LMFDB - Embedded newform 1323.2.o.e.440.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(440,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("1323.440");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 441)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			440.9
Character	$\chi$	$=$	1323.440
Dual form			1323.2.o.e.881.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.575298 - 0.332148i) q^{2} +(-0.779355 - 1.34988i) q^{4} +(-0.0141520 - 0.0245119i) q^{5} +2.36404i q^{8} +O(q^{10})$	\(q+(-0.575298 - 0.332148i) q^{2} +(-0.779355 - 1.34988i) q^{4} +(-0.0141520 - 0.0245119i) q^{5} +2.36404i q^{8} +0.0188022i q^{10} +(0.885324 + 0.511142i) q^{11} +(-4.87844 + 2.81657i) q^{13} +(-0.773498 + 1.33974i) q^{16} +5.67880 q^{17} -2.09274i q^{19} +(-0.0220588 + 0.0382070i) q^{20} +(-0.339550 - 0.588118i) q^{22} +(6.28849 - 3.63066i) q^{23} +(2.49960 - 4.32943i) q^{25} +3.74208 q^{26} +(3.52577 + 2.03560i) q^{29} +(2.87364 - 1.65910i) q^{31} +(4.98462 - 2.87787i) q^{32} +(-3.26700 - 1.88620i) q^{34} -2.47265 q^{37} +(-0.695101 + 1.20395i) q^{38} +(0.0579471 - 0.0334558i) q^{40} +(-3.52867 - 6.11183i) q^{41} +(-1.15994 + 2.00908i) q^{43} -1.59344i q^{44} -4.82367 q^{46} +(-5.43997 + 9.42231i) q^{47} +(-2.87603 + 1.66048i) q^{50} +(7.60408 + 4.39022i) q^{52} -11.5995i q^{53} -0.0289346i q^{55} +(-1.35224 - 2.34215i) q^{58} +(3.01111 + 5.21540i) q^{59} +(2.05220 + 1.18484i) q^{61} -2.20427 q^{62} -0.729528 q^{64} +(0.138079 + 0.0797200i) q^{65} +(-6.38995 - 11.0677i) q^{67} +(-4.42580 - 7.66571i) q^{68} -7.93415i q^{71} -10.8991i q^{73} +(1.42251 + 0.821285i) q^{74} +(-2.82496 + 1.63099i) q^{76} +(7.80018 - 13.5103i) q^{79} +0.0437861 q^{80} +4.68816i q^{82} +(-3.07406 + 5.32442i) q^{83} +(-0.0803661 - 0.139198i) q^{85} +(1.33463 - 0.770546i) q^{86} +(-1.20836 + 2.09294i) q^{88} +12.0516 q^{89} +(-9.80194 - 5.65915i) q^{92} +(6.25921 - 3.61376i) q^{94} +(-0.0512971 + 0.0296164i) q^{95} +(6.77565 + 3.91192i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4}+O(q^{10}) $ 48 * q + 24 * q^4	$ 48 q + 24 q^{4} + 24 q^{11} - 24 q^{16} + 48 q^{23} - 24 q^{25} - 120 q^{32} - 48 q^{50} - 48 q^{64} - 120 q^{65} + 168 q^{74} - 24 q^{79} - 24 q^{85} - 24 q^{86} + 144 q^{92} - 96 q^{95}+O(q^{100}) $ 48 * q + 24 * q^4 + 24 * q^11 - 24 * q^16 + 48 * q^23 - 24 * q^25 - 120 * q^32 - 48 * q^50 - 48 * q^64 - 120 * q^65 + 168 * q^74 - 24 * q^79 - 24 * q^85 - 24 * q^86 + 144 * q^92 - 96 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.575298	−	0.332148i	−0.406797	−	0.234864i	0.282616	−	0.959233i	$-0.408798\pi$
$2$	−0.575298	−	0.332148i	−0.406797	−	0.234864i	−0.689413	+	0.724369i	$0.742131\pi$
$3$		0			0
$3$		0			0
$4$	−0.779355	−	1.34988i	−0.389677	−	0.674941i
$5$	−0.0141520	−	0.0245119i	−0.00632895	−	0.0109621i	0.862844	−	0.505471i	$-0.168681\pi$
$5$	−0.0141520	−	0.0245119i	−0.00632895	−	0.0109621i	−0.869173	+	0.494509i	$0.835348\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			2.36404i			0.835814i
$9$		0			0
$10$			0.0188022i			0.00594578i
$11$	0.885324	+	0.511142i	0.266935	+	0.154115i	0.627494	−	0.778621i	$-0.284081\pi$
$11$	0.885324	+	0.511142i	0.266935	+	0.154115i	−0.360559	+	0.932736i	$0.617414\pi$
$12$		0			0
$13$	−4.87844	+	2.81657i	−1.35304	+	0.781176i	−0.988674	−	0.150081i	$-0.952047\pi$
$13$	−4.87844	+	2.81657i	−1.35304	+	0.781176i	−0.364363	+	0.931257i	$0.618713\pi$
$14$		0			0
$15$		0			0
$16$	−0.773498	+	1.33974i	−0.193375	+	0.334935i
$17$	5.67880			1.37731			0.688656	−	0.725089i	$-0.258201\pi$
$17$	5.67880			1.37731			0.688656	+	0.725089i	$0.258201\pi$
$18$		0			0
$19$		−	2.09274i		−	0.480108i	−0.970760	−	0.240054i	$-0.922835\pi$
$19$		−	2.09274i		−	0.480108i	0.970760	−	0.240054i	$-0.0771651\pi$
$20$	−0.0220588	+	0.0382070i	−0.00493250	+	0.00854334i
$21$		0			0
$22$	−0.339550	−	0.588118i	−0.0723923	−	0.125387i
$23$	6.28849	−	3.63066i	1.31124	−	0.757046i	0.328940	−	0.944351i	$-0.393309\pi$
$23$	6.28849	−	3.63066i	1.31124	−	0.757046i	0.982302	+	0.187305i	$0.0599754\pi$
$24$		0			0
$25$	2.49960	−	4.32943i	0.499920	−	0.865887i
$26$	3.74208			0.733882
$27$		0			0
$28$		0			0
$29$	3.52577	+	2.03560i	0.654718	+	0.378002i	0.790262	−	0.612770i	$-0.209945\pi$
$29$	3.52577	+	2.03560i	0.654718	+	0.378002i	−0.135543	+	0.990771i	$0.543278\pi$
$30$		0			0
$31$	2.87364	−	1.65910i	0.516122	−	0.297983i	−0.219225	−	0.975674i	$-0.570353\pi$
$31$	2.87364	−	1.65910i	0.516122	−	0.297983i	0.735346	+	0.677691i	$0.237019\pi$
$32$	4.98462	−	2.87787i	0.881165	−	0.508741i
$33$		0			0
$34$	−3.26700	−	1.88620i	−0.560286	−	0.323481i
$35$		0			0
$36$		0			0
$37$	−2.47265			−0.406501			−0.203250	−	0.979127i	$-0.565151\pi$
$37$	−2.47265			−0.406501			−0.203250	+	0.979127i	$0.565151\pi$
$38$	−0.695101	+	1.20395i	−0.112760	+	0.195306i
$39$		0			0
$40$	0.0579471	−	0.0334558i	0.00916224	−	0.00528982i
$41$	−3.52867	−	6.11183i	−0.551085	−	0.954508i	−0.998197	−	0.0600295i	$-0.980881\pi$
$41$	−3.52867	−	6.11183i	−0.551085	−	0.954508i	0.447111	−	0.894478i	$-0.352453\pi$
$42$		0			0
$43$	−1.15994	+	2.00908i	−0.176890	+	0.306382i	−0.940814	−	0.338924i	$-0.889937\pi$
$43$	−1.15994	+	2.00908i	−0.176890	+	0.306382i	0.763924	+	0.645306i	$0.223270\pi$
$44$		−	1.59344i		−	0.240221i
$45$		0			0
$46$	−4.82367			−0.711212
$47$	−5.43997	+	9.42231i	−0.793502	+	1.37439i	0.130285	+	0.991477i	$0.458411\pi$
$47$	−5.43997	+	9.42231i	−0.793502	+	1.37439i	−0.923786	+	0.382908i	$0.874922\pi$
$48$		0			0
$49$		0			0
$50$	−2.87603	+	1.66048i	−0.406732	+	0.234827i
$51$		0			0
$52$	7.60408	+	4.39022i	1.05450	+	0.608814i
$53$		−	11.5995i		−	1.59331i	−0.604435	−	0.796655i	$-0.706601\pi$
$53$		−	11.5995i		−	1.59331i	0.604435	−	0.796655i	$-0.293399\pi$
$54$		0			0
$55$		−	0.0289346i		−	0.00390155i
$56$		0			0
$57$		0			0
$58$	−1.35224	−	2.34215i	−0.177558	−	0.307540i
$59$	3.01111	+	5.21540i	0.392013	+	0.678987i	0.992715	−	0.120486i	$-0.0384454\pi$
$59$	3.01111	+	5.21540i	0.392013	+	0.678987i	−0.600702	+	0.799473i	$0.705112\pi$
$60$		0			0
$61$	2.05220	+	1.18484i	0.262757	+	0.151703i	0.625592	−	0.780151i	$-0.284858\pi$
$61$	2.05220	+	1.18484i	0.262757	+	0.151703i	−0.362834	+	0.931854i	$0.618191\pi$
$62$	−2.20427			−0.279942
$63$		0			0
$64$	−0.729528			−0.0911909
$65$	0.138079	+	0.0797200i	0.0171266	+	0.00988805i
$66$		0			0
$67$	−6.38995	−	11.0677i	−0.780656	−	1.35214i	−0.931560	−	0.363588i	$-0.881552\pi$
$67$	−6.38995	−	11.0677i	−0.780656	−	1.35214i	0.150903	−	0.988549i	$-0.451782\pi$
$68$	−4.42580	−	7.66571i	−0.536707	−	0.929604i
$69$		0			0
$70$		0			0
$71$		−	7.93415i		−	0.941610i	−0.882237	−	0.470805i	$-0.843964\pi$
$71$		−	7.93415i		−	0.941610i	0.882237	−	0.470805i	$-0.156036\pi$
$72$		0			0
$73$		−	10.8991i		−	1.27564i	−0.770185	−	0.637821i	$-0.779836\pi$
$73$		−	10.8991i		−	1.27564i	0.770185	−	0.637821i	$-0.220164\pi$
$74$	1.42251	+	0.821285i	0.165363	+	0.0954725i
$75$		0			0
$76$	−2.82496	+	1.63099i	−0.324045	+	0.187087i
$77$		0			0
$78$		0			0
$79$	7.80018	−	13.5103i	0.877588	−	1.52003i	0.0236086	−	0.999721i	$-0.492484\pi$
$79$	7.80018	−	13.5103i	0.877588	−	1.52003i	0.853980	−	0.520306i	$-0.174182\pi$
$80$	0.0437861			0.00489543
$81$		0			0
$82$			4.68816i			0.517721i
$83$	−3.07406	+	5.32442i	−0.337421	+	0.584431i	−0.983947	−	0.178461i	$-0.942888\pi$
$83$	−3.07406	+	5.32442i	−0.337421	+	0.584431i	0.646526	+	0.762892i	$0.276221\pi$
$84$		0			0
$85$	−0.0803661	−	0.139198i	−0.00871693	−	0.0150982i
$86$	1.33463	−	0.770546i	0.143916	−	0.0830902i
$87$		0			0
$88$	−1.20836	+	2.09294i	−0.128812	+	0.223108i
$89$	12.0516			1.27747			0.638736	−	0.769426i	$-0.279458\pi$
$89$	12.0516			1.27747			0.638736	+	0.769426i	$0.279458\pi$
$90$		0			0
$91$		0			0
$92$	−9.80194	−	5.65915i	−1.02192	−	0.590007i
$93$		0			0
$94$	6.25921	−	3.61376i	0.645588	−	0.372730i
$95$	−0.0512971	+	0.0296164i	−0.00526297	+	0.00303858i
$96$		0			0
$97$	6.77565	+	3.91192i	0.687963	+	0.397196i	0.802848	−	0.596183i	$-0.203317\pi$
$97$	6.77565	+	3.91192i	0.687963	+	0.397196i	−0.114885	+	0.993379i	$0.536650\pi$
$98$		0			0
$99$		0			0
$100$	−7.79230			−0.779230
$101$	0.226924	−	0.393043i	0.0225797	−	0.0391093i	−0.854515	−	0.519427i	$-0.826145\pi$
$101$	0.226924	−	0.393043i	0.0225797	−	0.0391093i	0.877094	+	0.480318i	$0.159479\pi$
$102$		0			0
$103$	4.58316	−	2.64609i	0.451592	−	0.260727i	−0.256910	−	0.966435i	$-0.582704\pi$
$103$	4.58316	−	2.64609i	0.451592	−	0.260727i	0.708502	+	0.705708i	$0.249371\pi$
$104$	−6.65848	−	11.5328i	−0.652918	−	1.13089i
$105$		0			0
$106$	−3.85274	+	6.67315i	−0.374212	+	0.648153i
$107$			9.06755i			0.876593i	0.898830	+	0.438296i	$0.144418\pi$
$107$			9.06755i			0.876593i	−0.898830	+	0.438296i	$0.855582\pi$
$108$		0			0
$109$	4.73027			0.453078			0.226539	−	0.974002i	$-0.427259\pi$
$109$	4.73027			0.453078			0.226539	+	0.974002i	$0.427259\pi$
$110$	−0.00961059	+	0.0166460i	−0.000916334	+	0.00158714i
$111$		0			0
$112$		0			0
$113$	8.21108	−	4.74067i	0.772433	−	0.445965i	−0.0613086	−	0.998119i	$-0.519527\pi$
$113$	8.21108	−	4.74067i	0.772433	−	0.445965i	0.833742	+	0.552154i	$0.186194\pi$
$114$		0			0
$115$	−0.177989	−	0.102762i	−0.0165976	−	0.00958261i
$116$		−	6.34583i		−	0.589195i
$117$		0			0
$118$		−	4.00054i		−	0.368280i
$119$		0			0
$120$		0			0
$121$	−4.97747	−	8.62123i	−0.452497	−	0.783748i
$122$	−0.787084	−	1.36327i	−0.0712593	−	0.123425i
$123$		0			0
$124$	−4.47918	−	2.58606i	−0.402242	−	0.232235i
$125$	−0.283017			−0.0253138
$126$		0			0
$127$	4.37297			0.388039			0.194019	−	0.980998i	$-0.437848\pi$
$127$	4.37297			0.388039			0.194019	+	0.980998i	$0.437848\pi$
$128$	−9.54954	−	5.51343i	−0.844068	−	0.487323i
$129$		0			0
$130$	−0.0529577	−	0.0917255i	−0.00464470	−	0.00804486i
$131$	−1.27231	−	2.20371i	−0.111162	−	0.192539i	0.805077	−	0.593171i	$-0.202124\pi$
$131$	−1.27231	−	2.20371i	−0.111162	−	0.192539i	−0.916239	+	0.400632i	$0.868791\pi$
$132$		0			0
$133$		0			0
$134$			8.48964i			0.733393i
$135$		0			0
$136$			13.4249i			1.15118i
$137$	9.82536	+	5.67267i	0.839437	+	0.484649i	0.857073	−	0.515195i	$-0.172281\pi$
$137$	9.82536	+	5.67267i	0.839437	+	0.484649i	−0.0176357	+	0.999844i	$0.505614\pi$
$138$		0			0
$139$	3.04891	−	1.76029i	0.258605	−	0.149306i	−0.365093	−	0.930971i	$-0.618963\pi$
$139$	3.04891	−	1.76029i	0.258605	−	0.149306i	0.623698	+	0.781665i	$0.285629\pi$
$140$		0			0
$141$		0			0
$142$	−2.63531	+	4.56450i	−0.221151	+	0.383044i
$143$	−5.75867			−0.481564
$144$		0			0
$145$		−	0.115231i		−	0.00956942i
$146$	−3.62012	+	6.27022i	−0.299603	+	0.518927i
$147$		0			0
$148$	1.92707	+	3.33778i	0.158404	+	0.274364i
$149$	13.7806	−	7.95623i	1.12895	−	0.651800i	0.185279	−	0.982686i	$-0.440681\pi$
$149$	13.7806	−	7.95623i	1.12895	−	0.651800i	0.943671	+	0.330886i	$0.107348\pi$
$150$		0			0
$151$	−1.73008	+	2.99659i	−0.140792	+	0.243859i	−0.927795	−	0.373090i	$-0.878298\pi$
$151$	−1.73008	+	2.99659i	−0.140792	+	0.243859i	0.787003	+	0.616949i	$0.211632\pi$
$152$	4.94732			0.401281
$153$		0			0
$154$		0			0
$155$	−0.0813354	−	0.0469590i	−0.00653302	−	0.00377184i
$156$		0			0
$157$	−14.1585	+	8.17442i	−1.12997	+	0.652390i	−0.943928	−	0.330151i	$-0.892900\pi$
$157$	−14.1585	+	8.17442i	−1.12997	+	0.652390i	−0.186045	+	0.982541i	$0.559567\pi$
$158$	−8.97485	+	5.18163i	−0.714001	+	0.412228i
$159$		0			0
$160$	−0.141084	−	0.0814550i	−0.0111537	−	0.00643959i
$161$		0			0
$162$		0			0
$163$	10.3556			0.811116			0.405558	−	0.914069i	$-0.367077\pi$
$163$	10.3556			0.811116			0.405558	+	0.914069i	$0.367077\pi$
$164$	−5.50017	+	9.52657i	−0.429491	+	0.743900i
$165$		0			0
$166$	3.53699	−	2.04208i	0.274524	−	0.158497i
$167$	2.94297	+	5.09738i	0.227734	+	0.394447i	0.957136	−	0.289638i	$-0.0935349\pi$
$167$	2.94297	+	5.09738i	0.227734	+	0.394447i	−0.729402	+	0.684085i	$0.760202\pi$
$168$		0			0
$169$	9.36614	−	16.2226i	0.720473	−	1.24790i
$170$			0.106774i			0.00818919i
$171$		0			0
$172$	3.61603			0.275720
$173$	−2.43276	+	4.21366i	−0.184959	+	0.320359i	−0.943563	−	0.331194i	$-0.892549\pi$
$173$	−2.43276	+	4.21366i	−0.184959	+	0.320359i	0.758604	+	0.651552i	$0.225882\pi$
$174$		0			0
$175$		0			0
$176$	−1.36959	+	0.790735i	−0.103237	+	0.0596039i
$177$		0			0
$178$	−6.93328	−	4.00293i	−0.519671	−	0.300032i
$179$		−	0.202645i		−	0.0151464i	−0.999971	−	0.00757319i	$-0.997589\pi$
$179$		−	0.202645i		−	0.0151464i	0.999971	−	0.00757319i	$-0.00241064\pi$
$180$		0			0
$181$			6.26273i			0.465505i	0.972536	+	0.232753i	$0.0747732\pi$
$181$			6.26273i			0.465505i	−0.972536	+	0.232753i	$0.925227\pi$
$182$		0			0
$183$		0			0
$184$	8.58303	+	14.8662i	0.632749	+	1.09595i
$185$	0.0349928	+	0.0606093i	0.00257272	+	0.00445608i
$186$		0			0
$187$	5.02758	+	2.90267i	0.367653	+	0.212264i
$188$	16.9587			1.23684
$189$		0			0
$190$	0.0393482			0.00285462
$191$	−11.9541	−	6.90168i	−0.864965	−	0.499388i	0.000706698	−	1.00000i	$-0.499775\pi$
$191$	−11.9541	−	6.90168i	−0.864965	−	0.499388i	−0.865672	+	0.500612i	$0.833108\pi$
$192$		0			0
$193$	10.5387	+	18.2536i	0.758593	+	1.31392i	0.943568	+	0.331178i	$0.107446\pi$
$193$	10.5387	+	18.2536i	0.758593	+	1.31392i	−0.184976	+	0.982743i	$0.559221\pi$
$194$	−2.59868	−	4.50104i	−0.186574	−	0.323156i
$195$		0			0
$196$		0			0
$197$			15.1679i			1.08067i	0.841451	+	0.540334i	$0.181702\pi$
$197$			15.1679i			1.08067i	−0.841451	+	0.540334i	$0.818298\pi$
$198$		0			0
$199$		−	9.68724i		−	0.686710i	−0.939206	−	0.343355i	$-0.888437\pi$
$199$		−	9.68724i		−	0.686710i	0.939206	−	0.343355i	$-0.111563\pi$
$200$	10.2349	+	5.90915i	0.723720	+	0.417840i
$201$		0			0
$202$	−0.261097	+	0.150745i	−0.0183707	+	0.0106064i
$203$		0			0
$204$		0			0
$205$	−0.0998751	+	0.172989i	−0.00697558	+	0.0120821i
$206$	−3.51558			−0.244942
$207$		0			0
$208$		−	8.71445i		−	0.604238i
$209$	1.06969	−	1.85275i	0.0739919	−	0.128158i
$210$		0			0
$211$	−7.05942	−	12.2273i	−0.485991	−	0.841761i	0.513880	−	0.857862i	$-0.328208\pi$
$211$	−7.05942	−	12.2273i	−0.485991	−	0.841761i	−0.999870	+	0.0161017i	$0.994874\pi$
$212$	−15.6579	+	9.04010i	−1.07539	+	0.620877i
$213$		0			0
$214$	3.01177	−	5.21654i	0.205880	−	0.356595i
$215$	0.0656619			0.00447810
$216$		0			0
$217$		0			0
$218$	−2.72132	−	1.57115i	−0.184311	−	0.106412i
$219$		0			0
$220$	−0.0390584	+	0.0225504i	−0.00263331	+	0.00152034i
$221$	−27.7037	+	15.9947i	−1.86355	+	1.07592i
$222$		0			0
$223$	−2.58777	−	1.49405i	−0.173290	−	0.100049i	0.410846	−	0.911705i	$-0.365233\pi$
$223$	−2.58777	−	1.49405i	−0.173290	−	0.100049i	−0.584136	+	0.811656i	$0.698567\pi$
$224$		0			0
$225$		0			0
$226$	−6.29842			−0.418965
$227$	14.3867	−	24.9184i	0.954876	−	1.65389i	0.220224	−	0.975449i	$-0.429321\pi$
$227$	14.3867	−	24.9184i	0.954876	−	1.65389i	0.734652	−	0.678444i	$-0.237346\pi$
$228$		0			0
$229$	−7.67401	+	4.43059i	−0.507113	+	0.292782i	−0.731646	−	0.681685i	$-0.761248\pi$
$229$	−7.67401	+	4.43059i	−0.507113	+	0.292782i	0.224533	+	0.974466i	$0.427914\pi$
$230$	0.0682645	+	0.118238i	0.00450122	+	0.00779635i
$231$		0			0
$232$	−4.81224	+	8.33505i	−0.315939	+	0.547223i
$233$			12.9082i			0.845646i	0.906212	+	0.422823i	$0.138961\pi$
$233$			12.9082i			0.845646i	−0.906212	+	0.422823i	$0.861039\pi$
$234$		0			0
$235$	0.307945			0.0200881
$236$	4.69345	−	8.12929i	0.305518	−	0.529172i
$237$		0			0
$238$		0			0
$239$	4.85712	−	2.80426i	0.314181	−	0.181392i	−0.334615	−	0.942355i	$-0.608606\pi$
$239$	4.85712	−	2.80426i	0.314181	−	0.181392i	0.648796	+	0.760963i	$0.275273\pi$
$240$		0			0
$241$	−9.51481	−	5.49338i	−0.612903	−	0.353860i	0.161198	−	0.986922i	$-0.448464\pi$
$241$	−9.51481	−	5.49338i	−0.612903	−	0.353860i	−0.774101	+	0.633063i	$0.781798\pi$
$242$			6.61303i			0.425102i
$243$		0			0
$244$		−	3.69364i		−	0.236461i
$245$		0			0
$246$		0			0
$247$	5.89436	+	10.2093i	0.375049	+	0.649604i
$248$	3.92218	+	6.79341i	0.249058	+	0.431382i
$249$		0			0
$250$	0.162819	+	0.0940035i	0.0102976	+	0.00594530i
$251$	24.2241			1.52901			0.764505	−	0.644618i	$-0.222984\pi$
$251$	24.2241			1.52901			0.764505	+	0.644618i	$0.222984\pi$
$252$		0			0
$253$	7.42314			0.466689
$254$	−2.51576	−	1.45248i	−0.157853	−	0.0911365i
$255$		0			0
$256$	4.39208	+	7.60731i	0.274505	+	0.475457i
$257$	−8.86142	−	15.3484i	−0.552760	−	0.957409i	−0.998074	−	0.0620341i	$-0.980241\pi$
$257$	−8.86142	−	15.3484i	−0.552760	−	0.957409i	0.445314	−	0.895375i	$-0.353092\pi$
$258$		0			0
$259$		0			0
$260$		−	0.248521i		−	0.0154126i
$261$		0			0
$262$			1.69039i			0.104432i
$263$	−2.51031	−	1.44933i	−0.154793	−	0.0893695i	0.420603	−	0.907245i	$-0.361819\pi$
$263$	−2.51031	−	1.44933i	−0.154793	−	0.0893695i	−0.575396	+	0.817875i	$0.695152\pi$
$264$		0			0
$265$	−0.284325	+	0.164155i	−0.0174660	+	0.0100840i
$266$		0			0
$267$		0			0
$268$	−9.96008	+	17.2514i	−0.608408	+	1.05379i
$269$	−21.8938			−1.33489			−0.667444	−	0.744660i	$-0.732612\pi$
$269$	−21.8938			−1.33489			−0.667444	+	0.744660i	$0.732612\pi$
$270$		0			0
$271$			8.98347i			0.545707i	0.962056	+	0.272854i	$0.0879675\pi$
$271$			8.98347i			0.545707i	−0.962056	+	0.272854i	$0.912033\pi$
$272$	−4.39254	+	7.60811i	−0.266337	+	0.461309i
$273$		0			0
$274$	−3.76834	−	6.52695i	−0.227654	−	0.394308i
$275$	4.42591	−	2.55530i	0.266892	−	0.154090i
$276$		0			0
$277$	−7.95091	+	13.7714i	−0.477724	+	0.827442i	−0.999674	−	0.0255339i	$-0.991871\pi$
$277$	−7.95091	+	13.7714i	−0.477724	+	0.827442i	0.521950	+	0.852976i	$0.325205\pi$
$278$	−2.33871			−0.140267
$279$		0			0
$280$		0			0
$281$	4.50324	+	2.59995i	0.268641	+	0.155100i	0.628270	−	0.777996i	$-0.283763\pi$
$281$	4.50324	+	2.59995i	0.268641	+	0.155100i	−0.359629	+	0.933095i	$0.617097\pi$
$282$		0			0
$283$	−16.2587	+	9.38694i	−0.966476	+	0.557995i	−0.898160	−	0.439668i	$-0.855096\pi$
$283$	−16.2587	+	9.38694i	−0.966476	+	0.557995i	−0.0683162	+	0.997664i	$0.521763\pi$
$284$	−10.7102	+	6.18352i	−0.635531	+	0.366924i
$285$		0			0
$286$	3.31295	+	1.91273i	0.195899	+	0.113102i
$287$		0			0
$288$		0			0
$289$	15.2488			0.896986
$290$	−0.0382738	+	0.0662922i	−0.00224751	+	0.00389281i
$291$		0			0
$292$	−14.7125	+	8.49426i	−0.860983	+	0.497089i
$293$	11.4201	+	19.7802i	0.667169	+	1.15557i	0.978692	+	0.205332i	$0.0658274\pi$
$293$	11.4201	+	19.7802i	0.667169	+	1.15557i	−0.311523	+	0.950238i	$0.600839\pi$
$294$		0			0
$295$	0.0852263	−	0.147616i	0.00496206	−	0.00859455i
$296$		−	5.84543i		−	0.339759i
$297$		0			0
$298$	−10.5706			−0.612338
$299$	−20.4520	+	35.4240i	−1.18277	+	2.04862i
$300$		0			0
$301$		0			0
$302$	1.99062	−	1.14929i	0.114548	−	0.0661341i
$303$		0			0
$304$	2.80373	+	1.61873i	0.160805	+	0.0928407i
$305$		−	0.0670711i		−	0.00384048i
$306$		0			0
$307$		−	18.6325i		−	1.06341i	−0.846928	−	0.531707i	$-0.821551\pi$
$307$		−	18.6325i		−	1.06341i	0.846928	−	0.531707i	$-0.178449\pi$
$308$		0			0
$309$		0			0
$310$	0.0311947	+	0.0540308i	0.00177174	+	0.00306875i
$311$	−10.2747	−	17.7964i	−0.582628	−	1.00914i	−0.995167	−	0.0982007i	$-0.968691\pi$
$311$	−10.2747	−	17.7964i	−0.582628	−	1.00914i	0.412539	−	0.910940i	$-0.364642\pi$
$312$		0			0
$313$	0.624466	+	0.360536i	0.0352969	+	0.0203787i	0.517545	−	0.855656i	$-0.326846\pi$
$313$	0.624466	+	0.360536i	0.0352969	+	0.0203787i	−0.482248	+	0.876035i	$0.660179\pi$
$314$	10.8605			0.612893
$315$		0			0
$316$	−24.3164			−1.36791
$317$	18.9915	+	10.9647i	1.06667	+	0.615841i	0.927269	−	0.374396i	$-0.122150\pi$
$317$	18.9915	+	10.9647i	1.06667	+	0.615841i	0.139398	+	0.990236i	$0.455483\pi$
$318$		0			0
$319$	2.08096	+	3.60433i	0.116512	+	0.201804i
$320$	0.0103242	+	0.0178821i	0.000577143	+	0.000999641i
$321$		0			0
$322$		0			0
$323$		−	11.8843i		−	0.661258i
$324$		0			0
$325$			28.1612i			1.56210i
$326$	−5.95757	−	3.43961i	−0.329959	−	0.190502i
$327$		0			0
$328$	14.4486	−	8.34191i	0.797791	−	0.460605i
$329$		0			0
$330$		0			0
$331$	−10.8338	+	18.7647i	−0.595480	+	1.03140i	0.397999	+	0.917386i	$0.369705\pi$
$331$	−10.8338	+	18.7647i	−0.595480	+	1.03140i	−0.993479	+	0.114016i	$0.963629\pi$
$332$	9.58312			0.525942
$333$		0			0
$334$		−	3.91002i		−	0.213947i
$335$	−0.180861	+	0.313260i	−0.00988147	+	0.0171152i
$336$		0			0
$337$	12.6455	+	21.9026i	0.688844	+	1.19311i	0.972212	+	0.234101i	$0.0752147\pi$
$337$	12.6455	+	21.9026i	0.688844	+	1.19311i	−0.283369	+	0.959011i	$0.591452\pi$
$338$	−10.7766	+	6.22190i	−0.586172	+	0.338427i
$339$		0			0
$340$	−0.125268	+	0.216970i	−0.00679358	+	0.0117668i
$341$	3.39214			0.183695
$342$		0			0
$343$		0			0
$344$	−4.74955	−	2.74215i	−0.256078	−	0.147847i
$345$		0			0
$346$	2.79912	−	1.61607i	0.150482	−	0.0868806i
$347$	4.92420	−	2.84299i	0.264345	−	0.152620i	−0.361970	−	0.932190i	$-0.617896\pi$
$347$	4.92420	−	2.84299i	0.264345	−	0.152620i	0.626315	+	0.779570i	$0.284562\pi$
$348$		0			0
$349$	9.68412	+	5.59113i	0.518379	+	0.299286i	0.736271	−	0.676687i	$-0.236585\pi$
$349$	9.68412	+	5.59113i	0.518379	+	0.299286i	−0.217892	+	0.975973i	$0.569918\pi$
$350$		0			0
$351$		0			0
$352$	5.88400			0.313618
$353$	7.02111	−	12.1609i	0.373696	−	0.647260i	−0.616435	−	0.787406i	$-0.711424\pi$
$353$	7.02111	−	12.1609i	0.373696	−	0.647260i	0.990131	+	0.140146i	$0.0447571\pi$
$354$		0			0
$355$	−0.194481	+	0.112284i	−0.0103220	+	0.00595940i
$356$	−9.39250	−	16.2683i	−0.497802	−	0.862218i
$357$		0			0
$358$	−0.0673081	+	0.116581i	−0.00355734	+	0.00616150i
$359$			27.1414i			1.43247i	0.697859	+	0.716235i	$0.254136\pi$
$359$			27.1414i			1.43247i	−0.697859	+	0.716235i	$0.745864\pi$
$360$		0			0
$361$	14.6204			0.769496
$362$	2.08016	−	3.60294i	0.109331	−	0.189366i
$363$		0			0
$364$		0			0
$365$	−0.267158	+	0.154244i	−0.0139837	+	0.00807347i
$366$		0			0
$367$	−5.95891	−	3.44038i	−0.311053	−	0.179586i	0.336345	−	0.941739i	$-0.390809\pi$
$367$	−5.95891	−	3.44038i	−0.311053	−	0.179586i	−0.647397	+	0.762153i	$0.724143\pi$
$368$			11.2332i			0.585573i
$369$		0			0
$370$		−	0.0464912i		−	0.00241696i
$371$		0			0
$372$		0			0
$373$	0.123926	+	0.214645i	0.00641662	+	0.0111139i	0.869216	−	0.494433i	$-0.164624\pi$
$373$	0.123926	+	0.214645i	0.00641662	+	0.0111139i	−0.862799	+	0.505547i	$0.831291\pi$
$374$	−1.92824	−	3.33980i	−0.0997067	−	0.172697i
$375$		0			0
$376$	−22.2747	−	12.8603i	−1.14873	−	0.663220i
$377$	−22.9337			−1.18114
$378$		0			0
$379$	−8.91863			−0.458119			−0.229060	−	0.973412i	$-0.573565\pi$
$379$	−8.91863			−0.458119			−0.229060	+	0.973412i	$0.573565\pi$
$380$	0.0799573	+	0.0461634i	0.00410172	+	0.00236813i
$381$		0			0
$382$	4.58476	+	7.94104i	0.234577	+	0.406299i
$383$	0.163545	+	0.283268i	0.00835675	+	0.0144743i	0.870174	−	0.492745i	$-0.164007\pi$
$383$	0.163545	+	0.283268i	0.00835675	+	0.0144743i	−0.861817	+	0.507220i	$0.830673\pi$
$384$		0			0
$385$		0			0
$386$		−	14.0017i		−	0.712665i
$387$		0			0
$388$		−	12.1951i		−	0.619113i
$389$	5.72348	+	3.30445i	0.290192	+	0.167542i	0.638028	−	0.770013i	$-0.279750\pi$
$389$	5.72348	+	3.30445i	0.290192	+	0.167542i	−0.347837	+	0.937555i	$0.613084\pi$
$390$		0			0
$391$	35.7111	−	20.6178i	1.80599	−	1.04269i
$392$		0			0
$393$		0			0
$394$	5.03799	−	8.72606i	0.253810	−	0.439613i
$395$	−0.441551			−0.0222168
$396$		0			0
$397$			7.51057i			0.376945i	0.982078	+	0.188472i	$0.0603536\pi$
$397$			7.51057i			0.376945i	−0.982078	+	0.188472i	$0.939646\pi$
$398$	−3.21760	+	5.57305i	−0.161284	+	0.279352i
$399$		0			0
$400$	3.86687	+	6.69762i	0.193344	+	0.334881i
$401$	5.48595	−	3.16732i	0.273956	−	0.158168i	−0.356728	−	0.934208i	$-0.616108\pi$
$401$	5.48595	−	3.16732i	0.273956	−	0.158168i	0.630684	+	0.776040i	$0.282774\pi$
$402$		0			0
$403$	−9.34594	+	16.1876i	−0.465555	+	0.806364i
$404$	−0.707416			−0.0351953
$405$		0			0
$406$		0			0
$407$	−2.18909	−	1.26387i	−0.108509	−	0.0626479i
$408$		0			0
$409$	29.0045	−	16.7457i	1.43418	−	0.828024i	0.436743	−	0.899586i	$-0.356132\pi$
$409$	29.0045	−	16.7457i	1.43418	−	0.828024i	0.997436	+	0.0715625i	$0.0227986\pi$
$410$	0.114916	−	0.0663467i	0.00567529	−	0.00327663i
$411$		0			0
$412$	−7.14382	−	4.12448i	−0.351951	−	0.203199i
$413$		0			0
$414$		0			0
$415$	0.174016			0.00854209
$416$	−16.2115	+	28.0791i	−0.794832	+	1.37669i
$417$		0			0
$418$	−1.23078	+	0.710590i	−0.0601993	+	0.0347561i
$419$	0.896459	+	1.55271i	0.0437949	+	0.0758550i	0.887092	−	0.461593i	$-0.152722\pi$
$419$	0.896459	+	1.55271i	0.0437949	+	0.0758550i	−0.843297	+	0.537448i	$0.819389\pi$
$420$		0			0
$421$	1.90262	−	3.29543i	0.0927278	−	0.160609i	−0.815930	−	0.578150i	$-0.803775\pi$
$421$	1.90262	−	3.29543i	0.0927278	−	0.160609i	0.908658	+	0.417541i	$0.137108\pi$
$422$			9.37910i			0.456568i
$423$		0			0
$424$	27.4216			1.33171
$425$	14.1947	−	24.5860i	0.688545	−	1.19260i
$426$		0			0
$427$		0			0
$428$	12.2401	−	7.06684i	0.591649	−	0.341589i
$429$		0			0
$430$	−0.0377751	−	0.0218095i	−0.00182168	−	0.00105175i
$431$		−	1.32957i		−	0.0640434i	−0.999487	−	0.0320217i	$-0.989805\pi$
$431$		−	1.32957i		−	0.0640434i	0.999487	−	0.0320217i	$-0.0101946\pi$
$432$		0			0
$433$			37.4292i			1.79873i	0.437194	+	0.899367i	$0.355972\pi$
$433$			37.4292i			1.79873i	−0.437194	+	0.899367i	$0.644028\pi$
$434$		0			0
$435$		0			0
$436$	−3.68656	−	6.38531i	−0.176554	−	0.305801i
$437$	−7.59804	−	13.1602i	−0.363464	−	0.629537i
$438$		0			0
$439$	20.5584	+	11.8694i	0.981201	+	0.566496i	0.902632	−	0.430412i	$-0.141632\pi$
$439$	20.5584	+	11.8694i	0.981201	+	0.566496i	0.0785682	+	0.996909i	$0.474965\pi$
$440$	0.0684026			0.00326097
$441$		0			0
$442$	21.2505			1.01078
$443$	−9.74317	−	5.62522i	−0.462912	−	0.267262i	0.250356	−	0.968154i	$-0.419452\pi$
$443$	−9.74317	−	5.62522i	−0.462912	−	0.267262i	−0.713268	+	0.700891i	$0.752786\pi$
$444$		0			0
$445$	−0.170554	−	0.295409i	−0.00808505	−	0.0140037i
$446$	0.992491	+	1.71904i	0.0469958	+	0.0813991i
$447$		0			0
$448$		0			0
$449$			14.3953i			0.679357i	0.940542	+	0.339679i	$0.110318\pi$
$449$			14.3953i			0.679357i	−0.940542	+	0.339679i	$0.889682\pi$
$450$		0			0
$451$		−	7.21460i		−	0.339722i
$452$	−12.7987	−	7.38933i	−0.602000	−	0.347565i
$453$		0			0
$454$	−16.5532	+	9.55701i	−0.776881	+	0.448533i
$455$		0			0
$456$		0			0
$457$	10.3135	−	17.8635i	0.482444	−	0.835617i	−0.517353	−	0.855772i	$-0.673083\pi$
$457$	10.3135	−	17.8635i	0.482444	−	0.835617i	0.999797	+	0.0201547i	$0.00641589\pi$
$458$	5.88646			0.275056
$459$		0			0
$460$			0.320352i			0.0149365i
$461$	−0.832511	+	1.44195i	−0.0387739	+	0.0671584i	−0.884761	−	0.466045i	$-0.845679\pi$
$461$	−0.832511	+	1.44195i	−0.0387739	+	0.0671584i	0.845987	+	0.533203i	$0.179012\pi$
$462$		0			0
$463$	0.604175	+	1.04646i	0.0280784	+	0.0486332i	0.879723	−	0.475486i	$-0.157728\pi$
$463$	0.604175	+	1.04646i	0.0280784	+	0.0486332i	−0.851645	+	0.524119i	$0.824395\pi$
$464$	−5.45435	+	3.14907i	−0.253212	+	0.146192i
$465$		0			0
$466$	4.28745	−	7.42608i	0.198612	−	0.344006i
$467$	−9.23988			−0.427571			−0.213785	−	0.976881i	$-0.568579\pi$
$467$	−9.23988			−0.427571			−0.213785	+	0.976881i	$0.568579\pi$
$468$		0			0
$469$		0			0
$470$	−0.177160	−	0.102283i	−0.00817179	−	0.00471798i
$471$		0			0
$472$	−12.3294	+	7.11839i	−0.567507	+	0.327650i
$473$	−2.05385	+	1.18579i	−0.0944361	+	0.0545227i
$474$		0			0
$475$	−9.06039	−	5.23102i	−0.415719	−	0.240016i
$476$		0			0
$477$		0			0
$478$	−3.72572			−0.170410
$479$	−8.77241	+	15.1943i	−0.400822	+	0.694243i	−0.993825	−	0.110956i	$-0.964609\pi$
$479$	−8.77241	+	15.1943i	−0.400822	+	0.694243i	0.593004	+	0.805200i	$0.297942\pi$
$480$		0			0
$481$	12.0627	−	6.96438i	0.550010	−	0.317549i
$482$	3.64923	+	6.32066i	0.166218	+	0.287898i
$483$		0			0
$484$	−7.75843	+	13.4380i	−0.352656	+	0.610818i
$485$		−	0.221446i		−	0.0100553i
$486$		0			0
$487$	−43.1898			−1.95712			−0.978558	−	0.205974i	$-0.933964\pi$
$487$	−43.1898			−1.95712			−0.978558	+	0.205974i	$0.933964\pi$
$488$	−2.80100	+	4.85148i	−0.126796	+	0.219616i
$489$		0			0
$490$		0			0
$491$	−23.0046	+	13.2817i	−1.03818	+	0.599396i	−0.919319	−	0.393514i	$-0.871259\pi$
$491$	−23.0046	+	13.2817i	−1.03818	+	0.599396i	−0.118866	+	0.992910i	$0.537926\pi$
$492$		0			0
$493$	20.0221	+	11.5598i	0.901751	+	0.520626i
$494$		−	7.83120i		−	0.352342i
$495$		0			0
$496$			5.13324i			0.230489i
$497$		0			0
$498$		0			0
$499$	−2.65759	−	4.60308i	−0.118970	−	0.206062i	0.800390	−	0.599480i	$-0.204626\pi$
$499$	−2.65759	−	4.60308i	−0.118970	−	0.206062i	−0.919360	+	0.393418i	$0.871293\pi$
$500$	0.220570	+	0.382039i	0.00986421	+	0.0170853i
$501$		0			0
$502$	−13.9361	−	8.04598i	−0.621996	−	0.359110i
$503$	−35.5334			−1.58436			−0.792178	−	0.610290i	$-0.791053\pi$
$503$	−35.5334			−1.58436			−0.792178	+	0.610290i	$0.791053\pi$
$504$		0			0
$505$	−0.0128457			−0.000571624
$506$	−4.27051	−	2.46558i	−0.189847	−	0.109608i
$507$		0			0
$508$	−3.40810	−	5.90300i	−0.151210	−	0.261903i
$509$	6.81654	+	11.8066i	0.302138	+	0.523318i	0.976620	−	0.214973i	$-0.0689663\pi$
$509$	6.81654	+	11.8066i	0.302138	+	0.523318i	−0.674482	+	0.738291i	$0.735633\pi$
$510$		0			0
$511$		0			0
$512$			16.2184i			0.716760i
$513$		0			0
$514$			11.7732i			0.519295i
$515$	−0.129721	−	0.0748947i	−0.00571621	−	0.00330025i
$516$		0			0
$517$	−9.63227	+	5.56120i	−0.423627	+	0.244581i
$518$		0			0
$519$		0			0
$520$	−0.188461	+	0.326424i	−0.00826457	+	0.0143147i
$521$	−10.2252			−0.447973			−0.223987	−	0.974592i	$-0.571907\pi$
$521$	−10.2252			−0.447973			−0.223987	+	0.974592i	$0.571907\pi$
$522$		0			0
$523$		−	5.17480i		−	0.226278i	−0.993579	−	0.113139i	$-0.963909\pi$
$523$		−	5.17480i		−	0.226278i	0.993579	−	0.113139i	$-0.0360905\pi$
$524$	−1.98317	+	3.43495i	−0.0866350	+	0.150056i
$525$		0			0
$526$	0.962785	+	1.66759i	0.0419794	+	0.0727105i
$527$	16.3189	−	9.42169i	0.710860	−	0.410415i
$528$		0			0
$529$	14.8634	−	25.7442i	0.646236	−	1.11931i
$530$	0.218096			0.00947346
$531$		0			0
$532$		0			0
$533$	34.4288	+	19.8775i	1.49128	+	0.860990i
$534$		0			0
$535$	0.222263	−	0.128324i	0.00960927	−	0.00554791i
$536$	26.1645	−	15.1061i	1.13013	−	0.652484i
$537$		0			0
$538$	12.5955	+	7.27199i	0.543029	+	0.313518i
$539$		0			0
$540$		0			0
$541$	−25.4395			−1.09373			−0.546864	−	0.837222i	$-0.684178\pi$
$541$	−25.4395			−1.09373			−0.546864	+	0.837222i	$0.684178\pi$
$542$	2.98385	−	5.16817i	0.128167	−	0.221992i
$543$		0			0
$544$	28.3067	−	16.3429i	1.21364	−	0.700694i
$545$	−0.0669427	−	0.115948i	−0.00286751	−	0.00496667i
$546$		0			0
$547$	14.7771	−	25.5947i	0.631824	−	1.09435i	−0.355355	−	0.934732i	$-0.615640\pi$
$547$	14.7771	−	25.5947i	0.631824	−	1.09435i	0.987179	−	0.159620i	$-0.0510267\pi$
$548$		−	17.6841i		−	0.755428i
$549$		0			0
$550$	−3.39495			−0.144761
$551$	4.25999	−	7.37852i	0.181482	−	0.314336i
$552$		0			0
$553$		0			0
$554$	9.14828	−	5.28176i	0.388673	−	0.224401i
$555$		0			0
$556$	−4.75237	−	2.74378i	−0.201545	−	0.116362i
$557$			19.6054i			0.830706i	0.909660	+	0.415353i	$0.136342\pi$
$557$			19.6054i			0.830706i	−0.909660	+	0.415353i	$0.863658\pi$
$558$		0			0
$559$		−	13.0683i		−	0.552728i
$560$		0			0
$561$		0			0
$562$	−1.72714	−	2.99149i	−0.0728548	−	0.126188i
$563$	7.23796	+	12.5365i	0.305044	+	0.528351i	0.977271	−	0.211994i	$-0.0679956\pi$
$563$	7.23796	+	12.5365i	0.305044	+	0.528351i	−0.672227	+	0.740345i	$0.734662\pi$
$564$		0			0
$565$	−0.232406	−	0.134180i	−0.00977738	−	0.00564497i
$566$	12.4714			0.524213
$567$		0			0
$568$	18.7566			0.787011
$569$	−6.70970	−	3.87385i	−0.281285	−	0.162400i	0.352720	−	0.935729i	$-0.385257\pi$
$569$	−6.70970	−	3.87385i	−0.281285	−	0.162400i	−0.634005	+	0.773329i	$0.718590\pi$
$570$		0			0
$571$	−8.06856	−	13.9752i	−0.337659	−	0.584842i	0.646333	−	0.763055i	$-0.276302\pi$
$571$	−8.06856	−	13.9752i	−0.337659	−	0.584842i	−0.983992	+	0.178213i	$0.942968\pi$
$572$	4.48805	+	7.77353i	0.187655	+	0.325027i
$573$		0			0
$574$		0			0
$575$		−	36.3008i		−	1.51385i
$576$		0			0
$577$		−	12.1708i		−	0.506679i	−0.967377	−	0.253339i	$-0.918471\pi$
$577$		−	12.1708i		−	0.506679i	0.967377	−	0.253339i	$-0.0815290\pi$
$578$	−8.77258	−	5.06485i	−0.364891	−	0.210670i
$579$		0			0
$580$	−0.155548	+	0.0898059i	−0.00645879	+	0.00372899i
$581$		0			0
$582$		0			0
$583$	5.92897	−	10.2693i	0.245553	−	0.425310i
$584$	25.7659			1.06620
$585$		0			0
$586$		−	15.1727i		−	0.626777i
$587$	16.8761	−	29.2302i	0.696550	−	1.20646i	−0.273106	−	0.961984i	$-0.588051\pi$
$587$	16.8761	−	29.2302i	0.696550	−	1.20646i	0.969655	−	0.244476i	$-0.0786158\pi$
$588$		0			0
$589$	−3.47207	−	6.01380i	−0.143064	−	0.247794i
$590$	−0.0980610	+	0.0566155i	−0.00403711	+	0.00233082i
$591$		0			0
$592$	1.91259	−	3.31270i	0.0786069	−	0.136151i
$593$	18.3025			0.751592			0.375796	−	0.926702i	$-0.377369\pi$
$593$	18.3025			0.751592			0.375796	+	0.926702i	$0.377369\pi$
$594$		0			0
$595$		0			0
$596$	−21.4799	−	12.4015i	−0.879853	−	0.507983i
$597$		0			0
$598$	23.5320	−	13.5862i	0.962296	−	0.555582i
$599$	34.1905	−	19.7399i	1.39699	−	0.806551i	0.402911	−	0.915239i	$-0.367998\pi$
$599$	34.1905	−	19.7399i	1.39699	−	0.806551i	0.994076	+	0.108689i	$0.0346651\pi$
$600$		0			0
$601$	−34.4865	−	19.9108i	−1.40673	−	0.812177i	−0.411661	−	0.911337i	$-0.635051\pi$
$601$	−34.4865	−	19.9108i	−1.40673	−	0.812177i	−0.995072	+	0.0991600i	$0.968384\pi$
$602$		0			0
$603$		0			0
$604$	5.39339			0.219454
$605$	−0.140882	+	0.244015i	−0.00572766	+	0.00992060i
$606$		0			0
$607$	−21.6104	+	12.4768i	−0.877140	+	0.506417i	−0.869714	−	0.493555i	$-0.835697\pi$
$607$	−21.6104	+	12.4768i	−0.877140	+	0.506417i	−0.00742570	+	0.999972i	$0.502364\pi$
$608$	−6.02264	−	10.4315i	−0.244250	−	0.423054i
$609$		0			0
$610$	−0.0222776	+	0.0385859i	−0.000901992	+	0.00156230i
$611$		−	61.2883i		−	2.47946i
$612$		0			0
$613$	28.0570			1.13321			0.566605	−	0.823990i	$-0.308257\pi$
$613$	28.0570			1.13321			0.566605	+	0.823990i	$0.308257\pi$
$614$	−6.18876	+	10.7192i	−0.249758	+	0.432594i
$615$		0			0
$616$		0			0
$617$	−29.8093	+	17.2104i	−1.20008	+	0.692865i	−0.960573	−	0.278030i	$-0.910319\pi$
$617$	−29.8093	+	17.2104i	−1.20008	+	0.692865i	−0.239506	+	0.970895i	$0.576985\pi$
$618$		0			0
$619$	−17.2889	−	9.98173i	−0.694898	−	0.401200i	0.110546	−	0.993871i	$-0.464740\pi$
$619$	−17.2889	−	9.98173i	−0.694898	−	0.401200i	−0.805444	+	0.592671i	$0.798073\pi$
$620$			0.146391i			0.00587920i
$621$		0			0
$622$			13.6510i			0.547354i
$623$		0			0
$624$		0			0
$625$	−12.4940	−	21.6402i	−0.499760	−	0.865609i
$626$	−0.239503	−	0.414831i	−0.00957245	−	0.0165800i
$627$		0			0
$628$	22.0690	+	12.7416i	0.880650	+	0.508443i
$629$	−14.0417			−0.559878
$630$		0			0
$631$	−46.8447			−1.86486			−0.932429	−	0.361354i	$-0.882314\pi$
$631$	−46.8447			−1.86486			−0.932429	+	0.361354i	$0.882314\pi$
$632$	31.9389	+	18.4399i	1.27046	+	0.733501i
$633$		0			0
$634$	−7.28384	−	12.6160i	−0.289278	−	0.501044i
$635$	−0.0618862	−	0.107190i	−0.00245588	−	0.00425370i
$636$		0			0
$637$		0			0
$638$		−	2.76475i		−	0.109458i
$639$		0			0
$640$			0.312103i			0.0123370i
$641$	3.34281	+	1.92997i	0.132033	+	0.0762293i	0.564562	−	0.825391i	$-0.309045\pi$
$641$	3.34281	+	1.92997i	0.132033	+	0.0762293i	−0.432529	+	0.901620i	$0.642379\pi$
$642$		0			0
$643$	−31.0233	+	17.9113i	−1.22344	+	0.706352i	−0.965649	−	0.259849i	$-0.916327\pi$
$643$	−31.0233	+	17.9113i	−1.22344	+	0.706352i	−0.257789	+	0.966201i	$0.582994\pi$
$644$		0			0
$645$		0			0
$646$	−3.94734	+	6.83699i	−0.155306	+	0.268998i
$647$	43.6492			1.71603			0.858013	−	0.513627i	$-0.171699\pi$
$647$	43.6492			1.71603			0.858013	+	0.513627i	$0.171699\pi$
$648$		0			0
$649$			6.15642i			0.241661i
$650$	9.35369	−	16.2011i	0.366882	−	0.635458i
$651$		0			0
$652$	−8.07072	−	13.9789i	−0.316074	−	0.547456i
$653$	−6.45191	+	3.72501i	−0.252483	+	0.145771i	−0.620901	−	0.783889i	$-0.713233\pi$
$653$	−6.45191	+	3.72501i	−0.252483	+	0.145771i	0.368418	+	0.929660i	$0.379900\pi$
$654$		0			0
$655$	−0.0360114	+	0.0623736i	−0.00140708	+	0.00243714i
$656$	10.9177			0.426264
$657$		0			0
$658$		0			0
$659$	7.52607	+	4.34518i	0.293174	+	0.169264i	0.639372	−	0.768897i	$-0.279194\pi$
$659$	7.52607	+	4.34518i	0.293174	+	0.169264i	−0.346198	+	0.938161i	$0.612528\pi$
$660$		0			0
$661$	−24.9853	+	14.4253i	−0.971815	+	0.561077i	−0.899789	−	0.436325i	$-0.856280\pi$
$661$	−24.9853	+	14.4253i	−0.971815	+	0.561077i	−0.0720256	+	0.997403i	$0.522946\pi$
$662$	12.4653	−	7.19686i	0.484479	−	0.279714i
$663$		0			0
$664$	−12.5871	−	7.26719i	−0.488476	−	0.282022i
$665$		0			0
$666$		0			0
$667$	29.5623			1.14466
$668$	4.58724	−	7.94534i	0.177486	−	0.307414i
$669$		0			0
$670$	0.208097	−	0.120145i	0.00803950	−	0.00464161i
$671$	1.21124	+	2.09793i	0.0467594	+	0.0809897i
$672$		0			0
$673$	−3.60695	+	6.24742i	−0.139038	+	0.240820i	−0.927133	−	0.374733i	$-0.877734\pi$
$673$	−3.60695	+	6.24742i	−0.139038	+	0.240820i	0.788095	+	0.615554i	$0.211068\pi$
$674$		−	16.8007i		−	0.647139i
$675$		0			0
$676$	−29.1982			−1.12301
$677$	18.1911	−	31.5079i	0.699140	−	1.21095i	−0.269626	−	0.962965i	$-0.586900\pi$
$677$	18.1911	−	31.5079i	0.699140	−	1.21095i	0.968765	−	0.247980i	$-0.0797667\pi$
$678$		0			0
$679$		0			0
$680$	0.329070	−	0.189989i	0.0126193	−	0.00728573i
$681$		0			0
$682$	−1.95149	−	1.12669i	−0.0747265	−	0.0431433i
$683$		−	23.7326i		−	0.908101i	−0.890976	−	0.454050i	$-0.849979\pi$
$683$		−	23.7326i		−	0.908101i	0.890976	−	0.454050i	$-0.150021\pi$
$684$		0			0
$685$		−	0.321118i		−	0.0122693i
$686$		0			0
$687$		0			0
$688$	−1.79443	−	3.10804i	−0.0684119	−	0.118493i
$689$	32.6707	+	56.5874i	1.24466	+	2.15581i
$690$		0			0
$691$	2.86127	+	1.65195i	0.108848	+	0.0628433i	0.553436	−	0.832892i	$-0.313316\pi$
$691$	2.86127	+	1.65195i	0.108848	+	0.0628433i	−0.444588	+	0.895735i	$0.646650\pi$
$692$	7.58393			0.288298
$693$		0			0
$694$	−3.77718			−0.143380
$695$	−0.0862962	−	0.0498231i	−0.00327340	−	0.00188990i
$696$		0			0
$697$	−20.0386	−	34.7079i	−0.759016	−	1.31465i
$698$	−3.71417	−	6.43313i	−0.140583	−	0.243498i
$699$		0			0
$700$		0			0
$701$			0.873603i			0.0329955i	0.999864	+	0.0164978i	$0.00525164\pi$
$701$			0.873603i			0.0329955i	−0.999864	+	0.0164978i	$0.994748\pi$
$702$		0			0
$703$			5.17461i			0.195164i
$704$	−0.645868	−	0.372892i	−0.0243421	−	0.0140539i
$705$		0			0
$706$	−8.07845	+	4.66410i	−0.304037	+	0.175536i
$707$		0			0
$708$		0			0
$709$	−8.07767	+	13.9909i	−0.303363	+	0.525441i	−0.976896	−	0.213717i	$-0.931443\pi$
$709$	−8.07767	+	13.9909i	−0.303363	+	0.525441i	0.673532	+	0.739158i	$0.264776\pi$
$710$	0.149179			0.00559860
$711$		0			0
$712$			28.4905i			1.06773i
$713$	12.0473	−	20.8665i	0.451174	−	0.781456i
$714$		0			0
$715$	0.0814965	+	0.141156i	0.00304779	+	0.00527894i
$716$	−0.273546	+	0.157932i	−0.0102229	+	0.00590220i
$717$		0			0
$718$	9.01498	−	15.6144i	0.336436	−	0.582724i
$719$	−45.1905			−1.68532			−0.842661	−	0.538445i	$-0.819012\pi$
$719$	−45.1905			−1.68532			−0.842661	+	0.538445i	$0.819012\pi$
$720$		0			0
$721$		0			0
$722$	−8.41110	−	4.85615i	−0.313029	−	0.180727i
$723$		0			0
$724$	8.45395	−	4.88089i	0.314189	−	0.181397i
$725$	17.6260	−	10.1764i	0.654613	−	0.377941i
$726$		0			0
$727$	7.15775	+	4.13253i	0.265466	+	0.153267i	0.626826	−	0.779160i	$-0.284354\pi$
$727$	7.15775	+	4.13253i	0.265466	+	0.153267i	−0.361359	+	0.932427i	$0.617687\pi$
$728$		0			0
$729$		0			0
$730$	0.204927			0.00758468
$731$	−6.58709	+	11.4092i	−0.243632	+	0.421983i
$732$		0			0
$733$	10.5799	−	6.10830i	0.390777	−	0.225615i	−0.291720	−	0.956504i	$-0.594227\pi$
$733$	10.5799	−	6.10830i	0.390777	−	0.225615i	0.682497	+	0.730889i	$0.260894\pi$
$734$	2.28543	+	3.95849i	0.0843569	+	0.146110i
$735$		0			0
$736$	20.8972	−	36.1949i	0.770280	−	1.33416i
$737$		−	13.0647i		−	0.481244i
$738$		0			0
$739$	−20.7072			−0.761726			−0.380863	−	0.924631i	$-0.624373\pi$
$739$	−20.7072			−0.761726			−0.380863	+	0.924631i	$0.624373\pi$
$740$	0.0545436	−	0.0944723i	0.00200506	−	0.00347287i
$741$		0			0
$742$		0			0
$743$	−10.2862	+	5.93873i	−0.377363	+	0.217871i	−0.676670	−	0.736286i	$-0.736578\pi$
$743$	−10.2862	+	5.93873i	−0.377363	+	0.217871i	0.299307	+	0.954157i	$0.403244\pi$
$744$		0			0
$745$	−0.390045	−	0.225192i	−0.0142901	−	0.00825041i
$746$		−	0.164647i		−	0.00602814i
$747$		0			0
$748$		−	9.04885i		−	0.330859i
$749$		0			0
$750$		0			0
$751$	−11.8554	−	20.5342i	−0.432610	−	0.749303i	0.564487	−	0.825442i	$-0.309074\pi$
$751$	−11.8554	−	20.5342i	−0.432610	−	0.749303i	−0.997097	+	0.0761390i	$0.975741\pi$
$752$	−8.41562	−	14.5763i	−0.306886	−	0.531542i
$753$		0			0
$754$	13.1937	+	7.61738i	0.480486	+	0.277409i
$755$	0.0979362			0.00356426
$756$		0			0
$757$	44.2494			1.60827			0.804136	−	0.594446i	$-0.202628\pi$
$757$	44.2494			1.60827			0.804136	+	0.594446i	$0.202628\pi$
$758$	5.13087	+	2.96231i	0.186362	+	0.107596i
$759$		0			0
$760$	−0.0700143	−	0.121268i	−0.00253969	−	0.00439887i
$761$	24.3767	+	42.2217i	0.883656	+	1.53054i	0.847246	+	0.531200i	$0.178259\pi$
$761$	24.3767	+	42.2217i	0.883656	+	1.53054i	0.0364098	+	0.999337i	$0.488408\pi$
$762$		0			0
$763$		0			0
$764$			21.5154i			0.778401i
$765$		0			0
$766$		−	0.217284i		−	0.00785081i
$767$	−29.3791	−	16.9620i	−1.06082	−	0.612463i
$768$		0			0
$769$	−23.3870	+	13.5025i	−0.843357	+	0.486912i	−0.858404	−	0.512975i	$-0.828543\pi$
$769$	−23.3870	+	13.5025i	−0.843357	+	0.486912i	0.0150472	+	0.999887i	$0.495210\pi$
$770$		0			0
$771$		0			0
$772$	16.4268	−	28.4520i	0.591213	−	1.02401i
$773$	−26.7135			−0.960817			−0.480408	−	0.877045i	$-0.659512\pi$
$773$	−26.7135			−0.960817			−0.480408	+	0.877045i	$0.659512\pi$
$774$		0			0
$775$		−	16.5883i		−	0.595871i
$776$	−9.24794	+	16.0179i	−0.331982	+	0.575009i
$777$		0			0
$778$	−2.19514	−	3.80209i	−0.0786994	−	0.136311i
$779$	−12.7905	+	7.38459i	−0.458267	+	0.264580i
$780$		0			0
$781$	4.05547	−	7.02429i	0.145116	−	0.251349i
$782$	−27.3927			−0.979560
$783$		0			0
$784$		0			0
$785$	0.400742	+	0.231368i	0.0143031	+	0.00825789i
$786$		0			0
$787$	41.0093	−	23.6767i	1.46182	−	0.843983i	0.462726	−	0.886501i	$-0.346871\pi$
$787$	41.0093	−	23.6767i	1.46182	−	0.843983i	0.999096	+	0.0425177i	$0.0135379\pi$
$788$	20.4749	−	11.8212i	0.729388	−	0.421112i
$789$		0			0
$790$	0.254023	+	0.146660i	0.00903775	+	0.00521795i
$791$		0			0
$792$		0			0
$793$	−13.3487			−0.474027
$794$	2.49462	−	4.32082i	0.0885309	−	0.153340i
$795$		0			0
$796$	−13.0766	+	7.54980i	−0.463489	+	0.267596i
$797$	−4.42781	−	7.66919i	−0.156841	−	0.271657i	0.776887	−	0.629640i	$-0.216798\pi$
$797$	−4.42781	−	7.66919i	−0.156841	−	0.271657i	−0.933728	+	0.357984i	$0.883464\pi$
$798$		0			0
$799$	−30.8925	+	53.5074i	−1.09290	+	1.89296i
$800$		−	28.7741i		−	1.01732i
$801$		0			0
$802$	−4.20808			−0.148592
$803$	5.57098	−	9.64922i	0.196596	−	0.340514i
$804$		0			0
$805$		0			0
$806$	10.7534	−	6.20848i	0.378772	−	0.218684i
$807$		0			0
$808$	0.929170	+	0.536456i	0.0326881	+	0.0188725i
$809$		−	7.40014i		−	0.260175i	−0.991503	−	0.130087i	$-0.958474\pi$
$809$		−	7.40014i		−	0.260175i	0.991503	−	0.130087i	$-0.0415258\pi$
$810$		0			0
$811$		−	25.0843i		−	0.880829i	−0.897794	−	0.440415i	$-0.854831\pi$
$811$		−	25.0843i		−	0.880829i	0.897794	−	0.440415i	$-0.145169\pi$
$812$		0			0
$813$		0			0
$814$	0.839587	+	1.45421i	0.0294275	+	0.0509699i
$815$	−0.146553	−	0.253836i	−0.00513351	−	0.00889150i
$816$		0			0
$817$	4.20449	+	2.42746i	0.147096	+	0.0849262i
$818$	−22.2483			−0.777893
$819$		0			0
$820$	0.311353			0.0108729
$821$	−18.3781	−	10.6106i	−0.641401	−	0.370313i	0.143753	−	0.989614i	$-0.454083\pi$
$821$	−18.3781	−	10.6106i	−0.641401	−	0.370313i	−0.785154	+	0.619300i	$0.787416\pi$
$822$		0			0
$823$	−8.47690	−	14.6824i	−0.295486	−	0.511797i	0.679612	−	0.733572i	$-0.262148\pi$
$823$	−8.47690	−	14.6824i	−0.295486	−	0.511797i	−0.975098	+	0.221775i	$0.928815\pi$
$824$	6.25546	+	10.8348i	0.217919	+	0.377447i
$825$		0			0
$826$		0			0
$827$		−	25.3052i		−	0.879949i	−0.898010	−	0.439975i	$-0.854987\pi$
$827$		−	25.3052i		−	0.879949i	0.898010	−	0.439975i	$-0.145013\pi$
$828$		0			0
$829$		−	41.5277i		−	1.44232i	−0.692770	−	0.721158i	$-0.743610\pi$
$829$		−	41.5277i		−	1.44232i	0.692770	−	0.721158i	$-0.256390\pi$
$830$	−0.100111	−	0.0577990i	−0.00347490	−	0.00200623i
$831$		0			0
$832$	3.55896	−	2.05477i	0.123385	−	0.0712362i
$833$		0			0
$834$		0			0
$835$	0.0832977	−	0.144276i	0.00288264	−	0.00499287i
$836$	−3.33467			−0.115332
$837$		0			0
$838$		−	1.19103i		−	0.0411434i
$839$	6.61780	−	11.4624i	0.228472	−	0.395725i	−0.728884	−	0.684638i	$-0.759960\pi$
$839$	6.61780	−	11.4624i	0.228472	−	0.395725i	0.957355	+	0.288913i	$0.0932938\pi$
$840$		0			0
$841$	−6.21265	−	10.7606i	−0.214229	−	0.371056i
$842$	−2.18914	+	1.26390i	−0.0754428	+	0.0435569i
$843$		0			0
$844$	−11.0036	+	19.0588i	−0.378759	+	0.656030i
$845$	−0.530197			−0.0182393
$846$		0			0
$847$		0			0
$848$	15.5403	+	8.97217i	0.533654	+	0.308106i
$849$		0			0
$850$	−16.3324	+	9.42951i	−0.560196	+	0.323429i
$851$	−15.5492	+	8.97735i	−0.533020	+	0.307739i
$852$		0			0
$853$	15.3814	+	8.88048i	0.526651	+	0.304062i	0.739651	−	0.672990i	$-0.234990\pi$
$853$	15.3814	+	8.88048i	0.526651	+	0.304062i	−0.213001	+	0.977052i	$0.568324\pi$
$854$		0			0
$855$		0			0
$856$	−21.4360			−0.732669
$857$	9.17157	−	15.8856i	0.313295	−	0.542643i	−0.665779	−	0.746149i	$-0.731900\pi$
$857$	9.17157	−	15.8856i	0.313295	−	0.542643i	0.979074	+	0.203507i	$0.0652338\pi$
$858$		0			0
$859$	2.69126	−	1.55380i	0.0918246	−	0.0530150i	−0.453385	−	0.891315i	$-0.649784\pi$
$859$	2.69126	−	1.55380i	0.0918246	−	0.0530150i	0.545209	+	0.838300i	$0.316450\pi$
$860$	−0.0511739	−	0.0886358i	−0.00174502	−	0.00302246i
$861$		0			0
$862$	−0.441616	+	0.764902i	−0.0150415	+	0.0260527i
$863$			41.4060i			1.40948i	0.709467	+	0.704739i	$0.248936\pi$
$863$			41.4060i			1.40948i	−0.709467	+	0.704739i	$0.751064\pi$
$864$		0			0
$865$	0.137713			0.00468239
$866$	12.4321	−	21.5330i	0.422458	−	0.731720i
$867$		0			0
$868$		0			0
$869$	13.8114	−	7.97399i	0.468518	−	0.270499i
$870$		0			0
$871$	62.3460	+	35.9955i	2.11251	+	1.21966i
$872$			11.1826i			0.378689i
$873$		0			0
$874$			10.0947i			0.341459i
$875$		0			0
$876$		0			0
$877$	11.3979	+	19.7417i	0.384878	+	0.666628i	0.991752	−	0.128170i	$-0.0409102\pi$
$877$	11.3979	+	19.7417i	0.384878	+	0.666628i	−0.606874	+	0.794798i	$0.707577\pi$
$878$	−7.88482	−	13.6569i	−0.266100	−	0.460898i
$879$		0			0
$880$	0.0387648	+	0.0223809i	0.00130676	+	0.000754460i
$881$	−43.4050			−1.46235			−0.731175	−	0.682190i	$-0.761028\pi$
$881$	−43.4050			−1.46235			−0.731175	+	0.682190i	$0.761028\pi$
$882$		0			0
$883$	−29.9309			−1.00725			−0.503627	−	0.863921i	$-0.668001\pi$
$883$	−29.9309			−1.00725			−0.503627	+	0.863921i	$0.668001\pi$
$884$	43.1820	+	24.9312i	1.45237	+	0.838526i
$885$		0			0
$886$	3.73682	+	6.47236i	0.125541	+	0.217443i
$887$	19.4788	+	33.7382i	0.654033	+	1.13282i	0.982135	+	0.188176i	$0.0602576\pi$
$887$	19.4788	+	33.7382i	0.654033	+	1.13282i	−0.328102	+	0.944642i	$0.606409\pi$
$888$		0			0
$889$		0			0
$890$			0.226597i			0.00759556i
$891$		0			0
$892$			4.65757i			0.155947i
$893$	19.7185	+	11.3845i	0.659853	+	0.380966i
$894$		0			0
$895$	−0.00496721	+	0.00286782i	−0.000166035	+	9.58606e-5i
$896$		0			0
$897$		0			0
$898$	4.78138	−	8.28160i	0.159557	−	0.276361i
$899$	13.5091			0.450553
$900$		0			0
$901$		−	65.8711i		−	2.19448i
$902$	−2.39632	+	4.15054i	−0.0797886	+	0.138198i
$903$		0			0
$904$	11.2071	+	19.4113i	0.372743	+	0.645611i
$905$	0.153512	−	0.0886299i	0.00510290	−	0.00294616i
$906$		0			0
$907$	14.0526	−	24.3399i	0.466610	−	0.808192i	−0.532663	−	0.846328i	$-0.678809\pi$
$907$	14.0526	−	24.3399i	0.466610	−	0.808192i	0.999273	+	0.0381355i	$0.0121419\pi$
$908$	−44.8493			−1.48837
$909$		0			0
$910$		0			0
$911$	−32.3883	−	18.6994i	−1.07307	−	0.619538i	−0.144052	−	0.989570i	$-0.546013\pi$
$911$	−32.3883	−	18.6994i	−1.07307	−	0.619538i	−0.929019	+	0.370032i	$0.879347\pi$
$912$		0			0
$913$	−5.44307	+	3.14256i	−0.180139	+	0.104003i
$914$	−11.8666	+	6.85121i	−0.392513	+	0.226618i
$915$		0			0
$916$	11.9616	+	6.90601i	0.395221	+	0.228181i
$917$		0			0
$918$		0			0
$919$	−25.8230			−0.851822			−0.425911	−	0.904765i	$-0.640046\pi$
$919$	−25.8230			−0.851822			−0.425911	+	0.904765i	$0.640046\pi$
$920$	0.242933	−	0.420773i	0.00800928	−	0.0138725i
$921$		0			0
$922$	0.957884	−	0.553034i	0.0315462	−	0.0182132i
$923$	22.3471	+	38.7063i	0.735563	+	1.27403i
$924$		0			0
$925$	−6.18063	+	10.7052i	−0.203218	+	0.351983i
$926$		−	0.802704i		−	0.0263785i
$927$		0			0
$928$	23.4328			0.769220
$929$	7.97094	−	13.8061i	0.261518	−	0.452963i	−0.705127	−	0.709081i	$-0.749110\pi$
$929$	7.97094	−	13.8061i	0.261518	−	0.452963i	0.966646	+	0.256118i	$0.0824435\pi$
$930$		0			0
$931$		0			0
$932$	17.4246	−	10.0601i	0.570762	−	0.329529i
$933$		0			0
$934$	5.31568	+	3.06901i	0.173934	+	0.100421i
$935$		−	0.164314i		−	0.00537364i
$936$		0			0
$937$			15.0698i			0.492308i	0.969231	+	0.246154i	$0.0791668\pi$
$937$			15.0698i			0.492308i	−0.969231	+	0.246154i	$0.920833\pi$
$938$		0			0
$939$		0			0
$940$	−0.239999	−	0.415690i	−0.00782789	−	0.0135583i
$941$	5.76861	+	9.99152i	0.188051	+	0.325714i	0.944600	−	0.328222i	$-0.106450\pi$
$941$	5.76861	+	9.99152i	0.188051	+	0.325714i	−0.756549	+	0.653937i	$0.773116\pi$
$942$		0			0
$943$	−44.3800	−	25.6228i	−1.44521	−	0.834393i
$944$	−9.31636			−0.303222
$945$		0			0
$946$	1.57543			0.0512218
$947$	24.5364	+	14.1661i	0.797325	+	0.460336i	0.842535	−	0.538642i	$-0.181062\pi$
$947$	24.5364	+	14.1661i	0.797325	+	0.460336i	−0.0452102	+	0.998977i	$0.514396\pi$
$948$		0			0
$949$	30.6981	+	53.1706i	0.996501	+	1.72599i
$950$	3.47495	+	6.01879i	0.112742	+	0.195275i
$951$		0			0
$952$		0			0
$953$			29.8498i			0.966931i	0.875364	+	0.483465i	$0.160622\pi$
$953$			29.8498i			0.966931i	−0.875364	+	0.483465i	$0.839378\pi$
$954$		0			0
$955$			0.390689i			0.0126424i
$956$	−7.57084	−	4.37102i	−0.244858	−	0.141369i
$957$		0			0
$958$	10.0935	−	5.82748i	0.326106	−	0.188277i
$959$		0			0
$960$		0			0
$961$	−9.99478	+	17.3115i	−0.322412	+	0.558434i
$962$	−9.25283			−0.298323
$963$		0			0
$964$			17.1252i			0.551564i
$965$	0.298287	−	0.516648i	0.00960219	−	0.0166315i
$966$		0			0
$967$	8.17864	+	14.1658i	0.263007	+	0.455542i	0.967040	−	0.254626i	$-0.0819523\pi$
$967$	8.17864	+	14.1658i	0.263007	+	0.455542i	−0.704032	+	0.710168i	$0.748619\pi$
$968$	20.3809	−	11.7669i	0.655068	−	0.378203i
$969$		0			0
$970$	−0.0735528	+	0.127397i	−0.00236164	+	0.00409048i
$971$	21.4630			0.688779			0.344390	−	0.938827i	$-0.388086\pi$
$971$	21.4630			0.688779			0.344390	+	0.938827i	$0.388086\pi$
$972$		0			0
$973$		0			0
$974$	24.8470	+	14.3454i	0.796148	+	0.459657i
$975$		0			0
$976$	−3.17475	+	1.83294i	−0.101621	+	0.0586710i
$977$	18.6219	−	10.7513i	0.595766	−	0.343966i	−0.171608	−	0.985165i	$-0.554896\pi$
$977$	18.6219	−	10.7513i	0.595766	−	0.343966i	0.767374	+	0.641199i	$0.221563\pi$
$978$		0			0
$979$	10.6696	+	6.16010i	0.341002	+	0.196878i
$980$		0			0
$981$		0			0
$982$	17.6460			0.563107
$983$	−12.7097	+	22.0138i	−0.405376	+	0.702131i	−0.994365	−	0.106009i	$-0.966193\pi$
$983$	−12.7097	+	22.0138i	−0.405376	+	0.702131i	0.588989	+	0.808141i	$0.299526\pi$
$984$		0			0
$985$	0.371794	−	0.214656i	0.0118464	−	0.00683949i
$986$	−7.67912	−	13.3006i	−0.244553	−	0.423578i
$987$		0			0
$988$	9.18759	−	15.9134i	0.292296	−	0.506272i
$989$			16.8455i			0.535654i
$990$		0			0
$991$	23.7537			0.754560			0.377280	−	0.926099i	$-0.376859\pi$
$991$	23.7537			0.754560			0.377280	+	0.926099i	$0.376859\pi$
$992$	9.54935	−	16.5400i	0.303192	−	0.525144i
$993$		0			0
$994$		0			0
$995$	−0.237453	+	0.137093i	−0.00752776	+	0.00434615i
$996$		0			0
$997$	−10.5366	−	6.08329i	−0.333697	−	0.192660i	0.323785	−	0.946131i	$-0.395045\pi$
$997$	−10.5366	−	6.08329i	−0.333697	−	0.192660i	−0.657481	+	0.753471i	$0.728378\pi$
$998$			3.53086i			0.111767i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.o.e.440.9		48
3.2	odd	2		441.2.o.e.146.15	✓	48
7.2	even	3		1323.2.i.d.521.9		48
7.3	odd	6		1323.2.s.d.656.16		48
7.4	even	3		1323.2.s.d.656.15		48
7.5	odd	6		1323.2.i.d.521.10		48
7.6	odd	2	inner	1323.2.o.e.440.10		48
9.4	even	3		441.2.o.e.293.16	yes	48
9.5	odd	6	inner	1323.2.o.e.881.10		48
21.2	odd	6		441.2.i.d.227.10		48
21.5	even	6		441.2.i.d.227.9		48
21.11	odd	6		441.2.s.d.362.10		48
21.17	even	6		441.2.s.d.362.9		48
21.20	even	2		441.2.o.e.146.16	yes	48
63.4	even	3		441.2.i.d.68.15		48
63.5	even	6		1323.2.s.d.962.15		48
63.13	odd	6		441.2.o.e.293.15	yes	48
63.23	odd	6		1323.2.s.d.962.16		48
63.31	odd	6		441.2.i.d.68.16		48
63.32	odd	6		1323.2.i.d.1097.10		48
63.40	odd	6		441.2.s.d.374.10		48
63.41	even	6	inner	1323.2.o.e.881.9		48
63.58	even	3		441.2.s.d.374.9		48
63.59	even	6		1323.2.i.d.1097.9		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.15		48	63.4	even	3
441.2.i.d.68.16		48	63.31	odd	6
441.2.i.d.227.9		48	21.5	even	6
441.2.i.d.227.10		48	21.2	odd	6
441.2.o.e.146.15	✓	48	3.2	odd	2
441.2.o.e.146.16	yes	48	21.20	even	2
441.2.o.e.293.15	yes	48	63.13	odd	6
441.2.o.e.293.16	yes	48	9.4	even	3
441.2.s.d.362.9		48	21.17	even	6
441.2.s.d.362.10		48	21.11	odd	6
441.2.s.d.374.9		48	63.58	even	3
441.2.s.d.374.10		48	63.40	odd	6
1323.2.i.d.521.9		48	7.2	even	3
1323.2.i.d.521.10		48	7.5	odd	6
1323.2.i.d.1097.9		48	63.59	even	6
1323.2.i.d.1097.10		48	63.32	odd	6
1323.2.o.e.440.9		48	1.1	even	1	trivial
1323.2.o.e.440.10		48	7.6	odd	2	inner
1323.2.o.e.881.9		48	63.41	even	6	inner
1323.2.o.e.881.10		48	9.5	odd	6	inner
1323.2.s.d.656.15		48	7.4	even	3
1323.2.s.d.656.16		48	7.3	odd	6
1323.2.s.d.962.15		48	63.5	even	6
1323.2.s.d.962.16		48	63.23	odd	6

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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.575298 - 0.332148i) q^{2} +(-0.779355 - 1.34988i) q^{4} +(-0.0141520 - 0.0245119i) q^{5} +2.36404i q^{8} +O(q^{10})\)	\(q+(-0.575298 - 0.332148i) q^{2} +(-0.779355 - 1.34988i) q^{4} +(-0.0141520 - 0.0245119i) q^{5} +2.36404i q^{8} +0.0188022i q^{10} +(0.885324 + 0.511142i) q^{11} +(-4.87844 + 2.81657i) q^{13} +(-0.773498 + 1.33974i) q^{16} +5.67880 q^{17} -2.09274i q^{19} +(-0.0220588 + 0.0382070i) q^{20} +(-0.339550 - 0.588118i) q^{22} +(6.28849 - 3.63066i) q^{23} +(2.49960 - 4.32943i) q^{25} +3.74208 q^{26} +(3.52577 + 2.03560i) q^{29} +(2.87364 - 1.65910i) q^{31} +(4.98462 - 2.87787i) q^{32} +(-3.26700 - 1.88620i) q^{34} -2.47265 q^{37} +(-0.695101 + 1.20395i) q^{38} +(0.0579471 - 0.0334558i) q^{40} +(-3.52867 - 6.11183i) q^{41} +(-1.15994 + 2.00908i) q^{43} -1.59344i q^{44} -4.82367 q^{46} +(-5.43997 + 9.42231i) q^{47} +(-2.87603 + 1.66048i) q^{50} +(7.60408 + 4.39022i) q^{52} -11.5995i q^{53} -0.0289346i q^{55} +(-1.35224 - 2.34215i) q^{58} +(3.01111 + 5.21540i) q^{59} +(2.05220 + 1.18484i) q^{61} -2.20427 q^{62} -0.729528 q^{64} +(0.138079 + 0.0797200i) q^{65} +(-6.38995 - 11.0677i) q^{67} +(-4.42580 - 7.66571i) q^{68} -7.93415i q^{71} -10.8991i q^{73} +(1.42251 + 0.821285i) q^{74} +(-2.82496 + 1.63099i) q^{76} +(7.80018 - 13.5103i) q^{79} +0.0437861 q^{80} +4.68816i q^{82} +(-3.07406 + 5.32442i) q^{83} +(-0.0803661 - 0.139198i) q^{85} +(1.33463 - 0.770546i) q^{86} +(-1.20836 + 2.09294i) q^{88} +12.0516 q^{89} +(-9.80194 - 5.65915i) q^{92} +(6.25921 - 3.61376i) q^{94} +(-0.0512971 + 0.0296164i) q^{95} +(6.77565 + 3.91192i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4}+O(q^{10}) \) 48 * q + 24 * q^4	\( 48 q + 24 q^{4} + 24 q^{11} - 24 q^{16} + 48 q^{23} - 24 q^{25} - 120 q^{32} - 48 q^{50} - 48 q^{64} - 120 q^{65} + 168 q^{74} - 24 q^{79} - 24 q^{85} - 24 q^{86} + 144 q^{92} - 96 q^{95}+O(q^{100}) \) 48 * q + 24 * q^4 + 24 * q^11 - 24 * q^16 + 48 * q^23 - 24 * q^25 - 120 * q^32 - 48 * q^50 - 48 * q^64 - 120 * q^65 + 168 * q^74 - 24 * q^79 - 24 * q^85 - 24 * q^86 + 144 * q^92 - 96 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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