LMFDB - Embedded newform 567.2.e.g.487.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(163,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("567.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.e (of order $3$, degree $2$, 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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 14x^{12} - 39x^{10} + 77x^{8} - 156x^{6} + 224x^{4} - 256x^{2} + 256 $ x^16 - 4x^14 + 14x^12 - 39x^10 + 77x^8 - 156x^6 + 224x^4 - 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			487.4
Root			$1.04779 - 0.949812i$ of defining polynomial
Character	$\chi$	$=$	567.487
Dual form			567.2.e.g.163.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.298668 - 0.517308i) q^{2} +(0.821595 - 1.42304i) q^{4} +(1.04779 + 1.81482i) q^{5} +(-1.12588 - 2.39424i) q^{7} -2.17621 q^{8} +(0.625881 - 1.08406i) q^{10} +(0.825707 - 1.43017i) q^{11} -0.426044 q^{13} +(-0.902296 + 1.29751i) q^{14} +(-0.993225 - 1.72032i) q^{16} +(3.03819 - 5.26230i) q^{17} +(-2.70625 - 4.68736i) q^{19} +3.44342 q^{20} -0.986450 q^{22} +(3.81729 + 6.61173i) q^{23} +(0.304286 - 0.527039i) q^{25} +(0.127246 + 0.220396i) q^{26} +(-4.33213 - 0.364918i) q^{28} -3.65377 q^{29} +(2.65372 - 4.59638i) q^{31} +(-2.76950 + 4.79691i) q^{32} -3.62964 q^{34} +(3.16543 - 4.55193i) q^{35} +(2.33890 + 4.05110i) q^{37} +(-1.61654 + 2.79993i) q^{38} +(-2.28020 - 3.94943i) q^{40} +1.48565 q^{41} +8.48997 q^{43} +(-1.35679 - 2.35004i) q^{44} +(2.28020 - 3.94943i) q^{46} +(-5.66624 - 9.81422i) q^{47} +(-4.46478 + 5.39126i) q^{49} -0.363522 q^{50} +(-0.350036 + 0.606280i) q^{52} +(-2.74496 + 4.75441i) q^{53} +3.46066 q^{55} +(2.45015 + 5.21037i) q^{56} +(1.09126 + 1.89013i) q^{58} +(0.779098 - 1.34944i) q^{59} +(-2.52408 - 4.37184i) q^{61} -3.17033 q^{62} -0.664256 q^{64} +(-0.446403 - 0.773193i) q^{65} +(2.61498 - 4.52928i) q^{67} +(-4.99232 - 8.64695i) q^{68} +(-3.30016 - 0.277990i) q^{70} -12.5604 q^{71} +(-0.793753 + 1.37482i) q^{73} +(1.39711 - 2.41987i) q^{74} -8.89375 q^{76} +(-4.35381 - 0.366745i) q^{77} +(3.81482 + 6.60746i) q^{79} +(2.08138 - 3.60505i) q^{80} +(-0.443717 - 0.768541i) q^{82} +5.25611 q^{83} +12.7335 q^{85} +(-2.53568 - 4.39193i) q^{86} +(-1.79691 + 3.11234i) q^{88} +(9.27808 + 16.0701i) q^{89} +(0.479675 + 1.02005i) q^{91} +12.5450 q^{92} +(-3.38465 + 5.86239i) q^{94} +(5.67114 - 9.82270i) q^{95} +13.7546 q^{97} +(4.12243 + 0.699472i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{4} + 6 q^{7} - 14 q^{10} + 12 q^{13} - 6 q^{16} - 24 q^{19} + 4 q^{22} - 26 q^{28} - 20 q^{31} + 4 q^{37} - 36 q^{40} + 20 q^{43} + 36 q^{46} - 14 q^{49} - 34 q^{52} + 8 q^{55} + 22 q^{58} - 36 q^{61}+ \cdots + 28 q^{97}+O(q^{100}) $ 16 * q - 6 * q^4 + 6 * q^7 - 14 * q^10 + 12 * q^13 - 6 * q^16 - 24 * q^19 + 4 * q^22 - 26 * q^28 - 20 * q^31 + 4 * q^37 - 36 * q^40 + 20 * q^43 + 36 * q^46 - 14 * q^49 - 34 * q^52 + 8 * q^55 + 22 * q^58 - 36 * q^61 + 76 * q^64 + 18 * q^67 - 58 * q^70 - 32 * q^73 + 116 * q^76 + 32 * q^79 + 2 * q^82 + 60 * q^85 + 72 * q^88 - 22 * q^91 - 54 * q^94 + 28 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.298668	−	0.517308i	−0.211190	−	0.365792i	0.740897	−	0.671619i	$-0.234401\pi$
$2$	−0.298668	−	0.517308i	−0.211190	−	0.365792i	−0.952087	+	0.305826i	$0.901067\pi$
$3$		0			0
$3$		0			0
$4$	0.821595	−	1.42304i	0.410797	−	0.711522i
$5$	1.04779	+	1.81482i	0.468584	+	0.811612i	0.999355	−	0.0359033i	$-0.0114308\pi$
$5$	1.04779	+	1.81482i	0.468584	+	0.811612i	−0.530771	+	0.847515i	$0.678098\pi$
$6$		0			0
$7$	−1.12588	−	2.39424i	−0.425543	−	0.904938i
$7$	−1.12588	−	2.39424i	−0.425543	−	0.904938i
$8$	−2.17621			−0.769406
$9$		0			0
$10$	0.625881	−	1.08406i	0.197921	−	0.342809i
$11$	0.825707	−	1.43017i	0.248960	−	0.431212i	−0.714277	−	0.699863i	$-0.753245\pi$
$11$	0.825707	−	1.43017i	0.248960	−	0.431212i	0.963238	+	0.268651i	$0.0865778\pi$
$12$		0			0
$13$	−0.426044			−0.118163			−0.0590817	−	0.998253i	$-0.518817\pi$
$13$	−0.426044			−0.118163			−0.0590817	+	0.998253i	$0.518817\pi$
$14$	−0.902296	+	1.29751i	−0.241149	+	0.346774i
$15$		0			0
$16$	−0.993225	−	1.72032i	−0.248306	−	0.430079i
$17$	3.03819	−	5.26230i	0.736869	−	1.27629i	−0.217030	−	0.976165i	$-0.569637\pi$
$17$	3.03819	−	5.26230i	0.736869	−	1.27629i	0.953899	−	0.300129i	$-0.0970298\pi$
$18$		0			0
$19$	−2.70625	−	4.68736i	−0.620856	−	1.07535i	−0.989327	−	0.145714i	$-0.953452\pi$
$19$	−2.70625	−	4.68736i	−0.620856	−	1.07535i	0.368471	−	0.929639i	$-0.379881\pi$
$20$	3.44342			0.769973
$21$		0			0
$22$	−0.986450			−0.210312
$23$	3.81729	+	6.61173i	0.795959	+	1.37864i	0.922228	+	0.386645i	$0.126366\pi$
$23$	3.81729	+	6.61173i	0.795959	+	1.37864i	−0.126269	+	0.991996i	$0.540300\pi$
$24$		0			0
$25$	0.304286	−	0.527039i	0.0608573	−	0.105408i
$26$	0.127246	+	0.220396i	0.0249550	+	0.0432233i
$27$		0			0
$28$	−4.33213	−	0.364918i	−0.818695	−	0.0689631i
$29$	−3.65377			−0.678488			−0.339244	−	0.940698i	$-0.610171\pi$
$29$	−3.65377			−0.678488			−0.339244	+	0.940698i	$0.610171\pi$
$30$		0			0
$31$	2.65372	−	4.59638i	0.476623	−	0.825535i	−0.523018	−	0.852321i	$-0.675194\pi$
$31$	2.65372	−	4.59638i	0.476623	−	0.825535i	0.999641	+	0.0267866i	$0.00852747\pi$
$32$	−2.76950	+	4.79691i	−0.489583	+	0.847982i
$33$		0			0
$34$	−3.62964			−0.622478
$35$	3.16543	−	4.55193i	0.535056	−	0.769416i
$36$		0			0
$37$	2.33890	+	4.05110i	0.384513	+	0.665997i	0.991702	−	0.128561i	$-0.0410360\pi$
$37$	2.33890	+	4.05110i	0.384513	+	0.665997i	−0.607188	+	0.794558i	$0.707703\pi$
$38$	−1.61654	+	2.79993i	−0.262237	+	0.454208i
$39$		0			0
$40$	−2.28020	−	3.94943i	−0.360532	−	0.624459i
$41$	1.48565			0.232020			0.116010	−	0.993248i	$-0.462990\pi$
$41$	1.48565			0.232020			0.116010	+	0.993248i	$0.462990\pi$
$42$		0			0
$43$	8.48997			1.29471			0.647354	−	0.762189i	$-0.275875\pi$
$43$	8.48997			1.29471			0.647354	+	0.762189i	$0.275875\pi$
$44$	−1.35679	−	2.35004i	−0.204544	−	0.354281i
$45$		0			0
$46$	2.28020	−	3.94943i	0.336198	−	0.582311i
$47$	−5.66624	−	9.81422i	−0.826506	−	1.43155i	−0.900763	−	0.434312i	$-0.856992\pi$
$47$	−5.66624	−	9.81422i	−0.826506	−	1.43155i	0.0742560	−	0.997239i	$-0.476342\pi$
$48$		0			0
$49$	−4.46478	+	5.39126i	−0.637826	+	0.770180i
$50$	−0.363522			−0.0514098
$51$		0			0
$52$	−0.350036	+	0.606280i	−0.0485412	+	0.0840758i
$53$	−2.74496	+	4.75441i	−0.377050	+	0.653069i	−0.990632	−	0.136562i	$-0.956395\pi$
$53$	−2.74496	+	4.75441i	−0.377050	+	0.653069i	0.613582	+	0.789631i	$0.289728\pi$
$54$		0			0
$55$	3.46066			0.466635
$56$	2.45015	+	5.21037i	0.327415	+	0.696265i
$57$		0			0
$58$	1.09126	+	1.89013i	0.143290	+	0.248186i
$59$	0.779098	−	1.34944i	0.101430	−	0.175682i	−0.810844	−	0.585262i	$-0.800992\pi$
$59$	0.779098	−	1.34944i	0.101430	−	0.175682i	0.912274	+	0.409581i	$0.134325\pi$
$60$		0			0
$61$	−2.52408	−	4.37184i	−0.323176	−	0.559757i	0.657966	−	0.753048i	$-0.271417\pi$
$61$	−2.52408	−	4.37184i	−0.323176	−	0.559757i	−0.981141	+	0.193291i	$0.938084\pi$
$62$	−3.17033			−0.402632
$63$		0			0
$64$	−0.664256			−0.0830320
$65$	−0.446403	−	0.773193i	−0.0553695	−	0.0959028i
$66$		0			0
$67$	2.61498	−	4.52928i	0.319471	−	0.553340i	−0.660907	−	0.750468i	$-0.729828\pi$
$67$	2.61498	−	4.52928i	0.319471	−	0.553340i	0.980378	+	0.197128i	$0.0631615\pi$
$68$	−4.99232	−	8.64695i	−0.605407	−	1.04860i
$69$		0			0
$70$	−3.30016	−	0.277990i	−0.394445	−	0.0332262i
$71$	−12.5604			−1.49065			−0.745324	−	0.666703i	$-0.767705\pi$
$71$	−12.5604			−1.49065			−0.745324	+	0.666703i	$0.767705\pi$
$72$		0			0
$73$	−0.793753	+	1.37482i	−0.0929017	+	0.160911i	−0.908731	−	0.417382i	$-0.862948\pi$
$73$	−0.793753	+	1.37482i	−0.0929017	+	0.160911i	0.815829	+	0.578293i	$0.196281\pi$
$74$	1.39711	−	2.41987i	0.162411	−	0.281304i
$75$		0			0
$76$	−8.89375			−1.02018
$77$	−4.35381	−	0.366745i	−0.496163	−	0.0417945i
$78$		0			0
$79$	3.81482	+	6.60746i	0.429201	+	0.743398i	0.996802	−	0.0799058i	$-0.0254620\pi$
$79$	3.81482	+	6.60746i	0.429201	+	0.743398i	−0.567602	+	0.823303i	$0.692129\pi$
$80$	2.08138	−	3.60505i	0.232705	−	0.403057i
$81$		0			0
$82$	−0.443717	−	0.768541i	−0.0490004	−	0.0848711i
$83$	5.25611			0.576933			0.288467	−	0.957490i	$-0.406855\pi$
$83$	5.25611			0.576933			0.288467	+	0.957490i	$0.406855\pi$
$84$		0			0
$85$	12.7335			1.38114
$86$	−2.53568	−	4.39193i	−0.273430	−	0.473595i
$87$		0			0
$88$	−1.79691	+	3.11234i	−0.191551	+	0.331777i
$89$	9.27808	+	16.0701i	0.983474	+	1.70343i	0.648528	+	0.761191i	$0.275385\pi$
$89$	9.27808	+	16.0701i	0.983474	+	1.70343i	0.334946	+	0.942237i	$0.391282\pi$
$90$		0			0
$91$	0.479675	+	1.02005i	0.0502836	+	0.106931i
$92$	12.5450			1.30791
$93$		0			0
$94$	−3.38465	+	5.86239i	−0.349100	+	0.604659i
$95$	5.67114	−	9.82270i	0.581847	−	1.00779i
$96$		0			0
$97$	13.7546			1.39656			0.698282	−	0.715823i	$-0.253948\pi$
$97$	13.7546			1.39656			0.698282	+	0.715823i	$0.253948\pi$
$98$	4.12243	+	0.699472i	0.416429	+	0.0706574i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−7.99423	+	13.8464i	−0.795456	+	1.37777i	0.127093	+	0.991891i	$0.459435\pi$
$101$	−7.99423	+	13.8464i	−0.795456	+	1.37777i	−0.922549	+	0.385879i	$0.873898\pi$
$102$		0			0
$103$	1.18156	+	2.04653i	0.116423	+	0.201651i	0.918348	−	0.395775i	$-0.129524\pi$
$103$	1.18156	+	2.04653i	0.116423	+	0.201651i	−0.801925	+	0.597425i	$0.796191\pi$
$104$	0.927161			0.0909156
$105$		0			0
$106$	3.27933			0.318517
$107$	2.27104	+	3.93356i	0.219550	+	0.380272i	0.954670	−	0.297665i	$-0.0962078\pi$
$107$	2.27104	+	3.93356i	0.219550	+	0.380272i	−0.735120	+	0.677936i	$0.762874\pi$
$108$		0			0
$109$	−8.62227	+	14.9342i	−0.825863	+	1.43044i	0.0753945	+	0.997154i	$0.475978\pi$
$109$	−8.62227	+	14.9342i	−0.825863	+	1.43044i	−0.901258	+	0.433283i	$0.857355\pi$
$110$	−1.03359	−	1.79023i	−0.0985489	−	0.170692i
$111$		0			0
$112$	−3.00060	+	4.31489i	−0.283530	+	0.407719i
$113$	10.6752			1.00424			0.502119	−	0.864799i	$-0.332554\pi$
$113$	10.6752			1.00424			0.502119	+	0.864799i	$0.332554\pi$
$114$		0			0
$115$	−7.99940	+	13.8554i	−0.745948	+	1.29202i
$116$	−3.00192	+	5.19947i	−0.278721	+	0.482759i
$117$		0			0
$118$	−0.930766			−0.0856840
$119$	−16.0198	−	1.34944i	−1.46854	−	0.123703i
$120$		0			0
$121$	4.13641	+	7.16448i	0.376038	+	0.651316i
$122$	−1.50773	+	2.61146i	−0.136503	+	0.236430i
$123$		0			0
$124$	−4.36057	−	7.55273i	−0.391591	−	0.678255i
$125$	11.7532			1.05124
$126$		0			0
$127$	14.4060			1.27833			0.639163	−	0.769072i	$-0.279281\pi$
$127$	14.4060			1.27833			0.639163	+	0.769072i	$0.279281\pi$
$128$	5.73739	+	9.93745i	0.507118	+	0.878355i
$129$		0			0
$130$	−0.266653	+	0.461856i	−0.0233870	+	0.0405075i
$131$	−5.09259	−	8.82063i	−0.444942	−	0.770662i	0.553106	−	0.833111i	$-0.313442\pi$
$131$	−5.09259	−	8.82063i	−0.444942	−	0.770662i	−0.998048	+	0.0624487i	$0.980109\pi$
$132$		0			0
$133$	−8.17575	+	11.7568i	−0.708928	+	1.01945i
$134$	−3.12405			−0.269877
$135$		0			0
$136$	−6.61173	+	11.4519i	−0.566951	+	0.981989i
$137$	−1.03116	+	1.78601i	−0.0880976	+	0.152589i	−0.906707	−	0.421761i	$-0.861412\pi$
$137$	−1.03116	+	1.78601i	−0.0880976	+	0.152589i	0.818609	+	0.574351i	$0.194745\pi$
$138$		0			0
$139$	6.63789			0.563018			0.281509	−	0.959559i	$-0.409165\pi$
$139$	6.63789			0.563018			0.281509	+	0.959559i	$0.409165\pi$
$140$	−3.87689	−	8.24439i	−0.327657	−	0.696778i
$141$		0			0
$142$	3.75140	+	6.49761i	0.314810	+	0.545267i
$143$	−0.351788	+	0.609314i	−0.0294180	+	0.0509534i
$144$		0			0
$145$	−3.82837	−	6.63093i	−0.317929	−	0.550669i
$146$	0.948275			0.0784798
$147$		0			0
$148$	7.68652			0.631828
$149$	−4.75850	−	8.24197i	−0.389832	−	0.675209i	0.602595	−	0.798047i	$-0.294134\pi$
$149$	−4.75850	−	8.24197i	−0.389832	−	0.675209i	−0.992427	+	0.122839i	$0.960800\pi$
$150$		0			0
$151$	5.54891	−	9.61099i	0.451564	−	0.782131i	−0.546920	−	0.837185i	$-0.684200\pi$
$151$	5.54891	−	9.61099i	0.451564	−	0.782131i	0.998483	+	0.0550537i	$0.0175330\pi$
$152$	5.88936	+	10.2007i	0.477690	+	0.827384i
$153$		0			0
$154$	1.11063	+	2.36180i	0.0894967	+	0.190319i
$155$	11.1221			0.893352
$156$		0			0
$157$	−12.1264	+	21.0035i	−0.967791	+	1.67626i	−0.265870	+	0.964009i	$0.585659\pi$
$157$	−12.1264	+	21.0035i	−0.967791	+	1.67626i	−0.701921	+	0.712255i	$0.747674\pi$
$158$	2.27873	−	3.94688i	0.181286	−	0.313997i
$159$		0			0
$160$	−11.6074			−0.917644
$161$	11.5323	−	16.5835i	0.908870	−	1.30696i
$162$		0			0
$163$	5.54515	+	9.60448i	0.434330	+	0.752281i	0.997241	−	0.0742364i	$-0.0236520\pi$
$163$	5.54515	+	9.60448i	0.434330	+	0.752281i	−0.562911	+	0.826518i	$0.690319\pi$
$164$	1.22060	−	2.11415i	0.0953132	−	0.165087i
$165$		0			0
$166$	−1.56983	−	2.71903i	−0.121843	−	0.211038i
$167$	2.45100			0.189664			0.0948321	−	0.995493i	$-0.469769\pi$
$167$	2.45100			0.189664			0.0948321	+	0.995493i	$0.469769\pi$
$168$		0			0
$169$	−12.8185			−0.986037
$170$	−3.80309	−	6.58714i	−0.291684	−	0.505211i
$171$		0			0
$172$	6.97532	−	12.0816i	0.531863	−	0.921214i
$173$	−4.64053	−	8.03763i	−0.352813	−	0.611090i	0.633928	−	0.773392i	$-0.281441\pi$
$173$	−4.64053	−	8.03763i	−0.352813	−	0.611090i	−0.986741	+	0.162302i	$0.948108\pi$
$174$		0			0
$175$	−1.60445	−	0.135151i	−0.121285	−	0.0102165i
$176$	−3.28045			−0.247273
$177$		0			0
$178$	5.54213	−	9.59926i	0.415400	−	0.719495i
$179$	−9.27808	+	16.0701i	−0.693476	+	1.20114i	0.277215	+	0.960808i	$0.410588\pi$
$179$	−9.27808	+	16.0701i	−0.693476	+	1.20114i	−0.970692	+	0.240328i	$0.922745\pi$
$180$		0			0
$181$	13.2382			0.983989			0.491994	−	0.870598i	$-0.336268\pi$
$181$	13.2382			0.983989			0.491994	+	0.870598i	$0.336268\pi$
$182$	0.384418	−	0.552797i	0.0284950	−	0.0409761i
$183$		0			0
$184$	−8.30721	−	14.3885i	−0.612416	−	1.06074i
$185$	−4.90134	+	8.48937i	−0.360354	+	0.624151i
$186$		0			0
$187$	−5.01731	−	8.69023i	−0.366902	−	0.635493i
$188$	−18.6214			−1.35811
$189$		0			0
$190$	−6.77515			−0.491521
$191$	5.29867	+	9.17757i	0.383399	+	0.664066i	0.991546	−	0.129759i	$-0.0414202\pi$
$191$	5.29867	+	9.17757i	0.383399	+	0.664066i	−0.608147	+	0.793824i	$0.708087\pi$
$192$		0			0
$193$	4.05981	−	7.03179i	0.292231	−	0.506159i	−0.682106	−	0.731254i	$-0.738936\pi$
$193$	4.05981	−	7.03179i	0.292231	−	0.506159i	0.974337	+	0.225094i	$0.0722690\pi$
$194$	−4.10805	−	7.11535i	−0.294941	−	0.510852i
$195$		0			0
$196$	4.00376	+	10.7830i	0.285983	+	0.770215i
$197$	−9.05534			−0.645166			−0.322583	−	0.946541i	$-0.604551\pi$
$197$	−9.05534			−0.645166			−0.322583	+	0.946541i	$0.604551\pi$
$198$		0			0
$199$	−3.71302	+	6.43114i	−0.263209	+	0.455892i	−0.967093	−	0.254424i	$-0.918114\pi$
$199$	−3.71302	+	6.43114i	−0.263209	+	0.455892i	0.703884	+	0.710315i	$0.251448\pi$
$200$	−0.662191	+	1.14695i	−0.0468239	+	0.0811015i
$201$		0			0
$202$	9.55049			0.671970
$203$	4.11371	+	8.74800i	0.288726	+	0.613989i
$204$		0			0
$205$	1.55665	+	2.69619i	0.108721	+	0.188310i
$206$	0.705791	−	1.22247i	0.0491748	−	0.0851733i
$207$		0			0
$208$	0.423158	+	0.732931i	0.0293407	+	0.0508196i
$209$	−8.93827			−0.618273
$210$		0			0
$211$	2.67781			0.184348			0.0921739	−	0.995743i	$-0.470618\pi$
$211$	2.67781			0.184348			0.0921739	+	0.995743i	$0.470618\pi$
$212$	4.51049	+	7.81240i	0.309782	+	0.536558i
$213$		0			0
$214$	1.35658	−	2.34966i	0.0927336	−	0.160619i
$215$	8.89568	+	15.4078i	0.606680	+	1.05080i
$216$		0			0
$217$	−13.9926	−	1.17867i	−0.949881	−	0.0800136i
$218$	10.3008			0.697657
$219$		0			0
$220$	2.84326	−	4.92467i	0.191693	−	0.332021i
$221$	−1.29440	+	2.24197i	−0.0870709	+	0.150811i
$222$		0			0
$223$	21.5369			1.44222			0.721110	−	0.692820i	$-0.243632\pi$
$223$	21.5369			1.44222			0.721110	+	0.692820i	$0.243632\pi$
$224$	14.6031	+	1.23010i	0.975710	+	0.0821892i
$225$		0			0
$226$	−3.18834	−	5.52237i	−0.212085	−	0.367342i
$227$	6.55051	−	11.3458i	0.434773	−	0.753049i	−0.562504	−	0.826794i	$-0.690162\pi$
$227$	6.55051	−	11.3458i	0.434773	−	0.753049i	0.997277	+	0.0737458i	$0.0234953\pi$
$228$		0			0
$229$	−8.41226	−	14.5705i	−0.555898	−	0.962843i	−0.997833	−	0.0657963i	$-0.979041\pi$
$229$	−8.41226	−	14.5705i	−0.555898	−	0.962843i	0.441935	−	0.897047i	$-0.354292\pi$
$230$	9.55666			0.630148
$231$		0			0
$232$	7.95136			0.522033
$233$	−11.3842	−	19.7180i	−0.745804	−	1.29177i	−0.949818	−	0.312803i	$-0.898732\pi$
$233$	−11.3842	−	19.7180i	−0.745804	−	1.29177i	0.204014	−	0.978968i	$-0.434601\pi$
$234$		0			0
$235$	11.8740	−	20.5664i	0.774576	−	1.34161i
$236$	−1.28020	−	2.21738i	−0.0833342	−	0.144339i
$237$		0			0
$238$	4.08654	+	8.69023i	0.264891	+	0.563304i
$239$	9.51810			0.615675			0.307837	−	0.951439i	$-0.400395\pi$
$239$	9.51810			0.615675			0.307837	+	0.951439i	$0.400395\pi$
$240$		0			0
$241$	−0.586542	+	1.01592i	−0.0377825	+	0.0654412i	−0.884298	−	0.466922i	$-0.845363\pi$
$241$	−0.586542	+	1.01592i	−0.0377825	+	0.0654412i	0.846516	+	0.532364i	$0.178696\pi$
$242$	2.47083	−	4.27960i	0.158831	−	0.275103i
$243$		0			0
$244$	−8.29509			−0.531039
$245$	−14.4623	−	2.45389i	−0.923963	−	0.156773i
$246$		0			0
$247$	1.15298	+	1.99702i	0.0733624	+	0.127067i
$248$	−5.77506	+	10.0027i	−0.366716	+	0.635171i
$249$		0			0
$250$	−3.51030	−	6.08002i	−0.222011	−	0.384534i
$251$	−7.59042			−0.479103			−0.239552	−	0.970884i	$-0.577000\pi$
$251$	−7.59042			−0.479103			−0.239552	+	0.970884i	$0.577000\pi$
$252$		0			0
$253$	12.6078			0.792648
$254$	−4.30261	−	7.45234i	−0.269970	−	0.467601i
$255$		0			0
$256$	2.76289	−	4.78547i	0.172681	−	0.299092i
$257$	11.6431	+	20.1665i	0.726277	+	1.25795i	0.958446	+	0.285273i	$0.0920844\pi$
$257$	11.6431	+	20.1665i	0.726277	+	1.25795i	−0.232169	+	0.972675i	$0.574582\pi$
$258$		0			0
$259$	7.06598	−	10.1610i	0.439059	−	0.631371i
$260$	−1.46705			−0.0909826
$261$		0			0
$262$	−3.04199	+	5.26888i	−0.187935	+	0.325513i
$263$	5.22230	−	9.04529i	0.322021	−	0.557757i	−0.658884	−	0.752245i	$-0.728971\pi$
$263$	5.22230	−	9.04529i	0.322021	−	0.557757i	0.980905	+	0.194488i	$0.0623045\pi$
$264$		0			0
$265$	−11.5045			−0.706718
$266$	8.52374	+	0.718000i	0.522624	+	0.0440234i
$267$		0			0
$268$	−4.29691	−	7.44247i	−0.262476	−	0.454621i
$269$	14.2349	−	24.6556i	0.867917	−	1.50328i	0.00379485	−	0.999993i	$-0.498792\pi$
$269$	14.2349	−	24.6556i	0.867917	−	1.50328i	0.864122	−	0.503283i	$-0.167875\pi$
$270$		0			0
$271$	−13.6962	−	23.7226i	−0.831986	−	1.44104i	−0.896461	−	0.443123i	$-0.853870\pi$
$271$	−13.6962	−	23.7226i	−0.831986	−	1.44104i	0.0644746	−	0.997919i	$-0.479463\pi$
$272$	−12.0704			−0.731876
$273$		0			0
$274$	1.23189			0.0744214
$275$	−0.502503	−	0.870361i	−0.0303021	−	0.0524847i
$276$		0			0
$277$	−2.05628	+	3.56159i	−0.123550	+	0.213995i	−0.921165	−	0.389172i	$-0.872761\pi$
$277$	−2.05628	+	3.56159i	−0.123550	+	0.213995i	0.797615	+	0.603167i	$0.206095\pi$
$278$	−1.98252	−	3.43383i	−0.118904	−	0.205948i
$279$		0			0
$280$	−6.88865	+	9.90594i	−0.411675	+	0.591993i
$281$	7.26126			0.433170			0.216585	−	0.976264i	$-0.430508\pi$
$281$	7.26126			0.433170			0.216585	+	0.976264i	$0.430508\pi$
$282$		0			0
$283$	0.640173	−	1.10881i	0.0380543	−	0.0659120i	−0.846371	−	0.532594i	$-0.821217\pi$
$283$	0.640173	−	1.10881i	0.0380543	−	0.0659120i	0.884425	+	0.466682i	$0.154551\pi$
$284$	−10.3196	+	17.8740i	−0.612354	+	1.06063i
$285$		0			0
$286$	0.420271			0.0248512
$287$	−1.67267	−	3.55701i	−0.0987345	−	0.209964i
$288$		0			0
$289$	−9.96117	−	17.2532i	−0.585951	−	1.01490i
$290$	−2.28682	+	3.96090i	−0.134287	+	0.232592i
$291$		0			0
$292$	1.30429	+	2.25909i	0.0763276	+	0.132203i
$293$	−20.0134			−1.16920			−0.584598	−	0.811323i	$-0.698748\pi$
$293$	−20.0134			−1.16920			−0.584598	+	0.811323i	$0.698748\pi$
$294$		0			0
$295$	3.26531			0.190114
$296$	−5.08994	−	8.81604i	−0.295847	−	0.512422i
$297$		0			0
$298$	−2.84243	+	4.92323i	−0.164657	+	0.285195i
$299$	−1.62633	−	2.81689i	−0.0940532	−	0.162905i
$300$		0			0
$301$	−9.55870	−	20.3270i	−0.550954	−	1.17163i
$302$	−6.62913			−0.381464
$303$		0			0
$304$	−5.37582	+	9.31120i	−0.308325	+	0.534034i
$305$	5.28940	−	9.16151i	0.302870	−	0.524587i
$306$		0			0
$307$	−2.19415			−0.125227			−0.0626134	−	0.998038i	$-0.519944\pi$
$307$	−2.19415			−0.125227			−0.0626134	+	0.998038i	$0.519944\pi$
$308$	−4.09896	+	5.89435i	−0.233560	+	0.335862i
$309$		0			0
$310$	−3.32183	−	5.75358i	−0.188667	−	0.326781i
$311$	−4.25439	+	7.36882i	−0.241244	+	0.417847i	−0.961069	−	0.276309i	$-0.910889\pi$
$311$	−4.25439	+	7.36882i	−0.241244	+	0.417847i	0.719825	+	0.694156i	$0.244222\pi$
$312$		0			0
$313$	−1.51731	−	2.62806i	−0.0857633	−	0.148546i	0.819953	−	0.572431i	$-0.194000\pi$
$313$	−1.51731	−	2.62806i	−0.0857633	−	0.148546i	−0.905716	+	0.423885i	$0.860666\pi$
$314$	14.4871			0.817552
$315$		0			0
$316$	12.5369			0.705258
$317$	2.64225	+	4.57652i	0.148404	+	0.257043i	0.930638	−	0.365942i	$-0.119253\pi$
$317$	2.64225	+	4.57652i	0.148404	+	0.257043i	−0.782234	+	0.622985i	$0.785920\pi$
$318$		0			0
$319$	−3.01694	+	5.22550i	−0.168916	+	0.292572i
$320$	−0.695999	−	1.20551i	−0.0389075	−	0.0673898i
$321$		0			0
$322$	−12.0231	−	1.01277i	−0.670022	−	0.0564395i
$323$	−32.8883			−1.82996
$324$		0			0
$325$	−0.129639	+	0.224542i	−0.00719110	+	0.0124554i
$326$	3.31232	−	5.73711i	0.183452	−	0.317749i
$327$		0			0
$328$	−3.23309			−0.178518
$329$	−17.1181	+	24.6160i	−0.943751	+	1.35712i
$330$		0			0
$331$	−10.6008	−	18.3612i	−0.582675	−	1.00922i	−0.995161	−	0.0982581i	$-0.968673\pi$
$331$	−10.6008	−	18.3612i	−0.582675	−	1.00922i	0.412486	−	0.910964i	$-0.364660\pi$
$332$	4.31839	−	7.47968i	0.237003	−	0.410500i
$333$		0			0
$334$	−0.732036	−	1.26792i	−0.0400552	−	0.0693777i
$335$	10.9598			0.598797
$336$		0			0
$337$	−14.0497			−0.765333			−0.382667	−	0.923886i	$-0.624994\pi$
$337$	−14.0497			−0.765333			−0.382667	+	0.923886i	$0.624994\pi$
$338$	3.82847	+	6.63111i	0.208242	+	0.360685i
$339$		0			0
$340$	10.4618	−	18.1203i	0.567369	−	0.982712i
$341$	−4.38240	−	7.59053i	−0.237320	−	0.411051i
$342$		0			0
$343$	17.9348	+	4.61985i	0.968388	+	0.249449i
$344$	−18.4760			−0.996157
$345$		0			0
$346$	−2.77196	+	4.80117i	−0.149021	+	0.258112i
$347$	10.0290	−	17.3707i	0.538385	−	0.932510i	−0.460606	−	0.887605i	$-0.652368\pi$
$347$	10.0290	−	17.3707i	0.538385	−	0.932510i	0.998991	−	0.0449055i	$-0.0142987\pi$
$348$		0			0
$349$	−27.9294			−1.49503			−0.747513	−	0.664247i	$-0.768752\pi$
$349$	−27.9294			−1.49503			−0.747513	+	0.664247i	$0.768752\pi$
$350$	0.409283	+	0.870361i	0.0218771	+	0.0465227i
$351$		0			0
$352$	4.57359	+	7.92169i	0.243773	+	0.422228i
$353$	−2.99626	+	5.18967i	−0.159475	+	0.276218i	−0.934679	−	0.355492i	$-0.884313\pi$
$353$	−2.99626	+	5.18967i	−0.159475	+	0.276218i	0.775205	+	0.631710i	$0.217647\pi$
$354$		0			0
$355$	−13.1606	−	22.7949i	−0.698494	−	1.20983i
$356$	30.4913			1.61603
$357$		0			0
$358$	11.0843			0.585822
$359$	8.30710	+	14.3883i	0.438432	+	0.759386i	0.997569	−	0.0696890i	$-0.0222007\pi$
$359$	8.30710	+	14.3883i	0.438432	+	0.759386i	−0.559137	+	0.829075i	$0.688867\pi$
$360$		0			0
$361$	−5.14755	+	8.91581i	−0.270924	+	0.469253i
$362$	−3.95383	−	6.84824i	−0.207809	−	0.359935i
$363$		0			0
$364$	1.84568	+	0.155471i	0.0967398	+	0.00814891i
$365$	−3.32673			−0.174129
$366$		0			0
$367$	−3.24764	+	5.62508i	−0.169525	+	0.293627i	−0.938253	−	0.345950i	$-0.887557\pi$
$367$	−3.24764	+	5.62508i	−0.169525	+	0.293627i	0.768728	+	0.639576i	$0.220890\pi$
$368$	7.58285	−	13.1339i	0.395283	−	0.684651i
$369$		0			0
$370$	5.85550			0.304413
$371$	14.4737	+	1.21920i	0.751438	+	0.0632976i
$372$		0			0
$373$	10.0805	+	17.4600i	0.521949	+	0.904042i	0.999674	+	0.0255327i	$0.00812820\pi$
$373$	10.0805	+	17.4600i	0.521949	+	0.904042i	−0.477725	+	0.878509i	$0.658538\pi$
$374$	−2.99702	+	5.19099i	−0.154972	+	0.268420i
$375$		0			0
$376$	12.3309	+	21.3578i	0.635919	+	1.10144i
$377$	1.55667			0.0801724
$378$		0			0
$379$	−15.3014			−0.785981			−0.392990	−	0.919543i	$-0.628559\pi$
$379$	−15.3014			−0.785981			−0.392990	+	0.919543i	$0.628559\pi$
$380$	−9.31876	−	16.1406i	−0.478042	−	0.827993i
$381$		0			0
$382$	3.16509	−	5.48210i	0.161940	−	0.280488i
$383$	3.39296	+	5.87677i	0.173372	+	0.300289i	0.939597	−	0.342284i	$-0.111200\pi$
$383$	3.39296	+	5.87677i	0.173372	+	0.300289i	−0.766225	+	0.642573i	$0.777867\pi$
$384$		0			0
$385$	−3.89629	−	8.28566i	−0.198573	−	0.422276i
$386$	−4.85014			−0.246866
$387$		0			0
$388$	11.3007	−	19.5733i	0.573705	−	0.993686i
$389$	−2.87957	+	4.98756i	−0.146000	+	0.252879i	−0.929746	−	0.368203i	$-0.879973\pi$
$389$	−2.87957	+	4.98756i	−0.146000	+	0.252879i	0.783746	+	0.621082i	$0.213307\pi$
$390$		0			0
$391$	46.3905			2.34607
$392$	9.71630	−	11.7325i	0.490747	−	0.592581i
$393$		0			0
$394$	2.70454	+	4.68440i	0.136253	+	0.235997i
$395$	−7.99423	+	13.8464i	−0.402234	+	0.696689i
$396$		0			0
$397$	0.247873	+	0.429329i	0.0124404	+	0.0215474i	0.872179	−	0.489188i	$-0.162707\pi$
$397$	0.247873	+	0.429329i	0.0124404	+	0.0215474i	−0.859738	+	0.510735i	$0.829373\pi$
$398$	4.43585			0.222349
$399$		0			0
$400$	−1.20890			−0.0604450
$401$	5.19147	+	8.99190i	0.259250	+	0.449034i	0.966041	−	0.258388i	$-0.0831914\pi$
$401$	5.19147	+	8.99190i	0.259250	+	0.449034i	−0.706791	+	0.707422i	$0.749858\pi$
$402$		0			0
$403$	−1.13060	+	1.95826i	−0.0563194	+	0.0975480i
$404$	13.1360	+	22.7523i	0.653542	+	1.13197i
$405$		0			0
$406$	3.29678	−	4.74081i	0.163617	−	0.235282i
$407$	7.72500			0.382914
$408$		0			0
$409$	15.0097	−	25.9976i	0.742182	−	1.28550i	−0.209318	−	0.977848i	$-0.567124\pi$
$409$	15.0097	−	25.9976i	0.742182	−	1.28550i	0.951500	−	0.307649i	$-0.0995423\pi$
$410$	0.929842	−	1.61053i	0.0459216	−	0.0795386i
$411$		0			0
$412$	3.88307			0.191305
$413$	−4.10805	−	0.346043i	−0.202144	−	0.0170276i
$414$		0			0
$415$	5.50728	+	9.53889i	0.270342	+	0.468246i
$416$	1.17993	−	2.04370i	0.0578508	−	0.100200i
$417$		0			0
$418$	2.66958	+	4.62384i	0.130573	+	0.226160i
$419$	−27.6495			−1.35077			−0.675384	−	0.737467i	$-0.736022\pi$
$419$	−27.6495			−1.35077			−0.675384	+	0.737467i	$0.736022\pi$
$420$		0			0
$421$	12.4621			0.607368			0.303684	−	0.952773i	$-0.401783\pi$
$421$	12.4621			0.607368			0.303684	+	0.952773i	$0.401783\pi$
$422$	−0.799775	−	1.38525i	−0.0389325	−	0.0674330i
$423$		0			0
$424$	5.97361	−	10.3466i	0.290104	−	0.502475i
$425$	−1.84896	−	3.20249i	−0.0896876	−	0.155344i
$426$		0			0
$427$	−7.62542	+	10.9654i	−0.369020	+	0.530655i
$428$	7.46351			0.360762
$429$		0			0
$430$	5.31371	−	9.20362i	0.256250	−	0.443838i
$431$	−7.05162	+	12.2138i	−0.339665	+	0.588316i	−0.984370	−	0.176115i	$-0.943647\pi$
$431$	−7.05162	+	12.2138i	−0.339665	+	0.588316i	0.644705	+	0.764431i	$0.276980\pi$
$432$		0			0
$433$	−15.3684			−0.738560			−0.369280	−	0.929318i	$-0.620396\pi$
$433$	−15.3684			−0.738560			−0.369280	+	0.929318i	$0.620396\pi$
$434$	3.56941	+	7.59053i	0.171337	+	0.364357i
$435$		0			0
$436$	14.1680	+	24.5397i	0.678525	+	1.17524i
$437$	20.6610	−	35.7860i	0.988351	−	1.71187i
$438$		0			0
$439$	−9.62286	−	16.6673i	−0.459274	−	0.795486i	0.539648	−	0.841890i	$-0.318557\pi$
$439$	−9.62286	−	16.6673i	−0.459274	−	0.795486i	−0.998923	+	0.0464041i	$0.985224\pi$
$440$	−7.53112			−0.359032
$441$		0			0
$442$	1.54639			0.0735541
$443$	12.2849	+	21.2781i	0.583673	+	1.01095i	0.995039	+	0.0994811i	$0.0317183\pi$
$443$	12.2849	+	21.2781i	0.583673	+	1.01095i	−0.411367	+	0.911470i	$0.634948\pi$
$444$		0			0
$445$	−19.4429	+	33.6761i	−0.921682	+	1.59640i
$446$	−6.43240	−	11.1412i	−0.304583	−	0.527553i
$447$		0			0
$448$	0.747873	+	1.59039i	0.0353337	+	0.0751389i
$449$	40.0045			1.88793			0.943965	−	0.330046i	$-0.107064\pi$
$449$	40.0045			1.88793			0.943965	+	0.330046i	$0.107064\pi$
$450$		0			0
$451$	1.22671	−	2.12473i	0.0577637	−	0.100050i
$452$	8.77068	−	15.1913i	0.412538	−	0.714537i
$453$		0			0
$454$	−7.82572			−0.367279
$455$	−1.34861	+	1.93932i	−0.0632240	+	0.0909168i
$456$		0			0
$457$	5.31807	+	9.21117i	0.248769	+	0.430880i	0.963184	−	0.268841i	$-0.0866407\pi$
$457$	5.31807	+	9.21117i	0.248769	+	0.430880i	−0.714416	+	0.699722i	$0.753307\pi$
$458$	−5.02495	+	8.70347i	−0.234800	+	0.406686i
$459$		0			0
$460$	13.1445	+	22.7670i	0.612867	+	1.06152i
$461$	16.4092			0.764251			0.382125	−	0.924111i	$-0.375192\pi$
$461$	16.4092			0.764251			0.382125	+	0.924111i	$0.375192\pi$
$462$		0			0
$463$	6.06393			0.281815			0.140907	−	0.990023i	$-0.454998\pi$
$463$	6.06393			0.281815			0.140907	+	0.990023i	$0.454998\pi$
$464$	3.62901	+	6.28564i	0.168473	+	0.291803i
$465$		0			0
$466$	−6.80020	+	11.7783i	−0.315013	+	0.545619i
$467$	−12.6433	−	21.8988i	−0.585062	−	1.01336i	−0.994868	−	0.101185i	$-0.967737\pi$
$467$	−12.6433	−	21.8988i	−0.585062	−	1.01336i	0.409805	−	0.912173i	$-0.365597\pi$
$468$		0			0
$469$	−13.7884	−	1.16147i	−0.636687	−	0.0536315i
$470$	−14.1856			−0.654332
$471$		0			0
$472$	−1.69548	+	2.93666i	−0.0780408	+	0.135171i
$473$	7.01023	−	12.1421i	0.322331	−	0.558294i
$474$		0			0
$475$	−3.29390			−0.151134
$476$	−15.0821	+	21.6882i	−0.691288	+	0.994079i
$477$		0			0
$478$	−2.84275	−	4.92379i	−0.130025	−	0.225209i
$479$	1.67124	−	2.89468i	0.0763611	−	0.132261i	−0.825316	−	0.564671i	$-0.809003\pi$
$479$	1.67124	−	2.89468i	0.0763611	−	0.132261i	0.901677	+	0.432409i	$0.142337\pi$
$480$		0			0
$481$	−0.996476	−	1.72595i	−0.0454354	−	0.0786964i
$482$	0.700726			0.0319172
$483$		0			0
$484$	13.5938			0.617901
$485$	14.4118	+	24.9620i	0.654408	+	1.13347i
$486$		0			0
$487$	−3.63943	+	6.30368i	−0.164918	+	0.285647i	−0.936626	−	0.350330i	$-0.886069\pi$
$487$	−3.63943	+	6.30368i	−0.164918	+	0.285647i	0.771708	+	0.635977i	$0.219403\pi$
$488$	5.49293	+	9.51404i	0.248653	+	0.430680i
$489$		0			0
$490$	3.05002	+	8.21437i	0.137786	+	0.371087i
$491$	−2.97131			−0.134093			−0.0670466	−	0.997750i	$-0.521358\pi$
$491$	−2.97131			−0.134093			−0.0670466	+	0.997750i	$0.521358\pi$
$492$		0			0
$493$	−11.1008	+	19.2272i	−0.499956	+	0.865950i
$494$	0.688717	−	1.19289i	0.0309869	−	0.0536708i
$495$		0			0
$496$	−10.5430			−0.473394
$497$	14.1415	+	30.0727i	0.634335	+	1.34894i
$498$		0			0
$499$	−6.24293	−	10.8131i	−0.279472	−	0.484060i	0.691782	−	0.722107i	$-0.256826\pi$
$499$	−6.24293	−	10.8131i	−0.279472	−	0.484060i	−0.971254	+	0.238047i	$0.923493\pi$
$500$	9.65635	−	16.7253i	0.431845	−	0.747977i
$501$		0			0
$502$	2.26702	+	3.92659i	0.101182	+	0.175252i
$503$	−17.4657			−0.778755			−0.389377	−	0.921078i	$-0.627310\pi$
$503$	−17.4657			−0.778755			−0.389377	+	0.921078i	$0.627310\pi$
$504$		0			0
$505$	−33.5050			−1.49095
$506$	−3.76556	−	6.52214i	−0.167400	−	0.289945i
$507$		0			0
$508$	11.8359	−	20.5004i	0.525133	−	0.909556i
$509$	−13.7671	−	23.8453i	−0.610215	−	1.05692i	−0.991204	−	0.132344i	$-0.957750\pi$
$509$	−13.7671	−	23.8453i	−0.610215	−	1.05692i	0.380989	−	0.924580i	$-0.375584\pi$
$510$		0			0
$511$	4.18532	+	0.352552i	0.185148	+	0.0155960i
$512$	19.6488			0.868363
$513$		0			0
$514$	6.95485	−	12.0462i	0.306765	−	0.531333i
$515$	−2.47606	+	4.28865i	−0.109108	+	0.188981i
$516$		0			0
$517$	−18.7146			−0.823069
$518$	−7.36673	−	0.620539i	−0.323676	−	0.0272649i
$519$		0			0
$520$	0.971467	+	1.68263i	0.0426017	+	0.0737882i
$521$	3.46252	−	5.99726i	0.151696	−	0.262745i	−0.780155	−	0.625586i	$-0.784860\pi$
$521$	3.46252	−	5.99726i	0.151696	−	0.262745i	0.931851	+	0.362841i	$0.118193\pi$
$522$		0			0
$523$	20.7968	+	36.0211i	0.909381	+	1.57509i	0.814925	+	0.579566i	$0.196778\pi$
$523$	20.7968	+	36.0211i	0.909381	+	1.57509i	0.0944561	+	0.995529i	$0.469889\pi$
$524$	−16.7362			−0.731124
$525$		0			0
$526$	−6.23894			−0.272031
$527$	−16.1250	−	27.9293i	−0.702417	−	1.21662i
$528$		0			0
$529$	−17.6433	+	30.5591i	−0.767101	+	1.32866i
$530$	3.43604	+	5.95139i	0.149252	+	0.258512i
$531$		0			0
$532$	10.0133	+	21.2938i	0.434132	+	0.923203i
$533$	−0.632954			−0.0274163
$534$		0			0
$535$	−4.75914	+	8.24307i	−0.205755	+	0.356379i
$536$	−5.69075	+	9.85667i	−0.245803	+	0.425743i
$537$		0			0
$538$	−17.0060			−0.733182
$539$	4.02380	+	10.8370i	0.173317	+	0.466782i
$540$		0			0
$541$	16.8944	+	29.2619i	0.726345	+	1.25807i	0.958418	+	0.285368i	$0.0921158\pi$
$541$	16.8944	+	29.2619i	0.726345	+	1.25807i	−0.232073	+	0.972698i	$0.574551\pi$
$542$	−8.18125	+	14.1703i	−0.351415	+	0.608668i
$543$		0			0
$544$	16.8285	+	29.1478i	0.721517	+	1.24970i
$545$	−36.1372			−1.54795
$546$		0			0
$547$	−14.1310			−0.604196			−0.302098	−	0.953277i	$-0.597687\pi$
$547$	−14.1310			−0.604196			−0.302098	+	0.953277i	$0.597687\pi$
$548$	1.69438	+	2.93476i	0.0723805	+	0.125367i
$549$		0			0
$550$	−0.300163	+	0.519898i	−0.0127990	+	0.0221685i
$551$	9.88800	+	17.1265i	0.421243	+	0.729614i
$552$		0			0
$553$	11.5248	−	16.5728i	0.490085	−	0.704748i
$554$	2.45658			0.104370
$555$		0			0
$556$	5.45365	−	9.44600i	0.231286	−	0.400600i
$557$	−3.74784	+	6.49145i	−0.158801	+	0.275051i	−0.934437	−	0.356130i	$-0.884096\pi$
$557$	−3.74784	+	6.49145i	−0.158801	+	0.275051i	0.775636	+	0.631181i	$0.217429\pi$
$558$		0			0
$559$	−3.61710			−0.152987
$560$	−10.9747	−	0.924461i	−0.463767	−	0.0390656i
$561$		0			0
$562$	−2.16871	−	3.75631i	−0.0914813	−	0.158450i
$563$	5.21120	−	9.02606i	0.219626	−	0.380403i	−0.735068	−	0.677994i	$-0.762850\pi$
$563$	5.21120	−	9.02606i	0.219626	−	0.380403i	0.954694	+	0.297591i	$0.0961830\pi$
$564$		0			0
$565$	11.1853	+	19.3735i	0.470570	+	0.815051i
$566$	−0.764797			−0.0321468
$567$		0			0
$568$	27.3341			1.14691
$569$	−14.9832	−	25.9517i	−0.628130	−	1.08795i	−0.987927	−	0.154923i	$-0.950487\pi$
$569$	−14.9832	−	25.9517i	−0.628130	−	1.08795i	0.359796	−	0.933031i	$-0.382846\pi$
$570$		0			0
$571$	−15.7168	+	27.2223i	−0.657727	+	1.13922i	0.323476	+	0.946236i	$0.395149\pi$
$571$	−15.7168	+	27.2223i	−0.657727	+	1.13922i	−0.981203	+	0.192980i	$0.938185\pi$
$572$	0.578054	+	1.00122i	0.0241697	+	0.0418631i
$573$		0			0
$574$	−1.34050	+	1.92765i	−0.0559514	+	0.0804586i
$575$	4.64619			0.193760
$576$		0			0
$577$	1.35570	−	2.34815i	0.0564387	−	0.0977547i	−0.836426	−	0.548080i	$-0.815359\pi$
$577$	1.35570	−	2.34815i	0.0564387	−	0.0977547i	0.892864	+	0.450326i	$0.148692\pi$
$578$	−5.95017	+	10.3060i	−0.247494	+	0.428673i
$579$		0			0
$580$	−12.5815			−0.522417
$581$	−5.91775	−	12.5844i	−0.245510	−	0.522089i
$582$		0			0
$583$	4.53307	+	7.85151i	0.187741	+	0.325176i
$584$	1.72737	−	2.99190i	0.0714792	−	0.123806i
$585$		0			0
$586$	5.97737	+	10.3531i	0.246923	+	0.427683i
$587$	−10.7040			−0.441800			−0.220900	−	0.975296i	$-0.570899\pi$
$587$	−10.7040			−0.441800			−0.220900	+	0.975296i	$0.570899\pi$
$588$		0			0
$589$	−28.7265			−1.18366
$590$	−0.975245	−	1.68917i	−0.0401502	−	0.0695422i
$591$		0			0
$592$	4.64611	−	8.04731i	0.190954	−	0.330742i
$593$	−14.8489	−	25.7191i	−0.609773	−	1.05616i	−0.991278	−	0.131791i	$-0.957927\pi$
$593$	−14.8489	−	25.7191i	−0.609773	−	1.05616i	0.381505	−	0.924367i	$-0.375406\pi$
$594$		0			0
$595$	−14.3364	−	30.4870i	−0.587735	−	1.24985i
$596$	−15.6382			−0.640568
$597$		0			0
$598$	−0.971467	+	1.68263i	−0.0397262	+	0.0688079i
$599$	7.19914	−	12.4693i	0.294149	−	0.509481i	−0.680638	−	0.732620i	$-0.738297\pi$
$599$	7.19914	−	12.4693i	0.294149	−	0.509481i	0.974787	+	0.223140i	$0.0716305\pi$
$600$		0			0
$601$	17.7120			0.722486			0.361243	−	0.932472i	$-0.382353\pi$
$601$	17.7120			0.722486			0.361243	+	0.932472i	$0.382353\pi$
$602$	−7.66047	+	11.0158i	−0.312218	+	0.448972i
$603$		0			0
$604$	−9.11791	−	15.7927i	−0.371002	−	0.642595i
$605$	−8.66816	+	15.0137i	−0.352411	+	0.610393i
$606$		0			0
$607$	2.57771	+	4.46473i	0.104626	+	0.181218i	0.913585	−	0.406647i	$-0.133302\pi$
$607$	2.57771	+	4.46473i	0.104626	+	0.181218i	−0.808959	+	0.587865i	$0.799969\pi$
$608$	29.9798			1.21584
$609$		0			0
$610$	−6.31910			−0.255853
$611$	2.41407	+	4.18129i	0.0976628	+	0.169157i
$612$		0			0
$613$	−5.62940	+	9.75042i	−0.227370	+	0.393816i	−0.957028	−	0.289996i	$-0.906346\pi$
$613$	−5.62940	+	9.75042i	−0.227370	+	0.393816i	0.729658	+	0.683812i	$0.239679\pi$
$614$	0.655323	+	1.13505i	0.0264467	+	0.0458070i
$615$		0			0
$616$	9.47481	+	0.798114i	0.381751	+	0.0321569i
$617$	0.520304			0.0209467			0.0104733	−	0.999945i	$-0.496666\pi$
$617$	0.520304			0.0209467			0.0104733	+	0.999945i	$0.496666\pi$
$618$		0			0
$619$	18.7370	−	32.4535i	0.753104	−	1.30441i	−0.193207	−	0.981158i	$-0.561889\pi$
$619$	18.7370	−	32.4535i	0.753104	−	1.30441i	0.946311	−	0.323257i	$-0.104778\pi$
$620$	9.13789	−	15.8273i	0.366987	−	0.635639i
$621$		0			0
$622$	5.08260			0.203794
$623$	28.0297	−	40.3070i	1.12299	−	1.61487i
$624$		0			0
$625$	10.7934	+	18.6947i	0.431736	+	0.747788i
$626$	−0.906343	+	1.56983i	−0.0362248	+	0.0627431i
$627$		0			0
$628$	19.9260	+	34.5128i	0.795132	+	1.37721i
$629$	28.4241			1.13334
$630$		0			0
$631$	0.502795			0.0200159			0.0100080	−	0.999950i	$-0.496814\pi$
$631$	0.502795			0.0200159			0.0100080	+	0.999950i	$0.496814\pi$
$632$	−8.30185	−	14.3792i	−0.330230	−	0.571975i
$633$		0			0
$634$	1.57831	−	2.73372i	0.0626828	−	0.108570i
$635$	15.0944	+	26.1443i	0.599003	+	1.03750i
$636$		0			0
$637$	1.90220	−	2.29692i	0.0753677	−	0.0910071i
$638$	3.60426			0.142694
$639$		0			0
$640$	−12.0231	+	20.8247i	−0.475256	+	0.823167i
$641$	−4.98058	+	8.62662i	−0.196721	+	0.340731i	−0.947463	−	0.319864i	$-0.896363\pi$
$641$	−4.98058	+	8.62662i	−0.196721	+	0.340731i	0.750742	+	0.660595i	$0.229696\pi$
$642$		0			0
$643$	21.6236			0.852752			0.426376	−	0.904546i	$-0.359790\pi$
$643$	21.6236			0.852752			0.426376	+	0.904546i	$0.359790\pi$
$644$	−14.1242	−	30.0359i	−0.556573	−	1.18358i
$645$		0			0
$646$	9.82270	+	17.0134i	0.386469	+	0.669384i
$647$	−19.3679	+	33.5462i	−0.761430	+	1.31884i	0.180683	+	0.983541i	$0.442169\pi$
$647$	−19.3679	+	33.5462i	−0.761430	+	1.31884i	−0.942113	+	0.335294i	$0.891164\pi$
$648$		0			0
$649$	−1.28661	−	2.22848i	−0.0505040	−	0.0874755i
$650$	0.154877			0.00607476
$651$		0			0
$652$	18.2235			0.713686
$653$	−10.8989	−	18.8774i	−0.426506	−	0.738731i	0.570053	−	0.821608i	$-0.306922\pi$
$653$	−10.8989	−	18.8774i	−0.426506	−	0.738731i	−0.996560	+	0.0828770i	$0.973589\pi$
$654$		0			0
$655$	10.6719	−	18.4843i	0.416986	−	0.722241i
$656$	−1.47559	−	2.55579i	−0.0576120	−	0.0997870i
$657$		0			0
$658$	17.8467	+	1.50332i	0.695737	+	0.0586056i
$659$	−5.13619			−0.200078			−0.100039	−	0.994984i	$-0.531897\pi$
$659$	−5.13619			−0.200078			−0.100039	+	0.994984i	$0.531897\pi$
$660$		0			0
$661$	−6.58087	+	11.3984i	−0.255966	+	0.443347i	−0.965158	−	0.261670i	$-0.915727\pi$
$661$	−6.58087	+	11.3984i	−0.255966	+	0.443347i	0.709191	+	0.705016i	$0.249060\pi$
$662$	−6.33226	+	10.9678i	−0.246110	+	0.426276i
$663$		0			0
$664$	−11.4384			−0.443896
$665$	−29.9029	−	2.51888i	−1.15959	−	0.0976781i
$666$		0			0
$667$	−13.9475	−	24.1577i	−0.540048	−	0.935391i
$668$	2.01373	−	3.48788i	0.0779136	−	0.134950i
$669$		0			0
$670$	−3.27334	−	5.66958i	−0.126460	−	0.219035i
$671$	−8.33662			−0.321832
$672$		0			0
$673$	−7.01209			−0.270296			−0.135148	−	0.990825i	$-0.543151\pi$
$673$	−7.01209			−0.270296			−0.135148	+	0.990825i	$0.543151\pi$
$674$	4.19618	+	7.26800i	0.161631	+	0.279953i
$675$		0			0
$676$	−10.5316	+	18.2413i	−0.405062	+	0.701587i
$677$	18.4481	+	31.9531i	0.709018	+	1.22806i	0.965222	+	0.261433i	$0.0841951\pi$
$677$	18.4481	+	31.9531i	0.709018	+	1.22806i	−0.256203	+	0.966623i	$0.582472\pi$
$678$		0			0
$679$	−15.4860	−	32.9317i	−0.594298	−	1.26380i
$680$	−27.7107			−1.06266
$681$		0			0
$682$	−2.61776	+	4.53410i	−0.100239	+	0.173620i
$683$	−2.79970	+	4.84921i	−0.107127	+	0.185550i	−0.914605	−	0.404348i	$-0.867499\pi$
$683$	−2.79970	+	4.84921i	−0.107127	+	0.185550i	0.807478	+	0.589898i	$0.200832\pi$
$684$		0			0
$685$	−4.32172			−0.165125
$686$	−2.96666	−	10.6576i	−0.113268	−	0.406910i
$687$		0			0
$688$	−8.43245	−	14.6054i	−0.321484	−	0.556827i
$689$	1.16948	−	2.02559i	0.0445535	−	0.0771689i
$690$		0			0
$691$	3.19219	+	5.52903i	0.121437	+	0.210334i	0.920334	−	0.391132i	$-0.127917\pi$
$691$	3.19219	+	5.52903i	0.121437	+	0.210334i	−0.798898	+	0.601467i	$0.794583\pi$
$692$	−15.2505			−0.579738
$693$		0			0
$694$	−11.9814			−0.454807
$695$	6.95509	+	12.0466i	0.263822	+	0.456952i
$696$		0			0
$697$	4.51369	−	7.81795i	0.170968	−	0.296126i
$698$	8.34162	+	14.4481i	0.315735	+	0.546869i
$699$		0			0
$700$	−1.51053	+	2.17216i	−0.0570928	+	0.0821000i
$701$	10.9860			0.414937			0.207468	−	0.978242i	$-0.433478\pi$
$701$	10.9860			0.414937			0.207468	+	0.978242i	$0.433478\pi$
$702$		0			0
$703$	12.6593	−	21.9265i	0.477455	−	0.826975i
$704$	−0.548481	+	0.949997i	−0.0206717	+	0.0358044i
$705$		0			0
$706$	3.57955			0.134718
$707$	42.1522	+	3.55071i	1.58530	+	0.133538i
$708$		0			0
$709$	−13.2658	−	22.9771i	−0.498208	−	0.862922i	0.501790	−	0.864990i	$-0.332675\pi$
$709$	−13.2658	−	22.9771i	−0.498208	−	0.862922i	−0.999998	+	0.00206764i	$0.999342\pi$
$710$	−7.86133	+	13.6162i	−0.295030	+	0.511008i
$711$		0			0
$712$	−20.1910	−	34.9719i	−0.756691	−	1.31063i
$713$	40.5201			1.51749
$714$		0			0
$715$	−1.47439			−0.0551392
$716$	15.2456	+	26.4062i	0.569756	+	0.986847i
$717$		0			0
$718$	4.96213	−	8.59466i	0.185185	−	0.320750i
$719$	−10.4980	−	18.1831i	−0.391510	−	0.678116i	0.601139	−	0.799145i	$-0.294714\pi$
$719$	−10.4980	−	18.1831i	−0.391510	−	0.678116i	−0.992649	+	0.121029i	$0.961381\pi$
$720$		0			0
$721$	3.56959	−	5.13310i	0.132938	−	0.191167i
$722$	6.14963			0.228866
$723$		0			0
$724$	10.8764	−	18.8386i	0.404220	−	0.700129i
$725$	−1.11179	+	1.92568i	−0.0412909	+	0.0715179i
$726$		0			0
$727$	17.0632			0.632839			0.316420	−	0.948619i	$-0.397519\pi$
$727$	17.0632			0.632839			0.316420	+	0.948619i	$0.397519\pi$
$728$	−1.04387	−	2.21985i	−0.0386885	−	0.0822730i
$729$		0			0
$730$	0.993590	+	1.72095i	0.0367744	+	0.0636951i
$731$	25.7941	−	44.6768i	0.954031	−	1.65243i
$732$		0			0
$733$	17.2403	+	29.8610i	0.636784	+	1.10294i	0.986134	+	0.165950i	$0.0530689\pi$
$733$	17.2403	+	29.8610i	0.636784	+	1.10294i	−0.349351	+	0.936992i	$0.613598\pi$
$734$	3.87987			0.143208
$735$		0			0
$736$	−42.2879			−1.55875
$737$	−4.31842	−	7.47973i	−0.159071	−	0.275519i
$738$		0			0
$739$	0.685922	−	1.18805i	0.0252321	−	0.0437032i	−0.853134	−	0.521692i	$-0.825301\pi$
$739$	0.685922	−	1.18805i	0.0252321	−	0.0437032i	0.878366	+	0.477989i	$0.158634\pi$
$740$	8.05383	+	13.9497i	0.296065	+	0.512799i
$741$		0			0
$742$	−3.69214	−	7.85151i	−0.135543	−	0.288238i
$743$	8.94248			0.328068			0.164034	−	0.986455i	$-0.447549\pi$
$743$	8.94248			0.328068			0.164034	+	0.986455i	$0.447549\pi$
$744$		0			0
$745$	9.97179	−	17.2717i	0.365338	−	0.632784i
$746$	6.02145	−	10.4295i	0.220461	−	0.381850i
$747$		0			0
$748$	−16.4888			−0.602889
$749$	6.86097	−	9.86615i	0.250694	−	0.360501i
$750$		0			0
$751$	−25.2856	−	43.7959i	−0.922683	−	1.59813i	−0.795246	−	0.606287i	$-0.792658\pi$
$751$	−25.2856	−	43.7959i	−0.922683	−	1.59813i	−0.127437	−	0.991847i	$-0.540675\pi$
$752$	−11.2557	+	19.4955i	−0.410453	+	0.710926i
$753$		0			0
$754$	−0.464927	−	0.805277i	−0.0169316	−	0.0293265i
$755$	23.2563			0.846383
$756$		0			0
$757$	9.56041			0.347479			0.173739	−	0.984792i	$-0.444415\pi$
$757$	9.56041			0.347479			0.173739	+	0.984792i	$0.444415\pi$
$758$	4.57004	+	7.91555i	0.165991	+	0.287506i
$759$		0			0
$760$	−12.3416	+	21.3763i	−0.447676	+	0.775398i
$761$	18.9406	+	32.8060i	0.686595	+	1.18922i	0.972933	+	0.231089i	$0.0742289\pi$
$761$	18.9406	+	32.8060i	0.686595	+	1.18922i	−0.286337	+	0.958129i	$0.592438\pi$
$762$		0			0
$763$	45.4637	+	3.82965i	1.64590	+	0.138643i
$764$	17.4134			0.629996
$765$		0			0
$766$	2.02674	−	3.51041i	0.0732289	−	0.126836i
$767$	−0.331930	+	0.574920i	−0.0119853	+	0.0207591i
$768$		0			0
$769$	−28.5588			−1.02986			−0.514928	−	0.857234i	$-0.672181\pi$
$769$	−28.5588			−1.02986			−0.514928	+	0.857234i	$0.672181\pi$
$770$	−3.12254	+	4.49025i	−0.112529	+	0.161817i
$771$		0			0
$772$	−6.67103	−	11.5546i	−0.240096	−	0.415858i
$773$	−5.35149	+	9.26905i	−0.192480	+	0.333385i	−0.946071	−	0.323958i	$-0.894986\pi$
$773$	−5.35149	+	9.26905i	−0.192480	+	0.333385i	0.753592	+	0.657343i	$0.228320\pi$
$774$		0			0
$775$	−1.61498	−	2.79723i	−0.0580119	−	0.100480i
$776$	−29.9328			−1.07452
$777$		0			0
$778$	3.44014			0.123335
$779$	−4.02054	−	6.96379i	−0.144051	−	0.249504i
$780$		0			0
$781$	−10.3712	+	17.9635i	−0.371112	+	0.642785i
$782$	−13.8554	−	23.9982i	−0.495467	−	0.858174i
$783$		0			0
$784$	13.7092	+	2.32610i	0.489615	+	0.0830752i
$785$	−50.8235			−1.81397
$786$		0			0
$787$	18.3183	−	31.7283i	0.652978	−	1.13099i	−0.329418	−	0.944184i	$-0.606853\pi$
$787$	18.3183	−	31.7283i	0.652978	−	1.13099i	0.982397	−	0.186808i	$-0.0598141\pi$
$788$	−7.43982	+	12.8861i	−0.265033	+	0.459050i
$789$		0			0
$790$	9.55049			0.339791
$791$	−12.0190	−	25.5590i	−0.427346	−	0.908773i
$792$		0			0
$793$	1.07537	+	1.86260i	0.0381875	+	0.0661428i
$794$	0.148064	−	0.256454i	0.00525459	−	0.00910121i
$795$		0			0
$796$	6.10120	+	10.5676i	0.216251	+	0.374558i
$797$	−19.0481			−0.674717			−0.337359	−	0.941376i	$-0.609533\pi$
$797$	−19.0481			−0.674717			−0.337359	+	0.941376i	$0.609533\pi$
$798$		0			0
$799$	−68.8604			−2.43611
$800$	1.68544	+	2.91927i	0.0595893	+	0.103212i
$801$		0			0
$802$	3.10106	−	5.37119i	0.109502	−	0.189663i
$803$	1.31082	+	2.27040i	0.0462577	+	0.0801206i
$804$		0			0
$805$	42.1795	+	3.55300i	1.48663	+	0.125227i
$806$	1.35070			0.0475764
$807$		0			0
$808$	17.3971	−	30.1327i	0.612029	−	1.06006i
$809$	9.24567	−	16.0140i	0.325060	−	0.563021i	−0.656464	−	0.754357i	$-0.727949\pi$
$809$	9.24567	−	16.0140i	0.325060	−	0.563021i	0.981525	+	0.191336i	$0.0612820\pi$
$810$		0			0
$811$	41.5033			1.45738			0.728690	−	0.684844i	$-0.240130\pi$
$811$	41.5033			1.45738			0.728690	+	0.684844i	$0.240130\pi$
$812$	15.8286	+	1.33333i	0.555475	+	0.0467906i
$813$		0			0
$814$	−2.30721	−	3.99621i	−0.0808677	−	0.140067i
$815$	−11.6203	+	20.1269i	−0.407040	+	0.705014i
$816$		0			0
$817$	−22.9760	−	39.7955i	−0.803827	−	1.39227i
$818$	−17.9317			−0.626966
$819$		0			0
$820$	5.11573			0.178649
$821$	−16.2444	−	28.1360i	−0.566932	−	0.981955i	−0.996867	−	0.0790951i	$-0.974797\pi$
$821$	−16.2444	−	28.1360i	−0.566932	−	0.981955i	0.429935	−	0.902860i	$-0.358536\pi$
$822$		0			0
$823$	7.86963	−	13.6306i	0.274318	−	0.475133i	−0.695645	−	0.718386i	$-0.744881\pi$
$823$	7.86963	−	13.6306i	0.274318	−	0.475133i	0.969963	+	0.243253i	$0.0782145\pi$
$824$	−2.57133	−	4.45368i	−0.0895766	−	0.155151i
$825$		0			0
$826$	1.04793	+	2.22848i	0.0364622	+	0.0775387i
$827$	40.6095			1.41213			0.706066	−	0.708146i	$-0.250468\pi$
$827$	40.6095			1.41213			0.706066	+	0.708146i	$0.250468\pi$
$828$		0			0
$829$	−12.7290	+	22.0473i	−0.442097	+	0.765734i	−0.997845	−	0.0656169i	$-0.979098\pi$
$829$	−12.7290	+	22.0473i	−0.442097	+	0.765734i	0.555748	+	0.831351i	$0.312432\pi$
$830$	3.28970	−	5.69793i	0.114187	−	0.197778i
$831$		0			0
$832$	0.283003			0.00981135
$833$	14.8056	+	39.8747i	0.512982	+	1.38158i
$834$		0			0
$835$	2.56813	+	4.44813i	0.0888737	+	0.153934i
$836$	−7.34364	+	12.7196i	−0.253985	+	0.439915i
$837$		0			0
$838$	8.25803	+	14.3033i	0.285269	+	0.494100i
$839$	−48.3492			−1.66920			−0.834600	−	0.550856i	$-0.814301\pi$
$839$	−48.3492			−1.66920			−0.834600	+	0.550856i	$0.814301\pi$
$840$		0			0
$841$	−15.6500			−0.539654
$842$	−3.72205	−	6.44677i	−0.128270	−	0.222170i
$843$		0			0
$844$	2.20007	−	3.81064i	0.0757296	−	0.131167i
$845$	−13.4310	−	23.2632i	−0.462042	−	0.800280i
$846$		0			0
$847$	12.4964	−	17.9699i	0.429381	−	0.617454i
$848$	10.9055			0.374495
$849$		0			0
$850$	−1.10445	+	1.91296i	−0.0378823	+	0.0656141i
$851$	−17.8565	+	30.9284i	−0.612114	+	1.06021i
$852$		0			0
$853$	−2.65867			−0.0910310			−0.0455155	−	0.998964i	$-0.514493\pi$
$853$	−2.65867			−0.0910310			−0.0455155	+	0.998964i	$0.514493\pi$
$854$	7.94998	+	0.669669i	0.272043	+	0.0229156i
$855$		0			0
$856$	−4.94226	−	8.56025i	−0.168923	−	0.292583i
$857$	7.03319	−	12.1818i	0.240249	−	0.416124i	−0.720536	−	0.693417i	$-0.756104\pi$
$857$	7.03319	−	12.1818i	0.240249	−	0.416124i	0.960785	+	0.277294i	$0.0894375\pi$
$858$		0			0
$859$	9.64635	+	16.7080i	0.329129	+	0.570068i	0.982339	−	0.187108i	$-0.0599115\pi$
$859$	9.64635	+	16.7080i	0.329129	+	0.570068i	−0.653210	+	0.757177i	$0.726578\pi$
$860$	29.2346			0.996891
$861$		0			0
$862$	8.42438			0.286935
$863$	−21.1692	−	36.6661i	−0.720608	−	1.24813i	−0.960756	−	0.277393i	$-0.910530\pi$
$863$	−21.1692	−	36.6661i	−0.720608	−	1.24813i	0.240149	−	0.970736i	$-0.422804\pi$
$864$		0			0
$865$	9.72457	−	16.8434i	0.330645	−	0.572694i
$866$	4.59006	+	7.95022i	0.155977	+	0.270159i
$867$		0			0
$868$	−13.1736	+	18.9437i	−0.447140	+	0.642992i
$869$	12.5997			0.427416
$870$		0			0
$871$	−1.11410	+	1.92967i	−0.0377498	+	0.0653845i
$872$	18.7639	−	32.4999i	0.635424	−	1.10059i
$873$		0			0
$874$	−24.6832			−0.834921
$875$	−13.2327	−	28.1399i	−0.447346	−	0.951304i
$876$		0			0
$877$	5.02542	+	8.70429i	0.169697	+	0.293923i	0.938313	−	0.345787i	$-0.112388\pi$
$877$	5.02542	+	8.70429i	0.169697	+	0.293923i	−0.768617	+	0.639710i	$0.779055\pi$
$878$	−5.74809	+	9.95598i	−0.193989	+	0.335998i
$879$		0			0
$880$	−3.43722	−	5.95343i	−0.115868	−	0.200690i
$881$	25.7602			0.867885			0.433942	−	0.900941i	$-0.357122\pi$
$881$	25.7602			0.867885			0.433942	+	0.900941i	$0.357122\pi$
$882$		0			0
$883$	−53.1876			−1.78991			−0.894953	−	0.446160i	$-0.852791\pi$
$883$	−53.1876			−1.78991			−0.894953	+	0.446160i	$0.852791\pi$
$884$	2.12695	+	3.68398i	0.0715370	+	0.123906i
$885$		0			0
$886$	7.33821	−	12.7102i	0.246532	−	0.427006i
$887$	10.4758	+	18.1447i	0.351745	+	0.609239i	0.986555	−	0.163428i	$-0.0522553\pi$
$887$	10.4758	+	18.1447i	0.351745	+	0.609239i	−0.634811	+	0.772668i	$0.718922\pi$
$888$		0			0
$889$	−16.2194	−	34.4914i	−0.543982	−	1.15681i
$890$	23.2279			0.778601
$891$		0			0
$892$	17.6946	−	30.6480i	0.592460	−	1.02617i
$893$	−30.6685	+	53.1194i	−1.02628	+	1.77757i
$894$		0			0
$895$	−38.8858			−1.29981
$896$	17.3330	−	24.9251i	0.579056	−	0.832688i
$897$		0			0
$898$	−11.9481	−	20.6947i	−0.398712	−	0.690590i
$899$	−9.69609	+	16.7941i	−0.323383	+	0.560115i
$900$		0			0
$901$	16.6794	+	28.8896i	0.555672	+	0.962452i
$902$	−1.46552			−0.0487966
$903$		0			0
$904$	−23.2314			−0.772667
$905$	13.8708	+	24.0250i	0.461082	+	0.798617i
$906$		0			0
$907$	−23.7927	+	41.2102i	−0.790024	+	1.36836i	0.135928	+	0.990719i	$0.456598\pi$
$907$	−23.7927	+	41.2102i	−0.790024	+	1.36836i	−0.925952	+	0.377642i	$0.876735\pi$
$908$	−10.7637	−	18.6433i	−0.357207	−	0.618701i
$909$		0			0
$910$	1.40602	+	0.118436i	0.0466090	+	0.00392612i
$911$	29.7720			0.986389			0.493194	−	0.869919i	$-0.335829\pi$
$911$	29.7720			0.986389			0.493194	+	0.869919i	$0.335829\pi$
$912$		0			0
$913$	4.34001	−	7.51712i	0.143633	−	0.248780i
$914$	3.17668	−	5.50217i	0.105075	−	0.181995i
$915$		0			0
$916$	−27.6459			−0.913445
$917$	−15.3851	+	22.1239i	−0.508060	+	0.730595i
$918$		0			0
$919$	−15.2293	−	26.3779i	−0.502367	−	0.870126i	−0.999996	−	0.00273583i	$-0.999129\pi$
$919$	−15.2293	−	26.3779i	−0.502367	−	0.870126i	0.497629	−	0.867390i	$-0.334204\pi$
$920$	17.4084	−	30.1522i	0.573937	−	0.994088i
$921$		0			0
$922$	−4.90089	−	8.48860i	−0.161402	−	0.279557i
$923$	5.35129			0.176140
$924$		0			0
$925$	2.84678			0.0936017
$926$	−1.81110	−	3.13692i	−0.0595165	−	0.103086i
$927$		0			0
$928$	10.1191	−	17.5268i	0.332176	−	0.575346i
$929$	−10.5830	−	18.3304i	−0.347218	−	0.601400i	0.638536	−	0.769592i	$-0.279540\pi$
$929$	−10.5830	−	18.3304i	−0.347218	−	0.601400i	−0.985754	+	0.168192i	$0.946207\pi$
$930$		0			0
$931$	37.3536	+	6.33795i	1.22421	+	0.207718i
$932$	−37.4128			−1.22550
$933$		0			0
$934$	−7.55230	+	13.0810i	−0.247119	+	0.428022i
$935$	10.5141	−	18.2110i	0.343849	−	0.595564i
$936$		0			0
$937$	40.2779			1.31582			0.657912	−	0.753095i	$-0.271440\pi$
$937$	40.2779			1.31582			0.657912	+	0.753095i	$0.271440\pi$
$938$	3.51731	+	7.47973i	0.114844	+	0.244222i
$939$		0			0
$940$	−19.5113	−	33.7945i	−0.636388	−	1.10226i
$941$	0.910476	−	1.57699i	0.0296807	−	0.0514084i	−0.850804	−	0.525484i	$-0.823884\pi$
$941$	0.910476	−	1.57699i	0.0296807	−	0.0514084i	0.880484	+	0.474076i	$0.157218\pi$
$942$		0			0
$943$	5.67116	+	9.82274i	0.184678	+	0.319872i
$944$	−3.09528			−0.100743
$945$		0			0
$946$	−8.37494			−0.272293
$947$	6.74590	+	11.6842i	0.219212	+	0.379687i	0.954567	−	0.297995i	$-0.0963180\pi$
$947$	6.74590	+	11.6842i	0.219212	+	0.379687i	−0.735355	+	0.677682i	$0.762985\pi$
$948$		0			0
$949$	0.338174	−	0.585734i	0.0109776	−	0.0190137i
$950$	0.983782	+	1.70396i	0.0319181	+	0.0552838i
$951$		0			0
$952$	34.8625	+	2.93666i	1.12990	+	0.0951776i
$953$	4.95309			0.160446			0.0802232	−	0.996777i	$-0.474437\pi$
$953$	4.95309			0.160446			0.0802232	+	0.996777i	$0.474437\pi$
$954$		0			0
$955$	−11.1038	+	19.2323i	−0.359309	+	0.622342i
$956$	7.82002	−	13.5447i	0.252918	−	0.438066i
$957$		0			0
$958$	−1.99659			−0.0645069
$959$	5.43711	+	0.457996i	0.175573	+	0.0147895i
$960$		0			0
$961$	1.41551	+	2.45174i	0.0456616	+	0.0790883i
$962$	−0.595231	+	1.03097i	−0.0191910	+	0.0332398i
$963$		0			0
$964$	0.963800	+	1.66935i	0.0310419	+	0.0537661i
$965$	17.0152			0.547740
$966$		0			0
$967$	17.2566			0.554936			0.277468	−	0.960735i	$-0.410505\pi$
$967$	17.2566			0.554936			0.277468	+	0.960735i	$0.410505\pi$
$968$	−9.00170	−	15.5914i	−0.289326	−	0.501127i
$969$		0			0
$970$	8.60872	−	14.9107i	0.276409	−	0.478755i
$971$	−23.4532	−	40.6221i	−0.752649	−	1.30363i	−0.946535	−	0.322602i	$-0.895442\pi$
$971$	−23.4532	−	40.6221i	−0.752649	−	1.30363i	0.193886	−	0.981024i	$-0.437891\pi$
$972$		0			0
$973$	−7.47347	−	15.8927i	−0.239588	−	0.509497i
$974$	4.34793			0.139317
$975$		0			0
$976$	−5.01397	+	8.68444i	−0.160493	+	0.277982i
$977$	−17.5817	+	30.4524i	−0.562488	+	0.974257i	0.434791	+	0.900531i	$0.356822\pi$
$977$	−17.5817	+	30.4524i	−0.562488	+	0.974257i	−0.997279	+	0.0737259i	$0.976511\pi$
$978$		0			0
$979$	30.6439			0.979384
$980$	−15.3741	+	18.5644i	−0.491109	+	0.593018i
$981$		0			0
$982$	0.887434	+	1.53708i	0.0283192	+	0.0490502i
$983$	6.04298	−	10.4667i	0.192741	−	0.333837i	−0.753417	−	0.657544i	$-0.771596\pi$
$983$	6.04298	−	10.4667i	0.192741	−	0.333837i	0.946158	+	0.323706i	$0.104929\pi$
$984$		0			0
$985$	−9.48806	−	16.4338i	−0.302315	−	0.523625i
$986$	13.2619			0.422344
$987$		0			0
$988$	3.78913			0.120548
$989$	32.4087	+	56.1334i	1.03054	+	1.78494i
$990$		0			0
$991$	−16.1874	+	28.0374i	−0.514209	+	0.890636i	0.485655	+	0.874150i	$0.338581\pi$
$991$	−16.1874	+	28.0374i	−0.514209	+	0.890636i	−0.999864	+	0.0164855i	$0.994752\pi$
$992$	14.6990	+	25.4594i	0.466693	+	0.808335i
$993$		0			0
$994$	11.3332	−	16.2973i	0.359468	−	0.516919i
$995$	−15.5618			−0.493343
$996$		0			0
$997$	7.36660	−	12.7593i	0.233303	−	0.404092i	−0.725475	−	0.688248i	$-0.758380\pi$
$997$	7.36660	−	12.7593i	0.233303	−	0.404092i	0.958778	+	0.284156i	$0.0917134\pi$
$998$	−3.72913	+	6.45904i	−0.118044	+	0.204457i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.e.g.487.4	yes	16
3.2	odd	2	inner	567.2.e.g.487.5	yes	16
7.2	even	3	inner	567.2.e.g.163.4	✓	16
7.3	odd	6		3969.2.a.bf.1.5		8
7.4	even	3		3969.2.a.bg.1.5		8
9.2	odd	6		567.2.g.l.109.5		16
9.4	even	3		567.2.h.l.298.5		16
9.5	odd	6		567.2.h.l.298.4		16
9.7	even	3		567.2.g.l.109.4		16
21.2	odd	6	inner	567.2.e.g.163.5	yes	16
21.11	odd	6		3969.2.a.bg.1.4		8
21.17	even	6		3969.2.a.bf.1.4		8
63.2	odd	6		567.2.h.l.352.4		16
63.16	even	3		567.2.h.l.352.5		16
63.23	odd	6		567.2.g.l.541.5		16
63.58	even	3		567.2.g.l.541.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.e.g.163.4	✓	16	7.2	even	3	inner
567.2.e.g.163.5	yes	16	21.2	odd	6	inner
567.2.e.g.487.4	yes	16	1.1	even	1	trivial
567.2.e.g.487.5	yes	16	3.2	odd	2	inner
567.2.g.l.109.4		16	9.7	even	3
567.2.g.l.109.5		16	9.2	odd	6
567.2.g.l.541.4		16	63.58	even	3
567.2.g.l.541.5		16	63.23	odd	6
567.2.h.l.298.4		16	9.5	odd	6
567.2.h.l.298.5		16	9.4	even	3
567.2.h.l.352.4		16	63.2	odd	6
567.2.h.l.352.5		16	63.16	even	3
3969.2.a.bf.1.4		8	21.17	even	6
3969.2.a.bf.1.5		8	7.3	odd	6
3969.2.a.bg.1.4		8	21.11	odd	6
3969.2.a.bg.1.5		8	7.4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.298668 - 0.517308i) q^{2} +(0.821595 - 1.42304i) q^{4} +(1.04779 + 1.81482i) q^{5} +(-1.12588 - 2.39424i) q^{7} -2.17621 q^{8} +(0.625881 - 1.08406i) q^{10} +(0.825707 - 1.43017i) q^{11} -0.426044 q^{13} +(-0.902296 + 1.29751i) q^{14} +(-0.993225 - 1.72032i) q^{16} +(3.03819 - 5.26230i) q^{17} +(-2.70625 - 4.68736i) q^{19} +3.44342 q^{20} -0.986450 q^{22} +(3.81729 + 6.61173i) q^{23} +(0.304286 - 0.527039i) q^{25} +(0.127246 + 0.220396i) q^{26} +(-4.33213 - 0.364918i) q^{28} -3.65377 q^{29} +(2.65372 - 4.59638i) q^{31} +(-2.76950 + 4.79691i) q^{32} -3.62964 q^{34} +(3.16543 - 4.55193i) q^{35} +(2.33890 + 4.05110i) q^{37} +(-1.61654 + 2.79993i) q^{38} +(-2.28020 - 3.94943i) q^{40} +1.48565 q^{41} +8.48997 q^{43} +(-1.35679 - 2.35004i) q^{44} +(2.28020 - 3.94943i) q^{46} +(-5.66624 - 9.81422i) q^{47} +(-4.46478 + 5.39126i) q^{49} -0.363522 q^{50} +(-0.350036 + 0.606280i) q^{52} +(-2.74496 + 4.75441i) q^{53} +3.46066 q^{55} +(2.45015 + 5.21037i) q^{56} +(1.09126 + 1.89013i) q^{58} +(0.779098 - 1.34944i) q^{59} +(-2.52408 - 4.37184i) q^{61} -3.17033 q^{62} -0.664256 q^{64} +(-0.446403 - 0.773193i) q^{65} +(2.61498 - 4.52928i) q^{67} +(-4.99232 - 8.64695i) q^{68} +(-3.30016 - 0.277990i) q^{70} -12.5604 q^{71} +(-0.793753 + 1.37482i) q^{73} +(1.39711 - 2.41987i) q^{74} -8.89375 q^{76} +(-4.35381 - 0.366745i) q^{77} +(3.81482 + 6.60746i) q^{79} +(2.08138 - 3.60505i) q^{80} +(-0.443717 - 0.768541i) q^{82} +5.25611 q^{83} +12.7335 q^{85} +(-2.53568 - 4.39193i) q^{86} +(-1.79691 + 3.11234i) q^{88} +(9.27808 + 16.0701i) q^{89} +(0.479675 + 1.02005i) q^{91} +12.5450 q^{92} +(-3.38465 + 5.86239i) q^{94} +(5.67114 - 9.82270i) q^{95} +13.7546 q^{97} +(4.12243 + 0.699472i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{4} + 6 q^{7} - 14 q^{10} + 12 q^{13} - 6 q^{16} - 24 q^{19} + 4 q^{22} - 26 q^{28} - 20 q^{31} + 4 q^{37} - 36 q^{40} + 20 q^{43} + 36 q^{46} - 14 q^{49} - 34 q^{52} + 8 q^{55} + 22 q^{58} - 36 q^{61}+ \cdots + 28 q^{97}+O(q^{100}) \) 16 * q - 6 * q^4 + 6 * q^7 - 14 * q^10 + 12 * q^13 - 6 * q^16 - 24 * q^19 + 4 * q^22 - 26 * q^28 - 20 * q^31 + 4 * q^37 - 36 * q^40 + 20 * q^43 + 36 * q^46 - 14 * q^49 - 34 * q^52 + 8 * q^55 + 22 * q^58 - 36 * q^61 + 76 * q^64 + 18 * q^67 - 58 * q^70 - 32 * q^73 + 116 * q^76 + 32 * q^79 + 2 * q^82 + 60 * q^85 + 72 * q^88 - 22 * q^91 - 54 * q^94 + 28 * q^97

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