LMFDB - Embedded newform 243.2.c.f.163.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,2,Mod(82,243)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(243, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("243.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.c (of order $3$, degree $2$, not minimal)

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:	no
Analytic conductor:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.3
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	243.163
Dual form			243.2.c.f.82.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.26604 - 2.19285i) q^{2} +(-2.20574 - 3.82045i) q^{4} +(0.233956 + 0.405223i) q^{5} +(1.61334 - 2.79439i) q^{7} -6.10607 q^{8} +1.18479 q^{10} +(-1.55303 + 2.68993i) q^{11} +(1.09240 + 1.89209i) q^{13} +(-4.08512 - 7.07564i) q^{14} +(-3.31908 + 5.74881i) q^{16} -3.00000 q^{17} +0.0418891 q^{19} +(1.03209 - 1.78763i) q^{20} +(3.93242 + 6.81115i) q^{22} +(3.05303 + 5.28801i) q^{23} +(2.39053 - 4.14052i) q^{25} +5.53209 q^{26} -14.2344 q^{28} +(3.28699 - 5.69323i) q^{29} +(3.11334 + 5.39246i) q^{31} +(2.29813 + 3.98048i) q^{32} +(-3.79813 + 6.57856i) q^{34} +1.50980 q^{35} +3.59627 q^{37} +(0.0530334 - 0.0918566i) q^{38} +(-1.42855 - 2.47432i) q^{40} +(3.85117 + 6.67042i) q^{41} +(0.294263 - 0.509678i) q^{43} +13.7023 q^{44} +15.4611 q^{46} +(-4.83022 + 8.36619i) q^{47} +(-1.70574 - 2.95442i) q^{49} +(-6.05303 - 10.4842i) q^{50} +(4.81908 - 8.34689i) q^{52} -4.95811 q^{53} -1.45336 q^{55} +(-9.85117 + 17.0627i) q^{56} +(-8.32295 - 14.4158i) q^{58} +(-4.26604 - 7.38901i) q^{59} +(0.634285 - 1.09861i) q^{61} +15.7665 q^{62} -1.63816 q^{64} +(-0.511144 + 0.885328i) q^{65} +(-5.00387 - 8.66696i) q^{67} +(6.61721 + 11.4613i) q^{68} +(1.91147 - 3.31077i) q^{70} -11.8307 q^{71} -8.23442 q^{73} +(4.55303 - 7.88609i) q^{74} +(-0.0923963 - 0.160035i) q^{76} +(5.01114 + 8.67956i) q^{77} +(-5.52481 + 9.56926i) q^{79} -3.10607 q^{80} +19.5030 q^{82} +(-0.754900 + 1.30753i) q^{83} +(-0.701867 - 1.21567i) q^{85} +(-0.745100 - 1.29055i) q^{86} +(9.48293 - 16.4249i) q^{88} +15.8726 q^{89} +7.04963 q^{91} +(13.4684 - 23.3279i) q^{92} +(12.2306 + 21.1839i) q^{94} +(0.00980018 + 0.0169744i) q^{95} +(-9.32295 + 16.1478i) q^{97} -8.63816 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} + 6 q^{5} + 3 q^{7} - 12 q^{8} + 3 q^{11} + 3 q^{13} - 3 q^{14} - 3 q^{16} - 18 q^{17} - 6 q^{19} - 3 q^{20} + 6 q^{23} - 3 q^{25} + 24 q^{26} - 24 q^{28} + 12 q^{29} + 12 q^{31}+ \cdots - 18 q^{98}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 + 3 * q^7 - 12 * q^8 + 3 * q^11 + 3 * q^13 - 3 * q^14 - 3 * q^16 - 18 * q^17 - 6 * q^19 - 3 * q^20 + 6 * q^23 - 3 * q^25 + 24 * q^26 - 24 * q^28 + 12 * q^29 + 12 * q^31 - 9 * q^34 + 12 * q^35 - 6 * q^37 - 12 * q^38 - 9 * q^40 - 3 * q^41 + 12 * q^43 + 30 * q^44 + 18 * q^46 - 6 * q^47 - 24 * q^50 + 12 * q^52 - 36 * q^53 + 18 * q^55 - 33 * q^56 - 9 * q^58 - 21 * q^59 - 6 * q^61 + 24 * q^62 + 24 * q^64 + 3 * q^65 - 6 * q^67 + 9 * q^68 - 9 * q^70 + 18 * q^71 + 12 * q^73 + 15 * q^74 + 3 * q^76 + 24 * q^77 - 6 * q^79 + 6 * q^80 + 36 * q^82 - 6 * q^83 - 18 * q^85 - 3 * q^86 + 36 * q^88 - 12 * q^91 + 24 * q^92 + 36 * q^94 + 3 * q^95 - 15 * q^97 - 18 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.26604	−	2.19285i	0.895229	−	1.55058i	0.0617072	−	0.998094i	$-0.480346\pi$
$2$	1.26604	−	2.19285i	0.895229	−	1.55058i	0.833521	−	0.552487i	$-0.186321\pi$
$3$		0			0
$3$		0			0
$4$	−2.20574	−	3.82045i	−1.10287	−	1.91022i
$5$	0.233956	+	0.405223i	0.104628	+	0.181221i	0.913586	−	0.406645i	$-0.133301\pi$
$5$	0.233956	+	0.405223i	0.104628	+	0.181221i	−0.808958	+	0.587866i	$0.799968\pi$
$6$		0			0
$7$	1.61334	−	2.79439i	0.609786	−	1.05618i	−0.381490	−	0.924373i	$-0.624589\pi$
$7$	1.61334	−	2.79439i	0.609786	−	1.05618i	0.991275	−	0.131806i	$-0.0420778\pi$
$8$	−6.10607			−2.15882
$9$		0			0
$10$	1.18479			0.374664
$11$	−1.55303	+	2.68993i	−0.468257	+	0.811045i	−0.999342	−	0.0362735i	$-0.988451\pi$
$11$	−1.55303	+	2.68993i	−0.468257	+	0.811045i	0.531085	+	0.847319i	$0.321785\pi$
$12$		0			0
$13$	1.09240	+	1.89209i	0.302976	+	0.524770i	0.976809	−	0.214114i	$-0.0686864\pi$
$13$	1.09240	+	1.89209i	0.302976	+	0.524770i	−0.673832	+	0.738884i	$0.735353\pi$
$14$	−4.08512	−	7.07564i	−1.09179	−	1.89104i
$15$		0			0
$16$	−3.31908	+	5.74881i	−0.829769	+	1.43720i
$17$	−3.00000			−0.727607			−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000			−0.727607			−0.363803	+	0.931476i	$0.618522\pi$
$18$		0			0
$19$	0.0418891			0.00961001			0.00480501	−	0.999988i	$-0.498471\pi$
$19$	0.0418891			0.00961001			0.00480501	+	0.999988i	$0.498471\pi$
$20$	1.03209	−	1.78763i	0.230782	−	0.399726i
$21$		0			0
$22$	3.93242	+	6.81115i	0.838394	+	1.45214i
$23$	3.05303	+	5.28801i	0.636601	+	1.10263i	0.986173	+	0.165717i	$0.0529937\pi$
$23$	3.05303	+	5.28801i	0.636601	+	1.10263i	−0.349572	+	0.936910i	$0.613673\pi$
$24$		0			0
$25$	2.39053	−	4.14052i	0.478106	−	0.828104i
$26$	5.53209			1.08493
$27$		0			0
$28$	−14.2344			−2.69005
$29$	3.28699	−	5.69323i	0.610379	−	1.05721i	−0.380798	−	0.924658i	$-0.624351\pi$
$29$	3.28699	−	5.69323i	0.610379	−	1.05721i	0.991177	−	0.132548i	$-0.0423160\pi$
$30$		0			0
$31$	3.11334	+	5.39246i	0.559173	+	0.968515i	0.997566	+	0.0697319i	$0.0222144\pi$
$31$	3.11334	+	5.39246i	0.559173	+	0.968515i	−0.438393	+	0.898783i	$0.644452\pi$
$32$	2.29813	+	3.98048i	0.406256	+	0.703657i
$33$		0			0
$34$	−3.79813	+	6.57856i	−0.651374	+	1.12821i
$35$	1.50980			0.255203
$36$		0			0
$37$	3.59627			0.591223			0.295611	−	0.955308i	$-0.404477\pi$
$37$	3.59627			0.591223			0.295611	+	0.955308i	$0.404477\pi$
$38$	0.0530334	−	0.0918566i	0.00860316	−	0.0149011i
$39$		0			0
$40$	−1.42855	−	2.47432i	−0.225873	−	0.391224i
$41$	3.85117	+	6.67042i	0.601451	+	1.04174i	0.992602	+	0.121417i	$0.0387439\pi$
$41$	3.85117	+	6.67042i	0.601451	+	1.04174i	−0.391150	+	0.920327i	$0.627923\pi$
$42$		0			0
$43$	0.294263	−	0.509678i	0.0448747	−	0.0777252i	−0.842716	−	0.538359i	$-0.819044\pi$
$43$	0.294263	−	0.509678i	0.0448747	−	0.0777252i	0.887590	+	0.460634i	$0.152378\pi$
$44$	13.7023			2.06570
$45$		0			0
$46$	15.4611			2.27962
$47$	−4.83022	+	8.36619i	−0.704560	+	1.22033i	0.262290	+	0.964989i	$0.415522\pi$
$47$	−4.83022	+	8.36619i	−0.704560	+	1.22033i	−0.966850	+	0.255345i	$0.917811\pi$
$48$		0			0
$49$	−1.70574	−	2.95442i	−0.243677	−	0.422060i
$50$	−6.05303	−	10.4842i	−0.856028	−	1.48268i
$51$		0			0
$52$	4.81908	−	8.34689i	0.668286	−	1.15751i
$53$	−4.95811			−0.681049			−0.340524	−	0.940236i	$-0.610605\pi$
$53$	−4.95811			−0.681049			−0.340524	+	0.940236i	$0.610605\pi$
$54$		0			0
$55$	−1.45336			−0.195971
$56$	−9.85117	+	17.0627i	−1.31642	+	2.28010i
$57$		0			0
$58$	−8.32295	−	14.4158i	−1.09286	−	1.89288i
$59$	−4.26604	−	7.38901i	−0.555392	−	0.961967i	−0.997873	−	0.0651889i	$-0.979235\pi$
$59$	−4.26604	−	7.38901i	−0.555392	−	0.961967i	0.442481	−	0.896778i	$-0.354098\pi$
$60$		0			0
$61$	0.634285	−	1.09861i	0.0812119	−	0.140663i	−0.822559	−	0.568680i	$-0.807454\pi$
$61$	0.634285	−	1.09861i	0.0812119	−	0.140663i	0.903771	+	0.428017i	$0.140788\pi$
$62$	15.7665			2.00235
$63$		0			0
$64$	−1.63816			−0.204769
$65$	−0.511144	+	0.885328i	−0.0633997	+	0.109811i
$66$		0			0
$67$	−5.00387	−	8.66696i	−0.611320	−	1.05884i	−0.991018	−	0.133727i	$-0.957305\pi$
$67$	−5.00387	−	8.66696i	−0.611320	−	1.05884i	0.379698	−	0.925110i	$-0.376028\pi$
$68$	6.61721	+	11.4613i	0.802455	+	1.38989i
$69$		0			0
$70$	1.91147	−	3.31077i	0.228465	−	0.395713i
$71$	−11.8307			−1.40404			−0.702022	−	0.712155i	$-0.747719\pi$
$71$	−11.8307			−1.40404			−0.702022	+	0.712155i	$0.747719\pi$
$72$		0			0
$73$	−8.23442			−0.963766			−0.481883	−	0.876236i	$-0.660047\pi$
$73$	−8.23442			−0.963766			−0.481883	+	0.876236i	$0.660047\pi$
$74$	4.55303	−	7.88609i	0.529279	−	0.916739i
$75$		0			0
$76$	−0.0923963	−	0.160035i	−0.0105986	−	0.0183573i
$77$	5.01114	+	8.67956i	0.571073	+	0.989127i
$78$		0			0
$79$	−5.52481	+	9.56926i	−0.621590	+	1.07663i	0.367599	+	0.929984i	$0.380180\pi$
$79$	−5.52481	+	9.56926i	−0.621590	+	1.07663i	−0.989190	+	0.146642i	$0.953154\pi$
$80$	−3.10607			−0.347269
$81$		0			0
$82$	19.5030			2.15375
$83$	−0.754900	+	1.30753i	−0.0828610	+	0.143520i	−0.904478	−	0.426521i	$-0.859739\pi$
$83$	−0.754900	+	1.30753i	−0.0828610	+	0.143520i	0.821617	+	0.570040i	$0.193072\pi$
$84$		0			0
$85$	−0.701867	−	1.21567i	−0.0761281	−	0.131858i
$86$	−0.745100	−	1.29055i	−0.0803462	−	0.139164i
$87$		0			0
$88$	9.48293	−	16.4249i	1.01088	−	1.75090i
$89$	15.8726			1.68249			0.841245	−	0.540654i	$-0.181823\pi$
$89$	15.8726			1.68249			0.841245	+	0.540654i	$0.181823\pi$
$90$		0			0
$91$	7.04963			0.739002
$92$	13.4684	−	23.3279i	1.40418	−	2.43210i
$93$		0			0
$94$	12.2306	+	21.1839i	1.26149	+	2.18496i
$95$	0.00980018	+	0.0169744i	0.00100548	+	0.00174154i
$96$		0			0
$97$	−9.32295	+	16.1478i	−0.946602	+	1.63956i	−0.194090	+	0.980984i	$0.562176\pi$
$97$	−9.32295	+	16.1478i	−0.946602	+	1.63956i	−0.752512	+	0.658579i	$0.771158\pi$
$98$	−8.63816			−0.872585
$99$		0			0
$100$	−21.0915			−2.10915
$101$	4.54323	−	7.86911i	0.452069	−	0.783006i	−0.546446	−	0.837494i	$-0.684020\pi$
$101$	4.54323	−	7.86911i	0.452069	−	0.783006i	0.998514	+	0.0544887i	$0.0173529\pi$
$102$		0			0
$103$	−0.130415	−	0.225885i	−0.0128502	−	0.0222571i	0.859529	−	0.511087i	$-0.170757\pi$
$103$	−0.130415	−	0.225885i	−0.0128502	−	0.0222571i	−0.872379	+	0.488830i	$0.837424\pi$
$104$	−6.67024	−	11.5532i	−0.654071	−	1.13288i
$105$		0			0
$106$	−6.27719	+	10.8724i	−0.609694	+	1.05602i
$107$	−4.04189			−0.390744			−0.195372	−	0.980729i	$-0.562591\pi$
$107$	−4.04189			−0.390744			−0.195372	+	0.980729i	$0.562591\pi$
$108$		0			0
$109$	−5.40373			−0.517584			−0.258792	−	0.965933i	$-0.583324\pi$
$109$	−5.40373			−0.517584			−0.258792	+	0.965933i	$0.583324\pi$
$110$	−1.84002	+	3.18701i	−0.175439	+	0.303870i
$111$		0			0
$112$	10.7096	+	18.5496i	1.01196	+	1.75277i
$113$	0.692066	+	1.19869i	0.0651041	+	0.112764i	0.896740	−	0.442557i	$-0.145929\pi$
$113$	0.692066	+	1.19869i	0.0651041	+	0.112764i	−0.831636	+	0.555321i	$0.812595\pi$
$114$		0			0
$115$	−1.42855	+	2.47432i	−0.133213	+	0.230731i
$116$	−29.0009			−2.69267
$117$		0			0
$118$	−21.6040			−1.98881
$119$	−4.84002	+	8.38316i	−0.443684	+	0.768483i
$120$		0			0
$121$	0.676174	+	1.17117i	0.0614704	+	0.106470i
$122$	−1.60607	−	2.78179i	−0.145406	−	0.251851i
$123$		0			0
$124$	13.7344	−	23.7887i	1.23339	−	2.13629i
$125$	4.57667			0.409349
$126$		0			0
$127$	−6.63816			−0.589041			−0.294521	−	0.955645i	$-0.595160\pi$
$127$	−6.63816			−0.589041			−0.294521	+	0.955645i	$0.595160\pi$
$128$	−6.67024	+	11.5532i	−0.589572	+	1.02117i
$129$		0			0
$130$	1.29426	+	2.24173i	0.113514	+	0.196613i
$131$	−6.32042	−	10.9473i	−0.552218	−	0.956469i	−0.998114	−	0.0613847i	$-0.980448\pi$
$131$	−6.32042	−	10.9473i	−0.552218	−	0.956469i	0.445896	−	0.895085i	$-0.352885\pi$
$132$		0			0
$133$	0.0675813	−	0.117054i	0.00586005	−	0.0101499i
$134$	−25.3405			−2.18908
$135$		0			0
$136$	18.3182			1.57077
$137$	5.30793	−	9.19361i	0.453487	−	0.785463i	−0.545112	−	0.838363i	$-0.683513\pi$
$137$	5.30793	−	9.19361i	0.453487	−	0.785463i	0.998600	+	0.0528998i	$0.0168464\pi$
$138$		0			0
$139$	3.73055	+	6.46151i	0.316421	+	0.548058i	0.979739	−	0.200281i	$-0.0641853\pi$
$139$	3.73055	+	6.46151i	0.316421	+	0.548058i	−0.663317	+	0.748338i	$0.730852\pi$
$140$	−3.33022	−	5.76811i	−0.281455	−	0.487495i
$141$		0			0
$142$	−14.9782	+	25.9430i	−1.25694	+	2.17709i
$143$	−6.78611			−0.567483
$144$		0			0
$145$	3.07604			0.255451
$146$	−10.4251	+	18.0569i	−0.862791	+	1.49440i
$147$		0			0
$148$	−7.93242	−	13.7394i	−0.652041	−	1.12937i
$149$	−2.12701	−	3.68409i	−0.174252	−	0.301813i	0.765650	−	0.643257i	$-0.222417\pi$
$149$	−2.12701	−	3.68409i	−0.174252	−	0.301813i	−0.939902	+	0.341444i	$0.889084\pi$
$150$		0			0
$151$	−0.0675813	+	0.117054i	−0.00549969	+	0.00952574i	−0.868762	−	0.495230i	$-0.835084\pi$
$151$	−0.0675813	+	0.117054i	−0.00549969	+	0.00952574i	0.863262	+	0.504755i	$0.168417\pi$
$152$	−0.255777			−0.0207463
$153$		0			0
$154$	25.3773			2.04496
$155$	−1.45677	+	2.52319i	−0.117010	+	0.202668i
$156$		0			0
$157$	−6.66297	−	11.5406i	−0.531763	−	0.921040i	−0.999313	−	0.0370736i	$-0.988196\pi$
$157$	−6.66297	−	11.5406i	−0.531763	−	0.921040i	0.467550	−	0.883967i	$-0.345137\pi$
$158$	13.9893	+	24.2302i	1.11293	+	1.92765i
$159$		0			0
$160$	−1.07532	+	1.86251i	−0.0850117	+	0.147245i
$161$	19.7023			1.55276
$162$		0			0
$163$	−9.76382			−0.764762			−0.382381	−	0.924005i	$-0.624896\pi$
$163$	−9.76382			−0.764762			−0.382381	+	0.924005i	$0.624896\pi$
$164$	16.9893	−	29.4264i	1.32664	−	2.29781i
$165$		0			0
$166$	1.91147	+	3.31077i	0.148359	+	0.256966i
$167$	−1.78699	−	3.09516i	−0.138281	−	0.239510i	0.788565	−	0.614952i	$-0.210824\pi$
$167$	−1.78699	−	3.09516i	−0.138281	−	0.239510i	−0.926846	+	0.375441i	$0.877491\pi$
$168$		0			0
$169$	4.11334	−	7.12452i	0.316411	−	0.548040i
$170$	−3.55438			−0.272608
$171$		0			0
$172$	−2.59627			−0.197963
$173$	9.38326	−	16.2523i	0.713396	−	1.23564i	−0.250179	−	0.968200i	$-0.580490\pi$
$173$	9.38326	−	16.2523i	0.713396	−	1.23564i	0.963575	−	0.267438i	$-0.0861771\pi$
$174$		0			0
$175$	−7.71348	−	13.3601i	−0.583084	−	1.00993i
$176$	−10.3093	−	17.8562i	−0.777091	−	1.34596i
$177$		0			0
$178$	20.0954	−	34.8062i	1.50621	−	2.60884i
$179$	5.08378			0.379979			0.189990	−	0.981786i	$-0.439155\pi$
$179$	5.08378			0.379979			0.189990	+	0.981786i	$0.439155\pi$
$180$		0			0
$181$	7.15064			0.531503			0.265752	−	0.964042i	$-0.414380\pi$
$181$	7.15064			0.531503			0.265752	+	0.964042i	$0.414380\pi$
$182$	8.92514	−	15.4588i	0.661576	−	1.14588i
$183$		0			0
$184$	−18.6420	−	32.2889i	−1.37431	−	2.38037i
$185$	0.841367	+	1.45729i	0.0618585	+	0.107142i
$186$		0			0
$187$	4.65910	−	8.06980i	0.340707	−	0.590122i
$188$	42.6168			3.10815
$189$		0			0
$190$	0.0496299			0.00360053
$191$	−5.25490	+	9.10175i	−0.380231	+	0.658580i	−0.991095	−	0.133156i	$-0.957489\pi$
$191$	−5.25490	+	9.10175i	−0.380231	+	0.658580i	0.610864	+	0.791736i	$0.290822\pi$
$192$		0			0
$193$	5.07145	+	8.78401i	0.365051	+	0.632287i	0.988784	−	0.149350i	$-0.0477182\pi$
$193$	5.07145	+	8.78401i	0.365051	+	0.632287i	−0.623733	+	0.781637i	$0.714385\pi$
$194$	23.6065	+	40.8877i	1.69485	+	2.93557i
$195$		0			0
$196$	−7.52481	+	13.0334i	−0.537487	+	0.930954i
$197$	−14.0838			−1.00343			−0.501714	−	0.865034i	$-0.667297\pi$
$197$	−14.0838			−1.00343			−0.501714	+	0.865034i	$0.667297\pi$
$198$		0			0
$199$	10.2763			0.728468			0.364234	−	0.931307i	$-0.381331\pi$
$199$	10.2763			0.728468			0.364234	+	0.931307i	$0.381331\pi$
$200$	−14.5967	+	25.2823i	−1.03214	+	1.78773i
$201$		0			0
$202$	−11.5039	−	19.9253i	−0.809409	−	1.40194i
$203$	−10.6061	−	18.3702i	−0.744400	−	1.28934i
$204$		0			0
$205$	−1.80200	+	3.12116i	−0.125857	+	0.217991i
$206$	−0.660444			−0.0460153
$207$		0			0
$208$	−14.5030			−1.00560
$209$	−0.0650551	+	0.112679i	−0.00449996	+	0.00779415i
$210$		0			0
$211$	3.57145	+	6.18594i	0.245869	+	0.425857i	0.962376	−	0.271723i	$-0.0875934\pi$
$211$	3.57145	+	6.18594i	0.245869	+	0.425857i	−0.716507	+	0.697580i	$0.754260\pi$
$212$	10.9363	+	18.9422i	0.751107	+	1.30096i
$213$		0			0
$214$	−5.11721	+	8.86327i	−0.349805	+	0.605881i
$215$	0.275378			0.0187806
$216$		0			0
$217$	20.0915			1.36390
$218$	−6.84137	+	11.8496i	−0.463356	+	0.802556i
$219$		0			0
$220$	3.20574	+	5.55250i	0.216131	+	0.374349i
$221$	−3.27719	−	5.67626i	−0.220448	−	0.381826i
$222$		0			0
$223$	5.16772	−	8.95075i	0.346056	−	0.599387i	−0.639489	−	0.768800i	$-0.720854\pi$
$223$	5.16772	−	8.95075i	0.346056	−	0.599387i	0.985545	+	0.169414i	$0.0541874\pi$
$224$	14.8307			0.990917
$225$		0			0
$226$	3.50475			0.233132
$227$	−6.51114	+	11.2776i	−0.432160	+	0.748523i	−0.997059	−	0.0766371i	$-0.975582\pi$
$227$	−6.51114	+	11.2776i	−0.432160	+	0.748523i	0.564899	+	0.825160i	$0.308915\pi$
$228$		0			0
$229$	14.0496	+	24.3347i	0.928426	+	1.60808i	0.785957	+	0.618281i	$0.212171\pi$
$229$	14.0496	+	24.3347i	0.928426	+	1.60808i	0.142469	+	0.989799i	$0.454496\pi$
$230$	3.61721	+	6.26519i	0.238512	+	0.413115i
$231$		0			0
$232$	−20.0706	+	34.7633i	−1.31770	+	2.28232i
$233$	13.9145			0.911567			0.455784	−	0.890091i	$-0.349359\pi$
$233$	13.9145			0.911567			0.455784	+	0.890091i	$0.349359\pi$
$234$		0			0
$235$	−4.52023			−0.294867
$236$	−18.8195	+	32.5964i	−1.22505	+	2.12185i
$237$		0			0
$238$	12.2554	+	21.2269i	0.794397	+	1.37594i
$239$	−7.50980	−	13.0074i	−0.485769	−	0.841376i	0.514098	−	0.857732i	$-0.328127\pi$
$239$	−7.50980	−	13.0074i	−0.485769	−	0.841376i	−0.999866	+	0.0163558i	$0.994794\pi$
$240$		0			0
$241$	6.48680	−	11.2355i	0.417851	−	0.723740i	−0.577872	−	0.816128i	$-0.696117\pi$
$241$	6.48680	−	11.2355i	0.417851	−	0.723740i	0.995723	+	0.0923879i	$0.0294500\pi$
$242$	3.42427			0.220120
$243$		0			0
$244$	−5.59627			−0.358264
$245$	0.798133	−	1.38241i	0.0509909	−	0.0883188i
$246$		0			0
$247$	0.0457595	+	0.0792577i	0.00291160	+	0.00504305i
$248$	−19.0103	−	32.9267i	−1.20715	−	2.09085i
$249$		0			0
$250$	5.79426	−	10.0360i	0.366461	−	0.634730i
$251$	−0.872578			−0.0550766			−0.0275383	−	0.999621i	$-0.508767\pi$
$251$	−0.872578			−0.0550766			−0.0275383	+	0.999621i	$0.508767\pi$
$252$		0			0
$253$	−18.9659			−1.19237
$254$	−8.40420	+	14.5565i	−0.527326	+	0.913356i
$255$		0			0
$256$	15.2515	+	26.4164i	0.953219	+	1.65102i
$257$	2.28833	+	3.96351i	0.142742	+	0.247237i	0.928528	−	0.371261i	$-0.121075\pi$
$257$	2.28833	+	3.96351i	0.142742	+	0.247237i	−0.785786	+	0.618498i	$0.787741\pi$
$258$		0			0
$259$	5.80200	−	10.0494i	0.360519	−	0.624437i
$260$	4.50980			0.279686
$261$		0			0
$262$	−32.0077			−1.97744
$263$	2.14883	−	3.72189i	0.132503	−	0.229501i	−0.792138	−	0.610342i	$-0.791032\pi$
$263$	2.14883	−	3.72189i	0.132503	−	0.229501i	0.924641	+	0.380841i	$0.124365\pi$
$264$		0			0
$265$	−1.15998	−	2.00914i	−0.0712569	−	0.123420i
$266$	−0.171122	−	0.296392i	−0.0104922	−	0.0181730i
$267$		0			0
$268$	−22.0744	+	38.2341i	−1.34841	+	2.33552i
$269$	−12.1257			−0.739315			−0.369657	−	0.929168i	$-0.620525\pi$
$269$	−12.1257			−0.739315			−0.369657	+	0.929168i	$0.620525\pi$
$270$		0			0
$271$	−0.319955			−0.0194359			−0.00971795	−	0.999953i	$-0.503093\pi$
$271$	−0.319955			−0.0194359			−0.00971795	+	0.999953i	$0.503093\pi$
$272$	9.95723	−	17.2464i	0.603746	−	1.04572i
$273$		0			0
$274$	−13.4402	−	23.2790i	−0.811950	−	1.40634i
$275$	7.42514	+	12.8607i	0.447753	+	0.775531i
$276$		0			0
$277$	13.4106	−	23.2278i	0.805765	−	1.39563i	−0.110009	−	0.993931i	$-0.535088\pi$
$277$	13.4106	−	23.2278i	0.805765	−	1.39563i	0.915774	−	0.401695i	$-0.131579\pi$
$278$	18.8922			1.13308
$279$		0			0
$280$	−9.21894			−0.550937
$281$	13.3405	−	23.1064i	0.795827	−	1.37841i	−0.126486	−	0.991968i	$-0.540370\pi$
$281$	13.3405	−	23.1064i	0.795827	−	1.37841i	0.922313	−	0.386444i	$-0.126297\pi$
$282$		0			0
$283$	4.64677	+	8.04845i	0.276222	+	0.478431i	0.970443	−	0.241332i	$-0.0775842\pi$
$283$	4.64677	+	8.04845i	0.276222	+	0.478431i	−0.694221	+	0.719762i	$0.744251\pi$
$284$	26.0954	+	45.1985i	1.54848	+	2.68204i
$285$		0			0
$286$	−8.59152	+	14.8809i	−0.508027	+	0.879929i
$287$	24.8530			1.46702
$288$		0			0
$289$	−8.00000			−0.470588
$290$	3.89440	−	6.74530i	0.228687	−	0.396098i
$291$		0			0
$292$	18.1630	+	31.4592i	1.06291	+	1.84101i
$293$	−9.81954	−	17.0080i	−0.573664	−	0.993615i	−0.996185	−	0.0872621i	$-0.972188\pi$
$293$	−9.81954	−	17.0080i	−0.573664	−	0.993615i	0.422521	−	0.906353i	$-0.361145\pi$
$294$		0			0
$295$	1.99613	−	3.45740i	0.116219	−	0.201297i
$296$	−21.9590			−1.27634
$297$		0			0
$298$	−10.7716			−0.623980
$299$	−6.67024	+	11.5532i	−0.385750	+	0.668139i
$300$		0			0
$301$	−0.949493	−	1.64457i	−0.0547279	−	0.0947914i
$302$	0.171122	+	0.296392i	0.00984696	+	0.0170554i
$303$		0			0
$304$	−0.139033	+	0.240812i	−0.00797409	+	0.0138115i
$305$	0.593578			0.0339882
$306$		0			0
$307$	28.3432			1.61763			0.808815	−	0.588063i	$-0.200109\pi$
$307$	28.3432			1.61763			0.808815	+	0.588063i	$0.200109\pi$
$308$	22.1065	−	38.2896i	1.25964	−	2.18175i
$309$		0			0
$310$	3.68866	+	6.38895i	0.209502	+	0.362868i
$311$	−1.02229	−	1.77066i	−0.0579687	−	0.100405i	0.835585	−	0.549362i	$-0.185129\pi$
$311$	−1.02229	−	1.77066i	−0.0579687	−	0.100405i	−0.893553	+	0.448957i	$0.851796\pi$
$312$		0			0
$313$	−4.20574	+	7.28455i	−0.237722	+	0.411747i	−0.960060	−	0.279793i	$-0.909734\pi$
$313$	−4.20574	+	7.28455i	−0.237722	+	0.411747i	0.722338	+	0.691540i	$0.243067\pi$
$314$	−33.7425			−1.90420
$315$		0			0
$316$	48.7452			2.74213
$317$	15.5642	−	26.9579i	0.874171	−	1.51411i	0.0165284	−	0.999863i	$-0.494739\pi$
$317$	15.5642	−	26.9579i	0.874171	−	1.51411i	0.857643	−	0.514246i	$-0.171928\pi$
$318$		0			0
$319$	10.2096	+	17.6836i	0.571628	+	0.990089i
$320$	−0.383256	−	0.663818i	−0.0214246	−	0.0371086i
$321$		0			0
$322$	24.9440	−	43.2043i	1.39008	−	2.40768i
$323$	−0.125667			−0.00699231
$324$		0			0
$325$	10.4456			0.579419
$326$	−12.3614	+	21.4106i	−0.684636	+	1.18583i
$327$		0			0
$328$	−23.5155	−	40.7300i	−1.29843	−	2.24894i
$329$	15.5856	+	26.9950i	0.859261	+	1.48828i
$330$		0			0
$331$	−15.5155	+	26.8736i	−0.852808	+	1.47711i	0.0258558	+	0.999666i	$0.491769\pi$
$331$	−15.5155	+	26.8736i	−0.852808	+	1.47711i	−0.878664	+	0.477441i	$0.841564\pi$
$332$	6.66044			0.365539
$333$		0			0
$334$	−9.04963			−0.495174
$335$	2.34137	−	4.05537i	0.127923	−	0.221568i
$336$		0			0
$337$	−11.8648	−	20.5505i	−0.646319	−	1.11946i	−0.983995	−	0.178195i	$-0.942974\pi$
$337$	−11.8648	−	20.5505i	−0.646319	−	1.11946i	0.337676	−	0.941262i	$-0.390359\pi$
$338$	−10.4153	−	18.0399i	−0.566520	−	0.981242i
$339$		0			0
$340$	−3.09627	+	5.36289i	−0.167919	+	0.290844i
$341$	−19.3405			−1.04735
$342$		0			0
$343$	11.5790			0.625209
$344$	−1.79679	+	3.11213i	−0.0968764	+	0.167795i
$345$		0			0
$346$	−23.7592	−	41.1522i	−1.27730	−	2.21236i
$347$	−0.904200	−	1.56612i	−0.0485400	−	0.0840738i	0.840735	−	0.541447i	$-0.182124\pi$
$347$	−0.904200	−	1.56612i	−0.0485400	−	0.0840738i	−0.889275	+	0.457374i	$0.848790\pi$
$348$		0			0
$349$	−7.63041	+	13.2163i	−0.408447	+	0.707451i	−0.994716	−	0.102666i	$-0.967263\pi$
$349$	−7.63041	+	13.2163i	−0.408447	+	0.707451i	0.586269	+	0.810116i	$0.300596\pi$
$350$	−39.0624			−2.08797
$351$		0			0
$352$	−14.2763			−0.760930
$353$	−16.1912	+	28.0440i	−0.861770	+	1.49263i	0.00844890	+	0.999964i	$0.497311\pi$
$353$	−16.1912	+	28.0440i	−0.861770	+	1.49263i	−0.870219	+	0.492665i	$0.836023\pi$
$354$		0			0
$355$	−2.76786	−	4.79407i	−0.146903	−	0.254443i
$356$	−35.0107	−	60.6404i	−1.85557	−	3.21393i
$357$		0			0
$358$	6.43629	−	11.1480i	0.340168	−	0.589189i
$359$	1.91447			0.101042			0.0505209	−	0.998723i	$-0.483912\pi$
$359$	1.91447			0.101042			0.0505209	+	0.998723i	$0.483912\pi$
$360$		0			0
$361$	−18.9982			−0.999908
$362$	9.05303	−	15.6803i	0.475817	−	0.824139i
$363$		0			0
$364$	−15.5496	−	26.9327i	−0.815022	−	1.41166i
$365$	−1.92649	−	3.33678i	−0.100837	−	0.174655i
$366$		0			0
$367$	13.4324	−	23.2656i	0.701167	−	1.21446i	−0.266891	−	0.963727i	$-0.585996\pi$
$367$	13.4324	−	23.2656i	0.701167	−	1.21446i	0.968057	−	0.250729i	$-0.0806704\pi$
$368$	−40.5330			−2.11293
$369$		0			0
$370$	4.26083			0.221510
$371$	−7.99912	+	13.8549i	−0.415294	+	0.719310i
$372$		0			0
$373$	−7.42009	−	12.8520i	−0.384198	−	0.665450i	0.607460	−	0.794350i	$-0.292189\pi$
$373$	−7.42009	−	12.8520i	−0.384198	−	0.665450i	−0.991658	+	0.128900i	$0.958855\pi$
$374$	−11.7973	−	20.4334i	−0.610022	−	1.05659i
$375$		0			0
$376$	29.4937	−	51.0845i	1.52102	−	2.63448i
$377$	14.3628			0.739721
$378$		0			0
$379$	−33.7870			−1.73552			−0.867762	−	0.496980i	$-0.834442\pi$
$379$	−33.7870			−1.73552			−0.867762	+	0.496980i	$0.834442\pi$
$380$	0.0432332	−	0.0748822i	0.00221782	−	0.00384137i
$381$		0			0
$382$	13.3059	+	23.0465i	0.680788	+	1.17916i
$383$	−4.63950	−	8.03585i	−0.237067	−	0.410613i	0.722804	−	0.691053i	$-0.242853\pi$
$383$	−4.63950	−	8.03585i	−0.237067	−	0.410613i	−0.959871	+	0.280440i	$0.909520\pi$
$384$		0			0
$385$	−2.34477	+	4.06126i	−0.119501	+	0.206981i
$386$	25.6827			1.30722
$387$		0			0
$388$	82.2559			4.17591
$389$	−7.98932	+	13.8379i	−0.405075	+	0.701610i	−0.994330	−	0.106337i	$-0.966088\pi$
$389$	−7.98932	+	13.8379i	−0.405075	+	0.701610i	0.589255	+	0.807947i	$0.299421\pi$
$390$		0			0
$391$	−9.15910	−	15.8640i	−0.463196	−	0.802278i
$392$	10.4153	+	18.0399i	0.526054	+	0.911153i
$393$		0			0
$394$	−17.8307	+	30.8837i	−0.898297	+	1.55590i
$395$	−5.17024			−0.260143
$396$		0			0
$397$	19.7050			0.988967			0.494483	−	0.869187i	$-0.335357\pi$
$397$	19.7050			0.988967			0.494483	+	0.869187i	$0.335357\pi$
$398$	13.0103	−	22.5344i	0.652146	−	1.12955i
$399$		0			0
$400$	15.8687	+	27.4854i	0.793435	+	1.37427i
$401$	0.573978	+	0.994159i	0.0286631	+	0.0496459i	0.880001	−	0.474972i	$-0.157542\pi$
$401$	0.573978	+	0.994159i	0.0286631	+	0.0496459i	−0.851338	+	0.524618i	$0.824208\pi$
$402$		0			0
$403$	−6.80200	+	11.7814i	−0.338832	+	0.586874i
$404$	−40.0847			−1.99429
$405$		0			0
$406$	−53.7110			−2.66563
$407$	−5.58512	+	9.67372i	−0.276844	+	0.479508i
$408$		0			0
$409$	1.55051	+	2.68556i	0.0766676	+	0.132792i	0.901810	−	0.432132i	$-0.142239\pi$
$409$	1.55051	+	2.68556i	0.0766676	+	0.132792i	−0.825143	+	0.564924i	$0.808905\pi$
$410$	4.56283	+	7.90306i	0.225342	+	0.390304i
$411$		0			0
$412$	−0.575322	+	0.996487i	−0.0283441	+	0.0490934i
$413$	−27.5303			−1.35468
$414$		0			0
$415$	−0.706452			−0.0346784
$416$	−5.02094	+	8.69653i	−0.246172	+	0.426383i
$417$		0			0
$418$	0.164725	+	0.285313i	0.00805698	+	0.0139551i
$419$	17.7246	+	30.6999i	0.865904	+	1.49979i	0.866146	+	0.499791i	$0.166590\pi$
$419$	17.7246	+	30.6999i	0.865904	+	1.49979i	−0.000241841		1.00000i	$0.500077\pi$
$420$		0			0
$421$	−4.60859	+	7.98232i	−0.224609	+	0.389034i	−0.956202	−	0.292707i	$-0.905444\pi$
$421$	−4.60859	+	7.98232i	−0.224609	+	0.389034i	0.731593	+	0.681742i	$0.238777\pi$
$422$	18.0865			0.880435
$423$		0			0
$424$	30.2746			1.47026
$425$	−7.17159	+	12.4216i	−0.347873	+	0.602534i
$426$		0			0
$427$	−2.04664	−	3.54488i	−0.0990437	−	0.171549i
$428$	8.91534	+	15.4418i	0.430939	+	0.746409i
$429$		0			0
$430$	0.348641	−	0.603863i	0.0168129	−	0.0291209i
$431$	−11.5794			−0.557758			−0.278879	−	0.960326i	$-0.589963\pi$
$431$	−11.5794			−0.557758			−0.278879	+	0.960326i	$0.589963\pi$
$432$		0			0
$433$	6.06511			0.291471			0.145735	−	0.989324i	$-0.453445\pi$
$433$	6.06511			0.291471			0.145735	+	0.989324i	$0.453445\pi$
$434$	25.4368	−	44.0578i	1.22100	−	2.11484i
$435$		0			0
$436$	11.9192	+	20.6447i	0.570827	+	0.988701i
$437$	0.127889	+	0.221510i	0.00611775	+	0.0105962i
$438$		0			0
$439$	−14.5030	+	25.1199i	−0.692190	+	1.19891i	0.278929	+	0.960312i	$0.410021\pi$
$439$	−14.5030	+	25.1199i	−0.692190	+	1.19891i	−0.971119	+	0.238597i	$0.923313\pi$
$440$	8.87433			0.423067
$441$		0			0
$442$	−16.5963			−0.789404
$443$	15.4461	−	26.7534i	0.733866	−	1.27109i	−0.221353	−	0.975194i	$-0.571047\pi$
$443$	15.4461	−	26.7534i	0.733866	−	1.27109i	0.955219	−	0.295899i	$-0.0956193\pi$
$444$		0			0
$445$	3.71348	+	6.43193i	0.176036	+	0.304903i
$446$	−13.0851	−	22.6641i	−0.619598	−	1.07318i
$447$		0			0
$448$	−2.64290	+	4.57764i	−0.124865	+	0.216273i
$449$	39.0820			1.84439			0.922197	−	0.386720i	$-0.126392\pi$
$449$	39.0820			1.84439			0.922197	+	0.386720i	$0.126392\pi$
$450$		0			0
$451$	−23.9240			−1.12654
$452$	3.05303	−	5.28801i	0.143603	−	0.248727i
$453$		0			0
$454$	16.4868	+	28.5560i	0.773764	+	1.34020i
$455$	1.64930	+	2.85667i	0.0773204	+	0.133923i
$456$		0			0
$457$	0.752374	−	1.30315i	0.0351946	−	0.0609588i	−0.847892	−	0.530170i	$-0.822128\pi$
$457$	0.752374	−	1.30315i	0.0351946	−	0.0609588i	0.883086	+	0.469211i	$0.155462\pi$
$458$	71.1498			3.32461
$459$		0			0
$460$	12.6040			0.587665
$461$	13.1186	−	22.7220i	0.610992	−	1.05827i	−0.380082	−	0.924953i	$-0.624104\pi$
$461$	13.1186	−	22.7220i	0.610992	−	1.05827i	0.991074	−	0.133316i	$-0.0425626\pi$
$462$		0			0
$463$	−3.37820	−	5.85122i	−0.156998	−	0.271929i	0.776786	−	0.629764i	$-0.216848\pi$
$463$	−3.37820	−	5.85122i	−0.156998	−	0.271929i	−0.933785	+	0.357835i	$0.883515\pi$
$464$	21.8195	+	37.7926i	1.01295	+	1.75448i
$465$		0			0
$466$	17.6163	−	30.5124i	0.816061	−	1.41346i
$467$	−33.7469			−1.56162			−0.780810	−	0.624768i	$-0.785194\pi$
$467$	−33.7469			−1.56162			−0.780810	+	0.624768i	$0.785194\pi$
$468$		0			0
$469$	−32.2918			−1.49110
$470$	−5.72281	+	9.91220i	−0.263974	+	0.457216i
$471$		0			0
$472$	26.0488	+	45.1178i	1.19899	+	2.07671i
$473$	0.914000	+	1.58310i	0.0420258	+	0.0727908i
$474$		0			0
$475$	0.100137	−	0.173442i	0.00459460	−	0.00795809i
$476$	42.7033			1.95730
$477$		0			0
$478$	−38.0310			−1.73950
$479$	5.56330	−	9.63592i	0.254194	−	0.440276i	−0.710483	−	0.703715i	$-0.751523\pi$
$479$	5.56330	−	9.63592i	0.254194	−	0.440276i	0.964676	+	0.263438i	$0.0848566\pi$
$480$		0			0
$481$	3.92855	+	6.80445i	0.179126	+	0.310256i
$482$	−16.4251	−	28.4492i	−0.748145	−	1.29582i
$483$		0			0
$484$	2.98293	−	5.16658i	0.135588	−	0.234845i
$485$	−8.72462			−0.396165
$486$		0			0
$487$	−4.74691			−0.215103			−0.107552	−	0.994200i	$-0.534301\pi$
$487$	−4.74691			−0.215103			−0.107552	+	0.994200i	$0.534301\pi$
$488$	−3.87299	+	6.70821i	−0.175322	+	0.303667i
$489$		0			0
$490$	−2.02094	−	3.50038i	−0.0912970	−	0.158131i
$491$	11.1702	+	19.3474i	0.504106	+	0.873137i	0.999989	+	0.00474780i	$0.00151128\pi$
$491$	11.1702	+	19.3474i	0.504106	+	0.873137i	−0.495883	+	0.868390i	$0.665155\pi$
$492$		0			0
$493$	−9.86097	+	17.0797i	−0.444116	+	0.769231i
$494$	0.231734			0.0104262
$495$		0			0
$496$	−41.3337			−1.85594
$497$	−19.0869	+	33.0595i	−0.856166	+	1.48292i
$498$		0			0
$499$	5.23055	+	9.05958i	0.234152	+	0.405563i	0.959026	−	0.283319i	$-0.0914354\pi$
$499$	5.23055	+	9.05958i	0.234152	+	0.405563i	−0.724874	+	0.688881i	$0.758102\pi$
$500$	−10.0949	−	17.4849i	−0.451459	−	0.781949i
$501$		0			0
$502$	−1.10472	+	1.91344i	−0.0493062	+	0.0854008i
$503$	−25.0419			−1.11656			−0.558281	−	0.829652i	$-0.688539\pi$
$503$	−25.0419			−1.11656			−0.558281	+	0.829652i	$0.688539\pi$
$504$		0			0
$505$	4.25166			0.189196
$506$	−24.0116	+	41.5893i	−1.06745	+	1.84887i
$507$		0			0
$508$	14.6420	+	25.3607i	0.649635	+	1.12520i
$509$	9.03121	+	15.6425i	0.400301	+	0.693342i	0.993762	−	0.111521i	$-0.0355721\pi$
$509$	9.03121	+	15.6425i	0.400301	+	0.693342i	−0.593461	+	0.804863i	$0.702239\pi$
$510$		0			0
$511$	−13.2849	+	23.0102i	−0.587691	+	1.01791i
$512$	50.5553			2.23425
$513$		0			0
$514$	11.5885			0.511148
$515$	0.0610226	−	0.105694i	0.00268898	−	0.00465744i
$516$		0			0
$517$	−15.0030	−	25.9859i	−0.659831	−	1.14286i
$518$	−14.6912	−	25.4459i	−0.645494	−	1.11803i
$519$		0			0
$520$	3.12108	−	5.40587i	0.136868	−	0.237063i
$521$	25.9581			1.13725			0.568623	−	0.822598i	$-0.307476\pi$
$521$	25.9581			1.13725			0.568623	+	0.822598i	$0.307476\pi$
$522$		0			0
$523$	25.5945			1.11917			0.559585	−	0.828773i	$-0.310961\pi$
$523$	25.5945			1.11917			0.559585	+	0.828773i	$0.310961\pi$
$524$	−27.8824	+	48.2937i	−1.21805	+	2.10972i
$525$		0			0
$526$	−5.44104	−	9.42415i	−0.237240	−	0.410913i
$527$	−9.34002	−	16.1774i	−0.406858	−	0.704698i
$528$		0			0
$529$	−7.14203	+	12.3704i	−0.310523	+	0.537841i
$530$	−5.87433			−0.255165
$531$		0			0
$532$	−0.596267			−0.0258514
$533$	−8.41400	+	14.5735i	−0.364451	+	0.631247i
$534$		0			0
$535$	−0.945622	−	1.63787i	−0.0408828	−	0.0708111i
$536$	30.5540	+	52.9210i	1.31973	+	2.28584i
$537$		0			0
$538$	−15.3516	+	26.5898i	−0.661856	+	1.14637i
$539$	10.5963			0.456414
$540$		0			0
$541$	27.8476			1.19726			0.598631	−	0.801025i	$-0.295712\pi$
$541$	27.8476			1.19726			0.598631	+	0.801025i	$0.295712\pi$
$542$	−0.405078	+	0.701615i	−0.0173996	+	0.0301369i
$543$		0			0
$544$	−6.89440	−	11.9415i	−0.295595	−	0.511985i
$545$	−1.26423	−	2.18972i	−0.0541538	−	0.0937972i
$546$		0			0
$547$	2.95424	−	5.11689i	0.126314	−	0.218783i	−0.795932	−	0.605386i	$-0.793019\pi$
$547$	2.95424	−	5.11689i	0.126314	−	0.218783i	0.922246	+	0.386604i	$0.126352\pi$
$548$	−46.8316			−2.00055
$549$		0			0
$550$	37.6023			1.60337
$551$	0.137689	−	0.238484i	0.00586574	−	0.0101598i
$552$		0			0
$553$	17.8268	+	30.8770i	0.758073	+	1.31302i
$554$	−33.9568	−	58.8149i	−1.44269	−	2.49881i
$555$		0			0
$556$	16.4572	−	28.5048i	0.697942	−	1.20887i
$557$	−26.7050			−1.13153			−0.565764	−	0.824567i	$-0.691419\pi$
$557$	−26.7050			−1.13153			−0.565764	+	0.824567i	$0.691419\pi$
$558$		0			0
$559$	1.28581			0.0543838
$560$	−5.01114	+	8.67956i	−0.211759	+	0.366778i
$561$		0			0
$562$	−33.7793	−	58.5075i	−1.42489	−	2.46799i
$563$	18.0312	+	31.2310i	0.759925	+	1.31623i	0.942888	+	0.333109i	$0.108098\pi$
$563$	18.0312	+	31.2310i	0.759925	+	1.31623i	−0.182963	+	0.983120i	$0.558569\pi$
$564$		0			0
$565$	−0.323826	+	0.560882i	−0.0136234	+	0.0235965i
$566$	23.5321			0.989127
$567$		0			0
$568$	72.2390			3.03108
$569$	−4.52363	+	7.83516i	−0.189641	+	0.328467i	−0.945130	−	0.326693i	$-0.894066\pi$
$569$	−4.52363	+	7.83516i	−0.189641	+	0.328467i	0.755490	+	0.655160i	$0.227399\pi$
$570$		0			0
$571$	−15.2895	−	26.4822i	−0.639846	−	1.10825i	−0.985466	−	0.169872i	$-0.945665\pi$
$571$	−15.2895	−	26.4822i	−0.639846	−	1.10825i	0.345620	−	0.938375i	$-0.387669\pi$
$572$	14.9684	+	25.9260i	0.625859	+	1.08402i
$573$		0			0
$574$	31.4650	−	54.4989i	1.31332	−	2.27474i
$575$	29.1935			1.21745
$576$		0			0
$577$	−25.1489			−1.04696			−0.523481	−	0.852037i	$-0.675367\pi$
$577$	−25.1489			−1.04696			−0.523481	+	0.852037i	$0.675367\pi$
$578$	−10.1284	+	17.5428i	−0.421284	+	0.729685i
$579$		0			0
$580$	−6.78493	−	11.7518i	−0.281729	−	0.487969i
$581$	2.43582	+	4.21897i	0.101055	+	0.175032i
$582$		0			0
$583$	7.70011	−	13.3370i	0.318906	−	0.552361i
$584$	50.2799			2.08060
$585$		0			0
$586$	−49.7279			−2.05424
$587$	10.4368	−	18.0770i	0.430771	−	0.746117i	−0.566169	−	0.824289i	$-0.691575\pi$
$587$	10.4368	−	18.0770i	0.430771	−	0.746117i	0.996940	+	0.0781720i	$0.0249083\pi$
$588$		0			0
$589$	0.130415	+	0.225885i	0.00537365	+	0.00930744i
$590$	−5.05438	−	8.75444i	−0.208085	−	0.360415i
$591$		0			0
$592$	−11.9363	+	20.6743i	−0.490578	+	0.849707i
$593$	−15.6212			−0.641488			−0.320744	−	0.947166i	$-0.603933\pi$
$593$	−15.6212			−0.641488			−0.320744	+	0.947166i	$0.603933\pi$
$594$		0			0
$595$	−4.52940			−0.185687
$596$	−9.38326	+	16.2523i	−0.384353	+	0.665719i
$597$		0			0
$598$	16.8897	+	29.2537i	0.690669	+	1.19627i
$599$	−0.224155	−	0.388249i	−0.00915874	−	0.0158634i	0.861410	−	0.507911i	$-0.169582\pi$
$599$	−0.224155	−	0.388249i	−0.00915874	−	0.0158634i	−0.870568	+	0.492047i	$0.836249\pi$
$600$		0			0
$601$	8.83615	−	15.3047i	0.360434	−	0.624290i	−0.627598	−	0.778537i	$-0.715962\pi$
$601$	8.83615	−	15.3047i	0.360434	−	0.624290i	0.988032	+	0.154247i	$0.0492952\pi$
$602$	−4.80840			−0.195976
$603$		0			0
$604$	0.596267			0.0242617
$605$	−0.316390	+	0.548003i	−0.0128631	+	0.0222795i
$606$		0			0
$607$	−13.0993	−	22.6886i	−0.531683	−	0.920901i	−0.999316	−	0.0369787i	$-0.988227\pi$
$607$	−13.0993	−	22.6886i	−0.531683	−	0.920901i	0.467634	−	0.883922i	$-0.345107\pi$
$608$	0.0962667	+	0.166739i	0.00390413	+	0.00676215i
$609$		0			0
$610$	0.751497	−	1.30163i	0.0304272	−	0.0527015i
$611$	−21.1061			−0.853860
$612$		0			0
$613$	14.5544			0.587846			0.293923	−	0.955829i	$-0.405039\pi$
$613$	14.5544			0.587846			0.293923	+	0.955829i	$0.405039\pi$
$614$	35.8837	−	62.1524i	1.44815	−	2.50827i
$615$		0			0
$616$	−30.5984	−	52.9980i	−1.23284	−	2.13535i
$617$	7.01027	+	12.1421i	0.282223	+	0.488824i	0.971932	−	0.235262i	$-0.0755950\pi$
$617$	7.01027	+	12.1421i	0.282223	+	0.488824i	−0.689709	+	0.724087i	$0.742262\pi$
$618$		0			0
$619$	15.8562	−	27.4638i	0.637315	−	1.10386i	−0.348704	−	0.937233i	$-0.613378\pi$
$619$	15.8562	−	27.4638i	0.637315	−	1.10386i	0.986020	−	0.166630i	$-0.0532884\pi$
$620$	12.8530			0.516188
$621$		0			0
$622$	−5.17705			−0.207581
$623$	25.6079	−	44.3541i	1.02596	−	1.77701i
$624$		0			0
$625$	−10.8819	−	18.8480i	−0.435276	−	0.753921i
$626$	10.6493	+	18.4451i	0.425632	+	0.737216i
$627$		0			0
$628$	−29.3935	+	50.9111i	−1.17293	+	2.03157i
$629$	−10.7888			−0.430178
$630$		0			0
$631$	−38.5758			−1.53568			−0.767840	−	0.640642i	$-0.778668\pi$
$631$	−38.5758			−1.53568			−0.767840	+	0.640642i	$0.778668\pi$
$632$	33.7349	−	58.4305i	1.34190	−	2.32424i
$633$		0			0
$634$	−39.4099	−	68.2599i	−1.56517	−	2.71095i
$635$	−1.55303	−	2.68993i	−0.0616303	−	0.106747i
$636$		0			0
$637$	3.72668	−	6.45480i	0.147657	−	0.255749i
$638$	51.7033			2.04695
$639$		0			0
$640$	−6.24216			−0.246743
$641$	−15.3084	+	26.5149i	−0.604645	+	1.04728i	0.387462	+	0.921886i	$0.373352\pi$
$641$	−15.3084	+	26.5149i	−0.604645	+	1.04728i	−0.992107	+	0.125391i	$0.959981\pi$
$642$		0			0
$643$	17.1125	+	29.6397i	0.674850	+	1.16887i	0.976513	+	0.215459i	$0.0691249\pi$
$643$	17.1125	+	29.6397i	0.674850	+	1.16887i	−0.301663	+	0.953415i	$0.597542\pi$
$644$	−43.4582	−	75.2718i	−1.71249	−	2.96612i
$645$		0			0
$646$	−0.159100	+	0.275570i	−0.00625972	+	0.0108421i
$647$	12.8726			0.506073			0.253037	−	0.967457i	$-0.418571\pi$
$647$	12.8726			0.506073			0.253037	+	0.967457i	$0.418571\pi$
$648$		0			0
$649$	26.5012			1.04026
$650$	13.2246	−	22.9057i	0.518712	−	0.898436i
$651$		0			0
$652$	21.5364	+	37.3022i	0.843432	+	1.46087i
$653$	−5.65957	−	9.80266i	−0.221476	−	0.383608i	0.733780	−	0.679387i	$-0.237754\pi$
$653$	−5.65957	−	9.80266i	−0.221476	−	0.383608i	−0.955256	+	0.295779i	$0.904421\pi$
$654$		0			0
$655$	2.95740	−	5.12236i	0.115555	−	0.200147i
$656$	−51.1293			−1.99626
$657$		0			0
$658$	78.9282			3.07694
$659$	−6.88460	+	11.9245i	−0.268186	+	0.464512i	−0.968393	−	0.249428i	$-0.919757\pi$
$659$	−6.88460	+	11.9245i	−0.268186	+	0.464512i	0.700207	+	0.713939i	$0.253091\pi$
$660$		0			0
$661$	10.1334	+	17.5516i	0.394144	+	0.682677i	0.992992	−	0.118186i	$-0.0377078\pi$
$661$	10.1334	+	17.5516i	0.394144	+	0.682677i	−0.598848	+	0.800863i	$0.704374\pi$
$662$	39.2866	+	68.0463i	1.52692	+	2.64470i
$663$		0			0
$664$	4.60947	−	7.98384i	0.178882	−	0.309833i
$665$	0.0632441			0.00245250
$666$		0			0
$667$	40.1411			1.55427
$668$	−7.88326	+	13.6542i	−0.305012	+	0.528297i
$669$		0			0
$670$	−5.92855	−	10.2685i	−0.229040	−	0.396709i
$671$	1.97013	+	3.41237i	0.0760561	+	0.131733i
$672$		0			0
$673$	15.2724	−	26.4526i	0.588709	−	1.01967i	−0.405692	−	0.914010i	$-0.632970\pi$
$673$	15.2724	−	26.4526i	0.588709	−	1.01967i	0.994402	−	0.105665i	$-0.0336971\pi$
$674$	−60.0856			−2.31441
$675$		0			0
$676$	−36.2918			−1.39584
$677$	−1.85962	+	3.22096i	−0.0714711	+	0.123792i	−0.899546	−	0.436826i	$-0.856103\pi$
$677$	−1.85962	+	3.22096i	−0.0714711	+	0.123792i	0.828075	+	0.560617i	$0.189436\pi$
$678$		0			0
$679$	30.0822	+	52.1039i	1.15445	+	1.99956i
$680$	4.28564	+	7.42295i	0.164347	+	0.284657i
$681$		0			0
$682$	−24.4859	+	42.4109i	−0.937614	+	1.62400i
$683$	21.7469			0.832122			0.416061	−	0.909337i	$-0.363410\pi$
$683$	21.7469			0.832122			0.416061	+	0.909337i	$0.363410\pi$
$684$		0			0
$685$	4.96728			0.189790
$686$	14.6596	−	25.3911i	0.559705	−	0.969437i
$687$		0			0
$688$	1.95336	+	3.38332i	0.0744713	+	0.128988i
$689$	−5.41622	−	9.38117i	−0.206342	−	0.357394i
$690$		0			0
$691$	18.7974	−	32.5581i	0.715087	−	1.23857i	−0.247838	−	0.968801i	$-0.579720\pi$
$691$	18.7974	−	32.5581i	0.715087	−	1.23857i	0.962926	−	0.269766i	$-0.0869465\pi$
$692$	−82.7880			−3.14713
$693$		0			0
$694$	−4.57903			−0.173818
$695$	−1.74557	+	3.02341i	−0.0662131	+	0.114684i
$696$		0			0
$697$	−11.5535	−	20.0112i	−0.437620	−	0.757980i
$698$	19.3209	+	33.4648i	0.731306	+	1.26666i
$699$		0			0
$700$	−34.0278	+	58.9379i	−1.28613	+	2.22764i
$701$	−23.3351			−0.881355			−0.440678	−	0.897665i	$-0.645262\pi$
$701$	−23.3351			−0.881355			−0.440678	+	0.897665i	$0.645262\pi$
$702$		0			0
$703$	0.150644			0.00568166
$704$	2.54411	−	4.40653i	0.0958848	−	0.166077i
$705$		0			0
$706$	40.9975	+	71.0098i	1.54296	+	2.67249i
$707$	−14.6596	−	25.3911i	−0.551330	−	0.954931i
$708$		0			0
$709$	−3.28952	+	5.69761i	−0.123540	+	0.213978i	−0.921161	−	0.389181i	$-0.872758\pi$
$709$	−3.28952	+	5.69761i	−0.123540	+	0.213978i	0.797621	+	0.603159i	$0.206091\pi$
$710$	−14.0169			−0.526045
$711$		0			0
$712$	−96.9190			−3.63219
$713$	−19.0103	+	32.9267i	−0.711940	+	1.23312i
$714$		0			0
$715$	−1.58765	−	2.74989i	−0.0593747	−	0.102840i
$716$	−11.2135	−	19.4223i	−0.419067	−	0.725846i
$717$		0			0
$718$	2.42380	−	4.19815i	0.0904554	−	0.156673i
$719$	16.8324			0.627744			0.313872	−	0.949465i	$-0.398374\pi$
$719$	16.8324			0.627744			0.313872	+	0.949465i	$0.398374\pi$
$720$		0			0
$721$	−0.841615			−0.0313434
$722$	−24.0526	+	41.6604i	−0.895146	+	1.55044i
$723$		0			0
$724$	−15.7724	−	27.3187i	−0.586178	−	1.01529i
$725$	−15.7153	−	27.2197i	−0.583651	−	1.01091i
$726$		0			0
$727$	−12.7811	+	22.1374i	−0.474023	+	0.821032i	−0.999558	−	0.0297400i	$-0.990532\pi$
$727$	−12.7811	+	22.1374i	−0.474023	+	0.821032i	0.525534	+	0.850772i	$0.323865\pi$
$728$	−43.0455			−1.59537
$729$		0			0
$730$	−9.75608			−0.361089
$731$	−0.882789	+	1.52904i	−0.0326511	+	0.0565534i
$732$		0			0
$733$	7.39899	+	12.8154i	0.273288	+	0.473348i	0.969702	−	0.244292i	$-0.0785555\pi$
$733$	7.39899	+	12.8154i	0.273288	+	0.473348i	−0.696414	+	0.717640i	$0.745222\pi$
$734$	−34.0121	−	58.9106i	−1.25541	−	2.17443i
$735$		0			0
$736$	−14.0326	+	24.3051i	−0.517247	+	0.895898i
$737$	31.0847			1.14502
$738$		0			0
$739$	9.19078			0.338088			0.169044	−	0.985608i	$-0.445932\pi$
$739$	9.19078			0.338088			0.169044	+	0.985608i	$0.445932\pi$
$740$	3.71167	−	6.42880i	0.136444	−	0.236327i
$741$		0			0
$742$	20.2545	+	35.0818i	0.743566	+	1.28789i
$743$	22.2246	+	38.4942i	0.815342	+	1.41221i	0.909082	+	0.416618i	$0.136785\pi$
$743$	22.2246	+	38.4942i	0.815342	+	1.41221i	−0.0937395	+	0.995597i	$0.529882\pi$
$744$		0			0
$745$	0.995252	−	1.72383i	0.0364632	−	0.0631562i
$746$	−37.5767			−1.37578
$747$		0			0
$748$	−41.1070			−1.50302
$749$	−6.52094	+	11.2946i	−0.238270	+	0.412696i
$750$		0			0
$751$	17.9030	+	31.0089i	0.653290	+	1.13153i	0.982319	+	0.187212i	$0.0599453\pi$
$751$	17.9030	+	31.0089i	0.653290	+	1.13153i	−0.329029	+	0.944320i	$0.606721\pi$
$752$	−32.0638	−	55.5361i	−1.16925	−	2.02519i
$753$		0			0
$754$	18.1839	−	31.4955i	0.662219	−	1.14700i
$755$	−0.0632441			−0.00230169
$756$		0			0
$757$	−45.8976			−1.66818			−0.834088	−	0.551632i	$-0.814005\pi$
$757$	−45.8976			−1.66818			−0.834088	+	0.551632i	$0.814005\pi$
$758$	−42.7759	+	74.0900i	−1.55369	+	2.69107i
$759$		0			0
$760$	−0.0598406	−	0.103647i	−0.00217064	−	0.00375967i
$761$	−18.5976	−	32.2120i	−0.674163	−	1.16768i	−0.976713	−	0.214551i	$-0.931171\pi$
$761$	−18.5976	−	32.2120i	−0.674163	−	1.16768i	0.302550	−	0.953134i	$-0.402162\pi$
$762$		0			0
$763$	−8.71806	+	15.1001i	−0.315615	+	0.546661i
$764$	46.3637			1.67738
$765$		0			0
$766$	−23.4953			−0.848918
$767$	9.32042	−	16.1434i	0.336541	−	0.582906i
$768$		0			0
$769$	19.1668	+	33.1979i	0.691174	+	1.19715i	0.971454	+	0.237230i	$0.0762395\pi$
$769$	19.1668	+	33.1979i	0.691174	+	1.19715i	−0.280280	+	0.959918i	$0.590427\pi$
$770$	5.93717	+	10.2835i	0.213961	+	0.370591i
$771$		0			0
$772$	22.3726	−	38.7504i	0.805207	−	1.39466i
$773$	−52.8272			−1.90006			−0.950031	−	0.312156i	$-0.898949\pi$
$773$	−52.8272			−1.90006			−0.950031	+	0.312156i	$0.898949\pi$
$774$		0			0
$775$	29.7701			1.06937
$776$	56.9265	−	98.5997i	2.04354	−	3.53952i
$777$		0			0
$778$	20.2297	+	35.0388i	0.725269	+	1.25620i
$779$	0.161322	+	0.279418i	0.00577995	+	0.0100112i
$780$		0			0
$781$	18.3735	−	31.8238i	0.657454	−	1.13874i
$782$	−46.3833			−1.65866
$783$		0			0
$784$	22.6459			0.808782
$785$	3.11768	−	5.39998i	0.111275	−	0.192733i
$786$

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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.26604 - 2.19285i) q^{2} +(-2.20574 - 3.82045i) q^{4} +(0.233956 + 0.405223i) q^{5} +(1.61334 - 2.79439i) q^{7} -6.10607 q^{8} +1.18479 q^{10} +(-1.55303 + 2.68993i) q^{11} +(1.09240 + 1.89209i) q^{13} +(-4.08512 - 7.07564i) q^{14} +(-3.31908 + 5.74881i) q^{16} -3.00000 q^{17} +0.0418891 q^{19} +(1.03209 - 1.78763i) q^{20} +(3.93242 + 6.81115i) q^{22} +(3.05303 + 5.28801i) q^{23} +(2.39053 - 4.14052i) q^{25} +5.53209 q^{26} -14.2344 q^{28} +(3.28699 - 5.69323i) q^{29} +(3.11334 + 5.39246i) q^{31} +(2.29813 + 3.98048i) q^{32} +(-3.79813 + 6.57856i) q^{34} +1.50980 q^{35} +3.59627 q^{37} +(0.0530334 - 0.0918566i) q^{38} +(-1.42855 - 2.47432i) q^{40} +(3.85117 + 6.67042i) q^{41} +(0.294263 - 0.509678i) q^{43} +13.7023 q^{44} +15.4611 q^{46} +(-4.83022 + 8.36619i) q^{47} +(-1.70574 - 2.95442i) q^{49} +(-6.05303 - 10.4842i) q^{50} +(4.81908 - 8.34689i) q^{52} -4.95811 q^{53} -1.45336 q^{55} +(-9.85117 + 17.0627i) q^{56} +(-8.32295 - 14.4158i) q^{58} +(-4.26604 - 7.38901i) q^{59} +(0.634285 - 1.09861i) q^{61} +15.7665 q^{62} -1.63816 q^{64} +(-0.511144 + 0.885328i) q^{65} +(-5.00387 - 8.66696i) q^{67} +(6.61721 + 11.4613i) q^{68} +(1.91147 - 3.31077i) q^{70} -11.8307 q^{71} -8.23442 q^{73} +(4.55303 - 7.88609i) q^{74} +(-0.0923963 - 0.160035i) q^{76} +(5.01114 + 8.67956i) q^{77} +(-5.52481 + 9.56926i) q^{79} -3.10607 q^{80} +19.5030 q^{82} +(-0.754900 + 1.30753i) q^{83} +(-0.701867 - 1.21567i) q^{85} +(-0.745100 - 1.29055i) q^{86} +(9.48293 - 16.4249i) q^{88} +15.8726 q^{89} +7.04963 q^{91} +(13.4684 - 23.3279i) q^{92} +(12.2306 + 21.1839i) q^{94} +(0.00980018 + 0.0169744i) q^{95} +(-9.32295 + 16.1478i) q^{97} -8.63816 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} + 6 q^{5} + 3 q^{7} - 12 q^{8} + 3 q^{11} + 3 q^{13} - 3 q^{14} - 3 q^{16} - 18 q^{17} - 6 q^{19} - 3 q^{20} + 6 q^{23} - 3 q^{25} + 24 q^{26} - 24 q^{28} + 12 q^{29} + 12 q^{31}+ \cdots - 18 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 + 3 * q^7 - 12 * q^8 + 3 * q^11 + 3 * q^13 - 3 * q^14 - 3 * q^16 - 18 * q^17 - 6 * q^19 - 3 * q^20 + 6 * q^23 - 3 * q^25 + 24 * q^26 - 24 * q^28 + 12 * q^29 + 12 * q^31 - 9 * q^34 + 12 * q^35 - 6 * q^37 - 12 * q^38 - 9 * q^40 - 3 * q^41 + 12 * q^43 + 30 * q^44 + 18 * q^46 - 6 * q^47 - 24 * q^50 + 12 * q^52 - 36 * q^53 + 18 * q^55 - 33 * q^56 - 9 * q^58 - 21 * q^59 - 6 * q^61 + 24 * q^62 + 24 * q^64 + 3 * q^65 - 6 * q^67 + 9 * q^68 - 9 * q^70 + 18 * q^71 + 12 * q^73 + 15 * q^74 + 3 * q^76 + 24 * q^77 - 6 * q^79 + 6 * q^80 + 36 * q^82 - 6 * q^83 - 18 * q^85 - 3 * q^86 + 36 * q^88 - 12 * q^91 + 24 * q^92 + 36 * q^94 + 3 * q^95 - 15 * q^97 - 18 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more