LMFDB - Embedded newform 560.2.t.a.43.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(43,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 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("560.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.t (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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$72$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.19
Character	$\chi$	$=$	560.43
Dual form			560.2.t.a.547.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.975664 - 1.02376i) q^{2} -0.864258i q^{3} +(-0.0961601 + 1.99769i) q^{4} +(-2.07047 - 0.844473i) q^{5} +(-0.884791 + 0.843225i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.13897 - 1.85063i) q^{8} +2.25306 q^{9} +O(q^{10})$	\(q+(-0.975664 - 1.02376i) q^{2} -0.864258i q^{3} +(-0.0961601 + 1.99769i) q^{4} +(-2.07047 - 0.844473i) q^{5} +(-0.884791 + 0.843225i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.13897 - 1.85063i) q^{8} +2.25306 q^{9} +(1.15555 + 2.94359i) q^{10} +(-1.00718 + 1.00718i) q^{11} +(1.72652 + 0.0831072i) q^{12} -4.85780 q^{13} +(1.41380 + 0.0340076i) q^{14} +(-0.729842 + 1.78942i) q^{15} +(-3.98151 - 0.384196i) q^{16} +(-1.58968 + 1.58968i) q^{17} +(-2.19823 - 2.30659i) q^{18} +(-2.19835 + 2.19835i) q^{19} +(1.88609 - 4.05496i) q^{20} +(0.611123 + 0.611123i) q^{21} +(2.01378 + 0.0484394i) q^{22} +(2.91715 + 2.91715i) q^{23} +(-1.59942 - 1.84862i) q^{24} +(3.57373 + 3.49692i) q^{25} +(4.73958 + 4.97321i) q^{26} -4.54000i q^{27} +(-1.34458 - 1.48057i) q^{28} +(6.04289 + 6.04289i) q^{29} +(2.54402 - 0.998695i) q^{30} +8.40005i q^{31} +(3.49129 + 4.45094i) q^{32} +(0.870465 + 0.870465i) q^{33} +(3.17844 + 0.0764540i) q^{34} +(2.06118 - 0.866915i) q^{35} +(-0.216654 + 4.50090i) q^{36} -10.5609 q^{37} +(4.39543 + 0.105727i) q^{38} +4.19839i q^{39} +(-5.99148 + 2.02538i) q^{40} -4.25256i q^{41} +(0.0293913 - 1.22189i) q^{42} +10.2395 q^{43} +(-1.91518 - 2.10889i) q^{44} +(-4.66490 - 1.90265i) q^{45} +(0.140297 - 5.83262i) q^{46} +(0.0941814 + 0.0941814i) q^{47} +(-0.332044 + 3.44105i) q^{48} -1.00000i q^{49} +(0.0932361 - 7.07045i) q^{50} +(1.37389 + 1.37389i) q^{51} +(0.467127 - 9.70436i) q^{52} -3.94479i q^{53} +(-4.64786 + 4.42951i) q^{54} +(2.93588 - 1.23481i) q^{55} +(-0.203888 + 2.82107i) q^{56} +(1.89994 + 1.89994i) q^{57} +(0.290627 - 12.0823i) q^{58} +(6.93924 + 6.93924i) q^{59} +(-3.50453 - 1.63007i) q^{60} +(-9.12105 + 9.12105i) q^{61} +(8.59962 - 8.19563i) q^{62} +(-1.59315 + 1.59315i) q^{63} +(1.15037 - 7.91686i) q^{64} +(10.0580 + 4.10228i) q^{65} +(0.0418641 - 1.74043i) q^{66} -11.8663 q^{67} +(-3.02282 - 3.32855i) q^{68} +(2.52117 - 2.52117i) q^{69} +(-2.89853 - 1.26433i) q^{70} +5.75655 q^{71} +(4.81922 - 4.16957i) q^{72} +(0.0114018 - 0.0114018i) q^{73} +(10.3039 + 10.8118i) q^{74} +(3.02224 - 3.08863i) q^{75} +(-4.18022 - 4.60301i) q^{76} -1.42437i q^{77} +(4.29814 - 4.09622i) q^{78} -10.5026 q^{79} +(7.91917 + 4.15774i) q^{80} +2.83544 q^{81} +(-4.35359 + 4.14907i) q^{82} +16.5380i q^{83} +(-1.27960 + 1.16207i) q^{84} +(4.63383 - 1.94895i) q^{85} +(-9.99031 - 10.4828i) q^{86} +(5.22262 - 5.22262i) q^{87} +(-0.290412 + 4.01825i) q^{88} -8.69343 q^{89} +(2.60353 + 6.63207i) q^{90} +(3.43498 - 3.43498i) q^{91} +(-6.10807 + 5.54704i) q^{92} +7.25981 q^{93} +(0.00452956 - 0.188308i) q^{94} +(6.40807 - 2.69518i) q^{95} +(3.84676 - 3.01737i) q^{96} +(2.30029 - 2.30029i) q^{97} +(-1.02376 + 0.975664i) q^{98} +(-2.26924 + 2.26924i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 8 q^{4} - 144 q^{9}+O(q^{10}) $ 144 * q + 8 * q^4 - 144 * q^9	$ 144 q + 8 q^{4} - 144 q^{9} - 16 q^{12} + 8 q^{16} - 28 q^{18} - 16 q^{19} + 4 q^{22} + 32 q^{26} - 36 q^{30} + 32 q^{34} - 32 q^{36} - 56 q^{38} + 8 q^{40} - 20 q^{42} + 64 q^{43} - 56 q^{44} - 32 q^{46} - 80 q^{48} - 48 q^{50} - 16 q^{51} - 16 q^{52} + 32 q^{54} - 24 q^{56} + 52 q^{58} + 72 q^{60} - 32 q^{61} - 40 q^{62} + 32 q^{64} + 32 q^{66} - 24 q^{68} - 32 q^{69} + 80 q^{72} - 16 q^{73} - 32 q^{74} - 88 q^{75} + 76 q^{78} + 128 q^{80} + 144 q^{81} + 56 q^{82} + 32 q^{86} - 112 q^{87} + 88 q^{88} + 88 q^{90} - 136 q^{92} - 8 q^{94} + 80 q^{95} + 32 q^{96} + 64 q^{99}+O(q^{100}) $ 144 * q + 8 * q^4 - 144 * q^9 - 16 * q^12 + 8 * q^16 - 28 * q^18 - 16 * q^19 + 4 * q^22 + 32 * q^26 - 36 * q^30 + 32 * q^34 - 32 * q^36 - 56 * q^38 + 8 * q^40 - 20 * q^42 + 64 * q^43 - 56 * q^44 - 32 * q^46 - 80 * q^48 - 48 * q^50 - 16 * q^51 - 16 * q^52 + 32 * q^54 - 24 * q^56 + 52 * q^58 + 72 * q^60 - 32 * q^61 - 40 * q^62 + 32 * q^64 + 32 * q^66 - 24 * q^68 - 32 * q^69 + 80 * q^72 - 16 * q^73 - 32 * q^74 - 88 * q^75 + 76 * q^78 + 128 * q^80 + 144 * q^81 + 56 * q^82 + 32 * q^86 - 112 * q^87 + 88 * q^88 + 88 * q^90 - 136 * q^92 - 8 * q^94 + 80 * q^95 + 32 * q^96 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.975664	−	1.02376i	−0.689899	−	0.723906i
$2$	−0.975664	−	1.02376i	−0.689899	−	0.723906i
$3$		−	0.864258i		−	0.498980i	−0.968377	−	0.249490i	$-0.919737\pi$
$3$		−	0.864258i		−	0.498980i	0.968377	−	0.249490i	$-0.0802629\pi$
$4$	−0.0961601	+	1.99769i	−0.0480801	+	0.998843i
$5$	−2.07047	−	0.844473i	−0.925945	−	0.377660i
$5$	−2.07047	−	0.844473i	−0.925945	−	0.377660i
$6$	−0.884791	+	0.843225i	−0.361214	+	0.344245i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	2.13897	−	1.85063i	0.756239	−	0.654295i
$9$	2.25306			0.751019
$10$	1.15555	+	2.94359i	0.365418	+	0.930844i
$11$	−1.00718	+	1.00718i	−0.303677	+	0.303677i	−0.842451	−	0.538774i	$-0.818888\pi$
$11$	−1.00718	+	1.00718i	−0.303677	+	0.303677i	0.538774	+	0.842451i	$0.318888\pi$
$12$	1.72652	+	0.0831072i	0.498403	+	0.0239910i
$13$	−4.85780			−1.34731			−0.673655	−	0.739046i	$-0.735277\pi$
$13$	−4.85780			−1.34731			−0.673655	+	0.739046i	$0.735277\pi$
$14$	1.41380	+	0.0340076i	0.377855	+	0.00908891i
$15$	−0.729842	+	1.78942i	−0.188444	+	0.462027i
$16$	−3.98151	−	0.384196i	−0.995377	−	0.0960489i
$17$	−1.58968	+	1.58968i	−0.385554	+	0.385554i	−0.873098	−	0.487544i	$-0.837893\pi$
$17$	−1.58968	+	1.58968i	−0.385554	+	0.385554i	0.487544	+	0.873098i	$0.337893\pi$
$18$	−2.19823	−	2.30659i	−0.518127	−	0.543667i
$19$	−2.19835	+	2.19835i	−0.504336	+	0.504336i	−0.912782	−	0.408446i	$-0.866071\pi$
$19$	−2.19835	+	2.19835i	−0.504336	+	0.504336i	0.408446	+	0.912782i	$0.366071\pi$
$20$	1.88609	−	4.05496i	0.421742	−	0.906716i
$21$	0.611123	+	0.611123i	0.133358	+	0.133358i
$22$	2.01378	+	0.0484394i	0.429340	+	0.0103273i
$23$	2.91715	+	2.91715i	0.608268	+	0.608268i	0.942493	−	0.334225i	$-0.108475\pi$
$23$	2.91715	+	2.91715i	0.608268	+	0.608268i	−0.334225	+	0.942493i	$0.608475\pi$
$24$	−1.59942	−	1.84862i	−0.326480	−	0.377348i
$25$	3.57373	+	3.49692i	0.714746	+	0.699384i
$26$	4.73958	+	4.97321i	0.929508	+	0.975327i
$27$		−	4.54000i		−	0.873723i
$28$	−1.34458	−	1.48057i	−0.254102	−	0.279802i
$29$	6.04289	+	6.04289i	1.12214	+	1.12214i	0.991420	+	0.130717i	$0.0417280\pi$
$29$	6.04289	+	6.04289i	1.12214	+	1.12214i	0.130717	+	0.991420i	$0.458272\pi$
$30$	2.54402	−	0.998695i	0.464472	−	0.182336i
$31$			8.40005i			1.50869i	0.656476	+	0.754347i	$0.272046\pi$
$31$			8.40005i			1.50869i	−0.656476	+	0.754347i	$0.727954\pi$
$32$	3.49129	+	4.45094i	0.617178	+	0.786823i
$33$	0.870465	+	0.870465i	0.151529	+	0.151529i
$34$	3.17844	+	0.0764540i	0.545098	+	0.0131118i
$35$	2.06118	−	0.866915i	0.348403	−	0.146535i
$36$	−0.216654	+	4.50090i	−0.0361091	+	0.750151i
$37$	−10.5609			−1.73621			−0.868104	−	0.496382i	$-0.834661\pi$
$37$	−10.5609			−1.73621			−0.868104	+	0.496382i	$0.834661\pi$
$38$	4.39543	+	0.105727i	0.713032	+	0.0171512i
$39$			4.19839i			0.672281i
$40$	−5.99148	+	2.02538i	−0.947336	+	0.320240i
$41$		−	4.25256i		−	0.664138i	−0.943255	−	0.332069i	$-0.892253\pi$
$41$		−	4.25256i		−	0.664138i	0.943255	−	0.332069i	$-0.107747\pi$
$42$	0.0293913	−	1.22189i	0.00453518	−	0.188542i
$43$	10.2395			1.56151			0.780755	−	0.624838i	$-0.214835\pi$
$43$	10.2395			1.56151			0.780755	+	0.624838i	$0.214835\pi$
$44$	−1.91518	−	2.10889i	−0.288725	−	0.317926i
$45$	−4.66490	−	1.90265i	−0.695402	−	0.283630i
$46$	0.140297	−	5.83262i	0.0206857	−	0.859972i
$47$	0.0941814	+	0.0941814i	0.0137378	+	0.0137378i	0.713942	−	0.700205i	$-0.246908\pi$
$47$	0.0941814	+	0.0941814i	0.0137378	+	0.0137378i	−0.700205	+	0.713942i	$0.746908\pi$
$48$	−0.332044	+	3.44105i	−0.0479265	+	0.496673i
$49$		−	1.00000i		−	0.142857i
$50$	0.0932361	−	7.07045i	0.0131856	−	0.999913i
$51$	1.37389	+	1.37389i	0.192384	+	0.192384i
$52$	0.467127	−	9.70436i	0.0647788	−	1.34575i
$53$		−	3.94479i		−	0.541858i	−0.962599	−	0.270929i	$-0.912669\pi$
$53$		−	3.94479i		−	0.541858i	0.962599	−	0.270929i	$-0.0873309\pi$
$54$	−4.64786	+	4.42951i	−0.632493	+	0.602780i
$55$	2.93588	−	1.23481i	0.395874	−	0.166501i
$56$	−0.203888	+	2.82107i	−0.0272457	+	0.376981i
$57$	1.89994	+	1.89994i	0.251653	+	0.251653i
$58$	0.290627	−	12.0823i	0.0381612	−	1.58648i
$59$	6.93924	+	6.93924i	0.903412	+	0.903412i	0.995730	−	0.0923180i	$-0.0294276\pi$
$59$	6.93924	+	6.93924i	0.903412	+	0.903412i	−0.0923180	+	0.995730i	$0.529428\pi$
$60$	−3.50453	−	1.63007i	−0.452433	−	0.210441i
$61$	−9.12105	+	9.12105i	−1.16783	+	1.16783i	−0.185114	+	0.982717i	$0.559265\pi$
$61$	−9.12105	+	9.12105i	−1.16783	+	1.16783i	−0.982717	+	0.185114i	$0.940735\pi$
$62$	8.59962	−	8.19563i	1.09215	−	1.04085i
$63$	−1.59315	+	1.59315i	−0.200718	+	0.200718i
$64$	1.15037	−	7.91686i	0.143796	−	0.989607i
$65$	10.0580	+	4.10228i	1.24754	+	0.508825i
$66$	0.0418641	−	1.74043i	0.00515312	−	0.214232i
$67$	−11.8663			−1.44970			−0.724851	−	0.688906i	$-0.758091\pi$
$67$	−11.8663			−1.44970			−0.724851	+	0.688906i	$0.758091\pi$
$68$	−3.02282	−	3.32855i	−0.366571	−	0.403645i
$69$	2.52117	−	2.52117i	0.303513	−	0.303513i
$70$	−2.89853	−	1.26433i	−0.346440	−	0.151116i
$71$	5.75655			0.683177			0.341588	−	0.939850i	$-0.389035\pi$
$71$	5.75655			0.683177			0.341588	+	0.939850i	$0.389035\pi$
$72$	4.81922	−	4.16957i	0.567950	−	0.491388i
$73$	0.0114018	−	0.0114018i	0.00133448	−	0.00133448i	−0.706439	−	0.707774i	$-0.749700\pi$
$73$	0.0114018	−	0.0114018i	0.00133448	−	0.00133448i	0.707774	+	0.706439i	$0.249700\pi$
$74$	10.3039	+	10.8118i	1.19781	+	1.25685i
$75$	3.02224	−	3.08863i	0.348978	−	0.356644i
$76$	−4.18022	−	4.60301i	−0.479504	−	0.528001i
$77$		−	1.42437i		−	0.162322i
$78$	4.29814	−	4.09622i	0.486668	−	0.463805i
$79$	−10.5026			−1.18163			−0.590815	−	0.806807i	$-0.701194\pi$
$79$	−10.5026			−1.18163			−0.590815	+	0.806807i	$0.701194\pi$
$80$	7.91917	+	4.15774i	0.885390	+	0.464850i
$81$	2.83544			0.315049
$82$	−4.35359	+	4.14907i	−0.480773	+	0.458188i
$83$			16.5380i			1.81528i	0.419751	+	0.907639i	$0.362117\pi$
$83$			16.5380i			1.81528i	−0.419751	+	0.907639i	$0.637883\pi$
$84$	−1.27960	+	1.16207i	−0.139616	+	0.126792i
$85$	4.63383	−	1.94895i	0.502610	−	0.211393i
$86$	−9.99031	−	10.4828i	−1.07728	−	1.13039i
$87$	5.22262	−	5.22262i	0.559923	−	0.559923i
$88$	−0.290412	+	4.01825i	−0.0309581	+	0.428347i
$89$	−8.69343			−0.921502			−0.460751	−	0.887529i	$-0.652420\pi$
$89$	−8.69343			−0.921502			−0.460751	+	0.887529i	$0.652420\pi$
$90$	2.60353	+	6.63207i	0.274436	+	0.699082i
$91$	3.43498	−	3.43498i	0.360084	−	0.360084i
$92$	−6.10807	+	5.54704i	−0.636810	+	0.578319i
$93$	7.25981			0.752807
$94$	0.00452956	−	0.188308i	0.000467188	−	0.0194225i
$95$	6.40807	−	2.69518i	0.657454	−	0.276520i
$96$	3.84676	−	3.01737i	0.392609	−	0.307959i
$97$	2.30029	−	2.30029i	0.233559	−	0.233559i	−0.580617	−	0.814177i	$-0.697189\pi$
$97$	2.30029	−	2.30029i	0.233559	−	0.233559i	0.814177	+	0.580617i	$0.197189\pi$
$98$	−1.02376	+	0.975664i	−0.103415	+	0.0985569i
$99$	−2.26924	+	2.26924i	−0.228067	+	0.228067i
$100$	−7.32940	+	6.80293i	−0.732940	+	0.680293i
$101$	−11.8936	−	11.8936i	−1.18346	−	1.18346i	−0.978842	−	0.204618i	$-0.934405\pi$
$101$	−11.8936	−	11.8936i	−1.18346	−	1.18346i	−0.204618	−	0.978842i	$-0.565595\pi$
$102$	0.0660760	−	2.74699i	0.00654250	−	0.271993i
$103$	6.48654	+	6.48654i	0.639138	+	0.639138i	0.950343	−	0.311205i	$-0.100733\pi$
$103$	6.48654	+	6.48654i	0.639138	+	0.639138i	−0.311205	+	0.950343i	$0.600733\pi$
$104$	−10.3907	+	8.98997i	−1.01889	+	0.881539i
$105$	−0.749238	−	1.78139i	−0.0731181	−	0.173846i
$106$	−4.03851	+	3.84879i	−0.392255	+	0.373827i
$107$		−	2.82779i		−	0.273372i	−0.990614	−	0.136686i	$-0.956355\pi$
$107$		−	2.82779i		−	0.273372i	0.990614	−	0.136686i	$-0.0436452\pi$
$108$	9.06949	+	0.436567i	0.872713	+	0.0420087i
$109$	−3.84958	−	3.84958i	−0.368723	−	0.368723i	0.498288	−	0.867011i	$-0.333962\pi$
$109$	−3.84958	−	3.84958i	−0.368723	−	0.368723i	−0.867011	+	0.498288i	$0.833962\pi$
$110$	−4.12858	−	1.80088i	−0.393645	−	0.171707i
$111$			9.12738i			0.866332i
$112$	3.08702	−	2.54368i	0.291696	−	0.240355i
$113$	−7.98251	−	7.98251i	−0.750932	−	0.750932i	0.223722	−	0.974653i	$-0.428179\pi$
$113$	−7.98251	−	7.98251i	−0.750932	−	0.750932i	−0.974653	+	0.223722i	$0.928179\pi$
$114$	0.0913757	−	3.79878i	0.00855812	−	0.355789i
$115$	−3.57643	−	8.50334i	−0.333504	−	0.792941i
$116$	−12.6529	+	11.4907i	−1.17479	+	1.06689i
$117$	−10.9449			−1.01186
$118$	0.333735	−	13.8745i	0.0307228	−	1.27725i
$119$		−	2.24815i		−	0.206087i
$120$	1.75045	+	5.17819i	0.159793	+	0.472702i
$121$			8.97117i			0.815561i
$122$	18.2368	+	0.438668i	1.65108	+	0.0397151i
$123$	−3.67531			−0.331391
$124$	−16.7807	−	0.807750i	−1.50695	−	0.0725381i
$125$	−4.44627	−	10.2582i	−0.397687	−	0.917521i
$126$	3.18538	+	0.0766210i	0.283777	+	0.00682595i
$127$	3.43559	+	3.43559i	0.304860	+	0.304860i	0.842912	−	0.538052i	$-0.180840\pi$
$127$	3.43559	+	3.43559i	0.304860	+	0.304860i	−0.538052	+	0.842912i	$0.680840\pi$
$128$	−9.22732	+	6.54650i	−0.815587	+	0.578634i
$129$		−	8.84957i		−	0.779161i
$130$	−5.61344	−	14.2993i	−0.492331	−	1.25414i
$131$	3.65545	+	3.65545i	0.319378	+	0.319378i	0.848528	−	0.529150i	$-0.177489\pi$
$131$	3.65545	+	3.65545i	0.319378	+	0.319378i	−0.529150	+	0.848528i	$0.677489\pi$
$132$	−1.82262	+	1.65521i	−0.158639	+	0.144068i
$133$		−	3.10894i		−	0.269579i
$134$	11.5775	+	12.1482i	1.00015	+	1.04945i
$135$	−3.83390	+	9.39995i	−0.329970	+	0.809019i
$136$	−0.458370	+	6.34218i	−0.0393049	+	0.543837i
$137$	−10.8381	−	10.8381i	−0.925959	−	0.925959i	0.0714828	−	0.997442i	$-0.477227\pi$
$137$	−10.8381	−	10.8381i	−0.925959	−	0.925959i	−0.997442	+	0.0714828i	$0.977227\pi$
$138$	−5.04089	−	0.121253i	−0.429109	−	0.0103218i
$139$	−1.33098	−	1.33098i	−0.112892	−	0.112892i	0.648404	−	0.761296i	$-0.275437\pi$
$139$	−1.33098	−	1.33098i	−0.112892	−	0.112892i	−0.761296	+	0.648404i	$0.775437\pi$
$140$	1.53362	+	4.20095i	0.129615	+	0.355045i
$141$	0.0813970	−	0.0813970i	0.00685486	−	0.00685486i
$142$	−5.61646	−	5.89331i	−0.471323	−	0.494556i
$143$	4.89269	−	4.89269i	0.409147	−	0.409147i
$144$	−8.97056	−	0.865615i	−0.747547	−	0.0721346i
$145$	−7.40860	−	17.6147i	−0.615251	−	1.46282i
$146$	−0.0227970		0.000548358i	−0.00188670		4.53825e-5i
$147$	−0.864258			−0.0712828
$148$	1.01554	−	21.0975i	0.0834770	−	1.73420i
$149$	2.18319	−	2.18319i	0.178854	−	0.178854i	−0.612002	−	0.790856i	$-0.709636\pi$
$149$	2.18319	−	2.18319i	0.178854	−	0.178854i	0.790856	+	0.612002i	$0.209636\pi$
$150$	−6.11070	−	0.0805801i	−0.498936	−	0.00657934i
$151$	−21.4144			−1.74268			−0.871340	−	0.490681i	$-0.836748\pi$
$151$	−21.4144			−1.74268			−0.871340	+	0.490681i	$0.836748\pi$
$152$	−0.633875	+	8.77052i	−0.0514141	+	0.711383i
$153$	−3.58164	+	3.58164i	−0.289558	+	0.289558i
$154$	−1.45821	+	1.38971i	−0.117506	+	0.111986i
$155$	7.09361	−	17.3921i	0.569773	−	1.39697i
$156$	−8.38707	−	0.403718i	−0.671503	−	0.0323233i
$157$		−	1.86675i		−	0.148983i	−0.997222	−	0.0744915i	$-0.976267\pi$
$157$		−	1.86675i		−	0.148983i	0.997222	−	0.0744915i	$-0.0237334\pi$
$158$	10.2470	+	10.7521i	0.815205	+	0.855390i
$159$	−3.40932			−0.270376
$160$	−3.46992	−	12.1639i	−0.274322	−	0.961638i
$161$	−4.12547			−0.325133
$162$	−2.76644	−	2.90281i	−0.217352	−	0.228066i
$163$			1.90675i			0.149348i	0.997208	+	0.0746742i	$0.0237917\pi$
$163$			1.90675i			0.149348i	−0.997208	+	0.0746742i	$0.976208\pi$
$164$	8.49528	+	0.408927i	0.663370	+	0.0319318i
$165$	−1.06719	−	2.53736i	−0.0830808	−	0.197533i
$166$	16.9309	−	16.1355i	1.31409	−	1.25236i
$167$	−3.51805	+	3.51805i	−0.272235	+	0.272235i	−0.829999	−	0.557764i	$-0.811659\pi$
$167$	−3.51805	+	3.51805i	−0.272235	+	0.272235i	0.557764	+	0.829999i	$0.311659\pi$
$168$	2.43813	+	0.176212i	0.188106	+	0.0135951i
$169$	10.5982			0.815247
$170$	−6.51632	−	2.84240i	−0.499779	−	0.218002i
$171$	−4.95301	+	4.95301i	−0.378766	+	0.378766i
$172$	−0.984632	+	20.4553i	−0.0750775	+	1.55970i
$173$	5.35618			0.407223			0.203612	−	0.979052i	$-0.434732\pi$
$173$	5.35618			0.407223			0.203612	+	0.979052i	$0.434732\pi$
$174$	−10.4422	−	0.251176i	−0.791622	−	0.0190416i
$175$	−4.99970	+	0.0543157i	−0.377942	+	0.00410588i
$176$	4.39706	−	3.62315i	0.331441	−	0.273105i
$177$	5.99729	−	5.99729i	0.450784	−	0.450784i
$178$	8.48187	+	8.89997i	0.635743	+	0.667081i
$179$	3.26190	−	3.26190i	0.243806	−	0.243806i	−0.574617	−	0.818423i	$-0.694849\pi$
$179$	3.26190	−	3.26190i	0.243806	−	0.243806i	0.818423	+	0.574617i	$0.194849\pi$
$180$	4.24947	−	9.13605i	0.316737	−	0.680961i
$181$	−7.29837	−	7.29837i	−0.542484	−	0.542484i	0.381773	−	0.924256i	$-0.375314\pi$
$181$	−7.29837	−	7.29837i	−0.542484	−	0.542484i	−0.924256	+	0.381773i	$0.875314\pi$
$182$	−6.86798	−	0.165202i	−0.509088	−	0.0122456i
$183$	7.88294	+	7.88294i	0.582724	+	0.582724i
$184$	11.6382	+	0.841135i	0.857983	+	0.0620093i
$185$	21.8662	+	8.91843i	1.60763	+	0.655696i
$186$	−7.08314	−	7.43229i	−0.519361	−	0.544962i
$187$		−	3.20219i		−	0.234168i
$188$	−0.197201	+	0.179088i	−0.0143824	+	0.0130614i
$189$	3.21026	+	3.21026i	0.233512	+	0.233512i
$190$	−9.01134	−	3.93072i	−0.653751	−	0.285165i
$191$			17.2712i			1.24970i	0.780744	+	0.624851i	$0.214840\pi$
$191$			17.2712i			1.24970i	−0.780744	+	0.624851i	$0.785160\pi$
$192$	−6.84221	−	0.994212i	−0.493794	−	0.0717511i
$193$	13.6300	+	13.6300i	0.981108	+	0.981108i	0.999825	−	0.0187168i	$-0.00595809\pi$
$193$	13.6300	+	13.6300i	0.981108	+	0.981108i	−0.0187168	+	0.999825i	$0.505958\pi$
$194$	−4.59925	−	0.110630i	−0.330207	−	0.00794278i
$195$	3.54543	−	8.69266i	0.253893	−	0.622495i
$196$	1.99769	+	0.0961601i	0.142692	+	0.00686858i
$197$	−18.4233			−1.31261			−0.656304	−	0.754497i	$-0.727881\pi$
$197$	−18.4233			−1.31261			−0.656304	+	0.754497i	$0.727881\pi$
$198$	4.53717	+	0.109137i	0.322442	+	0.00775601i
$199$		−	13.2003i		−	0.935744i	−0.883796	−	0.467872i	$-0.845021\pi$
$199$		−	13.2003i		−	0.935744i	0.883796	−	0.467872i	$-0.154979\pi$
$200$	14.1156	+	0.866152i	0.998123	+	0.0612462i
$201$			10.2556i			0.723372i
$202$	−0.572012	+	23.7804i	−0.0402466	+	1.67318i
$203$	−8.54594			−0.599807
$204$	−2.87672	+	2.61250i	−0.201411	+	0.182911i
$205$	−3.59117	+	8.80481i	−0.250818	+	0.614955i
$206$	0.311964	−	12.9693i	0.0217355	−	0.903616i
$207$	6.57251	+	6.57251i	0.456821	+	0.456821i
$208$	19.3414	+	1.86635i	1.34108	+	0.129408i
$209$		−	4.42828i		−	0.306310i
$210$	−1.09271	+	2.50508i	−0.0754040	+	0.172867i
$211$	8.67591	+	8.67591i	0.597275	+	0.597275i	0.939586	−	0.342312i	$-0.111210\pi$
$211$	8.67591	+	8.67591i	0.597275	+	0.597275i	−0.342312	+	0.939586i	$0.611210\pi$
$212$	7.88045	+	0.379332i	0.541232	+	0.0260526i
$213$		−	4.97514i		−	0.340891i
$214$	−2.89497	+	2.75897i	−0.197896	+	0.188599i
$215$	−21.2006	−	8.64698i	−1.44587	−	0.589719i
$216$	−8.40184	−	9.71091i	−0.571673	−	0.660744i
$217$	−5.93973	−	5.93973i	−0.403215	−	0.403215i
$218$	−0.185142	+	7.69694i	−0.0125394	+	0.521303i
$219$	−0.00985411	−	0.00985411i	−0.000665879	−	0.000665879i
$220$	2.18444	+	5.98371i	0.147275	+	0.403422i
$221$	7.72234	−	7.72234i	0.519461	−	0.519461i
$222$	9.34423	−	8.90525i	0.627143	−	0.597681i
$223$	−6.03462	+	6.03462i	−0.404108	+	0.404108i	−0.879678	−	0.475570i	$-0.842242\pi$
$223$	−6.03462	+	6.03462i	−0.404108	+	0.404108i	0.475570	+	0.879678i	$0.342242\pi$
$224$	−5.61601	−	0.678579i	−0.375235	−	0.0453395i
$225$	8.05183	+	7.87876i	0.536788	+	0.525251i
$226$	−0.383911	+	15.9604i	−0.0255374	+	1.06167i
$227$	−5.07018			−0.336520			−0.168260	−	0.985743i	$-0.553815\pi$
$227$	−5.07018			−0.336520			−0.168260	+	0.985743i	$0.553815\pi$
$228$	−3.97819	+	3.61279i	−0.263462	+	0.239263i
$229$	15.8996	−	15.8996i	1.05068	−	1.05068i	0.0520314	−	0.998645i	$-0.483430\pi$
$229$	15.8996	−	15.8996i	1.05068	−	1.05068i	0.998645	−	0.0520314i	$-0.0165696\pi$
$230$	−5.21597	+	11.9578i	−0.343931	+	0.788474i
$231$	−1.23102			−0.0809954
$232$	24.1087	+	1.74242i	1.58281	+	0.114395i
$233$	−2.90173	+	2.90173i	−0.190099	+	0.190099i	−0.795739	−	0.605640i	$-0.792917\pi$
$233$	−2.90173	+	2.90173i	−0.190099	+	0.190099i	0.605640	+	0.795739i	$0.292917\pi$
$234$	10.6785	+	11.2049i	0.698078	+	0.732489i
$235$	−0.115467	−	0.274534i	−0.00753221	−	0.0179086i
$236$	−14.5297	+	13.1951i	−0.945803	+	0.858931i
$237$			9.07692i			0.589610i
$238$	−2.30156	+	2.19344i	−0.149188	+	0.142179i
$239$	21.6701			1.40172			0.700862	−	0.713297i	$-0.252799\pi$
$239$	21.6701			1.40172			0.700862	+	0.713297i	$0.252799\pi$
$240$	3.59336	−	6.84420i	0.231950	−	0.441791i
$241$	−1.70672			−0.109939			−0.0549697	−	0.998488i	$-0.517506\pi$
$241$	−1.70672			−0.109939			−0.0549697	+	0.998488i	$0.517506\pi$
$242$	9.18430	−	8.75284i	0.590389	−	0.562654i
$243$		−	16.0705i		−	1.03093i
$244$	−17.3439	−	19.0981i	−1.11033	−	1.22263i
$245$	−0.844473	+	2.07047i	−0.0539514	+	0.132278i
$246$	3.58586	+	3.76262i	0.228626	+	0.239896i
$247$	10.6791	−	10.6791i	0.679497	−	0.679497i
$248$	15.5454	+	17.9674i	0.987131	+	1.14093i
$249$	14.2931			0.905787
$250$	−6.16385	+	14.5605i	−0.389836	+	0.920884i
$251$	22.2914	−	22.2914i	1.40702	−	1.40702i	0.632297	−	0.774726i	$-0.282112\pi$
$251$	22.2914	−	22.2914i	1.40702	−	1.40702i	0.774726	−	0.632297i	$-0.217888\pi$
$252$	−3.02942	−	3.33582i	−0.190836	−	0.210137i
$253$	−5.87620			−0.369434
$254$	0.165231	−	6.86920i	0.0103675	−	0.431012i
$255$	−1.68440	−	4.00483i	−0.105481	−	0.250792i
$256$	15.7048	+	3.05936i	0.981549	+	0.191210i
$257$	1.71366	−	1.71366i	0.106895	−	0.106895i	−0.651636	−	0.758531i	$-0.725917\pi$
$257$	1.71366	−	1.71366i	0.106895	−	0.106895i	0.758531	+	0.651636i	$0.225917\pi$
$258$	−9.05982	+	8.63421i	−0.564040	+	0.537542i
$259$	7.46771	−	7.46771i	0.464021	−	0.464021i
$260$	−9.16224	+	19.6982i	−0.568218	+	1.22163i
$261$	13.6150	+	13.6150i	0.842746	+	0.842746i
$262$	0.175805	−	7.30878i	0.0108613	−	0.451538i
$263$	−5.74534	−	5.74534i	−0.354273	−	0.354273i	0.507424	−	0.861697i	$-0.330598\pi$
$263$	−5.74534	−	5.74534i	−0.354273	−	0.354273i	−0.861697	+	0.507424i	$0.830598\pi$
$264$	3.47280	+	0.250991i	0.213736	+	0.0154474i
$265$	−3.33127	+	8.16759i	−0.204638	+	0.501731i
$266$	−3.18280	+	3.03328i	−0.195150	+	0.185982i
$267$			7.51337i			0.459811i
$268$	1.14107	−	23.7052i	0.0697018	−	1.44803i
$269$	2.38708	+	2.38708i	0.145543	+	0.145543i	0.776123	−	0.630581i	$-0.217183\pi$
$269$	2.38708	+	2.38708i	0.145543	+	0.145543i	−0.630581	+	0.776123i	$0.717183\pi$
$270$	13.3639	−	5.24620i	0.813300	−	0.319274i
$271$		−	12.2627i		−	0.744906i	−0.928051	−	0.372453i	$-0.878517\pi$
$271$		−	12.2627i		−	0.744906i	0.928051	−	0.372453i	$-0.121483\pi$
$272$	6.94007	−	5.71857i	0.420803	−	0.346739i
$273$	−2.96871	−	2.96871i	−0.179675	−	0.179675i
$274$	−0.521246	+	21.6699i	−0.0314896	+	1.30913i
$275$	−7.12143	+	0.0773656i	−0.429439	+	0.00466532i
$276$	4.79408	+	5.27895i	0.288569	+	0.317755i
$277$	24.6651			1.48198			0.740990	−	0.671516i	$-0.234357\pi$
$277$	24.6651			1.48198			0.740990	+	0.671516i	$0.234357\pi$
$278$	−0.0640120	+	2.66119i	−0.00383918	+	0.159607i
$279$			18.9258i			1.13306i
$280$	2.80446	−	5.66877i	0.167599	−	0.338774i
$281$		−	8.83874i		−	0.527275i	−0.964622	−	0.263638i	$-0.915078\pi$
$281$		−	8.83874i		−	0.527275i	0.964622	−	0.263638i	$-0.0849223\pi$
$282$	−0.162747	−	0.00391471i	−0.00969144	−	0.000233117i
$283$	−14.6105			−0.868502			−0.434251	−	0.900792i	$-0.642987\pi$
$283$	−14.6105			−0.868502			−0.434251	+	0.900792i	$0.642987\pi$
$284$	−0.553551	+	11.4998i	−0.0328472	+	0.682386i
$285$	−2.32933	−	5.53823i	−0.137978	−	0.328056i
$286$	−9.78255	−	0.235309i	−0.578454	−	0.0139141i
$287$	3.00701	+	3.00701i	0.177498	+	0.177498i
$288$	7.86608	+	10.0282i	0.463513	+	0.590919i
$289$			11.9458i			0.702696i
$290$	−10.8049	+	24.7706i	−0.634485	+	1.45458i
$291$	−1.98805	−	1.98805i	−0.116541	−	0.116541i
$292$	0.0216808	+	0.0238736i	0.00126878	+	0.00139710i
$293$			24.2065i			1.41416i	0.707134	+	0.707080i	$0.249988\pi$
$293$			24.2065i			1.41416i	−0.707134	+	0.707080i	$0.750012\pi$
$294$	0.843225	+	0.884791i	0.0491779	+	0.0516021i
$295$	−8.50752	−	20.2275i	−0.495327	−	1.17769i
$296$	−22.5895	+	19.5444i	−1.31299	+	1.13599i
$297$	4.57260	+	4.57260i	0.265329	+	0.265329i
$298$	−4.36512	−	0.104998i	−0.252865	−	0.00608239i
$299$	−14.1709	−	14.1709i	−0.819526	−	0.819526i
$300$	5.87949	+	6.33449i	0.339453	+	0.365722i
$301$	−7.24042	+	7.24042i	−0.417331	+	0.417331i
$302$	20.8933	+	21.9232i	1.20227	+	1.26154i
$303$	−10.2792	+	10.2792i	−0.590522	+	0.590522i
$304$	9.59734	−	7.90814i	0.550445	−	0.453563i
$305$	26.5874	−	11.1824i	1.52239	−	0.640304i
$306$	7.16121	+	0.172255i	0.409379	+	0.00984718i
$307$	16.2755			0.928893			0.464446	−	0.885601i	$-0.346253\pi$
$307$	16.2755			0.928893			0.464446	+	0.885601i	$0.346253\pi$
$308$	2.84545	+	0.136968i	0.162134	+	0.00780446i
$309$	5.60605	−	5.60605i	0.318917	−	0.318917i
$310$	−24.7263	+	9.70670i	−1.40436	+	0.551303i
$311$	7.09770			0.402474			0.201237	−	0.979543i	$-0.435504\pi$
$311$	7.09770			0.402474			0.201237	+	0.979543i	$0.435504\pi$
$312$	7.76965	+	8.98022i	0.439870	+	0.508405i
$313$	3.24842	−	3.24842i	0.183612	−	0.183612i	−0.609316	−	0.792928i	$-0.708556\pi$
$313$	3.24842	−	3.24842i	0.183612	−	0.183612i	0.792928	+	0.609316i	$0.208556\pi$
$314$	−1.91110	+	1.82132i	−0.107850	+	0.102783i
$315$	4.64396	−	1.95321i	0.261657	−	0.110051i
$316$	1.00993	−	20.9808i	0.0568129	−	1.18026i
$317$		−	9.86918i		−	0.554308i	−0.960825	−	0.277154i	$-0.910609\pi$
$317$		−	9.86918i		−	0.554308i	0.960825	−	0.277154i	$-0.0893913\pi$
$318$	3.32635	+	3.49031i	0.186532	+	0.195727i
$319$	−12.1726			−0.681534
$320$	−9.06737	+	15.4202i	−0.506882	+	0.862016i
$321$	−2.44394			−0.136407
$322$	4.02508	+	4.22349i	0.224309	+	0.235366i
$323$		−	6.98934i		−	0.388897i
$324$	−0.272657	+	5.66433i	−0.0151476	+	0.314685i
$325$	−17.3605	−	16.9873i	−0.962986	−	0.942287i
$326$	1.95205	−	1.86035i	0.108114	−	0.103035i
$327$	−3.32703	+	3.32703i	−0.183985	+	0.183985i
$328$	−7.86989	−	9.09608i	−0.434542	−	0.502247i
$329$	−0.133193			−0.00734314
$330$	−1.55642	+	3.56816i	−0.0856782	+	0.196421i
$331$	3.58279	−	3.58279i	0.196928	−	0.196928i	−0.601754	−	0.798682i	$-0.705531\pi$
$331$	3.58279	−	3.58279i	0.196928	−	0.196928i	0.798682	+	0.601754i	$0.205531\pi$
$332$	−33.0377	−	1.59029i	−1.81318	−	0.0872787i
$333$	−23.7944			−1.30393
$334$	7.03406	+	0.169197i	0.384887	+	0.00925805i
$335$	24.5689	+	10.0208i	1.34234	+	0.547494i
$336$	−2.19840	−	2.66798i	−0.119932	−	0.145550i
$337$	−17.0595	+	17.0595i	−0.929289	+	0.929289i	−0.997660	−	0.0683707i	$-0.978220\pi$
$337$	−17.0595	+	17.0595i	−0.929289	+	0.929289i	0.0683707	+	0.997660i	$0.478220\pi$
$338$	−10.3403	−	10.8500i	−0.562438	−	0.590162i
$339$	−6.89895	+	6.89895i	−0.374700	+	0.374700i
$340$	3.44780	+	9.44436i	0.186983	+	0.512192i
$341$	−8.46038	−	8.46038i	−0.458155	−	0.458155i
$342$	9.90315	+	0.238210i	0.535501	+	0.0128809i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	21.9020	−	18.9495i	1.18087	−	1.02169i
$345$	−7.34908	+	3.09096i	−0.395661	+	0.166412i
$346$	−5.22583	−	5.48343i	−0.280943	−	0.294791i
$347$			3.98115i			0.213719i	0.994274	+	0.106860i	$0.0340796\pi$
$347$			3.98115i			0.213719i	−0.994274	+	0.106860i	$0.965920\pi$
$348$	9.93095	+	10.9354i	0.532355	+	0.586197i
$349$	18.9861	+	18.9861i	1.01630	+	1.01630i	0.999865	+	0.0164395i	$0.00523308\pi$
$349$	18.9861	+	18.9861i	1.01630	+	1.01630i	0.0164395	+	0.999865i	$0.494767\pi$
$350$	4.93364	+	5.06549i	0.263714	+	0.270762i
$351$			22.0544i			1.17718i
$352$	−7.99927	−	0.966548i	−0.426363	−	0.0515172i
$353$	2.90130	+	2.90130i	0.154421	+	0.154421i	0.780089	−	0.625669i	$-0.215174\pi$
$353$	2.90130	+	2.90130i	0.154421	+	0.154421i	−0.625669	+	0.780089i	$0.715174\pi$
$354$	−11.9911	−	0.288434i	−0.637320	−	0.0153301i
$355$	−11.9188	−	4.86125i	−0.632584	−	0.258008i
$356$	0.835962	−	17.3668i	0.0443059	−	0.920436i
$357$	−1.94298			−0.102833
$358$	−6.52192	−	0.156878i	−0.344694	−	0.00829126i
$359$			13.1773i			0.695469i	0.937593	+	0.347735i	$0.113049\pi$
$359$			13.1773i			0.695469i	−0.937593	+	0.347735i	$0.886951\pi$
$360$	−13.4992	+	4.56329i	−0.711468	+	0.240506i
$361$			9.33452i			0.491291i
$362$	−0.351008	+	14.5925i	−0.0184486	+	0.766966i
$363$	7.75340			0.406948
$364$	6.53171	+	7.19233i	0.342355	+	0.376980i
$365$	−0.0332357	+	0.0139786i	−0.00173963	+	0.000731676i
$366$	0.379122	−	15.7613i	0.0198170	−	0.823858i
$367$	3.74719	+	3.74719i	0.195602	+	0.195602i	0.798111	−	0.602510i	$-0.205833\pi$
$367$	3.74719	+	3.74719i	0.195602	+	0.195602i	−0.602510	+	0.798111i	$0.705833\pi$
$368$	−10.4939	−	12.7354i	−0.547032	−	0.663879i
$369$		−	9.58126i		−	0.498780i
$370$	−12.2037	−	31.0870i	−0.634441	−	1.61614i
$371$	2.78939	+	2.78939i	0.144818	+	0.144818i
$372$	−0.698105	+	14.5028i	−0.0361950	+	0.751937i
$373$			17.6643i			0.914625i	0.889306	+	0.457313i	$0.151188\pi$
$373$			17.6643i			0.914625i	−0.889306	+	0.457313i	$0.848812\pi$
$374$	−3.27827	+	3.12426i	−0.169515	+	0.161552i
$375$	−8.86573	+	3.84273i	−0.457824	+	0.198438i
$376$	0.375745	+	0.0271564i	0.0193776	+	0.00140048i
$377$	−29.3552	−	29.3552i	−1.51187	−	1.51187i
$378$	0.154394	−	6.41867i	0.00794119	−	0.330141i
$379$	1.95440	+	1.95440i	0.100391	+	0.100391i	0.755518	−	0.655127i	$-0.227385\pi$
$379$	1.95440	+	1.95440i	0.100391	+	0.100391i	−0.655127	+	0.755518i	$0.727385\pi$
$380$	4.76793	+	13.0605i	0.244589	+	0.669989i
$381$	2.96924	−	2.96924i	0.152119	−	0.152119i
$382$	17.6816	−	16.8509i	0.904667	−	0.862168i
$383$	5.02757	−	5.02757i	0.256897	−	0.256897i	−0.566894	−	0.823791i	$-0.691855\pi$
$383$	5.02757	−	5.02757i	0.256897	−	0.256897i	0.823791	+	0.566894i	$0.191855\pi$
$384$	5.65786	+	7.97478i	0.288727	+	0.406961i
$385$	−1.20284	+	2.94912i	−0.0613025	+	0.150301i
$386$	0.655520	−	27.2521i	0.0333651	−	1.38710i
$387$	23.0702			1.17272
$388$	4.37407	+	4.81646i	0.222060	+	0.244519i
$389$	9.83599	−	9.83599i	0.498705	−	0.498705i	−0.412330	−	0.911035i	$-0.635285\pi$
$389$	9.83599	−	9.83599i	0.498705	−	0.498705i	0.911035	+	0.412330i	$0.135285\pi$
$390$	−12.3583	+	4.85146i	−0.625788	+	0.245663i
$391$	−9.27467			−0.469040
$392$	−1.85063	−	2.13897i	−0.0934707	−	0.108034i
$393$	3.15925	−	3.15925i	0.159363	−	0.159363i
$394$	17.9750	+	18.8610i	0.905566	+	0.950205i
$395$	21.7453	+	8.86913i	1.09412	+	0.446254i
$396$	−4.31502	−	4.75144i	−0.216838	−	0.238769i
$397$			17.0021i			0.853312i	0.904414	+	0.426656i	$0.140308\pi$
$397$			17.0021i			0.853312i	−0.904414	+	0.426656i	$0.859692\pi$
$398$	−13.5139	+	12.8790i	−0.677391	+	0.645568i
$399$	−2.68692			−0.134514
$400$	−12.8853	−	15.2960i	−0.644267	−	0.764801i
$401$	27.6629			1.38142			0.690710	−	0.723132i	$-0.257298\pi$
$401$	27.6629			1.38142			0.690710	+	0.723132i	$0.257298\pi$
$402$	10.4992	−	10.0060i	0.523653	−	0.499053i
$403$		−	40.8058i		−	2.03268i
$404$	24.9034	−	22.6160i	1.23899	−	1.12519i
$405$	−5.87072	−	2.39445i	−0.291718	−	0.118981i
$406$	8.33796	+	8.74897i	0.413806	+	0.434204i
$407$	10.6368	−	10.6368i	0.527246	−	0.527246i
$408$	5.48128	+	0.396150i	0.271364	+	0.0196124i
$409$	−1.58622			−0.0784338			−0.0392169	−	0.999231i	$-0.512486\pi$
$409$	−1.58622			−0.0784338			−0.0392169	+	0.999231i	$0.512486\pi$
$410$	12.5178	−	4.91405i	0.618209	−	0.242688i
$411$	−9.36689	+	9.36689i	−0.462035	+	0.462035i
$412$	−13.5818	+	12.3343i	−0.669129	+	0.607669i
$413$	−9.81356			−0.482894
$414$	0.316098	−	13.1412i	0.0155354	−	0.645856i
$415$	13.9659	−	34.2415i	0.685557	−	1.68085i
$416$	−16.9600	−	21.6218i	−0.831531	−	1.06010i
$417$	−1.15031	+	1.15031i	−0.0563308	+	0.0563308i
$418$	−4.53348	+	4.32051i	−0.221740	+	0.211323i
$419$	−7.62633	+	7.62633i	−0.372570	+	0.372570i	−0.868413	−	0.495842i	$-0.834859\pi$
$419$	−7.62633	+	7.62633i	−0.372570	+	0.372570i	0.495842	+	0.868413i	$0.334859\pi$
$420$	3.63071	−	1.32544i	0.177160	−	0.0646750i
$421$	−4.26245	−	4.26245i	−0.207739	−	0.207739i	0.595567	−	0.803306i	$-0.296928\pi$
$421$	−4.26245	−	4.26245i	−0.207739	−	0.207739i	−0.803306	+	0.595567i	$0.796928\pi$
$422$	0.417259	−	17.3468i	0.0203119	−	0.844430i
$423$	0.212196	+	0.212196i	0.0103173	+	0.0103173i
$424$	−7.30033	−	8.43778i	−0.354535	−	0.409775i
$425$	−11.2401	+	0.122110i	−0.545223	+	0.00592318i
$426$	−5.09334	+	4.85407i	−0.246773	+	0.235180i
$427$		−	12.8991i		−	0.624232i
$428$	5.64903	+	0.271920i	0.273056	+	0.0131438i
$429$	−4.22855	−	4.22855i	−0.204156	−	0.204156i
$430$	11.8323	+	30.1409i	0.570603	+	1.45352i
$431$		−	1.54488i		−	0.0744140i	−0.999308	−	0.0372070i	$-0.988154\pi$
$431$		−	1.54488i		−	0.0744140i	0.999308	−	0.0372070i	$-0.0118461\pi$
$432$	−1.74425	+	18.0760i	−0.0839202	+	0.869683i
$433$	−0.619886	−	0.619886i	−0.0297898	−	0.0297898i	0.692055	−	0.721845i	$-0.256706\pi$
$433$	−0.619886	−	0.619886i	−0.0297898	−	0.0297898i	−0.721845	+	0.692055i	$0.756706\pi$
$434$	−0.285665	+	11.8760i	−0.0137124	+	0.570068i
$435$	−15.2237	+	6.40294i	−0.729918	+	0.306998i
$436$	8.06044	−	7.32009i	0.386025	−	0.350569i
$437$	−12.8258			−0.613543
$438$	−0.000473923		0.0197025i	−2.26449e−5		0.000941422i
$439$		−	22.4362i		−	1.07082i	−0.844591	−	0.535412i	$-0.820157\pi$
$439$		−	22.4362i		−	1.07082i	0.844591	−	0.535412i	$-0.179843\pi$
$440$	3.99459	−	8.07444i	0.190435	−	0.384934i
$441$		−	2.25306i		−	0.107288i
$442$	−15.4402	−	0.371398i	−0.734416	−	0.0176656i
$443$	4.89359			0.232501			0.116251	−	0.993220i	$-0.462912\pi$
$443$	4.89359			0.232501			0.116251	+	0.993220i	$0.462912\pi$
$444$	−18.2336	−	0.877690i	−0.865331	−	0.0416533i
$445$	17.9995	+	7.34136i	0.853260	+	0.348014i
$446$	12.0657	+	0.290229i	0.571330	+	0.0137427i
$447$	−1.88684	−	1.88684i	−0.0892445	−	0.0892445i
$448$	4.78463	+	6.41150i	0.226053	+	0.302915i
$449$			10.9511i			0.516814i	0.966036	+	0.258407i	$0.0831976\pi$
$449$			10.9511i			0.516814i	−0.966036	+	0.258407i	$0.916802\pi$
$450$	0.210066	−	15.9301i	0.00990262	−	0.750954i
$451$	4.28310	+	4.28310i	0.201683	+	0.201683i
$452$	16.7142	−	15.1790i	0.786168	−	0.713958i
$453$			18.5076i			0.869561i
$454$	4.94679	+	5.19064i	0.232164	+	0.243609i
$455$	−10.0128	+	4.21130i	−0.469407	+	0.197429i
$456$	7.57999	+	0.547832i	0.354966	+	0.0256546i
$457$	0.308263	+	0.308263i	0.0144199	+	0.0144199i	0.714280	−	0.699860i	$-0.246754\pi$
$457$	0.308263	+	0.308263i	0.0144199	+	0.0144199i	−0.699860	+	0.714280i	$0.746754\pi$
$458$	−31.7901	−	0.764676i	−1.48545	−	0.0357310i
$459$	7.21714	+	7.21714i	0.336867	+	0.336867i
$460$	17.3309	−	6.32691i	0.808059	−	0.294994i
$461$	−8.75531	+	8.75531i	−0.407775	+	0.407775i	−0.880962	−	0.473187i	$-0.843104\pi$
$461$	−8.75531	+	8.75531i	−0.407775	+	0.407775i	0.473187	+	0.880962i	$0.343104\pi$
$462$	1.20107	+	1.26027i	0.0558786	+	0.0586331i
$463$	5.14440	−	5.14440i	0.239081	−	0.239081i	−0.577389	−	0.816469i	$-0.695928\pi$
$463$	5.14440	−	5.14440i	0.239081	−	0.239081i	0.816469	+	0.577389i	$0.195928\pi$
$464$	−21.7382	−	26.3815i	−1.00917	−	1.22473i
$465$	−15.0313	−	6.13071i	−0.697058	−	0.284305i
$466$	5.80178	+	0.139556i	0.268762	+	0.00646479i
$467$	−22.7611			−1.05326			−0.526628	−	0.850096i	$-0.676544\pi$
$467$	−22.7611			−1.05326			−0.526628	+	0.850096i	$0.676544\pi$
$468$	1.05246	−	21.8645i	0.0486501	−	1.01069i
$469$	8.39076	−	8.39076i	0.387449	−	0.387449i
$470$	−0.168399	+	0.386062i	−0.00776769	+	0.0178077i
$471$	−1.61335			−0.0743394
$472$	27.6847	+	2.00087i	1.27429	+	0.0920975i
$473$	−10.3130	+	10.3130i	−0.474194	+	0.474194i
$474$	9.29257	−	8.85603i	0.426822	−	0.406771i
$475$	−15.5438	+	0.168864i	−0.713197	+	0.00774801i
$476$	4.49109	+	0.216182i	0.205849	+	0.00990869i
$477$		−	8.88784i		−	0.406946i
$478$	−21.1428	−	22.1850i	−0.967047	−	1.01472i
$479$	−18.9488			−0.865794			−0.432897	−	0.901443i	$-0.642509\pi$
$479$	−18.9488			−0.865794			−0.432897	+	0.901443i	$0.642509\pi$
$480$	−10.5127	+	2.99891i	−0.479838	+	0.136881i
$481$	51.3029			2.33921
$482$	1.66518	+	1.74727i	0.0758470	+	0.0795857i
$483$			3.56548i			0.162235i
$484$	−17.9216	−	0.862669i	−0.814618	−	0.0392122i
$485$	−6.70523	+	2.82016i	−0.304469	+	0.128057i
$486$	−16.4524	+	15.6795i	−0.746294	+	0.711234i
$487$	−14.2888	+	14.2888i	−0.647485	+	0.647485i	−0.952385	−	0.304899i	$-0.901377\pi$
$487$	−14.2888	+	14.2888i	−0.647485	+	0.647485i	0.304899	+	0.952385i	$0.401377\pi$
$488$	−2.62998	+	36.3893i	−0.119053	+	1.64727i
$489$	1.64793			0.0745218
$490$	2.94359	−	1.15555i	0.132978	−	0.0522025i
$491$	5.97714	−	5.97714i	0.269745	−	0.269745i	−0.559253	−	0.828997i	$-0.688912\pi$
$491$	5.97714	−	5.97714i	0.269745	−	0.269745i	0.828997	+	0.559253i	$0.188912\pi$
$492$	0.353418	−	7.34211i	0.0159333	−	0.331008i
$493$	−19.2125			−0.865289
$494$	−21.3521	−	0.513602i	−0.960676	−	0.0231081i
$495$	6.61471	−	2.78209i	0.297309	−	0.125046i
$496$	3.22726	−	33.4449i	0.144908	−	1.50172i
$497$	−4.07049	+	4.07049i	−0.182587	+	0.182587i
$498$	−13.9452	−	14.6327i	−0.624901	−	0.655705i
$499$	−11.0776	+	11.0776i	−0.495900	+	0.495900i	−0.910159	−	0.414259i	$-0.864041\pi$
$499$	−11.0776	+	11.0776i	−0.495900	+	0.495900i	0.414259	+	0.910159i	$0.364041\pi$
$500$	20.9202	−	7.89583i	0.935581	−	0.353112i
$501$	3.04050	+	3.04050i	0.135840	+	0.135840i
$502$	−44.5700	−	1.07208i	−1.98926	−	0.0478494i
$503$	21.0606	+	21.0606i	0.939047	+	0.939047i	0.998246	−	0.0591995i	$-0.0188548\pi$
$503$	21.0606	+	21.0606i	0.939047	+	0.939047i	−0.0591995	+	0.998246i	$0.518855\pi$
$504$	−0.459372	+	6.35603i	−0.0204620	+	0.283120i
$505$	14.5816	+	34.6693i	0.648873	+	1.54276i
$506$	5.73320	+	6.01581i	0.254872	+	0.267435i
$507$		−	9.15959i		−	0.406792i
$508$	−7.19361	+	6.53287i	−0.319165	+	0.289849i
$509$	19.5994	+	19.5994i	0.868730	+	0.868730i	0.992332	−	0.123602i	$-0.0394447\pi$
$509$	19.5994	+	19.5994i	0.868730	+	0.868730i	−0.123602	+	0.992332i	$0.539445\pi$
$510$	−2.45657	+	5.63178i	−0.108779	+	0.249379i
$511$			0.0161246i			0.000713310i
$512$	−12.1906	−	19.0628i	−0.538751	−	0.842465i
$513$	9.98050	+	9.98050i	0.440650	+	0.440650i
$514$	−3.42633	−	0.0824167i	−0.151129	−	0.00363524i
$515$	−7.95252	−	18.9079i	−0.350430	−	0.833183i
$516$	17.6787	+	0.850976i	0.778260	+	0.0374621i
$517$	−0.189716			−0.00834368
$518$	−14.9311	−	0.359152i	−0.656035	−	0.0157802i
$519$		−	4.62912i		−	0.203196i
$520$	29.1054	−	9.83887i	1.27636	−	0.431463i
$521$			4.93923i			0.216392i	0.994130	+	0.108196i	$0.0345073\pi$
$521$			4.93923i			0.216392i	−0.994130	+	0.108196i	$0.965493\pi$
$522$	0.654799	−	27.2221i	0.0286598	−	1.19148i
$523$	−14.5371			−0.635664			−0.317832	−	0.948147i	$-0.602955\pi$
$523$	−14.5371			−0.635664			−0.317832	+	0.948147i	$0.602955\pi$
$524$	−7.65395	+	6.95093i	−0.334364	+	0.303653i
$525$	0.0469428	+	4.32104i	0.00204875	+	0.188585i
$526$	−0.276316	+	11.4874i	−0.0120480	+	0.500873i
$527$	−13.3534	−	13.3534i	−0.581683	−	0.581683i
$528$	−3.13133	−	3.80019i	−0.136274	−	0.165382i
$529$		−	5.98046i		−	0.260020i
$530$	11.6118	−	4.55841i	0.504386	−	0.198005i
$531$	15.6345	+	15.6345i	0.678480	+	0.678480i
$532$	6.21068	+	0.298956i	0.269267	+	0.0129614i
$533$			20.6581i			0.894800i
$534$	7.69187	−	7.33052i	0.332860	−	0.317223i
$535$	−2.38799	+	5.85486i	−0.103242	+	0.253128i
$536$	−25.3817	+	21.9601i	−1.09632	+	0.948533i
$537$	−2.81913	−	2.81913i	−0.121654	−	0.121654i
$538$	0.114804	−	4.77277i	0.00494955	−	0.205769i
$539$	1.00718	+	1.00718i	0.0433824	+	0.0433824i
$540$	−18.4095	−	8.56284i	−0.792218	−	0.368486i
$541$	−0.593239	+	0.593239i	−0.0255053	+	0.0255053i	−0.719744	−	0.694239i	$-0.755741\pi$
$541$	−0.593239	+	0.593239i	−0.0255053	+	0.0255053i	0.694239	+	0.719744i	$0.255741\pi$
$542$	−12.5540	+	11.9643i	−0.539242	+	0.513910i
$543$	−6.30768	+	6.30768i	−0.270688	+	0.270688i
$544$	−12.6256	−	1.52555i	−0.541318	−	0.0654072i
$545$	4.71960	+	11.2213i	0.202165	+	0.480669i
$546$	−0.142777	+	5.93571i	−0.00611030	+	0.254025i
$547$	−39.5697			−1.69188			−0.845938	−	0.533281i	$-0.820959\pi$
$547$	−39.5697			−1.69188			−0.845938	+	0.533281i	$0.820959\pi$
$548$	22.6933	−	20.6089i	0.969408	−	0.880368i
$549$	−20.5503	+	20.5503i	−0.877064	+	0.877064i
$550$	7.02733	+	7.21514i	0.299646	+	0.307655i
$551$	−26.5688			−1.13187
$552$	0.726958	−	10.0585i	0.0309414	−	0.428116i
$553$	7.42643	−	7.42643i	0.315804	−	0.315804i
$554$	−24.0648	−	25.2510i	−1.02242	−	1.07281i
$555$	7.70782	−	18.8980i	0.327179	−	0.802176i
$556$	2.78686	−	2.53089i	0.118189	−	0.107334i
$557$		−	34.6010i		−	1.46609i	−0.680179	−	0.733046i	$-0.738098\pi$
$557$		−	34.6010i		−	1.46609i	0.680179	−	0.733046i	$-0.261902\pi$
$558$	19.3754	−	18.4652i	0.820228	−	0.781695i
$559$	−49.7414			−2.10384
$560$	−8.53966	+	2.65973i	−0.360867	+	0.112394i
$561$	−2.76752			−0.116845
$562$	−9.04873	+	8.62364i	−0.381698	+	0.363766i
$563$		−	19.3057i		−	0.813640i	−0.913508	−	0.406820i	$-0.866638\pi$
$563$		−	19.3057i		−	0.813640i	0.913508	−	0.406820i	$-0.133362\pi$
$564$	0.154779	+	0.170433i	0.00651735	+	0.00717652i
$565$	9.78658	+	23.2686i	0.411724	+	0.978917i
$566$	14.2549	+	14.9576i	0.599178	+	0.628714i
$567$	−2.00496	+	2.00496i	−0.0842005	+	0.0842005i
$568$	12.3131	−	10.6532i	0.516645	−	0.446999i
$569$	−23.5212			−0.986062			−0.493031	−	0.870012i	$-0.664111\pi$
$569$	−23.5212			−0.986062			−0.493031	+	0.870012i	$0.664111\pi$
$570$	−3.39716	+	7.78812i	−0.142291	+	0.326208i
$571$	9.02087	−	9.02087i	0.377511	−	0.377511i	−0.492692	−	0.870204i	$-0.663987\pi$
$571$	9.02087	−	9.02087i	0.377511	−	0.377511i	0.870204	+	0.492692i	$0.163987\pi$
$572$	9.30358	+	10.2445i	0.389002	+	0.428346i
$573$	14.9268			0.623576
$574$	0.144619	−	6.01229i	0.00603629	−	0.250948i
$575$	0.224078	+	20.6262i	0.00934470	+	0.860170i
$576$	2.59184	−	17.8371i	0.107993	−	0.743214i
$577$	−16.9238	+	16.9238i	−0.704548	+	0.704548i	−0.965383	−	0.260835i	$-0.916002\pi$
$577$	−16.9238	+	16.9238i	−0.704548	+	0.704548i	0.260835	+	0.965383i	$0.416002\pi$
$578$	12.2296	−	11.6551i	0.508686	−	0.484789i
$579$	11.7798	−	11.7798i	0.489553	−	0.489553i
$580$	35.9011	−	13.1062i	1.49071	−	0.544207i
$581$	−11.6941	−	11.6941i	−0.485154	−	0.485154i
$582$	−0.0956130	+	3.97494i	−0.00396329	+	0.164767i
$583$	3.97312	+	3.97312i	0.164550	+	0.164550i
$584$	0.00328761	−	0.0454886i	0.000136042	−	0.00188233i
$585$	22.6611	+	9.24267i	0.936923	+	0.382137i
$586$	24.7816	−	23.6174i	1.02372	−	0.975626i
$587$			26.6128i			1.09843i	0.835682	+	0.549213i	$0.185073\pi$
$587$			26.6128i			1.09843i	−0.835682	+	0.549213i	$0.814927\pi$
$588$	0.0831072	−	1.72652i	0.00342728	−	0.0712004i
$589$	−18.4662	−	18.4662i	−0.760888	−	0.760888i
$590$	−12.4076	+	28.4449i	−0.510812	+	1.17106i
$591$			15.9225i			0.654964i
$592$	42.0485	+	4.05747i	1.72818	+	0.166761i
$593$	−4.94031	−	4.94031i	−0.202874	−	0.202874i	0.598356	−	0.801230i	$-0.295821\pi$
$593$	−4.94031	−	4.94031i	−0.202874	−	0.202874i	−0.801230	+	0.598356i	$0.795821\pi$
$594$	0.219915	−	9.14256i	0.00902321	−	0.375124i
$595$	−1.89850	+	4.65473i	−0.0778308	+	0.190825i
$596$	4.15140	+	4.57127i	0.170048	+	0.187247i
$597$	−11.4085			−0.466917
$598$	−0.681537	+	28.3337i	−0.0278701	+	1.15865i
$599$		−	14.3812i		−	0.587598i	−0.955867	−	0.293799i	$-0.905080\pi$
$599$		−	14.3812i		−	0.587598i	0.955867	−	0.293799i	$-0.0949197\pi$
$600$	0.748579	−	12.1995i	0.0305606	−	0.498043i
$601$		−	34.6711i		−	1.41426i	−0.707082	−	0.707132i	$-0.749989\pi$
$601$		−	34.6711i		−	1.41426i	0.707082	−	0.707132i	$-0.250011\pi$
$602$	14.4767	+	0.348221i	0.590024	+	0.0141924i
$603$	−26.7355			−1.08875
$604$	2.05921	−	42.7793i	0.0837881	−	1.74066i
$605$	7.57591	−	18.5746i	0.308004	−	0.755164i
$606$	20.5524	+	0.494366i	0.834883	+	0.0200822i
$607$	21.9851	+	21.9851i	0.892347	+	0.892347i	0.994744	−	0.102396i	$-0.0326510\pi$
$607$	21.9851	+	21.9851i	0.892347	+	0.892347i	−0.102396	+	0.994744i	$0.532651\pi$
$608$	−17.4598	−	2.10966i	−0.708088	−	0.0855579i
$609$			7.38590i			0.299292i
$610$	−37.3885	−	16.3088i	−1.51381	−	0.660322i
$611$	−0.457514	−	0.457514i	−0.0185090	−	0.0185090i
$612$	−6.81058	−	7.49941i	−0.275302	−	0.303146i
$613$			44.4578i			1.79563i	0.440369	+	0.897817i	$0.354848\pi$
$613$			44.4578i			1.79563i	−0.440369	+	0.897817i	$0.645152\pi$
$614$	−15.8794	−	16.6622i	−0.640842	−	0.672431i
$615$	7.60963	+	3.10370i	0.306850	+	0.125153i
$616$	−2.63598	−	3.04668i	−0.106207	−	0.122754i
$617$	−0.951682	−	0.951682i	−0.0383133	−	0.0383133i	0.687691	−	0.726004i	$-0.258625\pi$
$617$	−0.951682	−	0.951682i	−0.0383133	−	0.0383133i	−0.726004	+	0.687691i	$0.758625\pi$
$618$	−11.2089	−	0.269617i	−0.450886	−	0.0108456i
$619$	−1.30075	−	1.30075i	−0.0522814	−	0.0522814i	0.680483	−	0.732764i	$-0.261770\pi$
$619$	−1.30075	−	1.30075i	−0.0522814	−	0.0522814i	−0.732764	+	0.680483i	$0.761770\pi$
$620$	34.0618	+	15.8432i	1.36796	+	0.636280i
$621$	13.2439	−	13.2439i	0.531458	−	0.531458i
$622$	−6.92497	−	7.26633i	−0.277666	−	0.291353i
$623$	6.14718	−	6.14718i	0.246282	−	0.246282i
$624$	1.61300	−	16.7159i	0.0645718	−	0.669173i
$625$	0.543125	+	24.9941i	0.0217250	+	0.999764i
$626$	−6.49497	−	0.156230i	−0.259591	−	0.00624419i
$627$	−3.82717			−0.152843
$628$	3.72918	+	0.179507i	0.148811	+	0.00716311i
$629$	16.7885	−	16.7885i	0.669402	−	0.669402i
$630$	−6.53055	−	2.84861i	−0.260183	−	0.113491i
$631$	22.9478			0.913536			0.456768	−	0.889586i	$-0.349007\pi$
$631$	22.9478			0.913536			0.456768	+	0.889586i	$0.349007\pi$
$632$	−22.4646	+	19.4363i	−0.893595	+	0.773135i
$633$	7.49823	−	7.49823i	0.298028	−	0.298028i
$634$	−10.1037	+	9.62900i	−0.401267	+	0.382417i
$635$	−4.21204	−	10.0146i	−0.167150	−	0.397416i
$636$	0.327840	−	6.81075i	0.0129997	−	0.270064i
$637$			4.85780i			0.192473i
$638$	11.8764	+	12.4618i	0.470189	+	0.493367i
$639$	12.9698			0.513079
$640$	24.6333	−	5.76214i	0.973715	−	0.227769i
$641$	−4.87962			−0.192734			−0.0963668	−	0.995346i	$-0.530722\pi$
$641$	−4.87962			−0.192734			−0.0963668	+	0.995346i	$0.530722\pi$
$642$	2.38446	+	2.50200i	0.0941072	+	0.0987461i
$643$		−	27.9778i		−	1.10334i	−0.834063	−	0.551669i	$-0.813991\pi$
$643$		−	27.9778i		−	1.10334i	0.834063	−	0.551669i	$-0.186009\pi$
$644$	0.396706	−	8.24141i	0.0156324	−	0.324757i
$645$	−7.47322	+	18.3228i	−0.294258	+	0.721460i
$646$	−7.15539	+	6.81925i	−0.281525	+	0.268300i
$647$	34.4614	−	34.4614i	1.35482	−	1.35482i	0.474635	−	0.880183i	$-0.342580\pi$
$647$	34.4614	−	34.4614i	1.35482	−	1.35482i	0.880183	−	0.474635i	$-0.157420\pi$
$648$	6.06492	−	5.24735i	0.238253	−	0.206135i
$649$	−13.9781			−0.548690
$650$	−0.452922	+	34.3468i	−0.0177651	+	1.34719i
$651$	−5.13346	+	5.13346i	−0.201196	+	0.201196i
$652$	−3.80910	−	0.183354i	−0.149176	−	0.00718068i
$653$	1.87994			0.0735678			0.0367839	−	0.999323i	$-0.488289\pi$
$653$	1.87994			0.0735678			0.0367839	+	0.999323i	$0.488289\pi$
$654$	6.65214	+	0.160010i	0.260119	+	0.00625690i
$655$	−4.48159	−	10.6554i	−0.175110	−	0.416343i
$656$	−1.63381	+	16.9316i	−0.0637897	+	0.661067i
$657$	0.0256889	−	0.0256889i	0.00100222	−	0.00100222i
$658$	0.129951	+	0.136357i	0.00506602	+	0.00531575i
$659$	−12.2187	+	12.2187i	−0.475971	+	0.475971i	−0.903841	−	0.427869i	$-0.859264\pi$
$659$	−12.2187	+	12.2187i	−0.475971	+	0.475971i	0.427869	+	0.903841i	$0.359264\pi$
$660$	5.17147	−	1.88792i	0.201299	−	0.0734873i
$661$	0.933621	+	0.933621i	0.0363137	+	0.0363137i	0.725030	−	0.688717i	$-0.241826\pi$
$661$	0.933621	+	0.933621i	0.0363137	+	0.0363137i	−0.688717	+	0.725030i	$0.741826\pi$
$662$	−7.16352	−	0.172311i	−0.278418	−	0.00669705i
$663$	−6.67410	−	6.67410i	−0.259200	−	0.259200i
$664$	30.6056	+	35.3742i	1.18773	+	1.37279i
$665$	−2.62541	+	6.43697i	−0.101809	+	0.249615i
$666$	23.2153	+	24.3597i	0.899576	+	0.943920i
$667$			35.2561i			1.36512i
$668$	−6.68967	−	7.36626i	−0.258831	−	0.285009i
$669$	5.21547	+	5.21547i	0.201642	+	0.201642i
$670$	−13.7122	−	34.9295i	−0.529747	−	1.34945i
$671$		−	18.3731i		−	0.709286i
$672$	−0.586467	+	4.85368i	−0.0226235	+	0.187235i
$673$	−0.143700	−	0.143700i	−0.00553921	−	0.00553921i	0.704332	−	0.709871i	$-0.251247\pi$
$673$	−0.143700	−	0.143700i	−0.00553921	−	0.00553921i	−0.709871	+	0.704332i	$0.751247\pi$
$674$	34.1091	+	0.820458i	1.31383	+	0.0316029i
$675$	15.8760	−	16.2247i	0.611068	−	0.624490i
$676$	−1.01913	+	21.1719i	−0.0391971	+	0.814304i
$677$	41.3993			1.59110			0.795552	−	0.605885i	$-0.207181\pi$
$677$	41.3993			1.59110			0.795552	+	0.605885i	$0.207181\pi$
$678$	13.7939	+	0.331798i	0.529752	+	0.0127426i
$679$			3.25310i			0.124843i
$680$	6.30484	−	12.7442i	0.241779	−	0.488719i
$681$			4.38194i			0.167916i
$682$	−0.406893	+	16.9159i	−0.0155808	+	0.647742i
$683$	−32.8093			−1.25541			−0.627707	−	0.778450i	$-0.716006\pi$
$683$	−32.8093			−1.25541			−0.627707	+	0.778450i	$0.716006\pi$
$684$	−9.41828	−	10.3708i	−0.360117	−	0.396539i
$685$	13.2875	+	31.5924i	0.507689	+	1.20708i
$686$	0.0340076	−	1.41380i	0.00129842	−	0.0539793i
$687$	−13.7414	−	13.7414i	−0.524266	−	0.524266i
$688$	−40.7686	−	3.93397i	−1.55429	−	0.149981i
$689$			19.1630i			0.730052i
$690$	10.3346	+	4.50794i	0.393433	+	0.171614i
$691$	23.0675	+	23.0675i	0.877528	+	0.877528i	0.993278	−	0.115751i	$-0.0369273\pi$
$691$	23.0675	+	23.0675i	0.877528	+	0.877528i	−0.115751	+	0.993278i	$0.536927\pi$
$692$	−0.515051	+	10.7000i	−0.0195793	+	0.406752i
$693$		−	3.20919i		−	0.121907i
$694$	4.07574	−	3.88427i	0.154713	−	0.147445i
$695$	1.63178	+	3.87973i	0.0618970	+	0.147167i
$696$	1.50590	−	20.8361i	0.0570809	−	0.789791i
$697$	6.76020	+	6.76020i	0.256061	+	0.256061i
$698$	0.913119	−	37.9613i	0.0345621	−	1.43686i
$699$	2.50784	+	2.50784i	0.0948553	+	0.0948553i
$700$	0.372267	−	9.99307i	0.0140704	−	0.377702i
$701$	35.3546	−	35.3546i	1.33533	−	1.33533i	0.434798	−	0.900528i	$-0.356820\pi$
$701$	35.3546	−	35.3546i	1.33533	−	1.33533i	0.900528	−	0.434798i	$-0.143180\pi$
$702$	22.5784	−	21.5177i	0.852165	−	0.812132i
$703$	23.2166	−	23.2166i	0.875632	−	0.875632i
$704$	6.81509	+	9.13235i	0.256853	+	0.344188i
$705$	−0.237268	+	0.0997929i	−0.00893603	+	0.00375842i
$706$	0.139535	−	5.80092i	0.00525147	−	0.218320i
$707$	16.8201			0.632586
$708$	11.4040	+	12.5574i	0.428589	+	0.471936i
$709$	31.6538	−	31.6538i	1.18878	−	1.18878i	0.211378	−	0.977404i	$-0.432205\pi$
$709$	31.6538	−	31.6538i	1.18878	−	1.18878i	0.977404	−	0.211378i	$-0.0677951\pi$
$710$	6.65199	+	16.9449i	0.249645	+	0.635931i
$711$	−23.6629			−0.887427
$712$	−18.5950	+	16.0883i	−0.696876	+	0.602934i
$713$	−24.5042	+	24.5042i	−0.917690	+	0.917690i
$714$	1.89569	+	1.98914i	0.0709446	+	0.0744417i
$715$	−14.2619	+	5.99845i	−0.533366	+	0.224329i
$716$	6.20260	+	6.82993i	0.231802	+	0.255246i
$717$		−	18.7286i		−	0.699432i
$718$	13.4903	−	12.8566i	0.503454	−	0.479803i
$719$	−10.7756			−0.401862			−0.200931	−	0.979605i	$-0.564397\pi$
$719$	−10.7756			−0.401862			−0.200931	+	0.979605i	$0.564397\pi$
$720$	17.8423	+	9.36763i	0.664945	+	0.349111i
$721$	−9.17336			−0.341634
$722$	9.55629	−	9.10736i	0.355648	−	0.338941i
$723$			1.47504i			0.0548575i
$724$	15.2817	−	13.8781i	0.567939	−	0.515774i
$725$	0.464178	+	42.7272i	0.0172392	+	1.58685i
$726$	−7.56472	−	7.93761i	−0.280753	−	0.294592i
$727$	−0.396060	+	0.396060i	−0.0146891	+	0.0146891i	−0.714413	−	0.699724i	$-0.753306\pi$
$727$	−0.396060	+	0.396060i	−0.0146891	+	0.0146891i	0.699724	+	0.714413i	$0.253306\pi$
$728$	0.990448	−	13.7042i	0.0367084	−	0.507911i
$729$	−5.38277			−0.199362
$730$	0.0467376	+	0.0203868i	0.00172984	+	0.000754550i
$731$	−16.2775	+	16.2775i	−0.602046	+	0.602046i
$732$	−16.5057	+	14.9896i	−0.610067	+	0.554033i
$733$	43.2639			1.59799			0.798994	−	0.601339i	$-0.205366\pi$
$733$	43.2639			1.59799			0.798994	+	0.601339i	$0.205366\pi$
$734$	0.180217	−	7.49221i	0.00665194	−	0.276542i
$735$	1.78942	+	0.729842i	0.0660039	+	0.0269206i
$736$	−2.79946	+	23.1687i	−0.103190	+	0.854009i
$737$	11.9515	−	11.9515i	0.440241	−	0.440241i
$738$	−9.80889	+	9.34809i	−0.361070	+	0.344108i
$739$	−31.8860	+	31.8860i	−1.17295	+	1.17295i	−0.191441	+	0.981504i	$0.561316\pi$
$739$	−31.8860	+	31.8860i	−1.17295	+	1.17295i	−0.981504	+	0.191441i	$0.938684\pi$
$740$	−19.9189	+	42.8242i	−0.732232	+	1.57425i
$741$	−9.22953	−	9.22953i	−0.339055	−	0.339055i
$742$	0.134153	−	5.57716i	0.00492490	−	0.204744i
$743$	−6.24833	−	6.24833i	−0.229229	−	0.229229i	0.583142	−	0.812371i	$-0.301823\pi$
$743$	−6.24833	−	6.24833i	−0.229229	−	0.229229i	−0.812371	+	0.583142i	$0.801823\pi$
$744$	15.5285	−	13.4352i	0.569303	−	0.492558i
$745$	−6.36389	+	2.67660i	−0.233155	+	0.0980630i
$746$	18.0840	−	17.2345i	0.662103	−	0.630998i
$747$			37.2610i			1.36331i
$748$	6.39698	+	0.307923i	0.233897	+	0.0112588i
$749$	1.99955	+	1.99955i	0.0730619	+	0.0730619i
$750$	12.5840	+	5.32715i	0.459503	+	0.194520i
$751$			6.13136i			0.223737i	0.993723	+	0.111868i	$0.0356835\pi$
$751$			6.13136i			0.223737i	−0.993723	+	0.111868i	$0.964317\pi$
$752$	−0.338800	−	0.411168i	−0.0123548	−	0.0149937i
$753$	−19.2656	−	19.2656i	−0.702076	−	0.702076i
$754$	−1.41181	+	58.6933i	−0.0514149	+	2.13748i
$755$	44.3380	+	18.0839i	1.61362	+	0.658139i
$756$	−6.72180	+	6.10440i	−0.244470	+	0.222015i
$757$	−35.3503			−1.28483			−0.642414	−	0.766358i	$-0.722067\pi$
$757$	−35.3503			−1.28483			−0.642414	+	0.766358i	$0.722067\pi$
$758$	0.0939950	−	3.90768i	0.00341405	−	0.141933i
$759$			5.07856i			0.184340i
$760$	8.71889	−	17.6239i	0.316267	−	0.639284i
$761$		−	39.8267i		−	1.44372i	−0.692040	−	0.721859i	$-0.743288\pi$
$761$		−	39.8267i		−	1.44372i	0.692040	−	0.721859i	$-0.256712\pi$
$762$	−5.93676	−	0.142803i	−0.215066	−	0.00517319i
$763$	5.44413			0.197091
$764$	−34.5025	−	1.66080i	−1.24826	−	0.0600858i
$765$	10.4403	−	4.39110i	0.377470	−	0.158761i
$766$	−10.0522	−	0.241796i	−0.363202	−	0.00873645i
$767$	−33.7094	−	33.7094i	−1.21718	−	1.21718i
$768$	2.64407	−	13.5730i	0.0954098	−	0.489773i
$769$		−	12.5300i		−	0.451844i	−0.974145	−	0.225922i	$-0.927461\pi$
$769$		−	12.5300i		−	0.451844i	0.974145	−	0.225922i	$-0.0725394\pi$
$770$	4.19276	−	1.64593i	0.151096	−	0.0593154i
$771$	−1.48104	−	1.48104i	−0.0533385	−	0.0533385i
$772$	−28.5391	+	25.9178i	−1.02715	+	0.932802i
$773$		−	28.5452i		−	1.02670i	−0.858180	−	0.513349i	$-0.828404\pi$
$773$		−	28.5452i		−	1.02670i	0.858180	−	0.513349i	$-0.171596\pi$
$774$	−22.5088	−	23.6183i	−0.809060	−	0.848942i
$775$	−29.3743	+	30.0195i	−1.05516	+	1.07833i
$776$	0.663269	−	9.17723i	0.0238100	−	0.329443i
$777$	−6.45403	−	6.45403i	−0.231537	−	0.231537i
$778$	−19.6663	−	0.473052i	−0.705071	−	0.0169597i
$779$	9.34861	+	9.34861i	0.334949	+	0.334949i
$780$	17.0243	+	7.91854i	0.609568	+	0.283529i
$781$	−5.79789	+	5.79789i	−0.207465	+	0.207465i
$782$	9.04896	+	9.49502i	0.323590	+	0.339541i
$783$	27.4347	−	27.4347i	0.980437	−	0.980437i
$784$	−0.384196	+	3.98151i	−0.0137213	+	0.142197i
$785$	−1.57642	+	3.86506i	−0.0562648	+	0.137950i
$786$	−6.31668	−	0.151941i	−0.225308	−	0.00541956i
$787$	30.2894			1.07970			0.539851	−	0.841761i	$-0.318481\pi$
$787$	30.2894			1.07970			0.539851	+	0.841761i	$0.318481\pi$
$788$	1.77159	−	36.8040i	0.0631103	−	1.31109i
$789$	−4.96546	+	4.96546i	−0.176775	+	0.176775i
$790$	−12.1363	−	30.9152i	−0.431789	−	1.09991i
$791$	11.2890			0.401390
$792$	−0.654316	+	9.05334i	−0.0232501	+	0.321697i
$793$	44.3082	−	44.3082i	1.57343	−	1.57343i
$794$	17.4060	−	16.5883i	0.617717	−	0.588698i
$795$	7.05890	+	2.87907i	0.250353	+	0.102110i
$796$	26.3700	+	1.26934i	0.934661	+	0.0449906i
$797$			42.7438i			1.51406i	0.653379	+	0.757031i	$0.273351\pi$
$797$			42.7438i			1.51406i	−0.653379	+	0.757031i	$0.726649\pi$
$798$	2.62153	+	2.75076i	0.0928013	+	0.0973758i
$799$	−0.299436			−0.0105933
$800$	−3.08766	+	28.1152i	−0.109165	+	0.994024i
$801$	−19.5868			−0.692066
$802$	−26.9897	−	28.3201i	−0.953040	−	1.00002i
$803$			0.0229674i			0.000810502i
$804$	−20.4874	−	0.986177i	−0.722535	−	0.0347798i
$805$	8.54169	+	3.48385i	0.301055	+	0.122790i
$806$	−41.7752	+	39.8127i	−1.47147	+	1.40234i
$807$	2.06305	−	2.06305i	0.0726228	−	0.0726228i
$808$	−47.4507	−	3.42942i	−1.66931	−	0.120647i
$809$	10.0414			0.353038			0.176519	−	0.984297i	$-0.443516\pi$
$809$	10.0414			0.353038			0.176519	+	0.984297i	$0.443516\pi$
$810$	3.27650	+	8.34637i	0.115125	+	0.293262i
$811$	−7.06263	+	7.06263i	−0.248003	+	0.248003i	−0.820150	−	0.572148i	$-0.806110\pi$
$811$	−7.06263	+	7.06263i	−0.248003	+	0.248003i	0.572148	+	0.820150i	$0.306110\pi$
$812$	0.821779	−	17.0721i	0.0288388	−	0.599114i
$813$	−10.5981			−0.371693
$814$	−21.2674	−	0.511566i	−0.745423	−	0.0179304i
$815$	1.61020	−	3.94788i	0.0564029	−	0.138288i
$816$	−4.94232	−	5.99801i	−0.173016	−	0.209972i
$817$	−22.5100	+	22.5100i	−0.787525	+	0.787525i
$818$	1.54762	+	1.62391i	0.0541113	+	0.0567787i
$819$	7.73921	−	7.73921i	0.270430	−	0.270430i
$820$	−17.2439	−	8.02070i	−0.602184	−	0.280095i
$821$	30.0720	+	30.0720i	1.04952	+	1.04952i	0.998708	+	0.0508126i	$0.0161811\pi$
$821$	30.0720	+	30.0720i	1.04952	+	1.04952i	0.0508126	+	0.998708i	$0.483819\pi$
$822$	18.7284	+	0.450491i	0.653227	+	0.0157127i
$823$	−0.0366798	−	0.0366798i	−0.00127858	−	0.00127858i	0.706467	−	0.707746i	$-0.250288\pi$
$823$	−0.0366798	−	0.0366798i	−0.00127858	−	0.00127858i	−0.707746	+	0.706467i	$0.750288\pi$
$824$	25.8787	+	1.87034i	0.901526	+	0.0651563i
$825$	0.0668639	+	6.15476i	0.00232790	+	0.214281i
$826$	9.57474	+	10.0467i	0.333148	+	0.349570i
$827$			47.4262i			1.64917i	0.565738	+	0.824585i	$0.308592\pi$
$827$			47.4262i			1.64917i	−0.565738	+	0.824585i	$0.691408\pi$
$828$	−13.7618	+	12.4978i	−0.478257	+	0.434329i
$829$	−20.5221	−	20.5221i	−0.712761	−	0.712761i	0.254351	−	0.967112i	$-0.418138\pi$
$829$	−20.5221	−	20.5221i	−0.712761	−	0.712761i	−0.967112	+	0.254351i	$0.918138\pi$
$830$	−48.6810	+	19.1105i	−1.68974	+	0.663335i
$831$		−	21.3170i		−	0.739477i
$832$	−5.58824	+	38.4585i	−0.193737	+	1.33331i
$833$	1.58968	+	1.58968i	0.0550791	+	0.0550791i
$834$	2.29995	+	0.0553229i	0.0796408	+	0.00191568i
$835$	10.2549	−	4.31314i	0.354886	−	0.149262i
$836$	8.84631	+	0.425824i	0.305956	+	0.0147274i
$837$	38.1362			1.31818
$838$	15.2482	+	0.366780i	0.526742	+	0.0126702i
$839$		−	49.2729i		−	1.70109i	−0.525902	−	0.850545i	$-0.676272\pi$
$839$		−	49.2729i		−	1.70109i	0.525902	−	0.850545i	$-0.323728\pi$
$840$	−4.89928	−	2.42378i	−0.169041	−	0.0836283i
$841$			44.0331i			1.51838i
$842$	−0.204998	+	8.52244i	−0.00706471	+	0.293703i
$843$	−7.63896			−0.263100
$844$	−18.1660	+	16.4975i	−0.625301	+	0.567867i
$845$	−21.9433	−	8.94990i	−0.754873	−	0.307886i
$846$	0.0102054	−	0.424269i	0.000350867	−	0.0145867i
$847$	−6.34357	−	6.34357i	−0.217968	−	0.217968i
$848$	−1.51557	+	15.7062i	−0.0520449	+	0.539353i
$849$			12.6272i			0.433365i
$850$	11.0915	+	11.3880i	0.380437	+	0.390604i
$851$	−30.8079	−	30.8079i	−1.05608	−	1.05608i
$852$	9.93878	+	0.478411i	0.340497	+	0.0163901i
$853$			20.8078i			0.712445i	0.934401	+	0.356222i	$0.115935\pi$
$853$			20.8078i			0.712445i	−0.934401	+	0.356222i	$0.884065\pi$
$854$	−13.2056	+	12.5852i	−0.451885	+	0.430657i
$855$	14.4378	−	6.07240i	0.493761	−	0.207672i
$856$	−5.23318	−	6.04854i	−0.178866	−	0.206735i
$857$	2.57759	+	2.57759i	0.0880489	+	0.0880489i	0.749759	−	0.661711i	$-0.230169\pi$
$857$	2.57759	+	2.57759i	0.0880489	+	0.0880489i	−0.661711	+	0.749759i	$0.730169\pi$
$858$	−0.203368	+	8.45464i	−0.00694285	+	0.288637i
$859$	13.9667	+	13.9667i	0.476536	+	0.476536i	0.904022	−	0.427486i	$-0.140601\pi$
$859$	13.9667	+	13.9667i	0.476536	+	0.476536i	−0.427486	+	0.904022i	$0.640601\pi$
$860$	19.3126	−	41.5207i	0.658555	−	1.41585i
$861$	2.59883	−	2.59883i	0.0885680	−	0.0885680i
$862$	−1.58158	+	1.50728i	−0.0538688	+	0.0513381i
$863$	−2.19689	+	2.19689i	−0.0747832	+	0.0747832i	−0.743509	−	0.668726i	$-0.766840\pi$
$863$	−2.19689	+	2.19689i	−0.0747832	+	0.0747832i	0.668726	+	0.743509i	$0.266840\pi$
$864$	20.2073	−	15.8504i	0.687466	−	0.539243i
$865$	−11.0898	−	4.52315i	−0.377066	−	0.153792i
$866$	−0.0298128	+	1.23941i	−0.00101308	+	0.0421170i
$867$	10.3243			0.350631
$868$	12.4369	−	11.2946i	0.422136	−	0.383362i
$869$	10.5780	−	10.5780i	0.358834	−	0.358834i
$870$	21.4082	+	9.33822i	0.725807	+	0.316595i
$871$	57.6442			1.95320
$872$	−15.3583	−	1.10999i	−0.520097	−	0.0375892i
$873$	5.18269	−	5.18269i	0.175407	−	0.175407i
$874$	12.5137	+	13.1305i	0.423282	+	0.444147i
$875$	10.3976	+	4.10965i	0.351504	+	0.138932i
$876$	0.0206330	−	0.0187378i	0.000697124	−	0.000633093i
$877$			25.4716i			0.860114i	0.902802	+	0.430057i	$0.141507\pi$
$877$			25.4716i			0.860114i	−0.902802	+	0.430057i	$0.858493\pi$
$878$	−22.9693	+	21.8902i	−0.775175	+	0.738759i
$879$	20.9207			0.705637
$880$	−12.1636	+	3.78844i	−0.410036	+	0.127708i
$881$	−40.4199			−1.36178			−0.680891	−	0.732385i	$-0.738407\pi$
$881$	−40.4199			−1.36178			−0.680891	+	0.732385i	$0.738407\pi$
$882$	−2.30659	+	2.19823i	−0.0776668	+	0.0740182i
$883$			49.3699i			1.66143i	0.556698	+	0.830715i	$0.312068\pi$
$883$			49.3699i			1.66143i	−0.556698	+	0.830715i	$0.687932\pi$
$884$	14.6842	+	16.1694i	0.493885	+	0.543836i
$885$	−17.4818	+	7.35269i	−0.587644	+	0.247158i
$886$	−4.77450	−	5.00985i	−0.160402	−	0.168309i
$887$	−34.6395	+	34.6395i	−1.16308	+	1.16308i	−0.179283	+	0.983797i	$0.557378\pi$
$887$	−34.6395	+	34.6395i	−1.16308	+	1.16308i	−0.983797	+	0.179283i	$0.942622\pi$
$888$	16.8914	+	19.5232i	0.566837	+	0.655155i
$889$	−4.85866			−0.162954
$890$	−10.0457	−	25.5899i	−0.336733	−	0.857774i
$891$	−2.85581	+	2.85581i	−0.0956732	+	0.0956732i
$892$	−11.4750	−	12.6356i	−0.384211	−	0.423070i
$893$	−0.414087			−0.0138569
$894$	−0.0907457	+	3.77259i	−0.00303499	+	0.126174i
$895$	−9.50828	+	3.99910i	−0.317827	+	0.133675i
$896$	1.89562	−	11.1538i	0.0633284	−	0.372621i
$897$	−12.2473	+	12.2473i	−0.408927	+	0.408927i
$898$	11.2113	−	10.6846i	0.374125	−	0.356549i
$899$	−50.7606	+	50.7606i	−1.69296	+	1.69296i
$900$	−16.5136	+	15.3274i	−0.550452	+	0.510914i
$901$	6.27095	+	6.27095i	0.208916	+	0.208916i
$902$	0.205991	−	8.56372i	0.00685876	−	0.285141i
$903$	6.25759	+	6.25759i	0.208240	+	0.208240i
$904$	−31.8470	−	2.30169i	−1.05921	−	0.0765530i
$905$	8.94782	+	21.2744i	0.297436	+	0.707184i
$906$	18.9473	−	18.0572i	0.629481	−	0.599909i
$907$			25.4847i			0.846206i	0.906081	+	0.423103i	$0.139059\pi$
$907$			25.4847i			0.846206i	−0.906081	+	0.423103i	$0.860941\pi$
$908$	0.487549	−	10.1286i	0.0161799	−	0.336130i
$909$	−26.7970	−	26.7970i	−0.888801	−	0.888801i
$910$	14.0805	+	6.14187i	0.466763	+	0.203601i
$911$		−	52.0646i		−	1.72498i	−0.506076	−	0.862489i	$-0.668904\pi$
$911$		−	52.0646i		−	1.72498i	0.506076	−	0.862489i	$-0.331096\pi$
$912$	−6.83468	−	8.29458i	−0.226319	−	0.274661i
$913$	−16.6568	−	16.6568i	−0.551258	−	0.551258i
$914$	0.0148256	−	0.616348i	0.000490388	−	0.0203870i
$915$	−9.66451	−	22.9784i	−0.319499	−	0.759641i
$916$	30.2336	+	33.2914i	0.998945	+	1.09998i
$917$	−5.16959			−0.170715
$918$	0.347101	−	14.4301i	0.0114560	−	0.476265i
$919$			28.1746i			0.929393i	0.885470	+	0.464696i	$0.153837\pi$
$919$			28.1746i			0.929393i	−0.885470	+	0.464696i	$0.846163\pi$
$920$	−23.3864	−	11.5697i	−0.771026	−	0.381443i
$921$		−	14.0662i		−	0.463499i
$922$	17.5055	+	0.421078i	0.576515	+	0.0138675i
$923$	−27.9642			−0.920451
$924$	0.118375	−	2.45920i	0.00389427	−	0.0809017i
$925$	−37.7420	−	36.9308i	−1.24095	−	1.21428i
$926$	−10.2858	−	0.247415i	−0.338013	−	0.00813056i
$927$	14.6146	+	14.6146i	0.480005	+	0.480005i
$928$	−5.79910	+	47.9941i	−0.190365	+	1.57548i
$929$		−	53.2862i		−	1.74826i	−0.485690	−	0.874131i	$-0.661431\pi$
$929$		−	53.2862i		−	1.74826i	0.485690	−	0.874131i	$-0.338569\pi$
$930$	8.38909	+	21.3699i	0.275089	+	0.700746i
$931$	2.19835	+	2.19835i	0.0720480	+	0.0720480i
$932$	−5.51772	−	6.07578i	−0.180739	−	0.199019i
$933$		−	6.13425i		−	0.200826i
$934$	22.2071	+	23.3018i	0.726640	+	0.762458i
$935$	−2.70416	+	6.63006i	−0.0884356	+	0.216826i
$936$	−23.4108	+	20.2549i	−0.765206	+	0.662053i
$937$	19.2461	+	19.2461i	0.628742	+	0.628742i	0.947752	−	0.319009i	$-0.103350\pi$
$937$	19.2461	+	19.2461i	0.628742	+	0.628742i	−0.319009	+	0.947752i	$0.603350\pi$
$938$	−16.7767	−	0.403545i	−0.547777	−	0.0131762i
$939$	−2.80748	−	2.80748i	−0.0916185	−	0.0916185i
$940$	0.559536	−	0.204267i	0.0182500	−	0.00666245i
$941$	−21.9552	+	21.9552i	−0.715719	+	0.715719i	−0.967725	−	0.252007i	$-0.918909\pi$
$941$	−21.9552	+	21.9552i	−0.715719	+	0.715719i	0.252007	+	0.967725i	$0.418909\pi$
$942$	1.57409	+	1.65168i	0.0512867	+	0.0538148i
$943$	12.4054	−	12.4054i	0.403974	−	0.403974i
$944$	−24.9626	−	30.2946i	−0.812463	−	0.986006i
$945$	−3.93579	−	9.35775i	−0.128031	−	0.304408i
$946$	20.6201	+	0.495995i	0.670418	+	0.0161262i
$947$	37.7482			1.22665			0.613325	−	0.789831i	$-0.289832\pi$
$947$	37.7482			1.22665			0.613325	+	0.789831i	$0.289832\pi$
$948$	−18.1329	−	0.872838i	−0.588928	−	0.0283485i
$949$	−0.0553877	+	0.0553877i	−0.00179796	+	0.00179796i
$950$	15.3384	+	15.7483i	0.497642	+	0.510942i
$951$	−8.52952			−0.276589
$952$	−4.16048	−	4.80871i	−0.134842	−	0.155851i
$953$	35.9739	−	35.9739i	1.16531	−	1.16531i	0.182014	−	0.983296i	$-0.441738\pi$
$953$	35.9739	−	35.9739i	1.16531	−	1.16531i	0.983296	−	0.182014i	$-0.0582616\pi$
$954$	−9.09899	+	8.67154i	−0.294591	+	0.280752i
$955$	14.5851	−	35.7596i	0.471962	−	1.15715i
$956$	−2.08380	+	43.2901i	−0.0673950	+	1.40010i
$957$			10.5203i			0.340072i
$958$	18.4877	+	19.3990i	0.597310	+	0.626754i
$959$	15.3273			0.494946
$960$	13.3270	+	7.83655i	0.430128	+	0.252924i
$961$	−39.5609			−1.27616
$962$	−50.0544	−	52.5218i	−1.61382	−	1.69337i
$963$		−	6.37117i		−	0.205308i
$964$	0.164118	−	3.40949i	0.00528589	−	0.109812i
$965$	−16.7104	−	39.7307i	−0.537927	−	1.27898i
$966$	3.65018	−	3.47871i	0.117443	−	0.111925i
$967$	42.6553	−	42.6553i	1.37170	−	1.37170i	0.513778	−	0.857923i	$-0.328245\pi$
$967$	42.6553	−	42.6553i	1.37170	−	1.37170i	0.857923	−	0.513778i	$-0.171755\pi$
$968$	16.6023	+	19.1890i	0.533617	+	0.616759i
$969$	−6.04059			−0.194052
$970$	9.42921	+	4.11300i	0.302754	+	0.132060i
$971$	27.4169	−	27.4169i	0.879852	−	0.879852i	−0.113667	−	0.993519i	$-0.536260\pi$
$971$	27.4169	−	27.4169i	0.879852	−	0.879852i	0.993519	+	0.113667i	$0.0362598\pi$
$972$	32.1039	+	1.54535i	1.02973	+	0.0495670i
$973$	1.88229			0.0603433
$974$	28.5692	+	0.687203i	0.915418	+	0.0220194i
$975$	−14.6814	+	15.0039i	−0.470182	+	0.480510i
$976$	39.8198	−	32.8113i	1.27460	−	1.05026i
$977$	2.15875	−	2.15875i	0.0690644	−	0.0690644i	−0.671731	−	0.740795i	$-0.734449\pi$
$977$	2.15875	−	2.15875i	0.0690644	−	0.0690644i	0.740795	+	0.671731i	$0.234449\pi$
$978$	−1.60782	−	1.68708i	−0.0514125	−	0.0539468i
$979$	8.75587	−	8.75587i	0.279839	−	0.279839i
$980$	−4.05496	−	1.88609i	−0.129531	−	0.0602489i
$981$	−8.67334	−	8.67334i	−0.276918	−	0.276918i
$982$	−11.9508	−	0.287465i	−0.381366	−	0.00917336i
$983$	−18.9693	−	18.9693i	−0.605026	−	0.605026i	0.336616	−	0.941642i	$-0.390717\pi$
$983$	−18.9693	−	18.9693i	−0.605026	−	0.605026i	−0.941642	+	0.336616i	$0.890717\pi$
$984$	−7.86136	+	6.80162i	−0.250611	+	0.216828i
$985$	38.1450	+	15.5580i	1.21540	+	0.495719i
$986$	18.7450	+	19.6690i	0.596961	+	0.626388i
$987$			0.115113i			0.00366408i
$988$	20.3067	+	22.3605i	0.646041	+	0.711382i
$989$	29.8702	+	29.8702i	0.949816	+	0.949816i
$990$	−9.30193	−	4.05748i	−0.295635	−	0.128955i
$991$			25.5060i			0.810225i	0.914267	+	0.405113i	$0.132768\pi$
$991$			25.5060i			0.810225i	−0.914267	+	0.405113i	$0.867232\pi$
$992$	−37.3882	+	29.3270i	−1.18708	+	0.931133i
$993$	−3.09646	−	3.09646i	−0.0982632	−	0.0982632i
$994$	8.13863	+	0.195766i	0.258142	+	0.00620933i
$995$	−11.1473	+	27.3309i	−0.353393	+	0.866447i
$996$	−1.37442	+	28.5531i	−0.0435503	+	0.904740i
$997$	48.8422			1.54685			0.773424	−	0.633889i	$-0.218543\pi$
$997$	48.8422			1.54685			0.773424	+	0.633889i	$0.218543\pi$
$998$	22.1487	+	0.532764i	0.701106	+	0.0168644i
$999$			47.9467i			1.51696i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.t.a.43.19	✓	144
5.2	odd	4		560.2.bl.a.267.55	yes	144
16.3	odd	4		560.2.bl.a.323.55	yes	144
80.67	even	4	inner	560.2.t.a.547.19	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.t.a.43.19	✓	144	1.1	even	1	trivial
560.2.t.a.547.19	yes	144	80.67	even	4	inner
560.2.bl.a.267.55	yes	144	5.2	odd	4
560.2.bl.a.323.55	yes	144	16.3	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.975664 - 1.02376i) q^{2} -0.864258i q^{3} +(-0.0961601 + 1.99769i) q^{4} +(-2.07047 - 0.844473i) q^{5} +(-0.884791 + 0.843225i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.13897 - 1.85063i) q^{8} +2.25306 q^{9} +O(q^{10})\)	\(q+(-0.975664 - 1.02376i) q^{2} -0.864258i q^{3} +(-0.0961601 + 1.99769i) q^{4} +(-2.07047 - 0.844473i) q^{5} +(-0.884791 + 0.843225i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.13897 - 1.85063i) q^{8} +2.25306 q^{9} +(1.15555 + 2.94359i) q^{10} +(-1.00718 + 1.00718i) q^{11} +(1.72652 + 0.0831072i) q^{12} -4.85780 q^{13} +(1.41380 + 0.0340076i) q^{14} +(-0.729842 + 1.78942i) q^{15} +(-3.98151 - 0.384196i) q^{16} +(-1.58968 + 1.58968i) q^{17} +(-2.19823 - 2.30659i) q^{18} +(-2.19835 + 2.19835i) q^{19} +(1.88609 - 4.05496i) q^{20} +(0.611123 + 0.611123i) q^{21} +(2.01378 + 0.0484394i) q^{22} +(2.91715 + 2.91715i) q^{23} +(-1.59942 - 1.84862i) q^{24} +(3.57373 + 3.49692i) q^{25} +(4.73958 + 4.97321i) q^{26} -4.54000i q^{27} +(-1.34458 - 1.48057i) q^{28} +(6.04289 + 6.04289i) q^{29} +(2.54402 - 0.998695i) q^{30} +8.40005i q^{31} +(3.49129 + 4.45094i) q^{32} +(0.870465 + 0.870465i) q^{33} +(3.17844 + 0.0764540i) q^{34} +(2.06118 - 0.866915i) q^{35} +(-0.216654 + 4.50090i) q^{36} -10.5609 q^{37} +(4.39543 + 0.105727i) q^{38} +4.19839i q^{39} +(-5.99148 + 2.02538i) q^{40} -4.25256i q^{41} +(0.0293913 - 1.22189i) q^{42} +10.2395 q^{43} +(-1.91518 - 2.10889i) q^{44} +(-4.66490 - 1.90265i) q^{45} +(0.140297 - 5.83262i) q^{46} +(0.0941814 + 0.0941814i) q^{47} +(-0.332044 + 3.44105i) q^{48} -1.00000i q^{49} +(0.0932361 - 7.07045i) q^{50} +(1.37389 + 1.37389i) q^{51} +(0.467127 - 9.70436i) q^{52} -3.94479i q^{53} +(-4.64786 + 4.42951i) q^{54} +(2.93588 - 1.23481i) q^{55} +(-0.203888 + 2.82107i) q^{56} +(1.89994 + 1.89994i) q^{57} +(0.290627 - 12.0823i) q^{58} +(6.93924 + 6.93924i) q^{59} +(-3.50453 - 1.63007i) q^{60} +(-9.12105 + 9.12105i) q^{61} +(8.59962 - 8.19563i) q^{62} +(-1.59315 + 1.59315i) q^{63} +(1.15037 - 7.91686i) q^{64} +(10.0580 + 4.10228i) q^{65} +(0.0418641 - 1.74043i) q^{66} -11.8663 q^{67} +(-3.02282 - 3.32855i) q^{68} +(2.52117 - 2.52117i) q^{69} +(-2.89853 - 1.26433i) q^{70} +5.75655 q^{71} +(4.81922 - 4.16957i) q^{72} +(0.0114018 - 0.0114018i) q^{73} +(10.3039 + 10.8118i) q^{74} +(3.02224 - 3.08863i) q^{75} +(-4.18022 - 4.60301i) q^{76} -1.42437i q^{77} +(4.29814 - 4.09622i) q^{78} -10.5026 q^{79} +(7.91917 + 4.15774i) q^{80} +2.83544 q^{81} +(-4.35359 + 4.14907i) q^{82} +16.5380i q^{83} +(-1.27960 + 1.16207i) q^{84} +(4.63383 - 1.94895i) q^{85} +(-9.99031 - 10.4828i) q^{86} +(5.22262 - 5.22262i) q^{87} +(-0.290412 + 4.01825i) q^{88} -8.69343 q^{89} +(2.60353 + 6.63207i) q^{90} +(3.43498 - 3.43498i) q^{91} +(-6.10807 + 5.54704i) q^{92} +7.25981 q^{93} +(0.00452956 - 0.188308i) q^{94} +(6.40807 - 2.69518i) q^{95} +(3.84676 - 3.01737i) q^{96} +(2.30029 - 2.30029i) q^{97} +(-1.02376 + 0.975664i) q^{98} +(-2.26924 + 2.26924i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 8 q^{4} - 144 q^{9}+O(q^{10}) \) 144 * q + 8 * q^4 - 144 * q^9	\( 144 q + 8 q^{4} - 144 q^{9} - 16 q^{12} + 8 q^{16} - 28 q^{18} - 16 q^{19} + 4 q^{22} + 32 q^{26} - 36 q^{30} + 32 q^{34} - 32 q^{36} - 56 q^{38} + 8 q^{40} - 20 q^{42} + 64 q^{43} - 56 q^{44} - 32 q^{46} - 80 q^{48} - 48 q^{50} - 16 q^{51} - 16 q^{52} + 32 q^{54} - 24 q^{56} + 52 q^{58} + 72 q^{60} - 32 q^{61} - 40 q^{62} + 32 q^{64} + 32 q^{66} - 24 q^{68} - 32 q^{69} + 80 q^{72} - 16 q^{73} - 32 q^{74} - 88 q^{75} + 76 q^{78} + 128 q^{80} + 144 q^{81} + 56 q^{82} + 32 q^{86} - 112 q^{87} + 88 q^{88} + 88 q^{90} - 136 q^{92} - 8 q^{94} + 80 q^{95} + 32 q^{96} + 64 q^{99}+O(q^{100}) \) 144 * q + 8 * q^4 - 144 * q^9 - 16 * q^12 + 8 * q^16 - 28 * q^18 - 16 * q^19 + 4 * q^22 + 32 * q^26 - 36 * q^30 + 32 * q^34 - 32 * q^36 - 56 * q^38 + 8 * q^40 - 20 * q^42 + 64 * q^43 - 56 * q^44 - 32 * q^46 - 80 * q^48 - 48 * q^50 - 16 * q^51 - 16 * q^52 + 32 * q^54 - 24 * q^56 + 52 * q^58 + 72 * q^60 - 32 * q^61 - 40 * q^62 + 32 * q^64 + 32 * q^66 - 24 * q^68 - 32 * q^69 + 80 * q^72 - 16 * q^73 - 32 * q^74 - 88 * q^75 + 76 * q^78 + 128 * q^80 + 144 * q^81 + 56 * q^82 + 32 * q^86 - 112 * q^87 + 88 * q^88 + 88 * q^90 - 136 * q^92 - 8 * q^94 + 80 * q^95 + 32 * q^96 + 64 * q^99

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