LMFDB - Embedded newform 9.76.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,76,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, 76, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 76);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 76 $
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:	$320.605553540$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3 x^{5} + \cdots - 67\!\cdots\!50 $ x^6 - 3x^5 - 38457853073924058692x^4 - 10276556354621685339901678086x^3 + 371187556674475060057870954681799784505x^2 + 52686123927652036687598761277591247931691204025*x - 675344021115865838575279495800656435684060652010336995750
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	multiple of $ 2^{58}\cdot 3^{36}\cdot 5^{7}\cdot 7^{3}\cdot 11\cdot 13\cdot 19 $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.19848e9$ 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)

$f(q)$	$=$	$q-2.20777e11 q^{2} +1.09637e22 q^{4} +2.30711e25 q^{5} +1.96027e31 q^{7} +5.92020e33 q^{8} +O(q^{10})$	\(q-2.20777e11 q^{2} +1.09637e22 q^{4} +2.30711e25 q^{5} +1.96027e31 q^{7} +5.92020e33 q^{8} -5.09358e36 q^{10} -9.40509e38 q^{11} +1.14147e42 q^{13} -4.32784e42 q^{14} -1.72124e45 q^{16} -1.79040e46 q^{17} +1.43901e48 q^{19} +2.52945e47 q^{20} +2.07643e50 q^{22} +1.23136e51 q^{23} -2.59375e52 q^{25} -2.52010e53 q^{26} +2.14918e53 q^{28} +2.48097e54 q^{29} +1.95055e55 q^{31} +1.56352e56 q^{32} +3.95280e57 q^{34} +4.52257e56 q^{35} -2.65296e58 q^{37} -3.17702e59 q^{38} +1.36586e59 q^{40} -3.61594e59 q^{41} +8.98859e59 q^{43} -1.03115e61 q^{44} -2.71857e62 q^{46} -2.48355e62 q^{47} -2.02760e63 q^{49} +5.72641e63 q^{50} +1.25147e64 q^{52} -3.59994e64 q^{53} -2.16986e64 q^{55} +1.16052e65 q^{56} -5.47742e65 q^{58} +4.00811e66 q^{59} -1.59203e67 q^{61} -4.30637e66 q^{62} +3.05076e67 q^{64} +2.63349e67 q^{65} +1.61324e68 q^{67} -1.96294e68 q^{68} -9.98480e67 q^{70} -2.63303e69 q^{71} -2.52652e69 q^{73} +5.85713e69 q^{74} +1.57769e70 q^{76} -1.84365e70 q^{77} -9.29901e70 q^{79} -3.97110e70 q^{80} +7.98318e70 q^{82} +7.84087e71 q^{83} -4.13066e71 q^{85} -1.98448e71 q^{86} -5.56800e72 q^{88} -2.05618e73 q^{89} +2.23759e73 q^{91} +1.35003e73 q^{92} +5.48312e73 q^{94} +3.31997e73 q^{95} -4.10454e74 q^{97} +4.47648e74 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 57080822040 q^{2} + 17\!\cdots\!28 q^{4}+ \cdots - 44\!\cdots\!20 q^{8}+O(q^{10}) $ 6 * q + 57080822040 * q^2 + 172600466200162028593728 * q^4 + 38982947396479621874420940 * q^5 + 1924474634802918779239478643600 * q^7 - 4434903997968330342413437320645120 * q^8	$ 6 q + 57080822040 q^{2} + 17\!\cdots\!28 q^{4}+ \cdots + 16\!\cdots\!20 q^{98}+O(q^{100}) $ 6 * q + 57080822040 * q^2 + 172600466200162028593728 * q^4 + 38982947396479621874420940 * q^5 + 1924474634802918779239478643600 * q^7 - 4434903997968330342413437320645120 * q^8 + 133267935677460241037537052811576902960 * q^10 + 945659951949983071650740113735111214088 * q^11 + 533185179266852519941169625089098069764420 * q^13 - 8213946953162263647781694565284746353072576 * q^14 + 2681978005634517266622433394712415602648354816 * q^16 - 18261354095776132566172834671579513215483393580 * q^17 + 1061534856238354155312794852768417904375328867080 * q^19 - 9296557595621768320156983882258818695571369489280 * q^20 + 153315952874260268106194796405555863940172791589920 * q^22 - 1514929449877410771078348320690686508954384916853680 * q^23 + 19310380328261093150952553553121815533899364092239850 * q^25 - 117730941166816926498584842564210483616872200198362352 * q^26 + 1465885017268620651444113586751990931877154821040657920 * q^28 - 14718767377678125816030788545177391174717388984245534820 * q^29 - 41742874787360498453628839393549579933009794702042980288 * q^31 - 1174660148719991756036751189163540495635749096221862952960 * q^32 + 3034358950124956876257603978888653679838045546922892395856 * q^34 - 27299672493656883988453292135086250689495956464846953371360 * q^35 + 98517772547646219221591850851651469983797181732879949140340 * q^37 - 1257660981102762853948269222064665311191946222029530979162080 * q^38 + 8807901623729426290853411185831313455271917763097593104051200 * q^40 - 5039211762207387369185984529408567568647239506257650214613212 * q^41 + 27938749238581541451173935836639198120068956697568041153196600 * q^43 + 86388814623354110240559749283671522466589238091463431115801344 * q^44 - 824145803870667307795487213022331547039596870954611528203613888 * q^46 + 1386854970430427381646742231466788117324292253074354560479038880 * q^47 - 5707868790800975784856935495088511133239544554833878775910738442 * q^49 - 3144970672685230615695776810799603542575044196614572896663392600 * q^50 + 41677832028141179840113326797899392222702339479233001780216150400 * q^52 - 64283727174659970247345252518647455744441825702701764187054106260 * q^53 + 436876078674971654403803167180324983329224614451635548418098895120 * q^55 - 289950797286325881623798664040853221823087783432246887785270865920 * q^56 - 1763005756244374137396902189067511762184157619699352574614137403280 * q^58 + 2478360370933764187935912640189307752170553390931716617591182395560 * q^59 - 25641115321477658815889269525514418267074652297034046321782023152988 * q^61 + 29014701474354643819936101890527484086880802356768235703173807694080 * q^62 + 47683232974651133862719671893097862706511055838864188064811716968448 * q^64 - 122110621788131890149667214965152432737153070969379698276880591977720 * q^65 + 955579073553339181030887342220313909838725364297810737998207107813480 * q^67 - 1237210897217068882936524414359446185548686871817993659403939290386560 * q^68 - 3476902593928340346610001926714053112321275314411181267396530677050240 * q^70 + 255682319306096297182489045146623979225804710540351927309367569173488 * q^71 - 30605188898291905719532895918028188508004452865621142257485594115042020 * q^73 + 24065024027894599201472448362529876891121294631891709256708009194181584 * q^74 + 100020936372377387464010564774983213070641689274186088752725827576144640 * q^76 - 158930415774536768880543239288689183540801263714134710336228496440507200 * q^77 + 116627678166642324332643069323234092884951450625988452824960767925148320 * q^79 - 1239310052714502333188756625709169306278438274940582996524184215206748160 * q^80 - 2557649813228840791149140948716215474705151452500921688788291587877236080 * q^82 + 798780284119889426515570523310162377392459257634002033911814028088739960 * q^83 - 3615500806340871685633297735534398118961343923835923286123685237305018840 * q^85 - 7245194180836090971883743617494948296636529538939897523257528311698092832 * q^86 - 4827001398586167572057494186308233100206033194553368013345656010632181760 * q^88 - 53575610216125238704584826863934604186542249469498220298044079954014547260 * q^89 + 34502419684367451829908407139028781594042460695428817715772307436403470432 * q^91 - 187445224353587479072026786339601818260697439565538078689222489106585838080 * q^92 - 296189325151987924691405038954735773676385503565643130818482899021002578304 * q^94 - 194934959385332686251927514630723902507701573195047654345319995220933314800 * q^95 - 747928220344118582344222376208028579242743608466383778453296378427532508980 * q^97 + 1663265696927109513221859402309517858944410070626232817304447619248634722520 * 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 $

$2$	−2.20777e11	−1.13587	−0.567936	−	0.823072i	$-0.692258\pi$
$2$	−2.20777e11	−1.13587	−0.567936	+	0.823072i	$0.692258\pi$
$3$	0	0
$3$	0	0
$4$	1.09637e22	0.290207
$5$	2.30711e25	0.141806	0.0709028	−	0.997483i	$-0.477412\pi$
$5$	2.30711e25	0.141806	0.0709028	+	0.997483i	$0.477412\pi$
$6$	0	0
$7$	1.96027e31	0.399153	0.199577	−	0.979882i	$-0.436043\pi$
$7$	1.96027e31	0.399153	0.199577	+	0.979882i	$0.436043\pi$
$8$	5.92020e33	0.806235
$9$	0	0
$10$	−5.09358e36	−0.161073
$11$	−9.40509e38	−0.833945	−0.416972	−	0.908919i	$-0.636909\pi$
$11$	−9.40509e38	−0.833945	−0.416972	+	0.908919i	$0.636909\pi$
$12$	0	0
$13$	1.14147e42	1.92570	0.962848	−	0.270042i	$-0.0870377\pi$
$13$	1.14147e42	1.92570	0.962848	+	0.270042i	$0.0870377\pi$
$14$	−4.32784e42	−0.453387
$15$	0	0
$16$	−1.72124e45	−1.20599
$17$	−1.79040e46	−1.29156	−0.645782	−	0.763522i	$-0.723469\pi$
$17$	−1.79040e46	−1.29156	−0.645782	+	0.763522i	$0.723469\pi$
$18$	0	0
$19$	1.43901e48	1.60253	0.801263	−	0.598312i	$-0.204162\pi$
$19$	1.43901e48	1.60253	0.801263	+	0.598312i	$0.204162\pi$
$20$	2.52945e47	0.0411529
$21$	0	0
$22$	2.07643e50	0.947255
$23$	1.23136e51	1.06070	0.530349	−	0.847779i	$-0.322061\pi$
$23$	1.23136e51	1.06070	0.530349	+	0.847779i	$0.322061\pi$
$24$	0	0
$25$	−2.59375e52	−0.979891
$26$	−2.52010e53	−2.18735
$27$	0	0
$28$	2.14918e53	0.115837
$29$	2.48097e54	0.358671	0.179336	−	0.983788i	$-0.442605\pi$
$29$	2.48097e54	0.358671	0.179336	+	0.983788i	$0.442605\pi$
$30$	0	0
$31$	1.95055e55	0.231256	0.115628	−	0.993293i	$-0.463112\pi$
$31$	1.95055e55	0.231256	0.115628	+	0.993293i	$0.463112\pi$
$32$	1.56352e56	0.563613
$33$	0	0
$34$	3.95280e57	1.46705
$35$	4.52257e56	0.0566022
$36$	0	0
$37$	−2.65296e58	−0.413205	−0.206603	−	0.978425i	$-0.566241\pi$
$37$	−2.65296e58	−0.413205	−0.206603	+	0.978425i	$0.566241\pi$
$38$	−3.17702e59	−1.82027
$39$	0	0
$40$	1.36586e59	0.114329
$41$	−3.61594e59	−0.119902	−0.0599511	−	0.998201i	$-0.519094\pi$
$41$	−3.61594e59	−0.119902	−0.0599511	+	0.998201i	$0.519094\pi$
$42$	0	0
$43$	8.98859e59	0.0499603	0.0249801	−	0.999688i	$-0.492048\pi$
$43$	8.98859e59	0.0499603	0.0249801	+	0.999688i	$0.492048\pi$
$44$	−1.03115e61	−0.242016
$45$	0	0
$46$	−2.71857e62	−1.20482
$47$	−2.48355e62	−0.491364	−0.245682	−	0.969350i	$-0.579012\pi$
$47$	−2.48355e62	−0.491364	−0.245682	+	0.969350i	$0.579012\pi$
$48$	0	0
$49$	−2.02760e63	−0.840677
$50$	5.72641e63	1.11303
$51$	0	0
$52$	1.25147e64	0.558850
$53$	−3.59994e64	−0.786955	−0.393477	−	0.919334i	$-0.628728\pi$
$53$	−3.59994e64	−0.786955	−0.393477	+	0.919334i	$0.628728\pi$
$54$	0	0
$55$	−2.16986e64	−0.118258
$56$	1.16052e65	0.321811
$57$	0	0
$58$	−5.47742e65	−0.407405
$59$	4.00811e66	1.57032	0.785162	−	0.619291i	$-0.212580\pi$
$59$	4.00811e66	1.57032	0.785162	+	0.619291i	$0.212580\pi$
$60$	0	0
$61$	−1.59203e67	−1.78683	−0.893413	−	0.449237i	$-0.851696\pi$
$61$	−1.59203e67	−1.78683	−0.893413	+	0.449237i	$0.851696\pi$
$62$	−4.30637e66	−0.262678
$63$	0	0
$64$	3.05076e67	0.565795
$65$	2.63349e67	0.273075
$66$	0	0
$67$	1.61324e68	0.536900	0.268450	−	0.963294i	$-0.413489\pi$
$67$	1.61324e68	0.536900	0.268450	+	0.963294i	$0.413489\pi$
$68$	−1.96294e68	−0.374821
$69$	0	0
$70$	−9.98480e67	−0.0642929
$71$	−2.63303e69	−0.996020	−0.498010	−	0.867171i	$-0.665936\pi$
$71$	−2.63303e69	−0.996020	−0.498010	+	0.867171i	$0.665936\pi$
$72$	0	0
$73$	−2.52652e69	−0.337221	−0.168611	−	0.985683i	$-0.553928\pi$
$73$	−2.52652e69	−0.337221	−0.168611	+	0.985683i	$0.553928\pi$
$74$	5.85713e69	0.469348
$75$	0	0
$76$	1.57769e70	0.465064
$77$	−1.84365e70	−0.332872
$78$	0	0
$79$	−9.29901e70	−0.641831	−0.320916	−	0.947108i	$-0.603991\pi$
$79$	−9.29901e70	−0.641831	−0.320916	+	0.947108i	$0.603991\pi$
$80$	−3.97110e70	−0.171016
$81$	0	0
$82$	7.98318e70	0.136194
$83$	7.84087e71	0.849055	0.424528	−	0.905415i	$-0.360440\pi$
$83$	7.84087e71	0.849055	0.424528	+	0.905415i	$0.360440\pi$
$84$	0	0
$85$	−4.13066e71	−0.183151
$86$	−1.98448e71	−0.0567485
$87$	0	0
$88$	−5.56800e72	−0.672355
$89$	−2.05618e73	−1.62531	−0.812656	−	0.582744i	$-0.801979\pi$
$89$	−2.05618e73	−1.62531	−0.812656	+	0.582744i	$0.801979\pi$
$90$	0	0
$91$	2.23759e73	0.768648
$92$	1.35003e73	0.307822
$93$	0	0
$94$	5.48312e73	0.558127
$95$	3.31997e73	0.227247
$96$	0	0
$97$	−4.10454e74	−1.28625	−0.643123	−	0.765763i	$-0.722362\pi$
$97$	−4.10454e74	−1.28625	−0.643123	+	0.765763i	$0.722362\pi$
$98$	4.47648e74	0.954902
$99$	0	0
$100$	−2.84371e74	−0.284371
$101$	−1.81290e75	−1.24831	−0.624154	−	0.781302i	$-0.714556\pi$
$101$	−1.81290e75	−1.24831	−0.624154	+	0.781302i	$0.714556\pi$
$102$	0	0
$103$	−1.54416e75	−0.509677	−0.254839	−	0.966984i	$-0.582022\pi$
$103$	−1.54416e75	−0.509677	−0.254839	+	0.966984i	$0.582022\pi$
$104$	6.75771e75	1.55256
$105$	0	0
$106$	7.94784e75	0.893880
$107$	4.90777e73	0.00388144	0.00194072	−	0.999998i	$-0.499382\pi$
$107$	4.90777e73	0.00388144	0.00194072	+	0.999998i	$0.499382\pi$
$108$	0	0
$109$	−1.45643e76	−0.575171	−0.287586	−	0.957755i	$-0.592853\pi$
$109$	−1.45643e76	−0.575171	−0.287586	+	0.957755i	$0.592853\pi$
$110$	4.79056e75	0.134326
$111$	0	0
$112$	−3.37410e76	−0.481374
$113$	1.13049e77	1.15564	0.577822	−	0.816163i	$-0.303903\pi$
$113$	1.13049e77	1.15564	0.577822	+	0.816163i	$0.303903\pi$
$114$	0	0
$115$	2.84089e76	0.150413
$116$	2.72006e76	0.104089
$117$	0	0
$118$	−8.84899e77	−1.78369
$119$	−3.50968e77	−0.515532
$120$	0	0
$121$	−3.87338e77	−0.304536
$122$	3.51484e78	2.02961
$123$	0	0
$124$	2.13852e77	0.0671121
$125$	−1.20909e78	−0.280760
$126$	0	0
$127$	1.39623e78	0.178779	0.0893894	−	0.995997i	$-0.471508\pi$
$127$	1.39623e78	0.178779	0.0893894	+	0.995997i	$0.471508\pi$
$128$	−1.26422e79	−1.20628
$129$	0	0
$130$	−5.81416e78	−0.310178
$131$	3.06227e79	1.22566	0.612830	−	0.790215i	$-0.290031\pi$
$131$	3.06227e79	1.22566	0.612830	+	0.790215i	$0.290031\pi$
$132$	0	0
$133$	2.82086e79	0.639654
$134$	−3.56167e79	−0.609850
$135$	0	0
$136$	−1.05995e80	−1.04130
$137$	1.01580e80	0.758207	0.379103	−	0.925354i	$-0.376232\pi$
$137$	1.01580e80	0.758207	0.379103	+	0.925354i	$0.376232\pi$
$138$	0	0
$139$	2.74853e80	1.19137	0.595684	−	0.803219i	$-0.296881\pi$
$139$	2.74853e80	1.19137	0.595684	+	0.803219i	$0.296881\pi$
$140$	4.95840e78	0.0164263
$141$	0	0
$142$	5.81314e80	1.13135
$143$	−1.07356e81	−1.60592
$144$	0	0
$145$	5.72387e79	0.0508616
$146$	5.57798e80	0.383041
$147$	0	0
$148$	−2.90862e80	−0.119915
$149$	−3.12728e81	−1.00157	−0.500786	−	0.865571i	$-0.666955\pi$
$149$	−3.12728e81	−1.00157	−0.500786	+	0.865571i	$0.666955\pi$
$150$	0	0
$151$	3.88189e81	0.754062	0.377031	−	0.926201i	$-0.376945\pi$
$151$	3.88189e81	0.754062	0.377031	+	0.926201i	$0.376945\pi$
$152$	8.51925e81	1.29201
$153$	0	0
$154$	4.07037e81	0.378100
$155$	4.50014e80	0.0327934
$156$	0	0
$157$	−3.39510e81	−0.152973	−0.0764867	−	0.997071i	$-0.524370\pi$
$157$	−3.39510e81	−0.152973	−0.0764867	+	0.997071i	$0.524370\pi$
$158$	2.05301e82	0.729039
$159$	0	0
$160$	3.60723e81	0.0799234
$161$	2.41380e82	0.423381
$162$	0	0
$163$	8.90306e82	0.982888	0.491444	−	0.870909i	$-0.336469\pi$
$163$	8.90306e82	0.982888	0.491444	+	0.870909i	$0.336469\pi$
$164$	−3.96441e81	−0.0347964
$165$	0	0
$166$	−1.73109e83	−0.964419
$167$	3.38631e83	1.50612	0.753059	−	0.657952i	$-0.228577\pi$
$167$	3.38631e83	1.50612	0.753059	+	0.657952i	$0.228577\pi$
$168$	0	0
$169$	9.51589e83	2.70831
$170$	9.11956e82	0.208036
$171$	0	0
$172$	9.85482e81	0.0144988
$173$	−4.90633e83	−0.580801	−0.290401	−	0.956905i	$-0.593789\pi$
$173$	−4.90633e83	−0.580801	−0.290401	+	0.956905i	$0.593789\pi$
$174$	0	0
$175$	−5.08446e83	−0.391127
$176$	1.61884e84	1.00573
$177$	0	0
$178$	4.53959e84	1.84615
$179$	1.46434e84	0.482674	0.241337	−	0.970441i	$-0.422414\pi$
$179$	1.46434e84	0.482674	0.241337	+	0.970441i	$0.422414\pi$
$180$	0	0
$181$	5.14219e84	1.11738	0.558691	−	0.829376i	$-0.311304\pi$
$181$	5.14219e84	1.11738	0.558691	+	0.829376i	$0.311304\pi$
$182$	−4.94009e84	−0.873087
$183$	0	0
$184$	7.28990e84	0.855172
$185$	−6.12067e83	−0.0585948
$186$	0	0
$187$	1.68389e85	1.07709
$188$	−2.72289e84	−0.142597
$189$	0	0
$190$	−7.32973e84	−0.258124
$191$	3.57215e85	1.03318	0.516592	−	0.856231i	$-0.327200\pi$
$191$	3.57215e85	1.03318	0.516592	+	0.856231i	$0.327200\pi$
$192$	0	0
$193$	9.29438e84	0.181895	0.0909476	−	0.995856i	$-0.471010\pi$
$193$	9.29438e84	0.181895	0.0909476	+	0.995856i	$0.471010\pi$
$194$	9.06189e85	1.46101
$195$	0	0
$196$	−2.22300e85	−0.243970
$197$	−5.56745e85	−0.504862	−0.252431	−	0.967615i	$-0.581230\pi$
$197$	−5.56745e85	−0.504862	−0.252431	+	0.967615i	$0.581230\pi$
$198$	0	0
$199$	−2.63184e86	−1.63407	−0.817033	−	0.576591i	$-0.804382\pi$
$199$	−2.63184e86	−1.63407	−0.817033	+	0.576591i	$0.804382\pi$
$200$	−1.53555e86	−0.790022
$201$	0	0
$202$	4.00247e86	1.41792
$203$	4.86337e85	0.143165
$204$	0	0
$205$	−8.34238e84	−0.0170028
$206$	3.40915e86	0.578928
$207$	0	0
$208$	−1.96474e87	−2.32237
$209$	−1.35341e87	−1.33642
$210$	0	0
$211$	−5.62170e86	−0.388397	−0.194199	−	0.980962i	$-0.562211\pi$
$211$	−5.62170e86	−0.388397	−0.194199	+	0.980962i	$0.562211\pi$
$212$	−3.94686e86	−0.228379
$213$	0	0
$214$	−1.08353e85	−0.00440882
$215$	2.07377e85	0.00708465
$216$	0	0
$217$	3.82361e86	0.0923067
$218$	3.21548e87	0.653321
$219$	0	0
$220$	−2.37897e86	−0.0343193
$221$	−2.04369e88	−2.48716
$222$	0	0
$223$	2.95997e87	0.256954	0.128477	−	0.991712i	$-0.458991\pi$
$223$	2.95997e87	0.256954	0.128477	+	0.991712i	$0.458991\pi$
$224$	3.06493e87	0.224968
$225$	0	0
$226$	−2.49586e88	−1.31266
$227$	1.99529e88	0.889275	0.444638	−	0.895711i	$-0.353332\pi$
$227$	1.99529e88	0.889275	0.444638	+	0.895711i	$0.353332\pi$
$228$	0	0
$229$	6.29641e87	0.201959	0.100979	−	0.994889i	$-0.467802\pi$
$229$	6.29641e87	0.201959	0.100979	+	0.994889i	$0.467802\pi$
$230$	−6.27204e87	−0.170850
$231$	0	0
$232$	1.46878e88	0.289173
$233$	9.92233e87	0.166252	0.0831260	−	0.996539i	$-0.473510\pi$
$233$	9.92233e87	0.166252	0.0831260	+	0.996539i	$0.473510\pi$
$234$	0	0
$235$	−5.72983e87	−0.0696783
$236$	4.39437e88	0.455718
$237$	0	0
$238$	7.74857e88	0.585579
$239$	1.09445e89	0.706764	0.353382	−	0.935479i	$-0.385032\pi$
$239$	1.09445e89	0.706764	0.353382	+	0.935479i	$0.385032\pi$
$240$	0	0
$241$	−3.43159e88	−0.162127	−0.0810636	−	0.996709i	$-0.525832\pi$
$241$	−3.43159e88	−0.162127	−0.0810636	+	0.996709i	$0.525832\pi$
$242$	8.55155e88	0.345914
$243$	0	0
$244$	−1.74545e89	−0.518549
$245$	−4.67790e88	−0.119213
$246$	0	0
$247$	1.64259e90	3.08598
$248$	1.15476e89	0.186447
$249$	0	0
$250$	2.66941e89	0.318907
$251$	−3.39159e89	−0.348851	−0.174425	−	0.984670i	$-0.555807\pi$
$251$	−3.39159e89	−0.348851	−0.174425	+	0.984670i	$0.555807\pi$
$252$	0	0
$253$	−1.15811e90	−0.884564
$254$	−3.08255e89	−0.203070
$255$	0	0
$256$	1.63857e90	0.804389
$257$	4.75773e89	0.201794	0.100897	−	0.994897i	$-0.467829\pi$
$257$	4.75773e89	0.201794	0.100897	+	0.994897i	$0.467829\pi$
$258$	0	0
$259$	−5.20052e89	−0.164932
$260$	2.88728e89	0.0792481
$261$	0	0
$262$	−6.76080e90	−1.39219
$263$	−2.04074e90	−0.364289	−0.182145	−	0.983272i	$-0.558304\pi$
$263$	−2.04074e90	−0.364289	−0.182145	+	0.983272i	$0.558304\pi$
$264$	0	0
$265$	−8.30546e89	−0.111595
$266$	−6.22782e90	−0.726565
$267$	0	0
$268$	1.76871e90	0.155812
$269$	−1.37778e91	−1.05553	−0.527764	−	0.849391i	$-0.676969\pi$
$269$	−1.37778e91	−1.05553	−0.527764	+	0.849391i	$0.676969\pi$
$270$	0	0
$271$	−7.60957e90	−0.441582	−0.220791	−	0.975321i	$-0.570864\pi$
$271$	−7.60957e90	−0.441582	−0.220791	+	0.975321i	$0.570864\pi$
$272$	3.08172e91	1.55761
$273$	0	0
$274$	−2.24266e91	−0.861226
$275$	2.43945e91	0.817175
$276$	0	0
$277$	−4.78450e91	−1.22136	−0.610682	−	0.791876i	$-0.709105\pi$
$277$	−4.78450e91	−1.22136	−0.610682	+	0.791876i	$0.709105\pi$
$278$	−6.06814e91	−1.35324
$279$	0	0
$280$	2.67745e90	0.0456347
$281$	−1.67133e91	−0.249215	−0.124608	−	0.992206i	$-0.539767\pi$
$281$	−1.67133e91	−0.249215	−0.124608	+	0.992206i	$0.539767\pi$
$282$	0	0
$283$	−1.00325e92	−1.14662	−0.573310	−	0.819339i	$-0.694341\pi$
$283$	−1.00325e92	−1.14662	−0.573310	+	0.819339i	$0.694341\pi$
$284$	−2.88678e91	−0.289052
$285$	0	0
$286$	2.37018e92	1.82413
$287$	−7.08823e90	−0.0478593
$288$	0	0
$289$	1.28391e92	0.668138
$290$	−1.26370e91	−0.0577723
$291$	0	0
$292$	−2.77000e91	−0.0978639
$293$	−3.51636e92	−1.09284	−0.546421	−	0.837511i	$-0.684010\pi$
$293$	−3.51636e92	−1.09284	−0.546421	+	0.837511i	$0.684010\pi$
$294$	0	0
$295$	9.24715e91	0.222681
$296$	−1.57060e92	−0.333140
$297$	0	0
$298$	6.90433e92	1.13766
$299$	1.40556e93	2.04258
$300$	0	0
$301$	1.76201e91	0.0199418
$302$	−8.57032e92	−0.856519
$303$	0	0
$304$	−2.47689e93	−1.93263
$305$	−3.67299e92	−0.253382
$306$	0	0
$307$	2.83130e93	1.52861	0.764305	−	0.644855i	$-0.223082\pi$
$307$	2.83130e93	1.52861	0.764305	+	0.644855i	$0.223082\pi$
$308$	−2.02133e92	−0.0966016
$309$	0	0
$310$	−9.93528e91	−0.0372492
$311$	1.00581e93	0.334196	0.167098	−	0.985940i	$-0.446560\pi$
$311$	1.00581e93	0.334196	0.167098	+	0.985940i	$0.446560\pi$
$312$	0	0
$313$	−3.95730e93	−1.03392	−0.516959	−	0.856010i	$-0.672936\pi$
$313$	−3.95730e93	−1.03392	−0.516959	+	0.856010i	$0.672936\pi$
$314$	7.49562e92	0.173758
$315$	0	0
$316$	−1.01952e93	−0.186264
$317$	−1.02388e94	−1.66161	−0.830804	−	0.556565i	$-0.812119\pi$
$317$	−1.02388e94	−1.66161	−0.830804	+	0.556565i	$0.812119\pi$
$318$	0	0
$319$	−2.33337e93	−0.299112
$320$	7.03844e92	0.0802329
$321$	0	0
$322$	−5.32913e93	−0.480907
$323$	−2.57641e94	−2.06977
$324$	0	0
$325$	−2.96068e94	−1.88697
$326$	−1.96559e94	−1.11644
$327$	0	0
$328$	−2.14071e93	−0.0966693
$329$	−4.86844e93	−0.196130
$330$	0	0
$331$	4.19453e94	1.34627	0.673137	−	0.739518i	$-0.264947\pi$
$331$	4.19453e94	1.34627	0.673137	+	0.739518i	$0.264947\pi$
$332$	8.59650e93	0.246402
$333$	0	0
$334$	−7.47621e94	−1.71076
$335$	3.72192e93	0.0761355
$336$	0	0
$337$	−1.23784e94	−0.202554	−0.101277	−	0.994858i	$-0.532293\pi$
$337$	−1.23784e94	−0.202554	−0.101277	+	0.994858i	$0.532293\pi$
$338$	−2.10089e95	−3.07629
$339$	0	0
$340$	−4.52873e93	−0.0531517
$341$	−1.83451e94	−0.192855
$342$	0	0
$343$	−8.70256e94	−0.734712
$344$	5.32142e93	0.0402797
$345$	0	0
$346$	1.08321e95	0.659716
$347$	7.20855e93	0.0393996	0.0196998	−	0.999806i	$-0.493729\pi$
$347$	7.20855e93	0.0393996	0.0196998	+	0.999806i	$0.493729\pi$
$348$	0	0
$349$	−1.02804e95	−0.452958	−0.226479	−	0.974016i	$-0.572721\pi$
$349$	−1.02804e95	−0.452958	−0.226479	+	0.974016i	$0.572721\pi$
$350$	1.12253e95	0.444270
$351$	0	0
$352$	−1.47051e95	−0.470022
$353$	−2.67413e95	−0.768477	−0.384239	−	0.923234i	$-0.625536\pi$
$353$	−2.67413e95	−0.768477	−0.384239	+	0.923234i	$0.625536\pi$
$354$	0	0
$355$	−6.07470e94	−0.141241
$356$	−2.25434e95	−0.471676
$357$	0	0
$358$	−3.23294e95	−0.548257
$359$	−7.10202e95	−1.08478	−0.542388	−	0.840128i	$-0.682480\pi$
$359$	−7.10202e95	−1.08478	−0.542388	+	0.840128i	$0.682480\pi$
$360$	0	0
$361$	1.26442e96	1.56809
$362$	−1.13528e96	−1.26920
$363$	0	0
$364$	2.45322e95	0.223067
$365$	−5.82896e94	−0.0478199
$366$	0	0
$367$	−1.75912e96	−1.17576	−0.587878	−	0.808950i	$-0.700036\pi$
$367$	−1.75912e96	−1.17576	−0.587878	+	0.808950i	$0.700036\pi$
$368$	−2.11947e96	−1.27919
$369$	0	0
$370$	1.35130e95	0.0665562
$371$	−7.05685e95	−0.314116
$372$	0	0
$373$	−3.67079e96	−1.33561	−0.667803	−	0.744338i	$-0.732765\pi$
$373$	−3.67079e96	−1.33561	−0.667803	+	0.744338i	$0.732765\pi$
$374$	−3.71765e96	−1.22344
$375$	0	0
$376$	−1.47031e96	−0.396155
$377$	2.83195e96	0.690692
$378$	0	0
$379$	−4.49109e95	−0.0898217	−0.0449108	−	0.998991i	$-0.514300\pi$
$379$	−4.49109e95	−0.0898217	−0.0449108	+	0.998991i	$0.514300\pi$
$380$	3.63991e95	0.0659487
$381$	0	0
$382$	−7.88649e96	−1.17357
$383$	−1.26028e97	−1.70025	−0.850123	−	0.526583i	$-0.823473\pi$
$383$	−1.26028e97	−1.70025	−0.850123	+	0.526583i	$0.823473\pi$
$384$	0	0
$385$	−4.25351e95	−0.0472031
$386$	−2.05199e96	−0.206610
$387$	0	0
$388$	−4.50009e96	−0.373277
$389$	5.15319e96	0.388120	0.194060	−	0.980990i	$-0.437834\pi$
$389$	5.15319e96	0.388120	0.194060	+	0.980990i	$0.437834\pi$
$390$	0	0
$391$	−2.20463e97	−1.36996
$392$	−1.20038e97	−0.677783
$393$	0	0
$394$	1.22917e97	0.573459
$395$	−2.14539e96	−0.0910153
$396$	0	0
$397$	1.73194e97	0.607979	0.303989	−	0.952675i	$-0.401681\pi$
$397$	1.73194e97	0.607979	0.303989	+	0.952675i	$0.401681\pi$
$398$	5.81051e97	1.85609
$399$	0	0
$400$	4.46447e97	1.18174
$401$	8.61687e96	0.207700	0.103850	−	0.994593i	$-0.466884\pi$
$401$	8.61687e96	0.207700	0.103850	+	0.994593i	$0.466884\pi$
$402$	0	0
$403$	2.22649e97	0.445329
$404$	−1.98761e97	−0.362267
$405$	0	0
$406$	−1.07372e97	−0.162617
$407$	2.49513e97	0.344590
$408$	0	0
$409$	1.42017e98	1.63198	0.815990	−	0.578065i	$-0.196192\pi$
$409$	1.42017e98	1.63198	0.815990	+	0.578065i	$0.196192\pi$
$410$	1.84181e96	0.0193130
$411$	0	0
$412$	−1.69297e97	−0.147912
$413$	7.85698e97	0.626800
$414$	0	0
$415$	1.80898e97	0.120401
$416$	1.78471e98	1.08535
$417$	0	0
$418$	2.98801e98	1.51800
$419$	−5.15399e97	−0.239396	−0.119698	−	0.992810i	$-0.538193\pi$
$419$	−5.15399e97	−0.239396	−0.119698	+	0.992810i	$0.538193\pi$
$420$	0	0
$421$	−2.32868e97	−0.0904757	−0.0452378	−	0.998976i	$-0.514405\pi$
$421$	−2.32868e97	−0.0904757	−0.0452378	+	0.998976i	$0.514405\pi$
$422$	1.24114e98	0.441170
$423$	0	0
$424$	−2.13123e98	−0.634470
$425$	4.64386e98	1.26559
$426$	0	0
$427$	−3.12081e98	−0.713217
$428$	5.38074e95	0.00112642
$429$	0	0
$430$	−4.57841e96	−0.00804726
$431$	6.03815e98	0.972762	0.486381	−	0.873747i	$-0.338317\pi$
$431$	6.03815e98	0.972762	0.486381	+	0.873747i	$0.338317\pi$
$432$	0	0
$433$	−1.62785e98	−0.220455	−0.110227	−	0.993906i	$-0.535158\pi$
$433$	−1.62785e98	−0.220455	−0.110227	+	0.993906i	$0.535158\pi$
$434$	−8.44166e97	−0.104849
$435$	0	0
$436$	−1.59679e98	−0.166919
$437$	1.77195e99	1.69980
$438$	0	0
$439$	−1.67222e99	−1.35168	−0.675840	−	0.737048i	$-0.736219\pi$
$439$	−1.67222e99	−1.35168	−0.675840	+	0.737048i	$0.736219\pi$
$440$	−1.28460e98	−0.0953438
$441$	0	0
$442$	4.51200e99	2.82510
$443$	−2.94738e99	−1.69549	−0.847747	−	0.530401i	$-0.822041\pi$
$443$	−2.94738e99	−1.69549	−0.847747	+	0.530401i	$0.822041\pi$
$444$	0	0
$445$	−4.74385e98	−0.230478
$446$	−6.53495e98	−0.291867
$447$	0	0
$448$	5.98032e98	0.225839
$449$	2.98962e99	1.03843	0.519216	−	0.854643i	$-0.326224\pi$
$449$	2.98962e99	1.03843	0.519216	+	0.854643i	$0.326224\pi$
$450$	0	0
$451$	3.40083e98	0.0999917
$452$	1.23943e99	0.335376
$453$	0	0
$454$	−4.40515e99	−1.01010
$455$	5.16236e98	0.108999
$456$	0	0
$457$	5.57415e99	0.998438	0.499219	−	0.866476i	$-0.333620\pi$
$457$	5.57415e99	0.998438	0.499219	+	0.866476i	$0.333620\pi$
$458$	−1.39010e99	−0.229399
$459$	0	0
$460$	3.11467e98	0.0436508
$461$	7.38632e99	0.954209	0.477104	−	0.878847i	$-0.341686\pi$
$461$	7.38632e99	0.954209	0.477104	+	0.878847i	$0.341686\pi$
$462$	0	0
$463$	5.44068e99	0.597539	0.298769	−	0.954325i	$-0.403424\pi$
$463$	5.44068e99	0.597539	0.298769	+	0.954325i	$0.403424\pi$
$464$	−4.27035e99	−0.432553
$465$	0	0
$466$	−2.19063e99	−0.188841
$467$	−2.61476e99	−0.207993	−0.103996	−	0.994578i	$-0.533163\pi$
$467$	−2.61476e99	−0.207993	−0.103996	+	0.994578i	$0.533163\pi$
$468$	0	0
$469$	3.16239e99	0.214306
$470$	1.26502e99	0.0791456
$471$	0	0
$472$	2.37288e100	1.26605
$473$	−8.45385e98	−0.0416641
$474$	0	0
$475$	−3.73244e100	−1.57030
$476$	−3.84790e99	−0.149611
$477$	0	0
$478$	−2.41630e100	−0.802794
$479$	−4.90702e100	−1.50743	−0.753713	−	0.657204i	$-0.771739\pi$
$479$	−4.90702e100	−1.50743	−0.753713	+	0.657204i	$0.771739\pi$
$480$	0	0
$481$	−3.02827e100	−0.795708
$482$	7.57616e99	0.184156
$483$	0	0
$484$	−4.24666e99	−0.0883784
$485$	−9.46963e99	−0.182397
$486$	0	0
$487$	−2.18940e100	−0.361402	−0.180701	−	0.983538i	$-0.557837\pi$
$487$	−2.18940e100	−0.361402	−0.180701	+	0.983538i	$0.557837\pi$
$488$	−9.42512e100	−1.44060
$489$	0	0
$490$	1.03277e100	0.135410
$491$	5.47812e100	0.665389	0.332694	−	0.943035i	$-0.392042\pi$
$491$	5.47812e100	0.665389	0.332694	+	0.943035i	$0.392042\pi$
$492$	0	0
$493$	−4.44193e100	−0.463247
$494$	−3.62646e101	−3.50528
$495$	0	0
$496$	−3.35737e100	−0.278892
$497$	−5.16146e100	−0.397565
$498$	0	0
$499$	−1.49760e101	−0.992257	−0.496128	−	0.868249i	$-0.665246\pi$
$499$	−1.49760e101	−0.992257	−0.496128	+	0.868249i	$0.665246\pi$
$500$	−1.32561e100	−0.0814783
$501$	0	0
$502$	7.48787e100	0.396250
$503$	1.80374e101	0.885879	0.442939	−	0.896552i	$-0.353936\pi$
$503$	1.80374e101	0.885879	0.442939	+	0.896552i	$0.353936\pi$
$504$	0	0
$505$	−4.18256e100	−0.177017
$506$	2.55684e101	1.00475
$507$	0	0
$508$	1.53078e100	0.0518828
$509$	−2.40040e101	−0.755729	−0.377865	−	0.925861i	$-0.623342\pi$
$509$	−2.40040e101	−0.755729	−0.377865	+	0.925861i	$0.623342\pi$
$510$	0	0
$511$	−4.95266e100	−0.134603
$512$	1.15850e101	0.292599
$513$	0	0
$514$	−1.05040e101	−0.229212
$515$	−3.56254e100	−0.0722751
$516$	0	0
$517$	2.33580e101	0.409771
$518$	1.14816e101	0.187342
$519$	0	0
$520$	1.55908e101	0.220162
$521$	1.00783e102	1.32425	0.662126	−	0.749392i	$-0.269654\pi$
$521$	1.00783e102	1.32425	0.662126	+	0.749392i	$0.269654\pi$
$522$	0	0
$523$	9.80597e101	1.11603	0.558017	−	0.829830i	$-0.311562\pi$
$523$	9.80597e101	1.11603	0.558017	+	0.829830i	$0.311562\pi$
$524$	3.35738e101	0.355695
$525$	0	0
$526$	4.50548e101	0.413786
$527$	−3.49227e101	−0.298682
$528$	0	0
$529$	1.68569e101	0.125081
$530$	1.83366e101	0.126757
$531$	0	0
$532$	3.09271e101	0.185632
$533$	−4.12748e101	−0.230895
$534$	0	0
$535$	1.13228e99	0.000550410 0
$536$	9.55069e101	0.432868
$537$	0	0
$538$	3.04183e102	1.19894
$539$	1.90697e102	0.701078
$540$	0	0
$541$	1.90764e102	0.610378	0.305189	−	0.952292i	$-0.401280\pi$
$541$	1.90764e102	0.610378	0.305189	+	0.952292i	$0.401280\pi$
$542$	1.68002e102	0.501581
$543$	0	0
$544$	−2.79934e102	−0.727942
$545$	−3.36016e101	−0.0815625
$546$	0	0
$547$	−3.72021e102	−0.787123	−0.393562	−	0.919298i	$-0.628757\pi$
$547$	−3.72021e102	−0.787123	−0.393562	+	0.919298i	$0.628757\pi$
$548$	1.11369e102	0.220037
$549$	0	0
$550$	−5.38574e102	−0.928207
$551$	3.57015e102	0.574780
$552$	0	0
$553$	−1.82286e102	−0.256189
$554$	1.05631e103	1.38731
$555$	0	0
$556$	3.01341e102	0.345743
$557$	−9.39626e102	−1.00782	−0.503912	−	0.863755i	$-0.668107\pi$
$557$	−9.39626e102	−1.00782	−0.503912	+	0.863755i	$0.668107\pi$
$558$	0	0
$559$	1.02602e102	0.0962083
$560$	−7.78443e101	−0.0682615
$561$	0	0
$562$	3.68991e102	0.283077
$563$	−1.45593e103	−1.04490	−0.522450	−	0.852670i	$-0.674982\pi$
$563$	−1.45593e103	−1.04490	−0.522450	+	0.852670i	$0.674982\pi$
$564$	0	0
$565$	2.60816e102	0.163877
$566$	2.21496e103	1.30241
$567$	0	0
$568$	−1.55881e103	−0.803026
$569$	3.42122e103	1.64995	0.824976	−	0.565168i	$-0.191189\pi$
$569$	3.42122e103	1.64995	0.824976	+	0.565168i	$0.191189\pi$
$570$	0	0
$571$	4.10130e103	1.73407	0.867036	−	0.498245i	$-0.166022\pi$
$571$	4.10130e103	1.73407	0.867036	+	0.498245i	$0.166022\pi$
$572$	−1.17702e103	−0.466050
$573$	0	0
$574$	1.56492e102	0.0543621
$575$	−3.19385e103	−1.03937
$576$	0	0
$577$	−4.20900e103	−1.20250	−0.601251	−	0.799060i	$-0.705331\pi$
$577$	−4.20900e103	−1.20250	−0.601251	+	0.799060i	$0.705331\pi$
$578$	−2.83459e103	−0.758920
$579$	0	0
$580$	6.27548e101	0.0147604
$581$	1.53702e103	0.338903
$582$	0	0
$583$	3.38577e103	0.656277
$584$	−1.49575e103	−0.271880
$585$	0	0
$586$	7.76332e103	1.24133
$587$	−1.81185e103	−0.271764	−0.135882	−	0.990725i	$-0.543387\pi$
$587$	−1.81185e103	−0.271764	−0.135882	+	0.990725i	$0.543387\pi$
$588$	0	0
$589$	2.80687e103	0.370594
$590$	−2.04156e103	−0.252937
$591$	0	0
$592$	4.56638e103	0.498320
$593$	−5.45632e103	−0.558919	−0.279459	−	0.960158i	$-0.590155\pi$
$593$	−5.45632e103	−0.558919	−0.279459	+	0.960158i	$0.590155\pi$
$594$	0	0
$595$	−8.09721e102	−0.0731054
$596$	−3.42866e103	−0.290663
$597$	0	0
$598$	−3.10316e104	−2.32011
$599$	−1.50324e104	−1.05565	−0.527826	−	0.849352i	$-0.676993\pi$
$599$	−1.50324e104	−1.05565	−0.527826	+	0.849352i	$0.676993\pi$
$600$	0	0
$601$	−3.00993e104	−1.86536	−0.932682	−	0.360699i	$-0.882538\pi$
$601$	−3.00993e104	−1.86536	−0.932682	+	0.360699i	$0.882538\pi$
$602$	−3.89012e102	−0.0226514
$603$	0	0
$604$	4.25598e103	0.218834
$605$	−8.93632e102	−0.0431849
$606$	0	0
$607$	−2.70698e104	−1.15587	−0.577936	−	0.816082i	$-0.696142\pi$
$607$	−2.70698e104	−1.15587	−0.577936	+	0.816082i	$0.696142\pi$
$608$	2.24993e104	0.903204
$609$	0	0
$610$	8.10912e103	0.287810
$611$	−2.83490e104	−0.946219
$612$	0	0
$613$	1.37369e104	0.405621	0.202810	−	0.979218i	$-0.434993\pi$
$613$	1.37369e104	0.405621	0.202810	+	0.979218i	$0.434993\pi$
$614$	−6.25086e104	−1.73631
$615$	0	0
$616$	−1.09148e104	−0.268373
$617$	1.04793e104	0.242459	0.121229	−	0.992625i	$-0.461316\pi$
$617$	1.04793e104	0.242459	0.121229	+	0.992625i	$0.461316\pi$
$618$	0	0
$619$	−1.99374e104	−0.408573	−0.204286	−	0.978911i	$-0.565487\pi$
$619$	−1.99374e104	−0.408573	−0.204286	+	0.978911i	$0.565487\pi$
$620$	4.93381e102	0.00951687
$621$	0	0
$622$	−2.22060e104	−0.379604
$623$	−4.03068e104	−0.648749
$624$	0	0
$625$	6.58665e104	0.940078
$626$	8.73682e104	1.17440
$627$	0	0
$628$	−3.72229e103	−0.0443939
$629$	4.74986e104	0.533681
$630$	0	0
$631$	7.56039e104	0.754125	0.377062	−	0.926188i	$-0.376934\pi$
$631$	7.56039e104	0.754125	0.377062	+	0.926188i	$0.376934\pi$
$632$	−5.50520e104	−0.517467
$633$	0	0
$634$	2.26050e105	1.88738
$635$	3.22125e103	0.0253518
$636$	0	0
$637$	−2.31444e105	−1.61889
$638$	5.15156e104	0.339753
$639$	0	0
$640$	−2.91670e104	−0.171058
$641$	2.20699e105	1.22074	0.610371	−	0.792116i	$-0.291020\pi$
$641$	2.20699e105	1.22074	0.610371	+	0.792116i	$0.291020\pi$
$642$	0	0
$643$	1.66481e105	0.819317	0.409659	−	0.912239i	$-0.365648\pi$
$643$	1.66481e105	0.819317	0.409659	+	0.912239i	$0.365648\pi$
$644$	2.64642e104	0.122868
$645$	0	0
$646$	5.68814e105	2.35099
$647$	2.95788e104	0.115364	0.0576819	−	0.998335i	$-0.481629\pi$
$647$	2.95788e104	0.115364	0.0576819	+	0.998335i	$0.481629\pi$
$648$	0	0
$649$	−3.76966e105	−1.30956
$650$	6.53652e105	2.14336
$651$	0	0
$652$	9.76104e104	0.285241
$653$	1.46213e105	0.403406	0.201703	−	0.979447i	$-0.435352\pi$
$653$	1.46213e105	0.403406	0.201703	+	0.979447i	$0.435352\pi$
$654$	0	0
$655$	7.06500e104	0.173805
$656$	6.22391e104	0.144600
$657$	0	0
$658$	1.07484e105	0.222778
$659$	1.49655e105	0.293013	0.146507	−	0.989210i	$-0.453197\pi$
$659$	1.49655e105	0.293013	0.146507	+	0.989210i	$0.453197\pi$
$660$	0	0
$661$	−8.31783e105	−1.45363	−0.726817	−	0.686831i	$-0.759001\pi$
$661$	−8.31783e105	−1.45363	−0.726817	+	0.686831i	$0.759001\pi$
$662$	−9.26056e105	−1.52919
$663$	0	0
$664$	4.64195e105	0.684538
$665$	6.50804e104	0.0907065
$666$	0	0
$667$	3.05497e105	0.380442
$668$	3.71265e105	0.437086
$669$	0	0
$670$	−8.21716e104	−0.0864802
$671$	1.49732e106	1.49011
$672$	0	0
$673$	−1.42322e106	−1.26680	−0.633400	−	0.773824i	$-0.718341\pi$
$673$	−1.42322e106	−1.26680	−0.633400	+	0.773824i	$0.718341\pi$
$674$	2.73286e105	0.230076
$675$	0	0
$676$	1.04329e106	0.785969
$677$	−2.39084e106	−1.70402	−0.852012	−	0.523523i	$-0.824618\pi$
$677$	−2.39084e106	−1.70402	−0.852012	+	0.523523i	$0.824618\pi$
$678$	0	0
$679$	−8.04601e105	−0.513410
$680$	−2.44543e105	−0.147663
$681$	0	0
$682$	4.05018e105	0.219059
$683$	−2.42848e106	−1.24325	−0.621624	−	0.783316i	$-0.713527\pi$
$683$	−2.42848e106	−1.24325	−0.621624	+	0.783316i	$0.713527\pi$
$684$	0	0
$685$	2.34357e105	0.107518
$686$	1.92133e106	0.834540
$687$	0	0
$688$	−1.54715e105	−0.0602514
$689$	−4.10921e106	−1.51544
$690$	0	0
$691$	−1.62806e106	−0.538573	−0.269287	−	0.963060i	$-0.586788\pi$
$691$	−1.62806e106	−0.538573	−0.269287	+	0.963060i	$0.586788\pi$
$692$	−5.37915e105	−0.168552
$693$	0	0
$694$	−1.59148e105	−0.0447530
$695$	6.34118e105	0.168943
$696$	0	0
$697$	6.47399e105	0.154861
$698$	2.26968e106	0.514502
$699$	0	0
$700$	−5.57444e105	−0.113508
$701$	4.65996e106	0.899408	0.449704	−	0.893178i	$-0.351530\pi$
$701$	4.65996e106	0.899408	0.449704	+	0.893178i	$0.351530\pi$
$702$	0	0
$703$	−3.81764e106	−0.662172
$704$	−2.86927e106	−0.471842
$705$	0	0
$706$	5.90387e106	0.872892
$707$	−3.55377e106	−0.498266
$708$	0	0
$709$	5.38281e106	0.678853	0.339426	−	0.940633i	$-0.389767\pi$
$709$	5.38281e106	0.678853	0.339426	+	0.940633i	$0.389767\pi$
$710$	1.34116e106	0.160432
$711$	0	0
$712$	−1.21730e107	−1.31038
$713$	2.40183e106	0.245293
$714$	0	0
$715$	−2.47682e106	−0.227729
$716$	1.60546e106	0.140075
$717$	0	0
$718$	1.56796e107	1.23217
$719$	−2.39201e107	−1.78414	−0.892071	−	0.451895i	$-0.850748\pi$
$719$	−2.39201e107	−1.78414	−0.892071	+	0.451895i	$0.850748\pi$
$720$	0	0
$721$	−3.02697e106	−0.203439
$722$	−2.79155e107	−1.78115
$723$	0	0
$724$	5.63774e106	0.324272
$725$	−6.43501e106	−0.351459
$726$	0	0
$727$	−2.28277e107	−1.12440	−0.562202	−	0.827000i	$-0.690046\pi$
$727$	−2.28277e107	−1.12440	−0.562202	+	0.827000i	$0.690046\pi$
$728$	1.32470e107	0.619711
$729$	0	0
$730$	1.28690e106	0.0543173
$731$	−1.60932e106	−0.0645269
$732$	0	0
$733$	−1.58880e107	−0.575004	−0.287502	−	0.957780i	$-0.592825\pi$
$733$	−1.58880e107	−0.575004	−0.287502	+	0.957780i	$0.592825\pi$
$734$	3.88373e107	1.33551
$735$	0	0
$736$	1.92527e107	0.597823
$737$	−1.51727e107	−0.447745
$738$	0	0
$739$	−5.34509e107	−1.42491	−0.712457	−	0.701715i	$-0.752418\pi$
$739$	−5.34509e107	−1.42491	−0.712457	+	0.701715i	$0.752418\pi$
$740$	−6.71052e105	−0.0170046
$741$	0	0
$742$	1.55799e107	0.356795
$743$	−2.60517e107	−0.567226	−0.283613	−	0.958939i	$-0.591533\pi$
$743$	−2.60517e107	−0.567226	−0.283613	+	0.958939i	$0.591533\pi$
$744$	0	0
$745$	−7.21499e106	−0.142028
$746$	8.10428e107	1.51708
$747$	0	0
$748$	1.84617e107	0.312580
$749$	9.62057e104	0.00154929
$750$	0	0
$751$	3.70994e107	0.540592	0.270296	−	0.962777i	$-0.412879\pi$
$751$	3.70994e107	0.540592	0.270296	+	0.962777i	$0.412879\pi$
$752$	4.27480e107	0.592579
$753$	0	0
$754$	−6.25229e107	−0.784538
$755$	8.95595e106	0.106930
$756$	0	0
$757$	8.77971e107	0.949259	0.474629	−	0.880186i	$-0.342582\pi$
$757$	8.77971e107	0.949259	0.474629	+	0.880186i	$0.342582\pi$
$758$	9.91530e106	0.102026
$759$	0	0
$760$	1.96549e107	0.183215
$761$	5.45469e107	0.484000	0.242000	−	0.970276i	$-0.422197\pi$
$761$	5.45469e107	0.484000	0.242000	+	0.970276i	$0.422197\pi$
$762$	0	0
$763$	−2.85501e107	−0.229582
$764$	3.91639e107	0.299837
$765$	0	0
$766$	2.78241e108	1.93126
$767$	4.57513e108	3.02397
$768$	0	0
$769$	5.31194e107	0.318431	0.159215	−	0.987244i	$-0.449104\pi$
$769$	5.31194e107	0.318431	0.159215	+	0.987244i	$0.449104\pi$
$770$	9.39080e106	0.0536167
$771$	0	0
$772$	1.01901e107	0.0527872
$773$	−3.36099e108	−1.65858	−0.829290	−	0.558818i	$-0.811255\pi$
$773$	−3.36099e108	−1.65858	−0.829290	+	0.558818i	$0.811255\pi$
$774$	0	0
$775$	−5.05924e107	−0.226606
$776$	−2.42997e108	−1.03702
$777$	0	0
$778$	−1.13771e108	−0.440855
$779$	−5.20339e107	−0.192146
$780$	0	0
$781$	2.47639e108	0.830626
$782$	4.86733e108	1.55610
$783$	0	0
$784$	3.48999e108	1.01384
$785$	−7.83289e106	−0.0216925
$786$	0	0
$787$	3.71560e108	0.935356	0.467678	−	0.883899i	$-0.345091\pi$
$787$	3.71560e108	0.935356	0.467678	+	0.883899i	$0.345091\pi$
$788$	−6.10398e107	−0.146514
$789$	0	0
$790$	4.73653e107	0.103382
$791$	2.21606e108	0.461279
$792$	0	0
$793$	−1.81725e109	−3.44088
$794$	−3.82373e108	−0.690586
$795$	0	0
$796$	−2.88547e108	−0.474217
$797$	−8.59521e108	−1.34763	−0.673813	−	0.738901i	$-0.735345\pi$
$797$	−8.59521e108	−1.34763	−0.673813	+	0.738901i	$0.735345\pi$
$798$	0	0
$799$	4.44656e108	0.634629
$800$	−4.05539e108	−0.552279
$801$	0	0
$802$	−1.90241e108	−0.235920
$803$	2.37621e108	0.281224
$804$	0	0
$805$	5.56892e107	0.0600379
$806$	−4.91558e108	−0.505837
$807$	0	0
$808$	−1.07327e109	−1.00643
$809$	7.94957e108	0.711663	0.355831	−	0.934550i	$-0.384198\pi$
$809$	7.94957e108	0.711663	0.355831	+	0.934550i	$0.384198\pi$
$810$	0	0
$811$	−1.89106e109	−1.54320	−0.771602	−	0.636106i	$-0.780544\pi$
$811$	−1.89106e109	−1.54320	−0.771602	+	0.636106i	$0.780544\pi$
$812$	5.33206e107	0.0415474
$813$	0	0
$814$	−5.50868e108	−0.391411
$815$	2.05404e108	0.139379
$816$	0	0
$817$	1.29347e108	0.0800626
$818$	−3.13540e109	−1.85372
$819$	0	0
$820$	−9.14633e106	−0.00493432
$821$	−2.82901e109	−1.45803	−0.729015	−	0.684497i	$-0.760022\pi$
$821$	−2.82901e109	−1.45803	−0.729015	+	0.684497i	$0.760022\pi$
$822$	0	0
$823$	2.24716e109	1.05716	0.528579	−	0.848884i	$-0.322725\pi$
$823$	2.24716e109	1.05716	0.528579	+	0.848884i	$0.322725\pi$
$824$	−9.14170e108	−0.410919
$825$	0	0
$826$	−1.73464e109	−0.711965
$827$	1.40884e109	0.552591	0.276296	−	0.961073i	$-0.410893\pi$
$827$	1.40884e109	0.552591	0.276296	+	0.961073i	$0.410893\pi$
$828$	0	0
$829$	4.51132e109	1.61625	0.808125	−	0.589011i	$-0.200483\pi$
$829$	4.51132e109	1.61625	0.808125	+	0.589011i	$0.200483\pi$
$830$	−3.99381e108	−0.136760
$831$	0	0
$832$	3.48234e109	1.08955
$833$	3.63022e109	1.08579
$834$	0	0
$835$	7.81260e108	0.213576
$836$	−1.48383e109	−0.387837
$837$	0	0
$838$	1.13788e109	0.271924
$839$	−1.09964e109	−0.251290	−0.125645	−	0.992075i	$-0.540100\pi$
$839$	−1.09964e109	−0.251290	−0.125645	+	0.992075i	$0.540100\pi$
$840$	0	0
$841$	−4.16913e109	−0.871355
$842$	5.14120e108	0.102769
$843$	0	0
$844$	−6.16347e108	−0.112715
$845$	2.19542e109	0.384053
$846$	0	0
$847$	−7.59288e108	−0.121557
$848$	6.19636e109	0.949057
$849$	0	0
$850$	−1.02526e110	−1.43755
$851$	−3.26675e109	−0.438286
$852$	0	0
$853$	1.44601e110	1.77657	0.888287	−	0.459289i	$-0.151896\pi$
$853$	1.44601e110	1.77657	0.888287	+	0.459289i	$0.151896\pi$
$854$	6.89004e109	0.810124
$855$	0	0
$856$	2.90550e107	0.00312935
$857$	9.49435e109	0.978778	0.489389	−	0.872066i	$-0.337220\pi$
$857$	9.49435e109	0.978778	0.489389	+	0.872066i	$0.337220\pi$
$858$	0	0
$859$	9.18306e109	0.867449	0.433724	−	0.901046i	$-0.357199\pi$
$859$	9.18306e109	0.867449	0.433724	+	0.901046i	$0.357199\pi$
$860$	2.27362e107	0.00205601
$861$	0	0
$862$	−1.33309e110	−1.10493
$863$	−1.19495e110	−0.948299	−0.474150	−	0.880444i	$-0.657244\pi$
$863$	−1.19495e110	−0.948299	−0.474150	+	0.880444i	$0.657244\pi$
$864$	0	0
$865$	−1.13194e109	−0.0823609
$866$	3.59393e109	0.250408
$867$	0	0
$868$	4.19209e108	0.0267880
$869$	8.74581e109	0.535252
$870$	0	0
$871$	1.84146e110	1.03391
$872$	−8.62238e109	−0.463723
$873$	0	0
$874$	−3.91206e110	−1.93075
$875$	−2.37015e109	−0.112066
$876$	0	0
$877$	−1.79278e110	−0.778112	−0.389056	−	0.921214i	$-0.627199\pi$
$877$	−1.79278e110	−0.778112	−0.389056	+	0.921214i	$0.627199\pi$
$878$	3.69188e110	1.53534
$879$	0	0
$880$	3.73485e109	0.142618
$881$	1.61512e110	0.591030	0.295515	−	0.955338i	$-0.404509\pi$
$881$	1.61512e110	0.591030	0.295515	+	0.955338i	$0.404509\pi$
$882$	0	0
$883$	2.02977e110	0.682214	0.341107	−	0.940024i	$-0.389198\pi$
$883$	2.02977e110	0.682214	0.341107	+	0.940024i	$0.389198\pi$
$884$	−2.24064e110	−0.721791
$885$	0	0
$886$	6.50714e110	1.92586
$887$	1.52176e110	0.431729	0.215865	−	0.976423i	$-0.430743\pi$
$887$	1.52176e110	0.431729	0.215865	+	0.976423i	$0.430743\pi$
$888$	0	0
$889$	2.73698e109	0.0713601
$890$	1.04733e110	0.261794
$891$	0	0
$892$	3.24523e109	0.0745698
$893$	−3.57387e110	−0.787424
$894$	0	0
$895$	3.37840e109	0.0684459
$896$	−2.47822e110	−0.481492
$897$	0	0
$898$	−6.60040e110	−1.17953
$899$	4.83925e109	0.0829449
$900$	0	0
$901$	6.44533e110	1.01640
$902$	−7.50825e109	−0.113578
$903$	0	0
$904$	6.69271e110	0.931720
$905$	1.18636e110	0.158451
$906$	0	0
$907$	−4.71321e110	−0.579486	−0.289743	−	0.957104i	$-0.593570\pi$
$907$	−4.71321e110	−0.579486	−0.289743	+	0.957104i	$0.593570\pi$
$908$	2.18757e110	0.258074
$909$	0	0
$910$	−1.13973e110	−0.123809
$911$	1.43595e111	1.49693	0.748465	−	0.663174i	$-0.230791\pi$
$911$	1.43595e111	1.49693	0.748465	+	0.663174i	$0.230791\pi$
$912$	0	0
$913$	−7.37441e110	−0.708065
$914$	−1.23065e111	−1.13410
$915$	0	0
$916$	6.90319e109	0.0586097
$917$	6.00288e110	0.489226
$918$	0	0
$919$	4.57653e110	0.343720	0.171860	−	0.985121i	$-0.445022\pi$
$919$	4.57653e110	0.343720	0.171860	+	0.985121i	$0.445022\pi$
$920$	1.68186e110	0.121268
$921$	0	0
$922$	−1.63073e111	−1.08386
$923$	−3.00552e111	−1.91803
$924$	0	0
$925$	6.88111e110	0.404896
$926$	−1.20118e111	−0.678728
$927$	0	0
$928$	3.87906e110	0.202152
$929$	−1.05558e111	−0.528325	−0.264163	−	0.964478i	$-0.585096\pi$
$929$	−1.05558e111	−0.528325	−0.264163	+	0.964478i	$0.585096\pi$
$930$	0	0
$931$	−2.91774e111	−1.34721
$932$	1.08785e110	0.0482474
$933$	0	0
$934$	5.77279e110	0.236253
$935$	3.88492e110	0.152738
$936$	0	0
$937$	−8.13002e110	−0.295024	−0.147512	−	0.989060i	$-0.547126\pi$
$937$	−8.13002e110	−0.295024	−0.147512	+	0.989060i	$0.547126\pi$
$938$	−6.98183e110	−0.243424
$939$	0	0
$940$	−6.28202e109	−0.0202211
$941$	−1.60666e111	−0.496950	−0.248475	−	0.968638i	$-0.579929\pi$
$941$	−1.60666e111	−0.496950	−0.248475	+	0.968638i	$0.579929\pi$
$942$	0	0
$943$	−4.45253e110	−0.127180
$944$	−6.89892e111	−1.89379
$945$	0	0
$946$	1.86642e110	0.0473251
$947$	−1.93183e111	−0.470809	−0.235404	−	0.971898i	$-0.575641\pi$
$947$	−1.93183e111	−0.470809	−0.235404	+	0.971898i	$0.575641\pi$
$948$	0	0
$949$	−2.88394e111	−0.649386
$950$	8.24039e111	1.78366
$951$	0	0
$952$	−2.07780e111	−0.415640
$953$	−4.48955e111	−0.863414	−0.431707	−	0.902014i	$-0.642088\pi$
$953$	−4.48955e111	−0.863414	−0.431707	+	0.902014i	$0.642088\pi$
$954$	0	0
$955$	8.24134e110	0.146511
$956$	1.19992e111	0.205108
$957$	0	0
$958$	1.08336e112	1.71224
$959$	1.99125e111	0.302641
$960$	0	0
$961$	−6.73375e111	−0.946521
$962$	6.68572e111	0.903823
$963$	0	0
$964$	−3.76229e110	−0.0470504
$965$	2.14432e110	0.0257938
$966$	0	0
$967$	−1.19520e112	−1.33030	−0.665148	−	0.746712i	$-0.731631\pi$
$967$	−1.19520e112	−1.33030	−0.665148	+	0.746712i	$0.731631\pi$
$968$	−2.29312e111	−0.245528
$969$	0	0
$970$	2.09068e111	0.207180
$971$	2.02515e112	1.93079	0.965395	−	0.260790i	$-0.0839831\pi$
$971$	2.02515e112	1.93079	0.965395	+	0.260790i	$0.0839831\pi$
$972$	0	0
$973$	5.38788e111	0.475539
$974$	4.83371e111	0.410506
$975$	0	0
$976$	2.74027e112	2.15489
$977$	4.99871e111	0.378279	0.189140	−	0.981950i	$-0.439430\pi$
$977$	4.99871e111	0.378279	0.189140	+	0.981950i	$0.439430\pi$
$978$	0	0
$979$	1.93386e112	1.35542
$980$	−5.12870e110	−0.0345963
$981$	0	0
$982$	−1.20944e112	−0.755797
$983$	5.82663e111	0.350478	0.175239	−	0.984526i	$-0.443930\pi$
$983$	5.82663e111	0.350478	0.175239	+	0.984526i	$0.443930\pi$
$984$	0	0
$985$	−1.28447e111	−0.0715922
$986$	9.80678e111	0.526189
$987$	0	0
$988$	1.80088e112	0.895572
$989$	1.10682e111	0.0529928
$990$	0	0
$991$	5.49657e111	0.243966	0.121983	−	0.992532i	$-0.461075\pi$
$991$	5.49657e111	0.243966	0.121983	+	0.992532i	$0.461075\pi$
$992$	3.04973e111	0.130339
$993$	0	0
$994$	1.13953e112	0.451583
$995$	−6.07195e111	−0.231720
$996$	0	0
$997$	1.26397e112	0.447372	0.223686	−	0.974661i	$-0.428191\pi$
$997$	1.26397e112	0.447372	0.223686	+	0.974661i	$0.428191\pi$
$998$	3.30635e112	1.12708
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.76.a.c.1.2		6
3.2	odd	2		1.76.a.a.1.5	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.76.a.a.1.5	✓	6	3.2	odd	2
9.76.a.c.1.2		6	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:	\( k \)	\(=\)	\( 76 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q-2.20777e11 q^{2} +1.09637e22 q^{4} +2.30711e25 q^{5} +1.96027e31 q^{7} +5.92020e33 q^{8} +O(q^{10})\)	\(q-2.20777e11 q^{2} +1.09637e22 q^{4} +2.30711e25 q^{5} +1.96027e31 q^{7} +5.92020e33 q^{8} -5.09358e36 q^{10} -9.40509e38 q^{11} +1.14147e42 q^{13} -4.32784e42 q^{14} -1.72124e45 q^{16} -1.79040e46 q^{17} +1.43901e48 q^{19} +2.52945e47 q^{20} +2.07643e50 q^{22} +1.23136e51 q^{23} -2.59375e52 q^{25} -2.52010e53 q^{26} +2.14918e53 q^{28} +2.48097e54 q^{29} +1.95055e55 q^{31} +1.56352e56 q^{32} +3.95280e57 q^{34} +4.52257e56 q^{35} -2.65296e58 q^{37} -3.17702e59 q^{38} +1.36586e59 q^{40} -3.61594e59 q^{41} +8.98859e59 q^{43} -1.03115e61 q^{44} -2.71857e62 q^{46} -2.48355e62 q^{47} -2.02760e63 q^{49} +5.72641e63 q^{50} +1.25147e64 q^{52} -3.59994e64 q^{53} -2.16986e64 q^{55} +1.16052e65 q^{56} -5.47742e65 q^{58} +4.00811e66 q^{59} -1.59203e67 q^{61} -4.30637e66 q^{62} +3.05076e67 q^{64} +2.63349e67 q^{65} +1.61324e68 q^{67} -1.96294e68 q^{68} -9.98480e67 q^{70} -2.63303e69 q^{71} -2.52652e69 q^{73} +5.85713e69 q^{74} +1.57769e70 q^{76} -1.84365e70 q^{77} -9.29901e70 q^{79} -3.97110e70 q^{80} +7.98318e70 q^{82} +7.84087e71 q^{83} -4.13066e71 q^{85} -1.98448e71 q^{86} -5.56800e72 q^{88} -2.05618e73 q^{89} +2.23759e73 q^{91} +1.35003e73 q^{92} +5.48312e73 q^{94} +3.31997e73 q^{95} -4.10454e74 q^{97} +4.47648e74 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 57080822040 q^{2} + 17\!\cdots\!28 q^{4}+ \cdots - 44\!\cdots\!20 q^{8}+O(q^{10}) \) 6 * q + 57080822040 * q^2 + 172600466200162028593728 * q^4 + 38982947396479621874420940 * q^5 + 1924474634802918779239478643600 * q^7 - 4434903997968330342413437320645120 * q^8	\( 6 q + 57080822040 q^{2} + 17\!\cdots\!28 q^{4}+ \cdots + 16\!\cdots\!20 q^{98}+O(q^{100}) \) 6 * q + 57080822040 * q^2 + 172600466200162028593728 * q^4 + 38982947396479621874420940 * q^5 + 1924474634802918779239478643600 * q^7 - 4434903997968330342413437320645120 * q^8 + 133267935677460241037537052811576902960 * q^10 + 945659951949983071650740113735111214088 * q^11 + 533185179266852519941169625089098069764420 * q^13 - 8213946953162263647781694565284746353072576 * q^14 + 2681978005634517266622433394712415602648354816 * q^16 - 18261354095776132566172834671579513215483393580 * q^17 + 1061534856238354155312794852768417904375328867080 * q^19 - 9296557595621768320156983882258818695571369489280 * q^20 + 153315952874260268106194796405555863940172791589920 * q^22 - 1514929449877410771078348320690686508954384916853680 * q^23 + 19310380328261093150952553553121815533899364092239850 * q^25 - 117730941166816926498584842564210483616872200198362352 * q^26 + 1465885017268620651444113586751990931877154821040657920 * q^28 - 14718767377678125816030788545177391174717388984245534820 * q^29 - 41742874787360498453628839393549579933009794702042980288 * q^31 - 1174660148719991756036751189163540495635749096221862952960 * q^32 + 3034358950124956876257603978888653679838045546922892395856 * q^34 - 27299672493656883988453292135086250689495956464846953371360 * q^35 + 98517772547646219221591850851651469983797181732879949140340 * q^37 - 1257660981102762853948269222064665311191946222029530979162080 * q^38 + 8807901623729426290853411185831313455271917763097593104051200 * q^40 - 5039211762207387369185984529408567568647239506257650214613212 * q^41 + 27938749238581541451173935836639198120068956697568041153196600 * q^43 + 86388814623354110240559749283671522466589238091463431115801344 * q^44 - 824145803870667307795487213022331547039596870954611528203613888 * q^46 + 1386854970430427381646742231466788117324292253074354560479038880 * q^47 - 5707868790800975784856935495088511133239544554833878775910738442 * q^49 - 3144970672685230615695776810799603542575044196614572896663392600 * q^50 + 41677832028141179840113326797899392222702339479233001780216150400 * q^52 - 64283727174659970247345252518647455744441825702701764187054106260 * q^53 + 436876078674971654403803167180324983329224614451635548418098895120 * q^55 - 289950797286325881623798664040853221823087783432246887785270865920 * q^56 - 1763005756244374137396902189067511762184157619699352574614137403280 * q^58 + 2478360370933764187935912640189307752170553390931716617591182395560 * q^59 - 25641115321477658815889269525514418267074652297034046321782023152988 * q^61 + 29014701474354643819936101890527484086880802356768235703173807694080 * q^62 + 47683232974651133862719671893097862706511055838864188064811716968448 * q^64 - 122110621788131890149667214965152432737153070969379698276880591977720 * q^65 + 955579073553339181030887342220313909838725364297810737998207107813480 * q^67 - 1237210897217068882936524414359446185548686871817993659403939290386560 * q^68 - 3476902593928340346610001926714053112321275314411181267396530677050240 * q^70 + 255682319306096297182489045146623979225804710540351927309367569173488 * q^71 - 30605188898291905719532895918028188508004452865621142257485594115042020 * q^73 + 24065024027894599201472448362529876891121294631891709256708009194181584 * q^74 + 100020936372377387464010564774983213070641689274186088752725827576144640 * q^76 - 158930415774536768880543239288689183540801263714134710336228496440507200 * q^77 + 116627678166642324332643069323234092884951450625988452824960767925148320 * q^79 - 1239310052714502333188756625709169306278438274940582996524184215206748160 * q^80 - 2557649813228840791149140948716215474705151452500921688788291587877236080 * q^82 + 798780284119889426515570523310162377392459257634002033911814028088739960 * q^83 - 3615500806340871685633297735534398118961343923835923286123685237305018840 * q^85 - 7245194180836090971883743617494948296636529538939897523257528311698092832 * q^86 - 4827001398586167572057494186308233100206033194553368013345656010632181760 * q^88 - 53575610216125238704584826863934604186542249469498220298044079954014547260 * q^89 + 34502419684367451829908407139028781594042460695428817715772307436403470432 * q^91 - 187445224353587479072026786339601818260697439565538078689222489106585838080 * q^92 - 296189325151987924691405038954735773676385503565643130818482899021002578304 * q^94 - 194934959385332686251927514630723902507701573195047654345319995220933314800 * q^95 - 747928220344118582344222376208028579242743608466383778453296378427532508980 * q^97 + 1663265696927109513221859402309517858944410070626232817304447619248634722520 * q^98

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