LMFDB - Embedded newform 1.124.a.a.1.10

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			1.10
Root			$-8.41774e16$ 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)

$f(q)$	$=$	$q+6.28101e18 q^{2} +2.54101e29 q^{3} +2.88173e37 q^{4} -1.37149e43 q^{5} +1.59601e48 q^{6} +5.88359e51 q^{7} +1.14211e56 q^{8} +1.60483e58 q^{9} +O(q^{10})$	\(q+6.28101e18 q^{2} +2.54101e29 q^{3} +2.88173e37 q^{4} -1.37149e43 q^{5} +1.59601e48 q^{6} +5.88359e51 q^{7} +1.14211e56 q^{8} +1.60483e58 q^{9} -8.61436e61 q^{10} +8.14507e63 q^{11} +7.32252e66 q^{12} +4.84539e68 q^{13} +3.69549e70 q^{14} -3.48498e72 q^{15} +4.10920e74 q^{16} +1.33231e75 q^{17} +1.00799e77 q^{18} -1.53262e78 q^{19} -3.95227e80 q^{20} +1.49503e81 q^{21} +5.11593e82 q^{22} -3.99634e83 q^{23} +2.90211e85 q^{24} +9.40597e85 q^{25} +3.04340e87 q^{26} -8.25093e87 q^{27} +1.69549e89 q^{28} -8.68148e89 q^{29} -2.18892e91 q^{30} +4.77746e91 q^{31} +1.36650e93 q^{32} +2.06967e93 q^{33} +8.36826e93 q^{34} -8.06930e94 q^{35} +4.62467e95 q^{36} +2.08174e96 q^{37} -9.62638e96 q^{38} +1.23122e98 q^{39} -1.56639e99 q^{40} +1.76517e99 q^{41} +9.39029e99 q^{42} +9.95937e99 q^{43} +2.34719e101 q^{44} -2.20101e101 q^{45} -2.51011e102 q^{46} +3.47235e102 q^{47} +1.04415e104 q^{48} -5.39070e103 q^{49} +5.90790e104 q^{50} +3.38542e104 q^{51} +1.39631e106 q^{52} +1.95409e106 q^{53} -5.18242e106 q^{54} -1.11709e107 q^{55} +6.71968e107 q^{56} -3.89440e107 q^{57} -5.45285e108 q^{58} +7.27867e108 q^{59} -1.00428e110 q^{60} -3.89156e109 q^{61} +3.00073e110 q^{62} +9.44213e109 q^{63} +4.21335e111 q^{64} -6.64542e111 q^{65} +1.29997e112 q^{66} -4.59434e111 q^{67} +3.83936e112 q^{68} -1.01548e113 q^{69} -5.06834e113 q^{70} -8.85659e113 q^{71} +1.83288e114 q^{72} -4.60878e114 q^{73} +1.30755e115 q^{74} +2.39007e115 q^{75} -4.41659e115 q^{76} +4.79223e115 q^{77} +7.73331e116 q^{78} -1.49337e116 q^{79} -5.63574e117 q^{80} -2.87522e117 q^{81} +1.10871e118 q^{82} -5.33938e116 q^{83} +4.30827e118 q^{84} -1.82725e118 q^{85} +6.25550e118 q^{86} -2.20598e119 q^{87} +9.30254e119 q^{88} -7.66687e119 q^{89} -1.38245e120 q^{90} +2.85083e120 q^{91} -1.15164e121 q^{92} +1.21396e121 q^{93} +2.18099e121 q^{94} +2.10197e121 q^{95} +3.47230e122 q^{96} -6.12096e121 q^{97} -3.38590e122 q^{98} +1.30714e122 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	6.28101e18	1.92613	0.963064	−	0.269274i	$-0.0867838\pi$
$2$	6.28101e18	1.92613	0.963064	+	0.269274i	$0.0867838\pi$
$3$	2.54101e29	1.15359	0.576793	−	0.816890i	$-0.304304\pi$
$3$	2.54101e29	1.15359	0.576793	+	0.816890i	$0.304304\pi$
$4$	2.88173e37	2.70997
$5$	−1.37149e43	−1.41429	−0.707145	−	0.707069i	$-0.750017\pi$
$5$	−1.37149e43	−1.41429	−0.707145	+	0.707069i	$0.750017\pi$
$6$	1.59601e48	2.22195
$7$	5.88359e51	0.625335	0.312668	−	0.949863i	$-0.398777\pi$
$7$	5.88359e51	0.625335	0.312668	+	0.949863i	$0.398777\pi$
$8$	1.14211e56	3.29361
$9$	1.60483e58	0.330760
$10$	−8.61436e61	−2.72410
$11$	8.14507e63	0.733238	0.366619	−	0.930371i	$-0.380515\pi$
$11$	8.14507e63	0.733238	0.366619	+	0.930371i	$0.380515\pi$
$12$	7.32252e66	3.12618
$13$	4.84539e68	1.50596	0.752979	−	0.658045i	$-0.228616\pi$
$13$	4.84539e68	1.50596	0.752979	+	0.658045i	$0.228616\pi$
$14$	3.69549e70	1.20447
$15$	−3.48498e72	−1.63150
$16$	4.10920e74	3.63395
$17$	1.33231e75	0.283137	0.141569	−	0.989928i	$-0.454785\pi$
$17$	1.33231e75	0.283137	0.141569	+	0.989928i	$0.454785\pi$
$18$	1.00799e77	0.637086
$19$	−1.53262e78	−0.348407	−0.174204	−	0.984710i	$-0.555735\pi$
$19$	−1.53262e78	−0.348407	−0.174204	+	0.984710i	$0.555735\pi$
$20$	−3.95227e80	−3.83268
$21$	1.49503e81	0.721378
$22$	5.11593e82	1.41231
$23$	−3.99634e83	−0.716805	−0.358402	−	0.933567i	$-0.616678\pi$
$23$	−3.99634e83	−0.716805	−0.358402	+	0.933567i	$0.616678\pi$
$24$	2.90211e85	3.79946
$25$	9.40597e85	1.00021
$26$	3.04340e87	2.90067
$27$	−8.25093e87	−0.772025
$28$	1.69549e89	1.69464
$29$	−8.68148e89	−1.00258	−0.501288	−	0.865281i	$-0.667140\pi$
$29$	−8.68148e89	−1.00258	−0.501288	+	0.865281i	$0.667140\pi$
$30$	−2.18892e91	−3.14248
$31$	4.77746e91	0.912963	0.456481	−	0.889733i	$-0.349110\pi$
$31$	4.77746e91	0.912963	0.456481	+	0.889733i	$0.349110\pi$
$32$	1.36650e93	3.70583
$33$	2.06967e93	0.845853
$34$	8.36826e93	0.545358
$35$	−8.06930e94	−0.884405
$36$	4.62467e95	0.896349
$37$	2.08174e96	0.748206	0.374103	−	0.927387i	$-0.377951\pi$
$37$	2.08174e96	0.748206	0.374103	+	0.927387i	$0.377951\pi$
$38$	−9.62638e96	−0.671076
$39$	1.23122e98	1.73725
$40$	−1.56639e99	−4.65812
$41$	1.76517e99	1.14969	0.574844	−	0.818263i	$-0.305063\pi$
$41$	1.76517e99	1.14969	0.574844	+	0.818263i	$0.305063\pi$
$42$	9.39029e99	1.38947
$43$	9.95937e99	0.346675	0.173337	−	0.984863i	$-0.444545\pi$
$43$	9.95937e99	0.346675	0.173337	+	0.984863i	$0.444545\pi$
$44$	2.34719e101	1.98705
$45$	−2.20101e101	−0.467791
$46$	−2.51011e102	−1.38066
$47$	3.47235e102	0.508869	0.254434	−	0.967090i	$-0.418111\pi$
$47$	3.47235e102	0.508869	0.254434	+	0.967090i	$0.418111\pi$
$48$	1.04415e104	4.19207
$49$	−5.39070e103	−0.608956
$50$	5.90790e104	1.92654
$51$	3.38542e104	0.326623
$52$	1.39631e106	4.08109
$53$	1.95409e106	1.77003	0.885013	−	0.465567i	$-0.154149\pi$
$53$	1.95409e106	1.77003	0.885013	+	0.465567i	$0.154149\pi$
$54$	−5.18242e106	−1.48702
$55$	−1.11709e107	−1.03701
$56$	6.71968e107	2.05961
$57$	−3.89440e107	−0.401917
$58$	−5.45285e108	−1.93109
$59$	7.27867e108	0.900851	0.450426	−	0.892814i	$-0.351272\pi$
$59$	7.27867e108	0.900851	0.450426	+	0.892814i	$0.351272\pi$
$60$	−1.00428e110	−4.42132
$61$	−3.89156e109	−0.619924	−0.309962	−	0.950749i	$-0.600316\pi$
$61$	−3.89156e109	−0.619924	−0.309962	+	0.950749i	$0.600316\pi$
$62$	3.00073e110	1.75848
$63$	9.44213e109	0.206836
$64$	4.21335e111	3.50396
$65$	−6.64542e111	−2.12986
$66$	1.29997e112	1.62922
$67$	−4.59434e111	−0.228362	−0.114181	−	0.993460i	$-0.536424\pi$
$67$	−4.59434e111	−0.228362	−0.114181	+	0.993460i	$0.536424\pi$
$68$	3.83936e112	0.767292
$69$	−1.01548e113	−0.826896
$70$	−5.06834e113	−1.70348
$71$	−8.85659e113	−1.24416	−0.622082	−	0.782952i	$-0.713713\pi$
$71$	−8.85659e113	−1.24416	−0.622082	+	0.782952i	$0.713713\pi$
$72$	1.83288e114	1.08940
$73$	−4.60878e114	−1.17282	−0.586409	−	0.810015i	$-0.699459\pi$
$73$	−4.60878e114	−1.17282	−0.586409	+	0.810015i	$0.699459\pi$
$74$	1.30755e115	1.44114
$75$	2.39007e115	1.15383
$76$	−4.41659e115	−0.944171
$77$	4.79223e115	0.458519
$78$	7.73331e116	3.34617
$79$	−1.49337e116	−0.295190	−0.147595	−	0.989048i	$-0.547153\pi$
$79$	−1.49337e116	−0.295190	−0.147595	+	0.989048i	$0.547153\pi$
$80$	−5.63574e117	−5.13945
$81$	−2.87522e117	−1.22136
$82$	1.10871e118	2.21444
$83$	−5.33938e116	−0.0506044	−0.0253022	−	0.999680i	$-0.508055\pi$
$83$	−5.33938e116	−0.0506044	−0.0253022	+	0.999680i	$0.508055\pi$
$84$	4.30827e118	1.95491
$85$	−1.82725e118	−0.400438
$86$	6.25550e118	0.667739
$87$	−2.20598e119	−1.15656
$88$	9.30254e119	2.41500
$89$	−7.66687e119	−0.993419	−0.496710	−	0.867917i	$-0.665459\pi$
$89$	−7.66687e119	−0.993419	−0.496710	+	0.867917i	$0.665459\pi$
$90$	−1.38245e120	−0.901025
$91$	2.85083e120	0.941728
$92$	−1.15164e121	−1.94252
$93$	1.21396e121	1.05318
$94$	2.18099e121	0.980146
$95$	2.10197e121	0.492748
$96$	3.47230e122	4.27500
$97$	−6.12096e121	−0.398436	−0.199218	−	0.979955i	$-0.563840\pi$
$97$	−6.12096e121	−0.398436	−0.199218	+	0.979955i	$0.563840\pi$
$98$	−3.38590e122	−1.17293
$99$	1.30714e122	0.242526
$100$	2.71055e123	2.71055
$101$	−2.99821e123	−1.62592	−0.812958	−	0.582323i	$-0.802144\pi$
$101$	−2.99821e123	−1.62592	−0.812958	+	0.582323i	$0.802144\pi$
$102$	2.12639e123	0.629117
$103$	−4.95195e123	−0.804056	−0.402028	−	0.915627i	$-0.631695\pi$
$103$	−4.95195e123	−0.804056	−0.402028	+	0.915627i	$0.631695\pi$
$104$	5.53395e124	4.96004
$105$	−2.05042e124	−1.02024
$106$	1.22737e125	3.40929
$107$	7.36966e124	1.14907	0.574533	−	0.818482i	$-0.305184\pi$
$107$	7.36966e124	1.14907	0.574533	+	0.818482i	$0.305184\pi$
$108$	−2.37770e125	−2.09216
$109$	1.50132e124	0.0749454	0.0374727	−	0.999298i	$-0.488069\pi$
$109$	1.50132e124	0.0749454	0.0374727	+	0.999298i	$0.488069\pi$
$110$	−7.01646e125	−1.99741
$111$	5.28974e125	0.863120
$112$	2.41769e126	2.27243
$113$	−2.80875e126	−1.52823	−0.764116	−	0.645079i	$-0.776824\pi$
$113$	−2.80875e126	−1.52823	−0.764116	+	0.645079i	$0.776824\pi$
$114$	−2.44608e126	−0.774144
$115$	5.48096e126	1.01377
$116$	−2.50177e127	−2.71694
$117$	7.77601e126	0.498111
$118$	4.57174e127	1.73515
$119$	7.83877e126	0.177056
$120$	−3.98022e128	−5.37354
$121$	−5.70535e127	−0.462362
$122$	−2.44429e128	−1.19405
$123$	4.48533e128	1.32626
$124$	1.37674e129	2.47410
$125$	−2.76533e125	−0.000303237 0
$126$	5.93061e128	0.398393
$127$	−2.47206e129	−1.02125	−0.510624	−	0.859804i	$-0.670585\pi$
$127$	−2.47206e129	−1.02125	−0.510624	+	0.859804i	$0.670585\pi$
$128$	1.19330e130	3.04324
$129$	2.53069e129	0.399919
$130$	−4.17400e130	−4.10238
$131$	2.52715e130	1.55041	0.775205	−	0.631710i	$-0.217647\pi$
$131$	2.52715e130	1.55041	0.775205	+	0.631710i	$0.217647\pi$
$132$	5.96424e130	2.29223
$133$	−9.01728e129	−0.217871
$134$	−2.88571e130	−0.439854
$135$	1.13161e131	1.09187
$136$	1.52164e131	0.932544
$137$	1.16265e131	0.454082	0.227041	−	0.973885i	$-0.427095\pi$
$137$	1.16265e131	0.454082	0.227041	+	0.973885i	$0.427095\pi$
$138$	−6.37822e131	−1.59271
$139$	−5.92575e131	−0.949147	−0.474573	−	0.880216i	$-0.657398\pi$
$139$	−5.92575e131	−0.949147	−0.474573	+	0.880216i	$0.657398\pi$
$140$	−2.32535e132	−2.39671
$141$	8.82330e131	0.587024
$142$	−5.56283e132	−2.39642
$143$	3.94661e132	1.10423
$144$	6.59455e132	1.20197
$145$	1.19066e133	1.41793
$146$	−2.89478e133	−2.25899
$147$	−1.36978e133	−0.702483
$148$	5.99902e133	2.02761
$149$	3.11804e133	0.696507	0.348254	−	0.937400i	$-0.386775\pi$
$149$	3.11804e133	0.696507	0.348254	+	0.937400i	$0.386775\pi$
$150$	1.50121e134	2.22243
$151$	−1.85976e134	−1.82968	−0.914841	−	0.403815i	$-0.867684\pi$
$151$	−1.85976e134	−1.82968	−0.914841	+	0.403815i	$0.867684\pi$
$152$	−1.75041e134	−1.14752
$153$	2.13813e133	0.0936505
$154$	3.01000e134	0.883167
$155$	−6.55225e134	−1.29119
$156$	3.54805e135	4.70789
$157$	−1.12098e135	−1.00408	−0.502040	−	0.864844i	$-0.667417\pi$
$157$	−1.12098e135	−1.00408	−0.502040	+	0.864844i	$0.667417\pi$
$158$	−9.37990e134	−0.568574
$159$	4.96538e135	2.04188
$160$	−1.87414e136	−5.24112
$161$	−2.35128e135	−0.448243
$162$	−1.80593e136	−2.35249
$163$	7.99504e135	0.713318	0.356659	−	0.934235i	$-0.383916\pi$
$163$	7.99504e135	0.713318	0.356659	+	0.934235i	$0.383916\pi$
$164$	5.08675e136	3.11561
$165$	−2.83854e136	−1.19628
$166$	−3.35367e135	−0.0974705
$167$	−5.38464e136	−1.08167	−0.540834	−	0.841129i	$-0.681891\pi$
$167$	−5.38464e136	−1.08167	−0.540834	+	0.841129i	$0.681891\pi$
$168$	1.70748e137	2.37594
$169$	1.31256e137	1.26791
$170$	−1.14770e137	−0.771294
$171$	−2.45958e136	−0.115239
$172$	2.87002e137	0.939476
$173$	−1.97221e137	−0.451978	−0.225989	−	0.974130i	$-0.572561\pi$
$173$	−1.97221e137	−0.451978	−0.225989	+	0.974130i	$0.572561\pi$
$174$	−1.38558e138	−2.22767
$175$	5.53409e137	0.625469
$176$	3.34698e138	2.66455
$177$	1.84952e138	1.03921
$178$	−4.81557e138	−1.91345
$179$	1.49290e138	0.420311	0.210155	−	0.977668i	$-0.432603\pi$
$179$	1.49290e138	0.420311	0.210155	+	0.977668i	$0.432603\pi$
$180$	−6.34270e138	−1.26770
$181$	−1.11952e139	−1.59147	−0.795734	−	0.605646i	$-0.792915\pi$
$181$	−1.11952e139	−1.59147	−0.795734	+	0.605646i	$0.792915\pi$
$182$	1.79061e139	1.81389
$183$	−9.88851e138	−0.715136
$184$	−4.56425e139	−2.36088
$185$	−2.85510e139	−1.05818
$186$	7.62490e139	2.02856
$187$	1.08518e139	0.207607
$188$	1.00064e140	1.37902
$189$	−4.85451e139	−0.482775
$190$	1.32025e140	0.949096
$191$	−1.42810e140	−0.743374	−0.371687	−	0.928358i	$-0.621221\pi$
$191$	−1.42810e140	−0.743374	−0.371687	+	0.928358i	$0.621221\pi$
$192$	1.07062e141	4.04212
$193$	−1.24842e140	−0.342441	−0.171220	−	0.985233i	$-0.554771\pi$
$193$	−1.24842e140	−0.342441	−0.171220	+	0.985233i	$0.554771\pi$
$194$	−3.84458e140	−0.767437
$195$	−1.68861e141	−2.45698
$196$	−1.55345e141	−1.65025
$197$	−9.52451e139	−0.0739894	−0.0369947	−	0.999315i	$-0.511778\pi$
$197$	−9.52451e139	−0.0739894	−0.0369947	+	0.999315i	$0.511778\pi$
$198$	8.21018e140	0.467136
$199$	1.44330e141	0.602410	0.301205	−	0.953559i	$-0.402611\pi$
$199$	1.44330e141	0.602410	0.301205	+	0.953559i	$0.402611\pi$
$200$	1.07426e142	3.29432
$201$	−1.16743e141	−0.263435
$202$	−1.88318e142	−3.13172
$203$	−5.10783e141	−0.626945
$204$	9.75587e141	0.885137
$205$	−2.42092e142	−1.62599
$206$	−3.11032e142	−1.54871
$207$	−6.41343e141	−0.237091
$208$	1.99107e143	5.47257
$209$	−1.24833e142	−0.255465
$210$	−1.28787e143	−1.96511
$211$	−1.48002e143	−1.68615	−0.843074	−	0.537798i	$-0.819256\pi$
$211$	−1.48002e143	−1.68615	−0.843074	+	0.537798i	$0.819256\pi$
$212$	5.63117e143	4.79671
$213$	−2.25047e143	−1.43525
$214$	4.62889e143	2.21325
$215$	−1.36592e143	−0.490298
$216$	−9.42344e143	−2.54275
$217$	2.81086e143	0.570908
$218$	9.42983e142	0.144354
$219$	−1.17110e144	−1.35295
$220$	−3.21915e144	−2.81026
$221$	6.45557e143	0.426393
$222$	3.32249e144	1.66248
$223$	−1.06177e144	−0.402977	−0.201488	−	0.979491i	$-0.564578\pi$
$223$	−1.06177e144	−0.402977	−0.201488	+	0.979491i	$0.564578\pi$
$224$	8.03992e144	2.31739
$225$	1.50949e144	0.330831
$226$	−1.76418e145	−2.94357
$227$	1.13737e145	1.44648	0.723240	−	0.690596i	$-0.242652\pi$
$227$	1.13737e145	1.44648	0.723240	+	0.690596i	$0.242652\pi$
$228$	−1.12226e145	−1.08918
$229$	1.26033e145	0.934551	0.467276	−	0.884112i	$-0.345236\pi$
$229$	1.26033e145	0.934551	0.467276	+	0.884112i	$0.345236\pi$
$230$	3.44260e145	1.95265
$231$	1.21771e145	0.528942
$232$	−9.91517e145	−3.30209
$233$	2.92097e145	0.746687	0.373343	−	0.927693i	$-0.378211\pi$
$233$	2.92097e145	0.746687	0.373343	+	0.927693i	$0.378211\pi$
$234$	4.88412e145	0.959425
$235$	−4.76231e145	−0.719687
$236$	2.09751e146	2.44128
$237$	−3.79468e145	−0.340528
$238$	4.92354e145	0.341032
$239$	3.35714e146	1.79680	0.898399	−	0.439181i	$-0.144731\pi$
$239$	3.35714e146	1.79680	0.898399	+	0.439181i	$0.144731\pi$
$240$	−1.43205e147	−5.92880
$241$	3.58620e146	1.14971	0.574853	−	0.818257i	$-0.305059\pi$
$241$	3.58620e146	1.14971	0.574853	+	0.818257i	$0.305059\pi$
$242$	−3.58354e146	−0.890568
$243$	−3.30269e146	−0.636916
$244$	−1.12144e147	−1.67997
$245$	7.39330e146	0.861240
$246$	2.81724e147	2.55455
$247$	−7.42613e146	−0.524686
$248$	5.45637e147	3.00694
$249$	−1.35674e146	−0.0583765
$250$	−1.73691e144	−0.000584072 0
$251$	−3.07016e147	−0.807657	−0.403828	−	0.914835i	$-0.632321\pi$
$251$	−3.07016e147	−0.807657	−0.403828	+	0.914835i	$0.632321\pi$
$252$	2.72097e147	0.560519
$253$	−3.25505e147	−0.525588
$254$	−1.55271e148	−1.96705
$255$	−4.64308e147	−0.461940
$256$	3.01472e148	2.35770
$257$	4.68022e147	0.287991	0.143996	−	0.989578i	$-0.454005\pi$
$257$	4.68022e147	0.287991	0.143996	+	0.989578i	$0.454005\pi$
$258$	1.58953e148	0.770295
$259$	1.22481e148	0.467879
$260$	−1.91503e149	−5.77185
$261$	−1.39323e148	−0.331612
$262$	1.58731e149	2.98629
$263$	2.13714e148	0.318093	0.159046	−	0.987271i	$-0.449158\pi$
$263$	2.13714e148	0.318093	0.159046	+	0.987271i	$0.449158\pi$
$264$	2.36379e149	2.78591
$265$	−2.68003e149	−2.50333
$266$	−5.66377e148	−0.419648
$267$	−1.94816e149	−1.14599
$268$	−1.32397e149	−0.618852
$269$	−1.03121e149	−0.383338	−0.191669	−	0.981460i	$-0.561390\pi$
$269$	−1.03121e149	−0.383338	−0.191669	+	0.981460i	$0.561390\pi$
$270$	7.10765e149	2.10308
$271$	6.28280e148	0.148095	0.0740477	−	0.997255i	$-0.476408\pi$
$271$	6.28280e148	0.148095	0.0740477	+	0.997255i	$0.476408\pi$
$272$	5.47474e149	1.02891
$273$	7.24400e149	1.08636
$274$	7.30262e149	0.874620
$275$	7.66123e149	0.733395
$276$	−2.92633e150	−2.24086
$277$	1.64545e150	1.00874	0.504370	−	0.863488i	$-0.331725\pi$
$277$	1.64545e150	1.00874	0.504370	+	0.863488i	$0.331725\pi$
$278$	−3.72197e150	−1.82818
$279$	7.66699e149	0.301972
$280$	−9.21600e150	−2.91289
$281$	2.20237e150	0.559051	0.279525	−	0.960138i	$-0.409823\pi$
$281$	2.20237e150	0.559051	0.279525	+	0.960138i	$0.409823\pi$
$282$	5.54193e150	1.13068
$283$	2.33563e150	0.383299	0.191650	−	0.981463i	$-0.438616\pi$
$283$	2.33563e150	0.383299	0.191650	+	0.981463i	$0.438616\pi$
$284$	−2.55223e151	−3.37164
$285$	5.34114e150	0.568428
$286$	2.47887e151	2.12688
$287$	1.03855e151	0.718940
$288$	2.19299e151	1.22574
$289$	−2.03670e151	−0.919833
$290$	7.47854e151	2.73112
$291$	−1.55535e151	−0.459630
$292$	−1.32813e152	−3.17829
$293$	7.30840e151	1.41731	0.708653	−	0.705557i	$-0.249303\pi$
$293$	7.30840e151	1.41731	0.708653	+	0.705557i	$0.249303\pi$
$294$	−8.60363e151	−1.35307
$295$	−9.98264e151	−1.27406
$296$	2.37757e152	2.46430
$297$	−6.72045e151	−0.566078
$298$	1.95844e152	1.34156
$299$	−1.93639e152	−1.07948
$300$	6.88754e152	3.12685
$301$	5.85969e151	0.216788
$302$	−1.16812e153	−3.52420
$303$	−7.61850e152	−1.87563
$304$	−6.29783e152	−1.26609
$305$	5.33724e152	0.876752
$306$	1.34296e152	0.180383
$307$	1.34558e153	1.47877	0.739385	−	0.673283i	$-0.235116\pi$
$307$	1.34558e153	1.47877	0.739385	+	0.673283i	$0.235116\pi$
$308$	1.38099e153	1.24257
$309$	−1.25830e153	−0.927548
$310$	−4.11548e153	−2.48700
$311$	−1.55991e153	−0.773279	−0.386639	−	0.922231i	$-0.626364\pi$
$311$	−1.55991e153	−0.773279	−0.386639	+	0.922231i	$0.626364\pi$
$312$	1.40619e154	5.72183
$313$	3.32039e153	1.10972	0.554858	−	0.831945i	$-0.312773\pi$
$313$	3.32039e153	1.10972	0.554858	+	0.831945i	$0.312773\pi$
$314$	−7.04087e153	−1.93399
$315$	−1.29498e153	−0.292526
$316$	−4.30350e153	−0.799956
$317$	4.80548e152	0.0735516	0.0367758	−	0.999324i	$-0.488291\pi$
$317$	4.80548e152	0.0735516	0.0367758	+	0.999324i	$0.488291\pi$
$318$	3.11876e154	3.93291
$319$	−7.07113e153	−0.735126
$320$	−5.77858e154	−4.95561
$321$	1.87264e154	1.32555
$322$	−1.47684e154	−0.863373
$323$	−2.04192e153	−0.0986470
$324$	−8.28562e154	−3.30984
$325$	4.55756e154	1.50628
$326$	5.02170e154	1.37394
$327$	3.81489e153	0.0864559
$328$	2.01601e155	3.78662
$329$	2.04299e154	0.318213
$330$	−1.78289e155	−2.30419
$331$	−5.06406e154	−0.543347	−0.271673	−	0.962389i	$-0.587577\pi$
$331$	−5.06406e154	−0.543347	−0.271673	+	0.962389i	$0.587577\pi$
$332$	−1.53866e154	−0.137136
$333$	3.34083e154	0.247477
$334$	−3.38210e155	−2.08343
$335$	6.30111e154	0.322969
$336$	6.14337e155	2.62145
$337$	−6.39224e154	−0.227203	−0.113602	−	0.993526i	$-0.536239\pi$
$337$	−6.39224e154	−0.227203	−0.113602	+	0.993526i	$0.536239\pi$
$338$	8.24423e155	2.44215
$339$	−7.13708e155	−1.76295
$340$	−5.26565e155	−1.08517
$341$	3.89128e155	0.669419
$342$	−1.54487e155	−0.221965
$343$	−8.38003e155	−1.00614
$344$	1.13747e156	1.14181
$345$	1.39272e156	1.16947
$346$	−1.23875e156	−0.870567
$347$	−1.52957e156	−0.900134	−0.450067	−	0.892995i	$-0.648600\pi$
$347$	−1.52957e156	−0.900134	−0.450067	+	0.892995i	$0.648600\pi$
$348$	−6.35703e156	−3.13423
$349$	−2.71035e156	−1.12011	−0.560055	−	0.828455i	$-0.689220\pi$
$349$	−2.71035e156	−1.12011	−0.560055	+	0.828455i	$0.689220\pi$
$350$	3.47597e156	1.20473
$351$	−3.99790e156	−1.16264
$352$	1.11302e157	2.71726
$353$	4.72646e156	0.969152	0.484576	−	0.874749i	$-0.338974\pi$
$353$	4.72646e156	0.969152	0.484576	+	0.874749i	$0.338974\pi$
$354$	1.16169e157	2.00165
$355$	1.21467e157	1.75961
$356$	−2.20938e157	−2.69213
$357$	1.99184e156	0.204249
$358$	9.37694e156	0.809571
$359$	2.28300e157	1.66034	0.830170	−	0.557511i	$-0.188243\pi$
$359$	2.28300e157	1.66034	0.830170	+	0.557511i	$0.188243\pi$
$360$	−2.51378e157	−1.54072
$361$	−1.70016e157	−0.878613
$362$	−7.03169e157	−3.06537
$363$	−1.44974e157	−0.533374
$364$	8.21532e157	2.55205
$365$	6.32091e157	1.65870
$366$	−6.21098e157	−1.37744
$367$	4.65561e157	0.872999	0.436500	−	0.899704i	$-0.356218\pi$
$367$	4.65561e157	0.872999	0.436500	+	0.899704i	$0.356218\pi$
$368$	−1.64218e158	−2.60483
$369$	2.83279e157	0.380271
$370$	−1.79329e158	−2.03819
$371$	1.14971e158	1.10686
$372$	3.49830e158	2.85408
$373$	−1.44513e158	−0.999573	−0.499787	−	0.866149i	$-0.666588\pi$
$373$	−1.44513e158	−0.999573	−0.499787	+	0.866149i	$0.666588\pi$
$374$	6.81601e157	0.399877
$375$	−7.02675e154	−0.000349809 0
$376$	3.96580e158	1.67602
$377$	−4.20652e158	−1.50984
$378$	−3.04912e158	−0.929885
$379$	−1.05040e158	−0.272297	−0.136148	−	0.990688i	$-0.543472\pi$
$379$	−1.05040e158	−0.272297	−0.136148	+	0.990688i	$0.543472\pi$
$380$	6.05732e158	1.33533
$381$	−6.28155e158	−1.17810
$382$	−8.96993e158	−1.43183
$383$	1.44066e159	1.95810	0.979051	−	0.203614i	$-0.0652687\pi$
$383$	1.44066e159	1.95810	0.979051	+	0.203614i	$0.0652687\pi$
$384$	3.03219e159	3.51063
$385$	−6.57250e158	−0.648479
$386$	−7.84132e158	−0.659584
$387$	1.59831e158	0.114666
$388$	−1.76390e159	−1.07975
$389$	3.37385e159	1.76289	0.881445	−	0.472287i	$-0.156571\pi$
$389$	3.37385e159	1.76289	0.881445	+	0.472287i	$0.156571\pi$
$390$	−1.06062e160	−4.73245
$391$	−5.32437e158	−0.202954
$392$	−6.15675e159	−2.00566
$393$	6.42153e159	1.78853
$394$	−5.98235e158	−0.142513
$395$	2.04815e159	0.417485
$396$	3.76683e159	0.657237
$397$	1.25864e159	0.188056	0.0940278	−	0.995570i	$-0.470026\pi$
$397$	1.25864e159	0.188056	0.0940278	+	0.995570i	$0.470026\pi$
$398$	9.06539e159	1.16032
$399$	−2.29130e159	−0.251333
$400$	3.86510e160	3.63473
$401$	−1.07576e160	−0.867636	−0.433818	−	0.901001i	$-0.642834\pi$
$401$	−1.07576e160	−0.867636	−0.433818	+	0.901001i	$0.642834\pi$
$402$	−7.33264e159	−0.507409
$403$	2.31487e160	1.37488
$404$	−8.64004e160	−4.40617
$405$	3.94335e160	1.72735
$406$	−3.20823e160	−1.20758
$407$	1.69560e160	0.548613
$408$	3.86651e160	1.07577
$409$	4.90300e160	1.17349	0.586743	−	0.809773i	$-0.300410\pi$
$409$	4.90300e160	1.17349	0.586743	+	0.809773i	$0.300410\pi$
$410$	−1.52058e161	−3.13187
$411$	2.95431e160	0.523823
$412$	−1.42702e161	−2.17897
$413$	4.28247e160	0.563334
$414$	−4.02829e160	−0.456667
$415$	7.32292e159	0.0715692
$416$	6.62123e161	5.58083
$417$	−1.50574e161	−1.09492
$418$	−7.84076e160	−0.492059
$419$	−2.31678e161	−1.25523	−0.627614	−	0.778525i	$-0.715968\pi$
$419$	−2.31678e161	−1.25523	−0.627614	+	0.778525i	$0.715968\pi$
$420$	−5.90876e161	−2.76481
$421$	4.28614e161	1.73268	0.866338	−	0.499458i	$-0.166467\pi$
$421$	4.28614e161	1.73268	0.866338	+	0.499458i	$0.166467\pi$
$422$	−9.29600e161	−3.24773
$423$	5.57252e160	0.168314
$424$	2.23178e162	5.82978
$425$	1.25317e161	0.283198
$426$	−1.41352e162	−2.76448
$427$	−2.28963e161	−0.387661
$428$	2.12374e162	3.11393
$429$	1.00284e162	1.27382
$430$	−8.57937e161	−0.944377
$431$	−8.28865e161	−0.790919	−0.395459	−	0.918484i	$-0.629415\pi$
$431$	−8.28865e161	−0.790919	−0.395459	+	0.918484i	$0.629415\pi$
$432$	−3.39048e162	−2.80550
$433$	−1.16374e162	−0.835317	−0.417659	−	0.908604i	$-0.637149\pi$
$433$	−1.16374e162	−0.835317	−0.417659	+	0.908604i	$0.637149\pi$
$434$	1.76551e162	1.09964
$435$	3.02548e162	1.63571
$436$	4.32641e161	0.203099
$437$	6.12486e161	0.249740
$438$	−7.35568e162	−2.60594
$439$	3.31889e162	1.02194	0.510969	−	0.859599i	$-0.329287\pi$
$439$	3.31889e162	1.02194	0.510969	+	0.859599i	$0.329287\pi$
$440$	−1.27584e163	−3.41551
$441$	−8.65112e161	−0.201418
$442$	4.05475e162	0.821286
$443$	−3.49498e161	−0.0616049	−0.0308025	−	0.999525i	$-0.509806\pi$
$443$	−3.49498e161	−0.0616049	−0.0308025	+	0.999525i	$0.509806\pi$
$444$	1.52436e163	2.33902
$445$	1.05151e163	1.40498
$446$	−6.66897e162	−0.776184
$447$	7.92297e162	0.803481
$448$	2.47896e163	2.19115
$449$	−2.04381e161	−0.0157503	−0.00787516	−	0.999969i	$-0.502507\pi$
$449$	−2.04381e161	−0.0157503	−0.00787516	+	0.999969i	$0.502507\pi$
$450$	9.48115e162	0.637223
$451$	1.43775e163	0.842995
$452$	−8.09407e163	−4.14146
$453$	−4.72569e163	−2.11069
$454$	7.14385e163	2.78611
$455$	−3.90989e163	−1.33188
$456$	−4.44782e163	−1.32376
$457$	−6.52078e163	−1.69611	−0.848053	−	0.529911i	$-0.822225\pi$
$457$	−6.52078e163	−1.69611	−0.848053	+	0.529911i	$0.822225\pi$
$458$	7.91617e163	1.80006
$459$	−1.09928e163	−0.218589
$460$	1.57946e164	2.74728
$461$	7.02362e163	1.06894	0.534471	−	0.845187i	$-0.320511\pi$
$461$	7.02362e163	1.06894	0.534471	+	0.845187i	$0.320511\pi$
$462$	7.64846e163	1.01881
$463$	−9.80416e163	−1.14335	−0.571676	−	0.820480i	$-0.693706\pi$
$463$	−9.80416e163	−1.14335	−0.571676	+	0.820480i	$0.693706\pi$
$464$	−3.56740e164	−3.64331
$465$	−1.66494e164	−1.48950
$466$	1.83467e164	1.43821
$467$	1.28189e164	0.880771	0.440385	−	0.897809i	$-0.354842\pi$
$467$	1.28189e164	0.880771	0.440385	+	0.897809i	$0.354842\pi$
$468$	2.24083e164	1.34986
$469$	−2.70312e163	−0.142803
$470$	−2.99121e164	−1.38621
$471$	−2.84842e164	−1.15829
$472$	8.31301e164	2.96705
$473$	8.11198e163	0.254195
$474$	−2.38345e164	−0.655899
$475$	−1.44157e164	−0.348482
$476$	2.25892e164	0.479815
$477$	3.13598e164	0.585454
$478$	2.10863e165	3.46086
$479$	−1.44775e164	−0.208958	−0.104479	−	0.994527i	$-0.533317\pi$
$479$	−1.44775e164	−0.208958	−0.104479	+	0.994527i	$0.533317\pi$
$480$	−4.76223e165	−6.04608
$481$	1.00869e165	1.12677
$482$	2.25250e165	2.21448
$483$	−5.97465e164	−0.517087
$484$	−1.64413e165	−1.25299
$485$	8.39486e164	0.563503
$486$	−2.07442e165	−1.22678
$487$	−2.77538e165	−1.44641	−0.723204	−	0.690634i	$-0.757332\pi$
$487$	−2.77538e165	−1.44641	−0.723204	+	0.690634i	$0.757332\pi$
$488$	−4.44457e165	−2.04179
$489$	2.03155e165	0.822874
$490$	4.64374e165	1.65886
$491$	−1.79530e165	−0.565750	−0.282875	−	0.959157i	$-0.591288\pi$
$491$	−1.79530e165	−0.565750	−0.282875	+	0.959157i	$0.591288\pi$
$492$	1.29255e166	3.59413
$493$	−1.15664e165	−0.283866
$494$	−4.66436e165	−1.01061
$495$	−1.79274e165	−0.343002
$496$	1.96316e166	3.31766
$497$	−5.21085e165	−0.778020
$498$	−8.52173e164	−0.112441
$499$	1.54068e165	0.179692	0.0898462	−	0.995956i	$-0.471362\pi$
$499$	1.54068e165	0.179692	0.0898462	+	0.995956i	$0.471362\pi$
$500$	−7.96894e162	−0.000821761 0
$501$	−1.36825e166	−1.24780
$502$	−1.92837e166	−1.55565
$503$	−1.19018e166	−0.849534	−0.424767	−	0.905303i	$-0.639644\pi$
$503$	−1.19018e166	−0.849534	−0.424767	+	0.905303i	$0.639644\pi$
$504$	1.07839e166	0.681237
$505$	4.11203e166	2.29952
$506$	−2.04450e166	−1.01235
$507$	3.33524e166	1.46264
$508$	−7.12382e166	−2.76754
$509$	−9.70577e165	−0.334108	−0.167054	−	0.985948i	$-0.553425\pi$
$509$	−9.70577e165	−0.334108	−0.167054	+	0.985948i	$0.553425\pi$
$510$	−2.91632e166	−0.889754
$511$	−2.71162e166	−0.733404
$512$	6.24616e166	1.49800
$513$	1.26455e166	0.268979
$514$	2.93965e166	0.554708
$515$	6.79156e166	1.13717
$516$	7.29277e166	1.08377
$517$	2.82826e166	0.373122
$518$	7.69306e166	0.901195
$519$	−5.01141e166	−0.521396
$520$	−7.58978e167	−7.01493
$521$	1.48625e167	1.22060	0.610298	−	0.792172i	$-0.291050\pi$
$521$	1.48625e167	1.22060	0.610298	+	0.792172i	$0.291050\pi$
$522$	−8.75087e166	−0.638727
$523$	8.56212e166	0.555555	0.277778	−	0.960645i	$-0.410402\pi$
$523$	8.56212e166	0.555555	0.277778	+	0.960645i	$0.410402\pi$
$524$	7.28257e167	4.20156
$525$	1.40622e167	0.721532
$526$	1.34234e167	0.612687
$527$	6.36506e166	0.258494
$528$	8.50471e167	3.07378
$529$	−1.51123e167	−0.486191
$530$	−1.68333e168	−4.82173
$531$	1.16810e167	0.297966
$532$	−2.59854e167	−0.590423
$533$	8.55295e167	1.73138
$534$	−1.22364e168	−2.20733
$535$	−1.01074e168	−1.62511
$536$	−5.24723e167	−0.752134
$537$	3.79349e167	0.484864
$538$	−6.47704e167	−0.738357
$539$	−4.39076e167	−0.446510
$540$	3.26099e168	2.95892
$541$	1.51271e168	1.22496	0.612482	−	0.790484i	$-0.290171\pi$
$541$	1.51271e168	1.22496	0.612482	+	0.790484i	$0.290171\pi$
$542$	3.94623e167	0.285251
$543$	−2.84471e168	−1.83589
$544$	1.82060e168	1.04926
$545$	−2.05905e167	−0.105994
$546$	4.54996e168	2.09248
$547$	−4.51991e168	−1.85742	−0.928708	−	0.370811i	$-0.879080\pi$
$547$	−4.51991e168	−1.85742	−0.928708	+	0.370811i	$0.879080\pi$
$548$	3.35044e168	1.23055
$549$	−6.24527e167	−0.205046
$550$	4.81203e168	1.41261
$551$	1.33054e168	0.349304
$552$	−1.15978e169	−2.72347
$553$	−8.78639e167	−0.184593
$554$	1.03351e169	1.94296
$555$	−7.25484e168	−1.22070
$556$	−1.70764e169	−2.57215
$557$	8.96432e168	1.20899	0.604495	−	0.796609i	$-0.293375\pi$
$557$	8.96432e168	1.20899	0.604495	+	0.796609i	$0.293375\pi$
$558$	4.81565e168	0.581636
$559$	4.82571e168	0.522077
$560$	−3.31584e169	−3.21388
$561$	2.75745e168	0.239492
$562$	1.38331e169	1.07680
$563$	−1.98115e168	−0.138246	−0.0691229	−	0.997608i	$-0.522020\pi$
$563$	−1.98115e168	−0.138246	−0.0691229	+	0.997608i	$0.522020\pi$
$564$	2.54264e169	1.59081
$565$	3.85218e169	2.16136
$566$	1.46701e169	0.738283
$567$	−1.69166e169	−0.763758
$568$	−1.01152e170	−4.09779
$569$	−1.76449e169	−0.641527	−0.320764	−	0.947159i	$-0.603939\pi$
$569$	−1.76449e169	−0.641527	−0.320764	+	0.947159i	$0.603939\pi$
$570$	3.35478e169	1.09486
$571$	−3.50039e169	−1.02564	−0.512821	−	0.858496i	$-0.671399\pi$
$571$	−3.50039e169	−1.02564	−0.512821	+	0.858496i	$0.671399\pi$
$572$	1.13731e170	2.99241
$573$	−3.62883e169	−0.857546
$574$	6.52317e169	1.38477
$575$	−3.75895e169	−0.716958
$576$	6.76169e169	1.15897
$577$	−2.00413e169	−0.308754	−0.154377	−	0.988012i	$-0.549337\pi$
$577$	−2.00413e169	−0.308754	−0.154377	+	0.988012i	$0.549337\pi$
$578$	−1.27925e170	−1.77172
$579$	−3.17225e169	−0.395035
$580$	3.43116e170	3.84254
$581$	−3.14147e168	−0.0316447
$582$	−9.76914e169	−0.885305
$583$	1.59162e170	1.29785
$584$	−5.26372e170	−3.86280
$585$	−1.06647e170	−0.704473
$586$	4.59041e170	2.72991
$587$	−7.26482e169	−0.389028	−0.194514	−	0.980900i	$-0.562313\pi$
$587$	−7.26482e169	−0.389028	−0.194514	+	0.980900i	$0.562313\pi$
$588$	−3.94735e170	−1.90370
$589$	−7.32202e169	−0.318083
$590$	−6.27011e170	−2.45401
$591$	−2.42019e169	−0.0853531
$592$	8.55430e170	2.71894
$593$	−2.02317e169	−0.0579655	−0.0289827	−	0.999580i	$-0.509227\pi$
$593$	−2.02317e169	−0.0579655	−0.0289827	+	0.999580i	$0.509227\pi$
$594$	−4.22112e170	−1.09034
$595$	−1.07508e170	−0.250408
$596$	8.98534e170	1.88751
$597$	3.66745e170	0.694932
$598$	−1.21625e171	−2.07921
$599$	1.01373e171	1.56377	0.781885	−	0.623423i	$-0.214258\pi$
$599$	1.01373e171	1.56377	0.781885	+	0.623423i	$0.214258\pi$
$600$	2.72971e171	3.80028
$601$	1.48099e171	1.86111	0.930556	−	0.366150i	$-0.119324\pi$
$601$	1.48099e171	1.86111	0.930556	+	0.366150i	$0.119324\pi$
$602$	3.68048e170	0.417561
$603$	−7.37312e169	−0.0755330
$604$	−5.35934e171	−4.95837
$605$	7.82485e170	0.653914
$606$	−4.78519e171	−3.61271
$607$	1.89753e171	1.29444	0.647222	−	0.762301i	$-0.275931\pi$
$607$	1.89753e171	1.29444	0.647222	+	0.762301i	$0.275931\pi$
$608$	−2.09432e171	−1.29114
$609$	−1.29791e171	−0.723235
$610$	3.35233e171	1.68874
$611$	1.68249e171	0.766335
$612$	6.16150e170	0.253790
$613$	−2.22210e171	−0.827835	−0.413918	−	0.910314i	$-0.635840\pi$
$613$	−2.22210e171	−0.827835	−0.413918	+	0.910314i	$0.635840\pi$
$614$	8.45163e171	2.84830
$615$	−6.15159e171	−1.87572
$616$	5.47323e171	1.51018
$617$	2.23984e171	0.559344	0.279672	−	0.960096i	$-0.409774\pi$
$617$	2.23984e171	0.559344	0.279672	+	0.960096i	$0.409774\pi$
$618$	−7.90337e171	−1.78658
$619$	3.00498e171	0.614989	0.307494	−	0.951550i	$-0.400510\pi$
$619$	3.00498e171	0.614989	0.307494	+	0.951550i	$0.400510\pi$
$620$	−1.88818e172	−3.49909
$621$	3.29736e171	0.553392
$622$	−9.79782e171	−1.48943
$623$	−4.51087e171	−0.621220
$624$	5.05934e172	6.31308
$625$	−8.84154e171	−0.999786
$626$	2.08554e172	2.13745
$627$	−3.17202e171	−0.294701
$628$	−3.23035e172	−2.72102
$629$	2.77353e171	0.211845
$630$	−8.13380e171	−0.563442
$631$	2.00990e172	1.26290	0.631451	−	0.775416i	$-0.282460\pi$
$631$	2.00990e172	1.26290	0.631451	+	0.775416i	$0.282460\pi$
$632$	−1.70559e172	−0.972242
$633$	−3.76074e172	−1.94512
$634$	3.01833e171	0.141670
$635$	3.39042e172	1.44434
$636$	1.43089e173	5.53341
$637$	−2.61200e172	−0.917062
$638$	−4.44139e172	−1.41595
$639$	−1.42133e172	−0.411520
$640$	−1.63660e173	−4.30402
$641$	−6.88225e172	−1.64423	−0.822114	−	0.569324i	$-0.807205\pi$
$641$	−6.88225e172	−1.64423	−0.822114	+	0.569324i	$0.807205\pi$
$642$	1.17621e173	2.55317
$643$	3.66503e172	0.722941	0.361470	−	0.932384i	$-0.382275\pi$
$643$	3.66503e172	0.722941	0.361470	+	0.932384i	$0.382275\pi$
$644$	−6.77576e172	−1.21472
$645$	−3.47082e172	−0.565601
$646$	−1.28253e172	−0.190007
$647$	1.20583e173	1.62433	0.812164	−	0.583429i	$-0.198289\pi$
$647$	1.20583e173	1.62433	0.812164	+	0.583429i	$0.198289\pi$
$648$	−3.28381e173	−4.02268
$649$	5.92853e172	0.660538
$650$	2.86261e173	2.90129
$651$	7.14244e172	0.658591
$652$	2.30396e173	1.93307
$653$	2.16033e172	0.164953	0.0824765	−	0.996593i	$-0.473717\pi$
$653$	2.16033e172	0.164953	0.0824765	+	0.996593i	$0.473717\pi$
$654$	2.39613e172	0.166525
$655$	−3.46597e173	−2.19273
$656$	7.25345e173	4.17790
$657$	−7.39629e172	−0.387921
$658$	1.28320e173	0.612919
$659$	−2.94307e173	−1.28041	−0.640203	−	0.768206i	$-0.721150\pi$
$659$	−2.94307e173	−1.28041	−0.640203	+	0.768206i	$0.721150\pi$
$660$	−8.17992e173	−3.24188
$661$	1.01160e173	0.365276	0.182638	−	0.983180i	$-0.441536\pi$
$661$	1.01160e173	0.365276	0.182638	+	0.983180i	$0.441536\pi$
$662$	−3.18074e173	−1.04656
$663$	1.64037e173	0.491880
$664$	−6.09814e172	−0.166671
$665$	1.23671e173	0.308133
$666$	2.09838e173	0.476672
$667$	3.46942e173	0.718651
$668$	−1.55171e174	−2.93128
$669$	−2.69796e173	−0.464868
$670$	3.95774e173	0.622080
$671$	−3.16970e173	−0.454552
$672$	2.04296e174	2.67331
$673$	−9.67713e172	−0.115563	−0.0577817	−	0.998329i	$-0.518403\pi$
$673$	−9.67713e172	−0.115563	−0.0577817	+	0.998329i	$0.518403\pi$
$674$	−4.01497e173	−0.437622
$675$	−7.76080e173	−0.772191
$676$	3.78245e174	3.43599
$677$	1.26345e174	1.04799	0.523994	−	0.851722i	$-0.324441\pi$
$677$	1.26345e174	1.04799	0.523994	+	0.851722i	$0.324441\pi$
$678$	−4.48281e174	−3.39566
$679$	−3.60132e173	−0.249156
$680$	−2.08692e174	−1.31889
$681$	2.89008e174	1.66864
$682$	2.44412e174	1.28939
$683$	−2.78050e174	−1.34045	−0.670223	−	0.742160i	$-0.733802\pi$
$683$	−2.78050e174	−1.34045	−0.670223	+	0.742160i	$0.733802\pi$
$684$	−7.08785e173	−0.312294
$685$	−1.59457e174	−0.642203
$686$	−5.26350e174	−1.93795
$687$	3.20252e174	1.07809
$688$	4.09251e174	1.25980
$689$	9.46835e174	2.66558
$690$	8.74768e174	2.25255
$691$	−2.57828e174	−0.607338	−0.303669	−	0.952778i	$-0.598212\pi$
$691$	−2.57828e174	−0.607338	−0.303669	+	0.952778i	$0.598212\pi$
$692$	−5.68337e174	−1.22485
$693$	7.69069e173	0.151660
$694$	−9.60726e174	−1.73377
$695$	8.12713e174	1.34237
$696$	−2.51946e175	−3.80925
$697$	2.35176e174	0.325519
$698$	−1.70237e175	−2.15748
$699$	7.42223e174	0.861367
$700$	1.59477e175	1.69500
$701$	−3.61720e174	−0.352139	−0.176070	−	0.984378i	$-0.556338\pi$
$701$	−3.61720e174	−0.352139	−0.176070	+	0.984378i	$0.556338\pi$
$702$	−2.51109e175	−2.23939
$703$	−3.19051e174	−0.260680
$704$	3.43180e175	2.56924
$705$	−1.21011e175	−0.830221
$706$	2.96870e175	1.86671
$707$	−1.76403e175	−1.01674
$708$	5.32982e175	2.81622
$709$	−2.89754e175	−1.40374	−0.701868	−	0.712307i	$-0.747650\pi$
$709$	−2.89754e175	−1.40374	−0.701868	+	0.712307i	$0.747650\pi$
$710$	7.62938e175	3.38923
$711$	−2.39660e174	−0.0976373
$712$	−8.75638e175	−3.27194
$713$	−1.90924e175	−0.654416
$714$	1.25108e175	0.393409
$715$	−5.41274e175	−1.56169
$716$	4.30214e175	1.13903
$717$	8.53055e175	2.07276
$718$	1.43395e176	3.19802
$719$	−6.24158e175	−1.27781	−0.638907	−	0.769284i	$-0.720613\pi$
$719$	−6.24158e175	−1.27781	−0.638907	+	0.769284i	$0.720613\pi$
$720$	−9.04438e175	−1.69993
$721$	−2.91352e175	−0.502805
$722$	−1.06787e176	−1.69232
$723$	9.11260e175	1.32628
$724$	−3.22614e176	−4.31282
$725$	−8.16578e175	−1.00279
$726$	−9.10583e175	−1.02735
$727$	3.25718e174	0.0337657	0.0168829	−	0.999857i	$-0.494626\pi$
$727$	3.25718e174	0.0337657	0.0168829	+	0.999857i	$0.494626\pi$
$728$	3.25595e176	3.10169
$729$	5.55819e175	0.486621
$730$	3.97017e176	3.19487
$731$	1.32690e175	0.0981565
$732$	−2.84960e176	−1.93799
$733$	1.32124e176	0.826202	0.413101	−	0.910685i	$-0.364446\pi$
$733$	1.32124e176	0.826202	0.413101	+	0.910685i	$0.364446\pi$
$734$	2.92420e176	1.68151
$735$	1.87865e176	0.993514
$736$	−5.46100e176	−2.65636
$737$	−3.74213e175	−0.167443
$738$	1.77928e176	0.732450
$739$	−2.76212e176	−1.04619	−0.523094	−	0.852275i	$-0.675222\pi$
$739$	−2.76212e176	−1.04619	−0.523094	+	0.852275i	$0.675222\pi$
$740$	−8.22761e176	−2.86763
$741$	−1.88699e176	−0.605271
$742$	7.22133e176	2.13195
$743$	3.15416e176	0.857180	0.428590	−	0.903499i	$-0.359011\pi$
$743$	3.15416e176	0.857180	0.428590	+	0.903499i	$0.359011\pi$
$744$	1.38647e177	3.46877
$745$	−4.27636e176	−0.985063
$746$	−9.07690e176	−1.92531
$747$	−8.56877e174	−0.0167379
$748$	3.12719e176	0.562608
$749$	4.33600e176	0.718551
$750$	−4.41351e173	−0.000673778 0
$751$	−8.83325e176	−1.24241	−0.621204	−	0.783649i	$-0.713356\pi$
$751$	−8.83325e176	−1.24241	−0.621204	+	0.783649i	$0.713356\pi$
$752$	1.42686e177	1.84920
$753$	−7.80132e176	−0.931702
$754$	−2.64212e177	−2.90814
$755$	2.55065e177	2.58770
$756$	−1.39894e177	−1.30830
$757$	1.73175e176	0.149310	0.0746549	−	0.997209i	$-0.476214\pi$
$757$	1.73175e176	0.149310	0.0746549	+	0.997209i	$0.476214\pi$
$758$	−6.59757e176	−0.524478
$759$	−8.27113e176	−0.606311
$760$	2.40068e177	1.62292
$761$	−1.18435e177	−0.738452	−0.369226	−	0.929340i	$-0.620377\pi$
$761$	−1.18435e177	−0.738452	−0.369226	+	0.929340i	$0.620377\pi$
$762$	−3.94545e177	−2.26916
$763$	8.83317e175	0.0468660
$764$	−4.11541e177	−2.01452
$765$	−2.93242e176	−0.132449
$766$	9.04877e177	3.77155
$767$	3.52680e177	1.35664
$768$	7.66044e177	2.71981
$769$	2.81484e177	0.922537	0.461268	−	0.887261i	$-0.347395\pi$
$769$	2.81484e177	0.922537	0.461268	+	0.887261i	$0.347395\pi$
$770$	−4.12820e177	−1.24905
$771$	1.18925e177	0.332223
$772$	−3.59760e177	−0.928002
$773$	−3.81401e177	−0.908537	−0.454269	−	0.890865i	$-0.650099\pi$
$773$	−3.81401e177	−0.908537	−0.454269	+	0.890865i	$0.650099\pi$
$774$	1.00390e177	0.220862
$775$	4.49367e177	0.913158
$776$	−6.99079e177	−1.31229
$777$	3.11226e177	0.539739
$778$	2.11912e178	3.39555
$779$	−2.70533e177	−0.400559
$780$	−4.86612e178	−6.65832
$781$	−7.21375e177	−0.912269
$782$	−3.34424e177	−0.390915
$783$	7.16303e177	0.774014
$784$	−2.21515e178	−2.21291
$785$	1.53741e178	1.42006
$786$	4.03337e178	3.44494
$787$	4.06032e177	0.320712	0.160356	−	0.987059i	$-0.448736\pi$
$787$	4.06032e177	0.320712	0.160356	+	0.987059i	$0.448736\pi$
$788$	−2.74471e177	−0.200509
$789$	5.43049e177	0.366947
$790$	1.28645e178	0.804129
$791$	−1.65255e178	−0.955657
$792$	1.49289e178	0.798786
$793$	−1.88561e178	−0.933580
$794$	7.90555e177	0.362219
$795$	−6.80998e178	−2.88780
$796$	4.15920e178	1.63251
$797$	1.83721e178	0.667532	0.333766	−	0.942656i	$-0.391681\pi$
$797$	1.83721e178	0.667532	0.333766	+	0.942656i	$0.391681\pi$
$798$	−1.43917e178	−0.484100
$799$	4.62625e177	0.144080
$800$	1.28533e179	3.70663
$801$	−1.23040e178	−0.328584
$802$	−6.75688e178	−1.67118
$803$	−3.75389e178	−0.859954
$804$	−3.36422e178	−0.713899
$805$	3.22477e178	0.633946
$806$	1.45397e179	2.64820
$807$	−2.62032e178	−0.442213
$808$	−3.42428e179	−5.35513
$809$	3.33701e178	0.483641	0.241820	−	0.970321i	$-0.422256\pi$
$809$	3.33701e178	0.483641	0.241820	+	0.970321i	$0.422256\pi$
$810$	2.47682e179	3.32710
$811$	−1.72278e178	−0.214510	−0.107255	−	0.994232i	$-0.534206\pi$
$811$	−1.72278e178	−0.214510	−0.107255	+	0.994232i	$0.534206\pi$
$812$	−1.47194e179	−1.69900
$813$	1.59647e178	0.170841
$814$	1.06501e179	1.05670
$815$	−1.09651e179	−1.00884
$816$	1.39114e179	1.18693
$817$	−1.52639e178	−0.120784
$818$	3.07958e179	2.26028
$819$	4.57508e178	0.311486
$820$	−6.97644e179	−4.40638
$821$	−5.47085e178	−0.320591	−0.160295	−	0.987069i	$-0.551245\pi$
$821$	−5.47085e178	−0.320591	−0.160295	+	0.987069i	$0.551245\pi$
$822$	1.85561e179	1.00895
$823$	−1.52023e179	−0.767045	−0.383522	−	0.923532i	$-0.625289\pi$
$823$	−1.52023e179	−0.767045	−0.383522	+	0.923532i	$0.625289\pi$
$824$	−5.65565e179	−2.64825
$825$	1.94673e179	0.846034
$826$	2.68982e179	1.08505
$827$	2.73313e179	1.02346	0.511730	−	0.859146i	$-0.329005\pi$
$827$	2.73313e179	1.02346	0.511730	+	0.859146i	$0.329005\pi$
$828$	−1.84818e179	−0.642507
$829$	2.68325e179	0.866079	0.433040	−	0.901375i	$-0.357441\pi$
$829$	2.68325e179	0.866079	0.433040	+	0.901375i	$0.357441\pi$
$830$	4.59954e178	0.137851
$831$	4.18112e179	1.16367
$832$	2.04153e180	5.27681
$833$	−7.18208e178	−0.172418
$834$	−9.45759e179	−2.10896
$835$	7.38500e179	1.52979
$836$	−3.59734e179	−0.692302
$837$	−3.94185e179	−0.704830
$838$	−1.45517e180	−2.41773
$839$	−1.34849e179	−0.208203	−0.104102	−	0.994567i	$-0.533197\pi$
$839$	−1.34849e179	−0.208203	−0.104102	+	0.994567i	$0.533197\pi$
$840$	−2.34180e180	−3.36026
$841$	3.86672e177	0.00515691
$842$	2.69213e180	3.33736
$843$	5.59625e179	0.644913
$844$	−4.26501e180	−4.56940
$845$	−1.80017e180	−1.79319
$846$	3.50011e179	0.324193
$847$	−3.35680e179	−0.289131
$848$	8.02977e180	6.43218
$849$	5.93487e179	0.442169
$850$	7.87116e179	0.545475
$851$	−8.31936e179	−0.536317
$852$	−6.48525e180	−3.88948
$853$	−1.47202e180	−0.821389	−0.410694	−	0.911773i	$-0.634714\pi$
$853$	−1.47202e180	−0.821389	−0.410694	+	0.911773i	$0.634714\pi$
$854$	−1.43812e180	−0.746683
$855$	3.37330e179	0.162982
$856$	8.41693e180	3.78458
$857$	2.90308e179	0.121489	0.0607447	−	0.998153i	$-0.480652\pi$
$857$	2.90308e179	0.121489	0.0607447	+	0.998153i	$0.480652\pi$
$858$	6.29884e180	2.45354
$859$	3.16445e180	1.14741	0.573704	−	0.819062i	$-0.305506\pi$
$859$	3.16445e180	1.14741	0.573704	+	0.819062i	$0.305506\pi$
$860$	−3.93622e180	−1.32869
$861$	2.63898e180	0.829359
$862$	−5.20611e180	−1.52341
$863$	−8.27788e179	−0.225556	−0.112778	−	0.993620i	$-0.535975\pi$
$863$	−8.27788e179	−0.225556	−0.112778	+	0.993620i	$0.535975\pi$
$864$	−1.12749e181	−2.86100
$865$	2.70487e180	0.639228
$866$	−7.30948e180	−1.60893
$867$	−5.17528e180	−1.06111
$868$	8.10014e180	1.54714
$869$	−1.21636e180	−0.216445
$870$	1.90031e181	3.15058
$871$	−2.22614e180	−0.343903
$872$	1.71467e180	0.246841
$873$	−9.82307e179	−0.131787
$874$	3.84703e180	0.481031
$875$	−1.62701e177	−0.000189625 0
$876$	−3.37479e181	−3.66643
$877$	1.01192e181	1.02487	0.512436	−	0.858726i	$-0.328743\pi$
$877$	1.01192e181	1.02487	0.512436	+	0.858726i	$0.328743\pi$
$878$	2.08460e181	1.96838
$879$	1.85707e181	1.63498
$880$	−4.59035e181	−3.76844
$881$	−1.12249e181	−0.859339	−0.429670	−	0.902986i	$-0.641370\pi$
$881$	−1.12249e181	−0.859339	−0.429670	+	0.902986i	$0.641370\pi$
$882$	−5.43378e180	−0.387958
$883$	7.72901e180	0.514684	0.257342	−	0.966320i	$-0.417153\pi$
$883$	7.72901e180	0.514684	0.257342	+	0.966320i	$0.417153\pi$
$884$	1.86032e181	1.15551
$885$	−2.53660e181	−1.46974
$886$	−2.19520e180	−0.118659
$887$	−1.31789e181	−0.664623	−0.332311	−	0.943170i	$-0.607828\pi$
$887$	−1.31789e181	−0.664623	−0.332311	+	0.943170i	$0.607828\pi$
$888$	6.04144e181	2.84278
$889$	−1.45446e181	−0.638622
$890$	6.60452e181	2.70617
$891$	−2.34189e181	−0.895546
$892$	−3.05972e181	−1.09205
$893$	−5.32179e180	−0.177293
$894$	4.97643e181	1.54761
$895$	−2.04751e181	−0.594441
$896$	7.02087e181	1.90304
$897$	−4.92038e181	−1.24527
$898$	−1.28372e180	−0.0303371
$899$	−4.14754e181	−0.915314
$900$	4.34995e181	0.896541
$901$	2.60346e181	0.501160
$902$	9.03050e181	1.62371
$903$	1.48895e181	0.250083
$904$	−3.20789e182	−5.03340
$905$	1.53541e182	2.25080
$906$	−2.96821e182	−4.06547
$907$	1.04545e181	0.133800	0.0669000	−	0.997760i	$-0.478689\pi$
$907$	1.04545e181	0.133800	0.0669000	+	0.997760i	$0.478689\pi$
$908$	3.27760e182	3.91991
$909$	−4.81161e181	−0.537788
$910$	−2.45581e182	−2.56536
$911$	1.51147e182	1.47577	0.737886	−	0.674925i	$-0.235824\pi$
$911$	1.51147e182	1.47577	0.737886	+	0.674925i	$0.235824\pi$
$912$	−1.60029e182	−1.46055
$913$	−4.34896e180	−0.0371051
$914$	−4.09571e182	−3.26692
$915$	1.35620e182	1.01141
$916$	3.63194e182	2.53260
$917$	1.48687e182	0.969526
$918$	−6.90460e181	−0.421030
$919$	−1.33052e182	−0.758781	−0.379391	−	0.925237i	$-0.623866\pi$
$919$	−1.33052e182	−0.758781	−0.379391	+	0.925237i	$0.623866\pi$
$920$	6.25983e182	3.33896
$921$	3.41915e182	1.70589
$922$	4.41155e182	2.05892
$923$	−4.29136e182	−1.87366
$924$	3.50912e182	1.43341
$925$	1.95808e182	0.748366
$926$	−6.15801e182	−2.20224
$927$	−7.94701e181	−0.265950
$928$	−1.18632e183	−3.71538
$929$	−1.03681e181	−0.0303900	−0.0151950	−	0.999885i	$-0.504837\pi$
$929$	−1.03681e181	−0.0303900	−0.0151950	+	0.999885i	$0.504837\pi$
$930$	−1.04575e183	−2.86897
$931$	8.26187e181	0.212165
$932$	8.41745e182	2.02349
$933$	−3.96376e182	−0.892043
$934$	8.05157e182	1.69648
$935$	−1.48831e182	−0.293616
$936$	8.88103e182	1.64058
$937$	7.77855e182	1.34559	0.672797	−	0.739827i	$-0.265093\pi$
$937$	7.77855e182	1.34559	0.672797	+	0.739827i	$0.265093\pi$
$938$	−1.69784e182	−0.275056
$939$	8.43715e182	1.28015
$940$	−1.37237e183	−1.95033
$941$	−7.75525e182	−1.03237	−0.516184	−	0.856478i	$-0.672648\pi$
$941$	−7.75525e182	−1.03237	−0.516184	+	0.856478i	$0.672648\pi$
$942$	−1.78910e183	−2.23102
$943$	−7.05423e182	−0.824102
$944$	2.99095e183	3.27365
$945$	6.65793e182	0.682783
$946$	5.09515e182	0.489612
$947$	−9.38049e182	−0.844699	−0.422349	−	0.906433i	$-0.638795\pi$
$947$	−9.38049e182	−0.844699	−0.422349	+	0.906433i	$0.638795\pi$
$948$	−1.09352e183	−0.922818
$949$	−2.23314e183	−1.76621
$950$	−9.05455e182	−0.671220
$951$	1.22108e182	0.0848481
$952$	8.95271e182	0.583152
$953$	−9.89378e182	−0.604155	−0.302078	−	0.953283i	$-0.597680\pi$
$953$	−9.89378e182	−0.604155	−0.302078	+	0.953283i	$0.597680\pi$
$954$	1.96971e183	1.12766
$955$	1.95863e183	1.05135
$956$	9.67438e183	4.86926
$957$	−1.79678e183	−0.848031
$958$	−9.09331e182	−0.402479
$959$	6.84056e182	0.283953
$960$	−1.46834e184	−5.71672
$961$	−4.55932e182	−0.166499
$962$	6.33557e183	2.17029
$963$	1.18270e183	0.380065
$964$	1.03345e184	3.11566
$965$	1.71220e183	0.484310
$966$	−3.75268e183	−0.995975
$967$	−1.26063e183	−0.313950	−0.156975	−	0.987603i	$-0.550174\pi$
$967$	−1.26063e183	−0.313950	−0.156975	+	0.987603i	$0.550174\pi$
$968$	−6.51612e183	−1.52284
$969$	−5.18855e182	−0.113798
$970$	5.27282e183	1.08538
$971$	3.56075e180	0.000687952 0	0.000343976	−	1.00000i	$-0.499891\pi$
$971$	3.56075e180	0.000687952 0	0.000343976		1.00000i	$0.499891\pi$
$972$	−9.51746e183	−1.72602
$973$	−3.48647e183	−0.593535
$974$	−1.74322e184	−2.78597
$975$	1.15808e184	1.73762
$976$	−1.59912e184	−2.25277
$977$	−6.46619e183	−0.855328	−0.427664	−	0.903938i	$-0.640663\pi$
$977$	−6.46619e183	−0.855328	−0.427664	+	0.903938i	$0.640663\pi$
$978$	1.27602e184	1.58496
$979$	−6.24472e183	−0.728413
$980$	2.13055e184	2.33393
$981$	2.40936e182	0.0247890
$982$	−1.12763e184	−1.08971
$983$	1.44981e184	1.31605	0.658023	−	0.752998i	$-0.271393\pi$
$983$	1.44981e184	1.31605	0.658023	+	0.752998i	$0.271393\pi$
$984$	5.12272e184	4.36819
$985$	1.30628e183	0.104642
$986$	−7.26489e183	−0.546763
$987$	5.19127e183	0.367087
$988$	−2.14001e184	−1.42188
$989$	−3.98011e183	−0.248498
$990$	−1.12602e184	−0.660665
$991$	−2.64673e184	−1.45942	−0.729708	−	0.683759i	$-0.760344\pi$
$991$	−2.64673e184	−1.45942	−0.729708	+	0.683759i	$0.760344\pi$
$992$	6.52840e184	3.38329
$993$	−1.28678e184	−0.626797
$994$	−3.27294e184	−1.49857
$995$	−1.97948e184	−0.851983
$996$	−3.90977e183	−0.158198
$997$	5.11418e184	1.94547	0.972733	−	0.231926i	$-0.0745029\pi$
$997$	5.11418e184	1.94547	0.972733	+	0.231926i	$0.0745029\pi$
$998$	9.67705e183	0.346110
$999$	−1.71763e184	−0.577634

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.124.a.a.1.10	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.124.a.a.1.10	✓	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)

\(f(q)\)	\(=\)	\(q+6.28101e18 q^{2} +2.54101e29 q^{3} +2.88173e37 q^{4} -1.37149e43 q^{5} +1.59601e48 q^{6} +5.88359e51 q^{7} +1.14211e56 q^{8} +1.60483e58 q^{9} +O(q^{10})\)	\(q+6.28101e18 q^{2} +2.54101e29 q^{3} +2.88173e37 q^{4} -1.37149e43 q^{5} +1.59601e48 q^{6} +5.88359e51 q^{7} +1.14211e56 q^{8} +1.60483e58 q^{9} -8.61436e61 q^{10} +8.14507e63 q^{11} +7.32252e66 q^{12} +4.84539e68 q^{13} +3.69549e70 q^{14} -3.48498e72 q^{15} +4.10920e74 q^{16} +1.33231e75 q^{17} +1.00799e77 q^{18} -1.53262e78 q^{19} -3.95227e80 q^{20} +1.49503e81 q^{21} +5.11593e82 q^{22} -3.99634e83 q^{23} +2.90211e85 q^{24} +9.40597e85 q^{25} +3.04340e87 q^{26} -8.25093e87 q^{27} +1.69549e89 q^{28} -8.68148e89 q^{29} -2.18892e91 q^{30} +4.77746e91 q^{31} +1.36650e93 q^{32} +2.06967e93 q^{33} +8.36826e93 q^{34} -8.06930e94 q^{35} +4.62467e95 q^{36} +2.08174e96 q^{37} -9.62638e96 q^{38} +1.23122e98 q^{39} -1.56639e99 q^{40} +1.76517e99 q^{41} +9.39029e99 q^{42} +9.95937e99 q^{43} +2.34719e101 q^{44} -2.20101e101 q^{45} -2.51011e102 q^{46} +3.47235e102 q^{47} +1.04415e104 q^{48} -5.39070e103 q^{49} +5.90790e104 q^{50} +3.38542e104 q^{51} +1.39631e106 q^{52} +1.95409e106 q^{53} -5.18242e106 q^{54} -1.11709e107 q^{55} +6.71968e107 q^{56} -3.89440e107 q^{57} -5.45285e108 q^{58} +7.27867e108 q^{59} -1.00428e110 q^{60} -3.89156e109 q^{61} +3.00073e110 q^{62} +9.44213e109 q^{63} +4.21335e111 q^{64} -6.64542e111 q^{65} +1.29997e112 q^{66} -4.59434e111 q^{67} +3.83936e112 q^{68} -1.01548e113 q^{69} -5.06834e113 q^{70} -8.85659e113 q^{71} +1.83288e114 q^{72} -4.60878e114 q^{73} +1.30755e115 q^{74} +2.39007e115 q^{75} -4.41659e115 q^{76} +4.79223e115 q^{77} +7.73331e116 q^{78} -1.49337e116 q^{79} -5.63574e117 q^{80} -2.87522e117 q^{81} +1.10871e118 q^{82} -5.33938e116 q^{83} +4.30827e118 q^{84} -1.82725e118 q^{85} +6.25550e118 q^{86} -2.20598e119 q^{87} +9.30254e119 q^{88} -7.66687e119 q^{89} -1.38245e120 q^{90} +2.85083e120 q^{91} -1.15164e121 q^{92} +1.21396e121 q^{93} +2.18099e121 q^{94} +2.10197e121 q^{95} +3.47230e122 q^{96} -6.12096e121 q^{97} -3.38590e122 q^{98} +1.30714e122 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 22\!\cdots\!00 q^{2}+ \cdots + 11\!\cdots\!70 q^{9}+O(q^{10}) \) 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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