LMFDB - Embedded newform 1.116.a.a.1.4

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			1.4
Root			$5.63699e15$ 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)

$f(q)$	$=$	$q-1.48197e17 q^{2} +7.29391e26 q^{3} -1.95761e34 q^{4} +6.05511e39 q^{5} -1.08093e44 q^{6} -4.10385e48 q^{7} +9.05697e51 q^{8} -6.86309e54 q^{9} +O(q^{10})$	\(q-1.48197e17 q^{2} +7.29391e26 q^{3} -1.95761e34 q^{4} +6.05511e39 q^{5} -1.08093e44 q^{6} -4.10385e48 q^{7} +9.05697e51 q^{8} -6.86309e54 q^{9} -8.97348e56 q^{10} +6.80534e59 q^{11} -1.42786e61 q^{12} -2.20533e64 q^{13} +6.08178e65 q^{14} +4.41654e66 q^{15} -5.29056e68 q^{16} +2.09930e70 q^{17} +1.01709e72 q^{18} -1.06913e73 q^{19} -1.18535e74 q^{20} -2.99331e75 q^{21} -1.00853e77 q^{22} -2.36317e77 q^{23} +6.60607e78 q^{24} -2.04077e80 q^{25} +3.26823e81 q^{26} -1.03998e82 q^{27} +8.03373e82 q^{28} -3.92321e83 q^{29} -6.54518e83 q^{30} +8.07943e85 q^{31} -2.97807e86 q^{32} +4.96375e86 q^{33} -3.11110e87 q^{34} -2.48493e88 q^{35} +1.34352e89 q^{36} -4.38375e89 q^{37} +1.58442e90 q^{38} -1.60855e91 q^{39} +5.48409e91 q^{40} -5.70136e92 q^{41} +4.43600e92 q^{42} -1.08642e94 q^{43} -1.33222e94 q^{44} -4.15568e94 q^{45} +3.50215e94 q^{46} -2.05728e96 q^{47} -3.85889e95 q^{48} +1.48574e96 q^{49} +3.02436e97 q^{50} +1.53121e97 q^{51} +4.31717e98 q^{52} -2.60765e98 q^{53} +1.54122e99 q^{54} +4.12071e99 q^{55} -3.71685e100 q^{56} -7.79815e99 q^{57} +5.81408e100 q^{58} -6.32803e101 q^{59} -8.64585e100 q^{60} +5.74399e102 q^{61} -1.19735e103 q^{62} +2.81651e103 q^{63} +6.61102e103 q^{64} -1.33535e104 q^{65} -7.35612e103 q^{66} -6.22001e104 q^{67} -4.10960e104 q^{68} -1.72368e104 q^{69} +3.68259e105 q^{70} +2.47090e106 q^{71} -6.21588e106 q^{72} +1.45698e107 q^{73} +6.49658e106 q^{74} -1.48852e107 q^{75} +2.09294e107 q^{76} -2.79281e108 q^{77} +2.38382e108 q^{78} +1.16902e109 q^{79} -3.20349e108 q^{80} +4.31678e109 q^{81} +8.44924e109 q^{82} +2.26296e110 q^{83} +5.85973e109 q^{84} +1.27115e110 q^{85} +1.61004e111 q^{86} -2.86156e110 q^{87} +6.16357e111 q^{88} +2.37553e112 q^{89} +6.15858e111 q^{90} +9.05036e112 q^{91} +4.62617e111 q^{92} +5.89307e112 q^{93} +3.04882e113 q^{94} -6.47371e112 q^{95} -2.17218e113 q^{96} +1.57243e114 q^{97} -2.20182e113 q^{98} -4.67057e114 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.48197e17	−0.727134	−0.363567	−	0.931568i	$-0.618441\pi$
$2$	−1.48197e17	−0.727134	−0.363567	+	0.931568i	$0.618441\pi$
$3$	7.29391e26	0.268218	0.134109	−	0.990967i	$-0.457183\pi$
$3$	7.29391e26	0.268218	0.134109	+	0.990967i	$0.457183\pi$
$4$	−1.95761e34	−0.471277
$5$	6.05511e39	0.390254	0.195127	−	0.980778i	$-0.437488\pi$
$5$	6.05511e39	0.390254	0.195127	+	0.980778i	$0.437488\pi$
$6$	−1.08093e44	−0.195030
$7$	−4.10385e48	−1.04726	−0.523630	−	0.851946i	$-0.675423\pi$
$7$	−4.10385e48	−1.04726	−0.523630	+	0.851946i	$0.675423\pi$
$8$	9.05697e51	1.06981
$9$	−6.86309e54	−0.928059
$10$	−8.97348e56	−0.283766
$11$	6.80534e59	0.896954	0.448477	−	0.893794i	$-0.351967\pi$
$11$	6.80534e59	0.896954	0.448477	+	0.893794i	$0.351967\pi$
$12$	−1.42786e61	−0.126405
$13$	−2.20533e64	−1.95763	−0.978816	−	0.204742i	$-0.934364\pi$
$13$	−2.20533e64	−1.95763	−0.978816	+	0.204742i	$0.934364\pi$
$14$	6.08178e65	0.761498
$15$	4.41654e66	0.104673
$16$	−5.29056e68	−0.306622
$17$	2.09930e70	0.372616	0.186308	−	0.982491i	$-0.440348\pi$
$17$	2.09930e70	0.372616	0.186308	+	0.982491i	$0.440348\pi$
$18$	1.01709e72	0.674823
$19$	−1.06913e73	−0.316737	−0.158369	−	0.987380i	$-0.550623\pi$
$19$	−1.06913e73	−0.316737	−0.158369	+	0.987380i	$0.550623\pi$
$20$	−1.18535e74	−0.183917
$21$	−2.99331e75	−0.280894
$22$	−1.00853e77	−0.652206
$23$	−2.36317e77	−0.118617	−0.0593083	−	0.998240i	$-0.518889\pi$
$23$	−2.36317e77	−0.118617	−0.0593083	+	0.998240i	$0.518889\pi$
$24$	6.60607e78	0.286944
$25$	−2.04077e80	−0.847702
$26$	3.26823e81	1.42346
$27$	−1.03998e82	−0.517140
$28$	8.03373e82	0.493549
$29$	−3.92321e83	−0.320448	−0.160224	−	0.987081i	$-0.551222\pi$
$29$	−3.92321e83	−0.320448	−0.160224	+	0.987081i	$0.551222\pi$
$30$	−6.54518e83	−0.0761113
$31$	8.07943e85	1.42588	0.712941	−	0.701224i	$-0.247363\pi$
$31$	8.07943e85	1.42588	0.712941	+	0.701224i	$0.247363\pi$
$32$	−2.97807e86	−0.846860
$33$	4.96375e86	0.240579
$34$	−3.11110e87	−0.270942
$35$	−2.48493e88	−0.408697
$36$	1.34352e89	0.437373
$37$	−4.38375e89	−0.295288	−0.147644	−	0.989041i	$-0.547169\pi$
$37$	−4.38375e89	−0.295288	−0.147644	+	0.989041i	$0.547169\pi$
$38$	1.58442e90	0.230310
$39$	−1.60855e91	−0.525072
$40$	5.48409e91	0.417499
$41$	−5.70136e92	−1.04932	−0.524659	−	0.851313i	$-0.675807\pi$
$41$	−5.70136e92	−1.04932	−0.524659	+	0.851313i	$0.675807\pi$
$42$	4.43600e92	0.204248
$43$	−1.08642e94	−1.29289	−0.646446	−	0.762960i	$-0.723745\pi$
$43$	−1.08642e94	−1.29289	−0.646446	+	0.762960i	$0.723745\pi$
$44$	−1.33222e94	−0.422714
$45$	−4.15568e94	−0.362178
$46$	3.50215e94	0.0862501
$47$	−2.05728e96	−1.47118	−0.735590	−	0.677427i	$-0.763095\pi$
$47$	−2.05728e96	−1.47118	−0.735590	+	0.677427i	$0.763095\pi$
$48$	−3.85889e95	−0.0822415
$49$	1.48574e96	0.0967538
$50$	3.02436e97	0.616393
$51$	1.53121e97	0.0999423
$52$	4.31717e98	0.922586
$53$	−2.60765e98	−0.186375	−0.0931873	−	0.995649i	$-0.529706\pi$
$53$	−2.60765e98	−0.186375	−0.0931873	+	0.995649i	$0.529706\pi$
$54$	1.54122e99	0.376030
$55$	4.12071e99	0.350040
$56$	−3.71685e100	−1.12037
$57$	−7.79815e99	−0.0849547
$58$	5.81408e100	0.233008
$59$	−6.32803e101	−0.949026	−0.474513	−	0.880248i	$-0.657376\pi$
$59$	−6.32803e101	−0.949026	−0.474513	+	0.880248i	$0.657376\pi$
$60$	−8.64585e100	−0.0493300
$61$	5.74399e102	1.26692	0.633459	−	0.773776i	$-0.281635\pi$
$61$	5.74399e102	1.26692	0.633459	+	0.773776i	$0.281635\pi$
$62$	−1.19735e103	−1.03681
$63$	2.81651e103	0.971919
$64$	6.61102e103	0.922402
$65$	−1.33535e104	−0.763973
$66$	−7.35612e103	−0.174933
$67$	−6.22001e104	−0.623002	−0.311501	−	0.950246i	$-0.600832\pi$
$67$	−6.22001e104	−0.623002	−0.311501	+	0.950246i	$0.600832\pi$
$68$	−4.10960e104	−0.175605
$69$	−1.72368e104	−0.0318151
$70$	3.68259e105	0.297177
$71$	2.47090e106	0.882063	0.441031	−	0.897492i	$-0.354613\pi$
$71$	2.47090e106	0.882063	0.441031	+	0.897492i	$0.354613\pi$
$72$	−6.21588e106	−0.992851
$73$	1.45698e107	1.05291	0.526453	−	0.850204i	$-0.323522\pi$
$73$	1.45698e107	1.05291	0.526453	+	0.850204i	$0.323522\pi$
$74$	6.49658e106	0.214714
$75$	−1.48852e107	−0.227369
$76$	2.09294e107	0.149271
$77$	−2.79281e108	−0.939345
$78$	2.38382e108	0.381798
$79$	1.16902e109	0.900047	0.450024	−	0.893017i	$-0.351416\pi$
$79$	1.16902e109	0.900047	0.450024	+	0.893017i	$0.351416\pi$
$80$	−3.20349e108	−0.119660
$81$	4.31678e109	0.789353
$82$	8.44924e109	0.762994
$83$	2.26296e110	1.01785	0.508927	−	0.860809i	$-0.330042\pi$
$83$	2.26296e110	1.01785	0.508927	+	0.860809i	$0.330042\pi$
$84$	5.85973e109	0.132379
$85$	1.27115e110	0.145415
$86$	1.61004e111	0.940105
$87$	−2.86156e110	−0.0859499
$88$	6.16357e111	0.959575
$89$	2.37553e112	1.93123	0.965617	−	0.259969i	$-0.0837125\pi$
$89$	2.37553e112	1.93123	0.965617	+	0.259969i	$0.0837125\pi$
$90$	6.15858e111	0.263352
$91$	9.05036e112	2.05015
$92$	4.62617e111	0.0559012
$93$	5.89307e112	0.382447
$94$	3.04882e113	1.06974
$95$	−6.47371e112	−0.123608
$96$	−2.17218e113	−0.227143
$97$	1.57243e114	0.906141	0.453070	−	0.891475i	$-0.350329\pi$
$97$	1.57243e114	0.906141	0.453070	+	0.891475i	$0.350329\pi$
$98$	−2.20182e113	−0.0703529
$99$	−4.67057e114	−0.832427
$100$	3.99502e114	0.399502
$101$	−4.65500e114	−0.262688	−0.131344	−	0.991337i	$-0.541929\pi$
$101$	−4.65500e114	−0.262688	−0.131344	+	0.991337i	$0.541929\pi$
$102$	−2.26920e114	−0.0726714
$103$	−6.12632e115	−1.11959	−0.559795	−	0.828631i	$-0.689120\pi$
$103$	−6.12632e115	−1.11959	−0.559795	+	0.828631i	$0.689120\pi$
$104$	−1.99736e116	−2.09430
$105$	−1.81248e115	−0.109620
$106$	3.86446e115	0.135519
$107$	−7.26726e116	−1.48526	−0.742631	−	0.669700i	$-0.766423\pi$
$107$	−7.26726e116	−1.48526	−0.742631	+	0.669700i	$0.766423\pi$
$108$	2.03587e116	0.243716
$109$	1.57529e117	1.11003	0.555017	−	0.831839i	$-0.312712\pi$
$109$	1.57529e117	1.11003	0.555017	+	0.831839i	$0.312712\pi$
$110$	−6.10676e116	−0.254526
$111$	−3.19747e116	−0.0792017
$112$	2.17117e117	0.321112
$113$	1.10948e118	0.984262	0.492131	−	0.870521i	$-0.336218\pi$
$113$	1.10948e118	0.984262	0.492131	+	0.870521i	$0.336218\pi$
$114$	1.15566e117	0.0617734
$115$	−1.43093e117	−0.0462905
$116$	7.68011e117	0.151019
$117$	1.51354e119	1.81680
$118$	9.37795e118	0.690069
$119$	−8.61522e118	−0.390226
$120$	4.00005e118	0.111981
$121$	−1.12524e119	−0.195473
$122$	−8.51242e119	−0.921218
$123$	−4.15852e119	−0.281446
$124$	−1.58164e120	−0.671985
$125$	−2.69342e120	−0.721072
$126$	−4.17398e120	−0.706715
$127$	−4.53956e119	−0.0487866	−0.0243933	−	0.999702i	$-0.507765\pi$
$127$	−4.53956e119	−0.0487866	−0.0243933	+	0.999702i	$0.507765\pi$
$128$	2.57310e120	0.176151
$129$	−7.92426e120	−0.346777
$130$	1.97895e121	0.555510
$131$	2.04186e121	0.368915	0.184458	−	0.982840i	$-0.440947\pi$
$131$	2.04186e121	0.368915	0.184458	+	0.982840i	$0.440947\pi$
$132$	−9.71708e120	−0.113379
$133$	4.38756e121	0.331706
$134$	9.21785e121	0.453006
$135$	−6.29719e121	−0.201816
$136$	1.90133e122	0.398630
$137$	1.33547e123	1.83739	0.918696	−	0.394966i	$-0.129244\pi$
$137$	1.33547e123	1.83739	0.918696	+	0.394966i	$0.129244\pi$
$138$	2.55444e121	0.0231338
$139$	−6.39554e122	−0.382407	−0.191204	−	0.981550i	$-0.561239\pi$
$139$	−6.39554e122	−0.382407	−0.191204	+	0.981550i	$0.561239\pi$
$140$	4.86451e122	0.192609
$141$	−1.50056e123	−0.394597
$142$	−3.66179e123	−0.641377
$143$	−1.50080e124	−1.75591
$144$	3.63096e123	0.284563
$145$	−2.37555e123	−0.125056
$146$	−2.15920e124	−0.765603
$147$	1.08368e123	0.0259511
$148$	8.58165e123	0.139163
$149$	3.95861e124	0.435845	0.217922	−	0.975966i	$-0.430072\pi$
$149$	3.95861e124	0.435845	0.217922	+	0.975966i	$0.430072\pi$
$150$	2.20594e124	0.165328
$151$	2.15940e125	1.10448	0.552240	−	0.833685i	$-0.313773\pi$
$151$	2.15940e125	1.10448	0.552240	+	0.833685i	$0.313773\pi$
$152$	−9.68310e124	−0.338850
$153$	−1.44077e125	−0.345810
$154$	4.13886e125	0.683029
$155$	4.89219e125	0.556455
$156$	3.14890e125	0.247454
$157$	1.35019e126	0.734794	0.367397	−	0.930064i	$-0.380249\pi$
$157$	1.35019e126	0.734794	0.367397	+	0.930064i	$0.380249\pi$
$158$	−1.73246e126	−0.654455
$159$	−1.90200e125	−0.0499891
$160$	−1.80326e126	−0.330490
$161$	9.69812e125	0.124222
$162$	−6.39733e126	−0.573965
$163$	−3.03647e127	−1.91241	−0.956207	−	0.292691i	$-0.905449\pi$
$163$	−3.03647e127	−1.91241	−0.956207	+	0.292691i	$0.905449\pi$
$164$	1.11610e127	0.494519
$165$	3.00561e126	0.0938870
$166$	−3.35363e127	−0.740117
$167$	−1.96853e127	−0.307570	−0.153785	−	0.988104i	$-0.549146\pi$
$167$	−1.96853e127	−0.307570	−0.153785	+	0.988104i	$0.549146\pi$
$168$	−2.71103e127	−0.300505
$169$	3.59441e128	2.83232
$170$	−1.88380e127	−0.105736
$171$	7.33755e127	0.293951
$172$	2.12679e128	0.609310
$173$	−4.13957e128	−0.849776	−0.424888	−	0.905246i	$-0.639687\pi$
$173$	−4.13957e128	−0.849776	−0.424888	+	0.905246i	$0.639687\pi$
$174$	4.24073e127	0.0624970
$175$	8.37502e128	0.887765
$176$	−3.60041e128	−0.275026
$177$	−4.61561e128	−0.254546
$178$	−3.52046e129	−1.40426
$179$	4.91132e129	1.41954	0.709772	−	0.704431i	$-0.248798\pi$
$179$	4.91132e129	1.41954	0.709772	+	0.704431i	$0.248798\pi$
$180$	8.13519e128	0.170686
$181$	−6.27745e129	−0.957778	−0.478889	−	0.877875i	$-0.658960\pi$
$181$	−6.27745e129	−0.957778	−0.478889	+	0.877875i	$0.658960\pi$
$182$	−1.34123e130	−1.49073
$183$	4.18962e129	0.339810
$184$	−2.14032e129	−0.126898
$185$	−2.65441e129	−0.115237
$186$	−8.73334e129	−0.278090
$187$	1.42864e130	0.334220
$188$	4.02734e130	0.693333
$189$	4.26792e130	0.541581
$190$	9.59384e129	0.0898794
$191$	1.55182e131	1.07504	0.537519	−	0.843252i	$-0.319362\pi$
$191$	1.55182e131	1.07504	0.537519	+	0.843252i	$0.319362\pi$
$192$	4.82202e130	0.247405
$193$	1.62962e131	0.620212	0.310106	−	0.950702i	$-0.399635\pi$
$193$	1.62962e131	0.620212	0.310106	+	0.950702i	$0.399635\pi$
$194$	−2.33029e131	−0.658885
$195$	−9.73994e130	−0.204911
$196$	−2.90849e130	−0.0455978
$197$	−1.59108e132	−1.86159	−0.930793	−	0.365547i	$-0.880882\pi$
$197$	−1.59108e132	−1.86159	−0.930793	+	0.365547i	$0.880882\pi$
$198$	6.92163e131	0.605285
$199$	6.82092e129	0.00446469	0.00223234	−	0.999998i	$-0.499289\pi$
$199$	6.82092e129	0.00446469	0.00223234	+	0.999998i	$0.499289\pi$
$200$	−1.84832e132	−0.906884
$201$	−4.53682e131	−0.167101
$202$	6.89856e131	0.191009
$203$	1.61003e132	0.335592
$204$	−2.99751e131	−0.0471005
$205$	−3.45224e132	−0.409500
$206$	9.07901e132	0.814092
$207$	1.62187e132	0.110083
$208$	1.16674e133	0.600252
$209$	−7.27581e132	−0.284099
$210$	2.68604e132	0.0797083
$211$	2.50870e133	0.566511	0.283255	−	0.959045i	$-0.408586\pi$
$211$	2.50870e133	0.566511	0.283255	+	0.959045i	$0.408586\pi$
$212$	5.10475e132	0.0878340
$213$	1.80225e133	0.236585
$214$	1.07698e134	1.07998
$215$	−6.57840e133	−0.504556
$216$	−9.41906e133	−0.553244
$217$	−3.31568e134	−1.49327
$218$	−2.33453e134	−0.807144
$219$	1.06271e134	0.282408
$220$	−8.06673e133	−0.164966
$221$	−4.62965e134	−0.729445
$222$	4.73854e133	0.0575902
$223$	4.80964e134	0.451422	0.225711	−	0.974194i	$-0.427529\pi$
$223$	4.80964e134	0.451422	0.225711	+	0.974194i	$0.427529\pi$
$224$	1.22216e135	0.886883
$225$	1.40060e135	0.786718
$226$	−1.64422e135	−0.715690
$227$	2.75276e135	0.929570	0.464785	−	0.885424i	$-0.346132\pi$
$227$	2.75276e135	0.929570	0.464785	+	0.885424i	$0.346132\pi$
$228$	1.52657e134	0.0400372
$229$	2.88232e135	0.587762	0.293881	−	0.955842i	$-0.405053\pi$
$229$	2.88232e135	0.587762	0.293881	+	0.955842i	$0.405053\pi$
$230$	2.12059e134	0.0336594
$231$	−2.03705e135	−0.251949
$232$	−3.55324e135	−0.342820
$233$	9.61127e135	0.724128	0.362064	−	0.932153i	$-0.382072\pi$
$233$	9.61127e135	0.724128	0.362064	+	0.932153i	$0.382072\pi$
$234$	−2.24302e136	−1.32105
$235$	−1.24570e136	−0.574133
$236$	1.23878e136	0.447254
$237$	8.52675e135	0.241409
$238$	1.27675e136	0.283746
$239$	−9.76984e136	−1.70612	−0.853058	−	0.521817i	$-0.825254\pi$
$239$	−9.76984e136	−1.70612	−0.853058	+	0.521817i	$0.825254\pi$
$240$	−2.33660e135	−0.0320950
$241$	8.19549e135	0.0886329	0.0443164	−	0.999018i	$-0.485889\pi$
$241$	8.19549e135	0.0886329	0.0443164	+	0.999018i	$0.485889\pi$
$242$	1.66757e136	0.142135
$243$	1.08394e137	0.728859
$244$	−1.12445e137	−0.597069
$245$	8.99631e135	0.0377585
$246$	6.16280e136	0.204649
$247$	2.35779e137	0.620055
$248$	7.31752e137	1.52543
$249$	1.65058e137	0.273007
$250$	3.99157e137	0.524316
$251$	−1.01626e138	−1.06112	−0.530561	−	0.847647i	$-0.678019\pi$
$251$	−1.01626e138	−1.06112	−0.530561	+	0.847647i	$0.678019\pi$
$252$	−5.51363e137	−0.458043
$253$	−1.60822e137	−0.106394
$254$	6.72749e136	0.0354744
$255$	9.27164e136	0.0390029
$256$	−3.12744e138	−1.05049
$257$	−6.06267e138	−1.62746	−0.813728	−	0.581246i	$-0.802566\pi$
$257$	−6.06267e138	−1.62746	−0.813728	+	0.581246i	$0.802566\pi$
$258$	1.17435e138	0.252153
$259$	1.79903e138	0.309244
$260$	2.61409e138	0.360043
$261$	2.69254e138	0.297394
$262$	−3.02597e138	−0.268251
$263$	1.62398e139	1.15645	0.578223	−	0.815879i	$-0.303746\pi$
$263$	1.62398e139	1.15645	0.578223	+	0.815879i	$0.303746\pi$
$264$	4.49565e138	0.257375
$265$	−1.57896e138	−0.0727334
$266$	−6.50223e138	−0.241195
$267$	1.73269e139	0.517992
$268$	1.21763e139	0.293607
$269$	−4.13405e139	−0.804674	−0.402337	−	0.915492i	$-0.631802\pi$
$269$	−4.13405e139	−0.804674	−0.402337	+	0.915492i	$0.631802\pi$
$270$	9.33224e138	0.146747
$271$	8.34339e139	1.06074	0.530369	−	0.847767i	$-0.322053\pi$
$271$	8.34339e139	1.06074	0.530369	+	0.847767i	$0.322053\pi$
$272$	−1.11065e139	−0.114252
$273$	6.60125e139	0.549887
$274$	−1.97912e140	−1.33603
$275$	−1.38881e140	−0.760350
$276$	3.37428e138	0.0149937
$277$	−3.82205e139	−0.137946	−0.0689731	−	0.997619i	$-0.521972\pi$
$277$	−3.82205e139	−0.137946	−0.0689731	+	0.997619i	$0.521972\pi$
$278$	9.47798e139	0.278061
$279$	−5.54499e140	−1.32330
$280$	−2.25059e140	−0.437230
$281$	6.18517e140	0.978900	0.489450	−	0.872031i	$-0.337198\pi$
$281$	6.18517e140	0.978900	0.489450	+	0.872031i	$0.337198\pi$
$282$	2.22378e140	0.286925
$283$	1.28475e140	0.135238	0.0676191	−	0.997711i	$-0.478460\pi$
$283$	1.28475e140	0.135238	0.0676191	+	0.997711i	$0.478460\pi$
$284$	−4.83704e140	−0.415696
$285$	−4.72187e139	−0.0331539
$286$	2.22414e141	1.27678
$287$	2.33976e141	1.09891
$288$	2.04388e141	0.785936
$289$	−2.73343e141	−0.861157
$290$	3.52049e140	0.0909323
$291$	1.14691e141	0.243043
$292$	−2.85220e141	−0.496210
$293$	−7.49716e141	−1.07154	−0.535770	−	0.844364i	$-0.679979\pi$
$293$	−7.49716e141	−1.07154	−0.535770	+	0.844364i	$0.679979\pi$
$294$	−1.60599e140	−0.0188699
$295$	−3.83169e141	−0.370361
$296$	−3.97035e141	−0.315904
$297$	−7.07742e141	−0.463851
$298$	−5.86653e141	−0.316918
$299$	5.21158e141	0.232207
$300$	2.91393e141	0.107154
$301$	4.45852e142	1.35399
$302$	−3.20016e142	−0.803105
$303$	−3.39531e141	−0.0704577
$304$	5.65631e141	0.0971185
$305$	3.47805e142	0.494419
$306$	2.13517e142	0.251450
$307$	1.86191e142	0.181762	0.0908808	−	0.995862i	$-0.471032\pi$
$307$	1.86191e142	0.181762	0.0908808	+	0.995862i	$0.471032\pi$
$308$	5.46723e142	0.442691
$309$	−4.46848e142	−0.300295
$310$	−7.25007e142	−0.404617
$311$	2.60138e143	1.20637	0.603187	−	0.797600i	$-0.293897\pi$
$311$	2.60138e143	1.20637	0.603187	+	0.797600i	$0.293897\pi$
$312$	−1.45686e143	−0.561730
$313$	1.61650e143	0.518534	0.259267	−	0.965806i	$-0.416519\pi$
$313$	1.61650e143	0.518534	0.259267	+	0.965806i	$0.416519\pi$
$314$	−2.00094e143	−0.534294
$315$	1.70543e143	0.379295
$316$	−2.28849e143	−0.424171
$317$	−1.16259e144	−1.79688	−0.898439	−	0.439099i	$-0.855298\pi$
$317$	−1.16259e144	−1.79688	−0.898439	+	0.439099i	$0.855298\pi$
$318$	2.81870e142	0.0363487
$319$	−2.66988e143	−0.287427
$320$	4.00305e143	0.359971
$321$	−5.30067e143	−0.398374
$322$	−1.43723e143	−0.0903262
$323$	−2.24443e143	−0.118021
$324$	−8.45055e143	−0.372004
$325$	4.50057e144	1.65949
$326$	4.49995e144	1.39058
$327$	1.14900e144	0.297732
$328$	−5.16370e144	−1.12258
$329$	8.44276e144	1.54071
$330$	−4.45421e143	−0.0682684
$331$	−7.37132e144	−0.949370	−0.474685	−	0.880156i	$-0.657438\pi$
$331$	−7.37132e144	−0.949370	−0.474685	+	0.880156i	$0.657438\pi$
$332$	−4.42998e144	−0.479691
$333$	3.00861e144	0.274045
$334$	2.91730e144	0.223645
$335$	−3.76628e144	−0.243129
$336$	1.58363e144	0.0861282
$337$	−1.03506e145	−0.474509	−0.237254	−	0.971448i	$-0.576247\pi$
$337$	−1.03506e145	−0.474509	−0.237254	+	0.971448i	$0.576247\pi$
$338$	−5.32681e145	−2.05948
$339$	8.09248e144	0.263997
$340$	−2.48841e144	−0.0685305
$341$	5.49833e145	1.27895
$342$	−1.08740e145	−0.213742
$343$	5.69210e145	0.945934
$344$	−9.83969e145	−1.38315
$345$	−1.04371e144	−0.0124160
$346$	6.13471e145	0.617901
$347$	1.13849e146	0.971371	0.485686	−	0.874134i	$-0.338570\pi$
$347$	1.13849e146	0.971371	0.485686	+	0.874134i	$0.338570\pi$
$348$	5.60180e144	0.0405062
$349$	−4.54777e145	−0.278828	−0.139414	−	0.990234i	$-0.544522\pi$
$349$	−4.54777e145	−0.278828	−0.139414	+	0.990234i	$0.544522\pi$
$350$	−1.24115e146	−0.645524
$351$	2.29350e146	1.01237
$352$	−2.02668e146	−0.759595
$353$	4.74806e146	1.51172	0.755859	−	0.654734i	$-0.227220\pi$
$353$	4.74806e146	1.51172	0.755859	+	0.654734i	$0.227220\pi$
$354$	6.84019e145	0.185089
$355$	1.49615e146	0.344228
$356$	−4.65035e146	−0.910145
$357$	−6.28386e145	−0.104666
$358$	−7.27842e146	−1.03220
$359$	−2.02690e146	−0.244851	−0.122425	−	0.992478i	$-0.539067\pi$
$359$	−2.02690e146	−0.244851	−0.122425	+	0.992478i	$0.539067\pi$
$360$	−3.76378e146	−0.387464
$361$	−1.02506e147	−0.899677
$362$	9.30298e146	0.696433
$363$	−8.20739e145	−0.0524293
$364$	−1.77170e147	−0.966188
$365$	8.82218e146	0.410900
$366$	−6.20888e146	−0.247087
$367$	4.61004e147	1.56822	0.784108	−	0.620624i	$-0.213121\pi$
$367$	4.61004e147	1.56822	0.784108	+	0.620624i	$0.213121\pi$
$368$	1.25025e146	0.0363704
$369$	3.91290e147	0.973828
$370$	3.93375e146	0.0837929
$371$	1.07014e147	0.195183
$372$	−1.15363e147	−0.180239
$373$	7.37841e147	0.987882	0.493941	−	0.869496i	$-0.335556\pi$
$373$	7.37841e147	0.987882	0.493941	+	0.869496i	$0.335556\pi$
$374$	−2.11721e147	−0.243022
$375$	−1.96456e147	−0.193405
$376$	−1.86327e148	−1.57389
$377$	8.65198e147	0.627318
$378$	−6.32493e147	−0.393801
$379$	−8.05944e147	−0.431073	−0.215536	−	0.976496i	$-0.569150\pi$
$379$	−8.05944e147	−0.431073	−0.215536	+	0.976496i	$0.569150\pi$
$380$	1.26730e147	0.0582535
$381$	−3.31112e146	−0.0130854
$382$	−2.29975e148	−0.781696
$383$	1.63967e148	0.479544	0.239772	−	0.970829i	$-0.422927\pi$
$383$	1.63967e148	0.479544	0.239772	+	0.970829i	$0.422927\pi$
$384$	1.87680e147	0.0472468
$385$	−1.69108e148	−0.366583
$386$	−2.41504e148	−0.450977
$387$	7.45621e148	1.19988
$388$	−3.07819e148	−0.427043
$389$	6.56995e147	0.0786067	0.0393034	−	0.999227i	$-0.487486\pi$
$389$	6.56995e147	0.0786067	0.0393034	+	0.999227i	$0.487486\pi$
$390$	1.44343e148	0.148998
$391$	−4.96101e147	−0.0441984
$392$	1.34563e148	0.103509
$393$	1.48931e148	0.0989497
$394$	2.35793e149	1.35362
$395$	7.07856e148	0.351247
$396$	9.14314e148	0.392303
$397$	−3.69671e149	−1.37202	−0.686011	−	0.727591i	$-0.740640\pi$
$397$	−3.69671e149	−1.37202	−0.686011	+	0.727591i	$0.740640\pi$
$398$	−1.01084e147	−0.00324642
$399$	3.20025e148	0.0889697
$400$	1.07968e149	0.259924
$401$	2.91494e149	0.607895	0.303948	−	0.952689i	$-0.401695\pi$
$401$	2.91494e149	0.607895	0.303948	+	0.952689i	$0.401695\pi$
$402$	6.72342e148	0.121504
$403$	−1.78178e150	−2.79135
$404$	9.11265e148	0.123799
$405$	2.61386e149	0.308048
$406$	−2.38601e149	−0.244020
$407$	−2.98329e149	−0.264860
$408$	1.38681e149	0.106920
$409$	−1.24696e150	−0.835144	−0.417572	−	0.908644i	$-0.637119\pi$
$409$	−1.24696e150	−0.835144	−0.417572	+	0.908644i	$0.637119\pi$
$410$	5.11611e149	0.297761
$411$	9.74080e149	0.492822
$412$	1.19929e150	0.527637
$413$	2.59693e150	0.993877
$414$	−2.40356e149	−0.0800451
$415$	1.37025e150	0.397221
$416$	6.56764e150	1.65784
$417$	−4.66484e149	−0.102569
$418$	1.07825e150	0.206578
$419$	−1.06950e151	−1.78598	−0.892989	−	0.450078i	$-0.851396\pi$
$419$	−1.06950e151	−1.78598	−0.892989	+	0.450078i	$0.851396\pi$
$420$	3.54813e149	0.0516613
$421$	−7.55996e150	−0.960062	−0.480031	−	0.877252i	$-0.659375\pi$
$421$	−7.55996e150	−0.960062	−0.480031	+	0.877252i	$0.659375\pi$
$422$	−3.71782e150	−0.411929
$423$	1.41193e151	1.36534
$424$	−2.36174e150	−0.199386
$425$	−4.28418e150	−0.315867
$426$	−2.67088e150	−0.172029
$427$	−2.35725e151	−1.32679
$428$	1.42264e151	0.699970
$429$	−1.09467e151	−0.470966
$430$	9.74899e150	0.366879
$431$	1.67308e149	0.00550902	0.00275451	−	0.999996i	$-0.499123\pi$
$431$	1.67308e149	0.00550902	0.00275451	+	0.999996i	$0.499123\pi$
$432$	5.50208e150	0.158566
$433$	−1.88599e151	−0.475867	−0.237934	−	0.971281i	$-0.576470\pi$
$433$	−1.88599e151	−0.475867	−0.237934	+	0.971281i	$0.576470\pi$
$434$	4.91374e151	1.08581
$435$	−1.73270e150	−0.0335422
$436$	−3.08380e151	−0.523134
$437$	2.52655e150	0.0375703
$438$	−1.57490e151	−0.205349
$439$	1.28598e152	1.47070	0.735352	−	0.677685i	$-0.237017\pi$
$439$	1.28598e152	1.47070	0.735352	+	0.677685i	$0.237017\pi$
$440$	3.73211e151	0.374478
$441$	−1.01968e151	−0.0897932
$442$	6.86099e151	0.530404
$443$	−1.36069e152	−0.923731	−0.461865	−	0.886950i	$-0.652820\pi$
$443$	−1.36069e152	−0.923731	−0.461865	+	0.886950i	$0.652820\pi$
$444$	6.25938e150	0.0373259
$445$	1.43841e152	0.753671
$446$	−7.12773e151	−0.328244
$447$	2.88737e151	0.116902
$448$	−2.71307e152	−0.965995
$449$	−2.23655e151	−0.0700511	−0.0350255	−	0.999386i	$-0.511151\pi$
$449$	−2.23655e151	−0.0700511	−0.0350255	+	0.999386i	$0.511151\pi$
$450$	−2.07564e152	−0.572049
$451$	−3.87997e152	−0.941190
$452$	−2.17193e152	−0.463860
$453$	1.57504e152	0.296242
$454$	−4.07951e152	−0.675922
$455$	5.48009e152	0.800078
$456$	−7.06276e151	−0.0908858
$457$	1.46565e153	1.66283	0.831417	−	0.555649i	$-0.187530\pi$
$457$	1.46565e153	1.66283	0.831417	+	0.555649i	$0.187530\pi$
$458$	−4.27150e152	−0.427382
$459$	−2.18323e152	−0.192695
$460$	2.80119e151	0.0218156
$461$	7.37960e152	0.507259	0.253629	−	0.967301i	$-0.418376\pi$
$461$	7.37960e152	0.507259	0.253629	+	0.967301i	$0.418376\pi$
$462$	3.01885e152	0.183201
$463$	3.09025e153	1.65610	0.828051	−	0.560653i	$-0.189450\pi$
$463$	3.09025e153	1.65610	0.828051	+	0.560653i	$0.189450\pi$
$464$	2.07560e152	0.0982561
$465$	3.56832e152	0.149251
$466$	−1.42436e153	−0.526538
$467$	−3.75364e153	−1.22668	−0.613341	−	0.789818i	$-0.710175\pi$
$467$	−3.75364e153	−1.22668	−0.613341	+	0.789818i	$0.710175\pi$
$468$	−2.96291e153	−0.856215
$469$	2.55260e153	0.652446
$470$	1.84609e153	0.417472
$471$	9.84818e152	0.197085
$472$	−5.73128e153	−1.01528
$473$	−7.39347e153	−1.15967
$474$	−1.26364e153	−0.175537
$475$	2.18185e153	0.268499
$476$	1.68652e153	0.183904
$477$	1.78965e153	0.172967
$478$	1.44786e154	1.24057
$479$	−1.46491e154	−1.11306	−0.556531	−	0.830827i	$-0.687868\pi$
$479$	−1.46491e154	−1.11306	−0.556531	+	0.830827i	$0.687868\pi$
$480$	−1.31528e153	−0.0886434
$481$	9.66761e153	0.578066
$482$	−1.21455e153	−0.0644479
$483$	7.07372e152	0.0333187
$484$	2.20278e153	0.0921217
$485$	9.52122e153	0.353625
$486$	−1.60636e154	−0.529978
$487$	4.89637e153	0.143535	0.0717677	−	0.997421i	$-0.477136\pi$
$487$	4.89637e153	0.143535	0.0717677	+	0.997421i	$0.477136\pi$
$488$	5.20232e154	1.35537
$489$	−2.21477e154	−0.512944
$490$	−1.33323e153	−0.0274555
$491$	5.75175e154	1.05345	0.526725	−	0.850035i	$-0.323420\pi$
$491$	5.75175e154	1.05345	0.526725	+	0.850035i	$0.323420\pi$
$492$	8.14075e153	0.132639
$493$	−8.23600e153	−0.119404
$494$	−3.49417e154	−0.450863
$495$	−2.82808e154	−0.324857
$496$	−4.27447e154	−0.437206
$497$	−1.01402e155	−0.923749
$498$	−2.44611e154	−0.198513
$499$	−1.46769e155	−1.06134	−0.530668	−	0.847580i	$-0.678059\pi$
$499$	−1.46769e155	−1.06134	−0.530668	+	0.847580i	$0.678059\pi$
$500$	5.27266e154	0.339825
$501$	−1.43583e154	−0.0824959
$502$	1.50606e155	0.771577
$503$	−3.02897e155	−1.38400	−0.691999	−	0.721899i	$-0.743270\pi$
$503$	−3.02897e155	−1.38400	−0.691999	+	0.721899i	$0.743270\pi$
$504$	2.55091e155	1.03977
$505$	−2.81865e154	−0.102515
$506$	2.38333e154	0.0773624
$507$	2.62173e155	0.759680
$508$	8.88668e153	0.0229920
$509$	7.18272e155	1.65965	0.829825	−	0.558024i	$-0.188440\pi$
$509$	7.18272e155	1.65965	0.829825	+	0.558024i	$0.188440\pi$
$510$	−1.37403e154	−0.0283603
$511$	−5.97924e155	−1.10267
$512$	3.56594e155	0.587694
$513$	1.11188e155	0.163798
$514$	8.98469e155	1.18338
$515$	−3.70955e155	−0.436924
$516$	1.55126e155	0.163428
$517$	−1.40005e156	−1.31958
$518$	−2.66610e155	−0.224862
$519$	−3.01937e155	−0.227925
$520$	−1.20942e156	−0.817309
$521$	−1.15413e156	−0.698368	−0.349184	−	0.937054i	$-0.613541\pi$
$521$	−1.15413e156	−0.698368	−0.349184	+	0.937054i	$0.613541\pi$
$522$	−3.99026e155	−0.216245
$523$	2.89646e156	1.40612	0.703058	−	0.711133i	$-0.251818\pi$
$523$	2.89646e156	1.40612	0.703058	+	0.711133i	$0.251818\pi$
$524$	−3.99716e155	−0.173861
$525$	6.10866e155	0.238115
$526$	−2.40669e156	−0.840890
$527$	1.69612e156	0.531306
$528$	−2.62610e155	−0.0737668
$529$	−3.91334e156	−0.985930
$530$	2.33997e155	0.0528869
$531$	4.34299e156	0.880752
$532$	−8.58912e155	−0.156326
$533$	1.25734e157	2.05418
$534$	−2.56779e156	−0.376649
$535$	−4.40040e156	−0.579629
$536$	−5.63344e156	−0.666497
$537$	3.58227e156	0.380747
$538$	6.12654e156	0.585106
$539$	1.01110e156	0.0867837
$540$	1.23274e156	0.0951111
$541$	1.42832e157	0.990794	0.495397	−	0.868667i	$-0.335023\pi$
$541$	1.42832e157	0.990794	0.495397	+	0.868667i	$0.335023\pi$
$542$	−1.23646e157	−0.771299
$543$	−4.57871e156	−0.256893
$544$	−6.25187e156	−0.315553
$545$	9.53855e156	0.433195
$546$	−9.78284e156	−0.399842
$547$	−9.44842e155	−0.0347607	−0.0173803	−	0.999849i	$-0.505533\pi$
$547$	−9.44842e155	−0.0347607	−0.0173803	+	0.999849i	$0.505533\pi$
$548$	−2.61433e157	−0.865920
$549$	−3.94216e157	−1.17577
$550$	2.05818e157	0.552876
$551$	4.19443e156	0.101498
$552$	−1.56113e156	−0.0340363
$553$	−4.79750e157	−0.942583
$554$	5.66416e156	0.100305
$555$	−1.93610e156	−0.0309087
$556$	1.25199e157	0.180220
$557$	−1.16528e157	−0.151271	−0.0756357	−	0.997136i	$-0.524099\pi$
$557$	−1.16528e157	−0.151271	−0.0756357	+	0.997136i	$0.524099\pi$
$558$	8.21750e157	0.962218
$559$	2.39592e158	2.53101
$560$	1.31467e157	0.125315
$561$	1.04204e157	0.0896437
$562$	−9.16623e157	−0.711791
$563$	−3.73814e157	−0.262073	−0.131037	−	0.991378i	$-0.541831\pi$
$563$	−3.73814e157	−0.262073	−0.131037	+	0.991378i	$0.541831\pi$
$564$	2.93750e157	0.185965
$565$	6.71805e157	0.384112
$566$	−1.90396e157	−0.0983362
$567$	−1.77154e158	−0.826658
$568$	2.23788e158	0.943644
$569$	−4.11998e158	−1.57015	−0.785073	−	0.619403i	$-0.787375\pi$
$569$	−4.11998e158	−1.57015	−0.785073	+	0.619403i	$0.787375\pi$
$570$	6.99766e156	0.0241073
$571$	−4.23925e158	−1.32042	−0.660212	−	0.751080i	$-0.729533\pi$
$571$	−4.23925e158	−1.32042	−0.660212	+	0.751080i	$0.729533\pi$
$572$	2.93798e158	0.827518
$573$	1.13189e158	0.288345
$574$	−3.46744e158	−0.799053
$575$	4.82269e157	0.100551
$576$	−4.53721e158	−0.856043
$577$	5.16873e158	0.882622	0.441311	−	0.897354i	$-0.354514\pi$
$577$	5.16873e158	0.882622	0.441311	+	0.897354i	$0.354514\pi$
$578$	4.05086e158	0.626176
$579$	1.18863e158	0.166352
$580$	4.65039e157	0.0589359
$581$	−9.28684e158	−1.06596
$582$	−1.69969e158	−0.176725
$583$	−1.77459e158	−0.167170
$584$	1.31958e159	1.12641
$585$	9.16465e158	0.709012
$586$	1.11105e159	0.779153
$587$	−2.36162e158	−0.150148	−0.0750738	−	0.997178i	$-0.523919\pi$
$587$	−2.36162e158	−0.150148	−0.0750738	+	0.997178i	$0.523919\pi$
$588$	−2.12143e157	−0.0122302
$589$	−8.63798e158	−0.451630
$590$	5.67845e158	0.269302
$591$	−1.16052e159	−0.499311
$592$	2.31925e158	0.0905418
$593$	9.67649e158	0.342826	0.171413	−	0.985199i	$-0.445167\pi$
$593$	9.67649e158	0.342826	0.171413	+	0.985199i	$0.445167\pi$
$594$	1.04885e159	0.337282
$595$	−5.21661e158	−0.152287
$596$	−7.74940e158	−0.205404
$597$	4.97512e156	0.00119751
$598$	−7.72340e158	−0.168846
$599$	−3.27305e159	−0.649996	−0.324998	−	0.945715i	$-0.605364\pi$
$599$	−3.27305e159	−0.649996	−0.324998	+	0.945715i	$0.605364\pi$
$600$	−1.34815e159	−0.243243
$601$	−1.06278e159	−0.174245	−0.0871227	−	0.996198i	$-0.527767\pi$
$601$	−1.06278e159	−0.174245	−0.0871227	+	0.996198i	$0.527767\pi$
$602$	−6.60738e159	−0.984535
$603$	4.26885e159	0.578183
$604$	−4.22725e159	−0.520516
$605$	−6.81345e158	−0.0762839
$606$	5.03174e158	0.0512322
$607$	−3.44510e159	−0.319045	−0.159522	−	0.987194i	$-0.550995\pi$
$607$	−3.44510e159	−0.319045	−0.159522	+	0.987194i	$0.550995\pi$
$608$	3.18395e159	0.268232
$609$	1.17434e159	0.0900119
$610$	−5.15436e159	−0.359509
$611$	4.53698e160	2.88003
$612$	2.82046e159	0.162972
$613$	6.23107e159	0.327782	0.163891	−	0.986478i	$-0.447595\pi$
$613$	6.23107e159	0.327782	0.163891	+	0.986478i	$0.447595\pi$
$614$	−2.75929e159	−0.132165
$615$	−2.51803e159	−0.109835
$616$	−2.52944e160	−1.00492
$617$	1.96489e160	0.711118	0.355559	−	0.934654i	$-0.384291\pi$
$617$	1.96489e160	0.711118	0.355559	+	0.934654i	$0.384291\pi$
$618$	6.62215e159	0.218354
$619$	2.08863e160	0.627550	0.313775	−	0.949497i	$-0.398406\pi$
$619$	2.08863e160	0.627550	0.313775	+	0.949497i	$0.398406\pi$
$620$	−9.57698e159	−0.262244
$621$	2.45765e159	0.0613414
$622$	−3.85517e160	−0.877195
$623$	−9.74882e160	−2.02250
$624$	8.51012e159	0.160998
$625$	3.28208e160	0.566301
$626$	−2.39561e160	−0.377043
$627$	−5.30691e159	−0.0762005
$628$	−2.64315e160	−0.346291
$629$	−9.20280e159	−0.110029
$630$	−2.52739e160	−0.275798
$631$	−2.87682e160	−0.286566	−0.143283	−	0.989682i	$-0.545766\pi$
$631$	−2.87682e160	−0.286566	−0.143283	+	0.989682i	$0.545766\pi$
$632$	1.05878e161	0.962884
$633$	1.82983e160	0.151948
$634$	1.72292e161	1.30657
$635$	−2.74876e159	−0.0190391
$636$	3.72336e159	0.0235587
$637$	−3.27655e160	−0.189408
$638$	3.95668e160	0.208998
$639$	−1.69580e161	−0.818606
$640$	1.55804e160	0.0687434
$641$	3.49354e160	0.140906	0.0704529	−	0.997515i	$-0.477556\pi$
$641$	3.49354e160	0.140906	0.0704529	+	0.997515i	$0.477556\pi$
$642$	7.85543e160	0.289671
$643$	2.24340e161	0.756442	0.378221	−	0.925715i	$-0.376536\pi$
$643$	2.24340e161	0.756442	0.378221	+	0.925715i	$0.376536\pi$
$644$	−1.89851e160	−0.0585431
$645$	−4.79823e160	−0.135331
$646$	3.32617e160	0.0858173
$647$	1.26923e161	0.299601	0.149801	−	0.988716i	$-0.452137\pi$
$647$	1.26923e161	0.299601	0.149801	+	0.988716i	$0.452137\pi$
$648$	3.90969e161	0.844461
$649$	−4.30644e161	−0.851233
$650$	−6.66970e161	−1.20667
$651$	−2.41843e161	−0.400522
$652$	5.94422e161	0.901276
$653$	−4.47843e161	−0.621753	−0.310877	−	0.950450i	$-0.600623\pi$
$653$	−4.47843e161	−0.621753	−0.310877	+	0.950450i	$0.600623\pi$
$654$	−1.70278e161	−0.216491
$655$	1.23637e161	0.143970
$656$	3.01634e161	0.321743
$657$	−9.99940e161	−0.977159
$658$	−1.25119e162	−1.12030
$659$	−5.71805e161	−0.469177	−0.234589	−	0.972095i	$-0.575374\pi$
$659$	−5.71805e161	−0.469177	−0.234589	+	0.972095i	$0.575374\pi$
$660$	−5.88380e160	−0.0442467
$661$	1.83845e162	1.26727	0.633633	−	0.773634i	$-0.281563\pi$
$661$	1.83845e162	1.26727	0.633633	+	0.773634i	$0.281563\pi$
$662$	1.09241e162	0.690319
$663$	−3.37682e161	−0.195650
$664$	2.04955e162	1.08892
$665$	2.65672e161	0.129450
$666$	−4.45866e161	−0.199267
$667$	9.27123e160	0.0380104
$668$	3.85360e161	0.144951
$669$	3.50811e161	0.121080
$670$	5.58151e161	0.176787
$671$	3.90898e162	1.13637
$672$	8.91431e161	0.237878
$673$	−2.57574e162	−0.631009	−0.315505	−	0.948924i	$-0.602174\pi$
$673$	−2.57574e162	−0.631009	−0.315505	+	0.948924i	$0.602174\pi$
$674$	1.53392e162	0.345031
$675$	2.12236e162	0.438381
$676$	−7.03645e162	−1.33481
$677$	−4.39661e162	−0.766071	−0.383036	−	0.923734i	$-0.625121\pi$
$677$	−4.39661e162	−0.766071	−0.383036	+	0.923734i	$0.625121\pi$
$678$	−1.19928e162	−0.191961
$679$	−6.45301e162	−0.948965
$680$	1.15128e162	0.155567
$681$	2.00784e162	0.249328
$682$	−8.14835e162	−0.929968
$683$	3.74466e161	0.0392846	0.0196423	−	0.999807i	$-0.493747\pi$
$683$	3.74466e161	0.0392846	0.0196423	+	0.999807i	$0.493747\pi$
$684$	−1.43640e162	−0.138532
$685$	8.08642e162	0.717048
$686$	−8.43551e162	−0.687820
$687$	2.10234e162	0.157648
$688$	5.74778e162	0.396429
$689$	5.75073e162	0.364853
$690$	1.54674e161	0.00902806
$691$	1.71272e163	0.919811	0.459905	−	0.887968i	$-0.347883\pi$
$691$	1.71272e163	0.919811	0.459905	+	0.887968i	$0.347883\pi$
$692$	8.10365e162	0.400480
$693$	1.91673e163	0.871767
$694$	−1.68721e163	−0.706317
$695$	−3.87257e162	−0.149236
$696$	−2.59170e162	−0.0919504
$697$	−1.19689e163	−0.390992
$698$	6.73965e162	0.202745
$699$	7.01037e162	0.194224
$700$	−1.63950e163	−0.418383
$701$	4.36377e163	1.02583	0.512915	−	0.858439i	$-0.328566\pi$
$701$	4.36377e163	1.02583	0.512915	+	0.858439i	$0.328566\pi$
$702$	−3.39889e163	−0.736129
$703$	4.68681e162	0.0935289
$704$	4.49903e163	0.827352
$705$	−9.08605e162	−0.153993
$706$	−7.03648e163	−1.09922
$707$	1.91034e163	0.275103
$708$	9.03555e162	0.119962
$709$	−1.17769e164	−1.44169	−0.720843	−	0.693098i	$-0.756245\pi$
$709$	−1.17769e164	−1.44169	−0.720843	+	0.693098i	$0.756245\pi$
$710$	−2.21725e163	−0.250300
$711$	−8.02311e163	−0.835297
$712$	2.15151e164	2.06606
$713$	−1.90931e163	−0.169133
$714$	9.31248e162	0.0761059
$715$	−9.08752e163	−0.685249
$716$	−9.61443e163	−0.668998
$717$	−7.12603e163	−0.457611
$718$	3.00380e163	0.178039
$719$	7.97366e162	0.0436261	0.0218131	−	0.999762i	$-0.493056\pi$
$719$	7.97366e162	0.0436261	0.0218131	+	0.999762i	$0.493056\pi$
$720$	2.19859e163	0.111052
$721$	2.51415e164	1.17250
$722$	1.51911e164	0.654186
$723$	5.97771e162	0.0237729
$724$	1.22888e164	0.451379
$725$	8.00637e163	0.271644
$726$	1.21631e163	0.0381231
$727$	−1.51988e164	−0.440130	−0.220065	−	0.975485i	$-0.570627\pi$
$727$	−1.51988e164	−0.440130	−0.220065	+	0.975485i	$0.570627\pi$
$728$	8.19688e164	2.19328
$729$	−2.40169e164	−0.593859
$730$	−1.30742e164	−0.298779
$731$	−2.28072e164	−0.481752
$732$	−8.20162e163	−0.160145
$733$	−2.68363e164	−0.484445	−0.242223	−	0.970221i	$-0.577876\pi$
$733$	−2.68363e164	−0.484445	−0.242223	+	0.970221i	$0.577876\pi$
$734$	−6.83193e164	−1.14030
$735$	6.56183e162	0.0101275
$736$	7.03770e163	0.100452
$737$	−4.23293e164	−0.558805
$738$	−5.79879e164	−0.708103
$739$	−2.81348e164	−0.317825	−0.158913	−	0.987293i	$-0.550799\pi$
$739$	−2.81348e164	−0.317825	−0.158913	+	0.987293i	$0.550799\pi$
$740$	5.19629e163	0.0543087
$741$	1.71975e164	0.166310
$742$	−1.58592e164	−0.141924
$743$	1.39364e165	1.15423	0.577115	−	0.816663i	$-0.304178\pi$
$743$	1.39364e165	1.15423	0.577115	+	0.816663i	$0.304178\pi$
$744$	5.33733e164	0.409148
$745$	2.39698e164	0.170090
$746$	−1.09346e165	−0.718322
$747$	−1.55309e165	−0.944629
$748$	−2.79672e164	−0.157510
$749$	2.98238e165	1.55546
$750$	2.91141e164	0.140631
$751$	3.05307e165	1.36597	0.682985	−	0.730433i	$-0.260681\pi$
$751$	3.05307e165	1.36597	0.682985	+	0.730433i	$0.260681\pi$
$752$	1.08841e165	0.451096
$753$	−7.41249e164	−0.284612
$754$	−1.28220e165	−0.456144
$755$	1.30754e165	0.431027
$756$	−8.35492e164	−0.255234
$757$	−2.71337e165	−0.768239	−0.384120	−	0.923283i	$-0.625495\pi$
$757$	−2.71337e165	−0.768239	−0.384120	+	0.923283i	$0.625495\pi$
$758$	1.19438e165	0.313447
$759$	−1.17302e164	−0.0285367
$760$	−5.86322e164	−0.132238
$761$	2.17080e165	0.453944	0.226972	−	0.973901i	$-0.427117\pi$
$761$	2.17080e165	0.453944	0.226972	+	0.973901i	$0.427117\pi$
$762$	4.90697e163	0.00951486
$763$	−6.46476e165	−1.16250
$764$	−3.03786e165	−0.506640
$765$	−8.72401e164	−0.134953
$766$	−2.42995e165	−0.348692
$767$	1.39554e166	1.85784
$768$	−2.28112e165	−0.281760
$769$	−1.13798e166	−1.30428	−0.652141	−	0.758098i	$-0.726129\pi$
$769$	−1.13798e166	−1.30428	−0.652141	+	0.758098i	$0.726129\pi$
$770$	2.50612e165	0.266554
$771$	−4.42206e165	−0.436513
$772$	−3.19015e165	−0.292291
$773$	1.75539e166	1.49298	0.746489	−	0.665397i	$-0.231738\pi$
$773$	1.75539e166	1.49298	0.746489	+	0.665397i	$0.231738\pi$
$774$	−1.10499e166	−0.872473
$775$	−1.64883e166	−1.20872
$776$	1.42414e166	0.969403
$777$	1.31219e165	0.0829448
$778$	−9.73645e164	−0.0571576
$779$	6.09551e165	0.332358
$780$	1.90670e165	0.0965699
$781$	1.68153e166	0.791170
$782$	7.35206e164	0.0321381
$783$	4.08006e165	0.165716
$784$	−7.86039e164	−0.0296668
$785$	8.17556e165	0.286756
$786$	−2.20712e165	−0.0719497
$787$	3.66255e166	1.10978	0.554890	−	0.831924i	$-0.312760\pi$
$787$	3.66255e166	1.10978	0.554890	+	0.831924i	$0.312760\pi$
$788$	3.11470e166	0.877322
$789$	1.18452e166	0.310180
$790$	−1.04902e166	−0.255403
$791$	−4.55316e166	−1.03078
$792$	−4.23012e166	−0.890542
$793$	−1.26674e167	−2.48016
$794$	5.47841e166	0.997644
$795$	−1.15168e165	−0.0195084
$796$	−1.33527e164	−0.00210410
$797$	7.27867e165	0.106708	0.0533542	−	0.998576i	$-0.483009\pi$
$797$	7.27867e165	0.106708	0.0533542	+	0.998576i	$0.483009\pi$
$798$	−4.74267e165	−0.0646928
$799$	−4.31884e166	−0.548185
$800$	6.07756e166	0.717885
$801$	−1.63035e167	−1.79230
$802$	−4.31985e166	−0.442021
$803$	9.91525e166	0.944408
$804$	8.88130e165	0.0787506
$805$	5.87232e165	0.0484782
$806$	2.64055e167	2.02969
$807$	−3.01534e166	−0.215828
$808$	−4.21601e166	−0.281028
$809$	1.63119e167	1.01266	0.506331	−	0.862339i	$-0.331001\pi$
$809$	1.63119e167	1.01266	0.506331	+	0.862339i	$0.331001\pi$
$810$	−3.87365e166	−0.223992
$811$	9.83462e166	0.529735	0.264867	−	0.964285i	$-0.414672\pi$
$811$	9.83462e166	0.529735	0.264867	+	0.964285i	$0.414672\pi$
$812$	−3.15180e166	−0.158157
$813$	6.08559e166	0.284509
$814$	4.42114e166	0.192589
$815$	−1.83862e167	−0.746326
$816$	−8.10096e165	−0.0306445
$817$	1.16153e167	0.409507
$818$	1.84795e167	0.607262
$819$	−6.21134e167	−1.90266
$820$	6.75812e166	0.192988
$821$	4.99682e167	1.33034	0.665169	−	0.746693i	$-0.268359\pi$
$821$	4.99682e167	1.33034	0.665169	+	0.746693i	$0.268359\pi$
$822$	−1.44356e167	−0.358347
$823$	−4.10535e167	−0.950297	−0.475148	−	0.879906i	$-0.657606\pi$
$823$	−4.10535e167	−0.950297	−0.475148	+	0.879906i	$0.657606\pi$
$824$	−5.54859e167	−1.19775
$825$	−1.01299e167	−0.203940
$826$	−3.84857e167	−0.722681
$827$	1.12394e168	1.96868	0.984339	−	0.176288i	$-0.0564089\pi$
$827$	1.12394e168	1.96868	0.984339	+	0.176288i	$0.0564089\pi$
$828$	−3.17498e166	−0.0518796
$829$	5.14555e167	0.784416	0.392208	−	0.919877i	$-0.371711\pi$
$829$	5.14555e167	0.784416	0.392208	+	0.919877i	$0.371711\pi$
$830$	−2.03066e167	−0.288833
$831$	−2.78777e166	−0.0369997
$832$	−1.45795e168	−1.80572
$833$	3.11901e166	0.0360520
$834$	6.91315e166	0.0745810
$835$	−1.19197e167	−0.120030
$836$	1.42432e167	0.133889
$837$	−8.40245e167	−0.737381
$838$	1.58497e168	1.29864
$839$	2.21289e168	1.69296	0.846482	−	0.532417i	$-0.178716\pi$
$839$	2.21289e168	1.69296	0.846482	+	0.532417i	$0.178716\pi$
$840$	−1.64156e167	−0.117273
$841$	−1.34497e168	−0.897313
$842$	1.12036e168	0.698093
$843$	4.51141e167	0.262559
$844$	−4.91105e167	−0.266983
$845$	2.17646e168	1.10532
$846$	−2.09243e168	−0.992786
$847$	4.61782e167	0.204711
$848$	1.37959e167	0.0571465
$849$	9.37086e166	0.0362733
$850$	6.34903e167	0.229678
$851$	1.03596e167	0.0350261
$852$	−3.52810e167	−0.111497
$853$	−2.56484e168	−0.757689	−0.378844	−	0.925460i	$-0.623678\pi$
$853$	−2.56484e168	−0.757689	−0.378844	+	0.925460i	$0.623678\pi$
$854$	3.49337e168	0.964755
$855$	4.44297e167	0.114715
$856$	−6.58193e168	−1.58896
$857$	−1.74148e168	−0.393116	−0.196558	−	0.980492i	$-0.562976\pi$
$857$	−1.74148e168	−0.393116	−0.196558	+	0.980492i	$0.562976\pi$
$858$	1.62227e168	0.342455
$859$	−9.46367e168	−1.86833	−0.934163	−	0.356846i	$-0.883852\pi$
$859$	−9.46367e168	−1.86833	−0.934163	+	0.356846i	$0.883852\pi$
$860$	1.28779e168	0.237785
$861$	1.70660e168	0.294747
$862$	−2.47946e166	−0.00400579
$863$	−2.78076e168	−0.420284	−0.210142	−	0.977671i	$-0.567393\pi$
$863$	−2.78076e168	−0.420284	−0.210142	+	0.977671i	$0.567393\pi$
$864$	3.09714e168	0.437945
$865$	−2.50656e168	−0.331628
$866$	2.79498e168	0.346019
$867$	−1.99374e168	−0.230978
$868$	6.49080e168	0.703743
$869$	7.95560e168	0.807301
$870$	2.56781e167	0.0243897
$871$	1.37172e169	1.21961
$872$	1.42673e169	1.18753
$873$	−1.07917e169	−0.840952
$874$	−3.74426e167	−0.0273186
$875$	1.10534e169	0.755150
$876$	−2.08037e168	−0.133093
$877$	7.08897e167	0.0424724	0.0212362	−	0.999774i	$-0.493240\pi$
$877$	7.08897e167	0.0424724	0.0212362	+	0.999774i	$0.493240\pi$
$878$	−1.90579e169	−1.06940
$879$	−5.46836e168	−0.287406
$880$	−2.18009e168	−0.107330
$881$	−8.49061e168	−0.391583	−0.195792	−	0.980646i	$-0.562728\pi$
$881$	−8.49061e168	−0.391583	−0.195792	+	0.980646i	$0.562728\pi$
$882$	1.51113e168	0.0652917
$883$	−8.55801e168	−0.346444	−0.173222	−	0.984883i	$-0.555418\pi$
$883$	−8.55801e168	−0.346444	−0.173222	+	0.984883i	$0.555418\pi$
$884$	9.06303e168	0.343770
$885$	−2.79480e168	−0.0993375
$886$	2.01650e169	0.671676
$887$	−5.78367e169	−1.80549	−0.902745	−	0.430175i	$-0.858452\pi$
$887$	−5.78367e169	−1.80549	−0.902745	+	0.430175i	$0.858452\pi$
$888$	−2.89593e168	−0.0847312
$889$	1.86297e168	0.0510922
$890$	−2.13168e169	−0.548019
$891$	2.93771e169	0.708013
$892$	−9.41538e168	−0.212745
$893$	2.19950e169	0.465978
$894$	−4.27899e168	−0.0850030
$895$	2.97386e169	0.553982
$896$	−1.05596e169	−0.184475
$897$	3.80128e168	0.0622822
$898$	3.31450e168	0.0509365
$899$	−3.16973e169	−0.456920
$900$	−2.74182e169	−0.370762
$901$	−5.47424e168	−0.0694462
$902$	5.74999e169	0.684371
$903$	3.25200e169	0.363166
$904$	1.00486e170	1.05298
$905$	−3.80106e169	−0.373776
$906$	−2.33417e169	−0.215407
$907$	1.17501e170	1.01771	0.508855	−	0.860852i	$-0.330069\pi$
$907$	1.17501e170	1.01771	0.508855	+	0.860852i	$0.330069\pi$
$908$	−5.38883e169	−0.438085
$909$	3.19477e169	0.243790
$910$	−8.12132e169	−0.581764
$911$	6.09560e169	0.409930	0.204965	−	0.978769i	$-0.434292\pi$
$911$	6.09560e169	0.409930	0.204965	+	0.978769i	$0.434292\pi$
$912$	4.12566e168	0.0260489
$913$	1.54002e170	0.912970
$914$	−2.17205e170	−1.20910
$915$	2.53686e169	0.132612
$916$	−5.64245e169	−0.276999
$917$	−8.37950e169	−0.386350
$918$	3.23548e169	0.140115
$919$	−8.40951e169	−0.342081	−0.171040	−	0.985264i	$-0.554713\pi$
$919$	−8.40951e169	−0.342081	−0.171040	+	0.985264i	$0.554713\pi$
$920$	−1.29599e169	−0.0495223
$921$	1.35806e169	0.0487517
$922$	−1.09363e170	−0.368845
$923$	−5.44914e170	−1.72675
$924$	3.98775e169	0.118738
$925$	8.94622e169	0.250317
$926$	−4.57966e170	−1.20421
$927$	4.20455e170	1.03905
$928$	1.16836e170	0.271374
$929$	4.75134e170	1.03732	0.518660	−	0.854981i	$-0.326431\pi$
$929$	4.75134e170	1.03732	0.518660	+	0.854981i	$0.326431\pi$
$930$	−5.28813e169	−0.108526
$931$	−1.58845e169	−0.0306455
$932$	−1.88151e170	−0.341265
$933$	1.89742e170	0.323571
$934$	5.56278e170	0.891962
$935$	8.65060e169	0.130430
$936$	1.37081e171	1.94364
$937$	−1.27932e170	−0.170590	−0.0852949	−	0.996356i	$-0.527183\pi$
$937$	−1.27932e170	−0.170590	−0.0852949	+	0.996356i	$0.527183\pi$
$938$	−3.78287e170	−0.474415
$939$	1.17906e170	0.139080
$940$	2.43860e170	0.270576
$941$	−1.29835e171	−1.35515	−0.677577	−	0.735452i	$-0.736970\pi$
$941$	−1.29835e171	−1.35515	−0.677577	+	0.735452i	$0.736970\pi$
$942$	−1.45947e170	−0.143307
$943$	1.34733e170	0.124466
$944$	3.34788e170	0.290992
$945$	2.58428e170	0.211354
$946$	1.09569e171	0.843232
$947$	−9.04486e170	−0.655056	−0.327528	−	0.944842i	$-0.606216\pi$
$947$	−9.04486e170	−0.655056	−0.327528	+	0.944842i	$0.606216\pi$
$948$	−1.66920e170	−0.113770
$949$	−3.21313e171	−2.06120
$950$	−3.23344e170	−0.195235
$951$	−8.47981e170	−0.481955
$952$	−7.80277e170	−0.417469
$953$	5.36651e170	0.270302	0.135151	−	0.990825i	$-0.456848\pi$
$953$	5.36651e170	0.270302	0.135151	+	0.990825i	$0.456848\pi$
$954$	−2.65221e170	−0.125770
$955$	9.39646e170	0.419537
$956$	1.91255e171	0.804052
$957$	−1.94739e170	−0.0770931
$958$	2.17095e171	0.809345
$959$	−5.48057e171	−1.92423
$960$	2.91979e170	0.0965506
$961$	3.31706e171	1.03314
$962$	−1.43271e171	−0.420331
$963$	4.98759e171	1.37841
$964$	−1.60435e170	−0.0417706
$965$	9.86751e170	0.242040
$966$	−1.04830e170	−0.0242271
$967$	3.61793e171	0.787839	0.393919	−	0.919145i	$-0.371119\pi$
$967$	3.61793e171	0.787839	0.393919	+	0.919145i	$0.371119\pi$
$968$	−1.01913e171	−0.209120
$969$	−1.63707e170	−0.0316555
$970$	−1.41101e171	−0.257132
$971$	−4.66505e171	−0.801217	−0.400609	−	0.916249i	$-0.631201\pi$
$971$	−4.66505e171	−0.801217	−0.400609	+	0.916249i	$0.631201\pi$
$972$	−2.12192e171	−0.343494
$973$	2.62463e171	0.400480
$974$	−7.25627e170	−0.104369
$975$	3.28267e171	0.445105
$976$	−3.03889e171	−0.388464
$977$	5.36781e171	0.646934	0.323467	−	0.946239i	$-0.395152\pi$
$977$	5.36781e171	0.646934	0.323467	+	0.946239i	$0.395152\pi$
$978$	3.28223e171	0.372979
$979$	1.61663e172	1.73223
$980$	−1.76112e170	−0.0177947
$981$	−1.08114e172	−1.03018
$982$	−8.52391e171	−0.766000
$983$	−1.64979e172	−1.39831	−0.699153	−	0.714972i	$-0.746439\pi$
$983$	−1.64979e172	−1.39831	−0.699153	+	0.714972i	$0.746439\pi$
$984$	−3.76636e171	−0.301095
$985$	−9.63414e171	−0.726490
$986$	1.22055e171	0.0868226
$987$	6.15807e171	0.413246
$988$	−4.61563e171	−0.292218
$989$	2.56740e171	0.153358
$990$	4.19113e171	0.236215
$991$	4.72314e171	0.251186	0.125593	−	0.992082i	$-0.459917\pi$
$991$	4.72314e171	0.251186	0.125593	+	0.992082i	$0.459917\pi$
$992$	−2.40611e172	−1.20752
$993$	−5.37657e171	−0.254638
$994$	1.50275e172	0.671689
$995$	4.13014e169	0.00174236
$996$	−3.23119e171	−0.128662
$997$	2.37003e172	0.890806	0.445403	−	0.895330i	$-0.353060\pi$
$997$	2.37003e172	0.890806	0.445403	+	0.895330i	$0.353060\pi$
$998$	2.17507e172	0.771733
$999$	4.55901e171	0.152706

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.116.a.a.1.4	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.116.a.a.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-1.48197e17 q^{2} +7.29391e26 q^{3} -1.95761e34 q^{4} +6.05511e39 q^{5} -1.08093e44 q^{6} -4.10385e48 q^{7} +9.05697e51 q^{8} -6.86309e54 q^{9} +O(q^{10})\)	\(q-1.48197e17 q^{2} +7.29391e26 q^{3} -1.95761e34 q^{4} +6.05511e39 q^{5} -1.08093e44 q^{6} -4.10385e48 q^{7} +9.05697e51 q^{8} -6.86309e54 q^{9} -8.97348e56 q^{10} +6.80534e59 q^{11} -1.42786e61 q^{12} -2.20533e64 q^{13} +6.08178e65 q^{14} +4.41654e66 q^{15} -5.29056e68 q^{16} +2.09930e70 q^{17} +1.01709e72 q^{18} -1.06913e73 q^{19} -1.18535e74 q^{20} -2.99331e75 q^{21} -1.00853e77 q^{22} -2.36317e77 q^{23} +6.60607e78 q^{24} -2.04077e80 q^{25} +3.26823e81 q^{26} -1.03998e82 q^{27} +8.03373e82 q^{28} -3.92321e83 q^{29} -6.54518e83 q^{30} +8.07943e85 q^{31} -2.97807e86 q^{32} +4.96375e86 q^{33} -3.11110e87 q^{34} -2.48493e88 q^{35} +1.34352e89 q^{36} -4.38375e89 q^{37} +1.58442e90 q^{38} -1.60855e91 q^{39} +5.48409e91 q^{40} -5.70136e92 q^{41} +4.43600e92 q^{42} -1.08642e94 q^{43} -1.33222e94 q^{44} -4.15568e94 q^{45} +3.50215e94 q^{46} -2.05728e96 q^{47} -3.85889e95 q^{48} +1.48574e96 q^{49} +3.02436e97 q^{50} +1.53121e97 q^{51} +4.31717e98 q^{52} -2.60765e98 q^{53} +1.54122e99 q^{54} +4.12071e99 q^{55} -3.71685e100 q^{56} -7.79815e99 q^{57} +5.81408e100 q^{58} -6.32803e101 q^{59} -8.64585e100 q^{60} +5.74399e102 q^{61} -1.19735e103 q^{62} +2.81651e103 q^{63} +6.61102e103 q^{64} -1.33535e104 q^{65} -7.35612e103 q^{66} -6.22001e104 q^{67} -4.10960e104 q^{68} -1.72368e104 q^{69} +3.68259e105 q^{70} +2.47090e106 q^{71} -6.21588e106 q^{72} +1.45698e107 q^{73} +6.49658e106 q^{74} -1.48852e107 q^{75} +2.09294e107 q^{76} -2.79281e108 q^{77} +2.38382e108 q^{78} +1.16902e109 q^{79} -3.20349e108 q^{80} +4.31678e109 q^{81} +8.44924e109 q^{82} +2.26296e110 q^{83} +5.85973e109 q^{84} +1.27115e110 q^{85} +1.61004e111 q^{86} -2.86156e110 q^{87} +6.16357e111 q^{88} +2.37553e112 q^{89} +6.15858e111 q^{90} +9.05036e112 q^{91} +4.62617e111 q^{92} +5.89307e112 q^{93} +3.04882e113 q^{94} -6.47371e112 q^{95} -2.17218e113 q^{96} +1.57243e114 q^{97} -2.20182e113 q^{98} -4.67057e114 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 11\!\cdots\!44 q^{2}+ \cdots + 26\!\cdots\!13 q^{9}+O(q^{10}) \) 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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