LMFDB - Embedded newform 9.102.a.b.1.6

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			1.6
Root			$1.78363e13$ of defining polynomial
Character	$\chi$	$=$	9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.76666e15 q^{2} +5.85773e29 q^{4} +3.44135e35 q^{5} -5.35995e42 q^{7} -3.44415e45 q^{8} +O(q^{10})$	\(q+1.76666e15 q^{2} +5.85773e29 q^{4} +3.44135e35 q^{5} -5.35995e42 q^{7} -3.44415e45 q^{8} +6.07967e50 q^{10} +3.44385e52 q^{11} +3.09748e56 q^{13} -9.46918e57 q^{14} -7.56973e60 q^{16} +1.06203e62 q^{17} -6.11425e63 q^{19} +2.01585e65 q^{20} +6.08410e67 q^{22} +3.47561e68 q^{23} +7.89855e70 q^{25} +5.47219e71 q^{26} -3.13971e72 q^{28} -5.28104e73 q^{29} +2.84133e75 q^{31} -4.64116e75 q^{32} +1.87624e77 q^{34} -1.84454e78 q^{35} +1.90109e79 q^{37} -1.08018e79 q^{38} -1.18525e81 q^{40} -6.25482e80 q^{41} -1.65073e82 q^{43} +2.01731e82 q^{44} +6.14021e83 q^{46} +1.59905e84 q^{47} +6.08770e84 q^{49} +1.39540e86 q^{50} +1.81442e86 q^{52} -9.26087e86 q^{53} +1.18515e88 q^{55} +1.84604e88 q^{56} -9.32978e88 q^{58} +2.36767e89 q^{59} +8.85775e89 q^{61} +5.01965e90 q^{62} +1.09922e91 q^{64} +1.06595e92 q^{65} -3.21574e92 q^{67} +6.22108e91 q^{68} -3.25867e93 q^{70} -1.94954e93 q^{71} -1.32770e94 q^{73} +3.35857e94 q^{74} -3.58156e93 q^{76} -1.84589e95 q^{77} -3.38956e95 q^{79} -2.60501e96 q^{80} -1.10501e96 q^{82} +8.23897e95 q^{83} +3.65481e97 q^{85} -2.91628e97 q^{86} -1.18611e98 q^{88} -2.68359e98 q^{89} -1.66023e99 q^{91} +2.03592e98 q^{92} +2.82498e99 q^{94} -2.10412e99 q^{95} +1.33729e100 q^{97} +1.07549e100 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 434989091795040 q^{2} + 90\!\cdots\!96 q^{4}+ \cdots + 61\!\cdots\!20 q^{8}+O(q^{10}) $ 8 * q + 434989091795040 * q^2 + 9008967123164113911511576503296 * q^4 - 38238791540232828026421308589217200 * q^5 - 5786789720778120168956257648884421874283200 * q^7 + 6101688461407407841888405145259998920458731520 * q^8	$ 8 q + 434989091795040 q^{2} + 90\!\cdots\!96 q^{4}+ \cdots - 20\!\cdots\!20 q^{98}+O(q^{100}) $ 8 * q + 434989091795040 * q^2 + 9008967123164113911511576503296 * q^4 - 38238791540232828026421308589217200 * q^5 - 5786789720778120168956257648884421874283200 * q^7 + 6101688461407407841888405145259998920458731520 * q^8 - 376167658847177398692429835067300112512860198593600 * q^10 - 4622006661480385115355021397632645270205791478300896 * q^11 + 250316830865150221699601352256397536965043294984328650480 * q^13 + 4856789037716039923353321450215036970203737520869624889088 * q^14 - 10662656154906175558835021484824464714661655552497093859868672 * q^16 + 397968518694853312322660892941326449007299986932512193696587120 * q^17 - 21387776045417165942123954421061470474744368808488511816400717280 * q^19 - 1745002690168409059221421019241581897927614179506161156200285542400 * q^20 + 61357881995862711169740037407631980426480577127973320405539739944320 * q^22 + 1366243345208606848425464574347748611753917469593153677393324561698880 * q^23 + 77471873089568593564333770877949420045843582630742632687744142562715000 * q^25 + 97549630676937426518340388130407212490384846814009484188479115327886144 * q^26 + 9217624035174751886516129105576165061663773766415040330328487084880404480 * q^28 - 15465799862710125255662370242568323665682807414567501281109138719156160880 * q^29 - 6594370386043135339784923725045360443937393326734068279132668478779615001344 * q^31 - 12265519409733718324179959581296851912742484455832107241543734281342036213760 * q^32 + 9531455444774917507766540524882635666895777953789094347547215472626183995712 * q^34 + 1122850631208004175280217132184898888977788452428069383882586628450512616297600 * q^35 + 39729696767983511833540209209183332457877293383323859312175998401968644864715440 * q^37 + 70873740526925065519455012686645778106113298999572267198467188879790467046148480 * q^38 - 763642761360299050617237751714968411270996317577517686387843428508400019349504000 * q^40 - 5607291724825101314952096252772109505395882457063737303656079003304969203257094736 * q^41 - 28642921955044714117801359306021921736063108483729021321044095944585527287681223200 * q^43 + 207838425393205175674959052733026300855796348257745356716186803699782799277851086848 * q^44 + 1088094260619851586903932234100844276278561023621942541398958535856528393570339218176 * q^46 + 4595399220200007631460417274797048154524720407021496316223236391731855709593438718080 * q^47 + 12068461406676719302337658501270392621238416595305390197216228129207599916872005856456 * q^49 + 40493179837482260394665357435432250163405353367416857829233726008281167215503492420000 * q^50 - 736020167800817028850658909331852777746165402605863935107936992324104798352324258252800 * q^52 - 131026696145917691346168139299202731343660174597285772716290345361212508775951813313840 * q^53 - 14585157967675450217148723878599628333971210001615112897255333178063634767400530051473600 * q^55 + 23665562342657326400415121984960944704012341384928617813498515591030351969339927087022080 * q^56 + 29173417521771002425120779628349939892591335515731485644911210555324770598093888308326080 * q^58 - 212583149562022564923669670483574922097682552074321909615339251529169016840977455874187360 * q^59 - 3390796423636162146406492296389682436951029380958058095674208836333532599894943317230895504 * q^61 + 5878859817222970028213836429448832127296537243368792127423103234889716583457526212133370880 * q^62 - 74870090698021647967203019932764377907062372989513317693678846896652408519412785858115272704 * q^64 + 161067075283368767182138254547148962244907084326790507487294907612770451283405321317426536800 * q^65 - 618774503558862942537948810466095132313460919373052732511642097824837019429997681150398682720 * q^67 + 2182412150351293808121583165511486752102068977919329447376923905220322529537335456462676162560 * q^68 - 12923520657540473465038555822652190723092643731233782501675276653712048411292540691873715571200 * q^70 + 15797470289857673806303846655911576507977904169297655042639265226995032204172380517793831135424 * q^71 - 20462651635605668591994589976366754984142669867347912050159975933828495442291952971923777071280 * q^73 + 142953411935712165334538916257020870493984381200782662943456748743148514063783881306064429441088 * q^74 + 64556217054886497186737063238064337992823205997653378371004031509089422583081356800943896432640 * q^76 - 250231448169383959900618348975396989794902211753647918986458150866408618577007907131029306438400 * q^77 + 1474556321278768744579716979675929750918930811984805387023357390321899878561204701118206999166080 * q^79 - 6033438037435277941170744030808192554572458649979375320464765273747209092446481051552234550067200 * q^80 + 30083863369214129982421840097969977845328701273986110579467106900080547794123383776302929686086720 * q^82 - 33762254529254022439253159341806143692643909652777369725086142424861011401680843403961249425712160 * q^83 + 17314966267116570951109803841412092095679328201414316724042066880549149931729490643535478494114400 * q^85 - 67989564188024628582959760637462873453376851598916319417912395832044408164663357850732592560556416 * q^86 - 363099602372059077387783242048689913608334478213970275423791339756517232974574737922754584123146240 * q^88 + 620007165949691950044675276484549383308720953973642955804615855186521697520022438525123333812557360 * q^89 - 3685711793015793225308940042728501386995879977832891226647110522985454537354035281338855172828873344 * q^91 + 4618779932089713137770970202224414792688843158843334085630908366025929325979388063902511470793400320 * q^92 - 17371370943540992303713705925513939673302729250250795188383540356993592041601425149438637190677682688 * q^94 + 2642077700832720169247174948884057845373174576960370774287679094739730873649398763127258995555528000 * q^95 + 64020476116668335744724892375903667651900818166631138467214326399663196857065619648203365824701173520 * q^97 - 202971561788470754768820264959327860776947519106194867162872422213964707447467488105939520314595817120 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.76666e15	1.10953	0.554763	−	0.832009i	$-0.312809\pi$
$2$	1.76666e15	1.10953	0.554763	+	0.832009i	$0.312809\pi$
$3$	0	0
$3$	0	0
$4$	5.85773e29	0.231047
$5$	3.44135e35	1.73278	0.866389	−	0.499369i	$-0.166435\pi$
$5$	3.44135e35	1.73278	0.866389	+	0.499369i	$0.166435\pi$
$6$	0	0
$7$	−5.35995e42	−1.12644	−0.563222	−	0.826306i	$-0.690438\pi$
$7$	−5.35995e42	−1.12644	−0.563222	+	0.826306i	$0.690438\pi$
$8$	−3.44415e45	−0.853173
$9$	0	0
$10$	6.07967e50	1.92256
$11$	3.44385e52	0.884533	0.442267	−	0.896884i	$-0.354175\pi$
$11$	3.44385e52	0.884533	0.442267	+	0.896884i	$0.354175\pi$
$12$	0	0
$13$	3.09748e56	1.72532	0.862660	−	0.505785i	$-0.168797\pi$
$13$	3.09748e56	1.72532	0.862660	+	0.505785i	$0.168797\pi$
$14$	−9.46918e57	−1.24982
$15$	0	0
$16$	−7.56973e60	−1.17766
$17$	1.06203e62	0.773510	0.386755	−	0.922182i	$-0.373596\pi$
$17$	1.06203e62	0.773510	0.386755	+	0.922182i	$0.373596\pi$
$18$	0	0
$19$	−6.11425e63	−0.161915	−0.0809574	−	0.996718i	$-0.525798\pi$
$19$	−6.11425e63	−0.161915	−0.0809574	+	0.996718i	$0.525798\pi$
$20$	2.01585e65	0.400352
$21$	0	0
$22$	6.08410e67	0.981412
$23$	3.47561e68	0.593985	0.296992	−	0.954880i	$-0.404016\pi$
$23$	3.47561e68	0.593985	0.296992	+	0.954880i	$0.404016\pi$
$24$	0	0
$25$	7.89855e70	2.00252
$26$	5.47219e71	1.91429
$27$	0	0
$28$	−3.13971e72	−0.260261
$29$	−5.28104e73	−0.744082	−0.372041	−	0.928216i	$-0.621342\pi$
$29$	−5.28104e73	−0.744082	−0.372041	+	0.928216i	$0.621342\pi$
$30$	0	0
$31$	2.84133e75	1.37961	0.689805	−	0.723996i	$-0.257696\pi$
$31$	2.84133e75	1.37961	0.689805	+	0.723996i	$0.257696\pi$
$32$	−4.64116e75	−0.453475
$33$	0	0
$34$	1.87624e77	0.858229
$35$	−1.84454e78	−1.95188
$36$	0	0
$37$	1.90109e79	1.21567	0.607834	−	0.794064i	$-0.292039\pi$
$37$	1.90109e79	1.21567	0.607834	+	0.794064i	$0.292039\pi$
$38$	−1.08018e79	−0.179649
$39$	0	0
$40$	−1.18525e81	−1.47836
$41$	−6.25482e80	−0.224197	−0.112099	−	0.993697i	$-0.535757\pi$
$41$	−6.25482e80	−0.224197	−0.112099	+	0.993697i	$0.535757\pi$
$42$	0	0
$43$	−1.65073e82	−0.533974	−0.266987	−	0.963700i	$-0.586028\pi$
$43$	−1.65073e82	−0.533974	−0.266987	+	0.963700i	$0.586028\pi$
$44$	2.01731e82	0.204368
$45$	0	0
$46$	6.14021e83	0.659041
$47$	1.59905e84	0.579323	0.289662	−	0.957129i	$-0.406457\pi$
$47$	1.59905e84	0.579323	0.289662	+	0.957129i	$0.406457\pi$
$48$	0	0
$49$	6.08770e84	0.268876
$50$	1.39540e86	2.22185
$51$	0	0
$52$	1.81442e86	0.398629
$53$	−9.26087e86	−0.777536	−0.388768	−	0.921336i	$-0.627099\pi$
$53$	−9.26087e86	−0.777536	−0.388768	+	0.921336i	$0.627099\pi$
$54$	0	0
$55$	1.18515e88	1.53270
$56$	1.84604e88	0.961052
$57$	0	0
$58$	−9.32978e88	−0.825578
$59$	2.36767e89	0.883681	0.441840	−	0.897094i	$-0.354326\pi$
$59$	2.36767e89	0.883681	0.441840	+	0.897094i	$0.354326\pi$
$60$	0	0
$61$	8.85775e89	0.613998	0.306999	−	0.951710i	$-0.400675\pi$
$61$	8.85775e89	0.613998	0.306999	+	0.951710i	$0.400675\pi$
$62$	5.01965e90	1.53071
$63$	0	0
$64$	1.09922e91	0.674522
$65$	1.06595e92	2.98960
$66$	0	0
$67$	−3.21574e92	−1.95210	−0.976052	−	0.217537i	$-0.930198\pi$
$67$	−3.21574e92	−1.95210	−0.976052	+	0.217537i	$0.930198\pi$
$68$	6.22108e91	0.178717
$69$	0	0
$70$	−3.25867e93	−2.16566
$71$	−1.94954e93	−0.632974	−0.316487	−	0.948597i	$-0.602503\pi$
$71$	−1.94954e93	−0.632974	−0.316487	+	0.948597i	$0.602503\pi$
$72$	0	0
$73$	−1.32770e94	−1.05998	−0.529988	−	0.848005i	$-0.677804\pi$
$73$	−1.32770e94	−1.05998	−0.529988	+	0.848005i	$0.677804\pi$
$74$	3.35857e94	1.34881
$75$	0	0
$76$	−3.58156e93	−0.0374098
$77$	−1.84589e95	−0.996377
$78$	0	0
$79$	−3.38956e95	−0.501158	−0.250579	−	0.968096i	$-0.580621\pi$
$79$	−3.38956e95	−0.501158	−0.250579	+	0.968096i	$0.580621\pi$
$80$	−2.60501e96	−2.04063
$81$	0	0
$82$	−1.10501e96	−0.248752
$83$	8.23897e95	0.100561	0.0502805	−	0.998735i	$-0.483988\pi$
$83$	8.23897e95	0.100561	0.0502805	+	0.998735i	$0.483988\pi$
$84$	0	0
$85$	3.65481e97	1.34032
$86$	−2.91628e97	−0.592458
$87$	0	0
$88$	−1.18611e98	−0.754660
$89$	−2.68359e98	−0.964985	−0.482492	−	0.875900i	$-0.660268\pi$
$89$	−2.68359e98	−0.964985	−0.482492	+	0.875900i	$0.660268\pi$
$90$	0	0
$91$	−1.66023e99	−1.94348
$92$	2.03592e98	0.137238
$93$	0	0
$94$	2.82498e99	0.642774
$95$	−2.10412e99	−0.280562
$96$	0	0
$97$	1.33729e100	0.622664	0.311332	−	0.950301i	$-0.399225\pi$
$97$	1.33729e100	0.622664	0.311332	+	0.950301i	$0.399225\pi$
$98$	1.07549e100	0.298324
$99$	0	0
$100$	4.62676e100	0.462676
$101$	−3.34535e100	−0.202401	−0.101200	−	0.994866i	$-0.532268\pi$
$101$	−3.34535e100	−0.202401	−0.101200	+	0.994866i	$0.532268\pi$
$102$	0	0
$103$	3.42996e101	0.770919	0.385459	−	0.922725i	$-0.374043\pi$
$103$	3.42996e101	0.770919	0.385459	+	0.922725i	$0.374043\pi$
$104$	−1.06682e102	−1.47200
$105$	0	0
$106$	−1.63608e102	−0.862696
$107$	5.39428e102	1.77032	0.885162	−	0.465284i	$-0.154048\pi$
$107$	5.39428e102	1.77032	0.885162	+	0.465284i	$0.154048\pi$
$108$	0	0
$109$	1.02335e102	0.131822	0.0659108	−	0.997826i	$-0.479005\pi$
$109$	1.02335e102	0.131822	0.0659108	+	0.997826i	$0.479005\pi$
$110$	2.09375e103	1.70057
$111$	0	0
$112$	4.05734e103	1.32657
$113$	−3.86042e103	−0.805699	−0.402850	−	0.915266i	$-0.631980\pi$
$113$	−3.86042e103	−0.805699	−0.402850	+	0.915266i	$0.631980\pi$
$114$	0	0
$115$	1.19608e104	1.02924
$116$	−3.09349e103	−0.171918
$117$	0	0
$118$	4.18287e104	0.980466
$119$	−5.69242e104	−0.871316
$120$	0	0
$121$	−3.29855e104	−0.217601
$122$	1.56486e105	0.681246
$123$	0	0
$124$	1.66437e105	0.318754
$125$	1.36079e106	1.73715
$126$	0	0
$127$	1.39229e106	0.797339	0.398670	−	0.917095i	$-0.369472\pi$
$127$	1.39229e106	0.797339	0.398670	+	0.917095i	$0.369472\pi$
$128$	3.11862e106	1.20187
$129$	0	0
$130$	1.88317e107	3.31703
$131$	9.77949e106	1.16981	0.584905	−	0.811102i	$-0.301132\pi$
$131$	9.77949e106	1.16981	0.584905	+	0.811102i	$0.301132\pi$
$132$	0	0
$133$	3.27721e106	0.182388
$134$	−5.68110e107	−2.16591
$135$	0	0
$136$	−3.65778e107	−0.659938
$137$	4.26131e107	0.531073	0.265537	−	0.964101i	$-0.414451\pi$
$137$	4.26131e107	0.531073	0.265537	+	0.964101i	$0.414451\pi$
$138$	0	0
$139$	−1.67295e107	−0.100285	−0.0501425	−	0.998742i	$-0.515968\pi$
$139$	−1.67295e107	−0.100285	−0.0501425	+	0.998742i	$0.515968\pi$
$140$	−1.08048e108	−0.450975
$141$	0	0
$142$	−3.44417e108	−0.702301
$143$	1.06673e109	1.52610
$144$	0	0
$145$	−1.81739e109	−1.28933
$146$	−2.34559e109	−1.17607
$147$	0	0
$148$	1.11360e109	0.280876
$149$	−7.26079e109	−1.30340	−0.651700	−	0.758477i	$-0.725944\pi$
$149$	−7.26079e109	−1.30340	−0.651700	+	0.758477i	$0.725944\pi$
$150$	0	0
$151$	2.69592e109	0.246815	0.123408	−	0.992356i	$-0.460618\pi$
$151$	2.69592e109	0.246815	0.123408	+	0.992356i	$0.460618\pi$
$152$	2.10584e109	0.138141
$153$	0	0
$154$	−3.26105e110	−1.10551
$155$	9.77800e110	2.39056
$156$	0	0
$157$	4.68140e110	0.599023	0.299511	−	0.954093i	$-0.403176\pi$
$157$	4.68140e110	0.599023	0.299511	+	0.954093i	$0.403176\pi$
$158$	−5.98818e110	−0.556048
$159$	0	0
$160$	−1.59719e111	−0.785771
$161$	−1.86291e111	−0.669090
$162$	0	0
$163$	9.76956e111	1.88105	0.940526	−	0.339721i	$-0.110333\pi$
$163$	9.76956e111	1.88105	0.940526	+	0.339721i	$0.110333\pi$
$164$	−3.66390e110	−0.0518000
$165$	0	0
$166$	1.45554e111	0.111575
$167$	2.19092e111	0.124007	0.0620034	−	0.998076i	$-0.480251\pi$
$167$	2.19092e111	0.124007	0.0620034	+	0.998076i	$0.480251\pi$
$168$	0	0
$169$	6.37126e112	1.97673
$170$	6.45679e112	1.48712
$171$	0	0
$172$	−9.66955e111	−0.123373
$173$	1.20621e113	1.14840	0.574202	−	0.818714i	$-0.305312\pi$
$173$	1.20621e113	1.14840	0.574202	+	0.818714i	$0.305312\pi$
$174$	0	0
$175$	−4.23358e113	−2.25573
$176$	−2.60691e113	−1.04168
$177$	0	0
$178$	−4.74098e113	−1.07068
$179$	−7.66204e113	−1.30397	−0.651983	−	0.758234i	$-0.726063\pi$
$179$	−7.66204e113	−1.30397	−0.651983	+	0.758234i	$0.726063\pi$
$180$	0	0
$181$	5.31499e113	0.516101	0.258051	−	0.966131i	$-0.416920\pi$
$181$	5.31499e113	0.516101	0.258051	+	0.966131i	$0.416920\pi$
$182$	−2.93306e114	−2.15633
$183$	0	0
$184$	−1.19705e114	−0.506772
$185$	6.54230e114	2.10648
$186$	0	0
$187$	3.65747e114	0.684195
$188$	9.36682e113	0.133851
$189$	0	0
$190$	−3.71727e114	−0.311291
$191$	−8.28574e113	−0.0532288	−0.0266144	−	0.999646i	$-0.508473\pi$
$191$	−8.28574e113	−0.0532288	−0.0266144	+	0.999646i	$0.508473\pi$
$192$	0	0
$193$	3.05207e114	0.115865	0.0579323	−	0.998321i	$-0.481549\pi$
$193$	3.05207e114	0.115865	0.0579323	+	0.998321i	$0.481549\pi$
$194$	2.36254e115	0.690861
$195$	0	0
$196$	3.56601e114	0.0621228
$197$	4.98888e115	0.672139	0.336069	−	0.941837i	$-0.390902\pi$
$197$	4.98888e115	0.672139	0.336069	+	0.941837i	$0.390902\pi$
$198$	0	0
$199$	1.87907e116	1.52006	0.760032	−	0.649885i	$-0.225183\pi$
$199$	1.87907e116	1.52006	0.760032	+	0.649885i	$0.225183\pi$
$200$	−2.72038e116	−1.70850
$201$	0	0
$202$	−5.91008e115	−0.224569
$203$	2.83061e116	0.838166
$204$	0	0
$205$	−2.15250e116	−0.388484
$206$	6.05955e116	0.855354
$207$	0	0
$208$	−2.34471e117	−2.03185
$209$	−2.10566e116	−0.143219
$210$	0	0
$211$	−1.37595e117	−0.578548	−0.289274	−	0.957246i	$-0.593414\pi$
$211$	−1.37595e117	−0.578548	−0.289274	+	0.957246i	$0.593414\pi$
$212$	−5.42477e116	−0.179647
$213$	0	0
$214$	9.52984e117	1.96422
$215$	−5.68075e117	−0.925258
$216$	0	0
$217$	−1.52294e118	−1.55405
$218$	1.80791e117	0.146259
$219$	0	0
$220$	6.94228e117	0.354125
$221$	3.28962e118	1.33455
$222$	0	0
$223$	6.07548e118	1.56381	0.781907	−	0.623396i	$-0.214247\pi$
$223$	6.07548e118	1.56381	0.781907	+	0.623396i	$0.214247\pi$
$224$	2.48764e118	0.510814
$225$	0	0
$226$	−6.82003e118	−0.893944
$227$	−1.61334e119	−1.69207	−0.846037	−	0.533124i	$-0.821018\pi$
$227$	−1.61334e119	−1.69207	−0.846037	+	0.533124i	$0.821018\pi$
$228$	0	0
$229$	−7.19765e118	−0.484729	−0.242364	−	0.970185i	$-0.577923\pi$
$229$	−7.19765e118	−0.484729	−0.242364	+	0.970185i	$0.577923\pi$
$230$	2.11306e119	1.14197
$231$	0	0
$232$	1.81887e119	0.634831
$233$	−1.46080e119	−0.410314	−0.205157	−	0.978729i	$-0.565770\pi$
$233$	−1.46080e119	−0.410314	−0.205157	+	0.978729i	$0.565770\pi$
$234$	0	0
$235$	5.50289e119	1.00384
$236$	1.38692e119	0.204171
$237$	0	0
$238$	−1.00566e120	−0.966747
$239$	−7.43010e119	−0.577964	−0.288982	−	0.957334i	$-0.593317\pi$
$239$	−7.43010e119	−0.577964	−0.288982	+	0.957334i	$0.593317\pi$
$240$	0	0
$241$	−2.53445e120	−1.29427	−0.647133	−	0.762377i	$-0.724032\pi$
$241$	−2.53445e120	−1.29427	−0.647133	+	0.762377i	$0.724032\pi$
$242$	−5.82740e119	−0.241434
$243$	0	0
$244$	5.18863e119	0.141862
$245$	2.09499e120	0.465902
$246$	0	0
$247$	−1.89388e120	−0.279355
$248$	−9.78596e120	−1.17705
$249$	0	0
$250$	2.40405e121	1.92741
$251$	2.12075e121	1.38985	0.694923	−	0.719084i	$-0.255438\pi$
$251$	2.12075e121	1.38985	0.694923	+	0.719084i	$0.255438\pi$
$252$	0	0
$253$	1.19695e121	0.525399
$254$	2.45971e121	0.884668
$255$	0	0
$256$	2.72267e121	0.658988
$257$	−7.82104e121	−1.55468	−0.777341	−	0.629079i	$-0.783432\pi$
$257$	−7.82104e121	−1.55468	−0.777341	+	0.629079i	$0.783432\pi$
$258$	0	0
$259$	−1.01897e122	−1.36938
$260$	6.24405e121	0.690736
$261$	0	0
$262$	1.72770e122	1.29793
$263$	4.46862e121	0.276954	0.138477	−	0.990366i	$-0.455779\pi$
$263$	4.46862e121	0.276954	0.138477	+	0.990366i	$0.455779\pi$
$264$	0	0
$265$	−3.18699e122	−1.34730
$266$	5.78970e121	0.202364
$267$	0	0
$268$	−1.88369e122	−0.451027
$269$	−6.09483e122	−1.20913	−0.604563	−	0.796557i	$-0.706652\pi$
$269$	−6.09483e122	−1.20913	−0.604563	+	0.796557i	$0.706652\pi$
$270$	0	0
$271$	2.88488e122	0.393712	0.196856	−	0.980432i	$-0.436927\pi$
$271$	2.88488e122	0.393712	0.196856	+	0.980432i	$0.436927\pi$
$272$	−8.03928e122	−0.910935
$273$	0	0
$274$	7.52827e122	0.589239
$275$	2.72015e123	1.77130
$276$	0	0
$277$	−2.29440e123	−1.03619	−0.518097	−	0.855322i	$-0.673359\pi$
$277$	−2.29440e123	−1.03619	−0.518097	+	0.855322i	$0.673359\pi$
$278$	−2.95553e122	−0.111269
$279$	0	0
$280$	6.35288e123	1.66529
$281$	8.87210e123	1.94248	0.971242	−	0.238095i	$-0.0765231\pi$
$281$	8.87210e123	1.94248	0.971242	+	0.238095i	$0.0765231\pi$
$282$	0	0
$283$	3.63420e123	0.556152	0.278076	−	0.960559i	$-0.410303\pi$
$283$	3.63420e123	0.556152	0.278076	+	0.960559i	$0.410303\pi$
$284$	−1.14199e123	−0.146247
$285$	0	0
$286$	1.88454e124	1.69325
$287$	3.35255e123	0.252545
$288$	0	0
$289$	−7.57223e123	−0.401682
$290$	−3.21070e124	−1.43054
$291$	0	0
$292$	−7.77732e123	−0.244904
$293$	3.97733e124	1.05384	0.526922	−	0.849913i	$-0.323346\pi$
$293$	3.97733e124	1.05384	0.526922	+	0.849913i	$0.323346\pi$
$294$	0	0
$295$	8.14799e124	1.53122
$296$	−6.54762e124	−1.03718
$297$	0	0
$298$	−1.28273e125	−1.44615
$299$	1.07656e125	1.02481
$300$	0	0
$301$	8.84785e124	0.601492
$302$	4.76277e124	0.273848
$303$	0	0
$304$	4.62832e124	0.190681
$305$	3.04826e125	1.06392
$306$	0	0
$307$	6.37866e125	1.60045	0.800223	−	0.599702i	$-0.204714\pi$
$307$	6.37866e125	1.60045	0.800223	+	0.599702i	$0.204714\pi$
$308$	−1.08127e125	−0.230209
$309$	0	0
$310$	1.72744e126	2.65238
$311$	−4.16169e124	−0.0543088	−0.0271544	−	0.999631i	$-0.508645\pi$
$311$	−4.16169e124	−0.0543088	−0.0271544	+	0.999631i	$0.508645\pi$
$312$	0	0
$313$	9.78296e125	0.923594	0.461797	−	0.886986i	$-0.347205\pi$
$313$	9.78296e125	0.923594	0.461797	+	0.886986i	$0.347205\pi$
$314$	8.27042e125	0.664631
$315$	0	0
$316$	−1.98551e125	−0.115791
$317$	−1.90344e125	−0.0946336	−0.0473168	−	0.998880i	$-0.515067\pi$
$317$	−1.90344e125	−0.0946336	−0.0473168	+	0.998880i	$0.515067\pi$
$318$	0	0
$319$	−1.81871e126	−0.658165
$320$	3.78280e126	1.16880
$321$	0	0
$322$	−3.29112e126	−0.742373
$323$	−6.49351e125	−0.125243
$324$	0	0
$325$	2.44656e127	3.45499
$326$	1.72594e127	2.08708
$327$	0	0
$328$	2.15425e126	0.191279
$329$	−8.57084e126	−0.652575
$330$	0	0
$331$	−1.95148e127	−1.09409	−0.547043	−	0.837105i	$-0.684247\pi$
$331$	−1.95148e127	−1.09409	−0.547043	+	0.837105i	$0.684247\pi$
$332$	4.82616e125	0.0232343
$333$	0	0
$334$	3.87061e126	0.137589
$335$	−1.10665e128	−3.38256
$336$	0	0
$337$	−1.63331e126	−0.0369623	−0.0184811	−	0.999829i	$-0.505883\pi$
$337$	−1.63331e126	−0.0369623	−0.0184811	+	0.999829i	$0.505883\pi$
$338$	1.12558e128	2.19323
$339$	0	0
$340$	2.14089e127	0.309677
$341$	9.78512e127	1.22031
$342$	0	0
$343$	8.87266e127	0.823571
$344$	5.68537e127	0.455572
$345$	0	0
$346$	2.13096e128	1.27418
$347$	2.36944e128	1.22464	0.612319	−	0.790611i	$-0.290237\pi$
$347$	2.36944e128	1.22464	0.612319	+	0.790611i	$0.290237\pi$
$348$	0	0
$349$	−7.03918e126	−0.0272169	−0.0136084	−	0.999907i	$-0.504332\pi$
$349$	−7.03918e126	−0.0272169	−0.0136084	+	0.999907i	$0.504332\pi$
$350$	−7.47928e128	−2.50279
$351$	0	0
$352$	−1.59835e128	−0.401113
$353$	−2.29284e128	−0.498599	−0.249299	−	0.968426i	$-0.580200\pi$
$353$	−2.29284e128	−0.498599	−0.249299	+	0.968426i	$0.580200\pi$
$354$	0	0
$355$	−6.70905e128	−1.09680
$356$	−1.57197e128	−0.222956
$357$	0	0
$358$	−1.35362e129	−1.44678
$359$	5.85822e128	0.543871	0.271935	−	0.962316i	$-0.412336\pi$
$359$	5.85822e128	0.543871	0.271935	+	0.962316i	$0.412336\pi$
$360$	0	0
$361$	−1.38860e129	−0.973784
$362$	9.38977e128	0.572627
$363$	0	0
$364$	−9.72520e128	−0.449033
$365$	−4.56908e129	−1.83671
$366$	0	0
$367$	−3.80604e129	−1.16101	−0.580506	−	0.814256i	$-0.697145\pi$
$367$	−3.80604e129	−1.16101	−0.580506	+	0.814256i	$0.697145\pi$
$368$	−2.63094e129	−0.699514
$369$	0	0
$370$	1.15580e130	2.33720
$371$	4.96378e129	0.875851
$372$	0	0
$373$	−4.09983e129	−0.551404	−0.275702	−	0.961243i	$-0.588910\pi$
$373$	−4.09983e129	−0.551404	−0.275702	+	0.961243i	$0.588910\pi$
$374$	6.46150e129	0.759132
$375$	0	0
$376$	−5.50737e129	−0.494263
$377$	−1.63579e130	−1.28378
$378$	0	0
$379$	−1.69783e130	−1.02004	−0.510018	−	0.860164i	$-0.670361\pi$
$379$	−1.69783e130	−1.02004	−0.510018	+	0.860164i	$0.670361\pi$
$380$	−1.23254e129	−0.0648230
$381$	0	0
$382$	−1.46381e129	−0.0590587
$383$	2.79558e130	0.988403	0.494201	−	0.869347i	$-0.335461\pi$
$383$	2.79558e130	0.988403	0.494201	+	0.869347i	$0.335461\pi$
$384$	0	0
$385$	−6.35234e130	−1.72650
$386$	5.39196e129	0.128555
$387$	0	0
$388$	7.83349e129	0.143864
$389$	−1.02053e131	−1.64577	−0.822886	−	0.568206i	$-0.807638\pi$
$389$	−1.02053e131	−1.64577	−0.822886	+	0.568206i	$0.807638\pi$
$390$	0	0
$391$	3.69120e130	0.459453
$392$	−2.09669e130	−0.229397
$393$	0	0
$394$	8.81364e130	0.745755
$395$	−1.16646e131	−0.868396
$396$	0	0
$397$	2.41789e131	1.39481	0.697406	−	0.716676i	$-0.254337\pi$
$397$	2.41789e131	1.39481	0.697406	+	0.716676i	$0.254337\pi$
$398$	3.31967e131	1.68655
$399$	0	0
$400$	−5.97899e131	−2.35830
$401$	3.05800e131	1.06328	0.531638	−	0.846972i	$-0.321577\pi$
$401$	3.05800e131	1.06328	0.531638	+	0.846972i	$0.321577\pi$
$402$	0	0
$403$	8.80097e131	2.38027
$404$	−1.95961e130	−0.0467640
$405$	0	0
$406$	5.00072e131	0.929967
$407$	6.54706e131	1.07530
$408$	0	0
$409$	2.88971e131	0.370533	0.185267	−	0.982688i	$-0.440685\pi$
$409$	2.88971e131	0.370533	0.185267	+	0.982688i	$0.440685\pi$
$410$	−3.80273e131	−0.431033
$411$	0	0
$412$	2.00917e131	0.178118
$413$	−1.26906e132	−0.995417
$414$	0	0
$415$	2.83531e131	0.174250
$416$	−1.43759e132	−0.782389
$417$	0	0
$418$	−3.71997e131	−0.158905
$419$	4.10257e132	1.55327	0.776637	−	0.629948i	$-0.216924\pi$
$419$	4.10257e132	1.55327	0.776637	+	0.629948i	$0.216924\pi$
$420$	0	0
$421$	9.23486e131	0.274906	0.137453	−	0.990508i	$-0.456108\pi$
$421$	9.23486e131	0.274906	0.137453	+	0.990508i	$0.456108\pi$
$422$	−2.43083e132	−0.641913
$423$	0	0
$424$	3.18958e132	0.663373
$425$	8.38849e132	1.54897
$426$	0	0
$427$	−4.74771e132	−0.691634
$428$	3.15982e132	0.409027
$429$	0	0
$430$	−1.00359e133	−1.02660
$431$	4.45061e132	0.404872	0.202436	−	0.979295i	$-0.435114\pi$
$431$	4.45061e132	0.404872	0.202436	+	0.979295i	$0.435114\pi$
$432$	0	0
$433$	1.12944e133	0.813252	0.406626	−	0.913595i	$-0.366705\pi$
$433$	1.12944e133	0.813252	0.406626	+	0.913595i	$0.366705\pi$
$434$	−2.69051e133	−1.72426
$435$	0	0
$436$	5.99451e131	0.0304569
$437$	−2.12507e132	−0.0961749
$438$	0	0
$439$	−8.84001e130	−0.00317683	−0.00158842	−	0.999999i	$-0.500506\pi$
$439$	−8.84001e130	−0.00317683	−0.00158842	+	0.999999i	$0.500506\pi$
$440$	−4.08183e133	−1.30766
$441$	0	0
$442$	5.81162e133	1.48072
$443$	1.19259e133	0.271082	0.135541	−	0.990772i	$-0.456723\pi$
$443$	1.19259e133	0.271082	0.135541	+	0.990772i	$0.456723\pi$
$444$	0	0
$445$	−9.23515e133	−1.67210
$446$	1.07333e134	1.73509
$447$	0	0
$448$	−5.89177e133	−0.759811
$449$	3.96128e133	0.456452	0.228226	−	0.973608i	$-0.426707\pi$
$449$	3.96128e133	0.456452	0.228226	+	0.973608i	$0.426707\pi$
$450$	0	0
$451$	−2.15407e133	−0.198310
$452$	−2.26133e133	−0.186154
$453$	0	0
$454$	−2.85021e134	−1.87740
$455$	−5.71344e134	−3.36761
$456$	0	0
$457$	−1.35379e134	−0.639414	−0.319707	−	0.947516i	$-0.603585\pi$
$457$	−1.35379e134	−0.639414	−0.319707	+	0.947516i	$0.603585\pi$
$458$	−1.27158e134	−0.537819
$459$	0	0
$460$	7.00629e133	0.237803
$461$	6.86709e133	0.208870	0.104435	−	0.994532i	$-0.466697\pi$
$461$	6.86709e133	0.208870	0.104435	+	0.994532i	$0.466697\pi$
$462$	0	0
$463$	2.52099e134	0.616213	0.308107	−	0.951352i	$-0.400305\pi$
$463$	2.52099e134	0.616213	0.308107	+	0.951352i	$0.400305\pi$
$464$	3.99761e134	0.876278
$465$	0	0
$466$	−2.58073e134	−0.455253
$467$	6.60220e134	1.04517	0.522584	−	0.852588i	$-0.324968\pi$
$467$	6.60220e134	1.04517	0.522584	+	0.852588i	$0.324968\pi$
$468$	0	0
$469$	1.72362e135	2.19894
$470$	9.72172e134	1.11378
$471$	0	0
$472$	−8.15462e134	−0.753933
$473$	−5.68489e134	−0.472318
$474$	0	0
$475$	−4.82937e134	−0.324238
$476$	−3.33446e134	−0.201314
$477$	0	0
$478$	−1.31264e135	−0.641266
$479$	1.49265e135	0.656166	0.328083	−	0.944649i	$-0.393597\pi$
$479$	1.49265e135	0.656166	0.328083	+	0.944649i	$0.393597\pi$
$480$	0	0
$481$	5.88858e135	2.09741
$482$	−4.47751e135	−1.43602
$483$	0	0
$484$	−1.93220e134	−0.0502760
$485$	4.60208e135	1.07894
$486$	0	0
$487$	1.65892e135	0.315946	0.157973	−	0.987443i	$-0.449504\pi$
$487$	1.65892e135	0.315946	0.157973	+	0.987443i	$0.449504\pi$
$488$	−3.05074e135	−0.523847
$489$	0	0
$490$	3.70112e135	0.516930
$491$	5.07962e135	0.640053	0.320027	−	0.947409i	$-0.396308\pi$
$491$	5.07962e135	0.640053	0.320027	+	0.947409i	$0.396308\pi$
$492$	0	0
$493$	−5.60862e135	−0.575555
$494$	−3.34583e135	−0.309951
$495$	0	0
$496$	−2.15081e136	−1.62472
$497$	1.04494e136	0.713010
$498$	0	0
$499$	3.25310e136	1.81226	0.906130	−	0.422999i	$-0.139023\pi$
$499$	3.25310e136	1.81226	0.906130	+	0.422999i	$0.139023\pi$
$500$	7.97115e135	0.401362
$501$	0	0
$502$	3.74664e136	1.54207
$503$	−2.14382e136	−0.798006	−0.399003	−	0.916950i	$-0.630644\pi$
$503$	−2.14382e136	−0.798006	−0.399003	+	0.916950i	$0.630644\pi$
$504$	0	0
$505$	−1.15125e136	−0.350716
$506$	2.11460e136	0.582944
$507$	0	0
$508$	8.15568e135	0.184222
$509$	2.39037e136	0.488897	0.244448	−	0.969662i	$-0.421393\pi$
$509$	2.39037e136	0.488897	0.244448	+	0.969662i	$0.421393\pi$
$510$	0	0
$511$	7.11642e136	1.19400
$512$	−3.09661e136	−0.470711
$513$	0	0
$514$	−1.38171e137	−1.72496
$515$	1.18037e137	1.33583
$516$	0	0
$517$	5.50691e136	0.512431
$518$	−1.80017e137	−1.51936
$519$	0	0
$520$	−3.67129e137	−2.55064
$521$	−1.68827e137	−1.06448	−0.532239	−	0.846594i	$-0.678649\pi$
$521$	−1.68827e137	−1.06448	−0.532239	+	0.846594i	$0.678649\pi$
$522$	0	0
$523$	−2.56145e137	−1.33091	−0.665457	−	0.746436i	$-0.731763\pi$
$523$	−2.56145e137	−1.33091	−0.665457	+	0.746436i	$0.731763\pi$
$524$	5.72855e136	0.270281
$525$	0	0
$526$	7.89452e136	0.307288
$527$	3.01758e137	1.06714
$528$	0	0
$529$	−2.21584e137	−0.647182
$530$	−5.63031e137	−1.49486
$531$	0	0
$532$	1.91970e136	0.0421401
$533$	−1.93742e137	−0.386812
$534$	0	0
$535$	1.85636e138	3.06758
$536$	1.10755e138	1.66548
$537$	0	0
$538$	−1.07675e138	−1.34156
$539$	2.09652e137	0.237829
$540$	0	0
$541$	5.13635e137	0.483273	0.241636	−	0.970367i	$-0.422316\pi$
$541$	5.13635e137	0.483273	0.241636	+	0.970367i	$0.422316\pi$
$542$	5.09659e137	0.436833
$543$	0	0
$544$	−4.92905e137	−0.350767
$545$	3.52171e137	0.228418
$546$	0	0
$547$	−1.51606e138	−0.817251	−0.408626	−	0.912702i	$-0.633992\pi$
$547$	−1.51606e138	−0.817251	−0.408626	+	0.912702i	$0.633992\pi$
$548$	2.49616e137	0.122703
$549$	0	0
$550$	4.80556e138	1.96530
$551$	3.22896e137	0.120478
$552$	0	0
$553$	1.81679e138	0.564527
$554$	−4.05342e138	−1.14968
$555$	0	0
$556$	−9.79969e136	−0.0231705
$557$	2.27470e138	0.491175	0.245588	−	0.969374i	$-0.421019\pi$
$557$	2.27470e138	0.491175	0.245588	+	0.969374i	$0.421019\pi$
$558$	0	0
$559$	−5.11312e138	−0.921276
$560$	1.39627e139	2.29866
$561$	0	0
$562$	1.56740e139	2.15523
$563$	−2.50855e138	−0.315318	−0.157659	−	0.987494i	$-0.550395\pi$
$563$	−2.50855e138	−0.315318	−0.157659	+	0.987494i	$0.550395\pi$
$564$	0	0
$565$	−1.32850e139	−1.39610
$566$	6.42038e138	0.617065
$567$	0	0
$568$	6.71451e138	0.540037
$569$	5.91124e138	0.435020	0.217510	−	0.976058i	$-0.430207\pi$
$569$	5.91124e138	0.435020	0.217510	+	0.976058i	$0.430207\pi$
$570$	0	0
$571$	2.25293e139	1.38875	0.694375	−	0.719613i	$-0.255681\pi$
$571$	2.25293e139	1.38875	0.694375	+	0.719613i	$0.255681\pi$
$572$	6.24860e138	0.352601
$573$	0	0
$574$	5.92280e138	0.280206
$575$	2.74523e139	1.18947
$576$	0	0
$577$	2.94565e139	1.07103	0.535517	−	0.844525i	$-0.320117\pi$
$577$	2.94565e139	1.07103	0.535517	+	0.844525i	$0.320117\pi$
$578$	−1.33775e139	−0.445677
$579$	0	0
$580$	−1.06458e139	−0.297895
$581$	−4.41605e138	−0.113276
$582$	0	0
$583$	−3.18931e139	−0.687756
$584$	4.57280e139	0.904344
$585$	0	0
$586$	7.02657e139	1.16927
$587$	−4.14398e139	−0.632694	−0.316347	−	0.948644i	$-0.602456\pi$
$587$	−4.14398e139	−0.632694	−0.316347	+	0.948644i	$0.602456\pi$
$588$	0	0
$589$	−1.73726e139	−0.223379
$590$	1.43947e140	1.69893
$591$	0	0
$592$	−1.43907e140	−1.43165
$593$	4.72697e139	0.431838	0.215919	−	0.976411i	$-0.430725\pi$
$593$	4.72697e139	0.431838	0.215919	+	0.976411i	$0.430725\pi$
$594$	0	0
$595$	−1.95896e140	−1.50980
$596$	−4.25317e139	−0.301146
$597$	0	0
$598$	1.90192e140	1.13706
$599$	1.54853e139	0.0850875	0.0425438	−	0.999095i	$-0.486454\pi$
$599$	1.54853e139	0.0850875	0.0425438	+	0.999095i	$0.486454\pi$
$600$	0	0
$601$	−7.43424e139	−0.345204	−0.172602	−	0.984992i	$-0.555217\pi$
$601$	−7.43424e139	−0.345204	−0.172602	+	0.984992i	$0.555217\pi$
$602$	1.56311e140	0.667370
$603$	0	0
$604$	1.57920e139	0.0570258
$605$	−1.13514e140	−0.377055
$606$	0	0
$607$	6.16048e140	1.73215	0.866076	−	0.499913i	$-0.166635\pi$
$607$	6.16048e140	1.73215	0.866076	+	0.499913i	$0.166635\pi$
$608$	2.83772e139	0.0734243
$609$	0	0
$610$	5.38522e140	1.18045
$611$	4.95304e140	0.999518
$612$	0	0
$613$	−9.19299e140	−1.57291	−0.786453	−	0.617650i	$-0.788085\pi$
$613$	−9.19299e140	−1.57291	−0.786453	+	0.617650i	$0.788085\pi$
$614$	1.12689e141	1.77574
$615$	0	0
$616$	6.35751e140	0.850082
$617$	1.54803e140	0.190712	0.0953560	−	0.995443i	$-0.469601\pi$
$617$	1.54803e140	0.190712	0.0953560	+	0.995443i	$0.469601\pi$
$618$	0	0
$619$	5.82380e140	0.609297	0.304648	−	0.952465i	$-0.401461\pi$
$619$	5.82380e140	0.609297	0.304648	+	0.952465i	$0.401461\pi$
$620$	5.72768e140	0.552330
$621$	0	0
$622$	−7.35228e139	−0.0602570
$623$	1.43839e141	1.08700
$624$	0	0
$625$	1.56753e141	1.00757
$626$	1.72831e141	1.02475
$627$	0	0
$628$	2.74224e140	0.138402
$629$	2.01901e141	0.940331
$630$	0	0
$631$	2.40604e141	0.954597	0.477298	−	0.878741i	$-0.341616\pi$
$631$	2.40604e141	0.954597	0.477298	+	0.878741i	$0.341616\pi$
$632$	1.16741e141	0.427575
$633$	0	0
$634$	−3.36272e140	−0.104998
$635$	4.79137e141	1.38161
$636$	0	0
$637$	1.88565e141	0.463896
$638$	−3.21304e141	−0.730251
$639$	0	0
$640$	1.07322e142	2.08258
$641$	−8.62217e140	−0.154627	−0.0773136	−	0.997007i	$-0.524634\pi$
$641$	−8.62217e140	−0.154627	−0.0773136	+	0.997007i	$0.524634\pi$
$642$	0	0
$643$	−4.65858e141	−0.713838	−0.356919	−	0.934135i	$-0.616173\pi$
$643$	−4.65858e141	−0.713838	−0.356919	+	0.934135i	$0.616173\pi$
$644$	−1.09124e141	−0.154591
$645$	0	0
$646$	−1.14718e141	−0.138960
$647$	1.01951e142	1.14216	0.571078	−	0.820896i	$-0.306526\pi$
$647$	1.01951e142	1.14216	0.571078	+	0.820896i	$0.306526\pi$
$648$	0	0
$649$	8.15393e141	0.781645
$650$	4.32223e142	3.83340
$651$	0	0
$652$	5.72274e141	0.434611
$653$	6.34673e141	0.446102	0.223051	−	0.974807i	$-0.428398\pi$
$653$	6.34673e141	0.446102	0.223051	+	0.974807i	$0.428398\pi$
$654$	0	0
$655$	3.36546e142	2.02702
$656$	4.73473e141	0.264029
$657$	0	0
$658$	−1.51417e142	−0.724049
$659$	−2.68625e142	−1.18969	−0.594844	−	0.803841i	$-0.702786\pi$
$659$	−2.68625e142	−1.18969	−0.594844	+	0.803841i	$0.702786\pi$
$660$	0	0
$661$	−1.00522e142	−0.382021	−0.191010	−	0.981588i	$-0.561176\pi$
$661$	−1.00522e142	−0.382021	−0.191010	+	0.981588i	$0.561176\pi$
$662$	−3.44760e142	−1.21392
$663$	0	0
$664$	−2.83762e141	−0.0857959
$665$	1.12780e142	0.316038
$666$	0	0
$667$	−1.83548e142	−0.441973
$668$	1.28338e141	0.0286513
$669$	0	0
$670$	−1.95506e143	−3.75304
$671$	3.05048e142	0.543101
$672$	0	0
$673$	8.39160e142	1.28554	0.642768	−	0.766061i	$-0.277786\pi$
$673$	8.39160e142	1.28554	0.642768	+	0.766061i	$0.277786\pi$
$674$	−2.88550e141	−0.0410106
$675$	0	0
$676$	3.73211e142	0.456716
$677$	1.31642e143	1.49509	0.747546	−	0.664210i	$-0.231232\pi$
$677$	1.31642e143	1.49509	0.747546	+	0.664210i	$0.231232\pi$
$678$	0	0
$679$	−7.16781e142	−0.701396
$680$	−1.25877e143	−1.14353
$681$	0	0
$682$	1.72869e143	1.35396
$683$	1.72479e143	1.25456	0.627278	−	0.778795i	$-0.284169\pi$
$683$	1.72479e143	1.25456	0.627278	+	0.778795i	$0.284169\pi$
$684$	0	0
$685$	1.46646e143	0.920232
$686$	1.56749e143	0.913772
$687$	0	0
$688$	1.24956e143	0.628842
$689$	−2.86854e143	−1.34150
$690$	0	0
$691$	−2.96283e143	−1.19692	−0.598461	−	0.801152i	$-0.704221\pi$
$691$	−2.96283e143	−1.19692	−0.598461	+	0.801152i	$0.704221\pi$
$692$	7.06565e142	0.265335
$693$	0	0
$694$	4.18599e143	1.35877
$695$	−5.75720e142	−0.173772
$696$	0	0
$697$	−6.64280e142	−0.173419
$698$	−1.24358e142	−0.0301978
$699$	0	0
$700$	−2.47992e143	−0.521178
$701$	−6.60750e143	−1.29204	−0.646022	−	0.763319i	$-0.723568\pi$
$701$	−6.60750e143	−1.29204	−0.646022	+	0.763319i	$0.723568\pi$
$702$	0	0
$703$	−1.16237e143	−0.196835
$704$	3.78556e143	0.596637
$705$	0	0
$706$	−4.05066e143	−0.553208
$707$	1.79309e143	0.227993
$708$	0	0
$709$	−1.19409e144	−1.31644	−0.658221	−	0.752825i	$-0.728691\pi$
$709$	−1.19409e144	−1.31644	−0.658221	+	0.752825i	$0.728691\pi$
$710$	−1.18526e144	−1.21693
$711$	0	0
$712$	9.24267e143	0.823299
$713$	9.87535e143	0.819467
$714$	0	0
$715$	3.67098e144	2.64440
$716$	−4.48821e143	−0.301277
$717$	0	0
$718$	1.03495e144	0.603438
$719$	1.73333e143	0.0942047	0.0471023	−	0.998890i	$-0.485001\pi$
$719$	1.73333e143	0.0942047	0.0471023	+	0.998890i	$0.485001\pi$
$720$	0	0
$721$	−1.83844e144	−0.868397
$722$	−2.45317e144	−1.08044
$723$	0	0
$724$	3.11338e143	0.119243
$725$	−4.17126e144	−1.49004
$726$	0	0
$727$	−5.44264e144	−1.69169	−0.845847	−	0.533425i	$-0.820905\pi$
$727$	−5.44264e144	−1.69169	−0.845847	+	0.533425i	$0.820905\pi$
$728$	5.71809e144	1.65812
$729$	0	0
$730$	−8.07200e144	−2.03787
$731$	−1.75313e144	−0.413034
$732$	0	0
$733$	3.16959e144	0.650508	0.325254	−	0.945627i	$-0.394550\pi$
$733$	3.16959e144	0.650508	0.325254	+	0.945627i	$0.394550\pi$
$734$	−6.72396e144	−1.28817
$735$	0	0
$736$	−1.61309e144	−0.269357
$737$	−1.10745e145	−1.72670
$738$	0	0
$739$	−3.13110e144	−0.425748	−0.212874	−	0.977080i	$-0.568282\pi$
$739$	−3.13110e144	−0.425748	−0.212874	+	0.977080i	$0.568282\pi$
$740$	3.83230e144	0.486696
$741$	0	0
$742$	8.76929e144	0.971779
$743$	−5.48983e144	−0.568361	−0.284180	−	0.958771i	$-0.591721\pi$
$743$	−5.48983e144	−0.568361	−0.284180	+	0.958771i	$0.591721\pi$
$744$	0	0
$745$	−2.49869e145	−2.25850
$746$	−7.24299e144	−0.611797
$747$	0	0
$748$	2.14245e144	0.158081
$749$	−2.89131e145	−1.99417
$750$	0	0
$751$	−1.26915e145	−0.765061	−0.382531	−	0.923943i	$-0.624947\pi$
$751$	−1.26915e145	−0.765061	−0.382531	+	0.923943i	$0.624947\pi$
$752$	−1.21044e145	−0.682248
$753$	0	0
$754$	−2.88988e145	−1.42439
$755$	9.27760e144	0.427676
$756$	0	0
$757$	−4.29701e144	−0.173310	−0.0866552	−	0.996238i	$-0.527618\pi$
$757$	−4.29701e144	−0.173310	−0.0866552	+	0.996238i	$0.527618\pi$
$758$	−2.99949e145	−1.13176
$759$	0	0
$760$	7.24691e144	0.239368
$761$	4.62573e145	1.42973	0.714866	−	0.699261i	$-0.246488\pi$
$761$	4.62573e145	1.42973	0.714866	+	0.699261i	$0.246488\pi$
$762$	0	0
$763$	−5.48511e144	−0.148490
$764$	−4.85356e143	−0.0122983
$765$	0	0
$766$	4.93883e145	1.09666
$767$	7.33383e145	1.52463
$768$	0	0
$769$	5.22254e145	0.951922	0.475961	−	0.879466i	$-0.342100\pi$
$769$	5.22254e145	0.951922	0.475961	+	0.879466i	$0.342100\pi$
$770$	−1.12224e146	−1.91560
$771$	0	0
$772$	1.78782e144	0.0267701
$773$	−1.02627e145	−0.143945	−0.0719725	−	0.997407i	$-0.522929\pi$
$773$	−1.02627e145	−0.143945	−0.0719725	+	0.997407i	$0.522929\pi$
$774$	0	0
$775$	2.24424e146	2.76270
$776$	−4.60583e145	−0.531240
$777$	0	0
$778$	−1.80292e146	−1.82603
$779$	3.82435e144	0.0363008
$780$	0	0
$781$	−6.71394e145	−0.559887
$782$	6.52108e145	0.509775
$783$	0	0
$784$	−4.60823e145	−0.316645
$785$	1.61103e146	1.03797
$786$	0	0
$787$	4.14033e145	0.234591	0.117296	−	0.993097i	$-0.462578\pi$
$787$	4.14033e145	0.234591	0.117296	+	0.993097i	$0.462578\pi$
$788$	2.92235e145	0.155295
$789$	0	0
$790$	−2.06074e146	−0.963508
$791$	2.06916e146	0.907575
$792$	0	0
$793$	2.74367e146	1.05934
$794$	4.27158e146	1.54758
$795$	0	0
$796$	1.10071e146	0.351206
$797$	−5.59586e146	−1.67580	−0.837899	−	0.545825i	$-0.816216\pi$
$797$	−5.59586e146	−1.67580	−0.837899	+	0.545825i	$0.816216\pi$
$798$	0	0
$799$	1.69824e146	0.448113
$800$	−3.66585e146	−0.908093
$801$	0	0
$802$	5.40243e146	1.17973
$803$	−4.57241e146	−0.937585
$804$	0	0
$805$	−6.41091e146	−1.15939
$806$	1.55483e147	2.64097
$807$	0	0
$808$	1.15219e146	0.172683
$809$	−4.55725e146	−0.641657	−0.320828	−	0.947137i	$-0.603961\pi$
$809$	−4.55725e146	−0.641657	−0.320828	+	0.947137i	$0.603961\pi$
$810$	0	0
$811$	2.45816e146	0.305532	0.152766	−	0.988262i	$-0.451182\pi$
$811$	2.45816e146	0.305532	0.152766	+	0.988262i	$0.451182\pi$
$812$	1.65809e146	0.193655
$813$	0	0
$814$	1.15664e147	1.19307
$815$	3.36204e147	3.25945
$816$	0	0
$817$	1.00930e146	0.0864583
$818$	5.10512e146	0.411116
$819$	0	0
$820$	−1.26087e146	−0.0897579
$821$	−7.99047e146	−0.534863	−0.267432	−	0.963577i	$-0.586175\pi$
$821$	−7.99047e146	−0.534863	−0.267432	+	0.963577i	$0.586175\pi$
$822$	0	0
$823$	−3.10849e147	−1.84017	−0.920084	−	0.391721i	$-0.871880\pi$
$823$	−3.10849e147	−1.84017	−0.920084	+	0.391721i	$0.871880\pi$
$824$	−1.18133e147	−0.657727
$825$	0	0
$826$	−2.24199e147	−1.10444
$827$	−2.11410e147	−0.979709	−0.489854	−	0.871804i	$-0.662950\pi$
$827$	−2.11410e147	−0.979709	−0.489854	+	0.871804i	$0.662950\pi$
$828$	0	0
$829$	−1.42947e147	−0.586370	−0.293185	−	0.956056i	$-0.594715\pi$
$829$	−1.42947e147	−0.586370	−0.293185	+	0.956056i	$0.594715\pi$
$830$	5.00903e146	0.193335
$831$	0	0
$832$	3.40482e147	1.16377
$833$	6.46532e146	0.207978
$834$	0	0
$835$	7.53972e146	0.214876
$836$	−1.23344e146	−0.0330902
$837$	0	0
$838$	7.24784e147	1.72340
$839$	−1.47014e145	−0.00329138	−0.00164569	−	0.999999i	$-0.500524\pi$
$839$	−1.47014e145	−0.00329138	−0.00164569	+	0.999999i	$0.500524\pi$
$840$	0	0
$841$	−2.24836e147	−0.446342
$842$	1.63148e147	0.305016
$843$	0	0
$844$	−8.05994e146	−0.133671
$845$	2.19257e148	3.42523
$846$	0	0
$847$	1.76800e147	0.245116
$848$	7.01023e147	0.915676
$849$	0	0
$850$	1.48196e148	1.71862
$851$	6.60743e147	0.722088
$852$	0	0
$853$	8.51957e147	0.826974	0.413487	−	0.910510i	$-0.364311\pi$
$853$	8.51957e147	0.826974	0.413487	+	0.910510i	$0.364311\pi$
$854$	−8.38757e147	−0.767385
$855$	0	0
$856$	−1.85787e148	−1.51039
$857$	−2.41123e148	−1.84802	−0.924010	−	0.382368i	$-0.875109\pi$
$857$	−2.41123e148	−1.84802	−0.924010	+	0.382368i	$0.875109\pi$
$858$	0	0
$859$	1.06941e148	0.728601	0.364300	−	0.931282i	$-0.381308\pi$
$859$	1.06941e148	0.728601	0.364300	+	0.931282i	$0.381308\pi$
$860$	−3.32762e147	−0.213778
$861$	0	0
$862$	7.86270e147	0.449216
$863$	2.26991e147	0.122310	0.0611552	−	0.998128i	$-0.480522\pi$
$863$	2.26991e147	0.122310	0.0611552	+	0.998128i	$0.480522\pi$
$864$	0	0
$865$	4.15098e148	1.98993
$866$	1.99533e148	0.902323
$867$	0	0
$868$	−8.92095e147	−0.359058
$869$	−1.16731e148	−0.443291
$870$	0	0
$871$	−9.96069e148	−3.36800
$872$	−3.52457e147	−0.112467
$873$	0	0
$874$	−3.75428e147	−0.106708
$875$	−7.29378e148	−1.95680
$876$	0	0
$877$	3.37030e148	0.805728	0.402864	−	0.915260i	$-0.368015\pi$
$877$	3.37030e148	0.805728	0.402864	+	0.915260i	$0.368015\pi$
$878$	−1.56173e146	−0.00352478
$879$	0	0
$880$	−8.97126e148	−1.80501
$881$	7.25925e148	1.37914	0.689570	−	0.724219i	$-0.257799\pi$
$881$	7.25925e148	1.37914	0.689570	+	0.724219i	$0.257799\pi$
$882$	0	0
$883$	9.12520e148	1.54606	0.773031	−	0.634368i	$-0.218740\pi$
$883$	9.12520e148	1.54606	0.773031	+	0.634368i	$0.218740\pi$
$884$	1.92697e148	0.308344
$885$	0	0
$886$	2.10689e148	0.300773
$887$	−5.96302e148	−0.804124	−0.402062	−	0.915612i	$-0.631706\pi$
$887$	−5.96302e148	−0.804124	−0.402062	+	0.915612i	$0.631706\pi$
$888$	0	0
$889$	−7.46262e148	−0.898158
$890$	−1.63153e149	−1.85524
$891$	0	0
$892$	3.55885e148	0.361314
$893$	−9.77701e147	−0.0938010
$894$	0	0
$895$	−2.63677e149	−2.25948
$896$	−1.67156e149	−1.35384
$897$	0	0
$898$	6.99822e148	0.506446
$899$	−1.50052e149	−1.02654
$900$	0	0
$901$	−9.83532e148	−0.601432
$902$	−3.80550e148	−0.220030
$903$	0	0
$904$	1.32958e149	0.687401
$905$	1.82907e149	0.894289
$906$	0	0
$907$	2.15967e149	0.944540	0.472270	−	0.881454i	$-0.343435\pi$
$907$	2.15967e149	0.944540	0.472270	+	0.881454i	$0.343435\pi$
$908$	−9.45049e148	−0.390948
$909$	0	0
$910$	−1.00937e150	−3.73645
$911$	3.54148e149	1.24024	0.620121	−	0.784506i	$-0.287084\pi$
$911$	3.54148e149	1.24024	0.620121	+	0.784506i	$0.287084\pi$
$912$	0	0
$913$	2.83738e148	0.0889495
$914$	−2.39168e149	−0.709446
$915$	0	0
$916$	−4.21618e148	−0.111995
$917$	−5.24175e149	−1.31773
$918$	0	0
$919$	−3.46818e149	−0.781032	−0.390516	−	0.920596i	$-0.627703\pi$
$919$	−3.46818e149	−0.781032	−0.390516	+	0.920596i	$0.627703\pi$
$920$	−4.11947e149	−0.878123
$921$	0	0
$922$	1.21318e149	0.231747
$923$	−6.03867e149	−1.09208
$924$	0	0
$925$	1.50158e150	2.43440
$926$	4.45372e149	0.683704
$927$	0	0
$928$	2.45102e149	0.337422
$929$	1.59274e149	0.207659	0.103829	−	0.994595i	$-0.466890\pi$
$929$	1.59274e149	0.207659	0.103829	+	0.994595i	$0.466890\pi$
$930$	0	0
$931$	−3.72217e148	−0.0435349
$932$	−8.55695e148	−0.0948015
$933$	0	0
$934$	1.16638e150	1.15964
$935$	1.25866e150	1.18556
$936$	0	0
$937$	9.70291e149	0.820451	0.410226	−	0.911984i	$-0.365450\pi$
$937$	9.70291e149	0.820451	0.410226	+	0.911984i	$0.365450\pi$
$938$	3.04504e150	2.43977
$939$	0	0
$940$	3.22344e149	0.231934
$941$	−2.18073e149	−0.148705	−0.0743526	−	0.997232i	$-0.523689\pi$
$941$	−2.18073e149	−0.148705	−0.0743526	+	0.997232i	$0.523689\pi$
$942$	0	0
$943$	−2.17393e149	−0.133170
$944$	−1.79227e150	−1.04068
$945$	0	0
$946$	−1.00432e150	−0.524048
$947$	−2.56888e150	−1.27078	−0.635389	−	0.772192i	$-0.719160\pi$
$947$	−2.56888e150	−1.27078	−0.635389	+	0.772192i	$0.719160\pi$
$948$	0	0
$949$	−4.11254e150	−1.82880
$950$	−8.53184e149	−0.359750
$951$	0	0
$952$	1.96055e150	0.743383
$953$	4.47909e150	1.61064	0.805319	−	0.592842i	$-0.201994\pi$
$953$	4.47909e150	1.61064	0.805319	+	0.592842i	$0.201994\pi$
$954$	0	0
$955$	−2.85141e149	−0.0922337
$956$	−4.35235e149	−0.133537
$957$	0	0
$958$	2.63699e150	0.728033
$959$	−2.28404e150	−0.598224
$960$	0	0
$961$	3.83154e150	0.903322
$962$	1.04031e151	2.32714
$963$	0	0
$964$	−1.48461e150	−0.299036
$965$	1.05032e150	0.200768
$966$	0	0
$967$	−1.06296e151	−1.83012	−0.915060	−	0.403318i	$-0.867857\pi$
$967$	−1.06296e151	−1.83012	−0.915060	+	0.403318i	$0.867857\pi$
$968$	1.13607e150	0.185652
$969$	0	0
$970$	8.13030e150	1.19711
$971$	−2.05230e150	−0.286860	−0.143430	−	0.989660i	$-0.545813\pi$
$971$	−2.05230e150	−0.286860	−0.143430	+	0.989660i	$0.545813\pi$
$972$	0	0
$973$	8.96693e149	0.112965
$974$	2.93074e150	0.350550
$975$	0	0
$976$	−6.70508e150	−0.723083
$977$	1.45556e150	0.149058	0.0745289	−	0.997219i	$-0.476255\pi$
$977$	1.45556e150	0.149058	0.0745289	+	0.997219i	$0.476255\pi$
$978$	0	0
$979$	−9.24188e150	−0.853561
$980$	1.22719e150	0.107645
$981$	0	0
$982$	8.97394e150	0.710155
$983$	6.44594e150	0.484545	0.242272	−	0.970208i	$-0.422107\pi$
$983$	6.44594e150	0.484545	0.242272	+	0.970208i	$0.422107\pi$
$984$	0	0
$985$	1.71685e151	1.16467
$986$	−9.90851e150	−0.638593
$987$	0	0
$988$	−1.10938e150	−0.0645439
$989$	−5.73731e150	−0.317172
$990$	0	0
$991$	1.69874e151	0.848024	0.424012	−	0.905656i	$-0.360621\pi$
$991$	1.69874e151	0.848024	0.424012	+	0.905656i	$0.360621\pi$
$992$	−1.31871e151	−0.625618
$993$	0	0
$994$	1.84606e151	0.791103
$995$	6.46652e151	2.63394
$996$	0	0
$997$	−9.31202e150	−0.342719	−0.171360	−	0.985209i	$-0.554816\pi$
$997$	−9.31202e150	−0.342719	−0.171360	+	0.985209i	$0.554816\pi$
$998$	5.74712e151	2.01075
$999$	0	0

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 102 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q+1.76666e15 q^{2} +5.85773e29 q^{4} +3.44135e35 q^{5} -5.35995e42 q^{7} -3.44415e45 q^{8} +O(q^{10})\)	\(q+1.76666e15 q^{2} +5.85773e29 q^{4} +3.44135e35 q^{5} -5.35995e42 q^{7} -3.44415e45 q^{8} +6.07967e50 q^{10} +3.44385e52 q^{11} +3.09748e56 q^{13} -9.46918e57 q^{14} -7.56973e60 q^{16} +1.06203e62 q^{17} -6.11425e63 q^{19} +2.01585e65 q^{20} +6.08410e67 q^{22} +3.47561e68 q^{23} +7.89855e70 q^{25} +5.47219e71 q^{26} -3.13971e72 q^{28} -5.28104e73 q^{29} +2.84133e75 q^{31} -4.64116e75 q^{32} +1.87624e77 q^{34} -1.84454e78 q^{35} +1.90109e79 q^{37} -1.08018e79 q^{38} -1.18525e81 q^{40} -6.25482e80 q^{41} -1.65073e82 q^{43} +2.01731e82 q^{44} +6.14021e83 q^{46} +1.59905e84 q^{47} +6.08770e84 q^{49} +1.39540e86 q^{50} +1.81442e86 q^{52} -9.26087e86 q^{53} +1.18515e88 q^{55} +1.84604e88 q^{56} -9.32978e88 q^{58} +2.36767e89 q^{59} +8.85775e89 q^{61} +5.01965e90 q^{62} +1.09922e91 q^{64} +1.06595e92 q^{65} -3.21574e92 q^{67} +6.22108e91 q^{68} -3.25867e93 q^{70} -1.94954e93 q^{71} -1.32770e94 q^{73} +3.35857e94 q^{74} -3.58156e93 q^{76} -1.84589e95 q^{77} -3.38956e95 q^{79} -2.60501e96 q^{80} -1.10501e96 q^{82} +8.23897e95 q^{83} +3.65481e97 q^{85} -2.91628e97 q^{86} -1.18611e98 q^{88} -2.68359e98 q^{89} -1.66023e99 q^{91} +2.03592e98 q^{92} +2.82498e99 q^{94} -2.10412e99 q^{95} +1.33729e100 q^{97} +1.07549e100 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 434989091795040 q^{2} + 90\!\cdots\!96 q^{4}+ \cdots + 61\!\cdots\!20 q^{8}+O(q^{10}) \) 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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