LMFDB - Embedded newform 1.112.a.a.1.9

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			1.9
Root			$1.35766e15$ 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)

$f(q)$	$=$	$q+9.85626e16 q^{2} -3.53632e26 q^{3} +7.11844e33 q^{4} +7.51271e38 q^{5} -3.48549e43 q^{6} -5.05213e46 q^{7} +4.45728e50 q^{8} +3.37583e52 q^{9} +O(q^{10})$	\(q+9.85626e16 q^{2} -3.53632e26 q^{3} +7.11844e33 q^{4} +7.51271e38 q^{5} -3.48549e43 q^{6} -5.05213e46 q^{7} +4.45728e50 q^{8} +3.37583e52 q^{9} +7.40472e55 q^{10} +1.01538e58 q^{11} -2.51731e60 q^{12} -2.38289e61 q^{13} -4.97951e63 q^{14} -2.65674e65 q^{15} +2.54516e67 q^{16} +2.09592e67 q^{17} +3.32731e69 q^{18} -7.22081e69 q^{19} +5.34788e72 q^{20} +1.78660e73 q^{21} +1.00078e75 q^{22} -1.40540e75 q^{23} -1.57624e77 q^{24} +1.79222e77 q^{25} -2.34864e78 q^{26} +2.03477e79 q^{27} -3.59633e80 q^{28} -2.96869e80 q^{29} -2.61855e82 q^{30} +6.06335e82 q^{31} +1.35140e84 q^{32} -3.59071e84 q^{33} +2.06579e84 q^{34} -3.79552e85 q^{35} +2.40306e86 q^{36} +9.68639e86 q^{37} -7.11702e86 q^{38} +8.42668e87 q^{39} +3.34863e89 q^{40} +3.73593e89 q^{41} +1.76092e90 q^{42} -8.35551e90 q^{43} +7.22792e91 q^{44} +2.53617e91 q^{45} -1.38520e92 q^{46} +4.25353e92 q^{47} -9.00052e93 q^{48} -3.84322e93 q^{49} +1.76646e94 q^{50} -7.41184e93 q^{51} -1.69625e95 q^{52} +6.81823e95 q^{53} +2.00553e96 q^{54} +7.62826e96 q^{55} -2.25188e97 q^{56} +2.55351e96 q^{57} -2.92602e97 q^{58} +2.04459e98 q^{59} -1.89118e99 q^{60} +1.55667e98 q^{61} +5.97620e99 q^{62} -1.70551e99 q^{63} +6.71214e100 q^{64} -1.79020e100 q^{65} -3.53910e101 q^{66} +1.19121e101 q^{67} +1.49196e101 q^{68} +4.96996e101 q^{69} -3.74096e102 q^{70} +4.59631e102 q^{71} +1.50470e103 q^{72} +1.35334e103 q^{73} +9.54716e103 q^{74} -6.33789e103 q^{75} -5.14009e103 q^{76} -5.12983e104 q^{77} +8.30556e104 q^{78} -1.69183e105 q^{79} +1.91211e106 q^{80} -1.02777e106 q^{81} +3.68223e106 q^{82} +3.18814e106 q^{83} +1.27178e107 q^{84} +1.57460e106 q^{85} -8.23541e107 q^{86} +1.04982e107 q^{87} +4.52584e108 q^{88} -1.15017e108 q^{89} +2.49971e108 q^{90} +1.20387e108 q^{91} -1.00043e109 q^{92} -2.14420e109 q^{93} +4.19239e109 q^{94} -5.42479e108 q^{95} -4.77900e110 q^{96} +2.20139e110 q^{97} -3.78797e110 q^{98} +3.42775e110 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	9.85626e16	1.93440	0.967202	−	0.254007i	$-0.0817486\pi$
$2$	9.85626e16	1.93440	0.967202	+	0.254007i	$0.0817486\pi$
$3$	−3.53632e26	−1.17037	−0.585184	−	0.810901i	$-0.698978\pi$
$3$	−3.53632e26	−1.17037	−0.585184	+	0.810901i	$0.698978\pi$
$4$	7.11844e33	2.74192
$5$	7.51271e38	1.21049	0.605245	−	0.796039i	$-0.293075\pi$
$5$	7.51271e38	1.21049	0.605245	+	0.796039i	$0.293075\pi$
$6$	−3.48549e43	−2.26397
$7$	−5.05213e46	−0.631732	−0.315866	−	0.948804i	$-0.602295\pi$
$7$	−5.05213e46	−0.631732	−0.315866	+	0.948804i	$0.602295\pi$
$8$	4.45728e50	3.36958
$9$	3.37583e52	0.369761
$10$	7.40472e55	2.34158
$11$	1.01538e58	1.61933	0.809664	−	0.586894i	$-0.199650\pi$
$11$	1.01538e58	1.61933	0.809664	+	0.586894i	$0.199650\pi$
$12$	−2.51731e60	−3.20906
$13$	−2.38289e61	−0.357477	−0.178739	−	0.983897i	$-0.557202\pi$
$13$	−2.38289e61	−0.357477	−0.178739	+	0.983897i	$0.557202\pi$
$14$	−4.97951e63	−1.22203
$15$	−2.65674e65	−1.41672
$16$	2.54516e67	3.77621
$17$	2.09592e67	0.107512	0.0537562	−	0.998554i	$-0.482881\pi$
$17$	2.09592e67	0.107512	0.0537562	+	0.998554i	$0.482881\pi$
$18$	3.32731e69	0.715268
$19$	−7.22081e69	−0.0772256	−0.0386128	−	0.999254i	$-0.512294\pi$
$19$	−7.22081e69	−0.0772256	−0.0386128	+	0.999254i	$0.512294\pi$
$20$	5.34788e72	3.31907
$21$	1.78660e73	0.739359
$22$	1.00078e75	3.13243
$23$	−1.40540e75	−0.373169	−0.186585	−	0.982439i	$-0.559742\pi$
$23$	−1.40540e75	−0.373169	−0.186585	+	0.982439i	$0.559742\pi$
$24$	−1.57624e77	−3.94365
$25$	1.79222e77	0.465288
$26$	−2.34864e78	−0.691506
$27$	2.03477e79	0.737611
$28$	−3.59633e80	−1.73216
$29$	−2.96869e80	−0.203927	−0.101964	−	0.994788i	$-0.532513\pi$
$29$	−2.96869e80	−0.203927	−0.101964	+	0.994788i	$0.532513\pi$
$30$	−2.61855e82	−2.74051
$31$	6.06335e82	1.02835	0.514173	−	0.857687i	$-0.328099\pi$
$31$	6.06335e82	1.02835	0.514173	+	0.857687i	$0.328099\pi$
$32$	1.35140e84	3.93514
$33$	−3.59071e84	−1.89521
$34$	2.06579e84	0.207973
$35$	−3.79552e85	−0.764706
$36$	2.40306e86	1.01386
$37$	9.68639e86	0.893236	0.446618	−	0.894725i	$-0.352628\pi$
$37$	9.68639e86	0.893236	0.446618	+	0.894725i	$0.352628\pi$
$38$	−7.11702e86	−0.149385
$39$	8.42668e87	0.418380
$40$	3.34863e89	4.07885
$41$	3.73593e89	1.15583	0.577915	−	0.816097i	$-0.303866\pi$
$41$	3.73593e89	1.15583	0.577915	+	0.816097i	$0.303866\pi$
$42$	1.76092e90	1.43022
$43$	−8.35551e90	−1.83854	−0.919272	−	0.393624i	$-0.871221\pi$
$43$	−8.35551e90	−1.83854	−0.919272	+	0.393624i	$0.871221\pi$
$44$	7.22792e91	4.44007
$45$	2.53617e91	0.447593
$46$	−1.38520e92	−0.721861
$47$	4.25353e92	0.671921	0.335960	−	0.941876i	$-0.390939\pi$
$47$	4.25353e92	0.671921	0.335960	+	0.941876i	$0.390939\pi$
$48$	−9.00052e93	−4.41956
$49$	−3.84322e93	−0.600914
$50$	1.76646e94	0.900056
$51$	−7.41184e93	−0.125829
$52$	−1.69625e95	−0.980175
$53$	6.81823e95	1.36887	0.684433	−	0.729076i	$-0.260050\pi$
$53$	6.81823e95	1.36887	0.684433	+	0.729076i	$0.260050\pi$
$54$	2.00553e96	1.42684
$55$	7.62826e96	1.96018
$56$	−2.25188e97	−2.12867
$57$	2.55351e96	0.0903823
$58$	−2.92602e97	−0.394478
$59$	2.04459e98	1.06738	0.533692	−	0.845679i	$-0.320804\pi$
$59$	2.04459e98	1.06738	0.533692	+	0.845679i	$0.320804\pi$
$60$	−1.89118e99	−3.88454
$61$	1.55667e98	0.127759	0.0638794	−	0.997958i	$-0.479653\pi$
$61$	1.55667e98	0.127759	0.0638794	+	0.997958i	$0.479653\pi$
$62$	5.97620e99	1.98924
$63$	−1.70551e99	−0.233590
$64$	6.71214e100	3.83595
$65$	−1.79020e100	−0.432723
$66$	−3.53910e101	−3.66610
$67$	1.19121e101	0.535597	0.267799	−	0.963475i	$-0.413704\pi$
$67$	1.19121e101	0.535597	0.267799	+	0.963475i	$0.413704\pi$
$68$	1.49196e101	0.294791
$69$	4.96996e101	0.436746
$70$	−3.74096e102	−1.47925
$71$	4.59631e102	0.827125	0.413562	−	0.910476i	$-0.364284\pi$
$71$	4.59631e102	0.827125	0.413562	+	0.910476i	$0.364284\pi$
$72$	1.50470e103	1.24594
$73$	1.35334e103	0.521180	0.260590	−	0.965450i	$-0.416083\pi$
$73$	1.35334e103	0.521180	0.260590	+	0.965450i	$0.416083\pi$
$74$	9.54716e103	1.72788
$75$	−6.33789e103	−0.544558
$76$	−5.14009e103	−0.211746
$77$	−5.12983e104	−1.02298
$78$	8.30556e104	0.809316
$79$	−1.69183e105	−0.812932	−0.406466	−	0.913666i	$-0.633239\pi$
$79$	−1.69183e105	−0.812932	−0.406466	+	0.913666i	$0.633239\pi$
$80$	1.91211e106	4.57107
$81$	−1.02777e106	−1.23304
$82$	3.68223e106	2.23584
$83$	3.18814e106	0.987879	0.493940	−	0.869496i	$-0.335556\pi$
$83$	3.18814e106	0.987879	0.493940	+	0.869496i	$0.335556\pi$
$84$	1.27178e107	2.02727
$85$	1.57460e106	0.130143
$86$	−8.23541e107	−3.55649
$87$	1.04982e107	0.238670
$88$	4.52584e108	5.45646
$89$	−1.15017e108	−0.740655	−0.370328	−	0.928901i	$-0.620755\pi$
$89$	−1.15017e108	−0.740655	−0.370328	+	0.928901i	$0.620755\pi$
$90$	2.49971e108	0.865826
$91$	1.20387e108	0.225830
$92$	−1.00043e109	−1.02320
$93$	−2.14420e109	−1.20354
$94$	4.19239e109	1.29977
$95$	−5.42479e108	−0.0934808
$96$	−4.77900e110	−4.60557
$97$	2.20139e110	1.19362	0.596809	−	0.802383i	$-0.296435\pi$
$97$	2.20139e110	1.19362	0.596809	+	0.802383i	$0.296435\pi$
$98$	−3.78797e110	−1.16241
$99$	3.42775e110	0.598765
$100$	1.27578e111	1.27578
$101$	−6.10190e110	−0.351260	−0.175630	−	0.984456i	$-0.556196\pi$
$101$	−6.10190e110	−0.351260	−0.175630	+	0.984456i	$0.556196\pi$
$102$	−7.30530e110	−0.243404
$103$	−9.99504e111	−1.93784	−0.968922	−	0.247368i	$-0.920434\pi$
$103$	−9.99504e111	−1.93784	−0.968922	+	0.247368i	$0.920434\pi$
$104$	−1.06212e112	−1.20455
$105$	1.34222e112	0.894988
$106$	6.72022e112	2.64794
$107$	−3.23186e112	−0.756228	−0.378114	−	0.925759i	$-0.623427\pi$
$107$	−3.23186e112	−0.756228	−0.378114	+	0.925759i	$0.623427\pi$
$108$	1.44844e113	2.02247
$109$	−8.42763e112	−0.705561	−0.352781	−	0.935706i	$-0.614764\pi$
$109$	−8.42763e112	−0.705561	−0.352781	+	0.935706i	$0.614764\pi$
$110$	7.51861e113	3.79178
$111$	−3.42542e113	−1.04542
$112$	−1.28585e114	−2.38556
$113$	−2.67951e113	−0.303530	−0.151765	−	0.988417i	$-0.548496\pi$
$113$	−2.67951e113	−0.303530	−0.151765	+	0.988417i	$0.548496\pi$
$114$	2.51681e113	0.174836
$115$	−1.05584e114	−0.451718
$116$	−2.11324e114	−0.559153
$117$	−8.04425e113	−0.132181
$118$	2.01520e115	2.06475
$119$	−1.05888e114	−0.0679191
$120$	−1.18418e116	−4.77375
$121$	6.37820e115	1.62222
$122$	1.53429e115	0.247137
$123$	−1.32114e116	−1.35275
$124$	4.31616e116	2.81964
$125$	−1.54734e116	−0.647264
$126$	−1.68100e116	−0.451858
$127$	−3.13530e116	−0.543467	−0.271733	−	0.962373i	$-0.587597\pi$
$127$	−3.13530e116	−0.543467	−0.271733	+	0.962373i	$0.587597\pi$
$128$	3.10722e117	3.48513
$129$	2.95478e117	2.15177
$130$	−1.76447e117	−0.837062
$131$	8.41708e116	0.260979	0.130489	−	0.991450i	$-0.458345\pi$
$131$	8.41708e116	0.260979	0.130489	+	0.991450i	$0.458345\pi$
$132$	−2.55603e118	−5.19651
$133$	3.64805e116	0.0487859
$134$	1.17409e118	1.03606
$135$	1.52867e118	0.892872
$136$	9.34209e117	0.362272
$137$	−5.71963e118	−1.47699	−0.738493	−	0.674261i	$-0.764462\pi$
$137$	−5.71963e118	−1.47699	−0.738493	+	0.674261i	$0.764462\pi$
$138$	4.89852e118	0.844843
$139$	3.69513e118	0.426882	0.213441	−	0.976956i	$-0.431533\pi$
$139$	3.69513e118	0.426882	0.213441	+	0.976956i	$0.431533\pi$
$140$	−2.70182e119	−2.09677
$141$	−1.50418e119	−0.786394
$142$	4.53024e119	1.59999
$143$	−2.41954e119	−0.578873
$144$	8.59204e119	1.39630
$145$	−2.23029e119	−0.246852
$146$	1.33389e120	1.00817
$147$	1.35909e120	0.703291
$148$	6.89520e120	2.44918
$149$	−5.91164e120	−1.44501	−0.722503	−	0.691368i	$-0.757009\pi$
$149$	−5.91164e120	−1.44501	−0.722503	+	0.691368i	$0.757009\pi$
$150$	−6.24679e120	−1.05340
$151$	−1.37207e121	−1.60013	−0.800064	−	0.599915i	$-0.795201\pi$
$151$	−1.37207e121	−1.60013	−0.800064	+	0.599915i	$0.795201\pi$
$152$	−3.21852e120	−0.260218
$153$	7.07546e119	0.0397539
$154$	−5.05609e121	−1.97886
$155$	4.55522e121	1.24480
$156$	5.99848e121	1.14717
$157$	1.22958e121	0.164940	0.0824700	−	0.996594i	$-0.473719\pi$
$157$	1.22958e121	0.164940	0.0824700	+	0.996594i	$0.473719\pi$
$158$	−1.66752e122	−1.57254
$159$	−2.41115e122	−1.60208
$160$	1.01527e123	4.76346
$161$	7.10028e121	0.235743
$162$	−1.01299e123	−2.38519
$163$	−7.52728e122	−1.25958	−0.629791	−	0.776765i	$-0.716859\pi$
$163$	−7.52728e122	−1.25958	−0.629791	+	0.776765i	$0.716859\pi$
$164$	2.65940e123	3.16920
$165$	−2.69760e123	−2.29413
$166$	3.14232e123	1.91096
$167$	−1.70305e123	−0.742102	−0.371051	−	0.928612i	$-0.621003\pi$
$167$	−1.70305e123	−0.742102	−0.371051	+	0.928612i	$0.621003\pi$
$168$	7.96337e123	2.49133
$169$	−3.87555e123	−0.872210
$170$	1.55197e123	0.251749
$171$	−2.43762e122	−0.0285550
$172$	−5.94782e124	−5.04114
$173$	−1.69448e124	−1.04106	−0.520531	−	0.853843i	$-0.674266\pi$
$173$	−1.69448e124	−1.04106	−0.520531	+	0.853843i	$0.674266\pi$
$174$	1.03473e124	0.461685
$175$	−9.05455e123	−0.293938
$176$	2.58431e125	6.11493
$177$	−7.23035e124	−1.24923
$178$	−1.13364e125	−1.43273
$179$	−5.12712e124	−0.474822	−0.237411	−	0.971409i	$-0.576299\pi$
$179$	−5.12712e124	−0.474822	−0.237411	+	0.971409i	$0.576299\pi$
$180$	1.80535e125	1.22726
$181$	1.39900e125	0.699290	0.349645	−	0.936882i	$-0.386302\pi$
$181$	1.39900e125	0.699290	0.349645	+	0.936882i	$0.386302\pi$
$182$	1.18656e125	0.436847
$183$	−5.50489e124	−0.149525
$184$	−6.26428e125	−1.25743
$185$	7.27711e125	1.08125
$186$	−2.11338e126	−2.32814
$187$	2.12815e125	0.174098
$188$	3.02785e126	1.84235
$189$	−1.02799e126	−0.465973
$190$	−5.34681e125	−0.180830
$191$	7.50054e126	1.89557	0.947786	−	0.318906i	$-0.103316\pi$
$191$	7.50054e126	1.89557	0.947786	+	0.318906i	$0.103316\pi$
$192$	−2.37363e127	−4.48947
$193$	−5.81049e126	−0.823725	−0.411863	−	0.911246i	$-0.635122\pi$
$193$	−5.81049e126	−0.823725	−0.411863	+	0.911246i	$0.635122\pi$
$194$	2.16974e127	2.30894
$195$	6.33072e126	0.506445
$196$	−2.73577e127	−1.64766
$197$	1.44867e127	0.657799	0.328900	−	0.944365i	$-0.393322\pi$
$197$	1.44867e127	0.657799	0.328900	+	0.944365i	$0.393322\pi$
$198$	3.37848e127	1.15825
$199$	4.46207e127	1.15662	0.578309	−	0.815817i	$-0.303713\pi$
$199$	4.46207e127	1.15662	0.578309	+	0.815817i	$0.303713\pi$
$200$	7.98846e127	1.56783
$201$	−4.21252e127	−0.626846
$202$	−6.01420e127	−0.679480
$203$	1.49982e127	0.128828
$204$	−5.27607e127	−0.345014
$205$	2.80669e128	1.39912
$206$	−9.85137e128	−3.74857
$207$	−4.74441e127	−0.137984
$208$	−6.06485e128	−1.34991
$209$	−7.33187e127	−0.125053
$210$	1.32293e129	1.73127
$211$	4.55174e127	0.0457616	0.0228808	−	0.999738i	$-0.492716\pi$
$211$	4.55174e127	0.0457616	0.0228808	+	0.999738i	$0.492716\pi$
$212$	4.85351e129	3.75332
$213$	−1.62540e129	−0.968041
$214$	−3.18540e129	−1.46285
$215$	−6.27726e129	−2.22554
$216$	9.06957e129	2.48544
$217$	−3.06328e129	−0.649639
$218$	−8.30649e129	−1.36484
$219$	−4.78585e129	−0.609973
$220$	5.43013e130	5.37466
$221$	−4.99434e128	−0.0384332
$222$	−3.37618e130	−2.02226
$223$	2.34098e130	1.09264	0.546320	−	0.837576i	$-0.316028\pi$
$223$	2.34098e130	1.09264	0.546320	+	0.837576i	$0.316028\pi$
$224$	−6.82746e130	−2.48596
$225$	6.05025e129	0.172046
$226$	−2.64099e130	−0.587149
$227$	−2.69436e130	−0.468835	−0.234418	−	0.972136i	$-0.575318\pi$
$227$	−2.69436e130	−0.468835	−0.234418	+	0.972136i	$0.575318\pi$
$228$	1.81770e130	0.247821
$229$	−3.13059e130	−0.334778	−0.167389	−	0.985891i	$-0.553534\pi$
$229$	−3.13059e130	−0.334778	−0.167389	+	0.985891i	$0.553534\pi$
$230$	−1.04066e131	−0.873806
$231$	1.81407e131	1.19726
$232$	−1.32323e131	−0.687150
$233$	2.00804e131	0.821331	0.410665	−	0.911786i	$-0.365296\pi$
$233$	2.00804e131	0.821331	0.410665	+	0.911786i	$0.365296\pi$
$234$	−7.92862e130	−0.255692
$235$	3.19555e131	0.813354
$236$	1.45543e132	2.92668
$237$	5.98287e131	0.951430
$238$	−1.04366e131	−0.131383
$239$	−9.14942e131	−0.912662	−0.456331	−	0.889810i	$-0.650837\pi$
$239$	−9.14942e131	−0.912662	−0.456331	+	0.889810i	$0.650837\pi$
$240$	−6.76183e132	−5.34984
$241$	−6.32982e131	−0.397599	−0.198800	−	0.980040i	$-0.563704\pi$
$241$	−6.32982e131	−0.397599	−0.198800	+	0.980040i	$0.563704\pi$
$242$	6.28652e132	3.13803
$243$	1.77682e132	0.705497
$244$	1.10811e132	0.350305
$245$	−2.88730e132	−0.727401
$246$	−1.30215e133	−2.61676
$247$	1.72064e131	0.0276064
$248$	2.70261e133	3.46509
$249$	−1.12743e133	−1.15618
$250$	−1.52510e133	−1.25207
$251$	2.76120e133	1.81638	0.908189	−	0.418560i	$-0.137465\pi$
$251$	2.76120e133	1.81638	0.908189	+	0.418560i	$0.137465\pi$
$252$	−1.21406e133	−0.640486
$253$	−1.42702e133	−0.604284
$254$	−3.09023e133	−1.05128
$255$	−5.56830e132	−0.152315
$256$	1.31999e134	2.90571
$257$	−1.04925e134	−1.86033	−0.930165	−	0.367141i	$-0.880337\pi$
$257$	−1.04925e134	−1.86033	−0.930165	+	0.367141i	$0.880337\pi$
$258$	2.91231e134	4.16240
$259$	−4.89369e133	−0.564286
$260$	−1.27434e134	−1.18649
$261$	−1.00218e133	−0.0754045
$262$	8.29610e133	0.504838
$263$	−3.12572e133	−0.153959	−0.0769797	−	0.997033i	$-0.524528\pi$
$263$	−3.12572e133	−0.153959	−0.0769797	+	0.997033i	$0.524528\pi$
$264$	−1.60048e135	−6.38606
$265$	5.12234e134	1.65700
$266$	3.59561e133	0.0943717
$267$	4.06737e134	0.866839
$268$	8.47958e134	1.46857
$269$	−1.00474e135	−1.41515	−0.707573	−	0.706640i	$-0.750210\pi$
$269$	−1.00474e135	−1.41515	−0.707573	+	0.706640i	$0.750210\pi$
$270$	1.50669e135	1.72717
$271$	1.66241e135	1.55218	0.776090	−	0.630622i	$-0.217200\pi$
$271$	1.66241e135	1.55218	0.776090	+	0.630622i	$0.217200\pi$
$272$	5.33445e134	0.405990
$273$	−4.25727e134	−0.264304
$274$	−5.63741e135	−2.85709
$275$	1.81979e135	0.753454
$276$	3.53784e135	1.19752
$277$	1.59312e135	0.441186	0.220593	−	0.975366i	$-0.429201\pi$
$277$	1.59312e135	0.441186	0.220593	+	0.975366i	$0.429201\pi$
$278$	3.64201e135	0.825763
$279$	2.04689e135	0.380242
$280$	−1.69177e136	−2.57674
$281$	−5.49808e135	−0.687085	−0.343542	−	0.939137i	$-0.611627\pi$
$281$	−5.49808e135	−0.687085	−0.343542	+	0.939137i	$0.611627\pi$
$282$	−1.48256e136	−1.52121
$283$	1.20923e136	1.01944	0.509720	−	0.860340i	$-0.329749\pi$
$283$	1.20923e136	1.01944	0.509720	+	0.860340i	$0.329749\pi$
$284$	3.27186e136	2.26791
$285$	1.91838e135	0.109407
$286$	−2.38476e136	−1.11977
$287$	−1.88744e136	−0.730176
$288$	4.56211e136	1.45506
$289$	−3.75648e136	−0.988441
$290$	−2.19823e136	−0.477512
$291$	−7.78482e136	−1.39697
$292$	9.63366e136	1.42904
$293$	−1.22762e137	−1.50630	−0.753148	−	0.657851i	$-0.771466\pi$
$293$	−1.22762e137	−1.50630	−0.753148	+	0.657851i	$0.771466\pi$
$294$	1.33955e137	1.36045
$295$	1.53604e137	1.29206
$296$	4.31750e137	3.00983
$297$	2.06607e137	1.19443
$298$	−5.82666e137	−2.79523
$299$	3.34893e136	0.133400
$300$	−4.51159e137	−1.49314
$301$	4.22131e137	1.16147
$302$	−1.35234e138	−3.09530
$303$	2.15783e137	0.411104
$304$	−1.83781e137	−0.291620
$305$	1.16948e137	0.154651
$306$	6.97376e136	0.0769002
$307$	3.12961e137	0.287946	0.143973	−	0.989582i	$-0.454012\pi$
$307$	3.12961e137	0.287946	0.143973	+	0.989582i	$0.454012\pi$
$308$	−3.65164e138	−2.80494
$309$	3.53457e138	2.26799
$310$	4.48975e138	2.40795
$311$	−1.58640e138	−0.711559	−0.355780	−	0.934570i	$-0.615785\pi$
$311$	−1.58640e138	−0.711559	−0.355780	+	0.934570i	$0.615785\pi$
$312$	3.75601e138	1.40977
$313$	1.01974e138	0.320463	0.160232	−	0.987079i	$-0.448776\pi$
$313$	1.01974e138	0.320463	0.160232	+	0.987079i	$0.448776\pi$
$314$	1.21191e138	0.319061
$315$	−1.28130e138	−0.282759
$316$	−1.20432e139	−2.22900
$317$	2.89438e138	0.449538	0.224769	−	0.974412i	$-0.427837\pi$
$317$	2.89438e138	0.449538	0.224769	+	0.974412i	$0.427837\pi$
$318$	−2.37649e139	−3.09907
$319$	−3.01435e138	−0.330225
$320$	5.04264e139	4.64338
$321$	1.14289e139	0.885065
$322$	6.99822e138	0.456023
$323$	−1.51342e137	−0.00830270
$324$	−7.31610e139	−3.38089
$325$	−4.27068e138	−0.166330
$326$	−7.41909e139	−2.43654
$327$	2.98028e139	0.825766
$328$	1.66521e140	3.89467
$329$	−2.14894e139	−0.424474
$330$	−2.65882e140	−4.43778
$331$	5.98088e139	0.843940	0.421970	−	0.906610i	$-0.361339\pi$
$331$	5.98088e139	0.843940	0.421970	+	0.906610i	$0.361339\pi$
$332$	2.26946e140	2.70869
$333$	3.26996e139	0.330284
$334$	−1.67857e140	−1.43553
$335$	8.94925e139	0.648335
$336$	4.54718e140	2.79198
$337$	−1.07219e140	−0.558227	−0.279113	−	0.960258i	$-0.590040\pi$
$337$	−1.07219e140	−0.558227	−0.279113	+	0.960258i	$0.590040\pi$
$338$	−3.81984e140	−1.68721
$339$	9.47560e139	0.355241
$340$	1.12087e140	0.356841
$341$	6.15661e140	1.66523
$342$	−2.40259e139	−0.0552370
$343$	5.17279e140	1.01135
$344$	−3.72429e141	−6.19512
$345$	3.73379e140	0.528677
$346$	−1.67012e141	−2.01384
$347$	1.33861e141	1.37520	0.687602	−	0.726087i	$-0.258663\pi$
$347$	1.33861e141	1.37520	0.687602	+	0.726087i	$0.258663\pi$
$348$	7.47311e140	0.654415
$349$	1.26286e141	0.943070	0.471535	−	0.881847i	$-0.343700\pi$
$349$	1.26286e141	0.943070	0.471535	+	0.881847i	$0.343700\pi$
$350$	−8.92440e140	−0.568594
$351$	−4.84865e140	−0.263679
$352$	1.37219e142	6.37229
$353$	−3.73670e141	−1.48249	−0.741245	−	0.671235i	$-0.765764\pi$
$353$	−3.73670e141	−1.48249	−0.741245	+	0.671235i	$0.765764\pi$
$354$	−7.12642e141	−2.41652
$355$	3.45308e141	1.00123
$356$	−8.18740e141	−2.03082
$357$	3.74455e140	0.0794903
$358$	−5.05343e141	−0.918497
$359$	6.84872e141	1.06627	0.533135	−	0.846030i	$-0.321014\pi$
$359$	6.84872e141	1.06627	0.533135	+	0.846030i	$0.321014\pi$
$360$	1.13044e142	1.50820
$361$	−8.69064e141	−0.994036
$362$	1.37889e142	1.35271
$363$	−2.25554e142	−1.89860
$364$	8.56966e141	0.619208
$365$	1.01672e142	0.630884
$366$	−5.42576e141	−0.289241
$367$	−1.25937e142	−0.577014	−0.288507	−	0.957478i	$-0.593159\pi$
$367$	−1.25937e142	−0.577014	−0.288507	+	0.957478i	$0.593159\pi$
$368$	−3.57698e142	−1.40917
$369$	1.26119e142	0.427382
$370$	7.17250e142	2.09158
$371$	−3.44466e142	−0.864757
$372$	−1.52633e143	−3.30002
$373$	1.48553e142	0.276721	0.138360	−	0.990382i	$-0.455817\pi$
$373$	1.48553e142	0.276721	0.138360	+	0.990382i	$0.455817\pi$
$374$	2.09756e142	0.336776
$375$	5.47191e142	0.757537
$376$	1.89592e143	2.26409
$377$	7.07407e141	0.0728994
$378$	−1.01322e143	−0.901380
$379$	2.20431e143	1.69355	0.846773	−	0.531955i	$-0.178542\pi$
$379$	2.20431e143	1.69355	0.846773	+	0.531955i	$0.178542\pi$
$380$	−3.86160e142	−0.256317
$381$	1.10874e143	0.636056
$382$	7.39272e143	3.66680
$383$	−3.54148e143	−1.51933	−0.759665	−	0.650314i	$-0.774637\pi$
$383$	−3.54148e143	−1.51933	−0.759665	+	0.650314i	$0.774637\pi$
$384$	−1.09882e144	−4.07889
$385$	−3.85389e143	−1.23831
$386$	−5.72697e143	−1.59342
$387$	−2.82068e143	−0.679822
$388$	1.56704e144	3.27281
$389$	−1.77393e143	−0.321169	−0.160585	−	0.987022i	$-0.551338\pi$
$389$	−1.77393e143	−0.321169	−0.160585	+	0.987022i	$0.551338\pi$
$390$	6.23973e143	0.979670
$391$	−2.94561e142	−0.0401203
$392$	−1.71303e144	−2.02483
$393$	−2.97655e143	−0.305441
$394$	1.42784e144	1.27245
$395$	−1.27103e144	−0.984047
$396$	2.44002e144	1.64177
$397$	−1.18159e144	−0.691182	−0.345591	−	0.938385i	$-0.612322\pi$
$397$	−1.18159e144	−0.691182	−0.345591	+	0.938385i	$0.612322\pi$
$398$	4.39793e144	2.23737
$399$	−1.29007e143	−0.0570974
$400$	4.56150e144	1.75703
$401$	−3.41688e144	−1.14582	−0.572910	−	0.819618i	$-0.694186\pi$
$401$	−3.41688e144	−1.14582	−0.572910	+	0.819618i	$0.694186\pi$
$402$	−4.15197e144	−1.21257
$403$	−1.44483e144	−0.367610
$404$	−4.34360e144	−0.963128
$405$	−7.72132e144	−1.49258
$406$	1.47826e144	0.249205
$407$	9.83537e144	1.44644
$408$	−3.30367e144	−0.423991
$409$	8.41847e144	0.943169	0.471584	−	0.881821i	$-0.343682\pi$
$409$	8.41847e144	0.943169	0.471584	+	0.881821i	$0.343682\pi$
$410$	2.76635e145	2.70647
$411$	2.02265e145	1.72862
$412$	−7.11491e145	−5.31341
$413$	−1.03295e145	−0.674300
$414$	−4.67621e144	−0.266916
$415$	2.39516e145	1.19582
$416$	−3.22025e145	−1.40673
$417$	−1.30672e145	−0.499609
$418$	−7.22648e144	−0.241904
$419$	−3.76027e142	−0.00110240	−0.000551202	−	1.00000i	$-0.500175\pi$
$419$	−3.76027e142	−0.00110240	−0.000551202		1.00000i	$0.500175\pi$
$420$	9.55450e145	2.45399
$421$	−1.75764e145	−0.395616	−0.197808	−	0.980241i	$-0.563382\pi$
$421$	−1.75764e145	−0.395616	−0.197808	+	0.980241i	$0.563382\pi$
$422$	4.48631e144	0.0885215
$423$	1.43592e145	0.248450
$424$	3.03908e146	4.61251
$425$	3.75635e144	0.0500242
$426$	−1.60204e146	−1.87258
$427$	−7.86450e144	−0.0807094
$428$	−2.30058e146	−2.07352
$429$	8.55629e145	0.677494
$430$	−6.18703e146	−4.30510
$431$	1.43126e146	0.875450	0.437725	−	0.899109i	$-0.355784\pi$
$431$	1.43126e146	0.875450	0.437725	+	0.899109i	$0.355784\pi$
$432$	5.17883e146	2.78538
$433$	2.60531e145	0.123249	0.0616243	−	0.998099i	$-0.480372\pi$
$433$	2.60531e145	0.123249	0.0616243	+	0.998099i	$0.480372\pi$
$434$	−3.01925e146	−1.25666
$435$	7.88703e145	0.288908
$436$	−5.99915e146	−1.93459
$437$	1.01482e145	0.0288182
$438$	−4.71705e146	−1.17993
$439$	−3.69399e146	−0.814171	−0.407085	−	0.913390i	$-0.633455\pi$
$439$	−3.69399e146	−0.814171	−0.407085	+	0.913390i	$0.633455\pi$
$440$	3.40013e147	6.60499
$441$	−1.29741e146	−0.222195
$442$	−4.92255e145	−0.0743455
$443$	3.62346e146	0.482744	0.241372	−	0.970433i	$-0.422403\pi$
$443$	3.62346e146	0.482744	0.241372	+	0.970433i	$0.422403\pi$
$444$	−2.43836e147	−2.86645
$445$	−8.64089e146	−0.896557
$446$	2.30733e147	2.11361
$447$	2.09055e147	1.69119
$448$	−3.39106e147	−2.42329
$449$	−2.79783e147	−1.76665	−0.883324	−	0.468764i	$-0.844700\pi$
$449$	−2.79783e147	−1.76665	−0.883324	+	0.468764i	$0.844700\pi$
$450$	5.96328e146	0.332806
$451$	3.79339e147	1.87167
$452$	−1.90739e147	−0.832255
$453$	4.85207e147	1.87274
$454$	−2.65563e147	−0.906917
$455$	9.04432e146	0.273365
$456$	1.13817e147	0.304551
$457$	−6.28919e147	−1.49020	−0.745102	−	0.666951i	$-0.767599\pi$
$457$	−6.28919e147	−1.49020	−0.745102	+	0.666951i	$0.767599\pi$
$458$	−3.08559e147	−0.647596
$459$	4.26472e146	0.0793023
$460$	−7.51592e147	−1.23858
$461$	−3.91220e147	−0.571504	−0.285752	−	0.958304i	$-0.592243\pi$
$461$	−3.91220e147	−0.571504	−0.285752	+	0.958304i	$0.592243\pi$
$462$	1.78800e148	2.31599
$463$	5.51639e147	0.633738	0.316869	−	0.948469i	$-0.397368\pi$
$463$	5.51639e147	0.633738	0.316869	+	0.948469i	$0.397368\pi$
$464$	−7.55580e147	−0.770074
$465$	−1.61087e148	−1.45688
$466$	1.97917e148	1.58879
$467$	−3.61002e147	−0.257290	−0.128645	−	0.991691i	$-0.541063\pi$
$467$	−3.61002e147	−0.257290	−0.128645	+	0.991691i	$0.541063\pi$
$468$	−5.72625e147	−0.362431
$469$	−6.01817e147	−0.338354
$470$	3.14962e148	1.57336
$471$	−4.34819e147	−0.193041
$472$	9.11333e148	3.59663
$473$	−8.48402e148	−2.97720
$474$	5.89688e148	1.84045
$475$	−1.29413e147	−0.0359321
$476$	−7.53759e147	−0.186229
$477$	2.30172e148	0.506154
$478$	−9.01790e148	−1.76546
$479$	1.33846e148	0.233338	0.116669	−	0.993171i	$-0.462778\pi$
$479$	1.33846e148	0.233338	0.116669	+	0.993171i	$0.462778\pi$
$480$	−3.59032e149	−5.57500
$481$	−2.30816e148	−0.319312
$482$	−6.23884e148	−0.769118
$483$	−2.51089e148	−0.275906
$484$	4.54028e149	4.44800
$485$	1.65384e149	1.44486
$486$	1.75128e149	1.36472
$487$	−1.49987e149	−1.04279	−0.521396	−	0.853315i	$-0.674588\pi$
$487$	−1.49987e149	−1.04279	−0.521396	+	0.853315i	$0.674588\pi$
$488$	6.93852e148	0.430494
$489$	2.66189e149	1.47417
$490$	−2.84580e149	−1.40709
$491$	2.46766e149	1.08959	0.544795	−	0.838569i	$-0.316607\pi$
$491$	2.46766e149	1.08959	0.544795	+	0.838569i	$0.316607\pi$
$492$	−9.40448e149	−3.70913
$493$	−6.22212e147	−0.0219247
$494$	1.69591e148	0.0534019
$495$	2.57517e149	0.724799
$496$	1.54322e150	3.88325
$497$	−2.32212e149	−0.522522
$498$	−1.11123e150	−2.23652
$499$	−4.27209e149	−0.769236	−0.384618	−	0.923076i	$-0.625667\pi$
$499$	−4.27209e149	−0.769236	−0.384618	+	0.923076i	$0.625667\pi$
$500$	−1.10147e150	−1.77475
$501$	6.02255e149	0.868533
$502$	2.72151e150	3.51361
$503$	−8.56162e149	−0.989766	−0.494883	−	0.868960i	$-0.664789\pi$
$503$	−8.56162e149	−0.989766	−0.494883	+	0.868960i	$0.664789\pi$
$504$	−7.60196e149	−0.787102
$505$	−4.58419e149	−0.425197
$506$	−1.40651e150	−1.16893
$507$	1.37052e150	1.02081
$508$	−2.23184e150	−1.49014
$509$	1.41265e150	0.845661	0.422831	−	0.906209i	$-0.361036\pi$
$509$	1.41265e150	0.845661	0.422831	+	0.906209i	$0.361036\pi$
$510$	−5.48826e149	−0.294639
$511$	−6.83724e149	−0.329246
$512$	4.94333e150	2.13568
$513$	−1.46927e149	−0.0569624
$514$	−1.03417e151	−3.59863
$515$	−7.50899e150	−2.34574
$516$	2.10334e151	5.89999
$517$	4.31895e150	1.08806
$518$	−4.82335e150	−1.09156
$519$	5.99222e150	1.21843
$520$	−7.97943e150	−1.45810
$521$	6.38458e150	1.04867	0.524335	−	0.851512i	$-0.324314\pi$
$521$	6.38458e150	1.04867	0.524335	+	0.851512i	$0.324314\pi$
$522$	−9.87774e149	−0.145863
$523$	4.13536e150	0.549123	0.274562	−	0.961569i	$-0.411467\pi$
$523$	4.13536e150	0.549123	0.274562	+	0.961569i	$0.411467\pi$
$524$	5.99165e150	0.715583
$525$	3.20198e150	0.344015
$526$	−3.08079e150	−0.297820
$527$	1.27083e150	0.110560
$528$	−9.13895e151	−7.15671
$529$	−1.22085e151	−0.860745
$530$	5.04871e151	3.20531
$531$	6.90220e150	0.394677
$532$	2.59684e150	0.133767
$533$	−8.90231e150	−0.413183
$534$	4.00890e151	1.67682
$535$	−2.42800e151	−0.915407
$536$	5.30958e151	1.80474
$537$	1.81312e151	0.555716
$538$	−9.90296e151	−2.73746
$539$	−3.90233e151	−0.973077
$540$	1.08817e152	2.44818
$541$	3.00694e151	0.610487	0.305244	−	0.952274i	$-0.401262\pi$
$541$	3.00694e151	0.610487	0.305244	+	0.952274i	$0.401262\pi$
$542$	1.63851e152	3.00254
$543$	−4.94732e151	−0.818427
$544$	2.83242e151	0.423077
$545$	−6.33143e151	−0.854075
$546$	−4.19607e151	−0.511271
$547$	−7.46503e151	−0.821741	−0.410871	−	0.911694i	$-0.634775\pi$
$547$	−7.46503e151	−0.821741	−0.410871	+	0.911694i	$0.634775\pi$
$548$	−4.07148e152	−4.04978
$549$	5.25506e150	0.0472403
$550$	1.79363e152	1.45748
$551$	2.14363e150	0.0157484
$552$	2.21525e152	1.47165
$553$	8.54736e151	0.513556
$554$	1.57022e152	0.853433
$555$	−2.57342e152	−1.26547
$556$	2.63035e152	1.17048
$557$	−1.84620e152	−0.743561	−0.371780	−	0.928321i	$-0.621253\pi$
$557$	−1.84620e152	−0.743561	−0.371780	+	0.928321i	$0.621253\pi$
$558$	2.01746e152	0.735543
$559$	1.99103e152	0.657238
$560$	−9.66022e152	−2.88769
$561$	−7.52583e151	−0.203758
$562$	−5.41905e152	−1.32910
$563$	5.85179e152	1.30039	0.650193	−	0.759769i	$-0.274688\pi$
$563$	5.85179e152	1.30039	0.650193	+	0.759769i	$0.274688\pi$
$564$	−1.07074e153	−2.15623
$565$	−2.01304e152	−0.367420
$566$	1.19185e153	1.97201
$567$	5.19241e152	0.778950
$568$	2.04871e153	2.78707
$569$	1.21350e153	1.49730	0.748650	−	0.662966i	$-0.230703\pi$
$569$	1.21350e153	1.49730	0.748650	+	0.662966i	$0.230703\pi$
$570$	1.89081e152	0.211637
$571$	1.18098e153	1.19933	0.599663	−	0.800253i	$-0.295301\pi$
$571$	1.18098e153	1.19933	0.599663	+	0.800253i	$0.295301\pi$
$572$	−1.72234e153	−1.58722
$573$	−2.65243e153	−2.21852
$574$	−1.86031e153	−1.41246
$575$	−2.51880e152	−0.173631
$576$	2.26591e153	1.41839
$577$	1.10924e153	0.630618	0.315309	−	0.948989i	$-0.397892\pi$
$577$	1.10924e153	0.630618	0.315309	+	0.948989i	$0.397892\pi$
$578$	−3.70248e153	−1.91205
$579$	2.05478e153	0.964061
$580$	−1.58762e153	−0.676850
$581$	−1.61069e153	−0.624075
$582$	−7.67292e153	−2.70231
$583$	6.92309e153	2.21664
$584$	6.03222e153	1.75616
$585$	−6.04341e152	−0.160004
$586$	−1.20997e154	−2.91379
$587$	−4.53106e153	−0.992625	−0.496312	−	0.868144i	$-0.665313\pi$
$587$	−4.53106e153	−0.992625	−0.496312	+	0.868144i	$0.665313\pi$
$588$	9.67457e153	1.92837
$589$	−4.37823e152	−0.0794145
$590$	1.51396e154	2.49936
$591$	−5.12296e153	−0.769867
$592$	2.46534e154	3.37305
$593$	−7.40016e153	−0.921946	−0.460973	−	0.887414i	$-0.652500\pi$
$593$	−7.40016e153	−0.921946	−0.460973	+	0.887414i	$0.652500\pi$
$594$	2.03637e154	2.31052
$595$	−7.95509e152	−0.0822154
$596$	−4.20816e154	−3.96209
$597$	−1.57793e154	−1.35367
$598$	3.30079e153	0.258049
$599$	5.59902e153	0.398955	0.199477	−	0.979902i	$-0.436076\pi$
$599$	5.59902e153	0.398955	0.199477	+	0.979902i	$0.436076\pi$
$600$	−2.82498e154	−1.83493
$601$	1.96397e154	1.16306	0.581529	−	0.813526i	$-0.302455\pi$
$601$	1.96397e154	1.16306	0.581529	+	0.813526i	$0.302455\pi$
$602$	4.16064e154	2.24675
$603$	4.02134e153	0.198043
$604$	−9.76697e154	−4.38743
$605$	4.79176e154	1.96368
$606$	2.12681e154	0.795241
$607$	−2.94376e153	−0.100445	−0.0502227	−	0.998738i	$-0.515993\pi$
$607$	−2.94376e153	−0.100445	−0.0502227	+	0.998738i	$0.515993\pi$
$608$	−9.75821e153	−0.303894
$609$	−5.30385e153	−0.150776
$610$	1.15267e154	0.299157
$611$	−1.01357e154	−0.240196
$612$	5.03662e153	0.109002
$613$	8.46513e154	1.67331	0.836657	−	0.547727i	$-0.184507\pi$
$613$	8.46513e154	1.67331	0.836657	+	0.547727i	$0.184507\pi$
$614$	3.08463e154	0.557004
$615$	−9.92538e154	−1.63749
$616$	−2.28651e155	−3.44702
$617$	−7.28974e154	−1.00435	−0.502175	−	0.864766i	$-0.667467\pi$
$617$	−7.28974e154	−1.00435	−0.502175	+	0.864766i	$0.667467\pi$
$618$	3.48376e155	4.38721
$619$	−1.70911e155	−1.96761	−0.983806	−	0.179237i	$-0.942637\pi$
$619$	−1.70911e155	−1.96761	−0.983806	+	0.179237i	$0.942637\pi$
$620$	3.24261e155	3.41315
$621$	−2.85968e154	−0.275254
$622$	−1.56360e155	−1.37644
$623$	5.81080e154	0.467896
$624$	2.14473e155	1.57989
$625$	−1.85282e155	−1.24880
$626$	1.00508e155	0.619906
$627$	2.59279e154	0.146359
$628$	8.75269e154	0.452253
$629$	2.03019e154	0.0960340
$630$	−1.26289e155	−0.546970
$631$	2.06431e155	0.818740	0.409370	−	0.912369i	$-0.365749\pi$
$631$	2.06431e155	0.818740	0.409370	+	0.912369i	$0.365749\pi$
$632$	−7.54099e155	−2.73924
$633$	−1.60964e154	−0.0535579
$634$	2.85278e155	0.869589
$635$	−2.35546e155	−0.657861
$636$	−1.71636e156	−4.39277
$637$	9.15797e154	0.214813
$638$	−2.97102e155	−0.638789
$639$	1.55164e155	0.305839
$640$	2.33437e156	4.21872
$641$	−3.70625e155	−0.614206	−0.307103	−	0.951676i	$-0.599360\pi$
$641$	−3.70625e155	−0.614206	−0.307103	+	0.951676i	$0.599360\pi$
$642$	1.12646e156	1.71207
$643$	3.49915e155	0.487814	0.243907	−	0.969799i	$-0.421571\pi$
$643$	3.49915e155	0.487814	0.243907	+	0.969799i	$0.421571\pi$
$644$	5.05429e155	0.646390
$645$	2.21984e156	2.60470
$646$	−1.49167e154	−0.0160608
$647$	−8.30472e155	−0.820611	−0.410306	−	0.911948i	$-0.634578\pi$
$647$	−8.30472e155	−0.820611	−0.410306	+	0.911948i	$0.634578\pi$
$648$	−4.58105e156	−4.15482
$649$	2.07604e156	1.72844
$650$	−4.20929e155	−0.321749
$651$	1.08328e156	0.760317
$652$	−5.35825e156	−3.45367
$653$	−1.84053e156	−1.08958	−0.544792	−	0.838571i	$-0.683391\pi$
$653$	−1.84053e156	−1.08958	−0.544792	+	0.838571i	$0.683391\pi$
$654$	2.93744e156	1.59737
$655$	6.32351e155	0.315912
$656$	9.50854e156	4.36466
$657$	4.56865e155	0.192712
$658$	−2.11805e156	−0.821105
$659$	−4.97551e155	−0.177295	−0.0886477	−	0.996063i	$-0.528255\pi$
$659$	−4.97551e155	−0.177295	−0.0886477	+	0.996063i	$0.528255\pi$
$660$	−1.92027e157	−6.29033
$661$	−1.88696e156	−0.568305	−0.284153	−	0.958779i	$-0.591712\pi$
$661$	−1.88696e156	−0.568305	−0.284153	+	0.958779i	$0.591712\pi$
$662$	5.89491e156	1.63252
$663$	1.76616e155	0.0449810
$664$	1.42105e157	3.32874
$665$	2.74067e155	0.0590549
$666$	3.22296e156	0.638903
$667$	4.17220e155	0.0760995
$668$	−1.21231e157	−2.03479
$669$	−8.27845e156	−1.27879
$670$	8.82061e156	1.25414
$671$	1.58061e156	0.206883
$672$	2.41441e157	2.90949
$673$	−8.98860e156	−0.997370	−0.498685	−	0.866783i	$-0.666183\pi$
$673$	−8.98860e156	−0.997370	−0.498685	+	0.866783i	$0.666183\pi$
$674$	−1.05677e157	−1.07984
$675$	3.64677e156	0.343202
$676$	−2.75878e157	−2.39153
$677$	1.09573e157	0.875052	0.437526	−	0.899206i	$-0.355855\pi$
$677$	1.09573e157	0.875052	0.437526	+	0.899206i	$0.355855\pi$
$678$	9.33940e156	0.687181
$679$	−1.11217e157	−0.754047
$680$	7.01844e156	0.438527
$681$	9.52812e156	0.548710
$682$	6.06811e157	3.22122
$683$	1.57283e156	0.0769719	0.0384859	−	0.999259i	$-0.487747\pi$
$683$	1.57283e156	0.0769719	0.0384859	+	0.999259i	$0.487747\pi$
$684$	−1.73521e156	−0.0782957
$685$	−4.29699e157	−1.78788
$686$	5.09844e157	1.95636
$687$	1.10708e157	0.391814
$688$	−2.12661e158	−6.94273
$689$	−1.62471e157	−0.489339
$690$	3.68012e157	1.02267
$691$	5.20271e157	1.33413	0.667065	−	0.745000i	$-0.267550\pi$
$691$	5.20271e157	1.33413	0.667065	+	0.745000i	$0.267550\pi$
$692$	−1.20620e158	−2.85451
$693$	−1.73174e157	−0.378259
$694$	1.31937e158	2.66020
$695$	2.77604e157	0.516737
$696$	4.67937e157	0.804219
$697$	7.83018e156	0.124266
$698$	1.24471e158	1.82428
$699$	−7.10107e157	−0.961259
$700$	−6.44542e157	−0.805954
$701$	5.38723e157	0.622323	0.311161	−	0.950357i	$-0.399282\pi$
$701$	5.38723e157	0.622323	0.311161	+	0.950357i	$0.399282\pi$
$702$	−4.77896e157	−0.510062
$703$	−6.99436e156	−0.0689807
$704$	6.81538e158	6.21166
$705$	−1.13005e158	−0.951923
$706$	−3.68299e158	−2.86774
$707$	3.08276e157	0.221903
$708$	−5.14688e158	−3.42529
$709$	1.03664e158	0.637914	0.318957	−	0.947769i	$-0.396667\pi$
$709$	1.03664e158	0.637914	0.318957	+	0.947769i	$0.396667\pi$
$710$	3.40344e158	1.93678
$711$	−5.71135e157	−0.300591
$712$	−5.12663e158	−2.49570
$713$	−8.52146e157	−0.383747
$714$	3.69073e157	0.153766
$715$	−1.81773e158	−0.700720
$716$	−3.64971e158	−1.30192
$717$	3.23553e158	1.06815
$718$	6.75027e158	2.06260
$719$	−2.07012e158	−0.585520	−0.292760	−	0.956186i	$-0.594574\pi$
$719$	−2.07012e158	−0.585520	−0.292760	+	0.956186i	$0.594574\pi$
$720$	6.45496e158	1.69021
$721$	5.04962e158	1.22420
$722$	−8.56572e158	−1.92287
$723$	2.23843e158	0.465338
$724$	9.95870e158	1.91740
$725$	−5.32056e157	−0.0948850
$726$	−2.22312e159	−3.67265
$727$	−5.40917e158	−0.827887	−0.413943	−	0.910303i	$-0.635849\pi$
$727$	−5.40917e158	−0.827887	−0.413943	+	0.910303i	$0.635849\pi$
$728$	5.36598e158	0.760953
$729$	3.09986e158	0.407347
$730$	1.00211e159	1.22038
$731$	−1.75124e158	−0.197666
$732$	−3.91862e158	−0.409985
$733$	1.69454e159	1.64354	0.821770	−	0.569819i	$-0.192987\pi$
$733$	1.69454e159	1.64354	0.821770	+	0.569819i	$0.192987\pi$
$734$	−1.24127e159	−1.11618
$735$	1.02104e159	0.851327
$736$	−1.89926e159	−1.46848
$737$	1.20954e159	0.867307
$738$	1.24306e159	0.826729
$739$	−1.53257e158	−0.0945484	−0.0472742	−	0.998882i	$-0.515053\pi$
$739$	−1.53257e158	−0.0945484	−0.0472742	+	0.998882i	$0.515053\pi$
$740$	5.18016e159	2.96471
$741$	−6.08475e157	−0.0323096
$742$	−3.39514e159	−1.67279
$743$	−5.34682e158	−0.244465	−0.122232	−	0.992501i	$-0.539005\pi$
$743$	−5.34682e158	−0.244465	−0.122232	+	0.992501i	$0.539005\pi$
$744$	−9.55730e159	−4.05543
$745$	−4.44124e159	−1.74917
$746$	1.46418e159	0.535290
$747$	1.07626e159	0.365280
$748$	1.51491e159	0.477362
$749$	1.63278e159	0.477734
$750$	5.39326e159	1.46538
$751$	4.90914e157	0.0123876	0.00619382	−	0.999981i	$-0.498028\pi$
$751$	4.90914e157	0.0123876	0.00619382	+	0.999981i	$0.498028\pi$
$752$	1.08259e160	2.53732
$753$	−9.76450e159	−2.12583
$754$	6.97238e158	0.141017
$755$	−1.03079e160	−1.93694
$756$	−7.31771e159	−1.27766
$757$	5.97370e158	0.0969220	0.0484610	−	0.998825i	$-0.484568\pi$
$757$	5.97370e158	0.0969220	0.0484610	+	0.998825i	$0.484568\pi$
$758$	2.17263e160	3.27600
$759$	5.04640e159	0.707234
$760$	−2.41798e159	−0.314991
$761$	−9.53587e159	−1.15481	−0.577407	−	0.816457i	$-0.695935\pi$
$761$	−9.53587e159	−1.15481	−0.577407	+	0.816457i	$0.695935\pi$
$762$	1.09281e160	1.23039
$763$	4.25775e159	0.445726
$764$	5.33921e160	5.19751
$765$	5.31559e158	0.0481218
$766$	−3.49057e160	−2.93900
$767$	−4.87205e159	−0.381565
$768$	−4.66791e160	−3.40075
$769$	−1.17526e158	−0.00796570	−0.00398285	−	0.999992i	$-0.501268\pi$
$769$	−1.17526e158	−0.00796570	−0.00398285	+	0.999992i	$0.501268\pi$
$770$	−3.79850e160	−2.39539
$771$	3.71048e160	2.17727
$772$	−4.13616e160	−2.25859
$773$	−1.91699e160	−0.974224	−0.487112	−	0.873340i	$-0.661950\pi$
$773$	−1.91699e160	−0.974224	−0.487112	+	0.873340i	$0.661950\pi$
$774$	−2.78014e160	−1.31505
$775$	1.08669e160	0.478477
$776$	9.81221e160	4.02199
$777$	1.73057e160	0.660423
$778$	−1.74843e160	−0.621271
$779$	−2.69764e159	−0.0892597
$780$	4.50649e160	1.38863
$781$	4.66700e160	1.33939
$782$	−2.90327e159	−0.0776090
$783$	−6.04061e159	−0.150419
$784$	−9.78161e160	−2.26918
$785$	9.23748e159	0.199658
$786$	−2.93377e160	−0.590846
$787$	−1.16281e160	−0.218228	−0.109114	−	0.994029i	$-0.534801\pi$
$787$	−1.16281e160	−0.218228	−0.109114	+	0.994029i	$0.534801\pi$
$788$	1.03123e161	1.80363
$789$	1.10536e160	0.180189
$790$	−1.25276e161	−1.90354
$791$	1.35372e160	0.191750
$792$	1.52785e161	2.01759
$793$	−3.70938e159	−0.0456709
$794$	−1.16460e161	−1.33703
$795$	−1.81143e161	−1.93930
$796$	3.17629e161	3.17136
$797$	−6.52210e160	−0.607366	−0.303683	−	0.952773i	$-0.598216\pi$
$797$	−6.52210e160	−0.607366	−0.303683	+	0.952773i	$0.598216\pi$
$798$	−1.27152e160	−0.110450
$799$	8.91503e159	0.0722398
$800$	2.42202e161	1.83098
$801$	−3.88278e160	−0.273866
$802$	−3.36776e161	−2.21648
$803$	1.37415e161	0.843961
$804$	−2.99866e161	−1.71876
$805$	5.33424e160	0.285365
$806$	−1.42406e161	−0.711107
$807$	3.55308e161	1.65624
$808$	−2.71979e161	−1.18360
$809$	3.45708e161	1.40465	0.702323	−	0.711859i	$-0.252146\pi$
$809$	3.45708e161	1.40465	0.702323	+	0.711859i	$0.252146\pi$
$810$	−7.61034e161	−2.88726
$811$	1.71091e161	0.606134	0.303067	−	0.952969i	$-0.401989\pi$
$811$	1.71091e161	0.606134	0.303067	+	0.952969i	$0.401989\pi$
$812$	1.06764e161	0.353235
$813$	−5.87881e161	−1.81662
$814$	9.69399e161	2.79800
$815$	−5.65503e161	−1.52471
$816$	−1.88643e161	−0.475158
$817$	6.03336e160	0.141983
$818$	8.29746e161	1.82447
$819$	4.06406e160	0.0835032
$820$	1.99793e162	3.83628
$821$	7.53905e161	1.35292	0.676458	−	0.736481i	$-0.263514\pi$
$821$	7.53905e161	1.35292	0.676458	+	0.736481i	$0.263514\pi$
$822$	1.99357e162	3.34385
$823$	−3.89102e161	−0.610060	−0.305030	−	0.952343i	$-0.598667\pi$
$823$	−3.89102e161	−0.610060	−0.305030	+	0.952343i	$0.598667\pi$
$824$	−4.45507e162	−6.52972
$825$	−6.43537e161	−0.881818
$826$	−1.01811e162	−1.30437
$827$	−4.48123e161	−0.536836	−0.268418	−	0.963302i	$-0.586501\pi$
$827$	−4.48123e161	−0.536836	−0.268418	+	0.963302i	$0.586501\pi$
$828$	−3.37728e161	−0.378340
$829$	1.17405e162	1.23001	0.615007	−	0.788522i	$-0.289153\pi$
$829$	1.17405e162	1.23001	0.615007	+	0.788522i	$0.289153\pi$
$830$	2.36073e162	2.31320
$831$	−5.63380e161	−0.516350
$832$	−1.59943e162	−1.37126
$833$	−8.05506e160	−0.0646057
$834$	−1.28793e162	−0.966447
$835$	−1.27945e162	−0.898308
$836$	−5.21914e161	−0.342887
$837$	1.23376e162	0.758519
$838$	−3.70622e159	−0.00213249
$839$	6.62975e160	0.0357033	0.0178516	−	0.999841i	$-0.494317\pi$
$839$	6.62975e160	0.0357033	0.0178516	+	0.999841i	$0.494317\pi$
$840$	5.98265e162	3.01574
$841$	−2.03110e162	−0.958414
$842$	−1.73237e162	−0.765281
$843$	1.94430e162	0.804142
$844$	3.24013e161	0.125475
$845$	−2.91159e162	−1.05580
$846$	1.41528e162	0.480603
$847$	−3.22235e162	−1.02481
$848$	1.73535e163	5.16913
$849$	−4.27623e162	−1.19312
$850$	3.70236e161	0.0967671
$851$	−1.36133e162	−0.333328
$852$	−1.15703e163	−2.65429
$853$	5.64343e162	1.21303	0.606515	−	0.795072i	$-0.292567\pi$
$853$	5.64343e162	1.21303	0.606515	+	0.795072i	$0.292567\pi$
$854$	−7.75145e161	−0.156125
$855$	−1.83132e161	−0.0345656
$856$	−1.44053e163	−2.54817
$857$	9.25739e162	1.53480	0.767402	−	0.641166i	$-0.221549\pi$
$857$	9.25739e162	1.53480	0.767402	+	0.641166i	$0.221549\pi$
$858$	8.43330e162	1.31055
$859$	3.94546e162	0.574747	0.287374	−	0.957819i	$-0.407218\pi$
$859$	3.94546e162	0.574747	0.287374	+	0.957819i	$0.407218\pi$
$860$	−4.46843e163	−6.10226
$861$	6.67459e162	0.854574
$862$	1.41069e163	1.69348
$863$	1.46366e163	1.64756	0.823780	−	0.566909i	$-0.191861\pi$
$863$	1.46366e163	1.64756	0.823780	+	0.566909i	$0.191861\pi$
$864$	2.74980e163	2.90261
$865$	−1.27301e163	−1.26020
$866$	2.56786e162	0.238413
$867$	1.32841e163	1.15684
$868$	−2.18058e163	−1.78126
$869$	−1.71785e163	−1.31640
$870$	7.77366e162	0.558865
$871$	−2.83854e162	−0.191464
$872$	−3.75643e163	−2.37745
$873$	7.43151e162	0.441354
$874$	1.00023e162	0.0557461
$875$	7.81738e162	0.408898
$876$	−3.40677e163	−1.67250
$877$	−2.76429e163	−1.27382	−0.636908	−	0.770940i	$-0.719787\pi$
$877$	−2.76429e163	−1.27382	−0.636908	+	0.770940i	$0.719787\pi$
$878$	−3.64090e163	−1.57494
$879$	4.34126e163	1.76292
$880$	1.94152e164	7.40206
$881$	3.82698e163	1.36991	0.684957	−	0.728583i	$-0.259821\pi$
$881$	3.82698e163	1.36991	0.684957	+	0.728583i	$0.259821\pi$
$882$	−1.27876e163	−0.429815
$883$	1.62378e163	0.512516	0.256258	−	0.966608i	$-0.417510\pi$
$883$	1.62378e163	0.512516	0.256258	+	0.966608i	$0.417510\pi$
$884$	−3.55519e162	−0.105381
$885$	−5.43195e163	−1.51218
$886$	3.57137e163	0.933822
$887$	−3.49238e163	−0.857750	−0.428875	−	0.903364i	$-0.641090\pi$
$887$	−3.49238e163	−0.857750	−0.428875	+	0.903364i	$0.641090\pi$
$888$	−1.52681e164	−3.52261
$889$	1.58399e163	0.343325
$890$	−8.51668e163	−1.73430
$891$	−1.04357e164	−1.99669
$892$	1.66641e164	2.99593
$893$	−3.07139e162	−0.0518894
$894$	2.06050e164	3.27144
$895$	−3.85186e163	−0.574767
$896$	−1.56981e164	−2.20167
$897$	−1.18429e163	−0.156127
$898$	−2.75762e164	−3.41741
$899$	−1.80002e163	−0.209708
$900$	4.30683e163	0.471736
$901$	1.42904e163	0.147170
$902$	3.73886e164	3.62056
$903$	−1.49279e164	−1.35934
$904$	−1.19433e164	−1.02277
$905$	1.05103e164	0.846484
$906$	4.78233e164	3.62263
$907$	6.43412e163	0.458443	0.229221	−	0.973374i	$-0.426382\pi$
$907$	6.43412e163	0.458443	0.229221	+	0.973374i	$0.426382\pi$
$908$	−1.91796e164	−1.28551
$909$	−2.05990e163	−0.129883
$910$	8.91431e163	0.528799
$911$	4.13005e162	0.0230508	0.0115254	−	0.999934i	$-0.496331\pi$
$911$	4.13005e162	0.0230508	0.0115254	+	0.999934i	$0.496331\pi$
$912$	6.49911e163	0.341303
$913$	3.23718e164	1.59970
$914$	−6.19879e164	−2.88266
$915$	−4.13567e163	−0.180998
$916$	−2.22849e164	−0.917936
$917$	−4.25242e163	−0.164869
$918$	4.20341e163	0.153403
$919$	2.63394e164	0.904890	0.452445	−	0.891792i	$-0.350552\pi$
$919$	2.63394e164	0.904890	0.452445	+	0.891792i	$0.350552\pi$
$920$	−4.70618e164	−1.52210
$921$	−1.10673e164	−0.337003
$922$	−3.85597e164	−1.10552
$923$	−1.09525e164	−0.295678
$924$	1.29134e165	3.28281
$925$	1.73602e164	0.415612
$926$	5.43710e164	1.22591
$927$	−3.37416e164	−0.716540
$928$	−4.01189e164	−0.802484
$929$	−3.93844e164	−0.742083	−0.371042	−	0.928616i	$-0.620999\pi$
$929$	−3.93844e164	−0.742083	−0.371042	+	0.928616i	$0.620999\pi$
$930$	−1.58772e165	−2.81819
$931$	2.77511e163	0.0464059
$932$	1.42941e165	2.25202
$933$	5.61002e164	0.832786
$934$	−3.55813e164	−0.497703
$935$	1.59882e164	0.210744
$936$	−3.58555e164	−0.445396
$937$	−8.32831e164	−0.975011	−0.487505	−	0.873120i	$-0.662093\pi$
$937$	−8.32831e164	−0.975011	−0.487505	+	0.873120i	$0.662093\pi$
$938$	−5.93166e164	−0.654514
$939$	−3.60613e164	−0.375060
$940$	2.27473e165	2.23015
$941$	7.14440e164	0.660301	0.330150	−	0.943928i	$-0.392901\pi$
$941$	7.14440e164	0.660301	0.330150	+	0.943928i	$0.392901\pi$
$942$	−4.28569e164	−0.373419
$943$	−5.25048e164	−0.431321
$944$	5.20382e165	4.03067
$945$	−7.72303e164	−0.564056
$946$	−8.36207e165	−5.75912
$947$	2.09283e165	1.35929	0.679643	−	0.733543i	$-0.262135\pi$
$947$	2.09283e165	1.35929	0.679643	+	0.733543i	$0.262135\pi$
$948$	4.25887e165	2.60875
$949$	−3.22486e164	−0.186310
$950$	−1.27553e164	−0.0695073
$951$	−1.02355e165	−0.526125
$952$	−4.71974e164	−0.228859
$953$	4.80526e164	0.219817	0.109908	−	0.993942i	$-0.464944\pi$
$953$	4.80526e164	0.219817	0.109908	+	0.993942i	$0.464944\pi$
$954$	2.26863e165	0.979106
$955$	5.63494e165	2.29457
$956$	−6.51295e165	−2.50245
$957$	1.06597e165	0.386485
$958$	1.31922e165	0.451370
$959$	2.88963e165	0.933060
$960$	−1.78324e166	−5.43446
$961$	1.99880e164	0.0574937
$962$	−2.27499e165	−0.617678
$963$	−1.09102e165	−0.279624
$964$	−4.50584e165	−1.09019
$965$	−4.36526e165	−0.997112
$966$	−2.47480e165	−0.533715
$967$	−1.55505e165	−0.316648	−0.158324	−	0.987387i	$-0.550609\pi$
$967$	−1.55505e165	−0.316648	−0.158324	+	0.987387i	$0.550609\pi$
$968$	2.84294e166	5.46621
$969$	5.35195e163	0.00971722
$970$	1.63007e166	2.79495
$971$	−2.50410e165	−0.405494	−0.202747	−	0.979231i	$-0.564987\pi$
$971$	−2.50410e165	−0.405494	−0.202747	+	0.979231i	$0.564987\pi$
$972$	1.26482e166	1.93442
$973$	−1.86683e165	−0.269675
$974$	−1.47831e166	−2.01718
$975$	1.51025e165	0.194667
$976$	3.96198e165	0.482444
$977$	−7.45243e165	−0.857333	−0.428667	−	0.903463i	$-0.641016\pi$
$977$	−7.45243e165	−0.857333	−0.428667	+	0.903463i	$0.641016\pi$
$978$	2.62363e166	2.85165
$979$	−1.16786e166	−1.19936
$980$	−2.05530e166	−1.99448
$981$	−2.84503e165	−0.260889
$982$	2.43219e166	2.10771
$983$	−2.10138e166	−1.72101	−0.860506	−	0.509439i	$-0.829853\pi$
$983$	−2.10138e166	−1.72101	−0.860506	+	0.509439i	$0.829853\pi$
$984$	−5.88872e166	−4.55819
$985$	1.08834e166	0.796260
$986$	−6.13268e164	−0.0424113
$987$	7.59933e165	0.496791
$988$	1.22483e165	0.0756946
$989$	1.17429e166	0.686088
$990$	2.53816e166	1.40206
$991$	−1.91766e166	−1.00157	−0.500787	−	0.865571i	$-0.666956\pi$
$991$	−1.91766e166	−1.00157	−0.500787	+	0.865571i	$0.666956\pi$
$992$	8.19403e166	4.04669
$993$	−2.11503e166	−0.987720
$994$	−2.28874e166	−1.01077
$995$	3.35222e166	1.40008
$996$	−8.02555e166	−3.17016
$997$	8.17556e165	0.305447	0.152724	−	0.988269i	$-0.451196\pi$
$997$	8.17556e165	0.305447	0.152724	+	0.988269i	$0.451196\pi$
$998$	−4.21068e166	−1.48801
$999$	1.97096e166	0.658861

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.112.a.a.1.9	✓	9

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

\(f(q)\)	\(=\)	\(q+9.85626e16 q^{2} -3.53632e26 q^{3} +7.11844e33 q^{4} +7.51271e38 q^{5} -3.48549e43 q^{6} -5.05213e46 q^{7} +4.45728e50 q^{8} +3.37583e52 q^{9} +O(q^{10})\)	\(q+9.85626e16 q^{2} -3.53632e26 q^{3} +7.11844e33 q^{4} +7.51271e38 q^{5} -3.48549e43 q^{6} -5.05213e46 q^{7} +4.45728e50 q^{8} +3.37583e52 q^{9} +7.40472e55 q^{10} +1.01538e58 q^{11} -2.51731e60 q^{12} -2.38289e61 q^{13} -4.97951e63 q^{14} -2.65674e65 q^{15} +2.54516e67 q^{16} +2.09592e67 q^{17} +3.32731e69 q^{18} -7.22081e69 q^{19} +5.34788e72 q^{20} +1.78660e73 q^{21} +1.00078e75 q^{22} -1.40540e75 q^{23} -1.57624e77 q^{24} +1.79222e77 q^{25} -2.34864e78 q^{26} +2.03477e79 q^{27} -3.59633e80 q^{28} -2.96869e80 q^{29} -2.61855e82 q^{30} +6.06335e82 q^{31} +1.35140e84 q^{32} -3.59071e84 q^{33} +2.06579e84 q^{34} -3.79552e85 q^{35} +2.40306e86 q^{36} +9.68639e86 q^{37} -7.11702e86 q^{38} +8.42668e87 q^{39} +3.34863e89 q^{40} +3.73593e89 q^{41} +1.76092e90 q^{42} -8.35551e90 q^{43} +7.22792e91 q^{44} +2.53617e91 q^{45} -1.38520e92 q^{46} +4.25353e92 q^{47} -9.00052e93 q^{48} -3.84322e93 q^{49} +1.76646e94 q^{50} -7.41184e93 q^{51} -1.69625e95 q^{52} +6.81823e95 q^{53} +2.00553e96 q^{54} +7.62826e96 q^{55} -2.25188e97 q^{56} +2.55351e96 q^{57} -2.92602e97 q^{58} +2.04459e98 q^{59} -1.89118e99 q^{60} +1.55667e98 q^{61} +5.97620e99 q^{62} -1.70551e99 q^{63} +6.71214e100 q^{64} -1.79020e100 q^{65} -3.53910e101 q^{66} +1.19121e101 q^{67} +1.49196e101 q^{68} +4.96996e101 q^{69} -3.74096e102 q^{70} +4.59631e102 q^{71} +1.50470e103 q^{72} +1.35334e103 q^{73} +9.54716e103 q^{74} -6.33789e103 q^{75} -5.14009e103 q^{76} -5.12983e104 q^{77} +8.30556e104 q^{78} -1.69183e105 q^{79} +1.91211e106 q^{80} -1.02777e106 q^{81} +3.68223e106 q^{82} +3.18814e106 q^{83} +1.27178e107 q^{84} +1.57460e106 q^{85} -8.23541e107 q^{86} +1.04982e107 q^{87} +4.52584e108 q^{88} -1.15017e108 q^{89} +2.49971e108 q^{90} +1.20387e108 q^{91} -1.00043e109 q^{92} -2.14420e109 q^{93} +4.19239e109 q^{94} -5.42479e108 q^{95} -4.77900e110 q^{96} +2.20139e110 q^{97} -3.78797e110 q^{98} +3.42775e110 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 73\!\cdots\!76 q^{2}+ \cdots + 44\!\cdots\!13 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more