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Fisher zeros of the Ising model on finite rectangles with free boundaries
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Numbers
$m$
$n$
$j$ 
$b_{m,n,j}$
2
2
1:
0 + i * -2.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641573
comment: Multiplicity 1.
2
2
2:
0 + i * -0.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727
comment: Multiplicity 1.
2
2
3:
0 + i * 0.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727
comment: Multiplicity 1.
2
2
4:
0 + i * 2.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641573
comment: Multiplicity 1.
2
3
1:
-1
comment: Multiplicity 1.
2
3
2:
-0.3760858894420932720286410393918156187551122473163108902944444590597507799689994317542728773642059540 + i * -0.9265848065679415166334895496807616090580230781681989107398813869172600857321813903684660337681241365
comment: Multiplicity 1.
2
3
3:
-0.3760858894420932720286410393918156187551122473163108902944444590597507799689994317542728773642059540 + i * 0.9265848065679415166334895496807616090580230781681989107398813869172600857321813903684660337681241365
comment: Multiplicity 1.
2
3
4:
0.1118959241279502724104154530154523348283555151804687195733910518712485722048978895023709154641991517 + i * -0.3659283100347038394392151158709365150945602244423067559740111254946164377273621335034644423325034971
comment: Multiplicity 1.
2
3
5:
0.1118959241279502724104154530154523348283555151804687195733910518712485722048978895023709154641991517 + i * 0.3659283100347038394392151158709365150945602244423067559740111254946164377273621335034644423325034971
comment: Multiplicity 1.
2
3
6:
0.7641899653141429996182255863763632839267567321358421707210534071885022077641015422519019619000068023 + i * -2.499096769897741586347184015033281628392919550603163904691999914737746982715835953077016218675999194
comment: Multiplicity 1.
2
3
7:
0.7641899653141429996182255863763632839267567321358421707210534071885022077641015422519019619000068023 + i * 2.499096769897741586347184015033281628392919550603163904691999914737746982715835953077016218675999194
comment: Multiplicity 1.
2
4
1:
-1
comment: Multiplicity 2.
2
4
2:
-0.2047940572504313302745055894563902000430698943520502803456117329701958969926541839763908095983624669 + i * -1.694381773253064833143045200899301575391957459644433887641915512671969477781945409279088558322039577
comment: Multiplicity 1.
2
4
3:
-0.2047940572504313302745055894563902000430698943520502803456117329701958969926541839763908095983624669 + i * 1.694381773253064833143045200899301575391957459644433887641915512671969477781945409279088558322039577
comment: Multiplicity 1.
2
4
4:
-0.07030661966722700678257471883448226564134152866326171436465390129748836730192216430221785363894928884 + i * -0.5816880455545249912583323610771331279582569275166925667793464699285308467897597899043067700091556293
comment: Multiplicity 1.
2
4
5:
-0.07030661966722700678257471883448226564134152866326171436465390129748836730192216430221785363894928884 + i * 0.5816880455545249912583323610771331279582569275166925667793464699285308467897597899043067700091556293
comment: Multiplicity 1.
2
4
6:
0.1543790850315605588653115569262083045087192910976534785540273283854429317153373377217509677366264865 + i * -0.3375156554953382560380491851887352346272622127938007199299846265774189090601358667929884331500048025
comment: Multiplicity 1.
2
4
7:
0.1543790850315605588653115569262083045087192910976534785540273283854429317153373377217509677366264865 + i * 0.3375156554953382560380491851887352346272622127938007199299846265774189090601358667929884331500048025
comment: Multiplicity 1.
2
4
8:
1.120721591886097778191768751364664161175692131917658516156238305882241332579239010556857695500685269 + i * -2.450209383193878097922762025010903682060962744921542040792553669320857540052321486167770221462888750
comment: Multiplicity 1.
2
4
9:
1.120721591886097778191768751364664161175692131917658516156238305882241332579239010556857695500685269 + i * 2.450209383193878097922762025010903682060962744921542040792553669320857540052321486167770221462888750
comment: Multiplicity 1.
2
5
1:
-1
comment: Multiplicity 3.
2
5
2:
-0.2336189531598592598838743404801818851509592607695114276299876618392599912544150107602300892568471076 + i * -0.9723282289044638680969873469123042777613469520096674538706843934588552500864826731390699725897459240
comment: Multiplicity 1.
2
5
3:
-0.2336189531598592598838743404801818851509592607695114276299876618392599912544150107602300892568471076 + i * 0.9723282289044638680969873469123042777613469520096674538706843934588552500864826731390699725897459240
comment: Multiplicity 1.
2
5
4:
0.04540909939731060963388893425746474783738391686349217537695506181349081536860224971641817070337467527 + i * -0.4777653389603127530512477482985863130575668599838814890824432686272118877403639101070069867994159944
comment: Multiplicity 1.
2
5
5:
0.04540909939731060963388893425746474783738391686349217537695506181349081536860224971641817070337467527 + i * 0.4777653389603127530512477482985863130575668599838814890824432686272118877403639101070069867994159944
comment: Multiplicity 1.
2
5
6:
0.1752104141510476192347389667242876217944624605259672930004658604084823575404196786984145102078602401 + i * -0.3200869779879678454771978732607652439806523690662465060558729791388230361986935051630778875937226740
comment: Multiplicity 1.
2
5
7:
0.1752104141510476192347389667242876217944624605259672930004658604084823575404196786984145102078602401 + i * 0.3200869779879678454771978732607652439806523690662465060558729791388230361986935051630778875937226740
comment: Multiplicity 1.
2
5
8:
0.1971551023144684246718844389700398871451926456815426284708508768862521093583620941324787956889365250 + i * -2.074339186092861733974905023542074350928712658046102248615418892139962262481628571190325914646692035
comment: Multiplicity 1.
2
5
9:
0.1971551023144684246718844389700398871451926456815426284708508768862521093583620941324787956889365250 + i * 2.074339186092861733974905023542074350928712658046102248615418892139962262481628571190325914646692035
comment: Multiplicity 1.
2
5
10:
1.315844337297032606343362000528389628373920237698509330781715862731034708987030988212918612656675667 + i * -2.403879012950036241014424515034382746536830360600038909021298429687718673353464074922422576795435215
comment: Multiplicity 1.
2
5
11:
1.315844337297032606343362000528389628373920237698509330781715862731034708987030988212918612656675667 + i * 2.403879012950036241014424515034382746536830360600038909021298429687718673353464074922422576795435215
comment: Multiplicity 1.
2
6
1:
-1
comment: Multiplicity 4.
2
6
2:
-0.1739958578126563838253824094278421482148717317790626198328224578257764417230981880794130135065646223 + i * -1.436974610823395744106007683545509213906374662723042456321700352670126545539671054241391152788283947
comment: Multiplicity 1.
2
6
3:
-0.1739958578126563838253824094278421482148717317790626198328224578257764417230981880794130135065646223 + i * 1.436974610823395744106007683545509213906374662723042456321700352670126545539671054241391152788283947
comment: Multiplicity 1.
2
6
4:
-0.08304615318011059762007308110289651108146000452992620697698123012961418969318821241712411113382889082 + i * -0.6858508883289584999257339691775099630557076549836476916707453132539007353536775850210932046170899930
comment: Multiplicity 1.
2
6
5:
-0.08304615318011059762007308110289651108146000452992620697698123012961418969318821241712411113382889082 + i * 0.6858508883289584999257339691775099630557076549836476916707453132539007353536775850210932046170899930
comment: Multiplicity 1.
2
6
6:
0.1010424276673775088772951980248590856289846775068551506418674364993568012879413677967745294558704129 + i * -0.4231271371350168284414199940685066113174690869459050204080221231773041937645518351537595863049011330
comment: Multiplicity 1.
2
6
7:
0.1010424276673775088772951980248590856289846775068551506418674364993568012879413677967745294558704129 + i * 0.4231271371350168284414199940685066113174690869459050204080221231773041937645518351537595863049011330
comment: Multiplicity 1.
2
6
8:
0.1869165176768707182846711206410519813832056572524097725099099588529322378839139321869656677177030337 + i * -0.3087116593710191085426690249136401275571856092130277475402436210367213218289219620281077163498478741
comment: Multiplicity 1.
2
6
9:
0.1869165176768707182846711206410519813832056572524097725099099588529322378839139321869656677177030337 + i * 0.3087116593710191085426690249136401275571856092130277475402436210367213218289219620281077163498478741
comment: Multiplicity 1.
2
6
10:
0.5339206615619256037456198638003260239834787815072053924675261624321493139333791901738059086635133723 + i * -2.235856028000710801492508006967089096332366902779595701117665345237025280460349887057062496360492827
comment: Multiplicity 1.
2
6
11:
0.5339206615619256037456198638003260239834787815072053924675261624321493139333791901738059086635133723 + i * 2.235856028000710801492508006967089096332366902779595701117665345237025280460349887057062496360492827
comment: Multiplicity 1.
2
6
12:
1.435162404086593150537869308064501568300662620042518511190500130170952278311051910338991018803306694 + i * -2.370316827742275837413483323444223361721416417307323663598931803680216598338726544711112678234245615
comment: Multiplicity 1.
2
6
13:
1.435162404086593150537869308064501568300662620042518511190500130170952278311051910338991018803306694 + i * 2.370316827742275837413483323444223361721416417307323663598931803680216598338726544711112678234245615
comment: Multiplicity 1.
3
3
1:
-1
comment: Multiplicity 4.
3
3
2:
0.07832859875695279362931399949703201071178978455551420171437573958953798988010253960393022502054619079 + i * -0.5991017827424800107797909405027372644322028449932430626432188580932964121986333089961924145940881162
comment: Multiplicity 1.
3
3
3:
0.07832859875695279362931399949703201071178978455551420171437573958953798988010253960393022502054619079 + i * 0.5991017827424800107797909405027372644322028449932430626432188580932964121986333089961924145940881162
comment: Multiplicity 1.
3
3
4:
0.2012486345108661236597488252803140211889768865935676090649734826757262044890435424581499863298732844 + i * -0.3051930646596968102743329485273253382991436069606031900017784693315105894517713240497350320516831025
comment: Multiplicity 1.
3
3
5:
0.2012486345108661236597488252803140211889768865935676090649734826757262044890435424581499863298732844 + i * 0.3051930646596968102743329485273253382991436069606031900017784693315105894517713240497350320516831025
comment: Multiplicity 1.
3
3
6:
0.2145646200564996819698416383981189500033742777560117616972843914150957708888439409708760078156330228 + i * -1.641112549302454165060621193617305774821561797258625093494027428273875378988919456277603721563656598
comment: Multiplicity 1.
3
3
7:
0.2145646200564996819698416383981189500033742777560117616972843914150957708888439409708760078156330228 + i * 1.641112549302454165060621193617305774821561797258625093494027428273875378988919456277603721563656598
comment: Multiplicity 1.
3
3
8:
1.505858146675681400741095536824535018095859051094906427523366386319640034742009976967043780833947502 + i * -2.283630216143942227572199667578769445134451033192098412178503042032854551632896955598412252293796151
comment: Multiplicity 1.
3
3
9:
1.505858146675681400741095536824535018095859051094906427523366386319640034742009976967043780833947502 + i * 2.283630216143942227572199667578769445134451033192098412178503042032854551632896955598412252293796151
comment: Multiplicity 1.
3
4
1:
-1
comment: Multiplicity 5.
3
4
2:
-0.2252906317750145982810522684281535085379424629884409994649481310151576373943580854134299861882244512 + i * -1.293980400880815320432570035064108099179799164612973182760794092894411172412312970455801376969493691
comment: Multiplicity 1.
3
4
3:
-0.2252906317750145982810522684281535085379424629884409994649481310151576373943580854134299861882244512 + i * 1.293980400880815320432570035064108099179799164612973182760794092894411172412312970455801376969493691
comment: Multiplicity 1.
3
4
4:
-0.1305925791725553193334433406838510983974638452372522472744370997046046555246792640683254756261541500 + i * -0.7500721917213053003279616469559508008016039513185077893221871244985464439926047504894890497929682443
comment: Multiplicity 1.
3
4
5:
-0.1305925791725553193334433406838510983974638452372522472744370997046046555246792640683254756261541500 + i * 0.7500721917213053003279616469559508008016039513185077893221871244985464439926047504894890497929682443
comment: Multiplicity 1.
3
4
6:
0.1665781963347655757739856162172871230459366046318394993247482495984870229732216789210983309643923984 + i * -0.4830412586755967097405570569902759584068118277465594109600030383062410789987243474939623310171182469
comment: Multiplicity 1.
3
4
7:
0.1665781963347655757739856162172871230459366046318394993247482495984870229732216789210983309643923984 + i * 0.4830412586755967097405570569902759584068118277465594109600030383062410789987243474939623310171182469
comment: Multiplicity 1.
3
4
8:
0.2363654686028115443181050427698281158587090185593005553728277384794838923881573801357644684027544955 + i * -0.2727042853617133475941974982486088470162988755343415532858007098694414682728389990264496841449952009
comment: Multiplicity 1.
3
4
9:
0.2363654686028115443181050427698281158587090185593005553728277384794838923881573801357644684027544955 + i * 0.2727042853617133475941974982486088470162988755343415532858007098694414682728389990264496841449952009
comment: Multiplicity 1.
3
4
10:
0.6380420284635378727312479786209885269823675764579024079738058568609222497033988594436514262472245923 + i * -1.850185866447849509731742820976556804644571716358728455180631101353992038242427503749885327176131485
comment: Multiplicity 1.
3
4
11:
0.6380420284635378727312479786209885269823675764579024079738058568609222497033988594436514262472245923 + i * 1.850185866447849509731742820976556804644571716358728455180631101353992038242427503749885327176131485
comment: Multiplicity 1.
3
4
12:
1.814897517546454924791156971503900841048393108576650784068003385780869127854259430981241236200007115 + i * -2.093919782161303628325025466354806594542188884599789055656632441197895085780577794398578027385351884
comment: Multiplicity 1.
3
4
13:
1.814897517546454924791156971503900841048393108576650784068003385780869127854259430981241236200007115 + i * 2.093919782161303628325025466354806594542188884599789055656632441197895085780577794398578027385351884
comment: Multiplicity 1.
3
5
1:
-1
comment: Multiplicity 6.
3
5
2:
-0.6620598938904628088396601401838918430490477558679081768541838047646064794357822430808395764307697056 + i * -0.7494509302827965176088129095848119002273982175705804974026752022854904134425618329706124002862247188
comment: Multiplicity 1.
3
5
3:
-0.6620598938904628088396601401838918430490477558679081768541838047646064794357822430808395764307697056 + i * 0.7494509302827965176088129095848119002273982175705804974026752022854904134425618329706124002862247188
comment: Multiplicity 1.
3
5
4:
-0.1609817068083379258795307225450275635808096534560491240291251891094236532480150419742921946695966186 + i * -0.9869573902013573385578825279398547144744071681339474621853905820703821088832837572781642374377908151
comment: Multiplicity 1.
3
5
5:
-0.1609817068083379258795307225450275635808096534560491240291251891094236532480150419742921946695966186 + i * 0.9869573902013573385578825279398547144744071681339474621853905820703821088832837572781642374377908151
comment: Multiplicity 1.
3
5
6:
0.1139218137679146918860398343286572933332888184828199672174656456412103862023071483302326952211870843 + i * -0.5928038518459902011144598197837521443401386662154336245845148159121067565145611448457603603780035852
comment: Multiplicity 1.
3
5
7:
0.1139218137679146918860398343286572933332888184828199672174656456412103862023071483302326952211870843 + i * 0.5928038518459902011144598197837521443401386662154336245845148159121067565145611448457603603780035852
comment: Multiplicity 1.
3
5
8:
0.2011041400682613081588122402080480808170617037507320767791408719944261316783851503008765327661602519 + i * -0.4094966991611014955737978385678811429810584151222052627606311767889172404237507273582069526425004758
comment: Multiplicity 1.
3
5
9:
0.2011041400682613081588122402080480808170617037507320767791408719944261316783851503008765327661602519 + i * 0.4094966991611014955737978385678811429810584151222052627606311767889172404237507273582069526425004758
comment: Multiplicity 1.
3
5
10:
0.2538815005312574151150539821959085773270706165044569832460397780501351495367125581377999884012578892 + i * -0.2531301129449332414801329777866988359712818655918959300857975152380048343868321353028631153006301320
comment: Multiplicity 1.
3
5
11:
0.2538815005312574151150539821959085773270706165044569832460397780501351495367125581377999884012578892 + i * 0.2531301129449332414801329777866988359712818655918959300857975152380048343868321353028631153006301320
comment: Multiplicity 1.
3
5
12:
0.3126331126060691540048277219535788632377934925877480123181089072747082400523335199255125972650641724 + i * -1.626818492769432739325095618247127277156738195653621745401440257498461946796857688786188046591973328
comment: Multiplicity 1.
3
5
13:
0.3126331126060691540048277219535788632377934925877480123181089072747082400523335199255125972650641724 + i * 1.626818492769432739325095618247127277156738195653621745401440257498461946796857688786188046591973328
comment: Multiplicity 1.
3
5
14:
0.9662409673309621254224928415823162115022042557854829967839705037082040256191726045468019819163108867 + i * -1.967500453158023206486964348012649305555198355988018074254653754118386489924400861862583049674076996
comment: Multiplicity 1.
3
5
15:
0.9662409673309621254224928415823162115022042557854829967839705037082040256191726045468019819163108867 + i * 1.967500453158023206486964348012649305555198355988018074254653754118386489924400861862583049674076996
comment: Multiplicity 1.
3
5
16:
1.975260066394336040131964242460410380412438522212717264538583287205346199594886303813907975530386040 + i * -1.969414087500462924206114119080500059763425888350795997825692815319135960911308387843364985543363668
comment: Multiplicity 1.
3
5
17:
1.975260066394336040131964242460410380412438522212717264538583287205346199594886303813907975530386040 + i * 1.969414087500462924206114119080500059763425888350795997825692815319135960911308387843364985543363668
comment: Multiplicity 1.
3
6
1:
-1
comment: Multiplicity 7.
3
6
2:
-0.6549036169338613981173238925277483037836869175789987077524333116036255918205984414756812904284182449 + i * -0.8014819459401238696658775995101276816607023071560066278068833266513339326254280041091516917033595887
comment: Multiplicity 1.
3
6
3:
-0.6549036169338613981173238925277483037836869175789987077524333116036255918205984414756812904284182449 + i * 0.8014819459401238696658775995101276816607023071560066278068833266513339326254280041091516917033595887
comment: Multiplicity 1.
3
6
4:
-0.6113326792837744483649438140280840893638668157813378641547965563129718397207755145512390497137174106 + i * -0.7481591072944576411776859223309985702687610231987147709787372734618679190233679977918531300330385470
comment: Multiplicity 1.
3
6
5:
-0.6113326792837744483649438140280840893638668157813378641547965563129718397207755145512390497137174106 + i * 0.7481591072944576411776859223309985702687610231987147709787372734618679190233679977918531300330385470
comment: Multiplicity 1.
3
6
6:
0.05166393126598495098499913677115383355464901728930775043599608106828281107486495663860913131295643258 + i * -0.7200051812155994505291745091442172837368370389333335436777880878000506043893336791623678873986171304
comment: Multiplicity 1.
3
6
7:
0.05166393126598495098499913677115383355464901728930775043599608106828281107486495663860913131295643258 + i * 0.7200051812155994505291745091442172837368370389333335436777880878000506043893336791623678873986171304
comment: Multiplicity 1.
3
6
8:
0.09914843423838190585719581426733565886509088276639694592528521155312088267391678920933447679583387029 + i * -1.381764504011910075987807036564949602455844502359095523289166942542683021987240594270134376741153145
comment: Multiplicity 1.
3
6
9:
0.09914843423838190585719581426733565886509088276639694592528521155312088267391678920933447679583387029 + i * 1.381764504011910075987807036564949602455844502359095523289166942542683021987240594270134376741153145
comment: Multiplicity 1.
3
6
10:
0.1839610092100474573952288659912279247747259994182922369199343007634348284588179773976212844208809448 + i * -0.5092888502168081105784293380364574957453581363160007858121803743218877529097850921108047038839492775
comment: Multiplicity 1.
3
6
11:
0.1839610092100474573952288659912279247747259994182922369199343007634348284588179773976212844208809448 + i * 0.5092888502168081105784293380364574957453581363160007858121803743218877529097850921108047038839492775
comment: Multiplicity 1.
3
6
12:
0.2224342864073614413204319958965192223440766754481682068750713855292581825064397247372748306479068838 + i * -0.3590796453450027520971348063308213975234049111560083123001906117033668302519147967593097300258627039
comment: Multiplicity 1.
3
6
13:
0.2224342864073614413204319958965192223440766754481682068750713855292581825064397247372748306479068838 + i * 0.3590796453450027520971348063308213975234049111560083123001906117033668302519147967593097300258627039
comment: Multiplicity 1.
3
6
14:
0.2637756558400353460873063307920588515745725286541327677626191764420729524167899119557996447382601587 + i * -0.2403747997848321340453643454926778137363565421508410646393391056353073993327445644902990449787308322
comment: Multiplicity 1.
3
6
15:
0.2637756558400353460873063307920588515745725286541327677626191764420729524167899119557996447382601587 + i * 0.2403747997848321340453643454926778137363565421508410646393391056353073993327445644902990449787308322
comment: Multiplicity 1.
3
6
16:
0.6273890789284813572891151576202285797005368912669303470248966753091855289575349629930463254597304957 + i * -1.736902096907049875446543436788252255911636208234531133292711394731294210452432919610970861805610575
comment: Multiplicity 1.
3
6
17:
0.6273890789284813572891151576202285797005368912669303470248966753091855289575349629930463254597304957 + i * 1.736902096907049875446543436788252255911636208234531133292711394731294210452432919610970861805610575
comment: Multiplicity 1.
3
6
18:
1.246722712417044197644541066931109182438436108426560514466010362376136240129477277218947619787868204 + i * -2.012606764221652848252059853458542408348424865616193809455623504813862774560034198465383465364304709
comment: Multiplicity 1.
3
6
19:
1.246722712417044197644541066931109182438436108426560514466010362376136240129477277218947619787868204 + i * 2.012606764221652848252059853458542408348424865616193809455623504813862774560034198465383465364304709
comment: Multiplicity 1.
3
6
20:
2.071141187910299189903449338286199139895465630090547802497416674875106005323532355876287026978698666 + i * -1.887399907260489683625580299084352884948164317096463341944044389014862074970907691656444097546318783
comment: Multiplicity 1.
3
6
21:
2.071141187910299189903449338286199139895465630090547802497416674875106005323532355876287026978698666 + i * 1.887399907260489683625580299084352884948164317096463341944044389014862074970907691656444097546318783
comment: Multiplicity 1.
4
4
1:
-1.321883732568269187407173539204991509076806508908538102495105359001200640671081936527630216327463396 + i * -0.8132115383218487041620205392136454915632786995384549260299660477120276705589606444927361512066733463
comment: Multiplicity 1.
4
4
2:
-1.321883732568269187407173539204991509076806508908538102495105359001200640671081936527630216327463396 + i * 0.8132115383218487041620205392136454915632786995384549260299660477120276705589606444927361512066733463
comment: Multiplicity 1.
4
4
3:
-1
comment: Multiplicity 4.
4
4
4:
-0.5487978724655304179628844013562528896374626316891958351989475329570120435926188234433176730838006483 + i * -0.3376157456967592833757034868237046705680630358117192559660402362548874353566601685535203890404089860
comment: Multiplicity 1.
4
4
5:
-0.5487978724655304179628844013562528896374626316891958351989475329570120435926188234433176730838006483 + i * 0.3376157456967592833757034868237046705680630358117192559660402362548874353566601685535203890404089860
comment: Multiplicity 1.
4
4
6:
-0.1113168514638524458291198533428041948562521829991965027922869066531716753948051095208703483833014729 + i * -1.761645812565209289515900633392864722956941681807162501240469067641243039080605231170933508367942534
comment: Multiplicity 1.
4
4
7:
-0.1113168514638524458291198533428041948562521829991965027922869066531716753948051095208703483833014729 + i * 1.761645812565209289515900633392864722956941681807162501240469067641243039080605231170933508367942534
comment: Multiplicity 1.
4
4
8:
-0.03572671585171037700310539953341546973698409843178586951741974019262705937480227372077128794023829605 + i * -0.5653934561499007268614950932581716081652852166556043103296422974097979742027309773249729464181215910
comment: Multiplicity 1.
4
4
9:
-0.03572671585171037700310539953341546973698409843178586951741974019262705937480227372077128794023829605 + i * 0.5653934561499007268614950932581716081652852166556043103296422974097979742027309773249729464181215910
comment: Multiplicity 1.
4
4
10:
0.1127819945265776311216551706735581724406138695550352351440206551030461080100242894288680213377750659 + i * -0.6603391820064359256535127309709759682934373852628633585605953106278997196981386090332539648101954711
comment: Multiplicity 1.
4
4
11:
0.1127819945265776311216551706735581724406138695550352351440206551030461080100242894288680213377750659 + i * 0.6603391820064359256535127309709759682934373852628633585605953106278997196981386090332539648101954711
comment: Multiplicity 1.
4
4
12:
0.2385024398468503574515457942539274654415127078232986617492187252118955805015804160421865680457274623 + i * -0.4091492654587910378260753820406483546080063199039013390939271627392524969833583822600446389820040626
comment: Multiplicity 1.
4
4
13:
0.2385024398468503574515457942539274654415127078232986617492187252118955805015804160421865680457274623 + i * 0.4091492654587910378260753820406483546080063199039013390939271627392524969833583822600446389820040626
comment: Multiplicity 1.
4
4
14:
0.2513149146978025191660807341777935283863609635054748719479520400813146477770566361700908889783645177 + i * -1.471450171582632163293260606973259128827825886409529011066327127974043697016517483926755647842681044
comment: Multiplicity 1.
4
4
15:
0.2513149146978025191660807341777935283863609635054748719479520400813146477770566361700908889783645177 + i * 1.471450171582632163293260606973259128827825886409529011066327127974043697016517483926755647842681044
comment: Multiplicity 1.
4
4
16:
0.2698268914413946676582043865241992972425771883199284859023817095681364369731973012446519113188347325 + i * -0.2383244010982853161513117136423944102222576283304054438814569673951006385788911197212145851327441245
comment: Multiplicity 1.
4
4
17:
0.2698268914413946676582043865241992972425771883199284859023817095681364369731973012446519113188347325 + i * 0.2383244010982853161513117136423944102222576283304054438814569673951006385788911197212145851327441245
comment: Multiplicity 1.
4
4
18:
1.063382782178043608141704680187675533745508578295578346866033523500188018217167159749346160726839694 + i * -1.824225716554730626944635471222718187155425899965025267136449548425299099678668202742847441302846960
comment: Multiplicity 1.
4
4
19:
1.063382782178043608141704680187675533745508578295578346866033523500188018217167159749346160726839694 + i * 1.824225716554730626944635471222718187155425899965025267136449548425299099678668202742847441302846960
comment: Multiplicity 1.
4
4
20:
2.081916149658693644663092427620310066050932114529400708394152885339430627554282340577445975327262340 + i * -1.838850890116053432053204544628342821251625871303011707902647987905545418536996564317068828015176981
comment: Multiplicity 1.
4
4
21:
2.081916149658693644663092427620310066050932114529400708394152885339430627554282340577445975327262340 + i * 1.838850890116053432053204544628342821251625871303011707902647987905545418536996564317068828015176981
comment: Multiplicity 1.
4
5
1:
-1.139231934917025469654566593753700091079572717505258874503337165396160455696955108496180309622850030 + i * -1.036634105572539516615375929457985064670513016509314959407010473325160368972853886488558914989256439
comment: Multiplicity 1.
4
5
2:
-1.139231934917025469654566593753700091079572717505258874503337165396160455696955108496180309622850030 + i * 1.036634105572539516615375929457985064670513016509314959407010473325160368972853886488558914989256439
comment: Multiplicity 1.
4
5
3:
-1
comment: Multiplicity 7.
4
5
4:
-0.4801902216271983661476379717627415804292790140577088669461249307508229493331037544014481918843336430 + i * -0.4369448798303267328206951767436365462248471827351174665164018257193228143236831025974780784930768093
comment: Multiplicity 1.
4
5
5:
-0.4801902216271983661476379717627415804292790140577088669461249307508229493331037544014481918843336430 + i * 0.4369448798303267328206951767436365462248471827351174665164018257193228143236831025974780784930768093
comment: Multiplicity 1.
4
5
6:
-0.06403900357635011602581511514610967456379160555485051666892909655728284984686897726440642689006008562 + i * -1.208184865784237851238687822348085421384173757683534703742504924258968708398404941758862541540019620
comment: Multiplicity 1.
4
5
7:
-0.06403900357635011602581511514610967456379160555485051666892909655728284984686897726440642689006008562 + i * 1.208184865784237851238687822348085421384173757683534703742504924258968708398404941758862541540019620
comment: Multiplicity 1.
4
5
8:
-0.04374811675308561442815095177602286564273696223882752247768569857611749159624248279572474629324861195 + i * -0.8253690659727846409783055854557571042728236321117236603551108778201320963905654709878354253622891485
comment: Multiplicity 1.
4
5
9:
-0.04374811675308561442815095177602286564273696223882752247768569857611749159624248279572474629324861195 + i * 0.8253690659727846409783055854557571042728236321117236603551108778201320963905654709878354253622891485
comment: Multiplicity 1.
4
5
10:
0.07245838010142785358606880707996480157148093558615743536153490872018075542740688712963385774256559161 + i * -0.5425041642584351471193490913012954839980247146259789595290253835595644260436575058264495484237617571
comment: Multiplicity 1.
4
5
11:
0.07245838010142785358606880707996480157148093558615743536153490872018075542740688712963385774256559161 + i * 0.5425041642584351471193490913012954839980247146259789595290253835595644260436575058264495484237617571
comment: Multiplicity 1.
4
5
12:
0.1902189846138320767268075547787231501501358445310181741248033351407596931394776297233427485237727967 + i * -0.5199190372143699521140343143537664985003462498187310329419843621893007357113276007964057799539250026
comment: Multiplicity 1.
4
5
13:
0.1902189846138320767268075547787231501501358445310181741248033351407596931394776297233427485237727967 + i * 0.5199190372143699521140343143537664985003462498187310329419843621893007357113276007964057799539250026
comment: Multiplicity 1.
4
5
14:
0.2418818995435892207896298579327862773585855549950212394394564153386010013557430704885925363147206360 + i * -1.810997397091296510369358656252503843731596220128576043630027307392090881041766383640567266954867515
comment: Multiplicity 1.
4
5
15:
0.2418818995435892207896298579327862773585855549950212394394564153386010013557430704885925363147206360 + i * 1.810997397091296510369358656252503843731596220128576043630027307392090881041766383640567266954867515
comment: Multiplicity 1.
4
5
16:
0.2659461034909066407292828603087565650728758364778963939655281522969449339167546574194354189300430500 + i * -0.3582953201032266146402688417720570781588823034758281908812737176582468699010715643465718463294918583
comment: Multiplicity 1.
4
5
17:
0.2659461034909066407292828603087565650728758364778963939655281522969449339167546574194354189300430500 + i * 0.3582953201032266146402688417720570781588823034758281908812737176582468699010715643465718463294918583
comment: Multiplicity 1.
4
5
18:
0.2869845160491528430246287650728199572132797491834433987982023708239358994078959756078207040028886519 + i * -0.2174831108260953147969478493248750891595379091334046575618018721353307589680305830419261477777901555
comment: Multiplicity 1.
4
5
19:
0.2869845160491528430246287650728199572132797491834433987982023708239358994078959756078207040028886519 + i * 0.2174831108260953147969478493248750891595379091334046575618018721353307589680305830419261477777901555
comment: Multiplicity 1.
4
5
20:
0.6206184777294495149926170242128111459306734148408026039602604068757652163902309520899242635245390908 + i * -1.696315234116120548652527975596810064437542843088155552147650761208951089322319613698443026223833255
comment: Multiplicity 1.
4
5
21:
0.6206184777294495149926170242128111459306734148408026039602604068757652163902309520899242635245390908 + i * 1.696315234116120548652527975596810064437542843088155552147650761208951089322319613698443026223833255
comment: Multiplicity 1.
4
5
22:
1.335722123642678075689259610158485275985161582553924855807840598537109964060173672004370027119487875 + i * -1.799548779160356915264589674621993654106957571310211784672560115808649498070787651200952597731150581
comment: Multiplicity 1.
4
5
23:
1.335722123642678075689259610158485275985161582553924855807840598537109964060173672004370027119487875 + i * 1.799548779160356915264589674621993654106957571310211784672560115808649498070787651200952597731150581
comment: Multiplicity 1.
4
5
24:
2.213378791702623340717876152894227038433187381188381679138450703547086282775487478494640118532474679 + i * -1.677346609785540535523868180324375175068117835896386634389655278987208206003452749823699797894818729
comment: Multiplicity 1.
4
5
25:
2.213378791702623340717876152894227038433187381188381679138450703547086282775487478494640118532474679 + i * 1.677346609785540535523868180324375175068117835896386634389655278987208206003452749823699797894818729
comment: Multiplicity 1.
4
6
1:
-1.471580340364302081833948997201407901330259186951032092919222871836572677050904691227074884722279723 + i * -0.7288811976881560779287581001967784127827289612639301558913611568686028870461512421310423166393082227
comment: Multiplicity 1.
4
6
2:
-1.471580340364302081833948997201407901330259186951032092919222871836572677050904691227074884722279723 + i * 0.7288811976881560779287581001967784127827289612639301558913611568686028870461512421310423166393082227
comment: Multiplicity 1.
4
6
3:
-1
comment: Multiplicity 6.
4
6
4:
-0.8117927742039103151444909914525029519589624780369312596422669109561038160263910945984928314404228535 + i * -1.105481043759721835828421600746341512923104410197838947162565551324871346279567208718326264322810690
comment: Multiplicity 1.
4
6
5:
-0.8117927742039103151444909914525029519589624780369312596422669109561038160263910945984928314404228535 + i * 1.105481043759721835828421600746341512923104410197838947162565551324871346279567208718326264322810690
comment: Multiplicity 1.
4
6
6:
-0.5456731450538992450826323564446112424298025724841366424639219006357215680392932439299327275398027690 + i * -0.2702746731549073131183882120065864882080186403652592500094392075046002059313205137420618514507603725
comment: Multiplicity 1.
4
6
7:
-0.5456731450538992450826323564446112424298025724841366424639219006357215680392932439299327275398027690 + i * 0.2702746731549073131183882120065864882080186403652592500094392075046002059313205137420618514507603725
comment: Multiplicity 1.
4
6
8:
-0.4315531161126116948678093026860277800686138657284845297998528771377071682405385297919363061529948453 + i * -0.5876792752999998264294772800374803313714045898527793618774739198846145797789886856332750278991664673
comment: Multiplicity 1.
4
6
9:
-0.4315531161126116948678093026860277800686138657284845297998528771377071682405385297919363061529948453 + i * 0.5876792752999998264294772800374803313714045898527793618774739198846145797789886856332750278991664673
comment: Multiplicity 1.
4
6
10:
-0.1690344260982571993602810244853303212198720276814387376273337902730885625182751536173921496983258550 + i * -1.230219852123643090571783050133331514453256851281879115343925197011487746014149293504337254995418125
comment: Multiplicity 1.
4
6
11:
-0.1690344260982571993602810244853303212198720276814387376273337902730885625182751536173921496983258550 + i * 1.230219852123643090571783050133331514453256851281879115343925197011487746014149293504337254995418125
comment: Multiplicity 1.
4
6
12:
-0.1096192891387398079296245700146533886232036573308626423977633066143553730305889078058599781584247408 + i * -0.7978009497057698454161371976972025809579019674640143826687042001309194196333754727005100616814896112
comment: Multiplicity 1.
4
6
13:
-0.1096192891387398079296245700146533886232036573308626423977633066143553730305889078058599781584247408 + i * 0.7978009497057698454161371976972025809579019674640143826687042001309194196333754727005100616814896112
comment: Multiplicity 1.
4
6
14:
0.1057013977874212621252275021877329823785539258329113330647091218321155312837992491640935880606097817 + i * -0.6256604794808111698450402164414299217307405333165691131575734589235518720955633843223661634127173549
comment: Multiplicity 1.
4
6
15:
0.1057013977874212621252275021877329823785539258329113330647091218321155312837992491640935880606097817 + i * 0.6256604794808111698450402164414299217307405333165691131575734589235518720955633843223661634127173549
comment: Multiplicity 1.
4
6
16:
0.1308744031787449198075072827443481047665729866845424747940604015608314667988024853237188178467276050 + i * -0.5499851819996014677163975157355909890434435945248031325580655902454905665716227494502364190591396311
comment: Multiplicity 1.
4
6
17:
0.1308744031787449198075072827443481047665729866845424747940604015608314667988024853237188178467276050 + i * 0.5499851819996014677163975157355909890434435945248031325580655902454905665716227494502364190591396311
comment: Multiplicity 1.
4
6
18:
0.2429935316406965782904510991032178231171556854942176487410154837227920469561719994527150790004563642 + i * -0.4358793386389523661371294621130327420557054915539695523667225092155229912064222401691962227571420303
comment: Multiplicity 1.
4
6
19:
0.2429935316406965782904510991032178231171556854942176487410154837227920469561719994527150790004563642 + i * 0.4358793386389523661371294621130327420557054915539695523667225092155229912064222401691962227571420303
comment: Multiplicity 1.
4
6
20:
0.2625314058773632171828912009774215624810783999358913908164966130863156433940887179615113425598501132 + i * -1.553957929774409734131663901655872853191730791603413970649172385551252273392372106074210038706565927
comment: Multiplicity 1.
4
6
21:
0.2625314058773632171828912009774215624810783999358913908164966130863156433940887179615113425598501132 + i * 1.553957929774409734131663901655872853191730791603413970649172385551252273392372106074210038706565927
comment: Multiplicity 1.
4
6
22:
0.2781750635121444834066828326032669690091020243865914695485032206340793494925539153316255896939265592 + i * -0.3200134670824251787524232639591551817111086072624296305856349189572336113302626623887269555106071549
comment: Multiplicity 1.
4
6
23:
0.2781750635121444834066828326032669690091020243865914695485032206340793494925539153316255896939265592 + i * 0.3200134670824251787524232639591551817111086072624296305856349189572336113302626623887269555106071549
comment: Multiplicity 1.
4
6
24:
0.2968696273443089019652743779124911250418660792002637086916158743235671276922857911808603736978603553 + i * -0.2037753109162835907281154921135807068720727751927445562334090716554271650494112443781338661327262283
comment: Multiplicity 1.
4
6
25:
0.2968696273443089019652743779124911250418660792002637086916158743235671276922857911808603736978603553 + i * 0.2037753109162835907281154921135807068720727751927445562334090716554271650494112443781338661327262283
comment: Multiplicity 1.
4
6
26:
0.4094792468706908473401480528469077365352620230867296732055331284484842853179529322733999327542951478 + i * -1.720791175701897679215854498612043094240994983873365696766513900314803942512692181146643123574405964
comment: Multiplicity 1.
4
6
27:
0.4094792468706908473401480528469077365352620230867296732055331284484842853179529322733999327542951478 + i * 1.720791175701897679215854498612043094240994983873365696766513900314803942512692181146643123574405964
comment: Multiplicity 1.
4
6
28:
0.9757340032995193407257768400737567198851894609558316995698297276620225663457868943235460850343319853 + i * -1.750261783406674807080483254018530876426869887332354571453663207862073732015556269090760969536929822
comment: Multiplicity 1.
4
6
29:
0.9757340032995193407257768400737567198851894609558316995698297276620225663457868943235460850343319853 + i * 1.750261783406674807080483254018530876426869887332354571453663207862073732015556269090760969536929822
comment: Multiplicity 1.
4
6
30:
1.547222240423988313914874944062430011543289135145233880016935333217719738169743869177027751559679091 + i * -1.779929326711564848323432731240017275639920709186271912313001914050267991797073049843022731085740256
comment: Multiplicity 1.
4
6
31:
1.547222240423988313914874944062430011543289135145233880016935333217719738169743869177027751559679091 + i * 1.779929326711564848323432731240017275639920709186271912313001914050267991797073049843022731085740256
comment: Multiplicity 1.
4
6
32:
2.289672171036842479459953109772960550872644067490672626401662752965621409454805766782190317504513783 + i * -1.571661819106396765014055309565540463730944342305275957938827209495847378717240245783149650073928982
comment: Multiplicity 1.
4
6
33:
2.289672171036842479459953109772960550872644067490672626401662752965621409454805766782190317504513783 + i * 1.571661819106396765014055309565540463730944342305275957938827209495847378717240245783149650073928982
comment: Multiplicity 1.
5
5
1:
-1.326955559590357375774635146179919460557488176919503137175995131151904650104625191963328951203694898 + i * -0.8796105241148522407068629931563471634372265347028399035238142068299601219884303568821138998017268340
comment: Multiplicity 1.
5
5
2:
-1.326955559590357375774635146179919460557488176919503137175995131151904650104625191963328951203694898 + i * 0.8796105241148522407068629931563471634372265347028399035238142068299601219884303568821138998017268340
comment: Multiplicity 1.
5
5
3:
-1
comment: Multiplicity 8.
5
5
4:
-0.7863263802902427516217126888593754741977824287880157792110418699784749120910726646756275461481357865 + i * -1.236188439460251865759741160245168078286721641171041811294442354152804411577044069655010123812926359
comment: Multiplicity 1.
5
5
5:
-0.7863263802902427516217126888593754741977824287880157792110418699784749120910726646756275461481357865 + i * 1.236188439460251865759741160245168078286721641171041811294442354152804411577044069655010123812926359
comment: Multiplicity 1.
5
5
6:
-0.5235518200598295755960605574233835348729624774660473976582285229051396206445142389308078795030311083 + i * -0.3470513292745678093889680469935045192942146556608206007583864613924547990462658902429068259316579871
comment: Multiplicity 1.
5
5
7:
-0.5235518200598295755960605574233835348729624774660473976582285229051396206445142389308078795030311083 + i * 0.3470513292745678093889680469935045192942146556608206007583864613924547990462658902429068259316579871
comment: Multiplicity 1.
5
5
8:
-0.3663344940431253015666440997228877507291276735601699741222045130245919948332849512260228851970235118 + i * -0.5759166649661128780341931378287284837507355336166173836728491880150585860360175497388727437716721856
comment: Multiplicity 1.
5
5
9:
-0.3663344940431253015666440997228877507291276735601699741222045130245919948332849512260228851970235118 + i * 0.5759166649661128780341931378287284837507355336166173836728491880150585860360175497388727437716721856
comment: Multiplicity 1.
5
5
10:
0.04537497190559604956806851448877672018085536766437645280884690425837778201220738200735886721547410845 + i * -0.6919668790954023755149755531644760604170859710460958205501155260128160909194407913207408163730474008
comment: Multiplicity 1.
5
5
11:
0.04537497190559604956806851448877672018085536766437645280884690425837778201220738200735886721547410845 + i * 0.6919668790954023755149755531644760604170859710460958205501155260128160909194407913207408163730474008
comment: Multiplicity 1.
5
5
12:
0.09435878031744204198462198090429067052470989772664282743764328376542203981641842241147087831784834813 + i * -1.438968400186634878205552531204139389660344699469465983404069649790318541850732431298727222944657899
comment: Multiplicity 1.
5
5
13:
0.09435878031744204198462198090429067052470989772664282743764328376542203981641842241147087831784834813 + i * 1.438968400186634878205552531204139389660344699469465983404069649790318541850732431298727222944657899
comment: Multiplicity 1.
5
5
14:
0.1268401938455927426234859619779922130506160409214482743903247616803913292940421856164129902401777703 + i * -0.6881266043408210708617342502065424483462028580483174207790858117465757202654617245144973460096596590
comment: Multiplicity 1.
5
5
15:
0.1268401938455927426234859619779922130506160409214482743903247616803913292940421856164129902401777703 + i * 0.6881266043408210708617342502065424483462028580483174207790858117465757202654617245144973460096596590
comment: Multiplicity 1.
5
5
16:
0.1526578383477638558198207234740119324513069297567359852537573031905392774285008246123261639812371575 + i * -0.4440236398856600280039376619619321299381059762132704618113561322402531857113237409002815152732056061
comment: Multiplicity 1.
5
5
17:
0.1526578383477638558198207234740119324513069297567359852537573031905392774285008246123261639812371575 + i * 0.4440236398856600280039376619619321299381059762132704618113561322402531857113237409002815152732056061
comment: Multiplicity 1.
5
5
18:
0.2466010877040604514309610655325770792473354514618478007859426225025873833584916688351319255343784667 + i * -0.4623317706192098771434234627129733880585765413896007133655575966026100514596706040356594044487587820
comment: Multiplicity 1.
5
5
19:
0.2466010877040604514309610655325770792473354514618478007859426225025873833584916688351319255343784667 + i * 0.4623317706192098771434234627129733880585765413896007133655575966026100514596706040356594044487587820
comment: Multiplicity 1.
5
5
20:
0.2590655001837745155590841876519685567646759643709243400818741006418249018192994823031347172606671766 + i * -1.405468231626416540049101082860212141043445952655221728226387426817066221197020551525050613900942746
comment: Multiplicity 1.
5
5
21:
0.2590655001837745155590841876519685567646759643709243400818741006418249018192994823031347172606671766 + i * 1.405468231626416540049101082860212141043445952655221728226387426817066221197020551525050613900942746
comment: Multiplicity 1.
5
5
22:
0.2952444868584827398121600661419322282456547668252554760274696281097340360735374688876355857729452262 + i * -0.3188208657769811009485894760354044067895359533790066838158260085350372915214233229654859053408243318
comment: Multiplicity 1.
5
5
23:
0.2952444868584827398121600661419322282456547668252554760274696281097340360735374688876355857729452262 + i * 0.3188208657769811009485894760354044067895359533790066838158260085350372915214233229654859053408243318
comment: Multiplicity 1.
5
5
24:
0.3044025344716389242438750631074962145588344132304511713033033648380660643137535319669162048682189030 + i * -0.1957071083449249702144126310554778725376851059673215681170588380947636683383024425631550972950019656
comment: Multiplicity 1.
5
5
25:
0.3044025344716389242438750631074962145588344132304511713033033648380660643137535319669162048682189030 + i * 0.1957071083449249702144126310554778725376851059673215681170588380947636683383024425631550972950019656
comment: Multiplicity 1.
5
5
26:
0.6924469886369234416056774447353699757652181160443987176495464412186032841283834568580019348126814760 + i * -2.014065151518862416281866723561125602792804412879705225354266546500198245338497202735572306393261651
comment: Multiplicity 1.
5
5
27:
0.6924469886369234416056774447353699757652181160443987176495464412186032841283834568580019348126814760 + i * 2.014065151518862416281866723561125602792804412879705225354266546500198245338497202735572306393261651
comment: Multiplicity 1.
5
5
28:
0.8981592601493495095876612657947134006906343813849458335653056139410918934929053109743208441393120820 + i * -1.683883736722264993157433825750730630042463942896184191887930446799972566312808501936360001324755147
comment: Multiplicity 1.
5
5
29:
0.8981592601493495095876612657947134006906343813849458335653056139410918934929053109743208441393120820 + i * 1.683883736722264993157433825750730630042463942896184191887930446799972566312808501936360001324755147
comment: Multiplicity 1.
5
5
30:
1.563662011528708634586378448636163857256424851634008107620675732484464896764525658353024962562946989 + i * -1.688526284106752191185882912097491577748807513118691997070470152806946601841088020487269792340605905
comment: Multiplicity 1.
5
5
31:
1.563662011528708634586378448636163857256424851634008107620675732484464896764525658353024962562946989 + i * 1.688526284106752191185882912097491577748807513118691997070470152806946601841088020487269792340605905
comment: Multiplicity 1.
5
5
32:
2.324354600034222097737257769740273371621094575712701301242780280429008289171431653970052187345997601 + i * -1.494378876741265902613570502414612969100962467819120973218366275977268020043321157282165883820304687
comment: Multiplicity 1.
5
5
33:
2.324354600034222097737257769740273371621094575712701301242780280429008289171431653970052187345997601 + i * 1.494378876741265902613570502414612969100962467819120973218366275977268020043321157282165883820304687
comment: Multiplicity 1.
5
6
1:
-1.440475300308338024707008824855151152361202308470460005584741950129075618087129911638340329641884237 + i * -0.8742752343808977505659630602794267321370281866215293566802079377398365324870745265087291904671666881
comment: Multiplicity 1.
5
6
2:
-1.440475300308338024707008824855151152361202308470460005584741950129075618087129911638340329641884237 + i * 0.8742752343808977505659630602794267321370281866215293566802079377398365324870745265087291904671666881
comment: Multiplicity 1.
5
6
3:
-1.042054229763545760064838899353902162306165284048228149879516299302204270951242325048086724217230401 + i * -1.095256173045084467566176146649937222407037176482453478000220576510608851761943388573456038162729558
comment: Multiplicity 1.
5
6
4:
-1.042054229763545760064838899353902162306165284048228149879516299302204270951242325048086724217230401 + i * 1.095256173045084467566176146649937222407037176482453478000220576510608851761943388573456038162729558
comment: Multiplicity 1.
5
6
5:
-1
comment: Multiplicity 9.
5
6
6:
-0.5073299649840662159607684927902381735034765177505335950526492795661714944519640729757569051481925649 + i * -0.3079164383797173011594961762605444666828454474432331041805109494733303009205086319732596576891937787
comment: Multiplicity 1.
5
6
7:
-0.5073299649840662159607684927902381735034765177505335950526492795661714944519640729757569051481925649 + i * 0.3079164383797173011594961762605444666828454474432331041805109494733303009205086319732596576891937787
comment: Multiplicity 1.
5
6
8:
-0.4559488309773369547760191944163505026609903442875063337813499607124263434952042114957952330647046613 + i * -0.4792272392905438767079921145240215877868822578731179046160741688031034055383556521234532607839121690
comment: Multiplicity 1.
5
6
9:
-0.4559488309773369547760191944163505026609903442875063337813499607124263434952042114957952330647046613 + i * 0.4792272392905438767079921145240215877868822578731179046160741688031034055383556521234532607839121690
comment: Multiplicity 1.
5
6
10:
-0.3210201407589114259084772700978819801161186558781687714313936863013955744055146588978192898620278021 + i * -1.254869448586342815201392044098076263317265196284189856427719286137491053762293313520853441268067845
comment: Multiplicity 1.
5
6
11:
-0.3210201407589114259084772700978819801161186558781687714313936863013955744055146588978192898620278021 + i * 1.254869448586342815201392044098076263317265196284189856427719286137491053762293313520853441268067845
comment: Multiplicity 1.
5
6
12:
-0.1913395314856706926000474206723259046108245315636071874543315053096754715853202623917036347492810244 + i * -0.7479472527816075507617829163430509802204633007221537574160481785685273386732742153254164214690122102
comment: Multiplicity 1.
5
6
13:
-0.1913395314856706926000474206723259046108245315636071874543315053096754715853202623917036347492810244 + i * 0.7479472527816075507617829163430509802204633007221537574160481785685273386732742153254164214690122102
comment: Multiplicity 1.
5
6
14:
-0.01229600883097514939062499808000659940128259948851923343350132153328239506738783290613014933559038400 + i * -1.204996643118050593379185651822914492690719960308818058647275802891488230846984393293191721636897978
comment: Multiplicity 1.
5
6
15:
-0.01229600883097514939062499808000659940128259948851923343350132153328239506738783290613014933559038400 + i * 1.204996643118050593379185651822914492690719960308818058647275802891488230846984393293191721636897978
comment: Multiplicity 1.
5
6
16:
-0.008467345354908691336956028222786469264450653271195310825383936955009682956529801477650440022735130553 + i * -0.8297914281814175608811515463603883982139767417248259479985878466101000395918322978225349447795738240
comment: Multiplicity 1.
5
6
17:
-0.008467345354908691336956028222786469264450653271195310825383936955009682956529801477650440022735130553 + i * 0.8297914281814175608811515463603883982139767417248259479985878466101000395918322978225349447795738240
comment: Multiplicity 1.
5
6
18:
0.1089448185770945237466345691842097286103416102604848361700678646303620507502340842149316502892682979 + i * -0.6101862961639226374672432124943521113893206098353979635634450348893850531325800914561953520794012526
comment: Multiplicity 1.
5
6
19:
0.1089448185770945237466345691842097286103416102604848361700678646303620507502340842149316502892682979 + i * 0.6101862961639226374672432124943521113893206098353979635634450348893850531325800914561953520794012526
comment: Multiplicity 1.
5
6
20:
0.1967714263812103137485788545761035625858794345813974360781685681667143678834323835104921161438662395 + i * -0.4174657291435524230639627488845366774332413795192742080664325468475708950773767788008628402492315004
comment: Multiplicity 1.
5
6
21:
0.1967714263812103137485788545761035625858794345813974360781685681667143678834323835104921161438662395 + i * 0.4174657291435524230639627488845366774332413795192742080664325468475708950773767788008628402492315004
comment: Multiplicity 1.
5
6
22:
0.2082794537849534243290978603139473815658335004497555696968342124626826200957640490884519458106503631 + i * -0.5584681604883768270601244376612681743473179279466136874487568516228107982846018664222270789085009545
comment: Multiplicity 1.
5
6
23:
0.2082794537849534243290978603139473815658335004497555696968342124626826200957640490884519458106503631 + i * 0.5584681604883768270601244376612681743473179279466136874487568516228107982846018664222270789085009545
comment: Multiplicity 1.
5
6
24:
0.2735178561183997060310046801783445345154045227616905277872853624605149840541631721504981342928399291 + i * -0.4011558879023085666339511590199601624323208961646467825969483392652796131156672167324635653988257778
comment: Multiplicity 1.
5
6
25:
0.2735178561183997060310046801783445345154045227616905277872853624605149840541631721504981342928399291 + i * 0.4011558879023085666339511590199601624323208961646467825969483392652796131156672167324635653988257778
comment: Multiplicity 1.
5
6
26:
0.2835655146823786254306613066688637951767933693629919785837818794521596905211466834956585940546102542 + i * -1.588214964086744159558653486632782692904023396621756440622484050281143179440122172096370731632791161
comment: Multiplicity 1.
5
6
27:
0.2835655146823786254306613066688637951767933693629919785837818794521596905211466834956585940546102542 + i * 1.588214964086744159558653486632782692904023396621756440622484050281143179440122172096370731632791161
comment: Multiplicity 1.
5
6
28:
0.3085729161686157112144054197065173107824176483301053894865694275606671424837924175251355791757519718 + i * -0.2886992986257728618057054704491895436457270901487285744658330674939938784830382893679999639624291876
comment: Multiplicity 1.
5
6
29:
0.3085729161686157112144054197065173107824176483301053894865694275606671424837924175251355791757519718 + i * 0.2886992986257728618057054704491895436457270901487285744658330674939938784830382893679999639624291876
comment: Multiplicity 1.
5
6
30:
0.3146584788861420686842242615895822167371383294216051566816752882969181490798076908560886780485500512 + i * -0.1812624335684031815879890161224252177422356175220783961887813641238032501159650246964023298268860714
comment: Multiplicity 1.
5
6
31:
0.3146584788861420686842242615895822167371383294216051566816752882969181490798076908560886780485500512 + i * 0.1812624335684031815879890161224252177422356175220783961887813641238032501159650246964023298268860714
comment: Multiplicity 1.
5
6
32:
0.5862617235251305900182287031827206087836771804344273674855938326883755233068029720801562271207419491 + i * -1.571967375331564081499015067682352608312230747627545569161723115059721186875585918519038836657528182
comment: Multiplicity 1.
5
6
33:
0.5862617235251305900182287031827206087836771804344273674855938326883755233068029720801562271207419491 + i * 1.571967375331564081499015067682352608312230747627545569161723115059721186875585918519038836657528182
comment: Multiplicity 1.
5
6
34:
0.9238241331545145680167100607970984306490979557781262492159789650037788416167996377332561800720639867 + i * -1.959964017339596799951832121542072773132778656526297334309530675916632787173921991695625813946591081
comment: Multiplicity 1.
5
6
35:
0.9238241331545145680167100607970984306490979557781262492159789650037788416167996377332561800720639867 + i * 1.959964017339596799951832121542072773132778656526297334309530675916632787173921991695625813946591081
comment: Multiplicity 1.
5
6
36:
1.160261739070757697843529389701199057426430741841272273282798931473021252140206416455823729782351971 + i * -1.701701800172510396720838380417395615223796667591820803004152648487683758959870394323321936990748751
comment: Multiplicity 1.
5
6
37:
1.160261739070757697843529389701199057426430741841272273282798931473021252140206416455823729782351971 + i * 1.701701800172510396720838380417395615223796667591820803004152648487683758959870394323321936990748751
comment: Multiplicity 1.
5
6
38:
1.728075093220366753675622660140142320186406798836391026148653551764118765938379682758815936848477598 + i * -1.616778535134861528191969079704186862934187404302817248098880150872027655937872872521447426787616597
comment: Multiplicity 1.
5
6
39:
1.728075093220366753675622660140142320186406798836391026148653551764118765938379682758815936848477598 + i * 1.616778535134861528191969079704186862934187404302817248098880150872027655937872872521447426787616597
comment: Multiplicity 1.
5
6
40:
2.386198198894188932006043362449913997205089802699970776825460055849927463129763886961973934402473593 + i * -1.374595383665506850392048934851011830466350596298644605155527650740492808111700523964693858145814502
comment: Multiplicity 1.
5
6
41:
2.386198198894188932006043362449913997205089802699970776825460055849927463129763886961973934402473593 + i * 1.374595383665506850392048934851011830466350596298644605155527650740492808111700523964693858145814502
comment: Multiplicity 1.
6
6
1:
-1.684987005839314501179141795232063884257240248349538626088415378848345842072884156522004907879166254 + i * -0.6904503871156138551601864324070048493529863407653616468473019133422827151521956899114053702904953155
comment: Multiplicity 1.
6
6
2:
-1.684987005839314501179141795232063884257240248349538626088415378848345842072884156522004907879166254 + i * 0.6904503871156138551601864324070048493529863407653616468473019133422827151521956899114053702904953155
comment: Multiplicity 1.
6
6
3:
-1.218286978849634518655191327319109038486728396021563522592869342510484339311792364693316354122955671 + i * -1.077613543333278574448918008646388927472619672900444304273798050322967860577516814866396575974341919
comment: Multiplicity 1.
6
6
4:
-1.218286978849634518655191327319109038486728396021563522592869342510484339311792364693316354122955671 + i * 1.077613543333278574448918008646388927472619672900444304273798050322967860577516814866396575974341919
comment: Multiplicity 1.
6
6
5:
-1.061631591677744233072895836322748874550961486405644635051713078554365834851917210783469627643421297 + i * -1.047228487515974943431885307199215212377257903495949650133168914269388968985099287975960254092190432
comment: Multiplicity 1.
6
6
6:
-1.061631591677744233072895836322748874550961486405644635051713078554365834851917210783469627643421297 + i * 1.047228487515974943431885307199215212377257903495949650133168914269388968985099287975960254092190432
comment: Multiplicity 1.
6
6
7:
-1
comment: Multiplicity 8.
6
6
8:
-0.6855711754749302861213069411439252809575702962625395117317115332146225532267650698041288318973094030 + i * -1.168604907588597074053697525097149330497262289988167466169222070594374887121918247408508411972649726
comment: Multiplicity 1.
6
6
9:
-0.6855711754749302861213069411439252809575702962625395117317115332146225532267650698041288318973094030 + i * 1.168604907588597074053697525097149330497262289988167466169222070594374887121918247408508411972649726
comment: Multiplicity 1.
6
6
10:
-0.5081532942352080231099114943729904530003012058770052114582837483332428763027125254187321175405593177 + i * -0.2082239432724933299169969665080022189735526648134862687906910887062749629644110127946729208478652382
comment: Multiplicity 1.
6
6
11:
-0.5081532942352080231099114943729904530003012058770052114582837483332428763027125254187321175405593177 + i * 0.2082239432724933299169969665080022189735526648134862687906910887062749629644110127946729208478652382
comment: Multiplicity 1.
6
6
12:
-0.4774061839346343759765480503705722372870799300531052035755236627280203104885507398601712099059084676 + i * -0.4709292374603714277824572429467993895358222495069448797614952481282652975582803930633715983720282818
comment: Multiplicity 1.
6
6
13:
-0.4774061839346343759765480503705722372870799300531052035755236627280203104885507398601712099059084676 + i * 0.4709292374603714277824572429467993895358222495069448797614952481282652975582803930633715983720282818
comment: Multiplicity 1.
6
6
14:
-0.4605174450595018684181778362066760852804742088353249134607668231080285952558176949269826172602092337 + i * -0.4073423128973690482088306787393393338036777742738580121382604082002192141050153671135867057781863010
comment: Multiplicity 1.
6
6
15:
-0.4605174450595018684181778362066760852804742088353249134607668231080285952558176949269826172602092337 + i * 0.4073423128973690482088306787393393338036777742738580121382604082002192141050153671135867057781863010
comment: Multiplicity 1.
6
6
16:
-0.3734769391005705784875281613160389846245887760653088420703923183710132046292431711522886840840321863 + i * -0.6366180485953849884836342340978039412533884177126161160944042316303260055753525830531591087425851733
comment: Multiplicity 1.
6
6
17:
-0.3734769391005705784875281613160389846245887760653088420703923183710132046292431711522886840840321863 + i * 0.6366180485953849884836342340978039412533884177126161160944042316303260055753525830531591087425851733
comment: Multiplicity 1.
6
6
18:
-0.06139292324205990402370656948008759294331962626060189394009207013247222985448637551476244519654339872 + i * -1.515581672973391557488459926090154604747851976594557326321143766844465570225185284719974660179460320
comment: Multiplicity 1.
6
6
19:
-0.06139292324205990402370656948008759294331962626060189394009207013247222985448637551476244519654339872 + i * 1.515581672973391557488459926090154604747851976594557326321143766844465570225185284719974660179460320
comment: Multiplicity 1.
6
6
20:
-0.02668379405173076989834642152709685777650193626446513232757146105814741691129614362777674830905734740 + i * -0.6587317738682519584249736411738784366776912934782078179353317183588482665543225735055303995302533330
comment: Multiplicity 1.
6
6
21:
-0.02668379405173076989834642152709685777650193626446513232757146105814741691129614362777674830905734740 + i * 0.6587317738682519584249736411738784366776912934782078179353317183588482665543225735055303995302533330
comment: Multiplicity 1.
6
6
22:
0.07987020830572060074072048212615661870249751863298050182860108287719416302366215029351566839100358323 + i * -0.7329668045395261832668722939410997715455460668717980996821876649174392521278904902268357449161024459
comment: Multiplicity 1.
6
6
23:
0.07987020830572060074072048212615661870249751863298050182860108287719416302366215029351566839100358323 + i * 0.7329668045395261832668722939410997715455460668717980996821876649174392521278904902268357449161024459
comment: Multiplicity 1.
6
6
24:
0.1350120382126157763362773680959193170462948397177587111378367876306183378465549104262292294469886889 + i * -0.7039670852003550213507281915294626388019336118685006617155520358247567504687844565410846964706286763
comment: Multiplicity 1.
6
6
25:
0.1350120382126157763362773680959193170462948397177587111378367876306183378465549104262292294469886889 + i * 0.7039670852003550213507281915294626388019336118685006617155520358247567504687844565410846964706286763
comment: Multiplicity 1.
6
6
26:
0.1469229774922412917633193303076601100720464954969062147284494105010178089058711942976701311387038270 + i * -1.348308306818422235196301309047448750979940778014253643614675994533891394353849823824383938601106107
comment: Multiplicity 1.
6
6
27:
0.1469229774922412917633193303076601100720464954969062147284494105010178089058711942976701311387038270 + i * 1.348308306818422235196301309047448750979940778014253643614675994533891394353849823824383938601106107
comment: Multiplicity 1.
6
6
28:
0.1965806827690928980133450018353373299544368834660813383166562099407850406982582487293887977233714391 + i * -0.5186813579642245526240515005944828351398384400471037688112487159089654242216835160028081007199400080
comment: Multiplicity 1.
6
6
29:
0.1965806827690928980133450018353373299544368834660813383166562099407850406982582487293887977233714391 + i * 0.5186813579642245526240515005944828351398384400471037688112487159089654242216835160028081007199400080
comment: Multiplicity 1.
6
6
30:
0.2302356799533173180816807200902759922566199248394723412164081562476294143196607018285480466938920268 + i * -0.3652266624342361982585449040620829428039882027199551496413514033214213080467830940944398678145124642
comment: Multiplicity 1.
6
6
31:
0.2302356799533173180816807200902759922566199248394723412164081562476294143196607018285480466938920268 + i * 0.3652266624342361982585449040620829428039882027199551496413514033214213080467830940944398678145124642
comment: Multiplicity 1.
6
6
32:
0.2471403538490723761823949242896516520805434134859679527801763528123852357003558059994519168130839258 + i * -0.4949641627523506666745529864027751245680552405904100164481302925265441093730111815298918134616882944
comment: Multiplicity 1.
6
6
33:
0.2471403538490723761823949242896516520805434134859679527801763528123852357003558059994519168130839258 + i * 0.4949641627523506666745529864027751245680552405904100164481302925265441093730111815298918134616882944
comment: Multiplicity 1.
6
6
34:
0.2627726509582249633702081411916359722478125396473709652556852608114663062623552915753408157132580628 + i * -1.370124469005658789300787149300259940936320388828902462392347866115078930315856963832387628220179167
comment: Multiplicity 1.
6
6
35:
0.2627726509582249633702081411916359722478125396473709652556852608114663062623552915753408157132580628 + i * 1.370124469005658789300787149300259940936320388828902462392347866115078930315856963832387628220179167
comment: Multiplicity 1.
6
6
36:
0.2983823217864186984865149806620814925868049390149221340190937777031321260440893180885466907576560835 + i * -0.3667275930106299904773708417495067716516440132890846896365186306927129701836652935000707874790070172
comment: Multiplicity 1.
6
6
37:
0.2983823217864186984865149806620814925868049390149221340190937777031321260440893180885466907576560835 + i * 0.3667275930106299904773708417495067716516440132890846896365186306927129701836652935000707874790070172
comment: Multiplicity 1.
6
6
38:
0.3243363738654317610602454913483489937794089412116360923873559864963087356914082175126650422955020812 + i * -0.2634479984214338019458407643422874371055188765408754975274736059152522878379074948009038683718837170
comment: Multiplicity 1.
6
6
39:
0.3243363738654317610602454913483489937794089412116360923873559864963087356914082175126650422955020812 + i * 0.2634479984214338019458407643422874371055188765408754975274736059152522878379074948009038683718837170
comment: Multiplicity 1.
6
6
40:
0.3253400887805312159066560032070517338865134874239418484915735292605942399575945938437351011500059416 + i * -0.1662262944444239363916627511379016078015309314878736092873380948561407537251418047596699582663668945
comment: Multiplicity 1.
6
6
41:
0.3253400887805312159066560032070517338865134874239418484915735292605942399575945938437351011500059416 + i * 0.1662262944444239363916627511379016078015309314878736092873380948561407537251418047596699582663668945
comment: Multiplicity 1.
6
6
42:
0.6389245789660840636480197556039173416937529275274610202879471310252960038468661403235523501235029354 + i * -1.685812988268613844604866755537676085902497868019529609805606303803107935610985485054741448866228100
comment: Multiplicity 1.
6
6
43:
0.6389245789660840636480197556039173416937529275274610202879471310252960038468661403235523501235029354 + i * 1.685812988268613844604866755537676085902497868019529609805606303803107935610985485054741448866228100
comment: Multiplicity 1.
6
6
44:
0.8074691024237152837791007475107953476268765960924752196617128534022360765684803006802770105572752255 + i * -1.617171222768508828180127207144449543735342330670931006108593274384863726180550856087847417913626181
comment: Multiplicity 1.
6
6
45:
0.8074691024237152837791007475107953476268765960924752196617128534022360765684803006802770105572752255 + i * 1.617171222768508828180127207144449543735342330670931006108593274384863726180550856087847417913626181
comment: Multiplicity 1.
6
6
46:
1.235176694134068285926514677158182373432267931943433205826886691002435154693427280982688253316353888 + i * -1.959381194116430352710804032347124100246389495453926261373885998378139290910020708417014708965131416
comment: Multiplicity 1.
6
6
47:
1.235176694134068285926514677158182373432267931943433205826886691002435154693427280982688253316353888 + i * 1.959381194116430352710804032347124100246389495453926261373885998378139290910020708417014708965131416
comment: Multiplicity 1.
6
6
48:
1.334917696004614560390417081528422192613981611732798794943677891744098339022686075079937402602993739 + i * -1.640684175229012523534570813751277571634832747829717076255173085739605003258821829276633723775777869
comment: Multiplicity 1.
6
6
49:
1.334917696004614560390417081528422192613981611732798794943677891744098339022686075079937402602993739 + i * 1.640684175229012523534570813751277571634832747829717076255173085739605003258821829276633723775777869
comment: Multiplicity 1.
6
6
50:
1.857608013287661371452539051610795527858429064254371698099890488622878116641527421605001083806619122 + i * -1.508875206070156266952361308687856588250399627444226288927514149101883076913623849687149714248869192
comment: Multiplicity 1.
6
6
51:
1.857608013287661371452539051610795527858429064254371698099890488622878116641527421605001083806619122 + i * 1.508875206070156266952361308687856588250399627444226288927514149101883076913623849687149714248869192
comment: Multiplicity 1.
6
6
52:
2.437417870676518593804800676725077293326478995907519453315387806780668103682667801037086003308952006 + i * -1.245352032003936962160804613962039685579625022270293809152392297179782455546617407678341871494114024
comment: Multiplicity 1.
6
6
53:
2.437417870676518593804800676725077293326478995907519453315387806780668103682667801037086003308952006 + i * 1.245352032003936962160804613962039685579625022270293809152392297179782455546617407678341871494114024
comment: Multiplicity 1.
Definition
The Fisher zeros $b_{m,n,j}$ are the distinct complex roots of $F_{m,n}(b)=\sum_{S\subseteq V(G_{m,n})}b^{d(S)}$, where $G_{m,n}$ is the $m$ by $n$ vertex grid with free boundaries and $d(S)$ counts bonds with exactly one endpoint in $S$ [1]. The bond coordinate is $b=e^{-2K}$, with $K=J/(k_BT)$ [2].
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; roots are ordered lexicographically by their exact real and imaginary parts)
Formulas
(1)
$G_{m,n}=P_m\square P_n$, where $P_m$ is a path on $m$ vertices.
(2)
$Z_{m,n}(K,0)=e^{KE}F_{m,n}(e^{-2K})$, where $K=J/(k_BT)$ and $Z_{m,n}(K,0)=\sum_\sigma\exp(K\sum_{uv\in E(G_{m,n})}\sigma_u\sigma_v)$ [2].
(3)
$F_{m,n}(0)=2$, $F_{m,n}(1)=2^{mn}$, $\deg F_{m,n}=E$, and $b^E F_{m,n}(b^{-1})=F_{m,n}(b)$. The reciprocal symmetry follows by reversing the spins on one bipartite class of the rectangular graph.
(4)
$F_{m,n}(b)=2^{N-E}\sum_{\substack{A\subseteq E(G_{m,n})\\ \deg_A(v)\text{ even for every }v}}(1-b)^{|A|}(1+b)^{E-|A|}$, where $\deg_A(v)$ is the degree of vertex $v$ in the edge subset $A$. This is the zero-field high-temperature expansion.
(5)
$F_{2,2}(b)=2(1+6b^2+b^4)$, so its four simple zeros are $\pm i(\sqrt2-1)$ and $\pm i(\sqrt2+1)$.
Comments
(6)
There are $N=mn$ sites and $E=2mn-m-n$ bonds, with no wraparound bonds or fixed boundary spins. The spins are $\sigma_v\in\{-1,1\}$, every bond has the same coupling $J>0$, and the energy is $\mathcal H=-J\sum_{uv\in E(G_{m,n})}\sigma_u\sigma_v$; each bond is counted once. The external field is zero. The parameter $b$ is analytically continued to the complex plane.
(7)
Distinct roots are ordered lexicographically by $(\operatorname{Re}b,\operatorname{Im}b)$ using exact algebraic comparisons, with $j$ starting at $1$. Every conjugate and every real root is included. A repeated root has one entry, whose comment gives its multiplicity. Rectangles are ordered by $(m,n)$, with $m\le n$ to omit rotated copies.
(8)
Free rectangles form a finite-size Ising family in which changing the aspect ratio changes the boundary geometry [3]. Each finite polynomial is positive for real $b>0$, so no listed zero is a positive real thermodynamic singularity. The infinite square lattice has bulk critical coupling $K_c$$=\tfrac12\log(1+\sqrt2)$. The present table varies complex $b$ and does not fix it at $b_c=\sqrt2-1$.
Programs
(P1)
Sage
# With the attached generate.py in the current directory:
from generate import FisherZeros
g = FisherZeros()
p = {'m': 6, 'n': 6, 'j': 1}
g.value(p, 100)                  # certified value and multiplicity
list(g.enumerate())              # every distinct zero for 2 <= m <= n <= 6
References
[1]
J. Liu, A. Sinclair and P. Srivastava, Fisher zeros and correlation decay in the Ising model, 2018, Introduction, equation (1). (arXiv)
[2]
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). (arXiv) (doi)
[3]
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)
[4]
A. D. Sokal, The multivariate Tutte polynomial (alias Potts model) for graphs and matroids, Surveys in Combinatorics 2005, 173-226, Sections 2.2 and 2.5. (arXiv)
Links
Similar tables
Critical_couplings_of_the_Ising_model_on_lattices —   Bulk transition couplings for infinite Ising lattices, including the square lattice underlying these finite rectangles.
Critical_exponents_of_the_two-dimensional_universality_classes —   Critical exponents for the thermodynamic limit, including the two-dimensional Ising class.
Tutte_polynomials_of_connected_graphs —   Graph polynomials whose two-state Potts specialization gives the zero-field Ising partition function. [4]
Data properties
Entries are of type: complex number
digits: 100 (Unknown key)
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 the square sequence alone, and the noncanonical cutoff limits the transfer calculation to $64$ row states and the polynomial degree to $60$)
How they were obtained:

The attached generator constructs exact integer cut polynomials by row transfer. Sage isolates their algebraic roots and retains the multiplicities [5]; exact algebraic comparisons fix the indices [6]. Conversion to complex balls uses the precision needed for 100 decimal digits plus 96 guard bits, and exact rational values and exactly zero components are retained. Each nonzero inexact component was measured to retain at least 134 significant decimal digits before serialization.

more

The attached checks compare every polynomial with an independent even-subgraph parity transfer and reconstruct every coefficient from the certified roots with their multiplicities. They also check reciprocal and conjugate symmetry, the degree and the values at 0 and 1. Direct enumeration of every spin assignment verifies the full two-variable count polynomial for all nine rectangles with at most 16 sites. Writing $P(z,b)=\sum_{S\subseteq V(G_{m,n})}z^{|S|}b^{d(S)}$ for the two-variable count polynomial, the identities are $P(z,1)=(1+z)^N$, $P(z,0)=1+z^N$ and spin-reversal symmetry for all 15 rectangles. The four-cycle identity is a known-answer control. The exact count data and numerical evidence are attached.



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