LMFDB - Embedded newform 475.2.l.f.251.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [475,2,Mod(101,475)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(475, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 14])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("475.101"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.l (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			251.6
Character	$\chi$	$=$	475.251
Dual form			475.2.l.f.176.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.984236 + 0.358233i) q^{2} +(0.0922859 + 0.523379i) q^{3} +(-0.691698 - 0.580404i) q^{4} +(-0.0966605 + 0.548189i) q^{6} +(1.37016 - 2.37320i) q^{7} +(-1.52028 - 2.63320i) q^{8} +(2.55367 - 0.929459i) q^{9} +(-0.416418 - 0.721257i) q^{11} +(0.239937 - 0.415583i) q^{12} +(0.106070 - 0.601551i) q^{13} +(2.19872 - 1.84495i) q^{14} +(-0.239424 - 1.35784i) q^{16} +(-4.54662 - 1.65483i) q^{17} +2.84638 q^{18} +(4.35537 + 0.175314i) q^{19} +(1.36853 + 0.498103i) q^{21} +(-0.151476 - 0.859062i) q^{22} +(2.87338 + 2.41106i) q^{23} +(1.23786 - 1.03869i) q^{24} +(0.319893 - 0.554071i) q^{26} +(1.51931 + 2.63152i) q^{27} +(-2.32515 + 0.846286i) q^{28} +(3.73543 - 1.35958i) q^{29} +(3.46338 - 5.99875i) q^{31} +(-0.805200 + 4.56652i) q^{32} +(0.339061 - 0.284506i) q^{33} +(-3.88213 - 3.25750i) q^{34} +(-2.30583 - 0.839253i) q^{36} +4.33071 q^{37} +(4.22391 + 1.73279i) q^{38} +0.324628 q^{39} +(0.923271 + 5.23613i) q^{41} +(1.16852 + 0.980503i) q^{42} +(-8.01164 + 6.72257i) q^{43} +(-0.130585 + 0.740582i) q^{44} +(1.96437 + 3.40239i) q^{46} +(-3.19511 + 1.16292i) q^{47} +(0.688571 - 0.250619i) q^{48} +(-0.254704 - 0.441160i) q^{49} +(0.446517 - 2.53232i) q^{51} +(-0.422511 + 0.354529i) q^{52} +(-10.4702 - 8.78556i) q^{53} +(0.552662 + 3.13430i) q^{54} -8.33212 q^{56} +(0.310183 + 2.29569i) q^{57} +4.16359 q^{58} +(-9.41315 - 3.42610i) q^{59} +(6.94990 + 5.83166i) q^{61} +(5.55774 - 4.66350i) q^{62} +(1.29316 - 7.33387i) q^{63} +(-3.80717 + 6.59422i) q^{64} +(0.435636 - 0.158558i) q^{66} +(-10.2751 + 3.73984i) q^{67} +(2.18442 + 3.78352i) q^{68} +(-0.996723 + 1.72638i) q^{69} +(-0.519169 + 0.435634i) q^{71} +(-6.32974 - 5.31128i) q^{72} +(1.21787 + 6.90688i) q^{73} +(4.26244 + 1.55140i) q^{74} +(-2.91085 - 2.64914i) q^{76} -2.28224 q^{77} +(0.319511 + 0.116292i) q^{78} +(0.604220 + 3.42670i) q^{79} +(5.00824 - 4.20241i) q^{81} +(-0.967036 + 5.48434i) q^{82} +(2.48742 - 4.30834i) q^{83} +(-0.657507 - 1.13884i) q^{84} +(-10.2936 + 3.74656i) q^{86} +(1.05630 + 1.82957i) q^{87} +(-1.26614 + 2.19302i) q^{88} +(-1.02256 + 5.79921i) q^{89} +(-1.28227 - 1.07595i) q^{91} +(-0.588129 - 3.33544i) q^{92} +(3.45924 + 1.25906i) q^{93} -3.56134 q^{94} -2.46433 q^{96} +(11.6886 + 4.25430i) q^{97} +(-0.0926508 - 0.525449i) q^{98} +(-1.73377 - 1.45481i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9} - 12 q^{11} - 6 q^{14} - 42 q^{16} - 12 q^{19} - 54 q^{21} - 24 q^{24} + 12 q^{26} - 42 q^{31} + 36 q^{34} + 18 q^{36} + 48 q^{39} + 6 q^{41} + 6 q^{44} - 6 q^{46} - 12 q^{49}+ \cdots + 36 q^{99}+O(q^{100}) $ 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9 - 12 * q^11 - 6 * q^14 - 42 * q^16 - 12 * q^19 - 54 * q^21 - 24 * q^24 + 12 * q^26 - 42 * q^31 + 36 * q^34 + 18 * q^36 + 48 * q^39 + 6 * q^41 + 6 * q^44 - 6 * q^46 - 12 * q^49 + 108 * q^51 - 24 * q^54 + 36 * q^56 + 36 * q^59 + 48 * q^61 + 180 * q^66 - 66 * q^69 - 24 * q^71 - 84 * q^74 + 66 * q^76 - 48 * q^79 - 78 * q^81 + 54 * q^84 - 42 * q^86 + 12 * q^89 - 30 * q^91 + 72 * q^94 - 240 * q^96 + 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$

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 $

$2$	0.984236	+	0.358233i	0.695960	+	0.253309i	0.665685	−	0.746233i	$-0.268139\pi$
$2$	0.984236	+	0.358233i	0.695960	+	0.253309i	0.0302752	+	0.999542i	$0.490362\pi$
$3$	0.0922859	+	0.523379i	0.0532813	+	0.302173i	0.999790	−	0.0205059i	$-0.00652769\pi$
$3$	0.0922859	+	0.523379i	0.0532813	+	0.302173i	−0.946508	+	0.322679i	$0.895417\pi$
$4$	−0.691698	−	0.580404i	−0.345849	−	0.290202i
$5$		0			0
$5$		0			0
$6$	−0.0966605	+	0.548189i	−0.0394615	+	0.223797i
$7$	1.37016	−	2.37320i	0.517874	−	0.896983i	−0.481911	−	0.876220i	$-0.660057\pi$
$7$	1.37016	−	2.37320i	0.517874	−	0.896983i	0.999784	−	0.0207632i	$-0.00660960\pi$
$8$	−1.52028	−	2.63320i	−0.537499	−	0.930976i
$9$	2.55367	−	0.929459i	0.851223	−	0.309820i
$10$		0			0
$11$	−0.416418	−	0.721257i	−0.125555	−	0.217467i	0.796395	−	0.604777i	$-0.206738\pi$
$11$	−0.416418	−	0.721257i	−0.125555	−	0.217467i	−0.921950	+	0.387310i	$0.873404\pi$
$12$	0.239937	−	0.415583i	0.0692639	−	0.119969i
$13$	0.106070	−	0.601551i	0.0294185	−	0.166840i	−0.966559	−	0.256444i	$-0.917449\pi$
$13$	0.106070	−	0.601551i	0.0294185	−	0.166840i	0.995977	+	0.0896039i	$0.0285601\pi$
$14$	2.19872	−	1.84495i	0.587633	−	0.493083i
$15$		0			0
$16$	−0.239424	−	1.35784i	−0.0598561	−	0.339461i
$17$	−4.54662	−	1.65483i	−1.10272	−	0.401356i	−0.274400	−	0.961616i	$-0.588479\pi$
$17$	−4.54662	−	1.65483i	−1.10272	−	0.401356i	−0.828317	+	0.560259i	$0.810701\pi$
$18$	2.84638			0.670897
$19$	4.35537	+	0.175314i	0.999191	+	0.0402198i
$19$	4.35537	+	0.175314i	0.999191	+	0.0402198i
$20$		0			0
$21$	1.36853	+	0.498103i	0.298637	+	0.108695i
$22$	−0.151476	−	0.859062i	−0.0322947	−	0.183153i
$23$	2.87338	+	2.41106i	0.599142	+	0.502740i	0.891170	−	0.453670i	$-0.149886\pi$
$23$	2.87338	+	2.41106i	0.599142	+	0.502740i	−0.292028	+	0.956410i	$0.594330\pi$
$24$	1.23786	−	1.03869i	0.252677	−	0.212021i
$25$		0			0
$26$	0.319893	−	0.554071i	0.0627362	−	0.108662i
$27$	1.51931	+	2.63152i	0.292391	+	0.506436i
$28$	−2.32515	+	0.846286i	−0.439412	+	0.159933i
$29$	3.73543	−	1.35958i	0.693651	−	0.252468i	0.0289533	−	0.999581i	$-0.490783\pi$
$29$	3.73543	−	1.35958i	0.693651	−	0.252468i	0.664698	+	0.747112i	$0.268560\pi$
$30$		0			0
$31$	3.46338	−	5.99875i	0.622042	−	1.07741i	−0.367063	−	0.930196i	$-0.619637\pi$
$31$	3.46338	−	5.99875i	0.622042	−	1.07741i	0.989105	−	0.147212i	$-0.0470300\pi$
$32$	−0.805200	+	4.56652i	−0.142341	+	0.807254i
$33$	0.339061	−	0.284506i	0.0590230	−	0.0495262i
$34$	−3.88213	−	3.25750i	−0.665780	−	0.558656i
$35$		0			0
$36$	−2.30583	−	0.839253i	−0.384305	−	0.139876i
$37$	4.33071			0.711965			0.355982	−	0.934493i	$-0.384146\pi$
$37$	4.33071			0.711965			0.355982	+	0.934493i	$0.384146\pi$
$38$	4.22391	+	1.73279i	0.685209	+	0.281095i
$39$	0.324628			0.0519821
$40$		0			0
$41$	0.923271	+	5.23613i	0.144191	+	0.817746i	0.968013	+	0.250899i	$0.0807260\pi$
$41$	0.923271	+	5.23613i	0.144191	+	0.817746i	−0.823823	+	0.566848i	$0.808163\pi$
$42$	1.16852	+	0.980503i	0.180306	+	0.151295i
$43$	−8.01164	+	6.72257i	−1.22176	+	1.02518i	−0.223034	+	0.974811i	$0.571596\pi$
$43$	−8.01164	+	6.72257i	−1.22176	+	1.02518i	−0.998731	+	0.0503713i	$0.983960\pi$
$44$	−0.130585	+	0.740582i	−0.0196864	+	0.111647i
$45$		0			0
$46$	1.96437	+	3.40239i	0.289631	+	0.501655i
$47$	−3.19511	+	1.16292i	−0.466054	+	0.169630i	−0.564364	−	0.825526i	$-0.690879\pi$
$47$	−3.19511	+	1.16292i	−0.466054	+	0.169630i	0.0983098	+	0.995156i	$0.468656\pi$
$48$	0.688571	−	0.250619i	0.0993867	−	0.0361738i
$49$	−0.254704	−	0.441160i	−0.0363862	−	0.0630228i
$50$		0			0
$51$	0.446517	−	2.53232i	0.0625249	−	0.354596i
$52$	−0.422511	+	0.354529i	−0.0585917	+	0.0491643i
$53$	−10.4702	−	8.78556i	−1.43820	−	1.20679i	−0.940662	−	0.339346i	$-0.889794\pi$
$53$	−10.4702	−	8.78556i	−1.43820	−	1.20679i	−0.497535	−	0.867444i	$-0.665761\pi$
$54$	0.552662	+	3.13430i	0.0752077	+	0.426524i
$55$		0			0
$56$	−8.33212			−1.11343
$57$	0.310183	+	2.29569i	0.0410848	+	0.304072i
$58$	4.16359			0.546706
$59$	−9.41315	−	3.42610i	−1.22549	−	0.446041i	−0.353437	−	0.935458i	$-0.614987\pi$
$59$	−9.41315	−	3.42610i	−1.22549	−	0.446041i	−0.872050	+	0.489417i	$0.837210\pi$
$60$		0			0
$61$	6.94990	+	5.83166i	0.889844	+	0.746668i	0.968179	−	0.250260i	$-0.0805159\pi$
$61$	6.94990	+	5.83166i	0.889844	+	0.746668i	−0.0783350	+	0.996927i	$0.524960\pi$
$62$	5.55774	−	4.66350i	0.705833	−	0.592265i
$63$	1.29316	−	7.33387i	0.162923	−	0.923980i
$64$	−3.80717	+	6.59422i	−0.475897	+	0.824277i
$65$		0			0
$66$	0.435636	−	0.158558i	0.0536231	−	0.0195172i
$67$	−10.2751	+	3.73984i	−1.25531	+	0.456894i	−0.882191	−	0.470891i	$-0.843933\pi$
$67$	−10.2751	+	3.73984i	−1.25531	+	0.456894i	−0.373115	+	0.927785i	$0.621710\pi$
$68$	2.18442	+	3.78352i	0.264899	+	0.458819i
$69$	−0.996723	+	1.72638i	−0.119991	+	0.207831i
$70$		0			0
$71$	−0.519169	+	0.435634i	−0.0616140	+	0.0517003i	−0.673075	−	0.739575i	$-0.735027\pi$
$71$	−0.519169	+	0.435634i	−0.0616140	+	0.0517003i	0.611461	+	0.791275i	$0.290582\pi$
$72$	−6.32974	−	5.31128i	−0.745967	−	0.625940i
$73$	1.21787	+	6.90688i	0.142541	+	0.808389i	0.969309	+	0.245846i	$0.0790657\pi$
$73$	1.21787	+	6.90688i	0.142541	+	0.808389i	−0.826768	+	0.562543i	$0.809823\pi$
$74$	4.26244	+	1.55140i	0.495499	+	0.180347i
$75$		0			0
$76$	−2.91085	−	2.64914i	−0.333897	−	0.303877i
$77$	−2.28224			−0.260086
$78$	0.319511	+	0.116292i	0.0361775	+	0.0131675i
$79$	0.604220	+	3.42670i	0.0679801	+	0.385534i	0.999747	+	0.0224781i	$0.00715559\pi$
$79$	0.604220	+	3.42670i	0.0679801	+	0.385534i	−0.931767	+	0.363056i	$0.881733\pi$
$80$		0			0
$81$	5.00824	−	4.20241i	0.556471	−	0.466935i
$82$	−0.967036	+	5.48434i	−0.106791	+	0.605644i
$83$	2.48742	−	4.30834i	0.273030	−	0.472902i	−0.696606	−	0.717454i	$-0.745307\pi$
$83$	2.48742	−	4.30834i	0.273030	−	0.472902i	0.969636	+	0.244552i	$0.0786408\pi$
$84$	−0.657507	−	1.13884i	−0.0717399	−	0.124257i
$85$		0			0
$86$	−10.2936	+	3.74656i	−1.10999	+	0.404002i
$87$	1.05630	+	1.82957i	0.113248	+	0.196151i
$88$	−1.26614	+	2.19302i	−0.134971	+	0.233777i
$89$	−1.02256	+	5.79921i	−0.108391	+	0.614716i	0.881421	+	0.472332i	$0.156588\pi$
$89$	−1.02256	+	5.79921i	−0.108391	+	0.614716i	−0.989812	+	0.142383i	$0.954523\pi$
$90$		0			0
$91$	−1.28227	−	1.07595i	−0.134418	−	0.112790i
$92$	−0.588129	−	3.33544i	−0.0613167	−	0.347744i
$93$	3.45924	+	1.25906i	0.358707	+	0.130559i
$94$	−3.56134			−0.367324
$95$		0			0
$96$	−2.46433			−0.251514
$97$	11.6886	+	4.25430i	1.18680	+	0.431959i	0.858598	−	0.512649i	$-0.171336\pi$
$97$	11.6886	+	4.25430i	1.18680	+	0.431959i	0.328200	+	0.944608i	$0.393558\pi$
$98$	−0.0926508	−	0.525449i	−0.00935914	−	0.0530783i
$99$	−1.73377	−	1.45481i	−0.174251	−	0.146214i
$100$		0			0
$101$	−3.08004	+	17.4678i	−0.306475	+	1.73811i	0.310003	+	0.950736i	$0.399670\pi$
$101$	−3.08004	+	17.4678i	−0.306475	+	1.73811i	−0.616478	+	0.787372i	$0.711441\pi$
$102$	1.34664	−	2.33245i	0.133337	−	0.230947i
$103$	2.60925	+	4.51935i	0.257097	+	0.445305i	0.965463	−	0.260541i	$-0.0839008\pi$
$103$	2.60925	+	4.51935i	0.257097	+	0.445305i	−0.708366	+	0.705845i	$0.750567\pi$
$104$	−1.74526	+	0.635222i	−0.171137	+	0.0622887i
$105$		0			0
$106$	−7.15790	−	12.3979i	−0.695237	−	1.20419i
$107$	7.59356	−	13.1524i	0.734097	−	1.27149i	−0.221021	−	0.975269i	$-0.570939\pi$
$107$	7.59356	−	13.1524i	0.734097	−	1.27149i	0.955118	−	0.296225i	$-0.0957277\pi$
$108$	0.476440	−	2.70203i	0.0458455	−	0.260003i
$109$	3.00487	−	2.52138i	0.287814	−	0.241505i	−0.487437	−	0.873158i	$-0.662068\pi$
$109$	3.00487	−	2.52138i	0.287814	−	0.241505i	0.775251	+	0.631654i	$0.217624\pi$
$110$		0			0
$111$	0.399663	+	2.26660i	0.0379344	+	0.215137i
$112$	−3.55048	−	1.29227i	−0.335489	−	0.122108i
$113$	3.97342			0.373788			0.186894	−	0.982380i	$-0.440158\pi$
$113$	3.97342			0.373788			0.186894	+	0.982380i	$0.440158\pi$
$114$	−0.517097	+	2.37062i	−0.0484306	+	0.222029i
$115$		0			0
$116$	−3.37289	−	1.22763i	−0.313165	−	0.113983i
$117$	−0.288251	−	1.63475i	−0.0266488	−	0.151133i
$118$	−8.03742	−	6.74420i	−0.739904	−	0.620853i
$119$	−10.1569	+	8.52262i	−0.931078	+	0.781267i
$120$		0			0
$121$	5.15319	−	8.92559i	0.468472	−	0.811417i
$122$	4.75126	+	8.22942i	0.430158	+	0.745056i
$123$	−2.65528	+	0.966441i	−0.239418	+	0.0871411i
$124$	−5.87731	+	2.13917i	−0.527798	+	0.192103i
$125$		0			0
$126$	3.90001	−	6.75501i	0.347440	−	0.601784i
$127$	1.59495	−	9.04543i	0.141529	−	0.802652i	−0.828559	−	0.559901i	$-0.810839\pi$
$127$	1.59495	−	9.04543i	0.141529	−	0.802652i	0.970089	−	0.242751i	$-0.0780497\pi$
$128$	0.994815	−	0.834749i	0.0879301	−	0.0737821i
$129$	−4.25781	−	3.57273i	−0.374880	−	0.314561i
$130$		0			0
$131$	3.51355	+	1.27883i	0.306980	+	0.111732i	0.490917	−	0.871206i	$-0.336662\pi$
$131$	3.51355	+	1.27883i	0.306980	+	0.111732i	−0.183936	+	0.982938i	$0.558884\pi$
$132$	−0.399656			−0.0347856
$133$	6.38363	−	10.0959i	0.553531	−	0.875429i
$134$	−11.4529			−0.989379
$135$		0			0
$136$	2.55462	+	14.4880i	0.219057	+	1.24233i
$137$	1.81043	+	1.51913i	0.154675	+	0.129788i	0.716841	−	0.697237i	$-0.245587\pi$
$137$	1.81043	+	1.51913i	0.154675	+	0.129788i	−0.562166	+	0.827025i	$0.690032\pi$
$138$	−1.59946	+	1.34210i	−0.136155	+	0.114247i
$139$	0.424186	−	2.40568i	0.0359790	−	0.204047i	−0.961519	−	0.274737i	$-0.911409\pi$
$139$	0.424186	−	2.40568i	0.0359790	−	0.204047i	0.997498	+	0.0706903i	$0.0225202\pi$
$140$		0			0
$141$	−0.903514	−	1.56493i	−0.0760896	−	0.131791i
$142$	−0.667043	+	0.242784i	−0.0559770	+	0.0203740i
$143$	−0.478042	+	0.173993i	−0.0399759	+	0.0145500i
$144$	−1.87347	−	3.24495i	−0.156123	−	0.270412i
$145$		0			0
$146$	−1.27560	+	7.23428i	−0.105569	+	0.598713i
$147$	0.207388	−	0.174019i	0.0171051	−	0.0143529i
$148$	−2.99555	−	2.51356i	−0.246232	−	0.206613i
$149$	2.47773	+	14.0519i	0.202984	+	1.15118i	0.900581	+	0.434687i	$0.143141\pi$
$149$	2.47773	+	14.0519i	0.202984	+	1.15118i	−0.697598	+	0.716490i	$0.745748\pi$
$150$		0			0
$151$	2.34319			0.190686			0.0953432	−	0.995444i	$-0.469605\pi$
$151$	2.34319			0.190686			0.0953432	+	0.995444i	$0.469605\pi$
$152$	−6.15974	−	11.7351i	−0.499621	−	0.951841i
$153$	−13.1487			−1.06301
$154$	−2.24627	−	0.817575i	−0.181009	−	0.0658820i
$155$		0			0
$156$	−0.224545	−	0.188415i	−0.0179780	−	0.0150853i
$157$	−12.3906	+	10.3969i	−0.988875	+	0.829765i	−0.985405	−	0.170229i	$-0.945549\pi$
$157$	−12.3906	+	10.3969i	−0.988875	+	0.829765i	−0.00347076	+	0.999994i	$0.501105\pi$
$158$	−0.632862	+	3.58914i	−0.0503478	+	0.285536i
$159$	3.63193	−	6.29068i	0.288031	−	0.498884i
$160$		0			0
$161$	9.65891	−	3.51556i	0.761229	−	0.277065i
$162$	6.43473	−	2.34205i	0.505560	−	0.184009i
$163$	8.01289	+	13.8787i	0.627618	+	1.08707i	0.988028	+	0.154273i	$0.0493034\pi$
$163$	8.01289	+	13.8787i	0.627618	+	1.08707i	−0.360410	+	0.932794i	$0.617363\pi$
$164$	2.40044	−	4.15769i	0.187443	−	0.324661i
$165$		0			0
$166$	3.99160	−	3.34935i	0.309809	−	0.259960i
$167$	5.80391	+	4.87006i	0.449120	+	0.376856i	0.839109	−	0.543963i	$-0.183077\pi$
$167$	5.80391	+	4.87006i	0.449120	+	0.376856i	−0.389989	+	0.920819i	$0.627521\pi$
$168$	−0.768937	−	4.36086i	−0.0593248	−	0.336448i
$169$	11.8654	+	4.31865i	0.912722	+	0.332204i
$170$		0			0
$171$	11.2851	−	3.60045i	0.862995	−	0.275333i
$172$	9.44344			0.720056
$173$	8.32761	+	3.03100i	0.633136	+	0.230443i	0.638596	−	0.769542i	$-0.279516\pi$
$173$	8.32761	+	3.03100i	0.633136	+	0.230443i	−0.00545960	+	0.999985i	$0.501738\pi$
$174$	0.384240	+	2.17914i	0.0291292	+	0.165200i
$175$		0			0
$176$	−0.879653	+	0.738116i	−0.0663063	+	0.0556376i
$177$	0.924452	−	5.24283i	0.0694860	−	0.394075i
$178$	−3.08391	+	5.34148i	−0.231149	+	0.400361i
$179$	−2.73273	−	4.73323i	−0.204254	−	0.353778i	0.745641	−	0.666348i	$-0.232143\pi$
$179$	−2.73273	−	4.73323i	−0.204254	−	0.353778i	−0.949895	+	0.312570i	$0.898810\pi$
$180$		0			0
$181$	−17.6816	+	6.43559i	−1.31427	+	0.478354i	−0.901617	−	0.432536i	$-0.857619\pi$
$181$	−17.6816	+	6.43559i	−1.31427	+	0.478354i	−0.412650	+	0.910890i	$0.635397\pi$
$182$	−0.876613	−	1.51834i	−0.0649789	−	0.112547i
$183$	−2.41079	+	4.17561i	−0.178211	+	0.308670i
$184$	1.98044	−	11.2317i	0.146000	−	0.828009i
$185$		0			0
$186$	2.95368	+	2.47843i	0.216574	+	0.181727i
$187$	0.699733	+	3.96838i	0.0511695	+	0.290197i
$188$	2.88502	+	1.05006i	0.210411	+	0.0765835i
$189$	8.32680			0.605686
$190$		0			0
$191$	−17.2606			−1.24893			−0.624465	−	0.781053i	$-0.714683\pi$
$191$	−17.2606			−1.24893			−0.624465	+	0.781053i	$0.714683\pi$
$192$	−3.80262	−	1.38404i	−0.274431	−	0.0998846i
$193$	1.29789	+	7.36067i	0.0934238	+	0.529833i	0.995219	+	0.0976691i	$0.0311387\pi$
$193$	1.29789	+	7.36067i	0.0934238	+	0.529833i	−0.901795	+	0.432164i	$0.857750\pi$
$194$	9.98032	+	8.37448i	0.716545	+	0.601253i
$195$		0			0
$196$	−0.0798727	+	0.452980i	−0.00570519	+	0.0323557i
$197$	−6.10400	+	10.5724i	−0.434892	+	0.753255i	−0.997287	−	0.0736138i	$-0.976547\pi$
$197$	−6.10400	+	10.5724i	−0.434892	+	0.753255i	0.562395	+	0.826869i	$0.309880\pi$
$198$	−1.18528	−	2.05297i	−0.0842343	−	0.145898i
$199$	7.29002	−	2.65335i	0.516776	−	0.188091i	−0.0704481	−	0.997515i	$-0.522443\pi$
$199$	7.29002	−	2.65335i	0.516776	−	0.188091i	0.587224	+	0.809424i	$0.300221\pi$
$200$		0			0
$201$	−2.90560	−	5.03265i	−0.204945	−	0.354976i
$202$	−9.28901	+	16.0890i	−0.653573	+	1.13202i
$203$	1.89159	−	10.7277i	0.132764	−	0.752940i
$204$	−1.77862	+	1.49244i	−0.124529	+	0.104492i
$205$		0			0
$206$	0.949137	+	5.38282i	0.0661295	+	0.375039i
$207$	9.57865	+	3.48634i	0.665762	+	0.242318i
$208$	−0.842208			−0.0583966
$209$	−1.68721	−	3.21434i	−0.116707	−	0.222341i
$210$		0			0
$211$	−9.45058	−	3.43973i	−0.650605	−	0.236801i	−0.00442979	−	0.999990i	$-0.501410\pi$
$211$	−9.45058	−	3.43973i	−0.650605	−	0.236801i	−0.646175	+	0.763190i	$0.723632\pi$
$212$	2.14306	+	12.1539i	0.147186	+	0.834734i
$213$	−0.275914	−	0.231519i	−0.0189053	−	0.0158634i
$214$	12.1855	−	10.2248i	0.832983	−	0.698956i
$215$		0			0
$216$	4.61954	−	8.00127i	0.314320	−	0.544418i
$217$	−9.49081	−	16.4386i	−0.644278	−	1.11592i
$218$	3.86074	−	1.40519i	0.261482	−	0.0951718i
$219$	−3.50252	+	1.27481i	−0.236679	+	0.0861440i
$220$		0			0
$221$	−1.47773	+	2.55950i	−0.0994027	+	0.172170i
$222$	−0.418609	+	2.37405i	−0.0280952	+	0.159336i
$223$	21.6954	−	18.2046i	1.45283	−	1.21907i	0.522350	−	0.852731i	$-0.325056\pi$
$223$	21.6954	−	18.2046i	1.45283	−	1.21907i	0.930482	−	0.366339i	$-0.119389\pi$
$224$	9.73398	+	8.16778i	0.650379	+	0.545733i
$225$		0			0
$226$	3.91079	+	1.42341i	0.260142	+	0.0946839i
$227$	−15.8786			−1.05390			−0.526949	−	0.849897i	$-0.676664\pi$
$227$	−15.8786			−1.05390			−0.526949	+	0.849897i	$0.676664\pi$
$228$	1.11787	−	1.76796i	0.0740330	−	0.117086i
$229$	11.3865			0.752438			0.376219	−	0.926531i	$-0.377224\pi$
$229$	11.3865			0.752438			0.376219	+	0.926531i	$0.377224\pi$
$230$		0			0
$231$	−0.210619	−	1.19448i	−0.0138577	−	0.0785909i
$232$	−9.25894	−	7.76917i	−0.607879	−	0.510071i
$233$	−12.1527	+	10.1973i	−0.796151	+	0.668050i	−0.947260	−	0.320467i	$-0.896160\pi$
$233$	−12.1527	+	10.1973i	−0.796151	+	0.668050i	0.151109	+	0.988517i	$0.451716\pi$
$234$	0.301914	−	1.71224i	0.0197368	−	0.111933i
$235$		0			0
$236$	4.52253	+	7.83325i	0.294392	+	0.509901i
$237$	−1.73770	+	0.632473i	−0.112876	+	0.0410835i
$238$	−13.0498	+	4.74975i	−0.845895	+	0.307881i
$239$	−10.4324	−	18.0695i	−0.674817	−	1.16882i	−0.976522	−	0.215416i	$-0.930889\pi$
$239$	−10.4324	−	18.0695i	−0.674817	−	1.16882i	0.301705	−	0.953401i	$-0.402444\pi$
$240$		0			0
$241$	4.93664	−	27.9971i	0.317997	−	1.80345i	−0.236902	−	0.971533i	$-0.576132\pi$
$241$	4.93664	−	27.9971i	0.317997	−	1.80345i	0.554899	−	0.831917i	$-0.312757\pi$
$242$	8.26940	−	6.93885i	0.531577	−	0.446046i
$243$	9.64478	+	8.09293i	0.618713	+	0.519162i
$244$	−1.42252	−	8.06750i	−0.0910673	−	0.516469i
$245$		0			0
$246$	−2.95963			−0.188699
$247$	0.567434	−	2.60138i	0.0361049	−	0.165522i
$248$	−21.0612			−1.33739
$249$	2.48445	+	0.904266i	0.157446	+	0.0573056i
$250$		0			0
$251$	19.0083	+	15.9499i	1.19979	+	1.00675i	0.999636	+	0.0269823i	$0.00858979\pi$
$251$	19.0083	+	15.9499i	1.19979	+	1.00675i	0.200157	+	0.979764i	$0.435855\pi$
$252$	−5.15108	+	4.32227i	−0.324487	+	0.272277i
$253$	0.542462	−	3.07645i	0.0341043	−	0.193415i
$254$	4.81018	−	8.33148i	0.301818	−	0.522763i
$255$		0			0
$256$	15.5885	−	5.67373i	0.974279	−	0.354608i
$257$	5.11403	−	1.86135i	0.319004	−	0.116108i	−0.177555	−	0.984111i	$-0.556819\pi$
$257$	5.11403	−	1.86135i	0.319004	−	0.116108i	0.496559	+	0.868003i	$0.334597\pi$
$258$	−2.91083	−	5.04170i	−0.181220	−	0.313882i
$259$	5.93379	−	10.2776i	0.368708	−	0.638620i
$260$		0			0
$261$	8.27536	−	6.94385i	0.512232	−	0.429814i
$262$	3.00005	+	2.51734i	0.185344	+	0.155522i
$263$	−3.38955	−	19.2231i	−0.209009	−	1.18535i	−0.891006	−	0.453992i	$-0.849999\pi$
$263$	−3.38955	−	19.2231i	−0.209009	−	1.18535i	0.681997	−	0.731355i	$-0.261112\pi$
$264$	−1.26463	−	0.460287i	−0.0778325	−	0.0283287i
$265$		0			0
$266$	9.89970	−	7.64996i	0.606990	−	0.469049i
$267$	−3.12956			−0.191526
$268$	9.27790	+	3.37688i	0.566738	+	0.206276i
$269$	3.22722	+	18.3025i	0.196767	+	1.11592i	0.909880	+	0.414872i	$0.136174\pi$
$269$	3.22722	+	18.3025i	0.196767	+	1.11592i	−0.713113	+	0.701049i	$0.752715\pi$
$270$		0			0
$271$	1.44946	−	1.21624i	0.0880485	−	0.0738815i	−0.597701	−	0.801719i	$-0.703919\pi$
$271$	1.44946	−	1.21624i	0.0880485	−	0.0738815i	0.685749	+	0.727838i	$0.259475\pi$
$272$	−1.15843	+	6.56980i	−0.0702403	+	0.398353i
$273$	0.444794	−	0.770406i	0.0269202	−	0.0466271i
$274$	1.23769	+	2.14374i	0.0747715	+	0.129508i
$275$		0			0
$276$	1.69143	−	0.615629i	0.101812	−	0.0370565i
$277$	3.38944	+	5.87068i	0.203652	+	0.352735i	0.949702	−	0.313154i	$-0.101386\pi$
$277$	3.38944	+	5.87068i	0.203652	+	0.352735i	−0.746051	+	0.665889i	$0.768052\pi$
$278$	1.27929	−	2.21580i	0.0767269	−	0.132895i
$279$	3.26873	−	18.5379i	0.195694	−	1.10984i
$280$		0			0
$281$	−9.41170	−	7.89735i	−0.561455	−	0.471116i	0.317343	−	0.948311i	$-0.397209\pi$
$281$	−9.41170	−	7.89735i	−0.561455	−	0.471116i	−0.878798	+	0.477194i	$0.841654\pi$
$282$	−0.328661	−	1.86393i	−0.0195715	−	0.110995i
$283$	−24.1188	−	8.77851i	−1.43371	−	0.521829i	−0.495719	−	0.868483i	$-0.665095\pi$
$283$	−24.1188	−	8.77851i	−1.43371	−	0.521829i	−0.937993	+	0.346654i	$0.887318\pi$
$284$	0.611952			0.0363126
$285$		0			0
$286$	−0.532837			−0.0315073
$287$	13.6914	+	4.98326i	0.808177	+	0.294152i
$288$	2.18818	+	12.4098i	0.128940	+	0.731253i
$289$	4.91052	+	4.12042i	0.288854	+	0.242377i
$290$		0			0
$291$	−1.14792	+	6.51018i	−0.0672923	+	0.381634i
$292$	3.16638	−	5.48433i	0.185298	−	0.320946i
$293$	14.0560	+	24.3458i	0.821162	+	1.42229i	0.904817	+	0.425800i	$0.140007\pi$
$293$	14.0560	+	24.3458i	0.821162	+	1.42229i	−0.0836552	+	0.996495i	$0.526659\pi$
$294$	0.266459	−	0.0969830i	0.0155402	−	0.00565616i
$295$		0			0
$296$	−6.58388	−	11.4036i	−0.382680	−	0.662822i
$297$	1.26533	−	2.19162i	0.0734220	−	0.127171i
$298$	−2.59518	+	14.7180i	−0.150335	+	0.852591i
$299$	1.75515	−	1.47275i	0.101503	−	0.0851712i
$300$		0			0
$301$	4.97669	+	28.2242i	0.286852	+	1.62682i
$302$	2.30626	+	0.839409i	0.132710	+	0.0483025i
$303$	−9.42651			−0.541539
$304$	−0.804733	−	5.95588i	−0.0461546	−	0.341593i
$305$		0			0
$306$	−12.9414	−	4.71028i	−0.739810	−	0.269269i
$307$	−0.447450	−	2.53762i	−0.0255373	−	0.144829i	0.969373	−	0.245593i	$-0.0789826\pi$
$307$	−0.447450	−	2.53762i	−0.0255373	−	0.144829i	−0.994910	+	0.100763i	$0.967872\pi$
$308$	1.57862	+	1.32462i	0.0899504	+	0.0754774i
$309$	−2.12454	+	1.78270i	−0.120861	+	0.101414i
$310$		0			0
$311$	−7.31837	+	12.6758i	−0.414987	+	0.718778i	−0.995427	−	0.0955246i	$-0.969547\pi$
$311$	−7.31837	+	12.6758i	−0.414987	+	0.718778i	0.580440	+	0.814303i	$0.302880\pi$
$312$	−0.493525	−	0.854810i	−0.0279403	−	0.0483941i
$313$	−1.40398	+	0.511007i	−0.0793577	+	0.0288838i	−0.381394	−	0.924413i	$-0.624556\pi$
$313$	−1.40398	+	0.511007i	−0.0793577	+	0.0288838i	0.302036	+	0.953296i	$0.402334\pi$
$314$	−15.9198	+	5.79432i	−0.898405	+	0.326993i
$315$		0			0
$316$	1.57093	−	2.72094i	0.0883719	−	0.153065i
$317$	0.979782	−	5.55662i	0.0550301	−	0.312091i	−0.944851	−	0.327500i	$-0.893794\pi$
$317$	0.979782	−	5.55662i	0.0550301	−	0.312091i	0.999881	+	0.0154089i	$0.00490501\pi$
$318$	5.82820	−	4.89044i	0.326829	−	0.274242i
$319$	−2.53611	−	2.12805i	−0.141995	−	0.119148i
$320$		0			0
$321$	7.58449	+	2.76053i	0.423325	+	0.154078i
$322$	10.7660			0.599968
$323$	−19.5121	−	8.00451i	−1.08568	−	0.445383i
$324$	−5.90329			−0.327960
$325$		0			0
$326$	2.91476	+	16.5304i	0.161434	+	0.915536i
$327$	1.59694	+	1.34000i	0.0883113	+	0.0741019i
$328$	12.3841	−	10.3915i	0.683800	−	0.573776i
$329$	−1.61798	+	9.17601i	−0.0892021	+	0.505890i
$330$		0			0
$331$	−15.9460	−	27.6193i	−0.876472	−	1.51809i	−0.855186	−	0.518321i	$-0.826557\pi$
$331$	−15.9460	−	27.6193i	−0.876472	−	1.51809i	−0.0212866	−	0.999773i	$-0.506776\pi$
$332$	−4.22113	+	1.53636i	−0.231664	+	0.0843189i
$333$	11.0592	−	4.02522i	0.606041	−	0.220581i
$334$	3.96780	+	6.87244i	0.217109	+	0.376043i
$335$		0			0
$336$	0.348687	−	1.97750i	0.0190224	−	0.107882i
$337$	11.7495	−	9.85896i	0.640033	−	0.537052i	−0.263995	−	0.964524i	$-0.585040\pi$
$337$	11.7495	−	9.85896i	0.640033	−	0.537052i	0.904029	+	0.427472i	$0.140596\pi$
$338$	10.1313	+	8.50114i	0.551068	+	0.462401i
$339$	0.366691	+	2.07961i	0.0199159	+	0.112949i
$340$		0			0
$341$	−5.76886			−0.312401
$342$	12.3970	+	0.499010i	0.670355	+	0.0269834i
$343$	17.7864			0.960373
$344$	29.8818	+	10.8761i	1.61112	+	0.586399i
$345$		0			0
$346$	7.11053	+	5.96644i	0.382264	+	0.320758i
$347$	−0.0633501	+	0.0531571i	−0.00340081	+	0.00285362i	−0.644486	−	0.764616i	$-0.722929\pi$
$347$	−0.0633501	+	0.0531571i	−0.00340081	+	0.00285362i	0.641086	+	0.767469i	$0.278484\pi$
$348$	0.331247	−	1.87860i	0.0177567	−	0.100703i
$349$	2.32166	−	4.02124i	0.124276	−	0.215252i	−0.797174	−	0.603750i	$-0.793673\pi$
$349$	2.32166	−	4.02124i	0.124276	−	0.215252i	0.921450	+	0.388498i	$0.127006\pi$
$350$		0			0
$351$	1.74415	−	0.634817i	0.0930956	−	0.0338840i
$352$	3.62893	−	1.32082i	0.193423	−	0.0704001i
$353$	−1.99701	−	3.45892i	−0.106290	−	0.184100i	0.807974	−	0.589218i	$-0.200564\pi$
$353$	−1.99701	−	3.45892i	−0.106290	−	0.184100i	−0.914265	+	0.405118i	$0.867231\pi$
$354$	2.78803	−	4.82901i	0.148182	−	0.256659i
$355$		0			0
$356$	4.07319	−	3.41781i	0.215878	−	0.181144i
$357$	−5.39790	−	4.52937i	−0.285687	−	0.239720i
$358$	−0.994055	−	5.63757i	−0.0525374	−	0.297955i
$359$	−28.3973	−	10.3358i	−1.49875	−	0.545502i	−0.543017	−	0.839722i	$-0.682718\pi$
$359$	−28.3973	−	10.3358i	−1.49875	−	0.545502i	−0.955738	+	0.294220i	$0.904940\pi$
$360$		0			0
$361$	18.9385	+	1.52712i	0.996765	+	0.0803746i
$362$	−19.7084			−1.03585
$363$	5.14704	+	1.87337i	0.270149	+	0.0983263i
$364$	0.262456	+	1.48846i	0.0137564	+	0.0780167i
$365$		0			0
$366$	−3.86863	+	3.24617i	−0.202217	+	0.169680i
$367$	3.14996	−	17.8643i	0.164427	−	0.932511i	−0.785227	−	0.619208i	$-0.787454\pi$
$367$	3.14996	−	17.8643i	0.164427	−	0.932511i	0.949653	−	0.313302i	$-0.101435\pi$
$368$	2.58588	−	4.47887i	0.134798	−	0.233477i
$369$	7.22450	+	12.5132i	0.376092	+	0.651411i
$370$		0			0
$371$	−35.1958	+	12.8102i	−1.82727	+	0.665074i
$372$	−1.66199	−	2.87865i	−0.0861701	−	0.149251i
$373$	12.6075	−	21.8369i	0.652794	−	1.13067i	−0.329648	−	0.944104i	$-0.606930\pi$
$373$	12.6075	−	21.8369i	0.652794	−	1.13067i	0.982442	−	0.186568i	$-0.0597365\pi$
$374$	−0.732902	+	4.15649i	−0.0378975	+	0.214927i
$375$		0			0
$376$	7.91966	+	6.64538i	0.408425	+	0.342710i
$377$	−0.421644	−	2.39126i	−0.0217158	−	0.123156i
$378$	8.19554	+	2.98293i	0.421533	+	0.153426i
$379$	−27.5634			−1.41584			−0.707918	−	0.706294i	$-0.750366\pi$
$379$	−27.5634			−1.41584			−0.707918	+	0.706294i	$0.750366\pi$
$380$		0			0
$381$	4.88138			0.250081
$382$	−16.9885	−	6.18330i	−0.869206	−	0.316365i
$383$	3.18187	+	18.0453i	0.162586	+	0.922072i	0.951518	+	0.307592i	$0.0995230\pi$
$383$	3.18187	+	18.0453i	0.162586	+	0.922072i	−0.788932	+	0.614480i	$0.789366\pi$
$384$	0.528698	+	0.443630i	0.0269800	+	0.0226389i
$385$		0			0
$386$	−1.35941	+	7.70959i	−0.0691921	+	0.392408i
$387$	−14.2107	+	24.6137i	−0.722372	+	1.25119i
$388$	−5.61577	−	9.72680i	−0.285098	−	0.493803i
$389$	6.75172	−	2.45743i	0.342326	−	0.124596i	−0.165136	−	0.986271i	$-0.552806\pi$
$389$	6.75172	−	2.45743i	0.342326	−	0.124596i	0.507461	+	0.861674i	$0.330584\pi$
$390$		0			0
$391$	−9.07429	−	15.7171i	−0.458906	−	0.794849i
$392$	−0.774441	+	1.34137i	−0.0391152	+	0.0677495i
$393$	−0.345061	+	1.95694i	−0.0174060	+	0.0987144i
$394$	−9.79517	+	8.21913i	−0.493474	+	0.414074i
$395$		0			0
$396$	0.354871	+	2.01257i	0.0178330	+	0.101136i
$397$	11.0172	+	4.00993i	0.552937	+	0.201252i	0.603351	−	0.797476i	$-0.293832\pi$
$397$	11.0172	+	4.00993i	0.552937	+	0.201252i	−0.0504142	+	0.998728i	$0.516054\pi$
$398$	8.12562			0.407301
$399$	5.87312	+	2.40935i	0.294024	+	0.120618i
$400$		0			0
$401$	−36.8475	−	13.4114i	−1.84008	−	0.669734i	−0.989623	−	0.143686i	$-0.954105\pi$
$401$	−36.8475	−	13.4114i	−1.84008	−	0.669734i	−0.850455	−	0.526048i	$-0.823673\pi$
$402$	−1.05694	−	5.99420i	−0.0527154	−	0.298964i
$403$	−3.24120	−	2.71969i	−0.161456	−	0.135477i
$404$	12.2688	−	10.2948i	0.610396	−	0.512183i
$405$		0			0
$406$	5.70480	−	9.88101i	0.283125	−	0.490386i
$407$	−1.80339	−	3.12355i	−0.0893905	−	0.154829i
$408$	−7.34694	+	2.67407i	−0.363728	+	0.132386i
$409$	−8.34099	+	3.03587i	−0.412436	+	0.150114i	−0.539901	−	0.841729i	$-0.681538\pi$
$409$	−8.34099	+	3.03587i	−0.412436	+	0.150114i	0.127465	+	0.991843i	$0.459316\pi$
$410$		0			0
$411$	−0.628004	+	1.08773i	−0.0309772	+	0.0536540i
$412$	0.818235	−	4.64044i	0.0403115	−	0.228618i
$413$	−21.0284	+	17.6449i	−1.03474	+	0.868249i
$414$	8.17873	+	6.86277i	0.401963	+	0.337287i
$415$		0			0
$416$	2.66159	+	0.968738i	0.130495	+	0.0474963i
$417$	1.29823			0.0635745
$418$	−0.509128	−	3.76809i	−0.0249022	−	0.184303i
$419$	−7.80196			−0.381151			−0.190575	−	0.981673i	$-0.561035\pi$
$419$	−7.80196			−0.381151			−0.190575	+	0.981673i	$0.561035\pi$
$420$		0			0
$421$	6.00077	+	34.0320i	0.292459	+	1.65862i	0.677352	+	0.735659i	$0.263127\pi$
$421$	6.00077	+	34.0320i	0.292459	+	1.65862i	−0.384893	+	0.922961i	$0.625762\pi$
$422$	−8.06938	−	6.77101i	−0.392811	−	0.329608i
$423$	−7.07836	+	5.93945i	−0.344161	+	0.288786i
$424$	−7.21648	+	40.9267i	−0.350463	+	1.98758i
$425$		0			0
$426$	−0.188627	−	0.326711i	−0.00913899	−	0.0158292i
$427$	23.3622	−	8.50314i	1.13058	−	0.411496i
$428$	−12.8862	+	4.69018i	−0.622877	+	0.226709i
$429$	−0.135181	−	0.234140i	−0.00652660	−	0.0113044i
$430$		0			0
$431$	0.493077	−	2.79638i	0.0237507	−	0.134697i	−0.970627	−	0.240590i	$-0.922659\pi$
$431$	0.493077	−	2.79638i	0.0237507	−	0.134697i	0.994377	+	0.105893i	$0.0337702\pi$
$432$	3.20943	−	2.69303i	0.154414	−	0.129568i
$433$	−16.7402	−	14.0467i	−0.804481	−	0.675040i	0.144803	−	0.989461i	$-0.453745\pi$
$433$	−16.7402	−	14.0467i	−0.804481	−	0.675040i	−0.949284	+	0.314421i	$0.898190\pi$
$434$	−3.45237	−	19.5794i	−0.165719	−	0.939839i
$435$		0			0
$436$	−3.54188			−0.169625
$437$	12.0920	+	11.0048i	0.578437	+	0.526430i
$438$	−3.90399			−0.186540
$439$	−30.6114	−	11.1416i	−1.46100	−	0.531761i	−0.515361	−	0.856973i	$-0.672342\pi$
$439$	−30.6114	−	11.1416i	−1.46100	−	0.531761i	−0.945641	+	0.325212i	$0.894564\pi$
$440$		0			0
$441$	−1.06047	−	0.889839i	−0.0504985	−	0.0423733i
$442$	−2.37133	+	1.98978i	−0.112793	+	0.0946442i
$443$	1.34781	−	7.64381i	0.0640364	−	0.363169i	−0.935904	−	0.352255i	$-0.885415\pi$
$443$	1.34781	−	7.64381i	0.0640364	−	0.363169i	0.999940	−	0.0109135i	$-0.00347393\pi$
$444$	1.03910	−	1.79977i	0.0493134	−	0.0854134i
$445$		0			0
$446$	27.8749	−	10.1456i	1.31991	−	0.480409i
$447$	−7.12581	+	2.59358i	−0.337039	+	0.122672i
$448$	10.4329	+	18.0703i	0.492909	+	0.853743i
$449$	−11.4911	+	19.9031i	−0.542296	+	0.939285i	0.456475	+	0.889736i	$0.349112\pi$
$449$	−11.4911	+	19.9031i	−0.542296	+	0.939285i	−0.998772	+	0.0495489i	$0.984222\pi$
$450$		0			0
$451$	3.39213	−	2.84633i	0.159729	−	0.134029i
$452$	−2.74841	−	2.30619i	−0.129274	−	0.108474i
$453$	0.216244	+	1.22638i	0.0101600	+	0.0576203i
$454$	−15.6283	−	5.68822i	−0.733470	−	0.266961i
$455$		0			0
$456$	5.57344	−	4.30686i	0.261000	−	0.201687i
$457$	3.38866			0.158515			0.0792573	−	0.996854i	$-0.474745\pi$
$457$	3.38866			0.158515			0.0792573	+	0.996854i	$0.474745\pi$
$458$	11.2070	+	4.07900i	0.523667	+	0.190599i
$459$	−2.55299	−	14.4787i	−0.119163	−	0.675808i
$460$		0			0
$461$	−8.31382	+	6.97612i	−0.387213	+	0.324910i	−0.815526	−	0.578720i	$-0.803552\pi$
$461$	−8.31382	+	6.97612i	−0.387213	+	0.324910i	0.428313	+	0.903630i	$0.359108\pi$
$462$	0.220603	−	1.25110i	0.0102634	−	0.0582064i
$463$	−3.65586	+	6.33213i	−0.169902	+	0.294279i	−0.938385	−	0.345591i	$-0.887678\pi$
$463$	−3.65586	+	6.33213i	−0.169902	+	0.294279i	0.768483	+	0.639870i	$0.221012\pi$
$464$	−2.74045	−	4.74660i	−0.127222	−	0.220355i
$465$		0			0
$466$	−15.6142	+	5.68309i	−0.723313	+	0.263264i
$467$	5.42091	+	9.38929i	0.250850	+	0.434484i	0.963760	−	0.266771i	$-0.0859567\pi$
$467$	5.42091	+	9.38929i	0.250850	+	0.434484i	−0.712910	+	0.701255i	$0.752623\pi$
$468$	−0.749433	+	1.29806i	−0.0346425	+	0.0600026i
$469$	−5.20325	+	29.5091i	−0.240264	+	1.36260i
$470$		0			0
$471$	−6.58501	−	5.52548i	−0.303421	−	0.254601i
$472$	5.28898	+	29.9953i	0.243445	+	1.38065i
$473$	8.18489	+	2.97906i	0.376342	+	0.136977i
$474$	−1.93688			−0.0889640
$475$		0			0
$476$	11.9720			0.548738
$477$	−34.9033	−	12.7038i	−1.59811	−	0.581666i
$478$	−3.79489	−	21.5219i	−0.173574	−	0.984388i
$479$	2.64084	+	2.21593i	0.120663	+	0.101249i	0.701123	−	0.713041i	$-0.252683\pi$
$479$	2.64084	+	2.21593i	0.120663	+	0.101249i	−0.580459	+	0.814289i	$0.697127\pi$
$480$		0			0
$481$	0.459357	−	2.60515i	0.0209449	−	0.118784i
$482$	14.8883	−	25.7873i	0.678143	−	1.17458i
$483$	2.73135	+	4.73084i	0.124281	+	0.215261i
$484$	−8.74490	+	3.18288i	−0.397495	+	0.144677i
$485$		0			0
$486$	6.59359	+	11.4204i	0.299091	+	0.518042i
$487$	−13.4986	+	23.3802i	−0.611680	+	1.05946i	0.379278	+	0.925283i	$0.376172\pi$
$487$	−13.4986	+	23.3802i	−0.611680	+	1.05946i	−0.990957	+	0.134177i	$0.957161\pi$
$488$	4.79014	−	27.1662i	0.216839	−	1.22976i
$489$	−6.52436	+	5.47459i	−0.295042	+	0.247570i
$490$		0			0
$491$	0.0423665	+	0.240272i	0.00191197	+	0.0108433i	0.985749	−	0.168224i	$-0.0538032\pi$
$491$	0.0423665	+	0.240272i	0.00191197	+	0.0108433i	−0.983837	+	0.179067i	$0.942692\pi$
$492$	2.39758	+	0.872646i	0.108091	+	0.0393419i
$493$	−19.2334			−0.866231
$494$	1.49039	−	2.35710i	0.0670558	−	0.106051i
$495$		0			0
$496$	−8.97458	−	3.26648i	−0.402971	−	0.146669i
$497$	0.322498	+	1.82898i	0.0144660	+	0.0820409i
$498$	2.12135	+	1.78002i	0.0950600	+	0.0797648i
$499$	−2.48864	+	2.08821i	−0.111407	+	0.0934813i	−0.696789	−	0.717276i	$-0.745389\pi$
$499$	−2.48864	+	2.08821i	−0.111407	+	0.0934813i	0.585383	+	0.810757i	$0.300944\pi$
$500$		0			0
$501$	−2.01327	+	3.48708i	−0.0899462	+	0.155791i
$502$	12.9949	+	22.5078i	0.579991	+	1.00457i
$503$	−6.69573	+	2.43705i	−0.298548	+	0.108663i	−0.486951	−	0.873429i	$-0.661891\pi$
$503$	−6.69573	+	2.43705i	−0.298548	+	0.108663i	0.188403	+	0.982092i	$0.439669\pi$
$504$	−21.2775	+	7.74437i	−0.947774	+	0.344962i
$505$		0			0
$506$	1.63600	−	2.83363i	0.0727289	−	0.125970i
$507$	−1.16528	+	6.60865i	−0.0517520	+	0.293500i
$508$	−6.35323	+	5.33099i	−0.281879	+	0.236524i
$509$	1.32543	+	1.11216i	0.0587485	+	0.0492958i	0.671689	−	0.740833i	$-0.265569\pi$
$509$	1.32543	+	1.11216i	0.0587485	+	0.0492958i	−0.612941	+	0.790129i	$0.710014\pi$
$510$		0			0
$511$	18.0600	+	6.57332i	0.798929	+	0.290787i
$512$	14.7780			0.653100
$513$	6.15580	+	11.7276i	0.271785	+	0.517786i
$514$	5.70021			0.251426
$515$		0			0
$516$	0.871496	+	4.94250i	0.0383655	+	0.217581i
$517$	2.16927	+	1.82023i	0.0954042	+	0.0800537i
$518$	9.52203	−	7.98993i	0.418374	−	0.351058i
$519$	−0.817842	+	4.63821i	−0.0358993	+	0.203595i
$520$		0			0
$521$	−6.40164	−	11.0880i	−0.280461	−	0.485773i	0.691037	−	0.722819i	$-0.257154\pi$
$521$	−6.40164	−	11.0880i	−0.280461	−	0.485773i	−0.971498	+	0.237046i	$0.923821\pi$
$522$	10.6324	−	3.86989i	0.465369	−	0.169380i
$523$	−8.19075	+	2.98119i	−0.358157	+	0.130358i	−0.514830	−	0.857292i	$-0.672145\pi$
$523$	−8.19075	+	2.98119i	−0.358157	+	0.130358i	0.156674	+	0.987650i	$0.449923\pi$
$524$	−1.68808	−	2.92384i	−0.0737441	−	0.127729i
$525$		0			0
$526$	3.55023	−	20.1343i	0.154797	−	0.877898i
$527$	−25.6736	+	21.5427i	−1.11836	+	0.938416i
$528$	−0.467494	−	0.392274i	−0.0203451	−	0.0170715i
$529$	−1.55076	−	8.79481i	−0.0674244	−	0.382383i
$530$		0			0
$531$	−27.2225			−1.18136
$532$	−10.2753	+	3.27826i	−0.445489	+	0.142131i
$533$	3.24773			0.140675
$534$	−3.08022	−	1.12111i	−0.133294	−	0.0485151i
$535$		0			0
$536$	25.4688	+	21.3708i	1.10008	+	0.923080i
$537$	2.22508	−	1.86706i	0.0960193	−	0.0805697i
$538$	−3.38020	+	19.1701i	−0.145731	+	0.826480i
$539$	−0.212126	+	0.367414i	−0.00913693	+	0.0158256i
$540$		0			0
$541$	−10.3511	+	3.76748i	−0.445027	+	0.161977i	−0.554806	−	0.831979i	$-0.687208\pi$
$541$	−10.3511	+	3.76748i	−0.445027	+	0.161977i	0.109780	+	0.993956i	$0.464985\pi$
$542$	1.86231	−	0.677825i	0.0799931	−	0.0291151i
$543$	−5.00002	−	8.66029i	−0.214571	−	0.371649i
$544$	11.2178	−	19.4297i	0.480958	−	0.833043i
$545$		0			0
$546$	0.713767	−	0.598922i	0.0305464	−	0.0256315i
$547$	−14.0921	−	11.8246i	−0.602533	−	0.505585i	0.289726	−	0.957110i	$-0.406436\pi$
$547$	−14.0921	−	11.8246i	−0.602533	−	0.505585i	−0.892259	+	0.451525i	$0.850880\pi$
$548$	−0.370562	−	2.10156i	−0.0158296	−	0.0897741i
$549$	23.1680	+	8.43248i	0.988788	+	0.359889i
$550$		0			0
$551$	16.5075	−	5.26662i	0.703244	−	0.224366i
$552$	6.06118			0.257981
$553$	8.96012	+	3.26122i	0.381023	+	0.138681i
$554$	1.23294	+	6.99234i	0.0523825	+	0.297076i
$555$		0			0
$556$	−1.68967	+	1.41780i	−0.0716581	+	0.0601283i
$557$	0.0350939	−	0.199028i	0.00148698	−	0.00843307i	−0.984055	−	0.177863i	$-0.943082\pi$
$557$	0.0350939	−	0.199028i	0.00148698	−	0.00843307i	0.985542	+	0.169430i	$0.0541927\pi$
$558$	9.85809	−	17.0747i	0.417326	−	0.722830i
$559$	3.19418	+	5.53248i	0.135099	+	0.233999i
$560$		0			0
$561$	−2.01239	+	0.732451i	−0.0849633	+	0.0309241i
$562$	−6.43424	−	11.1444i	−0.271412	−	0.470100i
$563$	3.38187	−	5.85758i	0.142529	−	0.246867i	−0.785919	−	0.618329i	$-0.787810\pi$
$563$	3.38187	−	5.85758i	0.142529	−	0.246867i	0.928448	+	0.371462i	$0.121143\pi$
$564$	−0.283333	+	1.60686i	−0.0119305	+	0.0676611i
$565$		0			0
$566$	−20.5938	−	17.2803i	−0.865623	−	0.726344i
$567$	−3.11103	−	17.6435i	−0.130651	−	0.740958i
$568$	1.93639	+	0.704789i	0.0812492	+	0.0295723i
$569$	7.15701			0.300038			0.150019	−	0.988683i	$-0.452067\pi$
$569$	7.15701			0.300038			0.150019	+	0.988683i	$0.452067\pi$
$570$		0			0
$571$	−18.3153			−0.766471			−0.383236	−	0.923651i	$-0.625190\pi$
$571$	−18.3153			−0.766471			−0.383236	+	0.923651i	$0.625190\pi$
$572$	0.431647	+	0.157107i	0.0180481	+	0.00656896i
$573$	−1.59291	−	9.03382i	−0.0665446	−	0.377393i
$574$	11.6904	+	9.80941i	0.487948	+	0.409437i
$575$		0			0
$576$	−3.59320	+	20.3781i	−0.149717	+	0.849086i
$577$	10.7897	−	18.6883i	0.449182	−	0.778006i	−0.549151	−	0.835723i	$-0.685049\pi$
$577$	10.7897	−	18.6883i	0.449182	−	0.778006i	0.998333	+	0.0577173i	$0.0183822\pi$
$578$	3.35704	+	5.81457i	0.139635	+	0.241854i
$579$	−3.73265	+	1.35857i	−0.155124	+	0.0564603i
$580$		0			0
$581$	−6.81636	−	11.8063i	−0.282790	−	0.489807i
$582$	−3.46199	+	5.99634i	−0.143504	+	0.248556i
$583$	−1.97666	+	11.2102i	−0.0818648	+	0.464278i
$584$	16.3357	−	13.7073i	0.675975	−	0.567210i
$585$		0			0
$586$	5.11301	+	28.9973i	0.211216	+	1.19787i
$587$	−27.1976	−	9.89913i	−1.12257	−	0.408581i	−0.286978	−	0.957937i	$-0.592651\pi$
$587$	−27.1976	−	9.89913i	−1.12257	−	0.408581i	−0.835588	+	0.549356i	$0.814873\pi$
$588$	−0.244452			−0.0100810
$589$	16.1360	−	25.5196i	0.664872	−	1.05152i
$590$		0			0
$591$	−6.09671	−	2.21902i	−0.250785	−	0.0912783i
$592$	−1.03688	−	5.88043i	−0.0426154	−	0.241684i
$593$	13.6533	+	11.4565i	0.560674	+	0.470461i	0.878536	−	0.477676i	$-0.158521\pi$
$593$	13.6533	+	11.4565i	0.560674	+	0.470461i	−0.317863	+	0.948137i	$0.602965\pi$
$594$	2.03050	−	1.70379i	0.0833123	−	0.0699073i
$595$		0			0
$596$	6.44194	−	11.1578i	0.263872	−	0.457040i
$597$	2.06147	+	3.57058i	0.0843706	+	0.146134i
$598$	2.25507	−	0.820779i	0.0922167	−	0.0335642i
$599$	8.03512	−	2.92455i	0.328306	−	0.119494i	−0.172608	−	0.984991i	$-0.555219\pi$
$599$	8.03512	−	2.92455i	0.328306	−	0.119494i	0.500914	+	0.865497i	$0.332997\pi$
$600$		0			0
$601$	2.09514	−	3.62889i	0.0854627	−	0.148026i	−0.820126	−	0.572184i	$-0.806096\pi$
$601$	2.09514	−	3.62889i	0.0854627	−	0.148026i	0.905588	+	0.424158i	$0.139430\pi$
$602$	−5.21260	+	29.5621i	−0.212450	+	1.20486i
$603$	−22.7632	+	19.1006i	−0.926991	+	0.777838i
$604$	−1.62078	−	1.36000i	−0.0659487	−	0.0553375i
$605$		0			0
$606$	−9.27791	−	3.37688i	−0.376889	−	0.137177i
$607$	7.59458			0.308254			0.154127	−	0.988051i	$-0.450743\pi$
$607$	7.59458			0.308254			0.154127	+	0.988051i	$0.450743\pi$
$608$	−4.30752	+	19.7477i	−0.174693	+	0.800876i
$609$	5.78925			0.234592
$610$		0			0
$611$	0.360654	+	2.04537i	0.0145905	+	0.0827469i
$612$	9.09491	+	7.63153i	0.367640	+	0.308486i
$613$	13.7466	−	11.5348i	0.555220	−	0.465885i	−0.321484	−	0.946915i	$-0.604182\pi$
$613$	13.7466	−	11.5348i	0.555220	−	0.465885i	0.876704	+	0.481030i	$0.159737\pi$
$614$	0.468661	−	2.65791i	0.0189136	−	0.107264i
$615$		0			0
$616$	3.46964	+	6.00960i	0.139796	+	0.242134i
$617$	−38.1365	+	13.8805i	−1.53532	+	0.558809i	−0.964916	−	0.262558i	$-0.915434\pi$
$617$	−38.1365	+	13.8805i	−1.53532	+	0.558809i	−0.570400	+	0.821367i	$0.693212\pi$
$618$	−2.72967	+	0.993517i	−0.109803	+	0.0399651i
$619$	12.7804	+	22.1363i	0.513688	+	0.889733i	0.999874	+	0.0158781i	$0.00505438\pi$
$619$	12.7804	+	22.1363i	0.513688	+	0.889733i	−0.486186	+	0.873855i	$0.661612\pi$
$620$		0			0
$621$	−1.97918	+	11.2245i	−0.0794218	+	0.450423i
$622$	−11.7439	+	9.85430i	−0.470887	+	0.395121i
$623$	12.3616	+	10.3726i	0.495257	+	0.415570i
$624$	−0.0777239	−	0.440794i	−0.00311145	−	0.0176459i
$625$		0			0
$626$	−1.56491			−0.0625463
$627$	1.52662	−	1.17969i	0.0609672	−	0.0471122i
$628$	14.6049			0.582801
$629$	−19.6901	−	7.16661i	−0.785096	−	0.285751i
$630$		0			0
$631$	3.55051	+	2.97923i	0.141344	+	0.118601i	0.710718	−	0.703477i	$-0.248370\pi$
$631$	3.55051	+	2.97923i	0.141344	+	0.118601i	−0.569375	+	0.822078i	$0.692815\pi$
$632$	8.10461	−	6.80057i	0.322384	−	0.270512i
$633$	0.928128	−	5.26367i	0.0368898	−	0.209212i
$634$	2.95490	−	5.11804i	0.117354	−	0.203263i
$635$		0			0
$636$	−6.16333	+	2.24327i	−0.244392	+	0.0889514i
$637$	−0.292397	+	0.106424i	−0.0115852	+	0.00421666i
$638$	−1.73379	−	3.00302i	−0.0686415	−	0.118891i
$639$	−0.920880	+	1.59501i	−0.0364295	+	0.0630977i
$640$		0			0
$641$	17.7783	−	14.9178i	0.702201	−	0.589217i	−0.220198	−	0.975455i	$-0.570670\pi$
$641$	17.7783	−	14.9178i	0.702201	−	0.589217i	0.922399	+	0.386239i	$0.126226\pi$
$642$	6.47602	+	5.43402i	0.255588	+	0.214464i
$643$	2.64733	+	15.0138i	0.104401	+	0.592086i	0.991458	+	0.130426i	$0.0416346\pi$
$643$	2.64733	+	15.0138i	0.104401	+	0.592086i	−0.887057	+	0.461659i	$0.847254\pi$
$644$	−8.72149	−	3.17436i	−0.343675	−	0.125087i
$645$		0			0
$646$	−16.3370	−	14.8682i	−0.642773	−	0.584982i
$647$	17.6749			0.694872			0.347436	−	0.937704i	$-0.387052\pi$
$647$	17.6749			0.694872			0.347436	+	0.937704i	$0.387052\pi$
$648$	−18.6797	−	6.79885i	−0.733808	−	0.267084i
$649$	1.44870	+	8.21599i	0.0568664	+	0.322506i
$650$		0			0
$651$	7.72773	−	6.48434i	0.302874	−	0.254141i
$652$	2.51277	−	14.2506i	0.0984075	−	0.558097i
$653$	3.43228	−	5.94488i	0.134315	−	0.232641i	−0.791020	−	0.611790i	$-0.790450\pi$
$653$	3.43228	−	5.94488i	0.134315	−	0.232641i	0.925336	+	0.379149i	$0.123783\pi$
$654$	1.09174	+	1.89095i	0.0426905	+	0.0739420i
$655$		0			0
$656$	6.88879	−	2.50731i	0.268962	−	0.0978941i
$657$	9.52969	+	16.5059i	0.371789	+	0.643957i
$658$	−4.87962	+	8.45175i	−0.190227	+	0.329484i
$659$	4.75738	−	26.9804i	0.185321	−	1.05101i	−0.740221	−	0.672364i	$-0.765279\pi$
$659$	4.75738	−	26.9804i	0.185321	−	1.05101i	0.925542	−	0.378645i	$-0.123610\pi$
$660$		0			0
$661$	21.8707	+	18.3517i	0.850673	+	0.713800i	0.959938	−	0.280213i	$-0.0904051\pi$
$661$	21.8707	+	18.3517i	0.850673	+	0.713800i	−0.109265	+	0.994013i	$0.534850\pi$
$662$	−5.80051	−	32.8963i	−0.225443	−	1.27855i
$663$	−1.47596	−	0.537206i	−0.0573216	−	0.0208633i
$664$	−15.1263			−0.587014
$665$		0			0
$666$	12.3268			0.477655
$667$	14.0113	+	5.09971i	0.542521	+	0.197462i
$668$	−1.18795	−	6.73722i	−0.0459633	−	0.260671i
$669$	11.5301	+	9.67489i	0.445779	+	0.374053i
$670$		0			0
$671$	1.31206	−	7.44107i	0.0506516	−	0.287259i
$672$	−3.37654	+	5.84833i	−0.130253	+	0.225604i
$673$	−22.5844	−	39.1173i	−0.870565	−	1.50786i	−0.861414	−	0.507904i	$-0.830420\pi$
$673$	−22.5844	−	39.1173i	−0.870565	−	1.50786i	−0.00915115	−	0.999958i	$-0.502913\pi$
$674$	15.0960	−	5.49451i	0.581478	−	0.211641i
$675$		0			0
$676$	−5.70071	−	9.87392i	−0.219258	−	0.379766i
$677$	23.4814	−	40.6710i	0.902463	−	1.56311i	0.0781759	−	0.996940i	$-0.475090\pi$
$677$	23.4814	−	40.6710i	0.902463	−	1.56311i	0.824287	−	0.566172i	$-0.191576\pi$
$678$	−0.384073	+	2.17819i	−0.0147502	+	0.0836527i
$679$	26.1116	−	21.9102i	1.00207	−	0.840838i
$680$		0			0
$681$	−1.46537	−	8.31051i	−0.0561530	−	0.318459i
$682$	−5.67792	−	2.06659i	−0.217419	−	0.0791339i
$683$	19.4215			0.743142			0.371571	−	0.928405i	$-0.378819\pi$
$683$	19.4215			0.743142			0.371571	+	0.928405i	$0.378819\pi$
$684$	−9.89561	−	4.05951i	−0.378368	−	0.155219i
$685$		0			0
$686$	17.5060	+	6.37166i	0.668382	+	0.243271i
$687$	1.05081	+	5.95943i	0.0400909	+	0.227367i
$688$	11.0464	+	9.26901i	0.421139	+	0.353378i
$689$	−6.39554	+	5.36650i	−0.243651	+	0.204447i
$690$		0			0
$691$	8.93344	−	15.4732i	0.339844	−	0.588627i	−0.644559	−	0.764555i	$-0.722959\pi$
$691$	8.93344	−	15.4732i	0.339844	−	0.588627i	0.984403	+	0.175927i	$0.0562923\pi$
$692$	−4.00099	−	6.92991i	−0.152095	−	0.263436i
$693$	−5.82809	+	2.12125i	−0.221391	+	0.0805797i
$694$	−0.0813941	+	0.0296250i	−0.00308968	+	0.00112455i
$695$		0			0
$696$	3.21175	−	5.56292i	0.121741	−	0.210862i
$697$	4.46716	−	25.3346i	0.169206	−	0.959615i
$698$	3.72561	−	3.12615i	0.141016	−	0.118327i
$699$	−6.45860	−	5.41941i	−0.244287	−	0.204981i
$700$		0			0
$701$	−4.04522	−	1.47234i	−0.152786	−	0.0556096i	0.264495	−	0.964387i	$-0.414795\pi$
$701$	−4.04522	−	1.47234i	−0.152786	−	0.0556096i	−0.417281	+	0.908777i	$0.637017\pi$
$702$	1.94406			0.0733739
$703$	18.8619	+	0.759235i	0.711389	+	0.0286351i
$704$	6.34150			0.239004
$705$		0			0
$706$	−0.726431	−	4.11979i	−0.0273396	−	0.155050i
$707$	37.2343	+	31.2432i	1.40034	+	1.17502i
$708$	−3.68240	+	3.08990i	−0.138393	+	0.116125i
$709$	6.10059	−	34.5982i	0.229112	−	1.29936i	−0.625553	−	0.780182i	$-0.715127\pi$
$709$	6.10059	−	34.5982i	0.229112	−	1.29936i	0.854665	−	0.519179i	$-0.173762\pi$
$710$		0			0
$711$	4.72796	+	8.18907i	0.177312	+	0.307114i
$712$	16.8251	−	6.12382i	0.630545	−	0.229500i
$713$	24.4150	−	8.88632i	0.914347	−	0.332795i
$714$	−3.69024	−	6.39168i	−0.138104	−	0.239203i
$715$		0			0
$716$	−0.856958	+	4.86005i	−0.0320260	+	0.181629i
$717$	8.49442	−	7.12767i	0.317230	−	0.266188i
$718$	−24.2471	−	20.3457i	−0.904893	−	0.759295i
$719$	5.10577	+	28.9563i	0.190413	+	1.07989i	0.918801	+	0.394722i	$0.129159\pi$
$719$	5.10577	+	28.9563i	0.190413	+	1.07989i	−0.728388	+	0.685165i	$0.759730\pi$
$720$		0			0
$721$	14.3004			0.532574
$722$	18.0929	+	8.28745i	0.673349	+	0.308427i
$723$	15.1087			0.561898
$724$	15.9656	+	5.81100i	0.593357	+	0.215964i
$725$		0			0
$726$	4.39480	+	3.68767i	0.163106	+	0.136862i
$727$	17.2796	−	14.4993i	0.640864	−	0.537749i	−0.263419	−	0.964681i	$-0.584850\pi$
$727$	17.2796	−	14.4993i	0.640864	−	0.537749i	0.904283	+	0.426933i	$0.140406\pi$
$728$	−0.883786	+	5.01220i	−0.0327553	+	0.185765i
$729$	6.46109	−	11.1909i	0.239300	−	0.414479i
$730$		0			0
$731$	47.5506	−	17.3070i	1.75872	−	0.640123i
$732$	4.09108	−	1.48903i	0.151211	−	0.0550362i
$733$	−18.9501	−	32.8225i	−0.699938	−	1.21233i	−0.968488	−	0.249062i	$-0.919878\pi$
$733$	−18.9501	−	32.8225i	−0.699938	−	1.21233i	0.268550	−	0.963266i	$-0.413456\pi$
$734$	9.49990	−	16.4543i	0.350648	−	0.607340i
$735$		0			0
$736$	−13.3238	+	11.1800i	−0.491121	+	0.412099i
$737$	6.97613	+	5.85367i	0.256969	+	0.215623i
$738$	2.62798	+	14.9040i	0.0967372	+	0.548624i
$739$	24.4523	+	8.89989i	0.899491	+	0.327388i	0.750049	−	0.661383i	$-0.230030\pi$
$739$	24.4523	+	8.89989i	0.899491	+	0.327388i	0.149442	+	0.988770i	$0.452252\pi$
$740$		0			0
$741$	1.41388	+	0.0569119i	0.0519401	+	0.00209071i
$742$	−39.2300			−1.44018
$743$	−47.3487	−	17.2335i	−1.73706	−	0.632237i	−0.737964	−	0.674841i	$-0.764212\pi$
$743$	−47.3487	−	17.2335i	−1.73706	−	0.632237i	−0.999092	+	0.0426041i	$0.986435\pi$
$744$	−1.94365	−	11.0230i	−0.0712577	−	0.404123i
$745$		0			0
$746$	20.2315	−	16.9762i	0.740728	−	0.621544i
$747$	2.34763	−	13.3140i	0.0858951	−	0.487135i
$748$	1.81926	−	3.15105i	0.0665187	−	0.115214i
$749$	−20.8089	−	36.0420i	−0.760339	−	1.31695i
$750$		0			0
$751$	−25.5462	+	9.29806i	−0.932195	+	0.339291i	−0.763079	−	0.646305i	$-0.776313\pi$
$751$	−25.5462	+	9.29806i	−0.932195	+	0.339291i	−0.169116	+	0.985596i	$0.554091\pi$
$752$	2.34405	+	4.06002i	0.0854789	+	0.148054i
$753$	−6.59363	+	11.4205i	−0.240285	+	0.416186i
$754$	0.441631	−	2.50461i	0.0160832	−	0.0912126i
$755$		0			0
$756$	−5.75963	−	4.83291i	−0.209476	−	0.175771i
$757$	5.71273	+	32.3985i	0.207633	+	1.17754i	0.893243	+	0.449575i	$0.148424\pi$
$757$	5.71273	+	32.3985i	0.207633	+	1.17754i	−0.685610	+	0.727969i	$0.740464\pi$
$758$	−27.1289	−	9.87411i	−0.985366	−	0.358644i
$759$	1.66021			0.0602619
$760$		0			0
$761$	3.47213			0.125865			0.0629323	−	0.998018i	$-0.479955\pi$
$761$	3.47213			0.125865			0.0629323	+	0.998018i	$0.479955\pi$
$762$	4.80443	+	1.74867i	0.174046	+	0.0633476i
$763$	−1.86657	−	10.5858i	−0.0675743	−	0.383233i
$764$	11.9391	+	10.0181i	0.431941	+	0.362442i
$765$		0			0
$766$	−3.33270	+	18.9007i	−0.120415	+	0.682910i
$767$	−3.05943	+	5.29909i	−0.110470	+	0.191339i
$768$	4.40811	+	7.63507i	0.159064	+	0.275507i
$769$	29.7634	−	10.8330i	1.07330	−	0.390648i	0.255887	−	0.966707i	$-0.417632\pi$
$769$	29.7634	−	10.8330i	1.07330	−	0.390648i	0.817408	+	0.576059i	$0.195410\pi$
$770$		0			0
$771$	1.44615	+	2.50480i	0.0520817	+	0.0902081i
$772$	3.37442	−	5.84466i	0.121448	−	0.210354i
$773$	−6.08960	+	34.5358i	−0.219028	+	1.24217i	0.654752	+	0.755844i	$0.272773\pi$
$773$	−6.08960	+	34.5358i	−0.219028	+	1.24217i	−0.873779	+	0.486323i	$0.838338\pi$
$774$	−22.8042	+	19.1350i	−0.819679	+	0.687792i
$775$		0			0
$776$	−6.56750	−	37.2461i	−0.235759	−	1.33706i
$777$	5.92670	+	2.15714i	0.212619	+	0.0773870i
$778$	7.52562			0.269807
$779$	3.10322	+	22.9672i	0.111184	+	0.822884i
$780$		0			0
$781$	0.530395	+	0.193048i	0.0189790	+	0.00690780i
$782$	−3.30085	−	18.7201i	−0.118038	−	0.669428i
$783$	9.25302	+	7.76421i	0.330676	+	0.277470i
$784$	−0.538043	+	0.451472i	−0.0192158	+	0.0161240i
$785$		0			0
$786$	−1.04066	+	1.80248i	−0.0371191	+	0.0642922i
$787$	−21.0914	−	36.5314i	−0.751829	−	1.30221i	−0.946936	−	0.321424i	$-0.895839\pi$
$787$	−21.0914	−	36.5314i	−0.751829	−	1.30221i	0.195107	−	0.980782i	$-0.437495\pi$
$788$	10.3584	−	3.77015i	0.369003	−	0.134306i
$789$	9.74816	−	3.54804i	0.347044	−	0.126314i
$790$		0			0
$791$	5.44425	−	9.42971i	0.193575	−	0.335282i
$792$	−1.19498	+	6.77708i	−0.0424618	+	0.240813i
$793$	4.24522	−	3.56216i	0.150752	−	0.126496i
$794$	9.40703	+	7.89343i	0.333843	+	0.280127i
$795$		0			0
$796$	−6.58251	−	2.39584i	−0.233311	−	0.0849182i
$797$	−20.4194			−0.723291			−0.361646	−	0.932316i	$-0.617785\pi$
$797$	−20.4194			−0.723291			−0.361646	+	0.932316i	$0.617785\pi$
$798$	4.91743	+	4.47531i	0.174075	+	0.158424i
$799$	16.4514			0.582008
$800$		0			0
$801$	2.77886	+	15.7597i	0.0981862	+	0.556842i
$802$	−31.4623	−	26.4000i	−1.11097	−	0.932216i
$803$	4.47449	−	3.75454i	0.157901	−	0.132495i
$804$	−0.911169	+	5.16750i	−0.0321345	+	0.182244i
$805$		0			0
$806$	−2.21582	−	3.83792i	−0.0780491	−	0.135185i
$807$	−9.28131	+	3.37812i	−0.326717	+	0.118915i
$808$	50.6786	−	18.4455i	1.78287	−	0.648910i
$809$	−14.2768	−	24.7282i	−0.501946	−	0.869396i	−0.999997	−	0.00224865i	$-0.999284\pi$
$809$	−14.2768	−	24.7282i	−0.501946	−	0.869396i	0.498051	−	0.867148i	$-0.334049\pi$
$810$		0			0
$811$	−0.279849	+	1.58710i	−0.00982681	+	0.0557306i	−0.989327	−	0.145713i	$-0.953452\pi$
$811$	−0.279849	+	1.58710i	−0.00982681	+	0.0557306i	0.979500	+	0.201444i	$0.0645634\pi$
$812$	−7.53483	+	6.32248i	−0.264421	+	0.221875i
$813$	0.770321	+	0.646376i	0.0270163	+	0.0226694i
$814$	−0.655998	−	3.72035i	−0.0229927	−	0.130398i
$815$		0			0
$816$	−3.54540			−0.124114
$817$	−36.0723	+	27.8747i	−1.26201	+	0.975213i
$818$	−9.29706			−0.325064
$819$	−4.27453	−	1.55580i	−0.149364	−	0.0543642i
$820$		0			0
$821$	−6.16578	−	5.17371i	−0.215187	−	0.180564i	0.528822	−	0.848733i	$-0.322634\pi$
$821$	−6.16578	−	5.17371i	−0.215187	−	0.180564i	−0.744010	+	0.668169i	$0.767078\pi$
$822$	−1.00777	+	0.845617i	−0.0351499	+	0.0294943i
$823$	−6.48442	+	36.7750i	−0.226033	+	1.28189i	0.634669	+	0.772784i	$0.281137\pi$
$823$	−6.48442	+	36.7750i	−0.226033	+	1.28189i	−0.860701	+	0.509110i	$0.829975\pi$
$824$	7.93356	−	13.7413i	0.276379	−	0.478702i
$825$		0			0
$826$	−27.0179	+	9.83370i	−0.940072	+	0.342158i
$827$	10.2711	−	3.73836i	0.357160	−	0.129996i	−0.157207	−	0.987566i	$-0.550249\pi$
$827$	10.2711	−	3.73836i	0.357160	−	0.129996i	0.514367	+	0.857570i	$0.328027\pi$
$828$	−4.60205	−	7.97098i	−0.159932	−	0.277011i
$829$	−16.8187	+	29.1309i	−0.584139	+	1.01176i	0.410843	+	0.911706i	$0.365234\pi$
$829$	−16.8187	+	29.1309i	−0.584139	+	1.01176i	−0.994982	+	0.100052i	$0.968099\pi$
$830$		0			0
$831$	−2.75979	+	2.31574i	−0.0957361	+	0.0803322i
$832$	3.56293	+	2.98966i	0.123523	+	0.103648i
$833$	0.427995	+	2.42728i	0.0148291	+	0.0841002i
$834$	1.27776	+	0.465068i	0.0442454	+	0.0161040i
$835$		0			0
$836$	−0.698579	+	3.20262i	−0.0241609	+	0.110765i
$837$	21.0478			0.727517
$838$	−7.67897	−	2.79492i	−0.265266	−	0.0965488i
$839$	2.40910	+	13.6627i	0.0831714	+	0.471689i	0.997736	+	0.0672492i	$0.0214222\pi$
$839$	2.40910	+	13.6627i	0.0831714	+	0.471689i	−0.914565	+	0.404439i	$0.867467\pi$
$840$		0			0
$841$	−10.1104	+	8.48360i	−0.348633	+	0.292538i
$842$	−6.28522	+	35.6452i	−0.216603	+	1.22842i
$843$	3.26474	−	5.65470i	0.112444	−	0.194758i
$844$	4.54052	+	7.86440i	0.156291	+	0.270704i
$845$		0			0
$846$	−9.09448	+	3.31012i	−0.312675	+	0.113804i
$847$	−14.1214	−	24.4591i	−0.485219	−	0.840423i
$848$	−9.42259	+	16.3204i	−0.323573	+	0.560445i
$849$	2.36867	−	13.4334i	0.0812925	−	0.461033i
$850$		0			0
$851$	12.4438	+	10.4416i	0.426568	+	0.357933i
$852$	0.0564745	+	0.320283i	0.00193478	+	0.0109727i
$853$	27.7657	+	10.1059i	0.950680	+	0.346019i	0.770375	−	0.637591i	$-0.220069\pi$
$853$	27.7657	+	10.1059i	0.950680	+	0.346019i	0.180305	+	0.983611i	$0.442291\pi$
$854$	26.0400			0.891071
$855$		0			0
$856$	−46.1773			−1.57831
$857$	−4.02741	−	1.46586i	−0.137574	−	0.0500727i	0.272316	−	0.962208i	$-0.412210\pi$
$857$	−4.02741	−	1.46586i	−0.137574	−	0.0500727i	−0.409889	+	0.912135i	$0.634433\pi$
$858$	−0.0491733	−	0.278876i	−0.00167875	−	0.00952066i
$859$	−26.7935	−	22.4824i	−0.914181	−	0.767089i	0.0587290	−	0.998274i	$-0.481295\pi$
$859$	−26.7935	−	22.4824i	−0.914181	−	0.767089i	−0.972910	+	0.231185i	$0.925740\pi$
$860$		0			0
$861$	−1.34461	+	7.62567i	−0.0458243	+	0.259882i
$862$	1.48706	−	2.57566i	0.0506494	−	0.0877273i
$863$	−10.0153	−	17.3470i	−0.340924	−	0.590498i	0.643681	−	0.765294i	$-0.277407\pi$
$863$	−10.0153	−	17.3470i	−0.340924	−	0.590498i	−0.984605	+	0.174797i	$0.944073\pi$
$864$	−13.2402	+	4.81904i	−0.450441	+	0.163947i
$865$		0			0
$866$	−11.4443	−	19.8221i	−0.388893	−	0.673583i
$867$	−1.70337	+	2.95032i	−0.0578494	+	0.100198i
$868$	−2.97623	+	16.8790i	−0.101020	+	0.572911i
$869$	2.21992	−	1.86274i	0.0753058	−	0.0631891i
$870$		0			0
$871$	1.15983	+	6.57770i	0.0392992	+	0.222877i
$872$	−11.2075	−	4.07921i	−0.379535	−	0.138139i
$873$	33.8030			1.14406
$874$	7.95907	+	15.1630i	0.269220	+	0.512898i
$875$		0			0
$876$	3.16260	+	1.15109i	0.106854	+	0.0388917i
$877$	7.91697	+	44.8994i	0.267337	+	1.51614i	0.762297	+	0.647228i	$0.224072\pi$
$877$	7.91697	+	44.8994i	0.267337	+	1.51614i	−0.494959	+	0.868916i	$0.664817\pi$
$878$	−26.1376	−	21.9320i	−0.882100	−	0.740170i
$879$	−11.4449	+	9.60340i	−0.386027	+	0.323915i
$880$		0			0
$881$	8.63649	−	14.9588i	0.290971	−	0.503976i	−0.683069	−	0.730354i	$-0.739355\pi$
$881$	8.63649	−	14.9588i	0.290971	−	0.503976i	0.974040	+	0.226378i	$0.0726885\pi$
$882$	−0.724983	−	1.25571i	−0.0244114	−	0.0422819i
$883$	33.0707	−	12.0368i	1.11292	−	0.405069i	0.280856	−	0.959750i	$-0.409382\pi$
$883$	33.0707	−	12.0368i	1.11292	−	0.405069i	0.832063	+	0.554680i	$0.187160\pi$
$884$	2.50768	−	0.912722i	0.0843425	−	0.0306982i
$885$		0			0
$886$	4.06483	−	7.04049i	0.136561	−	0.236530i
$887$	0.548919	−	3.11307i	0.0184309	−	0.104527i	−0.974205	−	0.225667i	$-0.927544\pi$
$887$	0.548919	−	3.11307i	0.0184309	−	0.104527i	0.992635	+	0.121140i	$0.0386550\pi$
$888$	5.36082	−	4.49826i	0.179897	−	0.150952i
$889$	−19.2812	−	16.1789i	−0.646671	−	0.542622i
$890$		0			0
$891$	−5.11654	−	1.86227i	−0.171410	−	0.0623883i
$892$	−25.5727			−0.856237
$893$	−14.1198	+	4.50482i	−0.472500	+	0.150748i
$894$	−7.94259			−0.265640
$895$		0			0
$896$	−0.617962	−	3.50464i	−0.0206447	−	0.117082i
$897$	0.932781	+	0.782696i	0.0311447	+	0.0261335i
$898$	−18.4399	+	15.4729i	−0.615346	+	0.516337i
$899$	4.78140	−	27.1167i	0.159469	−	0.904391i
$900$		0			0
$901$	33.0655	+	57.2711i	1.10157	+	1.90798i
$902$	4.35830	−	1.58629i	0.145116	−	0.0528178i
$903$	−14.3127	+	5.20939i	−0.476297	+	0.173358i
$904$	−6.04071	−	10.4628i	−0.200911	−	0.347988i
$905$		0			0
$906$	−0.226494	+	1.28451i	−0.00752476	+	0.0426751i
$907$	−12.2041	+	10.2405i	−0.405230	+	0.340029i	−0.822511	−	0.568749i	$-0.807428\pi$
$907$	−12.2041	+	10.2405i	−0.405230	+	0.340029i	0.417281	+	0.908778i	$0.362983\pi$
$908$	10.9832	+	9.21597i	0.364489	+	0.305843i
$909$	8.37018	+	47.4697i	0.277621	+	1.57447i
$910$		0			0
$911$	0.0577380			0.00191294			0.000956472	−	1.00000i	$-0.499696\pi$
$911$	0.0577380			0.00191294			0.000956472		1.00000i	$0.499696\pi$
$912$	3.04292	−	0.970824i	0.100761	−	0.0321472i
$913$	−4.14323			−0.137121
$914$	3.33524	+	1.21393i	0.110320	+	0.0401532i
$915$		0			0
$916$	−7.87599	−	6.60874i	−0.260230	−	0.218359i
$917$	7.84905	−	6.58614i	0.259199	−	0.217493i
$918$	2.67400	−	15.1650i	0.0882553	−	0.500521i
$919$	−25.0245	+	43.3436i	−0.825481	+	1.42977i	0.0760708	+	0.997102i	$0.475762\pi$
$919$	−25.0245	+	43.3436i	−0.825481	+	1.42977i	−0.901551	+	0.432672i	$0.857571\pi$
$920$		0			0
$921$	1.28684	−	0.468372i	0.0424029	−	0.0154334i
$922$	−10.6818	+	3.88787i	−0.351788	+	0.128040i
$923$	0.206988	+	0.358514i	0.00681310	+	0.0118006i
$924$	−0.547595	+	0.948463i	−0.0180146	+	0.0312021i
$925$		0			0
$926$	−5.86660	+	4.92267i	−0.192789	+	0.161769i
$927$	10.8637	+	9.11573i	0.356811	+	0.299400i
$928$	3.20080	+	18.1526i	0.105071	+	0.595889i
$929$	15.9606	+	5.80920i	0.523652	+	0.190594i	0.590302	−	0.807183i	$-0.299009\pi$
$929$	15.9606	+	5.80920i	0.523652	+	0.190594i	−0.0666498	+	0.997776i	$0.521231\pi$
$930$		0			0
$931$	−1.03199	−	1.96607i	−0.0338220	−	0.0644353i
$932$	14.3246			0.469218
$933$	−7.30963	−	2.66049i	−0.239306	−	0.0871004i
$934$	1.97190	+	11.1832i	0.0645227	+	0.365926i
$935$		0			0
$936$	−3.86640	+	3.24430i	−0.126377	+	0.106043i
$937$	−5.85065	+	33.1807i	−0.191132	+	1.08397i	0.726687	+	0.686968i	$0.241059\pi$
$937$	−5.85065	+	33.1807i	−0.191132	+	1.08397i	−0.917820	+	0.396997i	$0.870052\pi$
$938$	−15.6923	+	27.1799i	−0.512373	+	0.887456i
$939$	−0.397018	−	0.687655i	−0.0129562	−	0.0224408i
$940$		0			0
$941$	25.5345	−	9.29380i	0.832401	−	0.302969i	0.109557	−	0.993980i	$-0.465057\pi$
$941$	25.5345	−	9.29380i	0.832401	−	0.302969i	0.722844	+	0.691011i	$0.242834\pi$
$942$	−4.50180	−	7.79734i	−0.146676	−	0.254051i
$943$	−9.97169	+	17.2715i	−0.324723	+	0.562436i
$944$	−2.39838	+	13.6019i	−0.0780605	+	0.442703i
$945$		0			0
$946$	6.98867	+	5.86419i	0.227221	+	0.190661i
$947$	−5.78183	−	32.7904i	−0.187884	−	1.06554i	−0.922193	−	0.386729i	$-0.873605\pi$
$947$	−5.78183	−	32.7904i	−0.187884	−	1.06554i	0.734309	−	0.678815i	$-0.237506\pi$
$948$	1.56906	+	0.571090i	0.0509606	+	0.0185481i
$949$	4.28402			0.139065
$950$		0			0
$951$	2.99864			0.0972376
$952$	37.8830	+	13.7883i	1.22780	+	0.446881i
$953$	−5.28039	−	29.9466i	−0.171049	−	0.970065i	−0.942606	−	0.333906i	$-0.891633\pi$
$953$	−5.28039	−	29.9466i	−0.171049	−	0.970065i	0.771558	−	0.636159i	$-0.219478\pi$
$954$	−29.8022	−	25.0070i	−0.964882	−	0.809632i
$955$		0			0
$956$	−3.27151	+	18.5536i	−0.105808	+	0.600068i
$957$	0.879728	−	1.52373i	0.0284376	−	0.0492553i
$958$	1.80540	+	3.12704i	0.0583297	+	0.101030i
$959$	6.08578	−	2.21504i	0.196520	−	0.0715274i
$960$		0			0
$961$	−8.49003	−	14.7052i	−0.273872	−	0.474360i
$962$	1.38536	−	2.39952i	0.0446660	−	0.0773637i
$963$	7.16679	−	40.6449i	0.230946	−	1.30976i
$964$	−19.6643	+	16.5003i	−0.633344	+	0.531438i
$965$		0			0
$966$	0.993554	+	5.63472i	0.0319671	+	0.181294i
$967$	55.3648	+	20.1511i	1.78041	+	0.648017i	0.999734	+	0.0230823i	$0.00734797\pi$
$967$	55.3648	+	20.1511i	1.78041	+	0.648017i	0.780677	+	0.624934i	$0.214874\pi$
$968$	−31.3371			−1.00721
$969$	2.38870	−	10.9509i	0.0767361	−	0.351795i
$970$		0			0
$971$	38.4033	+	13.9777i	1.23242	+	0.448564i	0.874426	−	0.485159i	$-0.161238\pi$
$971$	38.4033	+	13.9777i	1.23242	+	0.448564i	0.357995	+	0.933724i	$0.383461\pi$
$972$	−1.97411	−	11.1957i	−0.0633196	−	0.359103i
$973$	−5.12794	−	4.30285i	−0.164394	−	0.137943i
$974$	−21.6614	+	18.1761i	−0.694075	+	0.582398i
$975$		0			0
$976$	6.25450	−	10.8331i	0.200202	−	0.346760i
$977$	17.9716	+	31.1276i	0.574961	+	0.995862i	0.996046	+	0.0888405i	$0.0283161\pi$
$977$	17.9716	+	31.1276i	0.574961	+	0.995862i	−0.421085	+	0.907021i	$0.638351\pi$
$978$	−8.38270	+	3.05105i	−0.268049	+	0.0975619i
$979$	4.60853	−	1.67737i	0.147289	−	0.0536089i
$980$		0			0
$981$	5.32991	−	9.23167i	0.170171	−	0.294745i
$982$	−0.0443747	+	0.251662i	−0.00141606	+	0.00803085i
$983$	−7.71144	+	6.47067i	−0.245957	+	0.206382i	−0.757429	−	0.652918i	$-0.773545\pi$
$983$	−7.71144	+	6.47067i	−0.245957	+	0.206382i	0.511472	+	0.859300i	$0.329100\pi$
$984$	6.58159	+	5.52261i	0.209813	+	0.176054i
$985$		0			0
$986$	−18.9303	−	6.89005i	−0.602862	−	0.219424i
$987$	−4.95185			−0.157619
$988$	−1.90235	+	1.47003i	−0.0605217	+	0.0467680i
$989$	−39.2290			−1.24741
$990$		0			0
$991$	−3.13089	−	17.7562i	−0.0994561	−	0.564043i	−0.993290	−	0.115646i	$-0.963106\pi$
$991$	−3.13089	−	17.7562i	−0.0994561	−	0.564043i	0.893834	−	0.448397i	$-0.148005\pi$
$992$	24.6047	+	20.6458i	0.781200	+	0.655504i
$993$	12.9838	−	10.8947i	0.412028	−	0.345732i
$994$	−0.337786	+	1.91568i	−0.0107139	+	0.0607616i
$995$		0			0
$996$	−1.19365	−	2.06746i	−0.0378223	−	0.0655101i
$997$	−17.5954	+	6.40419i	−0.557251	+	0.202823i	−0.605265	−	0.796024i	$-0.706933\pi$
$997$	−17.5954	+	6.40419i	−0.557251	+	0.202823i	0.0480143	+	0.998847i	$0.484711\pi$
$998$	−3.19747	+	1.16378i	−0.101214	+	0.0368390i
$999$	6.57968	+	11.3963i	0.208172	+	0.360564i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.l.f.251.6		48
5.2	odd	4		95.2.p.a.4.3	✓	48
5.3	odd	4		95.2.p.a.4.6	yes	48
5.4	even	2	inner	475.2.l.f.251.3		48
15.2	even	4		855.2.da.b.289.6		48
15.8	even	4		855.2.da.b.289.3		48
19.5	even	9	inner	475.2.l.f.176.6		48
19.9	even	9		9025.2.a.cu.1.9		24
19.10	odd	18		9025.2.a.ct.1.16		24
95.9	even	18		9025.2.a.cu.1.16		24
95.24	even	18	inner	475.2.l.f.176.3		48
95.28	odd	36		1805.2.b.k.1084.16		24
95.29	odd	18		9025.2.a.ct.1.9		24
95.43	odd	36		95.2.p.a.24.3	yes	48
95.47	odd	36		1805.2.b.k.1084.9		24
95.48	even	36		1805.2.b.l.1084.9		24
95.62	odd	36		95.2.p.a.24.6	yes	48
95.67	even	36		1805.2.b.l.1084.16		24
285.62	even	36		855.2.da.b.784.3		48
285.233	even	36		855.2.da.b.784.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.4.3	✓	48	5.2	odd	4
95.2.p.a.4.6	yes	48	5.3	odd	4
95.2.p.a.24.3	yes	48	95.43	odd	36
95.2.p.a.24.6	yes	48	95.62	odd	36
475.2.l.f.176.3		48	95.24	even	18	inner
475.2.l.f.176.6		48	19.5	even	9	inner
475.2.l.f.251.3		48	5.4	even	2	inner
475.2.l.f.251.6		48	1.1	even	1	trivial
855.2.da.b.289.3		48	15.8	even	4
855.2.da.b.289.6		48	15.2	even	4
855.2.da.b.784.3		48	285.62	even	36
855.2.da.b.784.6		48	285.233	even	36
1805.2.b.k.1084.9		24	95.47	odd	36
1805.2.b.k.1084.16		24	95.28	odd	36
1805.2.b.l.1084.9		24	95.48	even	36
1805.2.b.l.1084.16		24	95.67	even	36
9025.2.a.ct.1.9		24	95.29	odd	18
9025.2.a.ct.1.16		24	19.10	odd	18
9025.2.a.cu.1.9		24	19.9	even	9
9025.2.a.cu.1.16		24	95.9	even	18

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.984236 + 0.358233i) q^{2} +(0.0922859 + 0.523379i) q^{3} +(-0.691698 - 0.580404i) q^{4} +(-0.0966605 + 0.548189i) q^{6} +(1.37016 - 2.37320i) q^{7} +(-1.52028 - 2.63320i) q^{8} +(2.55367 - 0.929459i) q^{9} +(-0.416418 - 0.721257i) q^{11} +(0.239937 - 0.415583i) q^{12} +(0.106070 - 0.601551i) q^{13} +(2.19872 - 1.84495i) q^{14} +(-0.239424 - 1.35784i) q^{16} +(-4.54662 - 1.65483i) q^{17} +2.84638 q^{18} +(4.35537 + 0.175314i) q^{19} +(1.36853 + 0.498103i) q^{21} +(-0.151476 - 0.859062i) q^{22} +(2.87338 + 2.41106i) q^{23} +(1.23786 - 1.03869i) q^{24} +(0.319893 - 0.554071i) q^{26} +(1.51931 + 2.63152i) q^{27} +(-2.32515 + 0.846286i) q^{28} +(3.73543 - 1.35958i) q^{29} +(3.46338 - 5.99875i) q^{31} +(-0.805200 + 4.56652i) q^{32} +(0.339061 - 0.284506i) q^{33} +(-3.88213 - 3.25750i) q^{34} +(-2.30583 - 0.839253i) q^{36} +4.33071 q^{37} +(4.22391 + 1.73279i) q^{38} +0.324628 q^{39} +(0.923271 + 5.23613i) q^{41} +(1.16852 + 0.980503i) q^{42} +(-8.01164 + 6.72257i) q^{43} +(-0.130585 + 0.740582i) q^{44} +(1.96437 + 3.40239i) q^{46} +(-3.19511 + 1.16292i) q^{47} +(0.688571 - 0.250619i) q^{48} +(-0.254704 - 0.441160i) q^{49} +(0.446517 - 2.53232i) q^{51} +(-0.422511 + 0.354529i) q^{52} +(-10.4702 - 8.78556i) q^{53} +(0.552662 + 3.13430i) q^{54} -8.33212 q^{56} +(0.310183 + 2.29569i) q^{57} +4.16359 q^{58} +(-9.41315 - 3.42610i) q^{59} +(6.94990 + 5.83166i) q^{61} +(5.55774 - 4.66350i) q^{62} +(1.29316 - 7.33387i) q^{63} +(-3.80717 + 6.59422i) q^{64} +(0.435636 - 0.158558i) q^{66} +(-10.2751 + 3.73984i) q^{67} +(2.18442 + 3.78352i) q^{68} +(-0.996723 + 1.72638i) q^{69} +(-0.519169 + 0.435634i) q^{71} +(-6.32974 - 5.31128i) q^{72} +(1.21787 + 6.90688i) q^{73} +(4.26244 + 1.55140i) q^{74} +(-2.91085 - 2.64914i) q^{76} -2.28224 q^{77} +(0.319511 + 0.116292i) q^{78} +(0.604220 + 3.42670i) q^{79} +(5.00824 - 4.20241i) q^{81} +(-0.967036 + 5.48434i) q^{82} +(2.48742 - 4.30834i) q^{83} +(-0.657507 - 1.13884i) q^{84} +(-10.2936 + 3.74656i) q^{86} +(1.05630 + 1.82957i) q^{87} +(-1.26614 + 2.19302i) q^{88} +(-1.02256 + 5.79921i) q^{89} +(-1.28227 - 1.07595i) q^{91} +(-0.588129 - 3.33544i) q^{92} +(3.45924 + 1.25906i) q^{93} -3.56134 q^{94} -2.46433 q^{96} +(11.6886 + 4.25430i) q^{97} +(-0.0926508 - 0.525449i) q^{98} +(-1.73377 - 1.45481i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9} - 12 q^{11} - 6 q^{14} - 42 q^{16} - 12 q^{19} - 54 q^{21} - 24 q^{24} + 12 q^{26} - 42 q^{31} + 36 q^{34} + 18 q^{36} + 48 q^{39} + 6 q^{41} + 6 q^{44} - 6 q^{46} - 12 q^{49}+ \cdots + 36 q^{99}+O(q^{100}) \) 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9 - 12 * q^11 - 6 * q^14 - 42 * q^16 - 12 * q^19 - 54 * q^21 - 24 * q^24 + 12 * q^26 - 42 * q^31 + 36 * q^34 + 18 * q^36 + 48 * q^39 + 6 * q^41 + 6 * q^44 - 6 * q^46 - 12 * q^49 + 108 * q^51 - 24 * q^54 + 36 * q^56 + 36 * q^59 + 48 * q^61 + 180 * q^66 - 66 * q^69 - 24 * q^71 - 84 * q^74 + 66 * q^76 - 48 * q^79 - 78 * q^81 + 54 * q^84 - 42 * q^86 + 12 * q^89 - 30 * q^91 + 72 * q^94 - 240 * q^96 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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