LMFDB - Embedded newform 1.112.a.a.1.4

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			1.4
Root			$-3.56630e14$ 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)

$f(q)$	$=$	$q-2.48662e16 q^{2} +5.20768e26 q^{3} -1.97782e33 q^{4} -7.34308e38 q^{5} -1.29495e43 q^{6} -1.22695e47 q^{7} +1.13737e50 q^{8} +1.79902e53 q^{9} +O(q^{10})$	\(q-2.48662e16 q^{2} +5.20768e26 q^{3} -1.97782e33 q^{4} -7.34308e38 q^{5} -1.29495e43 q^{6} -1.22695e47 q^{7} +1.13737e50 q^{8} +1.79902e53 q^{9} +1.82594e55 q^{10} -6.40567e57 q^{11} -1.02999e60 q^{12} -6.91792e61 q^{13} +3.05097e63 q^{14} -3.82404e65 q^{15} +2.30650e66 q^{16} -2.11423e68 q^{17} -4.47348e69 q^{18} +3.34195e70 q^{19} +1.45233e72 q^{20} -6.38959e73 q^{21} +1.59285e74 q^{22} -4.04428e74 q^{23} +5.92308e76 q^{24} +1.54022e77 q^{25} +1.72022e78 q^{26} +4.61425e79 q^{27} +2.42670e80 q^{28} +1.83961e81 q^{29} +9.50894e81 q^{30} -5.15527e82 q^{31} -3.52633e83 q^{32} -3.33587e84 q^{33} +5.25729e84 q^{34} +9.00962e85 q^{35} -3.55814e86 q^{36} +1.66082e87 q^{37} -8.31017e86 q^{38} -3.60263e88 q^{39} -8.35181e88 q^{40} -6.46319e88 q^{41} +1.58885e90 q^{42} -4.34991e90 q^{43} +1.26693e91 q^{44} -1.32104e92 q^{45} +1.00566e91 q^{46} +5.49999e92 q^{47} +1.20115e93 q^{48} +8.65856e93 q^{49} -3.82994e93 q^{50} -1.10102e95 q^{51} +1.36824e95 q^{52} +1.23885e95 q^{53} -1.14739e96 q^{54} +4.70373e96 q^{55} -1.39550e97 q^{56} +1.74038e97 q^{57} -4.57442e97 q^{58} -1.99367e97 q^{59} +7.56327e98 q^{60} +3.74129e98 q^{61} +1.28192e99 q^{62} -2.20732e100 q^{63} +2.78061e99 q^{64} +5.07988e100 q^{65} +8.29504e100 q^{66} -1.75123e101 q^{67} +4.18157e101 q^{68} -2.10613e101 q^{69} -2.24035e102 q^{70} +1.21022e102 q^{71} +2.04616e103 q^{72} -5.69248e102 q^{73} -4.12984e103 q^{74} +8.02098e103 q^{75} -6.60979e103 q^{76} +7.85947e104 q^{77} +8.95838e104 q^{78} +2.83877e105 q^{79} -1.69368e105 q^{80} +7.60490e105 q^{81} +1.60715e105 q^{82} +1.17958e106 q^{83} +1.26375e107 q^{84} +1.55250e107 q^{85} +1.08166e107 q^{86} +9.58012e107 q^{87} -7.28563e107 q^{88} -2.11765e108 q^{89} +3.28491e108 q^{90} +8.48797e108 q^{91} +7.99887e107 q^{92} -2.68470e109 q^{93} -1.36764e109 q^{94} -2.45402e109 q^{95} -1.83640e110 q^{96} +3.20630e110 q^{97} -2.15305e110 q^{98} -1.15239e111 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.48662e16	−0.488028	−0.244014	−	0.969772i	$-0.578464\pi$
$2$	−2.48662e16	−0.488028	−0.244014	+	0.969772i	$0.578464\pi$
$3$	5.20768e26	1.72351	0.861757	−	0.507321i	$-0.169364\pi$
$3$	5.20768e26	1.72351	0.861757	+	0.507321i	$0.169364\pi$
$4$	−1.97782e33	−0.761829
$5$	−7.34308e38	−1.18316	−0.591579	−	0.806247i	$-0.701495\pi$
$5$	−7.34308e38	−1.18316	−0.591579	+	0.806247i	$0.701495\pi$
$6$	−1.29495e43	−0.841123
$7$	−1.22695e47	−1.53422	−0.767109	−	0.641516i	$-0.778306\pi$
$7$	−1.22695e47	−1.53422	−0.767109	+	0.641516i	$0.778306\pi$
$8$	1.13737e50	0.859822
$9$	1.79902e53	1.97050
$10$	1.82594e55	0.577414
$11$	−6.40567e57	−1.02158	−0.510788	−	0.859707i	$-0.670646\pi$
$11$	−6.40567e57	−1.02158	−0.510788	+	0.859707i	$0.670646\pi$
$12$	−1.02999e60	−1.31302
$13$	−6.91792e61	−1.03781	−0.518907	−	0.854831i	$-0.673661\pi$
$13$	−6.91792e61	−1.03781	−0.518907	+	0.854831i	$0.673661\pi$
$14$	3.05097e63	0.748741
$15$	−3.82404e65	−2.03919
$16$	2.30650e66	0.342212
$17$	−2.11423e68	−1.08452	−0.542260	−	0.840211i	$-0.682431\pi$
$17$	−2.11423e68	−1.08452	−0.542260	+	0.840211i	$0.682431\pi$
$18$	−4.47348e69	−0.961660
$19$	3.34195e70	0.357417	0.178709	−	0.983902i	$-0.442808\pi$
$19$	3.34195e70	0.357417	0.178709	+	0.983902i	$0.442808\pi$
$20$	1.45233e72	0.901364
$21$	−6.38959e73	−2.64425
$22$	1.59285e74	0.498557
$23$	−4.04428e74	−0.107386	−0.0536929	−	0.998557i	$-0.517099\pi$
$23$	−4.04428e74	−0.107386	−0.0536929	+	0.998557i	$0.517099\pi$
$24$	5.92308e76	1.48192
$25$	1.54022e77	0.399864
$26$	1.72022e78	0.506482
$27$	4.61425e79	1.67268
$28$	2.42670e80	1.16881
$29$	1.83961e81	1.26368	0.631840	−	0.775098i	$-0.282300\pi$
$29$	1.83961e81	1.26368	0.631840	+	0.775098i	$0.282300\pi$
$30$	9.50894e81	0.995182
$31$	−5.15527e82	−0.874334	−0.437167	−	0.899380i	$-0.644018\pi$
$31$	−5.15527e82	−0.874334	−0.437167	+	0.899380i	$0.644018\pi$
$32$	−3.52633e83	−1.02683
$33$	−3.33587e84	−1.76070
$34$	5.25729e84	0.529276
$35$	9.00962e85	1.81522
$36$	−3.55814e86	−1.50119
$37$	1.66082e87	1.53154	0.765769	−	0.643116i	$-0.222359\pi$
$37$	1.66082e87	1.53154	0.765769	+	0.643116i	$0.222359\pi$
$38$	−8.31017e86	−0.174430
$39$	−3.60263e88	−1.78869
$40$	−8.35181e88	−1.01731
$41$	−6.46319e88	−0.199960	−0.0999800	−	0.994989i	$-0.531878\pi$
$41$	−6.46319e88	−0.199960	−0.0999800	+	0.994989i	$0.531878\pi$
$42$	1.58885e90	1.29047
$43$	−4.34991e90	−0.957152	−0.478576	−	0.878046i	$-0.658847\pi$
$43$	−4.34991e90	−0.957152	−0.478576	+	0.878046i	$0.658847\pi$
$44$	1.26693e91	0.778266
$45$	−1.32104e92	−2.33142
$46$	1.00566e91	0.0524072
$47$	5.49999e92	0.868822	0.434411	−	0.900715i	$-0.356957\pi$
$47$	5.49999e92	0.868822	0.434411	+	0.900715i	$0.356957\pi$
$48$	1.20115e93	0.589807
$49$	8.65856e93	1.35383
$50$	−3.82994e93	−0.195145
$51$	−1.10102e95	−1.86918
$52$	1.36824e95	0.790636
$53$	1.23885e95	0.248718	0.124359	−	0.992237i	$-0.460313\pi$
$53$	1.23885e95	0.248718	0.124359	+	0.992237i	$0.460313\pi$
$54$	−1.14739e96	−0.816312
$55$	4.70373e96	1.20869
$56$	−1.39550e97	−1.31915
$57$	1.74038e97	0.616014
$58$	−4.57442e97	−0.616712
$59$	−1.99367e97	−0.104080	−0.0520399	−	0.998645i	$-0.516572\pi$
$59$	−1.99367e97	−0.104080	−0.0520399	+	0.998645i	$0.516572\pi$
$60$	7.56327e98	1.55351
$61$	3.74129e98	0.307055	0.153527	−	0.988144i	$-0.450937\pi$
$61$	3.74129e98	0.307055	0.153527	+	0.988144i	$0.450937\pi$
$62$	1.28192e99	0.426699
$63$	−2.20732e100	−3.02318
$64$	2.78061e99	0.158910
$65$	5.07988e100	1.22790
$66$	8.29504e100	0.859271
$67$	−1.75123e101	−0.787393	−0.393697	−	0.919240i	$-0.628804\pi$
$67$	−1.75123e101	−0.787393	−0.393697	+	0.919240i	$0.628804\pi$
$68$	4.18157e101	0.826218
$69$	−2.10613e101	−0.185081
$70$	−2.24035e102	−0.885880
$71$	1.21022e102	0.217784	0.108892	−	0.994054i	$-0.465270\pi$
$71$	1.21022e102	0.217784	0.108892	+	0.994054i	$0.465270\pi$
$72$	2.04616e103	1.69428
$73$	−5.69248e102	−0.219221	−0.109611	−	0.993975i	$-0.534960\pi$
$73$	−5.69248e102	−0.219221	−0.109611	+	0.993975i	$0.534960\pi$
$74$	−4.12984e103	−0.747433
$75$	8.02098e103	0.689172
$76$	−6.60979e103	−0.272291
$77$	7.85947e104	1.56732
$78$	8.95838e104	0.872929
$79$	2.83877e105	1.36404	0.682020	−	0.731333i	$-0.261102\pi$
$79$	2.83877e105	1.36404	0.682020	+	0.731333i	$0.261102\pi$
$80$	−1.69368e105	−0.404891
$81$	7.60490e105	0.912379
$82$	1.60715e105	0.0975860
$83$	1.17958e106	0.365506	0.182753	−	0.983159i	$-0.441499\pi$
$83$	1.17958e106	0.365506	0.182753	+	0.983159i	$0.441499\pi$
$84$	1.26375e107	2.01446
$85$	1.55250e107	1.28316
$86$	1.08166e107	0.467117
$87$	9.58012e107	2.17797
$88$	−7.28563e107	−0.878373
$89$	−2.11765e108	−1.36367	−0.681835	−	0.731506i	$-0.738818\pi$
$89$	−2.11765e108	−1.36367	−0.681835	+	0.731506i	$0.738818\pi$
$90$	3.28491e108	1.13780
$91$	8.48797e108	1.59223
$92$	7.99887e107	0.0818096
$93$	−2.68470e109	−1.50693
$94$	−1.36764e109	−0.424009
$95$	−2.45402e109	−0.422881
$96$	−1.83640e110	−1.76976
$97$	3.20630e110	1.73850	0.869248	−	0.494377i	$-0.164604\pi$
$97$	3.20630e110	1.73850	0.869248	+	0.494377i	$0.164604\pi$
$98$	−2.15305e110	−0.660705
$99$	−1.15239e111	−2.01302
$100$	−3.04628e110	−0.304628
$101$	−2.11956e111	−1.22014	−0.610069	−	0.792349i	$-0.708858\pi$
$101$	−2.11956e111	−1.22014	−0.610069	+	0.792349i	$0.708858\pi$
$102$	2.73783e111	0.912214
$103$	1.15725e111	0.224368	0.112184	−	0.993687i	$-0.464215\pi$
$103$	1.15725e111	0.224368	0.112184	+	0.993687i	$0.464215\pi$
$104$	−7.86825e111	−0.892334
$105$	4.69193e112	3.12856
$106$	−3.08054e111	−0.121381
$107$	3.23538e111	0.0757051	0.0378526	−	0.999283i	$-0.487948\pi$
$107$	3.23538e111	0.0757051	0.0378526	+	0.999283i	$0.487948\pi$
$108$	−9.12615e112	−1.27429
$109$	1.99140e113	1.66720	0.833602	−	0.552366i	$-0.186275\pi$
$109$	1.99140e113	1.66720	0.833602	+	0.552366i	$0.186275\pi$
$110$	−1.16964e113	−0.589872
$111$	8.64904e113	2.63963
$112$	−2.82997e113	−0.525028
$113$	−4.38464e113	−0.496684	−0.248342	−	0.968672i	$-0.579886\pi$
$113$	−4.38464e113	−0.496684	−0.248342	+	0.968672i	$0.579886\pi$
$114$	−4.32767e113	−0.300632
$115$	2.96975e113	0.127054
$116$	−3.63842e114	−0.962708
$117$	−1.24455e115	−2.04501
$118$	4.95750e113	0.0507939
$119$	2.59406e115	1.66389
$120$	−4.34936e115	−1.75334
$121$	1.71491e114	0.0436168
$122$	−9.30317e114	−0.149851
$123$	−3.36583e115	−0.344634
$124$	1.01962e116	0.666093
$125$	1.69746e116	0.710056
$126$	5.48876e116	1.47540
$127$	6.78130e115	0.117546	0.0587728	−	0.998271i	$-0.481281\pi$
$127$	6.78130e115	0.117546	0.0587728	+	0.998271i	$0.481281\pi$
$128$	8.46344e116	0.949278
$129$	−2.26530e117	−1.64967
$130$	−1.26317e117	−0.599248
$131$	3.51066e117	1.08851	0.544254	−	0.838921i	$-0.316813\pi$
$131$	3.51066e117	1.08851	0.544254	+	0.838921i	$0.316813\pi$
$132$	6.59775e117	1.34135
$133$	−4.10043e117	−0.548356
$134$	4.35464e117	0.384270
$135$	−3.38828e118	−1.97904
$136$	−2.40467e118	−0.932493
$137$	−4.65642e118	−1.20243	−0.601216	−	0.799087i	$-0.705317\pi$
$137$	−4.65642e118	−1.20243	−0.601216	+	0.799087i	$0.705317\pi$
$138$	5.23716e117	0.0903247
$139$	1.15010e119	1.32867	0.664333	−	0.747437i	$-0.268716\pi$
$139$	1.15010e119	1.32867	0.664333	+	0.747437i	$0.268716\pi$
$140$	−1.78194e119	−1.38289
$141$	2.86422e119	1.49743
$142$	−3.00936e118	−0.106285
$143$	4.43139e119	1.06020
$144$	4.14945e119	0.674329
$145$	−1.35084e120	−1.49513
$146$	1.41550e119	0.106986
$147$	4.50910e120	2.33334
$148$	−3.28481e120	−1.16677
$149$	3.86935e120	0.945802	0.472901	−	0.881116i	$-0.343207\pi$
$149$	3.86935e120	0.945802	0.472901	+	0.881116i	$0.343207\pi$
$150$	−1.99451e120	−0.336335
$151$	−5.43708e120	−0.634081	−0.317041	−	0.948412i	$-0.602689\pi$
$151$	−5.43708e120	−0.634081	−0.317041	+	0.948412i	$0.602689\pi$
$152$	3.80105e120	0.307315
$153$	−3.80355e121	−2.13705
$154$	−1.95435e121	−0.764896
$155$	3.78555e121	1.03448
$156$	7.12536e121	1.36267
$157$	−1.42313e122	−1.90904	−0.954520	−	0.298148i	$-0.903631\pi$
$157$	−1.42313e122	−1.90904	−0.954520	+	0.298148i	$0.903631\pi$
$158$	−7.05895e121	−0.665690
$159$	6.45152e121	0.428669
$160$	2.58941e122	1.21490
$161$	4.96215e121	0.164753
$162$	−1.89105e122	−0.445266
$163$	7.01885e122	1.17450	0.587251	−	0.809405i	$-0.300210\pi$
$163$	7.01885e122	1.17450	0.587251	+	0.809405i	$0.300210\pi$
$164$	1.27830e122	0.152335
$165$	2.44956e123	2.08319
$166$	−2.93317e122	−0.178377
$167$	−2.13839e123	−0.931801	−0.465900	−	0.884837i	$-0.654269\pi$
$167$	−2.13839e123	−0.931801	−0.465900	+	0.884837i	$0.654269\pi$
$168$	−7.26734e123	−2.27358
$169$	3.42389e122	0.0770563
$170$	−3.86047e123	−0.626217
$171$	6.01225e123	0.704292
$172$	8.60334e123	0.729186
$173$	2.90506e123	0.178483	0.0892414	−	0.996010i	$-0.471556\pi$
$173$	2.90506e123	0.178483	0.0892414	+	0.996010i	$0.471556\pi$
$174$	−2.38221e124	−1.06291
$175$	−1.88978e124	−0.613479
$176$	−1.47747e124	−0.349595
$177$	−1.03824e124	−0.179383
$178$	5.26580e124	0.665509
$179$	4.52905e123	0.0419434	0.0209717	−	0.999780i	$-0.493324\pi$
$179$	4.52905e123	0.0419434	0.0209717	+	0.999780i	$0.493324\pi$
$180$	2.61277e125	1.77614
$181$	2.27550e125	1.13741	0.568703	−	0.822543i	$-0.307445\pi$
$181$	2.27550e125	1.13741	0.568703	+	0.822543i	$0.307445\pi$
$182$	−2.11063e125	−0.777054
$183$	1.94835e125	0.529213
$184$	−4.59986e124	−0.0923326
$185$	−1.21956e126	−1.81205
$186$	6.67583e125	0.735422
$187$	1.35431e126	1.10792
$188$	−1.08780e126	−0.661893
$189$	−5.66147e126	−2.56625
$190$	6.10222e125	0.206378
$191$	4.04208e126	1.02153	0.510767	−	0.859719i	$-0.329361\pi$
$191$	4.04208e126	1.02153	0.510767	+	0.859719i	$0.329361\pi$
$192$	1.44805e126	0.273884
$193$	−9.46896e126	−1.34237	−0.671184	−	0.741291i	$-0.734214\pi$
$193$	−9.46896e126	−1.34237	−0.671184	+	0.741291i	$0.734214\pi$
$194$	−7.97286e126	−0.848434
$195$	2.64544e127	2.11630
$196$	−1.71251e127	−1.03138
$197$	2.96196e127	1.34494	0.672471	−	0.740124i	$-0.265233\pi$
$197$	2.96196e127	1.34494	0.672471	+	0.740124i	$0.265233\pi$
$198$	2.86557e127	0.982409
$199$	1.59566e127	0.413613	0.206807	−	0.978382i	$-0.433693\pi$
$199$	1.59566e127	0.413613	0.206807	+	0.978382i	$0.433693\pi$
$200$	1.75180e127	0.343812
$201$	−9.11985e127	−1.35708
$202$	5.27053e127	0.595461
$203$	−2.25712e128	−1.93876
$204$	2.17763e128	1.42400
$205$	4.74597e127	0.236584
$206$	−2.87764e127	−0.109498
$207$	−7.27575e127	−0.211604
$208$	−1.59562e128	−0.355152
$209$	−2.14075e128	−0.365129
$210$	−1.16670e129	−1.52683
$211$	1.29421e128	0.130116	0.0650579	−	0.997881i	$-0.479277\pi$
$211$	1.29421e128	0.130116	0.0650579	+	0.997881i	$0.479277\pi$
$212$	−2.45022e128	−0.189480
$213$	6.30246e128	0.375355
$214$	−8.04515e127	−0.0369462
$215$	3.19417e129	1.13246
$216$	5.24811e129	1.43820
$217$	6.32528e129	1.34142
$218$	−4.95186e129	−0.813642
$219$	−2.96447e129	−0.377831
$220$	−9.30314e129	−0.920812
$221$	1.46261e130	1.12553
$222$	−2.15069e130	−1.28821
$223$	−3.22869e130	−1.50698	−0.753488	−	0.657462i	$-0.771630\pi$
$223$	−3.22869e130	−1.50698	−0.753488	+	0.657462i	$0.771630\pi$
$224$	4.32664e130	1.57538
$225$	2.77089e130	0.787933
$226$	1.09029e130	0.242395
$227$	−9.71528e130	−1.69052	−0.845260	−	0.534356i	$-0.820554\pi$
$227$	−9.71528e130	−1.69052	−0.845260	+	0.534356i	$0.820554\pi$
$228$	−3.44217e130	−0.469297
$229$	−1.85695e131	−1.98578	−0.992892	−	0.119021i	$-0.962025\pi$
$229$	−1.85695e131	−1.98578	−0.992892	+	0.119021i	$0.962025\pi$
$230$	−7.38464e129	−0.0620061
$231$	4.09296e131	2.70130
$232$	2.09232e131	1.08654
$233$	−2.70704e131	−1.10724	−0.553619	−	0.832770i	$-0.686754\pi$
$233$	−2.70704e131	−1.10724	−0.553619	+	0.832770i	$0.686754\pi$
$234$	3.09472e131	0.998024
$235$	−4.03868e131	−1.02795
$236$	3.94312e130	0.0792910
$237$	1.47834e132	2.35094
$238$	−6.45045e131	−0.812024
$239$	−7.63621e131	−0.761719	−0.380859	−	0.924633i	$-0.624372\pi$
$239$	−7.63621e131	−0.761719	−0.380859	+	0.924633i	$0.624372\pi$
$240$	−8.82017e131	−0.697835
$241$	1.87779e132	1.17951	0.589754	−	0.807583i	$-0.299225\pi$
$241$	1.87779e132	1.17951	0.589754	+	0.807583i	$0.299225\pi$
$242$	−4.26434e130	−0.0212862
$243$	−2.52302e131	−0.100178
$244$	−7.39960e131	−0.233923
$245$	−6.35805e132	−1.60179
$246$	8.36953e131	0.168191
$247$	−2.31194e132	−0.370933
$248$	−5.86346e132	−0.751771
$249$	6.14289e132	0.629954
$250$	−4.22093e132	−0.346527
$251$	−4.93887e132	−0.324890	−0.162445	−	0.986718i	$-0.551938\pi$
$251$	−4.93887e132	−0.324890	−0.162445	+	0.986718i	$0.551938\pi$
$252$	4.36568e133	2.30315
$253$	2.59063e132	0.109703
$254$	−1.68625e132	−0.0573655
$255$	8.08491e133	2.21154
$256$	−2.82642e133	−0.622184
$257$	−6.98797e133	−1.23897	−0.619487	−	0.785007i	$-0.712659\pi$
$257$	−6.98797e133	−1.23897	−0.619487	+	0.785007i	$0.712659\pi$
$258$	5.63293e133	0.805083
$259$	−2.03775e134	−2.34971
$260$	−1.00471e134	−0.935448
$261$	3.30950e134	2.49009
$262$	−8.72967e133	−0.531222
$263$	2.55380e134	1.25789	0.628945	−	0.777450i	$-0.283487\pi$
$263$	2.55380e134	1.25789	0.628945	+	0.777450i	$0.283487\pi$
$264$	−3.79413e134	−1.51389
$265$	−9.09695e133	−0.294273
$266$	1.01962e134	0.267613
$267$	−1.10281e135	−2.35031
$268$	3.46362e134	0.599859
$269$	4.83490e134	0.680982	0.340491	−	0.940248i	$-0.389407\pi$
$269$	4.83490e134	0.680982	0.340491	+	0.940248i	$0.389407\pi$
$270$	8.42536e134	0.965827
$271$	−1.21738e135	−1.13666	−0.568329	−	0.822802i	$-0.692410\pi$
$271$	−1.21738e135	−1.13666	−0.568329	+	0.822802i	$0.692410\pi$
$272$	−4.87648e134	−0.371135
$273$	4.42027e135	2.74424
$274$	1.15787e135	0.586820
$275$	−9.86614e134	−0.408491
$276$	4.16556e134	0.141000
$277$	5.52172e134	0.152914	0.0764569	−	0.997073i	$-0.475639\pi$
$277$	5.52172e134	0.152914	0.0764569	+	0.997073i	$0.475639\pi$
$278$	−2.85987e135	−0.648426
$279$	−9.27444e135	−1.72288
$280$	1.02473e136	1.56077
$281$	−1.47957e135	−0.184900	−0.0924498	−	0.995717i	$-0.529470\pi$
$281$	−1.47957e135	−0.184900	−0.0924498	+	0.995717i	$0.529470\pi$
$282$	−7.12223e135	−0.730786
$283$	5.75120e135	0.484854	0.242427	−	0.970170i	$-0.422057\pi$
$283$	5.75120e135	0.484854	0.242427	+	0.970170i	$0.422057\pi$
$284$	−2.39360e135	−0.165914
$285$	−1.27798e136	−0.728842
$286$	−1.10192e136	−0.517409
$287$	7.93004e135	0.306782
$288$	−6.34394e136	−2.02337
$289$	6.69562e135	0.176182
$290$	3.35903e136	0.729667
$291$	1.66974e137	2.99632
$292$	1.12587e136	0.167009
$293$	4.43220e136	0.543834	0.271917	−	0.962321i	$-0.412342\pi$
$293$	4.43220e136	0.543834	0.271917	+	0.962321i	$0.412342\pi$
$294$	−1.12124e137	−1.13873
$295$	1.46397e136	0.123143
$296$	1.88897e137	1.31685
$297$	−2.95573e137	−1.70876
$298$	−9.62161e136	−0.461578
$299$	2.79780e136	0.111446
$300$	−1.58641e137	−0.525031
$301$	5.33714e137	1.46848
$302$	1.35199e137	0.309449
$303$	−1.10380e138	−2.10292
$304$	7.70823e136	0.122312
$305$	−2.74726e137	−0.363294
$306$	9.45797e137	1.04294
$307$	−1.64265e137	−0.151135	−0.0755676	−	0.997141i	$-0.524077\pi$
$307$	−1.64265e137	−0.151135	−0.0755676	+	0.997141i	$0.524077\pi$
$308$	−1.55446e138	−1.19403
$309$	6.02659e137	0.386702
$310$	−9.41323e137	−0.504853
$311$	2.07244e138	0.929565	0.464782	−	0.885425i	$-0.346133\pi$
$311$	2.07244e138	0.929565	0.464782	+	0.885425i	$0.346133\pi$
$312$	−4.09753e138	−1.53795
$313$	3.70511e138	1.16437	0.582184	−	0.813057i	$-0.302198\pi$
$313$	3.70511e138	1.16437	0.582184	+	0.813057i	$0.302198\pi$
$314$	3.53879e138	0.931665
$315$	1.62085e139	3.57690
$316$	−5.61459e138	−1.03917
$317$	−5.51343e138	−0.856314	−0.428157	−	0.903704i	$-0.640837\pi$
$317$	−5.51343e138	−0.856314	−0.428157	+	0.903704i	$0.640837\pi$
$318$	−1.60425e138	−0.209202
$319$	−1.17839e139	−1.29095
$320$	−2.04182e138	−0.188016
$321$	1.68488e138	0.130479
$322$	−1.23390e138	−0.0804042
$323$	−7.06566e138	−0.387626
$324$	−1.50411e139	−0.695076
$325$	−1.06551e139	−0.414984
$326$	−1.74532e139	−0.573190
$327$	1.03706e140	2.87345
$328$	−7.35106e138	−0.171930
$329$	−6.74823e139	−1.33296
$330$	−6.09111e139	−1.01665
$331$	−3.26214e139	−0.460309	−0.230154	−	0.973154i	$-0.573923\pi$
$331$	−3.26214e139	−0.460309	−0.230154	+	0.973154i	$0.573923\pi$
$332$	−2.33300e139	−0.278453
$333$	2.98786e140	3.01790
$334$	5.31737e139	0.454745
$335$	1.28594e140	0.931611
$336$	−1.47376e140	−0.904893
$337$	1.03080e140	0.536677	0.268339	−	0.963325i	$-0.413525\pi$
$337$	1.03080e140	0.536677	0.268339	+	0.963325i	$0.413525\pi$
$338$	−8.51392e138	−0.0376056
$339$	−2.28338e140	−0.856042
$340$	−3.07056e140	−0.977547
$341$	3.30229e140	0.893198
$342$	−1.49502e140	−0.343714
$343$	−2.77652e140	−0.542847
$344$	−4.94747e140	−0.822980
$345$	1.54655e140	0.218980
$346$	−7.22378e139	−0.0871046
$347$	1.57845e141	1.62161	0.810803	−	0.585320i	$-0.199031\pi$
$347$	1.57845e141	1.62161	0.810803	+	0.585320i	$0.199031\pi$
$348$	−1.89478e141	−1.65924
$349$	9.28513e140	0.693389	0.346694	−	0.937978i	$-0.387304\pi$
$349$	9.28513e140	0.693389	0.346694	+	0.937978i	$0.387304\pi$
$350$	4.69917e140	0.299395
$351$	−3.19210e141	−1.73593
$352$	2.25885e141	1.04899
$353$	−1.77465e141	−0.704070	−0.352035	−	0.935987i	$-0.614510\pi$
$353$	−1.77465e141	−0.704070	−0.352035	+	0.935987i	$0.614510\pi$
$354$	2.58171e140	0.0875440
$355$	−8.88676e140	−0.257673
$356$	4.18834e141	1.03888
$357$	1.35091e142	2.86774
$358$	−1.12620e140	−0.0204696
$359$	8.61759e141	1.34166	0.670832	−	0.741609i	$-0.265937\pi$
$359$	8.61759e141	1.34166	0.670832	+	0.741609i	$0.265937\pi$
$360$	−1.50251e142	−2.00460
$361$	−7.62592e141	−0.872253
$362$	−5.65830e141	−0.555086
$363$	8.93072e140	0.0751742
$364$	−1.67877e142	−1.21301
$365$	4.18004e141	0.259374
$366$	−4.84479e141	−0.258271
$367$	−4.64736e141	−0.212931	−0.106466	−	0.994316i	$-0.533953\pi$
$367$	−4.64736e141	−0.212931	−0.106466	+	0.994316i	$0.533953\pi$
$368$	−9.32815e140	−0.0367487
$369$	−1.16274e142	−0.394022
$370$	3.03257e142	0.884332
$371$	−1.52001e142	−0.381587
$372$	5.30986e142	1.14802
$373$	−3.30742e142	−0.616096	−0.308048	−	0.951371i	$-0.599676\pi$
$373$	−3.30742e142	−0.616096	−0.308048	+	0.951371i	$0.599676\pi$
$374$	−3.36765e142	−0.540695
$375$	8.83981e142	1.22379
$376$	6.25553e142	0.747032
$377$	−1.27263e143	−1.31146
$378$	1.40779e143	1.25240
$379$	−8.09420e142	−0.621867	−0.310934	−	0.950432i	$-0.600642\pi$
$379$	−8.09420e142	−0.621867	−0.310934	+	0.950432i	$0.600642\pi$
$380$	4.85362e142	0.322163
$381$	3.53148e142	0.202591
$382$	−1.00511e143	−0.498537
$383$	1.64326e143	0.704977	0.352488	−	0.935816i	$-0.385336\pi$
$383$	1.64326e143	0.704977	0.352488	+	0.935816i	$0.385336\pi$
$384$	4.40749e143	1.63609
$385$	−5.77127e143	−1.85439
$386$	2.35457e143	0.655113
$387$	−7.82558e143	−1.88607
$388$	−6.34149e143	−1.32444
$389$	2.86845e143	0.519331	0.259666	−	0.965699i	$-0.416388\pi$
$389$	2.86845e143	0.519331	0.259666	+	0.965699i	$0.416388\pi$
$390$	−6.57821e143	−1.03281
$391$	8.55055e142	0.116462
$392$	9.84800e143	1.16405
$393$	1.82824e144	1.87606
$394$	−7.36526e143	−0.656369
$395$	−2.08453e144	−1.61388
$396$	2.27923e144	1.53357
$397$	2.42321e143	0.141748	0.0708742	−	0.997485i	$-0.477421\pi$
$397$	2.42321e143	0.141748	0.0708742	+	0.997485i	$0.477421\pi$
$398$	−3.96780e143	−0.201855
$399$	−2.13537e144	−0.945100
$400$	3.55252e143	0.136838
$401$	2.44524e144	0.819992	0.409996	−	0.912087i	$-0.365530\pi$
$401$	2.44524e144	0.819992	0.409996	+	0.912087i	$0.365530\pi$
$402$	2.26776e144	0.662295
$403$	3.56637e144	0.907395
$404$	4.19210e144	0.929535
$405$	−5.58434e144	−1.07949
$406$	5.61260e144	0.946170
$407$	−1.06387e145	−1.56458
$408$	−1.25227e145	−1.60717
$409$	8.06817e144	0.903922	0.451961	−	0.892038i	$-0.350725\pi$
$409$	8.06817e144	0.903922	0.451961	+	0.892038i	$0.350725\pi$
$410$	−1.18014e144	−0.115460
$411$	−2.42492e145	−2.07241
$412$	−2.28883e144	−0.170930
$413$	2.44614e144	0.159681
$414$	1.80920e144	0.103269
$415$	−8.66176e144	−0.432451
$416$	2.43948e145	1.06566
$417$	5.98938e145	2.28998
$418$	5.32322e144	0.178193
$419$	3.91013e145	1.14634	0.573169	−	0.819437i	$-0.305714\pi$
$419$	3.91013e145	1.14634	0.573169	+	0.819437i	$0.305714\pi$
$420$	−9.27979e145	−2.38343
$421$	−3.08094e145	−0.693470	−0.346735	−	0.937963i	$-0.612710\pi$
$421$	−3.08094e145	−0.693470	−0.346735	+	0.937963i	$0.612710\pi$
$422$	−3.21822e144	−0.0635001
$423$	9.89460e145	1.71202
$424$	1.40903e145	0.213853
$425$	−3.25638e145	−0.433660
$426$	−1.56718e145	−0.183184
$427$	−4.59039e145	−0.471089
$428$	−6.39899e144	−0.0576743
$429$	2.30773e146	1.82728
$430$	−7.94269e145	−0.552673
$431$	−2.79617e146	−1.71031	−0.855155	−	0.518372i	$-0.826538\pi$
$431$	−2.79617e146	−1.71031	−0.855155	+	0.518372i	$0.826538\pi$
$432$	1.06428e146	0.572409
$433$	3.39017e146	1.60377	0.801886	−	0.597477i	$-0.203830\pi$
$433$	3.39017e146	1.60377	0.801886	+	0.597477i	$0.203830\pi$
$434$	−1.57286e146	−0.654650
$435$	−7.03476e146	−2.57689
$436$	−3.93864e146	−1.27012
$437$	−1.35158e145	−0.0383815
$438$	7.37150e145	0.184392
$439$	3.80767e146	0.839226	0.419613	−	0.907703i	$-0.362166\pi$
$439$	3.80767e146	0.839226	0.419613	+	0.907703i	$0.362166\pi$
$440$	5.34990e146	1.03925
$441$	1.55769e147	2.66772
$442$	−3.63695e146	−0.549289
$443$	−8.44374e146	−1.12494	−0.562469	−	0.826819i	$-0.690148\pi$
$443$	−8.44374e146	−1.12494	−0.562469	+	0.826819i	$0.690148\pi$
$444$	−1.71063e147	−2.01094
$445$	1.55501e147	1.61344
$446$	8.02852e146	0.735446
$447$	2.01504e147	1.63010
$448$	−3.41168e146	−0.243803
$449$	−1.60638e147	−1.01432	−0.507162	−	0.861851i	$-0.669305\pi$
$449$	−1.60638e147	−1.01432	−0.507162	+	0.861851i	$0.669305\pi$
$450$	−6.89015e146	−0.384533
$451$	4.14011e146	0.204274
$452$	8.67202e146	0.378388
$453$	−2.83146e147	−1.09285
$454$	2.41582e147	0.825020
$455$	−6.23278e147	−1.88386
$456$	1.97946e147	0.529662
$457$	−9.87858e146	−0.234070	−0.117035	−	0.993128i	$-0.537339\pi$
$457$	−9.87858e146	−0.234070	−0.117035	+	0.993128i	$0.537339\pi$
$458$	4.61754e147	0.969118
$459$	−9.75558e147	−1.81405
$460$	−5.87363e146	−0.0967937
$461$	1.15263e148	1.68379	0.841897	−	0.539638i	$-0.181439\pi$
$461$	1.15263e148	1.68379	0.841897	+	0.539638i	$0.181439\pi$
$462$	−1.01776e148	−1.31831
$463$	−1.20613e148	−1.38563	−0.692816	−	0.721114i	$-0.743630\pi$
$463$	−1.20613e148	−1.38563	−0.692816	+	0.721114i	$0.743630\pi$
$464$	4.24307e147	0.432447
$465$	1.97140e148	1.78293
$466$	6.73138e147	0.540363
$467$	1.39556e147	0.0994629	0.0497315	−	0.998763i	$-0.484163\pi$
$467$	1.39556e147	0.0994629	0.0497315	+	0.998763i	$0.484163\pi$
$468$	2.46149e148	1.55795
$469$	2.14868e148	1.20803
$470$	1.00427e148	0.501670
$471$	−7.41123e148	−3.29026
$472$	−2.26755e147	−0.0894901
$473$	2.78641e148	0.977803
$474$	−3.67608e148	−1.14733
$475$	5.14735e147	0.142918
$476$	−5.13059e148	−1.26760
$477$	2.22871e148	0.490099
$478$	1.89884e148	0.371740
$479$	1.60728e148	0.280202	0.140101	−	0.990137i	$-0.455257\pi$
$479$	1.60728e148	0.280202	0.140101	+	0.990137i	$0.455257\pi$
$480$	1.34848e149	2.09390
$481$	−1.14894e149	−1.58945
$482$	−4.66935e148	−0.575633
$483$	2.58413e148	0.283955
$484$	−3.39179e147	−0.0332285
$485$	−2.35441e149	−2.05692
$486$	6.27379e147	0.0488897
$487$	−1.63488e149	−1.13666	−0.568328	−	0.822802i	$-0.692410\pi$
$487$	−1.63488e149	−1.13666	−0.568328	+	0.822802i	$0.692410\pi$
$488$	4.25524e148	0.264012
$489$	3.65519e149	2.02427
$490$	1.58100e149	0.781719
$491$	2.52836e149	1.11639	0.558195	−	0.829710i	$-0.311494\pi$
$491$	2.52836e149	1.11639	0.558195	+	0.829710i	$0.311494\pi$
$492$	6.65700e148	0.262552
$493$	−3.88936e149	−1.37049
$494$	5.74891e148	0.181025
$495$	8.46212e149	2.38172
$496$	−1.18906e149	−0.299207
$497$	−1.48489e149	−0.334129
$498$	−1.52750e149	−0.307435
$499$	−3.72000e149	−0.669827	−0.334914	−	0.942249i	$-0.608707\pi$
$499$	−3.72000e149	−0.669827	−0.334914	+	0.942249i	$0.608707\pi$
$500$	−3.35726e149	−0.540941
$501$	−1.11361e150	−1.60597
$502$	1.22811e149	0.158555
$503$	1.27407e150	1.47289	0.736443	−	0.676499i	$-0.236504\pi$
$503$	1.27407e150	1.47289	0.736443	+	0.676499i	$0.236504\pi$
$504$	−2.51054e150	−2.59940
$505$	1.55641e150	1.44362
$506$	−6.44192e148	−0.0535380
$507$	1.78306e149	0.132808
$508$	−1.34122e149	−0.0895496
$509$	1.08392e150	0.648875	0.324437	−	0.945907i	$-0.394825\pi$
$509$	1.08392e150	0.648875	0.324437	+	0.945907i	$0.394825\pi$
$510$	−2.01041e150	−1.07929
$511$	6.98442e149	0.336334
$512$	−1.49441e150	−0.645635
$513$	1.54206e150	0.597843
$514$	1.73764e150	0.604654
$515$	−8.49777e149	−0.265463
$516$	4.48035e150	1.25676
$517$	−3.52311e150	−0.887567
$518$	5.06712e150	1.14673
$519$	1.51286e150	0.307618
$520$	5.77771e150	1.05577
$521$	−4.49652e150	−0.738555	−0.369277	−	0.929319i	$-0.620395\pi$
$521$	−4.49652e150	−0.738555	−0.369277	+	0.929319i	$0.620395\pi$
$522$	−8.22947e150	−1.21523
$523$	1.01820e151	1.35204	0.676022	−	0.736881i	$-0.263702\pi$
$523$	1.01820e151	1.35204	0.676022	+	0.736881i	$0.263702\pi$
$524$	−6.94345e150	−0.829256
$525$	−9.84138e150	−1.05734
$526$	−6.35032e150	−0.613885
$527$	1.08994e151	0.948232
$528$	−7.69420e150	−0.602533
$529$	−1.40201e151	−0.988468
$530$	2.26207e150	0.143613
$531$	−3.58666e150	−0.205090
$532$	8.10991e150	0.417754
$533$	4.47118e150	0.207521
$534$	2.74226e151	1.14701
$535$	−2.37576e150	−0.0895711
$536$	−1.99180e151	−0.677018
$537$	2.35859e150	0.0722901
$538$	−1.20226e151	−0.332338
$539$	−5.54638e151	−1.38304
$540$	6.70140e151	1.50769
$541$	−9.67288e150	−0.196385	−0.0981924	−	0.995167i	$-0.531306\pi$
$541$	−9.67288e150	−0.196385	−0.0981924	+	0.995167i	$0.531306\pi$
$542$	3.02716e151	0.554721
$543$	1.18501e152	1.96034
$544$	7.45547e151	1.11362
$545$	−1.46230e152	−1.97257
$546$	−1.09915e152	−1.33926
$547$	5.62662e151	0.619372	0.309686	−	0.950839i	$-0.399776\pi$
$547$	5.62662e151	0.619372	0.309686	+	0.950839i	$0.399776\pi$
$548$	9.20956e151	0.916047
$549$	6.73066e151	0.605052
$550$	2.45334e151	0.199355
$551$	6.14790e151	0.451662
$552$	−2.39546e151	−0.159137
$553$	−3.48305e152	−2.09274
$554$	−1.37304e151	−0.0746262
$555$	−6.35106e152	−3.12310
$556$	−2.27470e152	−1.01222
$557$	1.52407e152	0.613822	0.306911	−	0.951738i	$-0.400705\pi$
$557$	1.52407e152	0.613822	0.306911	+	0.951738i	$0.400705\pi$
$558$	2.30620e152	0.840812
$559$	3.00923e152	0.993345
$560$	2.07807e152	0.621191
$561$	7.05280e152	1.90951
$562$	3.67914e151	0.0902362
$563$	2.64266e152	0.587254	0.293627	−	0.955920i	$-0.405138\pi$
$563$	2.64266e152	0.587254	0.293627	+	0.955920i	$0.405138\pi$
$564$	−5.66491e152	−1.14078
$565$	3.21967e152	0.587655
$566$	−1.43010e152	−0.236622
$567$	−9.33087e152	−1.39979
$568$	1.37647e152	0.187256
$569$	7.97260e152	0.983715	0.491858	−	0.870676i	$-0.336318\pi$
$569$	7.97260e152	0.983715	0.491858	+	0.870676i	$0.336318\pi$
$570$	3.17785e152	0.355695
$571$	−5.00611e152	−0.508389	−0.254194	−	0.967153i	$-0.581810\pi$
$571$	−5.00611e152	−0.508389	−0.254194	+	0.967153i	$0.581810\pi$
$572$	−8.76449e152	−0.807694
$573$	2.10499e153	1.76063
$574$	−1.97190e152	−0.149718
$575$	−6.22909e151	−0.0429397
$576$	5.00238e152	0.313133
$577$	−5.53466e152	−0.314654	−0.157327	−	0.987547i	$-0.550288\pi$
$577$	−5.53466e152	−0.314654	−0.157327	+	0.987547i	$0.550288\pi$
$578$	−1.66495e152	−0.0859816
$579$	−4.93113e153	−2.31359
$580$	2.67172e153	1.13904
$581$	−1.44729e153	−0.560765
$582$	−4.15201e153	−1.46229
$583$	−7.93564e152	−0.254084
$584$	−6.47447e152	−0.188491
$585$	9.13881e153	2.41958
$586$	−1.10212e153	−0.265406
$587$	4.76664e153	1.04423	0.522117	−	0.852874i	$-0.325142\pi$
$587$	4.76664e153	1.04423	0.522117	+	0.852874i	$0.325142\pi$
$588$	−8.91819e153	−1.77761
$589$	−1.72287e153	−0.312502
$590$	−3.64033e152	−0.0600972
$591$	1.54249e154	2.31803
$592$	3.83069e153	0.524110
$593$	9.25931e152	0.115357	0.0576784	−	0.998335i	$-0.481630\pi$
$593$	9.25931e152	0.115357	0.0576784	+	0.998335i	$0.481630\pi$
$594$	7.34979e153	0.833925
$595$	−1.90484e154	−1.96864
$596$	−7.65288e153	−0.720539
$597$	8.30969e153	0.712869
$598$	−6.95707e152	−0.0543889
$599$	1.28488e154	0.915532	0.457766	−	0.889073i	$-0.348650\pi$
$599$	1.28488e154	0.915532	0.457766	+	0.889073i	$0.348650\pi$
$600$	9.12284e153	0.592565
$601$	−2.63091e153	−0.155802	−0.0779009	−	0.996961i	$-0.524822\pi$
$601$	−2.63091e153	−0.155802	−0.0779009	+	0.996961i	$0.524822\pi$
$602$	−1.32714e154	−0.716659
$603$	−3.15050e154	−1.55156
$604$	1.07536e154	0.483061
$605$	−1.25927e153	−0.0516056
$606$	2.74473e154	1.02629
$607$	9.98361e153	0.340655	0.170328	−	0.985387i	$-0.445517\pi$
$607$	9.98361e153	0.340655	0.170328	+	0.985387i	$0.445517\pi$
$608$	−1.17848e154	−0.367007
$609$	−1.17544e155	−3.34149
$610$	6.83139e153	0.177298
$611$	−3.80485e154	−0.901675
$612$	7.52273e154	1.62806
$613$	−4.06990e153	−0.0804502	−0.0402251	−	0.999191i	$-0.512807\pi$
$613$	−4.06990e153	−0.0804502	−0.0402251	+	0.999191i	$0.512807\pi$
$614$	4.08465e153	0.0737582
$615$	2.47155e154	0.407757
$616$	8.93914e154	1.34762
$617$	9.21058e154	1.26900	0.634498	−	0.772925i	$-0.281207\pi$
$617$	9.21058e154	1.26900	0.634498	+	0.772925i	$0.281207\pi$
$618$	−1.49858e154	−0.188721
$619$	7.27636e154	0.837690	0.418845	−	0.908058i	$-0.362435\pi$
$619$	7.27636e154	0.837690	0.418845	+	0.908058i	$0.362435\pi$
$620$	−7.48715e154	−0.788093
$621$	−1.86613e154	−0.179622
$622$	−5.15336e154	−0.453654
$623$	2.59826e155	2.09217
$624$	−8.30948e154	−0.612110
$625$	−1.83973e155	−1.23997
$626$	−9.21320e154	−0.568244
$627$	−1.11483e155	−0.629305
$628$	2.81470e155	1.45436
$629$	−3.51136e155	−1.66098
$630$	−4.03044e155	−1.74563
$631$	2.61530e155	1.03727	0.518636	−	0.854995i	$-0.326440\pi$
$631$	2.61530e155	1.03727	0.518636	+	0.854995i	$0.326440\pi$
$632$	3.22874e155	1.17283
$633$	6.73986e154	0.224257
$634$	1.37098e155	0.417905
$635$	−4.97956e154	−0.139075
$636$	−1.27600e155	−0.326572
$637$	−5.98992e155	−1.40502
$638$	2.93022e155	0.630017
$639$	2.17722e155	0.429145
$640$	−6.21477e155	−1.12315
$641$	5.81662e155	0.963940	0.481970	−	0.876188i	$-0.339921\pi$
$641$	5.81662e155	0.963940	0.481970	+	0.876188i	$0.339921\pi$
$642$	−4.18966e154	−0.0636773
$643$	−9.13018e155	−1.27283	−0.636415	−	0.771347i	$-0.719583\pi$
$643$	−9.13018e155	−1.27283	−0.636415	+	0.771347i	$0.719583\pi$
$644$	−9.81424e154	−0.125514
$645$	1.66342e156	1.95182
$646$	1.75696e155	0.189172
$647$	−3.30430e154	−0.0326506	−0.0163253	−	0.999867i	$-0.505197\pi$
$647$	−3.30430e154	−0.0326506	−0.0163253	+	0.999867i	$0.505197\pi$
$648$	8.64960e155	0.784483
$649$	1.27708e155	0.106325
$650$	2.64952e155	0.202524
$651$	3.29401e156	2.31196
$652$	−1.38820e156	−0.894770
$653$	−2.20048e155	−0.130268	−0.0651338	−	0.997877i	$-0.520747\pi$
$653$	−2.20048e155	−0.130268	−0.0651338	+	0.997877i	$0.520747\pi$
$654$	−2.57877e156	−1.40232
$655$	−2.57790e156	−1.28788
$656$	−1.49074e155	−0.0684287
$657$	−1.02409e156	−0.431976
$658$	1.67803e156	0.650523
$659$	−3.84968e156	−1.37178	−0.685890	−	0.727705i	$-0.740587\pi$
$659$	−3.84968e156	−1.37178	−0.685890	+	0.727705i	$0.740587\pi$
$660$	−4.84478e156	−1.58703
$661$	3.29250e156	0.991619	0.495809	−	0.868431i	$-0.334871\pi$
$661$	3.29250e156	0.991619	0.495809	+	0.868431i	$0.334871\pi$
$662$	8.11171e155	0.224643
$663$	7.61679e156	1.93986
$664$	1.34162e156	0.314270
$665$	3.01098e156	0.648793
$666$	−7.42966e156	−1.47282
$667$	−7.43991e155	−0.135701
$668$	4.22935e156	0.709872
$669$	−1.68140e157	−2.59729
$670$	−3.19765e156	−0.454652
$671$	−2.39655e156	−0.313679
$672$	2.25318e157	2.71519
$673$	1.35473e157	1.50320	0.751601	−	0.659618i	$-0.229282\pi$
$673$	1.35473e157	1.50320	0.751601	+	0.659618i	$0.229282\pi$
$674$	−2.56320e156	−0.261913
$675$	7.10696e156	0.668843
$676$	−6.77185e155	−0.0587037
$677$	2.22344e157	1.77564	0.887818	−	0.460195i	$-0.152221\pi$
$677$	2.22344e157	1.77564	0.887818	+	0.460195i	$0.152221\pi$
$678$	5.67790e156	0.417772
$679$	−3.93399e157	−2.66723
$680$	1.76577e157	1.10329
$681$	−5.05941e157	−2.91363
$682$	−8.21155e156	−0.435906
$683$	3.49508e157	1.71044	0.855221	−	0.518263i	$-0.173421\pi$
$683$	3.49508e157	1.71044	0.855221	+	0.518263i	$0.173421\pi$
$684$	−1.18911e157	−0.536550
$685$	3.41924e157	1.42267
$686$	6.90416e156	0.264925
$687$	−9.67043e157	−3.42253
$688$	−1.00331e157	−0.327549
$689$	−8.57024e156	−0.258123
$690$	−3.84569e156	−0.106868
$691$	3.05453e157	0.783271	0.391636	−	0.920120i	$-0.371909\pi$
$691$	3.05453e157	0.783271	0.391636	+	0.920120i	$0.371909\pi$
$692$	−5.74569e156	−0.135973
$693$	1.41393e158	3.08841
$694$	−3.92501e157	−0.791389
$695$	−8.44531e157	−1.57202
$696$	1.08962e158	1.87267
$697$	1.36647e157	0.216860
$698$	−2.30886e157	−0.338393
$699$	−1.40974e158	−1.90834
$700$	3.73765e157	0.467366
$701$	4.91365e157	0.567616	0.283808	−	0.958881i	$-0.408402\pi$
$701$	4.91365e157	0.567616	0.283808	+	0.958881i	$0.408402\pi$
$702$	7.93753e157	0.847180
$703$	5.55040e157	0.547398
$704$	−1.78117e157	−0.162339
$705$	−2.10322e158	−1.77169
$706$	4.41287e157	0.343606
$707$	2.60060e158	1.87196
$708$	2.05345e157	0.136659
$709$	−2.07877e158	−1.27921	−0.639603	−	0.768705i	$-0.720901\pi$
$709$	−2.07877e158	−1.27921	−0.639603	+	0.768705i	$0.720901\pi$
$710$	2.20980e157	0.125752
$711$	5.10701e158	2.68785
$712$	−2.40856e158	−1.17251
$713$	2.08494e157	0.0938910
$714$	−3.35919e158	−1.39954
$715$	−3.25400e158	−1.25439
$716$	−8.95765e156	−0.0319537
$717$	−3.97670e158	−1.31283
$718$	−2.14287e158	−0.654769
$719$	4.16691e158	1.17858	0.589292	−	0.807920i	$-0.299407\pi$
$719$	4.16691e158	1.17858	0.589292	+	0.807920i	$0.299407\pi$
$720$	−3.04697e158	−0.797839
$721$	−1.41989e158	−0.344230
$722$	1.89628e158	0.425684
$723$	9.77894e158	2.03290
$724$	−4.50053e158	−0.866509
$725$	2.83341e158	0.505301
$726$	−2.22073e157	−0.0366871
$727$	6.15329e158	0.941776	0.470888	−	0.882193i	$-0.343934\pi$
$727$	6.15329e158	0.941776	0.470888	+	0.882193i	$0.343934\pi$
$728$	9.65398e158	1.36904
$729$	−8.25700e158	−1.08504
$730$	−1.03942e158	−0.126582
$731$	9.19671e158	1.03805
$732$	−3.85348e158	−0.403170
$733$	1.10124e159	1.06810	0.534049	−	0.845454i	$-0.320670\pi$
$733$	1.10124e159	1.06810	0.534049	+	0.845454i	$0.320670\pi$
$734$	1.15562e158	0.103916
$735$	−3.31107e159	−2.76071
$736$	1.42615e158	0.110267
$737$	1.12178e159	0.804382
$738$	2.89130e158	0.192294
$739$	−2.34177e159	−1.44470	−0.722352	−	0.691526i	$-0.756939\pi$
$739$	−2.34177e159	−1.44470	−0.722352	+	0.691526i	$0.756939\pi$
$740$	2.41206e159	1.38047
$741$	−1.20398e159	−0.639308
$742$	3.77968e158	0.186225
$743$	2.29031e159	1.04717	0.523583	−	0.851974i	$-0.324595\pi$
$743$	2.29031e159	1.04717	0.523583	+	0.851974i	$0.324595\pi$
$744$	−3.05350e159	−1.29569
$745$	−2.84129e159	−1.11903
$746$	8.22428e158	0.300672
$747$	2.12209e159	0.720230
$748$	−2.67857e159	−0.844044
$749$	−3.96966e158	−0.116148
$750$	−2.19812e159	−0.597245
$751$	−1.54156e159	−0.388996	−0.194498	−	0.980903i	$-0.562308\pi$
$751$	−1.54156e159	−0.388996	−0.194498	+	0.980903i	$0.562308\pi$
$752$	1.26857e159	0.297321
$753$	−2.57201e159	−0.559952
$754$	3.16454e159	0.640031
$755$	3.99249e159	0.750218
$756$	1.11974e160	1.95504
$757$	4.40154e159	0.714140	0.357070	−	0.934078i	$-0.383776\pi$
$757$	4.40154e159	0.714140	0.357070	+	0.934078i	$0.383776\pi$
$758$	2.01272e159	0.303488
$759$	1.34912e159	0.189074
$760$	−2.79114e159	−0.363603
$761$	1.66642e159	0.201807	0.100904	−	0.994896i	$-0.467827\pi$
$761$	1.66642e159	0.201807	0.100904	+	0.994896i	$0.467827\pi$
$762$	−8.78146e158	−0.0988703
$763$	−2.44336e160	−2.55786
$764$	−7.99451e159	−0.778234
$765$	2.79297e160	2.52847
$766$	−4.08617e159	−0.344048
$767$	1.37920e159	0.108015
$768$	−1.47191e160	−1.07234
$769$	−5.86634e159	−0.397608	−0.198804	−	0.980039i	$-0.563706\pi$
$769$	−5.86634e159	−0.397608	−0.198804	+	0.980039i	$0.563706\pi$
$770$	1.43509e160	0.904993
$771$	−3.63911e160	−2.13539
$772$	1.87279e160	1.02265
$773$	2.90909e160	1.47841	0.739205	−	0.673480i	$-0.235201\pi$
$773$	2.90909e160	1.47841	0.739205	+	0.673480i	$0.235201\pi$
$774$	1.94592e160	0.920455
$775$	−7.94025e159	−0.349615
$776$	3.64676e160	1.49480
$777$	−1.06120e161	−4.04977
$778$	−7.13275e159	−0.253448
$779$	−2.15997e159	−0.0714692
$780$	−5.23221e160	−1.61226
$781$	−7.75228e159	−0.222483
$782$	−2.12620e159	−0.0568367
$783$	8.48842e160	2.11373
$784$	1.99710e160	0.463295
$785$	1.04502e161	2.25870
$786$	−4.54613e160	−0.915569
$787$	7.23578e159	0.135796	0.0678981	−	0.997692i	$-0.478371\pi$
$787$	7.23578e159	0.135796	0.0678981	+	0.997692i	$0.478371\pi$
$788$	−5.85822e160	−1.02461
$789$	1.32994e161	2.16799
$790$	5.18344e160	0.787617
$791$	5.37975e160	0.762021
$792$	−1.31070e161	−1.73084
$793$	−2.58819e160	−0.318665
$794$	−6.02561e159	−0.0691772
$795$	−4.73740e160	−0.507183
$796$	−3.15593e160	−0.315102
$797$	1.26877e161	1.18154	0.590768	−	0.806841i	$-0.298825\pi$
$797$	1.26877e161	1.18154	0.590768	+	0.806841i	$0.298825\pi$
$798$	5.30986e160	0.461235
$799$	−1.16282e161	−0.942254
$800$	−5.43132e160	−0.410593
$801$	−3.80970e161	−2.68712
$802$	−6.08039e160	−0.400179
$803$	3.64642e160	0.223951
$804$	1.80374e161	1.03387
$805$	−3.64375e160	−0.194929
$806$	−8.86821e160	−0.442834
$807$	2.51786e161	1.17368
$808$	−2.41072e161	−1.04910
$809$	3.87066e161	1.57269	0.786344	−	0.617789i	$-0.211971\pi$
$809$	3.87066e161	1.57269	0.786344	+	0.617789i	$0.211971\pi$
$810$	1.38861e161	0.526821
$811$	5.33680e159	0.0189070	0.00945351	−	0.999955i	$-0.496991\pi$
$811$	5.33680e159	0.0189070	0.00945351	+	0.999955i	$0.496991\pi$
$812$	4.46418e161	1.47701
$813$	−6.33972e161	−1.95905
$814$	2.64544e161	0.763560
$815$	−5.15400e161	−1.38962
$816$	−2.53952e161	−0.639657
$817$	−1.45372e161	−0.342103
$818$	−2.00625e161	−0.441139
$819$	1.52700e162	3.13750
$820$	−9.38668e160	−0.180237
$821$	4.61794e161	0.828710	0.414355	−	0.910115i	$-0.364007\pi$
$821$	4.61794e161	0.828710	0.414355	+	0.910115i	$0.364007\pi$
$822$	6.02984e161	1.01139
$823$	−4.77194e161	−0.748177	−0.374088	−	0.927393i	$-0.622044\pi$
$823$	−4.77194e161	−0.748177	−0.374088	+	0.927393i	$0.622044\pi$
$824$	1.31622e161	0.192916
$825$	−5.13798e161	−0.704041
$826$	−6.08263e160	−0.0779289
$827$	−1.02394e162	−1.22664	−0.613322	−	0.789833i	$-0.710167\pi$
$827$	−1.02394e162	−1.22664	−0.613322	+	0.789833i	$0.710167\pi$
$828$	1.43901e161	0.161206
$829$	−8.64891e160	−0.0906118	−0.0453059	−	0.998973i	$-0.514426\pi$
$829$	−8.64891e160	−0.0906118	−0.0453059	+	0.998973i	$0.514426\pi$
$830$	2.15385e161	0.211048
$831$	2.87553e161	0.263549
$832$	−1.92360e161	−0.164919
$833$	−1.83062e162	−1.46825
$834$	−1.48933e162	−1.11757
$835$	1.57024e162	1.10247
$836$	4.23401e161	0.278166
$837$	−2.37877e162	−1.46248
$838$	−9.72301e161	−0.559445
$839$	−9.63574e160	−0.0518915	−0.0259457	−	0.999663i	$-0.508260\pi$
$839$	−9.63574e160	−0.0518915	−0.0259457	+	0.999663i	$0.508260\pi$
$840$	5.33647e162	2.69001
$841$	1.26494e162	0.596889
$842$	7.66114e161	0.338433
$843$	−7.70516e161	−0.318677
$844$	−2.55972e161	−0.0991260
$845$	−2.51419e161	−0.0911698
$846$	−2.46041e162	−0.835511
$847$	−2.10412e161	−0.0669177
$848$	2.85740e161	0.0851142
$849$	2.99504e162	0.835653
$850$	8.09738e161	0.211638
$851$	−6.71684e161	−0.164465
$852$	−1.24651e162	−0.285956
$853$	8.36078e162	1.79711	0.898557	−	0.438856i	$-0.144616\pi$
$853$	8.36078e162	1.79711	0.898557	+	0.438856i	$0.144616\pi$
$854$	1.14146e162	0.229904
$855$	−4.41484e162	−0.833289
$856$	3.67983e161	0.0650929
$857$	−1.67293e162	−0.277359	−0.138680	−	0.990337i	$-0.544286\pi$
$857$	−1.67293e162	−0.277359	−0.138680	+	0.990337i	$0.544286\pi$
$858$	−5.73844e162	−0.891763
$859$	1.07503e163	1.56603	0.783013	−	0.622005i	$-0.213682\pi$
$859$	1.07503e163	1.56603	0.783013	+	0.622005i	$0.213682\pi$
$860$	−6.31750e162	−0.862743
$861$	4.12972e162	0.528744
$862$	6.95301e162	0.834679
$863$	−1.75890e163	−1.97990	−0.989949	−	0.141424i	$-0.954832\pi$
$863$	−1.75890e163	−1.97990	−0.989949	+	0.141424i	$0.954832\pi$
$864$	−1.62713e163	−1.71755
$865$	−2.13321e162	−0.211173
$866$	−8.43005e162	−0.782686
$867$	3.48687e162	0.303652
$868$	−1.25103e163	−1.02193
$869$	−1.81842e163	−1.39347
$870$	1.74928e163	1.25759
$871$	1.21149e163	0.817167
$872$	2.26497e163	1.43350
$873$	5.76821e163	3.42571
$874$	3.36087e161	0.0187313
$875$	−2.08270e163	−1.08938
$876$	5.86318e162	0.287843
$877$	−2.27599e163	−1.04880	−0.524400	−	0.851472i	$-0.675710\pi$
$877$	−2.27599e163	−1.04880	−0.524400	+	0.851472i	$0.675710\pi$
$878$	−9.46823e162	−0.409565
$879$	2.30815e163	0.937306
$880$	1.08492e163	0.413627
$881$	3.21194e163	1.14975	0.574877	−	0.818240i	$-0.305050\pi$
$881$	3.21194e163	1.14975	0.574877	+	0.818240i	$0.305050\pi$
$882$	−3.87339e163	−1.30192
$883$	−4.65931e163	−1.47063	−0.735314	−	0.677727i	$-0.762965\pi$
$883$	−4.65931e163	−1.47063	−0.735314	+	0.677727i	$0.762965\pi$
$884$	−2.89277e163	−0.857460
$885$	7.62388e162	0.212239
$886$	2.09964e163	0.549001
$887$	−1.47634e163	−0.362598	−0.181299	−	0.983428i	$-0.558030\pi$
$887$	−1.47634e163	−0.362598	−0.181299	+	0.983428i	$0.558030\pi$
$888$	9.83718e163	2.26961
$889$	−8.32034e162	−0.180341
$890$	−3.86672e163	−0.787403
$891$	−4.87145e163	−0.932064
$892$	6.38577e163	1.14806
$893$	1.83807e163	0.310532
$894$	−5.01063e163	−0.795536
$895$	−3.32572e162	−0.0496257
$896$	−1.03843e164	−1.45640
$897$	1.45701e163	0.192079
$898$	3.99446e163	0.495018
$899$	−9.48369e163	−1.10488
$900$	−5.48032e163	−0.600270
$901$	−2.61921e163	−0.269739
$902$	−1.02949e163	−0.0996915
$903$	2.77941e164	2.53095
$904$	−4.98696e163	−0.427059
$905$	−1.67092e164	−1.34573
$906$	7.04076e163	0.533340
$907$	1.65157e164	1.17678	0.588388	−	0.808579i	$-0.299763\pi$
$907$	1.65157e164	1.17678	0.588388	+	0.808579i	$0.299763\pi$
$908$	1.92151e164	1.28789
$909$	−3.81313e164	−2.40428
$910$	1.54986e164	0.919378
$911$	3.20881e164	1.79091	0.895456	−	0.445150i	$-0.146850\pi$
$911$	3.20881e164	1.79091	0.895456	+	0.445150i	$0.146850\pi$
$912$	4.01420e163	0.210807
$913$	−7.55601e163	−0.373392
$914$	2.45643e163	0.114233
$915$	−1.43069e164	−0.626143
$916$	3.67272e164	1.51283
$917$	−4.30741e164	−1.67001
$918$	2.42584e164	0.885307
$919$	−1.34416e164	−0.461785	−0.230893	−	0.972979i	$-0.574165\pi$
$919$	−1.34416e164	−0.461785	−0.230893	+	0.972979i	$0.574165\pi$
$920$	3.37771e163	0.109244
$921$	−8.55441e163	−0.260484
$922$	−2.86616e164	−0.821738
$923$	−8.37222e163	−0.226020
$924$	−8.09514e164	−2.05793
$925$	2.55803e164	0.612407
$926$	2.99918e164	0.676228
$927$	2.08192e164	0.442118
$928$	−6.48707e164	−1.29759
$929$	4.58822e164	0.864515	0.432257	−	0.901750i	$-0.357717\pi$
$929$	4.58822e164	0.864515	0.432257	+	0.901750i	$0.357717\pi$
$930$	−4.90211e164	−0.870121
$931$	2.89365e164	0.483881
$932$	5.35404e164	0.843525
$933$	1.07926e165	1.60212
$934$	−3.47022e163	−0.0485407
$935$	−9.94478e164	−1.31084
$936$	−1.41551e165	−1.75835
$937$	−1.12368e165	−1.31551	−0.657754	−	0.753233i	$-0.728493\pi$
$937$	−1.12368e165	−1.31551	−0.657754	+	0.753233i	$0.728493\pi$
$938$	−5.34295e164	−0.589554
$939$	1.92950e165	2.00681
$940$	7.98779e164	0.783125
$941$	9.45412e164	0.873770	0.436885	−	0.899517i	$-0.356082\pi$
$941$	9.45412e164	0.873770	0.436885	+	0.899517i	$0.356082\pi$
$942$	1.84289e165	1.60574
$943$	2.61390e163	0.0214728
$944$	−4.59841e163	−0.0356174
$945$	4.15726e165	3.03628
$946$	−6.92874e164	−0.477195
$947$	−2.50899e165	−1.62958	−0.814788	−	0.579760i	$-0.803146\pi$
$947$	−2.50899e165	−1.62958	−0.814788	+	0.579760i	$0.803146\pi$
$948$	−2.92390e165	−1.79102
$949$	3.93801e164	0.227511
$950$	−1.27995e164	−0.0697482
$951$	−2.87122e165	−1.47587
$952$	2.95042e165	1.43065
$953$	−2.23026e164	−0.102023	−0.0510117	−	0.998698i	$-0.516245\pi$
$953$	−2.23026e164	−0.102023	−0.0510117	+	0.998698i	$0.516245\pi$
$954$	−5.54196e164	−0.239182
$955$	−2.96813e165	−1.20864
$956$	1.51031e165	0.580299
$957$	−6.13671e165	−2.22496
$958$	−3.99670e164	−0.136746
$959$	5.71321e165	1.84479
$960$	−1.06332e165	−0.324048
$961$	−8.18867e164	−0.235540
$962$	2.85699e165	0.775696
$963$	5.82051e164	0.149177
$964$	−3.71393e165	−0.898584
$965$	6.95313e165	1.58823
$966$	−6.42575e164	−0.138578
$967$	−1.65730e165	−0.337468	−0.168734	−	0.985662i	$-0.553968\pi$
$967$	−1.65730e165	−0.337468	−0.168734	+	0.985662i	$0.553968\pi$
$968$	1.95049e164	0.0375027
$969$	−3.67957e165	−0.668079
$970$	5.85453e165	1.00383
$971$	3.74092e165	0.605775	0.302888	−	0.953026i	$-0.402049\pi$
$971$	3.74092e165	0.605775	0.302888	+	0.953026i	$0.402049\pi$
$972$	4.99008e164	0.0763185
$973$	−1.41113e166	−2.03846
$974$	4.06533e165	0.554720
$975$	−5.54885e165	−0.715231
$976$	8.62930e164	0.105078
$977$	6.56544e165	0.755293	0.377647	−	0.925950i	$-0.376733\pi$
$977$	6.56544e165	0.755293	0.377647	+	0.925950i	$0.376733\pi$
$978$	−9.08908e165	−0.987901
$979$	1.35650e166	1.39309
$980$	1.25751e166	1.22029
$981$	3.58258e166	3.28523
$982$	−6.28706e165	−0.544829
$983$	−1.05824e166	−0.866691	−0.433345	−	0.901228i	$-0.642667\pi$
$983$	−1.05824e166	−0.866691	−0.433345	+	0.901228i	$0.642667\pi$
$984$	−3.82820e165	−0.296324
$985$	−2.17499e166	−1.59128
$986$	9.67137e165	0.668835
$987$	−3.51427e166	−2.29738
$988$	4.57259e165	0.282587
$989$	1.75923e165	0.102785
$990$	−2.10421e166	−1.16235
$991$	−1.54871e166	−0.808875	−0.404438	−	0.914566i	$-0.632533\pi$
$991$	−1.54871e166	−0.808875	−0.404438	+	0.914566i	$0.632533\pi$
$992$	1.81792e166	0.897793
$993$	−1.69882e166	−0.793349
$994$	3.69235e165	0.163064
$995$	−1.17171e166	−0.489370
$996$	−1.21495e166	−0.479917
$997$	3.29753e165	0.123199	0.0615995	−	0.998101i	$-0.480380\pi$
$997$	3.29753e165	0.123199	0.0615995	+	0.998101i	$0.480380\pi$
$998$	9.25023e165	0.326894
$999$	7.66345e166	2.56177

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.112.a.a.1.4	✓	9

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

\(f(q)\)	\(=\)	\(q-2.48662e16 q^{2} +5.20768e26 q^{3} -1.97782e33 q^{4} -7.34308e38 q^{5} -1.29495e43 q^{6} -1.22695e47 q^{7} +1.13737e50 q^{8} +1.79902e53 q^{9} +O(q^{10})\)	\(q-2.48662e16 q^{2} +5.20768e26 q^{3} -1.97782e33 q^{4} -7.34308e38 q^{5} -1.29495e43 q^{6} -1.22695e47 q^{7} +1.13737e50 q^{8} +1.79902e53 q^{9} +1.82594e55 q^{10} -6.40567e57 q^{11} -1.02999e60 q^{12} -6.91792e61 q^{13} +3.05097e63 q^{14} -3.82404e65 q^{15} +2.30650e66 q^{16} -2.11423e68 q^{17} -4.47348e69 q^{18} +3.34195e70 q^{19} +1.45233e72 q^{20} -6.38959e73 q^{21} +1.59285e74 q^{22} -4.04428e74 q^{23} +5.92308e76 q^{24} +1.54022e77 q^{25} +1.72022e78 q^{26} +4.61425e79 q^{27} +2.42670e80 q^{28} +1.83961e81 q^{29} +9.50894e81 q^{30} -5.15527e82 q^{31} -3.52633e83 q^{32} -3.33587e84 q^{33} +5.25729e84 q^{34} +9.00962e85 q^{35} -3.55814e86 q^{36} +1.66082e87 q^{37} -8.31017e86 q^{38} -3.60263e88 q^{39} -8.35181e88 q^{40} -6.46319e88 q^{41} +1.58885e90 q^{42} -4.34991e90 q^{43} +1.26693e91 q^{44} -1.32104e92 q^{45} +1.00566e91 q^{46} +5.49999e92 q^{47} +1.20115e93 q^{48} +8.65856e93 q^{49} -3.82994e93 q^{50} -1.10102e95 q^{51} +1.36824e95 q^{52} +1.23885e95 q^{53} -1.14739e96 q^{54} +4.70373e96 q^{55} -1.39550e97 q^{56} +1.74038e97 q^{57} -4.57442e97 q^{58} -1.99367e97 q^{59} +7.56327e98 q^{60} +3.74129e98 q^{61} +1.28192e99 q^{62} -2.20732e100 q^{63} +2.78061e99 q^{64} +5.07988e100 q^{65} +8.29504e100 q^{66} -1.75123e101 q^{67} +4.18157e101 q^{68} -2.10613e101 q^{69} -2.24035e102 q^{70} +1.21022e102 q^{71} +2.04616e103 q^{72} -5.69248e102 q^{73} -4.12984e103 q^{74} +8.02098e103 q^{75} -6.60979e103 q^{76} +7.85947e104 q^{77} +8.95838e104 q^{78} +2.83877e105 q^{79} -1.69368e105 q^{80} +7.60490e105 q^{81} +1.60715e105 q^{82} +1.17958e106 q^{83} +1.26375e107 q^{84} +1.55250e107 q^{85} +1.08166e107 q^{86} +9.58012e107 q^{87} -7.28563e107 q^{88} -2.11765e108 q^{89} +3.28491e108 q^{90} +8.48797e108 q^{91} +7.99887e107 q^{92} -2.68470e109 q^{93} -1.36764e109 q^{94} -2.45402e109 q^{95} -1.83640e110 q^{96} +3.20630e110 q^{97} -2.15305e110 q^{98} -1.15239e111 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 73\!\cdots\!76 q^{2}+ \cdots + 44\!\cdots\!13 q^{9}+O(q^{10}) \) 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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