LMFDB - Embedded newform 9.72.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,72,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, 72, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 72);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 72 $
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:	$287.321544505$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3 x^{5} + \cdots - 27\!\cdots\!00 $ x^6 - 3x^5 - 327712249929578892882x^4 - 247064970776889197907293537206x^3 + 25021443441555202497465421340907628615965x^2 + 14077016837018585361473224499724917623325562275625*x - 279259064416593965218586682187488478036140359478345093745500
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{49}\cdot 3^{29}\cdot 5^{7}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 3)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.55163e10$ 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)

$f(q)$	$=$	$q-8.09473e10 q^{2} +4.19128e21 q^{4} -7.59856e24 q^{5} +1.03665e30 q^{7} -1.48142e32 q^{8} +O(q^{10})$	\(q-8.09473e10 q^{2} +4.19128e21 q^{4} -7.59856e24 q^{5} +1.03665e30 q^{7} -1.48142e32 q^{8} +6.15083e35 q^{10} -1.84599e37 q^{11} +3.63924e39 q^{13} -8.39143e40 q^{14} +2.09527e42 q^{16} +6.76951e43 q^{17} -2.13387e45 q^{19} -3.18477e46 q^{20} +1.49428e48 q^{22} -4.23025e47 q^{23} +1.53864e49 q^{25} -2.94586e50 q^{26} +4.34490e51 q^{28} -3.95427e51 q^{29} -1.84438e52 q^{31} +1.80183e53 q^{32} -5.47974e54 q^{34} -7.87707e54 q^{35} +7.59903e55 q^{37} +1.72731e56 q^{38} +1.12566e57 q^{40} +1.64875e57 q^{41} -4.45136e57 q^{43} -7.73706e58 q^{44} +3.42428e58 q^{46} -1.38140e59 q^{47} +7.01241e58 q^{49} -1.24549e60 q^{50} +1.52531e61 q^{52} -1.74264e61 q^{53} +1.40269e62 q^{55} -1.53571e62 q^{56} +3.20087e62 q^{58} +1.37996e63 q^{59} +4.64940e62 q^{61} +1.49298e63 q^{62} -1.95326e64 q^{64} -2.76529e64 q^{65} +3.89158e63 q^{67} +2.83729e65 q^{68} +6.37627e65 q^{70} -7.57891e65 q^{71} -1.83450e66 q^{73} -6.15121e66 q^{74} -8.94366e66 q^{76} -1.91365e67 q^{77} +6.44832e66 q^{79} -1.59211e67 q^{80} -1.33462e68 q^{82} -8.97347e67 q^{83} -5.14385e68 q^{85} +3.60326e68 q^{86} +2.73468e69 q^{88} -2.67603e69 q^{89} +3.77263e69 q^{91} -1.77302e69 q^{92} +1.11821e70 q^{94} +1.62143e70 q^{95} -5.40339e69 q^{97} -5.67635e69 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 72903656826 q^{2} + 10\!\cdots\!32 q^{4}+ \cdots + 36\!\cdots\!32 q^{8}+O(q^{10}) $ 6 * q + 72903656826 * q^2 + 10314006409421274045732 * q^4 - 10108593794701196744004900 * q^5 + 599480901407450839419869685888 * q^7 + 366478583494279643287721499310632 * q^8	$ 6 q + 72903656826 q^{2} + 10\!\cdots\!32 q^{4}+ \cdots - 26\!\cdots\!26 q^{98}+O(q^{100}) $ 6 * q + 72903656826 * q^2 + 10314006409421274045732 * q^4 - 10108593794701196744004900 * q^5 + 599480901407450839419869685888 * q^7 + 366478583494279643287721499310632 * q^8 + 542868868744970666737312582578468900 * q^10 - 22151081175113604333940540682999237064 * q^11 - 3733792306574713187109013147800580842876 * q^13 + 32830507140759982684754962229979568501632 * q^14 + 21946377025014017232533669358468876656094480 * q^16 - 29728537162009030546400351590681521887294796 * q^17 - 3400191903952978211629854680984130031529265672 * q^19 - 67862977310829773665490051450873586512770090200 * q^20 + 944165659732727247119333482328915476491852443592 * q^22 + 241048097798755219551674687627695903843789894224 * q^23 + 147233544111014179651192740252202252138516733666250 * q^25 - 365811593583549796821577322473046008640162770663812 * q^26 + 7184703440899560087451639062714257068053559172254464 * q^28 - 14043556001266662709861160370005828332436911172303796 * q^29 - 270783306371944339515858500277888580308160694590498224 * q^31 + 1125690872219692784327995632757361168637025492519761312 * q^32 - 14624984721002826287006157938202770657423642866907848116 * q^34 - 1330179995756585937201666471865883862092414077711430400 * q^35 - 35792724481179188252370374519670456030630938465810079852 * q^37 + 40096713421645845706764919843501793548783513747008434184 * q^38 - 2479587661237177399988484749809178898031295693356625910000 * q^40 - 477389693785559225342921822791522325133674715121487806716 * q^41 + 11648760938240913572137172567293471863701640091329944903880 * q^43 - 74878798041661318901325225719624262581993699901301979154096 * q^44 - 22722764972174503220374661680362423965849207035012290901584 * q^46 + 74847986304767650251381147705131168308416847087017595772160 * q^47 - 688653477285391597239303104103354245619646953145790225785290 * q^49 + 15161902343877042722978992840348999467045739232226501266733750 * q^50 - 9233127809375467425363213342738333025041297615633059381760744 * q^52 - 54557017276559944552388010917280252208764745473331764291919716 * q^53 - 23377768702274474935917895870707480727711321830514284596005200 * q^55 - 52410231138004746064340786054323553480340549752421553548034560 * q^56 - 6869577034896111059681057797577176576414351550513678648728908 * q^58 + 2982562673835141937005021578485268051001526328776278691712555448 * q^59 + 2024766122758654206628711672366353464571765836352692052196097220 * q^61 - 6190527473014961587199547234678103673640494648116320147386047056 * q^62 + 45446447421689003372958411079333884263847638574085838786019075648 * q^64 - 48520756571856116218224136414427408842784606511438543051271531800 * q^65 - 35831986821500503360634896265657012310045332669260449034581275784 * q^67 - 185089183911227350024079142251468478888729548294423879590659066312 * q^68 - 344172356460367114079337658836072099942116692861986486268441785600 * q^70 + 51113783482860556737395980857143689650967786833886125865998410928 * q^71 - 1956710326081635365311373308078888669483174388894330237696366066724 * q^73 - 5709348546681615596063021572004447539391345291333750996512485900948 * q^74 - 23809271474859754704092582776426668087720715729896871772596110280752 * q^76 - 18917631699413080007630569020425573902563798951131161813579745527296 * q^77 + 48402596803386404034053884911414009193830041621338105095759924707760 * q^79 - 263392522337449869178773130835490329512120616670537417787135845410400 * q^80 - 304020075917296666161317294537198008494062493274925376834937204559364 * q^82 - 231863714798237849378047661016738227772765340915812707253802255256568 * q^83 - 153432496682031145548917546056875902159222382871180623315806512428600 * q^85 - 232789528332961926178362349658049178503816504422806394312074365597384 * q^86 + 5297065653948252699139641997691020789333729718805571695420136408677408 * q^88 - 4386397294164484419236854507748631162668647776406659364039350285963708 * q^89 + 10645224502890544811266185738918008251735428747945615198269035910167296 * q^91 - 3494882087686348167672392093650816456059296420998691954341908970318368 * q^92 + 212140324104529926314570388896027999493814139075827826098897565498112 * q^94 + 32230267438252135206013682642661075145567906057502744951334901038078000 * q^95 + 97296789347912261411847519869140120543815674831725660650989227379865996 * q^97 - 262411331100552434262334793443846407592764783361237538614096838440889526 * 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 $

$2$	−8.09473e10	−1.66586	−0.832928	−	0.553381i	$-0.813337\pi$
$2$	−8.09473e10	−1.66586	−0.832928	+	0.553381i	$0.813337\pi$
$3$	0	0
$3$	0	0
$4$	4.19128e21	1.77508
$5$	−7.59856e24	−1.16760	−0.583802	−	0.811896i	$-0.698436\pi$
$5$	−7.59856e24	−1.16760	−0.583802	+	0.811896i	$0.698436\pi$
$6$	0	0
$7$	1.03665e30	1.03432	0.517158	−	0.855890i	$-0.326990\pi$
$7$	1.03665e30	1.03432	0.517158	+	0.855890i	$0.326990\pi$
$8$	−1.48142e32	−1.29117
$9$	0	0
$10$	6.15083e35	1.94506
$11$	−1.84599e37	−1.98056	−0.990282	−	0.139075i	$-0.955587\pi$
$11$	−1.84599e37	−1.98056	−0.990282	+	0.139075i	$0.955587\pi$
$12$	0	0
$13$	3.63924e39	1.03758	0.518790	−	0.854902i	$-0.326383\pi$
$13$	3.63924e39	1.03758	0.518790	+	0.854902i	$0.326383\pi$
$14$	−8.39143e40	−1.72302
$15$	0	0
$16$	2.09527e42	0.375821
$17$	6.76951e43	1.41130	0.705652	−	0.708559i	$-0.250654\pi$
$17$	6.76951e43	1.41130	0.705652	+	0.708559i	$0.250654\pi$
$18$	0	0
$19$	−2.13387e45	−0.857858	−0.428929	−	0.903338i	$-0.641109\pi$
$19$	−2.13387e45	−0.857858	−0.428929	+	0.903338i	$0.641109\pi$
$20$	−3.18477e46	−2.07259
$21$	0	0
$22$	1.49428e48	3.29933
$23$	−4.23025e47	−0.192765	−0.0963825	−	0.995344i	$-0.530727\pi$
$23$	−4.23025e47	−0.192765	−0.0963825	+	0.995344i	$0.530727\pi$
$24$	0	0
$25$	1.53864e49	0.363301
$26$	−2.94586e50	−1.72846
$27$	0	0
$28$	4.34490e51	1.83599
$29$	−3.95427e51	−0.480770	−0.240385	−	0.970678i	$-0.577274\pi$
$29$	−3.95427e51	−0.480770	−0.240385	+	0.970678i	$0.577274\pi$
$30$	0	0
$31$	−1.84438e52	−0.210141	−0.105071	−	0.994465i	$-0.533507\pi$
$31$	−1.84438e52	−0.210141	−0.105071	+	0.994465i	$0.533507\pi$
$32$	1.80183e53	0.665103
$33$	0	0
$34$	−5.47974e54	−2.35103
$35$	−7.87707e54	−1.20767
$36$	0	0
$37$	7.59903e55	1.62031	0.810153	−	0.586219i	$-0.199384\pi$
$37$	7.59903e55	1.62031	0.810153	+	0.586219i	$0.199384\pi$
$38$	1.72731e56	1.42907
$39$	0	0
$40$	1.12566e57	1.50757
$41$	1.64875e57	0.919026	0.459513	−	0.888171i	$-0.348024\pi$
$41$	1.64875e57	0.919026	0.459513	+	0.888171i	$0.348024\pi$
$42$	0	0
$43$	−4.45136e57	−0.457470	−0.228735	−	0.973489i	$-0.573459\pi$
$43$	−4.45136e57	−0.457470	−0.228735	+	0.973489i	$0.573459\pi$
$44$	−7.73706e58	−3.51565
$45$	0	0
$46$	3.42428e58	0.321119
$47$	−1.38140e59	−0.603736	−0.301868	−	0.953350i	$-0.597610\pi$
$47$	−1.38140e59	−0.603736	−0.301868	+	0.953350i	$0.597610\pi$
$48$	0	0
$49$	7.01241e58	0.0698082
$50$	−1.24549e60	−0.605208
$51$	0	0
$52$	1.52531e61	1.84178
$53$	−1.74264e61	−1.07007	−0.535036	−	0.844829i	$-0.679702\pi$
$53$	−1.74264e61	−1.07007	−0.535036	+	0.844829i	$0.679702\pi$
$54$	0	0
$55$	1.40269e62	2.31252
$56$	−1.53571e62	−1.33547
$57$	0	0
$58$	3.20087e62	0.800894
$59$	1.37996e63	1.88201	0.941004	−	0.338395i	$-0.109884\pi$
$59$	1.37996e63	1.88201	0.941004	+	0.338395i	$0.109884\pi$
$60$	0	0
$61$	4.64940e62	0.194172	0.0970862	−	0.995276i	$-0.469048\pi$
$61$	4.64940e62	0.194172	0.0970862	+	0.995276i	$0.469048\pi$
$62$	1.49298e63	0.350065
$63$	0	0
$64$	−1.95326e64	−1.48379
$65$	−2.76529e64	−1.21148
$66$	0	0
$67$	3.89158e63	0.0581393	0.0290697	−	0.999577i	$-0.490746\pi$
$67$	3.89158e63	0.0581393	0.0290697	+	0.999577i	$0.490746\pi$
$68$	2.83729e65	2.50517
$69$	0	0
$70$	6.37627e65	2.01181
$71$	−7.57891e65	−1.44522	−0.722612	−	0.691254i	$-0.757059\pi$
$71$	−7.57891e65	−1.44522	−0.722612	+	0.691254i	$0.757059\pi$
$72$	0	0
$73$	−1.83450e66	−1.30484	−0.652419	−	0.757858i	$-0.726246\pi$
$73$	−1.83450e66	−1.30484	−0.652419	+	0.757858i	$0.726246\pi$
$74$	−6.15121e66	−2.69920
$75$	0	0
$76$	−8.94366e66	−1.52276
$77$	−1.91365e67	−2.04853
$78$	0	0
$79$	6.44832e66	0.277770	0.138885	−	0.990309i	$-0.455648\pi$
$79$	6.44832e66	0.277770	0.138885	+	0.990309i	$0.455648\pi$
$80$	−1.59211e67	−0.438811
$81$	0	0
$82$	−1.33462e68	−1.53096
$83$	−8.97347e67	−0.669404	−0.334702	−	0.942324i	$-0.608636\pi$
$83$	−8.97347e67	−0.669404	−0.334702	+	0.942324i	$0.608636\pi$
$84$	0	0
$85$	−5.14385e68	−1.64785
$86$	3.60326e68	0.762080
$87$	0	0
$88$	2.73468e69	2.55724
$89$	−2.67603e69	−1.67550	−0.837752	−	0.546051i	$-0.816130\pi$
$89$	−2.67603e69	−1.67550	−0.837752	+	0.546051i	$0.816130\pi$
$90$	0	0
$91$	3.77263e69	1.07318
$92$	−1.77302e69	−0.342173
$93$	0	0
$94$	1.11821e70	1.00574
$95$	1.62143e70	1.00164
$96$	0	0
$97$	−5.40339e69	−0.159320	−0.0796599	−	0.996822i	$-0.525383\pi$
$97$	−5.40339e69	−0.159320	−0.0796599	+	0.996822i	$0.525383\pi$
$98$	−5.67635e69	−0.116290
$99$	0	0
$100$	6.44888e70	0.644888
$101$	1.03525e71	0.727170	0.363585	−	0.931561i	$-0.381553\pi$
$101$	1.03525e71	0.727170	0.363585	+	0.931561i	$0.381553\pi$
$102$	0	0
$103$	−7.03177e70	−0.246231	−0.123116	−	0.992392i	$-0.539289\pi$
$103$	−7.03177e70	−0.246231	−0.123116	+	0.992392i	$0.539289\pi$
$104$	−5.39122e71	−1.33969
$105$	0	0
$106$	1.41062e72	1.78259
$107$	−1.09664e72	−0.992983	−0.496492	−	0.868042i	$-0.665379\pi$
$107$	−1.09664e72	−0.992983	−0.496492	+	0.868042i	$0.665379\pi$
$108$	0	0
$109$	2.99950e72	1.40737	0.703684	−	0.710513i	$-0.251537\pi$
$109$	2.99950e72	1.40737	0.703684	+	0.710513i	$0.251537\pi$
$110$	−1.13544e73	−3.85232
$111$	0	0
$112$	2.17207e72	0.388718
$113$	1.06159e73	1.38571	0.692853	−	0.721079i	$-0.256354\pi$
$113$	1.06159e73	1.38571	0.692853	+	0.721079i	$0.256354\pi$
$114$	0	0
$115$	3.21438e72	0.225073
$116$	−1.65735e73	−0.853404
$117$	0	0
$118$	−1.11704e74	−3.13516
$119$	7.01763e73	1.45973
$120$	0	0
$121$	2.53895e74	2.92263
$122$	−3.76356e73	−0.323463
$123$	0	0
$124$	−7.73034e73	−0.373017
$125$	2.04897e74	0.743413
$126$	0	0
$127$	−5.36800e74	−1.10861	−0.554307	−	0.832312i	$-0.687017\pi$
$127$	−5.36800e74	−1.10861	−0.554307	+	0.832312i	$0.687017\pi$
$128$	1.15567e75	1.80667
$129$	0	0
$130$	2.23843e75	2.01816
$131$	5.69097e74	0.390890	0.195445	−	0.980715i	$-0.437385\pi$
$131$	5.69097e74	0.390890	0.195445	+	0.980715i	$0.437385\pi$
$132$	0	0
$133$	−2.21208e75	−0.887296
$134$	−3.15012e74	−0.0968517
$135$	0	0
$136$	−1.00285e76	−1.82223
$137$	1.21672e76	1.70455	0.852277	−	0.523090i	$-0.175221\pi$
$137$	1.21672e76	1.70455	0.852277	+	0.523090i	$0.175221\pi$
$138$	0	0
$139$	4.97130e75	0.416337	0.208168	−	0.978093i	$-0.433250\pi$
$139$	4.97130e75	0.416337	0.208168	+	0.978093i	$0.433250\pi$
$140$	−3.30150e76	−2.14371
$141$	0	0
$142$	6.13492e76	2.40754
$143$	−6.71799e76	−2.05499
$144$	0	0
$145$	3.00467e76	0.561349
$146$	1.48498e77	2.17367
$147$	0	0
$148$	3.18497e77	2.87617
$149$	1.87555e77	1.33357	0.666784	−	0.745251i	$-0.267670\pi$
$149$	1.87555e77	1.33357	0.666784	+	0.745251i	$0.267670\pi$
$150$	0	0
$151$	6.89444e76	0.305364	0.152682	−	0.988275i	$-0.451209\pi$
$151$	6.89444e76	0.305364	0.152682	+	0.988275i	$0.451209\pi$
$152$	3.16115e77	1.10764
$153$	0	0
$154$	1.54905e78	3.41255
$155$	1.40147e77	0.245362
$156$	0	0
$157$	−6.16646e77	−0.684854	−0.342427	−	0.939544i	$-0.611249\pi$
$157$	−6.16646e77	−0.684854	−0.342427	+	0.939544i	$0.611249\pi$
$158$	−5.21974e77	−0.462725
$159$	0	0
$160$	−1.36913e78	−0.776577
$161$	−4.38530e77	−0.199380
$162$	0	0
$163$	6.27226e78	1.83977	0.919887	−	0.392184i	$-0.128280\pi$
$163$	6.27226e78	1.83977	0.919887	+	0.392184i	$0.128280\pi$
$164$	6.91037e78	1.63134
$165$	0	0
$166$	7.26378e78	1.11513
$167$	−6.69392e78	−0.830320	−0.415160	−	0.909748i	$-0.636274\pi$
$167$	−6.69392e78	−0.830320	−0.415160	+	0.909748i	$0.636274\pi$
$168$	0	0
$169$	9.41981e77	0.0765710
$170$	4.16381e79	2.74507
$171$	0	0
$172$	−1.86569e79	−0.812045
$173$	1.92433e79	0.681777	0.340889	−	0.940104i	$-0.389272\pi$
$173$	1.92433e79	0.681777	0.340889	+	0.940104i	$0.389272\pi$
$174$	0	0
$175$	1.59504e79	0.375768
$176$	−3.86785e79	−0.744338
$177$	0	0
$178$	2.16617e80	2.79115
$179$	1.10175e80	1.16360	0.581798	−	0.813334i	$-0.302350\pi$
$179$	1.10175e80	1.16360	0.581798	+	0.813334i	$0.302350\pi$
$180$	0	0
$181$	−3.57667e79	−0.254618	−0.127309	−	0.991863i	$-0.540634\pi$
$181$	−3.57667e79	−0.254618	−0.127309	+	0.991863i	$0.540634\pi$
$182$	−3.05384e80	−1.78777
$183$	0	0
$184$	6.26676e79	0.248892
$185$	−5.77416e80	−1.89188
$186$	0	0
$187$	−1.24964e81	−2.79518
$188$	−5.78985e80	−1.07168
$189$	0	0
$190$	−1.31251e81	−1.66859
$191$	2.20499e80	0.232660	0.116330	−	0.993211i	$-0.462887\pi$
$191$	2.20499e80	0.232660	0.116330	+	0.993211i	$0.462887\pi$
$192$	0	0
$193$	−3.61963e80	−0.263864	−0.131932	−	0.991259i	$-0.542118\pi$
$193$	−3.61963e80	−0.263864	−0.131932	+	0.991259i	$0.542118\pi$
$194$	4.37390e80	0.265404
$195$	0	0
$196$	2.93910e80	0.123915
$197$	2.77557e81	0.976788	0.488394	−	0.872623i	$-0.337583\pi$
$197$	2.77557e81	0.976788	0.488394	+	0.872623i	$0.337583\pi$
$198$	0	0
$199$	−1.40489e81	−0.345429	−0.172714	−	0.984972i	$-0.555254\pi$
$199$	−1.40489e81	−0.345429	−0.172714	+	0.984972i	$0.555254\pi$
$200$	−2.27937e81	−0.469082
$201$	0	0
$202$	−8.38005e81	−1.21136
$203$	−4.09920e81	−0.497268
$204$	0	0
$205$	−1.25281e82	−1.07306
$206$	5.69203e81	0.410186
$207$	0	0
$208$	7.62520e81	0.389944
$209$	3.93910e82	1.69904
$210$	0	0
$211$	−1.05750e82	−0.325276	−0.162638	−	0.986686i	$-0.552000\pi$
$211$	−1.05750e82	−0.325276	−0.162638	+	0.986686i	$0.552000\pi$
$212$	−7.30387e82	−1.89946
$213$	0	0
$214$	8.87704e82	1.65417
$215$	3.38239e82	0.534145
$216$	0	0
$217$	−1.91199e82	−0.217352
$218$	−2.42801e83	−2.34447
$219$	0	0
$220$	5.87905e83	4.10489
$221$	2.46359e83	1.46434
$222$	0	0
$223$	1.94708e83	0.840546	0.420273	−	0.907398i	$-0.361934\pi$
$223$	1.94708e83	0.840546	0.420273	+	0.907398i	$0.361934\pi$
$224$	1.86787e83	0.687926
$225$	0	0
$226$	−8.59326e83	−2.30839
$227$	3.59988e83	0.826743	0.413371	−	0.910562i	$-0.364351\pi$
$227$	3.59988e83	0.826743	0.413371	+	0.910562i	$0.364351\pi$
$228$	0	0
$229$	1.26233e83	0.212331	0.106165	−	0.994348i	$-0.466143\pi$
$229$	1.26233e83	0.212331	0.106165	+	0.994348i	$0.466143\pi$
$230$	−2.60195e83	−0.374940
$231$	0	0
$232$	5.85792e83	0.620754
$233$	9.85273e83	0.896234	0.448117	−	0.893975i	$-0.352095\pi$
$233$	9.85273e83	0.896234	0.448117	+	0.893975i	$0.352095\pi$
$234$	0	0
$235$	1.04967e84	0.704925
$236$	5.78382e84	3.34071
$237$	0	0
$238$	−5.68059e84	−2.43171
$239$	−3.19988e84	−1.18034	−0.590171	−	0.807278i	$-0.700940\pi$
$239$	−3.19988e84	−1.18034	−0.590171	+	0.807278i	$0.700940\pi$
$240$	0	0
$241$	−1.30522e83	−0.0358161	−0.0179080	−	0.999840i	$-0.505701\pi$
$241$	−1.30522e83	−0.0358161	−0.0179080	+	0.999840i	$0.505701\pi$
$242$	−2.05521e85	−4.86868
$243$	0	0
$244$	1.94869e84	0.344671
$245$	−5.32842e83	−0.0815084
$246$	0	0
$247$	−7.76566e84	−0.890096
$248$	2.73230e84	0.271327
$249$	0	0
$250$	−1.65859e85	−1.23842
$251$	−1.37585e85	−0.891570	−0.445785	−	0.895140i	$-0.647075\pi$
$251$	−1.37585e85	−0.891570	−0.445785	+	0.895140i	$0.647075\pi$
$252$	0	0
$253$	7.80900e84	0.381783
$254$	4.34525e85	1.84679
$255$	0	0
$256$	−4.74282e85	−1.52587
$257$	1.37641e84	0.0385586	0.0192793	−	0.999814i	$-0.493863\pi$
$257$	1.37641e84	0.0385586	0.0192793	+	0.999814i	$0.493863\pi$
$258$	0	0
$259$	7.87755e85	1.67591
$260$	−1.15901e86	−2.15048
$261$	0	0
$262$	−4.60668e85	−0.651167
$263$	−3.68940e85	−0.455541	−0.227770	−	0.973715i	$-0.573144\pi$
$263$	−3.68940e85	−0.455541	−0.227770	+	0.973715i	$0.573144\pi$
$264$	0	0
$265$	1.32415e86	1.24942
$266$	1.79062e86	1.47811
$267$	0	0
$268$	1.63107e85	0.103202
$269$	5.65675e85	0.313589	0.156795	−	0.987631i	$-0.449884\pi$
$269$	5.65675e85	0.313589	0.156795	+	0.987631i	$0.449884\pi$
$270$	0	0
$271$	9.90355e85	0.422067	0.211033	−	0.977479i	$-0.432317\pi$
$271$	9.90355e85	0.422067	0.211033	+	0.977479i	$0.432317\pi$
$272$	1.41840e86	0.530398
$273$	0	0
$274$	−9.84903e86	−2.83954
$275$	−2.84031e86	−0.719541
$276$	0	0
$277$	4.96677e86	0.972842	0.486421	−	0.873725i	$-0.338302\pi$
$277$	4.96677e86	0.972842	0.486421	+	0.873725i	$0.338302\pi$
$278$	−4.02413e86	−0.693557
$279$	0	0
$280$	1.16692e87	1.55931
$281$	9.77083e86	1.15042	0.575211	−	0.818005i	$-0.304920\pi$
$281$	9.77083e86	1.15042	0.575211	+	0.818005i	$0.304920\pi$
$282$	0	0
$283$	−1.60657e87	−1.47056	−0.735278	−	0.677766i	$-0.762948\pi$
$283$	−1.60657e87	−1.47056	−0.735278	+	0.677766i	$0.762948\pi$
$284$	−3.17653e87	−2.56538
$285$	0	0
$286$	5.43803e87	3.42332
$287$	1.70918e87	0.950563
$288$	0	0
$289$	2.28186e87	0.991779
$290$	−2.43220e87	−0.935127
$291$	0	0
$292$	−7.68892e87	−2.31619
$293$	−1.74289e87	−0.465018	−0.232509	−	0.972594i	$-0.574694\pi$
$293$	−1.74289e87	−0.465018	−0.232509	+	0.972594i	$0.574694\pi$
$294$	0	0
$295$	−1.04857e88	−2.19744
$296$	−1.12573e88	−2.09208
$297$	0	0
$298$	−1.51820e88	−2.22153
$299$	−1.53949e87	−0.200009
$300$	0	0
$301$	−4.61452e87	−0.473169
$302$	−5.58086e87	−0.508692
$303$	0	0
$304$	−4.47105e87	−0.322401
$305$	−3.53287e87	−0.226717
$306$	0	0
$307$	−3.34383e88	−1.70150	−0.850751	−	0.525569i	$-0.823852\pi$
$307$	−3.34383e88	−1.70150	−0.850751	+	0.525569i	$0.823852\pi$
$308$	−8.02065e88	−3.63629
$309$	0	0
$310$	−1.13445e88	−0.408738
$311$	2.61401e88	0.840066	0.420033	−	0.907509i	$-0.362019\pi$
$311$	2.61401e88	0.840066	0.420033	+	0.907509i	$0.362019\pi$
$312$	0	0
$313$	3.17000e88	0.811400	0.405700	−	0.914006i	$-0.367028\pi$
$313$	3.17000e88	0.811400	0.405700	+	0.914006i	$0.367028\pi$
$314$	4.99158e88	1.14087
$315$	0	0
$316$	2.70267e88	0.493063
$317$	−6.30501e88	−1.02821	−0.514106	−	0.857727i	$-0.671876\pi$
$317$	−6.30501e88	−1.02821	−0.514106	+	0.857727i	$0.671876\pi$
$318$	0	0
$319$	7.29954e88	0.952195
$320$	1.48420e89	1.73248
$321$	0	0
$322$	3.54978e88	0.332138
$323$	−1.44453e89	−1.21070
$324$	0	0
$325$	5.59948e88	0.376954
$326$	−5.07723e89	−3.06480
$327$	0	0
$328$	−2.44248e89	−1.18662
$329$	−1.43204e89	−0.624453
$330$	0	0
$331$	−1.52866e89	−0.537549	−0.268775	−	0.963203i	$-0.586619\pi$
$331$	−1.52866e89	−0.537549	−0.268775	+	0.963203i	$0.586619\pi$
$332$	−3.76103e89	−1.18824
$333$	0	0
$334$	5.41854e89	1.38319
$335$	−2.95704e88	−0.0678837
$336$	0	0
$337$	6.20666e89	1.15344	0.576722	−	0.816941i	$-0.304332\pi$
$337$	6.20666e89	1.15344	0.576722	+	0.816941i	$0.304332\pi$
$338$	−7.62508e88	−0.127556
$339$	0	0
$340$	−2.15593e90	−2.92505
$341$	3.40471e89	0.416198
$342$	0	0
$343$	−9.68650e89	−0.962112
$344$	6.59432e89	0.590671
$345$	0	0
$346$	−1.55769e90	−1.13574
$347$	2.25155e90	1.48179	0.740893	−	0.671623i	$-0.234402\pi$
$347$	2.25155e90	1.48179	0.740893	+	0.671623i	$0.234402\pi$
$348$	0	0
$349$	1.04948e90	0.563213	0.281606	−	0.959530i	$-0.409133\pi$
$349$	1.04948e90	0.563213	0.281606	+	0.959530i	$0.409133\pi$
$350$	−1.29114e90	−0.625975
$351$	0	0
$352$	−3.32615e90	−1.31728
$353$	−3.88135e90	−1.38989	−0.694946	−	0.719062i	$-0.744572\pi$
$353$	−3.88135e90	−1.38989	−0.694946	+	0.719062i	$0.744572\pi$
$354$	0	0
$355$	5.75888e90	1.68745
$356$	−1.12160e91	−2.97415
$357$	0	0
$358$	−8.91840e90	−1.93838
$359$	−1.60113e90	−0.315190	−0.157595	−	0.987504i	$-0.550374\pi$
$359$	−1.60113e90	−0.315190	−0.157595	+	0.987504i	$0.550374\pi$
$360$	0	0
$361$	−1.63396e90	−0.264080
$362$	2.89522e90	0.424157
$363$	0	0
$364$	1.58121e91	1.90498
$365$	1.39396e91	1.52354
$366$	0	0
$367$	−1.59612e91	−1.43688	−0.718438	−	0.695591i	$-0.755143\pi$
$367$	−1.59612e91	−1.43688	−0.718438	+	0.695591i	$0.755143\pi$
$368$	−8.86354e89	−0.0724452
$369$	0	0
$370$	4.67403e91	3.15159
$371$	−1.80651e91	−1.10679
$372$	0	0
$373$	−6.83531e90	−0.346015	−0.173007	−	0.984921i	$-0.555348\pi$
$373$	−6.83531e90	−0.346015	−0.173007	+	0.984921i	$0.555348\pi$
$374$	1.01155e92	4.65636
$375$	0	0
$376$	2.04643e91	0.779523
$377$	−1.43905e91	−0.498837
$378$	0	0
$379$	6.66619e90	0.191508	0.0957538	−	0.995405i	$-0.469474\pi$
$379$	6.66619e90	0.191508	0.0957538	+	0.995405i	$0.469474\pi$
$380$	6.79589e91	1.77799
$381$	0	0
$382$	−1.78488e91	−0.387578
$383$	1.62606e91	0.321795	0.160898	−	0.986971i	$-0.448561\pi$
$383$	1.62606e91	0.321795	0.160898	+	0.986971i	$0.448561\pi$
$384$	0	0
$385$	1.45410e92	2.39187
$386$	2.93000e91	0.439559
$387$	0	0
$388$	−2.26471e91	−0.282805
$389$	4.19375e91	0.477960	0.238980	−	0.971025i	$-0.423187\pi$
$389$	4.19375e91	0.477960	0.238980	+	0.971025i	$0.423187\pi$
$390$	0	0
$391$	−2.86367e91	−0.272050
$392$	−1.03883e91	−0.0901340
$393$	0	0
$394$	−2.24675e92	−1.62719
$395$	−4.89979e91	−0.324325
$396$	0	0
$397$	7.94566e91	0.439609	0.219805	−	0.975544i	$-0.429458\pi$
$397$	7.94566e91	0.439609	0.219805	+	0.975544i	$0.429458\pi$
$398$	1.13722e92	0.575434
$399$	0	0
$400$	3.22387e91	0.136536
$401$	−3.06655e92	−1.18857	−0.594284	−	0.804255i	$-0.702565\pi$
$401$	−3.06655e92	−1.18857	−0.594284	+	0.804255i	$0.702565\pi$
$402$	0	0
$403$	−6.71215e91	−0.218038
$404$	4.33902e92	1.29078
$405$	0	0
$406$	3.31820e92	0.828376
$407$	−1.40277e93	−3.20912
$408$	0	0
$409$	1.13654e92	0.218478	0.109239	−	0.994016i	$-0.465159\pi$
$409$	1.13654e92	0.218478	0.109239	+	0.994016i	$0.465159\pi$
$410$	1.01412e93	1.78756
$411$	0	0
$412$	−2.94721e92	−0.437079
$413$	1.43054e93	1.94659
$414$	0	0
$415$	6.81854e92	0.781599
$416$	6.55727e92	0.690097
$417$	0	0
$418$	−3.18860e93	−2.83036
$419$	−1.63357e93	−1.33211	−0.666055	−	0.745902i	$-0.732019\pi$
$419$	−1.63357e93	−1.33211	−0.666055	+	0.745902i	$0.732019\pi$
$420$	0	0
$421$	−5.83317e92	−0.401689	−0.200845	−	0.979623i	$-0.564369\pi$
$421$	−5.83317e92	−0.401689	−0.200845	+	0.979623i	$0.564369\pi$
$422$	8.56015e92	0.541863
$423$	0	0
$424$	2.58157e93	1.38164
$425$	1.04158e93	0.512728
$426$	0	0
$427$	4.81981e92	0.200836
$428$	−4.59635e93	−1.76262
$429$	0	0
$430$	−2.73796e93	−0.889808
$431$	−1.52684e92	−0.0456932	−0.0228466	−	0.999739i	$-0.507273\pi$
$431$	−1.52684e92	−0.0456932	−0.0228466	+	0.999739i	$0.507273\pi$
$432$	0	0
$433$	7.06740e93	1.79448	0.897241	−	0.441541i	$-0.145568\pi$
$433$	7.06740e93	1.79448	0.897241	+	0.441541i	$0.145568\pi$
$434$	1.54770e93	0.362078
$435$	0	0
$436$	1.25717e94	2.49819
$437$	9.02682e92	0.165365
$438$	0	0
$439$	−3.91121e93	−0.609285	−0.304642	−	0.952467i	$-0.598537\pi$
$439$	−3.91121e93	−0.609285	−0.304642	+	0.952467i	$0.598537\pi$
$440$	−2.07796e94	−2.98584
$441$	0	0
$442$	−1.99421e94	−2.43938
$443$	6.51372e93	0.735355	0.367677	−	0.929953i	$-0.380153\pi$
$443$	6.51372e93	0.735355	0.367677	+	0.929953i	$0.380153\pi$
$444$	0	0
$445$	2.03340e94	1.95633
$446$	−1.57611e94	−1.40023
$447$	0	0
$448$	−2.02485e94	−1.53470
$449$	−7.51651e93	−0.526346	−0.263173	−	0.964749i	$-0.584769\pi$
$449$	−7.51651e93	−0.526346	−0.263173	+	0.964749i	$0.584769\pi$
$450$	0	0
$451$	−3.04357e94	−1.82019
$452$	4.44941e94	2.45973
$453$	0	0
$454$	−2.91401e94	−1.37723
$455$	−2.86665e94	−1.25306
$456$	0	0
$457$	8.10540e93	0.303214	0.151607	−	0.988441i	$-0.451555\pi$
$457$	8.10540e93	0.303214	0.151607	+	0.988441i	$0.451555\pi$
$458$	−1.02182e94	−0.353713
$459$	0	0
$460$	1.34724e94	0.399522
$461$	−6.73106e94	−1.84799	−0.923997	−	0.382400i	$-0.875098\pi$
$461$	−6.73106e94	−1.84799	−0.923997	+	0.382400i	$0.875098\pi$
$462$	0	0
$463$	2.40928e94	0.567234	0.283617	−	0.958938i	$-0.408466\pi$
$463$	2.40928e94	0.567234	0.283617	+	0.958938i	$0.408466\pi$
$464$	−8.28528e93	−0.180684
$465$	0	0
$466$	−7.97552e94	−1.49300
$467$	−1.45676e94	−0.252720	−0.126360	−	0.991984i	$-0.540329\pi$
$467$	−1.45676e94	−0.252720	−0.126360	+	0.991984i	$0.540329\pi$
$468$	0	0
$469$	4.03421e93	0.0601344
$470$	−8.49678e94	−1.17430
$471$	0	0
$472$	−2.04430e95	−2.42999
$473$	8.21717e94	0.906049
$474$	0	0
$475$	−3.28326e94	−0.311661
$476$	2.94129e95	2.59114
$477$	0	0
$478$	2.59021e95	1.96628
$479$	1.30586e95	0.920420	0.460210	−	0.887810i	$-0.347774\pi$
$479$	1.30586e95	0.920420	0.460210	+	0.887810i	$0.347774\pi$
$480$	0	0
$481$	2.76547e95	1.68120
$482$	1.05654e94	0.0596644
$483$	0	0
$484$	1.06415e96	5.18790
$485$	4.10580e94	0.186023
$486$	0	0
$487$	−2.74082e95	−1.07301	−0.536503	−	0.843898i	$-0.680255\pi$
$487$	−2.74082e95	−1.07301	−0.536503	+	0.843898i	$0.680255\pi$
$488$	−6.88769e94	−0.250709
$489$	0	0
$490$	4.31321e94	0.135781
$491$	3.69071e94	0.108073	0.0540365	−	0.998539i	$-0.482791\pi$
$491$	3.69071e94	0.108073	0.0540365	+	0.998539i	$0.482791\pi$
$492$	0	0
$493$	−2.67685e95	−0.678513
$494$	6.28610e95	1.48277
$495$	0	0
$496$	−3.86449e94	−0.0789756
$497$	−7.85670e95	−1.49482
$498$	0	0
$499$	−6.69681e95	−1.10484	−0.552419	−	0.833567i	$-0.686295\pi$
$499$	−6.69681e95	−1.10484	−0.552419	+	0.833567i	$0.686295\pi$
$500$	8.58781e95	1.31961
$501$	0	0
$502$	1.11372e96	1.48523
$503$	4.64828e95	0.577602	0.288801	−	0.957389i	$-0.406743\pi$
$503$	4.64828e95	0.577602	0.288801	+	0.957389i	$0.406743\pi$
$504$	0	0
$505$	−7.86639e95	−0.849047
$506$	−6.32117e95	−0.635996
$507$	0	0
$508$	−2.24988e96	−1.96788
$509$	2.35898e96	1.92417	0.962083	−	0.272758i	$-0.0879358\pi$
$509$	2.35898e96	1.92417	0.962083	+	0.272758i	$0.0879358\pi$
$510$	0	0
$511$	−1.90174e96	−1.34961
$512$	1.11044e96	0.735208
$513$	0	0
$514$	−1.11416e95	−0.0642331
$515$	5.34313e95	0.287501
$516$	0	0
$517$	2.55006e96	1.19574
$518$	−6.37667e96	−2.79182
$519$	0	0
$520$	4.09655e96	1.56423
$521$	2.25201e95	0.0803215	0.0401607	−	0.999193i	$-0.487213\pi$
$521$	2.25201e95	0.0803215	0.0401607	+	0.999193i	$0.487213\pi$
$522$	0	0
$523$	6.44928e95	0.200771	0.100386	−	0.994949i	$-0.467992\pi$
$523$	6.44928e95	0.200771	0.100386	+	0.994949i	$0.467992\pi$
$524$	2.38524e96	0.693860
$525$	0	0
$526$	2.98647e96	0.758865
$527$	−1.24856e96	−0.296573
$528$	0	0
$529$	−4.63694e96	−0.962842
$530$	−1.07186e97	−2.08136
$531$	0	0
$532$	−9.27147e96	−1.57502
$533$	6.00019e96	0.953562
$534$	0	0
$535$	8.33292e96	1.15941
$536$	−5.76504e95	−0.0750676
$537$	0	0
$538$	−4.57899e96	−0.522395
$539$	−1.29448e96	−0.138260
$540$	0	0
$541$	−3.30152e96	−0.309179	−0.154590	−	0.987979i	$-0.549406\pi$
$541$	−3.30152e96	−0.309179	−0.154590	+	0.987979i	$0.549406\pi$
$542$	−8.01666e96	−0.703103
$543$	0	0
$544$	1.21975e97	0.938662
$545$	−2.27918e97	−1.64325
$546$	0	0
$547$	−1.71718e97	−1.08709	−0.543545	−	0.839380i	$-0.682918\pi$
$547$	−1.71718e97	−1.08709	−0.543545	+	0.839380i	$0.682918\pi$
$548$	5.09962e97	3.02572
$549$	0	0
$550$	2.29916e97	1.19865
$551$	8.43790e96	0.412432
$552$	0	0
$553$	6.68467e96	0.287302
$554$	−4.02047e97	−1.62061
$555$	0	0
$556$	2.08361e97	0.739030
$557$	−1.26148e97	−0.419779	−0.209890	−	0.977725i	$-0.567310\pi$
$557$	−1.26148e97	−0.419779	−0.209890	+	0.977725i	$0.567310\pi$
$558$	0	0
$559$	−1.61996e97	−0.474662
$560$	−1.65046e97	−0.453869
$561$	0	0
$562$	−7.90922e97	−1.91644
$563$	−1.27403e97	−0.289823	−0.144912	−	0.989445i	$-0.546290\pi$
$563$	−1.27403e97	−0.289823	−0.144912	+	0.989445i	$0.546290\pi$
$564$	0	0
$565$	−8.06653e97	−1.61796
$566$	1.30048e98	2.44973
$567$	0	0
$568$	1.12275e98	1.86603
$569$	−6.31265e97	−0.985659	−0.492829	−	0.870126i	$-0.664037\pi$
$569$	−6.31265e97	−0.985659	−0.492829	+	0.870126i	$0.664037\pi$
$570$	0	0
$571$	−4.55268e97	−0.627604	−0.313802	−	0.949488i	$-0.601603\pi$
$571$	−4.55268e97	−0.627604	−0.313802	+	0.949488i	$0.601603\pi$
$572$	−2.81570e98	−3.64777
$573$	0	0
$574$	−1.38354e98	−1.58350
$575$	−6.50884e96	−0.0700317
$576$	0	0
$577$	−1.54224e98	−1.46694	−0.733469	−	0.679723i	$-0.762100\pi$
$577$	−1.54224e98	−1.46694	−0.733469	+	0.679723i	$0.762100\pi$
$578$	−1.84710e98	−1.65216
$579$	0	0
$580$	1.25934e98	0.996438
$581$	−9.30237e97	−0.692375
$582$	0	0
$583$	3.21689e98	2.11935
$584$	2.71766e98	1.68476
$585$	0	0
$586$	1.41082e98	0.774654
$587$	3.03248e98	1.56727	0.783637	−	0.621220i	$-0.213362\pi$
$587$	3.03248e98	1.56727	0.783637	+	0.621220i	$0.213362\pi$
$588$	0	0
$589$	3.93568e97	0.180271
$590$	8.48792e98	3.66062
$591$	0	0
$592$	1.59220e98	0.608945
$593$	4.38798e97	0.158060	0.0790302	−	0.996872i	$-0.474818\pi$
$593$	4.38798e97	0.158060	0.0790302	+	0.996872i	$0.474818\pi$
$594$	0	0
$595$	−5.33239e98	−1.70439
$596$	7.86094e98	2.36719
$597$	0	0
$598$	1.24617e98	0.333186
$599$	1.67839e98	0.422904	0.211452	−	0.977388i	$-0.432181\pi$
$599$	1.67839e98	0.422904	0.211452	+	0.977388i	$0.432181\pi$
$600$	0	0
$601$	5.66573e98	1.26827	0.634135	−	0.773222i	$-0.281356\pi$
$601$	5.66573e98	1.26827	0.634135	+	0.773222i	$0.281356\pi$
$602$	3.73533e98	0.788231
$603$	0	0
$604$	2.88965e98	0.542044
$605$	−1.92924e99	−3.41248
$606$	0	0
$607$	−2.75702e97	−0.0433752	−0.0216876	−	0.999765i	$-0.506904\pi$
$607$	−2.75702e97	−0.0433752	−0.0216876	+	0.999765i	$0.506904\pi$
$608$	−3.84487e98	−0.570564
$609$	0	0
$610$	2.85976e98	0.377677
$611$	−5.02726e98	−0.626424
$612$	0	0
$613$	5.64289e98	0.626116	0.313058	−	0.949734i	$-0.398647\pi$
$613$	5.64289e98	0.626116	0.313058	+	0.949734i	$0.398647\pi$
$614$	2.70674e99	2.83446
$615$	0	0
$616$	2.83491e99	2.64499
$617$	−9.19226e98	−0.809653	−0.404826	−	0.914394i	$-0.632668\pi$
$617$	−9.19226e98	−0.809653	−0.404826	+	0.914394i	$0.632668\pi$
$618$	0	0
$619$	−1.49758e99	−1.17590	−0.587951	−	0.808896i	$-0.700065\pi$
$619$	−1.49758e99	−1.17590	−0.587951	+	0.808896i	$0.700065\pi$
$620$	5.87394e98	0.435536
$621$	0	0
$622$	−2.11597e99	−1.39943
$623$	−2.77411e99	−1.73300
$624$	0	0
$625$	−2.20856e99	−1.23131
$626$	−2.56603e99	−1.35168
$627$	0	0
$628$	−2.58454e99	−1.21567
$629$	5.14417e99	2.28674
$630$	0	0
$631$	−7.21240e98	−0.286443	−0.143221	−	0.989691i	$-0.545746\pi$
$631$	−7.21240e98	−0.286443	−0.143221	+	0.989691i	$0.545746\pi$
$632$	−9.55264e98	−0.358647
$633$	0	0
$634$	5.10374e99	1.71285
$635$	4.07890e99	1.29442
$636$	0	0
$637$	2.55198e98	0.0724315
$638$	−5.90878e99	−1.58622
$639$	0	0
$640$	−8.78141e99	−2.10948
$641$	1.12772e98	0.0256295	0.0128147	−	0.999918i	$-0.495921\pi$
$641$	1.12772e98	0.0256295	0.0128147	+	0.999918i	$0.495921\pi$
$642$	0	0
$643$	−9.14079e99	−1.85992	−0.929960	−	0.367660i	$-0.880159\pi$
$643$	−9.14079e99	−1.85992	−0.929960	+	0.367660i	$0.880159\pi$
$644$	−1.83800e99	−0.353914
$645$	0	0
$646$	1.16931e100	2.01685
$647$	−1.13923e100	−1.85998	−0.929990	−	0.367584i	$-0.880185\pi$
$647$	−1.13923e100	−1.85998	−0.929990	+	0.367584i	$0.880185\pi$
$648$	0	0
$649$	−2.54740e100	−3.72744
$650$	−4.53263e99	−0.627951
$651$	0	0
$652$	2.62888e100	3.26574
$653$	−8.91827e99	−1.04921	−0.524606	−	0.851345i	$-0.675787\pi$
$653$	−8.91827e99	−1.04921	−0.524606	+	0.851345i	$0.675787\pi$
$654$	0	0
$655$	−4.32431e99	−0.456405
$656$	3.45458e99	0.345389
$657$	0	0
$658$	1.15920e100	1.04025
$659$	1.20200e100	1.02205	0.511024	−	0.859566i	$-0.329266\pi$
$659$	1.20200e100	1.02205	0.511024	+	0.859566i	$0.329266\pi$
$660$	0	0
$661$	5.35859e99	0.409165	0.204583	−	0.978849i	$-0.434416\pi$
$661$	5.35859e99	0.409165	0.204583	+	0.978849i	$0.434416\pi$
$662$	1.23741e100	0.895480
$663$	0	0
$664$	1.32934e100	0.864312
$665$	1.68086e100	1.03601
$666$	0	0
$667$	1.67276e99	0.0926756
$668$	−2.80561e100	−1.47388
$669$	0	0
$670$	2.39364e99	0.113085
$671$	−8.58274e99	−0.384571
$672$	0	0
$673$	2.42021e100	0.975703	0.487852	−	0.872927i	$-0.337781\pi$
$673$	2.42021e100	0.975703	0.487852	+	0.872927i	$0.337781\pi$
$674$	−5.02412e100	−1.92147
$675$	0	0
$676$	3.94811e99	0.135919
$677$	−2.92966e99	−0.0957016	−0.0478508	−	0.998854i	$-0.515237\pi$
$677$	−2.92966e99	−0.0957016	−0.0478508	+	0.998854i	$0.515237\pi$
$678$	0	0
$679$	−5.60144e99	−0.164787
$680$	7.62018e100	2.12764
$681$	0	0
$682$	−2.75602e100	−0.693326
$683$	1.39931e100	0.334178	0.167089	−	0.985942i	$-0.446563\pi$
$683$	1.39931e100	0.334178	0.167089	+	0.985942i	$0.446563\pi$
$684$	0	0
$685$	−9.24533e100	−1.99025
$686$	7.84096e100	1.60274
$687$	0	0
$688$	−9.32683e99	−0.171927
$689$	−6.34186e100	−1.11028
$690$	0	0
$691$	1.43018e100	0.225902	0.112951	−	0.993601i	$-0.463970\pi$
$691$	1.43018e100	0.225902	0.112951	+	0.993601i	$0.463970\pi$
$692$	8.06540e100	1.21021
$693$	0	0
$694$	−1.82257e101	−2.46844
$695$	−3.77747e100	−0.486117
$696$	0	0
$697$	1.11612e101	1.29702
$698$	−8.49528e100	−0.938231
$699$	0	0
$700$	6.68525e100	0.667017
$701$	−1.19790e101	−1.13614	−0.568070	−	0.822980i	$-0.692310\pi$
$701$	−1.19790e101	−1.13614	−0.568070	+	0.822980i	$0.692310\pi$
$702$	0	0
$703$	−1.62153e101	−1.38999
$704$	3.60570e101	2.93873
$705$	0	0
$706$	3.14185e101	2.31536
$707$	1.07319e101	0.752123
$708$	0	0
$709$	−2.54319e101	−1.61227	−0.806135	−	0.591732i	$-0.798445\pi$
$709$	−2.54319e101	−1.61227	−0.806135	+	0.591732i	$0.798445\pi$
$710$	−4.66165e101	−2.81105
$711$	0	0
$712$	3.96431e101	2.16336
$713$	7.80221e99	0.0405079
$714$	0	0
$715$	5.10470e101	2.39942
$716$	4.61776e101	2.06547
$717$	0	0
$718$	1.29607e101	0.525062
$719$	4.25555e101	1.64089	0.820446	−	0.571724i	$-0.193725\pi$
$719$	4.25555e101	1.64089	0.820446	+	0.571724i	$0.193725\pi$
$720$	0	0
$721$	−7.28950e100	−0.254681
$722$	1.32264e101	0.439919
$723$	0	0
$724$	−1.49908e101	−0.451966
$725$	−6.08420e100	−0.174664
$726$	0	0
$727$	1.96540e101	0.511658	0.255829	−	0.966722i	$-0.417652\pi$
$727$	1.96540e101	0.511658	0.255829	+	0.966722i	$0.417652\pi$
$728$	−5.58883e101	−1.38566
$729$	0	0
$730$	−1.12837e102	−2.53799
$731$	−3.01336e101	−0.645630
$732$	0	0
$733$	4.65487e101	0.905141	0.452571	−	0.891729i	$-0.350507\pi$
$733$	4.65487e101	0.905141	0.452571	+	0.891729i	$0.350507\pi$
$734$	1.29201e102	2.39363
$735$	0	0
$736$	−7.62218e100	−0.128208
$737$	−7.18380e100	−0.115149
$738$	0	0
$739$	6.55112e101	0.953757	0.476879	−	0.878969i	$-0.341768\pi$
$739$	6.55112e101	0.953757	0.476879	+	0.878969i	$0.341768\pi$
$740$	−2.42011e102	−3.35823
$741$	0	0
$742$	1.46232e102	1.84376
$743$	2.79549e101	0.336013	0.168006	−	0.985786i	$-0.446267\pi$
$743$	2.79549e101	0.336013	0.168006	+	0.985786i	$0.446267\pi$
$744$	0	0
$745$	−1.42514e102	−1.55708
$746$	5.53300e101	0.576411
$747$	0	0
$748$	−5.23761e102	−4.96166
$749$	−1.13684e102	−1.02706
$750$	0	0
$751$	1.51149e102	1.24219	0.621093	−	0.783737i	$-0.286689\pi$
$751$	1.51149e102	1.24219	0.621093	+	0.783737i	$0.286689\pi$
$752$	−2.89442e101	−0.226897
$753$	0	0
$754$	1.16487e102	0.830991
$755$	−5.23878e101	−0.356544
$756$	0	0
$757$	−1.76935e102	−1.09625	−0.548126	−	0.836396i	$-0.684659\pi$
$757$	−1.76935e102	−1.09625	−0.548126	+	0.836396i	$0.684659\pi$
$758$	−5.39610e101	−0.319024
$759$	0	0
$760$	−2.40202e102	−1.29328
$761$	−1.85265e102	−0.952004	−0.476002	−	0.879444i	$-0.657914\pi$
$761$	−1.85265e102	−0.952004	−0.476002	+	0.879444i	$0.657914\pi$
$762$	0	0
$763$	3.10944e102	1.45566
$764$	9.24173e101	0.412990
$765$	0	0
$766$	−1.31625e102	−0.536064
$767$	5.02202e102	1.95273
$768$	0	0
$769$	3.11758e102	1.10518	0.552589	−	0.833454i	$-0.313640\pi$
$769$	3.11758e102	1.10518	0.552589	+	0.833454i	$0.313640\pi$
$770$	−1.17705e103	−3.98451
$771$	0	0
$772$	−1.51709e102	−0.468379
$773$	8.15788e101	0.240550	0.120275	−	0.992741i	$-0.461622\pi$
$773$	8.15788e101	0.240550	0.120275	+	0.992741i	$0.461622\pi$
$774$	0	0
$775$	−2.83784e101	−0.0763446
$776$	8.00466e101	0.205708
$777$	0	0
$778$	−3.39472e102	−0.796212
$779$	−3.51822e102	−0.788394
$780$	0	0
$781$	1.39906e103	2.86236
$782$	2.31807e102	0.453196
$783$	0	0
$784$	1.46929e101	0.0262354
$785$	4.68562e102	0.799639
$786$	0	0
$787$	−7.44955e102	−1.16152	−0.580761	−	0.814074i	$-0.697245\pi$
$787$	−7.44955e102	−1.16152	−0.580761	+	0.814074i	$0.697245\pi$
$788$	1.16332e103	1.73387
$789$	0	0
$790$	3.96625e102	0.540279
$791$	1.10050e103	1.43326
$792$	0	0
$793$	1.69203e102	0.201469
$794$	−6.43180e102	−0.732326
$795$	0	0
$796$	−5.88829e102	−0.613162
$797$	5.34875e102	0.532699	0.266350	−	0.963876i	$-0.414182\pi$
$797$	5.34875e102	0.532699	0.266350	+	0.963876i	$0.414182\pi$
$798$	0	0
$799$	−9.35143e102	−0.852055
$800$	2.77236e102	0.241633
$801$	0	0
$802$	2.48229e103	1.97998
$803$	3.38647e103	2.58432
$804$	0	0
$805$	3.33220e102	0.232797
$806$	5.43331e102	0.363220
$807$	0	0
$808$	−1.53363e103	−0.938897
$809$	6.34520e102	0.371769	0.185884	−	0.982572i	$-0.440485\pi$
$809$	6.34520e102	0.371769	0.185884	+	0.982572i	$0.440485\pi$
$810$	0	0
$811$	−4.13813e102	−0.222108	−0.111054	−	0.993814i	$-0.535423\pi$
$811$	−4.13813e102	−0.222108	−0.111054	+	0.993814i	$0.535423\pi$
$812$	−1.71809e103	−0.882688
$813$	0	0
$814$	1.13551e104	5.34593
$815$	−4.76601e103	−2.14813
$816$	0	0
$817$	9.49864e102	0.392445
$818$	−9.19997e102	−0.363952
$819$	0	0
$820$	−5.25089e103	−1.90476
$821$	−6.59788e101	−0.0229204	−0.0114602	−	0.999934i	$-0.503648\pi$
$821$	−6.59788e101	−0.0229204	−0.0114602	+	0.999934i	$0.503648\pi$
$822$	0	0
$823$	−5.99799e103	−1.91122	−0.955612	−	0.294628i	$-0.904804\pi$
$823$	−5.99799e103	−1.91122	−0.955612	+	0.294628i	$0.904804\pi$
$824$	1.04170e103	0.317926
$825$	0	0
$826$	−1.15799e104	−3.24274
$827$	−4.58671e103	−1.23043	−0.615213	−	0.788361i	$-0.710930\pi$
$827$	−4.58671e103	−1.23043	−0.615213	+	0.788361i	$0.710930\pi$
$828$	0	0
$829$	−1.62819e103	−0.400885	−0.200442	−	0.979706i	$-0.564238\pi$
$829$	−1.62819e103	−0.400885	−0.200442	+	0.979706i	$0.564238\pi$
$830$	−5.51942e103	−1.30203
$831$	0	0
$832$	−7.10838e103	−1.53955
$833$	4.74706e102	0.0985206
$834$	0	0
$835$	5.08641e103	0.969486
$836$	1.65099e104	3.01593
$837$	0	0
$838$	1.32233e104	2.21911
$839$	1.51975e103	0.244469	0.122234	−	0.992501i	$-0.460994\pi$
$839$	1.51975e103	0.244469	0.122234	+	0.992501i	$0.460994\pi$
$840$	0	0
$841$	−5.20122e103	−0.768860
$842$	4.72179e103	0.669157
$843$	0	0
$844$	−4.43227e103	−0.577390
$845$	−7.15770e102	−0.0894047
$846$	0	0
$847$	2.63201e104	3.02292
$848$	−3.65130e103	−0.402156
$849$	0	0
$850$	−8.43134e103	−0.854132
$851$	−3.21458e103	−0.312338
$852$	0	0
$853$	2.32517e103	0.207857	0.103929	−	0.994585i	$-0.466859\pi$
$853$	2.32517e103	0.207857	0.103929	+	0.994585i	$0.466859\pi$
$854$	−3.90151e103	−0.334563
$855$	0	0
$856$	1.62459e104	1.28211
$857$	−8.54167e103	−0.646731	−0.323365	−	0.946274i	$-0.604814\pi$
$857$	−8.54167e103	−0.646731	−0.323365	+	0.946274i	$0.604814\pi$
$858$	0	0
$859$	−1.07545e104	−0.749608	−0.374804	−	0.927104i	$-0.622290\pi$
$859$	−1.07545e104	−0.749608	−0.374804	+	0.927104i	$0.622290\pi$
$860$	1.41766e104	0.948148
$861$	0	0
$862$	1.23594e103	0.0761183
$863$	3.34468e103	0.197684	0.0988420	−	0.995103i	$-0.468486\pi$
$863$	3.34468e103	0.197684	0.0988420	+	0.995103i	$0.468486\pi$
$864$	0	0
$865$	−1.46221e104	−0.796046
$866$	−5.72087e104	−2.98935
$867$	0	0
$868$	−8.01368e103	−0.385817
$869$	−1.19035e104	−0.550141
$870$	0	0
$871$	1.41624e103	0.0603242
$872$	−4.44350e104	−1.81715
$873$	0	0
$874$	−7.30696e103	−0.275474
$875$	2.12407e104	0.768923
$876$	0	0
$877$	−4.01731e104	−1.34106	−0.670532	−	0.741881i	$-0.733934\pi$
$877$	−4.01731e104	−1.34106	−0.670532	+	0.741881i	$0.733934\pi$
$878$	3.16602e104	1.01498
$879$	0	0
$880$	2.93901e104	0.869093
$881$	−1.67336e104	−0.475275	−0.237638	−	0.971354i	$-0.576373\pi$
$881$	−1.67336e104	−0.475275	−0.237638	+	0.971354i	$0.576373\pi$
$882$	0	0
$883$	5.97846e104	1.56669	0.783347	−	0.621585i	$-0.213511\pi$
$883$	5.97846e104	1.56669	0.783347	+	0.621585i	$0.213511\pi$
$884$	1.03256e105	2.59932
$885$	0	0
$886$	−5.27268e104	−1.22499
$887$	−5.67147e104	−1.26592	−0.632961	−	0.774184i	$-0.718161\pi$
$887$	−5.67147e104	−1.26592	−0.632961	+	0.774184i	$0.718161\pi$
$888$	0	0
$889$	−5.56475e104	−1.14666
$890$	−1.64598e105	−3.25896
$891$	0	0
$892$	8.16076e104	1.49203
$893$	2.94774e104	0.517919
$894$	0	0
$895$	−8.37174e104	−1.35862
$896$	1.19803e105	1.86867
$897$	0	0
$898$	6.08441e104	0.876817
$899$	7.29319e103	0.101030
$900$	0	0
$901$	−1.17968e105	−1.51020
$902$	2.46369e105	3.03217
$903$	0	0
$904$	−1.57265e105	−1.78918
$905$	2.71775e104	0.297293
$906$	0	0
$907$	−5.37464e104	−0.543615	−0.271807	−	0.962352i	$-0.587621\pi$
$907$	−5.37464e104	−0.543615	−0.271807	+	0.962352i	$0.587621\pi$
$908$	1.50881e105	1.46753
$909$	0	0
$910$	2.32048e105	2.08741
$911$	−2.02280e105	−1.75005	−0.875027	−	0.484074i	$-0.839157\pi$
$911$	−2.02280e105	−1.75005	−0.875027	+	0.484074i	$0.839157\pi$
$912$	0	0
$913$	1.65649e105	1.32580
$914$	−6.56110e104	−0.505111
$915$	0	0
$916$	5.29078e104	0.376904
$917$	5.89956e104	0.404304
$918$	0	0
$919$	−1.34127e105	−0.850775	−0.425387	−	0.905011i	$-0.639862\pi$
$919$	−1.34127e105	−0.850775	−0.425387	+	0.905011i	$0.639862\pi$
$920$	−4.76183e104	−0.290607
$921$	0	0
$922$	5.44861e105	3.07849
$923$	−2.75814e105	−1.49954
$924$	0	0
$925$	1.16922e105	0.588659
$926$	−1.95025e105	−0.944931
$927$	0	0
$928$	−7.12490e104	−0.319761
$929$	9.89216e104	0.427300	0.213650	−	0.976910i	$-0.431465\pi$
$929$	9.89216e104	0.427300	0.213650	+	0.976910i	$0.431465\pi$
$930$	0	0
$931$	−1.49636e104	−0.0598855
$932$	4.12956e105	1.59088
$933$	0	0
$934$	1.17921e105	0.420995
$935$	9.49549e105	3.26366
$936$	0	0
$937$	3.45321e105	1.10019	0.550095	−	0.835102i	$-0.314592\pi$
$937$	3.45321e105	1.10019	0.550095	+	0.835102i	$0.314592\pi$
$938$	−3.26559e104	−0.100175
$939$	0	0
$940$	4.39945e105	1.25130
$941$	−5.44005e104	−0.148995	−0.0744974	−	0.997221i	$-0.523735\pi$
$941$	−5.44005e104	−0.148995	−0.0744974	+	0.997221i	$0.523735\pi$
$942$	0	0
$943$	−6.97463e104	−0.177156
$944$	2.89140e105	0.707299
$945$	0	0
$946$	−6.65158e105	−1.50935
$947$	−5.89362e105	−1.28812	−0.644062	−	0.764973i	$-0.722752\pi$
$947$	−5.89362e105	−1.28812	−0.644062	+	0.764973i	$0.722752\pi$
$948$	0	0
$949$	−6.67619e105	−1.35387
$950$	2.65771e105	0.519182
$951$	0	0
$952$	−1.03960e106	−1.88476
$953$	−3.31497e105	−0.579004	−0.289502	−	0.957177i	$-0.593490\pi$
$953$	−3.31497e105	−0.579004	−0.289502	+	0.957177i	$0.593490\pi$
$954$	0	0
$955$	−1.67547e105	−0.271655
$956$	−1.34116e106	−2.09520
$957$	0	0
$958$	−1.05706e106	−1.53329
$959$	1.26132e106	1.76305
$960$	0	0
$961$	−7.36319e105	−0.955841
$962$	−2.23857e106	−2.80063
$963$	0	0
$964$	−5.47054e104	−0.0635763
$965$	2.75040e105	0.308089
$966$	0	0
$967$	4.28185e105	0.445648	0.222824	−	0.974859i	$-0.428472\pi$
$967$	4.28185e105	0.445648	0.222824	+	0.974859i	$0.428472\pi$
$968$	−3.76125e106	−3.77361
$969$	0	0
$970$	−3.32353e105	−0.309887
$971$	−3.34549e105	−0.300730	−0.150365	−	0.988631i	$-0.548045\pi$
$971$	−3.34549e105	−0.300730	−0.150365	+	0.988631i	$0.548045\pi$
$972$	0	0
$973$	5.15351e105	0.430623
$974$	2.21862e106	1.78747
$975$	0	0
$976$	9.74176e104	0.0729741
$977$	−3.83131e105	−0.276752	−0.138376	−	0.990380i	$-0.544188\pi$
$977$	−3.83131e105	−0.276752	−0.138376	+	0.990380i	$0.544188\pi$
$978$	0	0
$979$	4.93992e106	3.31844
$980$	−2.23329e105	−0.144684
$981$	0	0
$982$	−2.98753e105	−0.180034
$983$	8.98586e105	0.522288	0.261144	−	0.965300i	$-0.415900\pi$
$983$	8.98586e105	0.522288	0.261144	+	0.965300i	$0.415900\pi$
$984$	0	0
$985$	−2.10903e106	−1.14050
$986$	2.16684e106	1.13030
$987$	0	0
$988$	−3.25481e106	−1.57999
$989$	1.88304e105	0.0881843
$990$	0	0
$991$	−2.72131e106	−1.18621	−0.593107	−	0.805124i	$-0.702099\pi$
$991$	−2.72131e106	−1.18621	−0.593107	+	0.805124i	$0.702099\pi$
$992$	−3.32326e105	−0.139766
$993$	0	0
$994$	6.35978e106	2.49015
$995$	1.06751e106	0.403324
$996$	0	0
$997$	4.43498e106	1.56032	0.780160	−	0.625581i	$-0.215138\pi$
$997$	4.43498e106	1.56032	0.780160	+	0.625581i	$0.215138\pi$
$998$	5.42089e106	1.84050
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.72.a.c.1.1		6
3.2	odd	2		3.72.a.b.1.6	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.72.a.b.1.6	✓	6	3.2	odd	2
9.72.a.c.1.1		6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 72 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q-8.09473e10 q^{2} +4.19128e21 q^{4} -7.59856e24 q^{5} +1.03665e30 q^{7} -1.48142e32 q^{8} +O(q^{10})\)	\(q-8.09473e10 q^{2} +4.19128e21 q^{4} -7.59856e24 q^{5} +1.03665e30 q^{7} -1.48142e32 q^{8} +6.15083e35 q^{10} -1.84599e37 q^{11} +3.63924e39 q^{13} -8.39143e40 q^{14} +2.09527e42 q^{16} +6.76951e43 q^{17} -2.13387e45 q^{19} -3.18477e46 q^{20} +1.49428e48 q^{22} -4.23025e47 q^{23} +1.53864e49 q^{25} -2.94586e50 q^{26} +4.34490e51 q^{28} -3.95427e51 q^{29} -1.84438e52 q^{31} +1.80183e53 q^{32} -5.47974e54 q^{34} -7.87707e54 q^{35} +7.59903e55 q^{37} +1.72731e56 q^{38} +1.12566e57 q^{40} +1.64875e57 q^{41} -4.45136e57 q^{43} -7.73706e58 q^{44} +3.42428e58 q^{46} -1.38140e59 q^{47} +7.01241e58 q^{49} -1.24549e60 q^{50} +1.52531e61 q^{52} -1.74264e61 q^{53} +1.40269e62 q^{55} -1.53571e62 q^{56} +3.20087e62 q^{58} +1.37996e63 q^{59} +4.64940e62 q^{61} +1.49298e63 q^{62} -1.95326e64 q^{64} -2.76529e64 q^{65} +3.89158e63 q^{67} +2.83729e65 q^{68} +6.37627e65 q^{70} -7.57891e65 q^{71} -1.83450e66 q^{73} -6.15121e66 q^{74} -8.94366e66 q^{76} -1.91365e67 q^{77} +6.44832e66 q^{79} -1.59211e67 q^{80} -1.33462e68 q^{82} -8.97347e67 q^{83} -5.14385e68 q^{85} +3.60326e68 q^{86} +2.73468e69 q^{88} -2.67603e69 q^{89} +3.77263e69 q^{91} -1.77302e69 q^{92} +1.11821e70 q^{94} +1.62143e70 q^{95} -5.40339e69 q^{97} -5.67635e69 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 72903656826 q^{2} + 10\!\cdots\!32 q^{4}+ \cdots + 36\!\cdots\!32 q^{8}+O(q^{10}) \) 6 * q + 72903656826 * q^2 + 10314006409421274045732 * q^4 - 10108593794701196744004900 * q^5 + 599480901407450839419869685888 * q^7 + 366478583494279643287721499310632 * q^8	\( 6 q + 72903656826 q^{2} + 10\!\cdots\!32 q^{4}+ \cdots - 26\!\cdots\!26 q^{98}+O(q^{100}) \) 6 * q + 72903656826 * q^2 + 10314006409421274045732 * q^4 - 10108593794701196744004900 * q^5 + 599480901407450839419869685888 * q^7 + 366478583494279643287721499310632 * q^8 + 542868868744970666737312582578468900 * q^10 - 22151081175113604333940540682999237064 * q^11 - 3733792306574713187109013147800580842876 * q^13 + 32830507140759982684754962229979568501632 * q^14 + 21946377025014017232533669358468876656094480 * q^16 - 29728537162009030546400351590681521887294796 * q^17 - 3400191903952978211629854680984130031529265672 * q^19 - 67862977310829773665490051450873586512770090200 * q^20 + 944165659732727247119333482328915476491852443592 * q^22 + 241048097798755219551674687627695903843789894224 * q^23 + 147233544111014179651192740252202252138516733666250 * q^25 - 365811593583549796821577322473046008640162770663812 * q^26 + 7184703440899560087451639062714257068053559172254464 * q^28 - 14043556001266662709861160370005828332436911172303796 * q^29 - 270783306371944339515858500277888580308160694590498224 * q^31 + 1125690872219692784327995632757361168637025492519761312 * q^32 - 14624984721002826287006157938202770657423642866907848116 * q^34 - 1330179995756585937201666471865883862092414077711430400 * q^35 - 35792724481179188252370374519670456030630938465810079852 * q^37 + 40096713421645845706764919843501793548783513747008434184 * q^38 - 2479587661237177399988484749809178898031295693356625910000 * q^40 - 477389693785559225342921822791522325133674715121487806716 * q^41 + 11648760938240913572137172567293471863701640091329944903880 * q^43 - 74878798041661318901325225719624262581993699901301979154096 * q^44 - 22722764972174503220374661680362423965849207035012290901584 * q^46 + 74847986304767650251381147705131168308416847087017595772160 * q^47 - 688653477285391597239303104103354245619646953145790225785290 * q^49 + 15161902343877042722978992840348999467045739232226501266733750 * q^50 - 9233127809375467425363213342738333025041297615633059381760744 * q^52 - 54557017276559944552388010917280252208764745473331764291919716 * q^53 - 23377768702274474935917895870707480727711321830514284596005200 * q^55 - 52410231138004746064340786054323553480340549752421553548034560 * q^56 - 6869577034896111059681057797577176576414351550513678648728908 * q^58 + 2982562673835141937005021578485268051001526328776278691712555448 * q^59 + 2024766122758654206628711672366353464571765836352692052196097220 * q^61 - 6190527473014961587199547234678103673640494648116320147386047056 * q^62 + 45446447421689003372958411079333884263847638574085838786019075648 * q^64 - 48520756571856116218224136414427408842784606511438543051271531800 * q^65 - 35831986821500503360634896265657012310045332669260449034581275784 * q^67 - 185089183911227350024079142251468478888729548294423879590659066312 * q^68 - 344172356460367114079337658836072099942116692861986486268441785600 * q^70 + 51113783482860556737395980857143689650967786833886125865998410928 * q^71 - 1956710326081635365311373308078888669483174388894330237696366066724 * q^73 - 5709348546681615596063021572004447539391345291333750996512485900948 * q^74 - 23809271474859754704092582776426668087720715729896871772596110280752 * q^76 - 18917631699413080007630569020425573902563798951131161813579745527296 * q^77 + 48402596803386404034053884911414009193830041621338105095759924707760 * q^79 - 263392522337449869178773130835490329512120616670537417787135845410400 * q^80 - 304020075917296666161317294537198008494062493274925376834937204559364 * q^82 - 231863714798237849378047661016738227772765340915812707253802255256568 * q^83 - 153432496682031145548917546056875902159222382871180623315806512428600 * q^85 - 232789528332961926178362349658049178503816504422806394312074365597384 * q^86 + 5297065653948252699139641997691020789333729718805571695420136408677408 * q^88 - 4386397294164484419236854507748631162668647776406659364039350285963708 * q^89 + 10645224502890544811266185738918008251735428747945615198269035910167296 * q^91 - 3494882087686348167672392093650816456059296420998691954341908970318368 * q^92 + 212140324104529926314570388896027999493814139075827826098897565498112 * q^94 + 32230267438252135206013682642661075145567906057502744951334901038078000 * q^95 + 97296789347912261411847519869140120543815674831725660650989227379865996 * q^97 - 262411331100552434262334793443846407592764783361237538614096838440889526 * q^98

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