LMFDB - Embedded newform 864.2.bi.a.767.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(95,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 17]))

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

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

chi := DirichletCharacter("864.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bi (of order $18$, degree $6$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$36$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			767.20
Character	$\chi$	$=$	864.767
Dual form			864.2.bi.a.383.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.139305 + 1.72644i) q^{3} +(0.518562 - 1.42474i) q^{5} +(-0.501230 - 0.0883804i) q^{7} +(-2.96119 + 0.481002i) q^{9} +O(q^{10})$	\(q+(0.139305 + 1.72644i) q^{3} +(0.518562 - 1.42474i) q^{5} +(-0.501230 - 0.0883804i) q^{7} +(-2.96119 + 0.481002i) q^{9} +(4.41709 - 1.60769i) q^{11} +(-3.89951 + 3.27207i) q^{13} +(2.53196 + 0.696793i) q^{15} +(1.93458 - 1.11693i) q^{17} +(7.05476 + 4.07307i) q^{19} +(0.0827598 - 0.877655i) q^{21} +(1.33011 + 7.54345i) q^{23} +(2.06925 + 1.73631i) q^{25} +(-1.24293 - 5.04531i) q^{27} +(-1.30648 + 1.55700i) q^{29} +(3.19967 - 0.564188i) q^{31} +(3.39090 + 7.40188i) q^{33} +(-0.385837 + 0.668290i) q^{35} +(-1.23366 - 2.13675i) q^{37} +(-6.19226 - 6.27645i) q^{39} +(6.02039 + 7.17482i) q^{41} +(-2.39164 - 6.57097i) q^{43} +(-0.850258 + 4.46834i) q^{45} +(-1.25088 + 7.09409i) q^{47} +(-6.33443 - 2.30554i) q^{49} +(2.19780 + 3.18433i) q^{51} -5.06730i q^{53} -7.12688i q^{55} +(-6.04915 + 12.7470i) q^{57} +(4.68437 + 1.70497i) q^{59} +(2.15983 - 12.2490i) q^{61} +(1.52675 + 0.0206185i) q^{63} +(2.63971 + 7.25254i) q^{65} +(1.40862 + 1.67872i) q^{67} +(-12.8380 + 3.34720i) q^{69} +(3.91962 + 6.78898i) q^{71} +(-5.20400 + 9.01360i) q^{73} +(-2.70938 + 3.81432i) q^{75} +(-2.35607 + 0.415438i) q^{77} +(0.00253083 - 0.00301612i) q^{79} +(8.53727 - 2.84867i) q^{81} +(-3.58383 - 3.00719i) q^{83} +(-0.588131 - 3.33546i) q^{85} +(-2.87006 - 2.03866i) q^{87} +(-5.26277 - 3.03846i) q^{89} +(2.24374 - 1.29542i) q^{91} +(1.41977 + 5.44544i) q^{93} +(9.46138 - 7.93904i) q^{95} +(-2.65220 + 0.965320i) q^{97} +(-12.3065 + 6.88530i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q+O(q^{10}) $ 216 * q	$ 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) $ 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{13}{18}\right)$	$-1$

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			0
$2$		0			0
$3$	0.139305	+	1.72644i	0.0804275	+	0.996760i
$3$	0.139305	+	1.72644i	0.0804275	+	0.996760i
$4$		0			0
$5$	0.518562	−	1.42474i	0.231908	−	0.637162i	−0.768087	−	0.640345i	$-0.778791\pi$
$5$	0.518562	−	1.42474i	0.231908	−	0.637162i	0.999995	+	0.00318383i	$0.00101345\pi$
$6$		0			0
$7$	−0.501230	−	0.0883804i	−0.189447	−	0.0334046i	0.0781195	−	0.996944i	$-0.475108\pi$
$7$	−0.501230	−	0.0883804i	−0.189447	−	0.0334046i	−0.267567	+	0.963539i	$0.586220\pi$
$8$		0			0
$9$	−2.96119	+	0.481002i	−0.987063	+	0.160334i
$10$		0			0
$11$	4.41709	−	1.60769i	1.33180	−	0.484737i	0.424582	−	0.905390i	$-0.360421\pi$
$11$	4.41709	−	1.60769i	1.33180	−	0.484737i	0.907222	+	0.420653i	$0.138199\pi$
$12$		0			0
$13$	−3.89951	+	3.27207i	−1.08153	+	0.907510i	−0.996047	−	0.0888299i	$-0.971687\pi$
$13$	−3.89951	+	3.27207i	−1.08153	+	0.907510i	−0.0854813	+	0.996340i	$0.527243\pi$
$14$		0			0
$15$	2.53196	+	0.696793i	0.653749	+	0.179911i
$16$		0			0
$17$	1.93458	−	1.11693i	0.469203	−	0.270895i	−0.246703	−	0.969091i	$-0.579347\pi$
$17$	1.93458	−	1.11693i	0.469203	−	0.270895i	0.715906	+	0.698196i	$0.246014\pi$
$18$		0			0
$19$	7.05476	+	4.07307i	1.61847	+	0.934426i	0.987315	+	0.158772i	$0.0507535\pi$
$19$	7.05476	+	4.07307i	1.61847	+	0.934426i	0.631158	+	0.775654i	$0.282580\pi$
$20$		0			0
$21$	0.0827598	−	0.877655i	0.0180597	−	0.191520i
$22$		0			0
$23$	1.33011	+	7.54345i	0.277348	+	1.57292i	0.731404	+	0.681944i	$0.238865\pi$
$23$	1.33011	+	7.54345i	0.277348	+	1.57292i	−0.454056	+	0.890973i	$0.650023\pi$
$24$		0			0
$25$	2.06925	+	1.73631i	0.413851	+	0.347262i
$26$		0			0
$27$	−1.24293	−	5.04531i	−0.239201	−	0.970970i
$28$		0			0
$29$	−1.30648	+	1.55700i	−0.242607	+	0.289127i	−0.873584	−	0.486674i	$-0.838210\pi$
$29$	−1.30648	+	1.55700i	−0.242607	+	0.289127i	0.630977	+	0.775802i	$0.282654\pi$
$30$		0			0
$31$	3.19967	−	0.564188i	0.574678	−	0.101331i	0.121246	−	0.992622i	$-0.461311\pi$
$31$	3.19967	−	0.564188i	0.574678	−	0.101331i	0.453431	+	0.891291i	$0.350200\pi$
$32$		0			0
$33$	3.39090	+	7.40188i	0.590280	+	1.28850i
$34$		0			0
$35$	−0.385837	+	0.668290i	−0.0652184	+	0.112962i
$36$		0			0
$37$	−1.23366	−	2.13675i	−0.202812	−	0.351280i	0.746622	−	0.665249i	$-0.231675\pi$
$37$	−1.23366	−	2.13675i	−0.202812	−	0.351280i	−0.949433	+	0.313969i	$0.898341\pi$
$38$		0			0
$39$	−6.19226	−	6.27645i	−0.991555	−	1.00504i
$40$		0			0
$41$	6.02039	+	7.17482i	0.940227	+	1.12052i	0.992544	+	0.121888i	$0.0388950\pi$
$41$	6.02039	+	7.17482i	0.940227	+	1.12052i	−0.0523169	+	0.998631i	$0.516661\pi$
$42$		0			0
$43$	−2.39164	−	6.57097i	−0.364721	−	1.00206i	−0.977338	−	0.211684i	$-0.932105\pi$
$43$	−2.39164	−	6.57097i	−0.364721	−	1.00206i	0.612617	−	0.790380i	$-0.290117\pi$
$44$		0			0
$45$	−0.850258	+	4.46834i	−0.126749	+	0.666101i
$46$		0			0
$47$	−1.25088	+	7.09409i	−0.182459	+	1.03478i	0.746717	+	0.665142i	$0.231629\pi$
$47$	−1.25088	+	7.09409i	−0.182459	+	1.03478i	−0.929176	+	0.369637i	$0.879482\pi$
$48$		0			0
$49$	−6.33443	−	2.30554i	−0.904918	−	0.329363i
$50$		0			0
$51$	2.19780	+	3.18433i	0.307754	+	0.445896i
$52$		0			0
$53$		−	5.06730i		−	0.696047i	−0.937486	−	0.348024i	$-0.886853\pi$
$53$		−	5.06730i		−	0.696047i	0.937486	−	0.348024i	$-0.113147\pi$
$54$		0			0
$55$		−	7.12688i		−	0.960988i
$56$		0			0
$57$	−6.04915	+	12.7470i	−0.801229	+	1.68838i
$58$		0			0
$59$	4.68437	+	1.70497i	0.609854	+	0.221969i	0.628439	−	0.777859i	$-0.283694\pi$
$59$	4.68437	+	1.70497i	0.609854	+	0.221969i	−0.0185856	+	0.999827i	$0.505916\pi$
$60$		0			0
$61$	2.15983	−	12.2490i	0.276537	−	1.56832i	−0.457498	−	0.889210i	$-0.651254\pi$
$61$	2.15983	−	12.2490i	0.276537	−	1.56832i	0.734036	−	0.679111i	$-0.237634\pi$
$62$		0			0
$63$	1.52675	+	0.0206185i	0.192352	+	0.00259768i
$64$		0			0
$65$	2.63971	+	7.25254i	0.327416	+	0.899567i
$66$		0			0
$67$	1.40862	+	1.67872i	0.172090	+	0.205089i	0.845195	−	0.534458i	$-0.179484\pi$
$67$	1.40862	+	1.67872i	0.172090	+	0.205089i	−0.673105	+	0.739547i	$0.735040\pi$
$68$		0			0
$69$	−12.8380	+	3.34720i	−1.54552	+	0.402955i
$70$		0			0
$71$	3.91962	+	6.78898i	0.465173	+	0.805703i	0.999209	−	0.0397583i	$-0.0126588\pi$
$71$	3.91962	+	6.78898i	0.465173	+	0.805703i	−0.534036	+	0.845462i	$0.679325\pi$
$72$		0			0
$73$	−5.20400	+	9.01360i	−0.609083	+	1.05496i	0.382309	+	0.924034i	$0.375129\pi$
$73$	−5.20400	+	9.01360i	−0.609083	+	1.05496i	−0.991392	+	0.130928i	$0.958204\pi$
$74$		0			0
$75$	−2.70938	+	3.81432i	−0.312852	+	0.440440i
$76$		0			0
$77$	−2.35607	+	0.415438i	−0.268499	+	0.0473436i
$78$		0			0
$79$	0.00253083	−	0.00301612i	0.000284740	−	0.000339340i	−0.765902	−	0.642957i	$-0.777707\pi$
$79$	0.00253083	−	0.00301612i	0.000284740	−	0.000339340i	0.766187	+	0.642618i	$0.222152\pi$
$80$		0			0
$81$	8.53727	−	2.84867i	0.948586	−	0.316519i
$82$		0			0
$83$	−3.58383	−	3.00719i	−0.393376	−	0.330082i	0.424550	−	0.905404i	$-0.360432\pi$
$83$	−3.58383	−	3.00719i	−0.393376	−	0.330082i	−0.817927	+	0.575322i	$0.804877\pi$
$84$		0			0
$85$	−0.588131	−	3.33546i	−0.0637918	−	0.361781i
$86$		0			0
$87$	−2.87006	−	2.03866i	−0.307703	−	0.218567i
$88$		0			0
$89$	−5.26277	−	3.03846i	−0.557852	−	0.322076i	0.194431	−	0.980916i	$-0.437714\pi$
$89$	−5.26277	−	3.03846i	−0.557852	−	0.322076i	−0.752283	+	0.658840i	$0.771047\pi$
$90$		0			0
$91$	2.24374	−	1.29542i	0.235207	−	0.135797i
$92$		0			0
$93$	1.41977	+	5.44544i	0.147223	+	0.564666i
$94$		0			0
$95$	9.46138	−	7.93904i	0.970717	−	0.814528i
$96$		0			0
$97$	−2.65220	+	0.965320i	−0.269290	+	0.0980134i	−0.473136	−	0.880990i	$-0.656878\pi$
$97$	−2.65220	+	0.965320i	−0.269290	+	0.0980134i	0.203846	+	0.979003i	$0.434656\pi$
$98$		0			0
$99$	−12.3065	+	6.88530i	−1.23685	+	0.691999i
$100$		0			0
$101$	10.3032	+	1.81673i	1.02521	+	0.180772i	0.660874	−	0.750497i	$-0.270186\pi$
$101$	10.3032	+	1.81673i	1.02521	+	0.180772i	0.364333	+	0.931269i	$0.381297\pi$
$102$		0			0
$103$	1.12558	−	3.09249i	0.110906	−	0.304712i	−0.871806	−	0.489851i	$-0.837051\pi$
$103$	1.12558	−	3.09249i	0.110906	−	0.304712i	0.982712	+	0.185139i	$0.0592734\pi$
$104$		0			0
$105$	−1.20751	−	0.573029i	−0.117841	−	0.0559219i
$106$		0			0
$107$	−11.4514			−1.10705			−0.553525	−	0.832833i	$-0.686718\pi$
$107$	−11.4514			−1.10705			−0.553525	+	0.832833i	$0.686718\pi$
$108$		0			0
$109$	−13.3373			−1.27748			−0.638739	−	0.769424i	$-0.720544\pi$
$109$	−13.3373			−1.27748			−0.638739	+	0.769424i	$0.720544\pi$
$110$		0			0
$111$	3.51712	−	2.42749i	0.333830	−	0.230407i
$112$		0			0
$113$	0.209824	−	0.576488i	0.0197386	−	0.0542314i	−0.929432	−	0.368993i	$-0.879702\pi$
$113$	0.209824	−	0.576488i	0.0197386	−	0.0542314i	0.949171	+	0.314762i	$0.101925\pi$
$114$		0			0
$115$	11.4372	+	2.01668i	1.06652	+	0.188057i
$116$		0			0
$117$	9.97330	−	11.5649i	0.922032	−	1.06917i
$118$		0			0
$119$	−1.06838	+	0.388859i	−0.0979384	+	0.0356466i
$120$		0			0
$121$	8.49954	−	7.13196i	0.772686	−	0.648360i
$122$		0			0
$123$	−11.5482	+	11.3933i	−1.04127	+	1.02730i
$124$		0			0
$125$	10.1120	−	5.83819i	0.904449	−	0.522184i
$126$		0			0
$127$	4.15798	+	2.40061i	0.368961	+	0.213020i	0.673004	−	0.739639i	$-0.265004\pi$
$127$	4.15798	+	2.40061i	0.368961	+	0.213020i	−0.304044	+	0.952658i	$0.598337\pi$
$128$		0			0
$129$	11.0112	−	5.04439i	0.969484	−	0.444133i
$130$		0			0
$131$	0.467939	+	2.65381i	0.0408840	+	0.231865i	0.998402	−	0.0565084i	$-0.0179968\pi$
$131$	0.467939	+	2.65381i	0.0408840	+	0.231865i	−0.957518	+	0.288373i	$0.906886\pi$
$132$		0			0
$133$	−3.17608	−	2.66505i	−0.275401	−	0.231089i
$134$		0			0
$135$	−7.83277	−	0.845459i	−0.674137	−	0.0727656i
$136$		0			0
$137$	11.9434	−	14.2336i	1.02039	−	1.21606i	0.0442291	−	0.999021i	$-0.485917\pi$
$137$	11.9434	−	14.2336i	1.02039	−	1.21606i	0.976164	−	0.217035i	$-0.0696387\pi$
$138$		0			0
$139$	10.6335	−	1.87498i	0.901923	−	0.159033i	0.296589	−	0.955005i	$-0.404151\pi$
$139$	10.6335	−	1.87498i	0.901923	−	0.159033i	0.605334	+	0.795972i	$0.293040\pi$
$140$		0			0
$141$	−12.4218	−	1.17133i	−1.04610	−	0.0986437i
$142$		0			0
$143$	−11.9640	+	20.7222i	−1.00048	+	1.73288i
$144$		0			0
$145$	1.54082	+	2.66879i	0.127958	+	0.221631i
$146$		0			0
$147$	3.09797	−	11.2572i	0.255516	−	0.928477i
$148$		0			0
$149$	5.55381	+	6.61877i	0.454986	+	0.542231i	0.943957	−	0.330069i	$-0.107072\pi$
$149$	5.55381	+	6.61877i	0.454986	+	0.542231i	−0.488971	+	0.872300i	$0.662628\pi$
$150$		0			0
$151$	−6.93484	−	19.0533i	−0.564349	−	1.55054i	−0.813194	−	0.581993i	$-0.802273\pi$
$151$	−6.93484	−	19.0533i	−0.564349	−	1.55054i	0.248844	−	0.968543i	$-0.419949\pi$
$152$		0			0
$153$	−5.19140	+	4.23797i	−0.419700	+	0.342619i
$154$		0			0
$155$	0.855407	−	4.85125i	0.0687079	−	0.389662i
$156$		0			0
$157$	−10.8184	−	3.93757i	−0.863400	−	0.314252i	−0.127909	−	0.991786i	$-0.540826\pi$
$157$	−10.8184	−	3.93757i	−0.863400	−	0.314252i	−0.735492	+	0.677534i	$0.763049\pi$
$158$		0			0
$159$	8.74839	−	0.705898i	0.693792	−	0.0559813i
$160$		0			0
$161$		−	3.89856i		−	0.307249i
$162$		0			0
$163$		−	7.27022i		−	0.569447i	−0.958610	−	0.284724i	$-0.908098\pi$
$163$		−	7.27022i		−	0.569447i	0.958610	−	0.284724i	$-0.0919018\pi$
$164$		0			0
$165$	12.3041	−	0.992806i	0.957875	−	0.0772899i
$166$		0			0
$167$	−1.37941	−	0.502065i	−0.106742	−	0.0388510i	0.288097	−	0.957601i	$-0.406977\pi$
$167$	−1.37941	−	0.502065i	−0.106742	−	0.0388510i	−0.394839	+	0.918750i	$0.629200\pi$
$168$		0			0
$169$	2.24225	−	12.7164i	0.172481	−	0.978187i
$170$		0			0
$171$	−22.8496	−	8.66777i	−1.74736	−	0.662841i
$172$		0			0
$173$	−8.65125	−	23.7691i	−0.657743	−	1.80713i	−0.586922	−	0.809644i	$-0.699660\pi$
$173$	−8.65125	−	23.7691i	−0.657743	−	1.80713i	−0.0708207	−	0.997489i	$-0.522562\pi$
$174$		0			0
$175$	−0.883716	−	1.05317i	−0.0668027	−	0.0796123i
$176$		0			0
$177$	−2.29098	+	8.32480i	−0.172200	+	0.625730i
$178$		0			0
$179$	−1.97000	−	3.41214i	−0.147245	−	0.255035i	0.782963	−	0.622068i	$-0.213707\pi$
$179$	−1.97000	−	3.41214i	−0.147245	−	0.255035i	−0.930208	+	0.367032i	$0.880374\pi$
$180$		0			0
$181$	12.5433	−	21.7256i	0.932334	−	1.61485i	0.153013	−	0.988224i	$-0.451103\pi$
$181$	12.5433	−	21.7256i	0.932334	−	1.61485i	0.779321	−	0.626625i	$-0.215564\pi$
$182$		0			0
$183$	21.4480	+	2.02247i	1.58548	+	0.149505i
$184$		0			0
$185$	−3.68404	+	0.649595i	−0.270856	+	0.0477592i
$186$		0			0
$187$	6.74952	−	8.04377i	0.493574	−	0.588219i
$188$		0			0
$189$	0.177086	+	2.63871i	0.0128811	+	0.191938i
$190$		0			0
$191$	7.28570	+	6.11343i	0.527175	+	0.442352i	0.867124	−	0.498091i	$-0.165966\pi$
$191$	7.28570	+	6.11343i	0.527175	+	0.442352i	−0.339950	+	0.940444i	$0.610410\pi$
$192$		0			0
$193$	−2.22671	−	12.6283i	−0.160282	−	0.909005i	−0.953797	−	0.300453i	$-0.902862\pi$
$193$	−2.22671	−	12.6283i	−0.160282	−	0.909005i	0.793514	−	0.608551i	$-0.208249\pi$
$194$		0			0
$195$	−12.1533	+	5.56761i	−0.870319	+	0.398705i
$196$		0			0
$197$	4.57077	+	2.63894i	0.325654	+	0.188017i	0.653910	−	0.756572i	$-0.273127\pi$
$197$	4.57077	+	2.63894i	0.325654	+	0.188017i	−0.328256	+	0.944589i	$0.606461\pi$
$198$		0			0
$199$	2.87678	−	1.66091i	0.203929	−	0.117739i	−0.394558	−	0.918871i	$-0.629102\pi$
$199$	2.87678	−	1.66091i	0.203929	−	0.117739i	0.598487	+	0.801132i	$0.295769\pi$
$200$		0			0
$201$	−2.70199	+	2.66574i	−0.190584	+	0.188027i
$202$		0			0
$203$	0.792453	−	0.664947i	0.0556193	−	0.0466702i
$204$		0			0
$205$	13.3442	−	4.85688i	0.931998	−	0.339219i
$206$		0			0
$207$	−7.56713	−	21.6978i	−0.525952	−	1.50810i
$208$		0			0
$209$	37.7098	+	6.64925i	2.60844	+	0.459938i
$210$		0			0
$211$	−7.57239	+	20.8050i	−0.521305	+	1.43227i	0.347764	+	0.937582i	$0.386941\pi$
$211$	−7.57239	+	20.8050i	−0.521305	+	1.43227i	−0.869069	+	0.494691i	$0.835281\pi$
$212$		0			0
$213$	−11.1747	+	7.71272i	−0.765680	+	0.528467i
$214$		0			0
$215$	−10.6021			−0.723058
$216$		0			0
$217$	−1.65363			−0.112256
$218$		0			0
$219$	−16.2864	−	7.72877i	−1.10053	−	0.522262i
$220$		0			0
$221$	−3.88922	+	10.6855i	−0.261617	+	0.718787i
$222$		0			0
$223$	−24.2048	−	4.26795i	−1.62087	−	0.285803i	−0.711781	−	0.702402i	$-0.752111\pi$
$223$	−24.2048	−	4.26795i	−1.62087	−	0.285803i	−0.909091	+	0.416598i	$0.863222\pi$
$224$		0			0
$225$	−6.96262	−	4.14623i	−0.464175	−	0.276415i
$226$		0			0
$227$	8.11984	−	2.95538i	0.538933	−	0.196156i	−0.0581897	−	0.998306i	$-0.518533\pi$
$227$	8.11984	−	2.95538i	0.538933	−	0.196156i	0.597123	+	0.802150i	$0.296311\pi$
$228$		0			0
$229$	−11.4209	+	9.58325i	−0.754712	+	0.633279i	−0.936745	−	0.350014i	$-0.886177\pi$
$229$	−11.4209	+	9.58325i	−0.754712	+	0.633279i	0.182032	+	0.983293i	$0.441732\pi$
$230$		0			0
$231$	−1.04544	−	4.00973i	−0.0687849	−	0.263821i
$232$		0			0
$233$	−14.1548	+	8.17227i	−0.927311	+	0.535383i	−0.885960	−	0.463762i	$-0.846499\pi$
$233$	−14.1548	+	8.17227i	−0.927311	+	0.535383i	−0.0413506	+	0.999145i	$0.513166\pi$
$234$		0			0
$235$	9.45854	+	5.46089i	0.617007	+	0.356229i
$236$		0			0
$237$	0.00555971	+	0.00394916i	0.000361142	+	0.000256526i
$238$		0			0
$239$	5.09290	+	28.8832i	0.329432	+	1.86830i	0.476499	+	0.879175i	$0.341906\pi$
$239$	5.09290	+	28.8832i	0.329432	+	1.86830i	−0.147067	+	0.989127i	$0.546983\pi$
$240$		0			0
$241$	−13.1975	−	11.0740i	−0.850123	−	0.713338i	0.109694	−	0.993965i	$-0.465013\pi$
$241$	−13.1975	−	11.0740i	−0.850123	−	0.713338i	−0.959817	+	0.280627i	$0.909457\pi$
$242$		0			0
$243$	6.10734	+	14.3423i	0.391786	+	0.920056i
$244$		0			0
$245$	−6.56958	+	7.82932i	−0.419715	+	0.500197i
$246$		0			0
$247$	−40.8375	+	7.20075i	−2.59843	+	0.458173i
$248$		0			0
$249$	4.69249	−	6.60618i	0.297374	−	0.418650i
$250$		0			0
$251$	−0.696958	+	1.20717i	−0.0439916	+	0.0761956i	−0.887183	−	0.461418i	$-0.847341\pi$
$251$	−0.696958	+	1.20717i	−0.0439916	+	0.0761956i	0.843191	+	0.537614i	$0.180674\pi$
$252$		0			0
$253$	18.0028	+	31.1817i	1.13182	+	1.96038i
$254$		0			0
$255$	5.67653	−	1.48002i	0.355478	−	0.0926822i
$256$		0			0
$257$	−11.6767	−	13.9158i	−0.728373	−	0.868042i	0.267042	−	0.963685i	$-0.413954\pi$
$257$	−11.6767	−	13.9158i	−0.728373	−	0.868042i	−0.995416	+	0.0956432i	$0.969509\pi$
$258$		0			0
$259$	0.429498	+	1.18004i	0.0266877	+	0.0733238i
$260$		0			0
$261$	3.11981	−	5.23898i	0.193111	−	0.324285i
$262$		0			0
$263$	3.45802	−	19.6114i	0.213231	−	1.20929i	−0.670720	−	0.741710i	$-0.734015\pi$
$263$	3.45802	−	19.6114i	0.213231	−	1.20929i	0.883951	−	0.467580i	$-0.154874\pi$
$264$		0			0
$265$	−7.21957	−	2.62771i	−0.443495	−	0.161419i
$266$		0			0
$267$	4.51259	−	9.50912i	0.276166	−	0.581949i
$268$		0			0
$269$		−	19.5616i		−	1.19269i	−0.802727	−	0.596347i	$-0.796618\pi$
$269$		−	19.5616i		−	1.19269i	0.802727	−	0.596347i	$-0.203382\pi$
$270$		0			0
$271$		−	6.55736i		−	0.398331i	−0.979966	−	0.199165i	$-0.936177\pi$
$271$		−	6.55736i		−	0.398331i	0.979966	−	0.199165i	$-0.0638231\pi$
$272$		0			0
$273$	2.54903	+	3.69322i	0.154274	+	0.223524i
$274$		0			0
$275$	11.9315	+	4.34272i	0.719499	+	0.261876i
$276$		0			0
$277$	−1.92524	+	10.9186i	−0.115677	+	0.656034i	0.870736	+	0.491750i	$0.163643\pi$
$277$	−1.92524	+	10.9186i	−0.115677	+	0.656034i	−0.986413	+	0.164284i	$0.947469\pi$
$278$		0			0
$279$	−9.20345	+	3.20971i	−0.550996	+	0.192161i
$280$		0			0
$281$	1.05582	+	2.90083i	0.0629847	+	0.173049i	0.967193	−	0.254043i	$-0.0817604\pi$
$281$	1.05582	+	2.90083i	0.0629847	+	0.173049i	−0.904208	+	0.427092i	$0.859538\pi$
$282$		0			0
$283$	6.88354	+	8.20348i	0.409184	+	0.487647i	0.930797	−	0.365535i	$-0.119114\pi$
$283$	6.88354	+	8.20348i	0.409184	+	0.487647i	−0.521613	+	0.853182i	$0.674670\pi$
$284$		0			0
$285$	15.0243	+	15.2286i	0.889962	+	0.902062i
$286$		0			0
$287$	−2.38349	−	4.12832i	−0.140693	−	0.243687i
$288$		0			0
$289$	−6.00495	+	10.4009i	−0.353232	+	0.611816i
$290$		0			0
$291$	−2.03603	−	4.44438i	−0.119354	−	0.260534i
$292$		0			0
$293$	−9.39323	+	1.65628i	−0.548758	+	0.0967609i	−0.441151	−	0.897433i	$-0.645430\pi$
$293$	−9.39323	+	1.65628i	−0.548758	+	0.0967609i	−0.107607	+	0.994194i	$0.534319\pi$
$294$		0			0
$295$	4.85827	−	5.78987i	0.282860	−	0.337099i
$296$		0			0
$297$	−13.6014	−	20.2873i	−0.789234	−	1.17719i
$298$		0			0
$299$	−29.8695	−	25.0635i	−1.72740	−	1.44946i
$300$		0			0
$301$	0.618016	+	3.50494i	0.0356218	+	0.202021i
$302$		0			0
$303$	−1.70120	+	18.0409i	−0.0977312	+	1.03643i
$304$		0			0
$305$	−16.3316	−	9.42904i	−0.935143	−	0.539905i
$306$		0			0
$307$	22.3083	−	12.8797i	1.27320	−	0.735085i	0.297614	−	0.954686i	$-0.403809\pi$
$307$	22.3083	−	12.8797i	1.27320	−	0.735085i	0.975590	+	0.219602i	$0.0704758\pi$
$308$		0			0
$309$	5.49580	+	1.51244i	0.312645	+	0.0860397i
$310$		0			0
$311$	−18.6602	+	15.6578i	−1.05812	+	0.887870i	−0.993924	−	0.110067i	$-0.964894\pi$
$311$	−18.6602	+	15.6578i	−1.05812	+	0.887870i	−0.0641985	+	0.997937i	$0.520449\pi$
$312$		0			0
$313$	16.6535	−	6.06137i	0.941310	−	0.342609i	0.174627	−	0.984635i	$-0.444128\pi$
$313$	16.6535	−	6.06137i	0.941310	−	0.342609i	0.766683	+	0.642026i	$0.221906\pi$
$314$		0			0
$315$	0.821089	−	2.16452i	0.0462631	−	0.121957i
$316$		0			0
$317$	2.68693	+	0.473778i	0.150913	+	0.0266100i	0.248594	−	0.968608i	$-0.420031\pi$
$317$	2.68693	+	0.473778i	0.150913	+	0.0266100i	−0.0976813	+	0.995218i	$0.531143\pi$
$318$		0			0
$319$	−3.26766	+	8.97782i	−0.182954	+	0.502661i
$320$		0			0
$321$	−1.59523	−	19.7702i	−0.0890372	−	1.10346i
$322$		0			0
$323$	18.1973			1.01252
$324$		0			0
$325$	−13.7504			−0.762735
$326$		0			0
$327$	−1.85794	−	23.0260i	−0.102744	−	1.27334i
$328$		0			0
$329$	1.25396	−	3.44521i	0.0691328	−	0.189941i
$330$		0			0
$331$	−22.1104	−	3.89867i	−1.21530	−	0.214290i	−0.470998	−	0.882134i	$-0.656106\pi$
$331$	−22.1104	−	3.89867i	−1.21530	−	0.214290i	−0.744301	+	0.667844i	$0.767217\pi$
$332$		0			0
$333$	4.68087	+	5.73394i	0.256510	+	0.314218i
$334$		0			0
$335$	3.12219	−	1.13638i	0.170584	−	0.0620873i
$336$		0			0
$337$	−2.99694	+	2.51473i	−0.163254	+	0.136986i	−0.720755	−	0.693190i	$-0.756205\pi$
$337$	−2.99694	+	2.51473i	−0.163254	+	0.136986i	0.557501	+	0.830176i	$0.311760\pi$
$338$		0			0
$339$	1.02450	+	0.281942i	0.0556433	+	0.0153130i
$340$		0			0
$341$	13.2262	−	7.63615i	0.716239	−	0.413520i
$342$		0			0
$343$	6.05666	+	3.49681i	0.327029	+	0.188810i
$344$		0			0
$345$	−1.88843	+	20.0265i	−0.101670	+	1.07819i
$346$		0			0
$347$	−3.72726	−	21.1384i	−0.200090	−	1.13477i	−0.904981	−	0.425452i	$-0.860115\pi$
$347$	−3.72726	−	21.1384i	−0.200090	−	1.13477i	0.704891	−	0.709315i	$-0.250996\pi$
$348$		0			0
$349$	26.2905	+	22.0603i	1.40730	+	1.18086i	0.957748	+	0.287608i	$0.0928600\pi$
$349$	26.2905	+	22.0603i	1.40730	+	1.18086i	0.449550	+	0.893255i	$0.351584\pi$
$350$		0			0
$351$	21.3554	+	15.6073i	1.13987	+	0.833054i
$352$		0			0
$353$	−10.8727	+	12.9575i	−0.578693	+	0.689660i	−0.973391	−	0.229151i	$-0.926405\pi$
$353$	−10.8727	+	12.9575i	−0.578693	+	0.689660i	0.394698	+	0.918811i	$0.370849\pi$
$354$		0			0
$355$	11.7051	−	2.06392i	0.621240	−	0.109541i
$356$		0			0
$357$	−0.820172	−	1.79033i	−0.0434081	−	0.0947541i
$358$		0			0
$359$	8.68903	−	15.0498i	0.458589	−	0.794300i	−0.540297	−	0.841474i	$-0.681688\pi$
$359$	8.68903	−	15.0498i	0.458589	−	0.794300i	0.998887	+	0.0471743i	$0.0150216\pi$
$360$		0			0
$361$	23.6798	+	41.0146i	1.24630	+	2.15866i
$362$		0			0
$363$	13.4969	+	13.6804i	0.708405	+	0.718036i
$364$		0			0
$365$	10.1434	+	12.0884i	0.530930	+	0.632738i
$366$		0			0
$367$	3.68181	+	10.1157i	0.192189	+	0.528035i	0.997935	−	0.0642257i	$-0.0204578\pi$
$367$	3.68181	+	10.1157i	0.192189	+	0.528035i	−0.805746	+	0.592261i	$0.798236\pi$
$368$		0			0
$369$	−21.2786	−	18.3502i	−1.10772	−	0.955272i
$370$		0			0
$371$	−0.447850	+	2.53988i	−0.0232512	+	0.131864i
$372$		0			0
$373$	−28.9939	−	10.5529i	−1.50125	−	0.546409i	−0.544864	−	0.838524i	$-0.683419\pi$
$373$	−28.9939	−	10.5529i	−1.50125	−	0.546409i	−0.956383	+	0.292115i	$0.905641\pi$
$374$		0			0
$375$	11.4879	+	16.6445i	0.593235	+	0.859521i
$376$		0			0
$377$		−	10.3464i		−	0.532867i
$378$		0			0
$379$		−	9.89616i		−	0.508331i	−0.967161	−	0.254166i	$-0.918199\pi$
$379$		−	9.89616i		−	0.508331i	0.967161	−	0.254166i	$-0.0818009\pi$
$380$		0			0
$381$	−3.56528	+	7.51291i	−0.182655	+	0.384898i
$382$		0			0
$383$	32.0568	+	11.6677i	1.63803	+	0.596193i	0.986692	−	0.162598i	$-0.0519875\pi$
$383$	32.0568	+	11.6677i	1.63803	+	0.596193i	0.651334	+	0.758791i	$0.274210\pi$
$384$		0			0
$385$	−0.629876	+	3.57220i	−0.0321015	+	0.182056i
$386$		0			0
$387$	10.2427	+	18.3075i	0.520668	+	0.930623i
$388$		0			0
$389$	12.1275	+	33.3200i	0.614888	+	1.68939i	0.719163	+	0.694841i	$0.244525\pi$
$389$	12.1275	+	33.3200i	0.614888	+	1.68939i	−0.104275	+	0.994548i	$0.533252\pi$
$390$		0			0
$391$	10.9987	+	13.1077i	0.556228	+	0.662886i
$392$		0			0
$393$	−4.51646	+	1.17756i	−0.227825	+	0.0593999i
$394$		0			0
$395$	−0.00298479	−	0.00516981i	−0.000150181	−	0.000260121i
$396$		0			0
$397$	6.61085	−	11.4503i	0.331789	−	0.574675i	−0.651074	−	0.759014i	$-0.725681\pi$
$397$	6.61085	−	11.4503i	0.331789	−	0.574675i	0.982863	+	0.184339i	$0.0590145\pi$
$398$		0			0
$399$	4.15860	−	5.85456i	0.208190	−	0.293095i
$400$		0			0
$401$	−5.39193	+	0.950743i	−0.269260	+	0.0474779i	−0.306648	−	0.951823i	$-0.599207\pi$
$401$	−5.39193	+	0.950743i	−0.269260	+	0.0474779i	0.0373877	+	0.999301i	$0.488096\pi$
$402$		0			0
$403$	−10.6311	+	12.6696i	−0.529571	+	0.631118i
$404$		0			0
$405$	0.368495	−	13.6406i	0.0183106	−	0.677806i
$406$		0			0
$407$	−8.88440	−	7.45490i	−0.440384	−	0.369526i
$408$		0			0
$409$	−4.37710	−	24.8238i	−0.216434	−	1.22746i	−0.878401	−	0.477924i	$-0.841389\pi$
$409$	−4.37710	−	24.8238i	−0.216434	−	1.22746i	0.661967	−	0.749533i	$-0.269722\pi$
$410$		0			0
$411$	26.2372	+	18.6367i	1.29418	+	0.919283i
$412$		0			0
$413$	−2.19726	−	1.26859i	−0.108120	−	0.0624232i
$414$		0			0
$415$	−6.14289	+	3.54660i	−0.301543	+	0.174096i
$416$		0			0
$417$	4.71833	+	18.0969i	0.231058	+	0.886211i
$418$		0			0
$419$	3.10945	−	2.60914i	0.151907	−	0.127465i	−0.563667	−	0.826002i	$-0.690610\pi$
$419$	3.10945	−	2.60914i	0.151907	−	0.127465i	0.715574	+	0.698537i	$0.246165\pi$
$420$		0			0
$421$	26.3131	−	9.57717i	1.28242	−	0.466763i	0.391188	−	0.920311i	$-0.372064\pi$
$421$	26.3131	−	9.57717i	1.28242	−	0.466763i	0.891232	+	0.453548i	$0.149842\pi$
$422$		0			0
$423$	0.291820	−	21.6086i	0.0141888	−	1.05065i
$424$		0			0
$425$	5.94246	+	1.04782i	0.288252	+	0.0508266i
$426$		0			0
$427$	−2.16514	+	5.94867i	−0.104778	+	0.287876i
$428$		0			0
$429$	−37.4423	−	17.7684i	−1.80773	−	0.857867i
$430$		0			0
$431$	−7.26000			−0.349702			−0.174851	−	0.984595i	$-0.555944\pi$
$431$	−7.26000			−0.349702			−0.174851	+	0.984595i	$0.555944\pi$
$432$		0			0
$433$	−9.09134			−0.436902			−0.218451	−	0.975848i	$-0.570100\pi$
$433$	−9.09134			−0.436902			−0.218451	+	0.975848i	$0.570100\pi$
$434$		0			0
$435$	−4.39285	+	3.03191i	−0.210621	+	0.145369i
$436$		0			0
$437$	−21.3413	+	58.6349i	−1.02090	+	2.80489i
$438$		0			0
$439$	1.43111	+	0.252343i	0.0683031	+	0.0120437i	0.207695	−	0.978194i	$-0.433404\pi$
$439$	1.43111	+	0.252343i	0.0683031	+	0.0120437i	−0.139392	+	0.990237i	$0.544515\pi$
$440$		0			0
$441$	19.8664	+	3.78028i	0.946019	+	0.180013i
$442$		0			0
$443$	20.9616	−	7.62941i	0.995917	−	0.362484i	0.207908	−	0.978148i	$-0.433334\pi$
$443$	20.9616	−	7.62941i	0.995917	−	0.362484i	0.788009	+	0.615664i	$0.211112\pi$
$444$		0			0
$445$	−7.05808	+	5.92243i	−0.334585	+	0.280750i
$446$		0			0
$447$	−10.6532	+	10.5103i	−0.503881	+	0.497122i
$448$		0			0
$449$	−14.8601	+	8.57950i	−0.701293	+	0.404892i	−0.807829	−	0.589417i	$-0.799357\pi$
$449$	−14.8601	+	8.57950i	−0.701293	+	0.404892i	0.106536	+	0.994309i	$0.466024\pi$
$450$		0			0
$451$	38.1275	+	22.0129i	1.79535	+	1.03655i
$452$		0			0
$453$	31.9283	−	14.6268i	1.50012	−	0.687227i
$454$		0			0
$455$	−0.682119	−	3.86849i	−0.0319782	−	0.181357i
$456$		0			0
$457$	−4.36732	−	3.66462i	−0.204295	−	0.171424i	0.534900	−	0.844915i	$-0.320349\pi$
$457$	−4.36732	−	3.66462i	−0.204295	−	0.171424i	−0.739195	+	0.673492i	$0.764794\pi$
$458$		0			0
$459$	−8.03978	−	8.37227i	−0.375265	−	0.390784i
$460$		0			0
$461$	15.7444	−	18.7634i	0.733290	−	0.873901i	−0.262560	−	0.964916i	$-0.584567\pi$
$461$	15.7444	−	18.7634i	0.733290	−	0.873901i	0.995850	+	0.0910148i	$0.0290111\pi$
$462$		0			0
$463$	8.07669	−	1.42414i	0.375356	−	0.0661854i	0.0172122	−	0.999852i	$-0.494521\pi$
$463$	8.07669	−	1.42414i	0.375356	−	0.0661854i	0.358144	+	0.933667i	$0.383410\pi$
$464$		0			0
$465$	8.49456	+	0.801007i	0.393926	+	0.0371458i
$466$		0			0
$467$	−8.87524	+	15.3724i	−0.410697	+	0.711348i	−0.994966	−	0.100212i	$-0.968048\pi$
$467$	−8.87524	+	15.3724i	−0.410697	+	0.711348i	0.584269	+	0.811560i	$0.301381\pi$
$468$		0			0
$469$	−0.557674	−	0.965920i	−0.0257510	−	0.0446020i
$470$		0			0
$471$	5.29092	−	19.2258i	0.243793	−	0.885878i
$472$		0			0
$473$	−21.1282	−	25.1796i	−0.971474	−	1.15776i
$474$		0			0
$475$	7.52598	+	20.6775i	0.345316	+	0.948748i
$476$		0			0
$477$	2.43738	+	15.0052i	0.111600	+	0.687042i
$478$		0			0
$479$	3.32838	−	18.8762i	0.152077	−	0.862474i	−0.809332	−	0.587352i	$-0.800171\pi$
$479$	3.32838	−	18.8762i	0.152077	−	0.862474i	0.961409	−	0.275122i	$-0.0887183\pi$
$480$		0			0
$481$	11.8023	+	4.29567i	0.538137	+	0.195866i
$482$		0			0
$483$	6.73062	−	0.543087i	0.306254	−	0.0247113i
$484$		0			0
$485$			4.27926i			0.194311i
$486$		0			0
$487$		−	19.6130i		−	0.888751i	−0.895841	−	0.444376i	$-0.853426\pi$
$487$		−	19.6130i		−	0.888751i	0.895841	−	0.444376i	$-0.146574\pi$
$488$		0			0
$489$	12.5516	−	1.01277i	0.567603	−	0.0457992i
$490$		0			0
$491$	6.31847	+	2.29974i	0.285149	+	0.103786i	0.480635	−	0.876921i	$-0.340406\pi$
$491$	6.31847	+	2.29974i	0.285149	+	0.103786i	−0.195486	+	0.980706i	$0.562628\pi$
$492$		0			0
$493$	−0.788424	+	4.47137i	−0.0355088	+	0.201380i
$494$		0			0
$495$	3.42804	+	21.1040i	0.154079	+	0.948556i
$496$		0			0
$497$	−1.36462	−	3.74925i	−0.0612114	−	0.168177i
$498$		0			0
$499$	−15.3202	−	18.2579i	−0.685828	−	0.817338i	0.305016	−	0.952347i	$-0.401338\pi$
$499$	−15.3202	−	18.2579i	−0.685828	−	0.817338i	−0.990844	+	0.135009i	$0.956894\pi$
$500$		0			0
$501$	0.674627	−	2.45141i	0.0301401	−	0.109521i
$502$		0			0
$503$	7.05932	+	12.2271i	0.314760	+	0.545180i	0.979386	−	0.201996i	$-0.0647428\pi$
$503$	7.05932	+	12.2271i	0.314760	+	0.545180i	−0.664627	+	0.747175i	$0.731409\pi$
$504$		0			0
$505$	7.93121	−	13.7373i	0.352934	−	0.611300i
$506$		0			0
$507$	22.2665	+	2.09965i	0.988890	+	0.0932489i
$508$		0			0
$509$	−8.71019	+	1.53584i	−0.386072	+	0.0680750i	−0.363316	−	0.931666i	$-0.618355\pi$
$509$	−8.71019	+	1.53584i	−0.386072	+	0.0680750i	−0.0227566	+	0.999741i	$0.507244\pi$
$510$		0			0
$511$	3.40503	−	4.05795i	0.150630	−	0.179513i
$512$		0			0
$513$	11.7813	−	40.6560i	0.520158	−	1.79501i
$514$		0			0
$515$	−3.82231	−	3.20730i	−0.168431	−	0.141330i
$516$		0			0
$517$	5.87984	+	33.3462i	0.258595	+	1.46657i
$518$		0			0
$519$	39.8308	−	18.2470i	1.74838	−	0.800955i
$520$		0			0
$521$	−23.2598	−	13.4291i	−1.01903	−	0.588338i	−0.105208	−	0.994450i	$-0.533551\pi$
$521$	−23.2598	−	13.4291i	−1.01903	−	0.588338i	−0.913823	+	0.406113i	$0.866884\pi$
$522$		0			0
$523$	−37.0164	+	21.3715i	−1.61862	+	0.934508i	−0.631338	+	0.775508i	$0.717494\pi$
$523$	−37.0164	+	21.3715i	−1.61862	+	0.934508i	−0.987279	+	0.159000i	$0.949173\pi$
$524$		0			0
$525$	1.69513	−	1.67239i	0.0739816	−	0.0729893i
$526$		0			0
$527$	5.55984	−	4.66526i	0.242191	−	0.203222i
$528$		0			0
$529$	−33.5215	+	12.2008i	−1.45745	+	0.530470i
$530$		0			0
$531$	−14.6914	−	2.79555i	−0.637553	−	0.121317i
$532$		0			0
$533$	−46.9531	−	8.27909i	−2.03376	−	0.358607i
$534$		0			0
$535$	−5.93826	+	16.3152i	−0.256733	+	0.705369i
$536$		0			0
$537$	5.61642	−	3.87641i	0.242367	−	0.167280i
$538$		0			0
$539$	−31.6863			−1.36483
$540$		0			0
$541$	7.20040			0.309569			0.154785	−	0.987948i	$-0.450532\pi$
$541$	7.20040			0.309569			0.154785	+	0.987948i	$0.450532\pi$
$542$		0			0
$543$	39.2552	+	18.6287i	1.68460	+	0.799435i
$544$		0			0
$545$	−6.91619	+	19.0021i	−0.296257	+	0.813960i
$546$		0			0
$547$	−9.06308	−	1.59807i	−0.387509	−	0.0683283i	−0.0235004	−	0.999724i	$-0.507481\pi$
$547$	−9.06308	−	1.59807i	−0.387509	−	0.0683283i	−0.364009	+	0.931395i	$0.618592\pi$
$548$		0			0
$549$	−0.503871	+	37.3104i	−0.0215047	+	1.59237i
$550$		0			0
$551$	−15.5586	+	5.66289i	−0.662821	+	0.241247i
$552$		0			0
$553$	−0.00153509	+	0.00128810i	−6.52788e−5	+	5.47754e-5i
$554$		0			0
$555$	−1.63469	−	6.26978i	−0.0693887	−	0.266137i
$556$		0			0
$557$	−27.4455	+	15.8457i	−1.16291	+	0.671404i	−0.951999	−	0.306103i	$-0.900975\pi$
$557$	−27.4455	+	15.8457i	−1.16291	+	0.671404i	−0.210907	+	0.977506i	$0.567642\pi$
$558$		0			0
$559$	30.8269	+	17.7979i	1.30384	+	0.752772i
$560$		0			0
$561$	14.8273	+	10.5321i	0.626010	+	0.444666i
$562$		0			0
$563$	−1.11021	−	6.29630i	−0.0467897	−	0.265357i	0.952434	−	0.304744i	$-0.0985708\pi$
$563$	−1.11021	−	6.29630i	−0.0467897	−	0.265357i	−0.999224	+	0.0393863i	$0.987460\pi$
$564$		0			0
$565$	−0.712537	−	0.597889i	−0.0299766	−	0.0251534i
$566$		0			0
$567$	−4.53090	+	0.673313i	−0.190280	+	0.0282765i
$568$		0			0
$569$	0.456296	−	0.543792i	0.0191289	−	0.0227969i	−0.756395	−	0.654115i	$-0.773041\pi$
$569$	0.456296	−	0.543792i	0.0191289	−	0.0227969i	0.775524	+	0.631318i	$0.217486\pi$
$570$		0			0
$571$	−30.2057	+	5.32608i	−1.26407	+	0.222890i	−0.765203	−	0.643789i	$-0.777361\pi$
$571$	−30.2057	+	5.32608i	−1.26407	+	0.222890i	−0.498867	+	0.866679i	$0.666250\pi$
$572$		0			0
$573$	−9.53953	+	13.4299i	−0.398520	+	0.561044i
$574$		0			0
$575$	−10.3454	+	17.9188i	−0.431434	+	0.747266i
$576$		0			0
$577$	14.9980	+	25.9773i	0.624376	+	1.08145i	0.988661	+	0.150163i	$0.0479799\pi$
$577$	14.9980	+	25.9773i	0.624376	+	1.08145i	−0.364285	+	0.931287i	$0.618687\pi$
$578$		0			0
$579$	21.4918	−	5.60346i	0.893169	−	0.232872i
$580$		0			0
$581$	1.53055	+	1.82403i	0.0634977	+	0.0756737i
$582$		0			0
$583$	−8.14665	−	22.3827i	−0.337400	−	0.926998i
$584$		0			0
$585$	−11.3052	−	20.2064i	−0.467411	−	0.835433i
$586$		0			0
$587$	3.84156	−	21.7866i	0.158558	−	0.899229i	−0.796902	−	0.604109i	$-0.793529\pi$
$587$	3.84156	−	21.7866i	0.158558	−	0.899229i	0.955460	−	0.295120i	$-0.0953597\pi$
$588$		0			0
$589$	24.8709	+	9.05226i	1.02479	+	0.372992i
$590$		0			0
$591$	−3.91924	+	8.25878i	−0.161216	+	0.339721i
$592$		0			0
$593$			42.7445i			1.75531i	0.479295	+	0.877654i	$0.340893\pi$
$593$			42.7445i			1.75531i	−0.479295	+	0.877654i	$0.659107\pi$
$594$		0			0
$595$			1.72381i			0.0706693i
$596$		0			0
$597$	3.26821	+	4.73521i	0.133759	+	0.193799i
$598$		0			0
$599$	0.587642	+	0.213884i	0.0240104	+	0.00873907i	0.353997	−	0.935246i	$-0.384822\pi$
$599$	0.587642	+	0.213884i	0.0240104	+	0.00873907i	−0.329987	+	0.943985i	$0.607044\pi$
$600$		0			0
$601$	−3.20985	+	18.2039i	−0.130932	+	0.742554i	0.846674	+	0.532112i	$0.178601\pi$
$601$	−3.20985	+	18.2039i	−0.130932	+	0.742554i	−0.977606	+	0.210442i	$0.932510\pi$
$602$		0			0
$603$	−4.97865	−	4.29347i	−0.202746	−	0.174844i
$604$		0			0
$605$	−5.75363	−	15.8080i	−0.233918	−	0.642685i
$606$		0			0
$607$	−6.95734	−	8.29144i	−0.282390	−	0.336539i	0.606140	−	0.795358i	$-0.292717\pi$
$607$	−6.95734	−	8.29144i	−0.282390	−	0.336539i	−0.888530	+	0.458819i	$0.848273\pi$
$608$		0			0
$609$	1.25838	+	1.27549i	0.0509923	+	0.0516856i
$610$		0			0
$611$	−18.3346	−	31.7564i	−0.741737	−	1.28473i
$612$		0			0
$613$	−21.0915	+	36.5316i	−0.851879	+	1.47550i	0.0276314	+	0.999618i	$0.491204\pi$
$613$	−21.0915	+	36.5316i	−0.851879	+	1.47550i	−0.879510	+	0.475880i	$0.842130\pi$
$614$		0			0
$615$	10.2440	+	22.3613i	0.413079	+	0.901696i
$616$		0			0
$617$	8.67931	−	1.53040i	0.349416	−	0.0616114i	0.00381403	−	0.999993i	$-0.498786\pi$
$617$	8.67931	−	1.53040i	0.349416	−	0.0616114i	0.345602	+	0.938381i	$0.387675\pi$
$618$		0			0
$619$	12.0477	−	14.3579i	0.484237	−	0.577091i	−0.467505	−	0.883990i	$-0.654847\pi$
$619$	12.0477	−	14.3579i	0.484237	−	0.577091i	0.951742	+	0.306899i	$0.0992915\pi$
$620$		0			0
$621$	36.4058	−	16.0868i	1.46091	−	0.645541i
$622$		0			0
$623$	2.36932	+	1.98809i	0.0949247	+	0.0796512i
$624$		0			0
$625$	−0.728856	−	4.13355i	−0.0291542	−	0.165342i
$626$		0			0
$627$	−6.22639	+	66.0299i	−0.248658	+	2.63698i
$628$		0			0
$629$	−4.77320	−	2.75581i	−0.190320	−	0.109881i
$630$		0			0
$631$	−34.1111	+	19.6940i	−1.35794	+	0.784007i	−0.989346	−	0.145584i	$-0.953494\pi$
$631$	−34.1111	+	19.6940i	−1.35794	+	0.784007i	−0.368594	+	0.929591i	$0.620161\pi$
$632$		0			0
$633$	−36.9734	−	10.1750i	−1.46956	−	0.404422i
$634$		0			0
$635$	5.57640	−	4.67916i	0.221293	−	0.185687i
$636$		0			0
$637$	32.2450	−	11.7362i	1.27760	−	0.465007i
$638$		0			0
$639$	−14.8722	−	18.2181i	−0.588337	−	0.720697i
$640$		0			0
$641$	5.31511	+	0.937197i	0.209934	+	0.0370171i	0.277626	−	0.960689i	$-0.410452\pi$
$641$	5.31511	+	0.937197i	0.209934	+	0.0370171i	−0.0676919	+	0.997706i	$0.521563\pi$
$642$		0			0
$643$	−9.12115	+	25.0601i	−0.359703	+	0.988276i	0.619430	+	0.785052i	$0.287364\pi$
$643$	−9.12115	+	25.0601i	−0.359703	+	0.988276i	−0.979132	+	0.203223i	$0.934858\pi$
$644$		0			0
$645$	−1.47692	−	18.3039i	−0.0581538	−	0.720716i
$646$		0			0
$647$	1.50379			0.0591200			0.0295600	−	0.999563i	$-0.490589\pi$
$647$	1.50379			0.0591200			0.0295600	+	0.999563i	$0.490589\pi$
$648$		0			0
$649$	23.4324			0.919801
$650$		0			0
$651$	−0.230359	−	2.85490i	−0.00902846	−	0.111892i
$652$		0			0
$653$	1.20984	−	3.32400i	0.0473446	−	0.130078i	−0.913767	−	0.406239i	$-0.866840\pi$
$653$	1.20984	−	3.32400i	0.0473446	−	0.130078i	0.961111	+	0.276161i	$0.0890622\pi$
$654$		0			0
$655$	4.02364	+	0.709476i	0.157217	+	0.0277215i
$656$		0			0
$657$	11.0745	−	29.1941i	0.432057	−	1.13897i
$658$		0			0
$659$	20.5734	−	7.48811i	0.801427	−	0.291695i	0.0913491	−	0.995819i	$-0.470882\pi$
$659$	20.5734	−	7.48811i	0.801427	−	0.291695i	0.710078	+	0.704123i	$0.248660\pi$
$660$		0			0
$661$	−10.2038	+	8.56203i	−0.396883	+	0.333024i	−0.819287	−	0.573383i	$-0.805631\pi$
$661$	−10.2038	+	8.56203i	−0.396883	+	0.333024i	0.422404	+	0.906407i	$0.361186\pi$
$662$		0			0
$663$	−18.9897	−	5.22596i	−0.737500	−	0.202959i
$664$		0			0
$665$	−5.44398	+	3.14308i	−0.211109	+	0.121884i
$666$		0			0
$667$	−13.4829	−	7.78436i	−0.522060	−	0.301411i
$668$		0			0
$669$	3.99653	−	42.3826i	0.154515	−	1.63861i
$670$		0			0
$671$	−10.1524	−	57.5772i	−0.391930	−	2.22274i
$672$		0			0
$673$	−11.9708	−	10.0447i	−0.461442	−	0.387196i	0.382219	−	0.924072i	$-0.375160\pi$
$673$	−11.9708	−	10.0447i	−0.461442	−	0.387196i	−0.843661	+	0.536876i	$0.819604\pi$
$674$		0			0
$675$	6.18829	−	12.5981i	0.238187	−	0.484902i
$676$		0			0
$677$	24.6017	−	29.3192i	0.945522	−	1.12683i	−0.0462656	−	0.998929i	$-0.514732\pi$
$677$	24.6017	−	29.3192i	0.945522	−	1.12683i	0.991787	−	0.127900i	$-0.0408235\pi$
$678$		0			0
$679$	1.41468	−	0.249445i	0.0542903	−	0.00957284i
$680$		0			0
$681$	6.23342	+	13.6067i	0.238865	+	0.521411i
$682$		0			0
$683$	12.8817	−	22.3118i	0.492906	−	0.853738i	−0.507061	−	0.861910i	$-0.669268\pi$
$683$	12.8817	−	22.3118i	0.492906	−	0.853738i	0.999967	+	0.00817252i	$0.00260142\pi$
$684$		0			0
$685$	−14.0857	−	24.3972i	−0.538188	−	0.932168i
$686$		0			0
$687$	−18.1359	−	18.3825i	−0.691927	−	0.701334i
$688$		0			0
$689$	16.5806	+	19.7600i	0.631670	+	0.752795i
$690$		0			0
$691$	−11.0848	−	30.4553i	−0.421687	−	1.15858i	−0.950741	−	0.309987i	$-0.899675\pi$
$691$	−11.0848	−	30.4553i	−0.421687	−	1.15858i	0.529054	−	0.848588i	$-0.322547\pi$
$692$		0			0
$693$	6.77693	−	2.36346i	0.257434	−	0.0897805i
$694$		0			0
$695$	2.84279	−	16.1223i	0.107833	−	0.611552i
$696$		0			0
$697$	19.6607	+	7.15589i	0.744700	+	0.271049i
$698$		0			0
$699$	−16.0808	−	23.2989i	−0.608230	−	0.881247i
$700$		0			0
$701$		−	26.8259i		−	1.01320i	−0.862181	−	0.506600i	$-0.830902\pi$
$701$		−	26.8259i		−	1.01320i	0.862181	−	0.506600i	$-0.169098\pi$
$702$		0			0
$703$		−	20.0990i		−	0.758050i
$704$		0			0
$705$	−8.11029	+	17.0903i	−0.305451	+	0.643659i
$706$		0			0
$707$	−5.00371	−	1.82120i	−0.188184	−	0.0684933i
$708$		0			0
$709$	3.92220	−	22.2439i	0.147301	−	0.835387i	−0.818189	−	0.574949i	$-0.805022\pi$
$709$	3.92220	−	22.2439i	0.147301	−	0.835387i	0.965491	−	0.260438i	$-0.0838670\pi$
$710$		0			0
$711$	−0.00604350	+	0.0101486i	−0.000226649	+	0.000380604i
$712$		0			0
$713$	8.51185	+	23.3861i	0.318771	+	0.875816i
$714$		0			0
$715$	23.3197	+	27.7913i	0.872106	+	1.03934i
$716$		0			0
$717$	−49.1557	+	12.8161i	−1.83575	+	0.478628i
$718$		0			0
$719$	−9.72854	−	16.8503i	−0.362813	−	0.628411i	0.625610	−	0.780136i	$-0.284850\pi$
$719$	−9.72854	−	16.8503i	−0.362813	−	0.628411i	−0.988423	+	0.151726i	$0.951517\pi$
$720$		0			0
$721$	−0.837488	+	1.45057i	−0.0311897	+	0.0540221i
$722$		0			0
$723$	17.2801	−	24.3273i	0.642654	−	0.904741i
$724$		0			0
$725$	−5.40687	+	0.953376i	−0.200806	+	0.0354075i
$726$		0			0
$727$	−13.7453	+	16.3810i	−0.509783	+	0.607536i	−0.958133	−	0.286322i	$-0.907567\pi$
$727$	−13.7453	+	16.3810i	−0.509783	+	0.607536i	0.448350	+	0.893858i	$0.352012\pi$
$728$		0			0
$729$	−23.9103	+	12.5419i	−0.885565	+	0.464515i
$730$		0			0
$731$	−11.9661	−	10.0408i	−0.442582	−	0.371371i
$732$		0			0
$733$	0.266433	+	1.51102i	0.00984092	+	0.0558107i	0.989333	−	0.145673i	$-0.0465348\pi$
$733$	0.266433	+	1.51102i	0.00984092	+	0.0558107i	−0.979492	+	0.201484i	$0.935424\pi$
$734$		0			0
$735$	−14.4320	−	10.2513i	−0.532333	−	0.378126i
$736$		0			0
$737$	8.92085	+	5.15046i	0.328604	+	0.189719i
$738$		0			0
$739$	−41.0294	+	23.6883i	−1.50929	+	0.871388i	−0.509348	+	0.860561i	$0.670113\pi$
$739$	−41.0294	+	23.6883i	−1.50929	+	0.871388i	−0.999941	+	0.0108277i	$0.996553\pi$
$740$		0			0
$741$	−18.1205	−	69.5003i	−0.665673	−	2.55316i
$742$		0			0
$743$	10.5869	−	8.88351i	0.388398	−	0.325904i	−0.427591	−	0.903972i	$-0.640638\pi$
$743$	10.5869	−	8.88351i	0.388398	−	0.325904i	0.815989	+	0.578068i	$0.196193\pi$
$744$		0			0
$745$	12.3100	−	4.48047i	0.451003	−	0.164152i
$746$		0			0
$747$	12.0589	+	7.18103i	0.441210	+	0.262740i
$748$		0			0
$749$	5.73979	+	1.01208i	0.209727	+	0.0369806i
$750$		0			0
$751$	3.51038	−	9.64468i	0.128096	−	0.351940i	−0.859022	−	0.511940i	$-0.828927\pi$
$751$	3.51038	−	9.64468i	0.128096	−	0.351940i	0.987117	+	0.160000i	$0.0511494\pi$
$752$		0			0
$753$	−2.18119	−	1.03509i	−0.0794869	−	0.0377208i
$754$		0			0
$755$	−30.7421			−1.11882
$756$		0			0
$757$	−42.4711			−1.54364			−0.771819	−	0.635843i	$-0.780653\pi$
$757$	−42.4711			−1.54364			−0.771819	+	0.635843i	$0.780653\pi$
$758$		0			0
$759$	−51.3254	+	35.4244i	−1.86300	+	1.28582i
$760$		0			0
$761$	16.3730	−	44.9845i	0.593522	−	1.63069i	−0.170396	−	0.985376i	$-0.554505\pi$
$761$	16.3730	−	44.9845i	0.593522	−	1.63069i	0.763918	−	0.645313i	$-0.223273\pi$
$762$		0			0
$763$	6.68503	+	1.17875i	0.242014	+	0.0426737i
$764$		0			0
$765$	3.34593	+	9.59402i	0.120972	+	0.346873i
$766$		0			0
$767$	−23.8455	+	8.67907i	−0.861012	+	0.313383i
$768$		0			0
$769$	19.5895	−	16.4375i	0.706414	−	0.592751i	−0.217177	−	0.976132i	$-0.569685\pi$
$769$	19.5895	−	16.4375i	0.706414	−	0.592751i	0.923590	+	0.383381i	$0.125240\pi$
$770$		0			0
$771$	22.3981	−	22.0977i	0.806648	−	0.795828i
$772$		0			0
$773$	32.2153	−	18.5995i	1.15871	−	0.668979i	0.207712	−	0.978190i	$-0.433398\pi$
$773$	32.2153	−	18.5995i	1.15871	−	0.668979i	0.950993	+	0.309211i	$0.100065\pi$
$774$		0			0
$775$	7.60053	+	4.38817i	0.273019	+	0.157628i
$776$		0			0
$777$	−1.97743	+	0.905886i	−0.0709399	+	0.0324985i
$778$		0			0
$779$	13.2489	+	75.1381i	0.474690	+	2.69210i
$780$		0			0
$781$	28.2279	+	23.6860i	1.01007	+	0.847552i
$782$		0			0
$783$	9.47939	+	4.65634i	0.338766	+	0.166404i
$784$		0			0
$785$	−11.2200	+	13.3715i	−0.400459	+	0.477248i
$786$		0			0
$787$	−12.5814	+	2.21844i	−0.448478	+	0.0790788i	−0.393326	−	0.919399i	$-0.628676\pi$
$787$	−12.5814	+	2.21844i	−0.448478	+	0.0790788i	−0.0551522	+	0.998478i	$0.517564\pi$
$788$		0			0
$789$	34.3396	+	3.23810i	1.22252	+	0.115280i
$790$		0			0
$791$	−0.156121	+	0.270409i	−0.00555101	+	0.00961462i
$792$		0			0
$793$	31.6573	+	54.8321i	1.12418	+	1.94714i
$794$		0			0
$795$	3.53086	−	12.8302i	0.125227	−	0.455040i
$796$		0			0
$797$	−7.60961	−	9.06878i	−0.269546	−	0.321233i	0.614244	−	0.789116i	$-0.289461\pi$
$797$	−7.60961	−	9.06878i	−0.269546	−	0.321233i	−0.883790	+	0.467884i	$0.845017\pi$
$798$		0			0
$799$	5.50366	+	15.1212i	0.194706	+	0.534949i
$800$		0			0
$801$	17.0456	+	6.46605i	0.602275	+	0.228467i
$802$		0			0
$803$	−8.49549	+	48.1803i	−0.299799	+	1.70025i
$804$		0			0
$805$	−5.55442	−	2.02164i	−0.195767	−	0.0712535i
$806$		0			0
$807$	33.7720	−	2.72502i	1.18883	−	0.0959254i
$808$		0			0
$809$		−	36.6666i		−	1.28913i	−0.764550	−	0.644565i	$-0.777039\pi$
$809$		−	36.6666i		−	1.28913i	0.764550	−	0.644565i	$-0.222961\pi$
$810$		0			0
$811$		−	47.6500i		−	1.67322i	−0.547800	−	0.836609i	$-0.684535\pi$
$811$		−	47.6500i		−	1.67322i	0.547800	−	0.836609i	$-0.315465\pi$
$812$		0			0
$813$	11.3209	−	0.913469i	0.397041	−	0.0320368i
$814$		0			0
$815$	−10.3581	−	3.77006i	−0.362830	−	0.132059i
$816$		0			0
$817$	9.89158	−	56.0980i	0.346063	−	1.96262i
$818$		0			0
$819$	−6.02102	+	4.91523i	−0.210392	+	0.171752i
$820$		0			0
$821$	−8.46614	−	23.2605i	−0.295470	−	0.811798i	−0.995242	−	0.0974316i	$-0.968937\pi$
$821$	−8.46614	−	23.2605i	−0.295470	−	0.811798i	0.699772	−	0.714366i	$-0.253285\pi$
$822$		0			0
$823$	34.3294	+	40.9122i	1.19665	+	1.42611i	0.878282	+	0.478143i	$0.158690\pi$
$823$	34.3294	+	40.9122i	1.19665	+	1.42611i	0.318367	+	0.947968i	$0.396866\pi$
$824$		0			0
$825$	−5.83533	+	21.2040i	−0.203160	+	0.738230i
$826$		0			0
$827$	21.6766	+	37.5449i	0.753768	+	1.30556i	0.945984	+	0.324212i	$0.105099\pi$
$827$	21.6766	+	37.5449i	0.753768	+	1.30556i	−0.192216	+	0.981353i	$0.561568\pi$
$828$		0			0
$829$	24.1358	−	41.8045i	0.838272	−	1.45193i	−0.0530670	−	0.998591i	$-0.516900\pi$
$829$	24.1358	−	41.8045i	0.838272	−	1.45193i	0.891339	−	0.453338i	$-0.149767\pi$
$830$		0			0
$831$	−19.1185	−	1.80281i	−0.663213	−	0.0625386i
$832$		0			0
$833$	−14.8296	+	2.61485i	−0.513814	+	0.0905992i
$834$		0			0
$835$	−1.43062	+	1.70495i	−0.0495087	+	0.0590021i
$836$		0			0
$837$	−6.82346	−	15.4421i	−0.235853	−	0.533756i
$838$		0			0
$839$	28.8687	+	24.2238i	0.996660	+	0.836297i	0.986518	−	0.163652i	$-0.0523273\pi$
$839$	28.8687	+	24.2238i	0.996660	+	0.836297i	0.0101417	+	0.999949i	$0.496772\pi$
$840$		0			0
$841$	4.31843	+	24.4911i	0.148912	+	0.844519i
$842$		0			0
$843$	−4.86103	+	2.22690i	−0.167423	+	0.0766985i
$844$		0			0
$845$	−16.9548	−	9.78887i	−0.583264	−	0.336747i
$846$		0			0
$847$	−4.89055	+	2.82356i	−0.168041	+	0.0970187i
$848$		0			0
$849$	−13.2039	+	13.0268i	−0.453157	+	0.447079i
$850$		0			0
$851$	14.4776	−	12.1481i	0.496285	−	0.416433i
$852$		0			0
$853$	−1.47527	+	0.536954i	−0.0505122	+	0.0183850i	−0.367153	−	0.930161i	$-0.619667\pi$
$853$	−1.47527	+	0.536954i	−0.0505122	+	0.0183850i	0.316640	+	0.948546i	$0.397445\pi$
$854$		0			0
$855$	−24.1982	+	28.0599i	−0.827562	+	0.959630i
$856$		0			0
$857$	10.3929	+	1.83256i	0.355016	+	0.0625990i	0.348312	−	0.937379i	$-0.386755\pi$
$857$	10.3929	+	1.83256i	0.355016	+	0.0625990i	0.00670407	+	0.999978i	$0.497866\pi$
$858$		0			0
$859$	5.67572	−	15.5939i	0.193653	−	0.532057i	−0.804423	−	0.594057i	$-0.797525\pi$
$859$	5.67572	−	15.5939i	0.193653	−	0.532057i	0.998076	+	0.0619994i	$0.0197477\pi$
$860$		0			0
$861$	6.79526	−	4.69004i	0.231582	−	0.159836i
$862$		0			0
$863$	−11.2876			−0.384235			−0.192118	−	0.981372i	$-0.561536\pi$
$863$	−11.2876			−0.384235			−0.192118	+	0.981372i	$0.561536\pi$
$864$		0			0
$865$	−38.3509			−1.30397
$866$		0			0
$867$	−18.7930	−	8.91829i	−0.638243	−	0.302881i
$868$		0			0
$869$	0.00632991	−	0.0173913i	0.000214727	−	0.000589959i
$870$		0			0
$871$	−10.9858	−	1.93709i	−0.372240	−	0.0656359i
$872$		0			0
$873$	7.38933	−	4.13421i	0.250091	−	0.139922i
$874$		0			0
$875$	−5.58444	+	2.03257i	−0.188788	+	0.0687134i
$876$		0			0
$877$	1.92658	−	1.61659i	0.0650561	−	0.0545885i	−0.609680	−	0.792648i	$-0.708702\pi$
$877$	1.92658	−	1.61659i	0.0650561	−	0.0545885i	0.674736	+	0.738059i	$0.264258\pi$
$878$		0			0
$879$	−4.16798	−	15.9861i	−0.140583	−	0.539198i
$880$		0			0
$881$	10.4007	−	6.00483i	0.350407	−	0.202308i	−0.314457	−	0.949272i	$-0.601823\pi$
$881$	10.4007	−	6.00483i	0.350407	−	0.202308i	0.664865	+	0.746964i	$0.268489\pi$
$882$		0			0
$883$	20.6073	+	11.8977i	0.693492	+	0.400388i	0.804919	−	0.593385i	$-0.202209\pi$
$883$	20.6073	+	11.8977i	0.693492	+	0.400388i	−0.111427	+	0.993773i	$0.535542\pi$
$884$		0			0
$885$	10.6726	+	7.58096i	0.358757	+	0.254831i
$886$		0			0
$887$	−5.01526	−	28.4430i	−0.168396	−	0.955022i	−0.945493	−	0.325641i	$-0.894420\pi$
$887$	−5.01526	−	28.4430i	−0.168396	−	0.955022i	0.777097	−	0.629380i	$-0.216691\pi$
$888$		0			0
$889$	−1.87194	−	1.57074i	−0.0627827	−	0.0526809i
$890$		0			0
$891$	33.1301	−	26.3081i	1.10990	−	0.881356i
$892$		0			0
$893$	−37.7194	+	44.9522i	−1.26223	+	1.50427i
$894$		0			0
$895$	−5.88297	+	1.03733i	−0.196646	+	0.0346740i
$896$		0			0
$897$	39.1096	−	55.0593i	1.30583	−	1.83838i
$898$		0			0
$899$	−3.30185	+	5.71898i	−0.110123	+	0.190739i
$900$		0			0
$901$	−5.65981	−	9.80307i	−0.188556	−	0.326588i
$902$		0			0
$903$	−5.96498	+	1.55522i	−0.198502	+	0.0517545i
$904$		0			0
$905$	−24.4488	−	29.1369i	−0.812704	−	0.968543i
$906$		0			0
$907$	−12.3117	−	33.8260i	−0.408802	−	1.12318i	−0.957821	−	0.287365i	$-0.907221\pi$
$907$	−12.3117	−	33.8260i	−0.408802	−	1.12318i	0.549019	−	0.835810i	$-0.315002\pi$
$908$		0			0
$909$	−31.3836	−	0.423830i	−1.04093	−	0.0140576i
$910$		0			0
$911$	6.37122	−	36.1330i	0.211088	−	1.19714i	−0.676480	−	0.736461i	$-0.736495\pi$
$911$	6.37122	−	36.1330i	0.211088	−	1.19714i	0.887568	−	0.460677i	$-0.152393\pi$
$912$		0			0
$913$	−20.6647	−	7.52135i	−0.683903	−	0.248920i
$914$		0			0
$915$	14.0036	−	29.5090i	0.462945	−	0.975537i
$916$		0			0
$917$		−	1.37153i		−	0.0452918i
$918$		0			0
$919$			11.5125i			0.379762i	0.981807	+	0.189881i	$0.0608102\pi$
$919$			11.5125i			0.379762i	−0.981807	+	0.189881i	$0.939190\pi$
$920$		0			0
$921$	25.3437	+	36.7198i	0.835104	+	1.20996i
$922$		0			0
$923$	−37.4986	−	13.6484i	−1.23428	−	0.449242i
$924$		0			0
$925$	1.15732	−	6.56349i	0.0380525	−	0.215806i
$926$		0			0
$927$	−1.84555	+	9.69886i	−0.0606157	+	0.318552i
$928$		0			0
$929$	9.88334	+	27.1543i	0.324262	+	0.890902i	0.989534	+	0.144301i	$0.0460934\pi$
$929$	9.88334	+	27.1543i	0.324262	+	0.890902i	−0.665272	+	0.746601i	$0.731684\pi$
$930$		0			0
$931$	−35.2972	−	42.0656i	−1.15682	−	1.37865i
$932$		0			0
$933$	−29.6316	−	30.0345i	−0.970096	−	0.983286i
$934$		0			0
$935$	−7.96021	−	13.7875i	−0.260327	−	0.450899i
$936$		0			0
$937$	18.2299	−	31.5750i	0.595543	−	1.03151i	−0.397926	−	0.917417i	$-0.630270\pi$
$937$	18.2299	−	31.5750i	0.595543	−	1.03151i	0.993470	−	0.114094i	$-0.0363966\pi$
$938$		0			0
$939$	12.7845	+	27.9069i	0.417206	+	0.910706i
$940$		0			0
$941$	−3.31442	+	0.584422i	−0.108047	+	0.0190516i	−0.227410	−	0.973799i	$-0.573026\pi$
$941$	−3.31442	+	0.584422i	−0.108047	+	0.0190516i	0.119363	+	0.992851i	$0.461915\pi$
$942$		0			0
$943$	−46.1151	+	54.9578i	−1.50171	+	1.78967i
$944$		0			0
$945$	3.85130	+	1.11603i	0.125283	+	0.0363045i
$946$		0			0
$947$	22.0991	+	18.5434i	0.718125	+	0.602578i	0.926866	−	0.375393i	$-0.122492\pi$
$947$	22.0991	+	18.5434i	0.718125	+	0.602578i	−0.208741	+	0.977971i	$0.566937\pi$
$948$		0			0
$949$	−9.20012	−	52.1765i	−0.298648	−	1.69372i
$950$		0			0
$951$	−0.443648	+	4.70482i	−0.0143863	+	0.152564i
$952$		0			0
$953$	13.1413	+	7.58714i	0.425689	+	0.245772i	0.697508	−	0.716577i	$-0.254292\pi$
$953$	13.1413	+	7.58714i	0.425689	+	0.245772i	−0.271819	+	0.962348i	$0.587625\pi$
$954$		0			0
$955$	12.4881	−	7.21001i	0.404106	−	0.233311i
$956$		0			0
$957$	−15.9549	−	4.39076i	−0.515747	−	0.141933i
$958$		0			0
$959$	−7.24435	+	6.07873i	−0.233932	+	0.196293i
$960$		0			0
$961$	−19.2109	+	6.99219i	−0.619706	+	0.225555i
$962$		0			0
$963$	33.9098	−	5.50815i	1.09273	−	0.177498i
$964$		0			0
$965$	−19.1467	−	3.37608i	−0.616353	−	0.108680i
$966$		0			0
$967$	15.0009	−	41.2145i	0.482395	−	1.32537i	−0.425039	−	0.905175i	$-0.639740\pi$
$967$	15.0009	−	41.2145i	0.482395	−	1.32537i	0.907434	−	0.420195i	$-0.138038\pi$
$968$		0			0
$969$	2.53496	+	31.4165i	0.0814348	+	1.00924i
$970$		0			0
$971$	48.1678			1.54578			0.772889	−	0.634541i	$-0.218811\pi$
$971$	48.1678			1.54578			0.772889	+	0.634541i	$0.218811\pi$
$972$		0			0
$973$	−5.49555			−0.176179
$974$		0			0
$975$	−1.91549	−	23.7392i	−0.0613449	−	0.760264i
$976$		0			0
$977$	4.28095	−	11.7618i	0.136960	−	0.376294i	−0.852185	−	0.523241i	$-0.824723\pi$
$977$	4.28095	−	11.7618i	0.136960	−	0.376294i	0.989144	+	0.146947i	$0.0469448\pi$
$978$		0			0
$979$	−28.1310	−	4.96026i	−0.899072	−	0.158531i
$980$		0			0
$981$	39.4941	−	6.41525i	1.26095	−	0.204823i
$982$		0			0
$983$	−18.4958	+	6.73190i	−0.589923	+	0.214714i	−0.619695	−	0.784842i	$-0.712744\pi$
$983$	−18.4958	+	6.73190i	−0.589923	+	0.214714i	0.0297726	+	0.999557i	$0.490522\pi$
$984$		0			0
$985$	6.13002	−	5.14370i	0.195319	−	0.163892i
$986$		0			0
$987$	6.12264	+	1.68494i	0.194886	+	0.0536324i
$988$		0			0
$989$	46.3866	−	26.7813i	1.47501	−	0.851597i
$990$		0			0
$991$	14.8346	+	8.56473i	0.471235	+	0.272068i	0.716757	−	0.697323i	$-0.245626\pi$
$991$	14.8346	+	8.56473i	0.471235	+	0.272068i	−0.245522	+	0.969391i	$0.578959\pi$
$992$		0			0
$993$	3.65073	−	38.7154i	0.115852	−	1.22860i
$994$		0			0
$995$	−0.874571	−	4.95994i	−0.0277257	−	0.157241i
$996$		0			0
$997$	13.7710	+	11.5553i	0.436133	+	0.365959i	0.834260	−	0.551371i	$-0.185895\pi$
$997$	13.7710	+	11.5553i	0.436133	+	0.365959i	−0.398127	+	0.917330i	$0.630340\pi$
$998$		0			0
$999$	−9.24723	+	8.88000i	−0.292570	+	0.280951i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bi.a.767.20	yes	216
4.3	odd	2	inner	864.2.bi.a.767.17	yes	216
27.5	odd	18	inner	864.2.bi.a.383.17	✓	216
108.59	even	18	inner	864.2.bi.a.383.20	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.bi.a.383.17	✓	216	27.5	odd	18	inner
864.2.bi.a.383.20	yes	216	108.59	even	18	inner
864.2.bi.a.767.17	yes	216	4.3	odd	2	inner
864.2.bi.a.767.20	yes	216	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bi (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.139305 + 1.72644i) q^{3} +(0.518562 - 1.42474i) q^{5} +(-0.501230 - 0.0883804i) q^{7} +(-2.96119 + 0.481002i) q^{9} +O(q^{10})\)	\(q+(0.139305 + 1.72644i) q^{3} +(0.518562 - 1.42474i) q^{5} +(-0.501230 - 0.0883804i) q^{7} +(-2.96119 + 0.481002i) q^{9} +(4.41709 - 1.60769i) q^{11} +(-3.89951 + 3.27207i) q^{13} +(2.53196 + 0.696793i) q^{15} +(1.93458 - 1.11693i) q^{17} +(7.05476 + 4.07307i) q^{19} +(0.0827598 - 0.877655i) q^{21} +(1.33011 + 7.54345i) q^{23} +(2.06925 + 1.73631i) q^{25} +(-1.24293 - 5.04531i) q^{27} +(-1.30648 + 1.55700i) q^{29} +(3.19967 - 0.564188i) q^{31} +(3.39090 + 7.40188i) q^{33} +(-0.385837 + 0.668290i) q^{35} +(-1.23366 - 2.13675i) q^{37} +(-6.19226 - 6.27645i) q^{39} +(6.02039 + 7.17482i) q^{41} +(-2.39164 - 6.57097i) q^{43} +(-0.850258 + 4.46834i) q^{45} +(-1.25088 + 7.09409i) q^{47} +(-6.33443 - 2.30554i) q^{49} +(2.19780 + 3.18433i) q^{51} -5.06730i q^{53} -7.12688i q^{55} +(-6.04915 + 12.7470i) q^{57} +(4.68437 + 1.70497i) q^{59} +(2.15983 - 12.2490i) q^{61} +(1.52675 + 0.0206185i) q^{63} +(2.63971 + 7.25254i) q^{65} +(1.40862 + 1.67872i) q^{67} +(-12.8380 + 3.34720i) q^{69} +(3.91962 + 6.78898i) q^{71} +(-5.20400 + 9.01360i) q^{73} +(-2.70938 + 3.81432i) q^{75} +(-2.35607 + 0.415438i) q^{77} +(0.00253083 - 0.00301612i) q^{79} +(8.53727 - 2.84867i) q^{81} +(-3.58383 - 3.00719i) q^{83} +(-0.588131 - 3.33546i) q^{85} +(-2.87006 - 2.03866i) q^{87} +(-5.26277 - 3.03846i) q^{89} +(2.24374 - 1.29542i) q^{91} +(1.41977 + 5.44544i) q^{93} +(9.46138 - 7.93904i) q^{95} +(-2.65220 + 0.965320i) q^{97} +(-12.3065 + 6.88530i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 216 * q	\( 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) \) 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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