LMFDB - Embedded newform 9.102.a.b.1.1

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			1.1
Root			$-2.72721e13$ 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)

$f(q)$	$=$	$q-2.56375e15 q^{2} +4.03750e30 q^{4} -2.88877e35 q^{5} -6.25978e42 q^{7} -3.85125e45 q^{8} +O(q^{10})$	\(q-2.56375e15 q^{2} +4.03750e30 q^{4} -2.88877e35 q^{5} -6.25978e42 q^{7} -3.85125e45 q^{8} +7.40607e50 q^{10} +2.44501e52 q^{11} -8.21796e55 q^{13} +1.60485e58 q^{14} -3.62648e59 q^{16} +1.73969e62 q^{17} -3.05406e64 q^{19} -1.16634e66 q^{20} -6.26838e67 q^{22} -2.17017e68 q^{23} +4.40068e70 q^{25} +2.10688e71 q^{26} -2.52738e73 q^{28} -1.39854e74 q^{29} -3.23973e75 q^{31} +1.06938e76 q^{32} -4.46012e77 q^{34} +1.80831e78 q^{35} +1.43241e79 q^{37} +7.82984e79 q^{38} +1.11254e81 q^{40} -4.24481e81 q^{41} +1.21927e82 q^{43} +9.87171e82 q^{44} +5.56377e83 q^{46} +3.72383e84 q^{47} +1.65435e85 q^{49} -1.12822e86 q^{50} -3.31800e86 q^{52} +1.31257e87 q^{53} -7.06306e87 q^{55} +2.41080e88 q^{56} +3.58550e89 q^{58} +2.92483e89 q^{59} -4.65268e89 q^{61} +8.30584e90 q^{62} -2.64968e91 q^{64} +2.37398e91 q^{65} +1.13200e92 q^{67} +7.02398e92 q^{68} -4.63604e93 q^{70} +1.95260e93 q^{71} -9.13236e93 q^{73} -3.67234e94 q^{74} -1.23308e95 q^{76} -1.53052e95 q^{77} -4.27479e95 q^{79} +1.04761e95 q^{80} +1.08826e97 q^{82} -1.25026e97 q^{83} -5.02556e97 q^{85} -3.12590e97 q^{86} -9.41633e97 q^{88} -1.65813e98 q^{89} +5.14426e98 q^{91} -8.76206e98 q^{92} -9.54696e99 q^{94} +8.82247e99 q^{95} +1.54750e100 q^{97} -4.24133e100 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.56375e15	−1.61013	−0.805064	−	0.593188i	$-0.797869\pi$
$2$	−2.56375e15	−1.61013	−0.805064	+	0.593188i	$0.797869\pi$
$3$	0	0
$3$	0	0
$4$	4.03750e30	1.59251
$5$	−2.88877e35	−1.45455	−0.727273	−	0.686348i	$-0.759213\pi$
$5$	−2.88877e35	−1.45455	−0.727273	+	0.686348i	$0.759213\pi$
$6$	0	0
$7$	−6.25978e42	−1.31555	−0.657776	−	0.753214i	$-0.728503\pi$
$7$	−6.25978e42	−1.31555	−0.657776	+	0.753214i	$0.728503\pi$
$8$	−3.85125e45	−0.954019
$9$	0	0
$10$	7.40607e50	2.34201
$11$	2.44501e52	0.627986	0.313993	−	0.949425i	$-0.398333\pi$
$11$	2.44501e52	0.627986	0.313993	+	0.949425i	$0.398333\pi$
$12$	0	0
$13$	−8.21796e55	−0.457746	−0.228873	−	0.973456i	$-0.573504\pi$
$13$	−8.21796e55	−0.457746	−0.228873	+	0.973456i	$0.573504\pi$
$14$	1.60485e58	2.11821
$15$	0	0
$16$	−3.62648e59	−0.0564191
$17$	1.73969e62	1.26707	0.633535	−	0.773714i	$-0.281603\pi$
$17$	1.73969e62	1.26707	0.633535	+	0.773714i	$0.281603\pi$
$18$	0	0
$19$	−3.05406e64	−0.808762	−0.404381	−	0.914591i	$-0.632513\pi$
$19$	−3.05406e64	−0.808762	−0.404381	+	0.914591i	$0.632513\pi$
$20$	−1.16634e66	−2.31638
$21$	0	0
$22$	−6.26838e67	−1.01114
$23$	−2.17017e68	−0.370884	−0.185442	−	0.982655i	$-0.559372\pi$
$23$	−2.17017e68	−0.370884	−0.185442	+	0.982655i	$0.559372\pi$
$24$	0	0
$25$	4.40068e70	1.11571
$26$	2.10688e71	0.737030
$27$	0	0
$28$	−2.52738e73	−2.09503
$29$	−1.39854e74	−1.97050	−0.985249	−	0.171125i	$-0.945260\pi$
$29$	−1.39854e74	−1.97050	−0.985249	+	0.171125i	$0.945260\pi$
$30$	0	0
$31$	−3.23973e75	−1.57305	−0.786526	−	0.617557i	$-0.788122\pi$
$31$	−3.23973e75	−1.57305	−0.786526	+	0.617557i	$0.788122\pi$
$32$	1.06938e76	1.04486
$33$	0	0
$34$	−4.46012e77	−2.04015
$35$	1.80831e78	1.91353
$36$	0	0
$37$	1.43241e79	0.915968	0.457984	−	0.888960i	$-0.348572\pi$
$37$	1.43241e79	0.915968	0.457984	+	0.888960i	$0.348572\pi$
$38$	7.82984e79	1.30221
$39$	0	0
$40$	1.11254e81	1.38766
$41$	−4.24481e81	−1.52151	−0.760753	−	0.649041i	$-0.775170\pi$
$41$	−4.24481e81	−1.52151	−0.760753	+	0.649041i	$0.775170\pi$
$42$	0	0
$43$	1.21927e82	0.394405	0.197202	−	0.980363i	$-0.436814\pi$
$43$	1.21927e82	0.394405	0.197202	+	0.980363i	$0.436814\pi$
$44$	9.87171e82	1.00007
$45$	0	0
$46$	5.56377e83	0.597171
$47$	3.72383e84	1.34911	0.674556	−	0.738223i	$-0.264335\pi$
$47$	3.72383e84	1.34911	0.674556	+	0.738223i	$0.264335\pi$
$48$	0	0
$49$	1.65435e85	0.730677
$50$	−1.12822e86	−1.79643
$51$	0	0
$52$	−3.31800e86	−0.728966
$53$	1.31257e87	1.10203	0.551013	−	0.834497i	$-0.314242\pi$
$53$	1.31257e87	1.10203	0.551013	+	0.834497i	$0.314242\pi$
$54$	0	0
$55$	−7.06306e87	−0.913434
$56$	2.41080e88	1.25506
$57$	0	0
$58$	3.58550e89	3.17275
$59$	2.92483e89	1.09163	0.545813	−	0.837907i	$-0.316221\pi$
$59$	2.92483e89	1.09163	0.545813	+	0.837907i	$0.316221\pi$
$60$	0	0
$61$	−4.65268e89	−0.322513	−0.161256	−	0.986913i	$-0.551555\pi$
$61$	−4.65268e89	−0.322513	−0.161256	+	0.986913i	$0.551555\pi$
$62$	8.30584e90	2.53281
$63$	0	0
$64$	−2.64968e91	−1.62594
$65$	2.37398e91	0.665813
$66$	0	0
$67$	1.13200e92	0.687180	0.343590	−	0.939120i	$-0.388357\pi$
$67$	1.13200e92	0.687180	0.343590	+	0.939120i	$0.388357\pi$
$68$	7.02398e92	2.01782
$69$	0	0
$70$	−4.63604e93	−3.08103
$71$	1.95260e93	0.633967	0.316984	−	0.948431i	$-0.397330\pi$
$71$	1.95260e93	0.633967	0.316984	+	0.948431i	$0.397330\pi$
$72$	0	0
$73$	−9.13236e93	−0.729086	−0.364543	−	0.931187i	$-0.618775\pi$
$73$	−9.13236e93	−0.729086	−0.364543	+	0.931187i	$0.618775\pi$
$74$	−3.67234e94	−1.47483
$75$	0	0
$76$	−1.23308e95	−1.28796
$77$	−1.53052e95	−0.826148
$78$	0	0
$79$	−4.27479e95	−0.632043	−0.316022	−	0.948752i	$-0.602347\pi$
$79$	−4.27479e95	−0.632043	−0.316022	+	0.948752i	$0.602347\pi$
$80$	1.04761e95	0.0820642
$81$	0	0
$82$	1.08826e97	2.44982
$83$	−1.25026e97	−1.52601	−0.763005	−	0.646392i	$-0.776277\pi$
$83$	−1.25026e97	−1.52601	−0.763005	+	0.646392i	$0.776277\pi$
$84$	0	0
$85$	−5.02556e97	−1.84301
$86$	−3.12590e97	−0.635042
$87$	0	0
$88$	−9.41633e97	−0.599110
$89$	−1.65813e98	−0.596242	−0.298121	−	0.954528i	$-0.596360\pi$
$89$	−1.65813e98	−0.596242	−0.298121	+	0.954528i	$0.596360\pi$
$90$	0	0
$91$	5.14426e98	0.602189
$92$	−8.76206e98	−0.590638
$93$	0	0
$94$	−9.54696e99	−2.17224
$95$	8.82247e99	1.17638
$96$	0	0
$97$	1.54750e100	0.720539	0.360269	−	0.932848i	$-0.382685\pi$
$97$	1.54750e100	0.720539	0.360269	+	0.932848i	$0.382685\pi$
$98$	−4.24133e100	−1.17648
$99$	0	0
$100$	1.77677e101	1.77677
$101$	3.42264e100	0.207077	0.103538	−	0.994625i	$-0.466984\pi$
$101$	3.42264e100	0.207077	0.103538	+	0.994625i	$0.466984\pi$
$102$	0	0
$103$	−3.65070e101	−0.820534	−0.410267	−	0.911965i	$-0.634564\pi$
$103$	−3.65070e101	−0.820534	−0.410267	+	0.911965i	$0.634564\pi$
$104$	3.16494e101	0.436699
$105$	0	0
$106$	−3.36510e102	−1.77440
$107$	−1.09596e102	−0.359679	−0.179839	−	0.983696i	$-0.557558\pi$
$107$	−1.09596e102	−0.359679	−0.179839	+	0.983696i	$0.557558\pi$
$108$	0	0
$109$	1.89257e102	0.243788	0.121894	−	0.992543i	$-0.461103\pi$
$109$	1.89257e102	0.243788	0.121894	+	0.992543i	$0.461103\pi$
$110$	1.81079e103	1.47075
$111$	0	0
$112$	2.27010e102	0.0742223
$113$	6.23836e103	1.30199	0.650997	−	0.759080i	$-0.274351\pi$
$113$	6.23836e103	1.30199	0.650997	+	0.759080i	$0.274351\pi$
$114$	0	0
$115$	6.26913e103	0.539469
$116$	−5.64660e104	−3.13804
$117$	0	0
$118$	−7.49853e104	−1.75766
$119$	−1.08901e105	−1.66690
$120$	0	0
$121$	−9.18061e104	−0.605634
$122$	1.19283e105	0.519287
$123$	0	0
$124$	−1.30804e106	−2.50510
$125$	−1.31837e105	−0.168300
$126$	0	0
$127$	1.87262e106	1.07241	0.536205	−	0.844088i	$-0.319857\pi$
$127$	1.87262e106	1.07241	0.536205	+	0.844088i	$0.319857\pi$
$128$	4.08190e106	1.57311
$129$	0	0
$130$	−6.08628e106	−1.07204
$131$	−5.76238e106	−0.689290	−0.344645	−	0.938733i	$-0.612001\pi$
$131$	−5.76238e106	−0.689290	−0.344645	+	0.938733i	$0.612001\pi$
$132$	0	0
$133$	1.91177e107	1.06397
$134$	−2.90217e107	−1.10645
$135$	0	0
$136$	−6.69997e107	−1.20881
$137$	−7.34857e107	−0.915829	−0.457914	−	0.888996i	$-0.651403\pi$
$137$	−7.34857e107	−0.915829	−0.457914	+	0.888996i	$0.651403\pi$
$138$	0	0
$139$	8.70128e106	0.0521598	0.0260799	−	0.999660i	$-0.491698\pi$
$139$	8.70128e106	0.0521598	0.0260799	+	0.999660i	$0.491698\pi$
$140$	7.30103e108	3.04732
$141$	0	0
$142$	−5.00597e108	−1.02077
$143$	−2.00930e108	−0.287458
$144$	0	0
$145$	4.04006e109	2.86618
$146$	2.34131e109	1.17392
$147$	0	0
$148$	5.78335e109	1.45869
$149$	3.67441e109	0.659600	0.329800	−	0.944051i	$-0.393019\pi$
$149$	3.67441e109	0.659600	0.329800	+	0.944051i	$0.393019\pi$
$150$	0	0
$151$	4.20738e109	0.385191	0.192595	−	0.981278i	$-0.438309\pi$
$151$	4.20738e109	0.385191	0.192595	+	0.981278i	$0.438309\pi$
$152$	1.17619e110	0.771574
$153$	0	0
$154$	3.92387e110	1.33020
$155$	9.35883e110	2.28808
$156$	0	0
$157$	2.25516e110	0.288566	0.144283	−	0.989536i	$-0.453912\pi$
$157$	2.25516e110	0.288566	0.144283	+	0.989536i	$0.453912\pi$
$158$	1.09595e111	1.01767
$159$	0	0
$160$	−3.08919e111	−1.51980
$161$	1.35848e111	0.487918
$162$	0	0
$163$	−5.79305e111	−1.11541	−0.557703	−	0.830040i	$-0.688317\pi$
$163$	−5.79305e111	−1.11541	−0.557703	+	0.830040i	$0.688317\pi$
$164$	−1.71384e112	−2.42302
$165$	0	0
$166$	3.20536e112	2.45707
$167$	2.04226e112	1.15592	0.577961	−	0.816064i	$-0.303848\pi$
$167$	2.04226e112	1.15592	0.577961	+	0.816064i	$0.303848\pi$
$168$	0	0
$169$	−2.54779e112	−0.790468
$170$	1.28843e113	2.96749
$171$	0	0
$172$	4.92279e112	0.628094
$173$	−1.08886e113	−1.03668	−0.518340	−	0.855174i	$-0.673450\pi$
$173$	−1.08886e113	−1.03668	−0.518340	+	0.855174i	$0.673450\pi$
$174$	0	0
$175$	−2.75473e113	−1.46777
$176$	−8.86677e111	−0.0354304
$177$	0	0
$178$	4.25102e113	0.960026
$179$	−8.45466e113	−1.43886	−0.719429	−	0.694566i	$-0.755597\pi$
$179$	−8.45466e113	−1.43886	−0.719429	+	0.694566i	$0.755597\pi$
$180$	0	0
$181$	−2.55677e113	−0.248269	−0.124135	−	0.992265i	$-0.539615\pi$
$181$	−2.55677e113	−0.248269	−0.124135	+	0.992265i	$0.539615\pi$
$182$	−1.31886e114	−0.969601
$183$	0	0
$184$	8.35787e113	0.353831
$185$	−4.13790e114	−1.33232
$186$	0	0
$187$	4.25355e114	0.795702
$188$	1.50350e115	2.14848
$189$	0	0
$190$	−2.26186e115	−1.89413
$191$	−7.87385e114	−0.505827	−0.252914	−	0.967489i	$-0.581389\pi$
$191$	−7.87385e114	−0.505827	−0.252914	+	0.967489i	$0.581389\pi$
$192$	0	0
$193$	−4.31049e115	−1.63637	−0.818187	−	0.574952i	$-0.805021\pi$
$193$	−4.31049e115	−1.63637	−0.818187	+	0.574952i	$0.805021\pi$
$194$	−3.96739e115	−1.16016
$195$	0	0
$196$	6.67943e115	1.16361
$197$	−1.14002e115	−0.153591	−0.0767957	−	0.997047i	$-0.524469\pi$
$197$	−1.14002e115	−0.153591	−0.0767957	+	0.997047i	$0.524469\pi$
$198$	0	0
$199$	−5.38798e115	−0.435859	−0.217929	−	0.975965i	$-0.569930\pi$
$199$	−5.38798e115	−0.435859	−0.217929	+	0.975965i	$0.569930\pi$
$200$	−1.69481e116	−1.06440
$201$	0	0
$202$	−8.77478e115	−0.333420
$203$	8.75456e116	2.59229
$204$	0	0
$205$	1.22623e117	2.21310
$206$	9.35948e116	1.32116
$207$	0	0
$208$	2.98023e115	0.0258256
$209$	−7.46720e116	−0.507891
$210$	0	0
$211$	−2.73700e117	−1.15083	−0.575414	−	0.817862i	$-0.695159\pi$
$211$	−2.73700e117	−1.15083	−0.575414	+	0.817862i	$0.695159\pi$
$212$	5.29950e117	1.75499
$213$	0	0
$214$	2.80977e117	0.579129
$215$	−3.52218e117	−0.573680
$216$	0	0
$217$	2.02800e118	2.06943
$218$	−4.85206e117	−0.392530
$219$	0	0
$220$	−2.85171e118	−1.45465
$221$	−1.42967e118	−0.579997
$222$	0	0
$223$	−5.94409e118	−1.52999	−0.764997	−	0.644034i	$-0.777259\pi$
$223$	−5.94409e118	−1.52999	−0.764997	+	0.644034i	$0.777259\pi$
$224$	−6.69409e118	−1.37457
$225$	0	0
$226$	−1.59936e119	−2.09638
$227$	−1.51279e118	−0.158662	−0.0793309	−	0.996848i	$-0.525278\pi$
$227$	−1.51279e118	−0.158662	−0.0793309	+	0.996848i	$0.525278\pi$
$228$	0	0
$229$	1.06684e119	0.718465	0.359232	−	0.933248i	$-0.383039\pi$
$229$	1.06684e119	0.718465	0.359232	+	0.933248i	$0.383039\pi$
$230$	−1.60725e119	−0.868614
$231$	0	0
$232$	5.38612e119	1.87989
$233$	−2.66360e118	−0.0748160	−0.0374080	−	0.999300i	$-0.511910\pi$
$233$	−2.66360e118	−0.0748160	−0.0374080	+	0.999300i	$0.511910\pi$
$234$	0	0
$235$	−1.07573e120	−1.96235
$236$	1.18090e120	1.73843
$237$	0	0
$238$	2.79194e120	2.68392
$239$	1.14147e119	0.0887912	0.0443956	−	0.999014i	$-0.485864\pi$
$239$	1.14147e119	0.0887912	0.0443956	+	0.999014i	$0.485864\pi$
$240$	0	0
$241$	−4.01998e119	−0.205288	−0.102644	−	0.994718i	$-0.532730\pi$
$241$	−4.01998e119	−0.205288	−0.102644	+	0.994718i	$0.532730\pi$
$242$	2.35368e120	0.975148
$243$	0	0
$244$	−1.87852e120	−0.513605
$245$	−4.77904e120	−1.06280
$246$	0	0
$247$	2.50982e120	0.370208
$248$	1.24770e121	1.50072
$249$	0	0
$250$	3.37998e120	0.270984
$251$	−6.98915e120	−0.458038	−0.229019	−	0.973422i	$-0.573552\pi$
$251$	−6.98915e120	−0.458038	−0.229019	+	0.973422i	$0.573552\pi$
$252$	0	0
$253$	−5.30609e120	−0.232910
$254$	−4.80092e121	−1.72672
$255$	0	0
$256$	−3.74723e121	−0.906969
$257$	1.41846e121	0.281964	0.140982	−	0.990012i	$-0.454974\pi$
$257$	1.41846e121	0.281964	0.140982	+	0.990012i	$0.454974\pi$
$258$	0	0
$259$	−8.96657e121	−1.20500
$260$	9.58493e121	1.06032
$261$	0	0
$262$	1.47733e122	1.10984
$263$	−2.18472e122	−1.35403	−0.677017	−	0.735967i	$-0.736728\pi$
$263$	−2.18472e122	−1.35403	−0.677017	+	0.735967i	$0.736728\pi$
$264$	0	0
$265$	−3.79172e122	−1.60295
$266$	−4.90130e122	−1.71313
$267$	0	0
$268$	4.57046e122	1.09434
$269$	5.08484e122	1.00876	0.504379	−	0.863482i	$-0.331721\pi$
$269$	5.08484e122	1.00876	0.504379	+	0.863482i	$0.331721\pi$
$270$	0	0
$271$	−5.98554e122	−0.816872	−0.408436	−	0.912787i	$-0.633926\pi$
$271$	−5.98554e122	−0.816872	−0.408436	+	0.912787i	$0.633926\pi$
$272$	−6.30894e121	−0.0714870
$273$	0	0
$274$	1.88399e123	1.47460
$275$	1.07597e123	0.700647
$276$	0	0
$277$	−1.50383e123	−0.679156	−0.339578	−	0.940578i	$-0.610284\pi$
$277$	−1.50383e123	−0.679156	−0.339578	+	0.940578i	$0.610284\pi$
$278$	−2.23079e122	−0.0839839
$279$	0	0
$280$	−6.96423e123	−1.82555
$281$	−2.37882e123	−0.520827	−0.260413	−	0.965497i	$-0.583859\pi$
$281$	−2.37882e123	−0.520827	−0.260413	+	0.965497i	$0.583859\pi$
$282$	0	0
$283$	−8.85918e123	−1.35575	−0.677874	−	0.735178i	$-0.737098\pi$
$283$	−8.85918e123	−1.35575	−0.677874	+	0.735178i	$0.737098\pi$
$284$	7.88362e123	1.00960
$285$	0	0
$286$	5.15133e123	0.462844
$287$	2.65716e124	2.00162
$288$	0	0
$289$	1.14139e124	0.605468
$290$	−1.03577e125	−4.61492
$291$	0	0
$292$	−3.68719e124	−1.16108
$293$	7.86213e123	0.208317	0.104159	−	0.994561i	$-0.466785\pi$
$293$	7.86213e123	0.208317	0.104159	+	0.994561i	$0.466785\pi$
$294$	0	0
$295$	−8.44916e124	−1.58782
$296$	−5.51656e124	−0.873851
$297$	0	0
$298$	−9.42025e124	−1.06204
$299$	1.78344e124	0.169771
$300$	0	0
$301$	−7.63235e124	−0.518860
$302$	−1.07867e125	−0.620207
$303$	0	0
$304$	1.10755e124	0.0456296
$305$	1.34405e125	0.469110
$306$	0	0
$307$	5.07790e124	0.127408	0.0637039	−	0.997969i	$-0.479709\pi$
$307$	5.07790e124	0.127408	0.0637039	+	0.997969i	$0.479709\pi$
$308$	−6.17947e125	−1.31565
$309$	0	0
$310$	−2.39937e126	−3.68410
$311$	−8.66949e125	−1.13134	−0.565671	−	0.824631i	$-0.691383\pi$
$311$	−8.66949e125	−1.13134	−0.565671	+	0.824631i	$0.691383\pi$
$312$	0	0
$313$	−2.59518e125	−0.245007	−0.122504	−	0.992468i	$-0.539092\pi$
$313$	−2.59518e125	−0.245007	−0.122504	+	0.992468i	$0.539092\pi$
$314$	−5.78167e125	−0.464629
$315$	0	0
$316$	−1.72594e126	−1.00654
$317$	−2.15142e126	−1.06963	−0.534813	−	0.844971i	$-0.679618\pi$
$317$	−2.15142e126	−1.06963	−0.534813	+	0.844971i	$0.679618\pi$
$318$	0	0
$319$	−3.41944e126	−1.23744
$320$	7.65431e126	2.36501
$321$	0	0
$322$	−3.48280e126	−0.785610
$323$	−5.31311e126	−1.02476
$324$	0	0
$325$	−3.61647e126	−0.510710
$326$	1.48519e127	1.79595
$327$	0	0
$328$	1.63478e127	1.45155
$329$	−2.33104e127	−1.77483
$330$	0	0
$331$	−1.15240e127	−0.646085	−0.323042	−	0.946385i	$-0.604706\pi$
$331$	−1.15240e127	−0.646085	−0.323042	+	0.946385i	$0.604706\pi$
$332$	−5.04793e127	−2.43019
$333$	0	0
$334$	−5.23583e127	−1.86118
$335$	−3.27010e127	−0.999536
$336$	0	0
$337$	−3.11810e127	−0.705635	−0.352817	−	0.935692i	$-0.614776\pi$
$337$	−3.11810e127	−0.705635	−0.352817	+	0.935692i	$0.614776\pi$
$338$	6.53188e127	1.27275
$339$	0	0
$340$	−2.02907e128	−2.93502
$341$	−7.92116e127	−0.987854
$342$	0	0
$343$	3.81711e127	0.354308
$344$	−4.69570e127	−0.376270
$345$	0	0
$346$	2.79157e128	1.66919
$347$	1.04259e128	0.538858	0.269429	−	0.963020i	$-0.413165\pi$
$347$	1.04259e128	0.538858	0.269429	+	0.963020i	$0.413165\pi$
$348$	0	0
$349$	4.27486e128	1.65287	0.826433	−	0.563036i	$-0.190367\pi$
$349$	4.27486e128	1.65287	0.826433	+	0.563036i	$0.190367\pi$
$350$	7.06243e128	2.36330
$351$	0	0
$352$	2.61464e128	0.656157
$353$	−3.37741e128	−0.734449	−0.367224	−	0.930132i	$-0.619692\pi$
$353$	−3.37741e128	−0.734449	−0.367224	+	0.930132i	$0.619692\pi$
$354$	0	0
$355$	−5.64061e128	−0.922135
$356$	−6.69469e128	−0.949523
$357$	0	0
$358$	2.16756e129	2.31675
$359$	2.13662e129	1.98362	0.991810	−	0.127724i	$-0.0407671\pi$
$359$	2.13662e129	1.98362	0.991810	+	0.127724i	$0.0407671\pi$
$360$	0	0
$361$	−4.93253e128	−0.345904
$362$	6.55490e128	0.399745
$363$	0	0
$364$	2.07699e129	0.958993
$365$	2.63813e129	1.06049
$366$	0	0
$367$	−8.11750e128	−0.247620	−0.123810	−	0.992306i	$-0.539511\pi$
$367$	−8.11750e128	−0.247620	−0.123810	+	0.992306i	$0.539511\pi$
$368$	7.87009e127	0.0209250
$369$	0	0
$370$	1.06085e130	2.14520
$371$	−8.21641e129	−1.44977
$372$	0	0
$373$	4.08727e129	0.549714	0.274857	−	0.961485i	$-0.411369\pi$
$373$	4.08727e129	0.549714	0.274857	+	0.961485i	$0.411369\pi$
$374$	−1.09050e130	−1.28118
$375$	0	0
$376$	−1.43414e130	−1.28708
$377$	1.14932e130	0.901989
$378$	0	0
$379$	−5.94249e129	−0.357017	−0.178508	−	0.983938i	$-0.557127\pi$
$379$	−5.94249e129	−0.357017	−0.178508	+	0.983938i	$0.557127\pi$
$380$	3.56207e130	1.87340
$381$	0	0
$382$	2.01866e130	0.814447
$383$	−3.05852e130	−1.08137	−0.540684	−	0.841226i	$-0.681834\pi$
$383$	−3.05852e130	−1.08137	−0.540684	+	0.841226i	$0.681834\pi$
$384$	0	0
$385$	4.42132e130	1.20167
$386$	1.10510e131	2.63477
$387$	0	0
$388$	6.24801e130	1.14747
$389$	−7.76173e130	−1.25171	−0.625855	−	0.779940i	$-0.715250\pi$
$389$	−7.76173e130	−1.25171	−0.625855	+	0.779940i	$0.715250\pi$
$390$	0	0
$391$	−3.77542e130	−0.469937
$392$	−6.37131e130	−0.697080
$393$	0	0
$394$	2.92271e130	0.247302
$395$	1.23489e131	0.919336
$396$	0	0
$397$	−1.13551e131	−0.655044	−0.327522	−	0.944844i	$-0.606214\pi$
$397$	−1.13551e131	−0.655044	−0.327522	+	0.944844i	$0.606214\pi$
$398$	1.38134e131	0.701789
$399$	0	0
$400$	−1.59590e130	−0.0629471
$401$	−4.48151e131	−1.55824	−0.779119	−	0.626876i	$-0.784333\pi$
$401$	−4.48151e131	−1.55824	−0.779119	+	0.626876i	$0.784333\pi$
$402$	0	0
$403$	2.66240e131	0.720059
$404$	1.38189e131	0.329772
$405$	0	0
$406$	−2.24445e132	−4.17392
$407$	3.50225e131	0.575215
$408$	0	0
$409$	−1.25927e132	−1.61469	−0.807347	−	0.590077i	$-0.799098\pi$
$409$	−1.25927e132	−1.61469	−0.807347	+	0.590077i	$0.799098\pi$
$410$	−3.14374e132	−3.56338
$411$	0	0
$412$	−1.47397e132	−1.30671
$413$	−1.83088e132	−1.43609
$414$	0	0
$415$	3.61172e132	2.21965
$416$	−8.78813e131	−0.478281
$417$	0	0
$418$	1.91440e132	0.817769
$419$	2.46484e132	0.933214	0.466607	−	0.884465i	$-0.345476\pi$
$419$	2.46484e132	0.933214	0.466607	+	0.884465i	$0.345476\pi$
$420$	0	0
$421$	−4.71464e132	−1.40347	−0.701734	−	0.712439i	$-0.747590\pi$
$421$	−4.71464e132	−1.40347	−0.701734	+	0.712439i	$0.747590\pi$
$422$	7.01697e132	1.85298
$423$	0	0
$424$	−5.05504e132	−1.05135
$425$	7.65582e132	1.41368
$426$	0	0
$427$	2.91248e132	0.424282
$428$	−4.42494e132	−0.572793
$429$	0	0
$430$	9.02999e132	0.923699
$431$	1.67772e133	1.52622	0.763111	−	0.646268i	$-0.223671\pi$
$431$	1.67772e133	1.52622	0.763111	+	0.646268i	$0.223671\pi$
$432$	0	0
$433$	−6.18307e129	−0.000445211 0	−0.000222605	−	1.00000i	$-0.500071\pi$
$433$	−6.18307e129	−0.000445211 0	−0.000222605		1.00000i	$0.500071\pi$
$434$	−5.19927e133	−3.33205
$435$	0	0
$436$	7.64123e132	0.388236
$437$	6.62784e132	0.299957
$438$	0	0
$439$	−3.77735e133	−1.35747	−0.678733	−	0.734385i	$-0.737470\pi$
$439$	−3.77735e133	−1.35747	−0.678733	+	0.734385i	$0.737470\pi$
$440$	2.72016e133	0.871433
$441$	0	0
$442$	3.66531e133	0.933869
$443$	−6.56580e133	−1.49245	−0.746224	−	0.665695i	$-0.768135\pi$
$443$	−6.56580e133	−1.49245	−0.746224	+	0.665695i	$0.768135\pi$
$444$	0	0
$445$	4.78995e133	0.867262
$446$	1.52391e134	2.46348
$447$	0	0
$448$	1.65864e134	2.13901
$449$	−7.19767e133	−0.829377	−0.414688	−	0.909963i	$-0.636109\pi$
$449$	−7.19767e133	−0.829377	−0.414688	+	0.909963i	$0.636109\pi$
$450$	0	0
$451$	−1.03786e134	−0.955484
$452$	2.51874e134	2.07344
$453$	0	0
$454$	3.87840e133	0.255466
$455$	−1.48606e134	−0.875912
$456$	0	0
$457$	1.64631e134	0.777576	0.388788	−	0.921327i	$-0.372894\pi$
$457$	1.64631e134	0.777576	0.388788	+	0.921327i	$0.372894\pi$
$458$	−2.73509e134	−1.15682
$459$	0	0
$460$	2.53116e134	0.859110
$461$	1.97585e134	0.600976	0.300488	−	0.953786i	$-0.402850\pi$
$461$	1.97585e134	0.600976	0.300488	+	0.953786i	$0.402850\pi$
$462$	0	0
$463$	5.15727e134	1.26061	0.630303	−	0.776349i	$-0.282930\pi$
$463$	5.15727e134	1.26061	0.630303	+	0.776349i	$0.282930\pi$
$464$	5.07178e133	0.111174
$465$	0	0
$466$	6.82879e133	0.120463
$467$	−2.94920e133	−0.0466876	−0.0233438	−	0.999727i	$-0.507431\pi$
$467$	−2.94920e133	−0.0466876	−0.0233438	+	0.999727i	$0.507431\pi$
$468$	0	0
$469$	−7.08610e134	−0.904021
$470$	2.75790e135	3.15963
$471$	0	0
$472$	−1.12642e135	−1.04143
$473$	2.98112e134	0.247681
$474$	0	0
$475$	−1.34400e135	−0.902340
$476$	−4.39686e135	−2.65455
$477$	0	0
$478$	−2.92643e134	−0.142965
$479$	−2.46547e135	−1.08382	−0.541909	−	0.840437i	$-0.682298\pi$
$479$	−2.46547e135	−1.08382	−0.541909	+	0.840437i	$0.682298\pi$
$480$	0	0
$481$	−1.17715e135	−0.419281
$482$	1.03062e135	0.330540
$483$	0	0
$484$	−3.70667e135	−0.964479
$485$	−4.47036e135	−1.04806
$486$	0	0
$487$	1.02728e134	0.0195649	0.00978245	−	0.999952i	$-0.496886\pi$
$487$	1.02728e134	0.0195649	0.00978245	+	0.999952i	$0.496886\pi$
$488$	1.79186e135	0.307683
$489$	0	0
$490$	1.22522e136	1.71125
$491$	8.92443e134	0.112451	0.0562257	−	0.998418i	$-0.482093\pi$
$491$	8.92443e134	0.112451	0.0562257	+	0.998418i	$0.482093\pi$
$492$	0	0
$493$	−2.43302e136	−2.49676
$494$	−6.43453e135	−0.596082
$495$	0	0
$496$	1.17488e135	0.0887502
$497$	−1.22229e136	−0.834017
$498$	0	0
$499$	−3.42871e136	−1.91009	−0.955044	−	0.296464i	$-0.904192\pi$
$499$	−3.42871e136	−1.91009	−0.955044	+	0.296464i	$0.904192\pi$
$500$	−5.32293e135	−0.268019
$501$	0	0
$502$	1.79184e136	0.737499
$503$	4.02932e136	1.49985	0.749926	−	0.661522i	$-0.230089\pi$
$503$	4.02932e136	1.49985	0.749926	+	0.661522i	$0.230089\pi$
$504$	0	0
$505$	−9.88721e135	−0.301203
$506$	1.36035e136	0.375015
$507$	0	0
$508$	7.56069e136	1.70783
$509$	−1.18185e136	−0.241721	−0.120861	−	0.992669i	$-0.538565\pi$
$509$	−1.18185e136	−0.241721	−0.120861	+	0.992669i	$0.538565\pi$
$510$	0	0
$511$	5.71666e136	0.959151
$512$	−7.41901e135	−0.112775
$513$	0	0
$514$	−3.63657e136	−0.453999
$515$	1.05460e137	1.19350
$516$	0	0
$517$	9.10480e136	0.847223
$518$	2.29880e137	1.94021
$519$	0	0
$520$	−9.14278e136	−0.635199
$521$	−9.59448e136	−0.604946	−0.302473	−	0.953158i	$-0.597812\pi$
$521$	−9.59448e136	−0.604946	−0.302473	+	0.953158i	$0.597812\pi$
$522$	0	0
$523$	1.10209e137	0.572642	0.286321	−	0.958134i	$-0.407568\pi$
$523$	1.10209e137	0.572642	0.286321	+	0.958134i	$0.407568\pi$
$524$	−2.32656e137	−1.09770
$525$	0	0
$526$	5.60106e137	2.18017
$527$	−5.63612e137	−1.99317
$528$	0	0
$529$	−2.95286e137	−0.862445
$530$	9.72100e137	2.58095
$531$	0	0
$532$	7.71878e137	1.69438
$533$	3.48837e137	0.696464
$534$	0	0
$535$	3.16598e137	0.523170
$536$	−4.35963e137	−0.655583
$537$	0	0
$538$	−1.30362e138	−1.62423
$539$	4.04490e137	0.458855
$540$	0	0
$541$	−6.70930e137	−0.631270	−0.315635	−	0.948881i	$-0.602218\pi$
$541$	−6.70930e137	−0.631270	−0.315635	+	0.948881i	$0.602218\pi$
$542$	1.53454e138	1.31527
$543$	0	0
$544$	1.86039e138	1.32391
$545$	−5.46719e137	−0.354601
$546$	0	0
$547$	−8.05553e137	−0.434244	−0.217122	−	0.976144i	$-0.569667\pi$
$547$	−8.05553e137	−0.434244	−0.217122	+	0.976144i	$0.569667\pi$
$548$	−2.96698e138	−1.45847
$549$	0	0
$550$	−2.75852e138	−1.12813
$551$	4.27123e138	1.59366
$552$	0	0
$553$	2.67592e138	0.831486
$554$	3.85543e138	1.09353
$555$	0	0
$556$	3.51314e137	0.0830651
$557$	−6.47956e138	−1.39913	−0.699565	−	0.714569i	$-0.746623\pi$
$557$	−6.47956e138	−1.39913	−0.699565	+	0.714569i	$0.746623\pi$
$558$	0	0
$559$	−1.00199e138	−0.180537
$560$	−6.55778e137	−0.107960
$561$	0	0
$562$	6.09870e138	0.838598
$563$	−4.45055e138	−0.559423	−0.279711	−	0.960084i	$-0.590239\pi$
$563$	−4.45055e138	−0.559423	−0.279711	+	0.960084i	$0.590239\pi$
$564$	0	0
$565$	−1.80212e139	−1.89381
$566$	2.27127e139	2.18293
$567$	0	0
$568$	−7.51995e138	−0.604817
$569$	−1.34965e139	−0.993237	−0.496618	−	0.867969i	$-0.665425\pi$
$569$	−1.34965e139	−0.993237	−0.496618	+	0.867969i	$0.665425\pi$
$570$	0	0
$571$	1.08594e139	0.669396	0.334698	−	0.942325i	$-0.391366\pi$
$571$	1.08594e139	0.669396	0.334698	+	0.942325i	$0.391366\pi$
$572$	−8.11253e138	−0.457780
$573$	0	0
$574$	−6.81229e139	−3.22287
$575$	−9.55024e138	−0.413798
$576$	0	0
$577$	−2.62894e139	−0.955876	−0.477938	−	0.878394i	$-0.658616\pi$
$577$	−2.62894e139	−0.955876	−0.477938	+	0.878394i	$0.658616\pi$
$578$	−2.92622e139	−0.974881
$579$	0	0
$580$	1.63117e140	4.56443
$581$	7.82637e139	2.00755
$582$	0	0
$583$	3.20925e139	0.692056
$584$	3.51710e139	0.695562
$585$	0	0
$586$	−2.01565e139	−0.335417
$587$	1.05231e140	1.60664	0.803321	−	0.595546i	$-0.203064\pi$
$587$	1.05231e140	1.60664	0.803321	+	0.595546i	$0.203064\pi$
$588$	0	0
$589$	9.89432e139	1.27222
$590$	2.16615e140	2.55660
$591$	0	0
$592$	−5.19461e138	−0.0516781
$593$	−6.79702e139	−0.620950	−0.310475	−	0.950582i	$-0.600488\pi$
$593$	−6.79702e139	−0.620950	−0.310475	+	0.950582i	$0.600488\pi$
$594$	0	0
$595$	3.14589e140	2.42458
$596$	1.48354e140	1.05042
$597$	0	0
$598$	−4.57229e139	−0.273353
$599$	1.50842e140	0.828835	0.414417	−	0.910087i	$-0.363985\pi$
$599$	1.50842e140	0.828835	0.414417	+	0.910087i	$0.363985\pi$
$600$	0	0
$601$	3.83968e140	1.78293	0.891464	−	0.453091i	$-0.149679\pi$
$601$	3.83968e140	1.78293	0.891464	+	0.453091i	$0.149679\pi$
$602$	1.95674e140	0.835431
$603$	0	0
$604$	1.69873e140	0.613421
$605$	2.65207e140	0.880923
$606$	0	0
$607$	8.64913e139	0.243189	0.121594	−	0.992580i	$-0.461199\pi$
$607$	8.64913e139	0.243189	0.121594	+	0.992580i	$0.461199\pi$
$608$	−3.26595e140	−0.845044
$609$	0	0
$610$	−3.44581e140	−0.755327
$611$	−3.06023e140	−0.617551
$612$	0	0
$613$	−7.96669e140	−1.36309	−0.681544	−	0.731777i	$-0.738691\pi$
$613$	−7.96669e140	−1.36309	−0.681544	+	0.731777i	$0.738691\pi$
$614$	−1.30184e140	−0.205143
$615$	0	0
$616$	5.89441e140	0.788160
$617$	−4.02335e140	−0.495664	−0.247832	−	0.968803i	$-0.579718\pi$
$617$	−4.02335e140	−0.495664	−0.247832	+	0.968803i	$0.579718\pi$
$618$	0	0
$619$	−8.10256e140	−0.847705	−0.423852	−	0.905731i	$-0.639322\pi$
$619$	−8.10256e140	−0.847705	−0.423852	+	0.905731i	$0.639322\pi$
$620$	3.77862e141	3.64379
$621$	0	0
$622$	2.22264e141	1.82161
$623$	1.03795e141	0.784388
$624$	0	0
$625$	−1.35492e141	−0.870906
$626$	6.65339e140	0.394493
$627$	0	0
$628$	9.10522e140	0.459545
$629$	2.49195e141	1.16060
$630$	0	0
$631$	1.26653e141	0.502496	0.251248	−	0.967923i	$-0.419159\pi$
$631$	1.26653e141	0.502496	0.251248	+	0.967923i	$0.419159\pi$
$632$	1.64633e141	0.602981
$633$	0	0
$634$	5.51569e141	1.72223
$635$	−5.40956e141	−1.55987
$636$	0	0
$637$	−1.35954e141	−0.334465
$638$	8.76658e141	1.99244
$639$	0	0
$640$	−1.17917e142	−2.28816
$641$	−2.46708e141	−0.442438	−0.221219	−	0.975224i	$-0.571004\pi$
$641$	−2.46708e141	−0.442438	−0.221219	+	0.975224i	$0.571004\pi$
$642$	0	0
$643$	−1.00891e142	−1.54596	−0.772981	−	0.634430i	$-0.781235\pi$
$643$	−1.00891e142	−1.54596	−0.772981	+	0.634430i	$0.781235\pi$
$644$	5.48486e141	0.777015
$645$	0	0
$646$	1.36215e142	1.64999
$647$	−5.47711e141	−0.613600	−0.306800	−	0.951774i	$-0.599258\pi$
$647$	−5.47711e141	−0.613600	−0.306800	+	0.951774i	$0.599258\pi$
$648$	0	0
$649$	7.15123e141	0.685526
$650$	9.27170e141	0.822309
$651$	0	0
$652$	−2.33894e142	−1.77630
$653$	1.55247e141	0.109121	0.0545605	−	0.998510i	$-0.482624\pi$
$653$	1.55247e141	0.109121	0.0545605	+	0.998510i	$0.482624\pi$
$654$	0	0
$655$	1.66462e142	1.00260
$656$	1.53937e141	0.0858420
$657$	0	0
$658$	5.97619e142	2.85770
$659$	3.76071e142	1.66554	0.832772	−	0.553616i	$-0.186752\pi$
$659$	3.76071e142	1.66554	0.832772	+	0.553616i	$0.186752\pi$
$660$	0	0
$661$	−3.14082e142	−1.19363	−0.596815	−	0.802379i	$-0.703567\pi$
$661$	−3.14082e142	−1.19363	−0.596815	+	0.802379i	$0.703567\pi$
$662$	2.95446e142	1.04028
$663$	0	0
$664$	4.81507e142	1.45584
$665$	−5.52267e142	−1.54759
$666$	0	0
$667$	3.03508e142	0.730827
$668$	8.24561e142	1.84082
$669$	0	0
$670$	8.38371e142	1.60938
$671$	−1.13758e142	−0.202533
$672$	0	0
$673$	5.72017e142	0.876290	0.438145	−	0.898904i	$-0.355636\pi$
$673$	5.72017e142	0.876290	0.438145	+	0.898904i	$0.355636\pi$
$674$	7.99402e142	1.13616
$675$	0	0
$676$	−1.02867e143	−1.25883
$677$	1.68388e143	1.91242	0.956211	−	0.292679i	$-0.0945467\pi$
$677$	1.68388e143	1.91242	0.956211	+	0.292679i	$0.0945467\pi$
$678$	0	0
$679$	−9.68699e142	−0.947906
$680$	1.93547e143	1.75827
$681$	0	0
$682$	2.03078e143	1.59057
$683$	−9.75485e142	−0.709537	−0.354769	−	0.934954i	$-0.615440\pi$
$683$	−9.75485e142	−0.709537	−0.354769	+	0.934954i	$0.615440\pi$
$684$	0	0
$685$	2.12283e143	1.33212
$686$	−9.78610e142	−0.570482
$687$	0	0
$688$	−4.42165e141	−0.0222520
$689$	−1.07867e143	−0.504448
$690$	0	0
$691$	−9.67210e142	−0.390732	−0.195366	−	0.980730i	$-0.562590\pi$
$691$	−9.67210e142	−0.390732	−0.195366	+	0.980730i	$0.562590\pi$
$692$	−4.39628e143	−1.65093
$693$	0	0
$694$	−2.67293e143	−0.867630
$695$	−2.51360e142	−0.0758689
$696$	0	0
$697$	−7.38465e143	−1.92786
$698$	−1.09596e144	−2.66132
$699$	0	0
$700$	−1.11222e144	−2.33744
$701$	6.48692e143	1.26847	0.634233	−	0.773142i	$-0.281316\pi$
$701$	6.48692e143	1.26847	0.634233	+	0.773142i	$0.281316\pi$
$702$	0	0
$703$	−4.37467e143	−0.740800
$704$	−6.47849e143	−1.02107
$705$	0	0
$706$	8.65883e143	1.18256
$707$	−2.14250e143	−0.272420
$708$	0	0
$709$	8.63719e143	0.952221	0.476111	−	0.879385i	$-0.342046\pi$
$709$	8.63719e143	0.952221	0.476111	+	0.879385i	$0.342046\pi$
$710$	1.44611e144	1.48476
$711$	0	0
$712$	6.38586e143	0.568826
$713$	7.03077e143	0.583420
$714$	0	0
$715$	5.80440e143	0.418121
$716$	−3.41357e144	−2.29140
$717$	0	0
$718$	−5.47776e144	−3.19388
$719$	−1.28977e143	−0.0700975	−0.0350488	−	0.999386i	$-0.511159\pi$
$719$	−1.28977e143	−0.0700975	−0.0350488	+	0.999386i	$0.511159\pi$
$720$	0	0
$721$	2.28526e144	1.07946
$722$	1.26457e144	0.556950
$723$	0	0
$724$	−1.03229e144	−0.395372
$725$	−6.15453e144	−2.19850
$726$	0	0
$727$	−1.32206e144	−0.410925	−0.205462	−	0.978665i	$-0.565870\pi$
$727$	−1.32206e144	−0.410925	−0.205462	+	0.978665i	$0.565870\pi$
$728$	−1.98118e144	−0.574500
$729$	0	0
$730$	−6.76350e144	−1.70752
$731$	2.12115e144	0.499739
$732$	0	0
$733$	2.44219e144	0.501220	0.250610	−	0.968088i	$-0.419369\pi$
$733$	2.44219e144	0.501220	0.250610	+	0.968088i	$0.419369\pi$
$734$	2.08112e144	0.398700
$735$	0	0
$736$	−2.32074e144	−0.387523
$737$	2.76776e144	0.431539
$738$	0	0
$739$	6.04415e144	0.821847	0.410924	−	0.911670i	$-0.365206\pi$
$739$	6.04415e144	0.821847	0.410924	+	0.911670i	$0.365206\pi$
$740$	−1.67068e145	−2.12173
$741$	0	0
$742$	2.10648e145	2.33432
$743$	−4.51166e144	−0.467091	−0.233546	−	0.972346i	$-0.575033\pi$
$743$	−4.51166e144	−0.467091	−0.233546	+	0.972346i	$0.575033\pi$
$744$	0	0
$745$	−1.06145e145	−0.959419
$746$	−1.04787e145	−0.885110
$747$	0	0
$748$	1.71737e145	1.26716
$749$	6.86048e144	0.473176
$750$	0	0
$751$	1.45207e145	0.875326	0.437663	−	0.899139i	$-0.355806\pi$
$751$	1.45207e145	0.875326	0.437663	+	0.899139i	$0.355806\pi$
$752$	−1.35044e144	−0.0761157
$753$	0	0
$754$	−2.94655e145	−1.45232
$755$	−1.21542e145	−0.560278
$756$	0	0
$757$	−1.20161e145	−0.484641	−0.242320	−	0.970196i	$-0.577909\pi$
$757$	−1.20161e145	−0.484641	−0.242320	+	0.970196i	$0.577909\pi$
$758$	1.52351e145	0.574843
$759$	0	0
$760$	−3.39775e145	−1.12229
$761$	3.90026e145	1.20550	0.602751	−	0.797929i	$-0.294071\pi$
$761$	3.90026e145	1.20550	0.602751	+	0.797929i	$0.294071\pi$
$762$	0	0
$763$	−1.18470e145	−0.320716
$764$	−3.17906e145	−0.805536
$765$	0	0
$766$	7.84127e145	1.74114
$767$	−2.40362e145	−0.499688
$768$	0	0
$769$	4.51695e144	0.0823313	0.0411656	−	0.999152i	$-0.486893\pi$
$769$	4.51695e144	0.0823313	0.0411656	+	0.999152i	$0.486893\pi$
$770$	−1.13351e146	−1.93484
$771$	0	0
$772$	−1.74036e146	−2.60594
$773$	−1.00998e145	−0.141661	−0.0708303	−	0.997488i	$-0.522565\pi$
$773$	−1.00998e145	−0.141661	−0.0708303	+	0.997488i	$0.522565\pi$
$774$	0	0
$775$	−1.42570e146	−1.75506
$776$	−5.95979e145	−0.687408
$777$	0	0
$778$	1.98991e146	2.01541
$779$	1.29639e146	1.23054
$780$	0	0
$781$	4.77412e145	0.398122
$782$	9.67923e145	0.756658
$783$	0	0
$784$	−5.99947e144	−0.0412241
$785$	−6.51465e145	−0.419733
$786$	0	0
$787$	−2.76862e146	−1.56870	−0.784350	−	0.620319i	$-0.787003\pi$
$787$	−2.76862e146	−1.56870	−0.784350	+	0.620319i	$0.787003\pi$
$788$	−4.60281e145	−0.244596
$789$	0	0
$790$	−3.16594e146	−1.48025
$791$	−3.90508e146	−1.71284
$792$	0	0
$793$	3.82356e145	0.147629
$794$	2.91116e146	1.05470
$795$	0	0
$796$	−2.17540e146	−0.694110
$797$	1.73951e146	0.520932	0.260466	−	0.965483i	$-0.416124\pi$
$797$	1.73951e146	0.520932	0.260466	+	0.965483i	$0.416124\pi$
$798$	0	0
$799$	6.47831e146	1.70942
$800$	4.70601e146	1.16576
$801$	0	0
$802$	1.14895e147	2.50896
$803$	−2.23287e146	−0.457855
$804$	0	0
$805$	−3.92434e146	−0.709699
$806$	−6.82571e146	−1.15939
$807$	0	0
$808$	−1.31814e146	−0.197555
$809$	−6.19950e146	−0.872883	−0.436442	−	0.899733i	$-0.643761\pi$
$809$	−6.19950e146	−0.872883	−0.436442	+	0.899733i	$0.643761\pi$
$810$	0	0
$811$	9.95522e146	1.23736	0.618682	−	0.785641i	$-0.287667\pi$
$811$	9.95522e146	1.23736	0.618682	+	0.785641i	$0.287667\pi$
$812$	3.53465e147	4.12826
$813$	0	0
$814$	−8.97889e146	−0.926169
$815$	1.67348e147	1.62241
$816$	0	0
$817$	−3.72372e146	−0.318980
$818$	3.22844e147	2.59986
$819$	0	0
$820$	4.95089e147	3.52439
$821$	−1.00145e147	−0.670349	−0.335174	−	0.942156i	$-0.608795\pi$
$821$	−1.00145e147	−0.670349	−0.335174	+	0.942156i	$0.608795\pi$
$822$	0	0
$823$	−3.42968e146	−0.203031	−0.101515	−	0.994834i	$-0.532369\pi$
$823$	−3.42968e146	−0.203031	−0.101515	+	0.994834i	$0.532369\pi$
$824$	1.40598e147	0.782805
$825$	0	0
$826$	4.69391e147	2.31229
$827$	2.19408e147	1.01677	0.508386	−	0.861129i	$-0.330242\pi$
$827$	2.19408e147	1.01677	0.508386	+	0.861129i	$0.330242\pi$
$828$	0	0
$829$	−1.42397e147	−0.584113	−0.292057	−	0.956401i	$-0.594340\pi$
$829$	−1.42397e147	−0.584113	−0.292057	+	0.956401i	$0.594340\pi$
$830$	−9.25953e147	−3.57393
$831$	0	0
$832$	2.17750e147	0.744268
$833$	2.87805e147	0.925819
$834$	0	0
$835$	−5.89961e147	−1.68134
$836$	−3.01488e147	−0.808822
$837$	0	0
$838$	−6.31924e147	−1.50259
$839$	−2.17760e147	−0.487528	−0.243764	−	0.969835i	$-0.578382\pi$
$839$	−2.17760e147	−0.487528	−0.243764	+	0.969835i	$0.578382\pi$
$840$	0	0
$841$	1.45219e148	2.88287
$842$	1.20871e148	2.25976
$843$	0	0
$844$	−1.10506e148	−1.83271
$845$	7.35997e147	1.14977
$846$	0	0
$847$	5.74686e147	0.796743
$848$	−4.76001e146	−0.0621753
$849$	0	0
$850$	−1.96276e148	−2.27620
$851$	−3.10858e147	−0.339718
$852$	0	0
$853$	2.39847e147	0.232814	0.116407	−	0.993202i	$-0.462862\pi$
$853$	2.39847e147	0.232814	0.116407	+	0.993202i	$0.462862\pi$
$854$	−7.46685e147	−0.683149
$855$	0	0
$856$	4.22082e147	0.343140
$857$	1.77495e148	1.36037	0.680183	−	0.733042i	$-0.261900\pi$
$857$	1.77495e148	1.36037	0.680183	+	0.733042i	$0.261900\pi$
$858$	0	0
$859$	−1.76032e148	−1.19933	−0.599664	−	0.800252i	$-0.704699\pi$
$859$	−1.76032e148	−1.19933	−0.599664	+	0.800252i	$0.704699\pi$
$860$	−1.42208e148	−0.913592
$861$	0	0
$862$	−4.30125e148	−2.45741
$863$	−2.64645e148	−1.42600	−0.712998	−	0.701166i	$-0.752663\pi$
$863$	−2.64645e148	−1.42600	−0.712998	+	0.701166i	$0.752663\pi$
$864$	0	0
$865$	3.14547e148	1.50790
$866$	1.58518e145	0.000716846 0
$867$	0	0
$868$	8.18803e148	3.29559
$869$	−1.04519e148	−0.396914
$870$	0	0
$871$	−9.30277e147	−0.314554
$872$	−7.28874e147	−0.232579
$873$	0	0
$874$	−1.69921e148	−0.482969
$875$	8.25273e147	0.221407
$876$	0	0
$877$	−7.77572e148	−1.85892	−0.929461	−	0.368920i	$-0.879728\pi$
$877$	−7.77572e148	−1.85892	−0.929461	+	0.368920i	$0.879728\pi$
$878$	9.68416e148	2.18569
$879$	0	0
$880$	2.56141e147	0.0515351
$881$	−5.10744e148	−0.970332	−0.485166	−	0.874422i	$-0.661241\pi$
$881$	−5.10744e148	−0.970332	−0.485166	+	0.874422i	$0.661241\pi$
$882$	0	0
$883$	−4.89678e148	−0.829650	−0.414825	−	0.909901i	$-0.636157\pi$
$883$	−4.89678e148	−0.829650	−0.414825	+	0.909901i	$0.636157\pi$
$884$	−5.77228e148	−0.923652
$885$	0	0
$886$	1.68330e149	2.40303
$887$	−8.91966e148	−1.20283	−0.601416	−	0.798936i	$-0.705397\pi$
$887$	−8.91966e148	−1.20283	−0.601416	+	0.798936i	$0.705397\pi$
$888$	0	0
$889$	−1.17222e149	−1.41081
$890$	−1.22802e149	−1.39640
$891$	0	0
$892$	−2.39992e149	−2.43653
$893$	−1.13728e149	−1.09111
$894$	0	0
$895$	2.44236e149	2.09289
$896$	−2.55518e149	−2.06951
$897$	0	0
$898$	1.84530e149	1.33540
$899$	4.53089e149	3.09970
$900$	0	0
$901$	2.28347e149	1.39634
$902$	2.66081e149	1.53845
$903$	0	0
$904$	−2.40255e149	−1.24213
$905$	7.38591e148	0.361119
$906$	0	0
$907$	−2.11629e149	−0.925567	−0.462784	−	0.886471i	$-0.653149\pi$
$907$	−2.11629e149	−0.925567	−0.462784	+	0.886471i	$0.653149\pi$
$908$	−6.10787e148	−0.252671
$909$	0	0
$910$	3.80988e149	1.41033
$911$	−2.22931e149	−0.780715	−0.390358	−	0.920663i	$-0.627649\pi$
$911$	−2.22931e149	−0.780715	−0.390358	+	0.920663i	$0.627649\pi$
$912$	0	0
$913$	−3.05690e149	−0.958312
$914$	−4.22072e149	−1.25200
$915$	0	0
$916$	4.30734e149	1.14416
$917$	3.60712e149	0.906796
$918$	0	0
$919$	−4.28888e149	−0.965852	−0.482926	−	0.875661i	$-0.660426\pi$
$919$	−4.28888e149	−0.965852	−0.482926	+	0.875661i	$0.660426\pi$
$920$	−2.41440e149	−0.514663
$921$	0	0
$922$	−5.06558e149	−0.967648
$923$	−1.60464e149	−0.290196
$924$	0	0
$925$	6.30358e149	1.02195
$926$	−1.32219e150	−2.02974
$927$	0	0
$928$	−1.49557e150	−2.05890
$929$	−1.69023e149	−0.220370	−0.110185	−	0.993911i	$-0.535144\pi$
$929$	−1.69023e149	−0.220370	−0.110185	+	0.993911i	$0.535144\pi$
$930$	0	0
$931$	−5.05249e149	−0.590944
$932$	−1.07543e149	−0.119145
$933$	0	0
$934$	7.56099e148	0.0751729
$935$	−1.22875e150	−1.15739
$936$	0	0
$937$	−1.59055e148	−0.0134492	−0.00672461	−	0.999977i	$-0.502141\pi$
$937$	−1.59055e148	−0.0134492	−0.00672461	+	0.999977i	$0.502141\pi$
$938$	1.81670e150	1.45559
$939$	0	0
$940$	−4.34325e150	−3.12506
$941$	−2.35520e150	−1.60602	−0.803012	−	0.595962i	$-0.796771\pi$
$941$	−2.35520e150	−1.60602	−0.803012	+	0.595962i	$0.796771\pi$
$942$	0	0
$943$	9.21198e149	0.564303
$944$	−1.06068e149	−0.0615886
$945$	0	0
$946$	−7.64284e149	−0.398797
$947$	1.39047e150	0.687838	0.343919	−	0.938999i	$-0.388245\pi$
$947$	1.39047e150	0.687838	0.343919	+	0.938999i	$0.388245\pi$
$948$	0	0
$949$	7.50494e149	0.333736
$950$	3.44566e150	1.45288
$951$	0	0
$952$	4.19403e150	1.59025
$953$	−9.30332e149	−0.334539	−0.167269	−	0.985911i	$-0.553495\pi$
$953$	−9.30332e149	−0.334539	−0.167269	+	0.985911i	$0.553495\pi$
$954$	0	0
$955$	2.27457e150	0.735749
$956$	4.60867e149	0.141401
$957$	0	0
$958$	6.32084e150	1.74509
$959$	4.60004e150	1.20482
$960$	0	0
$961$	6.25422e150	1.47449
$962$	3.01791e150	0.675096
$963$	0	0
$964$	−1.62307e150	−0.326923
$965$	1.24520e151	2.38018
$966$	0	0
$967$	−5.17125e150	−0.890345	−0.445172	−	0.895445i	$-0.646858\pi$
$967$	−5.17125e150	−0.890345	−0.445172	+	0.895445i	$0.646858\pi$
$968$	3.53568e150	0.577786
$969$	0	0
$970$	1.14609e151	1.68751
$971$	1.02064e151	1.42660	0.713302	−	0.700857i	$-0.247199\pi$
$971$	1.02064e151	1.42660	0.713302	+	0.700857i	$0.247199\pi$
$972$	0	0
$973$	−5.44681e149	−0.0686189
$974$	−2.63370e149	−0.0315020
$975$	0	0
$976$	1.68729e149	0.0181959
$977$	−1.19151e151	−1.22017	−0.610087	−	0.792334i	$-0.708866\pi$
$977$	−1.19151e151	−1.22017	−0.610087	+	0.792334i	$0.708866\pi$
$978$	0	0
$979$	−4.05414e150	−0.374432
$980$	−1.92953e151	−1.69253
$981$	0	0
$982$	−2.28800e150	−0.181061
$983$	−2.64030e151	−1.98473	−0.992364	−	0.123343i	$-0.960638\pi$
$983$	−2.64030e151	−1.98473	−0.992364	+	0.123343i	$0.960638\pi$
$984$	0	0
$985$	3.29324e150	0.223406
$986$	6.23766e151	4.02010
$987$	0	0
$988$	1.01334e151	0.589560
$989$	−2.64602e150	−0.146279
$990$	0	0
$991$	−1.12820e151	−0.563205	−0.281603	−	0.959531i	$-0.590866\pi$
$991$	−1.12820e151	−0.563205	−0.281603	+	0.959531i	$0.590866\pi$
$992$	−3.46450e151	−1.64362
$993$	0	0
$994$	3.13363e151	1.34287
$995$	1.55646e151	0.633977
$996$	0	0
$997$	1.50434e151	0.553656	0.276828	−	0.960920i	$-0.410717\pi$
$997$	1.50434e151	0.553656	0.276828	+	0.960920i	$0.410717\pi$
$998$	8.79035e151	3.07549
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.102.a.b.1.1		8
3.2	odd	2		1.102.a.a.1.8	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.102.a.a.1.8	✓	8	3.2	odd	2
9.102.a.b.1.1		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)

\(f(q)\)	\(=\)	\(q-2.56375e15 q^{2} +4.03750e30 q^{4} -2.88877e35 q^{5} -6.25978e42 q^{7} -3.85125e45 q^{8} +O(q^{10})\)	\(q-2.56375e15 q^{2} +4.03750e30 q^{4} -2.88877e35 q^{5} -6.25978e42 q^{7} -3.85125e45 q^{8} +7.40607e50 q^{10} +2.44501e52 q^{11} -8.21796e55 q^{13} +1.60485e58 q^{14} -3.62648e59 q^{16} +1.73969e62 q^{17} -3.05406e64 q^{19} -1.16634e66 q^{20} -6.26838e67 q^{22} -2.17017e68 q^{23} +4.40068e70 q^{25} +2.10688e71 q^{26} -2.52738e73 q^{28} -1.39854e74 q^{29} -3.23973e75 q^{31} +1.06938e76 q^{32} -4.46012e77 q^{34} +1.80831e78 q^{35} +1.43241e79 q^{37} +7.82984e79 q^{38} +1.11254e81 q^{40} -4.24481e81 q^{41} +1.21927e82 q^{43} +9.87171e82 q^{44} +5.56377e83 q^{46} +3.72383e84 q^{47} +1.65435e85 q^{49} -1.12822e86 q^{50} -3.31800e86 q^{52} +1.31257e87 q^{53} -7.06306e87 q^{55} +2.41080e88 q^{56} +3.58550e89 q^{58} +2.92483e89 q^{59} -4.65268e89 q^{61} +8.30584e90 q^{62} -2.64968e91 q^{64} +2.37398e91 q^{65} +1.13200e92 q^{67} +7.02398e92 q^{68} -4.63604e93 q^{70} +1.95260e93 q^{71} -9.13236e93 q^{73} -3.67234e94 q^{74} -1.23308e95 q^{76} -1.53052e95 q^{77} -4.27479e95 q^{79} +1.04761e95 q^{80} +1.08826e97 q^{82} -1.25026e97 q^{83} -5.02556e97 q^{85} -3.12590e97 q^{86} -9.41633e97 q^{88} -1.65813e98 q^{89} +5.14426e98 q^{91} -8.76206e98 q^{92} -9.54696e99 q^{94} +8.82247e99 q^{95} +1.54750e100 q^{97} -4.24133e100 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 434989091795040 q^{2} + 90\!\cdots\!96 q^{4}+ \cdots + 61\!\cdots\!20 q^{8}+O(q^{10}) \) 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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