LMFDB - Embedded newform 1.112.a.a.1.2

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			1.2
Root			$-1.03033e15$ 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)

$f(q)$	$=$	$q-7.33726e16 q^{2} -2.81001e26 q^{3} +2.78739e33 q^{4} +1.03167e38 q^{5} +2.06178e43 q^{6} -1.16535e47 q^{7} -1.40317e49 q^{8} -1.23360e52 q^{9} +O(q^{10})$	\(q-7.33726e16 q^{2} -2.81001e26 q^{3} +2.78739e33 q^{4} +1.03167e38 q^{5} +2.06178e43 q^{6} -1.16535e47 q^{7} -1.40317e49 q^{8} -1.23360e52 q^{9} -7.56964e54 q^{10} -4.47415e57 q^{11} -7.83259e59 q^{12} +4.56429e61 q^{13} +8.55050e63 q^{14} -2.89901e64 q^{15} -6.20693e66 q^{16} +1.57085e68 q^{17} +9.05124e68 q^{18} +5.23772e70 q^{19} +2.87567e71 q^{20} +3.27466e73 q^{21} +3.28280e74 q^{22} -4.90343e75 q^{23} +3.94291e75 q^{24} -3.74543e77 q^{25} -3.34893e78 q^{26} +2.91211e79 q^{27} -3.24829e80 q^{28} -1.78390e81 q^{29} +2.12708e81 q^{30} -1.77658e82 q^{31} +4.91847e83 q^{32} +1.25724e84 q^{33} -1.15257e85 q^{34} -1.20226e85 q^{35} -3.43852e85 q^{36} -8.04663e86 q^{37} -3.84305e87 q^{38} -1.28257e88 q^{39} -1.44761e87 q^{40} -4.83612e89 q^{41} -2.40270e90 q^{42} -6.78462e90 q^{43} -1.24712e91 q^{44} -1.27267e90 q^{45} +3.59777e92 q^{46} -8.63480e92 q^{47} +1.74415e93 q^{48} +7.18488e93 q^{49} +2.74812e94 q^{50} -4.41409e94 q^{51} +1.27224e95 q^{52} -6.44145e95 q^{53} -2.13669e96 q^{54} -4.61585e95 q^{55} +1.63519e96 q^{56} -1.47180e97 q^{57} +1.30889e98 q^{58} +2.31564e98 q^{59} -8.08066e97 q^{60} -1.67961e99 q^{61} +1.30352e99 q^{62} +1.43758e99 q^{63} -1.99740e100 q^{64} +4.70885e99 q^{65} -9.22469e100 q^{66} +2.49001e101 q^{67} +4.37856e101 q^{68} +1.37787e102 q^{69} +8.82131e101 q^{70} -8.70628e102 q^{71} +1.73095e101 q^{72} -2.93019e103 q^{73} +5.90402e103 q^{74} +1.05247e104 q^{75} +1.45995e104 q^{76} +5.21396e104 q^{77} +9.41054e104 q^{78} +2.11147e105 q^{79} -6.40352e104 q^{80} -7.05682e105 q^{81} +3.54839e106 q^{82} +8.08186e105 q^{83} +9.12774e106 q^{84} +1.62060e106 q^{85} +4.97805e107 q^{86} +5.01277e107 q^{87} +6.27797e106 q^{88} +8.02651e107 q^{89} +9.33791e106 q^{90} -5.31901e108 q^{91} -1.36678e109 q^{92} +4.99221e108 q^{93} +6.33557e109 q^{94} +5.40361e108 q^{95} -1.38209e110 q^{96} -2.46491e110 q^{97} -5.27173e110 q^{98} +5.51931e109 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−7.33726e16	−1.44002	−0.720011	−	0.693963i	$-0.755863\pi$
$2$	−7.33726e16	−1.44002	−0.720011	+	0.693963i	$0.755863\pi$
$3$	−2.81001e26	−0.929990	−0.464995	−	0.885313i	$-0.653944\pi$
$3$	−2.81001e26	−0.929990	−0.464995	+	0.885313i	$0.653944\pi$
$4$	2.78739e33	1.07366
$5$	1.03167e38	0.166229	0.0831144	−	0.996540i	$-0.473513\pi$
$5$	1.03167e38	0.166229	0.0831144	+	0.996540i	$0.473513\pi$
$6$	2.06178e43	1.33921
$7$	−1.16535e47	−1.45719	−0.728596	−	0.684944i	$-0.759827\pi$
$7$	−1.16535e47	−1.45719	−0.728596	+	0.684944i	$0.759827\pi$
$8$	−1.40317e49	−0.106075
$9$	−1.23360e52	−0.135119
$10$	−7.56964e54	−0.239373
$11$	−4.47415e57	−0.713536	−0.356768	−	0.934193i	$-0.616121\pi$
$11$	−4.47415e57	−0.713536	−0.356768	+	0.934193i	$0.616121\pi$
$12$	−7.83259e59	−0.998495
$13$	4.56429e61	0.684726	0.342363	−	0.939568i	$-0.388773\pi$
$13$	4.56429e61	0.684726	0.342363	+	0.939568i	$0.388773\pi$
$14$	8.55050e63	2.09839
$15$	−2.89901e64	−0.154591
$16$	−6.20693e66	−0.920911
$17$	1.57085e68	0.805784	0.402892	−	0.915248i	$-0.368005\pi$
$17$	1.57085e68	0.805784	0.402892	+	0.915248i	$0.368005\pi$
$18$	9.05124e68	0.194574
$19$	5.23772e70	0.560167	0.280083	−	0.959976i	$-0.409638\pi$
$19$	5.23772e70	0.560167	0.280083	+	0.959976i	$0.409638\pi$
$20$	2.87567e71	0.178474
$21$	3.27466e73	1.35517
$22$	3.28280e74	1.02751
$23$	−4.90343e75	−1.30198	−0.650991	−	0.759085i	$-0.725647\pi$
$23$	−4.90343e75	−1.30198	−0.650991	+	0.759085i	$0.725647\pi$
$24$	3.94291e75	0.0986491
$25$	−3.74543e77	−0.972368
$26$	−3.34893e78	−0.986020
$27$	2.91211e79	1.05565
$28$	−3.24829e80	−1.56453
$29$	−1.78390e81	−1.22541	−0.612704	−	0.790312i	$-0.709918\pi$
$29$	−1.78390e81	−1.22541	−0.612704	+	0.790312i	$0.709918\pi$
$30$	2.12708e81	0.222615
$31$	−1.77658e82	−0.301308	−0.150654	−	0.988587i	$-0.548138\pi$
$31$	−1.77658e82	−0.301308	−0.150654	+	0.988587i	$0.548138\pi$
$32$	4.91847e83	1.43221
$33$	1.25724e84	0.663582
$34$	−1.15257e85	−1.16035
$35$	−1.20226e85	−0.242227
$36$	−3.43852e85	−0.145072
$37$	−8.04663e86	−0.742025	−0.371012	−	0.928628i	$-0.620989\pi$
$37$	−8.04663e86	−0.742025	−0.371012	+	0.928628i	$0.620989\pi$
$38$	−3.84305e87	−0.806652
$39$	−1.28257e88	−0.636788
$40$	−1.44761e87	−0.0176328
$41$	−4.83612e89	−1.49621	−0.748106	−	0.663579i	$-0.769037\pi$
$41$	−4.83612e89	−1.49621	−0.748106	+	0.663579i	$0.769037\pi$
$42$	−2.40270e90	−1.95148
$43$	−6.78462e90	−1.49289	−0.746443	−	0.665450i	$-0.768240\pi$
$43$	−6.78462e90	−1.49289	−0.746443	+	0.665450i	$0.768240\pi$
$44$	−1.24712e91	−0.766097
$45$	−1.27267e90	−0.0224606
$46$	3.59777e92	1.87488
$47$	−8.63480e92	−1.36402	−0.682011	−	0.731342i	$-0.738894\pi$
$47$	−8.63480e92	−1.36402	−0.682011	+	0.731342i	$0.738894\pi$
$48$	1.74415e93	0.856438
$49$	7.18488e93	1.12341
$50$	2.74812e94	1.40023
$51$	−4.41409e94	−0.749371
$52$	1.27224e95	0.735165
$53$	−6.44145e95	−1.29322	−0.646611	−	0.762820i	$-0.723814\pi$
$53$	−6.44145e95	−1.29322	−0.646611	+	0.762820i	$0.723814\pi$
$54$	−2.13669e96	−1.52016
$55$	−4.61585e95	−0.118610
$56$	1.63519e96	0.154572
$57$	−1.47180e97	−0.520949
$58$	1.30889e98	1.76461
$59$	2.31564e98	1.20888	0.604442	−	0.796649i	$-0.293396\pi$
$59$	2.31564e98	1.20888	0.604442	+	0.796649i	$0.293396\pi$
$60$	−8.08066e97	−0.165979
$61$	−1.67961e99	−1.37848	−0.689241	−	0.724532i	$-0.742056\pi$
$61$	−1.67961e99	−1.37848	−0.689241	+	0.724532i	$0.742056\pi$
$62$	1.30352e99	0.433891
$63$	1.43758e99	0.196894
$64$	−1.99740e100	−1.14150
$65$	4.70885e99	0.113821
$66$	−9.22469e100	−0.955572
$67$	2.49001e101	1.11956	0.559782	−	0.828640i	$-0.310885\pi$
$67$	2.49001e101	1.11956	0.559782	+	0.828640i	$0.310885\pi$
$68$	4.37856e101	0.865140
$69$	1.37787e102	1.21083
$70$	8.82131e101	0.348813
$71$	−8.70628e102	−1.56673	−0.783365	−	0.621562i	$-0.786499\pi$
$71$	−8.70628e102	−1.56673	−0.783365	+	0.621562i	$0.786499\pi$
$72$	1.73095e101	0.0143328
$73$	−2.93019e103	−1.12843	−0.564217	−	0.825626i	$-0.690822\pi$
$73$	−2.93019e103	−1.12843	−0.564217	+	0.825626i	$0.690822\pi$
$74$	5.90402e103	1.06853
$75$	1.05247e104	0.904292
$76$	1.45995e104	0.601430
$77$	5.21396e104	1.03976
$78$	9.41054e104	0.916989
$79$	2.11147e105	1.01457	0.507284	−	0.861779i	$-0.330649\pi$
$79$	2.11147e105	1.01457	0.507284	+	0.861779i	$0.330649\pi$
$80$	−6.40352e104	−0.153082
$81$	−7.05682e105	−0.846624
$82$	3.54839e106	2.15458
$83$	8.08186e105	0.250425	0.125212	−	0.992130i	$-0.460039\pi$
$83$	8.08186e105	0.250425	0.125212	+	0.992130i	$0.460039\pi$
$84$	9.12774e106	1.45500
$85$	1.62060e106	0.133944
$86$	4.97805e107	2.14979
$87$	5.01277e107	1.13962
$88$	6.27797e106	0.0756887
$89$	8.02651e107	0.516870	0.258435	−	0.966029i	$-0.416793\pi$
$89$	8.02651e107	0.516870	0.258435	+	0.966029i	$0.416793\pi$
$90$	9.33791e106	0.0323438
$91$	−5.31901e108	−0.997777
$92$	−1.36678e109	−1.39789
$93$	4.99221e108	0.280214
$94$	6.33557e109	1.96422
$95$	5.40361e108	0.0931159
$96$	−1.38209e110	−1.33194
$97$	−2.46491e110	−1.33650	−0.668252	−	0.743935i	$-0.732957\pi$
$97$	−2.46491e110	−1.33650	−0.668252	+	0.743935i	$0.732957\pi$
$98$	−5.27173e110	−1.61773
$99$	5.51931e109	0.0964120
$100$	−1.04399e111	−1.04399
$101$	−1.59665e111	−0.919120	−0.459560	−	0.888147i	$-0.651993\pi$
$101$	−1.59665e111	−0.919120	−0.459560	+	0.888147i	$0.651993\pi$
$102$	3.23873e111	1.07911
$103$	3.72852e111	0.722887	0.361444	−	0.932394i	$-0.382284\pi$
$103$	3.72852e111	0.722887	0.361444	+	0.932394i	$0.382284\pi$
$104$	−6.40445e110	−0.0726326
$105$	3.37837e111	0.225269
$106$	4.72626e112	1.86227
$107$	−4.21312e112	−0.985836	−0.492918	−	0.870076i	$-0.664070\pi$
$107$	−4.21312e112	−0.985836	−0.492918	+	0.870076i	$0.664070\pi$
$108$	8.11719e112	1.13341
$109$	−7.20940e112	−0.603571	−0.301786	−	0.953376i	$-0.597583\pi$
$109$	−7.20940e112	−0.603571	−0.301786	+	0.953376i	$0.597583\pi$
$110$	3.38677e112	0.170801
$111$	2.26111e113	0.690075
$112$	7.23327e113	1.34194
$113$	−8.62149e113	−0.976627	−0.488314	−	0.872668i	$-0.662388\pi$
$113$	−8.62149e113	−0.976627	−0.488314	+	0.872668i	$0.662388\pi$
$114$	1.07990e114	0.750178
$115$	−5.05873e113	−0.216427
$116$	−4.97241e114	−1.31567
$117$	−5.63051e113	−0.0925192
$118$	−1.69905e115	−1.74082
$119$	−1.83059e115	−1.17418
$120$	4.06779e113	0.0163983
$121$	−1.92997e115	−0.490866
$122$	1.23237e116	1.98505
$123$	1.35896e116	1.39146
$124$	−4.95202e115	−0.323503
$125$	−7.83791e115	−0.327864
$126$	−1.05479e116	−0.283531
$127$	4.55346e115	0.0789288	0.0394644	−	0.999221i	$-0.487435\pi$
$127$	4.55346e115	0.0789288	0.0394644	+	0.999221i	$0.487435\pi$
$128$	1.88633e116	0.211575
$129$	1.90649e117	1.38837
$130$	−3.45500e116	−0.163905
$131$	1.77826e117	0.551365	0.275682	−	0.961249i	$-0.411096\pi$
$131$	1.77826e117	0.551365	0.275682	+	0.961249i	$0.411096\pi$
$132$	3.50441e117	0.712463
$133$	−6.10380e117	−0.816270
$134$	−1.82698e118	−1.61220
$135$	3.00435e117	0.175479
$136$	−2.20416e117	−0.0854739
$137$	−1.74406e118	−0.450371	−0.225186	−	0.974316i	$-0.572299\pi$
$137$	−1.74406e118	−0.450371	−0.225186	+	0.974316i	$0.572299\pi$
$138$	−1.01098e119	−1.74362
$139$	−2.01002e118	−0.232209	−0.116104	−	0.993237i	$-0.537041\pi$
$139$	−2.01002e118	−0.232209	−0.116104	+	0.993237i	$0.537041\pi$
$140$	−3.35117e118	−0.260070
$141$	2.42639e119	1.26853
$142$	6.38802e119	2.25613
$143$	−2.04213e119	−0.488577
$144$	7.65687e118	0.124432
$145$	−1.84040e119	−0.203698
$146$	2.14995e120	1.62497
$147$	−2.01896e120	−1.04476
$148$	−2.24291e120	−0.796684
$149$	3.14489e120	0.768720	0.384360	−	0.923183i	$-0.374422\pi$
$149$	3.14489e120	0.768720	0.384360	+	0.923183i	$0.374422\pi$
$150$	−7.72223e120	−1.30220
$151$	1.50620e121	1.75656	0.878280	−	0.478147i	$-0.158691\pi$
$151$	1.50620e121	1.75656	0.878280	+	0.478147i	$0.158691\pi$
$152$	−7.34939e119	−0.0594199
$153$	−1.93780e120	−0.108876
$154$	−3.82562e121	−1.49728
$155$	−1.83285e120	−0.0500861
$156$	−3.57502e121	−0.683696
$157$	−3.65233e121	−0.489936	−0.244968	−	0.969531i	$-0.578778\pi$
$157$	−3.65233e121	−0.489936	−0.244968	+	0.969531i	$0.578778\pi$
$158$	−1.54924e122	−1.46100
$159$	1.81005e122	1.20268
$160$	5.07425e121	0.238074
$161$	5.71423e122	1.89724
$162$	5.17777e122	1.21916
$163$	6.17387e122	1.03311	0.516553	−	0.856255i	$-0.327215\pi$
$163$	6.17387e122	1.03311	0.516553	+	0.856255i	$0.327215\pi$
$164$	−1.34801e123	−1.60643
$165$	1.29706e122	0.110306
$166$	−5.92987e122	−0.360617
$167$	4.50779e122	0.196426	0.0982132	−	0.995165i	$-0.468687\pi$
$167$	4.50779e122	0.196426	0.0982132	+	0.995165i	$0.468687\pi$
$168$	−4.59489e122	−0.143751
$169$	−2.36009e123	−0.531150
$170$	−1.18907e123	−0.192883
$171$	−6.46125e122	−0.0756889
$172$	−1.89114e124	−1.60285
$173$	2.60920e124	1.60305	0.801527	−	0.597958i	$-0.204021\pi$
$173$	2.60920e124	1.60305	0.801527	+	0.597958i	$0.204021\pi$
$174$	−3.67800e124	−1.64107
$175$	4.36475e124	1.41693
$176$	2.77707e124	0.657104
$177$	−6.50698e124	−1.12425
$178$	−5.88926e124	−0.744305
$179$	1.02561e125	0.949814	0.474907	−	0.880036i	$-0.342482\pi$
$179$	1.02561e125	0.949814	0.474907	+	0.880036i	$0.342482\pi$
$180$	−3.54743e123	−0.0241151
$181$	−1.23332e124	−0.0616475	−0.0308237	−	0.999525i	$-0.509813\pi$
$181$	−1.23332e124	−0.0616475	−0.0308237	+	0.999525i	$0.509813\pi$
$182$	3.90269e125	1.43682
$183$	4.71971e125	1.28198
$184$	6.88033e124	0.138108
$185$	−8.30148e124	−0.123346
$186$	−3.66292e125	−0.403514
$187$	−7.02819e125	−0.574956
$188$	−2.40685e126	−1.46450
$189$	−3.39364e126	−1.53828
$190$	−3.96477e125	−0.134089
$191$	2.26679e126	0.572875	0.286438	−	0.958099i	$-0.407529\pi$
$191$	2.26679e126	0.572875	0.286438	+	0.958099i	$0.407529\pi$
$192$	5.61270e126	1.06158
$193$	−1.35965e127	−1.92751	−0.963757	−	0.266780i	$-0.914040\pi$
$193$	−1.35965e127	−1.92751	−0.963757	+	0.266780i	$0.914040\pi$
$194$	1.80857e127	1.92459
$195$	−1.32319e126	−0.105853
$196$	2.00270e127	1.20616
$197$	8.77263e126	0.398340	0.199170	−	0.979965i	$-0.436175\pi$
$197$	8.77263e126	0.398340	0.199170	+	0.979965i	$0.436175\pi$
$198$	−4.04966e126	−0.138835
$199$	−3.74899e127	−0.971780	−0.485890	−	0.874020i	$-0.661504\pi$
$199$	−3.74899e127	−0.971780	−0.485890	+	0.874020i	$0.661504\pi$
$200$	5.25545e126	0.103144
$201$	−6.99694e127	−1.04118
$202$	1.17150e128	1.32355
$203$	2.07887e128	1.78565
$204$	−1.23038e128	−0.804571
$205$	−4.98929e127	−0.248714
$206$	−2.73571e128	−1.04097
$207$	6.04887e127	0.175922
$208$	−2.83302e128	−0.630572
$209$	−2.34343e128	−0.399699
$210$	−2.47880e128	−0.324392
$211$	−2.46502e128	−0.247824	−0.123912	−	0.992293i	$-0.539544\pi$
$211$	−2.46502e128	−0.247824	−0.123912	+	0.992293i	$0.539544\pi$
$212$	−1.79548e129	−1.38848
$213$	2.44647e129	1.45704
$214$	3.09128e129	1.41963
$215$	−6.99951e128	−0.248161
$216$	−4.08618e128	−0.111978
$217$	2.07035e129	0.439064
$218$	5.28972e129	0.869156
$219$	8.23385e129	1.04943
$220$	−1.28662e129	−0.127347
$221$	7.16979e129	0.551741
$222$	−1.65904e130	−0.993724
$223$	−3.56089e130	−1.66203	−0.831014	−	0.556251i	$-0.812239\pi$
$223$	−3.56089e130	−1.66203	−0.831014	+	0.556251i	$0.812239\pi$
$224$	−5.73176e130	−2.08700
$225$	4.62036e129	0.131385
$226$	6.32581e130	1.40636
$227$	1.35518e130	0.235811	0.117905	−	0.993025i	$-0.462382\pi$
$227$	1.35518e130	0.235811	0.117905	+	0.993025i	$0.462382\pi$
$228$	−4.10249e130	−0.559324
$229$	1.03957e131	1.11169	0.555845	−	0.831286i	$-0.312395\pi$
$229$	1.03957e131	1.11169	0.555845	+	0.831286i	$0.312395\pi$
$230$	3.71172e130	0.311660
$231$	−1.46513e131	−0.966966
$232$	2.50310e130	0.129986
$233$	−8.77503e130	−0.358918	−0.179459	−	0.983765i	$-0.557435\pi$
$233$	−8.77503e130	−0.358918	−0.179459	+	0.983765i	$0.557435\pi$
$234$	4.13125e130	0.133230
$235$	−8.90828e130	−0.226740
$236$	6.45459e131	1.29793
$237$	−5.93325e131	−0.943538
$238$	1.34315e132	1.69085
$239$	7.30543e131	0.728722	0.364361	−	0.931258i	$-0.381287\pi$
$239$	7.30543e131	0.728722	0.364361	+	0.931258i	$0.381287\pi$
$240$	1.79939e131	0.142365
$241$	−2.20787e132	−1.38685	−0.693424	−	0.720530i	$-0.743898\pi$
$241$	−2.20787e132	−1.38685	−0.693424	+	0.720530i	$0.743898\pi$
$242$	1.41607e132	0.706857
$243$	−6.75715e131	−0.268297
$244$	−4.68171e132	−1.48003
$245$	7.41244e131	0.186743
$246$	−9.97101e132	−2.00374
$247$	2.39064e132	0.383561
$248$	2.49284e131	0.0319614
$249$	−2.27101e132	−0.232893
$250$	5.75087e132	0.472132
$251$	2.20192e133	1.44847	0.724237	−	0.689551i	$-0.242192\pi$
$251$	2.20192e133	1.44847	0.724237	+	0.689551i	$0.242192\pi$
$252$	4.00709e132	0.211397
$253$	2.19387e133	0.929012
$254$	−3.34099e132	−0.113659
$255$	−4.55390e132	−0.124567
$256$	3.80148e133	0.836826
$257$	−8.22590e132	−0.145846	−0.0729231	−	0.997338i	$-0.523233\pi$
$257$	−8.22590e132	−0.145846	−0.0729231	+	0.997338i	$0.523233\pi$
$258$	−1.39884e134	−1.99928
$259$	9.37717e133	1.08127
$260$	1.31254e133	0.122206
$261$	2.20061e133	0.165575
$262$	−1.30476e134	−0.793977
$263$	−2.30362e134	−1.13466	−0.567331	−	0.823490i	$-0.692024\pi$
$263$	−2.30362e134	−1.13466	−0.567331	+	0.823490i	$0.692024\pi$
$264$	−1.76412e133	−0.0703897
$265$	−6.64546e133	−0.214971
$266$	4.47851e134	1.17545
$267$	−2.25546e134	−0.480684
$268$	6.94061e134	1.20203
$269$	−4.09995e134	−0.577467	−0.288734	−	0.957409i	$-0.593234\pi$
$269$	−4.09995e134	−0.577467	−0.288734	+	0.957409i	$0.593234\pi$
$270$	−2.20437e134	−0.252694
$271$	−9.99219e134	−0.932964	−0.466482	−	0.884531i	$-0.654479\pi$
$271$	−9.99219e134	−0.932964	−0.466482	+	0.884531i	$0.654479\pi$
$272$	−9.75013e134	−0.742055
$273$	1.49465e135	0.927923
$274$	1.27966e135	0.648544
$275$	1.67576e135	0.693820
$276$	3.84065e135	1.30002
$277$	−1.84923e134	−0.0512109	−0.0256055	−	0.999672i	$-0.508151\pi$
$277$	−1.84923e134	−0.0512109	−0.0256055	+	0.999672i	$0.508151\pi$
$278$	1.47480e135	0.334386
$279$	2.19159e134	0.0407124
$280$	1.68698e134	0.0256944
$281$	−7.99473e134	−0.0999087	−0.0499544	−	0.998752i	$-0.515908\pi$
$281$	−7.99473e134	−0.0999087	−0.0499544	+	0.998752i	$0.515908\pi$
$282$	−1.78030e136	−1.82670
$283$	−1.49271e136	−1.25843	−0.629216	−	0.777231i	$-0.716624\pi$
$283$	−1.49271e136	−1.25843	−0.629216	+	0.777231i	$0.716624\pi$
$284$	−2.42678e136	−1.68214
$285$	−1.51842e135	−0.0865968
$286$	1.49836e136	0.703561
$287$	5.63580e136	2.18027
$288$	−6.06742e135	−0.193518
$289$	−1.33285e136	−0.350713
$290$	1.35035e136	0.293330
$291$	6.92643e136	1.24293
$292$	−8.16756e136	−1.21156
$293$	1.18476e136	0.145371	0.0726857	−	0.997355i	$-0.476843\pi$
$293$	1.18476e136	0.145371	0.0726857	+	0.997355i	$0.476843\pi$
$294$	1.48136e137	1.50447
$295$	2.38898e136	0.200952
$296$	1.12908e136	0.0787106
$297$	−1.30292e137	−0.753244
$298$	−2.30749e137	−1.10697
$299$	−2.23807e137	−0.891501
$300$	2.93364e137	0.970905
$301$	7.90649e137	2.17542
$302$	−1.10514e138	−2.52948
$303$	4.48659e137	0.854772
$304$	−3.25102e137	−0.515864
$305$	−1.73280e137	−0.229144
$306$	1.42181e137	0.156784
$307$	−1.47670e138	−1.35867	−0.679334	−	0.733829i	$-0.737731\pi$
$307$	−1.47670e138	−1.35867	−0.679334	+	0.733829i	$0.737731\pi$
$308$	1.45333e138	1.11635
$309$	−1.04772e138	−0.672278
$310$	1.34481e137	0.0721251
$311$	5.36687e136	0.0240724	0.0120362	−	0.999928i	$-0.496169\pi$
$311$	5.36687e136	0.0240724	0.0120362	+	0.999928i	$0.496169\pi$
$312$	1.79966e137	0.0675476
$313$	2.15938e138	0.678607	0.339303	−	0.940677i	$-0.389809\pi$
$313$	2.15938e138	0.678607	0.339303	+	0.940677i	$0.389809\pi$
$314$	2.67981e138	0.705519
$315$	1.48311e137	0.0327294
$316$	5.88548e138	1.08930
$317$	5.83568e138	0.906364	0.453182	−	0.891418i	$-0.350289\pi$
$317$	5.83568e138	0.906364	0.453182	+	0.891418i	$0.350289\pi$
$318$	−1.32808e139	−1.73189
$319$	7.98141e138	0.874373
$320$	−2.06066e138	−0.189750
$321$	1.18389e139	0.916818
$322$	−4.19268e139	−2.73206
$323$	8.22765e138	0.451373
$324$	−1.96701e139	−0.908989
$325$	−1.70952e139	−0.665806
$326$	−4.52993e139	−1.48770
$327$	2.02585e139	0.561315
$328$	6.78589e138	0.158711
$329$	1.00626e140	1.98764
$330$	−9.51686e138	−0.158844
$331$	1.09986e140	1.55197	0.775983	−	0.630753i	$-0.217254\pi$
$331$	1.09986e140	1.55197	0.775983	+	0.630753i	$0.217254\pi$
$332$	2.25273e139	0.268872
$333$	9.92632e138	0.100261
$334$	−3.30749e139	−0.282858
$335$	2.56887e139	0.186104
$336$	−2.03256e140	−1.24799
$337$	−2.52008e140	−1.31206	−0.656031	−	0.754734i	$-0.727766\pi$
$337$	−2.52008e140	−1.31206	−0.656031	+	0.754734i	$0.727766\pi$
$338$	1.73166e140	0.764868
$339$	2.42265e140	0.908253
$340$	4.51723e139	0.143811
$341$	7.94869e139	0.214995
$342$	4.74079e139	0.108994
$343$	−9.19772e139	−0.179828
$344$	9.51996e139	0.158358
$345$	1.42151e140	0.201275
$346$	−1.91444e141	−2.30843
$347$	−8.57225e140	−0.880662	−0.440331	−	0.897836i	$-0.645139\pi$
$347$	−8.57225e140	−0.880662	−0.440331	+	0.897836i	$0.645139\pi$
$348$	1.39725e141	1.22356
$349$	1.51085e141	1.12826	0.564132	−	0.825685i	$-0.309211\pi$
$349$	1.51085e141	1.12826	0.564132	+	0.825685i	$0.309211\pi$
$350$	−3.20253e141	−2.04040
$351$	1.32917e141	0.722830
$352$	−2.20059e141	−1.02193
$353$	2.07819e141	0.824498	0.412249	−	0.911071i	$-0.364743\pi$
$353$	2.07819e141	0.824498	0.412249	+	0.911071i	$0.364743\pi$
$354$	4.77434e141	1.61895
$355$	−8.98203e140	−0.260436
$356$	2.23730e141	0.554944
$357$	5.14398e141	1.09198
$358$	−7.52516e141	−1.36775
$359$	9.29041e141	1.44642	0.723208	−	0.690631i	$-0.242667\pi$
$359$	9.29041e141	1.44642	0.723208	+	0.690631i	$0.242667\pi$
$360$	1.78577e139	0.00238252
$361$	−5.99941e141	−0.686213
$362$	9.04919e140	0.0887737
$363$	5.42324e141	0.456500
$364$	−1.48261e142	−1.07128
$365$	−3.02299e141	−0.187578
$366$	−3.46297e142	−1.84607
$367$	−4.11915e142	−1.88730	−0.943651	−	0.330941i	$-0.892634\pi$
$367$	−4.11915e142	−1.88730	−0.943651	+	0.330941i	$0.892634\pi$
$368$	3.04353e142	1.19901
$369$	5.96584e141	0.202166
$370$	6.09101e141	0.177621
$371$	7.50657e142	1.88447
$372$	1.39152e142	0.300855
$373$	−6.13584e142	−1.14297	−0.571484	−	0.820613i	$-0.693632\pi$
$373$	−6.13584e142	−1.14297	−0.571484	+	0.820613i	$0.693632\pi$
$374$	5.15677e142	0.827949
$375$	2.20246e142	0.304911
$376$	1.21161e142	0.144689
$377$	−8.14221e142	−0.839069
$378$	2.49000e143	2.21516
$379$	−1.19129e143	−0.915251	−0.457625	−	0.889145i	$-0.651300\pi$
$379$	−1.19129e143	−0.915251	−0.457625	+	0.889145i	$0.651300\pi$
$380$	1.50619e142	0.0999750
$381$	−1.27953e142	−0.0734030
$382$	−1.66320e143	−0.824952
$383$	−3.04385e143	−1.30585	−0.652923	−	0.757425i	$-0.726457\pi$
$383$	−3.04385e143	−1.30585	−0.652923	+	0.757425i	$0.726457\pi$
$384$	−5.30061e142	−0.196763
$385$	5.37910e142	0.172838
$386$	9.97613e143	2.77566
$387$	8.36951e142	0.201717
$388$	−6.87066e143	−1.43495
$389$	−1.87449e143	−0.339375	−0.169687	−	0.985498i	$-0.554276\pi$
$389$	−1.87449e143	−0.339375	−0.169687	+	0.985498i	$0.554276\pi$
$390$	9.70859e142	0.152430
$391$	−7.70253e143	−1.04912
$392$	−1.00816e143	−0.119166
$393$	−4.99694e143	−0.512764
$394$	−6.43670e143	−0.573618
$395$	2.17834e143	0.168651
$396$	1.53844e143	0.103514
$397$	−2.20741e143	−0.129125	−0.0645623	−	0.997914i	$-0.520565\pi$
$397$	−2.20741e143	−0.129125	−0.0645623	+	0.997914i	$0.520565\pi$
$398$	2.75073e144	1.39938
$399$	1.71517e144	0.759123
$400$	2.32476e144	0.895465
$401$	1.26098e144	0.422861	0.211430	−	0.977393i	$-0.432188\pi$
$401$	1.26098e144	0.422861	0.211430	+	0.977393i	$0.432188\pi$
$402$	5.13384e144	1.49933
$403$	−8.10883e143	−0.206314
$404$	−4.45047e144	−0.986825
$405$	−7.28033e143	−0.140733
$406$	−1.52532e145	−2.57138
$407$	3.60018e144	0.529462
$408$	6.19371e143	0.0794898
$409$	−1.09080e145	−1.22209	−0.611043	−	0.791597i	$-0.709250\pi$
$409$	−1.09080e145	−1.22209	−0.611043	+	0.791597i	$0.709250\pi$
$410$	3.66077e144	0.358153
$411$	4.90084e144	0.418841
$412$	1.03928e145	0.776137
$413$	−2.69854e145	−1.76158
$414$	−4.43821e144	−0.253332
$415$	8.33783e143	0.0416278
$416$	2.24493e145	0.980670
$417$	5.64817e144	0.215952
$418$	1.71944e145	0.575576
$419$	5.33990e144	0.156551	0.0782754	−	0.996932i	$-0.475059\pi$
$419$	5.33990e144	0.156551	0.0782754	+	0.996932i	$0.475059\pi$
$420$	9.41683e144	0.241863
$421$	2.48730e145	0.559849	0.279925	−	0.960022i	$-0.409691\pi$
$421$	2.48730e145	0.559849	0.279925	+	0.960022i	$0.409691\pi$
$422$	1.80865e145	0.356872
$423$	1.06519e145	0.184305
$424$	9.03843e144	0.137179
$425$	−5.88349e145	−0.783518
$426$	−1.79504e146	−2.09817
$427$	1.95733e146	2.00871
$428$	−1.17436e146	−1.05845
$429$	5.73840e145	0.454372
$430$	5.13572e145	0.357357
$431$	−4.17846e145	−0.255580	−0.127790	−	0.991801i	$-0.540788\pi$
$431$	−4.17846e145	−0.255580	−0.127790	+	0.991801i	$0.540788\pi$
$432$	−1.80753e146	−0.972159
$433$	3.59112e146	1.69884	0.849419	−	0.527718i	$-0.176952\pi$
$433$	3.59112e146	1.69884	0.849419	+	0.527718i	$0.176952\pi$
$434$	−1.51907e146	−0.632262
$435$	5.17153e145	0.189437
$436$	−2.00954e146	−0.648032
$437$	−2.56828e146	−0.729327
$438$	−6.04139e146	−1.51121
$439$	6.43626e146	1.41858	0.709288	−	0.704919i	$-0.249017\pi$
$439$	6.43626e146	1.41858	0.709288	+	0.704919i	$0.249017\pi$
$440$	6.47681e144	0.0125816
$441$	−8.86327e145	−0.151793
$442$	−5.26066e146	−0.794519
$443$	4.83539e146	0.644206	0.322103	−	0.946705i	$-0.395610\pi$
$443$	4.83539e146	0.644206	0.322103	+	0.946705i	$0.395610\pi$
$444$	6.30259e146	0.740908
$445$	8.28073e145	0.0859188
$446$	2.61272e147	2.39336
$447$	−8.83718e146	−0.714901
$448$	2.32767e147	1.66338
$449$	−1.86003e147	−1.17449	−0.587244	−	0.809410i	$-0.699787\pi$
$449$	−1.86003e147	−1.17449	−0.587244	+	0.809410i	$0.699787\pi$
$450$	−3.39008e146	−0.189197
$451$	2.16375e147	1.06760
$452$	−2.40314e147	−1.04857
$453$	−4.23245e147	−1.63358
$454$	−9.94334e146	−0.339572
$455$	−5.48747e146	−0.165859
$456$	2.06519e146	0.0552599
$457$	−3.32180e147	−0.787091	−0.393545	−	0.919305i	$-0.628752\pi$
$457$	−3.32180e147	−0.787091	−0.393545	+	0.919305i	$0.628752\pi$
$458$	−7.62758e147	−1.60086
$459$	4.57448e147	0.850625
$460$	−1.41006e147	−0.232370
$461$	−1.68247e146	−0.0245780	−0.0122890	−	0.999924i	$-0.503912\pi$
$461$	−1.68247e146	−0.0245780	−0.0122890	+	0.999924i	$0.503912\pi$
$462$	1.07500e148	1.39245
$463$	1.00810e148	1.15814	0.579068	−	0.815279i	$-0.303417\pi$
$463$	1.00810e148	1.15814	0.579068	+	0.815279i	$0.303417\pi$
$464$	1.10725e148	1.12849
$465$	5.15033e146	0.0465796
$466$	6.43847e147	0.516849
$467$	−1.58902e148	−1.13251	−0.566256	−	0.824230i	$-0.691609\pi$
$467$	−1.58902e148	−1.13251	−0.566256	+	0.824230i	$0.691609\pi$
$468$	−1.56944e147	−0.0993344
$469$	−2.90174e148	−1.63142
$470$	6.53623e147	0.326510
$471$	1.02631e148	0.455636
$472$	−3.24923e147	−0.128233
$473$	3.03554e148	1.06523
$474$	4.35338e148	1.35872
$475$	−1.96175e148	−0.544688
$476$	−5.10257e148	−1.26067
$477$	7.94617e147	0.174738
$478$	−5.36018e148	−1.04938
$479$	1.74839e148	0.304803	0.152401	−	0.988319i	$-0.451299\pi$
$479$	1.74839e148	0.304803	0.152401	+	0.988319i	$0.451299\pi$
$480$	−1.42587e148	−0.221407
$481$	−3.67271e148	−0.508084
$482$	1.61997e149	1.99709
$483$	−1.60570e149	−1.76441
$484$	−5.37958e148	−0.527024
$485$	−2.54298e148	−0.222165
$486$	4.95790e148	0.386353
$487$	7.45317e148	0.518184	0.259092	−	0.965853i	$-0.416577\pi$
$487$	7.45317e148	0.518184	0.259092	+	0.965853i	$0.416577\pi$
$488$	2.35677e148	0.146223
$489$	−1.73486e149	−0.960779
$490$	−5.43870e148	−0.268913
$491$	3.55474e149	1.56958	0.784792	−	0.619759i	$-0.212770\pi$
$491$	3.55474e149	1.56958	0.784792	+	0.619759i	$0.212770\pi$
$492$	3.78794e149	1.49396
$493$	−2.80223e149	−0.987414
$494$	−1.75408e149	−0.552336
$495$	5.69412e147	0.0160265
$496$	1.10271e149	0.277478
$497$	1.01459e150	2.28303
$498$	1.66630e149	0.335370
$499$	−2.03834e148	−0.0367026	−0.0183513	−	0.999832i	$-0.505842\pi$
$499$	−2.03834e148	−0.0367026	−0.0183513	+	0.999832i	$0.505842\pi$
$500$	−2.18473e149	−0.352016
$501$	−1.26669e149	−0.182675
$502$	−1.61561e150	−2.08583
$503$	−1.47352e150	−1.70347	−0.851733	−	0.523976i	$-0.824448\pi$
$503$	−1.47352e150	−1.70347	−0.851733	+	0.523976i	$0.824448\pi$
$504$	−2.01717e148	−0.0208856
$505$	−1.64721e149	−0.152784
$506$	−1.60970e150	−1.33780
$507$	6.63189e149	0.493964
$508$	1.26923e149	0.0847429
$509$	2.55193e150	1.52768	0.763839	−	0.645407i	$-0.223312\pi$
$509$	2.55193e150	1.52768	0.763839	+	0.645407i	$0.223312\pi$
$510$	3.34131e149	0.179379
$511$	3.41470e150	1.64435
$512$	−3.27897e150	−1.41662
$513$	1.52528e150	0.591339
$514$	6.03555e149	0.210022
$515$	3.84661e149	0.120165
$516$	5.31411e150	1.49064
$517$	3.86333e150	0.973279
$518$	−6.88027e150	−1.55706
$519$	−7.33187e150	−1.49082
$520$	−6.60730e148	−0.0120736
$521$	6.54328e150	1.07474	0.537368	−	0.843348i	$-0.319418\pi$
$521$	6.54328e150	1.07474	0.537368	+	0.843348i	$0.319418\pi$
$522$	−1.61465e150	−0.238432
$523$	−7.30109e150	−0.969491	−0.484746	−	0.874655i	$-0.661088\pi$
$523$	−7.30109e150	−0.969491	−0.484746	+	0.874655i	$0.661088\pi$
$524$	4.95671e150	0.591980
$525$	−1.22650e151	−1.31773
$526$	1.69022e151	1.63394
$527$	−2.79074e150	−0.242789
$528$	−7.80360e150	−0.611100
$529$	9.85992e150	0.695158
$530$	4.87595e150	0.309562
$531$	−2.85658e150	−0.163343
$532$	−1.70136e151	−0.876399
$533$	−2.20735e151	−1.02450
$534$	1.65489e151	0.692196
$535$	−4.34656e150	−0.163874
$536$	−3.49389e150	−0.118758
$537$	−2.88197e151	−0.883318
$538$	3.00824e151	0.831565
$539$	−3.21462e151	−0.801592
$540$	8.37428e150	0.188406
$541$	6.39247e151	1.29784	0.648919	−	0.760858i	$-0.275222\pi$
$541$	6.39247e151	1.29784	0.648919	+	0.760858i	$0.275222\pi$
$542$	7.33153e151	1.34349
$543$	3.46564e150	0.0573315
$544$	7.72616e151	1.15405
$545$	−7.43774e150	−0.100331
$546$	−1.09666e152	−1.33623
$547$	1.29503e152	1.42555	0.712775	−	0.701393i	$-0.247438\pi$
$547$	1.29503e152	1.42555	0.712775	+	0.701393i	$0.247438\pi$
$548$	−4.86138e151	−0.483547
$549$	2.07196e151	0.186259
$550$	−1.22955e152	−0.999116
$551$	−9.34355e151	−0.686433
$552$	−1.93338e151	−0.128439
$553$	−2.46061e152	−1.47842
$554$	1.35682e151	0.0737449
$555$	2.33273e151	0.114710
$556$	−5.60270e151	−0.249314
$557$	1.69460e152	0.682502	0.341251	−	0.939972i	$-0.389149\pi$
$557$	1.69460e152	0.682502	0.341251	+	0.939972i	$0.389149\pi$
$558$	−1.60803e151	−0.0586267
$559$	−3.09670e152	−1.02222
$560$	7.46236e151	0.223070
$561$	1.97493e152	0.534703
$562$	5.86594e151	0.143871
$563$	−3.57299e152	−0.793992	−0.396996	−	0.917820i	$-0.629947\pi$
$563$	−3.57299e152	−0.793992	−0.396996	+	0.917820i	$0.629947\pi$
$564$	6.76328e152	1.36197
$565$	−8.89455e151	−0.162344
$566$	1.09524e153	1.81217
$567$	8.22370e152	1.23369
$568$	1.22164e152	0.166192
$569$	−5.17186e152	−0.638139	−0.319070	−	0.947731i	$-0.603370\pi$
$569$	−5.17186e152	−0.638139	−0.319070	+	0.947731i	$0.603370\pi$
$570$	1.11410e152	0.124701
$571$	−4.67094e152	−0.474352	−0.237176	−	0.971467i	$-0.576222\pi$
$571$	−4.67094e152	−0.474352	−0.237176	+	0.971467i	$0.576222\pi$
$572$	−5.69220e152	−0.524567
$573$	−6.36971e152	−0.532768
$574$	−4.13513e153	−3.13963
$575$	1.83654e153	1.26601
$576$	2.46399e152	0.154238
$577$	−1.09945e152	−0.0625054	−0.0312527	−	0.999512i	$-0.509950\pi$
$577$	−1.09945e152	−0.0625054	−0.0312527	+	0.999512i	$0.509950\pi$
$578$	9.77948e152	0.505034
$579$	3.82064e153	1.79257
$580$	−5.12990e152	−0.218703
$581$	−9.41823e152	−0.364917
$582$	−5.08210e153	−1.78985
$583$	2.88200e153	0.922761
$584$	4.11154e152	0.119699
$585$	−5.80883e151	−0.0153794
$586$	−8.69292e152	−0.209338
$587$	2.31642e153	0.507460	0.253730	−	0.967275i	$-0.418342\pi$
$587$	2.31642e153	0.507460	0.253730	+	0.967275i	$0.418342\pi$
$588$	−5.62762e153	−1.12172
$589$	−9.30524e152	−0.168783
$590$	−1.75286e153	−0.289375
$591$	−2.46512e153	−0.370452
$592$	4.99449e153	0.683339
$593$	4.37743e153	0.545360	0.272680	−	0.962105i	$-0.412090\pi$
$593$	4.37743e153	0.545360	0.272680	+	0.962105i	$0.412090\pi$
$594$	9.55988e153	1.08469
$595$	−1.88857e153	−0.195183
$596$	8.76603e153	0.825345
$597$	1.05347e154	0.903746
$598$	1.64213e154	1.28378
$599$	−8.43252e153	−0.600854	−0.300427	−	0.953805i	$-0.597129\pi$
$599$	−8.43252e153	−0.600854	−0.300427	+	0.953805i	$0.597129\pi$
$600$	−1.47679e153	−0.0959232
$601$	−8.17370e153	−0.484045	−0.242022	−	0.970271i	$-0.577811\pi$
$601$	−8.17370e153	−0.484045	−0.242022	+	0.970271i	$0.577811\pi$
$602$	−5.80119e154	−3.13265
$603$	−3.07167e153	−0.151274
$604$	4.19837e154	1.88595
$605$	−1.99110e153	−0.0815961
$606$	−3.29193e154	−1.23089
$607$	−2.25267e154	−0.768643	−0.384321	−	0.923199i	$-0.625565\pi$
$607$	−2.25267e154	−0.768643	−0.384321	+	0.923199i	$0.625565\pi$
$608$	2.57615e154	0.802275
$609$	−5.84165e154	−1.66064
$610$	1.27140e154	0.329972
$611$	−3.94117e154	−0.933981
$612$	−5.40139e153	−0.116896
$613$	4.23322e154	0.836786	0.418393	−	0.908266i	$-0.362593\pi$
$613$	4.23322e154	0.836786	0.418393	+	0.908266i	$0.362593\pi$
$614$	1.08350e155	1.95651
$615$	1.40200e154	0.231301
$616$	−7.31606e153	−0.110293
$617$	8.69042e154	1.19733	0.598666	−	0.800999i	$-0.295698\pi$
$617$	8.69042e154	1.19733	0.598666	+	0.800999i	$0.295698\pi$
$618$	7.68738e154	0.968095
$619$	1.08449e153	0.0124851	0.00624257	−	0.999981i	$-0.498013\pi$
$619$	1.08449e153	0.0124851	0.00624257	+	0.999981i	$0.498013\pi$
$620$	−5.10886e153	−0.0537756
$621$	−1.42793e155	−1.37444
$622$	−3.93781e153	−0.0346648
$623$	−9.35373e154	−0.753179
$624$	7.96082e154	0.586426
$625$	1.36182e155	0.917867
$626$	−1.58439e155	−0.977209
$627$	6.58507e154	0.371716
$628$	−1.01805e155	−0.526026
$629$	−1.26400e155	−0.597911
$630$	−1.08820e154	−0.0471311
$631$	−2.43709e154	−0.0966589	−0.0483294	−	0.998831i	$-0.515390\pi$
$631$	−2.43709e154	−0.0966589	−0.0483294	+	0.998831i	$0.515390\pi$
$632$	−2.96274e154	−0.107621
$633$	6.92673e154	0.230474
$634$	−4.28179e155	−1.30518
$635$	4.69768e153	0.0131202
$636$	5.04532e155	1.29128
$637$	3.27939e155	0.769226
$638$	−5.85617e155	−1.25912
$639$	1.07401e155	0.211694
$640$	1.94608e154	0.0351699
$641$	5.10869e155	0.846621	0.423310	−	0.905985i	$-0.360868\pi$
$641$	5.10869e155	0.846621	0.423310	+	0.905985i	$0.360868\pi$
$642$	−8.68652e155	−1.32024
$643$	−1.83993e155	−0.256503	−0.128252	−	0.991742i	$-0.540937\pi$
$643$	−1.83993e155	−0.256503	−0.128252	+	0.991742i	$0.540937\pi$
$644$	1.59278e156	2.03699
$645$	1.96687e155	0.230787
$646$	−6.03684e155	−0.649987
$647$	−3.75949e155	−0.371485	−0.185742	−	0.982598i	$-0.559469\pi$
$647$	−3.75949e155	−0.371485	−0.185742	+	0.982598i	$0.559469\pi$
$648$	9.90190e154	0.0898061
$649$	−1.03605e156	−0.862583
$650$	1.25432e156	0.958775
$651$	−5.81770e155	−0.408325
$652$	1.72090e156	1.10921
$653$	2.06357e156	1.22162	0.610812	−	0.791775i	$-0.290843\pi$
$653$	2.06357e156	1.22162	0.610812	+	0.791775i	$0.290843\pi$
$654$	−1.48642e156	−0.808306
$655$	1.83458e155	0.0916528
$656$	3.00175e156	1.37788
$657$	3.61468e155	0.152473
$658$	−7.38319e156	−2.86224
$659$	2.03301e156	0.724433	0.362217	−	0.932094i	$-0.382020\pi$
$659$	2.03301e156	0.724433	0.362217	+	0.932094i	$0.382020\pi$
$660$	3.61541e155	0.118432
$661$	−3.89442e156	−1.17290	−0.586451	−	0.809985i	$-0.699475\pi$
$661$	−3.89442e156	−1.17290	−0.586451	+	0.809985i	$0.699475\pi$
$662$	−8.06993e156	−2.23487
$663$	−2.01472e156	−0.513114
$664$	−1.13402e155	−0.0265639
$665$	−6.29712e155	−0.135688
$666$	−7.28320e155	−0.144378
$667$	8.74721e156	1.59546
$668$	1.25650e156	0.210896
$669$	1.00061e157	1.54567
$670$	−1.88485e156	−0.267994
$671$	7.51480e156	0.983598
$672$	1.61063e157	1.94089
$673$	−1.11501e157	−1.23721	−0.618606	−	0.785702i	$-0.712302\pi$
$673$	−1.11501e157	−1.23721	−0.618606	+	0.785702i	$0.712302\pi$
$674$	1.84905e157	1.88940
$675$	−1.09071e157	−1.02648
$676$	−6.57850e156	−0.570276
$677$	−1.49317e157	−1.19244	−0.596221	−	0.802820i	$-0.703332\pi$
$677$	−1.49317e157	−1.19244	−0.596221	+	0.802820i	$0.703332\pi$
$678$	−1.77756e157	−1.30790
$679$	2.87249e157	1.94754
$680$	−2.27397e155	−0.0142082
$681$	−3.80808e156	−0.219302
$682$	−5.83216e156	−0.309597
$683$	−2.27958e157	−1.11559	−0.557796	−	0.829978i	$-0.688353\pi$
$683$	−2.27958e157	−1.11559	−0.557796	+	0.829978i	$0.688353\pi$
$684$	−1.80100e156	−0.0812644
$685$	−1.79930e156	−0.0748647
$686$	6.74861e156	0.258956
$687$	−2.92120e157	−1.03386
$688$	4.21117e157	1.37482
$689$	−2.94006e157	−0.885502
$690$	−1.04300e157	−0.289840
$691$	−2.96722e157	−0.760884	−0.380442	−	0.924805i	$-0.624228\pi$
$691$	−2.96722e157	−0.760884	−0.380442	+	0.924805i	$0.624228\pi$
$692$	7.27284e157	1.72114
$693$	−6.43195e156	−0.140491
$694$	6.28968e157	1.26817
$695$	−2.07368e156	−0.0385998
$696$	−7.03375e156	−0.120885
$697$	−7.59680e157	−1.20562
$698$	−1.10855e158	−1.62472
$699$	2.46579e157	0.333790
$700$	1.21662e158	1.52130
$701$	1.57857e158	1.82354	0.911769	−	0.410702i	$-0.134716\pi$
$701$	1.57857e158	1.82354	0.911769	+	0.410702i	$0.134716\pi$
$702$	−9.75248e157	−1.04089
$703$	−4.21460e157	−0.415657
$704$	8.93664e157	0.814501
$705$	2.50324e157	0.210866
$706$	−1.52482e158	−1.18730
$707$	1.86066e158	1.33933
$708$	−1.81375e158	−1.20707
$709$	1.54725e158	0.952124	0.476062	−	0.879412i	$-0.342064\pi$
$709$	1.54725e158	0.952124	0.476062	+	0.879412i	$0.342064\pi$
$710$	6.59034e157	0.375033
$711$	−2.60471e157	−0.137087
$712$	−1.12625e157	−0.0548273
$713$	8.71134e157	0.392298
$714$	−3.77427e158	−1.57247
$715$	−2.10681e157	−0.0812156
$716$	2.85877e158	1.01978
$717$	−2.05283e158	−0.677705
$718$	−6.81661e158	−2.08287
$719$	−1.18337e158	−0.334708	−0.167354	−	0.985897i	$-0.553522\pi$
$719$	−1.18337e158	−0.334708	−0.167354	+	0.985897i	$0.553522\pi$
$720$	7.89938e156	0.0206842
$721$	−4.34505e158	−1.05339
$722$	4.40192e158	0.988162
$723$	6.20415e158	1.28975
$724$	−3.43774e157	−0.0661886
$725$	6.68145e158	1.19155
$726$	−3.97917e158	−0.657370
$727$	−2.26518e158	−0.346691	−0.173345	−	0.984861i	$-0.555458\pi$
$727$	−2.26518e158	−0.346691	−0.173345	+	0.984861i	$0.555458\pi$
$728$	7.46346e157	0.105840
$729$	8.34148e158	1.09614
$730$	2.21805e158	0.270117
$731$	−1.06576e159	−1.20294
$732$	1.31557e159	1.37641
$733$	1.00328e159	0.973084	0.486542	−	0.873657i	$-0.338258\pi$
$733$	1.00328e159	0.973084	0.486542	+	0.873657i	$0.338258\pi$
$734$	3.02233e159	2.71776
$735$	−2.08290e158	−0.173669
$736$	−2.41174e159	−1.86471
$737$	−1.11407e159	−0.798850
$738$	−4.37729e158	−0.291124
$739$	−2.49257e159	−1.53774	−0.768868	−	0.639408i	$-0.779180\pi$
$739$	−2.49257e159	−1.53774	−0.768868	+	0.639408i	$0.779180\pi$
$740$	−2.31394e158	−0.132432
$741$	−6.71774e158	−0.356708
$742$	−5.50776e159	−2.71368
$743$	2.02643e159	0.926514	0.463257	−	0.886224i	$-0.346681\pi$
$743$	2.02643e159	0.926514	0.463257	+	0.886224i	$0.346681\pi$
$744$	−7.00491e157	−0.0297238
$745$	3.24450e158	0.127783
$746$	4.50203e159	1.64590
$747$	−9.96979e157	−0.0338370
$748$	−1.95903e159	−0.617309
$749$	4.90978e159	1.43655
$750$	−1.61600e159	−0.439078
$751$	8.30571e158	0.209585	0.104793	−	0.994494i	$-0.466582\pi$
$751$	8.30571e158	0.209585	0.104793	+	0.994494i	$0.466582\pi$
$752$	5.35956e159	1.25614
$753$	−6.18743e159	−1.34707
$754$	5.97415e159	1.20828
$755$	1.55391e159	0.291991
$756$	−9.45940e159	−1.65160
$757$	−1.32705e159	−0.215310	−0.107655	−	0.994188i	$-0.534334\pi$
$757$	−1.32705e159	−0.215310	−0.107655	+	0.994188i	$0.534334\pi$
$758$	8.74078e159	1.31798
$759$	−6.16479e159	−0.863972
$760$	−7.58216e157	−0.00987731
$761$	−9.00722e159	−1.09079	−0.545397	−	0.838178i	$-0.683621\pi$
$761$	−9.00722e159	−1.09079	−0.545397	+	0.838178i	$0.683621\pi$
$762$	9.38823e158	0.105702
$763$	8.40150e159	0.879519
$764$	6.31843e159	0.615074
$765$	−1.99917e158	−0.0180984
$766$	2.23335e160	1.88045
$767$	1.05693e160	0.827755
$768$	−1.06822e160	−0.778240
$769$	−1.61088e160	−1.09182	−0.545909	−	0.837845i	$-0.683815\pi$
$769$	−1.61088e160	−1.09182	−0.545909	+	0.837845i	$0.683815\pi$
$770$	−3.94679e159	−0.248890
$771$	2.31149e159	0.135635
$772$	−3.78988e160	−2.06950
$773$	4.20645e159	0.213773	0.106887	−	0.994271i	$-0.465912\pi$
$773$	4.20645e159	0.213773	0.106887	+	0.994271i	$0.465912\pi$
$774$	−6.14093e159	−0.290476
$775$	6.65405e159	0.292983
$776$	3.45868e159	0.141770
$777$	−2.63499e160	−1.00557
$778$	1.37536e160	0.488707
$779$	−2.53303e160	−0.838128
$780$	−3.68825e159	−0.113650
$781$	3.89532e160	1.11792
$782$	5.65155e160	1.51075
$783$	−5.19491e160	−1.29360
$784$	−4.45961e160	−1.03456
$785$	−3.76801e159	−0.0814415
$786$	3.66638e160	0.738391
$787$	5.91476e160	1.11004	0.555021	−	0.831836i	$-0.312710\pi$
$787$	5.91476e160	1.11004	0.555021	+	0.831836i	$0.312710\pi$
$788$	2.44527e160	0.427683
$789$	6.47319e160	1.05522
$790$	−1.59831e160	−0.242860
$791$	1.00471e161	1.42313
$792$	−7.74451e158	−0.0102270
$793$	−7.66620e160	−0.943883
$794$	1.61963e160	0.185942
$795$	1.86738e160	0.199921
$796$	−1.04499e161	−1.04336
$797$	1.37291e161	1.27851	0.639256	−	0.768994i	$-0.279242\pi$
$797$	1.37291e161	1.27851	0.639256	+	0.768994i	$0.279242\pi$
$798$	−1.25847e161	−1.09315
$799$	−1.35639e161	−1.09911
$800$	−1.84218e161	−1.39263
$801$	−9.90151e159	−0.0698388
$802$	−9.25217e160	−0.608928
$803$	1.31101e161	0.805179
$804$	−1.95032e161	−1.11788
$805$	5.89521e160	0.315376
$806$	5.94966e160	0.297096
$807$	1.15209e161	0.537039
$808$	2.24036e160	0.0974961
$809$	1.65308e160	0.0671662	0.0335831	−	0.999436i	$-0.489308\pi$
$809$	1.65308e160	0.0671662	0.0335831	+	0.999436i	$0.489308\pi$
$810$	5.34176e160	0.202659
$811$	−2.95175e161	−1.04574	−0.522868	−	0.852413i	$-0.675138\pi$
$811$	−2.95175e161	−1.04574	−0.522868	+	0.852413i	$0.675138\pi$
$812$	5.79462e161	1.91719
$813$	2.80782e161	0.867647
$814$	−2.64154e161	−0.762436
$815$	6.36941e160	0.171732
$816$	2.73980e161	0.690104
$817$	−3.55359e161	−0.836265
$818$	8.00349e161	1.75983
$819$	6.56153e160	0.134818
$820$	−1.39071e161	−0.267035
$821$	−6.93290e161	−1.24414	−0.622070	−	0.782961i	$-0.713708\pi$
$821$	−6.93290e161	−1.24414	−0.622070	+	0.782961i	$0.713708\pi$
$822$	−3.59587e161	−0.603140
$823$	−3.80398e161	−0.596413	−0.298207	−	0.954501i	$-0.596388\pi$
$823$	−3.80398e161	−0.596413	−0.298207	+	0.954501i	$0.596388\pi$
$824$	−5.23174e160	−0.0766806
$825$	−4.70890e161	−0.645246
$826$	1.97999e162	2.53671
$827$	−1.34459e162	−1.61078	−0.805389	−	0.592747i	$-0.798043\pi$
$827$	−1.34459e162	−1.61078	−0.805389	+	0.592747i	$0.798043\pi$
$828$	1.68605e161	0.188881
$829$	7.67087e161	0.803653	0.401826	−	0.915716i	$-0.368376\pi$
$829$	7.67087e161	0.803653	0.401826	+	0.915716i	$0.368376\pi$
$830$	−6.11768e160	−0.0599450
$831$	5.19634e160	0.0476257
$832$	−9.11669e161	−0.781614
$833$	1.12863e162	0.905223
$834$	−4.14421e161	−0.310975
$835$	4.65057e160	0.0326517
$836$	−6.53205e161	−0.429142
$837$	−5.17361e161	−0.318076
$838$	−3.91803e161	−0.225436
$839$	−1.81267e162	−0.976178	−0.488089	−	0.872794i	$-0.662306\pi$
$839$	−1.81267e162	−0.976178	−0.488089	+	0.872794i	$0.662306\pi$
$840$	−4.74042e160	−0.0238955
$841$	1.06306e162	0.501625
$842$	−1.82499e162	−0.806195
$843$	2.24653e161	0.0929141
$844$	−6.87096e161	−0.266080
$845$	−2.43484e161	−0.0882925
$846$	−7.81556e161	−0.265403
$847$	2.24910e162	0.715285
$848$	3.99816e162	1.19094
$849$	4.19454e162	1.17033
$850$	4.31687e162	1.12828
$851$	3.94561e162	0.966103
$852$	6.81927e162	1.56437
$853$	2.08445e162	0.448045	0.224022	−	0.974584i	$-0.428081\pi$
$853$	2.08445e162	0.448045	0.224022	+	0.974584i	$0.428081\pi$
$854$	−1.43615e163	−2.89259
$855$	−6.66589e160	−0.0125817
$856$	5.91171e161	0.104573
$857$	−8.05214e162	−1.33498	−0.667491	−	0.744618i	$-0.732632\pi$
$857$	−8.05214e162	−1.33498	−0.667491	+	0.744618i	$0.732632\pi$
$858$	−4.21041e162	−0.654305
$859$	−1.13807e162	−0.165786	−0.0828930	−	0.996558i	$-0.526416\pi$
$859$	−1.13807e162	−0.165786	−0.0828930	+	0.996558i	$0.526416\pi$
$860$	−1.95103e162	−0.266441
$861$	−1.58366e163	−2.02763
$862$	3.06584e162	0.368041
$863$	6.68941e162	0.752989	0.376494	−	0.926419i	$-0.377129\pi$
$863$	6.68941e162	0.752989	0.376494	+	0.926419i	$0.377129\pi$
$864$	1.43231e163	1.51191
$865$	2.69184e162	0.266474
$866$	−2.63490e163	−2.44636
$867$	3.74533e162	0.326159
$868$	5.77086e162	0.471407
$869$	−9.44703e162	−0.723932
$870$	−3.79449e162	−0.272794
$871$	1.13651e163	0.766595
$872$	1.01160e162	0.0640241
$873$	3.04071e162	0.180586
$874$	1.88441e163	1.05025
$875$	9.13394e162	0.477761
$876$	2.29509e163	1.12674
$877$	1.95614e163	0.901411	0.450706	−	0.892673i	$-0.351172\pi$
$877$	1.95614e163	0.901411	0.450706	+	0.892673i	$0.351172\pi$
$878$	−4.72245e163	−2.04278
$879$	−3.32920e162	−0.135194
$880$	2.86503e162	0.109230
$881$	3.64611e163	1.30517	0.652584	−	0.757716i	$-0.273685\pi$
$881$	3.64611e163	1.30517	0.652584	+	0.757716i	$0.273685\pi$
$882$	6.50321e162	0.218585
$883$	−2.91355e163	−0.919609	−0.459804	−	0.888020i	$-0.652081\pi$
$883$	−2.91355e163	−0.919609	−0.459804	+	0.888020i	$0.652081\pi$
$884$	1.99850e163	0.592384
$885$	−6.71307e162	−0.186883
$886$	−3.54785e163	−0.927670
$887$	−1.06500e163	−0.261571	−0.130785	−	0.991411i	$-0.541750\pi$
$887$	−1.06500e163	−0.261571	−0.130785	+	0.991411i	$0.541750\pi$
$888$	−3.17272e162	−0.0732001
$889$	−5.30640e162	−0.115014
$890$	−6.07579e162	−0.123725
$891$	3.15733e163	0.604097
$892$	−9.92557e163	−1.78446
$893$	−4.52266e163	−0.764079
$894$	6.48407e163	1.02947
$895$	1.05809e163	0.157887
$896$	−2.19825e163	−0.308306
$897$	6.28899e163	0.829087
$898$	1.36475e164	1.69129
$899$	3.16924e163	0.369226
$900$	1.28787e163	0.141063
$901$	−1.01185e164	−1.04206
$902$	−1.58760e164	−1.53737
$903$	−2.22173e164	−2.02312
$904$	1.20974e163	0.103596
$905$	−1.27238e162	−0.0102476
$906$	3.10545e164	2.35239
$907$	−7.54250e163	−0.537416	−0.268708	−	0.963222i	$-0.586597\pi$
$907$	−7.54250e163	−0.537416	−0.268708	+	0.963222i	$0.586597\pi$
$908$	3.77742e163	0.253181
$909$	1.96962e163	0.124190
$910$	4.02630e163	0.238841
$911$	3.76898e163	0.210356	0.105178	−	0.994453i	$-0.466459\pi$
$911$	3.76898e163	0.210356	0.105178	+	0.994453i	$0.466459\pi$
$912$	9.13539e163	0.479748
$913$	−3.61594e163	−0.178687
$914$	2.43729e164	1.13343
$915$	4.86919e163	0.213101
$916$	2.89768e164	1.19358
$917$	−2.07231e164	−0.803444
$918$	−3.35642e164	−1.22492
$919$	7.82986e163	0.268994	0.134497	−	0.990914i	$-0.457058\pi$
$919$	7.82986e163	0.268994	0.134497	+	0.990914i	$0.457058\pi$
$920$	7.09824e162	0.0229576
$921$	4.14955e164	1.26355
$922$	1.23447e163	0.0353928
$923$	−3.97380e164	−1.07278
$924$	−4.08388e164	−1.03819
$925$	3.01380e164	0.721521
$926$	−7.39670e164	−1.66774
$927$	−4.59950e163	−0.0976755
$928$	−8.77404e164	−1.75504
$929$	−3.13830e164	−0.591319	−0.295659	−	0.955293i	$-0.595539\pi$
$929$	−3.13830e164	−0.591319	−0.295659	+	0.955293i	$0.595539\pi$
$930$	−3.77893e163	−0.0670757
$931$	3.76324e164	0.629295
$932$	−2.44594e164	−0.385357
$933$	−1.50810e163	−0.0223871
$934$	1.16591e165	1.63084
$935$	−7.25079e163	−0.0955743
$936$	7.90054e162	0.00981402
$937$	8.31779e164	0.973779	0.486890	−	0.873464i	$-0.338131\pi$
$937$	8.31779e164	0.973779	0.486890	+	0.873464i	$0.338131\pi$
$938$	2.12908e165	2.34928
$939$	−6.06788e164	−0.631098
$940$	−2.48308e164	−0.243442
$941$	1.22077e165	1.12826	0.564132	−	0.825685i	$-0.309211\pi$
$941$	1.22077e165	1.12826	0.564132	+	0.825685i	$0.309211\pi$
$942$	−7.53030e164	−0.656125
$943$	2.37136e165	1.94804
$944$	−1.43730e165	−1.11328
$945$	−3.50113e164	−0.255707
$946$	−2.22725e165	−1.53395
$947$	9.51573e164	0.618043	0.309021	−	0.951055i	$-0.399999\pi$
$947$	9.51573e164	0.618043	0.309021	+	0.951055i	$0.399999\pi$
$948$	−1.65383e165	−1.01304
$949$	−1.33742e165	−0.772669
$950$	1.43939e165	0.784363
$951$	−1.63983e165	−0.842910
$952$	2.56862e164	0.124552
$953$	9.75657e164	0.446315	0.223157	−	0.974782i	$-0.428364\pi$
$953$	9.75657e164	0.446315	0.223157	+	0.974782i	$0.428364\pi$
$954$	−5.83031e164	−0.251627
$955$	2.33859e164	0.0952284
$956$	2.03631e165	0.782402
$957$	−2.24279e165	−0.813158
$958$	−1.28284e165	−0.438922
$959$	2.03245e165	0.656277
$960$	5.79047e164	0.176466
$961$	−3.16092e165	−0.909213
$962$	2.69476e165	0.731651
$963$	5.19731e164	0.133205
$964$	−6.15420e165	−1.48901
$965$	−1.40272e165	−0.320409
$966$	1.17815e166	2.54079
$967$	−9.63123e165	−1.96116	−0.980578	−	0.196128i	$-0.937163\pi$
$967$	−9.63123e165	−1.96116	−0.980578	+	0.196128i	$0.937163\pi$
$968$	2.70807e164	0.0520688
$969$	−2.31198e165	−0.419772
$970$	1.86585e165	0.319923
$971$	9.48314e165	1.53562	0.767812	−	0.640675i	$-0.221346\pi$
$971$	9.48314e165	1.53562	0.767812	+	0.640675i	$0.221346\pi$
$972$	−1.88348e165	−0.288060
$973$	2.34238e165	0.338373
$974$	−5.46858e165	−0.746196
$975$	4.80377e165	0.619193
$976$	1.04252e166	1.26946
$977$	−1.09593e166	−1.26076	−0.630380	−	0.776286i	$-0.717101\pi$
$977$	−1.09593e166	−1.26076	−0.630380	+	0.776286i	$0.717101\pi$
$978$	1.27291e166	1.38354
$979$	−3.59118e165	−0.368806
$980$	2.06613e165	0.200499
$981$	8.89352e164	0.0815537
$982$	−2.60820e166	−2.26024
$983$	1.38337e166	1.13297	0.566484	−	0.824073i	$-0.308303\pi$
$983$	1.38337e166	1.13297	0.566484	+	0.824073i	$0.308303\pi$
$984$	−1.90684e165	−0.147600
$985$	9.05047e164	0.0662156
$986$	2.05607e166	1.42190
$987$	−2.82760e166	−1.84849
$988$	6.66365e165	0.411815
$989$	3.32679e166	1.94371
$990$	−4.17792e164	−0.0230785
$991$	−8.26283e165	−0.431560	−0.215780	−	0.976442i	$-0.569229\pi$
$991$	−8.26283e165	−0.431560	−0.215780	+	0.976442i	$0.569229\pi$
$992$	−8.73806e165	−0.431536
$993$	−3.09061e166	−1.44331
$994$	−7.44431e166	−3.28761
$995$	−3.86772e165	−0.161538
$996$	−6.33019e165	−0.250048
$997$	4.58076e166	1.71142	0.855710	−	0.517455i	$-0.173121\pi$
$997$	4.58076e166	1.71142	0.855710	+	0.517455i	$0.173121\pi$
$998$	1.49559e165	0.0528526
$999$	−2.34327e166	−0.783317

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.112.a.a.1.2	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.112.a.a.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-7.33726e16 q^{2} -2.81001e26 q^{3} +2.78739e33 q^{4} +1.03167e38 q^{5} +2.06178e43 q^{6} -1.16535e47 q^{7} -1.40317e49 q^{8} -1.23360e52 q^{9} +O(q^{10})\)	\(q-7.33726e16 q^{2} -2.81001e26 q^{3} +2.78739e33 q^{4} +1.03167e38 q^{5} +2.06178e43 q^{6} -1.16535e47 q^{7} -1.40317e49 q^{8} -1.23360e52 q^{9} -7.56964e54 q^{10} -4.47415e57 q^{11} -7.83259e59 q^{12} +4.56429e61 q^{13} +8.55050e63 q^{14} -2.89901e64 q^{15} -6.20693e66 q^{16} +1.57085e68 q^{17} +9.05124e68 q^{18} +5.23772e70 q^{19} +2.87567e71 q^{20} +3.27466e73 q^{21} +3.28280e74 q^{22} -4.90343e75 q^{23} +3.94291e75 q^{24} -3.74543e77 q^{25} -3.34893e78 q^{26} +2.91211e79 q^{27} -3.24829e80 q^{28} -1.78390e81 q^{29} +2.12708e81 q^{30} -1.77658e82 q^{31} +4.91847e83 q^{32} +1.25724e84 q^{33} -1.15257e85 q^{34} -1.20226e85 q^{35} -3.43852e85 q^{36} -8.04663e86 q^{37} -3.84305e87 q^{38} -1.28257e88 q^{39} -1.44761e87 q^{40} -4.83612e89 q^{41} -2.40270e90 q^{42} -6.78462e90 q^{43} -1.24712e91 q^{44} -1.27267e90 q^{45} +3.59777e92 q^{46} -8.63480e92 q^{47} +1.74415e93 q^{48} +7.18488e93 q^{49} +2.74812e94 q^{50} -4.41409e94 q^{51} +1.27224e95 q^{52} -6.44145e95 q^{53} -2.13669e96 q^{54} -4.61585e95 q^{55} +1.63519e96 q^{56} -1.47180e97 q^{57} +1.30889e98 q^{58} +2.31564e98 q^{59} -8.08066e97 q^{60} -1.67961e99 q^{61} +1.30352e99 q^{62} +1.43758e99 q^{63} -1.99740e100 q^{64} +4.70885e99 q^{65} -9.22469e100 q^{66} +2.49001e101 q^{67} +4.37856e101 q^{68} +1.37787e102 q^{69} +8.82131e101 q^{70} -8.70628e102 q^{71} +1.73095e101 q^{72} -2.93019e103 q^{73} +5.90402e103 q^{74} +1.05247e104 q^{75} +1.45995e104 q^{76} +5.21396e104 q^{77} +9.41054e104 q^{78} +2.11147e105 q^{79} -6.40352e104 q^{80} -7.05682e105 q^{81} +3.54839e106 q^{82} +8.08186e105 q^{83} +9.12774e106 q^{84} +1.62060e106 q^{85} +4.97805e107 q^{86} +5.01277e107 q^{87} +6.27797e106 q^{88} +8.02651e107 q^{89} +9.33791e106 q^{90} -5.31901e108 q^{91} -1.36678e109 q^{92} +4.99221e108 q^{93} +6.33557e109 q^{94} +5.40361e108 q^{95} -1.38209e110 q^{96} -2.46491e110 q^{97} -5.27173e110 q^{98} +5.51931e109 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 73\!\cdots\!76 q^{2}+ \cdots + 44\!\cdots\!13 q^{9}+O(q^{10}) \) 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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