LMFDB - Embedded newform 1.112.a.a.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,112,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, 112, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 112);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 112 $
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:	$78.0257547452$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} + \cdots + 83\!\cdots\!00 $ x^9 - 3315922464294705608590165196340x^7 - 255555408771045262573740724659261076322467560x^6 + 3320202982441783582022071827204209719985134891553638695423030x^5 + 486090204777213459858612987370140469323683782886448261685463886479522250024x^4 - 993903666269142615407573465530289705623661908215275003413608826159739400453790801360794580x^3 - 213673821700016632402691584104288595326107445984799979280111640680075402748268946147918334592809157002200x^2 + 25978627876353238215912951424882678364963563964222013755846533827467381142125860355728302998720446833184794583100972625*x + 836305277856554948797002241464338930747139165236780477868307711306097431134007948005681053119621708958597452996847824637305875615000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{135}\cdot 3^{56}\cdot 5^{16}\cdot 7^{7}\cdot 11^{3}\cdot 13\cdot 19\cdot 37^{3} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-2.69685e13$ 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)

$f(q)$	$=$	$q-1.13057e15 q^{2} +1.34574e26 q^{3} -2.59487e33 q^{4} +1.00336e39 q^{5} -1.52145e41 q^{6} -8.67417e45 q^{7} +5.86879e48 q^{8} -7.31873e52 q^{9} +O(q^{10})$	\(q-1.13057e15 q^{2} +1.34574e26 q^{3} -2.59487e33 q^{4} +1.00336e39 q^{5} -1.52145e41 q^{6} -8.67417e45 q^{7} +5.86879e48 q^{8} -7.31873e52 q^{9} -1.13437e54 q^{10} +1.78506e57 q^{11} -3.49203e59 q^{12} +2.10514e61 q^{13} +9.80672e60 q^{14} +1.35027e65 q^{15} +6.73003e66 q^{16} +2.95295e68 q^{17} +8.27430e67 q^{18} -1.07798e71 q^{19} -2.60360e72 q^{20} -1.16732e72 q^{21} -2.01812e72 q^{22} -1.47561e75 q^{23} +7.89788e74 q^{24} +6.21551e77 q^{25} -2.38000e76 q^{26} -2.21355e79 q^{27} +2.25084e79 q^{28} +2.61440e81 q^{29} -1.52657e80 q^{30} -6.48392e82 q^{31} -2.28450e82 q^{32} +2.40223e83 q^{33} -3.33850e83 q^{34} -8.70334e84 q^{35} +1.89912e86 q^{36} -6.12579e86 q^{37} +1.21872e86 q^{38} +2.83298e87 q^{39} +5.88852e87 q^{40} -2.55361e89 q^{41} +1.31973e87 q^{42} +6.40828e90 q^{43} -4.63199e90 q^{44} -7.34334e91 q^{45} +1.66827e90 q^{46} +6.01122e92 q^{47} +9.05690e92 q^{48} -6.32038e93 q^{49} -7.02704e92 q^{50} +3.97391e94 q^{51} -5.46256e94 q^{52} -1.21175e95 q^{53} +2.50256e94 q^{54} +1.79106e96 q^{55} -5.09069e94 q^{56} -1.45068e97 q^{57} -2.95575e96 q^{58} +1.21787e98 q^{59} -3.50377e98 q^{60} +7.42509e98 q^{61} +7.33049e97 q^{62} +6.34839e98 q^{63} -1.74463e100 q^{64} +2.11222e100 q^{65} -2.71588e98 q^{66} +3.53383e101 q^{67} -7.66251e101 q^{68} -1.98579e101 q^{69} +9.83970e99 q^{70} +8.15428e102 q^{71} -4.29521e101 q^{72} -1.16063e103 q^{73} +6.92560e101 q^{74} +8.36449e103 q^{75} +2.79721e104 q^{76} -1.54839e103 q^{77} -3.20287e102 q^{78} +1.97268e105 q^{79} +6.75267e105 q^{80} +3.70296e105 q^{81} +2.88702e104 q^{82} +4.77769e106 q^{83} +3.02905e105 q^{84} +2.96288e107 q^{85} -7.24498e105 q^{86} +3.51832e107 q^{87} +1.04761e106 q^{88} +1.53326e108 q^{89} +8.30213e106 q^{90} -1.82603e107 q^{91} +3.82901e108 q^{92} -8.72570e108 q^{93} -6.79608e107 q^{94} -1.08160e110 q^{95} -3.07435e108 q^{96} -1.32081e110 q^{97} +7.14560e108 q^{98} -1.30643e110 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 73\!\cdots\!76 q^{2}+ \cdots + 44\!\cdots\!13 q^{9}+O(q^{10}) $ 9 * q + 7300500744476376 * q^2 + 233675452617241539765416652 * q^3 + 11020070169858572323722385321061952 * q^4 + 814194067724935025770916308591172296830 * q^5 - 21301527237484005705216688979545976184644832 * q^6 + 78389901636433627730832560362319405491179083256 * q^7 + 331917555337838634305814685721710111074446802593280 * q^8 + 448549390735821931740487725597506918142357121619864013 * q^9	$ 9 q + 73\!\cdots\!76 q^{2}+ \cdots - 30\!\cdots\!44 q^{99}+O(q^{100}) $ 9 * q + 7300500744476376 * q^2 + 233675452617241539765416652 * q^3 + 11020070169858572323722385321061952 * q^4 + 814194067724935025770916308591172296830 * q^5 - 21301527237484005705216688979545976184644832 * q^6 + 78389901636433627730832560362319405491179083256 * q^7 + 331917555337838634305814685721710111074446802593280 * q^8 + 448549390735821931740487725597506918142357121619864013 * q^9 + 70318383028880935426202467492101897354146229740372656080 * q^10 + 946977307561400491686882997086862420104457212380759419908 * q^11 + 621762406249451000840580799122879254067634743931860068057856 * q^12 - 105889073807861007951354048376593318148850899094543430238180938 * q^13 - 693200815745779812299859823081139405355406151517828024353685696 * q^14 - 263011530334644917620915776775966612573140691671014743658639898840 * q^15 + 27983078214052241229733802839129592879112204378169572191112640794624 * q^16 - 222105261114216680375344353232960019775132216853502752977555776836734 * q^17 + 13836898392348788400585588852374256049336540448485000158069800440043832 * q^18 - 84745728104868082450386145180218866587906565903531918441867146236497220 * q^19 + 7795554433199817270239288692578476214785961451581351341251140127219386240 * q^20 + 53447991875461898796552150181251304409032073759002376573082504235219586208 * q^21 + 1334480876839672633808741914071727189545841199132729059095736106759243606112 * q^22 - 4280804965700905487867557627761776334077515300975222519458633688084497477528 * q^23 - 129253468619699114441737651311892084919218132467191979241911494876891173877760 * q^24 - 456274260699810946496432078768368872244545007142930133725494539638375760654225 * q^25 + 9117596118629922830918453196718641926897783510547242670141134615123316525608208 * q^26 + 36009290264725541742540148694316715091842126661227810228968619953124574644440120 * q^27 + 389777110106676955938012042765885416118140162819674451900675730518240474989075968 * q^28 - 1612630879112671269089242330901312038613162417445580611832712505926453350563056730 * q^29 - 18167376599417385725382731299135244307087297190105602725235889269652594544837067840 * q^30 + 67559679369166080772885534172593278837571532071620973699499831976537741546761534688 * q^31 + 754093318949864663533121048615003094440304122496655835482200816722793265150805508096 * q^32 - 3133890070812326529166672578753895355679540062945915391855288247367239239009432080976 * q^33 - 24751022535879997806365605902203773919188021786642014954770492231640496515521010376656 * q^34 + 57944164206332657023724654984518766320829384409054668126147883688641566073099799278480 * q^35 + 328041564753120514775451575146434843390262564311310021231853773527241323710816435244864 * q^36 + 3043820559995771428343491307335152699983691109501186564620625804804431981535340669576286 * q^37 - 21382754992423793021134163907198673444659659051000850342253103089169961740533890647606880 * q^38 + 3273459216524867162345405450876825490686869325852879816870160180171296350982671401366216 * q^39 + 123460999717991511987771461057366625032200502337474727630106509260305540512417484610278400 * q^40 + 104629960197719783697927100274525225542843896456497561309270816521996960904985588920195178 * q^41 + 2027994299853353493651484516191980857294428743343203061454578749195409490693400034208902912 * q^42 - 19157176231150752403174922289745163210049080257481323543299910438470109245483512805859143708 * q^43 + 54900509500333144241574805152152293176467261284516409174290950395775810400803069025987309824 * q^44 + 15479509256451142996000421697851689107817887106618468041729343908392688500639929264156928310 * q^45 - 398788118873285310214184399746055204854113651152175668288210597675002274814165601481840895552 * q^46 + 1456966582071114763048986859064421525928331803997603240440970059620025856397045514594291849296 * q^47 - 7452969450778497532129812087184007504558526604092287637802268612794467934087599186261483798528 * q^48 + 17298008315064903937184133864291881308696588708445105876848488522049133450344930890256623872337 * q^49 + 20891593843500014301021428427705110541710363262225372510717283195064501890651418995923815351400 * q^50 - 85813999871822828588324201494589306593218994449334105811559220660851252439965047034531679254312 * q^51 - 228851992565399673815270028508808722169419264169266009042427250901076945058351740642305444481664 * q^52 - 330560931516346297292158383237634604339355604111254380988674341402404197811701576314208409413298 * q^53 + 4500007476747002196644470511723672131082224104684813911982619633059661906955824254260654375081280 * q^54 + 5411788085074080207797655602098900123199579033664526066719620291468503584226809836679744568059960 * q^55 - 42315784638223426280810136290704778028064917513845974684816911806737536885555338292253409336340480 * q^56 + 9918498856896672609870803756688673833744336383910153405185505298972528406991914653827866717244240 * q^57 + 32435179551725169564404757555461461839261719646775117357648454983301156661453863733221818065697680 * q^58 + 322553637419248081900645358050759529139017004186411501272056030884685696264538328889393003620694740 * q^59 - 132467389966865887348037310509899613119681515385419367203561785040397906770826770994985507300267520 * q^60 - 1759437984456387651106179880992119801754779277040263539338974358093077280629950964970586556177810042 * q^61 - 1712844297363572226123727147322557976426042183124057300794490386880408520919151071285053014838119168 * q^62 + 12759876033417698231199447475315412125628460028323317128859307435477632649190559962838360311186507992 * q^63 + 14281879241185987264094876187662890300953975181530786481128692077543427681889775277266607957835251712 * q^64 - 18446575904127982541910334362372985348294257469022062289060943594932692744923327761688031698818070540 * q^65 - 105227969740255769667487712999247235831860856852926275817422436766136475148421006520466387572795840384 * q^66 + 137686280746299018306956215858337887331602769875959175009115726791437961931237555780269025002728818316 * q^67 + 1157398196638034088725243365559060772268690235343345029534596768981482256873945115267239799529371269248 * q^68 + 1095507431560680024171724297772352455505639098885833012944706047494456930144134797052286618395241366496 * q^69 - 3640686416490340897700513163360856154742313115593190855720847062189976425143796505336061966373300603520 * q^70 + 9881612323140206421591424247232489623122284569259126072100461213939705350610294394975802208678001259448 * q^71 + 26396053480919173194166495118665950061506035792323405768129609103560026391739244345645460880788768488960 * q^72 + 68010594140875249475223137869343627059525985931897139097425407128220372890956239808513785565566231240522 * q^73 + 220837506033562453797347134849380708116539322544975559087316116631000736843141442638912881210212941372624 * q^74 + 181912260264814567208746612550869983753545991059523226326816406967698797635966067835830629689080707385300 * q^75 + 761174863647605635882918277985364633628165523124208915131122931858702438047845125322045601860264208695040 * q^76 + 1384642526997449454787538522373154719967650987275787604770256389537561344719927104096300078005408626536672 * q^77 + 10154718868595236540854386892056000355936883967938908970289471652675003137655678023153495552339085989663424 * q^78 + 7526673880001773966576204583811316437192125118919660383683770302134291678384367816740764114717599435401520 * q^79 + 32601244901804291407696890633217962008785625969393161121607747994402795735664787250217837405420588998778880 * q^80 + 48874282116782895668905156724559809826804317530845116719941792255495466449412888893127682785590511826600049 * q^81 + 113239522172902215034601434016259598176780723606704841332886416969022724124423260666831983947062879210014192 * q^82 + 199958416124075286987530689011944805825753524406236269102187579359597825528337021515595830260563921442487932 * q^83 + 880467563819420401586770374036347249339328631628161679582704747941404166343896577833615976614908144379930624 * q^84 + 707266002569821004378084548147696321676161909242361424333261618590644246794997074911164911557278987628650780 * q^85 + 749430950077361833338178064514980710590134374932604590973028338058871330476392166543416304708654721880933728 * q^86 + 2802132957491922284048190008280399903628415414482410070524683686927111831188200973776028254889144423439332360 * q^87 + 7195654272713601174999226937725203391076863795283476240434396643890296393716359696024184526976625256798607360 * q^88 + 3700827869341881331782801900641952675754040149647113243871021736652252631453067855946419168721111605247226810 * q^89 + 8997316939698708062605864942661951051594004217268128464090536667598399664816028357347925999912163977799180560 * q^90 - 254313076672373460593401973466735362362295247774148430702156053605292605984743534435031357382528251918280752 * q^91 - 16891756811302405862414651288981793929299127803233629387746389497252488943048833672780023478534318077838493184 * q^92 - 55378555126167982657281578020507978450769506755610812937817924402648049087367995838404448550854542227572273536 * q^93 - 71374169795251900964177147542915102589642305140612249128066111463360036313665875245965949313319551156299307136 * q^94 - 167271491201189176415157992539596873672401782137242927001530501790921136440405267833568144254517552969527081400 * q^95 - 1187167956876210917054814422873111467722801274363871607741943257050230342552379215783989919197651861627909046272 * q^96 - 631372797244867221191218982738135503959422268139699621925372110836288083138321626431181260783380505262640568654 * q^97 - 1898458058047689123148702915382067648076866113471255418148529297211872922066143741813213498341870918619707529832 * q^98 - 3056373683854811033724902889292841037638123003448050519838010864270837225210323694704228642303518682358171259244 * 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 $

$2$	−1.13057e15	−0.0221886	−0.0110943	−	0.999938i	$-0.503532\pi$
$2$	−1.13057e15	−0.0221886	−0.0110943	+	0.999938i	$0.503532\pi$
$3$	1.34574e26	0.445382	0.222691	−	0.974889i	$-0.428516\pi$
$3$	1.34574e26	0.445382	0.222691	+	0.974889i	$0.428516\pi$
$4$	−2.59487e33	−0.999508
$5$	1.00336e39	1.61668	0.808338	−	0.588719i	$-0.200368\pi$
$5$	1.00336e39	1.61668	0.808338	+	0.588719i	$0.200368\pi$
$6$	−1.52145e41	−0.00988243
$7$	−8.67417e45	−0.108464	−0.0542322	−	0.998528i	$-0.517271\pi$
$7$	−8.67417e45	−0.108464	−0.0542322	+	0.998528i	$0.517271\pi$
$8$	5.86879e48	0.0443664
$9$	−7.31873e52	−0.801635
$10$	−1.13437e54	−0.0358718
$11$	1.78506e57	0.284680	0.142340	−	0.989818i	$-0.454537\pi$
$11$	1.78506e57	0.284680	0.142340	+	0.989818i	$0.454537\pi$
$12$	−3.49203e59	−0.445163
$13$	2.10514e61	0.315809	0.157905	−	0.987454i	$-0.449526\pi$
$13$	2.10514e61	0.315809	0.157905	+	0.987454i	$0.449526\pi$
$14$	9.80672e60	0.00240668
$15$	1.35027e65	0.720038
$16$	6.73003e66	0.998523
$17$	2.95295e68	1.51475	0.757374	−	0.652981i	$-0.226482\pi$
$17$	2.95295e68	1.51475	0.757374	+	0.652981i	$0.226482\pi$
$18$	8.27430e67	0.0177872
$19$	−1.07798e71	−1.15288	−0.576440	−	0.817140i	$-0.695559\pi$
$19$	−1.07798e71	−1.15288	−0.576440	+	0.817140i	$0.695559\pi$
$20$	−2.60360e72	−1.61588
$21$	−1.16732e72	−0.0483081
$22$	−2.01812e72	−0.00631667
$23$	−1.47561e75	−0.391810	−0.195905	−	0.980623i	$-0.562764\pi$
$23$	−1.47561e75	−0.391810	−0.195905	+	0.980623i	$0.562764\pi$
$24$	7.89788e74	0.0197600
$25$	6.21551e77	1.61364
$26$	−2.38000e76	−0.00700738
$27$	−2.21355e79	−0.802416
$28$	2.25084e79	0.108411
$29$	2.61440e81	1.79591	0.897953	−	0.440092i	$-0.145054\pi$
$29$	2.61440e81	1.79591	0.897953	+	0.440092i	$0.145054\pi$
$30$	−1.52657e80	−0.0159767
$31$	−6.48392e82	−1.09967	−0.549836	−	0.835272i	$-0.685310\pi$
$31$	−6.48392e82	−1.09967	−0.549836	+	0.835272i	$0.685310\pi$
$32$	−2.28450e82	−0.0665223
$33$	2.40223e83	0.126792
$34$	−3.33850e83	−0.0336102
$35$	−8.70334e84	−0.175352
$36$	1.89912e86	0.801240
$37$	−6.12579e86	−0.564893	−0.282447	−	0.959283i	$-0.591146\pi$
$37$	−6.12579e86	−0.564893	−0.282447	+	0.959283i	$0.591146\pi$
$38$	1.21872e86	0.0255808
$39$	2.83298e87	0.140656
$40$	5.88852e87	0.0717260
$41$	−2.55361e89	−0.790042	−0.395021	−	0.918672i	$-0.629263\pi$
$41$	−2.55361e89	−0.790042	−0.395021	+	0.918672i	$0.629263\pi$
$42$	1.31973e87	0.00107189
$43$	6.40828e90	1.41007	0.705037	−	0.709170i	$-0.250930\pi$
$43$	6.40828e90	1.41007	0.705037	+	0.709170i	$0.250930\pi$
$44$	−4.63199e90	−0.284540
$45$	−7.34334e91	−1.29598
$46$	1.66827e90	0.00869374
$47$	6.01122e92	0.949580	0.474790	−	0.880099i	$-0.342524\pi$
$47$	6.01122e92	0.949580	0.474790	+	0.880099i	$0.342524\pi$
$48$	9.05690e92	0.444725
$49$	−6.32038e93	−0.988235
$50$	−7.02704e92	−0.0358045
$51$	3.97391e94	0.674642
$52$	−5.46256e94	−0.315654
$53$	−1.21175e95	−0.243277	−0.121639	−	0.992574i	$-0.538815\pi$
$53$	−1.21175e95	−0.243277	−0.121639	+	0.992574i	$0.538815\pi$
$54$	2.50256e94	0.0178045
$55$	1.79106e96	0.460236
$56$	−5.09069e94	−0.00481217
$57$	−1.45068e97	−0.513472
$58$	−2.95575e96	−0.0398487
$59$	1.21787e98	0.635789	0.317894	−	0.948126i	$-0.397024\pi$
$59$	1.21787e98	0.635789	0.317894	+	0.948126i	$0.397024\pi$
$60$	−3.50377e98	−0.719684
$61$	7.42509e98	0.609391	0.304695	−	0.952450i	$-0.401445\pi$
$61$	7.42509e98	0.609391	0.304695	+	0.952450i	$0.401445\pi$
$62$	7.33049e97	0.0244003
$63$	6.34839e98	0.0869488
$64$	−1.74463e100	−0.997047
$65$	2.11222e100	0.510561
$66$	−2.71588e98	−0.00281333
$67$	3.53383e101	1.58889	0.794445	−	0.607336i	$-0.207762\pi$
$67$	3.53383e101	1.58889	0.794445	+	0.607336i	$0.207762\pi$
$68$	−7.66251e101	−1.51400
$69$	−1.98579e101	−0.174505
$70$	9.83970e99	0.00389081
$71$	8.15428e102	1.46740	0.733698	−	0.679476i	$-0.237793\pi$
$71$	8.15428e102	1.46740	0.733698	+	0.679476i	$0.237793\pi$
$72$	−4.29521e101	−0.0355656
$73$	−1.16063e103	−0.446967	−0.223484	−	0.974708i	$-0.571743\pi$
$73$	−1.16063e103	−0.446967	−0.223484	+	0.974708i	$0.571743\pi$
$74$	6.92560e101	0.0125342
$75$	8.36449e103	0.718686
$76$	2.79721e104	1.15231
$77$	−1.54839e103	−0.0308777
$78$	−3.20287e102	−0.00312096
$79$	1.97268e105	0.947878	0.473939	−	0.880558i	$-0.342832\pi$
$79$	1.97268e105	0.947878	0.473939	+	0.880558i	$0.342832\pi$
$80$	6.75267e105	1.61429
$81$	3.70296e105	0.444253
$82$	2.88702e104	0.0175300
$83$	4.77769e106	1.48042	0.740208	−	0.672378i	$-0.234727\pi$
$83$	4.77769e106	1.48042	0.740208	+	0.672378i	$0.234727\pi$
$84$	3.02905e105	0.0482843
$85$	2.96288e107	2.44886
$86$	−7.24498e105	−0.0312877
$87$	3.51832e107	0.799865
$88$	1.04761e106	0.0126302
$89$	1.53326e108	0.987351	0.493676	−	0.869646i	$-0.335653\pi$
$89$	1.53326e108	0.987351	0.493676	+	0.869646i	$0.335653\pi$
$90$	8.30213e106	0.0287561
$91$	−1.82603e107	−0.0342540
$92$	3.82901e108	0.391617
$93$	−8.72570e108	−0.489775
$94$	−6.79608e107	−0.0210699
$95$	−1.08160e110	−1.86383
$96$	−3.07435e108	−0.0296278
$97$	−1.32081e110	−0.716157	−0.358078	−	0.933691i	$-0.616568\pi$
$97$	−1.32081e110	−0.716157	−0.358078	+	0.933691i	$0.616568\pi$
$98$	7.14560e108	0.0219276
$99$	−1.30643e110	−0.228210
$100$	−1.61284e111	−1.61284
$101$	−1.06114e111	−0.610854	−0.305427	−	0.952215i	$-0.598799\pi$
$101$	−1.06114e111	−0.610854	−0.305427	+	0.952215i	$0.598799\pi$
$102$	−4.49277e109	−0.0149694
$103$	7.30499e111	1.41629	0.708147	−	0.706065i	$-0.249531\pi$
$103$	7.30499e111	1.41629	0.708147	+	0.706065i	$0.249531\pi$
$104$	1.23546e110	0.0140113
$105$	−1.17125e111	−0.0780985
$106$	1.36996e110	0.00539799
$107$	4.27266e112	0.999767	0.499883	−	0.866093i	$-0.333376\pi$
$107$	4.27266e112	0.999767	0.499883	+	0.866093i	$0.333376\pi$
$108$	5.74386e112	0.802021
$109$	1.20079e113	1.00530	0.502652	−	0.864489i	$-0.332358\pi$
$109$	1.20079e113	1.00530	0.502652	+	0.864489i	$0.332358\pi$
$110$	−2.02491e111	−0.0102120
$111$	−8.24374e112	−0.251593
$112$	−5.83775e112	−0.108304
$113$	7.77458e113	0.880691	0.440345	−	0.897828i	$-0.354856\pi$
$113$	7.77458e113	0.880691	0.440345	+	0.897828i	$0.354856\pi$
$114$	1.64009e112	0.0113933
$115$	−1.48057e114	−0.633430
$116$	−6.78403e114	−1.79502
$117$	−1.54070e114	−0.253164
$118$	−1.37688e113	−0.0141073
$119$	−2.56144e114	−0.164296
$120$	7.92444e113	0.0319455
$121$	−3.61313e115	−0.918957
$122$	−8.39455e113	−0.0135216
$123$	−3.43650e115	−0.351871
$124$	1.68249e116	1.09913
$125$	2.37160e116	0.992054
$126$	−7.17727e113	−0.00192928
$127$	4.08716e116	0.708460	0.354230	−	0.935158i	$-0.384743\pi$
$127$	4.08716e116	0.708460	0.354230	+	0.935158i	$0.384743\pi$
$128$	7.90332e115	0.0886454
$129$	8.62391e116	0.628022
$130$	−2.38800e115	−0.0113287
$131$	−9.30119e116	−0.288391	−0.144196	−	0.989549i	$-0.546059\pi$
$131$	−9.30119e116	−0.288391	−0.144196	+	0.989549i	$0.546059\pi$
$132$	−6.23347e116	−0.126729
$133$	9.35055e116	0.125046
$134$	−3.99523e116	−0.0352553
$135$	−2.22099e118	−1.29725
$136$	1.73302e117	0.0672039
$137$	−6.27440e118	−1.62024	−0.810122	−	0.586261i	$-0.800599\pi$
$137$	−6.27440e118	−1.62024	−0.810122	+	0.586261i	$0.800599\pi$
$138$	2.24506e116	0.00387204
$139$	4.16536e118	0.481206	0.240603	−	0.970624i	$-0.422655\pi$
$139$	4.16536e118	0.481206	0.240603	+	0.970624i	$0.422655\pi$
$140$	2.25840e118	0.175265
$141$	8.08957e118	0.422926
$142$	−9.21895e117	−0.0325595
$143$	3.75779e118	0.0899047
$144$	−4.92553e119	−0.800451
$145$	2.62319e120	2.90340
$146$	1.31217e118	0.00991760
$147$	−8.50561e119	−0.440143
$148$	1.58956e120	0.564615
$149$	−3.78349e120	−0.924814	−0.462407	−	0.886668i	$-0.653014\pi$
$149$	−3.78349e120	−0.924814	−0.462407	+	0.886668i	$0.653014\pi$
$150$	−9.45660e118	−0.0159467
$151$	2.98158e120	0.347717	0.173859	−	0.984771i	$-0.444376\pi$
$151$	2.98158e120	0.347717	0.173859	+	0.984771i	$0.444376\pi$
$152$	−6.32641e119	−0.0511491
$153$	−2.16118e121	−1.21427
$154$	1.75055e118	0.000685134 0
$155$	−6.50572e121	−1.77781
$156$	−7.35121e120	−0.140587
$157$	1.19868e122	1.60795	0.803974	−	0.594664i	$-0.202715\pi$
$157$	1.19868e122	1.60795	0.803974	+	0.594664i	$0.202715\pi$
$158$	−2.23024e120	−0.0210321
$159$	−1.63070e121	−0.108351
$160$	−2.29218e121	−0.107545
$161$	1.27997e121	0.0424974
$162$	−4.18644e120	−0.00985737
$163$	9.11703e122	1.52560	0.762801	−	0.646633i	$-0.223824\pi$
$163$	9.11703e122	1.52560	0.762801	+	0.646633i	$0.223824\pi$
$164$	6.62628e122	0.789653
$165$	2.41031e122	0.204981
$166$	−5.40149e121	−0.0328484
$167$	−2.25099e123	−0.980867	−0.490434	−	0.871479i	$-0.663162\pi$
$167$	−2.25099e123	−0.980867	−0.490434	+	0.871479i	$0.663162\pi$
$168$	−6.85076e120	−0.00214325
$169$	−4.00020e123	−0.900265
$170$	−3.34973e122	−0.0543368
$171$	7.88941e123	0.924188
$172$	−1.66287e124	−1.40938
$173$	−8.20599e123	−0.504165	−0.252082	−	0.967706i	$-0.581115\pi$
$173$	−8.20599e123	−0.504165	−0.252082	+	0.967706i	$0.581115\pi$
$174$	−3.97769e122	−0.0177479
$175$	−5.39144e123	−0.175022
$176$	1.20135e124	0.284260
$177$	1.63894e124	0.283169
$178$	−1.73346e123	−0.0219080
$179$	2.47107e124	0.228845	0.114423	−	0.993432i	$-0.463498\pi$
$179$	2.47107e124	0.228845	0.114423	+	0.993432i	$0.463498\pi$
$180$	1.90550e125	1.29534
$181$	8.24759e124	0.412255	0.206128	−	0.978525i	$-0.433914\pi$
$181$	8.24759e124	0.412255	0.206128	+	0.978525i	$0.433914\pi$
$182$	2.06445e122	0.000760051 0
$183$	9.99227e124	0.271412
$184$	−8.66002e123	−0.0173832
$185$	−6.14639e125	−0.913249
$186$	9.86497e123	0.0108674
$187$	5.27117e125	0.431219
$188$	−1.55983e126	−0.949113
$189$	1.92007e125	0.0870335
$190$	1.22282e125	0.0413559
$191$	−7.07704e126	−1.78854	−0.894272	−	0.447523i	$-0.852306\pi$
$191$	−7.07704e126	−1.78854	−0.894272	+	0.447523i	$0.852306\pi$
$192$	−2.34783e126	−0.444067
$193$	8.55936e126	1.21342	0.606709	−	0.794924i	$-0.292489\pi$
$193$	8.55936e126	1.21342	0.606709	+	0.794924i	$0.292489\pi$
$194$	1.49326e125	0.0158906
$195$	2.84251e126	0.227395
$196$	1.64006e127	0.987749
$197$	−1.55618e127	−0.706617	−0.353309	−	0.935507i	$-0.614943\pi$
$197$	−1.55618e127	−0.706617	−0.353309	+	0.935507i	$0.614943\pi$
$198$	1.47701e125	0.00506367
$199$	4.81806e127	1.24890	0.624449	−	0.781066i	$-0.285324\pi$
$199$	4.81806e127	1.24890	0.624449	+	0.781066i	$0.285324\pi$
$200$	3.64775e126	0.0715913
$201$	4.75563e127	0.707664
$202$	1.19969e126	0.0135540
$203$	−2.26778e127	−0.194792
$204$	−1.03118e128	−0.674310
$205$	−2.56220e128	−1.27724
$206$	−8.25877e126	−0.0314257
$207$	1.07996e128	0.314089
$208$	1.41677e128	0.315343
$209$	−1.92425e128	−0.328202
$210$	1.32417e126	0.00173290
$211$	−1.93171e129	−1.94208	−0.971038	−	0.238923i	$-0.923205\pi$
$211$	−1.93171e129	−1.94208	−0.971038	+	0.238923i	$0.923205\pi$
$212$	3.14433e128	0.243157
$213$	1.09736e129	0.653552
$214$	−4.83052e127	−0.0221835
$215$	6.42983e129	2.27963
$216$	−1.29908e128	−0.0356003
$217$	5.62426e128	0.119275
$218$	−1.35758e128	−0.0223064
$219$	−1.56191e129	−0.199071
$220$	−4.64756e129	−0.460009
$221$	6.21636e129	0.478372
$222$	9.32009e127	0.00558252
$223$	3.15761e129	0.147380	0.0736900	−	0.997281i	$-0.476522\pi$
$223$	3.15761e129	0.147380	0.0736900	+	0.997281i	$0.476522\pi$
$224$	1.98161e128	0.00721529
$225$	−4.54896e130	−1.29355
$226$	−8.78967e128	−0.0195413
$227$	−7.69454e130	−1.33890	−0.669449	−	0.742858i	$-0.733470\pi$
$227$	−7.69454e130	−1.33890	−0.669449	+	0.742858i	$0.733470\pi$
$228$	3.76432e130	0.513219
$229$	9.69854e129	0.103714	0.0518570	−	0.998655i	$-0.483486\pi$
$229$	9.69854e129	0.103714	0.0518570	+	0.998655i	$0.483486\pi$
$230$	1.67388e129	0.0140549
$231$	−2.08373e129	−0.0137524
$232$	1.53434e130	0.0796778
$233$	1.59229e131	0.651282	0.325641	−	0.945493i	$-0.394420\pi$
$233$	1.59229e131	0.651282	0.325641	+	0.945493i	$0.394420\pi$
$234$	1.74186e129	0.00561736
$235$	6.03144e131	1.53516
$236$	−3.16020e131	−0.635476
$237$	2.65472e131	0.422168
$238$	2.89587e129	0.00364551
$239$	−1.69760e131	−0.169337	−0.0846687	−	0.996409i	$-0.526983\pi$
$239$	−1.69760e131	−0.169337	−0.0846687	+	0.996409i	$0.526983\pi$
$240$	9.08736e131	0.718975
$241$	−2.39713e132	−1.50573	−0.752863	−	0.658177i	$-0.771328\pi$
$241$	−2.39713e132	−1.50573	−0.752863	+	0.658177i	$0.771328\pi$
$242$	4.08488e130	0.0203904
$243$	2.51924e132	1.00028
$244$	−1.92671e132	−0.609091
$245$	−6.34163e132	−1.59766
$246$	3.88519e130	0.00780754
$247$	−2.26929e132	−0.364090
$248$	−3.80527e131	−0.0487885
$249$	6.42955e132	0.659351
$250$	−2.68125e131	−0.0220123
$251$	1.12360e133	0.739132	0.369566	−	0.929204i	$-0.379506\pi$
$251$	1.12360e133	0.739132	0.369566	+	0.929204i	$0.379506\pi$
$252$	−1.64733e132	−0.0869060
$253$	−2.63404e132	−0.111541
$254$	−4.62080e131	−0.0157198
$255$	3.98727e133	1.09068
$256$	4.52039e133	0.995080
$257$	−2.13648e133	−0.378801	−0.189400	−	0.981900i	$-0.560654\pi$
$257$	−2.13648e133	−0.378801	−0.189400	+	0.981900i	$0.560654\pi$
$258$	−9.74989e131	−0.0139350
$259$	5.31361e132	0.0612707
$260$	−5.48093e133	−0.510310
$261$	−1.91341e134	−1.43966
$262$	1.05156e132	0.00639901
$263$	9.21682e133	0.453980	0.226990	−	0.973897i	$-0.427111\pi$
$263$	9.21682e133	0.453980	0.226990	+	0.973897i	$0.427111\pi$
$264$	1.40982e132	0.00562528
$265$	−1.21582e134	−0.393300
$266$	−1.05714e132	−0.00277461
$267$	2.06338e134	0.439749
$268$	−9.16983e134	−1.58811
$269$	−4.40596e134	−0.620568	−0.310284	−	0.950644i	$-0.600424\pi$
$269$	−4.40596e134	−0.620568	−0.310284	+	0.950644i	$0.600424\pi$
$270$	2.51097e133	0.0287841
$271$	1.78768e135	1.66915	0.834573	−	0.550897i	$-0.185714\pi$
$271$	1.78768e135	1.66915	0.834573	+	0.550897i	$0.185714\pi$
$272$	1.98734e135	1.51251
$273$	−2.45738e133	−0.0152561
$274$	7.09362e133	0.0359510
$275$	1.10950e135	0.459371
$276$	5.15286e134	0.174419
$277$	−5.81952e135	−1.61161	−0.805805	−	0.592181i	$-0.798267\pi$
$277$	−5.81952e135	−1.61161	−0.805805	+	0.592181i	$0.798267\pi$
$278$	−4.70921e133	−0.0106773
$279$	4.74541e135	0.881536
$280$	−5.10781e133	−0.00777971
$281$	−2.48595e135	−0.310664	−0.155332	−	0.987862i	$-0.549645\pi$
$281$	−2.48595e135	−0.310664	−0.155332	+	0.987862i	$0.549645\pi$
$282$	−9.14578e133	−0.00938416
$283$	1.72091e135	0.145081	0.0725406	−	0.997365i	$-0.476889\pi$
$283$	1.72091e135	0.145081	0.0725406	+	0.997365i	$0.476889\pi$
$284$	−2.11593e136	−1.46667
$285$	−1.45556e136	−0.830118
$286$	−4.24843e133	−0.00199486
$287$	2.21504e135	0.0856914
$288$	1.67196e135	0.0533265
$289$	4.91948e136	1.29446
$290$	−2.96569e135	−0.0644224
$291$	−1.77747e136	−0.318964
$292$	3.01169e136	0.446747
$293$	3.53235e136	0.433422	0.216711	−	0.976236i	$-0.430467\pi$
$293$	3.53235e136	0.433422	0.216711	+	0.976236i	$0.430467\pi$
$294$	9.61615e134	0.00976617
$295$	1.22196e137	1.02786
$296$	−3.59509e135	−0.0250623
$297$	−3.95130e136	−0.228432
$298$	4.27748e135	0.0205204
$299$	−3.10636e136	−0.123737
$300$	−2.17048e137	−0.718332
$301$	−5.55865e136	−0.152943
$302$	−3.37087e135	−0.00771537
$303$	−1.42803e137	−0.272064
$304$	−7.25481e137	−1.15118
$305$	7.45006e137	0.985187
$306$	2.44336e136	0.0269431
$307$	−1.47005e138	−1.35255	−0.676275	−	0.736649i	$-0.736407\pi$
$307$	−1.47005e138	−1.35255	−0.676275	+	0.736649i	$0.736407\pi$
$308$	4.01787e136	0.0308625
$309$	9.83065e137	0.630792
$310$	7.35514e136	0.0394473
$311$	1.46188e138	0.655708	0.327854	−	0.944728i	$-0.393675\pi$
$311$	1.46188e138	0.655708	0.327854	+	0.944728i	$0.393675\pi$
$312$	1.66261e136	0.00624039
$313$	3.58880e138	1.12782	0.563909	−	0.825837i	$-0.309297\pi$
$313$	3.58880e138	1.12782	0.563909	+	0.825837i	$0.309297\pi$
$314$	−1.35518e137	−0.0356782
$315$	6.36974e137	0.140568
$316$	−5.11884e138	−0.947411
$317$	8.74575e138	1.35834	0.679169	−	0.733981i	$-0.262340\pi$
$317$	8.74575e138	1.35834	0.679169	+	0.733981i	$0.262340\pi$
$318$	1.84362e136	0.00240417
$319$	4.66685e138	0.511259
$320$	−1.75050e139	−1.61190
$321$	5.74991e138	0.445278
$322$	−1.44709e136	−0.000942960 0
$323$	−3.18320e139	−1.74632
$324$	−9.60869e138	−0.444034
$325$	1.30845e139	0.509602
$326$	−1.03074e138	−0.0338511
$327$	1.61596e139	0.447745
$328$	−1.49866e138	−0.0350513
$329$	−5.21424e138	−0.102996
$330$	−2.72501e137	−0.00454825
$331$	5.19978e139	0.733721	0.366861	−	0.930276i	$-0.380433\pi$
$331$	5.19978e139	0.733721	0.366861	+	0.930276i	$0.380433\pi$
$332$	−1.23975e140	−1.47969
$333$	4.48330e139	0.452838
$334$	2.54490e138	0.0217641
$335$	3.54571e140	2.56872
$336$	−7.85612e138	−0.0482367
$337$	7.42137e139	0.386389	0.193194	−	0.981160i	$-0.438115\pi$
$337$	7.42137e139	0.386389	0.193194	+	0.981160i	$0.438115\pi$
$338$	4.52249e138	0.0199757
$339$	1.04626e140	0.392244
$340$	−7.68828e140	−2.44765
$341$	−1.15742e140	−0.313055
$342$	−8.91949e138	−0.0205065
$343$	1.10301e140	0.215653
$344$	3.76088e139	0.0625599
$345$	−1.99247e140	−0.282118
$346$	9.27741e138	0.0111867
$347$	5.14927e140	0.529005	0.264502	−	0.964385i	$-0.414792\pi$
$347$	5.14927e140	0.529005	0.264502	+	0.964385i	$0.414792\pi$
$348$	−9.12958e140	−0.799471
$349$	−8.72784e140	−0.651772	−0.325886	−	0.945409i	$-0.605663\pi$
$349$	−8.72784e140	−0.651772	−0.325886	+	0.945409i	$0.605663\pi$
$350$	6.09538e138	0.00388351
$351$	−4.65982e140	−0.253410
$352$	−4.07795e139	−0.0189376
$353$	3.19681e141	1.26829	0.634147	−	0.773212i	$-0.281351\pi$
$353$	3.19681e141	1.26829	0.634147	+	0.773212i	$0.281351\pi$
$354$	−1.85292e139	−0.00628314
$355$	8.18170e141	2.37230
$356$	−3.97862e141	−0.986865
$357$	−3.44704e140	−0.0731746
$358$	−2.79371e139	−0.00507777
$359$	−1.41176e141	−0.219795	−0.109897	−	0.993943i	$-0.535052\pi$
$359$	−1.41176e141	−0.219795	−0.109897	+	0.993943i	$0.535052\pi$
$360$	−4.30965e140	−0.0574981
$361$	2.87753e141	0.329132
$362$	−9.32443e139	−0.00914738
$363$	−4.86235e141	−0.409287
$364$	4.73832e140	0.0342372
$365$	−1.16453e142	−0.722601
$366$	−1.12969e140	−0.00602226
$367$	−2.69770e142	−1.23602	−0.618012	−	0.786169i	$-0.712062\pi$
$367$	−2.69770e142	−1.23602	−0.618012	+	0.786169i	$0.712062\pi$
$368$	−9.93088e141	−0.391231
$369$	1.86892e142	0.633325
$370$	6.94889e140	0.0202638
$371$	1.05109e141	0.0263869
$372$	2.26420e142	0.489534
$373$	4.61617e141	0.0859888	0.0429944	−	0.999075i	$-0.486310\pi$
$373$	4.61617e141	0.0859888	0.0429944	+	0.999075i	$0.486310\pi$
$374$	−5.95940e140	−0.00956817
$375$	3.19156e142	0.441843
$376$	3.52786e141	0.0421294
$377$	5.50368e142	0.567164
$378$	−2.17076e140	−0.00193116
$379$	−1.08409e143	−0.832890	−0.416445	−	0.909161i	$-0.636724\pi$
$379$	−1.08409e143	−0.832890	−0.416445	+	0.909161i	$0.636724\pi$
$380$	2.80661e143	1.86291
$381$	5.50027e142	0.315535
$382$	8.00105e141	0.0396854
$383$	−3.57901e143	−1.53543	−0.767716	−	0.640790i	$-0.778607\pi$
$383$	−3.57901e143	−1.53543	−0.767716	+	0.640790i	$0.778607\pi$
$384$	1.06358e142	0.0394811
$385$	−1.55359e142	−0.0499192
$386$	−9.67692e141	−0.0269241
$387$	−4.69005e143	−1.13036
$388$	3.42732e143	0.715804
$389$	−4.20584e143	−0.761464	−0.380732	−	0.924685i	$-0.624328\pi$
$389$	−4.20584e143	−0.761464	−0.380732	+	0.924685i	$0.624328\pi$
$390$	−3.21364e141	−0.00504558
$391$	−4.35739e143	−0.593494
$392$	−3.70929e142	−0.0438444
$393$	−1.25170e143	−0.128444
$394$	1.75936e142	0.0156789
$395$	1.97931e144	1.53241
$396$	3.39003e143	0.228097
$397$	−1.18675e143	−0.0694201	−0.0347100	−	0.999397i	$-0.511051\pi$
$397$	−1.18675e143	−0.0694201	−0.0347100	+	0.999397i	$0.511051\pi$
$398$	−5.44713e142	−0.0277113
$399$	1.25834e143	0.0556934
$400$	4.18306e144	1.61126
$401$	−3.90384e144	−1.30912	−0.654560	−	0.756010i	$-0.727146\pi$
$401$	−3.90384e144	−1.30912	−0.654560	+	0.756010i	$0.727146\pi$
$402$	−5.37655e142	−0.0157021
$403$	−1.36496e144	−0.347287
$404$	2.75353e144	0.610553
$405$	3.71541e144	0.718213
$406$	2.56387e142	0.00432216
$407$	−1.09349e144	−0.160814
$408$	2.33220e143	0.0299314
$409$	−1.38876e145	−1.55591	−0.777955	−	0.628320i	$-0.783743\pi$
$409$	−1.38876e145	−1.55591	−0.777955	+	0.628320i	$0.783743\pi$
$410$	2.89673e143	0.0283403
$411$	−8.44373e144	−0.721628
$412$	−1.89555e145	−1.41560
$413$	−1.05640e144	−0.0689604
$414$	−1.22096e143	−0.00696920
$415$	4.79376e145	2.39335
$416$	−4.80919e143	−0.0210083
$417$	5.60550e144	0.214320
$418$	2.17549e143	0.00728237
$419$	−1.64295e145	−0.481666	−0.240833	−	0.970567i	$-0.577421\pi$
$419$	−1.64295e145	−0.481666	−0.240833	+	0.970567i	$0.577421\pi$
$420$	3.03924e144	0.0780600
$421$	2.49238e145	0.560995	0.280497	−	0.959855i	$-0.409501\pi$
$421$	2.49238e145	0.560995	0.280497	+	0.959855i	$0.409501\pi$
$422$	2.18393e144	0.0430921
$423$	−4.39945e145	−0.761216
$424$	−7.11149e143	−0.0107933
$425$	1.83541e146	2.44426
$426$	−1.24063e144	−0.0145014
$427$	−6.44065e144	−0.0660972
$428$	−1.10870e146	−0.999274
$429$	5.05702e144	0.0400420
$430$	−7.26934e144	−0.0505820
$431$	−2.11255e146	−1.29217	−0.646083	−	0.763268i	$-0.723594\pi$
$431$	−2.11255e146	−1.29217	−0.646083	+	0.763268i	$0.723594\pi$
$432$	−1.48972e146	−0.801231
$433$	−2.65803e145	−0.125742	−0.0628711	−	0.998022i	$-0.520026\pi$
$433$	−2.65803e145	−0.125742	−0.0628711	+	0.998022i	$0.520026\pi$
$434$	−6.35860e143	−0.00264656
$435$	3.53015e146	1.29312
$436$	−3.11590e146	−1.00481
$437$	1.59067e146	0.451710
$438$	1.76584e144	0.00441712
$439$	−4.26315e146	−0.939615	−0.469807	−	0.882769i	$-0.655677\pi$
$439$	−4.26315e146	−0.939615	−0.469807	+	0.882769i	$0.655677\pi$
$440$	1.05113e145	0.0204190
$441$	4.62571e146	0.792204
$442$	−7.02801e144	−0.0106144
$443$	3.01426e146	0.401581	0.200791	−	0.979634i	$-0.435649\pi$
$443$	3.01426e146	0.401581	0.200791	+	0.979634i	$0.435649\pi$
$444$	2.13914e146	0.251469
$445$	1.53842e147	1.59623
$446$	−3.56988e144	−0.00327016
$447$	−5.09160e146	−0.411896
$448$	1.51333e146	0.108144
$449$	−3.89035e146	−0.245650	−0.122825	−	0.992428i	$-0.539195\pi$
$449$	−3.89035e146	−0.245650	−0.122825	+	0.992428i	$0.539195\pi$
$450$	5.14290e145	0.0287021
$451$	−4.55833e146	−0.224910
$452$	−2.01740e147	−0.880257
$453$	4.01244e146	0.154867
$454$	8.69918e145	0.0297083
$455$	−1.83218e146	−0.0553777
$456$	−8.51372e145	−0.0227809
$457$	−1.32546e147	−0.314063	−0.157032	−	0.987594i	$-0.550192\pi$
$457$	−1.32546e147	−0.314063	−0.157032	+	0.987594i	$0.550192\pi$
$458$	−1.09648e145	−0.00230127
$459$	−6.53648e147	−1.21546
$460$	3.84188e147	0.633118
$461$	−8.05656e147	−1.17692	−0.588462	−	0.808525i	$-0.700266\pi$
$461$	−8.05656e147	−1.17692	−0.588462	+	0.808525i	$0.700266\pi$
$462$	2.35580e144	0.000305146 0
$463$	5.53658e147	0.636057	0.318029	−	0.948081i	$-0.396979\pi$
$463$	5.53658e147	0.636057	0.318029	+	0.948081i	$0.396979\pi$
$464$	1.75950e148	1.79325
$465$	−8.75504e147	−0.791807
$466$	−1.80019e146	−0.0144511
$467$	1.33793e148	0.953557	0.476779	−	0.879023i	$-0.341804\pi$
$467$	1.33793e148	0.953557	0.476779	+	0.879023i	$0.341804\pi$
$468$	3.99790e147	0.253039
$469$	−3.06531e147	−0.172338
$470$	−6.81893e146	−0.0340632
$471$	1.61312e148	0.716152
$472$	7.14739e146	0.0282076
$473$	1.14391e148	0.401421
$474$	−3.00133e146	−0.00936734
$475$	−6.70017e148	−1.86033
$476$	6.64660e147	0.164215
$477$	8.86845e147	0.195019
$478$	1.91925e146	0.00375737
$479$	−4.84135e148	−0.844007	−0.422003	−	0.906594i	$-0.638673\pi$
$479$	−4.84135e148	−0.844007	−0.422003	+	0.906594i	$0.638673\pi$
$480$	−3.08469e147	−0.0478986
$481$	−1.28956e148	−0.178398
$482$	2.71011e147	0.0334100
$483$	1.72251e147	0.0189276
$484$	9.37560e148	0.918505
$485$	−1.32525e149	−1.15779
$486$	−2.84816e147	−0.0221948
$487$	−6.20209e148	−0.431202	−0.215601	−	0.976482i	$-0.569171\pi$
$487$	−6.20209e148	−0.431202	−0.215601	+	0.976482i	$0.569171\pi$
$488$	4.35763e147	0.0270365
$489$	1.22692e149	0.679476
$490$	7.16963e147	0.0354498
$491$	3.71405e148	0.163993	0.0819963	−	0.996633i	$-0.473870\pi$
$491$	3.71405e148	0.163993	0.0819963	+	0.996633i	$0.473870\pi$
$492$	8.91728e148	0.351698
$493$	7.72019e149	2.72035
$494$	2.56558e147	0.00807867
$495$	−1.31083e149	−0.368941
$496$	−4.36370e149	−1.09805
$497$	−7.07316e148	−0.159160
$498$	−7.26903e147	−0.0146301
$499$	−1.19049e149	−0.214361	−0.107180	−	0.994240i	$-0.534182\pi$
$499$	−1.19049e149	−0.214361	−0.107180	+	0.994240i	$0.534182\pi$
$500$	−6.15399e149	−0.991566
$501$	−3.02926e149	−0.436861
$502$	−1.27031e148	−0.0164003
$503$	1.26079e150	1.45753	0.728767	−	0.684762i	$-0.240094\pi$
$503$	1.26079e150	1.45753	0.728767	+	0.684762i	$0.240094\pi$
$504$	3.72574e147	0.00385760
$505$	−1.06471e150	−0.987552
$506$	2.97795e147	0.00247494
$507$	−5.38325e149	−0.400962
$508$	−1.06057e150	−0.708111
$509$	−1.79207e149	−0.107280	−0.0536399	−	0.998560i	$-0.517082\pi$
$509$	−1.79207e149	−0.107280	−0.0536399	+	0.998560i	$0.517082\pi$
$510$	−4.50787e148	−0.0242006
$511$	1.00675e149	0.0484800
$512$	−2.56288e149	−0.110725
$513$	2.38615e150	0.925089
$514$	2.41543e148	0.00840508
$515$	7.32955e150	2.28969
$516$	−2.23779e150	−0.627713
$517$	1.07304e150	0.270327
$518$	−6.00739e147	−0.00135952
$519$	−1.10432e150	−0.224546
$520$	1.23962e149	0.0226517
$521$	−7.77547e150	−1.27712	−0.638562	−	0.769570i	$-0.720470\pi$
$521$	−7.77547e150	−1.27712	−0.638562	+	0.769570i	$0.720470\pi$
$522$	2.16324e149	0.0319441
$523$	1.05278e151	1.39796	0.698981	−	0.715141i	$-0.253637\pi$
$523$	1.05278e151	1.39796	0.698981	+	0.715141i	$0.253637\pi$
$524$	2.41354e150	0.288249
$525$	−7.25550e149	−0.0779518
$526$	−1.04202e149	−0.0100732
$527$	−1.91467e151	−1.66573
$528$	1.61671e150	0.126604
$529$	−1.20063e151	−0.846485
$530$	1.37457e149	0.00872680
$531$	−8.91323e150	−0.509670
$532$	−2.42635e150	−0.124985
$533$	−5.37570e150	−0.249503
$534$	−2.33279e149	−0.00975743
$535$	4.28703e151	1.61630
$536$	2.07393e150	0.0704933
$537$	3.32543e150	0.101924
$538$	4.98123e149	0.0137696
$539$	−1.12822e151	−0.281331
$540$	5.76318e151	1.29661
$541$	−4.75923e151	−0.966247	−0.483124	−	0.875552i	$-0.660498\pi$
$541$	−4.75923e151	−0.966247	−0.483124	+	0.875552i	$0.660498\pi$
$542$	−2.02109e150	−0.0370361
$543$	1.10991e151	0.183611
$544$	−6.74600e150	−0.100764
$545$	1.20483e152	1.62525
$546$	2.77822e148	0.000338513 0
$547$	−1.02815e152	−1.13178	−0.565889	−	0.824481i	$-0.691467\pi$
$547$	−1.02815e152	−1.13178	−0.565889	+	0.824481i	$0.691467\pi$
$548$	1.62812e152	1.61945
$549$	−5.43422e151	−0.488509
$550$	−1.25437e150	−0.0101928
$551$	−2.81826e152	−2.07046
$552$	−1.16542e150	−0.00774216
$553$	−1.71113e151	−0.102811
$554$	6.57935e150	0.0357594
$555$	−8.27147e151	−0.406745
$556$	−1.08086e152	−0.480969
$557$	5.71300e150	0.0230092	0.0115046	−	0.999934i	$-0.496338\pi$
$557$	5.71300e150	0.0230092	0.0115046	+	0.999934i	$0.496338\pi$
$558$	−5.36499e150	−0.0195601
$559$	1.34903e152	0.445315
$560$	−5.85738e151	−0.175093
$561$	7.09365e151	0.192057
$562$	2.81053e150	0.00689322
$563$	3.19132e152	0.709177	0.354589	−	0.935022i	$-0.384621\pi$
$563$	3.19132e152	0.709177	0.354589	+	0.935022i	$0.384621\pi$
$564$	−2.09914e152	−0.422718
$565$	7.80073e152	1.42379
$566$	−1.94560e150	−0.00321915
$567$	−3.21201e151	−0.0481856
$568$	4.78557e151	0.0651030
$569$	−3.33107e152	−0.411010	−0.205505	−	0.978656i	$-0.565884\pi$
$569$	−3.33107e152	−0.411010	−0.205505	+	0.978656i	$0.565884\pi$
$570$	1.64560e151	0.0184192
$571$	1.08228e153	1.09910	0.549549	−	0.835461i	$-0.314800\pi$
$571$	1.08228e153	1.09910	0.549549	+	0.835461i	$0.314800\pi$
$572$	−9.75098e151	−0.0898605
$573$	−9.52388e152	−0.796586
$574$	−2.50425e150	−0.00190138
$575$	−9.17164e152	−0.632240
$576$	1.27685e153	0.799268
$577$	3.30390e152	0.187832	0.0939158	−	0.995580i	$-0.470062\pi$
$577$	3.30390e152	0.187832	0.0939158	+	0.995580i	$0.470062\pi$
$578$	−5.56180e151	−0.0287224
$579$	1.15187e153	0.540435
$580$	−6.80685e153	−2.90197
$581$	−4.14425e152	−0.160572
$582$	2.00954e151	0.00707737
$583$	−2.16304e152	−0.0692563
$584$	−6.81150e151	−0.0198303
$585$	−1.54588e153	−0.409283
$586$	−3.99356e151	−0.00961706
$587$	6.31399e153	1.38321	0.691606	−	0.722275i	$-0.256903\pi$
$587$	6.31399e153	1.38321	0.691606	+	0.722275i	$0.256903\pi$
$588$	2.20710e153	0.439926
$589$	6.98951e153	1.26779
$590$	−1.38151e152	−0.0228069
$591$	−2.09422e153	−0.314715
$592$	−4.12268e153	−0.564059
$593$	2.19716e152	0.0273732	0.0136866	−	0.999906i	$-0.495643\pi$
$593$	2.19716e152	0.0273732	0.0136866	+	0.999906i	$0.495643\pi$
$594$	4.46720e151	0.00506860
$595$	−2.57005e153	−0.265613
$596$	9.81765e153	0.924358
$597$	6.48388e153	0.556237
$598$	3.51194e151	0.00274556
$599$	−9.10642e153	−0.648872	−0.324436	−	0.945908i	$-0.605175\pi$
$599$	−9.10642e153	−0.648872	−0.324436	+	0.945908i	$0.605175\pi$
$600$	4.90894e152	0.0318855
$601$	1.86785e154	1.10614	0.553069	−	0.833136i	$-0.313457\pi$
$601$	1.86785e154	1.10614	0.553069	+	0.833136i	$0.313457\pi$
$602$	6.28442e151	0.00339359
$603$	−2.58631e154	−1.27371
$604$	−7.73681e153	−0.347546
$605$	−3.62528e154	−1.48566
$606$	1.61448e152	0.00603672
$607$	−6.77722e153	−0.231249	−0.115624	−	0.993293i	$-0.536887\pi$
$607$	−6.77722e153	−0.231249	−0.115624	+	0.993293i	$0.536887\pi$
$608$	2.46263e153	0.0766922
$609$	−3.05185e153	−0.0867568
$610$	−8.42278e152	−0.0218600
$611$	1.26545e154	0.299886
$612$	5.60799e154	1.21368
$613$	−4.23393e153	−0.0836927	−0.0418464	−	0.999124i	$-0.513324\pi$
$613$	−4.23393e153	−0.0836927	−0.0418464	+	0.999124i	$0.513324\pi$
$614$	1.66199e153	0.0300112
$615$	−3.44806e154	−0.568861
$616$	−9.08716e151	−0.00136993
$617$	−3.10654e154	−0.428007	−0.214003	−	0.976833i	$-0.568650\pi$
$617$	−3.10654e154	−0.428007	−0.214003	+	0.976833i	$0.568650\pi$
$618$	−1.11142e153	−0.0139964
$619$	5.39853e154	0.621504	0.310752	−	0.950491i	$-0.399419\pi$
$619$	5.39853e154	0.621504	0.310752	+	0.950491i	$0.399419\pi$
$620$	1.68815e155	1.77694
$621$	3.26632e154	0.314395
$622$	−1.65275e153	−0.0145493
$623$	−1.32998e154	−0.107092
$624$	1.90660e154	0.140448
$625$	−1.45537e153	−0.00980914
$626$	−4.05738e153	−0.0250247
$627$	−2.58954e154	−0.146175
$628$	−3.11042e155	−1.60716
$629$	−1.80891e155	−0.855671
$630$	−7.20141e152	−0.00311901
$631$	1.51399e155	0.600472	0.300236	−	0.953865i	$-0.402935\pi$
$631$	1.51399e155	0.600472	0.300236	+	0.953865i	$0.402935\pi$
$632$	1.15772e154	0.0420539
$633$	−2.59959e155	−0.864966
$634$	−9.88764e153	−0.0301397
$635$	4.10090e155	1.14535
$636$	4.23146e154	0.108298
$637$	−1.33053e155	−0.312094
$638$	−5.27618e153	−0.0113442
$639$	−5.96790e155	−1.17632
$640$	7.92990e154	0.143311
$641$	−2.69579e155	−0.446750	−0.223375	−	0.974733i	$-0.571707\pi$
$641$	−2.69579e155	−0.446750	−0.223375	+	0.974733i	$0.571707\pi$
$642$	−6.50065e153	−0.00988012
$643$	9.34113e155	1.30224	0.651119	−	0.758976i	$-0.274300\pi$
$643$	9.34113e155	1.30224	0.651119	+	0.758976i	$0.274300\pi$
$644$	−3.32135e154	−0.0424765
$645$	8.65291e155	1.01531
$646$	3.59882e154	0.0387485
$647$	9.65671e155	0.954205	0.477102	−	0.878848i	$-0.341687\pi$
$647$	9.65671e155	0.954205	0.477102	+	0.878848i	$0.341687\pi$
$648$	2.17319e154	0.0197099
$649$	2.17396e155	0.180997
$650$	−1.47929e154	−0.0113074
$651$	7.56882e154	0.0531231
$652$	−2.36575e156	−1.52485
$653$	1.43448e156	0.849206	0.424603	−	0.905380i	$-0.360414\pi$
$653$	1.43448e156	0.849206	0.424603	+	0.905380i	$0.360414\pi$
$654$	−1.82695e154	−0.00993486
$655$	−9.33247e155	−0.466235
$656$	−1.71859e156	−0.788876
$657$	8.49435e155	0.358304
$658$	5.89504e153	0.00228533
$659$	−2.20830e156	−0.786895	−0.393447	−	0.919347i	$-0.628718\pi$
$659$	−2.20830e156	−0.786895	−0.393447	+	0.919347i	$0.628718\pi$
$660$	−6.25443e155	−0.204880
$661$	−1.24078e156	−0.373692	−0.186846	−	0.982389i	$-0.559827\pi$
$661$	−1.24078e156	−0.373692	−0.186846	+	0.982389i	$0.559827\pi$
$662$	−5.87869e154	−0.0162803
$663$	8.36564e155	0.213058
$664$	2.80392e155	0.0656807
$665$	9.38199e155	0.202159
$666$	−5.06866e154	−0.0100479
$667$	−3.85783e156	−0.703654
$668$	5.84104e156	0.980384
$669$	4.24933e155	0.0656404
$670$	−4.00866e155	−0.0569964
$671$	1.32542e156	0.173482
$672$	2.66674e154	0.00321356
$673$	1.04662e157	1.16133	0.580664	−	0.814144i	$-0.302793\pi$
$673$	1.04662e157	1.16133	0.580664	+	0.814144i	$0.302793\pi$
$674$	−8.39034e154	−0.00857345
$675$	−1.37583e157	−1.29481
$676$	1.03800e157	0.899821
$677$	1.52527e157	1.21808	0.609041	−	0.793139i	$-0.291554\pi$
$677$	1.52527e157	1.21808	0.609041	+	0.793139i	$0.291554\pi$
$678$	−1.18286e155	−0.00870336
$679$	1.14569e156	0.0776775
$680$	1.73885e156	0.108647
$681$	−1.03549e157	−0.596321
$682$	1.30853e155	0.00694628
$683$	8.34921e156	0.408598	0.204299	−	0.978909i	$-0.434509\pi$
$683$	8.34921e156	0.408598	0.204299	+	0.978909i	$0.434509\pi$
$684$	−2.04720e157	−0.923733
$685$	−6.29550e157	−2.61941
$686$	−1.24702e155	−0.00478504
$687$	1.30518e156	0.0461923
$688$	4.31279e157	1.40799
$689$	−2.55090e156	−0.0768292
$690$	2.25261e155	0.00625982
$691$	−3.40073e157	−0.872048	−0.436024	−	0.899935i	$-0.643614\pi$
$691$	−3.40073e157	−0.872048	−0.436024	+	0.899935i	$0.643614\pi$
$692$	2.12935e157	0.503916
$693$	1.13322e156	0.0247526
$694$	−5.82158e155	−0.0117379
$695$	4.17936e157	0.777953
$696$	2.06482e156	0.0354871
$697$	−7.54067e157	−1.19672
$698$	9.86740e155	0.0144619
$699$	2.14282e157	0.290070
$700$	1.39901e157	0.174936
$701$	1.35297e158	1.56292	0.781461	−	0.623954i	$-0.214475\pi$
$701$	1.35297e158	1.56292	0.781461	+	0.623954i	$0.214475\pi$
$702$	5.26823e155	0.00562284
$703$	6.60345e157	0.651254
$704$	−3.11427e157	−0.283840
$705$	8.11677e157	0.683734
$706$	−3.61420e156	−0.0281417
$707$	9.20453e156	0.0662559
$708$	−4.25283e157	−0.283030
$709$	−2.22378e158	−1.36844	−0.684219	−	0.729276i	$-0.739857\pi$
$709$	−2.22378e158	−1.36844	−0.684219	+	0.729276i	$0.739857\pi$
$710$	−9.24995e156	−0.0526382
$711$	−1.44375e158	−0.759852
$712$	8.99840e156	0.0438052
$713$	9.56771e157	0.430863
$714$	3.89710e155	0.00162365
$715$	3.77043e157	0.145347
$716$	−6.41211e157	−0.228733
$717$	−2.28454e157	−0.0754198
$718$	1.59608e156	0.00487695
$719$	−3.77497e157	−0.106773	−0.0533864	−	0.998574i	$-0.517001\pi$
$719$	−3.77497e157	−0.106773	−0.0533864	+	0.998574i	$0.517001\pi$
$720$	−4.94209e158	−1.29407
$721$	−6.33647e157	−0.153617
$722$	−3.25323e156	−0.00730299
$723$	−3.22593e158	−0.670624
$724$	−2.14014e158	−0.412052
$725$	1.62498e159	2.89794
$726$	5.49720e156	0.00908153
$727$	3.85921e158	0.590661	0.295331	−	0.955395i	$-0.404570\pi$
$727$	3.85921e158	0.590661	0.295331	+	0.955395i	$0.404570\pi$
$728$	−1.07166e156	−0.00151973
$729$	9.53810e155	0.00125338
$730$	1.31658e157	0.0160335
$731$	1.89233e159	2.13591
$732$	−2.59286e158	−0.271278
$733$	−1.82019e159	−1.76542	−0.882708	−	0.469921i	$-0.844282\pi$
$733$	−1.82019e159	−1.76542	−0.882708	+	0.469921i	$0.844282\pi$
$734$	3.04992e157	0.0274257
$735$	−8.53421e158	−0.711567
$736$	3.37102e157	0.0260641
$737$	6.30808e158	0.452326
$738$	−2.11293e157	−0.0140526
$739$	−1.20977e159	−0.746338	−0.373169	−	0.927763i	$-0.621729\pi$
$739$	−1.20977e159	−0.746338	−0.373169	+	0.927763i	$0.621729\pi$
$740$	1.59491e159	0.912799
$741$	−3.05388e158	−0.162159
$742$	−1.18833e156	−0.000585490 0
$743$	9.52974e158	0.435715	0.217857	−	0.975981i	$-0.430093\pi$
$743$	9.52974e158	0.435715	0.217857	+	0.975981i	$0.430093\pi$
$744$	−5.12092e157	−0.0217295
$745$	−3.79621e159	−1.49512
$746$	−5.21889e156	−0.00190798
$747$	−3.49666e159	−1.18675
$748$	−1.36780e159	−0.431007
$749$	−3.70618e158	−0.108439
$750$	−3.60827e157	−0.00980391
$751$	2.21943e159	0.560048	0.280024	−	0.959993i	$-0.409658\pi$
$751$	2.21943e159	0.560048	0.280024	+	0.959993i	$0.409658\pi$
$752$	4.04557e159	0.948178
$753$	1.51208e159	0.329196
$754$	−6.22227e157	−0.0125846
$755$	2.99161e159	0.562146
$756$	−4.98233e158	−0.0869907
$757$	6.32421e159	1.02609	0.513044	−	0.858362i	$-0.328518\pi$
$757$	6.32421e159	1.02609	0.513044	+	0.858362i	$0.328518\pi$
$758$	1.22563e158	0.0184807
$759$	−3.54474e158	−0.0496782
$760$	−6.34768e158	−0.0826915
$761$	−9.78502e158	−0.118499	−0.0592493	−	0.998243i	$-0.518871\pi$
$761$	−9.78502e158	−0.118499	−0.0592493	+	0.998243i	$0.518871\pi$
$762$	−6.21842e157	−0.00700130
$763$	−1.04159e159	−0.109040
$764$	1.83640e160	1.78766
$765$	−2.16845e160	−1.96309
$766$	4.04630e158	0.0340692
$767$	2.56378e159	0.200788
$768$	6.08329e159	0.443191
$769$	−1.50023e160	−1.01682	−0.508412	−	0.861114i	$-0.669767\pi$
$769$	−1.50023e160	−1.01682	−0.508412	+	0.861114i	$0.669767\pi$
$770$	1.75644e157	0.00110764
$771$	−2.87516e159	−0.168711
$772$	−2.22104e160	−1.21282
$773$	2.94606e160	1.49720	0.748600	−	0.663022i	$-0.230726\pi$
$773$	2.94606e160	1.49720	0.748600	+	0.663022i	$0.230726\pi$
$774$	5.30240e158	0.0250813
$775$	−4.03009e160	−1.77447
$776$	−7.75153e158	−0.0317733
$777$	7.15077e158	0.0272889
$778$	4.75497e158	0.0168959
$779$	2.75273e160	0.910824
$780$	−7.37594e159	−0.227283
$781$	1.45558e160	0.417739
$782$	4.92631e158	0.0131688
$783$	−5.78710e160	−1.44106
$784$	−4.25363e160	−0.986776
$785$	1.20271e161	2.59953
$786$	1.41513e158	0.00285000
$787$	4.54292e160	0.852585	0.426292	−	0.904585i	$-0.359819\pi$
$787$	4.54292e160	0.852585	0.426292	+	0.904585i	$0.359819\pi$
$788$	4.03808e160	0.706269
$789$	1.24035e160	0.202195
$790$	−2.23774e159	−0.0340021
$791$	−6.74381e159	−0.0955235
$792$	−7.66718e158	−0.0101248
$793$	1.56309e160	0.192451
$794$	1.34170e158	0.00154034
$795$	−1.63619e160	−0.175169
$796$	−1.25022e161	−1.24828
$797$	−9.86822e160	−0.918972	−0.459486	−	0.888185i	$-0.651966\pi$
$797$	−9.86822e160	−0.918972	−0.459486	+	0.888185i	$0.651966\pi$
$798$	−1.42264e158	−0.00123576
$799$	1.77508e161	1.43837
$800$	−1.41993e160	−0.107343
$801$	−1.12215e161	−0.791495
$802$	4.41355e159	0.0290476
$803$	−2.07179e160	−0.127243
$804$	−1.23402e161	−0.707315
$805$	1.28427e160	0.0687045
$806$	1.54317e159	0.00770583
$807$	−5.92930e160	−0.276390
$808$	−6.22762e159	−0.0271014
$809$	−1.60149e160	−0.0650700	−0.0325350	−	0.999471i	$-0.510358\pi$
$809$	−1.60149e160	−0.0650700	−0.0325350	+	0.999471i	$0.510358\pi$
$810$	−4.20051e159	−0.0159362
$811$	−1.90276e161	−0.674104	−0.337052	−	0.941486i	$-0.609430\pi$
$811$	−1.90276e161	−0.674104	−0.337052	+	0.941486i	$0.609430\pi$
$812$	5.88459e160	0.194696
$813$	2.40576e161	0.743408
$814$	1.23626e159	0.00356825
$815$	9.14769e161	2.46640
$816$	2.67446e161	0.673646
$817$	−6.90797e161	−1.62565
$818$	1.57009e160	0.0345235
$819$	1.33643e160	0.0274592
$820$	6.64857e161	1.27661
$821$	−4.92072e161	−0.883045	−0.441523	−	0.897250i	$-0.645562\pi$
$821$	−4.92072e161	−0.883045	−0.441523	+	0.897250i	$0.645562\pi$
$822$	9.54619e159	0.0160120
$823$	−5.15305e161	−0.807930	−0.403965	−	0.914775i	$-0.632368\pi$
$823$	−5.15305e161	−0.807930	−0.403965	+	0.914775i	$0.632368\pi$
$824$	4.28714e160	0.0628359
$825$	1.49311e161	0.204596
$826$	1.19433e159	0.00153014
$827$	8.74445e161	1.04756	0.523778	−	0.851855i	$-0.324522\pi$
$827$	8.74445e161	1.04756	0.523778	+	0.851855i	$0.324522\pi$
$828$	−2.80235e161	−0.313934
$829$	2.37845e161	0.249183	0.124591	−	0.992208i	$-0.460238\pi$
$829$	2.37845e161	0.249183	0.124591	+	0.992208i	$0.460238\pi$
$830$	−5.41966e160	−0.0531053
$831$	−7.83158e161	−0.717782
$832$	−3.67270e161	−0.314877
$833$	−1.86637e162	−1.49693
$834$	−6.33739e159	−0.00475548
$835$	−2.25856e162	−1.58574
$836$	4.99317e161	0.328041
$837$	1.43525e162	0.882395
$838$	1.85746e160	0.0106875
$839$	−1.22123e162	−0.657671	−0.328836	−	0.944387i	$-0.606656\pi$
$839$	−1.22123e162	−0.657671	−0.328836	+	0.944387i	$0.606656\pi$
$840$	−6.87380e159	−0.00346495
$841$	4.71587e162	2.22528
$842$	−2.81780e160	−0.0124477
$843$	−3.34545e161	−0.138364
$844$	5.01255e162	1.94112
$845$	−4.01366e162	−1.45544
$846$	4.97387e160	0.0168904
$847$	3.13409e161	0.0996741
$848$	−8.15510e161	−0.242918
$849$	2.31590e161	0.0646166
$850$	−2.07505e161	−0.0542347
$851$	9.03925e161	0.221331
$852$	−2.84750e162	−0.653230
$853$	2.01576e162	0.433280	0.216640	−	0.976252i	$-0.430490\pi$
$853$	2.01576e162	0.433280	0.216640	+	0.976252i	$0.430490\pi$
$854$	7.28158e159	0.00146661
$855$	7.91594e162	1.49411
$856$	2.50753e161	0.0443560
$857$	4.64993e162	0.770923	0.385462	−	0.922724i	$-0.374042\pi$
$857$	4.64993e162	0.770923	0.385462	+	0.922724i	$0.374042\pi$
$858$	−5.71730e159	−0.000888477 0
$859$	−4.69191e162	−0.683485	−0.341743	−	0.939794i	$-0.611017\pi$
$859$	−4.69191e162	−0.683485	−0.341743	+	0.939794i	$0.611017\pi$
$860$	−1.66846e163	−2.27851
$861$	2.98088e161	0.0381654
$862$	2.38837e161	0.0286714
$863$	−7.78382e162	−0.876180	−0.438090	−	0.898931i	$-0.644345\pi$
$863$	−7.78382e162	−0.876180	−0.438090	+	0.898931i	$0.644345\pi$
$864$	5.05684e161	0.0533785
$865$	−8.23359e162	−0.815070
$866$	3.00507e160	0.00279005
$867$	6.62037e162	0.576530
$868$	−1.45942e162	−0.119217
$869$	3.52134e162	0.269842
$870$	−3.99106e161	−0.0286926
$871$	7.43921e162	0.501786
$872$	7.04720e161	0.0446017
$873$	9.66663e162	0.574096
$874$	−1.79835e161	−0.0100228
$875$	−2.05717e162	−0.107602
$876$	4.05296e162	0.198973
$877$	9.51564e162	0.438491	0.219245	−	0.975670i	$-0.429640\pi$
$877$	9.51564e162	0.438491	0.219245	+	0.975670i	$0.429640\pi$
$878$	4.81977e161	0.0208488
$879$	4.75365e162	0.193039
$880$	1.20539e163	0.459556
$881$	−2.51275e163	−0.899470	−0.449735	−	0.893162i	$-0.648482\pi$
$881$	−2.51275e163	−0.899470	−0.449735	+	0.893162i	$0.648482\pi$
$882$	−5.22967e161	−0.0175779
$883$	5.66191e163	1.78708	0.893539	−	0.448985i	$-0.148214\pi$
$883$	5.66191e163	1.78708	0.893539	+	0.448985i	$0.148214\pi$
$884$	−1.61307e163	−0.478136
$885$	1.64445e163	0.457792
$886$	−3.40781e161	−0.00891055
$887$	−5.82201e163	−1.42992	−0.714961	−	0.699164i	$-0.753556\pi$
$887$	−5.82201e163	−1.42992	−0.714961	+	0.699164i	$0.753556\pi$
$888$	−4.83808e161	−0.0111623
$889$	−3.54527e162	−0.0768426
$890$	−1.73928e162	−0.0354181
$891$	6.60998e162	0.126470
$892$	−8.19358e162	−0.147307
$893$	−6.47995e163	−1.09475
$894$	5.75639e161	0.00913941
$895$	2.47938e163	0.369969
$896$	−6.85548e161	−0.00961486
$897$	−4.18036e162	−0.0551104
$898$	4.39829e161	0.00545064
$899$	−1.69516e164	−1.97491
$900$	1.18040e164	1.29291
$901$	−3.57823e163	−0.368504
$902$	5.15349e161	0.00499044
$903$	−7.48053e162	−0.0681180
$904$	4.56274e162	0.0390731
$905$	8.27532e163	0.666482
$906$	−4.53633e161	−0.00343629
$907$	9.23530e163	0.658031	0.329016	−	0.944324i	$-0.393283\pi$
$907$	9.23530e163	0.658031	0.329016	+	0.944324i	$0.393283\pi$
$908$	1.99663e164	1.33824
$909$	7.76622e163	0.489682
$910$	2.07139e161	0.00122876
$911$	−1.32120e164	−0.737390	−0.368695	−	0.929550i	$-0.620195\pi$
$911$	−1.32120e164	−0.737390	−0.368695	+	0.929550i	$0.620195\pi$
$912$	−9.76312e163	−0.512714
$913$	8.52844e163	0.421446
$914$	1.49852e162	0.00696863
$915$	1.00259e164	0.438785
$916$	−2.51665e163	−0.103663
$917$	8.06802e162	0.0312801
$918$	7.38992e162	0.0269694
$919$	−9.68585e163	−0.332757	−0.166378	−	0.986062i	$-0.553207\pi$
$919$	−9.68585e163	−0.332757	−0.166378	+	0.986062i	$0.553207\pi$
$920$	−8.68914e162	−0.0281030
$921$	−1.97832e164	−0.602402
$922$	9.10847e162	0.0261143
$923$	1.71659e164	0.463417
$924$	5.40702e162	0.0137456
$925$	−3.80749e164	−0.911533
$926$	−6.25946e162	−0.0141133
$927$	−5.34632e164	−1.13535
$928$	−5.97260e163	−0.119468
$929$	−3.35818e164	−0.632750	−0.316375	−	0.948634i	$-0.602466\pi$
$929$	−3.35818e164	−0.632750	−0.316375	+	0.948634i	$0.602466\pi$
$930$	9.89814e162	0.0175691
$931$	6.81321e164	1.13932
$932$	−4.13179e164	−0.650962
$933$	1.96732e164	0.292041
$934$	−1.51262e163	−0.0211582
$935$	5.28890e164	0.697141
$936$	−9.04201e162	−0.0112320
$937$	1.06842e165	1.25082	0.625410	−	0.780296i	$-0.284932\pi$
$937$	1.06842e165	1.25082	0.625410	+	0.780296i	$0.284932\pi$
$938$	3.46553e162	0.00382395
$939$	4.82961e164	0.502310
$940$	−1.56508e165	−1.53441
$941$	−7.60011e163	−0.0702418	−0.0351209	−	0.999383i	$-0.511182\pi$
$941$	−7.60011e163	−0.0702418	−0.0351209	+	0.999383i	$0.511182\pi$
$942$	−1.82373e163	−0.0158904
$943$	3.76812e164	0.309546
$944$	8.19628e164	0.634850
$945$	1.92652e164	0.140705
$946$	−1.29327e163	−0.00890698
$947$	2.50228e165	1.62522	0.812611	−	0.582806i	$-0.198045\pi$
$947$	2.50228e165	1.62522	0.812611	+	0.582806i	$0.198045\pi$
$948$	−6.88865e164	−0.421960
$949$	−2.44329e164	−0.141156
$950$	7.57498e163	0.0412782
$951$	1.17695e165	0.604980
$952$	−1.50325e163	−0.00728922
$953$	−2.38177e165	−1.08954	−0.544772	−	0.838584i	$-0.683384\pi$
$953$	−2.38177e165	−1.08954	−0.544772	+	0.838584i	$0.683384\pi$
$954$	−1.00264e163	−0.00432722
$955$	−7.10084e165	−2.89150
$956$	4.40506e164	0.169254
$957$	6.28039e164	0.227706
$958$	5.47347e163	0.0187274
$959$	5.44252e164	0.175739
$960$	−2.35573e165	−0.717912
$961$	7.27574e164	0.209281
$962$	1.45794e163	0.00395842
$963$	−3.12704e165	−0.801448
$964$	6.22024e165	1.50498
$965$	8.58814e165	1.96170
$966$	−1.94741e162	−0.000419978 0
$967$	−5.45138e165	−1.11004	−0.555018	−	0.831838i	$-0.687289\pi$
$967$	−5.45138e165	−1.11004	−0.555018	+	0.831838i	$0.687289\pi$
$968$	−2.12047e164	−0.0407708
$969$	−4.28378e165	−0.777781
$970$	1.49828e164	0.0256899
$971$	6.01930e165	0.974718	0.487359	−	0.873202i	$-0.337960\pi$
$971$	6.01930e165	0.974718	0.487359	+	0.873202i	$0.337960\pi$
$972$	−6.53709e165	−0.999786
$973$	−3.61310e164	−0.0521936
$974$	7.01187e163	0.00956779
$975$	1.76084e165	0.226968
$976$	4.99711e165	0.608491
$977$	1.41465e166	1.62742	0.813710	−	0.581271i	$-0.197444\pi$
$977$	1.41465e166	1.62742	0.813710	+	0.581271i	$0.197444\pi$
$978$	−1.38711e164	−0.0150767
$979$	2.73696e165	0.281080
$980$	1.64557e166	1.59687
$981$	−8.78829e165	−0.805887
$982$	−4.19897e163	−0.00363878
$983$	−1.98552e166	−1.62613	−0.813065	−	0.582174i	$-0.802202\pi$
$983$	−1.98552e166	−1.62613	−0.813065	+	0.582174i	$0.802202\pi$
$984$	−2.01681e164	−0.0156112
$985$	−1.56141e166	−1.14237
$986$	−8.72818e164	−0.0603608
$987$	−7.01703e164	−0.0458724
$988$	5.88851e165	0.363911
$989$	−9.45610e165	−0.552482
$990$	1.48198e164	0.00818630
$991$	−2.66398e166	−1.39137	−0.695686	−	0.718346i	$-0.744899\pi$
$991$	−2.66398e166	−1.39137	−0.695686	+	0.718346i	$0.744899\pi$
$992$	1.48125e165	0.0731527
$993$	6.99757e165	0.326786
$994$	7.99667e163	0.00353155
$995$	4.83427e166	2.01906
$996$	−1.66838e166	−0.659027
$997$	−3.76482e166	−1.40657	−0.703287	−	0.710906i	$-0.748285\pi$
$997$	−3.76482e166	−1.40657	−0.703287	+	0.710906i	$0.748285\pi$
$998$	1.34593e164	0.00475638
$999$	1.35597e166	0.453279

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.112.a.a.1.5	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.112.a.a.1.5	✓	9	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:	\( k \)	\(=\)	\( 112 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-1.13057e15 q^{2} +1.34574e26 q^{3} -2.59487e33 q^{4} +1.00336e39 q^{5} -1.52145e41 q^{6} -8.67417e45 q^{7} +5.86879e48 q^{8} -7.31873e52 q^{9} +O(q^{10})\)	\(q-1.13057e15 q^{2} +1.34574e26 q^{3} -2.59487e33 q^{4} +1.00336e39 q^{5} -1.52145e41 q^{6} -8.67417e45 q^{7} +5.86879e48 q^{8} -7.31873e52 q^{9} -1.13437e54 q^{10} +1.78506e57 q^{11} -3.49203e59 q^{12} +2.10514e61 q^{13} +9.80672e60 q^{14} +1.35027e65 q^{15} +6.73003e66 q^{16} +2.95295e68 q^{17} +8.27430e67 q^{18} -1.07798e71 q^{19} -2.60360e72 q^{20} -1.16732e72 q^{21} -2.01812e72 q^{22} -1.47561e75 q^{23} +7.89788e74 q^{24} +6.21551e77 q^{25} -2.38000e76 q^{26} -2.21355e79 q^{27} +2.25084e79 q^{28} +2.61440e81 q^{29} -1.52657e80 q^{30} -6.48392e82 q^{31} -2.28450e82 q^{32} +2.40223e83 q^{33} -3.33850e83 q^{34} -8.70334e84 q^{35} +1.89912e86 q^{36} -6.12579e86 q^{37} +1.21872e86 q^{38} +2.83298e87 q^{39} +5.88852e87 q^{40} -2.55361e89 q^{41} +1.31973e87 q^{42} +6.40828e90 q^{43} -4.63199e90 q^{44} -7.34334e91 q^{45} +1.66827e90 q^{46} +6.01122e92 q^{47} +9.05690e92 q^{48} -6.32038e93 q^{49} -7.02704e92 q^{50} +3.97391e94 q^{51} -5.46256e94 q^{52} -1.21175e95 q^{53} +2.50256e94 q^{54} +1.79106e96 q^{55} -5.09069e94 q^{56} -1.45068e97 q^{57} -2.95575e96 q^{58} +1.21787e98 q^{59} -3.50377e98 q^{60} +7.42509e98 q^{61} +7.33049e97 q^{62} +6.34839e98 q^{63} -1.74463e100 q^{64} +2.11222e100 q^{65} -2.71588e98 q^{66} +3.53383e101 q^{67} -7.66251e101 q^{68} -1.98579e101 q^{69} +9.83970e99 q^{70} +8.15428e102 q^{71} -4.29521e101 q^{72} -1.16063e103 q^{73} +6.92560e101 q^{74} +8.36449e103 q^{75} +2.79721e104 q^{76} -1.54839e103 q^{77} -3.20287e102 q^{78} +1.97268e105 q^{79} +6.75267e105 q^{80} +3.70296e105 q^{81} +2.88702e104 q^{82} +4.77769e106 q^{83} +3.02905e105 q^{84} +2.96288e107 q^{85} -7.24498e105 q^{86} +3.51832e107 q^{87} +1.04761e106 q^{88} +1.53326e108 q^{89} +8.30213e106 q^{90} -1.82603e107 q^{91} +3.82901e108 q^{92} -8.72570e108 q^{93} -6.79608e107 q^{94} -1.08160e110 q^{95} -3.07435e108 q^{96} -1.32081e110 q^{97} +7.14560e108 q^{98} -1.30643e110 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 73\!\cdots\!76 q^{2}+ \cdots + 44\!\cdots\!13 q^{9}+O(q^{10}) \) 9 * q + 7300500744476376 * q^2 + 233675452617241539765416652 * q^3 + 11020070169858572323722385321061952 * q^4 + 814194067724935025770916308591172296830 * q^5 - 21301527237484005705216688979545976184644832 * q^6 + 78389901636433627730832560362319405491179083256 * q^7 + 331917555337838634305814685721710111074446802593280 * q^8 + 448549390735821931740487725597506918142357121619864013 * q^9	\( 9 q + 73\!\cdots\!76 q^{2}+ \cdots - 30\!\cdots\!44 q^{99}+O(q^{100}) \) 9 * q + 7300500744476376 * q^2 + 233675452617241539765416652 * q^3 + 11020070169858572323722385321061952 * q^4 + 814194067724935025770916308591172296830 * q^5 - 21301527237484005705216688979545976184644832 * q^6 + 78389901636433627730832560362319405491179083256 * q^7 + 331917555337838634305814685721710111074446802593280 * q^8 + 448549390735821931740487725597506918142357121619864013 * q^9 + 70318383028880935426202467492101897354146229740372656080 * q^10 + 946977307561400491686882997086862420104457212380759419908 * q^11 + 621762406249451000840580799122879254067634743931860068057856 * q^12 - 105889073807861007951354048376593318148850899094543430238180938 * q^13 - 693200815745779812299859823081139405355406151517828024353685696 * q^14 - 263011530334644917620915776775966612573140691671014743658639898840 * q^15 + 27983078214052241229733802839129592879112204378169572191112640794624 * q^16 - 222105261114216680375344353232960019775132216853502752977555776836734 * q^17 + 13836898392348788400585588852374256049336540448485000158069800440043832 * q^18 - 84745728104868082450386145180218866587906565903531918441867146236497220 * q^19 + 7795554433199817270239288692578476214785961451581351341251140127219386240 * q^20 + 53447991875461898796552150181251304409032073759002376573082504235219586208 * q^21 + 1334480876839672633808741914071727189545841199132729059095736106759243606112 * q^22 - 4280804965700905487867557627761776334077515300975222519458633688084497477528 * q^23 - 129253468619699114441737651311892084919218132467191979241911494876891173877760 * q^24 - 456274260699810946496432078768368872244545007142930133725494539638375760654225 * q^25 + 9117596118629922830918453196718641926897783510547242670141134615123316525608208 * q^26 + 36009290264725541742540148694316715091842126661227810228968619953124574644440120 * q^27 + 389777110106676955938012042765885416118140162819674451900675730518240474989075968 * q^28 - 1612630879112671269089242330901312038613162417445580611832712505926453350563056730 * q^29 - 18167376599417385725382731299135244307087297190105602725235889269652594544837067840 * q^30 + 67559679369166080772885534172593278837571532071620973699499831976537741546761534688 * q^31 + 754093318949864663533121048615003094440304122496655835482200816722793265150805508096 * q^32 - 3133890070812326529166672578753895355679540062945915391855288247367239239009432080976 * q^33 - 24751022535879997806365605902203773919188021786642014954770492231640496515521010376656 * q^34 + 57944164206332657023724654984518766320829384409054668126147883688641566073099799278480 * q^35 + 328041564753120514775451575146434843390262564311310021231853773527241323710816435244864 * q^36 + 3043820559995771428343491307335152699983691109501186564620625804804431981535340669576286 * q^37 - 21382754992423793021134163907198673444659659051000850342253103089169961740533890647606880 * q^38 + 3273459216524867162345405450876825490686869325852879816870160180171296350982671401366216 * q^39 + 123460999717991511987771461057366625032200502337474727630106509260305540512417484610278400 * q^40 + 104629960197719783697927100274525225542843896456497561309270816521996960904985588920195178 * q^41 + 2027994299853353493651484516191980857294428743343203061454578749195409490693400034208902912 * q^42 - 19157176231150752403174922289745163210049080257481323543299910438470109245483512805859143708 * q^43 + 54900509500333144241574805152152293176467261284516409174290950395775810400803069025987309824 * q^44 + 15479509256451142996000421697851689107817887106618468041729343908392688500639929264156928310 * q^45 - 398788118873285310214184399746055204854113651152175668288210597675002274814165601481840895552 * q^46 + 1456966582071114763048986859064421525928331803997603240440970059620025856397045514594291849296 * q^47 - 7452969450778497532129812087184007504558526604092287637802268612794467934087599186261483798528 * q^48 + 17298008315064903937184133864291881308696588708445105876848488522049133450344930890256623872337 * q^49 + 20891593843500014301021428427705110541710363262225372510717283195064501890651418995923815351400 * q^50 - 85813999871822828588324201494589306593218994449334105811559220660851252439965047034531679254312 * q^51 - 228851992565399673815270028508808722169419264169266009042427250901076945058351740642305444481664 * q^52 - 330560931516346297292158383237634604339355604111254380988674341402404197811701576314208409413298 * q^53 + 4500007476747002196644470511723672131082224104684813911982619633059661906955824254260654375081280 * q^54 + 5411788085074080207797655602098900123199579033664526066719620291468503584226809836679744568059960 * q^55 - 42315784638223426280810136290704778028064917513845974684816911806737536885555338292253409336340480 * q^56 + 9918498856896672609870803756688673833744336383910153405185505298972528406991914653827866717244240 * q^57 + 32435179551725169564404757555461461839261719646775117357648454983301156661453863733221818065697680 * q^58 + 322553637419248081900645358050759529139017004186411501272056030884685696264538328889393003620694740 * q^59 - 132467389966865887348037310509899613119681515385419367203561785040397906770826770994985507300267520 * q^60 - 1759437984456387651106179880992119801754779277040263539338974358093077280629950964970586556177810042 * q^61 - 1712844297363572226123727147322557976426042183124057300794490386880408520919151071285053014838119168 * q^62 + 12759876033417698231199447475315412125628460028323317128859307435477632649190559962838360311186507992 * q^63 + 14281879241185987264094876187662890300953975181530786481128692077543427681889775277266607957835251712 * q^64 - 18446575904127982541910334362372985348294257469022062289060943594932692744923327761688031698818070540 * q^65 - 105227969740255769667487712999247235831860856852926275817422436766136475148421006520466387572795840384 * q^66 + 137686280746299018306956215858337887331602769875959175009115726791437961931237555780269025002728818316 * q^67 + 1157398196638034088725243365559060772268690235343345029534596768981482256873945115267239799529371269248 * q^68 + 1095507431560680024171724297772352455505639098885833012944706047494456930144134797052286618395241366496 * q^69 - 3640686416490340897700513163360856154742313115593190855720847062189976425143796505336061966373300603520 * q^70 + 9881612323140206421591424247232489623122284569259126072100461213939705350610294394975802208678001259448 * q^71 + 26396053480919173194166495118665950061506035792323405768129609103560026391739244345645460880788768488960 * q^72 + 68010594140875249475223137869343627059525985931897139097425407128220372890956239808513785565566231240522 * q^73 + 220837506033562453797347134849380708116539322544975559087316116631000736843141442638912881210212941372624 * q^74 + 181912260264814567208746612550869983753545991059523226326816406967698797635966067835830629689080707385300 * q^75 + 761174863647605635882918277985364633628165523124208915131122931858702438047845125322045601860264208695040 * q^76 + 1384642526997449454787538522373154719967650987275787604770256389537561344719927104096300078005408626536672 * q^77 + 10154718868595236540854386892056000355936883967938908970289471652675003137655678023153495552339085989663424 * q^78 + 7526673880001773966576204583811316437192125118919660383683770302134291678384367816740764114717599435401520 * q^79 + 32601244901804291407696890633217962008785625969393161121607747994402795735664787250217837405420588998778880 * q^80 + 48874282116782895668905156724559809826804317530845116719941792255495466449412888893127682785590511826600049 * q^81 + 113239522172902215034601434016259598176780723606704841332886416969022724124423260666831983947062879210014192 * q^82 + 199958416124075286987530689011944805825753524406236269102187579359597825528337021515595830260563921442487932 * q^83 + 880467563819420401586770374036347249339328631628161679582704747941404166343896577833615976614908144379930624 * q^84 + 707266002569821004378084548147696321676161909242361424333261618590644246794997074911164911557278987628650780 * q^85 + 749430950077361833338178064514980710590134374932604590973028338058871330476392166543416304708654721880933728 * q^86 + 2802132957491922284048190008280399903628415414482410070524683686927111831188200973776028254889144423439332360 * q^87 + 7195654272713601174999226937725203391076863795283476240434396643890296393716359696024184526976625256798607360 * q^88 + 3700827869341881331782801900641952675754040149647113243871021736652252631453067855946419168721111605247226810 * q^89 + 8997316939698708062605864942661951051594004217268128464090536667598399664816028357347925999912163977799180560 * q^90 - 254313076672373460593401973466735362362295247774148430702156053605292605984743534435031357382528251918280752 * q^91 - 16891756811302405862414651288981793929299127803233629387746389497252488943048833672780023478534318077838493184 * q^92 - 55378555126167982657281578020507978450769506755610812937817924402648049087367995838404448550854542227572273536 * q^93 - 71374169795251900964177147542915102589642305140612249128066111463360036313665875245965949313319551156299307136 * q^94 - 167271491201189176415157992539596873672401782137242927001530501790921136440405267833568144254517552969527081400 * q^95 - 1187167956876210917054814422873111467722801274363871607741943257050230342552379215783989919197651861627909046272 * q^96 - 631372797244867221191218982738135503959422268139699621925372110836288083138321626431181260783380505262640568654 * q^97 - 1898458058047689123148702915382067648076866113471255418148529297211872922066143741813213498341870918619707529832 * q^98 - 3056373683854811033724902889292841037638123003448050519838010864270837225210323694704228642303518682358171259244 * q^99

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