LMFDB - Embedded newform 1.112.a.a.1.7

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			1.7
Root			$7.31006e14$ 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)

$f(q)$	$=$	$q+5.34436e16 q^{2} -3.57964e25 q^{3} +2.60068e32 q^{4} -4.56192e38 q^{5} -1.91309e42 q^{6} -2.39634e46 q^{7} -1.24849e50 q^{8} -9.00162e52 q^{9} +O(q^{10})$	\(q+5.34436e16 q^{2} -3.57964e25 q^{3} +2.60068e32 q^{4} -4.56192e38 q^{5} -1.91309e42 q^{6} -2.39634e46 q^{7} -1.24849e50 q^{8} -9.00162e52 q^{9} -2.43805e55 q^{10} -2.36286e57 q^{11} -9.30949e57 q^{12} -5.27826e60 q^{13} -1.28069e63 q^{14} +1.63300e64 q^{15} -7.34753e66 q^{16} +3.40054e67 q^{17} -4.81079e69 q^{18} +1.10518e71 q^{19} -1.18641e71 q^{20} +8.57803e71 q^{21} -1.26280e74 q^{22} +1.40882e75 q^{23} +4.46913e75 q^{24} -1.77075e77 q^{25} -2.82089e77 q^{26} +6.49039e78 q^{27} -6.23209e78 q^{28} -7.61762e80 q^{29} +8.72736e80 q^{30} +2.31300e82 q^{31} -6.85528e82 q^{32} +8.45819e82 q^{33} +1.81737e84 q^{34} +1.09319e85 q^{35} -2.34103e85 q^{36} +6.32898e85 q^{37} +5.90648e87 q^{38} +1.88943e86 q^{39} +5.69549e88 q^{40} +5.31382e89 q^{41} +4.58440e88 q^{42} +6.52887e90 q^{43} -6.14503e89 q^{44} +4.10647e91 q^{45} +7.52924e91 q^{46} -1.03218e93 q^{47} +2.63015e92 q^{48} -5.82137e93 q^{49} -9.46351e93 q^{50} -1.21727e93 q^{51} -1.37271e93 q^{52} +5.63644e95 q^{53} +3.46869e95 q^{54} +1.07792e96 q^{55} +2.99179e96 q^{56} -3.95615e96 q^{57} -4.07113e97 q^{58} -1.83167e98 q^{59} +4.24692e96 q^{60} -2.77182e97 q^{61} +1.23615e99 q^{62} +2.15709e99 q^{63} +1.54116e100 q^{64} +2.40790e99 q^{65} +4.52036e99 q^{66} -2.58375e101 q^{67} +8.84371e99 q^{68} -5.04307e100 q^{69} +5.84239e101 q^{70} -8.44733e101 q^{71} +1.12384e103 q^{72} +2.87008e103 q^{73} +3.38243e102 q^{74} +6.33864e102 q^{75} +2.87422e103 q^{76} +5.66220e103 q^{77} +1.00978e103 q^{78} +2.48817e105 q^{79} +3.35188e105 q^{80} +7.98593e105 q^{81} +2.83990e106 q^{82} +4.12681e106 q^{83} +2.23087e104 q^{84} -1.55130e106 q^{85} +3.48926e107 q^{86} +2.72684e106 q^{87} +2.94999e107 q^{88} +1.87807e108 q^{89} +2.19464e108 q^{90} +1.26485e107 q^{91} +3.66389e107 q^{92} -8.27972e107 q^{93} -5.51633e109 q^{94} -5.04174e109 q^{95} +2.45395e108 q^{96} -1.71016e110 q^{97} -3.11115e110 q^{98} +2.12696e110 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	5.34436e16	1.04889	0.524446	−	0.851444i	$-0.324272\pi$
$2$	5.34436e16	1.04889	0.524446	+	0.851444i	$0.324272\pi$
$3$	−3.57964e25	−0.118470	−0.0592352	−	0.998244i	$-0.518866\pi$
$3$	−3.57964e25	−0.118470	−0.0592352	+	0.998244i	$0.518866\pi$
$4$	2.60068e32	0.100174
$5$	−4.56192e38	−0.735043	−0.367521	−	0.930015i	$-0.619794\pi$
$5$	−4.56192e38	−0.735043	−0.367521	+	0.930015i	$0.619794\pi$
$6$	−1.91309e42	−0.124263
$7$	−2.39634e46	−0.299645	−0.149822	−	0.988713i	$-0.547870\pi$
$7$	−2.39634e46	−0.299645	−0.149822	+	0.988713i	$0.547870\pi$
$8$	−1.24849e50	−0.943820
$9$	−9.00162e52	−0.985965
$10$	−2.43805e55	−0.770980
$11$	−2.36286e57	−0.376828	−0.188414	−	0.982090i	$-0.560335\pi$
$11$	−2.36286e57	−0.376828	−0.188414	+	0.982090i	$0.560335\pi$
$12$	−9.30949e57	−0.0118677
$13$	−5.27826e60	−0.0791836	−0.0395918	−	0.999216i	$-0.512606\pi$
$13$	−5.27826e60	−0.0791836	−0.0395918	+	0.999216i	$0.512606\pi$
$14$	−1.28069e63	−0.314295
$15$	1.63300e64	0.0870808
$16$	−7.34753e66	−1.09014
$17$	3.40054e67	0.174435	0.0872174	−	0.996189i	$-0.472203\pi$
$17$	3.40054e67	0.174435	0.0872174	+	0.996189i	$0.472203\pi$
$18$	−4.81079e69	−1.03417
$19$	1.10518e71	1.18197	0.590987	−	0.806681i	$-0.298738\pi$
$19$	1.10518e71	1.18197	0.590987	+	0.806681i	$0.298738\pi$
$20$	−1.18641e71	−0.0736325
$21$	8.57803e71	0.0354990
$22$	−1.26280e74	−0.395252
$23$	1.40882e75	0.374077	0.187038	−	0.982353i	$-0.440111\pi$
$23$	1.40882e75	0.374077	0.187038	+	0.982353i	$0.440111\pi$
$24$	4.46913e75	0.111815
$25$	−1.77075e77	−0.459712
$26$	−2.82089e77	−0.0830550
$27$	6.49039e78	0.235278
$28$	−6.23209e78	−0.0300167
$29$	−7.61762e80	−0.523276	−0.261638	−	0.965166i	$-0.584263\pi$
$29$	−7.61762e80	−0.523276	−0.261638	+	0.965166i	$0.584263\pi$
$30$	8.72736e80	0.0913384
$31$	2.31300e82	0.392285	0.196143	−	0.980575i	$-0.437158\pi$
$31$	2.31300e82	0.392285	0.196143	+	0.980575i	$0.437158\pi$
$32$	−6.85528e82	−0.199619
$33$	8.45819e82	0.0446430
$34$	1.81737e84	0.182963
$35$	1.09319e85	0.220252
$36$	−2.34103e85	−0.0987684
$37$	6.32898e85	0.0583630	0.0291815	−	0.999574i	$-0.490710\pi$
$37$	6.32898e85	0.0583630	0.0291815	+	0.999574i	$0.490710\pi$
$38$	5.90648e87	1.23976
$39$	1.88943e86	0.00938092
$40$	5.69549e88	0.693748
$41$	5.31382e89	1.64400	0.822002	−	0.569485i	$-0.192857\pi$
$41$	5.31382e89	1.64400	0.822002	+	0.569485i	$0.192857\pi$
$42$	4.58440e88	0.0372346
$43$	6.52887e90	1.43661	0.718305	−	0.695728i	$-0.244918\pi$
$43$	6.52887e90	1.43661	0.718305	+	0.695728i	$0.244918\pi$
$44$	−6.14503e89	−0.0377486
$45$	4.10647e91	0.724726
$46$	7.52924e91	0.392366
$47$	−1.03218e93	−1.63051	−0.815255	−	0.579102i	$-0.803403\pi$
$47$	−1.03218e93	−1.63051	−0.815255	+	0.579102i	$0.803403\pi$
$48$	2.63015e92	0.129149
$49$	−5.82137e93	−0.910213
$50$	−9.46351e93	−0.482189
$51$	−1.21727e93	−0.0206654
$52$	−1.37271e93	−0.00793217
$53$	5.63644e95	1.13160	0.565801	−	0.824542i	$-0.308567\pi$
$53$	5.63644e95	1.13160	0.565801	+	0.824542i	$0.308567\pi$
$54$	3.46869e95	0.246781
$55$	1.07792e96	0.276985
$56$	2.99179e96	0.282810
$57$	−3.95615e96	−0.140029
$58$	−4.07113e97	−0.548860
$59$	−1.83167e98	−0.956226	−0.478113	−	0.878298i	$-0.658679\pi$
$59$	−1.83167e98	−0.956226	−0.478113	+	0.878298i	$0.658679\pi$
$60$	4.24692e96	0.00872327
$61$	−2.77182e97	−0.0227488	−0.0113744	−	0.999935i	$-0.503621\pi$
$61$	−2.77182e97	−0.0227488	−0.0113744	+	0.999935i	$0.503621\pi$
$62$	1.23615e99	0.411465
$63$	2.15709e99	0.295439
$64$	1.54116e100	0.880761
$65$	2.40790e99	0.0582033
$66$	4.52036e99	0.0468257
$67$	−2.58375e101	−1.16172	−0.580858	−	0.814005i	$-0.697283\pi$
$67$	−2.58375e101	−1.16172	−0.580858	+	0.814005i	$0.697283\pi$
$68$	8.84371e99	0.0174739
$69$	−5.04307e100	−0.0443170
$70$	5.84239e101	0.231020
$71$	−8.44733e101	−0.152013	−0.0760066	−	0.997107i	$-0.524217\pi$
$71$	−8.44733e101	−0.152013	−0.0760066	+	0.997107i	$0.524217\pi$
$72$	1.12384e103	0.930573
$73$	2.87008e103	1.10529	0.552645	−	0.833417i	$-0.313619\pi$
$73$	2.87008e103	1.10529	0.552645	+	0.833417i	$0.313619\pi$
$74$	3.38243e102	0.0612165
$75$	6.33864e102	0.0544623
$76$	2.87422e103	0.118404
$77$	5.66220e103	0.112915
$78$	1.00978e103	0.00983957
$79$	2.48817e105	1.19558	0.597788	−	0.801654i	$-0.296046\pi$
$79$	2.48817e105	1.19558	0.597788	+	0.801654i	$0.296046\pi$
$80$	3.35188e105	0.801299
$81$	7.98593e105	0.958091
$82$	2.83990e106	1.72438
$83$	4.12681e106	1.27874	0.639368	−	0.768901i	$-0.279196\pi$
$83$	4.12681e106	1.27874	0.639368	+	0.768901i	$0.279196\pi$
$84$	2.23087e104	0.00355609
$85$	−1.55130e106	−0.128217
$86$	3.48926e107	1.50685
$87$	2.72684e106	0.0619927
$88$	2.94999e107	0.355658
$89$	1.87807e108	1.20939	0.604695	−	0.796457i	$-0.293295\pi$
$89$	1.87807e108	1.20939	0.604695	+	0.796457i	$0.293295\pi$
$90$	2.19464e108	0.760159
$91$	1.26485e107	0.0237269
$92$	3.66389e107	0.0374729
$93$	−8.27972e107	−0.0464742
$94$	−5.51633e109	−1.71023
$95$	−5.04174e109	−0.868802
$96$	2.45395e108	0.0236489
$97$	−1.71016e110	−0.927269	−0.463634	−	0.886027i	$-0.653455\pi$
$97$	−1.71016e110	−0.927269	−0.463634	+	0.886027i	$0.653455\pi$
$98$	−3.11115e110	−0.954715
$99$	2.12696e110	0.371540
$100$	−4.60514e109	−0.0460514
$101$	−6.38809e110	−0.367735	−0.183867	−	0.982951i	$-0.558862\pi$
$101$	−6.38809e110	−0.367735	−0.183867	+	0.982951i	$0.558862\pi$
$102$	−6.50554e109	−0.0216757
$103$	−4.63449e111	−0.898538	−0.449269	−	0.893397i	$-0.648315\pi$
$103$	−4.63449e111	−0.898538	−0.449269	+	0.893397i	$0.648315\pi$
$104$	6.58984e110	0.0747350
$105$	−3.91323e110	−0.0260933
$106$	3.01231e112	1.18693
$107$	4.78688e112	1.12009	0.560045	−	0.828462i	$-0.310784\pi$
$107$	4.78688e112	1.12009	0.560045	+	0.828462i	$0.310784\pi$
$108$	1.68794e111	0.0235689
$109$	1.94080e113	1.62484	0.812421	−	0.583071i	$-0.198149\pi$
$109$	1.94080e113	1.62484	0.812421	+	0.583071i	$0.198149\pi$
$110$	5.76078e112	0.290527
$111$	−2.26555e111	−0.00691430
$112$	1.76071e113	0.326654
$113$	−1.37358e114	−1.55596	−0.777982	−	0.628287i	$-0.783757\pi$
$113$	−1.37358e114	−1.55596	−0.777982	+	0.628287i	$0.783757\pi$
$114$	−2.11431e113	−0.146875
$115$	−6.42693e113	−0.274962
$116$	−1.98110e113	−0.0524188
$117$	4.75129e113	0.0780722
$118$	−9.78910e114	−1.00298
$119$	−8.14884e113	−0.0522684
$120$	−2.03878e114	−0.0821886
$121$	−3.37346e115	−0.858000
$122$	−1.48136e114	−0.0238611
$123$	−1.90216e115	−0.194766
$124$	6.01537e114	0.0392970
$125$	2.56499e116	1.07295
$126$	1.15283e116	0.309884
$127$	7.15774e116	1.24071	0.620353	−	0.784322i	$-0.286989\pi$
$127$	7.15774e116	1.24071	0.620353	+	0.784322i	$0.286989\pi$
$128$	1.00162e117	1.12344
$129$	−2.33710e116	−0.170196
$130$	1.28687e116	0.0610490
$131$	−2.34842e117	−0.728148	−0.364074	−	0.931370i	$-0.618614\pi$
$131$	−2.34842e117	−0.728148	−0.364074	+	0.931370i	$0.618614\pi$
$132$	2.19970e115	0.00447209
$133$	−2.64838e117	−0.354172
$134$	−1.38085e118	−1.21851
$135$	−2.96086e117	−0.172939
$136$	−4.24553e117	−0.164635
$137$	2.60288e118	0.672144	0.336072	−	0.941836i	$-0.390901\pi$
$137$	2.60288e118	0.672144	0.336072	+	0.941836i	$0.390901\pi$
$138$	−2.69520e117	−0.0464838
$139$	−1.02399e119	−1.18297	−0.591485	−	0.806316i	$-0.701458\pi$
$139$	−1.02399e119	−1.18297	−0.591485	+	0.806316i	$0.701458\pi$
$140$	2.84303e117	0.0220636
$141$	3.69483e118	0.193167
$142$	−4.51456e118	−0.159445
$143$	1.24718e118	0.0298386
$144$	6.61396e119	1.07484
$145$	3.47510e119	0.384630
$146$	1.53388e120	1.15933
$147$	2.08384e119	0.107833
$148$	1.64596e118	0.00584648
$149$	2.45647e120	0.600447	0.300223	−	0.953869i	$-0.402939\pi$
$149$	2.45647e120	0.600447	0.300223	+	0.953869i	$0.402939\pi$
$150$	3.38760e119	0.0571251
$151$	−1.49407e121	−1.74240	−0.871202	−	0.490924i	$-0.836659\pi$
$151$	−1.49407e121	−1.74240	−0.871202	+	0.490924i	$0.836659\pi$
$152$	−1.37980e121	−1.11557
$153$	−3.06104e120	−0.171987
$154$	3.02608e120	0.118435
$155$	−1.05517e121	−0.288346
$156$	4.91380e118	0.000939728 0
$157$	−4.18640e121	−0.561578	−0.280789	−	0.959770i	$-0.590596\pi$
$157$	−4.18640e121	−0.561578	−0.280789	+	0.959770i	$0.590596\pi$
$158$	1.32977e122	1.25403
$159$	−2.01764e121	−0.134062
$160$	3.12732e121	0.146728
$161$	−3.37601e121	−0.112090
$162$	4.26797e122	1.00493
$163$	−2.89307e122	−0.484113	−0.242056	−	0.970262i	$-0.577822\pi$
$163$	−2.89307e122	−0.484113	−0.242056	+	0.970262i	$0.577822\pi$
$164$	1.38195e122	0.164687
$165$	−3.85856e121	−0.0328145
$166$	2.20552e123	1.34126
$167$	6.80177e122	0.296386	0.148193	−	0.988958i	$-0.452654\pi$
$167$	6.80177e122	0.296386	0.148193	+	0.988958i	$0.452654\pi$
$168$	−1.07095e122	−0.0335047
$169$	−4.41551e123	−0.993730
$170$	−8.29071e122	−0.134486
$171$	−9.94841e123	−1.16539
$172$	1.69795e123	0.143912
$173$	−2.53918e124	−1.56004	−0.780019	−	0.625756i	$-0.784790\pi$
$173$	−2.53918e124	−1.56004	−0.780019	+	0.625756i	$0.784790\pi$
$174$	1.45732e123	0.0650237
$175$	4.24330e123	0.137750
$176$	1.73612e124	0.410796
$177$	6.55672e123	0.113285
$178$	1.00371e125	1.26852
$179$	8.20957e124	0.760287	0.380143	−	0.924928i	$-0.375875\pi$
$179$	8.20957e124	0.760287	0.380143	+	0.924928i	$0.375875\pi$
$180$	1.06796e124	0.0725990
$181$	1.48888e123	0.00744215	0.00372107	−	0.999993i	$-0.498816\pi$
$181$	1.48888e123	0.00744215	0.00372107	+	0.999993i	$0.498816\pi$
$182$	6.75981e123	0.0248870
$183$	9.92213e122	0.00269507
$184$	−1.75889e125	−0.353061
$185$	−2.88723e124	−0.0428993
$186$	−4.42498e124	−0.0487465
$187$	−8.03500e124	−0.0657320
$188$	−2.68436e125	−0.163335
$189$	−1.55531e125	−0.0704998
$190$	−2.69449e126	−0.911279
$191$	5.46909e125	0.138218	0.0691088	−	0.997609i	$-0.477984\pi$
$191$	5.46909e125	0.138218	0.0691088	+	0.997609i	$0.477984\pi$
$192$	−5.51679e125	−0.104344
$193$	2.13477e125	0.0302636	0.0151318	−	0.999886i	$-0.495183\pi$
$193$	2.13477e125	0.0302636	0.0151318	+	0.999886i	$0.495183\pi$
$194$	−9.13971e126	−0.972605
$195$	−8.61943e124	−0.00689537
$196$	−1.51395e126	−0.0911801
$197$	3.58980e127	1.63002	0.815012	−	0.579444i	$-0.196730\pi$
$197$	3.58980e127	1.63002	0.815012	+	0.579444i	$0.196730\pi$
$198$	1.13672e127	0.389705
$199$	3.11191e127	0.806644	0.403322	−	0.915058i	$-0.367855\pi$
$199$	3.11191e127	0.806644	0.403322	+	0.915058i	$0.367855\pi$
$200$	2.21075e127	0.433886
$201$	9.24892e126	0.137629
$202$	−3.41402e127	−0.385714
$203$	1.82544e127	0.156797
$204$	−3.16573e125	−0.00207014
$205$	−2.42412e128	−1.20841
$206$	−2.47684e128	−0.942469
$207$	−1.26817e128	−0.368826
$208$	3.87822e127	0.0863211
$209$	−2.61138e128	−0.445402
$210$	−2.09137e127	−0.0273691
$211$	9.12305e128	0.917199	0.458600	−	0.888643i	$-0.348351\pi$
$211$	9.12305e128	0.917199	0.458600	+	0.888643i	$0.348351\pi$
$212$	1.46586e128	0.113358
$213$	3.02384e127	0.0180091
$214$	2.55828e129	1.17485
$215$	−2.97842e129	−1.05597
$216$	−8.10315e128	−0.222060
$217$	−5.54273e128	−0.117546
$218$	1.03724e130	1.70428
$219$	−1.02739e129	−0.130944
$220$	2.80331e128	0.0277468
$221$	−1.79490e128	−0.0138124
$222$	−1.21079e128	−0.00725235
$223$	−4.15061e129	−0.193728	−0.0968640	−	0.995298i	$-0.530881\pi$
$223$	−4.15061e129	−0.193728	−0.0968640	+	0.995298i	$0.530881\pi$
$224$	1.64275e129	0.0598147
$225$	1.59396e130	0.453260
$226$	−7.34089e130	−1.63204
$227$	−6.19188e130	−1.07743	−0.538713	−	0.842489i	$-0.681089\pi$
$227$	−6.19188e130	−1.07743	−0.538713	+	0.842489i	$0.681089\pi$
$228$	−1.02887e129	−0.0140273
$229$	2.44280e129	0.0261227	0.0130614	−	0.999915i	$-0.495842\pi$
$229$	2.44280e129	0.0261227	0.0130614	+	0.999915i	$0.495842\pi$
$230$	−3.43478e130	−0.288406
$231$	−2.02687e129	−0.0133770
$232$	9.51049e130	0.493878
$233$	3.22185e131	1.31781	0.658904	−	0.752227i	$-0.271020\pi$
$233$	3.22185e131	1.31781	0.658904	+	0.752227i	$0.271020\pi$
$234$	2.53926e130	0.0818893
$235$	4.70872e131	1.19850
$236$	−4.76358e130	−0.0957893
$237$	−8.90677e130	−0.141640
$238$	−4.35503e130	−0.0548239
$239$	3.84696e131	0.383737	0.191869	−	0.981421i	$-0.438545\pi$
$239$	3.84696e131	0.383737	0.191869	+	0.981421i	$0.438545\pi$
$240$	−1.19985e131	−0.0949303
$241$	−1.48848e132	−0.934969	−0.467485	−	0.884001i	$-0.654840\pi$
$241$	−1.48848e132	−0.934969	−0.467485	+	0.884001i	$0.654840\pi$
$242$	−1.80290e132	−0.899950
$243$	−8.78424e131	−0.348784
$244$	−7.20861e129	−0.00227885
$245$	2.65567e132	0.669045
$246$	−1.01658e132	−0.204288
$247$	−5.83343e131	−0.0935930
$248$	−2.88775e132	−0.370247
$249$	−1.47725e132	−0.151492
$250$	1.37082e133	1.12541
$251$	−1.59684e133	−1.05043	−0.525217	−	0.850968i	$-0.676016\pi$
$251$	−1.59684e133	−1.05043	−0.525217	+	0.850968i	$0.676016\pi$
$252$	5.60989e131	0.0295954
$253$	−3.32884e132	−0.140963
$254$	3.82535e133	1.30137
$255$	5.55310e131	0.0151899
$256$	1.35196e133	0.297608
$257$	4.64499e133	0.823562	0.411781	−	0.911283i	$-0.364907\pi$
$257$	4.64499e133	0.823562	0.411781	+	0.911283i	$0.364907\pi$
$258$	−1.24903e133	−0.178517
$259$	−1.51664e132	−0.0174882
$260$	6.26218e131	0.00583048
$261$	6.85709e133	0.515931
$262$	−1.25508e134	−0.763749
$263$	−3.24421e134	−1.59795	−0.798977	−	0.601361i	$-0.794625\pi$
$263$	−3.24421e134	−1.59795	−0.798977	+	0.601361i	$0.794625\pi$
$264$	−1.05599e133	−0.0421350
$265$	−2.57130e134	−0.831776
$266$	−1.41539e134	−0.371488
$267$	−6.72282e133	−0.143277
$268$	−6.71951e133	−0.116374
$269$	1.30498e135	1.83803	0.919016	−	0.394220i	$-0.128985\pi$
$269$	1.30498e135	1.83803	0.919016	+	0.394220i	$0.128985\pi$
$270$	−1.58239e134	−0.181395
$271$	9.74078e134	0.909491	0.454745	−	0.890621i	$-0.349730\pi$
$271$	9.74078e134	0.909491	0.454745	+	0.890621i	$0.349730\pi$
$272$	−2.49856e134	−0.190158
$273$	−4.52771e132	−0.00281094
$274$	1.39107e135	0.705007
$275$	4.18403e134	0.173233
$276$	−1.31154e133	−0.00443943
$277$	1.98298e135	0.549150	0.274575	−	0.961566i	$-0.411463\pi$
$277$	1.98298e135	0.549150	0.274575	+	0.961566i	$0.411463\pi$
$278$	−5.47256e135	−1.24081
$279$	−2.08208e135	−0.386780
$280$	−1.36483e135	−0.207878
$281$	1.92173e135	0.240155	0.120077	−	0.992765i	$-0.461686\pi$
$281$	1.92173e135	0.240155	0.120077	+	0.992765i	$0.461686\pi$
$282$	1.97465e135	0.202612
$283$	−7.90343e135	−0.666298	−0.333149	−	0.942874i	$-0.608111\pi$
$283$	−7.90343e135	−0.666298	−0.333149	+	0.942874i	$0.608111\pi$
$284$	−2.19688e134	−0.0152278
$285$	1.80476e135	0.102927
$286$	6.66537e134	0.0312975
$287$	−1.27337e136	−0.492617
$288$	6.17086e135	0.196817
$289$	−3.68477e136	−0.969573
$290$	1.85722e136	0.403435
$291$	6.12176e135	0.109854
$292$	7.46416e135	0.110722
$293$	1.03292e137	1.26740	0.633700	−	0.773579i	$-0.281536\pi$
$293$	1.03292e137	1.26740	0.633700	+	0.773579i	$0.281536\pi$
$294$	1.11368e136	0.113106
$295$	8.35593e136	0.702867
$296$	−7.90164e135	−0.0550842
$297$	−1.53359e136	−0.0886595
$298$	1.31283e137	0.629804
$299$	−7.43613e135	−0.0296207
$300$	1.64848e135	0.00545573
$301$	−1.56454e137	−0.430472
$302$	−7.98482e137	−1.82759
$303$	2.28671e136	0.0435657
$304$	−8.12034e137	−1.28852
$305$	1.26448e136	0.0167214
$306$	−1.63593e137	−0.180395
$307$	1.30314e138	1.19897	0.599487	−	0.800384i	$-0.295371\pi$
$307$	1.30314e138	1.19897	0.599487	+	0.800384i	$0.295371\pi$
$308$	1.47256e136	0.0113112
$309$	1.65898e137	0.106450
$310$	−5.63923e137	−0.302444
$311$	3.28214e138	1.47216	0.736082	−	0.676892i	$-0.236674\pi$
$311$	3.28214e138	1.47216	0.736082	+	0.676892i	$0.236674\pi$
$312$	−2.35893e136	−0.00885389
$313$	2.85491e138	0.897185	0.448593	−	0.893736i	$-0.351925\pi$
$313$	2.85491e138	0.897185	0.448593	+	0.893736i	$0.351925\pi$
$314$	−2.23736e138	−0.589035
$315$	−9.84047e137	−0.217160
$316$	6.47093e137	0.119766
$317$	5.52179e137	0.0857613	0.0428806	−	0.999080i	$-0.486346\pi$
$317$	5.52179e137	0.0857613	0.0428806	+	0.999080i	$0.486346\pi$
$318$	−1.07830e138	−0.140616
$319$	1.79994e138	0.197185
$320$	−7.03063e138	−0.647397
$321$	−1.71353e138	−0.132698
$322$	−1.80426e138	−0.117570
$323$	3.75821e138	0.206177
$324$	2.07688e138	0.0959762
$325$	9.34647e137	0.0364017
$326$	−1.54616e139	−0.507782
$327$	−6.94739e138	−0.192496
$328$	−6.63423e139	−1.55164
$329$	2.47345e139	0.488574
$330$	−2.06215e138	−0.0344189
$331$	6.93834e139	0.979043	0.489521	−	0.871991i	$-0.337172\pi$
$331$	6.93834e139	0.979043	0.489521	+	0.871991i	$0.337172\pi$
$332$	1.07325e139	0.128097
$333$	−5.69711e138	−0.0575439
$334$	3.63511e139	0.310877
$335$	1.17869e140	0.853910
$336$	−6.30273e138	−0.0386989
$337$	3.33481e140	1.73625	0.868123	−	0.496349i	$-0.165326\pi$
$337$	3.33481e140	1.73625	0.868123	+	0.496349i	$0.165326\pi$
$338$	−2.35980e140	−1.04232
$339$	4.91692e139	0.184336
$340$	−4.03443e138	−0.0128441
$341$	−5.46530e139	−0.147824
$342$	−5.31679e140	−1.22236
$343$	2.92760e140	0.572385
$344$	−8.15120e140	−1.35590
$345$	2.30061e139	0.0325749
$346$	−1.35703e141	−1.63631
$347$	−6.95029e139	−0.0714031	−0.0357016	−	0.999362i	$-0.511367\pi$
$347$	−6.95029e139	−0.0714031	−0.0357016	+	0.999362i	$0.511367\pi$
$348$	7.09162e138	0.00621008
$349$	2.64284e141	1.97360	0.986801	−	0.161940i	$-0.0517751\pi$
$349$	2.64284e141	1.97360	0.986801	+	0.161940i	$0.0517751\pi$
$350$	2.26777e140	0.144485
$351$	−3.42580e139	−0.0186302
$352$	1.61981e140	0.0752220
$353$	1.11293e141	0.441543	0.220771	−	0.975326i	$-0.429143\pi$
$353$	1.11293e141	0.441543	0.220771	+	0.975326i	$0.429143\pi$
$354$	3.50415e140	0.118823
$355$	3.85360e140	0.111736
$356$	4.88425e140	0.121150
$357$	2.91699e139	0.00619227
$358$	4.38749e141	0.797458
$359$	−4.88931e141	−0.761212	−0.380606	−	0.924737i	$-0.624285\pi$
$359$	−4.88931e141	−0.761212	−0.380606	+	0.924737i	$0.624285\pi$
$360$	−5.12686e141	−0.684011
$361$	3.47144e141	0.397064
$362$	7.95710e139	0.00780601
$363$	1.20758e141	0.101648
$364$	3.28946e139	0.00237683
$365$	−1.30931e142	−0.812435
$366$	5.30274e139	0.00282683
$367$	2.44261e142	1.11915	0.559575	−	0.828780i	$-0.310965\pi$
$367$	2.44261e142	1.11915	0.559575	+	0.828780i	$0.310965\pi$
$368$	−1.03513e142	−0.407796
$369$	−4.78330e142	−1.62093
$370$	−1.54304e141	−0.0449968
$371$	−1.35068e142	−0.339079
$372$	−2.15329e140	−0.00465553
$373$	3.20357e142	0.596752	0.298376	−	0.954448i	$-0.403555\pi$
$373$	3.20357e142	0.596752	0.298376	+	0.954448i	$0.403555\pi$
$374$	−4.29419e141	−0.0689458
$375$	−9.18175e141	−0.127113
$376$	1.28866e143	1.53891
$377$	4.02078e141	0.0414348
$378$	−8.31216e141	−0.0739467
$379$	2.06241e143	1.58452	0.792262	−	0.610181i	$-0.208903\pi$
$379$	2.06241e143	1.58452	0.792262	+	0.610181i	$0.208903\pi$
$380$	−1.31119e142	−0.0870317
$381$	−2.56221e142	−0.146987
$382$	2.92288e142	0.144975
$383$	−2.12876e143	−0.913263	−0.456631	−	0.889656i	$-0.650944\pi$
$383$	−2.12876e143	−0.913263	−0.456631	+	0.889656i	$0.650944\pi$
$384$	−3.58545e142	−0.133095
$385$	−2.58305e142	−0.0829970
$386$	1.14090e142	0.0317432
$387$	−5.87704e143	−1.41645
$388$	−4.44757e142	−0.0928886
$389$	−6.73075e143	−1.21860	−0.609299	−	0.792941i	$-0.708549\pi$
$389$	−6.73075e143	−1.21860	−0.609299	+	0.792941i	$0.708549\pi$
$390$	−4.60653e141	−0.00723250
$391$	4.79075e142	0.0652520
$392$	7.26790e143	0.859077
$393$	8.40652e142	0.0862640
$394$	1.91851e144	1.70972
$395$	−1.13509e144	−0.878799
$396$	5.53152e142	0.0372188
$397$	−1.28955e143	−0.0754338	−0.0377169	−	0.999288i	$-0.512009\pi$
$397$	−1.28955e143	−0.0754338	−0.0377169	+	0.999288i	$0.512009\pi$
$398$	1.66312e144	0.846083
$399$	9.48026e142	0.0419589
$400$	1.30106e144	0.501151
$401$	−1.49726e144	−0.502094	−0.251047	−	0.967975i	$-0.580775\pi$
$401$	−1.49726e144	−0.502094	−0.251047	+	0.967975i	$0.580775\pi$
$402$	4.94295e143	0.144358
$403$	−1.22086e143	−0.0310626
$404$	−1.66133e143	−0.0368376
$405$	−3.64312e144	−0.704238
$406$	9.75579e143	0.164463
$407$	−1.49545e143	−0.0219929
$408$	1.51975e143	0.0195044
$409$	7.55497e144	0.846426	0.423213	−	0.906030i	$-0.360902\pi$
$409$	7.55497e144	0.846426	0.423213	+	0.906030i	$0.360902\pi$
$410$	−1.29554e145	−1.26749
$411$	−9.31738e143	−0.0796293
$412$	−1.20528e144	−0.0900105
$413$	4.38929e144	0.286528
$414$	−6.77753e144	−0.386859
$415$	−1.88262e145	−0.939925
$416$	3.61840e143	0.0158065
$417$	3.66551e144	0.140147
$418$	−1.39562e145	−0.467178
$419$	2.30213e145	0.674919	0.337460	−	0.941340i	$-0.390432\pi$
$419$	2.30213e145	0.674919	0.337460	+	0.941340i	$0.390432\pi$
$420$	−1.01770e143	−0.00261388
$421$	4.33827e145	0.976472	0.488236	−	0.872712i	$-0.337640\pi$
$421$	4.33827e145	0.976472	0.488236	+	0.872712i	$0.337640\pi$
$422$	4.87568e145	0.962043
$423$	9.29128e145	1.60763
$424$	−7.03701e145	−1.06803
$425$	−6.02150e144	−0.0801898
$426$	1.61605e144	0.0188896
$427$	6.64221e143	0.00681657
$428$	1.24491e145	0.112204
$429$	−4.46446e143	−0.00353500
$430$	−1.59177e146	−1.10760
$431$	−4.36552e145	−0.267022	−0.133511	−	0.991047i	$-0.542625\pi$
$431$	−4.36552e145	−0.267022	−0.133511	+	0.991047i	$0.542625\pi$
$432$	−4.76883e145	−0.256486
$433$	−2.99169e146	−1.41527	−0.707633	−	0.706580i	$-0.750237\pi$
$433$	−2.99169e146	−1.41527	−0.707633	+	0.706580i	$0.750237\pi$
$434$	−2.96223e145	−0.123293
$435$	−1.24396e145	−0.0455673
$436$	5.04740e145	0.162768
$437$	1.55700e146	0.442149
$438$	−5.49073e145	−0.137346
$439$	3.63494e146	0.801154	0.400577	−	0.916263i	$-0.368810\pi$
$439$	3.63494e146	0.801154	0.400577	+	0.916263i	$0.368810\pi$
$440$	−1.34576e146	−0.261424
$441$	5.24018e146	0.897438
$442$	−9.59257e144	−0.0144877
$443$	9.45240e146	1.25932	0.629659	−	0.776872i	$-0.283195\pi$
$443$	9.45240e146	1.25932	0.629659	+	0.776872i	$0.283195\pi$
$444$	−5.89196e143	−0.000692636 0
$445$	−8.56761e146	−0.888953
$446$	−2.21824e146	−0.203200
$447$	−8.79330e145	−0.0711352
$448$	−3.69313e146	−0.263915
$449$	1.39885e147	0.883283	0.441641	−	0.897192i	$-0.354396\pi$
$449$	1.39885e147	0.883283	0.441641	+	0.897192i	$0.354396\pi$
$450$	8.51869e146	0.475421
$451$	−1.25558e147	−0.619507
$452$	−3.57223e146	−0.155868
$453$	5.34822e146	0.206423
$454$	−3.30916e147	−1.13010
$455$	−5.77014e145	−0.0174403
$456$	4.93919e146	0.132162
$457$	4.78656e146	0.113416	0.0567080	−	0.998391i	$-0.481940\pi$
$457$	4.78656e146	0.113416	0.0567080	+	0.998391i	$0.481940\pi$
$458$	1.30552e146	0.0273999
$459$	2.20708e146	0.0410407
$460$	−1.67144e146	−0.0275442
$461$	−7.78882e147	−1.13781	−0.568906	−	0.822403i	$-0.692633\pi$
$461$	−7.78882e147	−1.13781	−0.568906	+	0.822403i	$0.692633\pi$
$462$	−1.08323e146	−0.0140311
$463$	−5.98097e147	−0.687111	−0.343555	−	0.939132i	$-0.611631\pi$
$463$	−5.98097e147	−0.687111	−0.343555	+	0.939132i	$0.611631\pi$
$464$	5.59707e147	0.570444
$465$	3.77714e146	0.0341605
$466$	1.72187e148	1.38224
$467$	−3.42519e147	−0.244117	−0.122058	−	0.992523i	$-0.538950\pi$
$467$	−3.42519e147	−0.244117	−0.122058	+	0.992523i	$0.538950\pi$
$468$	1.23566e146	0.00782084
$469$	6.19154e147	0.348102
$470$	2.51651e148	1.25709
$471$	1.49858e147	0.0665304
$472$	2.28681e148	0.902505
$473$	−1.54268e148	−0.541356
$474$	−4.76010e147	−0.148566
$475$	−1.95699e148	−0.543368
$476$	−2.11925e146	−0.00523596
$477$	−5.07371e148	−1.11572
$478$	2.05595e148	0.402499
$479$	−7.68061e148	−1.33898	−0.669491	−	0.742820i	$-0.733488\pi$
$479$	−7.68061e148	−1.33898	−0.669491	+	0.742820i	$0.733488\pi$
$480$	−1.11947e147	−0.0173830
$481$	−3.34060e146	−0.00462139
$482$	−7.95497e148	−0.980682
$483$	1.20849e147	0.0132794
$484$	−8.77328e147	−0.0859497
$485$	7.80162e148	0.681582
$486$	−4.69461e148	−0.365836
$487$	2.59840e149	1.80655	0.903273	−	0.429066i	$-0.141157\pi$
$487$	2.59840e149	1.80655	0.903273	+	0.429066i	$0.141157\pi$
$488$	3.46058e147	0.0214708
$489$	1.03561e148	0.0573531
$490$	1.41928e149	0.701756
$491$	3.04588e148	0.134490	0.0672449	−	0.997736i	$-0.478579\pi$
$491$	3.04588e148	0.134490	0.0672449	+	0.997736i	$0.478579\pi$
$492$	−4.94690e147	−0.0195106
$493$	−2.59041e148	−0.0912775
$494$	−3.11759e148	−0.0981689
$495$	−9.70300e148	−0.273097
$496$	−1.69948e149	−0.427646
$497$	2.02426e148	0.0455499
$498$	−7.89496e148	−0.158899
$499$	4.92976e149	0.887658	0.443829	−	0.896111i	$-0.353620\pi$
$499$	4.92976e149	0.887658	0.443829	+	0.896111i	$0.353620\pi$
$500$	6.67071e148	0.107482
$501$	−2.43479e148	−0.0351130
$502$	−8.53407e149	−1.10179
$503$	−1.94182e149	−0.224484	−0.112242	−	0.993681i	$-0.535803\pi$
$503$	−1.94182e149	−0.224484	−0.112242	+	0.993681i	$0.535803\pi$
$504$	−2.69309e149	−0.278841
$505$	2.91419e149	0.270301
$506$	−1.77905e149	−0.147855
$507$	1.58059e149	0.117728
$508$	1.86150e149	0.124287
$509$	−7.85118e149	−0.470000	−0.235000	−	0.971995i	$-0.575509\pi$
$509$	−7.85118e149	−0.470000	−0.235000	+	0.971995i	$0.575509\pi$
$510$	2.96778e148	0.0159326
$511$	−6.87769e149	−0.331194
$512$	−1.87783e150	−0.811283
$513$	7.17304e149	0.278093
$514$	2.48245e150	0.863828
$515$	2.11422e150	0.660464
$516$	−6.07805e148	−0.0170493
$517$	2.43889e150	0.614423
$518$	−8.10544e148	−0.0183432
$519$	9.08936e149	0.184818
$520$	−3.00623e149	−0.0549334
$521$	1.11447e151	1.83052	0.915261	−	0.402861i	$-0.131984\pi$
$521$	1.11447e151	1.83052	0.915261	+	0.402861i	$0.131984\pi$
$522$	3.66468e150	0.541156
$523$	−1.20337e151	−1.59793	−0.798964	−	0.601379i	$-0.794618\pi$
$523$	−1.20337e151	−1.59793	−0.798964	+	0.601379i	$0.794618\pi$
$524$	−6.10749e149	−0.0729418
$525$	−1.51895e149	−0.0163193
$526$	−1.73382e151	−1.67608
$527$	7.86546e149	0.0684282
$528$	−6.21468e149	−0.0486671
$529$	−1.21989e151	−0.860067
$530$	−1.37419e151	−0.872444
$531$	1.64880e151	0.942805
$532$	−6.88758e149	−0.0354790
$533$	−2.80477e150	−0.130178
$534$	−3.59292e150	−0.150282
$535$	−2.18374e151	−0.823314
$536$	3.22578e151	1.09645
$537$	−2.93873e150	−0.0900715
$538$	6.97429e151	1.92790
$539$	1.37551e151	0.342994
$540$	−7.70025e149	−0.0173241
$541$	−1.79940e151	−0.365324	−0.182662	−	0.983176i	$-0.558471\pi$
$541$	−1.79940e151	−0.365324	−0.182662	+	0.983176i	$0.558471\pi$
$542$	5.20582e151	0.953958
$543$	−5.32965e148	−0.000881675 0
$544$	−2.33117e150	−0.0348205
$545$	−8.85380e151	−1.19433
$546$	−2.41977e149	−0.00294837
$547$	−1.89946e151	−0.209090	−0.104545	−	0.994520i	$-0.533339\pi$
$547$	−1.89946e151	−0.209090	−0.104545	+	0.994520i	$0.533339\pi$
$548$	6.76925e150	0.0673317
$549$	2.49509e150	0.0224296
$550$	2.23609e151	0.181702
$551$	−8.41884e151	−0.618499
$552$	6.29620e150	0.0418273
$553$	−5.96250e151	−0.358248
$554$	1.05977e152	0.575999
$555$	1.03353e150	0.00508230
$556$	−2.66306e151	−0.118503
$557$	−9.27529e151	−0.373563	−0.186782	−	0.982401i	$-0.559806\pi$
$557$	−9.27529e151	−0.373563	−0.186782	+	0.982401i	$0.559806\pi$
$558$	−1.11274e152	−0.405690
$559$	−3.44611e151	−0.113756
$560$	−8.03224e151	−0.240105
$561$	2.87624e150	0.00778730
$562$	1.02704e152	0.251897
$563$	5.77012e151	0.128224	0.0641119	−	0.997943i	$-0.479579\pi$
$563$	5.77012e151	0.128224	0.0641119	+	0.997943i	$0.479579\pi$
$564$	9.60906e150	0.0193504
$565$	6.26615e152	1.14370
$566$	−4.22387e152	−0.698874
$567$	−1.91370e152	−0.287087
$568$	1.05464e152	0.143473
$569$	8.15675e152	1.00644	0.503218	−	0.864159i	$-0.332149\pi$
$569$	8.15675e152	1.00644	0.503218	+	0.864159i	$0.332149\pi$
$570$	9.64531e151	0.107960
$571$	1.62614e153	1.65141	0.825703	−	0.564106i	$-0.190779\pi$
$571$	1.62614e153	1.65141	0.825703	+	0.564106i	$0.190779\pi$
$572$	3.24351e150	0.00298907
$573$	−1.95774e151	−0.0163747
$574$	−6.80534e152	−0.516702
$575$	−2.49466e152	−0.171968
$576$	−1.38729e153	−0.868399
$577$	−8.44089e152	−0.479878	−0.239939	−	0.970788i	$-0.577127\pi$
$577$	−8.44089e152	−0.479878	−0.239939	+	0.970788i	$0.577127\pi$
$578$	−1.96927e153	−1.01698
$579$	−7.64172e150	−0.00358534
$580$	9.03761e151	0.0385301
$581$	−9.88923e152	−0.383166
$582$	3.27169e152	0.115225
$583$	−1.33181e153	−0.426420
$584$	−3.58326e153	−1.04319
$585$	−2.16750e152	−0.0573864
$586$	5.52029e153	1.32937
$587$	2.52144e153	0.552374	0.276187	−	0.961104i	$-0.410929\pi$
$587$	2.52144e153	0.552374	0.276187	+	0.961104i	$0.410929\pi$
$588$	5.41940e151	0.0108021
$589$	2.55628e153	0.463671
$590$	4.46571e153	0.737231
$591$	−1.28502e153	−0.193110
$592$	−4.65023e152	−0.0636239
$593$	9.68298e153	1.20635	0.603176	−	0.797608i	$-0.293902\pi$
$593$	9.68298e153	1.20635	0.603176	+	0.797608i	$0.293902\pi$
$594$	−8.19603e152	−0.0929942
$595$	3.71744e152	0.0384195
$596$	6.38850e152	0.0601494
$597$	−1.11395e153	−0.0955635
$598$	−3.97413e152	−0.0310689
$599$	−9.77515e153	−0.696522	−0.348261	−	0.937398i	$-0.613228\pi$
$599$	−9.77515e153	−0.696522	−0.348261	+	0.937398i	$0.613228\pi$
$600$	−7.91370e152	−0.0514026
$601$	−2.68769e154	−1.59164	−0.795822	−	0.605531i	$-0.792961\pi$
$601$	−2.68769e154	−1.59164	−0.795822	+	0.605531i	$0.792961\pi$
$602$	−8.36145e153	−0.451519
$603$	2.32580e154	1.14541
$604$	−3.88558e153	−0.174544
$605$	1.53895e154	0.630667
$606$	1.22210e153	0.0456957
$607$	−1.85080e154	−0.631519	−0.315759	−	0.948839i	$-0.602259\pi$
$607$	−1.85080e154	−0.631519	−0.315759	+	0.948839i	$0.602259\pi$
$608$	−7.57632e153	−0.235944
$609$	−6.53442e152	−0.0185758
$610$	6.75785e152	0.0175389
$611$	5.44811e153	0.129110
$612$	−7.96077e152	−0.0172287
$613$	−6.56124e154	−1.29697	−0.648484	−	0.761228i	$-0.724597\pi$
$613$	−6.56124e154	−1.29697	−0.648484	+	0.761228i	$0.724597\pi$
$614$	6.96443e154	1.25760
$615$	8.67749e153	0.143161
$616$	−7.06917e153	−0.106571
$617$	1.91681e154	0.264090	0.132045	−	0.991244i	$-0.457846\pi$
$617$	1.91681e154	0.264090	0.132045	+	0.991244i	$0.457846\pi$
$618$	8.86620e153	0.111655
$619$	−3.47345e153	−0.0399880	−0.0199940	−	0.999800i	$-0.506365\pi$
$619$	−3.47345e153	−0.0399880	−0.0199940	+	0.999800i	$0.506365\pi$
$620$	−2.74417e153	−0.0288849
$621$	9.14379e153	0.0880121
$622$	1.75410e155	1.54414
$623$	−4.50049e154	−0.362387
$624$	−1.38826e153	−0.0102265
$625$	−4.88061e154	−0.328952
$626$	1.52577e155	0.941051
$627$	9.34782e153	0.0527669
$628$	−1.08875e154	−0.0562557
$629$	2.15220e153	0.0101805
$630$	−5.25910e154	−0.227778
$631$	−3.38805e155	−1.34375	−0.671877	−	0.740662i	$-0.734512\pi$
$631$	−3.38805e155	−1.34375	−0.671877	+	0.740662i	$0.734512\pi$
$632$	−3.10645e155	−1.12841
$633$	−3.26573e154	−0.108661
$634$	2.95104e154	0.0899543
$635$	−3.26530e155	−0.911972
$636$	−5.24724e153	−0.0134295
$637$	3.07268e154	0.0720739
$638$	9.61950e154	0.206826
$639$	7.60396e154	0.149880
$640$	−4.56932e155	−0.825778
$641$	1.01586e156	1.68350	0.841749	−	0.539869i	$-0.181526\pi$
$641$	1.01586e156	1.68350	0.841749	+	0.539869i	$0.181526\pi$
$642$	−9.15773e154	−0.139185
$643$	1.24375e156	1.73390	0.866950	−	0.498396i	$-0.166077\pi$
$643$	1.24375e156	1.73390	0.866950	+	0.498396i	$0.166077\pi$
$644$	−8.77990e153	−0.0112286
$645$	1.06617e155	0.125101
$646$	2.00852e155	0.216258
$647$	4.94606e155	0.488734	0.244367	−	0.969683i	$-0.421420\pi$
$647$	4.94606e155	0.488734	0.244367	+	0.969683i	$0.421420\pi$
$648$	−9.97031e155	−0.904266
$649$	4.32798e155	0.360333
$650$	4.99509e154	0.0381814
$651$	1.98410e154	0.0139257
$652$	−7.52393e154	−0.0484957
$653$	−4.28612e155	−0.253736	−0.126868	−	0.991920i	$-0.540493\pi$
$653$	−4.28612e155	−0.253736	−0.126868	+	0.991920i	$0.540493\pi$
$654$	−3.71293e155	−0.201907
$655$	1.07133e156	0.535220
$656$	−3.90434e156	−1.79219
$657$	−2.58354e156	−1.08978
$658$	1.32190e156	0.512461
$659$	−5.85902e155	−0.208778	−0.104389	−	0.994537i	$-0.533289\pi$
$659$	−5.85902e155	−0.208778	−0.104389	+	0.994537i	$0.533289\pi$
$660$	−1.00349e154	−0.00328718
$661$	2.07235e156	0.624142	0.312071	−	0.950059i	$-0.398977\pi$
$661$	2.07235e156	0.624142	0.312071	+	0.950059i	$0.398977\pi$
$662$	3.70809e156	1.02691
$663$	6.42509e153	0.00163636
$664$	−5.15226e156	−1.20690
$665$	1.20817e156	0.260332
$666$	−3.04474e155	−0.0603573
$667$	−1.07319e156	−0.195745
$668$	1.76892e155	0.0296903
$669$	1.48577e155	0.0229510
$670$	6.29933e156	0.895659
$671$	6.54942e154	0.00857241
$672$	−5.88048e154	−0.00708627
$673$	−1.13628e157	−1.26081	−0.630406	−	0.776266i	$-0.717111\pi$
$673$	−1.13628e157	−1.26081	−0.630406	+	0.776266i	$0.717111\pi$
$674$	1.78224e157	1.82114
$675$	−1.14928e156	−0.108160
$676$	−1.14833e156	−0.0995463
$677$	2.68359e156	0.214311	0.107155	−	0.994242i	$-0.465826\pi$
$677$	2.68359e156	0.214311	0.107155	+	0.994242i	$0.465826\pi$
$678$	2.62778e156	0.193348
$679$	4.09812e156	0.277851
$680$	1.93678e156	0.121014
$681$	2.21647e156	0.127643
$682$	−2.92085e156	−0.155052
$683$	−7.20565e156	−0.352634	−0.176317	−	0.984333i	$-0.556418\pi$
$683$	−7.20565e156	−0.352634	−0.176317	+	0.984333i	$0.556418\pi$
$684$	−2.58726e156	−0.116742
$685$	−1.18741e157	−0.494055
$686$	1.56461e157	0.600370
$687$	−8.74435e154	−0.00309477
$688$	−4.79711e157	−1.56611
$689$	−2.97506e156	−0.0896044
$690$	1.22953e156	0.0341676
$691$	−5.23321e157	−1.34195	−0.670975	−	0.741480i	$-0.734124\pi$
$691$	−5.23321e157	−1.34195	−0.670975	+	0.741480i	$0.734124\pi$
$692$	−6.60359e156	−0.156276
$693$	−5.09690e156	−0.111330
$694$	−3.71448e156	−0.0748942
$695$	4.67135e157	0.869533
$696$	−3.40442e156	−0.0585100
$697$	1.80699e157	0.286771
$698$	1.41243e158	2.07009
$699$	−1.15331e157	−0.156121
$700$	1.10355e156	0.0137991
$701$	8.30755e157	0.959673	0.479836	−	0.877358i	$-0.340696\pi$
$701$	8.30755e157	0.959673	0.479836	+	0.877358i	$0.340696\pi$
$702$	−1.83087e156	−0.0195410
$703$	6.99466e156	0.0689836
$704$	−3.64153e157	−0.331896
$705$	−1.68555e157	−0.141986
$706$	5.94791e157	0.463131
$707$	1.53080e157	0.110190
$708$	1.70519e156	0.0113482
$709$	−1.08796e158	−0.669494	−0.334747	−	0.942308i	$-0.608651\pi$
$709$	−1.08796e158	−0.669494	−0.334747	+	0.942308i	$0.608651\pi$
$710$	2.05950e157	0.117199
$711$	−2.23976e158	−1.17880
$712$	−2.34474e158	−1.14145
$713$	3.25860e157	0.146745
$714$	1.55895e156	0.00649502
$715$	−5.68953e156	−0.0219327
$716$	2.13504e157	0.0761613
$717$	−1.37707e157	−0.0454615
$718$	−2.61302e158	−0.798429
$719$	5.50384e158	1.55673	0.778363	−	0.627814i	$-0.216050\pi$
$719$	5.50384e158	1.55673	0.778363	+	0.627814i	$0.216050\pi$
$720$	−3.01724e158	−0.790053
$721$	1.11058e158	0.269242
$722$	1.85526e158	0.416477
$723$	5.32823e157	0.110766
$724$	3.87209e155	0.000745513 0
$725$	1.34889e158	0.240556
$726$	6.45373e157	0.106617
$727$	4.79637e158	0.734096	0.367048	−	0.930202i	$-0.380368\pi$
$727$	4.79637e158	0.734096	0.367048	+	0.930202i	$0.380368\pi$
$728$	−1.57915e157	−0.0223939
$729$	−6.97652e158	−0.916771
$730$	−6.99742e158	−0.852156
$731$	2.22017e158	0.250595
$732$	2.58042e155	0.000269977 0
$733$	1.24852e159	1.21094	0.605471	−	0.795867i	$-0.292985\pi$
$733$	1.24852e159	1.21094	0.605471	+	0.795867i	$0.292985\pi$
$734$	1.30542e159	1.17387
$735$	−9.50633e157	−0.0792621
$736$	−9.65785e157	−0.0746727
$737$	6.10505e158	0.437767
$738$	−2.55637e159	−1.70018
$739$	6.30540e158	0.388997	0.194498	−	0.980903i	$-0.437692\pi$
$739$	6.30540e158	0.388997	0.194498	+	0.980903i	$0.437692\pi$
$740$	−7.50875e156	−0.00429741
$741$	2.08816e157	0.0110880
$742$	−7.21852e158	−0.355657
$743$	−7.63977e158	−0.349302	−0.174651	−	0.984630i	$-0.555880\pi$
$743$	−7.63977e158	−0.349302	−0.174651	+	0.984630i	$0.555880\pi$
$744$	1.03371e158	0.0438633
$745$	−1.12062e159	−0.441354
$746$	1.71210e159	0.625929
$747$	−3.71480e159	−1.26079
$748$	−2.08964e157	−0.00658466
$749$	−1.14710e159	−0.335629
$750$	−4.90705e158	−0.133328
$751$	−6.80212e159	−1.71644	−0.858219	−	0.513284i	$-0.828429\pi$
$751$	−6.80212e159	−1.71644	−0.858219	+	0.513284i	$0.828429\pi$
$752$	7.58396e159	1.77748
$753$	5.71611e158	0.124445
$754$	2.14885e158	0.0434607
$755$	6.81581e159	1.28074
$756$	−4.04487e157	−0.00706228
$757$	−5.64569e159	−0.916000	−0.458000	−	0.888952i	$-0.651434\pi$
$757$	−5.64569e159	−0.916000	−0.458000	+	0.888952i	$0.651434\pi$
$758$	1.10223e160	1.66199
$759$	1.19161e158	0.0166999
$760$	6.29454e159	0.819992
$761$	7.75612e159	0.939282	0.469641	−	0.882857i	$-0.344383\pi$
$761$	7.75612e159	0.939282	0.469641	+	0.882857i	$0.344383\pi$
$762$	−1.36934e159	−0.154174
$763$	−4.65082e159	−0.486875
$764$	1.42233e158	0.0138459
$765$	1.39642e159	0.126417
$766$	−1.13769e160	−0.957914
$767$	9.66804e158	0.0757174
$768$	−4.83952e158	−0.0352578
$769$	−2.50815e160	−1.69997	−0.849986	−	0.526804i	$-0.823390\pi$
$769$	−2.50815e160	−1.69997	−0.849986	+	0.526804i	$0.823390\pi$
$770$	−1.38048e159	−0.0870549
$771$	−1.66274e159	−0.0975678
$772$	5.55185e157	0.00303164
$773$	9.78960e159	0.497511	0.248756	−	0.968566i	$-0.419978\pi$
$773$	9.78960e159	0.497511	0.248756	+	0.968566i	$0.419978\pi$
$774$	−3.14090e160	−1.48570
$775$	−4.09574e159	−0.180338
$776$	2.13511e160	0.875175
$777$	5.42901e157	0.00207183
$778$	−3.59715e160	−1.27818
$779$	5.87273e160	1.94317
$780$	−2.24164e157	−0.000690740 0
$781$	1.99598e159	0.0572829
$782$	2.56035e159	0.0684423
$783$	−4.94413e159	−0.123115
$784$	4.27727e160	0.992259
$785$	1.90980e160	0.412784
$786$	4.49275e159	0.0904816
$787$	−2.42415e160	−0.454948	−0.227474	−	0.973784i	$-0.573047\pi$
$787$	−2.42415e160	−0.454948	−0.227474	+	0.973784i	$0.573047\pi$
$788$	9.33590e159	0.163287
$789$	1.16131e160	0.189310
$790$	−6.06630e160	−0.921765
$791$	3.29155e160	0.466236
$792$	−2.65547e160	−0.350666
$793$	1.46304e158	0.00180133
$794$	−6.89184e159	−0.0791220
$795$	9.20433e159	0.0985409
$796$	8.09308e159	0.0808051
$797$	1.35987e161	1.26637	0.633184	−	0.774001i	$-0.281748\pi$
$797$	1.35987e161	1.26637	0.633184	+	0.774001i	$0.281748\pi$
$798$	5.06659e159	0.0440104
$799$	−3.50997e160	−0.284418
$800$	1.21390e160	0.0917672
$801$	−1.69057e161	−1.19242
$802$	−8.00190e160	−0.526642
$803$	−6.78160e160	−0.416504
$804$	2.40534e159	0.0137869
$805$	1.54011e160	0.0823910
$806$	−6.52473e159	−0.0325813
$807$	−4.67137e160	−0.217753
$808$	7.97543e160	0.347075
$809$	−1.20710e161	−0.490456	−0.245228	−	0.969465i	$-0.578863\pi$
$809$	−1.20710e161	−0.490456	−0.245228	+	0.969465i	$0.578863\pi$
$810$	−1.94701e161	−0.738669
$811$	1.32817e161	0.470541	0.235271	−	0.971930i	$-0.424402\pi$
$811$	1.32817e161	0.470541	0.235271	+	0.971930i	$0.424402\pi$
$812$	4.74737e159	0.0157070
$813$	−3.48685e160	−0.107748
$814$	−7.99221e159	−0.0230681
$815$	1.31979e161	0.355843
$816$	8.94394e159	0.0225281
$817$	7.21558e161	1.69804
$818$	4.03765e161	0.887810
$819$	−1.13857e160	−0.0233939
$820$	−6.30436e160	−0.121052
$821$	−3.08347e160	−0.0553344	−0.0276672	−	0.999617i	$-0.508808\pi$
$821$	−3.08347e160	−0.0553344	−0.0276672	+	0.999617i	$0.508808\pi$
$822$	−4.97954e160	−0.0835225
$823$	2.46013e161	0.385716	0.192858	−	0.981227i	$-0.438224\pi$
$823$	2.46013e161	0.385716	0.192858	+	0.981227i	$0.438224\pi$
$824$	5.78610e161	0.848058
$825$	−1.49773e160	−0.0205230
$826$	2.34580e161	0.300537
$827$	−1.38302e162	−1.65681	−0.828403	−	0.560133i	$-0.810750\pi$
$827$	−1.38302e162	−1.65681	−0.828403	+	0.560133i	$0.810750\pi$
$828$	−3.29809e160	−0.0369470
$829$	−1.17575e162	−1.23180	−0.615900	−	0.787824i	$-0.711207\pi$
$829$	−1.17575e162	−1.23180	−0.615900	+	0.787824i	$0.711207\pi$
$830$	−1.00614e162	−0.985880
$831$	−7.09835e160	−0.0650580
$832$	−8.13463e160	−0.0697418
$833$	−1.97958e161	−0.158773
$834$	1.95898e161	0.146999
$835$	−3.10292e161	−0.217856
$836$	−6.79136e160	−0.0446178
$837$	1.50123e161	0.0922962
$838$	1.23034e162	0.707917
$839$	−2.36082e161	−0.127138	−0.0635689	−	0.997977i	$-0.520248\pi$
$839$	−2.36082e161	−0.127138	−0.0635689	+	0.997977i	$0.520248\pi$
$840$	4.88561e160	0.0246274
$841$	−1.53895e162	−0.726183
$842$	2.31852e162	1.02421
$843$	−6.87911e160	−0.0284513
$844$	2.37261e161	0.0918799
$845$	2.01432e162	0.730434
$846$	4.96559e162	1.68623
$847$	8.08394e161	0.257095
$848$	−4.14139e162	−1.23360
$849$	2.82914e161	0.0789366
$850$	−3.21811e161	−0.0841105
$851$	8.91639e160	0.0218323
$852$	7.86404e159	0.00180405
$853$	−2.28041e162	−0.490164	−0.245082	−	0.969502i	$-0.578815\pi$
$853$	−2.28041e162	−0.490164	−0.245082	+	0.969502i	$0.578815\pi$
$854$	3.54984e160	0.00714984
$855$	4.53839e162	0.856608
$856$	−5.97635e162	−1.05716
$857$	−3.75863e162	−0.623151	−0.311576	−	0.950221i	$-0.600857\pi$
$857$	−3.75863e162	−0.623151	−0.311576	+	0.950221i	$0.600857\pi$
$858$	−2.38597e160	−0.00370783
$859$	4.18442e162	0.609558	0.304779	−	0.952423i	$-0.401417\pi$
$859$	4.18442e162	0.609558	0.304779	+	0.952423i	$0.401417\pi$
$860$	−7.74591e161	−0.105781
$861$	4.55821e161	0.0583605
$862$	−2.33309e162	−0.280077
$863$	−7.54580e161	−0.0849388	−0.0424694	−	0.999098i	$-0.513522\pi$
$863$	−7.54580e161	−0.0849388	−0.0424694	+	0.999098i	$0.513522\pi$
$864$	−4.44934e161	−0.0469659
$865$	1.15835e163	1.14669
$866$	−1.59887e163	−1.48446
$867$	1.31902e162	0.114866
$868$	−1.44148e161	−0.0117751
$869$	−5.87920e162	−0.450527
$870$	−6.64818e161	−0.0477952
$871$	1.36377e162	0.0919888
$872$	−2.42307e163	−1.53356
$873$	1.53942e163	0.914254
$874$	8.32116e162	0.463767
$875$	−6.14657e162	−0.321504
$876$	−2.67190e161	−0.0131173
$877$	3.14908e163	1.45113	0.725566	−	0.688153i	$-0.241578\pi$
$877$	3.14908e163	1.45113	0.725566	+	0.688153i	$0.241578\pi$
$878$	1.94264e163	0.840324
$879$	−3.69748e162	−0.150149
$880$	−7.92003e162	−0.301952
$881$	−9.12306e162	−0.326571	−0.163285	−	0.986579i	$-0.552209\pi$
$881$	−9.12306e162	−0.326571	−0.163285	+	0.986579i	$0.552209\pi$
$882$	2.80054e163	0.941316
$883$	3.44556e162	0.108753	0.0543764	−	0.998521i	$-0.482683\pi$
$883$	3.44556e162	0.108753	0.0543764	+	0.998521i	$0.482683\pi$
$884$	−4.66795e160	−0.00138365
$885$	−2.99112e162	−0.0832689
$886$	5.05170e163	1.32089
$887$	−4.40074e162	−0.108085	−0.0540424	−	0.998539i	$-0.517211\pi$
$887$	−4.40074e162	−0.108085	−0.0540424	+	0.998539i	$0.517211\pi$
$888$	2.82850e161	0.00652585
$889$	−1.71523e163	−0.371771
$890$	−4.57884e163	−0.932416
$891$	−1.88696e163	−0.361036
$892$	−1.07944e162	−0.0194066
$893$	−1.14074e164	−1.92722
$894$	−4.69946e162	−0.0746131
$895$	−3.74514e163	−0.558843
$896$	−2.40022e163	−0.336633
$897$	2.66187e161	0.00350918
$898$	7.47596e163	0.926468
$899$	−1.76196e163	−0.205273
$900$	4.14537e162	0.0454051
$901$	1.91670e163	0.197391
$902$	−6.71027e163	−0.649796
$903$	5.60048e162	0.0509983
$904$	1.71489e164	1.46855
$905$	−6.79215e161	−0.00547030
$906$	2.85828e163	0.216516
$907$	2.00931e164	1.43167	0.715835	−	0.698269i	$-0.246046\pi$
$907$	2.00931e164	1.43167	0.715835	+	0.698269i	$0.246046\pi$
$908$	−1.61031e163	−0.107931
$909$	5.75031e163	0.362573
$910$	−3.08377e162	−0.0182930
$911$	−6.02724e163	−0.336394	−0.168197	−	0.985753i	$-0.553795\pi$
$911$	−6.02724e163	−0.336394	−0.168197	+	0.985753i	$0.553795\pi$
$912$	2.90679e163	0.152651
$913$	−9.75107e163	−0.481864
$914$	2.55811e163	0.118961
$915$	−4.52640e161	−0.00198099
$916$	6.35293e161	0.00261683
$917$	5.62761e163	0.218186
$918$	1.17954e163	0.0430473
$919$	−2.55068e164	−0.876284	−0.438142	−	0.898906i	$-0.644363\pi$
$919$	−2.55068e164	−0.876284	−0.438142	+	0.898906i	$0.644363\pi$
$920$	8.02392e163	0.259515
$921$	−4.66476e163	−0.142043
$922$	−4.16262e164	−1.19344
$923$	4.45872e162	0.0120369
$924$	−5.27122e161	−0.00134004
$925$	−1.12070e163	−0.0268302
$926$	−3.19645e164	−0.720705
$927$	4.17180e164	0.885927
$928$	5.22209e163	0.104456
$929$	5.00935e164	0.943864	0.471932	−	0.881635i	$-0.343557\pi$
$929$	5.00935e164	0.943864	0.471932	+	0.881635i	$0.343557\pi$
$930$	2.01864e163	0.0358307
$931$	−6.43367e164	−1.07585
$932$	8.37900e163	0.132011
$933$	−1.17489e164	−0.174408
$934$	−1.83054e164	−0.256052
$935$	3.66550e163	0.0483158
$936$	−5.93192e163	−0.0736861
$937$	−1.01592e164	−0.118936	−0.0594678	−	0.998230i	$-0.518940\pi$
$937$	−1.01592e164	−0.118936	−0.0594678	+	0.998230i	$0.518940\pi$
$938$	3.30898e164	0.365121
$939$	−1.02196e164	−0.106290
$940$	1.22458e164	0.120059
$941$	2.65618e164	0.245489	0.122745	−	0.992438i	$-0.460830\pi$
$941$	2.65618e164	0.245489	0.122745	+	0.992438i	$0.460830\pi$
$942$	8.00896e163	0.0697832
$943$	7.48622e164	0.614983
$944$	1.34582e165	1.04242
$945$	7.09522e163	0.0518204
$946$	−8.24464e164	−0.567824
$947$	1.23281e165	0.800707	0.400353	−	0.916361i	$-0.368887\pi$
$947$	1.23281e165	0.800707	0.400353	+	0.916361i	$0.368887\pi$
$948$	−2.31636e163	−0.0141887
$949$	−1.51491e164	−0.0875208
$950$	−1.04589e165	−0.569935
$951$	−1.97661e163	−0.0101602
$952$	1.01737e164	0.0493320
$953$	2.31069e165	1.05703	0.528513	−	0.848925i	$-0.322750\pi$
$953$	2.31069e165	1.05703	0.528513	+	0.848925i	$0.322750\pi$
$954$	−2.71157e165	−1.17027
$955$	−2.49496e164	−0.101596
$956$	1.00047e164	0.0384407
$957$	−6.44313e163	−0.0233606
$958$	−4.10479e165	−1.40445
$959$	−6.23737e164	−0.201404
$960$	2.51672e164	0.0766974
$961$	−2.94155e165	−0.846112
$962$	−1.78534e163	−0.00484734
$963$	−4.30897e165	−1.10437
$964$	−3.87106e164	−0.0936600
$965$	−9.73866e163	−0.0222450
$966$	6.45860e163	0.0139286
$967$	8.08781e165	1.64688	0.823440	−	0.567404i	$-0.192052\pi$
$967$	8.08781e165	1.64688	0.823440	+	0.567404i	$0.192052\pi$
$968$	4.21171e165	0.809798
$969$	−1.34531e164	−0.0244259
$970$	4.16946e165	0.714906
$971$	−2.32857e165	−0.377069	−0.188535	−	0.982067i	$-0.560374\pi$
$971$	−2.32857e165	−0.377069	−0.188535	+	0.982067i	$0.560374\pi$
$972$	−2.28450e164	−0.0349392
$973$	2.45382e165	0.354470
$974$	1.38868e166	1.89487
$975$	−3.34570e163	−0.00431252
$976$	2.03660e164	0.0247994
$977$	−1.26993e165	−0.146093	−0.0730467	−	0.997329i	$-0.523272\pi$
$977$	−1.26993e165	−0.146093	−0.0730467	+	0.997329i	$0.523272\pi$
$978$	5.53470e164	0.0601572
$979$	−4.43761e165	−0.455733
$980$	6.90653e164	0.0670212
$981$	−1.74704e166	−1.60204
$982$	1.62783e165	0.141065
$983$	5.21648e165	0.427226	0.213613	−	0.976918i	$-0.431477\pi$
$983$	5.21648e165	0.427226	0.213613	+	0.976918i	$0.431477\pi$
$984$	2.37482e165	0.183824
$985$	−1.63764e166	−1.19814
$986$	−1.38441e165	−0.0957402
$987$	−8.85405e164	−0.0578816
$988$	−1.51709e164	−0.00937562
$989$	9.19801e165	0.537402
$990$	−5.18563e165	−0.286450
$991$	−1.65064e166	−0.862115	−0.431058	−	0.902324i	$-0.641859\pi$
$991$	−1.65064e166	−0.862115	−0.431058	+	0.902324i	$0.641859\pi$
$992$	−1.58563e165	−0.0783075
$993$	−2.48368e165	−0.115988
$994$	1.08184e165	0.0477769
$995$	−1.41963e166	−0.592918
$996$	−3.84185e164	−0.0151757
$997$	4.67878e166	1.74804	0.874021	−	0.485888i	$-0.161504\pi$
$997$	4.67878e166	1.74804	0.874021	+	0.485888i	$0.161504\pi$
$998$	2.63464e166	0.931058
$999$	4.10775e164	0.0137315

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.112.a.a.1.7	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.112.a.a.1.7	✓	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)

\(f(q)\)	\(=\)	\(q+5.34436e16 q^{2} -3.57964e25 q^{3} +2.60068e32 q^{4} -4.56192e38 q^{5} -1.91309e42 q^{6} -2.39634e46 q^{7} -1.24849e50 q^{8} -9.00162e52 q^{9} +O(q^{10})\)	\(q+5.34436e16 q^{2} -3.57964e25 q^{3} +2.60068e32 q^{4} -4.56192e38 q^{5} -1.91309e42 q^{6} -2.39634e46 q^{7} -1.24849e50 q^{8} -9.00162e52 q^{9} -2.43805e55 q^{10} -2.36286e57 q^{11} -9.30949e57 q^{12} -5.27826e60 q^{13} -1.28069e63 q^{14} +1.63300e64 q^{15} -7.34753e66 q^{16} +3.40054e67 q^{17} -4.81079e69 q^{18} +1.10518e71 q^{19} -1.18641e71 q^{20} +8.57803e71 q^{21} -1.26280e74 q^{22} +1.40882e75 q^{23} +4.46913e75 q^{24} -1.77075e77 q^{25} -2.82089e77 q^{26} +6.49039e78 q^{27} -6.23209e78 q^{28} -7.61762e80 q^{29} +8.72736e80 q^{30} +2.31300e82 q^{31} -6.85528e82 q^{32} +8.45819e82 q^{33} +1.81737e84 q^{34} +1.09319e85 q^{35} -2.34103e85 q^{36} +6.32898e85 q^{37} +5.90648e87 q^{38} +1.88943e86 q^{39} +5.69549e88 q^{40} +5.31382e89 q^{41} +4.58440e88 q^{42} +6.52887e90 q^{43} -6.14503e89 q^{44} +4.10647e91 q^{45} +7.52924e91 q^{46} -1.03218e93 q^{47} +2.63015e92 q^{48} -5.82137e93 q^{49} -9.46351e93 q^{50} -1.21727e93 q^{51} -1.37271e93 q^{52} +5.63644e95 q^{53} +3.46869e95 q^{54} +1.07792e96 q^{55} +2.99179e96 q^{56} -3.95615e96 q^{57} -4.07113e97 q^{58} -1.83167e98 q^{59} +4.24692e96 q^{60} -2.77182e97 q^{61} +1.23615e99 q^{62} +2.15709e99 q^{63} +1.54116e100 q^{64} +2.40790e99 q^{65} +4.52036e99 q^{66} -2.58375e101 q^{67} +8.84371e99 q^{68} -5.04307e100 q^{69} +5.84239e101 q^{70} -8.44733e101 q^{71} +1.12384e103 q^{72} +2.87008e103 q^{73} +3.38243e102 q^{74} +6.33864e102 q^{75} +2.87422e103 q^{76} +5.66220e103 q^{77} +1.00978e103 q^{78} +2.48817e105 q^{79} +3.35188e105 q^{80} +7.98593e105 q^{81} +2.83990e106 q^{82} +4.12681e106 q^{83} +2.23087e104 q^{84} -1.55130e106 q^{85} +3.48926e107 q^{86} +2.72684e106 q^{87} +2.94999e107 q^{88} +1.87807e108 q^{89} +2.19464e108 q^{90} +1.26485e107 q^{91} +3.66389e107 q^{92} -8.27972e107 q^{93} -5.51633e109 q^{94} -5.04174e109 q^{95} +2.45395e108 q^{96} -1.71016e110 q^{97} -3.11115e110 q^{98} +2.12696e110 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 73\!\cdots\!76 q^{2}+ \cdots + 44\!\cdots\!13 q^{9}+O(q^{10}) \) 9 * q + 7300500744476376 * q^2 + 233675452617241539765416652 * q^3 + 11020070169858572323722385321061952 * q^4 + 814194067724935025770916308591172296830 * q^5 - 21301527237484005705216688979545976184644832 * q^6 + 78389901636433627730832560362319405491179083256 * q^7 + 331917555337838634305814685721710111074446802593280 * q^8 + 448549390735821931740487725597506918142357121619864013 * q^9	\( 9 q + 73\!\cdots\!76 q^{2}+ \cdots - 30\!\cdots\!44 q^{99}+O(q^{100}) \) 9 * q + 7300500744476376 * q^2 + 233675452617241539765416652 * q^3 + 11020070169858572323722385321061952 * q^4 + 814194067724935025770916308591172296830 * q^5 - 21301527237484005705216688979545976184644832 * q^6 + 78389901636433627730832560362319405491179083256 * q^7 + 331917555337838634305814685721710111074446802593280 * q^8 + 448549390735821931740487725597506918142357121619864013 * q^9 + 70318383028880935426202467492101897354146229740372656080 * q^10 + 946977307561400491686882997086862420104457212380759419908 * q^11 + 621762406249451000840580799122879254067634743931860068057856 * q^12 - 105889073807861007951354048376593318148850899094543430238180938 * q^13 - 693200815745779812299859823081139405355406151517828024353685696 * q^14 - 263011530334644917620915776775966612573140691671014743658639898840 * q^15 + 27983078214052241229733802839129592879112204378169572191112640794624 * q^16 - 222105261114216680375344353232960019775132216853502752977555776836734 * q^17 + 13836898392348788400585588852374256049336540448485000158069800440043832 * q^18 - 84745728104868082450386145180218866587906565903531918441867146236497220 * q^19 + 7795554433199817270239288692578476214785961451581351341251140127219386240 * q^20 + 53447991875461898796552150181251304409032073759002376573082504235219586208 * q^21 + 1334480876839672633808741914071727189545841199132729059095736106759243606112 * q^22 - 4280804965700905487867557627761776334077515300975222519458633688084497477528 * q^23 - 129253468619699114441737651311892084919218132467191979241911494876891173877760 * q^24 - 456274260699810946496432078768368872244545007142930133725494539638375760654225 * q^25 + 9117596118629922830918453196718641926897783510547242670141134615123316525608208 * q^26 + 36009290264725541742540148694316715091842126661227810228968619953124574644440120 * q^27 + 389777110106676955938012042765885416118140162819674451900675730518240474989075968 * q^28 - 1612630879112671269089242330901312038613162417445580611832712505926453350563056730 * q^29 - 18167376599417385725382731299135244307087297190105602725235889269652594544837067840 * q^30 + 67559679369166080772885534172593278837571532071620973699499831976537741546761534688 * q^31 + 754093318949864663533121048615003094440304122496655835482200816722793265150805508096 * q^32 - 3133890070812326529166672578753895355679540062945915391855288247367239239009432080976 * q^33 - 24751022535879997806365605902203773919188021786642014954770492231640496515521010376656 * q^34 + 57944164206332657023724654984518766320829384409054668126147883688641566073099799278480 * q^35 + 328041564753120514775451575146434843390262564311310021231853773527241323710816435244864 * q^36 + 3043820559995771428343491307335152699983691109501186564620625804804431981535340669576286 * q^37 - 21382754992423793021134163907198673444659659051000850342253103089169961740533890647606880 * q^38 + 3273459216524867162345405450876825490686869325852879816870160180171296350982671401366216 * q^39 + 123460999717991511987771461057366625032200502337474727630106509260305540512417484610278400 * q^40 + 104629960197719783697927100274525225542843896456497561309270816521996960904985588920195178 * q^41 + 2027994299853353493651484516191980857294428743343203061454578749195409490693400034208902912 * q^42 - 19157176231150752403174922289745163210049080257481323543299910438470109245483512805859143708 * q^43 + 54900509500333144241574805152152293176467261284516409174290950395775810400803069025987309824 * q^44 + 15479509256451142996000421697851689107817887106618468041729343908392688500639929264156928310 * q^45 - 398788118873285310214184399746055204854113651152175668288210597675002274814165601481840895552 * q^46 + 1456966582071114763048986859064421525928331803997603240440970059620025856397045514594291849296 * q^47 - 7452969450778497532129812087184007504558526604092287637802268612794467934087599186261483798528 * q^48 + 17298008315064903937184133864291881308696588708445105876848488522049133450344930890256623872337 * q^49 + 20891593843500014301021428427705110541710363262225372510717283195064501890651418995923815351400 * q^50 - 85813999871822828588324201494589306593218994449334105811559220660851252439965047034531679254312 * q^51 - 228851992565399673815270028508808722169419264169266009042427250901076945058351740642305444481664 * q^52 - 330560931516346297292158383237634604339355604111254380988674341402404197811701576314208409413298 * q^53 + 4500007476747002196644470511723672131082224104684813911982619633059661906955824254260654375081280 * q^54 + 5411788085074080207797655602098900123199579033664526066719620291468503584226809836679744568059960 * q^55 - 42315784638223426280810136290704778028064917513845974684816911806737536885555338292253409336340480 * q^56 + 9918498856896672609870803756688673833744336383910153405185505298972528406991914653827866717244240 * q^57 + 32435179551725169564404757555461461839261719646775117357648454983301156661453863733221818065697680 * q^58 + 322553637419248081900645358050759529139017004186411501272056030884685696264538328889393003620694740 * q^59 - 132467389966865887348037310509899613119681515385419367203561785040397906770826770994985507300267520 * q^60 - 1759437984456387651106179880992119801754779277040263539338974358093077280629950964970586556177810042 * q^61 - 1712844297363572226123727147322557976426042183124057300794490386880408520919151071285053014838119168 * q^62 + 12759876033417698231199447475315412125628460028323317128859307435477632649190559962838360311186507992 * q^63 + 14281879241185987264094876187662890300953975181530786481128692077543427681889775277266607957835251712 * q^64 - 18446575904127982541910334362372985348294257469022062289060943594932692744923327761688031698818070540 * q^65 - 105227969740255769667487712999247235831860856852926275817422436766136475148421006520466387572795840384 * q^66 + 137686280746299018306956215858337887331602769875959175009115726791437961931237555780269025002728818316 * q^67 + 1157398196638034088725243365559060772268690235343345029534596768981482256873945115267239799529371269248 * q^68 + 1095507431560680024171724297772352455505639098885833012944706047494456930144134797052286618395241366496 * q^69 - 3640686416490340897700513163360856154742313115593190855720847062189976425143796505336061966373300603520 * q^70 + 9881612323140206421591424247232489623122284569259126072100461213939705350610294394975802208678001259448 * q^71 + 26396053480919173194166495118665950061506035792323405768129609103560026391739244345645460880788768488960 * q^72 + 68010594140875249475223137869343627059525985931897139097425407128220372890956239808513785565566231240522 * q^73 + 220837506033562453797347134849380708116539322544975559087316116631000736843141442638912881210212941372624 * q^74 + 181912260264814567208746612550869983753545991059523226326816406967698797635966067835830629689080707385300 * q^75 + 761174863647605635882918277985364633628165523124208915131122931858702438047845125322045601860264208695040 * q^76 + 1384642526997449454787538522373154719967650987275787604770256389537561344719927104096300078005408626536672 * q^77 + 10154718868595236540854386892056000355936883967938908970289471652675003137655678023153495552339085989663424 * q^78 + 7526673880001773966576204583811316437192125118919660383683770302134291678384367816740764114717599435401520 * q^79 + 32601244901804291407696890633217962008785625969393161121607747994402795735664787250217837405420588998778880 * q^80 + 48874282116782895668905156724559809826804317530845116719941792255495466449412888893127682785590511826600049 * q^81 + 113239522172902215034601434016259598176780723606704841332886416969022724124423260666831983947062879210014192 * q^82 + 199958416124075286987530689011944805825753524406236269102187579359597825528337021515595830260563921442487932 * q^83 + 880467563819420401586770374036347249339328631628161679582704747941404166343896577833615976614908144379930624 * q^84 + 707266002569821004378084548147696321676161909242361424333261618590644246794997074911164911557278987628650780 * q^85 + 749430950077361833338178064514980710590134374932604590973028338058871330476392166543416304708654721880933728 * q^86 + 2802132957491922284048190008280399903628415414482410070524683686927111831188200973776028254889144423439332360 * q^87 + 7195654272713601174999226937725203391076863795283476240434396643890296393716359696024184526976625256798607360 * q^88 + 3700827869341881331782801900641952675754040149647113243871021736652252631453067855946419168721111605247226810 * q^89 + 8997316939698708062605864942661951051594004217268128464090536667598399664816028357347925999912163977799180560 * q^90 - 254313076672373460593401973466735362362295247774148430702156053605292605984743534435031357382528251918280752 * q^91 - 16891756811302405862414651288981793929299127803233629387746389497252488943048833672780023478534318077838493184 * q^92 - 55378555126167982657281578020507978450769506755610812937817924402648049087367995838404448550854542227572273536 * q^93 - 71374169795251900964177147542915102589642305140612249128066111463360036313665875245965949313319551156299307136 * q^94 - 167271491201189176415157992539596873672401782137242927001530501790921136440405267833568144254517552969527081400 * q^95 - 1187167956876210917054814422873111467722801274363871607741943257050230342552379215783989919197651861627909046272 * q^96 - 631372797244867221191218982738135503959422268139699621925372110836288083138321626431181260783380505262640568654 * q^97 - 1898458058047689123148702915382067648076866113471255418148529297211872922066143741813213498341870918619707529832 * q^98 - 3056373683854811033724902889292841037638123003448050519838010864270837225210323694704228642303518682358171259244 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more