LMFDB - Embedded newform 1.124.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,124,Mod(1,1)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1, base_ring=CyclotomicField(1))

chi = DirichletCharacter(H, H._module([]))

N = Newforms(chi, 124, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 124);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 124 $
Character orbit:	$[\chi]$	$=$	1.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$95.8076224914$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 5 x^{9} + \cdots - 30\!\cdots\!00 $ x^10 - 5x^9 - 15715453868021699710092772079092540x^8 - 26266124042812682998424571585089831590205068049060x^7 + 84121858174092336600113561613713972647563203512351912537270590353630x^6 + 379093517978966296102326874839864127890836652088481384034680507978226789995450963674x^5 - 178169460809783179009549624277289836654444059110978027273698418885123553241939688068575717934852189900x^4 - 1245636498979681226321614393524571589619504035401876840543009031333503086568636782764013392968027485700762127638413300x^3 + 129762452996526200398051897123036800060408807347851219771140695265257969506581377283936016647648702182046481807251218168548307972915625x^2 + 528571137862721172285166971123829130130230319341377634584297195173353067111023621859235329898258863701780917337311697625039368462612529429642669511875*x - 30099552861177981250053838955006077286296138508373520923076262019024824503038189462275061365602320269033953541177928036556554778705586348952495129790312912580886000000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{178}\cdot 3^{70}\cdot 5^{22}\cdot 7^{9}\cdot 11^{6}\cdot 13^{2}\cdot 17\cdot 31^{2}\cdot 41^{3} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$5.97127e16$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.07908e18 q^{2} +3.50571e29 q^{3} +6.00505e36 q^{4} -4.74746e42 q^{5} -1.43001e48 q^{6} -1.17353e51 q^{7} +1.88811e55 q^{8} +7.43807e58 q^{9} +O(q^{10})$	\(q-4.07908e18 q^{2} +3.50571e29 q^{3} +6.00505e36 q^{4} -4.74746e42 q^{5} -1.43001e48 q^{6} -1.17353e51 q^{7} +1.88811e55 q^{8} +7.43807e58 q^{9} +1.93653e61 q^{10} +1.35161e64 q^{11} +2.10520e66 q^{12} -1.52537e68 q^{13} +4.78693e69 q^{14} -1.66432e72 q^{15} -1.40874e74 q^{16} -5.29817e75 q^{17} -3.03405e77 q^{18} +6.94083e78 q^{19} -2.85088e79 q^{20} -4.11406e80 q^{21} -5.51332e82 q^{22} +9.79960e83 q^{23} +6.61917e84 q^{24} -7.15011e85 q^{25} +6.22212e86 q^{26} +9.06626e87 q^{27} -7.04712e87 q^{28} -7.09621e89 q^{29} +6.78890e90 q^{30} +6.10616e90 q^{31} +3.73858e92 q^{32} +4.73835e93 q^{33} +2.16117e94 q^{34} +5.57130e93 q^{35} +4.46660e95 q^{36} +3.84618e96 q^{37} -2.83122e97 q^{38} -5.34752e97 q^{39} -8.96374e97 q^{40} -1.40652e99 q^{41} +1.67816e99 q^{42} +4.40926e100 q^{43} +8.11648e100 q^{44} -3.53120e101 q^{45} -3.99733e102 q^{46} +4.08007e102 q^{47} -4.93864e103 q^{48} -8.71464e103 q^{49} +2.91659e104 q^{50} -1.85739e105 q^{51} -9.15995e104 q^{52} -1.87477e106 q^{53} -3.69820e106 q^{54} -6.41671e106 q^{55} -2.21576e106 q^{56} +2.43325e108 q^{57} +2.89460e108 q^{58} -8.99566e107 q^{59} -9.99434e108 q^{60} +5.11564e109 q^{61} -2.49075e109 q^{62} -8.72881e109 q^{63} -2.69659e109 q^{64} +7.24166e110 q^{65} -1.93281e112 q^{66} -3.71622e111 q^{67} -3.18158e112 q^{68} +3.43545e113 q^{69} -2.27258e112 q^{70} +2.34973e113 q^{71} +1.40439e114 q^{72} +6.07538e112 q^{73} -1.56889e115 q^{74} -2.50662e115 q^{75} +4.16800e115 q^{76} -1.58616e115 q^{77} +2.18130e116 q^{78} -4.96028e116 q^{79} +6.68795e116 q^{80} -4.30531e116 q^{81} +5.73729e117 q^{82} +1.89829e117 q^{83} -2.47052e117 q^{84} +2.51529e118 q^{85} -1.79857e119 q^{86} -2.48772e119 q^{87} +2.55199e119 q^{88} +1.50546e120 q^{89} +1.44040e120 q^{90} +1.79008e119 q^{91} +5.88471e120 q^{92} +2.14064e120 q^{93} -1.66429e121 q^{94} -3.29513e121 q^{95} +1.31064e122 q^{96} +3.72395e121 q^{97} +3.55477e122 q^{98} +1.00534e123 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 22\!\cdots\!00 q^{2}+ \cdots + 11\!\cdots\!70 q^{9}+O(q^{10}) $ 10 * q + 2202364291733634600 * q^2 + 134125909579478648360089344600 * q^3 + 57084626888206052159227531786235721280 * q^4 + 113311323144401441139520857445630379551020 * q^5 + 1704428975203488447105127830499670347572029831520 * q^6 - 588489927154562089895546247825497341684043299210000 * q^7 + 31510915218929096051805568530239002377664910158953331200 * q^8 + 110622019190242888335688316416186156626673662860821573119570 * q^9	$ 10 q + 22\!\cdots\!00 q^{2}+ \cdots + 42\!\cdots\!40 q^{99}+O(q^{100}) $ 10 * q + 2202364291733634600 * q^2 + 134125909579478648360089344600 * q^3 + 57084626888206052159227531786235721280 * q^4 + 113311323144401441139520857445630379551020 * q^5 + 1704428975203488447105127830499670347572029831520 * q^6 - 588489927154562089895546247825497341684043299210000 * q^7 + 31510915218929096051805568530239002377664910158953331200 * q^8 + 110622019190242888335688316416186156626673662860821573119570 * q^9 + 607459321076833386281292454084083169893966543300090109855920 * q^10 + 20273686763761435409423006911849218920389062193989167514770475720 * q^11 + 4052865973093508952389058638442895723286492489413158535125361555200 * q^12 - 291679396147681612979261456874156006927679666680520092295296904243300 * q^13 + 27976229889499855271101394813572915637495617130073041821451727626343360 * q^14 - 392991849187277904226922353724551866025786803779963352155457638870550960 * q^15 + 170537484653060213908677304907245043396278852268473637259293488813126389760 * q^16 + 12235102818717192622457093834992766133856671265915142264300826066878229357300 * q^17 - 3223507766001641523002467733734494312358127846172048898709172212524853129400 * q^18 + 1666536960290050807259098599664015537273272264625091908962591688248992033363000 * q^19 - 258603401942930436278392999359500188332957941397465316508154366680175868513395840 * q^20 + 4726509088722575910333056316070457676248231372641372129182198172427507924250822720 * q^21 + 36257825721047322261901872593889855345156787594610756475691779186002775337739623200 * q^22 + 608713231798404227050887650300591817769390426844961074649606092902614656957300110800 * q^23 + 19786957119488250790991083066821762146008515555201937981451455681676136224982485145600 * q^24 + 485472456776317058938705118138543671636666869772929691136469732236638136950683734854150 * q^25 + 5053774757641298124381938661884760040772792595111887036219927684117253575240872954270320 * q^26 + 7700604788205145137767150192913791419267884018867880017540340460394864815597243605954800 * q^27 + 74320574143924149311927158272423731357750692600077221984033474863771547722768608451827200 * q^28 - 2895686519348539858982198714566014333083121965126431872521364438276729233514966964861920900 * q^29 - 22262917949972607798281650542991372273227307551478322515015451194939644144287010568170260160 * q^30 + 8790022978579520754821177211313048365131172620195297293938358421085691479353060262526493120 * q^31 + 1751500200025709503299520819254071214160534691289882147163021909032725750364777638363998617600 * q^32 + 3377779222430911726674898641035883376428754579238816338112342781453942628724801459716957759200 * q^33 - 6225938074136149683378553996041283828179924226890449375819180913947978021351234695525912123440 * q^34 - 127563228852680813474013009675495155368791673351570943874124990036376129087211259153294998182880 * q^35 - 960607248812912772012251743514056985739786369519292450099978587362742327408164708696515631029440 * q^36 + 6228828125185127210799991385566665774174549878089400136396229638018645937962697518952494474353900 * q^37 + 28149067438989609944155252541609246090047173880579663465635025516156787837518279305588448239640800 * q^38 + 32959560456311799423446130174300373353905131721622845396992748686019716292294663425506424345860240 * q^39 - 1541102562733565575559372415349948151575063374670493456677530450911236708989098058436326331353216000 * q^40 - 1068152726446746563375131410189033727670864785235697564369168677061613108479021875193178691047211580 * q^41 + 20095761139727919770728604942082508129628376714407479872537782023853379601508712052049964889809772800 * q^42 + 46233404163387955795602164476169340298677865880468856734168936393238098987144594231102601675269093000 * q^43 - 52688891628643675175168725969332835598120041222275464101537283849644425575989226874013323217475715840 * q^44 - 276151139990973697058858962803580333632808711210368039524099465966592527069575726858161671366884559460 * q^45 - 4956167789256268893877918319143394669475196050553827727658680165816979401845732960931428427086369343680 * q^46 + 17772045268836184831844329814023597704806545621277768047420131448847122870736827620663655619725807063200 * q^47 + 51761953997683651012862563513543953819489370557013280319018667369358644539732537961201783057357284556800 * q^48 + 4842008461630476490563278611494437613501142312970195371812232417883349129579090018535857454479039263130 * q^49 - 330254069348074888508775695501771665236948121810497861745549014586967380406632858093596781115350317786600 * q^50 - 1686422005116992563499617363913766680527287395438410278431643755495206402676045225667531758007365026422480 * q^51 + 16611060975411842119131633337384601723518365602136815421052858543740989156971262266673653412429442118640000 * q^52 + 9865945778729587083239654534416850864601802213574882992654111630338605104546138239494501124975548493521100 * q^53 - 60640197068689493262198311334951229812788883593837286178369184088874735814592991608797792016104189923368000 * q^54 - 120361120762474187756245290834980454390752949663319471980043061592083830177139490905896370183199650052873360 * q^55 - 57015316450658072395870459826079095803920665182036397691229905074486924466540678768162486841164165128294400 * q^56 + 1396923092152977829208189007390918802999715037379682422426941467924623915894742262411280956401324684179725600 * q^57 + 2554207156866772251496945559844754999941265909370354854359543391556629115881092937374262646509059308353993200 * q^58 - 5145780721189304530977439106322232365186387161064437614606021967565628939238800130603665119360443691606408600 * q^59 - 66278076209627104092999016928275373331607580130420941011406364860535093218415612427322615235267206762608135680 * q^60 - 101263377816841551355083395298372952856192354301955205631542096828602753322654741755354533779833120948634218180 * q^61 + 490163771618275701978987843789963182098163324759510401318125961890059086504863674543728459156699482192104851200 * q^62 + 716994933719942928295473975746285250148612895023346279094238117312058943990010182273859915020097252421755028400 * q^63 + 977773622342975590017631946427418773791663923681070678728480268947054413114166828884752974664930456883519815680 * q^64 - 11968027825720175930231498946103877541009224034319106828760765788467265313917048983370089696694519867473256696760 * q^65 + 8356397123262354897793421823599928466576840588120328054964440488870910319312784016270333510655080761554879085440 * q^66 + 39912334137048450694568083884380942663008127500477138648875228077299015893249118799594117572286387201695784163800 * q^67 + 39810569882426825547153916716555119471846099090357174378729255654981318980810349722622634031376462141822712297600 * q^68 - 190987535400183650465933553655021226823555965329073635462561332226561638701086158395261700711827729370532705968960 * q^69 - 182874208614274419310812157137434002657108803954011080946993086754744195429788058628755429399392480183737020100480 * q^70 - 1491077405948495434941700576503681644378063798419124359800518573569171342873061633452931165399746735550688616916880 * q^71 + 3868752305234909303390161351576640709493783520411426900182416417888751619723371014253176886432068110318183269286400 * q^72 + 2192135974586112989195753785125121714230606008983301044356524322771675433811702392428103660396733638378012314983300 * q^73 - 1727512827049960711960442580477759342287747326769085411504653106770896005010199230748905559335798254942125500917840 * q^74 + 504885939682048274689087603051515462429637328904385746355242199239392653085717173946420202256812538173461328445800 * q^75 - 87242153455336999174915407092865037433520017247914052198234675064090961742425760253601031048397834372731494811884800 * q^76 + 125219039376054076906312524181774337606022429710014201552829418564774196434593400808568625172363524016803572381496000 * q^77 + 532021772270427326096828804708119000324560547259051767495862487744514269364113068456981059104472838417927263294440000 * q^78 + 791422870082819667716376764340803517880370192381122523208760361909337424612697174285245300530946528365443447973538400 * q^79 - 4085615693220605934319500471303383153704006928966377733020681159517376658700094137621404536087640933221508984164065280 * q^80 - 4901313048770605685168758293113604944951802904180679505379560996783873032337121922603323736534839244595242111670861990 * q^81 + 9412937760870473955022147090951043412853639579869374057740631037910279361456062862380973734854715629890526499271869200 * q^82 + 25598672435022890898365706131229485636670116907492184873375817087238430028799072047182092723440708545273457704582505400 * q^83 + 33174546777967500578087391267312861327420773111224581899833592957088759443575417585347553827589468266717940082704066560 * q^84 - 9635564759118842988822047485364075764019024326980604397537196383868268963111162554936571689782374441122549467080005480 * q^85 + 10863279313344256312123665865422603616515875103107232798448480961879504439581709207028323218422842324731614070800665120 * q^86 - 121620902589392915908211788499779291406085352403421659047183388653396698122624054668916792265905130473306827577981007600 * q^87 + 1658417872724710224316961024183068784782302432041532027143322435709213293291937227818245780162216280302401688092674918400 * q^88 + 1432769398908240147793761581541411990818735692935694485497792271884061431173833899064325508735771294071146532917448371300 * q^89 + 4242523397159088010711590897105749776230224908206487271625184482827883037969608572194218039560541845007789077503014537840 * q^90 + 3749197821974963786133178399116719947553345115682756250347057169251628507401139402810087270893048740655608748200953372320 * q^91 + 10615466523880625147148924876938816209748954360893793192595519658046375175603738111472483373680888517064089973142332940800 * q^92 + 44059413854358273427563101106184148636968023455699937482286003916513524569658318932628056672886084689799061193382440659200 * q^93 + 124806315412457573783492651738284236870157234824356474220743480912251201180129375425047875386957953704047914770947864658560 * q^94 + 266934808318153264777188286945199331781893495587515356911479003870672044191214686290176841073288939755251590483509109178000 * q^95 + 718345766812681622973438050365032032481440601133526400723013288803105919886348015012013492036267597486114877912972451512320 * q^96 + 151722902932344259186071782678082932585107678321580677399607057798381742852936340737162000675258065685590074813531733263700 * q^97 + 2158110007625946651882396712873921474356179378876735390584844074836963015629646171787464354973777052880845127577239492637800 * q^98 + 4265507899725315199945861403479494597528311025680927738450324529439136225728412750337207278998994765980992714808031550632040 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−4.07908e18	−1.25088	−0.625442	−	0.780270i	$-0.715081\pi$
$2$	−4.07908e18	−1.25088	−0.625442	+	0.780270i	$0.715081\pi$
$3$	3.50571e29	1.59154	0.795772	−	0.605596i	$-0.207065\pi$
$3$	3.50571e29	1.59154	0.795772	+	0.605596i	$0.207065\pi$
$4$	6.00505e36	0.564712
$5$	−4.74746e42	−0.489560	−0.244780	−	0.969579i	$-0.578716\pi$
$5$	−4.74746e42	−0.489560	−0.244780	+	0.969579i	$0.578716\pi$
$6$	−1.43001e48	−1.99084
$7$	−1.17353e51	−0.124728	−0.0623642	−	0.998053i	$-0.519864\pi$
$7$	−1.17353e51	−0.124728	−0.0623642	+	0.998053i	$0.519864\pi$
$8$	1.88811e55	0.544495
$9$	7.43807e58	1.53301
$10$	1.93653e61	0.612384
$11$	1.35161e64	1.21675	0.608374	−	0.793650i	$-0.291822\pi$
$11$	1.35161e64	1.21675	0.608374	+	0.793650i	$0.291822\pi$
$12$	2.10520e66	0.898765
$13$	−1.52537e68	−0.474090	−0.237045	−	0.971499i	$-0.576179\pi$
$13$	−1.52537e68	−0.474090	−0.237045	+	0.971499i	$0.576179\pi$
$14$	4.78693e69	0.156021
$15$	−1.66432e72	−0.779157
$16$	−1.40874e74	−1.24581
$17$	−5.29817e75	−1.12595	−0.562973	−	0.826475i	$-0.690343\pi$
$17$	−5.29817e75	−1.12595	−0.562973	+	0.826475i	$0.690343\pi$
$18$	−3.03405e77	−1.91762
$19$	6.94083e78	1.57785	0.788923	−	0.614492i	$-0.210639\pi$
$19$	6.94083e78	1.57785	0.788923	+	0.614492i	$0.210639\pi$
$20$	−2.85088e79	−0.276461
$21$	−4.11406e80	−0.198511
$22$	−5.51332e82	−1.52201
$23$	9.79960e83	1.75771	0.878853	−	0.477092i	$-0.158309\pi$
$23$	9.79960e83	1.75771	0.878853	+	0.477092i	$0.158309\pi$
$24$	6.61917e84	0.866587
$25$	−7.15011e85	−0.760331
$26$	6.22212e86	0.593031
$27$	9.06626e87	0.848314
$28$	−7.04712e87	−0.0704357
$29$	−7.09621e89	−0.819501	−0.409751	−	0.912198i	$-0.634384\pi$
$29$	−7.09621e89	−0.819501	−0.409751	+	0.912198i	$0.634384\pi$
$30$	6.78890e90	0.974636
$31$	6.10616e90	0.116687	0.0583437	−	0.998297i	$-0.481418\pi$
$31$	6.10616e90	0.116687	0.0583437	+	0.998297i	$0.481418\pi$
$32$	3.73858e92	1.01387
$33$	4.73835e93	1.93651
$34$	2.16117e94	1.40843
$35$	5.57130e93	0.0610621
$36$	4.46660e95	0.865711
$37$	3.84618e96	1.38237	0.691185	−	0.722678i	$-0.257089\pi$
$37$	3.84618e96	1.38237	0.691185	+	0.722678i	$0.257089\pi$
$38$	−2.83122e97	−1.97370
$39$	−5.34752e97	−0.754534
$40$	−8.96374e97	−0.266563
$41$	−1.40652e99	−0.916089	−0.458044	−	0.888929i	$-0.651450\pi$
$41$	−1.40652e99	−0.916089	−0.458044	+	0.888929i	$0.651450\pi$
$42$	1.67816e99	0.248314
$43$	4.40926e100	1.53481	0.767406	−	0.641161i	$-0.221547\pi$
$43$	4.40926e100	1.53481	0.767406	+	0.641161i	$0.221547\pi$
$44$	8.11648e100	0.687113
$45$	−3.53120e101	−0.750503
$46$	−3.99733e102	−2.19869
$47$	4.08007e102	0.597929	0.298965	−	0.954264i	$-0.403359\pi$
$47$	4.08007e102	0.597929	0.298965	+	0.954264i	$0.403359\pi$
$48$	−4.93864e103	−1.98277
$49$	−8.71464e103	−0.984443
$50$	2.91659e104	0.951086
$51$	−1.85739e105	−1.79199
$52$	−9.15995e104	−0.267724
$53$	−1.87477e106	−1.69817	−0.849087	−	0.528253i	$-0.822847\pi$
$53$	−1.87477e106	−1.69817	−0.849087	+	0.528253i	$0.822847\pi$
$54$	−3.69820e106	−1.06114
$55$	−6.41671e106	−0.595672
$56$	−2.21576e106	−0.0679140
$57$	2.43325e108	2.51121
$58$	2.89460e108	1.02510
$59$	−8.99566e107	−0.111336	−0.0556678	−	0.998449i	$-0.517729\pi$
$59$	−8.99566e107	−0.111336	−0.0556678	+	0.998449i	$0.517729\pi$
$60$	−9.99434e108	−0.440000
$61$	5.11564e109	0.814920	0.407460	−	0.913223i	$-0.366415\pi$
$61$	5.11564e109	0.814920	0.407460	+	0.913223i	$0.366415\pi$
$62$	−2.49075e109	−0.145962
$63$	−8.72881e109	−0.191210
$64$	−2.69659e109	−0.0224257
$65$	7.24166e110	0.232095
$66$	−1.93281e112	−2.42235
$67$	−3.71622e111	−0.184714	−0.0923572	−	0.995726i	$-0.529440\pi$
$67$	−3.71622e111	−0.184714	−0.0923572	+	0.995726i	$0.529440\pi$
$68$	−3.18158e112	−0.635836
$69$	3.43545e113	2.79747
$70$	−2.27258e112	−0.0763817
$71$	2.34973e113	0.330088	0.165044	−	0.986286i	$-0.447223\pi$
$71$	2.34973e113	0.330088	0.165044	+	0.986286i	$0.447223\pi$
$72$	1.40439e114	0.834717
$73$	6.07538e112	0.0154603	0.00773014	−	0.999970i	$-0.497539\pi$
$73$	6.07538e112	0.0154603	0.00773014	+	0.999970i	$0.497539\pi$
$74$	−1.56889e115	−1.72918
$75$	−2.50662e115	−1.21010
$76$	4.16800e115	0.891029
$77$	−1.58616e115	−0.151763
$78$	2.18130e116	0.943836
$79$	−4.96028e116	−0.980483	−0.490241	−	0.871587i	$-0.663091\pi$
$79$	−4.96028e116	−0.980483	−0.490241	+	0.871587i	$0.663091\pi$
$80$	6.68795e116	0.609900
$81$	−4.30531e116	−0.182884
$82$	5.73729e117	1.14592
$83$	1.89829e117	0.179912	0.0899558	−	0.995946i	$-0.471327\pi$
$83$	1.89829e117	0.179912	0.0899558	+	0.995946i	$0.471327\pi$
$84$	−2.47052e117	−0.112102
$85$	2.51529e118	0.551219
$86$	−1.79857e119	−1.91987
$87$	−2.48772e119	−1.30427
$88$	2.55199e119	0.662513
$89$	1.50546e120	1.95067	0.975333	−	0.220739i	$-0.0708468\pi$
$89$	1.50546e120	1.95067	0.975333	+	0.220739i	$0.0708468\pi$
$90$	1.44040e120	0.938792
$91$	1.79008e119	0.0591325
$92$	5.88471e120	0.992599
$93$	2.14064e120	0.185713
$94$	−1.66429e121	−0.747940
$95$	−3.29513e121	−0.772451
$96$	1.31064e122	1.61362
$97$	3.72395e121	0.242405	0.121203	−	0.992628i	$-0.461325\pi$
$97$	3.72395e121	0.242405	0.121203	+	0.992628i	$0.461325\pi$
$98$	3.55477e122	1.23142
$99$	1.00534e123	1.86529
$100$	−4.29368e122	−0.429368
$101$	1.47269e123	0.798634	0.399317	−	0.916813i	$-0.369247\pi$
$101$	1.47269e123	0.798634	0.399317	+	0.916813i	$0.369247\pi$
$102$	7.57642e123	2.24158
$103$	5.43611e123	0.882671	0.441335	−	0.897342i	$-0.354505\pi$
$103$	5.43611e123	0.882671	0.441335	+	0.897342i	$0.354505\pi$
$104$	−2.88008e123	−0.258139
$105$	1.95314e123	0.0971830
$106$	7.64734e124	2.12422
$107$	−6.41183e124	−0.999724	−0.499862	−	0.866105i	$-0.666616\pi$
$107$	−6.41183e124	−0.999724	−0.499862	+	0.866105i	$0.666616\pi$
$108$	5.44433e124	0.479053
$109$	−2.45008e124	−0.122307	−0.0611535	−	0.998128i	$-0.519478\pi$
$109$	−2.45008e124	−0.122307	−0.0611535	+	0.998128i	$0.519478\pi$
$110$	2.61743e125	0.745117
$111$	1.34836e126	2.20010
$112$	1.65320e125	0.155388
$113$	−4.10293e125	−0.223239	−0.111619	−	0.993751i	$-0.535604\pi$
$113$	−4.10293e125	−0.223239	−0.111619	+	0.993751i	$0.535604\pi$
$114$	−9.92542e126	−3.14124
$115$	−4.65232e126	−0.860504
$116$	−4.26131e126	−0.462782
$117$	−1.13458e127	−0.726785
$118$	3.66940e126	0.139268
$119$	6.21758e126	0.140437
$120$	−3.14243e127	−0.424247
$121$	5.92889e127	0.480477
$122$	−2.08671e128	−1.01937
$123$	−4.93084e128	−1.45800
$124$	3.66678e127	0.0658948
$125$	7.85898e128	0.861788
$126$	3.56055e128	0.239182
$127$	1.73379e129	0.716254	0.358127	−	0.933673i	$-0.383415\pi$
$127$	1.73379e129	0.716254	0.358127	+	0.933673i	$0.383415\pi$
$128$	−3.86555e129	−0.985821
$129$	1.54576e130	2.44272
$130$	−2.95393e129	−0.290325
$131$	1.84640e130	1.13277	0.566383	−	0.824142i	$-0.308342\pi$
$131$	1.84640e130	1.13277	0.566383	+	0.824142i	$0.308342\pi$
$132$	2.84540e130	1.09357
$133$	−8.14528e129	−0.196802
$134$	1.51587e130	0.231056
$135$	−4.30417e130	−0.415301
$136$	−1.00035e131	−0.613071
$137$	1.02034e131	0.398503	0.199251	−	0.979948i	$-0.436149\pi$
$137$	1.02034e131	0.398503	0.199251	+	0.979948i	$0.436149\pi$
$138$	−1.40135e132	−3.49931
$139$	9.32170e131	1.49309	0.746543	−	0.665337i	$-0.231712\pi$
$139$	9.32170e131	1.49309	0.746543	+	0.665337i	$0.231712\pi$
$140$	3.34559e130	0.0344825
$141$	1.43035e132	0.951631
$142$	−9.58473e131	−0.412902
$143$	−2.06171e132	−0.576848
$144$	−1.04783e133	−1.90985
$145$	3.36890e132	0.401195
$146$	−2.47819e131	−0.0193390
$147$	−3.05510e133	−1.56678
$148$	2.30965e133	0.780641
$149$	8.07218e133	1.80317	0.901583	−	0.432607i	$-0.142406\pi$
$149$	8.07218e133	1.80317	0.901583	+	0.432607i	$0.142406\pi$
$150$	1.02247e134	1.51370
$151$	1.05118e134	1.03417	0.517086	−	0.855933i	$-0.327017\pi$
$151$	1.05118e134	1.03417	0.517086	+	0.855933i	$0.327017\pi$
$152$	1.31051e134	0.859129
$153$	−3.94082e134	−1.72609
$154$	6.47006e133	0.189838
$155$	−2.89887e133	−0.0571255
$156$	−3.21121e134	−0.426095
$157$	6.66187e134	0.596716	0.298358	−	0.954454i	$-0.403561\pi$
$157$	6.66187e134	0.596716	0.298358	+	0.954454i	$0.403561\pi$
$158$	2.02334e135	1.22647
$159$	−6.57240e135	−2.70272
$160$	−1.77488e135	−0.496352
$161$	−1.15001e135	−0.219236
$162$	1.75617e135	0.228767
$163$	6.89825e135	0.615462	0.307731	−	0.951473i	$-0.400430\pi$
$163$	6.89825e135	0.615462	0.307731	+	0.951473i	$0.400430\pi$
$164$	−8.44620e135	−0.517327
$165$	−2.24951e136	−0.948038
$166$	−7.74326e135	−0.225049
$167$	5.97693e136	1.20065	0.600323	−	0.799757i	$-0.295039\pi$
$167$	5.97693e136	1.20065	0.600323	+	0.799757i	$0.295039\pi$
$168$	−7.76781e135	−0.108088
$169$	−8.02542e136	−0.775239
$170$	−1.02601e137	−0.689511
$171$	5.16263e137	2.41886
$172$	2.64778e137	0.866728
$173$	1.20289e137	0.275671	0.137835	−	0.990455i	$-0.455985\pi$
$173$	1.20289e137	0.275671	0.137835	+	0.990455i	$0.455985\pi$
$174$	1.01476e138	1.63149
$175$	8.39089e136	0.0948348
$176$	−1.90407e138	−1.51584
$177$	−3.15362e137	−0.177196
$178$	−6.14088e138	−2.44006
$179$	3.19140e138	0.898503	0.449251	−	0.893405i	$-0.351691\pi$
$179$	3.19140e138	0.898503	0.449251	+	0.893405i	$0.351691\pi$
$180$	−2.12050e138	−0.423818
$181$	−8.00108e138	−1.13741	−0.568704	−	0.822542i	$-0.692555\pi$
$181$	−8.00108e138	−1.13741	−0.568704	+	0.822542i	$0.692555\pi$
$182$	−7.30186e137	−0.0739679
$183$	1.79339e139	1.29698
$184$	1.85027e139	0.957062
$185$	−1.82596e139	−0.676753
$186$	−8.73184e138	−0.232306
$187$	−7.16106e139	−1.36999
$188$	2.45011e139	0.337658
$189$	−1.06395e139	−0.105809
$190$	1.34411e140	0.966247
$191$	2.82015e140	1.46798	0.733991	−	0.679159i	$-0.237655\pi$
$191$	2.82015e140	1.46798	0.733991	+	0.679159i	$0.237655\pi$
$192$	−9.45346e138	−0.0356915
$193$	2.93159e140	0.804134	0.402067	−	0.915610i	$-0.368292\pi$
$193$	2.93159e140	0.804134	0.402067	+	0.915610i	$0.368292\pi$
$194$	−1.51903e140	−0.303221
$195$	2.53872e140	0.369390
$196$	−5.23319e140	−0.555927
$197$	1.24210e141	0.964902	0.482451	−	0.875923i	$-0.339747\pi$
$197$	1.24210e141	0.964902	0.482451	+	0.875923i	$0.339747\pi$
$198$	−4.10084e141	−2.33326
$199$	1.31850e141	0.550321	0.275160	−	0.961398i	$-0.411269\pi$
$199$	1.31850e141	0.550321	0.275160	+	0.961398i	$0.411269\pi$
$200$	−1.35002e141	−0.413996
$201$	−1.30280e141	−0.293981
$202$	−6.00723e141	−0.999000
$203$	8.32763e140	0.102215
$204$	−1.11537e142	−1.01196
$205$	6.67738e141	0.448481
$206$	−2.21743e142	−1.10412
$207$	7.28901e142	2.69459
$208$	2.14886e142	0.590627
$209$	9.38128e142	1.91984
$210$	−7.96699e141	−0.121565
$211$	−1.64303e143	−1.87186	−0.935931	−	0.352184i	$-0.885439\pi$
$211$	−1.64303e143	−1.87186	−0.935931	+	0.352184i	$0.885439\pi$
$212$	−1.12581e143	−0.958980
$213$	8.23747e142	0.525349
$214$	2.61544e143	1.25054
$215$	−2.09328e143	−0.751384
$216$	1.71181e143	0.461902
$217$	−7.16577e141	−0.0145542
$218$	9.99409e142	0.152992
$219$	2.12985e142	0.0246057
$220$	−3.85327e143	−0.336383
$221$	8.08170e143	0.533799
$222$	−5.50007e144	−2.75207
$223$	−3.89007e143	−0.147641	−0.0738207	−	0.997272i	$-0.523519\pi$
$223$	−3.89007e143	−0.147641	−0.0738207	+	0.997272i	$0.523519\pi$
$224$	−4.38735e143	−0.126459
$225$	−5.31830e144	−1.16560
$226$	1.67362e144	0.279246
$227$	1.47914e145	1.88113	0.940565	−	0.339612i	$-0.110296\pi$
$227$	1.47914e145	1.88113	0.940565	+	0.339612i	$0.110296\pi$
$228$	1.46118e145	1.41811
$229$	1.91406e143	0.0141930	0.00709648	−	0.999975i	$-0.497741\pi$
$229$	1.91406e143	0.0141930	0.00709648	+	0.999975i	$0.497741\pi$
$230$	1.89772e145	1.07639
$231$	−5.56060e144	−0.241538
$232$	−1.33984e145	−0.446214
$233$	−1.17711e145	−0.300904	−0.150452	−	0.988617i	$-0.548073\pi$
$233$	−1.17711e145	−0.300904	−0.150452	+	0.988617i	$0.548073\pi$
$234$	4.62806e145	0.909125
$235$	−1.93700e145	−0.292722
$236$	−5.40194e144	−0.0628726
$237$	−1.73893e146	−1.56048
$238$	−2.53620e145	−0.175671
$239$	2.92835e145	0.156730	0.0783649	−	0.996925i	$-0.475030\pi$
$239$	2.92835e145	0.156730	0.0783649	+	0.996925i	$0.475030\pi$
$240$	2.34460e146	0.970683
$241$	−3.03376e146	−0.972599	−0.486299	−	0.873792i	$-0.661654\pi$
$241$	−3.03376e146	−0.972599	−0.486299	+	0.873792i	$0.661654\pi$
$242$	−2.41844e146	−0.601022
$243$	−5.90820e146	−1.13938
$244$	3.07197e146	0.460195
$245$	4.13724e146	0.481944
$246$	2.01133e147	1.82378
$247$	−1.05874e147	−0.748040
$248$	1.15291e146	0.0635356
$249$	6.65484e146	0.286337
$250$	−3.20574e147	−1.07800
$251$	1.10234e147	0.289990	0.144995	−	0.989432i	$-0.453683\pi$
$251$	1.10234e147	0.289990	0.144995	+	0.989432i	$0.453683\pi$
$252$	−5.24170e146	−0.107979
$253$	1.32452e148	2.13869
$254$	−7.07226e147	−0.895951
$255$	8.81787e147	0.877289
$256$	1.60546e148	1.25557
$257$	8.55597e147	0.526480	0.263240	−	0.964730i	$-0.415209\pi$
$257$	8.55597e147	0.526480	0.263240	+	0.964730i	$0.415209\pi$
$258$	−6.30526e148	−3.05556
$259$	−4.51362e147	−0.172421
$260$	4.34865e147	0.131067
$261$	−5.27821e148	−1.25631
$262$	−7.53160e148	−1.41696
$263$	−6.07178e148	−0.903728	−0.451864	−	0.892087i	$-0.649241\pi$
$263$	−6.07178e148	−0.903728	−0.451864	+	0.892087i	$0.649241\pi$
$264$	8.94653e148	1.05442
$265$	8.90041e148	0.831359
$266$	3.32252e148	0.246177
$267$	5.27769e149	3.10457
$268$	−2.23161e148	−0.104311
$269$	−4.70013e149	−1.74721	−0.873604	−	0.486637i	$-0.838223\pi$
$269$	−4.70013e149	−1.74721	−0.873604	+	0.486637i	$0.838223\pi$
$270$	1.75571e149	0.519493
$271$	−3.84447e149	−0.906202	−0.453101	−	0.891459i	$-0.649682\pi$
$271$	−3.84447e149	−0.906202	−0.453101	+	0.891459i	$0.649682\pi$
$272$	7.46376e149	1.40272
$273$	6.27549e148	0.0941119
$274$	−4.16206e149	−0.498481
$275$	−9.66416e149	−0.925131
$276$	2.06301e150	1.57976
$277$	5.65705e149	0.346804	0.173402	−	0.984851i	$-0.444524\pi$
$277$	5.65705e149	0.346804	0.173402	+	0.984851i	$0.444524\pi$
$278$	−3.80239e150	−1.86768
$279$	4.54180e149	0.178883
$280$	1.05192e149	0.0332480
$281$	5.67187e150	1.43975	0.719875	−	0.694103i	$-0.244199\pi$
$281$	5.67187e150	1.43975	0.719875	+	0.694103i	$0.244199\pi$
$282$	−5.83453e150	−1.19038
$283$	−9.33818e150	−1.53249	−0.766243	−	0.642551i	$-0.777876\pi$
$283$	−9.33818e150	−1.53249	−0.766243	+	0.642551i	$0.777876\pi$
$284$	1.41102e150	0.186405
$285$	−1.15518e151	−1.22939
$286$	8.40988e150	0.721570
$287$	1.65059e150	0.114262
$288$	2.78078e151	1.55428
$289$	5.92862e150	0.267754
$290$	−1.37420e151	−0.501849
$291$	1.30551e151	0.385799
$292$	3.64829e149	0.00873061
$293$	−3.24520e151	−0.629337	−0.314668	−	0.949202i	$-0.601893\pi$
$293$	−3.24520e151	−0.629337	−0.314668	+	0.949202i	$0.601893\pi$
$294$	1.24620e152	1.95987
$295$	4.27065e150	0.0545055
$296$	7.26203e151	0.752693
$297$	1.22540e152	1.03218
$298$	−3.29271e152	−2.25555
$299$	−1.49481e152	−0.833310
$300$	−1.50524e152	−0.683358
$301$	−5.17440e151	−0.191435
$302$	−4.28783e152	−1.29363
$303$	5.16284e152	1.27106
$304$	−9.77784e152	−1.96570
$305$	−2.42863e152	−0.398953
$306$	1.60749e153	2.15914
$307$	7.09431e152	0.779651	0.389826	−	0.920889i	$-0.372535\pi$
$307$	7.09431e152	0.779651	0.389826	+	0.920889i	$0.372535\pi$
$308$	−9.52495e151	−0.0857025
$309$	1.90574e153	1.40481
$310$	1.18247e152	0.0714574
$311$	−1.32805e153	−0.658343	−0.329171	−	0.944270i	$-0.606769\pi$
$311$	−1.32805e153	−0.658343	−0.329171	+	0.944270i	$0.606769\pi$
$312$	−1.00967e153	−0.410840
$313$	−1.77726e152	−0.0593984	−0.0296992	−	0.999559i	$-0.509455\pi$
$313$	−1.77726e152	−0.0593984	−0.0296992	+	0.999559i	$0.509455\pi$
$314$	−2.71743e153	−0.746423
$315$	4.14397e152	0.0936090
$316$	−2.97867e153	−0.553691
$317$	4.90600e153	0.750901	0.375450	−	0.926842i	$-0.377488\pi$
$317$	4.90600e153	0.750901	0.375450	+	0.926842i	$0.377488\pi$
$318$	2.68093e154	3.38079
$319$	−9.59130e153	−0.997127
$320$	1.28020e152	0.0109787
$321$	−2.24780e154	−1.59110
$322$	4.69100e153	0.274239
$323$	−3.67737e154	−1.77657
$324$	−2.58536e153	−0.103277
$325$	1.09066e154	0.360465
$326$	−2.81385e154	−0.769872
$327$	−8.58928e153	−0.194657
$328$	−2.65566e154	−0.498805
$329$	−4.78810e153	−0.0745788
$330$	9.17594e154	1.18589
$331$	8.61599e154	0.924450	0.462225	−	0.886763i	$-0.347051\pi$
$331$	8.61599e154	0.924450	0.462225	+	0.886763i	$0.347051\pi$
$332$	1.13993e154	0.101598
$333$	2.86082e155	2.11919
$334$	−2.43804e155	−1.50187
$335$	1.76426e154	0.0904289
$336$	5.79565e154	0.247307
$337$	−3.61617e154	−0.128532	−0.0642659	−	0.997933i	$-0.520471\pi$
$337$	−3.61617e154	−0.128532	−0.0642659	+	0.997933i	$0.520471\pi$
$338$	3.27363e155	0.969735
$339$	−1.43837e155	−0.355294
$340$	1.51044e155	0.311280
$341$	8.25313e154	0.141979
$342$	−2.10588e156	−3.02571
$343$	2.06154e155	0.247516
$344$	8.32517e155	0.835697
$345$	−1.63097e156	−1.36953
$346$	−4.90669e155	−0.344832
$347$	1.65487e156	0.973872	0.486936	−	0.873438i	$-0.338115\pi$
$347$	1.65487e156	0.973872	0.486936	+	0.873438i	$0.338115\pi$
$348$	−1.49389e156	−0.736539
$349$	2.97937e156	1.23129	0.615645	−	0.788023i	$-0.288895\pi$
$349$	2.97937e156	1.23129	0.615645	+	0.788023i	$0.288895\pi$
$350$	−3.42271e155	−0.118627
$351$	−1.38294e156	−0.402177
$352$	5.05310e156	1.23363
$353$	−2.17047e156	−0.445051	−0.222526	−	0.974927i	$-0.571430\pi$
$353$	−2.17047e156	−0.445051	−0.222526	+	0.974927i	$0.571430\pi$
$354$	1.28638e156	0.221651
$355$	−1.11553e156	−0.161598
$356$	9.04035e156	1.10157
$357$	2.17970e156	0.223512
$358$	−1.30180e157	−1.12392
$359$	−1.54651e157	−1.12472	−0.562358	−	0.826894i	$-0.690106\pi$
$359$	−1.54651e157	−1.12472	−0.562358	+	0.826894i	$0.690106\pi$
$360$	−6.66729e156	−0.408645
$361$	2.88245e157	1.48960
$362$	3.26370e157	1.42277
$363$	2.07850e157	0.764701
$364$	1.07495e156	0.0333928
$365$	−2.88426e155	−0.00756874
$366$	−7.31539e157	−1.62237
$367$	−1.39979e157	−0.262483	−0.131241	−	0.991350i	$-0.541896\pi$
$367$	−1.39979e157	−0.262483	−0.131241	+	0.991350i	$0.541896\pi$
$368$	−1.38051e158	−2.18977
$369$	−1.04618e158	−1.40438
$370$	7.44824e157	0.846540
$371$	2.20010e157	0.211811
$372$	1.28547e157	0.104874
$373$	−1.02366e158	−0.708046	−0.354023	−	0.935237i	$-0.615187\pi$
$373$	−1.02366e158	−0.708046	−0.354023	+	0.935237i	$0.615187\pi$
$374$	2.92105e158	1.71370
$375$	2.75513e158	1.37157
$376$	7.70363e157	0.325569
$377$	1.08244e158	0.388517
$378$	4.33995e157	0.132355
$379$	1.79026e158	0.464092	0.232046	−	0.972705i	$-0.425458\pi$
$379$	1.79026e158	0.464092	0.232046	+	0.972705i	$0.425458\pi$
$380$	−1.97874e158	−0.436213
$381$	6.07816e158	1.13995
$382$	−1.15036e159	−1.83628
$383$	3.15390e158	0.428670	0.214335	−	0.976760i	$-0.431242\pi$
$383$	3.15390e158	0.428670	0.214335	+	0.976760i	$0.431242\pi$
$384$	−1.35515e159	−1.56898
$385$	7.53022e157	0.0742972
$386$	−1.19582e159	−1.00588
$387$	3.27964e159	2.35289
$388$	2.23625e158	0.136889
$389$	−6.69930e158	−0.350049	−0.175025	−	0.984564i	$-0.556000\pi$
$389$	−6.69930e158	−0.350049	−0.175025	+	0.984564i	$0.556000\pi$
$390$	−1.03556e159	−0.462065
$391$	−5.19200e159	−1.97908
$392$	−1.64542e159	−0.536024
$393$	6.47293e159	1.80285
$394$	−5.06662e159	−1.20698
$395$	2.35487e159	0.480005
$396$	6.03709e159	1.05335
$397$	5.52673e159	0.825757	0.412879	−	0.910786i	$-0.364523\pi$
$397$	5.52673e159	0.825757	0.412879	+	0.910786i	$0.364523\pi$
$398$	−5.37827e159	−0.688388
$399$	−2.85550e159	−0.313220
$400$	1.00727e160	0.947229
$401$	−9.28251e159	−0.748663	−0.374332	−	0.927295i	$-0.622128\pi$
$401$	−9.28251e159	−0.748663	−0.374332	+	0.927295i	$0.622128\pi$
$402$	5.31421e159	0.367737
$403$	−9.31418e158	−0.0553202
$404$	8.84360e159	0.450999
$405$	2.04393e159	0.0895328
$406$	−3.39691e159	−0.127859
$407$	5.19854e160	1.68200
$408$	−3.50695e160	−0.975730
$409$	−2.58815e160	−0.619451	−0.309725	−	0.950826i	$-0.600237\pi$
$409$	−2.58815e160	−0.619451	−0.309725	+	0.950826i	$0.600237\pi$
$410$	−2.72376e160	−0.560998
$411$	3.57703e160	0.634235
$412$	3.26441e160	0.498455
$413$	1.05567e159	0.0138867
$414$	−2.97324e161	−3.37062
$415$	−9.01204e159	−0.0880776
$416$	−5.70274e160	−0.480667
$417$	3.26792e161	2.37631
$418$	−3.82670e161	−2.40150
$419$	5.73645e159	0.0310800	0.0155400	−	0.999879i	$-0.495053\pi$
$419$	5.73645e159	0.0310800	0.0155400	+	0.999879i	$0.495053\pi$
$420$	1.17287e160	0.0548805
$421$	4.49845e161	1.81850	0.909252	−	0.416245i	$-0.136654\pi$
$421$	4.49845e161	1.81850	0.909252	+	0.416245i	$0.136654\pi$
$422$	6.70203e161	2.34148
$423$	3.03479e161	0.916633
$424$	−3.53978e161	−0.924647
$425$	3.78826e161	0.856091
$426$	−3.36013e161	−0.657151
$427$	−6.00337e160	−0.101644
$428$	−3.85034e161	−0.564556
$429$	−7.22776e161	−0.918079
$430$	8.53865e161	0.939894
$431$	−4.19608e161	−0.400398	−0.200199	−	0.979755i	$-0.564159\pi$
$431$	−4.19608e161	−0.400398	−0.200199	+	0.979755i	$0.564159\pi$
$432$	−1.27720e162	−1.05684
$433$	−2.01659e162	−1.44748	−0.723740	−	0.690073i	$-0.757578\pi$
$433$	−2.01659e162	−1.44748	−0.723740	+	0.690073i	$0.757578\pi$
$434$	2.92297e160	0.0182057
$435$	1.18104e162	0.638520
$436$	−1.47129e161	−0.0690683
$437$	6.80173e162	2.77339
$438$	−8.68782e160	−0.0307789
$439$	−2.87850e162	−0.886336	−0.443168	−	0.896438i	$-0.646146\pi$
$439$	−2.87850e162	−0.886336	−0.443168	+	0.896438i	$0.646146\pi$
$440$	−1.21155e162	−0.324340
$441$	−6.48201e162	−1.50916
$442$	−3.29659e162	−0.667721
$443$	−1.22328e162	−0.215624	−0.107812	−	0.994171i	$-0.534384\pi$
$443$	−1.22328e162	−0.215624	−0.107812	+	0.994171i	$0.534384\pi$
$444$	8.09697e162	1.24242
$445$	−7.14710e162	−0.954969
$446$	1.58679e162	0.184682
$447$	2.82987e163	2.86982
$448$	3.16453e160	0.00279713
$449$	−8.69710e162	−0.670231	−0.335116	−	0.942177i	$-0.608775\pi$
$449$	−8.69710e162	−0.670231	−0.335116	+	0.942177i	$0.608775\pi$
$450$	2.16938e163	1.45803
$451$	−1.90106e163	−1.11465
$452$	−2.46383e162	−0.126066
$453$	3.68512e163	1.64593
$454$	−6.03353e163	−2.35308
$455$	−8.49832e161	−0.0289489
$456$	4.59425e163	1.36734
$457$	−2.28848e163	−0.595251	−0.297626	−	0.954683i	$-0.596195\pi$
$457$	−2.28848e163	−0.595251	−0.297626	+	0.954683i	$0.596195\pi$
$458$	−7.80759e161	−0.0177537
$459$	−4.80346e163	−0.955155
$460$	−2.79374e163	−0.485937
$461$	−2.22833e163	−0.339134	−0.169567	−	0.985519i	$-0.554237\pi$
$461$	−2.22833e163	−0.339134	−0.169567	+	0.985519i	$0.554237\pi$
$462$	2.26821e163	0.302136
$463$	−1.61260e164	−1.88060	−0.940300	−	0.340346i	$-0.889456\pi$
$463$	−1.61260e164	−1.88060	−0.940300	+	0.340346i	$0.889456\pi$
$464$	9.99673e163	1.02094
$465$	−1.01626e163	−0.0909178
$466$	4.80153e163	0.376397
$467$	8.69938e163	0.597724	0.298862	−	0.954296i	$-0.403393\pi$
$467$	8.69938e163	0.597724	0.298862	+	0.954296i	$0.403393\pi$
$468$	−6.81324e163	−0.410425
$469$	4.36110e162	0.0230391
$470$	7.90117e163	0.366162
$471$	2.33546e164	0.949700
$472$	−1.69848e163	−0.0606216
$473$	5.95959e164	1.86748
$474$	7.09323e164	1.95198
$475$	−4.96277e164	−1.19968
$476$	3.73369e163	0.0793068
$477$	−1.39447e165	−2.60332
$478$	−1.19450e164	−0.196051
$479$	−2.92128e164	−0.421638	−0.210819	−	0.977525i	$-0.567613\pi$
$479$	−2.92128e164	−0.421638	−0.210819	+	0.977525i	$0.567613\pi$
$480$	−6.22221e164	−0.789966
$481$	−5.86687e164	−0.655367
$482$	1.23750e165	1.21661
$483$	−4.03162e164	−0.348924
$484$	3.56033e164	0.271332
$485$	−1.76793e164	−0.118672
$486$	2.41000e165	1.42524
$487$	−2.88165e165	−1.50180	−0.750898	−	0.660419i	$-0.770379\pi$
$487$	−2.88165e165	−1.50180	−0.750898	+	0.660419i	$0.770379\pi$
$488$	9.65890e164	0.443720
$489$	2.41833e165	0.979535
$490$	−1.68761e165	−0.602857
$491$	−2.35310e165	−0.741529	−0.370764	−	0.928727i	$-0.620904\pi$
$491$	−2.35310e165	−0.741529	−0.370764	+	0.928727i	$0.620904\pi$
$492$	−2.96099e165	−0.823348
$493$	3.75970e165	0.922714
$494$	4.31867e165	0.935712
$495$	−4.77279e165	−0.913173
$496$	−8.60200e164	−0.145371
$497$	−2.75748e164	−0.0411713
$498$	−2.71456e165	−0.358175
$499$	1.13506e166	1.32384	0.661918	−	0.749576i	$-0.269743\pi$
$499$	1.13506e166	1.32384	0.661918	+	0.749576i	$0.269743\pi$
$500$	4.71936e165	0.486662
$501$	2.09534e166	1.91088
$502$	−4.49654e165	−0.362743
$503$	1.16413e166	0.830942	0.415471	−	0.909606i	$-0.363617\pi$
$503$	1.16413e166	0.830942	0.415471	+	0.909606i	$0.363617\pi$
$504$	−1.64810e165	−0.104113
$505$	−6.99156e165	−0.390980
$506$	−5.40283e166	−2.67525
$507$	−2.81348e166	−1.23383
$508$	1.04115e166	0.404478
$509$	8.96561e165	0.308629	0.154314	−	0.988022i	$-0.450683\pi$
$509$	8.96561e165	0.308629	0.154314	+	0.988022i	$0.450683\pi$
$510$	−3.59688e166	−1.09739
$511$	−7.12965e163	−0.00192834
$512$	−2.43825e166	−0.584757
$513$	6.29273e166	1.33851
$514$	−3.49005e166	−0.658566
$515$	−2.58077e166	−0.432121
$516$	9.28235e166	1.37944
$517$	5.51466e166	0.727529
$518$	1.84114e166	0.215679
$519$	4.21699e166	0.438742
$520$	1.36731e166	0.126375
$521$	−1.01757e167	−0.835691	−0.417846	−	0.908518i	$-0.637215\pi$
$521$	−1.01757e167	−0.835691	−0.417846	+	0.908518i	$0.637215\pi$
$522$	2.15302e167	1.57149
$523$	−2.11542e167	−1.37260	−0.686299	−	0.727320i	$-0.740766\pi$
$523$	−2.11542e167	−1.37260	−0.686299	+	0.727320i	$0.740766\pi$
$524$	1.10877e167	0.639687
$525$	2.94160e166	0.150934
$526$	2.47673e167	1.13046
$527$	−3.23515e166	−0.131384
$528$	−6.67511e167	−2.41253
$529$	6.49491e167	2.08953
$530$	−3.63054e167	−1.03993
$531$	−6.69103e166	−0.170679
$532$	−4.89128e166	−0.111137
$533$	2.14546e167	0.434308
$534$	−2.15281e168	−3.88346
$535$	3.04399e167	0.489425
$536$	−7.01664e166	−0.100576
$537$	1.11881e168	1.43001
$538$	1.91722e168	2.18556
$539$	−1.17788e168	−1.19782
$540$	−2.58468e167	−0.234526
$541$	1.72737e168	1.39879	0.699396	−	0.714734i	$-0.253452\pi$
$541$	1.72737e168	1.39879	0.699396	+	0.714734i	$0.253452\pi$
$542$	1.56819e168	1.13355
$543$	−2.80495e168	−1.81024
$544$	−1.98077e168	−1.14157
$545$	1.16317e167	0.0598767
$546$	−2.55982e167	−0.117723
$547$	−2.54175e167	−0.104451	−0.0522254	−	0.998635i	$-0.516631\pi$
$547$	−2.54175e167	−0.104451	−0.0522254	+	0.998635i	$0.516631\pi$
$548$	6.12721e167	0.225040
$549$	3.80505e168	1.24928
$550$	3.94209e168	1.15723
$551$	−4.92536e168	−1.29305
$552$	6.48652e168	1.52321
$553$	5.82104e167	0.122294
$554$	−2.30755e168	−0.433812
$555$	−6.40129e168	−1.07708
$556$	5.59773e168	0.843164
$557$	7.25186e168	0.978036	0.489018	−	0.872274i	$-0.337355\pi$
$557$	7.25186e168	0.978036	0.489018	+	0.872274i	$0.337355\pi$
$558$	−1.85264e168	−0.223762
$559$	−6.72577e168	−0.727639
$560$	−7.84853e167	−0.0760719
$561$	−2.51046e169	−2.18040
$562$	−2.31360e169	−1.80096
$563$	−1.46906e169	−1.02512	−0.512558	−	0.858653i	$-0.671302\pi$
$563$	−1.46906e169	−1.02512	−0.512558	+	0.858653i	$0.671302\pi$
$564$	8.58936e168	0.537398
$565$	1.94785e168	0.109289
$566$	3.80912e169	1.91696
$567$	5.05242e167	0.0228109
$568$	4.43655e168	0.179731
$569$	3.18292e169	1.15723	0.578616	−	0.815600i	$-0.303593\pi$
$569$	3.18292e169	1.15723	0.578616	+	0.815600i	$0.303593\pi$
$570$	4.71206e169	1.53783
$571$	−3.05271e169	−0.894469	−0.447235	−	0.894417i	$-0.647591\pi$
$571$	−3.05271e169	−0.894469	−0.447235	+	0.894417i	$0.647591\pi$
$572$	−1.23807e169	−0.325753
$573$	9.88664e169	2.33636
$574$	−6.73289e168	−0.142929
$575$	−7.00682e169	−1.33644
$576$	−2.00574e168	−0.0343789
$577$	−7.51389e169	−1.15758	−0.578792	−	0.815475i	$-0.696476\pi$
$577$	−7.51389e169	−1.15758	−0.578792	+	0.815475i	$0.696476\pi$
$578$	−2.41833e169	−0.334930
$579$	1.02773e170	1.27981
$580$	2.02304e169	0.226560
$581$	−2.22770e168	−0.0224401
$582$	−5.32527e169	−0.482590
$583$	−2.53396e170	−2.06625
$584$	1.14710e168	0.00841804
$585$	5.38640e169	0.355805
$586$	1.32374e170	0.787228
$587$	7.64060e169	0.409152	0.204576	−	0.978851i	$-0.434419\pi$
$587$	7.64060e169	0.409152	0.204576	+	0.978851i	$0.434419\pi$
$588$	−1.83460e170	−0.884782
$589$	4.23818e169	0.184115
$590$	−1.74203e169	−0.0681801
$591$	4.35444e170	1.53568
$592$	−5.41828e170	−1.72217
$593$	−3.88020e169	−0.111171	−0.0555853	−	0.998454i	$-0.517702\pi$
$593$	−3.88020e169	−0.111171	−0.0555853	+	0.998454i	$0.517702\pi$
$594$	−4.99852e170	−1.29114
$595$	−2.95177e169	−0.0687526
$596$	4.84739e170	1.01827
$597$	4.62228e170	0.875860
$598$	6.09743e170	1.04238
$599$	8.22113e170	1.26818	0.634091	−	0.773258i	$-0.281374\pi$
$599$	8.22113e170	1.26818	0.634091	+	0.773258i	$0.281374\pi$
$600$	−4.73278e170	−0.658893
$601$	−5.49414e170	−0.690431	−0.345215	−	0.938524i	$-0.612194\pi$
$601$	−5.49414e170	−0.690431	−0.345215	+	0.938524i	$0.612194\pi$
$602$	2.11068e170	0.239463
$603$	−2.76415e170	−0.283170
$604$	6.31236e170	0.584010
$605$	−2.81472e170	−0.235223
$606$	−2.10596e171	−1.58995
$607$	2.34356e170	0.159871	0.0799357	−	0.996800i	$-0.474528\pi$
$607$	2.34356e170	0.159871	0.0799357	+	0.996800i	$0.474528\pi$
$608$	2.59489e171	1.59974
$609$	2.91942e170	0.162680
$610$	9.90657e170	0.499044
$611$	−6.22364e170	−0.283472
$612$	−2.36648e171	−0.974744
$613$	−1.14374e171	−0.426096	−0.213048	−	0.977042i	$-0.568339\pi$
$613$	−1.14374e171	−0.426096	−0.213048	+	0.977042i	$0.568339\pi$
$614$	−2.89383e171	−0.975254
$615$	2.34090e171	0.713777
$616$	−2.99484e170	−0.0826342
$617$	−2.95411e171	−0.737716	−0.368858	−	0.929486i	$-0.620251\pi$
$617$	−2.95411e171	−0.737716	−0.368858	+	0.929486i	$0.620251\pi$
$618$	−7.77367e171	−1.75725
$619$	−2.24499e171	−0.459450	−0.229725	−	0.973256i	$-0.573783\pi$
$619$	−2.24499e171	−0.459450	−0.229725	+	0.973256i	$0.573783\pi$
$620$	−1.74079e170	−0.0322595
$621$	8.88457e171	1.49109
$622$	5.41724e171	0.823511
$623$	−1.76670e171	−0.243304
$624$	7.53328e171	0.940008
$625$	2.99291e171	0.338433
$626$	7.24959e170	0.0743005
$627$	3.28880e172	3.05551
$628$	4.00049e171	0.336973
$629$	−2.03778e172	−1.55647
$630$	−1.69036e171	−0.117094
$631$	2.95885e172	1.85916	0.929582	−	0.368615i	$-0.120168\pi$
$631$	2.95885e172	1.85916	0.929582	+	0.368615i	$0.120168\pi$
$632$	−9.36556e171	−0.533867
$633$	−5.75997e172	−2.97915
$634$	−2.00119e172	−0.939290
$635$	−8.23110e171	−0.350650
$636$	−3.94676e172	−1.52626
$637$	1.32931e172	0.466714
$638$	3.91237e172	1.24729
$639$	1.74774e172	0.506029
$640$	1.83515e172	0.482619
$641$	−3.94545e172	−0.942601	−0.471300	−	0.881973i	$-0.656215\pi$
$641$	−3.94545e172	−0.942601	−0.471300	+	0.881973i	$0.656215\pi$
$642$	9.16896e172	1.99029
$643$	−8.77105e172	−1.73012	−0.865061	−	0.501666i	$-0.832721\pi$
$643$	−8.77105e172	−1.73012	−0.865061	+	0.501666i	$0.832721\pi$
$644$	−6.90590e171	−0.123805
$645$	−7.33843e172	−1.19586
$646$	1.50003e173	2.22228
$647$	−2.40419e172	−0.323859	−0.161929	−	0.986802i	$-0.551772\pi$
$647$	−2.40419e172	−0.323859	−0.161929	+	0.986802i	$0.551772\pi$
$648$	−8.12891e171	−0.0995794
$649$	−1.21586e172	−0.135467
$650$	−4.44889e172	−0.450900
$651$	−2.51211e171	−0.0231637
$652$	4.14243e172	0.347559
$653$	−6.92929e171	−0.0529088	−0.0264544	−	0.999650i	$-0.508422\pi$
$653$	−6.92929e171	−0.0529088	−0.0264544	+	0.999650i	$0.508422\pi$
$654$	3.50364e172	0.243494
$655$	−8.76570e172	−0.554558
$656$	1.98142e173	1.14127
$657$	4.51891e171	0.0237008
$658$	1.95310e172	0.0932894
$659$	3.27918e173	1.42663	0.713316	−	0.700842i	$-0.247192\pi$
$659$	3.27918e173	1.42663	0.713316	+	0.700842i	$0.247192\pi$
$660$	−1.35084e173	−0.535369
$661$	2.02904e173	0.732658	0.366329	−	0.930485i	$-0.380615\pi$
$661$	2.02904e173	0.732658	0.366329	+	0.930485i	$0.380615\pi$
$662$	−3.51453e173	−1.15638
$663$	2.83321e173	0.849565
$664$	3.58418e172	0.0979609
$665$	3.86694e172	0.0963466
$666$	−1.16695e174	−2.65086
$667$	−6.95400e173	−1.44044
$668$	3.58918e173	0.678020
$669$	−1.36374e173	−0.234978
$670$	−7.19656e172	−0.113116
$671$	6.91434e173	0.991553
$672$	−1.53808e173	−0.201265
$673$	3.57687e173	0.427146	0.213573	−	0.976927i	$-0.431490\pi$
$673$	3.57687e173	0.427146	0.213573	+	0.976927i	$0.431490\pi$
$674$	1.47507e173	0.160778
$675$	−6.48248e173	−0.644999
$676$	−4.81931e173	−0.437787
$677$	−7.06172e173	−0.585743	−0.292872	−	0.956152i	$-0.594611\pi$
$677$	−7.06172e173	−0.585743	−0.292872	+	0.956152i	$0.594611\pi$
$678$	5.86721e173	0.444432
$679$	−4.37018e172	−0.0302349
$680$	4.74915e173	0.300136
$681$	5.18543e174	2.99390
$682$	−3.36652e173	−0.177600
$683$	−1.03101e174	−0.497040	−0.248520	−	0.968627i	$-0.579944\pi$
$683$	−1.03101e174	−0.497040	−0.248520	+	0.968627i	$0.579944\pi$
$684$	3.10019e174	1.36596
$685$	−4.84404e173	−0.195091
$686$	−8.40920e173	−0.309615
$687$	6.71013e172	0.0225887
$688$	−6.21151e174	−1.91209
$689$	2.85973e174	0.805087
$690$	6.65285e174	1.71312
$691$	−7.89744e174	−1.86031	−0.930157	−	0.367162i	$-0.880329\pi$
$691$	−7.89744e174	−1.86031	−0.930157	+	0.367162i	$0.880329\pi$
$692$	7.22342e173	0.155675
$693$	−1.17979e174	−0.232655
$694$	−6.75035e174	−1.21820
$695$	−4.42544e174	−0.730956
$696$	−4.69710e174	−0.710169
$697$	7.45197e174	1.03147
$698$	−1.21531e175	−1.54020
$699$	−4.12661e174	−0.478903
$700$	5.03877e173	0.0535544
$701$	1.78785e175	1.74049	0.870247	−	0.492616i	$-0.163959\pi$
$701$	1.78785e175	1.74049	0.870247	+	0.492616i	$0.163959\pi$
$702$	5.64114e174	0.503077
$703$	2.66957e175	2.18117
$704$	−3.64473e173	−0.0272865
$705$	−6.79056e174	−0.465881
$706$	8.85353e174	0.556708
$707$	−1.72825e174	−0.0996124
$708$	−1.89376e174	−0.100065
$709$	−3.39256e175	−1.64356	−0.821778	−	0.569808i	$-0.807017\pi$
$709$	−3.39256e175	−1.64356	−0.821778	+	0.569808i	$0.807017\pi$
$710$	4.55031e174	0.202140
$711$	−3.68949e175	−1.50309
$712$	2.84247e175	1.06213
$713$	5.98379e174	0.205102
$714$	−8.89117e174	−0.279588
$715$	9.78789e174	0.282402
$716$	1.91645e175	0.507396
$717$	1.02659e175	0.249442
$718$	6.30832e175	1.40689
$719$	2.62039e175	0.536462	0.268231	−	0.963355i	$-0.413561\pi$
$719$	2.62039e175	0.536462	0.268231	+	0.963355i	$0.413561\pi$
$720$	4.97454e175	0.934985
$721$	−6.37945e174	−0.110094
$722$	−1.17578e176	−1.86332
$723$	−1.06355e176	−1.54793
$724$	−4.80469e175	−0.642309
$725$	5.07387e175	0.623092
$726$	−8.47835e175	−0.956553
$727$	9.14836e175	0.948368	0.474184	−	0.880426i	$-0.342743\pi$
$727$	9.14836e175	0.948368	0.474184	+	0.880426i	$0.342743\pi$
$728$	3.37986e174	0.0321973
$729$	−1.86235e176	−1.63049
$730$	1.17651e174	0.00946762
$731$	−2.33610e176	−1.72812
$732$	1.07694e176	0.732421
$733$	1.15790e176	0.724061	0.362030	−	0.932166i	$-0.382084\pi$
$733$	1.15790e176	0.724061	0.362030	+	0.932166i	$0.382084\pi$
$734$	5.70987e175	0.328336
$735$	1.45040e176	0.767036
$736$	3.66366e176	1.78209
$737$	−5.02287e175	−0.224751
$738$	4.26744e176	1.75671
$739$	1.37876e175	0.0522224	0.0261112	−	0.999659i	$-0.491688\pi$
$739$	1.37876e175	0.0522224	0.0261112	+	0.999659i	$0.491688\pi$
$740$	−1.09650e176	−0.382171
$741$	−3.71162e176	−1.19054
$742$	−8.97440e175	−0.264951
$743$	3.39811e176	0.923477	0.461738	−	0.887016i	$-0.347226\pi$
$743$	3.39811e176	0.923477	0.461738	+	0.887016i	$0.347226\pi$
$744$	4.04177e175	0.101120
$745$	−3.83224e176	−0.882758
$746$	4.17558e176	0.885684
$747$	1.41196e176	0.275807
$748$	−4.30025e176	−0.773652
$749$	7.52449e175	0.124694
$750$	−1.12384e177	−1.71568
$751$	4.26430e176	0.599780	0.299890	−	0.953974i	$-0.403050\pi$
$751$	4.26430e176	0.599780	0.299890	+	0.953974i	$0.403050\pi$
$752$	−5.74777e176	−0.744907
$753$	3.86449e176	0.461531
$754$	−4.41535e176	−0.485990
$755$	−4.99042e176	−0.506290
$756$	−6.38910e175	−0.0597516
$757$	−1.55116e177	−1.33739	−0.668697	−	0.743535i	$-0.733147\pi$
$757$	−1.55116e177	−1.33739	−0.668697	+	0.743535i	$0.733147\pi$
$758$	−7.30260e176	−0.580525
$759$	4.64339e177	3.40382
$760$	−6.22158e176	−0.420595
$761$	9.13628e176	0.569656	0.284828	−	0.958579i	$-0.408063\pi$
$761$	9.13628e176	0.569656	0.284828	+	0.958579i	$0.408063\pi$
$762$	−2.47933e177	−1.42595
$763$	2.87525e175	0.0152552
$764$	1.69352e177	0.828988
$765$	1.87089e177	0.845025
$766$	−1.28650e177	−0.536216
$767$	1.37217e176	0.0527831
$768$	5.62828e177	1.99830
$769$	−4.97428e177	−1.63027	−0.815137	−	0.579268i	$-0.803338\pi$
$769$	−4.97428e177	−1.63027	−0.815137	+	0.579268i	$0.803338\pi$
$770$	−3.07163e176	−0.0929373
$771$	2.99947e177	0.837916
$772$	1.76043e177	0.454104
$773$	5.21997e177	1.24345	0.621726	−	0.783235i	$-0.286432\pi$
$773$	5.21997e177	1.24345	0.621726	+	0.783235i	$0.286432\pi$
$774$	−1.33779e178	−2.94319
$775$	−4.36597e176	−0.0887209
$776$	7.03124e176	0.131988
$777$	−1.58234e177	−0.274415
$778$	2.73270e177	0.437871
$779$	−9.76238e177	−1.44545
$780$	1.52451e177	0.208599
$781$	3.17591e177	0.401634
$782$	2.11786e178	2.47560
$783$	−6.43361e177	−0.695194
$784$	1.22767e178	1.22643
$785$	−3.16270e177	−0.292129
$786$	−2.64036e178	−2.25516
$787$	−9.37876e177	−0.740797	−0.370399	−	0.928873i	$-0.620779\pi$
$787$	−9.37876e177	−0.740797	−0.370399	+	0.928873i	$0.620779\pi$
$788$	7.45887e177	0.544892
$789$	−2.12859e178	−1.43832
$790$	−9.60571e177	−0.600431
$791$	4.81492e176	0.0278442
$792$	1.89819e178	1.01564
$793$	−7.80327e177	−0.386345
$794$	−2.25440e178	−1.03293
$795$	3.12022e178	1.32314
$796$	7.91766e177	0.310773
$797$	4.41390e178	1.60375	0.801873	−	0.597494i	$-0.203837\pi$
$797$	4.41390e178	1.60375	0.801873	+	0.597494i	$0.203837\pi$
$798$	1.16478e178	0.391802
$799$	−2.16169e178	−0.673236
$800$	−2.67313e178	−0.770879
$801$	1.11977e179	2.99040
$802$	3.78641e178	0.936492
$803$	8.21153e176	0.0188113
$804$	−7.82337e177	−0.166015
$805$	5.45965e177	0.107329
$806$	3.79932e177	0.0691992
$807$	−1.64773e179	−2.78076
$808$	2.78061e178	0.434852
$809$	−7.66029e178	−1.11022	−0.555112	−	0.831775i	$-0.687325\pi$
$809$	−7.66029e178	−1.11022	−0.555112	+	0.831775i	$0.687325\pi$
$810$	−8.33735e177	−0.111995
$811$	−4.64422e178	−0.578269	−0.289135	−	0.957288i	$-0.593368\pi$
$811$	−4.64422e178	−0.578269	−0.289135	+	0.957288i	$0.593368\pi$
$812$	5.00079e177	0.0577221
$813$	−1.34776e179	−1.44226
$814$	−2.12052e179	−2.10398
$815$	−3.27492e178	−0.301306
$816$	2.61658e179	2.23249
$817$	3.06039e179	2.42170
$818$	1.05573e179	0.774861
$819$	1.33147e178	0.0906508
$820$	4.00980e178	0.253263
$821$	−1.50011e179	−0.879062	−0.439531	−	0.898227i	$-0.644855\pi$
$821$	−1.50011e179	−0.879062	−0.439531	+	0.898227i	$0.644855\pi$
$822$	−1.45910e179	−0.793355
$823$	5.61480e178	0.283299	0.141649	−	0.989917i	$-0.454759\pi$
$823$	5.61480e178	0.283299	0.141649	+	0.989917i	$0.454759\pi$
$824$	1.02640e179	0.480609
$825$	−3.38797e179	−1.47239
$826$	−4.30616e177	−0.0173707
$827$	−1.04806e179	−0.392462	−0.196231	−	0.980558i	$-0.562870\pi$
$827$	−1.04806e179	−0.392462	−0.196231	+	0.980558i	$0.562870\pi$
$828$	4.37709e179	1.52167
$829$	4.03060e179	1.30097	0.650484	−	0.759520i	$-0.274566\pi$
$829$	4.03060e179	1.30097	0.650484	+	0.759520i	$0.274566\pi$
$830$	3.67608e178	0.110175
$831$	1.98320e179	0.551954
$832$	4.11331e177	0.0106318
$833$	4.61717e179	1.10843
$834$	−1.33301e180	−2.97249
$835$	−2.83753e179	−0.587789
$836$	5.63351e179	1.08416
$837$	5.53600e178	0.0989875
$838$	−2.33994e178	−0.0388775
$839$	2.33673e179	0.360784	0.180392	−	0.983595i	$-0.442263\pi$
$839$	2.33673e179	0.360784	0.180392	+	0.983595i	$0.442263\pi$
$840$	3.68774e178	0.0529156
$841$	−2.46252e179	−0.328418
$842$	−1.83495e180	−2.27474
$843$	1.98839e180	2.29143
$844$	−9.86646e179	−1.05706
$845$	3.81004e179	0.379526
$846$	−1.23791e180	−1.14660
$847$	−6.95774e178	−0.0599292
$848$	2.64107e180	2.11561
$849$	−3.27370e180	−2.43902
$850$	−1.54526e180	−1.07087
$851$	3.76911e180	2.42980
$852$	4.94664e179	0.296671
$853$	−8.65100e179	−0.482726	−0.241363	−	0.970435i	$-0.577594\pi$
$853$	−8.65100e179	−0.482726	−0.241363	+	0.970435i	$0.577594\pi$
$854$	2.44882e179	0.127145
$855$	−2.45094e180	−1.18418
$856$	−1.21063e180	−0.544344
$857$	3.21773e180	1.34657	0.673286	−	0.739382i	$-0.264882\pi$
$857$	3.21773e180	1.34657	0.673286	+	0.739382i	$0.264882\pi$
$858$	2.94826e180	1.14841
$859$	−1.58747e180	−0.575607	−0.287803	−	0.957690i	$-0.592925\pi$
$859$	−1.58747e180	−0.575607	−0.287803	+	0.957690i	$0.592925\pi$
$860$	−1.25702e180	−0.424316
$861$	5.78650e179	0.181854
$862$	1.71161e180	0.500851
$863$	3.86849e179	0.105409	0.0527045	−	0.998610i	$-0.483216\pi$
$863$	3.86849e179	0.105409	0.0527045	+	0.998610i	$0.483216\pi$
$864$	3.38950e180	0.860082
$865$	−5.71068e179	−0.134958
$866$	8.22583e180	1.81063
$867$	2.07840e180	0.426143
$868$	−4.30308e178	−0.00821895
$869$	−6.70436e180	−1.19300
$870$	−4.81755e180	−0.798715
$871$	5.66862e179	0.0875712
$872$	−4.62603e179	−0.0665955
$873$	2.76990e180	0.371611
$874$	−2.77448e181	−3.46919
$875$	−9.22277e179	−0.107490
$876$	1.27899e179	0.0138952
$877$	−7.71229e180	−0.781103	−0.390552	−	0.920581i	$-0.627716\pi$
$877$	−7.71229e180	−0.781103	−0.390552	+	0.920581i	$0.627716\pi$
$878$	1.17416e181	1.10870
$879$	−1.13767e181	−1.00162
$880$	9.03949e180	0.742096
$881$	−1.93191e181	−1.47900	−0.739499	−	0.673158i	$-0.764937\pi$
$881$	−1.93191e181	−1.47900	−0.739499	+	0.673158i	$0.764937\pi$
$882$	2.64406e181	1.88779
$883$	1.37642e178	0.000916574 0	0.000458287	−	1.00000i	$-0.499854\pi$
$883$	1.37642e178	0.000916574 0	0.000458287		1.00000i	$0.499854\pi$
$884$	4.85310e180	0.301443
$885$	1.49717e180	0.0867479
$886$	4.98986e180	0.269721
$887$	2.76845e181	1.39615	0.698077	−	0.716022i	$-0.254039\pi$
$887$	2.76845e181	1.39615	0.698077	+	0.716022i	$0.254039\pi$
$888$	2.54586e181	1.19794
$889$	−2.03466e180	−0.0893373
$890$	2.91536e181	1.19456
$891$	−5.81910e180	−0.222524
$892$	−2.33600e180	−0.0833749
$893$	2.83191e181	0.943440
$894$	−1.15433e182	−3.58981
$895$	−1.51510e181	−0.439871
$896$	4.53635e180	0.122960
$897$	−5.24035e181	−1.32625
$898$	3.54762e181	0.838382
$899$	−4.33306e180	−0.0956254
$900$	−3.19367e181	−0.658227
$901$	9.93286e181	1.91205
$902$	7.75457e181	1.39430
$903$	−1.81400e181	−0.304677
$904$	−7.74679e180	−0.121552
$905$	3.79848e181	0.556830
$906$	−1.50319e182	−2.05887
$907$	−1.07137e182	−1.37116	−0.685582	−	0.727995i	$-0.740452\pi$
$907$	−1.07137e182	−1.37116	−0.685582	+	0.727995i	$0.740452\pi$
$908$	8.88231e181	1.06230
$909$	1.09540e182	1.22432
$910$	3.46653e180	0.0362117
$911$	1.91047e181	0.186535	0.0932675	−	0.995641i	$-0.470269\pi$
$911$	1.91047e181	0.186535	0.0932675	+	0.995641i	$0.470269\pi$
$912$	−3.42782e182	−3.12850
$913$	2.56574e181	0.218907
$914$	9.33487e181	0.744590
$915$	−8.51407e181	−0.634951
$916$	1.14940e180	0.00801494
$917$	−2.16681e181	−0.141288
$918$	1.95937e182	1.19479
$919$	4.03068e181	0.229866	0.114933	−	0.993373i	$-0.463335\pi$
$919$	4.03068e181	0.229866	0.114933	+	0.993373i	$0.463335\pi$
$920$	−8.78411e181	−0.468540
$921$	2.48706e182	1.24085
$922$	9.08951e181	0.424218
$923$	−3.58422e181	−0.156491
$924$	−3.33917e181	−0.136399
$925$	−2.75007e182	−1.05106
$926$	6.57793e182	2.35241
$927$	4.04341e182	1.35315
$928$	−2.65298e182	−0.830870
$929$	1.47301e182	0.431757	0.215879	−	0.976420i	$-0.430738\pi$
$929$	1.47301e182	0.431757	0.215879	+	0.976420i	$0.430738\pi$
$930$	4.14541e181	0.113728
$931$	−6.04868e182	−1.55330
$932$	−7.06862e181	−0.169924
$933$	−4.65577e182	−1.04778
$934$	−3.54855e182	−0.747683
$935$	3.39969e182	0.670695
$936$	−2.14222e182	−0.395731
$937$	5.44976e182	0.942742	0.471371	−	0.881935i	$-0.343759\pi$
$937$	5.44976e182	0.942742	0.471371	+	0.881935i	$0.343759\pi$
$938$	−1.77893e181	−0.0288193
$939$	−6.23056e181	−0.0945351
$940$	−1.16318e182	−0.165304
$941$	6.12578e182	0.815454	0.407727	−	0.913104i	$-0.366322\pi$
$941$	6.12578e182	0.815454	0.407727	+	0.913104i	$0.366322\pi$
$942$	−9.52652e182	−1.18797
$943$	−1.37833e183	−1.61022
$944$	1.26726e182	0.138703
$945$	5.05108e181	0.0517998
$946$	−2.43096e183	−2.33600
$947$	2.12367e183	1.91233	0.956166	−	0.292825i	$-0.0945952\pi$
$947$	2.12367e183	1.91233	0.956166	+	0.292825i	$0.0945952\pi$
$948$	−1.04424e183	−0.881223
$949$	−9.26722e180	−0.00732956
$950$	2.02435e183	1.50067
$951$	1.71990e183	1.19509
$952$	1.17395e182	0.0764675
$953$	9.80747e182	0.598885	0.299443	−	0.954114i	$-0.403199\pi$
$953$	9.80747e182	0.598885	0.299443	+	0.954114i	$0.403199\pi$
$954$	5.68814e183	3.25646
$955$	−1.33886e183	−0.718666
$956$	1.75849e182	0.0885072
$957$	−3.36243e183	−1.58697
$958$	1.19161e183	0.527421
$959$	−1.19741e182	−0.0497046
$960$	4.48799e181	0.0174732
$961$	−2.70106e183	−0.986384
$962$	2.39314e183	0.819788
$963$	−4.76917e183	−1.53259
$964$	−1.82179e183	−0.549238
$965$	−1.39176e183	−0.393672
$966$	1.64453e183	0.436463
$967$	3.41603e183	0.850735	0.425367	−	0.905021i	$-0.360145\pi$
$967$	3.41603e183	0.850735	0.425367	+	0.905021i	$0.360145\pi$
$968$	1.11944e183	0.261617
$969$	−1.28918e184	−2.82749
$970$	7.21153e182	0.148445
$971$	4.60127e183	0.888986	0.444493	−	0.895782i	$-0.353384\pi$
$971$	4.60127e183	0.888986	0.444493	+	0.895782i	$0.353384\pi$
$972$	−3.54790e183	−0.643423
$973$	−1.09393e183	−0.186230
$974$	1.17545e184	1.87857
$975$	3.82354e183	0.573696
$976$	−7.20662e183	−1.01524
$977$	1.53204e181	0.00202653	0.00101327	−	0.999999i	$-0.499677\pi$
$977$	1.53204e181	0.00202653	0.00101327	+	0.999999i	$0.499677\pi$
$978$	−9.86454e183	−1.22529
$979$	2.03479e184	2.37347
$980$	2.48444e183	0.272160
$981$	−1.82239e183	−0.187498
$982$	9.59847e183	0.927567
$983$	−2.11877e184	−1.92328	−0.961640	−	0.274314i	$-0.911549\pi$
$983$	−2.11877e184	−1.92328	−0.961640	+	0.274314i	$0.911549\pi$
$984$	−9.30997e183	−0.793871
$985$	−5.89682e183	−0.472378
$986$	−1.53361e184	−1.15421
$987$	−1.67857e183	−0.118695
$988$	−6.35777e183	−0.422428
$989$	4.32090e184	2.69775
$990$	1.94686e184	1.14227
$991$	9.03221e182	0.0498040	0.0249020	−	0.999690i	$-0.492073\pi$
$991$	9.03221e182	0.0498040	0.0249020	+	0.999690i	$0.492073\pi$
$992$	2.28284e183	0.118306
$993$	3.02052e184	1.47130
$994$	1.12480e183	0.0515006
$995$	−6.25953e183	−0.269415
$996$	3.99627e183	0.161698
$997$	−3.43933e183	−0.130834	−0.0654171	−	0.997858i	$-0.520838\pi$
$997$	−3.43933e183	−0.130834	−0.0654171	+	0.997858i	$0.520838\pi$
$998$	−4.62999e184	−1.65597
$999$	3.48705e184	1.17268

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.124.a.a.1.3	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.124.a.a.1.3	✓	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 124 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-4.07908e18 q^{2} +3.50571e29 q^{3} +6.00505e36 q^{4} -4.74746e42 q^{5} -1.43001e48 q^{6} -1.17353e51 q^{7} +1.88811e55 q^{8} +7.43807e58 q^{9} +O(q^{10})\)	\(q-4.07908e18 q^{2} +3.50571e29 q^{3} +6.00505e36 q^{4} -4.74746e42 q^{5} -1.43001e48 q^{6} -1.17353e51 q^{7} +1.88811e55 q^{8} +7.43807e58 q^{9} +1.93653e61 q^{10} +1.35161e64 q^{11} +2.10520e66 q^{12} -1.52537e68 q^{13} +4.78693e69 q^{14} -1.66432e72 q^{15} -1.40874e74 q^{16} -5.29817e75 q^{17} -3.03405e77 q^{18} +6.94083e78 q^{19} -2.85088e79 q^{20} -4.11406e80 q^{21} -5.51332e82 q^{22} +9.79960e83 q^{23} +6.61917e84 q^{24} -7.15011e85 q^{25} +6.22212e86 q^{26} +9.06626e87 q^{27} -7.04712e87 q^{28} -7.09621e89 q^{29} +6.78890e90 q^{30} +6.10616e90 q^{31} +3.73858e92 q^{32} +4.73835e93 q^{33} +2.16117e94 q^{34} +5.57130e93 q^{35} +4.46660e95 q^{36} +3.84618e96 q^{37} -2.83122e97 q^{38} -5.34752e97 q^{39} -8.96374e97 q^{40} -1.40652e99 q^{41} +1.67816e99 q^{42} +4.40926e100 q^{43} +8.11648e100 q^{44} -3.53120e101 q^{45} -3.99733e102 q^{46} +4.08007e102 q^{47} -4.93864e103 q^{48} -8.71464e103 q^{49} +2.91659e104 q^{50} -1.85739e105 q^{51} -9.15995e104 q^{52} -1.87477e106 q^{53} -3.69820e106 q^{54} -6.41671e106 q^{55} -2.21576e106 q^{56} +2.43325e108 q^{57} +2.89460e108 q^{58} -8.99566e107 q^{59} -9.99434e108 q^{60} +5.11564e109 q^{61} -2.49075e109 q^{62} -8.72881e109 q^{63} -2.69659e109 q^{64} +7.24166e110 q^{65} -1.93281e112 q^{66} -3.71622e111 q^{67} -3.18158e112 q^{68} +3.43545e113 q^{69} -2.27258e112 q^{70} +2.34973e113 q^{71} +1.40439e114 q^{72} +6.07538e112 q^{73} -1.56889e115 q^{74} -2.50662e115 q^{75} +4.16800e115 q^{76} -1.58616e115 q^{77} +2.18130e116 q^{78} -4.96028e116 q^{79} +6.68795e116 q^{80} -4.30531e116 q^{81} +5.73729e117 q^{82} +1.89829e117 q^{83} -2.47052e117 q^{84} +2.51529e118 q^{85} -1.79857e119 q^{86} -2.48772e119 q^{87} +2.55199e119 q^{88} +1.50546e120 q^{89} +1.44040e120 q^{90} +1.79008e119 q^{91} +5.88471e120 q^{92} +2.14064e120 q^{93} -1.66429e121 q^{94} -3.29513e121 q^{95} +1.31064e122 q^{96} +3.72395e121 q^{97} +3.55477e122 q^{98} +1.00534e123 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 22\!\cdots\!00 q^{2}+ \cdots + 11\!\cdots\!70 q^{9}+O(q^{10}) \) 10 * q + 2202364291733634600 * q^2 + 134125909579478648360089344600 * q^3 + 57084626888206052159227531786235721280 * q^4 + 113311323144401441139520857445630379551020 * q^5 + 1704428975203488447105127830499670347572029831520 * q^6 - 588489927154562089895546247825497341684043299210000 * q^7 + 31510915218929096051805568530239002377664910158953331200 * q^8 + 110622019190242888335688316416186156626673662860821573119570 * q^9	\( 10 q + 22\!\cdots\!00 q^{2}+ \cdots + 42\!\cdots\!40 q^{99}+O(q^{100}) \) 10 * q + 2202364291733634600 * q^2 + 134125909579478648360089344600 * q^3 + 57084626888206052159227531786235721280 * q^4 + 113311323144401441139520857445630379551020 * q^5 + 1704428975203488447105127830499670347572029831520 * q^6 - 588489927154562089895546247825497341684043299210000 * q^7 + 31510915218929096051805568530239002377664910158953331200 * q^8 + 110622019190242888335688316416186156626673662860821573119570 * q^9 + 607459321076833386281292454084083169893966543300090109855920 * q^10 + 20273686763761435409423006911849218920389062193989167514770475720 * q^11 + 4052865973093508952389058638442895723286492489413158535125361555200 * q^12 - 291679396147681612979261456874156006927679666680520092295296904243300 * q^13 + 27976229889499855271101394813572915637495617130073041821451727626343360 * q^14 - 392991849187277904226922353724551866025786803779963352155457638870550960 * q^15 + 170537484653060213908677304907245043396278852268473637259293488813126389760 * q^16 + 12235102818717192622457093834992766133856671265915142264300826066878229357300 * q^17 - 3223507766001641523002467733734494312358127846172048898709172212524853129400 * q^18 + 1666536960290050807259098599664015537273272264625091908962591688248992033363000 * q^19 - 258603401942930436278392999359500188332957941397465316508154366680175868513395840 * q^20 + 4726509088722575910333056316070457676248231372641372129182198172427507924250822720 * q^21 + 36257825721047322261901872593889855345156787594610756475691779186002775337739623200 * q^22 + 608713231798404227050887650300591817769390426844961074649606092902614656957300110800 * q^23 + 19786957119488250790991083066821762146008515555201937981451455681676136224982485145600 * q^24 + 485472456776317058938705118138543671636666869772929691136469732236638136950683734854150 * q^25 + 5053774757641298124381938661884760040772792595111887036219927684117253575240872954270320 * q^26 + 7700604788205145137767150192913791419267884018867880017540340460394864815597243605954800 * q^27 + 74320574143924149311927158272423731357750692600077221984033474863771547722768608451827200 * q^28 - 2895686519348539858982198714566014333083121965126431872521364438276729233514966964861920900 * q^29 - 22262917949972607798281650542991372273227307551478322515015451194939644144287010568170260160 * q^30 + 8790022978579520754821177211313048365131172620195297293938358421085691479353060262526493120 * q^31 + 1751500200025709503299520819254071214160534691289882147163021909032725750364777638363998617600 * q^32 + 3377779222430911726674898641035883376428754579238816338112342781453942628724801459716957759200 * q^33 - 6225938074136149683378553996041283828179924226890449375819180913947978021351234695525912123440 * q^34 - 127563228852680813474013009675495155368791673351570943874124990036376129087211259153294998182880 * q^35 - 960607248812912772012251743514056985739786369519292450099978587362742327408164708696515631029440 * q^36 + 6228828125185127210799991385566665774174549878089400136396229638018645937962697518952494474353900 * q^37 + 28149067438989609944155252541609246090047173880579663465635025516156787837518279305588448239640800 * q^38 + 32959560456311799423446130174300373353905131721622845396992748686019716292294663425506424345860240 * q^39 - 1541102562733565575559372415349948151575063374670493456677530450911236708989098058436326331353216000 * q^40 - 1068152726446746563375131410189033727670864785235697564369168677061613108479021875193178691047211580 * q^41 + 20095761139727919770728604942082508129628376714407479872537782023853379601508712052049964889809772800 * q^42 + 46233404163387955795602164476169340298677865880468856734168936393238098987144594231102601675269093000 * q^43 - 52688891628643675175168725969332835598120041222275464101537283849644425575989226874013323217475715840 * q^44 - 276151139990973697058858962803580333632808711210368039524099465966592527069575726858161671366884559460 * q^45 - 4956167789256268893877918319143394669475196050553827727658680165816979401845732960931428427086369343680 * q^46 + 17772045268836184831844329814023597704806545621277768047420131448847122870736827620663655619725807063200 * q^47 + 51761953997683651012862563513543953819489370557013280319018667369358644539732537961201783057357284556800 * q^48 + 4842008461630476490563278611494437613501142312970195371812232417883349129579090018535857454479039263130 * q^49 - 330254069348074888508775695501771665236948121810497861745549014586967380406632858093596781115350317786600 * q^50 - 1686422005116992563499617363913766680527287395438410278431643755495206402676045225667531758007365026422480 * q^51 + 16611060975411842119131633337384601723518365602136815421052858543740989156971262266673653412429442118640000 * q^52 + 9865945778729587083239654534416850864601802213574882992654111630338605104546138239494501124975548493521100 * q^53 - 60640197068689493262198311334951229812788883593837286178369184088874735814592991608797792016104189923368000 * q^54 - 120361120762474187756245290834980454390752949663319471980043061592083830177139490905896370183199650052873360 * q^55 - 57015316450658072395870459826079095803920665182036397691229905074486924466540678768162486841164165128294400 * q^56 + 1396923092152977829208189007390918802999715037379682422426941467924623915894742262411280956401324684179725600 * q^57 + 2554207156866772251496945559844754999941265909370354854359543391556629115881092937374262646509059308353993200 * q^58 - 5145780721189304530977439106322232365186387161064437614606021967565628939238800130603665119360443691606408600 * q^59 - 66278076209627104092999016928275373331607580130420941011406364860535093218415612427322615235267206762608135680 * q^60 - 101263377816841551355083395298372952856192354301955205631542096828602753322654741755354533779833120948634218180 * q^61 + 490163771618275701978987843789963182098163324759510401318125961890059086504863674543728459156699482192104851200 * q^62 + 716994933719942928295473975746285250148612895023346279094238117312058943990010182273859915020097252421755028400 * q^63 + 977773622342975590017631946427418773791663923681070678728480268947054413114166828884752974664930456883519815680 * q^64 - 11968027825720175930231498946103877541009224034319106828760765788467265313917048983370089696694519867473256696760 * q^65 + 8356397123262354897793421823599928466576840588120328054964440488870910319312784016270333510655080761554879085440 * q^66 + 39912334137048450694568083884380942663008127500477138648875228077299015893249118799594117572286387201695784163800 * q^67 + 39810569882426825547153916716555119471846099090357174378729255654981318980810349722622634031376462141822712297600 * q^68 - 190987535400183650465933553655021226823555965329073635462561332226561638701086158395261700711827729370532705968960 * q^69 - 182874208614274419310812157137434002657108803954011080946993086754744195429788058628755429399392480183737020100480 * q^70 - 1491077405948495434941700576503681644378063798419124359800518573569171342873061633452931165399746735550688616916880 * q^71 + 3868752305234909303390161351576640709493783520411426900182416417888751619723371014253176886432068110318183269286400 * q^72 + 2192135974586112989195753785125121714230606008983301044356524322771675433811702392428103660396733638378012314983300 * q^73 - 1727512827049960711960442580477759342287747326769085411504653106770896005010199230748905559335798254942125500917840 * q^74 + 504885939682048274689087603051515462429637328904385746355242199239392653085717173946420202256812538173461328445800 * q^75 - 87242153455336999174915407092865037433520017247914052198234675064090961742425760253601031048397834372731494811884800 * q^76 + 125219039376054076906312524181774337606022429710014201552829418564774196434593400808568625172363524016803572381496000 * q^77 + 532021772270427326096828804708119000324560547259051767495862487744514269364113068456981059104472838417927263294440000 * q^78 + 791422870082819667716376764340803517880370192381122523208760361909337424612697174285245300530946528365443447973538400 * q^79 - 4085615693220605934319500471303383153704006928966377733020681159517376658700094137621404536087640933221508984164065280 * q^80 - 4901313048770605685168758293113604944951802904180679505379560996783873032337121922603323736534839244595242111670861990 * q^81 + 9412937760870473955022147090951043412853639579869374057740631037910279361456062862380973734854715629890526499271869200 * q^82 + 25598672435022890898365706131229485636670116907492184873375817087238430028799072047182092723440708545273457704582505400 * q^83 + 33174546777967500578087391267312861327420773111224581899833592957088759443575417585347553827589468266717940082704066560 * q^84 - 9635564759118842988822047485364075764019024326980604397537196383868268963111162554936571689782374441122549467080005480 * q^85 + 10863279313344256312123665865422603616515875103107232798448480961879504439581709207028323218422842324731614070800665120 * q^86 - 121620902589392915908211788499779291406085352403421659047183388653396698122624054668916792265905130473306827577981007600 * q^87 + 1658417872724710224316961024183068784782302432041532027143322435709213293291937227818245780162216280302401688092674918400 * q^88 + 1432769398908240147793761581541411990818735692935694485497792271884061431173833899064325508735771294071146532917448371300 * q^89 + 4242523397159088010711590897105749776230224908206487271625184482827883037969608572194218039560541845007789077503014537840 * q^90 + 3749197821974963786133178399116719947553345115682756250347057169251628507401139402810087270893048740655608748200953372320 * q^91 + 10615466523880625147148924876938816209748954360893793192595519658046375175603738111472483373680888517064089973142332940800 * q^92 + 44059413854358273427563101106184148636968023455699937482286003916513524569658318932628056672886084689799061193382440659200 * q^93 + 124806315412457573783492651738284236870157234824356474220743480912251201180129375425047875386957953704047914770947864658560 * q^94 + 266934808318153264777188286945199331781893495587515356911479003870672044191214686290176841073288939755251590483509109178000 * q^95 + 718345766812681622973438050365032032481440601133526400723013288803105919886348015012013492036267597486114877912972451512320 * q^96 + 151722902932344259186071782678082932585107678321580677399607057798381742852936340737162000675258065685590074813531733263700 * q^97 + 2158110007625946651882396712873921474356179378876735390584844074836963015629646171787464354973777052880845127577239492637800 * q^98 + 4265507899725315199945861403479494597528311025680927738450324529439136225728412750337207278998994765980992714808031550632040 * q^99

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