LMFDB - Embedded newform 441.2.s.d.374.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,2,Mod(362,441)] 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("441.362"); 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, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == 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			374.9
Character	$\chi$	$=$	441.374
Dual form			441.2.s.d.362.9

$q$-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} +(-0.537154 + 1.64665i) q^{3} +(-0.779355 - 1.34988i) q^{4} +0.0283039 q^{5} +(0.855956 - 0.768901i) q^{6} +2.36404i q^{8} +(-2.42293 - 1.76901i) q^{9} +(-0.0162832 - 0.00940110i) q^{10} -1.02228i q^{11} +(2.64142 - 0.558232i) q^{12} +(4.87844 + 2.81657i) q^{13} +(-0.0152036 + 0.0466067i) q^{15} +(-0.773498 + 1.33974i) q^{16} +(-2.83940 + 4.91798i) q^{17} +(0.806333 + 1.82248i) q^{18} +(-1.81237 + 1.04637i) q^{19} +(-0.0220588 - 0.0382070i) q^{20} +(-0.339550 + 0.588118i) q^{22} +7.26133i q^{23} +(-3.89275 - 1.26985i) q^{24} -4.99920 q^{25} +(-1.87104 - 3.24073i) q^{26} +(4.21444 - 3.03949i) q^{27} +(-3.52577 + 2.03560i) q^{29} +(0.0242269 - 0.0217629i) q^{30} +(2.87364 - 1.65910i) q^{31} +(4.98462 - 2.87787i) q^{32} +(1.68335 + 0.549124i) q^{33} +(3.26700 - 1.88620i) q^{34} +(-0.499635 + 4.64936i) q^{36} +(1.23632 + 2.14137i) q^{37} +1.39020 q^{38} +(-7.25839 + 6.52017i) q^{39} +0.0669116i q^{40} +(-3.52867 + 6.11183i) q^{41} +(-1.15994 - 2.00908i) q^{43} +(-1.37996 + 0.796722i) q^{44} +(-0.0685785 - 0.0500700i) q^{45} +(2.41184 - 4.17742i) q^{46} +(-5.43997 + 9.42231i) q^{47} +(-1.79060 - 1.99333i) q^{48} +(2.87603 + 1.66048i) q^{50} +(-6.57302 - 7.31722i) q^{51} -8.78043i q^{52} +(10.0454 + 5.79973i) q^{53} +(-3.43412 + 0.348797i) q^{54} -0.0289346i q^{55} +(-0.749489 - 3.54640i) q^{57} +2.70449 q^{58} +(3.01111 + 5.21540i) q^{59} +(0.0747626 - 0.0158002i) q^{60} +(2.05220 + 1.18484i) q^{61} -2.20427 q^{62} -0.729528 q^{64} +(0.138079 + 0.0797200i) q^{65} +(-0.786035 - 0.875030i) q^{66} +(-6.38995 - 11.0677i) q^{67} +8.85160 q^{68} +(-11.9569 - 3.90045i) q^{69} -7.93415i q^{71} +(4.18201 - 5.72790i) q^{72} +(9.43889 + 5.44955i) q^{73} -1.64257i q^{74} +(2.68534 - 8.23195i) q^{75} +(2.82496 + 1.63099i) q^{76} +(6.34140 - 1.34018i) q^{78} +(7.80018 - 13.5103i) q^{79} +(-0.0218930 + 0.0379198i) q^{80} +(2.74119 + 8.57239i) q^{81} +(4.06007 - 2.34408i) q^{82} +(-3.07406 - 5.32442i) q^{83} +(-0.0803661 + 0.139198i) q^{85} +1.54109i q^{86} +(-1.45805 - 6.89915i) q^{87} +2.41672 q^{88} +(-6.02582 - 10.4370i) q^{89} +(0.0228224 + 0.0515834i) q^{90} +(9.80194 - 5.65915i) q^{92} +(1.18837 + 5.62309i) q^{93} +(6.25921 - 3.61376i) q^{94} +(-0.0512971 + 0.0296164i) q^{95} +(2.06135 + 9.75380i) 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} - 8 q^{9} - 40 q^{15} - 24 q^{16} + 32 q^{18} + 48 q^{25} + 48 q^{30} - 120 q^{32} - 8 q^{36} - 32 q^{39} + 96 q^{44} + 48 q^{50} + 48 q^{53} + 80 q^{57} - 72 q^{60} - 48 q^{64} - 120 q^{65}+ \cdots - 72 q^{99}+O(q^{100}) $ 48 * q + 24 * q^4 - 8 * q^9 - 40 * q^15 - 24 * q^16 + 32 * q^18 + 48 * q^25 + 48 * q^30 - 120 * q^32 - 8 * q^36 - 32 * q^39 + 96 * q^44 + 48 * q^50 + 48 * q^53 + 80 * q^57 - 72 * q^60 - 48 * q^64 - 120 * q^65 + 32 * q^72 - 88 * q^78 - 24 * q^79 + 120 * q^81 - 24 * q^85 - 144 * q^92 + 16 * q^93 - 96 * q^95 - 72 * q^99

Character values

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

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

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	$-0.408798\pi$
$2$	−0.575298	−	0.332148i	−0.406797	−	0.234864i	−0.689413	+	0.724369i	$0.742131\pi$
$3$	−0.537154	+	1.64665i	−0.310126	+	0.950695i
$3$	−0.537154	+	1.64665i	−0.310126	+	0.950695i
$4$	−0.779355	−	1.34988i	−0.389677	−	0.674941i
$5$	0.0283039			0.0126579			0.00632895	−	0.999980i	$-0.497985\pi$
$5$	0.0283039			0.0126579			0.00632895	+	0.999980i	$0.497985\pi$
$6$	0.855956	−	0.768901i	0.349443	−	0.313903i
$7$		0			0
$7$		0			0
$8$			2.36404i			0.835814i
$9$	−2.42293	−	1.76901i	−0.807644	−	0.589671i
$10$	−0.0162832	−	0.00940110i	−0.00514919	−	0.00297289i
$11$		−	1.02228i		−	0.308230i	−0.988053	−	0.154115i	$-0.950747\pi$
$11$		−	1.02228i		−	0.308230i	0.988053	−	0.154115i	$-0.0492526\pi$
$12$	2.64142	−	0.558232i	0.762513	−	0.161148i
$13$	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
$17$	−2.83940	+	4.91798i	−0.688656	+	1.19279i	0.283617	+	0.958938i	$0.408465\pi$
$17$	−2.83940	+	4.91798i	−0.688656	+	1.19279i	−0.972273	+	0.233849i	$0.924868\pi$
$18$	0.806333	+	1.82248i	0.190054	+	0.429563i
$19$	−1.81237	+	1.04637i	−0.415786	+	0.240054i	−0.693273	−	0.720675i	$-0.743832\pi$
$19$	−1.81237	+	1.04637i	−0.415786	+	0.240054i	0.277487	+	0.960729i	$0.410498\pi$
$20$	−0.0220588	−	0.0382070i	−0.00493250	−	0.00854334i
$21$		0			0
$22$	−0.339550	+	0.588118i	−0.0723923	+	0.125387i
$23$			7.26133i			1.51409i	0.653362	+	0.757046i	$0.273358\pi$
$23$			7.26133i			1.51409i	−0.653362	+	0.757046i	$0.726642\pi$
$24$	−3.89275	−	1.26985i	−0.794605	−	0.259208i
$25$	−4.99920			−0.999840
$26$	−1.87104	−	3.24073i	−0.366941	−	0.635560i
$27$	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	$0.456722\pi$
$30$	0.0242269	−	0.0217629i	0.00442321	−	0.00397335i
$31$	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
$33$	1.68335	+	0.549124i	0.293033	+	0.0955902i
$34$	3.26700	−	1.88620i	0.560286	−	0.323481i
$35$		0			0
$36$	−0.499635	+	4.64936i	−0.0832725	+	0.774893i
$37$	1.23632	+	2.14137i	0.203250	+	0.352040i	0.949574	−	0.313543i	$-0.101516\pi$
$37$	1.23632	+	2.14137i	0.203250	+	0.352040i	−0.746324	+	0.665583i	$0.768183\pi$
$38$	1.39020			0.225520
$39$	−7.25839	+	6.52017i	−1.16227	+	1.04406i
$40$			0.0669116i			0.0105796i
$41$	−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	$0.889937\pi$
$44$	−1.37996	+	0.796722i	−0.208037	+	0.120110i
$45$	−0.0685785	−	0.0500700i	−0.0102231	−	0.00746399i
$46$	2.41184	−	4.17742i	0.355606	−	0.615928i
$47$	−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	$0.874922\pi$
$48$	−1.79060	−	1.99333i	−0.258450	−	0.287712i
$49$		0			0
$50$	2.87603	+	1.66048i	0.406732	+	0.234827i
$51$	−6.57302	−	7.31722i	−0.920407	−	1.02462i
$52$		−	8.78043i		−	1.21763i
$53$	10.0454	+	5.79973i	1.37985	+	0.796655i	0.992141	−	0.125128i	$-0.0399342\pi$
$53$	10.0454	+	5.79973i	1.37985	+	0.796655i	0.387706	+	0.921783i	$0.373268\pi$
$54$	−3.43412	+	0.348797i	−0.467324	+	0.0474652i
$55$		−	0.0289346i		−	0.00390155i
$56$		0			0
$57$	−0.749489	−	3.54640i	−0.0992723	−	0.469733i
$58$	2.70449			0.355117
$59$	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	$0.705112\pi$
$60$	0.0747626	−	0.0158002i	0.00965181	−	0.00203979i
$61$	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
$66$	−0.786035	−	0.875030i	−0.0967542	−	0.107709i
$67$	−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	$-0.451782\pi$
$68$	8.85160			1.07341
$69$	−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	$-0.156036\pi$
$72$	4.18201	−	5.72790i	0.492855	−	0.675040i
$73$	9.43889	+	5.44955i	1.10474	+	0.637821i	0.937462	−	0.348089i	$-0.113169\pi$
$73$	9.43889	+	5.44955i	1.10474	+	0.637821i	0.167277	+	0.985910i	$0.446503\pi$
$74$		−	1.64257i		−	0.190945i
$75$	2.68534	−	8.23195i	0.310076	−	0.950543i
$76$	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	0.0236086	−	0.999721i	$-0.492484\pi$
$79$	7.80018	−	13.5103i	0.877588	−	1.52003i	0.853980	−	0.520306i	$-0.174182\pi$
$80$	−0.0218930	+	0.0379198i	−0.00244772	+	0.00423957i
$81$	2.74119	+	8.57239i	0.304577	+	0.952488i
$82$	4.06007	−	2.34408i	0.448360	−	0.258861i
$83$	−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
$86$			1.54109i			0.166180i
$87$	−1.45805	−	6.89915i	−0.156319	−	0.739666i
$88$	2.41672			0.257623
$89$	−6.02582	−	10.4370i	−0.638736	−	1.10632i	−0.985711	−	0.168448i	$-0.946124\pi$
$89$	−6.02582	−	10.4370i	−0.638736	−	1.10632i	0.346975	−	0.937874i	$-0.387209\pi$
$90$	0.0228224	+	0.0515834i	0.00240569	+	0.00543736i
$91$		0			0
$92$	9.80194	−	5.65915i	1.02192	−	0.590007i
$93$	1.18837	+	5.62309i	0.123228	+	0.583087i
$94$	6.25921	−	3.61376i	0.645588	−	0.372730i
$95$	−0.0512971	+	0.0296164i	−0.00526297	+	0.00303858i
$96$	2.06135	+	9.75380i	0.210385	+	0.995493i
$97$	−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
$100$	3.89615	+	6.74833i	0.389615	+	0.674833i
$101$	−0.453847			−0.0451595			−0.0225797	−	0.999745i	$-0.507188\pi$
$101$	−0.453847			−0.0451595			−0.0225797	+	0.999745i	$0.507188\pi$
$102$	1.35104	+	6.39280i	0.133773	+	0.632981i
$103$			5.29218i			0.521454i	0.965413	+	0.260727i	$0.0839622\pi$
$103$			5.29218i			0.521454i	−0.965413	+	0.260727i	$0.916038\pi$
$104$	−6.65848	+	11.5328i	−0.652918	+	1.13089i
$105$		0			0
$106$	−3.85274	−	6.67315i	−0.374212	−	0.648153i
$107$	7.85273	−	4.53377i	0.759152	−	0.438296i	−0.0698394	−	0.997558i	$-0.522249\pi$
$107$	7.85273	−	4.53377i	0.759152	−	0.438296i	0.828991	+	0.559262i	$0.188915\pi$
$108$	−7.38750	−	3.32015i	−0.710863	−	0.319481i
$109$	−2.36514	+	4.09654i	−0.226539	+	0.392377i	−0.956780	−	0.290812i	$-0.906074\pi$
$109$	−2.36514	+	4.09654i	−0.226539	+	0.392377i	0.730241	+	0.683190i	$0.239408\pi$
$110$	−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	$0.813806\pi$
$114$	−0.746752	+	2.28918i	−0.0699398	+	0.214401i
$115$			0.205524i			0.0191652i
$116$	5.49565	+	3.17291i	0.510258	+	0.294598i
$117$	−6.83759	−	15.4544i	−0.632135	−	1.42876i
$118$		−	4.00054i		−	0.368280i
$119$		0			0
$120$	−0.110180	−	0.0359418i	−0.0100580	−	0.00328102i
$121$	9.95494			0.904994
$122$	−0.787084	−	1.36327i	−0.0712593	−	0.123425i
$123$	−8.16863	−	9.09349i	−0.736540	−	0.819932i
$124$	−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
$129$	3.93133	−	0.830838i	0.346134	−	0.0731512i
$130$	−0.0529577	−	0.0917255i	−0.00464470	−	0.00804486i
$131$	2.54463			0.222325			0.111162	−	0.993802i	$-0.464543\pi$
$131$	2.54463			0.222325			0.111162	+	0.993802i	$0.464543\pi$
$132$	−0.570672	−	2.70028i	−0.0496706	−	0.235029i
$133$		0			0
$134$			8.48964i			0.733393i
$135$	0.119285	−	0.0860296i	0.0102664	−	0.00740425i
$136$	−11.6263	−	6.71245i	−0.996948	−	0.575588i
$137$		−	11.3453i		−	0.969298i	−0.874709	−	0.484649i	$-0.838947\pi$
$137$		−	11.3453i		−	0.969298i	0.874709	−	0.484649i	$-0.161053\pi$
$138$	5.58324	+	6.21538i	0.475277	+	0.529088i
$139$	−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
$143$	2.87933	−	4.98715i	0.240782	−	0.417047i
$144$	4.24415	−	1.87777i	0.353679	−	0.156481i
$145$	−0.0997930	+	0.0576155i	−0.00828736	+	0.00478471i
$146$	−3.62012	−	6.27022i	−0.299603	−	0.518927i
$147$		0			0
$148$	1.92707	−	3.33778i	0.158404	−	0.274364i
$149$			15.9125i			1.30360i	0.758391	+	0.651800i	$0.225986\pi$
$149$			15.9125i			1.30360i	−0.758391	+	0.651800i	$0.774014\pi$
$150$	−4.27910	+	3.84389i	−0.349387	+	0.313852i
$151$	3.46016			0.281584			0.140792	−	0.990039i	$-0.455035\pi$
$151$	3.46016			0.281584			0.140792	+	0.990039i	$0.455035\pi$
$152$	−2.47366	−	4.28451i	−0.200640	−	0.347520i
$153$	15.5796	−	6.89301i	1.25954	−	0.557267i
$154$		0			0
$155$	0.0813354	−	0.0469590i	0.00653302	−	0.00377184i
$156$	14.4583	+	4.71644i	1.15759	+	0.377618i
$157$	−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
$159$	−14.9461	+	13.4260i	−1.18530	+	1.06475i
$160$	0.141084	−	0.0814550i	0.0111537	−	0.00643959i
$161$		0			0
$162$	1.27030	−	5.84216i	0.0998044	−	0.459003i
$163$	−5.17782	−	8.96824i	−0.405558	−	0.702447i	0.588828	−	0.808258i	$-0.299589\pi$
$163$	−5.17782	−	8.96824i	−0.405558	−	0.702447i	−0.994386	+	0.105811i	$0.966256\pi$
$164$	11.0003			0.858982
$165$	0.0476453	+	0.0155424i	0.00370918	+	0.00120997i
$166$			4.08417i			0.316993i
$167$	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
$170$	0.0924689	−	0.0533870i	0.00709204	−	0.00409459i
$171$	6.24229	+	0.670815i	0.477360	+	0.0512985i
$172$	−1.80802	+	3.13157i	−0.137860	+	0.238780i
$173$	−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	$0.225882\pi$
$174$	−1.45273	+	4.45335i	−0.110131	+	0.337608i
$175$		0			0
$176$	1.36959	+	0.790735i	0.103237	+	0.0596039i
$177$	−10.2054	+	2.15678i	−0.767083	+	0.162114i
$178$			8.00586i			0.600065i
$179$	0.175495	+	0.101322i	0.0131171	+	0.00757319i	0.506544	−	0.862214i	$-0.330923\pi$
$179$	0.175495	+	0.101322i	0.0131171	+	0.00757319i	−0.493427	+	0.869787i	$0.664256\pi$
$180$	−0.0141416	+	0.131595i	−0.00105405	+	0.00980852i
$181$			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
$184$	−17.1661			−1.26550
$185$	0.0349928	+	0.0606093i	0.00257272	+	0.00445608i
$186$	1.18403	−	3.62967i	0.0868174	−	0.266140i
$187$	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	$0.833108\pi$
$192$	0.391869	−	1.20128i	0.0282807	−	0.0866948i
$193$	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	$0.559221\pi$
$194$	5.19736			0.373148
$195$	−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	$0.818298\pi$
$198$	1.86309	−	0.824301i	0.132404	−	0.0585805i
$199$	8.38940	+	4.84362i	0.594709	+	0.343355i	0.766957	−	0.641698i	$-0.221770\pi$
$199$	8.38940	+	4.84362i	0.594709	+	0.343355i	−0.172249	+	0.985054i	$0.555103\pi$
$200$		−	11.8183i		−	0.835680i
$201$	21.6571	−	4.57696i	1.52757	−	0.322834i
$202$	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
$206$	1.75779	−	3.04458i	0.122471	−	0.212126i
$207$	12.8454	−	17.5937i	0.892815	−	1.22285i
$208$	−7.54694	+	4.35723i	−0.523286	+	0.302119i
$209$	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	$0.328208\pi$
$212$		−	18.0802i		−	1.24175i
$213$	13.0648	+	4.26186i	0.895184	+	0.292018i
$214$	−6.02354			−0.411761
$215$	−0.0328309	−	0.0568649i	−0.00223905	−	0.00387815i
$216$	7.18549	+	9.96309i	0.488910	+	0.677903i
$217$		0			0
$218$	2.72132	−	1.57115i	0.184311	−	0.106412i
$219$	−14.0436	+	12.6153i	−0.948982	+	0.852465i
$220$	−0.0390584	+	0.0225504i	−0.00263331	+	0.00152034i
$221$	−27.7037	+	15.9947i	−1.86355	+	1.07592i
$222$	2.70474	+	0.882313i	0.181531	+	0.0592170i
$223$	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
$226$	3.14921	+	5.45459i	0.209482	+	0.362834i
$227$	−28.7733			−1.90975			−0.954876	−	0.297005i	$-0.904012\pi$
$227$	−28.7733			−1.90975			−0.954876	+	0.297005i	$0.904012\pi$
$228$	−4.20311	+	3.77563i	−0.278358	+	0.250047i
$229$		−	8.86119i		−	0.585564i	−0.956179	−	0.292782i	$-0.905419\pi$
$229$		−	8.86119i		−	0.585564i	0.956179	−	0.292782i	$-0.0945810\pi$
$230$	0.0682645	−	0.118238i	0.00450122	−	0.00779635i
$231$		0			0
$232$	−4.81224	−	8.33505i	−0.315939	−	0.547223i
$233$	11.1789	−	6.45412i	0.732351	−	0.422823i	−0.0869305	−	0.996214i	$-0.527706\pi$
$233$	11.1789	−	6.45412i	0.732351	−	0.422823i	0.819282	+	0.573391i	$0.194372\pi$
$234$	−1.19950	+	11.1620i	−0.0784137	+	0.729681i
$235$	−0.153973	+	0.266688i	−0.0100441	+	0.0173968i
$236$	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	$0.724727\pi$
$240$	−0.0506809	−	0.0564190i	−0.00327144	−	0.00364183i
$241$			10.9868i			0.707719i	0.935299	+	0.353860i	$0.115131\pi$
$241$			10.9868i			0.707719i	−0.935299	+	0.353860i	$0.884869\pi$
$242$	−5.72705	−	3.30652i	−0.368149	−	0.212551i
$243$	−15.5882	−	0.0909006i	−0.999983	−	0.00583128i
$244$		−	3.69364i		−	0.236461i
$245$		0			0
$246$	1.67901	+	7.94466i	0.107050	+	0.506533i
$247$	−11.7887			−0.750098
$248$	3.92218	+	6.79341i	0.249058	+	0.431382i
$249$	10.4187	−	2.20187i	0.660259	−	0.139538i
$250$	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
$255$	−0.186042	−	0.207106i	−0.0116504	−	0.0129695i
$256$	4.39208	+	7.60731i	0.274505	+	0.475457i
$257$	17.7228			1.10552			0.552760	−	0.833340i	$-0.313575\pi$
$257$	17.7228			1.10552			0.552760	+	0.833340i	$0.313575\pi$
$258$	−2.53765	−	0.827804i	−0.157987	−	0.0515368i
$259$		0			0
$260$		−	0.248521i		−	0.0154126i
$261$	12.1437	+	1.30500i	0.751676	+	0.0807774i
$262$	−1.46392	−	0.845193i	−0.0904411	−	0.0522162i
$263$			2.89866i			0.178739i	0.995999	+	0.0893695i	$0.0284852\pi$
$263$			2.89866i			0.178739i	−0.995999	+	0.0893695i	$0.971515\pi$
$264$	−1.29815	+	3.97950i	−0.0798956	+	0.244921i
$265$	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
$269$	10.9469	−	18.9606i	0.667444	−	1.15605i	−0.311172	−	0.950354i	$-0.600722\pi$
$269$	10.9469	−	18.9606i	0.667444	−	1.15605i	0.978616	−	0.205694i	$-0.0659451\pi$
$270$	−0.0971990	+	0.00987232i	−0.00591534	+	0.000600810i
$271$	7.77992	−	4.49174i	0.472596	−	0.272854i	−0.244730	−	0.969591i	$-0.578699\pi$
$271$	7.77992	−	4.49174i	0.472596	−	0.272854i	0.717326	+	0.696738i	$0.245366\pi$
$272$	−4.39254	−	7.60811i	−0.266337	−	0.461309i
$273$		0			0
$274$	−3.76834	+	6.52695i	−0.227654	+	0.394308i
$275$			5.11060i			0.308181i
$276$	4.05351	+	19.1802i	0.243993	+	1.15451i
$277$	15.9018			0.955448			0.477724	−	0.878510i	$-0.341462\pi$
$277$	15.9018			0.955448			0.477724	+	0.878510i	$0.341462\pi$
$278$	1.16936	+	2.02538i	0.0701333	+	0.121474i
$279$	−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	$0.382903\pi$
$282$	2.58844	+	12.2479i	0.154140	+	0.729351i
$283$	−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
$285$	−0.0212135	−	0.100377i	−0.00125658	−	0.00594583i
$286$	−3.31295	+	1.91273i	−0.195899	+	0.113102i
$287$		0			0
$288$	−17.1684	−	1.84497i	−1.01166	−	0.108716i
$289$	−7.62438	−	13.2058i	−0.448493	−	0.776813i
$290$	0.0765476			0.00449503
$291$	−2.80201	−	13.2584i	−0.164257	−	0.777224i
$292$		−	16.9885i		−	0.994178i
$293$	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
$296$	−5.06229	+	2.92272i	−0.294240	+	0.169879i
$297$	−3.10723	−	4.30835i	−0.180300	−	0.249996i
$298$	5.28530	−	9.15440i	0.306169	−	0.530300i
$299$	−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
$303$	0.243786	−	0.747329i	0.0140051	−	0.0429329i
$304$		−	3.23746i		−	0.185681i
$305$	0.0580853	+	0.0335356i	0.00332596	+	0.00192024i
$306$	−11.2524	−	1.20922i	−0.643259	−	0.0691266i
$307$		−	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
$310$	−0.0623894			−0.00354348
$311$	−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	$-0.364642\pi$
$312$	−15.4139	−	17.1591i	−0.872643	−	0.971444i
$313$	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	$0.455483\pi$
$318$	13.0579	−	2.75962i	0.732249	−	0.154752i
$319$	2.08096	+	3.60433i	0.116512	+	0.201804i
$320$	−0.0206485			−0.00115429
$321$	3.24743	+	15.3660i	0.181254	+	0.857649i
$322$		0			0
$323$		−	11.8843i		−	0.661258i
$324$	9.43536	−	10.3812i	0.524186	−	0.576735i
$325$	−24.3883	−	14.0806i	−1.35282	−	0.781051i
$326$			6.87921i			0.381004i
$327$	−5.47513	−	6.09503i	−0.302776	−	0.337056i
$328$	−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	0.397999	+	0.917386i	$0.369705\pi$
$331$	−10.8338	+	18.7647i	−0.595480	+	1.03140i	−0.993479	+	0.114016i	$0.963629\pi$
$332$	−4.79156	+	8.29923i	−0.262971	+	0.455479i
$333$	0.792591	−	7.37547i	0.0434337	−	0.404174i
$334$	−3.38617	+	1.95501i	−0.185283	+	0.106973i
$335$	−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	$-0.0752147\pi$
$338$		−	12.4438i		−	0.676853i
$339$	12.2168	−	10.9743i	0.663528	−	0.596044i
$340$	0.250535			0.0135872
$341$	−1.69607	−	2.93768i	−0.0918474	−	0.159084i
$342$	−3.36836	−	2.45928i	−0.182140	−	0.132983i
$343$		0			0
$344$	4.74955	−	2.74215i	0.256078	−	0.147847i
$345$	−0.338427	−	0.110398i	−0.0182203	−	0.00594363i
$346$	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	$0.284562\pi$
$348$	−8.17670	+	7.34508i	−0.438317	+	0.393738i
$349$	−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
$352$	−2.94200	−	5.09570i	−0.156809	−	0.271601i
$353$	−14.0422			−0.747391			−0.373696	−	0.927551i	$-0.621910\pi$
$353$	−14.0422			−0.747391			−0.373696	+	0.927551i	$0.621910\pi$
$354$	6.58751	+	2.14891i	0.350122	+	0.114213i
$355$		−	0.224567i		−	0.0119188i
$356$	−9.39250	+	16.2683i	−0.497802	+	0.862218i
$357$		0			0
$358$	−0.0673081	−	0.116581i	−0.00355734	−	0.00616150i
$359$	23.5052	−	13.5707i	1.24056	−	0.716235i	0.271348	−	0.962481i	$-0.412531\pi$
$359$	23.5052	−	13.5707i	1.24056	−	0.716235i	0.969207	+	0.246246i	$0.0791973\pi$
$360$	0.118367	−	0.162122i	0.00623851	−	0.00854459i
$361$	−7.31022	+	12.6617i	−0.384748	+	0.666403i
$362$	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
$366$	2.66762	−	0.563769i	0.139439	−	0.0294687i
$367$			6.88076i			0.359173i	0.983742	+	0.179586i	$0.0574759\pi$
$367$			6.88076i			0.359173i	−0.983742	+	0.179586i	$0.942524\pi$
$368$	−9.72828	−	5.61662i	−0.507122	−	0.292787i
$369$	19.3616	−	8.56629i	1.00793	−	0.445943i
$370$		−	0.0464912i		−	0.00241696i
$371$		0			0
$372$	6.66434	−	5.98654i	0.345530	−	0.310388i
$373$	−0.247851			−0.0128332			−0.00641662	−	0.999979i	$-0.502042\pi$
$373$	−0.247851			−0.0128332			−0.00641662	+	0.999979i	$0.502042\pi$
$374$	−1.92824	−	3.33980i	−0.0997067	−	0.172697i
$375$	0.152023	−	0.466030i	0.00785046	−	0.0240657i
$376$	−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
$381$	−2.34896	+	7.20077i	−0.120341	+	0.368907i
$382$	4.58476	+	7.94104i	0.234577	+	0.406299i
$383$	−0.327089			−0.0167135			−0.00835675	−	0.999965i	$-0.502660\pi$
$383$	−0.327089			−0.0167135			−0.00835675	+	0.999965i	$0.502660\pi$
$384$	14.2083	−	12.7632i	0.725063	−	0.651320i
$385$		0			0
$386$		−	14.0017i		−	0.712665i
$387$	−0.743625	+	6.91982i	−0.0378006	+	0.351754i
$388$	10.5613	+	6.09755i	0.536167	+	0.309556i
$389$		−	6.60890i		−	0.335085i	−0.985865	−	0.167542i	$-0.946417\pi$
$389$		−	6.60890i		−	0.335085i	0.985865	−	0.167542i	$-0.0535831\pi$
$390$	0.179486	−	0.0379323i	0.00908865	−	0.00192078i
$391$	−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
$395$	0.220776	−	0.382394i	0.0111084	−	0.0192404i
$396$	4.75297	+	0.510768i	0.238846	+	0.0256671i
$397$	6.50435	−	3.75529i	0.326444	−	0.188472i	−0.327817	−	0.944741i	$-0.606313\pi$
$397$	6.50435	−	3.75529i	0.326444	−	0.188472i	0.654261	+	0.756269i	$0.272980\pi$
$398$	−3.21760	−	5.57305i	−0.161284	−	0.279352i
$399$		0			0
$400$	3.86687	−	6.69762i	0.193344	−	0.334881i
$401$			6.33464i			0.316337i	0.987412	+	0.158168i	$0.0505589\pi$
$401$			6.33464i			0.316337i	−0.987412	+	0.158168i	$0.949441\pi$
$402$	−13.9795	−	4.56024i	−0.697234	−	0.227444i
$403$	18.6919			0.931109
$404$	0.353708	+	0.612640i	0.0175976	+	0.0304800i
$405$	0.0775865	+	0.242632i	0.00385530	+	0.0120565i
$406$		0			0
$407$	2.18909	−	1.26387i	0.108509	−	0.0626479i
$408$	17.2982	−	15.5389i	0.856388	−	0.769289i
$409$	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
$411$	18.6818	+	6.09420i	0.921508	+	0.300605i
$412$	7.14382	−	4.12448i	0.351951	−	0.203199i
$413$		0			0
$414$	−13.2336	+	5.85504i	−0.650398	+	0.287760i
$415$	−0.0870078	−	0.150702i	−0.00427105	−	0.00739767i
$416$	32.4229			1.58966
$417$	4.53632	−	4.07496i	0.222145	−	0.199551i
$418$		−	1.42118i		−	0.0695122i
$419$	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	$0.803775\pi$
$422$	8.12254	−	4.68955i	0.395399	−	0.228284i
$423$	29.8489	−	13.2062i	1.45130	−	0.642109i
$424$	−13.7108	+	23.7478i	−0.665855	+	1.15330i
$425$	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
$429$	6.66547	+	7.42013i	0.321812	+	0.358247i
$430$			0.0436190i			0.00210349i
$431$	1.15145	+	0.664787i	0.0554632	+	0.0320217i	0.527475	−	0.849570i	$-0.323139\pi$
$431$	1.15145	+	0.664787i	0.0554632	+	0.0320217i	−0.472012	+	0.881592i	$0.656472\pi$
$432$	0.812269	+	7.99729i	0.0390803	+	0.384770i
$433$			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
$436$	7.37313			0.353109
$437$	−7.59804	−	13.1602i	−0.363464	−	0.629537i
$438$	12.2694	−	2.59300i	0.586257	−	0.123898i
$439$	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	$0.752786\pi$
$444$	4.46104	+	4.96612i	0.211711	+	0.235681i
$445$	−0.170554	−	0.295409i	−0.00808505	−	0.0140037i
$446$	−1.98498			−0.0939916
$447$	−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	$0.889682\pi$
$450$	−4.03102	−	9.11095i	−0.190024	−	0.429494i
$451$	6.24803	+	3.60730i	0.294208	+	0.169861i
$452$			14.7787i			0.695129i
$453$	−1.85864	+	5.69769i	−0.0873266	+	0.267701i
$454$	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	−0.517353	−	0.855772i	$-0.673083\pi$
$457$	10.3135	−	17.8635i	0.482444	−	0.835617i	0.999797	+	0.0201547i	$0.00641589\pi$
$458$	−2.94323	+	5.09782i	−0.137528	+	0.238206i
$459$	2.98172	+	29.3569i	0.139175	+	1.37026i
$460$	0.277433	−	0.160176i	0.0129354	−	0.00746825i
$461$	−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	$0.157728\pi$
$464$		−	6.29814i		−	0.292384i
$465$	0.0336356	+	0.159155i	0.00155981	+	0.00738066i
$466$	−8.57490			−0.397224
$467$	4.61994	+	8.00197i	0.213785	+	0.370287i	0.952896	−	0.303297i	$-0.0980874\pi$
$467$	4.61994	+	8.00197i	0.213785	+	0.370287i	−0.739111	+	0.673584i	$0.764754\pi$
$468$	−15.5327	+	21.2744i	−0.717999	+	0.983409i
$469$		0			0
$470$	0.177160	−	0.102283i	0.00817179	−	0.00471798i
$471$	−5.85514	−	27.7051i	−0.269790	−	1.27658i
$472$	−12.3294	+	7.11839i	−0.567507	+	0.327650i
$473$	−2.05385	+	1.18579i	−0.0944361	+	0.0545227i
$474$	−3.71147	−	17.5618i	−0.170474	−	0.806640i
$475$	9.06039	−	5.23102i	0.415719	−	0.240016i
$476$		0			0
$477$	−14.0796	−	31.8229i	−0.644660	−	1.45707i
$478$	1.86286	+	3.22657i	0.0852052	+	0.147580i
$479$	17.5448			0.801643			0.400822	−	0.916156i	$-0.368725\pi$
$479$	17.5448			0.801643			0.400822	+	0.916156i	$0.368725\pi$
$480$	0.0583442	+	0.276071i	0.00266304	+	0.0126008i
$481$			13.9288i			0.635097i
$482$	3.64923	−	6.32066i	0.166218	−	0.287898i
$483$		0			0
$484$	−7.75843	−	13.4380i	−0.352656	−	0.610818i
$485$	−0.191777	+	0.110723i	−0.00870817	+	0.00502766i
$486$	8.93766	+	5.22989i	0.405420	+	0.237232i
$487$	21.5949	−	37.4034i	0.978558	−	1.69491i	0.310900	−	0.950442i	$-0.399369\pi$
$487$	21.5949	−	37.4034i	0.978558	−	1.69491i	0.667657	−	0.744469i	$-0.267297\pi$
$488$	−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	$0.462074\pi$
$492$	−5.90888	+	18.1137i	−0.266393	+	0.816631i
$493$		−	23.1196i		−	1.04125i
$494$	6.78202	+	3.91560i	0.305138	+	0.176171i
$495$	−0.0511857	+	0.0701066i	−0.00230063	+	0.00315106i
$496$			5.13324i			0.230489i
$497$		0			0
$498$	−6.72521	−	2.19383i	−0.301364	−	0.0983078i
$499$	5.31518			0.237940			0.118970	−	0.992898i	$-0.462041\pi$
$499$	5.31518			0.237940			0.118970	+	0.992898i	$0.462041\pi$
$500$	0.220570	+	0.382039i	0.00986421	+	0.0170853i
$501$	6.81279	+	7.58414i	0.304373	+	0.338834i
$502$	−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
$507$	−31.7441	+	6.70873i	−1.40981	+	0.297945i
$508$	−3.40810	−	5.90300i	−0.151210	−	0.261903i
$509$	−13.6331			−0.604276			−0.302138	−	0.953264i	$-0.597700\pi$
$509$	−13.6331			−0.604276			−0.302138	+	0.953264i	$0.597700\pi$
$510$	0.0382397	+	0.180941i	0.00169328	+	0.00801221i
$511$		0			0
$512$			16.2184i			0.716760i
$513$	−4.45767	+	9.91855i	−0.196811	+	0.437915i
$514$	−10.1959	−	5.88661i	−0.449722	−	0.259647i
$515$			0.149789i			0.00660051i
$516$	−4.18543	−	4.65931i	−0.184253	−	0.205115i
$517$	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
$521$	5.11259	−	8.85526i	0.223987	−	0.387956i	−0.732028	−	0.681274i	$-0.761426\pi$
$521$	5.11259	−	8.85526i	0.223987	−	0.387956i	0.956015	+	0.293318i	$0.0947595\pi$
$522$	−6.55279	−	4.78427i	−0.286808	−	0.209402i
$523$	−4.48150	+	2.58740i	−0.195962	+	0.113139i	−0.594771	−	0.803895i	$-0.702757\pi$
$523$	−4.48150	+	2.58740i	−0.195962	+	0.113139i	0.398808	+	0.917034i	$0.369424\pi$
$524$	−1.98317	−	3.43495i	−0.0866350	−	0.150056i
$525$		0			0
$526$	0.962785	−	1.66759i	0.0419794	−	0.0727105i
$527$			18.8434i			0.820831i
$528$	−2.03775	+	1.83050i	−0.0886816	+	0.0796622i
$529$	−29.7269			−1.29247
$530$	−0.109048	−	0.188876i	−0.00473673	−	0.00820426i
$531$	1.93039	−	17.9632i	0.0837716	−	0.779538i
$532$		0			0
$533$	−34.4288	+	19.8775i	−1.49128	+	0.860990i
$534$	−13.1829	−	4.30038i	−0.570479	−	0.186096i
$535$	0.222263	−	0.128324i	0.00960927	−	0.00554791i
$536$	26.1645	−	15.1061i	1.13013	−	0.652484i
$537$	−0.261111	+	0.234554i	−0.0112678	+	0.0101218i
$538$	−12.5955	+	7.27199i	−0.543029	+	0.313518i
$539$		0			0
$540$	−0.209095	−	0.0939732i	−0.00899803	−	0.00404396i
$541$	12.7197	+	22.0312i	0.546864	+	0.947196i	0.998487	+	0.0549871i	$0.0175118\pi$
$541$	12.7197	+	22.0312i	0.546864	+	0.947196i	−0.451623	+	0.892209i	$0.649155\pi$
$542$	−5.96769			−0.256334
$543$	−10.3125	−	3.36405i	−0.442554	−	0.144365i
$544$			32.6857i			1.40139i
$545$	−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	$0.615640\pi$
$548$	−15.3149	+	8.84205i	−0.654219	+	0.377714i
$549$	−2.87635	−	6.50115i	−0.122759	−	0.277462i
$550$	1.69748	−	2.94012i	0.0723807	−	0.125367i
$551$	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
$555$	−0.118599	+	0.0250645i	−0.00503425	+	0.00106393i
$556$			5.48757i			0.232725i
$557$	−16.9788	−	9.80269i	−0.719413	−	0.415353i	0.0951237	−	0.995465i	$-0.469675\pi$
$557$	−16.9788	−	9.80269i	−0.719413	−	0.415353i	−0.814537	+	0.580112i	$0.803009\pi$
$558$	5.34079	+	3.89938i	0.226094	+	0.165074i
$559$		−	13.0683i		−	0.552728i
$560$		0			0
$561$	−7.48028	+	6.71949i	−0.315817	+	0.283697i
$562$	3.45427			0.145710
$563$	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	$0.734662\pi$
$564$	−9.10942	+	27.9251i	−0.383576	+	1.17586i
$565$	−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	$0.718590\pi$
$570$	−0.0211360	+	0.0647928i	−0.000885290	+	0.00271387i
$571$	−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	$0.942968\pi$
$572$	−8.97609			−0.375309
$573$	17.7858	−	15.9769i	0.743014	−	0.667445i
$574$		0			0
$575$		−	36.3008i		−	1.51385i
$576$	1.76760	+	1.29054i	0.0736498	+	0.0537726i
$577$	10.5403	+	6.08542i	0.438797	+	0.253339i	0.703087	−	0.711104i	$-0.251804\pi$
$577$	10.5403	+	6.08542i	0.438797	+	0.253339i	−0.264290	+	0.964443i	$0.585138\pi$
$578$			10.1297i			0.421340i
$579$	−35.7182	+	7.54861i	−1.48440	+	0.313710i
$580$	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
$584$	−12.8829	+	22.3139i	−0.533100	+	0.923356i
$585$	−0.193531	−	0.437420i	−0.00800150	−	0.0180851i
$586$	−13.1399	+	7.58633i	−0.542805	+	0.313388i
$587$	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
$590$		−	0.113231i		−	0.00466165i
$591$	−24.9763	−	8.14750i	−1.02739	−	0.335143i
$592$	−3.82518			−0.157214
$593$	−9.15123	−	15.8504i	−0.375796	−	0.650897i	0.614650	−	0.788800i	$-0.289297\pi$
$593$	−9.15123	−	15.8504i	−0.375796	−	0.650897i	−0.990446	+	0.137903i	$0.955964\pi$
$594$	0.356569	+	3.51064i	0.0146302	+	0.144043i
$595$		0			0
$596$	21.4799	−	12.4015i	0.879853	−	0.507983i
$597$	−12.4822	+	11.2127i	−0.510861	+	0.458903i
$598$	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	$0.0346651\pi$
$600$	19.4606	+	6.34825i	0.794477	+	0.259166i
$601$	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
$604$	−2.69670	−	4.67082i	−0.109727	−	0.190053i
$605$	0.281764			0.0114553
$606$	−0.388473	+	0.348964i	−0.0157807	+	0.0141757i
$607$		−	24.9536i		−	1.01283i	−0.862289	−	0.506417i	$-0.830970\pi$
$607$		−	24.9536i		−	1.01283i	0.862289	−	0.506417i	$-0.169030\pi$
$608$	−6.02264	+	10.4315i	−0.244250	+	0.423054i
$609$		0			0
$610$	−0.0222776	−	0.0385859i	−0.000901992	−	0.00156230i
$611$	−53.0772	+	30.6441i	−2.14727	+	1.23973i
$612$	−21.4468	−	15.6586i	−0.866936	−	0.632961i
$613$	−14.0285	+	24.2980i	−0.566605	+	0.981388i	0.430294	+	0.902689i	$0.358410\pi$
$613$	−14.0285	+	24.2980i	−0.566605	+	0.981388i	−0.996898	+	0.0786994i	$0.974923\pi$
$614$	−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	$0.423015\pi$
$618$	4.06916	+	4.52987i	0.163686	+	0.182218i
$619$			19.9635i			0.802399i	0.915991	+	0.401200i	$0.131407\pi$
$619$			19.9635i			0.802399i	−0.915991	+	0.401200i	$0.868593\pi$
$620$	−0.126778	−	0.0731955i	−0.00509154	−	0.00293960i
$621$	22.0708	+	30.6024i	0.885669	+	1.22803i
$622$			13.6510i			0.547354i
$623$		0			0
$624$	−3.12097	−	14.7677i	−0.124939	−	0.591181i
$625$	24.9880			0.999519
$626$	−0.239503	−	0.414831i	−0.00957245	−	0.0165800i
$627$	−3.62543	+	0.766191i	−0.144786	+	0.0305987i
$628$	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
$633$	−16.3421	−	18.1923i	−0.649540	−	0.723081i
$634$	−7.28384	−	12.6160i	−0.289278	−	0.501044i
$635$	0.123772			0.00491176
$636$	29.7718	+	9.71185i	1.18053	+	0.385100i
$637$		0			0
$638$		−	2.76475i		−	0.109458i
$639$	−14.0356	+	19.2239i	−0.555240	+	0.760485i
$640$	−0.270290	−	0.156052i	−0.0106841	−	0.00616849i
$641$		−	3.85994i		−	0.152459i	−0.997090	−	0.0762293i	$-0.975712\pi$
$641$		−	3.85994i		−	0.152459i	0.997090	−	0.0762293i	$-0.0242881\pi$
$642$	3.23557	−	9.91868i	0.127698	−	0.391459i
$643$	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
$647$	−21.8246	+	37.8013i	−0.858013	+	1.48612i	0.0158075	+	0.999875i	$0.494968\pi$
$647$	−21.8246	+	37.8013i	−0.858013	+	1.48612i	−0.873821	+	0.486248i	$0.838365\pi$
$648$	−20.2655	+	6.48029i	−0.796103	+	0.254570i
$649$	5.33162	−	3.07821i	0.209284	−	0.120830i
$650$	9.35369	+	16.2011i	0.366882	+	0.635458i
$651$		0			0
$652$	−8.07072	+	13.9789i	−0.316074	+	0.547456i
$653$		−	7.45002i		−	0.291542i	−0.989318	−	0.145771i	$-0.953434\pi$
$653$		−	7.45002i		−	0.291542i	0.989318	−	0.145771i	$-0.0465663\pi$
$654$	1.12538	+	5.32501i	0.0440057	+	0.208225i
$655$	0.0720229			0.00281417
$656$	−5.45884	−	9.45498i	−0.213132	−	0.369155i
$657$	−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	$0.387472\pi$
$660$	−0.0161523	−	0.0764286i	−0.000628726	−	0.00297498i
$661$	−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
$663$	−11.4566	−	54.2100i	−0.444939	−	2.10534i
$664$	12.5871	−	7.26719i	0.488476	−	0.282022i
$665$		0			0
$666$	−2.90573	+	3.97984i	−0.112595	+	0.154216i
$667$	−14.7812	−	25.6017i	−0.572329	−	0.991303i
$668$	−9.17449			−0.354972
$669$	1.07015	+	5.06369i	0.0413743	+	0.195773i
$670$			0.240290i			0.00928322i
$671$	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	$0.877734\pi$
$674$	−14.5498	+	8.40036i	−0.560439	+	0.323570i
$675$	−21.0688	+	15.1950i	−0.810939	+	0.584857i
$676$	14.5991	−	25.2864i	0.561504	−	0.972553i
$677$	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	$-0.0797667\pi$
$678$	−10.6734	+	2.25570i	−0.409911	+	0.0866297i
$679$		0			0
$680$	−0.329070	−	0.189989i	−0.0126193	−	0.00728573i
$681$	15.4557	−	47.3797i	0.592264	−	1.81559i
$682$			2.25339i			0.0862867i
$683$	20.5530	+	11.8663i	0.786438	+	0.454050i	0.838707	−	0.544583i	$-0.183312\pi$
$683$	20.5530	+	11.8663i	0.786438	+	0.454050i	−0.0522688	+	0.998633i	$0.516645\pi$
$684$	−3.95943	−	8.94916i	−0.151393	−	0.342180i
$685$		−	0.321118i		−	0.0122693i
$686$		0			0
$687$	14.5913	+	4.75982i	0.556693	+	0.181599i
$688$	3.58886			0.136824
$689$	32.6707	+	56.5874i	1.24466	+	2.15581i
$690$	0.158028	+	0.175920i	0.00601601	+	0.00669714i
$691$	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
$696$	16.3098	−	3.44689i	0.618223	−	0.130654i
$697$	−20.0386	−	34.7079i	−0.759016	−	1.31465i
$698$	7.42834			0.281167
$699$	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	$0.994748\pi$
$702$	−17.7356	−	7.97085i	−0.669386	−	0.300840i
$703$	−4.48135	−	2.58731i	−0.169017	−	0.0975821i
$704$			0.745784i			0.0281078i
$705$	−0.356436	−	0.396792i	−0.0134242	−	0.0149441i
$706$	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	−0.976896	−	0.213717i	$-0.931443\pi$
$709$	−8.07767	+	13.9909i	−0.303363	+	0.525441i	0.673532	+	0.739158i	$0.264776\pi$
$710$	−0.0745897	+	0.129193i	−0.00279930	+	0.00484853i
$711$	−42.7992	+	18.9359i	−1.60509	+	0.710153i
$712$	24.6735	−	14.2453i	0.924680	−	0.533864i
$713$	12.0473	+	20.8665i	0.451174	+	0.781456i
$714$		0			0
$715$	0.0814965	−	0.141156i	0.00304779	−	0.00527894i
$716$		−	0.315864i		−	0.0118044i
$717$	7.22666	−	6.49167i	0.269884	−	0.242436i
$718$	−18.0300			−0.672872
$719$	22.5953	+	39.1361i	0.842661	+	1.45953i	0.887637	+	0.460543i	$0.152345\pi$
$719$	22.5953	+	39.1361i	0.842661	+	1.45953i	−0.0449767	+	0.998988i	$0.514321\pi$
$720$	0.120126	−	0.0531481i	0.00447683	−	0.00198071i
$721$		0			0
$722$	8.41110	−	4.85615i	0.313029	−	0.180727i
$723$	−18.0914	−	5.90158i	−0.672825	−	0.219482i
$724$	8.45395	−	4.88089i	0.314189	−	0.181397i
$725$	17.6260	−	10.1764i	0.654613	−	0.377941i
$726$	8.52099	−	7.65436i	0.316244	−	0.284080i
$727$	−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
$730$	−0.102463	−	0.177472i	−0.00379234	−	0.00656853i
$731$	13.1742			0.487264
$732$	6.08214	+	1.98405i	0.224802	+	0.0733327i
$733$			12.2166i			0.451230i	0.974217	+	0.225615i	$0.0724392\pi$
$733$			12.2166i			0.451230i	−0.974217	+	0.225615i	$0.927561\pi$
$734$	2.28543	−	3.95849i	0.0843569	−	0.146110i
$735$		0			0
$736$	20.8972	+	36.1949i	0.770280	+	1.33416i
$737$	−11.3143	+	6.53234i	−0.416769	+	0.240622i
$738$	−13.9840	−	1.50276i	−0.514757	−	0.0553174i
$739$	10.3536	−	17.9330i	0.380863	−	0.659674i	−0.610323	−	0.792153i	$-0.708960\pi$
$739$	10.3536	−	17.9330i	0.380863	−	0.659674i	0.991186	+	0.132478i	$0.0422935\pi$
$740$	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	$0.596756\pi$
$744$	−13.2932	+	2.80936i	−0.487352	+	0.102996i
$745$			0.450385i			0.0165008i
$746$	0.142588	+	0.0823233i	0.00522053	+	0.00301407i
$747$	−1.97074	+	18.3387i	−0.0721056	+	0.670980i
$748$		−	9.04885i		−	0.330859i
$749$		0			0
$750$	−0.242250	+	0.217612i	−0.00884571	+	0.00794606i
$751$	23.7108			0.865221			0.432610	−	0.901581i	$-0.357593\pi$
$751$	23.7108			0.865221			0.432610	+	0.901581i	$0.357593\pi$
$752$	−8.41562	−	14.5763i	−0.306886	−	0.531542i
$753$	−13.0121	+	39.8886i	−0.474186	+	1.45362i
$754$	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
$759$	−3.98737	+	12.2233i	−0.144732	+	0.443679i
$760$	−0.0700143	−	0.121268i	−0.00253969	−	0.00439887i
$761$	−48.7535			−1.76731			−0.883656	−	0.468137i	$-0.844925\pi$
$761$	−48.7535			−1.76731			−0.883656	+	0.468137i	$0.844925\pi$
$762$	3.74308	−	3.36238i	0.135597	−	0.121806i
$763$		0			0
$764$			21.5154i			0.778401i
$765$	0.440965	−	0.195099i	0.0159431	−	0.00705382i
$766$	0.188174	+	0.108642i	0.00679900	+	0.00392540i
$767$			33.9240i			1.22493i
$768$	−14.8858	+	3.14594i	−0.537146	+	0.113519i
$769$	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
$773$	13.3567	−	23.1345i	0.480408	−	0.832092i	−0.519339	−	0.854568i	$-0.673822\pi$
$773$	13.3567	−	23.1345i	0.480408	−	0.832092i	0.999747	+	0.0224765i	$0.00715509\pi$
$774$	2.72621	−	3.73396i	0.0979917	−	0.134215i
$775$	−14.3659	+	8.29417i	−0.516039	+	0.297935i
$776$	−9.24794	−	16.0179i	−0.331982	−	0.575009i
$777$		0			0
$778$	−2.19514	+	3.80209i	−0.0786994	+	0.136311i
$779$		−	14.7692i		−	0.529161i
$780$	0.409227	+	0.133494i	0.0146527	+	0.00477985i
$781$	−8.11095			−0.290233
$782$	13.6963	+	23.7228i	0.489780	+	0.848324i
$783$	−8.67191	+	19.2955i	−0.309909	+	0.689564i
$784$		0			0
$785$	−0.400742	+	0.231368i	−0.0143031	+	0.00825789i
$786$	2.17809	−	1.95656i	0.0776898	−	0.0697884i
$787$	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
$789$	−4.77309	−	1.55703i	−0.169926	−	0.0554316i
$790$	−0.254023	+	0.146660i	−0.00903775	+	0.00521795i
$791$		0			0
$792$	−5.85554	−	4.27520i	−0.208068	−	0.151913i
$793$	6.67436	+	11.5603i	0.237014	+	0.410520i
$794$	−4.98925			−0.177062
$795$	−0.423033	+	0.380008i	−0.0150034	+	0.0134775i
$796$		−	15.0996i		−	0.535191i
$797$	−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
$800$	−24.9191	+	14.3871i	−0.881023	+	0.508659i
$801$	−3.86308	+	35.9479i	−0.136495	+	1.27016i
$802$	2.10404	−	3.64430i	0.0742962	−	0.128685i
$803$	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
$807$	25.3413	+	28.2105i	0.892057	+	0.993057i
$808$		−	1.07291i		−	0.0377449i
$809$	6.40871	+	3.70007i	0.225318	+	0.130087i	0.608410	−	0.793623i	$-0.291808\pi$
$809$	6.40871	+	3.70007i	0.225318	+	0.130087i	−0.383092	+	0.923710i	$0.625141\pi$
$810$	0.0359546	−	0.165356i	0.00126331	−	0.00581002i
$811$		−	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
$814$	−1.67917			−0.0588550
$815$	−0.146553	−	0.253836i	−0.00513351	−	0.00889150i
$816$	14.8874	−	3.14627i	0.521163	−	0.110141i
$817$	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	$0.787416\pi$
$822$	−8.72345	−	9.71112i	−0.304265	−	0.338714i
$823$	−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	$0.928815\pi$
$824$	−12.5109			−0.435838
$825$	−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	$-0.145013\pi$
$828$	−33.7605	−	3.62801i	−1.17326	−	0.126082i
$829$	35.9640	+	20.7638i	1.24908	+	0.721158i	0.970927	−	0.239378i	$-0.0769434\pi$
$829$	35.9640	+	20.7638i	1.24908	+	0.721158i	0.278156	+	0.960536i	$0.410277\pi$
$830$			0.115598i			0.00401247i
$831$	−8.54173	+	26.1848i	−0.296309	+	0.908340i
$832$	−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
$836$	1.66733	−	2.88791i	0.0576659	−	0.0998803i
$837$	7.06797	−	15.7266i	0.244305	−	0.543591i
$838$	−1.03146	+	0.595515i	−0.0356312	+	0.0205717i
$839$	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
$842$		−	2.52780i		−	0.0871138i
$843$	−1.86228	−	8.81184i	−0.0641402	−	0.303496i
$844$	22.0072			0.757519
$845$	0.265099	+	0.459164i	0.00911967	+	0.0157957i
$846$	−21.5584	−	2.31673i	−0.741193	−	0.0796509i
$847$		0			0
$848$	−15.5403	+	8.97217i	−0.533654	+	0.308106i
$849$	−6.72363	−	31.8146i	−0.230754	−	1.09187i
$850$	−16.3324	+	9.42951i	−0.560196	+	0.323429i
$851$	−15.5492	+	8.97735i	−0.533020	+	0.307739i
$852$	−4.42910	−	20.9574i	−0.151738	−	0.717989i
$853$	−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
$856$	10.7180	+	18.5642i	0.366334	+	0.634510i
$857$	−18.3431			−0.626590			−0.313295	−	0.949656i	$-0.601433\pi$
$857$	−18.3431			−0.626590			−0.313295	+	0.949656i	$0.601433\pi$
$858$	−1.37004	−	6.48271i	−0.0467725	−	0.221316i
$859$			3.10760i			0.106030i	0.998594	+	0.0530150i	$0.0168831\pi$
$859$			3.10760i			0.106030i	−0.998594	+	0.0530150i	$0.983117\pi$
$860$	−0.0511739	+	0.0886358i	−0.00174502	+	0.00302246i
$861$		0			0
$862$	−0.441616	−	0.764902i	−0.0150415	−	0.0260527i
$863$	35.8587	−	20.7030i	1.22064	−	0.704739i	0.255589	−	0.966786i	$-0.417731\pi$
$863$	35.8587	−	20.7030i	1.22064	−	0.704739i	0.965055	+	0.262047i	$0.0843974\pi$
$864$	12.2601	−	27.2793i	0.417097	−	0.928062i
$865$	−0.0688566	+	0.119263i	−0.00234119	+	0.00405507i
$866$	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
$870$	−0.0411178	+	0.126047i	−0.00139403	+	0.00427340i
$871$		−	71.9910i		−	2.43932i
$872$	−9.68438	−	5.59128i	−0.327954	−	0.189345i
$873$	23.3372	+	2.50789i	0.789844	+	0.0848791i
$874$			10.0947i			0.341459i
$875$		0			0
$876$	27.9742	+	9.12545i	0.945161	+	0.308320i
$877$	−22.7957			−0.769756			−0.384878	−	0.922967i	$-0.625756\pi$
$877$	−22.7957			−0.769756			−0.384878	+	0.922967i	$0.625756\pi$
$878$	−7.88482	−	13.6569i	−0.266100	−	0.460898i
$879$	26.4367	+	29.4299i	0.891689	+	0.992647i
$880$	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
$885$	−0.288852	+	0.0610454i	−0.00970966	+	0.00205202i
$886$	3.73682	+	6.47236i	0.125541	+	0.217443i
$887$	−38.9575			−1.30807			−0.654033	−	0.756466i	$-0.726924\pi$
$887$	−38.9575			−1.30807			−0.654033	+	0.756466i	$0.726924\pi$
$888$	−2.09347	−	9.90579i	−0.0702522	−	0.332417i
$889$		0			0
$890$			0.226597i			0.00759556i
$891$	8.76341	−	2.80228i	0.293585	−	0.0938798i
$892$	−4.03358	−	2.32879i	−0.135054	−	0.0779736i
$893$		−	22.7689i		−	0.761933i
$894$	12.2351	+	13.6204i	0.409203	+	0.455533i
$895$	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
$899$	−6.75453	+	11.6992i	−0.225276	+	0.390190i
$900$	2.49777	−	23.2431i	0.0832591	−	0.774769i
$901$	−57.0460	+	32.9355i	−1.90048	+	1.09724i
$902$	−2.39632	−	4.15054i	−0.0797886	−	0.138198i
$903$		0			0
$904$	11.2071	−	19.4113i	0.372743	−	0.645611i
$905$			0.177260i			0.00589232i
$906$	2.96175	−	2.66052i	0.0983976	−	0.0883900i
$907$	−28.1053			−0.933220			−0.466610	−	0.884463i	$-0.654525\pi$
$907$	−28.1053			−0.933220			−0.466610	+	0.884463i	$0.654525\pi$
$908$	22.4246	+	38.8406i	0.744187	+	1.28897i
$909$	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	$0.120653\pi$
$912$	5.33098	+	1.73902i	0.176526	+	0.0575846i
$913$	−5.44307	+	3.14256i	−0.180139	+	0.104003i
$914$	−11.8666	+	6.85121i	−0.392513	+	0.226618i
$915$	−0.0864222	+	0.0776326i	−0.00285703	+	0.00256645i
$916$	−11.9616	+	6.90601i	−0.395221	+	0.228181i
$917$		0			0
$918$	8.03546	−	17.8793i	0.265210	−	0.590105i
$919$	12.9115	+	22.3634i	0.425911	+	0.737699i	0.996505	−	0.0835328i	$-0.0266203\pi$
$919$	12.9115	+	22.3634i	0.425911	+	0.737699i	−0.570594	+	0.821232i	$0.693287\pi$
$920$	−0.485867			−0.0160186
$921$	30.6813	+	10.0085i	1.01098	+	0.329792i
$922$			1.10607i			0.0364264i
$923$	22.3471	−	38.7063i	0.735563	−	1.27403i
$924$		0			0
$925$	−6.18063	−	10.7052i	−0.203218	−	0.351983i
$926$	−0.695162	+	0.401352i	−0.0228444	+	0.0131892i
$927$	9.36193	−	12.8226i	0.307486	−	0.421149i
$928$	−11.7164	+	20.2934i	−0.384610	+	0.666164i
$929$	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	$0.0824435\pi$
$930$	0.0335127	−	0.102734i	0.00109893	−	0.00336877i
$931$		0			0
$932$	−17.4246	−	10.0601i	−0.570762	−	0.329529i
$933$	34.8236	−	7.35955i	1.14007	−	0.240941i
$934$		−	6.13802i		−	0.200842i
$935$	0.142300	+	0.0821570i	0.00465371	+	0.00268682i
$936$	36.5348	−	16.1643i	1.19418	−	0.528347i
$937$			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
$940$	0.479997			0.0156558
$941$	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	$0.773116\pi$
$942$	−5.83375	+	17.8834i	−0.190074	+	0.582674i
$943$	−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	$0.514396\pi$
$948$	13.0617	−	40.0407i	0.424223	−	1.30046i
$949$	30.6981	+	53.1706i	0.996501	+	1.72599i
$950$	−6.94989			−0.225484
$951$	−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	$0.839378\pi$
$954$	−2.46995	+	22.9841i	−0.0799675	+	0.744139i
$955$	−0.338347	−	0.195345i	−0.0109486	−	0.00632120i
$956$			8.74205i			0.282738i
$957$	−7.05288	+	1.49054i	−0.227987	+	0.0481824i
$958$	−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
$962$	4.62642	−	8.01319i	0.149162	−	0.258356i
$963$	−27.0469	−	2.90655i	−0.871575	−	0.0936621i
$964$	14.8308	−	8.56258i	0.477669	−	0.275782i
$965$	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	$0.0819523\pi$
$968$			23.5339i			0.756407i
$969$	19.5693	+	6.38368i	0.628655	+	0.205073i
$970$	0.147106			0.00472327
$971$	−10.7315	−	18.5875i	−0.344390	−	0.596500i	0.640853	−	0.767663i	$-0.278581\pi$
$971$	−10.7315	−	18.5875i	−0.344390	−	0.596500i	−0.985243	+	0.171163i	$0.945247\pi$
$972$	12.0260	+	21.1131i	0.385735	+	0.677202i
$973$		0			0
$974$	−24.8470	+	14.3454i	−0.796148	+	0.459657i
$975$	36.2861	−	32.5956i	1.16209	−	1.04390i
$976$	−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	$0.221563\pi$
$978$	−11.3277	−	3.69520i	−0.362219	−	0.118159i
$979$	−10.6696	+	6.16010i	−0.341002	+	0.196878i
$980$		0			0
$981$	12.9774	−	5.74167i	0.414336	−	0.183318i
$982$	−8.82301	−	15.2819i	−0.281554	−	0.487665i
$983$	25.4194			0.810752			0.405376	−	0.914150i	$-0.367141\pi$
$983$	25.4194			0.810752			0.405376	+	0.914150i	$0.367141\pi$
$984$	21.4974	−	19.3110i	0.685311	−	0.615611i
$985$			0.429311i			0.0136790i
$986$	−7.67912	+	13.3006i	−0.244553	+	0.423578i
$987$		0			0
$988$	9.18759	+	15.9134i	0.292296	+	0.506272i
$989$	14.5886	−	8.42273i	0.463890	−	0.267827i
$990$	0.0527328	−	0.0233309i	0.00167596	−	0.000741506i
$991$	−11.8768	+	20.5713i	−0.377280	+	0.653468i	−0.990665	−	0.136315i	$-0.956474\pi$
$991$	−11.8768	+	20.5713i	−0.377280	+	0.653468i	0.613385	+	0.789784i	$0.289807\pi$
$992$	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
$996$	−11.0921	−	12.3480i	−0.351468	−	0.391261i
$997$			12.1666i			0.385320i	0.981266	+	0.192660i	$0.0617114\pi$
$997$			12.1666i			0.385320i	−0.981266	+	0.192660i	$0.938289\pi$
$998$	−3.05781	−	1.76543i	−0.0967934	−	0.0558837i
$999$	11.7191	+	5.26689i	0.370776	+	0.166637i

Twists

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

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

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.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.575298 - 0.332148i) q^{2} +(-0.537154 + 1.64665i) q^{3} +(-0.779355 - 1.34988i) q^{4} +0.0283039 q^{5} +(0.855956 - 0.768901i) q^{6} +2.36404i q^{8} +(-2.42293 - 1.76901i) q^{9} +(-0.0162832 - 0.00940110i) q^{10} -1.02228i q^{11} +(2.64142 - 0.558232i) q^{12} +(4.87844 + 2.81657i) q^{13} +(-0.0152036 + 0.0466067i) q^{15} +(-0.773498 + 1.33974i) q^{16} +(-2.83940 + 4.91798i) q^{17} +(0.806333 + 1.82248i) q^{18} +(-1.81237 + 1.04637i) q^{19} +(-0.0220588 - 0.0382070i) q^{20} +(-0.339550 + 0.588118i) q^{22} +7.26133i q^{23} +(-3.89275 - 1.26985i) q^{24} -4.99920 q^{25} +(-1.87104 - 3.24073i) q^{26} +(4.21444 - 3.03949i) q^{27} +(-3.52577 + 2.03560i) q^{29} +(0.0242269 - 0.0217629i) q^{30} +(2.87364 - 1.65910i) q^{31} +(4.98462 - 2.87787i) q^{32} +(1.68335 + 0.549124i) q^{33} +(3.26700 - 1.88620i) q^{34} +(-0.499635 + 4.64936i) q^{36} +(1.23632 + 2.14137i) q^{37} +1.39020 q^{38} +(-7.25839 + 6.52017i) q^{39} +0.0669116i q^{40} +(-3.52867 + 6.11183i) q^{41} +(-1.15994 - 2.00908i) q^{43} +(-1.37996 + 0.796722i) q^{44} +(-0.0685785 - 0.0500700i) q^{45} +(2.41184 - 4.17742i) q^{46} +(-5.43997 + 9.42231i) q^{47} +(-1.79060 - 1.99333i) q^{48} +(2.87603 + 1.66048i) q^{50} +(-6.57302 - 7.31722i) q^{51} -8.78043i q^{52} +(10.0454 + 5.79973i) q^{53} +(-3.43412 + 0.348797i) q^{54} -0.0289346i q^{55} +(-0.749489 - 3.54640i) q^{57} +2.70449 q^{58} +(3.01111 + 5.21540i) q^{59} +(0.0747626 - 0.0158002i) q^{60} +(2.05220 + 1.18484i) q^{61} -2.20427 q^{62} -0.729528 q^{64} +(0.138079 + 0.0797200i) q^{65} +(-0.786035 - 0.875030i) q^{66} +(-6.38995 - 11.0677i) q^{67} +8.85160 q^{68} +(-11.9569 - 3.90045i) q^{69} -7.93415i q^{71} +(4.18201 - 5.72790i) q^{72} +(9.43889 + 5.44955i) q^{73} -1.64257i q^{74} +(2.68534 - 8.23195i) q^{75} +(2.82496 + 1.63099i) q^{76} +(6.34140 - 1.34018i) q^{78} +(7.80018 - 13.5103i) q^{79} +(-0.0218930 + 0.0379198i) q^{80} +(2.74119 + 8.57239i) q^{81} +(4.06007 - 2.34408i) q^{82} +(-3.07406 - 5.32442i) q^{83} +(-0.0803661 + 0.139198i) q^{85} +1.54109i q^{86} +(-1.45805 - 6.89915i) q^{87} +2.41672 q^{88} +(-6.02582 - 10.4370i) q^{89} +(0.0228224 + 0.0515834i) q^{90} +(9.80194 - 5.65915i) q^{92} +(1.18837 + 5.62309i) q^{93} +(6.25921 - 3.61376i) q^{94} +(-0.0512971 + 0.0296164i) q^{95} +(2.06135 + 9.75380i) q^{96} +(-6.77565 + 3.91192i) q^{97} +(-1.80843 + 2.47692i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4} - 8 q^{9} - 40 q^{15} - 24 q^{16} + 32 q^{18} + 48 q^{25} + 48 q^{30} - 120 q^{32} - 8 q^{36} - 32 q^{39} + 96 q^{44} + 48 q^{50} + 48 q^{53} + 80 q^{57} - 72 q^{60} - 48 q^{64} - 120 q^{65}+ \cdots - 72 q^{99}+O(q^{100}) \) 48 * q + 24 * q^4 - 8 * q^9 - 40 * q^15 - 24 * q^16 + 32 * q^18 + 48 * q^25 + 48 * q^30 - 120 * q^32 - 8 * q^36 - 32 * q^39 + 96 * q^44 + 48 * q^50 + 48 * q^53 + 80 * q^57 - 72 * q^60 - 48 * q^64 - 120 * q^65 + 32 * q^72 - 88 * q^78 - 24 * q^79 + 120 * q^81 - 24 * q^85 - 144 * q^92 + 16 * q^93 - 96 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

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Database

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