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{
"Title": "Fisher zeros of the Ising model on finite rectangles with free boundaries",
"Definition": "The Fisher zeros $b_{m,n,j}$ are the distinct complex roots of the zero-field Ising cut polynomial $F_{m,n}(b)$ on an $m$ by $n$ vertex rectangle with free boundaries CITE{LSS}.",
"Parameters": {
"m": {
"type": "Z",
"display": "$m$",
"title": "shorter side length in vertices",
"constraints": "$2\\le m\\le n$"
},
"n": {
"type": "Z",
"display": "$n$",
"title": "longer side length in vertices",
"constraints": "$n\\ge m$"
},
"j": {
"type": "Z",
"display": "$j$",
"title": "index of a distinct root",
"constraints": "$1\\le j\\le r_{m,n}$, where $r_{m,n}$ is the number of distinct roots; roots are ordered lexicographically by their exact real and imaginary parts"
}
},
"Tags": [
"statistical mechanics",
"physics",
"zero",
"algebraic"
],
"Data properties": {
"type": "C",
"digits": "100",
"rigour": "proven",
"complete": "no",
"complete-note": "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 $60$",
"rigour details": "The attached generator constructs exact integer cut polynomials by row transfer. Sage isolates their algebraic roots and retains the multiplicities CITE{SageRoots}; exact algebraic comparisons fix the indices CITE{SageAlgebraic}. 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.\n\nThe 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. The full count polynomial obeys $P(z,1)=(1+z)^N$, $P(z,0)=1+z^N$ 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."
},
"Display properties": {
"number-header": "$b_{m,n,j}$"
},
"Numbers": [
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "2",
"j": "1"
},
"number": "0 + i * -2.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641573"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "2",
"j": "2"
},
"number": "0 + i * -0.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "2",
"j": "3"
},
"number": "0 + i * 0.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "2",
"j": "4"
},
"number": "0 + i * 2.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641573"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "3",
"j": "1"
},
"number": "-1"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "3",
"j": "2"
},
"number": "-0.3760858894420932720286410393918156187551122473163108902944444590597507799689994317542728773642059540 + i * -0.9265848065679415166334895496807616090580230781681989107398813869172600857321813903684660337681241365"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "3",
"j": "3"
},
"number": "-0.3760858894420932720286410393918156187551122473163108902944444590597507799689994317542728773642059540 + i * 0.9265848065679415166334895496807616090580230781681989107398813869172600857321813903684660337681241365"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "3",
"j": "4"
},
"number": "0.1118959241279502724104154530154523348283555151804687195733910518712485722048978895023709154641991517 + i * -0.3659283100347038394392151158709365150945602244423067559740111254946164377273621335034644423325034971"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "3",
"j": "5"
},
"number": "0.1118959241279502724104154530154523348283555151804687195733910518712485722048978895023709154641991517 + i * 0.3659283100347038394392151158709365150945602244423067559740111254946164377273621335034644423325034971"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "3",
"j": "6"
},
"number": "0.7641899653141429996182255863763632839267567321358421707210534071885022077641015422519019619000068023 + i * -2.499096769897741586347184015033281628392919550603163904691999914737746982715835953077016218675999194"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "3",
"j": "7"
},
"number": "0.7641899653141429996182255863763632839267567321358421707210534071885022077641015422519019619000068023 + i * 2.499096769897741586347184015033281628392919550603163904691999914737746982715835953077016218675999194"
},
{
"comment": "Multiplicity 2.",
"params": {
"m": "2",
"n": "4",
"j": "1"
},
"number": "-1"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "4",
"j": "2"
},
"number": "-0.2047940572504313302745055894563902000430698943520502803456117329701958969926541839763908095983624669 + i * -1.694381773253064833143045200899301575391957459644433887641915512671969477781945409279088558322039577"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "4",
"j": "3"
},
"number": "-0.2047940572504313302745055894563902000430698943520502803456117329701958969926541839763908095983624669 + i * 1.694381773253064833143045200899301575391957459644433887641915512671969477781945409279088558322039577"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "4",
"j": "4"
},
"number": "-0.07030661966722700678257471883448226564134152866326171436465390129748836730192216430221785363894928884 + i * -0.5816880455545249912583323610771331279582569275166925667793464699285308467897597899043067700091556293"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "4",
"j": "5"
},
"number": "-0.07030661966722700678257471883448226564134152866326171436465390129748836730192216430221785363894928884 + i * 0.5816880455545249912583323610771331279582569275166925667793464699285308467897597899043067700091556293"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "4",
"j": "6"
},
"number": "0.1543790850315605588653115569262083045087192910976534785540273283854429317153373377217509677366264865 + i * -0.3375156554953382560380491851887352346272622127938007199299846265774189090601358667929884331500048025"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "4",
"j": "7"
},
"number": "0.1543790850315605588653115569262083045087192910976534785540273283854429317153373377217509677366264865 + i * 0.3375156554953382560380491851887352346272622127938007199299846265774189090601358667929884331500048025"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "4",
"j": "8"
},
"number": "1.120721591886097778191768751364664161175692131917658516156238305882241332579239010556857695500685269 + i * -2.450209383193878097922762025010903682060962744921542040792553669320857540052321486167770221462888750"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "4",
"j": "9"
},
"number": "1.120721591886097778191768751364664161175692131917658516156238305882241332579239010556857695500685269 + i * 2.450209383193878097922762025010903682060962744921542040792553669320857540052321486167770221462888750"
},
{
"comment": "Multiplicity 3.",
"params": {
"m": "2",
"n": "5",
"j": "1"
},
"number": "-1"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "5",
"j": "2"
},
"number": "-0.2336189531598592598838743404801818851509592607695114276299876618392599912544150107602300892568471076 + i * -0.9723282289044638680969873469123042777613469520096674538706843934588552500864826731390699725897459240"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "5",
"j": "3"
},
"number": "-0.2336189531598592598838743404801818851509592607695114276299876618392599912544150107602300892568471076 + i * 0.9723282289044638680969873469123042777613469520096674538706843934588552500864826731390699725897459240"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "5",
"j": "4"
},
"number": "0.04540909939731060963388893425746474783738391686349217537695506181349081536860224971641817070337467527 + i * -0.4777653389603127530512477482985863130575668599838814890824432686272118877403639101070069867994159944"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "5",
"j": "5"
},
"number": "0.04540909939731060963388893425746474783738391686349217537695506181349081536860224971641817070337467527 + i * 0.4777653389603127530512477482985863130575668599838814890824432686272118877403639101070069867994159944"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "5",
"j": "6"
},
"number": "0.1752104141510476192347389667242876217944624605259672930004658604084823575404196786984145102078602401 + i * -0.3200869779879678454771978732607652439806523690662465060558729791388230361986935051630778875937226740"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "5",
"j": "7"
},
"number": "0.1752104141510476192347389667242876217944624605259672930004658604084823575404196786984145102078602401 + i * 0.3200869779879678454771978732607652439806523690662465060558729791388230361986935051630778875937226740"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "5",
"j": "8"
},
"number": "0.1971551023144684246718844389700398871451926456815426284708508768862521093583620941324787956889365250 + i * -2.074339186092861733974905023542074350928712658046102248615418892139962262481628571190325914646692035"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "5",
"j": "9"
},
"number": "0.1971551023144684246718844389700398871451926456815426284708508768862521093583620941324787956889365250 + i * 2.074339186092861733974905023542074350928712658046102248615418892139962262481628571190325914646692035"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "5",
"j": "10"
},
"number": "1.315844337297032606343362000528389628373920237698509330781715862731034708987030988212918612656675667 + i * -2.403879012950036241014424515034382746536830360600038909021298429687718673353464074922422576795435215"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "5",
"j": "11"
},
"number": "1.315844337297032606343362000528389628373920237698509330781715862731034708987030988212918612656675667 + i * 2.403879012950036241014424515034382746536830360600038909021298429687718673353464074922422576795435215"
},
{
"comment": "Multiplicity 4.",
"params": {
"m": "2",
"n": "6",
"j": "1"
},
"number": "-1"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "6",
"j": "2"
},
"number": "-0.1739958578126563838253824094278421482148717317790626198328224578257764417230981880794130135065646223 + i * -1.436974610823395744106007683545509213906374662723042456321700352670126545539671054241391152788283947"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "6",
"j": "3"
},
"number": "-0.1739958578126563838253824094278421482148717317790626198328224578257764417230981880794130135065646223 + i * 1.436974610823395744106007683545509213906374662723042456321700352670126545539671054241391152788283947"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "6",
"j": "4"
},
"number": "-0.08304615318011059762007308110289651108146000452992620697698123012961418969318821241712411113382889082 + i * -0.6858508883289584999257339691775099630557076549836476916707453132539007353536775850210932046170899930"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "6",
"j": "5"
},
"number": "-0.08304615318011059762007308110289651108146000452992620697698123012961418969318821241712411113382889082 + i * 0.6858508883289584999257339691775099630557076549836476916707453132539007353536775850210932046170899930"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "6",
"j": "6"
},
"number": "0.1010424276673775088772951980248590856289846775068551506418674364993568012879413677967745294558704129 + i * -0.4231271371350168284414199940685066113174690869459050204080221231773041937645518351537595863049011330"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "6",
"j": "7"
},
"number": "0.1010424276673775088772951980248590856289846775068551506418674364993568012879413677967745294558704129 + i * 0.4231271371350168284414199940685066113174690869459050204080221231773041937645518351537595863049011330"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "6",
"j": "8"
},
"number": "0.1869165176768707182846711206410519813832056572524097725099099588529322378839139321869656677177030337 + i * -0.3087116593710191085426690249136401275571856092130277475402436210367213218289219620281077163498478741"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "6",
"j": "9"
},
"number": "0.1869165176768707182846711206410519813832056572524097725099099588529322378839139321869656677177030337 + i * 0.3087116593710191085426690249136401275571856092130277475402436210367213218289219620281077163498478741"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "6",
"j": "10"
},
"number": "0.5339206615619256037456198638003260239834787815072053924675261624321493139333791901738059086635133723 + i * -2.235856028000710801492508006967089096332366902779595701117665345237025280460349887057062496360492827"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "6",
"j": "11"
},
"number": "0.5339206615619256037456198638003260239834787815072053924675261624321493139333791901738059086635133723 + i * 2.235856028000710801492508006967089096332366902779595701117665345237025280460349887057062496360492827"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "6",
"j": "12"
},
"number": "1.435162404086593150537869308064501568300662620042518511190500130170952278311051910338991018803306694 + i * -2.370316827742275837413483323444223361721416417307323663598931803680216598338726544711112678234245615"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "2",
"n": "6",
"j": "13"
},
"number": "1.435162404086593150537869308064501568300662620042518511190500130170952278311051910338991018803306694 + i * 2.370316827742275837413483323444223361721416417307323663598931803680216598338726544711112678234245615"
},
{
"comment": "Multiplicity 4.",
"params": {
"m": "3",
"n": "3",
"j": "1"
},
"number": "-1"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "3",
"j": "2"
},
"number": "0.07832859875695279362931399949703201071178978455551420171437573958953798988010253960393022502054619079 + i * -0.5991017827424800107797909405027372644322028449932430626432188580932964121986333089961924145940881162"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "3",
"j": "3"
},
"number": "0.07832859875695279362931399949703201071178978455551420171437573958953798988010253960393022502054619079 + i * 0.5991017827424800107797909405027372644322028449932430626432188580932964121986333089961924145940881162"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "3",
"j": "4"
},
"number": "0.2012486345108661236597488252803140211889768865935676090649734826757262044890435424581499863298732844 + i * -0.3051930646596968102743329485273253382991436069606031900017784693315105894517713240497350320516831025"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "3",
"j": "5"
},
"number": "0.2012486345108661236597488252803140211889768865935676090649734826757262044890435424581499863298732844 + i * 0.3051930646596968102743329485273253382991436069606031900017784693315105894517713240497350320516831025"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "3",
"j": "6"
},
"number": "0.2145646200564996819698416383981189500033742777560117616972843914150957708888439409708760078156330228 + i * -1.641112549302454165060621193617305774821561797258625093494027428273875378988919456277603721563656598"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "3",
"j": "7"
},
"number": "0.2145646200564996819698416383981189500033742777560117616972843914150957708888439409708760078156330228 + i * 1.641112549302454165060621193617305774821561797258625093494027428273875378988919456277603721563656598"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "3",
"j": "8"
},
"number": "1.505858146675681400741095536824535018095859051094906427523366386319640034742009976967043780833947502 + i * -2.283630216143942227572199667578769445134451033192098412178503042032854551632896955598412252293796151"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "3",
"j": "9"
},
"number": "1.505858146675681400741095536824535018095859051094906427523366386319640034742009976967043780833947502 + i * 2.283630216143942227572199667578769445134451033192098412178503042032854551632896955598412252293796151"
},
{
"comment": "Multiplicity 5.",
"params": {
"m": "3",
"n": "4",
"j": "1"
},
"number": "-1"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "4",
"j": "2"
},
"number": "-0.2252906317750145982810522684281535085379424629884409994649481310151576373943580854134299861882244512 + i * -1.293980400880815320432570035064108099179799164612973182760794092894411172412312970455801376969493691"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "4",
"j": "3"
},
"number": "-0.2252906317750145982810522684281535085379424629884409994649481310151576373943580854134299861882244512 + i * 1.293980400880815320432570035064108099179799164612973182760794092894411172412312970455801376969493691"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "4",
"j": "4"
},
"number": "-0.1305925791725553193334433406838510983974638452372522472744370997046046555246792640683254756261541500 + i * -0.7500721917213053003279616469559508008016039513185077893221871244985464439926047504894890497929682443"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "4",
"j": "5"
},
"number": "-0.1305925791725553193334433406838510983974638452372522472744370997046046555246792640683254756261541500 + i * 0.7500721917213053003279616469559508008016039513185077893221871244985464439926047504894890497929682443"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "4",
"j": "6"
},
"number": "0.1665781963347655757739856162172871230459366046318394993247482495984870229732216789210983309643923984 + i * -0.4830412586755967097405570569902759584068118277465594109600030383062410789987243474939623310171182469"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "4",
"j": "7"
},
"number": "0.1665781963347655757739856162172871230459366046318394993247482495984870229732216789210983309643923984 + i * 0.4830412586755967097405570569902759584068118277465594109600030383062410789987243474939623310171182469"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "4",
"j": "8"
},
"number": "0.2363654686028115443181050427698281158587090185593005553728277384794838923881573801357644684027544955 + i * -0.2727042853617133475941974982486088470162988755343415532858007098694414682728389990264496841449952009"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "4",
"j": "9"
},
"number": "0.2363654686028115443181050427698281158587090185593005553728277384794838923881573801357644684027544955 + i * 0.2727042853617133475941974982486088470162988755343415532858007098694414682728389990264496841449952009"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "4",
"j": "10"
},
"number": "0.6380420284635378727312479786209885269823675764579024079738058568609222497033988594436514262472245923 + i * -1.850185866447849509731742820976556804644571716358728455180631101353992038242427503749885327176131485"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "4",
"j": "11"
},
"number": "0.6380420284635378727312479786209885269823675764579024079738058568609222497033988594436514262472245923 + i * 1.850185866447849509731742820976556804644571716358728455180631101353992038242427503749885327176131485"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "4",
"j": "12"
},
"number": "1.814897517546454924791156971503900841048393108576650784068003385780869127854259430981241236200007115 + i * -2.093919782161303628325025466354806594542188884599789055656632441197895085780577794398578027385351884"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "4",
"j": "13"
},
"number": "1.814897517546454924791156971503900841048393108576650784068003385780869127854259430981241236200007115 + i * 2.093919782161303628325025466354806594542188884599789055656632441197895085780577794398578027385351884"
},
{
"comment": "Multiplicity 6.",
"params": {
"m": "3",
"n": "5",
"j": "1"
},
"number": "-1"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "5",
"j": "2"
},
"number": "-0.6620598938904628088396601401838918430490477558679081768541838047646064794357822430808395764307697056 + i * -0.7494509302827965176088129095848119002273982175705804974026752022854904134425618329706124002862247188"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "5",
"j": "3"
},
"number": "-0.6620598938904628088396601401838918430490477558679081768541838047646064794357822430808395764307697056 + i * 0.7494509302827965176088129095848119002273982175705804974026752022854904134425618329706124002862247188"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "5",
"j": "4"
},
"number": "-0.1609817068083379258795307225450275635808096534560491240291251891094236532480150419742921946695966186 + i * -0.9869573902013573385578825279398547144744071681339474621853905820703821088832837572781642374377908151"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "5",
"j": "5"
},
"number": "-0.1609817068083379258795307225450275635808096534560491240291251891094236532480150419742921946695966186 + i * 0.9869573902013573385578825279398547144744071681339474621853905820703821088832837572781642374377908151"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "5",
"j": "6"
},
"number": "0.1139218137679146918860398343286572933332888184828199672174656456412103862023071483302326952211870843 + i * -0.5928038518459902011144598197837521443401386662154336245845148159121067565145611448457603603780035852"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "5",
"j": "7"
},
"number": "0.1139218137679146918860398343286572933332888184828199672174656456412103862023071483302326952211870843 + i * 0.5928038518459902011144598197837521443401386662154336245845148159121067565145611448457603603780035852"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "5",
"j": "8"
},
"number": "0.2011041400682613081588122402080480808170617037507320767791408719944261316783851503008765327661602519 + i * -0.4094966991611014955737978385678811429810584151222052627606311767889172404237507273582069526425004758"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "5",
"j": "9"
},
"number": "0.2011041400682613081588122402080480808170617037507320767791408719944261316783851503008765327661602519 + i * 0.4094966991611014955737978385678811429810584151222052627606311767889172404237507273582069526425004758"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "5",
"j": "10"
},
"number": "0.2538815005312574151150539821959085773270706165044569832460397780501351495367125581377999884012578892 + i * -0.2531301129449332414801329777866988359712818655918959300857975152380048343868321353028631153006301320"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "5",
"j": "11"
},
"number": "0.2538815005312574151150539821959085773270706165044569832460397780501351495367125581377999884012578892 + i * 0.2531301129449332414801329777866988359712818655918959300857975152380048343868321353028631153006301320"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "5",
"j": "12"
},
"number": "0.3126331126060691540048277219535788632377934925877480123181089072747082400523335199255125972650641724 + i * -1.626818492769432739325095618247127277156738195653621745401440257498461946796857688786188046591973328"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "5",
"j": "13"
},
"number": "0.3126331126060691540048277219535788632377934925877480123181089072747082400523335199255125972650641724 + i * 1.626818492769432739325095618247127277156738195653621745401440257498461946796857688786188046591973328"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "5",
"j": "14"
},
"number": "0.9662409673309621254224928415823162115022042557854829967839705037082040256191726045468019819163108867 + i * -1.967500453158023206486964348012649305555198355988018074254653754118386489924400861862583049674076996"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "5",
"j": "15"
},
"number": "0.9662409673309621254224928415823162115022042557854829967839705037082040256191726045468019819163108867 + i * 1.967500453158023206486964348012649305555198355988018074254653754118386489924400861862583049674076996"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "5",
"j": "16"
},
"number": "1.975260066394336040131964242460410380412438522212717264538583287205346199594886303813907975530386040 + i * -1.969414087500462924206114119080500059763425888350795997825692815319135960911308387843364985543363668"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "5",
"j": "17"
},
"number": "1.975260066394336040131964242460410380412438522212717264538583287205346199594886303813907975530386040 + i * 1.969414087500462924206114119080500059763425888350795997825692815319135960911308387843364985543363668"
},
{
"comment": "Multiplicity 7.",
"params": {
"m": "3",
"n": "6",
"j": "1"
},
"number": "-1"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "6",
"j": "2"
},
"number": "-0.6549036169338613981173238925277483037836869175789987077524333116036255918205984414756812904284182449 + i * -0.8014819459401238696658775995101276816607023071560066278068833266513339326254280041091516917033595887"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "6",
"j": "3"
},
"number": "-0.6549036169338613981173238925277483037836869175789987077524333116036255918205984414756812904284182449 + i * 0.8014819459401238696658775995101276816607023071560066278068833266513339326254280041091516917033595887"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "6",
"j": "4"
},
"number": "-0.6113326792837744483649438140280840893638668157813378641547965563129718397207755145512390497137174106 + i * -0.7481591072944576411776859223309985702687610231987147709787372734618679190233679977918531300330385470"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "6",
"j": "5"
},
"number": "-0.6113326792837744483649438140280840893638668157813378641547965563129718397207755145512390497137174106 + i * 0.7481591072944576411776859223309985702687610231987147709787372734618679190233679977918531300330385470"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "6",
"j": "6"
},
"number": "0.05166393126598495098499913677115383355464901728930775043599608106828281107486495663860913131295643258 + i * -0.7200051812155994505291745091442172837368370389333335436777880878000506043893336791623678873986171304"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "6",
"j": "7"
},
"number": "0.05166393126598495098499913677115383355464901728930775043599608106828281107486495663860913131295643258 + i * 0.7200051812155994505291745091442172837368370389333335436777880878000506043893336791623678873986171304"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "6",
"j": "8"
},
"number": "0.09914843423838190585719581426733565886509088276639694592528521155312088267391678920933447679583387029 + i * -1.381764504011910075987807036564949602455844502359095523289166942542683021987240594270134376741153145"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "6",
"j": "9"
},
"number": "0.09914843423838190585719581426733565886509088276639694592528521155312088267391678920933447679583387029 + i * 1.381764504011910075987807036564949602455844502359095523289166942542683021987240594270134376741153145"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "6",
"j": "10"
},
"number": "0.1839610092100474573952288659912279247747259994182922369199343007634348284588179773976212844208809448 + i * -0.5092888502168081105784293380364574957453581363160007858121803743218877529097850921108047038839492775"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "6",
"j": "11"
},
"number": "0.1839610092100474573952288659912279247747259994182922369199343007634348284588179773976212844208809448 + i * 0.5092888502168081105784293380364574957453581363160007858121803743218877529097850921108047038839492775"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "6",
"j": "12"
},
"number": "0.2224342864073614413204319958965192223440766754481682068750713855292581825064397247372748306479068838 + i * -0.3590796453450027520971348063308213975234049111560083123001906117033668302519147967593097300258627039"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "6",
"j": "13"
},
"number": "0.2224342864073614413204319958965192223440766754481682068750713855292581825064397247372748306479068838 + i * 0.3590796453450027520971348063308213975234049111560083123001906117033668302519147967593097300258627039"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "6",
"j": "14"
},
"number": "0.2637756558400353460873063307920588515745725286541327677626191764420729524167899119557996447382601587 + i * -0.2403747997848321340453643454926778137363565421508410646393391056353073993327445644902990449787308322"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "6",
"j": "15"
},
"number": "0.2637756558400353460873063307920588515745725286541327677626191764420729524167899119557996447382601587 + i * 0.2403747997848321340453643454926778137363565421508410646393391056353073993327445644902990449787308322"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "6",
"j": "16"
},
"number": "0.6273890789284813572891151576202285797005368912669303470248966753091855289575349629930463254597304957 + i * -1.736902096907049875446543436788252255911636208234531133292711394731294210452432919610970861805610575"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "6",
"j": "17"
},
"number": "0.6273890789284813572891151576202285797005368912669303470248966753091855289575349629930463254597304957 + i * 1.736902096907049875446543436788252255911636208234531133292711394731294210452432919610970861805610575"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "6",
"j": "18"
},
"number": "1.246722712417044197644541066931109182438436108426560514466010362376136240129477277218947619787868204 + i * -2.012606764221652848252059853458542408348424865616193809455623504813862774560034198465383465364304709"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "6",
"j": "19"
},
"number": "1.246722712417044197644541066931109182438436108426560514466010362376136240129477277218947619787868204 + i * 2.012606764221652848252059853458542408348424865616193809455623504813862774560034198465383465364304709"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "6",
"j": "20"
},
"number": "2.071141187910299189903449338286199139895465630090547802497416674875106005323532355876287026978698666 + i * -1.887399907260489683625580299084352884948164317096463341944044389014862074970907691656444097546318783"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "3",
"n": "6",
"j": "21"
},
"number": "2.071141187910299189903449338286199139895465630090547802497416674875106005323532355876287026978698666 + i * 1.887399907260489683625580299084352884948164317096463341944044389014862074970907691656444097546318783"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "4",
"j": "1"
},
"number": "-1.321883732568269187407173539204991509076806508908538102495105359001200640671081936527630216327463396 + i * -0.8132115383218487041620205392136454915632786995384549260299660477120276705589606444927361512066733463"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "4",
"j": "2"
},
"number": "-1.321883732568269187407173539204991509076806508908538102495105359001200640671081936527630216327463396 + i * 0.8132115383218487041620205392136454915632786995384549260299660477120276705589606444927361512066733463"
},
{
"comment": "Multiplicity 4.",
"params": {
"m": "4",
"n": "4",
"j": "3"
},
"number": "-1"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "4",
"j": "4"
},
"number": "-0.5487978724655304179628844013562528896374626316891958351989475329570120435926188234433176730838006483 + i * -0.3376157456967592833757034868237046705680630358117192559660402362548874353566601685535203890404089860"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "4",
"j": "5"
},
"number": "-0.5487978724655304179628844013562528896374626316891958351989475329570120435926188234433176730838006483 + i * 0.3376157456967592833757034868237046705680630358117192559660402362548874353566601685535203890404089860"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "4",
"j": "6"
},
"number": "-0.1113168514638524458291198533428041948562521829991965027922869066531716753948051095208703483833014729 + i * -1.761645812565209289515900633392864722956941681807162501240469067641243039080605231170933508367942534"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "4",
"j": "7"
},
"number": "-0.1113168514638524458291198533428041948562521829991965027922869066531716753948051095208703483833014729 + i * 1.761645812565209289515900633392864722956941681807162501240469067641243039080605231170933508367942534"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "4",
"j": "8"
},
"number": "-0.03572671585171037700310539953341546973698409843178586951741974019262705937480227372077128794023829605 + i * -0.5653934561499007268614950932581716081652852166556043103296422974097979742027309773249729464181215910"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "4",
"j": "9"
},
"number": "-0.03572671585171037700310539953341546973698409843178586951741974019262705937480227372077128794023829605 + i * 0.5653934561499007268614950932581716081652852166556043103296422974097979742027309773249729464181215910"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "4",
"j": "10"
},
"number": "0.1127819945265776311216551706735581724406138695550352351440206551030461080100242894288680213377750659 + i * -0.6603391820064359256535127309709759682934373852628633585605953106278997196981386090332539648101954711"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "4",
"j": "11"
},
"number": "0.1127819945265776311216551706735581724406138695550352351440206551030461080100242894288680213377750659 + i * 0.6603391820064359256535127309709759682934373852628633585605953106278997196981386090332539648101954711"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "4",
"j": "12"
},
"number": "0.2385024398468503574515457942539274654415127078232986617492187252118955805015804160421865680457274623 + i * -0.4091492654587910378260753820406483546080063199039013390939271627392524969833583822600446389820040626"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "4",
"j": "13"
},
"number": "0.2385024398468503574515457942539274654415127078232986617492187252118955805015804160421865680457274623 + i * 0.4091492654587910378260753820406483546080063199039013390939271627392524969833583822600446389820040626"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "4",
"j": "14"
},
"number": "0.2513149146978025191660807341777935283863609635054748719479520400813146477770566361700908889783645177 + i * -1.471450171582632163293260606973259128827825886409529011066327127974043697016517483926755647842681044"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "4",
"j": "15"
},
"number": "0.2513149146978025191660807341777935283863609635054748719479520400813146477770566361700908889783645177 + i * 1.471450171582632163293260606973259128827825886409529011066327127974043697016517483926755647842681044"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "4",
"j": "16"
},
"number": "0.2698268914413946676582043865241992972425771883199284859023817095681364369731973012446519113188347325 + i * -0.2383244010982853161513117136423944102222576283304054438814569673951006385788911197212145851327441245"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "4",
"j": "17"
},
"number": "0.2698268914413946676582043865241992972425771883199284859023817095681364369731973012446519113188347325 + i * 0.2383244010982853161513117136423944102222576283304054438814569673951006385788911197212145851327441245"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "4",
"j": "18"
},
"number": "1.063382782178043608141704680187675533745508578295578346866033523500188018217167159749346160726839694 + i * -1.824225716554730626944635471222718187155425899965025267136449548425299099678668202742847441302846960"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "4",
"j": "19"
},
"number": "1.063382782178043608141704680187675533745508578295578346866033523500188018217167159749346160726839694 + i * 1.824225716554730626944635471222718187155425899965025267136449548425299099678668202742847441302846960"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "4",
"j": "20"
},
"number": "2.081916149658693644663092427620310066050932114529400708394152885339430627554282340577445975327262340 + i * -1.838850890116053432053204544628342821251625871303011707902647987905545418536996564317068828015176981"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "4",
"j": "21"
},
"number": "2.081916149658693644663092427620310066050932114529400708394152885339430627554282340577445975327262340 + i * 1.838850890116053432053204544628342821251625871303011707902647987905545418536996564317068828015176981"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "5",
"j": "1"
},
"number": "-1.139231934917025469654566593753700091079572717505258874503337165396160455696955108496180309622850030 + i * -1.036634105572539516615375929457985064670513016509314959407010473325160368972853886488558914989256439"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "5",
"j": "2"
},
"number": "-1.139231934917025469654566593753700091079572717505258874503337165396160455696955108496180309622850030 + i * 1.036634105572539516615375929457985064670513016509314959407010473325160368972853886488558914989256439"
},
{
"comment": "Multiplicity 7.",
"params": {
"m": "4",
"n": "5",
"j": "3"
},
"number": "-1"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "5",
"j": "4"
},
"number": "-0.4801902216271983661476379717627415804292790140577088669461249307508229493331037544014481918843336430 + i * -0.4369448798303267328206951767436365462248471827351174665164018257193228143236831025974780784930768093"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "5",
"j": "5"
},
"number": "-0.4801902216271983661476379717627415804292790140577088669461249307508229493331037544014481918843336430 + i * 0.4369448798303267328206951767436365462248471827351174665164018257193228143236831025974780784930768093"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "5",
"j": "6"
},
"number": "-0.06403900357635011602581511514610967456379160555485051666892909655728284984686897726440642689006008562 + i * -1.208184865784237851238687822348085421384173757683534703742504924258968708398404941758862541540019620"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "5",
"j": "7"
},
"number": "-0.06403900357635011602581511514610967456379160555485051666892909655728284984686897726440642689006008562 + i * 1.208184865784237851238687822348085421384173757683534703742504924258968708398404941758862541540019620"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "5",
"j": "8"
},
"number": "-0.04374811675308561442815095177602286564273696223882752247768569857611749159624248279572474629324861195 + i * -0.8253690659727846409783055854557571042728236321117236603551108778201320963905654709878354253622891485"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "5",
"j": "9"
},
"number": "-0.04374811675308561442815095177602286564273696223882752247768569857611749159624248279572474629324861195 + i * 0.8253690659727846409783055854557571042728236321117236603551108778201320963905654709878354253622891485"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "5",
"j": "10"
},
"number": "0.07245838010142785358606880707996480157148093558615743536153490872018075542740688712963385774256559161 + i * -0.5425041642584351471193490913012954839980247146259789595290253835595644260436575058264495484237617571"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "5",
"j": "11"
},
"number": "0.07245838010142785358606880707996480157148093558615743536153490872018075542740688712963385774256559161 + i * 0.5425041642584351471193490913012954839980247146259789595290253835595644260436575058264495484237617571"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "5",
"j": "12"
},
"number": "0.1902189846138320767268075547787231501501358445310181741248033351407596931394776297233427485237727967 + i * -0.5199190372143699521140343143537664985003462498187310329419843621893007357113276007964057799539250026"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "5",
"j": "13"
},
"number": "0.1902189846138320767268075547787231501501358445310181741248033351407596931394776297233427485237727967 + i * 0.5199190372143699521140343143537664985003462498187310329419843621893007357113276007964057799539250026"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "5",
"j": "14"
},
"number": "0.2418818995435892207896298579327862773585855549950212394394564153386010013557430704885925363147206360 + i * -1.810997397091296510369358656252503843731596220128576043630027307392090881041766383640567266954867515"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "5",
"j": "15"
},
"number": "0.2418818995435892207896298579327862773585855549950212394394564153386010013557430704885925363147206360 + i * 1.810997397091296510369358656252503843731596220128576043630027307392090881041766383640567266954867515"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "5",
"j": "16"
},
"number": "0.2659461034909066407292828603087565650728758364778963939655281522969449339167546574194354189300430500 + i * -0.3582953201032266146402688417720570781588823034758281908812737176582468699010715643465718463294918583"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "5",
"j": "17"
},
"number": "0.2659461034909066407292828603087565650728758364778963939655281522969449339167546574194354189300430500 + i * 0.3582953201032266146402688417720570781588823034758281908812737176582468699010715643465718463294918583"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "5",
"j": "18"
},
"number": "0.2869845160491528430246287650728199572132797491834433987982023708239358994078959756078207040028886519 + i * -0.2174831108260953147969478493248750891595379091334046575618018721353307589680305830419261477777901555"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "5",
"j": "19"
},
"number": "0.2869845160491528430246287650728199572132797491834433987982023708239358994078959756078207040028886519 + i * 0.2174831108260953147969478493248750891595379091334046575618018721353307589680305830419261477777901555"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "5",
"j": "20"
},
"number": "0.6206184777294495149926170242128111459306734148408026039602604068757652163902309520899242635245390908 + i * -1.696315234116120548652527975596810064437542843088155552147650761208951089322319613698443026223833255"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "5",
"j": "21"
},
"number": "0.6206184777294495149926170242128111459306734148408026039602604068757652163902309520899242635245390908 + i * 1.696315234116120548652527975596810064437542843088155552147650761208951089322319613698443026223833255"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "5",
"j": "22"
},
"number": "1.335722123642678075689259610158485275985161582553924855807840598537109964060173672004370027119487875 + i * -1.799548779160356915264589674621993654106957571310211784672560115808649498070787651200952597731150581"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "5",
"j": "23"
},
"number": "1.335722123642678075689259610158485275985161582553924855807840598537109964060173672004370027119487875 + i * 1.799548779160356915264589674621993654106957571310211784672560115808649498070787651200952597731150581"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "5",
"j": "24"
},
"number": "2.213378791702623340717876152894227038433187381188381679138450703547086282775487478494640118532474679 + i * -1.677346609785540535523868180324375175068117835896386634389655278987208206003452749823699797894818729"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "5",
"j": "25"
},
"number": "2.213378791702623340717876152894227038433187381188381679138450703547086282775487478494640118532474679 + i * 1.677346609785540535523868180324375175068117835896386634389655278987208206003452749823699797894818729"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "1"
},
"number": "-1.471580340364302081833948997201407901330259186951032092919222871836572677050904691227074884722279723 + i * -0.7288811976881560779287581001967784127827289612639301558913611568686028870461512421310423166393082227"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "2"
},
"number": "-1.471580340364302081833948997201407901330259186951032092919222871836572677050904691227074884722279723 + i * 0.7288811976881560779287581001967784127827289612639301558913611568686028870461512421310423166393082227"
},
{
"comment": "Multiplicity 6.",
"params": {
"m": "4",
"n": "6",
"j": "3"
},
"number": "-1"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "4"
},
"number": "-0.8117927742039103151444909914525029519589624780369312596422669109561038160263910945984928314404228535 + i * -1.105481043759721835828421600746341512923104410197838947162565551324871346279567208718326264322810690"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "5"
},
"number": "-0.8117927742039103151444909914525029519589624780369312596422669109561038160263910945984928314404228535 + i * 1.105481043759721835828421600746341512923104410197838947162565551324871346279567208718326264322810690"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "6"
},
"number": "-0.5456731450538992450826323564446112424298025724841366424639219006357215680392932439299327275398027690 + i * -0.2702746731549073131183882120065864882080186403652592500094392075046002059313205137420618514507603725"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "7"
},
"number": "-0.5456731450538992450826323564446112424298025724841366424639219006357215680392932439299327275398027690 + i * 0.2702746731549073131183882120065864882080186403652592500094392075046002059313205137420618514507603725"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "8"
},
"number": "-0.4315531161126116948678093026860277800686138657284845297998528771377071682405385297919363061529948453 + i * -0.5876792752999998264294772800374803313714045898527793618774739198846145797789886856332750278991664673"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "9"
},
"number": "-0.4315531161126116948678093026860277800686138657284845297998528771377071682405385297919363061529948453 + i * 0.5876792752999998264294772800374803313714045898527793618774739198846145797789886856332750278991664673"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "10"
},
"number": "-0.1690344260982571993602810244853303212198720276814387376273337902730885625182751536173921496983258550 + i * -1.230219852123643090571783050133331514453256851281879115343925197011487746014149293504337254995418125"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "11"
},
"number": "-0.1690344260982571993602810244853303212198720276814387376273337902730885625182751536173921496983258550 + i * 1.230219852123643090571783050133331514453256851281879115343925197011487746014149293504337254995418125"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "12"
},
"number": "-0.1096192891387398079296245700146533886232036573308626423977633066143553730305889078058599781584247408 + i * -0.7978009497057698454161371976972025809579019674640143826687042001309194196333754727005100616814896112"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "13"
},
"number": "-0.1096192891387398079296245700146533886232036573308626423977633066143553730305889078058599781584247408 + i * 0.7978009497057698454161371976972025809579019674640143826687042001309194196333754727005100616814896112"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "14"
},
"number": "0.1057013977874212621252275021877329823785539258329113330647091218321155312837992491640935880606097817 + i * -0.6256604794808111698450402164414299217307405333165691131575734589235518720955633843223661634127173549"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "15"
},
"number": "0.1057013977874212621252275021877329823785539258329113330647091218321155312837992491640935880606097817 + i * 0.6256604794808111698450402164414299217307405333165691131575734589235518720955633843223661634127173549"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "16"
},
"number": "0.1308744031787449198075072827443481047665729866845424747940604015608314667988024853237188178467276050 + i * -0.5499851819996014677163975157355909890434435945248031325580655902454905665716227494502364190591396311"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "17"
},
"number": "0.1308744031787449198075072827443481047665729866845424747940604015608314667988024853237188178467276050 + i * 0.5499851819996014677163975157355909890434435945248031325580655902454905665716227494502364190591396311"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "18"
},
"number": "0.2429935316406965782904510991032178231171556854942176487410154837227920469561719994527150790004563642 + i * -0.4358793386389523661371294621130327420557054915539695523667225092155229912064222401691962227571420303"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "19"
},
"number": "0.2429935316406965782904510991032178231171556854942176487410154837227920469561719994527150790004563642 + i * 0.4358793386389523661371294621130327420557054915539695523667225092155229912064222401691962227571420303"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "20"
},
"number": "0.2625314058773632171828912009774215624810783999358913908164966130863156433940887179615113425598501132 + i * -1.553957929774409734131663901655872853191730791603413970649172385551252273392372106074210038706565927"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "21"
},
"number": "0.2625314058773632171828912009774215624810783999358913908164966130863156433940887179615113425598501132 + i * 1.553957929774409734131663901655872853191730791603413970649172385551252273392372106074210038706565927"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "22"
},
"number": "0.2781750635121444834066828326032669690091020243865914695485032206340793494925539153316255896939265592 + i * -0.3200134670824251787524232639591551817111086072624296305856349189572336113302626623887269555106071549"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "23"
},
"number": "0.2781750635121444834066828326032669690091020243865914695485032206340793494925539153316255896939265592 + i * 0.3200134670824251787524232639591551817111086072624296305856349189572336113302626623887269555106071549"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "24"
},
"number": "0.2968696273443089019652743779124911250418660792002637086916158743235671276922857911808603736978603553 + i * -0.2037753109162835907281154921135807068720727751927445562334090716554271650494112443781338661327262283"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "25"
},
"number": "0.2968696273443089019652743779124911250418660792002637086916158743235671276922857911808603736978603553 + i * 0.2037753109162835907281154921135807068720727751927445562334090716554271650494112443781338661327262283"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "26"
},
"number": "0.4094792468706908473401480528469077365352620230867296732055331284484842853179529322733999327542951478 + i * -1.720791175701897679215854498612043094240994983873365696766513900314803942512692181146643123574405964"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "27"
},
"number": "0.4094792468706908473401480528469077365352620230867296732055331284484842853179529322733999327542951478 + i * 1.720791175701897679215854498612043094240994983873365696766513900314803942512692181146643123574405964"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "28"
},
"number": "0.9757340032995193407257768400737567198851894609558316995698297276620225663457868943235460850343319853 + i * -1.750261783406674807080483254018530876426869887332354571453663207862073732015556269090760969536929822"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "29"
},
"number": "0.9757340032995193407257768400737567198851894609558316995698297276620225663457868943235460850343319853 + i * 1.750261783406674807080483254018530876426869887332354571453663207862073732015556269090760969536929822"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "30"
},
"number": "1.547222240423988313914874944062430011543289135145233880016935333217719738169743869177027751559679091 + i * -1.779929326711564848323432731240017275639920709186271912313001914050267991797073049843022731085740256"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "31"
},
"number": "1.547222240423988313914874944062430011543289135145233880016935333217719738169743869177027751559679091 + i * 1.779929326711564848323432731240017275639920709186271912313001914050267991797073049843022731085740256"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "32"
},
"number": "2.289672171036842479459953109772960550872644067490672626401662752965621409454805766782190317504513783 + i * -1.571661819106396765014055309565540463730944342305275957938827209495847378717240245783149650073928982"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "4",
"n": "6",
"j": "33"
},
"number": "2.289672171036842479459953109772960550872644067490672626401662752965621409454805766782190317504513783 + i * 1.571661819106396765014055309565540463730944342305275957938827209495847378717240245783149650073928982"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "1"
},
"number": "-1.326955559590357375774635146179919460557488176919503137175995131151904650104625191963328951203694898 + i * -0.8796105241148522407068629931563471634372265347028399035238142068299601219884303568821138998017268340"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "2"
},
"number": "-1.326955559590357375774635146179919460557488176919503137175995131151904650104625191963328951203694898 + i * 0.8796105241148522407068629931563471634372265347028399035238142068299601219884303568821138998017268340"
},
{
"comment": "Multiplicity 8.",
"params": {
"m": "5",
"n": "5",
"j": "3"
},
"number": "-1"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "4"
},
"number": "-0.7863263802902427516217126888593754741977824287880157792110418699784749120910726646756275461481357865 + i * -1.236188439460251865759741160245168078286721641171041811294442354152804411577044069655010123812926359"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "5"
},
"number": "-0.7863263802902427516217126888593754741977824287880157792110418699784749120910726646756275461481357865 + i * 1.236188439460251865759741160245168078286721641171041811294442354152804411577044069655010123812926359"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "6"
},
"number": "-0.5235518200598295755960605574233835348729624774660473976582285229051396206445142389308078795030311083 + i * -0.3470513292745678093889680469935045192942146556608206007583864613924547990462658902429068259316579871"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "7"
},
"number": "-0.5235518200598295755960605574233835348729624774660473976582285229051396206445142389308078795030311083 + i * 0.3470513292745678093889680469935045192942146556608206007583864613924547990462658902429068259316579871"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "8"
},
"number": "-0.3663344940431253015666440997228877507291276735601699741222045130245919948332849512260228851970235118 + i * -0.5759166649661128780341931378287284837507355336166173836728491880150585860360175497388727437716721856"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "9"
},
"number": "-0.3663344940431253015666440997228877507291276735601699741222045130245919948332849512260228851970235118 + i * 0.5759166649661128780341931378287284837507355336166173836728491880150585860360175497388727437716721856"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "10"
},
"number": "0.04537497190559604956806851448877672018085536766437645280884690425837778201220738200735886721547410845 + i * -0.6919668790954023755149755531644760604170859710460958205501155260128160909194407913207408163730474008"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "11"
},
"number": "0.04537497190559604956806851448877672018085536766437645280884690425837778201220738200735886721547410845 + i * 0.6919668790954023755149755531644760604170859710460958205501155260128160909194407913207408163730474008"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "12"
},
"number": "0.09435878031744204198462198090429067052470989772664282743764328376542203981641842241147087831784834813 + i * -1.438968400186634878205552531204139389660344699469465983404069649790318541850732431298727222944657899"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "13"
},
"number": "0.09435878031744204198462198090429067052470989772664282743764328376542203981641842241147087831784834813 + i * 1.438968400186634878205552531204139389660344699469465983404069649790318541850732431298727222944657899"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "14"
},
"number": "0.1268401938455927426234859619779922130506160409214482743903247616803913292940421856164129902401777703 + i * -0.6881266043408210708617342502065424483462028580483174207790858117465757202654617245144973460096596590"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "15"
},
"number": "0.1268401938455927426234859619779922130506160409214482743903247616803913292940421856164129902401777703 + i * 0.6881266043408210708617342502065424483462028580483174207790858117465757202654617245144973460096596590"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "16"
},
"number": "0.1526578383477638558198207234740119324513069297567359852537573031905392774285008246123261639812371575 + i * -0.4440236398856600280039376619619321299381059762132704618113561322402531857113237409002815152732056061"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "17"
},
"number": "0.1526578383477638558198207234740119324513069297567359852537573031905392774285008246123261639812371575 + i * 0.4440236398856600280039376619619321299381059762132704618113561322402531857113237409002815152732056061"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "18"
},
"number": "0.2466010877040604514309610655325770792473354514618478007859426225025873833584916688351319255343784667 + i * -0.4623317706192098771434234627129733880585765413896007133655575966026100514596706040356594044487587820"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "19"
},
"number": "0.2466010877040604514309610655325770792473354514618478007859426225025873833584916688351319255343784667 + i * 0.4623317706192098771434234627129733880585765413896007133655575966026100514596706040356594044487587820"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "20"
},
"number": "0.2590655001837745155590841876519685567646759643709243400818741006418249018192994823031347172606671766 + i * -1.405468231626416540049101082860212141043445952655221728226387426817066221197020551525050613900942746"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "21"
},
"number": "0.2590655001837745155590841876519685567646759643709243400818741006418249018192994823031347172606671766 + i * 1.405468231626416540049101082860212141043445952655221728226387426817066221197020551525050613900942746"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "22"
},
"number": "0.2952444868584827398121600661419322282456547668252554760274696281097340360735374688876355857729452262 + i * -0.3188208657769811009485894760354044067895359533790066838158260085350372915214233229654859053408243318"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "23"
},
"number": "0.2952444868584827398121600661419322282456547668252554760274696281097340360735374688876355857729452262 + i * 0.3188208657769811009485894760354044067895359533790066838158260085350372915214233229654859053408243318"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "24"
},
"number": "0.3044025344716389242438750631074962145588344132304511713033033648380660643137535319669162048682189030 + i * -0.1957071083449249702144126310554778725376851059673215681170588380947636683383024425631550972950019656"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "25"
},
"number": "0.3044025344716389242438750631074962145588344132304511713033033648380660643137535319669162048682189030 + i * 0.1957071083449249702144126310554778725376851059673215681170588380947636683383024425631550972950019656"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "26"
},
"number": "0.6924469886369234416056774447353699757652181160443987176495464412186032841283834568580019348126814760 + i * -2.014065151518862416281866723561125602792804412879705225354266546500198245338497202735572306393261651"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "27"
},
"number": "0.6924469886369234416056774447353699757652181160443987176495464412186032841283834568580019348126814760 + i * 2.014065151518862416281866723561125602792804412879705225354266546500198245338497202735572306393261651"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "28"
},
"number": "0.8981592601493495095876612657947134006906343813849458335653056139410918934929053109743208441393120820 + i * -1.683883736722264993157433825750730630042463942896184191887930446799972566312808501936360001324755147"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "29"
},
"number": "0.8981592601493495095876612657947134006906343813849458335653056139410918934929053109743208441393120820 + i * 1.683883736722264993157433825750730630042463942896184191887930446799972566312808501936360001324755147"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "30"
},
"number": "1.563662011528708634586378448636163857256424851634008107620675732484464896764525658353024962562946989 + i * -1.688526284106752191185882912097491577748807513118691997070470152806946601841088020487269792340605905"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "31"
},
"number": "1.563662011528708634586378448636163857256424851634008107620675732484464896764525658353024962562946989 + i * 1.688526284106752191185882912097491577748807513118691997070470152806946601841088020487269792340605905"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "32"
},
"number": "2.324354600034222097737257769740273371621094575712701301242780280429008289171431653970052187345997601 + i * -1.494378876741265902613570502414612969100962467819120973218366275977268020043321157282165883820304687"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "5",
"j": "33"
},
"number": "2.324354600034222097737257769740273371621094575712701301242780280429008289171431653970052187345997601 + i * 1.494378876741265902613570502414612969100962467819120973218366275977268020043321157282165883820304687"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "1"
},
"number": "-1.440475300308338024707008824855151152361202308470460005584741950129075618087129911638340329641884237 + i * -0.8742752343808977505659630602794267321370281866215293566802079377398365324870745265087291904671666881"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "2"
},
"number": "-1.440475300308338024707008824855151152361202308470460005584741950129075618087129911638340329641884237 + i * 0.8742752343808977505659630602794267321370281866215293566802079377398365324870745265087291904671666881"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "3"
},
"number": "-1.042054229763545760064838899353902162306165284048228149879516299302204270951242325048086724217230401 + i * -1.095256173045084467566176146649937222407037176482453478000220576510608851761943388573456038162729558"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "4"
},
"number": "-1.042054229763545760064838899353902162306165284048228149879516299302204270951242325048086724217230401 + i * 1.095256173045084467566176146649937222407037176482453478000220576510608851761943388573456038162729558"
},
{
"comment": "Multiplicity 9.",
"params": {
"m": "5",
"n": "6",
"j": "5"
},
"number": "-1"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "6"
},
"number": "-0.5073299649840662159607684927902381735034765177505335950526492795661714944519640729757569051481925649 + i * -0.3079164383797173011594961762605444666828454474432331041805109494733303009205086319732596576891937787"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "7"
},
"number": "-0.5073299649840662159607684927902381735034765177505335950526492795661714944519640729757569051481925649 + i * 0.3079164383797173011594961762605444666828454474432331041805109494733303009205086319732596576891937787"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "8"
},
"number": "-0.4559488309773369547760191944163505026609903442875063337813499607124263434952042114957952330647046613 + i * -0.4792272392905438767079921145240215877868822578731179046160741688031034055383556521234532607839121690"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "9"
},
"number": "-0.4559488309773369547760191944163505026609903442875063337813499607124263434952042114957952330647046613 + i * 0.4792272392905438767079921145240215877868822578731179046160741688031034055383556521234532607839121690"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "10"
},
"number": "-0.3210201407589114259084772700978819801161186558781687714313936863013955744055146588978192898620278021 + i * -1.254869448586342815201392044098076263317265196284189856427719286137491053762293313520853441268067845"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "11"
},
"number": "-0.3210201407589114259084772700978819801161186558781687714313936863013955744055146588978192898620278021 + i * 1.254869448586342815201392044098076263317265196284189856427719286137491053762293313520853441268067845"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "12"
},
"number": "-0.1913395314856706926000474206723259046108245315636071874543315053096754715853202623917036347492810244 + i * -0.7479472527816075507617829163430509802204633007221537574160481785685273386732742153254164214690122102"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "13"
},
"number": "-0.1913395314856706926000474206723259046108245315636071874543315053096754715853202623917036347492810244 + i * 0.7479472527816075507617829163430509802204633007221537574160481785685273386732742153254164214690122102"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "14"
},
"number": "-0.01229600883097514939062499808000659940128259948851923343350132153328239506738783290613014933559038400 + i * -1.204996643118050593379185651822914492690719960308818058647275802891488230846984393293191721636897978"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "15"
},
"number": "-0.01229600883097514939062499808000659940128259948851923343350132153328239506738783290613014933559038400 + i * 1.204996643118050593379185651822914492690719960308818058647275802891488230846984393293191721636897978"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "16"
},
"number": "-0.008467345354908691336956028222786469264450653271195310825383936955009682956529801477650440022735130553 + i * -0.8297914281814175608811515463603883982139767417248259479985878466101000395918322978225349447795738240"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "17"
},
"number": "-0.008467345354908691336956028222786469264450653271195310825383936955009682956529801477650440022735130553 + i * 0.8297914281814175608811515463603883982139767417248259479985878466101000395918322978225349447795738240"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "18"
},
"number": "0.1089448185770945237466345691842097286103416102604848361700678646303620507502340842149316502892682979 + i * -0.6101862961639226374672432124943521113893206098353979635634450348893850531325800914561953520794012526"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "19"
},
"number": "0.1089448185770945237466345691842097286103416102604848361700678646303620507502340842149316502892682979 + i * 0.6101862961639226374672432124943521113893206098353979635634450348893850531325800914561953520794012526"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "20"
},
"number": "0.1967714263812103137485788545761035625858794345813974360781685681667143678834323835104921161438662395 + i * -0.4174657291435524230639627488845366774332413795192742080664325468475708950773767788008628402492315004"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "21"
},
"number": "0.1967714263812103137485788545761035625858794345813974360781685681667143678834323835104921161438662395 + i * 0.4174657291435524230639627488845366774332413795192742080664325468475708950773767788008628402492315004"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "22"
},
"number": "0.2082794537849534243290978603139473815658335004497555696968342124626826200957640490884519458106503631 + i * -0.5584681604883768270601244376612681743473179279466136874487568516228107982846018664222270789085009545"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "23"
},
"number": "0.2082794537849534243290978603139473815658335004497555696968342124626826200957640490884519458106503631 + i * 0.5584681604883768270601244376612681743473179279466136874487568516228107982846018664222270789085009545"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "24"
},
"number": "0.2735178561183997060310046801783445345154045227616905277872853624605149840541631721504981342928399291 + i * -0.4011558879023085666339511590199601624323208961646467825969483392652796131156672167324635653988257778"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "25"
},
"number": "0.2735178561183997060310046801783445345154045227616905277872853624605149840541631721504981342928399291 + i * 0.4011558879023085666339511590199601624323208961646467825969483392652796131156672167324635653988257778"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "26"
},
"number": "0.2835655146823786254306613066688637951767933693629919785837818794521596905211466834956585940546102542 + i * -1.588214964086744159558653486632782692904023396621756440622484050281143179440122172096370731632791161"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "27"
},
"number": "0.2835655146823786254306613066688637951767933693629919785837818794521596905211466834956585940546102542 + i * 1.588214964086744159558653486632782692904023396621756440622484050281143179440122172096370731632791161"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "28"
},
"number": "0.3085729161686157112144054197065173107824176483301053894865694275606671424837924175251355791757519718 + i * -0.2886992986257728618057054704491895436457270901487285744658330674939938784830382893679999639624291876"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "29"
},
"number": "0.3085729161686157112144054197065173107824176483301053894865694275606671424837924175251355791757519718 + i * 0.2886992986257728618057054704491895436457270901487285744658330674939938784830382893679999639624291876"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "30"
},
"number": "0.3146584788861420686842242615895822167371383294216051566816752882969181490798076908560886780485500512 + i * -0.1812624335684031815879890161224252177422356175220783961887813641238032501159650246964023298268860714"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "31"
},
"number": "0.3146584788861420686842242615895822167371383294216051566816752882969181490798076908560886780485500512 + i * 0.1812624335684031815879890161224252177422356175220783961887813641238032501159650246964023298268860714"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "32"
},
"number": "0.5862617235251305900182287031827206087836771804344273674855938326883755233068029720801562271207419491 + i * -1.571967375331564081499015067682352608312230747627545569161723115059721186875585918519038836657528182"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "33"
},
"number": "0.5862617235251305900182287031827206087836771804344273674855938326883755233068029720801562271207419491 + i * 1.571967375331564081499015067682352608312230747627545569161723115059721186875585918519038836657528182"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "34"
},
"number": "0.9238241331545145680167100607970984306490979557781262492159789650037788416167996377332561800720639867 + i * -1.959964017339596799951832121542072773132778656526297334309530675916632787173921991695625813946591081"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "35"
},
"number": "0.9238241331545145680167100607970984306490979557781262492159789650037788416167996377332561800720639867 + i * 1.959964017339596799951832121542072773132778656526297334309530675916632787173921991695625813946591081"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "36"
},
"number": "1.160261739070757697843529389701199057426430741841272273282798931473021252140206416455823729782351971 + i * -1.701701800172510396720838380417395615223796667591820803004152648487683758959870394323321936990748751"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "37"
},
"number": "1.160261739070757697843529389701199057426430741841272273282798931473021252140206416455823729782351971 + i * 1.701701800172510396720838380417395615223796667591820803004152648487683758959870394323321936990748751"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "38"
},
"number": "1.728075093220366753675622660140142320186406798836391026148653551764118765938379682758815936848477598 + i * -1.616778535134861528191969079704186862934187404302817248098880150872027655937872872521447426787616597"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "39"
},
"number": "1.728075093220366753675622660140142320186406798836391026148653551764118765938379682758815936848477598 + i * 1.616778535134861528191969079704186862934187404302817248098880150872027655937872872521447426787616597"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "40"
},
"number": "2.386198198894188932006043362449913997205089802699970776825460055849927463129763886961973934402473593 + i * -1.374595383665506850392048934851011830466350596298644605155527650740492808111700523964693858145814502"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "5",
"n": "6",
"j": "41"
},
"number": "2.386198198894188932006043362449913997205089802699970776825460055849927463129763886961973934402473593 + i * 1.374595383665506850392048934851011830466350596298644605155527650740492808111700523964693858145814502"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "6",
"n": "6",
"j": "1"
},
"number": "-1.684987005839314501179141795232063884257240248349538626088415378848345842072884156522004907879166254 + i * -0.6904503871156138551601864324070048493529863407653616468473019133422827151521956899114053702904953155"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "6",
"n": "6",
"j": "2"
},
"number": "-1.684987005839314501179141795232063884257240248349538626088415378848345842072884156522004907879166254 + i * 0.6904503871156138551601864324070048493529863407653616468473019133422827151521956899114053702904953155"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "6",
"n": "6",
"j": "3"
},
"number": "-1.218286978849634518655191327319109038486728396021563522592869342510484339311792364693316354122955671 + i * -1.077613543333278574448918008646388927472619672900444304273798050322967860577516814866396575974341919"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "6",
"n": "6",
"j": "4"
},
"number": "-1.218286978849634518655191327319109038486728396021563522592869342510484339311792364693316354122955671 + i * 1.077613543333278574448918008646388927472619672900444304273798050322967860577516814866396575974341919"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "6",
"n": "6",
"j": "5"
},
"number": "-1.061631591677744233072895836322748874550961486405644635051713078554365834851917210783469627643421297 + i * -1.047228487515974943431885307199215212377257903495949650133168914269388968985099287975960254092190432"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "6",
"n": "6",
"j": "6"
},
"number": "-1.061631591677744233072895836322748874550961486405644635051713078554365834851917210783469627643421297 + i * 1.047228487515974943431885307199215212377257903495949650133168914269388968985099287975960254092190432"
},
{
"comment": "Multiplicity 8.",
"params": {
"m": "6",
"n": "6",
"j": "7"
},
"number": "-1"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "6",
"n": "6",
"j": "8"
},
"number": "-0.6855711754749302861213069411439252809575702962625395117317115332146225532267650698041288318973094030 + i * -1.168604907588597074053697525097149330497262289988167466169222070594374887121918247408508411972649726"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "6",
"n": "6",
"j": "9"
},
"number": "-0.6855711754749302861213069411439252809575702962625395117317115332146225532267650698041288318973094030 + i * 1.168604907588597074053697525097149330497262289988167466169222070594374887121918247408508411972649726"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "6",
"n": "6",
"j": "10"
},
"number": "-0.5081532942352080231099114943729904530003012058770052114582837483332428763027125254187321175405593177 + i * -0.2082239432724933299169969665080022189735526648134862687906910887062749629644110127946729208478652382"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "6",
"n": "6",
"j": "11"
},
"number": "-0.5081532942352080231099114943729904530003012058770052114582837483332428763027125254187321175405593177 + i * 0.2082239432724933299169969665080022189735526648134862687906910887062749629644110127946729208478652382"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "6",
"n": "6",
"j": "12"
},
"number": "-0.4774061839346343759765480503705722372870799300531052035755236627280203104885507398601712099059084676 + i * -0.4709292374603714277824572429467993895358222495069448797614952481282652975582803930633715983720282818"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "6",
"n": "6",
"j": "13"
},
"number": "-0.4774061839346343759765480503705722372870799300531052035755236627280203104885507398601712099059084676 + i * 0.4709292374603714277824572429467993895358222495069448797614952481282652975582803930633715983720282818"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "6",
"n": "6",
"j": "14"
},
"number": "-0.4605174450595018684181778362066760852804742088353249134607668231080285952558176949269826172602092337 + i * -0.4073423128973690482088306787393393338036777742738580121382604082002192141050153671135867057781863010"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "6",
"n": "6",
"j": "15"
},
"number": "-0.4605174450595018684181778362066760852804742088353249134607668231080285952558176949269826172602092337 + i * 0.4073423128973690482088306787393393338036777742738580121382604082002192141050153671135867057781863010"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "6",
"n": "6",
"j": "16"
},
"number": "-0.3734769391005705784875281613160389846245887760653088420703923183710132046292431711522886840840321863 + i * -0.6366180485953849884836342340978039412533884177126161160944042316303260055753525830531591087425851733"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "6",
"n": "6",
"j": "17"
},
"number": "-0.3734769391005705784875281613160389846245887760653088420703923183710132046292431711522886840840321863 + i * 0.6366180485953849884836342340978039412533884177126161160944042316303260055753525830531591087425851733"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "6",
"n": "6",
"j": "18"
},
"number": "-0.06139292324205990402370656948008759294331962626060189394009207013247222985448637551476244519654339872 + i * -1.515581672973391557488459926090154604747851976594557326321143766844465570225185284719974660179460320"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "6",
"n": "6",
"j": "19"
},
"number": "-0.06139292324205990402370656948008759294331962626060189394009207013247222985448637551476244519654339872 + i * 1.515581672973391557488459926090154604747851976594557326321143766844465570225185284719974660179460320"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "6",
"n": "6",
"j": "20"
},
"number": "-0.02668379405173076989834642152709685777650193626446513232757146105814741691129614362777674830905734740 + i * -0.6587317738682519584249736411738784366776912934782078179353317183588482665543225735055303995302533330"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "6",
"n": "6",
"j": "21"
},
"number": "-0.02668379405173076989834642152709685777650193626446513232757146105814741691129614362777674830905734740 + i * 0.6587317738682519584249736411738784366776912934782078179353317183588482665543225735055303995302533330"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "6",
"n": "6",
"j": "22"
},
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{
"comment": "Multiplicity 1.",
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{
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{
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{
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{
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{
"comment": "Multiplicity 1.",
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{
"comment": "Multiplicity 1.",
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{
"comment": "Multiplicity 1.",
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{
"comment": "Multiplicity 1.",
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{
"comment": "Multiplicity 1.",
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{
"comment": "Multiplicity 1.",
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},
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{
"comment": "Multiplicity 1.",
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{
"comment": "Multiplicity 1.",
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"m": "6",
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},
"number": "0.2627726509582249633702081411916359722478125396473709652556852608114663062623552915753408157132580628 + i * 1.370124469005658789300787149300259940936320388828902462392347866115078930315856963832387628220179167"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "6",
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"number": "0.2983823217864186984865149806620814925868049390149221340190937777031321260440893180885466907576560835 + i * -0.3667275930106299904773708417495067716516440132890846896365186306927129701836652935000707874790070172"
},
{
"comment": "Multiplicity 1.",
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"m": "6",
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},
"number": "0.2983823217864186984865149806620814925868049390149221340190937777031321260440893180885466907576560835 + i * 0.3667275930106299904773708417495067716516440132890846896365186306927129701836652935000707874790070172"
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{
"comment": "Multiplicity 1.",
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"number": "0.3243363738654317610602454913483489937794089412116360923873559864963087356914082175126650422955020812 + i * -0.2634479984214338019458407643422874371055188765408754975274736059152522878379074948009038683718837170"
},
{
"comment": "Multiplicity 1.",
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"m": "6",
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},
"number": "0.3243363738654317610602454913483489937794089412116360923873559864963087356914082175126650422955020812 + i * 0.2634479984214338019458407643422874371055188765408754975274736059152522878379074948009038683718837170"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "6",
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"j": "40"
},
"number": "0.3253400887805312159066560032070517338865134874239418484915735292605942399575945938437351011500059416 + i * -0.1662262944444239363916627511379016078015309314878736092873380948561407537251418047596699582663668945"
},
{
"comment": "Multiplicity 1.",
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},
"number": "0.3253400887805312159066560032070517338865134874239418484915735292605942399575945938437351011500059416 + i * 0.1662262944444239363916627511379016078015309314878736092873380948561407537251418047596699582663668945"
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{
"comment": "Multiplicity 1.",
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"number": "0.6389245789660840636480197556039173416937529275274610202879471310252960038468661403235523501235029354 + i * -1.685812988268613844604866755537676085902497868019529609805606303803107935610985485054741448866228100"
},
{
"comment": "Multiplicity 1.",
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},
"number": "0.6389245789660840636480197556039173416937529275274610202879471310252960038468661403235523501235029354 + i * 1.685812988268613844604866755537676085902497868019529609805606303803107935610985485054741448866228100"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "6",
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"j": "44"
},
"number": "0.8074691024237152837791007475107953476268765960924752196617128534022360765684803006802770105572752255 + i * -1.617171222768508828180127207144449543735342330670931006108593274384863726180550856087847417913626181"
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{
"comment": "Multiplicity 1.",
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},
"number": "0.8074691024237152837791007475107953476268765960924752196617128534022360765684803006802770105572752255 + i * 1.617171222768508828180127207144449543735342330670931006108593274384863726180550856087847417913626181"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "6",
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"number": "1.235176694134068285926514677158182373432267931943433205826886691002435154693427280982688253316353888 + i * -1.959381194116430352710804032347124100246389495453926261373885998378139290910020708417014708965131416"
},
{
"comment": "Multiplicity 1.",
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"number": "1.235176694134068285926514677158182373432267931943433205826886691002435154693427280982688253316353888 + i * 1.959381194116430352710804032347124100246389495453926261373885998378139290910020708417014708965131416"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "6",
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"number": "1.334917696004614560390417081528422192613981611732798794943677891744098339022686075079937402602993739 + i * -1.640684175229012523534570813751277571634832747829717076255173085739605003258821829276633723775777869"
},
{
"comment": "Multiplicity 1.",
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},
"number": "1.334917696004614560390417081528422192613981611732798794943677891744098339022686075079937402602993739 + i * 1.640684175229012523534570813751277571634832747829717076255173085739605003258821829276633723775777869"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "6",
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},
"number": "1.857608013287661371452539051610795527858429064254371698099890488622878116641527421605001083806619122 + i * -1.508875206070156266952361308687856588250399627444226288927514149101883076913623849687149714248869192"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "6",
"n": "6",
"j": "51"
},
"number": "1.857608013287661371452539051610795527858429064254371698099890488622878116641527421605001083806619122 + i * 1.508875206070156266952361308687856588250399627444226288927514149101883076913623849687149714248869192"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "6",
"n": "6",
"j": "52"
},
"number": "2.437417870676518593804800676725077293326478995907519453315387806780668103682667801037086003308952006 + i * -1.245352032003936962160804613962039685579625022270293809152392297179782455546617407678341871494114024"
},
{
"comment": "Multiplicity 1.",
"params": {
"m": "6",
"n": "6",
"j": "53"
},
"number": "2.437417870676518593804800676725077293326478995907519453315387806780668103682667801037086003308952006 + i * 1.245352032003936962160804613962039685579625022270293809152392297179782455546617407678341871494114024"
}
],
"Keywords": [
"Ising partition function",
"complex temperature zeros",
"open boundary conditions",
"finite square lattice"
],
"Comments": {
"conventions": "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.",
"indexing": "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.",
"finite-size": "Free rectangles form a finite-size Ising family in which changing the aspect ratio changes the boundary geometry CITE{WIG}. 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 $K_c=\\tfrac12\\log(1+\\sqrt2)$ in HREF{Critical_couplings_of_the_Ising_model_on_lattices#square,coupling}[$K_c$]. The present table varies complex $b$ and does not fix it at $b_c=\\sqrt2-1$."
},
"Formulas": {
"cut-polynomial": "$F_{m,n}(b)=\\sum_{S\\subseteq V(G_{m,n})}b^{d(S)}$, where $G_{m,n}=P_m\\square P_n$, $P_m$ is a path on $m$ vertices, and $d(S)$ counts edges with exactly one endpoint in $S$. The bond coordinate is $b=e^{-2K}$ with $K=J/(k_BT)$ CITE{PR}.",
"physical": "$Z_{m,n}(K,0)=e^{KE}F_{m,n}(e^{-2K})$, where $K=J/(k_BT)$ and $Z_{m,n}(K,0)=\\sum_\\sigma\\exp(K\\sum_{uv\\in E(G_{m,n})}\\sigma_u\\sigma_v)$ CITE{PR}.",
"controls": "$F_{m,n}(0)=2$, $F_{m,n}(1)=2^{mn}$, $\\deg F_{m,n}=E$, 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.",
"even-subgraphs": "$F_{m,n}(b)=2^{N-E}\\sum_{\\substack{A\\subseteq E(G_{m,n})\\\\ \\deg_A(v)\\text{ even for every }v}}(1-b)^{|A|}(1+b)^{E-|A|}$, where $\\deg_A(v)$ is the degree of vertex $v$ in the edge subset $A$. This is the zero-field high-temperature expansion.",
"small-square": "$F_{2,2}(b)=2(1+6b^2+b^4)$, so its four simple zeros are $\\pm i(\\sqrt2-1)$ and $\\pm i(\\sqrt2+1)$."
},
"Similar tables": [
{
"table": "HREF{Critical_couplings_of_the_Ising_model_on_lattices}",
"relation": "Bulk transition couplings for infinite Ising lattices, including the square lattice underlying these finite rectangles."
},
{
"table": "HREF{Critical_exponents_of_the_two-dimensional_universality_classes}",
"relation": "Critical exponents for the thermodynamic limit, including the two-dimensional Ising class."
},
{
"table": "HREF{Tutte_polynomials_of_connected_graphs}",
"relation": "Graph polynomials whose two-state Potts specialization gives the zero-field Ising partition function. CITE{Sokal}"
}
],
"References": {
"LSS": {
"bib": "J. Liu, A. Sinclair and P. Srivastava, Fisher zeros and correlation decay in the Ising model, 2018, Introduction, equation (1).",
"arxiv": "1807.06577"
},
"PR": {
"bib": "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": "1810.01699",
"doi": "10.1112/jlms.12286"
},
"WIG": {
"bib": "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": "1207.4540",
"doi": "10.1103/PhysRevE.86.041149"
},
"Sokal": {
"bib": "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": "math/0503607"
}
},
"Links": {
"SageRoots": {
"title": "SageMath: certified isolation of complex polynomial roots",
"url": "https://doc.sagemath.org/html/en/reference/polynomial_rings/sage/rings/polynomial/complex_roots.html"
},
"SageAlgebraic": {
"title": "SageMath: exact algebraic numbers and certified interval conversion",
"url": "https://doc.sagemath.org/html/en/reference/number_fields/sage/rings/qqbar.html"
}
},
"Programs": {
"program-sage": {
"language": "Sage",
"code": "# With the attached generate.py in the current directory:\nfrom generate import FisherZeros\ng = FisherZeros()\np = {'m': 6, 'n': 6, 'j': 1}\ng.value(p, 100) # certified value and multiplicity\nlist(g.enumerate()) # every distinct zero for 2 <= m <= n <= 6"
}
}
}