LMFDB - Embedded newform 1.124.a.a.1.4

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			1.4
Root			$2.18088e16$ 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)

$f(q)$	$=$	$q-1.35000e18 q^{2} +1.15541e28 q^{3} -8.81132e36 q^{4} +1.19036e42 q^{5} -1.55981e46 q^{6} +4.29022e51 q^{7} +2.62510e55 q^{8} -4.83858e58 q^{9} +O(q^{10})$	\(q-1.35000e18 q^{2} +1.15541e28 q^{3} -8.81132e36 q^{4} +1.19036e42 q^{5} -1.55981e46 q^{6} +4.29022e51 q^{7} +2.62510e55 q^{8} -4.83858e58 q^{9} -1.60698e60 q^{10} -6.95467e63 q^{11} -1.01807e65 q^{12} +4.61578e68 q^{13} -5.79180e69 q^{14} +1.37536e70 q^{15} +5.82593e73 q^{16} -3.52699e75 q^{17} +6.53208e76 q^{18} +5.44060e77 q^{19} -1.04886e79 q^{20} +4.95699e79 q^{21} +9.38880e81 q^{22} -5.17099e83 q^{23} +3.03307e83 q^{24} -9.26226e85 q^{25} -6.23130e86 q^{26} -1.11966e87 q^{27} -3.78026e88 q^{28} +8.59679e89 q^{29} -1.85673e88 q^{30} +2.75056e91 q^{31} -3.57798e92 q^{32} -8.03553e91 q^{33} +4.76144e93 q^{34} +5.10690e93 q^{35} +4.26343e95 q^{36} -2.58390e96 q^{37} -7.34481e95 q^{38} +5.33314e96 q^{39} +3.12480e97 q^{40} +4.18767e98 q^{41} -6.69193e97 q^{42} -2.45273e100 q^{43} +6.12798e100 q^{44} -5.75964e100 q^{45} +6.98084e101 q^{46} -6.57537e102 q^{47} +6.73136e101 q^{48} -7.01175e103 q^{49} +1.25041e104 q^{50} -4.07514e103 q^{51} -4.06711e105 q^{52} -2.38488e105 q^{53} +1.51153e105 q^{54} -8.27854e105 q^{55} +1.12622e107 q^{56} +6.28615e105 q^{57} -1.16057e108 q^{58} +8.41509e108 q^{59} -1.21187e107 q^{60} +2.09335e109 q^{61} -3.71325e109 q^{62} -2.07586e110 q^{63} -1.36492e110 q^{64} +5.49442e110 q^{65} +1.08480e110 q^{66} -1.87939e112 q^{67} +3.10775e112 q^{68} -5.97464e111 q^{69} -6.89432e111 q^{70} +1.00793e114 q^{71} -1.27017e114 q^{72} -2.35660e114 q^{73} +3.48827e114 q^{74} -1.07018e114 q^{75} -4.79389e114 q^{76} -2.98371e115 q^{77} -7.19973e114 q^{78} +1.72483e115 q^{79} +6.93494e115 q^{80} +2.33471e117 q^{81} -5.65335e116 q^{82} -4.88316e117 q^{83} -4.36776e116 q^{84} -4.19838e117 q^{85} +3.31118e118 q^{86} +9.93285e117 q^{87} -1.82567e119 q^{88} +6.06094e119 q^{89} +7.77551e118 q^{90} +1.98027e120 q^{91} +4.55633e120 q^{92} +3.17803e119 q^{93} +8.87675e120 q^{94} +6.47626e119 q^{95} -4.13405e120 q^{96} +2.90829e122 q^{97} +9.46587e121 q^{98} +3.36507e122 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.35000e18	−0.413989	−0.206995	−	0.978342i	$-0.566368\pi$
$2$	−1.35000e18	−0.413989	−0.206995	+	0.978342i	$0.566368\pi$
$3$	1.15541e28	0.0524543	0.0262271	−	0.999656i	$-0.491651\pi$
$3$	1.15541e28	0.0524543	0.0262271	+	0.999656i	$0.491651\pi$
$4$	−8.81132e36	−0.828613
$5$	1.19036e42	0.122750	0.0613751	−	0.998115i	$-0.480451\pi$
$5$	1.19036e42	0.122750	0.0613751	+	0.998115i	$0.480451\pi$
$6$	−1.55981e46	−0.0217155
$7$	4.29022e51	0.455985	0.227993	−	0.973663i	$-0.426784\pi$
$7$	4.29022e51	0.455985	0.227993	+	0.973663i	$0.426784\pi$
$8$	2.62510e55	0.757026
$9$	−4.83858e58	−0.997249
$10$	−1.60698e60	−0.0508173
$11$	−6.95467e63	−0.626075	−0.313037	−	0.949741i	$-0.601347\pi$
$11$	−6.95467e63	−0.626075	−0.313037	+	0.949741i	$0.601347\pi$
$12$	−1.01807e65	−0.0434643
$13$	4.61578e68	1.43459	0.717296	−	0.696768i	$-0.245379\pi$
$13$	4.61578e68	1.43459	0.717296	+	0.696768i	$0.245379\pi$
$14$	−5.79180e69	−0.188773
$15$	1.37536e70	0.00643877
$16$	5.82593e73	0.515212
$17$	−3.52699e75	−0.749541	−0.374771	−	0.927118i	$-0.622279\pi$
$17$	−3.52699e75	−0.749541	−0.374771	+	0.927118i	$0.622279\pi$
$18$	6.53208e76	0.412850
$19$	5.44060e77	0.123680	0.0618401	−	0.998086i	$-0.480303\pi$
$19$	5.44060e77	0.123680	0.0618401	+	0.998086i	$0.480303\pi$
$20$	−1.04886e79	−0.101712
$21$	4.95699e79	0.0239184
$22$	9.38880e81	0.259188
$23$	−5.17099e83	−0.927495	−0.463748	−	0.885967i	$-0.653496\pi$
$23$	−5.17099e83	−0.927495	−0.463748	+	0.885967i	$0.653496\pi$
$24$	3.03307e83	0.0397092
$25$	−9.26226e85	−0.984932
$26$	−6.23130e86	−0.593906
$27$	−1.11966e87	−0.104764
$28$	−3.78026e88	−0.377835
$29$	8.59679e89	0.992794	0.496397	−	0.868096i	$-0.334656\pi$
$29$	8.59679e89	0.992794	0.496397	+	0.868096i	$0.334656\pi$
$30$	−1.85673e88	−0.00266558
$31$	2.75056e91	0.525626	0.262813	−	0.964847i	$-0.415350\pi$
$31$	2.75056e91	0.525626	0.262813	+	0.964847i	$0.415350\pi$
$32$	−3.57798e92	−0.970318
$33$	−8.03553e91	−0.0328403
$34$	4.76144e93	0.310302
$35$	5.10690e93	0.0559722
$36$	4.26343e95	0.826333
$37$	−2.58390e96	−0.928689	−0.464345	−	0.885655i	$-0.653710\pi$
$37$	−2.58390e96	−0.928689	−0.464345	+	0.885655i	$0.653710\pi$
$38$	−7.34481e95	−0.0512023
$39$	5.33314e96	0.0752505
$40$	3.12480e97	0.0929251
$41$	4.18767e98	0.272750	0.136375	−	0.990657i	$-0.456455\pi$
$41$	4.18767e98	0.272750	0.136375	+	0.990657i	$0.456455\pi$
$42$	−6.69193e97	−0.00990194
$43$	−2.45273e100	−0.853767	−0.426883	−	0.904307i	$-0.640388\pi$
$43$	−2.45273e100	−0.853767	−0.426883	+	0.904307i	$0.640388\pi$
$44$	6.12798e100	0.518774
$45$	−5.75964e100	−0.122412
$46$	6.98084e101	0.383973
$47$	−6.57537e102	−0.963611	−0.481805	−	0.876278i	$-0.660019\pi$
$47$	−6.57537e102	−0.963611	−0.481805	+	0.876278i	$0.660019\pi$
$48$	6.73136e101	0.0270251
$49$	−7.01175e103	−0.792078
$50$	1.25041e104	0.407751
$51$	−4.07514e103	−0.0393166
$52$	−4.06711e105	−1.18872
$53$	−2.38488e105	−0.216023	−0.108012	−	0.994150i	$-0.534448\pi$
$53$	−2.38488e105	−0.216023	−0.108012	+	0.994150i	$0.534448\pi$
$54$	1.51153e105	0.0433712
$55$	−8.27854e105	−0.0768508
$56$	1.12622e107	0.345193
$57$	6.28615e105	0.00648756
$58$	−1.16057e108	−0.411006
$59$	8.41509e108	1.04150	0.520751	−	0.853709i	$-0.325652\pi$
$59$	8.41509e108	1.04150	0.520751	+	0.853709i	$0.325652\pi$
$60$	−1.21187e107	−0.00533525
$61$	2.09335e109	0.333470	0.166735	−	0.986002i	$-0.446678\pi$
$61$	2.09335e109	0.333470	0.166735	+	0.986002i	$0.446678\pi$
$62$	−3.71325e109	−0.217603
$63$	−2.07586e110	−0.454730
$64$	−1.36492e110	−0.113511
$65$	5.49442e110	0.176097
$66$	1.08480e110	0.0135955
$67$	−1.87939e112	−0.934150	−0.467075	−	0.884218i	$-0.654692\pi$
$67$	−1.87939e112	−0.934150	−0.467075	+	0.884218i	$0.654692\pi$
$68$	3.10775e112	0.621080
$69$	−5.97464e111	−0.0486511
$70$	−6.89432e111	−0.0231719
$71$	1.00793e114	1.41593	0.707966	−	0.706247i	$-0.249613\pi$
$71$	1.00793e114	1.41593	0.707966	+	0.706247i	$0.249613\pi$
$72$	−1.27017e114	−0.754943
$73$	−2.35660e114	−0.599695	−0.299848	−	0.953987i	$-0.596936\pi$
$73$	−2.35660e114	−0.599695	−0.299848	+	0.953987i	$0.596936\pi$
$74$	3.48827e114	0.384467
$75$	−1.07018e114	−0.0516639
$76$	−4.79389e114	−0.102483
$77$	−2.98371e115	−0.285481
$78$	−7.19973e114	−0.0311529
$79$	1.72483e115	0.0340943	0.0170471	−	0.999855i	$-0.494573\pi$
$79$	1.72483e115	0.0340943	0.0170471	+	0.999855i	$0.494573\pi$
$80$	6.93494e115	0.0632424
$81$	2.33471e117	0.991753
$82$	−5.65335e116	−0.112916
$83$	−4.88316e117	−0.462805	−0.231402	−	0.972858i	$-0.574331\pi$
$83$	−4.88316e117	−0.462805	−0.231402	+	0.972858i	$0.574331\pi$
$84$	−4.36776e116	−0.0198191
$85$	−4.19838e117	−0.0920063
$86$	3.31118e118	0.353450
$87$	9.93285e117	0.0520763
$88$	−1.82567e119	−0.473955
$89$	6.06094e119	0.785334	0.392667	−	0.919681i	$-0.371552\pi$
$89$	6.06094e119	0.785334	0.392667	+	0.919681i	$0.371552\pi$
$90$	7.77551e118	0.0506774
$91$	1.98027e120	0.654153
$92$	4.55633e120	0.768535
$93$	3.17803e119	0.0275713
$94$	8.87675e120	0.398925
$95$	6.47626e119	0.0151818
$96$	−4.13405e120	−0.0508973
$97$	2.90829e122	1.89311	0.946556	−	0.322539i	$-0.104536\pi$
$97$	2.90829e122	1.89311	0.946556	+	0.322539i	$0.104536\pi$
$98$	9.46587e121	0.327912
$99$	3.36507e122	0.624352
$100$	8.16128e122	0.816128
$101$	2.74239e123	1.48718	0.743591	−	0.668635i	$-0.233121\pi$
$101$	2.74239e123	1.48718	0.743591	+	0.668635i	$0.233121\pi$
$102$	5.50143e121	0.0162767
$103$	9.49511e123	1.54174	0.770869	−	0.636994i	$-0.219822\pi$
$103$	9.49511e123	1.54174	0.770869	+	0.636994i	$0.219822\pi$
$104$	1.21169e124	1.08602
$105$	5.90059e121	0.00293598
$106$	3.21959e123	0.0894314
$107$	7.03321e124	1.09661	0.548303	−	0.836279i	$-0.315274\pi$
$107$	7.03321e124	1.09661	0.548303	+	0.836279i	$0.315274\pi$
$108$	9.86565e123	0.0868090
$109$	2.48860e125	1.24230	0.621148	−	0.783693i	$-0.286666\pi$
$109$	2.48860e125	1.24230	0.621148	+	0.783693i	$0.286666\pi$
$110$	1.11760e124	0.0318154
$111$	−2.98548e124	−0.0487137
$112$	2.49945e125	0.234929
$113$	−2.43357e126	−1.32409	−0.662047	−	0.749462i	$-0.730312\pi$
$113$	−2.43357e126	−1.32409	−0.662047	+	0.749462i	$0.730312\pi$
$114$	−8.48630e123	−0.00268578
$115$	−6.15533e125	−0.113850
$116$	−7.57491e126	−0.822642
$117$	−2.23338e127	−1.43065
$118$	−1.13604e127	−0.431171
$119$	−1.51316e127	−0.341780
$120$	3.61044e125	0.00487432
$121$	−7.50284e127	−0.608030
$122$	−2.82602e127	−0.138053
$123$	4.83849e126	0.0143069
$124$	−2.42361e128	−0.435540
$125$	−2.22195e128	−0.243651
$126$	2.80241e128	0.188253
$127$	2.82965e129	1.16897	0.584485	−	0.811404i	$-0.301297\pi$
$127$	2.82965e129	1.16897	0.584485	+	0.811404i	$0.301297\pi$
$128$	3.98902e129	1.01731
$129$	−2.83392e128	−0.0447837
$130$	−7.41747e128	−0.0729021
$131$	3.09671e130	1.89983	0.949917	−	0.312504i	$-0.101168\pi$
$131$	3.09671e130	1.89983	0.949917	+	0.312504i	$0.101168\pi$
$132$	7.08036e128	0.0272119
$133$	2.33414e129	0.0563963
$134$	2.53718e130	0.386728
$135$	−1.33279e129	−0.0128598
$136$	−9.25868e130	−0.567422
$137$	−2.15203e131	−0.840493	−0.420247	−	0.907410i	$-0.638056\pi$
$137$	−2.15203e131	−0.840493	−0.420247	+	0.907410i	$0.638056\pi$
$138$	8.06576e129	0.0201410
$139$	−4.06654e131	−0.651351	−0.325675	−	0.945482i	$-0.605592\pi$
$139$	−4.06654e131	−0.651351	−0.325675	+	0.945482i	$0.605592\pi$
$140$	−4.49986e130	−0.0463793
$141$	−7.59728e130	−0.0505455
$142$	−1.36071e132	−0.586181
$143$	−3.21012e132	−0.898162
$144$	−2.81892e132	−0.513795
$145$	1.02333e132	0.121866
$146$	3.18141e132	0.248267
$147$	−8.10148e131	−0.0415478
$148$	2.27676e133	0.769524
$149$	1.13632e133	0.253832	0.126916	−	0.991913i	$-0.459492\pi$
$149$	1.13632e133	0.253832	0.126916	+	0.991913i	$0.459492\pi$
$150$	1.44474e132	0.0213883
$151$	1.48443e134	1.46042	0.730209	−	0.683224i	$-0.239423\pi$
$151$	1.48443e134	1.46042	0.730209	+	0.683224i	$0.239423\pi$
$152$	1.42821e133	0.0936292
$153$	1.70656e134	0.747479
$154$	4.02801e133	0.118186
$155$	3.27415e133	0.0645207
$156$	−4.69920e133	−0.0623535
$157$	−1.48840e135	−1.33319	−0.666595	−	0.745420i	$-0.732249\pi$
$157$	−1.48840e135	−1.33319	−0.666595	+	0.745420i	$0.732249\pi$
$158$	−2.32853e133	−0.0141147
$159$	−2.75553e133	−0.0113314
$160$	−4.25908e134	−0.119107
$161$	−2.21847e135	−0.422924
$162$	−3.15185e135	−0.410575
$163$	−8.72756e135	−0.778673	−0.389337	−	0.921096i	$-0.627296\pi$
$163$	−8.72756e135	−0.778673	−0.389337	+	0.921096i	$0.627296\pi$
$164$	−3.68989e135	−0.226004
$165$	−9.56515e133	−0.00403115
$166$	6.59226e135	0.191596
$167$	2.31137e135	0.0464308	0.0232154	−	0.999730i	$-0.492610\pi$
$167$	2.31137e135	0.0464308	0.0232154	+	0.999730i	$0.492610\pi$
$168$	1.30126e135	0.0181068
$169$	1.09532e137	1.05806
$170$	5.66781e135	0.0380896
$171$	−2.63248e136	−0.123340
$172$	2.16118e137	0.707442
$173$	7.24248e137	1.65978	0.829892	−	0.557924i	$-0.188402\pi$
$173$	7.24248e137	1.65978	0.829892	+	0.557924i	$0.188402\pi$
$174$	−1.34094e136	−0.0215590
$175$	−3.97372e137	−0.449114
$176$	−4.05174e137	−0.322561
$177$	9.72292e136	0.0546312
$178$	−8.18227e137	−0.325120
$179$	−5.81323e138	−1.63665	−0.818325	−	0.574755i	$-0.805097\pi$
$179$	−5.81323e138	−1.63665	−0.818325	+	0.574755i	$0.805097\pi$
$180$	5.07500e137	0.101433
$181$	7.72229e137	0.109778	0.0548888	−	0.998492i	$-0.482520\pi$
$181$	7.72229e137	0.109778	0.0548888	+	0.998492i	$0.482520\pi$
$182$	−2.67337e138	−0.270812
$183$	2.41869e137	0.0174919
$184$	−1.35743e139	−0.702138
$185$	−3.07577e138	−0.113997
$186$	−4.29035e137	−0.0114142
$187$	2.45290e139	0.469269
$188$	5.79377e139	0.798460
$189$	−4.80357e138	−0.0477709
$190$	−8.74295e137	−0.00628509
$191$	1.40010e140	0.728797	0.364398	−	0.931243i	$-0.381275\pi$
$191$	1.40010e140	0.728797	0.364398	+	0.931243i	$0.381275\pi$
$192$	−1.57704e138	−0.00595413
$193$	4.85849e140	1.33268	0.666341	−	0.745647i	$-0.267859\pi$
$193$	4.85849e140	1.33268	0.666341	+	0.745647i	$0.267859\pi$
$194$	−3.92619e140	−0.783728
$195$	6.34834e138	0.00923701
$196$	6.17828e140	0.656326
$197$	7.31143e139	0.0567975	0.0283988	−	0.999597i	$-0.490959\pi$
$197$	7.31143e139	0.0567975	0.0283988	+	0.999597i	$0.490959\pi$
$198$	−4.54285e140	−0.258475
$199$	−3.83561e141	−1.60092	−0.800462	−	0.599384i	$-0.795412\pi$
$199$	−3.83561e141	−1.60092	−0.800462	+	0.599384i	$0.795412\pi$
$200$	−2.43143e141	−0.745619
$201$	−2.17147e140	−0.0490001
$202$	−3.70222e141	−0.615677
$203$	3.68821e141	0.452699
$204$	3.59073e140	0.0325783
$205$	4.98482e140	0.0334801
$206$	−1.28184e142	−0.638263
$207$	2.50202e142	0.924943
$208$	2.68912e142	0.739120
$209$	−3.78376e141	−0.0774331
$210$	−7.96580e139	−0.00121547
$211$	1.04017e143	1.18504	0.592519	−	0.805557i	$-0.298134\pi$
$211$	1.04017e143	1.18504	0.592519	+	0.805557i	$0.298134\pi$
$212$	2.10140e142	0.179000
$213$	1.16458e142	0.0742716
$214$	−9.49483e142	−0.453983
$215$	−2.91962e142	−0.104800
$216$	−2.93920e142	−0.0793092
$217$	1.18005e143	0.239677
$218$	−3.35961e143	−0.514298
$219$	−2.72285e142	−0.0314566
$220$	7.29449e142	0.0636796
$221$	−1.62798e144	−1.07529
$222$	4.03040e142	0.0201670
$223$	−3.38499e144	−1.28472	−0.642359	−	0.766404i	$-0.722044\pi$
$223$	−3.38499e144	−1.28472	−0.642359	+	0.766404i	$0.722044\pi$
$224$	−1.53503e144	−0.442451
$225$	4.48162e144	0.982222
$226$	3.28531e144	0.548161
$227$	−4.85025e142	−0.00616842	−0.00308421	−	0.999995i	$-0.500982\pi$
$227$	−4.85025e142	−0.00616842	−0.00308421	+	0.999995i	$0.500982\pi$
$228$	−5.53893e142	−0.00537567
$229$	1.80240e145	1.33650	0.668252	−	0.743935i	$-0.267043\pi$
$229$	1.80240e145	1.33650	0.668252	+	0.743935i	$0.267043\pi$
$230$	8.30969e143	0.0471328
$231$	−3.44742e143	−0.0149747
$232$	2.25674e145	0.751571
$233$	−1.04691e145	−0.267622	−0.133811	−	0.991007i	$-0.542721\pi$
$233$	−1.04691e145	−0.267622	−0.133811	+	0.991007i	$0.542721\pi$
$234$	3.01506e145	0.592272
$235$	−7.82704e144	−0.118283
$236$	−7.41481e145	−0.863002
$237$	1.99290e143	0.00178839
$238$	2.04276e145	0.141493
$239$	−3.15188e146	−1.68693	−0.843467	−	0.537181i	$-0.819489\pi$
$239$	−3.15188e146	−1.68693	−0.843467	+	0.537181i	$0.819489\pi$
$240$	8.01273e143	0.00331733
$241$	−4.72368e145	−0.151437	−0.0757185	−	0.997129i	$-0.524125\pi$
$241$	−4.72368e145	−0.151437	−0.0757185	+	0.997129i	$0.524125\pi$
$242$	1.01288e146	0.251718
$243$	8.13004e145	0.156786
$244$	−1.84452e146	−0.276318
$245$	−8.34650e145	−0.0972277
$246$	−6.53196e144	−0.00592290
$247$	2.51126e146	0.177431
$248$	7.22048e146	0.397912
$249$	−5.64207e145	−0.0242761
$250$	2.99963e146	0.100869
$251$	4.33211e147	1.13964	0.569818	−	0.821771i	$-0.307014\pi$
$251$	4.33211e147	1.13964	0.569818	+	0.821771i	$0.307014\pi$
$252$	1.82911e147	0.376795
$253$	3.59625e147	0.580681
$254$	−3.82002e147	−0.483941
$255$	−4.85087e145	−0.00482612
$256$	−3.93376e147	−0.307645
$257$	−5.00581e147	−0.308026	−0.154013	−	0.988069i	$-0.549220\pi$
$257$	−5.00581e147	−0.308026	−0.154013	+	0.988069i	$0.549220\pi$
$258$	3.82579e146	0.0185400
$259$	−1.10855e148	−0.423468
$260$	−4.84132e147	−0.145916
$261$	−4.15962e148	−0.990063
$262$	−4.18055e148	−0.786510
$263$	2.63701e148	0.392494	0.196247	−	0.980554i	$-0.437124\pi$
$263$	2.63701e148	0.392494	0.196247	+	0.980554i	$0.437124\pi$
$264$	−2.10940e147	−0.0248610
$265$	−2.83886e147	−0.0265169
$266$	−3.15109e147	−0.0233475
$267$	7.00290e147	0.0411941
$268$	1.65599e149	0.774049
$269$	5.02813e149	1.86914	0.934568	−	0.355784i	$-0.115786\pi$
$269$	5.02813e149	1.86914	0.934568	+	0.355784i	$0.115786\pi$
$270$	1.79927e147	0.00532383
$271$	−2.53441e149	−0.597400	−0.298700	−	0.954347i	$-0.596553\pi$
$271$	−2.53441e149	−0.597400	−0.298700	+	0.954347i	$0.596553\pi$
$272$	−2.05480e149	−0.386173
$273$	2.28804e148	0.0343131
$274$	2.90525e149	0.347955
$275$	6.44159e149	0.616641
$276$	5.26445e148	0.0403129
$277$	−1.44550e150	−0.886161	−0.443080	−	0.896482i	$-0.646114\pi$
$277$	−1.44550e150	−0.886161	−0.443080	+	0.896482i	$0.646114\pi$
$278$	5.48983e149	0.269652
$279$	−1.33088e150	−0.524179
$280$	1.34061e149	0.0423725
$281$	−4.79224e150	−1.21646	−0.608232	−	0.793759i	$-0.708121\pi$
$281$	−4.79224e150	−1.21646	−0.608232	+	0.793759i	$0.708121\pi$
$282$	1.02563e149	0.0209253
$283$	3.54645e150	0.582006	0.291003	−	0.956722i	$-0.406011\pi$
$283$	3.54645e150	0.582006	0.291003	+	0.956722i	$0.406011\pi$
$284$	−8.88121e150	−1.17326
$285$	7.48277e147	0.000796349 0
$286$	4.33366e150	0.371830
$287$	1.79660e150	0.124370
$288$	1.73123e151	0.967649
$289$	−9.70236e150	−0.438188
$290$	−1.38149e150	−0.0504511
$291$	3.36028e150	0.0993018
$292$	2.07648e151	0.496915
$293$	8.74991e151	1.69686	0.848428	−	0.529310i	$-0.177549\pi$
$293$	8.74991e151	1.69686	0.848428	+	0.529310i	$0.177549\pi$
$294$	1.09370e150	0.0172004
$295$	1.00170e151	0.127845
$296$	−6.78300e151	−0.703042
$297$	7.78683e150	0.0655902
$298$	−1.53404e151	−0.105084
$299$	−2.38681e152	−1.33058
$300$	9.42966e150	0.0428094
$301$	−1.05227e152	−0.389305
$302$	−2.00398e152	−0.604598
$303$	3.16859e151	0.0780090
$304$	3.16966e151	0.0637216
$305$	2.49183e151	0.0409335
$306$	−2.30386e152	−0.309448
$307$	2.86249e152	0.314582	0.157291	−	0.987552i	$-0.449724\pi$
$307$	2.86249e152	0.314582	0.157291	+	0.987552i	$0.449724\pi$
$308$	2.62904e152	0.236553
$309$	1.09708e152	0.0808707
$310$	−4.42010e151	−0.0267109
$311$	2.08916e153	1.03564	0.517819	−	0.855490i	$-0.326744\pi$
$311$	2.08916e153	1.03564	0.517819	+	0.855490i	$0.326744\pi$
$312$	1.40000e152	0.0569666
$313$	3.04747e152	0.101850	0.0509251	−	0.998702i	$-0.483783\pi$
$313$	3.04747e152	0.101850	0.0509251	+	0.998702i	$0.483783\pi$
$314$	2.00934e153	0.551926
$315$	−2.47101e152	−0.0558182
$316$	−1.51981e152	−0.0282509
$317$	−4.34330e152	−0.0664776	−0.0332388	−	0.999447i	$-0.510582\pi$
$317$	−4.34330e152	−0.0664776	−0.0332388	+	0.999447i	$0.510582\pi$
$318$	3.71996e151	0.00469106
$319$	−5.97878e153	−0.621564
$320$	−1.62474e152	−0.0139335
$321$	8.12627e152	0.0575217
$322$	2.99494e153	0.175086
$323$	−1.91889e153	−0.0927035
$324$	−2.05719e154	−0.821780
$325$	−4.27525e154	−1.41298
$326$	1.17822e154	0.322362
$327$	2.87536e153	0.0651638
$328$	1.09930e154	0.206479
$329$	−2.82098e154	−0.439392
$330$	1.29130e152	0.00166885
$331$	1.20287e155	1.29062	0.645310	−	0.763921i	$-0.276728\pi$
$331$	1.20287e155	1.29062	0.645310	+	0.763921i	$0.276728\pi$
$332$	4.30271e154	0.383486
$333$	1.25024e155	0.926134
$334$	−3.12035e153	−0.0192218
$335$	−2.23715e154	−0.114667
$336$	2.88791e153	0.0123230
$337$	1.73074e155	0.615168	0.307584	−	0.951521i	$-0.400479\pi$
$337$	1.73074e155	0.615168	0.307584	+	0.951521i	$0.400479\pi$
$338$	−1.47868e155	−0.438024
$339$	−2.81178e154	−0.0694544
$340$	3.69933e154	0.0762376
$341$	−1.91292e155	−0.329081
$342$	3.55384e154	0.0510614
$343$	−6.80606e155	−0.817161
$344$	−6.43864e155	−0.646324
$345$	−7.11195e153	−0.00597193
$346$	−9.77734e155	−0.687133
$347$	2.57126e153	0.00151316	0.000756578	−	1.00000i	$-0.499759\pi$
$347$	2.57126e153	0.00151316	0.000756578		1.00000i	$0.499759\pi$
$348$	−8.75216e154	−0.0431511
$349$	1.37630e156	0.568786	0.284393	−	0.958708i	$-0.408208\pi$
$349$	1.37630e156	0.568786	0.284393	+	0.958708i	$0.408208\pi$
$350$	5.36452e155	0.185929
$351$	−5.16808e155	−0.150294
$352$	2.48837e156	0.607492
$353$	1.85229e156	0.379808	0.189904	−	0.981803i	$-0.439182\pi$
$353$	1.85229e156	0.379808	0.189904	+	0.981803i	$0.439182\pi$
$354$	−1.31259e155	−0.0226167
$355$	1.19980e156	0.173806
$356$	−5.34049e156	−0.650738
$357$	−1.74833e155	−0.0179278
$358$	7.84786e156	0.677556
$359$	2.39201e157	1.73962	0.869811	−	0.493385i	$-0.164241\pi$
$359$	2.39201e157	1.73962	0.869811	+	0.493385i	$0.164241\pi$
$360$	−1.51196e156	−0.0926694
$361$	−1.90545e157	−0.984703
$362$	−1.04251e156	−0.0454467
$363$	−8.66889e155	−0.0318938
$364$	−1.74488e157	−0.542039
$365$	−2.80520e156	−0.0736127
$366$	−3.26523e155	−0.00724147
$367$	−5.01985e157	−0.941299	−0.470650	−	0.882320i	$-0.655980\pi$
$367$	−5.01985e157	−0.941299	−0.470650	+	0.882320i	$0.655980\pi$
$368$	−3.01258e157	−0.477857
$369$	−2.02623e157	−0.272000
$370$	4.15229e156	0.0471934
$371$	−1.02317e157	−0.0985035
$372$	−2.80027e156	−0.0228459
$373$	1.60496e158	1.11013	0.555063	−	0.831808i	$-0.312694\pi$
$373$	1.60496e158	1.11013	0.555063	+	0.831808i	$0.312694\pi$
$374$	−3.31142e157	−0.194272
$375$	−2.56727e156	−0.0127805
$376$	−1.72610e158	−0.729479
$377$	3.96808e158	1.42426
$378$	6.48482e156	0.0197766
$379$	6.59802e158	1.71042	0.855208	−	0.518284i	$-0.173429\pi$
$379$	6.59802e158	1.71042	0.855208	+	0.518284i	$0.173429\pi$
$380$	−5.70644e156	−0.0125798
$381$	3.26942e157	0.0613175
$382$	−1.89013e158	−0.301714
$383$	−7.95829e158	−1.08167	−0.540835	−	0.841129i	$-0.681892\pi$
$383$	−7.95829e158	−1.08167	−0.540835	+	0.841129i	$0.681892\pi$
$384$	4.60898e157	0.0533623
$385$	−3.55168e157	−0.0350428
$386$	−6.55896e158	−0.551716
$387$	1.18677e159	0.851418
$388$	−2.56259e159	−1.56866
$389$	−4.66845e158	−0.243934	−0.121967	−	0.992534i	$-0.538920\pi$
$389$	−4.66845e158	−0.243934	−0.121967	+	0.992534i	$0.538920\pi$
$390$	−8.57026e156	−0.00382402
$391$	1.82380e159	0.695196
$392$	−1.84065e159	−0.599623
$393$	3.57798e158	0.0996543
$394$	−9.87043e157	−0.0235136
$395$	2.05317e157	0.00418508
$396$	−2.96507e159	−0.517346
$397$	2.78348e159	0.415884	0.207942	−	0.978141i	$-0.433324\pi$
$397$	2.78348e159	0.415884	0.207942	+	0.978141i	$0.433324\pi$
$398$	5.17808e159	0.662765
$399$	2.69690e157	0.00295823
$400$	−5.39613e159	−0.507449
$401$	2.29607e160	1.85185	0.925926	−	0.377706i	$-0.123287\pi$
$401$	2.29607e160	1.85185	0.925926	+	0.377706i	$0.123287\pi$
$402$	2.93149e158	0.0202855
$403$	1.26960e160	0.754059
$404$	−2.41640e160	−1.23230
$405$	2.77914e159	0.121738
$406$	−4.97909e159	−0.187413
$407$	1.79702e160	0.581429
$408$	−1.06976e159	−0.0297637
$409$	−2.39038e160	−0.572115	−0.286057	−	0.958212i	$-0.592345\pi$
$409$	−2.39038e160	−0.572115	−0.286057	+	0.958212i	$0.592345\pi$
$410$	−6.72951e158	−0.0138604
$411$	−2.48649e159	−0.0440874
$412$	−8.36645e160	−1.27750
$413$	3.61026e160	0.474909
$414$	−3.37773e160	−0.382917
$415$	−5.81270e159	−0.0568094
$416$	−1.65152e161	−1.39201
$417$	−4.69854e159	−0.0341661
$418$	5.10807e159	0.0320565
$419$	2.44400e161	1.32416	0.662078	−	0.749435i	$-0.269675\pi$
$419$	2.44400e161	1.32416	0.662078	+	0.749435i	$0.269675\pi$
$420$	−5.19920e158	−0.00243279
$421$	2.89517e161	1.17038	0.585188	−	0.810898i	$-0.301021\pi$
$421$	2.89517e161	1.17038	0.585188	+	0.810898i	$0.301021\pi$
$422$	−1.40423e161	−0.490593
$423$	3.18154e161	0.960960
$424$	−6.26054e160	−0.163535
$425$	3.26679e161	0.738248
$426$	−1.57218e160	−0.0307477
$427$	8.98094e160	0.152057
$428$	−6.19718e161	−0.908663
$429$	−3.70902e160	−0.0471124
$430$	3.94149e160	0.0433861
$431$	2.24782e161	0.214492	0.107246	−	0.994233i	$-0.465797\pi$
$431$	2.24782e161	0.214492	0.107246	+	0.994233i	$0.465797\pi$
$432$	−6.52303e160	−0.0539758
$433$	−8.10844e161	−0.582012	−0.291006	−	0.956721i	$-0.593990\pi$
$433$	−8.10844e161	−0.582012	−0.291006	+	0.956721i	$0.593990\pi$
$434$	−1.59307e161	−0.0992239
$435$	1.18236e160	0.00639237
$436$	−2.19279e162	−1.02938
$437$	−2.81333e161	−0.114713
$438$	3.67585e160	0.0130227
$439$	−1.38049e162	−0.425075	−0.212538	−	0.977153i	$-0.568173\pi$
$439$	−1.38049e162	−0.425075	−0.212538	+	0.977153i	$0.568173\pi$
$440$	−2.17320e161	−0.0581781
$441$	3.39269e162	0.789898
$442$	2.19777e162	0.445157
$443$	−1.58292e162	−0.279016	−0.139508	−	0.990221i	$-0.544552\pi$
$443$	−1.58292e162	−0.279016	−0.139508	+	0.990221i	$0.544552\pi$
$444$	2.63060e161	0.0403648
$445$	7.21469e161	0.0964000
$446$	4.56973e162	0.531860
$447$	1.31292e161	0.0133146
$448$	−5.85580e161	−0.0517593
$449$	1.09277e163	0.842131	0.421065	−	0.907030i	$-0.361656\pi$
$449$	1.09277e163	0.842131	0.421065	+	0.907030i	$0.361656\pi$
$450$	−6.05018e162	−0.406630
$451$	−2.91238e162	−0.170762
$452$	2.14429e163	1.09716
$453$	1.71513e162	0.0766052
$454$	6.54784e160	0.00255366
$455$	2.35723e162	0.0802974
$456$	1.65017e161	0.00491125
$457$	−6.18133e163	−1.60781	−0.803907	−	0.594755i	$-0.797249\pi$
$457$	−6.18133e163	−1.60781	−0.803907	+	0.594755i	$0.797249\pi$
$458$	−2.43325e163	−0.553298
$459$	3.94901e162	0.0785251
$460$	5.42366e162	0.0943378
$461$	−5.18425e163	−0.789003	−0.394502	−	0.918895i	$-0.629083\pi$
$461$	−5.18425e163	−0.789003	−0.394502	+	0.918895i	$0.629083\pi$
$462$	4.65402e161	0.00619936
$463$	−6.10085e163	−0.711475	−0.355737	−	0.934586i	$-0.615770\pi$
$463$	−6.10085e163	−0.711475	−0.355737	+	0.934586i	$0.615770\pi$
$464$	5.00843e163	0.511500
$465$	3.78300e161	0.00338438
$466$	1.41333e163	0.110793
$467$	5.60530e163	0.385133	0.192567	−	0.981284i	$-0.438319\pi$
$467$	5.60530e163	0.385133	0.192567	+	0.981284i	$0.438319\pi$
$468$	1.96790e164	1.18545
$469$	−8.06300e163	−0.425958
$470$	1.05665e163	0.0489681
$471$	−1.71972e163	−0.0699315
$472$	2.20904e164	0.788444
$473$	1.70579e164	0.534522
$474$	−2.69041e161	−0.000740374 0
$475$	−5.03923e163	−0.121817
$476$	1.33329e164	0.283203
$477$	1.15394e164	0.215429
$478$	4.25503e164	0.698373
$479$	−1.26103e165	−1.82008	−0.910042	−	0.414516i	$-0.863951\pi$
$479$	−1.26103e165	−1.82008	−0.910042	+	0.414516i	$0.863951\pi$
$480$	−4.92100e162	−0.00624766
$481$	−1.19267e165	−1.33229
$482$	6.37697e163	0.0626933
$483$	−2.56325e163	−0.0221842
$484$	6.61099e164	0.503822
$485$	3.46191e164	0.232380
$486$	−1.09756e164	−0.0649077
$487$	−2.36346e165	−1.23174	−0.615868	−	0.787850i	$-0.711194\pi$
$487$	−2.36346e165	−1.23174	−0.615868	+	0.787850i	$0.711194\pi$
$488$	5.49524e164	0.252446
$489$	−1.00840e164	−0.0408447
$490$	1.12678e164	0.0402512
$491$	3.96846e165	1.25058	0.625288	−	0.780394i	$-0.284981\pi$
$491$	3.96846e165	1.25058	0.625288	+	0.780394i	$0.284981\pi$
$492$	−4.26335e163	−0.0118549
$493$	−3.03208e165	−0.744140
$494$	−3.39020e164	−0.0734544
$495$	4.00564e164	0.0766394
$496$	1.60246e165	0.270809
$497$	4.32425e165	0.645644
$498$	7.61680e163	0.0100500
$499$	1.34804e166	1.57224	0.786118	−	0.618077i	$-0.212088\pi$
$499$	1.34804e166	1.57224	0.786118	+	0.618077i	$0.212088\pi$
$500$	1.95783e165	0.201892
$501$	2.67059e163	0.00243549
$502$	−5.84836e165	−0.471797
$503$	−1.22842e166	−0.876832	−0.438416	−	0.898772i	$-0.644460\pi$
$503$	−1.22842e166	−0.876832	−0.438416	+	0.898772i	$0.644460\pi$
$504$	−5.44933e165	−0.344243
$505$	3.26442e165	0.182552
$506$	−4.85494e165	−0.240396
$507$	1.26555e165	0.0554995
$508$	−2.49329e166	−0.968624
$509$	5.10455e165	0.175717	0.0878586	−	0.996133i	$-0.471998\pi$
$509$	5.10455e165	0.175717	0.0878586	+	0.996133i	$0.471998\pi$
$510$	6.54867e163	0.00199796
$511$	−1.01104e166	−0.273452
$512$	−3.71080e166	−0.889949
$513$	−6.09160e164	−0.0129573
$514$	6.75784e165	0.127519
$515$	1.13026e166	0.189249
$516$	2.49706e165	0.0371083
$517$	4.57295e166	0.603293
$518$	1.49655e166	0.175311
$519$	8.36806e165	0.0870628
$520$	1.44234e166	0.133310
$521$	1.22140e167	1.00309	0.501545	−	0.865132i	$-0.332765\pi$
$521$	1.22140e167	1.00309	0.501545	+	0.865132i	$0.332765\pi$
$522$	5.61549e166	0.409875
$523$	2.63026e167	1.70665	0.853327	−	0.521376i	$-0.174581\pi$
$523$	2.63026e167	1.70665	0.853327	+	0.521376i	$0.174581\pi$
$524$	−2.72861e167	−1.57423
$525$	−4.59129e165	−0.0235580
$526$	−3.55997e166	−0.162488
$527$	−9.70119e166	−0.393978
$528$	−4.68144e165	−0.0169197
$529$	−4.34394e166	−0.139753
$530$	3.83246e165	0.0109777
$531$	−4.07171e167	−1.03864
$532$	−2.05669e166	−0.0467307
$533$	1.93293e167	0.391285
$534$	−9.45392e165	−0.0170539
$535$	8.37203e166	0.134609
$536$	−4.93358e167	−0.707176
$537$	−6.71669e166	−0.0858493
$538$	−6.78797e167	−0.773802
$539$	4.87644e167	0.495900
$540$	1.17436e166	0.0106558
$541$	1.72950e166	0.0140052	0.00700259	−	0.999975i	$-0.497771\pi$
$541$	1.72950e166	0.0140052	0.00700259	+	0.999975i	$0.497771\pi$
$542$	3.42145e167	0.247317
$543$	8.92244e165	0.00575830
$544$	1.26195e168	0.727294
$545$	2.96232e167	0.152492
$546$	−3.08885e166	−0.0142053
$547$	1.32325e168	0.543778	0.271889	−	0.962329i	$-0.412352\pi$
$547$	1.32325e168	0.543778	0.271889	+	0.962329i	$0.412352\pi$
$548$	1.89623e168	0.696444
$549$	−1.01288e168	−0.332553
$550$	−8.69615e167	−0.255283
$551$	4.67717e167	0.122789
$552$	−1.56840e167	−0.0368301
$553$	7.39993e166	0.0155465
$554$	1.95143e168	0.366861
$555$	−3.55379e166	−0.00597962
$556$	3.58316e168	0.539718
$557$	−1.01453e169	−1.36826	−0.684131	−	0.729359i	$-0.739818\pi$
$557$	−1.01453e169	−1.36826	−0.684131	+	0.729359i	$0.739818\pi$
$558$	1.79669e168	0.217005
$559$	−1.13212e169	−1.22481
$560$	2.97524e167	0.0288376
$561$	2.83412e167	0.0246152
$562$	6.46952e168	0.503603
$563$	−2.49540e169	−1.74130	−0.870651	−	0.491901i	$-0.836302\pi$
$563$	−2.49540e169	−1.74130	−0.870651	+	0.491901i	$0.836302\pi$
$564$	6.69421e167	0.0418826
$565$	−2.89681e168	−0.162533
$566$	−4.78770e168	−0.240944
$567$	1.00164e169	0.452225
$568$	2.64591e169	1.07190
$569$	2.91935e169	1.06141	0.530703	−	0.847558i	$-0.321928\pi$
$569$	2.91935e169	1.06141	0.530703	+	0.847558i	$0.321928\pi$
$570$	−1.01017e166	−0.000329680 0
$571$	−1.12170e169	−0.328667	−0.164333	−	0.986405i	$-0.552547\pi$
$571$	−1.12170e169	−0.328667	−0.164333	+	0.986405i	$0.552547\pi$
$572$	2.82854e169	0.744229
$573$	1.61769e168	0.0382285
$574$	−2.42541e168	−0.0514878
$575$	4.78950e169	0.913520
$576$	6.60425e168	0.113199
$577$	−7.64139e169	−1.17723	−0.588613	−	0.808415i	$-0.700326\pi$
$577$	−7.64139e169	−1.17723	−0.588613	+	0.808415i	$0.700326\pi$
$578$	1.30982e169	0.181405
$579$	5.61357e168	0.0699049
$580$	−9.01685e168	−0.100979
$581$	−2.09498e169	−0.211032
$582$	−4.53638e168	−0.0411099
$583$	1.65861e169	0.135247
$584$	−6.18631e169	−0.453985
$585$	−2.65852e169	−0.175612
$586$	−1.18124e170	−0.702480
$587$	−1.12143e170	−0.600524	−0.300262	−	0.953857i	$-0.597074\pi$
$587$	−1.12143e170	−0.600524	−0.300262	+	0.953857i	$0.597074\pi$
$588$	7.13848e168	0.0344271
$589$	1.49647e169	0.0650095
$590$	−1.35229e169	−0.0529263
$591$	8.44773e167	0.00297927
$592$	−1.50536e170	−0.478472
$593$	5.66060e170	1.62181	0.810904	−	0.585180i	$-0.198976\pi$
$593$	5.66060e170	1.62181	0.810904	+	0.585180i	$0.198976\pi$
$594$	−1.05122e169	−0.0271536
$595$	−1.80120e169	−0.0419535
$596$	−1.00125e170	−0.210328
$597$	−4.43172e169	−0.0839752
$598$	3.22220e170	0.550845
$599$	1.17312e170	0.180965	0.0904825	−	0.995898i	$-0.471159\pi$
$599$	1.17312e170	0.180965	0.0904825	+	0.995898i	$0.471159\pi$
$600$	−2.80931e169	−0.0391109
$601$	3.25731e170	0.409335	0.204668	−	0.978832i	$-0.434389\pi$
$601$	3.25731e170	0.409335	0.204668	+	0.978832i	$0.434389\pi$
$602$	1.42057e170	0.161168
$603$	9.09357e170	0.931580
$604$	−1.30798e171	−1.21012
$605$	−8.93106e169	−0.0746358
$606$	−4.27760e169	−0.0322949
$607$	1.82912e171	1.24778	0.623889	−	0.781513i	$-0.285552\pi$
$607$	1.82912e171	1.24778	0.623889	+	0.781513i	$0.285552\pi$
$608$	−1.94664e170	−0.120009
$609$	4.26142e169	0.0237460
$610$	−3.36398e169	−0.0169460
$611$	−3.03504e171	−1.38239
$612$	−1.50371e171	−0.619371
$613$	−2.39664e171	−0.892859	−0.446429	−	0.894819i	$-0.647305\pi$
$613$	−2.39664e171	−0.892859	−0.446429	+	0.894819i	$0.647305\pi$
$614$	−3.86436e170	−0.130233
$615$	5.75953e168	0.00175617
$616$	−7.83252e170	−0.216116
$617$	3.82244e170	0.0954559	0.0477280	−	0.998860i	$-0.484802\pi$
$617$	3.82244e170	0.0954559	0.0477280	+	0.998860i	$0.484802\pi$
$618$	−1.48106e170	−0.0334796
$619$	5.08428e171	1.04053	0.520265	−	0.854005i	$-0.325833\pi$
$619$	5.08428e171	1.04053	0.520265	+	0.854005i	$0.325833\pi$
$620$	−2.88496e170	−0.0534626
$621$	5.78973e170	0.0971683
$622$	−2.82037e171	−0.428743
$623$	2.60028e171	0.358101
$624$	3.10705e170	0.0387700
$625$	8.44570e171	0.955024
$626$	−4.11408e170	−0.0421649
$627$	−4.37181e169	−0.00406170
$628$	1.31148e172	1.10470
$629$	9.11341e171	0.696091
$630$	3.33587e170	0.0231082
$631$	−2.13646e172	−1.34242	−0.671210	−	0.741267i	$-0.734225\pi$
$631$	−2.13646e172	−1.34242	−0.671210	+	0.741267i	$0.734225\pi$
$632$	4.52785e170	0.0258102
$633$	1.20182e171	0.0621602
$634$	5.86346e170	0.0275210
$635$	3.36829e171	0.143491
$636$	2.42798e170	0.00938930
$637$	−3.23647e172	−1.13631
$638$	8.07135e171	0.257321
$639$	−4.87695e172	−1.41204
$640$	4.74837e171	0.124875
$641$	−4.80302e172	−1.14748	−0.573740	−	0.819037i	$-0.694508\pi$
$641$	−4.80302e172	−1.14748	−0.573740	+	0.819037i	$0.694508\pi$
$642$	−1.09705e171	−0.0238134
$643$	9.01092e172	1.77744	0.888719	−	0.458453i	$-0.151596\pi$
$643$	9.01092e172	1.77744	0.888719	+	0.458453i	$0.151596\pi$
$644$	1.95477e172	0.350440
$645$	−3.37337e170	−0.00549721
$646$	2.59051e171	0.0383782
$647$	−8.43377e172	−1.13608	−0.568039	−	0.823001i	$-0.692298\pi$
$647$	−8.43377e172	−1.13608	−0.568039	+	0.823001i	$0.692298\pi$
$648$	6.12883e172	0.750783
$649$	−5.85242e172	−0.652058
$650$	5.77159e172	0.584957
$651$	1.36345e171	0.0125721
$652$	7.69014e172	0.645219
$653$	7.39243e171	0.0564452	0.0282226	−	0.999602i	$-0.491015\pi$
$653$	7.39243e171	0.0564452	0.0282226	+	0.999602i	$0.491015\pi$
$654$	−3.88174e171	−0.0269771
$655$	3.68619e172	0.233205
$656$	2.43970e172	0.140524
$657$	1.14026e173	0.598045
$658$	3.80832e172	0.181904
$659$	5.31616e172	0.231283	0.115642	−	0.993291i	$-0.463108\pi$
$659$	5.31616e172	0.231283	0.115642	+	0.993291i	$0.463108\pi$
$660$	8.42816e170	0.00334026
$661$	−3.10880e172	−0.112254	−0.0561272	−	0.998424i	$-0.517875\pi$
$661$	−3.10880e172	−0.112254	−0.0561272	+	0.998424i	$0.517875\pi$
$662$	−1.62388e173	−0.534303
$663$	−1.88099e172	−0.0564034
$664$	−1.28188e173	−0.350355
$665$	2.77846e171	0.00692266
$666$	−1.68783e173	−0.383410
$667$	−4.44539e173	−0.920812
$668$	−2.03662e172	−0.0384731
$669$	−3.91107e172	−0.0673890
$670$	3.02015e172	0.0474709
$671$	−1.45586e173	−0.208777
$672$	−1.77360e172	−0.0232084
$673$	1.04568e173	0.124874	0.0624368	−	0.998049i	$-0.480113\pi$
$673$	1.04568e173	0.124874	0.0624368	+	0.998049i	$0.480113\pi$
$674$	−2.33650e173	−0.254673
$675$	1.03705e173	0.103186
$676$	−9.65122e173	−0.876719
$677$	1.41595e174	1.17447	0.587237	−	0.809415i	$-0.300216\pi$
$677$	1.41595e174	1.17447	0.587237	+	0.809415i	$0.300216\pi$
$678$	3.79590e172	0.0287534
$679$	1.24772e174	0.863231
$680$	−1.10211e173	−0.0696512
$681$	−5.60405e170	−0.000323560 0
$682$	2.58244e173	0.136236
$683$	2.96475e174	1.42927	0.714637	−	0.699496i	$-0.246592\pi$
$683$	2.96475e174	1.42927	0.714637	+	0.699496i	$0.246592\pi$
$684$	2.31956e173	0.102201
$685$	−2.56169e173	−0.103171
$686$	9.18818e173	0.338296
$687$	2.08252e173	0.0701053
$688$	−1.42894e174	−0.439871
$689$	−1.10081e174	−0.309906
$690$	9.60114e171	0.00247231
$691$	−2.99309e174	−0.705051	−0.352525	−	0.935802i	$-0.614677\pi$
$691$	−2.99309e174	−0.705051	−0.352525	+	0.935802i	$0.614677\pi$
$692$	−6.38158e174	−1.37532
$693$	1.44369e174	0.284695
$694$	−3.47120e171	−0.000626430 0
$695$	−4.84064e173	−0.0799534
$696$	2.60747e173	0.0394231
$697$	−1.47699e174	−0.204437
$698$	−1.85800e174	−0.235471
$699$	−1.20962e173	−0.0140379
$700$	3.50137e174	0.372142
$701$	−1.44173e174	−0.140354	−0.0701770	−	0.997535i	$-0.522356\pi$
$701$	−1.44173e174	−0.140354	−0.0701770	+	0.997535i	$0.522356\pi$
$702$	6.97691e173	0.0622201
$703$	−1.40580e174	−0.114861
$704$	9.49254e173	0.0710663
$705$	−9.04347e172	−0.00620447
$706$	−2.50059e174	−0.157237
$707$	1.17654e175	0.678132
$708$	−8.56718e173	−0.0452681
$709$	2.28978e175	1.10930	0.554652	−	0.832082i	$-0.312851\pi$
$709$	2.28978e175	1.10930	0.554652	+	0.832082i	$0.312851\pi$
$710$	−1.61973e174	−0.0719538
$711$	−8.34574e173	−0.0340004
$712$	1.59105e175	0.594519
$713$	−1.42231e175	−0.487515
$714$	2.36024e173	0.00742191
$715$	−3.82119e174	−0.110250
$716$	5.12222e175	1.35615
$717$	−3.64172e174	−0.0884869
$718$	−3.22922e175	−0.720185
$719$	−7.94807e175	−1.62718	−0.813589	−	0.581441i	$-0.802489\pi$
$719$	−7.94807e175	−1.62718	−0.813589	+	0.581441i	$0.802489\pi$
$720$	−3.35552e174	−0.0630684
$721$	4.07362e175	0.703010
$722$	2.57236e175	0.407657
$723$	−5.45781e173	−0.00794352
$724$	−6.80436e174	−0.0909631
$725$	−7.96257e175	−0.977835
$726$	1.17030e174	0.0132037
$727$	−7.22576e175	−0.749062	−0.374531	−	0.927214i	$-0.622196\pi$
$727$	−7.22576e175	−0.749062	−0.374531	+	0.927214i	$0.622196\pi$
$728$	5.19840e175	0.495211
$729$	−1.12339e176	−0.983529
$730$	3.78702e174	0.0304749
$731$	8.65074e175	0.639933
$732$	−2.13118e174	−0.0144940
$733$	−1.46045e176	−0.913255	−0.456627	−	0.889658i	$-0.650943\pi$
$733$	−1.46045e176	−0.913255	−0.456627	+	0.889658i	$0.650943\pi$
$734$	6.77680e175	0.389688
$735$	−9.64366e173	−0.00510001
$736$	1.85017e176	0.899966
$737$	1.30705e176	0.584848
$738$	2.73542e175	0.112605
$739$	4.81140e176	1.82238	0.911190	−	0.411987i	$-0.135165\pi$
$739$	4.81140e176	1.82238	0.911190	+	0.411987i	$0.135165\pi$
$740$	2.71016e175	0.0944592
$741$	2.90155e174	0.00930700
$742$	1.38128e175	0.0407794
$743$	−3.95031e176	−1.07354	−0.536771	−	0.843728i	$-0.680356\pi$
$743$	−3.95031e176	−1.07354	−0.536771	+	0.843728i	$0.680356\pi$
$744$	8.34264e174	0.0208722
$745$	1.35263e175	0.0311579
$746$	−2.16670e176	−0.459580
$747$	2.36275e176	0.461532
$748$	−2.16133e176	−0.388842
$749$	3.01740e176	0.500036
$750$	3.46581e174	0.00529100
$751$	−9.12641e176	−1.28364	−0.641821	−	0.766854i	$-0.721821\pi$
$751$	−9.12641e176	−1.28364	−0.641821	+	0.766854i	$0.721821\pi$
$752$	−3.83076e176	−0.496464
$753$	5.00539e175	0.0597787
$754$	−5.35691e176	−0.589626
$755$	1.76700e176	0.179267
$756$	4.23258e175	0.0395836
$757$	2.56865e176	0.221467	0.110733	−	0.993850i	$-0.464680\pi$
$757$	2.56865e176	0.221467	0.110733	+	0.993850i	$0.464680\pi$
$758$	−8.90732e176	−0.708094
$759$	4.15516e175	0.0304592
$760$	1.70008e175	0.0114930
$761$	9.12474e176	0.568937	0.284468	−	0.958685i	$-0.408183\pi$
$761$	9.12474e176	0.568937	0.284468	+	0.958685i	$0.408183\pi$
$762$	−4.41371e175	−0.0253848
$763$	1.06767e177	0.566469
$764$	−1.23367e177	−0.603890
$765$	2.03142e176	0.0917532
$766$	1.07437e177	0.447800
$767$	3.88422e177	1.49413
$768$	−4.54512e175	−0.0161373
$769$	1.46574e177	0.480384	0.240192	−	0.970725i	$-0.422790\pi$
$769$	1.46574e177	0.480384	0.240192	+	0.970725i	$0.422790\pi$
$770$	4.79477e175	0.0145073
$771$	−5.78379e175	−0.0161573
$772$	−4.28097e177	−1.10428
$773$	−1.09501e176	−0.0260843	−0.0130422	−	0.999915i	$-0.504152\pi$
$773$	−1.09501e176	−0.0260843	−0.0130422	+	0.999915i	$0.504152\pi$
$774$	−1.60214e177	−0.352478
$775$	−2.54764e177	−0.517706
$776$	7.63454e177	1.43314
$777$	−1.28084e176	−0.0222127
$778$	6.30241e176	0.100986
$779$	2.27834e176	0.0337338
$780$	−5.59373e175	−0.00765391
$781$	−7.00983e177	−0.886479
$782$	−2.46213e177	−0.287804
$783$	−9.62544e176	−0.104009
$784$	−4.08500e177	−0.408088
$785$	−1.77173e177	−0.163649
$786$	−4.83027e176	−0.0412558
$787$	−6.05024e177	−0.477888	−0.238944	−	0.971033i	$-0.576801\pi$
$787$	−6.05024e177	−0.477888	−0.238944	+	0.971033i	$0.576801\pi$
$788$	−6.44234e176	−0.0470632
$789$	3.04684e176	0.0205880
$790$	−2.77178e175	−0.00173258
$791$	−1.04405e178	−0.603767
$792$	8.83363e177	0.472651
$793$	9.66243e177	0.478394
$794$	−3.75770e177	−0.172171
$795$	−3.28006e175	−0.00139093
$796$	3.37968e178	1.32655
$797$	9.16592e177	0.333035	0.166517	−	0.986039i	$-0.446748\pi$
$797$	9.16592e177	0.333035	0.166517	+	0.986039i	$0.446748\pi$
$798$	−3.64081e175	−0.00122467
$799$	2.31913e178	0.722266
$800$	3.31402e178	0.955698
$801$	−2.93263e178	−0.783174
$802$	−3.09969e178	−0.766647
$803$	1.63894e178	0.375454
$804$	1.91336e177	0.0406021
$805$	−2.64077e177	−0.0519140
$806$	−1.71395e178	−0.312172
$807$	5.80957e177	0.0980442
$808$	7.19902e178	1.12584
$809$	−3.90981e178	−0.566659	−0.283330	−	0.959023i	$-0.591439\pi$
$809$	−3.90981e178	−0.566659	−0.283330	+	0.959023i	$0.591439\pi$
$810$	−3.75183e177	−0.0503982
$811$	−1.47885e179	−1.84138	−0.920689	−	0.390297i	$-0.872372\pi$
$811$	−1.47885e179	−1.84138	−0.920689	+	0.390297i	$0.872372\pi$
$812$	−3.24981e178	−0.375113
$813$	−2.92829e177	−0.0313362
$814$	−2.42598e178	−0.240705
$815$	−1.03889e178	−0.0955823
$816$	−2.37415e177	−0.0202564
$817$	−1.33443e178	−0.105594
$818$	3.22701e178	0.236849
$819$	−9.58170e178	−0.652353
$820$	−4.39229e177	−0.0277421
$821$	4.57462e178	0.268071	0.134036	−	0.990977i	$-0.457206\pi$
$821$	4.57462e178	0.268071	0.134036	+	0.990977i	$0.457206\pi$
$822$	3.35676e177	0.0182517
$823$	2.05605e179	1.03739	0.518696	−	0.854959i	$-0.326418\pi$
$823$	2.05605e179	1.03739	0.518696	+	0.854959i	$0.326418\pi$
$824$	2.49256e179	1.16714
$825$	7.44271e177	0.0323455
$826$	−4.87386e178	−0.196607
$827$	1.83106e179	0.685668	0.342834	−	0.939396i	$-0.388613\pi$
$827$	1.83106e179	0.685668	0.342834	+	0.939396i	$0.388613\pi$
$828$	−2.20461e179	−0.766420
$829$	4.12949e178	0.133289	0.0666443	−	0.997777i	$-0.478771\pi$
$829$	4.12949e178	0.133289	0.0666443	+	0.997777i	$0.478771\pi$
$830$	7.84715e177	0.0235185
$831$	−1.67015e178	−0.0464829
$832$	−6.30015e178	−0.162842
$833$	2.47304e179	0.593695
$834$	6.34303e177	0.0141444
$835$	2.75135e177	0.00569939
$836$	3.33399e178	0.0641621
$837$	−3.07968e178	−0.0550667
$838$	−3.29940e179	−0.548186
$839$	2.17008e179	0.335054	0.167527	−	0.985867i	$-0.446422\pi$
$839$	2.17008e179	0.335054	0.167527	+	0.985867i	$0.446422\pi$
$840$	1.54896e177	0.00222262
$841$	−1.07669e178	−0.0143594
$842$	−3.90848e179	−0.484523
$843$	−5.53702e178	−0.0638088
$844$	−9.16525e179	−0.981937
$845$	1.30382e179	0.129877
$846$	−4.29508e179	−0.397827
$847$	−3.21889e179	−0.277253
$848$	−1.38942e179	−0.111298
$849$	4.09761e178	0.0305287
$850$	−4.41017e179	−0.305627
$851$	1.33613e180	0.861355
$852$	−1.02615e179	−0.0615424
$853$	−1.07110e179	−0.0597674	−0.0298837	−	0.999553i	$-0.509514\pi$
$853$	−1.07110e179	−0.0597674	−0.0298837	+	0.999553i	$0.509514\pi$
$854$	−1.21243e179	−0.0629501
$855$	−3.13359e178	−0.0151400
$856$	1.84628e180	0.830160
$857$	2.04472e180	0.855682	0.427841	−	0.903854i	$-0.359274\pi$
$857$	2.04472e180	0.855682	0.427841	+	0.903854i	$0.359274\pi$
$858$	5.00718e178	0.0195040
$859$	−1.90159e180	−0.689507	−0.344753	−	0.938693i	$-0.612037\pi$
$859$	−1.90159e180	−0.689507	−0.344753	+	0.938693i	$0.612037\pi$
$860$	2.57257e179	0.0868386
$861$	2.07582e178	0.00652373
$862$	−3.03456e179	−0.0887972
$863$	4.73695e180	1.29073	0.645365	−	0.763875i	$-0.276705\pi$
$863$	4.73695e180	1.29073	0.645365	+	0.763875i	$0.276705\pi$
$864$	4.00610e179	0.101655
$865$	8.62114e179	0.203739
$866$	1.09464e180	0.240947
$867$	−1.12103e179	−0.0229848
$868$	−1.03978e180	−0.198600
$869$	−1.19956e179	−0.0213456
$870$	−1.59619e178	−0.00264637
$871$	−8.67484e180	−1.34012
$872$	6.53281e180	0.940451
$873$	−1.40720e181	−1.88790
$874$	3.79799e179	0.0474899
$875$	−9.53265e179	−0.111101
$876$	2.39919e179	0.0260653
$877$	−1.50755e181	−1.52685	−0.763424	−	0.645898i	$-0.776483\pi$
$877$	−1.50755e181	−1.52685	−0.763424	+	0.645898i	$0.776483\pi$
$878$	1.86366e180	0.175977
$879$	1.01098e180	0.0890073
$880$	−4.82302e179	−0.0395945
$881$	2.11745e181	1.62105	0.810523	−	0.585707i	$-0.199183\pi$
$881$	2.11745e181	1.62105	0.810523	+	0.585707i	$0.199183\pi$
$882$	−4.58013e180	−0.327009
$883$	−1.17339e181	−0.781376	−0.390688	−	0.920523i	$-0.627763\pi$
$883$	−1.17339e181	−0.781376	−0.390688	+	0.920523i	$0.627763\pi$
$884$	1.43447e181	0.890996
$885$	1.15738e179	0.00670599
$886$	2.13694e180	0.115510
$887$	1.48546e181	0.749134	0.374567	−	0.927200i	$-0.377791\pi$
$887$	1.48546e181	0.749134	0.374567	+	0.927200i	$0.377791\pi$
$888$	−7.83717e179	−0.0368775
$889$	1.21398e181	0.533033
$890$	−9.73983e179	−0.0399085
$891$	−1.62371e181	−0.620912
$892$	2.98262e181	1.06453
$893$	−3.57739e180	−0.119180
$894$	−1.77245e179	−0.00551209
$895$	−6.91982e180	−0.200899
$896$	1.71138e181	0.463878
$897$	−2.75776e180	−0.0697945
$898$	−1.47524e181	−0.348633
$899$	2.36460e181	0.521838
$900$	−3.94890e181	−0.813882
$901$	8.41146e180	0.161919
$902$	3.93172e180	0.0706936
$903$	−1.21581e180	−0.0204207
$904$	−6.38834e181	−1.00237
$905$	9.19228e179	0.0134752
$906$	−2.31543e180	−0.0317137
$907$	−2.53418e181	−0.324332	−0.162166	−	0.986763i	$-0.551848\pi$
$907$	−2.53418e181	−0.324332	−0.162166	+	0.986763i	$0.551848\pi$
$908$	4.27371e179	0.00511123
$909$	−1.32692e182	−1.48309
$910$	−3.18226e180	−0.0332422
$911$	1.12329e182	1.09676	0.548382	−	0.836228i	$-0.315244\pi$
$911$	1.12329e182	1.09676	0.548382	+	0.836228i	$0.315244\pi$
$912$	3.66227e179	0.00334247
$913$	3.39607e181	0.289751
$914$	8.34480e181	0.665618
$915$	2.87910e179	0.00214714
$916$	−1.58816e182	−1.10744
$917$	1.32856e182	0.866295
$918$	−5.33117e180	−0.0325085
$919$	−1.60711e182	−0.916519	−0.458260	−	0.888818i	$-0.651527\pi$
$919$	−1.60711e182	−0.916519	−0.458260	+	0.888818i	$0.651527\pi$
$920$	−1.61583e181	−0.0861876
$921$	3.30736e180	0.0165011
$922$	6.99873e181	0.326639
$923$	4.65238e182	2.03129
$924$	3.03763e180	0.0124082
$925$	2.39328e182	0.914696
$926$	8.23615e181	0.294543
$927$	−4.59428e182	−1.53750
$928$	−3.07591e182	−0.963327
$929$	5.88179e182	1.72402	0.862011	−	0.506889i	$-0.169205\pi$
$929$	5.88179e182	1.72402	0.862011	+	0.506889i	$0.169205\pi$
$930$	−5.10705e179	−0.00140110
$931$	−3.81482e181	−0.0979644
$932$	9.22469e181	0.221755
$933$	2.41385e181	0.0543236
$934$	−7.56716e181	−0.159441
$935$	2.91983e181	0.0576029
$936$	−5.86283e182	−1.08304
$937$	−1.07177e183	−1.85403	−0.927016	−	0.375022i	$-0.877635\pi$
$937$	−1.07177e183	−1.85403	−0.927016	+	0.375022i	$0.877635\pi$
$938$	1.08851e182	0.176342
$939$	3.52109e180	0.00534248
$940$	6.89666e181	0.0980112
$941$	−4.32226e182	−0.575372	−0.287686	−	0.957725i	$-0.592886\pi$
$941$	−4.32226e182	−0.575372	−0.287686	+	0.957725i	$0.592886\pi$
$942$	2.32163e181	0.0289509
$943$	−2.16544e182	−0.252974
$944$	4.90257e182	0.536595
$945$	−5.71797e180	−0.00586389
$946$	−2.30282e182	−0.221286
$947$	1.73343e183	1.56093	0.780463	−	0.625202i	$-0.214983\pi$
$947$	1.73343e183	1.56093	0.780463	+	0.625202i	$0.214983\pi$
$948$	−1.75601e180	−0.00148188
$949$	−1.08776e183	−0.860318
$950$	6.80296e181	0.0504308
$951$	−5.01832e180	−0.00348703
$952$	−3.97218e182	−0.258736
$953$	1.90174e183	1.16128	0.580642	−	0.814159i	$-0.302802\pi$
$953$	1.90174e183	1.16128	0.580642	+	0.814159i	$0.302802\pi$
$954$	−1.55782e182	−0.0891853
$955$	1.66662e182	0.0894599
$956$	2.77722e183	1.39782
$957$	−6.90797e181	−0.0326037
$958$	1.70239e183	0.753495
$959$	−9.23271e182	−0.383252
$960$	−1.87725e180	−0.000730870 0
$961$	−1.98179e183	−0.723718
$962$	1.61011e183	0.551554
$963$	−3.40307e183	−1.09359
$964$	4.16219e182	0.125483
$965$	5.78334e182	0.163587
$966$	3.46039e181	0.00918400
$967$	−2.95800e183	−0.736664	−0.368332	−	0.929694i	$-0.620071\pi$
$967$	−2.95800e183	−0.736664	−0.368332	+	0.929694i	$0.620071\pi$
$968$	−1.96957e183	−0.460295
$969$	−2.21712e181	−0.00486269
$970$	−4.67358e182	−0.0962028
$971$	−3.34842e183	−0.646929	−0.323465	−	0.946240i	$-0.604848\pi$
$971$	−3.34842e183	−0.646929	−0.323465	+	0.946240i	$0.604848\pi$
$972$	−7.16364e182	−0.129915
$973$	−1.74464e183	−0.297006
$974$	3.19067e183	0.509925
$975$	−4.93969e182	−0.0741166
$976$	1.21957e183	0.171808
$977$	7.56696e183	1.00093	0.500467	−	0.865755i	$-0.333162\pi$
$977$	7.56696e183	1.00093	0.500467	+	0.865755i	$0.333162\pi$
$978$	1.36133e182	0.0169093
$979$	−4.21518e183	−0.491678
$980$	7.35437e182	0.0805641
$981$	−1.20413e184	−1.23888
$982$	−5.35742e183	−0.517725
$983$	1.70339e184	1.54623	0.773114	−	0.634268i	$-0.218698\pi$
$983$	1.70339e184	1.54623	0.773114	+	0.634268i	$0.218698\pi$
$984$	1.27015e182	0.0108307
$985$	8.70321e181	0.00697191
$986$	4.09331e183	0.308066
$987$	−3.25940e182	−0.0230480
$988$	−2.21275e183	−0.147021
$989$	1.26830e184	0.791864
$990$	−5.40761e182	−0.0317279
$991$	3.13740e184	1.72998	0.864988	−	0.501792i	$-0.167326\pi$
$991$	3.13740e184	1.72998	0.864988	+	0.501792i	$0.167326\pi$
$992$	−9.84144e183	−0.510024
$993$	1.38982e183	0.0676985
$994$	−5.83774e183	−0.267290
$995$	−4.56575e183	−0.196514
$996$	4.97141e182	0.0201155
$997$	8.44091e183	0.321098	0.160549	−	0.987028i	$-0.448674\pi$
$997$	8.44091e183	0.321098	0.160549	+	0.987028i	$0.448674\pi$
$998$	−1.81985e184	−0.650889
$999$	2.89308e183	0.0972934

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.124.a.a.1.4	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.124.a.a.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-1.35000e18 q^{2} +1.15541e28 q^{3} -8.81132e36 q^{4} +1.19036e42 q^{5} -1.55981e46 q^{6} +4.29022e51 q^{7} +2.62510e55 q^{8} -4.83858e58 q^{9} +O(q^{10})\)	\(q-1.35000e18 q^{2} +1.15541e28 q^{3} -8.81132e36 q^{4} +1.19036e42 q^{5} -1.55981e46 q^{6} +4.29022e51 q^{7} +2.62510e55 q^{8} -4.83858e58 q^{9} -1.60698e60 q^{10} -6.95467e63 q^{11} -1.01807e65 q^{12} +4.61578e68 q^{13} -5.79180e69 q^{14} +1.37536e70 q^{15} +5.82593e73 q^{16} -3.52699e75 q^{17} +6.53208e76 q^{18} +5.44060e77 q^{19} -1.04886e79 q^{20} +4.95699e79 q^{21} +9.38880e81 q^{22} -5.17099e83 q^{23} +3.03307e83 q^{24} -9.26226e85 q^{25} -6.23130e86 q^{26} -1.11966e87 q^{27} -3.78026e88 q^{28} +8.59679e89 q^{29} -1.85673e88 q^{30} +2.75056e91 q^{31} -3.57798e92 q^{32} -8.03553e91 q^{33} +4.76144e93 q^{34} +5.10690e93 q^{35} +4.26343e95 q^{36} -2.58390e96 q^{37} -7.34481e95 q^{38} +5.33314e96 q^{39} +3.12480e97 q^{40} +4.18767e98 q^{41} -6.69193e97 q^{42} -2.45273e100 q^{43} +6.12798e100 q^{44} -5.75964e100 q^{45} +6.98084e101 q^{46} -6.57537e102 q^{47} +6.73136e101 q^{48} -7.01175e103 q^{49} +1.25041e104 q^{50} -4.07514e103 q^{51} -4.06711e105 q^{52} -2.38488e105 q^{53} +1.51153e105 q^{54} -8.27854e105 q^{55} +1.12622e107 q^{56} +6.28615e105 q^{57} -1.16057e108 q^{58} +8.41509e108 q^{59} -1.21187e107 q^{60} +2.09335e109 q^{61} -3.71325e109 q^{62} -2.07586e110 q^{63} -1.36492e110 q^{64} +5.49442e110 q^{65} +1.08480e110 q^{66} -1.87939e112 q^{67} +3.10775e112 q^{68} -5.97464e111 q^{69} -6.89432e111 q^{70} +1.00793e114 q^{71} -1.27017e114 q^{72} -2.35660e114 q^{73} +3.48827e114 q^{74} -1.07018e114 q^{75} -4.79389e114 q^{76} -2.98371e115 q^{77} -7.19973e114 q^{78} +1.72483e115 q^{79} +6.93494e115 q^{80} +2.33471e117 q^{81} -5.65335e116 q^{82} -4.88316e117 q^{83} -4.36776e116 q^{84} -4.19838e117 q^{85} +3.31118e118 q^{86} +9.93285e117 q^{87} -1.82567e119 q^{88} +6.06094e119 q^{89} +7.77551e118 q^{90} +1.98027e120 q^{91} +4.55633e120 q^{92} +3.17803e119 q^{93} +8.87675e120 q^{94} +6.47626e119 q^{95} -4.13405e120 q^{96} +2.90829e122 q^{97} +9.46587e121 q^{98} +3.36507e122 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 22\!\cdots\!00 q^{2}+ \cdots + 11\!\cdots\!70 q^{9}+O(q^{10}) \) 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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