LMFDB - Embedded newform 576.2.y.a.239.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(47,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 2]))

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

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

chi := DirichletCharacter("576.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.y (of order $12$, degree $4$, 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:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			239.12
Character	$\chi$	$=$	576.239
Dual form			576.2.y.a.335.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.412428 + 1.68223i) q^{3} +(0.289971 - 0.0776974i) q^{5} +(0.374023 + 0.647827i) q^{7} +(-2.65981 + 1.38760i) q^{9} +O(q^{10})$	\(q+(0.412428 + 1.68223i) q^{3} +(0.289971 - 0.0776974i) q^{5} +(0.374023 + 0.647827i) q^{7} +(-2.65981 + 1.38760i) q^{9} +(2.23720 + 0.599457i) q^{11} +(1.60318 - 0.429571i) q^{13} +(0.250297 + 0.455753i) q^{15} +6.74518i q^{17} +(-0.621335 + 0.621335i) q^{19} +(-0.935537 + 0.896375i) q^{21} +(6.06191 + 3.49985i) q^{23} +(-4.25208 + 2.45494i) q^{25} +(-3.43124 - 3.90212i) q^{27} +(-5.44240 - 1.45829i) q^{29} +(-3.13647 - 1.81084i) q^{31} +(-0.0857395 + 4.01073i) q^{33} +(0.158790 + 0.158790i) q^{35} +(6.74053 - 6.74053i) q^{37} +(1.38383 + 2.51975i) q^{39} +(-1.39492 + 2.41607i) q^{41} +(-1.89907 + 7.08744i) q^{43} +(-0.663453 + 0.609023i) q^{45} +(-0.307120 - 0.531947i) q^{47} +(3.22021 - 5.57757i) q^{49} +(-11.3470 + 2.78190i) q^{51} +(2.68523 + 2.68523i) q^{53} +0.695300 q^{55} +(-1.30149 - 0.788974i) q^{57} +(0.00225603 + 0.00841962i) q^{59} +(2.72542 - 10.1714i) q^{61} +(-1.89375 - 1.20410i) q^{63} +(0.431499 - 0.249126i) q^{65} +(-2.35300 - 8.78151i) q^{67} +(-3.38745 + 11.6410i) q^{69} +15.9645i q^{71} +8.17785i q^{73} +(-5.88346 - 6.14050i) q^{75} +(0.448421 + 1.67353i) q^{77} +(7.67035 - 4.42848i) q^{79} +(5.14914 - 7.38149i) q^{81} +(0.353727 - 1.32013i) q^{83} +(0.524083 + 1.95590i) q^{85} +(0.208577 - 9.75681i) q^{87} +15.7852 q^{89} +(0.877914 + 0.877914i) q^{91} +(1.75268 - 6.02310i) q^{93} +(-0.131893 + 0.228445i) q^{95} +(-4.62075 - 8.00338i) q^{97} +(-6.78233 + 1.50990i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	0.412428	+	1.68223i	0.238116	+	0.971237i
$3$	0.412428	+	1.68223i	0.238116	+	0.971237i
$4$		0			0
$5$	0.289971	−	0.0776974i	0.129679	−	0.0347473i	−0.193396	−	0.981121i	$-0.561950\pi$
$5$	0.289971	−	0.0776974i	0.129679	−	0.0347473i	0.323075	+	0.946373i	$0.395283\pi$
$6$		0			0
$7$	0.374023	+	0.647827i	0.141367	+	0.244855i	0.928012	−	0.372551i	$-0.121517\pi$
$7$	0.374023	+	0.647827i	0.141367	+	0.244855i	−0.786644	+	0.617406i	$0.788183\pi$
$8$		0			0
$9$	−2.65981	+	1.38760i	−0.886602	+	0.462533i
$10$		0			0
$11$	2.23720	+	0.599457i	0.674542	+	0.180743i	0.579800	−	0.814759i	$-0.303131\pi$
$11$	2.23720	+	0.599457i	0.674542	+	0.180743i	0.0947421	+	0.995502i	$0.469797\pi$
$12$		0			0
$13$	1.60318	−	0.429571i	0.444642	−	0.119142i	−0.0295491	−	0.999563i	$-0.509407\pi$
$13$	1.60318	−	0.429571i	0.444642	−	0.119142i	0.474191	+	0.880422i	$0.342740\pi$
$14$		0			0
$15$	0.250297	+	0.455753i	0.0646264	+	0.117675i
$16$		0			0
$17$			6.74518i			1.63595i	0.575256	+	0.817973i	$0.304902\pi$
$17$			6.74518i			1.63595i	−0.575256	+	0.817973i	$0.695098\pi$
$18$		0			0
$19$	−0.621335	+	0.621335i	−0.142544	+	0.142544i	−0.774778	−	0.632234i	$-0.782138\pi$
$19$	−0.621335	+	0.621335i	−0.142544	+	0.142544i	0.632234	+	0.774778i	$0.282138\pi$
$20$		0			0
$21$	−0.935537	+	0.896375i	−0.204151	+	0.195605i
$22$		0			0
$23$	6.06191	+	3.49985i	1.26400	+	0.729769i	0.973845	−	0.227212i	$-0.0729611\pi$
$23$	6.06191	+	3.49985i	1.26400	+	0.729769i	0.290151	+	0.956981i	$0.406294\pi$
$24$		0			0
$25$	−4.25208	+	2.45494i	−0.850416	+	0.490988i
$26$		0			0
$27$	−3.43124	−	3.90212i	−0.660343	−	0.750964i
$28$		0			0
$29$	−5.44240	−	1.45829i	−1.01063	−	0.270797i	−0.284736	−	0.958606i	$-0.591906\pi$
$29$	−5.44240	−	1.45829i	−1.01063	−	0.270797i	−0.725892	+	0.687809i	$0.758573\pi$
$30$		0			0
$31$	−3.13647	−	1.81084i	−0.563326	−	0.325236i	0.191153	−	0.981560i	$-0.438777\pi$
$31$	−3.13647	−	1.81084i	−0.563326	−	0.325236i	−0.754479	+	0.656324i	$0.772111\pi$
$32$		0			0
$33$	−0.0857395	+	4.01073i	−0.0149253	+	0.698178i
$34$		0			0
$35$	0.158790	+	0.158790i	0.0268404	+	0.0268404i
$36$		0			0
$37$	6.74053	−	6.74053i	1.10814	−	1.10814i	0.114740	−	0.993396i	$-0.463396\pi$
$37$	6.74053	−	6.74053i	1.10814	−	1.10814i	0.993396	−	0.114740i	$-0.0366036\pi$
$38$		0			0
$39$	1.38383	+	2.51975i	0.221591	+	0.403483i
$40$		0			0
$41$	−1.39492	+	2.41607i	−0.217850	+	0.377327i	−0.954150	−	0.299328i	$-0.903238\pi$
$41$	−1.39492	+	2.41607i	−0.217850	+	0.377327i	0.736301	+	0.676655i	$0.236571\pi$
$42$		0			0
$43$	−1.89907	+	7.08744i	−0.289606	+	1.08082i	0.655801	+	0.754934i	$0.272331\pi$
$43$	−1.89907	+	7.08744i	−0.289606	+	1.08082i	−0.945407	+	0.325891i	$0.894336\pi$
$44$		0			0
$45$	−0.663453	+	0.609023i	−0.0989017	+	0.0907878i
$46$		0			0
$47$	−0.307120	−	0.531947i	−0.0447980	−	0.0775924i	0.842757	−	0.538294i	$-0.180931\pi$
$47$	−0.307120	−	0.531947i	−0.0447980	−	0.0775924i	−0.887555	+	0.460702i	$0.847598\pi$
$48$		0			0
$49$	3.22021	−	5.57757i	0.460031	−	0.796796i
$50$		0			0
$51$	−11.3470	+	2.78190i	−1.58889	+	0.389544i
$52$		0			0
$53$	2.68523	+	2.68523i	0.368844	+	0.368844i	0.867056	−	0.498211i	$-0.166010\pi$
$53$	2.68523	+	2.68523i	0.368844	+	0.368844i	−0.498211	+	0.867056i	$0.666010\pi$
$54$		0			0
$55$	0.695300			0.0937542
$56$		0			0
$57$	−1.30149	−	0.788974i	−0.172386	−	0.104502i
$58$		0			0
$59$	0.00225603	+	0.00841962i	0.000293710	+	0.00109614i	0.966073	−	0.258271i	$-0.0831527\pi$
$59$	0.00225603	+	0.00841962i	0.000293710	+	0.00109614i	−0.965779	+	0.259367i	$0.916486\pi$
$60$		0			0
$61$	2.72542	−	10.1714i	0.348955	−	1.30232i	−0.538969	−	0.842326i	$-0.681186\pi$
$61$	2.72542	−	10.1714i	0.348955	−	1.30232i	0.887924	−	0.459991i	$-0.152147\pi$
$62$		0			0
$63$	−1.89375	−	1.20410i	−0.238590	−	0.151702i
$64$		0			0
$65$	0.431499	−	0.249126i	0.0535208	−	0.0309003i
$66$		0			0
$67$	−2.35300	−	8.78151i	−0.287464	−	1.07283i	−0.947020	−	0.321176i	$-0.895922\pi$
$67$	−2.35300	−	8.78151i	−0.287464	−	1.07283i	0.659555	−	0.751656i	$-0.270745\pi$
$68$		0			0
$69$	−3.38745	+	11.6410i	−0.407801	+	1.40141i
$70$		0			0
$71$			15.9645i			1.89463i	0.320297	+	0.947317i	$0.396217\pi$
$71$			15.9645i			1.89463i	−0.320297	+	0.947317i	$0.603783\pi$
$72$		0			0
$73$			8.17785i			0.957145i	0.878048	+	0.478572i	$0.158846\pi$
$73$			8.17785i			0.957145i	−0.878048	+	0.478572i	$0.841154\pi$
$74$		0			0
$75$	−5.88346	−	6.14050i	−0.679363	−	0.709044i
$76$		0			0
$77$	0.448421	+	1.67353i	0.0511023	+	0.190717i
$78$		0			0
$79$	7.67035	−	4.42848i	0.862982	−	0.498243i	−0.00202794	−	0.999998i	$-0.500646\pi$
$79$	7.67035	−	4.42848i	0.862982	−	0.498243i	0.865010	+	0.501755i	$0.167312\pi$
$80$		0			0
$81$	5.14914	−	7.38149i	0.572126	−	0.820166i
$82$		0			0
$83$	0.353727	−	1.32013i	0.0388266	−	0.144903i	−0.943791	−	0.330541i	$-0.892769\pi$
$83$	0.353727	−	1.32013i	0.0388266	−	0.144903i	0.982618	+	0.185638i	$0.0594353\pi$
$84$		0			0
$85$	0.524083	+	1.95590i	0.0568448	+	0.212148i
$86$		0			0
$87$	0.208577	−	9.75681i	0.0223618	−	1.04604i
$88$		0			0
$89$	15.7852			1.67323			0.836613	−	0.547794i	$-0.184532\pi$
$89$	15.7852			1.67323			0.836613	+	0.547794i	$0.184532\pi$
$90$		0			0
$91$	0.877914	+	0.877914i	0.0920304	+	0.0920304i
$92$		0			0
$93$	1.75268	−	6.02310i	0.181745	−	0.624567i
$94$		0			0
$95$	−0.131893	+	0.228445i	−0.0135319	+	0.0234380i
$96$		0			0
$97$	−4.62075	−	8.00338i	−0.469166	−	0.812620i	0.530212	−	0.847865i	$-0.322112\pi$
$97$	−4.62075	−	8.00338i	−0.469166	−	0.812620i	−0.999379	+	0.0352448i	$0.988779\pi$
$98$		0			0
$99$	−6.78233	+	1.50990i	−0.681650	+	0.151751i
$100$		0			0
$101$	4.08762	−	15.2552i	0.406734	−	1.51795i	−0.394102	−	0.919067i	$-0.628944\pi$
$101$	4.08762	−	15.2552i	0.406734	−	1.51795i	0.800835	−	0.598885i	$-0.204389\pi$
$102$		0			0
$103$	5.63994	−	9.76866i	0.555720	−	0.962535i	−0.442127	−	0.896952i	$-0.645776\pi$
$103$	5.63994	−	9.76866i	0.555720	−	0.962535i	0.997847	−	0.0655828i	$-0.0208906\pi$
$104$		0			0
$105$	−0.201632	+	0.332611i	−0.0196773	+	0.0324595i
$106$		0			0
$107$	9.39963	−	9.39963i	0.908696	−	0.908696i	−0.0874707	−	0.996167i	$-0.527878\pi$
$107$	9.39963	−	9.39963i	0.908696	−	0.908696i	0.996167	+	0.0874707i	$0.0278784\pi$
$108$		0			0
$109$	0.535130	+	0.535130i	0.0512562	+	0.0512562i	0.732270	−	0.681014i	$-0.238461\pi$
$109$	0.535130	+	0.535130i	0.0512562	+	0.0512562i	−0.681014	+	0.732270i	$0.738461\pi$
$110$		0			0
$111$	14.1191	+	8.55914i	1.34013	+	0.812398i
$112$		0			0
$113$	3.53279	+	2.03966i	0.332337	+	0.191875i	0.656878	−	0.753997i	$-0.271877\pi$
$113$	3.53279	+	2.03966i	0.332337	+	0.191875i	−0.324541	+	0.945872i	$0.605210\pi$
$114$		0			0
$115$	2.02971	+	0.543858i	0.189271	+	0.0507150i
$116$		0			0
$117$	−3.66808	+	3.36715i	−0.339114	+	0.311293i
$118$		0			0
$119$	−4.36971	+	2.52285i	−0.400570	+	0.231269i
$120$		0			0
$121$	−4.88055	−	2.81779i	−0.443686	−	0.256162i
$122$		0			0
$123$	−4.63969	−	1.35012i	−0.418347	−	0.121736i
$124$		0			0
$125$	−2.10360	+	2.10360i	−0.188152	+	0.188152i
$126$		0			0
$127$		−	1.78789i		−	0.158650i	−0.996849	−	0.0793250i	$-0.974724\pi$
$127$		−	1.78789i		−	0.158650i	0.996849	−	0.0793250i	$-0.0252765\pi$
$128$		0			0
$129$	−12.7060	−	0.271622i	−1.11870	−	0.0239150i
$130$		0			0
$131$	−3.87165	+	1.03741i	−0.338268	+	0.0906386i	−0.423954	−	0.905684i	$-0.639358\pi$
$131$	−3.87165	+	1.03741i	−0.338268	+	0.0906386i	0.0856865	+	0.996322i	$0.472692\pi$
$132$		0			0
$133$	−0.634911	−	0.170124i	−0.0550538	−	0.0147516i
$134$		0			0
$135$	−1.29814	−	0.864903i	−0.111727	−	0.0744390i
$136$		0			0
$137$	0.396519	+	0.686792i	0.0338769	+	0.0586766i	0.882467	−	0.470375i	$-0.155881\pi$
$137$	0.396519	+	0.686792i	0.0338769	+	0.0586766i	−0.848590	+	0.529051i	$0.822548\pi$
$138$		0			0
$139$	17.7067	−	4.74448i	1.50186	−	0.402422i	0.588137	−	0.808762i	$-0.299862\pi$
$139$	17.7067	−	4.74448i	1.50186	−	0.402422i	0.913722	+	0.406340i	$0.133195\pi$
$140$		0			0
$141$	0.768193	−	0.736036i	0.0646935	−	0.0619854i
$142$		0			0
$143$	3.84415			0.321464
$144$		0			0
$145$	−1.69144			−0.140467
$146$		0			0
$147$	10.7109	+	3.11680i	0.883418	+	0.257069i
$148$		0			0
$149$	−12.6146	+	3.38007i	−1.03343	+	0.276906i	−0.735388	−	0.677647i	$-0.763000\pi$
$149$	−12.6146	+	3.38007i	−1.03343	+	0.276906i	−0.298041	+	0.954553i	$0.596333\pi$
$150$		0			0
$151$	−9.45023	−	16.3683i	−0.769049	−	1.33203i	−0.938079	−	0.346421i	$-0.887397\pi$
$151$	−9.45023	−	16.3683i	−0.769049	−	1.33203i	0.169030	−	0.985611i	$-0.445937\pi$
$152$		0			0
$153$	−9.35961	−	17.9409i	−0.756679	−	1.45043i
$154$		0			0
$155$	−1.05018	−	0.281395i	−0.0843526	−	0.0226022i
$156$		0			0
$157$	−9.20155	+	2.46555i	−0.734364	+	0.196772i	−0.606572	−	0.795029i	$-0.707456\pi$
$157$	−9.20155	+	2.46555i	−0.734364	+	0.196772i	−0.127792	+	0.991801i	$0.540789\pi$
$158$		0			0
$159$	−3.40971	+	5.62463i	−0.270408	+	0.446063i
$160$		0			0
$161$			5.23609i			0.412662i
$162$		0			0
$163$	6.24968	−	6.24968i	0.489512	−	0.489512i	−0.418640	−	0.908152i	$-0.637493\pi$
$163$	6.24968	−	6.24968i	0.489512	−	0.489512i	0.908152	+	0.418640i	$0.137493\pi$
$164$		0			0
$165$	0.286761	+	1.16965i	0.0223243	+	0.0910575i
$166$		0			0
$167$	−7.96426	−	4.59817i	−0.616293	−	0.355817i	0.159132	−	0.987257i	$-0.449131\pi$
$167$	−7.96426	−	4.59817i	−0.616293	−	0.355817i	−0.775424	+	0.631441i	$0.782464\pi$
$168$		0			0
$169$	−8.87267	+	5.12264i	−0.682513	+	0.394049i
$170$		0			0
$171$	0.790467	−	2.51480i	0.0604485	−	0.192311i
$172$		0			0
$173$	7.67137	+	2.05554i	0.583243	+	0.156280i	0.538363	−	0.842713i	$-0.319043\pi$
$173$	7.67137	+	2.05554i	0.583243	+	0.156280i	0.0448800	+	0.998992i	$0.485709\pi$
$174$		0			0
$175$	−3.18075	−	1.83641i	−0.240442	−	0.138819i
$176$		0			0
$177$	−0.0132333	+	0.00726765i	−0.000994675	+	0.000546270i
$178$		0			0
$179$	7.99447	+	7.99447i	0.597535	+	0.597535i	0.939656	−	0.342121i	$-0.111145\pi$
$179$	7.99447	+	7.99447i	0.597535	+	0.597535i	−0.342121	+	0.939656i	$0.611145\pi$
$180$		0			0
$181$	14.5271	−	14.5271i	1.07979	−	1.07979i	0.0832666	−	0.996527i	$-0.473465\pi$
$181$	14.5271	−	14.5271i	1.07979	−	1.07979i	0.996527	−	0.0832666i	$-0.0265353\pi$
$182$		0			0
$183$	18.2347	+	0.389813i	1.34795	+	0.0288158i
$184$		0			0
$185$	1.43083	−	2.47828i	0.105197	−	0.182207i
$186$		0			0
$187$	−4.04344	+	15.0903i	−0.295686	+	1.10351i
$188$		0			0
$189$	1.24454	−	3.68233i	0.0905268	−	0.267850i
$190$		0			0
$191$	−10.2382	−	17.7332i	−0.740813	−	1.28313i	−0.952125	−	0.305708i	$-0.901107\pi$
$191$	−10.2382	−	17.7332i	−0.740813	−	1.28313i	0.211312	−	0.977419i	$-0.432226\pi$
$192$		0			0
$193$	−2.37336	+	4.11078i	−0.170838	+	0.295901i	−0.938713	−	0.344699i	$-0.887981\pi$
$193$	−2.37336	+	4.11078i	−0.170838	+	0.295901i	0.767875	+	0.640600i	$0.221314\pi$
$194$		0			0
$195$	0.597050	+	0.623134i	0.0427556	+	0.0446236i
$196$		0			0
$197$	−6.65282	−	6.65282i	−0.473994	−	0.473994i	0.429210	−	0.903205i	$-0.358792\pi$
$197$	−6.65282	−	6.65282i	−0.473994	−	0.473994i	−0.903205	+	0.429210i	$0.858792\pi$
$198$		0			0
$199$	−22.8401			−1.61909			−0.809544	−	0.587059i	$-0.800286\pi$
$199$	−22.8401			−1.61909			−0.809544	+	0.587059i	$0.800286\pi$
$200$		0			0
$201$	13.8021	−	7.58003i	0.973524	−	0.534654i
$202$		0			0
$203$	−1.09087	−	4.07116i	−0.0765637	−	0.285740i
$204$		0			0
$205$	−0.216763	+	0.808971i	−0.0151394	+	0.0565010i
$206$		0			0
$207$	−20.9799	−	0.897407i	−1.45820	−	0.0623741i
$208$		0			0
$209$	−1.76252	+	1.01759i	−0.121916	+	0.0703881i
$210$		0			0
$211$	3.96884	+	14.8119i	0.273226	+	1.01969i	0.957021	+	0.290019i	$0.0936616\pi$
$211$	3.96884	+	14.8119i	0.273226	+	1.01969i	−0.683795	+	0.729674i	$0.739672\pi$
$212$		0			0
$213$	−26.8559	+	6.58420i	−1.84014	+	0.451142i
$214$		0			0
$215$			2.20270i			0.150223i
$216$		0			0
$217$		−	2.70918i		−	0.183911i
$218$		0			0
$219$	−13.7570	+	3.37277i	−0.929614	+	0.227911i
$220$		0			0
$221$	2.89753	+	10.8137i	0.194909	+	0.727411i
$222$		0			0
$223$	6.39965	−	3.69484i	0.428552	−	0.247425i	−0.270178	−	0.962811i	$-0.587082\pi$
$223$	6.39965	−	3.69484i	0.428552	−	0.247425i	0.698730	+	0.715386i	$0.253749\pi$
$224$		0			0
$225$	7.90324	−	12.4298i	0.526882	−	0.828657i
$226$		0			0
$227$	5.52301	−	20.6122i	0.366575	−	1.36808i	−0.498698	−	0.866776i	$-0.666188\pi$
$227$	5.52301	−	20.6122i	0.366575	−	1.36808i	0.865273	−	0.501301i	$-0.167145\pi$
$228$		0			0
$229$	4.76891	+	17.7978i	0.315138	+	1.17611i	0.923861	+	0.382729i	$0.125016\pi$
$229$	4.76891	+	17.7978i	0.315138	+	1.17611i	−0.608722	+	0.793383i	$0.708318\pi$
$230$		0			0
$231$	−2.63032	+	1.44456i	−0.173063	+	0.0950450i
$232$		0			0
$233$	14.3249			0.938455			0.469228	−	0.883077i	$-0.344532\pi$
$233$	14.3249			0.938455			0.469228	+	0.883077i	$0.344532\pi$
$234$		0			0
$235$	−0.130387	−	0.130387i	−0.00850548	−	0.00850548i
$236$		0			0
$237$	10.6132	+	11.0769i	0.689401	+	0.719520i
$238$		0			0
$239$	−11.4921	+	19.9049i	−0.743364	+	1.28754i	0.207592	+	0.978216i	$0.433438\pi$
$239$	−11.4921	+	19.9049i	−0.743364	+	1.28754i	−0.950955	+	0.309328i	$0.899896\pi$
$240$		0			0
$241$	10.2735	+	17.7943i	0.661777	+	1.14623i	0.980148	+	0.198265i	$0.0635306\pi$
$241$	10.2735	+	17.7943i	0.661777	+	1.14623i	−0.318372	+	0.947966i	$0.603136\pi$
$242$		0			0
$243$	14.5410	+	5.61770i	0.932807	+	0.360376i
$244$		0			0
$245$	0.500405	−	1.86754i	0.0319697	−	0.119312i
$246$		0			0
$247$	−0.729205	+	1.26302i	−0.0463982	+	0.0803640i
$248$		0			0
$249$	2.36665	+	0.0505931i	0.149980	+	0.00320621i
$250$		0			0
$251$	0.440838	−	0.440838i	0.0278255	−	0.0278255i	−0.693057	−	0.720883i	$-0.743737\pi$
$251$	0.440838	−	0.440838i	0.0278255	−	0.0278255i	0.720883	+	0.693057i	$0.243737\pi$
$252$		0			0
$253$	11.4637	+	11.4637i	0.720718	+	0.720718i
$254$		0			0
$255$	−3.07414	+	1.68830i	−0.192510	+	0.105725i
$256$		0			0
$257$	−4.78636	−	2.76341i	−0.298565	−	0.172377i	0.343233	−	0.939250i	$-0.388478\pi$
$257$	−4.78636	−	2.76341i	−0.298565	−	0.172377i	−0.641798	+	0.766874i	$0.721811\pi$
$258$		0			0
$259$	6.88781	+	1.84558i	0.427987	+	0.114679i
$260$		0			0
$261$	16.4992	−	3.67311i	1.02128	−	0.227360i
$262$		0			0
$263$	−4.83474	+	2.79134i	−0.298123	+	0.172121i	−0.641599	−	0.767040i	$-0.721729\pi$
$263$	−4.83474	+	2.79134i	−0.298123	+	0.172121i	0.343477	+	0.939161i	$0.388395\pi$
$264$		0			0
$265$	0.987272	+	0.570002i	0.0606476	+	0.0350149i
$266$		0			0
$267$	6.51026	+	26.5543i	0.398421	+	1.62510i
$268$		0			0
$269$	−1.66733	+	1.66733i	−0.101659	+	0.101659i	−0.756107	−	0.654448i	$-0.772901\pi$
$269$	−1.66733	+	1.66733i	−0.101659	+	0.101659i	0.654448	+	0.756107i	$0.272901\pi$
$270$		0			0
$271$			23.2740i			1.41379i	0.707317	+	0.706897i	$0.249905\pi$
$271$			23.2740i			1.41379i	−0.707317	+	0.706897i	$0.750095\pi$
$272$		0			0
$273$	−1.11478	+	1.83893i	−0.0674694	+	0.111297i
$274$		0			0
$275$	−10.9844	+	2.94326i	−0.662384	+	0.177485i
$276$		0			0
$277$	−0.684687	−	0.183461i	−0.0411389	−	0.0110231i	0.238191	−	0.971218i	$-0.423446\pi$
$277$	−0.684687	−	0.183461i	−0.0411389	−	0.0110231i	−0.279330	+	0.960195i	$0.590112\pi$
$278$		0			0
$279$	10.8551	+	0.464323i	0.649879	+	0.0277983i
$280$		0			0
$281$	2.29162	+	3.96921i	0.136707	+	0.236783i	0.926248	−	0.376914i	$-0.123015\pi$
$281$	2.29162	+	3.96921i	0.136707	+	0.236783i	−0.789541	+	0.613697i	$0.789682\pi$
$282$		0			0
$283$	−14.0269	+	3.75850i	−0.833814	+	0.223420i	−0.650377	−	0.759612i	$-0.725389\pi$
$283$	−14.0269	+	3.75850i	−0.833814	+	0.223420i	−0.183437	+	0.983031i	$0.558722\pi$
$284$		0			0
$285$	−0.438694	−	0.127657i	−0.0259860	−	0.00756176i
$286$		0			0
$287$	−2.08693			−0.123187
$288$		0			0
$289$	−28.4974			−1.67632
$290$		0			0
$291$	11.5578	−	11.0740i	0.677531	−	0.649169i
$292$		0			0
$293$	−6.04141	+	1.61879i	−0.352943	+	0.0945708i	−0.430934	−	0.902383i	$-0.641816\pi$
$293$	−6.04141	+	1.61879i	−0.352943	+	0.0945708i	0.0779914	+	0.996954i	$0.475149\pi$
$294$		0			0
$295$	0.00130836	+	0.00226615i	7.61760e−5	+	0.000131941i
$296$		0			0
$297$	−5.33723	−	10.7867i	−0.309698	−	0.625909i
$298$		0			0
$299$	11.2218	+	3.00687i	0.648972	+	0.173892i
$300$		0			0
$301$	−5.30173	+	1.42059i	−0.305587	+	0.0818817i
$302$		0			0
$303$	27.3487	+	0.584647i	1.57114	+	0.0335871i
$304$		0			0
$305$		−	3.16117i		−	0.181008i
$306$		0			0
$307$	4.52060	−	4.52060i	0.258004	−	0.258004i	−0.566238	−	0.824242i	$-0.691602\pi$
$307$	4.52060	−	4.52060i	0.258004	−	0.258004i	0.824242	+	0.566238i	$0.191602\pi$
$308$		0			0
$309$	18.7592	+	5.45881i	1.06718	+	0.310541i
$310$		0			0
$311$	−10.9637	−	6.32992i	−0.621697	−	0.358937i	0.155832	−	0.987784i	$-0.450194\pi$
$311$	−10.9637	−	6.32992i	−0.621697	−	0.358937i	−0.777529	+	0.628847i	$0.783527\pi$
$312$		0			0
$313$	16.6282	−	9.60027i	0.939879	−	0.542640i	0.0499568	−	0.998751i	$-0.484092\pi$
$313$	16.6282	−	9.60027i	0.939879	−	0.542640i	0.889922	+	0.456112i	$0.150758\pi$
$314$		0			0
$315$	−0.642688	−	0.202014i	−0.0362114	−	0.0113822i
$316$		0			0
$317$	−11.0834	−	2.96978i	−0.622504	−	0.166800i	−0.0662384	−	0.997804i	$-0.521100\pi$
$317$	−11.0834	−	2.96978i	−0.622504	−	0.166800i	−0.556266	+	0.831004i	$0.687766\pi$
$318$		0			0
$319$	−11.3016	−	6.52497i	−0.632767	−	0.365328i
$320$		0			0
$321$	19.6890	+	11.9357i	1.09893	+	0.666185i
$322$		0			0
$323$	−4.19102	−	4.19102i	−0.233194	−	0.233194i
$324$		0			0
$325$	−5.76228	+	5.76228i	−0.319634	+	0.319634i
$326$		0			0
$327$	−0.679510	+	1.12092i	−0.0375770	+	0.0619868i
$328$		0			0
$329$	0.229740	−	0.397921i	0.0126660	−	0.0219381i
$330$		0			0
$331$	−5.08741	+	18.9865i	−0.279630	+	1.04359i	0.673045	+	0.739601i	$0.264986\pi$
$331$	−5.08741	+	18.9865i	−0.279630	+	1.04359i	−0.952675	+	0.303991i	$0.901681\pi$
$332$		0			0
$333$	−8.57534	+	27.2816i	−0.469926	+	1.49502i
$334$		0			0
$335$	−1.36460	−	2.36356i	−0.0745561	−	0.129135i
$336$		0			0
$337$	4.99010	−	8.64310i	0.271828	−	0.470820i	−0.697502	−	0.716583i	$-0.745705\pi$
$337$	4.99010	−	8.64310i	0.271828	−	0.470820i	0.969330	+	0.245763i	$0.0790385\pi$
$338$		0			0
$339$	−1.97415	+	6.78418i	−0.107221	+	0.368466i
$340$		0			0
$341$	−5.93139	−	5.93139i	−0.321203	−	0.321203i
$342$		0			0
$343$	10.0541			0.542868
$344$		0			0
$345$	−0.0777873	+	3.63874i	−0.00418793	+	0.195903i
$346$		0			0
$347$	1.81153	+	6.76074i	0.0972483	+	0.362935i	0.997351	−	0.0727428i	$-0.0231752\pi$
$347$	1.81153	+	6.76074i	0.0972483	+	0.362935i	−0.900102	+	0.435678i	$0.856509\pi$
$348$		0			0
$349$	−5.23119	+	19.5231i	−0.280019	+	1.04505i	0.672383	+	0.740203i	$0.265271\pi$
$349$	−5.23119	+	19.5231i	−0.280019	+	1.04505i	−0.952403	+	0.304843i	$0.901396\pi$
$350$		0			0
$351$	−7.17714	−	4.78185i	−0.383087	−	0.255236i
$352$		0			0
$353$	8.37682	−	4.83636i	0.445853	−	0.257414i	−0.260224	−	0.965548i	$-0.583796\pi$
$353$	8.37682	−	4.83636i	0.445853	−	0.257414i	0.706077	+	0.708135i	$0.250463\pi$
$354$		0			0
$355$	1.24040	+	4.62923i	0.0658335	+	0.245694i
$356$		0			0
$357$	−6.04621	−	6.31037i	−0.319999	−	0.333980i
$358$		0			0
$359$			0.846908i			0.0446981i	0.999750	+	0.0223491i	$0.00711452\pi$
$359$			0.846908i			0.0446981i	−0.999750	+	0.0223491i	$0.992885\pi$
$360$		0			0
$361$			18.2279i			0.959362i
$362$		0			0
$363$	2.72729	−	9.37235i	0.143146	−	0.491921i
$364$		0			0
$365$	0.635398	+	2.37134i	0.0332582	+	0.124121i
$366$		0			0
$367$	15.5960	−	9.00434i	0.814103	−	0.470023i	−0.0342756	−	0.999412i	$-0.510912\pi$
$367$	15.5960	−	9.00434i	0.814103	−	0.470023i	0.848379	+	0.529390i	$0.177579\pi$
$368$		0			0
$369$	0.357676	−	8.36187i	0.0186199	−	0.435301i
$370$		0			0
$371$	−0.735225	+	2.74390i	−0.0381710	+	0.142456i
$372$		0			0
$373$	5.01296	+	18.7086i	0.259561	+	0.968696i	0.965496	+	0.260419i	$0.0838607\pi$
$373$	5.01296	+	18.7086i	0.259561	+	0.968696i	−0.705934	+	0.708277i	$0.749473\pi$
$374$		0			0
$375$	−4.40633	−	2.67116i	−0.227542	−	0.137938i
$376$		0			0
$377$	−9.35158			−0.481631
$378$		0			0
$379$	−7.14922	−	7.14922i	−0.367231	−	0.367231i	0.499235	−	0.866466i	$-0.333614\pi$
$379$	−7.14922	−	7.14922i	−0.367231	−	0.367231i	−0.866466	+	0.499235i	$0.833614\pi$
$380$		0			0
$381$	3.00765	−	0.737378i	0.154087	−	0.0377770i
$382$		0			0
$383$	−3.80911	+	6.59757i	−0.194636	+	0.337120i	−0.946781	−	0.321878i	$-0.895686\pi$
$383$	−3.80911	+	6.59757i	−0.194636	+	0.337120i	0.752145	+	0.658998i	$0.229019\pi$
$384$		0			0
$385$	0.260058	+	0.450434i	0.0132538	+	0.0229562i
$386$		0			0
$387$	−4.78336	−	21.4864i	−0.243152	−	1.09221i
$388$		0			0
$389$	−0.417448	+	1.55794i	−0.0211654	+	0.0789905i	−0.975701	−	0.219107i	$-0.929686\pi$
$389$	−0.417448	+	1.55794i	−0.0211654	+	0.0789905i	0.954535	+	0.298098i	$0.0963522\pi$
$390$		0			0
$391$	−23.6071	+	40.8887i	−1.19386	+	2.06783i
$392$		0			0
$393$	−3.34194	−	6.08516i	−0.168578	−	0.306956i
$394$		0			0
$395$	1.88010	−	1.88010i	0.0945979	−	0.0945979i
$396$		0			0
$397$	−20.8968	−	20.8968i	−1.04878	−	1.04878i	−0.998748	−	0.0500326i	$-0.984067\pi$
$397$	−20.8968	−	20.8968i	−1.04878	−	1.04878i	−0.0500326	−	0.998748i	$-0.515933\pi$
$398$		0			0
$399$	0.0243326	−	1.13823i	0.00121815	−	0.0569829i
$400$		0			0
$401$	−16.6619	−	9.61977i	−0.832057	−	0.480388i	0.0224993	−	0.999747i	$-0.492838\pi$
$401$	−16.6619	−	9.61977i	−0.832057	−	0.480388i	−0.854557	+	0.519358i	$0.826171\pi$
$402$		0			0
$403$	−5.80621	−	1.55577i	−0.289228	−	0.0774983i
$404$		0			0
$405$	0.919576	−	2.54049i	0.0456941	−	0.126238i
$406$		0			0
$407$	19.1206	−	11.0393i	0.947772	−	0.547196i
$408$		0			0
$409$	−4.69044	−	2.70803i	−0.231928	−	0.133903i	0.379533	−	0.925178i	$-0.376085\pi$
$409$	−4.69044	−	2.70803i	−0.231928	−	0.133903i	−0.611461	+	0.791275i	$0.709418\pi$
$410$		0			0
$411$	−0.991807	+	0.950290i	−0.0489222	+	0.0468743i
$412$		0			0
$413$	−0.00461065	+	0.00461065i	−0.000226875	+	0.000226875i
$414$		0			0
$415$		−	0.410282i		−	0.0201400i
$416$		0			0
$417$	15.2840	+	27.8299i	0.748463	+	1.36284i
$418$		0			0
$419$	−6.50669	+	1.74346i	−0.317873	+	0.0851738i	−0.414228	−	0.910173i	$-0.635948\pi$
$419$	−6.50669	+	1.74346i	−0.317873	+	0.0851738i	0.0963549	+	0.995347i	$0.469282\pi$
$420$		0			0
$421$	−19.0218	−	5.09689i	−0.927068	−	0.248407i	−0.236464	−	0.971640i	$-0.575989\pi$
$421$	−19.0218	−	5.09689i	−0.927068	−	0.248407i	−0.690604	+	0.723233i	$0.742655\pi$
$422$		0			0
$423$	1.55501	+	0.988716i	0.0756071	+	0.0480730i
$424$		0			0
$425$	−16.5590	−	28.6810i	−0.803230	−	1.39124i
$426$		0			0
$427$	7.60869	−	2.03874i	0.368210	−	0.0986616i
$428$		0			0
$429$	1.58544	+	6.46675i	0.0765456	+	0.312218i
$430$		0			0
$431$	22.9770			1.10676			0.553380	−	0.832929i	$-0.313338\pi$
$431$	22.9770			1.10676			0.553380	+	0.832929i	$0.313338\pi$
$432$		0			0
$433$	−9.38876			−0.451195			−0.225598	−	0.974221i	$-0.572433\pi$
$433$	−9.38876			−0.451195			−0.225598	+	0.974221i	$0.572433\pi$
$434$		0			0
$435$	−0.697598	−	2.84540i	−0.0334473	−	0.136426i
$436$		0			0
$437$	−5.94106	+	1.59190i	−0.284199	+	0.0761510i
$438$		0			0
$439$	2.64587	+	4.58278i	0.126281	+	0.218724i	0.922233	−	0.386635i	$-0.126363\pi$
$439$	2.64587	+	4.58278i	0.126281	+	0.218724i	−0.795952	+	0.605359i	$0.793029\pi$
$440$		0			0
$441$	−0.825706	+	19.3036i	−0.0393193	+	0.919220i
$442$		0			0
$443$	−20.7945	−	5.57188i	−0.987978	−	0.264728i	−0.271577	−	0.962417i	$-0.587545\pi$
$443$	−20.7945	−	5.57188i	−0.987978	−	0.264728i	−0.716401	+	0.697689i	$0.754212\pi$
$444$		0			0
$445$	4.57724	−	1.22647i	0.216982	−	0.0581402i
$446$		0			0
$447$	−10.8887	−	19.8267i	−0.515017	−	0.937769i
$448$		0			0
$449$		−	22.9162i		−	1.08148i	−0.841189	−	0.540742i	$-0.818144\pi$
$449$		−	22.9162i		−	1.08148i	0.841189	−	0.540742i	$-0.181856\pi$
$450$		0			0
$451$	−4.56905	+	4.56905i	−0.215148	+	0.215148i
$452$		0			0
$453$	23.6377	−	22.6482i	1.11060	−	1.06411i
$454$		0			0
$455$	0.322781	+	0.186358i	0.0151322	+	0.00873658i
$456$		0			0
$457$	2.67987	−	1.54723i	0.125359	−	0.0723761i	−0.436009	−	0.899942i	$-0.643608\pi$
$457$	2.67987	−	1.54723i	0.125359	−	0.0723761i	0.561368	+	0.827566i	$0.310275\pi$
$458$		0			0
$459$	26.3205	−	23.1443i	1.22854	−	1.08029i
$460$		0			0
$461$	1.53371	+	0.410957i	0.0714320	+	0.0191402i	0.294358	−	0.955695i	$-0.404894\pi$
$461$	1.53371	+	0.410957i	0.0714320	+	0.0191402i	−0.222926	+	0.974835i	$0.571561\pi$
$462$		0			0
$463$	0.0991508	+	0.0572447i	0.00460793	+	0.00266039i	0.502302	−	0.864692i	$-0.332487\pi$
$463$	0.0991508	+	0.0572447i	0.00460793	+	0.00266039i	−0.497694	+	0.867353i	$0.665820\pi$
$464$		0			0
$465$	0.0402475	−	1.88270i	0.00186644	−	0.0873082i
$466$		0			0
$467$	−0.325359	−	0.325359i	−0.0150558	−	0.0150558i	0.699539	−	0.714595i	$-0.253389\pi$
$467$	−0.325359	−	0.325359i	−0.0150558	−	0.0150558i	−0.714595	+	0.699539i	$0.753389\pi$
$468$		0			0
$469$	4.80882	−	4.80882i	0.222051	−	0.222051i
$470$		0			0
$471$	−7.94260	−	14.4623i	−0.365976	−	0.666387i
$472$		0			0
$473$	−8.49723	+	14.7176i	−0.390703	+	0.676718i
$474$		0			0
$475$	1.11663	−	4.16731i	0.0512344	−	0.191209i
$476$		0			0
$477$	−10.8682	−	3.41616i	−0.497621	−	0.156415i
$478$		0			0
$479$	9.17908	+	15.8986i	0.419403	+	0.726427i	0.995879	−	0.0906864i	$-0.0289061\pi$
$479$	9.17908	+	15.8986i	0.419403	+	0.726427i	−0.576476	+	0.817114i	$0.695573\pi$
$480$		0			0
$481$	7.91075	−	13.7018i	0.360699	−	0.624749i
$482$		0			0
$483$	−8.80832	+	2.15951i	−0.400793	+	0.0982612i
$484$		0			0
$485$	−1.96173	−	1.96173i	−0.0890774	−	0.0890774i
$486$		0			0
$487$	24.8691			1.12693			0.563464	−	0.826140i	$-0.309468\pi$
$487$	24.8691			1.12693			0.563464	+	0.826140i	$0.309468\pi$
$488$		0			0
$489$	13.0909	+	7.93586i	0.591993	+	0.358872i
$490$		0			0
$491$	−0.0538587	−	0.201003i	−0.00243061	−	0.00907115i	0.964700	−	0.263352i	$-0.0848280\pi$
$491$	−0.0538587	−	0.201003i	−0.00243061	−	0.00907115i	−0.967130	+	0.254281i	$0.918161\pi$
$492$		0			0
$493$	9.83640	−	36.7100i	0.443009	−	1.65333i
$494$		0			0
$495$	−1.84936	+	0.964797i	−0.0831226	+	0.0433644i
$496$		0			0
$497$	−10.3422	+	5.97108i	−0.463912	+	0.267840i
$498$		0			0
$499$	9.17443	+	34.2394i	0.410704	+	1.53277i	0.793288	+	0.608847i	$0.208368\pi$
$499$	9.17443	+	34.2394i	0.410704	+	1.53277i	−0.382584	+	0.923921i	$0.624966\pi$
$500$		0			0
$501$	4.45050	−	15.2941i	0.198833	−	0.683292i
$502$		0			0
$503$		−	39.4177i		−	1.75755i	−0.477239	−	0.878773i	$-0.658362\pi$
$503$		−	39.4177i		−	1.75755i	0.477239	−	0.878773i	$-0.341638\pi$
$504$		0			0
$505$		−	4.74117i		−	0.210979i
$506$		0			0
$507$	−12.2768	−	12.8132i	−0.545232	−	0.569053i
$508$		0			0
$509$	−10.2393	−	38.2137i	−0.453850	−	1.69379i	−0.691447	−	0.722427i	$-0.743027\pi$
$509$	−10.2393	−	38.2137i	−0.453850	−	1.69379i	0.237598	−	0.971364i	$-0.423640\pi$
$510$		0			0
$511$	−5.29783	+	3.05870i	−0.234362	+	0.135309i
$512$		0			0
$513$	4.55648	+	0.292576i	0.201173	+	0.0129175i
$514$		0			0
$515$	0.876418	−	3.27084i	0.0386196	−	0.144130i
$516$		0			0
$517$	−0.368210	−	1.37418i	−0.0161939	−	0.0604363i
$518$		0			0
$519$	−0.294001	+	13.7528i	−0.0129052	+	0.603680i
$520$		0			0
$521$	−21.5152			−0.942596			−0.471298	−	0.881974i	$-0.656214\pi$
$521$	−21.5152			−0.942596			−0.471298	+	0.881974i	$0.656214\pi$
$522$		0			0
$523$	−18.8248	−	18.8248i	−0.823149	−	0.823149i	0.163409	−	0.986558i	$-0.447751\pi$
$523$	−18.8248	−	18.8248i	−0.823149	−	0.823149i	−0.986558	+	0.163409i	$0.947751\pi$
$524$		0			0
$525$	1.77743	−	6.10815i	0.0775735	−	0.266581i
$526$		0			0
$527$	12.2144	−	21.1560i	0.532069	−	0.921571i
$528$		0			0
$529$	12.9979	+	22.5130i	0.565125	+	0.978825i
$530$		0			0
$531$	−0.0176837	−	0.0192641i	−0.000767405	−	0.000835990i
$532$		0			0
$533$	−1.19843	+	4.47261i	−0.0519099	+	0.193730i
$534$		0			0
$535$	1.99529	−	3.45594i	0.0862639	−	0.149413i
$536$		0			0
$537$	−10.1514	+	16.7457i	−0.438065	+	0.722630i
$538$		0			0
$539$	10.5478	−	10.5478i	0.454325	−	0.454325i
$540$		0			0
$541$	17.5988	+	17.5988i	0.756630	+	0.756630i	0.975707	−	0.219078i	$-0.0703048\pi$
$541$	17.5988	+	17.5988i	0.756630	+	0.756630i	−0.219078	+	0.975707i	$0.570305\pi$
$542$		0			0
$543$	30.4294	+	18.4466i	1.30585	+	0.791620i
$544$		0			0
$545$	0.196750	+	0.113594i	0.00842786	+	0.00486583i
$546$		0			0
$547$	−29.1328	−	7.80612i	−1.24563	−	0.333765i	−0.424983	−	0.905201i	$-0.639720\pi$
$547$	−29.1328	−	7.80612i	−1.24563	−	0.333765i	−0.820647	+	0.571436i	$0.806387\pi$
$548$		0			0
$549$	6.86476	+	30.8358i	0.292981	+	1.31604i
$550$		0			0
$551$	4.28764	−	2.47547i	0.182660	−	0.105459i
$552$		0			0
$553$	5.73777	+	3.31270i	0.243995	+	0.140871i
$554$		0			0
$555$	4.75915	+	1.38488i	0.202015	+	0.0587850i
$556$		0			0
$557$	25.0618	−	25.0618i	1.06190	−	1.06190i	0.0639497	−	0.997953i	$-0.479630\pi$
$557$	25.0618	−	25.0618i	1.06190	−	1.06190i	0.997953	−	0.0639497i	$-0.0203697\pi$
$558$		0			0
$559$			12.1782i			0.515084i
$560$		0			0
$561$	−27.0531	−	0.578328i	−1.14218	−	0.0244170i
$562$		0			0
$563$	−13.8780	+	3.71859i	−0.584886	+	0.156720i	−0.539115	−	0.842232i	$-0.681241\pi$
$563$	−13.8780	+	3.71859i	−0.584886	+	0.156720i	−0.0457710	+	0.998952i	$0.514574\pi$
$564$		0			0
$565$	1.18288	+	0.316952i	0.0497642	+	0.0133343i
$566$		0			0
$567$	6.70782	+	0.574901i	0.281702	+	0.0241436i
$568$		0			0
$569$	14.1987	+	24.5928i	0.595239	+	1.03098i	0.993513	+	0.113718i	$0.0362761\pi$
$569$	14.1987	+	24.5928i	0.595239	+	1.03098i	−0.398274	+	0.917267i	$0.630391\pi$
$570$		0			0
$571$	17.3238	−	4.64190i	0.724978	−	0.194257i	0.122586	−	0.992458i	$-0.460881\pi$
$571$	17.3238	−	4.64190i	0.724978	−	0.194257i	0.602392	+	0.798201i	$0.294214\pi$
$572$		0			0
$573$	25.6087	−	24.5368i	1.06982	−	1.02504i
$574$		0			0
$575$	−34.3677			−1.43323
$576$		0			0
$577$	−10.1199			−0.421295			−0.210648	−	0.977562i	$-0.567557\pi$
$577$	−10.1199			−0.421295			−0.210648	+	0.977562i	$0.567557\pi$
$578$		0			0
$579$	−7.89413	−	2.29714i	−0.328069	−	0.0954660i
$580$		0			0
$581$	0.987517	−	0.264604i	0.0409691	−	0.0109776i
$582$		0			0
$583$	4.39772	+	7.61707i	0.182135	+	0.315467i
$584$		0			0
$585$	−0.802016	+	1.26137i	−0.0331593	+	0.0521514i
$586$		0			0
$587$	20.9306	+	5.60833i	0.863897	+	0.231480i	0.663447	−	0.748224i	$-0.269093\pi$
$587$	20.9306	+	5.60833i	0.863897	+	0.231480i	0.200450	+	0.979704i	$0.435760\pi$
$588$		0			0
$589$	3.07394	−	0.823658i	0.126659	−	0.0339383i
$590$		0			0
$591$	8.44778	−	13.9354i	0.347495	−	0.573226i
$592$		0			0
$593$			20.8755i			0.857256i	0.903481	+	0.428628i	$0.141003\pi$
$593$			20.8755i			0.857256i	−0.903481	+	0.428628i	$0.858997\pi$
$594$		0			0
$595$	−1.07107	+	1.07107i	−0.0439095	+	0.0439095i
$596$		0			0
$597$	−9.41988	−	38.4223i	−0.385530	−	1.57252i
$598$		0			0
$599$	9.64766	+	5.57008i	0.394193	+	0.227587i	0.683975	−	0.729505i	$-0.260250\pi$
$599$	9.64766	+	5.57008i	0.394193	+	0.227587i	−0.289782	+	0.957093i	$0.593583\pi$
$600$		0			0
$601$	21.0323	−	12.1430i	0.857927	−	0.495324i	−0.00539080	−	0.999985i	$-0.501716\pi$
$601$	21.0323	−	12.1430i	0.857927	−	0.495324i	0.863317	+	0.504661i	$0.168383\pi$
$602$		0			0
$603$	18.4437	+	20.0921i	0.751087	+	0.818213i
$604$		0			0
$605$	−1.63415	−	0.437870i	−0.0664377	−	0.0178019i
$606$		0			0
$607$	−23.4924	−	13.5633i	−0.953525	−	0.550518i	−0.0593510	−	0.998237i	$-0.518903\pi$
$607$	−23.4924	−	13.5633i	−0.953525	−	0.550518i	−0.894174	+	0.447719i	$0.852236\pi$
$608$		0			0
$609$	6.39874	−	3.51415i	0.259290	−	0.142401i
$610$		0			0
$611$	−0.720877	−	0.720877i	−0.0291636	−	0.0291636i
$612$		0			0
$613$	−25.5272	+	25.5272i	−1.03103	+	1.03103i	−0.0315305	+	0.999503i	$0.510038\pi$
$613$	−25.5272	+	25.5272i	−1.03103	+	1.03103i	−0.999503	+	0.0315305i	$0.989962\pi$
$614$		0			0
$615$	−1.45028	−	0.0310033i	−0.0584808	−	0.00125017i
$616$		0			0
$617$	−3.82807	+	6.63041i	−0.154112	+	0.266930i	−0.932735	−	0.360562i	$-0.882585\pi$
$617$	−3.82807	+	6.63041i	−0.154112	+	0.266930i	0.778623	+	0.627492i	$0.215918\pi$
$618$		0			0
$619$	8.43446	−	31.4778i	0.339009	−	1.26520i	−0.560447	−	0.828190i	$-0.689371\pi$
$619$	8.43446	−	31.4778i	0.339009	−	1.26520i	0.899457	−	0.437010i	$-0.143963\pi$
$620$		0			0
$621$	−7.14306	−	35.6632i	−0.286641	−	1.43111i
$622$		0			0
$623$	5.90402	+	10.2261i	0.236540	+	0.409699i
$624$		0			0
$625$	11.8282	−	20.4870i	0.473126	−	0.819479i
$626$		0			0
$627$	−2.43873	−	2.54528i	−0.0973936	−	0.101649i
$628$		0			0
$629$	45.4661	+	45.4661i	1.81285	+	1.81285i
$630$		0			0
$631$	20.5675			0.818781			0.409390	−	0.912359i	$-0.365741\pi$
$631$	20.5675			0.818781			0.409390	+	0.912359i	$0.365741\pi$
$632$		0			0
$633$	−23.2802	+	12.7853i	−0.925304	+	0.508172i
$634$		0			0
$635$	−0.138915	−	0.518437i	−0.00551266	−	0.0205735i
$636$		0			0
$637$	2.76662	−	10.3252i	0.109617	−	0.409098i
$638$		0			0
$639$	−22.1523	−	42.4624i	−0.876331	−	1.67979i
$640$		0			0
$641$	12.3382	−	7.12347i	0.487330	−	0.281360i	−0.236136	−	0.971720i	$-0.575881\pi$
$641$	12.3382	−	7.12347i	0.487330	−	0.281360i	0.723466	+	0.690360i	$0.242548\pi$
$642$		0			0
$643$	−3.10018	−	11.5700i	−0.122259	−	0.456277i	0.877468	−	0.479635i	$-0.159231\pi$
$643$	−3.10018	−	11.5700i	−0.122259	−	0.456277i	−0.999727	+	0.0233581i	$0.992564\pi$
$644$		0			0
$645$	−3.70546	+	0.908457i	−0.145902	+	0.0357705i
$646$		0			0
$647$			3.24662i			0.127638i	0.997961	+	0.0638189i	$0.0203280\pi$
$647$			3.24662i			0.127638i	−0.997961	+	0.0638189i	$0.979672\pi$
$648$		0			0
$649$			0.0201888i			0.000792479i
$650$		0			0
$651$	4.55747	−	1.11734i	0.178621	−	0.0437921i
$652$		0			0
$653$	−0.0259859	−	0.0969809i	−0.00101691	−	0.00379516i	0.965416	−	0.260716i	$-0.0839587\pi$
$653$	−0.0259859	−	0.0969809i	−0.00101691	−	0.00379516i	−0.966432	+	0.256921i	$0.917292\pi$
$654$		0			0
$655$	−1.04206	+	0.601635i	−0.0407167	+	0.0235078i
$656$		0			0
$657$	−11.3476	−	21.7515i	−0.442711	−	0.848606i
$658$		0			0
$659$	−4.94194	+	18.4436i	−0.192511	+	0.718459i	0.800387	+	0.599484i	$0.204628\pi$
$659$	−4.94194	+	18.4436i	−0.192511	+	0.718459i	−0.992897	+	0.118975i	$0.962039\pi$
$660$		0			0
$661$	−7.13036	−	26.6109i	−0.277339	−	1.03504i	−0.954258	−	0.298985i	$-0.903352\pi$
$661$	−7.13036	−	26.6109i	−0.277339	−	1.03504i	0.676919	−	0.736058i	$-0.263315\pi$
$662$		0			0
$663$	−16.9962	+	9.33421i	−0.660077	+	0.362511i
$664$		0			0
$665$	−0.197324			−0.00765189
$666$		0			0
$667$	−27.8876	−	27.8876i	−1.07981	−	1.07981i
$668$		0			0
$669$	8.85497	+	9.24183i	0.342353	+	0.357310i
$670$		0			0
$671$	12.1947	−	21.1218i	0.470769	−	0.815396i
$672$		0			0
$673$	21.3890	+	37.0468i	0.824484	+	1.42805i	0.902313	+	0.431082i	$0.141868\pi$
$673$	21.3890	+	37.0468i	0.824484	+	1.42805i	−0.0778289	+	0.996967i	$0.524799\pi$
$674$		0			0
$675$	24.1694	+	8.16865i	0.930281	+	0.314412i
$676$		0			0
$677$	2.00745	−	7.49190i	0.0771525	−	0.287937i	−0.916560	−	0.399897i	$-0.869046\pi$
$677$	2.00745	−	7.49190i	0.0771525	−	0.287937i	0.993713	+	0.111960i	$0.0357127\pi$
$678$		0			0
$679$	3.45654	−	5.98690i	0.132650	−	0.229756i
$680$		0			0
$681$	36.9523	+	0.789949i	1.41601	+	0.0302709i
$682$		0			0
$683$	−31.9083	+	31.9083i	−1.22094	+	1.22094i	−0.253637	+	0.967299i	$0.581627\pi$
$683$	−31.9083	+	31.9083i	−1.22094	+	1.22094i	−0.967299	+	0.253637i	$0.918373\pi$
$684$		0			0
$685$	0.168341	+	0.168341i	0.00643198	+	0.00643198i
$686$		0			0
$687$	−27.9732	+	15.3627i	−1.06724	+	0.586125i
$688$		0			0
$689$	5.45840	+	3.15141i	0.207948	+	0.120059i
$690$		0			0
$691$	−29.1485	−	7.81032i	−1.10886	−	0.297118i	−0.342493	−	0.939520i	$-0.611271\pi$
$691$	−29.1485	−	7.81032i	−1.10886	−	0.297118i	−0.766368	+	0.642402i	$0.777938\pi$
$692$		0			0
$693$	−3.51490	−	3.82904i	−0.133520	−	0.145453i
$694$		0			0
$695$	4.76578	−	2.75152i	0.180776	−	0.104371i
$696$		0			0
$697$	−16.2968	−	9.40898i	−0.617286	−	0.356390i
$698$		0			0
$699$	5.90799	+	24.0978i	0.223461	+	0.911462i
$700$		0			0
$701$	−6.92803	+	6.92803i	−0.261668	+	0.261668i	−0.825732	−	0.564063i	$-0.809237\pi$
$701$	−6.92803	+	6.92803i	−0.261668	+	0.261668i	0.564063	+	0.825732i	$0.309237\pi$
$702$		0			0
$703$			8.37625i			0.315916i
$704$		0			0
$705$	0.165565	−	0.273116i	0.00623555	−	0.0102861i
$706$		0			0
$707$	11.4116	−	3.05773i	0.429178	−	0.114998i
$708$		0			0
$709$	−14.8255	−	3.97247i	−0.556782	−	0.149189i	−0.0305546	−	0.999533i	$-0.509727\pi$
$709$	−14.8255	−	3.97247i	−0.556782	−	0.149189i	−0.526228	+	0.850344i	$0.676394\pi$
$710$		0			0
$711$	−14.2567	+	22.4223i	−0.534668	+	0.840901i
$712$		0			0
$713$	−12.6753	−	21.9543i	−0.474695	−	0.822195i
$714$		0			0
$715$	1.11469	−	0.298680i	0.0416871	−	0.0111700i
$716$		0			0
$717$	−38.2244	−	11.1231i	−1.42752	−	0.415398i
$718$		0			0
$719$	6.93438			0.258609			0.129304	−	0.991605i	$-0.458726\pi$
$719$	6.93438			0.258609			0.129304	+	0.991605i	$0.458726\pi$
$720$		0			0
$721$	8.43787			0.314243
$722$		0			0
$723$	−25.6970	+	24.6213i	−0.955682	+	0.915677i
$724$		0			0
$725$	26.7215	−	7.16001i	0.992412	−	0.265916i
$726$		0			0
$727$	7.03023	+	12.1767i	0.260737	+	0.451610i	0.966438	−	0.256900i	$-0.0827011\pi$
$727$	7.03023	+	12.1767i	0.260737	+	0.451610i	−0.705701	+	0.708510i	$0.749368\pi$
$728$		0			0
$729$	−3.45315	+	26.7783i	−0.127894	+	0.991788i
$730$		0			0
$731$	−47.8061	−	12.8096i	−1.76817	−	0.473780i
$732$		0			0
$733$	0.233976	−	0.0626936i	0.00864209	−	0.00231564i	−0.254495	−	0.967074i	$-0.581909\pi$
$733$	0.233976	−	0.0626936i	0.00864209	−	0.00231564i	0.263138	+	0.964758i	$0.415243\pi$
$734$		0			0
$735$	3.34801	+	0.0715722i	0.123493	+	0.00263998i
$736$		0			0
$737$		−	21.0565i		−	0.775627i
$738$		0			0
$739$	6.77417	−	6.77417i	0.249192	−	0.249192i	−0.571447	−	0.820639i	$-0.693618\pi$
$739$	6.77417	−	6.77417i	0.249192	−	0.249192i	0.820639	+	0.571447i	$0.193618\pi$
$740$		0			0
$741$	−2.42544	−	0.705786i	−0.0891006	−	0.0259277i
$742$		0			0
$743$	5.26562	+	3.04011i	0.193177	+	0.111531i	0.593469	−	0.804857i	$-0.297758\pi$
$743$	5.26562	+	3.04011i	0.193177	+	0.111531i	−0.400292	+	0.916388i	$0.631091\pi$
$744$		0			0
$745$	−3.39524	+	1.96024i	−0.124392	+	0.0718178i
$746$		0			0
$747$	0.890964	+	4.00212i	0.0325987	+	0.146430i
$748$		0			0
$749$	9.60501	+	2.57365i	0.350959	+	0.0940393i
$750$		0			0
$751$	21.6001	+	12.4708i	0.788199	+	0.455067i	0.839328	−	0.543625i	$-0.182949\pi$
$751$	21.6001	+	12.4708i	0.788199	+	0.455067i	−0.0511293	+	0.998692i	$0.516282\pi$
$752$		0			0
$753$	0.923406	+	0.559778i	0.0336508	+	0.0203994i
$754$		0			0
$755$	−4.01206	−	4.01206i	−0.146014	−	0.146014i
$756$		0			0
$757$	27.5078	−	27.5078i	0.999789	−	0.999789i	−0.000211103	−	1.00000i	$-0.500067\pi$
$757$	27.5078	−	27.5078i	0.999789	−	0.999789i	1.00000		0.000211103i	$6.71963e-5\pi$
$758$		0			0
$759$	−14.5567	+	24.0126i	−0.528374	+	0.871602i
$760$		0			0
$761$	−3.41665	+	5.91781i	−0.123854	+	0.214521i	−0.921284	−	0.388890i	$-0.872859\pi$
$761$	−3.41665	+	5.91781i	−0.123854	+	0.214521i	0.797431	+	0.603411i	$0.206192\pi$
$762$		0			0
$763$	−0.146521	+	0.546823i	−0.00530440	+	0.0197963i
$764$		0			0
$765$	−4.10797	−	4.47511i	−0.148524	−	0.161798i
$766$		0			0
$767$	0.00723364	+	0.0125290i	0.000261192	+	0.000452397i
$768$		0			0
$769$	−1.16390	+	2.01594i	−0.0419714	+	0.0726966i	−0.886248	−	0.463211i	$-0.846697\pi$
$769$	−1.16390	+	2.01594i	−0.0419714	+	0.0726966i	0.844277	+	0.535908i	$0.180031\pi$
$770$		0			0
$771$	2.67466	−	9.19148i	0.0963256	−	0.331023i
$772$		0			0
$773$	4.66783	+	4.66783i	0.167890	+	0.167890i	0.786051	−	0.618161i	$-0.212122\pi$
$773$	4.66783	+	4.66783i	0.167890	+	0.167890i	−0.618161	+	0.786051i	$0.712122\pi$
$774$		0			0
$775$	17.7820			0.638749
$776$		0			0
$777$	−0.263971	+	12.3481i	−0.00946991	+	0.442984i
$778$		0			0
$779$	−0.634477	−	2.36790i	−0.0227325	−	0.0848389i
$780$		0			0
$781$	−9.57001	+	35.7158i	−0.342442	+	1.27801i
$782$		0			0
$783$	12.9838	+	26.2406i	0.464002	+	0.937764i
$784$		0			0
$785$	−2.47661	+	1.42987i	−0.0883942	+	0.0510344i
$786$		0			0
$787$	−7.60400	−	28.3785i	−0.271053	−	1.01158i	−0.958440	−	0.285293i	$-0.907909\pi$
$787$	−7.60400	−	28.3785i	−0.271053	−	1.01158i	0.687387	−	0.726291i	$-0.258758\pi$
$788$		0			0
$789$	−6.68965	−	6.98192i	−0.238158	−	0.248563i
$790$		0			0
$791$			3.05151i			0.108499i
$792$		0			0
$793$		−	17.4774i		−	0.620640i
$794$		0			0
$795$	−0.551696	+	1.89590i	−0.0195666	+	0.0672408i
$796$		0			0
$797$	12.9954	+	48.4997i	0.460322	+	1.71795i	0.671951	+	0.740596i	$0.265457\pi$
$797$	12.9954	+	48.4997i	0.460322	+	1.71795i	−0.211629	+	0.977350i	$0.567877\pi$
$798$		0			0
$799$	3.58808	−	2.07158i	0.126937	−	0.0732871i
$800$		0			0
$801$	−41.9855	+	21.9035i	−1.48349	+	0.773923i
$802$		0			0
$803$	−4.90227	+	18.2955i	−0.172997	+	0.645634i
$804$		0			0
$805$	0.406831	+	1.51831i	0.0143389	+	0.0535135i
$806$		0			0
$807$	−3.49249	−	2.11718i	−0.122942	−	0.0745284i
$808$		0			0
$809$	−54.3452			−1.91068			−0.955338	−	0.295515i	$-0.904509\pi$
$809$	−54.3452			−1.91068			−0.955338	+	0.295515i	$0.904509\pi$
$810$		0			0
$811$	22.9318	+	22.9318i	0.805245	+	0.805245i	0.983910	−	0.178665i	$-0.0571779\pi$
$811$	22.9318	+	22.9318i	0.805245	+	0.805245i	−0.178665	+	0.983910i	$0.557178\pi$
$812$		0			0
$813$	−39.1522	+	9.59884i	−1.37313	+	0.336646i
$814$		0			0
$815$	1.32664	−	2.29781i	0.0464701	−	0.0804886i
$816$		0			0
$817$	−3.22372	−	5.58364i	−0.112784	−	0.195347i
$818$		0			0
$819$	−3.55327	−	1.11689i	−0.124161	−	0.0390272i
$820$		0			0
$821$	−11.2724	+	42.0690i	−0.393408	+	1.46822i	0.431067	+	0.902320i	$0.358137\pi$
$821$	−11.2724	+	42.0690i	−0.393408	+	1.46822i	−0.824475	+	0.565899i	$0.808529\pi$
$822$		0			0
$823$	2.52571	−	4.37465i	0.0880406	−	0.152491i	−0.818642	−	0.574304i	$-0.805273\pi$
$823$	2.52571	−	4.37465i	0.0880406	−	0.152491i	0.906683	+	0.421813i	$0.138606\pi$
$824$		0			0
$825$	−9.48152	−	17.2644i	−0.330104	−	0.601070i
$826$		0			0
$827$	−27.8757	+	27.8757i	−0.969334	+	0.969334i	−0.999544	−	0.0302095i	$-0.990383\pi$
$827$	−27.8757	+	27.8757i	−0.969334	+	0.969334i	0.0302095	+	0.999544i	$0.490383\pi$
$828$		0			0
$829$	3.00281	+	3.00281i	0.104292	+	0.104292i	0.757327	−	0.653035i	$-0.226505\pi$
$829$	3.00281	+	3.00281i	0.104292	+	0.104292i	−0.653035	+	0.757327i	$0.726505\pi$
$830$		0			0
$831$	0.0262402	−	1.22747i	0.000910263	−	0.0425804i
$832$		0			0
$833$	37.6217	+	21.7209i	1.30352	+	0.752585i
$834$		0			0
$835$	−2.66667	−	0.714531i	−0.0922838	−	0.0247274i
$836$		0			0
$837$	3.69585	+	18.4523i	0.127747	+	0.637805i
$838$		0			0
$839$	−6.29143	+	3.63236i	−0.217204	+	0.125403i	−0.604655	−	0.796487i	$-0.706689\pi$
$839$	−6.29143	+	3.63236i	−0.217204	+	0.125403i	0.387451	+	0.921890i	$0.373356\pi$
$840$		0			0
$841$	2.37837	+	1.37315i	0.0820126	+	0.0473500i
$842$		0			0
$843$	−5.73200	+	5.49206i	−0.197420	+	0.189156i
$844$		0			0
$845$	−2.17480	+	2.17480i	−0.0748154	+	0.0748154i
$846$		0			0
$847$		−	4.21567i		−	0.144852i
$848$		0			0
$849$	−12.1078	−	22.0464i	−0.415538	−	0.756632i
$850$		0			0
$851$	64.4513	−	17.2697i	2.20936	−	0.591997i
$852$		0			0
$853$	−26.4188	−	7.07889i	−0.904562	−	0.242377i	−0.223587	−	0.974684i	$-0.571777\pi$
$853$	−26.4188	−	7.07889i	−0.904562	−	0.242377i	−0.680974	+	0.732307i	$0.738443\pi$
$854$		0			0
$855$	0.0338191	−	0.790634i	0.00115659	−	0.0270391i
$856$		0			0
$857$	3.27792	+	5.67752i	0.111971	+	0.193940i	0.916565	−	0.399886i	$-0.130950\pi$
$857$	3.27792	+	5.67752i	0.111971	+	0.193940i	−0.804594	+	0.593826i	$0.797617\pi$
$858$		0			0
$859$	33.2003	−	8.89601i	1.13278	−	0.303528i	0.356736	−	0.934205i	$-0.383890\pi$
$859$	33.2003	−	8.89601i	1.13278	−	0.303528i	0.776045	+	0.630677i	$0.217223\pi$
$860$		0			0
$861$	−0.860707	−	3.51069i	−0.0293328	−	0.119644i
$862$		0			0
$863$	39.5164			1.34515			0.672576	−	0.740028i	$-0.265188\pi$
$863$	39.5164			1.34515			0.672576	+	0.740028i	$0.265188\pi$
$864$		0			0
$865$	2.38418			0.0810646
$866$		0			0
$867$	−11.7532	−	47.9393i	−0.399158	−	1.62810i
$868$		0			0
$869$	19.8148	−	5.30936i	0.672171	−	0.180108i
$870$		0			0
$871$	−7.54456	−	13.0676i	−0.255638	−	0.442777i
$872$		0			0
$873$	23.3958	+	14.8757i	0.791828	+	0.503466i
$874$		0			0
$875$	−2.14957	−	0.575974i	−0.0726686	−	0.0194715i
$876$		0			0
$877$	−46.2823	+	12.4013i	−1.56284	+	0.418763i	−0.933562	−	0.358415i	$-0.883317\pi$
$877$	−46.2823	+	12.4013i	−1.56284	+	0.418763i	−0.629281	+	0.777178i	$0.716651\pi$
$878$		0			0
$879$	−5.21483	−	9.49542i	−0.175892	−	0.320273i
$880$		0			0
$881$			23.6718i			0.797522i	0.917055	+	0.398761i	$0.130560\pi$
$881$			23.6718i			0.797522i	−0.917055	+	0.398761i	$0.869440\pi$
$882$		0			0
$883$	7.40173	−	7.40173i	0.249088	−	0.249088i	−0.571508	−	0.820596i	$-0.693641\pi$
$883$	7.40173	−	7.40173i	0.249088	−	0.249088i	0.820596	+	0.571508i	$0.193641\pi$
$884$		0			0
$885$	−0.00327259	+	0.00313560i	−0.000110007	+	0.000105402i
$886$		0			0
$887$	19.6764	+	11.3602i	0.660669	+	0.381438i	0.792532	−	0.609830i	$-0.208762\pi$
$887$	19.6764	+	11.3602i	0.660669	+	0.381438i	−0.131863	+	0.991268i	$0.542096\pi$
$888$		0			0
$889$	1.15825	−	0.668713i	0.0388463	−	0.0224279i
$890$		0			0
$891$	15.9445	−	13.4272i	0.534162	−	0.449828i
$892$		0			0
$893$	0.521341	+	0.139693i	0.0174460	+	0.00467465i
$894$		0			0
$895$	2.93931	+	1.69701i	0.0982504	+	0.0567249i
$896$		0			0
$897$	−0.430068	+	20.1177i	−0.0143595	+	0.671712i
$898$		0			0
$899$	14.4292	+	14.4292i	0.481240	+	0.481240i
$900$		0			0
$901$	−18.1123	+	18.1123i	−0.603409	+	0.603409i
$902$		0			0
$903$	−4.57635	−	8.33285i	−0.152291	−	0.277300i
$904$		0			0
$905$	3.08372	−	5.34117i	0.102506	−	0.177546i
$906$		0			0
$907$	7.73443	−	28.8653i	0.256818	−	0.958456i	−0.710253	−	0.703947i	$-0.751419\pi$
$907$	7.73443	−	28.8653i	0.256818	−	0.958456i	0.967070	−	0.254509i	$-0.0819140\pi$
$908$		0			0
$909$	10.2959	+	46.2479i	0.341492	+	1.53395i
$910$		0			0
$911$	2.23081	+	3.86388i	0.0739100	+	0.128016i	0.900612	−	0.434625i	$-0.143119\pi$
$911$	2.23081	+	3.86388i	0.0739100	+	0.128016i	−0.826702	+	0.562640i	$0.809786\pi$
$912$		0			0
$913$	1.58272	−	2.74135i	0.0523804	−	0.0907255i
$914$		0			0
$915$	5.31782	−	1.30376i	0.175802	−	0.0431009i
$916$		0			0
$917$	−2.12015	−	2.12015i	−0.0700134	−	0.0700134i
$918$		0			0
$919$	43.4889			1.43457			0.717283	−	0.696782i	$-0.245385\pi$
$919$	43.4889			1.43457			0.717283	+	0.696782i	$0.245385\pi$
$920$		0			0
$921$	9.46912	+	5.74028i	0.312018	+	0.189149i
$922$		0			0
$923$	6.85787	+	25.5939i	0.225730	+	0.842435i
$924$		0			0
$925$	−12.1137	+	45.2089i	−0.398295	+	1.48646i
$926$		0			0
$927$	−1.44616	+	33.8087i	−0.0474980	+	1.11042i
$928$		0			0
$929$	33.8981	−	19.5711i	1.11216	−	0.642107i	0.172774	−	0.984962i	$-0.444727\pi$
$929$	33.8981	−	19.5711i	1.11216	−	0.642107i	0.939389	+	0.342854i	$0.111394\pi$
$930$		0			0
$931$	1.46471	+	5.46638i	0.0480040	+	0.179153i
$932$		0			0
$933$	6.12664	−	21.0542i	0.200577	−	0.689284i
$934$		0			0
$935$			4.68992i			0.153377i
$936$		0			0
$937$		−	34.6928i		−	1.13336i	−0.823936	−	0.566682i	$-0.808227\pi$
$937$		−	34.6928i		−	1.13336i	0.823936	−	0.566682i	$-0.191773\pi$
$938$		0			0
$939$	23.0078	+	24.0130i	0.750831	+	0.783634i
$940$		0			0
$941$	−6.32091	−	23.5900i	−0.206056	−	0.769011i	−0.989125	−	0.147076i	$-0.953014\pi$
$941$	−6.32091	−	23.5900i	−0.206056	−	0.769011i	0.783069	−	0.621934i	$-0.213653\pi$
$942$		0			0
$943$	−16.9118	+	9.76401i	−0.550723	+	0.317960i
$944$		0			0
$945$	0.0747714	−	1.16447i	0.00243231	−	0.0378801i
$946$		0			0
$947$	−13.8890	+	51.8344i	−0.451331	+	1.68439i	0.247325	+	0.968933i	$0.420449\pi$
$947$	−13.8890	+	51.8344i	−0.451331	+	1.68439i	−0.698656	+	0.715458i	$0.746218\pi$
$948$		0			0
$949$	3.51297	+	13.1106i	0.114036	+	0.425587i
$950$		0			0
$951$	0.424764	−	19.8696i	0.0137739	−	0.644317i
$952$		0			0
$953$	40.6369			1.31636			0.658180	−	0.752861i	$-0.271327\pi$
$953$	40.6369			1.31636			0.658180	+	0.752861i	$0.271327\pi$
$954$		0			0
$955$	−4.34661	−	4.34661i	−0.140653	−	0.140653i
$956$		0			0
$957$	6.31542	−	21.7029i	0.204148	−	0.701556i
$958$		0			0
$959$	−0.296615	+	0.513752i	−0.00957819	+	0.0165899i
$960$		0			0
$961$	−8.94172	−	15.4875i	−0.288443	−	0.499597i
$962$		0			0
$963$	−11.9583	+	38.0441i	−0.385350	+	1.22595i
$964$		0			0
$965$	−0.368808	+	1.37641i	−0.0118724	+	0.0443082i
$966$		0			0
$967$	2.97787	−	5.15783i	0.0957620	−	0.165865i	−0.814164	−	0.580634i	$-0.802805\pi$
$967$	2.97787	−	5.15783i	0.0957620	−	0.165865i	0.909926	+	0.414770i	$0.136138\pi$
$968$		0			0
$969$	5.32177	−	8.77876i	0.170960	−	0.282014i
$970$		0			0
$971$	−17.0165	+	17.0165i	−0.546085	+	0.546085i	−0.925306	−	0.379221i	$-0.876192\pi$
$971$	−17.0165	+	17.0165i	−0.546085	+	0.546085i	0.379221	+	0.925306i	$0.376192\pi$
$972$		0			0
$973$	9.69630	+	9.69630i	0.310849	+	0.310849i
$974$		0			0
$975$	−12.0700	−	7.31697i	−0.386550	−	0.234330i
$976$		0			0
$977$	−10.2439	−	5.91431i	−0.327731	−	0.189215i	0.327102	−	0.944989i	$-0.393928\pi$
$977$	−10.2439	−	5.91431i	−0.327731	−	0.189215i	−0.654833	+	0.755773i	$0.727261\pi$
$978$		0			0
$979$	35.3147	+	9.46254i	1.12866	+	0.302424i
$980$		0			0
$981$	−2.16589	−	0.680796i	−0.0691515	−	0.0217361i
$982$		0			0
$983$	−38.2947	+	22.1094i	−1.22141	+	0.705181i	−0.965218	−	0.261445i	$-0.915801\pi$
$983$	−38.2947	+	22.1094i	−1.22141	+	0.705181i	−0.256192	+	0.966626i	$0.582468\pi$
$984$		0			0
$985$	−2.44603	−	1.41222i	−0.0779370	−	0.0449970i
$986$		0			0
$987$	0.764146	+	0.222361i	0.0243230	+	0.00707784i
$988$		0			0
$989$	−36.3170	+	36.3170i	−1.15481	+	1.15481i
$990$		0			0
$991$			21.3026i			0.676701i	0.941020	+	0.338350i	$0.109869\pi$
$991$			21.3026i			0.676701i	−0.941020	+	0.338350i	$0.890131\pi$
$992$		0			0
$993$	−34.0379	−	0.727646i	−1.08016	−	0.0230911i
$994$		0			0
$995$	−6.62295	+	1.77461i	−0.209962	+	0.0562590i
$996$		0			0
$997$	−29.1547	−	7.81197i	−0.923338	−	0.247408i	−0.234326	−	0.972158i	$-0.575288\pi$
$997$	−29.1547	−	7.81197i	−0.923338	−	0.247408i	−0.689012	+	0.724750i	$0.741955\pi$
$998$		0			0
$999$	−49.4308	−	3.17399i	−1.56392	−	0.100421i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.y.a.239.12		88
3.2	odd	2		1728.2.z.a.1583.11		88
4.3	odd	2		144.2.u.a.131.21	yes	88
9.2	odd	6	inner	576.2.y.a.47.2		88
9.7	even	3		1728.2.z.a.1007.11		88
12.11	even	2		432.2.v.a.179.2		88
16.5	even	4		144.2.u.a.59.15	yes	88
16.11	odd	4	inner	576.2.y.a.527.2		88
36.7	odd	6		432.2.v.a.35.8		88
36.11	even	6		144.2.u.a.83.15	yes	88
48.5	odd	4		432.2.v.a.395.8		88
48.11	even	4		1728.2.z.a.719.11		88
144.11	even	12	inner	576.2.y.a.335.12		88
144.43	odd	12		1728.2.z.a.143.11		88
144.101	odd	12		144.2.u.a.11.21	✓	88
144.133	even	12		432.2.v.a.251.2		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.21	✓	88	144.101	odd	12
144.2.u.a.59.15	yes	88	16.5	even	4
144.2.u.a.83.15	yes	88	36.11	even	6
144.2.u.a.131.21	yes	88	4.3	odd	2
432.2.v.a.35.8		88	36.7	odd	6
432.2.v.a.179.2		88	12.11	even	2
432.2.v.a.251.2		88	144.133	even	12
432.2.v.a.395.8		88	48.5	odd	4
576.2.y.a.47.2		88	9.2	odd	6	inner
576.2.y.a.239.12		88	1.1	even	1	trivial
576.2.y.a.335.12		88	144.11	even	12	inner
576.2.y.a.527.2		88	16.11	odd	4	inner
1728.2.z.a.143.11		88	144.43	odd	12
1728.2.z.a.719.11		88	48.11	even	4
1728.2.z.a.1007.11		88	9.7	even	3
1728.2.z.a.1583.11		88	3.2	odd	2

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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.412428 + 1.68223i) q^{3} +(0.289971 - 0.0776974i) q^{5} +(0.374023 + 0.647827i) q^{7} +(-2.65981 + 1.38760i) q^{9} +O(q^{10})\)	\(q+(0.412428 + 1.68223i) q^{3} +(0.289971 - 0.0776974i) q^{5} +(0.374023 + 0.647827i) q^{7} +(-2.65981 + 1.38760i) q^{9} +(2.23720 + 0.599457i) q^{11} +(1.60318 - 0.429571i) q^{13} +(0.250297 + 0.455753i) q^{15} +6.74518i q^{17} +(-0.621335 + 0.621335i) q^{19} +(-0.935537 + 0.896375i) q^{21} +(6.06191 + 3.49985i) q^{23} +(-4.25208 + 2.45494i) q^{25} +(-3.43124 - 3.90212i) q^{27} +(-5.44240 - 1.45829i) q^{29} +(-3.13647 - 1.81084i) q^{31} +(-0.0857395 + 4.01073i) q^{33} +(0.158790 + 0.158790i) q^{35} +(6.74053 - 6.74053i) q^{37} +(1.38383 + 2.51975i) q^{39} +(-1.39492 + 2.41607i) q^{41} +(-1.89907 + 7.08744i) q^{43} +(-0.663453 + 0.609023i) q^{45} +(-0.307120 - 0.531947i) q^{47} +(3.22021 - 5.57757i) q^{49} +(-11.3470 + 2.78190i) q^{51} +(2.68523 + 2.68523i) q^{53} +0.695300 q^{55} +(-1.30149 - 0.788974i) q^{57} +(0.00225603 + 0.00841962i) q^{59} +(2.72542 - 10.1714i) q^{61} +(-1.89375 - 1.20410i) q^{63} +(0.431499 - 0.249126i) q^{65} +(-2.35300 - 8.78151i) q^{67} +(-3.38745 + 11.6410i) q^{69} +15.9645i q^{71} +8.17785i q^{73} +(-5.88346 - 6.14050i) q^{75} +(0.448421 + 1.67353i) q^{77} +(7.67035 - 4.42848i) q^{79} +(5.14914 - 7.38149i) q^{81} +(0.353727 - 1.32013i) q^{83} +(0.524083 + 1.95590i) q^{85} +(0.208577 - 9.75681i) q^{87} +15.7852 q^{89} +(0.877914 + 0.877914i) q^{91} +(1.75268 - 6.02310i) q^{93} +(-0.131893 + 0.228445i) q^{95} +(-4.62075 - 8.00338i) q^{97} +(-6.78233 + 1.50990i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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