LMFDB - Embedded newform 680.2.ba.b.21.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(21,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 2, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.21"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.ba (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [140] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$70$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			21.8
Character	$\chi$	$=$	680.21
Dual form			680.2.ba.b.421.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.33610 + 0.463502i) q^{2} +(0.494360 + 0.494360i) q^{3} +(1.57033 - 1.23857i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(-0.889652 - 0.431378i) q^{6} +(-0.414696 - 0.414696i) q^{7} +(-1.52404 + 2.38271i) q^{8} -2.51122i q^{9} +(1.27251 + 0.617020i) q^{10} +(-3.20488 + 3.20488i) q^{11} +(1.38861 + 0.164009i) q^{12} +1.30944i q^{13} +(0.746288 + 0.361863i) q^{14} -0.699131i q^{15} +(0.931882 - 3.88994i) q^{16} +(-0.762994 + 4.05189i) q^{17} +(1.16395 + 3.35524i) q^{18} -6.72670 q^{19} +(-1.98619 - 0.234590i) q^{20} -0.410018i q^{21} +(2.79657 - 5.76751i) q^{22} +(5.91974 + 5.91974i) q^{23} +(-1.93134 + 0.424491i) q^{24} +1.00000i q^{25} +(-0.606930 - 1.74955i) q^{26} +(2.72452 - 2.72452i) q^{27} +(-1.16484 - 0.137580i) q^{28} +(7.07289 + 7.07289i) q^{29} +(0.324049 + 0.934109i) q^{30} +(-6.42808 + 6.42808i) q^{31} +(0.557905 + 5.62928i) q^{32} -3.16873 q^{33} +(-0.858624 - 5.76739i) q^{34} +0.586469i q^{35} +(-3.11032 - 3.94344i) q^{36} +(1.46546 + 1.46546i) q^{37} +(8.98755 - 3.11784i) q^{38} +(-0.647336 + 0.647336i) q^{39} +(2.76249 - 0.607170i) q^{40} +(-0.620835 - 0.620835i) q^{41} +(0.190044 + 0.547826i) q^{42} +1.10981 q^{43} +(-1.06325 + 9.00220i) q^{44} +(-1.77570 + 1.77570i) q^{45} +(-10.6532 - 5.16556i) q^{46} +1.34367 q^{47} +(2.38371 - 1.46234i) q^{48} -6.65605i q^{49} +(-0.463502 - 1.33610i) q^{50} +(-2.38029 + 1.62590i) q^{51} +(1.62184 + 2.05626i) q^{52} -2.17870 q^{53} +(-2.37742 + 4.90306i) q^{54} +4.53238 q^{55} +(1.62011 - 0.356086i) q^{56} +(-3.32541 - 3.32541i) q^{57} +(-12.7284 - 6.17180i) q^{58} +3.33572 q^{59} +(-0.865923 - 1.09787i) q^{60} +(-2.21184 + 2.21184i) q^{61} +(5.60913 - 11.5680i) q^{62} +(-1.04139 + 1.04139i) q^{63} +(-3.35460 - 7.26269i) q^{64} +(0.925916 - 0.925916i) q^{65} +(4.23374 - 1.46871i) q^{66} +9.63230i q^{67} +(3.82041 + 7.30784i) q^{68} +5.85296i q^{69} +(-0.271830 - 0.783581i) q^{70} +(-2.86572 + 2.86572i) q^{71} +(5.98350 + 3.82720i) q^{72} +(-5.72848 + 5.72848i) q^{73} +(-2.63724 - 1.27876i) q^{74} +(-0.494360 + 0.494360i) q^{75} +(-10.5631 + 8.33150i) q^{76} +2.65810 q^{77} +(0.564865 - 1.16495i) q^{78} +(-6.52636 - 6.52636i) q^{79} +(-3.40954 + 2.09166i) q^{80} -4.83986 q^{81} +(1.11726 + 0.541740i) q^{82} -12.4258 q^{83} +(-0.507837 - 0.643865i) q^{84} +(3.40464 - 2.32560i) q^{85} +(-1.48282 + 0.514402i) q^{86} +6.99311i q^{87} +(-2.75193 - 12.5207i) q^{88} -16.7294 q^{89} +(1.54947 - 3.19555i) q^{90} +(0.543021 - 0.543021i) q^{91} +(16.6280 + 1.96393i) q^{92} -6.35557 q^{93} +(-1.79529 + 0.622796i) q^{94} +(4.75649 + 4.75649i) q^{95} +(-2.50708 + 3.05869i) q^{96} +(7.55413 - 7.55413i) q^{97} +(3.08510 + 8.89316i) q^{98} +(8.04815 + 8.04815i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 8 q^{4} - 4 q^{6} - 12 q^{7} + 20 q^{12} + 28 q^{14} - 24 q^{16} - 16 q^{17} - 8 q^{20} + 40 q^{22} + 4 q^{23} + 48 q^{24} - 20 q^{28} + 28 q^{31} - 8 q^{34} - 56 q^{38} + 24 q^{40} + 44 q^{41}+ \cdots + 176 q^{98}+O(q^{100}) $ 140 * q - 8 * q^4 - 4 * q^6 - 12 * q^7 + 20 * q^12 + 28 * q^14 - 24 * q^16 - 16 * q^17 - 8 * q^20 + 40 * q^22 + 4 * q^23 + 48 * q^24 - 20 * q^28 + 28 * q^31 - 8 * q^34 - 56 * q^38 + 24 * q^40 + 44 * q^41 + 28 * q^44 - 40 * q^46 - 120 * q^47 + 32 * q^48 - 48 * q^52 - 4 * q^54 + 16 * q^55 + 16 * q^56 - 16 * q^57 - 52 * q^58 - 72 * q^62 + 44 * q^63 - 104 * q^64 + 8 * q^68 + 12 * q^71 - 104 * q^72 + 36 * q^73 + 20 * q^74 + 28 * q^78 - 44 * q^79 - 76 * q^81 - 44 * q^82 + 48 * q^84 + 120 * q^86 + 28 * q^88 + 24 * q^89 + 28 * q^90 - 72 * q^92 + 8 * q^95 - 116 * q^96 + 12 * q^97 + 176 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−1.33610	+	0.463502i	−0.944766	+	0.327746i
$2$	−1.33610	+	0.463502i	−0.944766	+	0.327746i
$3$	0.494360	+	0.494360i	0.285419	+	0.285419i	0.835266	−	0.549847i	$-0.185314\pi$
$3$	0.494360	+	0.494360i	0.285419	+	0.285419i	−0.549847	+	0.835266i	$0.685314\pi$
$4$	1.57033	−	1.23857i	0.785166	−	0.619286i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$6$	−0.889652	−	0.431378i	−0.363199	−	0.176109i
$7$	−0.414696	−	0.414696i	−0.156740	−	0.156740i	0.624380	−	0.781121i	$-0.285352\pi$
$7$	−0.414696	−	0.414696i	−0.156740	−	0.156740i	−0.781121	+	0.624380i	$0.785352\pi$
$8$	−1.52404	+	2.38271i	−0.538830	+	0.842415i
$9$		−	2.51122i		−	0.837072i
$10$	1.27251	+	0.617020i	0.402403	+	0.195119i
$11$	−3.20488	+	3.20488i	−0.966308	+	0.966308i	−0.999451	−	0.0331430i	$-0.989448\pi$
$11$	−3.20488	+	3.20488i	−0.966308	+	0.966308i	0.0331430	+	0.999451i	$0.489448\pi$
$12$	1.38861	+	0.164009i	0.400857	+	0.0473453i
$13$			1.30944i			0.363174i	0.983375	+	0.181587i	$0.0581234\pi$
$13$			1.30944i			0.363174i	−0.983375	+	0.181587i	$0.941877\pi$
$14$	0.746288	+	0.361863i	0.199454	+	0.0967120i
$15$		−	0.699131i		−	0.180515i
$16$	0.931882	−	3.88994i	0.232970	−	0.972484i
$17$	−0.762994	+	4.05189i	−0.185053	+	0.982728i
$17$	−0.762994	+	4.05189i	−0.185053	+	0.982728i
$18$	1.16395	+	3.35524i	0.274347	+	0.790837i
$19$	−6.72670			−1.54321			−0.771605	−	0.636102i	$-0.780546\pi$
$19$	−6.72670			−1.54321			−0.771605	+	0.636102i	$0.780546\pi$
$20$	−1.98619	−	0.234590i	−0.444127	−	0.0524559i
$21$		−	0.410018i		−	0.0894733i
$22$	2.79657	−	5.76751i	0.596232	−	1.22964i
$23$	5.91974	+	5.91974i	1.23435	+	1.23435i	0.962276	+	0.272075i	$0.0877098\pi$
$23$	5.91974	+	5.91974i	1.23435	+	1.23435i	0.272075	+	0.962276i	$0.412290\pi$
$24$	−1.93134	+	0.424491i	−0.394233	+	0.0866489i
$25$			1.00000i			0.200000i
$26$	−0.606930	−	1.74955i	−0.119029	−	0.343115i
$27$	2.72452	−	2.72452i	0.524335	−	0.524335i
$28$	−1.16484	−	0.137580i	−0.220134	−	0.0260001i
$29$	7.07289	+	7.07289i	1.31340	+	1.31340i	0.918890	+	0.394513i	$0.129087\pi$
$29$	7.07289	+	7.07289i	1.31340	+	1.31340i	0.394513	+	0.918890i	$0.370913\pi$
$30$	0.324049	+	0.934109i	0.0591629	+	0.170544i
$31$	−6.42808	+	6.42808i	−1.15452	+	1.15452i	−0.168880	+	0.985637i	$0.554015\pi$
$31$	−6.42808	+	6.42808i	−1.15452	+	1.15452i	−0.985637	+	0.168880i	$0.945985\pi$
$32$	0.557905	+	5.62928i	0.0986247	+	0.995125i
$33$	−3.16873			−0.551605
$34$	−0.858624	−	5.76739i	−0.147253	−	0.989099i
$35$			0.586469i			0.0991313i
$36$	−3.11032	−	3.94344i	−0.518387	−	0.657240i
$37$	1.46546	+	1.46546i	0.240919	+	0.240919i	0.817230	−	0.576311i	$-0.195508\pi$
$37$	1.46546	+	1.46546i	0.240919	+	0.240919i	−0.576311	+	0.817230i	$0.695508\pi$
$38$	8.98755	−	3.11784i	1.45797	−	0.505780i
$39$	−0.647336	+	0.647336i	−0.103657	+	0.103657i
$40$	2.76249	−	0.607170i	0.436788	−	0.0960020i
$41$	−0.620835	−	0.620835i	−0.0969581	−	0.0969581i	0.656964	−	0.753922i	$-0.271840\pi$
$41$	−0.620835	−	0.620835i	−0.0969581	−	0.0969581i	−0.753922	+	0.656964i	$0.771840\pi$
$42$	0.190044	+	0.547826i	0.0293245	+	0.0845314i
$43$	1.10981			0.169245			0.0846226	−	0.996413i	$-0.473032\pi$
$43$	1.10981			0.169245			0.0846226	+	0.996413i	$0.473032\pi$
$44$	−1.06325	+	9.00220i	−0.160291	+	1.35713i
$45$	−1.77570	+	1.77570i	−0.264705	+	0.264705i
$46$	−10.6532	−	5.16556i	−1.57073	−	0.761620i
$47$	1.34367			0.195995			0.0979975	−	0.995187i	$-0.468756\pi$
$47$	1.34367			0.195995			0.0979975	+	0.995187i	$0.468756\pi$
$48$	2.38371	−	1.46234i	0.344059	−	0.211071i
$49$		−	6.65605i		−	0.950865i
$50$	−0.463502	−	1.33610i	−0.0655491	−	0.188953i
$51$	−2.38029	+	1.62590i	−0.333307	+	0.227672i
$52$	1.62184	+	2.05626i	0.224909	+	0.285152i
$53$	−2.17870			−0.299268			−0.149634	−	0.988741i	$-0.547810\pi$
$53$	−2.17870			−0.299268			−0.149634	+	0.988741i	$0.547810\pi$
$54$	−2.37742	+	4.90306i	−0.323525	+	0.667222i
$55$	4.53238			0.611147
$56$	1.62011	−	0.356086i	0.216497	−	0.0475840i
$57$	−3.32541	−	3.32541i	−0.440461	−	0.440461i
$58$	−12.7284	−	6.17180i	−1.67132	−	0.810397i
$59$	3.33572			0.434274			0.217137	−	0.976141i	$-0.430328\pi$
$59$	3.33572			0.434274			0.217137	+	0.976141i	$0.430328\pi$
$60$	−0.865923	−	1.09787i	−0.111790	−	0.141734i
$61$	−2.21184	+	2.21184i	−0.283197	+	0.283197i	−0.834383	−	0.551185i	$-0.814176\pi$
$61$	−2.21184	+	2.21184i	−0.283197	+	0.283197i	0.551185	+	0.834383i	$0.314176\pi$
$62$	5.60913	−	11.5680i	0.712361	−	1.46914i
$63$	−1.04139	+	1.04139i	−0.131203	+	0.131203i
$64$	−3.35460	−	7.26269i	−0.419325	−	0.907836i
$65$	0.925916	−	0.925916i	0.114846	−	0.114846i
$66$	4.23374	−	1.46871i	0.521138	−	0.180786i
$67$			9.63230i			1.17677i	0.808580	+	0.588387i	$0.200237\pi$
$67$			9.63230i			1.17677i	−0.808580	+	0.588387i	$0.799763\pi$
$68$	3.82041	+	7.30784i	0.463292	+	0.886206i
$69$			5.85296i			0.704614i
$70$	−0.271830	−	0.783581i	−0.0324898	−	0.0936559i
$71$	−2.86572	+	2.86572i	−0.340099	+	0.340099i	−0.856404	−	0.516306i	$-0.827307\pi$
$71$	−2.86572	+	2.86572i	−0.340099	+	0.340099i	0.516306	+	0.856404i	$0.327307\pi$
$72$	5.98350	+	3.82720i	0.705162	+	0.451039i
$73$	−5.72848	+	5.72848i	−0.670468	+	0.670468i	−0.957824	−	0.287356i	$-0.907224\pi$
$73$	−5.72848	+	5.72848i	−0.670468	+	0.670468i	0.287356	+	0.957824i	$0.407224\pi$
$74$	−2.63724	−	1.27876i	−0.306573	−	0.148652i
$75$	−0.494360	+	0.494360i	−0.0570838	+	0.0570838i
$76$	−10.5631	+	8.33150i	−1.21168	+	0.955688i
$77$	2.65810			0.302919
$78$	0.564865	−	1.16495i	0.0639583	−	0.131904i
$79$	−6.52636	−	6.52636i	−0.734273	−	0.734273i	0.237190	−	0.971463i	$-0.423774\pi$
$79$	−6.52636	−	6.52636i	−0.734273	−	0.734273i	−0.971463	+	0.237190i	$0.923774\pi$
$80$	−3.40954	+	2.09166i	−0.381198	+	0.233855i
$81$	−4.83986			−0.537762
$82$	1.11726	+	0.541740i	0.123380	+	0.0598251i
$83$	−12.4258			−1.36391			−0.681957	−	0.731392i	$-0.738871\pi$
$83$	−12.4258			−1.36391			−0.681957	+	0.731392i	$0.738871\pi$
$84$	−0.507837	−	0.643865i	−0.0554095	−	0.0702514i
$85$	3.40464	−	2.32560i	0.369285	−	0.252247i
$86$	−1.48282	+	0.514402i	−0.159897	+	0.0554694i
$87$			6.99311i			0.749740i
$88$	−2.75193	−	12.5207i	−0.293356	−	1.33471i
$89$	−16.7294			−1.77331			−0.886656	−	0.462429i	$-0.846978\pi$
$89$	−16.7294			−1.77331			−0.886656	+	0.462429i	$0.846978\pi$
$90$	1.54947	−	3.19555i	0.163329	−	0.336841i
$91$	0.543021	−	0.543021i	0.0569240	−	0.0569240i
$92$	16.6280	+	1.96393i	1.73359	+	0.204754i
$93$	−6.35557			−0.659042
$94$	−1.79529	+	0.622796i	−0.185170	+	0.0642365i
$95$	4.75649	+	4.75649i	0.488006	+	0.488006i
$96$	−2.50708	+	3.05869i	−0.255878	+	0.312177i
$97$	7.55413	−	7.55413i	0.767006	−	0.767006i	−0.210572	−	0.977578i	$-0.567533\pi$
$97$	7.55413	−	7.55413i	0.767006	−	0.767006i	0.977578	+	0.210572i	$0.0675328\pi$
$98$	3.08510	+	8.89316i	0.311642	+	0.898345i
$99$	8.04815	+	8.04815i	0.808869	+	0.808869i
$100$	1.23857	+	1.57033i	0.123857	+	0.157033i
$101$		−	4.14046i		−	0.411991i	−0.978553	−	0.205995i	$-0.933957\pi$
$101$		−	4.14046i		−	0.411991i	0.978553	−	0.205995i	$-0.0660432\pi$
$102$	2.42670	−	3.27564i	0.240279	−	0.324336i
$103$	−4.07974			−0.401989			−0.200995	−	0.979592i	$-0.564417\pi$
$103$	−4.07974			−0.401989			−0.200995	+	0.979592i	$0.564417\pi$
$104$	−3.12002	−	1.99564i	−0.305943	−	0.195689i
$105$	−0.289927	+	0.289927i	−0.0282939	+	0.0282939i
$106$	2.91097	−	1.00983i	0.282738	−	0.0980837i
$107$	8.38280	+	8.38280i	0.810396	+	0.810396i	0.984693	−	0.174297i	$-0.0557654\pi$
$107$	8.38280	+	8.38280i	0.810396	+	0.810396i	−0.174297	+	0.984693i	$0.555765\pi$
$108$	0.903889	−	7.65293i	0.0869767	−	0.736403i
$109$	11.9162	−	11.9162i	1.14137	−	1.14137i	0.153169	−	0.988200i	$-0.451052\pi$
$109$	11.9162	−	11.9162i	1.14137	−	1.14137i	0.988200	−	0.153169i	$-0.0489479\pi$
$110$	−6.05572	+	2.10077i	−0.577391	+	0.200301i
$111$			1.44893i			0.137526i
$112$	−1.99959	+	1.22669i	−0.188943	+	0.115912i
$113$	−9.79568	−	9.79568i	−0.921500	−	0.921500i	0.0756354	−	0.997136i	$-0.475901\pi$
$113$	−9.79568	−	9.79568i	−0.921500	−	0.921500i	−0.997136	+	0.0756354i	$0.975901\pi$
$114$	5.98442	+	2.90175i	0.560492	+	0.271774i
$115$		−	8.37177i		−	0.780672i
$116$	19.8671	+	2.34650i	1.84461	+	0.217867i
$117$	3.28829			0.304003
$118$	−4.45686	+	1.54611i	−0.410287	+	0.142331i
$119$	1.99671	−	1.36389i	0.183039	−	0.125028i
$120$	1.66582	+	1.06550i	0.152068	+	0.0972667i
$121$		−	9.54251i		−	0.867501i
$122$	1.93005	−	3.98044i	0.174739	−	0.360372i
$123$		−	0.613832i		−	0.0553473i
$124$	−2.13258	+	18.0558i	−0.191511	+	1.62146i
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$	0.908717	−	1.87409i	0.0809549	−	0.166957i
$127$			18.4352i			1.63586i	0.575317	+	0.817930i	$0.304879\pi$
$127$			18.4352i			1.63586i	−0.575317	+	0.817930i	$0.695121\pi$
$128$	7.84836	+	8.14882i	0.693703	+	0.720261i
$129$	0.548648	+	0.548648i	0.0483058	+	0.0483058i
$130$	−0.807953	+	1.66628i	−0.0708622	+	0.146143i
$131$	−13.5325	−	13.5325i	−1.18234	−	1.18234i	−0.979136	−	0.203207i	$-0.934864\pi$
$131$	−13.5325	−	13.5325i	−1.18234	−	1.18234i	−0.203207	−	0.979136i	$-0.565136\pi$
$132$	−4.97595	+	3.92470i	−0.433101	+	0.341601i
$133$	2.78954	+	2.78954i	0.241883	+	0.241883i
$134$	−4.46459	−	12.8697i	−0.385682	−	1.11178i
$135$	−3.85306			−0.331619
$136$	−8.49165	−	7.99324i	−0.728153	−	0.685415i
$137$	12.1908			1.04153			0.520763	−	0.853701i	$-0.325647\pi$
$137$	12.1908			1.04153			0.520763	+	0.853701i	$0.325647\pi$
$138$	−2.71286	−	7.82015i	−0.230934	−	0.665695i
$139$	9.18912	+	9.18912i	0.779411	+	0.779411i	0.979731	−	0.200319i	$-0.0641980\pi$
$139$	9.18912	+	9.18912i	0.779411	+	0.779411i	−0.200319	+	0.979731i	$0.564198\pi$
$140$	0.726383	+	0.920950i	0.0613906	+	0.0778345i
$141$	0.664259	+	0.664259i	0.0559407	+	0.0559407i
$142$	2.50063	−	5.15716i	0.209848	−	0.432780i
$143$	−4.19661	−	4.19661i	−0.350938	−	0.350938i
$144$	−9.76847	−	2.34016i	−0.814039	−	0.195013i
$145$		−	10.0026i		−	0.830669i
$146$	4.99867	−	10.3090i	0.413693	−	0.853178i
$147$	3.29049	−	3.29049i	0.271395	−	0.271395i
$148$	4.11632	+	0.486180i	0.338360	+	0.0399637i
$149$			11.7235i			0.960430i	0.877151	+	0.480215i	$0.159441\pi$
$149$			11.7235i			0.960430i	−0.877151	+	0.480215i	$0.840559\pi$
$150$	0.431378	−	0.889652i	0.0352219	−	0.0726398i
$151$			8.76515i			0.713298i	0.934238	+	0.356649i	$0.116081\pi$
$151$			8.76515i			0.713298i	−0.934238	+	0.356649i	$0.883919\pi$
$152$	10.2518	−	16.0278i	0.831528	−	1.30002i
$153$	10.1752	+	1.91604i	0.822615	+	0.154903i
$154$	−3.55149	+	1.23204i	−0.286187	+	0.0992803i
$155$	9.09067			0.730181
$156$	−0.214760	+	1.81830i	−0.0171946	+	0.145581i
$157$		−	20.6801i		−	1.65045i	−0.564805	−	0.825224i	$-0.691049\pi$
$157$		−	20.6801i		−	1.65045i	0.564805	−	0.825224i	$-0.308951\pi$
$158$	11.7449	+	5.69490i	0.934371	+	0.453062i
$159$	−1.07706	−	1.07706i	−0.0854167	−	0.0854167i
$160$	3.58600	−	4.37500i	0.283498	−	0.345874i
$161$		−	4.90978i		−	0.386945i
$162$	6.46654	−	2.24328i	0.508059	−	0.176249i
$163$	12.3217	−	12.3217i	0.965111	−	0.965111i	−0.0343004	−	0.999412i	$-0.510920\pi$
$163$	12.3217	−	12.3217i	0.965111	−	0.965111i	0.999412	+	0.0343004i	$0.0109203\pi$
$164$	−1.74386	−	0.205968i	−0.136173	−	0.0160834i
$165$	2.24063	+	2.24063i	0.174433	+	0.174433i
$166$	16.6022	−	5.75941i	1.28858	−	0.447017i
$167$	0.416614	−	0.416614i	0.0322386	−	0.0322386i	−0.690804	−	0.723042i	$-0.742743\pi$
$167$	0.416614	−	0.416614i	0.0322386	−	0.0322386i	0.723042	+	0.690804i	$0.242743\pi$
$168$	0.976954	+	0.624885i	0.0753736	+	0.0482109i
$169$	11.2854			0.868105
$170$	−3.47102	+	4.68530i	−0.266215	+	0.359346i
$171$			16.8922i			1.29178i
$172$	1.74278	−	1.37458i	0.132886	−	0.104811i
$173$	5.48975	+	5.48975i	0.417378	+	0.417378i	0.884299	−	0.466921i	$-0.154637\pi$
$173$	5.48975	+	5.48975i	0.417378	+	0.417378i	−0.466921	+	0.884299i	$0.654637\pi$
$174$	−3.24132	−	9.34350i	−0.245724	−	0.708329i
$175$	0.414696	−	0.414696i	0.0313481	−	0.0313481i
$176$	9.48021	+	15.4533i	0.714597	+	1.16484i
$177$	1.64905	+	1.64905i	0.123950	+	0.123950i
$178$	22.3522	−	7.75411i	1.67537	−	0.581195i
$179$	2.78878			0.208443			0.104222	−	0.994554i	$-0.466765\pi$
$179$	2.78878			0.208443			0.104222	+	0.994554i	$0.466765\pi$
$180$	−0.589106	+	4.98776i	−0.0439093	+	0.371766i
$181$	10.8676	−	10.8676i	0.807782	−	0.807782i	−0.176516	−	0.984298i	$-0.556483\pi$
$181$	10.8676	−	10.8676i	0.807782	−	0.807782i	0.984298	+	0.176516i	$0.0564826\pi$
$182$	−0.473839	+	0.977222i	−0.0351233	+	0.0724365i
$183$	−2.18689			−0.161660
$184$	−23.1269	+	5.08309i	−1.70494	+	0.374730i
$185$		−	2.07247i		−	0.152371i
$186$	8.49168	−	2.94582i	0.622640	−	0.215998i
$187$	−10.5405	−	15.4311i	−0.770800	−	1.12844i
$188$	2.11001	−	1.66424i	0.153889	−	0.121377i
$189$	−2.25970			−0.164369
$190$	−8.55980	−	4.15051i	−0.620993	−	0.301110i
$191$	5.18132			0.374907			0.187454	−	0.982273i	$-0.439977\pi$
$191$	5.18132			0.374907			0.187454	+	0.982273i	$0.439977\pi$
$192$	1.93200	−	5.24876i	0.139430	−	0.378797i
$193$	−13.1745	−	13.1745i	−0.948319	−	0.948319i	0.0504092	−	0.998729i	$-0.483947\pi$
$193$	−13.1745	−	13.1745i	−0.948319	−	0.948319i	−0.998729	+	0.0504092i	$0.983947\pi$
$194$	−6.59173	+	13.5944i	−0.473258	+	0.976024i
$195$	0.915472			0.0655583
$196$	−8.24400	−	10.4522i	−0.588857	−	0.746587i
$197$	2.67165	−	2.67165i	0.190347	−	0.190347i	−0.605499	−	0.795846i	$-0.707026\pi$
$197$	2.67165	−	2.67165i	0.190347	−	0.190347i	0.795846	+	0.605499i	$0.207026\pi$
$198$	−14.4835	−	7.02280i	−1.02930	−	0.499089i
$199$	12.4747	−	12.4747i	0.884310	−	0.884310i	−0.109659	−	0.993969i	$-0.534976\pi$
$199$	12.4747	−	12.4747i	0.884310	−	0.884310i	0.993969	+	0.109659i	$0.0349759\pi$
$200$	−2.38271	−	1.52404i	−0.168483	−	0.107766i
$201$	−4.76183	+	4.76183i	−0.335873	+	0.335873i
$202$	1.91911	+	5.53207i	0.135028	+	0.389235i
$203$		−	5.86620i		−	0.411727i
$204$	−1.72405	+	5.50136i	−0.120707	+	0.385172i
$205$			0.877993i			0.0613217i
$206$	5.45095	−	1.89097i	0.379786	−	0.131750i
$207$	14.8657	−	14.8657i	1.03324	−	1.03324i
$208$	5.09365	+	1.22025i	0.353181	+	0.0846088i
$209$	21.5583	−	21.5583i	1.49122	−	1.49122i
$210$	0.252990	−	0.521753i	0.0174579	−	0.0360044i
$211$	−7.62946	+	7.62946i	−0.525234	+	0.525234i	−0.919147	−	0.393914i	$-0.871121\pi$
$211$	−7.62946	+	7.62946i	−0.525234	+	0.525234i	0.393914	+	0.919147i	$0.371121\pi$
$212$	−3.42129	+	2.69848i	−0.234975	+	0.185332i
$213$	−2.83340			−0.194141
$214$	−15.0857	−	7.31482i	−1.03124	−	0.500031i
$215$	−0.784758	−	0.784758i	−0.0535200	−	0.0535200i
$216$	2.33946	+	10.6440i	0.159180	+	0.724235i
$217$	5.33140			0.361919
$218$	−10.3981	+	21.4445i	−0.704248	+	1.45241i
$219$	−5.66387			−0.382729
$220$	7.11735	−	5.61368i	0.479851	−	0.378474i
$221$	−5.30572	−	0.999097i	−0.356902	−	0.0672066i
$222$	−0.671580	−	1.93591i	−0.0450735	−	0.129930i
$223$			15.2834i			1.02345i	0.859148	+	0.511726i	$0.170994\pi$
$223$			15.2834i			1.02345i	−0.859148	+	0.511726i	$0.829006\pi$
$224$	2.10308	−	2.56580i	0.140518	−	0.171435i
$225$	2.51122			0.167414
$226$	17.6283	+	8.54770i	1.17262	+	0.568584i
$227$	−1.06058	+	1.06058i	−0.0703930	+	0.0703930i	−0.741427	−	0.671034i	$-0.765851\pi$
$227$	−1.06058	+	1.06058i	−0.0703930	+	0.0703930i	0.671034	+	0.741427i	$0.265851\pi$
$228$	−9.34076	−	1.10324i	−0.618607	−	0.0730637i
$229$	−17.2675			−1.14107			−0.570534	−	0.821274i	$-0.693264\pi$
$229$	−17.2675			−1.14107			−0.570534	+	0.821274i	$0.693264\pi$
$230$	3.88034	+	11.1855i	0.255862	+	0.737552i
$231$	1.31406	+	1.31406i	0.0864587	+	0.0864587i
$232$	−27.6320	+	6.07326i	−1.81413	+	0.398729i
$233$	−6.14273	+	6.14273i	−0.402424	+	0.402424i	−0.879086	−	0.476663i	$-0.841846\pi$
$233$	−6.14273	+	6.14273i	−0.402424	+	0.402424i	0.476663	+	0.879086i	$0.341846\pi$
$234$	−4.39349	+	1.52413i	−0.287212	+	0.0996356i
$235$	−0.950121	−	0.950121i	−0.0619791	−	0.0619791i
$236$	5.23818	−	4.13153i	0.340977	−	0.268939i
$237$		−	6.45275i		−	0.419151i
$238$	−2.03564	+	2.74778i	−0.131951	+	0.178112i
$239$	10.7634			0.696229			0.348114	−	0.937452i	$-0.386822\pi$
$239$	10.7634			0.696229			0.348114	+	0.937452i	$0.386822\pi$
$240$	−2.71957	−	0.651507i	−0.175548	−	0.0420546i
$241$	−9.90210	+	9.90210i	−0.637850	+	0.637850i	−0.950025	−	0.312175i	$-0.898943\pi$
$241$	−9.90210	+	9.90210i	−0.637850	+	0.637850i	0.312175	+	0.950025i	$0.398943\pi$
$242$	4.42297	+	12.7498i	0.284319	+	0.819585i
$243$	−10.5662	−	10.5662i	−0.677822	−	0.677822i
$244$	−0.733801	+	6.21285i	−0.0469768	+	0.397737i
$245$	−4.70654	+	4.70654i	−0.300690	+	0.300690i
$246$	0.284512	+	0.820141i	0.0181398	+	0.0522903i
$247$		−	8.80823i		−	0.560454i
$248$	−5.51958	−	25.1129i	−0.350494	−	1.59467i
$249$	−6.14284	−	6.14284i	−0.389287	−	0.389287i
$250$	−0.617020	+	1.27251i	−0.0390238	+	0.0804807i
$251$			18.6911i			1.17977i	0.807487	+	0.589885i	$0.200827\pi$
$251$			18.6911i			1.17977i	−0.807487	+	0.589885i	$0.799173\pi$
$252$	−0.345492	+	2.92517i	−0.0217640	+	0.184268i
$253$	−37.9441			−2.38553
$254$	−8.54476	−	24.6313i	−0.536146	−	1.54551i
$255$	2.83280	+	0.533433i	0.177397	+	0.0334048i
$256$	−14.2632	−	7.24992i	−0.891450	−	0.453120i
$257$			11.5619i			0.721211i	0.932719	+	0.360605i	$0.117430\pi$
$257$			11.5619i			0.721211i	−0.932719	+	0.360605i	$0.882570\pi$
$258$	−0.987349	−	0.478750i	−0.0614697	−	0.0298057i
$259$		−	1.21544i		−	0.0755236i
$260$	0.307182	−	2.60081i	0.0190506	−	0.161295i
$261$	17.7616	−	17.7616i	1.09941	−	1.09941i
$262$	24.3532	+	11.8085i	1.50454	+	0.729530i
$263$			25.4881i			1.57167i	0.618439	+	0.785833i	$0.287765\pi$
$263$			25.4881i			1.57167i	−0.618439	+	0.785833i	$0.712235\pi$
$264$	4.82927	−	7.55016i	0.297221	−	0.464680i
$265$	1.54058	+	1.54058i	0.0946368	+	0.0946368i
$266$	−5.02006	−	2.43414i	−0.307799	−	0.149247i
$267$	−8.27034	−	8.27034i	−0.506137	−	0.506137i
$268$	11.9303	+	15.1259i	0.728759	+	0.923962i
$269$	−4.56435	−	4.56435i	−0.278293	−	0.278293i	0.554134	−	0.832427i	$-0.313049\pi$
$269$	−4.56435	−	4.56435i	−0.278293	−	0.278293i	−0.832427	+	0.554134i	$0.813049\pi$
$270$	5.14808	−	1.78590i	0.313302	−	0.108687i
$271$	9.66938			0.587373			0.293686	−	0.955902i	$-0.405118\pi$
$271$	9.66938			0.587373			0.293686	+	0.955902i	$0.405118\pi$
$272$	15.0506	+	6.74388i	0.912576	+	0.408908i
$273$	0.536895			0.0324944
$274$	−16.2881	+	5.65044i	−0.983999	+	0.341356i
$275$	−3.20488	−	3.20488i	−0.193262	−	0.193262i
$276$	7.24931	+	9.19109i	0.436357	+	0.553239i
$277$	9.89970	+	9.89970i	0.594815	+	0.594815i	0.938928	−	0.344113i	$-0.111820\pi$
$277$	9.89970	+	9.89970i	0.594815	+	0.594815i	−0.344113	+	0.938928i	$0.611820\pi$
$278$	−16.5368	−	8.01842i	−0.991810	−	0.480913i
$279$	16.1423	+	16.1423i	0.966414	+	0.966414i
$280$	−1.39738	−	0.893802i	−0.0835097	−	0.0534149i
$281$		−	12.2163i		−	0.728763i	−0.931250	−	0.364382i	$-0.881280\pi$
$281$		−	12.2163i		−	0.728763i	0.931250	−	0.364382i	$-0.118720\pi$
$282$	−1.19540	−	0.579632i	−0.0711852	−	0.0345166i
$283$	2.57558	−	2.57558i	0.153102	−	0.153102i	−0.626400	−	0.779502i	$-0.715472\pi$
$283$	2.57558	−	2.57558i	0.153102	−	0.153102i	0.779502	+	0.626400i	$0.215472\pi$
$284$	−0.950732	+	8.04954i	−0.0564156	+	0.477652i
$285$			4.70284i			0.278572i
$286$	7.55223	+	3.66195i	0.446573	+	0.216536i
$287$			0.514915i			0.0303945i
$288$	14.1363	−	1.40102i	0.832991	−	0.0825560i
$289$	−15.8357	−	6.18314i	−0.931511	−	0.363714i
$290$	4.63622	+	13.3645i	0.272248	+	0.784788i
$291$	7.46892			0.437836
$292$	−1.90048	+	16.0908i	−0.111217	+	0.941640i
$293$			19.9362i			1.16468i	0.812944	+	0.582342i	$0.197864\pi$
$293$			19.9362i			1.16468i	−0.812944	+	0.582342i	$0.802136\pi$
$294$	−2.87127	+	5.92157i	−0.167456	+	0.345353i
$295$	−2.35871	−	2.35871i	−0.137329	−	0.137329i
$296$	−5.72517	+	1.25834i	−0.332769	+	0.0731395i
$297$			17.4635i			1.01334i
$298$	−5.43389	−	15.6638i	−0.314777	−	0.907382i
$299$	−7.75156	+	7.75156i	−0.448284	+	0.448284i
$300$	−0.164009	+	1.38861i	−0.00946906	+	0.0801714i
$301$	−0.460236	−	0.460236i	−0.0265276	−	0.0265276i
$302$	−4.06267	−	11.7111i	−0.233780	−	0.673900i
$303$	2.04688	−	2.04688i	0.117590	−	0.117590i
$304$	−6.26849	+	26.1664i	−0.359522	+	1.50075i
$305$	3.12802			0.179110
$306$	−14.4832	+	2.15619i	−0.827947	+	0.123261i
$307$		−	9.20696i		−	0.525469i	−0.964868	−	0.262734i	$-0.915376\pi$
$307$		−	9.20696i		−	0.525469i	0.964868	−	0.262734i	$-0.0846243\pi$
$308$	4.17410	−	3.29225i	0.237841	−	0.187593i
$309$	−2.01686	−	2.01686i	−0.114735	−	0.114735i
$310$	−12.1461	+	4.21355i	−0.689850	+	0.239313i
$311$	9.31837	−	9.31837i	0.528396	−	0.528396i	−0.391698	−	0.920094i	$-0.628112\pi$
$311$	9.31837	−	9.31837i	0.528396	−	0.528396i	0.920094	+	0.391698i	$0.128112\pi$
$312$	−0.555847	−	2.52898i	−0.0314686	−	0.143175i
$313$	19.7382	+	19.7382i	1.11567	+	1.11567i	0.992370	+	0.123299i	$0.0393475\pi$
$313$	19.7382	+	19.7382i	1.11567	+	1.11567i	0.123299	+	0.992370i	$0.460652\pi$
$314$	9.58526	+	27.6307i	0.540927	+	1.55929i
$315$	1.47275			0.0829801
$316$	−18.3319	−	2.16519i	−1.03125	−	0.121801i
$317$	−16.6969	+	16.6969i	−0.937789	+	0.937789i	−0.998175	−	0.0603861i	$-0.980767\pi$
$317$	−16.6969	+	16.6969i	−0.937789	+	0.937789i	0.0603861	+	0.998175i	$0.480767\pi$
$318$	1.93829	+	0.939845i	0.108694	+	0.0527039i
$319$	−45.3355			−2.53830
$320$	−2.76344	+	7.50756i	−0.154481	+	0.419685i
$321$			8.28824i			0.462604i
$322$	2.27570	+	6.55997i	0.126820	+	0.365573i
$323$	5.13243	−	27.2559i	0.285576	−	1.51656i
$324$	−7.60018	+	5.99451i	−0.422232	+	0.333028i
$325$	−1.30944			−0.0726348
$326$	−10.7519	+	22.1742i	−0.595493	+	1.22812i
$327$	11.7818			0.651537
$328$	2.42545	−	0.533091i	0.133923	−	0.0294350i
$329$	−0.557217	−	0.557217i	−0.0307203	−	0.0307203i
$330$	−4.03224	−	1.95517i	−0.221968	−	0.107629i
$331$	−2.15965			−0.118705			−0.0593526	−	0.998237i	$-0.518904\pi$
$331$	−2.15965			−0.118705			−0.0593526	+	0.998237i	$0.518904\pi$
$332$	−19.5127	+	15.3903i	−1.07090	+	0.844652i
$333$	3.68008	−	3.68008i	0.201667	−	0.201667i
$334$	−0.363537	+	0.749740i	−0.0198919	+	0.0410240i
$335$	6.81107	−	6.81107i	0.372128	−	0.372128i
$336$	−1.59494	−	0.382089i	−0.0870114	−	0.0208446i
$337$	−11.6091	+	11.6091i	−0.632387	+	0.632387i	−0.948666	−	0.316279i	$-0.897566\pi$
$337$	−11.6091	+	11.6091i	−0.632387	+	0.632387i	0.316279	+	0.948666i	$0.397566\pi$
$338$	−15.0784	+	5.23079i	−0.820156	+	0.284517i
$339$		−	9.68519i		−	0.526027i
$340$	2.46599	−	7.86886i	0.133737	−	0.426749i
$341$		−	41.2024i		−	2.23124i
$342$	−7.82957	−	22.5697i	−0.423375	−	1.22043i
$343$	−5.66311	+	5.66311i	−0.305779	+	0.305779i
$344$	−1.69140	+	2.64437i	−0.0911943	+	0.142575i
$345$	4.13867	−	4.13867i	0.222819	−	0.222819i
$346$	−9.87937	−	4.79035i	−0.531118	−	0.257531i
$347$	−19.9192	+	19.9192i	−1.06932	+	1.06932i	−0.0719045	+	0.997412i	$0.522908\pi$
$347$	−19.9192	+	19.9192i	−1.06932	+	1.06932i	−0.997412	+	0.0719045i	$0.977092\pi$
$348$	8.66147	+	10.9815i	0.464303	+	0.588670i
$349$	27.7385			1.48481			0.742405	−	0.669952i	$-0.233685\pi$
$349$	27.7385			1.48481			0.742405	+	0.669952i	$0.233685\pi$
$350$	−0.361863	+	0.746288i	−0.0193424	+	0.0398908i
$351$	3.56761	+	3.56761i	0.190425	+	0.190425i
$352$	−19.8292	−	16.2531i	−1.05690	−	0.866295i
$353$	−2.88487			−0.153546			−0.0767729	−	0.997049i	$-0.524462\pi$
$353$	−2.88487			−0.153546			−0.0767729	+	0.997049i	$0.524462\pi$
$354$	−2.96763	−	1.43896i	−0.157728	−	0.0764796i
$355$	4.05274			0.215097
$356$	−26.2707	+	20.7206i	−1.39234	+	1.09819i
$357$	1.66135	+	0.312842i	0.0879280	+	0.0165573i
$358$	−3.72609	+	1.29261i	−0.196930	+	0.0683163i
$359$		−	35.0920i		−	1.85209i	−0.377418	−	0.926043i	$-0.623188\pi$
$359$		−	35.0920i		−	1.85209i	0.377418	−	0.926043i	$-0.376812\pi$
$360$	−1.52473	−	6.93721i	−0.0803606	−	0.365623i
$361$	26.2485			1.38150
$362$	−9.48305	+	19.5574i	−0.498418	+	1.02791i
$363$	4.71743	−	4.71743i	0.247601	−	0.247601i
$364$	0.180153	−	1.52529i	0.00944256	−	0.0799470i
$365$	8.10130			0.424041
$366$	2.92191	−	1.01363i	0.152731	−	0.0529833i
$367$	−14.3435	−	14.3435i	−0.748724	−	0.748724i	0.225516	−	0.974240i	$-0.427593\pi$
$367$	−14.3435	−	14.3435i	−0.748724	−	0.748724i	−0.974240	+	0.225516i	$0.927593\pi$
$368$	28.5439	−	17.5109i	1.48795	−	0.912819i
$369$	−1.55905	+	1.55905i	−0.0811609	+	0.0811609i
$370$	0.960593	+	2.76903i	0.0499389	+	0.143955i
$371$	0.903500	+	0.903500i	0.0469074	+	0.0469074i
$372$	−9.98035	+	7.87183i	−0.517457	+	0.408135i
$373$			3.11844i			0.161467i	0.996736	+	0.0807334i	$0.0257262\pi$
$373$			3.11844i			0.161467i	−0.996736	+	0.0807334i	$0.974274\pi$
$374$	21.2356	+	15.7320i	1.09807	+	0.813482i
$375$	0.699131			0.0361030
$376$	−2.04782	+	3.20159i	−0.105608	+	0.165109i
$377$	−9.26155	+	9.26155i	−0.476994	+	0.476994i
$378$	3.01919	−	1.04738i	0.155290	−	0.0538712i
$379$	−2.10229	−	2.10229i	−0.107987	−	0.107987i	0.651049	−	0.759036i	$-0.274329\pi$
$379$	−2.10229	−	2.10229i	−0.107987	−	0.107987i	−0.759036	+	0.651049i	$0.774329\pi$
$380$	13.3605	+	1.57801i	0.685381	+	0.0809504i
$381$	−9.11363	+	9.11363i	−0.466906	+	0.466906i
$382$	−6.92277	+	2.40155i	−0.354200	+	0.122874i
$383$		−	14.3644i		−	0.733987i	−0.930223	−	0.366994i	$-0.880387\pi$
$383$		−	14.3644i		−	0.733987i	0.930223	−	0.366994i	$-0.119613\pi$
$384$	−0.148539	+	7.90837i	−0.00758008	+	0.403572i
$385$	−1.87956	−	1.87956i	−0.0957913	−	0.0957913i
$386$	23.7088	+	11.4960i	1.20675	+	0.585133i
$387$		−	2.78699i		−	0.141670i
$388$	2.50616	−	21.2188i	0.127231	−	1.07722i
$389$	−10.7331			−0.544191			−0.272096	−	0.962270i	$-0.587717\pi$
$389$	−10.7331			−0.544191			−0.272096	+	0.962270i	$0.587717\pi$
$390$	−1.22316	+	0.424323i	−0.0619372	+	0.0214864i
$391$	−28.5029	+	19.4694i	−1.44145	+	0.984611i
$392$	15.8594	+	10.1441i	0.801023	+	0.512354i
$393$		−	13.3799i		−	0.674926i
$394$	−2.33128	+	4.80791i	−0.117448	+	0.242219i
$395$			9.22967i			0.464395i
$396$	22.6065	+	2.67005i	1.13602	+	0.134175i
$397$	22.0133	−	22.0133i	1.10481	−	1.10481i	0.110992	−	0.993821i	$-0.464597\pi$
$397$	22.0133	−	22.0133i	1.10481	−	1.10481i	0.993821	−	0.110992i	$-0.0354029\pi$
$398$	−10.8854	+	22.4496i	−0.545638	+	1.12530i
$399$			2.75807i			0.138076i
$400$	3.88994	+	0.931882i	0.194497	+	0.0465941i
$401$	19.3728	+	19.3728i	0.967433	+	0.967433i	0.999486	−	0.0320527i	$-0.0102044\pi$
$401$	19.3728	+	19.3728i	0.967433	+	0.967433i	−0.0320527	+	0.999486i	$0.510204\pi$
$402$	4.15516	−	8.56940i	0.207241	−	0.427403i
$403$	−8.41720	−	8.41720i	−0.419291	−	0.419291i
$404$	−5.12825	−	6.50189i	−0.255140	−	0.323481i
$405$	3.42230	+	3.42230i	0.170055	+	0.170055i
$406$	2.71900	+	7.83784i	0.134942	+	0.388985i
$407$	−9.39322			−0.465605
$408$	−0.246390	−	8.14947i	−0.0121981	−	0.403459i
$409$	35.1770			1.73939			0.869695	−	0.493589i	$-0.164315\pi$
$409$	35.1770			1.73939			0.869695	+	0.493589i	$0.164315\pi$
$410$	−0.406952	−	1.17309i	−0.0200979	−	0.0579346i
$411$	6.02662	+	6.02662i	0.297271	+	0.297271i
$412$	−6.40655	+	5.05306i	−0.315628	+	0.248946i
$413$	−1.38331	−	1.38331i	−0.0680682	−	0.0680682i
$414$	−12.9718	+	26.7524i	−0.637531	+	1.31481i
$415$	8.78640	+	8.78640i	0.431307	+	0.431307i
$416$	−7.37121	+	0.730545i	−0.361404	+	0.0358179i
$417$			9.08547i			0.444917i
$418$	−18.8117	+	38.7963i	−0.920111	+	1.89759i
$419$	−9.52559	+	9.52559i	−0.465355	+	0.465355i	−0.900406	−	0.435051i	$-0.856730\pi$
$419$	−9.52559	+	9.52559i	−0.465355	+	0.465355i	0.435051	+	0.900406i	$0.356730\pi$
$420$	−0.0961861	+	0.814376i	−0.00469340	+	0.0397375i
$421$			14.9594i			0.729078i	0.931188	+	0.364539i	$0.118773\pi$
$421$			14.9594i			0.729078i	−0.931188	+	0.364539i	$0.881227\pi$
$422$	6.65746	−	13.7300i	0.324080	−	0.668366i
$423$		−	3.37426i		−	0.164062i
$424$	3.32043	−	5.19122i	0.161255	−	0.252108i
$425$	−4.05189	−	0.762994i	−0.196546	−	0.0370107i
$426$	3.78570	−	1.31329i	0.183418	−	0.0636289i
$427$	1.83448			0.0887769
$428$	23.5465	+	2.78108i	1.13816	+	0.134428i
$429$		−	4.14927i		−	0.200329i
$430$	1.41225	+	0.684779i	0.0681049	+	0.0330230i
$431$	−4.57187	−	4.57187i	−0.220219	−	0.220219i	0.588372	−	0.808591i	$-0.299769\pi$
$431$	−4.57187	−	4.57187i	−0.220219	−	0.220219i	−0.808591	+	0.588372i	$0.799769\pi$
$432$	−8.05929	−	13.1372i	−0.387753	−	0.632062i
$433$			14.1888i			0.681872i	0.940087	+	0.340936i	$0.110744\pi$
$433$			14.1888i			0.681872i	−0.940087	+	0.340936i	$0.889256\pi$
$434$	−7.12328	+	2.47111i	−0.341929	+	0.118617i
$435$	4.94488	−	4.94488i	0.237089	−	0.237089i
$436$	3.95333	−	33.4716i	0.189330	−	1.60300i
$437$	−39.8203	−	39.8203i	−1.90486	−	1.90486i
$438$	7.56750	−	2.62521i	0.361589	−	0.125438i
$439$	7.05143	−	7.05143i	0.336546	−	0.336546i	−0.518519	−	0.855066i	$-0.673517\pi$
$439$	7.05143	−	7.05143i	0.336546	−	0.336546i	0.855066	+	0.518519i	$0.173517\pi$
$440$	−6.90754	+	10.7994i	−0.329304	+	0.514839i
$441$	−16.7148			−0.795943
$442$	7.55206	−	1.12432i	0.359215	−	0.0534784i
$443$			8.10534i			0.385096i	0.981288	+	0.192548i	$0.0616752\pi$
$443$			8.10534i			0.385096i	−0.981288	+	0.192548i	$0.938325\pi$
$444$	1.79460	+	2.27529i	0.0851678	+	0.107981i
$445$	11.8295	+	11.8295i	0.560771	+	0.560771i
$446$	−7.08389	−	20.4202i	−0.335432	−	0.966924i
$447$	−5.79565	+	5.79565i	−0.274125	+	0.274125i
$448$	−1.62067	+	4.40295i	−0.0765694	+	0.208020i
$449$	−3.43582	−	3.43582i	−0.162146	−	0.162146i	0.621370	−	0.783517i	$-0.286576\pi$
$449$	−3.43582	−	3.43582i	−0.162146	−	0.162146i	−0.783517	+	0.621370i	$0.786576\pi$
$450$	−3.35524	+	1.16395i	−0.158167	+	0.0548693i
$451$	3.97940			0.187383
$452$	−27.5151	−	3.24982i	−1.29420	−	0.152858i
$453$	−4.33314	+	4.33314i	−0.203589	+	0.203589i
$454$	0.925458	−	1.90862i	0.0434339	−	0.0895759i
$455$	−0.767947			−0.0360019
$456$	12.9915	−	2.85542i	0.608385	−	0.133717i
$457$		−	38.0520i		−	1.78000i	−0.455963	−	0.889999i	$-0.650705\pi$
$457$		−	38.0520i		−	1.78000i	0.455963	−	0.889999i	$-0.349295\pi$
$458$	23.0711	−	8.00352i	1.07804	−	0.373980i
$459$	8.96069	+	13.1183i	0.418249	+	0.612309i
$460$	−10.3690	−	13.1465i	−0.483459	−	0.612957i
$461$	−6.87006			−0.319971			−0.159985	−	0.987119i	$-0.551145\pi$
$461$	−6.87006			−0.319971			−0.159985	+	0.987119i	$0.551145\pi$
$462$	−2.36479	−	1.14665i	−0.110020	−	0.0533468i
$463$	−7.76663			−0.360946			−0.180473	−	0.983580i	$-0.557763\pi$
$463$	−7.76663			−0.360946			−0.180473	+	0.983580i	$0.557763\pi$
$464$	34.1042	−	20.9220i	1.58325	−	0.971279i
$465$	4.49407	+	4.49407i	0.208407	+	0.208407i
$466$	5.36014	−	11.0545i	0.248304	−	0.512089i
$467$	−19.8238			−0.917335			−0.458667	−	0.888608i	$-0.651673\pi$
$467$	−19.8238			−0.917335			−0.458667	+	0.888608i	$0.651673\pi$
$468$	5.16371	−	4.07279i	0.238693	−	0.188265i
$469$	3.99448	−	3.99448i	0.184448	−	0.184448i
$470$	1.70984	+	0.829075i	0.0788691	+	0.0382424i
$471$	10.2234	−	10.2234i	0.471069	−	0.471069i
$472$	−5.08377	+	7.94804i	−0.234000	+	0.365838i
$473$	−3.55682	+	3.55682i	−0.163543	+	0.163543i
$474$	2.99086	+	8.62152i	0.137375	+	0.395999i
$475$		−	6.72670i		−	0.308642i
$476$	1.44622	−	4.61484i	0.0662876	−	0.211521i
$477$			5.47120i			0.250509i
$478$	−14.3810	+	4.98888i	−0.657773	+	0.228186i
$479$	21.1245	−	21.1245i	0.965201	−	0.965201i	−0.0342132	−	0.999415i	$-0.510893\pi$
$479$	21.1245	−	21.1245i	0.965201	−	0.965201i	0.999415	+	0.0342132i	$0.0108925\pi$
$480$	3.93560	−	0.390049i	0.179635	−	0.0178032i
$481$	−1.91893	+	1.91893i	−0.0874957	+	0.0874957i
$482$	8.64056	−	17.8198i	0.393567	−	0.811672i
$483$	2.42720	−	2.42720i	0.110441	−	0.110441i
$484$	−11.8191	−	14.9849i	−0.537231	−	0.681132i
$485$	−10.6832			−0.485097
$486$	19.0150	+	9.22006i	0.862537	+	0.418230i
$487$	11.1585	+	11.1585i	0.505638	+	0.505638i	0.913185	−	0.407546i	$-0.133616\pi$
$487$	11.1585	+	11.1585i	0.505638	+	0.505638i	−0.407546	+	0.913185i	$0.633616\pi$
$488$	−1.89924	−	8.64111i	−0.0859744	−	0.391165i
$489$	12.1827			0.550922
$490$	4.10692	−	8.46991i	0.185532	−	0.382631i
$491$	−21.2003			−0.956754			−0.478377	−	0.878154i	$-0.658775\pi$
$491$	−21.2003			−0.956754			−0.478377	+	0.878154i	$0.658775\pi$
$492$	−0.760274	−	0.963919i	−0.0342758	−	0.0434568i
$493$	−34.0552	+	23.2620i	−1.53377	+	1.04767i
$494$	4.08263	+	11.7687i	0.183686	+	0.529498i
$495$		−	11.3818i		−	0.511574i
$496$	19.0146	+	30.9950i	0.853781	+	1.39172i
$497$	2.37681			0.106614
$498$	11.0547	+	5.36024i	0.495372	+	0.240198i
$499$	26.2456	−	26.2456i	1.17492	−	1.17492i	0.193892	−	0.981023i	$-0.437889\pi$
$499$	26.2456	−	26.2456i	1.17492	−	1.17492i	0.981023	−	0.193892i	$-0.0621112\pi$
$500$	0.234590	−	1.98619i	0.0104912	−	0.0888253i
$501$	0.411915			0.0184030
$502$	−8.66335	−	24.9732i	−0.386664	−	1.11461i
$503$	15.5443	+	15.5443i	0.693086	+	0.693086i	0.962910	−	0.269824i	$-0.0869655\pi$
$503$	15.5443	+	15.5443i	0.693086	+	0.693086i	−0.269824	+	0.962910i	$0.586965\pi$
$504$	−0.894209	−	4.06846i	−0.0398312	−	0.181223i
$505$	−2.92775	+	2.92775i	−0.130283	+	0.130283i
$506$	50.6971	−	17.5872i	2.25376	−	0.781845i
$507$	5.57903	+	5.57903i	0.247773	+	0.247773i
$508$	22.8333	+	28.9494i	1.01307	+	1.28442i
$509$			14.6583i			0.649718i	0.945763	+	0.324859i	$0.105317\pi$
$509$			14.6583i			0.649718i	−0.945763	+	0.324859i	$0.894683\pi$
$510$	−4.03216	+	0.600290i	−0.178547	+	0.0265813i
$511$	4.75116			0.210179
$512$	22.4174	+	3.07560i	0.990719	+	0.135924i
$513$	−18.3271	+	18.3271i	−0.809159	+	0.809159i
$514$	−5.35896	−	15.4478i	−0.236374	−	0.681375i
$515$	2.88482	+	2.88482i	0.127120	+	0.127120i
$516$	1.54110	+	0.182020i	0.0678431	+	0.00801296i
$517$	−4.30632	+	4.30632i	−0.189392	+	0.189392i
$518$	0.563358	+	1.62395i	0.0247525	+	0.0713521i
$519$			5.42782i			0.238255i
$520$	0.795054	+	3.61732i	0.0348654	+	0.158630i
$521$	−5.50902	−	5.50902i	−0.241355	−	0.241355i	0.576056	−	0.817410i	$-0.304591\pi$
$521$	−5.50902	−	5.50902i	−0.241355	−	0.241355i	−0.817410	+	0.576056i	$0.804591\pi$
$522$	−15.4987	+	31.9638i	−0.678361	+	1.39902i
$523$		−	21.9472i		−	0.959683i	−0.877355	−	0.479842i	$-0.840694\pi$
$523$		−	21.9472i		−	0.959683i	0.877355	−	0.479842i	$-0.159306\pi$
$524$	−38.0116	−	4.48955i	−1.66054	−	0.196127i
$525$	0.410018			0.0178947
$526$	−11.8138	−	34.0547i	−0.515106	−	1.48486i
$527$	−21.1413	−	30.9505i	−0.920929	−	1.34822i
$528$	−2.95288	+	12.3261i	−0.128508	+	0.536427i
$529$			47.0866i			2.04724i
$530$	−2.77243	−	1.34430i	−0.120426	−	0.0583929i
$531$		−	8.37671i		−	0.363518i
$532$	7.83553	+	0.925456i	0.339713	+	0.0401236i
$533$	0.812948	−	0.812948i	0.0352127	−	0.0352127i
$534$	14.8833	+	7.21669i	0.644065	+	0.312297i
$535$		−	11.8551i		−	0.512539i
$536$	−22.9510	−	14.6800i	−0.991331	−	0.634080i
$537$	1.37866	+	1.37866i	0.0594936	+	0.0594936i
$538$	8.21402	+	3.98285i	0.354131	+	0.171713i
$539$	21.3319	+	21.3319i	0.918828	+	0.918828i
$540$	−6.05058	+	4.77229i	−0.260376	+	0.205367i
$541$	6.34924	+	6.34924i	0.272975	+	0.272975i	0.830297	−	0.557322i	$-0.188171\pi$
$541$	6.34924	+	6.34924i	0.272975	+	0.272975i	−0.557322	+	0.830297i	$0.688171\pi$
$542$	−12.9193	+	4.48178i	−0.554930	+	0.192509i
$543$	10.7450			0.461113
$544$	−23.2349	−	2.03453i	−0.996188	−	0.0872298i
$545$	−16.8521			−0.721865
$546$	−0.717347	+	0.248852i	−0.0306996	+	0.0106499i
$547$	−16.7869	−	16.7869i	−0.717755	−	0.717755i	0.250390	−	0.968145i	$-0.419441\pi$
$547$	−16.7869	−	16.7869i	−0.717755	−	0.717755i	−0.968145	+	0.250390i	$0.919441\pi$
$548$	19.1435	−	15.0991i	0.817771	−	0.645003i
$549$	5.55441	+	5.55441i	0.237057	+	0.237057i
$550$	5.76751	+	2.79657i	0.245928	+	0.119246i
$551$	−47.5772	−	47.5772i	−2.02686	−	2.02686i
$552$	−13.9459	−	8.92016i	−0.593577	−	0.379667i
$553$			5.41291i			0.230180i
$554$	−17.8155	−	8.63847i	−0.756910	−	0.367013i
$555$	1.02455	−	1.02455i	0.0434895	−	0.0434895i
$556$	25.8114	+	3.04858i	1.09465	+	0.129289i
$557$			16.0897i			0.681743i	0.940110	+	0.340872i	$0.110722\pi$
$557$			16.0897i			0.681743i	−0.940110	+	0.340872i	$0.889278\pi$
$558$	−29.0497	−	14.0857i	−1.22977	−	0.596297i
$559$			1.45324i			0.0614655i
$560$	2.28133	+	0.546520i	0.0964036	+	0.0230947i
$561$	2.41772	−	12.8394i	0.102076	−	0.542078i
$562$	5.66228	+	16.3222i	0.238849	+	0.688511i
$563$	23.1301			0.974815			0.487408	−	0.873174i	$-0.337943\pi$
$563$	23.1301			0.974815			0.487408	+	0.873174i	$0.337943\pi$
$564$	1.86584	+	0.220375i	0.0785660	+	0.00927944i
$565$			13.8532i			0.582808i
$566$	−2.24745	+	4.63503i	−0.0944674	+	0.194825i
$567$	2.00707	+	2.00707i	0.0842890	+	0.0842890i
$568$	−2.46070	−	11.1957i	−0.103249	−	0.469759i
$569$		−	16.3012i		−	0.683381i	−0.939813	−	0.341690i	$-0.889001\pi$
$569$		−	16.3012i		−	0.683381i	0.939813	−	0.341690i	$-0.110999\pi$
$570$	−2.17978	−	6.28347i	−0.0913008	−	0.263186i
$571$	−14.6592	+	14.6592i	−0.613468	+	0.613468i	−0.943848	−	0.330380i	$-0.892823\pi$
$571$	−14.6592	+	14.6592i	−0.613468	+	0.613468i	0.330380	+	0.943848i	$0.392823\pi$
$572$	−11.7879	−	1.39227i	−0.492875	−	0.0582136i
$573$	2.56144	+	2.56144i	0.107006	+	0.107006i
$574$	−0.238664	−	0.687979i	−0.00996166	−	0.0287157i
$575$	−5.91974	+	5.91974i	−0.246870	+	0.246870i
$576$	−18.2382	+	8.42412i	−0.759924	+	0.351005i
$577$	10.7253			0.446499			0.223249	−	0.974761i	$-0.428334\pi$
$577$	10.7253			0.446499			0.223249	+	0.974761i	$0.428334\pi$
$578$	24.0240	+	0.921430i	0.999265	+	0.0383264i
$579$		−	13.0259i		−	0.541337i
$580$	−12.3889	−	15.7074i	−0.514422	−	0.652213i
$581$	5.15295	+	5.15295i	0.213780	+	0.213780i
$582$	−9.97923	+	3.46186i	−0.413652	+	0.143499i
$583$	6.98248	−	6.98248i	0.289185	−	0.289185i
$584$	−4.91886	−	22.3797i	−0.203544	−	0.926080i
$585$	−2.32518	−	2.32518i	−0.0961342	−	0.0961342i
$586$	−9.24047	−	26.6368i	−0.381720	−	1.10035i
$587$	25.2433			1.04190			0.520951	−	0.853587i	$-0.325577\pi$
$587$	25.2433			1.04190			0.520951	+	0.853587i	$0.325577\pi$
$588$	1.09165	−	9.24266i	0.0450190	−	0.381161i
$589$	43.2397	−	43.2397i	1.78166	−	1.78166i
$590$	4.24474	+	2.05821i	0.174753	+	0.0847350i
$591$	2.64151			0.108657
$592$	7.06616	−	4.33490i	0.290417	−	0.178163i
$593$			4.45863i			0.183094i	0.995801	+	0.0915469i	$0.0291812\pi$
$593$			4.45863i			0.183094i	−0.995801	+	0.0915469i	$0.970819\pi$
$594$	−8.09439	−	23.3331i	−0.332117	−	0.957367i
$595$	−2.37631	−	0.447472i	−0.0974192	−	0.0183446i
$596$	14.5204	+	18.4098i	0.594781	+	0.754097i
$597$	12.3340			0.504798
$598$	6.76400	−	13.9497i	0.276601	−	0.570447i
$599$	8.32716			0.340239			0.170119	−	0.985423i	$-0.445585\pi$
$599$	8.32716			0.340239			0.170119	+	0.985423i	$0.445585\pi$
$600$	−0.424491	−	1.93134i	−0.0173298	−	0.0788467i
$601$	34.4763	+	34.4763i	1.40632	+	1.40632i	0.777778	+	0.628539i	$0.216347\pi$
$601$	34.4763	+	34.4763i	1.40632	+	1.40632i	0.628539	+	0.777778i	$0.283653\pi$
$602$	0.828242	+	0.401601i	0.0337566	+	0.0163680i
$603$	24.1888			0.985044
$604$	10.8563	+	13.7642i	0.441735	+	0.560057i
$605$	−6.74757	+	6.74757i	−0.274328	+	0.274328i
$606$	−1.78610	+	3.68357i	−0.0725554	+	0.149635i
$607$	−4.18159	+	4.18159i	−0.169726	+	0.169726i	−0.786859	−	0.617133i	$-0.788294\pi$
$607$	−4.18159	+	4.18159i	−0.169726	+	0.169726i	0.617133	+	0.786859i	$0.288294\pi$
$608$	−3.75286	−	37.8664i	−0.152199	−	1.53569i
$609$	2.90002	−	2.90002i	0.117515	−	0.117515i
$610$	−4.17935	+	1.44984i	−0.169217	+	0.0587024i
$611$			1.75947i			0.0711803i
$612$	18.3516	−	9.59386i	0.741818	−	0.387809i
$613$			27.4647i			1.10929i	0.832087	+	0.554645i	$0.187146\pi$
$613$			27.4647i			1.10929i	−0.832087	+	0.554645i	$0.812854\pi$
$614$	4.26744	+	12.3014i	0.172220	+	0.496445i
$615$	−0.434045	+	0.434045i	−0.0175024	+	0.0175024i
$616$	−4.05106	+	6.33348i	−0.163222	+	0.255183i
$617$	−4.45386	+	4.45386i	−0.179306	+	0.179306i	−0.791053	−	0.611748i	$-0.790467\pi$
$617$	−4.45386	+	4.45386i	−0.179306	+	0.179306i	0.611748	+	0.791053i	$0.290467\pi$
$618$	3.62955	+	1.75991i	0.146002	+	0.0707940i
$619$	5.18758	−	5.18758i	0.208506	−	0.208506i	−0.595126	−	0.803632i	$-0.702898\pi$
$619$	5.18758	−	5.18758i	0.208506	−	0.208506i	0.803632	+	0.595126i	$0.202898\pi$
$620$	14.2754	−	11.2594i	0.573313	−	0.452190i
$621$	32.2570			1.29443
$622$	−8.13120	+	16.7694i	−0.326031	+	0.672391i
$623$	6.93761	+	6.93761i	0.277950	+	0.277950i
$624$	1.91486	+	3.12134i	0.0766555	+	0.124953i
$625$	−1.00000			−0.0400000
$626$	−35.5209	−	17.2235i	−1.41970	−	0.688391i
$627$	21.3151			0.851242
$628$	−25.6137	−	32.4746i	−1.02210	−	1.29588i
$629$	−7.05601	+	4.81974i	−0.281341	+	0.192175i
$630$	−1.96774	+	0.682623i	−0.0783967	+	0.0271963i
$631$		−	8.92292i		−	0.355216i	−0.984101	−	0.177608i	$-0.943164\pi$
$631$		−	8.92292i		−	0.355216i	0.984101	−	0.177608i	$-0.0568359\pi$
$632$	25.4969	−	5.60398i	1.01421	−	0.222914i
$633$	−7.54340			−0.299823
$634$	14.5697	−	30.0477i	0.578635	−	1.19335i
$635$	13.0357	−	13.0357i	0.517305	−	0.517305i
$636$	−3.02537	−	0.357327i	−0.119964	−	0.0141689i
$637$	8.71572			0.345329
$638$	60.5729	−	21.0131i	2.39810	−	0.831918i
$639$	7.19645	+	7.19645i	0.284687	+	0.284687i
$640$	0.212462	−	11.3117i	0.00839830	−	0.447135i
$641$	4.21552	−	4.21552i	0.166503	−	0.166503i	−0.618937	−	0.785440i	$-0.712437\pi$
$641$	4.21552	−	4.21552i	0.166503	−	0.166503i	0.785440	+	0.618937i	$0.212437\pi$
$642$	−3.84162	−	11.0739i	−0.151617	−	0.437053i
$643$	−7.88865	−	7.88865i	−0.311098	−	0.311098i	0.534237	−	0.845335i	$-0.320599\pi$
$643$	−7.88865	−	7.88865i	−0.311098	−	0.311098i	−0.845335	+	0.534237i	$0.820599\pi$
$644$	−6.08112	−	7.70999i	−0.239630	−	0.303816i
$645$		−	0.775906i		−	0.0305513i
$646$	5.77571	+	38.7955i	0.227242	+	1.52639i
$647$	−13.5975			−0.534575			−0.267287	−	0.963617i	$-0.586127\pi$
$647$	−13.5975			−0.534575			−0.267287	+	0.963617i	$0.586127\pi$
$648$	7.37614	−	11.5320i	0.289762	−	0.453018i
$649$	−10.6906	+	10.6906i	−0.419642	+	0.419642i
$650$	1.74955	−	0.606930i	0.0686229	−	0.0238057i
$651$	2.63563	+	2.63563i	0.103298	+	0.103298i
$652$	4.08785	−	34.6105i	0.160093	−	1.35545i
$653$	−27.3424	+	27.3424i	−1.06999	+	1.06999i	−0.0726299	+	0.997359i	$0.523139\pi$
$653$	−27.3424	+	27.3424i	−1.06999	+	1.06999i	−0.997359	+	0.0726299i	$0.976861\pi$
$654$	−15.7417	+	5.46090i	−0.615550	+	0.213538i
$655$			19.1379i			0.747779i
$656$	−2.99355	+	1.83646i	−0.116879	+	0.0717018i
$657$	14.3855	+	14.3855i	0.561230	+	0.561230i
$658$	1.00277	+	0.486226i	0.0390920	+	0.0189551i
$659$			10.8432i			0.422393i	0.977444	+	0.211197i	$0.0677360\pi$
$659$			10.8432i			0.422393i	−0.977444	+	0.211197i	$0.932264\pi$
$660$	6.29371	+	0.743351i	0.244982	+	0.0289349i
$661$	−7.68911			−0.299072			−0.149536	−	0.988756i	$-0.547778\pi$
$661$	−7.68911			−0.299072			−0.149536	+	0.988756i	$0.547778\pi$
$662$	2.88551	−	1.00100i	0.112149	−	0.0389051i
$663$	−2.12902	−	3.11685i	−0.0826844	−	0.121048i
$664$	18.9375	−	29.6072i	0.734917	−	1.14898i
$665$		−	3.94500i		−	0.152980i
$666$	−3.21123	+	6.62268i	−0.124433	+	0.256624i
$667$			83.7394i			3.24240i
$668$	0.138216	−	1.17023i	0.00534773	−	0.0452775i
$669$	−7.55551	+	7.55551i	−0.292113	+	0.292113i
$670$	−5.94333	+	12.2572i	−0.229611	+	0.473538i
$671$		−	14.1774i		−	0.547311i
$672$	2.30811	−	0.228751i	0.0890371	−	0.00882428i
$673$	10.9503	+	10.9503i	0.422102	+	0.422102i	0.885927	−	0.463825i	$-0.153523\pi$
$673$	10.9503	+	10.9503i	0.422102	+	0.422102i	−0.463825	+	0.885927i	$0.653523\pi$
$674$	10.1301	−	20.8917i	0.390196	−	0.804719i
$675$	2.72452	+	2.72452i	0.104867	+	0.104867i
$676$	17.7218	−	13.9777i	0.681606	−	0.537605i
$677$	9.79402	+	9.79402i	0.376415	+	0.376415i	0.869807	−	0.493392i	$-0.164243\pi$
$677$	9.79402	+	9.79402i	0.376415	+	0.376415i	−0.493392	+	0.869807i	$0.664243\pi$
$678$	4.48910	+	12.9404i	0.172403	+	0.496973i
$679$	−6.26534			−0.240442
$680$	0.352424	+	11.6566i	0.0135148	+	0.447009i
$681$	−1.04861			−0.0401830
$682$	19.0974	+	55.0506i	0.731278	+	2.10800i
$683$	21.4331	+	21.4331i	0.820116	+	0.820116i	0.986124	−	0.166009i	$-0.0530879\pi$
$683$	21.4331	+	21.4331i	0.820116	+	0.820116i	−0.166009	+	0.986124i	$0.553088\pi$
$684$	20.9222	+	26.5263i	0.799980	+	1.01426i
$685$	−8.62017	−	8.62017i	−0.329360	−	0.329360i
$686$	4.94162	−	10.1914i	0.188672	−	0.389108i
$687$	−8.53636	−	8.53636i	−0.325682	−	0.325682i
$688$	1.03422	−	4.31711i	0.0394291	−	0.164588i
$689$		−	2.85289i		−	0.108686i
$690$	−3.61140	+	7.44796i	−0.137484	+	0.283539i
$691$	−2.68704	+	2.68704i	−0.102220	+	0.102220i	−0.756367	−	0.654147i	$-0.773028\pi$
$691$	−2.68704	+	2.68704i	−0.102220	+	0.102220i	0.654147	+	0.756367i	$0.273028\pi$
$692$	15.4202	+	1.82128i	0.586187	+	0.0692346i
$693$		−	6.67507i		−	0.253565i
$694$	17.3814	−	35.8466i	0.659790	−	1.36072i
$695$		−	12.9954i		−	0.492943i
$696$	−16.6625	−	10.6578i	−0.631592	−	0.403982i
$697$	2.98925	−	2.04186i	0.113226	−	0.0773411i
$698$	−37.0615	+	12.8569i	−1.40280	+	0.486640i
$699$	−6.07344			−0.229719
$700$	0.137580	−	1.16484i	0.00520002	−	0.0440268i
$701$		−	47.2568i		−	1.78487i	−0.451181	−	0.892433i	$-0.648997\pi$
$701$		−	47.2568i		−	1.78487i	0.451181	−	0.892433i	$-0.351003\pi$
$702$	−6.42028	−	3.11309i	−0.242318	−	0.117496i
$703$	−9.85768	−	9.85768i	−0.371789	−	0.371789i
$704$	34.0271	+	12.5250i	1.28245	+	0.472052i
$705$		−	0.939404i		−	0.0353800i
$706$	3.85447	−	1.33714i	0.145065	−	0.0503240i
$707$	−1.71703	+	1.71703i	−0.0645756	+	0.0645756i
$708$	4.63201	+	0.547088i	0.174082	+	0.0205608i
$709$	−10.6293	−	10.6293i	−0.399193	−	0.399193i	0.478755	−	0.877948i	$-0.341088\pi$
$709$	−10.6293	−	10.6293i	−0.399193	−	0.399193i	−0.877948	+	0.478755i	$0.841088\pi$
$710$	−5.41487	+	1.87846i	−0.203217	+	0.0704972i
$711$	−16.3891	+	16.3891i	−0.614640	+	0.614640i
$712$	25.4963	−	39.8613i	0.955514	−	1.49386i
$713$	−76.1051			−2.85016
$714$	−2.36473	+	0.352052i	−0.0884980	+	0.0131752i
$715$			5.93490i			0.221953i
$716$	4.37931	−	3.45410i	0.163662	−	0.129086i
$717$	5.32101	+	5.32101i	0.198717	+	0.198717i
$718$	16.2652	+	46.8865i	0.607013	+	1.74979i
$719$	−0.526091	+	0.526091i	−0.0196199	+	0.0196199i	−0.716849	−	0.697229i	$-0.754416\pi$
$719$	−0.526091	+	0.526091i	−0.0196199	+	0.0196199i	0.697229	+	0.716849i	$0.254416\pi$
$720$	5.25261	+	8.56209i	0.195753	+	0.319090i
$721$	1.69185	+	1.69185i	0.0630079	+	0.0630079i
$722$	−35.0706	+	12.1662i	−1.30519	+	0.452780i
$723$	−9.79040			−0.364109
$724$	3.60544	−	30.5260i	0.133995	−	1.13449i
$725$	−7.07289	+	7.07289i	−0.262681	+	0.262681i
$726$	−4.11643	+	8.48951i	−0.152775	+	0.315075i
$727$	−50.2791			−1.86475			−0.932375	−	0.361492i	$-0.882267\pi$
$727$	−50.2791			−1.86475			−0.932375	+	0.361492i	$0.882267\pi$
$728$	0.466274	+	2.12145i	0.0172813	+	0.0786260i
$729$			4.07255i			0.150835i
$730$	−10.8242	+	3.75497i	−0.400620	+	0.138978i
$731$	−0.846782	+	4.49685i	−0.0313194	+	0.166322i
$732$	−3.43415	+	2.70862i	−0.126930	+	0.100114i
$733$	21.4438			0.792047			0.396023	−	0.918240i	$-0.370390\pi$
$733$	21.4438			0.792047			0.396023	+	0.918240i	$0.370390\pi$
$734$	25.8126	+	12.5161i	0.952760	+	0.461978i
$735$	−4.65345			−0.171645
$736$	−30.0212	+	36.6265i	−1.10660	+	1.35007i
$737$	−30.8704	−	30.8704i	−1.13712	−	1.13712i
$738$	1.36043	−	2.80567i	0.0500780	−	0.103278i
$739$	10.9888			0.404230			0.202115	−	0.979362i	$-0.435219\pi$
$739$	10.9888			0.404230			0.202115	+	0.979362i	$0.435219\pi$
$740$	−2.56690	−	3.25446i	−0.0943611	−	0.119636i
$741$	4.35444	−	4.35444i	0.159964	−	0.159964i
$742$	−1.62594	−	0.788393i	−0.0596902	−	0.0289428i
$743$	16.1488	−	16.1488i	0.592440	−	0.592440i	−0.345850	−	0.938290i	$-0.612409\pi$
$743$	16.1488	−	16.1488i	0.592440	−	0.592440i	0.938290	+	0.345850i	$0.112409\pi$
$744$	9.68615	−	15.1435i	0.355111	−	0.555186i
$745$	8.28980	−	8.28980i	0.303715	−	0.303715i
$746$	−1.44540	−	4.16655i	−0.0529200	−	0.152548i
$747$			31.2040i			1.14169i
$748$	−35.6647	−	11.1768i	−1.30403	−	0.408664i
$749$		−	6.95263i		−	0.254043i
$750$	−0.934109	+	0.324049i	−0.0341088	+	0.0118326i
$751$	−6.50540	+	6.50540i	−0.237385	+	0.237385i	−0.815767	−	0.578381i	$-0.803685\pi$
$751$	−6.50540	+	6.50540i	−0.237385	+	0.237385i	0.578381	+	0.815767i	$0.303685\pi$
$752$	1.25215	−	5.22681i	0.0456611	−	0.190602i
$753$	−9.24012	+	9.24012i	−0.336729	+	0.336729i
$754$	8.08162	−	16.6671i	0.294315	−	0.606980i
$755$	6.19790	−	6.19790i	0.225565	−	0.225565i
$756$	−3.54848	+	2.79880i	−0.129057	+	0.101791i
$757$	−7.31906			−0.266016			−0.133008	−	0.991115i	$-0.542464\pi$
$757$	−7.31906			−0.266016			−0.133008	+	0.991115i	$0.542464\pi$
$758$	3.78328	+	1.83445i	0.137415	+	0.0666303i
$759$	−18.7580	−	18.7580i	−0.680874	−	0.680874i
$760$	−18.5824	+	4.08425i	−0.674056	+	0.148151i
$761$	−18.3027			−0.663472			−0.331736	−	0.943372i	$-0.607634\pi$
$761$	−18.3027			−0.663472			−0.331736	+	0.943372i	$0.607634\pi$
$762$	7.95254	−	16.4009i	0.288090	−	0.594143i
$763$	−9.88324			−0.357797
$764$	8.13639	−	6.41744i	0.294364	−	0.232175i
$765$	−5.84009	−	8.54979i	−0.211149	−	0.309118i
$766$	6.65794	+	19.1923i	0.240561	+	0.693446i
$767$			4.36793i			0.157717i
$768$	−3.46708	−	10.6352i	−0.125108	−	0.383766i
$769$	−7.38613			−0.266351			−0.133175	−	0.991092i	$-0.542517\pi$
$769$	−7.38613			−0.266351			−0.133175	+	0.991092i	$0.542517\pi$
$770$	3.38247	+	1.64010i	0.121896	+	0.0591052i
$771$	−5.71573	+	5.71573i	−0.205847	+	0.205847i
$772$	−37.0058	−	4.37076i	−1.33187	−	0.157307i
$773$	14.6520			0.526995			0.263498	−	0.964660i	$-0.415124\pi$
$773$	14.6520			0.526995			0.263498	+	0.964660i	$0.415124\pi$
$774$	1.29177	+	3.72369i	0.0464318	+	0.133845i
$775$	−6.42808	−	6.42808i	−0.230903	−	0.230903i
$776$	6.48649	+	29.5121i	0.232851	+	1.05942i
$777$	0.600864	−	0.600864i	0.0215559	−	0.0215559i
$778$	14.3405	−	4.97483i	0.514133	−	0.178356i
$779$	4.17617	+	4.17617i	0.149627	+	0.149627i
$780$	1.43759	−	1.13388i	0.0514741	−	0.0405993i
$781$		−	18.3686i		−	0.657280i
$782$	29.0586	−	39.2243i	1.03913	−	1.40266i
$783$	38.5405			1.37733
$784$	−25.8916	−	6.20266i	−0.924701	−	0.221523i
$785$	−14.6230	+	14.6230i	−0.521918	+	0.521918i
$786$	6.20160	+	17.8769i	0.221204	+	0.637647i
$787$	−6.38218	−	6.38218i	−0.227500	−	0.227500i	0.584147	−	0.811648i	$-0.301429\pi$
$787$	−6.38218	−	6.38218i	−0.227500	−	0.227500i	−0.811648	+	0.584147i	$0.801429\pi$
$788$	0.886347	−	7.50440i	0.0315748	−	0.267333i
$789$	−12.6003	+	12.6003i	−0.448583	+	0.448583i
$790$	−4.27797	−	12.3318i	−0.152203	−	0.438745i
$791$			8.12446i			0.288873i
$792$	−31.4421	+	6.91068i	−1.11725	+	0.245560i
$793$	−2.89628	−	2.89628i	−0.102850	−	0.102850i
$794$	−19.2087	+	39.6151i	−0.681693	+	1.40589i
$795$			1.52320i			0.0540223i
$796$	4.13862	−	35.0403i	0.146689	−	1.24197i
$797$	3.15865			0.111885			0.0559425	−	0.998434i	$-0.482184\pi$
$797$	3.15865			0.111885			0.0559425	+	0.998434i	$0.482184\pi$
$798$	−1.27837	−	3.68506i	−0.0452538	−	0.130450i
$799$	−1.02522	+	5.44443i	−0.0362695	+	0.192610i
$800$	−5.62928	+	0.557905i	−0.199025	+	0.0197249i
$801$			42.0111i			1.48439i
$802$	−34.8634	−	16.9047i	−1.23107	−	0.596926i
$803$		−	36.7182i		−	1.29576i
$804$	−1.57978	+	13.3755i	−0.0557147	+	0.471718i
$805$	−3.47174	+	3.47174i	−0.122363	+	0.122363i
$806$	15.1476	+	7.34484i	0.533552	+	0.258711i
$807$		−	4.51286i		−	0.158860i
$808$	9.86550	+	6.31023i	0.347067	+	0.221993i
$809$	22.3678	+	22.3678i	0.786409	+	0.786409i	0.980904	−	0.194495i	$-0.0623066\pi$
$809$	22.3678	+	22.3678i	0.786409	+	0.786409i	−0.194495	+	0.980904i	$0.562307\pi$
$810$	−6.15877	−	2.98629i	−0.216397	−	0.104928i
$811$	−4.84593	−	4.84593i	−0.170164	−	0.170164i	0.616888	−	0.787051i	$-0.288393\pi$
$811$	−4.84593	−	4.84593i	−0.170164	−	0.170164i	−0.787051	+	0.616888i	$0.788393\pi$
$812$	−7.26571	−	9.21188i	−0.254976	−	0.323274i
$813$	4.78015	+	4.78015i	0.167647	+	0.167647i
$814$	12.5503	−	4.35378i	0.439887	−	0.152600i
$815$	−17.4255			−0.610390
$816$	4.10650	+	10.7743i	0.143756	+	0.377176i
$817$	−7.46539			−0.261181
$818$	−47.0000	+	16.3046i	−1.64332	+	0.570078i
$819$	−1.36364	−	1.36364i	−0.0476495	−	0.0476495i
$820$	1.08746	+	1.37874i	0.0379756	+	0.0481477i
$821$	2.40790	+	2.40790i	0.0840364	+	0.0840364i	0.747875	−	0.663839i	$-0.231074\pi$
$821$	2.40790	+	2.40790i	0.0840364	+	0.0840364i	−0.663839	+	0.747875i	$0.731074\pi$
$822$	−10.8455	−	5.25882i	−0.378281	−	0.183423i
$823$	−22.0958	−	22.0958i	−0.770212	−	0.770212i	0.207931	−	0.978143i	$-0.433327\pi$
$823$	−22.0958	−	22.0958i	−0.770212	−	0.770212i	−0.978143	+	0.207931i	$0.933327\pi$
$824$	6.21770	−	9.72084i	0.216604	−	0.338642i
$825$		−	3.16873i		−	0.110321i
$826$	2.48941	+	1.20707i	0.0866176	+	0.0419995i
$827$	−3.78572	+	3.78572i	−0.131643	+	0.131643i	−0.769858	−	0.638215i	$-0.779673\pi$
$827$	−3.78572	+	3.78572i	−0.131643	+	0.131643i	0.638215	+	0.769858i	$0.279673\pi$
$828$	4.93186	−	41.7564i	0.171394	−	1.45114i
$829$			43.1749i			1.49953i	0.661706	+	0.749763i	$0.269833\pi$
$829$			43.1749i			1.49953i	−0.661706	+	0.749763i	$0.730167\pi$
$830$	−15.8120	−	7.66700i	−0.548844	−	0.266126i
$831$			9.78803i			0.339543i
$832$	9.51008	−	4.39266i	0.329703	−	0.152288i
$833$	26.9696	+	5.07853i	0.934442	+	0.175961i
$834$	−4.21114	−	12.1391i	−0.145820	−	0.420343i
$835$	−0.589181			−0.0203895
$836$	7.15217	−	60.5551i	0.247363	−	2.09434i
$837$			35.0269i			1.21071i
$838$	8.31202	−	17.1423i	0.287134	−	0.592170i
$839$	19.3498	+	19.3498i	0.668031	+	0.668031i	0.957260	−	0.289229i	$-0.0933990\pi$
$839$	19.3498	+	19.3498i	0.668031	+	0.668031i	−0.289229	+	0.957260i	$0.593399\pi$
$840$	−0.248951	−	1.13267i	−0.00858961	−	0.0390809i
$841$			71.0516i			2.45006i
$842$	−6.93373	−	19.9873i	−0.238952	−	0.688808i
$843$	6.03925	−	6.03925i	0.208003	−	0.208003i
$844$	−2.53115	+	21.4304i	−0.0871258	+	0.737665i
$845$	−7.97995	−	7.97995i	−0.274519	−	0.274519i
$846$	1.56398	+	4.50835i	0.0537706	+	0.155000i
$847$	−3.95724	+	3.95724i	−0.135972	+	0.135972i
$848$	−2.03029	+	8.47502i	−0.0697206	+	0.291033i
$849$	2.54653			0.0873967
$850$	5.76739	−	0.858624i	0.197820	−	0.0294506i
$851$			17.3502i			0.594758i
$852$	−4.44937	+	3.50936i	−0.152433	+	0.120229i
$853$	3.69875	+	3.69875i	0.126643	+	0.126643i	0.767587	−	0.640944i	$-0.221457\pi$
$853$	3.69875	+	3.69875i	0.126643	+	0.126643i	−0.640944	+	0.767587i	$0.721457\pi$
$854$	−2.45106	+	0.850287i	−0.0838734	+	0.0290962i
$855$	11.9446	−	11.9446i	0.408496	−	0.408496i
$856$	−32.7495	+	7.19804i	−1.11935	+	0.246024i
$857$	17.4953	+	17.4953i	0.597629	+	0.597629i	0.939681	−	0.342052i	$-0.111122\pi$
$857$	17.4953	+	17.4953i	0.597629	+	0.597629i	−0.342052	+	0.939681i	$0.611122\pi$
$858$	1.92320	+	5.54384i	0.0656568	+	0.189264i
$859$	8.46375			0.288779			0.144390	−	0.989521i	$-0.453878\pi$
$859$	8.46375			0.288779			0.144390	+	0.989521i	$0.453878\pi$
$860$	−2.20431	−	0.260351i	−0.0751663	−	0.00887790i
$861$	−0.254554	+	0.254554i	−0.00867516	+	0.00867516i
$862$	8.22755	+	3.98941i	0.280231	+	0.135880i
$863$	−11.1508			−0.379577			−0.189788	−	0.981825i	$-0.560780\pi$
$863$	−11.1508			−0.379577			−0.189788	+	0.981825i	$0.560780\pi$
$864$	16.8571	+	13.8171i	0.573491	+	0.470066i
$865$		−	7.76367i		−	0.263973i
$866$	−6.57655	−	18.9577i	−0.223480	−	0.644209i
$867$	−4.77183	−	10.8852i	−0.162060	−	0.369682i
$868$	8.37206	−	6.60332i	0.284166	−	0.224131i
$869$	41.8324			1.41907
$870$	−4.31489	+	8.89881i	−0.146289	+	0.301698i
$871$	−12.6130			−0.427374
$872$	10.2321	+	46.5538i	0.346502	+	1.57651i
$873$	−18.9701	−	18.9701i	−0.642039	−	0.642039i
$874$	71.6607	+	34.7471i	2.42396	+	1.17534i
$875$	−0.586469			−0.0198263
$876$	−8.89415	+	7.01510i	−0.300505	+	0.237018i
$877$	−16.2981	+	16.2981i	−0.550347	+	0.550347i	−0.926541	−	0.376194i	$-0.877233\pi$
$877$	−16.2981	+	16.2981i	−0.550347	+	0.550347i	0.376194	+	0.926541i	$0.377233\pi$
$878$	−6.15307	+	12.6898i	−0.207656	+	0.428259i
$879$	−9.85565	+	9.85565i	−0.332423	+	0.332423i
$880$	4.22365	−	17.6307i	0.142379	−	0.594330i
$881$	40.1622	−	40.1622i	1.35310	−	1.35310i	0.470927	−	0.882172i	$-0.343919\pi$
$881$	40.1622	−	40.1622i	1.35310	−	1.35310i	0.882172	−	0.470927i	$-0.156081\pi$
$882$	22.3327	−	7.74734i	0.751979	−	0.260867i
$883$		−	14.7072i		−	0.494938i	−0.968896	−	0.247469i	$-0.920401\pi$
$883$		−	14.7072i		−	0.494938i	0.968896	−	0.247469i	$-0.0795989\pi$
$884$	−9.56920	+	5.00260i	−0.321847	+	0.168256i
$885$		−	2.33210i		−	0.0783928i
$886$	−3.75684	−	10.8296i	−0.126214	−	0.363826i
$887$	21.5726	−	21.5726i	0.724338	−	0.724338i	−0.245148	−	0.969486i	$-0.578837\pi$
$887$	21.5726	−	21.5726i	0.724338	−	0.724338i	0.969486	+	0.245148i	$0.0788366\pi$
$888$	−3.45237	−	2.20822i	−0.115854	−	0.0741031i
$889$	7.64501	−	7.64501i	0.256405	−	0.256405i
$890$	−21.2883	−	10.3224i	−0.713587	−	0.346007i
$891$	15.5112	−	15.5112i	0.519643	−	0.519643i
$892$	18.9296	+	24.0000i	0.633810	+	0.803580i
$893$	−9.03849			−0.302462
$894$	5.05728	−	10.4299i	0.169141	−	0.348827i
$895$	−1.97196	−	1.97196i	−0.0659155	−	0.0659155i
$896$	0.124602	−	6.63397i	0.00416267	−	0.221625i
$897$	−7.66412			−0.255898
$898$	6.18311	+	2.99809i	0.206333	+	0.100048i
$899$	−90.9302			−3.03269
$900$	3.94344	−	3.11032i	0.131448	−	0.103677i
$901$	1.66234	−	8.82788i	0.0553805	−	0.294099i
$902$	−5.31688	+	1.84446i	−0.177033	+	0.0614138i
$903$		−	0.455044i		−	0.0151429i
$904$	38.2693	−	8.41123i	1.27282	−	0.279754i
$905$	−15.3691			−0.510886
$906$	3.78109	−	7.79793i	0.125618	−	0.259069i
$907$	27.1523	−	27.1523i	0.901578	−	0.901578i	−0.0939948	−	0.995573i	$-0.529964\pi$
$907$	27.1523	−	27.1523i	0.901578	−	0.901578i	0.995573	+	0.0939948i	$0.0299637\pi$
$908$	−0.351857	+	2.97906i	−0.0116768	+	0.0988635i
$909$	−10.3976			−0.344866
$910$	1.02606	−	0.355945i	0.0340134	−	0.0117995i
$911$	1.59868	+	1.59868i	0.0529666	+	0.0529666i	0.733094	−	0.680127i	$-0.238076\pi$
$911$	1.59868	+	1.59868i	0.0529666	+	0.0529666i	−0.680127	+	0.733094i	$0.738076\pi$
$912$	−16.0345	+	9.83674i	−0.530956	+	0.325727i
$913$	39.8233	−	39.8233i	1.31796	−	1.31796i
$914$	17.6372	+	50.8413i	0.583386	+	1.68168i
$915$	1.54637	+	1.54637i	0.0511213	+	0.0511213i
$916$	−27.1157	+	21.3870i	−0.895928	+	0.706647i
$917$			11.2238i			0.370642i
$918$	−18.0527	−	13.3740i	−0.595829	−	0.441409i
$919$	8.44961			0.278727			0.139363	−	0.990241i	$-0.455494\pi$
$919$	8.44961			0.278727			0.139363	+	0.990241i	$0.455494\pi$
$920$	19.9475	+	12.7589i	0.657650	+	0.420649i
$921$	4.55155	−	4.55155i	0.149979	−	0.149979i
$922$	9.17910	−	3.18429i	0.302297	−	0.104869i
$923$	−3.75250	−	3.75250i	−0.123515	−	0.123515i
$924$	3.69106	+	0.435952i	0.121427	+	0.0143418i
$925$	−1.46546	+	1.46546i	−0.0481839	+	0.0481839i
$926$	10.3770	−	3.59985i	0.341009	−	0.118298i
$927$			10.2451i			0.336494i
$928$	−35.8693	+	43.7613i	−1.17747	+	1.43653i
$929$	2.50421	+	2.50421i	0.0821606	+	0.0821606i	0.746993	−	0.664832i	$-0.231497\pi$
$929$	2.50421	+	2.50421i	0.0821606	+	0.0821606i	−0.664832	+	0.746993i	$0.731497\pi$
$930$	−8.08754	−	3.92152i	−0.265201	−	0.128592i
$931$			44.7733i			1.46738i
$932$	−2.03791	+	17.2543i	−0.0667540	+	0.565184i
$933$	9.21326			0.301629
$934$	26.4866	−	9.18836i	0.866667	−	0.300652i
$935$	−3.45818	+	18.3647i	−0.113095	+	0.600591i
$936$	−5.01149	+	7.83505i	−0.163806	+	0.256097i
$937$			3.25899i			0.106466i	0.998582	+	0.0532332i	$0.0169527\pi$
$937$			3.25899i			0.106466i	−0.998582	+	0.0532332i	$0.983047\pi$
$938$	−3.48558	+	7.18848i	−0.113808	+	0.234712i
$939$			19.5156i			0.636866i
$940$	−2.66880	−	0.315212i	−0.0870466	−	0.0102811i
$941$	−33.8759	+	33.8759i	−1.10432	+	1.10432i	−0.110441	+	0.993883i	$0.535226\pi$
$941$	−33.8759	+	33.8759i	−1.10432	+	1.10432i	−0.993883	+	0.110441i	$0.964774\pi$
$942$	−8.92092	+	18.3981i	−0.290659	+	0.599441i
$943$		−	7.35036i		−	0.239361i
$944$	3.10850	−	12.9757i	0.101173	−	0.422324i
$945$	1.59785	+	1.59785i	0.0519780	+	0.0519780i
$946$	3.10368	−	6.40087i	0.100909	−	0.208110i
$947$	0.877480	+	0.877480i	0.0285143	+	0.0285143i	0.721220	−	0.692706i	$-0.243582\pi$
$947$	0.877480	+	0.877480i	0.0285143	+	0.0285143i	−0.692706	+	0.721220i	$0.743582\pi$
$948$	−7.99219	−	10.1329i	−0.259574	−	0.329103i
$949$	−7.50112	−	7.50112i	−0.243497	−	0.243497i
$950$	3.11784	+	8.98755i	0.101156	+	0.291595i
$951$	−16.5085			−0.535325
$952$	0.206686	+	6.83622i	0.00669872	+	0.221563i
$953$	16.1289			0.522466			0.261233	−	0.965276i	$-0.415871\pi$
$953$	16.1289			0.522466			0.261233	+	0.965276i	$0.415871\pi$
$954$	−2.53591	−	7.31007i	−0.0821032	−	0.236672i
$955$	−3.66375	−	3.66375i	−0.118556	−	0.118556i
$956$	16.9022	−	13.3313i	0.546655	−	0.431164i
$957$	−22.4121	−	22.4121i	−0.724480	−	0.724480i
$958$	−18.4332	+	38.0156i	−0.595549	+	1.22823i
$959$	−5.05546	−	5.05546i	−0.163249	−	0.163249i
$960$	−5.07757	+	2.34530i	−0.163878	+	0.0756943i
$961$		−	51.6404i		−	1.66582i
$962$	1.67446	−	3.45331i	0.0539866	−	0.111339i
$963$	21.0510	−	21.0510i	0.678360	−	0.678360i
$964$	−3.28512	+	27.8140i	−0.105807	+	0.895829i
$965$			18.6315i			0.599770i
$966$	−2.11797	+	4.36800i	−0.0681446	+	0.140538i
$967$			30.0589i			0.966629i	0.875447	+	0.483314i	$0.160567\pi$
$967$			30.0589i			0.966629i	−0.875447	+	0.483314i	$0.839433\pi$
$968$	22.7370	+	14.5432i	0.730795	+	0.467435i
$969$	16.0115	−	10.9369i	0.514363	−	0.351345i
$970$	14.2738	−	4.95167i	0.458303	−	0.158988i
$971$	−5.94943			−0.190926			−0.0954631	−	0.995433i	$-0.530433\pi$
$971$	−5.94943			−0.190926			−0.0954631	+	0.995433i	$0.530433\pi$
$972$	−29.6794	−	3.50545i	−0.951969	−	0.112437i
$973$		−	7.62139i		−	0.244330i
$974$	−20.0808	−	9.73686i	−0.643430	−	0.311989i
$975$	−0.647336	−	0.647336i	−0.0207313	−	0.0207313i
$976$	6.54275	+	10.6651i	0.209428	+	0.341381i
$977$		−	42.7554i		−	1.36786i	−0.729545	−	0.683932i	$-0.760268\pi$
$977$		−	42.7554i		−	1.36786i	0.729545	−	0.683932i	$-0.239732\pi$
$978$	−16.2774	+	5.64672i	−0.520492	+	0.180562i
$979$	53.6157	−	53.6157i	1.71357	−	1.71357i
$980$	−1.56144	+	13.2202i	−0.0498784	+	0.422304i
$981$	−29.9243	−	29.9243i	−0.955408	−	0.955408i
$982$	28.3257	−	9.82637i	0.903909	−	0.313572i
$983$	−21.0767	+	21.0767i	−0.672241	+	0.672241i	−0.958232	−	0.285991i	$-0.907677\pi$
$983$	−21.0767	+	21.0767i	−0.672241	+	0.672241i	0.285991	+	0.958232i	$0.407677\pi$
$984$	1.46258	+	0.935505i	0.0466254	+	0.0298228i
$985$	−3.77828			−0.120386
$986$	34.7192	−	46.8651i	1.10568	−	1.49249i
$987$		−	0.550931i		−	0.0175363i
$988$	−10.9096	−	13.8318i	−0.347081	−	0.440049i
$989$	6.56981	+	6.56981i	0.208908	+	0.208908i
$990$	5.27549	+	15.2072i	0.167666	+	0.483318i
$991$	35.9599	−	35.9599i	1.14230	−	1.14230i	0.154276	−	0.988028i	$-0.450695\pi$
$991$	35.9599	−	35.9599i	1.14230	−	1.14230i	0.988028	−	0.154276i	$-0.0493045\pi$
$992$	−39.7717	−	32.5992i	−1.26275	−	1.03502i
$993$	−1.06765	−	1.06765i	−0.0338807	−	0.0338807i
$994$	−3.17565	+	1.10166i	−0.100726	+	0.0349424i
$995$	−17.6419			−0.559287
$996$	−17.2546	−	2.03795i	−0.546734	−	0.0645749i
$997$	28.2919	−	28.2919i	0.896015	−	0.896015i	−0.0990662	−	0.995081i	$-0.531586\pi$
$997$	28.2919	−	28.2919i	0.896015	−	0.896015i	0.995081	+	0.0990662i	$0.0315856\pi$
$998$	−22.9019	+	47.2317i	−0.724947	+	1.49509i
$999$	7.98534			0.252645

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.ba.b.21.8	✓	140
8.5	even	2	inner	680.2.ba.b.21.63	yes	140
17.13	even	4	inner	680.2.ba.b.421.63	yes	140
136.13	even	4	inner	680.2.ba.b.421.8	yes	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.ba.b.21.8	✓	140	1.1	even	1	trivial
680.2.ba.b.21.63	yes	140	8.5	even	2	inner
680.2.ba.b.421.8	yes	140	136.13	even	4	inner
680.2.ba.b.421.63	yes	140	17.13	even	4	inner

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:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.ba (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33610 + 0.463502i) q^{2} +(0.494360 + 0.494360i) q^{3} +(1.57033 - 1.23857i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(-0.889652 - 0.431378i) q^{6} +(-0.414696 - 0.414696i) q^{7} +(-1.52404 + 2.38271i) q^{8} -2.51122i q^{9} +(1.27251 + 0.617020i) q^{10} +(-3.20488 + 3.20488i) q^{11} +(1.38861 + 0.164009i) q^{12} +1.30944i q^{13} +(0.746288 + 0.361863i) q^{14} -0.699131i q^{15} +(0.931882 - 3.88994i) q^{16} +(-0.762994 + 4.05189i) q^{17} +(1.16395 + 3.35524i) q^{18} -6.72670 q^{19} +(-1.98619 - 0.234590i) q^{20} -0.410018i q^{21} +(2.79657 - 5.76751i) q^{22} +(5.91974 + 5.91974i) q^{23} +(-1.93134 + 0.424491i) q^{24} +1.00000i q^{25} +(-0.606930 - 1.74955i) q^{26} +(2.72452 - 2.72452i) q^{27} +(-1.16484 - 0.137580i) q^{28} +(7.07289 + 7.07289i) q^{29} +(0.324049 + 0.934109i) q^{30} +(-6.42808 + 6.42808i) q^{31} +(0.557905 + 5.62928i) q^{32} -3.16873 q^{33} +(-0.858624 - 5.76739i) q^{34} +0.586469i q^{35} +(-3.11032 - 3.94344i) q^{36} +(1.46546 + 1.46546i) q^{37} +(8.98755 - 3.11784i) q^{38} +(-0.647336 + 0.647336i) q^{39} +(2.76249 - 0.607170i) q^{40} +(-0.620835 - 0.620835i) q^{41} +(0.190044 + 0.547826i) q^{42} +1.10981 q^{43} +(-1.06325 + 9.00220i) q^{44} +(-1.77570 + 1.77570i) q^{45} +(-10.6532 - 5.16556i) q^{46} +1.34367 q^{47} +(2.38371 - 1.46234i) q^{48} -6.65605i q^{49} +(-0.463502 - 1.33610i) q^{50} +(-2.38029 + 1.62590i) q^{51} +(1.62184 + 2.05626i) q^{52} -2.17870 q^{53} +(-2.37742 + 4.90306i) q^{54} +4.53238 q^{55} +(1.62011 - 0.356086i) q^{56} +(-3.32541 - 3.32541i) q^{57} +(-12.7284 - 6.17180i) q^{58} +3.33572 q^{59} +(-0.865923 - 1.09787i) q^{60} +(-2.21184 + 2.21184i) q^{61} +(5.60913 - 11.5680i) q^{62} +(-1.04139 + 1.04139i) q^{63} +(-3.35460 - 7.26269i) q^{64} +(0.925916 - 0.925916i) q^{65} +(4.23374 - 1.46871i) q^{66} +9.63230i q^{67} +(3.82041 + 7.30784i) q^{68} +5.85296i q^{69} +(-0.271830 - 0.783581i) q^{70} +(-2.86572 + 2.86572i) q^{71} +(5.98350 + 3.82720i) q^{72} +(-5.72848 + 5.72848i) q^{73} +(-2.63724 - 1.27876i) q^{74} +(-0.494360 + 0.494360i) q^{75} +(-10.5631 + 8.33150i) q^{76} +2.65810 q^{77} +(0.564865 - 1.16495i) q^{78} +(-6.52636 - 6.52636i) q^{79} +(-3.40954 + 2.09166i) q^{80} -4.83986 q^{81} +(1.11726 + 0.541740i) q^{82} -12.4258 q^{83} +(-0.507837 - 0.643865i) q^{84} +(3.40464 - 2.32560i) q^{85} +(-1.48282 + 0.514402i) q^{86} +6.99311i q^{87} +(-2.75193 - 12.5207i) q^{88} -16.7294 q^{89} +(1.54947 - 3.19555i) q^{90} +(0.543021 - 0.543021i) q^{91} +(16.6280 + 1.96393i) q^{92} -6.35557 q^{93} +(-1.79529 + 0.622796i) q^{94} +(4.75649 + 4.75649i) q^{95} +(-2.50708 + 3.05869i) q^{96} +(7.55413 - 7.55413i) q^{97} +(3.08510 + 8.89316i) q^{98} +(8.04815 + 8.04815i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 8 q^{4} - 4 q^{6} - 12 q^{7} + 20 q^{12} + 28 q^{14} - 24 q^{16} - 16 q^{17} - 8 q^{20} + 40 q^{22} + 4 q^{23} + 48 q^{24} - 20 q^{28} + 28 q^{31} - 8 q^{34} - 56 q^{38} + 24 q^{40} + 44 q^{41}+ \cdots + 176 q^{98}+O(q^{100}) \) 140 * q - 8 * q^4 - 4 * q^6 - 12 * q^7 + 20 * q^12 + 28 * q^14 - 24 * q^16 - 16 * q^17 - 8 * q^20 + 40 * q^22 + 4 * q^23 + 48 * q^24 - 20 * q^28 + 28 * q^31 - 8 * q^34 - 56 * q^38 + 24 * q^40 + 44 * q^41 + 28 * q^44 - 40 * q^46 - 120 * q^47 + 32 * q^48 - 48 * q^52 - 4 * q^54 + 16 * q^55 + 16 * q^56 - 16 * q^57 - 52 * q^58 - 72 * q^62 + 44 * q^63 - 104 * q^64 + 8 * q^68 + 12 * q^71 - 104 * q^72 + 36 * q^73 + 20 * q^74 + 28 * q^78 - 44 * q^79 - 76 * q^81 - 44 * q^82 + 48 * q^84 + 120 * q^86 + 28 * q^88 + 24 * q^89 + 28 * q^90 - 72 * q^92 + 8 * q^95 - 116 * q^96 + 12 * q^97 + 176 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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