LMFDB - Embedded newform 441.2.s.d.362.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(362,441)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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			362.9
Character	$\chi$	$=$	441.362
Dual form			441.2.s.d.374.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.575298 + 0.332148i) q^{2} +(-0.537154 - 1.64665i) q^{3} +(-0.779355 + 1.34988i) q^{4} +0.0283039 q^{5} +(0.855956 + 0.768901i) q^{6} -2.36404i q^{8} +(-2.42293 + 1.76901i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 48 * q + 24 * q^4 - 8 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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	−0.689413	−	0.724369i	$-0.742131\pi$
$2$	−0.575298	+	0.332148i	−0.406797	+	0.234864i	0.282616	+	0.959233i	$0.408798\pi$
$3$	−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	$0.0492526\pi$
$11$			1.02228i			0.308230i	−0.988053	+	0.154115i	$0.950747\pi$
$12$	2.64142	+	0.558232i	0.762513	+	0.161148i
$13$	4.87844	−	2.81657i	1.35304	−	0.781176i	0.364363	−	0.931257i	$-0.381287\pi$
$13$	4.87844	−	2.81657i	1.35304	−	0.781176i	0.988674	+	0.150081i	$0.0479534\pi$
$14$		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	−0.972273	−	0.233849i	$-0.924868\pi$
$17$	−2.83940	−	4.91798i	−0.688656	−	1.19279i	0.283617	−	0.958938i	$-0.408465\pi$
$18$	0.806333	−	1.82248i	0.190054	−	0.429563i
$19$	−1.81237	−	1.04637i	−0.415786	−	0.240054i	0.277487	−	0.960729i	$-0.410498\pi$
$19$	−1.81237	−	1.04637i	−0.415786	−	0.240054i	−0.693273	+	0.720675i	$0.743832\pi$
$20$	−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	$-0.726642\pi$
$23$		−	7.26133i		−	1.51409i	0.653362	−	0.757046i	$-0.273358\pi$
$24$	−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	0.135543	−	0.990771i	$-0.456722\pi$
$29$	−3.52577	−	2.03560i	−0.654718	−	0.378002i	−0.790262	+	0.612770i	$0.790055\pi$
$30$	0.0242269	+	0.0217629i	0.00442321	+	0.00397335i
$31$	2.87364	+	1.65910i	0.516122	+	0.297983i	0.735346	−	0.677691i	$-0.237019\pi$
$31$	2.87364	+	1.65910i	0.516122	+	0.297983i	−0.219225	+	0.975674i	$0.570353\pi$
$32$	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	−0.746324	−	0.665583i	$-0.768183\pi$
$37$	1.23632	−	2.14137i	0.203250	−	0.352040i	0.949574	+	0.313543i	$0.101516\pi$
$38$	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	−0.998197	−	0.0600295i	$-0.980881\pi$
$41$	−3.52867	−	6.11183i	−0.551085	−	0.954508i	0.447111	−	0.894478i	$-0.352453\pi$
$42$		0			0
$43$	−1.15994	+	2.00908i	−0.176890	+	0.306382i	−0.940814	−	0.338924i	$-0.889937\pi$
$43$	−1.15994	+	2.00908i	−0.176890	+	0.306382i	0.763924	+	0.645306i	$0.223270\pi$
$44$	−1.37996	−	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	−0.923786	−	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
$51$	−6.57302	+	7.31722i	−0.920407	+	1.02462i
$52$			8.78043i			1.21763i
$53$	10.0454	−	5.79973i	1.37985	−	0.796655i	0.387706	−	0.921783i	$-0.373268\pi$
$53$	10.0454	−	5.79973i	1.37985	−	0.796655i	0.992141	+	0.125128i	$0.0399342\pi$
$54$	−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	−0.600702	−	0.799473i	$-0.705112\pi$
$59$	3.01111	−	5.21540i	0.392013	−	0.678987i	0.992715	+	0.120486i	$0.0384454\pi$
$60$	0.0747626	+	0.0158002i	0.00965181	+	0.00203979i
$61$	2.05220	−	1.18484i	0.262757	−	0.151703i	−0.362834	−	0.931854i	$-0.618191\pi$
$61$	2.05220	−	1.18484i	0.262757	−	0.151703i	0.625592	+	0.780151i	$0.284858\pi$
$62$	−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	0.150903	+	0.988549i	$0.451782\pi$
$67$	−6.38995	+	11.0677i	−0.780656	+	1.35214i	−0.931560	+	0.363588i	$0.881552\pi$
$68$	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	$0.156036\pi$
$71$			7.93415i			0.941610i	−0.882237	+	0.470805i	$0.843964\pi$
$72$	4.18201	+	5.72790i	0.492855	+	0.675040i
$73$	9.43889	−	5.44955i	1.10474	−	0.637821i	0.167277	−	0.985910i	$-0.446503\pi$
$73$	9.43889	−	5.44955i	1.10474	−	0.637821i	0.937462	+	0.348089i	$0.113169\pi$
$74$			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	0.853980	+	0.520306i	$0.174182\pi$
$79$	7.80018	+	13.5103i	0.877588	+	1.52003i	0.0236086	+	0.999721i	$0.492484\pi$
$80$	−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	−0.983947	−	0.178461i	$-0.942888\pi$
$83$	−3.07406	+	5.32442i	−0.337421	+	0.584431i	0.646526	+	0.762892i	$0.276221\pi$
$84$		0			0
$85$	−0.0803661	−	0.139198i	−0.00871693	−	0.0150982i
$86$		−	1.54109i		−	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	0.346975	+	0.937874i	$0.387209\pi$
$89$	−6.02582	+	10.4370i	−0.638736	+	1.10632i	−0.985711	+	0.168448i	$0.946124\pi$
$90$	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	0.114885	−	0.993379i	$-0.463350\pi$
$97$	−6.77565	−	3.91192i	−0.687963	−	0.397196i	−0.802848	+	0.596183i	$0.796683\pi$
$98$		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	$-0.916038\pi$
$103$		−	5.29218i		−	0.521454i	0.965413	−	0.260727i	$-0.0839622\pi$
$104$	−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	0.828991	−	0.559262i	$-0.188915\pi$
$107$	7.85273	+	4.53377i	0.759152	+	0.438296i	−0.0698394	+	0.997558i	$0.522249\pi$
$108$	−7.38750	+	3.32015i	−0.710863	+	0.319481i
$109$	−2.36514	−	4.09654i	−0.226539	−	0.392377i	0.730241	−	0.683190i	$-0.239408\pi$
$109$	−2.36514	−	4.09654i	−0.226539	−	0.392377i	−0.956780	+	0.290812i	$0.906074\pi$
$110$	−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	−0.833742	−	0.552154i	$-0.813806\pi$
$113$	−8.21108	+	4.74067i	−0.772433	+	0.445965i	0.0613086	+	0.998119i	$0.480473\pi$
$114$	−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	$0.161053\pi$
$137$			11.3453i			0.969298i	−0.874709	+	0.484649i	$0.838947\pi$
$138$	5.58324	−	6.21538i	0.475277	−	0.529088i
$139$	−3.04891	+	1.76029i	−0.258605	+	0.149306i	−0.623698	−	0.781665i	$-0.714371\pi$
$139$	−3.04891	+	1.76029i	−0.258605	+	0.149306i	0.365093	+	0.930971i	$0.381037\pi$
$140$		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	$-0.774014\pi$
$149$		−	15.9125i		−	1.30360i	0.758391	−	0.651800i	$-0.225986\pi$
$150$	−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	−0.186045	−	0.982541i	$-0.559567\pi$
$157$	−14.1585	−	8.17442i	−1.12997	−	0.652390i	−0.943928	+	0.330151i	$0.892900\pi$
$158$	−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	−0.994386	−	0.105811i	$-0.966256\pi$
$163$	−5.17782	+	8.96824i	−0.405558	+	0.702447i	0.588828	+	0.808258i	$0.299589\pi$
$164$	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	0.957136	−	0.289638i	$-0.0935349\pi$
$167$	2.94297	+	5.09738i	0.227734	+	0.394447i	−0.729402	+	0.684085i	$0.760202\pi$
$168$		0			0
$169$	9.36614	−	16.2226i	0.720473	−	1.24790i
$170$	0.0924689	+	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	0.758604	−	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
$177$	−10.2054	−	2.15678i	−0.767083	−	0.162114i
$178$		−	8.00586i		−	0.600065i
$179$	0.175495	−	0.101322i	0.0131171	−	0.00757319i	−0.493427	−	0.869787i	$-0.664256\pi$
$179$	0.175495	−	0.101322i	0.0131171	−	0.00757319i	0.506544	+	0.862214i	$0.330923\pi$
$180$	−0.0141416	−	0.131595i	−0.00105405	−	0.00980852i
$181$		−	6.26273i		−	0.465505i	−0.972536	−	0.232753i	$-0.925227\pi$
$181$		−	6.26273i		−	0.465505i	0.972536	−	0.232753i	$-0.0747732\pi$
$182$		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	−0.865672	−	0.500612i	$-0.833108\pi$
$191$	−11.9541	+	6.90168i	−0.864965	+	0.499388i	0.000706698		1.00000i	$0.499775\pi$
$192$	0.391869	+	1.20128i	0.0282807	+	0.0866948i
$193$	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	$-0.107446\pi$
$194$	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	$-0.818298\pi$
$197$		−	15.1679i		−	1.08067i	0.841451	−	0.540334i	$-0.181702\pi$
$198$	1.86309	+	0.824301i	0.132404	+	0.0585805i
$199$	8.38940	−	4.84362i	0.594709	−	0.343355i	−0.172249	−	0.985054i	$-0.555103\pi$
$199$	8.38940	−	4.84362i	0.594709	−	0.343355i	0.766957	+	0.641698i	$0.221770\pi$
$200$			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	0.513880	−	0.857862i	$-0.328208\pi$
$211$	−7.05942	−	12.2273i	−0.485991	−	0.841761i	−0.999870	+	0.0161017i	$0.994874\pi$
$212$			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	0.584136	−	0.811656i	$-0.301433\pi$
$223$	2.58777	+	1.49405i	0.173290	+	0.100049i	−0.410846	+	0.911705i	$0.634767\pi$
$224$		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	$0.0945810\pi$
$229$			8.86119i			0.585564i	−0.956179	+	0.292782i	$0.905419\pi$
$230$	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	0.819282	−	0.573391i	$-0.194372\pi$
$233$	11.1789	+	6.45412i	0.732351	+	0.422823i	−0.0869305	+	0.996214i	$0.527706\pi$
$234$	−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	−0.648796	−	0.760963i	$-0.724727\pi$
$239$	−4.85712	+	2.80426i	−0.314181	+	0.181392i	0.334615	+	0.942355i	$0.391394\pi$
$240$	−0.0506809	+	0.0564190i	−0.00327144	+	0.00364183i
$241$		−	10.9868i		−	0.707719i	−0.935299	−	0.353860i	$-0.884869\pi$
$241$		−	10.9868i		−	0.707719i	0.935299	−	0.353860i	$-0.115131\pi$
$242$	−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	$-0.971515\pi$
$263$		−	2.89866i		−	0.178739i	0.995999	−	0.0893695i	$-0.0284852\pi$
$264$	−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	0.978616	+	0.205694i	$0.0659451\pi$
$269$	10.9469	+	18.9606i	0.667444	+	1.15605i	−0.311172	+	0.950354i	$0.600722\pi$
$270$	−0.0971990	−	0.00987232i	−0.00591534	−	0.000600810i
$271$	7.77992	+	4.49174i	0.472596	+	0.272854i	0.717326	−	0.696738i	$-0.245366\pi$
$271$	7.77992	+	4.49174i	0.472596	+	0.272854i	−0.244730	+	0.969591i	$0.578699\pi$
$272$	−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	0.359629	−	0.933095i	$-0.382903\pi$
$281$	−4.50324	−	2.59995i	−0.268641	−	0.155100i	−0.628270	+	0.777996i	$0.716237\pi$
$282$	2.58844	−	12.2479i	0.154140	−	0.729351i
$283$	−16.2587	−	9.38694i	−0.966476	−	0.557995i	−0.0683162	−	0.997664i	$-0.521763\pi$
$283$	−16.2587	−	9.38694i	−0.966476	−	0.557995i	−0.898160	+	0.439668i	$0.855096\pi$
$284$	−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	0.978692	+	0.205332i	$0.0658274\pi$
$293$	11.4201	+	19.7802i	0.667169	+	1.15557i	−0.311523	+	0.950238i	$0.600839\pi$
$294$		0			0
$295$	0.0852263	−	0.147616i	0.00496206	−	0.00859455i
$296$	−5.06229	−	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	$0.178449\pi$
$307$			18.6325i			1.06341i	−0.846928	+	0.531707i	$0.821551\pi$
$308$		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	0.412539	+	0.910940i	$0.364642\pi$
$311$	−10.2747	+	17.7964i	−0.582628	+	1.00914i	−0.995167	+	0.0982007i	$0.968691\pi$
$312$	−15.4139	+	17.1591i	−0.872643	+	0.971444i
$313$	0.624466	−	0.360536i	0.0352969	−	0.0203787i	−0.482248	−	0.876035i	$-0.660179\pi$
$313$	0.624466	−	0.360536i	0.0352969	−	0.0203787i	0.517545	+	0.855656i	$0.326846\pi$
$314$	10.8605			0.612893
$315$		0			0
$316$	−24.3164			−1.36791
$317$	18.9915	−	10.9647i	1.06667	−	0.615841i	0.139398	−	0.990236i	$-0.455483\pi$
$317$	18.9915	−	10.9647i	1.06667	−	0.615841i	0.927269	+	0.374396i	$0.122150\pi$
$318$	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	−0.993479	−	0.114016i	$-0.963629\pi$
$331$	−10.8338	−	18.7647i	−0.595480	−	1.03140i	0.397999	−	0.917386i	$-0.369705\pi$
$332$	−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	0.972212	+	0.234101i	$0.0752147\pi$
$337$	12.6455	+	21.9026i	0.688844	+	1.19311i	−0.283369	+	0.959011i	$0.591452\pi$
$338$			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	0.626315	−	0.779570i	$-0.284562\pi$
$347$	4.92420	+	2.84299i	0.264345	+	0.152620i	−0.361970	+	0.932190i	$0.617896\pi$
$348$	−8.17670	−	7.34508i	−0.438317	−	0.393738i
$349$	−9.68412	−	5.59113i	−0.518379	−	0.299286i	0.217892	−	0.975973i	$-0.430082\pi$
$349$	−9.68412	−	5.59113i	−0.518379	−	0.299286i	−0.736271	+	0.676687i	$0.763415\pi$
$350$		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	0.969207	−	0.246246i	$-0.0791973\pi$
$359$	23.5052	+	13.5707i	1.24056	+	0.716235i	0.271348	+	0.962481i	$0.412531\pi$
$360$	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	$-0.942524\pi$
$367$		−	6.88076i		−	0.359173i	0.983742	−	0.179586i	$-0.0574759\pi$
$368$	−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	$0.0535831\pi$
$389$			6.60890i			0.335085i	−0.985865	+	0.167542i	$0.946417\pi$
$390$	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	0.654261	−	0.756269i	$-0.272980\pi$
$397$	6.50435	+	3.75529i	0.326444	+	0.188472i	−0.327817	+	0.944741i	$0.606313\pi$
$398$	−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	$-0.949441\pi$
$401$		−	6.33464i		−	0.316337i	0.987412	−	0.158168i	$-0.0505589\pi$
$402$	−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	0.997436	−	0.0715625i	$-0.0227986\pi$
$409$	29.0045	+	16.7457i	1.43418	+	0.828024i	0.436743	+	0.899586i	$0.356132\pi$
$410$	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	0.887092	−	0.461593i	$-0.152722\pi$
$419$	0.896459	+	1.55271i	0.0437949	+	0.0758550i	−0.843297	+	0.537448i	$0.819389\pi$
$420$		0			0
$421$	1.90262	−	3.29543i	0.0927278	−	0.160609i	−0.815930	−	0.578150i	$-0.803775\pi$
$421$	1.90262	−	3.29543i	0.0927278	−	0.160609i	0.908658	+	0.417541i	$0.137108\pi$
$422$	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	−0.472012	−	0.881592i	$-0.656472\pi$
$431$	1.15145	−	0.664787i	0.0554632	−	0.0320217i	0.527475	+	0.849570i	$0.323139\pi$
$432$	0.812269	−	7.99729i	0.0390803	−	0.384770i
$433$		−	37.4292i		−	1.79873i	−0.437194	−	0.899367i	$-0.644028\pi$
$433$		−	37.4292i		−	1.79873i	0.437194	−	0.899367i	$-0.355972\pi$
$434$		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	0.0785682	−	0.996909i	$-0.474965\pi$
$439$	20.5584	−	11.8694i	0.981201	−	0.566496i	0.902632	+	0.430412i	$0.141632\pi$
$440$	0.0684026			0.00326097
$441$		0			0
$442$	21.2505			1.01078
$443$	−9.74317	+	5.62522i	−0.462912	+	0.267262i	−0.713268	−	0.700891i	$-0.752786\pi$
$443$	−9.74317	+	5.62522i	−0.462912	+	0.267262i	0.250356	+	0.968154i	$0.419452\pi$
$444$	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	$-0.889682\pi$
$449$		−	14.3953i		−	0.679357i	0.940542	−	0.339679i	$-0.110318\pi$
$450$	−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	0.999797	−	0.0201547i	$-0.00641589\pi$
$457$	10.3135	+	17.8635i	0.482444	+	0.835617i	−0.517353	+	0.855772i	$0.673083\pi$
$458$	−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	−0.884761	−	0.466045i	$-0.845679\pi$
$461$	−0.832511	+	1.44195i	−0.0387739	+	0.0671584i	0.845987	+	0.533203i	$0.179012\pi$
$462$		0			0
$463$	0.604175	+	1.04646i	0.0280784	+	0.0486332i	0.879723	−	0.475486i	$-0.157728\pi$
$463$	0.604175	+	1.04646i	0.0280784	+	0.0486332i	−0.851645	+	0.524119i	$0.824395\pi$
$464$			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	−0.739111	−	0.673584i	$-0.764754\pi$
$467$	4.61994	−	8.00197i	0.213785	−	0.370287i	0.952896	+	0.303297i	$0.0980874\pi$
$468$	−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	0.667657	+	0.744469i	$0.267297\pi$
$487$	21.5949	+	37.4034i	0.978558	+	1.69491i	0.310900	+	0.950442i	$0.399369\pi$
$488$	−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	0.118866	−	0.992910i	$-0.462074\pi$
$491$	23.0046	−	13.2817i	1.03818	−	0.599396i	0.919319	+	0.393514i	$0.128741\pi$
$492$	−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	0.956015	−	0.293318i	$-0.0947595\pi$
$521$	5.11259	+	8.85526i	0.223987	+	0.387956i	−0.732028	+	0.681274i	$0.761426\pi$
$522$	−6.55279	+	4.78427i	−0.286808	+	0.209402i
$523$	−4.48150	−	2.58740i	−0.195962	−	0.113139i	0.398808	−	0.917034i	$-0.369424\pi$
$523$	−4.48150	−	2.58740i	−0.195962	−	0.113139i	−0.594771	+	0.803895i	$0.702757\pi$
$524$	−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	−0.451623	−	0.892209i	$-0.649155\pi$
$541$	12.7197	−	22.0312i	0.546864	−	0.947196i	0.998487	−	0.0549871i	$-0.0175118\pi$
$542$	−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	−0.355355	−	0.934732i	$-0.615640\pi$
$547$	14.7771	−	25.5947i	0.631824	−	1.09435i	0.987179	−	0.159620i	$-0.0510267\pi$
$548$	−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	−0.814537	−	0.580112i	$-0.803009\pi$
$557$	−16.9788	+	9.80269i	−0.719413	+	0.415353i	0.0951237	+	0.995465i	$0.469675\pi$
$558$	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	−0.672227	−	0.740345i	$-0.734662\pi$
$563$	7.23796	−	12.5365i	0.305044	−	0.528351i	0.977271	+	0.211994i	$0.0679956\pi$
$564$	−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	−0.634005	−	0.773329i	$-0.718590\pi$
$569$	−6.70970	+	3.87385i	−0.281285	+	0.162400i	0.352720	+	0.935729i	$0.385257\pi$
$570$	−0.0211360	−	0.0647928i	−0.000885290	−	0.00271387i
$571$	−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	$0.276302\pi$
$572$	−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	−0.264290	−	0.964443i	$-0.585138\pi$
$577$	10.5403	−	6.08542i	0.438797	−	0.253339i	0.703087	+	0.711104i	$0.251804\pi$
$578$		−	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	−0.273106	−	0.961984i	$-0.588051\pi$
$587$	16.8761	−	29.2302i	0.696550	−	1.20646i	0.969655	−	0.244476i	$-0.0786158\pi$
$588$		0			0
$589$	−3.47207	−	6.01380i	−0.143064	−	0.247794i
$590$			0.113231i			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	−0.990446	−	0.137903i	$-0.955964\pi$
$593$	−9.15123	+	15.8504i	−0.375796	+	0.650897i	0.614650	+	0.788800i	$0.289297\pi$
$594$	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	0.994076	−	0.108689i	$-0.0346651\pi$
$599$	34.1905	+	19.7399i	1.39699	+	0.806551i	0.402911	+	0.915239i	$0.367998\pi$
$600$	19.4606	−	6.34825i	0.794477	−	0.259166i
$601$	34.4865	+	19.9108i	1.40673	+	0.812177i	0.995072	−	0.0991600i	$-0.0316155\pi$
$601$	34.4865	+	19.9108i	1.40673	+	0.812177i	0.411661	+	0.911337i	$0.364949\pi$
$602$		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	$0.169030\pi$
$607$			24.9536i			1.01283i	−0.862289	+	0.506417i	$0.830970\pi$
$608$	−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	−0.996898	−	0.0786994i	$-0.974923\pi$
$613$	−14.0285	−	24.2980i	−0.566605	−	0.981388i	0.430294	−	0.902689i	$-0.358410\pi$
$614$	−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	0.239506	−	0.970895i	$-0.423015\pi$
$617$	29.8093	−	17.2104i	1.20008	−	0.692865i	0.960573	+	0.278030i	$0.0896813\pi$
$618$	4.06916	−	4.52987i	0.163686	−	0.182218i
$619$		−	19.9635i		−	0.802399i	−0.915991	−	0.401200i	$-0.868593\pi$
$619$		−	19.9635i		−	0.802399i	0.915991	−	0.401200i	$-0.131407\pi$
$620$	−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	$0.0242881\pi$
$641$			3.85994i			0.152459i	−0.997090	+	0.0762293i	$0.975712\pi$
$642$	3.23557	+	9.91868i	0.127698	+	0.391459i
$643$	31.0233	−	17.9113i	1.22344	−	0.706352i	0.257789	−	0.966201i	$-0.417006\pi$
$643$	31.0233	−	17.9113i	1.22344	−	0.706352i	0.965649	+	0.259849i	$0.0836727\pi$
$644$		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	−0.873821	−	0.486248i	$-0.838365\pi$
$647$	−21.8246	−	37.8013i	−0.858013	−	1.48612i	0.0158075	−	0.999875i	$-0.494968\pi$
$648$	−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	$0.0465663\pi$
$653$			7.45002i			0.291542i	−0.989318	+	0.145771i	$0.953434\pi$
$654$	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	0.346198	−	0.938161i	$-0.387472\pi$
$659$	−7.52607	−	4.34518i	−0.293174	−	0.169264i	−0.639372	+	0.768897i	$0.720806\pi$
$660$	−0.0161523	+	0.0764286i	−0.000628726	+	0.00297498i
$661$	−24.9853	−	14.4253i	−0.971815	−	0.561077i	−0.0720256	−	0.997403i	$-0.522946\pi$
$661$	−24.9853	−	14.4253i	−0.971815	−	0.561077i	−0.899789	+	0.436325i	$0.856280\pi$
$662$	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	−0.927133	−	0.374733i	$-0.877734\pi$
$673$	−3.60695	+	6.24742i	−0.139038	+	0.240820i	0.788095	+	0.615554i	$0.211068\pi$
$674$	−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	0.968765	+	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
$681$	15.4557	+	47.3797i	0.592264	+	1.81559i
$682$		−	2.25339i		−	0.0862867i
$683$	20.5530	−	11.8663i	0.786438	−	0.454050i	−0.0522688	−	0.998633i	$-0.516645\pi$
$683$	20.5530	−	11.8663i	0.786438	−	0.454050i	0.838707	+	0.544583i	$0.183312\pi$
$684$	−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	−0.444588	−	0.895735i	$-0.646650\pi$
$691$	2.86127	−	1.65195i	0.108848	−	0.0628433i	0.553436	+	0.832892i	$0.313316\pi$
$692$	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	$-0.994748\pi$
$701$		−	0.873603i		−	0.0329955i	0.999864	−	0.0164978i	$-0.00525164\pi$
$702$	−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	0.673532	−	0.739158i	$-0.264776\pi$
$709$	−8.07767	−	13.9909i	−0.303363	−	0.525441i	−0.976896	+	0.213717i	$0.931443\pi$
$710$	−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	−0.0449767	−	0.998988i	$-0.514321\pi$
$719$	22.5953	−	39.1361i	0.842661	−	1.45953i	0.887637	−	0.460543i	$-0.152345\pi$
$720$	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	0.361359	−	0.932427i	$-0.382313\pi$
$727$	−7.15775	−	4.13253i	−0.265466	−	0.153267i	−0.626826	+	0.779160i	$0.715646\pi$
$728$		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	$-0.927561\pi$
$733$		−	12.2166i		−	0.451230i	0.974217	−	0.225615i	$-0.0724392\pi$
$734$	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	0.991186	−	0.132478i	$-0.0422935\pi$
$739$	10.3536	+	17.9330i	0.380863	+	0.659674i	−0.610323	+	0.792153i	$0.708960\pi$
$740$	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	−0.299307	−	0.954157i	$-0.596756\pi$
$743$	10.2862	−	5.93873i	0.377363	−	0.217871i	0.676670	+	0.736286i	$0.263422\pi$
$744$	−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	−0.0150472	−	0.999887i	$-0.504790\pi$
$769$	23.3870	−	13.5025i	0.843357	−	0.486912i	0.858404	+	0.512975i	$0.171457\pi$
$770$		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	0.999747	−	0.0224765i	$-0.00715509\pi$
$773$	13.3567	+	23.1345i	0.480408	+	0.832092i	−0.519339	+	0.854568i	$0.673822\pi$
$774$	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	0.999096	−	0.0425177i	$-0.0135379\pi$
$787$	41.0093	+	23.6767i	1.46182	+	0.843983i	0.462726	+	0.886501i	$0.346871\pi$
$788$	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	0.776887	−	0.629640i	$-0.216798\pi$
$797$	−4.42781	−	7.66919i	−0.156841	−	0.271657i	−0.933728	+	0.357984i	$0.883464\pi$
$798$		0			0
$799$	−30.8925	+	53.5074i	−1.09290	+	1.89296i
$800$	−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	−0.383092	−	0.923710i	$-0.625141\pi$
$809$	6.40871	−	3.70007i	0.225318	−	0.130087i	0.608410	+	0.793623i	$0.291808\pi$
$810$	0.0359546	+	0.165356i	0.00126331	+	0.00581002i
$811$			25.0843i			0.880829i	0.897794	+	0.440415i	$0.145169\pi$
$811$			25.0843i			0.880829i	−0.897794	+	0.440415i	$0.854831\pi$
$812$		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	−0.785154	−	0.619300i	$-0.787416\pi$
$821$	−18.3781	+	10.6106i	−0.641401	+	0.370313i	0.143753	+	0.989614i	$0.454083\pi$
$822$	−8.72345	+	9.71112i	−0.304265	+	0.338714i
$823$	−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	$0.262148\pi$
$824$	−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	$0.145013\pi$
$827$			25.3052i			0.879949i	−0.898010	+	0.439975i	$0.854987\pi$
$828$	−33.7605	+	3.62801i	−1.17326	+	0.126082i
$829$	35.9640	−	20.7638i	1.24908	−	0.721158i	0.278156	−	0.960536i	$-0.410277\pi$
$829$	35.9640	−	20.7638i	1.24908	−	0.721158i	0.970927	+	0.239378i	$0.0769434\pi$
$830$		−	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	−0.728884	−	0.684638i	$-0.759960\pi$
$839$	6.61780	−	11.4624i	0.228472	−	0.395725i	0.957355	+	0.288913i	$0.0932938\pi$
$840$		0			0
$841$	−6.21265	−	10.7606i	−0.214229	−	0.371056i
$842$			2.52780i			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	0.213001	−	0.977052i	$-0.431676\pi$
$853$	−15.3814	−	8.88048i	−0.526651	−	0.304062i	−0.739651	+	0.672990i	$0.765010\pi$
$854$		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	$-0.983117\pi$
$859$		−	3.10760i		−	0.106030i	0.998594	−	0.0530150i	$-0.0168831\pi$
$860$	−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	0.965055	−	0.262047i	$-0.0843974\pi$
$863$	35.8587	+	20.7030i	1.22064	+	0.704739i	0.255589	+	0.966786i	$0.417731\pi$
$864$	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	0.929019	−	0.370032i	$-0.120653\pi$
$911$	32.3883	+	18.6994i	1.07307	+	0.619538i	0.144052	+	0.989570i	$0.453987\pi$
$912$	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	−0.570594	−	0.821232i	$-0.693287\pi$
$919$	12.9115	−	22.3634i	0.425911	−	0.737699i	0.996505	+	0.0835328i	$0.0266203\pi$
$920$	−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	0.966646	−	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
$933$	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	$-0.920833\pi$
$937$		−	15.0698i		−	0.492308i	0.969231	−	0.246154i	$-0.0791668\pi$
$938$		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	−0.756549	−	0.653937i	$-0.773116\pi$
$941$	5.76861	−	9.99152i	0.188051	−	0.325714i	0.944600	+	0.328222i	$0.106450\pi$
$942$	−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	−0.0452102	−	0.998977i	$-0.514396\pi$
$947$	24.5364	−	14.1661i	0.797325	−	0.460336i	0.842535	+	0.538642i	$0.181062\pi$
$948$	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	$-0.839378\pi$
$953$		−	29.8498i		−	0.966931i	0.875364	−	0.483465i	$-0.160622\pi$
$954$	−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	0.967040	−	0.254626i	$-0.0819523\pi$
$967$	8.17864	+	14.1658i	0.263007	+	0.455542i	−0.704032	+	0.710168i	$0.748619\pi$
$968$		−	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	−0.985243	−	0.171163i	$-0.945247\pi$
$971$	−10.7315	+	18.5875i	−0.344390	+	0.596500i	0.640853	+	0.767663i	$0.278581\pi$
$972$	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	0.767374	−	0.641199i	$-0.221563\pi$
$977$	18.6219	+	10.7513i	0.595766	+	0.343966i	−0.171608	+	0.985165i	$0.554896\pi$
$978$	−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	0.613385	−	0.789784i	$-0.289807\pi$
$991$	−11.8768	−	20.5713i	−0.377280	−	0.653468i	−0.990665	+	0.136315i	$0.956474\pi$
$992$	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	$-0.938289\pi$
$997$		−	12.1666i		−	0.385320i	0.981266	−	0.192660i	$-0.0617114\pi$
$998$	−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.362.9		48
3.2	odd	2		1323.2.s.d.656.16		48
7.2	even	3		441.2.o.e.146.16	yes	48
7.3	odd	6		441.2.i.d.227.10		48
7.4	even	3		441.2.i.d.227.9		48
7.5	odd	6		441.2.o.e.146.15	✓	48
7.6	odd	2	inner	441.2.s.d.362.10		48
9.4	even	3		1323.2.i.d.1097.9		48
9.5	odd	6		441.2.i.d.68.16		48
21.2	odd	6		1323.2.o.e.440.10		48
21.5	even	6		1323.2.o.e.440.9		48
21.11	odd	6		1323.2.i.d.521.10		48
21.17	even	6		1323.2.i.d.521.9		48
21.20	even	2		1323.2.s.d.656.15		48
63.4	even	3		1323.2.s.d.962.15		48
63.5	even	6		441.2.o.e.293.16	yes	48
63.13	odd	6		1323.2.i.d.1097.10		48
63.23	odd	6		441.2.o.e.293.15	yes	48
63.31	odd	6		1323.2.s.d.962.16		48
63.32	odd	6	inner	441.2.s.d.374.10		48
63.40	odd	6		1323.2.o.e.881.10		48
63.41	even	6		441.2.i.d.68.15		48
63.58	even	3		1323.2.o.e.881.9		48
63.59	even	6	inner	441.2.s.d.374.9		48

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.575298 + 0.332148i) q^{2} +(-0.537154 - 1.64665i) q^{3} +(-0.779355 + 1.34988i) q^{4} +0.0283039 q^{5} +(0.855956 + 0.768901i) q^{6} -2.36404i q^{8} +(-2.42293 + 1.76901i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4} - 8 q^{9}+O(q^{10}) \) 48 * q + 24 * q^4 - 8 * q^9	\( 48 q + 24 q^{4} - 8 q^{9} - 40 q^{15} - 24 q^{16} + 32 q^{18} + 48 q^{25} + 48 q^{30} - 120 q^{32} - 8 q^{36} - 32 q^{39} + 96 q^{44} + 48 q^{50} + 48 q^{53} + 80 q^{57} - 72 q^{60} - 48 q^{64} - 120 q^{65} + 32 q^{72} - 88 q^{78} - 24 q^{79} + 120 q^{81} - 24 q^{85} - 144 q^{92} + 16 q^{93} - 96 q^{95} - 72 q^{99}+O(q^{100}) \) 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

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