LMFDB - Embedded newform 9.102.a.b.1.5

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			1.5
Root			$2.10926e12$ 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)

$f(q)$	$=$	$q+2.56863e14 q^{2} -2.46932e30 q^{4} -1.16158e35 q^{5} +2.79663e42 q^{7} -1.28550e45 q^{8} +O(q^{10})$	\(q+2.56863e14 q^{2} -2.46932e30 q^{4} -1.16158e35 q^{5} +2.79663e42 q^{7} -1.28550e45 q^{8} -2.98366e49 q^{10} +9.95717e51 q^{11} -1.44350e56 q^{13} +7.18350e56 q^{14} +5.93028e60 q^{16} -1.59801e62 q^{17} +1.62028e64 q^{19} +2.86831e65 q^{20} +2.55763e66 q^{22} -7.65727e68 q^{23} -2.59504e70 q^{25} -3.70781e70 q^{26} -6.90578e72 q^{28} +7.16454e72 q^{29} +1.90510e75 q^{31} +4.78240e75 q^{32} -4.10469e76 q^{34} -3.24850e77 q^{35} -1.10721e79 q^{37} +4.16190e78 q^{38} +1.49321e80 q^{40} +1.87777e81 q^{41} +9.41841e81 q^{43} -2.45875e82 q^{44} -1.96687e83 q^{46} -3.14875e84 q^{47} -1.48202e85 q^{49} -6.66570e84 q^{50} +3.56447e86 q^{52} +4.00521e86 q^{53} -1.15660e87 q^{55} -3.59507e87 q^{56} +1.84030e87 q^{58} +2.34450e89 q^{59} -4.02186e89 q^{61} +4.89350e89 q^{62} -1.38066e91 q^{64} +1.67674e91 q^{65} -3.05726e92 q^{67} +3.94600e92 q^{68} -8.34418e91 q^{70} +5.37677e93 q^{71} -2.11035e94 q^{73} -2.84401e93 q^{74} -4.00100e94 q^{76} +2.78465e94 q^{77} +8.91772e95 q^{79} -6.88848e95 q^{80} +4.82328e95 q^{82} -7.50442e96 q^{83} +1.85621e97 q^{85} +2.41924e96 q^{86} -1.28000e97 q^{88} +3.83813e98 q^{89} -4.03693e98 q^{91} +1.89083e99 q^{92} -8.08797e98 q^{94} -1.88208e99 q^{95} +1.03291e100 q^{97} -3.80676e99 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.56863e14	0.161319	0.0806596	−	0.996742i	$-0.474297\pi$
$2$	2.56863e14	0.161319	0.0806596	+	0.996742i	$0.474297\pi$
$3$	0	0
$3$	0	0
$4$	−2.46932e30	−0.973976
$5$	−1.16158e35	−0.584875	−0.292437	−	0.956285i	$-0.594466\pi$
$5$	−1.16158e35	−0.584875	−0.292437	+	0.956285i	$0.594466\pi$
$6$	0	0
$7$	2.79663e42	0.587738	0.293869	−	0.955846i	$-0.405057\pi$
$7$	2.79663e42	0.587738	0.293869	+	0.955846i	$0.405057\pi$
$8$	−1.28550e45	−0.318440
$9$	0	0
$10$	−2.98366e49	−0.0943515
$11$	9.95717e51	0.255744	0.127872	−	0.991791i	$-0.459185\pi$
$11$	9.95717e51	0.255744	0.127872	+	0.991791i	$0.459185\pi$
$12$	0	0
$13$	−1.44350e56	−0.804039	−0.402020	−	0.915631i	$-0.631692\pi$
$13$	−1.44350e56	−0.804039	−0.402020	+	0.915631i	$0.631692\pi$
$14$	7.18350e56	0.0948135
$15$	0	0
$16$	5.93028e60	0.922606
$17$	−1.59801e62	−1.16388	−0.581941	−	0.813231i	$-0.697707\pi$
$17$	−1.59801e62	−1.16388	−0.581941	+	0.813231i	$0.697707\pi$
$18$	0	0
$19$	1.62028e64	0.429076	0.214538	−	0.976716i	$-0.431175\pi$
$19$	1.62028e64	0.429076	0.214538	+	0.976716i	$0.431175\pi$
$20$	2.86831e65	0.569654
$21$	0	0
$22$	2.55763e66	0.0412564
$23$	−7.65727e68	−1.30863	−0.654317	−	0.756220i	$-0.727044\pi$
$23$	−7.65727e68	−1.30863	−0.654317	+	0.756220i	$0.727044\pi$
$24$	0	0
$25$	−2.59504e70	−0.657922
$26$	−3.70781e70	−0.129707
$27$	0	0
$28$	−6.90578e72	−0.572443
$29$	7.16454e72	0.100946	0.0504730	−	0.998725i	$-0.483927\pi$
$29$	7.16454e72	0.100946	0.0504730	+	0.998725i	$0.483927\pi$
$30$	0	0
$31$	1.90510e75	0.925024	0.462512	−	0.886613i	$-0.346948\pi$
$31$	1.90510e75	0.925024	0.462512	+	0.886613i	$0.346948\pi$
$32$	4.78240e75	0.467274
$33$	0	0
$34$	−4.10469e76	−0.187757
$35$	−3.24850e77	−0.343753
$36$	0	0
$37$	−1.10721e79	−0.708017	−0.354009	−	0.935242i	$-0.615182\pi$
$37$	−1.10721e79	−0.708017	−0.354009	+	0.935242i	$0.615182\pi$
$38$	4.16190e78	0.0692182
$39$	0	0
$40$	1.49321e80	0.186248
$41$	1.87777e81	0.673064	0.336532	−	0.941672i	$-0.390746\pi$
$41$	1.87777e81	0.673064	0.336532	+	0.941672i	$0.390746\pi$
$42$	0	0
$43$	9.41841e81	0.304664	0.152332	−	0.988329i	$-0.451322\pi$
$43$	9.41841e81	0.304664	0.152332	+	0.988329i	$0.451322\pi$
$44$	−2.45875e82	−0.249088
$45$	0	0
$46$	−1.96687e83	−0.211108
$47$	−3.14875e84	−1.14077	−0.570383	−	0.821379i	$-0.693205\pi$
$47$	−3.14875e84	−1.14077	−0.570383	+	0.821379i	$0.693205\pi$
$48$	0	0
$49$	−1.48202e85	−0.654564
$50$	−6.66570e84	−0.106135
$51$	0	0
$52$	3.56447e86	0.783115
$53$	4.00521e86	0.336275	0.168137	−	0.985764i	$-0.446225\pi$
$53$	4.00521e86	0.336275	0.168137	+	0.985764i	$0.446225\pi$
$54$	0	0
$55$	−1.15660e87	−0.149578
$56$	−3.59507e87	−0.187160
$57$	0	0
$58$	1.84030e87	0.0162846
$59$	2.34450e89	0.875031	0.437516	−	0.899211i	$-0.355858\pi$
$59$	2.34450e89	0.875031	0.437516	+	0.899211i	$0.355858\pi$
$60$	0	0
$61$	−4.02186e89	−0.278785	−0.139393	−	0.990237i	$-0.544515\pi$
$61$	−4.02186e89	−0.278785	−0.139393	+	0.990237i	$0.544515\pi$
$62$	4.89350e89	0.149224
$63$	0	0
$64$	−1.38066e91	−0.847225
$65$	1.67674e91	0.470262
$66$	0	0
$67$	−3.05726e92	−1.85590	−0.927951	−	0.372702i	$-0.878432\pi$
$67$	−3.05726e92	−1.85590	−0.927951	+	0.372702i	$0.878432\pi$
$68$	3.94600e92	1.13359
$69$	0	0
$70$	−8.34418e91	−0.0554540
$71$	5.37677e93	1.74572	0.872861	−	0.487968i	$-0.162262\pi$
$71$	5.37677e93	1.74572	0.872861	+	0.487968i	$0.162262\pi$
$72$	0	0
$73$	−2.11035e94	−1.68480	−0.842402	−	0.538850i	$-0.818859\pi$
$73$	−2.11035e94	−1.68480	−0.842402	+	0.538850i	$0.818859\pi$
$74$	−2.84401e93	−0.114217
$75$	0	0
$76$	−4.00100e94	−0.417910
$77$	2.78465e94	0.150310
$78$	0	0
$79$	8.91772e95	1.31852	0.659259	−	0.751916i	$-0.270870\pi$
$79$	8.91772e95	1.31852	0.659259	+	0.751916i	$0.270870\pi$
$80$	−6.88848e95	−0.539608
$81$	0	0
$82$	4.82328e95	0.108578
$83$	−7.50442e96	−0.915954	−0.457977	−	0.888964i	$-0.651426\pi$
$83$	−7.50442e96	−0.915954	−0.457977	+	0.888964i	$0.651426\pi$
$84$	0	0
$85$	1.85621e97	0.680725
$86$	2.41924e96	0.0491481
$87$	0	0
$88$	−1.28000e97	−0.0814392
$89$	3.83813e98	1.38014	0.690072	−	0.723741i	$-0.257579\pi$
$89$	3.83813e98	1.38014	0.690072	+	0.723741i	$0.257579\pi$
$90$	0	0
$91$	−4.03693e98	−0.472565
$92$	1.89083e99	1.27458
$93$	0	0
$94$	−8.08797e98	−0.184028
$95$	−1.88208e99	−0.250956
$96$	0	0
$97$	1.03291e100	0.480937	0.240469	−	0.970657i	$-0.422699\pi$
$97$	1.03291e100	0.480937	0.240469	+	0.970657i	$0.422699\pi$
$98$	−3.80676e99	−0.105594
$99$	0	0
$100$	6.40800e100	0.640800
$101$	−2.39177e101	−1.44707	−0.723535	−	0.690288i	$-0.757484\pi$
$101$	−2.39177e101	−1.44707	−0.723535	+	0.690288i	$0.757484\pi$
$102$	0	0
$103$	−1.67545e101	−0.376575	−0.188288	−	0.982114i	$-0.560294\pi$
$103$	−1.67545e101	−0.376575	−0.188288	+	0.982114i	$0.560294\pi$
$104$	1.85562e101	0.256039
$105$	0	0
$106$	1.02879e101	0.0542476
$107$	9.91379e101	0.325356	0.162678	−	0.986679i	$-0.447987\pi$
$107$	9.91379e101	0.325356	0.162678	+	0.986679i	$0.447987\pi$
$108$	0	0
$109$	−1.40368e103	−1.80814	−0.904068	−	0.427390i	$-0.859433\pi$
$109$	−1.40368e103	−1.80814	−0.904068	+	0.427390i	$0.859433\pi$
$110$	−2.97088e101	−0.0241298
$111$	0	0
$112$	1.65848e103	0.542251
$113$	−1.51940e102	−0.0317110	−0.0158555	−	0.999874i	$-0.505047\pi$
$113$	−1.51940e102	−0.0317110	−0.0158555	+	0.999874i	$0.505047\pi$
$114$	0	0
$115$	8.89451e103	0.765387
$116$	−1.76916e103	−0.0983191
$117$	0	0
$118$	6.02215e103	0.141159
$119$	−4.46904e104	−0.684058
$120$	0	0
$121$	−1.41672e105	−0.934595
$122$	−1.03306e104	−0.0449734
$123$	0	0
$124$	−4.70432e105	−0.900952
$125$	7.59596e105	0.969676
$126$	0	0
$127$	−1.19794e106	−0.686034	−0.343017	−	0.939329i	$-0.611449\pi$
$127$	−1.19794e106	−0.686034	−0.343017	+	0.939329i	$0.611449\pi$
$128$	−1.56712e106	−0.603948
$129$	0	0
$130$	4.30691e105	0.0758623
$131$	−1.15584e107	−1.38261	−0.691304	−	0.722564i	$-0.742963\pi$
$131$	−1.15584e107	−1.38261	−0.691304	+	0.722564i	$0.742963\pi$
$132$	0	0
$133$	4.53133e106	0.252184
$134$	−7.85297e106	−0.299393
$135$	0	0
$136$	2.05424e107	0.370627
$137$	3.40012e107	0.423746	0.211873	−	0.977297i	$-0.432044\pi$
$137$	3.40012e107	0.423746	0.211873	+	0.977297i	$0.432044\pi$
$138$	0	0
$139$	−2.26071e108	−1.35518	−0.677592	−	0.735438i	$-0.736976\pi$
$139$	−2.26071e108	−1.35518	−0.677592	+	0.735438i	$0.736976\pi$
$140$	8.02159e107	0.334807
$141$	0	0
$142$	1.38109e108	0.281619
$143$	−1.43732e108	−0.205628
$144$	0	0
$145$	−8.32217e107	−0.0590408
$146$	−5.42069e108	−0.271791
$147$	0	0
$148$	2.73406e109	0.689592
$149$	−8.38640e109	−1.50546	−0.752730	−	0.658330i	$-0.771263\pi$
$149$	−8.38640e109	−1.50546	−0.752730	+	0.658330i	$0.771263\pi$
$150$	0	0
$151$	−9.80255e108	−0.0897436	−0.0448718	−	0.998993i	$-0.514288\pi$
$151$	−9.80255e108	−0.0897436	−0.0448718	+	0.998993i	$0.514288\pi$
$152$	−2.08288e109	−0.136635
$153$	0	0
$154$	7.15273e108	0.0242480
$155$	−2.21292e110	−0.541023
$156$	0	0
$157$	−1.27999e111	−1.63785	−0.818923	−	0.573903i	$-0.805429\pi$
$157$	−1.27999e111	−1.63785	−0.818923	+	0.573903i	$0.805429\pi$
$158$	2.29063e110	0.212702
$159$	0	0
$160$	−5.55513e110	−0.273297
$161$	−2.14146e111	−0.769135
$162$	0	0
$163$	1.59995e111	0.308058	0.154029	−	0.988066i	$-0.450775\pi$
$163$	1.59995e111	0.308058	0.154029	+	0.988066i	$0.450775\pi$
$164$	−4.63681e111	−0.655548
$165$	0	0
$166$	−1.92761e111	−0.147761
$167$	−2.33044e112	−1.31904	−0.659518	−	0.751689i	$-0.729239\pi$
$167$	−2.33044e112	−1.31904	−0.659518	+	0.751689i	$0.729239\pi$
$168$	0	0
$169$	−1.13945e112	−0.353521
$170$	4.76791e111	0.109814
$171$	0	0
$172$	−2.32571e112	−0.296735
$173$	8.33103e112	0.793178	0.396589	−	0.917996i	$-0.370194\pi$
$173$	8.33103e112	0.793178	0.396589	+	0.917996i	$0.370194\pi$
$174$	0	0
$175$	−7.25738e112	−0.386686
$176$	5.90488e112	0.235951
$177$	0	0
$178$	9.85873e112	0.222644
$179$	3.61084e113	0.614512	0.307256	−	0.951627i	$-0.400589\pi$
$179$	3.61084e113	0.614512	0.307256	+	0.951627i	$0.400589\pi$
$180$	0	0
$181$	1.67890e114	1.63026	0.815132	−	0.579275i	$-0.196664\pi$
$181$	1.67890e114	1.63026	0.815132	+	0.579275i	$0.196664\pi$
$182$	−1.03694e113	−0.0762338
$183$	0	0
$184$	9.84344e113	0.416722
$185$	1.28611e114	0.414101
$186$	0	0
$187$	−1.59117e114	−0.297656
$188$	7.77529e114	1.11108
$189$	0	0
$190$	−4.83437e113	−0.0404840
$191$	2.24809e114	0.144421	0.0722103	−	0.997389i	$-0.476995\pi$
$191$	2.24809e114	0.144421	0.0722103	+	0.997389i	$0.476995\pi$
$192$	0	0
$193$	−3.98577e115	−1.51310	−0.756551	−	0.653934i	$-0.773117\pi$
$193$	−3.98577e115	−1.51310	−0.756551	+	0.653934i	$0.773117\pi$
$194$	2.65315e114	0.0775844
$195$	0	0
$196$	3.65959e115	0.637529
$197$	−9.87434e115	−1.33034	−0.665171	−	0.746691i	$-0.731642\pi$
$197$	−9.87434e115	−1.33034	−0.665171	+	0.746691i	$0.731642\pi$
$198$	0	0
$199$	4.01699e115	0.324953	0.162476	−	0.986712i	$-0.448052\pi$
$199$	4.01699e115	0.324953	0.162476	+	0.986712i	$0.448052\pi$
$200$	3.33593e115	0.209509
$201$	0	0
$202$	−6.14356e115	−0.233440
$203$	2.00366e115	0.0593299
$204$	0	0
$205$	−2.18117e116	−0.393658
$206$	−4.30361e115	−0.0607489
$207$	0	0
$208$	−8.56035e116	−0.741811
$209$	1.61334e116	0.109734
$210$	0	0
$211$	4.53257e116	0.190581	0.0952907	−	0.995449i	$-0.469622\pi$
$211$	4.53257e116	0.190581	0.0952907	+	0.995449i	$0.469622\pi$
$212$	−9.89016e116	−0.327523
$213$	0	0
$214$	2.54648e116	0.0524862
$215$	−1.09402e117	−0.178190
$216$	0	0
$217$	5.32787e117	0.543672
$218$	−3.60554e117	−0.291687
$219$	0	0
$220$	2.85602e117	0.145685
$221$	2.30673e118	0.935807
$222$	0	0
$223$	−3.52241e118	−0.906660	−0.453330	−	0.891343i	$-0.649764\pi$
$223$	−3.52241e118	−0.906660	−0.453330	+	0.891343i	$0.649764\pi$
$224$	1.33746e118	0.274635
$225$	0	0
$226$	−3.90276e116	−0.00511559
$227$	1.25414e119	1.31535	0.657674	−	0.753302i	$-0.271540\pi$
$227$	1.25414e119	1.31535	0.657674	+	0.753302i	$0.271540\pi$
$228$	0	0
$229$	5.60999e118	0.377807	0.188904	−	0.981996i	$-0.439507\pi$
$229$	5.60999e118	0.377807	0.188904	+	0.981996i	$0.439507\pi$
$230$	2.28467e118	0.123472
$231$	0	0
$232$	−9.21003e117	−0.0321453
$233$	−4.54576e119	−1.27683	−0.638415	−	0.769693i	$-0.720409\pi$
$233$	−4.54576e119	−1.27683	−0.638415	+	0.769693i	$0.720409\pi$
$234$	0	0
$235$	3.65752e119	0.667205
$236$	−5.78933e119	−0.852260
$237$	0	0
$238$	−1.14793e119	−0.110352
$239$	1.02709e120	0.798939	0.399469	−	0.916747i	$-0.369194\pi$
$239$	1.02709e120	0.798939	0.399469	+	0.916747i	$0.369194\pi$
$240$	0	0
$241$	−8.90997e119	−0.455005	−0.227502	−	0.973778i	$-0.573056\pi$
$241$	−8.90997e119	−0.455005	−0.227502	+	0.973778i	$0.573056\pi$
$242$	−3.63903e119	−0.150768
$243$	0	0
$244$	9.93126e119	0.271530
$245$	1.72148e120	0.382838
$246$	0	0
$247$	−2.33888e120	−0.344994
$248$	−2.44901e120	−0.294565
$249$	0	0
$250$	1.95112e120	0.156427
$251$	−2.54170e121	−1.66572	−0.832860	−	0.553484i	$-0.813298\pi$
$251$	−2.54170e121	−1.66572	−0.832860	+	0.553484i	$0.813298\pi$
$252$	0	0
$253$	−7.62448e120	−0.334675
$254$	−3.07705e120	−0.110671
$255$	0	0
$256$	3.09786e121	0.749797
$257$	6.07536e121	1.20767	0.603836	−	0.797108i	$-0.293638\pi$
$257$	6.07536e121	1.20767	0.603836	+	0.797108i	$0.293638\pi$
$258$	0	0
$259$	−3.09646e121	−0.416129
$260$	−4.14040e121	−0.458024
$261$	0	0
$262$	−2.96893e121	−0.223041
$263$	2.58199e122	1.60026	0.800128	−	0.599829i	$-0.204765\pi$
$263$	2.58199e122	1.60026	0.800128	+	0.599829i	$0.204765\pi$
$264$	0	0
$265$	−4.65236e121	−0.196678
$266$	1.16393e121	0.0406822
$267$	0	0
$268$	7.54937e122	1.80760
$269$	2.19706e122	0.435865	0.217932	−	0.975964i	$-0.430069\pi$
$269$	2.19706e122	0.435865	0.217932	+	0.975964i	$0.430069\pi$
$270$	0	0
$271$	−2.27556e122	−0.310555	−0.155278	−	0.987871i	$-0.549627\pi$
$271$	−2.27556e122	−0.310555	−0.155278	+	0.987871i	$0.549627\pi$
$272$	−9.47664e122	−1.07380
$273$	0	0
$274$	8.73363e121	0.0683583
$275$	−2.58393e122	−0.168259
$276$	0	0
$277$	−2.83013e123	−1.27814	−0.639070	−	0.769148i	$-0.720681\pi$
$277$	−2.83013e123	−1.27814	−0.639070	+	0.769148i	$0.720681\pi$
$278$	−5.80693e122	−0.218617
$279$	0	0
$280$	4.17595e122	0.109465
$281$	5.27048e123	1.15393	0.576967	−	0.816768i	$-0.304236\pi$
$281$	5.27048e123	1.15393	0.576967	+	0.816768i	$0.304236\pi$
$282$	0	0
$283$	−4.08346e123	−0.624904	−0.312452	−	0.949934i	$-0.601150\pi$
$283$	−4.08346e123	−0.624904	−0.312452	+	0.949934i	$0.601150\pi$
$284$	−1.32770e124	−1.70029
$285$	0	0
$286$	−3.69193e122	−0.0331718
$287$	5.25141e123	0.395586
$288$	0	0
$289$	6.68506e123	0.354621
$290$	−2.13765e122	−0.00952442
$291$	0	0
$292$	5.21112e124	1.64096
$293$	6.02275e123	0.159580	0.0797902	−	0.996812i	$-0.474575\pi$
$293$	6.02275e123	0.159580	0.0797902	+	0.996812i	$0.474575\pi$
$294$	0	0
$295$	−2.72332e124	−0.511784
$296$	1.42332e124	0.225461
$297$	0	0
$298$	−2.15415e124	−0.242860
$299$	1.10533e125	1.05219
$300$	0	0
$301$	2.63398e124	0.179062
$302$	−2.51791e123	−0.0144774
$303$	0	0
$304$	9.60873e124	0.395868
$305$	4.67169e124	0.163054
$306$	0	0
$307$	2.01247e125	0.504943	0.252471	−	0.967604i	$-0.418757\pi$
$307$	2.01247e125	0.504943	0.252471	+	0.967604i	$0.418757\pi$
$308$	−6.87620e124	−0.146399
$309$	0	0
$310$	−5.68418e124	−0.0872775
$311$	−9.00803e125	−1.17552	−0.587760	−	0.809035i	$-0.699990\pi$
$311$	−9.00803e125	−1.17552	−0.587760	+	0.809035i	$0.699990\pi$
$312$	0	0
$313$	4.50650e125	0.425452	0.212726	−	0.977112i	$-0.431766\pi$
$313$	4.50650e125	0.425452	0.212726	+	0.977112i	$0.431766\pi$
$314$	−3.28781e125	−0.264216
$315$	0	0
$316$	−2.20207e126	−1.28420
$317$	1.39121e126	0.691671	0.345835	−	0.938295i	$-0.387596\pi$
$317$	1.39121e126	0.691671	0.345835	+	0.938295i	$0.387596\pi$
$318$	0	0
$319$	7.13386e124	0.0258163
$320$	1.60375e126	0.495520
$321$	0	0
$322$	−5.50060e125	−0.124076
$323$	−2.58923e126	−0.499394
$324$	0	0
$325$	3.74594e126	0.528995
$326$	4.10968e125	0.0496957
$327$	0	0
$328$	−2.41387e126	−0.214331
$329$	−8.80590e126	−0.670472
$330$	0	0
$331$	2.75350e127	1.54373	0.771864	−	0.635788i	$-0.219325\pi$
$331$	2.75350e127	1.54373	0.771864	+	0.635788i	$0.219325\pi$
$332$	1.85308e127	0.892117
$333$	0	0
$334$	−5.98604e126	−0.212786
$335$	3.55124e127	1.08547
$336$	0	0
$337$	7.77367e126	0.175920	0.0879602	−	0.996124i	$-0.471965\pi$
$337$	7.77367e126	0.175920	0.0879602	+	0.996124i	$0.471965\pi$
$338$	−2.92681e126	−0.0570297
$339$	0	0
$340$	−4.58358e127	−0.663010
$341$	1.89694e127	0.236569
$342$	0	0
$343$	−1.04766e128	−0.972450
$344$	−1.21074e127	−0.0970172
$345$	0	0
$346$	2.13993e127	0.127955
$347$	−2.37286e128	−1.22640	−0.613202	−	0.789926i	$-0.710119\pi$
$347$	−2.37286e128	−1.22640	−0.613202	+	0.789926i	$0.710119\pi$
$348$	0	0
$349$	3.72904e128	1.44183	0.720913	−	0.693026i	$-0.243723\pi$
$349$	3.72904e128	1.44183	0.720913	+	0.693026i	$0.243723\pi$
$350$	−1.86415e127	−0.0623799
$351$	0	0
$352$	4.76192e127	0.119503
$353$	−7.61652e126	−0.0165628	−0.00828140	−	0.999966i	$-0.502636\pi$
$353$	−7.61652e126	−0.0165628	−0.00828140	+	0.999966i	$0.502636\pi$
$354$	0	0
$355$	−6.24554e128	−1.02103
$356$	−9.47758e128	−1.34423
$357$	0	0
$358$	9.27491e127	0.0991327
$359$	1.27355e129	1.18235	0.591175	−	0.806543i	$-0.298664\pi$
$359$	1.27355e129	1.18235	0.591175	+	0.806543i	$0.298664\pi$
$360$	0	0
$361$	−1.16345e129	−0.815894
$362$	4.31248e128	0.262993
$363$	0	0
$364$	9.96849e128	0.460267
$365$	2.45133e129	0.985398
$366$	0	0
$367$	1.66816e129	0.508863	0.254431	−	0.967091i	$-0.418112\pi$
$367$	1.66816e129	0.508863	0.254431	+	0.967091i	$0.418112\pi$
$368$	−4.54098e129	−1.20735
$369$	0	0
$370$	3.30354e128	0.0668025
$371$	1.12011e129	0.197641
$372$	0	0
$373$	−3.54244e129	−0.476438	−0.238219	−	0.971211i	$-0.576564\pi$
$373$	−3.54244e129	−0.476438	−0.238219	+	0.971211i	$0.576564\pi$
$374$	−4.08711e128	−0.0480176
$375$	0	0
$376$	4.04773e129	0.363266
$377$	−1.03420e129	−0.0811646
$378$	0	0
$379$	−1.58386e130	−0.951561	−0.475781	−	0.879564i	$-0.657834\pi$
$379$	−1.58386e130	−0.951561	−0.475781	+	0.879564i	$0.657834\pi$
$380$	4.64747e129	0.244425
$381$	0	0
$382$	5.77451e128	0.0232978
$383$	3.23739e130	1.14461	0.572305	−	0.820041i	$-0.306049\pi$
$383$	3.23739e130	1.14461	0.572305	+	0.820041i	$0.306049\pi$
$384$	0	0
$385$	−3.23459e129	−0.0879128
$386$	−1.02380e130	−0.244093
$387$	0	0
$388$	−2.55058e130	−0.468421
$389$	−8.82272e130	−1.42281	−0.711406	−	0.702781i	$-0.751941\pi$
$389$	−8.82272e130	−1.42281	−0.711406	+	0.702781i	$0.751941\pi$
$390$	0	0
$391$	1.22364e131	1.52310
$392$	1.90514e130	0.208440
$393$	0	0
$394$	−2.53635e130	−0.214610
$395$	−1.03586e131	−0.771167
$396$	0	0
$397$	5.46354e130	0.315176	0.157588	−	0.987505i	$-0.449628\pi$
$397$	5.46354e130	0.315176	0.157588	+	0.987505i	$0.449628\pi$
$398$	1.03181e130	0.0524211
$399$	0	0
$400$	−1.53893e131	−0.607002
$401$	−1.18778e130	−0.0412996	−0.0206498	−	0.999787i	$-0.506574\pi$
$401$	−1.18778e130	−0.0412996	−0.0206498	+	0.999787i	$0.506574\pi$
$402$	0	0
$403$	−2.75002e131	−0.743756
$404$	5.90604e131	1.40941
$405$	0	0
$406$	5.14665e129	0.00957105
$407$	−1.10247e131	−0.181071
$408$	0	0
$409$	6.47684e131	0.830493	0.415247	−	0.909709i	$-0.363695\pi$
$409$	6.47684e131	0.830493	0.415247	+	0.909709i	$0.363695\pi$
$410$	−5.60261e130	−0.0635046
$411$	0	0
$412$	4.13723e131	0.366775
$413$	6.55670e131	0.514289
$414$	0	0
$415$	8.71696e131	0.535718
$416$	−6.90339e131	−0.375707
$417$	0	0
$418$	4.14408e130	0.0177021
$419$	−3.66872e131	−0.138901	−0.0694507	−	0.997585i	$-0.522125\pi$
$419$	−3.66872e131	−0.138901	−0.0694507	+	0.997585i	$0.522125\pi$
$420$	0	0
$421$	−1.22752e132	−0.365412	−0.182706	−	0.983168i	$-0.558486\pi$
$421$	−1.22752e132	−0.365412	−0.182706	+	0.983168i	$0.558486\pi$
$422$	1.16425e131	0.0307445
$423$	0	0
$424$	−5.14871e131	−0.107083
$425$	4.14691e132	0.765743
$426$	0	0
$427$	−1.12476e132	−0.163853
$428$	−2.44803e132	−0.316889
$429$	0	0
$430$	−2.81013e131	−0.0287455
$431$	−1.06447e133	−0.968344	−0.484172	−	0.874973i	$-0.660879\pi$
$431$	−1.06447e133	−0.968344	−0.484172	+	0.874973i	$0.660879\pi$
$432$	0	0
$433$	−2.64916e133	−1.90752	−0.953762	−	0.300564i	$-0.902825\pi$
$433$	−2.64916e133	−1.90752	−0.953762	+	0.300564i	$0.902825\pi$
$434$	1.36853e132	0.0877048
$435$	0	0
$436$	3.46615e133	1.76108
$437$	−1.24070e133	−0.561504
$438$	0	0
$439$	1.51769e133	0.545411	0.272706	−	0.962098i	$-0.412081\pi$
$439$	1.51769e133	0.545411	0.272706	+	0.962098i	$0.412081\pi$
$440$	1.48681e132	0.0476317
$441$	0	0
$442$	5.92512e132	0.150964
$443$	5.30570e133	1.20602	0.603010	−	0.797733i	$-0.293968\pi$
$443$	5.30570e133	1.20602	0.603010	+	0.797733i	$0.293968\pi$
$444$	0	0
$445$	−4.45828e133	−0.807211
$446$	−9.04776e132	−0.146262
$447$	0	0
$448$	−3.86120e133	−0.497947
$449$	−5.37070e131	−0.00618857	−0.00309429	−	0.999995i	$-0.500985\pi$
$449$	−5.37070e131	−0.00618857	−0.00309429	+	0.999995i	$0.500985\pi$
$450$	0	0
$451$	1.86972e133	0.172132
$452$	3.75188e132	0.0308857
$453$	0	0
$454$	3.22142e133	0.212191
$455$	4.68921e133	0.276391
$456$	0	0
$457$	2.17557e134	1.02755	0.513777	−	0.857924i	$-0.328246\pi$
$457$	2.17557e134	1.02755	0.513777	+	0.857924i	$0.328246\pi$
$458$	1.44100e133	0.0609476
$459$	0	0
$460$	−2.19634e134	−0.745469
$461$	−3.26419e134	−0.992838	−0.496419	−	0.868083i	$-0.665352\pi$
$461$	−3.26419e134	−0.992838	−0.496419	+	0.868083i	$0.665352\pi$
$462$	0	0
$463$	2.23237e134	0.545664	0.272832	−	0.962062i	$-0.412040\pi$
$463$	2.23237e134	0.545664	0.272832	+	0.962062i	$0.412040\pi$
$464$	4.24877e133	0.0931334
$465$	0	0
$466$	−1.16764e134	−0.205977
$467$	−1.51582e134	−0.239963	−0.119982	−	0.992776i	$-0.538284\pi$
$467$	−1.51582e134	−0.239963	−0.119982	+	0.992776i	$0.538284\pi$
$468$	0	0
$469$	−8.55003e134	−1.09078
$470$	9.39480e133	0.107633
$471$	0	0
$472$	−3.01386e134	−0.278645
$473$	9.37807e133	0.0779158
$474$	0	0
$475$	−4.20471e134	−0.282298
$476$	1.10355e135	0.666256
$477$	0	0
$478$	2.63820e134	0.128884
$479$	−1.07969e135	−0.474632	−0.237316	−	0.971432i	$-0.576268\pi$
$479$	−1.07969e135	−0.474632	−0.237316	+	0.971432i	$0.576268\pi$
$480$	0	0
$481$	1.59826e135	0.569273
$482$	−2.28864e134	−0.0734010
$483$	0	0
$484$	3.49834e135	0.910273
$485$	−1.19980e135	−0.281288
$486$	0	0
$487$	1.89475e135	0.360861	0.180430	−	0.983588i	$-0.442251\pi$
$487$	1.89475e135	0.360861	0.180430	+	0.983588i	$0.442251\pi$
$488$	5.17010e134	0.0887765
$489$	0	0
$490$	4.42184e134	0.0617591
$491$	1.35592e136	1.70851	0.854257	−	0.519852i	$-0.174013\pi$
$491$	1.35592e136	1.70851	0.854257	+	0.519852i	$0.174013\pi$
$492$	0	0
$493$	−1.14490e135	−0.117489
$494$	−6.00770e134	−0.0556541
$495$	0	0
$496$	1.12978e136	0.853433
$497$	1.50368e136	1.02603
$498$	0	0
$499$	−3.19004e136	−1.77713	−0.888563	−	0.458755i	$-0.848295\pi$
$499$	−3.19004e136	−1.77713	−0.888563	+	0.458755i	$0.848295\pi$
$500$	−1.87569e136	−0.944441
$501$	0	0
$502$	−6.52869e135	−0.268713
$503$	−4.79960e136	−1.78658	−0.893288	−	0.449485i	$-0.851608\pi$
$503$	−4.79960e136	−1.78658	−0.893288	+	0.449485i	$0.851608\pi$
$504$	0	0
$505$	2.77822e136	0.846354
$506$	−1.95844e135	−0.0539896
$507$	0	0
$508$	2.95809e136	0.668181
$509$	−1.97121e136	−0.403167	−0.201583	−	0.979471i	$-0.564609\pi$
$509$	−1.97121e136	−0.403167	−0.201583	+	0.979471i	$0.564609\pi$
$510$	0	0
$511$	−5.90185e136	−0.990223
$512$	4.76885e136	0.724905
$513$	0	0
$514$	1.56053e136	0.194821
$515$	1.94616e136	0.220249
$516$	0	0
$517$	−3.13527e136	−0.291744
$518$	−7.95366e135	−0.0671296
$519$	0	0
$520$	−2.15545e136	−0.149750
$521$	1.89189e137	1.19286	0.596430	−	0.802665i	$-0.296585\pi$
$521$	1.89189e137	1.19286	0.596430	+	0.802665i	$0.296585\pi$
$522$	0	0
$523$	6.85650e136	0.356260	0.178130	−	0.984007i	$-0.442995\pi$
$523$	6.85650e136	0.356260	0.178130	+	0.984007i	$0.442995\pi$
$524$	2.85415e137	1.34663
$525$	0	0
$526$	6.63217e136	0.258152
$527$	−3.04438e137	−1.07662
$528$	0	0
$529$	2.43956e137	0.712525
$530$	−1.19502e136	−0.0317280
$531$	0	0
$532$	−1.11893e137	−0.245621
$533$	−2.71055e137	−0.541170
$534$	0	0
$535$	−1.15156e137	−0.190293
$536$	3.93011e137	0.590994
$537$	0	0
$538$	5.64342e136	0.0703134
$539$	−1.47567e137	−0.167401
$540$	0	0
$541$	−1.17231e137	−0.110301	−0.0551506	−	0.998478i	$-0.517564\pi$
$541$	−1.17231e137	−0.110301	−0.0551506	+	0.998478i	$0.517564\pi$
$542$	−5.84506e136	−0.0500986
$543$	0	0
$544$	−7.64232e137	−0.543852
$545$	1.63049e138	1.05753
$546$	0	0
$547$	−1.71733e136	−0.00925751	−0.00462875	−	0.999989i	$-0.501473\pi$
$547$	−1.71733e136	−0.00925751	−0.00462875	+	0.999989i	$0.501473\pi$
$548$	−8.39599e137	−0.412718
$549$	0	0
$550$	−6.63715e136	−0.0271435
$551$	1.16086e137	0.0433135
$552$	0	0
$553$	2.49396e138	0.774943
$554$	−7.26956e137	−0.206189
$555$	0	0
$556$	5.58243e138	1.31992
$557$	1.70337e138	0.367808	0.183904	−	0.982944i	$-0.441126\pi$
$557$	1.70337e138	0.367808	0.183904	+	0.982944i	$0.441126\pi$
$558$	0	0
$559$	−1.35955e138	−0.244961
$560$	−1.92645e138	−0.317149
$561$	0	0
$562$	1.35379e138	0.186152
$563$	1.19099e139	1.49705	0.748523	−	0.663109i	$-0.230763\pi$
$563$	1.19099e139	1.49705	0.748523	+	0.663109i	$0.230763\pi$
$564$	0	0
$565$	1.76489e137	0.0185469
$566$	−1.04889e138	−0.100809
$567$	0	0
$568$	−6.91185e138	−0.555909
$569$	2.22588e139	1.63807	0.819034	−	0.573745i	$-0.194510\pi$
$569$	2.22588e139	1.63807	0.819034	+	0.573745i	$0.194510\pi$
$570$	0	0
$571$	7.96541e138	0.491004	0.245502	−	0.969396i	$-0.421047\pi$
$571$	7.96541e138	0.491004	0.245502	+	0.969396i	$0.421047\pi$
$572$	3.54920e138	0.200277
$573$	0	0
$574$	1.34889e138	0.0638156
$575$	1.98710e139	0.860979
$576$	0	0
$577$	2.07485e139	0.754411	0.377205	−	0.926130i	$-0.376885\pi$
$577$	2.07485e139	0.754411	0.377205	+	0.926130i	$0.376885\pi$
$578$	1.71714e138	0.0572072
$579$	0	0
$580$	2.05501e138	0.0575043
$581$	−2.09871e139	−0.538341
$582$	0	0
$583$	3.98806e138	0.0860002
$584$	2.71285e139	0.536509
$585$	0	0
$586$	1.54702e138	0.0257434
$587$	−2.85396e139	−0.435736	−0.217868	−	0.975978i	$-0.569910\pi$
$587$	−2.85396e139	−0.435736	−0.217868	+	0.975978i	$0.569910\pi$
$588$	0	0
$589$	3.08681e139	0.396906
$590$	−6.99519e138	−0.0825606
$591$	0	0
$592$	−6.56608e139	−0.653220
$593$	1.04560e140	0.955220	0.477610	−	0.878572i	$-0.341503\pi$
$593$	1.04560e140	0.955220	0.477610	+	0.878572i	$0.341503\pi$
$594$	0	0
$595$	5.19113e139	0.400088
$596$	2.07087e140	1.46628
$597$	0	0
$598$	2.83917e139	0.169739
$599$	1.21440e140	0.667277	0.333639	−	0.942701i	$-0.391723\pi$
$599$	1.21440e140	0.667277	0.333639	+	0.942701i	$0.391723\pi$
$600$	0	0
$601$	2.46874e140	1.14634	0.573171	−	0.819436i	$-0.305713\pi$
$601$	2.46874e140	1.14634	0.573171	+	0.819436i	$0.305713\pi$
$602$	6.76571e138	0.0288862
$603$	0	0
$604$	2.42057e139	0.0874081
$605$	1.64563e140	0.546621
$606$	0	0
$607$	1.09575e140	0.308093	0.154046	−	0.988064i	$-0.450770\pi$
$607$	1.09575e140	0.308093	0.154046	+	0.988064i	$0.450770\pi$
$608$	7.74884e139	0.200496
$609$	0	0
$610$	1.19998e139	0.0263038
$611$	4.54522e140	0.917221
$612$	0	0
$613$	7.23778e140	1.23837	0.619186	−	0.785244i	$-0.287463\pi$
$613$	7.23778e140	1.23837	0.619186	+	0.785244i	$0.287463\pi$
$614$	5.16929e139	0.0814570
$615$	0	0
$616$	−3.57967e139	−0.0478649
$617$	1.53781e141	1.89453	0.947265	−	0.320452i	$-0.103835\pi$
$617$	1.53781e141	1.89453	0.947265	+	0.320452i	$0.103835\pi$
$618$	0	0
$619$	−6.21672e140	−0.650404	−0.325202	−	0.945644i	$-0.605432\pi$
$619$	−6.21672e140	−0.650404	−0.325202	+	0.945644i	$0.605432\pi$
$620$	5.46443e140	0.526944
$621$	0	0
$622$	−2.31383e140	−0.189634
$623$	1.07338e141	0.811164
$624$	0	0
$625$	1.41236e140	0.0907829
$626$	1.15755e140	0.0686336
$627$	0	0
$628$	3.16070e141	1.59522
$629$	1.76934e141	0.824048
$630$	0	0
$631$	1.33263e141	0.528721	0.264360	−	0.964424i	$-0.414839\pi$
$631$	1.33263e141	0.528721	0.264360	+	0.964424i	$0.414839\pi$
$632$	−1.14637e141	−0.419869
$633$	0	0
$634$	3.57349e140	0.111580
$635$	1.39150e141	0.401244
$636$	0	0
$637$	2.13929e141	0.526295
$638$	1.83242e139	0.00416467
$639$	0	0
$640$	1.82033e141	0.353234
$641$	1.00041e142	1.79410	0.897049	−	0.441931i	$-0.145706\pi$
$641$	1.00041e142	1.79410	0.897049	+	0.441931i	$0.145706\pi$
$642$	0	0
$643$	6.42814e140	0.0984989	0.0492494	−	0.998787i	$-0.484317\pi$
$643$	6.42814e140	0.0984989	0.0492494	+	0.998787i	$0.484317\pi$
$644$	5.28795e141	0.749119
$645$	0	0
$646$	−6.65076e140	−0.0805618
$647$	1.06846e142	1.19699	0.598496	−	0.801126i	$-0.295765\pi$
$647$	1.06846e142	1.19699	0.598496	+	0.801126i	$0.295765\pi$
$648$	0	0
$649$	2.33446e141	0.223784
$650$	9.62193e140	0.0853371
$651$	0	0
$652$	−3.95080e141	−0.300041
$653$	8.23618e140	0.0578909	0.0289454	−	0.999581i	$-0.490785\pi$
$653$	8.23618e140	0.0578909	0.0289454	+	0.999581i	$0.490785\pi$
$654$	0	0
$655$	1.34260e142	0.808652
$656$	1.11357e142	0.620973
$657$	0	0
$658$	−2.26191e141	−0.108160
$659$	1.12345e142	0.497556	0.248778	−	0.968561i	$-0.419971\pi$
$659$	1.12345e142	0.497556	0.248778	+	0.968561i	$0.419971\pi$
$660$	0	0
$661$	4.11483e142	1.56379	0.781895	−	0.623410i	$-0.214253\pi$
$661$	4.11483e142	1.56379	0.781895	+	0.623410i	$0.214253\pi$
$662$	7.07271e141	0.249033
$663$	0	0
$664$	9.64694e141	0.291677
$665$	−5.26349e141	−0.147496
$666$	0	0
$667$	−5.48609e141	−0.132102
$668$	5.75461e142	1.28471
$669$	0	0
$670$	9.12182e141	0.175107
$671$	−4.00463e141	−0.0712976
$672$	0	0
$673$	−1.14033e143	−1.74691	−0.873456	−	0.486902i	$-0.838127\pi$
$673$	−1.14033e143	−1.74691	−0.873456	+	0.486902i	$0.838127\pi$
$674$	1.99677e141	0.0283793
$675$	0	0
$676$	2.81366e142	0.344321
$677$	1.56671e142	0.177935	0.0889673	−	0.996035i	$-0.471643\pi$
$677$	1.56671e142	0.177935	0.0889673	+	0.996035i	$0.471643\pi$
$678$	0	0
$679$	2.88866e142	0.282665
$680$	−2.38616e142	−0.216770
$681$	0	0
$682$	4.87254e141	0.0381632
$683$	2.23192e142	0.162343	0.0811714	−	0.996700i	$-0.474134\pi$
$683$	2.23192e142	0.162343	0.0811714	+	0.996700i	$0.474134\pi$
$684$	0	0
$685$	−3.94950e142	−0.247838
$686$	−2.69105e142	−0.156875
$687$	0	0
$688$	5.58538e142	0.281084
$689$	−5.78152e142	−0.270378
$690$	0	0
$691$	2.36035e143	0.953530	0.476765	−	0.879031i	$-0.341809\pi$
$691$	2.36035e143	0.953530	0.476765	+	0.879031i	$0.341809\pi$
$692$	−2.05720e143	−0.772537
$693$	0	0
$694$	−6.09499e142	−0.197843
$695$	2.62599e143	0.792612
$696$	0	0
$697$	−3.00069e143	−0.783367
$698$	9.57851e142	0.232594
$699$	0	0
$700$	1.79208e143	0.376623
$701$	6.16772e143	1.20605	0.603025	−	0.797723i	$-0.293962\pi$
$701$	6.16772e143	1.20605	0.603025	+	0.797723i	$0.293962\pi$
$702$	0	0
$703$	−1.79400e143	−0.303793
$704$	−1.37475e143	−0.216673
$705$	0	0
$706$	−1.95640e141	−0.00267190
$707$	−6.68888e143	−0.850498
$708$	0	0
$709$	4.62173e143	0.509529	0.254765	−	0.967003i	$-0.418002\pi$
$709$	4.62173e143	0.509529	0.254765	+	0.967003i	$0.418002\pi$
$710$	−1.60425e143	−0.164712
$711$	0	0
$712$	−4.93392e143	−0.439494
$713$	−1.45879e144	−1.21052
$714$	0	0
$715$	1.66955e143	0.120267
$716$	−8.91634e143	−0.598520
$717$	0	0
$718$	3.27127e143	0.190736
$719$	−3.09556e144	−1.68241	−0.841203	−	0.540719i	$-0.818152\pi$
$719$	−3.09556e144	−1.68241	−0.841203	+	0.540719i	$0.818152\pi$
$720$	0	0
$721$	−4.68562e143	−0.221328
$722$	−2.98847e143	−0.131619
$723$	0	0
$724$	−4.14576e144	−1.58784
$725$	−1.85923e143	−0.0664146
$726$	0	0
$727$	−3.18407e144	−0.989681	−0.494840	−	0.868984i	$-0.664773\pi$
$727$	−3.18407e144	−0.989681	−0.494840	+	0.868984i	$0.664773\pi$
$728$	5.18948e143	0.150484
$729$	0	0
$730$	6.29655e143	0.158964
$731$	−1.50507e144	−0.354592
$732$	0	0
$733$	8.96985e143	0.184092	0.0920459	−	0.995755i	$-0.470659\pi$
$733$	8.96985e143	0.184092	0.0920459	+	0.995755i	$0.470659\pi$
$734$	4.28487e143	0.0820894
$735$	0	0
$736$	−3.66202e144	−0.611492
$737$	−3.04417e144	−0.474636
$738$	0	0
$739$	−1.38916e144	−0.188889	−0.0944445	−	0.995530i	$-0.530107\pi$
$739$	−1.38916e144	−0.188889	−0.0944445	+	0.995530i	$0.530107\pi$
$740$	−3.17582e144	−0.403325
$741$	0	0
$742$	2.87714e143	0.0318834
$743$	−1.30796e145	−1.35413	−0.677066	−	0.735923i	$-0.736749\pi$
$743$	−1.30796e145	−1.35413	−0.677066	+	0.735923i	$0.736749\pi$
$744$	0	0
$745$	9.74145e144	0.880505
$746$	−9.09921e143	−0.0768587
$747$	0	0
$748$	3.92910e144	0.289910
$749$	2.77252e144	0.191224
$750$	0	0
$751$	−1.15451e145	−0.695954	−0.347977	−	0.937503i	$-0.613131\pi$
$751$	−1.15451e145	−0.695954	−0.347977	+	0.937503i	$0.613131\pi$
$752$	−1.86730e145	−1.05248
$753$	0	0
$754$	−2.65648e143	−0.0130934
$755$	1.13864e144	0.0524887
$756$	0	0
$757$	−3.83259e145	−1.54579	−0.772896	−	0.634533i	$-0.781193\pi$
$757$	−3.83259e145	−1.54579	−0.772896	+	0.634533i	$0.781193\pi$
$758$	−4.06835e144	−0.153505
$759$	0	0
$760$	2.41942e144	0.0799144
$761$	−2.11377e145	−0.653329	−0.326665	−	0.945140i	$-0.605925\pi$
$761$	−2.11377e145	−0.653329	−0.326665	+	0.945140i	$0.605925\pi$
$762$	0	0
$763$	−3.92558e145	−1.06271
$764$	−5.55126e144	−0.140662
$765$	0	0
$766$	8.31566e144	0.184648
$767$	−3.38428e145	−0.703560
$768$	0	0
$769$	9.71643e144	0.177103	0.0885516	−	0.996072i	$-0.471776\pi$
$769$	9.71643e144	0.177103	0.0885516	+	0.996072i	$0.471776\pi$
$770$	−8.30845e143	−0.0141820
$771$	0	0
$772$	9.84216e145	1.47373
$773$	−5.12373e145	−0.718657	−0.359328	−	0.933211i	$-0.616994\pi$
$773$	−5.12373e145	−0.718657	−0.359328	+	0.933211i	$0.616994\pi$
$774$	0	0
$775$	−4.94383e145	−0.608594
$776$	−1.32780e145	−0.153150
$777$	0	0
$778$	−2.26623e145	−0.229527
$779$	3.04251e145	0.288796
$780$	0	0
$781$	5.35375e145	0.446458
$782$	3.14307e145	0.245705
$783$	0	0
$784$	−8.78879e145	−0.603904
$785$	1.48680e146	0.957935
$786$	0	0
$787$	1.01267e146	0.573778	0.286889	−	0.957964i	$-0.407379\pi$
$787$	1.01267e146	0.573778	0.286889	+	0.957964i	$0.407379\pi$
$788$	2.43829e146	1.29572
$789$	0	0
$790$	−2.66074e145	−0.124404
$791$	−4.24919e144	−0.0186377
$792$	0	0
$793$	5.80554e145	0.224154
$794$	1.40338e145	0.0508440
$795$	0	0
$796$	−9.91924e145	−0.316496
$797$	2.74405e146	0.821764	0.410882	−	0.911688i	$-0.365221\pi$
$797$	2.74405e146	0.821764	0.410882	+	0.911688i	$0.365221\pi$
$798$	0	0
$799$	5.03174e146	1.32772
$800$	−1.24105e146	−0.307430
$801$	0	0
$802$	−3.05097e144	−0.00666242
$803$	−2.10131e146	−0.430878
$804$	0	0
$805$	2.48747e146	0.449847
$806$	−7.06377e145	−0.119982
$807$	0	0
$808$	3.07462e146	0.460805
$809$	7.66386e146	1.07906	0.539532	−	0.841965i	$-0.318601\pi$
$809$	7.66386e146	1.07906	0.539532	+	0.841965i	$0.318601\pi$
$810$	0	0
$811$	−1.19038e147	−1.47956	−0.739781	−	0.672848i	$-0.765071\pi$
$811$	−1.19038e147	−1.47956	−0.739781	+	0.672848i	$0.765071\pi$
$812$	−4.94768e145	−0.0577859
$813$	0	0
$814$	−2.83183e145	−0.0292103
$815$	−1.85847e146	−0.180175
$816$	0	0
$817$	1.52605e146	0.130724
$818$	1.66366e146	0.133975
$819$	0	0
$820$	5.38601e146	0.383414
$821$	1.88359e147	1.26083	0.630414	−	0.776259i	$-0.282885\pi$
$821$	1.88359e147	1.26083	0.630414	+	0.776259i	$0.282885\pi$
$822$	0	0
$823$	−4.64333e146	−0.274876	−0.137438	−	0.990510i	$-0.543887\pi$
$823$	−4.64333e146	−0.274876	−0.137438	+	0.990510i	$0.543887\pi$
$824$	2.15379e146	0.119917
$825$	0	0
$826$	1.68417e146	0.0829648
$827$	2.44457e147	1.13285	0.566427	−	0.824112i	$-0.308325\pi$
$827$	2.44457e147	1.13285	0.566427	+	0.824112i	$0.308325\pi$
$828$	0	0
$829$	4.20030e147	1.72297	0.861483	−	0.507786i	$-0.169536\pi$
$829$	4.20030e147	1.72297	0.861483	+	0.507786i	$0.169536\pi$
$830$	2.23906e146	0.0864216
$831$	0	0
$832$	1.99299e147	0.681202
$833$	2.36828e147	0.761835
$834$	0	0
$835$	2.70699e147	0.771470
$836$	−3.98387e146	−0.106878
$837$	0	0
$838$	−9.42358e145	−0.0224075
$839$	4.27111e147	0.956228	0.478114	−	0.878298i	$-0.341321\pi$
$839$	4.27111e147	0.956228	0.478114	+	0.878298i	$0.341321\pi$
$840$	0	0
$841$	−4.98597e147	−0.989810
$842$	−3.15304e146	−0.0589480
$843$	0	0
$844$	−1.11924e147	−0.185622
$845$	1.32355e147	0.206765
$846$	0	0
$847$	−3.96205e147	−0.549297
$848$	2.37520e147	0.310249
$849$	0	0
$850$	1.06519e147	0.123529
$851$	8.47823e147	0.926536
$852$	0	0
$853$	1.65370e147	0.160521	0.0802604	−	0.996774i	$-0.474425\pi$
$853$	1.65370e147	0.160521	0.0802604	+	0.996774i	$0.474425\pi$
$854$	−2.88910e146	−0.0264326
$855$	0	0
$856$	−1.27442e147	−0.103607
$857$	−2.26666e148	−1.73722	−0.868610	−	0.495497i	$-0.834986\pi$
$857$	−2.26666e148	−1.73722	−0.868610	+	0.495497i	$0.834986\pi$
$858$	0	0
$859$	1.45946e148	0.994344	0.497172	−	0.867652i	$-0.334372\pi$
$859$	1.45946e148	0.994344	0.497172	+	0.867652i	$0.334372\pi$
$860$	2.70149e147	0.173553
$861$	0	0
$862$	−2.73422e147	−0.156213
$863$	−1.99479e148	−1.07486	−0.537430	−	0.843308i	$-0.680605\pi$
$863$	−1.99479e148	−1.07486	−0.537430	+	0.843308i	$0.680605\pi$
$864$	0	0
$865$	−9.67714e147	−0.463910
$866$	−6.80471e147	−0.307720
$867$	0	0
$868$	−1.31562e148	−0.529524
$869$	8.87953e147	0.337203
$870$	0	0
$871$	4.41316e148	1.49222
$872$	1.80444e148	0.575783
$873$	0	0
$874$	−3.18688e147	−0.0905813
$875$	2.12431e148	0.569916
$876$	0	0
$877$	−9.73527e147	−0.232739	−0.116369	−	0.993206i	$-0.537126\pi$
$877$	−9.73527e147	−0.232739	−0.116369	+	0.993206i	$0.537126\pi$
$878$	3.89837e147	0.0879854
$879$	0	0
$880$	−6.85897e147	−0.138002
$881$	−6.24527e147	−0.118650	−0.0593250	−	0.998239i	$-0.518895\pi$
$881$	−6.24527e147	−0.118650	−0.0593250	+	0.998239i	$0.518895\pi$
$882$	0	0
$883$	−1.09918e149	−1.86232	−0.931159	−	0.364615i	$-0.881201\pi$
$883$	−1.09918e149	−1.86232	−0.931159	+	0.364615i	$0.881201\pi$
$884$	−5.69605e148	−0.911453
$885$	0	0
$886$	1.36284e148	0.194554
$887$	−1.10849e149	−1.49481	−0.747407	−	0.664366i	$-0.768702\pi$
$887$	−1.10849e149	−1.49481	−0.747407	+	0.664366i	$0.768702\pi$
$888$	0	0
$889$	−3.35018e148	−0.403209
$890$	−1.14517e148	−0.130219
$891$	0	0
$892$	8.69797e148	0.883065
$893$	−5.10187e148	−0.489475
$894$	0	0
$895$	−4.19427e148	−0.359413
$896$	−4.38266e148	−0.354963
$897$	0	0
$898$	−1.37953e146	−0.000998336 0
$899$	1.36492e148	0.0933776
$900$	0	0
$901$	−6.40037e148	−0.391384
$902$	4.80262e147	0.0277682
$903$	0	0
$904$	1.95318e147	0.0100981
$905$	−1.95018e149	−0.953500
$906$	0	0
$907$	−3.76928e149	−1.64851	−0.824253	−	0.566221i	$-0.808405\pi$
$907$	−3.76928e149	−1.64851	−0.824253	+	0.566221i	$0.808405\pi$
$908$	−3.09688e149	−1.28112
$909$	0	0
$910$	1.20448e148	0.0445872
$911$	2.36013e149	0.826528	0.413264	−	0.910611i	$-0.364389\pi$
$911$	2.36013e149	0.826528	0.413264	+	0.910611i	$0.364389\pi$
$912$	0	0
$913$	−7.47228e148	−0.234250
$914$	5.58822e148	0.165764
$915$	0	0
$916$	−1.38529e149	−0.367975
$917$	−3.23247e149	−0.812611
$918$	0	0
$919$	4.61378e149	1.03902	0.519510	−	0.854464i	$-0.326115\pi$
$919$	4.61378e149	1.03902	0.519510	+	0.854464i	$0.326115\pi$
$920$	−1.14339e149	−0.243730
$921$	0	0
$922$	−8.38448e148	−0.160164
$923$	−7.76137e149	−1.40363
$924$	0	0
$925$	2.87326e149	0.465820
$926$	5.73412e148	0.0880262
$927$	0	0
$928$	3.42637e148	0.0471695
$929$	6.15334e148	0.0802264	0.0401132	−	0.999195i	$-0.487228\pi$
$929$	6.15334e148	0.0802264	0.0401132	+	0.999195i	$0.487228\pi$
$930$	0	0
$931$	−2.40129e149	−0.280857
$932$	1.12250e150	1.24360
$933$	0	0
$934$	−3.89358e148	−0.0387107
$935$	1.84826e149	0.174091
$936$	0	0
$937$	9.87076e149	0.834644	0.417322	−	0.908759i	$-0.362969\pi$
$937$	9.87076e149	0.834644	0.417322	+	0.908759i	$0.362969\pi$
$938$	−2.19618e149	−0.175965
$939$	0	0
$940$	−9.03160e149	−0.649842
$941$	5.12586e149	0.349535	0.174768	−	0.984610i	$-0.444083\pi$
$941$	5.12586e149	0.349535	0.174768	+	0.984610i	$0.444083\pi$
$942$	0	0
$943$	−1.43786e150	−0.880795
$944$	1.39035e150	0.807309
$945$	0	0
$946$	2.40888e148	0.0125693
$947$	7.23652e149	0.357978	0.178989	−	0.983851i	$-0.442717\pi$
$947$	7.23652e149	0.357978	0.178989	+	0.983851i	$0.442717\pi$
$948$	0	0
$949$	3.04628e150	1.35465
$950$	−1.08003e149	−0.0455402
$951$	0	0
$952$	5.74496e149	0.217832
$953$	−1.33924e150	−0.481578	−0.240789	−	0.970578i	$-0.577406\pi$
$953$	−1.33924e150	−0.481578	−0.240789	+	0.970578i	$0.577406\pi$
$954$	0	0
$955$	−2.61133e149	−0.0844679
$956$	−2.53621e150	−0.778147
$957$	0	0
$958$	−2.77333e149	−0.0765673
$959$	9.50887e149	0.249052
$960$	0	0
$961$	−6.12191e149	−0.144330
$962$	4.10533e149	0.0918348
$963$	0	0
$964$	2.20016e150	0.443164
$965$	4.62978e150	0.884975
$966$	0	0
$967$	3.91457e150	0.673980	0.336990	−	0.941508i	$-0.390591\pi$
$967$	3.91457e150	0.673980	0.336990	+	0.941508i	$0.390591\pi$
$968$	1.82120e150	0.297613
$969$	0	0
$970$	−3.08184e149	−0.0453772
$971$	1.14003e151	1.59348	0.796740	−	0.604322i	$-0.206556\pi$
$971$	1.14003e151	1.59348	0.796740	+	0.604322i	$0.206556\pi$
$972$	0	0
$973$	−6.32238e150	−0.796493
$974$	4.86691e149	0.0582138
$975$	0	0
$976$	−2.38507e150	−0.257209
$977$	9.05921e150	0.927716	0.463858	−	0.885910i	$-0.346465\pi$
$977$	9.05921e150	0.927716	0.463858	+	0.885910i	$0.346465\pi$
$978$	0	0
$979$	3.82169e150	0.352964
$980$	−4.25089e150	−0.372875
$981$	0	0
$982$	3.48285e150	0.275616
$983$	1.35939e151	1.02186	0.510930	−	0.859623i	$-0.329301\pi$
$983$	1.35939e151	1.02186	0.510930	+	0.859623i	$0.329301\pi$
$984$	0	0
$985$	1.14698e151	0.778084
$986$	−2.94082e149	−0.0189533
$987$	0	0
$988$	5.77544e150	0.336016
$989$	−7.21193e150	−0.398693
$990$	0	0
$991$	1.59255e151	0.795010	0.397505	−	0.917600i	$-0.369876\pi$
$991$	1.59255e151	0.795010	0.397505	+	0.917600i	$0.369876\pi$
$992$	9.11097e150	0.432240
$993$	0	0
$994$	3.86241e150	0.165518
$995$	−4.66604e150	−0.190057
$996$	0	0
$997$	−7.11596e148	−0.00261896	−0.00130948	−	0.999999i	$-0.500417\pi$
$997$	−7.11596e148	−0.00261896	−0.00130948	+	0.999999i	$0.500417\pi$
$998$	−8.19401e150	−0.286685
$999$	0	0

Twists

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

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

\(f(q)\)	\(=\)	\(q+2.56863e14 q^{2} -2.46932e30 q^{4} -1.16158e35 q^{5} +2.79663e42 q^{7} -1.28550e45 q^{8} +O(q^{10})\)	\(q+2.56863e14 q^{2} -2.46932e30 q^{4} -1.16158e35 q^{5} +2.79663e42 q^{7} -1.28550e45 q^{8} -2.98366e49 q^{10} +9.95717e51 q^{11} -1.44350e56 q^{13} +7.18350e56 q^{14} +5.93028e60 q^{16} -1.59801e62 q^{17} +1.62028e64 q^{19} +2.86831e65 q^{20} +2.55763e66 q^{22} -7.65727e68 q^{23} -2.59504e70 q^{25} -3.70781e70 q^{26} -6.90578e72 q^{28} +7.16454e72 q^{29} +1.90510e75 q^{31} +4.78240e75 q^{32} -4.10469e76 q^{34} -3.24850e77 q^{35} -1.10721e79 q^{37} +4.16190e78 q^{38} +1.49321e80 q^{40} +1.87777e81 q^{41} +9.41841e81 q^{43} -2.45875e82 q^{44} -1.96687e83 q^{46} -3.14875e84 q^{47} -1.48202e85 q^{49} -6.66570e84 q^{50} +3.56447e86 q^{52} +4.00521e86 q^{53} -1.15660e87 q^{55} -3.59507e87 q^{56} +1.84030e87 q^{58} +2.34450e89 q^{59} -4.02186e89 q^{61} +4.89350e89 q^{62} -1.38066e91 q^{64} +1.67674e91 q^{65} -3.05726e92 q^{67} +3.94600e92 q^{68} -8.34418e91 q^{70} +5.37677e93 q^{71} -2.11035e94 q^{73} -2.84401e93 q^{74} -4.00100e94 q^{76} +2.78465e94 q^{77} +8.91772e95 q^{79} -6.88848e95 q^{80} +4.82328e95 q^{82} -7.50442e96 q^{83} +1.85621e97 q^{85} +2.41924e96 q^{86} -1.28000e97 q^{88} +3.83813e98 q^{89} -4.03693e98 q^{91} +1.89083e99 q^{92} -8.08797e98 q^{94} -1.88208e99 q^{95} +1.03291e100 q^{97} -3.80676e99 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 434989091795040 q^{2} + 90\!\cdots\!96 q^{4}+ \cdots + 61\!\cdots\!20 q^{8}+O(q^{10}) \) 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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