LMFDB - Embedded newform 1.124.a.a.1.9

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			1.9
Root			$-6.69543e16$ 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)

$f(q)$	$=$	$q+5.04095e18 q^{2} -1.36074e29 q^{3} +1.47773e37 q^{4} +1.38517e43 q^{5} -6.85941e47 q^{6} -1.32080e52 q^{7} +2.08873e55 q^{8} -3.00032e58 q^{9} +O(q^{10})$	\(q+5.04095e18 q^{2} -1.36074e29 q^{3} +1.47773e37 q^{4} +1.38517e43 q^{5} -6.85941e47 q^{6} -1.32080e52 q^{7} +2.08873e55 q^{8} -3.00032e58 q^{9} +6.98256e61 q^{10} -4.20436e63 q^{11} -2.01081e66 q^{12} +4.60485e68 q^{13} -6.65810e70 q^{14} -1.88485e72 q^{15} -5.18481e73 q^{16} +1.60960e75 q^{17} -1.51245e77 q^{18} +5.16000e78 q^{19} +2.04691e80 q^{20} +1.79727e81 q^{21} -2.11940e82 q^{22} +5.54302e83 q^{23} -2.84221e84 q^{24} +9.78297e85 q^{25} +2.32128e87 q^{26} +1.06849e88 q^{27} -1.95180e89 q^{28} +9.83495e88 q^{29} -9.50144e90 q^{30} +6.54554e91 q^{31} -4.83475e92 q^{32} +5.72104e92 q^{33} +8.11393e93 q^{34} -1.82954e95 q^{35} -4.43367e95 q^{36} +1.48661e96 q^{37} +2.60113e97 q^{38} -6.26600e97 q^{39} +2.89324e98 q^{40} -2.39944e99 q^{41} +9.05993e99 q^{42} +1.22512e100 q^{43} -6.21293e100 q^{44} -4.15595e101 q^{45} +2.79421e102 q^{46} +1.20430e103 q^{47} +7.05516e102 q^{48} +8.59286e103 q^{49} +4.93155e104 q^{50} -2.19025e104 q^{51} +6.80475e105 q^{52} +1.62098e106 q^{53} +5.38618e106 q^{54} -5.82375e106 q^{55} -2.75880e107 q^{56} -7.02140e107 q^{57} +4.95775e107 q^{58} -1.06817e109 q^{59} -2.78531e109 q^{60} -7.89623e109 q^{61} +3.29957e110 q^{62} +3.96283e110 q^{63} -1.88583e111 q^{64} +6.37850e111 q^{65} +2.88394e111 q^{66} +1.30157e112 q^{67} +2.37857e112 q^{68} -7.54259e112 q^{69} -9.22259e113 q^{70} +3.79687e113 q^{71} -6.26684e113 q^{72} +3.05102e114 q^{73} +7.49391e114 q^{74} -1.33121e115 q^{75} +7.62510e115 q^{76} +5.55314e115 q^{77} -3.15866e116 q^{78} +3.19616e116 q^{79} -7.18183e116 q^{80} +1.80496e114 q^{81} -1.20954e118 q^{82} +1.15425e118 q^{83} +2.65588e118 q^{84} +2.22957e118 q^{85} +6.17577e118 q^{86} -1.33828e118 q^{87} -8.78176e118 q^{88} +1.35923e120 q^{89} -2.09499e120 q^{90} -6.08211e120 q^{91} +8.19110e120 q^{92} -8.90676e120 q^{93} +6.07083e121 q^{94} +7.14747e121 q^{95} +6.57883e121 q^{96} -1.96075e122 q^{97} +4.33162e122 q^{98} +1.26144e122 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	5.04095e18	1.54585	0.772925	−	0.634497i	$-0.218793\pi$
$2$	5.04095e18	1.54585	0.772925	+	0.634497i	$0.218793\pi$
$3$	−1.36074e29	−0.617757	−0.308878	−	0.951102i	$-0.599954\pi$
$3$	−1.36074e29	−0.617757	−0.308878	+	0.951102i	$0.599954\pi$
$4$	1.47773e37	1.38965
$5$	1.38517e43	1.42839	0.714196	−	0.699946i	$-0.246792\pi$
$5$	1.38517e43	1.42839	0.714196	+	0.699946i	$0.246792\pi$
$6$	−6.85941e47	−0.954959
$7$	−1.32080e52	−1.40381	−0.701906	−	0.712270i	$-0.747667\pi$
$7$	−1.32080e52	−1.40381	−0.701906	+	0.712270i	$0.747667\pi$
$8$	2.08873e55	0.602348
$9$	−3.00032e58	−0.618377
$10$	6.98256e61	2.20808
$11$	−4.20436e63	−0.378486	−0.189243	−	0.981930i	$-0.560603\pi$
$11$	−4.20436e63	−0.378486	−0.189243	+	0.981930i	$0.560603\pi$
$12$	−2.01081e66	−0.858468
$13$	4.60485e68	1.43120	0.715599	−	0.698512i	$-0.246154\pi$
$13$	4.60485e68	1.43120	0.715599	+	0.698512i	$0.246154\pi$
$14$	−6.65810e70	−2.17008
$15$	−1.88485e72	−0.882399
$16$	−5.18481e73	−0.458515
$17$	1.60960e75	0.342066	0.171033	−	0.985265i	$-0.445289\pi$
$17$	1.60960e75	0.342066	0.171033	+	0.985265i	$0.445289\pi$
$18$	−1.51245e77	−0.955918
$19$	5.16000e78	1.17301	0.586507	−	0.809944i	$-0.300503\pi$
$19$	5.16000e78	1.17301	0.586507	+	0.809944i	$0.300503\pi$
$20$	2.04691e80	1.98497
$21$	1.79727e81	0.867214
$22$	−2.11940e82	−0.585083
$23$	5.54302e83	0.994224	0.497112	−	0.867686i	$-0.334394\pi$
$23$	5.54302e83	0.994224	0.497112	+	0.867686i	$0.334394\pi$
$24$	−2.84221e84	−0.372104
$25$	9.78297e85	1.04030
$26$	2.32128e87	2.21242
$27$	1.06849e88	0.999763
$28$	−1.95180e89	−1.95081
$29$	9.83495e88	0.113578	0.0567892	−	0.998386i	$-0.481914\pi$
$29$	9.83495e88	0.113578	0.0567892	+	0.998386i	$0.481914\pi$
$30$	−9.50144e90	−1.36406
$31$	6.54554e91	1.25084	0.625419	−	0.780289i	$-0.284928\pi$
$31$	6.54554e91	1.25084	0.625419	+	0.780289i	$0.284928\pi$
$32$	−4.83475e92	−1.31114
$33$	5.72104e92	0.233812
$34$	8.11393e93	0.528784
$35$	−1.82954e95	−2.00519
$36$	−4.43367e95	−0.859330
$37$	1.48661e96	0.534306	0.267153	−	0.963654i	$-0.413917\pi$
$37$	1.48661e96	0.534306	0.267153	+	0.963654i	$0.413917\pi$
$38$	2.60113e97	1.81330
$39$	−6.26600e97	−0.884132
$40$	2.89324e98	0.860389
$41$	−2.39944e99	−1.56280	−0.781398	−	0.624033i	$-0.785493\pi$
$41$	−2.39944e99	−1.56280	−0.781398	+	0.624033i	$0.785493\pi$
$42$	9.05993e99	1.34058
$43$	1.22512e100	0.426451	0.213225	−	0.977003i	$-0.431603\pi$
$43$	1.22512e100	0.426451	0.213225	+	0.977003i	$0.431603\pi$
$44$	−6.21293e100	−0.525965
$45$	−4.15595e101	−0.883285
$46$	2.79421e102	1.53692
$47$	1.20430e103	1.76489	0.882444	−	0.470417i	$-0.155896\pi$
$47$	1.20430e103	1.76489	0.882444	+	0.470417i	$0.155896\pi$
$48$	7.05516e102	0.283251
$49$	8.59286e103	0.970686
$50$	4.93155e104	1.60815
$51$	−2.19025e104	−0.211314
$52$	6.80475e105	1.98887
$53$	1.62098e106	1.46829	0.734147	−	0.678991i	$-0.237582\pi$
$53$	1.62098e106	1.46829	0.734147	+	0.678991i	$0.237582\pi$
$54$	5.38618e106	1.54548
$55$	−5.82375e106	−0.540627
$56$	−2.75880e107	−0.845582
$57$	−7.02140e107	−0.724637
$58$	4.95775e107	0.175575
$59$	−1.06817e109	−1.32204	−0.661018	−	0.750370i	$-0.729875\pi$
$59$	−1.06817e109	−1.32204	−0.661018	+	0.750370i	$0.729875\pi$
$60$	−2.78531e109	−1.22623
$61$	−7.89623e109	−1.25787	−0.628934	−	0.777459i	$-0.716508\pi$
$61$	−7.89623e109	−1.25787	−0.628934	+	0.777459i	$0.716508\pi$
$62$	3.29957e110	1.93361
$63$	3.96283e110	0.868084
$64$	−1.88583e111	−1.56832
$65$	6.37850e111	2.04431
$66$	2.88394e111	0.361439
$67$	1.30157e112	0.646943	0.323472	−	0.946238i	$-0.395150\pi$
$67$	1.30157e112	0.646943	0.323472	+	0.946238i	$0.395150\pi$
$68$	2.37857e112	0.475354
$69$	−7.54259e112	−0.614188
$70$	−9.22259e113	−3.09973
$71$	3.79687e113	0.533381	0.266690	−	0.963782i	$-0.414070\pi$
$71$	3.79687e113	0.533381	0.266690	+	0.963782i	$0.414070\pi$
$72$	−6.26684e113	−0.372478
$73$	3.05102e114	0.776406	0.388203	−	0.921574i	$-0.373096\pi$
$73$	3.05102e114	0.776406	0.388203	+	0.921574i	$0.373096\pi$
$74$	7.49391e114	0.825958
$75$	−1.33121e115	−0.642655
$76$	7.62510e115	1.63008
$77$	5.55314e115	0.531323
$78$	−3.15866e116	−1.36674
$79$	3.19616e116	0.631774	0.315887	−	0.948797i	$-0.397698\pi$
$79$	3.19616e116	0.631774	0.315887	+	0.948797i	$0.397698\pi$
$80$	−7.18183e116	−0.654939
$81$	1.80496e114	0.000766725 0
$82$	−1.20954e118	−2.41585
$83$	1.15425e118	1.09395	0.546975	−	0.837149i	$-0.315779\pi$
$83$	1.15425e118	1.09395	0.546975	+	0.837149i	$0.315779\pi$
$84$	2.65588e118	1.20513
$85$	2.22957e118	0.488605
$86$	6.17577e118	0.659229
$87$	−1.33828e118	−0.0701638
$88$	−8.78176e118	−0.227980
$89$	1.35923e120	1.76119	0.880596	−	0.473867i	$-0.157142\pi$
$89$	1.35923e120	1.76119	0.880596	+	0.473867i	$0.157142\pi$
$90$	−2.09499e120	−1.36543
$91$	−6.08211e120	−2.00913
$92$	8.19110e120	1.38163
$93$	−8.90676e120	−0.772713
$94$	6.07083e121	2.72825
$95$	7.14747e121	1.67552
$96$	6.57883e121	0.809967
$97$	−1.96075e122	−1.27632	−0.638160	−	0.769904i	$-0.720304\pi$
$97$	−1.96075e122	−1.27632	−0.638160	+	0.769904i	$0.720304\pi$
$98$	4.33162e122	1.50054
$99$	1.26144e122	0.234047
$100$	1.44566e123	1.44566
$101$	−1.98579e122	−0.107688	−0.0538441	−	0.998549i	$-0.517147\pi$
$101$	−1.98579e122	−0.107688	−0.0538441	+	0.998549i	$0.517147\pi$
$102$	−1.10409e123	−0.326659
$103$	1.06417e124	1.72791	0.863954	−	0.503571i	$-0.167981\pi$
$103$	1.06417e124	1.72791	0.863954	+	0.503571i	$0.167981\pi$
$104$	9.61827e123	0.862078
$105$	2.48952e124	1.23872
$106$	8.17130e124	2.26976
$107$	−1.59827e124	−0.249200	−0.124600	−	0.992207i	$-0.539765\pi$
$107$	−1.59827e124	−0.249200	−0.124600	+	0.992207i	$0.539765\pi$
$108$	1.57894e125	1.38932
$109$	−2.28160e125	−1.13896	−0.569481	−	0.822005i	$-0.692856\pi$
$109$	−2.28160e125	−1.13896	−0.569481	+	0.822005i	$0.692856\pi$
$110$	−2.93572e125	−0.835728
$111$	−2.02288e125	−0.330071
$112$	6.84811e125	0.643668
$113$	−6.45545e125	−0.351238	−0.175619	−	0.984458i	$-0.556193\pi$
$113$	−6.45545e125	−0.351238	−0.175619	+	0.984458i	$0.556193\pi$
$114$	−3.53945e126	−1.12018
$115$	7.67801e126	1.42014
$116$	1.45334e126	0.157835
$117$	−1.38160e127	−0.885019
$118$	−5.38461e127	−2.04367
$119$	−2.12597e127	−0.480197
$120$	−3.93694e127	−0.531511
$121$	−1.05719e128	−0.856748
$122$	−3.98045e128	−1.94448
$123$	3.26501e128	0.965428
$124$	9.67256e128	1.73823
$125$	5.25002e127	0.0575698
$126$	1.99764e129	1.34193
$127$	1.37391e128	0.0567582	0.0283791	−	0.999597i	$-0.490965\pi$
$127$	1.37391e128	0.0567582	0.0283791	+	0.999597i	$0.490965\pi$
$128$	−4.36518e129	−1.11324
$129$	−1.66707e129	−0.263443
$130$	3.21537e130	3.16020
$131$	−9.82058e129	−0.602493	−0.301247	−	0.953546i	$-0.597403\pi$
$131$	−9.82058e129	−0.602493	−0.301247	+	0.953546i	$0.597403\pi$
$132$	8.45417e129	0.324918
$133$	−6.81534e130	−1.64669
$134$	6.56113e130	1.00008
$135$	1.48003e131	1.42805
$136$	3.36202e130	0.206043
$137$	1.77463e131	0.693096	0.346548	−	0.938032i	$-0.387354\pi$
$137$	1.77463e131	0.693096	0.346548	+	0.938032i	$0.387354\pi$
$138$	−3.80218e131	−0.949443
$139$	−4.39183e131	−0.703453	−0.351727	−	0.936103i	$-0.614405\pi$
$139$	−4.39183e131	−0.703453	−0.351727	+	0.936103i	$0.614405\pi$
$140$	−2.70357e132	−2.78652
$141$	−1.63874e132	−1.09027
$142$	1.91398e132	0.824527
$143$	−1.93605e132	−0.541688
$144$	1.55561e132	0.283535
$145$	1.36231e132	0.162234
$146$	1.53800e133	1.20021
$147$	−1.16926e133	−0.599647
$148$	2.19681e133	0.742501
$149$	4.50415e133	1.00614	0.503069	−	0.864246i	$-0.332204\pi$
$149$	4.50415e133	1.00614	0.503069	+	0.864246i	$0.332204\pi$
$150$	−6.71054e133	−0.993448
$151$	−1.57643e133	−0.155093	−0.0775466	−	0.996989i	$-0.524709\pi$
$151$	−1.57643e133	−0.155093	−0.0775466	+	0.996989i	$0.524709\pi$
$152$	1.07778e134	0.706562
$153$	−4.82933e133	−0.211526
$154$	2.79931e134	0.821346
$155$	9.06667e134	1.78669
$156$	−9.25948e134	−1.22864
$157$	2.70485e134	0.242279	0.121139	−	0.992636i	$-0.461345\pi$
$157$	2.70485e134	0.242279	0.121139	+	0.992636i	$0.461345\pi$
$158$	1.61117e135	0.976628
$159$	−2.20574e135	−0.907048
$160$	−6.69694e135	−1.87283
$161$	−7.32123e135	−1.39570
$162$	9.09872e132	0.00118524
$163$	1.06647e136	0.951509	0.475754	−	0.879578i	$-0.342175\pi$
$163$	1.06647e136	0.951509	0.475754	+	0.879578i	$0.342175\pi$
$164$	−3.54573e136	−2.17175
$165$	7.92460e135	0.333976
$166$	5.81852e136	1.69108
$167$	−2.10867e136	−0.423590	−0.211795	−	0.977314i	$-0.567931\pi$
$167$	−2.10867e136	−0.423590	−0.211795	+	0.977314i	$0.567931\pi$
$168$	3.75400e136	0.522364
$169$	1.08525e137	1.04833
$170$	1.12392e137	0.755310
$171$	−1.54816e137	−0.725364
$172$	1.81040e137	0.592619
$173$	1.21858e136	0.0279266	0.0139633	−	0.999903i	$-0.495555\pi$
$173$	1.21858e136	0.0279266	0.0139633	+	0.999903i	$0.495555\pi$
$174$	−6.74620e136	−0.108463
$175$	−1.29214e138	−1.46039
$176$	2.17988e137	0.173542
$177$	1.45350e138	0.816696
$178$	6.85180e138	2.72254
$179$	−2.07474e138	−0.584119	−0.292059	−	0.956400i	$-0.594341\pi$
$179$	−2.07474e138	−0.584119	−0.292059	+	0.956400i	$0.594341\pi$
$180$	−6.14139e138	−1.22746
$181$	−9.05917e138	−1.28782	−0.643911	−	0.765100i	$-0.722689\pi$
$181$	−9.05917e138	−1.28782	−0.643911	+	0.765100i	$0.722689\pi$
$182$	−3.06596e139	−3.10582
$183$	1.07447e139	0.777056
$184$	1.15778e139	0.598868
$185$	2.05920e139	0.763199
$186$	−4.48985e139	−1.19450
$187$	−6.76736e138	−0.129467
$188$	1.77964e140	2.45259
$189$	−1.41126e140	−1.40348
$190$	3.60300e140	2.59011
$191$	−7.82953e139	−0.407553	−0.203776	−	0.979017i	$-0.565322\pi$
$191$	−7.82953e139	−0.407553	−0.203776	+	0.979017i	$0.565322\pi$
$192$	2.56612e140	0.968838
$193$	2.66103e140	0.729919	0.364960	−	0.931023i	$-0.381083\pi$
$193$	2.66103e140	0.729919	0.364960	+	0.931023i	$0.381083\pi$
$194$	−9.88402e140	−1.97300
$195$	−8.67947e140	−1.26289
$196$	1.26980e141	1.34892
$197$	−9.09388e140	−0.706441	−0.353221	−	0.935540i	$-0.614914\pi$
$197$	−9.09388e140	−0.706441	−0.353221	+	0.935540i	$0.614914\pi$
$198$	6.35887e140	0.361802
$199$	−1.83374e141	−0.765372	−0.382686	−	0.923878i	$-0.625001\pi$
$199$	−1.83374e141	−0.765372	−0.382686	+	0.923878i	$0.625001\pi$
$200$	2.04339e141	0.626625
$201$	−1.77109e141	−0.399653
$202$	−1.00102e141	−0.166470
$203$	−1.29900e141	−0.159443
$204$	−3.23661e141	−0.293653
$205$	−3.32363e142	−2.23229
$206$	5.36441e142	2.67109
$207$	−1.66308e142	−0.614805
$208$	−2.38753e142	−0.656226
$209$	−2.16945e142	−0.443969
$210$	1.25495e143	1.91488
$211$	2.53051e142	0.288295	0.144147	−	0.989556i	$-0.453956\pi$
$211$	2.53051e142	0.288295	0.144147	+	0.989556i	$0.453956\pi$
$212$	2.39538e143	2.04042
$213$	−5.16655e142	−0.329499
$214$	−8.05681e142	−0.385226
$215$	1.69700e143	0.609139
$216$	2.23177e143	0.602205
$217$	−8.64536e143	−1.75594
$218$	−1.15014e144	−1.76066
$219$	−4.15164e143	−0.479630
$220$	−8.60596e143	−0.751284
$221$	7.41199e143	0.489565
$222$	−1.01973e144	−0.510241
$223$	2.42618e144	0.920820	0.460410	−	0.887707i	$-0.347702\pi$
$223$	2.42618e144	0.920820	0.460410	+	0.887707i	$0.347702\pi$
$224$	6.38575e144	1.84060
$225$	−2.93520e144	−0.643300
$226$	−3.25416e144	−0.542962
$227$	3.45332e144	0.439184	0.219592	−	0.975592i	$-0.429527\pi$
$227$	3.45332e144	0.439184	0.219592	+	0.975592i	$0.429527\pi$
$228$	−1.03758e145	−1.00699
$229$	−9.36355e144	−0.694318	−0.347159	−	0.937806i	$-0.612854\pi$
$229$	−9.36355e144	−0.694318	−0.347159	+	0.937806i	$0.612854\pi$
$230$	3.87045e145	2.19533
$231$	−7.55636e144	−0.328228
$232$	2.05425e144	0.0684136
$233$	5.18001e145	1.32416	0.662082	−	0.749431i	$-0.269673\pi$
$233$	5.18001e145	1.32416	0.662082	+	0.749431i	$0.269673\pi$
$234$	−6.96459e145	−1.36811
$235$	1.66816e146	2.52095
$236$	−1.57848e146	−1.83717
$237$	−4.34913e145	−0.390283
$238$	−1.07169e146	−0.742312
$239$	2.61085e146	1.39737	0.698684	−	0.715430i	$-0.253769\pi$
$239$	2.61085e146	1.39737	0.698684	+	0.715430i	$0.253769\pi$
$240$	9.77259e145	0.404593
$241$	−4.98928e146	−1.59952	−0.799760	−	0.600320i	$-0.795040\pi$
$241$	−4.98928e146	−1.59952	−0.799760	+	0.600320i	$0.795040\pi$
$242$	−5.32925e146	−1.32440
$243$	−5.18667e146	−1.00024
$244$	−1.16685e147	−1.74800
$245$	1.19026e147	1.38652
$246$	1.64587e147	1.49241
$247$	2.37610e147	1.67881
$248$	1.36718e147	0.753439
$249$	−1.57063e147	−0.675795
$250$	2.64651e146	0.0889944
$251$	−4.32210e146	−0.113700	−0.0568501	−	0.998383i	$-0.518106\pi$
$251$	−4.32210e146	−0.113700	−0.0568501	+	0.998383i	$0.518106\pi$
$252$	5.85601e147	1.20634
$253$	−2.33048e147	−0.376300
$254$	6.92579e146	0.0877397
$255$	−3.03387e147	−0.301839
$256$	−1.95108e147	−0.152587
$257$	−2.79351e148	−1.71895	−0.859475	−	0.511177i	$-0.829210\pi$
$257$	−2.79351e148	−1.71895	−0.859475	+	0.511177i	$0.829210\pi$
$258$	−8.40361e147	−0.407243
$259$	−1.96352e148	−0.750065
$260$	9.42573e148	2.84089
$261$	−2.95080e147	−0.0702342
$262$	−4.95050e148	−0.931365
$263$	−6.41774e148	−0.955220	−0.477610	−	0.878572i	$-0.658497\pi$
$263$	−6.41774e148	−0.955220	−0.477610	+	0.878572i	$0.658497\pi$
$264$	1.19497e148	0.140836
$265$	2.24534e149	2.09730
$266$	−3.43558e149	−2.54554
$267$	−1.84955e149	−1.08799
$268$	1.92337e149	0.899028
$269$	−1.92853e149	−0.716905	−0.358453	−	0.933548i	$-0.616696\pi$
$269$	−1.92853e149	−0.716905	−0.358453	+	0.933548i	$0.616696\pi$
$270$	7.46077e149	2.20756
$271$	2.89975e149	0.683518	0.341759	−	0.939788i	$-0.388977\pi$
$271$	2.89975e149	0.683518	0.341759	+	0.939788i	$0.388977\pi$
$272$	−8.34548e148	−0.156843
$273$	8.27615e149	1.24115
$274$	8.94583e149	1.07142
$275$	−4.11312e149	−0.393741
$276$	−1.11459e150	−0.853510
$277$	−1.65087e149	−0.101206	−0.0506032	−	0.998719i	$-0.516114\pi$
$277$	−1.65087e149	−0.101206	−0.0506032	+	0.998719i	$0.516114\pi$
$278$	−2.21390e150	−1.08743
$279$	−1.96387e150	−0.773489
$280$	−3.82140e150	−1.20782
$281$	4.66150e150	1.18328	0.591639	−	0.806203i	$-0.298481\pi$
$281$	4.66150e150	1.18328	0.591639	+	0.806203i	$0.298481\pi$
$282$	−8.26081e150	−1.68540
$283$	5.32424e150	0.873759	0.436879	−	0.899520i	$-0.356084\pi$
$283$	5.32424e150	0.873759	0.436879	+	0.899520i	$0.356084\pi$
$284$	5.61076e150	0.741215
$285$	−9.72583e150	−1.03507
$286$	−9.75951e150	−0.837370
$287$	3.16919e151	2.19387
$288$	1.45058e151	0.810781
$289$	−1.95512e151	−0.882991
$290$	6.86732e150	0.250790
$291$	2.66806e151	0.788455
$292$	4.50860e151	1.07894
$293$	1.70376e150	0.0330407	0.0165204	−	0.999864i	$-0.494741\pi$
$293$	1.70376e150	0.0330407	0.0165204	+	0.999864i	$0.494741\pi$
$294$	−5.89419e151	−0.926965
$295$	−1.47960e152	−1.88838
$296$	3.10512e151	0.321838
$297$	−4.49230e151	−0.378396
$298$	2.27052e152	1.55534
$299$	2.55248e152	1.42293
$300$	−1.96717e152	−0.893068
$301$	−1.61814e152	−0.598656
$302$	−7.94671e151	−0.239751
$303$	2.70213e151	0.0665251
$304$	−2.67536e152	−0.537844
$305$	−1.09376e153	−1.79673
$306$	−2.43444e152	−0.326987
$307$	1.81160e152	0.199091	0.0995454	−	0.995033i	$-0.468261\pi$
$307$	1.81160e152	0.199091	0.0995454	+	0.995033i	$0.468261\pi$
$308$	8.20606e152	0.738355
$309$	−1.44805e153	−1.06743
$310$	4.57046e153	2.76195
$311$	3.76948e152	0.186860	0.0934302	−	0.995626i	$-0.470217\pi$
$311$	3.76948e152	0.186860	0.0934302	+	0.995626i	$0.470217\pi$
$312$	−1.30880e153	−0.532555
$313$	9.71055e152	0.324539	0.162270	−	0.986746i	$-0.448119\pi$
$313$	9.71055e152	0.324539	0.162270	+	0.986746i	$0.448119\pi$
$314$	1.36350e153	0.374527
$315$	5.48919e153	1.23996
$316$	4.72307e153	0.877948
$317$	1.35335e153	0.207141	0.103570	−	0.994622i	$-0.466973\pi$
$317$	1.35335e153	0.207141	0.103570	+	0.994622i	$0.466973\pi$
$318$	−1.11190e154	−1.40216
$319$	−4.13497e152	−0.0429878
$320$	−2.61219e154	−2.24017
$321$	2.17483e153	0.153945
$322$	−3.69060e154	−2.15755
$323$	8.30555e153	0.401248
$324$	2.66725e151	0.00106548
$325$	4.50491e154	1.48888
$326$	5.37604e154	1.47089
$327$	3.10465e154	0.703601
$328$	−5.01177e154	−0.941347
$329$	−1.59065e155	−2.47757
$330$	3.99475e154	0.516276
$331$	7.86763e154	0.844156	0.422078	−	0.906560i	$-0.361301\pi$
$331$	7.86763e154	0.844156	0.422078	+	0.906560i	$0.361301\pi$
$332$	1.70568e155	1.52021
$333$	−4.46030e154	−0.330403
$334$	−1.06297e155	−0.654808
$335$	1.80289e155	0.924089
$336$	−9.31848e154	−0.397630
$337$	−2.96778e155	−1.05485	−0.527427	−	0.849600i	$-0.676843\pi$
$337$	−2.96778e155	−1.05485	−0.527427	+	0.849600i	$0.676843\pi$
$338$	5.47068e155	1.62056
$339$	8.78417e154	0.216980
$340$	3.29472e155	0.678992
$341$	−2.75198e155	−0.473425
$342$	−7.80422e155	−1.12130
$343$	3.42749e154	0.0411517
$344$	2.55894e155	0.256872
$345$	−1.04478e156	−0.877302
$346$	6.14279e154	0.0431703
$347$	−8.45340e155	−0.497472	−0.248736	−	0.968571i	$-0.580015\pi$
$347$	−8.45340e155	−0.497472	−0.248736	+	0.968571i	$0.580015\pi$
$348$	−1.97762e155	−0.0975034
$349$	−4.86007e155	−0.200853	−0.100427	−	0.994944i	$-0.532021\pi$
$349$	−4.86007e155	−0.200853	−0.100427	+	0.994944i	$0.532021\pi$
$350$	−6.51360e156	−2.25755
$351$	4.92022e156	1.43086
$352$	2.03270e156	0.496250
$353$	−1.94425e156	−0.398665	−0.199332	−	0.979932i	$-0.563877\pi$
$353$	−1.94425e156	−0.398665	−0.199332	+	0.979932i	$0.563877\pi$
$354$	7.32704e156	1.26249
$355$	5.25931e156	0.761877
$356$	2.00858e157	2.44745
$357$	2.89289e156	0.296645
$358$	−1.04586e157	−0.902961
$359$	−1.44413e156	−0.105027	−0.0525133	−	0.998620i	$-0.516723\pi$
$359$	−1.44413e156	−0.105027	−0.0525133	+	0.998620i	$0.516723\pi$
$360$	−8.68064e156	−0.532044
$361$	7.27504e156	0.375961
$362$	−4.56668e157	−1.99078
$363$	1.43856e157	0.529262
$364$	−8.98773e157	−2.79200
$365$	4.22618e157	1.10901
$366$	5.41635e157	1.20121
$367$	−2.67237e157	−0.501111	−0.250555	−	0.968102i	$-0.580613\pi$
$367$	−2.67237e157	−0.501111	−0.250555	+	0.968102i	$0.580613\pi$
$368$	−2.87395e157	−0.455867
$369$	7.19908e157	0.966397
$370$	1.03803e158	1.17979
$371$	−2.14100e158	−2.06121
$372$	−1.31618e158	−1.07380
$373$	2.86141e158	1.97919	0.989593	−	0.143897i	$-0.0459634\pi$
$373$	2.86141e158	1.97919	0.989593	+	0.143897i	$0.0459634\pi$
$374$	−3.41139e157	−0.200137
$375$	−7.14390e156	−0.0355642
$376$	2.51546e158	1.06308
$377$	4.52885e157	0.162553
$378$	−7.11408e158	−2.16957
$379$	−4.17060e157	−0.108115	−0.0540577	−	0.998538i	$-0.517215\pi$
$379$	−4.17060e157	−0.108115	−0.0540577	+	0.998538i	$0.517215\pi$
$380$	1.05621e159	2.32840
$381$	−1.86953e157	−0.0350627
$382$	−3.94683e158	−0.630016
$383$	9.92434e157	0.134889	0.0674446	−	0.997723i	$-0.478515\pi$
$383$	9.92434e157	0.134889	0.0674446	+	0.997723i	$0.478515\pi$
$384$	5.93987e158	0.687712
$385$	7.69203e158	0.758938
$386$	1.34141e159	1.12835
$387$	−3.67575e158	−0.263707
$388$	−2.89746e159	−1.77364
$389$	−3.08543e159	−1.61219	−0.806094	−	0.591788i	$-0.798422\pi$
$389$	−3.08543e159	−1.61219	−0.806094	+	0.591788i	$0.798422\pi$
$390$	−4.37527e159	−1.95223
$391$	8.92206e158	0.340091
$392$	1.79481e159	0.584690
$393$	1.33632e159	0.372194
$394$	−4.58418e159	−1.09205
$395$	4.42721e159	0.902421
$396$	1.86408e159	0.325245
$397$	1.23573e160	1.84632	0.923158	−	0.384420i	$-0.125599\pi$
$397$	1.23573e160	1.84632	0.923158	+	0.384420i	$0.125599\pi$
$398$	−9.24377e159	−1.18315
$399$	9.27389e159	1.01725
$400$	−5.07228e159	−0.476995
$401$	1.11743e160	0.901245	0.450623	−	0.892715i	$-0.351202\pi$
$401$	1.11743e160	0.901245	0.450623	+	0.892715i	$0.351202\pi$
$402$	−8.92798e159	−0.617805
$403$	3.01412e160	1.79020
$404$	−2.93446e159	−0.149649
$405$	2.50018e157	0.00109518
$406$	−6.54821e159	−0.246474
$407$	−6.25024e159	−0.202228
$408$	−4.57483e159	−0.127284
$409$	−4.70431e160	−1.12593	−0.562967	−	0.826479i	$-0.690340\pi$
$409$	−4.70431e160	−1.12593	−0.562967	+	0.826479i	$0.690340\pi$
$410$	−1.67542e161	−3.45078
$411$	−2.41481e160	−0.428165
$412$	1.57256e161	2.40120
$413$	1.41085e161	1.85589
$414$	−8.38351e160	−0.950397
$415$	1.59883e161	1.56259
$416$	−2.22633e161	−1.87651
$417$	5.97613e160	0.434563
$418$	−1.09361e161	−0.686310
$419$	2.81552e160	0.152544	0.0762721	−	0.997087i	$-0.475698\pi$
$419$	2.81552e160	0.152544	0.0762721	+	0.997087i	$0.475698\pi$
$420$	3.67885e161	1.72139
$421$	−4.28945e161	−1.73401	−0.867007	−	0.498295i	$-0.833960\pi$
$421$	−4.28945e161	−1.73401	−0.867007	+	0.498295i	$0.833960\pi$
$422$	1.27562e161	0.445661
$423$	−3.61329e161	−1.09137
$424$	3.38579e161	0.884423
$425$	1.57467e161	0.355853
$426$	−2.60443e161	−0.509357
$427$	1.04294e162	1.76581
$428$	−2.36182e161	−0.346302
$429$	2.63445e161	0.334632
$430$	8.55448e161	0.941638
$431$	1.29306e162	1.23387	0.616933	−	0.787016i	$-0.288375\pi$
$431$	1.29306e162	1.23387	0.616933	+	0.787016i	$0.288375\pi$
$432$	−5.53989e161	−0.458406
$433$	−1.07508e162	−0.771678	−0.385839	−	0.922566i	$-0.626088\pi$
$433$	−1.07508e162	−0.771678	−0.385839	+	0.922566i	$0.626088\pi$
$434$	−4.35808e162	−2.71442
$435$	−1.85374e161	−0.100221
$436$	−3.37159e162	−1.58276
$437$	2.86019e162	1.16624
$438$	−2.09282e162	−0.741437
$439$	3.52834e162	1.08643	0.543215	−	0.839593i	$-0.317207\pi$
$439$	3.52834e162	1.08643	0.543215	+	0.839593i	$0.317207\pi$
$440$	−1.21642e162	−0.325645
$441$	−2.57813e162	−0.600250
$442$	3.73635e162	0.756794
$443$	−5.46459e162	−0.963227	−0.481613	−	0.876384i	$-0.659949\pi$
$443$	−5.46459e162	−0.963227	−0.481613	+	0.876384i	$0.659949\pi$
$444$	−2.98928e162	−0.458685
$445$	1.88276e163	2.51567
$446$	1.22303e163	1.42345
$447$	−6.12897e162	−0.621548
$448$	2.49081e163	2.20162
$449$	−1.51029e163	−1.16389	−0.581944	−	0.813229i	$-0.697708\pi$
$449$	−1.51029e163	−1.16389	−0.581944	+	0.813229i	$0.697708\pi$
$450$	−1.47962e163	−0.994446
$451$	1.00881e163	0.591497
$452$	−9.53943e162	−0.488100
$453$	2.14511e162	0.0958099
$454$	1.74080e163	0.678912
$455$	−8.42474e163	−2.86983
$456$	−1.46658e163	−0.436483
$457$	4.33830e163	1.12843	0.564213	−	0.825629i	$-0.309180\pi$
$457$	4.33830e163	1.12843	0.564213	+	0.825629i	$0.309180\pi$
$458$	−4.72012e163	−1.07331
$459$	1.71984e163	0.341985
$460$	1.13461e164	1.97351
$461$	−2.08641e163	−0.317535	−0.158768	−	0.987316i	$-0.550752\pi$
$461$	−2.08641e163	−0.317535	−0.158768	+	0.987316i	$0.550752\pi$
$462$	−3.80912e163	−0.507392
$463$	−5.62098e163	−0.655512	−0.327756	−	0.944762i	$-0.606292\pi$
$463$	−5.62098e163	−0.655512	−0.327756	+	0.944762i	$0.606292\pi$
$464$	−5.09923e162	−0.0520774
$465$	−1.23374e164	−1.10374
$466$	2.61122e164	2.04696
$467$	−9.38498e163	−0.644830	−0.322415	−	0.946598i	$-0.604495\pi$
$467$	−9.38498e163	−0.644830	−0.322415	+	0.946598i	$0.604495\pi$
$468$	−2.04164e164	−1.22987
$469$	−1.71911e164	−0.908186
$470$	8.40912e164	3.89702
$471$	−3.68060e163	−0.149669
$472$	−2.23112e164	−0.796325
$473$	−5.15085e163	−0.161406
$474$	−2.19237e164	−0.603319
$475$	5.04801e164	1.22029
$476$	−3.14162e164	−0.667307
$477$	−4.86347e164	−0.907959
$478$	1.31612e165	2.16012
$479$	−1.19226e164	−0.172083	−0.0860413	−	0.996292i	$-0.527422\pi$
$479$	−1.19226e164	−0.172083	−0.0860413	+	0.996292i	$0.527422\pi$
$480$	9.11278e164	1.15695
$481$	6.84561e164	0.764698
$482$	−2.51507e165	−2.47262
$483$	9.96228e164	0.862204
$484$	−1.56225e165	−1.19058
$485$	−2.71596e165	−1.82309
$486$	−2.61457e165	−1.54622
$487$	1.09263e165	0.569430	0.284715	−	0.958612i	$-0.408101\pi$
$487$	1.09263e165	0.569430	0.284715	+	0.958612i	$0.408101\pi$
$488$	−1.64931e165	−0.757674
$489$	−1.45119e165	−0.587801
$490$	6.00002e165	2.14335
$491$	−6.30702e164	−0.198752	−0.0993762	−	0.995050i	$-0.531685\pi$
$491$	−6.30702e164	−0.198752	−0.0993762	+	0.995050i	$0.531685\pi$
$492$	4.82481e165	1.34161
$493$	1.58304e164	0.0388513
$494$	1.19778e166	2.59520
$495$	1.74731e165	0.334311
$496$	−3.39373e165	−0.573528
$497$	−5.01492e165	−0.748766
$498$	−7.91749e165	−1.04468
$499$	7.78023e165	0.907421	0.453711	−	0.891149i	$-0.350100\pi$
$499$	7.78023e165	0.907421	0.453711	+	0.891149i	$0.350100\pi$
$500$	7.75813e164	0.0800022
$501$	2.86935e165	0.261676
$502$	−2.17875e165	−0.175763
$503$	−2.15868e166	−1.54084	−0.770420	−	0.637537i	$-0.779953\pi$
$503$	−2.15868e166	−1.54084	−0.770420	+	0.637537i	$0.779953\pi$
$504$	8.27727e165	0.522888
$505$	−2.75065e165	−0.153821
$506$	−1.17479e166	−0.581704
$507$	−1.47674e166	−0.647611
$508$	2.03027e165	0.0788743
$509$	3.89543e166	1.34095	0.670474	−	0.741933i	$-0.266091\pi$
$509$	3.89543e166	1.34095	0.670474	+	0.741933i	$0.266091\pi$
$510$	−1.52936e166	−0.466598
$511$	−4.02980e166	−1.08993
$512$	3.65833e166	0.877364
$513$	5.51338e166	1.17274
$514$	−1.40819e167	−2.65724
$515$	1.47405e167	2.46813
$516$	−2.46348e166	−0.366094
$517$	−5.06332e166	−0.667986
$518$	−9.89799e166	−1.15949
$519$	−1.65816e165	−0.0172518
$520$	1.33229e167	1.23139
$521$	7.22333e166	0.593222	0.296611	−	0.954998i	$-0.404143\pi$
$521$	7.22333e166	0.593222	0.296611	+	0.954998i	$0.404143\pi$
$522$	−1.48748e166	−0.108572
$523$	2.03091e167	1.31776	0.658881	−	0.752247i	$-0.271030\pi$
$523$	2.03091e167	1.31776	0.658881	+	0.752247i	$0.271030\pi$
$524$	−1.45122e167	−0.837258
$525$	1.75826e167	0.902166
$526$	−3.23515e167	−1.47663
$527$	1.05357e167	0.427870
$528$	−2.96625e166	−0.107206
$529$	−3.58044e165	−0.0115189
$530$	1.13186e168	3.24211
$531$	3.20486e167	0.817516
$532$	−1.00713e168	−2.28833
$533$	−1.10491e168	−2.23667
$534$	−9.32350e167	−1.68187
$535$	−2.21388e167	−0.355956
$536$	2.71862e167	0.389685
$537$	2.82317e167	0.360843
$538$	−9.72163e167	−1.10823
$539$	−3.61275e167	−0.367391
$540$	2.18709e168	1.98450
$541$	−5.23039e167	−0.423548	−0.211774	−	0.977319i	$-0.567924\pi$
$541$	−5.23039e167	−0.423548	−0.211774	+	0.977319i	$0.567924\pi$
$542$	1.46175e168	1.05662
$543$	1.23272e168	0.795561
$544$	−7.78203e167	−0.448498
$545$	−3.16040e168	−1.62688
$546$	4.17197e168	1.91864
$547$	1.55628e168	0.639538	0.319769	−	0.947496i	$-0.396395\pi$
$547$	1.55628e168	0.639538	0.319769	+	0.947496i	$0.396395\pi$
$548$	2.62244e168	0.963164
$549$	2.36912e168	0.777836
$550$	−2.07340e168	−0.608664
$551$	5.07483e167	0.133229
$552$	−1.57544e168	−0.369955
$553$	−4.22149e168	−0.886891
$554$	−8.32197e167	−0.156450
$555$	−2.80204e168	−0.471471
$556$	−6.48996e168	−0.977557
$557$	−5.76937e168	−0.778097	−0.389049	−	0.921217i	$-0.627196\pi$
$557$	−5.76937e168	−0.778097	−0.389049	+	0.921217i	$0.627196\pi$
$558$	−9.89977e168	−1.19570
$559$	5.64150e168	0.610335
$560$	9.48579e168	0.919411
$561$	9.20860e167	0.0799793
$562$	2.34984e169	1.82917
$563$	4.91542e168	0.343000	0.171500	−	0.985184i	$-0.445139\pi$
$563$	4.91542e168	0.343000	0.171500	+	0.985184i	$0.445139\pi$
$564$	−2.42162e169	−1.51510
$565$	−8.94188e168	−0.501706
$566$	2.68392e169	1.35070
$567$	−2.38400e166	−0.00107634
$568$	7.93062e168	0.321281
$569$	−1.55499e169	−0.565358	−0.282679	−	0.959215i	$-0.591223\pi$
$569$	−1.55499e169	−0.565358	−0.282679	+	0.959215i	$0.591223\pi$
$570$	−4.90274e169	−1.60006
$571$	−3.30919e169	−0.969618	−0.484809	−	0.874620i	$-0.661111\pi$
$571$	−3.30919e169	−0.969618	−0.484809	+	0.874620i	$0.661111\pi$
$572$	−2.86096e169	−0.752760
$573$	1.06539e169	0.251768
$574$	1.59757e170	3.39140
$575$	5.42272e169	1.03429
$576$	5.65809e169	0.969811
$577$	3.20200e169	0.493297	0.246648	−	0.969105i	$-0.420671\pi$
$577$	3.20200e169	0.493297	0.246648	+	0.969105i	$0.420671\pi$
$578$	−9.85566e169	−1.36497
$579$	−3.62096e169	−0.450912
$580$	2.01313e169	0.225450
$581$	−1.52454e170	−1.53570
$582$	1.34496e170	1.21883
$583$	−6.81521e169	−0.555729
$584$	6.37274e169	0.467667
$585$	−1.91375e170	−1.26415
$586$	8.58856e168	0.0510760
$587$	−5.58349e169	−0.298994	−0.149497	−	0.988762i	$-0.547765\pi$
$587$	−5.58349e169	−0.298994	−0.149497	+	0.988762i	$0.547765\pi$
$588$	−1.72786e170	−0.833303
$589$	3.37749e170	1.46725
$590$	−7.45859e170	−2.91916
$591$	1.23744e170	0.436409
$592$	−7.70777e169	−0.244987
$593$	5.08987e170	1.45829	0.729144	−	0.684361i	$-0.239919\pi$
$593$	5.08987e170	1.45829	0.729144	+	0.684361i	$0.239919\pi$
$594$	−2.26454e170	−0.584944
$595$	−2.94483e170	−0.685909
$596$	6.65594e170	1.39818
$597$	2.49523e170	0.472814
$598$	1.28669e171	2.19964
$599$	9.02625e168	0.0139238	0.00696190	−	0.999976i	$-0.497784\pi$
$599$	9.02625e168	0.0139238	0.00696190	+	0.999976i	$0.497784\pi$
$600$	−2.78052e170	−0.387101
$601$	1.38276e171	1.73767	0.868836	−	0.495099i	$-0.164868\pi$
$601$	1.38276e171	1.73767	0.868836	+	0.495099i	$0.164868\pi$
$602$	−8.15698e170	−0.925433
$603$	−3.90512e170	−0.400055
$604$	−2.32955e170	−0.215526
$605$	−1.46439e171	−1.22377
$606$	1.36213e170	0.102838
$607$	1.70745e171	1.16478	0.582390	−	0.812910i	$-0.302118\pi$
$607$	1.70745e171	1.16478	0.582390	+	0.812910i	$0.302118\pi$
$608$	−2.49473e171	−1.53799
$609$	1.76760e170	0.0984967
$610$	−5.51360e171	−2.77747
$611$	5.54564e171	2.52590
$612$	−7.13646e170	−0.293948
$613$	−4.47737e171	−1.66803	−0.834015	−	0.551742i	$-0.813963\pi$
$613$	−4.47737e171	−1.66803	−0.834015	+	0.551742i	$0.813963\pi$
$614$	9.13216e170	0.307765
$615$	4.52259e171	1.37901
$616$	1.15990e171	0.320041
$617$	1.97389e171	0.492930	0.246465	−	0.969152i	$-0.420731\pi$
$617$	1.97389e171	0.492930	0.246465	+	0.969152i	$0.420731\pi$
$618$	−7.29956e171	−1.65008
$619$	−4.28570e171	−0.877095	−0.438548	−	0.898708i	$-0.644507\pi$
$619$	−4.28570e171	−0.877095	−0.438548	+	0.898708i	$0.644507\pi$
$620$	1.33981e172	2.48288
$621$	5.92263e171	0.993988
$622$	1.90017e171	0.288858
$623$	−1.79527e172	−2.47238
$624$	3.24880e171	0.405388
$625$	−8.47265e171	−0.958072
$626$	4.89504e171	0.501689
$627$	2.95205e171	0.274265
$628$	3.99705e171	0.336684
$629$	2.39285e171	0.182768
$630$	2.76707e172	1.91680
$631$	−1.71770e172	−1.07930	−0.539648	−	0.841891i	$-0.681443\pi$
$631$	−1.71770e172	−1.07930	−0.539648	+	0.841891i	$0.681443\pi$
$632$	6.67589e171	0.380548
$633$	−3.44336e171	−0.178096
$634$	6.82217e171	0.320209
$635$	1.90309e171	0.0810729
$636$	−3.25949e172	−1.26048
$637$	3.95688e172	1.38924
$638$	−2.08442e171	−0.0664528
$639$	−1.13918e172	−0.329830
$640$	−6.04651e172	−1.59014
$641$	4.01079e172	0.958212	0.479106	−	0.877757i	$-0.340961\pi$
$641$	4.01079e172	0.958212	0.479106	+	0.877757i	$0.340961\pi$
$642$	1.09632e172	0.237976
$643$	−8.27282e172	−1.63185	−0.815923	−	0.578161i	$-0.803771\pi$
$643$	−8.27282e172	−1.63185	−0.815923	+	0.578161i	$0.803771\pi$
$644$	−1.08188e173	−1.93954
$645$	−2.30917e172	−0.376300
$646$	4.18679e172	0.620270
$647$	−5.44192e172	−0.733059	−0.366529	−	0.930406i	$-0.619454\pi$
$647$	−5.44192e172	−0.733059	−0.366529	+	0.930406i	$0.619454\pi$
$648$	3.77007e169	0.000461835 0
$649$	4.49099e172	0.500372
$650$	2.27090e173	2.30159
$651$	1.17641e173	1.08474
$652$	1.57597e173	1.32227
$653$	4.35137e172	0.332250	0.166125	−	0.986105i	$-0.446874\pi$
$653$	4.35137e172	0.332250	0.166125	+	0.986105i	$0.446874\pi$
$654$	1.56504e173	1.08766
$655$	−1.36032e173	−0.860597
$656$	1.24406e173	0.716566
$657$	−9.15403e172	−0.480112
$658$	−8.01837e173	−3.82995
$659$	1.11873e173	0.486712	0.243356	−	0.969937i	$-0.421752\pi$
$659$	1.11873e173	0.486712	0.243356	+	0.969937i	$0.421752\pi$
$660$	1.17105e173	0.464111
$661$	9.21909e172	0.332888	0.166444	−	0.986051i	$-0.446772\pi$
$661$	9.21909e172	0.332888	0.166444	+	0.986051i	$0.446772\pi$
$662$	3.96603e173	1.30494
$663$	−1.00858e173	−0.302432
$664$	2.41092e173	0.658939
$665$	−9.44040e173	−2.35212
$666$	−2.24841e173	−0.510753
$667$	5.45153e172	0.112922
$668$	−3.11606e173	−0.588644
$669$	−3.30140e173	−0.568842
$670$	9.08828e173	1.42850
$671$	3.31986e173	0.476086
$672$	−8.68933e173	−1.13704
$673$	8.75581e173	1.04561	0.522805	−	0.852452i	$-0.324885\pi$
$673$	8.75581e173	1.04561	0.522805	+	0.852452i	$0.324885\pi$
$674$	−1.49604e174	−1.63065
$675$	1.04530e174	1.04006
$676$	1.60371e174	1.45681
$677$	−1.47669e174	−1.22486	−0.612431	−	0.790524i	$-0.709808\pi$
$677$	−1.47669e174	−1.22486	−0.612431	+	0.790524i	$0.709808\pi$
$678$	4.42806e173	0.335418
$679$	2.58976e174	1.79171
$680$	4.65697e173	0.294310
$681$	−4.69906e173	−0.271309
$682$	−1.38726e174	−0.731844
$683$	−2.61613e174	−1.26120	−0.630602	−	0.776106i	$-0.717192\pi$
$683$	−2.61613e174	−1.26120	−0.630602	+	0.776106i	$0.717192\pi$
$684$	−2.28777e174	−1.00801
$685$	2.45817e174	0.990013
$686$	1.72778e173	0.0636144
$687$	1.27413e174	0.428919
$688$	−6.35201e173	−0.195534
$689$	7.46440e174	2.10142
$690$	−5.26666e174	−1.35618
$691$	7.68093e174	1.80931	0.904657	−	0.426141i	$-0.140127\pi$
$691$	7.68093e174	1.80931	0.904657	+	0.426141i	$0.140127\pi$
$692$	1.80073e173	0.0388083
$693$	−1.66612e174	−0.328558
$694$	−4.26132e174	−0.769018
$695$	−6.08343e174	−1.00481
$696$	−2.79530e173	−0.0422630
$697$	−3.86215e174	−0.534580
$698$	−2.44994e174	−0.310489
$699$	−7.04864e174	−0.818011
$700$	−1.90944e175	−2.02944
$701$	2.78861e173	0.0271475	0.0135738	−	0.999908i	$-0.495679\pi$
$701$	2.78861e173	0.0271475	0.0135738	+	0.999908i	$0.495679\pi$
$702$	2.48026e175	2.21189
$703$	7.67089e174	0.626749
$704$	7.92871e174	0.593586
$705$	−2.26993e175	−1.55734
$706$	−9.80087e174	−0.616276
$707$	2.62283e174	0.151174
$708$	2.14789e175	1.13493
$709$	2.01122e175	0.974351	0.487176	−	0.873304i	$-0.338027\pi$
$709$	2.01122e175	0.974351	0.487176	+	0.873304i	$0.338027\pi$
$710$	2.65119e175	1.17775
$711$	−9.58949e174	−0.390674
$712$	2.83905e175	1.06085
$713$	3.62820e175	1.24361
$714$	1.45829e175	0.458568
$715$	−2.68175e175	−0.773744
$716$	−3.06591e175	−0.811724
$717$	−3.55268e175	−0.863233
$718$	−7.27981e174	−0.162355
$719$	−3.78116e175	−0.774103	−0.387051	−	0.922058i	$-0.626506\pi$
$719$	−3.78116e175	−0.774103	−0.387051	+	0.922058i	$0.626506\pi$
$720$	2.15478e175	0.404999
$721$	−1.40556e176	−2.42566
$722$	3.66731e175	0.581179
$723$	6.78910e175	0.988114
$724$	−1.33870e176	−1.78963
$725$	9.62151e174	0.118156
$726$	7.25171e175	0.818160
$727$	−2.01660e175	−0.209051	−0.104526	−	0.994522i	$-0.533332\pi$
$727$	−2.01660e175	−0.209051	−0.104526	+	0.994522i	$0.533332\pi$
$728$	−1.27038e176	−1.21020
$729$	7.04894e175	0.617136
$730$	2.13039e176	1.71437
$731$	1.97196e175	0.145874
$732$	1.58778e176	1.07984
$733$	9.19181e175	0.574787	0.287393	−	0.957813i	$-0.407211\pi$
$733$	9.19181e175	0.574787	0.287393	+	0.957813i	$0.407211\pi$
$734$	−1.34713e176	−0.774642
$735$	−1.61963e176	−0.856532
$736$	−2.67991e176	−1.30357
$737$	−5.47226e175	−0.244859
$738$	3.62902e176	1.49391
$739$	3.86409e176	1.46357	0.731787	−	0.681534i	$-0.238687\pi$
$739$	3.86409e176	1.46357	0.731787	+	0.681534i	$0.238687\pi$
$740$	3.04295e176	1.06058
$741$	−3.23325e176	−1.03710
$742$	−1.07927e177	−3.18632
$743$	1.31118e176	0.356327	0.178164	−	0.984001i	$-0.442984\pi$
$743$	1.31118e176	0.356327	0.178164	+	0.984001i	$0.442984\pi$
$744$	−1.86038e176	−0.465442
$745$	6.23901e176	1.43716
$746$	1.44242e177	3.05953
$747$	−3.46312e176	−0.676474
$748$	−1.00004e176	−0.179915
$749$	2.11100e176	0.349830
$750$	−3.60120e175	−0.0549769
$751$	−1.06952e177	−1.50430	−0.752148	−	0.658994i	$-0.770982\pi$
$751$	−1.06952e177	−1.50430	−0.752148	+	0.658994i	$0.770982\pi$
$752$	−6.24407e176	−0.809228
$753$	5.88125e175	0.0702390
$754$	2.28297e176	0.251283
$755$	−2.18362e176	−0.221534
$756$	−2.08547e177	−1.95035
$757$	4.85169e176	0.418309	0.209154	−	0.977883i	$-0.432929\pi$
$757$	4.85169e176	0.418309	0.209154	+	0.977883i	$0.432929\pi$
$758$	−2.10238e176	−0.167130
$759$	3.17118e176	0.232462
$760$	1.49291e177	1.00925
$761$	−1.14920e177	−0.716540	−0.358270	−	0.933618i	$-0.616633\pi$
$761$	−1.14920e177	−0.716540	−0.358270	+	0.933618i	$0.616633\pi$
$762$	−9.42419e175	−0.0542018
$763$	3.01354e177	1.59889
$764$	−1.15700e177	−0.566357
$765$	−6.68943e176	−0.302142
$766$	5.00281e176	0.208519
$767$	−4.91878e177	−1.89209
$768$	2.65490e176	0.0942614
$769$	4.76086e177	1.56033	0.780164	−	0.625575i	$-0.215136\pi$
$769$	4.76086e177	1.56033	0.780164	+	0.625575i	$0.215136\pi$
$770$	3.87751e177	1.17320
$771$	3.80124e177	1.06189
$772$	3.93229e177	1.01434
$773$	2.59649e177	0.618511	0.309256	−	0.950979i	$-0.399920\pi$
$773$	2.59649e177	0.618511	0.309256	+	0.950979i	$0.399920\pi$
$774$	−1.85293e177	−0.407652
$775$	6.40348e177	1.30125
$776$	−4.09546e177	−0.768788
$777$	2.67183e177	0.463358
$778$	−1.55535e178	−2.49220
$779$	−1.23811e178	−1.83318
$780$	−1.28259e178	−1.75498
$781$	−1.59634e177	−0.201877
$782$	4.49756e177	0.525729
$783$	1.05085e177	0.113551
$784$	−4.45523e177	−0.445074
$785$	3.74668e177	0.346069
$786$	6.73634e177	0.575357
$787$	5.37341e177	0.424428	0.212214	−	0.977223i	$-0.431933\pi$
$787$	5.37341e177	0.424428	0.212214	+	0.977223i	$0.431933\pi$
$788$	−1.34383e178	−0.981709
$789$	8.73286e177	0.590094
$790$	2.23174e178	1.39501
$791$	8.52637e177	0.493072
$792$	2.63481e177	0.140978
$793$	−3.63610e178	−1.80026
$794$	6.22923e178	2.85413
$795$	−3.05532e178	−1.29562
$796$	−2.70977e178	−1.06360
$797$	1.17691e178	0.427619	0.213809	−	0.976875i	$-0.431413\pi$
$797$	1.17691e178	0.427619	0.213809	+	0.976875i	$0.431413\pi$
$798$	4.67492e178	1.57252
$799$	1.93845e178	0.603709
$800$	−4.72982e178	−1.36399
$801$	−4.07812e178	−1.08908
$802$	5.63293e178	1.39319
$803$	−1.28276e178	−0.293859
$804$	−2.61720e178	−0.555380
$805$	−1.01411e179	−1.99361
$806$	1.51940e179	2.76738
$807$	2.62423e178	0.442873
$808$	−4.14776e177	−0.0648657
$809$	−5.16964e178	−0.749249	−0.374624	−	0.927177i	$-0.622228\pi$
$809$	−5.16964e178	−0.749249	−0.374624	+	0.927177i	$0.622228\pi$
$810$	1.26033e176	0.00169299
$811$	−1.90882e178	−0.237674	−0.118837	−	0.992914i	$-0.537917\pi$
$811$	−1.90882e178	−0.237674	−0.118837	+	0.992914i	$0.537917\pi$
$812$	−1.91958e178	−0.221570
$813$	−3.94580e178	−0.422247
$814$	−3.15071e178	−0.312614
$815$	1.47725e179	1.35913
$816$	1.13560e178	0.0968905
$817$	6.32162e178	0.500232
$818$	−2.37142e179	−1.74053
$819$	1.82483e179	1.24240
$820$	−4.91144e179	−3.10211
$821$	8.61400e178	0.504778	0.252389	−	0.967626i	$-0.418784\pi$
$821$	8.61400e178	0.504778	0.252389	+	0.967626i	$0.418784\pi$
$822$	−1.21729e179	−0.661879
$823$	−3.11996e179	−1.57419	−0.787097	−	0.616829i	$-0.788417\pi$
$823$	−3.11996e179	−1.57419	−0.787097	+	0.616829i	$0.788417\pi$
$824$	2.22275e179	1.04080
$825$	5.59687e178	0.243236
$826$	7.11201e179	2.86893
$827$	1.37149e179	0.513576	0.256788	−	0.966468i	$-0.417336\pi$
$827$	1.37149e179	0.513576	0.256788	+	0.966468i	$0.417336\pi$
$828$	−2.45759e179	−0.854366
$829$	3.10846e179	1.00333	0.501663	−	0.865063i	$-0.332722\pi$
$829$	3.10846e179	1.00333	0.501663	+	0.865063i	$0.332722\pi$
$830$	8.05964e179	2.41553
$831$	2.24641e178	0.0625209
$832$	−8.68396e179	−2.24457
$833$	1.38311e179	0.332039
$834$	3.01254e179	0.671769
$835$	−2.92087e179	−0.605053
$836$	−3.20587e179	−0.616964
$837$	6.99381e179	1.25054
$838$	1.41929e179	0.235811
$839$	−6.72255e179	−1.03794	−0.518971	−	0.854792i	$-0.673685\pi$
$839$	−6.72255e179	−1.03794	−0.518971	+	0.854792i	$0.673685\pi$
$840$	5.19992e179	0.746141
$841$	−7.40142e179	−0.987100
$842$	−2.16229e180	−2.68053
$843$	−6.34308e179	−0.730978
$844$	3.73942e179	0.400630
$845$	1.50325e180	1.49742
$846$	−1.82144e180	−1.68709
$847$	1.39634e180	1.20271
$848$	−8.40449e179	−0.673235
$849$	−7.24489e179	−0.539770
$850$	7.93784e179	0.550096
$851$	8.24029e179	0.531220
$852$	−7.63478e179	−0.457890
$853$	4.77879e179	0.266657	0.133328	−	0.991072i	$-0.457434\pi$
$853$	4.77879e179	0.266657	0.133328	+	0.991072i	$0.457434\pi$
$854$	5.25739e180	2.72968
$855$	−2.14447e180	−1.03610
$856$	−3.33835e179	−0.150105
$857$	6.49820e179	0.271940	0.135970	−	0.990713i	$-0.456585\pi$
$857$	6.49820e179	0.271940	0.135970	+	0.990713i	$0.456585\pi$
$858$	1.32801e180	0.517291
$859$	−1.31804e180	−0.477914	−0.238957	−	0.971030i	$-0.576805\pi$
$859$	−1.31804e180	−0.477914	−0.238957	+	0.971030i	$0.576805\pi$
$860$	2.50771e180	0.846492
$861$	−4.31243e180	−1.35528
$862$	6.51827e180	1.90737
$863$	4.24755e180	1.15738	0.578688	−	0.815549i	$-0.303565\pi$
$863$	4.24755e180	1.15738	0.578688	+	0.815549i	$0.303565\pi$
$864$	−5.16586e180	−1.31083
$865$	1.68794e179	0.0398901
$866$	−5.41944e180	−1.19290
$867$	2.66041e180	0.545473
$868$	−1.27755e181	−2.44015
$869$	−1.34378e180	−0.239118
$870$	−9.34462e179	−0.154927
$871$	5.99353e180	0.925904
$872$	−4.76563e180	−0.686051
$873$	5.88286e180	0.789247
$874$	1.44181e181	1.80283
$875$	−6.93424e179	−0.0808172
$876$	−6.13502e180	−0.666520
$877$	−8.71730e180	−0.882891	−0.441445	−	0.897288i	$-0.645534\pi$
$877$	−8.71730e180	−0.882891	−0.441445	+	0.897288i	$0.645534\pi$
$878$	1.77862e181	1.67946
$879$	−2.31837e179	−0.0204111
$880$	3.01950e180	0.247885
$881$	−1.77057e181	−1.35549	−0.677744	−	0.735298i	$-0.737042\pi$
$881$	−1.77057e181	−1.35549	−0.677744	+	0.735298i	$0.737042\pi$
$882$	−1.29962e181	−0.927896
$883$	−2.21819e181	−1.47712	−0.738560	−	0.674188i	$-0.764494\pi$
$883$	−2.21819e181	−1.47712	−0.738560	+	0.674188i	$0.764494\pi$
$884$	1.09529e181	0.680326
$885$	2.01335e181	1.16656
$886$	−2.75467e181	−1.48900
$887$	−2.69390e181	−1.35856	−0.679281	−	0.733878i	$-0.737708\pi$
$887$	−2.69390e181	−1.35856	−0.679281	+	0.733878i	$0.737708\pi$
$888$	−4.22525e180	−0.198818
$889$	−1.81466e180	−0.0796778
$890$	9.49090e181	3.88886
$891$	−7.58871e177	−0.000290195 0
$892$	3.58525e181	1.27962
$893$	6.21420e181	2.07024
$894$	−3.08958e181	−0.960821
$895$	−2.87386e181	−0.834351
$896$	5.76554e181	1.56278
$897$	−3.47325e181	−0.879025
$898$	−7.61331e181	−1.79920
$899$	6.43750e180	0.142068
$900$	−4.33745e181	−0.893965
$901$	2.60914e181	0.502254
$902$	5.08536e181	0.914366
$903$	2.20187e181	0.369824
$904$	−1.34837e181	−0.211568
$905$	−1.25485e182	−1.83952
$906$	1.08134e181	0.148108
$907$	−4.52291e181	−0.578856	−0.289428	−	0.957200i	$-0.593465\pi$
$907$	−4.52291e181	−0.578856	−0.289428	+	0.957200i	$0.593465\pi$
$908$	5.10308e181	0.610313
$909$	5.95799e180	0.0665918
$910$	−4.24687e182	−4.43632
$911$	1.15320e182	1.12596	0.562980	−	0.826470i	$-0.309655\pi$
$911$	1.15320e182	1.12596	0.562980	+	0.826470i	$0.309655\pi$
$912$	3.64046e181	0.332257
$913$	−4.85289e181	−0.414045
$914$	2.18692e182	1.74438
$915$	1.48832e182	1.10994
$916$	−1.38368e182	−0.964861
$917$	1.29711e182	0.845787
$918$	8.66962e181	0.528658
$919$	2.41850e182	1.37925	0.689623	−	0.724168i	$-0.257776\pi$
$919$	2.41850e182	1.37925	0.689623	+	0.724168i	$0.257776\pi$
$920$	1.60373e182	0.855419
$921$	−2.46511e181	−0.122990
$922$	−1.05175e182	−0.490862
$923$	1.74840e182	0.763373
$924$	−1.11663e182	−0.456124
$925$	1.45434e182	0.555841
$926$	−2.83351e182	−1.01332
$927$	−3.19284e182	−1.06850
$928$	−4.75495e181	−0.148917
$929$	7.95882e181	0.233283	0.116641	−	0.993174i	$-0.462787\pi$
$929$	7.95882e181	0.233283	0.116641	+	0.993174i	$0.462787\pi$
$930$	−6.21920e182	−1.70621
$931$	4.43391e182	1.13863
$932$	7.65468e182	1.84013
$933$	−5.12927e181	−0.115434
$934$	−4.73092e182	−0.996810
$935$	−9.37393e181	−0.184930
$936$	−2.88579e182	−0.533089
$937$	−3.47259e182	−0.600715	−0.300358	−	0.953827i	$-0.597106\pi$
$937$	−3.47259e182	−0.600715	−0.300358	+	0.953827i	$0.597106\pi$
$938$	−8.66597e182	−1.40392
$939$	−1.32135e182	−0.200486
$940$	2.46510e183	3.50325
$941$	2.39463e182	0.318770	0.159385	−	0.987217i	$-0.449049\pi$
$941$	2.39463e182	0.318770	0.159385	+	0.987217i	$0.449049\pi$
$942$	−1.85537e182	−0.231366
$943$	−1.33001e183	−1.55377
$944$	5.53827e182	0.606173
$945$	−1.95483e183	−2.00472
$946$	−2.59652e182	−0.249509
$947$	6.93025e182	0.624059	0.312029	−	0.950072i	$-0.398991\pi$
$947$	6.93025e182	0.624059	0.312029	+	0.950072i	$0.398991\pi$
$948$	−6.42686e182	−0.542358
$949$	1.40495e183	1.11119
$950$	2.54468e183	1.88639
$951$	−1.84155e182	−0.127963
$952$	−4.44057e182	−0.289245
$953$	−4.40900e182	−0.269232	−0.134616	−	0.990898i	$-0.542980\pi$
$953$	−4.40900e182	−0.269232	−0.134616	+	0.990898i	$0.542980\pi$
$954$	−2.45165e183	−1.40357
$955$	−1.08452e183	−0.582145
$956$	3.85814e183	1.94186
$957$	5.62661e181	0.0265560
$958$	−6.01012e182	−0.266014
$959$	−2.34394e183	−0.972976
$960$	3.55451e183	1.38388
$961$	1.54606e183	0.564595
$962$	3.45084e183	1.18211
$963$	4.79533e182	0.154100
$964$	−7.37283e183	−2.22278
$965$	3.68597e183	1.04261
$966$	5.02193e183	1.33284
$967$	5.26220e183	1.31051	0.655253	−	0.755409i	$-0.272562\pi$
$967$	5.26220e183	1.31051	0.655253	+	0.755409i	$0.272562\pi$
$968$	−2.20818e183	−0.516060
$969$	−1.13017e183	−0.247874
$970$	−1.36910e184	−2.81822
$971$	−9.17010e183	−1.77171	−0.885853	−	0.463967i	$-0.846426\pi$
$971$	−9.17010e183	−1.77171	−0.885853	+	0.463967i	$0.846426\pi$
$972$	−7.66452e183	−1.38998
$973$	5.80074e183	0.987516
$974$	5.50787e183	0.880254
$975$	−6.13001e183	−0.919766
$976$	4.09404e183	0.576751
$977$	−7.51289e183	−0.993782	−0.496891	−	0.867813i	$-0.665525\pi$
$977$	−7.51289e183	−0.993782	−0.496891	+	0.867813i	$0.665525\pi$
$978$	−7.31539e183	−0.908652
$979$	−5.71469e183	−0.666587
$980$	1.75888e184	1.92678
$981$	6.84552e183	0.704307
$982$	−3.17934e183	−0.307242
$983$	1.79006e184	1.62490	0.812449	−	0.583033i	$-0.198134\pi$
$983$	1.79006e184	1.62490	0.812449	+	0.583033i	$0.198134\pi$
$984$	6.81970e183	0.581523
$985$	−1.25966e184	−1.00908
$986$	7.98001e182	0.0600583
$987$	2.16445e184	1.53054
$988$	3.51125e184	2.33297
$989$	6.79086e183	0.423987
$990$	8.80811e183	0.516795
$991$	−1.29328e184	−0.713120	−0.356560	−	0.934272i	$-0.616051\pi$
$991$	−1.29328e184	−0.713120	−0.356560	+	0.934272i	$0.616051\pi$
$992$	−3.16460e184	−1.64003
$993$	−1.07058e184	−0.521483
$994$	−2.52799e184	−1.15748
$995$	−2.54003e184	−1.09325
$996$	−2.32098e184	−0.939122
$997$	−1.18946e184	−0.452478	−0.226239	−	0.974072i	$-0.572643\pi$
$997$	−1.18946e184	−0.452478	−0.226239	+	0.974072i	$0.572643\pi$
$998$	3.92197e184	1.40274
$999$	1.58842e184	0.534180

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.124.a.a.1.9	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.124.a.a.1.9	✓	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)

\(f(q)\)	\(=\)	\(q+5.04095e18 q^{2} -1.36074e29 q^{3} +1.47773e37 q^{4} +1.38517e43 q^{5} -6.85941e47 q^{6} -1.32080e52 q^{7} +2.08873e55 q^{8} -3.00032e58 q^{9} +O(q^{10})\)	\(q+5.04095e18 q^{2} -1.36074e29 q^{3} +1.47773e37 q^{4} +1.38517e43 q^{5} -6.85941e47 q^{6} -1.32080e52 q^{7} +2.08873e55 q^{8} -3.00032e58 q^{9} +6.98256e61 q^{10} -4.20436e63 q^{11} -2.01081e66 q^{12} +4.60485e68 q^{13} -6.65810e70 q^{14} -1.88485e72 q^{15} -5.18481e73 q^{16} +1.60960e75 q^{17} -1.51245e77 q^{18} +5.16000e78 q^{19} +2.04691e80 q^{20} +1.79727e81 q^{21} -2.11940e82 q^{22} +5.54302e83 q^{23} -2.84221e84 q^{24} +9.78297e85 q^{25} +2.32128e87 q^{26} +1.06849e88 q^{27} -1.95180e89 q^{28} +9.83495e88 q^{29} -9.50144e90 q^{30} +6.54554e91 q^{31} -4.83475e92 q^{32} +5.72104e92 q^{33} +8.11393e93 q^{34} -1.82954e95 q^{35} -4.43367e95 q^{36} +1.48661e96 q^{37} +2.60113e97 q^{38} -6.26600e97 q^{39} +2.89324e98 q^{40} -2.39944e99 q^{41} +9.05993e99 q^{42} +1.22512e100 q^{43} -6.21293e100 q^{44} -4.15595e101 q^{45} +2.79421e102 q^{46} +1.20430e103 q^{47} +7.05516e102 q^{48} +8.59286e103 q^{49} +4.93155e104 q^{50} -2.19025e104 q^{51} +6.80475e105 q^{52} +1.62098e106 q^{53} +5.38618e106 q^{54} -5.82375e106 q^{55} -2.75880e107 q^{56} -7.02140e107 q^{57} +4.95775e107 q^{58} -1.06817e109 q^{59} -2.78531e109 q^{60} -7.89623e109 q^{61} +3.29957e110 q^{62} +3.96283e110 q^{63} -1.88583e111 q^{64} +6.37850e111 q^{65} +2.88394e111 q^{66} +1.30157e112 q^{67} +2.37857e112 q^{68} -7.54259e112 q^{69} -9.22259e113 q^{70} +3.79687e113 q^{71} -6.26684e113 q^{72} +3.05102e114 q^{73} +7.49391e114 q^{74} -1.33121e115 q^{75} +7.62510e115 q^{76} +5.55314e115 q^{77} -3.15866e116 q^{78} +3.19616e116 q^{79} -7.18183e116 q^{80} +1.80496e114 q^{81} -1.20954e118 q^{82} +1.15425e118 q^{83} +2.65588e118 q^{84} +2.22957e118 q^{85} +6.17577e118 q^{86} -1.33828e118 q^{87} -8.78176e118 q^{88} +1.35923e120 q^{89} -2.09499e120 q^{90} -6.08211e120 q^{91} +8.19110e120 q^{92} -8.90676e120 q^{93} +6.07083e121 q^{94} +7.14747e121 q^{95} +6.57883e121 q^{96} -1.96075e122 q^{97} +4.33162e122 q^{98} +1.26144e122 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 22\!\cdots\!00 q^{2}+ \cdots + 11\!\cdots\!70 q^{9}+O(q^{10}) \) 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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