LMFDB - Embedded newform 9.102.a.b.1.2

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			1.2
Root			$-2.32579e13$ 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)

$f(q)$	$=$	$q-2.17839e15 q^{2} +2.21006e30 q^{4} +2.56275e35 q^{5} +8.01618e42 q^{7} +7.08493e44 q^{8} +O(q^{10})$	\(q-2.17839e15 q^{2} +2.21006e30 q^{4} +2.56275e35 q^{5} +8.01618e42 q^{7} +7.08493e44 q^{8} -5.58265e50 q^{10} +9.55916e51 q^{11} +4.33831e54 q^{13} -1.74623e58 q^{14} -7.14655e60 q^{16} +7.76807e61 q^{17} +3.75637e64 q^{19} +5.66383e65 q^{20} -2.08235e67 q^{22} +1.01843e69 q^{23} +2.62336e70 q^{25} -9.45051e69 q^{26} +1.77163e73 q^{28} +3.74489e73 q^{29} -5.68206e74 q^{31} +1.37717e76 q^{32} -1.69219e77 q^{34} +2.05434e78 q^{35} -2.65734e79 q^{37} -8.18283e79 q^{38} +1.81569e80 q^{40} -3.81887e81 q^{41} -3.91159e82 q^{43} +2.11263e82 q^{44} -2.21854e84 q^{46} -2.04333e83 q^{47} +4.16178e85 q^{49} -5.71470e85 q^{50} +9.58794e84 q^{52} +5.06337e86 q^{53} +2.44977e87 q^{55} +5.67941e87 q^{56} -8.15782e88 q^{58} -5.27773e89 q^{59} -2.08484e90 q^{61} +1.23777e90 q^{62} -1.18814e91 q^{64} +1.11180e90 q^{65} -4.63082e91 q^{67} +1.71679e92 q^{68} -4.47515e93 q^{70} +3.91885e93 q^{71} +1.42179e94 q^{73} +5.78872e94 q^{74} +8.30182e94 q^{76} +7.66279e94 q^{77} -5.87787e95 q^{79} -1.83148e96 q^{80} +8.31898e96 q^{82} -6.23585e96 q^{83} +1.99076e97 q^{85} +8.52096e97 q^{86} +6.77260e96 q^{88} +4.22602e98 q^{89} +3.47767e97 q^{91} +2.25080e99 q^{92} +4.45116e98 q^{94} +9.62663e99 q^{95} +1.04471e100 q^{97} -9.06597e100 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.17839e15	−1.36811	−0.684053	−	0.729432i	$-0.739785\pi$
$2$	−2.17839e15	−1.36811	−0.684053	+	0.729432i	$0.739785\pi$
$3$	0	0
$3$	0	0
$4$	2.21006e30	0.871716
$5$	2.56275e35	1.29039	0.645194	−	0.764019i	$-0.276776\pi$
$5$	2.56275e35	1.29039	0.645194	+	0.764019i	$0.276776\pi$
$6$	0	0
$7$	8.01618e42	1.68468	0.842338	−	0.538949i	$-0.181179\pi$
$7$	8.01618e42	1.68468	0.842338	+	0.538949i	$0.181179\pi$
$8$	7.08493e44	0.175506
$9$	0	0
$10$	−5.58265e50	−1.76539
$11$	9.55916e51	0.245521	0.122761	−	0.992436i	$-0.460825\pi$
$11$	9.55916e51	0.245521	0.122761	+	0.992436i	$0.460825\pi$
$12$	0	0
$13$	4.33831e54	0.0241647	0.0120823	−	0.999927i	$-0.496154\pi$
$13$	4.33831e54	0.0241647	0.0120823	+	0.999927i	$0.496154\pi$
$14$	−1.74623e58	−2.30482
$15$	0	0
$16$	−7.14655e60	−1.11183
$17$	7.76807e61	0.565773	0.282887	−	0.959153i	$-0.408708\pi$
$17$	7.76807e61	0.565773	0.282887	+	0.959153i	$0.408708\pi$
$18$	0	0
$19$	3.75637e64	0.994745	0.497372	−	0.867537i	$-0.334298\pi$
$19$	3.75637e64	0.994745	0.497372	+	0.867537i	$0.334298\pi$
$20$	5.66383e65	1.12485
$21$	0	0
$22$	−2.08235e67	−0.335899
$23$	1.01843e69	1.74051	0.870254	−	0.492604i	$-0.163955\pi$
$23$	1.01843e69	1.74051	0.870254	+	0.492604i	$0.163955\pi$
$24$	0	0
$25$	2.62336e70	0.665102
$26$	−9.45051e69	−0.0330599
$27$	0	0
$28$	1.77163e73	1.46856
$29$	3.74489e73	0.527643	0.263822	−	0.964571i	$-0.415017\pi$
$29$	3.74489e73	0.527643	0.263822	+	0.964571i	$0.415017\pi$
$30$	0	0
$31$	−5.68206e74	−0.275893	−0.137946	−	0.990440i	$-0.544050\pi$
$31$	−5.68206e74	−0.275893	−0.137946	+	0.990440i	$0.544050\pi$
$32$	1.37717e76	1.34559
$33$	0	0
$34$	−1.69219e77	−0.774038
$35$	2.05434e78	2.17389
$36$	0	0
$37$	−2.65734e79	−1.69926	−0.849632	−	0.527377i	$-0.823176\pi$
$37$	−2.65734e79	−1.69926	−0.849632	+	0.527377i	$0.823176\pi$
$38$	−8.18283e79	−1.36092
$39$	0	0
$40$	1.81569e80	0.226471
$41$	−3.81887e81	−1.36883	−0.684417	−	0.729091i	$-0.739943\pi$
$41$	−3.81887e81	−1.36883	−0.684417	+	0.729091i	$0.739943\pi$
$42$	0	0
$43$	−3.91159e82	−1.26531	−0.632654	−	0.774434i	$-0.718035\pi$
$43$	−3.91159e82	−1.26531	−0.632654	+	0.774434i	$0.718035\pi$
$44$	2.11263e82	0.214025
$45$	0	0
$46$	−2.21854e84	−2.38120
$47$	−2.04333e83	−0.0740281	−0.0370140	−	0.999315i	$-0.511785\pi$
$47$	−2.04333e83	−0.0740281	−0.0370140	+	0.999315i	$0.511785\pi$
$48$	0	0
$49$	4.16178e85	1.83814
$50$	−5.71470e85	−0.909931
$51$	0	0
$52$	9.58794e84	0.0210648
$53$	5.06337e86	0.425116	0.212558	−	0.977148i	$-0.431820\pi$
$53$	5.06337e86	0.425116	0.212558	+	0.977148i	$0.431820\pi$
$54$	0	0
$55$	2.44977e87	0.316818
$56$	5.67941e87	0.295670
$57$	0	0
$58$	−8.15782e88	−0.721873
$59$	−5.27773e89	−1.96979	−0.984897	−	0.173141i	$-0.944608\pi$
$59$	−5.27773e89	−1.96979	−0.984897	+	0.173141i	$0.944608\pi$
$60$	0	0
$61$	−2.08484e90	−1.44516	−0.722581	−	0.691286i	$-0.757045\pi$
$61$	−2.08484e90	−1.44516	−0.722581	+	0.691286i	$0.757045\pi$
$62$	1.23777e90	0.377451
$63$	0	0
$64$	−1.18814e91	−0.729087
$65$	1.11180e90	0.0311818
$66$	0	0
$67$	−4.63082e91	−0.281113	−0.140556	−	0.990073i	$-0.544889\pi$
$67$	−4.63082e91	−0.281113	−0.140556	+	0.990073i	$0.544889\pi$
$68$	1.71679e92	0.493194
$69$	0	0
$70$	−4.47515e93	−2.97411
$71$	3.91885e93	1.27237	0.636183	−	0.771538i	$-0.280512\pi$
$71$	3.91885e93	1.27237	0.636183	+	0.771538i	$0.280512\pi$
$72$	0	0
$73$	1.42179e94	1.13509	0.567546	−	0.823341i	$-0.307893\pi$
$73$	1.42179e94	1.13509	0.567546	+	0.823341i	$0.307893\pi$
$74$	5.78872e94	2.32477
$75$	0	0
$76$	8.30182e94	0.867135
$77$	7.66279e94	0.413624
$78$	0	0
$79$	−5.87787e95	−0.869064	−0.434532	−	0.900656i	$-0.643086\pi$
$79$	−5.87787e95	−0.869064	−0.434532	+	0.900656i	$0.643086\pi$
$80$	−1.83148e96	−1.43469
$81$	0	0
$82$	8.31898e96	1.87271
$83$	−6.23585e96	−0.761118	−0.380559	−	0.924757i	$-0.624268\pi$
$83$	−6.23585e96	−0.761118	−0.380559	+	0.924757i	$0.624268\pi$
$84$	0	0
$85$	1.99076e97	0.730067
$86$	8.52096e97	1.73108
$87$	0	0
$88$	6.77260e96	0.0430904
$89$	4.22602e98	1.51963	0.759813	−	0.650142i	$-0.225291\pi$
$89$	4.22602e98	1.51963	0.759813	+	0.650142i	$0.225291\pi$
$90$	0	0
$91$	3.47767e97	0.0407097
$92$	2.25080e99	1.51723
$93$	0	0
$94$	4.45116e98	0.101278
$95$	9.62663e99	1.28361
$96$	0	0
$97$	1.04471e100	0.486432	0.243216	−	0.969972i	$-0.421798\pi$
$97$	1.04471e100	0.486432	0.243216	+	0.969972i	$0.421798\pi$
$98$	−9.06597e100	−2.51477
$99$	0	0
$100$	5.79780e100	0.579780
$101$	−1.04695e101	−0.633425	−0.316713	−	0.948522i	$-0.602579\pi$
$101$	−1.04695e101	−0.633425	−0.316713	+	0.948522i	$0.602579\pi$
$102$	0	0
$103$	2.23897e101	0.503232	0.251616	−	0.967827i	$-0.419038\pi$
$103$	2.23897e101	0.503232	0.251616	+	0.967827i	$0.419038\pi$
$104$	3.07366e99	0.00424104
$105$	0	0
$106$	−1.10300e102	−0.581605
$107$	−5.38178e101	−0.176622	−0.0883111	−	0.996093i	$-0.528147\pi$
$107$	−5.38178e101	−0.176622	−0.0883111	+	0.996093i	$0.528147\pi$
$108$	0	0
$109$	6.37162e102	0.820752	0.410376	−	0.911916i	$-0.365397\pi$
$109$	6.37162e102	0.820752	0.410376	+	0.911916i	$0.365397\pi$
$110$	−5.33654e102	−0.433440
$111$	0	0
$112$	−5.72880e103	−1.87307
$113$	4.48141e102	0.0935305	0.0467653	−	0.998906i	$-0.485109\pi$
$113$	4.48141e102	0.0935305	0.0467653	+	0.998906i	$0.485109\pi$
$114$	0	0
$115$	2.60998e104	2.24593
$116$	8.27645e103	0.459955
$117$	0	0
$118$	1.14969e105	2.69489
$119$	6.22703e104	0.953145
$120$	0	0
$121$	−1.42449e105	−0.939719
$122$	4.54159e105	1.97714
$123$	0	0
$124$	−1.25577e105	−0.240500
$125$	−3.38523e105	−0.432148
$126$	0	0
$127$	1.89098e106	1.08293	0.541463	−	0.840725i	$-0.317871\pi$
$127$	1.89098e106	1.08293	0.541463	+	0.840725i	$0.317871\pi$
$128$	−9.03309e105	−0.348123
$129$	0	0
$130$	−2.42193e105	−0.0426601
$131$	−1.48779e106	−0.177967	−0.0889836	−	0.996033i	$-0.528362\pi$
$131$	−1.48779e106	−0.177967	−0.0889836	+	0.996033i	$0.528362\pi$
$132$	0	0
$133$	3.01118e107	1.67582
$134$	1.00877e107	0.384592
$135$	0	0
$136$	5.50362e106	0.0992965
$137$	−2.05438e106	−0.0256031	−0.0128016	−	0.999918i	$-0.504075\pi$
$137$	−2.05438e106	−0.0256031	−0.0128016	+	0.999918i	$0.504075\pi$
$138$	0	0
$139$	1.46512e108	0.878265	0.439133	−	0.898422i	$-0.355286\pi$
$139$	1.46512e108	0.878265	0.439133	+	0.898422i	$0.355286\pi$
$140$	4.54023e108	1.89501
$141$	0	0
$142$	−8.53677e108	−1.74073
$143$	4.14706e106	0.00593294
$144$	0	0
$145$	9.59721e108	0.680865
$146$	−3.09721e109	−1.55293
$147$	0	0
$148$	−5.87290e109	−1.48128
$149$	4.96513e109	0.891300	0.445650	−	0.895207i	$-0.352973\pi$
$149$	4.96513e109	0.891300	0.445650	+	0.895207i	$0.352973\pi$
$150$	0	0
$151$	1.14116e110	1.04474	0.522372	−	0.852717i	$-0.325047\pi$
$151$	1.14116e110	1.04474	0.522372	+	0.852717i	$0.325047\pi$
$152$	2.66136e109	0.174583
$153$	0	0
$154$	−1.66925e110	−0.565882
$155$	−1.45617e110	−0.356009
$156$	0	0
$157$	−7.80595e110	−0.998834	−0.499417	−	0.866362i	$-0.666452\pi$
$157$	−7.80595e110	−0.998834	−0.499417	+	0.866362i	$0.666452\pi$
$158$	1.28043e111	1.18897
$159$	0	0
$160$	3.52934e111	1.73634
$161$	8.16393e111	2.93219
$162$	0	0
$163$	1.02381e112	1.97127	0.985636	−	0.168885i	$-0.0540167\pi$
$163$	1.02381e112	1.97127	0.985636	+	0.168885i	$0.0540167\pi$
$164$	−8.43995e111	−1.19323
$165$	0	0
$166$	1.35841e112	1.04129
$167$	9.04519e111	0.511960	0.255980	−	0.966682i	$-0.417602\pi$
$167$	9.04519e111	0.511960	0.255980	+	0.966682i	$0.417602\pi$
$168$	0	0
$169$	−3.22125e112	−0.999416
$170$	−4.33664e112	−0.998810
$171$	0	0
$172$	−8.64487e112	−1.10299
$173$	6.97539e112	0.664110	0.332055	−	0.943260i	$-0.392258\pi$
$173$	6.97539e112	0.664110	0.332055	+	0.943260i	$0.392258\pi$
$174$	0	0
$175$	2.10294e113	1.12048
$176$	−6.83150e112	−0.272977
$177$	0	0
$178$	−9.20591e113	−2.07901
$179$	4.15404e111	0.00706956	0.00353478	−	0.999994i	$-0.498875\pi$
$179$	4.15404e111	0.00706956	0.00353478	+	0.999994i	$0.498875\pi$
$180$	0	0
$181$	6.83567e113	0.663763	0.331882	−	0.943321i	$-0.392317\pi$
$181$	6.83567e113	0.663763	0.331882	+	0.943321i	$0.392317\pi$
$182$	−7.57570e112	−0.0556952
$183$	0	0
$184$	7.21551e113	0.305469
$185$	−6.81010e114	−2.19271
$186$	0	0
$187$	7.42562e113	0.138909
$188$	−4.51589e113	−0.0645315
$189$	0	0
$190$	−2.09705e115	−1.75611
$191$	6.49031e114	0.416946	0.208473	−	0.978028i	$-0.433151\pi$
$191$	6.49031e114	0.416946	0.208473	+	0.978028i	$0.433151\pi$
$192$	0	0
$193$	1.58395e115	0.601307	0.300654	−	0.953733i	$-0.402795\pi$
$193$	1.58395e115	0.601307	0.300654	+	0.953733i	$0.402795\pi$
$194$	−2.27578e115	−0.665491
$195$	0	0
$196$	9.19781e115	1.60233
$197$	4.98876e115	0.672122	0.336061	−	0.941840i	$-0.390905\pi$
$197$	4.98876e115	0.672122	0.336061	+	0.941840i	$0.390905\pi$
$198$	0	0
$199$	9.90704e115	0.801426	0.400713	−	0.916204i	$-0.368762\pi$
$199$	9.90704e115	0.801426	0.400713	+	0.916204i	$0.368762\pi$
$200$	1.85864e115	0.116729
$201$	0	0
$202$	2.28065e116	0.866593
$203$	3.00197e116	0.888909
$204$	0	0
$205$	−9.78681e116	−1.76633
$206$	−4.87734e116	−0.688475
$207$	0	0
$208$	−3.10039e115	−0.0268670
$209$	3.59077e116	0.244231
$210$	0	0
$211$	1.83494e117	0.771541	0.385770	−	0.922595i	$-0.373936\pi$
$211$	1.83494e117	0.771541	0.385770	+	0.922595i	$0.373936\pi$
$212$	1.11904e117	0.370581
$213$	0	0
$214$	1.17236e117	0.241638
$215$	−1.00244e118	−1.63274
$216$	0	0
$217$	−4.55485e117	−0.464790
$218$	−1.38799e118	−1.12288
$219$	0	0
$220$	5.41415e117	0.276175
$221$	3.37003e116	0.0136717
$222$	0	0
$223$	2.97933e118	0.766871	0.383436	−	0.923568i	$-0.374741\pi$
$223$	2.97933e118	0.766871	0.383436	+	0.923568i	$0.374741\pi$
$224$	1.10396e119	2.26689
$225$	0	0
$226$	−9.76224e117	−0.127960
$227$	7.51975e118	0.788674	0.394337	−	0.918966i	$-0.370974\pi$
$227$	7.51975e118	0.788674	0.394337	+	0.918966i	$0.370974\pi$
$228$	0	0
$229$	−2.60468e118	−0.175413	−0.0877067	−	0.996146i	$-0.527954\pi$
$229$	−2.60468e118	−0.175413	−0.0877067	+	0.996146i	$0.527954\pi$
$230$	−5.68554e119	−3.07267
$231$	0	0
$232$	2.65323e118	0.0926044
$233$	3.69783e119	1.03866	0.519330	−	0.854574i	$-0.326182\pi$
$233$	3.69783e119	1.03866	0.519330	+	0.854574i	$0.326182\pi$
$234$	0	0
$235$	−5.23653e118	−0.0955250
$236$	−1.16641e120	−1.71710
$237$	0	0
$238$	−1.35649e120	−1.30400
$239$	2.15076e119	0.167301	0.0836504	−	0.996495i	$-0.473342\pi$
$239$	2.15076e119	0.167301	0.0836504	+	0.996495i	$0.473342\pi$
$240$	0	0
$241$	2.22189e120	1.13465	0.567324	−	0.823495i	$-0.307979\pi$
$241$	2.22189e120	1.13465	0.567324	+	0.823495i	$0.307979\pi$
$242$	3.10309e120	1.28564
$243$	0	0
$244$	−4.60764e120	−1.25977
$245$	1.06656e121	2.37191
$246$	0	0
$247$	1.62963e119	0.0240377
$248$	−4.02570e119	−0.0484208
$249$	0	0
$250$	7.37434e120	0.591225
$251$	−8.35823e120	−0.547761	−0.273881	−	0.961764i	$-0.588307\pi$
$251$	−8.35823e120	−0.547761	−0.273881	+	0.961764i	$0.588307\pi$
$252$	0	0
$253$	9.73534e120	0.427331
$254$	−4.11928e121	−1.48156
$255$	0	0
$256$	4.98005e121	1.20536
$257$	1.29393e121	0.257210	0.128605	−	0.991696i	$-0.458950\pi$
$257$	1.29393e121	0.257210	0.128605	+	0.991696i	$0.458950\pi$
$258$	0	0
$259$	−2.13018e122	−2.86271
$260$	2.45715e120	0.0271817
$261$	0	0
$262$	3.24097e121	0.243478
$263$	1.95610e122	1.21235	0.606173	−	0.795333i	$-0.292704\pi$
$263$	1.95610e122	1.21235	0.606173	+	0.795333i	$0.292704\pi$
$264$	0	0
$265$	1.29761e122	0.548565
$266$	−6.55950e122	−2.29271
$267$	0	0
$268$	−1.02344e122	−0.245050
$269$	2.01646e122	0.400037	0.200018	−	0.979792i	$-0.435900\pi$
$269$	2.01646e122	0.400037	0.200018	+	0.979792i	$0.435900\pi$
$270$	0	0
$271$	−8.55915e122	−1.16810	−0.584052	−	0.811716i	$-0.698534\pi$
$271$	−8.55915e122	−1.16810	−0.584052	+	0.811716i	$0.698534\pi$
$272$	−5.55149e122	−0.629042
$273$	0	0
$274$	4.47524e121	0.0350278
$275$	2.50772e122	0.163297
$276$	0	0
$277$	2.86983e122	0.129607	0.0648035	−	0.997898i	$-0.479358\pi$
$277$	2.86983e122	0.129607	0.0648035	+	0.997898i	$0.479358\pi$
$278$	−3.19160e123	−1.20156
$279$	0	0
$280$	1.45549e123	0.381530
$281$	8.77608e123	1.92146	0.960730	−	0.277484i	$-0.0895005\pi$
$281$	8.77608e123	1.92146	0.960730	+	0.277484i	$0.0895005\pi$
$282$	0	0
$283$	−3.53849e123	−0.541506	−0.270753	−	0.962649i	$-0.587273\pi$
$283$	−3.53849e123	−0.541506	−0.270753	+	0.962649i	$0.587273\pi$
$284$	8.66091e123	1.10914
$285$	0	0
$286$	−9.03389e121	−0.00811690
$287$	−3.06128e124	−2.30604
$288$	0	0
$289$	−1.28170e124	−0.679900
$290$	−2.09064e124	−0.931496
$291$	0	0
$292$	3.14225e124	0.989479
$293$	3.24042e124	0.858592	0.429296	−	0.903164i	$-0.358762\pi$
$293$	3.24042e124	0.858592	0.429296	+	0.903164i	$0.358762\pi$
$294$	0	0
$295$	−1.35255e125	−2.54180
$296$	−1.88271e124	−0.298230
$297$	0	0
$298$	−1.08160e125	−1.21939
$299$	4.41827e123	0.0420588
$300$	0	0
$301$	−3.13560e125	−2.13164
$302$	−2.48588e125	−1.42932
$303$	0	0
$304$	−2.68451e125	−1.10598
$305$	−5.34293e125	−1.86482
$306$	0	0
$307$	−8.81457e124	−0.221163	−0.110582	−	0.993867i	$-0.535271\pi$
$307$	−8.81457e124	−0.221163	−0.110582	+	0.993867i	$0.535271\pi$
$308$	1.69353e125	0.360563
$309$	0	0
$310$	3.17210e125	0.487058
$311$	2.64772e125	0.345519	0.172760	−	0.984964i	$-0.444732\pi$
$311$	2.64772e125	0.345519	0.172760	+	0.984964i	$0.444732\pi$
$312$	0	0
$313$	2.92546e125	0.276189	0.138094	−	0.990419i	$-0.455902\pi$
$313$	2.92546e125	0.276189	0.138094	+	0.990419i	$0.455902\pi$
$314$	1.70044e126	1.36651
$315$	0	0
$316$	−1.29905e126	−0.757577
$317$	−1.43032e126	−0.711116	−0.355558	−	0.934654i	$-0.615709\pi$
$317$	−1.43032e126	−0.711116	−0.355558	+	0.934654i	$0.615709\pi$
$318$	0	0
$319$	3.57980e125	0.129548
$320$	−3.04491e126	−0.940806
$321$	0	0
$322$	−1.77842e127	−4.01155
$323$	2.91798e126	0.562800
$324$	0	0
$325$	1.13810e125	0.0160720
$326$	−2.23026e127	−2.69691
$327$	0	0
$328$	−2.70565e126	−0.240238
$329$	−1.63797e126	−0.124713
$330$	0	0
$331$	2.56318e126	0.143703	0.0718514	−	0.997415i	$-0.477109\pi$
$331$	2.56318e126	0.143703	0.0718514	+	0.997415i	$0.477109\pi$
$332$	−1.37816e127	−0.663479
$333$	0	0
$334$	−1.97039e127	−0.700415
$335$	−1.18676e127	−0.362744
$336$	0	0
$337$	−6.28379e127	−1.42204	−0.711020	−	0.703172i	$-0.751767\pi$
$337$	−6.28379e127	−1.42204	−0.711020	+	0.703172i	$0.751767\pi$
$338$	7.01713e127	1.36731
$339$	0	0
$340$	4.39970e127	0.636412
$341$	−5.43157e126	−0.0677376
$342$	0	0
$343$	1.52119e128	1.41199
$344$	−2.77134e127	−0.222069
$345$	0	0
$346$	−1.51951e128	−0.908573
$347$	7.50746e126	0.0388021	0.0194010	−	0.999812i	$-0.493824\pi$
$347$	7.50746e126	0.0388021	0.0194010	+	0.999812i	$0.493824\pi$
$348$	0	0
$349$	−1.53174e128	−0.592243	−0.296121	−	0.955150i	$-0.595693\pi$
$349$	−1.53174e128	−0.592243	−0.296121	+	0.955150i	$0.595693\pi$
$350$	−4.58101e128	−1.53294
$351$	0	0
$352$	1.31646e128	0.330371
$353$	8.51845e128	1.85241	0.926206	−	0.377017i	$-0.123050\pi$
$353$	8.51845e128	1.85241	0.926206	+	0.377017i	$0.123050\pi$
$354$	0	0
$355$	1.00430e129	1.64185
$356$	9.33978e128	1.32468
$357$	0	0
$358$	−9.04909e126	−0.00967191
$359$	6.93817e128	0.644133	0.322066	−	0.946717i	$-0.395623\pi$
$359$	6.93817e128	0.644133	0.322066	+	0.946717i	$0.395623\pi$
$360$	0	0
$361$	−1.49481e127	−0.0104827
$362$	−1.48907e129	−0.908099
$363$	0	0
$364$	7.68587e127	0.0354873
$365$	3.64369e129	1.46471
$366$	0	0
$367$	−3.99074e128	−0.121735	−0.0608677	−	0.998146i	$-0.519387\pi$
$367$	−3.99074e128	−0.121735	−0.0608677	+	0.998146i	$0.519387\pi$
$368$	−7.27827e129	−1.93514
$369$	0	0
$370$	1.48350e130	2.99986
$371$	4.05889e129	0.716184
$372$	0	0
$373$	9.72150e129	1.30749	0.653743	−	0.756716i	$-0.273198\pi$
$373$	9.72150e129	1.30749	0.653743	+	0.756716i	$0.273198\pi$
$374$	−1.61759e129	−0.190043
$375$	0	0
$376$	−1.44768e128	−0.0129923
$377$	1.62465e128	0.0127503
$378$	0	0
$379$	−5.91099e129	−0.355124	−0.177562	−	0.984110i	$-0.556821\pi$
$379$	−5.91099e129	−0.355124	−0.177562	+	0.984110i	$0.556821\pi$
$380$	2.12755e130	1.11894
$381$	0	0
$382$	−1.41384e130	−0.570427
$383$	1.38327e130	0.489066	0.244533	−	0.969641i	$-0.421365\pi$
$383$	1.38327e130	0.489066	0.244533	+	0.969641i	$0.421365\pi$
$384$	0	0
$385$	1.96378e130	0.533735
$386$	−3.45045e130	−0.822652
$387$	0	0
$388$	2.30887e130	0.424031
$389$	7.55228e130	1.21793	0.608966	−	0.793196i	$-0.291584\pi$
$389$	7.55228e130	1.21793	0.608966	+	0.793196i	$0.291584\pi$
$390$	0	0
$391$	7.91124e130	0.984733
$392$	2.94859e130	0.322603
$393$	0	0
$394$	−1.08674e131	−0.919535
$395$	−1.50635e131	−1.12143
$396$	0	0
$397$	−1.85454e131	−1.06983	−0.534917	−	0.844905i	$-0.679657\pi$
$397$	−1.85454e131	−1.06983	−0.534917	+	0.844905i	$0.679657\pi$
$398$	−2.15813e131	−1.09644
$399$	0	0
$400$	−1.87480e131	−0.739478
$401$	2.80194e131	0.974245	0.487123	−	0.873334i	$-0.338046\pi$
$401$	2.80194e131	0.974245	0.487123	+	0.873334i	$0.338046\pi$
$402$	0	0
$403$	−2.46506e129	−0.00666687
$404$	−2.31382e131	−0.552167
$405$	0	0
$406$	−6.53946e131	−1.21612
$407$	−2.54020e131	−0.417205
$408$	0	0
$409$	−1.45497e129	−0.00186564	−0.000932820	−	1.00000i	$-0.500297\pi$
$409$	−1.45497e129	−0.00186564	−0.000932820		1.00000i	$0.500297\pi$
$410$	2.13194e132	2.41652
$411$	0	0
$412$	4.94826e131	0.438675
$413$	−4.23073e132	−3.31847
$414$	0	0
$415$	−1.59809e132	−0.982138
$416$	5.97459e130	0.0325158
$417$	0	0
$418$	−7.82209e131	−0.334134
$419$	−2.79270e131	−0.105734	−0.0528671	−	0.998602i	$-0.516836\pi$
$419$	−2.79270e131	−0.105734	−0.0528671	+	0.998602i	$0.516836\pi$
$420$	0	0
$421$	−3.06040e132	−0.911029	−0.455514	−	0.890228i	$-0.650545\pi$
$421$	−3.06040e132	−0.911029	−0.455514	+	0.890228i	$0.650545\pi$
$422$	−3.99722e132	−1.05555
$423$	0	0
$424$	3.58736e131	0.0746104
$425$	2.03785e132	0.376297
$426$	0	0
$427$	−1.67125e133	−2.43463
$428$	−1.18941e132	−0.153964
$429$	0	0
$430$	2.18370e133	2.23376
$431$	2.83557e132	0.257951	0.128976	−	0.991648i	$-0.458831\pi$
$431$	2.83557e132	0.257951	0.128976	+	0.991648i	$0.458831\pi$
$432$	0	0
$433$	1.37181e133	0.987767	0.493883	−	0.869528i	$-0.335577\pi$
$433$	1.37181e133	0.987767	0.493883	+	0.869528i	$0.335577\pi$
$434$	9.92221e132	0.635883
$435$	0	0
$436$	1.40817e133	0.715463
$437$	3.82561e133	1.73136
$438$	0	0
$439$	2.79760e132	0.100537	0.0502686	−	0.998736i	$-0.483992\pi$
$439$	2.79760e132	0.100537	0.0502686	+	0.998736i	$0.483992\pi$
$440$	1.73564e132	0.0556033
$441$	0	0
$442$	−7.34122e131	−0.0187044
$443$	−1.81372e133	−0.412270	−0.206135	−	0.978524i	$-0.566089\pi$
$443$	−1.81372e133	−0.412270	−0.206135	+	0.978524i	$0.566089\pi$
$444$	0	0
$445$	1.08302e134	1.96091
$446$	−6.49012e133	−1.04916
$447$	0	0
$448$	−9.52436e133	−1.22828
$449$	4.40637e133	0.507740	0.253870	−	0.967238i	$-0.418297\pi$
$449$	4.40637e133	0.507740	0.253870	+	0.967238i	$0.418297\pi$
$450$	0	0
$451$	−3.65052e133	−0.336078
$452$	9.90421e132	0.0815321
$453$	0	0
$454$	−1.63809e134	−1.07899
$455$	8.91238e132	0.0525313
$456$	0	0
$457$	2.56573e134	1.21183	0.605916	−	0.795529i	$-0.292807\pi$
$457$	2.56573e134	1.21183	0.605916	+	0.795529i	$0.292807\pi$
$458$	5.67400e133	0.239984
$459$	0	0
$460$	5.76822e134	1.95781
$461$	2.76855e134	0.842084	0.421042	−	0.907041i	$-0.361664\pi$
$461$	2.76855e134	0.842084	0.421042	+	0.907041i	$0.361664\pi$
$462$	0	0
$463$	6.40865e134	1.56649	0.783243	−	0.621715i	$-0.213564\pi$
$463$	6.40865e134	1.56649	0.783243	+	0.621715i	$0.213564\pi$
$464$	−2.67631e134	−0.586648
$465$	0	0
$466$	−8.05530e134	−1.42100
$467$	7.65000e134	1.21104	0.605521	−	0.795829i	$-0.292965\pi$
$467$	7.65000e134	1.21104	0.605521	+	0.795829i	$0.292965\pi$
$468$	0	0
$469$	−3.71215e134	−0.473584
$470$	1.14072e134	0.130688
$471$	0	0
$472$	−3.73924e134	−0.345710
$473$	−3.73915e134	−0.310660
$474$	0	0
$475$	9.85433e134	0.661607
$476$	1.37621e135	0.830872
$477$	0	0
$478$	−4.68518e134	−0.228885
$479$	−4.32936e135	−1.90318	−0.951592	−	0.307364i	$-0.900553\pi$
$479$	−4.32936e135	−1.90318	−0.951592	+	0.307364i	$0.900553\pi$
$480$	0	0
$481$	−1.15284e134	−0.0410622
$482$	−4.84013e135	−1.55232
$483$	0	0
$484$	−3.14821e135	−0.819169
$485$	2.67732e135	0.627687
$486$	0	0
$487$	−2.22301e135	−0.423379	−0.211689	−	0.977337i	$-0.567896\pi$
$487$	−2.22301e135	−0.423379	−0.211689	+	0.977337i	$0.567896\pi$
$488$	−1.47710e135	−0.253634
$489$	0	0
$490$	−2.32338e136	−3.24502
$491$	−7.43679e135	−0.937066	−0.468533	−	0.883446i	$-0.655217\pi$
$491$	−7.43679e135	−0.937066	−0.468533	+	0.883446i	$0.655217\pi$
$492$	0	0
$493$	2.90906e135	0.298527
$494$	−3.54996e134	−0.0328861
$495$	0	0
$496$	4.06071e135	0.306745
$497$	3.14142e136	2.14352
$498$	0	0
$499$	−1.25878e135	−0.0701248	−0.0350624	−	0.999385i	$-0.511163\pi$
$499$	−1.25878e135	−0.0701248	−0.0350624	+	0.999385i	$0.511163\pi$
$500$	−7.48158e135	−0.376711
$501$	0	0
$502$	1.82075e136	0.749396
$503$	1.27338e136	0.473995	0.236997	−	0.971510i	$-0.423837\pi$
$503$	1.27338e136	0.473995	0.236997	+	0.971510i	$0.423837\pi$
$504$	0	0
$505$	−2.68306e136	−0.817365
$506$	−2.12073e136	−0.584635
$507$	0	0
$508$	4.17918e136	0.944004
$509$	−1.09464e136	−0.223885	−0.111943	−	0.993715i	$-0.535707\pi$
$509$	−1.09464e136	−0.223885	−0.111943	+	0.993715i	$0.535707\pi$
$510$	0	0
$511$	1.13973e137	1.91226
$512$	−8.55831e136	−1.30093
$513$	0	0
$514$	−2.81868e136	−0.351891
$515$	5.73791e136	0.649364
$516$	0	0
$517$	−1.95325e135	−0.0181755
$518$	4.64034e137	3.91649
$519$	0	0
$520$	7.87702e134	0.00547259
$521$	−2.10093e137	−1.32467	−0.662335	−	0.749208i	$-0.730434\pi$
$521$	−2.10093e137	−1.32467	−0.662335	+	0.749208i	$0.730434\pi$
$522$	0	0
$523$	1.58385e137	0.822958	0.411479	−	0.911419i	$-0.365012\pi$
$523$	1.58385e137	0.822958	0.411479	+	0.911419i	$0.365012\pi$
$524$	−3.28810e136	−0.155137
$525$	0	0
$526$	−4.26115e137	−1.65862
$527$	−4.41387e136	−0.156093
$528$	0	0
$529$	6.94819e137	2.02937
$530$	−2.82670e137	−0.750496
$531$	0	0
$532$	6.65489e137	1.46084
$533$	−1.65675e136	−0.0330774
$534$	0	0
$535$	−1.37921e137	−0.227911
$536$	−3.28090e136	−0.0493369
$537$	0	0
$538$	−4.39263e137	−0.547293
$539$	3.97831e137	0.451301
$540$	0	0
$541$	2.27932e137	0.214458	0.107229	−	0.994234i	$-0.465802\pi$
$541$	2.27932e137	0.214458	0.107229	+	0.994234i	$0.465802\pi$
$542$	1.86451e138	1.59809
$543$	0	0
$544$	1.06979e138	0.761300
$545$	1.63289e138	1.05909
$546$	0	0
$547$	−2.09237e137	−0.112792	−0.0563959	−	0.998408i	$-0.517961\pi$
$547$	−2.09237e137	−0.112792	−0.0563959	+	0.998408i	$0.517961\pi$
$548$	−4.54032e136	−0.0223187
$549$	0	0
$550$	−5.46277e137	−0.223407
$551$	1.40672e138	0.524871
$552$	0	0
$553$	−4.71180e138	−1.46409
$554$	−6.25160e137	−0.177316
$555$	0	0
$556$	3.23801e138	0.765598
$557$	1.72569e138	0.372629	0.186314	−	0.982490i	$-0.440346\pi$
$557$	1.72569e138	0.372629	0.186314	+	0.982490i	$0.440346\pi$
$558$	0	0
$559$	−1.69697e137	−0.0305758
$560$	−1.46815e139	−2.41699
$561$	0	0
$562$	−1.91177e139	−2.62876
$563$	−1.04160e139	−1.30927	−0.654633	−	0.755946i	$-0.727177\pi$
$563$	−1.04160e139	−1.30927	−0.654633	+	0.755946i	$0.727177\pi$
$564$	0	0
$565$	1.14847e138	0.120691
$566$	7.70820e138	0.740838
$567$	0	0
$568$	2.77648e138	0.223307
$569$	2.38659e139	1.75634	0.878170	−	0.478348i	$-0.158764\pi$
$569$	2.38659e139	1.75634	0.878170	+	0.478348i	$0.158764\pi$
$570$	0	0
$571$	−2.74087e139	−1.68953	−0.844764	−	0.535139i	$-0.820259\pi$
$571$	−2.74087e139	−1.68953	−0.844764	+	0.535139i	$0.820259\pi$
$572$	9.16526e136	0.00517184
$573$	0	0
$574$	6.66865e139	3.15491
$575$	2.67172e139	1.15761
$576$	0	0
$577$	3.12739e139	1.13711	0.568557	−	0.822644i	$-0.307502\pi$
$577$	3.12739e139	1.13711	0.568557	+	0.822644i	$0.307502\pi$
$578$	2.79204e139	0.930176
$579$	0	0
$580$	2.12104e139	0.593521
$581$	−4.99877e139	−1.28224
$582$	0	0
$583$	4.84015e138	0.104375
$584$	1.00733e139	0.199215
$585$	0	0
$586$	−7.05889e139	−1.17465
$587$	−6.93226e138	−0.105840	−0.0529201	−	0.998599i	$-0.516853\pi$
$587$	−6.93226e138	−0.105840	−0.0529201	+	0.998599i	$0.516853\pi$
$588$	0	0
$589$	−2.13439e139	−0.274443
$590$	2.94637e140	3.47745
$591$	0	0
$592$	1.89908e140	1.88929
$593$	5.93058e139	0.541795	0.270898	−	0.962608i	$-0.412680\pi$
$593$	5.93058e139	0.541795	0.270898	+	0.962608i	$0.412680\pi$
$594$	0	0
$595$	1.59583e140	1.22993
$596$	1.09733e140	0.776961
$597$	0	0
$598$	−9.62469e138	−0.0575410
$599$	−1.91583e140	−1.05269	−0.526346	−	0.850270i	$-0.676438\pi$
$599$	−1.91583e140	−1.05269	−0.526346	+	0.850270i	$0.676438\pi$
$600$	0	0
$601$	−1.85009e140	−0.859078	−0.429539	−	0.903048i	$-0.641324\pi$
$601$	−1.85009e140	−0.859078	−0.429539	+	0.903048i	$0.641324\pi$
$602$	6.83055e140	2.91631
$603$	0	0
$604$	2.52203e140	0.910721
$605$	−3.65061e140	−1.21260
$606$	0	0
$607$	3.03046e140	0.852077	0.426039	−	0.904705i	$-0.359909\pi$
$607$	3.03046e140	0.852077	0.426039	+	0.904705i	$0.359909\pi$
$608$	5.17316e140	1.33852
$609$	0	0
$610$	1.16390e141	2.55127
$611$	−8.86459e137	−0.00178887
$612$	0	0
$613$	2.63225e139	0.0450375	0.0225187	−	0.999746i	$-0.492831\pi$
$613$	2.63225e139	0.0450375	0.0225187	+	0.999746i	$0.492831\pi$
$614$	1.92015e140	0.302575
$615$	0	0
$616$	5.42904e139	0.0725933
$617$	9.13650e140	1.12559	0.562794	−	0.826597i	$-0.309727\pi$
$617$	9.13650e140	1.12559	0.562794	+	0.826597i	$0.309727\pi$
$618$	0	0
$619$	−3.85006e140	−0.402800	−0.201400	−	0.979509i	$-0.564549\pi$
$619$	−3.85006e140	−0.402800	−0.201400	+	0.979509i	$0.564549\pi$
$620$	−3.21823e140	−0.310339
$621$	0	0
$622$	−5.76775e140	−0.472707
$623$	3.38766e141	2.56008
$624$	0	0
$625$	−1.90228e141	−1.22274
$626$	−6.37279e140	−0.377856
$627$	0	0
$628$	−1.72516e141	−0.870700
$629$	−2.06424e141	−0.961398
$630$	0	0
$631$	3.45766e141	1.37183	0.685914	−	0.727683i	$-0.259403\pi$
$631$	3.45766e141	1.37183	0.685914	+	0.727683i	$0.259403\pi$
$632$	−4.16443e140	−0.152526
$633$	0	0
$634$	3.11579e141	0.972882
$635$	4.84610e141	1.39739
$636$	0	0
$637$	1.80551e140	0.0444180
$638$	−7.79819e140	−0.177235
$639$	0	0
$640$	−2.31495e141	−0.449214
$641$	7.54846e141	1.35372	0.676858	−	0.736113i	$-0.263341\pi$
$641$	7.54846e141	1.35372	0.676858	+	0.736113i	$0.263341\pi$
$642$	0	0
$643$	2.67416e141	0.409764	0.204882	−	0.978787i	$-0.434319\pi$
$643$	2.67416e141	0.409764	0.204882	+	0.978787i	$0.434319\pi$
$644$	1.80428e142	2.55604
$645$	0	0
$646$	−6.35648e141	−0.769971
$647$	−5.28331e141	−0.591888	−0.295944	−	0.955205i	$-0.595634\pi$
$647$	−5.28331e141	−0.591888	−0.295944	+	0.955205i	$0.595634\pi$
$648$	0	0
$649$	−5.04507e141	−0.483626
$650$	−2.47921e140	−0.0219882
$651$	0	0
$652$	2.26269e142	1.71839
$653$	−1.07024e142	−0.752255	−0.376127	−	0.926568i	$-0.622744\pi$
$653$	−1.07024e142	−0.752255	−0.376127	+	0.926568i	$0.622744\pi$
$654$	0	0
$655$	−3.81282e141	−0.229647
$656$	2.72918e142	1.52191
$657$	0	0
$658$	3.56813e141	0.170621
$659$	−5.07673e141	−0.224838	−0.112419	−	0.993661i	$-0.535860\pi$
$659$	−5.07673e141	−0.224838	−0.112419	+	0.993661i	$0.535860\pi$
$660$	0	0
$661$	3.54834e142	1.34850	0.674251	−	0.738503i	$-0.264467\pi$
$661$	3.54834e142	1.34850	0.674251	+	0.738503i	$0.264467\pi$
$662$	−5.58360e141	−0.196601
$663$	0	0
$664$	−4.41806e141	−0.133581
$665$	7.71688e142	2.16246
$666$	0	0
$667$	3.81391e142	0.918367
$668$	1.99904e142	0.446284
$669$	0	0
$670$	2.58523e142	0.496273
$671$	−1.99293e142	−0.354818
$672$	0	0
$673$	9.39782e142	1.43968	0.719841	−	0.694139i	$-0.244215\pi$
$673$	9.39782e142	1.43968	0.719841	+	0.694139i	$0.244215\pi$
$674$	1.36885e143	1.94550
$675$	0	0
$676$	−7.11918e142	−0.871207
$677$	8.56774e142	0.973058	0.486529	−	0.873664i	$-0.338263\pi$
$677$	8.56774e142	0.973058	0.486529	+	0.873664i	$0.338263\pi$
$678$	0	0
$679$	8.37457e142	0.819481
$680$	1.41044e142	0.128131
$681$	0	0
$682$	1.18321e142	0.0926722
$683$	−1.57442e143	−1.14518	−0.572592	−	0.819841i	$-0.694062\pi$
$683$	−1.57442e143	−1.14518	−0.572592	+	0.819841i	$0.694062\pi$
$684$	0	0
$685$	−5.26487e141	−0.0330380
$686$	−3.31374e143	−1.93175
$687$	0	0
$688$	2.79544e143	1.40680
$689$	2.19665e141	0.0102728
$690$	0	0
$691$	−3.69642e143	−1.49327	−0.746637	−	0.665232i	$-0.768333\pi$
$691$	−3.69642e143	−1.49327	−0.746637	+	0.665232i	$0.768333\pi$
$692$	1.54160e143	0.578916
$693$	0	0
$694$	−1.63542e142	−0.0530854
$695$	3.75473e143	1.13330
$696$	0	0
$697$	−2.96653e143	−0.774450
$698$	3.33671e143	0.810251
$699$	0	0
$700$	4.64762e143	0.976742
$701$	−6.83715e143	−1.33695	−0.668475	−	0.743735i	$-0.733052\pi$
$701$	−6.83715e143	−1.33695	−0.668475	+	0.743735i	$0.733052\pi$
$702$	0	0
$703$	−9.98197e143	−1.69033
$704$	−1.13576e143	−0.179006
$705$	0	0
$706$	−1.85565e144	−2.53430
$707$	−8.39252e143	−1.06712
$708$	0	0
$709$	−4.57737e143	−0.504640	−0.252320	−	0.967644i	$-0.581194\pi$
$709$	−4.57737e143	−0.504640	−0.252320	+	0.967644i	$0.581194\pi$
$710$	−2.18776e144	−2.24622
$711$	0	0
$712$	2.99411e143	0.266703
$713$	−5.78679e143	−0.480194
$714$	0	0
$715$	1.06279e142	0.00765580
$716$	9.18068e141	0.00616265
$717$	0	0
$718$	−1.51140e144	−0.881243
$719$	8.91079e142	0.0484292	0.0242146	−	0.999707i	$-0.492292\pi$
$719$	8.91079e142	0.0484292	0.0242146	+	0.999707i	$0.492292\pi$
$720$	0	0
$721$	1.79480e144	0.847783
$722$	3.25628e142	0.0143414
$723$	0	0
$724$	1.51073e144	0.578613
$725$	9.82422e143	0.350937
$726$	0	0
$727$	5.09087e144	1.58236	0.791178	−	0.611585i	$-0.209468\pi$
$727$	5.09087e144	1.58236	0.791178	+	0.611585i	$0.209468\pi$
$728$	2.46390e142	0.00714478
$729$	0	0
$730$	−7.93736e144	−2.00388
$731$	−3.03855e144	−0.715878
$732$	0	0
$733$	−8.05963e144	−1.65411	−0.827055	−	0.562121i	$-0.809985\pi$
$733$	−8.05963e144	−1.65411	−0.827055	+	0.562121i	$0.809985\pi$
$734$	8.69337e143	0.166547
$735$	0	0
$736$	1.40255e145	2.34201
$737$	−4.42667e143	−0.0690191
$738$	0	0
$739$	5.87280e143	0.0798547	0.0399274	−	0.999203i	$-0.487287\pi$
$739$	5.87280e143	0.0798547	0.0399274	+	0.999203i	$0.487287\pi$
$740$	−1.50508e145	−1.91142
$741$	0	0
$742$	−8.84182e144	−0.979816
$743$	−4.30726e144	−0.445929	−0.222965	−	0.974827i	$-0.571573\pi$
$743$	−4.30726e144	−0.445929	−0.222965	+	0.974827i	$0.571573\pi$
$744$	0	0
$745$	1.27244e145	1.15012
$746$	−2.11772e145	−1.78878
$747$	0	0
$748$	1.64111e144	0.121090
$749$	−4.31413e144	−0.297551
$750$	0	0
$751$	−1.39247e145	−0.839402	−0.419701	−	0.907662i	$-0.637865\pi$
$751$	−1.39247e145	−0.839402	−0.419701	+	0.907662i	$0.637865\pi$
$752$	1.46027e144	0.0823064
$753$	0	0
$754$	−3.53912e143	−0.0174438
$755$	2.92450e145	1.34813
$756$	0	0
$757$	−4.28990e145	−1.73024	−0.865118	−	0.501568i	$-0.832757\pi$
$757$	−4.28990e145	−1.73024	−0.865118	+	0.501568i	$0.832757\pi$
$758$	1.28764e145	0.485848
$759$	0	0
$760$	6.82040e144	0.225280
$761$	−2.43861e145	−0.753732	−0.376866	−	0.926268i	$-0.622998\pi$
$761$	−2.43861e145	−0.753732	−0.376866	+	0.926268i	$0.622998\pi$
$762$	0	0
$763$	5.10761e145	1.38270
$764$	1.43440e145	0.363459
$765$	0	0
$766$	−3.01329e145	−0.669095
$767$	−2.28964e144	−0.0475995
$768$	0	0
$769$	2.73166e145	0.497905	0.248952	−	0.968516i	$-0.419914\pi$
$769$	2.73166e145	0.497905	0.248952	+	0.968516i	$0.419914\pi$
$770$	−4.27787e145	−0.730207
$771$	0	0
$772$	3.50062e145	0.524169
$773$	3.79729e145	0.532611	0.266305	−	0.963889i	$-0.414197\pi$
$773$	3.79729e145	0.532611	0.266305	+	0.963889i	$0.414197\pi$
$774$	0	0
$775$	−1.49061e145	−0.183497
$776$	7.40168e144	0.0853716
$777$	0	0
$778$	−1.64518e146	−1.66626
$779$	−1.43451e146	−1.36164
$780$	0	0
$781$	3.74609e145	0.312393
$782$	−1.72337e146	−1.34722
$783$	0	0
$784$	−2.97424e146	−2.04369
$785$	−2.00047e146	−1.28888
$786$	0	0
$787$	−2.95088e146	−1.67197	−0.835984	−	0.548754i	$-0.815103\pi$
$787$	−2.95088e146	−1.67197	−0.835984	+	0.548754i	$0.815103\pi$
$788$	1.10255e146	0.585900
$789$	0	0
$790$	3.28141e146	1.53424
$791$	3.59238e145	0.157569
$792$	0	0
$793$	−9.04470e144	−0.0349219
$794$	4.03991e146	1.46365
$795$	0	0
$796$	2.18952e146	0.698616
$797$	9.14143e145	0.273759	0.136880	−	0.990588i	$-0.456293\pi$
$797$	9.14143e145	0.273759	0.136880	+	0.990588i	$0.456293\pi$
$798$	0	0
$799$	−1.58727e145	−0.0418831
$800$	3.61282e146	0.894956
$801$	0	0
$802$	−6.10371e146	−1.33287
$803$	1.35911e146	0.278689
$804$	0	0
$805$	2.09221e147	3.78367
$806$	5.36984e144	0.00912099
$807$	0	0
$808$	−7.41755e145	−0.111170
$809$	4.26379e146	0.600337	0.300168	−	0.953886i	$-0.402957\pi$
$809$	4.26379e146	0.600337	0.300168	+	0.953886i	$0.402957\pi$
$810$	0	0
$811$	1.42871e147	1.77579	0.887897	−	0.460043i	$-0.152166\pi$
$811$	1.42871e147	1.77579	0.887897	+	0.460043i	$0.152166\pi$
$812$	6.63455e146	0.774876
$813$	0	0
$814$	5.53353e146	0.570781
$815$	2.62377e147	2.54371
$816$	0	0
$817$	−1.46934e147	−1.25866
$818$	3.16949e144	0.00255240
$819$	0	0
$820$	−2.16295e147	−1.53974
$821$	5.19552e145	0.0347776	0.0173888	−	0.999849i	$-0.494465\pi$
$821$	5.19552e145	0.0347776	0.0173888	+	0.999849i	$0.494465\pi$
$822$	0	0
$823$	1.81447e146	0.107413	0.0537067	−	0.998557i	$-0.482896\pi$
$823$	1.81447e146	0.107413	0.0537067	+	0.998557i	$0.482896\pi$
$824$	1.58629e146	0.0883200
$825$	0	0
$826$	9.21615e147	4.54002
$827$	−2.36634e147	−1.09660	−0.548302	−	0.836280i	$-0.684726\pi$
$827$	−2.36634e147	−1.09660	−0.548302	+	0.836280i	$0.684726\pi$
$828$	0	0
$829$	−3.79588e147	−1.55707	−0.778536	−	0.627600i	$-0.784037\pi$
$829$	−3.79588e147	−1.55707	−0.778536	+	0.627600i	$0.784037\pi$
$830$	3.48126e147	1.34367
$831$	0	0
$832$	−5.15453e145	−0.0176182
$833$	3.23290e147	1.03997
$834$	0	0
$835$	2.31805e147	0.660627
$836$	7.93584e146	0.212900
$837$	0	0
$838$	6.08357e146	0.144656
$839$	2.25603e145	0.00505087	0.00252543	−	0.999997i	$-0.499196\pi$
$839$	2.25603e145	0.00505087	0.00252543	+	0.999997i	$0.499196\pi$
$840$	0	0
$841$	−3.63488e147	−0.721592
$842$	6.66673e147	1.24638
$843$	0	0
$844$	4.05534e147	0.672565
$845$	−8.25526e147	−1.28963
$846$	0	0
$847$	−1.14190e148	−1.58312
$848$	−3.61856e147	−0.472656
$849$	0	0
$850$	−4.43922e147	−0.514815
$851$	−2.70632e148	−2.95758
$852$	0	0
$853$	1.31386e148	1.27533	0.637664	−	0.770315i	$-0.279901\pi$
$853$	1.31386e148	1.27533	0.637664	+	0.770315i	$0.279901\pi$
$854$	3.64062e148	3.33084
$855$	0	0
$856$	−3.81295e146	−0.0309982
$857$	1.22789e148	0.941081	0.470541	−	0.882378i	$-0.344059\pi$
$857$	1.22789e148	0.941081	0.470541	+	0.882378i	$0.344059\pi$
$858$	0	0
$859$	−1.16067e148	−0.790778	−0.395389	−	0.918514i	$-0.629390\pi$
$859$	−1.16067e148	−0.790778	−0.395389	+	0.918514i	$0.629390\pi$
$860$	−2.21546e148	−1.42329
$861$	0	0
$862$	−6.17696e147	−0.352905
$863$	2.56604e148	1.38267	0.691336	−	0.722534i	$-0.257023\pi$
$863$	2.56604e148	1.38267	0.691336	+	0.722534i	$0.257023\pi$
$864$	0	0
$865$	1.78761e148	0.856960
$866$	−2.98833e148	−1.35137
$867$	0	0
$868$	−1.00665e148	−0.405165
$869$	−5.61874e147	−0.213374
$870$	0	0
$871$	−2.00899e146	−0.00679300
$872$	4.51425e147	0.144047
$873$	0	0
$874$	−8.33364e148	−2.36869
$875$	−2.71366e148	−0.728030
$876$	0	0
$877$	−6.08651e148	−1.45509	−0.727544	−	0.686061i	$-0.759338\pi$
$877$	−6.08651e148	−1.45509	−0.727544	+	0.686061i	$0.759338\pi$
$878$	−6.09425e147	−0.137546
$879$	0	0
$880$	−1.75074e148	−0.352246
$881$	−4.99456e148	−0.948885	−0.474443	−	0.880286i	$-0.657350\pi$
$881$	−4.99456e148	−0.948885	−0.474443	+	0.880286i	$0.657350\pi$
$882$	0	0
$883$	9.54085e148	1.61649	0.808243	−	0.588850i	$-0.200419\pi$
$883$	9.54085e148	1.61649	0.808243	+	0.588850i	$0.200419\pi$
$884$	7.44798e146	0.0119179
$885$	0	0
$886$	3.95098e148	0.564030
$887$	1.18543e149	1.59858	0.799290	−	0.600946i	$-0.205209\pi$
$887$	1.18543e149	1.59858	0.799290	+	0.600946i	$0.205209\pi$
$888$	0	0
$889$	1.51584e149	1.82438
$890$	−2.35924e149	−2.68273
$891$	0	0
$892$	6.58450e148	0.668494
$893$	−7.67550e147	−0.0736390
$894$	0	0
$895$	1.06457e147	0.00912247
$896$	−7.24109e148	−0.586475
$897$	0	0
$898$	−9.59878e148	−0.694642
$899$	−2.12787e148	−0.145573
$900$	0	0
$901$	3.93326e148	0.240520
$902$	7.95225e148	0.459790
$903$	0	0
$904$	3.17505e147	0.0164151
$905$	1.75181e149	0.856512
$906$	0	0
$907$	−7.81669e148	−0.341865	−0.170933	−	0.985283i	$-0.554678\pi$
$907$	−7.81669e148	−0.341865	−0.170933	+	0.985283i	$0.554678\pi$
$908$	1.66191e149	0.687500
$909$	0	0
$910$	−1.94146e148	−0.0718684
$911$	−2.35969e149	−0.826373	−0.413187	−	0.910646i	$-0.635584\pi$
$911$	−2.35969e149	−0.826373	−0.413187	+	0.910646i	$0.635584\pi$
$912$	0	0
$913$	−5.96095e148	−0.186871
$914$	−5.58914e149	−1.65792
$915$	0	0
$916$	−5.75651e148	−0.152911
$917$	−1.19264e149	−0.299817
$918$	0	0
$919$	−4.79004e149	−1.07871	−0.539356	−	0.842078i	$-0.681332\pi$
$919$	−4.79004e149	−1.07871	−0.539356	+	0.842078i	$0.681332\pi$
$920$	1.84915e149	0.394174
$921$	0	0
$922$	−6.03097e149	−1.15206
$923$	1.70012e148	0.0307463
$924$	0	0
$925$	−6.97118e149	−1.13018
$926$	−1.39605e150	−2.14312
$927$	0	0
$928$	5.15735e149	0.709993
$929$	−8.78242e149	−1.14504	−0.572520	−	0.819891i	$-0.694034\pi$
$929$	−8.78242e149	−1.14504	−0.572520	+	0.819891i	$0.694034\pi$
$930$	0	0
$931$	1.56332e150	1.82848
$932$	8.17244e149	0.905416
$933$	0	0
$934$	−1.66647e150	−1.65683
$935$	1.90300e149	0.179247
$936$	0	0
$937$	7.29911e149	0.617192	0.308596	−	0.951193i	$-0.400141\pi$
$937$	7.29911e149	0.617192	0.308596	+	0.951193i	$0.400141\pi$
$938$	8.08649e149	0.647913
$939$	0	0
$940$	−1.15731e149	−0.0832707
$941$	−7.72707e149	−0.526913	−0.263456	−	0.964671i	$-0.584862\pi$
$941$	−7.72707e149	−0.526913	−0.263456	+	0.964671i	$0.584862\pi$
$942$	0	0
$943$	−3.88926e150	−2.38246
$944$	3.77176e150	2.19007
$945$	0	0
$946$	8.14532e149	0.425016
$947$	−1.31603e150	−0.651019	−0.325509	−	0.945539i	$-0.605536\pi$
$947$	−1.31603e150	−0.651019	−0.325509	+	0.945539i	$0.605536\pi$
$948$	0	0
$949$	6.16817e148	0.0274292
$950$	−2.14665e150	−0.905149
$951$	0	0
$952$	4.41180e149	0.167282
$953$	2.13928e150	0.769266	0.384633	−	0.923070i	$-0.374328\pi$
$953$	2.13928e150	0.769266	0.384633	+	0.923070i	$0.374328\pi$
$954$	0	0
$955$	1.66330e150	0.538023
$956$	4.75332e149	0.145839
$957$	0	0
$958$	9.43103e150	2.60376
$959$	−1.64683e149	−0.0431330
$960$	0	0
$961$	−3.91875e150	−0.923883
$962$	2.51133e149	0.0561774
$963$	0	0
$964$	4.91051e150	0.989092
$965$	4.05925e150	0.775920
$966$	0	0
$967$	−3.54101e150	−0.609664	−0.304832	−	0.952406i	$-0.598600\pi$
$967$	−3.54101e150	−0.609664	−0.304832	+	0.952406i	$0.598600\pi$
$968$	−1.00924e150	−0.164926
$969$	0	0
$970$	−5.83224e150	−0.858742
$971$	1.11465e151	1.55799	0.778997	−	0.627028i	$-0.215729\pi$
$971$	1.11465e151	1.55799	0.778997	+	0.627028i	$0.215729\pi$
$972$	0	0
$973$	1.17447e151	1.47959
$974$	4.84257e150	0.579227
$975$	0	0
$976$	1.48994e151	1.60677
$977$	1.17628e151	1.20458	0.602289	−	0.798278i	$-0.294256\pi$
$977$	1.17628e151	1.20458	0.602289	+	0.798278i	$0.294256\pi$
$978$	0	0
$979$	4.03972e150	0.373100
$980$	2.35716e151	2.06763
$981$	0	0
$982$	1.62002e151	1.28201
$983$	4.21293e150	0.316688	0.158344	−	0.987384i	$-0.449385\pi$
$983$	4.21293e150	0.316688	0.158344	+	0.987384i	$0.449385\pi$
$984$	0	0
$985$	1.27849e151	0.867299
$986$	−6.33705e150	−0.408416
$987$	0	0
$988$	3.60159e149	0.0209541
$989$	−3.98369e151	−2.20228
$990$	0	0
$991$	−2.05203e151	−1.02439	−0.512193	−	0.858870i	$-0.671167\pi$
$991$	−2.05203e151	−1.02439	−0.512193	+	0.858870i	$0.671167\pi$
$992$	−7.82517e150	−0.371239
$993$	0	0
$994$	−6.84323e151	−2.93257
$995$	2.53892e151	1.03415
$996$	0	0
$997$	4.91493e151	1.80889	0.904444	−	0.426592i	$-0.140286\pi$
$997$	4.91493e151	1.80889	0.904444	+	0.426592i	$0.140286\pi$
$998$	2.74211e150	0.0959383
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.102.a.b.1.2		8
3.2	odd	2		1.102.a.a.1.7	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.102.a.a.1.7	✓	8	3.2	odd	2
9.102.a.b.1.2		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)

\(f(q)\)	\(=\)	\(q-2.17839e15 q^{2} +2.21006e30 q^{4} +2.56275e35 q^{5} +8.01618e42 q^{7} +7.08493e44 q^{8} +O(q^{10})\)	\(q-2.17839e15 q^{2} +2.21006e30 q^{4} +2.56275e35 q^{5} +8.01618e42 q^{7} +7.08493e44 q^{8} -5.58265e50 q^{10} +9.55916e51 q^{11} +4.33831e54 q^{13} -1.74623e58 q^{14} -7.14655e60 q^{16} +7.76807e61 q^{17} +3.75637e64 q^{19} +5.66383e65 q^{20} -2.08235e67 q^{22} +1.01843e69 q^{23} +2.62336e70 q^{25} -9.45051e69 q^{26} +1.77163e73 q^{28} +3.74489e73 q^{29} -5.68206e74 q^{31} +1.37717e76 q^{32} -1.69219e77 q^{34} +2.05434e78 q^{35} -2.65734e79 q^{37} -8.18283e79 q^{38} +1.81569e80 q^{40} -3.81887e81 q^{41} -3.91159e82 q^{43} +2.11263e82 q^{44} -2.21854e84 q^{46} -2.04333e83 q^{47} +4.16178e85 q^{49} -5.71470e85 q^{50} +9.58794e84 q^{52} +5.06337e86 q^{53} +2.44977e87 q^{55} +5.67941e87 q^{56} -8.15782e88 q^{58} -5.27773e89 q^{59} -2.08484e90 q^{61} +1.23777e90 q^{62} -1.18814e91 q^{64} +1.11180e90 q^{65} -4.63082e91 q^{67} +1.71679e92 q^{68} -4.47515e93 q^{70} +3.91885e93 q^{71} +1.42179e94 q^{73} +5.78872e94 q^{74} +8.30182e94 q^{76} +7.66279e94 q^{77} -5.87787e95 q^{79} -1.83148e96 q^{80} +8.31898e96 q^{82} -6.23585e96 q^{83} +1.99076e97 q^{85} +8.52096e97 q^{86} +6.77260e96 q^{88} +4.22602e98 q^{89} +3.47767e97 q^{91} +2.25080e99 q^{92} +4.45116e98 q^{94} +9.62663e99 q^{95} +1.04471e100 q^{97} -9.06597e100 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 434989091795040 q^{2} + 90\!\cdots\!96 q^{4}+ \cdots + 61\!\cdots\!20 q^{8}+O(q^{10}) \) 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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