LMFDB - Embedded newform 1.112.a.a.1.8

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			1.8
Root			$1.06213e15$ 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)

$f(q)$	$=$	$q+7.72845e16 q^{2} +5.46172e26 q^{3} +3.37675e33 q^{4} +2.64030e38 q^{5} +4.22106e43 q^{6} +1.15348e47 q^{7} +6.03282e49 q^{8} +2.07006e53 q^{9} +O(q^{10})$	\(q+7.72845e16 q^{2} +5.46172e26 q^{3} +3.37675e33 q^{4} +2.64030e38 q^{5} +4.22106e43 q^{6} +1.15348e47 q^{7} +6.03282e49 q^{8} +2.07006e53 q^{9} +2.04054e55 q^{10} +1.44065e57 q^{11} +1.84428e60 q^{12} +7.18299e61 q^{13} +8.91465e63 q^{14} +1.44206e65 q^{15} -4.10410e66 q^{16} -2.34132e68 q^{17} +1.59984e70 q^{18} -1.51112e71 q^{19} +8.91561e71 q^{20} +6.30001e73 q^{21} +1.11340e74 q^{22} -3.38533e75 q^{23} +3.29496e76 q^{24} -3.15474e77 q^{25} +5.55134e78 q^{26} +6.31969e79 q^{27} +3.89503e80 q^{28} -3.19272e80 q^{29} +1.11449e82 q^{30} -3.12606e82 q^{31} -4.73804e83 q^{32} +7.86845e83 q^{33} -1.80948e85 q^{34} +3.04554e85 q^{35} +6.99008e86 q^{36} +1.41760e87 q^{37} -1.16786e88 q^{38} +3.92315e88 q^{39} +1.59284e88 q^{40} +2.68935e89 q^{41} +4.86893e90 q^{42} +1.11115e90 q^{43} +4.86473e90 q^{44} +5.46558e91 q^{45} -2.61634e92 q^{46} -2.44186e92 q^{47} -2.24155e93 q^{48} +6.90966e93 q^{49} -2.43813e94 q^{50} -1.27876e95 q^{51} +2.42551e95 q^{52} -2.55871e95 q^{53} +4.88414e96 q^{54} +3.80375e95 q^{55} +6.95876e96 q^{56} -8.25333e97 q^{57} -2.46748e97 q^{58} +7.60791e96 q^{59} +4.86946e98 q^{60} -1.41871e99 q^{61} -2.41596e99 q^{62} +2.38779e100 q^{63} -2.59629e100 q^{64} +1.89652e100 q^{65} +6.08110e100 q^{66} +7.85405e100 q^{67} -7.90605e101 q^{68} -1.84897e102 q^{69} +2.35373e102 q^{70} +3.19368e102 q^{71} +1.24883e103 q^{72} +2.79589e103 q^{73} +1.09558e104 q^{74} -1.72303e104 q^{75} -5.10268e104 q^{76} +1.66177e104 q^{77} +3.03199e105 q^{78} +8.38653e104 q^{79} -1.08360e105 q^{80} +1.56172e106 q^{81} +2.07845e106 q^{82} -2.05152e106 q^{83} +2.12735e107 q^{84} -6.18178e106 q^{85} +8.58744e106 q^{86} -1.74377e107 q^{87} +8.69121e106 q^{88} +1.94865e108 q^{89} +4.22405e108 q^{90} +8.28547e108 q^{91} -1.14314e109 q^{92} -1.70737e109 q^{93} -1.88718e109 q^{94} -3.98981e109 q^{95} -2.58779e110 q^{96} -1.03356e110 q^{97} +5.34010e110 q^{98} +2.98225e110 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	7.72845e16	1.51680	0.758399	−	0.651791i	$-0.225982\pi$
$2$	7.72845e16	1.51680	0.758399	+	0.651791i	$0.225982\pi$
$3$	5.46172e26	1.80759	0.903795	−	0.427966i	$-0.140770\pi$
$3$	5.46172e26	1.80759	0.903795	+	0.427966i	$0.140770\pi$
$4$	3.37675e33	1.30068
$5$	2.64030e38	0.425419	0.212710	−	0.977115i	$-0.431771\pi$
$5$	2.64030e38	0.425419	0.212710	+	0.977115i	$0.431771\pi$
$6$	4.22106e43	2.74175
$7$	1.15348e47	1.44235	0.721175	−	0.692753i	$-0.243602\pi$
$7$	1.15348e47	1.44235	0.721175	+	0.692753i	$0.243602\pi$
$8$	6.03282e49	0.456064
$9$	2.07006e53	2.26738
$10$	2.04054e55	0.645275
$11$	1.44065e57	0.229755	0.114878	−	0.993380i	$-0.463352\pi$
$11$	1.44065e57	0.229755	0.114878	+	0.993380i	$0.463352\pi$
$12$	1.84428e60	2.35109
$13$	7.18299e61	1.07758	0.538790	−	0.842440i	$-0.318882\pi$
$13$	7.18299e61	1.07758	0.538790	+	0.842440i	$0.318882\pi$
$14$	8.91465e63	2.18775
$15$	1.44206e65	0.768984
$16$	−4.10410e66	−0.608919
$17$	−2.34132e68	−1.20101	−0.600504	−	0.799622i	$-0.705033\pi$
$17$	−2.34132e68	−1.20101	−0.600504	+	0.799622i	$0.705033\pi$
$18$	1.59984e70	3.43916
$19$	−1.51112e71	−1.61612	−0.808062	−	0.589098i	$-0.799483\pi$
$19$	−1.51112e71	−1.61612	−0.808062	+	0.589098i	$0.799483\pi$
$20$	8.91561e71	0.553333
$21$	6.30001e73	2.60718
$22$	1.11340e74	0.348493
$23$	−3.38533e75	−0.898889	−0.449445	−	0.893308i	$-0.648378\pi$
$23$	−3.38533e75	−0.898889	−0.449445	+	0.893308i	$0.648378\pi$
$24$	3.29496e76	0.824377
$25$	−3.15474e77	−0.819018
$26$	5.55134e78	1.63447
$27$	6.31969e79	2.29090
$28$	3.89503e80	1.87603
$29$	−3.19272e80	−0.219317	−0.109658	−	0.993969i	$-0.534976\pi$
$29$	−3.19272e80	−0.219317	−0.109658	+	0.993969i	$0.534976\pi$
$30$	1.11449e82	1.16639
$31$	−3.12606e82	−0.530180	−0.265090	−	0.964224i	$-0.585402\pi$
$31$	−3.12606e82	−0.530180	−0.265090	+	0.964224i	$0.585402\pi$
$32$	−4.73804e83	−1.37967
$33$	7.86845e83	0.415304
$34$	−1.80948e85	−1.82169
$35$	3.04554e85	0.613604
$36$	6.99008e86	2.94913
$37$	1.41760e87	1.30725	0.653623	−	0.756820i	$-0.273248\pi$
$37$	1.41760e87	1.30725	0.653623	+	0.756820i	$0.273248\pi$
$38$	−1.16786e88	−2.45133
$39$	3.92315e88	1.94782
$40$	1.59284e88	0.194019
$41$	2.68935e89	0.832040	0.416020	−	0.909356i	$-0.363425\pi$
$41$	2.68935e89	0.832040	0.416020	+	0.909356i	$0.363425\pi$
$42$	4.86893e90	3.95456
$43$	1.11115e90	0.244496	0.122248	−	0.992500i	$-0.460990\pi$
$43$	1.11115e90	0.244496	0.122248	+	0.992500i	$0.460990\pi$
$44$	4.86473e90	0.298837
$45$	5.46558e91	0.964587
$46$	−2.61634e92	−1.36343
$47$	−2.44186e92	−0.385736	−0.192868	−	0.981225i	$-0.561779\pi$
$47$	−2.44186e92	−0.385736	−0.192868	+	0.981225i	$0.561779\pi$
$48$	−2.24155e93	−1.10067
$49$	6.90966e93	1.08037
$50$	−2.43813e94	−1.24229
$51$	−1.27876e95	−2.17093
$52$	2.42551e95	1.40158
$53$	−2.55871e95	−0.513701	−0.256850	−	0.966451i	$-0.582685\pi$
$53$	−2.55871e95	−0.513701	−0.256850	+	0.966451i	$0.582685\pi$
$54$	4.88414e96	3.47484
$55$	3.80375e95	0.0977424
$56$	6.95876e96	0.657804
$57$	−8.25333e97	−2.92129
$58$	−2.46748e97	−0.332659
$59$	7.60791e96	0.0397172	0.0198586	−	0.999803i	$-0.493678\pi$
$59$	7.60791e96	0.0397172	0.0198586	+	0.999803i	$0.493678\pi$
$60$	4.86946e98	1.00020
$61$	−1.41871e99	−1.16436	−0.582182	−	0.813059i	$-0.697801\pi$
$61$	−1.41871e99	−1.16436	−0.582182	+	0.813059i	$0.697801\pi$
$62$	−2.41596e99	−0.804176
$63$	2.38779e100	3.27036
$64$	−2.59629e100	−1.48376
$65$	1.89652e100	0.458423
$66$	6.08110e100	0.629932
$67$	7.85405e100	0.353136	0.176568	−	0.984288i	$-0.443500\pi$
$67$	7.85405e100	0.353136	0.176568	+	0.984288i	$0.443500\pi$
$68$	−7.90605e101	−1.56212
$69$	−1.84897e102	−1.62482
$70$	2.35373e102	0.930713
$71$	3.19368e102	0.574715	0.287357	−	0.957823i	$-0.407223\pi$
$71$	3.19368e102	0.574715	0.287357	+	0.957823i	$0.407223\pi$
$72$	1.24883e103	1.03407
$73$	2.79589e103	1.07672	0.538358	−	0.842716i	$-0.319045\pi$
$73$	2.79589e103	1.07672	0.538358	+	0.842716i	$0.319045\pi$
$74$	1.09558e104	1.98283
$75$	−1.72303e104	−1.48045
$76$	−5.10268e104	−2.10205
$77$	1.66177e104	0.331388
$78$	3.03199e105	2.95445
$79$	8.38653e104	0.402976	0.201488	−	0.979491i	$-0.435422\pi$
$79$	8.38653e104	0.402976	0.201488	+	0.979491i	$0.435422\pi$
$80$	−1.08360e105	−0.259046
$81$	1.56172e106	1.87363
$82$	2.07845e106	1.26204
$83$	−2.05152e106	−0.635685	−0.317843	−	0.948143i	$-0.602958\pi$
$83$	−2.05152e106	−0.635685	−0.317843	+	0.948143i	$0.602958\pi$
$84$	2.12735e107	3.39109
$85$	−6.18178e106	−0.510932
$86$	8.58744e106	0.370851
$87$	−1.74377e107	−0.396435
$88$	8.69121e106	0.104783
$89$	1.94865e108	1.25484	0.627421	−	0.778680i	$-0.284110\pi$
$89$	1.94865e108	1.25484	0.627421	+	0.778680i	$0.284110\pi$
$90$	4.22405e108	1.46308
$91$	8.28547e108	1.55425
$92$	−1.14314e109	−1.16916
$93$	−1.70737e109	−0.958348
$94$	−1.88718e109	−0.585084
$95$	−3.98981e109	−0.687530
$96$	−2.58779e110	−2.49388
$97$	−1.03356e110	−0.560408	−0.280204	−	0.959940i	$-0.590402\pi$
$97$	−1.03356e110	−0.560408	−0.280204	+	0.959940i	$0.590402\pi$
$98$	5.34010e110	1.63871
$99$	2.98225e110	0.520943
$100$	−1.06528e111	−1.06528
$101$	5.22716e110	0.300905	0.150453	−	0.988617i	$-0.451927\pi$
$101$	5.22716e110	0.300905	0.150453	+	0.988617i	$0.451927\pi$
$102$	−9.88286e111	−3.29286
$103$	6.53103e111	1.26624	0.633120	−	0.774054i	$-0.281774\pi$
$103$	6.53103e111	1.26624	0.633120	+	0.774054i	$0.281774\pi$
$104$	4.33337e111	0.491445
$105$	1.66339e112	1.10914
$106$	−1.97749e112	−0.779180
$107$	2.71504e112	0.635296	0.317648	−	0.948209i	$-0.397107\pi$
$107$	2.71504e112	0.635296	0.317648	+	0.948209i	$0.397107\pi$
$108$	2.13400e113	2.97972
$109$	−1.68778e113	−1.41301	−0.706503	−	0.707710i	$-0.749728\pi$
$109$	−1.68778e113	−1.41301	−0.706503	+	0.707710i	$0.749728\pi$
$110$	2.93971e112	0.148256
$111$	7.74253e113	2.36297
$112$	−4.73402e113	−0.878274
$113$	1.31043e114	1.48443	0.742217	−	0.670159i	$-0.233774\pi$
$113$	1.31043e114	1.48443	0.742217	+	0.670159i	$0.233774\pi$
$114$	−6.37854e114	−4.43100
$115$	−8.93827e113	−0.382405
$116$	−1.07810e114	−0.285260
$117$	1.48692e115	2.44328
$118$	5.87974e113	0.0602430
$119$	−2.70068e115	−1.73227
$120$	8.69966e114	0.350706
$121$	−3.72422e115	−0.947212
$122$	−1.09644e116	−1.76610
$123$	1.46885e116	1.50399
$124$	−1.05559e116	−0.689593
$125$	−1.84995e116	−0.773846
$126$	1.84539e117	4.96047
$127$	−2.54820e115	−0.0441700	−0.0220850	−	0.999756i	$-0.507030\pi$
$127$	−2.54820e115	−0.0441700	−0.0220850	+	0.999756i	$0.507030\pi$
$128$	−7.76462e116	−0.870897
$129$	6.06877e116	0.441949
$130$	1.46572e117	0.695335
$131$	−4.25315e117	−1.31872	−0.659362	−	0.751825i	$-0.729174\pi$
$131$	−4.25315e117	−1.31872	−0.659362	+	0.751825i	$0.729174\pi$
$132$	2.65698e117	0.540175
$133$	−1.74306e118	−2.33102
$134$	6.06996e117	0.535636
$135$	1.66858e118	0.974595
$136$	−1.41248e118	−0.547737
$137$	−3.86790e117	−0.0998812	−0.0499406	−	0.998752i	$-0.515903\pi$
$137$	−3.86790e117	−0.0998812	−0.0499406	+	0.998752i	$0.515903\pi$
$138$	−1.42897e119	−2.46453
$139$	1.05527e119	1.21911	0.609553	−	0.792745i	$-0.291349\pi$
$139$	1.05527e119	1.21911	0.609553	+	0.792745i	$0.291349\pi$
$140$	1.02840e119	0.798099
$141$	−1.33368e119	−0.697252
$142$	2.46822e119	0.871726
$143$	1.03482e119	0.247580
$144$	−8.49575e119	−1.38065
$145$	−8.42972e118	−0.0933016
$146$	2.16079e120	1.63316
$147$	3.77386e120	1.95287
$148$	4.78687e120	1.70030
$149$	−3.46482e120	−0.846920	−0.423460	−	0.905915i	$-0.639185\pi$
$149$	−3.46482e120	−0.846920	−0.423460	+	0.905915i	$0.639185\pi$
$150$	−1.33164e121	−2.24554
$151$	2.44906e120	0.285614	0.142807	−	0.989751i	$-0.454387\pi$
$151$	2.44906e120	0.285614	0.142807	+	0.989751i	$0.454387\pi$
$152$	−9.11632e120	−0.737056
$153$	−4.84668e121	−2.72314
$154$	1.28429e121	0.502648
$155$	−8.25373e120	−0.225549
$156$	1.32475e122	2.53348
$157$	−3.10531e121	−0.416557	−0.208278	−	0.978070i	$-0.566786\pi$
$157$	−3.10531e121	−0.416557	−0.208278	+	0.978070i	$0.566786\pi$
$158$	6.48149e121	0.611232
$159$	−1.39750e122	−0.928560
$160$	−1.25098e122	−0.586939
$161$	−3.90493e122	−1.29651
$162$	1.20697e123	2.84192
$163$	−2.68202e122	−0.448798	−0.224399	−	0.974497i	$-0.572042\pi$
$163$	−2.68202e122	−0.448798	−0.224399	+	0.974497i	$0.572042\pi$
$164$	9.08127e122	1.08221
$165$	2.07750e122	0.176678
$166$	−1.58551e123	−0.964206
$167$	1.02267e123	0.445626	0.222813	−	0.974861i	$-0.428476\pi$
$167$	1.02267e123	0.445626	0.222813	+	0.974861i	$0.428476\pi$
$168$	3.80068e123	1.18904
$169$	7.16167e122	0.161177
$170$	−4.77756e123	−0.774980
$171$	−3.12812e124	−3.66437
$172$	3.75206e123	0.318010
$173$	2.95911e124	1.81803	0.909017	−	0.416760i	$-0.136834\pi$
$173$	2.95911e124	1.81803	0.909017	+	0.416760i	$0.136834\pi$
$174$	−1.34767e124	−0.601311
$175$	−3.63895e124	−1.18131
$176$	−5.91259e123	−0.139902
$177$	4.15523e123	0.0717925
$178$	1.50601e125	1.90334
$179$	6.90782e124	0.639732	0.319866	−	0.947463i	$-0.396362\pi$
$179$	6.90782e124	0.639732	0.319866	+	0.947463i	$0.396362\pi$
$180$	1.84559e125	1.25462
$181$	−2.79030e125	−1.39473	−0.697364	−	0.716718i	$-0.745644\pi$
$181$	−2.79030e125	−1.39473	−0.697364	+	0.716718i	$0.745644\pi$
$182$	6.40338e125	2.35748
$183$	−7.74861e125	−2.10469
$184$	−2.04231e125	−0.409951
$185$	3.74288e125	0.556128
$186$	−1.31953e126	−1.45362
$187$	−3.37303e125	−0.275938
$188$	−8.24555e125	−0.501717
$189$	7.28966e126	3.30428
$190$	−3.08350e126	−1.04284
$191$	4.67689e126	1.18197	0.590984	−	0.806683i	$-0.298740\pi$
$191$	4.67689e126	1.18197	0.590984	+	0.806683i	$0.298740\pi$
$192$	−1.41802e127	−2.68203
$193$	−1.37201e127	−1.94503	−0.972515	−	0.232840i	$-0.925198\pi$
$193$	−1.37201e127	−1.94503	−0.972515	+	0.232840i	$0.925198\pi$
$194$	−7.98782e126	−0.850026
$195$	1.03583e127	0.828641
$196$	2.33322e127	1.40522
$197$	3.75832e127	1.70655	0.853273	−	0.521464i	$-0.174614\pi$
$197$	3.75832e127	1.70655	0.853273	+	0.521464i	$0.174614\pi$
$198$	2.30481e127	0.790165
$199$	5.42417e126	0.140601	0.0703004	−	0.997526i	$-0.477604\pi$
$199$	5.42417e126	0.140601	0.0703004	+	0.997526i	$0.477604\pi$
$200$	−1.90320e127	−0.373525
$201$	4.28966e127	0.638325
$202$	4.03979e127	0.456412
$203$	−3.68275e127	−0.316331
$204$	−4.31806e128	−2.82367
$205$	7.10069e127	0.353966
$206$	5.04748e128	1.92063
$207$	−7.00785e128	−2.03812
$208$	−2.94797e128	−0.656158
$209$	−2.17700e128	−0.371313
$210$	1.28554e129	1.68235
$211$	−9.24485e128	−0.929445	−0.464722	−	0.885457i	$-0.653846\pi$
$211$	−9.24485e128	−0.929445	−0.464722	+	0.885457i	$0.653846\pi$
$212$	−8.64012e128	−0.668158
$213$	1.74430e129	1.03885
$214$	2.09830e129	0.963616
$215$	2.93376e128	0.104013
$216$	3.81255e129	1.04480
$217$	−3.60587e129	−0.764706
$218$	−1.30439e130	−2.14324
$219$	1.52704e130	1.94626
$220$	1.28443e129	0.127131
$221$	−1.68177e130	−1.29418
$222$	5.98377e130	3.58414
$223$	−1.52940e130	−0.713841	−0.356921	−	0.934135i	$-0.616173\pi$
$223$	−1.52940e130	−0.713841	−0.356921	+	0.934135i	$0.616173\pi$
$224$	−5.46526e130	−1.98997
$225$	−6.53052e130	−1.85703
$226$	1.01276e131	2.25159
$227$	9.48513e130	1.65047	0.825236	−	0.564788i	$-0.191042\pi$
$227$	9.48513e130	1.65047	0.825236	+	0.564788i	$0.191042\pi$
$228$	−2.78694e131	−3.79965
$229$	−8.03365e130	−0.859100	−0.429550	−	0.903043i	$-0.641328\pi$
$229$	−8.03365e130	−0.859100	−0.429550	+	0.903043i	$0.641328\pi$
$230$	−6.90790e130	−0.580031
$231$	9.07614e130	0.599013
$232$	−1.92611e130	−0.100022
$233$	2.94417e131	1.20423	0.602115	−	0.798409i	$-0.294325\pi$
$233$	2.94417e131	1.20423	0.602115	+	0.798409i	$0.294325\pi$
$234$	1.14916e132	3.70596
$235$	−6.44724e130	−0.164100
$236$	2.56900e130	0.0516592
$237$	4.58049e131	0.728414
$238$	−2.08721e132	−2.62751
$239$	−7.72398e131	−0.770474	−0.385237	−	0.922818i	$-0.625880\pi$
$239$	−7.72398e131	−0.770474	−0.385237	+	0.922818i	$0.625880\pi$
$240$	−5.91834e131	−0.468248
$241$	2.51722e132	1.58116	0.790578	−	0.612362i	$-0.209780\pi$
$241$	2.51722e132	1.58116	0.790578	+	0.612362i	$0.209780\pi$
$242$	−2.87825e132	−1.43673
$243$	2.75995e132	1.09586
$244$	−4.79063e132	−1.51446
$245$	1.82435e132	0.459612
$246$	1.13519e133	2.28124
$247$	−1.08544e133	−1.74150
$248$	−1.88590e132	−0.241796
$249$	−1.12048e133	−1.14906
$250$	−1.42973e133	−1.17377
$251$	−4.15793e132	−0.273518	−0.136759	−	0.990604i	$-0.543669\pi$
$251$	−4.15793e132	−0.273518	−0.136759	+	0.990604i	$0.543669\pi$
$252$	8.06295e133	4.25367
$253$	−4.87709e132	−0.206525
$254$	−1.96937e132	−0.0669970
$255$	−3.37631e133	−0.923555
$256$	7.39501e132	0.162787
$257$	−4.82220e133	−0.854982	−0.427491	−	0.904020i	$-0.640602\pi$
$257$	−4.82220e133	−0.854982	−0.427491	+	0.904020i	$0.640602\pi$
$258$	4.69022e133	0.670347
$259$	1.63518e134	1.88551
$260$	6.40407e133	0.596260
$261$	−6.60913e133	−0.497274
$262$	−3.28703e134	−2.00024
$263$	−7.10902e133	−0.350159	−0.175080	−	0.984554i	$-0.556018\pi$
$263$	−7.10902e133	−0.350159	−0.175080	+	0.984554i	$0.556018\pi$
$264$	4.74689e133	0.189405
$265$	−6.75575e133	−0.218538
$266$	−1.34711e135	−3.53568
$267$	1.06430e135	2.26824
$268$	2.65211e134	0.459315
$269$	−8.37325e134	−1.17935	−0.589675	−	0.807641i	$-0.700744\pi$
$269$	−8.37325e134	−1.17935	−0.589675	+	0.807641i	$0.700744\pi$
$270$	1.28956e135	1.47826
$271$	7.07063e133	0.0660180	0.0330090	−	0.999455i	$-0.489491\pi$
$271$	7.07063e133	0.0660180	0.0330090	+	0.999455i	$0.489491\pi$
$272$	9.60902e134	0.731316
$273$	4.52529e135	2.80944
$274$	−2.98929e134	−0.151500
$275$	−4.54490e134	−0.188174
$276$	−6.24351e135	−2.11337
$277$	−5.33984e135	−1.47877	−0.739386	−	0.673281i	$-0.764884\pi$
$277$	−5.33984e135	−1.47877	−0.739386	+	0.673281i	$0.764884\pi$
$278$	8.15559e135	1.84914
$279$	−6.47115e135	−1.20212
$280$	1.83732e135	0.279843
$281$	3.97801e135	0.497125	0.248562	−	0.968616i	$-0.420042\pi$
$281$	3.97801e135	0.497125	0.248562	+	0.968616i	$0.420042\pi$
$282$	−1.03073e136	−1.05759
$283$	1.06408e136	0.897069	0.448535	−	0.893765i	$-0.351946\pi$
$283$	1.06408e136	0.897069	0.448535	+	0.893765i	$0.351946\pi$
$284$	1.07842e136	0.747518
$285$	−2.17912e136	−1.24277
$286$	7.99756e135	0.375528
$287$	3.10213e136	1.20009
$288$	−9.80805e136	−3.12824
$289$	1.68137e136	0.442419
$290$	−6.51487e135	−0.141520
$291$	−5.64502e136	−1.01299
$292$	9.44101e136	1.40046
$293$	1.10399e136	0.135461	0.0677303	−	0.997704i	$-0.478424\pi$
$293$	1.10399e136	0.135461	0.0677303	+	0.997704i	$0.478424\pi$
$294$	2.91661e137	2.96211
$295$	2.00871e135	0.0168965
$296$	8.55211e136	0.596188
$297$	9.10449e136	0.526347
$298$	−2.67777e137	−1.28461
$299$	−2.43168e137	−0.968624
$300$	−5.81825e137	−1.92558
$301$	1.28169e137	0.352649
$302$	1.89275e137	0.433219
$303$	2.85493e137	0.543913
$304$	6.20180e137	0.984088
$305$	−3.74582e137	−0.495343
$306$	−3.74573e138	−4.13045
$307$	7.37205e137	0.678279	0.339139	−	0.940736i	$-0.389864\pi$
$307$	7.37205e137	0.678279	0.339139	+	0.940736i	$0.389864\pi$
$308$	5.61139e137	0.431028
$309$	3.56707e138	2.28884
$310$	−6.37885e137	−0.342112
$311$	4.10271e137	0.184022	0.0920109	−	0.995758i	$-0.470671\pi$
$311$	4.10271e137	0.184022	0.0920109	+	0.995758i	$0.470671\pi$
$312$	2.36676e138	0.888331
$313$	1.74273e138	0.547671	0.273835	−	0.961777i	$-0.411708\pi$
$313$	1.74273e138	0.547671	0.273835	+	0.961777i	$0.411708\pi$
$314$	−2.39992e138	−0.631832
$315$	6.30446e138	1.39127
$316$	2.83192e138	0.524140
$317$	−9.47538e138	−1.47166	−0.735830	−	0.677166i	$-0.763208\pi$
$317$	−9.47538e138	−1.47166	−0.735830	+	0.677166i	$0.763208\pi$
$318$	−1.08005e139	−1.40844
$319$	−4.59960e137	−0.0503892
$320$	−6.85497e138	−0.631221
$321$	1.48288e139	1.14835
$322$	−3.01790e139	−1.96655
$323$	3.53802e139	1.94098
$324$	5.27353e139	2.43699
$325$	−2.26605e139	−0.882557
$326$	−2.07279e139	−0.680735
$327$	−9.21816e139	−2.55413
$328$	1.62244e139	0.379463
$329$	−2.81665e139	−0.556366
$330$	1.60559e139	0.267985
$331$	−2.03506e139	−0.287160	−0.143580	−	0.989639i	$-0.545861\pi$
$331$	−2.03506e139	−0.287160	−0.143580	+	0.989639i	$0.545861\pi$
$332$	−6.92747e139	−0.826820
$333$	2.93452e140	2.96402
$334$	7.90364e139	0.675925
$335$	2.07370e139	0.150231
$336$	−2.58559e140	−1.58756
$337$	3.13043e140	1.62984	0.814918	−	0.579577i	$-0.196782\pi$
$337$	3.13043e140	1.62984	0.814918	+	0.579577i	$0.196782\pi$
$338$	5.53486e139	0.244472
$339$	7.15722e140	2.68325
$340$	−2.08743e140	−0.664557
$341$	−4.50358e139	−0.121812
$342$	−2.41755e141	−5.55810
$343$	5.92940e139	0.115928
$344$	6.70335e139	0.111506
$345$	−4.88184e140	−0.691231
$346$	2.28693e141	2.75759
$347$	−7.24586e140	−0.744396	−0.372198	−	0.928153i	$-0.621396\pi$
$347$	−7.24586e140	−0.744396	−0.372198	+	0.928153i	$0.621396\pi$
$348$	−5.88828e140	−0.515633
$349$	1.35577e141	1.01245	0.506225	−	0.862401i	$-0.331040\pi$
$349$	1.35577e141	1.01245	0.506225	+	0.862401i	$0.331040\pi$
$350$	−2.81234e141	−1.79181
$351$	4.53942e141	2.46863
$352$	−6.82589e140	−0.316987
$353$	−2.30005e140	−0.0912519	−0.0456260	−	0.998959i	$-0.514528\pi$
$353$	−2.30005e140	−0.0912519	−0.0456260	+	0.998959i	$0.514528\pi$
$354$	3.21135e140	0.108895
$355$	8.43225e140	0.244495
$356$	6.58011e141	1.63214
$357$	−1.47503e142	−3.13124
$358$	5.33868e141	0.970344
$359$	4.73871e141	0.737765	0.368883	−	0.929476i	$-0.379740\pi$
$359$	4.73871e141	0.737765	0.368883	+	0.929476i	$0.379740\pi$
$360$	3.29728e141	0.439914
$361$	1.40921e142	1.61186
$362$	−2.15647e142	−2.11552
$363$	−2.03407e142	−1.71217
$364$	2.79779e142	2.02157
$365$	7.38197e141	0.458056
$366$	−5.98847e142	−3.19239
$367$	−4.38893e141	−0.201091	−0.100545	−	0.994932i	$-0.532059\pi$
$367$	−4.38893e141	−0.201091	−0.100545	+	0.994932i	$0.532059\pi$
$368$	1.38937e142	0.547350
$369$	5.56713e142	1.88655
$370$	2.89267e142	0.843534
$371$	−2.95143e142	−0.740937
$372$	−5.76535e142	−1.24650
$373$	3.43254e141	0.0639404	0.0319702	−	0.999489i	$-0.489822\pi$
$373$	3.43254e141	0.0639404	0.0319702	+	0.999489i	$0.489822\pi$
$374$	−2.60683e142	−0.418542
$375$	−1.01039e143	−1.39880
$376$	−1.47313e142	−0.175920
$377$	−2.29333e142	−0.236331
$378$	5.63378e143	5.01193
$379$	1.17941e143	0.906123	0.453061	−	0.891479i	$-0.350332\pi$
$379$	1.17941e143	0.906123	0.453061	+	0.891479i	$0.350332\pi$
$380$	−1.34726e143	−0.894254
$381$	−1.39176e142	−0.0798413
$382$	3.61451e143	1.79281
$383$	−3.00959e143	−1.29115	−0.645573	−	0.763699i	$-0.723381\pi$
$383$	−3.00959e143	−1.29115	−0.645573	+	0.763699i	$0.723381\pi$
$384$	−4.24082e143	−1.57423
$385$	4.38757e142	0.140979
$386$	−1.06035e144	−2.95022
$387$	2.30014e143	0.554366
$388$	−3.49007e143	−0.728909
$389$	−5.10071e143	−0.923481	−0.461741	−	0.887015i	$-0.652775\pi$
$389$	−5.10071e143	−0.923481	−0.461741	+	0.887015i	$0.652775\pi$
$390$	8.00534e143	1.25688
$391$	7.92615e143	1.07957
$392$	4.16847e143	0.492720
$393$	−2.32295e144	−2.38371
$394$	2.90460e144	2.58849
$395$	2.21429e143	0.171434
$396$	1.00703e144	0.677578
$397$	2.39034e144	1.39826	0.699128	−	0.714996i	$-0.253572\pi$
$397$	2.39034e144	1.39826	0.699128	+	0.714996i	$0.253572\pi$
$398$	4.19204e143	0.213263
$399$	−9.52009e144	−4.21352
$400$	1.29474e144	0.498715
$401$	2.93366e144	0.983778	0.491889	−	0.870658i	$-0.336307\pi$
$401$	2.93366e144	0.983778	0.491889	+	0.870658i	$0.336307\pi$
$402$	3.31524e144	0.968210
$403$	−2.24545e144	−0.571311
$404$	1.76508e144	0.391380
$405$	4.12340e144	0.797079
$406$	−2.84620e144	−0.479811
$407$	2.04227e144	0.300347
$408$	−7.71455e144	−0.990083
$409$	−8.81721e144	−0.987842	−0.493921	−	0.869507i	$-0.664437\pi$
$409$	−8.81721e144	−0.987842	−0.493921	+	0.869507i	$0.664437\pi$
$410$	5.48773e144	0.536894
$411$	−2.11254e144	−0.180544
$412$	2.20536e145	1.64697
$413$	8.77562e143	0.0572862
$414$	−5.41598e145	−3.09142
$415$	−5.41663e144	−0.270433
$416$	−3.40333e145	−1.48670
$417$	5.76358e145	2.20364
$418$	−1.68249e145	−0.563207
$419$	5.10296e145	1.49604	0.748022	−	0.663674i	$-0.231004\pi$
$419$	5.10296e145	1.49604	0.748022	+	0.663674i	$0.231004\pi$
$420$	5.61685e145	1.44264
$421$	5.39517e145	1.21436	0.607182	−	0.794563i	$-0.292300\pi$
$421$	5.39517e145	1.21436	0.607182	+	0.794563i	$0.292300\pi$
$422$	−7.14483e145	−1.40978
$423$	−5.05481e145	−0.874610
$424$	−1.54362e145	−0.234281
$425$	7.38627e145	0.983647
$426$	1.34807e146	1.57572
$427$	−1.63646e146	−1.67942
$428$	9.16799e145	0.826314
$429$	5.65190e145	0.447522
$430$	2.26734e145	0.157767
$431$	−1.20323e146	−0.735972	−0.367986	−	0.929831i	$-0.619953\pi$
$431$	−1.20323e146	−0.735972	−0.367986	+	0.929831i	$0.619953\pi$
$432$	−2.59366e146	−1.39497
$433$	−1.88141e146	−0.890031	−0.445015	−	0.895523i	$-0.646802\pi$
$433$	−1.88141e146	−0.890031	−0.445015	+	0.895523i	$0.646802\pi$
$434$	−2.78678e146	−1.15990
$435$	−4.60408e145	−0.168651
$436$	−5.69919e146	−1.83786
$437$	5.11565e146	1.45272
$438$	1.18016e147	2.95208
$439$	−4.86267e146	−1.07175	−0.535875	−	0.844297i	$-0.680018\pi$
$439$	−4.86267e146	−1.07175	−0.535875	+	0.844297i	$0.680018\pi$
$440$	2.29474e145	0.0445768
$441$	1.43034e147	2.44962
$442$	−1.29975e147	−1.96301
$443$	−9.18192e144	−0.0122328	−0.00611641	−	0.999981i	$-0.501947\pi$
$443$	−9.18192e144	−0.0122328	−0.00611641	+	0.999981i	$0.501947\pi$
$444$	2.61445e147	3.07345
$445$	5.14502e146	0.533834
$446$	−1.18199e147	−1.08275
$447$	−1.89239e147	−1.53088
$448$	−2.99478e147	−2.14011
$449$	2.80895e147	1.77367	0.886833	−	0.462090i	$-0.152900\pi$
$449$	2.80895e147	1.77367	0.886833	+	0.462090i	$0.152900\pi$
$450$	−5.04708e147	−2.81673
$451$	3.87443e146	0.191166
$452$	4.42500e147	1.93077
$453$	1.33761e147	0.516273
$454$	7.33053e147	2.50343
$455$	2.18761e147	0.661207
$456$	−4.97908e147	−1.33230
$457$	−2.78314e147	−0.659457	−0.329729	−	0.944076i	$-0.606957\pi$
$457$	−2.78314e147	−0.659457	−0.329729	+	0.944076i	$0.606957\pi$
$458$	−6.20877e147	−1.30308
$459$	−1.47964e148	−2.75139
$460$	−3.01823e147	−0.497385
$461$	1.07180e148	1.56571	0.782857	−	0.622202i	$-0.213762\pi$
$461$	1.07180e148	1.56571	0.782857	+	0.622202i	$0.213762\pi$
$462$	7.01445e147	0.908582
$463$	−5.58821e147	−0.641989	−0.320995	−	0.947081i	$-0.604017\pi$
$463$	−5.58821e147	−0.641989	−0.320995	+	0.947081i	$0.604017\pi$
$464$	1.31032e147	0.133546
$465$	−4.50795e147	−0.407700
$466$	2.27539e148	1.82657
$467$	−2.67036e148	−1.90319	−0.951597	−	0.307350i	$-0.900558\pi$
$467$	−2.67036e148	−1.90319	−0.951597	+	0.307350i	$0.900558\pi$
$468$	5.02097e148	3.17792
$469$	9.05952e147	0.509346
$470$	−4.98272e147	−0.248906
$471$	−1.69603e148	−0.752963
$472$	4.58972e146	0.0181136
$473$	1.60078e147	0.0561744
$474$	3.54001e148	1.10486
$475$	4.76720e148	1.32364
$476$	−9.11951e148	−2.25313
$477$	−5.29669e148	−1.16476
$478$	−5.96944e148	−1.16865
$479$	−1.91802e148	−0.334374	−0.167187	−	0.985925i	$-0.553468\pi$
$479$	−1.91802e148	−0.334374	−0.167187	+	0.985925i	$0.553468\pi$
$480$	−6.83252e148	−1.06094
$481$	1.01826e149	1.40866
$482$	1.94542e149	2.39829
$483$	−2.13276e149	−2.34356
$484$	−1.25758e149	−1.23202
$485$	−2.72890e148	−0.238409
$486$	2.13301e149	1.66219
$487$	1.73004e149	1.20281	0.601407	−	0.798943i	$-0.294607\pi$
$487$	1.73004e149	1.20281	0.601407	+	0.798943i	$0.294607\pi$
$488$	−8.55883e148	−0.531024
$489$	−1.46485e149	−0.811242
$490$	1.40994e149	0.697139
$491$	2.17534e149	0.960515	0.480258	−	0.877128i	$-0.340543\pi$
$491$	2.17534e149	0.960515	0.480258	+	0.877128i	$0.340543\pi$
$492$	4.95994e149	1.95620
$493$	7.47518e148	0.263401
$494$	−8.38875e149	−2.64151
$495$	7.87401e148	0.221619
$496$	1.28297e149	0.322837
$497$	3.68386e149	0.828940
$498$	−8.65961e149	−1.74289
$499$	2.68868e149	0.484126	0.242063	−	0.970261i	$-0.422176\pi$
$499$	2.68868e149	0.484126	0.242063	+	0.970261i	$0.422176\pi$
$500$	−6.24681e149	−1.00652
$501$	5.58553e149	0.805509
$502$	−3.21344e149	−0.414871
$503$	−1.02195e150	−1.18143	−0.590714	−	0.806881i	$-0.701154\pi$
$503$	−1.02195e150	−1.18143	−0.590714	+	0.806881i	$0.701154\pi$
$504$	1.44051e150	1.49149
$505$	1.38013e149	0.128011
$506$	−3.76924e149	−0.313256
$507$	3.91150e149	0.291341
$508$	−8.60464e148	−0.0574509
$509$	3.76640e149	0.225470	0.112735	−	0.993625i	$-0.464039\pi$
$509$	3.76640e149	0.225470	0.112735	+	0.993625i	$0.464039\pi$
$510$	−2.60937e150	−1.40085
$511$	3.22502e150	1.55300
$512$	2.58733e150	1.11781
$513$	−9.54982e150	−3.70238
$514$	−3.72682e150	−1.29684
$515$	1.72439e150	0.538683
$516$	2.04927e150	0.574832
$517$	−3.51788e149	−0.0886250
$518$	1.26374e151	2.85993
$519$	1.61618e151	3.28626
$520$	1.14414e150	0.209070
$521$	−9.18377e148	−0.0150844	−0.00754219	−	0.999972i	$-0.502401\pi$
$521$	−9.18377e148	−0.0150844	−0.00754219	+	0.999972i	$0.502401\pi$
$522$	−5.10783e150	−0.754265
$523$	−6.29382e148	−0.00835739	−0.00417869	−	0.999991i	$-0.501330\pi$
$523$	−6.29382e148	−0.00835739	−0.00417869	+	0.999991i	$0.501330\pi$
$524$	−1.43618e151	−1.71523
$525$	−1.98749e151	−2.13533
$526$	−5.49417e150	−0.531121
$527$	7.31911e150	0.636751
$528$	−3.22929e150	−0.252886
$529$	−2.72324e150	−0.191998
$530$	−5.22115e150	−0.331478
$531$	1.57489e150	0.0900541
$532$	−5.88586e151	−3.03190
$533$	1.93176e151	0.896588
$534$	8.22539e151	3.44046
$535$	7.16850e150	0.270267
$536$	4.73820e150	0.161053
$537$	3.77286e151	1.15637
$538$	−6.47123e151	−1.78884
$539$	9.95443e150	0.248222
$540$	5.63439e151	1.26763
$541$	−3.41282e151	−0.692892	−0.346446	−	0.938070i	$-0.612612\pi$
$541$	−3.41282e151	−0.692892	−0.346446	+	0.938070i	$0.612612\pi$
$542$	5.46450e150	0.100136
$543$	−1.52398e152	−2.52109
$544$	1.10933e152	1.65699
$545$	−4.45623e151	−0.601120
$546$	3.49735e152	4.26135
$547$	−8.93792e151	−0.983875	−0.491937	−	0.870631i	$-0.663711\pi$
$547$	−8.93792e151	−0.983875	−0.491937	+	0.870631i	$0.663711\pi$
$548$	−1.30609e151	−0.129913
$549$	−2.93682e152	−2.64005
$550$	−3.51250e151	−0.285422
$551$	4.82459e151	0.354443
$552$	−1.11545e152	−0.741024
$553$	9.67373e151	0.581232
$554$	−4.12687e152	−2.24300
$555$	2.04426e152	1.00525
$556$	3.56337e152	1.58566
$557$	3.99221e152	1.60787	0.803933	−	0.594720i	$-0.202737\pi$
$557$	3.99221e152	1.60787	0.803933	+	0.594720i	$0.202737\pi$
$558$	−5.00119e152	−1.82337
$559$	7.98136e151	0.263464
$560$	−1.24992e152	−0.373635
$561$	−1.84226e152	−0.498783
$562$	3.07439e152	0.754038
$563$	−8.21746e152	−1.82609	−0.913044	−	0.407861i	$-0.866275\pi$
$563$	−8.21746e152	−1.82609	−0.913044	+	0.407861i	$0.866275\pi$
$564$	−4.50349e152	−0.906899
$565$	3.45993e152	0.631507
$566$	8.22367e152	1.36067
$567$	1.80142e153	2.70243
$568$	1.92669e152	0.262107
$569$	3.18212e151	0.0392632	0.0196316	−	0.999807i	$-0.493751\pi$
$569$	3.18212e151	0.0392632	0.0196316	+	0.999807i	$0.493751\pi$
$570$	−1.68412e153	−1.88504
$571$	−1.65282e153	−1.67850	−0.839248	−	0.543749i	$-0.817004\pi$
$571$	−1.65282e153	−1.67850	−0.839248	+	0.543749i	$0.817004\pi$
$572$	3.49433e152	0.322021
$573$	2.55439e153	2.13651
$574$	2.39747e153	1.82030
$575$	1.06799e153	0.736207
$576$	−5.37448e153	−3.36425
$577$	3.25453e153	1.85025	0.925125	−	0.379662i	$-0.123960\pi$
$577$	3.25453e153	1.85025	0.925125	+	0.379662i	$0.123960\pi$
$578$	1.29944e153	0.671061
$579$	−7.49353e153	−3.51582
$580$	−2.84650e152	−0.121355
$581$	−2.36640e153	−0.916881
$582$	−4.36272e153	−1.53650
$583$	−3.68622e152	−0.118026
$584$	1.68671e153	0.491052
$585$	3.92592e153	1.03942
$586$	8.53215e152	0.205466
$587$	−6.72912e153	−1.47416	−0.737079	−	0.675807i	$-0.763795\pi$
$587$	−6.72912e153	−1.47416	−0.737079	+	0.675807i	$0.763795\pi$
$588$	1.27434e154	2.54005
$589$	4.72386e153	0.856837
$590$	1.55242e152	0.0256285
$591$	2.05269e154	3.08474
$592$	−5.81797e153	−0.796007
$593$	−7.37543e153	−0.918866	−0.459433	−	0.888212i	$-0.651947\pi$
$593$	−7.37543e153	−0.918866	−0.459433	+	0.888212i	$0.651947\pi$
$594$	7.03636e153	0.798363
$595$	−7.13059e153	−0.736943
$596$	−1.16998e154	−1.10157
$597$	2.96253e153	0.254149
$598$	−1.87931e154	−1.46921
$599$	2.91989e153	0.208055	0.104027	−	0.994574i	$-0.466827\pi$
$599$	2.91989e153	0.208055	0.104027	+	0.994574i	$0.466827\pi$
$600$	−1.03947e154	−0.675180
$601$	−6.40222e153	−0.379138	−0.189569	−	0.981867i	$-0.560709\pi$
$601$	−6.40222e153	−0.379138	−0.189569	+	0.981867i	$0.560709\pi$
$602$	9.90549e153	0.534898
$603$	1.62584e154	0.800693
$604$	8.26987e153	0.371491
$605$	−9.83304e153	−0.402963
$606$	2.20642e154	0.825006
$607$	−3.30210e154	−1.12673	−0.563363	−	0.826210i	$-0.690493\pi$
$607$	−3.30210e154	−1.12673	−0.563363	+	0.826210i	$0.690493\pi$
$608$	7.15976e154	2.22972
$609$	−2.01142e154	−0.571797
$610$	−2.89494e154	−0.751335
$611$	−1.75399e154	−0.415661
$612$	−1.63660e155	−3.54192
$613$	4.11238e153	0.0812899	0.0406450	−	0.999174i	$-0.487059\pi$
$613$	4.11238e153	0.0812899	0.0406450	+	0.999174i	$0.487059\pi$
$614$	5.69745e154	1.02881
$615$	3.87820e154	0.639825
$616$	1.00252e154	0.151134
$617$	6.30634e154	0.868862	0.434431	−	0.900705i	$-0.356949\pi$
$617$	6.30634e154	0.868862	0.434431	+	0.900705i	$0.356949\pi$
$618$	2.75679e155	3.47171
$619$	−7.60559e154	−0.875592	−0.437796	−	0.899074i	$-0.644241\pi$
$619$	−7.60559e154	−0.875592	−0.437796	+	0.899074i	$0.644241\pi$
$620$	−2.78707e154	−0.293366
$621$	−2.13942e155	−2.05927
$622$	3.17076e154	0.279124
$623$	2.24774e155	1.80992
$624$	−1.61010e155	−1.18606
$625$	7.26722e154	0.489809
$626$	1.34686e155	0.830706
$627$	−1.18902e155	−0.671182
$628$	−1.04858e155	−0.541805
$629$	−3.31905e155	−1.57001
$630$	4.87237e155	2.11028
$631$	1.83855e155	0.729200	0.364600	−	0.931164i	$-0.381206\pi$
$631$	1.83855e155	0.729200	0.364600	+	0.931164i	$0.381206\pi$
$632$	5.05944e154	0.183783
$633$	−5.04928e155	−1.68005
$634$	−7.32300e155	−2.23221
$635$	−6.72801e153	−0.0187908
$636$	−4.71899e155	−1.20776
$637$	4.96320e155	1.16419
$638$	−3.55478e154	−0.0764302
$639$	6.61111e155	1.30310
$640$	−2.05009e155	−0.370497
$641$	−8.65682e155	−1.43462	−0.717312	−	0.696752i	$-0.754628\pi$
$641$	−8.65682e155	−1.43462	−0.717312	+	0.696752i	$0.754628\pi$
$642$	1.14603e156	1.74182
$643$	7.09901e155	0.989666	0.494833	−	0.868988i	$-0.335229\pi$
$643$	7.09901e155	0.989666	0.494833	+	0.868988i	$0.335229\pi$
$644$	−1.31860e156	−1.68634
$645$	1.60234e155	0.188014
$646$	2.73434e156	2.94407
$647$	1.48238e156	1.46478	0.732392	−	0.680884i	$-0.238404\pi$
$647$	1.48238e156	1.46478	0.732392	+	0.680884i	$0.238404\pi$
$648$	9.42157e155	0.854496
$649$	1.09604e154	0.00912525
$650$	−1.75130e156	−1.33866
$651$	−1.96942e156	−1.38227
$652$	−9.05651e155	−0.583740
$653$	2.26633e156	1.34166	0.670828	−	0.741613i	$-0.265939\pi$
$653$	2.26633e156	1.34166	0.670828	+	0.741613i	$0.265939\pi$
$654$	−7.12421e156	−3.87411
$655$	−1.12296e156	−0.561011
$656$	−1.10374e156	−0.506644
$657$	5.78767e156	2.44132
$658$	−2.17684e156	−0.843895
$659$	4.81803e156	1.71684	0.858419	−	0.512949i	$-0.171447\pi$
$659$	4.81803e156	1.71684	0.858419	+	0.512949i	$0.171447\pi$
$660$	7.01521e155	0.229801
$661$	4.83231e155	0.145537	0.0727686	−	0.997349i	$-0.476817\pi$
$661$	4.83231e155	0.145537	0.0727686	+	0.997349i	$0.476817\pi$
$662$	−1.57278e156	−0.435563
$663$	−9.18535e156	−2.33935
$664$	−1.23765e156	−0.289913
$665$	−4.60218e156	−0.991660
$666$	2.26793e157	4.49583
$667$	1.08084e156	0.197141
$668$	3.45329e156	0.579615
$669$	−8.35316e156	−1.29033
$670$	1.60265e156	0.227870
$671$	−2.04387e156	−0.267519
$672$	−2.98497e157	−3.59705
$673$	6.53460e156	0.725075	0.362538	−	0.931969i	$-0.381910\pi$
$673$	6.53460e156	0.725075	0.362538	+	0.931969i	$0.381910\pi$
$674$	2.41933e157	2.47213
$675$	−1.99370e157	−1.87629
$676$	2.41831e156	0.209639
$677$	−4.07162e156	−0.325159	−0.162580	−	0.986695i	$-0.551981\pi$
$677$	−4.07162e156	−0.325159	−0.162580	+	0.986695i	$0.551981\pi$
$678$	5.53142e157	4.06995
$679$	−1.19220e157	−0.808305
$680$	−3.72935e156	−0.233018
$681$	5.18051e157	2.98338
$682$	−3.48057e156	−0.184764
$683$	1.21083e157	0.592562	0.296281	−	0.955101i	$-0.404253\pi$
$683$	1.21083e157	0.592562	0.296281	+	0.955101i	$0.404253\pi$
$684$	−1.05629e158	−4.76615
$685$	−1.02124e156	−0.0424914
$686$	4.58251e156	0.175839
$687$	−4.38775e157	−1.55290
$688$	−4.56026e156	−0.148878
$689$	−1.83792e157	−0.553553
$690$	−3.77290e157	−1.04846
$691$	4.82493e155	0.0123725	0.00618627	−	0.999981i	$-0.498031\pi$
$691$	4.82493e155	0.0123725	0.00618627	+	0.999981i	$0.498031\pi$
$692$	9.99215e157	2.36467
$693$	3.43998e157	0.751382
$694$	−5.59993e157	−1.12910
$695$	2.78622e157	0.518631
$696$	−1.05199e157	−0.180800
$697$	−6.29664e157	−0.999286
$698$	1.04780e158	1.53568
$699$	1.60802e158	2.17675
$700$	−1.22878e158	−1.53650
$701$	−4.16519e157	−0.481155	−0.240577	−	0.970630i	$-0.577337\pi$
$701$	−4.16519e157	−0.481155	−0.240577	+	0.970630i	$0.577337\pi$
$702$	3.50827e158	3.74441
$703$	−2.14216e158	−2.11267
$704$	−3.74036e157	−0.340903
$705$	−3.52130e157	−0.296625
$706$	−1.77759e157	−0.138411
$707$	6.02945e157	0.434011
$708$	1.40312e157	0.0933787
$709$	−1.59499e158	−0.981501	−0.490751	−	0.871300i	$-0.663277\pi$
$709$	−1.59499e158	−0.981501	−0.490751	+	0.871300i	$0.663277\pi$
$710$	6.51682e157	0.370849
$711$	1.73606e158	0.913699
$712$	1.17559e158	0.572289
$713$	1.05828e158	0.476573
$714$	−1.13997e159	−4.74946
$715$	2.73223e157	0.105325
$716$	2.33260e158	0.832083
$717$	−4.21862e158	−1.39270
$718$	3.66229e158	1.11904
$719$	−5.50197e158	−1.55620	−0.778099	−	0.628142i	$-0.783816\pi$
$719$	−5.50197e158	−1.55620	−0.778099	+	0.628142i	$0.783816\pi$
$720$	−2.24313e158	−0.587355
$721$	7.53345e158	1.82636
$722$	1.08910e159	2.44486
$723$	1.37483e159	2.85808
$724$	−9.42212e158	−1.81409
$725$	1.00722e158	0.179624
$726$	−1.57202e159	−2.59702
$727$	4.58772e158	0.702162	0.351081	−	0.936345i	$-0.385814\pi$
$727$	4.58772e158	0.702162	0.351081	+	0.936345i	$0.385814\pi$
$728$	4.99847e158	0.708836
$729$	8.15962e157	0.107224
$730$	5.70512e158	0.694778
$731$	−2.60155e158	−0.293642
$732$	−2.61651e159	−2.73752
$733$	1.31294e158	0.127343	0.0636715	−	0.997971i	$-0.479719\pi$
$733$	1.31294e158	0.127343	0.0636715	+	0.997971i	$0.479719\pi$
$734$	−3.39196e158	−0.305014
$735$	9.96411e158	0.830790
$736$	1.60398e159	1.24017
$737$	1.13150e158	0.0811349
$738$	4.30253e159	2.86151
$739$	−6.63116e158	−0.409094	−0.204547	−	0.978857i	$-0.565572\pi$
$739$	−6.63116e158	−0.409094	−0.204547	+	0.978857i	$0.565572\pi$
$740$	1.26388e159	0.723342
$741$	−5.92835e159	−3.14792
$742$	−2.28100e159	−1.12385
$743$	3.72137e159	1.70147	0.850733	−	0.525598i	$-0.176159\pi$
$743$	3.72137e159	1.70147	0.850733	+	0.525598i	$0.176159\pi$
$744$	−1.03002e159	−0.437068
$745$	−9.14814e158	−0.360296
$746$	2.65282e158	0.0969846
$747$	−4.24678e159	−1.44134
$748$	−1.13899e159	−0.358906
$749$	3.13175e159	0.916319
$750$	−7.80876e159	−2.12169
$751$	4.71151e158	0.118890	0.0594448	−	0.998232i	$-0.481067\pi$
$751$	4.71151e158	0.118890	0.0594448	+	0.998232i	$0.481067\pi$
$752$	1.00217e159	0.234882
$753$	−2.27095e159	−0.494408
$754$	−1.77239e159	−0.358466
$755$	6.46625e158	0.121506
$756$	2.46154e160	4.29780
$757$	−3.99654e158	−0.0648430	−0.0324215	−	0.999474i	$-0.510322\pi$
$757$	−3.99654e158	−0.0648430	−0.0324215	+	0.999474i	$0.510322\pi$
$758$	9.11498e159	1.37441
$759$	−2.66373e159	−0.373312
$760$	−2.40698e159	−0.313558
$761$	1.27343e160	1.54215	0.771075	−	0.636744i	$-0.219719\pi$
$761$	1.27343e160	1.54215	0.771075	+	0.636744i	$0.219719\pi$
$762$	−1.07561e159	−0.121103
$763$	−1.94682e160	−2.03805
$764$	1.57927e160	1.53736
$765$	−1.27967e160	−1.15848
$766$	−2.32595e160	−1.95841
$767$	5.46476e158	0.0427985
$768$	4.03895e159	0.294253
$769$	1.43857e160	0.975033	0.487516	−	0.873114i	$-0.337903\pi$
$769$	1.43857e160	0.975033	0.487516	+	0.873114i	$0.337903\pi$
$770$	3.39091e159	0.213836
$771$	−2.63375e160	−1.54546
$772$	−4.63293e160	−2.52985
$773$	−3.31862e158	−0.0168654	−0.00843268	−	0.999964i	$-0.502684\pi$
$773$	−3.31862e158	−0.0168654	−0.00843268	+	0.999964i	$0.502684\pi$
$774$	1.77766e160	0.840861
$775$	9.86192e159	0.434227
$776$	−6.23528e159	−0.255582
$777$	8.93089e160	3.40822
$778$	−3.94206e160	−1.40073
$779$	−4.06394e160	−1.34468
$780$	3.49773e160	1.07779
$781$	4.60098e159	0.132044
$782$	6.12568e160	1.63749
$783$	−2.01770e160	−0.502433
$784$	−2.83580e160	−0.657860
$785$	−8.19893e159	−0.177211
$786$	−1.79528e161	−3.61561
$787$	8.36997e160	1.57082	0.785410	−	0.618976i	$-0.212452\pi$
$787$	8.36997e160	1.57082	0.785410	+	0.618976i	$0.212452\pi$
$788$	1.26909e161	2.21966
$789$	−3.88275e160	−0.632945
$790$	1.71130e160	0.260030
$791$	1.51156e161	2.14108
$792$	1.79913e160	0.237583
$793$	−1.01906e161	−1.25469
$794$	1.84736e161	2.12087
$795$	−3.68980e160	−0.395028
$796$	1.83161e160	0.182876
$797$	−1.47538e161	−1.37394	−0.686969	−	0.726687i	$-0.741059\pi$
$797$	−1.47538e161	−1.37394	−0.686969	+	0.726687i	$0.741059\pi$
$798$	−7.35755e161	−6.39106
$799$	5.71718e160	0.463272
$800$	1.49473e161	1.12998
$801$	4.03384e161	2.84520
$802$	2.26727e161	1.49219
$803$	4.02791e160	0.247381
$804$	1.44851e161	0.830253
$805$	−1.03102e161	−0.551562
$806$	−1.73538e161	−0.866563
$807$	−4.57324e161	−2.13178
$808$	3.15345e160	0.137232
$809$	−1.86211e161	−0.756592	−0.378296	−	0.925685i	$-0.623490\pi$
$809$	−1.86211e161	−0.756592	−0.378296	+	0.925685i	$0.623490\pi$
$810$	3.18675e161	1.20901
$811$	−2.62966e161	−0.931626	−0.465813	−	0.884883i	$-0.654238\pi$
$811$	−2.62966e161	−0.931626	−0.465813	+	0.884883i	$0.654238\pi$
$812$	−1.24357e161	−0.411445
$813$	3.86178e160	0.119334
$814$	1.57836e161	0.455566
$815$	−7.08133e160	−0.190927
$816$	5.24818e161	1.32192
$817$	−1.67908e161	−0.395136
$818$	−6.81434e161	−1.49836
$819$	1.71514e162	3.52407
$820$	2.39772e161	0.460395
$821$	−1.03407e161	−0.185569	−0.0927847	−	0.995686i	$-0.529577\pi$
$821$	−1.03407e161	−0.185569	−0.0927847	+	0.995686i	$0.529577\pi$
$822$	−1.63266e161	−0.273849
$823$	1.07145e162	1.67989	0.839943	−	0.542674i	$-0.182588\pi$
$823$	1.07145e162	1.67989	0.839943	+	0.542674i	$0.182588\pi$
$824$	3.94005e161	0.577486
$825$	−2.48230e161	−0.340141
$826$	6.78219e160	0.0868915
$827$	3.32028e161	0.397758	0.198879	−	0.980024i	$-0.436270\pi$
$827$	3.32028e161	0.397758	0.198879	+	0.980024i	$0.436270\pi$
$828$	−2.36637e162	−2.65094
$829$	−3.29721e161	−0.345438	−0.172719	−	0.984971i	$-0.555255\pi$
$829$	−3.29721e161	−0.345438	−0.172719	+	0.984971i	$0.555255\pi$
$830$	−4.18621e161	−0.410192
$831$	−2.91647e162	−2.67301
$832$	−1.86491e162	−1.59887
$833$	−1.61777e162	−1.29754
$834$	4.45435e162	3.34248
$835$	2.70015e161	0.189578
$836$	−7.35119e161	−0.482958
$837$	−1.97557e162	−1.21459
$838$	3.94380e162	2.26920
$839$	2.29592e162	1.23643	0.618213	−	0.786010i	$-0.287857\pi$
$839$	2.29592e162	1.23643	0.618213	+	0.786010i	$0.287857\pi$
$840$	1.00349e162	0.505841
$841$	−2.01729e162	−0.951900
$842$	4.16963e162	1.84194
$843$	2.17268e162	0.898597
$844$	−3.12175e162	−1.20891
$845$	1.89089e161	0.0685677
$846$	−3.90659e162	−1.32661
$847$	−4.29583e162	−1.36621
$848$	1.05012e162	0.312802
$849$	5.81169e162	1.62153
$850$	5.70844e162	1.49199
$851$	−4.79904e162	−1.17507
$852$	5.89005e162	1.35121
$853$	1.35980e162	0.292283	0.146141	−	0.989264i	$-0.453315\pi$
$853$	1.35980e162	0.292283	0.146141	+	0.989264i	$0.453315\pi$
$854$	−1.26473e163	−2.54734
$855$	−8.25916e162	−1.55889
$856$	1.63793e162	0.289736
$857$	7.45750e162	1.23640	0.618198	−	0.786022i	$-0.287863\pi$
$857$	7.45750e162	1.23640	0.618198	+	0.786022i	$0.287863\pi$
$858$	4.36804e162	0.678801
$859$	−5.62295e162	−0.819112	−0.409556	−	0.912285i	$-0.634316\pi$
$859$	−5.62295e162	−0.819112	−0.409556	+	0.912285i	$0.634316\pi$
$860$	9.90655e161	0.135288
$861$	1.69430e163	2.16927
$862$	−9.29913e162	−1.11632
$863$	1.46237e163	1.64611	0.823056	−	0.567960i	$-0.192267\pi$
$863$	1.46237e163	1.64611	0.823056	+	0.567960i	$0.192267\pi$
$864$	−2.99430e163	−3.16069
$865$	7.81291e162	0.773427
$866$	−1.45404e163	−1.35000
$867$	9.18319e162	0.799712
$868$	−1.21761e163	−0.994634
$869$	1.20821e162	0.0925858
$870$	−3.55824e162	−0.255809
$871$	5.64155e162	0.380532
$872$	−1.01820e163	−0.644421
$873$	−2.13953e163	−1.27066
$874$	3.95360e163	2.20348
$875$	−2.13389e163	−1.11616
$876$	5.15641e163	2.53145
$877$	2.51730e163	1.16000	0.579999	−	0.814617i	$-0.303053\pi$
$877$	2.51730e163	1.16000	0.579999	+	0.814617i	$0.303053\pi$
$878$	−3.75809e163	−1.62563
$879$	6.02970e162	0.244857
$880$	−1.56110e162	−0.0595172
$881$	−3.53698e163	−1.26610	−0.633052	−	0.774109i	$-0.718198\pi$
$881$	−3.53698e163	−1.26610	−0.633052	+	0.774109i	$0.718198\pi$
$882$	1.10543e164	3.71558
$883$	1.29185e163	0.407748	0.203874	−	0.978997i	$-0.434647\pi$
$883$	1.29185e163	0.407748	0.203874	+	0.978997i	$0.434647\pi$
$884$	−5.67891e163	−1.68331
$885$	1.09710e162	0.0305419
$886$	−7.09620e161	−0.0185547
$887$	−7.57654e163	−1.86084	−0.930422	−	0.366491i	$-0.880559\pi$
$887$	−7.57654e163	−1.86084	−0.930422	+	0.366491i	$0.880559\pi$
$888$	4.67092e163	1.07766
$889$	−2.93931e162	−0.0637086
$890$	3.97630e163	0.809719
$891$	2.24990e163	0.430477
$892$	−5.16440e163	−0.928476
$893$	3.68995e163	0.623397
$894$	−1.46252e164	−2.32204
$895$	1.82387e163	0.272154
$896$	−8.95637e163	−1.25614
$897$	−1.32812e164	−1.75088
$898$	2.17088e164	2.69029
$899$	9.98063e162	0.116277
$900$	−2.20519e164	−2.41539
$901$	5.99076e163	0.616959
$902$	2.99433e163	0.289960
$903$	7.00024e163	0.637445
$904$	7.90560e163	0.676998
$905$	−7.36720e163	−0.593344
$906$	1.03377e164	0.783082
$907$	−1.44259e164	−1.02787	−0.513936	−	0.857829i	$-0.671813\pi$
$907$	−1.44259e164	−1.02787	−0.513936	+	0.857829i	$0.671813\pi$
$908$	3.20289e164	2.14673
$909$	1.08206e164	0.682267
$910$	1.69068e164	1.00292
$911$	1.98406e164	1.10735	0.553675	−	0.832733i	$-0.313225\pi$
$911$	1.98406e164	1.10735	0.553675	+	0.832733i	$0.313225\pi$
$912$	3.38725e164	1.77883
$913$	−2.95554e163	−0.146052
$914$	−2.15094e164	−1.00026
$915$	−2.04586e164	−0.895376
$916$	−2.71276e164	−1.11741
$917$	−4.90595e164	−1.90206
$918$	−1.14353e165	−4.17331
$919$	1.67920e164	0.576889	0.288444	−	0.957497i	$-0.406862\pi$
$919$	1.67920e164	0.576889	0.288444	+	0.957497i	$0.406862\pi$
$920$	−5.39230e163	−0.174401
$921$	4.02641e164	1.22605
$922$	8.28335e164	2.37487
$923$	2.29401e164	0.619301
$924$	3.06478e164	0.779122
$925$	−4.47216e164	−1.07066
$926$	−4.31882e164	−0.973768
$927$	1.35196e165	2.87105
$928$	1.51272e164	0.302585
$929$	−6.74624e164	−1.27113	−0.635564	−	0.772048i	$-0.719232\pi$
$929$	−6.74624e164	−1.27113	−0.635564	+	0.772048i	$0.719232\pi$
$930$	−3.48395e164	−0.618398
$931$	−1.04413e165	−1.74602
$932$	9.94173e164	1.56631
$933$	2.24078e164	0.332636
$934$	−2.06377e165	−2.88676
$935$	−8.90581e163	−0.117389
$936$	8.97034e164	1.11429
$937$	−5.72108e164	−0.669778	−0.334889	−	0.942258i	$-0.608699\pi$
$937$	−5.72108e164	−0.669778	−0.334889	+	0.942258i	$0.608699\pi$
$938$	7.00161e164	0.772574
$939$	9.51831e164	0.989964
$940$	−2.17707e164	−0.213440
$941$	1.40898e165	1.30221	0.651106	−	0.758987i	$-0.274305\pi$
$941$	1.40898e165	1.30221	0.651106	+	0.758987i	$0.274305\pi$
$942$	−1.31077e165	−1.14209
$943$	−9.10435e164	−0.747911
$944$	−3.12237e163	−0.0241846
$945$	1.92469e165	1.40571
$946$	1.23715e164	0.0852051
$947$	1.36583e165	0.887103	0.443552	−	0.896249i	$-0.353718\pi$
$947$	1.36583e165	0.887103	0.443552	+	0.896249i	$0.353718\pi$
$948$	1.54671e165	0.947431
$949$	2.00828e165	1.16025
$950$	3.68431e165	2.00769
$951$	−5.17519e165	−2.66016
$952$	−1.62927e165	−0.790028
$953$	−1.29963e165	−0.594518	−0.297259	−	0.954797i	$-0.596073\pi$
$953$	−1.29963e165	−0.594518	−0.297259	+	0.954797i	$0.596073\pi$
$954$	−4.09352e165	−1.76670
$955$	1.23484e165	0.502832
$956$	−2.60819e165	−1.00214
$957$	−2.51218e164	−0.0910830
$958$	−1.48233e165	−0.507178
$959$	−4.46156e164	−0.144064
$960$	−3.74399e165	−1.14099
$961$	−2.49932e165	−0.718909
$962$	7.86957e165	2.13665
$963$	5.62030e165	1.44046
$964$	8.50000e165	2.05657
$965$	−3.62251e165	−0.827454
$966$	−1.64830e166	−3.55471
$967$	−8.22022e165	−1.67384	−0.836920	−	0.547325i	$-0.815646\pi$
$967$	−8.22022e165	−1.67384	−0.836920	+	0.547325i	$0.815646\pi$
$968$	−2.24675e165	−0.431990
$969$	1.93237e166	3.50849
$970$	−2.10902e165	−0.361618
$971$	−1.23089e164	−0.0199320	−0.00996601	−	0.999950i	$-0.503172\pi$
$971$	−1.23089e164	−0.0199320	−0.00996601	+	0.999950i	$0.503172\pi$
$972$	9.31966e165	1.42535
$973$	1.21724e166	1.75838
$974$	1.33705e166	1.82443
$975$	−1.23765e166	−1.59530
$976$	5.82254e165	0.709002
$977$	−5.24846e165	−0.603786	−0.301893	−	0.953342i	$-0.597619\pi$
$977$	−5.24846e165	−0.603786	−0.301893	+	0.953342i	$0.597619\pi$
$978$	−1.13210e166	−1.23049
$979$	2.80734e165	0.288307
$980$	6.16038e165	0.597806
$981$	−3.49380e166	−3.20382
$982$	1.68120e166	1.45691
$983$	−1.70165e165	−0.139364	−0.0696820	−	0.997569i	$-0.522198\pi$
$983$	−1.70165e165	−0.139364	−0.0696820	+	0.997569i	$0.522198\pi$
$984$	8.86131e165	0.685914
$985$	9.92307e165	0.725998
$986$	5.77715e165	0.399526
$987$	−1.53838e166	−1.00568
$988$	−3.66525e166	−2.26513
$989$	−3.76160e165	−0.219775
$990$	6.08539e165	0.336152
$991$	−1.26394e166	−0.660143	−0.330072	−	0.943956i	$-0.607073\pi$
$991$	−1.26394e166	−0.660143	−0.330072	+	0.943956i	$0.607073\pi$
$992$	1.48114e166	0.731474
$993$	−1.11149e166	−0.519067
$994$	2.84705e166	1.25733
$995$	1.43214e165	0.0598143
$996$	−3.78359e166	−1.49455
$997$	−2.85577e166	−1.06695	−0.533473	−	0.845817i	$-0.679113\pi$
$997$	−2.85577e166	−1.06695	−0.533473	+	0.845817i	$0.679113\pi$
$998$	2.07793e166	0.734321
$999$	8.95878e166	2.99477

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.112.a.a.1.8	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.112.a.a.1.8	✓	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)

\(f(q)\)	\(=\)	\(q+7.72845e16 q^{2} +5.46172e26 q^{3} +3.37675e33 q^{4} +2.64030e38 q^{5} +4.22106e43 q^{6} +1.15348e47 q^{7} +6.03282e49 q^{8} +2.07006e53 q^{9} +O(q^{10})\)	\(q+7.72845e16 q^{2} +5.46172e26 q^{3} +3.37675e33 q^{4} +2.64030e38 q^{5} +4.22106e43 q^{6} +1.15348e47 q^{7} +6.03282e49 q^{8} +2.07006e53 q^{9} +2.04054e55 q^{10} +1.44065e57 q^{11} +1.84428e60 q^{12} +7.18299e61 q^{13} +8.91465e63 q^{14} +1.44206e65 q^{15} -4.10410e66 q^{16} -2.34132e68 q^{17} +1.59984e70 q^{18} -1.51112e71 q^{19} +8.91561e71 q^{20} +6.30001e73 q^{21} +1.11340e74 q^{22} -3.38533e75 q^{23} +3.29496e76 q^{24} -3.15474e77 q^{25} +5.55134e78 q^{26} +6.31969e79 q^{27} +3.89503e80 q^{28} -3.19272e80 q^{29} +1.11449e82 q^{30} -3.12606e82 q^{31} -4.73804e83 q^{32} +7.86845e83 q^{33} -1.80948e85 q^{34} +3.04554e85 q^{35} +6.99008e86 q^{36} +1.41760e87 q^{37} -1.16786e88 q^{38} +3.92315e88 q^{39} +1.59284e88 q^{40} +2.68935e89 q^{41} +4.86893e90 q^{42} +1.11115e90 q^{43} +4.86473e90 q^{44} +5.46558e91 q^{45} -2.61634e92 q^{46} -2.44186e92 q^{47} -2.24155e93 q^{48} +6.90966e93 q^{49} -2.43813e94 q^{50} -1.27876e95 q^{51} +2.42551e95 q^{52} -2.55871e95 q^{53} +4.88414e96 q^{54} +3.80375e95 q^{55} +6.95876e96 q^{56} -8.25333e97 q^{57} -2.46748e97 q^{58} +7.60791e96 q^{59} +4.86946e98 q^{60} -1.41871e99 q^{61} -2.41596e99 q^{62} +2.38779e100 q^{63} -2.59629e100 q^{64} +1.89652e100 q^{65} +6.08110e100 q^{66} +7.85405e100 q^{67} -7.90605e101 q^{68} -1.84897e102 q^{69} +2.35373e102 q^{70} +3.19368e102 q^{71} +1.24883e103 q^{72} +2.79589e103 q^{73} +1.09558e104 q^{74} -1.72303e104 q^{75} -5.10268e104 q^{76} +1.66177e104 q^{77} +3.03199e105 q^{78} +8.38653e104 q^{79} -1.08360e105 q^{80} +1.56172e106 q^{81} +2.07845e106 q^{82} -2.05152e106 q^{83} +2.12735e107 q^{84} -6.18178e106 q^{85} +8.58744e106 q^{86} -1.74377e107 q^{87} +8.69121e106 q^{88} +1.94865e108 q^{89} +4.22405e108 q^{90} +8.28547e108 q^{91} -1.14314e109 q^{92} -1.70737e109 q^{93} -1.88718e109 q^{94} -3.98981e109 q^{95} -2.58779e110 q^{96} -1.03356e110 q^{97} +5.34010e110 q^{98} +2.98225e110 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 73\!\cdots\!76 q^{2}+ \cdots + 44\!\cdots\!13 q^{9}+O(q^{10}) \) 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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