LMFDB - Embedded newform 9.74.a.a.1.2

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			1.2
Root			$-6.50494e8$ 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)

$f(q)$	$=$	$q-1.28059e10 q^{2} -9.28074e21 q^{4} -4.05981e25 q^{5} -7.12492e30 q^{7} +2.39796e32 q^{8} +O(q^{10})$	\(q-1.28059e10 q^{2} -9.28074e21 q^{4} -4.05981e25 q^{5} -7.12492e30 q^{7} +2.39796e32 q^{8} +5.19894e35 q^{10} -5.42440e37 q^{11} +7.16246e40 q^{13} +9.12407e40 q^{14} +8.45834e43 q^{16} -1.30590e44 q^{17} -2.65578e46 q^{19} +3.76781e47 q^{20} +6.94640e47 q^{22} +6.34296e49 q^{23} +5.89418e50 q^{25} -9.17214e50 q^{26} +6.61246e52 q^{28} -8.00076e52 q^{29} -3.53071e54 q^{31} -3.34797e54 q^{32} +1.67231e54 q^{34} +2.89259e56 q^{35} +1.61097e56 q^{37} +3.40096e56 q^{38} -9.73526e57 q^{40} -6.62324e58 q^{41} +5.13946e57 q^{43} +5.03424e59 q^{44} -8.12270e59 q^{46} -1.87105e61 q^{47} +1.54278e60 q^{49} -7.54801e60 q^{50} -6.64729e62 q^{52} +2.36299e62 q^{53} +2.20220e63 q^{55} -1.70853e63 q^{56} +1.02457e63 q^{58} +2.19113e64 q^{59} -1.30217e65 q^{61} +4.52138e64 q^{62} -7.55994e65 q^{64} -2.90783e66 q^{65} -5.38484e66 q^{67} +1.21197e66 q^{68} -3.70420e66 q^{70} -3.88431e67 q^{71} -9.28505e67 q^{73} -2.06298e66 q^{74} +2.46476e68 q^{76} +3.86484e68 q^{77} -4.44441e68 q^{79} -3.43393e69 q^{80} +8.48163e68 q^{82} -9.20761e69 q^{83} +5.30170e69 q^{85} -6.58152e67 q^{86} -1.30075e70 q^{88} +3.27546e70 q^{89} -5.10320e71 q^{91} -5.88674e71 q^{92} +2.39603e71 q^{94} +1.07820e72 q^{95} -2.09156e72 q^{97} -1.97567e70 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.28059e10	−0.131769	−0.0658846	−	0.997827i	$-0.520987\pi$
$2$	−1.28059e10	−0.131769	−0.0658846	+	0.997827i	$0.520987\pi$
$3$	0	0
$3$	0	0
$4$	−9.28074e21	−0.982637
$5$	−4.05981e25	−1.24767	−0.623837	−	0.781555i	$-0.714427\pi$
$5$	−4.05981e25	−1.24767	−0.623837	+	0.781555i	$0.714427\pi$
$6$	0	0
$7$	−7.12492e30	−1.01555	−0.507775	−	0.861489i	$-0.669532\pi$
$7$	−7.12492e30	−1.01555	−0.507775	+	0.861489i	$0.669532\pi$
$8$	2.39796e32	0.261250
$9$	0	0
$10$	5.19894e35	0.164405
$11$	−5.42440e37	−0.529076	−0.264538	−	0.964375i	$-0.585220\pi$
$11$	−5.42440e37	−0.529076	−0.264538	+	0.964375i	$0.585220\pi$
$12$	0	0
$13$	7.16246e40	1.57083	0.785416	−	0.618968i	$-0.212449\pi$
$13$	7.16246e40	1.57083	0.785416	+	0.618968i	$0.212449\pi$
$14$	9.12407e40	0.133818
$15$	0	0
$16$	8.45834e43	0.948212
$17$	−1.30590e44	−0.160149	−0.0800744	−	0.996789i	$-0.525516\pi$
$17$	−1.30590e44	−0.160149	−0.0800744	+	0.996789i	$0.525516\pi$
$18$	0	0
$19$	−2.65578e46	−0.561935	−0.280968	−	0.959717i	$-0.590655\pi$
$19$	−2.65578e46	−0.561935	−0.280968	+	0.959717i	$0.590655\pi$
$20$	3.76781e47	1.22601
$21$	0	0
$22$	6.94640e47	0.0697159
$23$	6.34296e49	1.25668	0.628342	−	0.777937i	$-0.283734\pi$
$23$	6.34296e49	1.25668	0.628342	+	0.777937i	$0.283734\pi$
$24$	0	0
$25$	5.89418e50	0.556690
$26$	−9.17214e50	−0.206987
$27$	0	0
$28$	6.61246e52	0.997918
$29$	−8.00076e52	−0.335432	−0.167716	−	0.985835i	$-0.553639\pi$
$29$	−8.00076e52	−0.335432	−0.167716	+	0.985835i	$0.553639\pi$
$30$	0	0
$31$	−3.53071e54	−1.29766	−0.648829	−	0.760934i	$-0.724741\pi$
$31$	−3.53071e54	−1.29766	−0.648829	+	0.760934i	$0.724741\pi$
$32$	−3.34797e54	−0.386195
$33$	0	0
$34$	1.67231e54	0.0211027
$35$	2.89259e56	1.26708
$36$	0	0
$37$	1.61097e56	0.0928376	0.0464188	−	0.998922i	$-0.485219\pi$
$37$	1.61097e56	0.0928376	0.0464188	+	0.998922i	$0.485219\pi$
$38$	3.40096e56	0.0740457
$39$	0	0
$40$	−9.73526e57	−0.325955
$41$	−6.62324e58	−0.900450	−0.450225	−	0.892915i	$-0.648656\pi$
$41$	−6.62324e58	−0.900450	−0.450225	+	0.892915i	$0.648656\pi$
$42$	0	0
$43$	5.13946e57	0.0122834	0.00614171	−	0.999981i	$-0.498045\pi$
$43$	5.13946e57	0.0122834	0.00614171	+	0.999981i	$0.498045\pi$
$44$	5.03424e59	0.519890
$45$	0	0
$46$	−8.12270e59	−0.165592
$47$	−1.87105e61	−1.73985	−0.869927	−	0.493181i	$-0.835834\pi$
$47$	−1.87105e61	−1.73985	−0.869927	+	0.493181i	$0.835834\pi$
$48$	0	0
$49$	1.54278e60	0.0313436
$50$	−7.54801e60	−0.0733545
$51$	0	0
$52$	−6.64729e62	−1.54356
$53$	2.36299e62	0.273774	0.136887	−	0.990587i	$-0.456290\pi$
$53$	2.36299e62	0.273774	0.136887	+	0.990587i	$0.456290\pi$
$54$	0	0
$55$	2.20220e63	0.660115
$56$	−1.70853e63	−0.265313
$57$	0	0
$58$	1.02457e63	0.0441996
$59$	2.19113e64	0.506489	0.253244	−	0.967402i	$-0.418502\pi$
$59$	2.19113e64	0.506489	0.253244	+	0.967402i	$0.418502\pi$
$60$	0	0
$61$	−1.30217e65	−0.891513	−0.445756	−	0.895154i	$-0.647065\pi$
$61$	−1.30217e65	−0.891513	−0.445756	+	0.895154i	$0.647065\pi$
$62$	4.52138e64	0.170991
$63$	0	0
$64$	−7.55994e65	−0.897324
$65$	−2.90783e66	−1.95989
$66$	0	0
$67$	−5.38484e66	−1.20072	−0.600361	−	0.799729i	$-0.704977\pi$
$67$	−5.38484e66	−1.20072	−0.600361	+	0.799729i	$0.704977\pi$
$68$	1.21197e66	0.157368
$69$	0	0
$70$	−3.70420e66	−0.166962
$71$	−3.88431e67	−1.04324	−0.521620	−	0.853178i	$-0.674672\pi$
$71$	−3.88431e67	−1.04324	−0.521620	+	0.853178i	$0.674672\pi$
$72$	0	0
$73$	−9.28505e67	−0.904690	−0.452345	−	0.891843i	$-0.649412\pi$
$73$	−9.28505e67	−0.904690	−0.452345	+	0.891843i	$0.649412\pi$
$74$	−2.06298e66	−0.0122331
$75$	0	0
$76$	2.46476e68	0.552178
$77$	3.86484e68	0.537304
$78$	0	0
$79$	−4.44441e68	−0.242340	−0.121170	−	0.992632i	$-0.538665\pi$
$79$	−4.44441e68	−0.242340	−0.121170	+	0.992632i	$0.538665\pi$
$80$	−3.43393e69	−1.18306
$81$	0	0
$82$	8.48163e68	0.118652
$83$	−9.20761e69	−0.827555	−0.413777	−	0.910378i	$-0.635791\pi$
$83$	−9.20761e69	−0.827555	−0.413777	+	0.910378i	$0.635791\pi$
$84$	0	0
$85$	5.30170e69	0.199813
$86$	−6.58152e67	−0.00161858
$87$	0	0
$88$	−1.30075e70	−0.138221
$89$	3.27546e70	0.230429	0.115214	−	0.993341i	$-0.463245\pi$
$89$	3.27546e70	0.230429	0.115214	+	0.993341i	$0.463245\pi$
$90$	0	0
$91$	−5.10320e71	−1.59526
$92$	−5.88674e71	−1.23486
$93$	0	0
$94$	2.39603e71	0.229259
$95$	1.07820e72	0.701112
$96$	0	0
$97$	−2.09156e72	−0.635773	−0.317886	−	0.948129i	$-0.602973\pi$
$97$	−2.09156e72	−0.635773	−0.317886	+	0.948129i	$0.602973\pi$
$98$	−1.97567e70	−0.00413011
$99$	0	0
$100$	−5.47024e72	−0.547024
$101$	2.75339e73	1.91486	0.957430	−	0.288664i	$-0.0932111\pi$
$101$	2.75339e73	1.91486	0.957430	+	0.288664i	$0.0932111\pi$
$102$	0	0
$103$	4.01406e73	1.36466	0.682332	−	0.731043i	$-0.260966\pi$
$103$	4.01406e73	1.36466	0.682332	+	0.731043i	$0.260966\pi$
$104$	1.71753e73	0.410380
$105$	0	0
$106$	−3.02601e72	−0.0360750
$107$	1.95235e74	1.65215	0.826077	−	0.563557i	$-0.190568\pi$
$107$	1.95235e74	1.65215	0.826077	+	0.563557i	$0.190568\pi$
$108$	0	0
$109$	−2.72452e74	−1.17280	−0.586398	−	0.810023i	$-0.699454\pi$
$109$	−2.72452e74	−1.17280	−0.586398	+	0.810023i	$0.699454\pi$
$110$	−2.82011e73	−0.0869827
$111$	0	0
$112$	−6.02650e74	−0.962958
$113$	−4.60081e74	−0.531461	−0.265730	−	0.964047i	$-0.585613\pi$
$113$	−4.60081e74	−0.531461	−0.265730	+	0.964047i	$0.585613\pi$
$114$	0	0
$115$	−2.57512e75	−1.56793
$116$	7.42530e74	0.329608
$117$	0	0
$118$	−2.80593e74	−0.0667396
$119$	9.30442e74	0.162639
$120$	0	0
$121$	−7.56913e75	−0.720078
$122$	1.66754e75	0.117474
$123$	0	0
$124$	3.27676e76	1.27513
$125$	1.90557e76	0.553106
$126$	0	0
$127$	5.34262e75	0.0868798	0.0434399	−	0.999056i	$-0.486168\pi$
$127$	5.34262e75	0.0868798	0.0434399	+	0.999056i	$0.486168\pi$
$128$	4.13018e76	0.504435
$129$	0	0
$130$	3.72372e76	0.258252
$131$	−2.08365e77	−1.09250	−0.546252	−	0.837621i	$-0.683946\pi$
$131$	−2.08365e77	−1.09250	−0.546252	+	0.837621i	$0.683946\pi$
$132$	0	0
$133$	1.89222e77	0.570674
$134$	6.89575e76	0.158218
$135$	0	0
$136$	−3.13149e76	−0.0418389
$137$	−1.66251e76	−0.0170006	−0.00850030	−	0.999964i	$-0.502706\pi$
$137$	−1.66251e76	−0.0170006	−0.00850030	+	0.999964i	$0.502706\pi$
$138$	0	0
$139$	−9.14130e76	−0.0550767	−0.0275383	−	0.999621i	$-0.508767\pi$
$139$	−9.14130e76	−0.0550767	−0.0275383	+	0.999621i	$0.508767\pi$
$140$	−2.68454e78	−1.24508
$141$	0	0
$142$	4.97419e77	0.137467
$143$	−3.88520e78	−0.831090
$144$	0	0
$145$	3.24816e78	0.418510
$146$	1.18903e78	0.119210
$147$	0	0
$148$	−1.49510e78	−0.0912257
$149$	1.98294e79	0.946260	0.473130	−	0.880993i	$-0.343124\pi$
$149$	1.98294e79	0.946260	0.473130	+	0.880993i	$0.343124\pi$
$150$	0	0
$151$	−2.17790e79	−0.638821	−0.319410	−	0.947617i	$-0.603485\pi$
$151$	−2.17790e79	−0.638821	−0.319410	+	0.947617i	$0.603485\pi$
$152$	−6.36845e78	−0.146806
$153$	0	0
$154$	−4.94926e78	−0.0708001
$155$	1.43340e80	1.61905
$156$	0	0
$157$	−1.69128e80	−1.19641	−0.598204	−	0.801344i	$-0.704119\pi$
$157$	−1.69128e80	−1.19641	−0.598204	+	0.801344i	$0.704119\pi$
$158$	5.69145e78	0.0319330
$159$	0	0
$160$	1.35921e80	0.481846
$161$	−4.51931e80	−1.27623
$162$	0	0
$163$	−4.96403e80	−0.893279	−0.446640	−	0.894714i	$-0.647379\pi$
$163$	−4.96403e80	−0.893279	−0.446640	+	0.894714i	$0.647379\pi$
$164$	6.14686e80	0.884816
$165$	0	0
$166$	1.17911e80	0.109046
$167$	−1.76051e80	−0.130764	−0.0653818	−	0.997860i	$-0.520827\pi$
$167$	−1.76051e80	−0.130764	−0.0653818	+	0.997860i	$0.520827\pi$
$168$	0	0
$169$	3.05103e81	1.46751
$170$	−6.78928e79	−0.0263292
$171$	0	0
$172$	−4.76981e79	−0.0120701
$173$	−8.57658e81	−1.75643	−0.878216	−	0.478265i	$-0.841266\pi$
$173$	−8.57658e81	−1.75643	−0.878216	+	0.478265i	$0.841266\pi$
$174$	0	0
$175$	−4.19956e81	−0.565347
$176$	−4.58814e81	−0.501677
$177$	0	0
$178$	−4.19450e80	−0.0303634
$179$	1.04344e82	0.615646	0.307823	−	0.951444i	$-0.400400\pi$
$179$	1.04344e82	0.615646	0.307823	+	0.951444i	$0.400400\pi$
$180$	0	0
$181$	−5.37748e81	−0.211500	−0.105750	−	0.994393i	$-0.533724\pi$
$181$	−5.37748e81	−0.211500	−0.105750	+	0.994393i	$0.533724\pi$
$182$	6.53508e81	0.210206
$183$	0	0
$184$	1.52101e82	0.328309
$185$	−6.54023e81	−0.115831
$186$	0	0
$187$	7.08371e81	0.0847309
$188$	1.73647e83	1.70964
$189$	0	0
$190$	−1.38073e82	−0.0923849
$191$	−2.08649e82	−0.115265	−0.0576325	−	0.998338i	$-0.518355\pi$
$191$	−2.08649e82	−0.115265	−0.0576325	+	0.998338i	$0.518355\pi$
$192$	0	0
$193$	−1.09262e83	−0.412693	−0.206347	−	0.978479i	$-0.566157\pi$
$193$	−1.09262e83	−0.412693	−0.206347	+	0.978479i	$0.566157\pi$
$194$	2.67842e82	0.0837752
$195$	0	0
$196$	−1.43182e82	−0.0307993
$197$	−7.56333e83	−1.35113	−0.675563	−	0.737302i	$-0.736099\pi$
$197$	−7.56333e83	−1.35113	−0.675563	+	0.737302i	$0.736099\pi$
$198$	0	0
$199$	−7.27551e83	−0.898930	−0.449465	−	0.893298i	$-0.648385\pi$
$199$	−7.27551e83	−0.898930	−0.449465	+	0.893298i	$0.648385\pi$
$200$	1.41340e83	0.145435
$201$	0	0
$202$	−3.52595e83	−0.252320
$203$	5.70048e83	0.340648
$204$	0	0
$205$	2.68891e84	1.12347
$206$	−5.14035e83	−0.179820
$207$	0	0
$208$	6.05825e84	1.48948
$209$	1.44060e84	0.297307
$210$	0	0
$211$	−3.42639e84	−0.499491	−0.249745	−	0.968312i	$-0.580347\pi$
$211$	−3.42639e84	−0.499491	−0.249745	+	0.968312i	$0.580347\pi$
$212$	−2.19303e84	−0.269021
$213$	0	0
$214$	−2.50015e84	−0.217703
$215$	−2.08653e83	−0.0153257
$216$	0	0
$217$	2.51560e85	1.31784
$218$	3.48898e84	0.154538
$219$	0	0
$220$	−2.04381e85	−0.648653
$221$	−9.35344e84	−0.251567
$222$	0	0
$223$	−7.17475e85	−1.38893	−0.694463	−	0.719528i	$-0.744358\pi$
$223$	−7.17475e85	−1.38893	−0.694463	+	0.719528i	$0.744358\pi$
$224$	2.38540e85	0.392201
$225$	0	0
$226$	5.89173e84	0.0700301
$227$	−5.26645e85	−0.532813	−0.266406	−	0.963861i	$-0.585836\pi$
$227$	−5.26645e85	−0.532813	−0.266406	+	0.963861i	$0.585836\pi$
$228$	0	0
$229$	−1.96927e86	−1.44648	−0.723238	−	0.690599i	$-0.757347\pi$
$229$	−1.96927e86	−1.44648	−0.723238	+	0.690599i	$0.757347\pi$
$230$	3.29767e85	0.206605
$231$	0	0
$232$	−1.91855e85	−0.0876317
$233$	2.47311e86	0.965499	0.482750	−	0.875758i	$-0.339638\pi$
$233$	2.47311e86	0.965499	0.482750	+	0.875758i	$0.339638\pi$
$234$	0	0
$235$	7.59610e86	2.17077
$236$	−2.03353e86	−0.497695
$237$	0	0
$238$	−1.19151e85	−0.0214308
$239$	9.15532e85	0.141303	0.0706513	−	0.997501i	$-0.477492\pi$
$239$	9.15532e85	0.141303	0.0706513	+	0.997501i	$0.477492\pi$
$240$	0	0
$241$	−1.90452e86	−0.216852	−0.108426	−	0.994104i	$-0.534581\pi$
$241$	−1.90452e86	−0.216852	−0.108426	+	0.994104i	$0.534581\pi$
$242$	9.69291e85	0.0948841
$243$	0	0
$244$	1.20851e87	0.876033
$245$	−6.26342e85	−0.0391065
$246$	0	0
$247$	−1.90219e87	−0.882706
$248$	−8.46649e86	−0.339014
$249$	0	0
$250$	−2.44024e86	−0.0728823
$251$	−6.30464e87	−1.62768	−0.813841	−	0.581087i	$-0.802627\pi$
$251$	−6.30464e87	−1.62768	−0.813841	+	0.581087i	$0.802627\pi$
$252$	0	0
$253$	−3.44067e87	−0.664882
$254$	−6.84168e85	−0.0114481
$255$	0	0
$256$	6.61125e87	0.830855
$257$	6.84443e87	0.746068	0.373034	−	0.927818i	$-0.378317\pi$
$257$	6.84443e87	0.746068	0.373034	+	0.927818i	$0.378317\pi$
$258$	0	0
$259$	−1.14780e87	−0.0942814
$260$	2.69868e88	1.92586
$261$	0	0
$262$	2.66829e87	0.143958
$263$	7.68237e87	0.360670	0.180335	−	0.983605i	$-0.442282\pi$
$263$	7.68237e87	0.360670	0.180335	+	0.983605i	$0.442282\pi$
$264$	0	0
$265$	−9.59330e87	−0.341581
$266$	−2.42316e87	−0.0751972
$267$	0	0
$268$	4.99753e88	1.17987
$269$	6.48183e87	0.133579	0.0667897	−	0.997767i	$-0.478724\pi$
$269$	6.48183e87	0.133579	0.0667897	+	0.997767i	$0.478724\pi$
$270$	0	0
$271$	−7.02783e88	−1.10520	−0.552602	−	0.833445i	$-0.686365\pi$
$271$	−7.02783e88	−1.10520	−0.552602	+	0.833445i	$0.686365\pi$
$272$	−1.10457e88	−0.151855
$273$	0	0
$274$	2.12899e86	0.00224016
$275$	−3.19724e88	−0.294531
$276$	0	0
$277$	−2.35295e88	−0.166380	−0.0831901	−	0.996534i	$-0.526511\pi$
$277$	−2.35295e88	−0.166380	−0.0831901	+	0.996534i	$0.526511\pi$
$278$	1.17062e87	0.00725740
$279$	0	0
$280$	6.93630e88	0.331024
$281$	−3.29283e89	−1.37971	−0.689856	−	0.723947i	$-0.742326\pi$
$281$	−3.29283e89	−1.37971	−0.689856	+	0.723947i	$0.742326\pi$
$282$	0	0
$283$	5.00752e89	1.61964	0.809819	−	0.586680i	$-0.199565\pi$
$283$	5.00752e89	1.61964	0.809819	+	0.586680i	$0.199565\pi$
$284$	3.60493e89	1.02513
$285$	0	0
$286$	4.97533e88	0.109512
$287$	4.71901e89	0.914453
$288$	0	0
$289$	−6.47869e89	−0.974352
$290$	−4.15955e88	−0.0551467
$291$	0	0
$292$	8.61722e89	0.888982
$293$	6.16045e89	0.560976	0.280488	−	0.959858i	$-0.409504\pi$
$293$	6.16045e89	0.560976	0.280488	+	0.959858i	$0.409504\pi$
$294$	0	0
$295$	−8.89559e89	−0.631933
$296$	3.86303e88	0.0242539
$297$	0	0
$298$	−2.53932e89	−0.124688
$299$	4.54312e90	1.97404
$300$	0	0
$301$	−3.66183e88	−0.0124744
$302$	2.78898e89	0.0841768
$303$	0	0
$304$	−2.24635e90	−0.532834
$305$	5.28656e90	1.11232
$306$	0	0
$307$	9.29015e90	1.53983	0.769914	−	0.638148i	$-0.220299\pi$
$307$	9.29015e90	1.53983	0.769914	+	0.638148i	$0.220299\pi$
$308$	−3.58686e90	−0.527975
$309$	0	0
$310$	−1.83560e90	−0.213341
$311$	−2.50281e90	−0.258627	−0.129314	−	0.991604i	$-0.541277\pi$
$311$	−2.50281e90	−0.258627	−0.129314	+	0.991604i	$0.541277\pi$
$312$	0	0
$313$	1.82125e91	1.48937	0.744684	−	0.667417i	$-0.232600\pi$
$313$	1.82125e91	1.48937	0.744684	+	0.667417i	$0.232600\pi$
$314$	2.16583e90	0.157650
$315$	0	0
$316$	4.12475e90	0.238133
$317$	2.15612e91	1.10920	0.554601	−	0.832117i	$-0.312871\pi$
$317$	2.15612e91	1.10920	0.554601	+	0.832117i	$0.312871\pi$
$318$	0	0
$319$	4.33993e90	0.177469
$320$	3.06919e91	1.11957
$321$	0	0
$322$	5.78736e90	0.168167
$323$	3.46818e90	0.0899932
$324$	0	0
$325$	4.22168e91	0.874466
$326$	6.35687e90	0.117707
$327$	0	0
$328$	−1.58822e91	−0.235243
$329$	1.33311e92	1.76691
$330$	0	0
$331$	2.31408e91	0.245842	0.122921	−	0.992416i	$-0.460774\pi$
$331$	2.31408e91	0.245842	0.122921	+	0.992416i	$0.460774\pi$
$332$	8.54535e91	0.813186
$333$	0	0
$334$	2.25448e90	0.0172306
$335$	2.18615e92	1.49811
$336$	0	0
$337$	2.57115e91	0.141787	0.0708935	−	0.997484i	$-0.477415\pi$
$337$	2.57115e91	0.141787	0.0708935	+	0.997484i	$0.477415\pi$
$338$	−3.90710e91	−0.193373
$339$	0	0
$340$	−4.92037e91	−0.196344
$341$	1.91520e92	0.686560
$342$	0	0
$343$	3.39709e92	0.983720
$344$	1.23242e90	0.00320905
$345$	0	0
$346$	1.09830e92	0.231443
$347$	5.43093e92	1.03003	0.515013	−	0.857182i	$-0.327787\pi$
$347$	5.43093e92	1.03003	0.515013	+	0.857182i	$0.327787\pi$
$348$	0	0
$349$	−1.29977e90	−0.00199866	−0.000999328	−	1.00000i	$-0.500318\pi$
$349$	−1.29977e90	−0.00199866	−0.000999328		1.00000i	$0.500318\pi$
$350$	5.37790e91	0.0744953
$351$	0	0
$352$	1.81607e92	0.204327
$353$	1.12268e93	1.13888	0.569442	−	0.822032i	$-0.307159\pi$
$353$	1.12268e93	1.13888	0.569442	+	0.822032i	$0.307159\pi$
$354$	0	0
$355$	1.57696e93	1.30162
$356$	−3.03987e92	−0.226428
$357$	0	0
$358$	−1.33621e92	−0.0811231
$359$	−8.79228e91	−0.0482119	−0.0241059	−	0.999709i	$-0.507674\pi$
$359$	−8.79228e91	−0.0482119	−0.0241059	+	0.999709i	$0.507674\pi$
$360$	0	0
$361$	−1.52832e93	−0.684229
$362$	6.88633e91	0.0278692
$363$	0	0
$364$	4.73614e93	1.56756
$365$	3.76956e93	1.12876
$366$	0	0
$367$	3.02870e93	0.742925	0.371462	−	0.928448i	$-0.378856\pi$
$367$	3.02870e93	0.742925	0.371462	+	0.928448i	$0.378856\pi$
$368$	5.36509e93	1.19160
$369$	0	0
$370$	8.37533e91	0.0152630
$371$	−1.68361e93	−0.278032
$372$	0	0
$373$	−1.41066e94	−1.91448	−0.957239	−	0.289297i	$-0.906579\pi$
$373$	−1.41066e94	−1.91448	−0.957239	+	0.289297i	$0.906579\pi$
$374$	−9.07129e91	−0.0111649
$375$	0	0
$376$	−4.48669e93	−0.454537
$377$	−5.73051e93	−0.526907
$378$	0	0
$379$	3.09449e93	0.234562	0.117281	−	0.993099i	$-0.462582\pi$
$379$	3.09449e93	0.234562	0.117281	+	0.993099i	$0.462582\pi$
$380$	−1.00065e94	−0.688938
$381$	0	0
$382$	2.67192e92	0.0151884
$383$	5.62498e93	0.290647	0.145323	−	0.989384i	$-0.453578\pi$
$383$	5.62498e93	0.290647	0.145323	+	0.989384i	$0.453578\pi$
$384$	0	0
$385$	−1.56905e94	−0.670380
$386$	1.39919e93	0.0543802
$387$	0	0
$388$	1.94112e94	0.624734
$389$	−4.55175e94	−1.33358	−0.666789	−	0.745247i	$-0.732332\pi$
$389$	−4.55175e94	−1.33358	−0.666789	+	0.745247i	$0.732332\pi$
$390$	0	0
$391$	−8.28326e93	−0.201256
$392$	3.69953e92	0.00818852
$393$	0	0
$394$	9.68549e93	0.178037
$395$	1.80435e94	0.302362
$396$	0	0
$397$	6.04038e94	0.841804	0.420902	−	0.907106i	$-0.361714\pi$
$397$	6.04038e94	0.841804	0.420902	+	0.907106i	$0.361714\pi$
$398$	9.31691e93	0.118451
$399$	0	0
$400$	4.98550e94	0.527860
$401$	−1.81150e95	−1.75093	−0.875465	−	0.483281i	$-0.839445\pi$
$401$	−1.81150e95	−1.75093	−0.875465	+	0.483281i	$0.839445\pi$
$402$	0	0
$403$	−2.52886e95	−2.03840
$404$	−2.55535e95	−1.88161
$405$	0	0
$406$	−7.29995e93	−0.0448869
$407$	−8.73853e93	−0.0491182
$408$	0	0
$409$	−2.92901e95	−1.37664	−0.688318	−	0.725409i	$-0.741651\pi$
$409$	−2.92901e95	−1.37664	−0.688318	+	0.725409i	$0.741651\pi$
$410$	−3.44338e94	−0.148038
$411$	0	0
$412$	−3.72535e95	−1.34097
$413$	−1.56116e95	−0.514365
$414$	0	0
$415$	3.73812e95	1.03252
$416$	−2.39797e95	−0.606648
$417$	0	0
$418$	−1.84481e94	−0.0391758
$419$	8.12273e95	1.58085	0.790424	−	0.612560i	$-0.209860\pi$
$419$	8.12273e95	1.58085	0.790424	+	0.612560i	$0.209860\pi$
$420$	0	0
$421$	−1.37700e95	−0.225236	−0.112618	−	0.993638i	$-0.535924\pi$
$421$	−1.37700e95	−0.225236	−0.112618	+	0.993638i	$0.535924\pi$
$422$	4.38779e94	0.0658175
$423$	0	0
$424$	5.66635e94	0.0715236
$425$	−7.69720e94	−0.0891532
$426$	0	0
$427$	9.27784e95	0.905377
$428$	−1.81193e96	−1.62347
$429$	0	0
$430$	2.67198e93	0.00201945
$431$	−2.16300e95	−0.150189	−0.0750943	−	0.997176i	$-0.523926\pi$
$431$	−2.16300e95	−0.150189	−0.0750943	+	0.997176i	$0.523926\pi$
$432$	0	0
$433$	−1.06805e96	−0.626299	−0.313149	−	0.949704i	$-0.601384\pi$
$433$	−1.06805e96	−0.626299	−0.313149	+	0.949704i	$0.601384\pi$
$434$	−3.22145e95	−0.173650
$435$	0	0
$436$	2.52855e96	1.15243
$437$	−1.68455e96	−0.706175
$438$	0	0
$439$	−4.18327e96	−1.48443	−0.742217	−	0.670160i	$-0.766225\pi$
$439$	−4.18327e96	−1.48443	−0.742217	+	0.670160i	$0.766225\pi$
$440$	5.28079e95	0.172455
$441$	0	0
$442$	1.19779e95	0.0331487
$443$	1.44956e96	0.369403	0.184701	−	0.982795i	$-0.440868\pi$
$443$	1.44956e96	0.369403	0.184701	+	0.982795i	$0.440868\pi$
$444$	0	0
$445$	−1.32977e96	−0.287500
$446$	9.18788e95	0.183018
$447$	0	0
$448$	5.38640e96	0.911278
$449$	8.52316e95	0.132926	0.0664629	−	0.997789i	$-0.478829\pi$
$449$	8.52316e95	0.132926	0.0664629	+	0.997789i	$0.478829\pi$
$450$	0	0
$451$	3.59271e96	0.476407
$452$	4.26990e96	0.522233
$453$	0	0
$454$	6.74414e95	0.0702083
$455$	2.07180e97	1.99036
$456$	0	0
$457$	−1.28421e97	−1.05122	−0.525610	−	0.850726i	$-0.676163\pi$
$457$	−1.28421e97	−1.05122	−0.525610	+	0.850726i	$0.676163\pi$
$458$	2.52182e96	0.190601
$459$	0	0
$460$	2.38991e97	1.54071
$461$	2.16592e97	1.28991	0.644954	−	0.764221i	$-0.276876\pi$
$461$	2.16592e97	1.28991	0.644954	+	0.764221i	$0.276876\pi$
$462$	0	0
$463$	−7.61030e96	−0.386986	−0.193493	−	0.981102i	$-0.561982\pi$
$463$	−7.61030e96	−0.386986	−0.193493	+	0.981102i	$0.561982\pi$
$464$	−6.76731e96	−0.318061
$465$	0	0
$466$	−3.16703e96	−0.127223
$467$	2.32926e97	0.865270	0.432635	−	0.901569i	$-0.357584\pi$
$467$	2.32926e97	0.865270	0.432635	+	0.901569i	$0.357584\pi$
$468$	0	0
$469$	3.83666e97	1.21939
$470$	−9.72746e96	−0.286040
$471$	0	0
$472$	5.25424e96	0.132320
$473$	−2.78785e95	−0.00649887
$474$	0	0
$475$	−1.56537e97	−0.312824
$476$	−8.63519e96	−0.159815
$477$	0	0
$478$	−1.17242e96	−0.0186193
$479$	−2.29746e97	−0.338066	−0.169033	−	0.985610i	$-0.554064\pi$
$479$	−2.29746e97	−0.338066	−0.169033	+	0.985610i	$0.554064\pi$
$480$	0	0
$481$	1.15385e97	0.145832
$482$	2.43890e96	0.0285745
$483$	0	0
$484$	7.02471e97	0.707575
$485$	8.49134e97	0.793237
$486$	0	0
$487$	9.83578e97	0.790682	0.395341	−	0.918534i	$-0.370626\pi$
$487$	9.83578e97	0.790682	0.395341	+	0.918534i	$0.370626\pi$
$488$	−3.12254e97	−0.232908
$489$	0	0
$490$	8.02084e95	0.00515303
$491$	1.73954e98	1.03743	0.518716	−	0.854947i	$-0.326410\pi$
$491$	1.73954e98	1.03743	0.518716	+	0.854947i	$0.326410\pi$
$492$	0	0
$493$	1.04482e97	0.0537190
$494$	2.43592e97	0.116313
$495$	0	0
$496$	−2.98639e98	−1.23046
$497$	2.76754e98	1.05946
$498$	0	0
$499$	−4.48498e97	−0.148283	−0.0741413	−	0.997248i	$-0.523622\pi$
$499$	−4.48498e97	−0.148283	−0.0741413	+	0.997248i	$0.523622\pi$
$500$	−1.76851e98	−0.543503
$501$	0	0
$502$	8.07363e97	0.214478
$503$	−7.59682e98	−1.87672	−0.938362	−	0.345655i	$-0.887657\pi$
$503$	−7.59682e98	−1.87672	−0.938362	+	0.345655i	$0.887657\pi$
$504$	0	0
$505$	−1.11782e99	−2.38912
$506$	4.40608e97	0.0876109
$507$	0	0
$508$	−4.95835e97	−0.0853713
$509$	−1.10612e98	−0.177257	−0.0886284	−	0.996065i	$-0.528248\pi$
$509$	−1.10612e98	−0.177257	−0.0886284	+	0.996065i	$0.528248\pi$
$510$	0	0
$511$	6.61553e98	0.918759
$512$	−4.74747e98	−0.613916
$513$	0	0
$514$	−8.76488e97	−0.0983087
$515$	−1.62964e99	−1.70265
$516$	0	0
$517$	1.01493e99	0.920516
$518$	1.46986e97	0.0124234
$519$	0	0
$520$	−6.97284e98	−0.512021
$521$	−1.94380e99	−1.33068	−0.665341	−	0.746540i	$-0.731714\pi$
$521$	−1.94380e99	−1.33068	−0.665341	+	0.746540i	$0.731714\pi$
$522$	0	0
$523$	3.22586e98	0.192014	0.0960072	−	0.995381i	$-0.469393\pi$
$523$	3.22586e98	0.192014	0.0960072	+	0.995381i	$0.469393\pi$
$524$	1.93378e99	1.07353
$525$	0	0
$526$	−9.83793e97	−0.0475252
$527$	4.61075e98	0.207818
$528$	0	0
$529$	1.47571e99	0.579255
$530$	1.22850e98	0.0450098
$531$	0	0
$532$	−1.75613e99	−0.560765
$533$	−4.74387e99	−1.41446
$534$	0	0
$535$	−7.92619e99	−2.06135
$536$	−1.29126e99	−0.313689
$537$	0	0
$538$	−8.30054e97	−0.0176016
$539$	−8.36867e97	−0.0165831
$540$	0	0
$541$	2.75772e99	0.477364	0.238682	−	0.971098i	$-0.423285\pi$
$541$	2.75772e99	0.477364	0.238682	+	0.971098i	$0.423285\pi$
$542$	8.99974e98	0.145632
$543$	0	0
$544$	4.37210e98	0.0618487
$545$	1.10610e100	1.46327
$546$	0	0
$547$	2.20581e99	0.255288	0.127644	−	0.991820i	$-0.459258\pi$
$547$	2.20581e99	0.255288	0.127644	+	0.991820i	$0.459258\pi$
$548$	1.54294e98	0.0167054
$549$	0	0
$550$	4.09434e98	0.0388102
$551$	2.12483e99	0.188491
$552$	0	0
$553$	3.16661e99	0.246109
$554$	3.01316e98	0.0219238
$555$	0	0
$556$	8.48380e98	0.0541204
$557$	−3.12775e100	−1.86860	−0.934302	−	0.356482i	$-0.883976\pi$
$557$	−3.12775e100	−1.86860	−0.934302	+	0.356482i	$0.883976\pi$
$558$	0	0
$559$	3.68112e98	0.0192952
$560$	2.44665e100	1.20146
$561$	0	0
$562$	4.21674e99	0.181803
$563$	3.06947e100	1.24024	0.620122	−	0.784505i	$-0.287083\pi$
$563$	3.06947e100	1.24024	0.620122	+	0.784505i	$0.287083\pi$
$564$	0	0
$565$	1.86784e100	0.663090
$566$	−6.41256e99	−0.213418
$567$	0	0
$568$	−9.31441e99	−0.272547
$569$	−5.43050e99	−0.149019	−0.0745095	−	0.997220i	$-0.523739\pi$
$569$	−5.43050e99	−0.149019	−0.0745095	+	0.997220i	$0.523739\pi$
$570$	0	0
$571$	5.10752e100	1.23308	0.616541	−	0.787323i	$-0.288534\pi$
$571$	5.10752e100	1.23308	0.616541	+	0.787323i	$0.288534\pi$
$572$	3.60575e100	0.816660
$573$	0	0
$574$	−6.04309e99	−0.120497
$575$	3.73866e100	0.699583
$576$	0	0
$577$	1.75584e100	0.289447	0.144723	−	0.989472i	$-0.453771\pi$
$577$	1.75584e100	0.289447	0.144723	+	0.989472i	$0.453771\pi$
$578$	8.29652e99	0.128390
$579$	0	0
$580$	−3.01454e100	−0.411243
$581$	6.56035e100	0.840424
$582$	0	0
$583$	−1.28178e100	−0.144847
$584$	−2.22652e100	−0.236351
$585$	0	0
$586$	−7.88898e99	−0.0739193
$587$	1.85514e101	1.63337	0.816687	−	0.577081i	$-0.195808\pi$
$587$	1.85514e101	1.63337	0.816687	+	0.577081i	$0.195808\pi$
$588$	0	0
$589$	9.37680e100	0.729200
$590$	1.13916e100	0.0832693
$591$	0	0
$592$	1.36261e100	0.0880298
$593$	−2.31200e101	−1.40440	−0.702202	−	0.711978i	$-0.747800\pi$
$593$	−2.31200e101	−1.40440	−0.702202	+	0.711978i	$0.747800\pi$
$594$	0	0
$595$	−3.77742e100	−0.202921
$596$	−1.84031e101	−0.929830
$597$	0	0
$598$	−5.81785e100	−0.260117
$599$	2.30638e101	0.970178	0.485089	−	0.874465i	$-0.338787\pi$
$599$	2.30638e101	0.970178	0.485089	+	0.874465i	$0.338787\pi$
$600$	0	0
$601$	−3.98037e101	−1.48254	−0.741269	−	0.671209i	$-0.765775\pi$
$601$	−3.98037e101	−1.48254	−0.741269	+	0.671209i	$0.765775\pi$
$602$	4.68928e98	0.00164375
$603$	0	0
$604$	2.02125e101	0.627729
$605$	3.07292e101	0.898423
$606$	0	0
$607$	2.03446e101	0.527306	0.263653	−	0.964618i	$-0.415073\pi$
$607$	2.03446e101	0.527306	0.263653	+	0.964618i	$0.415073\pi$
$608$	8.89148e100	0.217017
$609$	0	0
$610$	−6.76989e100	−0.146569
$611$	−1.34013e102	−2.73302
$612$	0	0
$613$	8.11549e101	1.46895	0.734476	−	0.678635i	$-0.237428\pi$
$613$	8.11549e101	1.46895	0.734476	+	0.678635i	$0.237428\pi$
$614$	−1.18968e101	−0.202902
$615$	0	0
$616$	9.26772e100	0.140371
$617$	4.85215e101	0.692669	0.346335	−	0.938111i	$-0.387426\pi$
$617$	4.85215e101	0.692669	0.346335	+	0.938111i	$0.387426\pi$
$618$	0	0
$619$	−1.16809e102	−1.48173	−0.740864	−	0.671655i	$-0.765584\pi$
$619$	−1.16809e102	−1.48173	−0.740864	+	0.671655i	$0.765584\pi$
$620$	−1.33030e102	−1.59094
$621$	0	0
$622$	3.20507e100	0.0340791
$623$	−2.33374e101	−0.234012
$624$	0	0
$625$	−1.39770e102	−1.24679
$626$	−2.33227e101	−0.196253
$627$	0	0
$628$	1.56964e102	1.17563
$629$	−2.10376e100	−0.0148678
$630$	0	0
$631$	−2.95061e102	−1.85712	−0.928559	−	0.371185i	$-0.878952\pi$
$631$	−2.95061e102	−1.85712	−0.928559	+	0.371185i	$0.878952\pi$
$632$	−1.06575e101	−0.0633115
$633$	0	0
$634$	−2.76110e101	−0.146159
$635$	−2.16901e101	−0.108398
$636$	0	0
$637$	1.10501e101	0.0492355
$638$	−5.55765e100	−0.0233850
$639$	0	0
$640$	−1.67678e102	−0.629370
$641$	−4.29395e102	−1.52244	−0.761218	−	0.648496i	$-0.775398\pi$
$641$	−4.29395e102	−1.52244	−0.761218	+	0.648496i	$0.775398\pi$
$642$	0	0
$643$	1.03978e102	0.329034	0.164517	−	0.986374i	$-0.447393\pi$
$643$	1.03978e102	0.329034	0.164517	+	0.986374i	$0.447393\pi$
$644$	4.19426e102	1.25407
$645$	0	0
$646$	−4.44130e100	−0.0118583
$647$	9.92922e101	0.250558	0.125279	−	0.992122i	$-0.460017\pi$
$647$	9.92922e101	0.250558	0.125279	+	0.992122i	$0.460017\pi$
$648$	0	0
$649$	−1.18856e102	−0.267971
$650$	−5.40623e101	−0.115228
$651$	0	0
$652$	4.60699e102	0.877769
$653$	2.55572e102	0.460450	0.230225	−	0.973137i	$-0.426054\pi$
$653$	2.55572e102	0.460450	0.230225	+	0.973137i	$0.426054\pi$
$654$	0	0
$655$	8.45924e102	1.36309
$656$	−5.60216e102	−0.853818
$657$	0	0
$658$	−1.70716e102	−0.232824
$659$	9.61531e102	1.24064	0.620320	−	0.784349i	$-0.287003\pi$
$659$	9.61531e102	1.24064	0.620320	+	0.784349i	$0.287003\pi$
$660$	0	0
$661$	8.19473e102	0.946633	0.473316	−	0.880893i	$-0.343057\pi$
$661$	8.19473e102	0.946633	0.473316	+	0.880893i	$0.343057\pi$
$662$	−2.96337e101	−0.0323944
$663$	0	0
$664$	−2.20795e102	−0.216199
$665$	−7.68208e102	−0.712015
$666$	0	0
$667$	−5.07485e102	−0.421532
$668$	1.63388e102	0.128493
$669$	0	0
$670$	−2.79955e102	−0.197405
$671$	7.06347e102	0.471678
$672$	0	0
$673$	9.08707e102	0.544344	0.272172	−	0.962249i	$-0.412258\pi$
$673$	9.08707e102	0.544344	0.272172	+	0.962249i	$0.412258\pi$
$674$	−3.29258e101	−0.0186831
$675$	0	0
$676$	−2.83158e103	−1.44203
$677$	2.19434e103	1.05881	0.529405	−	0.848369i	$-0.322415\pi$
$677$	2.19434e103	1.05881	0.529405	+	0.848369i	$0.322415\pi$
$678$	0	0
$679$	1.49022e103	0.645659
$680$	1.27133e102	0.0522013
$681$	0	0
$682$	−2.45257e102	−0.0904675
$683$	3.52716e103	1.23330	0.616651	−	0.787236i	$-0.288489\pi$
$683$	3.52716e103	1.23330	0.616651	+	0.787236i	$0.288489\pi$
$684$	0	0
$685$	6.74950e101	0.0212112
$686$	−4.35026e102	−0.129624
$687$	0	0
$688$	4.34713e101	0.0116473
$689$	1.69248e103	0.430053
$690$	0	0
$691$	5.99882e103	1.37125	0.685626	−	0.727954i	$-0.259528\pi$
$691$	5.99882e103	1.37125	0.685626	+	0.727954i	$0.259528\pi$
$692$	7.95970e103	1.72593
$693$	0	0
$694$	−6.95477e102	−0.135726
$695$	3.71120e102	0.0687177
$696$	0	0
$697$	8.64928e102	0.144206
$698$	1.66446e100	0.000263361 0
$699$	0	0
$700$	3.89750e103	0.555531
$701$	−8.24063e103	−1.11494	−0.557472	−	0.830196i	$-0.688229\pi$
$701$	−8.24063e103	−1.11494	−0.557472	+	0.830196i	$0.688229\pi$
$702$	0	0
$703$	−4.27838e102	−0.0521687
$704$	4.10081e103	0.474753
$705$	0	0
$706$	−1.43769e103	−0.150070
$707$	−1.96177e104	−1.94464
$708$	0	0
$709$	−1.70430e104	−1.52391	−0.761953	−	0.647632i	$-0.775760\pi$
$709$	−1.70430e104	−1.52391	−0.761953	+	0.647632i	$0.775760\pi$
$710$	−2.01943e103	−0.171514
$711$	0	0
$712$	7.85440e102	0.0601996
$713$	−2.23952e104	−1.63075
$714$	0	0
$715$	1.57732e104	1.03693
$716$	−9.68387e103	−0.604956
$717$	0	0
$718$	1.12593e102	0.00635284
$719$	3.17489e104	1.70265	0.851323	−	0.524642i	$-0.175801\pi$
$719$	3.17489e104	1.70265	0.851323	+	0.524642i	$0.175801\pi$
$720$	0	0
$721$	−2.85999e104	−1.38588
$722$	1.95714e103	0.0901602
$723$	0	0
$724$	4.99070e103	0.207828
$725$	−4.71580e103	−0.186732
$726$	0	0
$727$	−2.53957e102	−0.00909398	−0.00454699	−	0.999990i	$-0.501447\pi$
$727$	−2.53957e102	−0.00909398	−0.00454699	+	0.999990i	$0.501447\pi$
$728$	−1.22372e104	−0.416762
$729$	0	0
$730$	−4.82724e103	−0.148736
$731$	−6.71162e101	−0.00196717
$732$	0	0
$733$	5.13601e104	1.36248	0.681242	−	0.732059i	$-0.261440\pi$
$733$	5.13601e104	1.36248	0.681242	+	0.732059i	$0.261440\pi$
$734$	−3.87851e103	−0.0978946
$735$	0	0
$736$	−2.12360e104	−0.485326
$737$	2.92095e104	0.635274
$738$	0	0
$739$	−8.61961e104	−1.69811	−0.849054	−	0.528306i	$-0.822828\pi$
$739$	−8.61961e104	−1.69811	−0.849054	+	0.528306i	$0.822828\pi$
$740$	6.06982e103	0.113820
$741$	0	0
$742$	2.15601e103	0.0366360
$743$	−8.31834e104	−1.34569	−0.672845	−	0.739784i	$-0.734928\pi$
$743$	−8.31834e104	−1.34569	−0.672845	+	0.739784i	$0.734928\pi$
$744$	0	0
$745$	−8.05036e104	−1.18062
$746$	1.80647e104	0.252269
$747$	0	0
$748$	−6.57421e103	−0.0832597
$749$	−1.39104e105	−1.67785
$750$	0	0
$751$	8.23505e104	0.901174	0.450587	−	0.892733i	$-0.351215\pi$
$751$	8.23505e104	0.901174	0.450587	+	0.892733i	$0.351215\pi$
$752$	−1.58259e105	−1.64975
$753$	0	0
$754$	7.33841e103	0.0694301
$755$	8.84186e104	0.797040
$756$	0	0
$757$	−2.18065e104	−0.178479	−0.0892394	−	0.996010i	$-0.528444\pi$
$757$	−2.18065e104	−0.178479	−0.0892394	+	0.996010i	$0.528444\pi$
$758$	−3.96275e103	−0.0309080
$759$	0	0
$760$	2.58547e104	0.183166
$761$	2.07078e105	1.39828	0.699140	−	0.714985i	$-0.253567\pi$
$761$	2.07078e105	1.39828	0.699140	+	0.714985i	$0.253567\pi$
$762$	0	0
$763$	1.94120e105	1.19103
$764$	1.93641e104	0.113264
$765$	0	0
$766$	−7.20327e103	−0.0382983
$767$	1.56939e105	0.795609
$768$	0	0
$769$	1.22335e105	0.563947	0.281973	−	0.959422i	$-0.409011\pi$
$769$	1.22335e105	0.563947	0.281973	+	0.959422i	$0.409011\pi$
$770$	2.00931e104	0.0883354
$771$	0	0
$772$	1.01403e105	0.405528
$773$	8.34378e104	0.318281	0.159141	−	0.987256i	$-0.449128\pi$
$773$	8.34378e104	0.318281	0.159141	+	0.987256i	$0.449128\pi$
$774$	0	0
$775$	−2.08107e105	−0.722393
$776$	−5.01547e104	−0.166096
$777$	0	0
$778$	5.82891e104	0.175724
$779$	1.75899e105	0.505995
$780$	0	0
$781$	2.10700e105	0.551953
$782$	1.06074e104	0.0265194
$783$	0	0
$784$	1.30494e104	0.0297203
$785$	6.86630e105	1.49273
$786$	0	0
$787$	−2.99942e105	−0.594236	−0.297118	−	0.954841i	$-0.596026\pi$
$787$	−2.99942e105	−0.594236	−0.297118	+	0.954841i	$0.596026\pi$
$788$	7.01933e105	1.32767
$789$	0	0
$790$	−2.31062e104	−0.0398419
$791$	3.27804e105	0.539726
$792$	0	0
$793$	−9.32671e105	−1.40042
$794$	−7.73522e104	−0.110924
$795$	0	0
$796$	6.75221e105	0.883322
$797$	−1.44943e106	−1.81121	−0.905604	−	0.424124i	$-0.860582\pi$
$797$	−1.44943e106	−1.81121	−0.905604	+	0.424124i	$0.860582\pi$
$798$	0	0
$799$	2.44340e105	0.278635
$800$	−1.97335e105	−0.214991
$801$	0	0
$802$	2.31978e105	0.230719
$803$	5.03658e105	0.478650
$804$	0	0
$805$	1.83476e106	1.59231
$806$	3.23842e105	0.268599
$807$	0	0
$808$	6.60250e105	0.500258
$809$	−1.25435e106	−0.908442	−0.454221	−	0.890889i	$-0.650082\pi$
$809$	−1.25435e106	−0.908442	−0.454221	+	0.890889i	$0.650082\pi$
$810$	0	0
$811$	−1.31775e106	−0.872112	−0.436056	−	0.899920i	$-0.643625\pi$
$811$	−1.31775e106	−0.872112	−0.436056	+	0.899920i	$0.643625\pi$
$812$	−5.29047e105	−0.334734
$813$	0	0
$814$	1.11904e104	0.00647226
$815$	2.01531e106	1.11452
$816$	0	0
$817$	−1.36493e104	−0.00690248
$818$	3.75084e105	0.181398
$819$	0	0
$820$	−2.49551e106	−1.10396
$821$	−2.12804e106	−0.900439	−0.450219	−	0.892918i	$-0.648654\pi$
$821$	−2.12804e106	−0.900439	−0.450219	+	0.892918i	$0.648654\pi$
$822$	0	0
$823$	2.97912e106	1.15344	0.576720	−	0.816942i	$-0.304333\pi$
$823$	2.97912e106	1.15344	0.576720	+	0.816942i	$0.304333\pi$
$824$	9.62555e105	0.356519
$825$	0	0
$826$	1.99920e105	0.0677775
$827$	−3.05296e106	−0.990306	−0.495153	−	0.868806i	$-0.664888\pi$
$827$	−3.05296e106	−0.990306	−0.495153	+	0.868806i	$0.664888\pi$
$828$	0	0
$829$	−3.55563e106	−1.05603	−0.528015	−	0.849235i	$-0.677064\pi$
$829$	−3.55563e106	−1.05603	−0.528015	+	0.849235i	$0.677064\pi$
$830$	−4.78698e105	−0.136054
$831$	0	0
$832$	−5.41477e106	−1.40954
$833$	−2.01472e104	−0.00501963
$834$	0	0
$835$	7.14734e105	0.163150
$836$	−1.33699e106	−0.292144
$837$	0	0
$838$	−1.04019e106	−0.208307
$839$	−1.13258e106	−0.217148	−0.108574	−	0.994088i	$-0.534628\pi$
$839$	−1.13258e106	−0.217148	−0.108574	+	0.994088i	$0.534628\pi$
$840$	0	0
$841$	−5.04911e106	−0.887485
$842$	1.76337e105	0.0296792
$843$	0	0
$844$	3.17995e106	0.490818
$845$	−1.23866e107	−1.83098
$846$	0	0
$847$	5.39294e106	0.731276
$848$	1.99870e106	0.259596
$849$	0	0
$850$	9.85692e104	0.0117476
$851$	1.02183e106	0.116668
$852$	0	0
$853$	−9.81188e106	−1.02828	−0.514141	−	0.857706i	$-0.671889\pi$
$853$	−9.81188e106	−1.02828	−0.514141	+	0.857706i	$0.671889\pi$
$854$	−1.18811e106	−0.119301
$855$	0	0
$856$	4.68166e106	0.431626
$857$	7.41614e106	0.655206	0.327603	−	0.944815i	$-0.393759\pi$
$857$	7.41614e106	0.655206	0.327603	+	0.944815i	$0.393759\pi$
$858$	0	0
$859$	8.57042e106	0.695427	0.347714	−	0.937601i	$-0.386958\pi$
$859$	8.57042e106	0.695427	0.347714	+	0.937601i	$0.386958\pi$
$860$	1.93645e105	0.0150596
$861$	0	0
$862$	2.76991e105	0.0197902
$863$	−7.22821e106	−0.495036	−0.247518	−	0.968883i	$-0.579615\pi$
$863$	−7.22821e106	−0.495036	−0.247518	+	0.968883i	$0.579615\pi$
$864$	0	0
$865$	3.48193e107	2.19145
$866$	1.36772e106	0.0825269
$867$	0	0
$868$	−2.33467e107	−1.29496
$869$	2.41083e106	0.128217
$870$	0	0
$871$	−3.85687e107	−1.88613
$872$	−6.53327e106	−0.306393
$873$	0	0
$874$	2.15721e106	0.0930520
$875$	−1.35770e107	−0.561708
$876$	0	0
$877$	1.98341e107	0.754967	0.377483	−	0.926016i	$-0.376790\pi$
$877$	1.98341e107	0.754967	0.377483	+	0.926016i	$0.376790\pi$
$878$	5.35703e106	0.195602
$879$	0	0
$880$	1.86270e107	0.625929
$881$	3.33655e107	1.07567	0.537833	−	0.843052i	$-0.319243\pi$
$881$	3.33655e107	1.07567	0.537833	+	0.843052i	$0.319243\pi$
$882$	0	0
$883$	−4.17223e106	−0.123823	−0.0619116	−	0.998082i	$-0.519720\pi$
$883$	−4.17223e106	−0.123823	−0.0619116	+	0.998082i	$0.519720\pi$
$884$	8.68068e106	0.247199
$885$	0	0
$886$	−1.85628e106	−0.0486759
$887$	5.76985e107	1.45195	0.725976	−	0.687720i	$-0.241388\pi$
$887$	5.76985e107	1.45195	0.725976	+	0.687720i	$0.241388\pi$
$888$	0	0
$889$	−3.80658e106	−0.0882308
$890$	1.70289e106	0.0378836
$891$	0	0
$892$	6.65870e107	1.36481
$893$	4.96909e107	0.977685
$894$	0	0
$895$	−4.23616e107	−0.768125
$896$	−2.94272e107	−0.512279
$897$	0	0
$898$	−1.09146e106	−0.0175155
$899$	2.82484e107	0.435276
$900$	0	0
$901$	−3.08582e106	−0.0438446
$902$	−4.60077e106	−0.0627757
$903$	0	0
$904$	−1.10325e107	−0.138844
$905$	2.18316e107	0.263883
$906$	0	0
$907$	−1.62085e107	−0.180749	−0.0903746	−	0.995908i	$-0.528806\pi$
$907$	−1.62085e107	−0.180749	−0.0903746	+	0.995908i	$0.528806\pi$
$908$	4.88766e107	0.523561
$909$	0	0
$910$	−2.65312e107	−0.262268
$911$	−7.78998e107	−0.739802	−0.369901	−	0.929071i	$-0.620608\pi$
$911$	−7.78998e107	−0.739802	−0.369901	+	0.929071i	$0.620608\pi$
$912$	0	0
$913$	4.99457e107	0.437840
$914$	1.64454e107	0.138518
$915$	0	0
$916$	1.82763e108	1.42136
$917$	1.48459e108	1.10949
$918$	0	0
$919$	1.01773e107	0.0702448	0.0351224	−	0.999383i	$-0.488818\pi$
$919$	1.01773e107	0.0702448	0.0351224	+	0.999383i	$0.488818\pi$
$920$	−6.17504e107	−0.409623
$921$	0	0
$922$	−2.77365e107	−0.169970
$923$	−2.78212e108	−1.63875
$924$	0	0
$925$	9.49534e106	0.0516818
$926$	9.74564e106	0.0509929
$927$	0	0
$928$	2.67863e107	0.129542
$929$	1.93150e108	0.898092	0.449046	−	0.893509i	$-0.351764\pi$
$929$	1.93150e108	0.898092	0.449046	+	0.893509i	$0.351764\pi$
$930$	0	0
$931$	−4.09730e106	−0.0176130
$932$	−2.29523e108	−0.948735
$933$	0	0
$934$	−2.98281e107	−0.114016
$935$	−2.87585e107	−0.105717
$936$	0	0
$937$	3.17605e108	1.07992	0.539960	−	0.841691i	$-0.318439\pi$
$937$	3.17605e108	1.07992	0.539960	+	0.841691i	$0.318439\pi$
$938$	−4.91317e107	−0.160679
$939$	0	0
$940$	−7.04975e108	−2.13308
$941$	−2.32516e108	−0.676756	−0.338378	−	0.941010i	$-0.609878\pi$
$941$	−2.32516e108	−0.676756	−0.338378	+	0.941010i	$0.609878\pi$
$942$	0	0
$943$	−4.20110e108	−1.13158
$944$	1.85333e108	0.480259
$945$	0	0
$946$	3.57008e105	0.000856350 0
$947$	−6.27531e108	−1.44831	−0.724154	−	0.689638i	$-0.757770\pi$
$947$	−6.27531e108	−1.44831	−0.724154	+	0.689638i	$0.757770\pi$
$948$	0	0
$949$	−6.65038e108	−1.42112
$950$	2.00459e107	0.0412205
$951$	0	0
$952$	2.23116e107	0.0424895
$953$	1.78151e107	0.0326511	0.0163255	−	0.999867i	$-0.494803\pi$
$953$	1.78151e107	0.0326511	0.0163255	+	0.999867i	$0.494803\pi$
$954$	0	0
$955$	8.47075e107	0.143813
$956$	−8.49682e107	−0.138849
$957$	0	0
$958$	2.94209e107	0.0445467
$959$	1.18453e107	0.0172650
$960$	0	0
$961$	5.06299e108	0.683917
$962$	−1.47760e107	−0.0192162
$963$	0	0
$964$	1.76754e108	0.213087
$965$	4.43584e108	0.514907
$966$	0	0
$967$	9.41056e108	1.01286	0.506430	−	0.862281i	$-0.330965\pi$
$967$	9.41056e108	1.01286	0.506430	+	0.862281i	$0.330965\pi$
$968$	−1.81504e108	−0.188121
$969$	0	0
$970$	−1.08739e108	−0.104524
$971$	−5.54960e107	−0.0513759	−0.0256879	−	0.999670i	$-0.508178\pi$
$971$	−5.54960e107	−0.0513759	−0.0256879	+	0.999670i	$0.508178\pi$
$972$	0	0
$973$	6.51310e107	0.0559331
$974$	−1.25956e108	−0.104187
$975$	0	0
$976$	−1.10142e109	−0.845343
$977$	−1.67241e109	−1.23649	−0.618245	−	0.785985i	$-0.712156\pi$
$977$	−1.67241e109	−1.23649	−0.618245	+	0.785985i	$0.712156\pi$
$978$	0	0
$979$	−1.77674e108	−0.121914
$980$	5.81292e107	0.0384275
$981$	0	0
$982$	−2.22763e108	−0.136701
$983$	−2.14789e108	−0.127002	−0.0635008	−	0.997982i	$-0.520227\pi$
$983$	−2.14789e108	−0.127002	−0.0635008	+	0.997982i	$0.520227\pi$
$984$	0	0
$985$	3.07057e109	1.68576
$986$	−1.33798e107	−0.00707851
$987$	0	0
$988$	1.76538e109	0.867379
$989$	3.25994e107	0.0154364
$990$	0	0
$991$	−2.88916e109	−1.27082	−0.635410	−	0.772175i	$-0.719169\pi$
$991$	−2.88916e109	−1.27082	−0.635410	+	0.772175i	$0.719169\pi$
$992$	1.18207e109	0.501150
$993$	0	0
$994$	−3.54407e108	−0.139605
$995$	2.95372e109	1.12157
$996$	0	0
$997$	−2.76095e109	−0.974284	−0.487142	−	0.873323i	$-0.661961\pi$
$997$	−2.76095e109	−0.974284	−0.487142	+	0.873323i	$0.661961\pi$
$998$	5.74340e107	0.0195391
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.74.a.a.1.2		5
3.2	odd	2		1.74.a.a.1.4	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.74.a.a.1.4	✓	5	3.2	odd	2
9.74.a.a.1.2		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)

\(f(q)\)	\(=\)	\(q-1.28059e10 q^{2} -9.28074e21 q^{4} -4.05981e25 q^{5} -7.12492e30 q^{7} +2.39796e32 q^{8} +O(q^{10})\)	\(q-1.28059e10 q^{2} -9.28074e21 q^{4} -4.05981e25 q^{5} -7.12492e30 q^{7} +2.39796e32 q^{8} +5.19894e35 q^{10} -5.42440e37 q^{11} +7.16246e40 q^{13} +9.12407e40 q^{14} +8.45834e43 q^{16} -1.30590e44 q^{17} -2.65578e46 q^{19} +3.76781e47 q^{20} +6.94640e47 q^{22} +6.34296e49 q^{23} +5.89418e50 q^{25} -9.17214e50 q^{26} +6.61246e52 q^{28} -8.00076e52 q^{29} -3.53071e54 q^{31} -3.34797e54 q^{32} +1.67231e54 q^{34} +2.89259e56 q^{35} +1.61097e56 q^{37} +3.40096e56 q^{38} -9.73526e57 q^{40} -6.62324e58 q^{41} +5.13946e57 q^{43} +5.03424e59 q^{44} -8.12270e59 q^{46} -1.87105e61 q^{47} +1.54278e60 q^{49} -7.54801e60 q^{50} -6.64729e62 q^{52} +2.36299e62 q^{53} +2.20220e63 q^{55} -1.70853e63 q^{56} +1.02457e63 q^{58} +2.19113e64 q^{59} -1.30217e65 q^{61} +4.52138e64 q^{62} -7.55994e65 q^{64} -2.90783e66 q^{65} -5.38484e66 q^{67} +1.21197e66 q^{68} -3.70420e66 q^{70} -3.88431e67 q^{71} -9.28505e67 q^{73} -2.06298e66 q^{74} +2.46476e68 q^{76} +3.86484e68 q^{77} -4.44441e68 q^{79} -3.43393e69 q^{80} +8.48163e68 q^{82} -9.20761e69 q^{83} +5.30170e69 q^{85} -6.58152e67 q^{86} -1.30075e70 q^{88} +3.27546e70 q^{89} -5.10320e71 q^{91} -5.88674e71 q^{92} +2.39603e71 q^{94} +1.07820e72 q^{95} -2.09156e72 q^{97} -1.97567e70 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 92089333488 q^{2} + 89\!\cdots\!60 q^{4}+ \cdots + 38\!\cdots\!80 q^{8}+O(q^{10}) \) 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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