LMFDB - Embedded newform 140.2.k.a.43.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,2,Mod(43,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([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("140.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	140.k (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:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.17
Character	$\chi$	$=$	140.43
Dual form			140.2.k.a.127.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34141 - 0.447909i) q^{2} +(-0.396892 + 0.396892i) q^{3} +(1.59875 - 1.20166i) q^{4} +(-0.137858 - 2.23181i) q^{5} +(-0.354623 + 0.710167i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(1.60635 - 2.32801i) q^{8} +2.68495i q^{9} +O(q^{10})$	\(q+(1.34141 - 0.447909i) q^{2} +(-0.396892 + 0.396892i) q^{3} +(1.59875 - 1.20166i) q^{4} +(-0.137858 - 2.23181i) q^{5} +(-0.354623 + 0.710167i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(1.60635 - 2.32801i) q^{8} +2.68495i q^{9} +(-1.18457 - 2.93203i) q^{10} +4.30996i q^{11} +(-0.157604 + 1.11146i) q^{12} +(1.27735 + 1.27735i) q^{13} +(-1.26524 - 0.631799i) q^{14} +(0.940505 + 0.831075i) q^{15} +(1.11203 - 3.84232i) q^{16} +(-0.355714 + 0.355714i) q^{17} +(1.20262 + 3.60162i) q^{18} -8.16424 q^{19} +(-2.90228 - 3.40246i) q^{20} +0.561291 q^{21} +(1.93047 + 5.78142i) q^{22} +(2.65723 - 2.65723i) q^{23} +(0.286423 + 1.56152i) q^{24} +(-4.96199 + 0.615348i) q^{25} +(2.28559 + 1.14131i) q^{26} +(-2.25631 - 2.25631i) q^{27} +(-1.98019 - 0.280789i) q^{28} +3.36420i q^{29} +(1.63385 + 0.693550i) q^{30} -0.150355i q^{31} +(-0.229322 - 5.65220i) q^{32} +(-1.71059 - 1.71059i) q^{33} +(-0.317830 + 0.636485i) q^{34} +(-1.48065 + 1.67561i) q^{35} +(3.22640 + 4.29258i) q^{36} +(-1.53414 + 1.53414i) q^{37} +(-10.9516 + 3.65684i) q^{38} -1.01394 q^{39} +(-5.41714 - 3.26414i) q^{40} +9.17384 q^{41} +(0.752920 - 0.251407i) q^{42} +(6.48688 - 6.48688i) q^{43} +(5.17911 + 6.89057i) q^{44} +(5.99232 - 0.370143i) q^{45} +(2.37423 - 4.75463i) q^{46} +(5.35960 + 5.35960i) q^{47} +(1.08363 + 1.96634i) q^{48} +1.00000i q^{49} +(-6.38044 + 3.04796i) q^{50} -0.282360i q^{51} +(3.57711 + 0.507230i) q^{52} +(-8.37980 - 8.37980i) q^{53} +(-4.03726 - 2.01602i) q^{54} +(9.61904 - 0.594164i) q^{55} +(-2.78201 + 0.510294i) q^{56} +(3.24033 - 3.24033i) q^{57} +(1.50686 + 4.51277i) q^{58} +0.357352 q^{59} +(2.50231 + 0.198519i) q^{60} -10.0316 q^{61} +(-0.0673452 - 0.201687i) q^{62} +(1.89855 - 1.89855i) q^{63} +(-2.83929 - 7.47920i) q^{64} +(2.67472 - 3.02690i) q^{65} +(-3.06079 - 1.52841i) q^{66} +(-5.33350 - 5.33350i) q^{67} +(-0.141252 + 0.996146i) q^{68} +2.10927i q^{69} +(-1.23564 + 2.91088i) q^{70} +2.69169i q^{71} +(6.25061 + 4.31297i) q^{72} +(-4.14495 - 4.14495i) q^{73} +(-1.37075 + 2.74506i) q^{74} +(1.72515 - 2.21360i) q^{75} +(-13.0526 + 9.81064i) q^{76} +(3.04760 - 3.04760i) q^{77} +(-1.36011 + 0.454154i) q^{78} +9.17393 q^{79} +(-8.72864 - 1.95215i) q^{80} -6.26383 q^{81} +(12.3059 - 4.10905i) q^{82} +(4.83885 - 4.83885i) q^{83} +(0.897366 - 0.674480i) q^{84} +(0.842925 + 0.744849i) q^{85} +(5.79603 - 11.6071i) q^{86} +(-1.33523 - 1.33523i) q^{87} +(10.0337 + 6.92330i) q^{88} +1.19198i q^{89} +(7.87235 - 3.18053i) q^{90} -1.80645i q^{91} +(1.05517 - 7.44135i) q^{92} +(0.0596746 + 0.0596746i) q^{93} +(9.59003 + 4.78880i) q^{94} +(1.12551 + 18.2211i) q^{95} +(2.33433 + 2.15230i) q^{96} +(-1.04890 + 1.04890i) q^{97} +(0.447909 + 1.34141i) q^{98} -11.5720 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 8 q^{6}+O(q^{10}) $ 36 * q - 8 * q^6	$ 36 q - 8 q^{6} - 16 q^{10} - 16 q^{12} - 4 q^{13} - 8 q^{16} - 20 q^{17} + 28 q^{18} + 20 q^{20} + 4 q^{22} - 20 q^{25} - 32 q^{26} - 4 q^{30} + 20 q^{37} - 36 q^{40} - 20 q^{42} + 20 q^{45} + 16 q^{46} - 24 q^{48} + 40 q^{50} + 16 q^{52} - 44 q^{53} - 24 q^{56} - 16 q^{57} - 4 q^{58} + 40 q^{60} - 64 q^{61} + 40 q^{62} + 4 q^{65} + 32 q^{66} + 80 q^{68} + 80 q^{72} + 52 q^{73} + 8 q^{76} - 76 q^{78} - 20 q^{80} - 36 q^{81} + 56 q^{82} - 20 q^{85} + 56 q^{86} - 40 q^{88} - 16 q^{90} - 56 q^{92} + 32 q^{93} + 120 q^{96} + 20 q^{97}+O(q^{100}) $ 36 * q - 8 * q^6 - 16 * q^10 - 16 * q^12 - 4 * q^13 - 8 * q^16 - 20 * q^17 + 28 * q^18 + 20 * q^20 + 4 * q^22 - 20 * q^25 - 32 * q^26 - 4 * q^30 + 20 * q^37 - 36 * q^40 - 20 * q^42 + 20 * q^45 + 16 * q^46 - 24 * q^48 + 40 * q^50 + 16 * q^52 - 44 * q^53 - 24 * q^56 - 16 * q^57 - 4 * q^58 + 40 * q^60 - 64 * q^61 + 40 * q^62 + 4 * q^65 + 32 * q^66 + 80 * q^68 + 80 * q^72 + 52 * q^73 + 8 * q^76 - 76 * q^78 - 20 * q^80 - 36 * q^81 + 56 * q^82 - 20 * q^85 + 56 * q^86 - 40 * q^88 - 16 * q^90 - 56 * q^92 + 32 * q^93 + 120 * q^96 + 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.34141	−	0.447909i	0.948519	−	0.316720i
$2$	1.34141	−	0.447909i	0.948519	−	0.316720i
$3$	−0.396892	+	0.396892i	−0.229146	+	0.229146i	−0.812336	−	0.583190i	$-0.801804\pi$
$3$	−0.396892	+	0.396892i	−0.229146	+	0.229146i	0.583190	+	0.812336i	$0.301804\pi$
$4$	1.59875	−	1.20166i	0.799377	−	0.600830i
$5$	−0.137858	−	2.23181i	−0.0616521	−	0.998098i
$5$	−0.137858	−	2.23181i	−0.0616521	−	0.998098i
$6$	−0.354623	+	0.710167i	−0.144774	+	0.289924i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	1.60635	−	2.32801i	0.567930	−	0.823077i
$9$			2.68495i			0.894984i
$10$	−1.18457	−	2.93203i	−0.374595	−	0.927188i
$11$			4.30996i			1.29950i	0.760147	+	0.649751i	$0.225127\pi$
$11$			4.30996i			1.29950i	−0.760147	+	0.649751i	$0.774873\pi$
$12$	−0.157604	+	1.11146i	−0.0454964	+	0.320852i
$13$	1.27735	+	1.27735i	0.354273	+	0.354273i	0.861697	−	0.507424i	$-0.169402\pi$
$13$	1.27735	+	1.27735i	0.354273	+	0.354273i	−0.507424	+	0.861697i	$0.669402\pi$
$14$	−1.26524	−	0.631799i	−0.338149	−	0.168855i
$15$	0.940505	+	0.831075i	0.242837	+	0.214583i
$16$	1.11203	−	3.84232i	0.278008	−	0.960579i
$17$	−0.355714	+	0.355714i	−0.0862733	+	0.0862733i	−0.748926	−	0.662653i	$-0.769430\pi$
$17$	−0.355714	+	0.355714i	−0.0862733	+	0.0862733i	0.662653	+	0.748926i	$0.269430\pi$
$18$	1.20262	+	3.60162i	0.283459	+	0.848910i
$19$	−8.16424			−1.87301			−0.936503	−	0.350660i	$-0.885957\pi$
$19$	−8.16424			−1.87301			−0.936503	+	0.350660i	$0.885957\pi$
$20$	−2.90228	−	3.40246i	−0.648970	−	0.760814i
$21$	0.561291			0.122484
$22$	1.93047	+	5.78142i	0.411578	+	1.23260i
$23$	2.65723	−	2.65723i	0.554071	−	0.554071i	−0.373542	−	0.927613i	$-0.621857\pi$
$23$	2.65723	−	2.65723i	0.554071	−	0.554071i	0.927613	+	0.373542i	$0.121857\pi$
$24$	0.286423	+	1.56152i	0.0584659	+	0.318744i
$25$	−4.96199	+	0.615348i	−0.992398	+	0.123070i
$26$	2.28559	+	1.14131i	0.448240	+	0.223830i
$27$	−2.25631	−	2.25631i	−0.434228	−	0.434228i
$28$	−1.98019	−	0.280789i	−0.374221	−	0.0530641i
$29$			3.36420i			0.624717i	0.949964	+	0.312359i	$0.101119\pi$
$29$			3.36420i			0.624717i	−0.949964	+	0.312359i	$0.898881\pi$
$30$	1.63385	+	0.693550i	0.298298	+	0.126624i
$31$		−	0.150355i		−	0.0270045i	−0.999909	−	0.0135022i	$-0.995702\pi$
$31$		−	0.150355i		−	0.0270045i	0.999909	−	0.0135022i	$-0.00429803\pi$
$32$	−0.229322	−	5.65220i	−0.0405388	−	0.999178i
$33$	−1.71059	−	1.71059i	−0.297776	−	0.297776i
$34$	−0.317830	+	0.636485i	−0.0545074	+	0.109156i
$35$	−1.48065	+	1.67561i	−0.250276	+	0.283230i
$36$	3.22640	+	4.29258i	0.537733	+	0.715430i
$37$	−1.53414	+	1.53414i	−0.252210	+	0.252210i	−0.821876	−	0.569666i	$-0.807073\pi$
$37$	−1.53414	+	1.53414i	−0.252210	+	0.252210i	0.569666	+	0.821876i	$0.307073\pi$
$38$	−10.9516	+	3.65684i	−1.77658	+	0.593218i
$39$	−1.01394			−0.162361
$40$	−5.41714	−	3.26414i	−0.856525	−	0.516105i
$41$	9.17384			1.43271			0.716357	−	0.697734i	$-0.245808\pi$
$41$	9.17384			1.43271			0.716357	+	0.697734i	$0.245808\pi$
$42$	0.752920	−	0.251407i	0.116178	−	0.0387930i
$43$	6.48688	−	6.48688i	0.989241	−	0.989241i	−0.0107022	−	0.999943i	$-0.503407\pi$
$43$	6.48688	−	6.48688i	0.989241	−	0.989241i	0.999943	+	0.0107022i	$0.00340667\pi$
$44$	5.17911	+	6.89057i	0.780780	+	1.03879i
$45$	5.99232	−	0.370143i	0.893282	−	0.0551776i
$46$	2.37423	−	4.75463i	0.350062	−	0.701032i
$47$	5.35960	+	5.35960i	0.781778	+	0.781778i	0.980131	−	0.198353i	$-0.0635591\pi$
$47$	5.35960	+	5.35960i	0.781778	+	0.781778i	−0.198353	+	0.980131i	$0.563559\pi$
$48$	1.08363	+	1.96634i	0.156408	+	0.283817i
$49$			1.00000i			0.142857i
$50$	−6.38044	+	3.04796i	−0.902330	+	0.431046i
$51$		−	0.282360i		−	0.0395383i
$52$	3.57711	+	0.507230i	0.496056	+	0.0703401i
$53$	−8.37980	−	8.37980i	−1.15105	−	1.15105i	−0.986342	−	0.164712i	$-0.947331\pi$
$53$	−8.37980	−	8.37980i	−1.15105	−	1.15105i	−0.164712	−	0.986342i	$-0.552669\pi$
$54$	−4.03726	−	2.01602i	−0.549402	−	0.274345i
$55$	9.61904	−	0.594164i	1.29703	−	0.0801171i
$56$	−2.78201	+	0.510294i	−0.371762	+	0.0681909i
$57$	3.24033	−	3.24033i	0.429192	−	0.429192i
$58$	1.50686	+	4.51277i	0.197860	+	0.592556i
$59$	0.357352			0.0465233			0.0232616	−	0.999729i	$-0.492595\pi$
$59$	0.357352			0.0465233			0.0232616	+	0.999729i	$0.492595\pi$
$60$	2.50231	+	0.198519i	0.323046	+	0.0256286i
$61$	−10.0316			−1.28442			−0.642210	−	0.766529i	$-0.721982\pi$
$61$	−10.0316			−1.28442			−0.642210	+	0.766529i	$0.721982\pi$
$62$	−0.0673452	−	0.201687i	−0.00855285	−	0.0256143i
$63$	1.89855	−	1.89855i	0.239195	−	0.239195i
$64$	−2.83929	−	7.47920i	−0.354911	−	0.934900i
$65$	2.67472	−	3.02690i	0.331758	−	0.375441i
$66$	−3.06079	−	1.52841i	−0.376758	−	0.188135i
$67$	−5.33350	−	5.33350i	−0.651591	−	0.651591i	0.301785	−	0.953376i	$-0.402418\pi$
$67$	−5.33350	−	5.33350i	−0.651591	−	0.651591i	−0.953376	+	0.301785i	$0.902418\pi$
$68$	−0.141252	+	0.996146i	−0.0171293	+	0.120800i
$69$			2.10927i			0.253926i
$70$	−1.23564	+	2.91088i	−0.147687	+	0.347916i
$71$			2.69169i			0.319445i	0.987162	+	0.159722i	$0.0510599\pi$
$71$			2.69169i			0.319445i	−0.987162	+	0.159722i	$0.948940\pi$
$72$	6.25061	+	4.31297i	0.736641	+	0.508288i
$73$	−4.14495	−	4.14495i	−0.485129	−	0.485129i	0.421636	−	0.906765i	$-0.361456\pi$
$73$	−4.14495	−	4.14495i	−0.485129	−	0.485129i	−0.906765	+	0.421636i	$0.861456\pi$
$74$	−1.37075	+	2.74506i	−0.159346	+	0.319106i
$75$	1.72515	−	2.21360i	0.199203	−	0.255605i
$76$	−13.0526	+	9.81064i	−1.49724	+	1.12536i
$77$	3.04760	−	3.04760i	0.347307	−	0.347307i
$78$	−1.36011	+	0.454154i	−0.154002	+	0.0514228i
$79$	9.17393			1.03215			0.516074	−	0.856544i	$-0.327393\pi$
$79$	9.17393			1.03215			0.516074	+	0.856544i	$0.327393\pi$
$80$	−8.72864	−	1.95215i	−0.975891	−	0.218257i
$81$	−6.26383			−0.695981
$82$	12.3059	−	4.10905i	1.35896	−	0.453769i
$83$	4.83885	−	4.83885i	0.531132	−	0.531132i	−0.389777	−	0.920909i	$-0.627448\pi$
$83$	4.83885	−	4.83885i	0.531132	−	0.531132i	0.920909	+	0.389777i	$0.127448\pi$
$84$	0.897366	−	0.674480i	0.0979106	−	0.0735918i
$85$	0.842925	+	0.744849i	0.0914281	+	0.0807902i
$86$	5.79603	−	11.6071i	0.625002	−	1.25163i
$87$	−1.33523	−	1.33523i	−0.143151	−	0.143151i
$88$	10.0337	+	6.92330i	1.06959	+	0.738027i
$89$			1.19198i			0.126350i	0.998002	+	0.0631750i	$0.0201226\pi$
$89$			1.19198i			0.126350i	−0.998002	+	0.0631750i	$0.979877\pi$
$90$	7.87235	−	3.18053i	0.829819	−	0.335257i
$91$		−	1.80645i		−	0.189367i
$92$	1.05517	−	7.44135i	0.110009	−	0.775814i
$93$	0.0596746	+	0.0596746i	0.00618797	+	0.00618797i
$94$	9.59003	+	4.78880i	0.989136	+	0.493927i
$95$	1.12551	+	18.2211i	0.115475	+	1.86944i
$96$	2.33433	+	2.15230i	0.238247	+	0.219668i
$97$	−1.04890	+	1.04890i	−0.106500	+	0.106500i	−0.758349	−	0.651849i	$-0.773994\pi$
$97$	−1.04890	+	1.04890i	−0.106500	+	0.106500i	0.651849	+	0.758349i	$0.273994\pi$
$98$	0.447909	+	1.34141i	0.0452457	+	0.135503i
$99$	−11.5720			−1.16303
$100$	−7.19356	+	6.94641i	−0.719356	+	0.694641i
$101$	15.2356			1.51599			0.757997	−	0.652258i	$-0.226178\pi$
$101$	15.2356			1.51599			0.757997	+	0.652258i	$0.226178\pi$
$102$	−0.126472	−	0.378760i	−0.0125226	−	0.0375029i
$103$	1.41071	−	1.41071i	0.139001	−	0.139001i	−0.634182	−	0.773183i	$-0.718663\pi$
$103$	1.41071	−	1.41071i	0.139001	−	0.139001i	0.773183	+	0.634182i	$0.218663\pi$
$104$	5.02556	−	0.921819i	0.492797	−	0.0903918i
$105$	−0.0773785	−	1.25270i	−0.00755137	−	0.122251i
$106$	−14.9941	−	7.48734i	−1.45636	−	0.727235i
$107$	−1.92951	−	1.92951i	−0.186533	−	0.186533i	0.607663	−	0.794195i	$-0.292107\pi$
$107$	−1.92951	−	1.92951i	−0.186533	−	0.186533i	−0.794195	+	0.607663i	$0.792107\pi$
$108$	−6.31861	−	0.895971i	−0.608009	−	0.0862149i
$109$		−	10.2471i		−	0.981494i	−0.871302	−	0.490747i	$-0.836724\pi$
$109$		−	10.2471i		−	0.981494i	0.871302	−	0.490747i	$-0.163276\pi$
$110$	12.6369	−	5.10547i	1.20488	−	0.486788i
$111$		−	1.21777i		−	0.115586i
$112$	−3.50325	+	1.93060i	−0.331026	+	0.182425i
$113$	8.33553	+	8.33553i	0.784141	+	0.784141i	0.980527	−	0.196386i	$-0.0629204\pi$
$113$	8.33553	+	8.33553i	0.784141	+	0.784141i	−0.196386	+	0.980527i	$0.562920\pi$
$114$	2.89523	−	5.79797i	0.271163	−	0.543030i
$115$	−6.29677	−	5.56413i	−0.587177	−	0.518858i
$116$	4.04263	+	5.37854i	0.375349	+	0.499385i
$117$	−3.42963	+	3.42963i	−0.317069	+	0.317069i
$118$	0.479355	−	0.160061i	0.0441282	−	0.0147348i
$119$	0.503055			0.0461150
$120$	3.44553	−	0.854512i	0.314533	−	0.0780059i
$121$	−7.57579			−0.688708
$122$	−13.4565	+	4.49327i	−1.21830	+	0.406801i
$123$	−3.64103	+	3.64103i	−0.328300	+	0.328300i
$124$	−0.180675	−	0.240380i	−0.0162251	−	0.0215868i
$125$	2.05739	+	10.9894i	0.184019	+	0.982923i
$126$	1.69635	−	3.39711i	0.151123	−	0.302638i
$127$	−5.10188	−	5.10188i	−0.452719	−	0.452719i	0.443537	−	0.896256i	$-0.353723\pi$
$127$	−5.10188	−	5.10188i	−0.452719	−	0.452719i	−0.896256	+	0.443537i	$0.853723\pi$
$128$	−7.15865	−	8.76092i	−0.632741	−	0.774363i
$129$			5.14919i			0.453361i
$130$	2.23211	−	5.25834i	0.195769	−	0.461187i
$131$			14.2250i			1.24284i	0.783477	+	0.621420i	$0.213444\pi$
$131$			14.2250i			1.24284i	−0.783477	+	0.621420i	$0.786556\pi$
$132$	−4.79036	−	0.679268i	−0.416948	−	0.0591227i
$133$	5.77299	+	5.77299i	0.500582	+	0.500582i
$134$	−9.54334	−	4.76548i	−0.824419	−	0.411675i
$135$	−4.72462	+	5.34673i	−0.406631	+	0.460173i
$136$	0.256706	+	1.39951i	0.0220124	+	0.120007i
$137$	−7.93760	+	7.93760i	−0.678155	+	0.678155i	−0.959583	−	0.281427i	$-0.909192\pi$
$137$	−7.93760	+	7.93760i	−0.678155	+	0.678155i	0.281427	+	0.959583i	$0.409192\pi$
$138$	0.944762	+	2.82939i	0.0804235	+	0.240854i
$139$	−12.9091			−1.09493			−0.547466	−	0.836828i	$-0.684408\pi$
$139$	−12.9091			−1.09493			−0.547466	+	0.836828i	$0.684408\pi$
$140$	−0.353682	+	4.45813i	−0.0298916	+	0.376781i
$141$	−4.25437			−0.358283
$142$	1.20563	+	3.61066i	0.101175	+	0.303000i
$143$	−5.50533	+	5.50533i	−0.460379	+	0.460379i
$144$	10.3164	+	2.98575i	0.859703	+	0.248812i
$145$	7.50828	−	0.463783i	0.623529	−	0.0385151i
$146$	−7.41663	−	3.70351i	−0.613805	−	0.306504i
$147$	−0.396892	−	0.396892i	−0.0327351	−	0.0327351i
$148$	−0.609198	+	4.29621i	−0.0500757	+	0.353147i
$149$			2.09688i			0.171783i	0.996304	+	0.0858916i	$0.0273739\pi$
$149$			2.09688i			0.171783i	−0.996304	+	0.0858916i	$0.972626\pi$
$150$	1.32264	−	3.74206i	0.107993	−	0.305538i
$151$		−	10.7851i		−	0.877677i	−0.898566	−	0.438838i	$-0.855390\pi$
$151$		−	10.7851i		−	0.877677i	0.898566	−	0.438838i	$-0.144610\pi$
$152$	−13.1146	+	19.0065i	−1.06374	+	1.54163i
$153$	−0.955075	−	0.955075i	−0.0772132	−	0.0772132i
$154$	2.72303	−	5.45313i	0.219428	−	0.439426i
$155$	−0.335563	+	0.0207276i	−0.0269531	+	0.00166488i
$156$	−1.62104	+	1.21841i	−0.129787	+	0.0975510i
$157$	−6.45101	+	6.45101i	−0.514846	+	0.514846i	−0.916007	−	0.401161i	$-0.868607\pi$
$157$	−6.45101	+	6.45101i	−0.514846	+	0.514846i	0.401161	+	0.916007i	$0.368607\pi$
$158$	12.3060	−	4.10909i	0.979012	−	0.326902i
$159$	6.65176			0.527519
$160$	−12.5831	+	1.29101i	−0.994778	+	0.102063i
$161$	−3.75789			−0.296163
$162$	−8.40236	+	2.80563i	−0.660151	+	0.220431i
$163$	−15.1687	+	15.1687i	−1.18811	+	1.18811i	−0.210517	+	0.977590i	$0.567515\pi$
$163$	−15.1687	+	15.1687i	−1.18811	+	1.18811i	−0.977590	+	0.210517i	$0.932485\pi$
$164$	14.6667	−	11.0238i	1.14528	−	0.860816i
$165$	−3.58190	+	4.05354i	−0.278851	+	0.315568i
$166$	4.32351	−	8.65824i	0.335569	−	0.672010i
$167$	−2.09436	−	2.09436i	−0.162067	−	0.162067i	0.621415	−	0.783482i	$-0.286558\pi$
$167$	−2.09436	−	2.09436i	−0.162067	−	0.162067i	−0.783482	+	0.621415i	$0.786558\pi$
$168$	0.901628	−	1.30669i	0.0695621	−	0.100813i
$169$		−	9.73675i		−	0.748981i
$170$	1.46433	+	0.621593i	0.112309	+	0.0476740i
$171$		−	21.9206i		−	1.67631i
$172$	2.57591	−	18.1660i	0.196411	−	1.38514i
$173$	−3.03416	−	3.03416i	−0.230683	−	0.230683i	0.582295	−	0.812978i	$-0.302155\pi$
$173$	−3.03416	−	3.03416i	−0.230683	−	0.230683i	−0.812978	+	0.582295i	$0.802155\pi$
$174$	−2.38915	−	1.19302i	−0.181121	−	0.0904429i
$175$	3.94377	+	3.07354i	0.298121	+	0.232338i
$176$	16.5602	+	4.79281i	1.24828	+	0.361272i
$177$	−0.141830	+	0.141830i	−0.0106606	+	0.0106606i
$178$	0.533900	+	1.59894i	0.0400175	+	0.119845i
$179$	−1.58383			−0.118381			−0.0591906	−	0.998247i	$-0.518852\pi$
$179$	−1.58383			−0.118381			−0.0591906	+	0.998247i	$0.518852\pi$
$180$	9.13546	−	7.79249i	0.680917	−	0.580818i
$181$	11.5907			0.861530			0.430765	−	0.902464i	$-0.358244\pi$
$181$	11.5907			0.861530			0.430765	+	0.902464i	$0.358244\pi$
$182$	−0.809124	−	2.42318i	−0.0599763	−	0.179618i
$183$	3.98148	−	3.98148i	0.294320	−	0.294320i
$184$	−1.91763	−	10.4545i	−0.141370	−	0.770717i
$185$	3.63540	+	3.21241i	0.267280	+	0.236181i
$186$	0.106777	+	0.0533192i	0.00782926	+	0.00390955i
$187$	−1.53311	−	1.53311i	−0.112112	−	0.112112i
$188$	15.0091	+	2.12827i	1.09465	+	0.155220i
$189$			3.19091i			0.232105i
$190$	9.67116	+	23.9378i	0.701619	+	1.73663i
$191$			5.02784i			0.363802i	0.983317	+	0.181901i	$0.0582250\pi$
$191$			5.02784i			0.363802i	−0.983317	+	0.181901i	$0.941775\pi$
$192$	4.09533	+	1.84154i	0.295555	+	0.132902i
$193$	9.38545	+	9.38545i	0.675580	+	0.675580i	0.958997	−	0.283417i	$-0.0914681\pi$
$193$	9.38545	+	9.38545i	0.675580	+	0.675580i	−0.283417	+	0.958997i	$0.591468\pi$
$194$	−0.937194	+	1.87682i	−0.0672866	+	0.134748i
$195$	0.139780	+	2.26293i	0.0100099	+	0.162052i
$196$	1.20166	+	1.59875i	0.0858328	+	0.114197i
$197$	0.573982	−	0.573982i	0.0408945	−	0.0408945i	−0.686364	−	0.727258i	$-0.740794\pi$
$197$	0.573982	−	0.573982i	0.0408945	−	0.0408945i	0.727258	+	0.686364i	$0.240794\pi$
$198$	−15.5228	+	5.18323i	−1.10316	+	0.368356i
$199$	26.4933			1.87806			0.939032	−	0.343830i	$-0.111725\pi$
$199$	26.4933			1.87806			0.939032	+	0.343830i	$0.111725\pi$
$200$	−6.53815	+	12.5400i	−0.462317	+	0.886715i
$201$	4.23365			0.298619
$202$	20.4371	−	6.82415i	1.43795	−	0.480145i
$203$	2.37885	−	2.37885i	0.166963	−	0.166963i
$204$	−0.339301	−	0.451425i	−0.0237558	−	0.0316060i
$205$	−1.26469	−	20.4743i	−0.0883297	−	1.42999i
$206$	1.26047	−	2.52420i	0.0878208	−	0.175870i
$207$	7.13454	+	7.13454i	0.495885	+	0.495885i
$208$	6.32844	−	3.48753i	0.438798	−	0.241817i
$209$		−	35.1876i		−	2.43398i
$210$	−0.664891	−	1.64572i	−0.0458818	−	0.113565i
$211$			19.9593i			1.37405i	0.726632	+	0.687027i	$0.241085\pi$
$211$			19.9593i			1.37405i	−0.726632	+	0.687027i	$0.758915\pi$
$212$	−23.4669	−	3.32758i	−1.61171	−	0.228539i
$213$	−1.06831	−	1.06831i	−0.0731995	−	0.0731995i
$214$	−3.45250	−	1.72401i	−0.236008	−	0.117851i
$215$	−15.3718	−	13.5833i	−1.04835	−	0.926370i
$216$	−8.87716	+	1.62830i	−0.604014	+	0.110792i
$217$	−0.106317	+	0.106317i	−0.00721725	+	0.00721725i
$218$	−4.58977	−	13.7455i	−0.310859	−	0.930966i
$219$	3.29020			0.222331
$220$	14.6645	−	12.5087i	0.988680	−	0.843338i
$221$	−0.908742			−0.0611286
$222$	−0.545452	−	1.63353i	−0.0366083	−	0.109635i
$223$	−11.8414	+	11.8414i	−0.792957	+	0.792957i	−0.981974	−	0.189017i	$-0.939470\pi$
$223$	−11.8414	+	11.8414i	−0.792957	+	0.792957i	0.189017	+	0.981974i	$0.439470\pi$
$224$	−3.83456	+	4.15887i	−0.256207	+	0.277876i
$225$	−1.65218	−	13.3227i	−0.110145	−	0.888181i
$226$	14.9149	+	7.44779i	0.992126	+	0.495420i
$227$	18.9838	+	18.9838i	1.26000	+	1.26000i	0.951094	+	0.308902i	$0.0999616\pi$
$227$	18.9838	+	18.9838i	1.26000	+	1.26000i	0.308902	+	0.951094i	$0.400038\pi$
$228$	1.28672	−	9.07425i	0.0852149	−	0.600957i
$229$			1.64815i			0.108913i	0.998516	+	0.0544563i	$0.0173426\pi$
$229$			1.64815i			0.108913i	−0.998516	+	0.0544563i	$0.982657\pi$
$230$	−10.9388	−	4.64339i	−0.721281	−	0.306176i
$231$			2.41914i			0.159168i
$232$	7.83191	+	5.40408i	0.514190	+	0.354796i
$233$	−3.20650	−	3.20650i	−0.210065	−	0.210065i	0.594230	−	0.804295i	$-0.297457\pi$
$233$	−3.20650	−	3.20650i	−0.210065	−	0.210065i	−0.804295	+	0.594230i	$0.797457\pi$
$234$	−3.06437	+	6.13669i	−0.200324	+	0.401168i
$235$	11.2228	−	12.7005i	0.732093	−	0.828489i
$236$	0.571318	−	0.429415i	0.0371896	−	0.0279526i
$237$	−3.64106	+	3.64106i	−0.236513	+	0.236513i
$238$	0.674803	−	0.225323i	0.0437410	−	0.0146055i
$239$	17.0886			1.10537			0.552685	−	0.833390i	$-0.313603\pi$
$239$	17.0886			1.10537			0.552685	+	0.833390i	$0.313603\pi$
$240$	4.23912	−	2.68954i	0.273634	−	0.173609i
$241$	−4.63841			−0.298786			−0.149393	−	0.988778i	$-0.547732\pi$
$241$	−4.63841			−0.298786			−0.149393	+	0.988778i	$0.547732\pi$
$242$	−10.1622	+	3.39327i	−0.653253	+	0.218127i
$243$	9.25501	−	9.25501i	0.593709	−	0.593709i
$244$	−16.0381	+	12.0546i	−1.02674	+	0.771717i
$245$	2.23181	−	0.137858i	0.142585	−	0.00880744i
$246$	−3.25325	+	6.51496i	−0.207420	+	0.415378i
$247$	−10.4286	−	10.4286i	−0.663556	−	0.663556i
$248$	−0.350027	−	0.241522i	−0.0222268	−	0.0153367i
$249$			3.84100i			0.243414i
$250$	7.68207	+	13.8198i	0.485857	+	0.874039i
$251$		−	15.8297i		−	0.999160i	−0.866268	−	0.499580i	$-0.833488\pi$
$251$		−	15.8297i		−	0.999160i	0.866268	−	0.499580i	$-0.166512\pi$
$252$	0.753904	−	5.31672i	0.0474915	−	0.334922i
$253$	11.4526	+	11.4526i	0.720017	+	0.720017i
$254$	−9.12889	−	4.55853i	−0.572797	−	0.286027i
$255$	−0.630175	+	0.0389257i	−0.0394631	+	0.00243762i
$256$	−13.5268	−	8.54554i	−0.845424	−	0.534096i
$257$	6.72940	−	6.72940i	0.419768	−	0.419768i	−0.465356	−	0.885124i	$-0.654074\pi$
$257$	6.72940	−	6.72940i	0.419768	−	0.419768i	0.885124	+	0.465356i	$0.154074\pi$
$258$	2.30637	+	6.90717i	0.143588	+	0.430021i
$259$	2.16959			0.134812
$260$	0.638908	−	8.05337i	0.0396234	−	0.499449i
$261$	−9.03273			−0.559112
$262$	6.37149	+	19.0815i	0.393632	+	1.17886i
$263$	11.4894	−	11.4894i	0.708470	−	0.708470i	−0.257744	−	0.966213i	$-0.582979\pi$
$263$	11.4894	−	11.4894i	0.708470	−	0.708470i	0.966213	+	0.257744i	$0.0829790\pi$
$264$	−6.73009	+	1.23447i	−0.414208	+	0.0759766i
$265$	−17.5469	+	19.8574i	−1.07790	+	1.21983i
$266$	10.3297	+	5.15816i	0.633356	+	0.316267i
$267$	−0.473089	−	0.473089i	−0.0289526	−	0.0289526i
$268$	−14.9360	−	2.11791i	−0.912362	−	0.129372i
$269$			16.9801i			1.03529i	0.855594	+	0.517647i	$0.173192\pi$
$269$			16.9801i			1.03529i	−0.855594	+	0.517647i	$0.826808\pi$
$270$	−3.94280	+	9.28835i	−0.239951	+	0.565271i
$271$		−	10.7726i		−	0.654386i	−0.944957	−	0.327193i	$-0.893897\pi$
$271$		−	10.7726i		−	0.654386i	0.944957	−	0.327193i	$-0.106103\pi$
$272$	0.971200	+	1.76233i	0.0588876	+	0.106857i
$273$	0.716965	+	0.716965i	0.0433927	+	0.0433927i
$274$	−7.09224	+	14.2029i	−0.428458	+	0.858028i
$275$	−2.65213	−	21.3860i	−0.159929	−	1.28962i
$276$	2.53462	+	3.37220i	0.152566	+	0.202983i
$277$	14.2950	−	14.2950i	0.858903	−	0.858903i	−0.132306	−	0.991209i	$-0.542238\pi$
$277$	14.2950	−	14.2950i	0.858903	−	0.858903i	0.991209	+	0.132306i	$0.0422380\pi$
$278$	−17.3163	+	5.78209i	−1.03856	+	0.346787i
$279$	0.403695			0.0241686
$280$	1.52241	+	6.13859i	0.0909811	+	0.366851i
$281$	−24.3209			−1.45086			−0.725430	−	0.688296i	$-0.758359\pi$
$281$	−24.3209			−1.45086			−0.725430	+	0.688296i	$0.758359\pi$
$282$	−5.70685	+	1.90557i	−0.339838	+	0.113475i
$283$	−14.6849	+	14.6849i	−0.872927	+	0.872927i	−0.992790	−	0.119864i	$-0.961754\pi$
$283$	−14.6849	+	14.6849i	−0.872927	+	0.872927i	0.119864	+	0.992790i	$0.461754\pi$
$284$	3.23449	+	4.30335i	0.191932	+	0.255357i
$285$	−7.67851	−	6.78510i	−0.454836	−	0.401915i
$286$	−4.91901	+	9.85079i	−0.290867	+	0.582490i
$287$	−6.48688	−	6.48688i	−0.382909	−	0.382909i
$288$	15.1759	−	0.615719i	0.894249	−	0.0362816i
$289$			16.7469i			0.985114i
$290$	9.86394	−	3.98515i	0.579230	−	0.234016i
$291$		−	0.832603i		−	0.0488080i
$292$	−11.6076	−	1.64594i	−0.679281	−	0.0963213i
$293$	−13.9330	−	13.9330i	−0.813975	−	0.813975i	0.171252	−	0.985227i	$-0.445219\pi$
$293$	−13.9330	−	13.9330i	−0.813975	−	0.813975i	−0.985227	+	0.171252i	$0.945219\pi$
$294$	−0.710167	−	0.354623i	−0.0414178	−	0.0206820i
$295$	−0.0492639	−	0.797544i	−0.00286826	−	0.0464348i
$296$	1.10713	+	6.03584i	0.0643507	+	0.350826i
$297$	9.72463	−	9.72463i	0.564280	−	0.564280i
$298$	0.939213	+	2.81277i	0.0544071	+	0.162940i
$299$	6.78843			0.392585
$300$	0.0980932	−	5.61205i	0.00566341	−	0.324012i
$301$	−9.17384			−0.528771
$302$	−4.83073	−	14.4672i	−0.277978	−	0.832493i
$303$	−6.04688	+	6.04688i	−0.347384	+	0.347384i
$304$	−9.07889	+	31.3696i	−0.520710	+	1.79917i
$305$	1.38294	+	22.3888i	0.0791872	+	1.28198i
$306$	−1.70893	−	0.853358i	−0.0976932	−	0.0487833i
$307$	18.4400	+	18.4400i	1.05243	+	1.05243i	0.998547	+	0.0538811i	$0.0171592\pi$
$307$	18.4400	+	18.4400i	1.05243	+	1.05243i	0.0538811	+	0.998547i	$0.482841\pi$
$308$	1.21019	−	8.53455i	0.0689569	−	0.486301i
$309$			1.11980i			0.0637031i
$310$	−0.440844	+	0.178106i	−0.0250382	+	0.0101158i
$311$		−	10.5963i		−	0.600863i	−0.953803	−	0.300431i	$-0.902869\pi$
$311$		−	10.5963i		−	0.600863i	0.953803	−	0.300431i	$-0.0971306\pi$
$312$	−1.62874	+	2.36047i	−0.0922094	+	0.133635i
$313$	16.8405	+	16.8405i	0.951879	+	0.951879i	0.998894	−	0.0470151i	$-0.0149709\pi$
$313$	16.8405	+	16.8405i	0.951879	+	0.951879i	−0.0470151	+	0.998894i	$0.514971\pi$
$314$	−5.76397	+	11.5429i	−0.325280	+	0.651404i
$315$	−4.49894	−	3.97548i	−0.253486	−	0.223993i
$316$	14.6669	−	11.0239i	0.825076	−	0.620145i
$317$	12.0012	−	12.0012i	0.674053	−	0.674053i	−0.284595	−	0.958648i	$-0.591859\pi$
$317$	12.0012	−	12.0012i	0.674053	−	0.674053i	0.958648	+	0.284595i	$0.0918591\pi$
$318$	8.92272	−	2.97938i	0.500361	−	0.167076i
$319$	−14.4996			−0.811822
$320$	−16.3008	+	7.36784i	−0.911241	+	0.411875i
$321$	1.53161			0.0854864
$322$	−5.04087	+	1.68320i	−0.280917	+	0.0938008i
$323$	2.90413	−	2.90413i	0.161590	−	0.161590i
$324$	−10.0143	+	7.52699i	−0.556351	+	0.418166i
$325$	−7.12422	−	5.55219i	−0.395180	−	0.307980i
$326$	−13.5533	+	27.1417i	−0.750646	+	1.50324i
$327$	4.06699	+	4.06699i	0.224905	+	0.224905i
$328$	14.7364	−	21.3568i	0.813681	−	1.17923i
$329$		−	7.57962i		−	0.417878i
$330$	−2.98918	+	7.04183i	−0.164549	+	0.387640i
$331$			7.88855i			0.433594i	0.976217	+	0.216797i	$0.0695610\pi$
$331$			7.88855i			0.433594i	−0.976217	+	0.216797i	$0.930439\pi$
$332$	1.92148	−	13.5508i	0.105455	−	0.743695i
$333$	−4.11908	−	4.11908i	−0.225724	−	0.225724i
$334$	−3.74748	−	1.87131i	−0.205053	−	0.102394i
$335$	−11.1681	+	12.6387i	−0.610180	+	0.690524i
$336$	0.624172	−	2.15666i	0.0340514	−	0.117655i
$337$	2.38503	−	2.38503i	0.129921	−	0.129921i	−0.639156	−	0.769077i	$-0.720716\pi$
$337$	2.38503	−	2.38503i	0.129921	−	0.129921i	0.769077	+	0.639156i	$0.220716\pi$
$338$	−4.36118	−	13.0610i	−0.237217	−	0.710423i
$339$	−6.61662			−0.359365
$340$	2.24268	+	0.177922i	0.121627	+	0.00964916i
$341$	0.648023			0.0350924
$342$	−9.81845	−	29.4045i	−0.530921	−	1.59001i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	−4.68136	−	25.5217i	−0.252402	−	1.37604i
$345$	4.70750	−	0.290780i	0.253443	−	0.0156551i
$346$	−5.42908	−	2.71102i	−0.291869	−	0.145745i
$347$	7.78620	+	7.78620i	0.417985	+	0.417985i	0.884509	−	0.466524i	$-0.154494\pi$
$347$	7.78620	+	7.78620i	0.417985	+	0.417985i	−0.466524	+	0.884509i	$0.654494\pi$
$348$	−3.73919	−	0.530212i	−0.200442	−	0.0284224i
$349$			5.15739i			0.276069i	0.990427	+	0.138034i	$0.0440785\pi$
$349$			5.15739i			0.276069i	−0.990427	+	0.138034i	$0.955922\pi$
$350$	6.66688	+	2.35642i	0.356360	+	0.125956i
$351$		−	5.76421i		−	0.307671i
$352$	24.3608	−	0.988370i	1.29843	−	0.0526803i
$353$	−21.1335	−	21.1335i	−1.12482	−	1.12482i	−0.991006	−	0.133818i	$-0.957276\pi$
$353$	−21.1335	−	21.1335i	−1.12482	−	1.12482i	−0.133818	−	0.991006i	$-0.542724\pi$
$354$	−0.126725	+	0.253780i	−0.00673537	+	0.0134882i
$355$	6.00735	−	0.371072i	0.318837	−	0.0196944i
$356$	1.43236	+	1.90569i	0.0759148	+	0.101001i
$357$	−0.199659	+	0.199659i	−0.0105671	+	0.0105671i
$358$	−2.12457	+	0.709414i	−0.112287	+	0.0374937i
$359$	4.82609			0.254711			0.127356	−	0.991857i	$-0.459351\pi$
$359$	4.82609			0.254711			0.127356	+	0.991857i	$0.459351\pi$
$360$	8.76405	−	14.5448i	0.461906	−	0.766577i
$361$	47.6548			2.50815
$362$	15.5479	−	5.19159i	0.817178	−	0.272864i
$363$	3.00677	−	3.00677i	0.157815	−	0.157815i
$364$	−2.17073	−	2.88806i	−0.113777	−	0.151376i
$365$	−8.67934	+	9.82217i	−0.454297	+	0.514116i
$366$	3.55745	−	7.12414i	0.185951	−	0.372385i
$367$	−2.80256	−	2.80256i	−0.146293	−	0.146293i	0.630167	−	0.776460i	$-0.282986\pi$
$367$	−2.80256	−	2.80256i	−0.146293	−	0.146293i	−0.776460	+	0.630167i	$0.782986\pi$
$368$	−7.25500	−	13.1648i	−0.378193	−	0.686265i
$369$			24.6313i			1.28226i
$370$	6.31542	+	2.68083i	0.328323	+	0.139370i
$371$			11.8508i			0.615264i
$372$	0.167114	+	0.0236965i	0.00866443	+	0.00122861i
$373$	15.9200	+	15.9200i	0.824309	+	0.824309i	0.986723	−	0.162414i	$-0.0519280\pi$
$373$	15.9200	+	15.9200i	0.824309	+	0.824309i	−0.162414	+	0.986723i	$0.551928\pi$
$374$	−2.74323	−	1.36984i	−0.141849	−	0.0708325i
$375$	−5.17818	−	3.54505i	−0.267400	−	0.183066i
$376$	21.0866	−	3.86784i	1.08746	−	0.199468i
$377$	−4.29727	+	4.29727i	−0.221321	+	0.221321i
$378$	1.42924	+	4.28031i	0.0735121	+	0.220156i
$379$	−12.6658			−0.650596			−0.325298	−	0.945612i	$-0.605465\pi$
$379$	−12.6658			−0.650596			−0.325298	+	0.945612i	$0.605465\pi$
$380$	23.6949	+	27.7785i	1.21552	+	1.42501i
$381$	4.04980			0.207477
$382$	2.25202	+	6.74439i	0.115223	+	0.345073i
$383$	−24.3066	+	24.3066i	−1.24201	+	1.24201i	−0.282845	+	0.959166i	$0.591278\pi$
$383$	−24.3066	+	24.3066i	−1.24201	+	1.24201i	−0.959166	+	0.282845i	$0.908722\pi$
$384$	6.31836	+	0.635927i	0.322432	+	0.0324520i
$385$	−7.22182	−	6.38155i	−0.368058	−	0.325234i
$386$	16.7936	+	8.38590i	0.854770	+	0.426831i
$387$	17.4170	+	17.4170i	0.885355	+	0.885355i
$388$	−0.416514	+	2.93736i	−0.0211453	+	0.149122i
$389$		−	19.6929i		−	0.998467i	−0.866467	−	0.499234i	$-0.833615\pi$
$389$		−	19.6929i		−	0.998467i	0.866467	−	0.499234i	$-0.166385\pi$
$390$	1.20109	+	2.97290i	0.0608195	+	0.150539i
$391$			1.89043i			0.0956031i
$392$	2.32801	+	1.60635i	0.117582	+	0.0811328i
$393$	−5.64578	−	5.64578i	−0.284792	−	0.284792i
$394$	0.512853	−	1.02704i	0.0258371	−	0.0517414i
$395$	−1.26470	−	20.4745i	−0.0636341	−	1.03018i
$396$	−18.5009	+	13.9057i	−0.929703	+	0.698786i
$397$	3.55904	−	3.55904i	0.178623	−	0.178623i	−0.612132	−	0.790755i	$-0.709688\pi$
$397$	3.55904	−	3.55904i	0.178623	−	0.178623i	0.790755	+	0.612132i	$0.209688\pi$
$398$	35.5384	−	11.8666i	1.78138	−	0.594820i
$399$	−4.58251			−0.229413
$400$	−3.15352	+	19.7498i	−0.157676	+	0.987491i
$401$	0.442108			0.0220778			0.0110389	−	0.999939i	$-0.496486\pi$
$401$	0.442108			0.0220778			0.0110389	+	0.999939i	$0.496486\pi$
$402$	5.67906	−	1.89629i	0.283246	−	0.0945785i
$403$	0.192055	−	0.192055i	0.00956696	−	0.00956696i
$404$	24.3579	−	18.3079i	1.21185	−	0.910854i
$405$	0.863521	+	13.9797i	0.0429087	+	0.694657i
$406$	2.12550	−	4.25652i	0.105487	−	0.211248i
$407$	−6.61207	−	6.61207i	−0.327748	−	0.327748i
$408$	−0.657338	−	0.453569i	−0.0325431	−	0.0224550i
$409$		−	17.2900i		−	0.854936i	−0.904031	−	0.427468i	$-0.859406\pi$
$409$		−	17.2900i		−	0.854936i	0.904031	−	0.427468i	$-0.140594\pi$
$410$	−10.8671	−	26.8979i	−0.536688	−	1.32839i
$411$		−	6.30075i		−	0.310793i
$412$	0.560185	−	3.95056i	0.0275983	−	0.194630i
$413$	−0.252686	−	0.252686i	−0.0124339	−	0.0124339i
$414$	12.7660	+	6.37471i	0.627413	+	0.313300i
$415$	−11.4665	−	10.1323i	−0.562868	−	0.497377i
$416$	6.92692	−	7.51277i	0.339620	−	0.368344i
$417$	5.12351	−	5.12351i	0.250899	−	0.250899i
$418$	−15.7609	−	47.2009i	−0.770888	−	2.30867i
$419$	−15.9655			−0.779965			−0.389982	−	0.920822i	$-0.627519\pi$
$419$	−15.9655			−0.779965			−0.389982	+	0.920822i	$0.627519\pi$
$420$	−1.62902	−	1.90977i	−0.0794882	−	0.0931873i
$421$	−18.9207			−0.922137			−0.461069	−	0.887364i	$-0.652534\pi$
$421$	−18.9207			−0.922137			−0.461069	+	0.887364i	$0.652534\pi$
$422$	8.93995	+	26.7736i	0.435190	+	1.30332i
$423$	−14.3903	+	14.3903i	−0.699679	+	0.699679i
$424$	−32.9692	+	6.04740i	−1.60112	+	0.293688i
$425$	1.54616	−	1.98394i	0.0749998	−	0.0962350i
$426$	−1.91155	−	0.954535i	−0.0926148	−	0.0462474i
$427$	7.09344	+	7.09344i	0.343276	+	0.343276i
$428$	−5.40342	−	0.766198i	−0.261184	−	0.0370356i
$429$		−	4.37005i		−	0.210988i
$430$	−26.7039	−	11.3355i	−1.28778	−	0.546647i
$431$		−	5.95579i		−	0.286880i	−0.989659	−	0.143440i	$-0.954184\pi$
$431$		−	5.95579i		−	0.286880i	0.989659	−	0.143440i	$-0.0458164\pi$
$432$	−11.1786	+	6.16038i	−0.537829	+	0.296391i
$433$	−21.6247	−	21.6247i	−1.03922	−	1.03922i	−0.999199	−	0.0400190i	$-0.987258\pi$
$433$	−21.6247	−	21.6247i	−1.03922	−	1.03922i	−0.0400190	−	0.999199i	$-0.512742\pi$
$434$	−0.0949939	+	0.190234i	−0.00455985	+	0.00913155i
$435$	−2.79591	+	3.16405i	−0.134053	+	0.151705i
$436$	−12.3135	−	16.3826i	−0.589711	−	0.784584i
$437$	−21.6943	+	21.6943i	−1.03778	+	1.03778i
$438$	4.41350	−	1.47371i	0.210885	−	0.0704166i
$439$	24.8255			1.18485			0.592427	−	0.805624i	$-0.298170\pi$
$439$	24.8255			1.18485			0.592427	+	0.805624i	$0.298170\pi$
$440$	14.0683	−	23.3477i	0.670680	−	1.11306i
$441$	−2.68495			−0.127855
$442$	−1.21899	+	0.407034i	−0.0579817	+	0.0193606i
$443$	21.8909	−	21.8909i	1.04007	−	1.04007i	0.0409038	−	0.999163i	$-0.486976\pi$
$443$	21.8909	−	21.8909i	1.04007	−	1.04007i	0.999163	−	0.0409038i	$-0.0130237\pi$
$444$	−1.46335	−	1.94692i	−0.0694474	−	0.0923967i
$445$	2.66028	−	0.164325i	0.126110	−	0.00778974i
$446$	−10.5803	+	21.1880i	−0.500990	+	1.00328i
$447$	−0.832236	−	0.832236i	−0.0393634	−	0.0393634i
$448$	−3.28091	+	7.29627i	−0.155009	+	0.344717i
$449$			29.8132i			1.40697i	0.710709	+	0.703487i	$0.248374\pi$
$449$			29.8132i			1.40697i	−0.710709	+	0.703487i	$0.751626\pi$
$450$	−8.18362	−	17.1312i	−0.385779	−	0.807571i
$451$			39.5389i			1.86181i
$452$	23.3429	+	3.31000i	1.09796	+	0.155689i
$453$	4.28051	+	4.28051i	0.201116	+	0.201116i
$454$	33.9680	+	16.9620i	1.59420	+	0.796065i
$455$	−4.03165	+	0.249034i	−0.189007	+	0.0116749i
$456$	−2.33843	−	12.7486i	−0.109507	−	0.597008i
$457$	−3.85045	+	3.85045i	−0.180117	+	0.180117i	−0.791407	−	0.611290i	$-0.790651\pi$
$457$	−3.85045	+	3.85045i	−0.180117	+	0.180117i	0.611290	+	0.791407i	$0.290651\pi$
$458$	0.738221	+	2.21084i	0.0344948	+	0.103306i
$459$	1.60520			0.0749245
$460$	−16.7532	−	1.32910i	−0.781121	−	0.0619696i
$461$	35.3477			1.64631			0.823153	−	0.567820i	$-0.192213\pi$
$461$	35.3477			1.64631			0.823153	+	0.567820i	$0.192213\pi$
$462$	1.08356	+	3.24506i	0.0504116	+	0.150974i
$463$	−17.1088	+	17.1088i	−0.795113	+	0.795113i	−0.982320	−	0.187208i	$-0.940056\pi$
$463$	−17.1088	+	17.1088i	−0.795113	+	0.795113i	0.187208	+	0.982320i	$0.440056\pi$
$464$	12.9263	+	3.74110i	0.600090	+	0.173676i
$465$	0.124956	−	0.141409i	0.00579469	−	0.00655770i
$466$	−5.73745	−	2.86500i	−0.265782	−	0.132719i
$467$	−10.3471	−	10.3471i	−0.478805	−	0.478805i	0.425944	−	0.904749i	$-0.359942\pi$
$467$	−10.3471	−	10.3471i	−0.478805	−	0.478805i	−0.904749	+	0.425944i	$0.859942\pi$
$468$	−1.36189	+	9.60437i	−0.0629533	+	0.443962i
$469$			7.54271i			0.348290i
$470$	9.36565	−	22.0633i	0.432005	−	1.01771i
$471$		−	5.12071i		−	0.235950i
$472$	0.574032	−	0.831920i	0.0264220	−	0.0382922i
$473$	27.9582	+	27.9582i	1.28552	+	1.28552i
$474$	−3.25329	+	6.51502i	−0.149428	+	0.299245i
$475$	40.5109	−	5.02385i	1.85877	−	0.230510i
$476$	0.804262	−	0.604501i	0.0368633	−	0.0277073i
$477$	22.4994	−	22.4994i	1.03017	−	1.03017i
$478$	22.9228	−	7.65414i	1.04846	−	0.350092i
$479$	−35.2550			−1.61084			−0.805422	−	0.592702i	$-0.798061\pi$
$479$	−35.2550			−1.61084			−0.805422	+	0.592702i	$0.798061\pi$
$480$	4.48173	−	5.50651i	0.204562	−	0.251337i
$481$	−3.91926			−0.178703
$482$	−6.22200	+	2.07759i	−0.283404	+	0.0946314i
$483$	1.49148	−	1.49148i	0.0678647	−	0.0678647i
$484$	−12.1118	+	9.10351i	−0.550537	+	0.413796i
$485$	2.48556	+	2.19636i	0.112863	+	0.0997314i
$486$	8.26934	−	16.5602i	0.375105	−	0.751184i
$487$	−23.9309	−	23.9309i	−1.08441	−	1.08441i	−0.996092	−	0.0883227i	$-0.971849\pi$
$487$	−23.9309	−	23.9309i	−1.08441	−	1.08441i	−0.0883227	−	0.996092i	$-0.528151\pi$
$488$	−16.1143	+	23.3538i	−0.729460	+	1.05718i
$489$		−	12.0407i		−	0.544500i
$490$	2.93203	−	1.18457i	0.132455	−	0.0535136i
$491$		−	2.82858i		−	0.127652i	−0.997961	−	0.0638260i	$-0.979670\pi$
$491$		−	2.82858i		−	0.127652i	0.997961	−	0.0638260i	$-0.0203303\pi$
$492$	−1.44583	+	10.1964i	−0.0651832	+	0.459688i
$493$	−1.19669	−	1.19669i	−0.0538964	−	0.0538964i
$494$	−18.6601	−	9.31794i	−0.839557	−	0.419234i
$495$	1.59530	+	25.8267i	0.0717035	+	1.16082i
$496$	−0.577710	−	0.167199i	−0.0259399	−	0.00750745i
$497$	1.90331	−	1.90331i	0.0853752	−	0.0853752i
$498$	1.72042	+	5.15235i	0.0770939	+	0.230883i
$499$	15.9947			0.716023			0.358012	−	0.933717i	$-0.383455\pi$
$499$	15.9947			0.716023			0.358012	+	0.933717i	$0.383455\pi$
$500$	16.4948	+	15.0971i	0.737670	+	0.675162i
$501$	1.66247			0.0742738
$502$	−7.09026	−	21.2341i	−0.316454	−	0.947722i
$503$	−7.59472	+	7.59472i	−0.338632	+	0.338632i	−0.855852	−	0.517221i	$-0.826967\pi$
$503$	−7.59472	+	7.59472i	−0.338632	+	0.338632i	0.517221	+	0.855852i	$0.326967\pi$
$504$	−1.37012	−	7.46958i	−0.0610298	−	0.332721i
$505$	−2.10035	−	34.0029i	−0.0934642	−	1.51311i
$506$	20.4923	+	10.2329i	0.910994	+	0.454906i
$507$	3.86444	+	3.86444i	0.171626	+	0.171626i
$508$	−14.2874	−	2.02593i	−0.633900	−	0.0898862i
$509$		−	17.1295i		−	0.759253i	−0.925140	−	0.379627i	$-0.876052\pi$
$509$		−	17.1295i		−	0.759253i	0.925140	−	0.379627i	$-0.123948\pi$
$510$	−0.827888	+	0.334477i	−0.0366595	+	0.0148109i
$511$			5.86184i			0.259313i
$512$	−21.9726	−	5.40430i	−0.971059	−	0.238838i
$513$	18.4211	+	18.4211i	0.813311	+	0.813311i
$514$	6.01271	−	12.0410i	0.265209	−	0.531107i
$515$	−3.34291	−	2.95396i	−0.147306	−	0.130167i
$516$	6.18757	+	8.23229i	0.272393	+	0.362406i
$517$	−23.0997	+	23.0997i	−1.01592	+	1.01592i
$518$	2.91031	−	0.971782i	0.127872	−	0.0426977i
$519$	2.40847			0.105720
$520$	−2.75014	−	11.0890i	−0.120602	−	0.486286i
$521$	−16.4925			−0.722548			−0.361274	−	0.932460i	$-0.617658\pi$
$521$	−16.4925			−0.722548			−0.361274	+	0.932460i	$0.617658\pi$
$522$	−12.1166	+	4.04585i	−0.530328	+	0.177082i
$523$	7.62703	−	7.62703i	0.333507	−	0.333507i	−0.520410	−	0.853917i	$-0.674221\pi$
$523$	7.62703	−	7.62703i	0.333507	−	0.333507i	0.853917	+	0.520410i	$0.174221\pi$
$524$	17.0936	+	22.7422i	0.746735	+	0.993498i
$525$	−2.78512	+	0.345389i	−0.121553	+	0.0150740i
$526$	10.2658	−	20.5583i	0.447611	−	0.896383i
$527$	0.0534832	+	0.0534832i	0.00232976	+	0.00232976i
$528$	−8.47486	+	4.67040i	−0.368821	+	0.203253i
$529$			8.87824i			0.386010i
$530$	−14.6433	+	34.4963i	−0.636064	+	1.49842i
$531$			0.959474i			0.0416376i
$532$	16.1668	+	2.29243i	0.700918	+	0.0993893i
$533$	11.7182	+	11.7182i	0.507572	+	0.507572i
$534$	−0.846506	−	0.422705i	−0.0366319	−	0.0182922i
$535$	−4.04031	+	4.57230i	−0.174678	+	0.197678i
$536$	−20.9839	+	3.84900i	−0.906368	+	0.166252i
$537$	0.628612	−	0.628612i	0.0271266	−	0.0271266i
$538$	7.60554	+	22.7772i	0.327898	+	0.981996i
$539$	−4.30996			−0.185643
$540$	−1.12857	+	14.2255i	−0.0485659	+	0.612168i
$541$	−3.69600			−0.158903			−0.0794517	−	0.996839i	$-0.525317\pi$
$541$	−3.69600			−0.158903			−0.0794517	+	0.996839i	$0.525317\pi$
$542$	−4.82513	−	14.4504i	−0.207257	−	0.620698i
$543$	−4.60026	+	4.60026i	−0.197416	+	0.197416i
$544$	2.09214	+	1.92899i	0.0896998	+	0.0827049i
$545$	−22.8696	+	1.41265i	−0.979627	+	0.0605111i
$546$	1.28288	+	0.640607i	0.0549021	+	0.0274155i
$547$	2.39361	+	2.39361i	0.102343	+	0.102343i	0.756424	−	0.654081i	$-0.226945\pi$
$547$	2.39361	+	2.39361i	0.102343	+	0.102343i	−0.654081	+	0.756424i	$0.726945\pi$
$548$	−3.15198	+	22.2286i	−0.134646	+	0.949557i
$549$		−	26.9345i		−	1.14954i
$550$	−13.1366	−	27.4994i	−0.560146	−	1.17258i
$551$		−	27.4662i		−	1.17010i
$552$	4.91041	+	3.38822i	0.209001	+	0.144212i
$553$	−6.48695	−	6.48695i	−0.275853	−	0.275853i
$554$	12.7726	−	25.5783i	0.542655	−	1.08672i
$555$	−2.71784	+	0.167880i	−0.115366	+	0.00712611i
$556$	−20.6384	+	15.5123i	−0.875264	+	0.657868i
$557$	−17.1208	+	17.1208i	−0.725433	+	0.725433i	−0.969706	−	0.244273i	$-0.921451\pi$
$557$	−17.1208	+	17.1208i	−0.725433	+	0.725433i	0.244273	+	0.969706i	$0.421451\pi$
$558$	0.541520	−	0.180819i	0.0229244	−	0.00765467i
$559$	16.5720			0.700923
$560$	4.79170	+	7.55246i	0.202486	+	0.319150i
$561$	1.21696			0.0513802
$562$	−32.6242	+	10.8935i	−1.37617	+	0.459516i
$563$	18.3059	−	18.3059i	0.771503	−	0.771503i	−0.206866	−	0.978369i	$-0.566326\pi$
$563$	18.3059	−	18.3059i	0.771503	−	0.771503i	0.978369	+	0.206866i	$0.0663264\pi$
$564$	−6.80169	+	5.11230i	−0.286403	+	0.215267i
$565$	17.4542	−	19.7525i	0.734306	−	0.830993i
$566$	−13.1209	+	26.2760i	−0.551515	+	1.10446i
$567$	4.42920	+	4.42920i	0.186009	+	0.186009i
$568$	6.26629	+	4.32379i	0.262928	+	0.181422i
$569$			17.5278i			0.734802i	0.930063	+	0.367401i	$0.119752\pi$
$569$			17.5278i			0.734802i	−0.930063	+	0.367401i	$0.880248\pi$
$570$	−13.3391	−	5.66231i	−0.558715	−	0.237168i
$571$		−	10.1133i		−	0.423227i	−0.977353	−	0.211614i	$-0.932128\pi$
$571$		−	10.1133i		−	0.423227i	0.977353	−	0.211614i	$-0.0678718\pi$
$572$	−2.18614	+	15.4172i	−0.0914072	+	0.644626i
$573$	−1.99551	−	1.99551i	−0.0833637	−	0.0833637i
$574$	−11.6071	−	5.79603i	−0.484471	−	0.241921i
$575$	−11.5500	+	14.8203i	−0.481670	+	0.618048i
$576$	20.0813	−	7.62336i	0.836721	−	0.317640i
$577$	−2.56471	+	2.56471i	−0.106770	+	0.106770i	−0.758474	−	0.651704i	$-0.774055\pi$
$577$	−2.56471	+	2.56471i	−0.106770	+	0.106770i	0.651704	+	0.758474i	$0.274055\pi$
$578$	7.50111	+	22.4645i	0.312005	+	0.934399i
$579$	−7.45003			−0.309613
$580$	11.4466	−	9.76387i	0.475294	−	0.405423i
$581$	−6.84316			−0.283902
$582$	−0.372931	−	1.11686i	−0.0154585	−	0.0462954i
$583$	36.1166	−	36.1166i	1.49580	−	1.49580i
$584$	−16.3077	+	2.99126i	−0.674818	+	0.123779i
$585$	8.12709	+	7.18149i	0.336014	+	0.296918i
$586$	−24.9306	−	12.4491i	−1.02987	−	0.514269i
$587$	−4.54357	−	4.54357i	−0.187533	−	0.187533i	0.607096	−	0.794629i	$-0.292334\pi$
$587$	−4.54357	−	4.54357i	−0.187533	−	0.187533i	−0.794629	+	0.607096i	$0.792334\pi$
$588$	−1.11146	−	0.157604i	−0.0458360	−	0.00649948i
$589$			1.22753i			0.0505795i
$590$	−0.423310	−	1.04777i	−0.0174274	−	0.0431358i
$591$			0.455618i			0.0187416i
$592$	4.18863	+	7.60064i	0.172151	+	0.312384i
$593$	−8.61195	−	8.61195i	−0.353650	−	0.353650i	0.507815	−	0.861466i	$-0.330453\pi$
$593$	−8.61195	−	8.61195i	−0.353650	−	0.353650i	−0.861466	+	0.507815i	$0.830453\pi$
$594$	8.68895	−	17.4005i	0.356512	−	0.713950i
$595$	−0.0693503	−	1.12273i	−0.00284309	−	0.0460273i
$596$	2.51974	+	3.35240i	0.103212	+	0.137320i
$597$	−10.5150	+	10.5150i	−0.430351	+	0.430351i
$598$	9.10606	−	3.04060i	0.372375	−	0.124340i
$599$	5.36339			0.219142			0.109571	−	0.993979i	$-0.465052\pi$
$599$	5.36339			0.219142			0.109571	+	0.993979i	$0.465052\pi$
$600$	−2.38211	−	7.57199i	−0.0972491	−	0.309125i
$601$	−6.54295			−0.266892			−0.133446	−	0.991056i	$-0.542604\pi$
$601$	−6.54295			−0.266892			−0.133446	+	0.991056i	$0.542604\pi$
$602$	−12.3059	+	4.10905i	−0.501550	+	0.167472i
$603$	14.3202	−	14.3202i	0.583164	−	0.583164i
$604$	−12.9600	−	17.2427i	−0.527334	−	0.701595i
$605$	1.04438	+	16.9078i	0.0424603	+	0.687398i
$606$	−5.40288	+	10.8198i	−0.219477	+	0.439524i
$607$	−28.3671	−	28.3671i	−1.15139	−	1.15139i	−0.986275	−	0.165110i	$-0.947202\pi$
$607$	−28.3671	−	28.3671i	−1.15139	−	1.15139i	−0.165110	−	0.986275i	$-0.552798\pi$
$608$	1.87224	+	46.1460i	0.0759294	+	1.87147i
$609$			1.88830i			0.0765176i
$610$	11.8832	+	29.4130i	0.481138	+	1.19090i
$611$			13.6922i			0.553926i
$612$	−2.67460	−	0.379255i	−0.108114	−	0.0153305i
$613$	−33.2293	−	33.2293i	−1.34212	−	1.34212i	−0.893950	−	0.448168i	$-0.852077\pi$
$613$	−33.2293	−	33.2293i	−1.34212	−	1.34212i	−0.448168	−	0.893950i	$-0.647923\pi$
$614$	32.9951	+	16.4762i	1.33157	+	0.664924i
$615$	8.62804	+	7.62415i	0.347916	+	0.307435i
$616$	−2.19935	−	11.9904i	−0.0886143	−	0.483106i
$617$	−17.0146	+	17.0146i	−0.684981	+	0.684981i	−0.961118	−	0.276137i	$-0.910945\pi$
$617$	−17.0146	+	17.0146i	−0.684981	+	0.684981i	0.276137	+	0.961118i	$0.410945\pi$
$618$	0.501568	+	1.50211i	0.0201760	+	0.0604236i
$619$	7.73369			0.310843			0.155422	−	0.987848i	$-0.450326\pi$
$619$	7.73369			0.310843			0.155422	+	0.987848i	$0.450326\pi$
$620$	−0.511576	+	0.436371i	−0.0205454	+	0.0175251i
$621$	−11.9911			−0.481186
$622$	−4.74620	−	14.2140i	−0.190305	−	0.569930i
$623$	0.842859	−	0.842859i	0.0337684	−	0.0337684i
$624$	−1.12753	+	3.89588i	−0.0451375	+	0.155960i
$625$	24.2427	−	6.10670i	0.969708	−	0.244268i
$626$	30.1329	+	15.0469i	1.20435	+	0.601397i
$627$	13.9657	+	13.9657i	0.557736	+	0.557736i
$628$	−2.56166	+	18.0655i	−0.102221	+	0.720891i
$629$		−	1.09143i		−	0.0435180i
$630$	−7.81557	−	3.31762i	−0.311380	−	0.132177i
$631$		−	11.7767i		−	0.468823i	−0.972137	−	0.234411i	$-0.924684\pi$
$631$		−	11.7767i		−	0.468823i	0.972137	−	0.234411i	$-0.0753163\pi$
$632$	14.7365	−	21.3570i	0.586188	−	0.849537i
$633$	−7.92169	−	7.92169i	−0.314859	−	0.314859i
$634$	10.7230	−	21.4739i	0.425866	−	0.852838i
$635$	−10.6831	+	12.0898i	−0.423946	+	0.479769i
$636$	10.6345	−	7.99314i	0.421686	−	0.316949i
$637$	−1.27735	+	1.27735i	−0.0506105	+	0.0506105i
$638$	−19.4499	+	6.49451i	−0.770028	+	0.257120i
$639$	−7.22706			−0.285898
$640$	−18.5659	+	17.1845i	−0.733880	+	0.679279i
$641$	14.5829			0.575989			0.287994	−	0.957632i	$-0.407012\pi$
$641$	14.5829			0.575989			0.287994	+	0.957632i	$0.407012\pi$
$642$	2.05452	−	0.686025i	0.0810855	−	0.0270752i
$643$	−17.6813	+	17.6813i	−0.697283	+	0.697283i	−0.963824	−	0.266541i	$-0.914119\pi$
$643$	−17.6813	+	17.6813i	−0.697283	+	0.697283i	0.266541	+	0.963824i	$0.414119\pi$
$644$	−6.00795	+	4.51571i	−0.236746	+	0.177944i
$645$	11.4920	−	0.709858i	0.452498	−	0.0279506i
$646$	2.59484	−	5.19642i	0.102093	−	0.204450i
$647$	−1.44929	−	1.44929i	−0.0569775	−	0.0569775i	0.678044	−	0.735021i	$-0.262828\pi$
$647$	−1.44929	−	1.44929i	−0.0569775	−	0.0569775i	−0.735021	+	0.678044i	$0.762828\pi$
$648$	−10.0619	+	14.5823i	−0.395269	+	0.572846i
$649$			1.54017i			0.0604571i
$650$	−12.0434	−	4.25675i	−0.472379	−	0.166963i
$651$		−	0.0843926i		−	0.00330761i
$652$	−6.02343	+	42.4787i	−0.235896	+	1.66360i
$653$	−6.44212	−	6.44212i	−0.252099	−	0.252099i	0.569731	−	0.821831i	$-0.307047\pi$
$653$	−6.44212	−	6.44212i	−0.252099	−	0.252099i	−0.821831	+	0.569731i	$0.807047\pi$
$654$	7.27715	+	3.63386i	0.284559	+	0.142095i
$655$	31.7475	−	1.96103i	1.24048	−	0.0766237i
$656$	10.2016	−	35.2488i	0.398305	−	1.37623i
$657$	11.1290	−	11.1290i	0.434183	−	0.434183i
$658$	−3.39498	−	10.1674i	−0.132350	−	0.396365i
$659$	37.8341			1.47381			0.736904	−	0.675997i	$-0.236287\pi$
$659$	37.8341			1.47381			0.736904	+	0.675997i	$0.236287\pi$
$660$	−0.855608	+	10.7848i	−0.0333045	+	0.419800i
$661$	13.3464			0.519114			0.259557	−	0.965728i	$-0.416423\pi$
$661$	13.3464			0.519114			0.259557	+	0.965728i	$0.416423\pi$
$662$	3.53336	+	10.5818i	0.137328	+	0.411272i
$663$	0.360673	−	0.360673i	0.0140074	−	0.0140074i
$664$	−3.49203	−	19.0378i	−0.135517	−	0.738809i
$665$	12.0884	−	13.6801i	0.468768	−	0.530491i
$666$	−7.37035	−	3.68040i	−0.285595	−	0.142612i
$667$	8.93947	+	8.93947i	0.346138	+	0.346138i
$668$	−5.86508	−	0.831661i	−0.226927	−	0.0321779i
$669$		−	9.39951i		−	0.363406i
$670$	−9.32004	+	21.9559i	−0.360065	+	0.848231i
$671$		−	43.2360i		−	1.66911i
$672$	−0.128716	−	3.17253i	−0.00496534	−	0.122383i
$673$	−15.8055	−	15.8055i	−0.609258	−	0.609258i	0.333494	−	0.942752i	$-0.391772\pi$
$673$	−15.8055	−	15.8055i	−0.609258	−	0.609258i	−0.942752	+	0.333494i	$0.891772\pi$
$674$	2.13102	−	4.26758i	0.0820840	−	0.164381i
$675$	12.5842	+	9.80739i	0.484367	+	0.377487i
$676$	−11.7003	−	15.5667i	−0.450010	−	0.598718i
$677$	28.3657	−	28.3657i	1.09018	−	1.09018i	0.0946735	−	0.995508i	$-0.469819\pi$
$677$	28.3657	−	28.3657i	1.09018	−	1.09018i	0.995508	−	0.0946735i	$-0.0301807\pi$
$678$	−8.87559	+	2.96365i	−0.340865	+	0.113818i
$679$	1.48337			0.0569266
$680$	3.08805	−	0.765854i	0.118421	−	0.0293692i
$681$	−15.0690			−0.577446
$682$	0.869263	−	0.290255i	0.0332858	−	0.0111145i
$683$	10.6192	−	10.6192i	0.406332	−	0.406332i	−0.474125	−	0.880457i	$-0.657236\pi$
$683$	10.6192	−	10.6192i	0.406332	−	0.406332i	0.880457	+	0.474125i	$0.157236\pi$
$684$	−26.3411	−	35.0457i	−1.00718	−	1.34000i
$685$	18.8095	+	16.6210i	0.718675	+	0.635055i
$686$	0.631799	−	1.26524i	0.0241222	−	0.0483070i
$687$	−0.654137	−	0.654137i	−0.0249569	−	0.0249569i
$688$	−17.7110	−	32.1383i	−0.675227	−	1.22526i
$689$		−	21.4079i		−	0.815575i
$690$	6.18444	−	2.49859i	0.235438	−	0.0951196i
$691$			41.5074i			1.57902i	0.613739	+	0.789509i	$0.289665\pi$
$691$			41.5074i			1.57902i	−0.613739	+	0.789509i	$0.710335\pi$
$692$	−8.49691	−	1.20485i	−0.323004	−	0.0458016i
$693$	8.18267	+	8.18267i	0.310834	+	0.310834i
$694$	13.9320	+	6.95697i	0.528851	+	0.264083i
$695$	1.77962	+	28.8106i	0.0675049	+	1.09285i
$696$	−5.25327	+	0.963586i	−0.199125	+	0.0365246i
$697$	−3.26326	+	3.26326i	−0.123605	+	0.123605i
$698$	2.31005	+	6.91817i	0.0874365	+	0.261857i
$699$	2.54527			0.0962709
$700$	9.99847	+	0.174764i	0.377907	+	0.00660545i
$701$	−3.56491			−0.134645			−0.0673224	−	0.997731i	$-0.521446\pi$
$701$	−3.56491			−0.134645			−0.0673224	+	0.997731i	$0.521446\pi$
$702$	−2.58184	−	7.73216i	−0.0974454	−	0.291832i
$703$	12.5251	−	12.5251i	0.472391	−	0.472391i
$704$	32.2351	−	12.2372i	1.21491	−	0.461208i
$705$	0.586500	+	9.49496i	0.0220889	+	0.357601i
$706$	−37.8146	−	18.8828i	−1.42317	−	0.710663i
$707$	−10.7732	−	10.7732i	−0.405167	−	0.405167i
$708$	−0.0563201	+	0.397184i	−0.00211664	+	0.0149271i
$709$			5.95148i			0.223513i	0.993736	+	0.111756i	$0.0356476\pi$
$709$			5.95148i			0.223513i	−0.993736	+	0.111756i	$0.964352\pi$
$710$	7.89211	−	3.18851i	0.296186	−	0.119663i
$711$			24.6316i			0.923756i
$712$	2.77495	+	1.91474i	0.103996	+	0.0717579i
$713$	−0.399527	−	0.399527i	−0.0149624	−	0.0149624i
$714$	−0.178395	+	0.357253i	−0.00667626	+	0.0133699i
$715$	13.0458	+	11.5279i	0.487887	+	0.431120i
$716$	−2.53216	+	1.90323i	−0.0946313	+	0.0711270i
$717$	−6.78233	+	6.78233i	−0.253291	+	0.253291i
$718$	6.47375	−	2.16165i	0.241598	−	0.0806720i
$719$	6.51438			0.242945			0.121473	−	0.992595i	$-0.461238\pi$
$719$	6.51438			0.242945			0.121473	+	0.992595i	$0.461238\pi$
$720$	5.24143	−	23.4360i	0.195337	−	0.873407i
$721$	−1.99504			−0.0742992
$722$	63.9246	−	21.3451i	2.37903	−	0.794381i
$723$	1.84095	−	1.84095i	0.0684656	−	0.0684656i
$724$	18.5307	−	13.9281i	0.688688	−	0.517633i
$725$	−2.07016	−	16.6931i	−0.0768837	−	0.619968i
$726$	2.68655	−	5.38007i	0.0997072	−	0.199673i
$727$	−24.9567	−	24.9567i	−0.925594	−	0.925594i	0.0718237	−	0.997417i	$-0.477118\pi$
$727$	−24.9567	−	24.9567i	−0.925594	−	0.925594i	−0.997417	+	0.0718237i	$0.977118\pi$
$728$	−4.20543	−	2.90178i	−0.155864	−	0.107547i
$729$		−	11.4450i		−	0.423889i
$730$	−7.24310	+	17.0631i	−0.268079	+	0.631534i
$731$			4.61495i			0.170690i
$732$	1.58103	−	11.1498i	0.0584364	−	0.412108i
$733$	7.44157	+	7.44157i	0.274861	+	0.274861i	0.831053	−	0.556193i	$-0.187738\pi$
$733$	7.44157	+	7.44157i	0.274861	+	0.274861i	−0.556193	+	0.831053i	$0.687738\pi$
$734$	−5.01468	−	2.50409i	−0.185095	−	0.0924276i
$735$	−0.831075	+	0.940505i	−0.0306547	+	0.0346910i
$736$	−15.6286	−	14.4099i	−0.576077	−	0.531154i
$737$	22.9872	−	22.9872i	0.846745	−	0.846745i
$738$	11.0326	+	33.0407i	0.406116	+	1.21624i
$739$	−28.7698			−1.05831			−0.529157	−	0.848524i	$-0.677492\pi$
$739$	−28.7698			−1.05831			−0.529157	+	0.848524i	$0.677492\pi$
$740$	9.67233	+	0.767348i	0.355562	+	0.0282083i
$741$	8.27806			0.304102
$742$	5.30810	+	15.8968i	0.194866	+	0.583590i
$743$	18.8941	−	18.8941i	0.693158	−	0.693158i	−0.269767	−	0.962926i	$-0.586947\pi$
$743$	18.8941	−	18.8941i	0.693158	−	0.693158i	0.962926	+	0.269767i	$0.0869467\pi$
$744$	0.234781	−	0.0430650i	0.00860750	−	0.00157884i
$745$	4.67985	−	0.289072i	0.171456	−	0.0105908i
$746$	28.4860	+	14.2245i	1.04295	+	0.520798i
$747$	12.9921	+	12.9921i	0.475355	+	0.475355i
$748$	−4.29335	−	0.608792i	−0.156980	−	0.0222596i
$749$			2.72874i			0.0997059i
$750$	−8.53391	−	2.43601i	−0.311614	−	0.0889503i
$751$			8.00352i			0.292053i	0.989281	+	0.146026i	$0.0466484\pi$
$751$			8.00352i			0.292053i	−0.989281	+	0.146026i	$0.953352\pi$
$752$	26.5533	−	14.6332i	0.968300	−	0.533619i
$753$	6.28267	+	6.28267i	0.228953	+	0.228953i
$754$	−3.83961	+	7.68918i	−0.139830	+	0.280023i
$755$	−24.0703	+	1.48681i	−0.876007	+	0.0541106i
$756$	3.83439	+	5.10148i	0.139455	+	0.185539i
$757$	−6.84570	+	6.84570i	−0.248811	+	0.248811i	−0.820483	−	0.571672i	$-0.806295\pi$
$757$	−6.84570	+	6.84570i	−0.248811	+	0.248811i	0.571672	+	0.820483i	$0.306295\pi$
$758$	−16.9900	+	5.67311i	−0.617103	+	0.206057i
$759$	−9.09088			−0.329978
$760$	44.2269	+	26.6492i	1.60428	+	0.966668i
$761$	−2.27505			−0.0824704			−0.0412352	−	0.999149i	$-0.513129\pi$
$761$	−2.27505			−0.0824704			−0.0412352	+	0.999149i	$0.513129\pi$
$762$	5.43243	−	1.81394i	0.196796	−	0.0657122i
$763$	−7.24579	+	7.24579i	−0.262315	+	0.262315i
$764$	6.04175	+	8.03828i	0.218583	+	0.290815i
$765$	−1.99988	+	2.26321i	−0.0723060	+	0.0818267i
$766$	−21.7179	+	43.4923i	−0.784701	+	1.57144i
$767$	0.456464	+	0.456464i	0.0164820	+	0.0164820i
$768$	8.76034	−	1.97701i	0.316111	−	0.0713393i
$769$		−	23.4892i		−	0.847041i	−0.905887	−	0.423520i	$-0.860794\pi$
$769$		−	23.4892i		−	0.847041i	0.905887	−	0.423520i	$-0.139206\pi$
$770$	−12.5458	−	5.32554i	−0.452118	−	0.191919i
$771$			5.34169i			0.192376i
$772$	26.2832	+	3.72692i	0.945951	+	0.134135i
$773$	36.2947	+	36.2947i	1.30543	+	1.30543i	0.924677	+	0.380751i	$0.124335\pi$
$773$	36.2947	+	36.2947i	1.30543	+	1.30543i	0.380751	+	0.924677i	$0.375665\pi$
$774$	31.1645	+	15.5621i	1.12019	+	0.559367i
$775$	0.0925204	+	0.746058i	0.00332343	+	0.0267992i
$776$	0.756956	+	4.12676i	0.0271731	+	0.148142i
$777$	−0.861096	+	0.861096i	−0.0308916	+	0.0308916i
$778$	−8.82062	−	26.4162i	−0.316234	−	0.947066i
$779$	−74.8974			−2.68348
$780$	2.94274	+	3.44990i	0.105367	+	0.123526i
$781$	−11.6011			−0.415120
$782$	0.846741	+	2.53584i	0.0302794	+	0.0906813i
$783$	7.59070	−	7.59070i	0.271270	−	0.271270i
$784$	3.84232	+	1.11203i	0.137226	+	0.0397154i
$785$	15.2868	+	13.5081i	0.545608	+	0.482126i
$786$	−10.1021	−	5.04450i	−0.360330	−	0.179931i
$787$	−36.2698	−	36.2698i	−1.29288	−	1.29288i	−0.932997	−	0.359883i	$-0.882817\pi$
$787$	−36.2698	−	36.2698i	−1.29288	−	1.29288i	−0.359883	−	0.932997i	$-0.617183\pi$
$788$	0.227926	−	1.60739i	0.00811951	−	0.0572608i
$789$			9.12015i			0.324686i
$790$	−10.8672	−	26.8982i	−0.386638	−	0.956996i
$791$		−	11.7882i		−	0.419141i
$792$	−18.5887	+	26.9399i	−0.660522	+	0.957267i
$793$	−12.8139	−	12.8139i	−0.455036	−	0.455036i
$794$	3.18000	−	6.36825i	0.112854	−	0.226001i
$795$	−0.916999	−	14.8455i	−0.0325226	−	0.526515i
$796$	42.3564	−	31.8360i	1.50128	−	1.12840i
$797$	−1.76536	+	1.76536i	−0.0625323	+	0.0625323i	−0.737681	−	0.675149i	$-0.764079\pi$
$797$	−1.76536	+	1.76536i	−0.0625323	+	0.0625323i	0.675149	+	0.737681i	$0.264079\pi$
$798$	−6.14702	+	2.05255i	−0.217602	+	0.0726595i
$799$	−3.81297			−0.134893
$800$	4.61597	+	27.9051i	0.163199	+	0.986593i
$801$	−3.20042			−0.113081
$802$	0.593047	−	0.198024i	0.0209412	−	0.00699248i
$803$	17.8646	−	17.8646i	0.630427	−	0.630427i
$804$	6.76857	−	5.08741i	0.238709	−	0.179419i
$805$	0.518057	+	8.38692i	0.0182591	+	0.295600i
$806$	0.171601	−	0.343648i	0.00604440	−	0.0121045i
$807$	−6.73926	−	6.73926i	−0.237233	−	0.237233i
$808$	24.4736	−	35.4686i	0.860979	−	1.24778i
$809$			24.8302i			0.872982i	0.899709	+	0.436491i	$0.143779\pi$
$809$			24.8302i			0.872982i	−0.899709	+	0.436491i	$0.856221\pi$
$810$	7.41998	+	18.3657i	0.260711	+	0.645306i
$811$			25.4473i			0.893576i	0.894640	+	0.446788i	$0.147432\pi$
$811$			25.4473i			0.893576i	−0.894640	+	0.446788i	$0.852568\pi$
$812$	0.944630	−	6.66177i	0.0331500	−	0.233782i
$813$	4.27555	+	4.27555i	0.149950	+	0.149950i
$814$	−11.8311	−	5.90788i	−0.414680	−	0.207071i
$815$	35.9449	+	31.7627i	1.25910	+	1.11260i
$816$	−1.08492	−	0.313993i	−0.0379797	−	0.0109920i
$817$	−52.9605	+	52.9605i	−1.85285	+	1.85285i
$818$	−7.74436	−	23.1930i	−0.270775	−	0.810923i
$819$	4.85022			0.169481
$820$	−26.6251	−	31.2137i	−0.929788	−	1.09003i
$821$	−55.9413			−1.95237			−0.976183	−	0.216948i	$-0.930390\pi$
$821$	−55.9413			−1.95237			−0.976183	+	0.216948i	$0.930390\pi$
$822$	−2.82216	−	8.45188i	−0.0984343	−	0.294793i
$823$	−31.9451	+	31.9451i	−1.11354	+	1.11354i	−0.120867	+	0.992669i	$0.538567\pi$
$823$	−31.9451	+	31.9451i	−1.11354	+	1.11354i	−0.992669	+	0.120867i	$0.961433\pi$
$824$	−1.01806	−	5.55023i	−0.0354657	−	0.193351i
$825$	9.54055	+	7.43533i	0.332159	+	0.258865i
$826$	−0.452136	−	0.225775i	−0.0157318	−	0.00785571i
$827$	5.59251	+	5.59251i	0.194471	+	0.194471i	0.797625	−	0.603154i	$-0.206090\pi$
$827$	5.59251	+	5.59251i	0.194471	+	0.194471i	−0.603154	+	0.797625i	$0.706090\pi$
$828$	19.9797	+	2.83309i	0.694341	+	0.0984568i
$829$			33.8082i			1.17421i	0.809512	+	0.587103i	$0.199732\pi$
$829$			33.8082i			1.17421i	−0.809512	+	0.587103i	$0.800268\pi$
$830$	−19.9196	−	8.45565i	−0.691420	−	0.293500i
$831$			11.3472i			0.393628i
$832$	5.92679	−	13.1803i	0.205474	−	0.456946i
$833$	−0.355714	−	0.355714i	−0.0123248	−	0.0123248i
$834$	4.57785	−	9.16759i	0.158518	−	0.317448i
$835$	−4.38550	+	4.96296i	−0.151767	+	0.171750i
$836$	−42.2835	−	56.2563i	−1.46240	−	1.94566i
$837$	−0.339247	+	0.339247i	−0.0117261	+	0.0117261i
$838$	−21.4162	+	7.15109i	−0.739811	+	0.247030i
$839$	−10.7222			−0.370170			−0.185085	−	0.982722i	$-0.559256\pi$
$839$	−10.7222			−0.370170			−0.185085	+	0.982722i	$0.559256\pi$
$840$	−3.04059	−	1.83213i	−0.104910	−	0.0632144i
$841$	17.6821			0.609729
$842$	−25.3804	+	8.47475i	−0.874665	+	0.292059i
$843$	9.65276	−	9.65276i	0.332459	−	0.332459i
$844$	23.9843	+	31.9100i	0.825572	+	1.09839i
$845$	−21.7306	+	1.34229i	−0.747556	+	0.0461762i
$846$	−12.8577	+	25.7488i	−0.442057	+	0.885261i
$847$	5.35689	+	5.35689i	0.184065	+	0.184065i
$848$	−41.5164	+	22.8792i	−1.42568	+	0.785676i
$849$		−	11.6566i		−	0.400055i
$850$	1.18541	−	3.35381i	0.0406592	−	0.115035i
$851$			8.15311i			0.279485i
$852$	−2.99171	−	0.424221i	−0.102494	−	0.0145336i
$853$	−6.50453	−	6.50453i	−0.222711	−	0.222711i	0.586928	−	0.809639i	$-0.300337\pi$
$853$	−6.50453	−	6.50453i	−0.222711	−	0.222711i	−0.809639	+	0.586928i	$0.800337\pi$
$854$	12.6924	+	6.33798i	0.434326	+	0.216881i
$855$	−48.9227	+	3.02194i	−1.67312	+	0.103348i
$856$	−7.59138	+	1.39246i	−0.259468	+	0.0475932i
$857$	17.3451	−	17.3451i	0.592498	−	0.592498i	−0.345808	−	0.938305i	$-0.612395\pi$
$857$	17.3451	−	17.3451i	0.592498	−	0.592498i	0.938305	+	0.345808i	$0.112395\pi$
$858$	−1.95739	−	5.86202i	−0.0668241	−	0.200126i
$859$	−15.3637			−0.524201			−0.262101	−	0.965041i	$-0.584415\pi$
$859$	−15.3637			−0.524201			−0.262101	+	0.965041i	$0.584415\pi$
$860$	−40.8982	−	3.24463i	−1.39462	−	0.110641i
$861$	5.14919			0.175484
$862$	−2.66765	−	7.98915i	−0.0908607	−	0.272111i
$863$	−37.0031	+	37.0031i	−1.25960	+	1.25960i	−0.308315	+	0.951284i	$0.599765\pi$
$863$	−37.0031	+	37.0031i	−1.25960	+	1.25960i	−0.951284	+	0.308315i	$0.900235\pi$
$864$	−12.2357	+	13.2706i	−0.416268	+	0.451474i
$865$	−6.35340	+	7.18997i	−0.216022	+	0.244466i
$866$	−38.6935	−	19.3217i	−1.31486	−	0.656577i
$867$	−6.64673	−	6.64673i	−0.225735	−	0.225735i
$868$	−0.0422179	+	0.297731i	−0.00143297	+	0.0101056i
$869$			39.5393i			1.34128i
$870$	−2.33325	+	5.49660i	−0.0791044	+	0.186352i
$871$		−	13.6255i		−	0.461683i
$872$	−23.8554	−	16.4604i	−0.807845	−	0.557420i
$873$	−2.81625	−	2.81625i	−0.0953157	−	0.0953157i
$874$	−19.3838	+	38.8180i	−0.655668	+	1.31304i
$875$	6.31589	−	9.22548i	0.213516	−	0.311878i
$876$	5.26022	−	3.95369i	0.177726	−	0.133583i
$877$	20.3030	−	20.3030i	0.685583	−	0.685583i	−0.275669	−	0.961253i	$-0.588899\pi$
$877$	20.3030	−	20.3030i	0.685583	−	0.685583i	0.961253	+	0.275669i	$0.0888995\pi$
$878$	33.3011	−	11.1196i	1.12386	−	0.375267i
$879$	11.0598			0.373038
$880$	8.41370	−	37.6201i	0.283626	−	1.26817i
$881$	25.0247			0.843102			0.421551	−	0.906805i	$-0.361486\pi$
$881$	25.0247			0.843102			0.421551	+	0.906805i	$0.361486\pi$
$882$	−3.60162	+	1.20262i	−0.121273	+	0.0404942i
$883$	−12.6604	+	12.6604i	−0.426055	+	0.426055i	−0.887282	−	0.461227i	$-0.847409\pi$
$883$	−12.6604	+	12.6604i	−0.426055	+	0.426055i	0.461227	+	0.887282i	$0.347409\pi$
$884$	−1.45286	+	1.09200i	−0.0488648	+	0.0367279i
$885$	0.336091	+	0.296986i	0.0112976	+	0.00998309i
$886$	19.5595	−	39.1697i	0.657114	−	1.31593i
$887$	−3.62337	−	3.62337i	−0.121661	−	0.121661i	0.643655	−	0.765316i	$-0.277417\pi$
$887$	−3.62337	−	3.62337i	−0.121661	−	0.121661i	−0.765316	+	0.643655i	$0.777417\pi$
$888$	−2.83499	−	1.95617i	−0.0951361	−	0.0656447i
$889$			7.21515i			0.241988i
$890$	3.49493	−	1.41199i	0.117150	−	0.0473301i
$891$		−	26.9969i		−	0.904430i
$892$	−4.70215	+	33.1608i	−0.157440	+	1.11030i
$893$	−43.7571	−	43.7571i	−1.46427	−	1.46427i
$894$	−1.48913	−	0.743602i	−0.0498041	−	0.0248698i
$895$	0.218345	+	3.53482i	0.00729845	+	0.118156i
$896$	−1.13297	+	11.2568i	−0.0378500	+	0.376065i
$897$	−2.69428	+	2.69428i	−0.0899593	+	0.0899593i
$898$	13.3536	+	39.9917i	0.445616	+	1.33454i
$899$	0.505824			0.0168702
$900$	−18.6508	−	19.3144i	−0.621693	−	0.643813i
$901$	5.96162			0.198610
$902$	17.7099	+	53.0378i	0.589674	+	1.76597i
$903$	3.64103	−	3.64103i	0.121166	−	0.121166i
$904$	32.7950	−	6.01546i	1.09075	−	0.200071i
$905$	−1.59787	−	25.8683i	−0.0531151	−	0.859892i
$906$	7.65920	+	3.82463i	0.254460	+	0.127065i
$907$	16.6559	+	16.6559i	0.553050	+	0.553050i	0.927320	−	0.374270i	$-0.122107\pi$
$907$	16.6559	+	16.6559i	0.553050	+	0.553050i	−0.374270	+	0.927320i	$0.622107\pi$
$908$	53.1624	+	7.53836i	1.76425	+	0.250169i
$909$			40.9067i			1.35679i
$910$	−5.29655	+	2.13987i	−0.175579	+	0.0709360i
$911$			36.8965i			1.22243i	0.791463	+	0.611217i	$0.209320\pi$
$911$			36.8965i			1.22243i	−0.791463	+	0.611217i	$0.790680\pi$
$912$	−8.84701	−	16.0537i	−0.292954	−	0.531591i
$913$	20.8553	+	20.8553i	0.690208	+	0.690208i
$914$	−3.44038	+	6.88969i	−0.113798	+	0.227891i
$915$	−9.43481	−	8.33705i	−0.311905	−	0.275614i
$916$	1.98051	+	2.63498i	0.0654380	+	0.0870623i
$917$	10.0586	−	10.0586i	0.332163	−	0.332163i
$918$	2.15323	−	0.718986i	0.0710673	−	0.0237301i
$919$	9.06905			0.299160			0.149580	−	0.988750i	$-0.452208\pi$
$919$	9.06905			0.299160			0.149580	+	0.988750i	$0.452208\pi$
$920$	−23.0682	+	5.72104i	−0.760535	+	0.188617i
$921$	−14.6374			−0.482319
$922$	47.4157	−	15.8326i	1.56155	−	0.521418i
$923$	−3.43823	+	3.43823i	−0.113171	+	0.113171i
$924$	2.90698	+	3.86761i	0.0956328	+	0.127235i
$925$	6.66834	−	8.55639i	0.219254	−	0.281332i
$926$	−15.2867	+	30.6131i	−0.502352	+	1.00601i
$927$	3.78768	+	3.78768i	0.124404	+	0.124404i
$928$	19.0152	−	0.771486i	0.624204	−	0.0253253i
$929$			33.1005i			1.08599i	0.839736	+	0.542996i	$0.182710\pi$
$929$			33.1005i			1.08599i	−0.839736	+	0.542996i	$0.817290\pi$
$930$	0.104278	−	0.245657i	0.00341943	−	0.00805539i
$931$		−	8.16424i		−	0.267572i
$932$	−8.97952	−	1.27328i	−0.294134	−	0.0417078i
$933$	4.20560	+	4.20560i	0.137685	+	0.137685i
$934$	−18.5142	−	9.24510i	−0.605803	−	0.302509i
$935$	−3.21027	+	3.63298i	−0.104987	+	0.118811i
$936$	2.47504	+	13.4934i	0.0808992	+	0.441045i
$937$	−5.66479	+	5.66479i	−0.185061	+	0.185061i	−0.793557	−	0.608496i	$-0.791773\pi$
$937$	−5.66479	+	5.66479i	−0.185061	+	0.185061i	0.608496	+	0.793557i	$0.291773\pi$
$938$	3.37845	+	10.1179i	0.110310	+	0.330360i
$939$	−13.3677			−0.436238
$940$	2.68078	−	33.7909i	0.0874373	−	1.10214i
$941$	15.8823			0.517747			0.258874	−	0.965911i	$-0.416649\pi$
$941$	15.8823			0.517747			0.258874	+	0.965911i	$0.416649\pi$
$942$	−2.29361	−	6.86896i	−0.0747300	−	0.223803i
$943$	24.3770	−	24.3770i	0.793825	−	0.793825i
$944$	0.397386	−	1.37306i	0.0129338	−	0.0446893i
$945$	7.12152	−	0.439893i	0.231663	−	0.0143097i
$946$	50.0262	+	24.9807i	1.62649	+	0.812191i
$947$	−17.5435	−	17.5435i	−0.570087	−	0.570087i	0.362066	−	0.932153i	$-0.382072\pi$
$947$	−17.5435	−	17.5435i	−0.570087	−	0.570087i	−0.932153	+	0.362066i	$0.882072\pi$
$948$	−1.44585	+	10.1965i	−0.0469590	+	0.331166i
$949$		−	10.5891i		−	0.343737i
$950$	52.0914	−	24.8842i	1.69007	−	0.807352i
$951$			9.52635i			0.308913i
$952$	0.808082	−	1.17112i	0.0261901	−	0.0379562i
$953$	−7.57040	−	7.57040i	−0.245229	−	0.245229i	0.573780	−	0.819009i	$-0.305476\pi$
$953$	−7.57040	−	7.57040i	−0.245229	−	0.245229i	−0.819009	+	0.573780i	$0.805476\pi$
$954$	20.1032	−	40.2585i	0.650864	−	1.30342i
$955$	11.2212	−	0.693129i	0.363110	−	0.0224291i
$956$	27.3205	−	20.5347i	0.883607	−	0.664139i
$957$	5.75478	−	5.75478i	0.186026	−	0.186026i
$958$	−47.2914	+	15.7911i	−1.52792	+	0.510186i
$959$	11.2255			0.362489
$960$	3.54541	−	9.39389i	0.114428	−	0.303186i
$961$	30.9774			0.999271
$962$	−5.25732	+	1.75547i	−0.169503	+	0.0565987i
$963$	5.18064	−	5.18064i	0.166944	−	0.166944i
$964$	−7.41567	+	5.57378i	−0.238843	+	0.179519i
$965$	19.6527	−	22.2405i	0.632644	−	0.715945i
$966$	1.33264	−	2.66873i	0.0428768	−	0.0858650i
$967$	5.93982	+	5.93982i	0.191012	+	0.191012i	0.796133	−	0.605121i	$-0.206875\pi$
$967$	5.93982	+	5.93982i	0.191012	+	0.191012i	−0.605121	+	0.796133i	$0.706875\pi$
$968$	−12.1694	+	17.6365i	−0.391138	+	0.566860i
$969$			2.30526i			0.0740555i
$970$	4.31791	+	1.83291i	0.138640	+	0.0588511i
$971$		−	19.4792i		−	0.625118i	−0.949898	−	0.312559i	$-0.898814\pi$
$971$		−	19.4792i		−	0.625118i	0.949898	−	0.312559i	$-0.101186\pi$
$972$	3.67512	−	25.9179i	0.117880	−	0.831316i
$973$	9.12809	+	9.12809i	0.292633	+	0.292633i
$974$	−42.8201	−	21.3823i	−1.37204	−	0.685132i
$975$	5.03117	−	0.623927i	0.161126	−	0.0199816i
$976$	−11.1555	+	38.5447i	−0.357079	+	1.23379i
$977$	−25.0324	+	25.0324i	−0.800859	+	0.800859i	−0.983230	−	0.182371i	$-0.941623\pi$
$977$	−25.0324	+	25.0324i	−0.800859	+	0.800859i	0.182371	+	0.983230i	$0.441623\pi$
$978$	−5.39315	−	16.1515i	−0.172454	−	0.516469i
$979$	−5.13740			−0.164192
$980$	3.40246	−	2.90228i	0.108688	−	0.0927100i
$981$	27.5130			0.878422
$982$	−1.26695	−	3.79428i	−0.0404299	−	0.121080i
$983$	17.1437	−	17.1437i	0.546798	−	0.546798i	−0.378715	−	0.925513i	$-0.623634\pi$
$983$	17.1437	−	17.1437i	0.546798	−	0.546798i	0.925513	+	0.378715i	$0.123634\pi$
$984$	2.62760	+	14.3251i	0.0837649	+	0.456668i
$985$	−1.36015	−	1.20189i	−0.0433380	−	0.0382955i
$986$	−2.14127	−	1.06924i	−0.0681918	−	0.0340517i
$987$	3.00829	+	3.00829i	0.0957550	+	0.0957550i
$988$	−29.2044	−	4.14115i	−0.929115	−	0.131747i
$989$		−	34.4743i		−	1.09622i
$990$	13.7080	+	33.9296i	0.435668	+	1.07835i
$991$		−	23.2266i		−	0.737816i	−0.929466	−	0.368908i	$-0.879732\pi$
$991$		−	23.2266i		−	0.737816i	0.929466	−	0.368908i	$-0.120268\pi$
$992$	−0.849835	+	0.0344796i	−0.0269823	+	0.00109473i
$993$	−3.13091	−	3.13091i	−0.0993563	−	0.0993563i
$994$	1.70061	−	3.40563i	0.0539400	−	0.108020i
$995$	−3.65233	−	59.1282i	−0.115787	−	1.87449i
$996$	4.61558	+	6.14082i	0.146250	+	0.194579i
$997$	35.3448	−	35.3448i	1.11938	−	1.11938i	0.127550	−	0.991832i	$-0.459289\pi$
$997$	35.3448	−	35.3448i	1.11938	−	1.11938i	0.991832	−	0.127550i	$-0.0407114\pi$
$998$	21.4555	−	7.16420i	0.679162	−	0.226779i
$999$	6.92298			0.219034

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.k.a.43.17	yes	36
4.3	odd	2	inner	140.2.k.a.43.11	✓	36
5.2	odd	4	inner	140.2.k.a.127.11	yes	36
5.3	odd	4		700.2.k.b.407.8		36
5.4	even	2		700.2.k.b.43.2		36
7.2	even	3		980.2.x.k.263.4		72
7.3	odd	6		980.2.x.l.863.8		72
7.4	even	3		980.2.x.k.863.8		72
7.5	odd	6		980.2.x.l.263.4		72
7.6	odd	2		980.2.k.l.883.17		36
20.3	even	4		700.2.k.b.407.2		36
20.7	even	4	inner	140.2.k.a.127.17	yes	36
20.19	odd	2		700.2.k.b.43.8		36
28.3	even	6		980.2.x.l.863.13		72
28.11	odd	6		980.2.x.k.863.13		72
28.19	even	6		980.2.x.l.263.2		72
28.23	odd	6		980.2.x.k.263.2		72
28.27	even	2		980.2.k.l.883.11		36
35.2	odd	12		980.2.x.k.67.13		72
35.12	even	12		980.2.x.l.67.13		72
35.17	even	12		980.2.x.l.667.2		72
35.27	even	4		980.2.k.l.687.11		36
35.32	odd	12		980.2.x.k.667.2		72
140.27	odd	4		980.2.k.l.687.17		36
140.47	odd	12		980.2.x.l.67.8		72
140.67	even	12		980.2.x.k.667.4		72
140.87	odd	12		980.2.x.l.667.4		72
140.107	even	12		980.2.x.k.67.8		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.k.a.43.11	✓	36	4.3	odd	2	inner
140.2.k.a.43.17	yes	36	1.1	even	1	trivial
140.2.k.a.127.11	yes	36	5.2	odd	4	inner
140.2.k.a.127.17	yes	36	20.7	even	4	inner
700.2.k.b.43.2		36	5.4	even	2
700.2.k.b.43.8		36	20.19	odd	2
700.2.k.b.407.2		36	20.3	even	4
700.2.k.b.407.8		36	5.3	odd	4
980.2.k.l.687.11		36	35.27	even	4
980.2.k.l.687.17		36	140.27	odd	4
980.2.k.l.883.11		36	28.27	even	2
980.2.k.l.883.17		36	7.6	odd	2
980.2.x.k.67.8		72	140.107	even	12
980.2.x.k.67.13		72	35.2	odd	12
980.2.x.k.263.2		72	28.23	odd	6
980.2.x.k.263.4		72	7.2	even	3
980.2.x.k.667.2		72	35.32	odd	12
980.2.x.k.667.4		72	140.67	even	12
980.2.x.k.863.8		72	7.4	even	3
980.2.x.k.863.13		72	28.11	odd	6
980.2.x.l.67.8		72	140.47	odd	12
980.2.x.l.67.13		72	35.12	even	12
980.2.x.l.263.2		72	28.19	even	6
980.2.x.l.263.4		72	7.5	odd	6
980.2.x.l.667.2		72	35.17	even	12
980.2.x.l.667.4		72	140.87	odd	12
980.2.x.l.863.8		72	7.3	odd	6
980.2.x.l.863.13		72	28.3	even	6

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:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34141 - 0.447909i) q^{2} +(-0.396892 + 0.396892i) q^{3} +(1.59875 - 1.20166i) q^{4} +(-0.137858 - 2.23181i) q^{5} +(-0.354623 + 0.710167i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(1.60635 - 2.32801i) q^{8} +2.68495i q^{9} +O(q^{10})\)	\(q+(1.34141 - 0.447909i) q^{2} +(-0.396892 + 0.396892i) q^{3} +(1.59875 - 1.20166i) q^{4} +(-0.137858 - 2.23181i) q^{5} +(-0.354623 + 0.710167i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(1.60635 - 2.32801i) q^{8} +2.68495i q^{9} +(-1.18457 - 2.93203i) q^{10} +4.30996i q^{11} +(-0.157604 + 1.11146i) q^{12} +(1.27735 + 1.27735i) q^{13} +(-1.26524 - 0.631799i) q^{14} +(0.940505 + 0.831075i) q^{15} +(1.11203 - 3.84232i) q^{16} +(-0.355714 + 0.355714i) q^{17} +(1.20262 + 3.60162i) q^{18} -8.16424 q^{19} +(-2.90228 - 3.40246i) q^{20} +0.561291 q^{21} +(1.93047 + 5.78142i) q^{22} +(2.65723 - 2.65723i) q^{23} +(0.286423 + 1.56152i) q^{24} +(-4.96199 + 0.615348i) q^{25} +(2.28559 + 1.14131i) q^{26} +(-2.25631 - 2.25631i) q^{27} +(-1.98019 - 0.280789i) q^{28} +3.36420i q^{29} +(1.63385 + 0.693550i) q^{30} -0.150355i q^{31} +(-0.229322 - 5.65220i) q^{32} +(-1.71059 - 1.71059i) q^{33} +(-0.317830 + 0.636485i) q^{34} +(-1.48065 + 1.67561i) q^{35} +(3.22640 + 4.29258i) q^{36} +(-1.53414 + 1.53414i) q^{37} +(-10.9516 + 3.65684i) q^{38} -1.01394 q^{39} +(-5.41714 - 3.26414i) q^{40} +9.17384 q^{41} +(0.752920 - 0.251407i) q^{42} +(6.48688 - 6.48688i) q^{43} +(5.17911 + 6.89057i) q^{44} +(5.99232 - 0.370143i) q^{45} +(2.37423 - 4.75463i) q^{46} +(5.35960 + 5.35960i) q^{47} +(1.08363 + 1.96634i) q^{48} +1.00000i q^{49} +(-6.38044 + 3.04796i) q^{50} -0.282360i q^{51} +(3.57711 + 0.507230i) q^{52} +(-8.37980 - 8.37980i) q^{53} +(-4.03726 - 2.01602i) q^{54} +(9.61904 - 0.594164i) q^{55} +(-2.78201 + 0.510294i) q^{56} +(3.24033 - 3.24033i) q^{57} +(1.50686 + 4.51277i) q^{58} +0.357352 q^{59} +(2.50231 + 0.198519i) q^{60} -10.0316 q^{61} +(-0.0673452 - 0.201687i) q^{62} +(1.89855 - 1.89855i) q^{63} +(-2.83929 - 7.47920i) q^{64} +(2.67472 - 3.02690i) q^{65} +(-3.06079 - 1.52841i) q^{66} +(-5.33350 - 5.33350i) q^{67} +(-0.141252 + 0.996146i) q^{68} +2.10927i q^{69} +(-1.23564 + 2.91088i) q^{70} +2.69169i q^{71} +(6.25061 + 4.31297i) q^{72} +(-4.14495 - 4.14495i) q^{73} +(-1.37075 + 2.74506i) q^{74} +(1.72515 - 2.21360i) q^{75} +(-13.0526 + 9.81064i) q^{76} +(3.04760 - 3.04760i) q^{77} +(-1.36011 + 0.454154i) q^{78} +9.17393 q^{79} +(-8.72864 - 1.95215i) q^{80} -6.26383 q^{81} +(12.3059 - 4.10905i) q^{82} +(4.83885 - 4.83885i) q^{83} +(0.897366 - 0.674480i) q^{84} +(0.842925 + 0.744849i) q^{85} +(5.79603 - 11.6071i) q^{86} +(-1.33523 - 1.33523i) q^{87} +(10.0337 + 6.92330i) q^{88} +1.19198i q^{89} +(7.87235 - 3.18053i) q^{90} -1.80645i q^{91} +(1.05517 - 7.44135i) q^{92} +(0.0596746 + 0.0596746i) q^{93} +(9.59003 + 4.78880i) q^{94} +(1.12551 + 18.2211i) q^{95} +(2.33433 + 2.15230i) q^{96} +(-1.04890 + 1.04890i) q^{97} +(0.447909 + 1.34141i) q^{98} -11.5720 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 8 q^{6}+O(q^{10}) \) 36 * q - 8 * q^6	\( 36 q - 8 q^{6} - 16 q^{10} - 16 q^{12} - 4 q^{13} - 8 q^{16} - 20 q^{17} + 28 q^{18} + 20 q^{20} + 4 q^{22} - 20 q^{25} - 32 q^{26} - 4 q^{30} + 20 q^{37} - 36 q^{40} - 20 q^{42} + 20 q^{45} + 16 q^{46} - 24 q^{48} + 40 q^{50} + 16 q^{52} - 44 q^{53} - 24 q^{56} - 16 q^{57} - 4 q^{58} + 40 q^{60} - 64 q^{61} + 40 q^{62} + 4 q^{65} + 32 q^{66} + 80 q^{68} + 80 q^{72} + 52 q^{73} + 8 q^{76} - 76 q^{78} - 20 q^{80} - 36 q^{81} + 56 q^{82} - 20 q^{85} + 56 q^{86} - 40 q^{88} - 16 q^{90} - 56 q^{92} + 32 q^{93} + 120 q^{96} + 20 q^{97}+O(q^{100}) \) 36 * q - 8 * q^6 - 16 * q^10 - 16 * q^12 - 4 * q^13 - 8 * q^16 - 20 * q^17 + 28 * q^18 + 20 * q^20 + 4 * q^22 - 20 * q^25 - 32 * q^26 - 4 * q^30 + 20 * q^37 - 36 * q^40 - 20 * q^42 + 20 * q^45 + 16 * q^46 - 24 * q^48 + 40 * q^50 + 16 * q^52 - 44 * q^53 - 24 * q^56 - 16 * q^57 - 4 * q^58 + 40 * q^60 - 64 * q^61 + 40 * q^62 + 4 * q^65 + 32 * q^66 + 80 * q^68 + 80 * q^72 + 52 * q^73 + 8 * q^76 - 76 * q^78 - 20 * q^80 - 36 * q^81 + 56 * q^82 - 20 * q^85 + 56 * q^86 - 40 * q^88 - 16 * q^90 - 56 * q^92 + 32 * q^93 + 120 * q^96 + 20 * q^97

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