LMFDB - Embedded newform 475.2.l.f.176.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(101,475)]

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

lf = mfeigenbasis(mf)

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")

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

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

Self dual:	no
Analytic conductor:	$3.79289409601$
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			176.6
Character	$\chi$	$=$	475.176
Dual form			475.2.l.f.251.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.984236 - 0.358233i) q^{2} +(0.0922859 - 0.523379i) q^{3} +(-0.691698 + 0.580404i) q^{4} +(-0.0966605 - 0.548189i) q^{6} +(1.37016 + 2.37320i) q^{7} +(-1.52028 + 2.63320i) q^{8} +(2.55367 + 0.929459i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{8}{9}\right)$

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	0.0302752	−	0.999542i	$-0.490362\pi$
$2$	0.984236	−	0.358233i	0.695960	−	0.253309i	0.665685	+	0.746233i	$0.268139\pi$
$3$	0.0922859	−	0.523379i	0.0532813	−	0.302173i	−0.946508	−	0.322679i	$-0.895417\pi$
$3$	0.0922859	−	0.523379i	0.0532813	−	0.302173i	0.999790	+	0.0205059i	$0.00652769\pi$
$4$	−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	0.999784	+	0.0207632i	$0.00660960\pi$
$7$	1.37016	+	2.37320i	0.517874	+	0.896983i	−0.481911	+	0.876220i	$0.660057\pi$
$8$	−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	−0.921950	−	0.387310i	$-0.873404\pi$
$11$	−0.416418	+	0.721257i	−0.125555	+	0.217467i	0.796395	+	0.604777i	$0.206738\pi$
$12$	0.239937	+	0.415583i	0.0692639	+	0.119969i
$13$	0.106070	+	0.601551i	0.0294185	+	0.166840i	0.995977	−	0.0896039i	$-0.0285601\pi$
$13$	0.106070	+	0.601551i	0.0294185	+	0.166840i	−0.966559	+	0.256444i	$0.917449\pi$
$14$	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	−0.828317	−	0.560259i	$-0.810701\pi$
$17$	−4.54662	+	1.65483i	−1.10272	+	0.401356i	−0.274400	+	0.961616i	$0.588479\pi$
$18$	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	−0.292028	−	0.956410i	$-0.594330\pi$
$23$	2.87338	−	2.41106i	0.599142	−	0.502740i	0.891170	+	0.453670i	$0.149886\pi$
$24$	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	0.664698	−	0.747112i	$-0.268560\pi$
$29$	3.73543	+	1.35958i	0.693651	+	0.252468i	0.0289533	+	0.999581i	$0.490783\pi$
$30$		0			0
$31$	3.46338	+	5.99875i	0.622042	+	1.07741i	0.989105	+	0.147212i	$0.0470300\pi$
$31$	3.46338	+	5.99875i	0.622042	+	1.07741i	−0.367063	+	0.930196i	$0.619637\pi$
$32$	−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	−0.823823	−	0.566848i	$-0.808163\pi$
$41$	0.923271	−	5.23613i	0.144191	−	0.817746i	0.968013	−	0.250899i	$-0.0807260\pi$
$42$	1.16852	−	0.980503i	0.180306	−	0.151295i
$43$	−8.01164	−	6.72257i	−1.22176	−	1.02518i	−0.998731	−	0.0503713i	$-0.983960\pi$
$43$	−8.01164	−	6.72257i	−1.22176	−	1.02518i	−0.223034	−	0.974811i	$-0.571596\pi$
$44$	−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	0.0983098	−	0.995156i	$-0.468656\pi$
$47$	−3.19511	−	1.16292i	−0.466054	−	0.169630i	−0.564364	+	0.825526i	$0.690879\pi$
$48$	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	−0.497535	+	0.867444i	$0.665761\pi$
$53$	−10.4702	+	8.78556i	−1.43820	+	1.20679i	−0.940662	+	0.339346i	$0.889794\pi$
$54$	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	−0.872050	−	0.489417i	$-0.837210\pi$
$59$	−9.41315	+	3.42610i	−1.22549	+	0.446041i	−0.353437	+	0.935458i	$0.614987\pi$
$60$		0			0
$61$	6.94990	−	5.83166i	0.889844	−	0.746668i	−0.0783350	−	0.996927i	$-0.524960\pi$
$61$	6.94990	−	5.83166i	0.889844	−	0.746668i	0.968179	+	0.250260i	$0.0805159\pi$
$62$	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	−0.373115	−	0.927785i	$-0.621710\pi$
$67$	−10.2751	−	3.73984i	−1.25531	−	0.456894i	−0.882191	+	0.470891i	$0.843933\pi$
$68$	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	0.611461	−	0.791275i	$-0.290582\pi$
$71$	−0.519169	−	0.435634i	−0.0616140	−	0.0517003i	−0.673075	+	0.739575i	$0.735027\pi$
$72$	−6.32974	+	5.31128i	−0.745967	+	0.625940i
$73$	1.21787	−	6.90688i	0.142541	−	0.808389i	−0.826768	−	0.562543i	$-0.809823\pi$
$73$	1.21787	−	6.90688i	0.142541	−	0.808389i	0.969309	−	0.245846i	$-0.0790657\pi$
$74$	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	−0.931767	−	0.363056i	$-0.881733\pi$
$79$	0.604220	−	3.42670i	0.0679801	−	0.385534i	0.999747	−	0.0224781i	$-0.00715559\pi$
$80$		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	0.969636	−	0.244552i	$-0.0786408\pi$
$83$	2.48742	+	4.30834i	0.273030	+	0.472902i	−0.696606	+	0.717454i	$0.745307\pi$
$84$	−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	−0.989812	−	0.142383i	$-0.954523\pi$
$89$	−1.02256	−	5.79921i	−0.108391	−	0.614716i	0.881421	−	0.472332i	$-0.156588\pi$
$90$		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	0.328200	−	0.944608i	$-0.393558\pi$
$97$	11.6886	−	4.25430i	1.18680	−	0.431959i	0.858598	+	0.512649i	$0.171336\pi$
$98$	−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	−0.616478	−	0.787372i	$-0.711441\pi$
$101$	−3.08004	−	17.4678i	−0.306475	−	1.73811i	0.310003	−	0.950736i	$-0.399670\pi$
$102$	1.34664	+	2.33245i	0.133337	+	0.230947i
$103$	2.60925	−	4.51935i	0.257097	−	0.445305i	−0.708366	−	0.705845i	$-0.750567\pi$
$103$	2.60925	−	4.51935i	0.257097	−	0.445305i	0.965463	+	0.260541i	$0.0839008\pi$
$104$	−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	0.955118	+	0.296225i	$0.0957277\pi$
$107$	7.59356	+	13.1524i	0.734097	+	1.27149i	−0.221021	+	0.975269i	$0.570939\pi$
$108$	0.476440	+	2.70203i	0.0458455	+	0.260003i
$109$	3.00487	+	2.52138i	0.287814	+	0.241505i	0.775251	−	0.631654i	$-0.217624\pi$
$109$	3.00487	+	2.52138i	0.287814	+	0.241505i	−0.487437	+	0.873158i	$0.662068\pi$
$110$		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	0.970089	+	0.242751i	$0.0780497\pi$
$127$	1.59495	+	9.04543i	0.141529	+	0.802652i	−0.828559	+	0.559901i	$0.810839\pi$
$128$	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	−0.183936	−	0.982938i	$-0.558884\pi$
$131$	3.51355	−	1.27883i	0.306980	−	0.111732i	0.490917	+	0.871206i	$0.336662\pi$
$132$	−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	−0.562166	−	0.827025i	$-0.690032\pi$
$137$	1.81043	−	1.51913i	0.154675	−	0.129788i	0.716841	+	0.697237i	$0.245587\pi$
$138$	−1.59946	−	1.34210i	−0.136155	−	0.114247i
$139$	0.424186	+	2.40568i	0.0359790	+	0.204047i	0.997498	−	0.0706903i	$-0.0225202\pi$
$139$	0.424186	+	2.40568i	0.0359790	+	0.204047i	−0.961519	+	0.274737i	$0.911409\pi$
$140$		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	−0.697598	−	0.716490i	$-0.745748\pi$
$149$	2.47773	−	14.0519i	0.202984	−	1.15118i	0.900581	−	0.434687i	$-0.143141\pi$
$150$		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	−0.00347076	−	0.999994i	$-0.501105\pi$
$157$	−12.3906	−	10.3969i	−0.988875	−	0.829765i	−0.985405	+	0.170229i	$0.945549\pi$
$158$	−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	−0.360410	−	0.932794i	$-0.617363\pi$
$163$	8.01289	−	13.8787i	0.627618	−	1.08707i	0.988028	−	0.154273i	$-0.0493034\pi$
$164$	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	−0.389989	−	0.920819i	$-0.627521\pi$
$167$	5.80391	−	4.87006i	0.449120	−	0.376856i	0.839109	+	0.543963i	$0.183077\pi$
$168$	−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	−0.00545960	−	0.999985i	$-0.501738\pi$
$173$	8.32761	−	3.03100i	0.633136	−	0.230443i	0.638596	+	0.769542i	$0.279516\pi$
$174$	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	−0.949895	−	0.312570i	$-0.898810\pi$
$179$	−2.73273	+	4.73323i	−0.204254	+	0.353778i	0.745641	+	0.666348i	$0.232143\pi$
$180$		0			0
$181$	−17.6816	−	6.43559i	−1.31427	−	0.478354i	−0.412650	−	0.910890i	$-0.635397\pi$
$181$	−17.6816	−	6.43559i	−1.31427	−	0.478354i	−0.901617	+	0.432536i	$0.857619\pi$
$182$	−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	−0.901795	−	0.432164i	$-0.857750\pi$
$193$	1.29789	−	7.36067i	0.0934238	−	0.529833i	0.995219	−	0.0976691i	$-0.0311387\pi$
$194$	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	0.562395	−	0.826869i	$-0.309880\pi$
$197$	−6.10400	−	10.5724i	−0.434892	−	0.753255i	−0.997287	+	0.0736138i	$0.976547\pi$
$198$	−1.18528	+	2.05297i	−0.0842343	+	0.145898i
$199$	7.29002	+	2.65335i	0.516776	+	0.188091i	0.587224	−	0.809424i	$-0.300221\pi$
$199$	7.29002	+	2.65335i	0.516776	+	0.188091i	−0.0704481	+	0.997515i	$0.522443\pi$
$200$		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	−0.646175	−	0.763190i	$-0.723632\pi$
$211$	−9.45058	+	3.43973i	−0.650605	+	0.236801i	−0.00442979	+	0.999990i	$0.501410\pi$
$212$	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	0.930482	+	0.366339i	$0.119389\pi$
$223$	21.6954	+	18.2046i	1.45283	+	1.21907i	0.522350	+	0.852731i	$0.325056\pi$
$224$	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	0.151109	−	0.988517i	$-0.451716\pi$
$233$	−12.1527	−	10.1973i	−0.796151	−	0.668050i	−0.947260	+	0.320467i	$0.896160\pi$
$234$	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	0.301705	+	0.953401i	$0.402444\pi$
$239$	−10.4324	+	18.0695i	−0.674817	+	1.16882i	−0.976522	+	0.215416i	$0.930889\pi$
$240$		0			0
$241$	4.93664	+	27.9971i	0.317997	+	1.80345i	0.554899	+	0.831917i	$0.312757\pi$
$241$	4.93664	+	27.9971i	0.317997	+	1.80345i	−0.236902	+	0.971533i	$0.576132\pi$
$242$	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	0.200157	−	0.979764i	$-0.435855\pi$
$251$	19.0083	−	15.9499i	1.19979	−	1.00675i	0.999636	−	0.0269823i	$-0.00858979\pi$
$252$	−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	0.496559	−	0.868003i	$-0.334597\pi$
$257$	5.11403	+	1.86135i	0.319004	+	0.116108i	−0.177555	+	0.984111i	$0.556819\pi$
$258$	−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	0.681997	+	0.731355i	$0.261112\pi$
$263$	−3.38955	+	19.2231i	−0.209009	+	1.18535i	−0.891006	+	0.453992i	$0.849999\pi$
$264$	−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	−0.713113	−	0.701049i	$-0.752715\pi$
$269$	3.22722	−	18.3025i	0.196767	−	1.11592i	0.909880	−	0.414872i	$-0.136174\pi$
$270$		0			0
$271$	1.44946	+	1.21624i	0.0880485	+	0.0738815i	0.685749	−	0.727838i	$-0.259475\pi$
$271$	1.44946	+	1.21624i	0.0880485	+	0.0738815i	−0.597701	+	0.801719i	$0.703919\pi$
$272$	−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	−0.746051	−	0.665889i	$-0.768052\pi$
$277$	3.38944	−	5.87068i	0.203652	−	0.352735i	0.949702	+	0.313154i	$0.101386\pi$
$278$	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	−0.878798	−	0.477194i	$-0.841654\pi$
$281$	−9.41170	+	7.89735i	−0.561455	+	0.471116i	0.317343	+	0.948311i	$0.397209\pi$
$282$	−0.328661	+	1.86393i	−0.0195715	+	0.110995i
$283$	−24.1188	+	8.77851i	−1.43371	+	0.521829i	−0.937993	−	0.346654i	$-0.887318\pi$
$283$	−24.1188	+	8.77851i	−1.43371	+	0.521829i	−0.495719	+	0.868483i	$0.665095\pi$
$284$	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	−0.0836552	−	0.996495i	$-0.526659\pi$
$293$	14.0560	−	24.3458i	0.821162	−	1.42229i	0.904817	−	0.425800i	$-0.140007\pi$
$294$	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	−0.994910	−	0.100763i	$-0.967872\pi$
$307$	−0.447450	+	2.53762i	−0.0255373	+	0.144829i	0.969373	+	0.245593i	$0.0789826\pi$
$308$	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	0.580440	−	0.814303i	$-0.302880\pi$
$311$	−7.31837	−	12.6758i	−0.414987	−	0.718778i	−0.995427	+	0.0955246i	$0.969547\pi$
$312$	−0.493525	+	0.854810i	−0.0279403	+	0.0483941i
$313$	−1.40398	−	0.511007i	−0.0793577	−	0.0288838i	0.302036	−	0.953296i	$-0.402334\pi$
$313$	−1.40398	−	0.511007i	−0.0793577	−	0.0288838i	−0.381394	+	0.924413i	$0.624556\pi$
$314$	−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	0.999881	−	0.0154089i	$-0.00490501\pi$
$317$	0.979782	+	5.55662i	0.0550301	+	0.312091i	−0.944851	+	0.327500i	$0.893794\pi$
$318$	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	−0.0212866	+	0.999773i	$0.506776\pi$
$331$	−15.9460	+	27.6193i	−0.876472	+	1.51809i	−0.855186	+	0.518321i	$0.826557\pi$
$332$	−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	0.904029	−	0.427472i	$-0.140596\pi$
$337$	11.7495	+	9.85896i	0.640033	+	0.537052i	−0.263995	+	0.964524i	$0.585040\pi$
$338$	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	0.641086	−	0.767469i	$-0.278484\pi$
$347$	−0.0633501	−	0.0531571i	−0.00340081	−	0.00285362i	−0.644486	+	0.764616i	$0.722929\pi$
$348$	0.331247	+	1.87860i	0.0177567	+	0.100703i
$349$	2.32166	+	4.02124i	0.124276	+	0.215252i	0.921450	−	0.388498i	$-0.127006\pi$
$349$	2.32166	+	4.02124i	0.124276	+	0.215252i	−0.797174	+	0.603750i	$0.793673\pi$
$350$		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	−0.914265	−	0.405118i	$-0.867231\pi$
$353$	−1.99701	+	3.45892i	−0.106290	+	0.184100i	0.807974	+	0.589218i	$0.200564\pi$
$354$	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	−0.955738	−	0.294220i	$-0.904940\pi$
$359$	−28.3973	+	10.3358i	−1.49875	+	0.545502i	−0.543017	+	0.839722i	$0.682718\pi$
$360$		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	0.949653	+	0.313302i	$0.101435\pi$
$367$	3.14996	+	17.8643i	0.164427	+	0.932511i	−0.785227	+	0.619208i	$0.787454\pi$
$368$	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	0.982442	+	0.186568i	$0.0597365\pi$
$373$	12.6075	+	21.8369i	0.652794	+	1.13067i	−0.329648	+	0.944104i	$0.606930\pi$
$374$	−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	−0.788932	−	0.614480i	$-0.789366\pi$
$383$	3.18187	−	18.0453i	0.162586	−	0.922072i	0.951518	−	0.307592i	$-0.0995230\pi$
$384$	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	0.507461	−	0.861674i	$-0.330584\pi$
$389$	6.75172	+	2.45743i	0.342326	+	0.124596i	−0.165136	+	0.986271i	$0.552806\pi$
$390$		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	−0.0504142	−	0.998728i	$-0.516054\pi$
$397$	11.0172	−	4.00993i	0.552937	−	0.201252i	0.603351	+	0.797476i	$0.293832\pi$
$398$	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	−0.850455	+	0.526048i	$0.823673\pi$
$401$	−36.8475	+	13.4114i	−1.84008	+	0.669734i	−0.989623	+	0.143686i	$0.954105\pi$
$402$	−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	0.127465	−	0.991843i	$-0.459316\pi$
$409$	−8.34099	−	3.03587i	−0.412436	−	0.150114i	−0.539901	+	0.841729i	$0.681538\pi$
$410$		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	−0.384893	−	0.922961i	$-0.625762\pi$
$421$	6.00077	−	34.0320i	0.292459	−	1.65862i	0.677352	−	0.735659i	$-0.263127\pi$
$422$	−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	0.994377	−	0.105893i	$-0.0337702\pi$
$431$	0.493077	+	2.79638i	0.0237507	+	0.134697i	−0.970627	+	0.240590i	$0.922659\pi$
$432$	3.20943	+	2.69303i	0.154414	+	0.129568i
$433$	−16.7402	+	14.0467i	−0.804481	+	0.675040i	−0.949284	−	0.314421i	$-0.898190\pi$
$433$	−16.7402	+	14.0467i	−0.804481	+	0.675040i	0.144803	+	0.989461i	$0.453745\pi$
$434$	−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	−0.945641	−	0.325212i	$-0.894564\pi$
$439$	−30.6114	+	11.1416i	−1.46100	+	0.531761i	−0.515361	+	0.856973i	$0.672342\pi$
$440$		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	0.999940	+	0.0109135i	$0.00347393\pi$
$443$	1.34781	+	7.64381i	0.0640364	+	0.363169i	−0.935904	+	0.352255i	$0.885415\pi$
$444$	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	−0.998772	−	0.0495489i	$-0.984222\pi$
$449$	−11.4911	−	19.9031i	−0.542296	−	0.939285i	0.456475	−	0.889736i	$-0.349112\pi$
$450$		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	0.428313	−	0.903630i	$-0.359108\pi$
$461$	−8.31382	−	6.97612i	−0.387213	−	0.324910i	−0.815526	+	0.578720i	$0.803552\pi$
$462$	0.220603	+	1.25110i	0.0102634	+	0.0582064i
$463$	−3.65586	−	6.33213i	−0.169902	−	0.294279i	0.768483	−	0.639870i	$-0.221012\pi$
$463$	−3.65586	−	6.33213i	−0.169902	−	0.294279i	−0.938385	+	0.345591i	$0.887678\pi$
$464$	−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	−0.712910	−	0.701255i	$-0.752623\pi$
$467$	5.42091	−	9.38929i	0.250850	−	0.434484i	0.963760	+	0.266771i	$0.0859567\pi$
$468$	−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	−0.580459	−	0.814289i	$-0.697127\pi$
$479$	2.64084	−	2.21593i	0.120663	−	0.101249i	0.701123	+	0.713041i	$0.252683\pi$
$480$		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	−0.990957	−	0.134177i	$-0.957161\pi$
$487$	−13.4986	−	23.3802i	−0.611680	−	1.05946i	0.379278	−	0.925283i	$-0.376172\pi$
$488$	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	−0.983837	−	0.179067i	$-0.942692\pi$
$491$	0.0423665	−	0.240272i	0.00191197	−	0.0108433i	0.985749	+	0.168224i	$0.0538032\pi$
$492$	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	0.585383	−	0.810757i	$-0.300944\pi$
$499$	−2.48864	−	2.08821i	−0.111407	−	0.0934813i	−0.696789	+	0.717276i	$0.745389\pi$
$500$		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	0.188403	−	0.982092i	$-0.439669\pi$
$503$	−6.69573	−	2.43705i	−0.298548	−	0.108663i	−0.486951	+	0.873429i	$0.661891\pi$
$504$	−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	−0.612941	−	0.790129i	$-0.710014\pi$
$509$	1.32543	−	1.11216i	0.0587485	−	0.0492958i	0.671689	+	0.740833i	$0.265569\pi$
$510$		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	−0.971498	−	0.237046i	$-0.923821\pi$
$521$	−6.40164	+	11.0880i	−0.280461	+	0.485773i	0.691037	+	0.722819i	$0.257154\pi$
$522$	10.6324	+	3.86989i	0.465369	+	0.169380i
$523$	−8.19075	−	2.98119i	−0.358157	−	0.130358i	0.156674	−	0.987650i	$-0.449923\pi$
$523$	−8.19075	−	2.98119i	−0.358157	−	0.130358i	−0.514830	+	0.857292i	$0.672145\pi$
$524$	−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	0.109780	−	0.993956i	$-0.464985\pi$
$541$	−10.3511	−	3.76748i	−0.445027	−	0.161977i	−0.554806	+	0.831979i	$0.687208\pi$
$542$	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	−0.892259	−	0.451525i	$-0.850880\pi$
$547$	−14.0921	+	11.8246i	−0.602533	+	0.505585i	0.289726	+	0.957110i	$0.406436\pi$
$548$	−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	0.985542	−	0.169430i	$-0.0541927\pi$
$557$	0.0350939	+	0.199028i	0.00148698	+	0.00843307i	−0.984055	+	0.177863i	$0.943082\pi$
$558$	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	0.928448	−	0.371462i	$-0.121143\pi$
$563$	3.38187	+	5.85758i	0.142529	+	0.246867i	−0.785919	+	0.618329i	$0.787810\pi$
$564$	−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	0.998333	−	0.0577173i	$-0.0183822\pi$
$577$	10.7897	+	18.6883i	0.449182	+	0.778006i	−0.549151	+	0.835723i	$0.685049\pi$
$578$	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	−0.835588	−	0.549356i	$-0.814873\pi$
$587$	−27.1976	+	9.89913i	−1.12257	+	0.408581i	−0.286978	+	0.957937i	$0.592651\pi$
$588$	−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	−0.317863	−	0.948137i	$-0.602965\pi$
$593$	13.6533	−	11.4565i	0.560674	−	0.470461i	0.878536	+	0.477676i	$0.158521\pi$
$594$	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	0.500914	−	0.865497i	$-0.332997\pi$
$599$	8.03512	+	2.92455i	0.328306	+	0.119494i	−0.172608	+	0.984991i	$0.555219\pi$
$600$		0			0
$601$	2.09514	+	3.62889i	0.0854627	+	0.148026i	0.905588	−	0.424158i	$-0.139430\pi$
$601$	2.09514	+	3.62889i	0.0854627	+	0.148026i	−0.820126	+	0.572184i	$0.806096\pi$
$602$	−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	0.876704	−	0.481030i	$-0.159737\pi$
$613$	13.7466	+	11.5348i	0.555220	+	0.465885i	−0.321484	+	0.946915i	$0.604182\pi$
$614$	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	−0.570400	−	0.821367i	$-0.693212\pi$
$617$	−38.1365	−	13.8805i	−1.53532	−	0.558809i	−0.964916	+	0.262558i	$0.915434\pi$
$618$	−2.72967	−	0.993517i	−0.109803	−	0.0399651i
$619$	12.7804	−	22.1363i	0.513688	−	0.889733i	−0.486186	−	0.873855i	$-0.661612\pi$
$619$	12.7804	−	22.1363i	0.513688	−	0.889733i	0.999874	−	0.0158781i	$-0.00505438\pi$
$620$		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	−0.569375	−	0.822078i	$-0.692815\pi$
$631$	3.55051	−	2.97923i	0.141344	−	0.118601i	0.710718	+	0.703477i	$0.248370\pi$
$632$	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	0.922399	−	0.386239i	$-0.126226\pi$
$641$	17.7783	+	14.9178i	0.702201	+	0.589217i	−0.220198	+	0.975455i	$0.570670\pi$
$642$	6.47602	−	5.43402i	0.255588	−	0.214464i
$643$	2.64733	−	15.0138i	0.104401	−	0.592086i	−0.887057	−	0.461659i	$-0.847254\pi$
$643$	2.64733	−	15.0138i	0.104401	−	0.592086i	0.991458	−	0.130426i	$-0.0416346\pi$
$644$	−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	0.925336	−	0.379149i	$-0.123783\pi$
$653$	3.43228	+	5.94488i	0.134315	+	0.232641i	−0.791020	+	0.611790i	$0.790450\pi$
$654$	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	0.925542	+	0.378645i	$0.123610\pi$
$659$	4.75738	+	26.9804i	0.185321	+	1.05101i	−0.740221	+	0.672364i	$0.765279\pi$
$660$		0			0
$661$	21.8707	−	18.3517i	0.850673	−	0.713800i	−0.109265	−	0.994013i	$-0.534850\pi$
$661$	21.8707	−	18.3517i	0.850673	−	0.713800i	0.959938	+	0.280213i	$0.0904051\pi$
$662$	−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	−0.00915115	+	0.999958i	$0.502913\pi$
$673$	−22.5844	+	39.1173i	−0.870565	+	1.50786i	−0.861414	+	0.507904i	$0.830420\pi$
$674$	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	0.824287	+	0.566172i	$0.191576\pi$
$677$	23.4814	+	40.6710i	0.902463	+	1.56311i	0.0781759	+	0.996940i	$0.475090\pi$
$678$	−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	0.984403	−	0.175927i	$-0.0562923\pi$
$691$	8.93344	+	15.4732i	0.339844	+	0.588627i	−0.644559	+	0.764555i	$0.722959\pi$
$692$	−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	−0.417281	−	0.908777i	$-0.637017\pi$
$701$	−4.04522	+	1.47234i	−0.152786	+	0.0556096i	0.264495	+	0.964387i	$0.414795\pi$
$702$	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	0.854665	+	0.519179i	$0.173762\pi$
$709$	6.10059	+	34.5982i	0.229112	+	1.29936i	−0.625553	+	0.780182i	$0.715127\pi$
$710$		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	−0.728388	−	0.685165i	$-0.759730\pi$
$719$	5.10577	−	28.9563i	0.190413	−	1.07989i	0.918801	−	0.394722i	$-0.129159\pi$
$720$		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	0.904283	−	0.426933i	$-0.140406\pi$
$727$	17.2796	+	14.4993i	0.640864	+	0.537749i	−0.263419	+	0.964681i	$0.584850\pi$
$728$	−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	0.268550	+	0.963266i	$0.413456\pi$
$733$	−18.9501	+	32.8225i	−0.699938	+	1.21233i	−0.968488	+	0.249062i	$0.919878\pi$
$734$	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	0.149442	−	0.988770i	$-0.452252\pi$
$739$	24.4523	−	8.89989i	0.899491	−	0.327388i	0.750049	+	0.661383i	$0.230030\pi$
$740$		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	−0.999092	−	0.0426041i	$-0.986435\pi$
$743$	−47.3487	+	17.2335i	−1.73706	+	0.632237i	−0.737964	+	0.674841i	$0.764212\pi$
$744$	−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	−0.169116	−	0.985596i	$-0.554091\pi$
$751$	−25.5462	−	9.29806i	−0.932195	−	0.339291i	−0.763079	+	0.646305i	$0.776313\pi$
$752$	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	−0.685610	−	0.727969i	$-0.740464\pi$
$757$	5.71273	−	32.3985i	0.207633	−	1.17754i	0.893243	−	0.449575i	$-0.148424\pi$
$758$	−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	0.817408	−	0.576059i	$-0.195410\pi$
$769$	29.7634	+	10.8330i	1.07330	+	0.390648i	0.255887	+	0.966707i	$0.417632\pi$
$770$		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	−0.873779	−	0.486323i	$-0.838338\pi$
$773$	−6.08960	−	34.5358i	−0.219028	−	1.24217i	0.654752	−	0.755844i	$-0.272773\pi$
$774$	−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	0.195107	+	0.980782i	$0.437495\pi$
$787$	−21.0914	+	36.5314i	−0.751829	+	1.30221i	−0.946936	+	0.321424i	$0.895839\pi$
$788$	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	0.498051	+	0.867148i	$0.334049\pi$
$809$	−14.2768	+	24.7282i	−0.501946	+	0.869396i	−0.999997	+	0.00224865i	$0.999284\pi$
$810$		0			0
$811$	−0.279849	−	1.58710i	−0.00982681	−	0.0557306i	0.979500	−	0.201444i	$-0.0645634\pi$
$811$	−0.279849	−	1.58710i	−0.00982681	−	0.0557306i	−0.989327	+	0.145713i	$0.953452\pi$
$812$	−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	−0.744010	−	0.668169i	$-0.767078\pi$
$821$	−6.16578	+	5.17371i	−0.215187	+	0.180564i	0.528822	+	0.848733i	$0.322634\pi$
$822$	−1.00777	−	0.845617i	−0.0351499	−	0.0294943i
$823$	−6.48442	−	36.7750i	−0.226033	−	1.28189i	−0.860701	−	0.509110i	$-0.829975\pi$
$823$	−6.48442	−	36.7750i	−0.226033	−	1.28189i	0.634669	−	0.772784i	$-0.281137\pi$
$824$	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	0.514367	−	0.857570i	$-0.328027\pi$
$827$	10.2711	+	3.73836i	0.357160	+	0.129996i	−0.157207	+	0.987566i	$0.550249\pi$
$828$	−4.60205	+	7.97098i	−0.159932	+	0.277011i
$829$	−16.8187	−	29.1309i	−0.584139	−	1.01176i	−0.994982	−	0.100052i	$-0.968099\pi$
$829$	−16.8187	−	29.1309i	−0.584139	−	1.01176i	0.410843	−	0.911706i	$-0.365234\pi$
$830$		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	−0.914565	−	0.404439i	$-0.867467\pi$
$839$	2.40910	−	13.6627i	0.0831714	−	0.471689i	0.997736	−	0.0672492i	$-0.0214222\pi$
$840$		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	0.180305	−	0.983611i	$-0.442291\pi$
$853$	27.7657	−	10.1059i	0.950680	−	0.346019i	0.770375	+	0.637591i	$0.220069\pi$
$854$	26.0400			0.891071
$855$		0			0
$856$	−46.1773			−1.57831
$857$	−4.02741	+	1.46586i	−0.137574	+	0.0500727i	−0.409889	−	0.912135i	$-0.634433\pi$
$857$	−4.02741	+	1.46586i	−0.137574	+	0.0500727i	0.272316	+	0.962208i	$0.412210\pi$
$858$	−0.0491733	+	0.278876i	−0.00167875	+	0.00952066i
$859$	−26.7935	+	22.4824i	−0.914181	+	0.767089i	−0.972910	−	0.231185i	$-0.925740\pi$
$859$	−26.7935	+	22.4824i	−0.914181	+	0.767089i	0.0587290	+	0.998274i	$0.481295\pi$
$860$		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	−0.984605	−	0.174797i	$-0.944073\pi$
$863$	−10.0153	+	17.3470i	−0.340924	+	0.590498i	0.643681	+	0.765294i	$0.277407\pi$
$864$	−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	−0.494959	−	0.868916i	$-0.664817\pi$
$877$	7.91697	−	44.8994i	0.267337	−	1.51614i	0.762297	−	0.647228i	$-0.224072\pi$
$878$	−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	0.974040	−	0.226378i	$-0.0726885\pi$
$881$	8.63649	+	14.9588i	0.290971	+	0.503976i	−0.683069	+	0.730354i	$0.739355\pi$
$882$	−0.724983	+	1.25571i	−0.0244114	+	0.0422819i
$883$	33.0707	+	12.0368i	1.11292	+	0.405069i	0.832063	−	0.554680i	$-0.187160\pi$
$883$	33.0707	+	12.0368i	1.11292	+	0.405069i	0.280856	+	0.959750i	$0.409382\pi$
$884$	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	0.992635	−	0.121140i	$-0.0386550\pi$
$887$	0.548919	+	3.11307i	0.0184309	+	0.104527i	−0.974205	+	0.225667i	$0.927544\pi$
$888$	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	0.417281	−	0.908778i	$-0.362983\pi$
$907$	−12.2041	−	10.2405i	−0.405230	−	0.340029i	−0.822511	+	0.568749i	$0.807428\pi$
$908$	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	−0.901551	−	0.432672i	$-0.857571\pi$
$919$	−25.0245	−	43.3436i	−0.825481	−	1.42977i	0.0760708	−	0.997102i	$-0.475762\pi$
$920$		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	−0.0666498	−	0.997776i	$-0.521231\pi$
$929$	15.9606	−	5.80920i	0.523652	−	0.190594i	0.590302	+	0.807183i	$0.299009\pi$
$930$		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	−0.917820	−	0.396997i	$-0.870052\pi$
$937$	−5.85065	−	33.1807i	−0.191132	−	1.08397i	0.726687	−	0.686968i	$-0.241059\pi$
$938$	−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	0.722844	−	0.691011i	$-0.242834\pi$
$941$	25.5345	+	9.29380i	0.832401	+	0.302969i	0.109557	+	0.993980i	$0.465057\pi$
$942$	−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	0.734309	+	0.678815i	$0.237506\pi$
$947$	−5.78183	+	32.7904i	−0.187884	+	1.06554i	−0.922193	+	0.386729i	$0.873605\pi$
$948$	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	0.771558	+	0.636159i	$0.219478\pi$
$953$	−5.28039	+	29.9466i	−0.171049	+	0.970065i	−0.942606	+	0.333906i	$0.891633\pi$
$954$	−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	0.780677	−	0.624934i	$-0.214874\pi$
$967$	55.3648	−	20.1511i	1.78041	−	0.648017i	0.999734	−	0.0230823i	$-0.00734797\pi$
$968$	−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	0.357995	−	0.933724i	$-0.383461\pi$
$971$	38.4033	−	13.9777i	1.23242	−	0.448564i	0.874426	+	0.485159i	$0.161238\pi$
$972$	−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	−0.421085	−	0.907021i	$-0.638351\pi$
$977$	17.9716	−	31.1276i	0.574961	−	0.995862i	0.996046	−	0.0888405i	$-0.0283161\pi$
$978$	−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	0.511472	−	0.859300i	$-0.329100\pi$
$983$	−7.71144	−	6.47067i	−0.245957	−	0.206382i	−0.757429	+	0.652918i	$0.773545\pi$
$984$	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	0.893834	+	0.448397i	$0.148005\pi$
$991$	−3.13089	+	17.7562i	−0.0994561	+	0.564043i	−0.993290	+	0.115646i	$0.963106\pi$
$992$	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	0.0480143	−	0.998847i	$-0.484711\pi$
$997$	−17.5954	−	6.40419i	−0.557251	−	0.202823i	−0.605265	+	0.796024i	$0.706933\pi$
$998$	−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.176.6		48
5.2	odd	4		95.2.p.a.24.6	yes	48
5.3	odd	4		95.2.p.a.24.3	yes	48
5.4	even	2	inner	475.2.l.f.176.3		48
15.2	even	4		855.2.da.b.784.3		48
15.8	even	4		855.2.da.b.784.6		48
19.2	odd	18		9025.2.a.ct.1.16		24
19.4	even	9	inner	475.2.l.f.251.6		48
19.17	even	9		9025.2.a.cu.1.9		24
95.2	even	36		1805.2.b.l.1084.16		24
95.4	even	18	inner	475.2.l.f.251.3		48
95.17	odd	36		1805.2.b.k.1084.9		24
95.23	odd	36		95.2.p.a.4.6	yes	48
95.42	odd	36		95.2.p.a.4.3	✓	48
95.59	odd	18		9025.2.a.ct.1.9		24
95.74	even	18		9025.2.a.cu.1.16		24
95.78	even	36		1805.2.b.l.1084.9		24
95.93	odd	36		1805.2.b.k.1084.16		24
285.23	even	36		855.2.da.b.289.3		48
285.137	even	36		855.2.da.b.289.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.4.3	✓	48	95.42	odd	36
95.2.p.a.4.6	yes	48	95.23	odd	36
95.2.p.a.24.3	yes	48	5.3	odd	4
95.2.p.a.24.6	yes	48	5.2	odd	4
475.2.l.f.176.3		48	5.4	even	2	inner
475.2.l.f.176.6		48	1.1	even	1	trivial
475.2.l.f.251.3		48	95.4	even	18	inner
475.2.l.f.251.6		48	19.4	even	9	inner
855.2.da.b.289.3		48	285.23	even	36
855.2.da.b.289.6		48	285.137	even	36
855.2.da.b.784.3		48	15.2	even	4
855.2.da.b.784.6		48	15.8	even	4
1805.2.b.k.1084.9		24	95.17	odd	36
1805.2.b.k.1084.16		24	95.93	odd	36
1805.2.b.l.1084.9		24	95.78	even	36
1805.2.b.l.1084.16		24	95.2	even	36
9025.2.a.ct.1.9		24	95.59	odd	18
9025.2.a.ct.1.16		24	19.2	odd	18
9025.2.a.cu.1.9		24	19.17	even	9
9025.2.a.cu.1.16		24	95.74	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.984236 - 0.358233i) q^{2} +(0.0922859 - 0.523379i) q^{3} +(-0.691698 + 0.580404i) q^{4} +(-0.0966605 - 0.548189i) q^{6} +(1.37016 + 2.37320i) q^{7} +(-1.52028 + 2.63320i) q^{8} +(2.55367 + 0.929459i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9}+O(q^{10}) \) 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9	\( 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9} - 12 q^{11} - 6 q^{14} - 42 q^{16} - 12 q^{19} - 54 q^{21} - 24 q^{24} + 12 q^{26} - 42 q^{31} + 36 q^{34} + 18 q^{36} + 48 q^{39} + 6 q^{41} + 6 q^{44} - 6 q^{46} - 12 q^{49} + 108 q^{51} - 24 q^{54} + 36 q^{56} + 36 q^{59} + 48 q^{61} + 180 q^{66} - 66 q^{69} - 24 q^{71} - 84 q^{74} + 66 q^{76} - 48 q^{79} - 78 q^{81} + 54 q^{84} - 42 q^{86} + 12 q^{89} - 30 q^{91} + 72 q^{94} - 240 q^{96} + 36 q^{99}+O(q^{100}) \) 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

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