LMFDB - Embedded newform 9.90.a.b.1.2

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			1.2
Root			$-4.94369e11$ of defining polynomial
Character	$\chi$	$=$	9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.92430e13 q^{2} -2.48679e26 q^{4} +3.02831e30 q^{5} +1.70526e37 q^{7} +1.66961e40 q^{8} +O(q^{10})$	\(q-1.92430e13 q^{2} -2.48679e26 q^{4} +3.02831e30 q^{5} +1.70526e37 q^{7} +1.66961e40 q^{8} -5.82737e43 q^{10} -1.93063e46 q^{11} +1.74324e49 q^{13} -3.28142e50 q^{14} -1.67358e53 q^{16} +6.51031e54 q^{17} -9.59966e56 q^{19} -7.53078e56 q^{20} +3.71509e59 q^{22} +9.89412e59 q^{23} -1.52388e62 q^{25} -3.35451e62 q^{26} -4.24062e63 q^{28} +1.35771e65 q^{29} +1.59360e66 q^{31} -7.11394e66 q^{32} -1.25278e68 q^{34} +5.16406e67 q^{35} -2.47785e68 q^{37} +1.84726e70 q^{38} +5.05611e70 q^{40} -4.58319e71 q^{41} -7.07930e72 q^{43} +4.80106e72 q^{44} -1.90392e73 q^{46} -1.32347e74 q^{47} -1.34499e75 q^{49} +2.93240e75 q^{50} -4.33507e75 q^{52} +9.22610e76 q^{53} -5.84654e76 q^{55} +2.84712e77 q^{56} -2.61263e78 q^{58} +8.06039e78 q^{59} +4.49999e79 q^{61} -3.06655e79 q^{62} +2.40483e80 q^{64} +5.27908e79 q^{65} +1.54319e81 q^{67} -1.61898e81 q^{68} -9.93718e80 q^{70} +2.24358e82 q^{71} -1.49797e83 q^{73} +4.76812e81 q^{74} +2.38723e83 q^{76} -3.29222e83 q^{77} +3.12365e84 q^{79} -5.06813e83 q^{80} +8.81941e84 q^{82} -3.77338e85 q^{83} +1.97153e85 q^{85} +1.36227e86 q^{86} -3.22340e86 q^{88} -2.53389e85 q^{89} +2.97268e86 q^{91} -2.46046e86 q^{92} +2.54675e87 q^{94} -2.90708e87 q^{95} +3.77341e87 q^{97} +2.58816e88 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.92430e13	−0.773458	−0.386729	−	0.922193i	$-0.626395\pi$
$2$	−1.92430e13	−0.773458	−0.386729	+	0.922193i	$0.626395\pi$
$3$	0	0
$3$	0	0
$4$	−2.48679e26	−0.401762
$5$	3.02831e30	0.238252	0.119126	−	0.992879i	$-0.461991\pi$
$5$	3.02831e30	0.238252	0.119126	+	0.992879i	$0.461991\pi$
$6$	0	0
$7$	1.70526e37	0.421626	0.210813	−	0.977526i	$-0.432389\pi$
$7$	1.70526e37	0.421626	0.210813	+	0.977526i	$0.432389\pi$
$8$	1.66961e40	1.08420
$9$	0	0
$10$	−5.82737e43	−0.184278
$11$	−1.93063e46	−0.878463	−0.439232	−	0.898374i	$-0.644749\pi$
$11$	−1.93063e46	−0.878463	−0.439232	+	0.898374i	$0.644749\pi$
$12$	0	0
$13$	1.74324e49	0.468682	0.234341	−	0.972155i	$-0.424707\pi$
$13$	1.74324e49	0.468682	0.234341	+	0.972155i	$0.424707\pi$
$14$	−3.28142e50	−0.326110
$15$	0	0
$16$	−1.67358e53	−0.436825
$17$	6.51031e54	1.14452	0.572262	−	0.820071i	$-0.306066\pi$
$17$	6.51031e54	1.14452	0.572262	+	0.820071i	$0.306066\pi$
$18$	0	0
$19$	−9.59966e56	−1.19597	−0.597985	−	0.801507i	$-0.704032\pi$
$19$	−9.59966e56	−1.19597	−0.597985	+	0.801507i	$0.704032\pi$
$20$	−7.53078e56	−0.0957205
$21$	0	0
$22$	3.71509e59	0.679455
$23$	9.89412e59	0.250316	0.125158	−	0.992137i	$-0.460056\pi$
$23$	9.89412e59	0.250316	0.125158	+	0.992137i	$0.460056\pi$
$24$	0	0
$25$	−1.52388e62	−0.943236
$26$	−3.35451e62	−0.362506
$27$	0	0
$28$	−4.24062e63	−0.169394
$29$	1.35771e65	1.13788	0.568938	−	0.822381i	$-0.307355\pi$
$29$	1.35771e65	1.13788	0.568938	+	0.822381i	$0.307355\pi$
$30$	0	0
$31$	1.59360e66	0.686725	0.343363	−	0.939203i	$-0.388434\pi$
$31$	1.59360e66	0.686725	0.343363	+	0.939203i	$0.388434\pi$
$32$	−7.11394e66	−0.746339
$33$	0	0
$34$	−1.25278e68	−0.885242
$35$	5.16406e67	0.100453
$36$	0	0
$37$	−2.47785e68	−0.0406535	−0.0203268	−	0.999793i	$-0.506471\pi$
$37$	−2.47785e68	−0.0406535	−0.0203268	+	0.999793i	$0.506471\pi$
$38$	1.84726e70	0.925033
$39$	0	0
$40$	5.05611e70	0.258313
$41$	−4.58319e71	−0.780344	−0.390172	−	0.920742i	$-0.627584\pi$
$41$	−4.58319e71	−0.780344	−0.390172	+	0.920742i	$0.627584\pi$
$42$	0	0
$43$	−7.07930e72	−1.44758	−0.723792	−	0.690018i	$-0.757603\pi$
$43$	−7.07930e72	−1.44758	−0.723792	+	0.690018i	$0.757603\pi$
$44$	4.80106e72	0.352933
$45$	0	0
$46$	−1.90392e73	−0.193609
$47$	−1.32347e74	−0.516844	−0.258422	−	0.966032i	$-0.583203\pi$
$47$	−1.32347e74	−0.516844	−0.258422	+	0.966032i	$0.583203\pi$
$48$	0	0
$49$	−1.34499e75	−0.822231
$50$	2.93240e75	0.729554
$51$	0	0
$52$	−4.33507e75	−0.188299
$53$	9.22610e76	1.71689	0.858444	−	0.512907i	$-0.171432\pi$
$53$	9.22610e76	1.71689	0.858444	+	0.512907i	$0.171432\pi$
$54$	0	0
$55$	−5.84654e76	−0.209295
$56$	2.84712e77	0.457129
$57$	0	0
$58$	−2.61263e78	−0.880099
$59$	8.06039e78	1.26894	0.634471	−	0.772947i	$-0.281218\pi$
$59$	8.06039e78	1.26894	0.634471	+	0.772947i	$0.281218\pi$
$60$	0	0
$61$	4.49999e79	1.60707	0.803534	−	0.595259i	$-0.202951\pi$
$61$	4.49999e79	1.60707	0.803534	+	0.595259i	$0.202951\pi$
$62$	−3.06655e79	−0.531153
$63$	0	0
$64$	2.40483e80	1.01409
$65$	5.27908e79	0.111664
$66$	0	0
$67$	1.54319e81	0.847404	0.423702	−	0.905802i	$-0.360730\pi$
$67$	1.54319e81	0.847404	0.423702	+	0.905802i	$0.360730\pi$
$68$	−1.61898e81	−0.459827
$69$	0	0
$70$	−9.93718e80	−0.0776963
$71$	2.24358e82	0.933136	0.466568	−	0.884485i	$-0.345490\pi$
$71$	2.24358e82	0.933136	0.466568	+	0.884485i	$0.345490\pi$
$72$	0	0
$73$	−1.49797e83	−1.80982	−0.904908	−	0.425607i	$-0.860061\pi$
$73$	−1.49797e83	−1.80982	−0.904908	+	0.425607i	$0.860061\pi$
$74$	4.76812e81	0.0314438
$75$	0	0
$76$	2.38723e83	0.480496
$77$	−3.29222e83	−0.370383
$78$	0	0
$79$	3.12365e84	1.12268	0.561342	−	0.827584i	$-0.310285\pi$
$79$	3.12365e84	1.12268	0.561342	+	0.827584i	$0.310285\pi$
$80$	−5.06813e83	−0.104074
$81$	0	0
$82$	8.81941e84	0.603564
$83$	−3.77338e85	−1.50576	−0.752880	−	0.658158i	$-0.771336\pi$
$83$	−3.77338e85	−1.50576	−0.752880	+	0.658158i	$0.771336\pi$
$84$	0	0
$85$	1.97153e85	0.272685
$86$	1.36227e86	1.11965
$87$	0	0
$88$	−3.22340e86	−0.952434
$89$	−2.53389e85	−0.0452828	−0.0226414	−	0.999744i	$-0.507208\pi$
$89$	−2.53389e85	−0.0452828	−0.0226414	+	0.999744i	$0.507208\pi$
$90$	0	0
$91$	2.97268e86	0.197609
$92$	−2.46046e86	−0.100567
$93$	0	0
$94$	2.54675e87	0.399758
$95$	−2.90708e87	−0.284942
$96$	0	0
$97$	3.77341e87	0.146350	0.0731749	−	0.997319i	$-0.476687\pi$
$97$	3.77341e87	0.146350	0.0731749	+	0.997319i	$0.476687\pi$
$98$	2.58816e88	0.635962
$99$	0	0
$100$	3.78957e88	0.378957
$101$	6.63329e88	0.426018	0.213009	−	0.977050i	$-0.431674\pi$
$101$	6.63329e88	0.426018	0.213009	+	0.977050i	$0.431674\pi$
$102$	0	0
$103$	−6.09276e88	−0.163515	−0.0817575	−	0.996652i	$-0.526053\pi$
$103$	−6.09276e88	−0.163515	−0.0817575	+	0.996652i	$0.526053\pi$
$104$	2.91053e89	0.508147
$105$	0	0
$106$	−1.77537e90	−1.32794
$107$	−3.96513e90	−1.95290	−0.976448	−	0.215751i	$-0.930780\pi$
$107$	−3.96513e90	−1.95290	−0.976448	+	0.215751i	$0.930780\pi$
$108$	0	0
$109$	7.03908e90	1.52068	0.760338	−	0.649528i	$-0.225034\pi$
$109$	7.03908e90	1.52068	0.760338	+	0.649528i	$0.225034\pi$
$110$	1.12505e90	0.161881
$111$	0	0
$112$	−2.85389e90	−0.184177
$113$	1.14772e91	0.498706	0.249353	−	0.968413i	$-0.419782\pi$
$113$	1.14772e91	0.498706	0.249353	+	0.968413i	$0.419782\pi$
$114$	0	0
$115$	2.99625e90	0.0596381
$116$	−3.37633e91	−0.457156
$117$	0	0
$118$	−1.55106e92	−0.981473
$119$	1.11018e92	0.482562
$120$	0	0
$121$	−1.10271e92	−0.228302
$122$	−8.65932e92	−1.24300
$123$	0	0
$124$	−3.96294e92	−0.275900
$125$	−9.50730e92	−0.462979
$126$	0	0
$127$	2.56627e93	0.616648	0.308324	−	0.951281i	$-0.400232\pi$
$127$	2.56627e93	0.616648	0.308324	+	0.951281i	$0.400232\pi$
$128$	−2.24284e92	−0.0380149
$129$	0	0
$130$	−1.01585e93	−0.0863675
$131$	1.52696e94	0.923114	0.461557	−	0.887110i	$-0.347291\pi$
$131$	1.52696e94	0.923114	0.461557	+	0.887110i	$0.347291\pi$
$132$	0	0
$133$	−1.63699e94	−0.504253
$134$	−2.96955e94	−0.655432
$135$	0	0
$136$	1.08697e95	1.24090
$137$	−4.13375e94	−0.340627	−0.170313	−	0.985390i	$-0.554478\pi$
$137$	−4.13375e94	−0.340627	−0.170313	+	0.985390i	$0.554478\pi$
$138$	0	0
$139$	−4.37002e94	−0.188940	−0.0944701	−	0.995528i	$-0.530116\pi$
$139$	−4.37002e94	−0.188940	−0.0944701	+	0.995528i	$0.530116\pi$
$140$	−1.28419e94	−0.0403583
$141$	0	0
$142$	−4.31731e95	−0.721742
$143$	−3.36554e95	−0.411719
$144$	0	0
$145$	4.11156e95	0.271101
$146$	2.88253e96	1.39982
$147$	0	0
$148$	6.16189e94	0.0163331
$149$	−2.82695e94	−0.00555303	−0.00277651	−	0.999996i	$-0.500884\pi$
$149$	−2.82695e94	−0.00555303	−0.00277651	+	0.999996i	$0.500884\pi$
$150$	0	0
$151$	1.26902e97	1.37720	0.688598	−	0.725143i	$-0.258226\pi$
$151$	1.26902e97	1.37720	0.688598	+	0.725143i	$0.258226\pi$
$152$	−1.60277e97	−1.29668
$153$	0	0
$154$	6.33520e96	0.286476
$155$	4.82591e96	0.163613
$156$	0	0
$157$	−2.10812e97	−0.403981	−0.201990	−	0.979387i	$-0.564741\pi$
$157$	−2.10812e97	−0.403981	−0.201990	+	0.979387i	$0.564741\pi$
$158$	−6.01083e97	−0.868349
$159$	0	0
$160$	−2.15432e97	−0.177816
$161$	1.68720e97	0.105540
$162$	0	0
$163$	1.44678e98	0.522462	0.261231	−	0.965276i	$-0.415872\pi$
$163$	1.44678e98	0.522462	0.261231	+	0.965276i	$0.415872\pi$
$164$	1.13974e98	0.313513
$165$	0	0
$166$	7.26110e98	1.16464
$167$	−9.38473e98	−1.15223	−0.576115	−	0.817369i	$-0.695432\pi$
$167$	−9.38473e98	−1.15223	−0.576115	+	0.817369i	$0.695432\pi$
$168$	0	0
$169$	−1.07955e99	−0.780338
$170$	−3.79380e98	−0.210910
$171$	0	0
$172$	1.76047e99	0.581585
$173$	−3.32605e99	−0.848941	−0.424471	−	0.905442i	$-0.639540\pi$
$173$	−3.32605e99	−0.848941	−0.424471	+	0.905442i	$0.639540\pi$
$174$	0	0
$175$	−2.59861e99	−0.397693
$176$	3.23106e99	0.383734
$177$	0	0
$178$	4.87596e98	0.0350243
$179$	1.11777e100	0.625736	0.312868	−	0.949797i	$-0.398710\pi$
$179$	1.11777e100	0.625736	0.312868	+	0.949797i	$0.398710\pi$
$180$	0	0
$181$	2.69295e100	0.919457	0.459728	−	0.888060i	$-0.347947\pi$
$181$	2.69295e100	0.919457	0.459728	+	0.888060i	$0.347947\pi$
$182$	−5.72031e99	−0.152842
$183$	0	0
$184$	1.65193e100	0.271394
$185$	−7.50371e98	−0.00968577
$186$	0	0
$187$	−1.25690e101	−1.00542
$188$	3.29119e100	0.207649
$189$	0	0
$190$	5.59408e100	0.220391
$191$	2.28014e101	0.711177	0.355588	−	0.934643i	$-0.384281\pi$
$191$	2.28014e101	0.711177	0.355588	+	0.934643i	$0.384281\pi$
$192$	0	0
$193$	−6.90447e101	−1.35466	−0.677330	−	0.735679i	$-0.736863\pi$
$193$	−6.90447e101	−1.35466	−0.677330	+	0.735679i	$0.736863\pi$
$194$	−7.26116e100	−0.113195
$195$	0	0
$196$	3.34471e101	0.330341
$197$	3.78554e100	0.0298113	0.0149056	−	0.999889i	$-0.495255\pi$
$197$	3.78554e100	0.0298113	0.0149056	+	0.999889i	$0.495255\pi$
$198$	0	0
$199$	2.74343e101	0.137826	0.0689132	−	0.997623i	$-0.478047\pi$
$199$	2.74343e101	0.137826	0.0689132	+	0.997623i	$0.478047\pi$
$200$	−2.54429e102	−1.02266
$201$	0	0
$202$	−1.27644e102	−0.329507
$203$	2.31524e102	0.479758
$204$	0	0
$205$	−1.38793e102	−0.185918
$206$	1.17243e102	0.126472
$207$	0	0
$208$	−2.91745e102	−0.204732
$209$	1.85333e103	1.05062
$210$	0	0
$211$	−3.13690e103	−1.16394	−0.581971	−	0.813209i	$-0.697718\pi$
$211$	−3.13690e103	−1.16394	−0.581971	+	0.813209i	$0.697718\pi$
$212$	−2.29434e103	−0.689781
$213$	0	0
$214$	7.63008e103	1.51048
$215$	−2.14383e103	−0.344889
$216$	0	0
$217$	2.71750e103	0.289542
$218$	−1.35453e104	−1.17618
$219$	0	0
$220$	1.45391e103	0.0840869
$221$	1.13490e104	0.536417
$222$	0	0
$223$	−2.51321e104	−0.795539	−0.397770	−	0.917485i	$-0.630216\pi$
$223$	−2.51321e104	−0.795539	−0.397770	+	0.917485i	$0.630216\pi$
$224$	−1.21311e104	−0.314676
$225$	0	0
$226$	−2.20855e104	−0.385729
$227$	−3.43863e104	−0.493440	−0.246720	−	0.969087i	$-0.579353\pi$
$227$	−3.43863e104	−0.493440	−0.246720	+	0.969087i	$0.579353\pi$
$228$	0	0
$229$	−1.97608e105	−1.91922	−0.959610	−	0.281334i	$-0.909223\pi$
$229$	−1.97608e105	−1.91922	−0.959610	+	0.281334i	$0.909223\pi$
$230$	−5.76567e103	−0.0461276
$231$	0	0
$232$	2.26684e105	1.23369
$233$	−4.43243e104	−0.199206	−0.0996032	−	0.995027i	$-0.531757\pi$
$233$	−4.43243e104	−0.199206	−0.0996032	+	0.995027i	$0.531757\pi$
$234$	0	0
$235$	−4.00789e104	−0.123139
$236$	−2.00445e105	−0.509813
$237$	0	0
$238$	−2.13631e105	−0.373241
$239$	1.01112e105	0.146587	0.0732933	−	0.997310i	$-0.476649\pi$
$239$	1.01112e105	0.146587	0.0732933	+	0.997310i	$0.476649\pi$
$240$	0	0
$241$	−1.92058e106	−1.92165	−0.960823	−	0.277163i	$-0.910606\pi$
$241$	−1.92058e106	−1.92165	−0.960823	+	0.277163i	$0.910606\pi$
$242$	2.12193e105	0.176582
$243$	0	0
$244$	−1.11905e106	−0.645659
$245$	−4.07306e105	−0.195898
$246$	0	0
$247$	−1.67345e106	−0.560529
$248$	2.66069e106	0.744551
$249$	0	0
$250$	1.82948e106	0.358095
$251$	−6.63724e106	−1.08769	−0.543847	−	0.839184i	$-0.683033\pi$
$251$	−6.63724e106	−1.08769	−0.543847	+	0.839184i	$0.683033\pi$
$252$	0	0
$253$	−1.91018e106	−0.219893
$254$	−4.93827e106	−0.476951
$255$	0	0
$256$	−1.44536e107	−0.984684
$257$	5.06905e106	0.290337	0.145168	−	0.989407i	$-0.453628\pi$
$257$	5.06905e106	0.290337	0.145168	+	0.989407i	$0.453628\pi$
$258$	0	0
$259$	−4.22538e105	−0.0171406
$260$	−1.31279e106	−0.0448624
$261$	0	0
$262$	−2.93832e107	−0.713990
$263$	−7.92155e107	−1.62472	−0.812362	−	0.583154i	$-0.801819\pi$
$263$	−7.92155e107	−1.62472	−0.812362	+	0.583154i	$0.801819\pi$
$264$	0	0
$265$	2.79395e107	0.409051
$266$	3.15005e107	0.390019
$267$	0	0
$268$	−3.83759e107	−0.340455
$269$	−1.49563e107	−0.112421	−0.0562104	−	0.998419i	$-0.517902\pi$
$269$	−1.49563e107	−0.112421	−0.0562104	+	0.998419i	$0.517902\pi$
$270$	0	0
$271$	2.64960e108	1.43234	0.716171	−	0.697925i	$-0.245893\pi$
$271$	2.64960e108	1.43234	0.716171	+	0.697925i	$0.245893\pi$
$272$	−1.08955e108	−0.499956
$273$	0	0
$274$	7.95455e107	0.263461
$275$	2.94204e108	0.828598
$276$	0	0
$277$	−8.85589e108	−1.80668	−0.903342	−	0.428921i	$-0.858894\pi$
$277$	−8.85589e108	−1.80668	−0.903342	+	0.428921i	$0.858894\pi$
$278$	8.40920e107	0.146137
$279$	0	0
$280$	8.62199e107	0.108912
$281$	1.15862e109	1.24885	0.624426	−	0.781084i	$-0.285333\pi$
$281$	1.15862e109	1.24885	0.624426	+	0.781084i	$0.285333\pi$
$282$	0	0
$283$	1.13837e109	0.894930	0.447465	−	0.894302i	$-0.352327\pi$
$283$	1.13837e109	0.894930	0.447465	+	0.894302i	$0.352327\pi$
$284$	−5.57931e108	−0.374899
$285$	0	0
$286$	6.47630e108	0.318448
$287$	−7.81553e108	−0.329014
$288$	0	0
$289$	1.00282e109	0.309935
$290$	−7.91186e108	−0.209685
$291$	0	0
$292$	3.72512e109	0.727116
$293$	8.89977e109	1.49200	0.746002	−	0.665944i	$-0.231971\pi$
$293$	8.89977e109	1.49200	0.746002	+	0.665944i	$0.231971\pi$
$294$	0	0
$295$	2.44094e109	0.302327
$296$	−4.13705e108	−0.0440768
$297$	0	0
$298$	5.43989e107	0.00429504
$299$	1.72478e109	0.117318
$300$	0	0
$301$	−1.20720e110	−0.610340
$302$	−2.44198e110	−1.06520
$303$	0	0
$304$	1.60658e110	0.522430
$305$	1.36274e110	0.382887
$306$	0	0
$307$	5.02296e110	1.05512	0.527560	−	0.849518i	$-0.323107\pi$
$307$	5.02296e110	1.05512	0.527560	+	0.849518i	$0.323107\pi$
$308$	8.18705e109	0.148806
$309$	0	0
$310$	−9.28648e109	−0.126548
$311$	−5.98946e110	−0.707213	−0.353606	−	0.935394i	$-0.615045\pi$
$311$	−5.98946e110	−0.707213	−0.353606	+	0.935394i	$0.615045\pi$
$312$	0	0
$313$	7.96129e110	0.706741	0.353371	−	0.935483i	$-0.385035\pi$
$313$	7.96129e110	0.706741	0.353371	+	0.935483i	$0.385035\pi$
$314$	4.05665e110	0.312462
$315$	0	0
$316$	−7.76786e110	−0.451052
$317$	1.75038e111	0.883068	0.441534	−	0.897244i	$-0.354434\pi$
$317$	1.75038e111	0.883068	0.441534	+	0.897244i	$0.354434\pi$
$318$	0	0
$319$	−2.62122e111	−0.999582
$320$	7.28258e110	0.241608
$321$	0	0
$322$	−3.24668e110	−0.0816306
$323$	−6.24968e111	−1.36882
$324$	0	0
$325$	−2.65649e111	−0.442077
$326$	−2.78403e111	−0.404102
$327$	0	0
$328$	−7.65215e111	−0.846053
$329$	−2.25686e111	−0.217915
$330$	0	0
$331$	−1.64032e112	−1.20943	−0.604717	−	0.796441i	$-0.706714\pi$
$331$	−1.64032e112	−1.20943	−0.604717	+	0.796441i	$0.706714\pi$
$332$	9.38361e111	0.604958
$333$	0	0
$334$	1.80590e112	0.891201
$335$	4.67327e111	0.201895
$336$	0	0
$337$	−8.55619e110	−0.0283628	−0.0141814	−	0.999899i	$-0.504514\pi$
$337$	−8.55619e110	−0.0283628	−0.0141814	+	0.999899i	$0.504514\pi$
$338$	2.07736e112	0.603559
$339$	0	0
$340$	−4.90277e111	−0.109554
$341$	−3.07664e112	−0.603263
$342$	0	0
$343$	−5.08299e112	−0.768301
$344$	−1.18197e113	−1.56948
$345$	0	0
$346$	6.40031e112	0.656621
$347$	8.64589e112	0.780096	0.390048	−	0.920795i	$-0.372458\pi$
$347$	8.64589e112	0.780096	0.390048	+	0.920795i	$0.372458\pi$
$348$	0	0
$349$	8.46384e112	0.591338	0.295669	−	0.955290i	$-0.404457\pi$
$349$	8.46384e112	0.591338	0.295669	+	0.955290i	$0.404457\pi$
$350$	5.00050e112	0.307599
$351$	0	0
$352$	1.37344e113	0.655631
$353$	3.61884e112	0.152263	0.0761316	−	0.997098i	$-0.475743\pi$
$353$	3.61884e112	0.152263	0.0761316	+	0.997098i	$0.475743\pi$
$354$	0	0
$355$	6.79427e112	0.222321
$356$	6.30125e111	0.0181929
$357$	0	0
$358$	−2.15091e113	−0.483980
$359$	5.09085e113	1.01178	0.505891	−	0.862597i	$-0.331164\pi$
$359$	5.09085e113	1.01178	0.505891	+	0.862597i	$0.331164\pi$
$360$	0	0
$361$	2.77261e113	0.430346
$362$	−5.18203e113	−0.711161
$363$	0	0
$364$	−7.39242e112	−0.0793916
$365$	−4.53631e113	−0.431192
$366$	0	0
$367$	1.40897e114	1.05017	0.525087	−	0.851048i	$-0.324033\pi$
$367$	1.40897e114	1.05017	0.525087	+	0.851048i	$0.324033\pi$
$368$	−1.65586e113	−0.109344
$369$	0	0
$370$	1.44394e112	0.00749154
$371$	1.57329e114	0.723885
$372$	0	0
$373$	−1.68014e114	−0.608557	−0.304279	−	0.952583i	$-0.598415\pi$
$373$	−1.68014e114	−0.608557	−0.304279	+	0.952583i	$0.598415\pi$
$374$	2.41864e114	0.777652
$375$	0	0
$376$	−2.20968e114	−0.560365
$377$	2.36681e114	0.533301
$378$	0	0
$379$	6.69736e114	1.19250	0.596251	−	0.802798i	$-0.296656\pi$
$379$	6.69736e114	1.19250	0.596251	+	0.802798i	$0.296656\pi$
$380$	7.22929e113	0.114479
$381$	0	0
$382$	−4.38767e114	−0.550065
$383$	−6.76908e114	−0.755413	−0.377706	−	0.925925i	$-0.623287\pi$
$383$	−6.76908e114	−0.755413	−0.377706	+	0.925925i	$0.623287\pi$
$384$	0	0
$385$	−9.96987e113	−0.0882444
$386$	1.32862e115	1.04777
$387$	0	0
$388$	−9.38368e113	−0.0587978
$389$	−2.97836e115	−1.66425	−0.832127	−	0.554585i	$-0.812877\pi$
$389$	−2.97836e115	−1.66425	−0.832127	+	0.554585i	$0.812877\pi$
$390$	0	0
$391$	6.44138e114	0.286492
$392$	−2.24561e115	−0.891467
$393$	0	0
$394$	−7.28449e113	−0.0230578
$395$	9.45941e114	0.267481
$396$	0	0
$397$	−7.96520e115	−1.79895	−0.899475	−	0.436973i	$-0.856051\pi$
$397$	−7.96520e115	−1.79895	−0.899475	+	0.436973i	$0.856051\pi$
$398$	−5.27918e114	−0.106603
$399$	0	0
$400$	2.55034e115	0.412029
$401$	5.80386e115	0.839059	0.419530	−	0.907742i	$-0.362195\pi$
$401$	5.80386e115	0.839059	0.419530	+	0.907742i	$0.362195\pi$
$402$	0	0
$403$	2.77802e115	0.321856
$404$	−1.64956e115	−0.171158
$405$	0	0
$406$	−4.45521e115	−0.371073
$407$	4.78380e114	0.0357126
$408$	0	0
$409$	1.48135e116	0.889139	0.444570	−	0.895744i	$-0.353357\pi$
$409$	1.48135e116	0.889139	0.444570	+	0.895744i	$0.353357\pi$
$410$	2.67079e115	0.143800
$411$	0	0
$412$	1.51514e115	0.0656942
$413$	1.37451e116	0.535019
$414$	0	0
$415$	−1.14270e116	−0.358750
$416$	−1.24013e116	−0.349795
$417$	0	0
$418$	−3.56636e116	−0.812608
$419$	6.48329e116	1.32822	0.664112	−	0.747633i	$-0.268810\pi$
$419$	6.48329e116	1.32822	0.664112	+	0.747633i	$0.268810\pi$
$420$	0	0
$421$	6.60560e114	0.0109486	0.00547430	−	0.999985i	$-0.498257\pi$
$421$	6.60560e114	0.0109486	0.00547430	+	0.999985i	$0.498257\pi$
$422$	6.03632e116	0.900261
$423$	0	0
$424$	1.54040e117	1.86146
$425$	−9.92094e116	−1.07956
$426$	0	0
$427$	7.67366e116	0.677582
$428$	9.86044e116	0.784600
$429$	0	0
$430$	4.12537e116	0.266757
$431$	1.17992e117	0.688042	0.344021	−	0.938962i	$-0.388211\pi$
$431$	1.17992e117	0.688042	0.344021	+	0.938962i	$0.388211\pi$
$432$	0	0
$433$	4.77799e116	0.226743	0.113372	−	0.993553i	$-0.463835\pi$
$433$	4.77799e116	0.226743	0.113372	+	0.993553i	$0.463835\pi$
$434$	−5.22927e116	−0.223948
$435$	0	0
$436$	−1.75047e117	−0.610950
$437$	−9.49801e116	−0.299370
$438$	0	0
$439$	5.26626e117	1.35466	0.677332	−	0.735678i	$-0.263136\pi$
$439$	5.26626e117	1.35466	0.677332	+	0.735678i	$0.263136\pi$
$440$	−9.76146e116	−0.226919
$441$	0	0
$442$	−2.18389e117	−0.414896
$443$	1.09118e118	1.87469	0.937344	−	0.348406i	$-0.113277\pi$
$443$	1.09118e118	1.87469	0.937344	+	0.348406i	$0.113277\pi$
$444$	0	0
$445$	−7.67343e115	−0.0107887
$446$	4.83615e117	0.615317
$447$	0	0
$448$	4.10086e117	0.427566
$449$	−4.36528e117	−0.412145	−0.206073	−	0.978537i	$-0.566068\pi$
$449$	−4.36528e117	−0.412145	−0.206073	+	0.978537i	$0.566068\pi$
$450$	0	0
$451$	8.84842e117	0.685504
$452$	−2.85413e117	−0.200361
$453$	0	0
$454$	6.61694e117	0.381655
$455$	9.00220e116	0.0470805
$456$	0	0
$457$	−3.59688e118	−1.54759	−0.773793	−	0.633438i	$-0.781643\pi$
$457$	−3.59688e118	−1.54759	−0.773793	+	0.633438i	$0.781643\pi$
$458$	3.80255e118	1.48444
$459$	0	0
$460$	−7.45104e116	−0.0239604
$461$	5.08794e118	1.48542	0.742712	−	0.669611i	$-0.233539\pi$
$461$	5.08794e118	1.48542	0.742712	+	0.669611i	$0.233539\pi$
$462$	0	0
$463$	−3.69277e118	−0.889196	−0.444598	−	0.895730i	$-0.646654\pi$
$463$	−3.69277e118	−0.889196	−0.444598	+	0.895730i	$0.646654\pi$
$464$	−2.27223e118	−0.497052
$465$	0	0
$466$	8.52930e117	0.154078
$467$	2.67556e118	0.439352	0.219676	−	0.975573i	$-0.429500\pi$
$467$	2.67556e118	0.439352	0.219676	+	0.975573i	$0.429500\pi$
$468$	0	0
$469$	2.63154e118	0.357288
$470$	7.71236e117	0.0952429
$471$	0	0
$472$	1.34577e119	1.37579
$473$	1.36675e119	1.27165
$474$	0	0
$475$	1.46287e119	1.12808
$476$	−2.76078e118	−0.193875
$477$	0	0
$478$	−1.94569e118	−0.113379
$479$	−2.72713e118	−0.144802	−0.0724011	−	0.997376i	$-0.523066\pi$
$479$	−2.72713e118	−0.144802	−0.0724011	+	0.997376i	$0.523066\pi$
$480$	0	0
$481$	−4.31949e117	−0.0190536
$482$	3.69576e119	1.48631
$483$	0	0
$484$	2.74219e118	0.0917233
$485$	1.14271e118	0.0348681
$486$	0	0
$487$	5.36131e119	1.36217	0.681087	−	0.732203i	$-0.261508\pi$
$487$	5.36131e119	1.36217	0.681087	+	0.732203i	$0.261508\pi$
$488$	7.51325e119	1.74239
$489$	0	0
$490$	7.83776e118	0.151519
$491$	8.26069e119	1.45844	0.729222	−	0.684277i	$-0.239882\pi$
$491$	8.26069e119	1.45844	0.729222	+	0.684277i	$0.239882\pi$
$492$	0	0
$493$	8.83909e119	1.30233
$494$	3.22021e119	0.433546
$495$	0	0
$496$	−2.66701e119	−0.299979
$497$	3.82589e119	0.393435
$498$	0	0
$499$	9.69692e119	0.833987	0.416994	−	0.908909i	$-0.363084\pi$
$499$	9.69692e119	0.833987	0.416994	+	0.908909i	$0.363084\pi$
$500$	2.36426e119	0.186008
$501$	0	0
$502$	1.27720e120	0.841286
$503$	8.76853e119	0.528629	0.264315	−	0.964436i	$-0.414854\pi$
$503$	8.76853e119	0.528629	0.264315	+	0.964436i	$0.414854\pi$
$504$	0	0
$505$	2.00877e119	0.101499
$506$	3.67576e119	0.170078
$507$	0	0
$508$	−6.38178e119	−0.247746
$509$	4.82992e120	1.71790	0.858951	−	0.512057i	$-0.171117\pi$
$509$	4.82992e120	1.71790	0.858951	+	0.512057i	$0.171117\pi$
$510$	0	0
$511$	−2.55442e120	−0.763066
$512$	2.92012e120	0.799627
$513$	0	0
$514$	−9.75434e119	−0.224564
$515$	−1.84508e119	−0.0389577
$516$	0	0
$517$	2.55513e120	0.454029
$518$	8.13088e118	0.0132575
$519$	0	0
$520$	8.81401e119	0.121067
$521$	2.52036e120	0.317822	0.158911	−	0.987293i	$-0.449202\pi$
$521$	2.52036e120	0.317822	0.158911	+	0.987293i	$0.449202\pi$
$522$	0	0
$523$	1.51452e120	0.161046	0.0805229	−	0.996753i	$-0.474341\pi$
$523$	1.51452e120	0.161046	0.0805229	+	0.996753i	$0.474341\pi$
$524$	−3.79723e120	−0.370872
$525$	0	0
$526$	1.52434e121	1.25666
$527$	1.03748e121	0.785974
$528$	0	0
$529$	−1.46445e121	−0.937342
$530$	−5.37639e120	−0.316384
$531$	0	0
$532$	4.07085e120	0.202590
$533$	−7.98960e120	−0.365733
$534$	0	0
$535$	−1.20077e121	−0.465281
$536$	2.57653e121	0.918760
$537$	0	0
$538$	2.87803e120	0.0869528
$539$	2.59667e121	0.722300
$540$	0	0
$541$	2.85949e121	0.674544	0.337272	−	0.941407i	$-0.390496\pi$
$541$	2.85949e121	0.674544	0.337272	+	0.941407i	$0.390496\pi$
$542$	−5.09861e121	−1.10786
$543$	0	0
$544$	−4.63140e121	−0.854203
$545$	2.13165e121	0.362303
$546$	0	0
$547$	8.63056e121	1.24624	0.623122	−	0.782125i	$-0.285864\pi$
$547$	8.63056e121	1.24624	0.623122	+	0.782125i	$0.285864\pi$
$548$	1.02798e121	0.136851
$549$	0	0
$550$	−5.66136e121	−0.640886
$551$	−1.30335e122	−1.36087
$552$	0	0
$553$	5.32664e121	0.473353
$554$	1.70413e122	1.39740
$555$	0	0
$556$	1.08673e121	0.0759091
$557$	−5.63943e120	−0.0363646	−0.0181823	−	0.999835i	$-0.505788\pi$
$557$	−5.63943e120	−0.0363646	−0.0181823	+	0.999835i	$0.505788\pi$
$558$	0	0
$559$	−1.23409e122	−0.678456
$560$	−8.64247e120	−0.0438804
$561$	0	0
$562$	−2.22953e122	−0.965934
$563$	4.00702e121	0.160397	0.0801987	−	0.996779i	$-0.474445\pi$
$563$	4.00702e121	0.160397	0.0801987	+	0.996779i	$0.474445\pi$
$564$	0	0
$565$	3.47565e121	0.118818
$566$	−2.19057e122	−0.692191
$567$	0	0
$568$	3.74591e122	1.01171
$569$	−7.53120e122	−1.88091	−0.940455	−	0.339918i	$-0.889601\pi$
$569$	−7.53120e122	−1.88091	−0.940455	+	0.339918i	$0.889601\pi$
$570$	0	0
$571$	2.54331e122	0.543366	0.271683	−	0.962387i	$-0.412420\pi$
$571$	2.54331e122	0.543366	0.271683	+	0.962387i	$0.412420\pi$
$572$	8.36939e121	0.165413
$573$	0	0
$574$	1.50394e122	0.254478
$575$	−1.50774e122	−0.236107
$576$	0	0
$577$	−6.75470e122	−0.906321	−0.453161	−	0.891429i	$-0.649704\pi$
$577$	−6.75470e122	−0.906321	−0.453161	+	0.891429i	$0.649704\pi$
$578$	−1.92973e122	−0.239722
$579$	0	0
$580$	−1.02246e122	−0.108918
$581$	−6.43460e122	−0.634868
$582$	0	0
$583$	−1.78121e123	−1.50822
$584$	−2.50102e123	−1.96221
$585$	0	0
$586$	−1.71258e123	−1.15400
$587$	−3.95250e121	−0.0246875	−0.0123437	−	0.999924i	$-0.503929\pi$
$587$	−3.95250e121	−0.0246875	−0.0123437	+	0.999924i	$0.503929\pi$
$588$	0	0
$589$	−1.52980e123	−0.821304
$590$	−4.69709e122	−0.233838
$591$	0	0
$592$	4.14688e121	0.0177585
$593$	−2.53221e123	−1.00593	−0.502963	−	0.864308i	$-0.667757\pi$
$593$	−2.53221e123	−1.00593	−0.502963	+	0.864308i	$0.667757\pi$
$594$	0	0
$595$	3.36197e122	0.114971
$596$	7.03004e120	0.00223100
$597$	0	0
$598$	−3.31899e122	−0.0907409
$599$	−4.15936e123	−1.05568	−0.527840	−	0.849344i	$-0.676998\pi$
$599$	−4.15936e123	−1.05568	−0.527840	+	0.849344i	$0.676998\pi$
$600$	0	0
$601$	2.63415e123	0.576404	0.288202	−	0.957570i	$-0.406943\pi$
$601$	2.63415e123	0.576404	0.288202	+	0.957570i	$0.406943\pi$
$602$	2.32302e123	0.472072
$603$	0	0
$604$	−3.15580e123	−0.553306
$605$	−3.33934e122	−0.0543934
$606$	0	0
$607$	−6.29951e122	−0.0885952	−0.0442976	−	0.999018i	$-0.514105\pi$
$607$	−6.29951e122	−0.0885952	−0.0442976	+	0.999018i	$0.514105\pi$
$608$	6.82914e123	0.892599
$609$	0	0
$610$	−2.62231e123	−0.296147
$611$	−2.30713e123	−0.242235
$612$	0	0
$613$	−9.19228e123	−0.834511	−0.417256	−	0.908789i	$-0.637008\pi$
$613$	−9.19228e123	−0.834511	−0.417256	+	0.908789i	$0.637008\pi$
$614$	−9.66565e123	−0.816091
$615$	0	0
$616$	−5.49673e123	−0.401571
$617$	4.08750e123	0.277823	0.138911	−	0.990305i	$-0.455640\pi$
$617$	4.08750e123	0.277823	0.138911	+	0.990305i	$0.455640\pi$
$618$	0	0
$619$	2.80595e124	1.65138	0.825688	−	0.564127i	$-0.190787\pi$
$619$	2.80595e124	1.65138	0.825688	+	0.564127i	$0.190787\pi$
$620$	−1.20010e123	−0.0657337
$621$	0	0
$622$	1.15255e124	0.547000
$623$	−4.32095e122	−0.0190924
$624$	0	0
$625$	2.17405e124	0.832931
$626$	−1.53199e124	−0.546635
$627$	0	0
$628$	5.24245e123	0.162304
$629$	−1.61316e123	−0.0465289
$630$	0	0
$631$	2.74236e124	0.686781	0.343391	−	0.939193i	$-0.388425\pi$
$631$	2.74236e124	0.686781	0.343391	+	0.939193i	$0.388425\pi$
$632$	5.21529e124	1.21722
$633$	0	0
$634$	−3.36824e124	−0.683017
$635$	7.77148e123	0.146917
$636$	0	0
$637$	−2.34464e124	−0.385365
$638$	5.04400e124	0.773135
$639$	0	0
$640$	−6.79202e122	−0.00905712
$641$	−1.82007e124	−0.226415	−0.113207	−	0.993571i	$-0.536112\pi$
$641$	−1.82007e124	−0.226415	−0.113207	+	0.993571i	$0.536112\pi$
$642$	0	0
$643$	1.88790e124	0.204452	0.102226	−	0.994761i	$-0.467404\pi$
$643$	1.88790e124	0.204452	0.102226	+	0.994761i	$0.467404\pi$
$644$	−4.19572e123	−0.0424019
$645$	0	0
$646$	1.20262e125	1.05872
$647$	2.17534e125	1.78766	0.893832	−	0.448402i	$-0.148007\pi$
$647$	2.17534e125	1.78766	0.893832	+	0.448402i	$0.148007\pi$
$648$	0	0
$649$	−1.55616e125	−1.11472
$650$	5.11187e124	0.341928
$651$	0	0
$652$	−3.59784e124	−0.209905
$653$	−1.56942e125	−0.855268	−0.427634	−	0.903952i	$-0.640653\pi$
$653$	−1.56942e125	−0.855268	−0.427634	+	0.903952i	$0.640653\pi$
$654$	0	0
$655$	4.62412e124	0.219933
$656$	7.67033e124	0.340874
$657$	0	0
$658$	4.34287e124	0.168548
$659$	3.65512e125	1.32587	0.662935	−	0.748677i	$-0.269310\pi$
$659$	3.65512e125	1.32587	0.662935	+	0.748677i	$0.269310\pi$
$660$	0	0
$661$	3.53397e125	1.12021	0.560104	−	0.828423i	$-0.310761\pi$
$661$	3.53397e125	1.12021	0.560104	+	0.828423i	$0.310761\pi$
$662$	3.15645e125	0.935447
$663$	0	0
$664$	−6.30009e125	−1.63255
$665$	−4.95733e124	−0.120139
$666$	0	0
$667$	1.34333e125	0.284828
$668$	2.33378e125	0.462922
$669$	0	0
$670$	−8.99274e124	−0.156158
$671$	−8.68780e125	−1.41175
$672$	0	0
$673$	9.88007e125	1.40634	0.703169	−	0.711023i	$-0.251768\pi$
$673$	9.88007e125	1.40634	0.703169	+	0.711023i	$0.251768\pi$
$674$	1.64646e124	0.0219375
$675$	0	0
$676$	2.68460e125	0.313510
$677$	5.70038e125	0.623316	0.311658	−	0.950194i	$-0.399116\pi$
$677$	5.70038e125	0.623316	0.311658	+	0.950194i	$0.399116\pi$
$678$	0	0
$679$	6.43465e124	0.0617050
$680$	3.29169e125	0.295646
$681$	0	0
$682$	5.92036e125	0.466599
$683$	3.27309e125	0.241678	0.120839	−	0.992672i	$-0.461442\pi$
$683$	3.27309e125	0.241678	0.120839	+	0.992672i	$0.461442\pi$
$684$	0	0
$685$	−1.25183e125	−0.0811548
$686$	9.78118e125	0.594249
$687$	0	0
$688$	1.18478e126	0.632341
$689$	1.60833e126	0.804674
$690$	0	0
$691$	2.05988e126	0.905877	0.452938	−	0.891542i	$-0.350376\pi$
$691$	2.05988e126	0.905877	0.452938	+	0.891542i	$0.350376\pi$
$692$	8.27119e125	0.341073
$693$	0	0
$694$	−1.66372e126	−0.603372
$695$	−1.32338e125	−0.0450153
$696$	0	0
$697$	−2.98380e126	−0.893123
$698$	−1.62869e126	−0.457376
$699$	0	0
$700$	6.46220e125	0.159778
$701$	−4.71347e126	−1.09368	−0.546839	−	0.837238i	$-0.684169\pi$
$701$	−4.71347e126	−1.09368	−0.546839	+	0.837238i	$0.684169\pi$
$702$	0	0
$703$	2.37865e125	0.0486204
$704$	−4.64282e126	−0.890838
$705$	0	0
$706$	−6.96371e125	−0.117769
$707$	1.13115e126	0.179620
$708$	0	0
$709$	−7.09898e126	−0.994120	−0.497060	−	0.867716i	$-0.665587\pi$
$709$	−7.09898e126	−0.994120	−0.497060	+	0.867716i	$0.665587\pi$
$710$	−1.30742e126	−0.171956
$711$	0	0
$712$	−4.23062e125	−0.0490958
$713$	1.57672e126	0.171898
$714$	0	0
$715$	−1.01919e126	−0.0980928
$716$	−2.77965e126	−0.251397
$717$	0	0
$718$	−9.79630e126	−0.782572
$719$	−1.17855e127	−0.884939	−0.442470	−	0.896783i	$-0.645898\pi$
$719$	−1.17855e127	−0.884939	−0.442470	+	0.896783i	$0.645898\pi$
$720$	0	0
$721$	−1.03897e126	−0.0689423
$722$	−5.33531e126	−0.332855
$723$	0	0
$724$	−6.69679e126	−0.369403
$725$	−2.06898e127	−1.07329
$726$	0	0
$727$	−1.19951e127	−0.550458	−0.275229	−	0.961379i	$-0.588754\pi$
$727$	−1.19951e127	−0.550458	−0.275229	+	0.961379i	$0.588754\pi$
$728$	4.96322e126	0.214248
$729$	0	0
$730$	8.72920e126	0.333509
$731$	−4.60884e127	−1.65679
$732$	0	0
$733$	8.96644e125	0.0285426	0.0142713	−	0.999898i	$-0.495457\pi$
$733$	8.96644e125	0.0285426	0.0142713	+	0.999898i	$0.495457\pi$
$734$	−2.71127e127	−0.812266
$735$	0	0
$736$	−7.03861e126	−0.186820
$737$	−2.97932e127	−0.744414
$738$	0	0
$739$	−1.58170e127	−0.350306	−0.175153	−	0.984541i	$-0.556042\pi$
$739$	−1.58170e127	−0.350306	−0.175153	+	0.984541i	$0.556042\pi$
$740$	1.86601e125	0.00389138
$741$	0	0
$742$	−3.02747e127	−0.559895
$743$	1.06713e128	1.85872	0.929360	−	0.369176i	$-0.120360\pi$
$743$	1.06713e128	1.85872	0.929360	+	0.369176i	$0.120360\pi$
$744$	0	0
$745$	−8.56091e124	−0.00132302
$746$	3.23308e127	0.470693
$747$	0	0
$748$	3.12564e127	0.403941
$749$	−6.76158e127	−0.823393
$750$	0	0
$751$	5.91843e127	0.640072	0.320036	−	0.947405i	$-0.396305\pi$
$751$	5.91843e127	0.640072	0.320036	+	0.947405i	$0.396305\pi$
$752$	2.21493e127	0.225770
$753$	0	0
$754$	−4.55443e127	−0.412486
$755$	3.84301e127	0.328119
$756$	0	0
$757$	1.35916e127	0.103158	0.0515792	−	0.998669i	$-0.483575\pi$
$757$	1.35916e127	0.103158	0.0515792	+	0.998669i	$0.483575\pi$
$758$	−1.28877e128	−0.922350
$759$	0	0
$760$	−4.85370e127	−0.308935
$761$	1.07211e128	0.643607	0.321804	−	0.946806i	$-0.395711\pi$
$761$	1.07211e128	0.643607	0.321804	+	0.946806i	$0.395711\pi$
$762$	0	0
$763$	1.20035e128	0.641157
$764$	−5.67023e127	−0.285724
$765$	0	0
$766$	1.30257e128	0.584280
$767$	1.40512e128	0.594729
$768$	0	0
$769$	−6.47273e124	−0.000243986 0	−0.000121993	−	1.00000i	$-0.500039\pi$
$769$	−6.47273e124	−0.000243986 0	−0.000121993		1.00000i	$0.500039\pi$
$770$	1.91850e127	0.0682534
$771$	0	0
$772$	1.71700e128	0.544251
$773$	3.33193e128	0.997030	0.498515	−	0.866881i	$-0.333879\pi$
$773$	3.33193e128	0.997030	0.498515	+	0.866881i	$0.333879\pi$
$774$	0	0
$775$	−2.42845e128	−0.647744
$776$	6.30014e127	0.158673
$777$	0	0
$778$	5.73124e128	1.28723
$779$	4.39971e128	0.933269
$780$	0	0
$781$	−4.33151e128	−0.819726
$782$	−1.23951e128	−0.221590
$783$	0	0
$784$	2.25095e128	0.359171
$785$	−6.38405e127	−0.0962491
$786$	0	0
$787$	8.30772e127	0.111842	0.0559212	−	0.998435i	$-0.482190\pi$
$787$	8.30772e127	0.111842	0.0559212	+	0.998435i	$0.482190\pi$
$788$	−9.41383e126	−0.0119770
$789$	0	0
$790$	−1.82027e128	−0.206885
$791$	1.95716e128	0.210268
$792$	0	0
$793$	7.84457e128	0.753203
$794$	1.53274e129	1.39141
$795$	0	0
$796$	−6.82234e127	−0.0553735
$797$	−2.28637e129	−1.75490	−0.877448	−	0.479671i	$-0.840756\pi$
$797$	−2.28637e129	−1.75490	−0.877448	+	0.479671i	$0.840756\pi$
$798$	0	0
$799$	−8.61621e128	−0.591541
$800$	1.08408e129	0.703974
$801$	0	0
$802$	−1.11683e129	−0.648977
$803$	2.89201e129	1.58986
$804$	0	0
$805$	5.10938e127	0.0251450
$806$	−5.34573e128	−0.248942
$807$	0	0
$808$	1.10750e129	0.461891
$809$	1.46938e129	0.579997	0.289999	−	0.957027i	$-0.406345\pi$
$809$	1.46938e129	0.579997	0.289999	+	0.957027i	$0.406345\pi$
$810$	0	0
$811$	−8.00048e128	−0.282936	−0.141468	−	0.989943i	$-0.545182\pi$
$811$	−8.00048e128	−0.282936	−0.141468	+	0.989943i	$0.545182\pi$
$812$	−5.75751e128	−0.192749
$813$	0	0
$814$	−9.20545e127	−0.0276222
$815$	4.38131e128	0.124477
$816$	0	0
$817$	6.79588e129	1.73127
$818$	−2.85055e129	−0.687712
$819$	0	0
$820$	3.45150e128	0.0746949
$821$	4.07345e129	0.835010	0.417505	−	0.908675i	$-0.362905\pi$
$821$	4.07345e129	0.835010	0.417505	+	0.908675i	$0.362905\pi$
$822$	0	0
$823$	−7.86998e129	−1.44771	−0.723854	−	0.689953i	$-0.757631\pi$
$823$	−7.86998e129	−1.44771	−0.723854	+	0.689953i	$0.757631\pi$
$824$	−1.01726e129	−0.177284
$825$	0	0
$826$	−2.64496e129	−0.413815
$827$	4.50103e129	0.667293	0.333646	−	0.942698i	$-0.391721\pi$
$827$	4.50103e129	0.667293	0.333646	+	0.942698i	$0.391721\pi$
$828$	0	0
$829$	1.34040e130	1.78467	0.892336	−	0.451371i	$-0.149065\pi$
$829$	1.34040e130	1.78467	0.892336	+	0.451371i	$0.149065\pi$
$830$	2.19889e129	0.277478
$831$	0	0
$832$	4.19219e129	0.475284
$833$	−8.75631e129	−0.941063
$834$	0	0
$835$	−2.84199e129	−0.274520
$836$	−4.60885e129	−0.422098
$837$	0	0
$838$	−1.24758e130	−1.02733
$839$	−1.46067e130	−1.14063	−0.570315	−	0.821426i	$-0.693179\pi$
$839$	−1.46067e130	−1.14063	−0.570315	+	0.821426i	$0.693179\pi$
$840$	0	0
$841$	4.19654e129	0.294761
$842$	−1.27111e128	−0.00846829
$843$	0	0
$844$	7.80081e129	0.467628
$845$	−3.26920e129	−0.185917
$846$	0	0
$847$	−1.88040e129	−0.0962583
$848$	−1.54406e130	−0.749979
$849$	0	0
$850$	1.90908e130	0.834992
$851$	−2.45161e128	−0.0101762
$852$	0	0
$853$	−1.41360e130	−0.528562	−0.264281	−	0.964446i	$-0.585135\pi$
$853$	−1.41360e130	−0.528562	−0.264281	+	0.964446i	$0.585135\pi$
$854$	−1.47664e130	−0.524082
$855$	0	0
$856$	−6.62023e130	−2.11734
$857$	−3.80993e130	−1.15683	−0.578417	−	0.815742i	$-0.696329\pi$
$857$	−3.80993e130	−1.15683	−0.578417	+	0.815742i	$0.696329\pi$
$858$	0	0
$859$	−5.21106e130	−1.42636	−0.713182	−	0.700979i	$-0.752746\pi$
$859$	−5.21106e130	−1.42636	−0.713182	+	0.700979i	$0.752746\pi$
$860$	5.33126e129	0.138563
$861$	0	0
$862$	−2.27052e130	−0.532172
$863$	1.19612e130	0.266253	0.133127	−	0.991099i	$-0.457498\pi$
$863$	1.19612e130	0.266253	0.133127	+	0.991099i	$0.457498\pi$
$864$	0	0
$865$	−1.00723e130	−0.202262
$866$	−9.19427e129	−0.175376
$867$	0	0
$868$	−6.75784e129	−0.116327
$869$	−6.03061e130	−0.986236
$870$	0	0
$871$	2.69015e130	0.397163
$872$	1.17525e131	1.64872
$873$	0	0
$874$	1.82770e130	0.231551
$875$	−1.62124e130	−0.195204
$876$	0	0
$877$	1.16850e131	1.27101	0.635503	−	0.772099i	$-0.280793\pi$
$877$	1.16850e131	1.27101	0.635503	+	0.772099i	$0.280793\pi$
$878$	−1.01338e131	−1.04778
$879$	0	0
$880$	9.78466e129	0.0914254
$881$	−1.91284e131	−1.69923	−0.849614	−	0.527406i	$-0.823165\pi$
$881$	−1.91284e131	−1.69923	−0.849614	+	0.527406i	$0.823165\pi$
$882$	0	0
$883$	−3.55710e130	−0.285657	−0.142828	−	0.989747i	$-0.545620\pi$
$883$	−3.55710e130	−0.285657	−0.142828	+	0.989747i	$0.545620\pi$
$884$	−2.82226e130	−0.215512
$885$	0	0
$886$	−2.09974e131	−1.44999
$887$	2.68906e131	1.76603	0.883017	−	0.469341i	$-0.155508\pi$
$887$	2.68906e131	1.76603	0.883017	+	0.469341i	$0.155508\pi$
$888$	0	0
$889$	4.37616e130	0.259995
$890$	1.47659e129	0.00834460
$891$	0	0
$892$	6.24981e130	0.319618
$893$	1.27049e131	0.618131
$894$	0	0
$895$	3.38495e130	0.149083
$896$	−3.82462e129	−0.0160281
$897$	0	0
$898$	8.40009e130	0.318777
$899$	2.16364e131	0.781408
$900$	0	0
$901$	6.00648e131	1.96502
$902$	−1.70270e131	−0.530208
$903$	0	0
$904$	1.91625e131	0.540700
$905$	8.15509e130	0.219062
$906$	0	0
$907$	−4.49131e131	−1.09357	−0.546787	−	0.837272i	$-0.684149\pi$
$907$	−4.49131e131	−1.09357	−0.546787	+	0.837272i	$0.684149\pi$
$908$	8.55114e130	0.198246
$909$	0	0
$910$	−1.73229e130	−0.0364148
$911$	2.09946e131	0.420282	0.210141	−	0.977671i	$-0.432608\pi$
$911$	2.09946e131	0.420282	0.210141	+	0.977671i	$0.432608\pi$
$912$	0	0
$913$	7.28499e131	1.32276
$914$	6.92146e131	1.19699
$915$	0	0
$916$	4.91408e131	0.771070
$917$	2.60387e131	0.389209
$918$	0	0
$919$	−3.59597e131	−0.487839	−0.243919	−	0.969796i	$-0.578433\pi$
$919$	−3.59597e131	−0.487839	−0.243919	+	0.969796i	$0.578433\pi$
$920$	5.00258e130	0.0646600
$921$	0	0
$922$	−9.79069e131	−1.14891
$923$	3.91110e131	0.437344
$924$	0	0
$925$	3.77595e130	0.0383459
$926$	7.10597e131	0.687756
$927$	0	0
$928$	−9.65864e131	−0.849241
$929$	1.24505e132	1.04349	0.521745	−	0.853102i	$-0.325281\pi$
$929$	1.24505e132	1.04349	0.521745	+	0.853102i	$0.325281\pi$
$930$	0	0
$931$	1.29115e132	0.983364
$932$	1.10225e131	0.0800336
$933$	0	0
$934$	−5.14856e131	−0.339821
$935$	−3.80628e131	−0.239543
$936$	0	0
$937$	1.91446e132	1.09555	0.547777	−	0.836624i	$-0.315474\pi$
$937$	1.91446e132	1.09555	0.547777	+	0.836624i	$0.315474\pi$
$938$	−5.06386e131	−0.276347
$939$	0	0
$940$	9.96676e130	0.0494726
$941$	−2.75820e132	−1.30583	−0.652916	−	0.757431i	$-0.726454\pi$
$941$	−2.75820e132	−1.30583	−0.652916	+	0.757431i	$0.726454\pi$
$942$	0	0
$943$	−4.53466e131	−0.195332
$944$	−1.34897e132	−0.554305
$945$	0	0
$946$	−2.63003e132	−0.983568
$947$	1.89826e132	0.677300	0.338650	−	0.940912i	$-0.390030\pi$
$947$	1.89826e132	0.677300	0.338650	+	0.940912i	$0.390030\pi$
$948$	0	0
$949$	−2.61131e132	−0.848227
$950$	−2.81500e132	−0.872525
$951$	0	0
$952$	1.85357e132	0.523195
$953$	2.66119e132	0.716871	0.358436	−	0.933554i	$-0.383310\pi$
$953$	2.66119e132	0.716871	0.358436	+	0.933554i	$0.383310\pi$
$954$	0	0
$955$	6.90499e131	0.169439
$956$	−2.51443e131	−0.0588930
$957$	0	0
$958$	5.24780e131	0.111999
$959$	−7.04911e131	−0.143617
$960$	0	0
$961$	−2.84551e132	−0.528408
$962$	8.31197e130	0.0147371
$963$	0	0
$964$	4.77607e132	0.772045
$965$	−2.09089e132	−0.322750
$966$	0	0
$967$	5.83176e132	0.820959	0.410480	−	0.911870i	$-0.365361\pi$
$967$	5.83176e132	0.820959	0.410480	+	0.911870i	$0.365361\pi$
$968$	−1.84109e132	−0.247527
$969$	0	0
$970$	−2.19891e131	−0.0269690
$971$	5.38578e132	0.630947	0.315473	−	0.948934i	$-0.397837\pi$
$971$	5.38578e132	0.630947	0.315473	+	0.948934i	$0.397837\pi$
$972$	0	0
$973$	−7.45201e131	−0.0796622
$974$	−1.03167e133	−1.05358
$975$	0	0
$976$	−7.53110e132	−0.702007
$977$	−4.38063e132	−0.390147	−0.195073	−	0.980789i	$-0.562495\pi$
$977$	−4.38063e132	−0.390147	−0.195073	+	0.980789i	$0.562495\pi$
$978$	0	0
$979$	4.89200e131	0.0397792
$980$	1.01288e132	0.0787044
$981$	0	0
$982$	−1.58960e133	−1.12805
$983$	1.19142e133	0.808042	0.404021	−	0.914750i	$-0.367612\pi$
$983$	1.19142e133	0.808042	0.404021	+	0.914750i	$0.367612\pi$
$984$	0	0
$985$	1.14638e131	0.00710258
$986$	−1.70090e133	−1.00729
$987$	0	0
$988$	4.16152e132	0.225200
$989$	−7.00434e132	−0.362353
$990$	0	0
$991$	−2.01317e132	−0.0951923	−0.0475962	−	0.998867i	$-0.515156\pi$
$991$	−2.01317e132	−0.0951923	−0.0475962	+	0.998867i	$0.515156\pi$
$992$	−1.13368e133	−0.512530
$993$	0	0
$994$	−7.36214e132	−0.304305
$995$	8.30798e131	0.0328374
$996$	0	0
$997$	−9.22203e132	−0.333344	−0.166672	−	0.986012i	$-0.553302\pi$
$997$	−9.22203e132	−0.333344	−0.166672	+	0.986012i	$0.553302\pi$
$998$	−1.86597e133	−0.645054
$999$	0	0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.90.a.a.1.6	✓	7	3.2	odd	2
9.90.a.b.1.2		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)

\(f(q)\)	\(=\)	\(q-1.92430e13 q^{2} -2.48679e26 q^{4} +3.02831e30 q^{5} +1.70526e37 q^{7} +1.66961e40 q^{8} +O(q^{10})\)	\(q-1.92430e13 q^{2} -2.48679e26 q^{4} +3.02831e30 q^{5} +1.70526e37 q^{7} +1.66961e40 q^{8} -5.82737e43 q^{10} -1.93063e46 q^{11} +1.74324e49 q^{13} -3.28142e50 q^{14} -1.67358e53 q^{16} +6.51031e54 q^{17} -9.59966e56 q^{19} -7.53078e56 q^{20} +3.71509e59 q^{22} +9.89412e59 q^{23} -1.52388e62 q^{25} -3.35451e62 q^{26} -4.24062e63 q^{28} +1.35771e65 q^{29} +1.59360e66 q^{31} -7.11394e66 q^{32} -1.25278e68 q^{34} +5.16406e67 q^{35} -2.47785e68 q^{37} +1.84726e70 q^{38} +5.05611e70 q^{40} -4.58319e71 q^{41} -7.07930e72 q^{43} +4.80106e72 q^{44} -1.90392e73 q^{46} -1.32347e74 q^{47} -1.34499e75 q^{49} +2.93240e75 q^{50} -4.33507e75 q^{52} +9.22610e76 q^{53} -5.84654e76 q^{55} +2.84712e77 q^{56} -2.61263e78 q^{58} +8.06039e78 q^{59} +4.49999e79 q^{61} -3.06655e79 q^{62} +2.40483e80 q^{64} +5.27908e79 q^{65} +1.54319e81 q^{67} -1.61898e81 q^{68} -9.93718e80 q^{70} +2.24358e82 q^{71} -1.49797e83 q^{73} +4.76812e81 q^{74} +2.38723e83 q^{76} -3.29222e83 q^{77} +3.12365e84 q^{79} -5.06813e83 q^{80} +8.81941e84 q^{82} -3.77338e85 q^{83} +1.97153e85 q^{85} +1.36227e86 q^{86} -3.22340e86 q^{88} -2.53389e85 q^{89} +2.97268e86 q^{91} -2.46046e86 q^{92} +2.54675e87 q^{94} -2.90708e87 q^{95} +3.77341e87 q^{97} +2.58816e88 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 31407330351408 q^{2} + 22\!\cdots\!04 q^{4}+ \cdots + 17\!\cdots\!20 q^{8}+O(q^{10}) \) 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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