LMFDB - Embedded newform 9.90.a.b.1.5

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			1.5
Root			$3.74539e11$ of defining polynomial
Character	$\chi$	$=$	9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.24646e13 q^{2} -1.14310e26 q^{4} +1.81181e31 q^{5} -2.76134e37 q^{7} -1.64729e40 q^{8} +O(q^{10})$	\(q+2.24646e13 q^{2} -1.14310e26 q^{4} +1.81181e31 q^{5} -2.76134e37 q^{7} -1.64729e40 q^{8} +4.07017e44 q^{10} -2.89211e46 q^{11} -2.93091e49 q^{13} -6.20325e50 q^{14} -2.99303e53 q^{16} -3.53494e54 q^{17} -2.73074e56 q^{19} -2.07108e57 q^{20} -6.49703e59 q^{22} -5.99973e60 q^{23} +1.66707e62 q^{25} -6.58419e62 q^{26} +3.15649e63 q^{28} -2.05712e65 q^{29} -1.59142e66 q^{31} +3.47249e66 q^{32} -7.94112e67 q^{34} -5.00303e68 q^{35} +1.13777e69 q^{37} -6.13450e69 q^{38} -2.98457e71 q^{40} -8.14082e70 q^{41} +3.18229e72 q^{43} +3.30598e72 q^{44} -1.34782e74 q^{46} +3.19743e74 q^{47} -8.73283e74 q^{49} +3.74502e75 q^{50} +3.35033e75 q^{52} +1.04143e77 q^{53} -5.23996e77 q^{55} +4.54872e77 q^{56} -4.62126e78 q^{58} -8.65856e78 q^{59} -3.87413e79 q^{61} -3.57506e79 q^{62} +2.63268e80 q^{64} -5.31026e80 q^{65} +1.41209e81 q^{67} +4.04080e80 q^{68} -1.12391e82 q^{70} -1.52471e82 q^{71} -5.28056e82 q^{73} +2.55595e82 q^{74} +3.12151e82 q^{76} +7.98611e83 q^{77} +4.95085e84 q^{79} -5.42280e84 q^{80} -1.82881e84 q^{82} -5.30230e84 q^{83} -6.40465e85 q^{85} +7.14891e85 q^{86} +4.76414e86 q^{88} +6.27807e86 q^{89} +8.09324e86 q^{91} +6.85829e86 q^{92} +7.18291e87 q^{94} -4.94758e87 q^{95} +2.15232e88 q^{97} -1.96180e88 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.24646e13	0.902952	0.451476	−	0.892283i	$-0.350898\pi$
$2$	2.24646e13	0.902952	0.451476	+	0.892283i	$0.350898\pi$
$3$	0	0
$3$	0	0
$4$	−1.14310e26	−0.184678
$5$	1.81181e31	1.42544	0.712718	−	0.701451i	$-0.247464\pi$
$5$	1.81181e31	1.42544	0.712718	+	0.701451i	$0.247464\pi$
$6$	0	0
$7$	−2.76134e37	−0.682743	−0.341371	−	0.939929i	$-0.610891\pi$
$7$	−2.76134e37	−0.682743	−0.341371	+	0.939929i	$0.610891\pi$
$8$	−1.64729e40	−1.06971
$9$	0	0
$10$	4.07017e44	1.28710
$11$	−2.89211e46	−1.31595	−0.657977	−	0.753038i	$-0.728588\pi$
$11$	−2.89211e46	−1.31595	−0.657977	+	0.753038i	$0.728588\pi$
$12$	0	0
$13$	−2.93091e49	−0.787995	−0.393998	−	0.919111i	$-0.628908\pi$
$13$	−2.93091e49	−0.787995	−0.393998	+	0.919111i	$0.628908\pi$
$14$	−6.20325e50	−0.616484
$15$	0	0
$16$	−2.99303e53	−0.781216
$17$	−3.53494e54	−0.621449	−0.310725	−	0.950500i	$-0.600572\pi$
$17$	−3.53494e54	−0.621449	−0.310725	+	0.950500i	$0.600572\pi$
$18$	0	0
$19$	−2.73074e56	−0.340208	−0.170104	−	0.985426i	$-0.554410\pi$
$19$	−2.73074e56	−0.340208	−0.170104	+	0.985426i	$0.554410\pi$
$20$	−2.07108e57	−0.263246
$21$	0	0
$22$	−6.49703e59	−1.18824
$23$	−5.99973e60	−1.51790	−0.758949	−	0.651150i	$-0.774287\pi$
$23$	−5.99973e60	−1.51790	−0.758949	+	0.651150i	$0.774287\pi$
$24$	0	0
$25$	1.66707e62	1.03187
$26$	−6.58419e62	−0.711522
$27$	0	0
$28$	3.15649e63	0.126087
$29$	−2.05712e65	−1.72405	−0.862025	−	0.506867i	$-0.830804\pi$
$29$	−2.05712e65	−1.72405	−0.862025	+	0.506867i	$0.830804\pi$
$30$	0	0
$31$	−1.59142e66	−0.685786	−0.342893	−	0.939375i	$-0.611407\pi$
$31$	−1.59142e66	−0.685786	−0.342893	+	0.939375i	$0.611407\pi$
$32$	3.47249e66	0.364306
$33$	0	0
$34$	−7.94112e67	−0.561139
$35$	−5.00303e68	−0.973206
$36$	0	0
$37$	1.13777e69	0.186671	0.0933353	−	0.995635i	$-0.470247\pi$
$37$	1.13777e69	0.186671	0.0933353	+	0.995635i	$0.470247\pi$
$38$	−6.13450e69	−0.307191
$39$	0	0
$40$	−2.98457e71	−1.52480
$41$	−8.14082e70	−0.138607	−0.0693037	−	0.997596i	$-0.522078\pi$
$41$	−8.14082e70	−0.138607	−0.0693037	+	0.997596i	$0.522078\pi$
$42$	0	0
$43$	3.18229e72	0.650720	0.325360	−	0.945590i	$-0.394515\pi$
$43$	3.18229e72	0.650720	0.325360	+	0.945590i	$0.394515\pi$
$44$	3.30598e72	0.243028
$45$	0	0
$46$	−1.34782e74	−1.37059
$47$	3.19743e74	1.24867	0.624333	−	0.781159i	$-0.285371\pi$
$47$	3.19743e74	1.24867	0.624333	+	0.781159i	$0.285371\pi$
$48$	0	0
$49$	−8.73283e74	−0.533862
$50$	3.74502e75	0.931727
$51$	0	0
$52$	3.35033e75	0.145525
$53$	1.04143e77	1.93800	0.968999	−	0.247063i	$-0.0794655\pi$
$53$	1.04143e77	1.93800	0.968999	+	0.247063i	$0.0794655\pi$
$54$	0	0
$55$	−5.23996e77	−1.87581
$56$	4.54872e77	0.730335
$57$	0	0
$58$	−4.62126e78	−1.55673
$59$	−8.65856e78	−1.36311	−0.681556	−	0.731766i	$-0.738696\pi$
$59$	−8.65856e78	−1.36311	−0.681556	+	0.731766i	$0.738696\pi$
$60$	0	0
$61$	−3.87413e79	−1.38356	−0.691778	−	0.722110i	$-0.743172\pi$
$61$	−3.87413e79	−1.38356	−0.691778	+	0.722110i	$0.743172\pi$
$62$	−3.57506e79	−0.619231
$63$	0	0
$64$	2.63268e80	1.11017
$65$	−5.31026e80	−1.12324
$66$	0	0
$67$	1.41209e81	0.775416	0.387708	−	0.921782i	$-0.373267\pi$
$67$	1.41209e81	0.775416	0.387708	+	0.921782i	$0.373267\pi$
$68$	4.04080e80	0.114768
$69$	0	0
$70$	−1.12391e82	−0.878758
$71$	−1.52471e82	−0.634148	−0.317074	−	0.948401i	$-0.602700\pi$
$71$	−1.52471e82	−0.634148	−0.317074	+	0.948401i	$0.602700\pi$
$72$	0	0
$73$	−5.28056e82	−0.637989	−0.318994	−	0.947757i	$-0.603345\pi$
$73$	−5.28056e82	−0.637989	−0.318994	+	0.947757i	$0.603345\pi$
$74$	2.55595e82	0.168555
$75$	0	0
$76$	3.12151e82	0.0628289
$77$	7.98611e83	0.898458
$78$	0	0
$79$	4.95085e84	1.77940	0.889702	−	0.456542i	$-0.150912\pi$
$79$	4.95085e84	1.77940	0.889702	+	0.456542i	$0.150912\pi$
$80$	−5.42280e84	−1.11357
$81$	0	0
$82$	−1.82881e84	−0.125156
$83$	−5.30230e84	−0.211587	−0.105794	−	0.994388i	$-0.533738\pi$
$83$	−5.30230e84	−0.211587	−0.105794	+	0.994388i	$0.533738\pi$
$84$	0	0
$85$	−6.40465e85	−0.885836
$86$	7.14891e85	0.587568
$87$	0	0
$88$	4.76414e86	1.40769
$89$	6.27807e86	1.12194	0.560972	−	0.827835i	$-0.310428\pi$
$89$	6.27807e86	1.12194	0.560972	+	0.827835i	$0.310428\pi$
$90$	0	0
$91$	8.09324e86	0.537998
$92$	6.85829e86	0.280322
$93$	0	0
$94$	7.18291e87	1.12748
$95$	−4.94758e87	−0.484945
$96$	0	0
$97$	2.15232e88	0.834766	0.417383	−	0.908731i	$-0.362947\pi$
$97$	2.15232e88	0.834766	0.417383	+	0.908731i	$0.362947\pi$
$98$	−1.96180e88	−0.482052
$99$	0	0
$100$	−1.90563e88	−0.190563
$101$	2.76146e89	1.77353	0.886763	−	0.462225i	$-0.152949\pi$
$101$	2.76146e89	1.77353	0.886763	+	0.462225i	$0.152949\pi$
$102$	0	0
$103$	1.89577e89	0.508780	0.254390	−	0.967102i	$-0.418125\pi$
$103$	1.89577e89	0.508780	0.254390	+	0.967102i	$0.418125\pi$
$104$	4.82805e89	0.842924
$105$	0	0
$106$	2.33953e90	1.74992
$107$	3.99265e89	0.196645	0.0983226	−	0.995155i	$-0.468652\pi$
$107$	3.99265e89	0.196645	0.0983226	+	0.995155i	$0.468652\pi$
$108$	0	0
$109$	−3.60049e90	−0.777826	−0.388913	−	0.921274i	$-0.627149\pi$
$109$	−3.60049e90	−0.777826	−0.388913	+	0.921274i	$0.627149\pi$
$110$	−1.17714e91	−1.69376
$111$	0	0
$112$	8.26476e90	0.533370
$113$	−1.16933e91	−0.508095	−0.254047	−	0.967192i	$-0.581762\pi$
$113$	−1.16933e91	−0.508095	−0.254047	+	0.967192i	$0.581762\pi$
$114$	0	0
$115$	−1.08704e92	−2.16367
$116$	2.35150e91	0.318394
$117$	0	0
$118$	−1.94511e92	−1.23082
$119$	9.76118e91	0.424290
$120$	0	0
$121$	3.53430e92	0.731735
$122$	−8.70310e92	−1.24928
$123$	0	0
$124$	1.81915e92	0.126649
$125$	9.32811e91	0.0454253
$126$	0	0
$127$	4.35388e93	1.04619	0.523096	−	0.852274i	$-0.324777\pi$
$127$	4.35388e93	1.04619	0.523096	+	0.852274i	$0.324777\pi$
$128$	3.76484e93	0.638121
$129$	0	0
$130$	−1.19293e94	−1.01423
$131$	−2.78935e93	−0.168628	−0.0843141	−	0.996439i	$-0.526870\pi$
$131$	−2.78935e93	−0.168628	−0.0843141	+	0.996439i	$0.526870\pi$
$132$	0	0
$133$	7.54049e93	0.232274
$134$	3.17222e94	0.700164
$135$	0	0
$136$	5.82307e94	0.664769
$137$	−1.13533e95	−0.935530	−0.467765	−	0.883853i	$-0.654941\pi$
$137$	−1.13533e95	−0.935530	−0.467765	+	0.883853i	$0.654941\pi$
$138$	0	0
$139$	2.67554e95	1.15679	0.578394	−	0.815758i	$-0.303680\pi$
$139$	2.67554e95	1.15679	0.578394	+	0.815758i	$0.303680\pi$
$140$	5.71896e94	0.179730
$141$	0	0
$142$	−3.42520e95	−0.572605
$143$	8.47653e95	1.03697
$144$	0	0
$145$	−3.72712e96	−2.45752
$146$	−1.18626e96	−0.576073
$147$	0	0
$148$	−1.30058e95	−0.0344739
$149$	−1.67237e96	−0.328505	−0.164253	−	0.986418i	$-0.552521\pi$
$149$	−1.67237e96	−0.328505	−0.164253	+	0.986418i	$0.552521\pi$
$150$	0	0
$151$	5.57662e96	0.605197	0.302599	−	0.953118i	$-0.402146\pi$
$151$	5.57662e96	0.605197	0.302599	+	0.953118i	$0.402146\pi$
$152$	4.49831e96	0.363923
$153$	0	0
$154$	1.79405e97	0.811264
$155$	−2.88335e97	−0.977543
$156$	0	0
$157$	1.11335e96	0.0213351	0.0106676	−	0.999943i	$-0.496604\pi$
$157$	1.11335e96	0.0213351	0.0106676	+	0.999943i	$0.496604\pi$
$158$	1.11219e98	1.60672
$159$	0	0
$160$	6.29149e97	0.519295
$161$	1.65673e98	1.03633
$162$	0	0
$163$	−2.70141e98	−0.975534	−0.487767	−	0.872974i	$-0.662188\pi$
$163$	−2.70141e98	−0.975534	−0.487767	+	0.872974i	$0.662188\pi$
$164$	9.30578e96	0.0255977
$165$	0	0
$166$	−1.19114e98	−0.191053
$167$	−1.44407e99	−1.77299	−0.886493	−	0.462743i	$-0.846865\pi$
$167$	−1.44407e99	−1.77299	−0.886493	+	0.462743i	$0.846865\pi$
$168$	0	0
$169$	−5.24409e98	−0.379063
$170$	−1.43878e99	−0.799867
$171$	0	0
$172$	−3.63768e98	−0.120173
$173$	6.16711e99	1.57409	0.787046	−	0.616895i	$-0.211610\pi$
$173$	6.16711e99	1.57409	0.787046	+	0.616895i	$0.211610\pi$
$174$	0	0
$175$	−4.60335e99	−0.704500
$176$	8.65617e99	1.02804
$177$	0	0
$178$	1.41035e100	1.01306
$179$	−2.48664e100	−1.39204	−0.696022	−	0.718020i	$-0.745049\pi$
$179$	−2.48664e100	−1.39204	−0.696022	+	0.718020i	$0.745049\pi$
$180$	0	0
$181$	−3.55444e100	−1.21360	−0.606799	−	0.794856i	$-0.707547\pi$
$181$	−3.55444e100	−1.21360	−0.606799	+	0.794856i	$0.707547\pi$
$182$	1.81812e100	0.485786
$183$	0	0
$184$	9.88328e100	1.62371
$185$	2.06142e100	0.266087
$186$	0	0
$187$	1.02235e101	0.817799
$188$	−3.65498e100	−0.230601
$189$	0	0
$190$	−1.11146e101	−0.437882
$191$	4.56087e100	0.142253	0.0711267	−	0.997467i	$-0.477341\pi$
$191$	4.56087e100	0.142253	0.0711267	+	0.997467i	$0.477341\pi$
$192$	0	0
$193$	−3.40846e101	−0.668740	−0.334370	−	0.942442i	$-0.608524\pi$
$193$	−3.40846e101	−0.668740	−0.334370	+	0.942442i	$0.608524\pi$
$194$	4.83511e101	0.753753
$195$	0	0
$196$	9.98250e100	0.0985926
$197$	−1.93426e102	−1.52324	−0.761619	−	0.648025i	$-0.775595\pi$
$197$	−1.93426e102	−1.52324	−0.761619	+	0.648025i	$0.775595\pi$
$198$	0	0
$199$	−2.15474e102	−1.08251	−0.541257	−	0.840857i	$-0.682051\pi$
$199$	−2.15474e102	−1.08251	−0.541257	+	0.840857i	$0.682051\pi$
$200$	−2.74615e102	−1.10380
$201$	0	0
$202$	6.20352e102	1.60141
$203$	5.68042e102	1.17708
$204$	0	0
$205$	−1.47496e102	−0.197576
$206$	4.25878e102	0.459404
$207$	0	0
$208$	8.77230e102	0.615595
$209$	7.89760e102	0.447698
$210$	0	0
$211$	8.21019e101	0.0304638	0.0152319	−	0.999884i	$-0.495151\pi$
$211$	8.21019e101	0.0304638	0.0152319	+	0.999884i	$0.495151\pi$
$212$	−1.19046e103	−0.357905
$213$	0	0
$214$	8.96935e102	0.177561
$215$	5.76571e103	0.927559
$216$	0	0
$217$	4.39444e103	0.468215
$218$	−8.08837e103	−0.702340
$219$	0	0
$220$	5.98980e103	0.346420
$221$	1.03606e104	0.489699
$222$	0	0
$223$	−1.00410e104	−0.317842	−0.158921	−	0.987291i	$-0.550801\pi$
$223$	−1.00410e104	−0.317842	−0.158921	+	0.987291i	$0.550801\pi$
$224$	−9.58872e103	−0.248728
$225$	0	0
$226$	−2.62685e104	−0.458785
$227$	1.08320e105	1.55439	0.777194	−	0.629261i	$-0.216642\pi$
$227$	1.08320e105	1.55439	0.777194	+	0.629261i	$0.216642\pi$
$228$	0	0
$229$	−3.66875e104	−0.356319	−0.178160	−	0.984002i	$-0.557014\pi$
$229$	−3.66875e104	−0.356319	−0.178160	+	0.984002i	$0.557014\pi$
$230$	−2.44199e105	−1.95369
$231$	0	0
$232$	3.38867e105	1.84423
$233$	3.17011e105	1.42474	0.712371	−	0.701803i	$-0.247621\pi$
$233$	3.17011e105	1.42474	0.712371	+	0.701803i	$0.247621\pi$
$234$	0	0
$235$	5.79313e105	1.77989
$236$	9.89761e104	0.251736
$237$	0	0
$238$	2.19281e105	0.383113
$239$	3.35013e105	0.485686	0.242843	−	0.970066i	$-0.421920\pi$
$239$	3.35013e105	0.485686	0.242843	+	0.970066i	$0.421920\pi$
$240$	0	0
$241$	2.48905e105	0.249044	0.124522	−	0.992217i	$-0.460260\pi$
$241$	2.48905e105	0.249044	0.124522	+	0.992217i	$0.460260\pi$
$242$	7.93967e105	0.660722
$243$	0	0
$244$	4.42852e105	0.255512
$245$	−1.58222e106	−0.760987
$246$	0	0
$247$	8.00355e105	0.268082
$248$	2.62152e106	0.733590
$249$	0	0
$250$	2.09553e105	0.0410169
$251$	−4.34459e106	−0.711981	−0.355991	−	0.934490i	$-0.615857\pi$
$251$	−4.34459e106	−0.711981	−0.355991	+	0.934490i	$0.615857\pi$
$252$	0	0
$253$	1.73519e107	1.99749
$254$	9.78084e106	0.944660
$255$	0	0
$256$	−7.83789e106	−0.533974
$257$	1.84254e106	0.105534	0.0527671	−	0.998607i	$-0.483196\pi$
$257$	1.84254e106	0.105534	0.0527671	+	0.998607i	$0.483196\pi$
$258$	0	0
$259$	−3.14176e106	−0.127448
$260$	6.07016e106	0.207437
$261$	0	0
$262$	−6.26617e106	−0.152263
$263$	5.95118e107	1.22060	0.610299	−	0.792171i	$-0.291049\pi$
$263$	5.95118e107	1.22060	0.610299	+	0.792171i	$0.291049\pi$
$264$	0	0
$265$	1.88687e108	2.76249
$266$	1.69394e107	0.209733
$267$	0	0
$268$	−1.61417e107	−0.143202
$269$	−1.60452e108	−1.20606	−0.603028	−	0.797720i	$-0.706039\pi$
$269$	−1.60452e108	−1.20606	−0.603028	+	0.797720i	$0.706039\pi$
$270$	0	0
$271$	−1.64745e108	−0.890591	−0.445296	−	0.895384i	$-0.646901\pi$
$271$	−1.64745e108	−0.890591	−0.445296	+	0.895384i	$0.646901\pi$
$272$	1.05802e108	0.485486
$273$	0	0
$274$	−2.55048e108	−0.844739
$275$	−4.82136e108	−1.35789
$276$	0	0
$277$	−7.83782e108	−1.59899	−0.799495	−	0.600673i	$-0.794899\pi$
$277$	−7.83782e108	−1.59899	−0.799495	+	0.600673i	$0.794899\pi$
$278$	6.01051e108	1.04452
$279$	0	0
$280$	8.24142e108	1.04105
$281$	5.27154e107	0.0568206	0.0284103	−	0.999596i	$-0.490955\pi$
$281$	5.27154e107	0.0568206	0.0284103	+	0.999596i	$0.490955\pi$
$282$	0	0
$283$	−3.88406e108	−0.305344	−0.152672	−	0.988277i	$-0.548788\pi$
$283$	−3.88406e108	−0.305344	−0.152672	+	0.988277i	$0.548788\pi$
$284$	1.74290e108	0.117113
$285$	0	0
$286$	1.90422e109	0.936330
$287$	2.24796e108	0.0946332
$288$	0	0
$289$	−1.98601e109	−0.613801
$290$	−8.37284e109	−2.21902
$291$	0	0
$292$	6.03621e108	0.117822
$293$	1.22983e109	0.206174	0.103087	−	0.994672i	$-0.467128\pi$
$293$	1.22983e109	0.206174	0.103087	+	0.994672i	$0.467128\pi$
$294$	0	0
$295$	−1.56877e110	−1.94303
$296$	−1.87423e109	−0.199683
$297$	0	0
$298$	−3.75691e109	−0.296624
$299$	1.75847e110	1.19610
$300$	0	0
$301$	−8.78739e109	−0.444274
$302$	1.25277e110	0.546464
$303$	0	0
$304$	8.17316e109	0.265776
$305$	−7.01920e110	−1.97217
$306$	0	0
$307$	9.59258e109	0.201501	0.100751	−	0.994912i	$-0.467876\pi$
$307$	9.59258e109	0.201501	0.100751	+	0.994912i	$0.467876\pi$
$308$	−9.12892e109	−0.165925
$309$	0	0
$310$	−6.47733e110	−0.882675
$311$	4.76737e110	0.562914	0.281457	−	0.959574i	$-0.409182\pi$
$311$	4.76737e110	0.562914	0.281457	+	0.959574i	$0.409182\pi$
$312$	0	0
$313$	5.26526e109	0.0467409	0.0233704	−	0.999727i	$-0.492560\pi$
$313$	5.26526e109	0.0467409	0.0233704	+	0.999727i	$0.492560\pi$
$314$	2.50109e109	0.0192646
$315$	0	0
$316$	−5.65932e110	−0.328616
$317$	2.68580e110	0.135499	0.0677494	−	0.997702i	$-0.478418\pi$
$317$	2.68580e110	0.135499	0.0677494	+	0.997702i	$0.478418\pi$
$318$	0	0
$319$	5.94944e111	2.26877
$320$	4.76991e111	1.58247
$321$	0	0
$322$	3.72178e111	0.935760
$323$	9.65300e110	0.211422
$324$	0	0
$325$	−4.88604e111	−0.813107
$326$	−6.06862e111	−0.880860
$327$	0	0
$328$	1.34103e111	0.148269
$329$	−8.82918e111	−0.852517
$330$	0	0
$331$	1.92028e112	1.41586	0.707928	−	0.706284i	$-0.249630\pi$
$331$	1.92028e112	1.41586	0.707928	+	0.706284i	$0.249630\pi$
$332$	6.06106e110	0.0390754
$333$	0	0
$334$	−3.24405e112	−1.60092
$335$	2.55845e112	1.10531
$336$	0	0
$337$	3.45050e111	0.114381	0.0571903	−	0.998363i	$-0.481786\pi$
$337$	3.45050e111	0.114381	0.0571903	+	0.998363i	$0.481786\pi$
$338$	−1.17807e112	−0.342276
$339$	0	0
$340$	7.32116e111	0.163594
$341$	4.60256e112	0.902462
$342$	0	0
$343$	6.92838e112	1.04723
$344$	−5.24215e112	−0.696079
$345$	0	0
$346$	1.38542e113	1.42133
$347$	8.88897e112	0.802028	0.401014	−	0.916072i	$-0.368658\pi$
$347$	8.88897e112	0.802028	0.401014	+	0.916072i	$0.368658\pi$
$348$	0	0
$349$	−1.03428e113	−0.722615	−0.361308	−	0.932447i	$-0.617670\pi$
$349$	−1.03428e113	−0.722615	−0.361308	+	0.932447i	$0.617670\pi$
$350$	−1.03413e113	−0.636130
$351$	0	0
$352$	−1.00428e113	−0.479411
$353$	1.22789e113	0.516637	0.258318	−	0.966060i	$-0.416832\pi$
$353$	1.22789e113	0.516637	0.258318	+	0.966060i	$0.416832\pi$
$354$	0	0
$355$	−2.76248e113	−0.903937
$356$	−7.17647e112	−0.207198
$357$	0	0
$358$	−5.58615e113	−1.25695
$359$	−6.91261e112	−0.137385	−0.0686924	−	0.997638i	$-0.521883\pi$
$359$	−6.91261e112	−0.137385	−0.0686924	+	0.997638i	$0.521883\pi$
$360$	0	0
$361$	−5.69705e113	−0.884259
$362$	−7.98492e113	−1.09582
$363$	0	0
$364$	−9.25139e112	−0.0993563
$365$	−9.56738e113	−0.909412
$366$	0	0
$367$	1.07815e114	0.803600	0.401800	−	0.915727i	$-0.368385\pi$
$367$	1.07815e114	0.803600	0.401800	+	0.915727i	$0.368385\pi$
$368$	1.79573e114	1.18581
$369$	0	0
$370$	4.63090e113	0.240264
$371$	−2.87574e114	−1.32315
$372$	0	0
$373$	2.32613e114	0.842542	0.421271	−	0.906935i	$-0.361584\pi$
$373$	2.32613e114	0.842542	0.421271	+	0.906935i	$0.361584\pi$
$374$	2.29666e114	0.738433
$375$	0	0
$376$	−5.26708e114	−1.33571
$377$	6.02925e114	1.35854
$378$	0	0
$379$	−1.50115e114	−0.267288	−0.133644	−	0.991029i	$-0.542668\pi$
$379$	−1.50115e114	−0.267288	−0.133644	+	0.991029i	$0.542668\pi$
$380$	5.65558e113	0.0895585
$381$	0	0
$382$	1.02458e114	0.128448
$383$	−4.26852e114	−0.476357	−0.238178	−	0.971221i	$-0.576550\pi$
$383$	−4.26852e114	−0.476357	−0.238178	+	0.971221i	$0.576550\pi$
$384$	0	0
$385$	1.44693e115	1.28069
$386$	−7.65697e114	−0.603840
$387$	0	0
$388$	−2.46032e114	−0.154163
$389$	−1.36736e115	−0.764054	−0.382027	−	0.924151i	$-0.624774\pi$
$389$	−1.36736e115	−0.764054	−0.382027	+	0.924151i	$0.624774\pi$
$390$	0	0
$391$	2.12087e115	0.943297
$392$	1.43855e115	0.571076
$393$	0	0
$394$	−4.34524e115	−1.37541
$395$	8.97001e115	2.53643
$396$	0	0
$397$	5.64489e115	1.27491	0.637453	−	0.770489i	$-0.279988\pi$
$397$	5.64489e115	1.27491	0.637453	+	0.770489i	$0.279988\pi$
$398$	−4.84055e115	−0.977458
$399$	0	0
$400$	−4.98959e115	−0.806112
$401$	5.09288e115	0.736274	0.368137	−	0.929772i	$-0.379996\pi$
$401$	5.09288e115	0.736274	0.368137	+	0.929772i	$0.379996\pi$
$402$	0	0
$403$	4.66430e115	0.540396
$404$	−3.15662e115	−0.327531
$405$	0	0
$406$	1.27609e116	1.06285
$407$	−3.29055e115	−0.245650
$408$	0	0
$409$	1.50131e116	0.901120	0.450560	−	0.892746i	$-0.351224\pi$
$409$	1.50131e116	0.901120	0.450560	+	0.892746i	$0.351224\pi$
$410$	−3.31345e115	−0.178402
$411$	0	0
$412$	−2.16706e115	−0.0939603
$413$	2.39092e116	0.930654
$414$	0	0
$415$	−9.60676e115	−0.301604
$416$	−1.01776e116	−0.287072
$417$	0	0
$418$	1.77417e116	0.404250
$419$	2.86274e116	0.586487	0.293244	−	0.956038i	$-0.405265\pi$
$419$	2.86274e116	0.586487	0.293244	+	0.956038i	$0.405265\pi$
$420$	0	0
$421$	−9.74749e116	−1.61562	−0.807811	−	0.589442i	$-0.799348\pi$
$421$	−9.74749e116	−1.61562	−0.807811	+	0.589442i	$0.799348\pi$
$422$	1.84439e115	0.0275073
$423$	0	0
$424$	−1.71553e117	−2.07309
$425$	−5.89301e116	−0.641253
$426$	0	0
$427$	1.06978e117	0.944613
$428$	−4.56400e115	−0.0363160
$429$	0	0
$430$	1.29525e117	0.837541
$431$	−8.68467e116	−0.506425	−0.253212	−	0.967411i	$-0.581487\pi$
$431$	−8.68467e116	−0.506425	−0.253212	+	0.967411i	$0.581487\pi$
$432$	0	0
$433$	1.47184e117	0.698471	0.349235	−	0.937035i	$-0.386441\pi$
$433$	1.47184e117	0.698471	0.349235	+	0.937035i	$0.386441\pi$
$434$	9.87195e116	0.422776
$435$	0	0
$436$	4.11572e116	0.143647
$437$	1.63837e117	0.516401
$438$	0	0
$439$	−6.00723e117	−1.54527	−0.772633	−	0.634853i	$-0.781061\pi$
$439$	−6.00723e117	−1.54527	−0.772633	+	0.634853i	$0.781061\pi$
$440$	8.63172e117	2.00657
$441$	0	0
$442$	2.32747e117	0.442175
$443$	1.62705e117	0.279535	0.139767	−	0.990184i	$-0.455365\pi$
$443$	1.62705e117	0.279535	0.139767	+	0.990184i	$0.455365\pi$
$444$	0	0
$445$	1.13747e118	1.59926
$446$	−2.25567e117	−0.286996
$447$	0	0
$448$	−7.26971e117	−0.757959
$449$	1.55698e117	0.147001	0.0735006	−	0.997295i	$-0.476583\pi$
$449$	1.55698e117	0.147001	0.0735006	+	0.997295i	$0.476583\pi$
$450$	0	0
$451$	2.35442e117	0.182401
$452$	1.33666e117	0.0938339
$453$	0	0
$454$	2.43338e118	1.40354
$455$	1.46634e118	0.766882
$456$	0	0
$457$	−8.39164e117	−0.361057	−0.180529	−	0.983570i	$-0.557781\pi$
$457$	−8.39164e117	−0.361057	−0.180529	+	0.983570i	$0.557781\pi$
$458$	−8.24172e117	−0.321739
$459$	0	0
$460$	1.24259e118	0.399581
$461$	5.23843e118	1.52936	0.764680	−	0.644410i	$-0.222897\pi$
$461$	5.23843e118	1.52936	0.764680	+	0.644410i	$0.222897\pi$
$462$	0	0
$463$	4.31741e118	1.03961	0.519804	−	0.854286i	$-0.326005\pi$
$463$	4.31741e118	1.03961	0.519804	+	0.854286i	$0.326005\pi$
$464$	6.15703e118	1.34686
$465$	0	0
$466$	7.12154e118	1.28647
$467$	2.94860e118	0.484189	0.242094	−	0.970253i	$-0.422166\pi$
$467$	2.94860e118	0.484189	0.242094	+	0.970253i	$0.422166\pi$
$468$	0	0
$469$	−3.89927e118	−0.529410
$470$	1.30141e119	1.60716
$471$	0	0
$472$	1.42631e119	1.45813
$473$	−9.20355e118	−0.856317
$474$	0	0
$475$	−4.55233e118	−0.351050
$476$	−1.11580e118	−0.0783569
$477$	0	0
$478$	7.52596e118	0.438551
$479$	1.88316e119	0.999899	0.499950	−	0.866054i	$-0.333352\pi$
$479$	1.88316e119	0.999899	0.499950	+	0.866054i	$0.333352\pi$
$480$	0	0
$481$	−3.33469e118	−0.147096
$482$	5.59156e118	0.224874
$483$	0	0
$484$	−4.04006e118	−0.135135
$485$	3.89960e119	1.18991
$486$	0	0
$487$	−3.85031e119	−0.978266	−0.489133	−	0.872209i	$-0.662687\pi$
$487$	−3.85031e119	−0.978266	−0.489133	+	0.872209i	$0.662687\pi$
$488$	6.38181e119	1.48000
$489$	0	0
$490$	−3.55441e119	−0.687134
$491$	−2.29064e119	−0.404417	−0.202209	−	0.979342i	$-0.564812\pi$
$491$	−2.29064e119	−0.404417	−0.202209	+	0.979342i	$0.564812\pi$
$492$	0	0
$493$	7.27182e119	1.07141
$494$	1.79797e119	0.242065
$495$	0	0
$496$	4.76315e119	0.535747
$497$	4.21024e119	0.432960
$498$	0	0
$499$	3.59737e119	0.309393	0.154697	−	0.987962i	$-0.450560\pi$
$499$	3.59737e119	0.309393	0.154697	+	0.987962i	$0.450560\pi$
$500$	−1.06630e118	−0.00838905
$501$	0	0
$502$	−9.75997e119	−0.642885
$503$	8.86242e119	0.534290	0.267145	−	0.963656i	$-0.413920\pi$
$503$	8.86242e119	0.534290	0.267145	+	0.963656i	$0.413920\pi$
$504$	0	0
$505$	5.00324e120	2.52805
$506$	3.89804e120	1.80363
$507$	0	0
$508$	−4.97692e119	−0.193208
$509$	4.22196e120	1.50166	0.750832	−	0.660493i	$-0.229653\pi$
$509$	4.22196e120	1.50166	0.750832	+	0.660493i	$0.229653\pi$
$510$	0	0
$511$	1.45814e120	0.435582
$512$	−4.09108e120	−1.12027
$513$	0	0
$514$	4.13920e119	0.0952923
$515$	3.43478e120	0.725233
$516$	0	0
$517$	−9.24732e120	−1.64319
$518$	−7.05784e119	−0.115079
$519$	0	0
$520$	8.74752e120	1.20153
$521$	6.53932e120	0.824620	0.412310	−	0.911044i	$-0.364722\pi$
$521$	6.53932e120	0.824620	0.412310	+	0.911044i	$0.364722\pi$
$522$	0	0
$523$	2.91241e120	0.309690	0.154845	−	0.987939i	$-0.450512\pi$
$523$	2.91241e120	0.309690	0.154845	+	0.987939i	$0.450512\pi$
$524$	3.18850e119	0.0311419
$525$	0	0
$526$	1.33691e121	1.10214
$527$	5.62557e120	0.426181
$528$	0	0
$529$	2.03733e121	1.30402
$530$	4.23879e121	2.49440
$531$	0	0
$532$	−8.61954e119	−0.0428960
$533$	2.38600e120	0.109222
$534$	0	0
$535$	7.23393e120	0.280305
$536$	−2.32612e121	−0.829468
$537$	0	0
$538$	−3.60449e121	−1.08901
$539$	2.52563e121	0.702538
$540$	0	0
$541$	1.96807e121	0.464260	0.232130	−	0.972685i	$-0.425430\pi$
$541$	1.96807e121	0.464260	0.232130	+	0.972685i	$0.425430\pi$
$542$	−3.70093e121	−0.804161
$543$	0	0
$544$	−1.22751e121	−0.226398
$545$	−6.52341e121	−1.10874
$546$	0	0
$547$	5.06309e121	0.731105	0.365552	−	0.930791i	$-0.380880\pi$
$547$	5.06309e121	0.731105	0.365552	+	0.930791i	$0.380880\pi$
$548$	1.29780e121	0.172772
$549$	0	0
$550$	−1.08310e122	−1.22611
$551$	5.61746e121	0.586535
$552$	0	0
$553$	−1.36710e122	−1.21487
$554$	−1.76074e122	−1.44381
$555$	0	0
$556$	−3.05842e121	−0.213633
$557$	−7.70908e121	−0.497103	−0.248551	−	0.968619i	$-0.579955\pi$
$557$	−7.70908e121	−0.497103	−0.248551	+	0.968619i	$0.579955\pi$
$558$	0	0
$559$	−9.32702e121	−0.512764
$560$	1.49742e122	0.760284
$561$	0	0
$562$	1.18423e121	0.0513063
$563$	−3.40007e122	−1.36102	−0.680509	−	0.732740i	$-0.738241\pi$
$563$	−3.40007e122	−1.36102	−0.680509	+	0.732740i	$0.738241\pi$
$564$	0	0
$565$	−2.11860e122	−0.724257
$566$	−8.72541e121	−0.275711
$567$	0	0
$568$	2.51163e122	0.678352
$569$	1.07140e122	0.267580	0.133790	−	0.991010i	$-0.457285\pi$
$569$	1.07140e122	0.267580	0.133790	+	0.991010i	$0.457285\pi$
$570$	0	0
$571$	4.63901e121	0.0991103	0.0495551	−	0.998771i	$-0.484220\pi$
$571$	4.63901e121	0.0991103	0.0495551	+	0.998771i	$0.484220\pi$
$572$	−9.68952e121	−0.191505
$573$	0	0
$574$	5.04995e121	0.0854493
$575$	−1.00020e123	−1.56627
$576$	0	0
$577$	4.29228e121	0.0575922	0.0287961	−	0.999585i	$-0.490833\pi$
$577$	4.29228e121	0.0575922	0.0287961	+	0.999585i	$0.490833\pi$
$578$	−4.46150e122	−0.554233
$579$	0	0
$580$	4.26047e122	0.453850
$581$	1.46414e122	0.144460
$582$	0	0
$583$	−3.01193e123	−2.55032
$584$	8.69860e122	0.682461
$585$	0	0
$586$	2.76276e122	0.186166
$587$	5.10199e122	0.318672	0.159336	−	0.987224i	$-0.449065\pi$
$587$	5.10199e122	0.318672	0.159336	+	0.987224i	$0.449065\pi$
$588$	0	0
$589$	4.34574e122	0.233310
$590$	−3.52418e123	−1.75446
$591$	0	0
$592$	−3.40536e122	−0.145830
$593$	−3.16373e123	−1.25680	−0.628400	−	0.777891i	$-0.716290\pi$
$593$	−3.16373e123	−1.25680	−0.628400	+	0.777891i	$0.716290\pi$
$594$	0	0
$595$	1.76854e123	0.604798
$596$	1.91168e122	0.0606676
$597$	0	0
$598$	3.95033e123	1.08002
$599$	−2.38447e123	−0.605199	−0.302599	−	0.953118i	$-0.597854\pi$
$599$	−2.38447e123	−0.605199	−0.302599	+	0.953118i	$0.597854\pi$
$600$	0	0
$601$	−2.41864e123	−0.529245	−0.264623	−	0.964352i	$-0.585247\pi$
$601$	−2.41864e123	−0.529245	−0.264623	+	0.964352i	$0.585247\pi$
$602$	−1.97406e123	−0.401158
$603$	0	0
$604$	−6.37464e122	−0.111766
$605$	6.40348e123	1.04304
$606$	0	0
$607$	2.86566e123	0.403021	0.201511	−	0.979486i	$-0.435415\pi$
$607$	2.86566e123	0.403021	0.201511	+	0.979486i	$0.435415\pi$
$608$	−9.48245e122	−0.123940
$609$	0	0
$610$	−1.57684e124	−1.78078
$611$	−9.37138e123	−0.983942
$612$	0	0
$613$	5.03326e123	0.456939	0.228469	−	0.973551i	$-0.426628\pi$
$613$	5.03326e123	0.456939	0.228469	+	0.973551i	$0.426628\pi$
$614$	2.15494e123	0.181946
$615$	0	0
$616$	−1.31554e124	−0.961087
$617$	−2.23873e122	−0.0152164	−0.00760819	−	0.999971i	$-0.502422\pi$
$617$	−2.23873e122	−0.0152164	−0.00760819	+	0.999971i	$0.502422\pi$
$618$	0	0
$619$	5.07827e123	0.298870	0.149435	−	0.988772i	$-0.452255\pi$
$619$	5.07827e123	0.298870	0.149435	+	0.988772i	$0.452255\pi$
$620$	3.29595e123	0.180531
$621$	0	0
$622$	1.07097e124	0.508284
$623$	−1.73359e124	−0.765999
$624$	0	0
$625$	−2.52429e124	−0.967117
$626$	1.18282e123	0.0422048
$627$	0	0
$628$	−1.27267e122	−0.00394013
$629$	−4.02194e123	−0.116006
$630$	0	0
$631$	−6.55453e124	−1.64148	−0.820739	−	0.571304i	$-0.806438\pi$
$631$	−6.55453e124	−1.64148	−0.820739	+	0.571304i	$0.806438\pi$
$632$	−8.15548e124	−1.90344
$633$	0	0
$634$	6.03354e123	0.122349
$635$	7.88841e124	1.49128
$636$	0	0
$637$	2.55952e124	0.420681
$638$	1.33652e125	2.04859
$639$	0	0
$640$	6.82119e124	0.909601
$641$	1.12609e125	1.40085	0.700426	−	0.713725i	$-0.252994\pi$
$641$	1.12609e125	1.40085	0.700426	+	0.713725i	$0.252994\pi$
$642$	0	0
$643$	1.67853e125	1.81777	0.908886	−	0.417044i	$-0.136934\pi$
$643$	1.67853e125	1.81777	0.908886	+	0.417044i	$0.136934\pi$
$644$	−1.89381e124	−0.191388
$645$	0	0
$646$	2.16851e124	0.190904
$647$	1.03514e125	0.850666	0.425333	−	0.905037i	$-0.360157\pi$
$647$	1.03514e125	0.850666	0.425333	+	0.905037i	$0.360157\pi$
$648$	0	0
$649$	2.50415e125	1.79379
$650$	−1.09763e125	−0.734196
$651$	0	0
$652$	3.08798e124	0.180159
$653$	1.56383e125	0.852222	0.426111	−	0.904671i	$-0.359883\pi$
$653$	1.56383e125	0.852222	0.426111	+	0.904671i	$0.359883\pi$
$654$	0	0
$655$	−5.05377e124	−0.240369
$656$	2.43657e124	0.108282
$657$	0	0
$658$	−1.98344e125	−0.769782
$659$	−1.26588e125	−0.459191	−0.229595	−	0.973286i	$-0.573740\pi$
$659$	−1.26588e125	−0.459191	−0.229595	+	0.973286i	$0.573740\pi$
$660$	0	0
$661$	−5.50470e125	−1.74489	−0.872447	−	0.488709i	$-0.837468\pi$
$661$	−5.50470e125	−1.74489	−0.872447	+	0.488709i	$0.837468\pi$
$662$	4.31384e125	1.27845
$663$	0	0
$664$	8.73441e124	0.226336
$665$	1.36619e125	0.331092
$666$	0	0
$667$	1.23422e126	2.61693
$668$	1.65072e125	0.327431
$669$	0	0
$670$	5.74746e125	0.998038
$671$	1.12044e126	1.82070
$672$	0	0
$673$	−1.57404e125	−0.224050	−0.112025	−	0.993705i	$-0.535734\pi$
$673$	−1.57404e125	−0.224050	−0.112025	+	0.993705i	$0.535734\pi$
$674$	7.75143e124	0.103280
$675$	0	0
$676$	5.99452e124	0.0700046
$677$	−1.04038e126	−1.13762	−0.568809	−	0.822470i	$-0.692595\pi$
$677$	−1.04038e126	−1.13762	−0.568809	+	0.822470i	$0.692595\pi$
$678$	0	0
$679$	−5.94329e125	−0.569930
$680$	1.05503e126	0.947585
$681$	0	0
$682$	1.03395e126	0.814880
$683$	−1.23854e126	−0.914513	−0.457256	−	0.889335i	$-0.651168\pi$
$683$	−1.23854e126	−0.914513	−0.457256	+	0.889335i	$0.651168\pi$
$684$	0	0
$685$	−2.05701e126	−1.33354
$686$	1.55644e126	0.945601
$687$	0	0
$688$	−9.52469e125	−0.508353
$689$	−3.05234e126	−1.52713
$690$	0	0
$691$	−3.68627e126	−1.62111	−0.810557	−	0.585659i	$-0.800836\pi$
$691$	−3.68627e126	−1.62111	−0.810557	+	0.585659i	$0.800836\pi$
$692$	−7.04962e125	−0.290700
$693$	0	0
$694$	1.99687e126	0.724193
$695$	4.84758e126	1.64893
$696$	0	0
$697$	2.87773e125	0.0861375
$698$	−2.32347e126	−0.652487
$699$	0	0
$700$	5.26209e125	0.130106
$701$	−4.13787e125	−0.0960119	−0.0480059	−	0.998847i	$-0.515287\pi$
$701$	−4.13787e125	−0.0960119	−0.0480059	+	0.998847i	$0.515287\pi$
$702$	0	0
$703$	−3.10694e125	−0.0635068
$704$	−7.61399e126	−1.46093
$705$	0	0
$706$	2.75841e126	0.466498
$707$	−7.62532e126	−1.21086
$708$	0	0
$709$	−3.99945e126	−0.560070	−0.280035	−	0.959990i	$-0.590346\pi$
$709$	−3.99945e126	−0.560070	−0.280035	+	0.959990i	$0.590346\pi$
$710$	−6.20582e126	−0.816212
$711$	0	0
$712$	−1.03418e127	−1.20015
$713$	9.54806e126	1.04095
$714$	0	0
$715$	1.53579e127	1.47813
$716$	2.84248e126	0.257080
$717$	0	0
$718$	−1.55289e126	−0.124052
$719$	2.03979e127	1.53162	0.765808	−	0.643070i	$-0.222339\pi$
$719$	2.03979e127	1.53162	0.765808	+	0.643070i	$0.222339\pi$
$720$	0	0
$721$	−5.23487e126	−0.347366
$722$	−1.27982e127	−0.798443
$723$	0	0
$724$	4.06308e126	0.224124
$725$	−3.42937e127	−1.77899
$726$	0	0
$727$	1.86391e127	0.855350	0.427675	−	0.903933i	$-0.359333\pi$
$727$	1.86391e127	0.855350	0.427675	+	0.903933i	$0.359333\pi$
$728$	−1.33319e127	−0.575500
$729$	0	0
$730$	−2.14928e127	−0.821155
$731$	−1.12492e127	−0.404389
$732$	0	0
$733$	2.07676e126	0.0661089	0.0330544	−	0.999454i	$-0.489477\pi$
$733$	2.07676e126	0.0661089	0.0330544	+	0.999454i	$0.489477\pi$
$734$	2.42203e127	0.725612
$735$	0	0
$736$	−2.08340e127	−0.552980
$737$	−4.08394e127	−1.02041
$738$	0	0
$739$	2.17012e127	0.480624	0.240312	−	0.970696i	$-0.422750\pi$
$739$	2.17012e127	0.480624	0.240312	+	0.970696i	$0.422750\pi$
$740$	−2.35641e126	−0.0491404
$741$	0	0
$742$	−6.46024e127	−1.19474
$743$	−3.44373e127	−0.599828	−0.299914	−	0.953966i	$-0.596958\pi$
$743$	−3.44373e127	−0.599828	−0.299914	+	0.953966i	$0.596958\pi$
$744$	0	0
$745$	−3.03001e127	−0.468263
$746$	5.22557e127	0.760775
$747$	0	0
$748$	−1.16864e127	−0.151029
$749$	−1.10251e127	−0.134258
$750$	0	0
$751$	−9.41430e127	−1.01815	−0.509074	−	0.860723i	$-0.670012\pi$
$751$	−9.41430e127	−1.01815	−0.509074	+	0.860723i	$0.670012\pi$
$752$	−9.56998e127	−0.975478
$753$	0	0
$754$	1.35445e128	1.22670
$755$	1.01038e128	0.862670
$756$	0	0
$757$	−8.67950e124	−0.000658761 0	−0.000329381	−	1.00000i	$-0.500105\pi$
$757$	−8.67950e124	−0.000658761 0	−0.000329381		1.00000i	$0.500105\pi$
$758$	−3.37228e127	−0.241348
$759$	0	0
$760$	8.15008e127	0.518749
$761$	−2.99513e128	−1.79804	−0.899018	−	0.437911i	$-0.855718\pi$
$761$	−2.99513e128	−1.79804	−0.899018	+	0.437911i	$0.855718\pi$
$762$	0	0
$763$	9.94218e127	0.531055
$764$	−5.21353e126	−0.0262711
$765$	0	0
$766$	−9.58909e127	−0.430127
$767$	2.53775e128	1.07413
$768$	0	0
$769$	−1.81575e128	−0.684439	−0.342220	−	0.939620i	$-0.611179\pi$
$769$	−1.81575e128	−0.684439	−0.342220	+	0.939620i	$0.611179\pi$
$770$	3.25048e128	1.15641
$771$	0	0
$772$	3.89621e127	0.123502
$773$	4.64806e128	1.39086	0.695432	−	0.718592i	$-0.255213\pi$
$773$	4.64806e128	1.39086	0.695432	+	0.718592i	$0.255213\pi$
$774$	0	0
$775$	−2.65301e128	−0.707640
$776$	−3.54549e128	−0.892955
$777$	0	0
$778$	−3.07171e128	−0.689904
$779$	2.22304e127	0.0471554
$780$	0	0
$781$	4.40963e128	0.834509
$782$	4.76446e128	0.851752
$783$	0	0
$784$	2.61376e128	0.417062
$785$	2.01717e127	0.0304119
$786$	0	0
$787$	1.58248e128	0.213040	0.106520	−	0.994311i	$-0.466029\pi$
$787$	1.58248e128	0.213040	0.106520	+	0.994311i	$0.466029\pi$
$788$	2.21105e128	0.281308
$789$	0	0
$790$	2.01508e129	2.29027
$791$	3.22891e128	0.346898
$792$	0	0
$793$	1.13547e129	1.09024
$794$	1.26810e129	1.15118
$795$	0	0
$796$	2.46309e128	0.199916
$797$	9.45352e128	0.725602	0.362801	−	0.931867i	$-0.381821\pi$
$797$	9.45352e128	0.725602	0.362801	+	0.931867i	$0.381821\pi$
$798$	0	0
$799$	−1.13027e129	−0.775982
$800$	5.78889e128	0.375916
$801$	0	0
$802$	1.14410e129	0.664820
$803$	1.52720e129	0.839564
$804$	0	0
$805$	3.00168e129	1.47723
$806$	1.04782e129	0.487951
$807$	0	0
$808$	−4.54891e129	−1.89715
$809$	−1.50426e129	−0.593762	−0.296881	−	0.954914i	$-0.595946\pi$
$809$	−1.50426e129	−0.593762	−0.296881	+	0.954914i	$0.595946\pi$
$810$	0	0
$811$	−1.51351e129	−0.535249	−0.267625	−	0.963523i	$-0.586239\pi$
$811$	−1.51351e129	−0.535249	−0.267625	+	0.963523i	$0.586239\pi$
$812$	−6.49329e128	−0.217381
$813$	0	0
$814$	−7.39209e128	−0.221810
$815$	−4.89445e129	−1.39056
$816$	0	0
$817$	−8.69000e128	−0.221380
$818$	3.37264e129	0.813668
$819$	0	0
$820$	1.68603e128	0.0364879
$821$	−6.94292e129	−1.42322	−0.711609	−	0.702575i	$-0.752033\pi$
$821$	−6.94292e129	−1.42322	−0.711609	+	0.702575i	$0.752033\pi$
$822$	0	0
$823$	3.78802e129	0.696818	0.348409	−	0.937343i	$-0.386722\pi$
$823$	3.78802e129	0.696818	0.348409	+	0.937343i	$0.386722\pi$
$824$	−3.12288e129	−0.544245
$825$	0	0
$826$	5.37112e129	0.840336
$827$	1.29618e130	1.92163	0.960816	−	0.277185i	$-0.0894016\pi$
$827$	1.29618e130	1.92163	0.960816	+	0.277185i	$0.0894016\pi$
$828$	0	0
$829$	−7.78087e129	−1.03598	−0.517990	−	0.855386i	$-0.673320\pi$
$829$	−7.78087e129	−1.03598	−0.517990	+	0.855386i	$0.673320\pi$
$830$	−2.15812e129	−0.272334
$831$	0	0
$832$	−7.71614e129	−0.874807
$833$	3.08701e129	0.331768
$834$	0	0
$835$	−2.61638e130	−2.52728
$836$	−9.02775e128	−0.0826799
$837$	0	0
$838$	6.43105e129	0.529570
$839$	−2.28971e129	−0.178802	−0.0894011	−	0.995996i	$-0.528495\pi$
$839$	−2.28971e129	−0.178802	−0.0894011	+	0.995996i	$0.528495\pi$
$840$	0	0
$841$	2.80805e130	1.97235
$842$	−2.18974e130	−1.45883
$843$	0	0
$844$	−9.38507e127	−0.00562599
$845$	−9.50130e129	−0.540331
$846$	0	0
$847$	−9.75939e129	−0.499587
$848$	−3.11702e130	−1.51400
$849$	0	0
$850$	−1.32384e130	−0.579021
$851$	−6.82628e129	−0.283347
$852$	0	0
$853$	1.69945e130	0.635443	0.317722	−	0.948184i	$-0.397082\pi$
$853$	1.69945e130	0.635443	0.317722	+	0.948184i	$0.397082\pi$
$854$	2.40322e130	0.852940
$855$	0	0
$856$	−6.57705e129	−0.210353
$857$	−3.15524e130	−0.958044	−0.479022	−	0.877803i	$-0.659009\pi$
$857$	−3.15524e130	−0.958044	−0.479022	+	0.877803i	$0.659009\pi$
$858$	0	0
$859$	−7.05135e130	−1.93008	−0.965042	−	0.262095i	$-0.915587\pi$
$859$	−7.05135e130	−1.93008	−0.965042	+	0.262095i	$0.915587\pi$
$860$	−6.59079e129	−0.171300
$861$	0	0
$862$	−1.95098e130	−0.457277
$863$	5.08141e130	1.13111	0.565554	−	0.824711i	$-0.308662\pi$
$863$	5.08141e130	1.13111	0.565554	+	0.824711i	$0.308662\pi$
$864$	0	0
$865$	1.11736e131	2.24377
$866$	3.30643e130	0.630686
$867$	0	0
$868$	−5.02329e129	−0.0864690
$869$	−1.43184e131	−2.34161
$870$	0	0
$871$	−4.13872e130	−0.611024
$872$	5.93104e130	0.832046
$873$	0	0
$874$	3.68053e130	0.466286
$875$	−2.57581e129	−0.0310138
$876$	0	0
$877$	6.84567e130	0.744618	0.372309	−	0.928109i	$-0.378566\pi$
$877$	6.84567e130	0.744618	0.372309	+	0.928109i	$0.378566\pi$
$878$	−1.34950e131	−1.39530
$879$	0	0
$880$	1.56833e131	1.46541
$881$	1.42433e131	1.26526	0.632632	−	0.774453i	$-0.281975\pi$
$881$	1.42433e131	1.26526	0.632632	+	0.774453i	$0.281975\pi$
$882$	0	0
$883$	−1.48435e131	−1.19202	−0.596012	−	0.802975i	$-0.703249\pi$
$883$	−1.48435e131	−1.19202	−0.596012	+	0.802975i	$0.703249\pi$
$884$	−1.18432e130	−0.0904366
$885$	0	0
$886$	3.65511e130	0.252406
$887$	−8.44535e130	−0.554647	−0.277323	−	0.960777i	$-0.589447\pi$
$887$	−8.44535e130	−0.554647	−0.277323	+	0.960777i	$0.589447\pi$
$888$	0	0
$889$	−1.20225e131	−0.714279
$890$	2.55528e131	1.44405
$891$	0	0
$892$	1.14779e130	0.0586983
$893$	−8.73133e130	−0.424806
$894$	0	0
$895$	−4.50532e131	−1.98427
$896$	−1.03960e131	−0.435673
$897$	0	0
$898$	3.49770e130	0.132735
$899$	3.27374e131	1.18233
$900$	0	0
$901$	−3.68139e131	−1.20437
$902$	5.28911e130	0.164699
$903$	0	0
$904$	1.92622e131	0.543513
$905$	−6.43997e131	−1.72990
$906$	0	0
$907$	3.96830e131	0.966229	0.483114	−	0.875557i	$-0.339506\pi$
$907$	3.96830e131	0.966229	0.483114	+	0.875557i	$0.339506\pi$
$908$	−1.23821e131	−0.287061
$909$	0	0
$910$	3.29409e131	0.692457
$911$	9.54692e131	1.91115	0.955577	−	0.294742i	$-0.0952338\pi$
$911$	9.54692e131	1.91115	0.955577	+	0.294742i	$0.0952338\pi$
$912$	0	0
$913$	1.53348e131	0.278439
$914$	−1.88515e131	−0.326017
$915$	0	0
$916$	4.19375e130	0.0658043
$917$	7.70234e130	0.115130
$918$	0	0
$919$	3.40413e130	0.0461812	0.0230906	−	0.999733i	$-0.492649\pi$
$919$	3.40413e130	0.0461812	0.0230906	+	0.999733i	$0.492649\pi$
$920$	1.79066e132	2.31449
$921$	0	0
$922$	1.17679e132	1.38094
$923$	4.46879e131	0.499705
$924$	0	0
$925$	1.89674e131	0.192619
$926$	9.69891e131	0.938716
$927$	0	0
$928$	−7.14334e131	−0.628082
$929$	−1.84470e132	−1.54606	−0.773032	−	0.634368i	$-0.781261\pi$
$929$	−1.84470e132	−1.54606	−0.773032	+	0.634368i	$0.781261\pi$
$930$	0	0
$931$	2.38470e131	0.181624
$932$	−3.62376e131	−0.263118
$933$	0	0
$934$	6.62393e131	0.437199
$935$	1.85230e132	1.16572
$936$	0	0
$937$	1.38071e132	0.790114	0.395057	−	0.918657i	$-0.370725\pi$
$937$	1.38071e132	0.790114	0.395057	+	0.918657i	$0.370725\pi$
$938$	−8.75957e131	−0.478032
$939$	0	0
$940$	−6.62213e131	−0.328707
$941$	8.90199e131	0.421453	0.210726	−	0.977545i	$-0.432417\pi$
$941$	8.90199e131	0.421453	0.210726	+	0.977545i	$0.432417\pi$
$942$	0	0
$943$	4.88427e131	0.210392
$944$	2.59153e132	1.06488
$945$	0	0
$946$	−2.06754e132	−0.773213
$947$	−3.43186e132	−1.22449	−0.612245	−	0.790668i	$-0.709734\pi$
$947$	−3.43186e132	−1.22449	−0.612245	+	0.790668i	$0.709734\pi$
$948$	0	0
$949$	1.54769e132	0.502732
$950$	−1.02267e132	−0.316981
$951$	0	0
$952$	−1.60795e132	−0.453866
$953$	2.81753e132	0.758987	0.379493	−	0.925194i	$-0.376098\pi$
$953$	2.81753e132	0.758987	0.379493	+	0.925194i	$0.376098\pi$
$954$	0	0
$955$	8.26343e131	0.202773
$956$	−3.82954e131	−0.0896955
$957$	0	0
$958$	4.23044e132	0.902861
$959$	3.13504e132	0.638726
$960$	0	0
$961$	−2.85246e132	−0.529698
$962$	−7.49126e131	−0.132820
$963$	0	0
$964$	−2.84524e131	−0.0459929
$965$	−6.17548e132	−0.953247
$966$	0	0
$967$	−1.21293e133	−1.70748	−0.853742	−	0.520697i	$-0.825672\pi$
$967$	−1.21293e133	−1.70748	−0.853742	+	0.520697i	$0.825672\pi$
$968$	−5.82200e132	−0.782743
$969$	0	0
$970$	8.76030e132	1.07443
$971$	−7.55835e132	−0.885465	−0.442733	−	0.896654i	$-0.645991\pi$
$971$	−7.55835e132	−0.885465	−0.442733	+	0.896654i	$0.645991\pi$
$972$	0	0
$973$	−7.38809e132	−0.789788
$974$	−8.64958e132	−0.883327
$975$	0	0
$976$	1.15954e133	1.08086
$977$	−3.97667e132	−0.354170	−0.177085	−	0.984196i	$-0.556667\pi$
$977$	−3.97667e132	−0.354170	−0.177085	+	0.984196i	$0.556667\pi$
$978$	0	0
$979$	−1.81569e133	−1.47643
$980$	1.80864e132	0.140537
$981$	0	0
$982$	−5.14583e132	−0.365169
$983$	−6.63961e132	−0.450310	−0.225155	−	0.974323i	$-0.572289\pi$
$983$	−6.63961e132	−0.450310	−0.225155	+	0.974323i	$0.572289\pi$
$984$	0	0
$985$	−3.50451e133	−2.17128
$986$	1.63359e133	0.967431
$987$	0	0
$988$	−9.14886e131	−0.0495089
$989$	−1.90929e133	−0.987727
$990$	0	0
$991$	1.70757e133	0.807423	0.403712	−	0.914886i	$-0.367720\pi$
$991$	1.70757e133	0.807423	0.403712	+	0.914886i	$0.367720\pi$
$992$	−5.52617e132	−0.249836
$993$	0	0
$994$	9.45815e132	0.390942
$995$	−3.90399e133	−1.54305
$996$	0	0
$997$	−1.42027e133	−0.513378	−0.256689	−	0.966494i	$-0.582632\pi$
$997$	−1.42027e133	−0.513378	−0.256689	+	0.966494i	$0.582632\pi$
$998$	8.08136e132	0.279367
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.90.a.b.1.5		7
3.2	odd	2		1.90.a.a.1.3	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.90.a.a.1.3	✓	7	3.2	odd	2
9.90.a.b.1.5		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)

\(f(q)\)	\(=\)	\(q+2.24646e13 q^{2} -1.14310e26 q^{4} +1.81181e31 q^{5} -2.76134e37 q^{7} -1.64729e40 q^{8} +O(q^{10})\)	\(q+2.24646e13 q^{2} -1.14310e26 q^{4} +1.81181e31 q^{5} -2.76134e37 q^{7} -1.64729e40 q^{8} +4.07017e44 q^{10} -2.89211e46 q^{11} -2.93091e49 q^{13} -6.20325e50 q^{14} -2.99303e53 q^{16} -3.53494e54 q^{17} -2.73074e56 q^{19} -2.07108e57 q^{20} -6.49703e59 q^{22} -5.99973e60 q^{23} +1.66707e62 q^{25} -6.58419e62 q^{26} +3.15649e63 q^{28} -2.05712e65 q^{29} -1.59142e66 q^{31} +3.47249e66 q^{32} -7.94112e67 q^{34} -5.00303e68 q^{35} +1.13777e69 q^{37} -6.13450e69 q^{38} -2.98457e71 q^{40} -8.14082e70 q^{41} +3.18229e72 q^{43} +3.30598e72 q^{44} -1.34782e74 q^{46} +3.19743e74 q^{47} -8.73283e74 q^{49} +3.74502e75 q^{50} +3.35033e75 q^{52} +1.04143e77 q^{53} -5.23996e77 q^{55} +4.54872e77 q^{56} -4.62126e78 q^{58} -8.65856e78 q^{59} -3.87413e79 q^{61} -3.57506e79 q^{62} +2.63268e80 q^{64} -5.31026e80 q^{65} +1.41209e81 q^{67} +4.04080e80 q^{68} -1.12391e82 q^{70} -1.52471e82 q^{71} -5.28056e82 q^{73} +2.55595e82 q^{74} +3.12151e82 q^{76} +7.98611e83 q^{77} +4.95085e84 q^{79} -5.42280e84 q^{80} -1.82881e84 q^{82} -5.30230e84 q^{83} -6.40465e85 q^{85} +7.14891e85 q^{86} +4.76414e86 q^{88} +6.27807e86 q^{89} +8.09324e86 q^{91} +6.85829e86 q^{92} +7.18291e87 q^{94} -4.94758e87 q^{95} +2.15232e88 q^{97} -1.96180e88 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 31407330351408 q^{2} + 22\!\cdots\!04 q^{4}+ \cdots + 17\!\cdots\!20 q^{8}+O(q^{10}) \) 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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