LMFDB - Embedded newform 9.90.a.b.1.4

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			1.4
Root			$1.22894e11$ 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)

$f(q)$	$=$	$q+1.03857e13 q^{2} -5.11108e26 q^{4} -2.06848e31 q^{5} -1.95248e37 q^{7} -1.17366e40 q^{8} +O(q^{10})$	\(q+1.03857e13 q^{2} -5.11108e26 q^{4} -2.06848e31 q^{5} -1.95248e37 q^{7} -1.17366e40 q^{8} -2.14826e44 q^{10} +3.33800e46 q^{11} +6.87926e49 q^{13} -2.02778e50 q^{14} +1.94468e53 q^{16} +2.38635e54 q^{17} +1.04038e57 q^{19} +1.05722e58 q^{20} +3.46674e59 q^{22} +1.76924e60 q^{23} +2.66302e62 q^{25} +7.14457e62 q^{26} +9.97926e63 q^{28} -3.58840e64 q^{29} -5.07783e65 q^{31} +9.28429e66 q^{32} +2.47839e67 q^{34} +4.03866e68 q^{35} +3.65900e69 q^{37} +1.08050e70 q^{38} +2.42770e71 q^{40} +8.30251e71 q^{41} +1.00136e72 q^{43} -1.70608e73 q^{44} +1.83748e73 q^{46} +1.68772e74 q^{47} -1.25457e75 q^{49} +2.76573e75 q^{50} -3.51604e76 q^{52} +3.74926e76 q^{53} -6.90459e77 q^{55} +2.29155e77 q^{56} -3.72680e77 q^{58} +6.54064e78 q^{59} +6.58668e78 q^{61} -5.27367e78 q^{62} -2.39460e79 q^{64} -1.42296e81 q^{65} -6.71698e80 q^{67} -1.21968e81 q^{68} +4.19442e81 q^{70} +3.76636e82 q^{71} +8.64712e81 q^{73} +3.80012e82 q^{74} -5.31745e83 q^{76} -6.51737e83 q^{77} +1.41908e84 q^{79} -4.02252e84 q^{80} +8.62271e84 q^{82} +6.96531e84 q^{83} -4.93612e85 q^{85} +1.03998e85 q^{86} -3.91768e86 q^{88} +1.63496e86 q^{89} -1.34316e87 q^{91} -9.04273e86 q^{92} +1.75281e87 q^{94} -2.15200e88 q^{95} -3.58411e88 q^{97} -1.30295e88 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.03857e13	0.417446	0.208723	−	0.977975i	$-0.433069\pi$
$2$	1.03857e13	0.417446	0.208723	+	0.977975i	$0.433069\pi$
$3$	0	0
$3$	0	0
$4$	−5.11108e26	−0.825739
$5$	−2.06848e31	−1.62737	−0.813685	−	0.581307i	$-0.802542\pi$
$5$	−2.06848e31	−1.62737	−0.813685	+	0.581307i	$0.802542\pi$
$6$	0	0
$7$	−1.95248e37	−0.482751	−0.241376	−	0.970432i	$-0.577599\pi$
$7$	−1.95248e37	−0.482751	−0.241376	+	0.970432i	$0.577599\pi$
$8$	−1.17366e40	−0.762147
$9$	0	0
$10$	−2.14826e44	−0.679338
$11$	3.33800e46	1.51884	0.759420	−	0.650601i	$-0.225483\pi$
$11$	3.33800e46	1.51884	0.759420	+	0.650601i	$0.225483\pi$
$12$	0	0
$13$	6.87926e49	1.84953	0.924767	−	0.380534i	$-0.124260\pi$
$13$	6.87926e49	1.84953	0.924767	+	0.380534i	$0.124260\pi$
$14$	−2.02778e50	−0.201522
$15$	0	0
$16$	1.94468e53	0.507584
$17$	2.38635e54	0.419525	0.209762	−	0.977752i	$-0.432731\pi$
$17$	2.38635e54	0.419525	0.209762	+	0.977752i	$0.432731\pi$
$18$	0	0
$19$	1.04038e57	1.29615	0.648075	−	0.761576i	$-0.275574\pi$
$19$	1.04038e57	1.29615	0.648075	+	0.761576i	$0.275574\pi$
$20$	1.05722e58	1.34378
$21$	0	0
$22$	3.46674e59	0.634033
$23$	1.76924e60	0.447609	0.223804	−	0.974634i	$-0.428152\pi$
$23$	1.76924e60	0.447609	0.223804	+	0.974634i	$0.428152\pi$
$24$	0	0
$25$	2.66302e62	1.64833
$26$	7.14457e62	0.772080
$27$	0	0
$28$	9.97926e63	0.398626
$29$	−3.58840e64	−0.300739	−0.150370	−	0.988630i	$-0.548046\pi$
$29$	−3.58840e64	−0.300739	−0.150370	+	0.988630i	$0.548046\pi$
$30$	0	0
$31$	−5.07783e65	−0.218818	−0.109409	−	0.993997i	$-0.534896\pi$
$31$	−5.07783e65	−0.218818	−0.109409	+	0.993997i	$0.534896\pi$
$32$	9.28429e66	0.974036
$33$	0	0
$34$	2.47839e67	0.175129
$35$	4.03866e68	0.785614
$36$	0	0
$37$	3.65900e69	0.600324	0.300162	−	0.953888i	$-0.402959\pi$
$37$	3.65900e69	0.600324	0.300162	+	0.953888i	$0.402959\pi$
$38$	1.08050e70	0.541072
$39$	0	0
$40$	2.42770e71	1.24029
$41$	8.30251e71	1.41360	0.706802	−	0.707412i	$-0.250137\pi$
$41$	8.30251e71	1.41360	0.706802	+	0.707412i	$0.250137\pi$
$42$	0	0
$43$	1.00136e72	0.204760	0.102380	−	0.994745i	$-0.467354\pi$
$43$	1.00136e72	0.204760	0.102380	+	0.994745i	$0.467354\pi$
$44$	−1.70608e73	−1.25417
$45$	0	0
$46$	1.83748e73	0.186852
$47$	1.68772e74	0.659091	0.329545	−	0.944140i	$-0.393105\pi$
$47$	1.68772e74	0.659091	0.329545	+	0.944140i	$0.393105\pi$
$48$	0	0
$49$	−1.25457e75	−0.766951
$50$	2.76573e75	0.688089
$51$	0	0
$52$	−3.51604e76	−1.52723
$53$	3.74926e76	0.697701	0.348851	−	0.937178i	$-0.386572\pi$
$53$	3.74926e76	0.697701	0.348851	+	0.937178i	$0.386572\pi$
$54$	0	0
$55$	−6.90459e77	−2.47171
$56$	2.29155e77	0.367927
$57$	0	0
$58$	−3.72680e77	−0.125542
$59$	6.54064e78	1.02969	0.514844	−	0.857284i	$-0.327850\pi$
$59$	6.54064e78	1.02969	0.514844	+	0.857284i	$0.327850\pi$
$60$	0	0
$61$	6.58668e78	0.235228	0.117614	−	0.993059i	$-0.462475\pi$
$61$	6.58668e78	0.235228	0.117614	+	0.993059i	$0.462475\pi$
$62$	−5.27367e78	−0.0913446
$63$	0	0
$64$	−2.39460e79	−0.100977
$65$	−1.42296e81	−3.00987
$66$	0	0
$67$	−6.71698e80	−0.368846	−0.184423	−	0.982847i	$-0.559042\pi$
$67$	−6.71698e80	−0.368846	−0.184423	+	0.982847i	$0.559042\pi$
$68$	−1.21968e81	−0.346418
$69$	0	0
$70$	4.19442e81	0.327951
$71$	3.76636e82	1.56648	0.783240	−	0.621719i	$-0.213566\pi$
$71$	3.76636e82	1.56648	0.783240	+	0.621719i	$0.213566\pi$
$72$	0	0
$73$	8.64712e81	0.104473	0.0522365	−	0.998635i	$-0.483365\pi$
$73$	8.64712e81	0.104473	0.0522365	+	0.998635i	$0.483365\pi$
$74$	3.80012e82	0.250603
$75$	0	0
$76$	−5.31745e83	−1.07028
$77$	−6.51737e83	−0.733221
$78$	0	0
$79$	1.41908e84	0.510037	0.255019	−	0.966936i	$-0.417918\pi$
$79$	1.41908e84	0.510037	0.255019	+	0.966936i	$0.417918\pi$
$80$	−4.02252e84	−0.826027
$81$	0	0
$82$	8.62271e84	0.590103
$83$	6.96531e84	0.277949	0.138975	−	0.990296i	$-0.455619\pi$
$83$	6.96531e84	0.277949	0.138975	+	0.990296i	$0.455619\pi$
$84$	0	0
$85$	−4.93612e85	−0.682722
$86$	1.03998e85	0.0854761
$87$	0	0
$88$	−3.91768e86	−1.15758
$89$	1.63496e86	0.292182	0.146091	−	0.989271i	$-0.453331\pi$
$89$	1.63496e86	0.292182	0.146091	+	0.989271i	$0.453331\pi$
$90$	0	0
$91$	−1.34316e87	−0.892864
$92$	−9.04273e86	−0.369608
$93$	0	0
$94$	1.75281e87	0.275135
$95$	−2.15200e88	−2.10932
$96$	0	0
$97$	−3.58411e88	−1.39008	−0.695038	−	0.718973i	$-0.744612\pi$
$97$	−3.58411e88	−1.39008	−0.695038	+	0.718973i	$0.744612\pi$
$98$	−1.30295e88	−0.320161
$99$	0	0
$100$	−1.36109e89	−1.36109
$101$	1.52336e89	0.978368	0.489184	−	0.872181i	$-0.337295\pi$
$101$	1.52336e89	0.978368	0.489184	+	0.872181i	$0.337295\pi$
$102$	0	0
$103$	−6.65603e89	−1.78632	−0.893159	−	0.449740i	$-0.851517\pi$
$103$	−6.65603e89	−1.78632	−0.893159	+	0.449740i	$0.851517\pi$
$104$	−8.07392e89	−1.40962
$105$	0	0
$106$	3.89386e89	0.291252
$107$	8.04305e89	0.396135	0.198067	−	0.980188i	$-0.436534\pi$
$107$	8.04305e89	0.396135	0.198067	+	0.980188i	$0.436534\pi$
$108$	0	0
$109$	6.24667e90	1.34949	0.674745	−	0.738051i	$-0.264254\pi$
$109$	6.24667e90	1.34949	0.674745	+	0.738051i	$0.264254\pi$
$110$	−7.17088e90	−1.03181
$111$	0	0
$112$	−3.79694e90	−0.245037
$113$	−1.14980e89	−0.00499610	−0.00249805	−	0.999997i	$-0.500795\pi$
$113$	−1.14980e89	−0.00499610	−0.00249805	+	0.999997i	$0.500795\pi$
$114$	0	0
$115$	−3.65964e91	−0.728424
$116$	1.83406e91	0.248332
$117$	0	0
$118$	6.79290e91	0.429839
$119$	−4.65930e91	−0.202526
$120$	0	0
$121$	6.31222e92	1.30687
$122$	6.84072e91	0.0981949
$123$	0	0
$124$	2.59532e92	0.180687
$125$	−2.16660e93	−1.05507
$126$	0	0
$127$	−6.09607e93	−1.46482	−0.732411	−	0.680863i	$-0.761605\pi$
$127$	−6.09607e93	−1.46482	−0.732411	+	0.680863i	$0.761605\pi$
$128$	−5.99540e93	−1.01619
$129$	0	0
$130$	−1.47784e94	−1.25646
$131$	−1.93866e93	−0.117201	−0.0586003	−	0.998282i	$-0.518664\pi$
$131$	−1.93866e93	−0.117201	−0.0586003	+	0.998282i	$0.518664\pi$
$132$	0	0
$133$	−2.03131e94	−0.625718
$134$	−6.97603e93	−0.153973
$135$	0	0
$136$	−2.80077e94	−0.319740
$137$	−3.30510e94	−0.272345	−0.136172	−	0.990685i	$-0.543480\pi$
$137$	−3.30510e94	−0.272345	−0.136172	+	0.990685i	$0.543480\pi$
$138$	0	0
$139$	2.72553e95	1.17840	0.589200	−	0.807987i	$-0.299443\pi$
$139$	2.72553e95	1.17840	0.589200	+	0.807987i	$0.299443\pi$
$140$	−2.06419e95	−0.648712
$141$	0	0
$142$	3.91162e95	0.653920
$143$	2.29630e96	2.80915
$144$	0	0
$145$	7.42253e95	0.489414
$146$	8.98062e94	0.0436118
$147$	0	0
$148$	−1.87014e96	−0.495711
$149$	2.76855e96	0.543830	0.271915	−	0.962321i	$-0.412343\pi$
$149$	2.76855e96	0.543830	0.271915	+	0.962321i	$0.412343\pi$
$150$	0	0
$151$	6.33879e96	0.687910	0.343955	−	0.938986i	$-0.388233\pi$
$151$	6.33879e96	0.687910	0.343955	+	0.938986i	$0.388233\pi$
$152$	−1.22105e97	−0.987857
$153$	0	0
$154$	−6.76873e96	−0.306080
$155$	1.05034e97	0.356098
$156$	0	0
$157$	1.38061e97	0.264567	0.132283	−	0.991212i	$-0.457769\pi$
$157$	1.38061e97	0.264567	0.132283	+	0.991212i	$0.457769\pi$
$158$	1.47381e97	0.212913
$159$	0	0
$160$	−1.92044e98	−1.58512
$161$	−3.45440e97	−0.216084
$162$	0	0
$163$	−3.99376e98	−1.44223	−0.721113	−	0.692817i	$-0.756369\pi$
$163$	−3.99376e98	−1.44223	−0.721113	+	0.692817i	$0.756369\pi$
$164$	−4.24348e98	−1.16727
$165$	0	0
$166$	7.23395e97	0.116029
$167$	5.58501e98	0.685711	0.342855	−	0.939388i	$-0.388606\pi$
$167$	5.58501e98	0.685711	0.342855	+	0.939388i	$0.388606\pi$
$168$	0	0
$169$	3.34898e99	2.42078
$170$	−5.12650e98	−0.284999
$171$	0	0
$172$	−5.11804e98	−0.169078
$173$	5.30954e98	0.135521	0.0677603	−	0.997702i	$-0.478415\pi$
$173$	5.30954e98	0.135521	0.0677603	+	0.997702i	$0.478415\pi$
$174$	0	0
$175$	−5.19949e99	−0.795733
$176$	6.49133e99	0.770939
$177$	0	0
$178$	1.69802e99	0.121970
$179$	1.66743e100	0.933442	0.466721	−	0.884405i	$-0.345435\pi$
$179$	1.66743e100	0.933442	0.466721	+	0.884405i	$0.345435\pi$
$180$	0	0
$181$	−2.59959e99	−0.0887581	−0.0443790	−	0.999015i	$-0.514131\pi$
$181$	−2.59959e99	−0.0887581	−0.0443790	+	0.999015i	$0.514131\pi$
$182$	−1.39496e100	−0.372722
$183$	0	0
$184$	−2.07649e100	−0.341143
$185$	−7.56857e100	−0.976949
$186$	0	0
$187$	7.96565e100	0.637191
$188$	−8.62606e100	−0.544237
$189$	0	0
$190$	−2.23500e101	−0.880525
$191$	5.02287e101	1.56663	0.783315	−	0.621624i	$-0.213527\pi$
$191$	5.02287e101	1.56663	0.783315	+	0.621624i	$0.213527\pi$
$192$	0	0
$193$	5.15777e100	0.101196	0.0505979	−	0.998719i	$-0.483887\pi$
$193$	5.15777e100	0.101196	0.0505979	+	0.998719i	$0.483887\pi$
$194$	−3.72234e101	−0.580281
$195$	0	0
$196$	6.41218e101	0.633302
$197$	3.96960e101	0.312608	0.156304	−	0.987709i	$-0.450042\pi$
$197$	3.96960e101	0.312608	0.156304	+	0.987709i	$0.450042\pi$
$198$	0	0
$199$	2.43079e102	1.22119	0.610597	−	0.791941i	$-0.290929\pi$
$199$	2.43079e102	1.22119	0.610597	+	0.791941i	$0.290929\pi$
$200$	−3.12549e102	−1.25627
$201$	0	0
$202$	1.58211e102	0.408415
$203$	7.00627e101	0.145182
$204$	0	0
$205$	−1.71736e103	−2.30046
$206$	−6.91274e102	−0.745691
$207$	0	0
$208$	1.33779e103	0.938794
$209$	3.47278e103	1.96864
$210$	0	0
$211$	−1.60967e103	−0.597265	−0.298633	−	0.954368i	$-0.596531\pi$
$211$	−1.60967e103	−0.597265	−0.298633	+	0.954368i	$0.596531\pi$
$212$	−1.91628e103	−0.576119
$213$	0	0
$214$	8.35325e102	0.165365
$215$	−2.07130e103	−0.333220
$216$	0	0
$217$	9.91435e102	0.105635
$218$	6.48759e103	0.563339
$219$	0	0
$220$	3.52899e104	2.04099
$221$	1.64163e104	0.775926
$222$	0	0
$223$	−3.21841e104	−1.01877	−0.509384	−	0.860539i	$-0.670127\pi$
$223$	−3.21841e104	−1.01877	−0.509384	+	0.860539i	$0.670127\pi$
$224$	−1.81274e104	−0.470217
$225$	0	0
$226$	−1.19414e102	−0.00208560
$227$	6.65358e104	0.954783	0.477392	−	0.878691i	$-0.341582\pi$
$227$	6.65358e104	0.954783	0.477392	+	0.878691i	$0.341582\pi$
$228$	0	0
$229$	6.59926e104	0.640938	0.320469	−	0.947259i	$-0.396159\pi$
$229$	6.59926e104	0.640938	0.320469	+	0.947259i	$0.396159\pi$
$230$	−3.80078e104	−0.304078
$231$	0	0
$232$	4.21157e104	0.229207
$233$	−2.60299e105	−1.16986	−0.584931	−	0.811083i	$-0.698878\pi$
$233$	−2.60299e105	−1.16986	−0.584931	+	0.811083i	$0.698878\pi$
$234$	0	0
$235$	−3.49101e105	−1.07258
$236$	−3.34297e105	−0.850254
$237$	0	0
$238$	−4.83900e104	−0.0845436
$239$	6.66813e105	0.966713	0.483357	−	0.875424i	$-0.339417\pi$
$239$	6.66813e105	0.966713	0.483357	+	0.875424i	$0.339417\pi$
$240$	0	0
$241$	1.08349e106	1.08409	0.542045	−	0.840350i	$-0.317650\pi$
$241$	1.08349e106	1.08409	0.542045	+	0.840350i	$0.317650\pi$
$242$	6.55567e105	0.545549
$243$	0	0
$244$	−3.36651e105	−0.194237
$245$	2.59504e106	1.24811
$246$	0	0
$247$	7.15702e106	2.39727
$248$	5.95966e105	0.166771
$249$	0	0
$250$	−2.25016e106	−0.440436
$251$	−2.49391e106	−0.408696	−0.204348	−	0.978898i	$-0.565507\pi$
$251$	−2.49391e106	−0.408696	−0.204348	+	0.978898i	$0.565507\pi$
$252$	0	0
$253$	5.90573e106	0.679846
$254$	−6.33118e106	−0.611483
$255$	0	0
$256$	−4.74444e106	−0.323226
$257$	−3.95594e106	−0.226582	−0.113291	−	0.993562i	$-0.536139\pi$
$257$	−3.95594e106	−0.226582	−0.113291	+	0.993562i	$0.536139\pi$
$258$	0	0
$259$	−7.14411e106	−0.289807
$260$	7.27286e107	2.48537
$261$	0	0
$262$	−2.01343e106	−0.0489249
$263$	−7.74466e107	−1.58844	−0.794221	−	0.607629i	$-0.792121\pi$
$263$	−7.74466e107	−1.58844	−0.794221	+	0.607629i	$0.792121\pi$
$264$	0	0
$265$	−7.75527e107	−1.13542
$266$	−2.10965e107	−0.261203
$267$	0	0
$268$	3.43310e107	0.304571
$269$	−1.98879e108	−1.49490	−0.747449	−	0.664319i	$-0.768722\pi$
$269$	−1.98879e108	−1.49490	−0.747449	+	0.664319i	$0.768722\pi$
$270$	0	0
$271$	1.60523e108	0.867768	0.433884	−	0.900969i	$-0.357143\pi$
$271$	1.60523e108	0.867768	0.433884	+	0.900969i	$0.357143\pi$
$272$	4.64069e107	0.212944
$273$	0	0
$274$	−3.43257e107	−0.113689
$275$	8.88917e108	2.50355
$276$	0	0
$277$	7.19461e108	1.46777	0.733885	−	0.679274i	$-0.237705\pi$
$277$	7.19461e108	1.46777	0.733885	+	0.679274i	$0.237705\pi$
$278$	2.83065e108	0.491918
$279$	0	0
$280$	−4.74002e108	−0.598753
$281$	−1.68676e108	−0.181812	−0.0909061	−	0.995859i	$-0.528976\pi$
$281$	−1.68676e108	−0.181812	−0.0909061	+	0.995859i	$0.528976\pi$
$282$	0	0
$283$	−1.91816e109	−1.50796	−0.753979	−	0.656899i	$-0.771868\pi$
$283$	−1.91816e109	−1.50796	−0.753979	+	0.656899i	$0.771868\pi$
$284$	−1.92501e109	−1.29350
$285$	0	0
$286$	2.38486e109	1.17267
$287$	−1.62105e109	−0.682419
$288$	0	0
$289$	−2.66613e109	−0.823999
$290$	7.70880e108	0.204304
$291$	0	0
$292$	−4.41961e108	−0.0862675
$293$	−4.27672e109	−0.716972	−0.358486	−	0.933535i	$-0.616707\pi$
$293$	−4.27672e109	−0.716972	−0.358486	+	0.933535i	$0.616707\pi$
$294$	0	0
$295$	−1.35292e110	−1.67568
$296$	−4.29443e109	−0.457535
$297$	0	0
$298$	2.87532e109	0.227019
$299$	1.21711e110	0.827867
$300$	0	0
$301$	−1.95514e109	−0.0988480
$302$	6.58326e109	0.287165
$303$	0	0
$304$	2.02320e110	0.657906
$305$	−1.36244e110	−0.382803
$306$	0	0
$307$	7.49397e110	1.57418	0.787090	−	0.616838i	$-0.211587\pi$
$307$	7.49397e110	1.57418	0.787090	+	0.616838i	$0.211587\pi$
$308$	3.33108e110	0.605450
$309$	0	0
$310$	1.09085e110	0.148651
$311$	2.85176e109	0.0336725	0.0168362	−	0.999858i	$-0.494641\pi$
$311$	2.85176e109	0.0336725	0.0168362	+	0.999858i	$0.494641\pi$
$312$	0	0
$313$	−2.07857e111	−1.84520	−0.922598	−	0.385764i	$-0.873938\pi$
$313$	−2.07857e111	−1.84520	−0.922598	+	0.385764i	$0.873938\pi$
$314$	1.43385e110	0.110442
$315$	0	0
$316$	−7.25304e110	−0.421158
$317$	−9.87009e110	−0.497948	−0.248974	−	0.968510i	$-0.580093\pi$
$317$	−9.87009e110	−0.497948	−0.248974	+	0.968510i	$0.580093\pi$
$318$	0	0
$319$	−1.19781e111	−0.456775
$320$	4.95318e110	0.164327
$321$	0	0
$322$	−3.58763e110	−0.0902031
$323$	2.48271e111	0.543767
$324$	0	0
$325$	1.83196e112	3.04864
$326$	−4.14779e111	−0.602051
$327$	0	0
$328$	−9.74434e111	−1.07737
$329$	−3.29523e111	−0.318177
$330$	0	0
$331$	9.02317e111	0.665293	0.332647	−	0.943052i	$-0.392058\pi$
$331$	9.02317e111	0.665293	0.332647	+	0.943052i	$0.392058\pi$
$332$	−3.56003e111	−0.229514
$333$	0	0
$334$	5.80041e111	0.286247
$335$	1.38939e112	0.600249
$336$	0	0
$337$	−4.14663e112	−1.37456	−0.687281	−	0.726392i	$-0.741196\pi$
$337$	−4.14663e112	−1.37456	−0.687281	+	0.726392i	$0.741196\pi$
$338$	3.47815e112	1.01054
$339$	0	0
$340$	2.52289e112	0.563750
$341$	−1.69498e112	−0.332349
$342$	0	0
$343$	5.64334e112	0.852998
$344$	−1.17526e112	−0.156057
$345$	0	0
$346$	5.51432e111	0.0565725
$347$	−4.79621e112	−0.432749	−0.216375	−	0.976310i	$-0.569423\pi$
$347$	−4.79621e112	−0.432749	−0.216375	+	0.976310i	$0.569423\pi$
$348$	0	0
$349$	−1.99610e113	−1.39461	−0.697303	−	0.716776i	$-0.745617\pi$
$349$	−1.99610e113	−1.39461	−0.697303	+	0.716776i	$0.745617\pi$
$350$	−5.40002e112	−0.332175
$351$	0	0
$352$	3.09910e113	1.47940
$353$	3.89397e113	1.63840	0.819198	−	0.573512i	$-0.194419\pi$
$353$	3.89397e113	1.63840	0.819198	+	0.573512i	$0.194419\pi$
$354$	0	0
$355$	−7.79063e113	−2.54924
$356$	−8.35643e112	−0.241266
$357$	0	0
$358$	1.73174e113	0.389661
$359$	−6.09419e113	−1.21119	−0.605596	−	0.795772i	$-0.707065\pi$
$359$	−6.09419e113	−1.21119	−0.605596	+	0.795772i	$0.707065\pi$
$360$	0	0
$361$	4.38110e113	0.680006
$362$	−2.69985e112	−0.0370517
$363$	0	0
$364$	6.86499e113	0.737273
$365$	−1.78864e113	−0.170016
$366$	0	0
$367$	3.55965e112	0.0265318	0.0132659	−	0.999912i	$-0.495777\pi$
$367$	3.55965e112	0.0265318	0.0132659	+	0.999912i	$0.495777\pi$
$368$	3.44060e113	0.227199
$369$	0	0
$370$	−7.86047e113	−0.407823
$371$	−7.32035e113	−0.336816
$372$	0	0
$373$	−1.39504e114	−0.505294	−0.252647	−	0.967559i	$-0.581301\pi$
$373$	−1.39504e114	−0.505294	−0.252647	+	0.967559i	$0.581301\pi$
$374$	8.27286e113	0.265993
$375$	0	0
$376$	−1.98081e114	−0.502324
$377$	−2.46855e114	−0.556227
$378$	0	0
$379$	−6.43130e114	−1.14513	−0.572564	−	0.819860i	$-0.694051\pi$
$379$	−6.43130e114	−1.14513	−0.572564	+	0.819860i	$0.694051\pi$
$380$	1.09990e115	1.74174
$381$	0	0
$382$	5.21658e114	0.653983
$383$	−1.10630e115	−1.23460	−0.617301	−	0.786727i	$-0.711774\pi$
$383$	−1.10630e115	−1.23460	−0.617301	+	0.786727i	$0.711774\pi$
$384$	0	0
$385$	1.34810e115	1.19322
$386$	5.35670e113	0.0422437
$387$	0	0
$388$	1.83186e115	1.14784
$389$	1.57957e115	0.882638	0.441319	−	0.897350i	$-0.354511\pi$
$389$	1.57957e115	0.882638	0.441319	+	0.897350i	$0.354511\pi$
$390$	0	0
$391$	4.22204e114	0.187783
$392$	1.47244e115	0.584530
$393$	0	0
$394$	4.12270e114	0.130497
$395$	−2.93534e115	−0.830019
$396$	0	0
$397$	−6.52560e115	−1.47381	−0.736907	−	0.675994i	$-0.763715\pi$
$397$	−6.52560e115	−1.47381	−0.736907	+	0.675994i	$0.763715\pi$
$398$	2.52454e115	0.509782
$399$	0	0
$400$	5.17872e115	0.836667
$401$	2.09460e115	0.302815	0.151407	−	0.988471i	$-0.451619\pi$
$401$	2.09460e115	0.302815	0.151407	+	0.988471i	$0.451619\pi$
$402$	0	0
$403$	−3.49317e115	−0.404711
$404$	−7.78602e115	−0.807876
$405$	0	0
$406$	7.27649e114	0.0606057
$407$	1.22137e116	0.911796
$408$	0	0
$409$	−1.11593e116	−0.669808	−0.334904	−	0.942252i	$-0.608704\pi$
$409$	−1.11593e116	−0.669808	−0.334904	+	0.942252i	$0.608704\pi$
$410$	−1.78359e116	−0.960315
$411$	0	0
$412$	3.40195e116	1.47503
$413$	−1.27705e116	−0.497083
$414$	0	0
$415$	−1.44076e116	−0.452326
$416$	6.38690e116	1.80151
$417$	0	0
$418$	3.60671e116	0.821802
$419$	5.10063e116	1.04496	0.522480	−	0.852652i	$-0.325007\pi$
$419$	5.10063e116	1.04496	0.522480	+	0.852652i	$0.325007\pi$
$420$	0	0
$421$	1.89402e116	0.313929	0.156965	−	0.987604i	$-0.449829\pi$
$421$	1.89402e116	0.313929	0.156965	+	0.987604i	$0.449829\pi$
$422$	−1.67175e116	−0.249326
$423$	0	0
$424$	−4.40036e116	−0.531751
$425$	6.35491e116	0.691516
$426$	0	0
$427$	−1.28604e116	−0.113557
$428$	−4.11087e116	−0.327104
$429$	0	0
$430$	−2.15118e116	−0.139101
$431$	−3.16057e117	−1.84301	−0.921503	−	0.388371i	$-0.873038\pi$
$431$	−3.16057e117	−1.84301	−0.921503	+	0.388371i	$0.873038\pi$
$432$	0	0
$433$	6.43348e116	0.305306	0.152653	−	0.988280i	$-0.451218\pi$
$433$	6.43348e116	0.305306	0.152653	+	0.988280i	$0.451218\pi$
$434$	1.02967e116	0.0440967
$435$	0	0
$436$	−3.19272e117	−1.11433
$437$	1.84068e117	0.580168
$438$	0	0
$439$	9.35169e116	0.240558	0.120279	−	0.992740i	$-0.461621\pi$
$439$	9.35169e116	0.240558	0.120279	+	0.992740i	$0.461621\pi$
$440$	8.10365e117	1.88381
$441$	0	0
$442$	1.70495e117	0.323907
$443$	1.84634e117	0.317210	0.158605	−	0.987342i	$-0.449300\pi$
$443$	1.84634e117	0.317210	0.158605	+	0.987342i	$0.449300\pi$
$444$	0	0
$445$	−3.38189e117	−0.475488
$446$	−3.34254e117	−0.425280
$447$	0	0
$448$	4.67540e116	0.0487469
$449$	1.21900e118	1.15091	0.575457	−	0.817832i	$-0.304824\pi$
$449$	1.21900e118	1.15091	0.575457	+	0.817832i	$0.304824\pi$
$450$	0	0
$451$	2.77138e118	2.14704
$452$	5.87672e115	0.00412548
$453$	0	0
$454$	6.91019e117	0.398570
$455$	2.77830e118	1.45302
$456$	0	0
$457$	3.95962e118	1.70366	0.851829	−	0.523820i	$-0.175493\pi$
$457$	3.95962e118	1.70366	0.851829	+	0.523820i	$0.175493\pi$
$458$	6.85378e117	0.267557
$459$	0	0
$460$	1.87047e118	0.601489
$461$	2.43828e118	0.711857	0.355928	−	0.934513i	$-0.384165\pi$
$461$	2.43828e118	0.711857	0.355928	+	0.934513i	$0.384165\pi$
$462$	0	0
$463$	−6.30692e118	−1.51867	−0.759335	−	0.650700i	$-0.774476\pi$
$463$	−6.30692e118	−1.51867	−0.759335	+	0.650700i	$0.774476\pi$
$464$	−6.97828e117	−0.152650
$465$	0	0
$466$	−2.70339e118	−0.488354
$467$	7.19968e118	1.18226	0.591129	−	0.806577i	$-0.298682\pi$
$467$	7.19968e118	1.18226	0.591129	+	0.806577i	$0.298682\pi$
$468$	0	0
$469$	1.31147e118	0.178061
$470$	−3.62565e118	−0.447746
$471$	0	0
$472$	−7.67651e118	−0.784774
$473$	3.34255e118	0.310997
$474$	0	0
$475$	2.77055e119	2.13648
$476$	2.38140e118	0.167234
$477$	0	0
$478$	6.92531e118	0.403550
$479$	2.34376e119	1.24446	0.622232	−	0.782833i	$-0.286226\pi$
$479$	2.34376e119	1.24446	0.622232	+	0.782833i	$0.286226\pi$
$480$	0	0
$481$	2.51712e119	1.11032
$482$	1.12527e119	0.452549
$483$	0	0
$484$	−3.22623e119	−1.07914
$485$	7.41365e119	2.26217
$486$	0	0
$487$	2.11455e119	0.537253	0.268627	−	0.963244i	$-0.413430\pi$
$487$	2.11455e119	0.537253	0.268627	+	0.963244i	$0.413430\pi$
$488$	−7.73054e118	−0.179278
$489$	0	0
$490$	2.69513e119	0.521019
$491$	6.64397e119	1.17301	0.586504	−	0.809946i	$-0.300504\pi$
$491$	6.64397e119	1.17301	0.586504	+	0.809946i	$0.300504\pi$
$492$	0	0
$493$	−8.56319e118	−0.126168
$494$	7.43305e119	1.00073
$495$	0	0
$496$	−9.87474e118	−0.111069
$497$	−7.35372e119	−0.756220
$498$	0	0
$499$	1.68726e120	1.45114	0.725568	−	0.688150i	$-0.241577\pi$
$499$	1.68726e120	1.45114	0.725568	+	0.688150i	$0.241577\pi$
$500$	1.10737e120	0.871216
$501$	0	0
$502$	−2.59009e119	−0.170608
$503$	−9.10170e118	−0.0548715	−0.0274358	−	0.999624i	$-0.508734\pi$
$503$	−9.10170e118	−0.0548715	−0.0274358	+	0.999624i	$0.508734\pi$
$504$	0	0
$505$	−3.15104e120	−1.59217
$506$	6.13350e119	0.283799
$507$	0	0
$508$	3.11575e120	1.20956
$509$	−1.64557e120	−0.585295	−0.292647	−	0.956220i	$-0.594536\pi$
$509$	−1.64557e120	−0.585295	−0.292647	+	0.956220i	$0.594536\pi$
$510$	0	0
$511$	−1.68833e119	−0.0504345
$512$	3.21823e120	0.881259
$513$	0	0
$514$	−4.10851e119	−0.0945857
$515$	1.37679e121	2.90700
$516$	0	0
$517$	5.63360e120	1.00105
$518$	−7.41965e119	−0.120979
$519$	0	0
$520$	1.67007e121	2.29397
$521$	3.57068e120	0.450269	0.225135	−	0.974328i	$-0.427718\pi$
$521$	3.57068e120	0.450269	0.225135	+	0.974328i	$0.427718\pi$
$522$	0	0
$523$	6.21466e120	0.660834	0.330417	−	0.943835i	$-0.392811\pi$
$523$	6.21466e120	0.660834	0.330417	+	0.943835i	$0.392811\pi$
$524$	9.90866e119	0.0967771
$525$	0	0
$526$	−8.04335e120	−0.663088
$527$	−1.21175e120	−0.0917996
$528$	0	0
$529$	−1.24933e121	−0.799647
$530$	−8.05437e120	−0.473975
$531$	0	0
$532$	1.03822e121	0.516680
$533$	5.71151e121	2.61451
$534$	0	0
$535$	−1.66369e121	−0.644657
$536$	7.88346e120	0.281115
$537$	0	0
$538$	−2.06549e121	−0.624039
$539$	−4.18774e121	−1.16488
$540$	0	0
$541$	2.95502e121	0.697079	0.348539	−	0.937294i	$-0.386678\pi$
$541$	2.95502e121	0.697079	0.348539	+	0.937294i	$0.386678\pi$
$542$	1.66714e121	0.362246
$543$	0	0
$544$	2.21556e121	0.408632
$545$	−1.29211e122	−2.19612
$546$	0	0
$547$	−6.53228e121	−0.943255	−0.471627	−	0.881798i	$-0.656333\pi$
$547$	−6.53228e121	−0.943255	−0.471627	+	0.881798i	$0.656333\pi$
$548$	1.68926e121	0.224886
$549$	0	0
$550$	9.23200e121	1.04510
$551$	−3.73329e121	−0.389803
$552$	0	0
$553$	−2.77072e121	−0.246221
$554$	7.47209e121	0.612714
$555$	0	0
$556$	−1.39304e122	−0.973051
$557$	−4.41176e120	−0.0284483	−0.0142241	−	0.999899i	$-0.504528\pi$
$557$	−4.41176e120	−0.0284483	−0.0142241	+	0.999899i	$0.504528\pi$
$558$	0	0
$559$	6.88863e121	0.378710
$560$	7.85389e121	0.398765
$561$	0	0
$562$	−1.75182e121	−0.0758967
$563$	−6.13774e121	−0.245688	−0.122844	−	0.992426i	$-0.539202\pi$
$563$	−6.13774e121	−0.245688	−0.122844	+	0.992426i	$0.539202\pi$
$564$	0	0
$565$	2.37834e120	0.00813051
$566$	−1.99214e122	−0.629490
$567$	0	0
$568$	−4.42043e122	−1.19389
$569$	−3.46558e122	−0.865526	−0.432763	−	0.901508i	$-0.642461\pi$
$569$	−3.46558e122	−0.865526	−0.432763	+	0.901508i	$0.642461\pi$
$570$	0	0
$571$	−1.51810e122	−0.324335	−0.162167	−	0.986763i	$-0.551848\pi$
$571$	−1.51810e122	−0.324335	−0.162167	+	0.986763i	$0.551848\pi$
$572$	−1.17365e123	−2.31962
$573$	0	0
$574$	−1.68357e122	−0.284873
$575$	4.71153e122	0.737807
$576$	0	0
$577$	−3.65421e122	−0.490309	−0.245155	−	0.969484i	$-0.578839\pi$
$577$	−3.65421e122	−0.490309	−0.245155	+	0.969484i	$0.578839\pi$
$578$	−2.76895e122	−0.343975
$579$	0	0
$580$	−3.79372e122	−0.404128
$581$	−1.35996e122	−0.134180
$582$	0	0
$583$	1.25150e123	1.05970
$584$	−1.01488e122	−0.0796238
$585$	0	0
$586$	−4.44166e122	−0.299297
$587$	4.37714e122	0.273398	0.136699	−	0.990613i	$-0.456351\pi$
$587$	4.37714e122	0.273398	0.136699	+	0.990613i	$0.456351\pi$
$588$	0	0
$589$	−5.28286e122	−0.283621
$590$	−1.40510e123	−0.699507
$591$	0	0
$592$	7.11557e122	0.304715
$593$	−3.28296e123	−1.30416	−0.652082	−	0.758148i	$-0.726104\pi$
$593$	−3.28296e123	−1.30416	−0.652082	+	0.758148i	$0.726104\pi$
$594$	0	0
$595$	9.63767e122	0.329585
$596$	−1.41503e123	−0.449062
$597$	0	0
$598$	1.26405e123	0.345590
$599$	−1.53295e123	−0.389077	−0.194538	−	0.980895i	$-0.562321\pi$
$599$	−1.53295e123	−0.389077	−0.194538	+	0.980895i	$0.562321\pi$
$600$	0	0
$601$	−6.22438e123	−1.36202	−0.681008	−	0.732276i	$-0.738458\pi$
$601$	−6.22438e123	−1.36202	−0.681008	+	0.732276i	$0.738458\pi$
$602$	−2.03054e122	−0.0412637
$603$	0	0
$604$	−3.23980e123	−0.568035
$605$	−1.30567e124	−2.12677
$606$	0	0
$607$	−4.03681e123	−0.567730	−0.283865	−	0.958864i	$-0.591617\pi$
$607$	−4.03681e123	−0.567730	−0.283865	+	0.958864i	$0.591617\pi$
$608$	9.65917e123	1.26250
$609$	0	0
$610$	−1.41499e123	−0.159799
$611$	1.16102e124	1.21901
$612$	0	0
$613$	3.27247e123	0.297087	0.148544	−	0.988906i	$-0.452541\pi$
$613$	3.27247e123	0.297087	0.148544	+	0.988906i	$0.452541\pi$
$614$	7.78300e123	0.657135
$615$	0	0
$616$	7.64919e123	0.558822
$617$	−1.99774e124	−1.35784	−0.678921	−	0.734211i	$-0.737552\pi$
$617$	−1.99774e124	−1.35784	−0.678921	+	0.734211i	$0.737552\pi$
$618$	0	0
$619$	−3.28784e123	−0.193498	−0.0967491	−	0.995309i	$-0.530844\pi$
$619$	−3.28784e123	−0.193498	−0.0967491	+	0.995309i	$0.530844\pi$
$620$	−5.36837e123	−0.294044
$621$	0	0
$622$	2.96174e122	0.0140564
$623$	−3.19223e123	−0.141051
$624$	0	0
$625$	1.79220e123	0.0686635
$626$	−2.15874e124	−0.770269
$627$	0	0
$628$	−7.05638e123	−0.218463
$629$	8.73167e123	0.251851
$630$	0	0
$631$	1.80467e124	0.451952	0.225976	−	0.974133i	$-0.427443\pi$
$631$	1.80467e124	0.451952	0.225976	+	0.974133i	$0.427443\pi$
$632$	−1.66552e124	−0.388723
$633$	0	0
$634$	−1.02508e124	−0.207866
$635$	1.26096e125	2.38381
$636$	0	0
$637$	−8.63048e124	−1.41850
$638$	−1.24400e124	−0.190679
$639$	0	0
$640$	1.24014e125	1.65371
$641$	8.89073e124	1.10600	0.553000	−	0.833181i	$-0.313483\pi$
$641$	8.89073e124	1.10600	0.553000	+	0.833181i	$0.313483\pi$
$642$	0	0
$643$	−9.77592e124	−1.05869	−0.529345	−	0.848406i	$-0.677562\pi$
$643$	−9.77592e124	−1.05869	−0.529345	+	0.848406i	$0.677562\pi$
$644$	1.76557e124	0.178429
$645$	0	0
$646$	2.57846e124	0.226993
$647$	−1.88260e125	−1.54710	−0.773550	−	0.633735i	$-0.781521\pi$
$647$	−1.88260e125	−1.54710	−0.773550	+	0.633735i	$0.781521\pi$
$648$	0	0
$649$	2.18327e125	1.56393
$650$	1.90262e125	1.27264
$651$	0	0
$652$	2.04124e125	1.19090
$653$	1.38084e125	0.752503	0.376252	−	0.926518i	$-0.377213\pi$
$653$	1.38084e125	0.752503	0.376252	+	0.926518i	$0.377213\pi$
$654$	0	0
$655$	4.01009e124	0.190729
$656$	1.61457e125	0.717523
$657$	0	0
$658$	−3.42232e124	−0.132821
$659$	3.19975e125	1.16069	0.580344	−	0.814372i	$-0.302918\pi$
$659$	3.19975e125	1.16069	0.580344	+	0.814372i	$0.302918\pi$
$660$	0	0
$661$	2.58615e125	0.819764	0.409882	−	0.912139i	$-0.365570\pi$
$661$	2.58615e125	0.819764	0.409882	+	0.912139i	$0.365570\pi$
$662$	9.37117e124	0.277724
$663$	0	0
$664$	−8.17492e124	−0.211838
$665$	4.20173e125	1.01827
$666$	0	0
$667$	−6.34875e124	−0.134613
$668$	−2.85454e125	−0.566218
$669$	0	0
$670$	1.44298e125	0.250571
$671$	2.19864e125	0.357274
$672$	0	0
$673$	6.54859e125	0.932132	0.466066	−	0.884750i	$-0.345671\pi$
$673$	6.54859e125	0.932132	0.466066	+	0.884750i	$0.345671\pi$
$674$	−4.30655e125	−0.573805
$675$	0	0
$676$	−1.71169e126	−1.99893
$677$	−7.59313e125	−0.830281	−0.415140	−	0.909757i	$-0.636268\pi$
$677$	−7.59313e125	−0.830281	−0.415140	+	0.909757i	$0.636268\pi$
$678$	0	0
$679$	6.99788e125	0.671061
$680$	5.79334e125	0.520334
$681$	0	0
$682$	−1.76035e125	−0.138738
$683$	9.21145e125	0.680153	0.340077	−	0.940398i	$-0.389547\pi$
$683$	9.21145e125	0.680153	0.340077	+	0.940398i	$0.389547\pi$
$684$	0	0
$685$	6.83653e125	0.443206
$686$	5.86099e125	0.356080
$687$	0	0
$688$	1.94733e125	0.103933
$689$	2.57921e126	1.29042
$690$	0	0
$691$	−3.51288e126	−1.54487	−0.772433	−	0.635096i	$-0.780960\pi$
$691$	−3.51288e126	−1.54487	−0.772433	+	0.635096i	$0.780960\pi$
$692$	−2.71375e125	−0.111905
$693$	0	0
$694$	−4.98118e125	−0.180649
$695$	−5.63771e126	−1.91769
$696$	0	0
$697$	1.98127e126	0.593042
$698$	−2.07309e126	−0.582173
$699$	0	0
$700$	2.65750e126	0.657068
$701$	5.19129e126	1.20455	0.602273	−	0.798290i	$-0.294262\pi$
$701$	5.19129e126	1.20455	0.602273	+	0.798290i	$0.294262\pi$
$702$	0	0
$703$	3.80674e126	0.778110
$704$	−7.99317e125	−0.153368
$705$	0	0
$706$	4.04415e126	0.683941
$707$	−2.97433e126	−0.472308
$708$	0	0
$709$	7.37489e125	0.103276	0.0516378	−	0.998666i	$-0.483556\pi$
$709$	7.37489e125	0.103276	0.0516378	+	0.998666i	$0.483556\pi$
$710$	−8.09110e126	−1.06417
$711$	0	0
$712$	−1.91890e126	−0.222685
$713$	−8.98391e125	−0.0979448
$714$	0	0
$715$	−4.74984e127	−4.57152
$716$	−8.52236e126	−0.770780
$717$	0	0
$718$	−6.32923e126	−0.505607
$719$	−2.06006e127	−1.54684	−0.773419	−	0.633895i	$-0.781455\pi$
$719$	−2.06006e127	−1.54684	−0.773419	+	0.633895i	$0.781455\pi$
$720$	0	0
$721$	1.29958e127	0.862347
$722$	4.55007e126	0.283866
$723$	0	0
$724$	1.32867e126	0.0732910
$725$	−9.55599e126	−0.495718
$726$	0	0
$727$	3.42949e127	1.57380	0.786898	−	0.617083i	$-0.211686\pi$
$727$	3.42949e127	1.57380	0.786898	+	0.617083i	$0.211686\pi$
$728$	1.57642e127	0.680494
$729$	0	0
$730$	−1.85762e126	−0.0709725
$731$	2.38960e126	0.0859019
$732$	0	0
$733$	3.37168e127	1.07330	0.536649	−	0.843806i	$-0.319690\pi$
$733$	3.37168e127	1.07330	0.536649	+	0.843806i	$0.319690\pi$
$734$	3.69694e125	0.0110756
$735$	0	0
$736$	1.64262e127	0.435987
$737$	−2.24213e127	−0.560218
$738$	0	0
$739$	−5.17935e127	−1.14709	−0.573546	−	0.819174i	$-0.694432\pi$
$739$	−5.17935e127	−1.14709	−0.573546	+	0.819174i	$0.694432\pi$
$740$	3.86835e127	0.806705
$741$	0	0
$742$	−7.60267e126	−0.140602
$743$	−7.49695e127	−1.30582	−0.652909	−	0.757437i	$-0.726451\pi$
$743$	−7.49695e127	−1.30582	−0.652909	+	0.757437i	$0.726451\pi$
$744$	0	0
$745$	−5.72669e127	−0.885012
$746$	−1.44884e127	−0.210933
$747$	0	0
$748$	−4.07130e127	−0.526154
$749$	−1.57039e127	−0.191234
$750$	0	0
$751$	−8.01748e127	−0.867083	−0.433542	−	0.901134i	$-0.642736\pi$
$751$	−8.01748e127	−0.867083	−0.433542	+	0.901134i	$0.642736\pi$
$752$	3.28207e127	0.334544
$753$	0	0
$754$	−2.56376e127	−0.232195
$755$	−1.31116e128	−1.11948
$756$	0	0
$757$	2.70790e127	0.205525	0.102763	−	0.994706i	$-0.467232\pi$
$757$	2.70790e127	0.205525	0.102763	+	0.994706i	$0.467232\pi$
$758$	−6.67934e127	−0.478029
$759$	0	0
$760$	2.52572e128	1.60761
$761$	2.72586e127	0.163639	0.0818195	−	0.996647i	$-0.473927\pi$
$761$	2.72586e127	0.163639	0.0818195	+	0.996647i	$0.473927\pi$
$762$	0	0
$763$	−1.21965e128	−0.651468
$764$	−2.56723e128	−1.29363
$765$	0	0
$766$	−1.14897e128	−0.515379
$767$	4.49948e128	1.90444
$768$	0	0
$769$	1.43554e128	0.541118	0.270559	−	0.962703i	$-0.412791\pi$
$769$	1.43554e128	0.541118	0.270559	+	0.962703i	$0.412791\pi$
$770$	1.40010e128	0.498105
$771$	0	0
$772$	−2.63618e127	−0.0835613
$773$	1.30472e128	0.390419	0.195210	−	0.980762i	$-0.437461\pi$
$773$	1.30472e128	0.390419	0.195210	+	0.980762i	$0.437461\pi$
$774$	0	0
$775$	−1.35224e128	−0.360684
$776$	4.20653e128	1.05944
$777$	0	0
$778$	1.64049e128	0.368454
$779$	8.63774e128	1.83224
$780$	0	0
$781$	1.25721e129	2.37923
$782$	4.38487e127	0.0783892
$783$	0	0
$784$	−2.43972e128	−0.389292
$785$	−2.85575e128	−0.430547
$786$	0	0
$787$	3.37148e128	0.453884	0.226942	−	0.973908i	$-0.427127\pi$
$787$	3.37148e128	0.453884	0.226942	+	0.973908i	$0.427127\pi$
$788$	−2.02889e128	−0.258133
$789$	0	0
$790$	−3.04855e128	−0.346488
$791$	2.24496e126	0.00241187
$792$	0	0
$793$	4.53115e128	0.435062
$794$	−6.77727e128	−0.615237
$795$	0	0
$796$	−1.24239e129	−1.00839
$797$	1.75623e129	1.34799	0.673993	−	0.738738i	$-0.264578\pi$
$797$	1.75623e129	1.34799	0.673993	+	0.738738i	$0.264578\pi$
$798$	0	0
$799$	4.02749e128	0.276505
$800$	2.47243e129	1.60553
$801$	0	0
$802$	2.17539e128	0.126409
$803$	2.88641e128	0.158678
$804$	0	0
$805$	7.14536e128	0.351648
$806$	−3.62789e128	−0.168945
$807$	0	0
$808$	−1.78791e129	−0.745660
$809$	−4.20411e129	−1.65945	−0.829726	−	0.558171i	$-0.811503\pi$
$809$	−4.20411e129	−1.65945	−0.829726	+	0.558171i	$0.811503\pi$
$810$	0	0
$811$	2.68092e129	0.948104	0.474052	−	0.880497i	$-0.342791\pi$
$811$	2.68092e129	0.948104	0.474052	+	0.880497i	$0.342791\pi$
$812$	−3.58096e128	−0.119883
$813$	0	0
$814$	1.26848e129	0.380625
$815$	8.26101e129	2.34704
$816$	0	0
$817$	1.04179e129	0.265400
$818$	−1.15897e129	−0.279609
$819$	0	0
$820$	8.77755e129	1.89958
$821$	−7.91079e129	−1.62162	−0.810810	−	0.585309i	$-0.800973\pi$
$821$	−7.91079e129	−1.62162	−0.810810	+	0.585309i	$0.800973\pi$
$822$	0	0
$823$	−5.95240e129	−1.09496	−0.547481	−	0.836818i	$-0.684413\pi$
$823$	−5.95240e129	−1.09496	−0.547481	+	0.836818i	$0.684413\pi$
$824$	7.81193e129	1.36144
$825$	0	0
$826$	−1.32630e129	−0.207505
$827$	6.51955e128	0.0966546	0.0483273	−	0.998832i	$-0.484611\pi$
$827$	6.51955e128	0.0966546	0.0483273	+	0.998832i	$0.484611\pi$
$828$	0	0
$829$	−1.23651e130	−1.64634	−0.823170	−	0.567795i	$-0.807797\pi$
$829$	−1.23651e130	−1.64634	−0.823170	+	0.567795i	$0.807797\pi$
$830$	−1.49633e129	−0.188822
$831$	0	0
$832$	−1.64731e129	−0.186761
$833$	−2.99384e129	−0.321755
$834$	0	0
$835$	−1.15525e130	−1.11591
$836$	−1.77496e130	−1.62559
$837$	0	0
$838$	5.29735e129	0.436214
$839$	1.77540e130	1.38641	0.693203	−	0.720743i	$-0.256199\pi$
$839$	1.77540e130	1.38641	0.693203	+	0.720743i	$0.256199\pi$
$840$	0	0
$841$	−1.29494e130	−0.909556
$842$	1.96707e129	0.131048
$843$	0	0
$844$	8.22714e129	0.493185
$845$	−6.92731e130	−3.93950
$846$	0	0
$847$	−1.23245e130	−0.630894
$848$	7.29110e129	0.354142
$849$	0	0
$850$	6.60000e129	0.288670
$851$	6.47365e129	0.268710
$852$	0	0
$853$	2.44364e130	0.913704	0.456852	−	0.889543i	$-0.348977\pi$
$853$	2.44364e130	0.913704	0.456852	+	0.889543i	$0.348977\pi$
$854$	−1.33563e129	−0.0474037
$855$	0	0
$856$	−9.43982e129	−0.301913
$857$	3.08645e129	0.0937159	0.0468579	−	0.998902i	$-0.485079\pi$
$857$	3.08645e129	0.0937159	0.0468579	+	0.998902i	$0.485079\pi$
$858$	0	0
$859$	3.12518e130	0.855421	0.427710	−	0.903916i	$-0.359320\pi$
$859$	3.12518e130	0.855421	0.427710	+	0.903916i	$0.359320\pi$
$860$	1.05866e130	0.275153
$861$	0	0
$862$	−3.28246e130	−0.769355
$863$	−4.69595e130	−1.04530	−0.522652	−	0.852546i	$-0.675057\pi$
$863$	−4.69595e130	−1.04530	−0.522652	+	0.852546i	$0.675057\pi$
$864$	0	0
$865$	−1.09827e130	−0.220542
$866$	6.68161e129	0.127448
$867$	0	0
$868$	−5.06730e129	−0.0872266
$869$	4.73689e130	0.774665
$870$	0	0
$871$	−4.62078e130	−0.682193
$872$	−7.33149e130	−1.02851
$873$	0	0
$874$	1.91167e130	0.242189
$875$	4.23023e130	0.509338
$876$	0	0
$877$	1.47350e131	1.60276	0.801382	−	0.598153i	$-0.204099\pi$
$877$	1.47350e131	1.60276	0.801382	+	0.598153i	$0.204099\pi$
$878$	9.71237e129	0.100420
$879$	0	0
$880$	−1.34272e131	−1.25460
$881$	−1.74519e131	−1.55030	−0.775149	−	0.631778i	$-0.782325\pi$
$881$	−1.74519e131	−1.55030	−0.775149	+	0.631778i	$0.782325\pi$
$882$	0	0
$883$	−1.48587e131	−1.19324	−0.596621	−	0.802523i	$-0.703490\pi$
$883$	−1.48587e131	−1.19324	−0.596621	+	0.802523i	$0.703490\pi$
$884$	−8.39052e130	−0.640712
$885$	0	0
$886$	1.91755e130	0.132418
$887$	1.59345e131	1.04649	0.523246	−	0.852182i	$-0.324721\pi$
$887$	1.59345e131	1.04649	0.523246	+	0.852182i	$0.324721\pi$
$888$	0	0
$889$	1.19024e131	0.707144
$890$	−3.51232e130	−0.198490
$891$	0	0
$892$	1.64496e131	0.841237
$893$	1.75586e131	0.854281
$894$	0	0
$895$	−3.44904e131	−1.51906
$896$	1.17059e131	0.490566
$897$	0	0
$898$	1.26602e131	0.480444
$899$	1.82213e130	0.0658071
$900$	0	0
$901$	8.94706e130	0.292703
$902$	2.87826e131	0.896271
$903$	0	0
$904$	1.34948e129	0.00380776
$905$	5.37719e130	0.144442
$906$	0	0
$907$	1.57911e131	0.384492	0.192246	−	0.981347i	$-0.438423\pi$
$907$	1.57911e131	0.384492	0.192246	+	0.981347i	$0.438423\pi$
$908$	−3.40070e131	−0.788402
$909$	0	0
$910$	2.88545e131	0.606557
$911$	−2.16123e131	−0.432647	−0.216324	−	0.976322i	$-0.569407\pi$
$911$	−2.16123e131	−0.432647	−0.216324	+	0.976322i	$0.569407\pi$
$912$	0	0
$913$	2.32502e131	0.422160
$914$	4.11233e131	0.711185
$915$	0	0
$916$	−3.37293e131	−0.529248
$917$	3.78520e130	0.0565787
$918$	0	0
$919$	−3.78728e131	−0.513792	−0.256896	−	0.966439i	$-0.582700\pi$
$919$	−3.78728e131	−0.513792	−0.256896	+	0.966439i	$0.582700\pi$
$920$	4.29518e131	0.555166
$921$	0	0
$922$	2.53232e131	0.297162
$923$	2.59097e132	2.89726
$924$	0	0
$925$	9.74400e131	0.989533
$926$	−6.55016e131	−0.633962
$927$	0	0
$928$	−3.33158e131	−0.292931
$929$	−4.01039e131	−0.336115	−0.168057	−	0.985777i	$-0.553749\pi$
$929$	−4.01039e131	−0.336115	−0.168057	+	0.985777i	$0.553749\pi$
$930$	0	0
$931$	−1.30522e132	−0.994085
$932$	1.33041e132	0.966001
$933$	0	0
$934$	7.47736e131	0.493528
$935$	−1.64768e132	−1.03695
$936$	0	0
$937$	1.77275e132	1.01446	0.507230	−	0.861811i	$-0.330669\pi$
$937$	1.77275e132	1.01446	0.507230	+	0.861811i	$0.330669\pi$
$938$	1.36205e131	0.0743307
$939$	0	0
$940$	1.78428e132	0.885675
$941$	−1.19449e132	−0.565517	−0.282759	−	0.959191i	$-0.591250\pi$
$941$	−1.19449e132	−0.565517	−0.282759	+	0.959191i	$0.591250\pi$
$942$	0	0
$943$	1.46891e132	0.632741
$944$	1.27194e132	0.522654
$945$	0	0
$946$	3.47146e131	0.129824
$947$	3.58699e132	1.27984	0.639921	−	0.768441i	$-0.278967\pi$
$947$	3.58699e132	1.27984	0.639921	+	0.768441i	$0.278967\pi$
$948$	0	0
$949$	5.94858e131	0.193226
$950$	2.87740e132	0.891866
$951$	0	0
$952$	5.46844e131	0.154355
$953$	−6.31274e132	−1.70053	−0.850264	−	0.526357i	$-0.823558\pi$
$953$	−6.31274e132	−1.70053	−0.850264	+	0.526357i	$0.823558\pi$
$954$	0	0
$955$	−1.03897e133	−2.54949
$956$	−3.40813e132	−0.798253
$957$	0	0
$958$	2.43415e132	0.519496
$959$	6.45313e131	0.131475
$960$	0	0
$961$	−5.12722e132	−0.952119
$962$	2.61420e132	0.463498
$963$	0	0
$964$	−5.53778e132	−0.895175
$965$	−1.06688e132	−0.164683
$966$	0	0
$967$	2.25037e132	0.316793	0.158396	−	0.987376i	$-0.449368\pi$
$967$	2.25037e132	0.316793	0.158396	+	0.987376i	$0.449368\pi$
$968$	−7.40842e132	−0.996029
$969$	0	0
$970$	7.69958e132	0.944332
$971$	−1.34386e133	−1.57434	−0.787168	−	0.616739i	$-0.788453\pi$
$971$	−1.34386e133	−1.57434	−0.787168	+	0.616739i	$0.788453\pi$
$972$	0	0
$973$	−5.32154e132	−0.568874
$974$	2.19610e132	0.224274
$975$	0	0
$976$	1.28090e132	0.119398
$977$	1.09375e133	0.974118	0.487059	−	0.873369i	$-0.338070\pi$
$977$	1.09375e133	0.974118	0.487059	+	0.873369i	$0.338070\pi$
$978$	0	0
$979$	5.45751e132	0.443777
$980$	−1.32635e133	−1.03062
$981$	0	0
$982$	6.90021e132	0.489667
$983$	−1.10364e132	−0.0748505	−0.0374253	−	0.999299i	$-0.511916\pi$
$983$	−1.10364e132	−0.0748505	−0.0374253	+	0.999299i	$0.511916\pi$
$984$	0	0
$985$	−8.21104e132	−0.508728
$986$	−8.89345e131	−0.0526681
$987$	0	0
$988$	−3.65801e133	−1.97952
$989$	1.77165e132	0.0916523
$990$	0	0
$991$	7.24307e132	0.342488	0.171244	−	0.985229i	$-0.445221\pi$
$991$	7.24307e132	0.342488	0.171244	+	0.985229i	$0.445221\pi$
$992$	−4.71441e132	−0.213136
$993$	0	0
$994$	−7.63734e132	−0.315681
$995$	−5.02803e133	−1.98733
$996$	0	0
$997$	−2.56102e132	−0.0925716	−0.0462858	−	0.998928i	$-0.514738\pi$
$997$	−2.56102e132	−0.0925716	−0.0462858	+	0.998928i	$0.514738\pi$
$998$	1.75234e133	0.605771
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.90.a.b.1.4		7
3.2	odd	2		1.90.a.a.1.4	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.90.a.a.1.4	✓	7	3.2	odd	2
9.90.a.b.1.4		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)

\(f(q)\)	\(=\)	\(q+1.03857e13 q^{2} -5.11108e26 q^{4} -2.06848e31 q^{5} -1.95248e37 q^{7} -1.17366e40 q^{8} +O(q^{10})\)	\(q+1.03857e13 q^{2} -5.11108e26 q^{4} -2.06848e31 q^{5} -1.95248e37 q^{7} -1.17366e40 q^{8} -2.14826e44 q^{10} +3.33800e46 q^{11} +6.87926e49 q^{13} -2.02778e50 q^{14} +1.94468e53 q^{16} +2.38635e54 q^{17} +1.04038e57 q^{19} +1.05722e58 q^{20} +3.46674e59 q^{22} +1.76924e60 q^{23} +2.66302e62 q^{25} +7.14457e62 q^{26} +9.97926e63 q^{28} -3.58840e64 q^{29} -5.07783e65 q^{31} +9.28429e66 q^{32} +2.47839e67 q^{34} +4.03866e68 q^{35} +3.65900e69 q^{37} +1.08050e70 q^{38} +2.42770e71 q^{40} +8.30251e71 q^{41} +1.00136e72 q^{43} -1.70608e73 q^{44} +1.83748e73 q^{46} +1.68772e74 q^{47} -1.25457e75 q^{49} +2.76573e75 q^{50} -3.51604e76 q^{52} +3.74926e76 q^{53} -6.90459e77 q^{55} +2.29155e77 q^{56} -3.72680e77 q^{58} +6.54064e78 q^{59} +6.58668e78 q^{61} -5.27367e78 q^{62} -2.39460e79 q^{64} -1.42296e81 q^{65} -6.71698e80 q^{67} -1.21968e81 q^{68} +4.19442e81 q^{70} +3.76636e82 q^{71} +8.64712e81 q^{73} +3.80012e82 q^{74} -5.31745e83 q^{76} -6.51737e83 q^{77} +1.41908e84 q^{79} -4.02252e84 q^{80} +8.62271e84 q^{82} +6.96531e84 q^{83} -4.93612e85 q^{85} +1.03998e85 q^{86} -3.91768e86 q^{88} +1.63496e86 q^{89} -1.34316e87 q^{91} -9.04273e86 q^{92} +1.75281e87 q^{94} -2.15200e88 q^{95} -3.58411e88 q^{97} -1.30295e88 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 31407330351408 q^{2} + 22\!\cdots\!04 q^{4}+ \cdots + 17\!\cdots\!20 q^{8}+O(q^{10}) \) 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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