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Normalised Hecke eigenvalues of level one cusp forms
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Numbers
$k$
$i$
$p$ 
$a_p/p^{(k-1)/2}$
12
1
2:
-0.5303300858899106433006332715786367794636269532663555274412549017465246794232901395688953253728655898
comment: $a_2=-24$, the root of $\chi_{12,2}$.
12
1
3:
0.5987336124929452372687468834835114354864018161319834269822542645019027712771160622008900398667032113
comment: $a_2=-24$, the root of $\chi_{12,2}$.
12
1
5:
0.6912133332047349909540037644782121098994039473231148318866197565013002285331582505069837819180491768
comment: $a_2=-24$, the root of $\chi_{12,2}$.
12
1
7:
-0.3765476965589635683036749498842810101921187580135194164003722274295803311219633746416885693132092769
comment: $a_2=-24$, the root of $\chi_{12,2}$.
12
1
11:
1.000872909497037372201709351366952167872079291390257239367279015229860043066259727424970513177233932
comment: $a_2=-24$, the root of $\chi_{12,2}$.
12
1
13:
-0.4315613032925094500793614697879840256772811147033588560141724538506849925847298429649124751377563915
comment: $a_2=-24$, the root of $\chi_{12,2}$.
12
1
17:
-1.179650499416253268565296209088267407814883849126701535726662993525898587750106750281795551718469753
comment: $a_2=-24$, the root of $\chi_{12,2}$.
12
1
19:
0.9878027871269624608218178433593492187049581745222646186402897376171373576796598553989516818142493371
comment: $a_2=-24$, the root of $\chi_{12,2}$.
12
1
23:
0.6039751046808208209140173592184700225176129315948113185560554294015688964112683493941956400315663262
comment: $a_2=-24$, the root of $\chi_{12,2}$.
12
1
29:
1.162514717338632422877579844123726324800993580078314702977416929836581763729813349975384622906645272
comment: $a_2=-24$, the root of $\chi_{12,2}$.
12
1
31:
-0.3315122110568911588257876058543706824657705225732363299281988553439305445301072538749844503262298464
comment: $a_2=-24$, the root of $\chi_{12,2}$.
12
1
37:
-0.4319869472570346910408567304386573194573007766713625873755839216890840139405566455558323097887019712
comment: $a_2=-24$, the root of $\chi_{12,2}$.
12
1
41:
0.4153452998335415440833204775340603490359265084786771856233937510483154592296031633612439461207671479
comment: $a_2=-24$, the root of $\chi_{12,2}$.
12
1
43:
-0.01776527886859974698913306210573175610806495707096420203283013005980400219189627621963859609956120900
comment: $a_2=-24$, the root of $\chi_{12,2}$.
12
1
47:
1.709172005305176414105573550060353324469808786775944071172584250096155742995936582713829317540728689
comment: $a_2=-24$, the root of $\chi_{12,2}$.
12
1
53:
-0.5242407305685585099265397533232602208943059602157070654311094051502656177247561486689991491072625938
comment: $a_2=-24$, the root of $\chi_{12,2}$.
12
1
59:
-0.9449626830605435624175307069296804801073408113814191457344121507235239079791321233746040555825713398
comment: $a_2=-24$, the root of $\chi_{12,2}$.
12
1
61:
1.054569884035339663097444438060698301915856918487749666113869196070530567518665725291324765383820971
comment: $a_2=-24$, the root of $\chi_{12,2}$.
16
1
2:
1.193242693252298947426424861051932753793160644849299936742823528929680528702402814030014482088947577
comment: $a_2=216$, the root of $\chi_{16,2}$.
16
1
3:
-0.8838448565372048740633882565708978333370693476234041064976134380742374242662189489632186302794190263
comment: $a_2=216$, the root of $\chi_{16,2}$.
16
1
5:
0.2982950459072359451644980220866222198497551941615529100588965259733561483135641940697219451407829615
comment: $a_2=216$, the root of $\chi_{16,2}$.
16
1
7:
1.295364169972583632931098296984345586969693367185816129001103039702291875563311449410671324957686217
comment: $a_2=216$, the root of $\chi_{16,2}$.
16
1
11:
0.3185259382772092568189486454717703042141638660585435472501590669207796624841742830972589661402041404
comment: $a_2=216$, the root of $\chi_{16,2}$.
16
1
13:
-0.8401291610268996400093050047930069082435017506453939756447322031033318262698186371099146601072418216
comment: $a_2=216$, the root of $\chi_{16,2}$.
16
1
17:
0.9732002380002932546245193662027657524487725796908464139039761170875865273133183987554213542517473096
comment: $a_2=216$, the root of $\chi_{16,2}$.
16
1
19:
0.4012161672986115865868364663962970060486234096940814432808438472029833930378969513949028719366645002
comment: $a_2=216$, the root of $\chi_{16,2}$.
16
1
23:
0.5787944082933429787812098443751235852886773502427195741635731097429813650907029927451064934574117069
comment: $a_2=216$, the root of $\chi_{16,2}$.
16
1
29:
-0.3972570459572397399803487429191191409417360478052746599810752332880976279562090981311856347402588390
comment: $a_2=216$, the root of $\chi_{16,2}$.
16
1
31:
0.4673373150992241328767667111301962692872163689519683760185319084992692349649214172513472938285225367
comment: $a_2=216$, the root of $\chi_{16,2}$.
16
1
37:
-1.790034712949766770717726086089315617920960121724193993105053934214300348798752294539806394995473860
comment: $a_2=216$, the root of $\chi_{16,2}$.
16
1
41:
1.316701575969749230097415213089433437183169385660604114074027298384076798938469642523082380957378659
comment: $a_2=216$, the root of $\chi_{16,2}$.
16
1
43:
-0.2762532333271328704825270035399768160615906492648095002949959981377136608859527044432492490925268710
comment: $a_2=216$, the root of $\chi_{16,2}$.
16
1
47:
-0.9819913689723332250999307166780014025833808059346814944544923837036400894109800970677605276363452060
comment: $a_2=216$, the root of $\chi_{16,2}$.
16
1
53:
0.7948001453608557647812060664080828638100698835021717742360991245924745184606473899699150860024742211
comment: $a_2=216$, the root of $\chi_{16,2}$.
16
1
59:
0.5157467167100643210178415844237116958016559955075851410836114316650250560904031928815695885751300053
comment: $a_2=216$, the root of $\chi_{16,2}$.
16
1
61:
0.2009256802787188690624692529609652117201632048392638743660672282379892775671830836775061954641791919
comment: $a_2=216$, the root of $\chi_{16,2}$.
18
1
2:
-1.458407736197254269076741496841251143524974121482477700463450979802942868414047883814462144775380372
comment: $a_2=-528$, the root of $\chi_{18,2}$.
18
1
3:
-0.3769804226807432975395813710822109038247715138608784540258637961678647078411471502746344695457020220
comment: $a_2=-528$, the root of $\chi_{18,2}$.
18
1
5:
-1.174461611375697541151411613730805619776900272234231636092569568872644040481557583904909834667711384
comment: $a_2=-528$, the root of $\chi_{18,2}$.
18
1
7:
0.2115095328029506935584094975280456346630399221202337531380231764339424333292017524204467117059395927
comment: $a_2=-528$, the root of $\chi_{18,2}$.
18
1
11:
-1.060018806604012966003266175657055115852580018462396786681214825546162736292965932691261807291957922
comment: $a_2=-528$, the root of $\chi_{18,2}$.
18
1
13:
0.8639670879780245693253311347537985281038850984430620292002710999233454648238626564777981019604206863
comment: $a_2=-528$, the root of $\chi_{18,2}$.
18
1
17:
-0.1887832193164064796579241881979268234812103940796308753851638132618447829814453809797239843396632495
comment: $a_2=-528$, the root of $\chi_{18,2}$.
18
1
19:
0.02009330263563849804938743421426720616406378659610633544766121166105715613756618391561221338477485071
comment: $a_2=-528$, the root of $\chi_{18,2}$.
18
1
23:
-0.8443032038817561849926416212559773548327475466030070835129221991703311688330936383164316068773020307
comment: $a_2=-528$, the root of $\chi_{18,2}$.
18
1
29:
0.9033008394740900204089654775014695778521328773815554262104658132768061793765468131834636737052512520
comment: $a_2=-528$, the root of $\chi_{18,2}$.
18
1
31:
-1.863610862844638278658911943350798107715808612255624838497266765054915421098294834841482073746245905
comment: $a_2=-528$, the root of $\chi_{18,2}$.
18
1
37:
0.5940233726728624483463091466786848270033948053091223514396920415404459129848269654227234053983526624
comment: $a_2=-528$, the root of $\chi_{18,2}$.
18
1
41:
0.9557131800919007948201208923398492023011764547328238156721172476195816178932079969621701294853737584
comment: $a_2=-528$, the root of $\chi_{18,2}$.
18
1
43:
-1.187558017959507052170630819530571926504124141251280230201176422029015053892652401786836965260007474
comment: $a_2=-528$, the root of $\chi_{18,2}$.
18
1
47:
-0.3020362852726075812758212307897945200879342291595098002476556442023471638084496631718349997519633169
comment: $a_2=-528$, the root of $\chi_{18,2}$.
18
1
53:
0.05061241980788769593429897472022451747275448159079251810499614149019723920550850807894729327371288847
comment: $a_2=-528$, the root of $\chi_{18,2}$.
18
1
59:
0.02898948151353914037843028790613535496720129067046951296279716373259269829561252573870379226969281230
comment: $a_2=-528$, the root of $\chi_{18,2}$.
18
1
61:
-0.8737738602605760237218366311300710484029862714470458957460737748431182527319079945055358546295811992
comment: $a_2=-528$, the root of $\chi_{18,2}$.
20
1
2:
0.6297669769942688889195020099996311756130570070037971888364901958239980568151570407380631988802778879
comment: $a_2=456$, the root of $\chi_{20,2}$.
20
1
3:
1.485746371741752996185408933088713562132923025216403318807816137838055025020991709905912321150707969
comment: $a_2=456$, the root of $\chi_{20,2}$.
20
1
5:
-0.5443635579277081622671496777501105597336453626187814269070206791896500791112267515818826709630771987
comment: $a_2=456$, the root of $\chi_{20,2}$.
20
1
7:
-0.1584549951772691353811217158473426051548043452869083285742646939670466018919291063448750800613334318
comment: $a_2=456$, the root of $\chi_{20,2}$.
20
1
11:
-0.002073046191897018740447267659688674923195695716970366766819766312638937301958664134974316208972445078
comment: $a_2=456$, the root of $\chi_{20,2}$.
20
1
13:
1.318727022611535414117896397368131990350672400418945494914891462738880567235643316813843343192572350
comment: $a_2=456$, the root of $\chi_{20,2}$.
20
1
17:
0.4603127981810038196424923070421074184522494651729783812019015089317779788948604290005056219766806477
comment: $a_2=456$, the root of $\chi_{20,2}$.
20
1
19:
-1.215927401541693572492080955479943654764125197606602704522684590721273490463438700264422782879811818
comment: $a_2=456$, the root of $\chi_{20,2}$.
20
1
23:
1.624970436718039737946458294473438208103601498427966992820042886474612429059552029286975776238263308
comment: $a_2=456$, the root of $\chi_{20,2}$.
20
1
29:
0.01456459495981460721329463982494094957866859104311392566971925839367384902141908104634975307630140955
comment: $a_2=456$, the root of $\chi_{20,2}$.
20
1
31:
-0.7107341509564648012475803973230805963560835029542765850406863209579181737652362428380709361994844306
comment: $a_2=456$, the root of $\chi_{20,2}$.
20
1
37:
-0.2142778876378053771952494930517375774977596466446563569962921688376553646734957521002711728768204784
comment: $a_2=456$, the root of $\chi_{20,2}$.
20
1
41:
-1.578989907448420819042739211717980380484291922496054684831486930778964321452503784343280510656762908
comment: $a_2=456$, the root of $\chi_{20,2}$.
20
1
43:
0.3422358328258123814772079097150723012067941376081342601990171023452884302080282056221385400086343469
comment: $a_2=456$, the root of $\chi_{20,2}$.
20
1
47:
0.4560120388384573656618423471052279057084079408089725979420469591428079253417952129429780135815576977
comment: $a_2=456$, the root of $\chi_{20,2}$.
20
1
53:
1.247002501450263882654081161015914935127913076836275140241665430328846596666195623654486135435020067
comment: $a_2=456$, the root of $\chi_{20,2}$.
20
1
59:
0.8775154264054454335905292486317530779691180025793531791501571764735361602182979263170715532626274482
comment: $a_2=456$, the root of $\chi_{20,2}$.
20
1
61:
0.2559138301474767779102097823332701296136939866332475910386477885518874110281518727224598063682136155
comment: $a_2=456$, the root of $\chi_{20,2}$.
22
1
2:
-0.1988737822087164912377374768419887922988601074748833227904705881549467547837338023383357470148245962
comment: $a_2=-288$, the root of $\chi_{22,2}$.
22
1
3:
-1.259769311647413876651878363308340639392023574330610632080827755821463855614813866323918549490259138
comment: $a_2=-288$, the root of $\chi_{22,2}$.
22
1
5:
0.9910402108963650320487650694416407029219051497356297753120824062580083266699561766498789681357784734
comment: $a_2=-288$, the root of $\chi_{22,2}$.
22
1
7:
-1.027723678173571312366808539204218313544100195641273486916418715714745974116771938239100768514233754
comment: $a_2=-288$, the root of $\chi_{22,2}$.
22
1
11:
-1.101136338856333121668729325424789771746039864752560145346534554877307556121333029096734238237447256
comment: $a_2=-288$, the root of $\chi_{22,2}$.
22
1
13:
-0.1621986502933202219542363457646379777558623748380508684415826205080799031755773745858356426152893127
comment: $a_2=-288$, the root of $\chi_{22,2}$.
22
1
17:
0.3672071369119166638572280950150066425365665974101878361668863230625960543556215368422391535132911980
comment: $a_2=-288$, the root of $\chi_{22,2}$.
22
1
19:
-0.2963845758860839815261642524249345533376138065332954455085151884374846769045466595551887834041668929
comment: $a_2=-288$, the root of $\chi_{22,2}$.
22
1
23:
-0.3716904386542675975984169412019415127043783812721226150838006938504808813280880767361460396529796643
comment: $a_2=-288$, the root of $\chi_{22,2}$.
22
1
29:
-1.877239334313507764290059756942048418275793700131801501092109386090210103809719702727887629523436025
comment: $a_2=-288$, the root of $\chi_{22,2}$.
22
1
31:
0.4164659485374165913262626627373381739012092165238386017076890385425710606187515106643327945337681926
comment: $a_2=-288$, the root of $\chi_{22,2}$.
22
1
37:
0.7586949342768825519322246554197825208217037794320724982621470254424989373610057239838508871662392657
comment: $a_2=-288$, the root of $\chi_{22,2}$.
22
1
41:
-0.2399480366260902296071180646844143552035413332614789411467542175052950813091446586589263568769134655
comment: $a_2=-288$, the root of $\chi_{22,2}$.
22
1
43:
-1.366154140637430707070560348318909833133085075419835037062387470072374257238196668844976894947362422
comment: $a_2=-288$, the root of $\chi_{22,2}$.
22
1
47:
0.4075427065300653713119573878364765247496568467690262572565364801929170860005339989914541609820432840
comment: $a_2=-288$, the root of $\chi_{22,2}$.
22
1
53:
1.600900963146133584319719519231187729083953288181754385318676646645841330682031230994492541686937834
comment: $a_2=-288$, the root of $\chi_{22,2}$.
22
1
59:
-1.522144718212955987072306876680531403205156999973695678591912299748290508229937246754906376595264489
comment: $a_2=-288$, the root of $\chi_{22,2}$.
22
1
61:
1.111144853841389519846148897788037134664759787852813984898616616663159353927798256396041237388136591
comment: $a_2=-288$, the root of $\chi_{22,2}$.
24
1
2:
-1.386713451731978864295125080733199128653280597657630418797748428242657257494258153087934954779003296
comment: $a_2$ is the first root of $\chi_{24,2}$ in increasing order, with $a_2\approx -4016.351171716245$.
24
1
3:
1.266003614607435860226755548889435212319869803028098255179693667656341140882694669252494286781659412
comment: $a_2$ is the first root of $\chi_{24,2}$ in increasing order, with $a_2\approx -4016.351171716245$.
24
1
5:
0.9622562593275645712172889997740843445437802629540908812930035075720286803226014910169685839917050603
comment: $a_2$ is the first root of $\chi_{24,2}$ in increasing order, with $a_2\approx -4016.351171716245$.
24
1
7:
0.7286929821871229913895460085939896252097904273639934320514336503034625979878336751807263970042821771
comment: $a_2$ is the first root of $\chi_{24,2}$ in increasing order, with $a_2\approx -4016.351171716245$.
24
1
11:
0.2665192018758358943338300067295906843350802124468332276293385331690666904764573794659843347383676960
comment: $a_2$ is the first root of $\chi_{24,2}$ in increasing order, with $a_2\approx -4016.351171716245$.
24
1
13:
-0.5557330160428562979299393551528560071582404066154034589775862471358895871505070493903697657121823538
comment: $a_2$ is the first root of $\chi_{24,2}$ in increasing order, with $a_2\approx -4016.351171716245$.
24
1
17:
1.657314946255125131717092622913138341437045737014457877810402561060762609247634034554503317356938563
comment: $a_2$ is the first root of $\chi_{24,2}$ in increasing order, with $a_2\approx -4016.351171716245$.
24
1
19:
-1.227104205980233712360223074993434707160166250344377315336341135741037424495001678921679435351525607
comment: $a_2$ is the first root of $\chi_{24,2}$ in increasing order, with $a_2\approx -4016.351171716245$.
24
1
23:
-0.7851733143026698802972183914349125882377825698426322031834950573318569343058656452502429312437162497
comment: $a_2$ is the first root of $\chi_{24,2}$ in increasing order, with $a_2\approx -4016.351171716245$.
24
1
29:
-0.3134207440437849937908341051325398444306984050465224695835326506528331389590823667875306963292439940
comment: $a_2$ is the first root of $\chi_{24,2}$ in increasing order, with $a_2\approx -4016.351171716245$.
24
1
31:
0.9638702104739258909721234290850150890460836209017431575872157617060622926452701835844477915479149909
comment: $a_2$ is the first root of $\chi_{24,2}$ in increasing order, with $a_2\approx -4016.351171716245$.
24
1
37:
-1.144838243792219520864031191087631567181272639921644130735299369415105094172485995192767259312601378
comment: $a_2$ is the first root of $\chi_{24,2}$ in increasing order, with $a_2\approx -4016.351171716245$.
24
1
41:
0.3975060713523978014822944408263180283507694337296047453236010924031669963328898161571948336532200591
comment: $a_2$ is the first root of $\chi_{24,2}$ in increasing order, with $a_2\approx -4016.351171716245$.
24
1
43:
0.03590430628680864112302591985365631162283605120989535132535130198883202665905412223612558168330367400
comment: $a_2$ is the first root of $\chi_{24,2}$ in increasing order, with $a_2\approx -4016.351171716245$.
24
1
47:
-0.5120500125566444887603935557554327016520425128097402780011759044151853674027829410697519376628432724
comment: $a_2$ is the first root of $\chi_{24,2}$ in increasing order, with $a_2\approx -4016.351171716245$.
24
1
53:
-1.131357516517204103798609712301610662062297241540331187312117512837669305090562533252354794997742126
comment: $a_2$ is the first root of $\chi_{24,2}$ in increasing order, with $a_2\approx -4016.351171716245$.
24
1
59:
-0.004397596720133884519141760932862397836917388051207753980949104152381954158934486125913542718165163768
comment: $a_2$ is the first root of $\chi_{24,2}$ in increasing order, with $a_2\approx -4016.351171716245$.
24
1
61:
0.8454717480974119786683922489441562783923141240253072478793376463182977936654650980979437221805917912
comment: $a_2$ is the first root of $\chi_{24,2}$ in increasing order, with $a_2\approx -4016.351171716245$.
24
2
2:
1.759601793373322285365882849811928114213643299173036649029880781033182422713759032472314480431799414
comment: $a_2$ is the second root of $\chi_{24,2}$ in increasing order, with $a_2\approx 5096.351171716245$.
24
2
3:
-0.1595842601476134836944641298713061046113122631251776758258512780320136603529661827632932136985688220
comment: $a_2$ is the second root of $\chi_{24,2}$ in increasing order, with $a_2\approx 5096.351171716245$.
24
2
5:
-0.2930218958565458363274449232956244492562374718646449303077273936813303922935310364319939010846001505
comment: $a_2$ is the second root of $\chi_{24,2}$ in increasing order, with $a_2\approx 5096.351171716245$.
24
2
7:
-0.9885000258570738525584865277945294044119879962721953101271681508384124621396308613756299868215837849
comment: $a_2$ is the second root of $\chi_{24,2}$ in increasing order, with $a_2\approx 5096.351171716245$.
24
2
11:
0.6389310130940702246290392849420136772633754517252143692202321726541778820182561437775763692416603969
comment: $a_2$ is the second root of $\chi_{24,2}$ in increasing order, with $a_2\approx 5096.351171716245$.
24
2
13:
1.232968353830267799343686703867922371129000077320669831883616620836484138772515628051905753152733269
comment: $a_2$ is the second root of $\chi_{24,2}$ in increasing order, with $a_2\approx 5096.351171716245$.
24
2
17:
0.1403934443561437923395685585939698095824470723229308689826679623081165233165153004112731031979011060
comment: $a_2$ is the second root of $\chi_{24,2}$ in increasing order, with $a_2\approx 5096.351171716245$.
24
2
19:
1.235495026893432850899234193223603573964412410063643180591061081754732877850941430663908169410863020
comment: $a_2$ is the second root of $\chi_{24,2}$ in increasing order, with $a_2\approx 5096.351171716245$.
24
2
23:
-0.9972287457378191760330996701728666470349572600271183029119012104647062459886445585625663459187642163
comment: $a_2$ is the second root of $\chi_{24,2}$ in increasing order, with $a_2\approx 5096.351171716245$.
24
2
29:
0.6302834114412152574174587873559123071799962826432111450630639684111259631064493421907899482942322387
comment: $a_2$ is the second root of $\chi_{24,2}$ in increasing order, with $a_2\approx 5096.351171716245$.
24
2
31:
0.009591038275517184201618615830780305427680936928798877901120381775139908175572374927986873168456402648
comment: $a_2$ is the second root of $\chi_{24,2}$ in increasing order, with $a_2\approx 5096.351171716245$.
24
2
37:
0.3153281296436670732891672833073426094859206249942533439823762103419795625066648203272512940553233532
comment: $a_2$ is the second root of $\chi_{24,2}$ in increasing order, with $a_2\approx 5096.351171716245$.
24
2
41:
-1.048626763209357966520606434576822150523766603552032730453526652955562104706520949948093205509442685
comment: $a_2$ is the second root of $\chi_{24,2}$ in increasing order, with $a_2\approx 5096.351171716245$.
24
2
43:
-0.3232069134913499945301862782142526861264994125658270856934328703063367879509321763484762206343344650
comment: $a_2$ is the second root of $\chi_{24,2}$ in increasing order, with $a_2\approx 5096.351171716245$.
24
2
47:
1.441923356591801400061414959409923215698048127195325735254764137721135920869567194304241785506207677
comment: $a_2$ is the second root of $\chi_{24,2}$ in increasing order, with $a_2\approx 5096.351171716245$.
24
2
53:
-0.9476004666964863713016065709863660260702934723484678783239038914779318149556669231649933236609587547
comment: $a_2$ is the second root of $\chi_{24,2}$ in increasing order, with $a_2\approx 5096.351171716245$.
24
2
59:
1.216981625053662440990161505693251687797595084390318308303628706663218435660883585111733066213483971
comment: $a_2$ is the second root of $\chi_{24,2}$ in increasing order, with $a_2\approx 5096.351171716245$.
24
2
61:
-1.376442678800444786733256058636870042920433289598502943190413989900418297543699908430469907329853258
comment: $a_2$ is the second root of $\chi_{24,2}$ in increasing order, with $a_2\approx 5096.351171716245$.
26
1
2:
-0.008286407592029853801572394868416199679119171144786805116269607839789448115988908430763989458951024840
comment: $a_2=-48$, the root of $\chi_{26,2}$.
26
1
3:
-0.2127188005976307495920513618960623618531935121785784740581671529574661423330220303292599730116270669
comment: $a_2=-48$, the root of $\chi_{26,2}$.
26
1
5:
-1.359167277641623414268058262803144166803987743174985343322443289794613747741373244740211863315096702
comment: $a_2=-48$, the root of $\chi_{26,2}$.
26
1
7:
1.067175119485490500224870012621816959806788994898400711285351514055433764840518283986237880906978060
comment: $a_2=-48$, the root of $\chi_{26,2}$.
26
1
11:
0.8088696231973608397151592712897576611727510048291167075827445212867675535693055745956130972695157192
comment: $a_2=-48$, the root of $\chi_{26,2}$.
26
1
13:
-0.9720080133493531294141202643219812586868651700269461015672801895500067962395739188070429240291030271
comment: $a_2=-48$, the root of $\chi_{26,2}$.
26
1
17:
-1.048991077745249899013013097947591921143584913070329466500594192331600626425283253419947411707171785
comment: $a_2=-48$, the root of $\chi_{26,2}$.
26
1
19:
-0.6304206480590941067704999598191026409209304908683029976622913308084169168623856123429639033452909272
comment: $a_2=-48$, the root of $\chi_{26,2}$.
26
1
23:
-0.9038660585135445584200765084673958600113254726665652082531204099842397605906047618787296780218304740
comment: $a_2=-48$, the root of $\chi_{26,2}$.
26
1
29:
-0.1423606312127414237068725060652353443954910641018267045292650692000128665446384102666730341336810942
comment: $a_2=-48$, the root of $\chi_{26,2}$.
26
1
31:
0.9785989589958676521132566053307857458463420768735398766371708042848814948374576421506720364721347763
comment: $a_2=-48$, the root of $\chi_{26,2}$.
26
1
37:
0.5069979973687969510046054047821983548479005676242916213837382361620239952645634315573044572580213885
comment: $a_2=-48$, the root of $\chi_{26,2}$.
26
1
41:
-1.271790414487243312543058522870743921147138109312802401543065122696206910230478320572805694638898089
comment: $a_2=-48$, the root of $\chi_{26,2}$.
26
1
43:
1.148336385578371378952183695405075539163724379730550093693834108589435482690576143420462341932171395
comment: $a_2=-48$, the root of $\chi_{26,2}$.
26
1
47:
-1.160428568508038010587923701758909991652186599988955322247304761289114329080549948421692370312014451
comment: $a_2=-48$, the root of $\chi_{26,2}$.
26
1
53:
-0.2768949217008764812289171007574650819236884929070388933896418206979032372588122833643513281475158427
comment: $a_2=-48$, the root of $\chi_{26,2}$.
26
1
59:
0.9550934485455756703279617693733821635889082443484052355934175958799348878918500714301685714916143292
comment: $a_2=-48$, the root of $\chi_{26,2}$.
26
1
61:
0.4348750888354600263855480478714595105019830875244743068039334868651629930667764907562343242128062146
comment: $a_2=-48$, the root of $\chi_{26,2}$.
28
1
2:
-1.615296931973749712110209788411903186406380594941535114820284668996984846689879945662685032982611027
comment: $a_2$ is the first root of $\chi_{28,2}$ in increasing order, with $a_2\approx -18713.59859471915$.
28
1
3:
-1.246183300308259589535809378998312351319827457345540951518056842356595465240779787695676695350508971
comment: $a_2$ is the first root of $\chi_{28,2}$ in increasing order, with $a_2\approx -18713.59859471915$.
28
1
5:
0.2112270963075308384096834364530986645007984663243843144233466463942903041663851427964243204635313432
comment: $a_2$ is the first root of $\chi_{28,2}$ in increasing order, with $a_2\approx -18713.59859471915$.
28
1
7:
-0.7680042467362946817272963117745778542709266689085190099450156647946807996059868336405307704906336416
comment: $a_2$ is the first root of $\chi_{28,2}$ in increasing order, with $a_2\approx -18713.59859471915$.
28
1
11:
1.805381738710423818573982616551089979197530184829663417731595304565683948490623845724821100633940241
comment: $a_2$ is the first root of $\chi_{28,2}$ in increasing order, with $a_2\approx -18713.59859471915$.
28
1
13:
-0.1526113057217544765028857479998890357093464847388599763633559708781611934099872492235978917998703323
comment: $a_2$ is the first root of $\chi_{28,2}$ in increasing order, with $a_2\approx -18713.59859471915$.
28
1
17:
-0.1339987404592490651576601263693478068973365420970062951851984469066225758506737598774430251011856909
comment: $a_2$ is the first root of $\chi_{28,2}$ in increasing order, with $a_2\approx -18713.59859471915$.
28
1
19:
0.8808905998366487024966023723080335212997328717882538396847985888495239404257589667771117858742596989
comment: $a_2$ is the first root of $\chi_{28,2}$ in increasing order, with $a_2\approx -18713.59859471915$.
28
1
23:
1.159740709850372370546622566516789907593922108629293178958305738089594602912148326304071465222975214
comment: $a_2$ is the first root of $\chi_{28,2}$ in increasing order, with $a_2\approx -18713.59859471915$.
28
1
29:
-0.05426503282386875030950861247325996663025942402320731415470215902494578550237108289841851534453591199
comment: $a_2$ is the first root of $\chi_{28,2}$ in increasing order, with $a_2\approx -18713.59859471915$.
28
1
31:
0.6687625833396147341401039737460355480505981127749290317997912889661916857094504126563948364200641170
comment: $a_2$ is the first root of $\chi_{28,2}$ in increasing order, with $a_2\approx -18713.59859471915$.
28
1
37:
1.012440470348131447241516914054201501575287503285477728691440741408468970738432390399419832231030380
comment: $a_2$ is the first root of $\chi_{28,2}$ in increasing order, with $a_2\approx -18713.59859471915$.
28
1
41:
0.9236793194333443126455264562878159132835096176192678713354878821657628979470178347939010370379704848
comment: $a_2$ is the first root of $\chi_{28,2}$ in increasing order, with $a_2\approx -18713.59859471915$.
28
1
43:
-0.6044290235512866516946554321212293051373921243626881790146005776804349075150256266104769961253098153
comment: $a_2$ is the first root of $\chi_{28,2}$ in increasing order, with $a_2\approx -18713.59859471915$.
28
1
47:
-0.2515195659012758748268519692540324437675537898797127048380291096586175450762320332134870894969430858
comment: $a_2$ is the first root of $\chi_{28,2}$ in increasing order, with $a_2\approx -18713.59859471915$.
28
1
53:
-0.2827408645667824049816758079632896171274750323331771589507767503078673470181260865054098762885599940
comment: $a_2$ is the first root of $\chi_{28,2}$ in increasing order, with $a_2\approx -18713.59859471915$.
28
1
59:
1.136359650941572072741750944056607841140262349278990072593035789664360059888666462160465560746338365
comment: $a_2$ is the first root of $\chi_{28,2}$ in increasing order, with $a_2\approx -18713.59859471915$.
28
1
61:
1.165285889644322503321319116247862395307145981558191784931787237506318720866628120334826786847919891
comment: $a_2$ is the first root of $\chi_{28,2}$ in increasing order, with $a_2\approx -18713.59859471915$.
28
2
2:
0.9005942771611748217245907310110059640823520837036731735420309928151449466858365935092909421480851348
comment: $a_2$ is the second root of $\chi_{28,2}$ in increasing order, with $a_2\approx 10433.59859471915$.
28
2
3:
0.7803842719725761499988849958061625573004241240035902940382313612528223901927392689934361587503107054
comment: $a_2$ is the second root of $\chi_{28,2}$ in increasing order, with $a_2\approx 10433.59859471915$.
28
2
5:
1.783071490565559610001784541414850787468057805899732443396830567825595017008450799892429426680992074
comment: $a_2$ is the second root of $\chi_{28,2}$ in increasing order, with $a_2\approx 10433.59859471915$.
28
2
7:
0.08379939405324849044370683281961203959523792128935353999576441302672968606128240775162099142821082438
comment: $a_2$ is the second root of $\chi_{28,2}$ in increasing order, with $a_2\approx 10433.59859471915$.
28
2
11:
-0.5986683266660720637019032008043881969668423857898127378066161675467939969864745976690942909017610632
comment: $a_2$ is the second root of $\chi_{28,2}$ in increasing order, with $a_2\approx 10433.59859471915$.
28
2
13:
-0.5373263423570909022779338706510642341779955781549133719803431357574569084532397400939823351325327539
comment: $a_2$ is the second root of $\chi_{28,2}$ in increasing order, with $a_2\approx 10433.59859471915$.
28
2
17:
-0.5945848377710350941811268904944255760025908151095605272955585890384993053397178695111783690205490353
comment: $a_2$ is the second root of $\chi_{28,2}$ in increasing order, with $a_2\approx 10433.59859471915$.
28
2
19:
1.326176643534780876255053102307888316284100171086770095297402738738823376317043530724234021311367899
comment: $a_2$ is the second root of $\chi_{28,2}$ in increasing order, with $a_2\approx 10433.59859471915$.
28
2
23:
0.05198769211466836451619744759321631758856626054070792140960785395980614496867821635413024264900108816
comment: $a_2$ is the second root of $\chi_{28,2}$ in increasing order, with $a_2\approx 10433.59859471915$.
28
2
29:
-0.2270964782538272249175635331177214969023806447321016993383022058152581453350579389234117968449858584
comment: $a_2$ is the second root of $\chi_{28,2}$ in increasing order, with $a_2\approx 10433.59859471915$.
28
2
31:
-0.4588007269472087767830452214965586375336372947233840923412044275734839407082640030421562099779143770
comment: $a_2$ is the second root of $\chi_{28,2}$ in increasing order, with $a_2\approx 10433.59859471915$.
28
2
37:
0.2481766294974023277063348358868471671145984713378397532775859619304123343184168374614935829457420210
comment: $a_2$ is the second root of $\chi_{28,2}$ in increasing order, with $a_2\approx 10433.59859471915$.
28
2
41:
0.6094120784640162992218021039153049372393134874321296486352998122591694032333969028543956834508934795
comment: $a_2$ is the second root of $\chi_{28,2}$ in increasing order, with $a_2\approx 10433.59859471915$.
28
2
43:
1.061110016176858372175972703704643198086233870925923605351495521010414077197133258416582994143823282
comment: $a_2$ is the second root of $\chi_{28,2}$ in increasing order, with $a_2\approx 10433.59859471915$.
28
2
47:
0.2207959928061740148273597625729343420425885700397736063868539755884638341655710172643335723556520756
comment: $a_2$ is the second root of $\chi_{28,2}$ in increasing order, with $a_2\approx 10433.59859471915$.
28
2
53:
0.8469910600883175384177766959521732343348782074707513285341363524008091072228114631952570528991653424
comment: $a_2$ is the second root of $\chi_{28,2}$ in increasing order, with $a_2\approx 10433.59859471915$.
28
2
59:
1.356007383262304272239322473825524074424720028628370964054287247577424885395134801617778484497469551
comment: $a_2$ is the second root of $\chi_{28,2}$ in increasing order, with $a_2\approx 10433.59859471915$.
28
2
61:
-1.048365468547328918883547355793816038523318543163087670390226707137625558350749343032530166273481508
comment: $a_2$ is the second root of $\chi_{28,2}$ in increasing order, with $a_2\approx 10433.59859471915$.
30
1
2:
-0.7524189739009653217833804476440777294975683435523585425055725341113470409849593734818857821049995626
comment: $a_2$ is the first root of $\chi_{30,2}$ in increasing order, with $a_2\approx -17433.90502875288$.
30
1
3:
1.149678726452501121879860532400169824060946419299013974295060114294214673810555394244895242391959484
comment: $a_2$ is the first root of $\chi_{30,2}$ in increasing order, with $a_2\approx -17433.90502875288$.
30
1
5:
-0.8252087992301811627618036617889158112555181659898522072112595038405871810433411019224947971250354724
comment: $a_2$ is the first root of $\chi_{30,2}$ in increasing order, with $a_2\approx -17433.90502875288$.
30
1
7:
-1.664212704579535917913520707242837800789020769056109695364744225796842579937553028892942285159838873
comment: $a_2$ is the first root of $\chi_{30,2}$ in increasing order, with $a_2\approx -17433.90502875288$.
30
1
11:
-0.9989058233626319306250085647578711291067408921769379904885901982908614122636298583979932875238329577
comment: $a_2$ is the first root of $\chi_{30,2}$ in increasing order, with $a_2\approx -17433.90502875288$.
30
1
13:
0.4290069416948860505463130555736296651175368028094058959304027487105758257884648698810653783009866672
comment: $a_2$ is the first root of $\chi_{30,2}$ in increasing order, with $a_2\approx -17433.90502875288$.
30
1
17:
0.1194042791858177778366675758649081006519707075911004311213426566120971792399557020922387710424328008
comment: $a_2$ is the first root of $\chi_{30,2}$ in increasing order, with $a_2\approx -17433.90502875288$.
30
1
19:
1.068847867571145427599699283926833751129432088516410861468212309280969647938929691427971497573806522
comment: $a_2$ is the first root of $\chi_{30,2}$ in increasing order, with $a_2\approx -17433.90502875288$.
30
1
23:
-0.3048944598046837680946049390298311005830494169817089341590770850986820480794977103007654694575225675
comment: $a_2$ is the first root of $\chi_{30,2}$ in increasing order, with $a_2\approx -17433.90502875288$.
30
1
29:
-0.5500511581912282607063155384299115005580936307812183267848180035983828138011180217808697563976414800
comment: $a_2$ is the first root of $\chi_{30,2}$ in increasing order, with $a_2\approx -17433.90502875288$.
30
1
31:
0.8805181399190703772604069829267625749271325418036276702083829315690589414276626684951987940575921082
comment: $a_2$ is the first root of $\chi_{30,2}$ in increasing order, with $a_2\approx -17433.90502875288$.
30
1
37:
0.3607298350227331127514072805657925372564790938347576732868989862467473029579689739385877218452968811
comment: $a_2$ is the first root of $\chi_{30,2}$ in increasing order, with $a_2\approx -17433.90502875288$.
30
1
41:
-0.4143669007531177475074960516318730664103372656638111865872466714741082497235072206713336401411663802
comment: $a_2$ is the first root of $\chi_{30,2}$ in increasing order, with $a_2\approx -17433.90502875288$.
30
1
43:
-0.3341310211017978877716986474619492945925284414120460720567138632244360166037427055587873177060874507
comment: $a_2$ is the first root of $\chi_{30,2}$ in increasing order, with $a_2\approx -17433.90502875288$.
30
1
47:
-1.487509440644847374949048815969264960862017671104510164047602546731061040788948268703977771653672172
comment: $a_2$ is the first root of $\chi_{30,2}$ in increasing order, with $a_2\approx -17433.90502875288$.
30
1
53:
-1.441901575317273056307974425838292421176477636075138716557720214263263306496422840080713835663629304
comment: $a_2$ is the first root of $\chi_{30,2}$ in increasing order, with $a_2\approx -17433.90502875288$.
30
1
59:
0.1234173233914681222214118382324426482204849666604696800627687777570794310345038701111254639508192381
comment: $a_2$ is the first root of $\chi_{30,2}$ in increasing order, with $a_2\approx -17433.90502875288$.
30
1
61:
-0.8020319917826961641500862326534030376139371686743112238059962489356506433951462337332566023961292937
comment: $a_2$ is the first root of $\chi_{30,2}$ in increasing order, with $a_2\approx -17433.90502875288$.
30
2
2:
1.125307315542308742854138216722806715057931045067764772737704886901872206204460252866265307757795680
comment: $a_2$ is the second root of $\chi_{30,2}$ in increasing order, with $a_2\approx 26073.90502875288$.
30
2
3:
-1.749320557967017007892550108262514726353487383641357208044860638013868061494846010680403887279181787
comment: $a_2$ is the second root of $\chi_{30,2}$ in increasing order, with $a_2\approx 26073.90502875288$.
30
2
5:
-0.4554145524095251125315850347249661984463028889372313544406715096240561707338334387334540890874737154
comment: $a_2$ is the second root of $\chi_{30,2}$ in increasing order, with $a_2\approx 26073.90502875288$.
30
2
7:
-0.01896638085353562502921756442131902680091391046565552229082834203359190315025675316545045636091143610
comment: $a_2$ is the second root of $\chi_{30,2}$ in increasing order, with $a_2\approx 26073.90502875288$.
30
2
11:
-0.6330120585559747717168975625100503455676938259172371903054269099981657135801745072152293469614252607
comment: $a_2$ is the second root of $\chi_{30,2}$ in increasing order, with $a_2\approx 26073.90502875288$.
30
2
13:
0.7782960470266394515708045261384339841219620743996182860160978686721688922697736385309254081458028309
comment: $a_2$ is the second root of $\chi_{30,2}$ in increasing order, with $a_2\approx 26073.90502875288$.
30
2
17:
-1.076992930799832055907045399379935629798806841490352849794028988915934464735854688836840348925040826
comment: $a_2$ is the second root of $\chi_{30,2}$ in increasing order, with $a_2\approx 26073.90502875288$.
30
2
19:
-0.7150597671570491470101828024551363827720219320902051819156934371912635478263436187935032412224194495
comment: $a_2$ is the second root of $\chi_{30,2}$ in increasing order, with $a_2\approx 26073.90502875288$.
30
2
23:
-0.02944612660176609477513898239984602048500376235676904157758152383349159891389917798039958324961174889
comment: $a_2$ is the second root of $\chi_{30,2}$ in increasing order, with $a_2\approx 26073.90502875288$.
30
2
29:
1.171678929974289924656893146124778475868517017409335467912188456144628176878582738968385866952570396
comment: $a_2$ is the second root of $\chi_{30,2}$ in increasing order, with $a_2\approx 26073.90502875288$.
30
2
31:
-1.138499493194146103622964041345963338499500056431202286817090707124763374521689815660392204711369378
comment: $a_2$ is the second root of $\chi_{30,2}$ in increasing order, with $a_2\approx 26073.90502875288$.
30
2
37:
1.443015560884481066351826555164625135922214022449795417443045175129254942635252357859397914392546869
comment: $a_2$ is the second root of $\chi_{30,2}$ in increasing order, with $a_2\approx 26073.90502875288$.
30
2
41:
-0.02497015433903390903495713111987546182620425252523953602577877921616174694265947670987995868762372284
comment: $a_2$ is the second root of $\chi_{30,2}$ in increasing order, with $a_2\approx 26073.90502875288$.
30
2
43:
1.388087296109694793889370203119129290849961774221996975749165216546917438779170008679090941706352729
comment: $a_2$ is the second root of $\chi_{30,2}$ in increasing order, with $a_2\approx 26073.90502875288$.
30
2
47:
-1.081856186788493056795111716601051053214371597461455959312334390217467308006676713421055188659334552
comment: $a_2$ is the second root of $\chi_{30,2}$ in increasing order, with $a_2\approx 26073.90502875288$.
30
2
53:
-0.1648361175177164738515902452120459825206132020054620168788671018082072951431599342448748672883866882
comment: $a_2$ is the second root of $\chi_{30,2}$ in increasing order, with $a_2\approx 26073.90502875288$.
30
2
59:
-1.878583411636523081309623543412831444328377534446564070800417321615687554051162093154643834270445847
comment: $a_2$ is the second root of $\chi_{30,2}$ in increasing order, with $a_2\approx 26073.90502875288$.
30
2
61:
0.5962158879033281489706597584719276861935568474084639202126755609488721446195576555907772411828517231
comment: $a_2$ is the second root of $\chi_{30,2}$ in increasing order, with $a_2\approx 26073.90502875288$.
32
1
2:
-0.6764615684132934787532143262164313825021937676823302919189058362357233517726515121933871577980404866
comment: $a_2$ is the first root of $\chi_{32,2}$ in increasing order, with $a_2\approx -31347.87172677239$.
32
1
3:
-0.5428737402249537018396293897663308615215780316045316425519782699403914915135592848006807596325035306
comment: $a_2$ is the first root of $\chi_{32,2}$ in increasing order, with $a_2\approx -31347.87172677239$.
32
1
5:
0.9249213203610357808745509441184148141718497878161243754734210157654984034094033115232948902256192973
comment: $a_2$ is the first root of $\chi_{32,2}$ in increasing order, with $a_2\approx -31347.87172677239$.
32
1
7:
1.498361471358111133858378580055695571330990272328975388935328052761461240877646968779783483148945396
comment: $a_2$ is the first root of $\chi_{32,2}$ in increasing order, with $a_2\approx -31347.87172677239$.
32
1
11:
-0.3883059154524253149426616333471598202393563283757669411567315268487959293479778549863552398545064482
comment: $a_2$ is the first root of $\chi_{32,2}$ in increasing order, with $a_2\approx -31347.87172677239$.
32
1
13:
1.498723876894326604873427850818377677688796157687273454547327919054930378416984674816816091566874279
comment: $a_2$ is the first root of $\chi_{32,2}$ in increasing order, with $a_2\approx -31347.87172677239$.
32
1
17:
0.5336493996807846764483461955180579905674925475923412701787704795192815772066059853407916866894612391
comment: $a_2$ is the first root of $\chi_{32,2}$ in increasing order, with $a_2\approx -31347.87172677239$.
32
1
19:
0.02893255354989983887711807295010560755749045207852637974004409910159423687274571236732946998393738995
comment: $a_2$ is the first root of $\chi_{32,2}$ in increasing order, with $a_2\approx -31347.87172677239$.
32
1
23:
1.486775211855176598558151890631372076532005205246826786595049236110215746963176410161358426470020359
comment: $a_2$ is the first root of $\chi_{32,2}$ in increasing order, with $a_2\approx -31347.87172677239$.
32
1
29:
1.124767005264094331178262204060798086121886721127242178287877812384322925427084146818071524786313898
comment: $a_2$ is the first root of $\chi_{32,2}$ in increasing order, with $a_2\approx -31347.87172677239$.
32
1
31:
-0.4666543421009590112860376933916210581234838159512056953236241786008810501209978133376485771520591117
comment: $a_2$ is the first root of $\chi_{32,2}$ in increasing order, with $a_2\approx -31347.87172677239$.
32
1
37:
-1.021020334309156856453140327235654680170805133235643749100966766603952580672564339536666768942187101
comment: $a_2$ is the first root of $\chi_{32,2}$ in increasing order, with $a_2\approx -31347.87172677239$.
32
1
41:
-0.5116730487997672157708534503269726595380341358807029597867982817694280246683662422697341163417978562
comment: $a_2$ is the first root of $\chi_{32,2}$ in increasing order, with $a_2\approx -31347.87172677239$.
32
1
43:
0.4027189765447091716064920894699071273677475641327906723335075965220591125772572099847393819957588266
comment: $a_2$ is the first root of $\chi_{32,2}$ in increasing order, with $a_2\approx -31347.87172677239$.
32
1
47:
0.2582609438620404824015581732240233359235115291998377110802026186599908316957579806076379419167637082
comment: $a_2$ is the first root of $\chi_{32,2}$ in increasing order, with $a_2\approx -31347.87172677239$.
32
1
53:
0.2990222024403797247407486011039315400745132134606990177378666244654797774739872895417152865848781500
comment: $a_2$ is the first root of $\chi_{32,2}$ in increasing order, with $a_2\approx -31347.87172677239$.
32
1
59:
0.7704585291644269137447195596846020313439985044892682391355025377929793353472956804338462996359083950
comment: $a_2$ is the first root of $\chi_{32,2}$ in increasing order, with $a_2\approx -31347.87172677239$.
32
1
61:
-1.404250510743589330326710812985742091270277138870715068491831650796440563943906523384005210269526942
comment: $a_2$ is the first root of $\chi_{32,2}$ in increasing order, with $a_2\approx -31347.87172677239$.
32
2
2:
1.538765858458900139979341667210992161610532514936707199330711902063812796342747295769764810870131509
comment: $a_2$ is the second root of $\chi_{32,2}$ in increasing order, with $a_2\approx 71307.87172677239$.
32
2
3:
1.241507099545112546641862182804878509478472087965996398620935659594777136400894616377872765129414391
comment: $a_2$ is the second root of $\chi_{32,2}$ in increasing order, with $a_2\approx 71307.87172677239$.
32
2
5:
-1.209085951523023681952267265936867989831731096794287974909936746987356990333655724549723933723003852
comment: $a_2$ is the second root of $\chi_{32,2}$ in increasing order, with $a_2\approx 71307.87172677239$.
32
2
7:
0.9105110501094124393597329803239736509651121309196865569418155189712307786371039678820184994902964964
comment: $a_2$ is the second root of $\chi_{32,2}$ in increasing order, with $a_2\approx 71307.87172677239$.
32
2
11:
-0.1734198538831323508780925451635810812099672216195695495029958436055852601709656578380556579127804825
comment: $a_2$ is the second root of $\chi_{32,2}$ in increasing order, with $a_2\approx 71307.87172677239$.
32
2
13:
-1.093914382749593687534967776660441764510631573541198469832839131451217983795170520809935212581551570
comment: $a_2$ is the second root of $\chi_{32,2}$ in increasing order, with $a_2\approx 71307.87172677239$.
32
2
17:
0.9258067850385174067823529802973293370356660080649111002830388415796238461260861691143651854901620789
comment: $a_2$ is the second root of $\chi_{32,2}$ in increasing order, with $a_2\approx 71307.87172677239$.
32
2
19:
-0.2158753186493279813852488267311208234046606022688782063760421907360950893478116619150197663662648065
comment: $a_2$ is the second root of $\chi_{32,2}$ in increasing order, with $a_2\approx 71307.87172677239$.
32
2
23:
-0.003011270068966485470399027742513325649715323356693350281250663652051177219311834591669544308709651918
comment: $a_2$ is the second root of $\chi_{32,2}$ in increasing order, with $a_2\approx 71307.87172677239$.
32
2
29:
1.642120042902868623455698210436327982548848432698499281671609020579164386325887946368784294887621589
comment: $a_2$ is the second root of $\chi_{32,2}$ in increasing order, with $a_2\approx 71307.87172677239$.
32
2
31:
1.429030478902833579991324476138654646699770212405989865114010397347936359922904665204427843123179807
comment: $a_2$ is the second root of $\chi_{32,2}$ in increasing order, with $a_2\approx 71307.87172677239$.
32
2
37:
0.6099244882482985216528042522636848917949821621426486336603415318372927456579132310723832276423672743
comment: $a_2$ is the second root of $\chi_{32,2}$ in increasing order, with $a_2\approx 71307.87172677239$.
32
2
41:
1.387890483130496892319257919794275802228473080362069410556408121731263663023268426616031140432239859
comment: $a_2$ is the second root of $\chi_{32,2}$ in increasing order, with $a_2\approx 71307.87172677239$.
32
2
43:
-1.285775356334748076875679467625647208140808105595641497620645536546883965204466132783304399113473814
comment: $a_2$ is the second root of $\chi_{32,2}$ in increasing order, with $a_2\approx 71307.87172677239$.
32
2
47:
0.8958924174021028294225540087725873860797612125847566158442764893645519078910718013338341544140555972
comment: $a_2$ is the second root of $\chi_{32,2}$ in increasing order, with $a_2\approx 71307.87172677239$.
32
2
53:
0.06687842320133344651257846265602364425069360947208913709037416606706319278772133990737032520168076387
comment: $a_2$ is the second root of $\chi_{32,2}$ in increasing order, with $a_2\approx 71307.87172677239$.
32
2
59:
-0.8412600408353439995394841304150651246727864161768919878960477490530935799815249148629517741963257592
comment: $a_2$ is the second root of $\chi_{32,2}$ in increasing order, with $a_2\approx 71307.87172677239$.
32
2
61:
-1.157864712168695595111190445490945637684435886056072776851468892934990516973413275140605441273049175
comment: $a_2$ is the second root of $\chi_{32,2}$ in increasing order, with $a_2\approx 71307.87172677239$.
34
1
2:
-1.848898620856169496761129324880648902757869677180751135863396704525469641722765053371303406830737626
comment: $a_2$ is the first root of $\chi_{34,2}$ in increasing order, with $a_2\approx -171359.4371321172$.
34
1
3:
0.7167736566471636612898075772038009354414923291012731542388664243495029192365061413259753646199306577
comment: $a_2$ is the first root of $\chi_{34,2}$ in increasing order, with $a_2\approx -171359.4371321172$.
34
1
5:
-0.5905454753667583730977408539082283578731459328228363939072113271226017367065370005737953860376367723
comment: $a_2$ is the first root of $\chi_{34,2}$ in increasing order, with $a_2\approx -171359.4371321172$.
34
1
7:
0.6256992195658007985704573750185906492568464618693653107329612738199276061620064232303055519925539998
comment: $a_2$ is the first root of $\chi_{34,2}$ in increasing order, with $a_2\approx -171359.4371321172$.
34
1
11:
-0.5373486626580254591073246051105931402463589517557059811087275624764777973452234166279878230522882235
comment: $a_2$ is the first root of $\chi_{34,2}$ in increasing order, with $a_2\approx -171359.4371321172$.
34
1
13:
-0.7935969264563423248452452810051332407136978298790346079785915152597130945276759161817930085751334412
comment: $a_2$ is the first root of $\chi_{34,2}$ in increasing order, with $a_2\approx -171359.4371321172$.
34
1
17:
-1.664180973207459127382287120984364251832261050623402965365603229227032353585279646634788161326831530
comment: $a_2$ is the first root of $\chi_{34,2}$ in increasing order, with $a_2\approx -171359.4371321172$.
34
1
19:
-0.1117434458255125205267807491555114940230532771539109387971625630474934880437813659247064917400315133
comment: $a_2$ is the first root of $\chi_{34,2}$ in increasing order, with $a_2\approx -171359.4371321172$.
34
1
23:
1.063435069076848668665373676437737734108907837819101833607464919410355358447182596647556389798191041
comment: $a_2$ is the first root of $\chi_{34,2}$ in increasing order, with $a_2\approx -171359.4371321172$.
34
1
29:
-1.120336966534024686434620110455787780291672395289831191465904704858498392424183534801203093847247496
comment: $a_2$ is the first root of $\chi_{34,2}$ in increasing order, with $a_2\approx -171359.4371321172$.
34
1
31:
0.1280855991110528763833102522520557705688532571405208047923944813110471852718326864417412893275088596
comment: $a_2$ is the first root of $\chi_{34,2}$ in increasing order, with $a_2\approx -171359.4371321172$.
34
1
37:
-0.4017621735513896811097982242375293917522205426593931459582650687956919679194342226972843941186418641
comment: $a_2$ is the first root of $\chi_{34,2}$ in increasing order, with $a_2\approx -171359.4371321172$.
34
1
41:
-0.5361492848180820407335988950886688605064288342513390985796499125240235814341114243137367089506447387
comment: $a_2$ is the first root of $\chi_{34,2}$ in increasing order, with $a_2\approx -171359.4371321172$.
34
1
43:
1.972463363721027499835548198307171929666127739216933863256692573773309748811643114999144671417364223
comment: $a_2$ is the first root of $\chi_{34,2}$ in increasing order, with $a_2\approx -171359.4371321172$.
34
1
47:
0.8378024547653931984441946570209689583597427098854492102486086945737899075328100627823809622429513448
comment: $a_2$ is the first root of $\chi_{34,2}$ in increasing order, with $a_2\approx -171359.4371321172$.
34
1
53:
0.3251816376456476596192111948935771440404974507387097346290438438945760730852319307042747273437614880
comment: $a_2$ is the first root of $\chi_{34,2}$ in increasing order, with $a_2\approx -171359.4371321172$.
34
1
59:
-0.7141737018905793295598450247902660911434365293077327050769996738234570733775491144404740346720914997
comment: $a_2$ is the first root of $\chi_{34,2}$ in increasing order, with $a_2\approx -171359.4371321172$.
34
1
61:
-0.03459204531796642306764603984564602327965051763961455660958570242549875853764397656009314355342608933
comment: $a_2$ is the first root of $\chi_{34,2}$ in increasing order, with $a_2\approx -171359.4371321172$.
34
2
2:
0.5360209179939395350745030129159572660974259989285917002544307124088289558457723738721338269281846281
comment: $a_2$ is the second root of $\chi_{34,2}$ in increasing order, with $a_2\approx 49679.43713211717$.
34
2
3:
-0.2081854897194595456826006854458766446862828743334394155575792250761075018153614247120385085522141014
comment: $a_2$ is the second root of $\chi_{34,2}$ in increasing order, with $a_2\approx 49679.43713211717$.
34
2
5:
0.05987963803690394074020787270174294867776717640145357390892354033559372663184081584802685255732699732
comment: $a_2$ is the second root of $\chi_{34,2}$ in increasing order, with $a_2\approx 49679.43713211717$.
34
2
7:
-1.389444037833846718506910792013802753784446983927006168917542617920152573990580581317312916278639337
comment: $a_2$ is the second root of $\chi_{34,2}$ in increasing order, with $a_2\approx 49679.43713211717$.
34
2
11:
1.415784100576830144743514810396745290177282962544881174637815071784883870760920964036154232556364598
comment: $a_2$ is the second root of $\chi_{34,2}$ in increasing order, with $a_2\approx 49679.43713211717$.
34
2
13:
-0.4491582847397892392606464551772850161125662598063345173879075192776854918097488031506435697609997731
comment: $a_2$ is the second root of $\chi_{34,2}$ in increasing order, with $a_2\approx 49679.43713211717$.
34
2
17:
1.268631559028685657490111931086900667987242468050912434537081674118523997941595250766151669667155676
comment: $a_2$ is the second root of $\chi_{34,2}$ in increasing order, with $a_2\approx 49679.43713211717$.
34
2
19:
-0.9705046585448785364165316968422831320293438114012416473551728600379730492947097083597190090175566975
comment: $a_2$ is the second root of $\chi_{34,2}$ in increasing order, with $a_2\approx 49679.43713211717$.
34
2
23:
-0.1738398840432379868784163619311588247867102106204505712495288274324392280234979917575234243691739683
comment: $a_2$ is the second root of $\chi_{34,2}$ in increasing order, with $a_2\approx 49679.43713211717$.
34
2
29:
-0.1222401928681393180959248477791801158867382428027119557672584528454977123281761773779611643498676639
comment: $a_2$ is the second root of $\chi_{34,2}$ in increasing order, with $a_2\approx 49679.43713211717$.
34
2
31:
-1.668361048548165189898395885417119035448731749321909774966533517443344010232308210258816981800658942
comment: $a_2$ is the second root of $\chi_{34,2}$ in increasing order, with $a_2\approx 49679.43713211717$.
34
2
37:
-0.9947482972774771716683118117175019880714242053389944204732221849501546816142306647085209447430128334
comment: $a_2$ is the second root of $\chi_{34,2}$ in increasing order, with $a_2\approx 49679.43713211717$.
34
2
41:
1.216031358125483637022431665950015710343258141343754756668457127743537339650078396580368049334043845
comment: $a_2$ is the second root of $\chi_{34,2}$ in increasing order, with $a_2\approx 49679.43713211717$.
34
2
43:
-0.2225252525487807121315388773270310913010448143938634218727653773672580486116691577410349547319763334
comment: $a_2$ is the second root of $\chi_{34,2}$ in increasing order, with $a_2\approx 49679.43713211717$.
34
2
47:
0.5568618164215350163822452543070427216446530474167392557649607722847903477131417823313033320304432490
comment: $a_2$ is the second root of $\chi_{34,2}$ in increasing order, with $a_2\approx 49679.43713211717$.
34
2
53:
-1.277262930009159234754718766872174182642264322972224949294312745440972321508253477589694558801665994
comment: $a_2$ is the second root of $\chi_{34,2}$ in increasing order, with $a_2\approx 49679.43713211717$.
34
2
59:
-1.132371688569852206988062990782117539177196705236147472326069956379042177975881271169982163134441026
comment: $a_2$ is the second root of $\chi_{34,2}$ in increasing order, with $a_2\approx 49679.43713211717$.
34
2
61:
0.01457429209736033573682785099640916912073930943243693686202683777963831734770485872566822126214654998
comment: $a_2$ is the second root of $\chi_{34,2}$ in increasing order, with $a_2\approx 49679.43713211717$.
36
1
2:
-0.8907303788026748798365876000415771459612265770283242731433568535591302247470510906439556827878022928
comment: $a_2$ is the first root of $\chi_{36,2}$ in increasing order, with $a_2\approx -165109.1678324939$.
36
1
3:
-1.546483971391031178480522651848652075701574086891417606065984528488308890345548125298240382215854245
comment: $a_2$ is the first root of $\chi_{36,2}$ in increasing order, with $a_2\approx -165109.1678324939$.
36
1
5:
-1.201731497612590880730596101885344209219998854068594208067727450612953025831483841765470277728594119
comment: $a_2$ is the first root of $\chi_{36,2}$ in increasing order, with $a_2\approx -165109.1678324939$.
36
1
7:
-0.2033526154694013978442626962747203628138430027148003699818564905199009939421518598977454204652387333
comment: $a_2$ is the first root of $\chi_{36,2}$ in increasing order, with $a_2\approx -165109.1678324939$.
36
1
11:
-1.019113952381924827671296710878531495652760232068292752473762657616627481601209119807828132169424962
comment: $a_2$ is the first root of $\chi_{36,2}$ in increasing order, with $a_2\approx -165109.1678324939$.
36
1
13:
-1.587027442320132380914828823174323401359078663290293608639006117277135983792195755518532120595025763
comment: $a_2$ is the first root of $\chi_{36,2}$ in increasing order, with $a_2\approx -165109.1678324939$.
36
1
17:
0.3871373113299478681537133246507136687746546727567962908436523578836747564845797038286289545313608204
comment: $a_2$ is the first root of $\chi_{36,2}$ in increasing order, with $a_2\approx -165109.1678324939$.
36
1
19:
0.1650957387617458703854439461129865646759282447855869267754406230441716908291630202836346173852425569
comment: $a_2$ is the first root of $\chi_{36,2}$ in increasing order, with $a_2\approx -165109.1678324939$.
36
1
23:
-0.5157504696391517347806425872885648307351330341406135566833795935795919103598800767968529730862797818
comment: $a_2$ is the first root of $\chi_{36,2}$ in increasing order, with $a_2\approx -165109.1678324939$.
36
1
29:
0.8229789650283930316094066920082935391868740138580332175245419542517041483203272957770771514410254353
comment: $a_2$ is the first root of $\chi_{36,2}$ in increasing order, with $a_2\approx -165109.1678324939$.
36
1
31:
0.2716322833195114733133465159118984134822051262539217396720404775221345366408462152523034327543103303
comment: $a_2$ is the first root of $\chi_{36,2}$ in increasing order, with $a_2\approx -165109.1678324939$.
36
1
37:
-1.453607329526677387439171479914665630309896901197767802690330815284868587122085659284004842568264739
comment: $a_2$ is the first root of $\chi_{36,2}$ in increasing order, with $a_2\approx -165109.1678324939$.
36
1
41:
0.5172833716807605389636421668697949384743502545004143275757922708367892408193449352672739996915726940
comment: $a_2$ is the first root of $\chi_{36,2}$ in increasing order, with $a_2\approx -165109.1678324939$.
36
1
43:
0.02568437271405625104525756548056350881046714112543195109309212417475854680651634329679307226497315032
comment: $a_2$ is the first root of $\chi_{36,2}$ in increasing order, with $a_2\approx -165109.1678324939$.
36
1
47:
1.072049666300293933468071782126733667571260436693514898310031901007914268335070813410521978495545716
comment: $a_2$ is the first root of $\chi_{36,2}$ in increasing order, with $a_2\approx -165109.1678324939$.
36
1
53:
-0.6665427479764315999145850862796821694039320586007704770138531164325954883763184777570906508565435831
comment: $a_2$ is the first root of $\chi_{36,2}$ in increasing order, with $a_2\approx -165109.1678324939$.
36
1
59:
0.4011655824250842657870093399625640679385708721619626709809534312739828764748108641967100612252791594
comment: $a_2$ is the first root of $\chi_{36,2}$ in increasing order, with $a_2\approx -165109.1678324939$.
36
1
61:
0.04368553145789431559948919188001845797597186191947520603222099044119990926387888441049964964707332878
comment: $a_2$ is the first root of $\chi_{36,2}$ in increasing order, with $a_2\approx -165109.1678324939$.
36
2
2:
-0.1446237485637502892162510108806274840944682287737576161708806880815505807834391609099062742343222392
comment: $a_2$ is the second root of $\chi_{36,2}$ in increasing order, with $a_2\approx -26808.00761087159$.
36
2
3:
1.769195139733115872292762713822899569723685188919137449419029673230062853846222697153966612758062561
comment: $a_2$ is the second root of $\chi_{36,2}$ in increasing order, with $a_2\approx -26808.00761087159$.
36
2
5:
0.4814821027860211222559557171669681498591327770158271339976039269710636551335071096776060335687943514
comment: $a_2$ is the second root of $\chi_{36,2}$ in increasing order, with $a_2\approx -26808.00761087159$.
36
2
7:
0.9861240742127249114786108901669930613676202817626902065666470603432812415321877720571509773103288884
comment: $a_2$ is the second root of $\chi_{36,2}$ in increasing order, with $a_2\approx -26808.00761087159$.
36
2
11:
0.7356070797534798866386105439645897099603115783169783824649616921407253359147713919321213264145601214
comment: $a_2$ is the second root of $\chi_{36,2}$ in increasing order, with $a_2\approx -26808.00761087159$.
36
2
13:
-0.02712701963205320414839006734107141398619412552542775500149738479334360081264465277216721977923352592
comment: $a_2$ is the second root of $\chi_{36,2}$ in increasing order, with $a_2\approx -26808.00761087159$.
36
2
17:
-1.149952601741555918867045311160816835547153959821101285644073917933517593494955144779113526075515474
comment: $a_2$ is the second root of $\chi_{36,2}$ in increasing order, with $a_2\approx -26808.00761087159$.
36
2
19:
-0.01476683220568040134981803220199973687949330814392328471452801842828794393261278495740073570330250762
comment: $a_2$ is the second root of $\chi_{36,2}$ in increasing order, with $a_2\approx -26808.00761087159$.
36
2
23:
-1.268584457920206606335995525435627259189759946951738737488993733060714114886539555534484828222520714
comment: $a_2$ is the second root of $\chi_{36,2}$ in increasing order, with $a_2\approx -26808.00761087159$.
36
2
29:
-0.3548121664911002300778615207188077425537166145293754475736413493559282752518631480546021235991536163
comment: $a_2$ is the second root of $\chi_{36,2}$ in increasing order, with $a_2\approx -26808.00761087159$.
36
2
31:
-0.2654829123043728875066426218745182385563163549442119420965617560591835237799235321257247508179001895
comment: $a_2$ is the second root of $\chi_{36,2}$ in increasing order, with $a_2\approx -26808.00761087159$.
36
2
37:
0.7191020858470917571011593202451874856826417882203227469311513432813100046375582573239258203393044857
comment: $a_2$ is the second root of $\chi_{36,2}$ in increasing order, with $a_2\approx -26808.00761087159$.
36
2
41:
1.260292880013555338768460212553163935743989359240574835911911223550419668579373913453286366954413923
comment: $a_2$ is the second root of $\chi_{36,2}$ in increasing order, with $a_2\approx -26808.00761087159$.
36
2
43:
-1.187597026617968249566976758587835700155403355995869684921661341045702240342132704207481472094540589
comment: $a_2$ is the second root of $\chi_{36,2}$ in increasing order, with $a_2\approx -26808.00761087159$.
36
2
47:
-0.9448162779814578978610415169176826506475290353704750254777066284058682849735994481699224135607134627
comment: $a_2$ is the second root of $\chi_{36,2}$ in increasing order, with $a_2\approx -26808.00761087159$.
36
2
53:
1.211154788734123960634161370553905970101559904068039343225846634445843241782957833797636920490084599
comment: $a_2$ is the second root of $\chi_{36,2}$ in increasing order, with $a_2\approx -26808.00761087159$.
36
2
59:
-0.5142036792930590861101326808237648486979847994890633038517384689343012027961553658326369387178385720
comment: $a_2$ is the second root of $\chi_{36,2}$ in increasing order, with $a_2\approx -26808.00761087159$.
36
2
61:
-0.01860378286045443505745032224082394398660015928313023276859642470189858291795954045016911012171623422
comment: $a_2$ is the second root of $\chi_{36,2}$ in increasing order, with $a_2\approx -26808.00761087159$.
36
3
2:
1.788769842648014532667678700598983785255608194731994685745063291949037033451419285282231561110187244
comment: $a_2$ is the third root of $\chi_{36,2}$ in increasing order, with $a_2\approx 331573.1754433655$.
36
3
3:
-0.6915799222489921247532436533431633189459078384914483839584084252536712006493779069529482758357187629
comment: $a_2$ is the third root of $\chi_{36,2}$ in increasing order, with $a_2\approx 331573.1754433655$.
36
3
5:
1.243496859575032326545528728660257860912185827749201544409435702800956253548051654347421750993421468
comment: $a_2$ is the third root of $\chi_{36,2}$ in increasing order, with $a_2\approx 331573.1754433655$.
36
3
7:
0.6444375477908452422811361264073348655999573213723351428234211233036657313906382797618766935075471604
comment: $a_2$ is the third root of $\chi_{36,2}$ in increasing order, with $a_2\approx 331573.1754433655$.
36
3
11:
-0.4072355067389493075719847578578774074675778412229641066905475505414508490100076607409505001038799492
comment: $a_2$ is the third root of $\chi_{36,2}$ in increasing order, with $a_2\approx 331573.1754433655$.
36
3
13:
-0.3781690567800454635268938950843978648841067485498497393682655087093419848847996123290837569762799830
comment: $a_2$ is the third root of $\chi_{36,2}$ in increasing order, with $a_2\approx 331573.1754433655$.
36
3
17:
-0.3901805196936937894905450008034727919455653672735420229092512746266665384741242607849731217396208075
comment: $a_2$ is the third root of $\chi_{36,2}$ in increasing order, with $a_2\approx 331573.1754433655$.
36
3
19:
-1.502588801321946446596393202333814320663794951824135816380445902100604993811452184640094464408484978
comment: $a_2$ is the third root of $\chi_{36,2}$ in increasing order, with $a_2\approx 331573.1754433655$.
36
3
23:
1.023272949247183243950058584051747932049395446052341076675591255179240359608198258367708043802003393
comment: $a_2$ is the third root of $\chi_{36,2}$ in increasing order, with $a_2\approx 331573.1754433655$.
36
3
29:
-1.452288534039482295821874975689817033674205270736791152460171242068172484476847043988364586004207195
comment: $a_2$ is the third root of $\chi_{36,2}$ in increasing order, with $a_2\approx 331573.1754433655$.
36
3
31:
0.8200434402204684127760553237848468364112031387024827333366384516979888773880403102344902981586324505
comment: $a_2$ is the third root of $\chi_{36,2}$ in increasing order, with $a_2\approx 331573.1754433655$.
36
3
37:
1.622107901920786021516347869628016119984896672080990191679475665956613720898335053744640343851769131
comment: $a_2$ is the third root of $\chi_{36,2}$ in increasing order, with $a_2\approx 331573.1754433655$.
36
3
41:
-0.3722570889023515092984213599931184885219697459577601259535277257043521715592743413656524668824766186
comment: $a_2$ is the third root of $\chi_{36,2}$ in increasing order, with $a_2\approx 331573.1754433655$.
36
3
43:
-0.07160286238892634263784798227643279109706310458605008369731389253070904514791904136324247665161353036
comment: $a_2$ is the third root of $\chi_{36,2}$ in increasing order, with $a_2\approx 331573.1754433655$.
36
3
47:
0.7723649739589430456096278270680697195320688278111432898374697512421491415422858568627075816524585728
comment: $a_2$ is the third root of $\chi_{36,2}$ in increasing order, with $a_2\approx 331573.1754433655$.
36
3
53:
-1.661510535497391838180734364262840429247189555957971650417147902343665775347512931123869556042276577
comment: $a_2$ is the third root of $\chi_{36,2}$ in increasing order, with $a_2\approx 331573.1754433655$.
36
3
59:
0.5603637050951589332267015354651276629330657871258724314913695470650283168949862950047240030399566822
comment: $a_2$ is the third root of $\chi_{36,2}$ in increasing order, with $a_2\approx 331573.1754433655$.
36
3
61:
1.319169470388452947068869602193488929981305910990916320276511777126874450456921112826567228121921459
comment: $a_2$ is the third root of $\chi_{36,2}$ in increasing order, with $a_2\approx 331573.1754433655$.
38
1
2:
-1.295861850726684650267541184015646258884143375923880751986007994780191361699156952930217217896797514
comment: $a_2$ is the first root of $\chi_{38,2}$ in increasing order, with $a_2\approx -480411.7539742225$.
38
1
3:
0.05154291865227699716712941811803034858018440130861615487530340846133060020305117012491081186057012951
comment: $a_2$ is the first root of $\chi_{38,2}$ in increasing order, with $a_2\approx -480411.7539742225$.
38
1
5:
1.620968552849841124765559726027324842524851115138421014347910153284223534275633763412300818580393100
comment: $a_2$ is the first root of $\chi_{38,2}$ in increasing order, with $a_2\approx -480411.7539742225$.
38
1
7:
-1.258528802413531800236946354652244590480279181751604019529688159611007232787478448913758325008213106
comment: $a_2$ is the first root of $\chi_{38,2}$ in increasing order, with $a_2\approx -480411.7539742225$.
38
1
11:
-0.05601075280510592369834802356312816670638958758536182103847605804235735245939528028563605563666018078
comment: $a_2$ is the first root of $\chi_{38,2}$ in increasing order, with $a_2\approx -480411.7539742225$.
38
1
13:
-0.03039570330656262739846148091764848677846810110596753176613087736227899689452039676509408244263919132
comment: $a_2$ is the first root of $\chi_{38,2}$ in increasing order, with $a_2\approx -480411.7539742225$.
38
1
17:
-0.9340468005188976787180195368005322594742634932304287782845959114713820744467410717920321800192012844
comment: $a_2$ is the first root of $\chi_{38,2}$ in increasing order, with $a_2\approx -480411.7539742225$.
38
1
19:
-0.6804552546974617450219774603475763820349397585345065283137878884798679742295461386413593594583568452
comment: $a_2$ is the first root of $\chi_{38,2}$ in increasing order, with $a_2\approx -480411.7539742225$.
38
1
23:
-1.681356917355910803949715363305719858555116457309631023133253047263552861204289881096051228210359142
comment: $a_2$ is the first root of $\chi_{38,2}$ in increasing order, with $a_2\approx -480411.7539742225$.
38
1
29:
0.2199134742737444311600131952677248338266457698677768274169950440523555026819381815538923708269132866
comment: $a_2$ is the first root of $\chi_{38,2}$ in increasing order, with $a_2\approx -480411.7539742225$.
38
1
31:
-0.6028586414428873079583583167173223678631309586208953410494567408838410622415631631413030302423737327
comment: $a_2$ is the first root of $\chi_{38,2}$ in increasing order, with $a_2\approx -480411.7539742225$.
38
1
37:
0.6052200115137969480306554889650859410542875049981590361392315144643787539117708165154179643684553698
comment: $a_2$ is the first root of $\chi_{38,2}$ in increasing order, with $a_2\approx -480411.7539742225$.
38
1
41:
-1.243521366907364540594822996320850679091372758640842075081150165523555663998502097679903008759825972
comment: $a_2$ is the first root of $\chi_{38,2}$ in increasing order, with $a_2\approx -480411.7539742225$.
38
1
43:
0.2137125646286646378426163749634182584079720464208497494941048317231582957038789734829014163380232180
comment: $a_2$ is the first root of $\chi_{38,2}$ in increasing order, with $a_2\approx -480411.7539742225$.
38
1
47:
0.07791145044885296633640609193355207473088944545195662885094154662346894100811768325000787601106704890
comment: $a_2$ is the first root of $\chi_{38,2}$ in increasing order, with $a_2\approx -480411.7539742225$.
38
1
53:
1.565911437132625951210515590592903692561363843680091492116827150753930988537390577814480465570351725
comment: $a_2$ is the first root of $\chi_{38,2}$ in increasing order, with $a_2\approx -480411.7539742225$.
38
1
59:
0.1139789655517196438066833364960172277859322444949171257818497717213138049992642721799970635676767931
comment: $a_2$ is the first root of $\chi_{38,2}$ in increasing order, with $a_2\approx -480411.7539742225$.
38
1
61:
-0.9927583501868274116451462997457226163508955323644573054351001694471441110268745273561972087282410052
comment: $a_2$ is the first root of $\chi_{38,2}$ in increasing order, with $a_2\approx -480411.7539742225$.
38
2
2:
0.7714876202935454643867880712486836229398833269178407407220718736685153481092338412959335099475529733
comment: $a_2$ is the second root of $\chi_{38,2}$ in increasing order, with $a_2\approx 286011.7539742225$.
38
2
3:
-0.03069234728164479004719750288183052140752329008194364615022492509085525808902255040227386690075295292
comment: $a_2$ is the second root of $\chi_{38,2}$ in increasing order, with $a_2\approx 286011.7539742225$.
38
2
5:
-0.9727112619967476700805284633828349428154363209158528650161955380043277246016072943513996909440964054
comment: $a_2$ is the second root of $\chi_{38,2}$ in increasing order, with $a_2\approx 286011.7539742225$.
38
2
7:
0.4581244682482572313972334855045602892170901200098865451946942298772214666141786521784184852020019712
comment: $a_2$ is the second root of $\chi_{38,2}$ in increasing order, with $a_2\approx 286011.7539742225$.
38
2
11:
-1.393761751505440403151084041612544887003520475894057969769443077610158574068299196671427000539057174
comment: $a_2$ is the second root of $\chi_{38,2}$ in increasing order, with $a_2\approx 286011.7539742225$.
38
2
13:
1.338975718203915444037649949883429547562980750146818821041822583267712503281821462758959692883338527
comment: $a_2$ is the second root of $\chi_{38,2}$ in increasing order, with $a_2\approx 286011.7539742225$.
38
2
17:
-0.6084428119526850102574024746222353653133096045134001001894109519033507667993202105106532910213358346
comment: $a_2$ is the second root of $\chi_{38,2}$ in increasing order, with $a_2\approx 286011.7539742225$.
38
2
19:
1.502866410559374323226757546680966159374314654965625302585442428112441617595542233928493415653246637
comment: $a_2$ is the second root of $\chi_{38,2}$ in increasing order, with $a_2\approx 286011.7539742225$.
38
2
23:
-0.005267550833912544050034828885123348641117189281035023778916493562262061091867536872567737041311728042
comment: $a_2$ is the second root of $\chi_{38,2}$ in increasing order, with $a_2\approx 286011.7539742225$.
38
2
29:
-1.341082583495213676343133717189157833462697021619324590098060911644644410782276380361331875416747254
comment: $a_2$ is the second root of $\chi_{38,2}$ in increasing order, with $a_2\approx 286011.7539742225$.
38
2
31:
0.6700245410984659816965582182936034611445112587209492319628132120955783075378918905687825545963805074
comment: $a_2$ is the second root of $\chi_{38,2}$ in increasing order, with $a_2\approx 286011.7539742225$.
38
2
37:
-1.267343474482780834023611464633013617157220212448131065195104807412652796203715402194555705242093301
comment: $a_2$ is the second root of $\chi_{38,2}$ in increasing order, with $a_2\approx 286011.7539742225$.
38
2
41:
-0.5931681416898510282091841497124529431117024393486979700635872524865955949318460476977402136001154683
comment: $a_2$ is the second root of $\chi_{38,2}$ in increasing order, with $a_2\approx 286011.7539742225$.
38
2
43:
-1.765411359304014846005709983635114386519660637167710852569637941791746777018916235983868266397032559
comment: $a_2$ is the second root of $\chi_{38,2}$ in increasing order, with $a_2\approx 286011.7539742225$.
38
2
47:
0.4173152062912311390115707317685417133387995840041612129402398130465333914263362875145875093864168313
comment: $a_2$ is the second root of $\chi_{38,2}$ in increasing order, with $a_2\approx 286011.7539742225$.
38
2
53:
0.4500047429223205315112491014784244181338451771088151963087571451570611702927563234249110831349635210
comment: $a_2$ is the second root of $\chi_{38,2}$ in increasing order, with $a_2\approx 286011.7539742225$.
38
2
59:
-0.5267851868509207762849727199124828869112532762301157129115515705044618704350991965959941460851347862
comment: $a_2$ is the second root of $\chi_{38,2}$ in increasing order, with $a_2\approx 286011.7539742225$.
38
2
61:
1.088068880807194134485625301863928490508751934651059555207611056985032495090185498759968042871884013
comment: $a_2$ is the second root of $\chi_{38,2}$ in increasing order, with $a_2\approx 286011.7539742225$.
40
1
2:
-1.077815305491872856846310363452715742490418266302905256503173946502571264868800574935493252354512574
comment: $a_2$ is the first root of $\chi_{40,2}$ in increasing order, with $a_2\approx -799151.7631007462$.
40
1
3:
0.6314465362261163034619764575476713477329431759079600618597937304344845880506102284578178253776806251
comment: $a_2$ is the first root of $\chi_{40,2}$ in increasing order, with $a_2\approx -799151.7631007462$.
40
1
5:
-1.445377543611898645607301396414588049772336605081308878680879817762433437219498866550466434970397519
comment: $a_2$ is the first root of $\chi_{40,2}$ in increasing order, with $a_2\approx -799151.7631007462$.
40
1
7:
0.4767438387188188741690329951752283020043453796180242747737949216053143310638640449021376293993841468
comment: $a_2$ is the first root of $\chi_{40,2}$ in increasing order, with $a_2\approx -799151.7631007462$.
40
1
11:
1.654325758157396572621658551626470935021008660095007140234192270840472336941817215140724893528494171
comment: $a_2$ is the first root of $\chi_{40,2}$ in increasing order, with $a_2\approx -799151.7631007462$.
40
1
13:
0.5719435283259639217532180202980158432037300154985173877767189348807440402154650750257883133473376344
comment: $a_2$ is the first root of $\chi_{40,2}$ in increasing order, with $a_2\approx -799151.7631007462$.
40
1
17:
1.465983605409172063626140635244425591484415806999385591808678447128578415909885646094087527107021485
comment: $a_2$ is the first root of $\chi_{40,2}$ in increasing order, with $a_2\approx -799151.7631007462$.
40
1
19:
-0.1851741859930711050766029069368351127954042358653117809386460502505470772720376926850376178718176887
comment: $a_2$ is the first root of $\chi_{40,2}$ in increasing order, with $a_2\approx -799151.7631007462$.
40
1
23:
0.7673347793621872081631694095102125076778745349153894423272162317841750060506804255680684336927967009
comment: $a_2$ is the first root of $\chi_{40,2}$ in increasing order, with $a_2\approx -799151.7631007462$.
40
1
29:
-0.2672076130058885583750458387379811578257885259391985038740961315869665334132905766232849221239362220
comment: $a_2$ is the first root of $\chi_{40,2}$ in increasing order, with $a_2\approx -799151.7631007462$.
40
1
31:
-0.3775469525226551883057988264120617790902323443623517583843327080187752268130906388159044796149382057
comment: $a_2$ is the first root of $\chi_{40,2}$ in increasing order, with $a_2\approx -799151.7631007462$.
40
1
37:
1.475078946370887437167783627587280014911095103705585583813544332548183932051037436657906525581332419
comment: $a_2$ is the first root of $\chi_{40,2}$ in increasing order, with $a_2\approx -799151.7631007462$.
40
1
41:
0.3210509752568237361815903573240565931432716755243690442350149406358264146438031090672446047504481196
comment: $a_2$ is the first root of $\chi_{40,2}$ in increasing order, with $a_2\approx -799151.7631007462$.
40
1
43:
-0.2668028290766666606176368522209435467511133534522378626770687691134163409535051455997049175324894105
comment: $a_2$ is the first root of $\chi_{40,2}$ in increasing order, with $a_2\approx -799151.7631007462$.
40
1
47:
1.547503705467737339378117700007600715784691593747186910215441982444761001451739369813276917168844344
comment: $a_2$ is the first root of $\chi_{40,2}$ in increasing order, with $a_2\approx -799151.7631007462$.
40
1
53:
1.113724073278660367591395165665365113501135736442425047597241244689134790202809510069711823529896510
comment: $a_2$ is the first root of $\chi_{40,2}$ in increasing order, with $a_2\approx -799151.7631007462$.
40
1
59:
-0.5546956720232208936694052732919723557571123487604872821236360235806697755934751783523148788671347754
comment: $a_2$ is the first root of $\chi_{40,2}$ in increasing order, with $a_2\approx -799151.7631007462$.
40
1
61:
0.8595039187374796058546016102971210194576397566562844988611413880961621614011481965532847593101563872
comment: $a_2$ is the first root of $\chi_{40,2}$ in increasing order, with $a_2\approx -799151.7631007462$.
40
2
2:
0.3256943162527601758535614071303904146835971940406618976334142580068711244657560358575366773739937072
comment: $a_2$ is the second root of $\chi_{40,2}$ in increasing order, with $a_2\approx 241487.7444577613$.
40
2
3:
-1.564566767895857530643793181440808121843786086937816276683235681206619783307637042266595353957013697
comment: $a_2$ is the second root of $\chi_{40,2}$ in increasing order, with $a_2\approx 241487.7444577613$.
40
2
5:
1.257271694539006598437745945744437692376863061865342957724736306849450976881187782632631821495516604
comment: $a_2$ is the second root of $\chi_{40,2}$ in increasing order, with $a_2\approx 241487.7444577613$.
40
2
7:
0.6037524410520824523986697778985994009311482317787462438590077652751472225771065883942956689656084385
comment: $a_2$ is the second root of $\chi_{40,2}$ in increasing order, with $a_2\approx 241487.7444577613$.
40
2
11:
1.266449866641736094409145736785007839778080338376052375087901897129084303816294922736068819156534792
comment: $a_2$ is the second root of $\chi_{40,2}$ in increasing order, with $a_2\approx 241487.7444577613$.
40
2
13:
-0.5563193792239405041535105287965594780073287265839306367564664144579015586963864067078891099415761920
comment: $a_2$ is the second root of $\chi_{40,2}$ in increasing order, with $a_2\approx 241487.7444577613$.
40
2
17:
-0.1003518910565435450733995456426227271016964189832889521530607260015389072399671381797455272340381907
comment: $a_2$ is the second root of $\chi_{40,2}$ in increasing order, with $a_2\approx 241487.7444577613$.
40
2
19:
1.444249178418742916656085784711068220980389649146851860171927040219470454118089686227539836881541500
comment: $a_2$ is the second root of $\chi_{40,2}$ in increasing order, with $a_2\approx 241487.7444577613$.
40
2
23:
-0.5205796985733647729078060254112437765108403701319833350302726784787716665353023988936792348703507301
comment: $a_2$ is the second root of $\chi_{40,2}$ in increasing order, with $a_2\approx 241487.7444577613$.
40
2
29:
0.4009324319333008972853699524968185402341063222661339051715600746468418824508511199518516982658346500
comment: $a_2$ is the second root of $\chi_{40,2}$ in increasing order, with $a_2\approx 241487.7444577613$.
40
2
31:
1.566633603740819449761804610706763317989633487223577297492320710628039339496840542739607476918959513
comment: $a_2$ is the second root of $\chi_{40,2}$ in increasing order, with $a_2\approx 241487.7444577613$.
40
2
37:
0.8495930046624595698839606355635223771846275866271040258400928523378491793252824511854328799711311362
comment: $a_2$ is the second root of $\chi_{40,2}$ in increasing order, with $a_2\approx 241487.7444577613$.
40
2
41:
-0.8067934670562684991121843644677779960531119888488639675667308779686471959274635028660711361358891740
comment: $a_2$ is the second root of $\chi_{40,2}$ in increasing order, with $a_2\approx 241487.7444577613$.
40
2
43:
0.7533572792219916729835289452484189401187875954600937765374269423853641980749853509970348939651084525
comment: $a_2$ is the second root of $\chi_{40,2}$ in increasing order, with $a_2\approx 241487.7444577613$.
40
2
47:
0.4644418762575507592527731356343631574395934513712382208128030352783534288666909835144410011093204696
comment: $a_2$ is the second root of $\chi_{40,2}$ in increasing order, with $a_2\approx 241487.7444577613$.
40
2
53:
-0.07674904871521866966072296594075993855808451651895403073821767866787018496037393617409453668441573770
comment: $a_2$ is the second root of $\chi_{40,2}$ in increasing order, with $a_2\approx 241487.7444577613$.
40
2
59:
0.2978699023148304843967383595793198785209463749290879216991013697076788288311026690170478279110439600
comment: $a_2$ is the second root of $\chi_{40,2}$ in increasing order, with $a_2\approx 241487.7444577613$.
40
2
61:
-1.329767767417701658519195848235228453182197223380635873429125834425706138657015605498816205499351615
comment: $a_2$ is the second root of $\chi_{40,2}$ in increasing order, with $a_2\approx 241487.7444577613$.
40
3
2:
1.492362611200560831727745433845020915548134841442436508104016179465016112920819331668353742702202410
comment: $a_2$ is the third root of $\chi_{40,2}$ in increasing order, with $a_2\approx 1106520.018642985$.
40
3
3:
1.484232995397548902139099294745512516837190040190358774728001335212451774266599862841416177482387658
comment: $a_2$ is the third root of $\chi_{40,2}$ in increasing order, with $a_2\approx 1106520.018642985$.
40
3
5:
0.5967125323287798004535337551991934607188511452627711653948448906554946041885218369463728314438613969
comment: $a_2$ is the third root of $\chi_{40,2}$ in increasing order, with $a_2\approx 1106520.018642985$.
40
3
7:
-1.677217371835103800997432784007438098625277480651147763198669619158070234503950207235922991630598463
comment: $a_2$ is the third root of $\chi_{40,2}$ in increasing order, with $a_2\approx 1106520.018642985$.
40
3
11:
0.3715197238505965083802053339504201713017356940575084094204438227598160711032071145834749656496378952
comment: $a_2$ is the third root of $\chi_{40,2}$ in increasing order, with $a_2\approx 1106520.018642985$.
40
3
13:
0.5831357819015479299482910705128364397280136524400406426188508259461130514410161717396925511047798695
comment: $a_2$ is the third root of $\chi_{40,2}$ in increasing order, with $a_2\approx 1106520.018642985$.
40
3
17:
-0.4627130616767625490111344907201383627748333784603324189704922030810731117623879322882927970232737931
comment: $a_2$ is the third root of $\chi_{40,2}$ in increasing order, with $a_2\approx 1106520.018642985$.
40
3
19:
-0.1890495227333346971811456950059616062958298497867928108317407677970340345938871171922447991919154365
comment: $a_2$ is the third root of $\chi_{40,2}$ in increasing order, with $a_2\approx 1106520.018642985$.
40
3
23:
0.6064358361314574861171896516525323917221311593368847663810857131005872870595368506569485028350478811
comment: $a_2$ is the third root of $\chi_{40,2}$ in increasing order, with $a_2\approx 1106520.018642985$.
40
3
29:
-0.2095661517774158387421496142718820383228507701455980890800155893207199066465263902885069675939444451
comment: $a_2$ is the third root of $\chi_{40,2}$ in increasing order, with $a_2\approx 1106520.018642985$.
40
3
31:
1.347917538082317215231517361967709891013431332512015977747366217107026547841381468549290999661130711
comment: $a_2$ is the third root of $\chi_{40,2}$ in increasing order, with $a_2\approx 1106520.018642985$.
40
3
37:
-0.3256064663859441596135444202464528156463965168178852770544582069390599408711142084059255295220727129
comment: $a_2$ is the third root of $\chi_{40,2}$ in increasing order, with $a_2\approx 1106520.018642985$.
40
3
41:
0.5707509633904393634321151068835835514240809048458259895600520077593806161600379282133538687088630336
comment: $a_2$ is the third root of $\chi_{40,2}$ in increasing order, with $a_2\approx 1106520.018642985$.
40
3
43:
1.800072632122094310867812279822086542864239919906189080705172792986007332851415223382578337273324327
comment: $a_2$ is the third root of $\chi_{40,2}$ in increasing order, with $a_2\approx 1106520.018642985$.
40
3
47:
-1.509707556253413678551569799338768964523055797314294206545323376322196040777355696479495257595719925
comment: $a_2$ is the third root of $\chi_{40,2}$ in increasing order, with $a_2\approx 1106520.018642985$.
40
3
53:
0.3600062065512081620396404980655658060053607593807932986498106088078982972119551213243033094077322337
comment: $a_2$ is the third root of $\chi_{40,2}$ in increasing order, with $a_2\approx 1106520.018642985$.
40
3
59:
-1.392151019508250843141690511800469726035553369376879953405980213002355478223965108023460841528911981
comment: $a_2$ is the third root of $\chi_{40,2}$ in increasing order, with $a_2\approx 1106520.018642985$.
40
3
61:
1.077724991238206957380224342653173652902661676997053673354073518456173956294496792101654751068382490
comment: $a_2$ is the third root of $\chi_{40,2}$ in increasing order, with $a_2\approx 1106520.018642985$.
Definition
For the $i$th normalised Hecke eigenform $f_{k,i}(q)=\sum_{m\geq1}a_mq^m$ in $S_k(\mathrm{SL}_2(\mathbb{Z}))$ [1], ordered by increasing real $T_2$-eigenvalue $a_2$ [2], this table gives the Deligne-normalised eigenvalue $a_p/p^{(k-1)/2}$ for primes $p$.
Parameters
$k$
—   weight ($k$ is even and $\dim S_k(\mathrm{SL}_2(\mathbb{Z}))>0$)
$i$
—   position by increasing $a_2$ ($1\leq i\leq\dim S_k(\mathrm{SL}_2(\mathbb{Z}))$)
$p$
—   prime ($p$ is prime)
Formulas
(1)
For $\operatorname{Re}s>(k+1)/2$, the Euler factor of $L(f_{k,i},s)$ at $p$ is $(1-a_pp^{-s}+p^{k-1-2s})^{-1}$.
(2)
$a_p/p^{(k-1)/2}=2\cos\theta_p$, where $\theta_p$ is the Satake angle [4] in $[0,\pi]$.
(3)
For a normalised eigenform, $a_{p^2}=a_p^2-p^{k-1}$.
Comments
(4)
The eigenform is normalised so that $a_1=1$, and the stored value is the analytic normalisation $a_p/p^{(k-1)/2}$. It lies in $[-2,2]$ by the Ramanujan-Petersson theorem [3], and is not divided by an additional factor of $2$.
(5)
In each weight, the eigenforms are ordered by the real roots of the Hecke polynomial $\chi_{k,2}$, whose roots are the $a_2$ values in that weight. This is not necessarily the order Sage or PARI lists the eigenforms in.
(6)
The Satake angle $\theta_p\in[0,\pi]$ [4] is determined by $a_p/p^{(k-1)/2}=2\cos\theta_p$. This table stores the normalised eigenvalue rather than the angle.
Programs
(P1)
Sage
import numberdb.sage
import sage.symbolic.expression
from sage.modular.modform.constructor import CuspForms
from sage.rings.qqbar import AA
from sage.rings.rational_field import QQ
k = 24; i = 2; p = 2
roots = sorted(
    CuspForms(1, k).hecke_matrix(2).charpoly().roots(
        ring=AA, multiplicities=False))
(roots[i - 1] / (AA(p) ** (QQ(k - 1) / 2))).n(110)       # 1.759601793373322...
(P2)
PARI/GP
default(realbitprecision, 330);
k = 24; i = 2; p = 2;
mf = mfinit([1,k], 0);
F = mfeigenbasis(mf)[1];
a2 = mfcoefs(F, 2)[3];
ap = mfcoefs(F, p)[p+1];
nf = nfinit(component(a2, 1));
A2 = nfeltembed(nf, a2);
Ap = nfeltembed(nf, ap);
P = vecsort(vector(#A2, j, [real(A2[j]), real(Ap[j])]), 1);
P[i][2] / p^((k-1)/2)       \\ 1.759601793373322...
Links
Similar tables
Hecke polynomials of level one cusp forms —   stores the characteristic polynomials whose roots are the unnormalised eigenvalues used here
Special values of the $L$-functions of level one cusp forms —   stores critical values of the same eigenforms in the same ordering
Zeros of the $L$-functions of level one cusp forms —   stores critical-line zero ordinates of the same eigenforms in the same ordering
$q$-expansion of the modular discriminant $\Delta$ —   stores the coefficients of the weight $12$ eigenform whose normalised prime coefficients are the $k=12$ rows here
Frobenius angles of abelian varieties over prime fields —   stores angles in another family governed by a Sato-Tate distribution [4]
Algebraic numbers of degree $2$ —   contains low-degree algebraic numbers of the kind that occur in the two-dimensional Hecke fields
Data properties
Entries are of type: real number
How well the digits are known: proven
Table is complete: no (it holds every even weight $12\leq k\leq40$ with $\dim S_k(\mathrm{SL}_2(\mathbb{Z}))>0$, every eigenform, and every prime $p\leq61$)
How they were obtained:

The generator computes exact Hecke matrices with Sage and checks their characteristic polynomials against PARI/GP's mfheckemat [5].

more

For each prime $p$, it expresses $T_p$ exactly as a polynomial in $T_2$, evaluates that polynomial at the exact algebraic roots of the $T_2$ characteristic polynomial in increasing real order, and only then coerces $a_p/p^{(k-1)/2}$ into Sage's real ball field before writing the stored digits. It checks Deligne's bound on every entry. The weight $12$ rows were checked against the Ramanujan tau values in the modular discriminant table, and an independent run compared every row with Sage's Newforms coefficient embeddings [6].



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