LMFDB - Embedded newform 1.116.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,116,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, 116, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 116);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 116 $
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:	$83.7504016273$
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} - 2 x^{8} + \cdots + 17\!\cdots\!50 $ x^9 - 2x^8 - 414076092797094884588270368040436x^7 + 207885950141989247333601728603350570907316559312x^6 + 53953056107747668024828577555978295738884933497151315454381156886x^5 - 39336141962639287206411519462083835839620927164943264814333421249916046093973300x^4 - 2533518066854386914668551089531708845226628134530725297100926671028265843202987733859009561529300x^3 + 490964205010322004682419127624980798498399412112911264185935626548027088494947196860262385130972000357947992000x^2 + 38262806893998180073611796677487723511025244043210521534516185790505315041447776458181906288587312474432220588758515963555640625x + 17621806778630140635149450041757730400137842910015553441183676408184188481669177964095541530125144445707343612831547087968976539961942089843750
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{142}\cdot 3^{52}\cdot 5^{17}\cdot 7^{8}\cdot 11^{3}\cdot 13^{3}\cdot 17\cdot 19^{3}\cdot 23^{3}\cdot 29^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$9.00047e15$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.28920e17 q^{2} -5.05419e27 q^{3} +1.08661e34 q^{4} -2.40937e40 q^{5} +1.15700e45 q^{6} -2.38510e48 q^{7} +7.02151e51 q^{8} +1.81497e55 q^{9} +O(q^{10})$	\(q-2.28920e17 q^{2} -5.05419e27 q^{3} +1.08661e34 q^{4} -2.40937e40 q^{5} +1.15700e45 q^{6} -2.38510e48 q^{7} +7.02151e51 q^{8} +1.81497e55 q^{9} +5.51552e57 q^{10} +1.20710e59 q^{11} -5.49191e61 q^{12} +2.13264e63 q^{13} +5.45998e65 q^{14} +1.21774e68 q^{15} -2.05872e69 q^{16} -6.67628e70 q^{17} -4.15483e72 q^{18} +4.80941e73 q^{19} -2.61803e74 q^{20} +1.20548e76 q^{21} -2.76329e76 q^{22} +9.19672e77 q^{23} -3.54880e79 q^{24} +3.39763e80 q^{25} -4.88205e80 q^{26} -5.43556e82 q^{27} -2.59167e82 q^{28} -2.85164e82 q^{29} -2.78765e85 q^{30} -8.05350e85 q^{31} +1.79621e86 q^{32} -6.10089e86 q^{33} +1.52834e88 q^{34} +5.74659e88 q^{35} +1.97216e89 q^{36} -9.49437e89 q^{37} -1.10097e91 q^{38} -1.07788e91 q^{39} -1.69174e92 q^{40} +1.04533e93 q^{41} -2.75958e93 q^{42} -4.52080e93 q^{43} +1.31164e93 q^{44} -4.37292e95 q^{45} -2.10532e95 q^{46} -8.34733e95 q^{47} +1.04052e97 q^{48} -9.66716e96 q^{49} -7.77786e97 q^{50} +3.37432e98 q^{51} +2.31734e97 q^{52} -1.33157e99 q^{53} +1.24431e100 q^{54} -2.90834e99 q^{55} -1.67470e100 q^{56} -2.43076e101 q^{57} +6.52798e99 q^{58} -1.17247e101 q^{59} +1.32320e102 q^{60} +1.55293e102 q^{61} +1.84361e103 q^{62} -4.32889e103 q^{63} +4.43971e103 q^{64} -5.13832e103 q^{65} +1.39662e104 q^{66} -3.39216e103 q^{67} -7.25449e104 q^{68} -4.64820e105 q^{69} -1.31551e106 q^{70} +2.06325e106 q^{71} +1.27438e107 q^{72} +8.37405e106 q^{73} +2.17345e107 q^{74} -1.71723e108 q^{75} +5.22593e107 q^{76} -2.87905e107 q^{77} +2.46748e108 q^{78} -9.00747e108 q^{79} +4.96022e109 q^{80} +1.40505e110 q^{81} -2.39296e110 q^{82} +1.51752e110 q^{83} +1.30988e110 q^{84} +1.60856e111 q^{85} +1.03490e111 q^{86} +1.44127e110 q^{87} +8.47564e110 q^{88} -4.43962e111 q^{89} +1.00105e113 q^{90} -5.08657e111 q^{91} +9.99322e111 q^{92} +4.07039e113 q^{93} +1.91087e113 q^{94} -1.15876e114 q^{95} -9.07840e113 q^{96} +2.50229e114 q^{97} +2.21301e114 q^{98} +2.19084e114 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 11\!\cdots\!44 q^{2}+ \cdots + 26\!\cdots\!13 q^{9}+O(q^{10}) $ 9 * q - 116180770089455544 * q^2 + 344843759214607763941669692 * q^3 + 104670059680921154232978400984552512 * q^4 - 9416265734776133053944609096571667575890 * q^5 + 256991120598421923060797165626503750361356768 * q^6 + 1823100316304157772850498188908022382936745628056 * q^7 - 219342532030837467786318171319354148041440220761600 * q^8 + 26072637303355254030743970272505117374453788742960594013 * q^9	$ 9 q - 11\!\cdots\!44 q^{2}+ \cdots - 81\!\cdots\!24 q^{99}+O(q^{100}) $ 9 * q - 116180770089455544 * q^2 + 344843759214607763941669692 * q^3 + 104670059680921154232978400984552512 * q^4 - 9416265734776133053944609096571667575890 * q^5 + 256991120598421923060797165626503750361356768 * q^6 + 1823100316304157772850498188908022382936745628056 * q^7 - 219342532030837467786318171319354148041440220761600 * q^8 + 26072637303355254030743970272505117374453788742960594013 * q^9 + 6889731598544239023205889874968132433435838108852679867760 * q^10 - 445517152984004554452882006139810856593102366136026223610732 * q^11 - 42821766403658150616877740531461298756313417540328083617855744 * q^12 + 19120191369167112279983663882072248970668936436622013715636775942 * q^13 - 874484410352602036165423857414222226528651993964136670010092090176 * q^14 + 57599849217209390109884779325066884761013420104089343277210728579720 * q^15 - 1898660452996213931642847506744088625997939708105388690720226275618816 * q^16 + 33419179892190498379140269229352347311321292371418143383895702694253506 * q^17 - 2890446730701337146666584437647276674841816394744930484862532014864739608 * q^18 + 56323667191172324184321794810244934428905386312408168014796206412959893100 * q^19 - 120777388922455433799357146114685194143652980138750550147727102823046920320 * q^20 + 28176272485874451401581069312956900459966003840123920247504389614132269060768 * q^21 + 210984989629936406579159416842818263081445382036693993098790665852739866289312 * q^22 + 5043025461154544652592399598502520927437665517917355864726536202832817581701192 * q^23 - 7479406270402029067027148815379966966654468567388028134173932380834142711449600 * q^24 + 121685992880890163904850134332941584046982669818587694611007334128142016185838975 * q^25 - 5914878085893066644910373209258644573936085196716403877449593179133594373009735632 * q^26 - 5437898471824326237019158372464459291991052787593142902719608572344381893810183400 * q^27 + 134945777488992574285149234278139874324546574917240128067914181134023530915243857408 * q^28 + 2439895086110265548692574276791512440826974071718418782816151860616339046059592317750 * q^29 - 1116585539518521415480577570330322838097236714153628065703800981349351376364839660480 * q^30 - 115077428025700644556762203100792633275869803062860787032812289936236157369971844291232 * q^31 + 182002942689670990671600876052552389114866685587533572692282985590686349099701286240256 * q^32 + 369141873981337522256423851297810174364779891698538054811380159251387321031750289147184 * q^33 + 16133584300638755367079868159687776681138177363676896002357157762964033939697234321079824 * q^34 - 52628449929177569411912369226649064291208149114238009380905357827049459818370441573185840 * q^35 - 343110691203669342080842230156946587735541070043733921826769094626380948288641172661825216 * q^36 + 287193704739393607505131056484688448302333303851532744432838755870145511209962195474555406 * q^37 + 1887285676044348998237316198233063024983501152361943246105012398202088272208210660325749600 * q^38 + 57495405068562246295455616507616293122146350008991254547433422285102442790821436306805531176 * q^39 - 377538131908105786834217342693439591573182569233316142689856344096115044105226591101231948800 * q^40 + 450036474709634029239457226906183730406636229485540132536579898525082307383544109285527636618 * q^41 - 3614527346318500983114558586611383169745609085282334175950975443992847582191151261402533817088 * q^42 + 11238467180897591407367974873375005136437267786775173672510908822395481702707823219190726952692 * q^43 + 8699999971697013733855125470633863112208674234411673595635316509240061153413462554031896481024 * q^44 - 354262889245566735270191791009177826124944074544236912619488508381128369609584375919402912590330 * q^45 + 211097623274700628625262911429039098879374408053211152239698326314586272783546202145178950255168 * q^46 - 316976878807259053071085359106141878112628948954523917108980455021512269952447135287167972348144 * q^47 + 4410525927214080719418968105605950188534122907207757808623172340024505114953341149753389138952192 * q^48 - 5402924848400424806022935001474260663230730313005626183937801432100886221124285978670797398474063 * q^49 - 107358804410623226001357232665018218738784300597386966398329608024306023910080977639712704319931400 * q^50 + 392230202654118035824948006166789320012418877782515914171168122937227894930092554264584283119946168 * q^51 + 186847646489930730643602674069595365244797337372298185295802970592172751947352587676622924463312256 * q^52 + 334496168286075107324733466358006346326362975568659741057867434494885827999701558072502824894138942 * q^53 + 815273172520443779763028707379283569820579781203093260711879845468622355550376013747519262940305600 * q^54 - 23563721346912912517453864325899810796736448452180735731334842246903047272785132546150581553652938280 * q^55 + 50501579633901923276218857218558899542358162690763518272752547626356309717401481440460372264435200000 * q^56 + 19326182159286888425606068195996356732391193445128832852476856331643144551112440129841029596191125200 * q^57 - 276537143978921040553065169225197607521839521198309506889392716069666566548578247536870903521071531600 * q^58 + 26559202104122447477824144844523074937734984825144901102500175836351773839109503993732582002313425700 * q^59 - 1442907433717223203332783871119423031323933407363314628882895297513470975585089853716965229400414768640 * q^60 + 466761553545603468366117849047093343161086980381148338979195572768003416466078862368134301594309428118 * q^61 + 28949531649262422331932844636470226821904033422254832199912074503071191433543806733834531878575668538112 * q^62 - 26525953947162098838236213455266609374207032849533466856093515022060397668973168836773250206710710550408 * q^63 - 46169280478215780445338819251740629236256446911950466222769056677599024448485239500558186236965165989888 * q^64 + 30622590124662743929353875752733901757221609411050393019261768040290807869865915951670063818998022920820 * q^65 + 58885521825482117580183439615438901701040523699794385163331031210597262925198785331149493283518615857536 * q^66 + 522391041991614299569962418777982996178060317974008251288477038656645322955247899200108470501056740725756 * q^67 - 963970789349034201430960171930241226642674599765083803055821765339886224671560293508121902691671583492992 * q^68 - 4768744134714834748105886788969216829087468736062331961872791186003972694205687719806877940995404594939424 * q^69 + 648102273330646244918318234903390383158022917116167184817069407742837923825354916186559362576551723218560 * q^70 + 32114907384466138287517273839727096331385168126590004271972827521185198833360861938868844865182495384954968 * q^71 + 134036350375106083011376263362911564045625075783489246636869772536858707114389024728586916900414866675980800 * q^72 - 111532806797088262693446813432847569894350723689665928769373202408064805330900544787546502644693976667521558 * q^73 + 146367501244421643149579339910137613783225032865117034030178763862717664956463164057696425085332997488423024 * q^74 + 191011236006610982766017086665378142663007338029810651608018025472800438314119281980403153054303538075361700 * q^75 + 1898752275573850608619854563706181213417282281074664303825494148687676736613874275716737807304301723964896000 * q^76 + 8547320523119144259127272245019592075910296652673224064175151890175172791298973939747111362021472266254476512 * q^77 + 8439857258376544014998782670363733435136214517799335731701302157574158558998894356877778911194771366104305984 * q^78 - 2698128344097500588934092059818825897117643397087596829234810281027633187083900600989280771432492738133389200 * q^79 + 117204555830492291605465104654149864678123037973909556311887751421858566469073727335484870898703213772212264960 * q^80 + 243844251998840861544064848215817562747898683224158368441742398035262682571557660719126722958354994801550865809 * q^81 + 473149820338187161445671999094492312190196735403799620250132055162721259658633637951105669203590924984388498512 * q^82 + 976812723170338476169372114700471197638723418120402034771092851931233919858674637831041045969218865325658875692 * q^83 + 2539321467869080915143952852614384190778021160799093130626725907993426541237386266518480321379169708798426343424 * q^84 + 3552505762114082405879304975670471704857686108558874865895506783571862811153977851101780608475304927035932222460 * q^85 + 11838276402773622473531002179261101730801162542213640979598425595359582429205612657343793928842614227749715441568 * q^86 + 27897493284886904362947680243525683713496258927093426130335092322232937971279756139421073573801725541246460925800 * q^87 + 52038964178994366220097267685544117931455067665556497129662971665594737875310678877513435089254305724995593676800 * q^88 + 59446666639398225412533241825642117887211504765823780420331081870088511796669962981765187912981764097798200324250 * q^89 + 259316827454272274338207071834855070930759935980768037766603430323600593416394106984590468235314680478785223708720 * q^90 + 245939937247192661534362402615346617600082162228156200993853962356431783555050183953904527617619011036872688337168 * q^91 + 613988446074365886926604878609711354412545763779069644197907853873975238992484853992399764939548985670950928032256 * q^92 + 1223125501788227369263854591107492905645880857959405771691286774974787266171291063996752221071041873907531275398784 * q^93 + 1499086835290066702674923853658203297973424744123451952620504314323336222430358359629023729105486706372629303556224 * q^94 + 799041738816013640930530159507467835290369458135599646151456080273195210563093613872275650940535406365162133749800 * q^95 + 3260013267518849074696485824622037660135078104167613123139522044708136137474372602480504246720813695045123797024768 * q^96 + 2523963432996685893503346240622778846413532532685755052598994124525775010632417867867345710038197597044049732141106 * q^97 + 585262872930561598617358018346679967180230161387125148358962641400172126269413925011919715802450101152197028464008 * q^98 - 8131297049226938077737975811278315123841467115358913895092773707388454338324871486984094251614634664934679647525724 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.28920e17	−1.12321	−0.561603	−	0.827407i	$-0.689815\pi$
$2$	−2.28920e17	−1.12321	−0.561603	+	0.827407i	$0.689815\pi$
$3$	−5.05419e27	−1.85857	−0.929285	−	0.369363i	$-0.879576\pi$
$3$	−5.05419e27	−1.85857	−0.929285	+	0.369363i	$0.879576\pi$
$4$	1.08661e34	0.261591
$5$	−2.40937e40	−1.55284	−0.776421	−	0.630214i	$-0.782967\pi$
$5$	−2.40937e40	−1.55284	−0.776421	+	0.630214i	$0.782967\pi$
$6$	1.15700e45	2.08756
$7$	−2.38510e48	−0.608653	−0.304327	−	0.952568i	$-0.598431\pi$
$7$	−2.38510e48	−0.608653	−0.304327	+	0.952568i	$0.598431\pi$
$8$	7.02151e51	0.829385
$9$	1.81497e55	2.45428
$10$	5.51552e57	1.74416
$11$	1.20710e59	0.159097	0.0795486	−	0.996831i	$-0.474652\pi$
$11$	1.20710e59	0.159097	0.0795486	+	0.996831i	$0.474652\pi$
$12$	−5.49191e61	−0.486185
$13$	2.13264e63	0.189311	0.0946554	−	0.995510i	$-0.469825\pi$
$13$	2.13264e63	0.189311	0.0946554	+	0.995510i	$0.469825\pi$
$14$	5.45998e65	0.683643
$15$	1.21774e68	2.88607
$16$	−2.05872e69	−1.19316
$17$	−6.67628e70	−1.18501	−0.592505	−	0.805567i	$-0.701861\pi$
$17$	−6.67628e70	−1.18501	−0.592505	+	0.805567i	$0.701861\pi$
$18$	−4.15483e72	−2.75667
$19$	4.80941e73	1.42482	0.712409	−	0.701764i	$-0.247604\pi$
$19$	4.80941e73	1.42482	0.712409	+	0.701764i	$0.247604\pi$
$20$	−2.61803e74	−0.406210
$21$	1.20548e76	1.13122
$22$	−2.76329e76	−0.178699
$23$	9.19672e77	0.461618	0.230809	−	0.972999i	$-0.425863\pi$
$23$	9.19672e77	0.461618	0.230809	+	0.972999i	$0.425863\pi$
$24$	−3.54880e79	−1.54147
$25$	3.39763e80	1.41132
$26$	−4.88205e80	−0.212635
$27$	−5.43556e82	−2.70289
$28$	−2.59167e82	−0.159218
$29$	−2.85164e82	−0.0232922	−0.0116461	−	0.999932i	$-0.503707\pi$
$29$	−2.85164e82	−0.0232922	−0.0116461	+	0.999932i	$0.503707\pi$
$30$	−2.78765e85	−3.24165
$31$	−8.05350e85	−1.42131	−0.710653	−	0.703543i	$-0.751600\pi$
$31$	−8.05350e85	−1.42131	−0.710653	+	0.703543i	$0.751600\pi$
$32$	1.79621e86	0.510780
$33$	−6.10089e86	−0.295693
$34$	1.52834e88	1.33101
$35$	5.74659e88	0.945143
$36$	1.97216e89	0.642019
$37$	−9.49437e89	−0.639539	−0.319770	−	0.947495i	$-0.603605\pi$
$37$	−9.49437e89	−0.639539	−0.319770	+	0.947495i	$0.603605\pi$
$38$	−1.10097e91	−1.60036
$39$	−1.07788e91	−0.351847
$40$	−1.69174e92	−1.28790
$41$	1.04533e93	1.92389	0.961945	−	0.273242i	$-0.0880961\pi$
$41$	1.04533e93	1.92389	0.961945	+	0.273242i	$0.0880961\pi$
$42$	−2.75958e93	−1.27060
$43$	−4.52080e93	−0.537996	−0.268998	−	0.963141i	$-0.586693\pi$
$43$	−4.52080e93	−0.537996	−0.268998	+	0.963141i	$0.586693\pi$
$44$	1.31164e93	0.0416184
$45$	−4.37292e95	−3.81112
$46$	−2.10532e95	−0.518492
$47$	−8.34733e95	−0.596926	−0.298463	−	0.954421i	$-0.596474\pi$
$47$	−8.34733e95	−0.596926	−0.298463	+	0.954421i	$0.596474\pi$
$48$	1.04052e97	2.21757
$49$	−9.66716e96	−0.629541
$50$	−7.77786e97	−1.58520
$51$	3.37432e98	2.20242
$52$	2.31734e97	0.0495220
$53$	−1.33157e99	−0.951702	−0.475851	−	0.879526i	$-0.657860\pi$
$53$	−1.33157e99	−0.951702	−0.475851	+	0.879526i	$0.657860\pi$
$54$	1.24431e100	3.03590
$55$	−2.90834e99	−0.247053
$56$	−1.67470e100	−0.504808
$57$	−2.43076e101	−2.64813
$58$	6.52798e99	0.0261619
$59$	−1.17247e101	−0.175837	−0.0879187	−	0.996128i	$-0.528022\pi$
$59$	−1.17247e101	−0.175837	−0.0879187	+	0.996128i	$0.528022\pi$
$60$	1.32320e102	0.754970
$61$	1.55293e102	0.342519	0.171260	−	0.985226i	$-0.445216\pi$
$61$	1.55293e102	0.342519	0.171260	+	0.985226i	$0.445216\pi$
$62$	1.84361e103	1.59642
$63$	−4.32889e103	−1.49381
$64$	4.43971e103	0.619450
$65$	−5.13832e103	−0.293970
$66$	1.39662e104	0.332124
$67$	−3.39216e103	−0.0339762	−0.0169881	−	0.999856i	$-0.505408\pi$
$67$	−3.39216e103	−0.0339762	−0.0169881	+	0.999856i	$0.505408\pi$
$68$	−7.25449e104	−0.309988
$69$	−4.64820e105	−0.857949
$70$	−1.31551e106	−1.06159
$71$	2.06325e106	0.736540	0.368270	−	0.929719i	$-0.379950\pi$
$71$	2.06325e106	0.736540	0.368270	+	0.929719i	$0.379950\pi$
$72$	1.27438e107	2.03555
$73$	8.37405e106	0.605161	0.302581	−	0.953124i	$-0.402152\pi$
$73$	8.37405e106	0.605161	0.302581	+	0.953124i	$0.402152\pi$
$74$	2.17345e107	0.718334
$75$	−1.71723e108	−2.62304
$76$	5.22593e107	0.372720
$77$	−2.87905e107	−0.0968350
$78$	2.46748e108	0.395197
$79$	−9.00747e108	−0.693498	−0.346749	−	0.937958i	$-0.612714\pi$
$79$	−9.00747e108	−0.693498	−0.346749	+	0.937958i	$0.612714\pi$
$80$	4.96022e109	1.85279
$81$	1.40505e110	2.56923
$82$	−2.39296e110	−2.16092
$83$	1.51752e110	0.682566	0.341283	−	0.939961i	$-0.389138\pi$
$83$	1.51752e110	0.682566	0.341283	+	0.939961i	$0.389138\pi$
$84$	1.30988e110	0.295918
$85$	1.60856e111	1.84013
$86$	1.03490e111	0.604281
$87$	1.44127e110	0.0432901
$88$	8.47564e110	0.131953
$89$	−4.43962e111	−0.360928	−0.180464	−	0.983582i	$-0.557760\pi$
$89$	−4.43962e111	−0.360928	−0.180464	+	0.983582i	$0.557760\pi$
$90$	1.00105e113	4.28067
$91$	−5.08657e111	−0.115225
$92$	9.99322e111	0.120755
$93$	4.07039e113	2.64160
$94$	1.91087e113	0.670471
$95$	−1.15876e114	−2.21252
$96$	−9.07840e113	−0.949321
$97$	2.50229e114	1.44199	0.720996	−	0.692939i	$-0.243684\pi$
$97$	2.50229e114	1.44199	0.720996	+	0.692939i	$0.243684\pi$
$98$	2.21301e114	0.707104
$99$	2.19084e114	0.390470
$100$	3.69189e114	0.369189
$101$	−3.12738e114	−0.176483	−0.0882414	−	0.996099i	$-0.528125\pi$
$101$	−3.12738e114	−0.176483	−0.0882414	+	0.996099i	$0.528125\pi$
$102$	−7.72449e115	−2.47377
$103$	−6.12792e115	−1.11988	−0.559942	−	0.828532i	$-0.689177\pi$
$103$	−6.12792e115	−1.11988	−0.559942	+	0.828532i	$0.689177\pi$
$104$	1.49744e115	0.157012
$105$	−2.90443e116	−1.75661
$106$	3.04823e116	1.06896
$107$	−3.43255e116	−0.701535	−0.350768	−	0.936463i	$-0.614079\pi$
$107$	−3.43255e116	−0.701535	−0.350768	+	0.936463i	$0.614079\pi$
$108$	−5.90632e116	−0.707052
$109$	−6.50465e115	−0.0458353	−0.0229177	−	0.999737i	$-0.507296\pi$
$109$	−6.50465e115	−0.0458353	−0.0229177	+	0.999737i	$0.507296\pi$
$110$	6.65777e116	0.277491
$111$	4.79863e117	1.18863
$112$	4.91027e117	0.726221
$113$	−2.16880e118	−1.92402	−0.962009	−	0.273017i	$-0.911979\pi$
$113$	−2.16880e118	−1.92402	−0.962009	+	0.273017i	$0.911979\pi$
$114$	5.56451e118	2.97439
$115$	−2.21583e118	−0.716820
$116$	−3.09861e116	−0.00609302
$117$	3.87068e118	0.464622
$118$	2.68402e118	0.197502
$119$	1.59236e119	0.721260
$120$	8.55036e119	2.39366
$121$	−5.61080e119	−0.974688
$122$	−3.55496e119	−0.384720
$123$	−5.28328e120	−3.57569
$124$	−8.75099e119	−0.371801
$125$	−2.38580e120	−0.638716
$126$	9.90970e120	1.67785
$127$	−2.53704e120	−0.272655	−0.136327	−	0.990664i	$-0.543530\pi$
$127$	−2.53704e120	−0.272655	−0.136327	+	0.990664i	$0.543530\pi$
$128$	−1.76246e121	−1.20655
$129$	2.28490e121	0.999904
$130$	1.17626e121	0.330189
$131$	−2.31169e121	−0.417667	−0.208834	−	0.977951i	$-0.566967\pi$
$131$	−2.31169e121	−0.417667	−0.208834	+	0.977951i	$0.566967\pi$
$132$	−6.62927e120	−0.0773507
$133$	−1.14709e122	−0.867220
$134$	7.76533e120	0.0381623
$135$	1.30963e123	4.19716
$136$	−4.68776e122	−0.982829
$137$	−2.12787e122	−0.292760	−0.146380	−	0.989228i	$-0.546762\pi$
$137$	−2.12787e122	−0.292760	−0.146380	+	0.989228i	$0.546762\pi$
$138$	1.06407e123	0.963654
$139$	−2.34313e123	−1.40102	−0.700510	−	0.713642i	$-0.747044\pi$
$139$	−2.34313e123	−1.40102	−0.700510	+	0.713642i	$0.747044\pi$
$140$	6.24428e122	0.247241
$141$	4.21890e123	1.10943
$142$	−4.72319e123	−0.827286
$143$	2.57430e122	0.0301188
$144$	−3.73652e124	−2.92836
$145$	6.87064e122	0.0361691
$146$	−1.91699e124	−0.679720
$147$	4.88596e124	1.17005
$148$	−1.03166e124	−0.167298
$149$	−8.10227e124	−0.892065	−0.446032	−	0.895017i	$-0.647163\pi$
$149$	−8.10227e124	−0.892065	−0.446032	+	0.895017i	$0.647163\pi$
$150$	3.93107e125	2.94621
$151$	−4.18179e124	−0.213889	−0.106944	−	0.994265i	$-0.534107\pi$
$151$	−4.18179e124	−0.213889	−0.106944	+	0.994265i	$0.534107\pi$
$152$	3.37693e125	1.18172
$153$	−1.21172e126	−2.90835
$154$	6.59073e124	0.108766
$155$	1.94038e126	2.20706
$156$	−1.17123e125	−0.0920401
$157$	−1.20791e126	−0.657362	−0.328681	−	0.944441i	$-0.606604\pi$
$157$	−1.20791e126	−0.657362	−0.328681	+	0.944441i	$0.606604\pi$
$158$	2.06199e126	0.778941
$159$	6.72999e126	1.76881
$160$	−4.32774e126	−0.793162
$161$	−2.19351e126	−0.280965
$162$	−3.21644e127	−2.88577
$163$	−2.12174e127	−1.33630	−0.668152	−	0.744025i	$-0.732915\pi$
$163$	−2.12174e127	−1.33630	−0.668152	+	0.744025i	$0.732915\pi$
$164$	1.13586e127	0.503273
$165$	1.46993e127	0.459165
$166$	−3.47392e127	−0.766663
$167$	1.17628e128	1.83786	0.918929	−	0.394422i	$-0.129055\pi$
$167$	1.17628e128	1.83786	0.918929	+	0.394422i	$0.129055\pi$
$168$	8.46426e127	0.938221
$169$	−1.22359e128	−0.964161
$170$	−3.68232e128	−2.06685
$171$	8.72892e128	3.49691
$172$	−4.91234e127	−0.140735
$173$	3.53335e128	0.725331	0.362665	−	0.931919i	$-0.381867\pi$
$173$	3.53335e128	0.725331	0.362665	+	0.931919i	$0.381867\pi$
$174$	−3.29936e127	−0.0486237
$175$	−8.10370e128	−0.859005
$176$	−2.48508e128	−0.189829
$177$	5.92589e128	0.326806
$178$	1.01632e129	0.405397
$179$	−4.12864e129	−1.19332	−0.596661	−	0.802493i	$-0.703506\pi$
$179$	−4.12864e129	−1.19332	−0.596661	+	0.802493i	$0.703506\pi$
$180$	−4.75165e129	−0.996954
$181$	4.52368e129	0.690198	0.345099	−	0.938566i	$-0.387845\pi$
$181$	4.52368e129	0.690198	0.345099	+	0.938566i	$0.387845\pi$
$182$	1.16442e129	0.129421
$183$	−7.84878e129	−0.636596
$184$	6.45749e129	0.382859
$185$	2.28754e130	0.993104
$186$	−9.31794e130	−2.96706
$187$	−8.05892e129	−0.188532
$188$	−9.07027e129	−0.156151
$189$	1.29644e131	1.64512
$190$	2.65264e131	2.48511
$191$	2.44486e131	1.69370	0.846849	−	0.531834i	$-0.178497\pi$
$191$	2.44486e131	1.69370	0.846849	+	0.531834i	$0.178497\pi$
$192$	−2.24391e131	−1.15129
$193$	5.80694e130	0.221005	0.110503	−	0.993876i	$-0.464754\pi$
$193$	5.80694e130	0.221005	0.110503	+	0.993876i	$0.464754\pi$
$194$	−5.72825e131	−1.61965
$195$	2.59700e131	0.546364
$196$	−1.05044e131	−0.164682
$197$	−1.23927e132	−1.44996	−0.724981	−	0.688769i	$-0.758152\pi$
$197$	−1.23927e132	−1.44996	−0.724981	+	0.688769i	$0.758152\pi$
$198$	−5.01528e131	−0.438578
$199$	−1.06085e132	−0.694388	−0.347194	−	0.937793i	$-0.612865\pi$
$199$	−1.06085e132	−0.694388	−0.347194	+	0.937793i	$0.612865\pi$
$200$	2.38565e132	1.17053
$201$	1.71446e131	0.0631472
$202$	7.15921e131	0.198226
$203$	6.80146e130	0.0141769
$204$	3.66656e132	0.576134
$205$	−2.51857e133	−2.98750
$206$	1.40281e133	1.25786
$207$	1.66918e133	1.13294
$208$	−4.39052e132	−0.225878
$209$	5.80542e132	0.226685
$210$	6.64883e133	1.97304
$211$	−7.72272e131	−0.0174393	−0.00871966	−	0.999962i	$-0.502776\pi$
$211$	−7.72272e131	−0.0174393	−0.00871966	+	0.999962i	$0.502776\pi$
$212$	−1.44689e133	−0.248957
$213$	−1.04280e134	−1.36891
$214$	7.85779e133	0.787968
$215$	1.08923e134	0.835424
$216$	−3.81659e134	−2.24174
$217$	1.92084e134	0.865082
$218$	1.48905e133	0.0514825
$219$	−4.23240e134	−1.12473
$220$	−3.16022e133	−0.0646268
$221$	−1.42381e134	−0.224335
$222$	−1.09850e135	−1.33507
$223$	−5.64542e134	−0.529867	−0.264933	−	0.964267i	$-0.585350\pi$
$223$	−5.64542e134	−0.529867	−0.264933	+	0.964267i	$0.585350\pi$
$224$	−4.28416e134	−0.310888
$225$	6.16659e135	3.46378
$226$	4.96482e135	2.16107
$227$	−1.92698e135	−0.650713	−0.325357	−	0.945591i	$-0.605484\pi$
$227$	−1.92698e135	−0.650713	−0.325357	+	0.945591i	$0.605484\pi$
$228$	−2.64128e135	−0.692726
$229$	−4.06266e135	−0.828458	−0.414229	−	0.910173i	$-0.635949\pi$
$229$	−4.06266e135	−0.828458	−0.414229	+	0.910173i	$0.635949\pi$
$230$	5.07248e135	0.805136
$231$	1.45513e135	0.179975
$232$	−2.00228e134	−0.0193182
$233$	−2.43219e136	−1.83245	−0.916224	−	0.400667i	$-0.868778\pi$
$233$	−2.43219e136	−1.83245	−0.916224	+	0.400667i	$0.868778\pi$
$234$	−8.86076e135	−0.521866
$235$	2.01118e136	0.926933
$236$	−1.27402e135	−0.0459975
$237$	4.55254e136	1.28891
$238$	−3.64524e136	−0.810123
$239$	8.58360e136	1.49896	0.749481	−	0.662026i	$-0.230303\pi$
$239$	8.58360e136	1.49896	0.749481	+	0.662026i	$0.230303\pi$
$240$	−2.50699e137	−3.44354
$241$	−1.31115e136	−0.141799	−0.0708995	−	0.997483i	$-0.522587\pi$
$241$	−1.31115e136	−0.141799	−0.0708995	+	0.997483i	$0.522587\pi$
$242$	1.28442e137	1.09478
$243$	−3.08171e137	−2.07220
$244$	1.68742e136	0.0896000
$245$	2.32917e137	0.977578
$246$	1.20945e138	4.01623
$247$	1.02567e137	0.269733
$248$	−5.65477e137	−1.17881
$249$	−7.66984e137	−1.26860
$250$	5.46157e137	0.717409
$251$	7.47209e137	0.780195	0.390097	−	0.920774i	$-0.372441\pi$
$251$	7.47209e137	0.780195	0.390097	+	0.920774i	$0.372441\pi$
$252$	−4.70380e137	−0.390767
$253$	1.11013e137	0.0734421
$254$	5.80780e137	0.306248
$255$	−8.12996e138	−3.42002
$256$	2.19044e138	0.735754
$257$	3.13793e138	0.842342	0.421171	−	0.906981i	$-0.361619\pi$
$257$	3.13793e138	0.842342	0.421171	+	0.906981i	$0.361619\pi$
$258$	−5.23059e138	−1.12310
$259$	2.26451e138	0.389258
$260$	−5.58333e137	−0.0768999
$261$	−5.17564e137	−0.0571656
$262$	5.29193e138	0.469126
$263$	−4.18832e138	−0.298252	−0.149126	−	0.988818i	$-0.547646\pi$
$263$	−4.18832e138	−0.298252	−0.149126	+	0.988818i	$0.547646\pi$
$264$	−4.28374e138	−0.245244
$265$	3.20824e139	1.47784
$266$	2.62593e139	0.974067
$267$	2.24387e139	0.670810
$268$	−3.68594e137	−0.00888787
$269$	2.73613e139	0.532574	0.266287	−	0.963894i	$-0.414203\pi$
$269$	2.73613e139	0.532574	0.266287	+	0.963894i	$0.414203\pi$
$270$	−2.99800e140	−4.71428
$271$	9.58126e139	1.21812	0.609058	−	0.793126i	$-0.291548\pi$
$271$	9.58126e139	1.21812	0.609058	+	0.793126i	$0.291548\pi$
$272$	1.37446e140	1.41391
$273$	2.57085e139	0.214153
$274$	4.87112e139	0.328830
$275$	4.10127e139	0.224537
$276$	−5.05076e139	−0.224432
$277$	−3.42272e140	−1.23534	−0.617668	−	0.786439i	$-0.711922\pi$
$277$	−3.42272e140	−1.23534	−0.617668	+	0.786439i	$0.711922\pi$
$278$	5.36389e140	1.57363
$279$	−1.46169e141	−3.48829
$280$	4.03497e140	0.783887
$281$	−1.29251e140	−0.204560	−0.102280	−	0.994756i	$-0.532614\pi$
$281$	−1.29251e140	−0.204560	−0.102280	+	0.994756i	$0.532614\pi$
$282$	−9.65790e140	−1.24612
$283$	5.38652e140	0.567006	0.283503	−	0.958971i	$-0.408503\pi$
$283$	5.38652e140	0.567006	0.283503	+	0.958971i	$0.408503\pi$
$284$	2.24194e140	0.192672
$285$	5.85660e141	4.11212
$286$	−5.89310e139	−0.0338296
$287$	−2.49321e141	−1.17098
$288$	3.26007e141	1.25360
$289$	1.28313e141	0.404247
$290$	−1.57283e140	−0.0406253
$291$	−1.26470e142	−2.68005
$292$	9.09930e140	0.158305
$293$	5.81577e141	0.831226	0.415613	−	0.909542i	$-0.363567\pi$
$293$	5.81577e141	0.831226	0.415613	+	0.909542i	$0.363567\pi$
$294$	−1.11849e142	−1.31420
$295$	2.82491e141	0.273048
$296$	−6.66648e141	−0.530424
$297$	−6.56125e141	−0.430022
$298$	1.85477e142	1.00197
$299$	1.96133e141	0.0873892
$300$	−1.86595e142	−0.686163
$301$	1.07826e142	0.327453
$302$	9.57296e141	0.240241
$303$	1.58064e142	0.328006
$304$	−9.90124e142	−1.70004
$305$	−3.74157e142	−0.531879
$306$	2.77388e143	3.26667
$307$	4.32832e141	0.0422535	0.0211268	−	0.999777i	$-0.493275\pi$
$307$	4.32832e141	0.0422535	0.0211268	+	0.999777i	$0.493275\pi$
$308$	−3.12840e141	−0.0253312
$309$	3.09717e143	2.08138
$310$	−4.44193e143	−2.47899
$311$	−1.09977e143	−0.510010	−0.255005	−	0.966940i	$-0.582077\pi$
$311$	−1.09977e143	−0.510010	−0.255005	+	0.966940i	$0.582077\pi$
$312$	−7.56832e142	−0.291817
$313$	−2.25775e143	−0.724231	−0.362115	−	0.932133i	$-0.617945\pi$
$313$	−2.25775e143	−0.724231	−0.362115	+	0.932133i	$0.617945\pi$
$314$	2.76515e143	0.738353
$315$	1.04299e144	2.31965
$316$	−9.78758e142	−0.181413
$317$	−8.37236e143	−1.29402	−0.647009	−	0.762482i	$-0.723980\pi$
$317$	−8.37236e143	−1.29402	−0.647009	+	0.762482i	$0.723980\pi$
$318$	−1.54063e144	−1.98673
$319$	−3.44220e141	−0.00370572
$320$	−1.06969e144	−0.961908
$321$	1.73487e144	1.30385
$322$	5.02140e143	0.315582
$323$	−3.21090e144	−1.68842
$324$	1.52673e144	0.672087
$325$	7.24593e143	0.267178
$326$	4.85710e144	1.50095
$327$	3.28757e143	0.0851882
$328$	7.33977e144	1.59565
$329$	1.99092e144	0.363321
$330$	−3.36496e144	−0.515737
$331$	7.54208e144	0.971363	0.485681	−	0.874136i	$-0.338572\pi$
$331$	7.54208e144	0.971363	0.485681	+	0.874136i	$0.338572\pi$
$332$	1.64895e144	0.178553
$333$	−1.72320e145	−1.56961
$334$	−2.69273e145	−2.06429
$335$	8.17295e143	0.0527597
$336$	−2.48174e145	−1.34973
$337$	−2.13907e145	−0.980632	−0.490316	−	0.871545i	$-0.663119\pi$
$337$	−2.13907e145	−0.980632	−0.490316	+	0.871545i	$0.663119\pi$
$338$	2.80104e145	1.08295
$339$	1.09615e146	3.57592
$340$	1.74787e145	0.481362
$341$	−9.72135e144	−0.226126
$342$	−1.99823e146	−3.92775
$343$	5.96825e145	0.991826
$344$	−3.17429e145	−0.446206
$345$	1.11992e146	1.33226
$346$	−8.08856e145	−0.814696
$347$	5.74175e145	0.489891	0.244946	−	0.969537i	$-0.421230\pi$
$347$	5.74175e145	0.489891	0.244946	+	0.969537i	$0.421230\pi$
$348$	1.56610e144	0.0113243
$349$	1.15077e146	0.705545	0.352773	−	0.935709i	$-0.385239\pi$
$349$	1.15077e146	0.705545	0.352773	+	0.935709i	$0.385239\pi$
$350$	1.85510e146	0.964839
$351$	−1.15921e146	−0.511686
$352$	2.16820e145	0.0812637
$353$	5.34973e146	1.70328	0.851640	−	0.524127i	$-0.175608\pi$
$353$	5.34973e146	1.70328	0.851640	+	0.524127i	$0.175608\pi$
$354$	−1.35655e146	−0.367071
$355$	−4.97112e146	−1.14373
$356$	−4.82413e145	−0.0944156
$357$	−8.04809e146	−1.34051
$358$	9.45129e146	1.34035
$359$	6.95439e145	0.0840094	0.0420047	−	0.999117i	$-0.486626\pi$
$359$	6.95439e145	0.0840094	0.0420047	+	0.999117i	$0.486626\pi$
$360$	−3.07045e147	−3.16088
$361$	1.17367e147	1.03011
$362$	−1.03556e147	−0.775234
$363$	2.83580e147	1.81153
$364$	−5.52711e145	−0.0301417
$365$	−2.01761e147	−0.939720
$366$	1.79674e147	0.715029
$367$	−5.28355e147	−1.79733	−0.898664	−	0.438638i	$-0.855461\pi$
$367$	−5.28355e147	−1.79733	−0.898664	+	0.438638i	$0.855461\pi$
$368$	−1.89335e147	−0.550785
$369$	1.89724e148	4.72177
$370$	−5.23664e147	−1.11546
$371$	3.17593e147	0.579257
$372$	4.42291e147	0.691018
$373$	−9.04078e147	−1.21045	−0.605227	−	0.796053i	$-0.706918\pi$
$373$	−9.04078e147	−1.21045	−0.605227	+	0.796053i	$0.706918\pi$
$374$	1.84485e147	0.211760
$375$	1.20583e148	1.18710
$376$	−5.86109e147	−0.495082
$377$	−6.08153e145	−0.00440946
$378$	−2.96781e148	−1.84781
$379$	−2.06906e148	−1.10667	−0.553335	−	0.832959i	$-0.686645\pi$
$379$	−2.06906e148	−1.10667	−0.553335	+	0.832959i	$0.686645\pi$
$380$	−1.25912e148	−0.578775
$381$	1.28227e148	0.506748
$382$	−5.59678e148	−1.90237
$383$	6.34800e148	1.85655	0.928277	−	0.371890i	$-0.121290\pi$
$383$	6.34800e148	1.85655	0.928277	+	0.371890i	$0.121290\pi$
$384$	8.90778e148	2.24246
$385$	6.93668e147	0.150370
$386$	−1.32933e148	−0.248234
$387$	−8.20512e148	−1.32040
$388$	2.71901e148	0.377213
$389$	4.46834e147	0.0534619	0.0267309	−	0.999643i	$-0.491490\pi$
$389$	4.46834e147	0.0534619	0.0267309	+	0.999643i	$0.491490\pi$
$390$	−5.94506e148	−0.613679
$391$	−6.13999e148	−0.547021
$392$	−6.78780e148	−0.522132
$393$	1.16837e149	0.776264
$394$	2.83693e149	1.62861
$395$	2.17023e149	1.07689
$396$	2.38058e148	0.102143
$397$	−3.89829e149	−1.44684	−0.723420	−	0.690408i	$-0.757431\pi$
$397$	−3.89829e149	−1.44684	−0.723420	+	0.690408i	$0.757431\pi$
$398$	2.42850e149	0.779941
$399$	5.79762e149	1.61179
$400$	−6.99478e149	−1.68393
$401$	−6.08075e147	−0.0126811	−0.00634053	−	0.999980i	$-0.502018\pi$
$401$	−6.08075e147	−0.0126811	−0.00634053	+	0.999980i	$0.502018\pi$
$402$	−3.92474e148	−0.0709273
$403$	−1.71752e149	−0.269068
$404$	−3.39824e148	−0.0461663
$405$	−3.38527e150	−3.98960
$406$	−1.55699e148	−0.0159235
$407$	−1.14606e149	−0.101749
$408$	2.36928e150	1.82666
$409$	−1.35823e150	−0.909670	−0.454835	−	0.890576i	$-0.650302\pi$
$409$	−1.35823e150	−0.909670	−0.454835	+	0.890576i	$0.650302\pi$
$410$	5.76552e150	3.35558
$411$	1.07546e150	0.544115
$412$	−6.65864e149	−0.292952
$413$	2.79646e149	0.107024
$414$	−3.82108e150	−1.27253
$415$	−3.65627e150	−1.05992
$416$	3.83068e149	0.0966962
$417$	1.18426e151	2.60390
$418$	−1.32898e150	−0.254613
$419$	2.69917e150	0.450738	0.225369	−	0.974273i	$-0.427641\pi$
$419$	2.69917e150	0.450738	0.225369	+	0.974273i	$0.427641\pi$
$420$	−3.15598e150	−0.459515
$421$	3.83975e150	0.487620	0.243810	−	0.969823i	$-0.421603\pi$
$421$	3.83975e150	0.487620	0.243810	+	0.969823i	$0.421603\pi$
$422$	1.76789e149	0.0195879
$423$	−1.51501e151	−1.46503
$424$	−9.34962e150	−0.789327
$425$	−2.26835e151	−1.67243
$426$	2.38719e151	1.53757
$427$	−3.70389e150	−0.208476
$428$	−3.72983e150	−0.183515
$429$	−1.30110e150	−0.0559779
$430$	−2.49346e151	−0.938353
$431$	1.93138e151	0.635952	0.317976	−	0.948099i	$-0.396997\pi$
$431$	1.93138e151	0.635952	0.317976	+	0.948099i	$0.396997\pi$
$432$	1.11903e152	3.22498
$433$	−6.56914e151	−1.65750	−0.828752	−	0.559616i	$-0.810949\pi$
$433$	−6.56914e151	−1.65750	−0.828752	+	0.559616i	$0.810949\pi$
$434$	−4.39720e151	−0.971665
$435$	−3.47255e150	−0.0672228
$436$	−7.06800e149	−0.0119901
$437$	4.42308e151	0.657722
$438$	9.68881e151	1.26331
$439$	−9.58044e150	−0.109566	−0.0547830	−	0.998498i	$-0.517447\pi$
$439$	−9.58044e150	−0.109566	−0.0547830	+	0.998498i	$0.517447\pi$
$440$	−2.04209e151	−0.204902
$441$	−1.75456e152	−1.54507
$442$	3.25939e151	0.251974
$443$	1.09467e152	0.743138	0.371569	−	0.928405i	$-0.378820\pi$
$443$	1.09467e152	0.743138	0.371569	+	0.928405i	$0.378820\pi$
$444$	5.21423e151	0.310935
$445$	1.06967e152	0.560465
$446$	1.29235e152	0.595149
$447$	4.09504e152	1.65797
$448$	−1.05892e152	−0.377030
$449$	−4.65768e152	−1.45883	−0.729415	−	0.684072i	$-0.760208\pi$
$449$	−4.65768e152	−1.45883	−0.729415	+	0.684072i	$0.760208\pi$
$450$	−1.41166e153	−3.89054
$451$	1.26181e152	0.306086
$452$	−2.35663e152	−0.503306
$453$	2.11355e152	0.397527
$454$	4.41124e152	0.730885
$455$	1.22554e152	0.178926
$456$	−1.70676e153	−2.19632
$457$	1.09049e153	1.23720	0.618601	−	0.785706i	$-0.287700\pi$
$457$	1.09049e153	1.23720	0.618601	+	0.785706i	$0.287700\pi$
$458$	9.30026e152	0.930529
$459$	3.62894e153	3.20295
$460$	−2.40773e152	−0.187514
$461$	−8.47963e151	−0.0582873	−0.0291436	−	0.999575i	$-0.509278\pi$
$461$	−8.47963e151	−0.0582873	−0.0291436	+	0.999575i	$0.509278\pi$
$462$	−3.33107e152	−0.202149
$463$	2.28684e153	1.22554	0.612772	−	0.790259i	$-0.290054\pi$
$463$	2.28684e153	1.22554	0.612772	+	0.790259i	$0.290054\pi$
$464$	5.87074e151	0.0277913
$465$	−9.80706e153	−4.10198
$466$	5.56777e153	2.05822
$467$	−1.92859e153	−0.630260	−0.315130	−	0.949049i	$-0.602048\pi$
$467$	−1.92859e153	−0.630260	−0.315130	+	0.949049i	$0.602048\pi$
$468$	4.20591e152	0.121541
$469$	8.09065e151	0.0206797
$470$	−4.60399e153	−1.04114
$471$	6.10500e153	1.22175
$472$	−8.23252e152	−0.145837
$473$	−5.45704e152	−0.0855937
$474$	−1.04217e154	−1.44772
$475$	1.63406e154	2.01087
$476$	1.73027e153	0.188675
$477$	−2.41675e154	−2.33575
$478$	−1.96496e154	−1.68364
$479$	1.94859e154	1.48057	0.740284	−	0.672294i	$-0.234691\pi$
$479$	1.94859e154	1.48057	0.740284	+	0.672294i	$0.234691\pi$
$480$	2.18732e154	1.47415
$481$	−2.02481e153	−0.121072
$482$	3.00149e153	0.159269
$483$	1.10864e154	0.522194
$484$	−6.09673e153	−0.254970
$485$	−6.02893e154	−2.23919
$486$	7.05466e154	2.32750
$487$	1.10319e154	0.323396	0.161698	−	0.986840i	$-0.448303\pi$
$487$	1.10319e154	0.323396	0.161698	+	0.986840i	$0.448303\pi$
$488$	1.09039e154	0.284081
$489$	1.07237e155	2.48362
$490$	−5.33194e154	−1.09802
$491$	−7.48198e154	−1.37035	−0.685174	−	0.728379i	$-0.740274\pi$
$491$	−7.48198e154	−1.37035	−0.685174	+	0.728379i	$0.740274\pi$
$492$	−5.74084e154	−0.935368
$493$	1.90384e153	0.0276014
$494$	−2.34798e154	−0.302966
$495$	−5.27854e154	−0.606338
$496$	1.65799e155	1.69585
$497$	−4.92106e154	−0.448297
$498$	1.75578e155	1.42490
$499$	−5.31550e154	−0.384382	−0.192191	−	0.981358i	$-0.561559\pi$
$499$	−5.31550e154	−0.384382	−0.192191	+	0.981358i	$0.561559\pi$
$500$	−2.59242e154	−0.167082
$501$	−5.94512e155	−3.41579
$502$	−1.71051e155	−0.876319
$503$	3.39710e155	1.55220	0.776102	−	0.630607i	$-0.217194\pi$
$503$	3.39710e155	1.55220	0.776102	+	0.630607i	$0.217194\pi$
$504$	−3.03953e155	−1.23894
$505$	7.53501e154	0.274050
$506$	−2.54132e154	−0.0824906
$507$	6.18424e155	1.79196
$508$	−2.75677e154	−0.0713241
$509$	4.85532e155	1.12188	0.560938	−	0.827858i	$-0.310440\pi$
$509$	4.85532e155	1.12188	0.560938	+	0.827858i	$0.310440\pi$
$510$	1.86111e156	3.84138
$511$	−1.99730e155	−0.368333
$512$	2.30661e155	0.380147
$513$	−2.61418e156	−3.85113
$514$	−7.18335e155	−0.946123
$515$	1.47644e156	1.73900
$516$	2.48279e155	0.261566
$517$	−1.00760e155	−0.0949693
$518$	−5.18391e155	−0.437216
$519$	−1.78582e156	−1.34808
$520$	−3.60787e155	−0.243814
$521$	−3.56343e155	−0.215625	−0.107813	−	0.994171i	$-0.534385\pi$
$521$	−3.56343e155	−0.215625	−0.107813	+	0.994171i	$0.534385\pi$
$522$	1.18481e155	0.0642087
$523$	−2.32519e156	−1.12879	−0.564393	−	0.825506i	$-0.690890\pi$
$523$	−2.32519e156	−1.12879	−0.564393	+	0.825506i	$0.690890\pi$
$524$	−2.51190e155	−0.109258
$525$	4.09576e156	1.59652
$526$	9.58790e155	0.334999
$527$	5.37675e156	1.68426
$528$	1.25600e156	0.352810
$529$	−3.12339e156	−0.786909
$530$	−7.34430e156	−1.65992
$531$	−2.12800e156	−0.431555
$532$	−1.24644e156	−0.226857
$533$	2.22931e156	0.364213
$534$	−5.13667e156	−0.753458
$535$	8.27026e156	1.08937
$536$	−2.38181e155	−0.0281794
$537$	2.08669e157	2.21787
$538$	−6.26354e156	−0.598190
$539$	−1.16692e156	−0.100158
$540$	1.42305e157	1.09794
$541$	2.33291e157	1.61828	0.809142	−	0.587613i	$-0.199932\pi$
$541$	2.33291e157	1.61828	0.809142	+	0.587613i	$0.199932\pi$
$542$	−2.19334e157	−1.36819
$543$	−2.28635e157	−1.28278
$544$	−1.19920e157	−0.605279
$545$	1.56721e156	0.0711751
$546$	−5.88519e156	−0.240538
$547$	−4.03407e157	−1.48413	−0.742065	−	0.670327i	$-0.766154\pi$
$547$	−4.03407e157	−1.48413	−0.742065	+	0.670327i	$0.766154\pi$
$548$	−2.31215e156	−0.0765834
$549$	2.81851e157	0.840640
$550$	−9.38863e156	−0.252201
$551$	−1.37147e156	−0.0331871
$552$	−3.26373e157	−0.711570
$553$	2.14838e157	0.422100
$554$	7.83530e157	1.38754
$555$	−1.15617e158	−1.84575
$556$	−2.54606e157	−0.366495
$557$	−3.55776e157	−0.461853	−0.230926	−	0.972971i	$-0.574176\pi$
$557$	−3.55776e157	−0.461853	−0.230926	+	0.972971i	$0.574176\pi$
$558$	3.34609e158	3.91806
$559$	−9.64126e156	−0.101849
$560$	−1.18306e158	−1.12771
$561$	4.07313e157	0.350399
$562$	2.95882e157	0.229764
$563$	−1.11685e158	−0.783000	−0.391500	−	0.920178i	$-0.628044\pi$
$563$	−1.11685e158	−0.783000	−0.391500	+	0.920178i	$0.628044\pi$
$564$	4.58428e157	0.290217
$565$	5.22543e158	2.98770
$566$	−1.23308e158	−0.636865
$567$	−3.35118e158	−1.56377
$568$	1.44871e158	0.610875
$569$	4.27804e158	1.63038	0.815192	−	0.579191i	$-0.196631\pi$
$569$	4.27804e158	1.63038	0.815192	+	0.579191i	$0.196631\pi$
$570$	−1.34069e159	−4.61876
$571$	2.25483e158	0.702326	0.351163	−	0.936314i	$-0.385786\pi$
$571$	2.25483e158	0.702326	0.351163	+	0.936314i	$0.385786\pi$
$572$	2.79726e156	0.00787881
$573$	−1.23568e159	−3.14786
$574$	5.70747e158	1.31525
$575$	3.12471e158	0.651491
$576$	8.05793e158	1.52031
$577$	3.11939e157	0.0532673	0.0266337	−	0.999645i	$-0.491521\pi$
$577$	3.11939e157	0.0532673	0.0266337	+	0.999645i	$0.491521\pi$
$578$	−2.93735e158	−0.454052
$579$	−2.93494e158	−0.410753
$580$	7.46569e156	0.00946151
$581$	−3.61945e158	−0.415446
$582$	2.89516e159	3.01024
$583$	−1.60733e158	−0.151413
$584$	5.87985e158	0.501912
$585$	−9.32588e158	−0.721485
$586$	−1.33135e159	−0.933638
$587$	−1.09717e159	−0.697563	−0.348781	−	0.937204i	$-0.613404\pi$
$587$	−1.09717e159	−0.697563	−0.348781	+	0.937204i	$0.613404\pi$
$588$	5.30912e158	0.306074
$589$	−3.87326e159	−2.02510
$590$	−6.46679e158	−0.306689
$591$	6.26348e159	2.69486
$592$	1.95463e159	0.763073
$593$	3.00781e159	1.06563	0.532814	−	0.846232i	$-0.321134\pi$
$593$	3.00781e159	1.06563	0.532814	+	0.846232i	$0.321134\pi$
$594$	1.50200e159	0.483003
$595$	−3.83658e159	−1.12000
$596$	−8.80398e158	−0.233356
$597$	5.36173e159	1.29057
$598$	−4.48989e158	−0.0981561
$599$	−5.17844e159	−1.02839	−0.514194	−	0.857674i	$-0.671909\pi$
$599$	−5.17844e159	−1.02839	−0.514194	+	0.857674i	$0.671909\pi$
$600$	−1.20575e160	−2.17551
$601$	−9.14758e159	−1.49977	−0.749884	−	0.661570i	$-0.769891\pi$
$601$	−9.14758e159	−1.49977	−0.749884	+	0.661570i	$0.769891\pi$
$602$	−2.46835e159	−0.367797
$603$	−6.15666e158	−0.0833873
$604$	−4.54396e158	−0.0559514
$605$	1.35185e160	1.51354
$606$	−3.61840e159	−0.368418
$607$	8.02223e159	0.742926	0.371463	−	0.928448i	$-0.378856\pi$
$607$	8.02223e159	0.742926	0.371463	+	0.928448i	$0.378856\pi$
$608$	8.63872e159	0.727769
$609$	−3.43758e158	−0.0263487
$610$	8.56520e159	0.597409
$611$	−1.78019e159	−0.113005
$612$	−1.31667e160	−0.760798
$613$	−6.16186e159	−0.324141	−0.162071	−	0.986779i	$-0.551817\pi$
$613$	−6.16186e159	−0.324141	−0.162071	+	0.986779i	$0.551817\pi$
$614$	−9.90841e158	−0.0474594
$615$	1.27293e161	5.55248
$616$	−2.02153e159	−0.0803135
$617$	−3.11778e160	−1.12836	−0.564180	−	0.825651i	$-0.690808\pi$
$617$	−3.11778e160	−1.12836	−0.564180	+	0.825651i	$0.690808\pi$
$618$	−7.09004e160	−2.33782
$619$	−5.42840e160	−1.63102	−0.815510	−	0.578743i	$-0.803543\pi$
$619$	−5.42840e160	−1.63102	−0.815510	+	0.578743i	$0.803543\pi$
$620$	2.10843e160	0.577348
$621$	−4.99894e160	−1.24770
$622$	2.51759e160	0.572846
$623$	1.05890e160	0.219680
$624$	2.21905e160	0.419811
$625$	−2.43124e160	−0.419495
$626$	5.16845e160	0.813460
$627$	−2.93417e160	−0.421309
$628$	−1.31252e160	−0.171960
$629$	6.33871e160	0.757860
$630$	−2.38761e161	−2.60544
$631$	2.09102e160	0.208291	0.104145	−	0.994562i	$-0.466789\pi$
$631$	2.09102e160	0.208291	0.104145	+	0.994562i	$0.466789\pi$
$632$	−6.32461e160	−0.575177
$633$	3.90321e159	0.0324122
$634$	1.91660e161	1.45345
$635$	6.11266e160	0.423390
$636$	7.31286e160	0.462704
$637$	−2.06166e160	−0.119179
$638$	7.87990e158	0.00416228
$639$	3.74473e161	1.80768
$640$	4.24640e161	1.87358
$641$	−1.73677e161	−0.700496	−0.350248	−	0.936657i	$-0.613903\pi$
$641$	−1.73677e161	−0.700496	−0.350248	+	0.936657i	$0.613903\pi$
$642$	−3.97148e161	−1.46449
$643$	−5.35423e161	−1.80537	−0.902686	−	0.430301i	$-0.858407\pi$
$643$	−5.35423e161	−1.80537	−0.902686	+	0.430301i	$0.858407\pi$
$644$	−2.38349e160	−0.0734980
$645$	−5.50515e161	−1.55269
$646$	7.35039e161	1.89645
$647$	−1.24596e161	−0.294110	−0.147055	−	0.989128i	$-0.546979\pi$
$647$	−1.24596e161	−0.294110	−0.147055	+	0.989128i	$0.546979\pi$
$648$	9.86555e161	2.13088
$649$	−1.41529e160	−0.0279752
$650$	−1.65874e161	−0.300096
$651$	−9.70830e161	−1.60782
$652$	−2.30550e161	−0.349565
$653$	7.67229e161	1.06517	0.532583	−	0.846378i	$-0.321221\pi$
$653$	7.67229e161	1.06517	0.532583	+	0.846378i	$0.321221\pi$
$654$	−7.52591e160	−0.0956839
$655$	5.56971e161	0.648571
$656$	−2.15204e162	−2.29551
$657$	1.51986e162	1.48524
$658$	−4.55763e161	−0.408084
$659$	−1.15576e162	−0.948320	−0.474160	−	0.880439i	$-0.657248\pi$
$659$	−1.15576e162	−0.948320	−0.474160	+	0.880439i	$0.657248\pi$
$660$	1.59723e161	0.120114
$661$	−1.72713e162	−1.19053	−0.595267	−	0.803528i	$-0.702954\pi$
$661$	−1.72713e162	−1.19053	−0.595267	+	0.803528i	$0.702954\pi$
$662$	−1.72653e162	−1.09104
$663$	7.19621e161	0.416942
$664$	1.06553e162	0.566110
$665$	2.76377e162	1.34666
$666$	3.94475e162	1.76300
$667$	−2.62258e160	−0.0107521
$668$	1.27815e162	0.480768
$669$	2.85330e162	0.984795
$670$	−1.87095e161	−0.0592600
$671$	1.87453e161	0.0544939
$672$	2.16529e162	0.577807
$673$	6.78263e161	0.166162	0.0830811	−	0.996543i	$-0.473524\pi$
$673$	6.78263e161	0.166162	0.0830811	+	0.996543i	$0.473524\pi$
$674$	4.89677e162	1.10145
$675$	−1.84680e163	−3.81464
$676$	−1.32956e162	−0.252216
$677$	7.52027e162	1.31034	0.655172	−	0.755480i	$-0.272596\pi$
$677$	7.52027e162	1.31034	0.655172	+	0.755480i	$0.272596\pi$
$678$	−2.50931e163	−4.01650
$679$	−5.96822e162	−0.877674
$680$	1.12945e163	1.52618
$681$	9.73930e162	1.20940
$682$	2.22541e162	0.253986
$683$	−1.04849e163	−1.09995	−0.549976	−	0.835180i	$-0.685363\pi$
$683$	−1.04849e163	−1.09995	−0.549976	+	0.835180i	$0.685363\pi$
$684$	9.48491e162	0.914760
$685$	5.12681e162	0.454610
$686$	−1.36625e163	−1.11402
$687$	2.05335e163	1.53975
$688$	9.30709e162	0.641917
$689$	−2.83976e162	−0.180167
$690$	−2.56372e163	−1.49640
$691$	1.22950e163	0.660302	0.330151	−	0.943928i	$-0.392900\pi$
$691$	1.22950e163	0.660302	0.330151	+	0.943928i	$0.392900\pi$
$692$	3.83937e162	0.189740
$693$	−5.22538e162	−0.237661
$694$	−1.31440e163	−0.550249
$695$	5.64545e163	2.17556
$696$	1.01199e162	0.0359042
$697$	−6.97890e163	−2.27983
$698$	−2.63433e163	−0.792472
$699$	1.22927e164	3.40573
$700$	−8.80554e162	−0.224708
$701$	2.67997e163	0.630005	0.315002	−	0.949091i	$-0.397995\pi$
$701$	2.67997e163	0.630005	0.315002	+	0.949091i	$0.397995\pi$
$702$	2.65367e163	0.574729
$703$	−4.56623e163	−0.911227
$704$	5.35916e162	0.0985527
$705$	−1.01649e164	−1.72277
$706$	−1.22466e164	−1.91313
$707$	7.45914e162	0.107417
$708$	6.43911e162	0.0854896
$709$	1.33884e164	1.63897	0.819483	−	0.573103i	$-0.194261\pi$
$709$	1.33884e164	1.63897	0.819483	+	0.573103i	$0.194261\pi$
$710$	1.13799e164	1.28464
$711$	−1.63483e164	−1.70204
$712$	−3.11729e163	−0.299348
$713$	−7.40658e163	−0.656100
$714$	1.84237e164	1.50567
$715$	−6.20244e162	−0.0467698
$716$	−4.48621e163	−0.312162
$717$	−4.33831e164	−2.78592
$718$	−1.59200e163	−0.0943599
$719$	−9.19371e163	−0.503014	−0.251507	−	0.967856i	$-0.580926\pi$
$719$	−9.19371e163	−0.503014	−0.251507	+	0.967856i	$0.580926\pi$
$720$	9.00264e164	4.54728
$721$	1.46157e164	0.681621
$722$	−2.68677e164	−1.15702
$723$	6.62680e163	0.263543
$724$	4.91546e163	0.180550
$725$	−9.68882e162	−0.0328727
$726$	−6.49172e164	−2.03472
$727$	3.96782e164	1.14901	0.574504	−	0.818502i	$-0.305195\pi$
$727$	3.96782e164	1.14901	0.574504	+	0.818502i	$0.305195\pi$
$728$	−3.57154e163	−0.0955656
$729$	5.18507e164	1.28210
$730$	4.61873e164	1.05550
$731$	3.01822e164	0.637531
$732$	−8.52853e163	−0.166528
$733$	−1.03536e165	−1.86902	−0.934508	−	0.355941i	$-0.884160\pi$
$733$	−1.03536e165	−1.86902	−0.934508	+	0.355941i	$0.884160\pi$
$734$	1.20951e165	2.01877
$735$	−1.17721e165	−1.81690
$736$	1.65193e164	0.235785
$737$	−4.09466e162	−0.00540552
$738$	−4.34315e165	−5.30352
$739$	9.41614e164	1.06370	0.531848	−	0.846840i	$-0.321498\pi$
$739$	9.41614e164	1.06370	0.531848	+	0.846840i	$0.321498\pi$
$740$	2.48566e164	0.259787
$741$	−5.18395e164	−0.501319
$742$	−7.27034e164	−0.650624
$743$	−4.71091e164	−0.390165	−0.195083	−	0.980787i	$-0.562497\pi$
$743$	−4.71091e164	−0.390165	−0.195083	+	0.980787i	$0.562497\pi$
$744$	2.85803e165	2.19090
$745$	1.95213e165	1.38524
$746$	2.06962e165	1.35959
$747$	2.75426e165	1.67521
$748$	−8.75687e163	−0.0493182
$749$	8.18698e164	0.426992
$750$	−2.76038e165	−1.33336
$751$	−2.71492e165	−1.21468	−0.607338	−	0.794444i	$-0.707762\pi$
$751$	−2.71492e165	−1.21468	−0.607338	+	0.794444i	$0.707762\pi$
$752$	1.71848e165	0.712229
$753$	−3.77653e165	−1.45005
$754$	1.39218e163	0.00495273
$755$	1.00755e165	0.332135
$756$	1.40872e165	0.430349
$757$	1.82760e165	0.517449	0.258725	−	0.965951i	$-0.416698\pi$
$757$	1.82760e165	0.517449	0.258725	+	0.965951i	$0.416698\pi$
$758$	4.73649e165	1.24302
$759$	−5.61082e164	−0.136497
$760$	−8.13626e165	−1.83503
$761$	−4.53824e165	−0.949008	−0.474504	−	0.880253i	$-0.657373\pi$
$761$	−4.53824e165	−0.949008	−0.474504	+	0.880253i	$0.657373\pi$
$762$	−2.93537e165	−0.569183
$763$	1.55143e164	0.0278978
$764$	2.65660e165	0.443056
$765$	2.91949e166	4.51621
$766$	−1.45319e166	−2.08529
$767$	−2.50046e164	−0.0332879
$768$	−1.10709e166	−1.36745
$769$	1.50222e165	0.172174	0.0860872	−	0.996288i	$-0.472564\pi$
$769$	1.50222e165	0.172174	0.0860872	+	0.996288i	$0.472564\pi$
$770$	−1.58795e165	−0.168896
$771$	−1.58597e166	−1.56555
$772$	6.30986e164	0.0578129
$773$	−8.97300e165	−0.763162	−0.381581	−	0.924335i	$-0.624620\pi$
$773$	−8.97300e165	−0.763162	−0.381581	+	0.924335i	$0.624620\pi$
$774$	1.87832e166	1.48308
$775$	−2.73628e166	−2.00592
$776$	1.75699e166	1.19597
$777$	−1.14452e166	−0.723463
$778$	−1.02289e165	−0.0600487
$779$	5.02740e166	2.74119
$780$	2.82192e165	0.142924
$781$	2.49054e165	0.117181
$782$	1.40557e166	0.614418
$783$	1.55003e165	0.0629561
$784$	1.99020e166	0.751144
$785$	2.91030e166	1.02078
$786$	−2.67464e166	−0.871904
$787$	−5.88325e166	−1.78267	−0.891333	−	0.453349i	$-0.850229\pi$
$787$	−5.88325e166	−1.78267	−0.891333	+	0.453349i	$0.850229\pi$
$788$	−1.34660e166	−0.379297
$789$	2.11685e166	0.554323
$790$	−4.96809e166	−1.20957
$791$	5.17282e166	1.17106
$792$	1.53830e166	0.323850
$793$	3.31184e165	0.0648426
$794$	8.92398e166	1.62510
$795$	−1.62150e167	−2.74668
$796$	−1.15273e166	−0.181646
$797$	−7.45350e165	−0.109271	−0.0546357	−	0.998506i	$-0.517400\pi$
$797$	−7.45350e165	−0.109271	−0.0546357	+	0.998506i	$0.517400\pi$
$798$	−1.32719e167	−1.81037
$799$	5.57291e166	0.707363
$800$	6.10287e166	0.720875
$801$	−8.05778e166	−0.885820
$802$	1.39201e165	0.0142434
$803$	1.01083e166	0.0962794
$804$	1.86294e165	0.0165187
$805$	5.28498e166	0.436295
$806$	3.93176e166	0.302219
$807$	−1.38289e167	−0.989826
$808$	−2.19590e166	−0.146372
$809$	−4.30973e166	−0.267553	−0.133777	−	0.991012i	$-0.542710\pi$
$809$	−4.30973e166	−0.267553	−0.133777	+	0.991012i	$0.542710\pi$
$810$	7.74957e167	4.48115
$811$	2.50824e167	1.35105	0.675523	−	0.737339i	$-0.263918\pi$
$811$	2.50824e167	1.35105	0.675523	+	0.737339i	$0.263918\pi$
$812$	7.39051e164	0.00370854
$813$	−4.84255e167	−2.26395
$814$	2.62357e166	0.114285
$815$	5.11205e167	2.07507
$816$	−6.94679e167	−2.62785
$817$	−2.17424e167	−0.766547
$818$	3.10927e167	1.02175
$819$	−9.23197e166	−0.282794
$820$	−2.73670e167	−0.781503
$821$	−2.73261e167	−0.727522	−0.363761	−	0.931492i	$-0.618508\pi$
$821$	−2.73261e167	−0.727522	−0.363761	+	0.931492i	$0.618508\pi$
$822$	−2.46195e167	−0.611153
$823$	5.96060e167	1.37975	0.689874	−	0.723930i	$-0.257666\pi$
$823$	5.96060e167	1.37975	0.689874	+	0.723930i	$0.257666\pi$
$824$	−4.30273e167	−0.928815
$825$	−2.07286e167	−0.417318
$826$	−6.40167e166	−0.120210
$827$	3.90468e167	0.683940	0.341970	−	0.939711i	$-0.388906\pi$
$827$	3.90468e167	0.683940	0.341970	+	0.939711i	$0.388906\pi$
$828$	1.81374e167	0.296367
$829$	−9.96715e167	−1.51945	−0.759724	−	0.650246i	$-0.774666\pi$
$829$	−9.96715e167	−1.51945	−0.759724	+	0.650246i	$0.774666\pi$
$830$	8.36993e167	1.19051
$831$	1.72991e168	2.29596
$832$	9.46831e166	0.117268
$833$	6.45407e167	0.746012
$834$	−2.71101e168	−2.92471
$835$	−2.83408e168	−2.85391
$836$	6.30821e166	0.0592987
$837$	4.37753e168	3.84163
$838$	−6.17895e167	−0.506271
$839$	1.21000e168	0.925701	0.462851	−	0.886436i	$-0.346827\pi$
$839$	1.21000e168	0.925701	0.462851	+	0.886436i	$0.346827\pi$
$840$	−2.03935e168	−1.45691
$841$	−1.49808e168	−0.999457
$842$	−8.78995e167	−0.547698
$843$	6.53260e167	0.380190
$844$	−8.39157e165	−0.00456197
$845$	2.94807e168	1.49719
$846$	3.46817e168	1.64553
$847$	1.33823e168	0.593247
$848$	2.74133e168	1.13553
$849$	−2.72245e168	−1.05382
$850$	5.19272e168	1.87848
$851$	−8.73171e167	−0.295223
$852$	−1.13312e168	−0.358095
$853$	−3.73963e168	−1.10474	−0.552370	−	0.833599i	$-0.686276\pi$
$853$	−3.73963e168	−1.10474	−0.552370	+	0.833599i	$0.686276\pi$
$854$	8.47895e167	0.234161
$855$	−2.10312e169	−5.43015
$856$	−2.41017e168	−0.581843
$857$	−3.81490e166	−0.00861164	−0.00430582	−	0.999991i	$-0.501371\pi$
$857$	−3.81490e166	−0.00861164	−0.00430582	+	0.999991i	$0.501371\pi$
$858$	2.97848e167	0.0628747
$859$	5.16815e168	1.02030	0.510150	−	0.860085i	$-0.329590\pi$
$859$	5.16815e168	1.02030	0.510150	+	0.860085i	$0.329590\pi$
$860$	1.18356e168	0.218539
$861$	1.26012e169	2.17635
$862$	−4.42131e168	−0.714305
$863$	8.64922e168	1.30724	0.653621	−	0.756822i	$-0.273249\pi$
$863$	8.64922e168	1.30724	0.653621	+	0.756822i	$0.273249\pi$
$864$	−9.76344e168	−1.38058
$865$	−8.51314e168	−1.12632
$866$	1.50381e169	1.86172
$867$	−6.48520e168	−0.751321
$868$	2.08720e168	0.226298
$869$	−1.08729e168	−0.110334
$870$	7.94937e167	0.0755050
$871$	−7.23426e166	−0.00643206
$872$	−4.56725e167	−0.0380151
$873$	4.54158e169	3.53906
$874$	−1.01253e169	−0.738757
$875$	5.69037e168	0.388756
$876$	−4.59895e168	−0.294221
$877$	−1.64432e169	−0.985166	−0.492583	−	0.870265i	$-0.663947\pi$
$877$	−1.64432e169	−0.985166	−0.492583	+	0.870265i	$0.663947\pi$
$878$	2.19316e168	0.123065
$879$	−2.93940e169	−1.54489
$880$	5.98746e168	0.294774
$881$	−2.30769e169	−1.06429	−0.532147	−	0.846652i	$-0.678615\pi$
$881$	−2.30769e169	−1.06429	−0.532147	+	0.846652i	$0.678615\pi$
$882$	4.01654e169	1.73543
$883$	1.52838e169	0.618714	0.309357	−	0.950946i	$-0.399886\pi$
$883$	1.52838e169	0.618714	0.309357	+	0.950946i	$0.399886\pi$
$884$	−1.54712e168	−0.0586840
$885$	−1.42776e169	−0.507479
$886$	−2.50592e169	−0.834697
$887$	−5.45018e169	−1.70139	−0.850693	−	0.525662i	$-0.823818\pi$
$887$	−5.45018e169	−1.70139	−0.850693	+	0.525662i	$0.823818\pi$
$888$	3.36936e169	0.985831
$889$	6.05110e168	0.165952
$890$	−2.44869e169	−0.629517
$891$	1.69603e169	0.408757
$892$	−6.13435e168	−0.138608
$893$	−4.01457e169	−0.850512
$894$	−9.37437e169	−1.86224
$895$	9.94740e169	1.85304
$896$	4.20364e169	0.734370
$897$	−9.91294e168	−0.162419
$898$	1.06624e170	1.63857
$899$	2.29657e168	0.0331053
$900$	6.70066e169	0.906094
$901$	8.88993e169	1.12778
$902$	−2.88854e169	−0.343797
$903$	−5.44972e169	−0.608595
$904$	−1.52283e170	−1.59575
$905$	−1.08992e170	−1.07177
$906$	−4.83835e169	−0.446505
$907$	1.43816e170	1.24563	0.622815	−	0.782369i	$-0.285989\pi$
$907$	1.43816e170	1.24563	0.622815	+	0.782369i	$0.285989\pi$
$908$	−2.09387e169	−0.170221
$909$	−5.67610e169	−0.433139
$910$	−2.80551e169	−0.200970
$911$	9.92930e169	0.667747	0.333874	−	0.942618i	$-0.391644\pi$
$911$	9.92930e169	0.667747	0.333874	+	0.942618i	$0.391644\pi$
$912$	5.00427e170	3.15964
$913$	1.83180e169	0.108594
$914$	−2.49635e170	−1.38963
$915$	1.89106e170	0.988534
$916$	−4.41452e169	−0.216717
$917$	5.51362e169	0.254214
$918$	−8.30737e170	−3.59757
$919$	3.28948e170	1.33809	0.669046	−	0.743221i	$-0.266703\pi$
$919$	3.28948e170	1.33809	0.669046	+	0.743221i	$0.266703\pi$
$920$	−1.55585e170	−0.594520
$921$	−2.18762e169	−0.0785312
$922$	1.94116e169	0.0654686
$923$	4.40017e169	0.139435
$924$	1.58115e169	0.0470798
$925$	−3.22584e170	−0.902594
$926$	−5.23504e170	−1.37654
$927$	−1.11220e171	−2.74851
$928$	−5.12216e168	−0.0118972
$929$	5.99376e170	1.30857	0.654283	−	0.756250i	$-0.272971\pi$
$929$	5.99376e170	1.30857	0.654283	+	0.756250i	$0.272971\pi$
$930$	2.24503e171	4.60737
$931$	−4.64933e170	−0.896982
$932$	−2.64283e170	−0.479352
$933$	5.55843e170	0.947889
$934$	4.41493e170	0.707911
$935$	1.94169e170	0.292760
$936$	2.71780e170	0.385351
$937$	2.78075e170	0.370796	0.185398	−	0.982664i	$-0.440643\pi$
$937$	2.78075e170	0.370796	0.185398	+	0.982664i	$0.440643\pi$
$938$	−1.85211e169	−0.0232276
$939$	1.14111e171	1.34603
$940$	2.18536e170	0.242477
$941$	−1.36748e171	−1.42730	−0.713651	−	0.700501i	$-0.752960\pi$
$941$	−1.36748e171	−1.42730	−0.713651	+	0.700501i	$0.752960\pi$
$942$	−1.39756e171	−1.37228
$943$	9.61358e170	0.888102
$944$	2.41379e170	0.209802
$945$	−3.12359e171	−2.55462
$946$	1.24923e170	0.0961394
$947$	−1.15070e171	−0.833373	−0.416686	−	0.909050i	$-0.636809\pi$
$947$	−1.15070e171	−0.833373	−0.416686	+	0.909050i	$0.636809\pi$
$948$	4.94683e170	0.337169
$949$	1.78588e170	0.114563
$950$	−3.74069e171	−2.25863
$951$	4.23155e171	2.40502
$952$	1.11808e171	0.598202
$953$	−1.01050e171	−0.508973	−0.254486	−	0.967076i	$-0.581906\pi$
$953$	−1.01050e171	−0.508973	−0.254486	+	0.967076i	$0.581906\pi$
$954$	5.53244e171	2.62352
$955$	−5.89057e171	−2.63005
$956$	9.32700e170	0.392115
$957$	1.73975e169	0.00688734
$958$	−4.46072e171	−1.66298
$959$	5.07518e170	0.178189
$960$	5.40640e171	1.78777
$961$	3.27523e171	1.02011
$962$	4.63520e170	0.135988
$963$	−6.22997e171	−1.72177
$964$	−1.42471e170	−0.0370933
$965$	−1.39910e171	−0.343186
$966$	−2.53791e171	−0.586531
$967$	−1.36547e171	−0.297345	−0.148673	−	0.988886i	$-0.547500\pi$
$967$	−1.36547e171	−0.297345	−0.148673	+	0.988886i	$0.547500\pi$
$968$	−3.93963e171	−0.808392
$969$	1.62285e172	3.13805
$970$	1.38014e172	2.51507
$971$	−3.45776e171	−0.593866	−0.296933	−	0.954898i	$-0.595964\pi$
$971$	−3.45776e171	−0.593866	−0.296933	+	0.954898i	$0.595964\pi$
$972$	−3.34861e171	−0.542069
$973$	5.58860e171	0.852736
$974$	−2.52542e171	−0.363241
$975$	−3.66223e171	−0.496569
$976$	−3.19705e171	−0.408681
$977$	1.57762e171	0.190137	0.0950684	−	0.995471i	$-0.469693\pi$
$977$	1.57762e171	0.190137	0.0950684	+	0.995471i	$0.469693\pi$
$978$	−2.45487e172	−2.78961
$979$	−5.35905e170	−0.0574227
$980$	2.53089e171	0.255726
$981$	−1.18057e171	−0.112493
$982$	1.71278e172	1.53918
$983$	8.38422e171	0.710616	0.355308	−	0.934749i	$-0.384376\pi$
$983$	8.38422e171	0.710616	0.355308	+	0.934749i	$0.384376\pi$
$984$	−3.70966e172	−2.96562
$985$	2.98585e172	2.25156
$986$	−4.35826e170	−0.0310021
$987$	−1.00625e172	−0.675258
$988$	1.11451e171	0.0705599
$989$	−4.15766e171	−0.248349
$990$	1.20836e172	0.681042
$991$	−7.35123e171	−0.390953	−0.195477	−	0.980708i	$-0.562625\pi$
$991$	−7.35123e171	−0.390953	−0.195477	+	0.980708i	$0.562625\pi$
$992$	−1.44658e172	−0.725975
$993$	−3.81191e172	−1.80535
$994$	1.12653e172	0.503530
$995$	2.55598e172	1.07828
$996$	−8.33410e171	−0.331854
$997$	−3.14216e172	−1.18102	−0.590508	−	0.807032i	$-0.701073\pi$
$997$	−3.14216e172	−1.18102	−0.590508	+	0.807032i	$0.701073\pi$
$998$	1.21683e172	0.431740
$999$	5.16073e172	1.72860

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.116.a.a.1.3	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.116.a.a.1.3	✓	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:	\( k \)	\(=\)	\( 116 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-2.28920e17 q^{2} -5.05419e27 q^{3} +1.08661e34 q^{4} -2.40937e40 q^{5} +1.15700e45 q^{6} -2.38510e48 q^{7} +7.02151e51 q^{8} +1.81497e55 q^{9} +O(q^{10})\)	\(q-2.28920e17 q^{2} -5.05419e27 q^{3} +1.08661e34 q^{4} -2.40937e40 q^{5} +1.15700e45 q^{6} -2.38510e48 q^{7} +7.02151e51 q^{8} +1.81497e55 q^{9} +5.51552e57 q^{10} +1.20710e59 q^{11} -5.49191e61 q^{12} +2.13264e63 q^{13} +5.45998e65 q^{14} +1.21774e68 q^{15} -2.05872e69 q^{16} -6.67628e70 q^{17} -4.15483e72 q^{18} +4.80941e73 q^{19} -2.61803e74 q^{20} +1.20548e76 q^{21} -2.76329e76 q^{22} +9.19672e77 q^{23} -3.54880e79 q^{24} +3.39763e80 q^{25} -4.88205e80 q^{26} -5.43556e82 q^{27} -2.59167e82 q^{28} -2.85164e82 q^{29} -2.78765e85 q^{30} -8.05350e85 q^{31} +1.79621e86 q^{32} -6.10089e86 q^{33} +1.52834e88 q^{34} +5.74659e88 q^{35} +1.97216e89 q^{36} -9.49437e89 q^{37} -1.10097e91 q^{38} -1.07788e91 q^{39} -1.69174e92 q^{40} +1.04533e93 q^{41} -2.75958e93 q^{42} -4.52080e93 q^{43} +1.31164e93 q^{44} -4.37292e95 q^{45} -2.10532e95 q^{46} -8.34733e95 q^{47} +1.04052e97 q^{48} -9.66716e96 q^{49} -7.77786e97 q^{50} +3.37432e98 q^{51} +2.31734e97 q^{52} -1.33157e99 q^{53} +1.24431e100 q^{54} -2.90834e99 q^{55} -1.67470e100 q^{56} -2.43076e101 q^{57} +6.52798e99 q^{58} -1.17247e101 q^{59} +1.32320e102 q^{60} +1.55293e102 q^{61} +1.84361e103 q^{62} -4.32889e103 q^{63} +4.43971e103 q^{64} -5.13832e103 q^{65} +1.39662e104 q^{66} -3.39216e103 q^{67} -7.25449e104 q^{68} -4.64820e105 q^{69} -1.31551e106 q^{70} +2.06325e106 q^{71} +1.27438e107 q^{72} +8.37405e106 q^{73} +2.17345e107 q^{74} -1.71723e108 q^{75} +5.22593e107 q^{76} -2.87905e107 q^{77} +2.46748e108 q^{78} -9.00747e108 q^{79} +4.96022e109 q^{80} +1.40505e110 q^{81} -2.39296e110 q^{82} +1.51752e110 q^{83} +1.30988e110 q^{84} +1.60856e111 q^{85} +1.03490e111 q^{86} +1.44127e110 q^{87} +8.47564e110 q^{88} -4.43962e111 q^{89} +1.00105e113 q^{90} -5.08657e111 q^{91} +9.99322e111 q^{92} +4.07039e113 q^{93} +1.91087e113 q^{94} -1.15876e114 q^{95} -9.07840e113 q^{96} +2.50229e114 q^{97} +2.21301e114 q^{98} +2.19084e114 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 11\!\cdots\!44 q^{2}+ \cdots + 26\!\cdots\!13 q^{9}+O(q^{10}) \) 9 * q - 116180770089455544 * q^2 + 344843759214607763941669692 * q^3 + 104670059680921154232978400984552512 * q^4 - 9416265734776133053944609096571667575890 * q^5 + 256991120598421923060797165626503750361356768 * q^6 + 1823100316304157772850498188908022382936745628056 * q^7 - 219342532030837467786318171319354148041440220761600 * q^8 + 26072637303355254030743970272505117374453788742960594013 * q^9	\( 9 q - 11\!\cdots\!44 q^{2}+ \cdots - 81\!\cdots\!24 q^{99}+O(q^{100}) \) 9 * q - 116180770089455544 * q^2 + 344843759214607763941669692 * q^3 + 104670059680921154232978400984552512 * q^4 - 9416265734776133053944609096571667575890 * q^5 + 256991120598421923060797165626503750361356768 * q^6 + 1823100316304157772850498188908022382936745628056 * q^7 - 219342532030837467786318171319354148041440220761600 * q^8 + 26072637303355254030743970272505117374453788742960594013 * q^9 + 6889731598544239023205889874968132433435838108852679867760 * q^10 - 445517152984004554452882006139810856593102366136026223610732 * q^11 - 42821766403658150616877740531461298756313417540328083617855744 * q^12 + 19120191369167112279983663882072248970668936436622013715636775942 * q^13 - 874484410352602036165423857414222226528651993964136670010092090176 * q^14 + 57599849217209390109884779325066884761013420104089343277210728579720 * q^15 - 1898660452996213931642847506744088625997939708105388690720226275618816 * q^16 + 33419179892190498379140269229352347311321292371418143383895702694253506 * q^17 - 2890446730701337146666584437647276674841816394744930484862532014864739608 * q^18 + 56323667191172324184321794810244934428905386312408168014796206412959893100 * q^19 - 120777388922455433799357146114685194143652980138750550147727102823046920320 * q^20 + 28176272485874451401581069312956900459966003840123920247504389614132269060768 * q^21 + 210984989629936406579159416842818263081445382036693993098790665852739866289312 * q^22 + 5043025461154544652592399598502520927437665517917355864726536202832817581701192 * q^23 - 7479406270402029067027148815379966966654468567388028134173932380834142711449600 * q^24 + 121685992880890163904850134332941584046982669818587694611007334128142016185838975 * q^25 - 5914878085893066644910373209258644573936085196716403877449593179133594373009735632 * q^26 - 5437898471824326237019158372464459291991052787593142902719608572344381893810183400 * q^27 + 134945777488992574285149234278139874324546574917240128067914181134023530915243857408 * q^28 + 2439895086110265548692574276791512440826974071718418782816151860616339046059592317750 * q^29 - 1116585539518521415480577570330322838097236714153628065703800981349351376364839660480 * q^30 - 115077428025700644556762203100792633275869803062860787032812289936236157369971844291232 * q^31 + 182002942689670990671600876052552389114866685587533572692282985590686349099701286240256 * q^32 + 369141873981337522256423851297810174364779891698538054811380159251387321031750289147184 * q^33 + 16133584300638755367079868159687776681138177363676896002357157762964033939697234321079824 * q^34 - 52628449929177569411912369226649064291208149114238009380905357827049459818370441573185840 * q^35 - 343110691203669342080842230156946587735541070043733921826769094626380948288641172661825216 * q^36 + 287193704739393607505131056484688448302333303851532744432838755870145511209962195474555406 * q^37 + 1887285676044348998237316198233063024983501152361943246105012398202088272208210660325749600 * q^38 + 57495405068562246295455616507616293122146350008991254547433422285102442790821436306805531176 * q^39 - 377538131908105786834217342693439591573182569233316142689856344096115044105226591101231948800 * q^40 + 450036474709634029239457226906183730406636229485540132536579898525082307383544109285527636618 * q^41 - 3614527346318500983114558586611383169745609085282334175950975443992847582191151261402533817088 * q^42 + 11238467180897591407367974873375005136437267786775173672510908822395481702707823219190726952692 * q^43 + 8699999971697013733855125470633863112208674234411673595635316509240061153413462554031896481024 * q^44 - 354262889245566735270191791009177826124944074544236912619488508381128369609584375919402912590330 * q^45 + 211097623274700628625262911429039098879374408053211152239698326314586272783546202145178950255168 * q^46 - 316976878807259053071085359106141878112628948954523917108980455021512269952447135287167972348144 * q^47 + 4410525927214080719418968105605950188534122907207757808623172340024505114953341149753389138952192 * q^48 - 5402924848400424806022935001474260663230730313005626183937801432100886221124285978670797398474063 * q^49 - 107358804410623226001357232665018218738784300597386966398329608024306023910080977639712704319931400 * q^50 + 392230202654118035824948006166789320012418877782515914171168122937227894930092554264584283119946168 * q^51 + 186847646489930730643602674069595365244797337372298185295802970592172751947352587676622924463312256 * q^52 + 334496168286075107324733466358006346326362975568659741057867434494885827999701558072502824894138942 * q^53 + 815273172520443779763028707379283569820579781203093260711879845468622355550376013747519262940305600 * q^54 - 23563721346912912517453864325899810796736448452180735731334842246903047272785132546150581553652938280 * q^55 + 50501579633901923276218857218558899542358162690763518272752547626356309717401481440460372264435200000 * q^56 + 19326182159286888425606068195996356732391193445128832852476856331643144551112440129841029596191125200 * q^57 - 276537143978921040553065169225197607521839521198309506889392716069666566548578247536870903521071531600 * q^58 + 26559202104122447477824144844523074937734984825144901102500175836351773839109503993732582002313425700 * q^59 - 1442907433717223203332783871119423031323933407363314628882895297513470975585089853716965229400414768640 * q^60 + 466761553545603468366117849047093343161086980381148338979195572768003416466078862368134301594309428118 * q^61 + 28949531649262422331932844636470226821904033422254832199912074503071191433543806733834531878575668538112 * q^62 - 26525953947162098838236213455266609374207032849533466856093515022060397668973168836773250206710710550408 * q^63 - 46169280478215780445338819251740629236256446911950466222769056677599024448485239500558186236965165989888 * q^64 + 30622590124662743929353875752733901757221609411050393019261768040290807869865915951670063818998022920820 * q^65 + 58885521825482117580183439615438901701040523699794385163331031210597262925198785331149493283518615857536 * q^66 + 522391041991614299569962418777982996178060317974008251288477038656645322955247899200108470501056740725756 * q^67 - 963970789349034201430960171930241226642674599765083803055821765339886224671560293508121902691671583492992 * q^68 - 4768744134714834748105886788969216829087468736062331961872791186003972694205687719806877940995404594939424 * q^69 + 648102273330646244918318234903390383158022917116167184817069407742837923825354916186559362576551723218560 * q^70 + 32114907384466138287517273839727096331385168126590004271972827521185198833360861938868844865182495384954968 * q^71 + 134036350375106083011376263362911564045625075783489246636869772536858707114389024728586916900414866675980800 * q^72 - 111532806797088262693446813432847569894350723689665928769373202408064805330900544787546502644693976667521558 * q^73 + 146367501244421643149579339910137613783225032865117034030178763862717664956463164057696425085332997488423024 * q^74 + 191011236006610982766017086665378142663007338029810651608018025472800438314119281980403153054303538075361700 * q^75 + 1898752275573850608619854563706181213417282281074664303825494148687676736613874275716737807304301723964896000 * q^76 + 8547320523119144259127272245019592075910296652673224064175151890175172791298973939747111362021472266254476512 * q^77 + 8439857258376544014998782670363733435136214517799335731701302157574158558998894356877778911194771366104305984 * q^78 - 2698128344097500588934092059818825897117643397087596829234810281027633187083900600989280771432492738133389200 * q^79 + 117204555830492291605465104654149864678123037973909556311887751421858566469073727335484870898703213772212264960 * q^80 + 243844251998840861544064848215817562747898683224158368441742398035262682571557660719126722958354994801550865809 * q^81 + 473149820338187161445671999094492312190196735403799620250132055162721259658633637951105669203590924984388498512 * q^82 + 976812723170338476169372114700471197638723418120402034771092851931233919858674637831041045969218865325658875692 * q^83 + 2539321467869080915143952852614384190778021160799093130626725907993426541237386266518480321379169708798426343424 * q^84 + 3552505762114082405879304975670471704857686108558874865895506783571862811153977851101780608475304927035932222460 * q^85 + 11838276402773622473531002179261101730801162542213640979598425595359582429205612657343793928842614227749715441568 * q^86 + 27897493284886904362947680243525683713496258927093426130335092322232937971279756139421073573801725541246460925800 * q^87 + 52038964178994366220097267685544117931455067665556497129662971665594737875310678877513435089254305724995593676800 * q^88 + 59446666639398225412533241825642117887211504765823780420331081870088511796669962981765187912981764097798200324250 * q^89 + 259316827454272274338207071834855070930759935980768037766603430323600593416394106984590468235314680478785223708720 * q^90 + 245939937247192661534362402615346617600082162228156200993853962356431783555050183953904527617619011036872688337168 * q^91 + 613988446074365886926604878609711354412545763779069644197907853873975238992484853992399764939548985670950928032256 * q^92 + 1223125501788227369263854591107492905645880857959405771691286774974787266171291063996752221071041873907531275398784 * q^93 + 1499086835290066702674923853658203297973424744123451952620504314323336222430358359629023729105486706372629303556224 * q^94 + 799041738816013640930530159507467835290369458135599646151456080273195210563093613872275650940535406365162133749800 * q^95 + 3260013267518849074696485824622037660135078104167613123139522044708136137474372602480504246720813695045123797024768 * q^96 + 2523963432996685893503346240622778846413532532685755052598994124525775010632417867867345710038197597044049732141106 * q^97 + 585262872930561598617358018346679967180230161387125148358962641400172126269413925011919715802450101152197028464008 * q^98 - 8131297049226938077737975811278315123841467115358913895092773707388454338324871486984094251614634664934679647525724 * q^99

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