LMFDB - Embedded newform 9.102.a.b.1.3

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			1.3
Root			$-1.40661e13$ 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)

$f(q)$	$=$	$q-1.29597e15 q^{2} -8.55769e29 q^{4} +1.52987e35 q^{5} -2.30272e42 q^{7} +4.39472e45 q^{8} +O(q^{10})$	\(q-1.29597e15 q^{2} -8.55769e29 q^{4} +1.52987e35 q^{5} -2.30272e42 q^{7} +4.39472e45 q^{8} -1.98266e50 q^{10} -7.37923e52 q^{11} +1.08138e56 q^{13} +2.98425e57 q^{14} -3.52578e60 q^{16} +7.80096e61 q^{17} -2.75511e64 q^{19} -1.30921e65 q^{20} +9.56325e67 q^{22} -8.02073e68 q^{23} -1.60381e70 q^{25} -1.40143e71 q^{26} +1.97059e72 q^{28} +4.17708e73 q^{29} +1.32596e74 q^{31} -6.57264e75 q^{32} -1.01098e77 q^{34} -3.52285e77 q^{35} +7.61174e78 q^{37} +3.57054e79 q^{38} +6.72333e80 q^{40} -4.16079e81 q^{41} -6.23745e81 q^{43} +6.31492e82 q^{44} +1.03946e84 q^{46} +9.39126e83 q^{47} -1.73388e85 q^{49} +2.07849e85 q^{50} -9.25410e85 q^{52} -1.74117e87 q^{53} -1.12892e88 q^{55} -1.01198e88 q^{56} -5.41336e88 q^{58} -2.25849e89 q^{59} -2.74167e90 q^{61} -1.71840e89 q^{62} +1.74568e91 q^{64} +1.65436e91 q^{65} +8.52043e91 q^{67} -6.67582e91 q^{68} +4.56550e92 q^{70} +3.72400e93 q^{71} -2.87380e93 q^{73} -9.86457e93 q^{74} +2.35774e94 q^{76} +1.69923e95 q^{77} +4.49556e95 q^{79} -5.39397e95 q^{80} +5.39225e96 q^{82} -1.36723e96 q^{83} +1.19344e97 q^{85} +8.08353e96 q^{86} -3.24296e98 q^{88} -2.37256e98 q^{89} -2.49011e98 q^{91} +6.86390e98 q^{92} -1.21708e99 q^{94} -4.21495e99 q^{95} -7.96305e99 q^{97} +2.24706e100 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.29597e15	−0.813916	−0.406958	−	0.913447i	$-0.633410\pi$
$2$	−1.29597e15	−0.813916	−0.406958	+	0.913447i	$0.633410\pi$
$3$	0	0
$3$	0	0
$4$	−8.55769e29	−0.337541
$5$	1.52987e35	0.770315	0.385157	−	0.922851i	$-0.374147\pi$
$5$	1.52987e35	0.770315	0.385157	+	0.922851i	$0.374147\pi$
$6$	0	0
$7$	−2.30272e42	−0.483938	−0.241969	−	0.970284i	$-0.577793\pi$
$7$	−2.30272e42	−0.483938	−0.241969	+	0.970284i	$0.577793\pi$
$8$	4.39472e45	1.08865
$9$	0	0
$10$	−1.98266e50	−0.626971
$11$	−7.37923e52	−1.89531	−0.947656	−	0.319293i	$-0.896554\pi$
$11$	−7.37923e52	−1.89531	−0.947656	+	0.319293i	$0.896554\pi$
$12$	0	0
$13$	1.08138e56	0.602335	0.301167	−	0.953571i	$-0.402624\pi$
$13$	1.08138e56	0.602335	0.301167	+	0.953571i	$0.402624\pi$
$14$	2.98425e57	0.393884
$15$	0	0
$16$	−3.52578e60	−0.548524
$17$	7.80096e61	0.568169	0.284084	−	0.958799i	$-0.408310\pi$
$17$	7.80096e61	0.568169	0.284084	+	0.958799i	$0.408310\pi$
$18$	0	0
$19$	−2.75511e64	−0.729596	−0.364798	−	0.931087i	$-0.618862\pi$
$19$	−2.75511e64	−0.729596	−0.364798	+	0.931087i	$0.618862\pi$
$20$	−1.30921e65	−0.260013
$21$	0	0
$22$	9.56325e67	1.54262
$23$	−8.02073e68	−1.37075	−0.685375	−	0.728190i	$-0.740362\pi$
$23$	−8.02073e68	−1.37075	−0.685375	+	0.728190i	$0.740362\pi$
$24$	0	0
$25$	−1.60381e70	−0.406615
$26$	−1.40143e71	−0.490250
$27$	0	0
$28$	1.97059e72	0.163349
$29$	4.17708e73	0.588537	0.294268	−	0.955723i	$-0.404924\pi$
$29$	4.17708e73	0.588537	0.294268	+	0.955723i	$0.404924\pi$
$30$	0	0
$31$	1.32596e74	0.0643821	0.0321910	−	0.999482i	$-0.489752\pi$
$31$	1.32596e74	0.0643821	0.0321910	+	0.999482i	$0.489752\pi$
$32$	−6.57264e75	−0.642193
$33$	0	0
$34$	−1.01098e77	−0.462441
$35$	−3.52285e77	−0.372784
$36$	0	0
$37$	7.61174e78	0.486740	0.243370	−	0.969934i	$-0.421747\pi$
$37$	7.61174e78	0.486740	0.243370	+	0.969934i	$0.421747\pi$
$38$	3.57054e79	0.593830
$39$	0	0
$40$	6.72333e80	0.838600
$41$	−4.16079e81	−1.49139	−0.745694	−	0.666288i	$-0.767882\pi$
$41$	−4.16079e81	−1.49139	−0.745694	+	0.666288i	$0.767882\pi$
$42$	0	0
$43$	−6.23745e81	−0.201767	−0.100883	−	0.994898i	$-0.532167\pi$
$43$	−6.23745e81	−0.201767	−0.100883	+	0.994898i	$0.532167\pi$
$44$	6.31492e82	0.639746
$45$	0	0
$46$	1.03946e84	1.11568
$47$	9.39126e83	0.340237	0.170119	−	0.985424i	$-0.445585\pi$
$47$	9.39126e83	0.340237	0.170119	+	0.985424i	$0.445585\pi$
$48$	0	0
$49$	−1.73388e85	−0.765804
$50$	2.07849e85	0.330950
$51$	0	0
$52$	−9.25410e85	−0.203313
$53$	−1.74117e87	−1.46187	−0.730935	−	0.682447i	$-0.760916\pi$
$53$	−1.74117e87	−1.46187	−0.730935	+	0.682447i	$0.760916\pi$
$54$	0	0
$55$	−1.12892e88	−1.45999
$56$	−1.01198e88	−0.526837
$57$	0	0
$58$	−5.41336e88	−0.479019
$59$	−2.25849e89	−0.842930	−0.421465	−	0.906845i	$-0.638484\pi$
$59$	−2.25849e89	−0.842930	−0.421465	+	0.906845i	$0.638484\pi$
$60$	0	0
$61$	−2.74167e90	−1.90046	−0.950229	−	0.311553i	$-0.899151\pi$
$61$	−2.74167e90	−1.90046	−0.950229	+	0.311553i	$0.899151\pi$
$62$	−1.71840e89	−0.0524016
$63$	0	0
$64$	1.74568e91	1.07122
$65$	1.65436e91	0.463988
$66$	0	0
$67$	8.52043e91	0.517230	0.258615	−	0.965980i	$-0.416734\pi$
$67$	8.52043e91	0.517230	0.258615	+	0.965980i	$0.416734\pi$
$68$	−6.67582e91	−0.191780
$69$	0	0
$70$	4.56550e92	0.303415
$71$	3.72400e93	1.20910	0.604551	−	0.796566i	$-0.293352\pi$
$71$	3.72400e93	1.20910	0.604551	+	0.796566i	$0.293352\pi$
$72$	0	0
$73$	−2.87380e93	−0.229431	−0.114715	−	0.993398i	$-0.536596\pi$
$73$	−2.87380e93	−0.229431	−0.114715	+	0.993398i	$0.536596\pi$
$74$	−9.86457e93	−0.396165
$75$	0	0
$76$	2.35774e94	0.246269
$77$	1.69923e95	0.917213
$78$	0	0
$79$	4.49556e95	0.664685	0.332343	−	0.943159i	$-0.392161\pi$
$79$	4.49556e95	0.664685	0.332343	+	0.943159i	$0.392161\pi$
$80$	−5.39397e95	−0.422536
$81$	0	0
$82$	5.39225e96	1.21386
$83$	−1.36723e96	−0.166877	−0.0834386	−	0.996513i	$-0.526590\pi$
$83$	−1.36723e96	−0.166877	−0.0834386	+	0.996513i	$0.526590\pi$
$84$	0	0
$85$	1.19344e97	0.437669
$86$	8.08353e96	0.164221
$87$	0	0
$88$	−3.24296e98	−2.06332
$89$	−2.37256e98	−0.853143	−0.426571	−	0.904454i	$-0.640279\pi$
$89$	−2.37256e98	−0.853143	−0.426571	+	0.904454i	$0.640279\pi$
$90$	0	0
$91$	−2.49011e98	−0.291493
$92$	6.86390e98	0.462685
$93$	0	0
$94$	−1.21708e99	−0.276924
$95$	−4.21495e99	−0.562019
$96$	0	0
$97$	−7.96305e99	−0.370772	−0.185386	−	0.982666i	$-0.559354\pi$
$97$	−7.96305e99	−0.370772	−0.185386	+	0.982666i	$0.559354\pi$
$98$	2.24706e100	0.623300
$99$	0	0
$100$	1.37249e100	0.137249
$101$	7.62399e100	0.461268	0.230634	−	0.973041i	$-0.425920\pi$
$101$	7.62399e100	0.461268	0.230634	+	0.973041i	$0.425920\pi$
$102$	0	0
$103$	−3.82780e101	−0.860339	−0.430169	−	0.902748i	$-0.641546\pi$
$103$	−3.82780e101	−0.860339	−0.430169	+	0.902748i	$0.641546\pi$
$104$	4.75235e101	0.655729
$105$	0	0
$106$	2.25649e102	1.18984
$107$	2.91169e102	0.955576	0.477788	−	0.878475i	$-0.341439\pi$
$107$	2.91169e102	0.955576	0.477788	+	0.878475i	$0.341439\pi$
$108$	0	0
$109$	−8.50797e102	−1.09594	−0.547971	−	0.836497i	$-0.684600\pi$
$109$	−8.50797e102	−1.09594	−0.547971	+	0.836497i	$0.684600\pi$
$110$	1.46305e103	1.18831
$111$	0	0
$112$	8.11887e102	0.265452
$113$	−5.83476e103	−1.21776	−0.608880	−	0.793262i	$-0.708381\pi$
$113$	−5.83476e103	−1.21776	−0.608880	+	0.793262i	$0.708381\pi$
$114$	0	0
$115$	−1.22707e104	−1.05591
$116$	−3.57461e103	−0.198656
$117$	0	0
$118$	2.92693e104	0.686074
$119$	−1.79634e104	−0.274958
$120$	0	0
$121$	3.92944e105	2.59221
$122$	3.55311e105	1.54681
$123$	0	0
$124$	−1.13472e104	−0.0217316
$125$	−8.48788e105	−1.08354
$126$	0	0
$127$	9.46785e105	0.542205	0.271102	−	0.962551i	$-0.412612\pi$
$127$	9.46785e105	0.542205	0.271102	+	0.962551i	$0.412612\pi$
$128$	−5.95988e105	−0.229686
$129$	0	0
$130$	−2.14400e106	−0.377647
$131$	9.25172e106	1.10668	0.553340	−	0.832955i	$-0.313353\pi$
$131$	9.25172e106	1.10668	0.553340	+	0.832955i	$0.313353\pi$
$132$	0	0
$133$	6.34424e106	0.353079
$134$	−1.10422e107	−0.420982
$135$	0	0
$136$	3.42830e107	0.618534
$137$	5.67560e107	0.707331	0.353666	−	0.935372i	$-0.384935\pi$
$137$	5.67560e107	0.707331	0.353666	+	0.935372i	$0.384935\pi$
$138$	0	0
$139$	−1.48585e108	−0.890690	−0.445345	−	0.895359i	$-0.646919\pi$
$139$	−1.48585e108	−0.890690	−0.445345	+	0.895359i	$0.646919\pi$
$140$	3.01474e107	0.125830
$141$	0	0
$142$	−4.82618e108	−0.984107
$143$	−7.97974e108	−1.14161
$144$	0	0
$145$	6.39037e108	0.453359
$146$	3.72435e108	0.186737
$147$	0	0
$148$	−6.51389e108	−0.164295
$149$	−2.67615e109	−0.480400	−0.240200	−	0.970723i	$-0.577213\pi$
$149$	−2.67615e109	−0.480400	−0.240200	+	0.970723i	$0.577213\pi$
$150$	0	0
$151$	−1.18193e109	−0.108207	−0.0541037	−	0.998535i	$-0.517230\pi$
$151$	−1.18193e109	−0.108207	−0.0541037	+	0.998535i	$0.517230\pi$
$152$	−1.21079e110	−0.794272
$153$	0	0
$154$	−2.20214e110	−0.746534
$155$	2.02854e109	0.0495945
$156$	0	0
$157$	4.49535e110	0.575216	0.287608	−	0.957748i	$-0.407140\pi$
$157$	4.49535e110	0.575216	0.287608	+	0.957748i	$0.407140\pi$
$158$	−5.82611e110	−0.540998
$159$	0	0
$160$	−1.00553e111	−0.494691
$161$	1.84695e111	0.663358
$162$	0	0
$163$	2.42594e111	0.467097	0.233548	−	0.972345i	$-0.424966\pi$
$163$	2.42594e111	0.467097	0.233548	+	0.972345i	$0.424966\pi$
$164$	3.56067e111	0.503405
$165$	0	0
$166$	1.77188e111	0.135824
$167$	−5.27032e111	−0.298302	−0.149151	−	0.988814i	$-0.547654\pi$
$167$	−5.27032e111	−0.298302	−0.149151	+	0.988814i	$0.547654\pi$
$168$	0	0
$169$	−2.05376e112	−0.637193
$170$	−1.54666e112	−0.356225
$171$	0	0
$172$	5.33782e111	0.0681047
$173$	−2.18981e112	−0.208486	−0.104243	−	0.994552i	$-0.533242\pi$
$173$	−2.18981e112	−0.208486	−0.104243	+	0.994552i	$0.533242\pi$
$174$	0	0
$175$	3.69313e112	0.196776
$176$	2.60175e113	1.03962
$177$	0	0
$178$	3.07476e113	0.694386
$179$	−4.11936e113	−0.701055	−0.350527	−	0.936553i	$-0.613998\pi$
$179$	−4.11936e113	−0.701055	−0.350527	+	0.936553i	$0.613998\pi$
$180$	0	0
$181$	−3.60610e113	−0.350163	−0.175081	−	0.984554i	$-0.556019\pi$
$181$	−3.60610e113	−0.350163	−0.175081	+	0.984554i	$0.556019\pi$
$182$	3.22710e113	0.237250
$183$	0	0
$184$	−3.52489e114	−1.49226
$185$	1.16449e114	0.374943
$186$	0	0
$187$	−5.75651e114	−1.07686
$188$	−8.03675e113	−0.114844
$189$	0	0
$190$	5.46244e114	0.457436
$191$	3.07102e115	1.97286	0.986432	−	0.164171i	$-0.0524948\pi$
$191$	3.07102e115	1.97286	0.986432	+	0.164171i	$0.0524948\pi$
$192$	0	0
$193$	2.25699e115	0.856811	0.428406	−	0.903587i	$-0.359075\pi$
$193$	2.25699e115	0.856811	0.428406	+	0.903587i	$0.359075\pi$
$194$	1.03199e115	0.301777
$195$	0	0
$196$	1.48380e115	0.258491
$197$	2.88844e115	0.389152	0.194576	−	0.980887i	$-0.437667\pi$
$197$	2.88844e115	0.389152	0.194576	+	0.980887i	$0.437667\pi$
$198$	0	0
$199$	−1.43998e116	−1.16486	−0.582432	−	0.812880i	$-0.697899\pi$
$199$	−1.43998e116	−1.16486	−0.582432	+	0.812880i	$0.697899\pi$
$200$	−7.04831e115	−0.442660
$201$	0	0
$202$	−9.88045e115	−0.375433
$203$	−9.61862e115	−0.284815
$204$	0	0
$205$	−6.36545e116	−1.14884
$206$	4.96070e116	0.700243
$207$	0	0
$208$	−3.81270e116	−0.330395
$209$	2.03306e117	1.38281
$210$	0	0
$211$	−3.37109e117	−1.41744	−0.708722	−	0.705488i	$-0.750728\pi$
$211$	−3.37109e117	−1.41744	−0.708722	+	0.705488i	$0.750728\pi$
$212$	1.49004e117	0.493442
$213$	0	0
$214$	−3.77346e117	−0.777758
$215$	−9.54246e116	−0.155424
$216$	0	0
$217$	−3.05331e116	−0.0311569
$218$	1.10260e118	0.892004
$219$	0	0
$220$	9.66099e117	0.492806
$221$	8.43578e117	0.342228
$222$	0	0
$223$	−2.91997e118	−0.751594	−0.375797	−	0.926702i	$-0.622631\pi$
$223$	−2.91997e118	−0.751594	−0.375797	+	0.926702i	$0.622631\pi$
$224$	1.51349e118	0.310781
$225$	0	0
$226$	7.56166e118	0.991154
$227$	−4.57961e118	−0.480311	−0.240155	−	0.970734i	$-0.577198\pi$
$227$	−4.57961e118	−0.480311	−0.240155	+	0.970734i	$0.577198\pi$
$228$	0	0
$229$	−1.61593e119	−1.08825	−0.544127	−	0.839003i	$-0.683139\pi$
$229$	−1.61593e119	−1.08825	−0.544127	+	0.839003i	$0.683139\pi$
$230$	1.59024e119	0.859421
$231$	0	0
$232$	1.83571e119	0.640708
$233$	−1.44890e119	−0.406972	−0.203486	−	0.979078i	$-0.565227\pi$
$233$	−1.44890e119	−0.406972	−0.203486	+	0.979078i	$0.565227\pi$
$234$	0	0
$235$	1.43674e119	0.262090
$236$	1.93275e119	0.284524
$237$	0	0
$238$	2.32800e119	0.223793
$239$	5.74092e118	0.0446568	0.0223284	−	0.999751i	$-0.492892\pi$
$239$	5.74092e118	0.0446568	0.0223284	+	0.999751i	$0.492892\pi$
$240$	0	0
$241$	−1.31918e120	−0.673666	−0.336833	−	0.941564i	$-0.609356\pi$
$241$	−1.31918e120	−0.673666	−0.336833	+	0.941564i	$0.609356\pi$
$242$	−5.09243e120	−2.10984
$243$	0	0
$244$	2.34623e120	0.641483
$245$	−2.65261e120	−0.589911
$246$	0	0
$247$	−2.97932e120	−0.439461
$248$	5.82722e119	0.0700893
$249$	0	0
$250$	1.10000e121	0.881907
$251$	−8.00520e120	−0.524625	−0.262313	−	0.964983i	$-0.584485\pi$
$251$	−8.00520e120	−0.524625	−0.262313	+	0.964983i	$0.584485\pi$
$252$	0	0
$253$	5.91869e121	2.59800
$254$	−1.22700e121	−0.441309
$255$	0	0
$256$	−3.65345e121	−0.884271
$257$	5.16612e121	1.02693	0.513466	−	0.858110i	$-0.328361\pi$
$257$	5.16612e121	1.02693	0.513466	+	0.858110i	$0.328361\pi$
$258$	0	0
$259$	−1.75277e121	−0.235552
$260$	−1.41575e121	−0.156615
$261$	0	0
$262$	−1.19899e122	−0.900744
$263$	1.02351e122	0.634347	0.317174	−	0.948368i	$-0.397266\pi$
$263$	1.02351e122	0.634347	0.317174	+	0.948368i	$0.397266\pi$
$264$	0	0
$265$	−2.66375e122	−1.12610
$266$	−8.22193e121	−0.287376
$267$	0	0
$268$	−7.29152e121	−0.174587
$269$	−5.17382e121	−0.102641	−0.0513205	−	0.998682i	$-0.516343\pi$
$269$	−5.17382e121	−0.102641	−0.0513205	+	0.998682i	$0.516343\pi$
$270$	0	0
$271$	4.55314e122	0.621387	0.310693	−	0.950510i	$-0.399439\pi$
$271$	4.55314e122	0.621387	0.310693	+	0.950510i	$0.399439\pi$
$272$	−2.75044e122	−0.311654
$273$	0	0
$274$	−7.35539e122	−0.575708
$275$	1.18349e123	0.770662
$276$	0	0
$277$	−1.61307e123	−0.728490	−0.364245	−	0.931303i	$-0.618673\pi$
$277$	−1.61307e123	−0.728490	−0.364245	+	0.931303i	$0.618673\pi$
$278$	1.92561e123	0.724946
$279$	0	0
$280$	−1.54819e123	−0.405830
$281$	−1.39882e123	−0.306263	−0.153131	−	0.988206i	$-0.548936\pi$
$281$	−1.39882e123	−0.306263	−0.153131	+	0.988206i	$0.548936\pi$
$282$	0	0
$283$	−8.50004e123	−1.30079	−0.650394	−	0.759597i	$-0.725396\pi$
$283$	−8.50004e123	−1.30079	−0.650394	+	0.759597i	$0.725396\pi$
$284$	−3.18688e123	−0.408122
$285$	0	0
$286$	1.03415e124	0.929176
$287$	9.58111e123	0.721739
$288$	0	0
$289$	−1.27658e124	−0.677184
$290$	−8.28171e123	−0.368996
$291$	0	0
$292$	2.45931e123	0.0774425
$293$	−6.76033e124	−1.79124	−0.895619	−	0.444822i	$-0.853267\pi$
$293$	−6.76033e124	−1.79124	−0.895619	+	0.444822i	$0.853267\pi$
$294$	0	0
$295$	−3.45519e124	−0.649322
$296$	3.34514e124	0.529887
$297$	0	0
$298$	3.46820e124	0.391005
$299$	−8.67344e124	−0.825651
$300$	0	0
$301$	1.43631e124	0.0976426
$302$	1.53175e124	0.0880717
$303$	0	0
$304$	9.71392e124	0.400201
$305$	−4.19438e125	−1.46395
$306$	0	0
$307$	−6.79538e125	−1.70500	−0.852502	−	0.522723i	$-0.824916\pi$
$307$	−6.79538e125	−1.70500	−0.852502	+	0.522723i	$0.824916\pi$
$308$	−1.45415e125	−0.309597
$309$	0	0
$310$	−2.62892e124	−0.0403657
$311$	5.79067e125	0.755665	0.377832	−	0.925874i	$-0.376670\pi$
$311$	5.79067e125	0.755665	0.377832	+	0.925874i	$0.376670\pi$
$312$	0	0
$313$	−4.76409e125	−0.449770	−0.224885	−	0.974385i	$-0.572201\pi$
$313$	−4.76409e125	−0.449770	−0.224885	+	0.974385i	$0.572201\pi$
$314$	−5.82583e125	−0.468177
$315$	0	0
$316$	−3.84717e125	−0.224359
$317$	−8.81971e125	−0.438492	−0.219246	−	0.975670i	$-0.570360\pi$
$317$	−8.81971e125	−0.438492	−0.219246	+	0.975670i	$0.570360\pi$
$318$	0	0
$319$	−3.08236e126	−1.11546
$320$	2.67066e126	0.825173
$321$	0	0
$322$	−2.39358e126	−0.539917
$323$	−2.14925e126	−0.414534
$324$	0	0
$325$	−1.73433e126	−0.244918
$326$	−3.14394e126	−0.380177
$327$	0	0
$328$	−1.82855e127	−1.62359
$329$	−2.16254e126	−0.164654
$330$	0	0
$331$	−2.21975e127	−1.24449	−0.622244	−	0.782823i	$-0.713779\pi$
$331$	−2.21975e127	−1.24449	−0.622244	+	0.782823i	$0.713779\pi$
$332$	1.17003e126	0.0563280
$333$	0	0
$334$	6.83017e126	0.242792
$335$	1.30351e127	0.398430
$336$	0	0
$337$	2.66317e127	0.602684	0.301342	−	0.953516i	$-0.402565\pi$
$337$	2.66317e127	0.602684	0.301342	+	0.953516i	$0.402565\pi$
$338$	2.66160e127	0.518621
$339$	0	0
$340$	−1.02131e127	−0.147731
$341$	−9.78457e126	−0.122024
$342$	0	0
$343$	9.20630e127	0.854539
$344$	−2.74118e127	−0.219653
$345$	0	0
$346$	2.83792e127	0.169690
$347$	−1.75162e128	−0.905317	−0.452658	−	0.891684i	$-0.649524\pi$
$347$	−1.75162e128	−0.905317	−0.452658	+	0.891684i	$0.649524\pi$
$348$	0	0
$349$	−2.08861e128	−0.807559	−0.403780	−	0.914856i	$-0.632304\pi$
$349$	−2.08861e128	−0.807559	−0.403780	+	0.914856i	$0.632304\pi$
$350$	−4.78617e127	−0.160159
$351$	0	0
$352$	4.85010e128	1.21716
$353$	−5.13773e128	−1.11725	−0.558623	−	0.829422i	$-0.688670\pi$
$353$	−5.13773e128	−1.11725	−0.558623	+	0.829422i	$0.688670\pi$
$354$	0	0
$355$	5.69722e128	0.931390
$356$	2.03036e128	0.287971
$357$	0	0
$358$	5.33856e128	0.570599
$359$	7.54531e128	0.700499	0.350250	−	0.936656i	$-0.386097\pi$
$359$	7.54531e128	0.700499	0.350250	+	0.936656i	$0.386097\pi$
$360$	0	0
$361$	−6.66916e128	−0.467690
$362$	4.67339e128	0.285003
$363$	0	0
$364$	2.13096e128	0.0983908
$365$	−4.39653e128	−0.176734
$366$	0	0
$367$	−2.00122e129	−0.610463	−0.305231	−	0.952278i	$-0.598734\pi$
$367$	−2.00122e129	−0.610463	−0.305231	+	0.952278i	$0.598734\pi$
$368$	2.82793e129	0.751890
$369$	0	0
$370$	−1.50915e129	−0.305172
$371$	4.00941e129	0.707454
$372$	0	0
$373$	1.38653e130	1.86480	0.932400	−	0.361428i	$-0.117711\pi$
$373$	1.38653e130	1.86480	0.932400	+	0.361428i	$0.117711\pi$
$374$	7.46025e129	0.876471
$375$	0	0
$376$	4.12719e129	0.370398
$377$	4.51700e129	0.354496
$378$	0	0
$379$	1.21170e130	0.727971	0.363986	−	0.931405i	$-0.381416\pi$
$379$	1.21170e130	0.727971	0.363986	+	0.931405i	$0.381416\pi$
$380$	3.60703e129	0.189705
$381$	0	0
$382$	−3.97994e130	−1.60574
$383$	3.71125e129	0.131215	0.0656073	−	0.997846i	$-0.479102\pi$
$383$	3.71125e129	0.131215	0.0656073	+	0.997846i	$0.479102\pi$
$384$	0	0
$385$	2.59959e130	0.706543
$386$	−2.92498e130	−0.697372
$387$	0	0
$388$	6.81453e129	0.125151
$389$	−2.40999e130	−0.388651	−0.194325	−	0.980937i	$-0.562252\pi$
$389$	−2.40999e130	−0.388651	−0.194325	+	0.980937i	$0.562252\pi$
$390$	0	0
$391$	−6.25694e130	−0.778817
$392$	−7.61993e130	−0.833690
$393$	0	0
$394$	−3.74333e130	−0.316737
$395$	6.87761e130	0.512017
$396$	0	0
$397$	1.41143e131	0.814216	0.407108	−	0.913380i	$-0.366537\pi$
$397$	1.41143e131	0.814216	0.407108	+	0.913380i	$0.366537\pi$
$398$	1.86616e131	0.948100
$399$	0	0
$400$	5.65469e130	0.223038
$401$	−5.27775e131	−1.83509	−0.917546	−	0.397629i	$-0.869833\pi$
$401$	−5.27775e131	−1.83509	−0.917546	+	0.397629i	$0.869833\pi$
$402$	0	0
$403$	1.43386e130	0.0387796
$404$	−6.52438e130	−0.155697
$405$	0	0
$406$	1.24654e131	0.231815
$407$	−5.61688e131	−0.922524
$408$	0	0
$409$	−6.90731e131	−0.885690	−0.442845	−	0.896598i	$-0.646031\pi$
$409$	−6.90731e131	−0.885690	−0.442845	+	0.896598i	$0.646031\pi$
$410$	8.24942e131	0.935058
$411$	0	0
$412$	3.27571e131	0.290400
$413$	5.20066e131	0.407926
$414$	0	0
$415$	−2.09167e131	−0.128548
$416$	−7.10750e131	−0.386815
$417$	0	0
$418$	−2.63478e132	−1.12549
$419$	−1.10295e132	−0.417589	−0.208795	−	0.977960i	$-0.566954\pi$
$419$	−1.10295e132	−0.417589	−0.208795	+	0.977960i	$0.566954\pi$
$420$	0	0
$421$	−5.00940e132	−1.49122	−0.745608	−	0.666385i	$-0.767841\pi$
$421$	−5.00940e132	−1.49122	−0.745608	+	0.666385i	$0.767841\pi$
$422$	4.36882e132	1.15368
$423$	0	0
$424$	−7.65193e132	−1.59146
$425$	−1.25113e132	−0.231026
$426$	0	0
$427$	6.31328e132	0.919703
$428$	−2.49174e132	−0.322546
$429$	0	0
$430$	1.23667e132	0.126502
$431$	3.12141e132	0.283954	0.141977	−	0.989870i	$-0.454654\pi$
$431$	3.12141e132	0.283954	0.141977	+	0.989870i	$0.454654\pi$
$432$	0	0
$433$	1.09298e133	0.787000	0.393500	−	0.919325i	$-0.371264\pi$
$433$	1.09298e133	0.787000	0.393500	+	0.919325i	$0.371264\pi$
$434$	3.95699e131	0.0253591
$435$	0	0
$436$	7.28085e132	0.369926
$437$	2.20980e133	1.00009
$438$	0	0
$439$	4.51566e133	1.62279	0.811396	−	0.584497i	$-0.198708\pi$
$439$	4.51566e133	1.62279	0.811396	+	0.584497i	$0.198708\pi$
$440$	−4.96130e133	−1.58941
$441$	0	0
$442$	−1.09325e133	−0.278545
$443$	−2.94289e133	−0.668938	−0.334469	−	0.942407i	$-0.608557\pi$
$443$	−2.94289e133	−0.668938	−0.334469	+	0.942407i	$0.608557\pi$
$444$	0	0
$445$	−3.62970e133	−0.657188
$446$	3.78419e133	0.611734
$447$	0	0
$448$	−4.01981e133	−0.518401
$449$	6.58528e133	0.758812	0.379406	−	0.925230i	$-0.376128\pi$
$449$	6.58528e133	0.758812	0.379406	+	0.925230i	$0.376128\pi$
$450$	0	0
$451$	3.07034e134	2.82665
$452$	4.99321e133	0.411045
$453$	0	0
$454$	5.93502e133	0.390932
$455$	−3.80953e133	−0.224541
$456$	0	0
$457$	−1.30627e134	−0.616971	−0.308486	−	0.951229i	$-0.599822\pi$
$457$	−1.30627e134	−0.616971	−0.308486	+	0.951229i	$0.599822\pi$
$458$	2.09419e134	0.885747
$459$	0	0
$460$	1.05008e134	0.356413
$461$	−5.34670e134	−1.62626	−0.813129	−	0.582084i	$-0.802237\pi$
$461$	−5.34670e134	−1.62626	−0.813129	+	0.582084i	$0.802237\pi$
$462$	0	0
$463$	−3.58951e134	−0.877396	−0.438698	−	0.898635i	$-0.644560\pi$
$463$	−3.58951e134	−0.877396	−0.438698	+	0.898635i	$0.644560\pi$
$464$	−1.47275e134	−0.322827
$465$	0	0
$466$	1.87773e134	0.331241
$467$	8.01039e134	1.26809	0.634047	−	0.773295i	$-0.281393\pi$
$467$	8.01039e134	1.26809	0.634047	+	0.773295i	$0.281393\pi$
$468$	0	0
$469$	−1.96201e134	−0.250307
$470$	−1.86196e134	−0.213319
$471$	0	0
$472$	−9.92543e134	−0.917652
$473$	4.60276e134	0.382411
$474$	0	0
$475$	4.41869e134	0.296665
$476$	1.53725e134	0.0928098
$477$	0	0
$478$	−7.44005e133	−0.0363469
$479$	1.89509e135	0.833078	0.416539	−	0.909118i	$-0.363243\pi$
$479$	1.89509e135	0.833078	0.416539	+	0.909118i	$0.363243\pi$
$480$	0	0
$481$	8.23116e134	0.293180
$482$	1.70962e135	0.548308
$483$	0	0
$484$	−3.36270e135	−0.874977
$485$	−1.21824e135	−0.285611
$486$	0	0
$487$	−8.27291e135	−1.57560	−0.787799	−	0.615932i	$-0.788780\pi$
$487$	−8.27291e135	−1.57560	−0.787799	+	0.615932i	$0.788780\pi$
$488$	−1.20489e136	−2.06892
$489$	0	0
$490$	3.43770e135	0.480137
$491$	−6.23886e135	−0.786122	−0.393061	−	0.919512i	$-0.628584\pi$
$491$	−6.23886e135	−0.786122	−0.393061	+	0.919512i	$0.628584\pi$
$492$	0	0
$493$	3.25852e135	0.334388
$494$	3.86110e135	0.357684
$495$	0	0
$496$	−4.67504e134	−0.0353151
$497$	−8.57531e135	−0.585130
$498$	0	0
$499$	1.23647e136	0.688823	0.344411	−	0.938819i	$-0.388079\pi$
$499$	1.23647e136	0.688823	0.344411	+	0.938819i	$0.388079\pi$
$500$	7.26367e135	0.365738
$501$	0	0
$502$	1.03745e136	0.427001
$503$	3.60863e136	1.34326	0.671628	−	0.740889i	$-0.265595\pi$
$503$	3.60863e136	1.34326	0.671628	+	0.740889i	$0.265595\pi$
$504$	0	0
$505$	1.16637e136	0.355321
$506$	−7.67043e136	−2.11455
$507$	0	0
$508$	−8.10229e135	−0.183017
$509$	5.84391e136	1.19524	0.597621	−	0.801779i	$-0.296113\pi$
$509$	5.84391e136	1.19524	0.597621	+	0.801779i	$0.296113\pi$
$510$	0	0
$511$	6.61754e135	0.111030
$512$	6.24577e136	0.949407
$513$	0	0
$514$	−6.69512e136	−0.835836
$515$	−5.85602e136	−0.662732
$516$	0	0
$517$	−6.93003e136	−0.644856
$518$	2.27153e136	0.191719
$519$	0	0
$520$	7.27046e136	0.505118
$521$	2.75937e137	1.73982	0.869912	−	0.493208i	$-0.164176\pi$
$521$	2.75937e137	1.73982	0.869912	+	0.493208i	$0.164176\pi$
$522$	0	0
$523$	2.02120e137	1.05020	0.525102	−	0.851039i	$-0.324027\pi$
$523$	2.02120e137	1.05020	0.525102	+	0.851039i	$0.324027\pi$
$524$	−7.91734e136	−0.373550
$525$	0	0
$526$	−1.32644e137	−0.516305
$527$	1.03438e136	0.0365799
$528$	0	0
$529$	3.00939e137	0.878957
$530$	3.45214e137	0.916550
$531$	0	0
$532$	−5.42921e136	−0.119179
$533$	−4.49938e137	−0.898315
$534$	0	0
$535$	4.45450e137	0.736094
$536$	3.74449e137	0.563081
$537$	0	0
$538$	6.70510e136	0.0835412
$539$	1.27947e138	1.45144
$540$	0	0
$541$	7.54522e137	0.709921	0.354960	−	0.934881i	$-0.384494\pi$
$541$	7.54522e137	0.709921	0.354960	+	0.934881i	$0.384494\pi$
$542$	−5.90072e137	−0.505756
$543$	0	0
$544$	−5.12729e137	−0.364874
$545$	−1.30160e138	−0.844220
$546$	0	0
$547$	1.00720e138	0.542946	0.271473	−	0.962446i	$-0.412489\pi$
$547$	1.00720e138	0.542946	0.271473	+	0.962446i	$0.412489\pi$
$548$	−4.85700e137	−0.238754
$549$	0	0
$550$	−1.53377e138	−0.627254
$551$	−1.15083e138	−0.429394
$552$	0	0
$553$	−1.03520e138	−0.321666
$554$	2.09048e138	0.592930
$555$	0	0
$556$	1.27154e138	0.300645
$557$	−3.76306e138	−0.812556	−0.406278	−	0.913749i	$-0.633174\pi$
$557$	−3.76306e138	−0.812556	−0.406278	+	0.913749i	$0.633174\pi$
$558$	0	0
$559$	−6.74504e137	−0.121531
$560$	1.24208e138	0.204481
$561$	0	0
$562$	1.81283e138	0.249272
$563$	6.33267e138	0.796000	0.398000	−	0.917385i	$-0.369704\pi$
$563$	6.33267e138	0.796000	0.398000	+	0.917385i	$0.369704\pi$
$564$	0	0
$565$	−8.92641e138	−0.938059
$566$	1.10158e139	1.05873
$567$	0	0
$568$	1.63659e139	1.31628
$569$	9.81189e138	0.722077	0.361038	−	0.932551i	$-0.382422\pi$
$569$	9.81189e138	0.722077	0.361038	+	0.932551i	$0.382422\pi$
$570$	0	0
$571$	−2.82442e139	−1.74103	−0.870515	−	0.492141i	$-0.836214\pi$
$571$	−2.82442e139	−1.74103	−0.870515	+	0.492141i	$0.836214\pi$
$572$	6.82881e138	0.385342
$573$	0	0
$574$	−1.24168e139	−0.587435
$575$	1.28638e139	0.557368
$576$	0	0
$577$	−8.15873e138	−0.296650	−0.148325	−	0.988939i	$-0.547388\pi$
$577$	−8.15873e138	−0.296650	−0.148325	+	0.988939i	$0.547388\pi$
$578$	1.65441e139	0.551171
$579$	0	0
$580$	−5.46868e138	−0.153027
$581$	3.14834e138	0.0807581
$582$	0	0
$583$	1.28485e140	2.77070
$584$	−1.26295e139	−0.249769
$585$	0	0
$586$	8.76117e139	1.45792
$587$	1.00425e140	1.53327	0.766633	−	0.642086i	$-0.221931\pi$
$587$	1.00425e140	1.53327	0.766633	+	0.642086i	$0.221931\pi$
$588$	0	0
$589$	−3.65317e138	−0.0469729
$590$	4.47781e139	0.528493
$591$	0	0
$592$	−2.68373e139	−0.266989
$593$	−8.91714e139	−0.814636	−0.407318	−	0.913286i	$-0.633536\pi$
$593$	−8.91714e139	−0.814636	−0.407318	+	0.913286i	$0.633536\pi$
$594$	0	0
$595$	−2.74816e139	−0.211804
$596$	2.29016e139	0.162155
$597$	0	0
$598$	1.12405e140	0.672010
$599$	1.43219e140	0.786949	0.393475	−	0.919335i	$-0.371273\pi$
$599$	1.43219e140	0.786949	0.393475	+	0.919335i	$0.371273\pi$
$600$	0	0
$601$	2.96889e140	1.37859	0.689293	−	0.724483i	$-0.257921\pi$
$601$	2.96889e140	1.37859	0.689293	+	0.724483i	$0.257921\pi$
$602$	−1.86141e139	−0.0794728
$603$	0	0
$604$	1.01146e139	0.0365245
$605$	6.01152e140	1.99682
$606$	0	0
$607$	1.14900e140	0.323067	0.161534	−	0.986867i	$-0.448356\pi$
$607$	1.14900e140	0.323067	0.161534	+	0.986867i	$0.448356\pi$
$608$	1.81084e140	0.468542
$609$	0	0
$610$	5.43579e140	1.19153
$611$	1.01555e140	0.204937
$612$	0	0
$613$	2.62097e140	0.448444	0.224222	−	0.974538i	$-0.428016\pi$
$613$	2.62097e140	0.448444	0.224222	+	0.974538i	$0.428016\pi$
$614$	8.80659e140	1.38773
$615$	0	0
$616$	7.46763e140	0.998520
$617$	1.16164e141	1.43110	0.715552	−	0.698559i	$-0.246175\pi$
$617$	1.16164e141	1.43110	0.715552	+	0.698559i	$0.246175\pi$
$618$	0	0
$619$	−1.09614e141	−1.14680	−0.573402	−	0.819274i	$-0.694377\pi$
$619$	−1.09614e141	−1.14680	−0.573402	+	0.819274i	$0.694377\pi$
$620$	−1.73596e139	−0.0167402
$621$	0	0
$622$	−7.50452e140	−0.615047
$623$	5.46333e140	0.412868
$624$	0	0
$625$	−6.65939e140	−0.428049
$626$	6.17410e140	0.366075
$627$	0	0
$628$	−3.84698e140	−0.194159
$629$	5.93788e140	0.276550
$630$	0	0
$631$	1.04696e141	0.415381	0.207691	−	0.978195i	$-0.433405\pi$
$631$	1.04696e141	0.415381	0.207691	+	0.978195i	$0.433405\pi$
$632$	1.97567e141	0.723607
$633$	0	0
$634$	1.14301e141	0.356895
$635$	1.44845e141	0.417668
$636$	0	0
$637$	−1.87498e141	−0.461271
$638$	3.99464e141	0.907891
$639$	0	0
$640$	−9.11782e140	−0.176930
$641$	−9.77655e140	−0.175329	−0.0876647	−	0.996150i	$-0.527940\pi$
$641$	−9.77655e140	−0.175329	−0.0876647	+	0.996150i	$0.527940\pi$
$642$	0	0
$643$	5.45078e141	0.835227	0.417614	−	0.908625i	$-0.362867\pi$
$643$	5.45078e141	0.835227	0.417614	+	0.908625i	$0.362867\pi$
$644$	−1.58056e141	−0.223911
$645$	0	0
$646$	2.78536e141	0.337395
$647$	1.17949e142	1.32138	0.660692	−	0.750657i	$-0.270263\pi$
$647$	1.17949e142	1.32138	0.660692	+	0.750657i	$0.270263\pi$
$648$	0	0
$649$	1.66659e142	1.59762
$650$	2.24763e141	0.199343
$651$	0	0
$652$	−2.07605e141	−0.157664
$653$	1.63413e142	1.14861	0.574303	−	0.818643i	$-0.305273\pi$
$653$	1.63413e142	1.14861	0.574303	+	0.818643i	$0.305273\pi$
$654$	0	0
$655$	1.41539e142	0.852492
$656$	1.46700e142	0.818063
$657$	0	0
$658$	2.80258e141	0.134014
$659$	−3.81560e142	−1.68985	−0.844927	−	0.534881i	$-0.820356\pi$
$659$	−3.81560e142	−1.68985	−0.844927	+	0.534881i	$0.820356\pi$
$660$	0	0
$661$	4.39849e142	1.67159	0.835795	−	0.549041i	$-0.185007\pi$
$661$	4.39849e142	1.67159	0.835795	+	0.549041i	$0.185007\pi$
$662$	2.87673e142	1.01291
$663$	0	0
$664$	−6.00858e141	−0.181670
$665$	9.70584e141	0.271982
$666$	0	0
$667$	−3.35032e142	−0.806737
$668$	4.51018e141	0.100689
$669$	0	0
$670$	−1.68931e142	−0.324289
$671$	2.02314e143	3.60196
$672$	0	0
$673$	−4.95594e140	−0.00759216	−0.00379608	−	0.999993i	$-0.501208\pi$
$673$	−4.95594e140	−0.00759216	−0.00379608	+	0.999993i	$0.501208\pi$
$674$	−3.45139e142	−0.490534
$675$	0	0
$676$	1.75754e142	0.215079
$677$	−8.50309e142	−0.965715	−0.482857	−	0.875699i	$-0.660401\pi$
$677$	−8.50309e142	−0.965715	−0.482857	+	0.875699i	$0.660401\pi$
$678$	0	0
$679$	1.83366e142	0.179430
$680$	5.24484e142	0.476466
$681$	0	0
$682$	1.26805e142	0.0993173
$683$	2.16958e143	1.57809	0.789043	−	0.614339i	$-0.210577\pi$
$683$	2.16958e143	1.57809	0.789043	+	0.614339i	$0.210577\pi$
$684$	0	0
$685$	8.68291e142	0.544868
$686$	−1.19311e143	−0.695523
$687$	0	0
$688$	2.19919e142	0.110674
$689$	−1.88286e143	−0.880535
$690$	0	0
$691$	−5.23754e142	−0.211586	−0.105793	−	0.994388i	$-0.533738\pi$
$691$	−5.23754e142	−0.211586	−0.105793	+	0.994388i	$0.533738\pi$
$692$	1.87397e142	0.0703727
$693$	0	0
$694$	2.27004e143	0.736851
$695$	−2.27315e143	−0.686112
$696$	0	0
$697$	−3.24581e143	−0.847360
$698$	2.70678e143	0.657285
$699$	0	0
$700$	−3.16046e142	−0.0664201
$701$	9.46919e141	0.0185162	0.00925812	−	0.999957i	$-0.497053\pi$
$701$	9.46919e141	0.0185162	0.00925812	+	0.999957i	$0.497053\pi$
$702$	0	0
$703$	−2.09712e143	−0.355123
$704$	−1.28818e144	−2.03029
$705$	0	0
$706$	6.65833e143	0.909344
$707$	−1.75559e143	−0.223225
$708$	0	0
$709$	−1.18469e144	−1.30608	−0.653039	−	0.757324i	$-0.726506\pi$
$709$	−1.18469e144	−1.30608	−0.653039	+	0.757324i	$0.726506\pi$
$710$	−7.38342e143	−0.758072
$711$	0	0
$712$	−1.04267e144	−0.928770
$713$	−1.06352e143	−0.0882517
$714$	0	0
$715$	−1.22079e144	−0.879401
$716$	3.52522e143	0.236635
$717$	0	0
$718$	−9.77848e143	−0.570147
$719$	−3.12750e144	−1.69976	−0.849881	−	0.526974i	$-0.823326\pi$
$719$	−3.12750e144	−1.69976	−0.849881	+	0.526974i	$0.823326\pi$
$720$	0	0
$721$	8.81434e143	0.416350
$722$	8.64302e143	0.380660
$723$	0	0
$724$	3.08599e143	0.118195
$725$	−6.69925e143	−0.239308
$726$	0	0
$727$	6.15549e143	0.191326	0.0956632	−	0.995414i	$-0.469503\pi$
$727$	6.15549e143	0.191326	0.0956632	+	0.995414i	$0.469503\pi$
$728$	−1.09433e144	−0.317332
$729$	0	0
$730$	5.69776e143	0.143847
$731$	−4.86581e143	−0.114638
$732$	0	0
$733$	−2.88576e144	−0.592255	−0.296128	−	0.955148i	$-0.595695\pi$
$733$	−2.88576e144	−0.592255	−0.296128	+	0.955148i	$0.595695\pi$
$734$	2.59352e144	0.496865
$735$	0	0
$736$	5.27174e144	0.880287
$737$	−6.28742e144	−0.980313
$738$	0	0
$739$	−1.27820e145	−1.73802	−0.869008	−	0.494798i	$-0.835242\pi$
$739$	−1.27820e145	−1.73802	−0.869008	+	0.494798i	$0.835242\pi$
$740$	−9.96538e143	−0.126559
$741$	0	0
$742$	−5.19607e144	−0.575808
$743$	4.61819e144	0.478120	0.239060	−	0.971005i	$-0.423161\pi$
$743$	4.61819e144	0.478120	0.239060	+	0.971005i	$0.423161\pi$
$744$	0	0
$745$	−4.09415e144	−0.370060
$746$	−1.79689e145	−1.51779
$747$	0	0
$748$	4.92624e144	0.363484
$749$	−6.70481e144	−0.462439
$750$	0	0
$751$	1.60089e145	0.965041	0.482521	−	0.875885i	$-0.339721\pi$
$751$	1.60089e145	0.965041	0.482521	+	0.875885i	$0.339721\pi$
$752$	−3.31115e144	−0.186628
$753$	0	0
$754$	−5.85388e144	−0.288530
$755$	−1.80820e144	−0.0833538
$756$	0	0
$757$	4.02375e145	1.62289	0.811445	−	0.584429i	$-0.198681\pi$
$757$	4.02375e145	1.62289	0.811445	+	0.584429i	$0.198681\pi$
$758$	−1.57032e145	−0.592507
$759$	0	0
$760$	−1.85235e145	−0.611839
$761$	−2.36459e145	−0.730854	−0.365427	−	0.930840i	$-0.619077\pi$
$761$	−2.36459e145	−0.730854	−0.365427	+	0.930840i	$0.619077\pi$
$762$	0	0
$763$	1.95914e145	0.530368
$764$	−2.62808e145	−0.665923
$765$	0	0
$766$	−4.80966e144	−0.106798
$767$	−2.44228e145	−0.507726
$768$	0	0
$769$	−9.23730e145	−1.68370	−0.841851	−	0.539710i	$-0.818534\pi$
$769$	−9.23730e145	−1.68370	−0.841851	+	0.539710i	$0.818534\pi$
$770$	−3.36899e145	−0.575066
$771$	0	0
$772$	−1.93146e145	−0.289209
$773$	2.95288e145	0.414173	0.207086	−	0.978323i	$-0.433602\pi$
$773$	2.95288e145	0.414173	0.207086	+	0.978323i	$0.433602\pi$
$774$	0	0
$775$	−2.12659e144	−0.0261787
$776$	−3.49953e145	−0.403639
$777$	0	0
$778$	3.12326e145	0.316329
$779$	1.14634e146	1.08811
$780$	0	0
$781$	−2.74803e146	−2.29163
$782$	8.10879e145	0.633892
$783$	0	0
$784$	6.11329e145	0.420062
$785$	6.87728e145	0.443098
$786$	0	0
$787$	1.33841e146	0.758343	0.379171	−	0.925326i	$-0.376209\pi$
$787$	1.33841e146	0.758343	0.379171	+	0.925326i	$0.376209\pi$
$788$	−2.47184e145	−0.131355
$789$	0	0
$790$	−8.91316e145	−0.416739
$791$	1.34358e146	0.589320
$792$	0	0
$793$	−2.96478e146	−1.14471
$794$	−1.82917e146	−0.662703
$795$	0	0
$796$	1.23229e146	0.393190
$797$	−2.71043e144	−0.00811696	−0.00405848	−	0.999992i	$-0.501292\pi$
$797$	−2.71043e144	−0.00811696	−0.00405848	+	0.999992i	$0.501292\pi$
$798$	0	0
$799$	7.32608e145	0.193312
$800$	1.05413e146	0.261125
$801$	0	0
$802$	6.83979e146	1.49361
$803$	2.12064e146	0.434843
$804$	0	0
$805$	2.82558e146	0.510994
$806$	−1.85824e145	−0.0315633
$807$	0	0
$808$	3.35053e146	0.502157
$809$	7.92293e146	1.11554	0.557771	−	0.829995i	$-0.311657\pi$
$809$	7.92293e146	1.11554	0.557771	+	0.829995i	$0.311657\pi$
$810$	0	0
$811$	4.85339e146	0.603243	0.301621	−	0.953428i	$-0.402472\pi$
$811$	4.85339e146	0.603243	0.301621	+	0.953428i	$0.402472\pi$
$812$	8.23132e145	0.0961369
$813$	0	0
$814$	7.27929e146	0.750856
$815$	3.71137e146	0.359811
$816$	0	0
$817$	1.71849e146	0.147208
$818$	8.95164e146	0.720877
$819$	0	0
$820$	5.44736e146	0.387781
$821$	1.28716e147	0.861593	0.430796	−	0.902449i	$-0.358233\pi$
$821$	1.28716e147	0.861593	0.430796	+	0.902449i	$0.358233\pi$
$822$	0	0
$823$	6.44259e146	0.381389	0.190695	−	0.981649i	$-0.438926\pi$
$823$	6.44259e146	0.381389	0.190695	+	0.981649i	$0.438926\pi$
$824$	−1.68221e147	−0.936604
$825$	0	0
$826$	−6.73989e146	−0.332017
$827$	3.99006e147	1.84906	0.924531	−	0.381107i	$-0.124457\pi$
$827$	3.99006e147	1.84906	0.924531	+	0.381107i	$0.124457\pi$
$828$	0	0
$829$	1.05489e147	0.432717	0.216359	−	0.976314i	$-0.430582\pi$
$829$	1.05489e147	0.432717	0.216359	+	0.976314i	$0.430582\pi$
$830$	2.71074e146	0.104627
$831$	0	0
$832$	1.88774e147	0.645231
$833$	−1.35259e147	−0.435106
$834$	0	0
$835$	−8.06289e146	−0.229786
$836$	−1.73983e147	−0.466756
$837$	0	0
$838$	1.42939e147	0.339882
$839$	8.81853e147	1.97432	0.987160	−	0.159737i	$-0.0510647\pi$
$839$	8.81853e147	1.97432	0.987160	+	0.159737i	$0.0510647\pi$
$840$	0	0
$841$	−3.29250e147	−0.653624
$842$	6.49203e147	1.21372
$843$	0	0
$844$	2.88487e147	0.478446
$845$	−3.14198e147	−0.490839
$846$	0	0
$847$	−9.04839e147	−1.25447
$848$	6.13897e147	0.801871
$849$	0	0
$850$	1.62142e147	0.188036
$851$	−6.10517e147	−0.667199
$852$	0	0
$853$	−1.29264e148	−1.25474	−0.627369	−	0.778722i	$-0.715868\pi$
$853$	−1.29264e148	−1.25474	−0.627369	+	0.778722i	$0.715868\pi$
$854$	−8.18181e147	−0.748560
$855$	0	0
$856$	1.27961e148	1.04028
$857$	1.60312e148	1.22867	0.614333	−	0.789047i	$-0.289425\pi$
$857$	1.60312e148	1.22867	0.614333	+	0.789047i	$0.289425\pi$
$858$	0	0
$859$	5.02898e147	0.342630	0.171315	−	0.985216i	$-0.445198\pi$
$859$	5.02898e147	0.342630	0.171315	+	0.985216i	$0.445198\pi$
$860$	8.16615e146	0.0524621
$861$	0	0
$862$	−4.04524e147	−0.231115
$863$	−1.54202e148	−0.830890	−0.415445	−	0.909618i	$-0.636374\pi$
$863$	−1.54202e148	−0.830890	−0.415445	+	0.909618i	$0.636374\pi$
$864$	0	0
$865$	−3.35011e147	−0.160600
$866$	−1.41647e148	−0.640551
$867$	0	0
$868$	2.61293e146	0.0105167
$869$	−3.31738e148	−1.25979
$870$	0	0
$871$	9.21380e147	0.311546
$872$	−3.73901e148	−1.19309
$873$	0	0
$874$	−2.86383e148	−0.813992
$875$	1.95452e148	0.524364
$876$	0	0
$877$	−7.14743e148	−1.70872	−0.854359	−	0.519684i	$-0.826050\pi$
$877$	−7.14743e148	−1.70872	−0.854359	+	0.519684i	$0.826050\pi$
$878$	−5.85215e148	−1.32082
$879$	0	0
$880$	3.98034e148	0.800838
$881$	2.08981e148	0.397030	0.198515	−	0.980098i	$-0.436388\pi$
$881$	2.08981e148	0.397030	0.198515	+	0.980098i	$0.436388\pi$
$882$	0	0
$883$	1.01269e149	1.71577	0.857886	−	0.513840i	$-0.171778\pi$
$883$	1.01269e149	1.71577	0.857886	+	0.513840i	$0.171778\pi$
$884$	−7.21908e147	−0.115516
$885$	0	0
$886$	3.81389e148	0.544459
$887$	8.02411e148	1.08207	0.541034	−	0.841001i	$-0.318033\pi$
$887$	8.02411e148	1.08207	0.541034	+	0.841001i	$0.318033\pi$
$888$	0	0
$889$	−2.18018e148	−0.262393
$890$	4.70397e148	0.534896
$891$	0	0
$892$	2.49882e148	0.253694
$893$	−2.58740e148	−0.248236
$894$	0	0
$895$	−6.30207e148	−0.540033
$896$	1.37239e148	0.111154
$897$	0	0
$898$	−8.53432e148	−0.617609
$899$	5.53864e147	0.0378912
$900$	0	0
$901$	−1.35828e149	−0.830589
$902$	−3.97906e149	−2.30065
$903$	0	0
$904$	−2.56421e149	−1.32571
$905$	−5.51686e148	−0.269736
$906$	0	0
$907$	5.06153e148	0.221368	0.110684	−	0.993856i	$-0.464696\pi$
$907$	5.06153e148	0.221368	0.110684	+	0.993856i	$0.464696\pi$
$908$	3.91909e148	0.162125
$909$	0	0
$910$	4.93703e148	0.182757
$911$	−2.45697e149	−0.860444	−0.430222	−	0.902723i	$-0.641565\pi$
$911$	−2.45697e149	−0.860444	−0.430222	+	0.902723i	$0.641565\pi$
$912$	0	0
$913$	1.00891e149	0.316284
$914$	1.69288e149	0.502162
$915$	0	0
$916$	1.38286e149	0.367331
$917$	−2.13041e149	−0.535564
$918$	0	0
$919$	−5.29393e149	−1.19219	−0.596095	−	0.802914i	$-0.703282\pi$
$919$	−5.29393e149	−1.19219	−0.596095	+	0.802914i	$0.703282\pi$
$920$	−5.39260e149	−1.14951
$921$	0	0
$922$	6.92915e149	1.32364
$923$	4.02705e149	0.728285
$924$	0	0
$925$	−1.22078e149	−0.197916
$926$	4.65189e149	0.714126
$927$	0	0
$928$	−2.74544e149	−0.377954
$929$	−1.40418e150	−1.83075	−0.915376	−	0.402600i	$-0.868107\pi$
$929$	−1.40418e150	−1.83075	−0.915376	+	0.402600i	$0.868107\pi$
$930$	0	0
$931$	4.77704e149	0.558728
$932$	1.23992e149	0.137370
$933$	0	0
$934$	−1.03812e150	−1.03212
$935$	−8.80669e149	−0.829519
$936$	0	0
$937$	−1.68453e150	−1.42439	−0.712196	−	0.701981i	$-0.752299\pi$
$937$	−1.68453e150	−1.42439	−0.712196	+	0.701981i	$0.752299\pi$
$938$	2.54271e149	0.203729
$939$	0	0
$940$	−1.22952e149	−0.0884662
$941$	−2.17412e149	−0.148254	−0.0741272	−	0.997249i	$-0.523617\pi$
$941$	−2.17412e149	−0.148254	−0.0741272	+	0.997249i	$0.523617\pi$
$942$	0	0
$943$	3.33726e150	2.04432
$944$	7.96294e149	0.462368
$945$	0	0
$946$	−5.96503e149	−0.311250
$947$	2.61387e150	1.29303	0.646516	−	0.762900i	$-0.276225\pi$
$947$	2.61387e150	1.29303	0.646516	+	0.762900i	$0.276225\pi$
$948$	0	0
$949$	−3.10766e149	−0.138194
$950$	−5.72647e149	−0.241460
$951$	0	0
$952$	−7.89440e149	−0.299332
$953$	2.67818e150	0.963050	0.481525	−	0.876432i	$-0.340083\pi$
$953$	2.67818e150	0.963050	0.481525	+	0.876432i	$0.340083\pi$
$954$	0	0
$955$	4.69825e150	1.51973
$956$	−4.91290e148	−0.0150735
$957$	0	0
$958$	−2.45597e150	−0.678055
$959$	−1.30693e150	−0.342304
$960$	0	0
$961$	−4.22403e150	−0.995855
$962$	−1.06673e150	−0.238624
$963$	0	0
$964$	1.12892e150	0.227390
$965$	3.45289e150	0.660014
$966$	0	0
$967$	−1.44436e150	−0.248678	−0.124339	−	0.992240i	$-0.539681\pi$
$967$	−1.44436e150	−0.248678	−0.124339	+	0.992240i	$0.539681\pi$
$968$	1.72688e151	2.82200
$969$	0	0
$970$	1.57880e150	0.232463
$971$	−2.05283e150	−0.286934	−0.143467	−	0.989655i	$-0.545825\pi$
$971$	−2.05283e150	−0.286934	−0.143467	+	0.989655i	$0.545825\pi$
$972$	0	0
$973$	3.42148e150	0.431038
$974$	1.07214e151	1.28240
$975$	0	0
$976$	9.66651e150	1.04245
$977$	−8.85563e150	−0.906868	−0.453434	−	0.891290i	$-0.649801\pi$
$977$	−8.85563e150	−0.906868	−0.453434	+	0.891290i	$0.649801\pi$
$978$	0	0
$979$	1.75077e151	1.61697
$980$	2.27002e150	0.199119
$981$	0	0
$982$	8.08536e150	0.639837
$983$	1.64570e151	1.23708	0.618542	−	0.785752i	$-0.287724\pi$
$983$	1.64570e151	1.23708	0.618542	+	0.785752i	$0.287724\pi$
$984$	0	0
$985$	4.41893e150	0.299770
$986$	−4.22294e150	−0.272164
$987$	0	0
$988$	2.54961e150	0.148336
$989$	5.00289e150	0.276572
$990$	0	0
$991$	−1.18475e150	−0.0591437	−0.0295718	−	0.999563i	$-0.509414\pi$
$991$	−1.18475e150	−0.0591437	−0.0295718	+	0.999563i	$0.509414\pi$
$992$	−8.71505e149	−0.0413457
$993$	0	0
$994$	1.11133e151	0.476247
$995$	−2.20297e151	−0.897311
$996$	0	0
$997$	2.26170e151	0.832396	0.416198	−	0.909274i	$-0.363362\pi$
$997$	2.26170e151	0.832396	0.416198	+	0.909274i	$0.363362\pi$
$998$	−1.60243e151	−0.560644
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.102.a.b.1.3		8
3.2	odd	2		1.102.a.a.1.6	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.102.a.a.1.6	✓	8	3.2	odd	2
9.102.a.b.1.3		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)

\(f(q)\)	\(=\)	\(q-1.29597e15 q^{2} -8.55769e29 q^{4} +1.52987e35 q^{5} -2.30272e42 q^{7} +4.39472e45 q^{8} +O(q^{10})\)	\(q-1.29597e15 q^{2} -8.55769e29 q^{4} +1.52987e35 q^{5} -2.30272e42 q^{7} +4.39472e45 q^{8} -1.98266e50 q^{10} -7.37923e52 q^{11} +1.08138e56 q^{13} +2.98425e57 q^{14} -3.52578e60 q^{16} +7.80096e61 q^{17} -2.75511e64 q^{19} -1.30921e65 q^{20} +9.56325e67 q^{22} -8.02073e68 q^{23} -1.60381e70 q^{25} -1.40143e71 q^{26} +1.97059e72 q^{28} +4.17708e73 q^{29} +1.32596e74 q^{31} -6.57264e75 q^{32} -1.01098e77 q^{34} -3.52285e77 q^{35} +7.61174e78 q^{37} +3.57054e79 q^{38} +6.72333e80 q^{40} -4.16079e81 q^{41} -6.23745e81 q^{43} +6.31492e82 q^{44} +1.03946e84 q^{46} +9.39126e83 q^{47} -1.73388e85 q^{49} +2.07849e85 q^{50} -9.25410e85 q^{52} -1.74117e87 q^{53} -1.12892e88 q^{55} -1.01198e88 q^{56} -5.41336e88 q^{58} -2.25849e89 q^{59} -2.74167e90 q^{61} -1.71840e89 q^{62} +1.74568e91 q^{64} +1.65436e91 q^{65} +8.52043e91 q^{67} -6.67582e91 q^{68} +4.56550e92 q^{70} +3.72400e93 q^{71} -2.87380e93 q^{73} -9.86457e93 q^{74} +2.35774e94 q^{76} +1.69923e95 q^{77} +4.49556e95 q^{79} -5.39397e95 q^{80} +5.39225e96 q^{82} -1.36723e96 q^{83} +1.19344e97 q^{85} +8.08353e96 q^{86} -3.24296e98 q^{88} -2.37256e98 q^{89} -2.49011e98 q^{91} +6.86390e98 q^{92} -1.21708e99 q^{94} -4.21495e99 q^{95} -7.96305e99 q^{97} +2.24706e100 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 434989091795040 q^{2} + 90\!\cdots\!96 q^{4}+ \cdots + 61\!\cdots\!20 q^{8}+O(q^{10}) \) 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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