LMFDB - Embedded newform 9.74.a.a.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,74,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, 74, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 74);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 74 $
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:	$303.735576363$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} + \cdots + 17\!\cdots\!00 $ x^5 - x^4 - 10073499617947743056x^3 + 1429272143092482488433869600x^2 + 7661214288514935343595600445215756800*x + 1722510836040319301450745177697157900206688000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{39}\cdot 3^{22}\cdot 5^{6}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$2.93794e9$ 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)

$f(q)$	$=$	$q+1.59439e11 q^{2} +1.59761e22 q^{4} -2.70839e25 q^{5} -5.83802e30 q^{7} +1.04135e33 q^{8} +O(q^{10})$	\(q+1.59439e11 q^{2} +1.59761e22 q^{4} -2.70839e25 q^{5} -5.83802e30 q^{7} +1.04135e33 q^{8} -4.31824e36 q^{10} -1.33163e38 q^{11} -6.53481e40 q^{13} -9.30808e41 q^{14} +1.51423e43 q^{16} -1.34700e45 q^{17} +4.71630e46 q^{19} -4.32695e47 q^{20} -2.12314e49 q^{22} +7.28068e48 q^{23} -3.25252e50 q^{25} -1.04190e52 q^{26} -9.32686e52 q^{28} +1.30886e53 q^{29} -6.62177e53 q^{31} -7.42102e54 q^{32} -2.14764e56 q^{34} +1.58116e56 q^{35} +1.59006e57 q^{37} +7.51962e57 q^{38} -2.82039e58 q^{40} +1.09204e59 q^{41} +6.52415e59 q^{43} -2.12743e60 q^{44} +1.16082e60 q^{46} -6.06379e60 q^{47} -1.51393e61 q^{49} -5.18579e61 q^{50} -1.04401e63 q^{52} +1.02494e63 q^{53} +3.60659e63 q^{55} -6.07943e63 q^{56} +2.08683e64 q^{58} +2.47662e64 q^{59} -8.75008e64 q^{61} -1.05577e65 q^{62} -1.32621e66 q^{64} +1.76988e66 q^{65} -2.58164e66 q^{67} -2.15197e67 q^{68} +2.52099e67 q^{70} +4.91723e67 q^{71} -1.02422e68 q^{73} +2.53517e68 q^{74} +7.53479e68 q^{76} +7.77410e68 q^{77} -2.22461e69 q^{79} -4.10112e68 q^{80} +1.74113e70 q^{82} +1.44102e70 q^{83} +3.64820e70 q^{85} +1.04020e71 q^{86} -1.38670e71 q^{88} -3.70525e70 q^{89} +3.81503e71 q^{91} +1.16317e71 q^{92} -9.66804e71 q^{94} -1.27736e72 q^{95} +3.38939e71 q^{97} -2.41379e72 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 92089333488 q^{2} + 89\!\cdots\!60 q^{4}+ \cdots + 38\!\cdots\!80 q^{8}+O(q^{10}) $ 5 * q + 92089333488 * q^2 + 891110479259563516160 * q^4 - 23099529720469471562826750 * q^5 - 4356178487147579439806268090008 * q^7 + 382321348565178801062509850849280 * q^8	$ 5 q + 92089333488 q^{2} + 89\!\cdots\!60 q^{4}+ \cdots + 76\!\cdots\!16 q^{98}+O(q^{100}) $ 5 * q + 92089333488 * q^2 + 891110479259563516160 * q^4 - 23099529720469471562826750 * q^5 - 4356178487147579439806268090008 * q^7 + 382321348565178801062509850849280 * q^8 - 1082726120403847340426026649690244000 * q^10 - 50083756421782317855880849016778496860 * q^11 + 4753748397471720291047553799357192278886 * q^13 - 263363595637460329420141722180437171694720 * q^14 + 57509595349357883169785087518099233197588480 * q^16 - 663279725175909884624200257401822351394256602 * q^17 + 31387402430958534058855312636541530201995765700 * q^19 - 68535205735011202400715856751699460073169856000 * q^20 - 9492394168845783423791120540922405517833204177216 * q^22 + 41173446223173693726617088414497261153026772718024 * q^23 + 321010940201155914585034686800814006311220324546875 * q^25 - 4496438035379975943261998606627087983483848085006560 * q^26 - 37814301174111882879202704910382387341459683517577216 * q^28 + 217397685843681573854388291537651452827057882148450250 * q^29 - 3959918978904396097569386510196715694840286709585401440 * q^31 + 9479144378484593489541015426974249650207814007382867968 * q^32 - 324638192385754362369074018224584035205208569018875155680 * q^34 + 1051811671165262926972759981500117019527196204743409914000 * q^35 - 6710426612911460903226679780416929578822322356442579950178 * q^37 + 20075776649866586500887218371135359952534984707306414947520 * q^38 - 87443314425210154156114784714128373503740284779633935360000 * q^40 + 89999556000464227434562342749528590851939245788450434103790 * q^41 + 1171421579861687300375905115748875459141635816468653452284156 * q^43 - 3620387401482413711753562750789250834104238410455247119723520 * q^44 + 13122337792181100518478081314861771936057558300377044573644160 * q^46 - 26407117391117866585989236437476333636637017745173062895096432 * q^47 - 47859785088079990485612756297590896342589260563105328803969315 * q^49 + 198341627273982740927873511630518057650356858808871192258250000 * q^50 - 1819820853930882517149424007699825989256997486995920851867734528 * q^52 + 2253672757277210109476755074185818948452790752453662372858468754 * q^53 + 5272301841223840031246441919708126997046467528986443289345081000 * q^55 - 17369101267271748189623122493455314696373137673860233497989120000 * q^56 + 63080485469034924979732075223792805715626817023343777138220605920 * q^58 - 49827032054541030737892137385762950528020446432538215007741437900 * q^59 - 200207946356755779993110124671040230418699916707275462827300034090 * q^61 + 456512716932753516995161459627410738703514050956609499700325060096 * q^62 - 2671988611100492125931167910213768824231319631401339943695669002240 * q^64 + 2221078323698894670419341126197735507928898751783246157619800369500 * q^65 + 1726934463658866670044856129309631728944059099751189118466533017652 * q^67 - 25844159932565717701710366021885253281928511625890180327915132834304 * q^68 + 60019715162941233136874683443010604187189046779871920798680662752000 * q^70 - 29528228383509762365399718501357560736875772117852859701209862331560 * q^71 - 237248424072934328617284197336037660641948064767277176027665176375374 * q^73 + 385668396032745357868624366253781435784895053179379214963132226802080 * q^74 - 402469771116557587325960702574461860644965601604695023105081798528000 * q^76 + 1160921420345569675442649510235573702285949327395662717704239852301856 * q^77 + 1210019475236668608258558597507004925943189831192425236151129201347600 * q^79 - 7695510793835037324754830224890315360926193938062866122926593916928000 * q^80 + 19869905655996015892436375229312420723635630923691072274009372051144864 * q^82 - 10633758535693793129462935403233565634399957806616398467042339222483716 * q^83 - 28641392301460491393930553180957463692521548910270676165772874742366500 * q^85 + 130748824105220136322401247193488038601024385677355691179590030869522240 * q^86 - 221808067516055560593893382793377773024661552295403957235825845052456960 * q^88 + 44230399340933247556508628049428956972940692248797881370004235332026750 * q^89 + 503963419362898329804217905595235878617892804641236823955454638331741360 * q^91 - 1056276182251025158869277711594662138415929570173882076378175681365399552 * q^92 + 1211599009021421323842808603980852406277919665987296133682388929757489920 * q^94 - 1134809355692277446299742482002998127744674957590385906379174039024255000 * q^95 - 4705643796144250410051227741367571092615369303801441364082016351450032918 * q^97 + 7645702282951838206479981702299956043322685777549671658293752892775157616 * 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 $

$2$	1.59439e11	1.64059	0.820295	−	0.571941i	$-0.193809\pi$
$2$	1.59439e11	1.64059	0.820295	+	0.571941i	$0.193809\pi$
$3$	0	0
$3$	0	0
$4$	1.59761e22	1.69153
$5$	−2.70839e25	−0.832351	−0.416175	−	0.909284i	$-0.636630\pi$
$5$	−2.70839e25	−0.832351	−0.416175	+	0.909284i	$0.636630\pi$
$6$	0	0
$7$	−5.83802e30	−0.832122	−0.416061	−	0.909337i	$-0.636590\pi$
$7$	−5.83802e30	−0.832122	−0.416061	+	0.909337i	$0.636590\pi$
$8$	1.04135e33	1.13452
$9$	0	0
$10$	−4.31824e36	−1.36555
$11$	−1.33163e38	−1.29883	−0.649414	−	0.760435i	$-0.724986\pi$
$11$	−1.33163e38	−1.29883	−0.649414	+	0.760435i	$0.724986\pi$
$12$	0	0
$13$	−6.53481e40	−1.43318	−0.716590	−	0.697495i	$-0.754298\pi$
$13$	−6.53481e40	−1.43318	−0.716590	+	0.697495i	$0.754298\pi$
$14$	−9.30808e41	−1.36517
$15$	0	0
$16$	1.51423e43	0.169750
$17$	−1.34700e45	−1.65189	−0.825945	−	0.563750i	$-0.809358\pi$
$17$	−1.34700e45	−1.65189	−0.825945	+	0.563750i	$0.809358\pi$
$18$	0	0
$19$	4.71630e46	0.997918	0.498959	−	0.866626i	$-0.333716\pi$
$19$	4.71630e46	0.997918	0.498959	+	0.866626i	$0.333716\pi$
$20$	−4.32695e47	−1.40795
$21$	0	0
$22$	−2.12314e49	−2.13084
$23$	7.28068e48	0.144247	0.0721234	−	0.997396i	$-0.477022\pi$
$23$	7.28068e48	0.144247	0.0721234	+	0.997396i	$0.477022\pi$
$24$	0	0
$25$	−3.25252e50	−0.307192
$26$	−1.04190e52	−2.35126
$27$	0	0
$28$	−9.32686e52	−1.40756
$29$	1.30886e53	0.548738	0.274369	−	0.961624i	$-0.411531\pi$
$29$	1.30886e53	0.548738	0.274369	+	0.961624i	$0.411531\pi$
$30$	0	0
$31$	−6.62177e53	−0.243373	−0.121686	−	0.992569i	$-0.538830\pi$
$31$	−6.62177e53	−0.243373	−0.121686	+	0.992569i	$0.538830\pi$
$32$	−7.42102e54	−0.856030
$33$	0	0
$34$	−2.14764e56	−2.71007
$35$	1.58116e56	0.692618
$36$	0	0
$37$	1.59006e57	0.916326	0.458163	−	0.888868i	$-0.348508\pi$
$37$	1.59006e57	0.916326	0.458163	+	0.888868i	$0.348508\pi$
$38$	7.51962e57	1.63717
$39$	0	0
$40$	−2.82039e58	−0.944320
$41$	1.09204e59	1.48466	0.742328	−	0.670036i	$-0.233722\pi$
$41$	1.09204e59	1.48466	0.742328	+	0.670036i	$0.233722\pi$
$42$	0	0
$43$	6.52415e59	1.55928	0.779642	−	0.626225i	$-0.215401\pi$
$43$	6.52415e59	1.55928	0.779642	+	0.626225i	$0.215401\pi$
$44$	−2.12743e60	−2.19701
$45$	0	0
$46$	1.16082e60	0.236650
$47$	−6.06379e60	−0.563861	−0.281931	−	0.959435i	$-0.590975\pi$
$47$	−6.06379e60	−0.563861	−0.281931	+	0.959435i	$0.590975\pi$
$48$	0	0
$49$	−1.51393e61	−0.307573
$50$	−5.18579e61	−0.503976
$51$	0	0
$52$	−1.04401e63	−2.42427
$53$	1.02494e63	1.18749	0.593745	−	0.804654i	$-0.297649\pi$
$53$	1.02494e63	1.18749	0.593745	+	0.804654i	$0.297649\pi$
$54$	0	0
$55$	3.60659e63	1.08108
$56$	−6.07943e63	−0.944060
$57$	0	0
$58$	2.08683e64	0.900254
$59$	2.47662e64	0.572481	0.286241	−	0.958158i	$-0.407594\pi$
$59$	2.47662e64	0.572481	0.286241	+	0.958158i	$0.407594\pi$
$60$	0	0
$61$	−8.75008e64	−0.599064	−0.299532	−	0.954086i	$-0.596831\pi$
$61$	−8.75008e64	−0.599064	−0.299532	+	0.954086i	$0.596831\pi$
$62$	−1.05577e65	−0.399275
$63$	0	0
$64$	−1.32621e66	−1.57414
$65$	1.76988e66	1.19291
$66$	0	0
$67$	−2.58164e66	−0.575659	−0.287830	−	0.957682i	$-0.592934\pi$
$67$	−2.58164e66	−0.575659	−0.287830	+	0.957682i	$0.592934\pi$
$68$	−2.15197e67	−2.79423
$69$	0	0
$70$	2.52099e67	1.13630
$71$	4.91723e67	1.32066	0.660330	−	0.750975i	$-0.270416\pi$
$71$	4.91723e67	1.32066	0.660330	+	0.750975i	$0.270416\pi$
$72$	0	0
$73$	−1.02422e68	−0.997948	−0.498974	−	0.866617i	$-0.666290\pi$
$73$	−1.02422e68	−0.997948	−0.498974	+	0.866617i	$0.666290\pi$
$74$	2.53517e68	1.50332
$75$	0	0
$76$	7.53479e68	1.68801
$77$	7.77410e68	1.08078
$78$	0	0
$79$	−2.22461e69	−1.21301	−0.606505	−	0.795080i	$-0.707429\pi$
$79$	−2.22461e69	−1.21301	−0.606505	+	0.795080i	$0.707429\pi$
$80$	−4.10112e68	−0.141292
$81$	0	0
$82$	1.74113e70	2.43571
$83$	1.44102e70	1.29515	0.647575	−	0.762001i	$-0.275783\pi$
$83$	1.44102e70	1.29515	0.647575	+	0.762001i	$0.275783\pi$
$84$	0	0
$85$	3.64820e70	1.37495
$86$	1.04020e71	2.55815
$87$	0	0
$88$	−1.38670e71	−1.47355
$89$	−3.70525e70	−0.260664	−0.130332	−	0.991470i	$-0.541604\pi$
$89$	−3.70525e70	−0.260664	−0.130332	+	0.991470i	$0.541604\pi$
$90$	0	0
$91$	3.81503e71	1.19258
$92$	1.16317e71	0.243998
$93$	0	0
$94$	−9.66804e71	−0.925064
$95$	−1.27736e72	−0.830618
$96$	0	0
$97$	3.38939e71	0.103027	0.0515137	−	0.998672i	$-0.483595\pi$
$97$	3.38939e71	0.103027	0.0515137	+	0.998672i	$0.483595\pi$
$98$	−2.41379e72	−0.504601
$99$	0	0
$100$	−5.19625e72	−0.519625
$101$	6.71007e71	0.0466656	0.0233328	−	0.999728i	$-0.492572\pi$
$101$	6.71007e71	0.0466656	0.0233328	+	0.999728i	$0.492572\pi$
$102$	0	0
$103$	−2.69369e73	−0.915775	−0.457888	−	0.889010i	$-0.651394\pi$
$103$	−2.69369e73	−0.915775	−0.457888	+	0.889010i	$0.651394\pi$
$104$	−6.80503e73	−1.62597
$105$	0	0
$106$	1.63416e74	1.94818
$107$	−4.79460e73	−0.405737	−0.202869	−	0.979206i	$-0.565026\pi$
$107$	−4.79460e73	−0.405737	−0.202869	+	0.979206i	$0.565026\pi$
$108$	0	0
$109$	−2.34717e74	−1.01036	−0.505182	−	0.863013i	$-0.668575\pi$
$109$	−2.34717e74	−1.01036	−0.505182	+	0.863013i	$0.668575\pi$
$110$	5.75031e74	1.77361
$111$	0	0
$112$	−8.84007e73	−0.141253
$113$	−1.03352e75	−1.19386	−0.596931	−	0.802293i	$-0.703613\pi$
$113$	−1.03352e75	−1.19386	−0.596931	+	0.802293i	$0.703613\pi$
$114$	0	0
$115$	−1.97189e74	−0.120064
$116$	2.09104e75	0.928209
$117$	0	0
$118$	3.94870e75	0.939207
$119$	7.86380e75	1.37457
$120$	0	0
$121$	7.22094e75	0.686954
$122$	−1.39510e76	−0.982818
$123$	0	0
$124$	−1.05790e76	−0.411673
$125$	3.74853e76	1.08804
$126$	0	0
$127$	−6.92602e76	−1.12628	−0.563142	−	0.826360i	$-0.690408\pi$
$127$	−6.92602e76	−1.12628	−0.563142	+	0.826360i	$0.690408\pi$
$128$	−1.41361e77	−1.72649
$129$	0	0
$130$	2.82188e77	1.95707
$131$	1.76015e76	0.0922887	0.0461444	−	0.998935i	$-0.485307\pi$
$131$	1.76015e76	0.0922887	0.0461444	+	0.998935i	$0.485307\pi$
$132$	0	0
$133$	−2.75338e77	−0.830389
$134$	−4.11614e77	−0.944420
$135$	0	0
$136$	−1.40270e78	−1.87411
$137$	4.61954e77	0.472387	0.236193	−	0.971706i	$-0.424100\pi$
$137$	4.61954e77	0.472387	0.236193	+	0.971706i	$0.424100\pi$
$138$	0	0
$139$	2.47006e78	1.48822	0.744111	−	0.668056i	$-0.232873\pi$
$139$	2.47006e78	1.48822	0.744111	+	0.668056i	$0.232873\pi$
$140$	2.52608e78	1.17159
$141$	0	0
$142$	7.83999e78	2.16666
$143$	8.70197e78	1.86145
$144$	0	0
$145$	−3.54490e78	−0.456743
$146$	−1.63300e79	−1.63722
$147$	0	0
$148$	2.54029e79	1.55000
$149$	2.10744e79	1.00567	0.502835	−	0.864382i	$-0.332290\pi$
$149$	2.10744e79	1.00567	0.502835	+	0.864382i	$0.332290\pi$
$150$	0	0
$151$	−2.80175e79	−0.821808	−0.410904	−	0.911679i	$-0.634787\pi$
$151$	−2.80175e79	−0.821808	−0.410904	+	0.911679i	$0.634787\pi$
$152$	4.91132e79	1.13216
$153$	0	0
$154$	1.23949e80	1.77312
$155$	1.79344e79	0.202572
$156$	0	0
$157$	4.31233e79	0.305053	0.152526	−	0.988299i	$-0.451259\pi$
$157$	4.31233e79	0.305053	0.152526	+	0.988299i	$0.451259\pi$
$158$	−3.54689e80	−1.99005
$159$	0	0
$160$	2.00990e80	0.712518
$161$	−4.25048e79	−0.120031
$162$	0	0
$163$	2.42638e80	0.436628	0.218314	−	0.975879i	$-0.429944\pi$
$163$	2.42638e80	0.436628	0.218314	+	0.975879i	$0.429944\pi$
$164$	1.74464e81	2.51135
$165$	0	0
$166$	2.29755e81	2.12481
$167$	7.19837e80	0.534666	0.267333	−	0.963604i	$-0.413858\pi$
$167$	7.19837e80	0.534666	0.267333	+	0.963604i	$0.413858\pi$
$168$	0	0
$169$	2.19132e81	1.05400
$170$	5.81666e81	2.25573
$171$	0	0
$172$	1.04230e82	2.63758
$173$	7.61563e80	0.155963	0.0779817	−	0.996955i	$-0.475152\pi$
$173$	7.61563e80	0.155963	0.0779817	+	0.996955i	$0.475152\pi$
$174$	0	0
$175$	1.89883e81	0.255621
$176$	−2.01639e81	−0.220477
$177$	0	0
$178$	−5.90761e81	−0.427643
$179$	−2.45288e82	−1.44724	−0.723621	−	0.690197i	$-0.757524\pi$
$179$	−2.45288e82	−1.44724	−0.723621	+	0.690197i	$0.757524\pi$
$180$	0	0
$181$	−1.01305e82	−0.398442	−0.199221	−	0.979955i	$-0.563841\pi$
$181$	−1.01305e82	−0.398442	−0.199221	+	0.979955i	$0.563841\pi$
$182$	6.08265e82	1.95653
$183$	0	0
$184$	7.58174e81	0.163651
$185$	−4.30650e82	−0.762705
$186$	0	0
$187$	1.79371e83	2.14552
$188$	−9.68755e82	−0.953790
$189$	0	0
$190$	−2.03661e83	−1.36270
$191$	1.22649e83	0.677559	0.338780	−	0.940866i	$-0.389986\pi$
$191$	1.22649e83	0.677559	0.338780	+	0.940866i	$0.389986\pi$
$192$	0	0
$193$	−2.37981e82	−0.0898876	−0.0449438	−	0.998990i	$-0.514311\pi$
$193$	−2.37981e82	−0.0898876	−0.0449438	+	0.998990i	$0.514311\pi$
$194$	5.40401e82	0.169026
$195$	0	0
$196$	−2.41866e83	−0.520270
$197$	1.97247e83	0.352366	0.176183	−	0.984357i	$-0.443625\pi$
$197$	1.97247e83	0.352366	0.176183	+	0.984357i	$0.443625\pi$
$198$	0	0
$199$	−1.25645e84	−1.55241	−0.776206	−	0.630480i	$-0.782858\pi$
$199$	−1.25645e84	−1.55241	−0.776206	+	0.630480i	$0.782858\pi$
$200$	−3.38702e83	−0.348516
$201$	0	0
$202$	1.06985e83	0.0765591
$203$	−7.64113e83	−0.456617
$204$	0	0
$205$	−2.95766e84	−1.23576
$206$	−4.29479e84	−1.50241
$207$	0	0
$208$	−9.89517e83	−0.243283
$209$	−6.28038e84	−1.29612
$210$	0	0
$211$	−1.14628e85	−1.67101	−0.835505	−	0.549482i	$-0.814825\pi$
$211$	−1.14628e85	−1.67101	−0.835505	+	0.549482i	$0.814825\pi$
$212$	1.63745e85	2.00868
$213$	0	0
$214$	−7.64447e84	−0.665648
$215$	−1.76700e85	−1.29787
$216$	0	0
$217$	3.86580e84	0.202516
$218$	−3.74231e85	−1.65759
$219$	0	0
$220$	5.76191e85	1.82868
$221$	8.80238e85	2.36746
$222$	0	0
$223$	6.90864e85	1.33741	0.668705	−	0.743527i	$-0.266849\pi$
$223$	6.90864e85	1.33741	0.668705	+	0.743527i	$0.266849\pi$
$224$	4.33240e85	0.712322
$225$	0	0
$226$	−1.64783e86	−1.95864
$227$	1.09495e86	1.10777	0.553885	−	0.832593i	$-0.313145\pi$
$227$	1.09495e86	1.10777	0.553885	+	0.832593i	$0.313145\pi$
$228$	0	0
$229$	2.05799e86	1.51164	0.755819	−	0.654781i	$-0.227239\pi$
$229$	2.05799e86	1.51164	0.755819	+	0.654781i	$0.227239\pi$
$230$	−3.14397e85	−0.196976
$231$	0	0
$232$	1.36298e86	0.622555
$233$	−3.11195e86	−1.21490	−0.607451	−	0.794358i	$-0.707808\pi$
$233$	−3.11195e86	−1.21490	−0.607451	+	0.794358i	$0.707808\pi$
$234$	0	0
$235$	1.64231e86	0.469330
$236$	3.95667e86	0.968371
$237$	0	0
$238$	1.25380e87	2.25511
$239$	−5.50425e86	−0.849522	−0.424761	−	0.905305i	$-0.639642\pi$
$239$	−5.50425e86	−0.849522	−0.424761	+	0.905305i	$0.639642\pi$
$240$	0	0
$241$	−3.36564e86	−0.383218	−0.191609	−	0.981471i	$-0.561371\pi$
$241$	−3.36564e86	−0.383218	−0.191609	+	0.981471i	$0.561371\pi$
$242$	1.15130e87	1.12701
$243$	0	0
$244$	−1.39792e87	−1.01334
$245$	4.10031e86	0.256009
$246$	0	0
$247$	−3.08201e87	−1.43020
$248$	−6.89559e86	−0.276112
$249$	0	0
$250$	5.97662e87	1.78503
$251$	2.95049e87	0.761735	0.380867	−	0.924630i	$-0.375625\pi$
$251$	2.95049e87	0.761735	0.380867	+	0.924630i	$0.375625\pi$
$252$	0	0
$253$	−9.69520e86	−0.187352
$254$	−1.10428e88	−1.84777
$255$	0	0
$256$	−1.00127e88	−1.25832
$257$	3.50489e87	0.382046	0.191023	−	0.981586i	$-0.438819\pi$
$257$	3.50489e87	0.382046	0.191023	+	0.981586i	$0.438819\pi$
$258$	0	0
$259$	−9.28279e87	−0.762495
$260$	2.82758e88	2.01784
$261$	0	0
$262$	2.80637e87	0.151408
$263$	−3.88636e88	−1.82456	−0.912279	−	0.409569i	$-0.865679\pi$
$263$	−3.88636e88	−1.82456	−0.912279	+	0.409569i	$0.865679\pi$
$264$	0	0
$265$	−2.77594e88	−0.988408
$266$	−4.38997e88	−1.36233
$267$	0	0
$268$	−4.12445e88	−0.973746
$269$	−9.19679e87	−0.189530	−0.0947650	−	0.995500i	$-0.530210\pi$
$269$	−9.19679e87	−0.189530	−0.0947650	+	0.995500i	$0.530210\pi$
$270$	0	0
$271$	−4.14063e87	−0.0651159	−0.0325580	−	0.999470i	$-0.510365\pi$
$271$	−4.14063e87	−0.0651159	−0.0325580	+	0.999470i	$0.510365\pi$
$272$	−2.03966e88	−0.280409
$273$	0	0
$274$	7.36535e88	0.774993
$275$	4.33116e88	0.398989
$276$	0	0
$277$	1.14938e89	0.812737	0.406369	−	0.913709i	$-0.366795\pi$
$277$	1.14938e89	0.812737	0.406369	+	0.913709i	$0.366795\pi$
$278$	3.93825e89	2.44156
$279$	0	0
$280$	1.64655e89	0.785789
$281$	4.90170e88	0.205384	0.102692	−	0.994713i	$-0.467254\pi$
$281$	4.90170e88	0.205384	0.102692	+	0.994713i	$0.467254\pi$
$282$	0	0
$283$	−2.46352e89	−0.796805	−0.398402	−	0.917211i	$-0.630435\pi$
$283$	−2.46352e89	−0.796805	−0.398402	+	0.917211i	$0.630435\pi$
$284$	7.85581e89	2.23394
$285$	0	0
$286$	1.38743e90	3.05388
$287$	−6.37532e89	−1.23542
$288$	0	0
$289$	1.14948e90	1.72874
$290$	−5.65195e89	−0.749328
$291$	0	0
$292$	−1.63630e90	−1.68806
$293$	1.49279e90	1.35935	0.679675	−	0.733514i	$-0.262121\pi$
$293$	1.49279e90	1.35935	0.679675	+	0.733514i	$0.262121\pi$
$294$	0	0
$295$	−6.70767e89	−0.476506
$296$	1.65581e90	1.03959
$297$	0	0
$298$	3.36008e90	1.64989
$299$	−4.75779e89	−0.206731
$300$	0	0
$301$	−3.80881e90	−1.29751
$302$	−4.46708e90	−1.34825
$303$	0	0
$304$	7.14154e89	0.169397
$305$	2.36987e90	0.498631
$306$	0	0
$307$	−3.33315e90	−0.552464	−0.276232	−	0.961091i	$-0.589086\pi$
$307$	−3.33315e90	−0.552464	−0.276232	+	0.961091i	$0.589086\pi$
$308$	1.24200e91	1.82818
$309$	0	0
$310$	2.85944e90	0.332337
$311$	7.99091e90	0.825738	0.412869	−	0.910791i	$-0.364527\pi$
$311$	7.99091e90	0.825738	0.412869	+	0.910791i	$0.364527\pi$
$312$	0	0
$313$	2.38998e91	1.95445	0.977227	−	0.212197i	$-0.0680620\pi$
$313$	2.38998e91	1.95445	0.977227	+	0.212197i	$0.0680620\pi$
$314$	6.87555e90	0.500466
$315$	0	0
$316$	−3.55405e91	−2.05185
$317$	−3.26000e90	−0.167708	−0.0838542	−	0.996478i	$-0.526723\pi$
$317$	−3.26000e90	−0.167708	−0.0838542	+	0.996478i	$0.526723\pi$
$318$	0	0
$319$	−1.74292e91	−0.712717
$320$	3.59191e91	1.31024
$321$	0	0
$322$	−6.77692e90	−0.196921
$323$	−6.35284e91	−1.64845
$324$	0	0
$325$	2.12546e91	0.440261
$326$	3.86860e91	0.716328
$327$	0	0
$328$	1.13719e92	1.68437
$329$	3.54005e91	0.469201
$330$	0	0
$331$	−8.71306e90	−0.0925654	−0.0462827	−	0.998928i	$-0.514738\pi$
$331$	−8.71306e90	−0.0925654	−0.0462827	+	0.998928i	$0.514738\pi$
$332$	2.30219e92	2.19079
$333$	0	0
$334$	1.14770e92	0.877168
$335$	6.99210e91	0.479150
$336$	0	0
$337$	9.82568e91	0.541840	0.270920	−	0.962602i	$-0.412672\pi$
$337$	9.82568e91	0.541840	0.270920	+	0.962602i	$0.412672\pi$
$338$	3.49383e92	1.72919
$339$	0	0
$340$	5.82839e92	2.32578
$341$	8.81777e91	0.316099
$342$	0	0
$343$	3.75741e92	1.08806
$344$	6.79393e92	1.76904
$345$	0	0
$346$	1.21423e92	0.255872
$347$	5.42783e92	1.02944	0.514719	−	0.857359i	$-0.327896\pi$
$347$	5.42783e92	1.02944	0.514719	+	0.857359i	$0.327896\pi$
$348$	0	0
$349$	−1.13207e92	−0.174079	−0.0870395	−	0.996205i	$-0.527741\pi$
$349$	−1.13207e92	−0.174079	−0.0870395	+	0.996205i	$0.527741\pi$
$350$	3.02747e92	0.419369
$351$	0	0
$352$	9.88207e92	1.11184
$353$	−2.43382e92	−0.246895	−0.123447	−	0.992351i	$-0.539395\pi$
$353$	−2.43382e92	−0.246895	−0.123447	+	0.992351i	$0.539395\pi$
$354$	0	0
$355$	−1.33178e93	−1.09925
$356$	−5.91953e92	−0.440922
$357$	0	0
$358$	−3.91085e93	−2.37433
$359$	−1.41112e92	−0.0773776	−0.0386888	−	0.999251i	$-0.512318\pi$
$359$	−1.41112e92	−0.0773776	−0.0386888	+	0.999251i	$0.512318\pi$
$360$	0	0
$361$	−9.29175e90	−0.00415991
$362$	−1.61520e93	−0.653679
$363$	0	0
$364$	6.09493e93	2.01729
$365$	2.77399e93	0.830643
$366$	0	0
$367$	−1.09116e93	−0.267656	−0.133828	−	0.991005i	$-0.542727\pi$
$367$	−1.09116e93	−0.267656	−0.133828	+	0.991005i	$0.542727\pi$
$368$	1.10246e92	0.0244860
$369$	0	0
$370$	−6.86625e93	−1.25129
$371$	−5.98363e93	−0.988136
$372$	0	0
$373$	−1.92037e93	−0.260623	−0.130311	−	0.991473i	$-0.541598\pi$
$373$	−1.92037e93	−0.260623	−0.130311	+	0.991473i	$0.541598\pi$
$374$	2.85987e94	3.51992
$375$	0	0
$376$	−6.31453e93	−0.639712
$377$	−8.55313e93	−0.786441
$378$	0	0
$379$	1.21975e94	0.924567	0.462283	−	0.886732i	$-0.347030\pi$
$379$	1.21975e94	0.924567	0.462283	+	0.886732i	$0.347030\pi$
$380$	−2.04072e94	−1.40502
$381$	0	0
$382$	1.95551e94	1.11160
$383$	−1.64774e94	−0.851400	−0.425700	−	0.904864i	$-0.639972\pi$
$383$	−1.64774e94	−0.851400	−0.425700	+	0.904864i	$0.639972\pi$
$384$	0	0
$385$	−2.10553e94	−0.899591
$386$	−3.79434e93	−0.147469
$387$	0	0
$388$	5.41491e93	0.174274
$389$	1.57842e93	0.0462447	0.0231223	−	0.999733i	$-0.492639\pi$
$389$	1.57842e93	0.0462447	0.0231223	+	0.999733i	$0.492639\pi$
$390$	0	0
$391$	−9.80706e93	−0.238280
$392$	−1.57653e94	−0.348948
$393$	0	0
$394$	3.14489e94	0.578087
$395$	6.02511e94	1.00965
$396$	0	0
$397$	4.97423e94	0.693223	0.346611	−	0.938009i	$-0.387332\pi$
$397$	4.97423e94	0.693223	0.346611	+	0.938009i	$0.387332\pi$
$398$	−2.00327e95	−2.54687
$399$	0	0
$400$	−4.92505e93	−0.0521460
$401$	1.84398e95	1.78233	0.891163	−	0.453682i	$-0.149890\pi$
$401$	1.84398e95	1.78233	0.891163	+	0.453682i	$0.149890\pi$
$402$	0	0
$403$	4.32720e94	0.348797
$404$	1.07201e94	0.0789364
$405$	0	0
$406$	−1.21830e95	−0.749121
$407$	−2.11737e95	−1.19015
$408$	0	0
$409$	3.46318e94	0.162770	0.0813850	−	0.996683i	$-0.474066\pi$
$409$	3.46318e94	0.162770	0.0813850	+	0.996683i	$0.474066\pi$
$410$	−4.71567e95	−2.02737
$411$	0	0
$412$	−4.30346e95	−1.54906
$413$	−1.44586e95	−0.476374
$414$	0	0
$415$	−3.90285e95	−1.07802
$416$	4.84949e95	1.22685
$417$	0	0
$418$	−1.00134e96	−2.12641
$419$	−4.03746e95	−0.785772	−0.392886	−	0.919587i	$-0.628523\pi$
$419$	−4.03746e95	−0.785772	−0.392886	+	0.919587i	$0.628523\pi$
$420$	0	0
$421$	7.10860e94	0.116275	0.0581377	−	0.998309i	$-0.481484\pi$
$421$	7.10860e94	0.116275	0.0581377	+	0.998309i	$0.481484\pi$
$422$	−1.82761e96	−2.74144
$423$	0	0
$424$	1.06732e96	1.34723
$425$	4.38114e95	0.507447
$426$	0	0
$427$	5.10831e95	0.498494
$428$	−7.65989e95	−0.686318
$429$	0	0
$430$	−2.81728e96	−2.12927
$431$	−8.97999e95	−0.623528	−0.311764	−	0.950160i	$-0.600920\pi$
$431$	−8.97999e95	−0.623528	−0.311764	+	0.950160i	$0.600920\pi$
$432$	0	0
$433$	5.49073e95	0.321975	0.160987	−	0.986956i	$-0.448532\pi$
$433$	5.49073e95	0.321975	0.160987	+	0.986956i	$0.448532\pi$
$434$	6.16360e95	0.332245
$435$	0	0
$436$	−3.74986e96	−1.70906
$437$	3.43379e95	0.143946
$438$	0	0
$439$	2.02667e96	0.719165	0.359583	−	0.933113i	$-0.382919\pi$
$439$	2.02667e96	0.719165	0.359583	+	0.933113i	$0.382919\pi$
$440$	3.75572e96	1.22651
$441$	0	0
$442$	1.40344e97	3.88402
$443$	6.68470e96	1.70351	0.851757	−	0.523937i	$-0.175537\pi$
$443$	6.68470e96	1.70351	0.851757	+	0.523937i	$0.175537\pi$
$444$	0	0
$445$	1.00353e96	0.216964
$446$	1.10151e97	2.19414
$447$	0	0
$448$	7.74246e96	1.30988
$449$	−4.18030e96	−0.651953	−0.325976	−	0.945378i	$-0.605693\pi$
$449$	−4.18030e96	−0.651953	−0.325976	+	0.945378i	$0.605693\pi$
$450$	0	0
$451$	−1.45419e97	−1.92831
$452$	−1.65115e97	−2.01946
$453$	0	0
$454$	1.74577e97	1.81740
$455$	−1.03326e97	−0.992645
$456$	0	0
$457$	−1.11555e97	−0.913162	−0.456581	−	0.889682i	$-0.650926\pi$
$457$	−1.11555e97	−0.913162	−0.456581	+	0.889682i	$0.650926\pi$
$458$	3.28124e97	2.47998
$459$	0	0
$460$	−3.15031e96	−0.203092
$461$	2.25234e97	1.34137	0.670687	−	0.741740i	$-0.265999\pi$
$461$	2.25234e97	1.34137	0.670687	+	0.741740i	$0.265999\pi$
$462$	0	0
$463$	3.51982e97	1.78984	0.894919	−	0.446228i	$-0.147233\pi$
$463$	3.51982e97	1.78984	0.894919	+	0.446228i	$0.147233\pi$
$464$	1.98190e96	0.0931486
$465$	0	0
$466$	−4.96166e97	−1.99315
$467$	−1.56243e97	−0.580410	−0.290205	−	0.956965i	$-0.593723\pi$
$467$	−1.56243e97	−0.580410	−0.290205	+	0.956965i	$0.593723\pi$
$468$	0	0
$469$	1.50717e97	0.479019
$470$	2.61849e97	0.769978
$471$	0	0
$472$	2.57903e97	0.649492
$473$	−8.68777e97	−2.02524
$474$	0	0
$475$	−1.53399e97	−0.306552
$476$	1.25633e98	2.32514
$477$	0	0
$478$	−8.77592e97	−1.39372
$479$	9.54291e97	1.40422	0.702109	−	0.712069i	$-0.252242\pi$
$479$	9.54291e97	1.40422	0.702109	+	0.712069i	$0.252242\pi$
$480$	0	0
$481$	−1.03907e98	−1.31326
$482$	−5.36615e97	−0.628704
$483$	0	0
$484$	1.15362e98	1.16200
$485$	−9.17979e96	−0.0857550
$486$	0	0
$487$	1.64586e98	1.32308	0.661539	−	0.749911i	$-0.269904\pi$
$487$	1.64586e98	1.32308	0.661539	+	0.749911i	$0.269904\pi$
$488$	−9.11191e97	−0.679651
$489$	0	0
$490$	6.53749e97	0.420005
$491$	2.78063e98	1.65832	0.829159	−	0.559012i	$-0.188820\pi$
$491$	2.78063e98	1.65832	0.829159	+	0.559012i	$0.188820\pi$
$492$	0	0
$493$	−1.76303e98	−0.906456
$494$	−4.91393e98	−2.34636
$495$	0	0
$496$	−1.00268e97	−0.0413127
$497$	−2.87069e98	−1.09895
$498$	0	0
$499$	1.33205e98	0.440404	0.220202	−	0.975454i	$-0.429328\pi$
$499$	1.33205e98	0.440404	0.220202	+	0.975454i	$0.429328\pi$
$500$	5.98868e98	1.84046
$501$	0	0
$502$	4.70424e98	1.24969
$503$	−8.13928e96	−0.0201073	−0.0100537	−	0.999949i	$-0.503200\pi$
$503$	−8.13928e96	−0.0201073	−0.0100537	+	0.999949i	$0.503200\pi$
$504$	0	0
$505$	−1.81735e97	−0.0388422
$506$	−1.54579e98	−0.307367
$507$	0	0
$508$	−1.10651e99	−1.90515
$509$	1.29772e98	0.207961	0.103981	−	0.994579i	$-0.466842\pi$
$509$	1.29772e98	0.207961	0.103981	+	0.994579i	$0.466842\pi$
$510$	0	0
$511$	5.97941e98	0.830415
$512$	−2.61299e98	−0.337897
$513$	0	0
$514$	5.58817e98	0.626781
$515$	7.29557e98	0.762247
$516$	0	0
$517$	8.07474e98	0.732358
$518$	−1.48004e99	−1.25094
$519$	0	0
$520$	1.84307e99	1.35338
$521$	−1.96905e99	−1.34797	−0.673984	−	0.738746i	$-0.735418\pi$
$521$	−1.96905e99	−1.34797	−0.673984	+	0.738746i	$0.735418\pi$
$522$	0	0
$523$	−2.52411e99	−1.50244	−0.751220	−	0.660052i	$-0.770534\pi$
$523$	−2.52411e99	−1.50244	−0.751220	+	0.660052i	$0.770534\pi$
$524$	2.81204e98	0.156109
$525$	0	0
$526$	−6.19637e99	−2.99335
$527$	8.91951e98	0.402025
$528$	0	0
$529$	−2.49460e99	−0.979193
$530$	−4.42594e99	−1.62157
$531$	0	0
$532$	−4.39883e99	−1.40463
$533$	−7.13624e99	−2.12778
$534$	0	0
$535$	1.29857e99	0.337716
$536$	−2.68839e99	−0.653098
$537$	0	0
$538$	−1.46633e99	−0.310941
$539$	2.01600e99	0.399484
$540$	0	0
$541$	2.76758e99	0.479071	0.239536	−	0.970888i	$-0.423005\pi$
$541$	2.76758e99	0.479071	0.239536	+	0.970888i	$0.423005\pi$
$542$	−6.60178e98	−0.106828
$543$	0	0
$544$	9.99610e99	1.41407
$545$	6.35706e99	0.840977
$546$	0	0
$547$	−1.06027e100	−1.22710	−0.613549	−	0.789657i	$-0.710259\pi$
$547$	−1.06027e100	−1.22710	−0.613549	+	0.789657i	$0.710259\pi$
$548$	7.38021e99	0.799058
$549$	0	0
$550$	6.90557e99	0.654578
$551$	6.17296e99	0.547596
$552$	0	0
$553$	1.29873e100	1.00937
$554$	1.83255e100	1.33337
$555$	0	0
$556$	3.94619e100	2.51738
$557$	2.06065e100	1.23109	0.615544	−	0.788102i	$-0.288936\pi$
$557$	2.06065e100	1.23109	0.615544	+	0.788102i	$0.288936\pi$
$558$	0	0
$559$	−4.26341e100	−2.23473
$560$	2.39424e99	0.117572
$561$	0	0
$562$	7.81523e99	0.336951
$563$	−1.21330e100	−0.490245	−0.245122	−	0.969492i	$-0.578828\pi$
$563$	−1.21330e100	−0.490245	−0.245122	+	0.969492i	$0.578828\pi$
$564$	0	0
$565$	2.79917e100	0.993711
$566$	−3.92782e100	−1.30723
$567$	0	0
$568$	5.12057e100	1.49832
$569$	−4.59237e100	−1.26020	−0.630100	−	0.776514i	$-0.716986\pi$
$569$	−4.59237e100	−1.26020	−0.630100	+	0.776514i	$0.716986\pi$
$570$	0	0
$571$	1.78384e100	0.430664	0.215332	−	0.976541i	$-0.430917\pi$
$571$	1.78384e100	0.430664	0.215332	+	0.976541i	$0.430917\pi$
$572$	1.39023e101	3.14871
$573$	0	0
$574$	−1.01648e101	−2.02681
$575$	−2.36806e99	−0.0443114
$576$	0	0
$577$	8.01529e100	1.32130	0.660651	−	0.750693i	$-0.270280\pi$
$577$	8.01529e100	1.32130	0.660651	+	0.750693i	$0.270280\pi$
$578$	1.83272e101	2.83616
$579$	0	0
$580$	−5.66336e100	−0.772596
$581$	−8.41272e100	−1.07772
$582$	0	0
$583$	−1.36485e101	−1.54234
$584$	−1.06657e101	−1.13219
$585$	0	0
$586$	2.38009e101	2.23013
$587$	7.04852e100	0.620594	0.310297	−	0.950640i	$-0.399572\pi$
$587$	7.04852e100	0.620594	0.310297	+	0.950640i	$0.399572\pi$
$588$	0	0
$589$	−3.12302e100	−0.242866
$590$	−1.06946e101	−0.781750
$591$	0	0
$592$	2.40771e100	0.155547
$593$	−9.98127e99	−0.0606303	−0.0303151	−	0.999540i	$-0.509651\pi$
$593$	−9.98127e99	−0.0606303	−0.0303151	+	0.999540i	$0.509651\pi$
$594$	0	0
$595$	−2.12983e101	−1.14413
$596$	3.36686e101	1.70113
$597$	0	0
$598$	−7.58577e100	−0.339161
$599$	1.09544e101	0.460799	0.230399	−	0.973096i	$-0.425997\pi$
$599$	1.09544e101	0.460799	0.230399	+	0.973096i	$0.425997\pi$
$600$	0	0
$601$	1.50406e100	0.0560205	0.0280103	−	0.999608i	$-0.491083\pi$
$601$	1.50406e100	0.0560205	0.0280103	+	0.999608i	$0.491083\pi$
$602$	−6.07273e101	−2.12869
$603$	0	0
$604$	−4.47609e101	−1.39011
$605$	−1.95571e101	−0.571787
$606$	0	0
$607$	−5.22503e101	−1.35426	−0.677129	−	0.735864i	$-0.736776\pi$
$607$	−5.22503e101	−1.35426	−0.677129	+	0.735864i	$0.736776\pi$
$608$	−3.49997e101	−0.854248
$609$	0	0
$610$	3.77849e101	0.818049
$611$	3.96257e101	0.808114
$612$	0	0
$613$	7.48452e101	1.35474	0.677371	−	0.735641i	$-0.263119\pi$
$613$	7.48452e101	1.35474	0.677371	+	0.735641i	$0.263119\pi$
$614$	−5.31434e101	−0.906367
$615$	0	0
$616$	8.09557e101	1.22617
$617$	−6.91230e101	−0.986765	−0.493383	−	0.869812i	$-0.664240\pi$
$617$	−6.91230e101	−0.986765	−0.493383	+	0.869812i	$0.664240\pi$
$618$	0	0
$619$	−3.46069e101	−0.438989	−0.219495	−	0.975614i	$-0.570441\pi$
$619$	−3.46069e101	−0.438989	−0.219495	+	0.975614i	$0.570441\pi$
$620$	2.86521e101	0.342657
$621$	0	0
$622$	1.27406e102	1.35470
$623$	2.16313e101	0.216905
$624$	0	0
$625$	−6.70876e101	−0.598441
$626$	3.81056e102	3.20646
$627$	0	0
$628$	6.88942e101	0.516007
$629$	−2.14181e102	−1.51367
$630$	0	0
$631$	−2.33316e102	−1.46849	−0.734247	−	0.678882i	$-0.762465\pi$
$631$	−2.33316e102	−1.46849	−0.734247	+	0.678882i	$0.762465\pi$
$632$	−2.31660e102	−1.37619
$633$	0	0
$634$	−5.19772e101	−0.275141
$635$	1.87584e102	0.937464
$636$	0	0
$637$	9.89323e101	0.440807
$638$	−2.77889e102	−1.16928
$639$	0	0
$640$	3.82861e102	1.43705
$641$	−4.71888e102	−1.67310	−0.836548	−	0.547893i	$-0.815430\pi$
$641$	−4.71888e102	−1.67310	−0.836548	+	0.547893i	$0.815430\pi$
$642$	0	0
$643$	−4.02862e102	−1.27484	−0.637420	−	0.770516i	$-0.719998\pi$
$643$	−4.02862e102	−1.27484	−0.637420	+	0.770516i	$0.719998\pi$
$644$	−6.79059e101	−0.203036
$645$	0	0
$646$	−1.01289e103	−2.70443
$647$	−3.84535e102	−0.970353	−0.485177	−	0.874416i	$-0.661245\pi$
$647$	−3.84535e102	−0.970353	−0.485177	+	0.874416i	$0.661245\pi$
$648$	0	0
$649$	−3.29795e102	−0.743555
$650$	3.38881e102	0.722287
$651$	0	0
$652$	3.87641e102	0.738571
$653$	−4.39591e101	−0.0791986	−0.0395993	−	0.999216i	$-0.512608\pi$
$653$	−4.39591e101	−0.0791986	−0.0395993	+	0.999216i	$0.512608\pi$
$654$	0	0
$655$	−4.76719e101	−0.0768166
$656$	1.65359e102	0.252021
$657$	0	0
$658$	5.64422e102	0.769767
$659$	2.74596e102	0.354305	0.177153	−	0.984183i	$-0.443311\pi$
$659$	2.74596e102	0.354305	0.177153	+	0.984183i	$0.443311\pi$
$660$	0	0
$661$	−1.38738e103	−1.60267	−0.801334	−	0.598217i	$-0.795876\pi$
$661$	−1.38738e103	−1.60267	−0.801334	+	0.598217i	$0.795876\pi$
$662$	−1.38920e102	−0.151862
$663$	0	0
$664$	1.50061e103	1.46938
$665$	7.45724e102	0.691175
$666$	0	0
$667$	9.52937e101	0.0791537
$668$	1.15002e103	0.904406
$669$	0	0
$670$	1.11481e103	0.786089
$671$	1.16519e103	0.778081
$672$	0	0
$673$	−3.23651e102	−0.193877	−0.0969387	−	0.995290i	$-0.530905\pi$
$673$	−3.23651e102	−0.193877	−0.0969387	+	0.995290i	$0.530905\pi$
$674$	1.56660e103	0.888938
$675$	0	0
$676$	3.50088e103	1.78288
$677$	−1.27970e103	−0.617479	−0.308740	−	0.951147i	$-0.599907\pi$
$677$	−1.27970e103	−0.617479	−0.308740	+	0.951147i	$0.599907\pi$
$678$	0	0
$679$	−1.97873e102	−0.0857314
$680$	3.79906e103	1.55991
$681$	0	0
$682$	1.40590e103	0.518589
$683$	−5.71497e102	−0.199829	−0.0999144	−	0.994996i	$-0.531857\pi$
$683$	−5.71497e102	−0.199829	−0.0999144	+	0.994996i	$0.531857\pi$
$684$	0	0
$685$	−1.25115e103	−0.393192
$686$	5.99077e103	1.78506
$687$	0	0
$688$	9.87903e102	0.264689
$689$	−6.69780e103	−1.70189
$690$	0	0
$691$	4.49013e103	1.02639	0.513193	−	0.858273i	$-0.328463\pi$
$691$	4.49013e103	1.02639	0.513193	+	0.858273i	$0.328463\pi$
$692$	1.21668e103	0.263817
$693$	0	0
$694$	8.65408e103	1.68889
$695$	−6.68990e103	−1.23872
$696$	0	0
$697$	−1.47097e104	−2.45249
$698$	−1.80497e103	−0.285592
$699$	0	0
$700$	3.03358e103	0.432391
$701$	1.08120e104	1.46284	0.731422	−	0.681925i	$-0.238857\pi$
$701$	1.08120e104	1.46284	0.731422	+	0.681925i	$0.238857\pi$
$702$	0	0
$703$	7.49919e103	0.914419
$704$	1.76603e104	2.04454
$705$	0	0
$706$	−3.88046e103	−0.405053
$707$	−3.91735e102	−0.0388315
$708$	0	0
$709$	−1.89558e104	−1.69494	−0.847470	−	0.530843i	$-0.821875\pi$
$709$	−1.89558e104	−1.69494	−0.847470	+	0.530843i	$0.821875\pi$
$710$	−2.12338e104	−1.80342
$711$	0	0
$712$	−3.85846e103	−0.295729
$713$	−4.82110e102	−0.0351057
$714$	0	0
$715$	−2.35683e104	−1.54938
$716$	−3.91875e104	−2.44806
$717$	0	0
$718$	−2.24987e103	−0.126945
$719$	−2.05381e103	−0.110143	−0.0550713	−	0.998482i	$-0.517539\pi$
$719$	−2.05381e103	−0.110143	−0.0550713	+	0.998482i	$0.517539\pi$
$720$	0	0
$721$	1.57258e104	0.762037
$722$	−1.48147e102	−0.00682471
$723$	0	0
$724$	−1.61846e104	−0.673977
$725$	−4.25708e103	−0.168568
$726$	0	0
$727$	−2.37156e104	−0.849235	−0.424617	−	0.905373i	$-0.639591\pi$
$727$	−2.37156e104	−0.849235	−0.424617	+	0.905373i	$0.639591\pi$
$728$	3.97279e104	1.35301
$729$	0	0
$730$	4.42282e104	1.36274
$731$	−8.78802e104	−2.57577
$732$	0	0
$733$	−3.38968e104	−0.899215	−0.449607	−	0.893226i	$-0.648436\pi$
$733$	−3.38968e104	−0.899215	−0.449607	+	0.893226i	$0.648436\pi$
$734$	−1.73974e104	−0.439114
$735$	0	0
$736$	−5.40301e103	−0.123480
$737$	3.43780e104	0.747682
$738$	0	0
$739$	7.30628e104	1.43938	0.719689	−	0.694297i	$-0.244285\pi$
$739$	7.30628e104	1.43938	0.719689	+	0.694297i	$0.244285\pi$
$740$	−6.88010e104	−1.29014
$741$	0	0
$742$	−9.54024e104	−1.62113
$743$	5.81323e104	0.940429	0.470214	−	0.882552i	$-0.344177\pi$
$743$	5.81323e104	0.940429	0.470214	+	0.882552i	$0.344177\pi$
$744$	0	0
$745$	−5.70777e104	−0.837071
$746$	−3.06182e104	−0.427575
$747$	0	0
$748$	2.86564e105	3.62922
$749$	2.79910e104	0.337623
$750$	0	0
$751$	2.16876e104	0.237331	0.118665	−	0.992934i	$-0.462138\pi$
$751$	2.16876e104	0.237331	0.118665	+	0.992934i	$0.462138\pi$
$752$	−9.18194e103	−0.0957157
$753$	0	0
$754$	−1.36370e105	−1.29023
$755$	7.58823e104	0.684032
$756$	0	0
$757$	1.98343e105	1.62337	0.811686	−	0.584095i	$-0.198550\pi$
$757$	1.98343e105	1.62337	0.811686	+	0.584095i	$0.198550\pi$
$758$	1.94475e105	1.51683
$759$	0	0
$760$	−1.33018e105	−0.942354
$761$	4.55380e104	0.307492	0.153746	−	0.988110i	$-0.450866\pi$
$761$	4.55380e104	0.307492	0.153746	+	0.988110i	$0.450866\pi$
$762$	0	0
$763$	1.37028e105	0.840746
$764$	1.95945e105	1.14611
$765$	0	0
$766$	−2.62714e105	−1.39680
$767$	−1.61843e105	−0.820469
$768$	0	0
$769$	5.60355e104	0.258316	0.129158	−	0.991624i	$-0.458773\pi$
$769$	5.60355e104	0.258316	0.129158	+	0.991624i	$0.458773\pi$
$770$	−3.35704e105	−1.47586
$771$	0	0
$772$	−3.80200e104	−0.152048
$773$	−3.54192e105	−1.35110	−0.675549	−	0.737315i	$-0.736093\pi$
$773$	−3.54192e105	−1.35110	−0.675549	+	0.737315i	$0.736093\pi$
$774$	0	0
$775$	2.15374e104	0.0747622
$776$	3.52954e104	0.116887
$777$	0	0
$778$	2.51661e104	0.0758685
$779$	5.15036e105	1.48157
$780$	0	0
$781$	−6.54795e105	−1.71531
$782$	−1.56363e105	−0.390919
$783$	0	0
$784$	−2.29243e104	−0.0522106
$785$	−1.16795e105	−0.253911
$786$	0	0
$787$	−3.56055e105	−0.705407	−0.352704	−	0.935735i	$-0.614738\pi$
$787$	−3.56055e105	−0.705407	−0.352704	+	0.935735i	$0.614738\pi$
$788$	3.15124e105	0.596038
$789$	0	0
$790$	9.60638e105	1.65642
$791$	6.03368e105	0.993438
$792$	0	0
$793$	5.71801e105	0.858566
$794$	7.93087e105	1.13729
$795$	0	0
$796$	−2.00731e106	−2.62596
$797$	−5.25518e104	−0.0656688	−0.0328344	−	0.999461i	$-0.510453\pi$
$797$	−5.25518e104	−0.0656688	−0.0328344	+	0.999461i	$0.510453\pi$
$798$	0	0
$799$	8.16791e105	0.931437
$800$	2.41370e105	0.262966
$801$	0	0
$802$	2.94003e106	2.92407
$803$	1.36388e106	1.29616
$804$	0	0
$805$	1.15120e105	0.0999078
$806$	6.89925e105	0.572233
$807$	0	0
$808$	6.98754e104	0.0529431
$809$	−1.82851e106	−1.32427	−0.662136	−	0.749384i	$-0.730350\pi$
$809$	−1.82851e106	−1.32427	−0.662136	+	0.749384i	$0.730350\pi$
$810$	0	0
$811$	2.89168e106	1.91376	0.956882	−	0.290477i	$-0.0938139\pi$
$811$	2.89168e106	1.91376	0.956882	+	0.290477i	$0.0938139\pi$
$812$	−1.22075e106	−0.772383
$813$	0	0
$814$	−3.37592e106	−1.95255
$815$	−6.57160e105	−0.363428
$816$	0	0
$817$	3.07698e106	1.55604
$818$	5.52166e105	0.267039
$819$	0	0
$820$	−4.72518e106	−2.09032
$821$	8.16158e105	0.345342	0.172671	−	0.984980i	$-0.444760\pi$
$821$	8.16158e105	0.345342	0.172671	+	0.984980i	$0.444760\pi$
$822$	0	0
$823$	−2.88771e106	−1.11805	−0.559024	−	0.829152i	$-0.688824\pi$
$823$	−2.88771e106	−1.11805	−0.559024	+	0.829152i	$0.688824\pi$
$824$	−2.80508e106	−1.03897
$825$	0	0
$826$	−2.30526e106	−0.781535
$827$	3.86945e106	1.25516	0.627579	−	0.778553i	$-0.284046\pi$
$827$	3.86945e106	1.25516	0.627579	+	0.778553i	$0.284046\pi$
$828$	0	0
$829$	4.59567e106	1.36492	0.682461	−	0.730922i	$-0.260910\pi$
$829$	4.59567e106	1.36492	0.682461	+	0.730922i	$0.260910\pi$
$830$	−6.22267e106	−1.76859
$831$	0	0
$832$	8.66656e106	2.25603
$833$	2.03926e106	0.508077
$834$	0	0
$835$	−1.94960e106	−0.445030
$836$	−1.00336e107	−2.19244
$837$	0	0
$838$	−6.43729e106	−1.28913
$839$	2.07164e106	0.397193	0.198597	−	0.980081i	$-0.436362\pi$
$839$	2.07164e106	0.397193	0.198597	+	0.980081i	$0.436362\pi$
$840$	0	0
$841$	−3.97613e106	−0.698886
$842$	1.13339e106	0.190760
$843$	0	0
$844$	−1.83130e107	−2.82657
$845$	−5.93497e106	−0.877301
$846$	0	0
$847$	−4.21560e106	−0.571629
$848$	1.55199e106	0.201577
$849$	0	0
$850$	6.98525e106	0.832513
$851$	1.15767e106	0.132177
$852$	0	0
$853$	1.22138e107	1.28000	0.640002	−	0.768373i	$-0.278934\pi$
$853$	1.22138e107	1.28000	0.640002	+	0.768373i	$0.278934\pi$
$854$	8.14465e106	0.817824
$855$	0	0
$856$	−4.99286e106	−0.460317
$857$	−6.15560e106	−0.543839	−0.271920	−	0.962320i	$-0.587659\pi$
$857$	−6.15560e106	−0.543839	−0.271920	+	0.962320i	$0.587659\pi$
$858$	0	0
$859$	−8.34532e105	−0.0677162	−0.0338581	−	0.999427i	$-0.510779\pi$
$859$	−8.34532e105	−0.0677162	−0.0338581	+	0.999427i	$0.510779\pi$
$860$	−2.82297e107	−2.19539
$861$	0	0
$862$	−1.43176e107	−1.02295
$863$	−3.81216e106	−0.261082	−0.130541	−	0.991443i	$-0.541671\pi$
$863$	−3.81216e106	−0.261082	−0.130541	+	0.991443i	$0.541671\pi$
$864$	0	0
$865$	−2.06261e106	−0.129816
$866$	8.75436e106	0.528228
$867$	0	0
$868$	6.17603e106	0.342562
$869$	2.96236e107	1.57549
$870$	0	0
$871$	1.68705e107	0.825023
$872$	−2.44423e107	−1.14628
$873$	0	0
$874$	5.47480e106	0.236157
$875$	−2.18840e107	−0.905384
$876$	0	0
$877$	8.06360e105	0.0306933	0.0153467	−	0.999882i	$-0.495115\pi$
$877$	8.06360e105	0.0306933	0.0153467	+	0.999882i	$0.495115\pi$
$878$	3.23131e107	1.17985
$879$	0	0
$880$	5.46118e106	0.183514
$881$	−1.01969e107	−0.328735	−0.164367	−	0.986399i	$-0.552558\pi$
$881$	−1.01969e107	−0.328735	−0.164367	+	0.986399i	$0.552558\pi$
$882$	0	0
$883$	−2.99686e107	−0.889408	−0.444704	−	0.895678i	$-0.646691\pi$
$883$	−2.99686e107	−0.889408	−0.444704	+	0.895678i	$0.646691\pi$
$884$	1.40627e108	4.00463
$885$	0	0
$886$	1.06580e108	2.79477
$887$	4.43897e107	1.11704	0.558522	−	0.829490i	$-0.311369\pi$
$887$	4.43897e107	1.11704	0.558522	+	0.829490i	$0.311369\pi$
$888$	0	0
$889$	4.04343e107	0.937206
$890$	1.60001e107	0.355949
$891$	0	0
$892$	1.10373e108	2.26227
$893$	−2.85986e107	−0.562687
$894$	0	0
$895$	6.64337e107	1.20461
$896$	8.25267e107	1.43665
$897$	0	0
$898$	−6.66503e107	−1.06959
$899$	−8.66695e106	−0.133548
$900$	0	0
$901$	−1.38059e108	−1.96160
$902$	−2.31855e108	−3.16357
$903$	0	0
$904$	−1.07625e108	−1.35446
$905$	2.74375e107	0.331643
$906$	0	0
$907$	−5.06142e106	−0.0564426	−0.0282213	−	0.999602i	$-0.508984\pi$
$907$	−5.06142e106	−0.0564426	−0.0282213	+	0.999602i	$0.508984\pi$
$908$	1.74930e108	1.87383
$909$	0	0
$910$	−1.64742e108	−1.62852
$911$	−6.00813e107	−0.570583	−0.285291	−	0.958441i	$-0.592090\pi$
$911$	−6.00813e107	−0.570583	−0.285291	+	0.958441i	$0.592090\pi$
$912$	0	0
$913$	−1.91891e108	−1.68218
$914$	−1.77862e108	−1.49812
$915$	0	0
$916$	3.28786e108	2.55698
$917$	−1.02758e107	−0.0767955
$918$	0	0
$919$	−2.62509e108	−1.81187	−0.905937	−	0.423413i	$-0.860832\pi$
$919$	−2.62509e108	−1.81187	−0.905937	+	0.423413i	$0.860832\pi$
$920$	−2.05343e107	−0.136215
$921$	0	0
$922$	3.59111e108	2.20064
$923$	−3.21332e108	−1.89274
$924$	0	0
$925$	−5.17170e107	−0.281488
$926$	5.61196e108	2.93639
$927$	0	0
$928$	−9.71305e107	−0.469737
$929$	3.15796e108	1.46836	0.734181	−	0.678954i	$-0.237566\pi$
$929$	3.15796e108	1.46836	0.734181	+	0.678954i	$0.237566\pi$
$930$	0	0
$931$	−7.14013e107	−0.306932
$932$	−4.97167e108	−2.05505
$933$	0	0
$934$	−2.49113e108	−0.952214
$935$	−4.85806e108	−1.78583
$936$	0	0
$937$	4.12136e108	1.40135	0.700673	−	0.713482i	$-0.252883\pi$
$937$	4.12136e108	1.40135	0.700673	+	0.713482i	$0.252883\pi$
$938$	2.40301e108	0.785873
$939$	0	0
$940$	2.62377e108	0.793888
$941$	3.47164e108	1.01045	0.505224	−	0.862989i	$-0.331410\pi$
$941$	3.47164e108	1.01045	0.505224	+	0.862989i	$0.331410\pi$
$942$	0	0
$943$	7.95076e107	0.214157
$944$	3.75016e107	0.0971790
$945$	0	0
$946$	−1.38517e109	−3.32259
$947$	−6.22124e107	−0.143583	−0.0717914	−	0.997420i	$-0.522872\pi$
$947$	−6.22124e107	−0.143583	−0.0717914	+	0.997420i	$0.522872\pi$
$948$	0	0
$949$	6.69307e108	1.43024
$950$	−2.44577e108	−0.502926
$951$	0	0
$952$	8.18898e108	1.55948
$953$	1.83299e108	0.335946	0.167973	−	0.985792i	$-0.446278\pi$
$953$	1.83299e108	0.335946	0.167973	+	0.985792i	$0.446278\pi$
$954$	0	0
$955$	−3.32182e108	−0.563967
$956$	−8.79363e108	−1.43699
$957$	0	0
$958$	1.52151e109	2.30375
$959$	−2.69689e108	−0.393083
$960$	0	0
$961$	−6.96445e108	−0.940770
$962$	−1.65669e109	−2.15452
$963$	0	0
$964$	−5.37698e108	−0.648226
$965$	6.44545e107	0.0748181
$966$	0	0
$967$	−7.58384e108	−0.816250	−0.408125	−	0.912926i	$-0.633817\pi$
$967$	−7.58384e108	−0.816250	−0.408125	+	0.912926i	$0.633817\pi$
$968$	7.51953e108	0.779364
$969$	0	0
$970$	−1.46362e108	−0.140689
$971$	1.18116e108	0.109347	0.0546737	−	0.998504i	$-0.482588\pi$
$971$	1.18116e108	0.109347	0.0546737	+	0.998504i	$0.482588\pi$
$972$	0	0
$973$	−1.44203e109	−1.23838
$974$	2.62414e109	2.17063
$975$	0	0
$976$	−1.32496e108	−0.101691
$977$	2.49823e108	0.184706	0.0923528	−	0.995726i	$-0.470561\pi$
$977$	2.49823e108	0.184706	0.0923528	+	0.995726i	$0.470561\pi$
$978$	0	0
$979$	4.93403e108	0.338558
$980$	6.55069e108	0.433047
$981$	0	0
$982$	4.43340e109	2.72062
$983$	−1.72004e109	−1.01703	−0.508517	−	0.861052i	$-0.669806\pi$
$983$	−1.72004e109	−1.01703	−0.508517	+	0.861052i	$0.669806\pi$
$984$	0	0
$985$	−5.34223e108	−0.293292
$986$	−2.81096e109	−1.48712
$987$	0	0
$988$	−4.92384e109	−2.41922
$989$	4.75003e108	0.224922
$990$	0	0
$991$	−1.06575e108	−0.0468777	−0.0234389	−	0.999725i	$-0.507462\pi$
$991$	−1.06575e108	−0.0468777	−0.0234389	+	0.999725i	$0.507462\pi$
$992$	4.91403e108	0.208335
$993$	0	0
$994$	−4.57700e109	−1.80293
$995$	3.40295e109	1.29215
$996$	0	0
$997$	3.85126e109	1.35903	0.679517	−	0.733660i	$-0.262190\pi$
$997$	3.85126e109	1.35903	0.679517	+	0.733660i	$0.262190\pi$
$998$	2.12381e109	0.722522
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.74.a.a.1.5		5
3.2	odd	2		1.74.a.a.1.1	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.74.a.a.1.1	✓	5	3.2	odd	2
9.74.a.a.1.5		5	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:	\( k \)	\(=\)	\( 74 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q+1.59439e11 q^{2} +1.59761e22 q^{4} -2.70839e25 q^{5} -5.83802e30 q^{7} +1.04135e33 q^{8} +O(q^{10})\)	\(q+1.59439e11 q^{2} +1.59761e22 q^{4} -2.70839e25 q^{5} -5.83802e30 q^{7} +1.04135e33 q^{8} -4.31824e36 q^{10} -1.33163e38 q^{11} -6.53481e40 q^{13} -9.30808e41 q^{14} +1.51423e43 q^{16} -1.34700e45 q^{17} +4.71630e46 q^{19} -4.32695e47 q^{20} -2.12314e49 q^{22} +7.28068e48 q^{23} -3.25252e50 q^{25} -1.04190e52 q^{26} -9.32686e52 q^{28} +1.30886e53 q^{29} -6.62177e53 q^{31} -7.42102e54 q^{32} -2.14764e56 q^{34} +1.58116e56 q^{35} +1.59006e57 q^{37} +7.51962e57 q^{38} -2.82039e58 q^{40} +1.09204e59 q^{41} +6.52415e59 q^{43} -2.12743e60 q^{44} +1.16082e60 q^{46} -6.06379e60 q^{47} -1.51393e61 q^{49} -5.18579e61 q^{50} -1.04401e63 q^{52} +1.02494e63 q^{53} +3.60659e63 q^{55} -6.07943e63 q^{56} +2.08683e64 q^{58} +2.47662e64 q^{59} -8.75008e64 q^{61} -1.05577e65 q^{62} -1.32621e66 q^{64} +1.76988e66 q^{65} -2.58164e66 q^{67} -2.15197e67 q^{68} +2.52099e67 q^{70} +4.91723e67 q^{71} -1.02422e68 q^{73} +2.53517e68 q^{74} +7.53479e68 q^{76} +7.77410e68 q^{77} -2.22461e69 q^{79} -4.10112e68 q^{80} +1.74113e70 q^{82} +1.44102e70 q^{83} +3.64820e70 q^{85} +1.04020e71 q^{86} -1.38670e71 q^{88} -3.70525e70 q^{89} +3.81503e71 q^{91} +1.16317e71 q^{92} -9.66804e71 q^{94} -1.27736e72 q^{95} +3.38939e71 q^{97} -2.41379e72 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 92089333488 q^{2} + 89\!\cdots\!60 q^{4}+ \cdots + 38\!\cdots\!80 q^{8}+O(q^{10}) \) 5 * q + 92089333488 * q^2 + 891110479259563516160 * q^4 - 23099529720469471562826750 * q^5 - 4356178487147579439806268090008 * q^7 + 382321348565178801062509850849280 * q^8	\( 5 q + 92089333488 q^{2} + 89\!\cdots\!60 q^{4}+ \cdots + 76\!\cdots\!16 q^{98}+O(q^{100}) \) 5 * q + 92089333488 * q^2 + 891110479259563516160 * q^4 - 23099529720469471562826750 * q^5 - 4356178487147579439806268090008 * q^7 + 382321348565178801062509850849280 * q^8 - 1082726120403847340426026649690244000 * q^10 - 50083756421782317855880849016778496860 * q^11 + 4753748397471720291047553799357192278886 * q^13 - 263363595637460329420141722180437171694720 * q^14 + 57509595349357883169785087518099233197588480 * q^16 - 663279725175909884624200257401822351394256602 * q^17 + 31387402430958534058855312636541530201995765700 * q^19 - 68535205735011202400715856751699460073169856000 * q^20 - 9492394168845783423791120540922405517833204177216 * q^22 + 41173446223173693726617088414497261153026772718024 * q^23 + 321010940201155914585034686800814006311220324546875 * q^25 - 4496438035379975943261998606627087983483848085006560 * q^26 - 37814301174111882879202704910382387341459683517577216 * q^28 + 217397685843681573854388291537651452827057882148450250 * q^29 - 3959918978904396097569386510196715694840286709585401440 * q^31 + 9479144378484593489541015426974249650207814007382867968 * q^32 - 324638192385754362369074018224584035205208569018875155680 * q^34 + 1051811671165262926972759981500117019527196204743409914000 * q^35 - 6710426612911460903226679780416929578822322356442579950178 * q^37 + 20075776649866586500887218371135359952534984707306414947520 * q^38 - 87443314425210154156114784714128373503740284779633935360000 * q^40 + 89999556000464227434562342749528590851939245788450434103790 * q^41 + 1171421579861687300375905115748875459141635816468653452284156 * q^43 - 3620387401482413711753562750789250834104238410455247119723520 * q^44 + 13122337792181100518478081314861771936057558300377044573644160 * q^46 - 26407117391117866585989236437476333636637017745173062895096432 * q^47 - 47859785088079990485612756297590896342589260563105328803969315 * q^49 + 198341627273982740927873511630518057650356858808871192258250000 * q^50 - 1819820853930882517149424007699825989256997486995920851867734528 * q^52 + 2253672757277210109476755074185818948452790752453662372858468754 * q^53 + 5272301841223840031246441919708126997046467528986443289345081000 * q^55 - 17369101267271748189623122493455314696373137673860233497989120000 * q^56 + 63080485469034924979732075223792805715626817023343777138220605920 * q^58 - 49827032054541030737892137385762950528020446432538215007741437900 * q^59 - 200207946356755779993110124671040230418699916707275462827300034090 * q^61 + 456512716932753516995161459627410738703514050956609499700325060096 * q^62 - 2671988611100492125931167910213768824231319631401339943695669002240 * q^64 + 2221078323698894670419341126197735507928898751783246157619800369500 * q^65 + 1726934463658866670044856129309631728944059099751189118466533017652 * q^67 - 25844159932565717701710366021885253281928511625890180327915132834304 * q^68 + 60019715162941233136874683443010604187189046779871920798680662752000 * q^70 - 29528228383509762365399718501357560736875772117852859701209862331560 * q^71 - 237248424072934328617284197336037660641948064767277176027665176375374 * q^73 + 385668396032745357868624366253781435784895053179379214963132226802080 * q^74 - 402469771116557587325960702574461860644965601604695023105081798528000 * q^76 + 1160921420345569675442649510235573702285949327395662717704239852301856 * q^77 + 1210019475236668608258558597507004925943189831192425236151129201347600 * q^79 - 7695510793835037324754830224890315360926193938062866122926593916928000 * q^80 + 19869905655996015892436375229312420723635630923691072274009372051144864 * q^82 - 10633758535693793129462935403233565634399957806616398467042339222483716 * q^83 - 28641392301460491393930553180957463692521548910270676165772874742366500 * q^85 + 130748824105220136322401247193488038601024385677355691179590030869522240 * q^86 - 221808067516055560593893382793377773024661552295403957235825845052456960 * q^88 + 44230399340933247556508628049428956972940692248797881370004235332026750 * q^89 + 503963419362898329804217905595235878617892804641236823955454638331741360 * q^91 - 1056276182251025158869277711594662138415929570173882076378175681365399552 * q^92 + 1211599009021421323842808603980852406277919665987296133682388929757489920 * q^94 - 1134809355692277446299742482002998127744674957590385906379174039024255000 * q^95 - 4705643796144250410051227741367571092615369303801441364082016351450032918 * q^97 + 7645702282951838206479981702299956043322685777549671658293752892775157616 * q^98

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