LMFDB - Embedded newform 9.90.a.b.1.3

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			1.3
Root			$-4.68207e11$ 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)

$f(q)$	$=$	$q-1.79872e13 q^{2} -2.95431e26 q^{4} +4.75717e30 q^{5} +3.90338e37 q^{7} +1.64475e40 q^{8} +O(q^{10})$	\(q-1.79872e13 q^{2} -2.95431e26 q^{4} +4.75717e30 q^{5} +3.90338e37 q^{7} +1.64475e40 q^{8} -8.55680e43 q^{10} +2.01197e45 q^{11} -1.05046e49 q^{13} -7.02109e50 q^{14} -1.12982e53 q^{16} -1.05148e55 q^{17} +1.08050e57 q^{19} -1.40541e57 q^{20} -3.61897e58 q^{22} +5.03802e60 q^{23} -1.38928e62 q^{25} +1.88949e62 q^{26} -1.15318e64 q^{28} -1.12164e65 q^{29} -3.18722e66 q^{31} -8.14829e66 q^{32} +1.89132e68 q^{34} +1.85690e68 q^{35} -6.99627e69 q^{37} -1.94351e70 q^{38} +7.82435e70 q^{40} +7.38883e70 q^{41} +4.97212e72 q^{43} -5.94398e71 q^{44} -9.06197e73 q^{46} -5.91267e73 q^{47} -1.12142e74 q^{49} +2.49893e75 q^{50} +3.10339e75 q^{52} -2.39386e76 q^{53} +9.57127e75 q^{55} +6.42009e77 q^{56} +2.01752e78 q^{58} +1.72292e78 q^{59} +1.90453e79 q^{61} +5.73291e79 q^{62} +2.16497e80 q^{64} -4.99723e79 q^{65} +7.04228e80 q^{67} +3.10640e81 q^{68} -3.34005e81 q^{70} +1.27373e82 q^{71} -3.75786e82 q^{73} +1.25843e83 q^{74} -3.19212e83 q^{76} +7.85349e82 q^{77} +3.21546e83 q^{79} -5.37472e83 q^{80} -1.32904e84 q^{82} +2.22227e85 q^{83} -5.00207e85 q^{85} -8.94344e85 q^{86} +3.30919e85 q^{88} +5.54352e86 q^{89} -4.10036e86 q^{91} -1.48839e87 q^{92} +1.06352e87 q^{94} +5.14011e87 q^{95} +4.88818e88 q^{97} +2.01713e87 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.79872e13	−0.722984	−0.361492	−	0.932375i	$-0.617732\pi$
$2$	−1.79872e13	−0.722984	−0.361492	+	0.932375i	$0.617732\pi$
$3$	0	0
$3$	0	0
$4$	−2.95431e26	−0.477294
$5$	4.75717e30	0.374268	0.187134	−	0.982334i	$-0.440080\pi$
$5$	4.75717e30	0.374268	0.187134	+	0.982334i	$0.440080\pi$
$6$	0	0
$7$	3.90338e37	0.965114	0.482557	−	0.875865i	$-0.339708\pi$
$7$	3.90338e37	0.965114	0.482557	+	0.875865i	$0.339708\pi$
$8$	1.64475e40	1.06806
$9$	0	0
$10$	−8.55680e43	−0.270590
$11$	2.01197e45	0.0915476	0.0457738	−	0.998952i	$-0.485425\pi$
$11$	2.01197e45	0.0915476	0.0457738	+	0.998952i	$0.485425\pi$
$12$	0	0
$13$	−1.05046e49	−0.282424	−0.141212	−	0.989979i	$-0.545100\pi$
$13$	−1.05046e49	−0.282424	−0.141212	+	0.989979i	$0.545100\pi$
$14$	−7.02109e50	−0.697761
$15$	0	0
$16$	−1.12982e53	−0.294895
$17$	−1.05148e55	−1.84852	−0.924260	−	0.381763i	$-0.875317\pi$
$17$	−1.05148e55	−1.84852	−0.924260	+	0.381763i	$0.875317\pi$
$18$	0	0
$19$	1.08050e57	1.34613	0.673067	−	0.739581i	$-0.264976\pi$
$19$	1.08050e57	1.34613	0.673067	+	0.739581i	$0.264976\pi$
$20$	−1.40541e57	−0.178636
$21$	0	0
$22$	−3.61897e58	−0.0661874
$23$	5.03802e60	1.27459	0.637295	−	0.770620i	$-0.280053\pi$
$23$	5.03802e60	1.27459	0.637295	+	0.770620i	$0.280053\pi$
$24$	0	0
$25$	−1.38928e62	−0.859923
$26$	1.88949e62	0.204188
$27$	0	0
$28$	−1.15318e64	−0.460643
$29$	−1.12164e65	−0.940032	−0.470016	−	0.882658i	$-0.655752\pi$
$29$	−1.12164e65	−0.940032	−0.470016	+	0.882658i	$0.655752\pi$
$30$	0	0
$31$	−3.18722e66	−1.37346	−0.686731	−	0.726912i	$-0.740955\pi$
$31$	−3.18722e66	−1.37346	−0.686731	+	0.726912i	$0.740955\pi$
$32$	−8.14829e66	−0.854855
$33$	0	0
$34$	1.89132e68	1.33645
$35$	1.85690e68	0.361211
$36$	0	0
$37$	−6.99627e69	−1.14786	−0.573931	−	0.818904i	$-0.694582\pi$
$37$	−6.99627e69	−1.14786	−0.573931	+	0.818904i	$0.694582\pi$
$38$	−1.94351e70	−0.973233
$39$	0	0
$40$	7.82435e70	0.399741
$41$	7.38883e70	0.125804	0.0629020	−	0.998020i	$-0.479964\pi$
$41$	7.38883e70	0.125804	0.0629020	+	0.998020i	$0.479964\pi$
$42$	0	0
$43$	4.97212e72	1.01671	0.508353	−	0.861149i	$-0.330255\pi$
$43$	4.97212e72	1.01671	0.508353	+	0.861149i	$0.330255\pi$
$44$	−5.94398e71	−0.0436952
$45$	0	0
$46$	−9.06197e73	−0.921508
$47$	−5.91267e73	−0.230903	−0.115451	−	0.993313i	$-0.536831\pi$
$47$	−5.91267e73	−0.230903	−0.115451	+	0.993313i	$0.536831\pi$
$48$	0	0
$49$	−1.12142e74	−0.0685558
$50$	2.49893e75	0.621711
$51$	0	0
$52$	3.10339e75	0.134799
$53$	−2.39386e76	−0.445475	−0.222738	−	0.974878i	$-0.571499\pi$
$53$	−2.39386e76	−0.445475	−0.222738	+	0.974878i	$0.571499\pi$
$54$	0	0
$55$	9.57127e75	0.0342634
$56$	6.42009e77	1.03080
$57$	0	0
$58$	2.01752e78	0.679628
$59$	1.72292e78	0.271239	0.135619	−	0.990761i	$-0.456698\pi$
$59$	1.72292e78	0.271239	0.135619	+	0.990761i	$0.456698\pi$
$60$	0	0
$61$	1.90453e79	0.680158	0.340079	−	0.940397i	$-0.389546\pi$
$61$	1.90453e79	0.680158	0.340079	+	0.940397i	$0.389546\pi$
$62$	5.73291e79	0.992990
$63$	0	0
$64$	2.16497e80	0.912942
$65$	−4.99723e79	−0.105702
$66$	0	0
$67$	7.04228e80	0.386709	0.193355	−	0.981129i	$-0.438063\pi$
$67$	7.04228e80	0.386709	0.193355	+	0.981129i	$0.438063\pi$
$68$	3.10640e81	0.882289
$69$	0	0
$70$	−3.34005e81	−0.261150
$71$	1.27373e82	0.529762	0.264881	−	0.964281i	$-0.414667\pi$
$71$	1.27373e82	0.529762	0.264881	+	0.964281i	$0.414667\pi$
$72$	0	0
$73$	−3.75786e82	−0.454018	−0.227009	−	0.973893i	$-0.572895\pi$
$73$	−3.75786e82	−0.454018	−0.227009	+	0.973893i	$0.572895\pi$
$74$	1.25843e83	0.829886
$75$	0	0
$76$	−3.19212e83	−0.642503
$77$	7.85349e82	0.0883538
$78$	0	0
$79$	3.21546e83	0.115568	0.0577840	−	0.998329i	$-0.481597\pi$
$79$	3.21546e83	0.115568	0.0577840	+	0.998329i	$0.481597\pi$
$80$	−5.37472e83	−0.110370
$81$	0	0
$82$	−1.32904e84	−0.0909542
$83$	2.22227e85	0.886793	0.443396	−	0.896326i	$-0.353773\pi$
$83$	2.22227e85	0.886793	0.443396	+	0.896326i	$0.353773\pi$
$84$	0	0
$85$	−5.00207e85	−0.691843
$86$	−8.94344e85	−0.735062
$87$	0	0
$88$	3.30919e85	0.0977783
$89$	5.54352e86	0.990672	0.495336	−	0.868701i	$-0.335045\pi$
$89$	5.54352e86	0.990672	0.495336	+	0.868701i	$0.335045\pi$
$90$	0	0
$91$	−4.10036e86	−0.272571
$92$	−1.48839e87	−0.608355
$93$	0	0
$94$	1.06352e87	0.166939
$95$	5.14011e87	0.503816
$96$	0	0
$97$	4.88818e88	1.89585	0.947927	−	0.318488i	$-0.103175\pi$
$97$	4.88818e88	1.89585	0.947927	+	0.318488i	$0.103175\pi$
$98$	2.01713e87	0.0495647
$99$	0	0
$100$	4.10437e88	0.410437
$101$	−6.30836e88	−0.405150	−0.202575	−	0.979267i	$-0.564931\pi$
$101$	−6.30836e88	−0.405150	−0.202575	+	0.979267i	$0.564931\pi$
$102$	0	0
$103$	−3.95925e89	−1.06257	−0.531284	−	0.847194i	$-0.678290\pi$
$103$	−3.95925e89	−1.06257	−0.531284	+	0.847194i	$0.678290\pi$
$104$	−1.72775e89	−0.301646
$105$	0	0
$106$	4.30589e89	0.322071
$107$	−5.08196e88	−0.0250296	−0.0125148	−	0.999922i	$-0.503984\pi$
$107$	−5.08196e88	−0.0250296	−0.0125148	+	0.999922i	$0.503984\pi$
$108$	0	0
$109$	−3.00179e90	−0.648487	−0.324244	−	0.945974i	$-0.605110\pi$
$109$	−3.00179e90	−0.648487	−0.324244	+	0.945974i	$0.605110\pi$
$110$	−1.72160e89	−0.0247719
$111$	0	0
$112$	−4.41010e90	−0.284608
$113$	1.01787e91	0.442284	0.221142	−	0.975242i	$-0.429022\pi$
$113$	1.01787e91	0.442284	0.221142	+	0.975242i	$0.429022\pi$
$114$	0	0
$115$	2.39667e91	0.477039
$116$	3.31367e91	0.448672
$117$	0	0
$118$	−3.09906e91	−0.196101
$119$	−4.10433e92	−1.78403
$120$	0	0
$121$	−4.78954e92	−0.991619
$122$	−3.42571e92	−0.491743
$123$	0	0
$124$	9.41603e92	0.655546
$125$	−1.42947e93	−0.696110
$126$	0	0
$127$	−3.42465e93	−0.822908	−0.411454	−	0.911431i	$-0.634979\pi$
$127$	−3.42465e93	−0.822908	−0.411454	+	0.911431i	$0.634979\pi$
$128$	1.14937e93	0.194813
$129$	0	0
$130$	8.98861e92	0.0764211
$131$	2.21360e94	1.33821	0.669107	−	0.743166i	$-0.266677\pi$
$131$	2.21360e94	1.33821	0.669107	+	0.743166i	$0.266677\pi$
$132$	0	0
$133$	4.21760e94	1.29917
$134$	−1.26671e94	−0.279585
$135$	0	0
$136$	−1.72942e95	−1.97433
$137$	−1.50357e93	−0.0123896	−0.00619482	−	0.999981i	$-0.501972\pi$
$137$	−1.50357e93	−0.0123896	−0.00619482	+	0.999981i	$0.501972\pi$
$138$	0	0
$139$	1.85854e95	0.803550	0.401775	−	0.915738i	$-0.368393\pi$
$139$	1.85854e95	0.803550	0.401775	+	0.915738i	$0.368393\pi$
$140$	−5.48587e94	−0.172404
$141$	0	0
$142$	−2.29108e95	−0.383009
$143$	−2.11350e94	−0.0258552
$144$	0	0
$145$	−5.33583e95	−0.351824
$146$	6.75933e95	0.328248
$147$	0	0
$148$	2.06691e96	0.547868
$149$	6.69346e96	1.31481	0.657403	−	0.753539i	$-0.271655\pi$
$149$	6.69346e96	1.31481	0.657403	+	0.753539i	$0.271655\pi$
$150$	0	0
$151$	−8.94714e96	−0.970980	−0.485490	−	0.874242i	$-0.661359\pi$
$151$	−8.94714e96	−0.970980	−0.485490	+	0.874242i	$0.661359\pi$
$152$	1.77715e97	1.43775
$153$	0	0
$154$	−1.41262e96	−0.0638784
$155$	−1.51621e97	−0.514043
$156$	0	0
$157$	−7.99466e97	−1.53202	−0.766012	−	0.642826i	$-0.777762\pi$
$157$	−7.99466e97	−1.53202	−0.766012	+	0.642826i	$0.777762\pi$
$158$	−5.78371e96	−0.0835538
$159$	0	0
$160$	−3.87628e97	−0.319945
$161$	1.96653e98	1.23012
$162$	0	0
$163$	8.25331e97	0.298044	0.149022	−	0.988834i	$-0.452388\pi$
$163$	8.25331e97	0.298044	0.149022	+	0.988834i	$0.452388\pi$
$164$	−2.18289e97	−0.0600455
$165$	0	0
$166$	−3.99724e98	−0.641137
$167$	2.58266e98	0.317091	0.158546	−	0.987352i	$-0.449320\pi$
$167$	2.58266e98	0.317091	0.158546	+	0.987352i	$0.449320\pi$
$168$	0	0
$169$	−1.27309e99	−0.920237
$170$	8.99732e98	0.500191
$171$	0	0
$172$	−1.46892e99	−0.485268
$173$	2.87467e99	0.733730	0.366865	−	0.930274i	$-0.380431\pi$
$173$	2.87467e99	0.733730	0.366865	+	0.930274i	$0.380431\pi$
$174$	0	0
$175$	−5.42290e99	−0.829924
$176$	−2.27315e98	−0.0269970
$177$	0	0
$178$	−9.97123e99	−0.716240
$179$	7.10087e99	0.397513	0.198757	−	0.980049i	$-0.436310\pi$
$179$	7.10087e99	0.397513	0.198757	+	0.980049i	$0.436310\pi$
$180$	0	0
$181$	3.14165e100	1.07266	0.536329	−	0.844009i	$-0.319811\pi$
$181$	3.14165e100	1.07266	0.536329	+	0.844009i	$0.319811\pi$
$182$	7.37540e99	0.197065
$183$	0	0
$184$	8.28628e100	1.36134
$185$	−3.32824e100	−0.429608
$186$	0	0
$187$	−2.11555e100	−0.169228
$188$	1.74679e100	0.110209
$189$	0	0
$190$	−9.24561e100	−0.364250
$191$	−1.75148e101	−0.546285	−0.273142	−	0.961974i	$-0.588063\pi$
$191$	−1.75148e101	−0.546285	−0.273142	+	0.961974i	$0.588063\pi$
$192$	0	0
$193$	3.08614e101	0.605502	0.302751	−	0.953070i	$-0.402095\pi$
$193$	3.08614e101	0.605502	0.302751	+	0.953070i	$0.402095\pi$
$194$	−8.79246e101	−1.37067
$195$	0	0
$196$	3.31303e100	0.0327213
$197$	6.10297e101	0.480612	0.240306	−	0.970697i	$-0.422752\pi$
$197$	6.10297e101	0.480612	0.240306	+	0.970697i	$0.422752\pi$
$198$	0	0
$199$	9.92591e100	0.0498665	0.0249332	−	0.999689i	$-0.492063\pi$
$199$	9.92591e100	0.0498665	0.0249332	+	0.999689i	$0.492063\pi$
$200$	−2.28502e102	−0.918450
$201$	0	0
$202$	1.13470e102	0.292917
$203$	−4.37819e102	−0.907238
$204$	0	0
$205$	3.51499e101	0.0470844
$206$	7.12158e102	0.768219
$207$	0	0
$208$	1.18683e102	0.0832856
$209$	2.17393e102	0.123235
$210$	0	0
$211$	−8.33167e102	−0.309145	−0.154573	−	0.987981i	$-0.549400\pi$
$211$	−8.33167e102	−0.309145	−0.154573	+	0.987981i	$0.549400\pi$
$212$	7.07222e102	0.212623
$213$	0	0
$214$	9.14103e101	0.0180960
$215$	2.36532e103	0.380521
$216$	0	0
$217$	−1.24409e104	−1.32555
$218$	5.39938e103	0.468846
$219$	0	0
$220$	−2.82765e102	−0.0163537
$221$	1.10454e104	0.522067
$222$	0	0
$223$	−5.60785e104	−1.77513	−0.887564	−	0.460684i	$-0.847604\pi$
$223$	−5.60785e104	−1.77513	−0.887564	+	0.460684i	$0.847604\pi$
$224$	−3.18059e104	−0.825032
$225$	0	0
$226$	−1.83086e104	−0.319764
$227$	4.37425e104	0.627701	0.313851	−	0.949472i	$-0.398381\pi$
$227$	4.37425e104	0.627701	0.313851	+	0.949472i	$0.398381\pi$
$228$	0	0
$229$	6.98125e104	0.678038	0.339019	−	0.940779i	$-0.389905\pi$
$229$	6.98125e104	0.678038	0.339019	+	0.940779i	$0.389905\pi$
$230$	−4.31093e104	−0.344891
$231$	0	0
$232$	−1.84482e105	−1.00401
$233$	−2.70074e105	−1.21379	−0.606897	−	0.794781i	$-0.707586\pi$
$233$	−2.70074e105	−1.21379	−0.606897	+	0.794781i	$0.707586\pi$
$234$	0	0
$235$	−2.81276e104	−0.0864196
$236$	−5.09005e104	−0.129461
$237$	0	0
$238$	7.38254e105	1.28983
$239$	−8.33363e105	−1.20817	−0.604084	−	0.796920i	$-0.706461\pi$
$239$	−8.33363e105	−1.20817	−0.604084	+	0.796920i	$0.706461\pi$
$240$	0	0
$241$	−1.56610e106	−1.56697	−0.783487	−	0.621408i	$-0.786561\pi$
$241$	−1.56610e106	−1.56697	−0.783487	+	0.621408i	$0.786561\pi$
$242$	8.61504e105	0.716924
$243$	0	0
$244$	−5.62657e105	−0.324636
$245$	−5.33480e104	−0.0256583
$246$	0	0
$247$	−1.13502e106	−0.380181
$248$	−5.24218e106	−1.46694
$249$	0	0
$250$	2.57121e106	0.503276
$251$	1.03640e106	0.169843	0.0849217	−	0.996388i	$-0.472936\pi$
$251$	1.03640e106	0.169843	0.0849217	+	0.996388i	$0.472936\pi$
$252$	0	0
$253$	1.01363e106	0.116686
$254$	6.15999e106	0.594949
$255$	0	0
$256$	−1.54679e107	−1.05379
$257$	−2.59608e107	−1.48694	−0.743471	−	0.668768i	$-0.766822\pi$
$257$	−2.59608e107	−1.48694	−0.743471	+	0.668768i	$0.766822\pi$
$258$	0	0
$259$	−2.73091e107	−1.10782
$260$	1.47634e106	0.0504512
$261$	0	0
$262$	−3.98164e107	−0.967508
$263$	9.18230e107	1.88331	0.941653	−	0.336586i	$-0.109272\pi$
$263$	9.18230e107	1.88331	0.941653	+	0.336586i	$0.109272\pi$
$264$	0	0
$265$	−1.13880e107	−0.166727
$266$	−7.58627e107	−0.939281
$267$	0	0
$268$	−2.08051e107	−0.184574
$269$	4.34307e107	0.326453	0.163227	−	0.986589i	$-0.447810\pi$
$269$	4.34307e107	0.326453	0.163227	+	0.986589i	$0.447810\pi$
$270$	0	0
$271$	−2.01852e107	−0.109119	−0.0545595	−	0.998511i	$-0.517375\pi$
$271$	−2.01852e107	−0.109119	−0.0545595	+	0.998511i	$0.517375\pi$
$272$	1.18798e108	0.545120
$273$	0	0
$274$	2.70450e106	0.00895751
$275$	−2.79519e107	−0.0787239
$276$	0	0
$277$	6.30470e108	1.28622	0.643109	−	0.765774i	$-0.277644\pi$
$277$	6.30470e108	1.28622	0.643109	+	0.765774i	$0.277644\pi$
$278$	−3.34299e108	−0.580954
$279$	0	0
$280$	3.05414e108	0.385795
$281$	−2.21025e108	−0.238238	−0.119119	−	0.992880i	$-0.538007\pi$
$281$	−2.21025e108	−0.238238	−0.119119	+	0.992880i	$0.538007\pi$
$282$	0	0
$283$	−5.73795e108	−0.451087	−0.225544	−	0.974233i	$-0.572416\pi$
$283$	−5.73795e108	−0.451087	−0.225544	+	0.974233i	$0.572416\pi$
$284$	−3.76299e108	−0.252853
$285$	0	0
$286$	3.80159e107	0.0186929
$287$	2.88414e108	0.121415
$288$	0	0
$289$	7.82052e109	2.41703
$290$	9.59766e108	0.254363
$291$	0	0
$292$	1.11019e109	0.216700
$293$	8.06470e109	1.35201	0.676004	−	0.736898i	$-0.263710\pi$
$293$	8.06470e109	1.35201	0.676004	+	0.736898i	$0.263710\pi$
$294$	0	0
$295$	8.19624e108	0.101516
$296$	−1.15071e110	−1.22599
$297$	0	0
$298$	−1.20397e110	−0.950584
$299$	−5.29225e109	−0.359975
$300$	0	0
$301$	1.94081e110	0.981236
$302$	1.60934e110	0.702002
$303$	0	0
$304$	−1.22076e110	−0.396969
$305$	9.06015e109	0.254562
$306$	0	0
$307$	−5.28891e110	−1.11099	−0.555493	−	0.831521i	$-0.687471\pi$
$307$	−5.28891e110	−1.11099	−0.555493	+	0.831521i	$0.687471\pi$
$308$	−2.32016e109	−0.0421708
$309$	0	0
$310$	2.72724e110	0.371645
$311$	1.09333e111	1.29097	0.645484	−	0.763773i	$-0.276656\pi$
$311$	1.09333e111	1.29097	0.645484	+	0.763773i	$0.276656\pi$
$312$	0	0
$313$	4.11236e110	0.365063	0.182531	−	0.983200i	$-0.441571\pi$
$313$	4.11236e110	0.365063	0.182531	+	0.983200i	$0.441571\pi$
$314$	1.43802e111	1.10763
$315$	0	0
$316$	−9.49947e109	−0.0551600
$317$	−1.98612e111	−1.00200	−0.501000	−	0.865447i	$-0.667034\pi$
$317$	−1.98612e111	−1.00200	−0.501000	+	0.865447i	$0.667034\pi$
$318$	0	0
$319$	−2.25671e110	−0.0860577
$320$	1.02991e111	0.341685
$321$	0	0
$322$	−3.53724e111	−0.889360
$323$	−1.13612e112	−2.48836
$324$	0	0
$325$	1.45939e111	0.242863
$326$	−1.48454e111	−0.215481
$327$	0	0
$328$	1.21528e111	0.134366
$329$	−2.30794e111	−0.222847
$330$	0	0
$331$	6.49334e110	0.0478765	0.0239383	−	0.999713i	$-0.492379\pi$
$331$	6.49334e110	0.0478765	0.0239383	+	0.999713i	$0.492379\pi$
$332$	−6.56528e111	−0.423261
$333$	0	0
$334$	−4.64548e111	−0.229252
$335$	3.35013e111	0.144733
$336$	0	0
$337$	−1.31744e112	−0.436718	−0.218359	−	0.975869i	$-0.570070\pi$
$337$	−1.31744e112	−0.436718	−0.218359	+	0.975869i	$0.570070\pi$
$338$	2.28992e112	0.665316
$339$	0	0
$340$	1.47777e112	0.330213
$341$	−6.41259e111	−0.125737
$342$	0	0
$343$	−6.82282e112	−1.03128
$344$	8.17789e112	1.08590
$345$	0	0
$346$	−5.17072e112	−0.530475
$347$	−1.51622e113	−1.36805	−0.684023	−	0.729461i	$-0.739771\pi$
$347$	−1.51622e113	−1.36805	−0.684023	+	0.729461i	$0.739771\pi$
$348$	0	0
$349$	1.52478e113	1.06531	0.532653	−	0.846334i	$-0.321195\pi$
$349$	1.52478e113	1.06531	0.532653	+	0.846334i	$0.321195\pi$
$350$	9.75427e112	0.600021
$351$	0	0
$352$	−1.63941e112	−0.0782600
$353$	2.78663e113	1.17248	0.586239	−	0.810138i	$-0.300608\pi$
$353$	2.78663e113	1.17248	0.586239	+	0.810138i	$0.300608\pi$
$354$	0	0
$355$	6.05934e112	0.198273
$356$	−1.63773e113	−0.472842
$357$	0	0
$358$	−1.27725e113	−0.287396
$359$	5.91157e113	1.17490	0.587448	−	0.809262i	$-0.300133\pi$
$359$	5.91157e113	1.17490	0.587448	+	0.809262i	$0.300133\pi$
$360$	0	0
$361$	5.23201e113	0.812078
$362$	−5.65094e113	−0.775514
$363$	0	0
$364$	1.21137e113	0.130097
$365$	−1.78768e113	−0.169925
$366$	0	0
$367$	−2.85230e113	−0.212596	−0.106298	−	0.994334i	$-0.533900\pi$
$367$	−2.85230e113	−0.212596	−0.106298	+	0.994334i	$0.533900\pi$
$368$	−5.69203e113	−0.375871
$369$	0	0
$370$	5.98657e113	0.310600
$371$	−9.34417e113	−0.429934
$372$	0	0
$373$	4.52146e114	1.63770	0.818852	−	0.574005i	$-0.194611\pi$
$373$	4.52146e114	1.63770	0.818852	+	0.574005i	$0.194611\pi$
$374$	3.80528e113	0.122349
$375$	0	0
$376$	−9.72487e113	−0.246618
$377$	1.17824e114	0.265488
$378$	0	0
$379$	9.92623e113	0.176742	0.0883709	−	0.996088i	$-0.471834\pi$
$379$	9.92623e113	0.176742	0.0883709	+	0.996088i	$0.471834\pi$
$380$	−1.51855e114	−0.240468
$381$	0	0
$382$	3.15041e114	0.394955
$383$	1.05705e115	1.17964	0.589821	−	0.807534i	$-0.299198\pi$
$383$	1.05705e115	1.17964	0.589821	+	0.807534i	$0.299198\pi$
$384$	0	0
$385$	3.73604e113	0.0330680
$386$	−5.55110e114	−0.437768
$387$	0	0
$388$	−1.44412e115	−0.904881
$389$	2.17710e114	0.121653	0.0608263	−	0.998148i	$-0.480626\pi$
$389$	2.17710e114	0.121653	0.0608263	+	0.998148i	$0.480626\pi$
$390$	0	0
$391$	−5.29738e115	−2.35611
$392$	−1.84446e114	−0.0732217
$393$	0	0
$394$	−1.09775e115	−0.347475
$395$	1.52965e114	0.0432535
$396$	0	0
$397$	4.00607e113	0.00904776	0.00452388	−	0.999990i	$-0.498560\pi$
$397$	4.00607e113	0.00904776	0.00452388	+	0.999990i	$0.498560\pi$
$398$	−1.78539e114	−0.0360526
$399$	0	0
$400$	1.56963e115	0.253587
$401$	−6.23287e114	−0.0901080	−0.0450540	−	0.998985i	$-0.514346\pi$
$401$	−6.23287e114	−0.0901080	−0.0450540	+	0.998985i	$0.514346\pi$
$402$	0	0
$403$	3.34806e115	0.387899
$404$	1.86368e115	0.193376
$405$	0	0
$406$	7.87514e115	0.655918
$407$	−1.40763e115	−0.105084
$408$	0	0
$409$	−6.55225e115	−0.393281	−0.196641	−	0.980476i	$-0.563003\pi$
$409$	−6.55225e115	−0.393281	−0.196641	+	0.980476i	$0.563003\pi$
$410$	−6.32248e114	−0.0340413
$411$	0	0
$412$	1.16969e116	0.507158
$413$	6.72523e115	0.261776
$414$	0	0
$415$	1.05717e116	0.331898
$416$	8.55948e115	0.241432
$417$	0	0
$418$	−3.91029e115	−0.0890972
$419$	−3.38221e116	−0.692909	−0.346454	−	0.938067i	$-0.612614\pi$
$419$	−3.38221e116	−0.692909	−0.346454	+	0.938067i	$0.612614\pi$
$420$	0	0
$421$	7.60301e116	1.26018	0.630090	−	0.776522i	$-0.283018\pi$
$421$	7.60301e116	1.26018	0.630090	+	0.776522i	$0.283018\pi$
$422$	1.49863e116	0.223507
$423$	0	0
$424$	−3.93731e116	−0.475794
$425$	1.46080e117	1.58959
$426$	0	0
$427$	7.43410e116	0.656430
$428$	1.50137e115	0.0119465
$429$	0	0
$430$	−4.25454e116	−0.275110
$431$	−1.02975e117	−0.600470	−0.300235	−	0.953865i	$-0.597065\pi$
$431$	−1.02975e117	−0.600470	−0.300235	+	0.953865i	$0.597065\pi$
$432$	0	0
$433$	2.72587e117	1.29358	0.646791	−	0.762668i	$-0.276111\pi$
$433$	2.72587e117	1.29358	0.646791	+	0.762668i	$0.276111\pi$
$434$	2.23777e117	0.958348
$435$	0	0
$436$	8.86823e116	0.309519
$437$	5.44356e117	1.71577
$438$	0	0
$439$	−5.39464e117	−1.38769	−0.693843	−	0.720126i	$-0.744084\pi$
$439$	−5.39464e117	−1.38769	−0.693843	+	0.720126i	$0.744084\pi$
$440$	1.57424e116	0.0365953
$441$	0	0
$442$	−1.98676e117	−0.377446
$443$	−5.69469e117	−0.978372	−0.489186	−	0.872179i	$-0.662706\pi$
$443$	−5.69469e117	−0.978372	−0.489186	+	0.872179i	$0.662706\pi$
$444$	0	0
$445$	2.63714e117	0.370777
$446$	1.00869e118	1.28339
$447$	0	0
$448$	8.45071e117	0.881093
$449$	1.50535e118	1.42126	0.710631	−	0.703565i	$-0.248410\pi$
$449$	1.50535e118	1.42126	0.710631	+	0.703565i	$0.248410\pi$
$450$	0	0
$451$	1.48661e116	0.0115170
$452$	−3.00710e117	−0.211100
$453$	0	0
$454$	−7.86805e117	−0.453818
$455$	−1.95061e117	−0.102015
$456$	0	0
$457$	2.94233e118	1.26596	0.632980	−	0.774168i	$-0.281831\pi$
$457$	2.94233e118	1.26596	0.632980	+	0.774168i	$0.281831\pi$
$458$	−1.25573e118	−0.490211
$459$	0	0
$460$	−7.08050e117	−0.227688
$461$	−1.09403e117	−0.0319402	−0.0159701	−	0.999872i	$-0.505084\pi$
$461$	−1.09403e117	−0.0319402	−0.0159701	+	0.999872i	$0.505084\pi$
$462$	0	0
$463$	−1.51518e118	−0.364847	−0.182423	−	0.983220i	$-0.558394\pi$
$463$	−1.51518e118	−0.364847	−0.182423	+	0.983220i	$0.558394\pi$
$464$	1.26725e118	0.277211
$465$	0	0
$466$	4.85788e118	0.877553
$467$	8.24498e118	1.35391	0.676953	−	0.736026i	$-0.263300\pi$
$467$	8.24498e118	1.35391	0.676953	+	0.736026i	$0.263300\pi$
$468$	0	0
$469$	2.74887e118	0.373219
$470$	5.05936e117	0.0624799
$471$	0	0
$472$	2.83378e118	0.289699
$473$	1.00038e118	0.0930770
$474$	0	0
$475$	−1.50111e119	−1.15757
$476$	1.21255e119	0.851509
$477$	0	0
$478$	1.49899e119	0.873487
$479$	3.05065e119	1.61980	0.809900	−	0.586567i	$-0.199521\pi$
$479$	3.05065e119	1.61980	0.809900	+	0.586567i	$0.199521\pi$
$480$	0	0
$481$	7.34932e118	0.324184
$482$	2.81698e119	1.13290
$483$	0	0
$484$	1.41498e119	0.473294
$485$	2.32539e119	0.709558
$486$	0	0
$487$	−1.88865e118	−0.0479857	−0.0239929	−	0.999712i	$-0.507638\pi$
$487$	−1.88865e118	−0.0479857	−0.0239929	+	0.999712i	$0.507638\pi$
$488$	3.13247e119	0.726449
$489$	0	0
$490$	9.59580e117	0.0185505
$491$	7.35262e119	1.29812	0.649061	−	0.760736i	$-0.275162\pi$
$491$	7.35262e119	1.29812	0.649061	+	0.760736i	$0.275162\pi$
$492$	0	0
$493$	1.17938e120	1.73767
$494$	2.04159e119	0.274865
$495$	0	0
$496$	3.60097e119	0.405028
$497$	4.97186e119	0.511281
$498$	0	0
$499$	1.88248e120	1.61903	0.809515	−	0.587099i	$-0.199730\pi$
$499$	1.88248e120	1.61903	0.809515	+	0.587099i	$0.199730\pi$
$500$	4.22308e119	0.332250
$501$	0	0
$502$	−1.86420e119	−0.122794
$503$	2.65462e119	0.160039	0.0800197	−	0.996793i	$-0.474502\pi$
$503$	2.65462e119	0.160039	0.0800197	+	0.996793i	$0.474502\pi$
$504$	0	0
$505$	−3.00099e119	−0.151635
$506$	−1.82324e119	−0.0843619
$507$	0	0
$508$	1.01175e120	0.392769
$509$	3.57212e120	1.27053	0.635265	−	0.772294i	$-0.280891\pi$
$509$	3.57212e120	1.27053	0.635265	+	0.772294i	$0.280891\pi$
$510$	0	0
$511$	−1.46684e120	−0.438179
$512$	2.07082e120	0.567059
$513$	0	0
$514$	4.66962e120	1.07503
$515$	−1.88348e120	−0.397685
$516$	0	0
$517$	−1.18961e119	−0.0211386
$518$	4.91214e120	0.800934
$519$	0	0
$520$	−8.21919e119	−0.112896
$521$	−9.79424e119	−0.123507	−0.0617535	−	0.998091i	$-0.519669\pi$
$521$	−9.79424e119	−0.123507	−0.0617535	+	0.998091i	$0.519669\pi$
$522$	0	0
$523$	1.44190e120	0.153324	0.0766618	−	0.997057i	$-0.475574\pi$
$523$	1.44190e120	0.153324	0.0766618	+	0.997057i	$0.475574\pi$
$524$	−6.53965e120	−0.638722
$525$	0	0
$526$	−1.65164e121	−1.36160
$527$	3.35130e121	2.53887
$528$	0	0
$529$	9.75813e120	0.624582
$530$	2.04838e120	0.120541
$531$	0	0
$532$	−1.24601e121	−0.620088
$533$	−7.76170e119	−0.0355301
$534$	0	0
$535$	−2.41757e119	−0.00936778
$536$	1.15828e121	0.413029
$537$	0	0
$538$	−7.81197e120	−0.236020
$539$	−2.25627e119	−0.00627612
$540$	0	0
$541$	−3.32756e121	−0.784960	−0.392480	−	0.919761i	$-0.628383\pi$
$541$	−3.32756e121	−0.784960	−0.392480	+	0.919761i	$0.628383\pi$
$542$	3.63076e120	0.0788913
$543$	0	0
$544$	8.56777e121	1.58022
$545$	−1.42800e121	−0.242708
$546$	0	0
$547$	8.03429e121	1.16014	0.580072	−	0.814565i	$-0.303025\pi$
$547$	8.03429e121	1.16014	0.580072	+	0.814565i	$0.303025\pi$
$548$	4.44201e119	0.00591351
$549$	0	0
$550$	5.02776e120	0.0569161
$551$	−1.21193e122	−1.26541
$552$	0	0
$553$	1.25512e121	0.111536
$554$	−1.13404e122	−0.929915
$555$	0	0
$556$	−5.49070e121	−0.383530
$557$	−4.95449e121	−0.319479	−0.159740	−	0.987159i	$-0.551065\pi$
$557$	−4.95449e121	−0.319479	−0.159740	+	0.987159i	$0.551065\pi$
$558$	0	0
$559$	−5.22303e121	−0.287142
$560$	−2.09796e121	−0.106520
$561$	0	0
$562$	3.97562e121	0.172242
$563$	1.54057e122	0.616679	0.308340	−	0.951276i	$-0.400227\pi$
$563$	1.54057e122	0.616679	0.308340	+	0.951276i	$0.400227\pi$
$564$	0	0
$565$	4.84217e121	0.165533
$566$	1.03210e122	0.326129
$567$	0	0
$568$	2.09497e122	0.565818
$569$	5.08576e121	0.127017	0.0635083	−	0.997981i	$-0.479771\pi$
$569$	5.08576e121	0.127017	0.0635083	+	0.997981i	$0.479771\pi$
$570$	0	0
$571$	−6.07440e122	−1.29777	−0.648883	−	0.760888i	$-0.724764\pi$
$571$	−6.07440e122	−1.29777	−0.648883	+	0.760888i	$0.724764\pi$
$572$	6.24394e120	0.0123406
$573$	0	0
$574$	−5.18777e121	−0.0877811
$575$	−6.99922e122	−1.09605
$576$	0	0
$577$	−9.97444e122	−1.33834	−0.669168	−	0.743111i	$-0.733349\pi$
$577$	−9.97444e122	−1.33834	−0.669168	+	0.743111i	$0.733349\pi$
$578$	−1.40669e123	−1.74747
$579$	0	0
$580$	1.57637e122	0.167924
$581$	8.67438e122	0.855856
$582$	0	0
$583$	−4.81638e121	−0.0407822
$584$	−6.18074e122	−0.484919
$585$	0	0
$586$	−1.45061e123	−0.977479
$587$	−3.03625e123	−1.89645	−0.948226	−	0.317595i	$-0.897125\pi$
$587$	−3.03625e123	−1.89645	−0.948226	+	0.317595i	$0.897125\pi$
$588$	0	0
$589$	−3.44378e123	−1.84886
$590$	−1.47427e122	−0.0733945
$591$	0	0
$592$	7.90449e122	0.338499
$593$	−3.31837e123	−1.31823	−0.659114	−	0.752043i	$-0.729069\pi$
$593$	−3.31837e123	−1.31823	−0.659114	+	0.752043i	$0.729069\pi$
$594$	0	0
$595$	−1.95250e123	−0.667707
$596$	−1.97746e123	−0.627550
$597$	0	0
$598$	9.51927e122	0.260256
$599$	4.88132e123	1.23892	0.619460	−	0.785028i	$-0.287352\pi$
$599$	4.88132e123	1.23892	0.619460	+	0.785028i	$0.287352\pi$
$600$	0	0
$601$	6.45254e123	1.41194	0.705970	−	0.708241i	$-0.250511\pi$
$601$	6.45254e123	1.41194	0.705970	+	0.708241i	$0.250511\pi$
$602$	−3.49097e123	−0.709418
$603$	0	0
$604$	2.64326e123	0.463443
$605$	−2.27846e123	−0.371132
$606$	0	0
$607$	−3.71680e123	−0.522724	−0.261362	−	0.965241i	$-0.584172\pi$
$607$	−3.71680e123	−0.522724	−0.261362	+	0.965241i	$0.584172\pi$
$608$	−8.80421e123	−1.15075
$609$	0	0
$610$	−1.62967e123	−0.184044
$611$	6.21104e122	0.0652125
$612$	0	0
$613$	−2.51871e123	−0.228658	−0.114329	−	0.993443i	$-0.536472\pi$
$613$	−2.51871e123	−0.228658	−0.114329	+	0.993443i	$0.536472\pi$
$614$	9.51327e123	0.803225
$615$	0	0
$616$	1.29170e123	0.0943672
$617$	−1.46315e124	−0.994484	−0.497242	−	0.867612i	$-0.665654\pi$
$617$	−1.46315e124	−0.994484	−0.497242	+	0.867612i	$0.665654\pi$
$618$	0	0
$619$	7.24631e123	0.426465	0.213232	−	0.977002i	$-0.431601\pi$
$619$	7.24631e123	0.426465	0.213232	+	0.977002i	$0.431601\pi$
$620$	4.47936e123	0.245350
$621$	0	0
$622$	−1.96660e124	−0.933350
$623$	2.16385e124	0.956111
$624$	0	0
$625$	1.56448e124	0.599391
$626$	−7.39697e123	−0.263935
$627$	0	0
$628$	2.36187e124	0.731227
$629$	7.35644e124	2.12185
$630$	0	0
$631$	−4.53146e124	−1.13483	−0.567416	−	0.823431i	$-0.692057\pi$
$631$	−4.53146e124	−1.13483	−0.567416	+	0.823431i	$0.692057\pi$
$632$	5.28863e123	0.123434
$633$	0	0
$634$	3.57247e124	0.724430
$635$	−1.62916e124	−0.307988
$636$	0	0
$637$	1.17801e123	0.0193618
$638$	4.05918e123	0.0622183
$639$	0	0
$640$	5.46777e123	0.0729124
$641$	7.56055e124	0.940526	0.470263	−	0.882526i	$-0.344159\pi$
$641$	7.56055e124	0.940526	0.470263	+	0.882526i	$0.344159\pi$
$642$	0	0
$643$	−4.06237e124	−0.439937	−0.219969	−	0.975507i	$-0.570596\pi$
$643$	−4.06237e124	−0.439937	−0.219969	+	0.975507i	$0.570596\pi$
$644$	−5.80974e124	−0.587132
$645$	0	0
$646$	2.04356e125	1.79904
$647$	−7.70585e124	−0.633257	−0.316629	−	0.948550i	$-0.602551\pi$
$647$	−7.70585e124	−0.633257	−0.316629	+	0.948550i	$0.602551\pi$
$648$	0	0
$649$	3.46647e123	0.0248313
$650$	−2.62503e124	−0.175586
$651$	0	0
$652$	−2.43828e124	−0.142255
$653$	2.83307e125	1.54391	0.771954	−	0.635678i	$-0.219279\pi$
$653$	2.83307e125	1.54391	0.771954	+	0.635678i	$0.219279\pi$
$654$	0	0
$655$	1.05304e125	0.500851
$656$	−8.34801e123	−0.0370990
$657$	0	0
$658$	4.15134e124	0.161115
$659$	3.52918e125	1.28018	0.640092	−	0.768298i	$-0.278896\pi$
$659$	3.52918e125	1.28018	0.640092	+	0.768298i	$0.278896\pi$
$660$	0	0
$661$	−1.91190e125	−0.606037	−0.303019	−	0.952985i	$-0.597994\pi$
$661$	−1.91190e125	−0.606037	−0.303019	+	0.952985i	$0.597994\pi$
$662$	−1.16797e124	−0.0346139
$663$	0	0
$664$	3.65508e125	0.947148
$665$	2.00638e125	0.486239
$666$	0	0
$667$	−5.65084e125	−1.19816
$668$	−7.62998e124	−0.151346
$669$	0	0
$670$	−6.02594e124	−0.104640
$671$	3.83185e124	0.0622668
$672$	0	0
$673$	−6.51200e125	−0.926924	−0.463462	−	0.886117i	$-0.653393\pi$
$673$	−6.51200e125	−0.926924	−0.463462	+	0.886117i	$0.653393\pi$
$674$	2.36971e125	0.315740
$675$	0	0
$676$	3.76109e125	0.439224
$677$	7.27595e125	0.795599	0.397799	−	0.917472i	$-0.369774\pi$
$677$	7.27595e125	0.795599	0.397799	+	0.917472i	$0.369774\pi$
$678$	0	0
$679$	1.90804e126	1.82971
$680$	−8.22715e125	−0.738930
$681$	0	0
$682$	1.15344e125	0.0909059
$683$	2.25576e126	1.66560	0.832802	−	0.553571i	$-0.186735\pi$
$683$	2.25576e126	1.66560	0.832802	+	0.553571i	$0.186735\pi$
$684$	0	0
$685$	−7.15274e123	−0.00463705
$686$	1.22723e126	0.745597
$687$	0	0
$688$	−5.61757e125	−0.299822
$689$	2.51467e125	0.125813
$690$	0	0
$691$	9.57630e125	0.421138	0.210569	−	0.977579i	$-0.432468\pi$
$691$	9.57630e125	0.421138	0.210569	+	0.977579i	$0.432468\pi$
$692$	−8.49267e125	−0.350205
$693$	0	0
$694$	2.72725e126	0.989075
$695$	8.84137e125	0.300743
$696$	0	0
$697$	−7.76921e125	−0.232551
$698$	−2.74264e126	−0.770199
$699$	0	0
$700$	1.60209e126	0.396118
$701$	−7.40940e126	−1.71922	−0.859610	−	0.510951i	$-0.829293\pi$
$701$	−7.40940e126	−1.71922	−0.859610	+	0.510951i	$0.829293\pi$
$702$	0	0
$703$	−7.55945e126	−1.54518
$704$	4.35586e125	0.0835777
$705$	0	0
$706$	−5.01237e126	−0.847683
$707$	−2.46239e126	−0.391015
$708$	0	0
$709$	5.85411e126	0.819792	0.409896	−	0.912132i	$-0.365565\pi$
$709$	5.85411e126	0.819792	0.409896	+	0.912132i	$0.365565\pi$
$710$	−1.08991e126	−0.143348
$711$	0	0
$712$	9.11770e126	1.05810
$713$	−1.60573e127	−1.75060
$714$	0	0
$715$	−1.00543e125	−0.00967680
$716$	−2.09782e126	−0.189731
$717$	0	0
$718$	−1.06332e127	−0.849431
$719$	8.16889e126	0.613377	0.306689	−	0.951810i	$-0.400779\pi$
$719$	8.16889e126	0.613377	0.306689	+	0.951810i	$0.400779\pi$
$720$	0	0
$721$	−1.54545e127	−1.02550
$722$	−9.41091e126	−0.587119
$723$	0	0
$724$	−9.28141e126	−0.511974
$725$	1.55827e127	0.808356
$726$	0	0
$727$	−3.60710e127	−1.65530	−0.827651	−	0.561243i	$-0.810323\pi$
$727$	−3.60710e127	−1.65530	−0.827651	+	0.561243i	$0.810323\pi$
$728$	−6.74407e126	−0.291122
$729$	0	0
$730$	3.21553e126	0.122853
$731$	−5.22809e127	−1.87940
$732$	0	0
$733$	−1.35200e127	−0.430377	−0.215188	−	0.976573i	$-0.569037\pi$
$733$	−1.35200e127	−0.430377	−0.215188	+	0.976573i	$0.569037\pi$
$734$	5.13048e126	0.153703
$735$	0	0
$736$	−4.10512e127	−1.08959
$737$	1.41689e126	0.0354023
$738$	0	0
$739$	2.74269e127	0.607434	0.303717	−	0.952762i	$-0.401772\pi$
$739$	2.74269e127	0.607434	0.303717	+	0.952762i	$0.401772\pi$
$740$	9.83265e126	0.205050
$741$	0	0
$742$	1.68075e127	0.310835
$743$	3.00345e126	0.0523139	0.0261570	−	0.999658i	$-0.491673\pi$
$743$	3.00345e126	0.0523139	0.0261570	+	0.999658i	$0.491673\pi$
$744$	0	0
$745$	3.18419e127	0.492091
$746$	−8.13283e127	−1.18403
$747$	0	0
$748$	6.24998e126	0.0807714
$749$	−1.98369e126	−0.0241564
$750$	0	0
$751$	7.58766e127	0.820599	0.410299	−	0.911951i	$-0.365424\pi$
$751$	7.58766e127	0.820599	0.410299	+	0.911951i	$0.365424\pi$
$752$	6.68022e126	0.0680922
$753$	0	0
$754$	−2.11933e127	−0.191943
$755$	−4.25630e127	−0.363407
$756$	0	0
$757$	1.94772e128	1.47829	0.739145	−	0.673546i	$-0.235230\pi$
$757$	1.94772e128	1.47829	0.739145	+	0.673546i	$0.235230\pi$
$758$	−1.78545e127	−0.127782
$759$	0	0
$760$	8.45419e127	0.538105
$761$	9.33020e127	0.560111	0.280055	−	0.959984i	$-0.409647\pi$
$761$	9.33020e127	0.560111	0.280055	+	0.959984i	$0.409647\pi$
$762$	0	0
$763$	−1.17171e128	−0.625864
$764$	5.17440e127	0.260739
$765$	0	0
$766$	−1.90134e128	−0.852861
$767$	−1.80987e127	−0.0766043
$768$	0	0
$769$	1.54824e127	0.0583602	0.0291801	−	0.999574i	$-0.490710\pi$
$769$	1.54824e127	0.0583602	0.0291801	+	0.999574i	$0.490710\pi$
$770$	−6.72008e126	−0.0239077
$771$	0	0
$772$	−9.11742e127	−0.289003
$773$	5.49356e127	0.164387	0.0821933	−	0.996616i	$-0.473808\pi$
$773$	5.49356e127	0.164387	0.0821933	+	0.996616i	$0.473808\pi$
$774$	0	0
$775$	4.42794e128	1.18107
$776$	8.03983e128	2.02489
$777$	0	0
$778$	−3.91599e127	−0.0879528
$779$	7.98361e127	0.169349
$780$	0	0
$781$	2.56271e127	0.0484985
$782$	9.52849e128	1.70343
$783$	0	0
$784$	1.26700e127	0.0202168
$785$	−3.80319e128	−0.573388
$786$	0	0
$787$	−3.53123e128	−0.475391	−0.237695	−	0.971340i	$-0.576392\pi$
$787$	−3.53123e128	−0.475391	−0.237695	+	0.971340i	$0.576392\pi$
$788$	−1.80301e128	−0.229393
$789$	0	0
$790$	−2.75141e127	−0.0312716
$791$	3.97313e128	0.426854
$792$	0	0
$793$	−2.00064e128	−0.192093
$794$	−7.20579e126	−0.00654138
$795$	0	0
$796$	−2.93242e127	−0.0238010
$797$	7.97738e127	0.0612301	0.0306151	−	0.999531i	$-0.490253\pi$
$797$	7.97738e127	0.0612301	0.0306151	+	0.999531i	$0.490253\pi$
$798$	0	0
$799$	6.21706e128	0.426828
$800$	1.13203e129	0.735110
$801$	0	0
$802$	1.12112e128	0.0651466
$803$	−7.56070e127	−0.0415643
$804$	0	0
$805$	9.35511e128	0.460397
$806$	−6.02221e128	−0.280444
$807$	0	0
$808$	−1.03757e129	−0.432724
$809$	−1.78703e129	−0.705379	−0.352690	−	0.935740i	$-0.614733\pi$
$809$	−1.78703e129	−0.705379	−0.352690	+	0.935740i	$0.614733\pi$
$810$	0	0
$811$	1.09543e129	0.387396	0.193698	−	0.981061i	$-0.437952\pi$
$811$	1.09543e129	0.387396	0.193698	+	0.981061i	$0.437952\pi$
$812$	1.29345e129	0.433020
$813$	0	0
$814$	2.53193e128	0.0759740
$815$	3.92624e128	0.111548
$816$	0	0
$817$	5.37236e129	1.36862
$818$	1.17857e129	0.284336
$819$	0	0
$820$	−1.03844e128	−0.0224731
$821$	3.64821e129	0.747840	0.373920	−	0.927461i	$-0.378013\pi$
$821$	3.64821e129	0.747840	0.373920	+	0.927461i	$0.378013\pi$
$822$	0	0
$823$	3.97364e129	0.730964	0.365482	−	0.930818i	$-0.380904\pi$
$823$	3.97364e129	0.730964	0.365482	+	0.930818i	$0.380904\pi$
$824$	−6.51198e129	−1.13489
$825$	0	0
$826$	−1.20968e129	−0.189260
$827$	5.47831e129	0.812178	0.406089	−	0.913834i	$-0.366892\pi$
$827$	5.47831e129	0.812178	0.406089	+	0.913834i	$0.366892\pi$
$828$	0	0
$829$	−1.19299e130	−1.58840	−0.794199	−	0.607658i	$-0.792109\pi$
$829$	−1.19299e130	−1.58840	−0.794199	+	0.607658i	$0.792109\pi$
$830$	−1.90155e129	−0.239957
$831$	0	0
$832$	−2.27422e129	−0.257837
$833$	1.17916e129	0.126727
$834$	0	0
$835$	1.22861e129	0.118677
$836$	−6.42246e128	−0.0588196
$837$	0	0
$838$	6.08364e129	0.500962
$839$	9.99439e129	0.780457	0.390228	−	0.920718i	$-0.372396\pi$
$839$	9.99439e129	0.780457	0.390228	+	0.920718i	$0.372396\pi$
$840$	0	0
$841$	−1.65633e129	−0.116339
$842$	−1.36757e130	−0.911089
$843$	0	0
$844$	2.46143e129	0.147553
$845$	−6.05628e129	−0.344415
$846$	0	0
$847$	−1.86954e130	−0.957025
$848$	2.70462e129	0.131369
$849$	0	0
$850$	−2.62757e130	−1.14924
$851$	−3.52473e130	−1.46305
$852$	0	0
$853$	1.76906e130	0.661470	0.330735	−	0.943724i	$-0.392703\pi$
$853$	1.76906e130	0.661470	0.330735	+	0.943724i	$0.392703\pi$
$854$	−1.33719e130	−0.474588
$855$	0	0
$856$	−8.35856e128	−0.0267331
$857$	−4.47933e130	−1.36009	−0.680044	−	0.733171i	$-0.738039\pi$
$857$	−4.47933e130	−1.36009	−0.680044	+	0.733171i	$0.738039\pi$
$858$	0	0
$859$	−4.95328e130	−1.35580	−0.677902	−	0.735152i	$-0.737111\pi$
$859$	−4.95328e130	−1.35580	−0.677902	+	0.735152i	$0.737111\pi$
$860$	−6.98789e129	−0.181620
$861$	0	0
$862$	1.85222e130	0.434130
$863$	−2.69455e129	−0.0599798	−0.0299899	−	0.999550i	$-0.509548\pi$
$863$	−2.69455e129	−0.0599798	−0.0299899	+	0.999550i	$0.509548\pi$
$864$	0	0
$865$	1.36753e130	0.274612
$866$	−4.90307e130	−0.935238
$867$	0	0
$868$	3.67544e130	0.632676
$869$	6.46941e128	0.0105800
$870$	0	0
$871$	−7.39766e129	−0.109216
$872$	−4.93720e130	−0.692623
$873$	0	0
$874$	−9.79144e130	−1.24047
$875$	−5.57975e130	−0.671826
$876$	0	0
$877$	2.89651e130	0.315060	0.157530	−	0.987514i	$-0.449647\pi$
$877$	2.89651e130	0.315060	0.157530	+	0.987514i	$0.449647\pi$
$878$	9.70344e130	1.00327
$879$	0	0
$880$	−1.08138e129	−0.0101041
$881$	1.34623e131	1.19589	0.597944	−	0.801538i	$-0.295985\pi$
$881$	1.34623e131	1.19589	0.597944	+	0.801538i	$0.295985\pi$
$882$	0	0
$883$	−8.82317e130	−0.708554	−0.354277	−	0.935140i	$-0.615273\pi$
$883$	−8.82317e130	−0.708554	−0.354277	+	0.935140i	$0.615273\pi$
$884$	−3.26316e130	−0.249180
$885$	0	0
$886$	1.02431e131	0.707347
$887$	8.56098e130	0.562241	0.281120	−	0.959673i	$-0.409294\pi$
$887$	8.56098e130	0.562241	0.281120	+	0.959673i	$0.409294\pi$
$888$	0	0
$889$	−1.33677e131	−0.794199
$890$	−4.74348e130	−0.268066
$891$	0	0
$892$	1.65673e131	0.847259
$893$	−6.38863e130	−0.310826
$894$	0	0
$895$	3.37800e130	0.148777
$896$	4.48645e130	0.188017
$897$	0	0
$898$	−2.70769e131	−1.02755
$899$	3.57491e131	1.29110
$900$	0	0
$901$	2.51710e131	0.823470
$902$	−2.67400e129	−0.00832664
$903$	0	0
$904$	1.67414e131	0.472386
$905$	1.49453e131	0.401462
$906$	0	0
$907$	5.43134e131	1.32246	0.661230	−	0.750184i	$-0.270035\pi$
$907$	5.43134e131	1.32246	0.661230	+	0.750184i	$0.270035\pi$
$908$	−1.29229e131	−0.299598
$909$	0	0
$910$	3.50860e130	0.0737550
$911$	6.55369e131	1.31195	0.655976	−	0.754782i	$-0.272257\pi$
$911$	6.55369e131	1.31195	0.655976	+	0.754782i	$0.272257\pi$
$912$	0	0
$913$	4.47114e130	0.0811837
$914$	−5.29242e131	−0.915269
$915$	0	0
$916$	−2.06248e131	−0.323624
$917$	8.64052e131	1.29153
$918$	0	0
$919$	3.69672e131	0.501506	0.250753	−	0.968051i	$-0.419322\pi$
$919$	3.69672e131	0.501506	0.250753	+	0.968051i	$0.419322\pi$
$920$	3.94192e131	0.509506
$921$	0	0
$922$	1.96785e130	0.0230922
$923$	−1.33801e131	−0.149618
$924$	0	0
$925$	9.71978e131	0.987073
$926$	2.72539e131	0.263778
$927$	0	0
$928$	9.13946e131	0.803592
$929$	−2.08057e131	−0.174375	−0.0871873	−	0.996192i	$-0.527788\pi$
$929$	−2.08057e131	−0.174375	−0.0871873	+	0.996192i	$0.527788\pi$
$930$	0	0
$931$	−1.21170e131	−0.0922853
$932$	7.97883e131	0.579337
$933$	0	0
$934$	−1.48304e132	−0.978852
$935$	−1.00640e131	−0.0633366
$936$	0	0
$937$	−1.38597e132	−0.793124	−0.396562	−	0.918008i	$-0.629797\pi$
$937$	−1.38597e132	−0.793124	−0.396562	+	0.918008i	$0.629797\pi$
$938$	−4.94445e131	−0.269831
$939$	0	0
$940$	8.30975e130	0.0412476
$941$	−1.36215e132	−0.644890	−0.322445	−	0.946588i	$-0.604505\pi$
$941$	−1.36215e132	−0.644890	−0.322445	+	0.946588i	$0.604505\pi$
$942$	0	0
$943$	3.72250e131	0.160349
$944$	−1.94659e131	−0.0799871
$945$	0	0
$946$	−1.79939e131	−0.0672931
$947$	−1.23478e130	−0.00440572	−0.00220286	−	0.999998i	$-0.500701\pi$
$947$	−1.23478e130	−0.00440572	−0.00220286	+	0.999998i	$0.500701\pi$
$948$	0	0
$949$	3.94749e131	0.128226
$950$	2.70008e132	0.836906
$951$	0	0
$952$	−6.75060e132	−1.90545
$953$	2.21160e130	0.00595762	0.00297881	−	0.999996i	$-0.499052\pi$
$953$	2.21160e130	0.00595762	0.00297881	+	0.999996i	$0.499052\pi$
$954$	0	0
$955$	−8.33206e131	−0.204457
$956$	2.46201e132	0.576652
$957$	0	0
$958$	−5.48726e132	−1.17109
$959$	−5.86901e130	−0.0119574
$960$	0	0
$961$	4.77330e132	0.886396
$962$	−1.32194e132	−0.234380
$963$	0	0
$964$	4.62675e132	0.747908
$965$	1.46813e132	0.226620
$966$	0	0
$967$	1.28780e133	1.81288	0.906440	−	0.422334i	$-0.138789\pi$
$967$	1.28780e133	1.81288	0.906440	+	0.422334i	$0.138789\pi$
$968$	−7.87760e132	−1.05911
$969$	0	0
$970$	−4.18272e132	−0.512999
$971$	−1.86631e132	−0.218639	−0.109320	−	0.994007i	$-0.534867\pi$
$971$	−1.86631e132	−0.218639	−0.109320	+	0.994007i	$0.534867\pi$
$972$	0	0
$973$	7.25459e132	0.775517
$974$	3.39715e131	0.0346929
$975$	0	0
$976$	−2.15176e132	−0.200575
$977$	−1.65586e133	−1.47474	−0.737370	−	0.675489i	$-0.763933\pi$
$977$	−1.65586e133	−1.47474	−0.737370	+	0.675489i	$0.763933\pi$
$978$	0	0
$979$	1.11534e132	0.0906937
$980$	1.57606e131	0.0122465
$981$	0	0
$982$	−1.32253e133	−0.938522
$983$	−2.57060e133	−1.74342	−0.871711	−	0.490021i	$-0.836989\pi$
$983$	−2.57060e133	−1.74342	−0.871711	+	0.490021i	$0.836989\pi$
$984$	0	0
$985$	2.90329e132	0.179878
$986$	−2.12138e133	−1.25631
$987$	0	0
$988$	3.35321e132	0.181458
$989$	2.50496e133	1.29588
$990$	0	0
$991$	−2.75768e133	−1.30397	−0.651984	−	0.758233i	$-0.726063\pi$
$991$	−2.75768e133	−1.30397	−0.651984	+	0.758233i	$0.726063\pi$
$992$	2.59704e133	1.17411
$993$	0	0
$994$	−8.94297e132	−0.369648
$995$	4.72192e131	0.0186634
$996$	0	0
$997$	3.36932e133	1.21789	0.608945	−	0.793213i	$-0.291593\pi$
$997$	3.36932e133	1.21789	0.608945	+	0.793213i	$0.291593\pi$
$998$	−3.38604e133	−1.17053
$999$	0	0

Twists

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

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

\(f(q)\)	\(=\)	\(q-1.79872e13 q^{2} -2.95431e26 q^{4} +4.75717e30 q^{5} +3.90338e37 q^{7} +1.64475e40 q^{8} +O(q^{10})\)	\(q-1.79872e13 q^{2} -2.95431e26 q^{4} +4.75717e30 q^{5} +3.90338e37 q^{7} +1.64475e40 q^{8} -8.55680e43 q^{10} +2.01197e45 q^{11} -1.05046e49 q^{13} -7.02109e50 q^{14} -1.12982e53 q^{16} -1.05148e55 q^{17} +1.08050e57 q^{19} -1.40541e57 q^{20} -3.61897e58 q^{22} +5.03802e60 q^{23} -1.38928e62 q^{25} +1.88949e62 q^{26} -1.15318e64 q^{28} -1.12164e65 q^{29} -3.18722e66 q^{31} -8.14829e66 q^{32} +1.89132e68 q^{34} +1.85690e68 q^{35} -6.99627e69 q^{37} -1.94351e70 q^{38} +7.82435e70 q^{40} +7.38883e70 q^{41} +4.97212e72 q^{43} -5.94398e71 q^{44} -9.06197e73 q^{46} -5.91267e73 q^{47} -1.12142e74 q^{49} +2.49893e75 q^{50} +3.10339e75 q^{52} -2.39386e76 q^{53} +9.57127e75 q^{55} +6.42009e77 q^{56} +2.01752e78 q^{58} +1.72292e78 q^{59} +1.90453e79 q^{61} +5.73291e79 q^{62} +2.16497e80 q^{64} -4.99723e79 q^{65} +7.04228e80 q^{67} +3.10640e81 q^{68} -3.34005e81 q^{70} +1.27373e82 q^{71} -3.75786e82 q^{73} +1.25843e83 q^{74} -3.19212e83 q^{76} +7.85349e82 q^{77} +3.21546e83 q^{79} -5.37472e83 q^{80} -1.32904e84 q^{82} +2.22227e85 q^{83} -5.00207e85 q^{85} -8.94344e85 q^{86} +3.30919e85 q^{88} +5.54352e86 q^{89} -4.10036e86 q^{91} -1.48839e87 q^{92} +1.06352e87 q^{94} +5.14011e87 q^{95} +4.88818e88 q^{97} +2.01713e87 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 31407330351408 q^{2} + 22\!\cdots\!04 q^{4}+ \cdots + 17\!\cdots\!20 q^{8}+O(q^{10}) \) 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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