LMFDB - Embedded newform 9.102.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,102,Mod(1,9)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 102, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 102);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 102 $
Character orbit:	$[\chi]$	$=$	9.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:	$581.406281043$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + \cdots + 14\!\cdots\!00 $ x^8 - x^7 - 1587875693797102871013870264x^6 - 1330672377046512025083958312008691941376x^5 + 791445357227345439680707260473135602197341722594809856x^4 + 1619878418527606484256994450085468366256752280708006567605868625920x^3 - 123437551313054499723143526216928211228510769023293658451121904309621876706508800x^2 - 461414543589146449205827365849494496729755778377708510322901762861807152038306434693201920000x + 1491743821439154656522591042817873299711189313438184985174364653060384818799349544894763946517463040000000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	multiple of $ 2^{119}\cdot 3^{56}\cdot 5^{14}\cdot 7^{7}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2} $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$2.42719e13$ of defining polynomial
Character	$\chi$	$=$	9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.38447e15 q^{2} +3.15040e30 q^{4} -7.99157e34 q^{5} +3.14769e42 q^{7} +1.46670e45 q^{8} +O(q^{10})$	\(q+2.38447e15 q^{2} +3.15040e30 q^{4} -7.99157e34 q^{5} +3.14769e42 q^{7} +1.46670e45 q^{8} -1.90557e50 q^{10} -6.08310e52 q^{11} -2.09809e56 q^{13} +7.50557e57 q^{14} -4.48993e60 q^{16} +1.97536e62 q^{17} -2.54133e64 q^{19} -2.51767e65 q^{20} -1.45050e68 q^{22} +6.11246e68 q^{23} -3.30565e70 q^{25} -5.00284e71 q^{26} +9.91648e72 q^{28} -7.52088e73 q^{29} -1.26748e75 q^{31} -1.44246e76 q^{32} +4.71018e77 q^{34} -2.51550e77 q^{35} +1.84306e79 q^{37} -6.05972e79 q^{38} -1.17212e80 q^{40} +3.79846e81 q^{41} -1.82567e82 q^{43} -1.91642e83 q^{44} +1.45750e84 q^{46} +1.21503e84 q^{47} -1.27334e85 q^{49} -7.88223e85 q^{50} -6.60984e86 q^{52} -1.92092e87 q^{53} +4.86136e87 q^{55} +4.61670e87 q^{56} -1.79333e89 q^{58} +9.03706e88 q^{59} -9.82351e89 q^{61} -3.02228e90 q^{62} -2.30118e91 q^{64} +1.67671e91 q^{65} +1.68394e92 q^{67} +6.22317e92 q^{68} -5.99813e92 q^{70} -2.66050e92 q^{71} -1.19661e94 q^{73} +4.39473e94 q^{74} -8.00620e94 q^{76} -1.91477e95 q^{77} +8.68984e95 q^{79} +3.58816e95 q^{80} +9.05733e96 q^{82} +2.05551e96 q^{83} -1.57862e97 q^{85} -4.35327e97 q^{86} -8.92207e97 q^{88} +4.58460e98 q^{89} -6.60413e98 q^{91} +1.92567e99 q^{92} +2.89721e99 q^{94} +2.03092e99 q^{95} -9.41618e99 q^{97} -3.03625e100 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 434989091795040 q^{2} + 90\!\cdots\!96 q^{4}+ \cdots + 61\!\cdots\!20 q^{8}+O(q^{10}) $ 8 * q + 434989091795040 * q^2 + 9008967123164113911511576503296 * q^4 - 38238791540232828026421308589217200 * q^5 - 5786789720778120168956257648884421874283200 * q^7 + 6101688461407407841888405145259998920458731520 * q^8	$ 8 q + 434989091795040 q^{2} + 90\!\cdots\!96 q^{4}+ \cdots - 20\!\cdots\!20 q^{98}+O(q^{100}) $ 8 * q + 434989091795040 * q^2 + 9008967123164113911511576503296 * q^4 - 38238791540232828026421308589217200 * q^5 - 5786789720778120168956257648884421874283200 * q^7 + 6101688461407407841888405145259998920458731520 * q^8 - 376167658847177398692429835067300112512860198593600 * q^10 - 4622006661480385115355021397632645270205791478300896 * q^11 + 250316830865150221699601352256397536965043294984328650480 * q^13 + 4856789037716039923353321450215036970203737520869624889088 * q^14 - 10662656154906175558835021484824464714661655552497093859868672 * q^16 + 397968518694853312322660892941326449007299986932512193696587120 * q^17 - 21387776045417165942123954421061470474744368808488511816400717280 * q^19 - 1745002690168409059221421019241581897927614179506161156200285542400 * q^20 + 61357881995862711169740037407631980426480577127973320405539739944320 * q^22 + 1366243345208606848425464574347748611753917469593153677393324561698880 * q^23 + 77471873089568593564333770877949420045843582630742632687744142562715000 * q^25 + 97549630676937426518340388130407212490384846814009484188479115327886144 * q^26 + 9217624035174751886516129105576165061663773766415040330328487084880404480 * q^28 - 15465799862710125255662370242568323665682807414567501281109138719156160880 * q^29 - 6594370386043135339784923725045360443937393326734068279132668478779615001344 * q^31 - 12265519409733718324179959581296851912742484455832107241543734281342036213760 * q^32 + 9531455444774917507766540524882635666895777953789094347547215472626183995712 * q^34 + 1122850631208004175280217132184898888977788452428069383882586628450512616297600 * q^35 + 39729696767983511833540209209183332457877293383323859312175998401968644864715440 * q^37 + 70873740526925065519455012686645778106113298999572267198467188879790467046148480 * q^38 - 763642761360299050617237751714968411270996317577517686387843428508400019349504000 * q^40 - 5607291724825101314952096252772109505395882457063737303656079003304969203257094736 * q^41 - 28642921955044714117801359306021921736063108483729021321044095944585527287681223200 * q^43 + 207838425393205175674959052733026300855796348257745356716186803699782799277851086848 * q^44 + 1088094260619851586903932234100844276278561023621942541398958535856528393570339218176 * q^46 + 4595399220200007631460417274797048154524720407021496316223236391731855709593438718080 * q^47 + 12068461406676719302337658501270392621238416595305390197216228129207599916872005856456 * q^49 + 40493179837482260394665357435432250163405353367416857829233726008281167215503492420000 * q^50 - 736020167800817028850658909331852777746165402605863935107936992324104798352324258252800 * q^52 - 131026696145917691346168139299202731343660174597285772716290345361212508775951813313840 * q^53 - 14585157967675450217148723878599628333971210001615112897255333178063634767400530051473600 * q^55 + 23665562342657326400415121984960944704012341384928617813498515591030351969339927087022080 * q^56 + 29173417521771002425120779628349939892591335515731485644911210555324770598093888308326080 * q^58 - 212583149562022564923669670483574922097682552074321909615339251529169016840977455874187360 * q^59 - 3390796423636162146406492296389682436951029380958058095674208836333532599894943317230895504 * q^61 + 5878859817222970028213836429448832127296537243368792127423103234889716583457526212133370880 * q^62 - 74870090698021647967203019932764377907062372989513317693678846896652408519412785858115272704 * q^64 + 161067075283368767182138254547148962244907084326790507487294907612770451283405321317426536800 * q^65 - 618774503558862942537948810466095132313460919373052732511642097824837019429997681150398682720 * q^67 + 2182412150351293808121583165511486752102068977919329447376923905220322529537335456462676162560 * q^68 - 12923520657540473465038555822652190723092643731233782501675276653712048411292540691873715571200 * q^70 + 15797470289857673806303846655911576507977904169297655042639265226995032204172380517793831135424 * q^71 - 20462651635605668591994589976366754984142669867347912050159975933828495442291952971923777071280 * q^73 + 142953411935712165334538916257020870493984381200782662943456748743148514063783881306064429441088 * q^74 + 64556217054886497186737063238064337992823205997653378371004031509089422583081356800943896432640 * q^76 - 250231448169383959900618348975396989794902211753647918986458150866408618577007907131029306438400 * q^77 + 1474556321278768744579716979675929750918930811984805387023357390321899878561204701118206999166080 * q^79 - 6033438037435277941170744030808192554572458649979375320464765273747209092446481051552234550067200 * q^80 + 30083863369214129982421840097969977845328701273986110579467106900080547794123383776302929686086720 * q^82 - 33762254529254022439253159341806143692643909652777369725086142424861011401680843403961249425712160 * q^83 + 17314966267116570951109803841412092095679328201414316724042066880549149931729490643535478494114400 * q^85 - 67989564188024628582959760637462873453376851598916319417912395832044408164663357850732592560556416 * q^86 - 363099602372059077387783242048689913608334478213970275423791339756517232974574737922754584123146240 * q^88 + 620007165949691950044675276484549383308720953973642955804615855186521697520022438525123333812557360 * q^89 - 3685711793015793225308940042728501386995879977832891226647110522985454537354035281338855172828873344 * q^91 + 4618779932089713137770970202224414792688843158843334085630908366025929325979388063902511470793400320 * q^92 - 17371370943540992303713705925513939673302729250250795188383540356993592041601425149438637190677682688 * q^94 + 2642077700832720169247174948884057845373174576960370774287679094739730873649398763127258995555528000 * q^95 + 64020476116668335744724892375903667651900818166631138467214326399663196857065619648203365824701173520 * q^97 - 202971561788470754768820264959327860776947519106194867162872422213964707447467488105939520314595817120 * q^98

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 $

$2$	2.38447e15	1.49754	0.748768	−	0.662832i	$-0.230646\pi$
$2$	2.38447e15	1.49754	0.748768	+	0.662832i	$0.230646\pi$
$3$	0	0
$3$	0	0
$4$	3.15040e30	1.24262
$5$	−7.99157e34	−0.402390	−0.201195	−	0.979551i	$-0.564482\pi$
$5$	−7.99157e34	−0.402390	−0.201195	+	0.979551i	$0.564482\pi$
$6$	0	0
$7$	3.14769e42	0.661516	0.330758	−	0.943716i	$-0.392696\pi$
$7$	3.14769e42	0.661516	0.330758	+	0.943716i	$0.392696\pi$
$8$	1.46670e45	0.363326
$9$	0	0
$10$	−1.90557e50	−0.602594
$11$	−6.08310e52	−1.56241	−0.781204	−	0.624276i	$-0.785394\pi$
$11$	−6.08310e52	−1.56241	−0.781204	+	0.624276i	$0.785394\pi$
$12$	0	0
$13$	−2.09809e56	−1.16865	−0.584326	−	0.811519i	$-0.698641\pi$
$13$	−2.09809e56	−1.16865	−0.584326	+	0.811519i	$0.698641\pi$
$14$	7.50557e57	0.990644
$15$	0	0
$16$	−4.48993e60	−0.698522
$17$	1.97536e62	1.43872	0.719358	−	0.694640i	$-0.244436\pi$
$17$	1.97536e62	1.43872	0.719358	+	0.694640i	$0.244436\pi$
$18$	0	0
$19$	−2.54133e64	−0.672982	−0.336491	−	0.941687i	$-0.609240\pi$
$19$	−2.54133e64	−0.672982	−0.336491	+	0.941687i	$0.609240\pi$
$20$	−2.51767e65	−0.500016
$21$	0	0
$22$	−1.45050e68	−2.33976
$23$	6.11246e68	1.04462	0.522312	−	0.852754i	$-0.325070\pi$
$23$	6.11246e68	1.04462	0.522312	+	0.852754i	$0.325070\pi$
$24$	0	0
$25$	−3.30565e70	−0.838082
$26$	−5.00284e71	−1.75010
$27$	0	0
$28$	9.91648e72	0.822010
$29$	−7.52088e73	−1.05967	−0.529834	−	0.848101i	$-0.677746\pi$
$29$	−7.52088e73	−1.05967	−0.529834	+	0.848101i	$0.677746\pi$
$30$	0	0
$31$	−1.26748e75	−0.615428	−0.307714	−	0.951479i	$-0.599564\pi$
$31$	−1.26748e75	−0.615428	−0.307714	+	0.951479i	$0.599564\pi$
$32$	−1.44246e76	−1.40939
$33$	0	0
$34$	4.71018e77	2.15453
$35$	−2.51550e77	−0.266187
$36$	0	0
$37$	1.84306e79	1.17856	0.589281	−	0.807928i	$-0.299411\pi$
$37$	1.84306e79	1.17856	0.589281	+	0.807928i	$0.299411\pi$
$38$	−6.05972e79	−1.00781
$39$	0	0
$40$	−1.17212e80	−0.146199
$41$	3.79846e81	1.36152	0.680758	−	0.732508i	$-0.261650\pi$
$41$	3.79846e81	1.36152	0.680758	+	0.732508i	$0.261650\pi$
$42$	0	0
$43$	−1.82567e82	−0.590563	−0.295282	−	0.955410i	$-0.595413\pi$
$43$	−1.82567e82	−0.590563	−0.295282	+	0.955410i	$0.595413\pi$
$44$	−1.91642e83	−1.94147
$45$	0	0
$46$	1.45750e84	1.56436
$47$	1.21503e84	0.440196	0.220098	−	0.975478i	$-0.429362\pi$
$47$	1.21503e84	0.440196	0.220098	+	0.975478i	$0.429362\pi$
$48$	0	0
$49$	−1.27334e85	−0.562397
$50$	−7.88223e85	−1.25506
$51$	0	0
$52$	−6.60984e86	−1.45219
$53$	−1.92092e87	−1.61279	−0.806393	−	0.591380i	$-0.798584\pi$
$53$	−1.92092e87	−1.61279	−0.806393	+	0.591380i	$0.798584\pi$
$54$	0	0
$55$	4.86136e87	0.628697
$56$	4.61670e87	0.240346
$57$	0	0
$58$	−1.79333e89	−1.58689
$59$	9.03706e88	0.337288	0.168644	−	0.985677i	$-0.446061\pi$
$59$	9.03706e88	0.337288	0.168644	+	0.985677i	$0.446061\pi$
$60$	0	0
$61$	−9.82351e89	−0.680942	−0.340471	−	0.940255i	$-0.610586\pi$
$61$	−9.82351e89	−0.680942	−0.340471	+	0.940255i	$0.610586\pi$
$62$	−3.02228e90	−0.921625
$63$	0	0
$64$	−2.30118e91	−1.41209
$65$	1.67671e91	0.470254
$66$	0	0
$67$	1.68394e92	1.02223	0.511116	−	0.859512i	$-0.329232\pi$
$67$	1.68394e92	1.02223	0.511116	+	0.859512i	$0.329232\pi$
$68$	6.22317e92	1.78777
$69$	0	0
$70$	−5.99813e92	−0.398625
$71$	−2.66050e92	−0.0863806	−0.0431903	−	0.999067i	$-0.513752\pi$
$71$	−2.66050e92	−0.0863806	−0.0431903	+	0.999067i	$0.513752\pi$
$72$	0	0
$73$	−1.19661e94	−0.955316	−0.477658	−	0.878546i	$-0.658514\pi$
$73$	−1.19661e94	−0.955316	−0.477658	+	0.878546i	$0.658514\pi$
$74$	4.39473e94	1.76494
$75$	0	0
$76$	−8.00620e94	−0.836258
$77$	−1.91477e95	−1.03356
$78$	0	0
$79$	8.68984e95	1.28482	0.642412	−	0.766360i	$-0.277934\pi$
$79$	8.68984e95	1.28482	0.642412	+	0.766360i	$0.277934\pi$
$80$	3.58816e95	0.281078
$81$	0	0
$82$	9.05733e96	2.03892
$83$	2.05551e96	0.250885	0.125443	−	0.992101i	$-0.459965\pi$
$83$	2.05551e96	0.250885	0.125443	+	0.992101i	$0.459965\pi$
$84$	0	0
$85$	−1.57862e97	−0.578925
$86$	−4.35327e97	−0.884390
$87$	0	0
$88$	−8.92207e97	−0.567663
$89$	4.58460e98	1.64857	0.824283	−	0.566178i	$-0.191579\pi$
$89$	4.58460e98	1.64857	0.824283	+	0.566178i	$0.191579\pi$
$90$	0	0
$91$	−6.60413e98	−0.773082
$92$	1.92567e99	1.29807
$93$	0	0
$94$	2.89721e99	0.659210
$95$	2.03092e99	0.270801
$96$	0	0
$97$	−9.41618e99	−0.438432	−0.219216	−	0.975676i	$-0.570350\pi$
$97$	−9.41618e99	−0.438432	−0.219216	+	0.975676i	$0.570350\pi$
$98$	−3.03625e100	−0.842210
$99$	0	0
$100$	−1.04141e101	−1.04141
$101$	1.91765e101	1.16022	0.580110	−	0.814538i	$-0.303009\pi$
$101$	1.91765e101	1.16022	0.580110	+	0.814538i	$0.303009\pi$
$102$	0	0
$103$	5.30544e101	1.19245	0.596227	−	0.802816i	$-0.296666\pi$
$103$	5.30544e101	1.19245	0.596227	+	0.802816i	$0.296666\pi$
$104$	−3.07727e101	−0.424601
$105$	0	0
$106$	−4.58037e102	−2.41521
$107$	2.09657e102	0.688064	0.344032	−	0.938958i	$-0.388207\pi$
$107$	2.09657e102	0.688064	0.344032	+	0.938958i	$0.388207\pi$
$108$	0	0
$109$	1.37901e101	0.0177636	0.00888179	−	0.999961i	$-0.497173\pi$
$109$	1.37901e101	0.0177636	0.00888179	+	0.999961i	$0.497173\pi$
$110$	1.15918e103	0.941497
$111$	0	0
$112$	−1.41329e103	−0.462083
$113$	−4.37593e102	−0.0913290	−0.0456645	−	0.998957i	$-0.514541\pi$
$113$	−4.37593e102	−0.0913290	−0.0456645	+	0.998957i	$0.514541\pi$
$114$	0	0
$115$	−4.88482e103	−0.420346
$116$	−2.36938e104	−1.31676
$117$	0	0
$118$	2.15486e104	0.505101
$119$	6.21780e104	0.951733
$120$	0	0
$121$	2.18454e105	1.44112
$122$	−2.34239e105	−1.01973
$123$	0	0
$124$	−3.99309e105	−0.764740
$125$	5.79386e105	0.739626
$126$	0	0
$127$	−2.11318e106	−1.21018	−0.605088	−	0.796159i	$-0.706862\pi$
$127$	−2.11318e106	−1.21018	−0.605088	+	0.796159i	$0.706862\pi$
$128$	−1.83002e106	−0.705265
$129$	0	0
$130$	3.99806e106	0.704222
$131$	−1.48036e107	−1.77079	−0.885393	−	0.464842i	$-0.846111\pi$
$131$	−1.48036e107	−1.77079	−0.885393	+	0.464842i	$0.846111\pi$
$132$	0	0
$133$	−7.99929e106	−0.445188
$134$	4.01531e107	1.53083
$135$	0	0
$136$	2.89725e107	0.522722
$137$	1.25472e108	1.56372	0.781859	−	0.623455i	$-0.214272\pi$
$137$	1.25472e108	1.56372	0.781859	+	0.623455i	$0.214272\pi$
$138$	0	0
$139$	−1.05964e108	−0.635199	−0.317599	−	0.948225i	$-0.602877\pi$
$139$	−1.05964e108	−0.635199	−0.317599	+	0.948225i	$0.602877\pi$
$140$	−7.92483e107	−0.330769
$141$	0	0
$142$	−6.34388e107	−0.129358
$143$	1.27629e109	1.82591
$144$	0	0
$145$	6.01037e108	0.426400
$146$	−2.85327e109	−1.43062
$147$	0	0
$148$	5.80639e109	1.46450
$149$	8.73079e109	1.56728	0.783641	−	0.621214i	$-0.213360\pi$
$149$	8.73079e109	1.56728	0.783641	+	0.621214i	$0.213360\pi$
$150$	0	0
$151$	1.82348e110	1.66942	0.834708	−	0.550693i	$-0.185637\pi$
$151$	1.82348e110	1.66942	0.834708	+	0.550693i	$0.185637\pi$
$152$	−3.72735e109	−0.244512
$153$	0	0
$154$	−4.56571e110	−1.54779
$155$	1.01292e110	0.247642
$156$	0	0
$157$	6.49484e110	0.831067	0.415533	−	0.909578i	$-0.363595\pi$
$157$	6.49484e110	0.831067	0.415533	+	0.909578i	$0.363595\pi$
$158$	2.07207e111	1.92407
$159$	0	0
$160$	1.15275e111	0.567124
$161$	1.92401e111	0.691036
$162$	0	0
$163$	−2.38327e111	−0.458880	−0.229440	−	0.973323i	$-0.573689\pi$
$163$	−2.38327e111	−0.458880	−0.229440	+	0.973323i	$0.573689\pi$
$164$	1.19667e112	1.69184
$165$	0	0
$166$	4.90130e111	0.375710
$167$	−1.51500e112	−0.857491	−0.428746	−	0.903425i	$-0.641044\pi$
$167$	−1.51500e112	−0.857491	−0.428746	+	0.903425i	$0.641044\pi$
$168$	0	0
$169$	1.17885e112	0.365747
$170$	−3.76418e112	−0.866961
$171$	0	0
$172$	−5.75162e112	−0.733843
$173$	−8.48260e110	−0.00807609	−0.00403804	−	0.999992i	$-0.501285\pi$
$173$	−8.48260e110	−0.00807609	−0.00403804	+	0.999992i	$0.501285\pi$
$174$	0	0
$175$	−1.04052e113	−0.554405
$176$	2.73127e113	1.09138
$177$	0	0
$178$	1.09319e114	2.46879
$179$	−7.70832e113	−1.31184	−0.655921	−	0.754829i	$-0.727720\pi$
$179$	−7.70832e113	−1.31184	−0.655921	+	0.754829i	$0.727720\pi$
$180$	0	0
$181$	−9.10499e113	−0.884121	−0.442060	−	0.896985i	$-0.645752\pi$
$181$	−9.10499e113	−0.884121	−0.442060	+	0.896985i	$0.645752\pi$
$182$	−1.57474e114	−1.15772
$183$	0	0
$184$	8.96512e113	0.379539
$185$	−1.47290e114	−0.474242
$186$	0	0
$187$	−1.20163e115	−2.24786
$188$	3.82785e114	0.546995
$189$	0	0
$190$	4.84267e114	0.405535
$191$	−1.29493e115	−0.831879	−0.415939	−	0.909392i	$-0.636547\pi$
$191$	−1.29493e115	−0.831879	−0.415939	+	0.909392i	$0.636547\pi$
$192$	0	0
$193$	2.90903e115	1.10434	0.552171	−	0.833731i	$-0.313799\pi$
$193$	2.90903e115	1.10434	0.552171	+	0.833731i	$0.313799\pi$
$194$	−2.24526e115	−0.656568
$195$	0	0
$196$	−4.01154e115	−0.698843
$197$	−1.44395e115	−0.194539	−0.0972697	−	0.995258i	$-0.531011\pi$
$197$	−1.44395e115	−0.194539	−0.0972697	+	0.995258i	$0.531011\pi$
$198$	0	0
$199$	1.20582e116	0.975440	0.487720	−	0.873000i	$-0.337829\pi$
$199$	1.20582e116	0.975440	0.487720	+	0.873000i	$0.337829\pi$
$200$	−4.84839e115	−0.304497
$201$	0	0
$202$	4.57259e116	1.73747
$203$	−2.36734e116	−0.700987
$204$	0	0
$205$	−3.03557e116	−0.547861
$206$	1.26507e117	1.78574
$207$	0	0
$208$	9.42028e116	0.816329
$209$	1.54591e117	1.05147
$210$	0	0
$211$	−3.28579e116	−0.138158	−0.0690789	−	0.997611i	$-0.522006\pi$
$211$	−3.28579e116	−0.138158	−0.0690789	+	0.997611i	$0.522006\pi$
$212$	−6.05166e117	−2.00407
$213$	0	0
$214$	4.99922e117	1.03040
$215$	1.45900e117	0.237637
$216$	0	0
$217$	−3.98964e117	−0.407115
$218$	3.28822e116	0.0266016
$219$	0	0
$220$	1.53152e118	0.781229
$221$	−4.14448e118	−1.68136
$222$	0	0
$223$	−7.08484e117	−0.182362	−0.0911810	−	0.995834i	$-0.529064\pi$
$223$	−7.08484e117	−0.182362	−0.0911810	+	0.995834i	$0.529064\pi$
$224$	−4.54042e118	−0.932333
$225$	0	0
$226$	−1.04343e118	−0.136769
$227$	7.11138e118	0.745844	0.372922	−	0.927863i	$-0.378356\pi$
$227$	7.11138e118	0.745844	0.372922	+	0.927863i	$0.378356\pi$
$228$	0	0
$229$	−7.22725e118	−0.486722	−0.243361	−	0.969936i	$-0.578250\pi$
$229$	−7.22725e118	−0.486722	−0.243361	+	0.969936i	$0.578250\pi$
$230$	−1.16477e119	−0.629484
$231$	0	0
$232$	−1.10309e119	−0.385005
$233$	−1.44195e119	−0.405020	−0.202510	−	0.979280i	$-0.564910\pi$
$233$	−1.44195e119	−0.405020	−0.202510	+	0.979280i	$0.564910\pi$
$234$	0	0
$235$	−9.71003e118	−0.177131
$236$	2.84704e119	0.419119
$237$	0	0
$238$	1.48262e120	1.42526
$239$	7.34680e119	0.571484	0.285742	−	0.958307i	$-0.407760\pi$
$239$	7.34680e119	0.571484	0.285742	+	0.958307i	$0.407760\pi$
$240$	0	0
$241$	−1.91398e120	−0.977411	−0.488706	−	0.872449i	$-0.662531\pi$
$241$	−1.91398e120	−0.977411	−0.488706	+	0.872449i	$0.662531\pi$
$242$	5.20899e120	2.15813
$243$	0	0
$244$	−3.09480e120	−0.846149
$245$	1.01760e120	0.226303
$246$	0	0
$247$	5.33193e120	0.786482
$248$	−1.85902e120	−0.223601
$249$	0	0
$250$	1.38153e121	1.10762
$251$	1.31699e121	0.863098	0.431549	−	0.902089i	$-0.357967\pi$
$251$	1.31699e121	0.863098	0.431549	+	0.902089i	$0.357967\pi$
$252$	0	0
$253$	−3.71827e121	−1.63213
$254$	−5.03881e121	−1.81228
$255$	0	0
$256$	1.47055e121	0.355928
$257$	3.41822e121	0.679480	0.339740	−	0.940519i	$-0.389661\pi$
$257$	3.41822e121	0.679480	0.339740	+	0.940519i	$0.389661\pi$
$258$	0	0
$259$	5.80137e121	0.779638
$260$	5.28230e121	0.584345
$261$	0	0
$262$	−3.52987e122	−2.65182
$263$	−4.70322e121	−0.291494	−0.145747	−	0.989322i	$-0.546559\pi$
$263$	−4.70322e121	−0.291494	−0.145747	+	0.989322i	$0.546559\pi$
$264$	0	0
$265$	1.53511e122	0.648969
$266$	−1.90741e122	−0.666686
$267$	0	0
$268$	5.30509e122	1.27024
$269$	−3.47750e121	−0.0689886	−0.0344943	−	0.999405i	$-0.510982\pi$
$269$	−3.47750e121	−0.0689886	−0.0344943	+	0.999405i	$0.510982\pi$
$270$	0	0
$271$	8.93405e122	1.21927	0.609634	−	0.792683i	$-0.291317\pi$
$271$	8.93405e122	1.21927	0.609634	+	0.792683i	$0.291317\pi$
$272$	−8.86921e122	−1.00497
$273$	0	0
$274$	2.99185e123	2.34173
$275$	2.01086e123	1.30943
$276$	0	0
$277$	−2.61374e123	−1.18042	−0.590208	−	0.807252i	$-0.700954\pi$
$277$	−2.61374e123	−1.18042	−0.590208	+	0.807252i	$0.700954\pi$
$278$	−2.52667e123	−0.951233
$279$	0	0
$280$	−3.68947e122	−0.0967127
$281$	7.67814e123	1.68108	0.840538	−	0.541753i	$-0.182239\pi$
$281$	7.67814e123	1.68108	0.840538	+	0.541753i	$0.182239\pi$
$282$	0	0
$283$	−3.67598e123	−0.562546	−0.281273	−	0.959628i	$-0.590757\pi$
$283$	−3.67598e123	−0.562546	−0.281273	+	0.959628i	$0.590757\pi$
$284$	−8.38165e122	−0.107338
$285$	0	0
$286$	3.04328e124	2.73437
$287$	1.19564e124	0.900665
$288$	0	0
$289$	2.01690e124	1.06990
$290$	1.43316e124	0.638549
$291$	0	0
$292$	−3.76980e124	−1.18709
$293$	−1.82743e124	−0.484201	−0.242100	−	0.970251i	$-0.577836\pi$
$293$	−1.82743e124	−0.484201	−0.242100	+	0.970251i	$0.577836\pi$
$294$	0	0
$295$	−7.22204e123	−0.135721
$296$	2.70321e124	0.428202
$297$	0	0
$298$	2.08183e125	2.34706
$299$	−1.28245e125	−1.22080
$300$	0	0
$301$	−5.74665e124	−0.390667
$302$	4.34803e125	2.50001
$303$	0	0
$304$	1.14104e125	0.470093
$305$	7.85053e124	0.274004
$306$	0	0
$307$	4.99534e125	1.25336	0.626681	−	0.779276i	$-0.284413\pi$
$307$	4.99534e125	1.25336	0.626681	+	0.779276i	$0.284413\pi$
$308$	−6.03230e125	−1.28431
$309$	0	0
$310$	2.41528e125	0.370853
$311$	1.21415e126	1.58443	0.792215	−	0.610243i	$-0.208928\pi$
$311$	1.21415e126	1.58443	0.792215	+	0.610243i	$0.208928\pi$
$312$	0	0
$313$	4.93941e125	0.466322	0.233161	−	0.972438i	$-0.425093\pi$
$313$	4.93941e125	0.466322	0.233161	+	0.972438i	$0.425093\pi$
$314$	1.54868e126	1.24455
$315$	0	0
$316$	2.73765e126	1.59654
$317$	3.07972e126	1.53115	0.765576	−	0.643346i	$-0.222454\pi$
$317$	3.07972e126	1.53115	0.765576	+	0.643346i	$0.222454\pi$
$318$	0	0
$319$	4.57503e126	1.65563
$320$	1.83900e126	0.568210
$321$	0	0
$322$	4.58775e126	1.03485
$323$	−5.02002e126	−0.968230
$324$	0	0
$325$	6.93556e126	0.979427
$326$	−5.68283e126	−0.687189
$327$	0	0
$328$	5.57119e126	0.494674
$329$	3.82454e126	0.291197
$330$	0	0
$331$	2.91257e127	1.63291	0.816456	−	0.577407i	$-0.195936\pi$
$331$	2.91257e127	1.63291	0.816456	+	0.577407i	$0.195936\pi$
$332$	6.47568e126	0.311754
$333$	0	0
$334$	−3.61247e127	−1.28412
$335$	−1.34573e127	−0.411336
$336$	0	0
$337$	7.69384e127	1.74114	0.870568	−	0.492047i	$-0.163751\pi$
$337$	7.69384e127	1.74114	0.870568	+	0.492047i	$0.163751\pi$
$338$	2.81094e127	0.547720
$339$	0	0
$340$	−4.97329e127	−0.719381
$341$	7.71024e127	0.961549
$342$	0	0
$343$	−1.11349e128	−1.03355
$344$	−2.67771e127	−0.214567
$345$	0	0
$346$	−2.02265e126	−0.0120942
$347$	−5.05616e127	−0.261326	−0.130663	−	0.991427i	$-0.541711\pi$
$347$	−5.05616e127	−0.261326	−0.130663	+	0.991427i	$0.541711\pi$
$348$	0	0
$349$	−3.51214e128	−1.35796	−0.678981	−	0.734156i	$-0.737578\pi$
$349$	−3.51214e128	−1.35796	−0.678981	+	0.734156i	$0.737578\pi$
$350$	−2.48108e128	−0.830241
$351$	0	0
$352$	8.77464e128	2.20204
$353$	5.20749e127	0.113242	0.0566208	−	0.998396i	$-0.481967\pi$
$353$	5.20749e127	0.113242	0.0566208	+	0.998396i	$0.481967\pi$
$354$	0	0
$355$	2.12616e127	0.0347587
$356$	1.44433e129	2.04853
$357$	0	0
$358$	−1.83803e129	−1.96453
$359$	−1.83400e128	−0.170267	−0.0851336	−	0.996370i	$-0.527132\pi$
$359$	−1.83400e128	−0.170267	−0.0851336	+	0.996370i	$0.527132\pi$
$360$	0	0
$361$	−7.80148e128	−0.547095
$362$	−2.17106e129	−1.32400
$363$	0	0
$364$	−2.08057e129	−0.960643
$365$	9.56277e128	0.384409
$366$	0	0
$367$	−2.13701e129	−0.651884	−0.325942	−	0.945390i	$-0.605681\pi$
$367$	−2.13701e129	−0.651884	−0.325942	+	0.945390i	$0.605681\pi$
$368$	−2.74445e129	−0.729693
$369$	0	0
$370$	−3.51208e129	−0.710194
$371$	−6.04644e129	−1.06688
$372$	0	0
$373$	−6.00257e129	−0.807311	−0.403656	−	0.914911i	$-0.632261\pi$
$373$	−6.00257e129	−0.807311	−0.403656	+	0.914911i	$0.632261\pi$
$374$	−2.86525e130	−3.36625
$375$	0	0
$376$	1.78209e129	0.159935
$377$	1.57795e130	1.23838
$378$	0	0
$379$	1.67101e129	0.100392	0.0501959	−	0.998739i	$-0.484015\pi$
$379$	1.67101e129	0.100392	0.0501959	+	0.998739i	$0.484015\pi$
$380$	6.39822e129	0.336502
$381$	0	0
$382$	−3.08772e130	−1.24577
$383$	−4.14692e130	−1.46618	−0.733091	−	0.680131i	$-0.761923\pi$
$383$	−4.14692e130	−1.46618	−0.733091	+	0.680131i	$0.761923\pi$
$384$	0	0
$385$	1.53020e130	0.415893
$386$	6.93649e130	1.65379
$387$	0	0
$388$	−2.96648e130	−0.544802
$389$	6.92348e130	1.11653	0.558264	−	0.829663i	$-0.311468\pi$
$389$	6.92348e130	1.11653	0.558264	+	0.829663i	$0.311468\pi$
$390$	0	0
$391$	1.20743e131	1.50292
$392$	−1.86761e130	−0.204333
$393$	0	0
$394$	−3.44306e130	−0.291330
$395$	−6.94455e130	−0.517000
$396$	0	0
$397$	−8.86213e130	−0.511231	−0.255616	−	0.966778i	$-0.582278\pi$
$397$	−8.86213e130	−0.511231	−0.255616	+	0.966778i	$0.582278\pi$
$398$	2.87523e131	1.46076
$399$	0	0
$400$	1.48421e131	0.585419
$401$	6.21084e129	0.0215953	0.0107977	−	0.999942i	$-0.496563\pi$
$401$	6.21084e129	0.0215953	0.0107977	+	0.999942i	$0.496563\pi$
$402$	0	0
$403$	2.65930e131	0.719221
$404$	6.04138e131	1.44171
$405$	0	0
$406$	−5.64485e131	−1.04975
$407$	−1.12115e132	−1.84140
$408$	0	0
$409$	1.03956e132	1.33297	0.666487	−	0.745517i	$-0.267797\pi$
$409$	1.03956e132	1.33297	0.666487	+	0.745517i	$0.267797\pi$
$410$	−7.23823e131	−0.820441
$411$	0	0
$412$	1.67143e132	1.48176
$413$	2.84458e131	0.223121
$414$	0	0
$415$	−1.64267e131	−0.100954
$416$	3.02642e132	1.64708
$417$	0	0
$418$	3.68619e132	1.57462
$419$	1.38531e132	0.524491	0.262246	−	0.965001i	$-0.415537\pi$
$419$	1.38531e132	0.524491	0.262246	+	0.965001i	$0.415537\pi$
$420$	0	0
$421$	1.31976e132	0.392869	0.196435	−	0.980517i	$-0.437064\pi$
$421$	1.31976e132	0.392869	0.196435	+	0.980517i	$0.437064\pi$
$422$	−7.83486e131	−0.206896
$423$	0	0
$424$	−2.81740e132	−0.585967
$425$	−6.52984e132	−1.20576
$426$	0	0
$427$	−3.09213e132	−0.450454
$428$	6.60505e132	0.855000
$429$	0	0
$430$	3.47895e132	0.355870
$431$	1.47645e133	1.34313	0.671564	−	0.740946i	$-0.265623\pi$
$431$	1.47645e133	1.34313	0.671564	+	0.740946i	$0.265623\pi$
$432$	0	0
$433$	2.39695e133	1.72592	0.862958	−	0.505276i	$-0.168609\pi$
$433$	2.39695e133	1.72592	0.862958	+	0.505276i	$0.168609\pi$
$434$	−9.51319e132	−0.609670
$435$	0	0
$436$	4.34445e131	0.0220733
$437$	−1.55337e133	−0.703013
$438$	0	0
$439$	−1.80750e133	−0.649563	−0.324781	−	0.945789i	$-0.605291\pi$
$439$	−1.80750e133	−0.649563	−0.324781	+	0.945789i	$0.605291\pi$
$440$	7.13014e132	0.228422
$441$	0	0
$442$	−9.88239e133	−2.51789
$443$	−5.76910e133	−1.31135	−0.655677	−	0.755041i	$-0.727617\pi$
$443$	−5.76910e133	−1.31135	−0.655677	+	0.755041i	$0.727617\pi$
$444$	0	0
$445$	−3.66382e133	−0.663366
$446$	−1.68936e133	−0.273094
$447$	0	0
$448$	−7.24339e133	−0.934119
$449$	1.99115e133	0.229437	0.114718	−	0.993398i	$-0.463403\pi$
$449$	1.99115e133	0.229437	0.114718	+	0.993398i	$0.463403\pi$
$450$	0	0
$451$	−2.31064e134	−2.12724
$452$	−1.37859e133	−0.113487
$453$	0	0
$454$	1.69569e134	1.11693
$455$	5.27774e133	0.311080
$456$	0	0
$457$	3.63995e133	0.171921	0.0859603	−	0.996299i	$-0.472604\pi$
$457$	3.63995e133	0.171921	0.0859603	+	0.996299i	$0.472604\pi$
$458$	−1.72332e134	−0.728884
$459$	0	0
$460$	−1.53891e134	−0.522329
$461$	−7.99190e133	−0.243082	−0.121541	−	0.992586i	$-0.538784\pi$
$461$	−7.99190e133	−0.243082	−0.121541	+	0.992586i	$0.538784\pi$
$462$	0	0
$463$	3.09340e134	0.756129	0.378064	−	0.925779i	$-0.376590\pi$
$463$	3.09340e134	0.756129	0.378064	+	0.925779i	$0.376590\pi$
$464$	3.37682e134	0.740202
$465$	0	0
$466$	−3.43829e134	−0.606532
$467$	−6.56173e134	−1.03876	−0.519381	−	0.854543i	$-0.673837\pi$
$467$	−6.56173e134	−1.03876	−0.519381	+	0.854543i	$0.673837\pi$
$468$	0	0
$469$	5.30051e134	0.676222
$470$	−2.31533e134	−0.265259
$471$	0	0
$472$	1.32546e134	0.122545
$473$	1.11058e135	0.922701
$474$	0	0
$475$	8.40074e134	0.564014
$476$	1.95886e135	1.18264
$477$	0	0
$478$	1.75182e135	0.855819
$479$	7.37311e134	0.324121	0.162061	−	0.986781i	$-0.448186\pi$
$479$	7.37311e134	0.324121	0.162061	+	0.986781i	$0.448186\pi$
$480$	0	0
$481$	−3.86691e135	−1.37733
$482$	−4.56384e135	−1.46371
$483$	0	0
$484$	6.88220e135	1.79076
$485$	7.52501e134	0.176421
$486$	0	0
$487$	6.08383e135	1.15868	0.579341	−	0.815085i	$-0.303310\pi$
$487$	6.08383e135	1.15868	0.579341	+	0.815085i	$0.303310\pi$
$488$	−1.44081e135	−0.247404
$489$	0	0
$490$	2.42644e135	0.338897
$491$	4.22617e135	0.532514	0.266257	−	0.963902i	$-0.414213\pi$
$491$	4.22617e135	0.532514	0.266257	+	0.963902i	$0.414213\pi$
$492$	0	0
$493$	−1.48564e136	−1.52456
$494$	1.27138e136	1.17778
$495$	0	0
$496$	5.69091e135	0.429890
$497$	−8.37441e134	−0.0571422
$498$	0	0
$499$	1.79965e136	1.00256	0.501279	−	0.865286i	$-0.332863\pi$
$499$	1.79965e136	1.00256	0.501279	+	0.865286i	$0.332863\pi$
$500$	1.82530e136	0.919071
$501$	0	0
$502$	3.14033e136	1.29252
$503$	3.61622e136	1.34608	0.673041	−	0.739605i	$-0.264988\pi$
$503$	3.61622e136	1.34608	0.673041	+	0.739605i	$0.264988\pi$
$504$	0	0
$505$	−1.53251e136	−0.466861
$506$	−8.86611e136	−2.44417
$507$	0	0
$508$	−6.65737e136	−1.50378
$509$	3.70155e135	0.0757069	0.0378535	−	0.999283i	$-0.487948\pi$
$509$	3.70155e135	0.0757069	0.0378535	+	0.999283i	$0.487948\pi$
$510$	0	0
$511$	−3.76654e136	−0.631957
$512$	8.14614e136	1.23828
$513$	0	0
$514$	8.15064e136	1.01755
$515$	−4.23989e136	−0.479832
$516$	0	0
$517$	−7.39117e136	−0.687766
$518$	1.38332e137	1.16754
$519$	0	0
$520$	2.45922e136	0.170855
$521$	−1.29061e137	−0.813746	−0.406873	−	0.913485i	$-0.633381\pi$
$521$	−1.29061e137	−0.813746	−0.406873	+	0.913485i	$0.633381\pi$
$522$	0	0
$523$	−1.43042e137	−0.743240	−0.371620	−	0.928385i	$-0.621198\pi$
$523$	−1.43042e137	−0.743240	−0.371620	+	0.928385i	$0.621198\pi$
$524$	−4.66373e137	−2.20041
$525$	0	0
$526$	−1.12147e137	−0.436523
$527$	−2.50373e137	−0.885425
$528$	0	0
$529$	3.12389e136	0.0912399
$530$	3.66044e137	0.971855
$531$	0	0
$532$	−2.52010e137	−0.553198
$533$	−7.96952e137	−1.59114
$534$	0	0
$535$	−1.67549e137	−0.276870
$536$	2.46983e137	0.371403
$537$	0	0
$538$	−8.29201e136	−0.103313
$539$	7.74587e137	0.878693
$540$	0	0
$541$	4.27854e136	0.0402563	0.0201282	−	0.999797i	$-0.493593\pi$
$541$	4.27854e136	0.0402563	0.0201282	+	0.999797i	$0.493593\pi$
$542$	2.13030e138	1.82590
$543$	0	0
$544$	−2.84938e138	−2.02771
$545$	−1.10205e136	−0.00714789
$546$	0	0
$547$	2.81194e138	1.51582	0.757908	−	0.652361i	$-0.226221\pi$
$547$	2.81194e138	1.51582	0.757908	+	0.652361i	$0.226221\pi$
$548$	3.95288e138	1.94310
$549$	0	0
$550$	4.79484e138	1.96091
$551$	1.91130e138	0.713137
$552$	0	0
$553$	2.73529e138	0.849931
$554$	−6.23240e138	−1.76771
$555$	0	0
$556$	−3.33828e138	−0.789308
$557$	4.55257e138	0.983036	0.491518	−	0.870867i	$-0.336442\pi$
$557$	4.55257e138	0.983036	0.491518	+	0.870867i	$0.336442\pi$
$558$	0	0
$559$	3.83043e138	0.690163
$560$	1.12944e138	0.185938
$561$	0	0
$562$	1.83083e139	2.51747
$563$	1.09186e139	1.37243	0.686217	−	0.727397i	$-0.259270\pi$
$563$	1.09186e139	1.37243	0.686217	+	0.727397i	$0.259270\pi$
$564$	0	0
$565$	3.49705e137	0.0367499
$566$	−8.76527e138	−0.842433
$567$	0	0
$568$	−3.90215e137	−0.0313843
$569$	−1.38183e139	−1.01692	−0.508460	−	0.861086i	$-0.669785\pi$
$569$	−1.38183e139	−1.01692	−0.508460	+	0.861086i	$0.669785\pi$
$570$	0	0
$571$	−1.25037e139	−0.770750	−0.385375	−	0.922760i	$-0.625928\pi$
$571$	−1.25037e139	−0.770750	−0.385375	+	0.922760i	$0.625928\pi$
$572$	4.02083e139	2.26891
$573$	0	0
$574$	2.85096e139	1.34878
$575$	−2.02057e139	−0.875481
$576$	0	0
$577$	−4.89173e139	−1.77862	−0.889312	−	0.457301i	$-0.848816\pi$
$577$	−4.89173e139	−1.77862	−0.889312	+	0.457301i	$0.848816\pi$
$578$	4.80925e139	1.60222
$579$	0	0
$580$	1.89351e139	0.529851
$581$	6.47009e138	0.165965
$582$	0	0
$583$	1.16851e140	2.51983
$584$	−1.75506e139	−0.347091
$585$	0	0
$586$	−4.35745e139	−0.725109
$587$	3.73373e139	0.570057	0.285029	−	0.958519i	$-0.407997\pi$
$587$	3.73373e139	0.570057	0.285029	+	0.958519i	$0.407997\pi$
$588$	0	0
$589$	3.22109e139	0.414172
$590$	−1.72207e139	−0.203248
$591$	0	0
$592$	−8.27521e139	−0.823252
$593$	8.44292e139	0.771313	0.385656	−	0.922642i	$-0.373975\pi$
$593$	8.44292e139	0.771313	0.385656	+	0.922642i	$0.373975\pi$
$594$	0	0
$595$	−4.96900e139	−0.382968
$596$	2.75055e140	1.94753
$597$	0	0
$598$	−3.05797e140	−1.82820
$599$	1.37418e140	0.755074	0.377537	−	0.925995i	$-0.376771\pi$
$599$	1.37418e140	0.755074	0.377537	+	0.925995i	$0.376771\pi$
$600$	0	0
$601$	−2.04647e140	−0.950264	−0.475132	−	0.879914i	$-0.657600\pi$
$601$	−2.04647e140	−0.950264	−0.475132	+	0.879914i	$0.657600\pi$
$602$	−1.37027e140	−0.585038
$603$	0	0
$604$	5.74469e140	2.07444
$605$	−1.74580e140	−0.579892
$606$	0	0
$607$	−1.81132e140	−0.509292	−0.254646	−	0.967034i	$-0.581959\pi$
$607$	−1.81132e140	−0.509292	−0.254646	+	0.967034i	$0.581959\pi$
$608$	3.66577e140	0.948493
$609$	0	0
$610$	1.87194e140	0.410331
$611$	−2.54925e140	−0.514436
$612$	0	0
$613$	−5.22003e139	−0.0893139	−0.0446570	−	0.999002i	$-0.514219\pi$
$613$	−5.22003e139	−0.0893139	−0.0446570	+	0.999002i	$0.514219\pi$
$614$	1.19112e141	1.87696
$615$	0	0
$616$	−2.80839e140	−0.375518
$617$	−4.53230e140	−0.558365	−0.279182	−	0.960238i	$-0.590063\pi$
$617$	−4.53230e140	−0.558365	−0.279182	+	0.960238i	$0.590063\pi$
$618$	0	0
$619$	4.58319e140	0.479502	0.239751	−	0.970834i	$-0.422934\pi$
$619$	4.58319e140	0.479502	0.239751	+	0.970834i	$0.422934\pi$
$620$	3.19111e140	0.307724
$621$	0	0
$622$	2.89511e141	2.37274
$623$	1.44309e141	1.09055
$624$	0	0
$625$	8.40829e140	0.540464
$626$	1.17779e141	0.698334
$627$	0	0
$628$	2.04614e141	1.03270
$629$	3.64070e141	1.69562
$630$	0	0
$631$	1.90514e140	0.0755866	0.0377933	−	0.999286i	$-0.487967\pi$
$631$	1.90514e140	0.0755866	0.0377933	+	0.999286i	$0.487967\pi$
$632$	1.27454e141	0.466809
$633$	0	0
$634$	7.34350e141	2.29296
$635$	1.68876e141	0.486962
$636$	0	0
$637$	2.67159e141	0.657246
$638$	1.09090e142	2.47937
$639$	0	0
$640$	1.46247e141	0.283792
$641$	2.72348e141	0.488421	0.244210	−	0.969722i	$-0.421471\pi$
$641$	2.72348e141	0.488421	0.244210	+	0.969722i	$0.421471\pi$
$642$	0	0
$643$	5.31375e141	0.814230	0.407115	−	0.913377i	$-0.366535\pi$
$643$	5.31375e141	0.814230	0.407115	+	0.913377i	$0.366535\pi$
$644$	6.06141e141	0.858691
$645$	0	0
$646$	−1.19701e142	−1.44996
$647$	−6.34797e140	−0.0711162	−0.0355581	−	0.999368i	$-0.511321\pi$
$647$	−6.34797e140	−0.0711162	−0.0355581	+	0.999368i	$0.511321\pi$
$648$	0	0
$649$	−5.49734e141	−0.526981
$650$	1.65377e142	1.46673
$651$	0	0
$652$	−7.50826e141	−0.570211
$653$	−1.11233e142	−0.781837	−0.390919	−	0.920425i	$-0.627843\pi$
$653$	−1.11233e142	−0.781837	−0.390919	+	0.920425i	$0.627843\pi$
$654$	0	0
$655$	1.18304e142	0.712547
$656$	−1.70548e142	−0.951050
$657$	0	0
$658$	9.11951e141	0.436078
$659$	−2.40144e142	−1.06355	−0.531776	−	0.846885i	$-0.678475\pi$
$659$	−2.40144e142	−1.06355	−0.531776	+	0.846885i	$0.678475\pi$
$660$	0	0
$661$	2.18550e142	0.830571	0.415285	−	0.909691i	$-0.363682\pi$
$661$	2.18550e142	0.830571	0.415285	+	0.909691i	$0.363682\pi$
$662$	6.94494e142	2.44535
$663$	0	0
$664$	3.01481e141	0.0911531
$665$	6.39269e141	0.179139
$666$	0	0
$667$	−4.59711e142	−1.10695
$668$	−4.77285e142	−1.06553
$669$	0	0
$670$	−3.20886e142	−0.615990
$671$	5.97574e142	1.06391
$672$	0	0
$673$	−3.76621e142	−0.576958	−0.288479	−	0.957486i	$-0.593150\pi$
$673$	−3.76621e142	−0.576958	−0.288479	+	0.957486i	$0.593150\pi$
$674$	1.83457e143	2.60742
$675$	0	0
$676$	3.71387e142	0.454483
$677$	−9.42279e142	−1.07017	−0.535084	−	0.844799i	$-0.679720\pi$
$677$	−9.42279e142	−1.07017	−0.535084	+	0.844799i	$0.679720\pi$
$678$	0	0
$679$	−2.96392e142	−0.290030
$680$	−2.31536e142	−0.210338
$681$	0	0
$682$	1.83848e143	1.43995
$683$	−1.77484e143	−1.29096	−0.645481	−	0.763777i	$-0.723343\pi$
$683$	−1.77484e143	−1.29096	−0.645481	+	0.763777i	$0.723343\pi$
$684$	0	0
$685$	−1.00272e143	−0.629225
$686$	−2.65508e143	−1.54778
$687$	0	0
$688$	8.19715e142	0.412522
$689$	4.03026e143	1.88479
$690$	0	0
$691$	−2.13672e143	−0.863190	−0.431595	−	0.902068i	$-0.642049\pi$
$691$	−2.13672e143	−0.863190	−0.431595	+	0.902068i	$0.642049\pi$
$692$	−2.67236e141	−0.0100355
$693$	0	0
$694$	−1.20563e143	−0.391345
$695$	8.46817e142	0.255598
$696$	0	0
$697$	7.50332e143	1.95884
$698$	−8.37459e143	−2.03360
$699$	0	0
$700$	−3.27804e143	−0.688912
$701$	1.00021e143	0.195582	0.0977912	−	0.995207i	$-0.468822\pi$
$701$	1.00021e143	0.195582	0.0977912	+	0.995207i	$0.468822\pi$
$702$	0	0
$703$	−4.68382e143	−0.793151
$704$	1.39983e144	2.20626
$705$	0	0
$706$	1.24171e143	0.169583
$707$	6.03617e143	0.767504
$708$	0	0
$709$	1.19635e144	1.31893	0.659466	−	0.751735i	$-0.270783\pi$
$709$	1.19635e144	1.31893	0.659466	+	0.751735i	$0.270783\pi$
$710$	5.06976e142	0.0520524
$711$	0	0
$712$	6.72422e143	0.598966
$713$	−7.74744e143	−0.642891
$714$	0	0
$715$	−1.01996e144	−0.734728
$716$	−2.42843e144	−1.63012
$717$	0	0
$718$	−4.37313e143	−0.254981
$719$	−6.63155e143	−0.360418	−0.180209	−	0.983628i	$-0.557677\pi$
$719$	−6.63155e143	−0.360418	−0.180209	+	0.983628i	$0.557677\pi$
$720$	0	0
$721$	1.66999e144	0.788828
$722$	−1.86024e144	−0.819295
$723$	0	0
$724$	−2.86844e144	−1.09862
$725$	2.48614e144	0.888089
$726$	0	0
$727$	2.70060e144	0.839407	0.419704	−	0.907661i	$-0.362134\pi$
$727$	2.70060e144	0.839407	0.419704	+	0.907661i	$0.362134\pi$
$728$	−9.68626e143	−0.280880
$729$	0	0
$730$	2.28022e144	0.575667
$731$	−3.60636e144	−0.849653
$732$	0	0
$733$	−7.92252e144	−1.62597	−0.812985	−	0.582284i	$-0.802159\pi$
$733$	−7.92252e144	−1.62597	−0.812985	+	0.582284i	$0.802159\pi$
$734$	−5.09564e144	−0.976220
$735$	0	0
$736$	−8.81699e144	−1.47228
$737$	−1.02436e145	−1.59714
$738$	0	0
$739$	4.09564e144	0.556900	0.278450	−	0.960451i	$-0.410179\pi$
$739$	4.09564e144	0.556900	0.278450	+	0.960451i	$0.410179\pi$
$740$	−4.64022e144	−0.589300
$741$	0	0
$742$	−1.44176e145	−1.59770
$743$	−1.16041e145	−1.20136	−0.600682	−	0.799488i	$-0.705104\pi$
$743$	−1.16041e145	−1.20136	−0.600682	+	0.799488i	$0.705104\pi$
$744$	0	0
$745$	−6.97728e144	−0.630658
$746$	−1.43130e145	−1.20898
$747$	0	0
$748$	−3.78562e145	−2.79323
$749$	6.59935e144	0.455166
$750$	0	0
$751$	1.16350e144	0.0701371	0.0350686	−	0.999385i	$-0.488835\pi$
$751$	1.16350e144	0.0701371	0.0350686	+	0.999385i	$0.488835\pi$
$752$	−5.45541e144	−0.307487
$753$	0	0
$754$	3.76258e145	1.85452
$755$	−1.45725e145	−0.671756
$756$	0	0
$757$	−5.51960e144	−0.222621	−0.111310	−	0.993786i	$-0.535505\pi$
$757$	−5.51960e144	−0.222621	−0.111310	+	0.993786i	$0.535505\pi$
$758$	3.98447e144	0.150340
$759$	0	0
$760$	2.97874e144	0.0983890
$761$	5.40410e145	1.67031	0.835157	−	0.550011i	$-0.185377\pi$
$761$	5.40410e145	1.67031	0.835157	+	0.550011i	$0.185377\pi$
$762$	0	0
$763$	4.34070e143	0.0117509
$764$	−4.07954e145	−1.03371
$765$	0	0
$766$	−9.88822e145	−2.19566
$767$	−1.89606e145	−0.394172
$768$	0	0
$769$	2.96750e145	0.540891	0.270446	−	0.962735i	$-0.412829\pi$
$769$	2.96750e145	0.540891	0.270446	+	0.962735i	$0.412829\pi$
$770$	3.64872e145	0.622815
$771$	0	0
$772$	9.16461e145	1.37227
$773$	−9.98016e144	−0.139982	−0.0699911	−	0.997548i	$-0.522297\pi$
$773$	−9.98016e144	−0.139982	−0.0699911	+	0.997548i	$0.522297\pi$
$774$	0	0
$775$	4.18986e145	0.515779
$776$	−1.38107e145	−0.159294
$777$	0	0
$778$	1.65089e146	1.67204
$779$	−9.65313e145	−0.916276
$780$	0	0
$781$	1.61841e145	0.134962
$782$	2.87908e146	2.25067
$783$	0	0
$784$	5.71721e145	0.392847
$785$	−5.19040e145	−0.334413
$786$	0	0
$787$	−1.20626e146	−0.683465	−0.341732	−	0.939797i	$-0.611014\pi$
$787$	−1.20626e146	−0.683465	−0.341732	+	0.939797i	$0.611014\pi$
$788$	−4.54902e145	−0.241738
$789$	0	0
$790$	−1.65591e146	−0.774227
$791$	−1.37740e145	−0.0604156
$792$	0	0
$793$	2.06106e146	0.795784
$794$	−2.11315e146	−0.765587
$795$	0	0
$796$	3.79881e146	1.21210
$797$	−2.00327e146	−0.599921	−0.299961	−	0.953952i	$-0.596974\pi$
$797$	−2.00327e146	−0.599921	−0.299961	+	0.953952i	$0.596974\pi$
$798$	0	0
$799$	2.40012e146	0.633317
$800$	4.76828e146	1.18118
$801$	0	0
$802$	1.48096e145	0.0323398
$803$	7.27908e146	1.49259
$804$	0	0
$805$	−1.53759e146	−0.278066
$806$	6.34102e146	1.07706
$807$	0	0
$808$	2.81262e146	0.421538
$809$	−2.46422e145	−0.0346960	−0.0173480	−	0.999850i	$-0.505522\pi$
$809$	−2.46422e145	−0.0346960	−0.0173480	+	0.999850i	$0.505522\pi$
$810$	0	0
$811$	−4.96232e146	−0.616781	−0.308391	−	0.951260i	$-0.599790\pi$
$811$	−4.96232e146	−0.616781	−0.308391	+	0.951260i	$0.599790\pi$
$812$	−7.45807e146	−0.871058
$813$	0	0
$814$	−2.67336e147	−2.75756
$815$	1.90461e146	0.184649
$816$	0	0
$817$	4.63963e146	0.397438
$818$	2.47880e147	1.99618
$819$	0	0
$820$	−9.56327e146	−0.680780
$821$	2.07513e147	1.38904	0.694522	−	0.719472i	$-0.255616\pi$
$821$	2.07513e147	1.38904	0.694522	+	0.719472i	$0.255616\pi$
$822$	0	0
$823$	2.08912e147	1.23672	0.618361	−	0.785894i	$-0.287797\pi$
$823$	2.08912e147	1.23672	0.618361	+	0.785894i	$0.287797\pi$
$824$	7.78148e146	0.433249
$825$	0	0
$826$	6.78283e146	0.334132
$827$	−3.48507e147	−1.61504	−0.807521	−	0.589839i	$-0.799191\pi$
$827$	−3.48507e147	−1.61504	−0.807521	+	0.589839i	$0.799191\pi$
$828$	0	0
$829$	−3.30518e147	−1.35579	−0.677894	−	0.735160i	$-0.737107\pi$
$829$	−3.30518e147	−1.35579	−0.677894	+	0.735160i	$0.737107\pi$
$830$	−3.91691e146	−0.151182
$831$	0	0
$832$	4.82809e147	1.65024
$833$	−2.51530e147	−0.809129
$834$	0	0
$835$	1.21072e147	0.345046
$836$	4.87025e147	1.30658
$837$	0	0
$838$	3.30323e147	0.785445
$839$	−4.20113e147	−0.940561	−0.470281	−	0.882517i	$-0.655847\pi$
$839$	−4.20113e147	−0.940561	−0.470281	+	0.882517i	$0.655847\pi$
$840$	0	0
$841$	6.19065e146	0.122896
$842$	3.14692e147	0.588336
$843$	0	0
$844$	−1.03516e147	−0.171677
$845$	−9.42090e146	−0.147173
$846$	0	0
$847$	6.87626e147	0.953323
$848$	8.62477e147	1.12657
$849$	0	0
$850$	−1.55702e148	−1.80567
$851$	1.12656e148	1.23115
$852$	0	0
$853$	1.14274e148	1.10923	0.554614	−	0.832108i	$-0.312866\pi$
$853$	1.14274e148	1.10923	0.554614	+	0.832108i	$0.312866\pi$
$854$	−7.37310e147	−0.674571
$855$	0	0
$856$	3.07504e147	0.249991
$857$	1.25430e148	0.961328	0.480664	−	0.876905i	$-0.340396\pi$
$857$	1.25430e148	0.961328	0.480664	+	0.876905i	$0.340396\pi$
$858$	0	0
$859$	2.03083e148	1.38362	0.691812	−	0.722078i	$-0.256813\pi$
$859$	2.03083e148	1.38362	0.691812	+	0.722078i	$0.256813\pi$
$860$	4.59645e147	0.295291
$861$	0	0
$862$	3.52056e148	2.01138
$863$	−8.95017e147	−0.482266	−0.241133	−	0.970492i	$-0.577519\pi$
$863$	−8.95017e147	−0.482266	−0.241133	+	0.970492i	$0.577519\pi$
$864$	0	0
$865$	6.77894e145	0.00324974
$866$	5.71545e148	2.58462
$867$	0	0
$868$	−1.25690e148	−0.505888
$869$	−5.28612e148	−2.00742
$870$	0	0
$871$	−3.53306e148	−1.19463
$872$	2.02260e146	0.00645397
$873$	0	0
$874$	−3.70398e148	−1.05279
$875$	1.82372e148	0.489274
$876$	0	0
$877$	2.88741e148	0.690285	0.345142	−	0.938550i	$-0.387831\pi$
$877$	2.88741e148	0.690285	0.345142	+	0.938550i	$0.387831\pi$
$878$	−4.30994e148	−0.972744
$879$	0	0
$880$	−2.18271e148	−0.439159
$881$	−6.06187e148	−1.15166	−0.575828	−	0.817571i	$-0.695320\pi$
$881$	−6.06187e148	−1.15166	−0.575828	+	0.817571i	$0.695320\pi$
$882$	0	0
$883$	−1.10147e148	−0.186619	−0.0933097	−	0.995637i	$-0.529745\pi$
$883$	−1.10147e148	−0.186619	−0.0933097	+	0.995637i	$0.529745\pi$
$884$	−1.30568e149	−2.08928
$885$	0	0
$886$	−1.37563e149	−1.96380
$887$	4.72512e148	0.637192	0.318596	−	0.947891i	$-0.396789\pi$
$887$	4.72512e148	0.637192	0.318596	+	0.947891i	$0.396789\pi$
$888$	0	0
$889$	−6.65162e148	−0.800550
$890$	−8.73627e148	−0.993415
$891$	0	0
$892$	−2.23201e148	−0.226606
$893$	−3.08779e148	−0.296244
$894$	0	0
$895$	6.16016e148	0.527872
$896$	−5.76033e148	−0.466544
$897$	0	0
$898$	4.74784e148	0.343590
$899$	9.53260e148	0.652149
$900$	0	0
$901$	−3.79449e149	−2.32034
$902$	−5.50966e149	−3.18563
$903$	0	0
$904$	−6.41816e147	−0.0331822
$905$	7.27632e148	0.355761
$906$	0	0
$907$	1.12427e149	0.491703	0.245852	−	0.969307i	$-0.420932\pi$
$907$	1.12427e149	0.491703	0.245852	+	0.969307i	$0.420932\pi$
$908$	2.24037e149	0.926797
$909$	0	0
$910$	1.25846e149	0.465854
$911$	−4.17428e148	−0.146185	−0.0730926	−	0.997325i	$-0.523287\pi$
$911$	−4.17428e148	−0.146185	−0.0730926	+	0.997325i	$0.523287\pi$
$912$	0	0
$913$	−1.25039e149	−0.391985
$914$	8.67937e148	0.257457
$915$	0	0
$916$	−2.27688e149	−0.604809
$917$	−4.65970e149	−1.17140
$918$	0	0
$919$	8.30867e149	1.87111	0.935553	−	0.353186i	$-0.114902\pi$
$919$	8.30867e149	1.87111	0.935553	+	0.353186i	$0.114902\pi$
$920$	−7.16454e148	−0.152723
$921$	0	0
$922$	−1.90564e149	−0.364024
$923$	5.58197e148	0.100949
$924$	0	0
$925$	−6.09252e149	−0.987732
$926$	7.37612e149	1.13233
$927$	0	0
$928$	1.08486e150	1.49348
$929$	−7.17354e149	−0.935277	−0.467638	−	0.883920i	$-0.654895\pi$
$929$	−7.17354e149	−0.935277	−0.467638	+	0.883920i	$0.654895\pi$
$930$	0	0
$931$	3.23597e149	0.378483
$932$	−4.54272e149	−0.503284
$933$	0	0
$934$	−1.56463e150	−1.55558
$935$	9.60291e149	0.904517
$936$	0	0
$937$	−1.12560e150	−0.951774	−0.475887	−	0.879507i	$-0.657873\pi$
$937$	−1.12560e150	−0.951774	−0.475887	+	0.879507i	$0.657873\pi$
$938$	1.26389e150	1.01267
$939$	0	0
$940$	−3.05905e149	−0.220105
$941$	−8.61109e149	−0.587195	−0.293597	−	0.955929i	$-0.594853\pi$
$941$	−8.61109e149	−0.587195	−0.293597	+	0.955929i	$0.594853\pi$
$942$	0	0
$943$	2.32179e150	1.42227
$944$	−4.05758e149	−0.235603
$945$	0	0
$946$	2.64814e150	1.38178
$947$	1.36513e150	0.675307	0.337654	−	0.941270i	$-0.390367\pi$
$947$	1.36513e150	0.675307	0.337654	+	0.941270i	$0.390367\pi$
$948$	0	0
$949$	2.51059e150	1.11643
$950$	2.00313e150	0.844632
$951$	0	0
$952$	9.11963e149	0.345789
$953$	−4.18075e149	−0.150336	−0.0751680	−	0.997171i	$-0.523949\pi$
$953$	−4.18075e149	−0.150336	−0.0751680	+	0.997171i	$0.523949\pi$
$954$	0	0
$955$	1.03485e150	0.334740
$956$	2.31454e150	0.710135
$957$	0	0
$958$	1.75810e150	0.485383
$959$	3.94947e150	1.03442
$960$	0	0
$961$	−2.63510e150	−0.621249
$962$	−9.22054e150	−2.06260
$963$	0	0
$964$	−6.02982e150	−1.21455
$965$	−2.32477e150	−0.444376
$966$	0	0
$967$	−1.04342e150	−0.179648	−0.0898238	−	0.995958i	$-0.528630\pi$
$967$	−1.04342e150	−0.179648	−0.0898238	+	0.995958i	$0.528630\pi$
$968$	3.20407e150	0.523595
$969$	0	0
$970$	1.79432e150	0.264196
$971$	3.53326e150	0.493861	0.246930	−	0.969033i	$-0.420578\pi$
$971$	3.53326e150	0.493861	0.246930	+	0.969033i	$0.420578\pi$
$972$	0	0
$973$	−3.33540e150	−0.420194
$974$	1.45067e151	1.73517
$975$	0	0
$976$	4.41068e150	0.475653
$977$	1.53694e151	1.57392	0.786960	−	0.617004i	$-0.211654\pi$
$977$	1.53694e151	1.57392	0.786960	+	0.617004i	$0.211654\pi$
$978$	0	0
$979$	−2.78886e151	−2.57573
$980$	3.20585e150	0.281207
$981$	0	0
$982$	1.00772e151	0.797460
$983$	−9.55031e150	−0.717901	−0.358951	−	0.933357i	$-0.616865\pi$
$983$	−9.55031e150	−0.717901	−0.358951	+	0.933357i	$0.616865\pi$
$984$	0	0
$985$	1.15394e150	0.0782807
$986$	−3.54247e151	−2.28309
$987$	0	0
$988$	1.67977e151	0.977294
$989$	−1.11594e151	−0.616917
$990$	0	0
$991$	−5.87889e150	−0.293478	−0.146739	−	0.989175i	$-0.546878\pi$
$991$	−5.87889e150	−0.293478	−0.146739	+	0.989175i	$0.546878\pi$
$992$	1.82830e151	0.867376
$993$	0	0
$994$	−1.99685e150	−0.0855725
$995$	−9.63637e150	−0.392507
$996$	0	0
$997$	−3.59519e150	−0.132317	−0.0661586	−	0.997809i	$-0.521074\pi$
$997$	−3.59519e150	−0.132317	−0.0661586	+	0.997809i	$0.521074\pi$
$998$	4.29120e151	1.50137
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.102.a.b.1.7		8
3.2	odd	2		1.102.a.a.1.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.102.a.a.1.2	✓	8	3.2	odd	2
9.102.a.b.1.7		8	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:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 102 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q+2.38447e15 q^{2} +3.15040e30 q^{4} -7.99157e34 q^{5} +3.14769e42 q^{7} +1.46670e45 q^{8} +O(q^{10})\)	\(q+2.38447e15 q^{2} +3.15040e30 q^{4} -7.99157e34 q^{5} +3.14769e42 q^{7} +1.46670e45 q^{8} -1.90557e50 q^{10} -6.08310e52 q^{11} -2.09809e56 q^{13} +7.50557e57 q^{14} -4.48993e60 q^{16} +1.97536e62 q^{17} -2.54133e64 q^{19} -2.51767e65 q^{20} -1.45050e68 q^{22} +6.11246e68 q^{23} -3.30565e70 q^{25} -5.00284e71 q^{26} +9.91648e72 q^{28} -7.52088e73 q^{29} -1.26748e75 q^{31} -1.44246e76 q^{32} +4.71018e77 q^{34} -2.51550e77 q^{35} +1.84306e79 q^{37} -6.05972e79 q^{38} -1.17212e80 q^{40} +3.79846e81 q^{41} -1.82567e82 q^{43} -1.91642e83 q^{44} +1.45750e84 q^{46} +1.21503e84 q^{47} -1.27334e85 q^{49} -7.88223e85 q^{50} -6.60984e86 q^{52} -1.92092e87 q^{53} +4.86136e87 q^{55} +4.61670e87 q^{56} -1.79333e89 q^{58} +9.03706e88 q^{59} -9.82351e89 q^{61} -3.02228e90 q^{62} -2.30118e91 q^{64} +1.67671e91 q^{65} +1.68394e92 q^{67} +6.22317e92 q^{68} -5.99813e92 q^{70} -2.66050e92 q^{71} -1.19661e94 q^{73} +4.39473e94 q^{74} -8.00620e94 q^{76} -1.91477e95 q^{77} +8.68984e95 q^{79} +3.58816e95 q^{80} +9.05733e96 q^{82} +2.05551e96 q^{83} -1.57862e97 q^{85} -4.35327e97 q^{86} -8.92207e97 q^{88} +4.58460e98 q^{89} -6.60413e98 q^{91} +1.92567e99 q^{92} +2.89721e99 q^{94} +2.03092e99 q^{95} -9.41618e99 q^{97} -3.03625e100 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 434989091795040 q^{2} + 90\!\cdots\!96 q^{4}+ \cdots + 61\!\cdots\!20 q^{8}+O(q^{10}) \) 8 * q + 434989091795040 * q^2 + 9008967123164113911511576503296 * q^4 - 38238791540232828026421308589217200 * q^5 - 5786789720778120168956257648884421874283200 * q^7 + 6101688461407407841888405145259998920458731520 * q^8	\( 8 q + 434989091795040 q^{2} + 90\!\cdots\!96 q^{4}+ \cdots - 20\!\cdots\!20 q^{98}+O(q^{100}) \) 8 * q + 434989091795040 * q^2 + 9008967123164113911511576503296 * q^4 - 38238791540232828026421308589217200 * q^5 - 5786789720778120168956257648884421874283200 * q^7 + 6101688461407407841888405145259998920458731520 * q^8 - 376167658847177398692429835067300112512860198593600 * q^10 - 4622006661480385115355021397632645270205791478300896 * q^11 + 250316830865150221699601352256397536965043294984328650480 * q^13 + 4856789037716039923353321450215036970203737520869624889088 * q^14 - 10662656154906175558835021484824464714661655552497093859868672 * q^16 + 397968518694853312322660892941326449007299986932512193696587120 * q^17 - 21387776045417165942123954421061470474744368808488511816400717280 * q^19 - 1745002690168409059221421019241581897927614179506161156200285542400 * q^20 + 61357881995862711169740037407631980426480577127973320405539739944320 * q^22 + 1366243345208606848425464574347748611753917469593153677393324561698880 * q^23 + 77471873089568593564333770877949420045843582630742632687744142562715000 * q^25 + 97549630676937426518340388130407212490384846814009484188479115327886144 * q^26 + 9217624035174751886516129105576165061663773766415040330328487084880404480 * q^28 - 15465799862710125255662370242568323665682807414567501281109138719156160880 * q^29 - 6594370386043135339784923725045360443937393326734068279132668478779615001344 * q^31 - 12265519409733718324179959581296851912742484455832107241543734281342036213760 * q^32 + 9531455444774917507766540524882635666895777953789094347547215472626183995712 * q^34 + 1122850631208004175280217132184898888977788452428069383882586628450512616297600 * q^35 + 39729696767983511833540209209183332457877293383323859312175998401968644864715440 * q^37 + 70873740526925065519455012686645778106113298999572267198467188879790467046148480 * q^38 - 763642761360299050617237751714968411270996317577517686387843428508400019349504000 * q^40 - 5607291724825101314952096252772109505395882457063737303656079003304969203257094736 * q^41 - 28642921955044714117801359306021921736063108483729021321044095944585527287681223200 * q^43 + 207838425393205175674959052733026300855796348257745356716186803699782799277851086848 * q^44 + 1088094260619851586903932234100844276278561023621942541398958535856528393570339218176 * q^46 + 4595399220200007631460417274797048154524720407021496316223236391731855709593438718080 * q^47 + 12068461406676719302337658501270392621238416595305390197216228129207599916872005856456 * q^49 + 40493179837482260394665357435432250163405353367416857829233726008281167215503492420000 * q^50 - 736020167800817028850658909331852777746165402605863935107936992324104798352324258252800 * q^52 - 131026696145917691346168139299202731343660174597285772716290345361212508775951813313840 * q^53 - 14585157967675450217148723878599628333971210001615112897255333178063634767400530051473600 * q^55 + 23665562342657326400415121984960944704012341384928617813498515591030351969339927087022080 * q^56 + 29173417521771002425120779628349939892591335515731485644911210555324770598093888308326080 * q^58 - 212583149562022564923669670483574922097682552074321909615339251529169016840977455874187360 * q^59 - 3390796423636162146406492296389682436951029380958058095674208836333532599894943317230895504 * q^61 + 5878859817222970028213836429448832127296537243368792127423103234889716583457526212133370880 * q^62 - 74870090698021647967203019932764377907062372989513317693678846896652408519412785858115272704 * q^64 + 161067075283368767182138254547148962244907084326790507487294907612770451283405321317426536800 * q^65 - 618774503558862942537948810466095132313460919373052732511642097824837019429997681150398682720 * q^67 + 2182412150351293808121583165511486752102068977919329447376923905220322529537335456462676162560 * q^68 - 12923520657540473465038555822652190723092643731233782501675276653712048411292540691873715571200 * q^70 + 15797470289857673806303846655911576507977904169297655042639265226995032204172380517793831135424 * q^71 - 20462651635605668591994589976366754984142669867347912050159975933828495442291952971923777071280 * q^73 + 142953411935712165334538916257020870493984381200782662943456748743148514063783881306064429441088 * q^74 + 64556217054886497186737063238064337992823205997653378371004031509089422583081356800943896432640 * q^76 - 250231448169383959900618348975396989794902211753647918986458150866408618577007907131029306438400 * q^77 + 1474556321278768744579716979675929750918930811984805387023357390321899878561204701118206999166080 * q^79 - 6033438037435277941170744030808192554572458649979375320464765273747209092446481051552234550067200 * q^80 + 30083863369214129982421840097969977845328701273986110579467106900080547794123383776302929686086720 * q^82 - 33762254529254022439253159341806143692643909652777369725086142424861011401680843403961249425712160 * q^83 + 17314966267116570951109803841412092095679328201414316724042066880549149931729490643535478494114400 * q^85 - 67989564188024628582959760637462873453376851598916319417912395832044408164663357850732592560556416 * q^86 - 363099602372059077387783242048689913608334478213970275423791339756517232974574737922754584123146240 * q^88 + 620007165949691950044675276484549383308720953973642955804615855186521697520022438525123333812557360 * q^89 - 3685711793015793225308940042728501386995879977832891226647110522985454537354035281338855172828873344 * q^91 + 4618779932089713137770970202224414792688843158843334085630908366025929325979388063902511470793400320 * q^92 - 17371370943540992303713705925513939673302729250250795188383540356993592041601425149438637190677682688 * q^94 + 2642077700832720169247174948884057845373174576960370774287679094739730873649398763127258995555528000 * q^95 + 64020476116668335744724892375903667651900818166631138467214326399663196857065619648203365824701173520 * q^97 - 202971561788470754768820264959327860776947519106194867162872422213964707447467488105939520314595817120 * q^98

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