608611513981702101254863823384364797308198888678991 + i * 0.1525770861520716973678244295551519583985906990392299568026188681593845010288994817784575747337062795
comment: Multiplicity 1.
4
5
3:
-0.9040820842030914578868434240744239236195431044239631249514862703230322736751925005497572635617082433 + i * -0.4273588480691539946495975049048218602639201841070453634792987698741444903733338401238875788895813017
comment: Multiplicity 1.
4
5
4:
-0.9040820842030914578868434240744239236195431044239631249514862703230322736751925005497572635617082433 + i * 0.4273588480691539946495975049048218602639201841070453634792987698741444903733338401238875788895813017
comment: Multiplicity 1.
4
5
5:
-0.7467348514913746746232304956689111493906083637395798509637914301681416511573343050522437228797342081 + i * -0.6651218396415461336754170816371864855915686651452128952609843215654682850085388774914003019765451333
comment: Multiplicity 1.
4
5
6:
-0.7467348514913746746232304956689111493906083637395798509637914301681416511573343050522437228797342081 + i * 0.6651218396415461336754170816371864855915686651452128952609843215654682850085388774914003019765451333
comment: Multiplicity 1.
4
5
7:
-0.5281315545043520634834573739357043306086815358025381635001042462909967144913340282493044145900217619 + i * -0.8491625646110505533726026486161543836047212300160312220804770586344627546716723620221564595150105888
comment: Multiplicity 1.
4
5
8:
-0.5281315545043520634834573739357043306086815358025381635001042462909967144913340282493044145900217619 + i * 0.8491625646110505533726026486161543836047212300160312220804770586344627546716723620221564595150105888
comment: Multiplicity 1.
4
5
9:
-0.2677612950945014822480006363196826966061271030077152024482107794771389477013092373072766819870487256 + i * -0.9634852821134920151514575545255851681045143130311006439005700166700036864516569520643626129047776405
comment: Multiplicity 1.
4
5
10:
-0.2677612950945014822480006363196826966061271030077152024482107794771389477013092373072766819870487256 + i * 0.9634852821134920151514575545255851681045143130311006439005700166700036864516569520643626129047776405
comment: Multiplicity 1.
4
5
11:
0.01966368835268006067821128947248970853023237947919004656577167329869350836147769308291721953971776465 + i * -0.9998066509882641676492929304640722258844490983009444179829309573322341158501646797635686540927751079
comment: Multiplicity 1.
4
5
12:
0.01966368835268006067821128947248970853023237947919004656577167329869350836147769308291721953971776465 + i * 0.9998066509882641676492929304640722258844490983009444179829309573322341158501646797635686540927751079
comment: Multiplicity 1.
4
5
13:
0.3048120385036061744669305022597934840777639216727354581858811739677017319627102982439016451970236005 + i * -0.9524125267883009669423778171519728613284341458925643598981554840529420647820384319123573789011173627
comment: Multiplicity 1.
4
5
14:
0.3048120385036061744669305022597934840777639216727354581858811739677017319627102982439016451970236005 + i * 0.9524125267883009669423778171519728613284341458925643598981554840529420647820384319123573789011173627
comment: Multiplicity 1.
4
5
15:
0.5716458966125135124598746740598602507299080029615323882632265018024986394317229984647493126643007783 + i * -0.8205004380779302864517725116109554671607440944621902289665040695913529653511970205693267592110957221
comment: Multiplicity 1.
4
5
16:
0.5716458966125135124598746740598602507299080029615323882632265018024986394317229984647493126643007783 + i * 0.8205004380779302864517725116109554671607440944621902289665040695913529653511970205693267592110957221
comment: Multiplicity 1.
4
5
17:
0.7977321086282251482311038033996967615100396342321887542385229042361046513215497801724830556970281359 + i * -0.6030120088883517351300760011695120488043796859080757894211647661785032863642886278055887523617274096
comment: Multiplicity 1.
4
5
18:
0.7977321086282251482311038033996967615100396342321887542385229042361046513215497801724830556970281359 + i * 0.6030120088883517351300760011695120488043796859080757894211647661785032863642886278055887523617274096
comment: Multiplicity 1.
4
5
19:
0.9543510615491329684417342088204617567384770763102316534117847130254237192616533204300746847239341497 + i * -0.2986872131847009894250836404907598280604070156798877805191214263772832387660803291293397197271204443
comment: Multiplicity 1.
4
5
20:
0.9543510615491329684417342088204617567384770763102316534117847130254237192616533204300746847239341497 + i * 0.2986872131847009894250836404907598280604070156798877805191214263772832387660803291293397197271204443
comment: Multiplicity 1.
4
6
1:
-0.9916977871812599371112988166667254197820665987880505329906781468690092501222629349663574373609992294 + i * -0.1285904308251297288462187559538951644793522328382339182047918182707104689167419648736973037753447619
comment: Multiplicity 1.
4
6
2:
-0.9916977871812599371112988166667254197820665987880505329906781468690092501222629349663574373609992294 + i * 0.1285904308251297288462187559538951644793522328382339182047918182707104689167419648736973037753447619
comment: Multiplicity 1.
4
6
3:
-0.9320036490831283284727443003506549082846100693221595568786691628345716158769124615808255264412752587 + i * -0.3624488903221156063487939599019762889707465670826095663442111149510607251187422700315053637078844800
comment: Multiplicity 1.
4
6
4:
-0.9320036490831283284727443003506549082846100693221595568786691628345716158769124615808255264412752587 + i * 0.3624488903221156063487939599019762889707465670826095663442111149510607251187422700315053637078844800
comment: Multiplicity 1.
4
6
5:
-0.8194158520622403663736419887616524027759835128183439340661714274967561539798656363738179597250719069 + i * -0.5731994952798829971370540404776935107713675289644018484698218911195092987178682016707779544726922180
comment: Multiplicity 1.
4
6
6:
-0.8194158520622403663736419887616524027759835128183439340661714274967561539798656363738179597250719069 + i * 0.5731994952798829971370540404776935107713675289644018484698218911195092987178682016707779544726922180
comment: Multiplicity 1.
4
6
7:
-0.6601537990302281335804827183964992965437192061927444948319668073959488622646110564831084071286178654 + i * -0.7511304557970986470812515045438322411778140997633216171395540112313209166316141934767729303624738636
comment: Multiplicity 1.
4
6
8:
-0.6601537990302281335804827183964992965437192061927444948319668073959488622646110564831084071286178654 + i * 0.7511304557970986470812515045438322411778140997633216171395540112313209166316141934767729303624738636
comment: Multiplicity 1.
4
6
9:
-0.4615810420575636622655268684737418505431012294637339658825946698266064198244998198792211769467689236 + i * -0.8870980450959485941420174963921475770257195872809343819697174724353403094475868795284114821635586399
comment: Multiplicity 1.
4
6
10:
-0.4615810420575636622655268684737418505431012294637339658825946698266064198244998198792211769467689236 + i * 0.8870980450959485941420174963921475770257195872809343819697174724353403094475868795284114821635586399
comment: Multiplicity 1.
4
6
11:
-0.2389629750093514256490735107458071033481468021308110845328465662548631139742221808998159069888110743 + i * -0.9710286795840172742578947814803334408516426312101775520106792980300390826786756166044208448969811870
comment: Multiplicity 1.
4
6
12:
-0.2389629750093514256490735107458071033481468021308110845328465662548631139742221808998159069888110743 + i * 0.9710286795840172742578947814803334408516426312101775520106792980300390826786756166044208448969811870
comment: Multiplicity 1.
4
6
13:
0.003793397352982836717931142076529741789434260974134769583708719689435622704667063320549081195182441315 + i * -0.9999928050423774838089423484239298241960562919360338890134950930934700778727696492137358497946681985
comment: Multiplicity 1.
4
6
14:
0.003793397352982836717931142076529741789434260974134769583708719689435622704667063320549081195182441315 + i * 0.9999928050423774838089423484239298241960562919360338890134950930934700778727696492137358497946681985
comment: Multiplicity 1.
4
6
15:
0.2424918003181560025715624750092712384474290322570484703437476404531304371758790951723961375792218147 + i * -0.9701534552731642755090700624564504585828023198468635383460651141385336515189000740701815642650521762
comment: Multiplicity 1.
4
6
16:
0.2424918003181560025715624750092712384474290322570484703437476404531304371758790951723961375792218147 + i * 0.9701534552731642755090700624564504585828023198468635383460651141385336515189000740701815642650521762
comment: Multiplicity 1.
4
6
17:
0.4732304196495258690215443494325280773647511571509267026942555733538599495568433571816642441775404815 + i * -0.8809386868098901014919130614495178536073751305156765765449604510604670427429525013223760883391038514
comment: Multiplicity 1.
4
6
18:
0.4732304196495258690215443494325280773647511571509267026942555733538599495568433571816642441775404815 + i * 0.8809386868098901014919130614495178536073751305156765765449604510604670427429525013223760883391038514
comment: Multiplicity 1.
4
6
19:
0.6803998916936893384260004040706909455178642345041336205144089232326897875493953829936594834708543595 + i * -0.7328410382772077114055704761856388288968136368880347534535169016196525623406179665506958773111535056
comment: Multiplicity 1.
4
6
20:
0.6803998916936893384260004040706909455178642345041336205144089232326897875493953829936594834708543595 + i * 0.7328410382772077114055704761856388288968136368880347534535169016196525623406179665506958773111535056
comment: Multiplicity 1.
4
6
21:
0.8511722768563592670427829948717227673448905986103792326358664012643593745965093682325541593383239434 + i * -0.5248864211533398874478988497487649844164862495288441761695183915612153733761339637939025205481677769
comment: Multiplicity 1.
4
6
22:
0.8511722768563592670427829948717227673448905986103792326358664012643593745965093682325541593383239434 + i * 0.5248864211533398874478988497487649844164862495288441761695183915612153733761339637939025205481677769
comment: Multiplicity 1.
4
6
23:
0.9654256907611496133100987705476959393460393935120783832978937584803947706254346779908490640385358182 + i * -0.2606784141780003965780928564488019348033282505308950807829699297675164210209459379971485539433646696
comment: Multiplicity 1.
4
6
24:
0.9654256907611496133100987705476959393460393935120783832978937584803947706254346779908490640385358182 + i * 0.2606784141780003965780928564488019348033282505308950807829699297675164210209459379971485539433646696
comment: Multiplicity 1.
5
5
1:
-1
comment: Multiplicity 1. The root is exactly $-1$; spin reversal makes every odd-degree field polynomial divisible by $z+1$.
5
5
2:
-0.9714950861757157134574441979161361489386961212315657822373706437900352175236283587149790908824461498 + i * -0.2370596919268197725701643651169163725822503533615562535123208307708663627329618667563763134227282985
comment: Multiplicity 1.
5
5
3:
-0.9714950861757157134574441979161361489386961212315657822373706437900352175236283587149790908824461498 + i * 0.2370596919268197725701643651169163725822503533615562535123208307708663627329618667563763134227282985
comment: Multiplicity 1.
5
5
4:
-0.8910835180388356207400206112391925700400528047400558564840476498461177021024560929999376073187757966 + i * -0.4538393591123759209703105406915045583750781472878774942583205358984483517992751719989853671180503274
comment: Multiplicity 1.
5
5
5:
-0.8910835180388356207400206112391925700400528047400558564840476498461177021024560929999376073187757966 + i * 0.4538393591123759209703105406915045583750781472878774942583205358984483517992751719989853671180503274
comment: Multiplicity 1.
5
5
6:
-0.7626908779032180093623239736732426005247336301890723775114476121255759828705686858330873275543442880 + i * -0.6467631906372057896590217547095117967324061089480119080128515018316829473536406570842724631503616861
comment: Multiplicity 1.
5
5
7:
-0.7626908779032180093623239736732426005247336301890723775114476121255759828705686858330873275543442880 + i * 0.6467631906372057896590217547095117967324061089480119080128515018316829473536406570842724631503616861
comment: Multiplicity 1.
5
5
8:
-0.5950931588722995590622994704616647711306702014540231926001286980480545832988494336943188473962440000 + i * -0.8036567253892597373827660776900101781535245117207799473916496295546638571339714067838858005169323273
comment: Multiplicity 1.
5
5
9:
-0.5950931588722995590622994704616647711306702014540231926001286980480545832988494336943188473962440000 + i * 0.8036567253892597373827660776900101781535245117207799473916496295546638571339714067838858005169323273
comment: Multiplicity 1.
5
5
10:
-0.3944054559518213837480901076147204000639576217406052818455066780634598916462507054255100604312408301 + i * -0.9189365246389088229417472804995922027880669614848059941546876990682643894065375086558259583628207613
comment: Multiplicity 1.
5
5
11:
-0.3944054559518213837480901076147204000639576217406052818455066780634598916462507054255100604312408301 + i * 0.9189365246389088229417472804995922027880669614848059941546876990682643894065375086558259583628207613
comment: Multiplicity 1.
5
5
12:
-0.1736350469402748203580469568269552576587175478846466094305129342945229498228939716921880338680133865 + i * -0.9848100682233344022306352819208335683423249645553031363337184148967669496814803248250618557198105313
comment: Multiplicity 1.
5
5
13:
-0.1736350469402748203580469568269552576587175478846466094305129342945229498228939716921880338680133865 + i * 0.9848100682233344022306352819208335683423249645553031363337184148967669496814803248250618557198105313
comment: Multiplicity 1.
5
5
14:
0.05696021899595251244502566765443164703573454864168712232775865463491856411668162109527117080506623071 + i * -0.9983764487666629301171544635877849621420167171562283953652247845088934211800879723130510908928174418
comment: Multiplicity 1.
5
5
15:
0.05696021899595251244502566765443164703573454864168712232775865463491856411668162109527117080506623071 + i * 0.9983764487666629301171544635877849621420167171562283953652247845088934211800879723130510908928174418
comment: Multiplicity 1.
5
5
16:
0.2895845777548446561313984115064065855237436003995696752500087672680842719715005060769225600872663205 + i * -0.9571524289926596271204326292352492325051239241279918596902318576969933116347459255892664595752836390
comment: Multiplicity 1.
5
5
17:
0.2895845777548446561313984115064065855237436003995696752500087672680842719715005060769225600872663205 + i * 0.9571524289926596271204326292352492325051239241279918596902318576969933116347459255892664595752836390
comment: Multiplicity 1.
5
5
18:
0.5073918244160104016511056945857284491015066763920279891005475000006468850299184588761044898674190057 + i * -0.8617154614580107850842583445762891249620937505057059217237312891300367592699299810827720102713935344
comment: Multiplicity 1.
5
5
19:
0.5073918244160104016511056945857284491015066763920279891005475000006468850299184588761044898674190057 + i * 0.8617154614580107850842583445762891249620937505057059217237312891300367592699299810827720102713935344
comment: Multiplicity 1.
5
5
20:
0.7021883162595576292598228427941575426259237519540237973906766775046122590275026270579071476666417735 + i * -0.7119912699665407236957383319055941455013633245225765820787381133223797407781928221387727865042952790
comment: Multiplicity 1.
5
5
21:
0.7021883162595576292598228427941575426259237519540237973906766775046122590275026270579071476666417735 + i * 0.7119912699665407236957383319055941455013633245225765820787381133223797407781928221387727865042952790
comment: Multiplicity 1.
5
5
22:
0.8609484372911734840639291136563837244297060159059494914094132417646347378571950675143120164301397410 + i * -0.5086922334043309520615052583480193513449007890018291279876853827457118334672564885402401355643100556
comment: Multiplicity 1.
5
5
23:
0.8609484372911734840639291136563837244297060159059494914094132417646347378571950675143120164301397410 + i * 0.5086922334043309520615052583480193513449007890018291279876853827457118334672564885402401355643100556
comment: Multiplicity 1.
5
5
24:
0.9693095156112877896242278654063499995910258445012570735776420387353790062008460555503545437684954161 + i * -0.2458435741389443614964225457681647500533671513278002677736725417520647460071835526989816418478655157
comment: Multiplicity 1.
5
5
25:
0.9693095156112877896242278654063499995910258445012570735776420387353790062008460555503545437684954161 + i * 0.2458435741389443614964225457681647500533671513278002677736725417520647460071835526989816418478655157
comment: Multiplicity 1.
5
6
1:
-0.9949084196631567804446315075418100739303121996751151387058128163786543459415035644978442843512742314 + i * -0.1007831160629592291711953002150778846357573157064939053389547869561344475558530519801363784527096110
comment: Multiplicity 1.
5
6
2:
-0.9949084196631567804446315075418100739303121996751151387058128163786543459415035644978442843512742314 + i * 0.1007831160629592291711953002150778846357573157064939053389547869561344475558530519801363784527096110
comment: Multiplicity 1.
5
6
3:
-0.9557989013658811495997455193153472112390259062415079835604648961770233006414593324020698558012596223 + i * -0.2940211899638775992586103097699876918686778410883232045047801355629082058725774472431649656689069202
comment: Multiplicity 1.
5
6
4:
-0.9557989013658811495997455193153472112390259062415079835604648961770233006414593324020698558012596223 + i * 0.2940211899638775992586103097699876918686778410883232045047801355629082058725774472431649656689069202
comment: Multiplicity 1.
5
6
5:
-0.8814121319309558776269356154432223090757003092226049151325495367507431594600913327844165880199270656 + i * -0.4723480217857668028460170026220947747148093559858955690423452979800310119967747872776028650451582510
comment: Multiplicity 1.
5
6
6:
-0.8814121319309558776269356154432223090757003092226049151325495367507431594600913327844165880199270656 + i * 0.4723480217857668028460170026220947747148093559858955690423452979800310119967747872776028650451582510
comment: Multiplicity 1.
5
6
7:
-0.7738409921694105766371934405915160858386060588485225323389968558119346660742284209024740322321518849 + i * -0.6333799166679207540303080359533965790082719230205849087061258437611374407648312148707239177540820096
comment: Multiplicity 1.
5
6
8:
-0.7738409921694105766371934405915160858386060588485225323389968558119346660742284209024740322321518849 + i * 0.6333799166679207540303080359533965790082719230205849087061258437611374407648312148707239177540820096
comment: Multiplicity 1.
5
6
9:
-0.6382938656728483351270928563770877806975973287764694311579483552646966691045504864265909541761299898 + i * -0.7697927909797621934164688858977275172352767942604363617579783530852831757149550498095322165921529680
comment: Multiplicity 1.
5
6
10:
-0.6382938656728483351270928563770877806975973287764694311579483552646966691045504864265909541761299898 + i * 0.7697927909797621934164688858977275172352767942604363617579783530852831757149550498095322165921529680
comment: Multiplicity 1.
5
6
11:
-0.4772890094378351933213577250192609168652091779306321798699457040173226457934169299533079570579565727 + i * -0.8787463806297298586654730539979792246212013035133217125836092672089231961311688895900329801243366593
comment: Multiplicity 1.
5
6
12:
-0.4772890094378351933213577250192609168652091779306321798699457040173226457934169299533079570579565727 + i * 0.8787463806297298586654730539979792246212013035133217125836092672089231961311688895900329801243366593
comment: Multiplicity 1.
5
6
13:
-0.2994717642770091146906066506253417205540879882903197762864652525644939342708279111076788125012500884 + i * -0.9541051631768981719948120704894532893739692448951157224814591788793863508573629500202540735448272160
comment: Multiplicity 1.
5
6
14:
-0.2994717642770091146906066506253417205540879882903197762864652525644939342708279111076788125012500884 + i * 0.9541051631768981719948120704894532893739692448951157224814591788793863508573629500202540735448272160
comment: Multiplicity 1.
5
6
15:
-0.1100992821084267270228039079650908797536414332514086780438204134226829300842571607121857249313787789 + i * -0.9939205944537063803875426840563360005365510204985044815708758850669666446860667773024477528628754657
comment: Multiplicity 1.
5
6
16:
-0.1100992821084267270228039079650908797536414332514086780438204134226829300842571607121857249313787789 + i * 0.9939205944537063803875426840563360005365510204985044815708758850669666446860667773024477528628754657
comment: Multiplicity 1.
5
6
17:
0.08420381440227090022891493686067540637035769694587716298829671348010237738787287776907321121441139503 + i * -0.9964485524301332014641671787469908546424582094705188792061554669018412461255806699295871427141372572
comment: Multiplicity 1.
5
6
18:
0.08420381440227090022891493686067540637035769694587716298829671348010237738787287776907321121441139503 + i * 0.9964485524301332014641671787469908546424582094705188792061554669018412461255806699295871427141372572
comment: Multiplicity 1.
5
6
19:
0.2782210777421366358849235163122805207750607025976490896378198938737893077145476835421192221406462280 + i * -0.9605170648666289896667920469159224572085698863225892424504669194760157779271658363072547297747945106
comment: Multiplicity 1.
5
6
20:
0.2782210777421366358849235163122805207750607025976490896378198938737893077145476835421192221406462280 + i * 0.9605170648666289896667920469159224572085698863225892424504669194760157779271658363072547297747945106
comment: Multiplicity 1.
5
6
21:
0.4629631232556948355322637806945765104922641012596519725652101708197980399444867524319672337659692137 + i * -0.8863775417424181961518466309856954368168320324097297167591398522164317438432221883307604368216285295
comment: Multiplicity 1.
5
6
22:
0.4629631232556948355322637806945765104922641012596519725652101708197980399444867524319672337659692137 + i * 0.8863775417424181961518466309856954368168320324097297167591398522164317438432221883307604368216285295
comment: Multiplicity 1.
5
6
23:
0.6327663604648402547257720514025520274376363334260479135667097219423023851591560905087380170170259643 + i * -0.7743427749156570052895570947364376660657537447083244858591380404411555467817823526789810010747072271
comment: Multiplicity 1.
5
6
24:
0.6327663604648402547257720514025520274376363334260479135667097219423023851591560905087380170170259643 + i * 0.7743427749156570052895570947364376660657537447083244858591380404411555467817823526789810010747072271
comment: Multiplicity 1.
5
6
25:
0.7801507708054174810122253950110136481103224245007186115797190357608915459378525390692031054653512867 + i * -0.6255915399137946809331654977157410832318694907093694216457581490650867257053762848064340489555590558
comment: Multiplicity 1.
5
6
26:
0.7801507708054174810122253950110136481103224245007186115797190357608915459378525390692031054653512867 + i * 0.6255915399137946809331654977157410832318694907093694216457581490650867257053762848064340489555590558
comment: Multiplicity 1.
5
6
27:
0.8981863998531761699756530730882863474385376448752816567514055949560614009379182676471759997972476176 + i * -0.4396148213138296075867673005577622879101818148469841078949162947440365369432629827387676802956451255
comment: Multiplicity 1.
5
6
28:
0.8981863998531761699756530730882863474385376448752816567514055949560614009379182676471759997972476176 + i * 0.4396148213138296075867673005577622879101818148469841078949162947440365369432629827387676802956451255
comment: Multiplicity 1.
5
6
29:
0.9773788773988844779798521621069137386865483890862252282507119571746382112348895206841803271039810108 + i * -0.2114959338013294868355789070951402146498615159724756952340970982102977571378222373217034767952644274
comment: Multiplicity 1.
5
6
30:
0.9773788773988844779798521621069137386865483890862252282507119571746382112348895206841803271039810108 + i * 0.2114959338013294868355789070951402146498615159724756952340970982102977571378222373217034767952644274
comment: Multiplicity 1.
6
6
1:
-0.9964167907938231884749232512428559558979330757138346759920301034665021324446348953623436376614245183 + i * -0.08457883319210778042683151669545193801156198159884868934625493025623391376507742102041203095512541475
comment: Multiplicity 1.
6
6
2:
-0.9964167907938231884749232512428559558979330757138346759920301034665021324446348953623436376614245183 + i * 0.08457883319210778042683151669545193801156198159884868934625493025623391376507742102041203095512541475
comment: Multiplicity 1.
6
6
3:
-0.9689620644248055817570901232667495096693531059929727868949235323292542483710837577800496996273302198 + i * -0.2472094611976226876372338882489785620432035303811561253126161464648276910170197241979542934470377948
comment: Multiplicity 1.
6
6
4:
-0.9689620644248055817570901232667495096693531059929727868949235323292542483710837577800496996273302198 + i * 0.2472094611976226876372338882489785620432035303811561253126161464648276910170197241979542934470377948
comment: Multiplicity 1.
6
6
5:
-0.9160199205122663351992119991516864200054154097428018416337818866440440410710707676108510664552789696 + i * -0.4011327775496553272929271296473212476772493920245890764524375741016102478632082933338915752535035904
comment: Multiplicity 1.
6
6
6:
-0.9160199205122663351992119991516864200054154097428018416337818866440440410710707676108510664552789696 + i * 0.4011327775496553272929271296473212476772493920245890764524375741016102478632082933338915752535035904
comment: Multiplicity 1.
6
6
7:
-0.8394902897289078539065581503203744062074170455922423829575078336716090068540545976859691816370702958 + i * -0.5433746897407665864421462256486084486719271926009419350177619753873960017258174910858754507073901930
comment: Multiplicity 1.
6
6
8:
-0.8394902897289078539065581503203744062074170455922423829575078336716090068540545976859691816370702958 + i * 0.5433746897407665864421462256486084486719271926009419350177619753873960017258174910858754507073901930
comment: Multiplicity 1.
6
6
9:
-0.7412313437491916423695404452289093860348255554181099208471799912366233976324186729064170765069682963 + i * -0.6712496518015988482951560122269807882915127198697121410823229539213875832296107502471321327772914252
comment: Multiplicity 1.
6
6
10:
-0.7412313437491916423695404452289093860348255554181099208471799912366233976324186729064170765069682963 + i * 0.6712496518015988482951560122269807882915127198697121410823229539213875832296107502471321327772914252
comment: Multiplicity 1.
6
6
11:
-0.6234664836992205835917125214009152712852044416574371531059102384121042902038692365524525025932834681 + i * -0.7818500775108547076755311336994540193283492184247874215592278802284975639909384445945208031004760634
comment: Multiplicity 1.
6
6
12:
-0.6234664836992205835917125214009152712852044416574371531059102384121042902038692365524525025932834681 + i * 0.7818500775108547076755311336994540193283492184247874215592278802284975639909384445945208031004760634
comment: Multiplicity 1.
6
6
13:
-0.4878882101288201061311705029385201185601638717913572234946155886028452823276337934508495913930212028 + i * -0.8729061200480245676341491438924488013161706680505106345600795531859079673529961482351599693118699511
comment: Multiplicity 1.
6
6
14:
-0.4878882101288201061311705029385201185601638717913572234946155886028452823276337934508495913930212028 + i * 0.8729061200480245676341491438924488013161706680505106345600795531859079673529961482351599693118699511
comment: Multiplicity 1.
6
6
15:
-0.3409084318525184835431970019137823927949414567356975716529242534875302849224562125664112548543355692 + i * -0.9400965062651050832415870657240884531783807840935435979571848532045415366515557758955440330828459455
comment: Multiplicity 1.
6
6
16:
-0.3409084318525184835431970019137823927949414567356975716529242534875302849224562125664112548543355692 + i * 0.9400965062651050832415870657240884531783807840935435979571848532045415366515557758955440330828459455
comment: Multiplicity 1.
6
6
17:
-0.1846785953199100681369224272517321107933440793681833773403783686358367109011247248844131269326124779 + i * -0.9827989705075320697681981410113602934846245287206870272880743220496719476506357569904147514674247056
comment: Multiplicity 1.
6
6
18:
-0.1846785953199100681369224272517321107933440793681833773403783686358367109011247248844131269326124779 + i * 0.9827989705075320697681981410113602934846245287206870272880743220496719476506357569904147514674247056
comment: Multiplicity 1.
6
6
19:
-0.02270772616731906816912827440243366358278984105522972976923302358865991668783184802350621943166990109 + i * -0.9997421463419005287919454106973480329759262529015533622354893769223055857584417686615101183239950932
comment: Multiplicity 1.
6
6
20:
-0.02270772616731906816912827440243366358278984105522972976923302358865991668783184802350621943166990109 + i * 0.9997421463419005287919454106973480329759262529015533622354893769223055857584417686615101183239950932
comment: Multiplicity 1.
6
6
21:
0.1404961584919474488005576820867983812632086207602545530244865757378321650101858535069543812740507982 + i * -0.9900812236624859773400327945949152913235220460280640767098837746039483334813118376344092604739437108
comment: Multiplicity 1.
6
6
22:
0.1404961584919474488005576820867983812632086207602545530244865757378321650101858535069543812740507982 + i * 0.9900812236624859773400327945949152913235220460280640767098837746039483334813118376344092604739437108
comment: Multiplicity 1.
6
6
23:
0.3010821386845571671040329145532540774664153857977439912783935308352507386994923409509373191994385600 + i * -0.9535982098164473193526018162940581168630064418683965497739532745636325512013776884198298576356327413
comment: Multiplicity 1.
6
6
24:
0.3010821386845571671040329145532540774664153857977439912783935308352507386994923409509373191994385600 + i * 0.9535982098164473193526018162940581168630064418683965497739532745636325512013776884198298576356327413
comment: Multiplicity 1.
6
6
25:
0.4560488081192373771609960277005043662805562105861047003929094788557317756374107814176267640149170191 + i * -0.8899547654870010349919161985460400353835399011532955164459120603498271752417824097488782011224293852
comment: Multiplicity 1.
6
6
26:
0.4560488081192373771609960277005043662805562105861047003929094788557317756374107814176267640149170191 + i * 0.8899547654870010349919161985460400353835399011532955164459120603498271752417824097488782011224293852
comment: Multiplicity 1.
6
6
27:
0.5997583618132892462614009014783350246102476384936132961080365491549316821124153299261828103034967678 + i * -0.8001811716324245201623679943750036172876986803346438462746270951440182853351741941545271978856888124
comment: Multiplicity 1.
6
6
28:
0.5997583618132892462614009014783350246102476384936132961080365491549316821124153299261828103034967678 + i * 0.8001811716324245201623679943750036172876986803346438462746270951440182853351741941545271978856888124
comment: Multiplicity 1.
6
6
29:
0.7289631663874888050361920621562437787739959065492081171229070601614418507533829969302199593115053795 + i * -0.6845529212926684396886234234291449525640046135515567569655015575517527383836052371447927912203552839
comment: Multiplicity 1.
6
6
30:
0.7289631663874888050361920621562437787739959065492081171229070601614418507533829969302199593115053795 + i * 0.6845529212926684396886234234291449525640046135515567569655015575517527383836052371447927912203552839
comment: Multiplicity 1.
6
6
31:
0.8388843833895137225605923509418980447990934620870244415854675663037714913043953345953530920586252978 + i * -0.5443096465296158548393929412109864883585889250700187706220106284688937675799278056369921030926239251
comment: Multiplicity 1.
6
6
32:
0.8388843833895137225605923509418980447990934620870244415854675663037714913043953345953530920586252978 + i * 0.5443096465296158548393929412109864883585889250700187706220106284688937675799278056369921030926239251
comment: Multiplicity 1.
6
6
33:
0.9256512288102385381083527271699928207199993674401180791037387657226784657739119591046611068812786433 + i * -0.3783778569130273772734357924332719793525665385896630132105455444123156033276996309881015280916239352
comment: Multiplicity 1.
6
6
34:
0.9256512288102385381083527271699928207199993674401180791037387657226784657739119591046611068812786433 + i * 0.3783778569130273772734357924332719793525665385896630132105455444123156033276996309881015280916239352
comment: Multiplicity 1.
6
6
35:
0.9836993530662135343486534836128174550981838139706838756733295727473198498514062414145799837081768172 + i * -0.1798209742413630935514013188420053664518988353692939543865338629898108200548569141832481509956178326
comment: Multiplicity 1.
6
6
36:
0.9836993530662135343486534836128174550981838139706838756733295727473198498514062414145799837081768172 + i * 0.1798209742413630935514013188420053664518988353692939543865338629898108200548569141832481509956178326
comment: Multiplicity 1.
Definition
The Lee–Yang zeros $z_{m,n,j}$ are the distinct roots in $z$ of $P_{m,n}(z,\sqrt2-1)$, the field-fugacity polynomial of the ferromagnetic Ising model on the $m$ by $n$ vertex grid with free boundaries [1].
Parameters
$m$
—   shorter side length in vertices ($2\le m\le n$)
$n$
—   longer side length in vertices ($n\ge m$)
$j$
—   index of a distinct root ($1\le j\le r_{m,n}$, where $r_{m,n}$ is the number of distinct roots, ordered lexicographically by their exact real and imaginary parts)
Formulas
(1)
$P_{m,n}(z,b)=\sum_{S\subseteq V(G_{m,n})}z^{|S|}b^{d(S)}$, where $G_{m,n}=P_m\square P_n$, $P_m$ is a path on $m$ vertices, and $d(S)$ counts bonds with exactly one endpoint in $S$ [1].
(2)
$Z_{m,n}(K,H)=e^{KE+HN}P_{m,n}(e^{-2H},e^{-2K})$, where $Z_{m,n}(K,H)=\sum_\sigma e^{KB(\sigma)+HM(\sigma)}$ [1].
(3)
$z^NP_{m,n}(z^{-1},b)=P_{m,n}(z,b)$, $P_{m,n}(z,1)=(1+z)^N$, and $P_{m,n}(z,0)=1+z^N$.
(4)
$P_{2,2}(z,b)=1+4b^2z+(4b^2+2b^4)z^2+4b^2z^3+z^4$.
Comments
(5)
There are $N=mn$ sites and $E=2mn-m-n$ bonds, with no wraparound bonds or fixed boundary spins. Each spin is $\sigma_v\in\{-1,1\}$, all bonds have the same ferromagnetic coupling $J>0$, and each bond is counted once. The energy is $\mathcal H=-JB-hM$, where $B=\sum_{uv\in E(G_{m,n})}\sigma_u\sigma_v$ and $M=\sum_v\sigma_v$. The dimensionless coupling and field are $K=J/(k_BT)$ and $H=h/(k_BT)$; the field fugacity is $z=e^{-2H}$ and the bond weight is $b=e^{-2K}$ [1].
(6)
The fixed coupling is the infinite square lattice's bulk critical coupling $K_c$$=\tfrac12\log(1+\sqrt2)$, so $b_c=\sqrt2-1$. A finite rectangle has no thermodynamic singularity; critical coupling means this bulk value, not the location of a finite-size response maximum. Free rectangles with different aspect ratios form a finite-size Ising family [2].
(7)
Distinct roots are ordered lexicographically by $(\operatorname{Re}z,\operatorname{Im}z)$ using exact algebraic comparisons, with $j$ starting at $1$. Both conjugates and every real root are included. Each entry comment records the multiplicity; repeated roots have one index. Rectangles are ordered by $(m,n)$, with $m\le n$ omitting rotated copies.
(8)
The Lee–Yang circle theorem places these zeros on $|z|=1$ because $0<b_c<1$ [1]. Positive coefficients exclude $z=1$, and spin reversal gives the root $z=-1$ whenever $mn$ is odd.
Programs
(P1)
Sage
# With the attached generate.py in the current directory:
from generate import LeeYangZeros
g = LeeYangZeros()
g.value({'m': 6, 'n': 6, 'j': 36}, 100)
list(g.enumerate())  # every distinct root for 2 <= m <= n <= 6
References
[1]
H. Peters and G. Regts, Location of zeros for the partition function of the Ising model on bounded degree graphs, 2019, equations (1.1)-(1.2) and the Introduction. (arXiv) (doi)
[2]
X. Wu, N. Izmailian and W. Guo, Finite-size behavior of the critical Ising model on a rectangle with free boundaries, Physical Review E 86 (2012), 041149; erratum, Physical Review E 87 (2013), 019901. (arXiv) (doi)
Links
Similar tables
Fisher_zeros_of_the_Ising_model_on_finite_rectangles_with_free_boundaries —   Zeros of the same finite-rectangle partition function in the bond coordinate at zero external field.
Critical_couplings_of_the_Ising_model_on_lattices —   Bulk transition couplings, including the square-lattice coupling fixed in this table.
Critical_exponents_of_the_two-dimensional_universality_classes —   Critical exponents for the thermodynamic limit, including the two-dimensional Ising universality class.
Data properties
Entries are of type: complex number
How well the digits are known: proven
Table is complete: no (it holds every distinct zero for every rectangle with $2\le m\le n\le6$, including five squares and ten nonsquare rectangles; these discrete sizes cover ladders and intermediate aspect ratios before extending only the square sequence, and the practical, noncanonical cutoff bounds row transfer by $64$ states and the field polynomial degree by $36$)
How they were obtained:

The attached generator constructs exact integer cut counts by row transfer and substitutes $b_c$ in the positive real embedding of $\mathbb Q(\sqrt2)$. Spin-reversal symmetry reduces each polynomial to an exact polynomial in $t=z+z^{-1}$ after removing $z+1$ factors. Sage isolates all its real algebraic roots, determines their multiplicities and orders them by exact comparisons [3] [4]. Each reduced root lies in $(-2,2)$, and $z=t/2\pm i\sqrt{1-t^2/4}$ is converted to certified complex balls. The working precision is 445 bits for 100 requested decimal digits, including 112 guard bits. Every inexact component retains at least 133 decimal digits before serialization. The root $-1$ is stored exactly.

more

The attached checks independently enumerate every spin assignment for all nine rectangles with at most 16 sites. An independent edge-parity transfer verifies the zero-field even-subgraph expansion for every one of the 15 rectangles. Known four-cycle counts provide controls. Further checks establish spin-reversal symmetry, the specializations at $b=0$ and $b=1$, root multiplicities, conjugate symmetry, the unit circle, and reconstruction of every coefficient from the serialized root enclosures. The exact counts and numerical evidence are attached.



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