LMFDB - Embedded newform 576.2.y.a.47.2

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			47.2
Character	$\chi$	$=$	576.47
Dual form			576.2.y.a.527.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.68223 - 0.412428i) q^{3} +(0.0776974 - 0.289971i) q^{5} +(0.374023 - 0.647827i) q^{7} +(2.65981 + 1.38760i) q^{9} +O(q^{10})$	\(q+(-1.68223 - 0.412428i) q^{3} +(0.0776974 - 0.289971i) q^{5} +(0.374023 - 0.647827i) q^{7} +(2.65981 + 1.38760i) q^{9} +(0.599457 + 2.23720i) q^{11} +(-0.429571 + 1.60318i) q^{13} +(-0.250297 + 0.455753i) q^{15} -6.74518i q^{17} +(-0.621335 + 0.621335i) q^{19} +(-0.896375 + 0.935537i) q^{21} +(6.06191 - 3.49985i) q^{23} +(4.25208 + 2.45494i) q^{25} +(-3.90212 - 3.43124i) q^{27} +(-1.45829 - 5.44240i) q^{29} +(3.13647 - 1.81084i) q^{31} +(-0.0857395 - 4.01073i) q^{33} +(-0.158790 - 0.158790i) q^{35} +(6.74053 - 6.74053i) q^{37} +(1.38383 - 2.51975i) q^{39} +(1.39492 + 2.41607i) q^{41} +(7.08744 - 1.89907i) q^{43} +(0.609023 - 0.663453i) q^{45} +(0.307120 - 0.531947i) q^{47} +(3.22021 + 5.57757i) q^{49} +(-2.78190 + 11.3470i) q^{51} +(-2.68523 - 2.68523i) q^{53} +0.695300 q^{55} +(1.30149 - 0.788974i) q^{57} +(0.00841962 + 0.00225603i) q^{59} +(-10.1714 + 2.72542i) q^{61} +(1.89375 - 1.20410i) q^{63} +(0.431499 + 0.249126i) q^{65} +(8.78151 + 2.35300i) q^{67} +(-11.6410 + 3.38745i) q^{69} -15.9645i q^{71} +8.17785i q^{73} +(-6.14050 - 5.88346i) q^{75} +(1.67353 + 0.448421i) q^{77} +(-7.67035 - 4.42848i) q^{79} +(5.14914 + 7.38149i) q^{81} +(1.32013 - 0.353727i) q^{83} +(-1.95590 - 0.524083i) q^{85} +(0.208577 + 9.75681i) q^{87} -15.7852 q^{89} +(0.877914 + 0.877914i) q^{91} +(-6.02310 + 1.75268i) q^{93} +(0.131893 + 0.228445i) q^{95} +(-4.62075 + 8.00338i) q^{97} +(-1.50990 + 6.78233i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

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

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
$3$	−1.68223	−	0.412428i	−0.971237	−	0.238116i
$3$	−1.68223	−	0.412428i	−0.971237	−	0.238116i
$4$		0			0
$5$	0.0776974	−	0.289971i	0.0347473	−	0.129679i	−0.946373	−	0.323075i	$-0.895283\pi$
$5$	0.0776974	−	0.289971i	0.0347473	−	0.129679i	0.981121	+	0.193396i	$0.0619502\pi$
$6$		0			0
$7$	0.374023	−	0.647827i	0.141367	−	0.244855i	−0.786644	−	0.617406i	$-0.788183\pi$
$7$	0.374023	−	0.647827i	0.141367	−	0.244855i	0.928012	+	0.372551i	$0.121517\pi$
$8$		0			0
$9$	2.65981	+	1.38760i	0.886602	+	0.462533i
$10$		0			0
$11$	0.599457	+	2.23720i	0.180743	+	0.674542i	0.995502	+	0.0947421i	$0.0302027\pi$
$11$	0.599457	+	2.23720i	0.180743	+	0.674542i	−0.814759	+	0.579800i	$0.803131\pi$
$12$		0			0
$13$	−0.429571	+	1.60318i	−0.119142	+	0.444642i	−0.999563	−	0.0295491i	$-0.990593\pi$
$13$	−0.429571	+	1.60318i	−0.119142	+	0.444642i	0.880422	+	0.474191i	$0.157260\pi$
$14$		0			0
$15$	−0.250297	+	0.455753i	−0.0646264	+	0.117675i
$16$		0			0
$17$		−	6.74518i		−	1.63595i	−0.575256	−	0.817973i	$-0.695098\pi$
$17$		−	6.74518i		−	1.63595i	0.575256	−	0.817973i	$-0.304902\pi$
$18$		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
$21$	−0.896375	+	0.935537i	−0.195605	+	0.204151i
$22$		0			0
$23$	6.06191	−	3.49985i	1.26400	−	0.729769i	0.290151	−	0.956981i	$-0.406294\pi$
$23$	6.06191	−	3.49985i	1.26400	−	0.729769i	0.973845	+	0.227212i	$0.0729611\pi$
$24$		0			0
$25$	4.25208	+	2.45494i	0.850416	+	0.490988i
$26$		0			0
$27$	−3.90212	−	3.43124i	−0.750964	−	0.660343i
$28$		0			0
$29$	−1.45829	−	5.44240i	−0.270797	−	1.01063i	−0.958606	−	0.284736i	$-0.908094\pi$
$29$	−1.45829	−	5.44240i	−0.270797	−	1.01063i	0.687809	−	0.725892i	$-0.258573\pi$
$30$		0			0
$31$	3.13647	−	1.81084i	0.563326	−	0.325236i	−0.191153	−	0.981560i	$-0.561223\pi$
$31$	3.13647	−	1.81084i	0.563326	−	0.325236i	0.754479	+	0.656324i	$0.227889\pi$
$32$		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	$-0.0967624\pi$
$41$	1.39492	+	2.41607i	0.217850	+	0.377327i	−0.736301	+	0.676655i	$0.763429\pi$
$42$		0			0
$43$	7.08744	−	1.89907i	1.08082	−	0.289606i	0.325891	−	0.945407i	$-0.394336\pi$
$43$	7.08744	−	1.89907i	1.08082	−	0.289606i	0.754934	+	0.655801i	$0.227669\pi$
$44$		0			0
$45$	0.609023	−	0.663453i	0.0907878	−	0.0989017i
$46$		0			0
$47$	0.307120	−	0.531947i	0.0447980	−	0.0775924i	−0.842757	−	0.538294i	$-0.819069\pi$
$47$	0.307120	−	0.531947i	0.0447980	−	0.0775924i	0.887555	+	0.460702i	$0.152402\pi$
$48$		0			0
$49$	3.22021	+	5.57757i	0.460031	+	0.796796i
$50$		0			0
$51$	−2.78190	+	11.3470i	−0.389544	+	1.58889i
$52$		0			0
$53$	−2.68523	−	2.68523i	−0.368844	−	0.368844i	0.498211	−	0.867056i	$-0.333990\pi$
$53$	−2.68523	−	2.68523i	−0.368844	−	0.368844i	−0.867056	+	0.498211i	$0.833990\pi$
$54$		0			0
$55$	0.695300			0.0937542
$56$		0			0
$57$	1.30149	−	0.788974i	0.172386	−	0.104502i
$58$		0			0
$59$	0.00841962	+	0.00225603i	0.00109614	+	0.000293710i	0.259367	−	0.965779i	$-0.416486\pi$
$59$	0.00841962	+	0.00225603i	0.00109614	+	0.000293710i	−0.258271	+	0.966073i	$0.583153\pi$
$60$		0			0
$61$	−10.1714	+	2.72542i	−1.30232	+	0.348955i	−0.842326	−	0.538969i	$-0.818814\pi$
$61$	−10.1714	+	2.72542i	−1.30232	+	0.348955i	−0.459991	+	0.887924i	$0.652147\pi$
$62$		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
$67$	8.78151	+	2.35300i	1.07283	+	0.287464i	0.751656	−	0.659555i	$-0.229255\pi$
$67$	8.78151	+	2.35300i	1.07283	+	0.287464i	0.321176	+	0.947020i	$0.395922\pi$
$68$		0			0
$69$	−11.6410	+	3.38745i	−1.40141	+	0.407801i
$70$		0			0
$71$		−	15.9645i		−	1.89463i	−0.320297	−	0.947317i	$-0.603783\pi$
$71$		−	15.9645i		−	1.89463i	0.320297	−	0.947317i	$-0.396217\pi$
$72$		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
$75$	−6.14050	−	5.88346i	−0.709044	−	0.679363i
$76$		0			0
$77$	1.67353	+	0.448421i	0.190717	+	0.0511023i
$78$		0			0
$79$	−7.67035	−	4.42848i	−0.862982	−	0.498243i	0.00202794	−	0.999998i	$-0.499354\pi$
$79$	−7.67035	−	4.42848i	−0.862982	−	0.498243i	−0.865010	+	0.501755i	$0.832688\pi$
$80$		0			0
$81$	5.14914	+	7.38149i	0.572126	+	0.820166i
$82$		0			0
$83$	1.32013	−	0.353727i	0.144903	−	0.0388266i	−0.185638	−	0.982618i	$-0.559435\pi$
$83$	1.32013	−	0.353727i	0.144903	−	0.0388266i	0.330541	+	0.943791i	$0.392769\pi$
$84$		0			0
$85$	−1.95590	−	0.524083i	−0.212148	−	0.0568448i
$86$		0			0
$87$	0.208577	+	9.75681i	0.0223618	+	1.04604i
$88$		0			0
$89$	−15.7852			−1.67323			−0.836613	−	0.547794i	$-0.815468\pi$
$89$	−15.7852			−1.67323			−0.836613	+	0.547794i	$0.815468\pi$
$90$		0			0
$91$	0.877914	+	0.877914i	0.0920304	+	0.0920304i
$92$		0			0
$93$	−6.02310	+	1.75268i	−0.624567	+	0.181745i
$94$		0			0
$95$	0.131893	+	0.228445i	0.0135319	+	0.0234380i
$96$		0			0
$97$	−4.62075	+	8.00338i	−0.469166	+	0.812620i	−0.999379	−	0.0352448i	$-0.988779\pi$
$97$	−4.62075	+	8.00338i	−0.469166	+	0.812620i	0.530212	+	0.847865i	$0.322112\pi$
$98$		0			0
$99$	−1.50990	+	6.78233i	−0.151751	+	0.681650i
$100$		0			0
$101$	15.2552	−	4.08762i	1.51795	−	0.406734i	0.598885	−	0.800835i	$-0.295611\pi$
$101$	15.2552	−	4.08762i	1.51795	−	0.406734i	0.919067	+	0.394102i	$0.128944\pi$
$102$		0			0
$103$	5.63994	+	9.76866i	0.555720	+	0.962535i	0.997847	+	0.0655828i	$0.0208906\pi$
$103$	5.63994	+	9.76866i	0.555720	+	0.962535i	−0.442127	+	0.896952i	$0.645776\pi$
$104$		0			0
$105$	0.201632	+	0.332611i	0.0196773	+	0.0324595i
$106$		0			0
$107$	−9.39963	+	9.39963i	−0.908696	+	0.908696i	−0.996167	−	0.0874707i	$-0.972122\pi$
$107$	−9.39963	+	9.39963i	−0.908696	+	0.908696i	0.0874707	+	0.996167i	$0.472122\pi$
$108$		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	−0.324541	−	0.945872i	$-0.605210\pi$
$113$	3.53279	−	2.03966i	0.332337	−	0.191875i	0.656878	+	0.753997i	$0.271877\pi$
$114$		0			0
$115$	−0.543858	−	2.02971i	−0.0507150	−	0.189271i
$116$		0			0
$117$	−3.36715	+	3.66808i	−0.311293	+	0.339114i
$118$		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
$123$	−1.35012	−	4.63969i	−0.121736	−	0.418347i
$124$		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
$131$	−1.03741	+	3.87165i	−0.0906386	+	0.338268i	−0.996322	−	0.0856865i	$-0.972692\pi$
$131$	−1.03741	+	3.87165i	−0.0906386	+	0.338268i	0.905684	+	0.423954i	$0.139358\pi$
$132$		0			0
$133$	0.170124	+	0.634911i	0.0147516	+	0.0550538i
$134$		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	$-0.844119\pi$
$137$	−0.396519	+	0.686792i	−0.0338769	+	0.0586766i	0.848590	+	0.529051i	$0.177452\pi$
$138$		0			0
$139$	−4.74448	+	17.7067i	−0.402422	+	1.50186i	0.406340	+	0.913722i	$0.366805\pi$
$139$	−4.74448	+	17.7067i	−0.402422	+	1.50186i	−0.808762	+	0.588137i	$0.799862\pi$
$140$		0			0
$141$	−0.736036	+	0.768193i	−0.0619854	+	0.0646935i
$142$		0			0
$143$	−3.84415			−0.321464
$144$		0			0
$145$	−1.69144			−0.140467
$146$		0			0
$147$	−3.11680	−	10.7109i	−0.257069	−	0.883418i
$148$		0			0
$149$	−3.38007	+	12.6146i	−0.276906	+	1.03343i	0.677647	+	0.735388i	$0.263000\pi$
$149$	−3.38007	+	12.6146i	−0.276906	+	1.03343i	−0.954553	+	0.298041i	$0.903667\pi$
$150$		0			0
$151$	−9.45023	+	16.3683i	−0.769049	+	1.33203i	0.169030	+	0.985611i	$0.445937\pi$
$151$	−9.45023	+	16.3683i	−0.769049	+	1.33203i	−0.938079	+	0.346421i	$0.887397\pi$
$152$		0			0
$153$	9.35961	−	17.9409i	0.756679	−	1.45043i
$154$		0			0
$155$	−0.281395	−	1.05018i	−0.0226022	−	0.0843526i
$156$		0			0
$157$	2.46555	−	9.20155i	0.196772	−	0.734364i	−0.795029	−	0.606572i	$-0.792544\pi$
$157$	2.46555	−	9.20155i	0.196772	−	0.734364i	0.991801	−	0.127792i	$-0.0407891\pi$
$158$		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
$165$	−1.16965	−	0.286761i	−0.0910575	−	0.0223243i
$166$		0			0
$167$	−7.96426	+	4.59817i	−0.616293	+	0.355817i	−0.775424	−	0.631441i	$-0.782464\pi$
$167$	−7.96426	+	4.59817i	−0.616293	+	0.355817i	0.159132	+	0.987257i	$0.449131\pi$
$168$		0			0
$169$	8.87267	+	5.12264i	0.682513	+	0.394049i
$170$		0			0
$171$	−2.51480	+	0.790467i	−0.192311	+	0.0604485i
$172$		0			0
$173$	2.05554	+	7.67137i	0.156280	+	0.583243i	0.998992	+	0.0448800i	$0.0142906\pi$
$173$	2.05554	+	7.67137i	0.156280	+	0.583243i	−0.842713	+	0.538363i	$0.819043\pi$
$174$		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	0.342121	−	0.939656i	$-0.388855\pi$
$179$	−7.99447	−	7.99447i	−0.597535	−	0.597535i	−0.939656	+	0.342121i	$0.888855\pi$
$180$		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
$187$	15.0903	−	4.04344i	1.10351	−	0.295686i
$188$		0			0
$189$	−3.68233	+	1.24454i	−0.267850	+	0.0905268i
$190$		0			0
$191$	10.2382	−	17.7332i	0.740813	−	1.28313i	−0.211312	−	0.977419i	$-0.567774\pi$
$191$	10.2382	−	17.7332i	0.740813	−	1.28313i	0.952125	−	0.305708i	$-0.0988930\pi$
$192$		0			0
$193$	−2.37336	−	4.11078i	−0.170838	−	0.295901i	0.767875	−	0.640600i	$-0.221314\pi$
$193$	−2.37336	−	4.11078i	−0.170838	−	0.295901i	−0.938713	+	0.344699i	$0.887981\pi$
$194$		0			0
$195$	−0.623134	−	0.597050i	−0.0446236	−	0.0427556i
$196$		0			0
$197$	6.65282	+	6.65282i	0.473994	+	0.473994i	0.903205	−	0.429210i	$-0.141208\pi$
$197$	6.65282	+	6.65282i	0.473994	+	0.473994i	−0.429210	+	0.903205i	$0.641208\pi$
$198$		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
$203$	−4.07116	−	1.09087i	−0.285740	−	0.0765637i
$204$		0			0
$205$	0.808971	−	0.216763i	0.0565010	−	0.0151394i
$206$		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
$211$	−14.8119	−	3.96884i	−1.01969	−	0.273226i	−0.290019	−	0.957021i	$-0.593662\pi$
$211$	−14.8119	−	3.96884i	−1.01969	−	0.273226i	−0.729674	+	0.683795i	$0.760328\pi$
$212$		0			0
$213$	−6.58420	+	26.8559i	−0.451142	+	1.84014i
$214$		0			0
$215$		−	2.20270i		−	0.150223i
$216$		0			0
$217$		−	2.70918i		−	0.183911i
$218$		0			0
$219$	3.37277	−	13.7570i	0.227911	−	0.929614i
$220$		0			0
$221$	10.8137	+	2.89753i	0.727411	+	0.194909i
$222$		0			0
$223$	−6.39965	−	3.69484i	−0.428552	−	0.247425i	0.270178	−	0.962811i	$-0.412918\pi$
$223$	−6.39965	−	3.69484i	−0.428552	−	0.247425i	−0.698730	+	0.715386i	$0.746251\pi$
$224$		0			0
$225$	7.90324	+	12.4298i	0.526882	+	0.828657i
$226$		0			0
$227$	20.6122	−	5.52301i	1.36808	−	0.366575i	0.501301	−	0.865273i	$-0.332855\pi$
$227$	20.6122	−	5.52301i	1.36808	−	0.366575i	0.866776	+	0.498698i	$0.166188\pi$
$228$		0			0
$229$	−17.7978	−	4.76891i	−1.17611	−	0.315138i	−0.382729	−	0.923861i	$-0.625016\pi$
$229$	−17.7978	−	4.76891i	−1.17611	−	0.315138i	−0.793383	+	0.608722i	$0.791682\pi$
$230$		0			0
$231$	−2.63032	−	1.44456i	−0.173063	−	0.0950450i
$232$		0			0
$233$	−14.3249			−0.938455			−0.469228	−	0.883077i	$-0.655468\pi$
$233$	−14.3249			−0.938455			−0.469228	+	0.883077i	$0.655468\pi$
$234$		0			0
$235$	−0.130387	−	0.130387i	−0.00850548	−	0.00850548i
$236$		0			0
$237$	11.0769	+	10.6132i	0.719520	+	0.689401i
$238$		0			0
$239$	11.4921	+	19.9049i	0.743364	+	1.28754i	0.950955	+	0.309328i	$0.100104\pi$
$239$	11.4921	+	19.9049i	0.743364	+	1.28754i	−0.207592	+	0.978216i	$0.566562\pi$
$240$		0			0
$241$	10.2735	−	17.7943i	0.661777	−	1.14623i	−0.318372	−	0.947966i	$-0.603136\pi$
$241$	10.2735	−	17.7943i	0.661777	−	1.14623i	0.980148	−	0.198265i	$-0.0635306\pi$
$242$		0			0
$243$	−5.61770	−	14.5410i	−0.360376	−	0.932807i
$244$		0			0
$245$	1.86754	−	0.500405i	0.119312	−	0.0319697i
$246$		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	−0.720883	−	0.693057i	$-0.756263\pi$
$251$	−0.440838	+	0.440838i	−0.0278255	+	0.0278255i	0.693057	+	0.720883i	$0.256263\pi$
$252$		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	−0.641798	−	0.766874i	$-0.721811\pi$
$257$	−4.78636	+	2.76341i	−0.298565	+	0.172377i	0.343233	+	0.939250i	$0.388478\pi$
$258$		0			0
$259$	−1.84558	−	6.88781i	−0.114679	−	0.427987i
$260$		0			0
$261$	3.67311	−	16.4992i	0.227360	−	1.02128i
$262$		0			0
$263$	−4.83474	−	2.79134i	−0.298123	−	0.172121i	0.343477	−	0.939161i	$-0.388395\pi$
$263$	−4.83474	−	2.79134i	−0.298123	−	0.172121i	−0.641599	+	0.767040i	$0.721729\pi$
$264$		0			0
$265$	−0.987272	+	0.570002i	−0.0606476	+	0.0350149i
$266$		0			0
$267$	26.5543	+	6.51026i	1.62510	+	0.398421i
$268$		0			0
$269$	1.66733	−	1.66733i	0.101659	−	0.101659i	−0.654448	−	0.756107i	$-0.727099\pi$
$269$	1.66733	−	1.66733i	0.101659	−	0.101659i	0.756107	+	0.654448i	$0.227099\pi$
$270$		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
$275$	−2.94326	+	10.9844i	−0.177485	+	0.662384i
$276$		0			0
$277$	0.183461	+	0.684687i	0.0110231	+	0.0411389i	0.971218	−	0.238191i	$-0.0765544\pi$
$277$	0.183461	+	0.684687i	0.0110231	+	0.0411389i	−0.960195	+	0.279330i	$0.909888\pi$
$278$		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	$-0.876985\pi$
$281$	−2.29162	+	3.96921i	−0.136707	+	0.236783i	0.789541	+	0.613697i	$0.210318\pi$
$282$		0			0
$283$	3.75850	−	14.0269i	0.223420	−	0.833814i	−0.759612	−	0.650377i	$-0.774611\pi$
$283$	3.75850	−	14.0269i	0.223420	−	0.833814i	0.983031	−	0.183437i	$-0.0587224\pi$
$284$		0			0
$285$	−0.127657	−	0.438694i	−0.00756176	−	0.0259860i
$286$		0			0
$287$	2.08693			0.123187
$288$		0			0
$289$	−28.4974			−1.67632
$290$		0			0
$291$	11.0740	−	11.5578i	0.649169	−	0.677531i
$292$		0			0
$293$	−1.61879	+	6.04141i	−0.0945708	+	0.352943i	−0.996954	−	0.0779914i	$-0.975149\pi$
$293$	−1.61879	+	6.04141i	−0.0945708	+	0.352943i	0.902383	+	0.430934i	$0.141816\pi$
$294$		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
$299$	3.00687	+	11.2218i	0.173892	+	0.648972i
$300$		0			0
$301$	1.42059	−	5.30173i	0.0818817	−	0.305587i
$302$		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
$309$	−5.45881	−	18.7592i	−0.310541	−	1.06718i
$310$		0			0
$311$	−10.9637	+	6.32992i	−0.621697	+	0.358937i	−0.777529	−	0.628847i	$-0.783527\pi$
$311$	−10.9637	+	6.32992i	−0.621697	+	0.358937i	0.155832	+	0.987784i	$0.450194\pi$
$312$		0			0
$313$	−16.6282	−	9.60027i	−0.939879	−	0.542640i	−0.0499568	−	0.998751i	$-0.515908\pi$
$313$	−16.6282	−	9.60027i	−0.939879	−	0.542640i	−0.889922	+	0.456112i	$0.849242\pi$
$314$		0			0
$315$	−0.202014	−	0.642688i	−0.0113822	−	0.0362114i
$316$		0			0
$317$	−2.96978	−	11.0834i	−0.166800	−	0.622504i	−0.997804	−	0.0662384i	$-0.978900\pi$
$317$	−2.96978	−	11.0834i	−0.166800	−	0.622504i	0.831004	−	0.556266i	$-0.187766\pi$
$318$		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
$331$	18.9865	−	5.08741i	1.04359	−	0.279630i	0.303991	−	0.952675i	$-0.401681\pi$
$331$	18.9865	−	5.08741i	1.04359	−	0.279630i	0.739601	+	0.673045i	$0.235014\pi$
$332$		0			0
$333$	27.2816	−	8.57534i	1.49502	−	0.469926i
$334$		0			0
$335$	1.36460	−	2.36356i	0.0745561	−	0.129135i
$336$		0			0
$337$	4.99010	+	8.64310i	0.271828	+	0.470820i	0.969330	−	0.245763i	$-0.0790385\pi$
$337$	4.99010	+	8.64310i	0.271828	+	0.470820i	−0.697502	+	0.716583i	$0.745705\pi$
$338$		0			0
$339$	−6.78418	+	1.97415i	−0.368466	+	0.107221i
$340$		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
$347$	6.76074	+	1.81153i	0.362935	+	0.0972483i	0.435678	−	0.900102i	$-0.356509\pi$
$347$	6.76074	+	1.81153i	0.362935	+	0.0972483i	−0.0727428	+	0.997351i	$0.523175\pi$
$348$		0			0
$349$	19.5231	−	5.23119i	1.04505	−	0.280019i	0.304843	−	0.952403i	$-0.401396\pi$
$349$	19.5231	−	5.23119i	1.04505	−	0.280019i	0.740203	+	0.672383i	$0.234729\pi$
$350$		0			0
$351$	7.17714	−	4.78185i	0.383087	−	0.255236i
$352$		0			0
$353$	8.37682	+	4.83636i	0.445853	+	0.257414i	0.706077	−	0.708135i	$-0.250463\pi$
$353$	8.37682	+	4.83636i	0.445853	+	0.257414i	−0.260224	+	0.965548i	$0.583796\pi$
$354$		0			0
$355$	−4.62923	−	1.24040i	−0.245694	−	0.0658335i
$356$		0			0
$357$	6.31037	+	6.04621i	0.333980	+	0.319999i
$358$		0			0
$359$		−	0.846908i		−	0.0446981i	−0.999750	−	0.0223491i	$-0.992885\pi$
$359$		−	0.846908i		−	0.0446981i	0.999750	−	0.0223491i	$-0.00711452\pi$
$360$		0			0
$361$			18.2279i			0.959362i
$362$		0			0
$363$	−9.37235	+	2.72729i	−0.491921	+	0.143146i
$364$		0			0
$365$	2.37134	+	0.635398i	0.124121	+	0.0332582i
$366$		0			0
$367$	−15.5960	−	9.00434i	−0.814103	−	0.470023i	0.0342756	−	0.999412i	$-0.489088\pi$
$367$	−15.5960	−	9.00434i	−0.814103	−	0.470023i	−0.848379	+	0.529390i	$0.822421\pi$
$368$		0			0
$369$	0.357676	+	8.36187i	0.0186199	+	0.435301i
$370$		0			0
$371$	−2.74390	+	0.735225i	−0.142456	+	0.0381710i
$372$		0			0
$373$	−18.7086	−	5.01296i	−0.968696	−	0.259561i	−0.260419	−	0.965496i	$-0.583861\pi$
$373$	−18.7086	−	5.01296i	−0.968696	−	0.259561i	−0.708277	+	0.705934i	$0.750527\pi$
$374$		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
$381$	−0.737378	+	3.00765i	−0.0377770	+	0.154087i
$382$		0			0
$383$	3.80911	+	6.59757i	0.194636	+	0.337120i	0.946781	−	0.321878i	$-0.104314\pi$
$383$	3.80911	+	6.59757i	0.194636	+	0.337120i	−0.752145	+	0.658998i	$0.770981\pi$
$384$		0			0
$385$	0.260058	−	0.450434i	0.0132538	−	0.0229562i
$386$		0			0
$387$	21.4864	+	4.78336i	1.09221	+	0.243152i
$388$		0			0
$389$	−1.55794	+	0.417448i	−0.0789905	+	0.0211654i	−0.298098	−	0.954535i	$-0.596352\pi$
$389$	−1.55794	+	0.417448i	−0.0789905	+	0.0211654i	0.219107	+	0.975701i	$0.429686\pi$
$390$		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	−0.854557	−	0.519358i	$-0.826171\pi$
$401$	−16.6619	+	9.61977i	−0.832057	+	0.480388i	0.0224993	+	0.999747i	$0.492838\pi$
$402$		0			0
$403$	1.55577	+	5.80621i	0.0774983	+	0.289228i
$404$		0			0
$405$	2.54049	−	0.919576i	0.126238	−	0.0456941i
$406$		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	$-0.623915\pi$
$409$	4.69044	−	2.70803i	0.231928	−	0.133903i	0.611461	+	0.791275i	$0.290582\pi$
$410$		0			0
$411$	0.950290	−	0.991807i	0.0468743	−	0.0489222i
$412$		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
$419$	−1.74346	+	6.50669i	−0.0851738	+	0.317873i	−0.995347	−	0.0963549i	$-0.969282\pi$
$419$	−1.74346	+	6.50669i	−0.0851738	+	0.317873i	0.910173	+	0.414228i	$0.135948\pi$
$420$		0			0
$421$	5.09689	+	19.0218i	0.248407	+	0.927068i	0.971640	+	0.236464i	$0.0759886\pi$
$421$	5.09689	+	19.0218i	0.248407	+	0.927068i	−0.723233	+	0.690604i	$0.757345\pi$
$422$		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
$427$	−2.03874	+	7.60869i	−0.0986616	+	0.368210i
$428$		0			0
$429$	6.46675	+	1.58544i	0.312218	+	0.0765456i
$430$		0			0
$431$	−22.9770			−1.10676			−0.553380	−	0.832929i	$-0.686662\pi$
$431$	−22.9770			−1.10676			−0.553380	+	0.832929i	$0.686662\pi$
$432$		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
$435$	2.84540	+	0.697598i	0.136426	+	0.0334473i
$436$		0			0
$437$	−1.59190	+	5.94106i	−0.0761510	+	0.284199i
$438$		0			0
$439$	2.64587	−	4.58278i	0.126281	−	0.218724i	−0.795952	−	0.605359i	$-0.793029\pi$
$439$	2.64587	−	4.58278i	0.126281	−	0.218724i	0.922233	+	0.386635i	$0.126363\pi$
$440$		0			0
$441$	0.825706	+	19.3036i	0.0393193	+	0.919220i
$442$		0			0
$443$	−5.57188	−	20.7945i	−0.264728	−	0.987978i	−0.962417	−	0.271577i	$-0.912455\pi$
$443$	−5.57188	−	20.7945i	−0.264728	−	0.987978i	0.697689	−	0.716401i	$-0.254212\pi$
$444$		0			0
$445$	−1.22647	+	4.57724i	−0.0581402	+	0.216982i
$446$		0			0
$447$	10.8887	−	19.8267i	0.515017	−	0.937769i
$448$		0			0
$449$			22.9162i			1.08148i	0.841189	+	0.540742i	$0.181856\pi$
$449$			22.9162i			1.08148i	−0.841189	+	0.540742i	$0.818144\pi$
$450$		0			0
$451$	−4.56905	+	4.56905i	−0.215148	+	0.215148i
$452$		0			0
$453$	22.6482	−	23.6377i	1.06411	−	1.11060i
$454$		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	$-0.356392\pi$
$457$	−2.67987	−	1.54723i	−0.125359	−	0.0723761i	−0.561368	+	0.827566i	$0.689725\pi$
$458$		0			0
$459$	−23.1443	+	26.3205i	−1.08029	+	1.22854i
$460$		0			0
$461$	0.410957	+	1.53371i	0.0191402	+	0.0714320i	0.974835	−	0.222926i	$-0.0715608\pi$
$461$	0.410957	+	1.53371i	0.0191402	+	0.0714320i	−0.955695	+	0.294358i	$0.904894\pi$
$462$		0			0
$463$	−0.0991508	+	0.0572447i	−0.00460793	+	0.00266039i	−0.502302	−	0.864692i	$-0.667513\pi$
$463$	−0.0991508	+	0.0572447i	−0.00460793	+	0.00266039i	0.497694	+	0.867353i	$0.334180\pi$
$464$		0			0
$465$	0.0402475	+	1.88270i	0.00186644	+	0.0873082i
$466$		0			0
$467$	0.325359	+	0.325359i	0.0150558	+	0.0150558i	0.714595	−	0.699539i	$-0.246611\pi$
$467$	0.325359	+	0.325359i	0.0150558	+	0.0150558i	−0.699539	+	0.714595i	$0.746611\pi$
$468$		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
$475$	−4.16731	+	1.11663i	−0.191209	+	0.0512344i
$476$		0			0
$477$	−3.41616	−	10.8682i	−0.156415	−	0.497621i
$478$		0			0
$479$	−9.17908	+	15.8986i	−0.419403	+	0.726427i	−0.995879	−	0.0906864i	$-0.971094\pi$
$479$	−9.17908	+	15.8986i	−0.419403	+	0.726427i	0.576476	+	0.817114i	$0.304427\pi$
$480$		0			0
$481$	7.91075	+	13.7018i	0.360699	+	0.624749i
$482$		0			0
$483$	−2.15951	+	8.80832i	−0.0982612	+	0.400793i
$484$		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
$491$	−0.201003	−	0.0538587i	−0.00907115	−	0.00243061i	0.254281	−	0.967130i	$-0.418161\pi$
$491$	−0.201003	−	0.0538587i	−0.00907115	−	0.00243061i	−0.263352	+	0.964700i	$0.584828\pi$
$492$		0			0
$493$	−36.7100	+	9.83640i	−1.65333	+	0.443009i
$494$		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
$499$	−34.2394	−	9.17443i	−1.53277	−	0.410704i	−0.608847	−	0.793288i	$-0.708368\pi$
$499$	−34.2394	−	9.17443i	−1.53277	−	0.410704i	−0.923921	+	0.382584i	$0.875034\pi$
$500$		0			0
$501$	15.2941	−	4.45050i	0.683292	−	0.198833i
$502$		0			0
$503$			39.4177i			1.75755i	0.477239	+	0.878773i	$0.341638\pi$
$503$			39.4177i			1.75755i	−0.477239	+	0.878773i	$0.658362\pi$
$504$		0			0
$505$		−	4.74117i		−	0.210979i
$506$		0			0
$507$	−12.8132	−	12.2768i	−0.569053	−	0.545232i
$508$		0			0
$509$	−38.2137	−	10.2393i	−1.69379	−	0.453850i	−0.722427	−	0.691447i	$-0.756973\pi$
$509$	−38.2137	−	10.2393i	−1.69379	−	0.453850i	−0.971364	+	0.237598i	$0.923640\pi$
$510$		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
$515$	3.27084	−	0.876418i	0.144130	−	0.0386196i
$516$		0			0
$517$	1.37418	+	0.368210i	0.0604363	+	0.0161939i
$518$		0			0
$519$	−0.294001	−	13.7528i	−0.0129052	−	0.603680i
$520$		0			0
$521$	21.5152			0.942596			0.471298	−	0.881974i	$-0.343786\pi$
$521$	21.5152			0.942596			0.471298	+	0.881974i	$0.343786\pi$
$522$		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
$525$	−6.10815	+	1.77743i	−0.266581	+	0.0775735i
$526$		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
$531$	0.0192641	+	0.0176837i	0.000835990	+	0.000767405i
$532$		0			0
$533$	−4.47261	+	1.19843i	−0.193730	+	0.0519099i
$534$		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
$547$	7.80612	+	29.1328i	0.333765	+	1.24563i	0.905201	+	0.424983i	$0.139720\pi$
$547$	7.80612	+	29.1328i	0.333765	+	1.24563i	−0.571436	+	0.820647i	$0.693613\pi$
$548$		0			0
$549$	−30.8358	−	6.86476i	−1.31604	−	0.292981i
$550$		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
$555$	1.38488	+	4.75915i	0.0587850	+	0.202015i
$556$		0			0
$557$	−25.0618	+	25.0618i	−1.06190	+	1.06190i	−0.0639497	+	0.997953i	$0.520370\pi$
$557$	−25.0618	+	25.0618i	−1.06190	+	1.06190i	−0.997953	+	0.0639497i	$0.979630\pi$
$558$		0			0
$559$			12.1782i			0.515084i
$560$		0			0
$561$	−27.0531	+	0.578328i	−1.14218	+	0.0244170i
$562$		0			0
$563$	−3.71859	+	13.8780i	−0.156720	+	0.584886i	0.842232	+	0.539115i	$0.181241\pi$
$563$	−3.71859	+	13.8780i	−0.156720	+	0.584886i	−0.998952	+	0.0457710i	$0.985426\pi$
$564$		0			0
$565$	−0.316952	−	1.18288i	−0.0133343	−	0.0497642i
$566$		0			0
$567$	6.70782	−	0.574901i	0.281702	−	0.0241436i
$568$		0			0
$569$	−14.1987	+	24.5928i	−0.595239	+	1.03098i	0.398274	+	0.917267i	$0.369609\pi$
$569$	−14.1987	+	24.5928i	−0.595239	+	1.03098i	−0.993513	+	0.113718i	$0.963724\pi$
$570$		0			0
$571$	−4.64190	+	17.3238i	−0.194257	+	0.724978i	0.798201	+	0.602392i	$0.205786\pi$
$571$	−4.64190	+	17.3238i	−0.194257	+	0.724978i	−0.992458	+	0.122586i	$0.960881\pi$
$572$		0			0
$573$	−24.5368	+	25.6087i	−1.02504	+	1.06982i
$574$		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
$579$	2.29714	+	7.89413i	0.0954660	+	0.328069i
$580$		0			0
$581$	0.264604	−	0.987517i	0.0109776	−	0.0409691i
$582$		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
$587$	5.60833	+	20.9306i	0.231480	+	0.863897i	0.979704	+	0.200450i	$0.0642404\pi$
$587$	5.60833	+	20.9306i	0.231480	+	0.863897i	−0.748224	+	0.663447i	$0.769093\pi$
$588$		0			0
$589$	−0.823658	+	3.07394i	−0.0339383	+	0.126659i
$590$		0			0
$591$	−8.44778	−	13.9354i	−0.347495	−	0.573226i
$592$		0			0
$593$		−	20.8755i		−	0.857256i	−0.903481	−	0.428628i	$-0.858997\pi$
$593$		−	20.8755i		−	0.857256i	0.903481	−	0.428628i	$-0.141003\pi$
$594$		0			0
$595$	−1.07107	+	1.07107i	−0.0439095	+	0.0439095i
$596$		0			0
$597$	38.4223	+	9.41988i	1.57252	+	0.385530i
$598$		0			0
$599$	9.64766	−	5.57008i	0.394193	−	0.227587i	−0.289782	−	0.957093i	$-0.593583\pi$
$599$	9.64766	−	5.57008i	0.394193	−	0.227587i	0.683975	+	0.729505i	$0.260250\pi$
$600$		0			0
$601$	−21.0323	−	12.1430i	−0.857927	−	0.495324i	0.00539080	−	0.999985i	$-0.498284\pi$
$601$	−21.0323	−	12.1430i	−0.857927	−	0.495324i	−0.863317	+	0.504661i	$0.831617\pi$
$602$		0			0
$603$	20.0921	+	18.4437i	0.818213	+	0.751087i
$604$		0			0
$605$	−0.437870	−	1.63415i	−0.0178019	−	0.0664377i
$606$		0			0
$607$	23.4924	−	13.5633i	0.953525	−	0.550518i	0.0593510	−	0.998237i	$-0.481097\pi$
$607$	23.4924	−	13.5633i	0.953525	−	0.550518i	0.894174	+	0.447719i	$0.147764\pi$
$608$		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	$-0.117415\pi$
$617$	3.82807	+	6.63041i	0.154112	+	0.266930i	−0.778623	+	0.627492i	$0.784082\pi$
$618$		0			0
$619$	−31.4778	+	8.43446i	−1.26520	+	0.339009i	−0.828190	−	0.560447i	$-0.810629\pi$
$619$	−31.4778	+	8.43446i	−1.26520	+	0.339009i	−0.437010	+	0.899457i	$0.643963\pi$
$620$		0			0
$621$	−35.6632	−	7.14306i	−1.43111	−	0.286641i
$622$		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
$627$	2.54528	+	2.43873i	0.101649	+	0.0973936i
$628$		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
$635$	−0.518437	−	0.138915i	−0.0205735	−	0.00551266i
$636$		0			0
$637$	−10.3252	+	2.76662i	−0.409098	+	0.109617i
$638$		0			0
$639$	22.1523	−	42.4624i	0.876331	−	1.67979i
$640$		0			0
$641$	12.3382	+	7.12347i	0.487330	+	0.281360i	0.723466	−	0.690360i	$-0.242548\pi$
$641$	12.3382	+	7.12347i	0.487330	+	0.281360i	−0.236136	+	0.971720i	$0.575881\pi$
$642$		0			0
$643$	11.5700	+	3.10018i	0.456277	+	0.122259i	0.479635	−	0.877468i	$-0.340769\pi$
$643$	11.5700	+	3.10018i	0.456277	+	0.122259i	−0.0233581	+	0.999727i	$0.507436\pi$
$644$		0			0
$645$	−0.908457	+	3.70546i	−0.0357705	+	0.145902i
$646$		0			0
$647$		−	3.24662i		−	0.127638i	−0.997961	−	0.0638189i	$-0.979672\pi$
$647$		−	3.24662i		−	0.127638i	0.997961	−	0.0638189i	$-0.0203280\pi$
$648$		0			0
$649$			0.0201888i			0.000792479i
$650$		0			0
$651$	−1.11734	+	4.55747i	−0.0437921	+	0.178621i
$652$		0			0
$653$	−0.0969809	−	0.0259859i	−0.00379516	−	0.00101691i	0.256921	−	0.966432i	$-0.417292\pi$
$653$	−0.0969809	−	0.0259859i	−0.00379516	−	0.00101691i	−0.260716	+	0.965416i	$0.583959\pi$
$654$		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
$659$	−18.4436	+	4.94194i	−0.718459	+	0.192511i	−0.599484	−	0.800387i	$-0.704628\pi$
$659$	−18.4436	+	4.94194i	−0.718459	+	0.192511i	−0.118975	+	0.992897i	$0.537961\pi$
$660$		0			0
$661$	26.6109	+	7.13036i	1.03504	+	0.277339i	0.736058	−	0.676919i	$-0.236685\pi$
$661$	26.6109	+	7.13036i	1.03504	+	0.277339i	0.298985	+	0.954258i	$0.403352\pi$
$662$		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
$669$	9.24183	+	8.85497i	0.357310	+	0.342353i
$670$		0			0
$671$	−12.1947	−	21.1218i	−0.470769	−	0.815396i
$672$		0			0
$673$	21.3890	−	37.0468i	0.824484	−	1.42805i	−0.0778289	−	0.996967i	$-0.524799\pi$
$673$	21.3890	−	37.0468i	0.824484	−	1.42805i	0.902313	−	0.431082i	$-0.141868\pi$
$674$		0			0
$675$	−8.16865	−	24.1694i	−0.314412	−	0.930281i
$676$		0			0
$677$	7.49190	−	2.00745i	0.287937	−	0.0771525i	−0.111960	−	0.993713i	$-0.535713\pi$
$677$	7.49190	−	2.00745i	0.287937	−	0.0771525i	0.399897	+	0.916560i	$0.369046\pi$
$678$		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	$-0.418373\pi$
$683$	31.9083	−	31.9083i	1.22094	−	1.22094i	0.967299	−	0.253637i	$-0.0816269\pi$
$684$		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
$691$	7.81032	+	29.1485i	0.297118	+	1.10886i	0.939520	+	0.342493i	$0.111271\pi$
$691$	7.81032	+	29.1485i	0.297118	+	1.10886i	−0.642402	+	0.766368i	$0.722062\pi$
$692$		0			0
$693$	3.82904	+	3.51490i	0.145453	+	0.133520i
$694$		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
$699$	24.0978	+	5.90799i	0.911462	+	0.223461i
$700$		0			0
$701$	6.92803	−	6.92803i	0.261668	−	0.261668i	−0.564063	−	0.825732i	$-0.690763\pi$
$701$	6.92803	−	6.92803i	0.261668	−	0.261668i	0.825732	+	0.564063i	$0.190763\pi$
$702$		0			0
$703$			8.37625i			0.315916i
$704$		0			0
$705$	0.165565	+	0.273116i	0.00623555	+	0.0102861i
$706$		0			0
$707$	3.05773	−	11.4116i	0.114998	−	0.429178i
$708$		0			0
$709$	3.97247	+	14.8255i	0.149189	+	0.556782i	0.999533	+	0.0305546i	$0.00972734\pi$
$709$	3.97247	+	14.8255i	0.149189	+	0.556782i	−0.850344	+	0.526228i	$0.823606\pi$
$710$		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
$715$	−0.298680	+	1.11469i	−0.0111700	+	0.0416871i
$716$		0			0
$717$	−11.1231	−	38.2244i	−0.415398	−	1.42752i
$718$		0			0
$719$	−6.93438			−0.258609			−0.129304	−	0.991605i	$-0.541274\pi$
$719$	−6.93438			−0.258609			−0.129304	+	0.991605i	$0.541274\pi$
$720$		0			0
$721$	8.43787			0.314243
$722$		0			0
$723$	−24.6213	+	25.6970i	−0.915677	+	0.955682i
$724$		0			0
$725$	7.16001	−	26.7215i	0.265916	−	0.992412i
$726$		0			0
$727$	7.03023	−	12.1767i	0.260737	−	0.451610i	−0.705701	−	0.708510i	$-0.749368\pi$
$727$	7.03023	−	12.1767i	0.260737	−	0.451610i	0.966438	+	0.256900i	$0.0827011\pi$
$728$		0			0
$729$	3.45315	+	26.7783i	0.127894	+	0.991788i
$730$		0			0
$731$	−12.8096	−	47.8061i	−0.473780	−	1.76817i
$732$		0			0
$733$	−0.0626936	+	0.233976i	−0.00231564	+	0.00864209i	−0.967074	−	0.254495i	$-0.918091\pi$
$733$	−0.0626936	+	0.233976i	−0.00231564	+	0.00864209i	0.964758	+	0.263138i	$0.0847573\pi$
$734$		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
$741$	0.705786	+	2.42544i	0.0259277	+	0.0891006i
$742$		0			0
$743$	5.26562	−	3.04011i	0.193177	−	0.111531i	−0.400292	−	0.916388i	$-0.631091\pi$
$743$	5.26562	−	3.04011i	0.193177	−	0.111531i	0.593469	+	0.804857i	$0.297758\pi$
$744$		0			0
$745$	3.39524	+	1.96024i	0.124392	+	0.0718178i
$746$		0			0
$747$	4.00212	+	0.890964i	0.146430	+	0.0325987i
$748$		0			0
$749$	2.57365	+	9.60501i	0.0940393	+	0.350959i
$750$		0			0
$751$	−21.6001	+	12.4708i	−0.788199	+	0.455067i	−0.839328	−	0.543625i	$-0.817051\pi$
$751$	−21.6001	+	12.4708i	−0.788199	+	0.455067i	0.0511293	+	0.998692i	$0.483718\pi$
$752$		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	$-0.127141\pi$
$761$	3.41665	+	5.91781i	0.123854	+	0.214521i	−0.797431	+	0.603411i	$0.793808\pi$
$762$		0			0
$763$	0.546823	−	0.146521i	0.0197963	−	0.00530440i
$764$		0			0
$765$	−4.47511	−	4.10797i	−0.161798	−	0.148524i
$766$		0			0
$767$	−0.00723364	+	0.0125290i	−0.000261192	+	0.000452397i
$768$		0			0
$769$	−1.16390	−	2.01594i	−0.0419714	−	0.0726966i	0.844277	−	0.535908i	$-0.180031\pi$
$769$	−1.16390	−	2.01594i	−0.0419714	−	0.0726966i	−0.886248	+	0.463211i	$0.846697\pi$
$770$		0			0
$771$	9.19148	−	2.67466i	0.331023	−	0.0963256i
$772$		0			0
$773$	−4.66783	−	4.66783i	−0.167890	−	0.167890i	0.618161	−	0.786051i	$-0.287878\pi$
$773$	−4.66783	−	4.66783i	−0.167890	−	0.167890i	−0.786051	+	0.618161i	$0.787878\pi$
$774$		0			0
$775$	17.7820			0.638749
$776$		0			0
$777$	0.263971	+	12.3481i	0.00946991	+	0.442984i
$778$		0			0
$779$	−2.36790	−	0.634477i	−0.0848389	−	0.0227325i
$780$		0			0
$781$	35.7158	−	9.57001i	1.27801	−	0.342442i
$782$		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
$787$	28.3785	+	7.60400i	1.01158	+	0.271053i	0.726291	−	0.687387i	$-0.241242\pi$
$787$	28.3785	+	7.60400i	1.01158	+	0.271053i	0.285293	+	0.958440i	$0.407909\pi$
$788$		0			0
$789$	6.98192	+	6.68965i	0.248563	+	0.238158i
$790$		0			0
$791$		−	3.05151i		−	0.108499i
$792$		0			0
$793$		−	17.4774i		−	0.620640i
$794$		0			0
$795$	1.89590	−	0.551696i	0.0672408	−	0.0195666i
$796$		0			0
$797$	48.4997	+	12.9954i	1.71795	+	0.460322i	0.977350	−	0.211629i	$-0.0678767\pi$
$797$	48.4997	+	12.9954i	1.71795	+	0.460322i	0.740596	+	0.671951i	$0.234543\pi$
$798$		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
$803$	−18.2955	+	4.90227i	−0.645634	+	0.172997i
$804$		0			0
$805$	−1.51831	−	0.406831i	−0.0535135	−	0.0143389i
$806$		0			0
$807$	−3.49249	+	2.11718i	−0.122942	+	0.0745284i
$808$		0			0
$809$	54.3452			1.91068			0.955338	−	0.295515i	$-0.0954911\pi$
$809$	54.3452			1.91068			0.955338	+	0.295515i	$0.0954911\pi$
$810$		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
$813$	9.59884	−	39.1522i	0.336646	−	1.37313i
$814$		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
$819$	1.11689	+	3.55327i	0.0390272	+	0.124161i
$820$		0			0
$821$	−42.0690	+	11.2724i	−1.46822	+	0.393408i	−0.902320	−	0.431067i	$-0.858137\pi$
$821$	−42.0690	+	11.2724i	−1.46822	+	0.393408i	−0.565899	+	0.824475i	$0.691471\pi$
$822$		0			0
$823$	2.52571	+	4.37465i	0.0880406	+	0.152491i	0.906683	−	0.421813i	$-0.138606\pi$
$823$	2.52571	+	4.37465i	0.0880406	+	0.152491i	−0.818642	+	0.574304i	$0.805273\pi$
$824$		0			0
$825$	9.48152	−	17.2644i	0.330104	−	0.601070i
$826$		0			0
$827$	27.8757	−	27.8757i	0.969334	−	0.969334i	−0.0302095	−	0.999544i	$-0.509617\pi$
$827$	27.8757	−	27.8757i	0.969334	−	0.969334i	0.999544	+	0.0302095i	$0.00961743\pi$
$828$		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
$835$	0.714531	+	2.66667i	0.0247274	+	0.0922838i
$836$		0			0
$837$	−18.4523	−	3.69585i	−0.637805	−	0.127747i
$838$		0			0
$839$	−6.29143	−	3.63236i	−0.217204	−	0.125403i	0.387451	−	0.921890i	$-0.373356\pi$
$839$	−6.29143	−	3.63236i	−0.217204	−	0.125403i	−0.604655	+	0.796487i	$0.706689\pi$
$840$		0			0
$841$	−2.37837	+	1.37315i	−0.0820126	+	0.0473500i
$842$		0			0
$843$	5.49206	−	5.73200i	0.189156	−	0.197420i
$844$		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
$851$	17.2697	−	64.4513i	0.591997	−	2.20936i
$852$		0			0
$853$	7.07889	+	26.4188i	0.242377	+	0.904562i	0.974684	+	0.223587i	$0.0717768\pi$
$853$	7.07889	+	26.4188i	0.242377	+	0.904562i	−0.732307	+	0.680974i	$0.761557\pi$
$854$		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	$-0.869050\pi$
$857$	−3.27792	+	5.67752i	−0.111971	+	0.193940i	0.804594	+	0.593826i	$0.202383\pi$
$858$		0			0
$859$	−8.89601	+	33.2003i	−0.303528	+	1.13278i	0.630677	+	0.776045i	$0.282777\pi$
$859$	−8.89601	+	33.2003i	−0.303528	+	1.13278i	−0.934205	+	0.356736i	$0.883890\pi$
$860$		0			0
$861$	−3.51069	−	0.860707i	−0.119644	−	0.0293328i
$862$		0			0
$863$	−39.5164			−1.34515			−0.672576	−	0.740028i	$-0.734812\pi$
$863$	−39.5164			−1.34515			−0.672576	+	0.740028i	$0.734812\pi$
$864$		0			0
$865$	2.38418			0.0810646
$866$		0			0
$867$	47.9393	+	11.7532i	1.62810	+	0.399158i
$868$		0			0
$869$	5.30936	−	19.8148i	0.180108	−	0.672171i
$870$		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
$875$	−0.575974	−	2.14957i	−0.0194715	−	0.0726686i
$876$		0			0
$877$	12.4013	−	46.2823i	0.418763	−	1.56284i	−0.358415	−	0.933562i	$-0.616683\pi$
$877$	12.4013	−	46.2823i	0.418763	−	1.56284i	0.777178	−	0.629281i	$-0.216651\pi$
$878$		0			0
$879$	5.21483	−	9.49542i	0.175892	−	0.320273i
$880$		0			0
$881$		−	23.6718i		−	0.797522i	−0.917055	−	0.398761i	$-0.869440\pi$
$881$		−	23.6718i		−	0.797522i	0.917055	−	0.398761i	$-0.130560\pi$
$882$		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
$885$	−0.00313560	+	0.00327259i	−0.000105402	+	0.000110007i
$886$		0			0
$887$	19.6764	−	11.3602i	0.660669	−	0.381438i	−0.131863	−	0.991268i	$-0.542096\pi$
$887$	19.6764	−	11.3602i	0.660669	−	0.381438i	0.792532	+	0.609830i	$0.208762\pi$
$888$		0			0
$889$	−1.15825	−	0.668713i	−0.0388463	−	0.0224279i
$890$		0			0
$891$	−13.4272	+	15.9445i	−0.449828	+	0.534162i
$892$		0			0
$893$	0.139693	+	0.521341i	0.00467465	+	0.0174460i
$894$		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
$907$	−28.8653	+	7.73443i	−0.958456	+	0.256818i	−0.703947	−	0.710253i	$-0.748581\pi$
$907$	−28.8653	+	7.73443i	−0.958456	+	0.256818i	−0.254509	+	0.967070i	$0.581914\pi$
$908$		0			0
$909$	46.2479	+	10.2959i	1.53395	+	0.341492i
$910$		0			0
$911$	−2.23081	+	3.86388i	−0.0739100	+	0.128016i	−0.900612	−	0.434625i	$-0.856881\pi$
$911$	−2.23081	+	3.86388i	−0.0739100	+	0.128016i	0.826702	+	0.562640i	$0.190214\pi$
$912$		0			0
$913$	1.58272	+	2.74135i	0.0523804	+	0.0907255i
$914$		0			0
$915$	1.30376	−	5.31782i	0.0431009	−	0.175802i
$916$		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
$923$	25.5939	+	6.85787i	0.842435	+	0.225730i
$924$		0			0
$925$	45.2089	−	12.1137i	1.48646	−	0.398295i
$926$		0			0
$927$	1.44616	+	33.8087i	0.0474980	+	1.11042i
$928$		0			0
$929$	33.8981	+	19.5711i	1.11216	+	0.642107i	0.939389	−	0.342854i	$-0.111394\pi$
$929$	33.8981	+	19.5711i	1.11216	+	0.642107i	0.172774	+	0.984962i	$0.444727\pi$
$930$		0			0
$931$	−5.46638	−	1.46471i	−0.179153	−	0.0480040i
$932$		0			0
$933$	21.0542	−	6.12664i	0.689284	−	0.200577i
$934$		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
$939$	24.0130	+	23.0078i	0.783634	+	0.750831i
$940$		0			0
$941$	−23.5900	−	6.32091i	−0.769011	−	0.206056i	−0.147076	−	0.989125i	$-0.546986\pi$
$941$	−23.5900	−	6.32091i	−0.769011	−	0.206056i	−0.621934	+	0.783069i	$0.713653\pi$
$942$		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
$947$	−51.8344	+	13.8890i	−1.68439	+	0.451331i	−0.968933	−	0.247325i	$-0.920449\pi$
$947$	−51.8344	+	13.8890i	−1.68439	+	0.451331i	−0.715458	+	0.698656i	$0.753782\pi$
$948$		0			0
$949$	−13.1106	−	3.51297i	−0.425587	−	0.114036i
$950$		0			0
$951$	0.424764	+	19.8696i	0.0137739	+	0.644317i
$952$		0			0
$953$	−40.6369			−1.31636			−0.658180	−	0.752861i	$-0.728673\pi$
$953$	−40.6369			−1.31636			−0.658180	+	0.752861i	$0.728673\pi$
$954$		0			0
$955$	−4.34661	−	4.34661i	−0.140653	−	0.140653i
$956$		0			0
$957$	−21.7029	+	6.31542i	−0.701556	+	0.204148i
$958$		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
$963$	−38.0441	+	11.9583i	−1.22595	+	0.385350i
$964$		0			0
$965$	−1.37641	+	0.368808i	−0.0443082	+	0.0118724i
$966$		0			0
$967$	2.97787	+	5.15783i	0.0957620	+	0.165865i	0.909926	−	0.414770i	$-0.136138\pi$
$967$	2.97787	+	5.15783i	0.0957620	+	0.165865i	−0.814164	+	0.580634i	$0.802805\pi$
$968$		0			0
$969$	−5.32177	−	8.77876i	−0.170960	−	0.282014i
$970$		0			0
$971$	17.0165	−	17.0165i	0.546085	−	0.546085i	−0.379221	−	0.925306i	$-0.623808\pi$
$971$	17.0165	−	17.0165i	0.546085	−	0.546085i	0.925306	+	0.379221i	$0.123808\pi$
$972$		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	−0.654833	−	0.755773i	$-0.727261\pi$
$977$	−10.2439	+	5.91431i	−0.327731	+	0.189215i	0.327102	+	0.944989i	$0.393928\pi$
$978$		0			0
$979$	−9.46254	−	35.3147i	−0.302424	−	1.12866i
$980$		0			0
$981$	0.680796	+	2.16589i	0.0217361	+	0.0691515i
$982$		0			0
$983$	−38.2947	−	22.1094i	−1.22141	−	0.705181i	−0.256192	−	0.966626i	$-0.582468\pi$
$983$	−38.2947	−	22.1094i	−1.22141	−	0.705181i	−0.965218	+	0.261445i	$0.915801\pi$
$984$		0			0
$985$	2.44603	−	1.41222i	0.0779370	−	0.0449970i
$986$		0			0
$987$	0.222361	+	0.764146i	0.00707784	+	0.0243230i
$988$		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
$995$	−1.77461	+	6.62295i	−0.0562590	+	0.209962i
$996$		0			0
$997$	7.81197	+	29.1547i	0.247408	+	0.923338i	0.972158	+	0.234326i	$0.0752884\pi$
$997$	7.81197	+	29.1547i	0.247408	+	0.923338i	−0.724750	+	0.689012i	$0.758045\pi$
$998$		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.47.2		88
3.2	odd	2		1728.2.z.a.1007.11		88
4.3	odd	2		144.2.u.a.83.15	yes	88
9.4	even	3		1728.2.z.a.1583.11		88
9.5	odd	6	inner	576.2.y.a.239.12		88
12.11	even	2		432.2.v.a.35.8		88
16.5	even	4		144.2.u.a.11.21	✓	88
16.11	odd	4	inner	576.2.y.a.335.12		88
36.23	even	6		144.2.u.a.131.21	yes	88
36.31	odd	6		432.2.v.a.179.2		88
48.5	odd	4		432.2.v.a.251.2		88
48.11	even	4		1728.2.z.a.143.11		88
144.5	odd	12		144.2.u.a.59.15	yes	88
144.59	even	12	inner	576.2.y.a.527.2		88
144.85	even	12		432.2.v.a.395.8		88
144.139	odd	12		1728.2.z.a.719.11		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.21	✓	88	16.5	even	4
144.2.u.a.59.15	yes	88	144.5	odd	12
144.2.u.a.83.15	yes	88	4.3	odd	2
144.2.u.a.131.21	yes	88	36.23	even	6
432.2.v.a.35.8		88	12.11	even	2
432.2.v.a.179.2		88	36.31	odd	6
432.2.v.a.251.2		88	48.5	odd	4
432.2.v.a.395.8		88	144.85	even	12
576.2.y.a.47.2		88	1.1	even	1	trivial
576.2.y.a.239.12		88	9.5	odd	6	inner
576.2.y.a.335.12		88	16.11	odd	4	inner
576.2.y.a.527.2		88	144.59	even	12	inner
1728.2.z.a.143.11		88	48.11	even	4
1728.2.z.a.719.11		88	144.139	odd	12
1728.2.z.a.1007.11		88	3.2	odd	2
1728.2.z.a.1583.11		88	9.4	even	3

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)

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