LMFDB - Embedded newform 272.2.l.b.205.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [272,2,Mod(69,272)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(272, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("272.69"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 272 = 2^{4} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	272.l (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [30] 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:	$2.17193093498$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			205.3
Character	$\chi$	$=$	272.205
Dual form			272.2.l.b.69.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.13198 - 0.847715i) q^{2} +(0.907888 + 0.907888i) q^{3} +(0.562758 + 1.91919i) q^{4} +(0.218362 - 0.218362i) q^{5} +(-0.258081 - 1.79734i) q^{6} +4.34872i q^{7} +(0.989900 - 2.64955i) q^{8} -1.35148i q^{9} +(-0.432289 + 0.0620725i) q^{10} +(-3.20019 + 3.20019i) q^{11} +(-1.23149 + 2.25333i) q^{12} +(1.70475 + 1.70475i) q^{13} +(3.68647 - 4.92266i) q^{14} +0.396496 q^{15} +(-3.36661 + 2.16008i) q^{16} -1.00000 q^{17} +(-1.14567 + 1.52985i) q^{18} +(0.630802 + 0.630802i) q^{19} +(0.541963 + 0.296193i) q^{20} +(-3.94815 + 3.94815i) q^{21} +(6.33541 - 0.909702i) q^{22} -0.799019i q^{23} +(3.30421 - 1.50677i) q^{24} +4.90464i q^{25} +(-0.484599 - 3.37488i) q^{26} +(3.95066 - 3.95066i) q^{27} +(-8.34603 + 2.44727i) q^{28} +(2.21985 + 2.21985i) q^{29} +(-0.448825 - 0.336116i) q^{30} +6.06127 q^{31} +(5.64207 + 0.408756i) q^{32} -5.81084 q^{33} +(1.13198 + 0.847715i) q^{34} +(0.949593 + 0.949593i) q^{35} +(2.59375 - 0.760554i) q^{36} +(4.96211 - 4.96211i) q^{37} +(-0.179315 - 1.24879i) q^{38} +3.09544i q^{39} +(-0.362403 - 0.794715i) q^{40} -11.0340i q^{41} +(7.81613 - 1.12232i) q^{42} +(-4.85759 + 4.85759i) q^{43} +(-7.94273 - 4.34086i) q^{44} +(-0.295111 - 0.295111i) q^{45} +(-0.677341 + 0.904474i) q^{46} +10.8190 q^{47} +(-5.01762 - 1.09539i) q^{48} -11.9113 q^{49} +(4.15774 - 5.55195i) q^{50} +(-0.907888 - 0.907888i) q^{51} +(-2.31238 + 4.23110i) q^{52} +(-3.33187 + 3.33187i) q^{53} +(-7.82109 + 1.12303i) q^{54} +1.39760i q^{55} +(11.5221 + 4.30479i) q^{56} +1.14539i q^{57} +(-0.631026 - 4.39463i) q^{58} +(-3.82207 + 3.82207i) q^{59} +(0.223131 + 0.760952i) q^{60} +(-3.16363 - 3.16363i) q^{61} +(-6.86123 - 5.13823i) q^{62} +5.87719 q^{63} +(-6.04020 - 5.24557i) q^{64} +0.744502 q^{65} +(6.57775 + 4.92594i) q^{66} +(-7.94007 - 7.94007i) q^{67} +(-0.562758 - 1.91919i) q^{68} +(0.725420 - 0.725420i) q^{69} +(-0.269936 - 1.87990i) q^{70} -6.71291i q^{71} +(-3.58080 - 1.33783i) q^{72} -10.1781i q^{73} +(-9.82346 + 1.41055i) q^{74} +(-4.45286 + 4.45286i) q^{75} +(-0.855642 + 1.56562i) q^{76} +(-13.9167 - 13.9167i) q^{77} +(2.62405 - 3.50397i) q^{78} +1.19136 q^{79} +(-0.263459 + 1.20682i) q^{80} +3.11908 q^{81} +(-9.35371 + 12.4903i) q^{82} +(-0.310373 - 0.310373i) q^{83} +(-9.79912 - 5.35541i) q^{84} +(-0.218362 + 0.218362i) q^{85} +(9.61654 - 1.38084i) q^{86} +4.03076i q^{87} +(5.31119 + 11.6469i) q^{88} +0.417625i q^{89} +(0.0838896 + 0.584229i) q^{90} +(-7.41346 + 7.41346i) q^{91} +(1.53347 - 0.449654i) q^{92} +(5.50295 + 5.50295i) q^{93} +(-12.2469 - 9.17146i) q^{94} +0.275486 q^{95} +(4.75126 + 5.49347i) q^{96} +1.28394 q^{97} +(13.4834 + 10.0974i) q^{98} +(4.32499 + 4.32499i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} + 8 q^{6} + 2 q^{8} - 6 q^{10} - 10 q^{11} - 2 q^{12} - 6 q^{13} - 22 q^{14} - 28 q^{15} + 2 q^{16} - 30 q^{17} + 8 q^{18} + 10 q^{19} - 10 q^{20} - 4 q^{21}+ \cdots + 54 q^{99}+O(q^{100}) $ 30 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 + 8 * q^6 + 2 * q^8 - 6 * q^10 - 10 * q^11 - 2 * q^12 - 6 * q^13 - 22 * q^14 - 28 * q^15 + 2 * q^16 - 30 * q^17 + 8 * q^18 + 10 * q^19 - 10 * q^20 - 4 * q^21 + 28 * q^22 + 18 * q^24 + 6 * q^26 + 4 * q^27 + 8 * q^28 - 18 * q^29 - 56 * q^30 + 48 * q^31 - 38 * q^32 - 12 * q^33 - 2 * q^34 + 16 * q^35 + 20 * q^36 + 6 * q^37 + 42 * q^38 + 10 * q^40 + 12 * q^42 + 2 * q^43 + 22 * q^44 + 42 * q^45 - 14 * q^46 - 32 * q^47 - 62 * q^48 - 38 * q^49 - 28 * q^50 + 2 * q^51 - 10 * q^52 - 6 * q^53 + 40 * q^54 + 96 * q^56 + 62 * q^58 - 14 * q^59 - 28 * q^60 + 6 * q^61 - 74 * q^62 + 84 * q^63 - 38 * q^64 - 12 * q^65 + 26 * q^67 + 2 * q^68 + 12 * q^69 + 48 * q^70 + 44 * q^72 + 42 * q^74 - 26 * q^75 - 38 * q^76 - 28 * q^77 - 56 * q^78 - 72 * q^79 - 38 * q^80 - 10 * q^81 - 76 * q^82 - 34 * q^83 + 104 * q^84 + 2 * q^85 + 34 * q^86 - 2 * q^88 + 70 * q^90 + 16 * q^91 - 40 * q^92 - 24 * q^93 - 44 * q^94 + 76 * q^95 - 126 * q^96 - 28 * q^97 - 30 * q^98 + 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/272\mathbb{Z}\right)^\times$.

$n$	$69$	$239$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$	−1.13198	−	0.847715i	−0.800431	−	0.599425i
$2$	−1.13198	−	0.847715i	−0.800431	−	0.599425i
$3$	0.907888	+	0.907888i	0.524170	+	0.524170i	0.918828	−	0.394658i	$-0.129137\pi$
$3$	0.907888	+	0.907888i	0.524170	+	0.524170i	−0.394658	+	0.918828i	$0.629137\pi$
$4$	0.562758	+	1.91919i	0.281379	+	0.959597i
$5$	0.218362	−	0.218362i	0.0976542	−	0.0976542i	−0.656592	−	0.754246i	$-0.728003\pi$
$5$	0.218362	−	0.218362i	0.0976542	−	0.0976542i	0.754246	+	0.656592i	$0.228003\pi$
$6$	−0.258081	−	1.79734i	−0.105361	−	0.733762i
$7$			4.34872i			1.64366i	0.569732	+	0.821830i	$0.307047\pi$
$7$			4.34872i			1.64366i	−0.569732	+	0.821830i	$0.692953\pi$
$8$	0.989900	−	2.64955i	0.349982	−	0.936756i
$9$		−	1.35148i		−	0.450493i
$10$	−0.432289	+	0.0620725i	−0.136702	+	0.0196290i
$11$	−3.20019	+	3.20019i	−0.964895	+	0.964895i	−0.999404	−	0.0345093i	$-0.989013\pi$
$11$	−3.20019	+	3.20019i	−0.964895	+	0.964895i	0.0345093	+	0.999404i	$0.489013\pi$
$12$	−1.23149	+	2.25333i	−0.355501	+	0.650482i
$13$	1.70475	+	1.70475i	0.472812	+	0.472812i	0.902823	−	0.430012i	$-0.141491\pi$
$13$	1.70475	+	1.70475i	0.472812	+	0.472812i	−0.430012	+	0.902823i	$0.641491\pi$
$14$	3.68647	−	4.92266i	0.985252	−	1.31564i
$15$	0.396496			0.102375
$16$	−3.36661	+	2.16008i	−0.841652	+	0.540020i
$17$	−1.00000			−0.242536
$17$	−1.00000			−0.242536
$18$	−1.14567	+	1.52985i	−0.270037	+	0.360588i
$19$	0.630802	+	0.630802i	0.144716	+	0.144716i	0.775753	−	0.631037i	$-0.217370\pi$
$19$	0.630802	+	0.630802i	0.144716	+	0.144716i	−0.631037	+	0.775753i	$0.717370\pi$
$20$	0.541963	+	0.296193i	0.121187	+	0.0662309i
$21$	−3.94815	+	3.94815i	−0.861557	+	0.861557i
$22$	6.33541	−	0.909702i	1.35071	−	0.193949i
$23$		−	0.799019i		−	0.166607i	−0.996524	−	0.0833035i	$-0.973453\pi$
$23$		−	0.799019i		−	0.166607i	0.996524	−	0.0833035i	$-0.0265471\pi$
$24$	3.30421	−	1.50677i	0.674469	−	0.307569i
$25$			4.90464i			0.980927i
$26$	−0.484599	−	3.37488i	−0.0950377	−	0.661868i
$27$	3.95066	−	3.95066i	0.760304	−	0.760304i
$28$	−8.34603	+	2.44727i	−1.57725	+	0.462491i
$29$	2.21985	+	2.21985i	0.412217	+	0.412217i	0.882510	−	0.470294i	$-0.155852\pi$
$29$	2.21985	+	2.21985i	0.412217	+	0.412217i	−0.470294	+	0.882510i	$0.655852\pi$
$30$	−0.448825	−	0.336116i	−0.0819439	−	0.0613660i
$31$	6.06127			1.08864			0.544318	−	0.838879i	$-0.316789\pi$
$31$	6.06127			1.08864			0.544318	+	0.838879i	$0.316789\pi$
$32$	5.64207	+	0.408756i	0.997386	+	0.0722586i
$33$	−5.81084			−1.01154
$34$	1.13198	+	0.847715i	0.194133	+	0.145382i
$35$	0.949593	+	0.949593i	0.160510	+	0.160510i
$36$	2.59375	−	0.760554i	0.432291	−	0.126759i
$37$	4.96211	−	4.96211i	0.815765	−	0.815765i	−0.169726	−	0.985491i	$-0.554288\pi$
$37$	4.96211	−	4.96211i	0.815765	−	0.815765i	0.985491	+	0.169726i	$0.0542883\pi$
$38$	−0.179315	−	1.24879i	−0.0290887	−	0.202581i
$39$			3.09544i			0.495667i
$40$	−0.362403	−	0.794715i	−0.0573010	−	0.125655i
$41$		−	11.0340i		−	1.72322i	−0.507567	−	0.861612i	$-0.669455\pi$
$41$		−	11.0340i		−	1.72322i	0.507567	−	0.861612i	$-0.330545\pi$
$42$	7.81613	−	1.12232i	1.20606	−	0.173178i
$43$	−4.85759	+	4.85759i	−0.740775	+	0.740775i	−0.972727	−	0.231952i	$-0.925489\pi$
$43$	−4.85759	+	4.85759i	−0.740775	+	0.740775i	0.231952	+	0.972727i	$0.425489\pi$
$44$	−7.94273	−	4.34086i	−1.19741	−	0.654409i
$45$	−0.295111	−	0.295111i	−0.0439925	−	0.0439925i
$46$	−0.677341	+	0.904474i	−0.0998685	+	0.133357i
$47$	10.8190			1.57812			0.789059	−	0.614318i	$-0.210569\pi$
$47$	10.8190			1.57812			0.789059	+	0.614318i	$0.210569\pi$
$48$	−5.01762	−	1.09539i	−0.724231	−	0.158106i
$49$	−11.9113			−1.70162
$50$	4.15774	−	5.55195i	0.587993	−	0.785164i
$51$	−0.907888	−	0.907888i	−0.127130	−	0.127130i
$52$	−2.31238	+	4.23110i	−0.320669	+	0.586748i
$53$	−3.33187	+	3.33187i	−0.457668	+	0.457668i	−0.897889	−	0.440222i	$-0.854900\pi$
$53$	−3.33187	+	3.33187i	−0.457668	+	0.457668i	0.440222	+	0.897889i	$0.354900\pi$
$54$	−7.82109	+	1.12303i	−1.06432	+	0.152825i
$55$			1.39760i			0.188452i
$56$	11.5221	+	4.30479i	1.53971	+	0.575252i
$57$			1.14539i			0.151711i
$58$	−0.631026	−	4.39463i	−0.0828578	−	0.577044i
$59$	−3.82207	+	3.82207i	−0.497591	+	0.497591i	−0.910687	−	0.413096i	$-0.864447\pi$
$59$	−3.82207	+	3.82207i	−0.497591	+	0.497591i	0.413096	+	0.910687i	$0.364447\pi$
$60$	0.223131	+	0.760952i	0.0288061	+	0.0982385i
$61$	−3.16363	−	3.16363i	−0.405061	−	0.405061i	0.474951	−	0.880012i	$-0.342466\pi$
$61$	−3.16363	−	3.16363i	−0.405061	−	0.405061i	−0.880012	+	0.474951i	$0.842466\pi$
$62$	−6.86123	−	5.13823i	−0.871378	−	0.652556i
$63$	5.87719			0.740457
$64$	−6.04020	−	5.24557i	−0.755025	−	0.655696i
$65$	0.744502			0.0923441
$66$	6.57775	+	4.92594i	0.809666	+	0.606341i
$67$	−7.94007	−	7.94007i	−0.970034	−	0.970034i	0.0295295	−	0.999564i	$-0.490599\pi$
$67$	−7.94007	−	7.94007i	−0.970034	−	0.970034i	−0.999564	+	0.0295295i	$0.990599\pi$
$68$	−0.562758	−	1.91919i	−0.0682444	−	0.232736i
$69$	0.725420	−	0.725420i	0.0873304	−	0.0873304i
$70$	−0.269936	−	1.87990i	−0.0322635	−	0.224692i
$71$		−	6.71291i		−	0.796676i	−0.917239	−	0.398338i	$-0.869587\pi$
$71$		−	6.71291i		−	0.796676i	0.917239	−	0.398338i	$-0.130413\pi$
$72$	−3.58080	−	1.33783i	−0.422002	−	0.157664i
$73$		−	10.1781i		−	1.19126i	−0.803260	−	0.595629i	$-0.796903\pi$
$73$		−	10.1781i		−	1.19126i	0.803260	−	0.595629i	$-0.203097\pi$
$74$	−9.82346	+	1.41055i	−1.14195	+	0.163973i
$75$	−4.45286	+	4.45286i	−0.514172	+	0.514172i
$76$	−0.855642	+	1.56562i	−0.0981489	+	0.179589i
$77$	−13.9167	−	13.9167i	−1.58596	−	1.58596i
$78$	2.62405	−	3.50397i	0.297115	−	0.396747i
$79$	1.19136			0.134038			0.0670192	−	0.997752i	$-0.478651\pi$
$79$	1.19136			0.134038			0.0670192	+	0.997752i	$0.478651\pi$
$80$	−0.263459	+	1.20682i	−0.0294556	+	0.134926i
$81$	3.11908			0.346564
$82$	−9.35371	+	12.4903i	−1.03294	+	1.37932i
$83$	−0.310373	−	0.310373i	−0.0340679	−	0.0340679i	0.689868	−	0.723936i	$-0.257669\pi$
$83$	−0.310373	−	0.310373i	−0.0340679	−	0.0340679i	−0.723936	+	0.689868i	$0.757669\pi$
$84$	−9.79912	−	5.35541i	−1.06917	−	0.584324i
$85$	−0.218362	+	0.218362i	−0.0236846	+	0.0236846i
$86$	9.61654	−	1.38084i	1.03698	−	0.148900i
$87$			4.03076i			0.432143i
$88$	5.31119	+	11.6469i	0.566175	+	1.24157i
$89$			0.417625i			0.0442682i	0.999755	+	0.0221341i	$0.00704607\pi$
$89$			0.417625i			0.0442682i	−0.999755	+	0.0221341i	$0.992954\pi$
$90$	0.0838896	+	0.584229i	0.00884274	+	0.0615832i
$91$	−7.41346	+	7.41346i	−0.777142	+	0.777142i
$92$	1.53347	−	0.449654i	0.159876	−	0.0468797i
$93$	5.50295	+	5.50295i	0.570630	+	0.570630i
$94$	−12.2469	−	9.17146i	−1.26317	−	0.945964i
$95$	0.275486			0.0282642
$96$	4.75126	+	5.49347i	0.484924	+	0.560675i
$97$	1.28394			0.130364			0.0651820	−	0.997873i	$-0.479237\pi$
$97$	1.28394			0.130364			0.0651820	+	0.997873i	$0.479237\pi$
$98$	13.4834	+	10.0974i	1.36203	+	1.01999i
$99$	4.32499	+	4.32499i	0.434678	+	0.434678i
$100$	−9.41295	+	2.76012i	−0.941295	+	0.276012i
$101$	−4.33008	+	4.33008i	−0.430859	+	0.430859i	−0.888921	−	0.458061i	$-0.848544\pi$
$101$	−4.33008	+	4.33008i	−0.430859	+	0.430859i	0.458061	+	0.888921i	$0.348544\pi$
$102$	0.258081	+	1.79734i	0.0255538	+	0.177963i
$103$		−	11.1306i		−	1.09673i	−0.836239	−	0.548366i	$-0.815250\pi$
$103$		−	11.1306i		−	1.09673i	0.836239	−	0.548366i	$-0.184750\pi$
$104$	6.20433	−	2.82928i	0.608385	−	0.277434i
$105$			1.72425i			0.168269i
$106$	6.59609	−	0.947133i	0.640669	−	0.0919937i
$107$	9.53747	−	9.53747i	0.922022	−	0.922022i	−0.0751502	−	0.997172i	$-0.523944\pi$
$107$	9.53747	−	9.53747i	0.922022	−	0.922022i	0.997172	+	0.0751502i	$0.0239436\pi$
$108$	9.80533	+	5.35881i	0.943519	+	0.515652i
$109$	8.07061	+	8.07061i	0.773025	+	0.773025i	0.978634	−	0.205609i	$-0.0659177\pi$
$109$	8.07061	+	8.07061i	0.773025	+	0.773025i	−0.205609	+	0.978634i	$0.565918\pi$
$110$	1.18477	−	1.58205i	0.112963	−	0.150843i
$111$	9.01008			0.855199
$112$	−9.39358	−	14.6404i	−0.887610	−	1.38339i
$113$	13.9211			1.30959			0.654795	−	0.755806i	$-0.272755\pi$
$113$	13.9211			1.30959			0.654795	+	0.755806i	$0.272755\pi$
$114$	0.970969	−	1.29656i	0.0909395	−	0.121434i
$115$	−0.174475	−	0.174475i	−0.0162699	−	0.0162699i
$116$	−3.01109	+	5.50957i	−0.279573	+	0.511551i
$117$	2.30393	−	2.30393i	0.212998	−	0.212998i
$118$	7.56653	−	1.08648i	0.696555	−	0.100018i
$119$		−	4.34872i		−	0.398646i
$120$	0.392491	−	1.05053i	0.0358294	−	0.0959002i
$121$		−	9.48249i		−	0.862045i
$122$	0.899308	+	6.26302i	0.0814195	+	0.567027i
$123$	10.0177	−	10.0177i	0.903262	−	0.903262i
$124$	3.41102	+	11.6327i	0.306319	+	1.04465i
$125$	2.16279	+	2.16279i	0.193446	+	0.193446i
$126$	−6.65287	−	4.98219i	−0.592684	−	0.443849i
$127$	16.7206			1.48371			0.741857	−	0.670558i	$-0.233945\pi$
$127$	16.7206			1.48371			0.741857	+	0.670558i	$0.233945\pi$
$128$	2.39063	+	11.0582i	0.211304	+	0.977420i
$129$	−8.82029			−0.776584
$130$	−0.842761	−	0.631126i	−0.0739151	−	0.0553534i
$131$	13.1402	+	13.1402i	1.14806	+	1.14806i	0.986933	+	0.161129i	$0.0515135\pi$
$131$	13.1402	+	13.1402i	1.14806	+	1.14806i	0.161129	+	0.986933i	$0.448486\pi$
$132$	−3.27009	−	11.1521i	−0.284625	−	0.970668i
$133$	−2.74318	+	2.74318i	−0.237864	+	0.237864i
$134$	2.25708	+	15.7189i	0.194982	+	1.35791i
$135$		−	1.72534i		−	0.148494i
$136$	−0.989900	+	2.64955i	−0.0848832	+	0.227197i
$137$		−	19.2469i		−	1.64438i	−0.569215	−	0.822189i	$-0.692753\pi$
$137$		−	19.2469i		−	1.64438i	0.569215	−	0.822189i	$-0.307247\pi$
$138$	−1.43611	+	0.206211i	−0.122250	+	0.0175539i
$139$	−10.1679	+	10.1679i	−0.862432	+	0.862432i	−0.991620	−	0.129188i	$-0.958763\pi$
$139$	−10.1679	+	10.1679i	−0.862432	+	0.862432i	0.129188	+	0.991620i	$0.458763\pi$
$140$	−1.28806	+	2.35684i	−0.108861	+	0.199190i
$141$	9.82247	+	9.82247i	0.827201	+	0.827201i
$142$	−5.69064	+	7.59888i	−0.477548	+	0.637684i
$143$	−10.9110			−0.912427
$144$	2.91930	+	4.54989i	0.243275	+	0.379158i
$145$	0.969461			0.0805094
$146$	−8.62814	+	11.5214i	−0.714070	+	0.953519i
$147$	−10.8142	−	10.8142i	−0.891938	−	0.891938i
$148$	12.3157	+	6.73078i	1.01234	+	0.553267i
$149$	−15.5419	+	15.5419i	−1.27324	+	1.27324i	−0.328869	+	0.944375i	$0.606668\pi$
$149$	−15.5419	+	15.5419i	−1.27324	+	1.27324i	−0.944375	+	0.328869i	$0.893332\pi$
$150$	8.81531	−	1.26579i	0.719767	−	0.103351i
$151$			11.7132i			0.953210i	0.879118	+	0.476605i	$0.158133\pi$
$151$			11.7132i			0.953210i	−0.879118	+	0.476605i	$0.841867\pi$
$152$	2.29577	−	1.04691i	0.186211	−	0.0849155i
$153$			1.35148i			0.109260i
$154$	3.95604	+	27.5509i	0.318787	+	2.22012i
$155$	1.32355	−	1.32355i	0.106310	−	0.106310i
$156$	−5.94075	+	1.74198i	−0.475640	+	0.139470i
$157$	10.3731	+	10.3731i	0.827862	+	0.827862i	0.987221	−	0.159359i	$-0.0509426\pi$
$157$	10.3731	+	10.3731i	0.827862	+	0.827862i	−0.159359	+	0.987221i	$0.550943\pi$
$158$	−1.34859	−	1.00993i	−0.107288	−	0.0803460i
$159$	−6.04993			−0.479791
$160$	1.32127	−	1.14275i	0.104455	−	0.0903426i
$161$	3.47471			0.273846
$162$	−3.53073	−	2.64409i	−0.277400	−	0.207739i
$163$	−8.39724	−	8.39724i	−0.657723	−	0.657723i	0.297118	−	0.954841i	$-0.403974\pi$
$163$	−8.39724	−	8.39724i	−0.657723	−	0.657723i	−0.954841	+	0.297118i	$0.903974\pi$
$164$	21.1764	−	6.20948i	1.65360	−	0.484879i
$165$	−1.26886	+	1.26886i	−0.0987809	+	0.0987809i
$166$	0.0882282	+	0.614445i	0.00684784	+	0.0476902i
$167$		−	15.5541i		−	1.20361i	−0.798642	−	0.601807i	$-0.794448\pi$
$167$		−	15.5541i		−	1.20361i	0.798642	−	0.601807i	$-0.205552\pi$
$168$	6.55254	+	14.3691i	0.505539	+	1.10860i
$169$		−	7.18768i		−	0.552898i
$170$	0.432289	−	0.0620725i	0.0331551	−	0.00476074i
$171$	0.852514	−	0.852514i	0.0651934	−	0.0651934i
$172$	−12.0563	−	6.58901i	−0.919284	−	0.502407i
$173$	−4.32493	−	4.32493i	−0.328818	−	0.328818i	0.523319	−	0.852137i	$-0.324694\pi$
$173$	−4.32493	−	4.32493i	−0.328818	−	0.328818i	−0.852137	+	0.523319i	$0.824694\pi$
$174$	3.41694	−	4.56274i	0.259037	−	0.345900i
$175$	−21.3289			−1.61231
$176$	3.86112	−	17.6865i	0.291043	−	1.33317i
$177$	−6.94002			−0.521644
$178$	0.354027	−	0.472743i	0.0265355	−	0.0354336i
$179$	−7.50749	−	7.50749i	−0.561136	−	0.561136i	0.368494	−	0.929630i	$-0.379874\pi$
$179$	−7.50749	−	7.50749i	−0.561136	−	0.561136i	−0.929630	+	0.368494i	$0.879874\pi$
$180$	0.400299	−	0.732450i	0.0298365	−	0.0545936i
$181$	11.2316	−	11.2316i	0.834842	−	0.834842i	−0.153333	−	0.988175i	$-0.549001\pi$
$181$	11.2316	−	11.2316i	0.834842	−	0.834842i	0.988175	+	0.153333i	$0.0490006\pi$
$182$	14.6764	−	2.10739i	1.08789	−	0.156210i
$183$		−	5.74444i		−	0.424641i
$184$	−2.11704	−	0.790949i	−0.156070	−	0.0583095i
$185$		−	2.16707i		−	0.159326i
$186$	−1.56430	−	10.8942i	−0.114700	−	0.798800i
$187$	3.20019	−	3.20019i	0.234021	−	0.234021i
$188$	6.08849	+	20.7638i	0.444049	+	1.51436i
$189$	17.1803	+	17.1803i	1.24968	+	1.24968i
$190$	−0.311844	−	0.233533i	−0.0226236	−	0.0169423i
$191$	−21.5439			−1.55886			−0.779431	−	0.626489i	$-0.784491\pi$
$191$	−21.5439			−1.55886			−0.779431	+	0.626489i	$0.784491\pi$
$192$	−0.721433	−	10.2462i	−0.0520649	−	0.739457i
$193$	6.73755			0.484980			0.242490	−	0.970154i	$-0.422036\pi$
$193$	6.73755			0.484980			0.242490	+	0.970154i	$0.422036\pi$
$194$	−1.45339	−	1.08841i	−0.104347	−	0.0781435i
$195$	0.675925	+	0.675925i	0.0484040	+	0.0484040i
$196$	−6.70320	−	22.8602i	−0.478800	−	1.63287i
$197$	−4.29287	+	4.29287i	−0.305854	+	0.305854i	−0.843299	−	0.537445i	$-0.819390\pi$
$197$	−4.29287	+	4.29287i	−0.305854	+	0.305854i	0.537445	+	0.843299i	$0.319390\pi$
$198$	−1.22944	−	8.56217i	−0.0873727	−	0.608487i
$199$			12.1391i			0.860521i	0.902705	+	0.430260i	$0.141578\pi$
$199$			12.1391i			0.860521i	−0.902705	+	0.430260i	$0.858422\pi$
$200$	12.9951	+	4.85510i	0.918890	+	0.343307i
$201$		−	14.4174i		−	1.01693i
$202$	8.57224	−	1.23089i	0.603141	−	0.0866051i
$203$	−9.65352	+	9.65352i	−0.677544	+	0.677544i
$204$	1.23149	−	2.25333i	0.0862217	−	0.157765i
$205$	−2.40940	−	2.40940i	−0.168280	−	0.168280i
$206$	−9.43559	+	12.5996i	−0.657409	+	0.877858i
$207$	−1.07986			−0.0750552
$208$	−9.42160	−	2.05682i	−0.653271	−	0.142615i
$209$	−4.03738			−0.279271
$210$	1.46167	−	1.95181i	0.100865	−	0.134688i
$211$	13.1133	+	13.1133i	0.902755	+	0.902755i	0.995674	−	0.0929183i	$-0.0296195\pi$
$211$	13.1133	+	13.1133i	0.902755	+	0.902755i	−0.0929183	+	0.995674i	$0.529620\pi$
$212$	−8.26954	−	4.51947i	−0.567954	−	0.310398i
$213$	6.09457	−	6.09457i	0.417593	−	0.417593i
$214$	−18.8813	+	2.71117i	−1.29070	+	0.185332i
$215$			2.12142i			0.144680i
$216$	−6.55670	−	14.3782i	−0.446127	−	0.978313i
$217$			26.3587i			1.78935i
$218$	−2.29419	−	15.9774i	−0.155382	−	1.08212i
$219$	9.24058	−	9.24058i	0.624421	−	0.624421i
$220$	−2.68226	+	0.786509i	−0.180838	+	0.0530264i
$221$	−1.70475	−	1.70475i	−0.114674	−	0.114674i
$222$	−10.1992	−	7.63798i	−0.684527	−	0.512628i
$223$	−6.52936			−0.437238			−0.218619	−	0.975810i	$-0.570155\pi$
$223$	−6.52936			−0.437238			−0.218619	+	0.975810i	$0.570155\pi$
$224$	−1.77757	+	24.5358i	−0.118769	+	1.63936i
$225$	6.62851			0.441900
$226$	−15.7585	−	11.8012i	−1.04824	−	0.785002i
$227$	−12.5151	−	12.5151i	−0.830656	−	0.830656i	0.156951	−	0.987606i	$-0.449834\pi$
$227$	−12.5151	−	12.5151i	−0.830656	−	0.830656i	−0.987606	+	0.156951i	$0.949834\pi$
$228$	−2.19823	+	0.644579i	−0.145582	+	0.0426883i
$229$	2.02898	−	2.02898i	0.134079	−	0.134079i	−0.636882	−	0.770961i	$-0.719776\pi$
$229$	2.02898	−	2.02898i	0.134079	−	0.134079i	0.770961	+	0.636882i	$0.219776\pi$
$230$	0.0495971	+	0.345408i	0.00327034	+	0.0227755i
$231$		−	25.2697i		−	1.66262i
$232$	8.07904	−	3.68418i	0.530415	−	0.241878i
$233$			15.3064i			1.00276i	0.865228	+	0.501379i	$0.167174\pi$
$233$			15.3064i			1.00276i	−0.865228	+	0.501379i	$0.832826\pi$
$234$	−4.56107	+	0.654925i	−0.298167	+	0.0428138i
$235$	2.36246	−	2.36246i	0.154110	−	0.154110i
$236$	−9.48618	−	5.18439i	−0.617498	−	0.337475i
$237$	1.08162	+	1.08162i	0.0702588	+	0.0702588i
$238$	−3.68647	+	4.92266i	−0.238959	+	0.319089i
$239$	−6.69415			−0.433009			−0.216504	−	0.976282i	$-0.569466\pi$
$239$	−6.69415			−0.433009			−0.216504	+	0.976282i	$0.569466\pi$
$240$	−1.33485	+	0.856463i	−0.0861639	+	0.0552845i
$241$	27.6474			1.78093			0.890464	−	0.455054i	$-0.150380\pi$
$241$	27.6474			1.78093			0.890464	+	0.455054i	$0.150380\pi$
$242$	−8.03845	+	10.7340i	−0.516731	+	0.690007i
$243$	−9.02019	−	9.02019i	−0.578646	−	0.578646i
$244$	4.29126	−	7.85197i	0.274720	−	0.502671i
$245$	−2.60098	+	2.60098i	−0.166171	+	0.166171i
$246$	−19.8319	+	2.84767i	−1.26444	+	0.181561i
$247$			2.15071i			0.136847i
$248$	6.00005	−	16.0596i	0.381003	−	1.01979i
$249$		−	0.563569i		−	0.0357147i
$250$	−0.614805	−	4.28167i	−0.0388837	−	0.270796i
$251$	−14.5898	+	14.5898i	−0.920900	+	0.920900i	−0.997093	−	0.0761933i	$-0.975723\pi$
$251$	−14.5898	+	14.5898i	−0.920900	+	0.920900i	0.0761933	+	0.997093i	$0.475723\pi$
$252$	3.30744	+	11.2795i	0.208349	+	0.710540i
$253$	2.55702	+	2.55702i	0.160758	+	0.160758i
$254$	−18.9274	−	14.1743i	−1.18761	−	0.889376i
$255$	−0.396496			−0.0248295
$256$	6.66810	−	14.5443i	0.416756	−	0.909018i
$257$	−1.86651			−0.116429			−0.0582147	−	0.998304i	$-0.518541\pi$
$257$	−1.86651			−0.116429			−0.0582147	+	0.998304i	$0.518541\pi$
$258$	9.98440	+	7.47710i	0.621601	+	0.465504i
$259$	21.5788	+	21.5788i	1.34084	+	1.34084i
$260$	0.418974	+	1.42884i	0.0259837	+	0.0886131i
$261$	3.00008	−	3.00008i	0.185700	−	0.185700i
$262$	−3.73529	−	26.0135i	−0.230767	−	1.60712i
$263$			20.7112i			1.27711i	0.769577	+	0.638553i	$0.220467\pi$
$263$			20.7112i			1.27711i	−0.769577	+	0.638553i	$0.779533\pi$
$264$	−5.75215	+	15.3961i	−0.354020	+	0.947564i
$265$			1.45510i			0.0893864i
$266$	5.43066	−	0.779789i	0.332975	−	0.0478119i
$267$	−0.379157	+	0.379157i	−0.0232040	+	0.0232040i
$268$	10.7702	−	19.7069i	0.657895	−	1.20379i
$269$	−1.46061	−	1.46061i	−0.0890551	−	0.0890551i	0.661176	−	0.750231i	$-0.270058\pi$
$269$	−1.46061	−	1.46061i	−0.0890551	−	0.0890551i	−0.750231	+	0.661176i	$0.770058\pi$
$270$	−1.46260	+	1.95305i	−0.0890110	+	0.118859i
$271$	5.12993			0.311621			0.155810	−	0.987787i	$-0.450201\pi$
$271$	5.12993			0.311621			0.155810	+	0.987787i	$0.450201\pi$
$272$	3.36661	−	2.16008i	0.204131	−	0.130974i
$273$	−13.4612			−0.814708
$274$	−16.3159	+	21.7872i	−0.985681	+	1.31621i
$275$	−15.6958	−	15.6958i	−0.946492	−	0.946492i
$276$	1.80046	+	0.983986i	0.108375	+	0.0592290i
$277$	10.4664	−	10.4664i	0.628866	−	0.628866i	−0.318917	−	0.947783i	$-0.603319\pi$
$277$	10.4664	−	10.4664i	0.628866	−	0.628866i	0.947783	+	0.318917i	$0.103319\pi$
$278$	20.1294	−	2.89038i	1.20728	−	0.173354i
$279$		−	8.19167i		−	0.490422i
$280$	3.45599	−	1.57599i	0.206535	−	0.0941834i
$281$			19.3081i			1.15183i	0.817511	+	0.575913i	$0.195353\pi$
$281$			19.3081i			1.15183i	−0.817511	+	0.575913i	$0.804647\pi$
$282$	−2.79218	−	19.4455i	−0.166272	−	1.15796i
$283$	−13.2247	+	13.2247i	−0.786124	+	0.786124i	−0.980856	−	0.194732i	$-0.937616\pi$
$283$	−13.2247	+	13.2247i	−0.786124	+	0.786124i	0.194732	+	0.980856i	$0.437616\pi$
$284$	12.8834	−	3.77774i	0.764487	−	0.224168i
$285$	0.250110	+	0.250110i	0.0148152	+	0.0148152i
$286$	12.3511	+	9.24946i	0.730335	+	0.546932i
$287$	47.9838			2.83240
$288$	0.552425	−	7.62513i	0.0325520	−	0.449315i
$289$	1.00000			0.0588235
$290$	−1.09741	−	0.821827i	−0.0644422	−	0.0482594i
$291$	1.16567	+	1.16567i	0.0683329	+	0.0683329i
$292$	19.5338	−	5.72781i	1.14313	−	0.335194i
$293$	−6.75051	+	6.75051i	−0.394369	+	0.394369i	−0.876241	−	0.481872i	$-0.839957\pi$
$293$	−6.75051	+	6.75051i	−0.394369	+	0.394369i	0.481872	+	0.876241i	$0.339957\pi$
$294$	3.07409	+	21.4088i	0.179284	+	1.24858i
$295$			1.66918i			0.0971837i
$296$	−8.23535	−	18.0593i	−0.478670	−	1.04968i
$297$			25.2857i			1.46723i
$298$	30.7683	−	4.41802i	1.78236	−	0.255929i
$299$	1.36213	−	1.36213i	0.0787737	−	0.0787737i
$300$	−11.0518	−	6.04002i	−0.638075	−	0.348721i
$301$	−21.1243	−	21.1243i	−1.21758	−	1.21758i
$302$	9.92949	−	13.2592i	0.571378	−	0.762978i
$303$	−7.86246			−0.451687
$304$	−3.48624	−	0.761079i	−0.199950	−	0.0436509i
$305$	−1.38163			−0.0791119
$306$	1.14567	−	1.52985i	0.0654935	−	0.0874554i
$307$	−4.76317	−	4.76317i	−0.271848	−	0.271848i	0.557996	−	0.829844i	$-0.311571\pi$
$307$	−4.76317	−	4.76317i	−0.271848	−	0.271848i	−0.829844	+	0.557996i	$0.811571\pi$
$308$	18.8772	−	34.5407i	1.07563	−	1.96814i
$309$	10.1054	−	10.1054i	0.574873	−	0.574873i
$310$	−2.62022	+	0.376238i	−0.148819	+	0.0213689i
$311$			4.29643i			0.243628i	0.992553	+	0.121814i	$0.0388712\pi$
$311$			4.29643i			0.243628i	−0.992553	+	0.121814i	$0.961129\pi$
$312$	8.20151	+	3.06417i	0.464319	+	0.173475i
$313$		−	3.56363i		−	0.201428i	−0.994915	−	0.100714i	$-0.967887\pi$
$313$		−	3.56363i		−	0.201428i	0.994915	−	0.100714i	$-0.0321127\pi$
$314$	−2.94870	−	20.5355i	−0.166405	−	1.15889i
$315$	1.28335	−	1.28335i	0.0723088	−	0.0723088i
$316$	0.670446	+	2.28645i	0.0377155	+	0.128623i
$317$	3.97879	+	3.97879i	0.223471	+	0.223471i	0.809959	−	0.586487i	$-0.199490\pi$
$317$	3.97879	+	3.97879i	0.223471	+	0.223471i	−0.586487	+	0.809959i	$0.699490\pi$
$318$	6.84840	+	5.12862i	0.384039	+	0.287599i
$319$	−14.2079			−0.795491
$320$	−2.46438	+	0.173516i	−0.137763	+	0.00969984i
$321$	17.3179			0.966592
$322$	−3.93330	−	2.94556i	−0.219194	−	0.164150i
$323$	−0.630802	−	0.630802i	−0.0350987	−	0.0350987i
$324$	1.75528	+	5.98611i	0.0975157	+	0.332562i
$325$	−8.36116	+	8.36116i	−0.463794	+	0.463794i
$326$	2.38704	+	16.6240i	0.132206	+	0.920717i
$327$			14.6544i			0.810392i
$328$	−29.2351	−	10.9226i	−1.61424	−	0.603098i
$329$			47.0489i			2.59389i
$330$	2.51196	−	0.360693i	0.138279	−	0.0198555i
$331$	−7.16883	+	7.16883i	−0.394035	+	0.394035i	−0.876123	−	0.482088i	$-0.839879\pi$
$331$	−7.16883	+	7.16883i	−0.394035	+	0.394035i	0.482088	+	0.876123i	$0.339879\pi$
$332$	0.421002	−	0.770332i	0.0231055	−	0.0422774i
$333$	−6.70618	−	6.70618i	−0.367496	−	0.367496i
$334$	−13.1855	+	17.6069i	−0.721476	+	0.963409i
$335$	−3.46761			−0.189456
$336$	4.76355	−	21.8202i	0.259873	−	1.19039i
$337$	−10.8336			−0.590146			−0.295073	−	0.955475i	$-0.595344\pi$
$337$	−10.8336			−0.590146			−0.295073	+	0.955475i	$0.595344\pi$
$338$	−6.09311	+	8.13631i	−0.331421	+	0.442557i
$339$	12.6388	+	12.6388i	0.686448	+	0.686448i
$340$	−0.541963	−	0.296193i	−0.0293920	−	0.0160633i
$341$	−19.3972	+	19.3972i	−1.05042	+	1.05042i
$342$	−1.68772	+	0.242340i	−0.0912613	+	0.0131042i
$343$		−	21.3581i		−	1.15323i
$344$	8.06188	+	17.6789i	0.434668	+	0.953184i
$345$		−	0.316808i		−	0.0170564i
$346$	1.22942	+	8.56204i	0.0660943	+	0.460298i
$347$	12.0092	−	12.0092i	0.644686	−	0.644686i	−0.307018	−	0.951704i	$-0.599331\pi$
$347$	12.0092	−	12.0092i	0.644686	−	0.644686i	0.951704	+	0.307018i	$0.0993310\pi$
$348$	−7.73581	+	2.26834i	−0.414683	+	0.121596i
$349$	−19.9188	−	19.9188i	−1.06623	−	1.06623i	−0.997645	−	0.0685821i	$-0.978152\pi$
$349$	−19.9188	−	19.9188i	−1.06623	−	1.06623i	−0.0685821	−	0.997645i	$-0.521848\pi$
$350$	24.1439	+	18.0808i	1.29054	+	0.966460i
$351$	13.4697			0.718961
$352$	−19.3638	+	16.7476i	−1.03209	+	0.892651i
$353$	18.3604			0.977226			0.488613	−	0.872501i	$-0.337503\pi$
$353$	18.3604			0.977226			0.488613	+	0.872501i	$0.337503\pi$
$354$	7.85596	+	5.88316i	0.417540	+	0.312687i
$355$	−1.46584	−	1.46584i	−0.0777988	−	0.0777988i
$356$	−0.801504	+	0.235022i	−0.0424796	+	0.0124561i
$357$	3.94815	−	3.94815i	0.208958	−	0.208958i
$358$	2.13412	+	14.8626i	0.112792	+	0.785510i
$359$			0.624108i			0.0329391i	0.999864	+	0.0164696i	$0.00524266\pi$
$359$			0.624108i			0.0329391i	−0.999864	+	0.0164696i	$0.994757\pi$
$360$	−1.07404	+	0.489780i	−0.0566069	+	0.0258137i
$361$		−	18.2042i		−	0.958115i
$362$	−22.2352	+	3.19276i	−1.16866	+	0.167808i
$363$	8.60905	−	8.60905i	0.451858	−	0.451858i
$364$	−18.3998	−	10.0559i	−0.964414	−	0.527072i
$365$	−2.22251	−	2.22251i	−0.116331	−	0.116331i
$366$	−4.86965	+	6.50259i	−0.254541	+	0.339896i
$367$	−3.47800			−0.181550			−0.0907750	−	0.995871i	$-0.528934\pi$
$367$	−3.47800			−0.181550			−0.0907750	+	0.995871i	$0.528934\pi$
$368$	1.72595	+	2.68999i	0.0899712	+	0.140225i
$369$	−14.9122			−0.776300
$370$	−1.83706	+	2.45308i	−0.0955040	+	0.127529i
$371$	−14.4894	−	14.4894i	−0.752250	−	0.752250i
$372$	−7.46441	+	13.6581i	−0.387011	+	0.708138i
$373$	14.8724	−	14.8724i	0.770064	−	0.770064i	−0.208054	−	0.978117i	$-0.566713\pi$
$373$	14.8724	−	14.8724i	0.770064	−	0.770064i	0.978117	+	0.208054i	$0.0667128\pi$
$374$	−6.33541	+	0.909702i	−0.327596	+	0.0470396i
$375$			3.92715i			0.202797i
$376$	10.7098	−	28.6655i	0.552313	−	1.47831i
$377$			7.56858i			0.389802i
$378$	−4.88375	−	34.0117i	−0.251193	−	1.74937i
$379$	12.2779	−	12.2779i	0.630675	−	0.630675i	−0.317562	−	0.948237i	$-0.602864\pi$
$379$	12.2779	−	12.2779i	0.630675	−	0.630675i	0.948237	+	0.317562i	$0.102864\pi$
$380$	0.155032	+	0.528710i	0.00795295	+	0.0271223i
$381$	15.1804	+	15.1804i	0.777718	+	0.777718i
$382$	24.3873	+	18.2631i	1.24776	+	0.934421i
$383$	6.42453			0.328278			0.164139	−	0.986437i	$-0.447515\pi$
$383$	6.42453			0.328278			0.164139	+	0.986437i	$0.447515\pi$
$384$	−7.86923	+	12.2101i	−0.401575	+	0.623093i
$385$	−6.07776			−0.309751
$386$	−7.62677	−	5.71153i	−0.388193	−	0.290709i
$387$	6.56492	+	6.56492i	0.333714	+	0.333714i
$388$	0.722545	+	2.46412i	0.0366817	+	0.125097i
$389$	2.70168	−	2.70168i	0.136980	−	0.136980i	−0.635292	−	0.772272i	$-0.719120\pi$
$389$	2.70168	−	2.70168i	0.136980	−	0.136980i	0.772272	+	0.635292i	$0.219120\pi$
$390$	−0.192142	−	1.33813i	−0.00972947	−	0.0677586i
$391$			0.799019i			0.0404081i
$392$	−11.7910	+	31.5597i	−0.595537	+	1.59400i
$393$			23.8596i			1.20356i
$394$	8.49857	−	1.22031i	0.428152	−	0.0614783i
$395$	0.260147	−	0.260147i	0.0130894	−	0.0130894i
$396$	−5.86657	+	10.7344i	−0.294806	+	0.539425i
$397$	23.4561	+	23.4561i	1.17723	+	1.17723i	0.980448	+	0.196779i	$0.0630482\pi$
$397$	23.4561	+	23.4561i	1.17723	+	1.17723i	0.196779	+	0.980448i	$0.436952\pi$
$398$	10.2905	−	13.7413i	0.515818	−	0.688787i
$399$	−4.98100			−0.249362
$400$	−10.5944	−	16.5120i	−0.529721	−	0.825599i
$401$	−1.78480			−0.0891287			−0.0445644	−	0.999007i	$-0.514190\pi$
$401$	−1.78480			−0.0891287			−0.0445644	+	0.999007i	$0.514190\pi$
$402$	−12.2219	+	16.3202i	−0.609571	+	0.813978i
$403$	10.3329	+	10.3329i	0.514720	+	0.514720i
$404$	−10.7470	−	5.87348i	−0.534686	−	0.292216i
$405$	0.681086	−	0.681086i	0.0338434	−	0.0338434i
$406$	19.1110	−	2.74415i	0.948464	−	0.136190i
$407$			31.7594i			1.57426i
$408$	−3.30421	+	1.50677i	−0.163583	+	0.0745965i
$409$		−	31.5259i		−	1.55886i	−0.626492	−	0.779428i	$-0.715510\pi$
$409$		−	31.5259i		−	1.55886i	0.626492	−	0.779428i	$-0.284490\pi$
$410$	0.684909	+	4.76989i	0.0338252	+	0.235568i
$411$	17.4741	−	17.4741i	0.861932	−	0.861932i
$412$	21.3618	−	6.26383i	1.05242	−	0.308597i
$413$	−16.6211	−	16.6211i	−0.817871	−	0.817871i
$414$	1.22238	+	0.915411i	0.0600765	+	0.0449900i
$415$	−0.135547			−0.00665375
$416$	8.92147	+	10.3151i	0.437411	+	0.505740i
$417$	−18.4627			−0.904121
$418$	4.57023	+	3.42255i	0.223537	+	0.167402i
$419$	−14.4975	−	14.4975i	−0.708248	−	0.708248i	0.257918	−	0.966167i	$-0.416963\pi$
$419$	−14.4975	−	14.4975i	−0.708248	−	0.708248i	−0.966167	+	0.257918i	$0.916963\pi$
$420$	−3.30917	+	0.970334i	−0.161471	+	0.0473474i
$421$	12.0990	−	12.0990i	0.589667	−	0.589667i	−0.347874	−	0.937541i	$-0.613096\pi$
$421$	12.0990	−	12.0990i	0.589667	−	0.589667i	0.937541	+	0.347874i	$0.113096\pi$
$422$	−3.72764	−	25.9603i	−0.181459	−	1.26373i
$423$		−	14.6217i		−	0.710930i
$424$	5.52973	+	12.1262i	0.268547	+	0.588899i
$425$		−	4.90464i		−	0.237910i
$426$	−12.0654	+	1.73247i	−0.584570	+	0.0839385i
$427$	13.7577	−	13.7577i	0.665783	−	0.665783i
$428$	23.6715	+	12.9370i	1.14421	+	0.625332i
$429$	−9.90601	−	9.90601i	−0.478267	−	0.478267i
$430$	1.79836	−	2.40141i	0.0867246	−	0.115806i
$431$	−25.8793			−1.24656			−0.623281	−	0.781998i	$-0.714201\pi$
$431$	−25.8793			−1.24656			−0.623281	+	0.781998i	$0.714201\pi$
$432$	−4.76657	+	21.8340i	−0.229332	+	1.05049i
$433$	−19.2252			−0.923904			−0.461952	−	0.886905i	$-0.652851\pi$
$433$	−19.2252			−0.923904			−0.461952	+	0.886905i	$0.652851\pi$
$434$	22.3447	−	29.8376i	1.07258	−	1.43225i
$435$	0.880163	+	0.880163i	0.0422006	+	0.0422006i
$436$	−10.9473	+	20.0309i	−0.524279	+	0.959305i
$437$	0.504023	−	0.504023i	0.0241107	−	0.0241107i
$438$	−18.2935	+	2.62677i	−0.874099	+	0.125512i
$439$			32.8584i			1.56825i	0.620606	+	0.784123i	$0.286887\pi$
$439$			32.8584i			1.56825i	−0.620606	+	0.784123i	$0.713113\pi$
$440$	3.70300	+	1.38348i	0.176534	+	0.0659549i
$441$			16.0979i			0.766568i
$442$	0.484599	+	3.37488i	0.0230500	+	0.160527i
$443$	9.79263	−	9.79263i	0.465262	−	0.465262i	−0.435114	−	0.900375i	$-0.643292\pi$
$443$	9.79263	−	9.79263i	0.465262	−	0.465262i	0.900375	+	0.435114i	$0.143292\pi$
$444$	5.07049	+	17.2921i	0.240635	+	0.820646i
$445$	0.0911933	+	0.0911933i	0.00432298	+	0.00432298i
$446$	7.39111	+	5.53504i	0.349979	+	0.262092i
$447$	−28.2207			−1.33479
$448$	22.8115	−	26.2671i	1.07774	−	1.24100i
$449$	−19.2899			−0.910349			−0.455174	−	0.890402i	$-0.650423\pi$
$449$	−19.2899			−0.910349			−0.455174	+	0.890402i	$0.650423\pi$
$450$	−7.50334	−	5.61909i	−0.353711	−	0.264886i
$451$	35.3110	+	35.3110i	1.66273	+	1.66273i
$452$	7.83423	+	26.7174i	0.368491	+	1.25668i
$453$	−10.6343	+	10.6343i	−0.499644	+	0.499644i
$454$	3.55760	+	24.7761i	0.166966	+	1.16280i
$455$			3.23763i			0.151782i
$456$	3.03478	+	1.13383i	0.142116	+	0.0530963i
$457$		−	0.0860321i		−	0.00402441i	−0.999998	−	0.00201221i	$-0.999359\pi$
$457$		−	0.0860321i		−	0.00402441i	0.999998	−	0.00201221i	$-0.000640505\pi$
$458$	−4.01676	+	0.576767i	−0.187691	+	0.0269505i
$459$	−3.95066	+	3.95066i	−0.184401	+	0.184401i
$460$	0.236664	−	0.433039i	0.0110345	−	0.0201905i
$461$	−10.2169	−	10.2169i	−0.475851	−	0.475851i	0.427951	−	0.903802i	$-0.359236\pi$
$461$	−10.2169	−	10.2169i	−0.475851	−	0.475851i	−0.903802	+	0.427951i	$0.859236\pi$
$462$	−21.4215	+	28.6048i	−0.996619	+	1.33082i
$463$	−31.6625			−1.47148			−0.735741	−	0.677263i	$-0.763166\pi$
$463$	−31.6625			−1.47148			−0.735741	+	0.677263i	$0.763166\pi$
$464$	−12.2684	−	2.67831i	−0.569548	−	0.124338i
$465$	2.40327			0.111449
$466$	12.9755	−	17.3266i	0.601078	−	0.802638i
$467$	4.61581	+	4.61581i	0.213594	+	0.213594i	0.805792	−	0.592198i	$-0.201740\pi$
$467$	4.61581	+	4.61581i	0.213594	+	0.213594i	−0.592198	+	0.805792i	$0.701740\pi$
$468$	5.71823	+	3.12513i	0.264325	+	0.144459i
$469$	34.5291	−	34.5291i	1.59441	−	1.59441i
$470$	−4.67695	+	0.671564i	−0.215732	+	0.0309769i
$471$			18.8352i			0.867880i
$472$	6.34328	+	13.9102i	0.291973	+	0.640269i
$473$		−	31.0904i		−	1.42954i
$474$	−0.307467	−	2.14128i	−0.0141224	−	0.0983522i
$475$	−3.09385	+	3.09385i	−0.141956	+	0.141956i
$476$	8.34603	−	2.44727i	0.382540	−	0.112171i
$477$	4.50295	+	4.50295i	0.206176	+	0.206176i
$478$	7.57765	+	5.67474i	0.346594	+	0.259556i
$479$	−8.41813			−0.384634			−0.192317	−	0.981333i	$-0.561600\pi$
$479$	−8.41813			−0.384634			−0.192317	+	0.981333i	$0.561600\pi$
$480$	2.23706	+	0.162070i	0.102107	+	0.00739746i
$481$	16.9183			0.771407
$482$	−31.2963	−	23.4371i	−1.42551	−	1.06753i
$483$	3.15465	+	3.15465i	0.143541	+	0.143541i
$484$	18.1987	−	5.33634i	0.827215	−	0.242561i
$485$	0.280363	−	0.280363i	0.0127306	−	0.0127306i
$486$	2.56412	+	17.8572i	0.116311	+	0.810021i
$487$		−	39.1242i		−	1.77289i	−0.462836	−	0.886444i	$-0.653168\pi$
$487$		−	39.1242i		−	1.77289i	0.462836	−	0.886444i	$-0.346832\pi$
$488$	−11.5139	+	5.25051i	−0.521208	+	0.237679i
$489$		−	15.2475i		−	0.689516i
$490$	5.14915	−	0.739367i	0.232615	−	0.0334012i
$491$	−9.80593	+	9.80593i	−0.442536	+	0.442536i	−0.892863	−	0.450328i	$-0.851307\pi$
$491$	−9.80593	+	9.80593i	−0.442536	+	0.442536i	0.450328	+	0.892863i	$0.351307\pi$
$492$	24.8633	+	13.5883i	1.12093	+	0.612608i
$493$	−2.21985	−	2.21985i	−0.0999772	−	0.0999772i
$494$	1.82319	−	2.43456i	0.0820293	−	0.109536i
$495$	1.88882			0.0848963
$496$	−20.4059	+	13.0928i	−0.916253	+	0.587885i
$497$	29.1925			1.30946
$498$	−0.477746	+	0.637949i	−0.0214083	+	0.0285872i
$499$	0.119096	+	0.119096i	0.00533148	+	0.00533148i	0.709767	−	0.704436i	$-0.248800\pi$
$499$	0.119096	+	0.119096i	0.00533148	+	0.00533148i	−0.704436	+	0.709767i	$0.748800\pi$
$500$	−2.93369	+	5.36794i	−0.131199	+	0.240062i
$501$	14.1214	−	14.1214i	0.630898	−	0.630898i
$502$	28.8834	−	4.14736i	1.28913	−	0.185106i
$503$			20.4936i			0.913763i	0.889527	+	0.456882i	$0.151034\pi$
$503$			20.4936i			0.913763i	−0.889527	+	0.456882i	$0.848966\pi$
$504$	5.81783	−	15.5719i	0.259147	−	0.693628i
$505$			1.89105i			0.0841505i
$506$	−0.726870	−	5.06212i	−0.0323133	−	0.225039i
$507$	6.52561	−	6.52561i	0.289813	−	0.289813i
$508$	9.40965	+	32.0901i	0.417486	+	1.42377i
$509$	−16.4317	−	16.4317i	−0.728323	−	0.728323i	0.241963	−	0.970286i	$-0.422209\pi$
$509$	−16.4317	−	16.4317i	−0.728323	−	0.728323i	−0.970286	+	0.241963i	$0.922209\pi$
$510$	0.448825	+	0.336116i	0.0198743	+	0.0148834i
$511$	44.2617			1.95802
$512$	−19.8776	+	10.8112i	−0.878473	+	0.477792i
$513$	4.98416			0.220056
$514$	2.11285	+	1.58227i	0.0931937	+	0.0697907i
$515$	−2.43050	−	2.43050i	−0.107100	−	0.107100i
$516$	−4.96369	−	16.9279i	−0.218514	−	0.745207i
$517$	−34.6230	+	34.6230i	−1.52272	+	1.52272i
$518$	−6.13409	−	42.7195i	−0.269517	−	1.87698i
$519$		−	7.85311i		−	0.344713i
$520$	0.736982	−	1.97259i	0.0323188	−	0.0865039i
$521$			1.65317i			0.0724268i	0.999344	+	0.0362134i	$0.0115296\pi$
$521$			1.65317i			0.0724268i	−0.999344	+	0.0362134i	$0.988470\pi$
$522$	−5.93925	+	0.852818i	−0.259954	+	0.0373268i
$523$	−11.5020	+	11.5020i	−0.502945	+	0.502945i	−0.912352	−	0.409407i	$-0.865736\pi$
$523$	−11.5020	+	11.5020i	−0.502945	+	0.502945i	0.409407	+	0.912352i	$0.365736\pi$
$524$	−17.8238	+	32.6133i	−0.778637	+	1.42472i
$525$	−19.3642	−	19.3642i	−0.845125	−	0.845125i
$526$	17.5572	−	23.4447i	0.765530	−	1.02224i
$527$	−6.06127			−0.264033
$528$	19.5628	−	12.5519i	0.851362	−	0.546251i
$529$	22.3616			0.972242
$530$	1.23351	−	1.64715i	0.0535804	−	0.0715476i
$531$	5.16544	+	5.16544i	0.224161	+	0.224161i
$532$	−6.80843	−	3.72095i	−0.295183	−	0.161323i
$533$	18.8102	−	18.8102i	0.814760	−	0.814760i
$534$	0.750615	−	0.107781i	0.0324823	−	0.00466414i
$535$		−	4.16523i		−	0.180079i
$536$	−28.8975	+	13.1777i	−1.24818	+	0.569191i
$537$		−	13.6319i		−	0.588261i
$538$	0.415201	+	2.89157i	0.0179006	+	0.124664i
$539$	38.1186	−	38.1186i	1.64189	−	1.64189i
$540$	3.31127	−	0.970949i	0.142494	−	0.0417830i
$541$	−22.1142	−	22.1142i	−0.950762	−	0.950762i	0.0480817	−	0.998843i	$-0.484689\pi$
$541$	−22.1142	−	22.1142i	−0.950762	−	0.950762i	−0.998843	+	0.0480817i	$0.984689\pi$
$542$	−5.80697	−	4.34872i	−0.249431	−	0.186793i
$543$	20.3942			0.875197
$544$	−5.64207	−	0.408756i	−0.241902	−	0.0175253i
$545$	3.52462			0.150978
$546$	15.2378	+	11.4113i	0.652118	+	0.488357i
$547$	−2.21494	−	2.21494i	−0.0947040	−	0.0947040i	0.658167	−	0.752872i	$-0.271332\pi$
$547$	−2.21494	−	2.21494i	−0.0947040	−	0.0947040i	−0.752872	+	0.658167i	$0.771332\pi$
$548$	36.9386	−	10.8314i	1.57794	−	0.462693i
$549$	−4.27557	+	4.27557i	−0.182477	+	0.182477i
$550$	4.46176	+	31.0729i	0.190250	+	1.32495i
$551$			2.80057i			0.119308i
$552$	−1.20394	−	2.64013i	−0.0512432	−	0.112371i
$553$			5.18088i			0.220314i
$554$	−20.7203	+	2.97523i	−0.880322	+	0.126405i
$555$	1.96745	−	1.96745i	0.0835138	−	0.0835138i
$556$	−25.2363	−	13.7921i	−1.07026	−	0.584917i
$557$	31.2307	+	31.2307i	1.32329	+	1.32329i	0.911099	+	0.412188i	$0.135235\pi$
$557$	31.2307	+	31.2307i	1.32329	+	1.32329i	0.412188	+	0.911099i	$0.364765\pi$
$558$	−6.94420	+	9.27280i	−0.293972	+	0.392549i
$559$	−16.5619			−0.700494
$560$	−5.24810	−	1.14571i	−0.221773	−	0.0484150i
$561$	5.81084			0.245334
$562$	16.3678	−	21.8564i	0.690434	−	0.921958i
$563$	−6.90605	−	6.90605i	−0.291055	−	0.291055i	0.546442	−	0.837497i	$-0.315982\pi$
$563$	−6.90605	−	6.90605i	−0.291055	−	0.291055i	−0.837497	+	0.546442i	$0.815982\pi$
$564$	−13.3236	+	24.3789i	−0.561023	+	1.02654i
$565$	3.03984	−	3.03984i	0.127887	−	0.127887i
$566$	26.1808	−	3.75930i	1.10046	−	0.158015i
$567$			13.5640i			0.569634i
$568$	−17.7862	−	6.64511i	−0.746291	−	0.278822i
$569$		−	15.2242i		−	0.638231i	−0.947716	−	0.319116i	$-0.896614\pi$
$569$		−	15.2242i		−	0.638231i	0.947716	−	0.319116i	$-0.103386\pi$
$570$	−0.0710975	−	0.495142i	−0.00297795	−	0.0207392i
$571$	12.3088	−	12.3088i	0.515106	−	0.515106i	−0.400981	−	0.916087i	$-0.631331\pi$
$571$	12.3088	−	12.3088i	0.515106	−	0.515106i	0.916087	+	0.400981i	$0.131331\pi$
$572$	−6.14027	−	20.9404i	−0.256738	−	0.875562i
$573$	−19.5594	−	19.5594i	−0.817108	−	0.817108i
$574$	−54.3167	−	40.6766i	−2.26714	−	1.69781i
$575$	3.91890			0.163429
$576$	−7.08927	+	8.16319i	−0.295386	+	0.340133i
$577$	17.0577			0.710120			0.355060	−	0.934844i	$-0.384460\pi$
$577$	17.0577			0.710120			0.355060	+	0.934844i	$0.384460\pi$
$578$	−1.13198	−	0.847715i	−0.0470842	−	0.0352603i
$579$	6.11694	+	6.11694i	0.254212	+	0.254212i
$580$	0.545572	+	1.86058i	0.0226536	+	0.0772566i
$581$	1.34973	−	1.34973i	0.0559961	−	0.0559961i
$582$	−0.331359	−	2.30768i	−0.0137353	−	0.0956562i
$583$		−	21.3253i		−	0.883202i
$584$	−26.9674	−	10.0753i	−1.11592	−	0.416919i
$585$		−	1.00618i		−	0.0416003i
$586$	13.3640	−	1.91893i	0.552060	−	0.0792704i
$587$	12.0018	−	12.0018i	0.495368	−	0.495368i	−0.414625	−	0.909993i	$-0.636087\pi$
$587$	12.0018	−	12.0018i	0.495368	−	0.495368i	0.909993	+	0.414625i	$0.136087\pi$
$588$	14.6687	−	26.8402i	0.604928	−	1.10687i
$589$	3.82346	+	3.82346i	0.157543	+	0.157543i
$590$	1.41499	−	1.88948i	0.0582544	−	0.0777888i
$591$	−7.79489			−0.320639
$592$	−5.98691	+	27.4240i	−0.246061	+	1.12712i
$593$	−46.6598			−1.91609			−0.958044	−	0.286622i	$-0.907468\pi$
$593$	−46.6598			−1.91609			−0.958044	+	0.286622i	$0.907468\pi$
$594$	21.4351	−	28.6229i	0.879493	−	1.17441i
$595$	−0.949593	−	0.949593i	−0.0389295	−	0.0389295i
$596$	−38.5743	−	21.0816i	−1.58007	−	0.863538i
$597$	−11.0210	+	11.0210i	−0.451059	+	0.451059i
$598$	−2.69659	+	0.387204i	−0.110272	+	0.0158340i
$599$		−	1.28453i		−	0.0524844i	−0.999656	−	0.0262422i	$-0.991646\pi$
$599$		−	1.28453i		−	0.0524844i	0.999656	−	0.0262422i	$-0.00835411\pi$
$600$	7.39018	+	16.2060i	0.301703	+	0.661605i
$601$			39.8860i			1.62698i	0.581576	+	0.813492i	$0.302436\pi$
$601$			39.8860i			1.62698i	−0.581576	+	0.813492i	$0.697564\pi$
$602$	6.00489	+	41.8196i	0.244741	+	1.70444i
$603$	−10.7308	+	10.7308i	−0.436993	+	0.436993i
$604$	−22.4800	+	6.59171i	−0.914697	+	0.268213i
$605$	−2.07061	−	2.07061i	−0.0841823	−	0.0841823i
$606$	8.90015	+	6.66513i	0.361544	+	0.270752i
$607$	−23.5272			−0.954940			−0.477470	−	0.878648i	$-0.658446\pi$
$607$	−23.5272			−0.954940			−0.477470	+	0.878648i	$0.658446\pi$
$608$	3.30118	+	3.81687i	0.133881	+	0.154794i
$609$	−17.5286			−0.710296
$610$	1.56398	+	1.17123i	0.0633236	+	0.0474216i
$611$	18.4437	+	18.4437i	0.746152	+	0.746152i
$612$	−2.59375	+	0.760554i	−0.104846	+	0.0307436i
$613$	12.5637	−	12.5637i	0.507444	−	0.507444i	−0.406297	−	0.913741i	$-0.633180\pi$
$613$	12.5637	−	12.5637i	0.507444	−	0.507444i	0.913741	+	0.406297i	$0.133180\pi$
$614$	1.35400	+	9.42962i	0.0546430	+	0.380549i
$615$		−	4.37494i		−	0.176415i
$616$	−50.6492	+	23.0969i	−2.04072	+	0.930600i
$617$			21.4382i			0.863069i	0.902096	+	0.431535i	$0.142028\pi$
$617$			21.4382i			0.863069i	−0.902096	+	0.431535i	$0.857972\pi$
$618$	−20.0055	+	2.87259i	−0.804740	+	0.115553i
$619$	−24.6780	+	24.6780i	−0.991891	+	0.991891i	−0.999967	−	0.00807682i	$-0.997429\pi$
$619$	−24.6780	+	24.6780i	−0.991891	+	0.991891i	0.00807682	+	0.999967i	$0.497429\pi$
$620$	3.28498	+	1.79531i	0.131928	+	0.0721013i
$621$	−3.15665	−	3.15665i	−0.126672	−	0.126672i
$622$	3.64215	−	4.86347i	0.146037	−	0.195008i
$623$	−1.81613			−0.0727619
$624$	−6.68640	−	10.4211i	−0.267670	−	0.417179i
$625$	−23.5786			−0.943146
$626$	−3.02094	+	4.03395i	−0.120741	+	0.161229i
$627$	−3.66549	−	3.66549i	−0.146385	−	0.146385i
$628$	−14.0704	+	25.7455i	−0.561471	+	1.02736i
$629$	−4.96211	+	4.96211i	−0.197852	+	0.197852i
$630$	−2.54065	+	0.364812i	−0.101222	+	0.0145345i
$631$		−	41.8888i		−	1.66757i	−0.552091	−	0.833784i	$-0.686170\pi$
$631$		−	41.8888i		−	1.66757i	0.552091	−	0.833784i	$-0.313830\pi$
$632$	1.17933	−	3.15656i	0.0469111	−	0.125561i
$633$			23.8108i			0.946394i
$634$	−1.13103	−	7.87680i	−0.0449190	−	0.312828i
$635$	3.65114	−	3.65114i	0.144891	−	0.144891i
$636$	−3.40465	−	11.6110i	−0.135003	−	0.460406i
$637$	−20.3058	−	20.3058i	−0.804546	−	0.804546i
$638$	16.0831	+	12.0443i	0.636736	+	0.476838i
$639$	−9.07235			−0.358896
$640$	2.93672	+	1.89267i	0.116084	+	0.0748145i
$641$	−13.0370			−0.514931			−0.257466	−	0.966287i	$-0.582887\pi$
$641$	−13.0370			−0.514931			−0.257466	+	0.966287i	$0.582887\pi$
$642$	−19.6035	−	14.6807i	−0.773690	−	0.579400i
$643$	23.2630	+	23.2630i	0.917403	+	0.917403i	0.996840	−	0.0794366i	$-0.0253121\pi$
$643$	23.2630	+	23.2630i	0.917403	+	0.917403i	−0.0794366	+	0.996840i	$0.525312\pi$
$644$	1.95542	+	6.66864i	0.0770543	+	0.262781i
$645$	−1.92601	+	1.92601i	−0.0758367	+	0.0758367i
$646$	0.179315	+	1.24879i	0.00705504	+	0.0491332i
$647$		−	16.7115i		−	0.656995i	−0.944505	−	0.328498i	$-0.893458\pi$
$647$		−	16.7115i		−	0.656995i	0.944505	−	0.328498i	$-0.106542\pi$
$648$	3.08757	−	8.26414i	0.121291	−	0.324646i
$649$		−	24.4627i		−	0.960246i
$650$	16.5526	−	2.37678i	0.649245	−	0.0932251i
$651$	−23.9308	+	23.9308i	−0.937922	+	0.937922i
$652$	11.3903	−	20.8415i	0.446079	−	0.816218i
$653$	−29.3006	−	29.3006i	−1.14662	−	1.14662i	−0.987213	−	0.159410i	$-0.949041\pi$
$653$	−29.3006	−	29.3006i	−1.14662	−	1.14662i	−0.159410	−	0.987213i	$-0.550959\pi$
$654$	12.4228	−	16.5885i	0.485769	−	0.648663i
$655$	5.73862			0.224226
$656$	23.8344	+	37.1472i	0.930576	+	1.45035i
$657$	−13.7555			−0.536652
$658$	39.8841	−	53.2584i	1.55484	−	2.07623i
$659$	−13.1348	−	13.1348i	−0.511658	−	0.511658i	0.403376	−	0.915034i	$-0.367837\pi$
$659$	−13.1348	−	13.1348i	−0.511658	−	0.511658i	−0.915034	+	0.403376i	$0.867837\pi$
$660$	−3.14926	−	1.72113i	−0.122585	−	0.0669950i
$661$	7.62442	−	7.62442i	0.296556	−	0.296556i	−0.543107	−	0.839663i	$-0.682752\pi$
$661$	7.62442	−	7.62442i	0.296556	−	0.296556i	0.839663	+	0.543107i	$0.182752\pi$
$662$	14.1921	−	2.03785i	0.551592	−	0.0792032i
$663$		−	3.09544i		−	0.120217i
$664$	−1.12959	+	0.515110i	−0.0438365	+	0.0199902i
$665$			1.19801i			0.0464568i
$666$	1.90633	+	13.2762i	0.0738687	+	0.514442i
$667$	1.77371	−	1.77371i	0.0686782	−	0.0686782i
$668$	29.8514	−	8.75319i	1.15498	−	0.338671i
$669$	−5.92793	−	5.92793i	−0.229187	−	0.229187i
$670$	3.92527	+	2.93955i	0.151646	+	0.113565i
$671$	20.2485			0.781683
$672$	−23.8896	+	20.6619i	−0.921560	+	0.797050i
$673$	22.8894			0.882321			0.441161	−	0.897428i	$-0.354567\pi$
$673$	22.8894			0.882321			0.441161	+	0.897428i	$0.354567\pi$
$674$	12.2635	+	9.18384i	0.472371	+	0.353748i
$675$	19.3765	+	19.3765i	0.745803	+	0.745803i
$676$	13.7945	−	4.04492i	0.530560	−	0.155574i
$677$	14.2701	−	14.2701i	0.548445	−	0.548445i	−0.377546	−	0.925991i	$-0.623232\pi$
$677$	14.2701	−	14.2701i	0.548445	−	0.548445i	0.925991	+	0.377546i	$0.123232\pi$
$678$	−3.59278	−	25.0211i	−0.137980	−	0.960928i
$679$			5.58348i			0.214274i
$680$	0.362403	+	0.794715i	0.0138975	+	0.0304759i
$681$		−	22.7246i		−	0.870809i
$682$	38.4006	−	5.51395i	1.47044	−	0.211140i
$683$	25.2551	−	25.2551i	0.966359	−	0.966359i	−0.0330936	−	0.999452i	$-0.510536\pi$
$683$	25.2551	−	25.2551i	0.966359	−	0.966359i	0.999452	+	0.0330936i	$0.0105360\pi$
$684$	2.11590	+	1.15638i	0.0809034	+	0.0442153i
$685$	−4.20279	−	4.20279i	−0.160580	−	0.160580i
$686$	−18.1056	+	24.1769i	−0.691273	+	0.923078i
$687$	3.68417			0.140560
$688$	5.86081	−	26.8464i	0.223441	−	1.02351i
$689$	−11.3600			−0.432781
$690$	−0.268563	+	0.358620i	−0.0102240	+	0.0136524i
$691$	−12.1865	−	12.1865i	−0.463598	−	0.463598i	0.436235	−	0.899833i	$-0.356312\pi$
$691$	−12.1865	−	12.1865i	−0.463598	−	0.463598i	−0.899833	+	0.436235i	$0.856312\pi$
$692$	5.86649	−	10.7343i	0.223011	−	0.408056i
$693$	−18.8082	+	18.8082i	−0.714463	+	0.714463i
$694$	−23.7745	+	3.41378i	−0.902468	+	0.129586i
$695$			4.44057i			0.168440i
$696$	10.6797	+	3.99005i	0.404812	+	0.151242i
$697$			11.0340i			0.417943i
$698$	5.66220	+	39.4331i	0.214318	+	1.49257i
$699$	−13.8965	+	13.8965i	−0.525615	+	0.525615i
$700$	−12.0030	−	40.9343i	−0.453670	−	1.54717i
$701$	−9.64948	−	9.64948i	−0.364456	−	0.364456i	0.500995	−	0.865450i	$-0.332968\pi$
$701$	−9.64948	−	9.64948i	−0.364456	−	0.364456i	−0.865450	+	0.500995i	$0.832968\pi$
$702$	−15.2475	−	11.4185i	−0.575479	−	0.430963i
$703$	6.26021			0.236108
$704$	36.1167	−	2.54296i	1.36120	−	0.0958415i
$705$	4.28970			0.161559
$706$	−20.7836	−	15.5644i	−0.782201	−	0.585774i
$707$	−18.8303	−	18.8303i	−0.708186	−	0.708186i
$708$	−3.90555	−	13.3192i	−0.146780	−	0.500568i
$709$	8.08220	−	8.08220i	0.303533	−	0.303533i	−0.538861	−	0.842395i	$-0.681145\pi$
$709$	8.08220	−	8.08220i	0.303533	−	0.303533i	0.842395	+	0.538861i	$0.181145\pi$
$710$	0.416687	+	2.90192i	0.0156380	+	0.108907i
$711$		−	1.61009i		−	0.0603833i
$712$	1.10652	+	0.413407i	0.0414685	+	0.0154931i
$713$		−	4.84307i		−	0.181374i
$714$	−7.81613	+	1.12232i	−0.292511	+	0.0420018i
$715$	−2.38255	+	2.38255i	−0.0891024	+	0.0891024i
$716$	10.1834	−	18.6332i	0.380573	−	0.696357i
$717$	−6.07754	−	6.07754i	−0.226970	−	0.226970i
$718$	0.529066	−	0.706477i	0.0197446	−	0.0263655i
$719$	51.5501			1.92249			0.961246	−	0.275691i	$-0.0889067\pi$
$719$	51.5501			1.92249			0.961246	+	0.275691i	$0.0889067\pi$
$720$	1.63099	+	0.356059i	0.0607832	+	0.0132695i
$721$	48.4039			1.80265
$722$	−15.4320	+	20.6068i	−0.574318	+	0.766904i
$723$	25.1008	+	25.1008i	0.933508	+	0.933508i
$724$	27.8764	+	15.2350i	1.03602	+	0.566205i
$725$	−10.8876	+	10.8876i	−0.404354	+	0.404354i
$726$	−17.0433	+	2.44725i	−0.632536	+	0.0908259i
$727$			38.5213i			1.42868i	0.699801	+	0.714338i	$0.253272\pi$
$727$			38.5213i			1.42868i	−0.699801	+	0.714338i	$0.746728\pi$
$728$	12.3037	+	26.9809i	0.456007	+	0.999979i
$729$		−	25.7359i		−	0.953181i
$730$	0.631780	+	4.39989i	0.0233832	+	0.162847i
$731$	4.85759	−	4.85759i	0.179664	−	0.179664i
$732$	11.0247	−	3.23273i	0.407485	−	0.119485i
$733$	19.0332	+	19.0332i	0.703006	+	0.703006i	0.965055	−	0.262049i	$-0.0843981\pi$
$733$	19.0332	+	19.0332i	0.703006	+	0.703006i	−0.262049	+	0.965055i	$0.584398\pi$
$734$	3.93703	+	2.94835i	0.145318	+	0.108826i
$735$	−4.72280			−0.174203
$736$	0.326604	−	4.50812i	0.0120388	−	0.166172i
$737$	50.8196			1.87196
$738$	16.8803	+	12.6413i	0.621374	+	0.465334i
$739$	−21.8630	−	21.8630i	−0.804244	−	0.804244i	0.179512	−	0.983756i	$-0.442548\pi$
$739$	−21.8630	−	21.8630i	−0.804244	−	0.804244i	−0.983756	+	0.179512i	$0.942548\pi$
$740$	4.15902	−	1.21953i	0.152889	−	0.0448309i
$741$	−1.95261	+	1.95261i	−0.0717308	+	0.0717308i
$742$	4.11882	+	28.6845i	0.151206	+	1.05304i
$743$			7.33947i			0.269259i	0.990896	+	0.134629i	$0.0429844\pi$
$743$			7.33947i			0.269259i	−0.990896	+	0.134629i	$0.957016\pi$
$744$	20.0277	−	9.13296i	0.734251	−	0.334831i
$745$			6.78752i			0.248675i
$746$	−29.4428	+	4.22770i	−1.07798	+	0.154787i
$747$	−0.419463	+	0.419463i	−0.0153473	+	0.0153473i
$748$	7.94273	+	4.34086i	0.290415	+	0.158718i
$749$	41.4758	+	41.4758i	1.51549	+	1.51549i
$750$	3.32910	−	4.44545i	0.121562	−	0.162325i
$751$	−52.9939			−1.93378			−0.966888	−	0.255201i	$-0.917858\pi$
$751$	−52.9939			−1.93378			−0.966888	+	0.255201i	$0.917858\pi$
$752$	−36.4234	+	23.3700i	−1.32823	+	0.852216i
$753$	−26.4918			−0.965415
$754$	6.41600	−	8.56748i	0.233657	−	0.312009i
$755$	2.55772	+	2.55772i	0.0930850	+	0.0930850i
$756$	−23.3040	+	42.6406i	−0.847557	+	1.55082i
$757$	−24.6626	+	24.6626i	−0.896378	+	0.896378i	−0.995114	−	0.0987356i	$-0.968520\pi$
$757$	−24.6626	+	24.6626i	−0.896378	+	0.896378i	0.0987356	+	0.995114i	$0.468520\pi$
$758$	−24.3066	+	3.49018i	−0.882855	+	0.126769i
$759$			4.64297i			0.168529i
$760$	0.272703	−	0.729912i	0.00989198	−	0.0264767i
$761$		−	30.0495i		−	1.08929i	−0.838666	−	0.544646i	$-0.816664\pi$
$761$		−	30.0495i		−	1.08929i	0.838666	−	0.544646i	$-0.183336\pi$
$762$	−4.31526	−	30.0527i	−0.156326	−	1.08869i
$763$	−35.0968	+	35.0968i	−1.27059	+	1.27059i
$764$	−12.1240	−	41.3469i	−0.438630	−	1.49588i
$765$	0.295111	+	0.295111i	0.0106697	+	0.0106697i
$766$	−7.27243	−	5.44617i	−0.262764	−	0.196778i
$767$	−13.0313			−0.470533
$768$	19.2585	−	7.15071i	0.694931	−	0.258029i
$769$	−33.9419			−1.22398			−0.611988	−	0.790867i	$-0.709630\pi$
$769$	−33.9419			−1.22398			−0.611988	+	0.790867i	$0.709630\pi$
$770$	6.87991	+	5.15221i	0.247935	+	0.185673i
$771$	−1.69458	−	1.69458i	−0.0610288	−	0.0610288i
$772$	3.79161	+	12.9307i	0.136463	+	0.465385i
$773$	−22.2311	+	22.2311i	−0.799596	+	0.799596i	−0.983032	−	0.183436i	$-0.941278\pi$
$773$	−22.2311	+	22.2311i	−0.799596	+	0.799596i	0.183436	+	0.983032i	$0.441278\pi$
$774$	−1.86617	−	12.9965i	−0.0670783	−	0.467151i
$775$			29.7283i			1.06787i
$776$	1.27097	−	3.40185i	0.0456251	−	0.122119i
$777$			39.1823i			1.40566i
$778$	−5.34850	+	0.767991i	−0.191753	+	0.0275338i
$779$	6.96028	−	6.96028i	0.249378	−	0.249378i
$780$	−0.916849	+	1.67761i	−0.0328284	+	0.0600682i
$781$	21.4826	+	21.4826i	0.768708	+	0.768708i
$782$	0.677341	−	0.904474i	0.0242217	−	0.0323439i
$783$	17.5398			0.626820
$784$	40.1008	−	25.7295i	1.43217	−	0.918910i
$785$	4.53016			0.161688
$786$	20.2262	−	27.0086i	0.721444	−	0.963365i
$787$	2.95532	+	2.95532i	0.105346	+	0.105346i	0.757815	−	0.652469i	$-0.226267\pi$
$787$	2.95532	+	2.95532i	0.105346	+	0.105346i	−0.652469	+	0.757815i	$0.726267\pi$
$788$	−10.6547	−	5.82300i	−0.379557	−	0.207436i
$789$	−18.8035	+	18.8035i	−0.669421	+	0.669421i
$790$	−0.515012	+	0.0739506i	−0.0183233	+	0.00263104i
$791$			60.5391i			2.15252i
$792$	15.7406	−	7.17796i	0.559317	−	0.255058i
$793$		−	10.7864i		−	0.383035i
$794$	−6.66774	−	46.4359i	−0.236629	−	1.64795i
$795$	−1.32107	+	1.32107i	−0.0468536	+	0.0468536i
$796$	−23.2974	+	6.83139i	−0.825753	+	0.242132i
$797$	−34.3544	−	34.3544i	−1.21690	−	1.21690i	−0.968713	−	0.248183i	$-0.920166\pi$
$797$	−34.3544	−	34.3544i	−1.21690	−	1.21690i	−0.248183	−	0.968713i	$-0.579834\pi$
$798$	5.63839	+	4.22247i	0.199597	+	0.149474i
$799$	−10.8190			−0.382750
$800$	−2.00480	+	27.6723i	−0.0708804	+	0.978363i
$801$	0.564411			0.0199425
$802$	2.02036	+	1.51300i	0.0713414	+	0.0534260i
$803$	32.5719	+	32.5719i	1.14944	+	1.14944i
$804$	27.6698	−	8.11350i	0.975838	−	0.286141i
$805$	0.758743	−	0.758743i	0.0267422	−	0.0267422i
$806$	−2.93729	−	20.4560i	−0.103461	−	0.720533i
$807$		−	2.65215i		−	0.0933600i
$808$	7.18641	+	15.7591i	0.252817	+	0.554403i
$809$			47.8299i			1.68161i	0.541338	+	0.840805i	$0.317918\pi$
$809$			47.8299i			1.68161i	−0.541338	+	0.840805i	$0.682082\pi$
$810$	−1.34834	+	0.193609i	−0.0473759	+	0.00680272i
$811$	4.34921	−	4.34921i	0.152721	−	0.152721i	−0.626611	−	0.779332i	$-0.715558\pi$
$811$	4.34921	−	4.34921i	0.152721	−	0.152721i	0.779332	+	0.626611i	$0.215558\pi$
$812$	−23.9596	−	13.0944i	−0.840816	−	0.459523i
$813$	4.65740	+	4.65740i	0.163342	+	0.163342i
$814$	26.9229	−	35.9510i	0.943649	−	1.26008i
$815$	−3.66727			−0.128459
$816$	5.01762	+	1.09539i	0.175652	+	0.0383464i
$817$	−6.12835			−0.214404
$818$	−26.7250	+	35.6867i	−0.934418	+	1.24776i
$819$	10.0191	+	10.0191i	0.350097	+	0.350097i
$820$	3.26820	−	5.98003i	0.114131	−	0.208832i
$821$	18.0908	−	18.0908i	0.631373	−	0.631373i	−0.317040	−	0.948412i	$-0.602689\pi$
$821$	18.0908	−	18.0908i	0.631373	−	0.631373i	0.948412	+	0.317040i	$0.102689\pi$
$822$	−34.5933	+	4.96726i	−1.20658	+	0.173253i
$823$			7.20992i			0.251322i	0.992073	+	0.125661i	$0.0401052\pi$
$823$			7.20992i			0.251322i	−0.992073	+	0.125661i	$0.959895\pi$
$824$	−29.4911	−	11.0182i	−1.02737	−	0.383837i
$825$		−	28.5001i		−	0.992245i
$826$	4.72479	+	32.9047i	0.164396	+	1.14490i
$827$	22.4550	−	22.4550i	0.780838	−	0.780838i	−0.199134	−	0.979972i	$-0.563813\pi$
$827$	22.4550	−	22.4550i	0.780838	−	0.780838i	0.979972	+	0.199134i	$0.0638129\pi$
$828$	−0.607697	−	2.07245i	−0.0211189	−	0.0720228i
$829$	39.3070	+	39.3070i	1.36519	+	1.36519i	0.867164	+	0.498023i	$0.165941\pi$
$829$	39.3070	+	39.3070i	1.36519	+	1.36519i	0.498023	+	0.867164i	$0.334059\pi$
$830$	0.153437	+	0.114905i	0.00532587	+	0.00398843i
$831$	19.0047			0.659265
$832$	−1.35464	−	19.2394i	−0.0469636	−	0.667005i
$833$	11.9113			0.412704
$834$	20.8994	+	15.6511i	0.723686	+	0.541953i
$835$	−3.39642	−	3.39642i	−0.117538	−	0.117538i
$836$	−2.27206	−	7.74851i	−0.0785810	−	0.267988i
$837$	23.9460	−	23.9460i	0.827694	−	0.827694i
$838$	4.12112	+	28.7006i	0.142362	+	0.991446i
$839$			3.29065i			0.113606i	0.998385	+	0.0568030i	$0.0180907\pi$
$839$			3.29065i			0.113606i	−0.998385	+	0.0568030i	$0.981909\pi$
$840$	4.56848	+	1.70683i	0.157627	+	0.0588913i
$841$		−	19.1445i		−	0.660155i
$842$	−23.9522	+	3.43931i	−0.825449	+	0.118526i
$843$	−17.5296	+	17.5296i	−0.603753	+	0.603753i
$844$	−17.7873	+	32.5465i	−0.612265	+	1.12030i
$845$	−1.56951	−	1.56951i	−0.0539929	−	0.0539929i
$846$	−12.3950	+	16.5514i	−0.426149	+	0.569050i
$847$	41.2367			1.41691
$848$	4.01999	−	18.4142i	0.138047	−	0.632347i
$849$	−24.0130			−0.824125
$850$	−4.15774	+	5.55195i	−0.142609	+	0.190430i
$851$	−3.96482	−	3.96482i	−0.135912	−	0.135912i
$852$	15.1264	+	8.26690i	0.518223	+	0.283219i
$853$	−1.60651	+	1.60651i	−0.0550057	+	0.0550057i	−0.734075	−	0.679069i	$-0.762384\pi$
$853$	−1.60651	+	1.60651i	−0.0550057	+	0.0550057i	0.679069	+	0.734075i	$0.262384\pi$
$854$	−27.2361	+	3.91084i	−0.932000	+	0.133826i
$855$		−	0.372313i		−	0.0127328i
$856$	−15.8288	−	34.7111i	−0.541019	−	1.18640i
$857$		−	12.2042i		−	0.416888i	−0.978034	−	0.208444i	$-0.933160\pi$
$857$		−	12.2042i		−	0.416888i	0.978034	−	0.208444i	$-0.0668399\pi$
$858$	2.81593	+	19.6109i	0.0961342	+	0.669504i
$859$	34.5224	−	34.5224i	1.17789	−	1.17789i	0.197610	−	0.980281i	$-0.436682\pi$
$859$	34.5224	−	34.5224i	1.17789	−	1.17789i	0.980281	−	0.197610i	$-0.0633179\pi$
$860$	−4.07142	+	1.19385i	−0.138834	+	0.0407098i
$861$	43.5640	+	43.5640i	1.48466	+	1.48466i
$862$	29.2949	+	21.9383i	0.997787	+	0.747221i
$863$	−10.3155			−0.351145			−0.175573	−	0.984466i	$-0.556178\pi$
$863$	−10.3155			−0.351145			−0.175573	+	0.984466i	$0.556178\pi$
$864$	23.9047	−	20.6750i	0.813255	−	0.703378i
$865$	−1.88880			−0.0642210
$866$	21.7625	+	16.2975i	0.739521	+	0.553811i
$867$	0.907888	+	0.907888i	0.0308335	+	0.0308335i
$868$	−50.5875	+	14.8336i	−1.71705	+	0.503485i
$869$	−3.81258	+	3.81258i	−0.129333	+	0.129333i
$870$	−0.250199	−	1.74245i	−0.00848255	−	0.0590747i
$871$		−	27.0716i		−	0.917287i
$872$	29.3726	−	13.3944i	0.994681	−	0.453591i
$873$		−	1.73521i		−	0.0587280i
$874$	−0.997811	+	0.143276i	−0.0337515	+	0.00484638i
$875$	−9.40537	+	9.40537i	−0.317960	+	0.317960i
$876$	22.9347	+	12.5343i	0.774891	+	0.423493i
$877$	21.8446	+	21.8446i	0.737640	+	0.737640i	0.972121	−	0.234481i	$-0.0753390\pi$
$877$	21.8446	+	21.8446i	0.737640	+	0.737640i	−0.234481	+	0.972121i	$0.575339\pi$
$878$	27.8546	−	37.1950i	0.940046	−	1.25527i
$879$	−12.2574			−0.413433
$880$	−3.01893	−	4.70517i	−0.101768	−	0.158611i
$881$	16.4331			0.553646			0.276823	−	0.960921i	$-0.410718\pi$
$881$	16.4331			0.553646			0.276823	+	0.960921i	$0.410718\pi$
$882$	13.6465	−	18.2225i	0.459500	−	0.613584i
$883$	−17.9848	−	17.9848i	−0.605237	−	0.605237i	0.336460	−	0.941698i	$-0.390770\pi$
$883$	−17.9848	−	17.9848i	−0.605237	−	0.605237i	−0.941698	+	0.336460i	$0.890770\pi$
$884$	2.31238	−	4.23110i	0.0777737	−	0.142307i
$885$	−1.51543	+	1.51543i	−0.0509407	+	0.0509407i
$886$	−19.3864	+	2.78370i	−0.651299	+	0.0935202i
$887$		−	15.6846i		−	0.526636i	−0.964709	−	0.263318i	$-0.915183\pi$
$887$		−	15.6846i		−	0.526636i	0.964709	−	0.263318i	$-0.0848169\pi$
$888$	8.91907	−	23.8726i	0.299304	−	0.801113i
$889$			72.7132i			2.43872i
$890$	−0.0259230	−	0.180535i	−0.000868942	−	0.00605154i
$891$	−9.98165	+	9.98165i	−0.334398	+	0.334398i
$892$	−3.67445	−	12.5311i	−0.123030	−	0.419572i
$893$	6.82466	+	6.82466i	0.228379	+	0.228379i
$894$	31.9452	+	23.9231i	1.06841	+	0.800108i
$895$	−3.27870			−0.109595
$896$	−48.0892	+	10.3962i	−1.60655	+	0.347312i
$897$	2.47332			0.0825816
$898$	21.8358	+	16.3524i	0.728671	+	0.545686i
$899$	13.4551	+	13.4551i	0.448754	+	0.448754i
$900$	3.73024	+	12.7214i	0.124341	+	0.424046i
$901$	3.33187	−	3.33187i	0.111001	−	0.111001i
$902$	−10.0377	−	69.9050i	−0.334218	−	2.32758i
$903$		−	38.3570i		−	1.27644i
$904$	13.7805	−	36.8847i	0.458334	−	1.22677i
$905$		−	4.90512i		−	0.163052i
$906$	21.0527	−	3.02296i	0.699429	−	0.100431i
$907$	−10.0361	+	10.0361i	−0.333243	+	0.333243i	−0.853817	−	0.520574i	$-0.825718\pi$
$907$	−10.0361	+	10.0361i	−0.333243	+	0.333243i	0.520574	+	0.853817i	$0.325718\pi$
$908$	16.9759	−	31.0618i	0.563366	−	1.03082i
$909$	5.85201	+	5.85201i	0.194099	+	0.194099i
$910$	2.74459	−	3.66493i	0.0909822	−	0.121491i
$911$	−12.7630			−0.422858			−0.211429	−	0.977393i	$-0.567812\pi$
$911$	−12.7630			−0.422858			−0.211429	+	0.977393i	$0.567812\pi$
$912$	−2.47415	−	3.85609i	−0.0819271	−	0.127688i
$913$	1.98651			0.0657439
$914$	−0.0729307	+	0.0973866i	−0.00241233	+	0.00322126i
$915$	−1.25437	−	1.25437i	−0.0414680	−	0.0414680i
$916$	5.03582	+	2.75218i	0.166388	+	0.0909345i
$917$	−57.1429	+	57.1429i	−1.88703	+	1.88703i
$918$	7.82109	−	1.12303i	0.258135	−	0.0370656i
$919$		−	17.9165i		−	0.591012i	−0.955341	−	0.295506i	$-0.904512\pi$
$919$		−	17.9165i		−	0.591012i	0.955341	−	0.295506i	$-0.0954882\pi$
$920$	−0.634993	+	0.289567i	−0.0209351	+	0.00954675i
$921$		−	8.64885i		−	0.284989i
$922$	2.90432	+	20.2264i	0.0956486	+	0.666123i
$923$	11.4438	−	11.4438i	0.376678	−	0.376678i
$924$	48.4974	−	14.2207i	1.59545	−	0.467827i
$925$	24.3373	+	24.3373i	0.800206	+	0.800206i
$926$	35.8413	+	26.8408i	1.17782	+	0.882043i
$927$	−15.0428			−0.494069
$928$	11.6172	+	13.4319i	0.381353	+	0.440925i
$929$	−6.07092			−0.199180			−0.0995902	−	0.995029i	$-0.531753\pi$
$929$	−6.07092			−0.199180			−0.0995902	+	0.995029i	$0.531753\pi$
$930$	−2.72045	−	2.03729i	−0.0892071	−	0.0668052i
$931$	−7.51370	−	7.51370i	−0.246251	−	0.246251i
$932$	−29.3760	+	8.61381i	−0.962243	+	0.282155i
$933$	−3.90068	+	3.90068i	−0.127703	+	0.127703i
$934$	−1.31211	−	9.13789i	−0.0429336	−	0.299001i
$935$		−	1.39760i		−	0.0457064i
$936$	−3.82371	−	8.38502i	−0.124982	−	0.274073i
$937$		−	6.43148i		−	0.210107i	−0.994467	−	0.105054i	$-0.966499\pi$
$937$		−	6.43148i		−	0.210107i	0.994467	−	0.105054i	$-0.0335014\pi$
$938$	−68.3572	+	9.81542i	−2.23194	+	0.320485i
$939$	3.23538	−	3.23538i	0.105582	−	0.105582i
$940$	5.86351	+	3.20453i	0.191247	+	0.104520i
$941$	29.4367	+	29.4367i	0.959609	+	0.959609i	0.999215	−	0.0396060i	$-0.0126103\pi$
$941$	29.4367	+	29.4367i	0.959609	+	0.959609i	−0.0396060	+	0.999215i	$0.512610\pi$
$942$	15.9669	−	21.3211i	0.520229	−	0.694678i
$943$	−8.81639			−0.287101
$944$	4.61143	−	21.1234i	0.150089	−	0.687507i
$945$	7.50303			0.244073
$946$	−26.3559	+	35.1938i	−0.856903	+	1.14425i
$947$	−19.5143	−	19.5143i	−0.634129	−	0.634129i	0.314972	−	0.949101i	$-0.398005\pi$
$947$	−19.5143	−	19.5143i	−0.634129	−	0.634129i	−0.949101	+	0.314972i	$0.898005\pi$
$948$	−1.46715	+	2.68453i	−0.0476508	+	0.0871895i
$949$	17.3511	−	17.3511i	0.563240	−	0.563240i
$950$	6.12488	−	0.879473i	0.198717	−	0.0285339i
$951$			7.22460i			0.234274i
$952$	−11.5221	−	4.30479i	−0.373434	−	0.139519i
$953$			23.1990i			0.751488i	0.926723	+	0.375744i	$0.122613\pi$
$953$			23.1990i			0.751488i	−0.926723	+	0.375744i	$0.877387\pi$
$954$	−1.28003	−	8.91447i	−0.0414425	−	0.288616i
$955$	−4.70436	+	4.70436i	−0.152229	+	0.152229i
$956$	−3.76719	−	12.8474i	−0.121839	−	0.415514i
$957$	−12.8992	−	12.8992i	−0.416972	−	0.416972i
$958$	9.52916	+	7.13618i	0.307873	+	0.230560i
$959$	83.6995			2.70280
$960$	−2.39491	−	2.07985i	−0.0772955	−	0.0671268i
$961$	5.73897			0.185128
$962$	−19.1511	−	14.3419i	−0.617458	−	0.462401i
$963$	−12.8897	−	12.8897i	−0.415364	−	0.415364i
$964$	15.5588	+	53.0608i	0.501115	+	1.70897i
$965$	1.47122	−	1.47122i	0.0473603	−	0.0473603i
$966$	−0.896755	−	6.24524i	−0.0288526	−	0.200937i
$967$		−	10.6813i		−	0.343489i	−0.985142	−	0.171744i	$-0.945060\pi$
$967$		−	10.6813i		−	0.343489i	0.985142	−	0.171744i	$-0.0549403\pi$
$968$	−25.1243	−	9.38672i	−0.807526	−	0.301700i
$969$		−	1.14539i		−	0.0367954i
$970$	−0.555032	+	0.0796972i	−0.0178210	+	0.00255892i
$971$	−15.7703	+	15.7703i	−0.506093	+	0.506093i	−0.913325	−	0.407232i	$-0.866494\pi$
$971$	−15.7703	+	15.7703i	−0.506093	+	0.506093i	0.407232	+	0.913325i	$0.366494\pi$
$972$	12.2353	−	22.3877i	0.392448	−	0.718085i
$973$	−44.2174	−	44.2174i	−1.41755	−	1.41755i
$974$	−33.1662	+	44.2878i	−1.06271	+	1.41907i
$975$	−15.1820			−0.486213
$976$	17.4844	+	3.81700i	0.559662	+	0.122179i
$977$	11.7332			0.375378			0.187689	−	0.982229i	$-0.439900\pi$
$977$	11.7332			0.375378			0.187689	+	0.982229i	$0.439900\pi$
$978$	−12.9255	+	17.2599i	−0.413313	+	0.551910i
$979$	−1.33648	−	1.33648i	−0.0427141	−	0.0427141i
$980$	−6.45551	−	3.52806i	−0.206214	−	0.112700i
$981$	10.9073	−	10.9073i	0.348242	−	0.348242i
$982$	19.4128	−	2.78748i	0.619486	−	0.0889521i
$983$			3.41187i			0.108822i	0.998519	+	0.0544108i	$0.0173281\pi$
$983$			3.41187i			0.108822i	−0.998519	+	0.0544108i	$0.982672\pi$
$984$	−16.6258	−	36.4587i	−0.530010	−	1.16226i
$985$			1.87479i			0.0597359i
$986$	0.631026	+	4.39463i	0.0200960	+	0.139954i
$987$	−42.7152	+	42.7152i	−1.35964	+	1.35964i
$988$	−4.12764	+	1.21033i	−0.131318	+	0.0385057i
$989$	3.88131	+	3.88131i	0.123418	+	0.123418i
$990$	−2.13811	−	1.60118i	−0.0679536	−	0.0508890i
$991$	−12.5692			−0.399272			−0.199636	−	0.979870i	$-0.563976\pi$
$991$	−12.5692			−0.399272			−0.199636	+	0.979870i	$0.563976\pi$
$992$	34.1981	+	2.47758i	1.08579	+	0.0786633i
$993$	−13.0170			−0.413082
$994$	−33.0454	−	24.7470i	−1.04814	−	0.784926i
$995$	2.65072	+	2.65072i	0.0840335	+	0.0840335i
$996$	1.08160	−	0.317153i	0.0342717	−	0.0100494i
$997$	−22.4744	+	22.4744i	−0.711773	+	0.711773i	−0.966906	−	0.255133i	$-0.917881\pi$
$997$	−22.4744	+	22.4744i	−0.711773	+	0.711773i	0.255133	+	0.966906i	$0.417881\pi$
$998$	−0.0338548	−	0.235774i	−0.00107166	−	0.00746330i
$999$		−	39.2071i		−	1.24046i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	272.2.l.b.205.3	yes	30
4.3	odd	2		1088.2.l.b.273.5		30
16.5	even	4	inner	272.2.l.b.69.3	✓	30
16.11	odd	4		1088.2.l.b.817.5		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
272.2.l.b.69.3	✓	30	16.5	even	4	inner
272.2.l.b.205.3	yes	30	1.1	even	1	trivial
1088.2.l.b.273.5		30	4.3	odd	2
1088.2.l.b.817.5		30	16.11	odd	4

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:	\( N \)	\(=\)	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	272.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13198 - 0.847715i) q^{2} +(0.907888 + 0.907888i) q^{3} +(0.562758 + 1.91919i) q^{4} +(0.218362 - 0.218362i) q^{5} +(-0.258081 - 1.79734i) q^{6} +4.34872i q^{7} +(0.989900 - 2.64955i) q^{8} -1.35148i q^{9} +(-0.432289 + 0.0620725i) q^{10} +(-3.20019 + 3.20019i) q^{11} +(-1.23149 + 2.25333i) q^{12} +(1.70475 + 1.70475i) q^{13} +(3.68647 - 4.92266i) q^{14} +0.396496 q^{15} +(-3.36661 + 2.16008i) q^{16} -1.00000 q^{17} +(-1.14567 + 1.52985i) q^{18} +(0.630802 + 0.630802i) q^{19} +(0.541963 + 0.296193i) q^{20} +(-3.94815 + 3.94815i) q^{21} +(6.33541 - 0.909702i) q^{22} -0.799019i q^{23} +(3.30421 - 1.50677i) q^{24} +4.90464i q^{25} +(-0.484599 - 3.37488i) q^{26} +(3.95066 - 3.95066i) q^{27} +(-8.34603 + 2.44727i) q^{28} +(2.21985 + 2.21985i) q^{29} +(-0.448825 - 0.336116i) q^{30} +6.06127 q^{31} +(5.64207 + 0.408756i) q^{32} -5.81084 q^{33} +(1.13198 + 0.847715i) q^{34} +(0.949593 + 0.949593i) q^{35} +(2.59375 - 0.760554i) q^{36} +(4.96211 - 4.96211i) q^{37} +(-0.179315 - 1.24879i) q^{38} +3.09544i q^{39} +(-0.362403 - 0.794715i) q^{40} -11.0340i q^{41} +(7.81613 - 1.12232i) q^{42} +(-4.85759 + 4.85759i) q^{43} +(-7.94273 - 4.34086i) q^{44} +(-0.295111 - 0.295111i) q^{45} +(-0.677341 + 0.904474i) q^{46} +10.8190 q^{47} +(-5.01762 - 1.09539i) q^{48} -11.9113 q^{49} +(4.15774 - 5.55195i) q^{50} +(-0.907888 - 0.907888i) q^{51} +(-2.31238 + 4.23110i) q^{52} +(-3.33187 + 3.33187i) q^{53} +(-7.82109 + 1.12303i) q^{54} +1.39760i q^{55} +(11.5221 + 4.30479i) q^{56} +1.14539i q^{57} +(-0.631026 - 4.39463i) q^{58} +(-3.82207 + 3.82207i) q^{59} +(0.223131 + 0.760952i) q^{60} +(-3.16363 - 3.16363i) q^{61} +(-6.86123 - 5.13823i) q^{62} +5.87719 q^{63} +(-6.04020 - 5.24557i) q^{64} +0.744502 q^{65} +(6.57775 + 4.92594i) q^{66} +(-7.94007 - 7.94007i) q^{67} +(-0.562758 - 1.91919i) q^{68} +(0.725420 - 0.725420i) q^{69} +(-0.269936 - 1.87990i) q^{70} -6.71291i q^{71} +(-3.58080 - 1.33783i) q^{72} -10.1781i q^{73} +(-9.82346 + 1.41055i) q^{74} +(-4.45286 + 4.45286i) q^{75} +(-0.855642 + 1.56562i) q^{76} +(-13.9167 - 13.9167i) q^{77} +(2.62405 - 3.50397i) q^{78} +1.19136 q^{79} +(-0.263459 + 1.20682i) q^{80} +3.11908 q^{81} +(-9.35371 + 12.4903i) q^{82} +(-0.310373 - 0.310373i) q^{83} +(-9.79912 - 5.35541i) q^{84} +(-0.218362 + 0.218362i) q^{85} +(9.61654 - 1.38084i) q^{86} +4.03076i q^{87} +(5.31119 + 11.6469i) q^{88} +0.417625i q^{89} +(0.0838896 + 0.584229i) q^{90} +(-7.41346 + 7.41346i) q^{91} +(1.53347 - 0.449654i) q^{92} +(5.50295 + 5.50295i) q^{93} +(-12.2469 - 9.17146i) q^{94} +0.275486 q^{95} +(4.75126 + 5.49347i) q^{96} +1.28394 q^{97} +(13.4834 + 10.0974i) q^{98} +(4.32499 + 4.32499i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} + 8 q^{6} + 2 q^{8} - 6 q^{10} - 10 q^{11} - 2 q^{12} - 6 q^{13} - 22 q^{14} - 28 q^{15} + 2 q^{16} - 30 q^{17} + 8 q^{18} + 10 q^{19} - 10 q^{20} - 4 q^{21}+ \cdots + 54 q^{99}+O(q^{100}) \) 30 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 + 8 * q^6 + 2 * q^8 - 6 * q^10 - 10 * q^11 - 2 * q^12 - 6 * q^13 - 22 * q^14 - 28 * q^15 + 2 * q^16 - 30 * q^17 + 8 * q^18 + 10 * q^19 - 10 * q^20 - 4 * q^21 + 28 * q^22 + 18 * q^24 + 6 * q^26 + 4 * q^27 + 8 * q^28 - 18 * q^29 - 56 * q^30 + 48 * q^31 - 38 * q^32 - 12 * q^33 - 2 * q^34 + 16 * q^35 + 20 * q^36 + 6 * q^37 + 42 * q^38 + 10 * q^40 + 12 * q^42 + 2 * q^43 + 22 * q^44 + 42 * q^45 - 14 * q^46 - 32 * q^47 - 62 * q^48 - 38 * q^49 - 28 * q^50 + 2 * q^51 - 10 * q^52 - 6 * q^53 + 40 * q^54 + 96 * q^56 + 62 * q^58 - 14 * q^59 - 28 * q^60 + 6 * q^61 - 74 * q^62 + 84 * q^63 - 38 * q^64 - 12 * q^65 + 26 * q^67 + 2 * q^68 + 12 * q^69 + 48 * q^70 + 44 * q^72 + 42 * q^74 - 26 * q^75 - 38 * q^76 - 28 * q^77 - 56 * q^78 - 72 * q^79 - 38 * q^80 - 10 * q^81 - 76 * q^82 - 34 * q^83 + 104 * q^84 + 2 * q^85 + 34 * q^86 - 2 * q^88 + 70 * q^90 + 16 * q^91 - 40 * q^92 - 24 * q^93 - 44 * q^94 + 76 * q^95 - 126 * q^96 - 28 * q^97 - 30 * q^98 + 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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