LMFDB - Embedded newform 441.2.o.e.293.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,2,Mod(146,441)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("441.146"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(441, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.o (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			293.16
Character	$\chi$	$=$	441.293
Dual form			441.2.o.e.146.16

$q$-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} +(1.69462 - 0.358137i) q^{3} +(-0.779355 + 1.34988i) q^{4} +(-0.0141520 + 0.0245119i) q^{5} +(0.855956 - 0.768901i) q^{6} +2.36404i q^{8} +(2.74348 - 1.21381i) q^{9} +0.0188022i q^{10} +(-0.885324 + 0.511142i) q^{11} +(-0.837267 + 2.56665i) q^{12} +(4.87844 + 2.81657i) q^{13} +(-0.0152036 + 0.0466067i) q^{15} +(-0.773498 - 1.33974i) q^{16} +5.67880 q^{17} +(1.17515 - 1.60955i) q^{18} -2.09274i q^{19} +(-0.0220588 - 0.0382070i) q^{20} +(-0.339550 + 0.588118i) q^{22} +(-6.28849 - 3.63066i) q^{23} +(0.846651 + 4.00615i) q^{24} +(2.49960 + 4.32943i) q^{25} +3.74208 q^{26} +(4.21444 - 3.03949i) q^{27} +(-3.52577 + 2.03560i) q^{29} +(0.00673377 + 0.0318626i) q^{30} +(-2.87364 - 1.65910i) q^{31} +(-4.98462 - 2.87787i) q^{32} +(-1.31723 + 1.18326i) q^{33} +(3.26700 - 1.88620i) q^{34} +(-0.499635 + 4.64936i) q^{36} -2.47265 q^{37} +(-0.695101 - 1.20395i) q^{38} +(9.27583 + 3.02586i) q^{39} +(-0.0579471 - 0.0334558i) q^{40} +(-3.52867 + 6.11183i) q^{41} +(-1.15994 - 2.00908i) q^{43} -1.59344i q^{44} +(-0.00907265 + 0.0844257i) q^{45} -4.82367 q^{46} +(-5.43997 - 9.42231i) q^{47} +(-1.79060 - 1.99333i) q^{48} +(2.87603 + 1.66048i) q^{50} +(9.62341 - 2.03379i) q^{51} +(-7.60408 + 4.39022i) q^{52} -11.5995i q^{53} +(1.41499 - 3.14843i) q^{54} -0.0289346i q^{55} +(-0.749489 - 3.54640i) q^{57} +(-1.35224 + 2.34215i) q^{58} +(3.01111 - 5.21540i) q^{59} +(-0.0510646 - 0.0568462i) q^{60} +(-2.05220 + 1.18484i) q^{61} -2.20427 q^{62} -0.729528 q^{64} +(-0.138079 + 0.0797200i) q^{65} +(-0.364781 + 1.11824i) q^{66} +(-6.38995 + 11.0677i) q^{67} +(-4.42580 + 7.66571i) q^{68} +(-11.9569 - 3.90045i) q^{69} -7.93415i q^{71} +(2.86950 + 6.48568i) q^{72} -10.8991i q^{73} +(-1.42251 + 0.821285i) q^{74} +(5.78640 + 6.44154i) q^{75} +(2.82496 + 1.63099i) q^{76} +(6.34140 - 1.34018i) q^{78} +(7.80018 + 13.5103i) q^{79} +0.0437861 q^{80} +(6.05331 - 6.66014i) q^{81} +4.68816i q^{82} +(-3.07406 - 5.32442i) q^{83} +(-0.0803661 + 0.139198i) q^{85} +(-1.33463 - 0.770546i) q^{86} +(-5.24581 + 4.71228i) q^{87} +(-1.20836 - 2.09294i) q^{88} +12.0516 q^{89} +(0.0228224 + 0.0515834i) q^{90} +(9.80194 - 5.65915i) q^{92} +(-5.46392 - 1.78238i) q^{93} +(-6.25921 - 3.61376i) q^{94} +(0.0512971 + 0.0296164i) q^{95} +(-9.47771 - 3.09172i) q^{96} +(-6.77565 + 3.91192i) q^{97} +(-1.80843 + 2.47692i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4} + 16 q^{9} - 24 q^{11} - 40 q^{15} - 24 q^{16} - 16 q^{18} - 48 q^{23} - 24 q^{25} - 24 q^{30} + 120 q^{32} - 8 q^{36} + 88 q^{39} + 48 q^{50} + 24 q^{51} + 80 q^{57} - 96 q^{60} - 48 q^{64}+ \cdots - 72 q^{99}+O(q^{100}) $ 48 * q + 24 * q^4 + 16 * q^9 - 24 * q^11 - 40 * q^15 - 24 * q^16 - 16 * q^18 - 48 * q^23 - 24 * q^25 - 24 * q^30 + 120 * q^32 - 8 * q^36 + 88 * q^39 + 48 * q^50 + 24 * q^51 + 80 * q^57 - 96 * q^60 - 48 * q^64 + 120 * q^65 + 56 * q^72 - 168 * q^74 - 88 * q^78 - 24 * q^79 - 96 * q^81 - 24 * q^85 + 24 * q^86 - 144 * q^92 - 32 * q^93 + 96 * q^95 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.575298	−	0.332148i	0.406797	−	0.234864i	−0.282616	−	0.959233i	$-0.591202\pi$
$2$	0.575298	−	0.332148i	0.406797	−	0.234864i	0.689413	+	0.724369i	$0.257869\pi$
$3$	1.69462	−	0.358137i	0.978389	−	0.206771i
$3$	1.69462	−	0.358137i	0.978389	−	0.206771i
$4$	−0.779355	+	1.34988i	−0.389677	+	0.674941i
$5$	−0.0141520	+	0.0245119i	−0.00632895	+	0.0109621i	−0.869173	−	0.494509i	$-0.835348\pi$
$5$	−0.0141520	+	0.0245119i	−0.00632895	+	0.0109621i	0.862844	+	0.505471i	$0.168681\pi$
$6$	0.855956	−	0.768901i	0.349443	−	0.313903i
$7$		0			0
$7$		0			0
$8$			2.36404i			0.835814i
$9$	2.74348	−	1.21381i	0.914492	−	0.404605i
$10$			0.0188022i			0.00594578i
$11$	−0.885324	+	0.511142i	−0.266935	+	0.154115i	−0.627494	−	0.778621i	$-0.715919\pi$
$11$	−0.885324	+	0.511142i	−0.266935	+	0.154115i	0.360559	+	0.932736i	$0.382586\pi$
$12$	−0.837267	+	2.56665i	−0.241698	+	0.740929i
$13$	4.87844	+	2.81657i	1.35304	+	0.781176i	0.988674	−	0.150081i	$-0.0479534\pi$
$13$	4.87844	+	2.81657i	1.35304	+	0.781176i	0.364363	+	0.931257i	$0.381287\pi$
$14$		0			0
$15$	−0.0152036	+	0.0466067i	−0.00392554	+	0.0120338i
$16$	−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	$0.258201\pi$
$18$	1.17515	−	1.60955i	0.276985	−	0.379373i
$19$		−	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	$-0.606691\pi$
$23$	−6.28849	−	3.63066i	−1.31124	−	0.757046i	−0.982302	+	0.187305i	$0.940025\pi$
$24$	0.846651	+	4.00615i	0.172822	+	0.817752i
$25$	2.49960	+	4.32943i	0.499920	+	0.865887i
$26$	3.74208			0.733882
$27$	4.21444	−	3.03949i	0.811069	−	0.584951i
$28$		0			0
$29$	−3.52577	+	2.03560i	−0.654718	+	0.378002i	−0.790262	−	0.612770i	$-0.790055\pi$
$29$	−3.52577	+	2.03560i	−0.654718	+	0.378002i	0.135543	+	0.990771i	$0.456722\pi$
$30$	0.00673377	+	0.0318626i	0.00122941	+	0.00581729i
$31$	−2.87364	−	1.65910i	−0.516122	−	0.297983i	0.219225	−	0.975674i	$-0.429647\pi$
$31$	−2.87364	−	1.65910i	−0.516122	−	0.297983i	−0.735346	+	0.677691i	$0.762981\pi$
$32$	−4.98462	−	2.87787i	−0.881165	−	0.508741i
$33$	−1.31723	+	1.18326i	−0.229300	+	0.205979i
$34$	3.26700	−	1.88620i	0.560286	−	0.323481i
$35$		0			0
$36$	−0.499635	+	4.64936i	−0.0832725	+	0.774893i
$37$	−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
$39$	9.27583	+	3.02586i	1.48532	+	0.484526i
$40$	−0.0579471	−	0.0334558i	−0.00916224	−	0.00528982i
$41$	−3.52867	+	6.11183i	−0.551085	+	0.954508i	0.447111	+	0.894478i	$0.352453\pi$
$41$	−3.52867	+	6.11183i	−0.551085	+	0.954508i	−0.998197	+	0.0600295i	$0.980881\pi$
$42$		0			0
$43$	−1.15994	−	2.00908i	−0.176890	−	0.306382i	0.763924	−	0.645306i	$-0.223270\pi$
$43$	−1.15994	−	2.00908i	−0.176890	−	0.306382i	−0.940814	+	0.338924i	$0.889937\pi$
$44$		−	1.59344i		−	0.240221i
$45$	−0.00907265	+	0.0844257i	−0.00135247	+	0.0125854i
$46$	−4.82367			−0.711212
$47$	−5.43997	−	9.42231i	−0.793502	−	1.37439i	−0.923786	−	0.382908i	$-0.874922\pi$
$47$	−5.43997	−	9.42231i	−0.793502	−	1.37439i	0.130285	−	0.991477i	$-0.458411\pi$
$48$	−1.79060	−	1.99333i	−0.258450	−	0.287712i
$49$		0			0
$50$	2.87603	+	1.66048i	0.406732	+	0.234827i
$51$	9.62341	−	2.03379i	1.34755	−	0.284788i
$52$	−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	$-0.293399\pi$
$54$	1.41499	−	3.14843i	0.192556	−	0.428447i
$55$		−	0.0289346i		−	0.00390155i
$56$		0			0
$57$	−0.749489	−	3.54640i	−0.0992723	−	0.469733i
$58$	−1.35224	+	2.34215i	−0.177558	+	0.307540i
$59$	3.01111	−	5.21540i	0.392013	−	0.678987i	−0.600702	−	0.799473i	$-0.705112\pi$
$59$	3.01111	−	5.21540i	0.392013	−	0.678987i	0.992715	+	0.120486i	$0.0384454\pi$
$60$	−0.0510646	−	0.0568462i	−0.00659242	−	0.00733881i
$61$	−2.05220	+	1.18484i	−0.262757	+	0.151703i	−0.625592	−	0.780151i	$-0.715142\pi$
$61$	−2.05220	+	1.18484i	−0.262757	+	0.151703i	0.362834	+	0.931854i	$0.381809\pi$
$62$	−2.20427			−0.279942
$63$		0			0
$64$	−0.729528			−0.0911909
$65$	−0.138079	+	0.0797200i	−0.0171266	+	0.00988805i
$66$	−0.364781	+	1.11824i	−0.0449014	+	0.137646i
$67$	−6.38995	+	11.0677i	−0.780656	+	1.35214i	0.150903	+	0.988549i	$0.451782\pi$
$67$	−6.38995	+	11.0677i	−0.780656	+	1.35214i	−0.931560	+	0.363588i	$0.881552\pi$
$68$	−4.42580	+	7.66571i	−0.536707	+	0.929604i
$69$	−11.9569	−	3.90045i	−1.43944	−	0.469559i
$70$		0			0
$71$		−	7.93415i		−	0.941610i	−0.882237	−	0.470805i	$-0.843964\pi$
$71$		−	7.93415i		−	0.941610i	0.882237	−	0.470805i	$-0.156036\pi$
$72$	2.86950	+	6.48568i	0.338174	+	0.764345i
$73$		−	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
$75$	5.78640	+	6.44154i	0.668156	+	0.743806i
$76$	2.82496	+	1.63099i	0.324045	+	0.187087i
$77$		0			0
$78$	6.34140	−	1.34018i	0.718022	−	0.151745i
$79$	7.80018	+	13.5103i	0.877588	+	1.52003i	0.853980	+	0.520306i	$0.174182\pi$
$79$	7.80018	+	13.5103i	0.877588	+	1.52003i	0.0236086	+	0.999721i	$0.492484\pi$
$80$	0.0437861			0.00489543
$81$	6.05331	−	6.66014i	0.672590	−	0.740015i
$82$			4.68816i			0.517721i
$83$	−3.07406	−	5.32442i	−0.337421	−	0.584431i	0.646526	−	0.762892i	$-0.276221\pi$
$83$	−3.07406	−	5.32442i	−0.337421	−	0.584431i	−0.983947	+	0.178461i	$0.942888\pi$
$84$		0			0
$85$	−0.0803661	+	0.139198i	−0.00871693	+	0.0150982i
$86$	−1.33463	−	0.770546i	−0.143916	−	0.0830902i
$87$	−5.24581	+	4.71228i	−0.562410	+	0.505210i
$88$	−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	$0.279458\pi$
$90$	0.0228224	+	0.0515834i	0.00240569	+	0.00543736i
$91$		0			0
$92$	9.80194	−	5.65915i	1.02192	−	0.590007i
$93$	−5.46392	−	1.78238i	−0.566582	−	0.184825i
$94$	−6.25921	−	3.61376i	−0.645588	−	0.372730i
$95$	0.0512971	+	0.0296164i	0.00526297	+	0.00303858i
$96$	−9.47771	−	3.09172i	−0.967315	−	0.315547i
$97$	−6.77565	+	3.91192i	−0.687963	+	0.397196i	−0.802848	−	0.596183i	$-0.796683\pi$
$97$	−6.77565	+	3.91192i	−0.687963	+	0.397196i	0.114885	+	0.993379i	$0.463350\pi$
$98$		0			0
$99$	−1.80843	+	2.47692i	−0.181754	+	0.248940i
$100$	−7.79230			−0.779230
$101$	0.226924	+	0.393043i	0.0225797	+	0.0391093i	0.877094	−	0.480318i	$-0.159479\pi$
$101$	0.226924	+	0.393043i	0.0225797	+	0.0391093i	−0.854515	+	0.519427i	$0.826145\pi$
$102$	4.86081	−	4.36643i	0.481291	−	0.432341i
$103$	−4.58316	−	2.64609i	−0.451592	−	0.260727i	0.256910	−	0.966435i	$-0.417296\pi$
$103$	−4.58316	−	2.64609i	−0.451592	−	0.260727i	−0.708502	+	0.705708i	$0.750629\pi$
$104$	−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	$0.855582\pi$
$108$	0.818419	+	8.05784i	0.0787524	+	0.775366i
$109$	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
$111$	−4.19020	+	0.885547i	−0.397716	+	0.0840524i
$112$		0			0
$113$	−8.21108	−	4.74067i	−0.772433	−	0.445965i	0.0613086	−	0.998119i	$-0.480473\pi$
$113$	−8.21108	−	4.74067i	−0.772433	−	0.445965i	−0.833742	+	0.552154i	$0.813806\pi$
$114$	−1.60911	−	1.79130i	−0.150707	−	0.167770i
$115$	0.177989	−	0.102762i	0.0165976	−	0.00958261i
$116$		−	6.34583i		−	0.589195i
$117$	16.8027	+	1.80567i	1.55341	+	0.166934i
$118$		−	4.00054i		−	0.368280i
$119$		0			0
$120$	−0.110180	−	0.0359418i	−0.0100580	−	0.00328102i
$121$	−4.97747	+	8.62123i	−0.452497	+	0.783748i
$122$	−0.787084	+	1.36327i	−0.0712593	+	0.123425i
$123$	−3.79088	+	11.6210i	−0.341812	+	1.04783i
$124$	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
$129$	−2.68519	−	2.98921i	−0.236418	−	0.263185i
$130$	−0.0529577	+	0.0917255i	−0.00464470	+	0.00804486i
$131$	−1.27231	+	2.20371i	−0.111162	+	0.192539i	−0.916239	−	0.400632i	$-0.868791\pi$
$131$	−1.27231	+	2.20371i	−0.111162	+	0.192539i	0.805077	+	0.593171i	$0.202124\pi$
$132$	−0.570672	−	2.70028i	−0.0496706	−	0.235029i
$133$		0			0
$134$			8.48964i			0.733393i
$135$	0.0148613	+	0.146319i	0.00127906	+	0.0125931i
$136$			13.4249i			1.15118i
$137$	−9.82536	+	5.67267i	−0.839437	+	0.484649i	−0.857073	−	0.515195i	$-0.827719\pi$
$137$	−9.82536	+	5.67267i	−0.839437	+	0.484649i	0.0176357	+	0.999844i	$0.494386\pi$
$138$	−8.17430	+	1.72754i	−0.695842	+	0.147058i
$139$	−3.04891	−	1.76029i	−0.258605	−	0.149306i	0.365093	−	0.930971i	$-0.381037\pi$
$139$	−3.04891	−	1.76029i	−0.258605	−	0.149306i	−0.623698	+	0.781665i	$0.714371\pi$
$140$		0			0
$141$	−12.5932	−	14.0190i	−1.06054	−	1.18061i
$142$	−2.63531	−	4.56450i	−0.221151	−	0.383044i
$143$	−5.75867			−0.481564
$144$	−3.74827	−	2.73666i	−0.312356	−	0.228055i
$145$		−	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	$-0.559319\pi$
$149$	−13.7806	−	7.95623i	−1.12895	−	0.651800i	−0.943671	+	0.330886i	$0.892652\pi$
$150$	5.46845	+	1.78386i	0.446497	+	0.145652i
$151$	−1.73008	−	2.99659i	−0.140792	−	0.243859i	0.787003	−	0.616949i	$-0.211632\pi$
$151$	−1.73008	−	2.99659i	−0.140792	−	0.243859i	−0.927795	+	0.373090i	$0.878298\pi$
$152$	4.94732			0.401281
$153$	15.5796	−	6.89301i	1.25954	−	0.557267i
$154$		0			0
$155$	0.0813354	−	0.0469590i	0.00653302	−	0.00377184i
$156$	−11.3137	+	10.1631i	−0.905823	+	0.813696i
$157$	14.1585	+	8.17442i	1.12997	+	0.652390i	0.943928	−	0.330151i	$-0.107100\pi$
$157$	14.1585	+	8.17442i	1.12997	+	0.652390i	0.186045	+	0.982541i	$0.440433\pi$
$158$	8.97485	+	5.18163i	0.714001	+	0.412228i
$159$	−4.15420	−	19.6567i	−0.329450	−	1.55888i
$160$	0.141084	−	0.0814550i	0.0111537	−	0.00643959i
$161$		0			0
$162$	1.27030	−	5.84216i	0.0998044	−	0.459003i
$163$	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
$165$	−0.0103626	−	0.0490332i	−0.000806726	−	0.00381723i
$166$	−3.53699	−	2.04208i	−0.274524	−	0.158497i
$167$	2.94297	−	5.09738i	0.227734	−	0.394447i	−0.729402	−	0.684085i	$-0.760202\pi$
$167$	2.94297	−	5.09738i	0.227734	−	0.394447i	0.957136	+	0.289638i	$0.0935349\pi$
$168$		0			0
$169$	9.36614	+	16.2226i	0.720473	+	1.24790i
$170$			0.106774i			0.00818919i
$171$	−2.54020	−	5.74139i	−0.194254	−	0.439055i
$172$	3.61603			0.275720
$173$	−2.43276	−	4.21366i	−0.184959	−	0.320359i	0.758604	−	0.651552i	$-0.225882\pi$
$173$	−2.43276	−	4.21366i	−0.184959	−	0.320359i	−0.943563	+	0.331194i	$0.892549\pi$
$174$	−1.45273	+	4.45335i	−0.110131	+	0.337608i
$175$		0			0
$176$	1.36959	+	0.790735i	0.103237	+	0.0596039i
$177$	3.23486	−	9.91651i	0.243147	−	0.745371i
$178$	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	$-0.00241064\pi$
$180$	−0.106894	−	0.0780446i	−0.00796740	−	0.00581710i
$181$			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
$183$	−3.05337	+	2.74282i	−0.225711	+	0.202755i
$184$	8.58303	−	14.8662i	0.632749	−	1.09595i
$185$	0.0349928	−	0.0606093i	0.00257272	−	0.00445608i
$186$	−3.73540	+	0.789431i	−0.273893	+	0.0578839i
$187$	−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	$-0.500225\pi$
$191$	11.9541	−	6.90168i	0.864965	−	0.499388i	0.865672	+	0.500612i	$0.166892\pi$
$192$	−1.23627	+	0.261271i	−0.0892203	+	0.0188556i
$193$	10.5387	−	18.2536i	0.758593	−	1.31392i	−0.184976	−	0.982743i	$-0.559221\pi$
$193$	10.5387	−	18.2536i	0.758593	−	1.31392i	0.943568	−	0.331178i	$-0.107446\pi$
$194$	−2.59868	+	4.50104i	−0.186574	+	0.323156i
$195$	−0.205441	+	0.184546i	−0.0147119	+	0.0132156i
$196$		0			0
$197$			15.1679i			1.08067i	0.841451	+	0.540334i	$0.181702\pi$
$197$			15.1679i			1.08067i	−0.841451	+	0.540334i	$0.818298\pi$
$198$	−0.217681	+	2.02564i	−0.0154699	+	0.143956i
$199$		−	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
$201$	−6.86477	+	21.0441i	−0.484204	+	1.48433i
$202$	0.261097	+	0.150745i	0.0183707	+	0.0106064i
$203$		0			0
$204$	−4.75467	+	14.5755i	−0.332894	+	1.02049i
$205$	−0.0998751	−	0.172989i	−0.00697558	−	0.0120821i
$206$	−3.51558			−0.244942
$207$	−21.6593	−	2.32757i	−1.50542	−	0.161777i
$208$		−	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	−0.999870	−	0.0161017i	$-0.994874\pi$
$211$	−7.05942	+	12.2273i	−0.485991	+	0.841761i	0.513880	+	0.857862i	$0.328208\pi$
$212$	15.6579	+	9.04010i	1.07539	+	0.620877i
$213$	−2.84152	−	13.4454i	−0.194697	−	0.921261i
$214$	3.01177	+	5.21654i	0.205880	+	0.356595i
$215$	0.0656619			0.00447810
$216$	7.18549	+	9.96309i	0.488910	+	0.677903i
$217$		0			0
$218$	2.72132	−	1.57115i	0.184311	−	0.106412i
$219$	−3.90337	−	18.4698i	−0.263766	−	1.24807i
$220$	0.0390584	+	0.0225504i	0.00263331	+	0.00152034i
$221$	27.7037	+	15.9947i	1.86355	+	1.07592i
$222$	−2.11648	+	1.90122i	−0.142049	+	0.127602i
$223$	2.58777	−	1.49405i	0.173290	−	0.100049i	−0.410846	−	0.911705i	$-0.634767\pi$
$223$	2.58777	−	1.49405i	0.173290	−	0.100049i	0.584136	+	0.811656i	$0.301433\pi$
$224$		0			0
$225$	12.1127	+	8.84364i	0.807514	+	0.589576i
$226$	−6.29842			−0.418965
$227$	14.3867	+	24.9184i	0.954876	+	1.65389i	0.734652	+	0.678444i	$0.237346\pi$
$227$	14.3867	+	24.9184i	0.954876	+	1.65389i	0.220224	+	0.975449i	$0.429321\pi$
$228$	5.37135	+	1.75218i	0.355726	+	0.116041i
$229$	7.67401	+	4.43059i	0.507113	+	0.292782i	0.731646	−	0.681685i	$-0.238752\pi$
$229$	7.67401	+	4.43059i	0.507113	+	0.292782i	−0.224533	+	0.974466i	$0.572086\pi$
$230$	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	$0.861039\pi$
$234$	10.2663	−	4.54219i	0.671129	−	0.296932i
$235$	0.307945			0.0200881
$236$	4.69345	+	8.12929i	0.305518	+	0.529172i
$237$	18.0569	+	20.1013i	1.17292	+	1.30572i
$238$		0			0
$239$	−4.85712	−	2.80426i	−0.314181	−	0.181392i	0.334615	−	0.942355i	$-0.391394\pi$
$239$	−4.85712	−	2.80426i	−0.314181	−	0.181392i	−0.648796	+	0.760963i	$0.724727\pi$
$240$	0.0742008	−	0.0156814i	0.00478964	−	0.00101223i
$241$	9.51481	−	5.49338i	0.612903	−	0.353860i	−0.161198	−	0.986922i	$-0.551536\pi$
$241$	9.51481	−	5.49338i	0.612903	−	0.353860i	0.774101	+	0.633063i	$0.218202\pi$
$242$			6.61303i			0.425102i
$243$	7.87282	−	13.4543i	0.505042	−	0.863095i
$244$		−	3.69364i		−	0.236461i
$245$		0			0
$246$	1.67901	+	7.94466i	0.107050	+	0.506533i
$247$	5.89436	−	10.2093i	0.375049	−	0.649604i
$248$	3.92218	−	6.79341i	0.249058	−	0.431382i
$249$	−7.11623	−	7.92193i	−0.450973	−	0.502032i
$250$	−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
$255$	−0.0863380	+	0.264670i	−0.00540669	+	0.0165743i
$256$	4.39208	−	7.60731i	0.274505	−	0.475457i
$257$	−8.86142	+	15.3484i	−0.552760	+	0.957409i	0.445314	+	0.895375i	$0.353092\pi$
$257$	−8.86142	+	15.3484i	−0.552760	+	0.957409i	−0.998074	+	0.0620341i	$0.980241\pi$
$258$	−2.53765	−	0.827804i	−0.157987	−	0.0515368i
$259$		0			0
$260$		−	0.248521i		−	0.0154126i
$261$	−7.20201	+	9.86425i	−0.445793	+	0.610582i
$262$			1.69039i			0.104432i
$263$	2.51031	−	1.44933i	0.154793	−	0.0893695i	−0.420603	−	0.907245i	$-0.638181\pi$
$263$	2.51031	−	1.44933i	0.154793	−	0.0893695i	0.575396	+	0.817875i	$0.304848\pi$
$264$	−2.79727	−	3.11398i	−0.172160	−	0.191652i
$265$	0.284325	+	0.164155i	0.0174660	+	0.0100840i
$266$		0			0
$267$	20.4230	−	4.31614i	1.24986	−	0.264144i
$268$	−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	$0.732612\pi$
$270$	0.0571492	+	0.0792407i	0.00347799	+	0.00482243i
$271$			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
$276$	14.5838	−	13.1006i	0.877842	−	0.788561i
$277$	−7.95091	−	13.7714i	−0.477724	−	0.827442i	0.521950	−	0.852976i	$-0.325205\pi$
$277$	−7.95091	−	13.7714i	−0.477724	−	0.827442i	−0.999674	+	0.0255339i	$0.991871\pi$
$278$	−2.33871			−0.140267
$279$	−9.89761	−	1.06363i	−0.592554	−	0.0636777i
$280$		0			0
$281$	−4.50324	+	2.59995i	−0.268641	+	0.155100i	−0.628270	−	0.777996i	$-0.716237\pi$
$281$	−4.50324	+	2.59995i	−0.268641	+	0.155100i	0.359629	+	0.933095i	$0.382903\pi$
$282$	−11.9012	−	3.88229i	−0.708706	−	0.231187i
$283$	16.2587	+	9.38694i	0.966476	+	0.557995i	0.898160	−	0.439668i	$-0.144904\pi$
$283$	16.2587	+	9.38694i	0.966476	+	0.557995i	0.0683162	+	0.997664i	$0.478237\pi$
$284$	10.7102	+	6.18352i	0.635531	+	0.366924i
$285$	0.0975359	+	0.0318171i	0.00577753	+	0.00188468i
$286$	−3.31295	+	1.91273i	−0.195899	+	0.113102i
$287$		0			0
$288$	−17.1684	−	1.84497i	−1.01166	−	0.108716i
$289$	15.2488			0.896986
$290$	−0.0382738	−	0.0662922i	−0.00224751	−	0.00389281i
$291$	−10.0811	+	9.05584i	−0.590967	+	0.530863i
$292$	14.7125	+	8.49426i	0.860983	+	0.497089i
$293$	11.4201	−	19.7802i	0.667169	−	1.15557i	−0.311523	−	0.950238i	$-0.600839\pi$
$293$	11.4201	−	19.7802i	0.667169	−	1.15557i	0.978692	−	0.205332i	$-0.0658274\pi$
$294$		0			0
$295$	0.0852263	+	0.147616i	0.00496206	+	0.00859455i
$296$		−	5.84543i		−	0.339759i
$297$	−2.17753	+	4.84511i	−0.126353	+	0.281142i
$298$	−10.5706			−0.612338
$299$	−20.4520	−	35.4240i	−1.18277	−	2.04862i
$300$	−13.2050	+	2.79072i	−0.762390	+	0.161122i
$301$		0			0
$302$	−1.99062	−	1.14929i	−0.114548	−	0.0661341i
$303$	0.525313	+	0.584789i	0.0301784	+	0.0335953i
$304$	−2.80373	+	1.61873i	−0.160805	+	0.0928407i
$305$		−	0.0670711i		−	0.00384048i
$306$	6.67343	−	9.14028i	0.381495	−	0.522515i
$307$		−	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
$309$	−8.71438	−	2.84271i	−0.495744	−	0.161716i
$310$	0.0311947	−	0.0540308i	0.00177174	−	0.00306875i
$311$	−10.2747	+	17.7964i	−0.582628	+	1.00914i	0.412539	+	0.910940i	$0.364642\pi$
$311$	−10.2747	+	17.7964i	−0.582628	+	1.00914i	−0.995167	+	0.0982007i	$0.968691\pi$
$312$	−7.15326	+	21.9284i	−0.404974	+	1.24145i
$313$	−0.624466	+	0.360536i	−0.0352969	+	0.0203787i	−0.517545	−	0.855656i	$-0.673154\pi$
$313$	−0.624466	+	0.360536i	−0.0352969	+	0.0203787i	0.482248	+	0.876035i	$0.339821\pi$
$314$	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	$-0.877850\pi$
$317$	−18.9915	+	10.9647i	−1.06667	+	0.615841i	−0.139398	+	0.990236i	$0.544517\pi$
$318$	−8.91884	−	9.92864i	−0.500144	−	0.556770i
$319$	2.08096	−	3.60433i	0.116512	−	0.201804i
$320$	0.0103242	−	0.0178821i	0.000577143	−	0.000999641i
$321$	3.24743	+	15.3660i	0.181254	+	0.857649i
$322$		0			0
$323$		−	11.8843i		−	0.661258i
$324$	4.27272	+	13.3619i	0.237374	+	0.742326i
$325$			28.1612i			1.56210i
$326$	5.95757	−	3.43961i	0.329959	−	0.190502i
$327$	8.01602	−	1.69409i	0.443287	−	0.0936833i
$328$	−14.4486	−	8.34191i	−0.797791	−	0.460605i
$329$		0			0
$330$	−0.0222479	−	0.0247668i	−0.00122470	−	0.00136337i
$331$	−10.8338	−	18.7647i	−0.595480	−	1.03140i	−0.993479	−	0.114016i	$-0.963629\pi$
$331$	−10.8338	−	18.7647i	−0.595480	−	1.03140i	0.397999	−	0.917386i	$-0.369705\pi$
$332$	9.58312			0.525942
$333$	−6.78364	+	3.00133i	−0.371741	+	0.164472i
$334$		−	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	−0.283369	−	0.959011i	$-0.591452\pi$
$337$	12.6455	−	21.9026i	0.688844	−	1.19311i	0.972212	−	0.234101i	$-0.0752147\pi$
$338$	10.7766	+	6.22190i	0.586172	+	0.338427i
$339$	−15.6125	−	5.09294i	−0.847953	−	0.276610i
$340$	−0.125268	−	0.216970i	−0.00679358	−	0.0117668i
$341$	3.39214			0.183695
$342$	−3.36836	−	2.45928i	−0.182140	−	0.132983i
$343$		0			0
$344$	4.74955	−	2.74215i	0.256078	−	0.147847i
$345$	0.264821	−	0.237887i	0.0142575	−	0.0128074i
$346$	−2.79912	−	1.61607i	−0.150482	−	0.0868806i
$347$	−4.92420	−	2.84299i	−0.264345	−	0.152620i	0.361970	−	0.932190i	$-0.382104\pi$
$347$	−4.92420	−	2.84299i	−0.264345	−	0.152620i	−0.626315	+	0.779570i	$0.715438\pi$
$348$	−2.27268	−	10.7538i	−0.121828	−	0.576462i
$349$	−9.68412	+	5.59113i	−0.518379	+	0.299286i	−0.736271	−	0.676687i	$-0.763415\pi$
$349$	−9.68412	+	5.59113i	−0.518379	+	0.299286i	0.217892	+	0.975973i	$0.430082\pi$
$350$		0			0
$351$	29.1208	−	2.95775i	1.55436	−	0.157873i
$352$	5.88400			0.313618
$353$	7.02111	+	12.1609i	0.373696	+	0.647260i	0.990131	−	0.140146i	$-0.0447571\pi$
$353$	7.02111	+	12.1609i	0.373696	+	0.647260i	−0.616435	+	0.787406i	$0.711424\pi$
$354$	−1.43274	−	6.77940i	−0.0761495	−	0.360321i
$355$	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	$0.745864\pi$
$360$	−0.199586	−	0.0214481i	−0.0105191	−	0.00113041i
$361$	14.6204			0.769496
$362$	2.08016	+	3.60294i	0.109331	+	0.189366i
$363$	−5.34733	+	16.3923i	−0.280662	+	0.860374i
$364$		0			0
$365$	0.267158	+	0.154244i	0.0139837	+	0.00807347i
$366$	−0.845571	+	2.59211i	−0.0441987	+	0.135492i
$367$	5.95891	−	3.44038i	0.311053	−	0.179586i	−0.336345	−	0.941739i	$-0.609191\pi$
$367$	5.95891	−	3.44038i	0.311053	−	0.179586i	0.647397	+	0.762153i	$0.275857\pi$
$368$			11.2332i			0.585573i
$369$	−2.26219	+	21.0508i	−0.117765	+	1.09586i
$370$		−	0.0464912i		−	0.00241696i
$371$		0			0
$372$	6.66434	−	5.98654i	0.345530	−	0.310388i
$373$	0.123926	−	0.214645i	0.00641662	−	0.0111139i	−0.862799	−	0.505547i	$-0.831291\pi$
$373$	0.123926	−	0.214645i	0.00641662	−	0.0111139i	0.869216	+	0.494433i	$0.164624\pi$
$374$	−1.92824	+	3.33980i	−0.0997067	+	0.172697i
$375$	−0.479606	+	0.101359i	−0.0247667	+	0.00523415i
$376$	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
$381$	7.41053	−	1.56613i	0.379653	−	0.0802351i
$382$	4.58476	−	7.94104i	0.234577	−	0.406299i
$383$	0.163545	−	0.283268i	0.00835675	−	0.0144743i	−0.861817	−	0.507220i	$-0.830673\pi$
$383$	0.163545	−	0.283268i	0.00835675	−	0.0144743i	0.870174	+	0.492745i	$0.164007\pi$
$384$	14.2083	−	12.7632i	0.725063	−	0.651320i
$385$		0			0
$386$		−	14.0017i		−	0.712665i
$387$	−5.62093	−	4.10391i	−0.285728	−	0.208613i
$388$		−	12.1951i		−	0.619113i
$389$	−5.72348	+	3.30445i	−0.290192	+	0.167542i	−0.638028	−	0.770013i	$-0.720250\pi$
$389$	−5.72348	+	3.30445i	−0.290192	+	0.167542i	0.347837	+	0.937555i	$0.386916\pi$
$390$	−0.0568929	+	0.174406i	−0.00288088	+	0.00883139i
$391$	−35.7111	−	20.6178i	−1.80599	−	1.04269i
$392$		0			0
$393$	−1.36686	+	4.19011i	−0.0689487	+	0.211363i
$394$	5.03799	+	8.72606i	0.253810	+	0.439613i
$395$	−0.441551			−0.0222168
$396$	−1.93414	−	4.37157i	−0.0971944	−	0.219680i
$397$			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	$-0.383892\pi$
$401$	−5.48595	−	3.16732i	−0.273956	−	0.158168i	−0.630684	+	0.776040i	$0.717226\pi$
$402$	3.04046	+	14.3867i	0.151644	+	0.717544i
$403$	−9.34594	−	16.1876i	−0.465555	−	0.806364i
$404$	−0.707416			−0.0351953
$405$	0.0775865	+	0.242632i	0.00385530	+	0.0120565i
$406$		0			0
$407$	2.18909	−	1.26387i	0.108509	−	0.0626479i
$408$	4.80796	+	22.7501i	0.238030	+	1.12630i
$409$	−29.0045	−	16.7457i	−1.43418	−	0.828024i	−0.436743	−	0.899586i	$-0.643868\pi$
$409$	−29.0045	−	16.7457i	−1.43418	−	0.828024i	−0.997436	+	0.0715625i	$0.977201\pi$
$410$	−0.114916	−	0.0663467i	−0.00567529	−	0.00327663i
$411$	−14.6187	+	13.1319i	−0.721085	+	0.647747i
$412$	7.14382	−	4.12448i	0.351951	−	0.203199i
$413$		0			0
$414$	−13.2336	+	5.85504i	−0.650398	+	0.287760i
$415$	0.174016			0.00854209
$416$	−16.2115	−	28.0791i	−0.794832	−	1.37669i
$417$	−5.79718	−	1.89109i	−0.283889	−	0.0926073i
$418$	1.23078	+	0.710590i	0.0601993	+	0.0347561i
$419$	0.896459	−	1.55271i	0.0437949	−	0.0758550i	−0.843297	−	0.537448i	$-0.819389\pi$
$419$	0.896459	−	1.55271i	0.0437949	−	0.0758550i	0.887092	+	0.461593i	$0.152722\pi$
$420$		0			0
$421$	1.90262	+	3.29543i	0.0927278	+	0.160609i	0.908658	−	0.417541i	$-0.137108\pi$
$421$	1.90262	+	3.29543i	0.0927278	+	0.160609i	−0.815930	+	0.578150i	$0.803775\pi$
$422$			9.37910i			0.456568i
$423$	−26.3614	−	19.2468i	−1.28173	−	0.935809i
$424$	27.4216			1.33171
$425$	14.1947	+	24.5860i	0.688545	+	1.19260i
$426$	−6.10057	−	6.79128i	−0.295574	−	0.329039i
$427$		0			0
$428$	−12.2401	−	7.06684i	−0.591649	−	0.341589i
$429$	−9.75876	+	2.06240i	−0.471157	+	0.0995734i
$430$	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	$-0.0101946\pi$
$432$	−7.33199	−	3.29520i	−0.352760	−	0.158540i
$433$			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
$435$	−0.0412686	−	0.195273i	−0.00197868	−	0.00936262i
$436$	−3.68656	+	6.38531i	−0.176554	+	0.305801i
$437$	−7.59804	+	13.1602i	−0.363464	+	0.629537i
$438$	−8.38032	−	9.32915i	−0.400427	−	0.445764i
$439$	−20.5584	+	11.8694i	−0.981201	+	0.566496i	−0.902632	−	0.430412i	$-0.858368\pi$
$439$	−20.5584	+	11.8694i	−0.981201	+	0.566496i	−0.0785682	+	0.996909i	$0.525035\pi$
$440$	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	$-0.580548\pi$
$443$	9.74317	−	5.62522i	0.462912	−	0.267262i	0.713268	+	0.700891i	$0.247214\pi$
$444$	2.07027	−	6.34643i	0.0982505	−	0.301188i
$445$	−0.170554	+	0.295409i	−0.00808505	+	0.0140037i
$446$	0.992491	−	1.71904i	0.0469958	−	0.0813991i
$447$	−26.2023	−	8.54744i	−1.23933	−	0.404280i
$448$		0			0
$449$			14.3953i			0.679357i	0.940542	+	0.339679i	$0.110318\pi$
$449$			14.3953i			0.679357i	−0.940542	+	0.339679i	$0.889682\pi$
$450$	9.90582	+	1.06451i	0.466965	+	0.0501815i
$451$		−	7.21460i		−	0.339722i
$452$	12.7987	−	7.38933i	0.602000	−	0.347565i
$453$	−4.00502	−	4.45848i	−0.188172	−	0.209477i
$454$	16.5532	+	9.55701i	0.776881	+	0.448533i
$455$		0			0
$456$	8.38384	−	1.77182i	0.392609	−	0.0829732i
$457$	10.3135	+	17.8635i	0.482444	+	0.835617i	0.999797	−	0.0201547i	$-0.00641589\pi$
$457$	10.3135	+	17.8635i	0.482444	+	0.835617i	−0.517353	+	0.855772i	$0.673083\pi$
$458$	5.88646			0.275056
$459$	23.9329	−	17.2607i	1.11709	−	0.805660i
$460$			0.320352i			0.0149365i
$461$	−0.832511	−	1.44195i	−0.0387739	−	0.0671584i	0.845987	−	0.533203i	$-0.179012\pi$
$461$	−0.832511	−	1.44195i	−0.0387739	−	0.0671584i	−0.884761	+	0.466045i	$0.845679\pi$
$462$		0			0
$463$	0.604175	−	1.04646i	0.0280784	−	0.0486332i	−0.851645	−	0.524119i	$-0.824395\pi$
$463$	0.604175	−	1.04646i	0.0280784	−	0.0486332i	0.879723	+	0.475486i	$0.157728\pi$
$464$	5.45435	+	3.14907i	0.253212	+	0.146192i
$465$	0.121015	−	0.108707i	0.00561193	−	0.00504116i
$466$	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	$0.568579\pi$
$468$	−15.5327	+	21.2744i	−0.717999	+	0.983409i
$469$		0			0
$470$	0.177160	−	0.102283i	0.00817179	−	0.00471798i
$471$	26.9209	+	8.78185i	1.24045	+	0.404646i
$472$	12.3294	+	7.11839i	0.567507	+	0.327650i
$473$	2.05385	+	1.18579i	0.0944361	+	0.0545227i
$474$	17.0647	+	5.56667i	0.783807	+	0.255685i
$475$	9.06039	−	5.23102i	0.415719	−	0.240016i
$476$		0			0
$477$	−14.0796	−	31.8229i	−0.644660	−	1.45707i
$478$	−3.72572			−0.170410
$479$	−8.77241	−	15.1943i	−0.400822	−	0.694243i	0.593004	−	0.805200i	$-0.297942\pi$
$479$	−8.77241	−	15.1943i	−0.400822	−	0.694243i	−0.993825	+	0.110956i	$0.964609\pi$
$480$	0.209912	−	0.188563i	0.00958114	−	0.00860668i
$481$	−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
$486$	0.0603850	−	10.3552i	0.00273912	−	0.469721i
$487$	−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
$489$	17.5489	−	3.70874i	0.793587	−	0.167715i
$490$		0			0
$491$	23.0046	+	13.2817i	1.03818	+	0.599396i	0.919319	−	0.393514i	$-0.128741\pi$
$491$	23.0046	+	13.2817i	1.03818	+	0.599396i	0.118866	+	0.992910i	$0.462074\pi$
$492$	−12.7325	−	14.1741i	−0.574026	−	0.639018i
$493$	−20.0221	+	11.5598i	−0.901751	+	0.520626i
$494$		−	7.83120i		−	0.352342i
$495$	−0.0351213	−	0.0793815i	−0.00157858	−	0.00356793i
$496$			5.13324i			0.230489i
$497$		0			0
$498$	−6.72521	−	2.19383i	−0.301364	−	0.0983078i
$499$	−2.65759	+	4.60308i	−0.118970	+	0.206062i	−0.919360	−	0.393418i	$-0.871293\pi$
$499$	−2.65759	+	4.60308i	−0.118970	+	0.206062i	0.800390	+	0.599480i	$0.204626\pi$
$500$	0.220570	−	0.382039i	0.00986421	−	0.0170853i
$501$	3.16166	−	9.69212i	0.141253	−	0.433012i
$502$	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
$507$	21.6820	+	24.1368i	0.962931	+	1.07195i
$508$	−3.40810	+	5.90300i	−0.151210	+	0.261903i
$509$	6.81654	−	11.8066i	0.302138	−	0.523318i	−0.674482	−	0.738291i	$-0.735633\pi$
$509$	6.81654	−	11.8066i	0.302138	−	0.523318i	0.976620	+	0.214973i	$0.0689663\pi$
$510$	0.0382397	+	0.180941i	0.00169328	+	0.00801221i
$511$		0			0
$512$			16.2184i			0.716760i
$513$	−6.36088	−	8.81973i	−0.280840	−	0.389400i
$514$			11.7732i			0.519295i
$515$	0.129721	−	0.0748947i	0.00571621	−	0.00330025i
$516$	6.12780	−	1.29504i	0.269761	−	0.0570108i
$517$	9.63227	+	5.56120i	0.423627	+	0.244581i
$518$		0			0
$519$	−5.63167	−	6.26929i	−0.247203	−	0.275191i
$520$	−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	$0.571907\pi$
$522$	−0.866907	+	8.06702i	−0.0379435	+	0.353084i
$523$		−	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
$528$	2.60413	+	0.849493i	0.113330	+	0.0369694i
$529$	14.8634	+	25.7442i	0.646236	+	1.11931i
$530$	0.218096			0.00947346
$531$	1.93039	−	17.9632i	0.0837716	−	0.779538i
$532$		0			0
$533$	−34.4288	+	19.8775i	−1.49128	+	0.860990i
$534$	10.3157	−	9.26652i	0.446403	−	0.401001i
$535$	−0.222263	−	0.128324i	−0.00960927	−	0.00554791i
$536$	−26.1645	−	15.1061i	−1.13013	−	0.652484i
$537$	−0.0725746	−	0.343406i	−0.00313183	−	0.0148191i
$538$	−12.5955	+	7.27199i	−0.543029	+	0.313518i
$539$		0			0
$540$	−0.209095	−	0.0939732i	−0.00899803	−	0.00404396i
$541$	−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
$543$	2.24292	+	10.6130i	0.0962529	+	0.455445i
$544$	−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	0.987179	+	0.159620i	$0.0510267\pi$
$547$	14.7771	+	25.5947i	0.631824	+	1.09435i	−0.355355	+	0.934732i	$0.615640\pi$
$548$		−	17.6841i		−	0.755428i
$549$	−4.19199	+	5.74156i	−0.178910	+	0.245044i
$550$	−3.39495			−0.144761
$551$	4.25999	+	7.37852i	0.181482	+	0.314336i
$552$	9.22082	−	28.2665i	0.392464	−	1.20310i
$553$		0			0
$554$	−9.14828	−	5.28176i	−0.388673	−	0.224401i
$555$	0.0375930	−	0.115242i	0.00159574	−	0.00489175i
$556$	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	$0.863658\pi$
$558$	−6.04736	+	2.67557i	−0.256005	+	0.113266i
$559$		−	13.0683i		−	0.552728i
$560$		0			0
$561$	−7.48028	+	6.71949i	−0.315817	+	0.283697i
$562$	−1.72714	+	2.99149i	−0.0728548	+	0.126188i
$563$	7.23796	−	12.5365i	0.305044	−	0.528351i	−0.672227	−	0.740345i	$-0.734662\pi$
$563$	7.23796	−	12.5365i	0.305044	−	0.528351i	0.977271	+	0.211994i	$0.0679956\pi$
$564$	28.7385	−	6.07354i	1.21011	−	0.255742i
$565$	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	$-0.614743\pi$
$569$	6.70970	−	3.87385i	0.281285	−	0.162400i	0.634005	+	0.773329i	$0.281410\pi$
$570$	0.0666802	−	0.0140920i	0.00279293	−	0.000590251i
$571$	−8.06856	+	13.9752i	−0.337659	+	0.584842i	−0.983992	−	0.178213i	$-0.942968\pi$
$571$	−8.06856	+	13.9752i	−0.337659	+	0.584842i	0.646333	+	0.763055i	$0.276302\pi$
$572$	4.48805	−	7.77353i	0.187655	−	0.325027i
$573$	17.7858	−	15.9769i	0.743014	−	0.667445i
$574$		0			0
$575$		−	36.3008i		−	1.51385i
$576$	−2.00144	+	0.885511i	−0.0833934	+	0.0368963i
$577$		−	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
$579$	11.3218	−	34.7072i	0.470519	−	1.44238i
$580$	0.155548	+	0.0898059i	0.00645879	+	0.00372899i
$581$		0			0
$582$	−2.79178	+	8.55824i	−0.115723	+	0.354750i
$583$	5.92897	+	10.2693i	0.245553	+	0.425310i
$584$	25.7659			1.06620
$585$	−0.282051	+	0.386312i	−0.0116614	+	0.0159720i
$586$		−	15.1727i		−	0.626777i
$587$	16.8761	+	29.2302i	0.696550	+	1.20646i	0.969655	+	0.244476i	$0.0786158\pi$
$587$	16.8761	+	29.2302i	0.696550	+	1.20646i	−0.273106	+	0.961984i	$0.588051\pi$
$588$		0			0
$589$	−3.47207	+	6.01380i	−0.143064	+	0.247794i
$590$	0.0980610	+	0.0566155i	0.00403711	+	0.00233082i
$591$	5.43219	+	25.7038i	0.223451	+	1.05731i
$592$	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	$0.377369\pi$
$594$	0.356569	+	3.51064i	0.0146302	+	0.144043i
$595$		0			0
$596$	21.4799	−	12.4015i	0.879853	−	0.507983i
$597$	−3.46936	−	16.4162i	−0.141992	−	0.671870i
$598$	−23.5320	−	13.5862i	−0.962296	−	0.555582i
$599$	−34.1905	−	19.7399i	−1.39699	−	0.806551i	−0.402911	−	0.915239i	$-0.632002\pi$
$599$	−34.1905	−	19.7399i	−1.39699	−	0.806551i	−0.994076	+	0.108689i	$0.965335\pi$
$600$	−15.2281	+	13.6793i	−0.621683	+	0.558454i
$601$	34.4865	−	19.9108i	1.40673	−	0.812177i	0.411661	−	0.911337i	$-0.364949\pi$
$601$	34.4865	−	19.9108i	1.40673	−	0.812177i	0.995072	+	0.0991600i	$0.0316155\pi$
$602$		0			0
$603$	−4.09652	+	38.1202i	−0.166823	+	1.55237i
$604$	5.39339			0.219454
$605$	−0.140882	−	0.244015i	−0.00572766	−	0.00992060i
$606$	0.496448	+	0.161946i	0.0201668	+	0.00657861i
$607$	21.6104	+	12.4768i	0.877140	+	0.506417i	0.869714	−	0.493555i	$-0.164303\pi$
$607$	21.6104	+	12.4768i	0.877140	+	0.506417i	0.00742570	+	0.999972i	$0.497636\pi$
$608$	−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
$612$	−2.83733	+	26.4028i	−0.114692	+	1.06727i
$613$	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
$615$	−0.231204	−	0.257381i	−0.00932305	−	0.0103786i
$616$		0			0
$617$	29.8093	+	17.2104i	1.20008	+	0.692865i	0.960573	−	0.278030i	$-0.0896813\pi$
$617$	29.8093	+	17.2104i	1.20008	+	0.692865i	0.239506	+	0.970895i	$0.423015\pi$
$618$	−5.95757	+	1.25906i	−0.239648	+	0.0506468i
$619$	17.2889	−	9.98173i	0.694898	−	0.401200i	−0.110546	−	0.993871i	$-0.535260\pi$
$619$	17.2889	−	9.98173i	0.694898	−	0.401200i	0.805444	+	0.592671i	$0.201927\pi$
$620$			0.146391i			0.00587920i
$621$	−37.5378	+	3.81265i	−1.50634	+	0.152996i
$622$			13.6510i			0.547354i
$623$		0			0
$624$	−3.12097	−	14.7677i	−0.124939	−	0.591181i
$625$	−12.4940	+	21.6402i	−0.499760	+	0.865609i
$626$	−0.239503	+	0.414831i	−0.00957245	+	0.0165800i
$627$	2.47626	+	2.75662i	0.0988921	+	0.110089i
$628$	−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
$633$	−7.58399	+	23.2488i	−0.301437	+	0.924058i
$634$	−7.28384	+	12.6160i	−0.289278	+	0.501044i
$635$	−0.0618862	+	0.107190i	−0.00245588	+	0.00425370i
$636$	29.7718	+	9.71185i	1.18053	+	0.385100i
$637$		0			0
$638$		−	2.76475i		−	0.109458i
$639$	−9.63058	−	21.7671i	−0.380980	−	0.861094i
$640$			0.312103i			0.0123370i
$641$	−3.34281	+	1.92997i	−0.132033	+	0.0762293i	−0.564562	−	0.825391i	$-0.690955\pi$
$641$	−3.34281	+	1.92997i	−0.132033	+	0.0762293i	0.432529	+	0.901620i	$0.357621\pi$
$642$	6.97205	+	7.76143i	0.275165	+	0.306319i
$643$	31.0233	+	17.9113i	1.22344	+	0.706352i	0.965649	−	0.259849i	$-0.0836727\pi$
$643$	31.0233	+	17.9113i	1.22344	+	0.706352i	0.257789	+	0.966201i	$0.417006\pi$
$644$		0			0
$645$	0.111272	−	0.0235160i	0.00438133	−	0.000925941i
$646$	−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	$0.171699\pi$
$648$	15.7448	+	14.3103i	0.618515	+	0.562160i
$649$			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	$-0.286767\pi$
$653$	6.45191	+	3.72501i	0.252483	+	0.145771i	−0.368418	+	0.929660i	$0.620100\pi$
$654$	4.04891	−	3.63711i	0.158325	−	0.142222i
$655$	−0.0360114	−	0.0623736i	−0.00140708	−	0.00243714i
$656$	10.9177			0.426264
$657$	−13.2295	−	29.9014i	−0.516131	−	1.16656i
$658$		0			0
$659$	−7.52607	+	4.34518i	−0.293174	+	0.169264i	−0.639372	−	0.768897i	$-0.720806\pi$
$659$	−7.52607	+	4.34518i	−0.293174	+	0.169264i	0.346198	+	0.938161i	$0.387472\pi$
$660$	0.0742652	+	0.0242260i	0.00289077	+	0.000942997i
$661$	24.9853	+	14.4253i	0.971815	+	0.561077i	0.899789	−	0.436325i	$-0.143720\pi$
$661$	24.9853	+	14.4253i	0.971815	+	0.561077i	0.0720256	+	0.997403i	$0.477054\pi$
$662$	−12.4653	−	7.19686i	−0.484479	−	0.279714i
$663$	52.6756	+	17.1833i	2.04575	+	0.667343i
$664$	12.5871	−	7.26719i	0.488476	−	0.282022i
$665$		0			0
$666$	−2.90573	+	3.97984i	−0.112595	+	0.154216i
$667$	29.5623			1.14466
$668$	4.58724	+	7.94534i	0.177486	+	0.307414i
$669$	3.85021	−	3.45862i	0.148858	−	0.133718i
$670$	−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	0.788095	−	0.615554i	$-0.211068\pi$
$673$	−3.60695	−	6.24742i	−0.139038	−	0.240820i	−0.927133	+	0.374733i	$0.877734\pi$
$674$		−	16.8007i		−	0.647139i
$675$	23.6937	+	10.6486i	0.911971	+	0.409865i
$676$	−29.1982			−1.12301
$677$	18.1911	+	31.5079i	0.699140	+	1.21095i	0.968765	+	0.247980i	$0.0797667\pi$
$677$	18.1911	+	31.5079i	0.699140	+	1.21095i	−0.269626	+	0.962965i	$0.586900\pi$
$678$	−10.6734	+	2.25570i	−0.409911	+	0.0866297i
$679$		0			0
$680$	−0.329070	−	0.189989i	−0.0126193	−	0.00728573i
$681$	33.3041	+	37.0749i	1.27622	+	1.42071i
$682$	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	$-0.150021\pi$
$684$	9.72991	+	1.04561i	0.372033	+	0.0399798i
$685$		−	0.321118i		−	0.0122693i
$686$		0			0
$687$	14.5913	+	4.75982i	0.556693	+	0.181599i
$688$	−1.79443	+	3.10804i	−0.0684119	+	0.118493i
$689$	32.6707	−	56.5874i	1.24466	−	2.15581i
$690$	0.0733370	−	0.224816i	0.00279189	−	0.00855859i
$691$	−2.86127	+	1.65195i	−0.108848	+	0.0628433i	−0.553436	−	0.832892i	$-0.686684\pi$
$691$	−2.86127	+	1.65195i	−0.108848	+	0.0628433i	0.444588	+	0.895735i	$0.353350\pi$
$692$	7.58393			0.288298
$693$		0			0
$694$	−3.77718			−0.143380
$695$	0.0862962	−	0.0498231i	0.00327340	−	0.00188990i
$696$	−11.1400	−	12.4013i	−0.422261	−	0.470070i
$697$	−20.0386	+	34.7079i	−0.759016	+	1.31465i
$698$	−3.71417	+	6.43313i	−0.140583	+	0.243498i
$699$	4.62292	+	21.8746i	0.174855	+	0.827371i
$700$		0			0
$701$			0.873603i			0.0329955i	0.999864	+	0.0164978i	$0.00525164\pi$
$701$			0.873603i			0.0329955i	−0.999864	+	0.0164978i	$0.994748\pi$
$702$	15.7707	−	11.3740i	0.595228	−	0.429285i
$703$			5.17461i			0.195164i
$704$	0.645868	−	0.372892i	0.0243421	−	0.0140539i
$705$	0.521850	−	0.110287i	0.0196540	−	0.00415364i
$706$	8.07845	+	4.66410i	0.304037	+	0.175536i
$707$		0			0
$708$	10.8650	+	12.0952i	0.408332	+	0.454564i
$709$	−8.07767	−	13.9909i	−0.303363	−	0.525441i	0.673532	−	0.739158i	$-0.264776\pi$
$709$	−8.07767	−	13.9909i	−0.303363	−	0.525441i	−0.976896	+	0.213717i	$0.931443\pi$
$710$	0.149179			0.00559860
$711$	37.7986	+	27.5972i	1.41756	+	1.03498i
$712$			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
$717$	−9.23528	−	3.01264i	−0.344898	−	0.112509i
$718$	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	$0.819012\pi$
$720$	0.120126	−	0.0531481i	0.00447683	−	0.00198071i
$721$		0			0
$722$	8.41110	−	4.85615i	0.313029	−	0.180727i
$723$	14.1566	−	12.7168i	0.526490	−	0.472943i
$724$	−8.45395	−	4.88089i	−0.314189	−	0.181397i
$725$	−17.6260	−	10.1764i	−0.654613	−	0.377941i
$726$	2.36837	+	11.2066i	0.0878986	+	0.415915i
$727$	−7.15775	+	4.13253i	−0.265466	+	0.153267i	−0.626826	−	0.779160i	$-0.715646\pi$
$727$	−7.15775	+	4.13253i	−0.265466	+	0.153267i	0.361359	+	0.932427i	$0.382313\pi$
$728$		0			0
$729$	8.52294	−	25.6195i	0.315664	−	0.948871i
$730$	0.204927			0.00758468
$731$	−6.58709	−	11.4092i	−0.243632	−	0.421983i
$732$	−1.32283	−	6.25931i	−0.0488932	−	0.231351i
$733$	−10.5799	−	6.10830i	−0.390777	−	0.225615i	0.291720	−	0.956504i	$-0.405773\pi$
$733$	−10.5799	−	6.10830i	−0.390777	−	0.225615i	−0.682497	+	0.730889i	$0.739106\pi$
$734$	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
$738$	5.69056	+	12.8619i	0.209472	+	0.473452i
$739$	−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
$741$	6.33235	−	19.4119i	0.232625	−	0.713115i
$742$		0			0
$743$	10.2862	+	5.93873i	0.377363	+	0.217871i	0.676670	−	0.736286i	$-0.263422\pi$
$743$	10.2862	+	5.93873i	0.377363	+	0.217871i	−0.299307	+	0.954157i	$0.596756\pi$
$744$	4.21362	−	12.9169i	0.154479	−	0.473557i
$745$	0.390045	−	0.225192i	0.0142901	−	0.00825041i
$746$		−	0.164647i		−	0.00602814i
$747$	−14.8964	−	10.8761i	−0.545033	−	0.397935i
$748$		−	9.04885i		−	0.330859i
$749$		0			0
$750$	−0.242250	+	0.217612i	−0.00884571	+	0.00794606i
$751$	−11.8554	+	20.5342i	−0.432610	+	0.749303i	−0.997097	−	0.0761390i	$-0.975741\pi$
$751$	−11.8554	+	20.5342i	−0.432610	+	0.749303i	0.564487	+	0.825442i	$0.309074\pi$
$752$	−8.41562	+	14.5763i	−0.306886	+	0.531542i
$753$	41.0506	−	8.67555i	1.49597	−	0.316154i
$754$	−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
$759$	12.5794	−	2.65850i	0.456603	−	0.0964975i
$760$	−0.0700143	+	0.121268i	−0.00253969	+	0.00439887i
$761$	24.3767	−	42.2217i	0.883656	−	1.53054i	0.0364098	−	0.999337i	$-0.488408\pi$
$761$	24.3767	−	42.2217i	0.883656	−	1.53054i	0.847246	−	0.531200i	$-0.178259\pi$
$762$	3.74308	−	3.36238i	0.135597	−	0.121806i
$763$		0			0
$764$			21.5154i			0.778401i
$765$	−0.0515217	+	0.479436i	−0.00186277	+	0.0173341i
$766$		−	0.217284i		−	0.00785081i
$767$	29.3791	−	16.9620i	1.06082	−	0.612463i
$768$	4.71845	−	14.4645i	0.170262	−	0.521942i
$769$	23.3870	+	13.5025i	0.843357	+	0.486912i	0.858404	−	0.512975i	$-0.171457\pi$
$769$	23.3870	+	13.5025i	0.843357	+	0.486912i	−0.0150472	+	0.999887i	$0.504790\pi$
$770$		0			0
$771$	−9.51989	+	29.1834i	−0.342851	+	1.05101i
$772$	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	$0.659512\pi$
$774$	−4.59681	−	0.493988i	−0.165229	−	0.0177560i
$775$		−	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
$780$	−0.0890046	−	0.421148i	−0.00318688	−	0.0150795i
$781$	4.05547	+	7.02429i	0.145116	+	0.251349i
$782$	−27.3927			−0.979560
$783$	−8.67191	+	19.2955i	−0.309909	+	0.689564i
$784$		0			0
$785$	−0.400742	+	0.231368i	−0.0143031	+	0.00825789i
$786$	0.605391	+	2.86456i	0.0215936	+	0.102176i
$787$	−41.0093	−	23.6767i	−1.46182	−	0.843983i	−0.462726	−	0.886501i	$-0.653129\pi$
$787$	−41.0093	−	23.6767i	−1.46182	−	0.843983i	−0.999096	+	0.0425177i	$0.986462\pi$
$788$	−20.4749	−	11.8212i	−0.729388	−	0.421112i
$789$	3.73497	−	3.35510i	0.132968	−	0.119445i
$790$	−0.254023	+	0.146660i	−0.00903775	+	0.00521795i
$791$		0			0
$792$	−5.85554	−	4.27520i	−0.208068	−	0.151913i
$793$	−13.3487			−0.474027
$794$	2.49462	+	4.32082i	0.0885309	+	0.153340i
$795$	0.540613	+	0.176353i	0.0191736	+	0.00625461i
$796$	13.0766	+	7.54980i	0.463489	+	0.267596i
$797$	−4.42781	+	7.66919i	−0.156841	+	0.271657i	−0.933728	−	0.357984i	$-0.883464\pi$
$797$	−4.42781	+	7.66919i	−0.156841	+	0.271657i	0.776887	+	0.629640i	$0.216798\pi$
$798$		0			0
$799$	−30.8925	−	53.5074i	−1.09290	−	1.89296i
$800$		−	28.7741i		−	1.01732i
$801$	33.0634	−	14.6284i	1.16824	−	0.516871i
$802$	−4.20808			−0.148592
$803$	5.57098	+	9.64922i	0.196596	+	0.340514i
$804$	−23.0569	−	25.6674i	−0.813154	−	0.905220i
$805$		0			0
$806$	−10.7534	−	6.20848i	−0.378772	−	0.218684i
$807$	−37.1017	+	7.84099i	−1.30604	+	0.276016i
$808$	−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	$-0.0415258\pi$
$810$	0.125225	+	0.113816i	0.00439997	+	0.00399907i
$811$		−	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
$813$	3.21732	+	15.2236i	0.112836	+	0.533914i
$814$	0.839587	−	1.45421i	0.0294275	−	0.0509699i
$815$	−0.146553	+	0.253836i	−0.00513351	+	0.00889150i
$816$	−10.1684	−	11.3197i	−0.355967	−	0.396269i
$817$	−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	$-0.545917\pi$
$821$	18.3781	−	10.6106i	0.641401	−	0.370313i	0.785154	+	0.619300i	$0.212584\pi$
$822$	−4.04836	+	12.4103i	−0.141203	+	0.432859i
$823$	−8.47690	+	14.6824i	−0.295486	+	0.511797i	−0.975098	−	0.221775i	$-0.928815\pi$
$823$	−8.47690	+	14.6824i	−0.295486	+	0.511797i	0.679612	+	0.733572i	$0.262148\pi$
$824$	6.25546	−	10.8348i	0.217919	−	0.377447i
$825$	−8.41538	−	2.74518i	−0.292986	−	0.0955749i
$826$		0			0
$827$		−	25.3052i		−	0.879949i	−0.898010	−	0.439975i	$-0.854987\pi$
$827$		−	25.3052i		−	0.879949i	0.898010	−	0.439975i	$-0.145013\pi$
$828$	20.0222	−	27.4235i	0.695820	−	0.953031i
$829$		−	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
$831$	−18.4058	−	20.4897i	−0.638491	−	0.710781i
$832$	−3.55896	−	2.05477i	−0.123385	−	0.0712362i
$833$		0			0
$834$	−3.96323	+	0.837580i	−0.137235	+	0.0290030i
$835$	0.0832977	+	0.144276i	0.00288264	+	0.00499287i
$836$	−3.33467			−0.115332
$837$	−17.1536	+	1.74226i	−0.592916	+	0.0602213i
$838$		−	1.19103i		−	0.0411434i
$839$	6.61780	+	11.4624i	0.228472	+	0.395725i	0.957355	−	0.288913i	$-0.0932938\pi$
$839$	6.61780	+	11.4624i	0.228472	+	0.395725i	−0.728884	+	0.684638i	$0.759960\pi$
$840$		0			0
$841$	−6.21265	+	10.7606i	−0.214229	+	0.371056i
$842$	2.18914	+	1.26390i	0.0754428	+	0.0435569i
$843$	−6.70014	+	6.01870i	−0.230765	+	0.207295i
$844$	−11.0036	−	19.0588i	−0.378759	−	0.656030i
$845$	−0.530197			−0.0182393
$846$	−21.5584	−	2.31673i	−0.741193	−	0.0796509i
$847$		0			0
$848$	−15.5403	+	8.97217i	−0.533654	+	0.308106i
$849$	30.9141	+	10.0845i	1.06097	+	0.346098i
$850$	16.3324	+	9.42951i	0.560196	+	0.323429i
$851$	15.5492	+	8.97735i	0.533020	+	0.307739i
$852$	20.3642	+	6.64300i	0.697666	+	0.227585i
$853$	−15.3814	+	8.88048i	−0.526651	+	0.304062i	−0.739651	−	0.672990i	$-0.765010\pi$
$853$	−15.3814	+	8.88048i	−0.526651	+	0.304062i	0.213001	+	0.977052i	$0.431676\pi$
$854$		0			0
$855$	0.176681	+	0.0189867i	0.00604237	+	0.000649332i
$856$	−21.4360			−0.732669
$857$	9.17157	+	15.8856i	0.313295	+	0.542643i	0.979074	−	0.203507i	$-0.0652338\pi$
$857$	9.17157	+	15.8856i	0.313295	+	0.542643i	−0.665779	+	0.746149i	$0.731900\pi$
$858$	−4.92917	+	4.42785i	−0.168279	+	0.151164i
$859$	−2.69126	−	1.55380i	−0.0918246	−	0.0530150i	0.453385	−	0.891315i	$-0.350216\pi$
$859$	−2.69126	−	1.55380i	−0.0918246	−	0.0530150i	−0.545209	+	0.838300i	$0.683550\pi$
$860$	−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	$0.751064\pi$
$864$	−29.7546	+	3.02212i	−1.01227	+	0.102815i
$865$	0.137713			0.00468239
$866$	12.4321	+	21.5330i	0.422458	+	0.731720i
$867$	25.8409	−	5.46115i	0.877602	−	0.185471i
$868$		0			0
$869$	−13.8114	−	7.97399i	−0.468518	−	0.270499i
$870$	−0.0886013	−	0.0986328i	−0.00300386	−	0.00334396i
$871$	−62.3460	+	35.9955i	−2.11251	+	1.21966i
$872$			11.1826i			0.378689i
$873$	−13.8405	+	18.9566i	−0.468429	+	0.641585i
$874$			10.0947i			0.341459i
$875$		0			0
$876$	27.9742	+	9.12545i	0.945161	+	0.308320i
$877$	11.3979	−	19.7417i	0.384878	−	0.666628i	−0.606874	−	0.794798i	$-0.707577\pi$
$877$	11.3979	−	19.7417i	0.384878	−	0.666628i	0.991752	+	0.128170i	$0.0409102\pi$
$878$	−7.88482	+	13.6569i	−0.266100	+	0.460898i
$879$	12.2687	−	37.6099i	0.413813	−	1.26855i
$880$	−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
$885$	0.197293	+	0.219631i	0.00663193	+	0.00738281i
$886$	3.73682	−	6.47236i	0.125541	−	0.217443i
$887$	19.4788	−	33.7382i	0.654033	−	1.13282i	−0.328102	−	0.944642i	$-0.606409\pi$
$887$	19.4788	−	33.7382i	0.654033	−	1.13282i	0.982135	−	0.188176i	$-0.0602576\pi$
$888$	−2.09347	−	9.90579i	−0.0702522	−	0.332417i
$889$		0			0
$890$			0.226597i			0.00759556i
$891$	−1.95486	+	8.99048i	−0.0654904	+	0.301192i
$892$			4.65757i			0.155947i
$893$	−19.7185	+	11.3845i	−0.659853	+	0.380966i
$894$	−17.9131	+	3.78572i	−0.599105	+	0.126614i
$895$	0.00496721	+	0.00286782i	0.000166035	+	9.58606e-5i
$896$		0			0
$897$	−47.3451	−	52.7055i	−1.58081	−	1.75979i
$898$	4.78138	+	8.28160i	0.159557	+	0.276361i
$899$	13.5091			0.450553
$900$	−21.3780	+	9.45840i	−0.712599	+	0.315280i
$901$		−	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
$906$	−3.78496	−	1.23469i	−0.125747	−	0.0410198i
$907$	14.0526	+	24.3399i	0.466610	+	0.808192i	0.999273	−	0.0381355i	$-0.0121419\pi$
$907$	14.0526	+	24.3399i	0.466610	+	0.808192i	−0.532663	+	0.846328i	$0.678809\pi$
$908$	−44.8493			−1.48837
$909$	1.09964	+	0.802861i	0.0364728	+	0.0266292i
$910$		0			0
$911$	32.3883	−	18.6994i	1.07307	−	0.619538i	0.144052	−	0.989570i	$-0.453987\pi$
$911$	32.3883	−	18.6994i	1.07307	−	0.619538i	0.929019	+	0.370032i	$0.120653\pi$
$912$	−4.17152	+	3.74726i	−0.138133	+	0.124084i
$913$	5.44307	+	3.14256i	0.180139	+	0.104003i
$914$	11.8666	+	6.85121i	0.392513	+	0.226618i
$915$	−0.0240207	−	0.113660i	−0.000794100	−	0.00375749i
$916$	−11.9616	+	6.90601i	−0.395221	+	0.228181i
$917$		0			0
$918$	8.03546	−	17.8793i	0.265210	−	0.590105i
$919$	−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
$921$	−6.67300	−	31.5750i	−0.219883	−	1.04043i
$922$	−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
$927$	−15.7856	−	1.69637i	−0.518469	−	0.0557162i
$928$	23.4328			0.769220
$929$	7.97094	+	13.8061i	0.261518	+	0.452963i	0.966646	−	0.256118i	$-0.0824435\pi$
$929$	7.97094	+	13.8061i	0.261518	+	0.452963i	−0.705127	+	0.709081i	$0.749110\pi$
$930$	0.0335127	−	0.102734i	0.00109893	−	0.00336877i
$931$		0			0
$932$	−17.4246	−	10.0601i	−0.570762	−	0.329529i
$933$	−11.0382	+	33.8379i	−0.361376	+	1.10780i
$934$	−5.31568	+	3.06901i	−0.173934	+	0.100421i
$935$		−	0.164314i		−	0.00537364i
$936$	−4.26867	+	39.7222i	−0.139526	+	1.29836i
$937$			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
$939$	−0.929112	+	0.834616i	−0.0303204	+	0.0272367i
$940$	−0.239999	+	0.415690i	−0.00782789	+	0.0135583i
$941$	5.76861	−	9.99152i	0.188051	−	0.325714i	−0.756549	−	0.653937i	$-0.773116\pi$
$941$	5.76861	−	9.99152i	0.188051	−	0.325714i	0.944600	+	0.328222i	$0.106450\pi$
$942$	18.4044	−	3.88955i	0.599648	−	0.126728i
$943$	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	$-0.818938\pi$
$947$	−24.5364	+	14.1661i	−0.797325	+	0.460336i	0.0452102	+	0.998977i	$0.485604\pi$
$948$	−41.2071	+	8.70862i	−1.33834	+	0.282843i
$949$	30.6981	−	53.1706i	0.996501	−	1.72599i
$950$	3.47495	−	6.01879i	0.112742	−	0.195275i
$951$	−28.2565	+	25.3826i	−0.916278	+	0.823088i
$952$		0			0
$953$			29.8498i			0.966931i	0.875364	+	0.483465i	$0.160622\pi$
$953$			29.8498i			0.966931i	−0.875364	+	0.483465i	$0.839378\pi$
$954$	−18.6699	−	13.6311i	−0.604459	−	0.441323i
$955$			0.390689i			0.0126424i
$956$	7.57084	−	4.37102i	0.244858	−	0.141369i
$957$	2.23559	−	6.85325i	0.0722665	−	0.221534i
$958$	−10.0935	−	5.82748i	−0.326106	−	0.188277i
$959$		0			0
$960$	0.0110914	−	0.0340009i	0.000357974	−	0.00109737i
$961$	−9.99478	−	17.3115i	−0.322412	−	0.558434i
$962$	−9.25283			−0.298323
$963$	11.0063	+	24.8766i	0.354674	+	0.801637i
$964$			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	−0.704032	−	0.710168i	$-0.748619\pi$
$967$	8.17864	−	14.1658i	0.263007	−	0.455542i	0.967040	+	0.254626i	$0.0819523\pi$
$968$	−20.3809	−	11.7669i	−0.655068	−	0.378203i
$969$	−4.25620	−	20.1393i	−0.136729	−	0.646968i
$970$	−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	$0.388086\pi$
$972$	12.0260	+	21.1131i	0.385735	+	0.677202i
$973$		0			0
$974$	−24.8470	+	14.3454i	−0.796148	+	0.459657i
$975$	10.0856	+	47.7225i	0.322997	+	1.52834i
$976$	3.17475	+	1.83294i	0.101621	+	0.0586710i
$977$	−18.6219	−	10.7513i	−0.595766	−	0.343966i	0.171608	−	0.985165i	$-0.445104\pi$
$977$	−18.6219	−	10.7513i	−0.595766	−	0.343966i	−0.767374	+	0.641199i	$0.778437\pi$
$978$	8.86397	−	7.96246i	0.283439	−	0.254611i
$979$	−10.6696	+	6.16010i	−0.341002	+	0.196878i
$980$		0			0
$981$	12.9774	−	5.74167i	0.414336	−	0.183318i
$982$	17.6460			0.563107
$983$	−12.7097	−	22.0138i	−0.405376	−	0.702131i	0.588989	−	0.808141i	$-0.299526\pi$
$983$	−12.7097	−	22.0138i	−0.405376	−	0.702131i	−0.994365	+	0.106009i	$0.966193\pi$
$984$	−27.4725	−	8.96178i	−0.875790	−	0.285691i
$985$	−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
$990$	−0.0465716	−	0.0340025i	−0.00148014	−	0.00108067i
$991$	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
$993$	−25.0795	−	27.9191i	−0.795875	−	0.885985i
$994$		0			0
$995$	0.237453	+	0.137093i	0.00752776	+	0.00434615i
$996$	16.2398	−	3.43207i	0.514576	−	0.108749i
$997$	10.5366	−	6.08329i	0.333697	−	0.192660i	−0.323785	−	0.946131i	$-0.604955\pi$
$997$	10.5366	−	6.08329i	0.333697	−	0.192660i	0.657481	+	0.753471i	$0.271622\pi$
$998$			3.53086i			0.111767i
$999$	−10.4208	+	7.51560i	−0.329700	+	0.237783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.o.e.293.16	yes	48
3.2	odd	2		1323.2.o.e.881.10		48
7.2	even	3		441.2.s.d.374.9		48
7.3	odd	6		441.2.i.d.68.16		48
7.4	even	3		441.2.i.d.68.15		48
7.5	odd	6		441.2.s.d.374.10		48
7.6	odd	2	inner	441.2.o.e.293.15	yes	48
9.2	odd	6	inner	441.2.o.e.146.15	✓	48
9.7	even	3		1323.2.o.e.440.9		48
21.2	odd	6		1323.2.s.d.962.16		48
21.5	even	6		1323.2.s.d.962.15		48
21.11	odd	6		1323.2.i.d.1097.10		48
21.17	even	6		1323.2.i.d.1097.9		48
21.20	even	2		1323.2.o.e.881.9		48
63.2	odd	6		441.2.i.d.227.10		48
63.11	odd	6		441.2.s.d.362.10		48
63.16	even	3		1323.2.i.d.521.9		48
63.20	even	6	inner	441.2.o.e.146.16	yes	48
63.25	even	3		1323.2.s.d.656.15		48
63.34	odd	6		1323.2.o.e.440.10		48
63.38	even	6		441.2.s.d.362.9		48
63.47	even	6		441.2.i.d.227.9		48
63.52	odd	6		1323.2.s.d.656.16		48
63.61	odd	6		1323.2.i.d.521.10		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.15		48	7.4	even	3
441.2.i.d.68.16		48	7.3	odd	6
441.2.i.d.227.9		48	63.47	even	6
441.2.i.d.227.10		48	63.2	odd	6
441.2.o.e.146.15	✓	48	9.2	odd	6	inner
441.2.o.e.146.16	yes	48	63.20	even	6	inner
441.2.o.e.293.15	yes	48	7.6	odd	2	inner
441.2.o.e.293.16	yes	48	1.1	even	1	trivial
441.2.s.d.362.9		48	63.38	even	6
441.2.s.d.362.10		48	63.11	odd	6
441.2.s.d.374.9		48	7.2	even	3
441.2.s.d.374.10		48	7.5	odd	6
1323.2.i.d.521.9		48	63.16	even	3
1323.2.i.d.521.10		48	63.61	odd	6
1323.2.i.d.1097.9		48	21.17	even	6
1323.2.i.d.1097.10		48	21.11	odd	6
1323.2.o.e.440.9		48	9.7	even	3
1323.2.o.e.440.10		48	63.34	odd	6
1323.2.o.e.881.9		48	21.20	even	2
1323.2.o.e.881.10		48	3.2	odd	2
1323.2.s.d.656.15		48	63.25	even	3
1323.2.s.d.656.16		48	63.52	odd	6
1323.2.s.d.962.15		48	21.5	even	6
1323.2.s.d.962.16		48	21.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.575298 - 0.332148i) q^{2} +(1.69462 - 0.358137i) q^{3} +(-0.779355 + 1.34988i) q^{4} +(-0.0141520 + 0.0245119i) q^{5} +(0.855956 - 0.768901i) q^{6} +2.36404i q^{8} +(2.74348 - 1.21381i) q^{9} +0.0188022i q^{10} +(-0.885324 + 0.511142i) q^{11} +(-0.837267 + 2.56665i) q^{12} +(4.87844 + 2.81657i) q^{13} +(-0.0152036 + 0.0466067i) q^{15} +(-0.773498 - 1.33974i) q^{16} +5.67880 q^{17} +(1.17515 - 1.60955i) q^{18} -2.09274i q^{19} +(-0.0220588 - 0.0382070i) q^{20} +(-0.339550 + 0.588118i) q^{22} +(-6.28849 - 3.63066i) q^{23} +(0.846651 + 4.00615i) q^{24} +(2.49960 + 4.32943i) q^{25} +3.74208 q^{26} +(4.21444 - 3.03949i) q^{27} +(-3.52577 + 2.03560i) q^{29} +(0.00673377 + 0.0318626i) q^{30} +(-2.87364 - 1.65910i) q^{31} +(-4.98462 - 2.87787i) q^{32} +(-1.31723 + 1.18326i) q^{33} +(3.26700 - 1.88620i) q^{34} +(-0.499635 + 4.64936i) q^{36} -2.47265 q^{37} +(-0.695101 - 1.20395i) q^{38} +(9.27583 + 3.02586i) q^{39} +(-0.0579471 - 0.0334558i) q^{40} +(-3.52867 + 6.11183i) q^{41} +(-1.15994 - 2.00908i) q^{43} -1.59344i q^{44} +(-0.00907265 + 0.0844257i) q^{45} -4.82367 q^{46} +(-5.43997 - 9.42231i) q^{47} +(-1.79060 - 1.99333i) q^{48} +(2.87603 + 1.66048i) q^{50} +(9.62341 - 2.03379i) q^{51} +(-7.60408 + 4.39022i) q^{52} -11.5995i q^{53} +(1.41499 - 3.14843i) q^{54} -0.0289346i q^{55} +(-0.749489 - 3.54640i) q^{57} +(-1.35224 + 2.34215i) q^{58} +(3.01111 - 5.21540i) q^{59} +(-0.0510646 - 0.0568462i) q^{60} +(-2.05220 + 1.18484i) q^{61} -2.20427 q^{62} -0.729528 q^{64} +(-0.138079 + 0.0797200i) q^{65} +(-0.364781 + 1.11824i) q^{66} +(-6.38995 + 11.0677i) q^{67} +(-4.42580 + 7.66571i) q^{68} +(-11.9569 - 3.90045i) q^{69} -7.93415i q^{71} +(2.86950 + 6.48568i) q^{72} -10.8991i q^{73} +(-1.42251 + 0.821285i) q^{74} +(5.78640 + 6.44154i) q^{75} +(2.82496 + 1.63099i) q^{76} +(6.34140 - 1.34018i) q^{78} +(7.80018 + 13.5103i) q^{79} +0.0437861 q^{80} +(6.05331 - 6.66014i) q^{81} +4.68816i q^{82} +(-3.07406 - 5.32442i) q^{83} +(-0.0803661 + 0.139198i) q^{85} +(-1.33463 - 0.770546i) q^{86} +(-5.24581 + 4.71228i) q^{87} +(-1.20836 - 2.09294i) q^{88} +12.0516 q^{89} +(0.0228224 + 0.0515834i) q^{90} +(9.80194 - 5.65915i) q^{92} +(-5.46392 - 1.78238i) q^{93} +(-6.25921 - 3.61376i) q^{94} +(0.0512971 + 0.0296164i) q^{95} +(-9.47771 - 3.09172i) q^{96} +(-6.77565 + 3.91192i) q^{97} +(-1.80843 + 2.47692i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4} + 16 q^{9} - 24 q^{11} - 40 q^{15} - 24 q^{16} - 16 q^{18} - 48 q^{23} - 24 q^{25} - 24 q^{30} + 120 q^{32} - 8 q^{36} + 88 q^{39} + 48 q^{50} + 24 q^{51} + 80 q^{57} - 96 q^{60} - 48 q^{64}+ \cdots - 72 q^{99}+O(q^{100}) \) 48 * q + 24 * q^4 + 16 * q^9 - 24 * q^11 - 40 * q^15 - 24 * q^16 - 16 * q^18 - 48 * q^23 - 24 * q^25 - 24 * q^30 + 120 * q^32 - 8 * q^36 + 88 * q^39 + 48 * q^50 + 24 * q^51 + 80 * q^57 - 96 * q^60 - 48 * q^64 + 120 * q^65 + 56 * q^72 - 168 * q^74 - 88 * q^78 - 24 * q^79 - 96 * q^81 - 24 * q^85 + 24 * q^86 - 144 * q^92 - 32 * q^93 + 96 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

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