LMFDB - Embedded newform 280.2.w.a.43.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(43,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("280.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.w (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.5
Character	$\chi$	$=$	280.43
Dual form			280.2.w.a.267.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27334 - 0.615319i) q^{2} +(-1.25131 - 1.25131i) q^{3} +(1.24277 + 1.56701i) q^{4} +(-0.429301 + 2.19447i) q^{5} +(0.823380 + 2.36328i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.618244 - 2.76003i) q^{8} +0.131530i q^{9} +O(q^{10})$	\(q+(-1.27334 - 0.615319i) q^{2} +(-1.25131 - 1.25131i) q^{3} +(1.24277 + 1.56701i) q^{4} +(-0.429301 + 2.19447i) q^{5} +(0.823380 + 2.36328i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.618244 - 2.76003i) q^{8} +0.131530i q^{9} +(1.89694 - 2.53014i) q^{10} +5.96709 q^{11} +(0.405734 - 3.51589i) q^{12} +(-1.91409 + 1.91409i) q^{13} +(0.465288 + 1.33548i) q^{14} +(3.28314 - 2.20877i) q^{15} +(-0.911068 + 3.89486i) q^{16} +(3.17333 - 3.17333i) q^{17} +(0.0809332 - 0.167482i) q^{18} -5.13375i q^{19} +(-3.97229 + 2.05449i) q^{20} +1.76961i q^{21} +(-7.59811 - 3.67166i) q^{22} +(5.58599 - 5.58599i) q^{23} +(-2.68003 + 4.22725i) q^{24} +(-4.63140 - 1.88418i) q^{25} +(3.61505 - 1.25950i) q^{26} +(-3.58933 + 3.58933i) q^{27} +(0.229279 - 1.98681i) q^{28} -1.99216 q^{29} +(-5.53963 + 0.792322i) q^{30} -7.70084i q^{31} +(3.55668 - 4.39887i) q^{32} +(-7.46666 - 7.46666i) q^{33} +(-5.99332 + 2.08810i) q^{34} +(1.85529 - 1.24816i) q^{35} +(-0.206110 + 0.163462i) q^{36} +(3.10699 + 3.10699i) q^{37} +(-3.15889 + 6.53699i) q^{38} +4.79022 q^{39} +(6.32222 - 0.171833i) q^{40} +4.51513 q^{41} +(1.08888 - 2.25331i) q^{42} +(2.55955 + 2.55955i) q^{43} +(7.41570 + 9.35052i) q^{44} +(-0.288640 - 0.0564662i) q^{45} +(-10.5500 + 3.67567i) q^{46} +(3.82891 + 3.82891i) q^{47} +(6.01369 - 3.73364i) q^{48} +1.00000i q^{49} +(4.73796 + 5.24898i) q^{50} -7.94161 q^{51} +(-5.37817 - 0.620641i) q^{52} +(6.09013 - 6.09013i) q^{53} +(6.77901 - 2.36184i) q^{54} +(-2.56168 + 13.0946i) q^{55} +(-1.51447 + 2.38880i) q^{56} +(-6.42389 + 6.42389i) q^{57} +(2.53669 + 1.22582i) q^{58} +7.52612i q^{59} +(7.54134 + 2.39975i) q^{60} +5.45245i q^{61} +(-4.73847 + 9.80576i) q^{62} +(0.0930061 - 0.0930061i) q^{63} +(-7.23555 + 3.41274i) q^{64} +(-3.37869 - 5.02213i) q^{65} +(4.91318 + 14.1019i) q^{66} +(6.27455 - 6.27455i) q^{67} +(8.91636 + 1.02895i) q^{68} -13.9796 q^{69} +(-3.13042 + 0.447737i) q^{70} -4.59614i q^{71} +(0.363028 - 0.0813179i) q^{72} +(2.07406 + 2.07406i) q^{73} +(-2.04445 - 5.86803i) q^{74} +(3.43762 + 8.15298i) q^{75} +(8.04466 - 6.38005i) q^{76} +(-4.21937 - 4.21937i) q^{77} +(-6.09955 - 2.94751i) q^{78} -8.45199 q^{79} +(-8.15604 - 3.67138i) q^{80} +9.37729 q^{81} +(-5.74928 - 2.77825i) q^{82} +(-4.80743 - 4.80743i) q^{83} +(-2.77301 + 2.19921i) q^{84} +(5.60146 + 8.32609i) q^{85} +(-1.68422 - 4.83410i) q^{86} +(2.49280 + 2.49280i) q^{87} +(-3.68912 - 16.4694i) q^{88} +3.08788i q^{89} +(0.332790 + 0.249506i) q^{90} +2.70693 q^{91} +(15.6954 + 1.81125i) q^{92} +(-9.63611 + 9.63611i) q^{93} +(-2.51949 - 7.23149i) q^{94} +(11.2659 + 2.20393i) q^{95} +(-9.95482 + 1.05384i) q^{96} +(-9.27909 + 9.27909i) q^{97} +(0.615319 - 1.27334i) q^{98} +0.784855i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 8 q^{6}+O(q^{10}) $ 72 * q + 8 * q^6	$ 72 q + 8 q^{6} + 16 q^{10} - 16 q^{12} - 8 q^{16} + 8 q^{17} - 28 q^{18} - 20 q^{20} - 36 q^{22} - 8 q^{25} - 32 q^{26} - 4 q^{30} + 40 q^{32} + 64 q^{36} - 4 q^{40} + 20 q^{42} - 64 q^{43} + 48 q^{46} - 80 q^{48} - 32 q^{51} + 16 q^{52} - 24 q^{56} + 4 q^{58} - 80 q^{60} - 40 q^{62} - 8 q^{65} + 32 q^{66} - 24 q^{68} + 40 q^{72} - 40 q^{73} + 112 q^{75} - 8 q^{76} + 28 q^{78} - 20 q^{80} - 72 q^{81} + 24 q^{82} + 80 q^{83} + 8 q^{86} - 88 q^{88} + 136 q^{90} - 96 q^{92} - 56 q^{96} - 8 q^{97}+O(q^{100}) $ 72 * q + 8 * q^6 + 16 * q^10 - 16 * q^12 - 8 * q^16 + 8 * q^17 - 28 * q^18 - 20 * q^20 - 36 * q^22 - 8 * q^25 - 32 * q^26 - 4 * q^30 + 40 * q^32 + 64 * q^36 - 4 * q^40 + 20 * q^42 - 64 * q^43 + 48 * q^46 - 80 * q^48 - 32 * q^51 + 16 * q^52 - 24 * q^56 + 4 * q^58 - 80 * q^60 - 40 * q^62 - 8 * q^65 + 32 * q^66 - 24 * q^68 + 40 * q^72 - 40 * q^73 + 112 * q^75 - 8 * q^76 + 28 * q^78 - 20 * q^80 - 72 * q^81 + 24 * q^82 + 80 * q^83 + 8 * q^86 - 88 * q^88 + 136 * q^90 - 96 * q^92 - 56 * q^96 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$	$1$

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 $

$2$	−1.27334	−	0.615319i	−0.900384	−	0.435096i
$2$	−1.27334	−	0.615319i	−0.900384	−	0.435096i
$3$	−1.25131	−	1.25131i	−0.722442	−	0.722442i	0.246660	−	0.969102i	$-0.420667\pi$
$3$	−1.25131	−	1.25131i	−0.722442	−	0.722442i	−0.969102	+	0.246660i	$0.920667\pi$
$4$	1.24277	+	1.56701i	0.621383	+	0.783507i
$5$	−0.429301	+	2.19447i	−0.191989	+	0.981397i
$5$	−0.429301	+	2.19447i	−0.191989	+	0.981397i
$6$	0.823380	+	2.36328i	0.336143	+	0.964806i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	−0.618244	−	2.76003i	−0.218582	−	0.975819i
$9$			0.131530i			0.0438435i
$10$	1.89694	−	2.53014i	0.599866	−	0.800100i
$11$	5.96709			1.79915			0.899573	−	0.436770i	$-0.143878\pi$
$11$	5.96709			1.79915			0.899573	+	0.436770i	$0.143878\pi$
$12$	0.405734	−	3.51589i	0.117125	−	1.01495i
$13$	−1.91409	+	1.91409i	−0.530873	+	0.530873i	−0.920832	−	0.389959i	$-0.872489\pi$
$13$	−1.91409	+	1.91409i	−0.530873	+	0.530873i	0.389959	+	0.920832i	$0.372489\pi$
$14$	0.465288	+	1.33548i	0.124353	+	0.356922i
$15$	3.28314	−	2.20877i	0.847703	−	0.570301i
$16$	−0.911068	+	3.89486i	−0.227767	+	0.973716i
$17$	3.17333	−	3.17333i	0.769645	−	0.769645i	−0.208399	−	0.978044i	$-0.566825\pi$
$17$	3.17333	−	3.17333i	0.769645	−	0.769645i	0.978044	+	0.208399i	$0.0668251\pi$
$18$	0.0809332	−	0.167482i	0.0190761	−	0.0394760i
$19$		−	5.13375i		−	1.17776i	−0.808219	−	0.588882i	$-0.799568\pi$
$19$		−	5.13375i		−	1.17776i	0.808219	−	0.588882i	$-0.200432\pi$
$20$	−3.97229	+	2.05449i	−0.888230	+	0.459398i
$21$			1.76961i			0.386161i
$22$	−7.59811	−	3.67166i	−1.61992	−	0.782801i
$23$	5.58599	−	5.58599i	1.16476	−	1.16476i	0.181338	−	0.983421i	$-0.441957\pi$
$23$	5.58599	−	5.58599i	1.16476	−	1.16476i	0.983421	−	0.181338i	$-0.0580430\pi$
$24$	−2.68003	+	4.22725i	−0.547059	+	0.862885i
$25$	−4.63140	−	1.88418i	−0.926280	−	0.376835i
$26$	3.61505	−	1.25950i	0.708970	−	0.247009i
$27$	−3.58933	+	3.58933i	−0.690767	+	0.690767i
$28$	0.229279	−	1.98681i	0.0433296	−	0.375473i
$29$	−1.99216			−0.369935			−0.184968	−	0.982745i	$-0.559218\pi$
$29$	−1.99216			−0.369935			−0.184968	+	0.982745i	$0.559218\pi$
$30$	−5.53963	+	0.792322i	−1.01139	+	0.144658i
$31$		−	7.70084i		−	1.38311i	−0.722323	−	0.691556i	$-0.756925\pi$
$31$		−	7.70084i		−	1.38311i	0.722323	−	0.691556i	$-0.243075\pi$
$32$	3.55668	−	4.39887i	0.628738	−	0.777618i
$33$	−7.46666	−	7.46666i	−1.29978	−	1.29978i
$34$	−5.99332	+	2.08810i	−1.02785	+	0.358107i
$35$	1.85529	−	1.24816i	0.313601	−	0.210978i
$36$	−0.206110	+	0.163462i	−0.0343517	+	0.0272436i
$37$	3.10699	+	3.10699i	0.510786	+	0.510786i	0.914767	−	0.403981i	$-0.132374\pi$
$37$	3.10699	+	3.10699i	0.510786	+	0.510786i	−0.403981	+	0.914767i	$0.632374\pi$
$38$	−3.15889	+	6.53699i	−0.512440	+	1.06044i
$39$	4.79022			0.767049
$40$	6.32222	−	0.171833i	0.999631	−	0.0271692i
$41$	4.51513			0.705145			0.352573	−	0.935784i	$-0.385307\pi$
$41$	4.51513			0.705145			0.352573	+	0.935784i	$0.385307\pi$
$42$	1.08888	−	2.25331i	0.168017	−	0.347693i
$43$	2.55955	+	2.55955i	0.390327	+	0.390327i	0.874804	−	0.484477i	$-0.160990\pi$
$43$	2.55955	+	2.55955i	0.390327	+	0.390327i	−0.484477	+	0.874804i	$0.660990\pi$
$44$	7.41570	+	9.35052i	1.11796	+	1.40964i
$45$	−0.288640	−	0.0564662i	−0.0430279	−	0.00841748i
$46$	−10.5500	+	3.67567i	−1.55551	+	0.541948i
$47$	3.82891	+	3.82891i	0.558504	+	0.558504i	0.928881	−	0.370378i	$-0.120772\pi$
$47$	3.82891	+	3.82891i	0.558504	+	0.558504i	−0.370378	+	0.928881i	$0.620772\pi$
$48$	6.01369	−	3.73364i	0.868001	−	0.538904i
$49$			1.00000i			0.142857i
$50$	4.73796	+	5.24898i	0.670048	+	0.742318i
$51$	−7.94161			−1.11205
$52$	−5.37817	−	0.620641i	−0.745818	−	0.0860674i
$53$	6.09013	−	6.09013i	0.836544	−	0.836544i	−0.151859	−	0.988402i	$-0.548526\pi$
$53$	6.09013	−	6.09013i	0.836544	−	0.836544i	0.988402	+	0.151859i	$0.0485258\pi$
$54$	6.77901	−	2.36184i	0.922506	−	0.321406i
$55$	−2.56168	+	13.0946i	−0.345417	+	1.76568i
$56$	−1.51447	+	2.38880i	−0.202380	+	0.319217i
$57$	−6.42389	+	6.42389i	−0.850865	+	0.850865i
$58$	2.53669	+	1.22582i	0.333084	+	0.160957i
$59$			7.52612i			0.979818i	0.871774	+	0.489909i	$0.162970\pi$
$59$			7.52612i			0.979818i	−0.871774	+	0.489909i	$0.837030\pi$
$60$	7.54134	+	2.39975i	0.973583	+	0.309806i
$61$			5.45245i			0.698115i	0.937101	+	0.349057i	$0.113498\pi$
$61$			5.45245i			0.698115i	−0.937101	+	0.349057i	$0.886502\pi$
$62$	−4.73847	+	9.80576i	−0.601787	+	1.24533i
$63$	0.0930061	−	0.0930061i	0.0117177	−	0.0117177i
$64$	−7.23555	+	3.41274i	−0.904444	+	0.426593i
$65$	−3.37869	−	5.02213i	−0.419075	−	0.622919i
$66$	4.91318	+	14.1019i	0.604771	+	1.73583i
$67$	6.27455	−	6.27455i	0.766558	−	0.766558i	−0.210941	−	0.977499i	$-0.567653\pi$
$67$	6.27455	−	6.27455i	0.766558	−	0.766558i	0.977499	+	0.210941i	$0.0676527\pi$
$68$	8.91636	+	1.02895i	1.08127	+	0.124778i
$69$	−13.9796			−1.68294
$70$	−3.13042	+	0.447737i	−0.374157	+	0.0535149i
$71$		−	4.59614i		−	0.545461i	−0.962090	−	0.272731i	$-0.912073\pi$
$71$		−	4.59614i		−	0.545461i	0.962090	−	0.272731i	$-0.0879268\pi$
$72$	0.363028	−	0.0813179i	0.0427833	−	0.00958341i
$73$	2.07406	+	2.07406i	0.242750	+	0.242750i	0.817987	−	0.575237i	$-0.195090\pi$
$73$	2.07406	+	2.07406i	0.242750	+	0.242750i	−0.575237	+	0.817987i	$0.695090\pi$
$74$	−2.04445	−	5.86803i	−0.237663	−	0.682145i
$75$	3.43762	+	8.15298i	0.396942	+	0.941425i
$76$	8.04466	−	6.38005i	0.922786	−	0.731842i
$77$	−4.21937	−	4.21937i	−0.480842	−	0.480842i
$78$	−6.09955	−	2.94751i	−0.690639	−	0.333740i
$79$	−8.45199			−0.950923			−0.475462	−	0.879736i	$-0.657719\pi$
$79$	−8.45199			−0.950923			−0.475462	+	0.879736i	$0.657719\pi$
$80$	−8.15604	−	3.67138i	−0.911873	−	0.410473i
$81$	9.37729			1.04192
$82$	−5.74928	−	2.77825i	−0.634902	−	0.306806i
$83$	−4.80743	−	4.80743i	−0.527684	−	0.527684i	0.392197	−	0.919881i	$-0.371715\pi$
$83$	−4.80743	−	4.80743i	−0.527684	−	0.527684i	−0.919881	+	0.392197i	$0.871715\pi$
$84$	−2.77301	+	2.19921i	−0.302560	+	0.239954i
$85$	5.60146	+	8.32609i	0.607564	+	0.903091i
$86$	−1.68422	−	4.83410i	−0.181614	−	0.521274i
$87$	2.49280	+	2.49280i	0.267257	+	0.267257i
$88$	−3.68912	−	16.4694i	−0.393261	−	1.75564i
$89$			3.08788i			0.327314i	0.986517	+	0.163657i	$0.0523291\pi$
$89$			3.08788i			0.327314i	−0.986517	+	0.163657i	$0.947671\pi$
$90$	0.332790	+	0.249506i	0.0350792	+	0.0263002i
$91$	2.70693			0.283763
$92$	15.6954	+	1.81125i	1.63636	+	0.188836i
$93$	−9.63611	+	9.63611i	−0.999218	+	0.999218i
$94$	−2.51949	−	7.23149i	−0.259865	−	0.745871i
$95$	11.2659	+	2.20393i	1.15585	+	0.226118i
$96$	−9.95482	+	1.05384i	−1.01601	+	0.107557i
$97$	−9.27909	+	9.27909i	−0.942148	+	0.942148i	−0.998416	−	0.0562673i	$-0.982080\pi$
$97$	−9.27909	+	9.27909i	−0.942148	+	0.942148i	0.0562673	+	0.998416i	$0.482080\pi$
$98$	0.615319	−	1.27334i	0.0621566	−	0.128626i
$99$			0.784855i			0.0788809i
$100$	−2.80321	−	9.59906i	−0.280321	−	0.959906i
$101$		−	9.21539i		−	0.916965i	−0.888703	−	0.458483i	$-0.848393\pi$
$101$		−	9.21539i		−	0.916965i	0.888703	−	0.458483i	$-0.151607\pi$
$102$	10.1123	+	4.88662i	1.00127	+	0.483848i
$103$	−0.616495	+	0.616495i	−0.0607451	+	0.0607451i	−0.736827	−	0.676082i	$-0.763677\pi$
$103$	−0.616495	+	0.616495i	−0.0607451	+	0.0607451i	0.676082	+	0.736827i	$0.263677\pi$
$104$	6.46632	+	4.09957i	0.634075	+	0.401996i
$105$	−3.88336	−	0.759697i	−0.378977	−	0.0741388i
$106$	−11.5021	+	4.00741i	−1.11719	+	0.389234i
$107$	−7.57562	+	7.57562i	−0.732363	+	0.732363i	−0.971087	−	0.238724i	$-0.923271\pi$
$107$	−7.57562	+	7.57562i	−0.732363	+	0.732363i	0.238724	+	0.971087i	$0.423271\pi$
$108$	−10.0852	−	1.16384i	−0.970452	−	0.111990i
$109$	−10.4490			−1.00083			−0.500415	−	0.865786i	$-0.666819\pi$
$109$	−10.4490			−1.00083			−0.500415	+	0.865786i	$0.666819\pi$
$110$	11.3192	−	15.0976i	1.07925	−	1.43950i
$111$		−	7.77559i		−	0.738026i
$112$	3.39831	−	2.10986i	0.321110	−	0.199363i
$113$	9.49671	+	9.49671i	0.893375	+	0.893375i	0.994839	−	0.101464i	$-0.0323526\pi$
$113$	9.49671	+	9.49671i	0.893375	+	0.893375i	−0.101464	+	0.994839i	$0.532353\pi$
$114$	12.1325	−	4.22703i	1.13631	−	0.395897i
$115$	9.86022	+	14.6564i	0.919470	+	1.36671i
$116$	−2.47579	−	3.12175i	−0.229871	−	0.289847i
$117$	−0.251761	−	0.251761i	−0.0232753	−	0.0232753i
$118$	4.63096	−	9.58328i	0.426315	−	0.882212i
$119$	−4.48777			−0.411393
$120$	−8.12604	−	7.69601i	−0.741803	−	0.702547i
$121$	24.6062			2.23693
$122$	3.35500	−	6.94280i	0.303747	−	0.628571i
$123$	−5.64981	−	5.64981i	−0.509426	−	0.509426i
$124$	12.0673	−	9.57034i	1.08368	−	0.859442i
$125$	6.12304	−	9.35459i	0.547661	−	0.836700i
$126$	−0.175656	+	0.0611995i	−0.0156487	+	0.00545209i
$127$	−0.551000	−	0.551000i	−0.0488933	−	0.0488933i	0.682237	−	0.731131i	$-0.261007\pi$
$127$	−0.551000	−	0.551000i	−0.0488933	−	0.0488933i	−0.731131	+	0.682237i	$0.761007\pi$
$128$	11.3132	+	0.106601i	0.999956	+	0.00942232i
$129$		−	6.40555i		−	0.563977i
$130$	1.21199	+	8.47383i	0.106299	+	0.743204i
$131$	−14.3346			−1.25242			−0.626208	−	0.779656i	$-0.715394\pi$
$131$	−14.3346			−1.25242			−0.626208	+	0.779656i	$0.715394\pi$
$132$	2.42105	−	20.9797i	0.210726	−	1.82604i
$133$	−3.63011	+	3.63011i	−0.314770	+	0.314770i
$134$	−11.8505	+	4.12876i	−1.02372	+	0.356670i
$135$	−6.33578	−	9.41759i	−0.545297	−	0.810537i
$136$	−10.7204	−	6.79660i	−0.919265	−	0.582804i
$137$	−8.15088	+	8.15088i	−0.696377	+	0.696377i	−0.963627	−	0.267250i	$-0.913885\pi$
$137$	−8.15088	+	8.15088i	−0.696377	+	0.696377i	0.267250	+	0.963627i	$0.413885\pi$
$138$	17.8007	+	8.60188i	1.51529	+	0.732241i
$139$		−	11.9519i		−	1.01375i	−0.862021	−	0.506873i	$-0.830801\pi$
$139$		−	11.9519i		−	1.01375i	0.862021	−	0.506873i	$-0.169199\pi$
$140$	4.26158	+	1.35609i	0.360169	+	0.114610i
$141$		−	9.58227i		−	0.806973i
$142$	−2.82809	+	5.85242i	−0.237328	+	0.491125i
$143$	−11.4215	+	11.4215i	−0.955117	+	0.955117i
$144$	−0.512293	−	0.119833i	−0.0426911	−	0.00998610i
$145$	0.855238	−	4.37174i	0.0710236	−	0.363053i
$146$	−1.36476	−	3.91717i	−0.112949	−	0.324188i
$147$	1.25131	−	1.25131i	0.103206	−	0.103206i
$148$	−1.00744	+	8.72996i	−0.0828109	+	0.717598i
$149$	8.65497			0.709043			0.354522	−	0.935048i	$-0.384644\pi$
$149$	8.65497			0.709043			0.354522	+	0.935048i	$0.384644\pi$
$150$	0.639444	−	12.4967i	0.0522104	−	1.02035i
$151$		−	2.98172i		−	0.242649i	−0.992613	−	0.121325i	$-0.961286\pi$
$151$		−	2.98172i		−	0.242649i	0.992613	−	0.121325i	$-0.0387142\pi$
$152$	−14.1693	+	3.17391i	−1.14928	+	0.257438i
$153$	0.417390	+	0.417390i	0.0337439	+	0.0337439i
$154$	2.77642	+	7.96893i	0.223730	+	0.642155i
$155$	16.8993	+	3.30598i	1.35738	+	0.265543i
$156$	5.95312	+	7.50634i	0.476631	+	0.600988i
$157$	−0.861084	−	0.861084i	−0.0687220	−	0.0687220i	0.671910	−	0.740632i	$-0.265474\pi$
$157$	−0.861084	−	0.861084i	−0.0687220	−	0.0687220i	−0.740632	+	0.671910i	$0.765474\pi$
$158$	10.7622	+	5.20067i	0.856196	+	0.413743i
$159$	−15.2412			−1.20871
$160$	8.12630	+	9.69346i	0.642441	+	0.766335i
$161$	−7.89978			−0.622590
$162$	−11.9404	−	5.77002i	−0.938129	−	0.453336i
$163$	−7.07960	−	7.07960i	−0.554517	−	0.554517i	0.373224	−	0.927741i	$-0.378252\pi$
$163$	−7.07960	−	7.07960i	−0.554517	−	0.554517i	−0.927741	+	0.373224i	$0.878252\pi$
$164$	5.61125	+	7.07528i	0.438165	+	0.552486i
$165$	19.5908	−	13.1799i	1.52514	−	1.02605i
$166$	3.16337	+	9.07957i	0.245525	+	0.704711i
$167$	−7.34834	−	7.34834i	−0.568631	−	0.568631i	0.363114	−	0.931745i	$-0.381714\pi$
$167$	−7.34834	−	7.34834i	−0.568631	−	0.568631i	−0.931745	+	0.363114i	$0.881714\pi$
$168$	4.88419	−	1.09405i	0.376823	−	0.0844080i
$169$			5.67253i			0.436349i
$170$	−2.00934	−	14.0486i	−0.154109	−	1.07748i
$171$	0.675245			0.0516373
$172$	−0.829930	+	7.19176i	−0.0632815	+	0.548367i
$173$	−8.02384	+	8.02384i	−0.610041	+	0.610041i	−0.942957	−	0.332915i	$-0.891968\pi$
$173$	−8.02384	+	8.02384i	−0.610041	+	0.610041i	0.332915	+	0.942957i	$0.391968\pi$
$174$	−1.64031	−	4.70804i	−0.124351	−	0.356916i
$175$	1.94258	+	4.60721i	0.146845	+	0.348272i
$176$	−5.43643	+	23.2410i	−0.409786	+	1.75186i
$177$	9.41748	−	9.41748i	0.707861	−	0.707861i
$178$	1.90003	−	3.93190i	0.142413	−	0.294709i
$179$			5.53708i			0.413860i	0.978356	+	0.206930i	$0.0663473\pi$
$179$			5.53708i			0.413860i	−0.978356	+	0.206930i	$0.933653\pi$
$180$	−0.270228	−	0.522477i	−0.0201416	−	0.0389431i
$181$			3.82887i			0.284598i	0.989824	+	0.142299i	$0.0454494\pi$
$181$			3.82887i			0.284598i	−0.989824	+	0.142299i	$0.954551\pi$
$182$	−3.44683	−	1.66562i	−0.255496	−	0.123464i
$183$	6.82268	−	6.82268i	0.504347	−	0.504347i
$184$	−18.8710	−	11.9640i	−1.39119	−	0.881998i
$185$	−8.15203	+	5.48436i	−0.599349	+	0.403218i
$186$	18.1993	−	6.34072i	1.33444	−	0.464924i
$187$	18.9356	−	18.9356i	1.38470	−	1.38470i
$188$	−1.24152	+	10.7584i	−0.0905471	+	0.784636i
$189$	5.07608			0.369231
$190$	−12.9891	−	9.73843i	−0.942329	−	0.706500i
$191$			4.01180i			0.290283i	0.989411	+	0.145142i	$0.0463638\pi$
$191$			4.01180i			0.290283i	−0.989411	+	0.145142i	$0.953636\pi$
$192$	13.3243	+	4.78350i	0.961596	+	0.345219i
$193$	−9.52035	−	9.52035i	−0.685290	−	0.685290i	0.275897	−	0.961187i	$-0.411025\pi$
$193$	−9.52035	−	9.52035i	−0.685290	−	0.685290i	−0.961187	+	0.275897i	$0.911025\pi$
$194$	17.5250	−	6.10579i	1.25822	−	0.438370i
$195$	−2.05645	+	10.5120i	−0.147265	+	0.752779i
$196$	−1.56701	+	1.24277i	−0.111930	+	0.0887690i
$197$	−8.07812	−	8.07812i	−0.575542	−	0.575542i	0.358130	−	0.933672i	$-0.383415\pi$
$197$	−8.07812	−	8.07812i	−0.575542	−	0.575542i	−0.933672	+	0.358130i	$0.883415\pi$
$198$	0.482936	−	0.999383i	0.0343208	−	0.0710231i
$199$	4.24109			0.300643			0.150322	−	0.988637i	$-0.451969\pi$
$199$	4.24109			0.300643			0.150322	+	0.988637i	$0.451969\pi$
$200$	−2.33705	+	13.9477i	−0.165255	+	0.986251i
$201$	−15.7028			−1.10759
$202$	−5.67040	+	11.7343i	−0.398968	+	0.825621i
$203$	1.40867	+	1.40867i	0.0988694	+	0.0988694i
$204$	−9.86956	−	12.4446i	−0.691007	−	0.871297i
$205$	−1.93835	+	9.90833i	−0.135380	+	0.692028i
$206$	1.16435	−	0.405664i	0.0811238	−	0.0282639i
$207$	0.734728	+	0.734728i	0.0510671	+	0.0510671i
$208$	−5.71125	−	9.19898i	−0.396004	−	0.637834i
$209$		−	30.6336i		−	2.11897i
$210$	4.47737	+	3.35686i	0.308968	+	0.231645i
$211$	−6.57474			−0.452624			−0.226312	−	0.974055i	$-0.572667\pi$
$211$	−6.57474			−0.452624			−0.226312	+	0.974055i	$0.572667\pi$
$212$	17.1119	+	1.97472i	1.17525	+	0.135624i
$213$	−5.75117	+	5.75117i	−0.394064	+	0.394064i
$214$	14.3077	−	4.98488i	0.978056	−	0.340760i
$215$	−6.71566	+	4.51803i	−0.458004	+	0.308127i
$216$	12.1258	+	7.68759i	0.825053	+	0.523074i
$217$	−5.44532	+	5.44532i	−0.369652	+	0.369652i
$218$	13.3050	+	6.42944i	0.901131	+	0.435457i
$219$		−	5.19055i		−	0.350745i
$220$	−23.7030	+	12.2593i	−1.59806	+	0.826524i
$221$			12.1481i			0.817167i
$222$	−4.78446	+	9.90093i	−0.321112	+	0.664507i
$223$	−7.41104	+	7.41104i	−0.496280	+	0.496280i	−0.910278	−	0.413998i	$-0.864132\pi$
$223$	−7.41104	+	7.41104i	−0.496280	+	0.496280i	0.413998	+	0.910278i	$0.364132\pi$
$224$	−5.62542	+	0.595520i	−0.375864	+	0.0397898i
$225$	0.247827	−	0.609170i	0.0165218	−	0.0406114i
$226$	−6.24899	−	17.9360i	−0.415677	−	1.19309i
$227$	−0.188519	+	0.188519i	−0.0125124	+	0.0125124i	−0.713335	−	0.700823i	$-0.752816\pi$
$227$	−0.188519	+	0.188519i	−0.0125124	+	0.0125124i	0.700823	+	0.713335i	$0.252816\pi$
$228$	−18.0497	−	2.08294i	−1.19537	−	0.137946i
$229$	12.6007			0.832677			0.416338	−	0.909210i	$-0.363313\pi$
$229$	12.6007			0.832677			0.416338	+	0.909210i	$0.363313\pi$
$230$	−3.53703	−	24.7296i	−0.233225	−	1.63062i
$231$			10.5594i			0.694760i
$232$	1.23164	+	5.49843i	0.0808613	+	0.360990i
$233$	17.3698	+	17.3698i	1.13793	+	1.13793i	0.988820	+	0.149113i	$0.0476418\pi$
$233$	17.3698	+	17.3698i	1.13793	+	1.13793i	0.149113	+	0.988820i	$0.452358\pi$
$234$	0.165663	+	0.475489i	0.0108297	+	0.0310837i
$235$	−10.0462	+	6.75867i	−0.655341	+	0.440887i
$236$	−11.7935	+	9.35320i	−0.767694	+	0.608842i
$237$	10.5760	+	10.5760i	0.686986	+	0.686986i
$238$	5.71443	+	2.76141i	0.370411	+	0.178995i
$239$	18.1545			1.17432			0.587159	−	0.809471i	$-0.300246\pi$
$239$	18.1545			1.17432			0.587159	+	0.809471i	$0.300246\pi$
$240$	5.61168	+	14.7997i	0.362232	+	0.955317i
$241$	4.33837			0.279459			0.139729	−	0.990190i	$-0.455377\pi$
$241$	4.33837			0.279459			0.139729	+	0.990190i	$0.455377\pi$
$242$	−31.3319	−	15.1407i	−2.01409	−	0.973278i
$243$	−0.965861	−	0.965861i	−0.0619600	−	0.0619600i
$244$	−8.54407	+	6.77612i	−0.546978	+	0.433796i
$245$	−2.19447	−	0.429301i	−0.140200	−	0.0274270i
$246$	3.71767	+	10.6705i	0.237030	+	0.680329i
$247$	9.82645	+	9.82645i	0.625242	+	0.625242i
$248$	−21.2546	+	4.76100i	−1.34967	+	0.302324i
$249$			12.0311i			0.762441i
$250$	−13.5527	+	8.14391i	−0.857150	+	0.515066i
$251$	−4.49506			−0.283726			−0.141863	−	0.989886i	$-0.545309\pi$
$251$	−4.49506			−0.283726			−0.141863	+	0.989886i	$0.545309\pi$
$252$	0.261327	+	0.0301571i	0.0164620	+	0.00189972i
$253$	33.3321	−	33.3321i	2.09557	−	2.09557i
$254$	0.362567	+	1.04065i	0.0227495	+	0.0652961i
$255$	3.40934	−	17.4276i	0.213501	−	1.09136i
$256$	−14.3399	−	7.09697i	−0.896244	−	0.443561i
$257$	1.70450	−	1.70450i	0.106324	−	0.106324i	−0.651943	−	0.758268i	$-0.726046\pi$
$257$	1.70450	−	1.70450i	0.106324	−	0.106324i	0.758268	+	0.651943i	$0.226046\pi$
$258$	−3.94145	+	8.15641i	−0.245384	+	0.507796i
$259$		−	4.39395i		−	0.273027i
$260$	3.67083	−	11.5358i	0.227655	−	0.715419i
$261$		−	0.262030i		−	0.0162193i
$262$	18.2527	+	8.82032i	1.12766	+	0.544921i
$263$	−8.32401	+	8.32401i	−0.513280	+	0.513280i	−0.915530	−	0.402250i	$-0.868228\pi$
$263$	−8.32401	+	8.32401i	−0.513280	+	0.513280i	0.402250	+	0.915530i	$0.368228\pi$
$264$	−15.9920	+	25.2244i	−0.984239	+	1.55246i
$265$	10.7501	+	15.9791i	0.660374	+	0.981589i
$266$	6.85602	−	2.38867i	0.420370	−	0.146459i
$267$	3.86388	−	3.86388i	0.236466	−	0.236466i
$268$	17.6301	+	2.03451i	1.07693	+	0.124278i
$269$	32.1282			1.95889			0.979446	−	0.201705i	$-0.0646484\pi$
$269$	32.1282			1.95889			0.979446	+	0.201705i	$0.0646484\pi$
$270$	2.27275	+	15.8903i	0.138315	+	0.967051i
$271$			11.7684i			0.714881i	0.933936	+	0.357440i	$0.116350\pi$
$271$			11.7684i			0.714881i	−0.933936	+	0.357440i	$0.883650\pi$
$272$	9.46856	+	15.2508i	0.574116	+	0.924716i
$273$	−3.38720	−	3.38720i	−0.205002	−	0.205002i
$274$	15.3942	−	5.36342i	0.929998	−	0.324016i
$275$	−27.6360	−	11.2431i	−1.66651	−	0.677982i
$276$	−17.3733	−	21.9062i	−1.04575	−	1.31860i
$277$	3.07987	+	3.07987i	0.185051	+	0.185051i	0.793553	−	0.608501i	$-0.208229\pi$
$277$	3.07987	+	3.07987i	0.185051	+	0.185051i	−0.608501	+	0.793553i	$0.708229\pi$
$278$	−7.35423	+	15.2188i	−0.441077	+	0.912761i
$279$	1.01290			0.0606405
$280$	−4.59199	−	4.34898i	−0.274424	−	0.259901i
$281$	9.35098			0.557833			0.278916	−	0.960315i	$-0.410025\pi$
$281$	9.35098			0.557833			0.278916	+	0.960315i	$0.410025\pi$
$282$	−5.89615	+	12.2014i	−0.351111	+	0.726585i
$283$	9.23567	+	9.23567i	0.549004	+	0.549004i	0.926153	−	0.377149i	$-0.123096\pi$
$283$	9.23567	+	9.23567i	0.549004	+	0.549004i	−0.377149	+	0.926153i	$0.623096\pi$
$284$	7.20221	−	5.71192i	0.427373	−	0.338940i
$285$	−11.3393	−	16.8548i	−0.671679	−	0.998393i
$286$	21.5713	−	7.51556i	1.27554	−	0.444405i
$287$	−3.19268	−	3.19268i	−0.188458	−	0.188458i
$288$	0.578585	+	0.467811i	0.0340935	+	0.0275661i
$289$		−	3.14004i		−	0.184708i
$290$	−3.77902	+	5.04045i	−0.221912	+	0.295985i
$291$	23.2219			1.36129
$292$	−0.672510	+	5.82764i	−0.0393557	+	0.341037i
$293$	−13.5179	+	13.5179i	−0.789727	+	0.789727i	−0.981449	−	0.191722i	$-0.938593\pi$
$293$	−13.5179	+	13.5179i	−0.789727	+	0.789727i	0.191722	+	0.981449i	$0.438593\pi$
$294$	−2.36328	+	0.823380i	−0.137829	+	0.0480205i
$295$	−16.5159	−	3.23097i	−0.961590	−	0.188115i
$296$	6.65451	−	10.4963i	0.386786	−	0.610083i
$297$	−21.4179	+	21.4179i	−1.24279	+	1.24279i
$298$	−11.0207	−	5.32557i	−0.638411	−	0.308502i
$299$			21.3842i			1.23668i
$300$	−8.50368	+	15.5190i	−0.490960	+	0.895992i
$301$		−	3.61974i		−	0.208639i
$302$	−1.83471	+	3.79673i	−0.105576	+	0.218477i
$303$	−11.5313	+	11.5313i	−0.662454	+	0.662454i
$304$	19.9953	+	4.67719i	1.14681	+	0.268256i
$305$	−11.9652	−	2.34074i	−0.685128	−	0.134031i
$306$	−0.274649	−	0.788305i	−0.0157007	−	0.0450644i
$307$	9.29059	−	9.29059i	0.530242	−	0.530242i	−0.390402	−	0.920644i	$-0.627664\pi$
$307$	9.29059	−	9.29059i	0.530242	−	0.530242i	0.920644	+	0.390402i	$0.127664\pi$
$308$	1.36813	−	11.8555i	0.0779562	−	0.675530i
$309$	1.54285			0.0877695
$310$	−19.4842	−	14.6081i	−1.10663	−	0.829682i
$311$			12.0624i			0.683993i	0.939701	+	0.341997i	$0.111103\pi$
$311$			12.0624i			0.683993i	−0.939701	+	0.341997i	$0.888897\pi$
$312$	−2.96152	−	13.2212i	−0.167663	−	0.748500i
$313$	0.831582	+	0.831582i	0.0470038	+	0.0470038i	0.730218	−	0.683214i	$-0.239418\pi$
$313$	0.831582	+	0.831582i	0.0470038	+	0.0470038i	−0.683214	+	0.730218i	$0.739418\pi$
$314$	0.566607	+	1.62629i	0.0319755	+	0.0917768i
$315$	0.164172	+	0.244027i	0.00925002	+	0.0137494i
$316$	−10.5038	−	13.2444i	−0.590887	−	0.745055i
$317$	−11.2922	−	11.2922i	−0.634234	−	0.634234i	0.314893	−	0.949127i	$-0.398031\pi$
$317$	−11.2922	−	11.2922i	−0.634234	−	0.634234i	−0.949127	+	0.314893i	$0.898031\pi$
$318$	19.4072	+	9.37821i	1.08830	+	0.525904i
$319$	−11.8874			−0.665568
$320$	−4.38294	−	17.3433i	−0.245014	−	0.969520i
$321$	18.9588			1.05818
$322$	10.0591	+	4.86088i	0.560570	+	0.270886i
$323$	−16.2911	−	16.2911i	−0.906460	−	0.906460i
$324$	11.6538	+	14.6943i	0.647432	+	0.816353i
$325$	12.4714	−	5.25843i	0.691788	−	0.291685i
$326$	4.65849	+	13.3709i	0.258010	+	0.740546i
$327$	13.0748	+	13.0748i	0.723041	+	0.723041i
$328$	−2.79145	−	12.4619i	−0.154132	−	0.688094i
$329$		−	5.41490i		−	0.298533i
$330$	−33.0555	+	4.72786i	−1.81965	+	0.260260i
$331$	−34.2993			−1.88526			−0.942629	−	0.333841i	$-0.891655\pi$
$331$	−34.2993			−1.88526			−0.942629	+	0.333841i	$0.891655\pi$
$332$	1.55880	−	13.5078i	0.0855504	−	0.741338i
$333$	−0.408664	+	0.408664i	−0.0223946	+	0.0223946i
$334$	4.83533	+	13.8785i	0.264577	+	0.759396i
$335$	11.0756	+	16.4630i	0.605127	+	0.899469i
$336$	−6.89240	−	1.61224i	−0.376011	−	0.0879548i
$337$	20.3846	−	20.3846i	1.11042	−	1.11042i	0.117324	−	0.993094i	$-0.462568\pi$
$337$	20.3846	−	20.3846i	1.11042	−	1.11042i	0.993094	−	0.117324i	$-0.0374317\pi$
$338$	3.49042	−	7.22303i	0.189854	−	0.392881i
$339$		−	23.7666i		−	1.29082i
$340$	−6.08580	+	19.1250i	−0.330049	+	1.03720i
$341$		−	45.9516i		−	2.48842i
$342$	−0.859813	−	0.415491i	−0.0464934	−	0.0224672i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	5.48200	−	8.64685i	0.295570	−	0.466207i
$345$	6.00144	−	30.6777i	0.323107	−	1.65163i
$346$	15.1543	−	5.27982i	0.814698	−	0.283845i
$347$	12.2251	−	12.2251i	0.656278	−	0.656278i	−0.298220	−	0.954497i	$-0.596393\pi$
$347$	12.2251	−	12.2251i	0.656278	−	0.656278i	0.954497	+	0.298220i	$0.0963928\pi$
$348$	−0.808289	+	7.00423i	−0.0433288	+	0.375466i
$349$	7.42220			0.397301			0.198651	−	0.980070i	$-0.436344\pi$
$349$	7.42220			0.397301			0.198651	+	0.980070i	$0.436344\pi$
$350$	0.361347	−	7.06183i	0.0193148	−	0.377471i
$351$		−	13.7406i		−	0.733419i
$352$	21.2230	−	26.2485i	1.13119	−	1.39905i
$353$	−3.67043	−	3.67043i	−0.195357	−	0.195357i	0.602649	−	0.798006i	$-0.294112\pi$
$353$	−3.67043	−	3.67043i	−0.195357	−	0.195357i	−0.798006	+	0.602649i	$0.794112\pi$
$354$	−17.7864	+	6.19686i	−0.945334	+	0.329359i
$355$	10.0861	+	1.97313i	0.535314	+	0.104723i
$356$	−4.83875	+	3.83751i	−0.256453	+	0.203388i
$357$	5.61557	+	5.61557i	0.297207	+	0.297207i
$358$	3.40707	−	7.05055i	0.180069	−	0.372633i
$359$	−4.89000			−0.258084			−0.129042	−	0.991639i	$-0.541190\pi$
$359$	−4.89000			−0.258084			−0.129042	+	0.991639i	$0.541190\pi$
$360$	0.0226013	+	0.831565i	0.00119119	+	0.0438273i
$361$	−7.35540			−0.387126
$362$	2.35598	−	4.87544i	0.123827	−	0.256247i
$363$	−30.7899	−	30.7899i	−1.61605	−	1.61605i
$364$	3.36408	+	4.24180i	0.176326	+	0.222331i
$365$	−5.44185	+	3.66106i	−0.284839	+	0.191629i
$366$	−12.8857	+	4.48944i	−0.673545	+	0.234667i
$367$	9.23935	+	9.23935i	0.482290	+	0.482290i	0.905862	−	0.423572i	$-0.139224\pi$
$367$	9.23935	+	9.23935i	0.482290	+	0.482290i	−0.423572	+	0.905862i	$0.639224\pi$
$368$	16.6674	+	26.8459i	0.868851	+	1.39944i
$369$			0.593878i			0.0309160i
$370$	13.7549	−	1.96733i	0.715083	−	0.102277i
$371$	−8.61274			−0.447151
$372$	−27.0753	−	3.12450i	−1.40379	−	0.161998i
$373$	−6.52245	+	6.52245i	−0.337720	+	0.337720i	−0.855508	−	0.517789i	$-0.826755\pi$
$373$	−6.52245	+	6.52245i	−0.337720	+	0.337720i	0.517789	+	0.855508i	$0.326755\pi$
$374$	−35.7627	+	12.4599i	−1.84925	+	0.644286i
$375$	−19.3672	+	4.04366i	−1.00012	+	0.208814i
$376$	8.20071	−	12.9351i	0.422919	−	0.667077i
$377$	3.81318	−	3.81318i	0.196389	−	0.196389i
$378$	−6.46355	−	3.12341i	−0.332449	−	0.160651i
$379$			28.3055i			1.45395i	0.686662	+	0.726977i	$0.259075\pi$
$379$			28.3055i			1.45395i	−0.686662	+	0.726977i	$0.740925\pi$
$380$	10.5472	+	20.3927i	0.541062	+	1.04613i
$381$			1.37894i			0.0706452i
$382$	2.46853	−	5.10836i	0.126301	−	0.261366i
$383$	18.2785	−	18.2785i	0.933990	−	0.933990i	−0.0639623	−	0.997952i	$-0.520374\pi$
$383$	18.2785	−	18.2785i	0.933990	−	0.933990i	0.997952	+	0.0639623i	$0.0203737\pi$
$384$	−14.0229	−	14.2897i	−0.715602	−	0.729217i
$385$	11.0707	−	7.44791i	0.564213	−	0.379580i
$386$	6.26455	+	17.9806i	0.318857	+	0.915191i
$387$	−0.336658	+	0.336658i	−0.0171133	+	0.0171133i
$388$	−26.0722	−	3.00873i	−1.32361	−	0.152745i
$389$	−27.9535			−1.41730			−0.708649	−	0.705561i	$-0.750695\pi$
$389$	−27.9535			−1.41730			−0.708649	+	0.705561i	$0.750695\pi$
$390$	9.08677	−	12.1199i	0.460127	−	0.613716i
$391$		−	35.4524i		−	1.79290i
$392$	2.76003	−	0.618244i	0.139403	−	0.0312260i
$393$	17.9369	+	17.9369i	0.904797	+	0.904797i
$394$	5.31554	+	15.2568i	0.267793	+	0.768625i
$395$	3.62845	−	18.5476i	0.182567	−	0.933233i
$396$	−1.22988	+	0.975390i	−0.0618037	+	0.0490152i
$397$	9.81583	+	9.81583i	0.492642	+	0.492642i	0.909138	−	0.416495i	$-0.136742\pi$
$397$	9.81583	+	9.81583i	0.492642	+	0.492642i	−0.416495	+	0.909138i	$0.636742\pi$
$398$	−5.40033	−	2.60962i	−0.270694	−	0.130809i
$399$	9.08475			0.454806
$400$	11.5581	−	16.3221i	0.577907	−	0.816103i
$401$	5.63983			0.281640			0.140820	−	0.990035i	$-0.455026\pi$
$401$	5.63983			0.281640			0.140820	+	0.990035i	$0.455026\pi$
$402$	19.9949	+	9.66220i	0.997253	+	0.481907i
$403$	14.7401	+	14.7401i	0.734256	+	0.734256i
$404$	14.4406	−	11.4526i	0.718449	−	0.569786i
$405$	−4.02568	+	20.5782i	−0.200038	+	1.02254i
$406$	−0.926929	−	2.66049i	−0.0460027	−	0.132038i
$407$	18.5397	+	18.5397i	0.918979	+	0.918979i
$408$	4.90985	+	21.9191i	0.243074	+	1.08516i
$409$		−	18.4878i		−	0.914165i	−0.889424	−	0.457082i	$-0.848894\pi$
$409$		−	18.4878i		−	0.914165i	0.889424	−	0.457082i	$-0.151106\pi$
$410$	8.56495	−	11.4239i	0.422993	−	0.564187i
$411$	20.3985			1.00618
$412$	−1.73222	−	0.199898i	−0.0853401	−	0.00984826i
$413$	5.32177	−	5.32177i	0.261867	−	0.261867i
$414$	−0.483463	−	1.38765i	−0.0237609	−	0.0681991i
$415$	12.6136	−	8.48593i	0.619177	−	0.416558i
$416$	1.61203	+	15.2276i	0.0790363	+	0.746595i
$417$	−14.9555	+	14.9555i	−0.732373	+	0.732373i
$418$	−18.8494	+	39.0068i	−0.921955	+	1.90788i
$419$			17.8426i			0.871669i	0.900027	+	0.435835i	$0.143547\pi$
$419$			17.8426i			0.871669i	−0.900027	+	0.435835i	$0.856453\pi$
$420$	−3.63565	−	7.02941i	−0.177402	−	0.343000i
$421$			35.0932i			1.71034i	0.518351	+	0.855168i	$0.326546\pi$
$421$			35.0932i			1.71034i	−0.518351	+	0.855168i	$0.673454\pi$
$422$	8.37185	+	4.04556i	0.407535	+	0.196935i
$423$	−0.503618	+	0.503618i	−0.0244868	+	0.0244868i
$424$	−20.5741	−	13.0438i	−0.999168	−	0.633461i
$425$	−20.6761	+	8.71785i	−1.00294	+	0.422878i
$426$	10.8620	−	3.78437i	0.526264	−	0.183353i
$427$	3.85546	−	3.85546i	0.186579	−	0.186579i
$428$	−21.2858	−	2.45639i	−1.02889	−	0.118734i
$429$	28.5837			1.38003
$430$	11.3313	−	1.62069i	0.546445	−	0.0781569i
$431$			2.61849i			0.126128i	0.998009	+	0.0630640i	$0.0200872\pi$
$431$			2.61849i			0.126128i	−0.998009	+	0.0630640i	$0.979913\pi$
$432$	−10.7098	−	17.2501i	−0.515277	−	0.829945i
$433$	6.27906	+	6.27906i	0.301752	+	0.301752i	0.841699	−	0.539947i	$-0.181556\pi$
$433$	6.27906	+	6.27906i	0.301752	+	0.301752i	−0.539947	+	0.841699i	$0.681556\pi$
$434$	10.2843	−	3.58311i	0.493663	−	0.171995i
$435$	−6.54055	+	4.40022i	−0.313595	+	0.210974i
$436$	−12.9856	−	16.3737i	−0.621898	−	0.784157i
$437$	−28.6771	−	28.6771i	−1.37181	−	1.37181i
$438$	−3.19384	+	6.60931i	−0.152608	+	0.315805i
$439$	−32.3107			−1.54210			−0.771052	−	0.636772i	$-0.780269\pi$
$439$	−32.3107			−1.54210			−0.771052	+	0.636772i	$0.780269\pi$
$440$	37.7253	−	1.02534i	1.79848	−	0.0488813i
$441$	−0.131530			−0.00626336
$442$	7.47493	−	15.4686i	0.355546	−	0.735764i
$443$	6.86960	+	6.86960i	0.326384	+	0.326384i	0.851210	−	0.524825i	$-0.175869\pi$
$443$	6.86960	+	6.86960i	0.326384	+	0.326384i	−0.524825	+	0.851210i	$0.675869\pi$
$444$	12.1845	−	9.66323i	0.578249	−	0.458597i
$445$	−6.77626	−	1.32563i	−0.321225	−	0.0628409i
$446$	13.9969	−	4.87658i	0.662772	−	0.230913i
$447$	−10.8300	−	10.8300i	−0.512242	−	0.512242i
$448$	7.52948	+	2.70313i	0.355735	+	0.127711i
$449$		−	15.1408i		−	0.714541i	−0.934001	−	0.357270i	$-0.883708\pi$
$449$		−	15.1408i		−	0.714541i	0.934001	−	0.357270i	$-0.116292\pi$
$450$	−0.690401	+	0.623186i	−0.0325458	+	0.0293773i
$451$	26.9422			1.26866
$452$	−3.07930	+	26.6837i	−0.144838	+	1.25509i
$453$	−3.73104	+	3.73104i	−0.175300	+	0.175300i
$454$	0.356047	−	0.124049i	0.0167101	−	0.00582189i
$455$	−1.16209	+	5.94028i	−0.0544795	+	0.278485i
$456$	21.7017	+	13.7586i	1.01627	+	0.644306i
$457$	−24.1987	+	24.1987i	−1.13197	+	1.13197i	−0.142119	+	0.989850i	$0.545392\pi$
$457$	−24.1987	+	24.1987i	−1.13197	+	1.13197i	−0.989850	+	0.142119i	$0.954608\pi$
$458$	−16.0449	−	7.75344i	−0.749729	−	0.362294i
$459$			22.7803i			1.06329i
$460$	−10.7128	+	33.6655i	−0.499486	+	1.56966i
$461$		−	12.2551i		−	0.570775i	−0.958412	−	0.285387i	$-0.907878\pi$
$461$		−	12.2551i		−	0.570775i	0.958412	−	0.285387i	$-0.0921223\pi$
$462$	6.49743	−	13.4457i	0.302288	−	0.625551i
$463$	−9.51345	+	9.51345i	−0.442128	+	0.442128i	−0.892727	−	0.450599i	$-0.851210\pi$
$463$	−9.51345	+	9.51345i	−0.442128	+	0.442128i	0.450599	+	0.892727i	$0.351210\pi$
$464$	1.81500	−	7.75920i	0.0842590	−	0.360212i
$465$	−17.0094	−	25.2829i	−0.788790	−	1.17247i
$466$	−11.4296	−	32.8055i	−0.529467	−	1.51969i
$467$	21.1636	−	21.1636i	0.979333	−	0.979333i	−0.0204578	−	0.999791i	$-0.506512\pi$
$467$	21.1636	−	21.1636i	0.979333	−	0.979333i	0.999791	+	0.0204578i	$0.00651237\pi$
$468$	0.0816332	−	0.707393i	0.00377350	−	0.0326993i
$469$	−8.87355			−0.409742
$470$	16.9509	−	2.42445i	0.781887	−	0.111832i
$471$			2.15496i			0.0992952i
$472$	20.7723	−	4.65298i	0.956124	−	0.214171i
$473$	15.2730	+	15.2730i	0.702255	+	0.702255i
$474$	−6.95920	−	19.9744i	−0.319647	−	0.917457i
$475$	−9.67290	+	23.7765i	−0.443823	+	1.09094i
$476$	−5.57724	−	7.03239i	−0.255632	−	0.322329i
$477$	0.801038	+	0.801038i	0.0366770	+	0.0366770i
$478$	−23.1168	−	11.1708i	−1.05734	−	0.510942i
$479$	22.2444			1.01637			0.508186	−	0.861247i	$-0.330316\pi$
$479$	22.2444			1.01637			0.508186	+	0.861247i	$0.330316\pi$
$480$	1.96100	−	22.2980i	0.0895068	−	1.01776i
$481$	−11.8941			−0.542325
$482$	−5.52420	−	2.66948i	−0.251620	−	0.121591i
$483$	9.88504	+	9.88504i	0.449785	+	0.449785i
$484$	30.5797	+	38.5583i	1.38999	+	1.75265i
$485$	−16.3792	−	24.3462i	−0.743739	−	1.10550i
$486$	0.635552	+	1.82418i	0.0288292	+	0.0827464i
$487$	−3.90518	−	3.90518i	−0.176960	−	0.176960i	0.613069	−	0.790029i	$-0.289935\pi$
$487$	−3.90518	−	3.90518i	−0.176960	−	0.176960i	−0.790029	+	0.613069i	$0.789935\pi$
$488$	15.0489	−	3.37094i	0.681233	−	0.152595i
$489$			17.7175i			0.801212i
$490$	2.53014	+	1.89694i	0.114300	+	0.0856952i
$491$	−27.5353			−1.24265			−0.621325	−	0.783553i	$-0.713405\pi$
$491$	−27.5353			−1.24265			−0.621325	+	0.783553i	$0.713405\pi$
$492$	1.83194	−	15.8747i	0.0825904	−	0.715688i
$493$	−6.32179	+	6.32179i	−0.284719	+	0.284719i
$494$	−6.46597	−	18.5588i	−0.290918	−	0.834999i
$495$	−1.72234	−	0.336939i	−0.0774134	−	0.0151443i
$496$	29.9937	+	7.01599i	1.34676	+	0.315027i
$497$	−3.24996	+	3.24996i	−0.145781	+	0.145781i
$498$	7.40298	−	15.3197i	0.331735	−	0.686490i
$499$			13.4558i			0.602365i	0.953566	+	0.301183i	$0.0973814\pi$
$499$			13.4558i			0.602365i	−0.953566	+	0.301183i	$0.902619\pi$
$500$	22.2683	−	2.03068i	0.995868	−	0.0908147i
$501$			18.3900i			0.821606i
$502$	5.72372	+	2.76590i	0.255462	+	0.123448i
$503$	23.1597	−	23.1597i	1.03264	−	1.03264i	0.0331899	−	0.999449i	$-0.489433\pi$
$503$	23.1597	−	23.1597i	1.03264	−	1.03264i	0.999449	−	0.0331899i	$-0.0105666\pi$
$504$	−0.314200	−	0.199199i	−0.0139956	−	0.00887304i
$505$	20.2229	+	3.95618i	0.899907	+	0.176048i
$506$	−62.9528	+	21.9331i	−2.79859	+	0.975044i
$507$	7.09807	−	7.09807i	0.315236	−	0.315236i
$508$	0.178661	−	1.54819i	0.00792680	−	0.0686898i
$509$	−22.1067			−0.979864			−0.489932	−	0.871761i	$-0.662978\pi$
$509$	−22.1067			−0.979864			−0.489932	+	0.871761i	$0.662978\pi$
$510$	−15.0648	+	20.0934i	−0.667080	+	0.889750i
$511$		−	2.93316i		−	0.129755i
$512$	13.8926	+	17.8604i	0.613973	+	0.789327i
$513$	18.4267	+	18.4267i	0.813560	+	0.813560i
$514$	−3.21922	+	1.12159i	−0.141994	+	0.0494713i
$515$	−1.08822	−	1.61754i	−0.0479526	−	0.0712774i
$516$	10.0376	−	7.96059i	0.441880	−	0.350446i
$517$	22.8475	+	22.8475i	1.00483	+	1.00483i
$518$	−2.70368	+	5.59497i	−0.118793	+	0.245829i
$519$	20.0805			0.881438
$520$	−11.7724	+	12.4302i	−0.516253	+	0.545100i
$521$	−21.3058			−0.933424			−0.466712	−	0.884409i	$-0.654562\pi$
$521$	−21.3058			−0.933424			−0.466712	+	0.884409i	$0.654562\pi$
$522$	−0.161232	+	0.333652i	−0.00705694	+	0.0146036i
$523$	−4.41565	−	4.41565i	−0.193083	−	0.193083i	0.603944	−	0.797027i	$-0.293595\pi$
$523$	−4.41565	−	4.41565i	−0.193083	−	0.193083i	−0.797027	+	0.603944i	$0.793595\pi$
$524$	−17.8145	−	22.4625i	−0.778230	−	0.981277i
$525$	3.33426	−	8.19579i	0.145519	−	0.357694i
$526$	15.7212	−	5.47733i	0.685475	−	0.238823i
$527$	−24.4373	−	24.4373i	−1.06451	−	1.06451i
$528$	35.8842	−	22.2790i	1.56166	−	0.969568i
$529$		−	39.4065i		−	1.71333i
$530$	−3.85625	−	26.9615i	−0.167505	−	1.17113i
$531$	−0.989915			−0.0429586
$532$	−10.1998	−	1.17706i	−0.442218	−	0.0510320i
$533$	−8.64236	+	8.64236i	−0.374342	+	0.374342i
$534$	−7.29753	+	2.54250i	−0.315795	+	0.110025i
$535$	−13.3723	−	19.8767i	−0.578133	−	0.859345i
$536$	−21.1971	−	13.4387i	−0.915577	−	0.580466i
$537$	6.92857	−	6.92857i	0.298990	−	0.298990i
$538$	−40.9100	−	19.7691i	−1.76376	−	0.852306i
$539$			5.96709i			0.257021i
$540$	6.88361	−	21.6321i	0.296223	−	0.930898i
$541$			44.7274i			1.92298i	0.274838	+	0.961491i	$0.411376\pi$
$541$			44.7274i			1.92298i	−0.274838	+	0.961491i	$0.588624\pi$
$542$	7.24133	−	14.9851i	0.311042	−	0.643667i
$543$	4.79109	−	4.79109i	0.205605	−	0.205605i
$544$	−2.67255	−	25.2456i	−0.114585	−	1.08239i
$545$	4.48575	−	22.9299i	0.192148	−	0.982211i
$546$	2.22883	+	6.39724i	0.0953851	+	0.273777i
$547$	4.23856	−	4.23856i	0.181228	−	0.181228i	−0.610663	−	0.791891i	$-0.709097\pi$
$547$	4.23856	−	4.23856i	0.181228	−	0.181228i	0.791891	+	0.610663i	$0.209097\pi$
$548$	−22.9022	−	2.64291i	−0.978333	−	0.112900i
$549$	−0.717163			−0.0306078
$550$	28.2718	+	31.3211i	1.20551	+	1.33554i
$551$			10.2273i			0.435696i
$552$	8.64277	+	38.5840i	0.367861	+	1.64224i
$553$	5.97646	+	5.97646i	0.254145	+	0.254145i
$554$	−2.02660	−	5.81681i	−0.0861021	−	0.247132i
$555$	17.0633	+	3.33807i	0.724297	+	0.141693i
$556$	18.7288	−	14.8534i	0.794278	−	0.629925i
$557$	−22.2112	−	22.2112i	−0.941120	−	0.941120i	0.0572403	−	0.998360i	$-0.481770\pi$
$557$	−22.2112	−	22.2112i	−0.941120	−	0.941120i	−0.998360	+	0.0572403i	$0.981770\pi$
$558$	−1.28976	−	0.623254i	−0.0545997	−	0.0263844i
$559$	−9.79839			−0.414428
$560$	3.17113	+	8.36325i	0.134005	+	0.353412i
$561$	−47.3883			−2.00074
$562$	−11.9069	−	5.75383i	−0.502264	−	0.242711i
$563$	19.0121	+	19.0121i	0.801264	+	0.801264i	0.983293	−	0.182029i	$-0.0582666\pi$
$563$	19.0121	+	19.0121i	0.801264	+	0.801264i	−0.182029	+	0.983293i	$0.558267\pi$
$564$	15.0156	−	11.9085i	0.632269	−	0.501439i
$565$	−24.9172	+	16.7633i	−1.04827	+	0.705237i
$566$	−6.07722	−	17.4430i	−0.255445	−	0.733183i
$567$	−6.63075	−	6.63075i	−0.278465	−	0.278465i
$568$	−12.6855	+	2.84153i	−0.532271	+	0.119228i
$569$			33.4627i			1.40283i	0.712753	+	0.701415i	$0.247448\pi$
$569$			33.4627i			1.40283i	−0.712753	+	0.701415i	$0.752552\pi$
$570$	4.06758	+	28.4391i	0.170372	+	1.19118i
$571$	−2.60942			−0.109201			−0.0546005	−	0.998508i	$-0.517389\pi$
$571$	−2.60942			−0.109201			−0.0546005	+	0.998508i	$0.517389\pi$
$572$	−32.0920	−	3.70342i	−1.34183	−	0.154848i
$573$	5.01998	−	5.01998i	0.209713	−	0.209713i
$574$	2.10084	+	6.02987i	0.0876872	+	0.251682i
$575$	−36.3959	+	15.3460i	−1.51782	+	0.639971i
$576$	−0.448880	−	0.951695i	−0.0187033	−	0.0396540i
$577$	−25.9115	+	25.9115i	−1.07871	+	1.07871i	−0.0820828	+	0.996626i	$0.526157\pi$
$577$	−25.9115	+	25.9115i	−1.07871	+	1.07871i	−0.996626	+	0.0820828i	$0.973843\pi$
$578$	−1.93213	+	3.99832i	−0.0803658	+	0.166308i
$579$			23.8257i			0.990164i
$580$	7.91344	−	4.09288i	0.328588	−	0.169948i
$581$			6.79873i			0.282059i
$582$	−29.5693	−	14.2889i	−1.22569	−	0.592294i
$583$	36.3404	−	36.3404i	1.50506	−	1.50506i
$584$	4.44219	−	7.00673i	0.183819	−	0.289941i
$585$	0.660563	−	0.444401i	0.0273109	−	0.0183737i
$586$	25.5307	−	8.89503i	1.05466	−	0.367450i
$587$	−13.3816	+	13.3816i	−0.552320	+	0.552320i	−0.927110	−	0.374790i	$-0.877715\pi$
$587$	−13.3816	+	13.3816i	−0.552320	+	0.552320i	0.374790	+	0.927110i	$0.377715\pi$
$588$	3.51589	+	0.405734i	0.144993	+	0.0167322i
$589$	−39.5342			−1.62898
$590$	19.0421	+	14.2766i	0.783952	+	0.587759i
$591$			20.2164i			0.831591i
$592$	−14.9320	+	9.27062i	−0.613701	+	0.381020i
$593$	−16.8820	−	16.8820i	−0.693260	−	0.693260i	0.269688	−	0.962948i	$-0.413080\pi$
$593$	−16.8820	−	16.8820i	−0.693260	−	0.693260i	−0.962948	+	0.269688i	$0.913080\pi$
$594$	40.4510	−	14.0933i	1.65972	−	0.578256i
$595$	1.92660	−	9.84827i	0.0789830	−	0.403740i
$596$	10.7561	+	13.5625i	0.440587	+	0.555540i
$597$	−5.30690	−	5.30690i	−0.217197	−	0.217197i
$598$	13.1581	−	27.2292i	0.538074	−	1.11348i
$599$	10.9277			0.446494			0.223247	−	0.974762i	$-0.428334\pi$
$599$	10.9277			0.446494			0.223247	+	0.974762i	$0.428334\pi$
$600$	20.3772	−	14.5285i	0.831895	−	0.593122i
$601$	3.80159			0.155070			0.0775351	−	0.996990i	$-0.475295\pi$
$601$	3.80159			0.155070			0.0775351	+	0.996990i	$0.475295\pi$
$602$	−2.22730	+	4.60915i	−0.0907778	+	0.187855i
$603$	0.825294	+	0.825294i	0.0336086	+	0.0336086i
$604$	4.67240	−	3.70558i	0.190117	−	0.150778i
$605$	−10.5635	+	53.9976i	−0.429466	+	2.19531i
$606$	21.7786	−	7.58776i	0.884694	−	0.308232i
$607$	−12.0874	−	12.0874i	−0.490611	−	0.490611i	0.417887	−	0.908499i	$-0.362771\pi$
$607$	−12.0874	−	12.0874i	−0.490611	−	0.490611i	−0.908499	+	0.417887i	$0.862771\pi$
$608$	−22.5827	−	18.2591i	−0.915849	−	0.740504i
$609$		−	3.52536i		−	0.142855i
$610$	13.7955	+	10.3430i	0.558562	+	0.418775i
$611$	−14.6577			−0.592989
$612$	−0.135338	+	1.17277i	−0.00547072	+	0.0474065i
$613$	−5.61506	+	5.61506i	−0.226790	+	0.226790i	−0.811350	−	0.584560i	$-0.801267\pi$
$613$	−5.61506	+	5.61506i	−0.226790	+	0.226790i	0.584560	+	0.811350i	$0.301267\pi$
$614$	−17.5467	+	6.11336i	−0.708128	+	0.246715i
$615$	14.8238	−	9.97287i	0.597754	−	0.402145i
$616$	−9.03700	+	14.2542i	−0.364111	+	0.574318i
$617$	1.40675	−	1.40675i	0.0566337	−	0.0566337i	−0.678223	−	0.734856i	$-0.737250\pi$
$617$	1.40675	−	1.40675i	0.0566337	−	0.0566337i	0.734856	+	0.678223i	$0.237250\pi$
$618$	−1.96456	−	0.949343i	−0.0790262	−	0.0381882i
$619$		−	28.1868i		−	1.13292i	−0.824089	−	0.566461i	$-0.808312\pi$
$619$		−	28.1868i		−	1.13292i	0.824089	−	0.566461i	$-0.191688\pi$
$620$	15.8213	+	30.5900i	0.635399	+	1.22852i
$621$			40.0999i			1.60915i
$622$	7.42219	−	15.3594i	0.297603	−	0.615857i
$623$	2.18346	−	2.18346i	0.0874785	−	0.0874785i
$624$	−4.36421	+	18.6572i	−0.174708	+	0.746887i
$625$	17.8998	+	17.4528i	0.715990	+	0.698110i
$626$	−0.547195	−	1.57057i	−0.0218703	−	0.0627726i
$627$	−38.3319	+	38.3319i	−1.53083	+	1.53083i
$628$	0.279205	−	2.41946i	0.0111415	−	0.0965468i
$629$	19.7190			0.786248
$630$	−0.0588911	−	0.411746i	−0.00234628	−	0.0164043i
$631$		−	30.5820i		−	1.21745i	−0.793382	−	0.608725i	$-0.791681\pi$
$631$		−	30.5820i		−	1.21745i	0.793382	−	0.608725i	$-0.208319\pi$
$632$	5.22539	+	23.3278i	0.207855	+	0.927929i
$633$	8.22700	+	8.22700i	0.326994	+	0.326994i
$634$	7.43046	+	21.3271i	0.295101	+	0.847006i
$635$	1.44570	−	0.972608i	0.0573708	−	0.0385968i
$636$	−18.9413	−	23.8832i	−0.751070	−	0.947031i
$637$	−1.91409	−	1.91409i	−0.0758389	−	0.0758389i
$638$	15.1367	+	7.31455i	0.599267	+	0.289586i
$639$	0.604532			0.0239149
$640$	−5.09071	+	24.7807i	−0.201228	+	0.979544i
$641$	34.3944			1.35850			0.679249	−	0.733908i	$-0.262306\pi$
$641$	34.3944			1.35850			0.679249	+	0.733908i	$0.262306\pi$
$642$	−24.1410	−	11.6657i	−0.952767	−	0.460410i
$643$	30.4856	+	30.4856i	1.20223	+	1.20223i	0.973485	+	0.228750i	$0.0734637\pi$
$643$	30.4856	+	30.4856i	1.20223	+	1.20223i	0.228750	+	0.973485i	$0.426536\pi$
$644$	−9.81758	−	12.3791i	−0.386867	−	0.487804i
$645$	14.0568	+	2.74991i	0.553485	+	0.108278i
$646$	10.7198	+	30.7682i	0.421765	+	1.21056i
$647$	29.8629	+	29.8629i	1.17403	+	1.17403i	0.981239	+	0.192793i	$0.0617546\pi$
$647$	29.8629	+	29.8629i	1.17403	+	1.17403i	0.192793	+	0.981239i	$0.438245\pi$
$648$	−5.79745	−	25.8816i	−0.227745	−	1.01673i
$649$			44.9091i			1.76284i
$650$	−19.1159	−	0.978140i	−0.749786	−	0.0383658i
$651$	13.6275			0.534104
$652$	2.29555	−	19.8921i	0.0899007	−	0.779035i
$653$	−8.04076	+	8.04076i	−0.314659	+	0.314659i	−0.846712	−	0.532052i	$-0.821421\pi$
$653$	−8.04076	+	8.04076i	−0.314659	+	0.314659i	0.532052	+	0.846712i	$0.321421\pi$
$654$	−8.60346	−	24.6939i	−0.336422	−	0.965606i
$655$	6.15384	−	31.4568i	0.240450	−	1.22912i
$656$	−4.11359	+	17.5858i	−0.160609	+	0.686611i
$657$	−0.272801	+	0.272801i	−0.0106430	+	0.0106430i
$658$	−3.33189	+	6.89498i	−0.129890	+	0.268794i
$659$			16.8820i			0.657631i	0.944394	+	0.328816i	$0.106649\pi$
$659$			16.8820i			0.657631i	−0.944394	+	0.328816i	$0.893351\pi$
$660$	44.9999	+	14.3195i	1.75162	+	0.557387i
$661$		−	36.6473i		−	1.42542i	−0.701461	−	0.712708i	$-0.747469\pi$
$661$		−	36.6473i		−	1.42542i	0.701461	−	0.712708i	$-0.252531\pi$
$662$	43.6745	+	21.1050i	1.69746	+	0.820269i
$663$	15.2009	−	15.2009i	0.590356	−	0.590356i
$664$	−10.2965	+	16.2408i	−0.399581	+	0.630266i
$665$	−6.40776	−	9.52458i	−0.248482	−	0.369347i
$666$	0.771825	−	0.268908i	0.0299076	−	0.0104200i
$667$	−11.1282	+	11.1282i	−0.430886	+	0.430886i
$668$	2.38269	−	20.6472i	0.0921890	−	0.798864i
$669$	18.5469			0.717066
$670$	−3.97302	−	27.7779i	−0.153491	−	1.07316i
$671$			32.5353i			1.25601i
$672$	7.78430	+	6.29394i	0.300286	+	0.242794i
$673$	−25.2704	−	25.2704i	−0.974102	−	0.974102i	0.0255714	−	0.999673i	$-0.491859\pi$
$673$	−25.2704	−	25.2704i	−0.974102	−	0.974102i	−0.999673	+	0.0255714i	$0.991859\pi$
$674$	−38.4994	+	13.4134i	−1.48294	+	0.516664i
$675$	23.3866	−	9.86070i	0.900150	−	0.379538i
$676$	−8.88894	+	7.04963i	−0.341882	+	0.271139i
$677$	19.3899	+	19.3899i	0.745215	+	0.745215i	0.973576	−	0.228362i	$-0.0733369\pi$
$677$	19.3899	+	19.3899i	0.745215	+	0.745215i	−0.228362	+	0.973576i	$0.573337\pi$
$678$	−14.6240	+	30.2628i	−0.561632	+	1.16224i
$679$	13.1226			0.503600
$680$	19.5172	−	20.6078i	0.748451	−	0.790272i
$681$	0.471790			0.0180790
$682$	−28.2749	+	58.5119i	−1.08270	+	2.24053i
$683$	−20.2968	−	20.2968i	−0.776634	−	0.776634i	0.202623	−	0.979257i	$-0.435054\pi$
$683$	−20.2968	−	20.2968i	−0.776634	−	0.776634i	−0.979257	+	0.202623i	$0.935054\pi$
$684$	0.839171	+	1.05812i	0.0320865	+	0.0404582i
$685$	−14.3877	−	21.3861i	−0.549725	−	0.817119i
$686$	−1.33548	+	0.465288i	−0.0509889	+	0.0177648i
$687$	−15.7673	−	15.7673i	−0.601560	−	0.601560i
$688$	−12.3010	+	7.63716i	−0.468971	+	0.291164i
$689$			23.3141i			0.888196i
$690$	−26.5184	+	35.3702i	−1.00954	+	1.34652i
$691$	−24.2104			−0.921007			−0.460504	−	0.887658i	$-0.652331\pi$
$691$	−24.2104			−0.921007			−0.460504	+	0.887658i	$0.652331\pi$
$692$	−22.5452	−	2.60172i	−0.857041	−	0.0989026i
$693$	0.554976	−	0.554976i	0.0210818	−	0.0210818i
$694$	−23.0890	+	8.04431i	−0.876446	+	0.305358i
$695$	26.2281	+	5.13096i	0.994888	+	0.194629i
$696$	5.33906	−	8.42138i	0.202376	−	0.319212i
$697$	14.3280	−	14.3280i	0.542712	−	0.542712i
$698$	−9.45095	−	4.56702i	−0.357724	−	0.172864i
$699$		−	43.4698i		−	1.64418i
$700$	−4.80539	+	8.76973i	−0.181627	+	0.331465i
$701$			49.5132i			1.87009i	0.354531	+	0.935044i	$0.384641\pi$
$701$			49.5132i			1.87009i	−0.354531	+	0.935044i	$0.615359\pi$
$702$	−8.45485	+	17.4964i	−0.319108	+	0.660358i
$703$	15.9505	−	15.9505i	0.601585	−	0.601585i
$704$	−43.1752	+	20.3642i	−1.62723	+	0.767503i
$705$	21.0280	+	4.11368i	0.791961	+	0.154930i
$706$	2.41520	+	6.93217i	0.0908973	+	0.260896i
$707$	−6.51626	+	6.51626i	−0.245069	+	0.245069i
$708$	26.4610	+	3.05361i	0.994467	+	0.114762i
$709$	−9.15317			−0.343755			−0.171877	−	0.985118i	$-0.554983\pi$
$709$	−9.15317			−0.343755			−0.171877	+	0.985118i	$0.554983\pi$
$710$	−11.6289	−	8.71861i	−0.436424	−	0.327204i
$711$		−	1.11169i		−	0.0416918i
$712$	8.52264	−	1.90906i	0.319400	−	0.0715451i
$713$	−43.0168	−	43.0168i	−1.61099	−	1.61099i
$714$	−3.69513	−	10.6059i	−0.138287	−	0.396914i
$715$	−20.1610	−	29.9675i	−0.753977	−	1.12072i
$716$	−8.67668	+	6.88129i	−0.324263	+	0.257166i
$717$	−22.7169	−	22.7169i	−0.848377	−	0.848377i
$718$	6.22661	+	3.00891i	0.232375	+	0.112291i
$719$	50.9056			1.89846			0.949229	−	0.314587i	$-0.101866\pi$
$719$	50.9056			1.89846			0.949229	+	0.314587i	$0.101866\pi$
$720$	0.482898	−	1.07277i	0.0179966	−	0.0399797i
$721$	0.871855			0.0324696
$722$	9.36589	+	4.52591i	0.348562	+	0.168437i
$723$	−5.42862	−	5.42862i	−0.201893	−	0.201893i
$724$	−5.99990	+	4.75839i	−0.222984	+	0.176844i
$725$	9.22650	+	3.75359i	0.342664	+	0.139405i
$726$	20.2602	+	58.1514i	0.751928	+	2.15820i
$727$	34.7785	+	34.7785i	1.28986	+	1.28986i	0.934868	+	0.354996i	$0.115518\pi$
$727$	34.7785	+	34.7785i	1.28986	+	1.28986i	0.354996	+	0.934868i	$0.384482\pi$
$728$	−1.67354	−	7.47121i	−0.0620256	−	0.276902i
$729$		−	25.7147i		−	0.952396i
$730$	9.18201	−	1.31328i	0.339842	−	0.0486068i
$731$	16.2446			0.600827
$732$	19.1702	+	2.21225i	0.708552	+	0.0817670i
$733$	34.3469	−	34.3469i	1.26863	−	1.26863i	0.321836	−	0.946795i	$-0.395700\pi$
$733$	34.3469	−	34.3469i	1.26863	−	1.26863i	0.946795	−	0.321836i	$-0.104300\pi$
$734$	−6.07964	−	17.4499i	−0.224404	−	0.644089i
$735$	2.20877	+	3.28314i	0.0814716	+	0.121100i
$736$	−4.70447	−	44.4396i	−0.173409	−	1.63807i
$737$	37.4408	−	37.4408i	1.37915	−	1.37915i
$738$	0.365424	−	0.756205i	0.0134514	−	0.0278363i
$739$		−	20.3807i		−	0.749717i	−0.927082	−	0.374858i	$-0.877691\pi$
$739$		−	20.3807i		−	0.749717i	0.927082	−	0.374858i	$-0.122309\pi$
$740$	−18.7251	−	5.95857i	−0.688350	−	0.219042i
$741$		−	24.5918i		−	0.903402i
$742$	10.9669	+	5.29958i	0.402608	+	0.194554i
$743$	−24.0469	+	24.0469i	−0.882195	+	0.882195i	−0.993757	−	0.111562i	$-0.964415\pi$
$743$	−24.0469	+	24.0469i	−0.882195	+	0.882195i	0.111562	+	0.993757i	$0.464415\pi$
$744$	32.5534	+	20.6385i	1.19347	+	0.756644i
$745$	−3.71559	+	18.9931i	−0.136129	+	0.695853i
$746$	12.3187	−	4.29188i	0.451018	−	0.157137i
$747$	0.632323	−	0.632323i	0.0231355	−	0.0231355i
$748$	53.2047	+	6.13983i	1.94536	+	0.224494i
$749$	10.7135			0.391464
$750$	27.1491	+	6.76809i	0.991346	+	0.247136i
$751$			52.0925i			1.90088i	0.310906	+	0.950441i	$0.399367\pi$
$751$			52.0925i			1.90088i	−0.310906	+	0.950441i	$0.600633\pi$
$752$	−18.4015	+	11.4247i	−0.671033	+	0.416615i
$753$	5.62470	+	5.62470i	0.204975	+	0.204975i
$754$	−7.20177	+	2.50913i	−0.262273	+	0.0913772i
$755$	6.54330	+	1.28006i	0.238135	+	0.0465860i
$756$	6.30838	+	7.95429i	0.229434	+	0.289295i
$757$	11.3468	+	11.3468i	0.412407	+	0.412407i	0.882576	−	0.470169i	$-0.155807\pi$
$757$	11.3468	+	11.3468i	0.412407	+	0.412407i	−0.470169	+	0.882576i	$0.655807\pi$
$758$	17.4169	−	36.0423i	0.632610	−	1.30912i
$759$	−83.4173			−3.02786
$760$	−0.882147	−	32.4567i	−0.0319988	−	1.17733i
$761$	−10.6758			−0.386999			−0.193500	−	0.981100i	$-0.561984\pi$
$761$	−10.6758			−0.386999			−0.193500	+	0.981100i	$0.561984\pi$
$762$	0.848487	−	1.75585i	0.0307374	−	0.0636078i
$763$	7.38853	+	7.38853i	0.267483	+	0.267483i
$764$	−6.28654	+	4.98572i	−0.227439	+	0.180377i
$765$	−1.09513	+	0.736763i	−0.0395947	+	0.0266377i
$766$	−34.5218	+	12.0276i	−1.24733	+	0.434574i
$767$	−14.4057	−	14.4057i	−0.520158	−	0.520158i
$768$	9.06313	+	26.8241i	0.327038	+	0.967931i
$769$			4.73034i			0.170580i	0.996356	+	0.0852902i	$0.0271817\pi$
$769$			4.73034i			0.170580i	−0.996356	+	0.0852902i	$0.972818\pi$
$770$	−18.6795	+	2.67169i	−0.673163	+	0.0962810i
$771$	−4.26571			−0.153626
$772$	3.08696	−	26.7501i	0.111102	−	0.962757i
$773$	15.5911	−	15.5911i	0.560772	−	0.560772i	−0.368755	−	0.929527i	$-0.620216\pi$
$773$	15.5911	−	15.5911i	0.560772	−	0.560772i	0.929527	+	0.368755i	$0.120216\pi$
$774$	0.635831	−	0.221527i	0.0228545	−	0.00796261i
$775$	−14.5098	+	35.6657i	−0.521206	+	1.28115i
$776$	31.3473	+	19.8738i	1.12530	+	0.713429i
$777$	−5.49817	+	5.49817i	−0.197246	+	0.197246i
$778$	35.5942	+	17.2003i	1.27611	+	0.616661i
$779$		−	23.1796i		−	0.830494i
$780$	−19.0281	+	9.84146i	−0.681316	+	0.352381i
$781$		−	27.4256i		−	0.981364i
$782$	−21.8145	+	45.1427i	−0.780085	+	1.61430i
$783$	7.15053	−	7.15053i	0.255539	−	0.255539i
$784$	−3.89486	−	0.911068i	−0.139102	−	0.0325381i
$785$	2.25929	−	1.51996i	0.0806374	−	0.0542496i
$786$	−11.8028	−	33.8766i	−0.420991	−	1.20834i
$787$	−7.86946	+	7.86946i	−0.280516	+	0.280516i	−0.833315	−	0.552799i	$-0.813560\pi$
$787$	−7.86946	+	7.86946i	−0.280516	+	0.280516i	0.552799	+	0.833315i	$0.313560\pi$
$788$	2.61932	−	22.6977i	0.0933095	−	0.808574i
$789$	20.8317			0.741630
$790$	−16.0329	+	21.3847i	−0.570427	+	0.760834i
$791$		−	13.4304i		−	0.477529i
$792$	2.16622	−	0.485231i	0.0769734	−	0.0172419i
$793$	−10.4365	−	10.4365i	−0.370610	−	0.370610i
$794$	−6.45898	−	18.5387i	−0.229221	−	0.657914i
$795$	6.54308	−	33.4464i	0.232059	−	1.18622i
$796$	5.27068	+	6.64585i	0.186814	+	0.235556i
$797$	−34.2043	−	34.2043i	−1.21158	−	1.21158i	−0.970507	−	0.241072i	$-0.922501\pi$
$797$	−34.2043	−	34.2043i	−1.21158	−	1.21158i	−0.241072	−	0.970507i	$-0.577499\pi$
$798$	−11.5679	−	5.59002i	−0.409500	−	0.197885i
$799$	24.3008			0.859700
$800$	−24.7606	+	13.6715i	−0.875421	+	0.483361i
$801$	−0.406150			−0.0143506
$802$	−7.18140	−	3.47029i	−0.253584	−	0.122540i
$803$	12.3761	+	12.3761i	0.436742	+	0.436742i
$804$	−19.5148	−	24.6064i	−0.688235	−	0.867802i
$805$	3.39139	−	17.3358i	0.119531	−	0.611008i
$806$	−9.69923	−	27.8389i	−0.341641	−	0.980585i
$807$	−40.2022	−	40.2022i	−1.41519	−	1.41519i
$808$	−25.4348	+	5.69736i	−0.894792	+	0.200432i
$809$		−	15.4940i		−	0.544740i	−0.962193	−	0.272370i	$-0.912192\pi$
$809$		−	15.4940i		−	0.544740i	0.962193	−	0.272370i	$-0.0878075\pi$
$810$	17.7882	−	23.7259i	0.625013	−	0.833642i
$811$	−30.6872			−1.07757			−0.538787	−	0.842442i	$-0.681117\pi$
$811$	−30.6872			−1.07757			−0.538787	+	0.842442i	$0.681117\pi$
$812$	−0.456760	+	3.95806i	−0.0160291	+	0.138901i
$813$	14.7259	−	14.7259i	0.516459	−	0.516459i
$814$	−12.1994	−	35.0151i	−0.427590	−	1.22728i
$815$	18.5752	−	12.4967i	0.650662	−	0.437740i
$816$	7.23534	−	30.9315i	0.253288	−	1.08282i
$817$	13.1401	−	13.1401i	0.459713	−	0.459713i
$818$	−11.3759	+	23.5412i	−0.397749	+	0.823099i
$819$			0.356044i			0.0124412i
$820$	−17.9354	+	9.27630i	−0.626332	+	0.323942i
$821$		−	23.7738i		−	0.829710i	−0.909888	−	0.414855i	$-0.863832\pi$
$821$		−	23.7738i		−	0.829710i	0.909888	−	0.414855i	$-0.136168\pi$
$822$	−25.9741	−	12.5516i	−0.905951	−	0.437787i
$823$	−18.0970	+	18.0970i	−0.630821	+	0.630821i	−0.948274	−	0.317453i	$-0.897173\pi$
$823$	−18.0970	+	18.0970i	−0.630821	+	0.630821i	0.317453	+	0.948274i	$0.397173\pi$
$824$	2.08269	+	1.32040i	0.0725539	+	0.0459984i
$825$	20.5126	+	48.6496i	0.714156	+	1.69376i
$826$	−10.0510	+	3.50181i	−0.349719	+	0.121844i
$827$	16.1168	−	16.1168i	0.560437	−	0.560437i	−0.368995	−	0.929431i	$-0.620298\pi$
$827$	16.1168	−	16.1168i	0.560437	−	0.560437i	0.929431	+	0.368995i	$0.120298\pi$
$828$	−0.238235	+	2.06442i	−0.00827923	+	0.0717437i
$829$	−8.67660			−0.301351			−0.150675	−	0.988583i	$-0.548145\pi$
$829$	−8.67660			−0.301351			−0.150675	+	0.988583i	$0.548145\pi$
$830$	−21.2829	+	3.04405i	−0.738740	+	0.105660i
$831$		−	7.70771i		−	0.267378i
$832$	7.31719	−	20.3818i	0.253678	−	0.706611i
$833$	3.17333	+	3.17333i	0.109949	+	0.109949i
$834$	28.2457	−	9.84095i	0.978069	−	0.340764i
$835$	19.2804	−	12.9711i	0.667224	−	0.448882i
$836$	48.0032	−	38.0703i	1.66023	−	1.31669i
$837$	27.6409	+	27.6409i	0.955409	+	0.955409i
$838$	10.9789	−	22.7196i	0.379260	−	0.784837i
$839$	−20.1640			−0.696138			−0.348069	−	0.937469i	$-0.613163\pi$
$839$	−20.1640			−0.696138			−0.348069	+	0.937469i	$0.613163\pi$
$840$	0.304078	+	11.1879i	0.0104917	+	0.386019i
$841$	−25.0313			−0.863148
$842$	21.5935	−	44.6854i	0.744161	−	1.53996i
$843$	−11.7009	−	11.7009i	−0.403001	−	0.403001i
$844$	−8.17086	−	10.3027i	−0.281253	−	0.354634i
$845$	−12.4482	−	2.43522i	−0.428231	−	0.0837743i
$846$	0.951161	−	0.331389i	0.0327016	−	0.0113934i
$847$	−17.3992	−	17.3992i	−0.597844	−	0.597844i
$848$	18.1717	+	29.2687i	0.624019	+	1.00509i
$849$		−	23.1133i		−	0.793246i
$850$	31.6918	+	1.62164i	1.08702	+	0.0556217i
$851$	34.7112			1.18989
$852$	−16.1595	−	1.86481i	−0.553616	−	0.0638874i
$853$	−2.19308	+	2.19308i	−0.0750895	+	0.0750895i	−0.743654	−	0.668565i	$-0.766909\pi$
$853$	−2.19308	+	2.19308i	−0.0750895	+	0.0750895i	0.668565	+	0.743654i	$0.266909\pi$
$854$	−7.28164	+	2.53696i	−0.249173	+	0.0868130i
$855$	−0.289883	+	1.48180i	−0.00991380	+	0.0506766i
$856$	25.5925	+	16.2254i	0.874735	+	0.554572i
$857$	36.4894	−	36.4894i	1.24645	−	1.24645i	0.289178	−	0.957275i	$-0.406618\pi$
$857$	36.4894	−	36.4894i	1.24645	−	1.24645i	0.957275	−	0.289178i	$-0.0933818\pi$
$858$	−36.3966	−	17.5881i	−1.24256	−	0.600447i
$859$		−	10.4649i		−	0.357058i	−0.983935	−	0.178529i	$-0.942866\pi$
$859$		−	10.4649i		−	0.357058i	0.983935	−	0.178529i	$-0.0571338\pi$
$860$	−15.4258	−	4.90869i	−0.526016	−	0.167385i
$861$			7.99004i			0.272300i
$862$	1.61120	−	3.33421i	0.0548778	−	0.113564i
$863$	−1.00046	+	1.00046i	−0.0340560	+	0.0340560i	−0.723930	−	0.689874i	$-0.757666\pi$
$863$	−1.00046	+	1.00046i	−0.0340560	+	0.0340560i	0.689874	+	0.723930i	$0.257666\pi$
$864$	3.02291	+	28.5551i	0.102841	+	0.971464i
$865$	−14.1634	−	21.0527i	−0.481571	−	0.715814i
$866$	−4.13172	−	11.8590i	−0.140402	−	0.402984i
$867$	−3.92915	+	3.92915i	−0.133441	+	0.133441i
$868$	−15.3001	−	1.76564i	−0.519321	−	0.0599297i
$869$	−50.4338			−1.71085
$870$	11.0359	−	1.57843i	0.374150	−	0.0535139i
$871$			24.0201i			0.813889i
$872$	6.46001	+	28.8395i	0.218763	+	0.976628i
$873$	−1.22048	−	1.22048i	−0.0413071	−	0.0413071i
$874$	18.8700	+	54.1611i	0.638287	+	1.83203i
$875$	−10.9443	+	2.28505i	−0.369986	+	0.0772490i
$876$	8.13367	−	6.45064i	0.274811	−	0.217947i
$877$	3.79667	+	3.79667i	0.128205	+	0.128205i	0.768298	−	0.640093i	$-0.221104\pi$
$877$	3.79667	+	3.79667i	0.128205	+	0.128205i	−0.640093	+	0.768298i	$0.721104\pi$
$878$	41.1423	+	19.8814i	1.38849	+	0.670963i
$879$	33.8302			1.14106
$880$	−48.6678	−	21.9075i	−1.64059	−	0.738501i
$881$	26.5704			0.895180			0.447590	−	0.894239i	$-0.352282\pi$
$881$	26.5704			0.895180			0.447590	+	0.894239i	$0.352282\pi$
$882$	0.167482	+	0.0809332i	0.00563943	+	0.00272516i
$883$	−19.0483	−	19.0483i	−0.641025	−	0.641025i	0.309782	−	0.950808i	$-0.399744\pi$
$883$	−19.0483	−	19.0483i	−0.641025	−	0.641025i	−0.950808	+	0.309782i	$0.899744\pi$
$884$	−19.0362	+	15.0972i	−0.640256	+	0.507774i
$885$	16.6234	+	24.7093i	0.558791	+	0.830594i
$886$	−4.52031	−	12.9743i	−0.151863	−	0.435880i
$887$	6.60791	+	6.60791i	0.221872	+	0.221872i	0.809286	−	0.587414i	$-0.199854\pi$
$887$	6.60791	+	6.60791i	0.221872	+	0.221872i	−0.587414	+	0.809286i	$0.699854\pi$
$888$	−21.4609	+	4.80721i	−0.720179	+	0.161319i
$889$			0.779232i			0.0261346i
$890$	7.81276	+	5.85753i	0.261884	+	0.196345i
$891$	55.9552			1.87457
$892$	−20.8234	−	2.40302i	−0.697218	−	0.0804591i
$893$	19.6567	−	19.6567i	0.657785	−	0.657785i
$894$	7.12633	+	20.4542i	0.238340	+	0.684089i
$895$	−12.1509	−	2.37707i	−0.406161	−	0.0794568i
$896$	−7.92427	−	8.07502i	−0.264731	−	0.269768i
$897$	26.7581	−	26.7581i	0.893427	−	0.893427i
$898$	−9.31645	+	19.2794i	−0.310894	+	0.643361i
$899$			15.3413i			0.511662i
$900$	1.26257	−	0.368708i	0.0420856	−	0.0122903i
$901$		−	38.6520i		−	1.28768i
$902$	−34.3065	−	16.5781i	−1.14228	−	0.551989i
$903$	−4.52941	+	4.52941i	−0.150729	+	0.150729i
$904$	20.3399	−	32.0825i	0.676496	−	1.06705i
$905$	−8.40234	−	1.64374i	−0.279303	−	0.0546397i
$906$	7.04665	−	2.45509i	0.234109	−	0.0815648i
$907$	−19.0548	+	19.0548i	−0.632706	+	0.632706i	−0.948746	−	0.316040i	$-0.897647\pi$
$907$	−19.0548	+	19.0548i	−0.632706	+	0.632706i	0.316040	+	0.948746i	$0.397647\pi$
$908$	−0.529697	−	0.0611270i	−0.0175786	−	0.00202857i
$909$	1.21210			0.0402030
$910$	5.13489	−	6.84891i	0.170220	−	0.227039i
$911$			16.8983i			0.559864i	0.960020	+	0.279932i	$0.0903120\pi$
$911$			16.8983i			0.559864i	−0.960020	+	0.279932i	$0.909688\pi$
$912$	−19.1676	−	30.8728i	−0.634702	−	1.02230i
$913$	−28.6864	−	28.6864i	−0.949380	−	0.949380i
$914$	45.7030	−	15.9232i	1.51172	−	0.526691i
$915$	12.0432	+	17.9012i	0.398135	+	0.591794i
$916$	15.6597	+	19.7454i	0.517411	+	0.652408i
$917$	10.1361	+	10.1361i	0.334722	+	0.334722i
$918$	14.0171	−	29.0069i	0.462634	−	0.957371i
$919$	36.5640			1.20613			0.603067	−	0.797691i	$-0.293945\pi$
$919$	36.5640			1.20613			0.603067	+	0.797691i	$0.293945\pi$
$920$	34.3560	−	36.2757i	1.13268	−	1.19597i
$921$	−23.2507			−0.766138
$922$	−7.54077	+	15.6048i	−0.248342	+	0.513917i
$923$	8.79741	+	8.79741i	0.289570	+	0.289570i
$924$	−16.5468	+	13.1229i	−0.544350	+	0.431712i
$925$	−8.53560	−	20.2438i	−0.280649	−	0.665613i
$926$	17.9676	−	6.26001i	0.590453	−	0.205717i
$927$	−0.0810879	−	0.0810879i	−0.00266328	−	0.00266328i
$928$	−7.08548	+	8.76326i	−0.232592	+	0.287668i
$929$			27.3379i			0.896929i	0.893801	+	0.448464i	$0.148029\pi$
$929$			27.3379i			0.896929i	−0.893801	+	0.448464i	$0.851971\pi$
$930$	6.10155	+	42.6598i	0.200078	+	1.39887i
$931$	5.13375			0.168252
$932$	−5.63214	+	48.8053i	−0.184487	+	1.59867i
$933$	15.0937	−	15.0937i	0.494145	−	0.494145i
$934$	−39.9707	+	13.9260i	−1.30788	+	0.455672i
$935$	33.4245	+	49.6826i	1.09310	+	1.62479i
$936$	−0.539219	+	0.850518i	−0.0176249	+	0.0278000i
$937$	30.7841	−	30.7841i	1.00567	−	1.00567i	0.00568761	−	0.999984i	$-0.498190\pi$
$937$	30.7841	−	30.7841i	1.00567	−	1.00567i	0.999984	−	0.00568761i	$-0.00181043\pi$
$938$	11.2990	+	5.46006i	0.368926	+	0.178277i
$939$		−	2.08113i		−	0.0679150i
$940$	−23.0760	−	7.34307i	−0.752656	−	0.239504i
$941$			39.9120i			1.30109i	0.759466	+	0.650547i	$0.225460\pi$
$941$			39.9120i			1.30109i	−0.759466	+	0.650547i	$0.774540\pi$
$942$	1.32599	−	2.74398i	0.0432029	−	0.0894038i
$943$	25.2215	−	25.2215i	0.821325	−	0.821325i
$944$	−29.3132	−	6.85681i	−0.954064	−	0.223170i
$945$	−2.17917	+	11.1393i	−0.0708883	+	0.362362i
$946$	−10.0499	−	28.8455i	−0.326751	−	0.937848i
$947$	14.8395	−	14.8395i	0.482219	−	0.482219i	−0.423620	−	0.905840i	$-0.639241\pi$
$947$	14.8395	−	14.8395i	0.482219	−	0.482219i	0.905840	+	0.423620i	$0.139241\pi$
$948$	−3.42926	+	29.7163i	−0.111377	+	0.965140i
$949$	−7.93985			−0.257738
$950$	26.9469	−	24.3235i	0.874274	−	0.789158i
$951$			28.2600i			0.916393i
$952$	2.77453	+	12.3864i	0.0899231	+	0.401445i
$953$	−4.99989	−	4.99989i	−0.161962	−	0.161962i	0.621473	−	0.783435i	$-0.286534\pi$
$953$	−4.99989	−	4.99989i	−0.161962	−	0.161962i	−0.783435	+	0.621473i	$0.786534\pi$
$954$	−0.527096	−	1.51288i	−0.0170654	−	0.0489814i
$955$	−8.80377	−	1.72227i	−0.284883	−	0.0557313i
$956$	22.5618	+	28.4484i	0.729701	+	0.920087i
$957$	14.8748	+	14.8748i	0.480834	+	0.480834i
$958$	−28.3246	−	13.6874i	−0.915126	−	0.442220i
$959$	11.5271			0.372229
$960$	−16.2174	+	27.1862i	−0.523413	+	0.877429i
$961$	−28.3030			−0.913000
$962$	15.1452	+	7.31867i	0.488300	+	0.235963i
$963$	−0.996425	−	0.996425i	−0.0321094	−	0.0321094i
$964$	5.39157	+	6.79829i	0.173651	+	0.218958i
$965$	24.9792	−	16.8050i	0.804110	−	0.540973i
$966$	−6.50452	−	18.6694i	−0.209279	−	0.600679i
$967$	−12.1191	−	12.1191i	−0.389724	−	0.389724i	0.484865	−	0.874589i	$-0.338869\pi$
$967$	−12.1191	−	12.1191i	−0.389724	−	0.389724i	−0.874589	+	0.484865i	$0.838869\pi$
$968$	−15.2126	−	67.9139i	−0.488952	−	2.18283i
$969$			40.7702i			1.30973i
$970$	5.87548	+	41.0793i	0.188650	+	1.31898i
$971$	−27.9027			−0.895440			−0.447720	−	0.894174i	$-0.647764\pi$
$971$	−27.9027			−0.895440			−0.447720	+	0.894174i	$0.647764\pi$
$972$	0.313179	−	2.71386i	0.0100452	−	0.0870470i
$973$	−8.45127	+	8.45127i	−0.270935	+	0.270935i
$974$	2.56967	+	7.37553i	0.0823375	+	0.236327i
$975$	−22.1854	−	9.02562i	−0.710502	−	0.289051i
$976$	−21.2365	−	4.96755i	−0.679765	−	0.159007i
$977$	−26.0184	+	26.0184i	−0.832402	+	0.832402i	−0.987845	−	0.155443i	$-0.950320\pi$
$977$	−26.0184	+	26.0184i	−0.832402	+	0.832402i	0.155443	+	0.987845i	$0.450320\pi$
$978$	10.9019	−	22.5603i	0.348604	−	0.721398i
$979$			18.4257i			0.588887i
$980$	−2.05449	−	3.97229i	−0.0656283	−	0.126890i
$981$		−	1.37436i		−	0.0438798i
$982$	35.0617	+	16.9430i	1.11886	+	0.540672i
$983$	−20.5832	+	20.5832i	−0.656503	+	0.656503i	−0.954551	−	0.298048i	$-0.903664\pi$
$983$	−20.5832	+	20.5832i	−0.656503	+	0.656503i	0.298048	+	0.954551i	$0.403664\pi$
$984$	−12.1007	+	19.0866i	−0.385756	+	0.608459i
$985$	21.1951	−	14.2593i	0.675334	−	0.454338i
$986$	11.9397	−	4.15984i	0.380237	−	0.132476i
$987$	−6.77569	+	6.77569i	−0.215673	+	0.215673i
$988$	−3.18622	+	27.6102i	−0.101367	+	0.878396i
$989$	28.5952			0.909274
$990$	1.98579	+	1.48882i	0.0631126	+	0.0473180i
$991$			19.7638i			0.627817i	0.949453	+	0.313908i	$0.101638\pi$
$991$			19.7638i			0.627817i	−0.949453	+	0.313908i	$0.898362\pi$
$992$	−33.8750	−	27.3894i	−1.07553	−	0.869615i
$993$	42.9189	+	42.9189i	1.36199	+	1.36199i
$994$	6.13805	−	2.13853i	0.194687	−	0.0678300i
$995$	−1.82071	+	9.30695i	−0.0577203	+	0.295050i
$996$	−18.8529	+	14.9519i	−0.597378	+	0.473768i
$997$	−21.3923	−	21.3923i	−0.677501	−	0.677501i	0.281933	−	0.959434i	$-0.409024\pi$
$997$	−21.3923	−	21.3923i	−0.677501	−	0.677501i	−0.959434	+	0.281933i	$0.909024\pi$
$998$	8.27962	−	17.1338i	0.262087	−	0.542360i
$999$	−22.3040			−0.705668

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.w.a.43.5	✓	72
4.3	odd	2		1120.2.bi.a.463.28		72
5.2	odd	4	inner	280.2.w.a.267.24	yes	72
8.3	odd	2	inner	280.2.w.a.43.24	yes	72
8.5	even	2		1120.2.bi.a.463.27		72
20.7	even	4		1120.2.bi.a.687.27		72
40.27	even	4	inner	280.2.w.a.267.5	yes	72
40.37	odd	4		1120.2.bi.a.687.28		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.w.a.43.5	✓	72	1.1	even	1	trivial
280.2.w.a.43.24	yes	72	8.3	odd	2	inner
280.2.w.a.267.5	yes	72	40.27	even	4	inner
280.2.w.a.267.24	yes	72	5.2	odd	4	inner
1120.2.bi.a.463.27		72	8.5	even	2
1120.2.bi.a.463.28		72	4.3	odd	2
1120.2.bi.a.687.27		72	20.7	even	4
1120.2.bi.a.687.28		72	40.37	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27334 - 0.615319i) q^{2} +(-1.25131 - 1.25131i) q^{3} +(1.24277 + 1.56701i) q^{4} +(-0.429301 + 2.19447i) q^{5} +(0.823380 + 2.36328i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.618244 - 2.76003i) q^{8} +0.131530i q^{9} +O(q^{10})\)	\(q+(-1.27334 - 0.615319i) q^{2} +(-1.25131 - 1.25131i) q^{3} +(1.24277 + 1.56701i) q^{4} +(-0.429301 + 2.19447i) q^{5} +(0.823380 + 2.36328i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.618244 - 2.76003i) q^{8} +0.131530i q^{9} +(1.89694 - 2.53014i) q^{10} +5.96709 q^{11} +(0.405734 - 3.51589i) q^{12} +(-1.91409 + 1.91409i) q^{13} +(0.465288 + 1.33548i) q^{14} +(3.28314 - 2.20877i) q^{15} +(-0.911068 + 3.89486i) q^{16} +(3.17333 - 3.17333i) q^{17} +(0.0809332 - 0.167482i) q^{18} -5.13375i q^{19} +(-3.97229 + 2.05449i) q^{20} +1.76961i q^{21} +(-7.59811 - 3.67166i) q^{22} +(5.58599 - 5.58599i) q^{23} +(-2.68003 + 4.22725i) q^{24} +(-4.63140 - 1.88418i) q^{25} +(3.61505 - 1.25950i) q^{26} +(-3.58933 + 3.58933i) q^{27} +(0.229279 - 1.98681i) q^{28} -1.99216 q^{29} +(-5.53963 + 0.792322i) q^{30} -7.70084i q^{31} +(3.55668 - 4.39887i) q^{32} +(-7.46666 - 7.46666i) q^{33} +(-5.99332 + 2.08810i) q^{34} +(1.85529 - 1.24816i) q^{35} +(-0.206110 + 0.163462i) q^{36} +(3.10699 + 3.10699i) q^{37} +(-3.15889 + 6.53699i) q^{38} +4.79022 q^{39} +(6.32222 - 0.171833i) q^{40} +4.51513 q^{41} +(1.08888 - 2.25331i) q^{42} +(2.55955 + 2.55955i) q^{43} +(7.41570 + 9.35052i) q^{44} +(-0.288640 - 0.0564662i) q^{45} +(-10.5500 + 3.67567i) q^{46} +(3.82891 + 3.82891i) q^{47} +(6.01369 - 3.73364i) q^{48} +1.00000i q^{49} +(4.73796 + 5.24898i) q^{50} -7.94161 q^{51} +(-5.37817 - 0.620641i) q^{52} +(6.09013 - 6.09013i) q^{53} +(6.77901 - 2.36184i) q^{54} +(-2.56168 + 13.0946i) q^{55} +(-1.51447 + 2.38880i) q^{56} +(-6.42389 + 6.42389i) q^{57} +(2.53669 + 1.22582i) q^{58} +7.52612i q^{59} +(7.54134 + 2.39975i) q^{60} +5.45245i q^{61} +(-4.73847 + 9.80576i) q^{62} +(0.0930061 - 0.0930061i) q^{63} +(-7.23555 + 3.41274i) q^{64} +(-3.37869 - 5.02213i) q^{65} +(4.91318 + 14.1019i) q^{66} +(6.27455 - 6.27455i) q^{67} +(8.91636 + 1.02895i) q^{68} -13.9796 q^{69} +(-3.13042 + 0.447737i) q^{70} -4.59614i q^{71} +(0.363028 - 0.0813179i) q^{72} +(2.07406 + 2.07406i) q^{73} +(-2.04445 - 5.86803i) q^{74} +(3.43762 + 8.15298i) q^{75} +(8.04466 - 6.38005i) q^{76} +(-4.21937 - 4.21937i) q^{77} +(-6.09955 - 2.94751i) q^{78} -8.45199 q^{79} +(-8.15604 - 3.67138i) q^{80} +9.37729 q^{81} +(-5.74928 - 2.77825i) q^{82} +(-4.80743 - 4.80743i) q^{83} +(-2.77301 + 2.19921i) q^{84} +(5.60146 + 8.32609i) q^{85} +(-1.68422 - 4.83410i) q^{86} +(2.49280 + 2.49280i) q^{87} +(-3.68912 - 16.4694i) q^{88} +3.08788i q^{89} +(0.332790 + 0.249506i) q^{90} +2.70693 q^{91} +(15.6954 + 1.81125i) q^{92} +(-9.63611 + 9.63611i) q^{93} +(-2.51949 - 7.23149i) q^{94} +(11.2659 + 2.20393i) q^{95} +(-9.95482 + 1.05384i) q^{96} +(-9.27909 + 9.27909i) q^{97} +(0.615319 - 1.27334i) q^{98} +0.784855i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 8 q^{6}+O(q^{10}) \) 72 * q + 8 * q^6	\( 72 q + 8 q^{6} + 16 q^{10} - 16 q^{12} - 8 q^{16} + 8 q^{17} - 28 q^{18} - 20 q^{20} - 36 q^{22} - 8 q^{25} - 32 q^{26} - 4 q^{30} + 40 q^{32} + 64 q^{36} - 4 q^{40} + 20 q^{42} - 64 q^{43} + 48 q^{46} - 80 q^{48} - 32 q^{51} + 16 q^{52} - 24 q^{56} + 4 q^{58} - 80 q^{60} - 40 q^{62} - 8 q^{65} + 32 q^{66} - 24 q^{68} + 40 q^{72} - 40 q^{73} + 112 q^{75} - 8 q^{76} + 28 q^{78} - 20 q^{80} - 72 q^{81} + 24 q^{82} + 80 q^{83} + 8 q^{86} - 88 q^{88} + 136 q^{90} - 96 q^{92} - 56 q^{96} - 8 q^{97}+O(q^{100}) \) 72 * q + 8 * q^6 + 16 * q^10 - 16 * q^12 - 8 * q^16 + 8 * q^17 - 28 * q^18 - 20 * q^20 - 36 * q^22 - 8 * q^25 - 32 * q^26 - 4 * q^30 + 40 * q^32 + 64 * q^36 - 4 * q^40 + 20 * q^42 - 64 * q^43 + 48 * q^46 - 80 * q^48 - 32 * q^51 + 16 * q^52 - 24 * q^56 + 4 * q^58 - 80 * q^60 - 40 * q^62 - 8 * q^65 + 32 * q^66 - 24 * q^68 + 40 * q^72 - 40 * q^73 + 112 * q^75 - 8 * q^76 + 28 * q^78 - 20 * q^80 - 72 * q^81 + 24 * q^82 + 80 * q^83 + 8 * q^86 - 88 * q^88 + 136 * q^90 - 96 * q^92 - 56 * q^96 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more