LMFDB - Embedded newform 9.90.a.b.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,90,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, 90, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 90);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 90 $
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:	$451.461862736$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3 x^{6} + \cdots + 56\!\cdots\!00 $ x^7 - 3x^6 - 1400531600527934473811256x^5 + 92429106535860966322690362643440028x^4 + 486502004825754823566786579226467181483733375376x^3 - 41390338158988484679355574715314473323669246141474080139600x^2 - 47785461930919140795588898989186212855196409324706742802409577734342400x + 5612439960923763868733925256800794059272997589318959539312206365735127554315560000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	multiple of $ 2^{83}\cdot 3^{43}\cdot 5^{9}\cdot 7^{5}\cdot 11^{2}\cdot 13^{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			$5.71170e11$ 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)

$f(q)$	$=$	$q+3.19029e13 q^{2} +3.98828e26 q^{4} -1.00222e30 q^{5} +1.60489e37 q^{7} -7.02319e39 q^{8} +O(q^{10})$	\(q+3.19029e13 q^{2} +3.98828e26 q^{4} -1.00222e30 q^{5} +1.60489e37 q^{7} -7.02319e39 q^{8} -3.19739e43 q^{10} +3.40556e46 q^{11} -5.21527e49 q^{13} +5.12007e50 q^{14} -4.70923e53 q^{16} +3.62126e53 q^{17} -5.12451e56 q^{19} -3.99715e56 q^{20} +1.08647e60 q^{22} +4.07651e60 q^{23} -1.60554e62 q^{25} -1.66382e63 q^{26} +6.40074e63 q^{28} +1.51052e64 q^{29} -6.54829e65 q^{31} -1.06767e67 q^{32} +1.15529e67 q^{34} -1.60846e67 q^{35} +3.74749e69 q^{37} -1.63487e70 q^{38} +7.03881e69 q^{40} -4.56036e71 q^{41} +6.44841e72 q^{43} +1.35823e73 q^{44} +1.30053e74 q^{46} +3.14673e74 q^{47} -1.37822e75 q^{49} -5.12215e75 q^{50} -2.07999e76 q^{52} +1.60814e76 q^{53} -3.41313e76 q^{55} -1.12714e77 q^{56} +4.81900e77 q^{58} +3.75851e78 q^{59} -8.19597e78 q^{61} -2.08910e79 q^{62} -4.91303e79 q^{64} +5.22687e79 q^{65} -2.77246e80 q^{67} +1.44426e80 q^{68} -5.13146e80 q^{70} +2.48739e82 q^{71} +1.94198e82 q^{73} +1.19556e83 q^{74} -2.04380e83 q^{76} +5.46555e83 q^{77} -3.70591e84 q^{79} +4.71970e83 q^{80} -1.45489e85 q^{82} +1.07302e85 q^{83} -3.62931e83 q^{85} +2.05723e86 q^{86} -2.39179e86 q^{88} -7.67903e86 q^{89} -8.36993e86 q^{91} +1.62582e87 q^{92} +1.00390e88 q^{94} +5.13591e86 q^{95} +1.74718e88 q^{97} -4.39691e88 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 31407330351408 q^{2} + 22\!\cdots\!04 q^{4}+ \cdots + 17\!\cdots\!20 q^{8}+O(q^{10}) $ 7 * q + 31407330351408 * q^2 + 2261776677705673116713576704 * q^4 - 10232470009089362495458987082250 * q^5 + 38501341543555466088619988316514959992 * q^7 + 17954070319777658933153680910224754257920 * q^8	$ 7 q + 31407330351408 q^{2} + 22\!\cdots\!04 q^{4}+ \cdots + 17\!\cdots\!56 q^{98}+O(q^{100}) $ 7 * q + 31407330351408 * q^2 + 2261776677705673116713576704 * q^4 - 10232470009089362495458987082250 * q^5 + 38501341543555466088619988316514959992 * q^7 + 17954070319777658933153680910224754257920 * q^8 - 339886969508111355644737639996417314840948000 * q^10 + 33185398429231418991729589216300973489966079756 * q^11 - 103208963062610039235367083636366996420076737975934 * q^13 + 3327254465892753266340667920543396227686510656335232 * q^14 + 1162914962909596823700454711087105707311468348200517632 * q^16 - 8319478335928844788789086096491382896131016464480742142 * q^17 + 566291740319213482378495952187194771397009633898137615980 * q^19 - 17240116916193408372006373658712519601040539123805641152000 * q^20 - 572030171884928043470630402880877439080047260844354367465536 * q^22 + 1162243907076079309616831317442805749267469267057101679089304 * q^23 - 212322678457531006783078558385295515929862869778299899884234375 * q^25 - 256954281475267715641749604093742676189922873609159508555728224 * q^26 + 42271634017038816624971599134243423766860094950653754695170525184 * q^28 + 141971615822865442921693407341400369750322173654805889340125766030 * q^29 + 683664012826903943332640912357777981916064560235376021892996967904 * q^31 + 18295616415211966307849618677858007212056173228946481610958698446848 * q^32 + 310076023324380793221121009797602653729382139402481891183326564397728 * q^34 - 330170304491374501797216156307803170564453659546779205972398673602000 * q^35 - 54562371243327727239087361205689070078467002527262667251534613287958 * q^37 - 45443543517981085735407850236293406047335765118416513555057178362067520 * q^38 - 361606215568925170012071637858292899677067482636237269829164280222720000 * q^40 + 657970372131031022656393678727303783670430723595160145307484502660397466 * q^41 + 3219260988489925248073148176207907480629490254450229462745931521229023956 * q^43 + 15518629834856028222698238418543583045824703222318379119582671434892588032 * q^44 - 56495859283654895727924020960810320205382055229302825603343235358563739776 * q^46 + 589986405817377998239864975519322982713028461832176517663311475432884156208 * q^47 - 3087918931516952942471049623523578487683423584779916315782412290559435137201 * q^49 + 11186377093883721132072449077187321801629226446489467367094029042775729250000 * q^50 - 195074413541392068451275175025603658303895820240091441880921515457689944416768 * q^52 + 181430063765559371241038742666701312033549399057740391278794421145415983301414 * q^53 - 1251959124114414009910203618775792485005181014548185493458611647835407269933000 * q^55 + 5833843183212315752254903583581814862872931164492369538677714690034795155128320 * q^56 - 3085757480392710136283141086455357758895171179069060863542747741259905831138720 * q^58 + 9086646688135460130541149101651496775878005651006843822379595086967226946739260 * q^59 + 8774545844023482806788207542368099480171833682235332719617911769894989384384594 * q^61 - 169526530141162019514362685680407627845528510541984421132250792903222430290676224 * q^62 + 1452176441912468141297252840801366807510309025606268702123180748140039039923257344 * q^64 - 1324597647382660271811574639166235036730362819738030027679321346411726630592583500 * q^65 + 5843793535214317245370457729815716742376089805910350107798697912590172409883288892 * q^67 - 3383522446313435458738303622044969561038087184549368481666865721250715220292329984 * q^68 - 48530199945646178573467957795368744286471165824229177345686884714666072932491936000 * q^70 + 54831722251632385251791847370899308335600102141533329655944703784411212003030405576 * q^71 - 199687593578972105167207004100293505918603845674208378633352670689487827039532442554 * q^73 + 965066694195901068911432718812601386557508653596585879236882657245078468484355531552 * q^74 - 624789819902471734428103435859366276136204176410553236414159885942801809403293936640 * q^76 - 1343091849772730830408738350805190184311976794055420918621708129900429278982204783264 * q^77 + 2673613187258858564803647217355170619960582874636639491339476674654505245882753222320 * q^79 - 27680777280715589878137850302356927719666260300976702690203906698201250115244507136000 * q^80 + 63127032979305734173962933747182283580799525530431609292523424735220314498528511785504 * q^82 + 35017619719051015255233069909205249521130641969249674783596011796500257235899597331924 * q^83 - 141384913067859944856588220403027346022605850144801355881993121940858052671602572135500 * q^85 + 246618390628075722158819620850499384970086160242141588082920865473574265424952752922176 * q^86 - 1874747156501905660418588549009712256169985369393565612731235328175018372894817920368640 * q^88 + 1625431592570174192786638376427668495469444301472287736732287307560402850485922205836490 * q^89 - 304928345599594097428899578613442396706625647498145800328408392926012721126646204980336 * q^91 - 7281329003117440073848907204538369781556431009214831685528490675028895216006021740500992 * q^92 + 22964567086699943860517240071514688733928422760236698641236969735081204002206026310078208 * q^94 - 22546113414761055806340378014072491896390775587517280959221325649524340597082183574485000 * q^95 + 71386807957160533061753038101994485650273149078658846323482657056181047793902162983463342 * q^97 + 17615586549862077419320336328445909012296979015379167958274818444332513071671081562433456 * 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 $

$2$	3.19029e13	1.28232	0.641159	−	0.767408i	$-0.278454\pi$
$2$	3.19029e13	1.28232	0.641159	+	0.767408i	$0.278454\pi$
$3$	0	0
$3$	0	0
$4$	3.98828e26	0.644341
$5$	−1.00222e30	−0.0788496	−0.0394248	−	0.999223i	$-0.512553\pi$
$5$	−1.00222e30	−0.0788496	−0.0394248	+	0.999223i	$0.512553\pi$
$6$	0	0
$7$	1.60489e37	0.396810	0.198405	−	0.980120i	$-0.436424\pi$
$7$	1.60489e37	0.396810	0.198405	+	0.980120i	$0.436424\pi$
$8$	−7.02319e39	−0.456068
$9$	0	0
$10$	−3.19739e43	−0.101110
$11$	3.40556e46	1.54958	0.774790	−	0.632219i	$-0.217856\pi$
$11$	3.40556e46	1.54958	0.774790	+	0.632219i	$0.217856\pi$
$12$	0	0
$13$	−5.21527e49	−1.40216	−0.701080	−	0.713083i	$-0.747298\pi$
$13$	−5.21527e49	−1.40216	−0.701080	+	0.713083i	$0.747298\pi$
$14$	5.12007e50	0.508837
$15$	0	0
$16$	−4.70923e53	−1.22917
$17$	3.62126e53	0.0636623	0.0318311	−	0.999493i	$-0.489866\pi$
$17$	3.62126e53	0.0636623	0.0318311	+	0.999493i	$0.489866\pi$
$18$	0	0
$19$	−5.12451e56	−0.638436	−0.319218	−	0.947681i	$-0.603420\pi$
$19$	−5.12451e56	−0.638436	−0.319218	+	0.947681i	$0.603420\pi$
$20$	−3.99715e56	−0.0508060
$21$	0	0
$22$	1.08647e60	1.98705
$23$	4.07651e60	1.03134	0.515668	−	0.856789i	$-0.327544\pi$
$23$	4.07651e60	1.03134	0.515668	+	0.856789i	$0.327544\pi$
$24$	0	0
$25$	−1.60554e62	−0.993783
$26$	−1.66382e63	−1.79802
$27$	0	0
$28$	6.40074e63	0.255681
$29$	1.51052e64	0.126595	0.0632973	−	0.997995i	$-0.479838\pi$
$29$	1.51052e64	0.126595	0.0632973	+	0.997995i	$0.479838\pi$
$30$	0	0
$31$	−6.54829e65	−0.282184	−0.141092	−	0.989996i	$-0.545061\pi$
$31$	−6.54829e65	−0.282184	−0.141092	+	0.989996i	$0.545061\pi$
$32$	−1.06767e67	−1.12011
$33$	0	0
$34$	1.15529e67	0.0816353
$35$	−1.60846e67	−0.0312883
$36$	0	0
$37$	3.74749e69	0.614842	0.307421	−	0.951574i	$-0.400534\pi$
$37$	3.74749e69	0.614842	0.307421	+	0.951574i	$0.400534\pi$
$38$	−1.63487e70	−0.818678
$39$	0	0
$40$	7.03881e69	0.0359608
$41$	−4.56036e71	−0.776457	−0.388228	−	0.921563i	$-0.626913\pi$
$41$	−4.56036e71	−0.776457	−0.388228	+	0.921563i	$0.626913\pi$
$42$	0	0
$43$	6.44841e72	1.31858	0.659290	−	0.751889i	$-0.270857\pi$
$43$	6.44841e72	1.31858	0.659290	+	0.751889i	$0.270857\pi$
$44$	1.35823e73	0.998457
$45$	0	0
$46$	1.30053e74	1.32250
$47$	3.14673e74	1.22886	0.614432	−	0.788969i	$-0.289385\pi$
$47$	3.14673e74	1.22886	0.614432	+	0.788969i	$0.289385\pi$
$48$	0	0
$49$	−1.37822e75	−0.842542
$50$	−5.12215e75	−1.27435
$51$	0	0
$52$	−2.07999e76	−0.903468
$53$	1.60814e76	0.299260	0.149630	−	0.988742i	$-0.452192\pi$
$53$	1.60814e76	0.299260	0.149630	+	0.988742i	$0.452192\pi$
$54$	0	0
$55$	−3.41313e76	−0.122184
$56$	−1.12714e77	−0.180972
$57$	0	0
$58$	4.81900e77	0.162335
$59$	3.75851e78	0.591700	0.295850	−	0.955234i	$-0.404397\pi$
$59$	3.75851e78	0.591700	0.295850	+	0.955234i	$0.404397\pi$
$60$	0	0
$61$	−8.19597e78	−0.292700	−0.146350	−	0.989233i	$-0.546753\pi$
$61$	−8.19597e78	−0.292700	−0.146350	+	0.989233i	$0.546753\pi$
$62$	−2.08910e79	−0.361850
$63$	0	0
$64$	−4.91303e79	−0.207176
$65$	5.22687e79	0.110560
$66$	0	0
$67$	−2.77246e80	−0.152243	−0.0761214	−	0.997099i	$-0.524254\pi$
$67$	−2.77246e80	−0.152243	−0.0761214	+	0.997099i	$0.524254\pi$
$68$	1.44426e80	0.0410202
$69$	0	0
$70$	−5.13146e80	−0.0401216
$71$	2.48739e82	1.03454	0.517271	−	0.855822i	$-0.326948\pi$
$71$	2.48739e82	1.03454	0.517271	+	0.855822i	$0.326948\pi$
$72$	0	0
$73$	1.94198e82	0.234627	0.117313	−	0.993095i	$-0.462572\pi$
$73$	1.94198e82	0.234627	0.117313	+	0.993095i	$0.462572\pi$
$74$	1.19556e83	0.788423
$75$	0	0
$76$	−2.04380e83	−0.411370
$77$	5.46555e83	0.614888
$78$	0	0
$79$	−3.70591e84	−1.33196	−0.665978	−	0.745972i	$-0.731985\pi$
$79$	−3.70591e84	−1.33196	−0.665978	+	0.745972i	$0.731985\pi$
$80$	4.71970e83	0.0969192
$81$	0	0
$82$	−1.45489e85	−0.995665
$83$	1.07302e85	0.428185	0.214093	−	0.976813i	$-0.431321\pi$
$83$	1.07302e85	0.428185	0.214093	+	0.976813i	$0.431321\pi$
$84$	0	0
$85$	−3.62931e83	−0.00501975
$86$	2.05723e86	1.69084
$87$	0	0
$88$	−2.39179e86	−0.706714
$89$	−7.67903e86	−1.37231	−0.686153	−	0.727457i	$-0.740702\pi$
$89$	−7.67903e86	−1.37231	−0.686153	+	0.727457i	$0.740702\pi$
$90$	0	0
$91$	−8.36993e86	−0.556391
$92$	1.62582e87	0.664531
$93$	0	0
$94$	1.00390e88	1.57580
$95$	5.13591e86	0.0503404
$96$	0	0
$97$	1.74718e88	0.677635	0.338818	−	0.940852i	$-0.389973\pi$
$97$	1.74718e88	0.677635	0.338818	+	0.940852i	$0.389973\pi$
$98$	−4.39691e88	−1.08041
$99$	0	0
$100$	−6.40335e88	−0.640335
$101$	−1.19479e89	−0.767343	−0.383671	−	0.923470i	$-0.625340\pi$
$101$	−1.19479e89	−0.767343	−0.383671	+	0.923470i	$0.625340\pi$
$102$	0	0
$103$	−1.38153e88	−0.0370769	−0.0185385	−	0.999828i	$-0.505901\pi$
$103$	−1.38153e88	−0.0370769	−0.0185385	+	0.999828i	$0.505901\pi$
$104$	3.66278e89	0.639481
$105$	0	0
$106$	5.13045e89	0.383747
$107$	1.99720e90	0.983656	0.491828	−	0.870692i	$-0.336329\pi$
$107$	1.99720e90	0.983656	0.491828	+	0.870692i	$0.336329\pi$
$108$	0	0
$109$	−1.48917e90	−0.321711	−0.160855	−	0.986978i	$-0.551425\pi$
$109$	−1.48917e90	−0.321711	−0.160855	+	0.986978i	$0.551425\pi$
$110$	−1.08889e90	−0.156678
$111$	0	0
$112$	−7.55779e90	−0.487745
$113$	2.72847e91	1.18557	0.592787	−	0.805359i	$-0.298027\pi$
$113$	2.72847e91	1.18557	0.592787	+	0.805359i	$0.298027\pi$
$114$	0	0
$115$	−4.08558e90	−0.0813204
$116$	6.02436e90	0.0815700
$117$	0	0
$118$	1.19908e92	0.758747
$119$	5.81172e90	0.0252618
$120$	0	0
$121$	6.76780e92	1.40120
$122$	−2.61476e92	−0.375335
$123$	0	0
$124$	−2.61164e92	−0.181823
$125$	3.22829e92	0.157209
$126$	0	0
$127$	−8.97792e92	−0.215730	−0.107865	−	0.994166i	$-0.534401\pi$
$127$	−8.97792e92	−0.215730	−0.107865	+	0.994166i	$0.534401\pi$
$128$	5.04114e93	0.854447
$129$	0	0
$130$	1.66752e93	0.141773
$131$	1.51084e94	0.913370	0.456685	−	0.889628i	$-0.349037\pi$
$131$	1.51084e94	0.913370	0.456685	+	0.889628i	$0.349037\pi$
$132$	0	0
$133$	−8.22428e93	−0.253338
$134$	−8.84496e93	−0.195224
$135$	0	0
$136$	−2.54328e93	−0.0290344
$137$	−4.03766e94	−0.332709	−0.166355	−	0.986066i	$-0.553200\pi$
$137$	−4.03766e94	−0.332709	−0.166355	+	0.986066i	$0.553200\pi$
$138$	0	0
$139$	−2.42776e94	−0.104965	−0.0524827	−	0.998622i	$-0.516713\pi$
$139$	−2.42776e94	−0.104965	−0.0524827	+	0.998622i	$0.516713\pi$
$140$	−6.41498e93	−0.0201603
$141$	0	0
$142$	7.93551e95	1.32661
$143$	−1.77609e96	−2.17276
$144$	0	0
$145$	−1.51388e94	−0.00998193
$146$	6.19548e95	0.300866
$147$	0	0
$148$	1.49460e96	0.396168
$149$	−4.62119e96	−0.907746	−0.453873	−	0.891066i	$-0.649958\pi$
$149$	−4.62119e96	−0.907746	−0.453873	+	0.891066i	$0.649958\pi$
$150$	0	0
$151$	−9.15258e96	−0.993275	−0.496638	−	0.867958i	$-0.665432\pi$
$151$	−9.15258e96	−0.993275	−0.496638	+	0.867958i	$0.665432\pi$
$152$	3.59904e96	0.291170
$153$	0	0
$154$	1.74367e97	0.788483
$155$	6.56286e95	0.0222501
$156$	0	0
$157$	5.65103e97	1.08291	0.541456	−	0.840729i	$-0.317873\pi$
$157$	5.65103e97	1.08291	0.541456	+	0.840729i	$0.317873\pi$
$158$	−1.18230e98	−1.70799
$159$	0	0
$160$	1.07004e97	0.0883205
$161$	6.54235e97	0.409244
$162$	0	0
$163$	3.56675e98	1.28802	0.644012	−	0.765015i	$-0.277269\pi$
$163$	3.56675e98	1.28802	0.644012	+	0.765015i	$0.277269\pi$
$164$	−1.81880e98	−0.500303
$165$	0	0
$166$	3.42324e98	0.549070
$167$	−1.30174e99	−1.59824	−0.799121	−	0.601170i	$-0.794702\pi$
$167$	−1.30174e99	−1.59824	−0.799121	+	0.601170i	$0.794702\pi$
$168$	0	0
$169$	1.33647e99	0.966051
$170$	−1.15786e97	−0.00643691
$171$	0	0
$172$	2.57180e99	0.849614
$173$	6.61614e99	1.68870	0.844351	−	0.535791i	$-0.179986\pi$
$173$	6.61614e99	1.68870	0.844351	+	0.535791i	$0.179986\pi$
$174$	0	0
$175$	−2.57672e99	−0.394343
$176$	−1.60375e100	−1.90469
$177$	0	0
$178$	−2.44984e100	−1.75973
$179$	1.26918e99	0.0710497	0.0355249	−	0.999369i	$-0.488690\pi$
$179$	1.26918e99	0.0710497	0.0355249	+	0.999369i	$0.488690\pi$
$180$	0	0
$181$	5.28698e100	1.80514	0.902571	−	0.430541i	$-0.141677\pi$
$181$	5.28698e100	1.80514	0.902571	+	0.430541i	$0.141677\pi$
$182$	−2.67025e100	−0.713470
$183$	0	0
$184$	−2.86301e100	−0.470360
$185$	−3.75582e99	−0.0484801
$186$	0	0
$187$	1.23324e100	0.0986498
$188$	1.25500e101	0.791808
$189$	0	0
$190$	1.63851e100	0.0645524
$191$	2.70845e100	0.0844764	0.0422382	−	0.999108i	$-0.486551\pi$
$191$	2.70845e100	0.0844764	0.0422382	+	0.999108i	$0.486551\pi$
$192$	0	0
$193$	−7.69721e101	−1.51019	−0.755097	−	0.655613i	$-0.772410\pi$
$193$	−7.69721e101	−1.51019	−0.755097	+	0.655613i	$0.772410\pi$
$194$	5.57403e101	0.868944
$195$	0	0
$196$	−5.49670e101	−0.542884
$197$	1.82807e102	1.43961	0.719805	−	0.694176i	$-0.244231\pi$
$197$	1.82807e102	1.43961	0.719805	+	0.694176i	$0.244231\pi$
$198$	0	0
$199$	1.85967e102	0.934273	0.467137	−	0.884185i	$-0.345286\pi$
$199$	1.85967e102	0.934273	0.467137	+	0.884185i	$0.345286\pi$
$200$	1.12760e102	0.453233
$201$	0	0
$202$	−3.81172e102	−0.983978
$203$	2.42421e101	0.0502340
$204$	0	0
$205$	4.57050e101	0.0612233
$206$	−4.40749e101	−0.0475444
$207$	0	0
$208$	2.45599e103	1.72349
$209$	−1.74518e103	−0.989307
$210$	0	0
$211$	−1.52726e103	−0.566688	−0.283344	−	0.959018i	$-0.591444\pi$
$211$	−1.52726e103	−0.566688	−0.283344	+	0.959018i	$0.591444\pi$
$212$	6.41372e102	0.192825
$213$	0	0
$214$	6.37165e103	1.26136
$215$	−6.46275e102	−0.103969
$216$	0	0
$217$	−1.05093e103	−0.111973
$218$	−4.75089e103	−0.412535
$219$	0	0
$220$	−1.36125e103	−0.0787279
$221$	−1.88858e103	−0.0892647
$222$	0	0
$223$	3.56431e104	1.12826	0.564130	−	0.825686i	$-0.309212\pi$
$223$	3.56431e104	1.12826	0.564130	+	0.825686i	$0.309212\pi$
$224$	−1.71349e104	−0.444472
$225$	0	0
$226$	8.70463e104	1.52028
$227$	1.20998e105	1.73631	0.868154	−	0.496294i	$-0.165306\pi$
$227$	1.20998e105	1.73631	0.868154	+	0.496294i	$0.165306\pi$
$228$	0	0
$229$	1.82845e105	1.77584	0.887922	−	0.459994i	$-0.152148\pi$
$229$	1.82845e105	1.77584	0.887922	+	0.459994i	$0.152148\pi$
$230$	−1.30342e104	−0.104279
$231$	0	0
$232$	−1.06087e104	−0.0577358
$233$	−4.63528e104	−0.208323	−0.104162	−	0.994560i	$-0.533216\pi$
$233$	−4.63528e104	−0.208323	−0.104162	+	0.994560i	$0.533216\pi$
$234$	0	0
$235$	−3.15372e104	−0.0968955
$236$	1.49900e105	0.381256
$237$	0	0
$238$	1.85411e104	0.0323937
$239$	9.19408e105	1.33291	0.666456	−	0.745544i	$-0.267810\pi$
$239$	9.19408e105	1.33291	0.666456	+	0.745544i	$0.267810\pi$
$240$	0	0
$241$	9.93847e105	0.994400	0.497200	−	0.867636i	$-0.334362\pi$
$241$	9.93847e105	0.994400	0.497200	+	0.867636i	$0.334362\pi$
$242$	2.15913e106	1.79678
$243$	0	0
$244$	−3.26878e105	−0.188599
$245$	1.38128e105	0.0664341
$246$	0	0
$247$	2.67257e106	0.895189
$248$	4.59899e105	0.128695
$249$	0	0
$250$	1.02992e106	0.201592
$251$	−6.45749e105	−0.105824	−0.0529119	−	0.998599i	$-0.516850\pi$
$251$	−6.45749e105	−0.105824	−0.0529119	+	0.998599i	$0.516850\pi$
$252$	0	0
$253$	1.38828e107	1.59814
$254$	−2.86422e106	−0.276634
$255$	0	0
$256$	1.91237e107	1.30285
$257$	1.37257e107	0.786159	0.393079	−	0.919504i	$-0.371410\pi$
$257$	1.37257e107	0.786159	0.393079	+	0.919504i	$0.371410\pi$
$258$	0	0
$259$	6.01431e106	0.243975
$260$	2.08462e106	0.0712381
$261$	0	0
$262$	4.82003e107	1.17123
$263$	1.85087e107	0.379616	0.189808	−	0.981821i	$-0.439213\pi$
$263$	1.85087e107	0.379616	0.189808	+	0.981821i	$0.439213\pi$
$264$	0	0
$265$	−1.61172e106	−0.0235965
$266$	−2.62379e107	−0.324860
$267$	0	0
$268$	−1.10573e107	−0.0980962
$269$	7.26822e107	0.546326	0.273163	−	0.961968i	$-0.411930\pi$
$269$	7.26822e107	0.546326	0.273163	+	0.961968i	$0.411930\pi$
$270$	0	0
$271$	2.62902e108	1.42122	0.710610	−	0.703586i	$-0.248419\pi$
$271$	2.62902e108	1.42122	0.710610	+	0.703586i	$0.248419\pi$
$272$	−1.70533e107	−0.0782515
$273$	0	0
$274$	−1.28813e108	−0.426639
$275$	−5.46777e108	−1.53995
$276$	0	0
$277$	−6.85250e108	−1.39797	−0.698987	−	0.715134i	$-0.746366\pi$
$277$	−6.85250e108	−1.39797	−0.698987	+	0.715134i	$0.746366\pi$
$278$	−7.74525e107	−0.134599
$279$	0	0
$280$	1.12965e107	0.0142696
$281$	2.51845e108	0.271457	0.135729	−	0.990746i	$-0.456662\pi$
$281$	2.51845e108	0.271457	0.135729	+	0.990746i	$0.456662\pi$
$282$	0	0
$283$	1.20621e108	0.0948254	0.0474127	−	0.998875i	$-0.484902\pi$
$283$	1.20621e108	0.0948254	0.0474127	+	0.998875i	$0.484902\pi$
$284$	9.92041e108	0.666597
$285$	0	0
$286$	−5.66625e109	−2.78617
$287$	−7.31887e108	−0.308106
$288$	0	0
$289$	−3.22248e109	−0.995947
$290$	−4.82971e107	−0.0128000
$291$	0	0
$292$	7.74514e108	0.151179
$293$	5.59855e109	0.938570	0.469285	−	0.883047i	$-0.344512\pi$
$293$	5.59855e109	0.938570	0.469285	+	0.883047i	$0.344512\pi$
$294$	0	0
$295$	−3.76687e108	−0.0466553
$296$	−2.63193e109	−0.280410
$297$	0	0
$298$	−1.47429e110	−1.16402
$299$	−2.12601e110	−1.44610
$300$	0	0
$301$	1.03490e110	0.523225
$302$	−2.91994e110	−1.27370
$303$	0	0
$304$	2.41325e110	0.784744
$305$	8.21420e108	0.0230793
$306$	0	0
$307$	−2.89040e110	−0.607157	−0.303578	−	0.952806i	$-0.598181\pi$
$307$	−2.89040e110	−0.607157	−0.303578	+	0.952806i	$0.598181\pi$
$308$	2.17981e110	0.396198
$309$	0	0
$310$	2.09374e109	0.0285317
$311$	−1.10485e111	−1.30456	−0.652282	−	0.757977i	$-0.726188\pi$
$311$	−1.10485e111	−1.30456	−0.652282	+	0.757977i	$0.726188\pi$
$312$	0	0
$313$	7.78951e110	0.691492	0.345746	−	0.938328i	$-0.387626\pi$
$313$	7.78951e110	0.691492	0.345746	+	0.938328i	$0.387626\pi$
$314$	1.80285e111	1.38864
$315$	0	0
$316$	−1.47802e111	−0.858233
$317$	−3.26678e110	−0.164810	−0.0824049	−	0.996599i	$-0.526260\pi$
$317$	−3.26678e110	−0.164810	−0.0824049	+	0.996599i	$0.526260\pi$
$318$	0	0
$319$	5.14416e110	0.196168
$320$	4.92395e109	0.0163358
$321$	0	0
$322$	2.08720e111	0.524781
$323$	−1.85572e110	−0.0406443
$324$	0	0
$325$	8.37333e111	1.39344
$326$	1.13790e112	1.65166
$327$	0	0
$328$	3.20283e111	0.354117
$329$	5.05015e111	0.487626
$330$	0	0
$331$	1.61579e112	1.19135	0.595675	−	0.803226i	$-0.296885\pi$
$331$	1.61579e112	1.19135	0.595675	+	0.803226i	$0.296885\pi$
$332$	4.27949e111	0.275897
$333$	0	0
$334$	−4.15295e112	−2.04946
$335$	2.77863e110	0.0120043
$336$	0	0
$337$	3.52838e112	1.16962	0.584810	−	0.811170i	$-0.301169\pi$
$337$	3.52838e112	1.16962	0.584810	+	0.811170i	$0.301169\pi$
$338$	4.26373e112	1.23879
$339$	0	0
$340$	−1.44747e110	−0.00323443
$341$	−2.23006e112	−0.437267
$342$	0	0
$343$	−4.83713e112	−0.731139
$344$	−4.52884e112	−0.601363
$345$	0	0
$346$	2.11074e113	2.16545
$347$	−1.07241e113	−0.967612	−0.483806	−	0.875175i	$-0.660746\pi$
$347$	−1.07241e113	−0.967612	−0.483806	+	0.875175i	$0.660746\pi$
$348$	0	0
$349$	5.96829e112	0.416983	0.208491	−	0.978024i	$-0.433145\pi$
$349$	5.96829e112	0.416983	0.208491	+	0.978024i	$0.433145\pi$
$350$	−8.22049e112	−0.505673
$351$	0	0
$352$	−3.63600e113	−1.73570
$353$	−1.30915e113	−0.550827	−0.275414	−	0.961326i	$-0.588815\pi$
$353$	−1.30915e113	−0.550827	−0.275414	+	0.961326i	$0.588815\pi$
$354$	0	0
$355$	−2.49292e112	−0.0815732
$356$	−3.06261e113	−0.884233
$357$	0	0
$358$	4.04905e112	0.0911084
$359$	4.82670e112	0.0959284	0.0479642	−	0.998849i	$-0.484727\pi$
$359$	4.82670e112	0.0959284	0.0479642	+	0.998849i	$0.484727\pi$
$360$	0	0
$361$	−3.81668e113	−0.592400
$362$	1.68670e114	2.31477
$363$	0	0
$364$	−3.33816e113	−0.358505
$365$	−1.94630e112	−0.0185002
$366$	0	0
$367$	−2.20853e114	−1.64613	−0.823063	−	0.567950i	$-0.807737\pi$
$367$	−2.20853e114	−1.64613	−0.823063	+	0.567950i	$0.807737\pi$
$368$	−1.91972e114	−1.26768
$369$	0	0
$370$	−1.19822e113	−0.0621669
$371$	2.58089e113	0.118749
$372$	0	0
$373$	−2.99699e114	−1.08553	−0.542765	−	0.839884i	$-0.682623\pi$
$373$	−2.99699e114	−1.08553	−0.542765	+	0.839884i	$0.682623\pi$
$374$	3.93440e113	0.126500
$375$	0	0
$376$	−2.21001e114	−0.560447
$377$	−7.87775e113	−0.177506
$378$	0	0
$379$	1.07738e115	1.91834	0.959170	−	0.282829i	$-0.0912727\pi$
$379$	1.07738e115	1.91834	0.959170	+	0.282829i	$0.0912727\pi$
$380$	2.04834e113	0.0324364
$381$	0	0
$382$	8.64074e113	0.108326
$383$	7.15115e114	0.798051	0.399025	−	0.916940i	$-0.369349\pi$
$383$	7.15115e114	0.798051	0.399025	+	0.916940i	$0.369349\pi$
$384$	0	0
$385$	−5.47770e113	−0.0484837
$386$	−2.45563e115	−1.93655
$387$	0	0
$388$	6.96825e114	0.436628
$389$	2.74793e115	1.53549	0.767747	−	0.640753i	$-0.221378\pi$
$389$	2.74793e115	1.53549	0.767747	+	0.640753i	$0.221378\pi$
$390$	0	0
$391$	1.47621e114	0.0656572
$392$	9.67947e114	0.384257
$393$	0	0
$394$	5.83207e115	1.84604
$395$	3.71415e114	0.105024
$396$	0	0
$397$	7.31767e114	0.165270	0.0826352	−	0.996580i	$-0.473666\pi$
$397$	7.31767e114	0.165270	0.0826352	+	0.996580i	$0.473666\pi$
$398$	5.93289e115	1.19804
$399$	0	0
$400$	7.56087e115	1.22152
$401$	−6.87201e115	−0.993480	−0.496740	−	0.867899i	$-0.665470\pi$
$401$	−6.87201e115	−0.993480	−0.496740	+	0.867899i	$0.665470\pi$
$402$	0	0
$403$	3.41511e115	0.395667
$404$	−4.76514e115	−0.494430
$405$	0	0
$406$	7.73396e114	0.0644159
$407$	1.27623e116	0.952746
$408$	0	0
$409$	−1.57330e116	−0.944328	−0.472164	−	0.881511i	$-0.656527\pi$
$409$	−1.57330e116	−0.944328	−0.472164	+	0.881511i	$0.656527\pi$
$410$	1.45812e115	0.0785078
$411$	0	0
$412$	−5.50992e114	−0.0238902
$413$	6.03200e115	0.234792
$414$	0	0
$415$	−1.07540e115	−0.0337622
$416$	5.56817e116	1.57058
$417$	0	0
$418$	−5.56764e116	−1.26861
$419$	−2.45919e116	−0.503811	−0.251906	−	0.967752i	$-0.581057\pi$
$419$	−2.45919e116	−0.503811	−0.251906	+	0.967752i	$0.581057\pi$
$420$	0	0
$421$	−5.39311e116	−0.893893	−0.446947	−	0.894561i	$-0.647489\pi$
$421$	−5.39311e116	−0.893893	−0.446947	+	0.894561i	$0.647489\pi$
$422$	−4.87241e116	−0.726675
$423$	0	0
$424$	−1.12943e116	−0.136483
$425$	−5.81408e115	−0.0632665
$426$	0	0
$427$	−1.31536e116	−0.116146
$428$	7.96538e116	0.633809
$429$	0	0
$430$	−2.06181e116	−0.133322
$431$	−2.12129e116	−0.123698	−0.0618489	−	0.998086i	$-0.519700\pi$
$431$	−2.12129e116	−0.123698	−0.0618489	+	0.998086i	$0.519700\pi$
$432$	0	0
$433$	3.26732e117	1.55053	0.775265	−	0.631636i	$-0.217616\pi$
$433$	3.26732e117	1.55053	0.775265	+	0.631636i	$0.217616\pi$
$434$	−3.35277e116	−0.143586
$435$	0	0
$436$	−5.93922e116	−0.207291
$437$	−2.08901e117	−0.658441
$438$	0	0
$439$	2.12142e117	0.545702	0.272851	−	0.962056i	$-0.412033\pi$
$439$	2.12142e117	0.545702	0.272851	+	0.962056i	$0.412033\pi$
$440$	2.39711e116	0.0557241
$441$	0	0
$442$	−6.02513e116	−0.114466
$443$	4.42831e117	0.760802	0.380401	−	0.924822i	$-0.375786\pi$
$443$	4.42831e117	0.760802	0.380401	+	0.924822i	$0.375786\pi$
$444$	0	0
$445$	7.69611e116	0.108206
$446$	1.13712e118	1.44679
$447$	0	0
$448$	−7.88487e116	−0.0822097
$449$	−4.39818e117	−0.415251	−0.207626	−	0.978208i	$-0.566574\pi$
$449$	−4.39818e117	−0.415251	−0.207626	+	0.978208i	$0.566574\pi$
$450$	0	0
$451$	−1.55306e118	−1.20318
$452$	1.08819e118	0.763914
$453$	0	0
$454$	3.86019e118	2.22650
$455$	8.38854e116	0.0438712
$456$	0	0
$457$	2.74806e118	1.18238	0.591188	−	0.806533i	$-0.298659\pi$
$457$	2.74806e118	1.18238	0.591188	+	0.806533i	$0.298659\pi$
$458$	5.83330e118	2.27720
$459$	0	0
$460$	−1.62944e117	−0.0523980
$461$	2.01568e118	0.588477	0.294239	−	0.955732i	$-0.404934\pi$
$461$	2.01568e118	0.588477	0.294239	+	0.955732i	$0.404934\pi$
$462$	0	0
$463$	6.20126e118	1.49323	0.746613	−	0.665258i	$-0.231679\pi$
$463$	6.20126e118	1.49323	0.746613	+	0.665258i	$0.231679\pi$
$464$	−7.11337e117	−0.155606
$465$	0	0
$466$	−1.47879e118	−0.267137
$467$	1.14327e119	1.87735	0.938676	−	0.344800i	$-0.112053\pi$
$467$	1.14327e119	1.87735	0.938676	+	0.344800i	$0.112053\pi$
$468$	0	0
$469$	−4.44949e117	−0.0604114
$470$	−1.00613e118	−0.124251
$471$	0	0
$472$	−2.63967e118	−0.269856
$473$	2.19604e119	2.04324
$474$	0	0
$475$	8.22762e118	0.634467
$476$	2.31787e117	0.0162772
$477$	0	0
$478$	2.93318e119	1.70922
$479$	−1.95218e119	−1.03655	−0.518273	−	0.855215i	$-0.673425\pi$
$479$	−1.95218e119	−1.03655	−0.518273	+	0.855215i	$0.673425\pi$
$480$	0	0
$481$	−1.95442e119	−0.862107
$482$	3.17066e119	1.27514
$483$	0	0
$484$	2.69919e119	0.902847
$485$	−1.75107e118	−0.0534313
$486$	0	0
$487$	−2.36047e119	−0.599736	−0.299868	−	0.953981i	$-0.596943\pi$
$487$	−2.36047e119	−0.599736	−0.299868	+	0.953981i	$0.596943\pi$
$488$	5.75619e118	0.133491
$489$	0	0
$490$	4.40669e118	0.0851897
$491$	−4.48321e119	−0.791522	−0.395761	−	0.918354i	$-0.629519\pi$
$491$	−4.48321e119	−0.791522	−0.395761	+	0.918354i	$0.629519\pi$
$492$	0	0
$493$	5.46997e117	0.00805930
$494$	8.52628e119	1.14792
$495$	0	0
$496$	3.08374e119	0.346851
$497$	3.99199e119	0.410516
$498$	0	0
$499$	−9.47256e119	−0.814692	−0.407346	−	0.913274i	$-0.633546\pi$
$499$	−9.47256e119	−0.814692	−0.407346	+	0.913274i	$0.633546\pi$
$500$	1.28753e119	0.101296
$501$	0	0
$502$	−2.06013e119	−0.135700
$503$	3.20241e120	1.93064	0.965321	−	0.261065i	$-0.0840737\pi$
$503$	3.20241e120	1.93064	0.965321	+	0.261065i	$0.0840737\pi$
$504$	0	0
$505$	1.19744e119	0.0605047
$506$	4.42902e120	2.04932
$507$	0	0
$508$	−3.58064e119	−0.139003
$509$	1.53283e120	0.545196	0.272598	−	0.962128i	$-0.412117\pi$
$509$	1.53283e120	0.545196	0.272598	+	0.962128i	$0.412117\pi$
$510$	0	0
$511$	3.11666e119	0.0931021
$512$	2.98072e120	0.816221
$513$	0	0
$514$	4.37890e120	1.00811
$515$	1.38460e118	0.00292350
$516$	0	0
$517$	1.07164e121	1.90422
$518$	1.91874e120	0.312854
$519$	0	0
$520$	−3.67093e119	−0.0504228
$521$	−2.75020e120	−0.346805	−0.173403	−	0.984851i	$-0.555476\pi$
$521$	−2.75020e120	−0.346805	−0.173403	+	0.984851i	$0.555476\pi$
$522$	0	0
$523$	1.45893e121	1.55135	0.775674	−	0.631134i	$-0.217410\pi$
$523$	1.45893e121	1.55135	0.775674	+	0.631134i	$0.217410\pi$
$524$	6.02566e120	0.588522
$525$	0	0
$526$	5.90481e120	0.486789
$527$	−2.37130e119	−0.0179645
$528$	0	0
$529$	9.94471e119	0.0636524
$530$	−5.14186e119	−0.0302583
$531$	0	0
$532$	−3.28007e120	−0.163236
$533$	2.37835e121	1.08872
$534$	0	0
$535$	−2.00164e120	−0.0775609
$536$	1.94715e120	0.0694331
$537$	0	0
$538$	2.31878e121	0.700564
$539$	−4.69359e121	−1.30559
$540$	0	0
$541$	−5.02723e120	−0.118591	−0.0592953	−	0.998240i	$-0.518885\pi$
$541$	−5.02723e120	−0.118591	−0.0592953	+	0.998240i	$0.518885\pi$
$542$	8.38736e121	1.82246
$543$	0	0
$544$	−3.86630e120	−0.0713090
$545$	1.49248e120	0.0253668
$546$	0	0
$547$	1.81478e121	0.262053	0.131026	−	0.991379i	$-0.458173\pi$
$547$	1.81478e121	0.262053	0.131026	+	0.991379i	$0.458173\pi$
$548$	−1.61033e121	−0.214378
$549$	0	0
$550$	−1.74438e122	−1.97470
$551$	−7.74067e120	−0.0808225
$552$	0	0
$553$	−5.94758e121	−0.528533
$554$	−2.18615e122	−1.79265
$555$	0	0
$556$	−9.68256e120	−0.0676335
$557$	−4.76949e121	−0.307550	−0.153775	−	0.988106i	$-0.549143\pi$
$557$	−4.76949e121	−0.307550	−0.153775	+	0.988106i	$0.549143\pi$
$558$	0	0
$559$	−3.36302e122	−1.84886
$560$	7.57460e120	0.0384585
$561$	0	0
$562$	8.03458e121	0.348095
$563$	6.41763e121	0.256892	0.128446	−	0.991716i	$-0.459001\pi$
$563$	6.41763e121	0.256892	0.128446	+	0.991716i	$0.459001\pi$
$564$	0	0
$565$	−2.73454e121	−0.0934821
$566$	3.84815e121	0.121596
$567$	0	0
$568$	−1.74694e122	−0.471822
$569$	−3.36684e122	−0.840867	−0.420433	−	0.907323i	$-0.638122\pi$
$569$	−3.36684e122	−0.840867	−0.420433	+	0.907323i	$0.638122\pi$
$570$	0	0
$571$	−2.53729e122	−0.542080	−0.271040	−	0.962568i	$-0.587368\pi$
$571$	−2.53729e122	−0.542080	−0.271040	+	0.962568i	$0.587368\pi$
$572$	−7.08354e122	−1.40000
$573$	0	0
$574$	−2.33493e122	−0.395090
$575$	−6.54501e122	−1.02492
$576$	0	0
$577$	1.10107e123	1.47737	0.738687	−	0.674049i	$-0.235446\pi$
$577$	1.10107e123	1.47737	0.738687	+	0.674049i	$0.235446\pi$
$578$	−1.02807e123	−1.27712
$579$	0	0
$580$	−6.03776e120	−0.00643176
$581$	1.72207e122	0.169908
$582$	0	0
$583$	5.47663e122	0.463727
$584$	−1.36389e122	−0.107006
$585$	0	0
$586$	1.78610e123	1.20355
$587$	−3.13449e122	−0.195781	−0.0978905	−	0.995197i	$-0.531210\pi$
$587$	−3.13449e122	−0.195781	−0.0978905	+	0.995197i	$0.531210\pi$
$588$	0	0
$589$	3.35568e122	0.180157
$590$	−1.20174e122	−0.0598269
$591$	0	0
$592$	−1.76478e123	−0.755743
$593$	3.85499e123	1.53140	0.765702	−	0.643196i	$-0.222392\pi$
$593$	3.85499e123	1.53140	0.765702	+	0.643196i	$0.222392\pi$
$594$	0	0
$595$	−5.82464e120	−0.00199188
$596$	−1.84306e123	−0.584898
$597$	0	0
$598$	−6.78259e123	−1.85436
$599$	−6.84145e123	−1.73642	−0.868210	−	0.496198i	$-0.834729\pi$
$599$	−6.84145e123	−1.73642	−0.868210	+	0.496198i	$0.834729\pi$
$600$	0	0
$601$	5.81715e122	0.127291	0.0636453	−	0.997973i	$-0.479727\pi$
$601$	5.81715e122	0.127291	0.0636453	+	0.997973i	$0.479727\pi$
$602$	3.30163e123	0.670941
$603$	0	0
$604$	−3.65030e123	−0.640008
$605$	−6.78285e122	−0.110484
$606$	0	0
$607$	7.22901e122	0.101667	0.0508337	−	0.998707i	$-0.483812\pi$
$607$	7.22901e122	0.101667	0.0508337	+	0.998707i	$0.483812\pi$
$608$	5.47128e123	0.715121
$609$	0	0
$610$	2.62057e122	0.0295950
$611$	−1.64110e124	−1.72306
$612$	0	0
$613$	−1.46296e123	−0.132814	−0.0664068	−	0.997793i	$-0.521154\pi$
$613$	−1.46296e123	−0.132814	−0.0664068	+	0.997793i	$0.521154\pi$
$614$	−9.22124e123	−0.778569
$615$	0	0
$616$	−3.83856e123	−0.280431
$617$	−8.13622e123	−0.553010	−0.276505	−	0.961013i	$-0.589176\pi$
$617$	−8.13622e123	−0.553010	−0.276505	+	0.961013i	$0.589176\pi$
$618$	0	0
$619$	4.24524e123	0.249844	0.124922	−	0.992167i	$-0.460132\pi$
$619$	4.24524e123	0.249844	0.124922	+	0.992167i	$0.460132\pi$
$620$	2.61745e122	0.0143367
$621$	0	0
$622$	−3.52479e124	−1.67287
$623$	−1.23240e124	−0.544545
$624$	0	0
$625$	2.56154e124	0.981387
$626$	2.48508e124	0.886712
$627$	0	0
$628$	2.25379e124	0.697765
$629$	1.35706e123	0.0391422
$630$	0	0
$631$	−4.16093e124	−1.04204	−0.521019	−	0.853545i	$-0.674448\pi$
$631$	−4.16093e124	−1.04204	−0.521019	+	0.853545i	$0.674448\pi$
$632$	2.60273e124	0.607463
$633$	0	0
$634$	−1.04220e124	−0.211339
$635$	8.99788e122	0.0170102
$636$	0	0
$637$	7.18776e124	1.18138
$638$	1.64114e124	0.251550
$639$	0	0
$640$	−5.05235e123	−0.0673728
$641$	5.88543e124	0.732144	0.366072	−	0.930587i	$-0.380702\pi$
$641$	5.88543e124	0.732144	0.366072	+	0.930587i	$0.380702\pi$
$642$	0	0
$643$	1.22279e124	0.132423	0.0662116	−	0.997806i	$-0.478909\pi$
$643$	1.22279e124	0.132423	0.0662116	+	0.997806i	$0.478909\pi$
$644$	2.60927e124	0.263693
$645$	0	0
$646$	−5.92028e123	−0.0521189
$647$	−1.38772e125	−1.14041	−0.570204	−	0.821503i	$-0.693136\pi$
$647$	−1.38772e125	−1.14041	−0.570204	+	0.821503i	$0.693136\pi$
$648$	0	0
$649$	1.27998e125	0.916885
$650$	2.67134e125	1.78684
$651$	0	0
$652$	1.42252e125	0.829926
$653$	1.57716e125	0.859487	0.429743	−	0.902951i	$-0.358604\pi$
$653$	1.57716e125	0.859487	0.429743	+	0.902951i	$0.358604\pi$
$654$	0	0
$655$	−1.51420e124	−0.0720189
$656$	2.14758e125	0.954394
$657$	0	0
$658$	1.61115e125	0.625291
$659$	3.75748e125	1.36300	0.681500	−	0.731818i	$-0.261328\pi$
$659$	3.75748e125	1.36300	0.681500	+	0.731818i	$0.261328\pi$
$660$	0	0
$661$	1.24288e125	0.393970	0.196985	−	0.980406i	$-0.436885\pi$
$661$	1.24288e125	0.393970	0.196985	+	0.980406i	$0.436885\pi$
$662$	5.15485e125	1.52769
$663$	0	0
$664$	−7.53601e124	−0.195282
$665$	8.24257e123	0.0199756
$666$	0	0
$667$	6.15764e124	0.130561
$668$	−5.19172e125	−1.02981
$669$	0	0
$670$	8.86463e123	0.0153933
$671$	−2.79119e125	−0.453562
$672$	0	0
$673$	9.59713e125	1.36606	0.683032	−	0.730389i	$-0.260661\pi$
$673$	9.59713e125	1.36606	0.683032	+	0.730389i	$0.260661\pi$
$674$	1.12566e126	1.49983
$675$	0	0
$676$	5.33020e125	0.622466
$677$	−4.24330e125	−0.463989	−0.231994	−	0.972717i	$-0.574525\pi$
$677$	−4.24330e125	−0.463989	−0.231994	+	0.972717i	$0.574525\pi$
$678$	0	0
$679$	2.80404e125	0.268892
$680$	2.54893e123	0.00228935
$681$	0	0
$682$	−7.11454e125	−0.560715
$683$	−1.36159e126	−1.00536	−0.502682	−	0.864471i	$-0.667653\pi$
$683$	−1.36159e126	−1.00536	−0.502682	+	0.864471i	$0.667653\pi$
$684$	0	0
$685$	4.04664e124	0.0262340
$686$	−1.54319e126	−0.937553
$687$	0	0
$688$	−3.03670e126	−1.62075
$689$	−8.38690e125	−0.419610
$690$	0	0
$691$	−6.63422e125	−0.291754	−0.145877	−	0.989303i	$-0.546600\pi$
$691$	−6.63422e125	−0.291754	−0.145877	+	0.989303i	$0.546600\pi$
$692$	2.63870e126	1.08810
$693$	0	0
$694$	−3.42132e126	−1.24079
$695$	2.43315e124	0.00827648
$696$	0	0
$697$	−1.65142e125	−0.0494310
$698$	1.90406e126	0.534705
$699$	0	0
$700$	−1.02767e126	−0.254091
$701$	−1.31009e126	−0.303984	−0.151992	−	0.988382i	$-0.548569\pi$
$701$	−1.31009e126	−0.303984	−0.151992	+	0.988382i	$0.548569\pi$
$702$	0	0
$703$	−1.92040e126	−0.392537
$704$	−1.67316e126	−0.321036
$705$	0	0
$706$	−4.17658e126	−0.706336
$707$	−1.91750e126	−0.304489
$708$	0	0
$709$	5.61717e126	0.786611	0.393305	−	0.919408i	$-0.371332\pi$
$709$	5.61717e126	0.786611	0.393305	+	0.919408i	$0.371332\pi$
$710$	−7.95316e125	−0.104603
$711$	0	0
$712$	5.39313e126	0.625866
$713$	−2.66942e126	−0.291027
$714$	0	0
$715$	1.78004e126	0.171321
$716$	5.06183e125	0.0457802
$717$	0	0
$718$	1.53986e126	0.123011
$719$	−1.05953e127	−0.795569	−0.397784	−	0.917479i	$-0.630221\pi$
$719$	−1.05953e127	−0.795569	−0.397784	+	0.917479i	$0.630221\pi$
$720$	0	0
$721$	−2.21720e125	−0.0147125
$722$	−1.21763e127	−0.759645
$723$	0	0
$724$	2.10860e127	1.16313
$725$	−2.42520e126	−0.125807
$726$	0	0
$727$	−1.34692e127	−0.618104	−0.309052	−	0.951045i	$-0.600012\pi$
$727$	−1.34692e127	−0.618104	−0.309052	+	0.951045i	$0.600012\pi$
$728$	5.87836e126	0.253752
$729$	0	0
$730$	−6.20926e125	−0.0237232
$731$	2.33513e126	0.0839438
$732$	0	0
$733$	3.56447e127	1.13467	0.567333	−	0.823489i	$-0.307975\pi$
$733$	3.56447e127	1.13467	0.567333	+	0.823489i	$0.307975\pi$
$734$	−7.04586e127	−2.11086
$735$	0	0
$736$	−4.35236e127	−1.15521
$737$	−9.44177e126	−0.235912
$738$	0	0
$739$	−2.93556e127	−0.650150	−0.325075	−	0.945688i	$-0.605390\pi$
$739$	−2.93556e127	−0.650150	−0.325075	+	0.945688i	$0.605390\pi$
$740$	−1.49793e126	−0.0312377
$741$	0	0
$742$	8.23381e126	0.152274
$743$	6.01913e127	1.04841	0.524206	−	0.851592i	$-0.324362\pi$
$743$	6.01913e127	1.04841	0.524206	+	0.851592i	$0.324362\pi$
$744$	0	0
$745$	4.63146e126	0.0715754
$746$	−9.56128e127	−1.39200
$747$	0	0
$748$	4.91850e126	0.0635640
$749$	3.20528e127	0.390324
$750$	0	0
$751$	−1.76278e128	−1.90643	−0.953217	−	0.302287i	$-0.902250\pi$
$751$	−1.76278e128	−1.90643	−0.953217	+	0.302287i	$0.902250\pi$
$752$	−1.48186e128	−1.51048
$753$	0	0
$754$	−2.51324e127	−0.227619
$755$	9.17294e126	0.0783194
$756$	0	0
$757$	−1.57049e127	−0.119198	−0.0595988	−	0.998222i	$-0.518982\pi$
$757$	−1.57049e127	−0.119198	−0.0595988	+	0.998222i	$0.518982\pi$
$758$	3.43717e128	2.45992
$759$	0	0
$760$	−3.60705e126	−0.0229587
$761$	6.19247e127	0.371746	0.185873	−	0.982574i	$-0.440489\pi$
$761$	6.19247e127	0.371746	0.185873	+	0.982574i	$0.440489\pi$
$762$	0	0
$763$	−2.38996e127	−0.127658
$764$	1.08020e127	0.0544316
$765$	0	0
$766$	2.28143e128	1.02336
$767$	−1.96016e128	−0.829657
$768$	0	0
$769$	−5.08598e128	−1.91714	−0.958568	−	0.284864i	$-0.908051\pi$
$769$	−5.08598e128	−1.91714	−0.958568	+	0.284864i	$0.908051\pi$
$770$	−1.74755e127	−0.0621715
$771$	0	0
$772$	−3.06986e128	−0.973080
$773$	1.07698e128	0.322270	0.161135	−	0.986932i	$-0.448485\pi$
$773$	1.07698e128	0.322270	0.161135	+	0.986932i	$0.448485\pi$
$774$	0	0
$775$	1.05136e128	0.280430
$776$	−1.22708e128	−0.309048
$777$	0	0
$778$	8.76670e128	1.96899
$779$	2.33696e128	0.495718
$780$	0	0
$781$	8.47096e128	1.60310
$782$	4.70954e127	0.0841934
$783$	0	0
$784$	6.49033e128	1.03562
$785$	−5.66360e127	−0.0853872
$786$	0	0
$787$	4.48703e128	0.604065	0.302032	−	0.953298i	$-0.402335\pi$
$787$	4.48703e128	0.604065	0.302032	+	0.953298i	$0.402335\pi$
$788$	7.29083e128	0.927599
$789$	0	0
$790$	1.18492e128	0.134674
$791$	4.37890e128	0.470448
$792$	0	0
$793$	4.27442e128	0.410412
$794$	2.33455e128	0.211929
$795$	0	0
$796$	7.41687e128	0.601990
$797$	1.23563e129	0.948402	0.474201	−	0.880417i	$-0.342737\pi$
$797$	1.23563e129	0.948402	0.474201	+	0.880417i	$0.342737\pi$
$798$	0	0
$799$	1.13951e128	0.0782323
$800$	1.71419e129	1.11315
$801$	0	0
$802$	−2.19237e129	−1.27396
$803$	6.61352e128	0.363572
$804$	0	0
$805$	−6.55690e127	−0.0322687
$806$	1.08952e129	0.507372
$807$	0	0
$808$	8.39122e128	0.349961
$809$	4.09545e129	1.61656	0.808281	−	0.588797i	$-0.200398\pi$
$809$	4.09545e129	1.61656	0.808281	+	0.588797i	$0.200398\pi$
$810$	0	0
$811$	−5.08524e128	−0.179839	−0.0899195	−	0.995949i	$-0.528661\pi$
$811$	−5.08524e128	−0.179839	−0.0899195	+	0.995949i	$0.528661\pi$
$812$	9.66844e127	0.0323678
$813$	0	0
$814$	4.07155e129	1.22172
$815$	−3.57468e128	−0.101560
$816$	0	0
$817$	−3.30449e129	−0.841828
$818$	−5.01927e129	−1.21093
$819$	0	0
$820$	1.82284e128	0.0394487
$821$	−7.00375e129	−1.43569	−0.717844	−	0.696204i	$-0.754871\pi$
$821$	−7.00375e129	−1.43569	−0.717844	+	0.696204i	$0.754871\pi$
$822$	0	0
$823$	−1.04462e130	−1.92162	−0.960808	−	0.277214i	$-0.910589\pi$
$823$	−1.04462e130	−1.92162	−0.960808	+	0.277214i	$0.910589\pi$
$824$	9.70275e127	0.0169096
$825$	0	0
$826$	1.92438e129	0.301078
$827$	−5.36964e129	−0.796068	−0.398034	−	0.917371i	$-0.630307\pi$
$827$	−5.36964e129	−0.796068	−0.398034	+	0.917371i	$0.630307\pi$
$828$	0	0
$829$	−8.74341e128	−0.116414	−0.0582069	−	0.998305i	$-0.518538\pi$
$829$	−8.74341e128	−0.116414	−0.0582069	+	0.998305i	$0.518538\pi$
$830$	−3.43085e128	−0.0432939
$831$	0	0
$832$	2.56228e129	0.290494
$833$	−4.99087e128	−0.0536381
$834$	0	0
$835$	1.30464e129	0.126021
$836$	−6.96027e129	−0.637451
$837$	0	0
$838$	−7.84554e129	−0.646047
$839$	−1.06592e129	−0.0832369	−0.0416185	−	0.999134i	$-0.513251\pi$
$839$	−1.06592e129	−0.0832369	−0.0416185	+	0.999134i	$0.513251\pi$
$840$	0	0
$841$	−1.40089e130	−0.983974
$842$	−1.72056e130	−1.14626
$843$	0	0
$844$	−6.09114e129	−0.365140
$845$	−1.33944e129	−0.0761728
$846$	0	0
$847$	1.08616e130	0.556008
$848$	−7.57312e129	−0.367840
$849$	0	0
$850$	−1.85486e129	−0.0811278
$851$	1.52767e130	0.634108
$852$	0	0
$853$	1.93219e130	0.722467	0.361233	−	0.932475i	$-0.382356\pi$
$853$	1.93219e130	0.722467	0.361233	+	0.932475i	$0.382356\pi$
$854$	−4.19639e129	−0.148936
$855$	0	0
$856$	−1.40267e130	−0.448614
$857$	−7.26166e129	−0.220490	−0.110245	−	0.993904i	$-0.535164\pi$
$857$	−7.26166e129	−0.220490	−0.110245	+	0.993904i	$0.535164\pi$
$858$	0	0
$859$	3.54047e130	0.969091	0.484545	−	0.874766i	$-0.338985\pi$
$859$	3.54047e130	0.969091	0.484545	+	0.874766i	$0.338985\pi$
$860$	−2.57752e129	−0.0669918
$861$	0	0
$862$	−6.76755e129	−0.158620
$863$	−3.76103e130	−0.837195	−0.418598	−	0.908172i	$-0.637478\pi$
$863$	−3.76103e130	−0.837195	−0.418598	+	0.908172i	$0.637478\pi$
$864$	0	0
$865$	−6.63085e129	−0.133153
$866$	1.04237e131	1.98827
$867$	0	0
$868$	−4.19139e129	−0.0721491
$869$	−1.26207e131	−2.06397
$870$	0	0
$871$	1.44591e130	0.213469
$872$	1.04587e130	0.146722
$873$	0	0
$874$	−6.66456e130	−0.844332
$875$	5.18105e129	0.0623821
$876$	0	0
$877$	−1.55152e131	−1.68762	−0.843811	−	0.536641i	$-0.819693\pi$
$877$	−1.55152e131	−1.68762	−0.843811	+	0.536641i	$0.819693\pi$
$878$	6.76796e130	0.699764
$879$	0	0
$880$	1.60732e130	0.150184
$881$	−9.08036e130	−0.806631	−0.403316	−	0.915061i	$-0.632142\pi$
$881$	−9.08036e130	−0.806631	−0.403316	+	0.915061i	$0.632142\pi$
$882$	0	0
$883$	1.55010e131	1.24482	0.622411	−	0.782690i	$-0.286153\pi$
$883$	1.55010e131	1.24482	0.622411	+	0.782690i	$0.286153\pi$
$884$	−7.53219e129	−0.0575169
$885$	0	0
$886$	1.41276e131	0.975591
$887$	6.55371e130	0.430414	0.215207	−	0.976568i	$-0.430957\pi$
$887$	6.55371e130	0.430414	0.215207	+	0.976568i	$0.430957\pi$
$888$	0	0
$889$	−1.44086e130	−0.0856037
$890$	2.45528e130	0.138754
$891$	0	0
$892$	1.42155e131	0.726984
$893$	−1.61254e131	−0.784551
$894$	0	0
$895$	−1.27200e129	−0.00560224
$896$	8.09048e130	0.339053
$897$	0	0
$898$	−1.40315e131	−0.532484
$899$	−9.89131e129	−0.0357230
$900$	0	0
$901$	5.82350e129	0.0190516
$902$	−4.95471e131	−1.54286
$903$	0	0
$904$	−1.91626e131	−0.540703
$905$	−5.29874e130	−0.142335
$906$	0	0
$907$	−5.61057e131	−1.36610	−0.683051	−	0.730371i	$-0.739347\pi$
$907$	−5.61057e131	−1.36610	−0.683051	+	0.730371i	$0.739347\pi$
$908$	4.82573e131	1.11877
$909$	0	0
$910$	2.67619e130	0.0562568
$911$	7.85678e131	1.57281	0.786406	−	0.617710i	$-0.211940\pi$
$911$	7.85678e131	1.57281	0.786406	+	0.617710i	$0.211940\pi$
$912$	0	0
$913$	3.65422e131	0.663507
$914$	8.76713e131	1.51618
$915$	0	0
$916$	7.29238e131	1.14425
$917$	2.42474e131	0.362434
$918$	0	0
$919$	−1.20827e132	−1.63917	−0.819587	−	0.572955i	$-0.805797\pi$
$919$	−1.20827e132	−1.63917	−0.819587	+	0.572955i	$0.805797\pi$
$920$	2.86938e130	0.0370877
$921$	0	0
$922$	6.43060e131	0.754615
$923$	−1.29724e132	−1.45059
$924$	0	0
$925$	−6.01675e131	−0.611019
$926$	1.97838e132	1.91479
$927$	0	0
$928$	−1.61273e131	−0.141800
$929$	8.48290e131	0.710960	0.355480	−	0.934684i	$-0.384317\pi$
$929$	8.48290e131	0.710960	0.355480	+	0.934684i	$0.384317\pi$
$930$	0	0
$931$	7.06268e131	0.537909
$932$	−1.84868e131	−0.134231
$933$	0	0
$934$	3.64735e132	2.40736
$935$	−1.23598e130	−0.00777849
$936$	0	0
$937$	1.06062e132	0.606941	0.303470	−	0.952841i	$-0.401855\pi$
$937$	1.06062e132	0.606941	0.303470	+	0.952841i	$0.401855\pi$
$938$	−1.41952e131	−0.0774667
$939$	0	0
$940$	−1.25779e131	−0.0624337
$941$	2.79020e132	1.32098	0.660492	−	0.750833i	$-0.270348\pi$
$941$	2.79020e132	1.32098	0.660492	+	0.750833i	$0.270348\pi$
$942$	0	0
$943$	−1.85903e132	−0.800787
$944$	−1.76997e132	−0.727297
$945$	0	0
$946$	7.00602e132	2.62009
$947$	−1.84501e132	−0.658302	−0.329151	−	0.944277i	$-0.606762\pi$
$947$	−1.84501e132	−0.658302	−0.329151	+	0.944277i	$0.606762\pi$
$948$	0	0
$949$	−1.01279e132	−0.328984
$950$	2.62485e132	0.813588
$951$	0	0
$952$	−4.08168e130	−0.0115211
$953$	−3.12272e132	−0.841199	−0.420599	−	0.907246i	$-0.638180\pi$
$953$	−3.12272e132	−0.841199	−0.420599	+	0.907246i	$0.638180\pi$
$954$	0	0
$955$	−2.71447e130	−0.00666093
$956$	3.66685e132	0.858850
$957$	0	0
$958$	−6.22802e132	−1.32918
$959$	−6.48000e131	−0.132022
$960$	0	0
$961$	−4.95626e132	−0.920372
$962$	−6.23516e132	−1.10550
$963$	0	0
$964$	3.96374e132	0.640732
$965$	7.71432e131	0.119078
$966$	0	0
$967$	−9.50210e132	−1.33765	−0.668823	−	0.743421i	$-0.733202\pi$
$967$	−9.50210e132	−1.33765	−0.668823	+	0.743421i	$0.733202\pi$
$968$	−4.75316e132	−0.639041
$969$	0	0
$970$	−5.58642e131	−0.0685159
$971$	−8.78389e132	−1.02904	−0.514518	−	0.857479i	$-0.672029\pi$
$971$	−8.78389e132	−1.02904	−0.514518	+	0.857479i	$0.672029\pi$
$972$	0	0
$973$	−3.89628e131	−0.0416513
$974$	−7.53060e132	−0.769053
$975$	0	0
$976$	3.85967e132	0.359777
$977$	−1.26615e133	−1.12765	−0.563827	−	0.825893i	$-0.690672\pi$
$977$	−1.26615e133	−1.12765	−0.563827	+	0.825893i	$0.690672\pi$
$978$	0	0
$979$	−2.61514e133	−2.12650
$980$	5.50893e131	0.0428062
$981$	0	0
$982$	−1.43028e133	−1.01498
$983$	−3.88384e132	−0.263408	−0.131704	−	0.991289i	$-0.542045\pi$
$983$	−3.88384e132	−0.263408	−0.131704	+	0.991289i	$0.542045\pi$
$984$	0	0
$985$	−1.83213e132	−0.113513
$986$	1.74508e131	0.0103346
$987$	0	0
$988$	1.06589e133	0.576807
$989$	2.62870e133	1.35990
$990$	0	0
$991$	−2.30184e133	−1.08842	−0.544211	−	0.838948i	$-0.683171\pi$
$991$	−2.30184e133	−1.08842	−0.544211	+	0.838948i	$0.683171\pi$
$992$	6.99140e132	0.316078
$993$	0	0
$994$	1.27356e133	0.526412
$995$	−1.86380e132	−0.0736671
$996$	0	0
$997$	−3.12858e132	−0.113087	−0.0565435	−	0.998400i	$-0.518008\pi$
$997$	−3.12858e132	−0.113087	−0.0565435	+	0.998400i	$0.518008\pi$
$998$	−3.02203e133	−1.04469
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.90.a.b.1.6		7
3.2	odd	2		1.90.a.a.1.2	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.90.a.a.1.2	✓	7	3.2	odd	2
9.90.a.b.1.6		7	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:	\( k \)	\(=\)	\( 90 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q+3.19029e13 q^{2} +3.98828e26 q^{4} -1.00222e30 q^{5} +1.60489e37 q^{7} -7.02319e39 q^{8} +O(q^{10})\)	\(q+3.19029e13 q^{2} +3.98828e26 q^{4} -1.00222e30 q^{5} +1.60489e37 q^{7} -7.02319e39 q^{8} -3.19739e43 q^{10} +3.40556e46 q^{11} -5.21527e49 q^{13} +5.12007e50 q^{14} -4.70923e53 q^{16} +3.62126e53 q^{17} -5.12451e56 q^{19} -3.99715e56 q^{20} +1.08647e60 q^{22} +4.07651e60 q^{23} -1.60554e62 q^{25} -1.66382e63 q^{26} +6.40074e63 q^{28} +1.51052e64 q^{29} -6.54829e65 q^{31} -1.06767e67 q^{32} +1.15529e67 q^{34} -1.60846e67 q^{35} +3.74749e69 q^{37} -1.63487e70 q^{38} +7.03881e69 q^{40} -4.56036e71 q^{41} +6.44841e72 q^{43} +1.35823e73 q^{44} +1.30053e74 q^{46} +3.14673e74 q^{47} -1.37822e75 q^{49} -5.12215e75 q^{50} -2.07999e76 q^{52} +1.60814e76 q^{53} -3.41313e76 q^{55} -1.12714e77 q^{56} +4.81900e77 q^{58} +3.75851e78 q^{59} -8.19597e78 q^{61} -2.08910e79 q^{62} -4.91303e79 q^{64} +5.22687e79 q^{65} -2.77246e80 q^{67} +1.44426e80 q^{68} -5.13146e80 q^{70} +2.48739e82 q^{71} +1.94198e82 q^{73} +1.19556e83 q^{74} -2.04380e83 q^{76} +5.46555e83 q^{77} -3.70591e84 q^{79} +4.71970e83 q^{80} -1.45489e85 q^{82} +1.07302e85 q^{83} -3.62931e83 q^{85} +2.05723e86 q^{86} -2.39179e86 q^{88} -7.67903e86 q^{89} -8.36993e86 q^{91} +1.62582e87 q^{92} +1.00390e88 q^{94} +5.13591e86 q^{95} +1.74718e88 q^{97} -4.39691e88 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 31407330351408 q^{2} + 22\!\cdots\!04 q^{4}+ \cdots + 17\!\cdots\!20 q^{8}+O(q^{10}) \) 7 * q + 31407330351408 * q^2 + 2261776677705673116713576704 * q^4 - 10232470009089362495458987082250 * q^5 + 38501341543555466088619988316514959992 * q^7 + 17954070319777658933153680910224754257920 * q^8	\( 7 q + 31407330351408 q^{2} + 22\!\cdots\!04 q^{4}+ \cdots + 17\!\cdots\!56 q^{98}+O(q^{100}) \) 7 * q + 31407330351408 * q^2 + 2261776677705673116713576704 * q^4 - 10232470009089362495458987082250 * q^5 + 38501341543555466088619988316514959992 * q^7 + 17954070319777658933153680910224754257920 * q^8 - 339886969508111355644737639996417314840948000 * q^10 + 33185398429231418991729589216300973489966079756 * q^11 - 103208963062610039235367083636366996420076737975934 * q^13 + 3327254465892753266340667920543396227686510656335232 * q^14 + 1162914962909596823700454711087105707311468348200517632 * q^16 - 8319478335928844788789086096491382896131016464480742142 * q^17 + 566291740319213482378495952187194771397009633898137615980 * q^19 - 17240116916193408372006373658712519601040539123805641152000 * q^20 - 572030171884928043470630402880877439080047260844354367465536 * q^22 + 1162243907076079309616831317442805749267469267057101679089304 * q^23 - 212322678457531006783078558385295515929862869778299899884234375 * q^25 - 256954281475267715641749604093742676189922873609159508555728224 * q^26 + 42271634017038816624971599134243423766860094950653754695170525184 * q^28 + 141971615822865442921693407341400369750322173654805889340125766030 * q^29 + 683664012826903943332640912357777981916064560235376021892996967904 * q^31 + 18295616415211966307849618677858007212056173228946481610958698446848 * q^32 + 310076023324380793221121009797602653729382139402481891183326564397728 * q^34 - 330170304491374501797216156307803170564453659546779205972398673602000 * q^35 - 54562371243327727239087361205689070078467002527262667251534613287958 * q^37 - 45443543517981085735407850236293406047335765118416513555057178362067520 * q^38 - 361606215568925170012071637858292899677067482636237269829164280222720000 * q^40 + 657970372131031022656393678727303783670430723595160145307484502660397466 * q^41 + 3219260988489925248073148176207907480629490254450229462745931521229023956 * q^43 + 15518629834856028222698238418543583045824703222318379119582671434892588032 * q^44 - 56495859283654895727924020960810320205382055229302825603343235358563739776 * q^46 + 589986405817377998239864975519322982713028461832176517663311475432884156208 * q^47 - 3087918931516952942471049623523578487683423584779916315782412290559435137201 * q^49 + 11186377093883721132072449077187321801629226446489467367094029042775729250000 * q^50 - 195074413541392068451275175025603658303895820240091441880921515457689944416768 * q^52 + 181430063765559371241038742666701312033549399057740391278794421145415983301414 * q^53 - 1251959124114414009910203618775792485005181014548185493458611647835407269933000 * q^55 + 5833843183212315752254903583581814862872931164492369538677714690034795155128320 * q^56 - 3085757480392710136283141086455357758895171179069060863542747741259905831138720 * q^58 + 9086646688135460130541149101651496775878005651006843822379595086967226946739260 * q^59 + 8774545844023482806788207542368099480171833682235332719617911769894989384384594 * q^61 - 169526530141162019514362685680407627845528510541984421132250792903222430290676224 * q^62 + 1452176441912468141297252840801366807510309025606268702123180748140039039923257344 * q^64 - 1324597647382660271811574639166235036730362819738030027679321346411726630592583500 * q^65 + 5843793535214317245370457729815716742376089805910350107798697912590172409883288892 * q^67 - 3383522446313435458738303622044969561038087184549368481666865721250715220292329984 * q^68 - 48530199945646178573467957795368744286471165824229177345686884714666072932491936000 * q^70 + 54831722251632385251791847370899308335600102141533329655944703784411212003030405576 * q^71 - 199687593578972105167207004100293505918603845674208378633352670689487827039532442554 * q^73 + 965066694195901068911432718812601386557508653596585879236882657245078468484355531552 * q^74 - 624789819902471734428103435859366276136204176410553236414159885942801809403293936640 * q^76 - 1343091849772730830408738350805190184311976794055420918621708129900429278982204783264 * q^77 + 2673613187258858564803647217355170619960582874636639491339476674654505245882753222320 * q^79 - 27680777280715589878137850302356927719666260300976702690203906698201250115244507136000 * q^80 + 63127032979305734173962933747182283580799525530431609292523424735220314498528511785504 * q^82 + 35017619719051015255233069909205249521130641969249674783596011796500257235899597331924 * q^83 - 141384913067859944856588220403027346022605850144801355881993121940858052671602572135500 * q^85 + 246618390628075722158819620850499384970086160242141588082920865473574265424952752922176 * q^86 - 1874747156501905660418588549009712256169985369393565612731235328175018372894817920368640 * q^88 + 1625431592570174192786638376427668495469444301472287736732287307560402850485922205836490 * q^89 - 304928345599594097428899578613442396706625647498145800328408392926012721126646204980336 * q^91 - 7281329003117440073848907204538369781556431009214831685528490675028895216006021740500992 * q^92 + 22964567086699943860517240071514688733928422760236698641236969735081204002206026310078208 * q^94 - 22546113414761055806340378014072491896390775587517280959221325649524340597082183574485000 * q^95 + 71386807957160533061753038101994485650273149078658846323482657056181047793902162983463342 * q^97 + 17615586549862077419320336328445909012296979015379167958274818444332513071671081562433456 * q^98

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