LMFDB - Embedded newform 9.102.a.b.1.4

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			1.4
Root			$-6.74954e12$ 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)

$f(q)$	$=$	$q-5.93582e14 q^{2} -2.18296e30 q^{4} -2.07725e34 q^{5} -6.15512e42 q^{7} +2.80068e45 q^{8} +O(q^{10})$	\(q-5.93582e14 q^{2} -2.18296e30 q^{4} -2.07725e34 q^{5} -6.15512e42 q^{7} +2.80068e45 q^{8} +1.23302e49 q^{10} +1.93541e51 q^{11} +2.07990e56 q^{13} +3.65357e57 q^{14} +3.87203e60 q^{16} -9.51139e61 q^{17} -2.07479e64 q^{19} +4.53455e64 q^{20} -1.14883e66 q^{22} +1.01002e69 q^{23} -3.90116e70 q^{25} -1.23459e71 q^{26} +1.34364e73 q^{28} +1.12007e74 q^{29} -3.39166e75 q^{31} -9.39893e75 q^{32} +5.64580e76 q^{34} +1.27857e77 q^{35} -2.80250e78 q^{37} +1.23156e79 q^{38} -5.81770e79 q^{40} +2.18595e81 q^{41} +4.27840e82 q^{43} -4.22493e81 q^{44} -5.99533e83 q^{46} +4.06463e84 q^{47} +1.52441e85 q^{49} +2.31566e85 q^{50} -4.54035e86 q^{52} +1.28592e87 q^{53} -4.02033e85 q^{55} -1.72385e88 q^{56} -6.64855e88 q^{58} -2.29239e88 q^{59} +1.48144e90 q^{61} +2.01323e90 q^{62} -4.23772e90 q^{64} -4.32047e90 q^{65} -1.12651e92 q^{67} +2.07630e92 q^{68} -7.58936e91 q^{70} +1.07138e93 q^{71} +8.88946e92 q^{73} +1.66351e93 q^{74} +4.52919e94 q^{76} -1.19127e94 q^{77} +3.94018e95 q^{79} -8.04316e94 q^{80} -1.29754e96 q^{82} -7.91760e96 q^{83} +1.97575e96 q^{85} -2.53958e97 q^{86} +5.42047e96 q^{88} -1.56456e98 q^{89} -1.28020e99 q^{91} -2.20484e99 q^{92} -2.41269e99 q^{94} +4.30986e98 q^{95} +6.75748e99 q^{97} -9.04864e99 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.93582e14	−0.372792	−0.186396	−	0.982475i	$-0.559681\pi$
$2$	−5.93582e14	−0.372792	−0.186396	+	0.982475i	$0.559681\pi$
$3$	0	0
$3$	0	0
$4$	−2.18296e30	−0.861026
$5$	−2.07725e34	−0.104593	−0.0522965	−	0.998632i	$-0.516654\pi$
$5$	−2.07725e34	−0.104593	−0.0522965	+	0.998632i	$0.516654\pi$
$6$	0	0
$7$	−6.15512e42	−1.29356	−0.646778	−	0.762678i	$-0.723884\pi$
$7$	−6.15512e42	−1.29356	−0.646778	+	0.762678i	$0.723884\pi$
$8$	2.80068e45	0.693775
$9$	0	0
$10$	1.23302e49	0.0389914
$11$	1.93541e51	0.0497099	0.0248550	−	0.999691i	$-0.492088\pi$
$11$	1.93541e51	0.0497099	0.0248550	+	0.999691i	$0.492088\pi$
$12$	0	0
$13$	2.07990e56	1.15852	0.579260	−	0.815143i	$-0.303341\pi$
$13$	2.07990e56	1.15852	0.579260	+	0.815143i	$0.303341\pi$
$14$	3.65357e57	0.482227
$15$	0	0
$16$	3.87203e60	0.602393
$17$	−9.51139e61	−0.692745	−0.346373	−	0.938097i	$-0.612587\pi$
$17$	−9.51139e61	−0.692745	−0.346373	+	0.938097i	$0.612587\pi$
$18$	0	0
$19$	−2.07479e64	−0.549437	−0.274719	−	0.961525i	$-0.588585\pi$
$19$	−2.07479e64	−0.549437	−0.274719	+	0.961525i	$0.588585\pi$
$20$	4.53455e64	0.0900573
$21$	0	0
$22$	−1.14883e66	−0.0185314
$23$	1.01002e69	1.72614	0.863070	−	0.505084i	$-0.168539\pi$
$23$	1.01002e69	1.72614	0.863070	+	0.505084i	$0.168539\pi$
$24$	0	0
$25$	−3.90116e70	−0.989060
$26$	−1.23459e71	−0.431887
$27$	0	0
$28$	1.34364e73	1.11379
$29$	1.12007e74	1.57815	0.789073	−	0.614299i	$-0.210561\pi$
$29$	1.12007e74	1.57815	0.789073	+	0.614299i	$0.210561\pi$
$30$	0	0
$31$	−3.39166e75	−1.64682	−0.823410	−	0.567447i	$-0.807931\pi$
$31$	−3.39166e75	−1.64682	−0.823410	+	0.567447i	$0.807931\pi$
$32$	−9.39893e75	−0.918342
$33$	0	0
$34$	5.64580e76	0.258250
$35$	1.27857e77	0.135297
$36$	0	0
$37$	−2.80250e78	−0.179208	−0.0896041	−	0.995977i	$-0.528560\pi$
$37$	−2.80250e78	−0.179208	−0.0896041	+	0.995977i	$0.528560\pi$
$38$	1.23156e79	0.204826
$39$	0	0
$40$	−5.81770e79	−0.0725640
$41$	2.18595e81	0.783531	0.391765	−	0.920065i	$-0.371864\pi$
$41$	2.18595e81	0.783531	0.391765	+	0.920065i	$0.371864\pi$
$42$	0	0
$43$	4.27840e82	1.38396	0.691981	−	0.721916i	$-0.256738\pi$
$43$	4.27840e82	1.38396	0.691981	+	0.721916i	$0.256738\pi$
$44$	−4.22493e81	−0.0428015
$45$	0	0
$46$	−5.99533e83	−0.643491
$47$	4.06463e84	1.47258	0.736291	−	0.676665i	$-0.236576\pi$
$47$	4.06463e84	1.47258	0.736291	+	0.676665i	$0.236576\pi$
$48$	0	0
$49$	1.52441e85	0.673287
$50$	2.31566e85	0.368714
$51$	0	0
$52$	−4.54035e86	−0.997517
$53$	1.28592e87	1.07965	0.539824	−	0.841778i	$-0.318491\pi$
$53$	1.28592e87	1.07965	0.539824	+	0.841778i	$0.318491\pi$
$54$	0	0
$55$	−4.02033e85	−0.00519931
$56$	−1.72385e88	−0.897437
$57$	0	0
$58$	−6.64855e88	−0.588320
$59$	−2.29239e88	−0.0855583	−0.0427792	−	0.999085i	$-0.513621\pi$
$59$	−2.29239e88	−0.0855583	−0.0427792	+	0.999085i	$0.513621\pi$
$60$	0	0
$61$	1.48144e90	1.02690	0.513451	−	0.858119i	$-0.328367\pi$
$61$	1.48144e90	1.02690	0.513451	+	0.858119i	$0.328367\pi$
$62$	2.01323e90	0.613921
$63$	0	0
$64$	−4.23772e90	−0.260042
$65$	−4.32047e90	−0.121173
$66$	0	0
$67$	−1.12651e92	−0.683844	−0.341922	−	0.939728i	$-0.611078\pi$
$67$	−1.12651e92	−0.683844	−0.341922	+	0.939728i	$0.611078\pi$
$68$	2.07630e92	0.596472
$69$	0	0
$70$	−7.58936e91	−0.0504376
$71$	1.07138e93	0.347852	0.173926	−	0.984759i	$-0.444355\pi$
$71$	1.07138e93	0.347852	0.173926	+	0.984759i	$0.444355\pi$
$72$	0	0
$73$	8.88946e92	0.0709694	0.0354847	−	0.999370i	$-0.488703\pi$
$73$	8.88946e92	0.0709694	0.0354847	+	0.999370i	$0.488703\pi$
$74$	1.66351e93	0.0668074
$75$	0	0
$76$	4.52919e94	0.473080
$77$	−1.19127e94	−0.0643026
$78$	0	0
$79$	3.94018e95	0.582570	0.291285	−	0.956636i	$-0.405917\pi$
$79$	3.94018e95	0.582570	0.291285	+	0.956636i	$0.405917\pi$
$80$	−8.04316e94	−0.0630060
$81$	0	0
$82$	−1.29754e96	−0.292094
$83$	−7.91760e96	−0.966385	−0.483192	−	0.875514i	$-0.660523\pi$
$83$	−7.91760e96	−0.966385	−0.483192	+	0.875514i	$0.660523\pi$
$84$	0	0
$85$	1.97575e96	0.0724563
$86$	−2.53958e97	−0.515930
$87$	0	0
$88$	5.42047e96	0.0344875
$89$	−1.56456e98	−0.562596	−0.281298	−	0.959620i	$-0.590765\pi$
$89$	−1.56456e98	−0.562596	−0.281298	+	0.959620i	$0.590765\pi$
$90$	0	0
$91$	−1.28020e99	−1.49861
$92$	−2.20484e99	−1.48625
$93$	0	0
$94$	−2.41269e99	−0.548966
$95$	4.30986e98	0.0574673
$96$	0	0
$97$	6.75748e99	0.314639	0.157319	−	0.987548i	$-0.449715\pi$
$97$	6.75748e99	0.314639	0.157319	+	0.987548i	$0.449715\pi$
$98$	−9.04864e99	−0.250996
$99$	0	0
$100$	8.51607e100	0.851607
$101$	−6.91980e100	−0.418663	−0.209331	−	0.977845i	$-0.567129\pi$
$101$	−6.91980e100	−0.418663	−0.209331	+	0.977845i	$0.567129\pi$
$102$	0	0
$103$	3.86032e101	0.867647	0.433823	−	0.900998i	$-0.357164\pi$
$103$	3.86032e101	0.867647	0.433823	+	0.900998i	$0.357164\pi$
$104$	5.82514e101	0.803753
$105$	0	0
$106$	−7.63299e101	−0.402484
$107$	2.00326e102	0.657441	0.328720	−	0.944427i	$-0.393383\pi$
$107$	2.00326e102	0.657441	0.328720	+	0.944427i	$0.393383\pi$
$108$	0	0
$109$	7.50780e102	0.967107	0.483553	−	0.875315i	$-0.339346\pi$
$109$	7.50780e102	0.967107	0.483553	+	0.875315i	$0.339346\pi$
$110$	2.38640e100	0.00193826
$111$	0	0
$112$	−2.38328e103	−0.779229
$113$	−2.79242e103	−0.582800	−0.291400	−	0.956601i	$-0.594121\pi$
$113$	−2.79242e103	−0.582800	−0.291400	+	0.956601i	$0.594121\pi$
$114$	0	0
$115$	−2.09807e103	−0.180542
$116$	−2.44507e104	−1.35883
$117$	0	0
$118$	1.36072e103	0.0318954
$119$	5.85437e104	0.896105
$120$	0	0
$121$	−1.51212e105	−0.997529
$122$	−8.79360e104	−0.382820
$123$	0	0
$124$	7.40385e105	1.41796
$125$	1.62969e105	0.208042
$126$	0	0
$127$	−2.25447e106	−1.29109	−0.645544	−	0.763723i	$-0.723369\pi$
$127$	−2.25447e106	−1.29109	−0.645544	+	0.763723i	$0.723369\pi$
$128$	2.63446e106	1.01528
$129$	0	0
$130$	2.56456e105	0.0451724
$131$	−4.52448e106	−0.541213	−0.270606	−	0.962690i	$-0.587224\pi$
$131$	−4.52448e106	−0.541213	−0.270606	+	0.962690i	$0.587224\pi$
$132$	0	0
$133$	1.27706e107	0.710728
$134$	6.68676e106	0.254931
$135$	0	0
$136$	−2.66383e107	−0.480610
$137$	−1.30756e108	−1.62957	−0.814787	−	0.579761i	$-0.803146\pi$
$137$	−1.30756e108	−1.62957	−0.814787	+	0.579761i	$0.803146\pi$
$138$	0	0
$139$	−1.97428e107	−0.118348	−0.0591742	−	0.998248i	$-0.518847\pi$
$139$	−1.97428e107	−0.118348	−0.0591742	+	0.998248i	$0.518847\pi$
$140$	−2.79107e107	−0.116494
$141$	0	0
$142$	−6.35950e107	−0.129677
$143$	4.02547e107	0.0575900
$144$	0	0
$145$	−2.32667e108	−0.165063
$146$	−5.27663e107	−0.0264568
$147$	0	0
$148$	6.11774e108	0.154303
$149$	−3.36638e109	−0.604305	−0.302153	−	0.953260i	$-0.597705\pi$
$149$	−3.36638e109	−0.604305	−0.302153	+	0.953260i	$0.597705\pi$
$150$	0	0
$151$	−7.09829e109	−0.649857	−0.324929	−	0.945739i	$-0.605340\pi$
$151$	−7.09829e109	−0.649857	−0.324929	+	0.945739i	$0.605340\pi$
$152$	−5.81083e109	−0.381186
$153$	0	0
$154$	7.07116e108	0.0239715
$155$	7.04530e109	0.172246
$156$	0	0
$157$	−3.72274e110	−0.476354	−0.238177	−	0.971222i	$-0.576550\pi$
$157$	−3.72274e110	−0.476354	−0.238177	+	0.971222i	$0.576550\pi$
$158$	−2.33882e110	−0.217177
$159$	0	0
$160$	1.95239e110	0.0960522
$161$	−6.21682e111	−2.23286
$162$	0	0
$163$	−4.16933e111	−0.802771	−0.401386	−	0.915909i	$-0.631471\pi$
$163$	−4.16933e111	−0.802771	−0.401386	+	0.915909i	$0.631471\pi$
$164$	−4.77185e111	−0.674641
$165$	0	0
$166$	4.69975e111	0.360260
$167$	9.93308e111	0.562215	0.281107	−	0.959676i	$-0.409298\pi$
$167$	9.93308e111	0.562215	0.281107	+	0.959676i	$0.409298\pi$
$168$	0	0
$169$	1.10286e112	0.342171
$170$	−1.17277e111	−0.0270111
$171$	0	0
$172$	−9.33958e112	−1.19163
$173$	5.87533e112	0.559377	0.279688	−	0.960091i	$-0.409769\pi$
$173$	5.87533e112	0.559377	0.279688	+	0.960091i	$0.409769\pi$
$174$	0	0
$175$	2.40121e113	1.27940
$176$	7.49398e111	0.0299449
$177$	0	0
$178$	9.28695e112	0.209731
$179$	−2.72675e113	−0.464053	−0.232027	−	0.972709i	$-0.574536\pi$
$179$	−2.72675e113	−0.464053	−0.232027	+	0.972709i	$0.574536\pi$
$180$	0	0
$181$	−4.92080e113	−0.477823	−0.238912	−	0.971041i	$-0.576791\pi$
$181$	−4.92080e113	−0.477823	−0.238912	+	0.971041i	$0.576791\pi$
$182$	7.59907e113	0.558670
$183$	0	0
$184$	2.82875e114	1.19755
$185$	5.82147e112	0.0187439
$186$	0	0
$187$	−1.84085e113	−0.0344363
$188$	−8.87293e114	−1.26793
$189$	0	0
$190$	−2.55826e113	−0.0214233
$191$	2.75631e115	1.77069	0.885346	−	0.464933i	$-0.153921\pi$
$191$	2.75631e115	1.77069	0.885346	+	0.464933i	$0.153921\pi$
$192$	0	0
$193$	4.98329e115	1.89179	0.945893	−	0.324479i	$-0.105189\pi$
$193$	4.98329e115	1.89179	0.945893	+	0.324479i	$0.105189\pi$
$194$	−4.01112e114	−0.117295
$195$	0	0
$196$	−3.32773e115	−0.579718
$197$	−7.76102e115	−1.04562	−0.522810	−	0.852449i	$-0.675116\pi$
$197$	−7.76102e115	−1.04562	−0.522810	+	0.852449i	$0.675116\pi$
$198$	0	0
$199$	3.53197e115	0.285717	0.142859	−	0.989743i	$-0.454371\pi$
$199$	3.53197e115	0.285717	0.142859	+	0.989743i	$0.454371\pi$
$200$	−1.09259e116	−0.686186
$201$	0	0
$202$	4.10747e115	0.156074
$203$	−6.89418e116	−2.04142
$204$	0	0
$205$	−4.54076e115	−0.0819518
$206$	−2.29142e116	−0.323452
$207$	0	0
$208$	8.05345e116	0.697884
$209$	−4.01558e115	−0.0273125
$210$	0	0
$211$	2.23121e117	0.938158	0.469079	−	0.883156i	$-0.344586\pi$
$211$	2.23121e117	0.938158	0.469079	+	0.883156i	$0.344586\pi$
$212$	−2.80711e117	−0.929606
$213$	0	0
$214$	−1.18910e117	−0.245088
$215$	−8.88728e116	−0.144753
$216$	0	0
$217$	2.08760e118	2.13025
$218$	−4.45650e117	−0.360529
$219$	0	0
$220$	8.77622e115	0.00447674
$221$	−1.97828e118	−0.802560
$222$	0	0
$223$	−3.91127e118	−1.00675	−0.503376	−	0.864068i	$-0.667909\pi$
$223$	−3.91127e118	−1.00675	−0.503376	+	0.864068i	$0.667909\pi$
$224$	5.78515e118	1.18793
$225$	0	0
$226$	1.65753e118	0.217263
$227$	−7.18962e118	−0.754050	−0.377025	−	0.926203i	$-0.623053\pi$
$227$	−7.18962e118	−0.754050	−0.377025	+	0.926203i	$0.623053\pi$
$228$	0	0
$229$	2.25539e118	0.151890	0.0759452	−	0.997112i	$-0.475803\pi$
$229$	2.25539e118	0.151890	0.0759452	+	0.997112i	$0.475803\pi$
$230$	1.24538e118	0.0673046
$231$	0	0
$232$	3.13696e119	1.09488
$233$	4.34636e119	1.22082	0.610410	−	0.792085i	$-0.291005\pi$
$233$	4.34636e119	1.22082	0.610410	+	0.792085i	$0.291005\pi$
$234$	0	0
$235$	−8.44324e118	−0.154022
$236$	5.00420e118	0.0736680
$237$	0	0
$238$	−3.47505e119	−0.334061
$239$	−5.86452e119	−0.456183	−0.228091	−	0.973640i	$-0.573248\pi$
$239$	−5.86452e119	−0.456183	−0.228091	+	0.973640i	$0.573248\pi$
$240$	0	0
$241$	−2.33319e120	−1.19149	−0.595743	−	0.803175i	$-0.703142\pi$
$241$	−2.33319e120	−1.19149	−0.595743	+	0.803175i	$0.703142\pi$
$242$	8.97569e119	0.371871
$243$	0	0
$244$	−3.23394e120	−0.884189
$245$	−3.16658e119	−0.0704211
$246$	0	0
$247$	−4.31537e120	−0.636535
$248$	−9.49893e120	−1.14252
$249$	0	0
$250$	−9.67358e119	−0.0775563
$251$	2.88476e121	1.89055	0.945273	−	0.326280i	$-0.105795\pi$
$251$	2.88476e121	1.89055	0.945273	+	0.326280i	$0.105795\pi$
$252$	0	0
$253$	1.95481e120	0.0858063
$254$	1.33821e121	0.481307
$255$	0	0
$256$	−4.89376e120	−0.118447
$257$	−1.22979e120	−0.0244461	−0.0122230	−	0.999925i	$-0.503891\pi$
$257$	−1.22979e120	−0.0244461	−0.0122230	+	0.999925i	$0.503891\pi$
$258$	0	0
$259$	1.72497e121	0.231816
$260$	9.43142e120	0.104333
$261$	0	0
$262$	2.68565e121	0.201760
$263$	3.92088e121	0.243006	0.121503	−	0.992591i	$-0.461229\pi$
$263$	3.92088e121	0.243006	0.121503	+	0.992591i	$0.461229\pi$
$264$	0	0
$265$	−2.67117e121	−0.112924
$266$	−7.58040e121	−0.264954
$267$	0	0
$268$	2.45912e122	0.588808
$269$	−4.57510e122	−0.907634	−0.453817	−	0.891095i	$-0.649938\pi$
$269$	−4.57510e122	−0.907634	−0.453817	+	0.891095i	$0.649938\pi$
$270$	0	0
$271$	−1.82542e122	−0.249123	−0.124562	−	0.992212i	$-0.539752\pi$
$271$	−1.82542e122	−0.249123	−0.124562	+	0.992212i	$0.539752\pi$
$272$	−3.68284e122	−0.417305
$273$	0	0
$274$	7.76146e122	0.607492
$275$	−7.55035e121	−0.0491661
$276$	0	0
$277$	1.06562e123	0.481256	0.240628	−	0.970617i	$-0.422647\pi$
$277$	1.06562e123	0.481256	0.240628	+	0.970617i	$0.422647\pi$
$278$	1.17190e122	0.0441193
$279$	0	0
$280$	3.58086e122	0.0938656
$281$	−3.52617e123	−0.772029	−0.386015	−	0.922493i	$-0.626149\pi$
$281$	−3.52617e123	−0.772029	−0.386015	+	0.922493i	$0.626149\pi$
$282$	0	0
$283$	−5.45476e123	−0.834758	−0.417379	−	0.908732i	$-0.637051\pi$
$283$	−5.45476e123	−0.834758	−0.417379	+	0.908732i	$0.637051\pi$
$284$	−2.33877e123	−0.299510
$285$	0	0
$286$	−2.38945e122	−0.0214691
$287$	−1.34548e124	−1.01354
$288$	0	0
$289$	−9.80463e123	−0.520104
$290$	1.38107e123	0.0615341
$291$	0	0
$292$	−1.94053e123	−0.0611065
$293$	3.35595e124	0.889203	0.444601	−	0.895729i	$-0.353345\pi$
$293$	3.35595e124	0.889203	0.444601	+	0.895729i	$0.353345\pi$
$294$	0	0
$295$	4.76186e122	0.00894880
$296$	−7.84889e123	−0.124330
$297$	0	0
$298$	1.99822e124	0.225280
$299$	2.10075e125	1.99977
$300$	0	0
$301$	−2.63340e125	−1.79023
$302$	4.21342e124	0.242261
$303$	0	0
$304$	−8.03367e124	−0.330977
$305$	−3.07732e124	−0.107407
$306$	0	0
$307$	7.02970e124	0.176380	0.0881900	−	0.996104i	$-0.471892\pi$
$307$	7.02970e124	0.176380	0.0881900	+	0.996104i	$0.471892\pi$
$308$	2.60049e124	0.0553662
$309$	0	0
$310$	−4.18197e124	−0.0642118
$311$	−1.14224e126	−1.49058	−0.745291	−	0.666739i	$-0.767690\pi$
$311$	−1.14224e126	−1.49058	−0.745291	+	0.666739i	$0.767690\pi$
$312$	0	0
$313$	−6.45867e125	−0.609753	−0.304876	−	0.952392i	$-0.598615\pi$
$313$	−6.45867e125	−0.609753	−0.304876	+	0.952392i	$0.598615\pi$
$314$	2.20975e125	0.177581
$315$	0	0
$316$	−8.60126e125	−0.501608
$317$	−2.85359e126	−1.41873	−0.709364	−	0.704843i	$-0.751018\pi$
$317$	−2.85359e126	−1.41873	−0.709364	+	0.704843i	$0.751018\pi$
$318$	0	0
$319$	2.16780e125	0.0784495
$320$	8.80279e124	0.0271986
$321$	0	0
$322$	3.69019e126	0.832391
$323$	1.97342e126	0.380620
$324$	0	0
$325$	−8.11403e126	−1.14585
$326$	2.47484e126	0.299266
$327$	0	0
$328$	6.12215e126	0.543594
$329$	−2.50183e127	−1.90487
$330$	0	0
$331$	1.94587e127	1.09094	0.545469	−	0.838131i	$-0.316351\pi$
$331$	1.94587e127	1.09094	0.545469	+	0.838131i	$0.316351\pi$
$332$	1.72838e127	0.832083
$333$	0	0
$334$	−5.89610e126	−0.209589
$335$	2.34004e126	0.0715253
$336$	0	0
$337$	−3.84815e127	−0.870848	−0.435424	−	0.900225i	$-0.643402\pi$
$337$	−3.84815e127	−0.870848	−0.435424	+	0.900225i	$0.643402\pi$
$338$	−6.54640e126	−0.127558
$339$	0	0
$340$	−4.31298e126	−0.0623868
$341$	−6.56425e126	−0.0818633
$342$	0	0
$343$	4.55307e127	0.422621
$344$	1.19824e128	0.960159
$345$	0	0
$346$	−3.48749e127	−0.208531
$347$	5.10458e127	0.263828	0.131914	−	0.991261i	$-0.457888\pi$
$347$	5.10458e127	0.263828	0.131914	+	0.991261i	$0.457888\pi$
$348$	0	0
$349$	−2.94005e128	−1.13677	−0.568383	−	0.822764i	$-0.692431\pi$
$349$	−2.94005e128	−1.13677	−0.568383	+	0.822764i	$0.692431\pi$
$350$	−1.42531e128	−0.476952
$351$	0	0
$352$	−1.81908e127	−0.0456507
$353$	3.11192e128	0.676714	0.338357	−	0.941018i	$-0.390129\pi$
$353$	3.11192e128	0.676714	0.338357	+	0.941018i	$0.390129\pi$
$354$	0	0
$355$	−2.22551e127	−0.0363829
$356$	3.41537e128	0.484410
$357$	0	0
$358$	1.61855e128	0.172995
$359$	−1.27605e129	−1.18467	−0.592336	−	0.805691i	$-0.701794\pi$
$359$	−1.27605e129	−1.18467	−0.592336	+	0.805691i	$0.701794\pi$
$360$	0	0
$361$	−9.95504e128	−0.698119
$362$	2.92090e128	0.178129
$363$	0	0
$364$	2.79464e129	1.29034
$365$	−1.84656e127	−0.00742290
$366$	0	0
$367$	3.07513e129	0.938052	0.469026	−	0.883184i	$-0.344605\pi$
$367$	3.07513e129	0.938052	0.469026	+	0.883184i	$0.344605\pi$
$368$	3.91084e129	1.03981
$369$	0	0
$370$	−3.45552e127	−0.00698758
$371$	−7.91499e129	−1.39659
$372$	0	0
$373$	−9.10110e128	−0.122405	−0.0612023	−	0.998125i	$-0.519493\pi$
$373$	−9.10110e128	−0.122405	−0.0612023	+	0.998125i	$0.519493\pi$
$374$	1.09269e128	0.0128376
$375$	0	0
$376$	1.13837e130	1.02164
$377$	2.32964e130	1.82832
$378$	0	0
$379$	1.67118e130	1.00402	0.502011	−	0.864861i	$-0.332594\pi$
$379$	1.67118e130	1.00402	0.502011	+	0.864861i	$0.332594\pi$
$380$	−9.40825e128	−0.0494809
$381$	0	0
$382$	−1.63610e130	−0.660099
$383$	−4.34816e130	−1.53733	−0.768666	−	0.639650i	$-0.779079\pi$
$383$	−4.34816e130	−1.53733	−0.768666	+	0.639650i	$0.779079\pi$
$384$	0	0
$385$	2.47456e128	0.00672560
$386$	−2.95799e130	−0.705242
$387$	0	0
$388$	−1.47513e130	−0.270912
$389$	2.46326e130	0.397242	0.198621	−	0.980076i	$-0.436354\pi$
$389$	2.46326e130	0.397242	0.198621	+	0.980076i	$0.436354\pi$
$390$	0	0
$391$	−9.60674e130	−1.19578
$392$	4.26939e130	0.467110
$393$	0	0
$394$	4.60680e130	0.389799
$395$	−8.18472e129	−0.0609327
$396$	0	0
$397$	1.12850e131	0.651001	0.325500	−	0.945542i	$-0.394467\pi$
$397$	1.12850e131	0.651001	0.325500	+	0.945542i	$0.394467\pi$
$398$	−2.09651e130	−0.106513
$399$	0	0
$400$	−1.51054e131	−0.595803
$401$	2.71882e131	0.945343	0.472672	−	0.881239i	$-0.343290\pi$
$401$	2.71882e131	0.945343	0.472672	+	0.881239i	$0.343290\pi$
$402$	0	0
$403$	−7.05431e131	−1.90788
$404$	1.51057e131	0.360480
$405$	0	0
$406$	4.09226e131	0.761025
$407$	−5.42399e129	−0.00890843
$408$	0	0
$409$	4.67974e131	0.600059	0.300030	−	0.953930i	$-0.403003\pi$
$409$	4.67974e131	0.600059	0.300030	+	0.953930i	$0.403003\pi$
$410$	2.69532e130	0.0305510
$411$	0	0
$412$	−8.42692e131	−0.747067
$413$	1.41099e131	0.110674
$414$	0	0
$415$	1.64468e131	0.101077
$416$	−1.95489e132	−1.06392
$417$	0	0
$418$	2.38358e130	0.0101819
$419$	−1.77543e132	−0.672194	−0.336097	−	0.941827i	$-0.609107\pi$
$419$	−1.77543e132	−0.672194	−0.336097	+	0.941827i	$0.609107\pi$
$420$	0	0
$421$	2.58058e132	0.768194	0.384097	−	0.923293i	$-0.374513\pi$
$421$	2.58058e132	0.768194	0.384097	+	0.923293i	$0.374513\pi$
$422$	−1.32441e132	−0.349738
$423$	0	0
$424$	3.60145e132	0.749034
$425$	3.71054e132	0.685167
$426$	0	0
$427$	−9.11847e132	−1.32835
$428$	−4.37304e132	−0.566074
$429$	0	0
$430$	5.27534e131	0.0539626
$431$	6.70076e132	0.609568	0.304784	−	0.952422i	$-0.401416\pi$
$431$	6.70076e132	0.609568	0.304784	+	0.952422i	$0.401416\pi$
$432$	0	0
$433$	2.06034e133	1.48354	0.741771	−	0.670653i	$-0.233986\pi$
$433$	2.06034e133	1.48354	0.741771	+	0.670653i	$0.233986\pi$
$434$	−1.23916e133	−0.794141
$435$	0	0
$436$	−1.63892e133	−0.832704
$437$	−2.09559e133	−0.948406
$438$	0	0
$439$	−2.98273e133	−1.07190	−0.535952	−	0.844249i	$-0.680047\pi$
$439$	−2.98273e133	−1.07190	−0.535952	+	0.844249i	$0.680047\pi$
$440$	−1.12596e131	−0.00360715
$441$	0	0
$442$	1.17427e133	0.299188
$443$	8.60604e133	1.95621	0.978105	−	0.208113i	$-0.0667323\pi$
$443$	8.60604e133	1.95621	0.978105	+	0.208113i	$0.0667323\pi$
$444$	0	0
$445$	3.24997e132	0.0588436
$446$	2.32166e133	0.375308
$447$	0	0
$448$	2.60837e133	0.336379
$449$	7.10386e133	0.818567	0.409283	−	0.912407i	$-0.365779\pi$
$449$	7.10386e133	0.818567	0.409283	+	0.912407i	$0.365779\pi$
$450$	0	0
$451$	4.23072e132	0.0389493
$452$	6.09574e133	0.501806
$453$	0	0
$454$	4.26763e133	0.281104
$455$	2.65930e133	0.156744
$456$	0	0
$457$	1.42058e134	0.670962	0.335481	−	0.942047i	$-0.391101\pi$
$457$	1.42058e134	0.670962	0.335481	+	0.942047i	$0.391101\pi$
$458$	−1.33876e133	−0.0566235
$459$	0	0
$460$	4.58000e133	0.155452
$461$	−6.35945e134	−1.93430	−0.967148	−	0.254214i	$-0.918183\pi$
$461$	−6.35945e134	−1.93430	−0.967148	+	0.254214i	$0.918183\pi$
$462$	0	0
$463$	−4.26577e134	−1.04270	−0.521348	−	0.853344i	$-0.674571\pi$
$463$	−4.26577e134	−1.04270	−0.521348	+	0.853344i	$0.674571\pi$
$464$	4.33696e134	0.950664
$465$	0	0
$466$	−2.57992e134	−0.455112
$467$	−7.39973e134	−1.17142	−0.585711	−	0.810520i	$-0.699185\pi$
$467$	−7.39973e134	−1.17142	−0.585711	+	0.810520i	$0.699185\pi$
$468$	0	0
$469$	6.93379e134	0.884591
$470$	5.01176e133	0.0574180
$471$	0	0
$472$	−6.42025e133	−0.0593582
$473$	8.28047e133	0.0687966
$474$	0	0
$475$	8.09409e134	0.543427
$476$	−1.27799e135	−0.771570
$477$	0	0
$478$	3.48108e134	0.170061
$479$	7.32367e134	0.321948	0.160974	−	0.986959i	$-0.448536\pi$
$479$	7.32367e134	0.321948	0.160974	+	0.986959i	$0.448536\pi$
$480$	0	0
$481$	−5.82892e134	−0.207617
$482$	1.38494e135	0.444176
$483$	0	0
$484$	3.30090e135	0.858899
$485$	−1.40369e134	−0.0329090
$486$	0	0
$487$	−5.67086e135	−1.08003	−0.540016	−	0.841655i	$-0.681582\pi$
$487$	−5.67086e135	−1.08003	−0.540016	+	0.841655i	$0.681582\pi$
$488$	4.14905e135	0.712439
$489$	0	0
$490$	1.87963e134	0.0262524
$491$	−1.09683e135	−0.138205	−0.0691027	−	0.997610i	$-0.522014\pi$
$491$	−1.09683e135	−0.138205	−0.0691027	+	0.997610i	$0.522014\pi$
$492$	0	0
$493$	−1.06535e136	−1.09325
$494$	2.56153e135	0.237295
$495$	0	0
$496$	−1.31326e136	−0.992032
$497$	−6.59444e135	−0.449967
$498$	0	0
$499$	1.68834e136	0.940550	0.470275	−	0.882520i	$-0.344155\pi$
$499$	1.68834e136	0.940550	0.470275	+	0.882520i	$0.344155\pi$
$500$	−3.55756e135	−0.179129
$501$	0	0
$502$	−1.71235e136	−0.704780
$503$	4.59541e136	1.71057	0.855285	−	0.518158i	$-0.173382\pi$
$503$	4.59541e136	1.71057	0.855285	+	0.518158i	$0.173382\pi$
$504$	0	0
$505$	1.43741e135	0.0437892
$506$	−1.16034e135	−0.0319879
$507$	0	0
$508$	4.92141e136	1.11166
$509$	−3.06425e136	−0.626724	−0.313362	−	0.949634i	$-0.601455\pi$
$509$	−3.06425e136	−0.626724	−0.313362	+	0.949634i	$0.601455\pi$
$510$	0	0
$511$	−5.47157e135	−0.0918029
$512$	−6.38865e136	−0.971128
$513$	0	0
$514$	7.29983e134	0.00911329
$515$	−8.01882e135	−0.0907498
$516$	0	0
$517$	7.86674e135	0.0732019
$518$	−1.02391e136	−0.0864191
$519$	0	0
$520$	−1.21002e136	−0.0840669
$521$	−4.01949e136	−0.253435	−0.126717	−	0.991939i	$-0.540444\pi$
$521$	−4.01949e136	−0.253435	−0.126717	+	0.991939i	$0.540444\pi$
$522$	0	0
$523$	1.74801e137	0.908256	0.454128	−	0.890937i	$-0.349951\pi$
$523$	1.74801e137	0.908256	0.454128	+	0.890937i	$0.349951\pi$
$524$	9.87676e136	0.465999
$525$	0	0
$526$	−2.32736e136	−0.0905908
$527$	3.22594e137	1.14083
$528$	0	0
$529$	6.77766e137	1.97956
$530$	1.58556e136	0.0420970
$531$	0	0
$532$	−2.78777e137	−0.611956
$533$	4.54657e137	0.907737
$534$	0	0
$535$	−4.16126e136	−0.0687637
$536$	−3.15499e137	−0.474434
$537$	0	0
$538$	2.71570e137	0.338359
$539$	2.95037e136	0.0334691
$540$	0	0
$541$	−1.25633e138	−1.18207	−0.591034	−	0.806647i	$-0.701280\pi$
$541$	−1.25633e138	−1.18207	−0.591034	+	0.806647i	$0.701280\pi$
$542$	1.08354e137	0.0928711
$543$	0	0
$544$	8.93969e137	0.636177
$545$	−1.55955e137	−0.101153
$546$	0	0
$547$	−2.40142e138	−1.29452	−0.647259	−	0.762270i	$-0.724085\pi$
$547$	−2.40142e138	−1.29452	−0.647259	+	0.762270i	$0.724085\pi$
$548$	2.85436e138	1.40311
$549$	0	0
$550$	4.48175e136	0.0183287
$551$	−2.32392e138	−0.867093
$552$	0	0
$553$	−2.42523e138	−0.753587
$554$	−6.32536e137	−0.179408
$555$	0	0
$556$	4.30979e137	0.101901
$557$	2.32646e138	0.502353	0.251176	−	0.967941i	$-0.419183\pi$
$557$	2.32646e138	0.502353	0.251176	+	0.967941i	$0.419183\pi$
$558$	0	0
$559$	8.89866e138	1.60335
$560$	4.95066e137	0.0815019
$561$	0	0
$562$	2.09307e138	0.287806
$563$	1.12700e139	1.41661	0.708306	−	0.705906i	$-0.249460\pi$
$563$	1.12700e139	1.41661	0.708306	+	0.705906i	$0.249460\pi$
$564$	0	0
$565$	5.80054e137	0.0609568
$566$	3.23785e138	0.311191
$567$	0	0
$568$	3.00058e138	0.241331
$569$	6.22965e138	0.458452	0.229226	−	0.973373i	$-0.426380\pi$
$569$	6.22965e138	0.458452	0.229226	+	0.973373i	$0.426380\pi$
$570$	0	0
$571$	−1.06373e139	−0.655704	−0.327852	−	0.944729i	$-0.606325\pi$
$571$	−1.06373e139	−0.655704	−0.327852	+	0.944729i	$0.606325\pi$
$572$	−8.78745e137	−0.0495865
$573$	0	0
$574$	7.98653e138	0.377840
$575$	−3.94026e139	−1.70726
$576$	0	0
$577$	3.61142e139	1.31310	0.656552	−	0.754281i	$-0.272014\pi$
$577$	3.61142e139	1.31310	0.656552	+	0.754281i	$0.272014\pi$
$578$	5.81986e138	0.193890
$579$	0	0
$580$	5.07902e138	0.142124
$581$	4.87338e139	1.25007
$582$	0	0
$583$	2.48879e138	0.0536692
$584$	2.48965e138	0.0492368
$585$	0	0
$586$	−1.99203e139	−0.331487
$587$	9.37398e139	1.43120	0.715599	−	0.698511i	$-0.246154\pi$
$587$	9.37398e139	1.43120	0.715599	+	0.698511i	$0.246154\pi$
$588$	0	0
$589$	7.03699e139	0.904824
$590$	−2.82656e137	−0.00333604
$591$	0	0
$592$	−1.08514e139	−0.107954
$593$	1.79083e140	1.63603	0.818015	−	0.575197i	$-0.195074\pi$
$593$	1.79083e140	1.63603	0.818015	+	0.575197i	$0.195074\pi$
$594$	0	0
$595$	−1.21610e139	−0.0937263
$596$	7.34868e139	0.520323
$597$	0	0
$598$	−1.24697e140	−0.745497
$599$	8.24207e139	0.452879	0.226439	−	0.974025i	$-0.427291\pi$
$599$	8.24207e139	0.452879	0.226439	+	0.974025i	$0.427291\pi$
$600$	0	0
$601$	1.29641e140	0.601980	0.300990	−	0.953627i	$-0.402683\pi$
$601$	1.29641e140	0.601980	0.300990	+	0.953627i	$0.402683\pi$
$602$	1.56314e140	0.667384
$603$	0	0
$604$	1.54953e140	0.559544
$605$	3.14105e139	0.104335
$606$	0	0
$607$	4.97901e140	1.39996	0.699978	−	0.714164i	$-0.253193\pi$
$607$	4.97901e140	1.39996	0.699978	+	0.714164i	$0.253193\pi$
$608$	1.95008e140	0.504572
$609$	0	0
$610$	1.82665e139	0.0400403
$611$	8.45404e140	1.70602
$612$	0	0
$613$	2.08079e140	0.356019	0.178010	−	0.984029i	$-0.443034\pi$
$613$	2.08079e140	0.356019	0.178010	+	0.984029i	$0.443034\pi$
$614$	−4.17271e139	−0.0657530
$615$	0	0
$616$	−3.33636e139	−0.0446115
$617$	8.92522e140	1.09956	0.549779	−	0.835310i	$-0.314712\pi$
$617$	8.92522e140	1.09956	0.549779	+	0.835310i	$0.314712\pi$
$618$	0	0
$619$	4.62079e140	0.483436	0.241718	−	0.970347i	$-0.422289\pi$
$619$	4.62079e140	0.483436	0.241718	+	0.970347i	$0.422289\pi$
$620$	−1.53796e140	−0.148308
$621$	0	0
$622$	6.78011e140	0.555677
$623$	9.63005e140	0.727750
$624$	0	0
$625$	1.50488e141	0.967301
$626$	3.83375e140	0.227311
$627$	0	0
$628$	8.12660e140	0.410154
$629$	2.66556e140	0.124146
$630$	0	0
$631$	−3.56470e141	−1.41430	−0.707148	−	0.707066i	$-0.750018\pi$
$631$	−3.56470e141	−1.41430	−0.707148	+	0.707066i	$0.750018\pi$
$632$	1.10352e141	0.404173
$633$	0	0
$634$	1.69384e141	0.528890
$635$	4.68308e140	0.135039
$636$	0	0
$637$	3.17063e141	0.780017
$638$	−1.28677e140	−0.0292453
$639$	0	0
$640$	−5.47241e140	−0.106192
$641$	1.80821e140	0.0324278	0.0162139	−	0.999869i	$-0.494839\pi$
$641$	1.80821e140	0.0324278	0.0162139	+	0.999869i	$0.494839\pi$
$642$	0	0
$643$	5.93023e140	0.0908693	0.0454347	−	0.998967i	$-0.485533\pi$
$643$	5.93023e140	0.0908693	0.0454347	+	0.998967i	$0.485533\pi$
$644$	1.35711e142	1.92255
$645$	0	0
$646$	−1.17139e141	−0.141892
$647$	1.30820e142	1.46558	0.732788	−	0.680457i	$-0.238219\pi$
$647$	1.30820e142	1.46558	0.732788	+	0.680457i	$0.238219\pi$
$648$	0	0
$649$	−4.43672e139	−0.00425310
$650$	4.81634e141	0.427162
$651$	0	0
$652$	9.10148e141	0.691207
$653$	2.39043e142	1.68020	0.840100	−	0.542431i	$-0.182496\pi$
$653$	2.39043e142	1.68020	0.840100	+	0.542431i	$0.182496\pi$
$654$	0	0
$655$	9.39845e140	0.0566071
$656$	8.46408e141	0.471993
$657$	0	0
$658$	1.48504e142	0.710119
$659$	2.10277e142	0.931278	0.465639	−	0.884975i	$-0.345825\pi$
$659$	2.10277e142	0.931278	0.465639	+	0.884975i	$0.345825\pi$
$660$	0	0
$661$	−1.91977e142	−0.729583	−0.364792	−	0.931089i	$-0.618860\pi$
$661$	−1.91977e142	−0.729583	−0.364792	+	0.931089i	$0.618860\pi$
$662$	−1.15503e142	−0.406693
$663$	0	0
$664$	−2.21747e142	−0.670454
$665$	−2.65277e141	−0.0743372
$666$	0	0
$667$	1.13130e143	2.72410
$668$	−2.16835e142	−0.484082
$669$	0	0
$670$	−1.38900e141	−0.0266640
$671$	2.86721e141	0.0510472
$672$	0	0
$673$	5.63386e142	0.863069	0.431534	−	0.902096i	$-0.357972\pi$
$673$	5.63386e142	0.863069	0.431534	+	0.902096i	$0.357972\pi$
$674$	2.28420e142	0.324645
$675$	0	0
$676$	−2.40751e142	−0.294618
$677$	−6.51705e141	−0.0740157	−0.0370078	−	0.999315i	$-0.511783\pi$
$677$	−6.51705e141	−0.0740157	−0.0370078	+	0.999315i	$0.511783\pi$
$678$	0	0
$679$	−4.15931e142	−0.407003
$680$	5.53344e141	0.0502684
$681$	0	0
$682$	3.89643e141	0.0305180
$683$	−1.77465e142	−0.129083	−0.0645413	−	0.997915i	$-0.520558\pi$
$683$	−1.77465e142	−0.129083	−0.0645413	+	0.997915i	$0.520558\pi$
$684$	0	0
$685$	2.71613e142	0.170442
$686$	−2.70262e142	−0.157550
$687$	0	0
$688$	1.65661e143	0.833689
$689$	2.67459e143	1.25080
$690$	0	0
$691$	−7.60623e142	−0.307275	−0.153638	−	0.988127i	$-0.549099\pi$
$691$	−7.60623e142	−0.307275	−0.153638	+	0.988127i	$0.549099\pi$
$692$	−1.28256e143	−0.481638
$693$	0	0
$694$	−3.02999e142	−0.0983530
$695$	4.10107e141	0.0123784
$696$	0	0
$697$	−2.07915e143	−0.542787
$698$	1.74516e143	0.423777
$699$	0	0
$700$	−5.24174e143	−1.10160
$701$	−2.53234e143	−0.495179	−0.247590	−	0.968865i	$-0.579638\pi$
$701$	−2.53234e143	−0.495179	−0.247590	+	0.968865i	$0.579638\pi$
$702$	0	0
$703$	5.81460e142	0.0984637
$704$	−8.20174e141	−0.0129267
$705$	0	0
$706$	−1.84718e143	−0.252274
$707$	4.25922e143	0.541564
$708$	0	0
$709$	−4.79369e143	−0.528488	−0.264244	−	0.964456i	$-0.585122\pi$
$709$	−4.79369e143	−0.528488	−0.264244	+	0.964456i	$0.585122\pi$
$710$	1.32102e142	0.0135633
$711$	0	0
$712$	−4.38183e143	−0.390315
$713$	−3.42565e144	−2.84264
$714$	0	0
$715$	−8.36189e141	−0.00602351
$716$	5.95240e143	0.399562
$717$	0	0
$718$	7.57440e143	0.441636
$719$	−2.96453e143	−0.161119	−0.0805595	−	0.996750i	$-0.525671\pi$
$719$	−2.96453e143	−0.161119	−0.0805595	+	0.996750i	$0.525671\pi$
$720$	0	0
$721$	−2.37607e144	−1.12235
$722$	5.90914e143	0.260253
$723$	0	0
$724$	1.07419e144	0.411418
$725$	−4.36958e144	−1.56088
$726$	0	0
$727$	−5.04268e143	−0.156738	−0.0783689	−	0.996924i	$-0.524971\pi$
$727$	−5.04268e143	−0.156738	−0.0783689	+	0.996924i	$0.524971\pi$
$728$	−3.58544e144	−1.03970
$729$	0	0
$730$	1.09609e142	0.00276720
$731$	−4.06935e144	−0.958733
$732$	0	0
$733$	1.13594e144	0.233134	0.116567	−	0.993183i	$-0.462811\pi$
$733$	1.13594e144	0.233134	0.116567	+	0.993183i	$0.462811\pi$
$734$	−1.82534e144	−0.349698
$735$	0	0
$736$	−9.49315e144	−1.58519
$737$	−2.18026e143	−0.0339938
$738$	0	0
$739$	9.39645e144	1.27767	0.638836	−	0.769343i	$-0.279416\pi$
$739$	9.39645e144	1.27767	0.638836	+	0.769343i	$0.279416\pi$
$740$	−1.27080e143	−0.0161390
$741$	0	0
$742$	4.69820e144	0.520636
$743$	−3.87882e144	−0.401574	−0.200787	−	0.979635i	$-0.564350\pi$
$743$	−3.87882e144	−0.401574	−0.200787	+	0.979635i	$0.564350\pi$
$744$	0	0
$745$	6.99280e143	0.0632061
$746$	5.40226e143	0.0456315
$747$	0	0
$748$	4.01850e143	0.0296506
$749$	−1.23303e145	−0.850436
$750$	0	0
$751$	−1.87721e145	−1.13161	−0.565804	−	0.824540i	$-0.691434\pi$
$751$	−1.87721e145	−1.13161	−0.565804	+	0.824540i	$0.691434\pi$
$752$	1.57384e145	0.887072
$753$	0	0
$754$	−1.38284e145	−0.681581
$755$	1.47449e144	0.0679705
$756$	0	0
$757$	−6.72388e144	−0.271193	−0.135596	−	0.990764i	$-0.543295\pi$
$757$	−6.72388e144	−0.271193	−0.135596	+	0.990764i	$0.543295\pi$
$758$	−9.91984e144	−0.374291
$759$	0	0
$760$	1.20705e144	0.0398694
$761$	−2.75168e144	−0.0850496	−0.0425248	−	0.999095i	$-0.513540\pi$
$761$	−2.75168e144	−0.0850496	−0.0425248	+	0.999095i	$0.513540\pi$
$762$	0	0
$763$	−4.62114e145	−1.25101
$764$	−6.01692e145	−1.52461
$765$	0	0
$766$	2.58099e145	0.573105
$767$	−4.76795e144	−0.0991211
$768$	0	0
$769$	−8.90258e144	−0.162269	−0.0811345	−	0.996703i	$-0.525854\pi$
$769$	−8.90258e144	−0.162269	−0.0811345	+	0.996703i	$0.525854\pi$
$770$	−1.46885e143	−0.00250725
$771$	0	0
$772$	−1.08783e146	−1.62888
$773$	−6.30125e145	−0.883816	−0.441908	−	0.897060i	$-0.645698\pi$
$773$	−6.30125e145	−0.883816	−0.441908	+	0.897060i	$0.645698\pi$
$774$	0	0
$775$	1.32314e146	1.62880
$776$	1.89255e145	0.218289
$777$	0	0
$778$	−1.46215e145	−0.148088
$779$	−4.53540e145	−0.430501
$780$	0	0
$781$	2.07355e144	0.0172917
$782$	5.70239e145	0.445775
$783$	0	0
$784$	5.90257e145	0.405583
$785$	7.73304e144	0.0498233
$786$	0	0
$787$	1.04521e146	0.592216	0.296108	−	0.955154i	$-0.404311\pi$
$787$	1.04521e146	0.592216	0.296108	+	0.955154i	$0.404311\pi$
$788$	1.69420e146	0.900307
$789$	0	0
$790$	4.85831e144	0.0227152
$791$	1.71877e146	0.753884
$792$	0	0
$793$	3.08126e146	1.18969
$794$	−6.69859e145	−0.242688
$795$	0	0
$796$	−7.71014e145	−0.246010
$797$	−4.25964e146	−1.27564	−0.637820	−	0.770186i	$-0.720164\pi$
$797$	−4.25964e146	−1.27564	−0.637820	+	0.770186i	$0.720164\pi$
$798$	0	0
$799$	−3.86603e146	−1.02012
$800$	3.66667e146	0.908296
$801$	0	0
$802$	−1.61384e146	−0.352416
$803$	1.72048e144	0.00352788
$804$	0	0
$805$	1.29139e146	0.233541
$806$	4.18732e146	0.711240
$807$	0	0
$808$	−1.93801e146	−0.290458
$809$	3.72784e146	0.524877	0.262438	−	0.964949i	$-0.415473\pi$
$809$	3.72784e146	0.524877	0.262438	+	0.964949i	$0.415473\pi$
$810$	0	0
$811$	1.18387e147	1.47147	0.735735	−	0.677270i	$-0.236837\pi$
$811$	1.18387e147	1.47147	0.735735	+	0.677270i	$0.236837\pi$
$812$	1.50497e147	1.75772
$813$	0	0
$814$	3.21958e144	0.00332099
$815$	8.66071e145	0.0839642
$816$	0	0
$817$	−8.87680e146	−0.760401
$818$	−2.77781e146	−0.223697
$819$	0	0
$820$	9.91231e145	0.0705627
$821$	1.48927e147	0.996885	0.498442	−	0.866923i	$-0.333906\pi$
$821$	1.48927e147	0.996885	0.498442	+	0.866923i	$0.333906\pi$
$822$	0	0
$823$	2.78199e147	1.64689	0.823443	−	0.567399i	$-0.192050\pi$
$823$	2.78199e147	1.64689	0.823443	+	0.567399i	$0.192050\pi$
$824$	1.08115e147	0.601952
$825$	0	0
$826$	−8.37541e145	−0.0412585
$827$	2.17061e147	1.00590	0.502950	−	0.864316i	$-0.332248\pi$
$827$	2.17061e147	1.00590	0.502950	+	0.864316i	$0.332248\pi$
$828$	0	0
$829$	1.19927e147	0.491941	0.245970	−	0.969277i	$-0.420893\pi$
$829$	1.19927e147	0.491941	0.245970	+	0.969277i	$0.420893\pi$
$830$	−9.76254e145	−0.0376807
$831$	0	0
$832$	−8.81405e146	−0.301264
$833$	−1.44993e147	−0.466417
$834$	0	0
$835$	−2.06335e146	−0.0588037
$836$	8.76586e145	0.0235168
$837$	0	0
$838$	1.05386e147	0.250588
$839$	4.40608e147	0.986445	0.493223	−	0.869903i	$-0.335819\pi$
$839$	4.40608e147	0.986445	0.493223	+	0.869903i	$0.335819\pi$
$840$	0	0
$841$	7.50833e147	1.49055
$842$	−1.53179e147	−0.286377
$843$	0	0
$844$	−4.87064e147	−0.807779
$845$	−2.29092e146	−0.0357886
$846$	0	0
$847$	9.30728e147	1.29036
$848$	4.97912e147	0.650372
$849$	0	0
$850$	−2.20251e147	−0.255425
$851$	−2.83059e147	−0.309339
$852$	0	0
$853$	−1.23230e148	−1.19616	−0.598082	−	0.801435i	$-0.704070\pi$
$853$	−1.23230e148	−1.19616	−0.598082	+	0.801435i	$0.704070\pi$
$854$	5.41256e147	0.495200
$855$	0	0
$856$	5.61049e147	0.456116
$857$	−9.78619e147	−0.750036	−0.375018	−	0.927018i	$-0.622363\pi$
$857$	−9.78619e147	−0.750036	−0.375018	+	0.927018i	$0.622363\pi$
$858$	0	0
$859$	1.54130e147	0.105010	0.0525052	−	0.998621i	$-0.483279\pi$
$859$	1.54130e147	0.105010	0.0525052	+	0.998621i	$0.483279\pi$
$860$	1.94006e147	0.124636
$861$	0	0
$862$	−3.97746e147	−0.227242
$863$	−1.29970e148	−0.700321	−0.350160	−	0.936690i	$-0.613873\pi$
$863$	−1.29970e148	−0.700321	−0.350160	+	0.936690i	$0.613873\pi$
$864$	0	0
$865$	−1.22045e147	−0.0585069
$866$	−1.22298e148	−0.553053
$867$	0	0
$868$	−4.55716e148	−1.83420
$869$	7.62588e146	0.0289595
$870$	0	0
$871$	−2.34303e148	−0.792248
$872$	2.10269e148	0.670955
$873$	0	0
$874$	1.24391e148	0.353558
$875$	−1.00310e148	−0.269114
$876$	0	0
$877$	3.62999e148	0.867813	0.433906	−	0.900958i	$-0.357135\pi$
$877$	3.62999e148	0.867813	0.433906	+	0.900958i	$0.357135\pi$
$878$	1.77050e148	0.399597
$879$	0	0
$880$	−1.55668e146	−0.00313203
$881$	−3.01535e148	−0.572869	−0.286434	−	0.958100i	$-0.592470\pi$
$881$	−3.01535e148	−0.572869	−0.286434	+	0.958100i	$0.592470\pi$
$882$	0	0
$883$	−5.32283e148	−0.901835	−0.450917	−	0.892566i	$-0.648903\pi$
$883$	−5.32283e148	−0.901835	−0.450917	+	0.892566i	$0.648903\pi$
$884$	4.31850e148	0.691025
$885$	0	0
$886$	−5.10840e148	−0.729259
$887$	−2.38497e147	−0.0321618	−0.0160809	−	0.999871i	$-0.505119\pi$
$887$	−2.38497e147	−0.0321618	−0.0160809	+	0.999871i	$0.505119\pi$
$888$	0	0
$889$	1.38765e149	1.67009
$890$	−1.92913e147	−0.0219364
$891$	0	0
$892$	8.53815e148	0.866839
$893$	−8.43327e148	−0.809091
$894$	0	0
$895$	5.66414e147	0.0485367
$896$	−1.62154e149	−1.31333
$897$	0	0
$898$	−4.21673e148	−0.305155
$899$	−3.79890e149	−2.59892
$900$	0	0
$901$	−1.22309e149	−0.747922
$902$	−2.51128e147	−0.0145200
$903$	0	0
$904$	−7.82067e148	−0.404332
$905$	1.02217e148	0.0499770
$906$	0	0
$907$	−1.47830e149	−0.646541	−0.323270	−	0.946307i	$-0.604782\pi$
$907$	−1.47830e149	−0.646541	−0.323270	+	0.946307i	$0.604782\pi$
$908$	1.56947e149	0.649257
$909$	0	0
$910$	−1.57851e148	−0.0584330
$911$	−4.77532e149	−1.67234	−0.836170	−	0.548470i	$-0.815210\pi$
$911$	−4.77532e149	−1.67234	−0.836170	+	0.548470i	$0.815210\pi$
$912$	0	0
$913$	−1.53238e148	−0.0480389
$914$	−8.43232e148	−0.250129
$915$	0	0
$916$	−4.92344e148	−0.130782
$917$	2.78487e149	0.700089
$918$	0	0
$919$	−2.19568e148	−0.0494465	−0.0247232	−	0.999694i	$-0.507870\pi$
$919$	−2.19568e148	−0.0494465	−0.0247232	+	0.999694i	$0.507870\pi$
$920$	−5.87601e148	−0.125256
$921$	0	0
$922$	3.77486e149	0.721090
$923$	2.22836e149	0.402994
$924$	0	0
$925$	1.09330e149	0.177248
$926$	2.53209e149	0.388708
$927$	0	0
$928$	−1.05275e150	−1.44928
$929$	1.54224e149	0.201076	0.100538	−	0.994933i	$-0.467944\pi$
$929$	1.54224e149	0.201076	0.100538	+	0.994933i	$0.467944\pi$
$930$	0	0
$931$	−3.16284e149	−0.369929
$932$	−9.48794e149	−1.05116
$933$	0	0
$934$	4.39235e149	0.436696
$935$	3.82389e147	0.00360180
$936$	0	0
$937$	−2.20649e150	−1.86574	−0.932871	−	0.360210i	$-0.882705\pi$
$937$	−2.20649e150	−1.86574	−0.932871	+	0.360210i	$0.882705\pi$
$938$	−4.11578e149	−0.329768
$939$	0	0
$940$	1.84313e149	0.132617
$941$	2.68784e150	1.83285	0.916426	−	0.400205i	$-0.131061\pi$
$941$	2.68784e150	1.83285	0.916426	+	0.400205i	$0.131061\pi$
$942$	0	0
$943$	2.20787e150	1.35248
$944$	−8.87621e148	−0.0515397
$945$	0	0
$946$	−4.91514e148	−0.0256468
$947$	2.21163e149	0.109406	0.0547028	−	0.998503i	$-0.482579\pi$
$947$	2.21163e149	0.109406	0.0547028	+	0.998503i	$0.482579\pi$
$948$	0	0
$949$	1.84892e149	0.0822195
$950$	−4.80451e149	−0.202585
$951$	0	0
$952$	1.63962e150	0.621695
$953$	−4.98371e150	−1.79210	−0.896048	−	0.443957i	$-0.853574\pi$
$953$	−4.98371e150	−1.79210	−0.896048	+	0.443957i	$0.853574\pi$
$954$	0	0
$955$	−5.72553e149	−0.185202
$956$	1.28020e150	0.392785
$957$	0	0
$958$	−4.34720e149	−0.120020
$959$	8.04820e150	2.10794
$960$	0	0
$961$	7.26171e150	1.71202
$962$	3.45995e149	0.0773977
$963$	0	0
$964$	5.09325e150	1.02590
$965$	−1.03515e150	−0.197868
$966$	0	0
$967$	−6.03489e150	−1.03904	−0.519520	−	0.854458i	$-0.673889\pi$
$967$	−6.03489e150	−1.03904	−0.519520	+	0.854458i	$0.673889\pi$
$968$	−4.23497e150	−0.692061
$969$	0	0
$970$	8.33209e148	0.0122682
$971$	1.06084e151	1.48278	0.741392	−	0.671072i	$-0.234166\pi$
$971$	1.06084e151	1.48278	0.741392	+	0.671072i	$0.234166\pi$
$972$	0	0
$973$	1.21520e150	0.153090
$974$	3.36612e150	0.402627
$975$	0	0
$976$	5.73620e150	0.618598
$977$	−5.88403e149	−0.0602559	−0.0301279	−	0.999546i	$-0.509591\pi$
$977$	−5.88403e149	−0.0602559	−0.0301279	+	0.999546i	$0.509591\pi$
$978$	0	0
$979$	−3.02807e149	−0.0279666
$980$	6.91252e149	0.0606344
$981$	0	0
$982$	6.51061e149	0.0515218
$983$	5.74386e150	0.431769	0.215884	−	0.976419i	$-0.430737\pi$
$983$	5.74386e150	0.431769	0.215884	+	0.976419i	$0.430737\pi$
$984$	0	0
$985$	1.61215e150	0.109365
$986$	6.32370e150	0.407556
$987$	0	0
$988$	9.42029e150	0.548073
$989$	4.32129e151	2.38891
$990$	0	0
$991$	−6.60511e150	−0.329731	−0.164866	−	0.986316i	$-0.552719\pi$
$991$	−6.60511e150	−0.329731	−0.164866	+	0.986316i	$0.552719\pi$
$992$	3.18779e151	1.51234
$993$	0	0
$994$	3.91434e150	0.167744
$995$	−7.33676e149	−0.0298840
$996$	0	0
$997$	−6.44459e150	−0.237186	−0.118593	−	0.992943i	$-0.537838\pi$
$997$	−6.44459e150	−0.237186	−0.118593	+	0.992943i	$0.537838\pi$
$998$	−1.00217e151	−0.350629
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.102.a.b.1.4		8
3.2	odd	2		1.102.a.a.1.5	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.102.a.a.1.5	✓	8	3.2	odd	2
9.102.a.b.1.4		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)

\(f(q)\)	\(=\)	\(q-5.93582e14 q^{2} -2.18296e30 q^{4} -2.07725e34 q^{5} -6.15512e42 q^{7} +2.80068e45 q^{8} +O(q^{10})\)	\(q-5.93582e14 q^{2} -2.18296e30 q^{4} -2.07725e34 q^{5} -6.15512e42 q^{7} +2.80068e45 q^{8} +1.23302e49 q^{10} +1.93541e51 q^{11} +2.07990e56 q^{13} +3.65357e57 q^{14} +3.87203e60 q^{16} -9.51139e61 q^{17} -2.07479e64 q^{19} +4.53455e64 q^{20} -1.14883e66 q^{22} +1.01002e69 q^{23} -3.90116e70 q^{25} -1.23459e71 q^{26} +1.34364e73 q^{28} +1.12007e74 q^{29} -3.39166e75 q^{31} -9.39893e75 q^{32} +5.64580e76 q^{34} +1.27857e77 q^{35} -2.80250e78 q^{37} +1.23156e79 q^{38} -5.81770e79 q^{40} +2.18595e81 q^{41} +4.27840e82 q^{43} -4.22493e81 q^{44} -5.99533e83 q^{46} +4.06463e84 q^{47} +1.52441e85 q^{49} +2.31566e85 q^{50} -4.54035e86 q^{52} +1.28592e87 q^{53} -4.02033e85 q^{55} -1.72385e88 q^{56} -6.64855e88 q^{58} -2.29239e88 q^{59} +1.48144e90 q^{61} +2.01323e90 q^{62} -4.23772e90 q^{64} -4.32047e90 q^{65} -1.12651e92 q^{67} +2.07630e92 q^{68} -7.58936e91 q^{70} +1.07138e93 q^{71} +8.88946e92 q^{73} +1.66351e93 q^{74} +4.52919e94 q^{76} -1.19127e94 q^{77} +3.94018e95 q^{79} -8.04316e94 q^{80} -1.29754e96 q^{82} -7.91760e96 q^{83} +1.97575e96 q^{85} -2.53958e97 q^{86} +5.42047e96 q^{88} -1.56456e98 q^{89} -1.28020e99 q^{91} -2.20484e99 q^{92} -2.41269e99 q^{94} +4.30986e98 q^{95} +6.75748e99 q^{97} -9.04864e99 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 434989091795040 q^{2} + 90\!\cdots\!96 q^{4}+ \cdots + 61\!\cdots\!20 q^{8}+O(q^{10}) \) 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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