LMFDB - Embedded newform 1338.2.e.i.931.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1338,2,Mod(931,1338)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1338.931"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1338, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1338 = 2 \cdot 3 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1338.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,14,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$10.6839837904$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 25 x^{12} - 30 x^{11} + 502 x^{10} - 434 x^{9} + 3060 x^{8} - 1136 x^{7} + 13014 x^{6} + \cdots + 961 $ x^14 + 25x^12 - 30x^11 + 502x^10 - 434x^9 + 3060x^8 - 1136x^7 + 13014x^6 - 2882x^5 + 18706x^4 + 14706x^3 + 12571x^2 + 3720x + 961
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			931.5
Root			$1.86875 - 3.23677i$ of defining polynomial
Character	$\chi$	$=$	1338.931
Dual form			1338.2.e.i.1075.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +(0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(0.887260 + 1.53678i) q^{5} +(0.500000 - 0.866025i) q^{6} -3.74585 q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.887260 + 1.53678i) q^{10} +(2.36875 + 4.10280i) q^{11} +(0.500000 - 0.866025i) q^{12} +2.39040 q^{13} -3.74585 q^{14} +1.77452 q^{15} +1.00000 q^{16} +4.75863 q^{17} +(-0.500000 - 0.866025i) q^{18} +(1.21405 - 2.10279i) q^{19} +(0.887260 + 1.53678i) q^{20} +(-1.87292 + 3.24400i) q^{21} +(2.36875 + 4.10280i) q^{22} +(-4.36080 + 7.55313i) q^{23} +(0.500000 - 0.866025i) q^{24} +(0.925541 - 1.60308i) q^{25} +2.39040 q^{26} -1.00000 q^{27} -3.74585 q^{28} +(1.36875 + 2.37075i) q^{29} +1.77452 q^{30} +(2.90277 - 5.02774i) q^{31} +1.00000 q^{32} +4.73750 q^{33} +4.75863 q^{34} +(-3.32354 - 5.75654i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(4.83896 + 8.38133i) q^{37} +(1.21405 - 2.10279i) q^{38} +(1.19520 - 2.07015i) q^{39} +(0.887260 + 1.53678i) q^{40} -0.632448 q^{41} +(-1.87292 + 3.24400i) q^{42} +(3.14676 - 5.45034i) q^{43} +(2.36875 + 4.10280i) q^{44} +(0.887260 - 1.53678i) q^{45} +(-4.36080 + 7.55313i) q^{46} +(5.30059 + 9.18089i) q^{47} +(0.500000 - 0.866025i) q^{48} +7.03138 q^{49} +(0.925541 - 1.60308i) q^{50} +(2.37931 - 4.12109i) q^{51} +2.39040 q^{52} +(-0.401996 - 0.696278i) q^{53} -1.00000 q^{54} +(-4.20339 + 7.28049i) q^{55} -3.74585 q^{56} +(-1.21405 - 2.10279i) q^{57} +(1.36875 + 2.37075i) q^{58} -0.772969 q^{59} +1.77452 q^{60} +(-2.78610 + 4.82566i) q^{61} +(2.90277 - 5.02774i) q^{62} +(1.87292 + 3.24400i) q^{63} +1.00000 q^{64} +(2.12091 + 3.67352i) q^{65} +4.73750 q^{66} +(-2.20654 + 3.82184i) q^{67} +4.75863 q^{68} +(4.36080 + 7.55313i) q^{69} +(-3.32354 - 5.75654i) q^{70} +(0.965893 - 1.67297i) q^{71} +(-0.500000 - 0.866025i) q^{72} +(-8.22631 - 14.2484i) q^{73} +(4.83896 + 8.38133i) q^{74} +(-0.925541 - 1.60308i) q^{75} +(1.21405 - 2.10279i) q^{76} +(-8.87298 - 15.3685i) q^{77} +(1.19520 - 2.07015i) q^{78} +(-6.71908 - 11.6378i) q^{79} +(0.887260 + 1.53678i) q^{80} +(-0.500000 + 0.866025i) q^{81} -0.632448 q^{82} +(-8.19331 - 14.1912i) q^{83} +(-1.87292 + 3.24400i) q^{84} +(4.22214 + 7.31296i) q^{85} +(3.14676 - 5.45034i) q^{86} +2.73750 q^{87} +(2.36875 + 4.10280i) q^{88} +(-7.04593 + 12.2039i) q^{89} +(0.887260 - 1.53678i) q^{90} -8.95408 q^{91} +(-4.36080 + 7.55313i) q^{92} +(-2.90277 - 5.02774i) q^{93} +(5.30059 + 9.18089i) q^{94} +4.30870 q^{95} +(0.500000 - 0.866025i) q^{96} +(-6.85370 - 11.8710i) q^{97} +7.03138 q^{98} +(2.36875 - 4.10280i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 14 q^{2} + 7 q^{3} + 14 q^{4} + 3 q^{5} + 7 q^{6} + 4 q^{7} + 14 q^{8} - 7 q^{9} + 3 q^{10} + 7 q^{11} + 7 q^{12} - 12 q^{13} + 4 q^{14} + 6 q^{15} + 14 q^{16} + 6 q^{17} - 7 q^{18} - 6 q^{19} + 3 q^{20}+ \cdots + 7 q^{99}+O(q^{100}) $ 14 * q + 14 * q^2 + 7 * q^3 + 14 * q^4 + 3 * q^5 + 7 * q^6 + 4 * q^7 + 14 * q^8 - 7 * q^9 + 3 * q^10 + 7 * q^11 + 7 * q^12 - 12 * q^13 + 4 * q^14 + 6 * q^15 + 14 * q^16 + 6 * q^17 - 7 * q^18 - 6 * q^19 + 3 * q^20 + 2 * q^21 + 7 * q^22 - 14 * q^23 + 7 * q^24 - 16 * q^25 - 12 * q^26 - 14 * q^27 + 4 * q^28 - 7 * q^29 + 6 * q^30 - 19 * q^31 + 14 * q^32 + 14 * q^33 + 6 * q^34 + q^35 - 7 * q^36 - 9 * q^37 - 6 * q^38 - 6 * q^39 + 3 * q^40 + 10 * q^41 + 2 * q^42 + 20 * q^43 + 7 * q^44 + 3 * q^45 - 14 * q^46 + q^47 + 7 * q^48 + 62 * q^49 - 16 * q^50 + 3 * q^51 - 12 * q^52 + 10 * q^53 - 14 * q^54 - 24 * q^55 + 4 * q^56 + 6 * q^57 - 7 * q^58 - 6 * q^59 + 6 * q^60 + 4 * q^61 - 19 * q^62 - 2 * q^63 + 14 * q^64 + 3 * q^65 + 14 * q^66 + 3 * q^67 + 6 * q^68 + 14 * q^69 + q^70 + 31 * q^71 - 7 * q^72 - 45 * q^73 - 9 * q^74 + 16 * q^75 - 6 * q^76 - 14 * q^77 - 6 * q^78 - 41 * q^79 + 3 * q^80 - 7 * q^81 + 10 * q^82 - q^83 + 2 * q^84 - 9 * q^85 + 20 * q^86 - 14 * q^87 + 7 * q^88 - 24 * q^89 + 3 * q^90 + 74 * q^91 - 14 * q^92 + 19 * q^93 + q^94 - 8 * q^95 + 7 * q^96 - 13 * q^97 + 62 * q^98 + 7 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1338\mathbb{Z}\right)^\times$.

$n$	$893$	$895$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	1.00000			0.500000
$5$	0.887260	+	1.53678i	0.396795	+	0.687268i	0.993328	−	0.115320i	$-0.0367892\pi$
$5$	0.887260	+	1.53678i	0.396795	+	0.687268i	−0.596534	+	0.802588i	$0.703456\pi$
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	−3.74585			−1.41580			−0.707899	−	0.706314i	$-0.750357\pi$
$7$	−3.74585			−1.41580			−0.707899	+	0.706314i	$0.750357\pi$
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.887260	+	1.53678i	0.280576	+	0.485972i
$11$	2.36875	+	4.10280i	0.714205	+	1.23704i	0.963265	+	0.268552i	$0.0865450\pi$
$11$	2.36875	+	4.10280i	0.714205	+	1.23704i	−0.249060	+	0.968488i	$0.580122\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	2.39040			0.662978			0.331489	−	0.943459i	$-0.392449\pi$
$13$	2.39040			0.662978			0.331489	+	0.943459i	$0.392449\pi$
$14$	−3.74585			−1.00112
$15$	1.77452			0.458179
$16$	1.00000			0.250000
$17$	4.75863			1.15414			0.577068	−	0.816696i	$-0.304197\pi$
$17$	4.75863			1.15414			0.577068	+	0.816696i	$0.304197\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	1.21405	−	2.10279i	0.278521	−	0.482413i	−0.692496	−	0.721422i	$-0.743489\pi$
$19$	1.21405	−	2.10279i	0.278521	−	0.482413i	0.971017	+	0.239008i	$0.0768224\pi$
$20$	0.887260	+	1.53678i	0.198397	+	0.343634i
$21$	−1.87292	+	3.24400i	−0.408706	+	0.707899i
$22$	2.36875	+	4.10280i	0.505019	+	0.874719i
$23$	−4.36080	+	7.55313i	−0.909291	+	1.57494i	−0.0942385	+	0.995550i	$0.530042\pi$
$23$	−4.36080	+	7.55313i	−0.909291	+	1.57494i	−0.815052	+	0.579388i	$0.803292\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	0.925541	−	1.60308i	0.185108	−	0.320617i
$26$	2.39040			0.468796
$27$	−1.00000			−0.192450
$28$	−3.74585			−0.707899
$29$	1.36875	+	2.37075i	0.254171	+	0.440236i	0.964670	−	0.263462i	$-0.0848642\pi$
$29$	1.36875	+	2.37075i	0.254171	+	0.440236i	−0.710499	+	0.703698i	$0.751531\pi$
$30$	1.77452			0.323981
$31$	2.90277	−	5.02774i	0.521353	−	0.903009i	−0.478339	−	0.878175i	$-0.658761\pi$
$31$	2.90277	−	5.02774i	0.521353	−	0.903009i	0.999692	−	0.0248338i	$-0.00790567\pi$
$32$	1.00000			0.176777
$33$	4.73750			0.824693
$34$	4.75863			0.816098
$35$	−3.32354	−	5.75654i	−0.561781	−	0.973033i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	4.83896	+	8.38133i	0.795520	+	1.37788i	0.922508	+	0.385977i	$0.126136\pi$
$37$	4.83896	+	8.38133i	0.795520	+	1.37788i	−0.126988	+	0.991904i	$0.540531\pi$
$38$	1.21405	−	2.10279i	0.196944	−	0.341118i
$39$	1.19520	−	2.07015i	0.191385	−	0.331489i
$40$	0.887260	+	1.53678i	0.140288	+	0.242986i
$41$	−0.632448			−0.0987717			−0.0493859	−	0.998780i	$-0.515726\pi$
$41$	−0.632448			−0.0987717			−0.0493859	+	0.998780i	$0.515726\pi$
$42$	−1.87292	+	3.24400i	−0.288998	+	0.500560i
$43$	3.14676	−	5.45034i	0.479876	−	0.831170i	−0.519857	−	0.854253i	$-0.674015\pi$
$43$	3.14676	−	5.45034i	0.479876	−	0.831170i	0.999734	+	0.0230833i	$0.00734828\pi$
$44$	2.36875	+	4.10280i	0.357103	+	0.618520i
$45$	0.887260	−	1.53678i	0.132265	−	0.229089i
$46$	−4.36080	+	7.55313i	−0.642966	+	1.11365i
$47$	5.30059	+	9.18089i	0.773171	+	1.33917i	0.935817	+	0.352486i	$0.114664\pi$
$47$	5.30059	+	9.18089i	0.773171	+	1.33917i	−0.162646	+	0.986684i	$0.552003\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	7.03138			1.00448
$50$	0.925541	−	1.60308i	0.130891	−	0.226710i
$51$	2.37931	−	4.12109i	0.333171	−	0.577068i
$52$	2.39040			0.331489
$53$	−0.401996	−	0.696278i	−0.0552184	−	0.0956411i	0.837095	−	0.547058i	$-0.184252\pi$
$53$	−0.401996	−	0.696278i	−0.0552184	−	0.0956411i	−0.892313	+	0.451417i	$0.850919\pi$
$54$	−1.00000			−0.136083
$55$	−4.20339	+	7.28049i	−0.566785	+	0.981701i
$56$	−3.74585			−0.500560
$57$	−1.21405	−	2.10279i	−0.160804	−	0.278521i
$58$	1.36875	+	2.37075i	0.179726	+	0.311294i
$59$	−0.772969			−0.100632			−0.0503160	−	0.998733i	$-0.516023\pi$
$59$	−0.772969			−0.100632			−0.0503160	+	0.998733i	$0.516023\pi$
$60$	1.77452			0.229089
$61$	−2.78610	+	4.82566i	−0.356723	+	0.617863i	−0.987411	−	0.158174i	$-0.949439\pi$
$61$	−2.78610	+	4.82566i	−0.356723	+	0.617863i	0.630688	+	0.776037i	$0.282773\pi$
$62$	2.90277	−	5.02774i	0.368652	−	0.638524i
$63$	1.87292	+	3.24400i	0.235966	+	0.408706i
$64$	1.00000			0.125000
$65$	2.12091	+	3.67352i	0.263066	+	0.455644i
$66$	4.73750			0.583146
$67$	−2.20654	+	3.82184i	−0.269572	+	0.466912i	−0.968751	−	0.248034i	$-0.920215\pi$
$67$	−2.20654	+	3.82184i	−0.269572	+	0.466912i	0.699180	+	0.714946i	$0.253549\pi$
$68$	4.75863			0.577068
$69$	4.36080	+	7.55313i	0.524979	+	0.909291i
$70$	−3.32354	−	5.75654i	−0.397239	−	0.688038i
$71$	0.965893	−	1.67297i	0.114630	−	0.198546i	−0.803002	−	0.595977i	$-0.796765\pi$
$71$	0.965893	−	1.67297i	0.114630	−	0.198546i	0.917632	+	0.397431i	$0.130098\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	−8.22631	−	14.2484i	−0.962817	−	1.66765i	−0.715369	−	0.698746i	$-0.753742\pi$
$73$	−8.22631	−	14.2484i	−0.962817	−	1.66765i	−0.247447	−	0.968901i	$-0.579592\pi$
$74$	4.83896	+	8.38133i	0.562518	+	0.974309i
$75$	−0.925541	−	1.60308i	−0.106872	−	0.185108i
$76$	1.21405	−	2.10279i	0.139261	−	0.241207i
$77$	−8.87298	−	15.3685i	−1.01117	−	1.75140i
$78$	1.19520	−	2.07015i	0.135330	−	0.234398i
$79$	−6.71908	−	11.6378i	−0.755956	−	1.30935i	−0.944898	−	0.327366i	$-0.893839\pi$
$79$	−6.71908	−	11.6378i	−0.755956	−	1.30935i	0.188942	−	0.981988i	$-0.439494\pi$
$80$	0.887260	+	1.53678i	0.0991986	+	0.171817i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−0.632448			−0.0698421
$83$	−8.19331	−	14.1912i	−0.899333	−	1.55769i	−0.828349	−	0.560213i	$-0.810719\pi$
$83$	−8.19331	−	14.1912i	−0.899333	−	1.55769i	−0.0709840	−	0.997477i	$-0.522614\pi$
$84$	−1.87292	+	3.24400i	−0.204353	+	0.353949i
$85$	4.22214	+	7.31296i	0.457955	+	0.793202i
$86$	3.14676	−	5.45034i	0.339324	−	0.587726i
$87$	2.73750			0.293491
$88$	2.36875	+	4.10280i	0.252510	+	0.437360i
$89$	−7.04593	+	12.2039i	−0.746867	+	1.29361i	0.202450	+	0.979293i	$0.435110\pi$
$89$	−7.04593	+	12.2039i	−0.746867	+	1.29361i	−0.949317	+	0.314320i	$0.898224\pi$
$90$	0.887260	−	1.53678i	0.0935254	−	0.161991i
$91$	−8.95408			−0.938643
$92$	−4.36080	+	7.55313i	−0.454645	+	0.787469i
$93$	−2.90277	−	5.02774i	−0.301003	−	0.521353i
$94$	5.30059	+	9.18089i	0.546714	+	0.946937i
$95$	4.30870			0.442063
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	−6.85370	−	11.8710i	−0.695888	−	1.20531i	−0.969881	−	0.243581i	$-0.921678\pi$
$97$	−6.85370	−	11.8710i	−0.695888	−	1.20531i	0.273993	−	0.961732i	$-0.411655\pi$
$98$	7.03138			0.710276
$99$	2.36875	−	4.10280i	0.238068	−	0.412347i
$100$	0.925541	−	1.60308i	0.0925541	−	0.160308i
$101$	9.00074	−	15.5897i	0.895607	−	1.55124i	0.0625550	−	0.998042i	$-0.480075\pi$
$101$	9.00074	−	15.5897i	0.895607	−	1.55124i	0.833052	−	0.553195i	$-0.186592\pi$
$102$	2.37931	−	4.12109i	0.235587	−	0.408049i
$103$	−2.30804			−0.227418			−0.113709	−	0.993514i	$-0.536273\pi$
$103$	−2.30804			−0.227418			−0.113709	+	0.993514i	$0.536273\pi$
$104$	2.39040			0.234398
$105$	−6.64708			−0.648689
$106$	−0.401996	−	0.696278i	−0.0390453	−	0.0676285i
$107$	0.952509	+	1.64979i	0.0920825	+	0.159492i	0.908387	−	0.418130i	$-0.137314\pi$
$107$	0.952509	+	1.64979i	0.0920825	+	0.159492i	−0.816305	+	0.577621i	$0.803981\pi$
$108$	−1.00000			−0.0962250
$109$	5.57998	+	9.66480i	0.534465	+	0.925720i	0.999189	+	0.0402647i	$0.0128201\pi$
$109$	5.57998	+	9.66480i	0.534465	+	0.925720i	−0.464724	+	0.885455i	$0.653847\pi$
$110$	−4.20339	+	7.28049i	−0.400778	+	0.694168i
$111$	9.67792			0.918588
$112$	−3.74585			−0.353949
$113$	0.0278961	−	0.0483175i	0.00262424	−	0.00454533i	−0.864710	−	0.502271i	$-0.832498\pi$
$113$	0.0278961	−	0.0483175i	0.00262424	−	0.00454533i	0.867335	+	0.497726i	$0.165831\pi$
$114$	−1.21405	−	2.10279i	−0.113706	−	0.196944i
$115$	−15.4767			−1.44321
$116$	1.36875	+	2.37075i	0.127085	+	0.220118i
$117$	−1.19520	−	2.07015i	−0.110496	−	0.191385i
$118$	−0.772969			−0.0711575
$119$	−17.8251			−1.63402
$120$	1.77452			0.161991
$121$	−5.72196	+	9.91072i	−0.520178	+	0.900975i
$122$	−2.78610	+	4.82566i	−0.252242	+	0.436895i
$123$	−0.316224	+	0.547716i	−0.0285129	+	0.0493859i
$124$	2.90277	−	5.02774i	0.260676	−	0.451505i
$125$	12.1574			1.08739
$126$	1.87292	+	3.24400i	0.166853	+	0.288998i
$127$	−9.70566	+	16.8107i	−0.861238	+	1.49171i	0.00949578	+	0.999955i	$0.496977\pi$
$127$	−9.70566	+	16.8107i	−0.861238	+	1.49171i	−0.870734	+	0.491754i	$0.836356\pi$
$128$	1.00000			0.0883883
$129$	−3.14676	−	5.45034i	−0.277057	−	0.479876i
$130$	2.12091	+	3.67352i	0.186016	+	0.322189i
$131$	−0.740902	+	1.28328i	−0.0647329	+	0.112121i	−0.896575	−	0.442891i	$-0.853953\pi$
$131$	−0.740902	+	1.28328i	−0.0647329	+	0.112121i	0.831843	+	0.555012i	$0.187286\pi$
$132$	4.73750			0.412347
$133$	−4.54763	+	7.87673i	−0.394330	+	0.682999i
$134$	−2.20654	+	3.82184i	−0.190616	+	0.330157i
$135$	−0.887260	−	1.53678i	−0.0763632	−	0.132265i
$136$	4.75863			0.408049
$137$	7.78257	−	13.4798i	0.664910	−	1.15166i	−0.314400	−	0.949291i	$-0.601803\pi$
$137$	7.78257	−	13.4798i	0.664910	−	1.15166i	0.979310	−	0.202367i	$-0.0648635\pi$
$138$	4.36080	+	7.55313i	0.371216	+	0.642966i
$139$	−4.96109	+	8.59286i	−0.420794	+	0.728837i	−0.996017	−	0.0891598i	$-0.971582\pi$
$139$	−4.96109	+	8.59286i	−0.420794	+	0.728837i	0.575223	+	0.817996i	$0.304915\pi$
$140$	−3.32354	−	5.75654i	−0.280890	−	0.486516i
$141$	10.6012			0.892781
$142$	0.965893	−	1.67297i	0.0810559	−	0.140393i
$143$	5.66227	+	9.80733i	0.473502	+	0.820130i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−2.42887	+	4.20693i	−0.201707	+	0.349367i
$146$	−8.22631	−	14.2484i	−0.680814	−	1.17921i
$147$	3.51569	−	6.08935i	0.289969	−	0.502241i
$148$	4.83896	+	8.38133i	0.397760	+	0.688941i
$149$	3.99258	+	6.91535i	0.327085	+	0.566528i	0.981932	−	0.189234i	$-0.0606004\pi$
$149$	3.99258	+	6.91535i	0.327085	+	0.566528i	−0.654847	+	0.755761i	$0.727267\pi$
$150$	−0.925541	−	1.60308i	−0.0755701	−	0.130891i
$151$	−5.95146	−	10.3082i	−0.484323	−	0.838872i	0.515515	−	0.856881i	$-0.327601\pi$
$151$	−5.95146	−	10.3082i	−0.484323	−	0.838872i	−0.999838	+	0.0180089i	$0.994267\pi$
$152$	1.21405	−	2.10279i	0.0984722	−	0.170559i
$153$	−2.37931	−	4.12109i	−0.192356	−	0.333171i
$154$	−8.87298	−	15.3685i	−0.715005	−	1.23843i
$155$	10.3020			0.827479
$156$	1.19520	−	2.07015i	0.0956927	−	0.165745i
$157$	3.63665			0.290236			0.145118	−	0.989414i	$-0.453644\pi$
$157$	3.63665			0.290236			0.145118	+	0.989414i	$0.453644\pi$
$158$	−6.71908	−	11.6378i	−0.534541	−	0.925853i
$159$	−0.803992			−0.0637607
$160$	0.887260	+	1.53678i	0.0701440	+	0.121493i
$161$	16.3349	−	28.2929i	1.28737	−	2.22979i
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	6.95712			0.544923			0.272462	−	0.962167i	$-0.412162\pi$
$163$	6.95712			0.544923			0.272462	+	0.962167i	$0.412162\pi$
$164$	−0.632448			−0.0493859
$165$	4.20339	+	7.28049i	0.327234	+	0.566785i
$166$	−8.19331	−	14.1912i	−0.635924	−	1.10145i
$167$	−18.8502			−1.45867			−0.729337	−	0.684155i	$-0.760171\pi$
$167$	−18.8502			−1.45867			−0.729337	+	0.684155i	$0.760171\pi$
$168$	−1.87292	+	3.24400i	−0.144499	+	0.250280i
$169$	−7.28598			−0.560460
$170$	4.22214	+	7.31296i	0.323823	+	0.560878i
$171$	−2.42809			−0.185681
$172$	3.14676	−	5.45034i	0.239938	−	0.415585i
$173$	9.13704	−	15.8258i	0.694676	−	1.20321i	−0.275614	−	0.961268i	$-0.588881\pi$
$173$	9.13704	−	15.8258i	0.694676	−	1.20321i	0.970290	−	0.241946i	$-0.0777856\pi$
$174$	2.73750			0.207529
$175$	−3.46693	+	6.00491i	−0.262076	+	0.453928i
$176$	2.36875	+	4.10280i	0.178551	+	0.309260i
$177$	−0.386484	+	0.669411i	−0.0290499	+	0.0503160i
$178$	−7.04593	+	12.2039i	−0.528115	+	0.914722i
$179$	1.31142	+	2.27145i	0.0980201	+	0.169776i	0.910865	−	0.412704i	$-0.135416\pi$
$179$	1.31142	+	2.27145i	0.0980201	+	0.169776i	−0.812845	+	0.582480i	$0.802082\pi$
$180$	0.887260	−	1.53678i	0.0661324	−	0.114545i
$181$	9.83095	−	17.0277i	0.730729	−	1.26566i	−0.225844	−	0.974164i	$-0.572514\pi$
$181$	9.83095	−	17.0277i	0.730729	−	1.26566i	0.956572	−	0.291495i	$-0.0941528\pi$
$182$	−8.95408			−0.663721
$183$	2.78610	+	4.82566i	0.205954	+	0.356723i
$184$	−4.36080	+	7.55313i	−0.321483	+	0.556824i
$185$	−8.58683	+	14.8728i	−0.631316	+	1.09347i
$186$	−2.90277	−	5.02774i	−0.212841	−	0.368652i
$187$	11.2720	+	19.5237i	0.824290	+	1.42771i
$188$	5.30059	+	9.18089i	0.386585	+	0.669585i
$189$	3.74585			0.272470
$190$	4.30870			0.312586
$191$	−8.84394			−0.639925			−0.319963	−	0.947430i	$-0.603670\pi$
$191$	−8.84394			−0.639925			−0.319963	+	0.947430i	$0.603670\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−10.4172			−0.749844			−0.374922	−	0.927056i	$-0.622331\pi$
$193$	−10.4172			−0.749844			−0.374922	+	0.927056i	$0.622331\pi$
$194$	−6.85370	−	11.8710i	−0.492067	−	0.852285i
$195$	4.24181			0.303763
$196$	7.03138			0.502241
$197$	10.6771			0.760713			0.380356	−	0.924840i	$-0.375801\pi$
$197$	10.6771			0.760713			0.380356	+	0.924840i	$0.375801\pi$
$198$	2.36875	−	4.10280i	0.168340	−	0.291573i
$199$	0.216180	−	0.374435i	0.0153246	−	0.0265430i	−0.858261	−	0.513213i	$-0.828455\pi$
$199$	0.216180	−	0.374435i	0.0153246	−	0.0265430i	0.873586	+	0.486670i	$0.161788\pi$
$200$	0.925541	−	1.60308i	0.0654456	−	0.113355i
$201$	2.20654	+	3.82184i	0.155637	+	0.269572i
$202$	9.00074	−	15.5897i	0.633290	−	1.09689i
$203$	−5.12713	−	8.88045i	−0.359854	−	0.623286i
$204$	2.37931	−	4.12109i	0.166585	−	0.288534i
$205$	−0.561145	−	0.971932i	−0.0391921	−	0.0678827i
$206$	−2.30804			−0.160809
$207$	8.72161			0.606194
$208$	2.39040			0.165745
$209$	11.5031			0.795685
$210$	−6.64708			−0.458692
$211$	2.78934	−	4.83127i	0.192026	−	0.332598i	−0.753896	−	0.656994i	$-0.771828\pi$
$211$	2.78934	−	4.83127i	0.192026	−	0.332598i	0.945921	+	0.324396i	$0.105161\pi$
$212$	−0.401996	−	0.696278i	−0.0276092	−	0.0478205i
$213$	−0.965893	−	1.67297i	−0.0661819	−	0.114630i
$214$	0.952509	+	1.64979i	0.0651122	+	0.112778i
$215$	11.1680			0.761649
$216$	−1.00000			−0.0680414
$217$	−10.8733	+	18.8332i	−0.738130	+	1.27848i
$218$	5.57998	+	9.66480i	0.377924	+	0.654583i
$219$	−16.4526			−1.11177
$220$	−4.20339	+	7.28049i	−0.283393	+	0.490851i
$221$	11.3750			0.765167
$222$	9.67792			0.649540
$223$	0.344793	+	14.9292i	0.0230890	+	0.999733i
$223$	0.344793	+	14.9292i	0.0230890	+	0.999733i
$224$	−3.74585			−0.250280
$225$	−1.85108			−0.123405
$226$	0.0278961	−	0.0483175i	0.00185562	−	0.00321403i
$227$	−6.99895			−0.464537			−0.232268	−	0.972652i	$-0.574615\pi$
$227$	−6.99895			−0.464537			−0.232268	+	0.972652i	$0.574615\pi$
$228$	−1.21405	−	2.10279i	−0.0804022	−	0.139261i
$229$	10.9526	−	18.9705i	0.723769	−	1.25361i	−0.235709	−	0.971824i	$-0.575741\pi$
$229$	10.9526	−	18.9705i	0.723769	−	1.25361i	0.959479	−	0.281782i	$-0.0909254\pi$
$230$	−15.4767			−1.02050
$231$	−17.7460			−1.16760
$232$	1.36875	+	2.37075i	0.0898629	+	0.155647i
$233$	8.65849	+	14.9970i	0.567237	+	0.982483i	0.996838	+	0.0794641i	$0.0253209\pi$
$233$	8.65849	+	14.9970i	0.567237	+	0.982483i	−0.429601	+	0.903019i	$0.641346\pi$
$234$	−1.19520	−	2.07015i	−0.0781327	−	0.135330i
$235$	−9.40600	+	16.2917i	−0.613580	+	1.06275i
$236$	−0.772969			−0.0503160
$237$	−13.4382			−0.872903
$238$	−17.8251			−1.15543
$239$	−18.4003			−1.19022			−0.595108	−	0.803646i	$-0.702891\pi$
$239$	−18.4003			−1.19022			−0.595108	+	0.803646i	$0.702891\pi$
$240$	1.77452			0.114545
$241$	1.57469	+	2.72745i	0.101435	+	0.175691i	0.912276	−	0.409576i	$-0.134323\pi$
$241$	1.57469	+	2.72745i	0.101435	+	0.175691i	−0.810841	+	0.585266i	$0.800990\pi$
$242$	−5.72196	+	9.91072i	−0.367821	+	0.637085i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−2.78610	+	4.82566i	−0.178362	+	0.308932i
$245$	6.23866	+	10.8057i	0.398573	+	0.690349i
$246$	−0.316224	+	0.547716i	−0.0201617	+	0.0349211i
$247$	2.90206	−	5.02651i	0.184654	−	0.319829i
$248$	2.90277	−	5.02774i	0.184326	−	0.319262i
$249$	−16.3866			−1.03846
$250$	12.1574			0.768900
$251$	−17.4639			−1.10231			−0.551156	−	0.834402i	$-0.685813\pi$
$251$	−17.4639			−1.10231			−0.551156	+	0.834402i	$0.685813\pi$
$252$	1.87292	+	3.24400i	0.117983	+	0.204353i
$253$	−41.3186			−2.59768
$254$	−9.70566	+	16.8107i	−0.608988	+	1.05480i
$255$	8.44428			0.528801
$256$	1.00000			0.0625000
$257$	1.19413			0.0744879			0.0372440	−	0.999306i	$-0.488142\pi$
$257$	1.19413			0.0744879			0.0372440	+	0.999306i	$0.488142\pi$
$258$	−3.14676	−	5.45034i	−0.195909	−	0.339324i
$259$	−18.1260	−	31.3952i	−1.12630	−	1.95080i
$260$	2.12091	+	3.67352i	0.131533	+	0.227822i
$261$	1.36875	−	2.37075i	0.0847235	−	0.146745i
$262$	−0.740902	+	1.28328i	−0.0457731	+	0.0792813i
$263$	−10.2134	−	17.6900i	−0.629782	−	1.09081i	−0.987595	−	0.157022i	$-0.949811\pi$
$263$	−10.2134	−	17.6900i	−0.629782	−	1.09081i	0.357813	−	0.933793i	$-0.383523\pi$
$264$	4.73750			0.291573
$265$	0.713350	−	1.23556i	0.0438207	−	0.0758997i
$266$	−4.54763	+	7.87673i	−0.278833	+	0.482953i
$267$	7.04593	+	12.2039i	0.431204	+	0.746867i
$268$	−2.20654	+	3.82184i	−0.134786	+	0.233456i
$269$	−2.79455	+	4.84030i	−0.170387	+	0.295118i	−0.938555	−	0.345130i	$-0.887835\pi$
$269$	−2.79455	+	4.84030i	−0.170387	+	0.295118i	0.768169	+	0.640248i	$0.221168\pi$
$270$	−0.887260	−	1.53678i	−0.0539969	−	0.0935254i
$271$	11.4081	−	19.7594i	0.692992	−	1.20030i	−0.277861	−	0.960621i	$-0.589626\pi$
$271$	11.4081	−	19.7594i	0.692992	−	1.20030i	0.970853	−	0.239676i	$-0.0770411\pi$
$272$	4.75863			0.288534
$273$	−4.47704	+	7.75446i	−0.270963	+	0.469321i
$274$	7.78257	−	13.4798i	0.470162	−	0.814345i
$275$	8.76950			0.528821
$276$	4.36080	+	7.55313i	0.262490	+	0.454645i
$277$	−14.4006			−0.865249			−0.432624	−	0.901574i	$-0.642412\pi$
$277$	−14.4006			−0.865249			−0.432624	+	0.901574i	$0.642412\pi$
$278$	−4.96109	+	8.59286i	−0.297546	+	0.515365i
$279$	−5.80554			−0.347568
$280$	−3.32354	−	5.75654i	−0.198619	−	0.344019i
$281$	−15.7826	−	27.3363i	−0.941512	−	1.63075i	−0.762589	−	0.646884i	$-0.776072\pi$
$281$	−15.7826	−	27.3363i	−0.941512	−	1.63075i	−0.178923	−	0.983863i	$-0.557261\pi$
$282$	10.6012			0.631291
$283$	13.8005			0.820356			0.410178	−	0.912006i	$-0.365467\pi$
$283$	13.8005			0.820356			0.410178	+	0.912006i	$0.365467\pi$
$284$	0.965893	−	1.67297i	0.0573152	−	0.0992728i
$285$	2.15435	−	3.73144i	0.127613	−	0.221032i
$286$	5.66227	+	9.80733i	0.334817	+	0.579920i
$287$	2.36905			0.139841
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	5.64453			0.332031
$290$	−2.42887	+	4.20693i	−0.142628	+	0.247040i
$291$	−13.7074			−0.803542
$292$	−8.22631	−	14.2484i	−0.481408	−	0.833824i
$293$	9.59900	+	16.6260i	0.560780	+	0.971299i	0.997429	+	0.0716669i	$0.0228319\pi$
$293$	9.59900	+	16.6260i	0.560780	+	0.971299i	−0.436649	+	0.899632i	$0.643835\pi$
$294$	3.51569	−	6.08935i	0.205039	−	0.355138i
$295$	−0.685824	−	1.18788i	−0.0399302	−	0.0691612i
$296$	4.83896	+	8.38133i	0.281259	+	0.487155i
$297$	−2.36875	−	4.10280i	−0.137449	−	0.238068i
$298$	3.99258	+	6.91535i	0.231284	+	0.400596i
$299$	−10.4241	+	18.0550i	−0.602840	+	1.04415i
$300$	−0.925541	−	1.60308i	−0.0534361	−	0.0925541i
$301$	−11.7873	+	20.4162i	−0.679407	+	1.17677i
$302$	−5.95146	−	10.3082i	−0.342468	−	0.593172i
$303$	−9.00074	−	15.5897i	−0.517079	−	0.895607i
$304$	1.21405	−	2.10279i	0.0696303	−	0.120603i
$305$	−9.88797			−0.566184
$306$	−2.37931	−	4.12109i	−0.136016	−	0.235587i
$307$	−1.57486	+	2.72774i	−0.0898822	+	0.155681i	−0.907461	−	0.420136i	$-0.861982\pi$
$307$	−1.57486	+	2.72774i	−0.0898822	+	0.155681i	0.817579	+	0.575816i	$0.195316\pi$
$308$	−8.87298	−	15.3685i	−0.505585	−	0.875699i
$309$	−1.15402	+	1.99882i	−0.0656498	+	0.113709i
$310$	10.3020			0.585116
$311$	−6.93960	−	12.0197i	−0.393509	−	0.681577i	0.599401	−	0.800449i	$-0.295406\pi$
$311$	−6.93960	−	12.0197i	−0.393509	−	0.681577i	−0.992910	+	0.118872i	$0.962072\pi$
$312$	1.19520	−	2.07015i	0.0676649	−	0.117199i
$313$	−15.3020	+	26.5038i	−0.864920	+	1.49809i	0.00220623	+	0.999998i	$0.499298\pi$
$313$	−15.3020	+	26.5038i	−0.864920	+	1.49809i	−0.867126	+	0.498088i	$0.834036\pi$
$314$	3.63665			0.205228
$315$	−3.32354	+	5.75654i	−0.187260	+	0.324344i
$316$	−6.71908	−	11.6378i	−0.377978	−	0.654677i
$317$	−3.77596	−	6.54015i	−0.212079	−	0.367332i	0.740286	−	0.672292i	$-0.234690\pi$
$317$	−3.77596	−	6.54015i	−0.212079	−	0.367332i	−0.952365	+	0.304961i	$0.901357\pi$
$318$	−0.803992			−0.0450856
$319$	−6.48446	+	11.2314i	−0.363060	+	0.628838i
$320$	0.887260	+	1.53678i	0.0495993	+	0.0859085i
$321$	1.90502			0.106328
$322$	16.3349	−	28.2929i	0.910309	−	1.57670i
$323$	5.77719	−	10.0064i	0.321452	−	0.556771i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	2.21241	−	3.83201i	0.122723	−	0.212562i
$326$	6.95712			0.385319
$327$	11.1600			0.617147
$328$	−0.632448			−0.0349211
$329$	−19.8552	−	34.3902i	−1.09465	−	1.89599i
$330$	4.20339	+	7.28049i	0.231389	+	0.400778i
$331$	6.63419			0.364648			0.182324	−	0.983238i	$-0.441638\pi$
$331$	6.63419			0.364648			0.182324	+	0.983238i	$0.441638\pi$
$332$	−8.19331	−	14.1912i	−0.449666	−	0.778845i
$333$	4.83896	−	8.38133i	0.265173	−	0.459294i
$334$	−18.8502			−1.03144
$335$	−7.83109			−0.427858
$336$	−1.87292	+	3.24400i	−0.102176	+	0.176975i
$337$	10.5094	+	18.2029i	0.572485	+	0.991574i	0.996310	+	0.0858296i	$0.0273541\pi$
$337$	10.5094	+	18.2029i	0.572485	+	0.991574i	−0.423824	+	0.905744i	$0.639313\pi$
$338$	−7.28598			−0.396305
$339$	−0.0278961	−	0.0483175i	−0.00151511	−	0.00262424i
$340$	4.22214	+	7.31296i	0.228978	+	0.396601i
$341$	27.5037			1.48941
$342$	−2.42809			−0.131296
$343$	−0.117532			−0.00634611
$344$	3.14676	−	5.45034i	0.169662	−	0.293863i
$345$	−7.73833	+	13.4032i	−0.416618	+	0.721603i
$346$	9.13704	−	15.8258i	0.491210	−	0.850801i
$347$	1.71558	−	2.97147i	0.0920970	−	0.159517i	−0.816296	−	0.577633i	$-0.803976\pi$
$347$	1.71558	−	2.97147i	0.0920970	−	0.159517i	0.908393	+	0.418117i	$0.137310\pi$
$348$	2.73750			0.146745
$349$	2.22641	+	3.85625i	0.119177	+	0.206420i	0.919442	−	0.393226i	$-0.128641\pi$
$349$	2.22641	+	3.85625i	0.119177	+	0.206420i	−0.800265	+	0.599647i	$0.795308\pi$
$350$	−3.46693	+	6.00491i	−0.185315	+	0.320976i
$351$	−2.39040			−0.127590
$352$	2.36875	+	4.10280i	0.126255	+	0.218680i
$353$	−4.81975	−	8.34806i	−0.256530	−	0.444322i	0.708780	−	0.705429i	$-0.249246\pi$
$353$	−4.81975	−	8.34806i	−0.256530	−	0.444322i	−0.965310	+	0.261107i	$0.915912\pi$
$354$	−0.386484	+	0.669411i	−0.0205414	+	0.0355788i
$355$	3.42799			0.181939
$356$	−7.04593	+	12.2039i	−0.373434	+	0.646806i
$357$	−8.91255	+	15.4370i	−0.471702	+	0.817012i
$358$	1.31142	+	2.27145i	0.0693107	+	0.120050i
$359$	30.0913			1.58816			0.794079	−	0.607814i	$-0.207953\pi$
$359$	30.0913			1.58816			0.794079	+	0.607814i	$0.207953\pi$
$360$	0.887260	−	1.53678i	0.0467627	−	0.0809954i
$361$	6.55218	+	11.3487i	0.344852	+	0.597301i
$362$	9.83095	−	17.0277i	0.516703	−	0.894956i
$363$	5.72196	+	9.91072i	0.300325	+	0.520178i
$364$	−8.95408			−0.469321
$365$	14.5977	−	25.2840i	0.764081	−	1.32343i
$366$	2.78610	+	4.82566i	0.145632	+	0.252242i
$367$	4.75430	+	8.23468i	0.248172	+	0.429847i	0.963019	−	0.269435i	$-0.0868368\pi$
$367$	4.75430	+	8.23468i	0.248172	+	0.429847i	−0.714847	+	0.699281i	$0.753503\pi$
$368$	−4.36080	+	7.55313i	−0.227323	+	0.393734i
$369$	0.316224	+	0.547716i	0.0164620	+	0.0285129i
$370$	−8.58683	+	14.8728i	−0.446408	+	0.773201i
$371$	1.50582	+	2.60815i	0.0781781	+	0.135408i
$372$	−2.90277	−	5.02774i	−0.150502	−	0.260676i
$373$	−9.70475	−	16.8091i	−0.502493	−	0.870343i	−0.999996	−	0.00288109i	$-0.999083\pi$
$373$	−9.70475	−	16.8091i	−0.502493	−	0.870343i	0.497503	−	0.867462i	$-0.334250\pi$
$374$	11.2720	+	19.5237i	0.582861	+	1.00955i
$375$	6.07869	−	10.5286i	0.313902	−	0.543694i
$376$	5.30059	+	9.18089i	0.273357	+	0.473468i
$377$	3.27186	+	5.66703i	0.168510	+	0.291867i
$378$	3.74585			0.192666
$379$	0.939270	−	1.62686i	0.0482471	−	0.0835664i	−0.840893	−	0.541201i	$-0.817970\pi$
$379$	0.939270	−	1.62686i	0.0482471	−	0.0835664i	0.889140	+	0.457635i	$0.151303\pi$
$380$	4.30870			0.221032
$381$	9.70566	+	16.8107i	0.497236	+	0.861238i
$382$	−8.84394			−0.452496
$383$	−2.17888	−	3.77392i	−0.111335	−	0.192839i	0.804974	−	0.593311i	$-0.202179\pi$
$383$	−2.17888	−	3.77392i	−0.111335	−	0.192839i	−0.916309	+	0.400472i	$0.868846\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	15.7453	−	27.2716i	0.802453	−	1.38989i
$386$	−10.4172			−0.530220
$387$	−6.29352			−0.319917
$388$	−6.85370	−	11.8710i	−0.347944	−	0.602656i
$389$	12.8343	+	22.2297i	0.650726	+	1.12709i	0.982947	+	0.183888i	$0.0588685\pi$
$389$	12.8343	+	22.2297i	0.650726	+	1.12709i	−0.332222	+	0.943201i	$0.607798\pi$
$390$	4.24181			0.214793
$391$	−20.7514	+	35.9425i	−1.04945	+	1.81769i
$392$	7.03138			0.355138
$393$	0.740902	+	1.28328i	0.0373736	+	0.0647329i
$394$	10.6771			0.537905
$395$	11.9231	−	20.6515i	0.599918	−	1.03909i
$396$	2.36875	−	4.10280i	0.119034	−	0.206173i
$397$	21.8495			1.09659			0.548297	−	0.836283i	$-0.315276\pi$
$397$	21.8495			1.09659			0.548297	+	0.836283i	$0.315276\pi$
$398$	0.216180	−	0.374435i	0.0108361	−	0.0187687i
$399$	4.54763	+	7.87673i	0.227666	+	0.394330i
$400$	0.925541	−	1.60308i	0.0462770	−	0.0801542i
$401$	7.09149	−	12.2828i	0.354132	−	0.613375i	−0.632837	−	0.774285i	$-0.718110\pi$
$401$	7.09149	−	12.2828i	0.354132	−	0.613375i	0.986969	+	0.160910i	$0.0514429\pi$
$402$	2.20654	+	3.82184i	0.110052	+	0.190616i
$403$	6.93878	−	12.0183i	0.345645	−	0.598675i
$404$	9.00074	−	15.5897i	0.447803	−	0.775618i
$405$	−1.77452			−0.0881766
$406$	−5.12713	−	8.88045i	−0.254455	−	0.440729i
$407$	−22.9246	+	39.7065i	−1.13633	+	1.96818i
$408$	2.37931	−	4.12109i	0.117794	−	0.204024i
$409$	−18.2433	−	31.5984i	−0.902075	−	1.56244i	−0.824797	−	0.565429i	$-0.808711\pi$
$409$	−18.2433	−	31.5984i	−0.902075	−	1.56244i	−0.0772778	−	0.997010i	$-0.524623\pi$
$410$	−0.561145	−	0.971932i	−0.0277130	−	0.0480003i
$411$	−7.78257	−	13.4798i	−0.383886	−	0.664910i
$412$	−2.30804			−0.113709
$413$	2.89542			0.142474
$414$	8.72161			0.428644
$415$	14.5392	−	25.1826i	0.713701	−	1.23617i
$416$	2.39040			0.117199
$417$	4.96109	+	8.59286i	0.242946	+	0.420794i
$418$	11.5031			0.562635
$419$	3.27422			0.159956			0.0799781	−	0.996797i	$-0.474515\pi$
$419$	3.27422			0.159956			0.0799781	+	0.996797i	$0.474515\pi$
$420$	−6.64708			−0.324344
$421$	7.43351	−	12.8752i	0.362287	−	0.627499i	−0.626050	−	0.779783i	$-0.715329\pi$
$421$	7.43351	−	12.8752i	0.362287	−	0.627499i	0.988337	+	0.152284i	$0.0486627\pi$
$422$	2.78934	−	4.83127i	0.135783	−	0.235183i
$423$	5.30059	−	9.18089i	0.257724	−	0.446390i
$424$	−0.401996	−	0.696278i	−0.0195227	−	0.0338142i
$425$	4.40430	−	7.62848i	0.213640	−	0.370035i
$426$	−0.965893	−	1.67297i	−0.0467976	−	0.0810559i
$427$	10.4363	−	18.0762i	0.505048	−	0.874769i
$428$	0.952509	+	1.64979i	0.0460412	+	0.0797458i
$429$	11.3245			0.546754
$430$	11.1680			0.538567
$431$	18.7446			0.902897			0.451449	−	0.892297i	$-0.350907\pi$
$431$	18.7446			0.902897			0.451449	+	0.892297i	$0.350907\pi$
$432$	−1.00000			−0.0481125
$433$	−36.0021			−1.73015			−0.865074	−	0.501644i	$-0.832729\pi$
$433$	−36.0021			−1.73015			−0.865074	+	0.501644i	$0.832729\pi$
$434$	−10.8733	+	18.8332i	−0.521936	+	0.904020i
$435$	2.42887	+	4.20693i	0.116456	+	0.201707i
$436$	5.57998	+	9.66480i	0.267232	+	0.462860i
$437$	10.5884	+	18.3397i	0.506514	+	0.877307i
$438$	−16.4526			−0.786137
$439$	1.35629			0.0647322			0.0323661	−	0.999476i	$-0.489696\pi$
$439$	1.35629			0.0647322			0.0323661	+	0.999476i	$0.489696\pi$
$440$	−4.20339	+	7.28049i	−0.200389	+	0.347084i
$441$	−3.51569	−	6.08935i	−0.167414	−	0.289969i
$442$	11.3750			0.541055
$443$	−13.9058	+	24.0855i	−0.660684	+	1.14434i	0.319753	+	0.947501i	$0.396400\pi$
$443$	−13.9058	+	24.0855i	−0.660684	+	1.14434i	−0.980436	+	0.196837i	$0.936933\pi$
$444$	9.67792			0.459294
$445$	−25.0063			−1.18541
$446$	0.344793	+	14.9292i	0.0163264	+	0.706918i
$447$	7.98516			0.377685
$448$	−3.74585			−0.176975
$449$	1.51834	−	2.62983i	0.0716547	−	0.124110i	−0.827972	−	0.560770i	$-0.810505\pi$
$449$	1.51834	−	2.62983i	0.0716547	−	0.124110i	0.899627	+	0.436660i	$0.143839\pi$
$450$	−1.85108			−0.0872608
$451$	−1.49811	−	2.59480i	−0.0705433	−	0.122185i
$452$	0.0278961	−	0.0483175i	0.00131212	−	0.00227266i
$453$	−11.9029			−0.559248
$454$	−6.99895			−0.328477
$455$	−7.94460	−	13.7604i	−0.372448	−	0.645100i
$456$	−1.21405	−	2.10279i	−0.0568529	−	0.0984722i
$457$	6.67371	+	11.5592i	0.312183	+	0.540717i	0.978835	−	0.204653i	$-0.0656065\pi$
$457$	6.67371	+	11.5592i	0.312183	+	0.540717i	−0.666652	+	0.745369i	$0.732273\pi$
$458$	10.9526	−	18.9705i	0.511782	−	0.886433i
$459$	−4.75863			−0.222114
$460$	−15.4767			−0.721603
$461$	29.6966			1.38311			0.691555	−	0.722324i	$-0.256926\pi$
$461$	29.6966			1.38311			0.691555	+	0.722324i	$0.256926\pi$
$462$	−17.7460			−0.825617
$463$	−2.66639			−0.123918			−0.0619589	−	0.998079i	$-0.519735\pi$
$463$	−2.66639			−0.123918			−0.0619589	+	0.998079i	$0.519735\pi$
$464$	1.36875	+	2.37075i	0.0635426	+	0.110059i
$465$	5.15102	−	8.92182i	0.238873	−	0.413740i
$466$	8.65849	+	14.9970i	0.401097	+	0.694720i
$467$	18.0945	−	31.3406i	0.837315	−	1.45027i	−0.0548172	−	0.998496i	$-0.517458\pi$
$467$	18.0945	−	31.3406i	0.837315	−	1.45027i	0.892132	−	0.451775i	$-0.149209\pi$
$468$	−1.19520	−	2.07015i	−0.0552482	−	0.0956927i
$469$	8.26536	−	14.3160i	0.381659	−	0.661053i
$470$	−9.40600	+	16.2917i	−0.433866	+	0.751479i
$471$	1.81832	−	3.14943i	0.0837840	−	0.145118i
$472$	−0.772969			−0.0355788
$473$	29.8155			1.37092
$474$	−13.4382			−0.617235
$475$	−2.24730	−	3.89244i	−0.103113	−	0.178597i
$476$	−17.8251			−0.817012
$477$	−0.401996	+	0.696278i	−0.0184061	+	0.0318804i
$478$	−18.4003			−0.841609
$479$	1.35910			0.0620987			0.0310493	−	0.999518i	$-0.490115\pi$
$479$	1.35910			0.0620987			0.0310493	+	0.999518i	$0.490115\pi$
$480$	1.77452			0.0809954
$481$	11.5671	+	20.0347i	0.527413	+	0.913506i
$482$	1.57469	+	2.72745i	0.0717254	+	0.124232i
$483$	−16.3349	−	28.2929i	−0.743264	−	1.28737i
$484$	−5.72196	+	9.91072i	−0.260089	+	0.450487i
$485$	12.1620	−	21.0652i	0.552249	−	0.956523i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−35.1048			−1.59075			−0.795375	−	0.606118i	$-0.792726\pi$
$487$	−35.1048			−1.59075			−0.795375	+	0.606118i	$0.792726\pi$
$488$	−2.78610	+	4.82566i	−0.126121	+	0.218448i
$489$	3.47856	−	6.02504i	0.157306	−	0.272462i
$490$	6.23866	+	10.8057i	0.281834	+	0.488150i
$491$	17.5638	−	30.4214i	0.792643	−	1.37290i	−0.131682	−	0.991292i	$-0.542038\pi$
$491$	17.5638	−	30.4214i	0.792643	−	1.37290i	0.924325	−	0.381606i	$-0.124629\pi$
$492$	−0.316224	+	0.547716i	−0.0142565	+	0.0246929i
$493$	6.51337	+	11.2815i	0.293348	+	0.508093i
$494$	2.90206	−	5.02651i	0.130570	−	0.226154i
$495$	8.40679			0.377857
$496$	2.90277	−	5.02774i	0.130338	−	0.225752i
$497$	−3.61809	+	6.26671i	−0.162293	+	0.281100i
$498$	−16.3866			−0.734302
$499$	−18.0271	−	31.2239i	−0.807006	−	1.39778i	−0.914928	−	0.403616i	$-0.867753\pi$
$499$	−18.0271	−	31.2239i	−0.807006	−	1.39778i	0.107922	−	0.994159i	$-0.465580\pi$
$500$	12.1574			0.543694
$501$	−9.42511	+	16.3248i	−0.421083	+	0.729337i
$502$	−17.4639			−0.779452
$503$	11.4549	+	19.8405i	0.510749	+	0.884643i	0.999922	+	0.0124563i	$0.00396505\pi$
$503$	11.4549	+	19.8405i	0.510749	+	0.884643i	−0.489174	+	0.872186i	$0.662702\pi$
$504$	1.87292	+	3.24400i	0.0834267	+	0.144499i
$505$	31.9440			1.42149
$506$	−41.3186			−1.83684
$507$	−3.64299	+	6.30984i	−0.161791	+	0.280230i
$508$	−9.70566	+	16.8107i	−0.430619	+	0.745854i
$509$	4.38330	+	7.59210i	0.194286	+	0.336514i	0.946666	−	0.322215i	$-0.104428\pi$
$509$	4.38330	+	7.59210i	0.194286	+	0.336514i	−0.752380	+	0.658729i	$0.771094\pi$
$510$	8.44428			0.373919
$511$	30.8145	+	53.3723i	1.36315	+	2.36105i
$512$	1.00000			0.0441942
$513$	−1.21405	+	2.10279i	−0.0536015	+	0.0928404i
$514$	1.19413			0.0526709
$515$	−2.04783	−	3.54694i	−0.0902381	−	0.156297i
$516$	−3.14676	−	5.45034i	−0.138528	−	0.239938i
$517$	−25.1116	+	43.4945i	−1.10440	+	1.91289i
$518$	−18.1260	−	31.3952i	−0.796411	−	1.37942i
$519$	−9.13704	−	15.8258i	−0.401071	−	0.694676i
$520$	2.12091	+	3.67352i	0.0930079	+	0.161094i
$521$	0.409003	+	0.708414i	0.0179187	+	0.0310362i	0.874846	−	0.484402i	$-0.160963\pi$
$521$	0.409003	+	0.708414i	0.0179187	+	0.0310362i	−0.856927	+	0.515438i	$0.827629\pi$
$522$	1.36875	−	2.37075i	0.0599086	−	0.103765i
$523$	14.2201	+	24.6299i	0.621800	+	1.07699i	0.989150	+	0.146906i	$0.0469315\pi$
$523$	14.2201	+	24.6299i	0.621800	+	1.07699i	−0.367351	+	0.930082i	$0.619735\pi$
$524$	−0.740902	+	1.28328i	−0.0323665	+	0.0560604i
$525$	3.46693	+	6.00491i	0.151309	+	0.262076i
$526$	−10.2134	−	17.6900i	−0.445323	−	0.771323i
$527$	13.8132	−	23.9251i	0.601712	−	1.04220i
$528$	4.73750			0.206173
$529$	−26.5332	−	45.9569i	−1.15362	−	1.99813i
$530$	0.713350	−	1.23556i	0.0309859	−	0.0536692i
$531$	0.386484	+	0.669411i	0.0167720	+	0.0290499i
$532$	−4.54763	+	7.87673i	−0.197165	+	0.341500i
$533$	−1.51180			−0.0654835
$534$	7.04593	+	12.2039i	0.304907	+	0.528115i
$535$	−1.69025	+	2.92759i	−0.0730757	+	0.126571i
$536$	−2.20654	+	3.82184i	−0.0953080	+	0.165078i
$537$	2.62284			0.113184
$538$	−2.79455	+	4.84030i	−0.120481	+	0.208680i
$539$	16.6556	+	28.8483i	0.717406	+	1.24258i
$540$	−0.887260	−	1.53678i	−0.0381816	−	0.0661324i
$541$	−31.5738			−1.35747			−0.678733	−	0.734386i	$-0.737470\pi$
$541$	−31.5738			−1.35747			−0.678733	+	0.734386i	$0.737470\pi$
$542$	11.4081	−	19.7594i	0.490019	−	0.848738i
$543$	−9.83095	−	17.0277i	−0.421886	−	0.730729i
$544$	4.75863			0.204024
$545$	−9.90178	+	17.1504i	−0.424145	+	0.734641i
$546$	−4.47704	+	7.75446i	−0.191600	+	0.331860i
$547$	−11.4521	+	19.8356i	−0.489657	+	0.848111i	−0.999929	−	0.0119020i	$-0.996211\pi$
$547$	−11.4521	+	19.8356i	−0.489657	+	0.848111i	0.510272	+	0.860013i	$0.329545\pi$
$548$	7.78257	−	13.4798i	0.332455	−	0.575829i
$549$	5.57220			0.237816
$550$	8.76950			0.373933
$551$	6.64691			0.283168
$552$	4.36080	+	7.55313i	0.185608	+	0.321483i
$553$	25.1687	+	43.5934i	1.07028	+	1.85378i
$554$	−14.4006			−0.611823
$555$	8.58683	+	14.8728i	0.364491	+	0.631316i
$556$	−4.96109	+	8.59286i	−0.210397	+	0.364418i
$557$	−39.9594			−1.69313			−0.846567	−	0.532282i	$-0.821335\pi$
$557$	−39.9594			−1.69313			−0.846567	+	0.532282i	$0.821335\pi$
$558$	−5.80554			−0.245768
$559$	7.52202	−	13.0285i	0.318147	−	0.551047i
$560$	−3.32354	−	5.75654i	−0.140445	−	0.243258i
$561$	22.5440			0.951808
$562$	−15.7826	−	27.3363i	−0.665750	−	1.15311i
$563$	3.50732	+	6.07485i	0.147816	+	0.256024i	0.930420	−	0.366495i	$-0.119442\pi$
$563$	3.50732	+	6.07485i	0.147816	+	0.256024i	−0.782604	+	0.622520i	$0.786109\pi$
$564$	10.6012			0.446390
$565$	0.0990044			0.00416514
$566$	13.8005			0.580079
$567$	1.87292	−	3.24400i	0.0786554	−	0.136235i
$568$	0.965893	−	1.67297i	0.0405279	−	0.0701965i
$569$	7.81595	−	13.5376i	0.327662	−	0.567526i	−0.654386	−	0.756161i	$-0.727073\pi$
$569$	7.81595	−	13.5376i	0.327662	−	0.567526i	0.982047	+	0.188634i	$0.0604061\pi$
$570$	2.15435	−	3.73144i	0.0902357	−	0.156293i
$571$	11.0692			0.463230			0.231615	−	0.972808i	$-0.425599\pi$
$571$	11.0692			0.463230			0.231615	+	0.972808i	$0.425599\pi$
$572$	5.66227	+	9.80733i	0.236751	+	0.410065i
$573$	−4.42197	+	7.65908i	−0.184731	+	0.319963i
$574$	2.36905			0.0988823
$575$	8.07220	+	13.9815i	0.336634	+	0.583067i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−8.18546	+	14.1776i	−0.340765	+	0.590223i	−0.984575	−	0.174963i	$-0.944019\pi$
$577$	−8.18546	+	14.1776i	−0.340765	+	0.590223i	0.643810	+	0.765186i	$0.277353\pi$
$578$	5.64453			0.234781
$579$	−5.20858	+	9.02153i	−0.216461	+	0.374922i
$580$	−2.42887	+	4.20693i	−0.100854	+	0.174683i
$581$	30.6909	+	53.1582i	1.27327	+	2.20537i
$582$	−13.7074			−0.568190
$583$	1.90446	−	3.29862i	0.0788745	−	0.136615i
$584$	−8.22631	−	14.2484i	−0.340407	−	0.589603i
$585$	2.12091	−	3.67352i	0.0876887	−	0.151881i
$586$	9.59900	+	16.6260i	0.396531	+	0.686812i
$587$	1.13628			0.0468991			0.0234496	−	0.999725i	$-0.492535\pi$
$587$	1.13628			0.0468991			0.0234496	+	0.999725i	$0.492535\pi$
$588$	3.51569	−	6.08935i	0.144985	−	0.251121i
$589$	−7.04819	−	12.2078i	−0.290416	−	0.503015i
$590$	−0.685824	−	1.18788i	−0.0282349	−	0.0489043i
$591$	5.33856	−	9.24665i	0.219599	−	0.380356i
$592$	4.83896	+	8.38133i	0.198880	+	0.344470i
$593$	−11.2720	+	19.5237i	−0.462886	+	0.801742i	−0.999103	−	0.0423378i	$-0.986519\pi$
$593$	−11.2720	+	19.5237i	−0.462886	+	0.801742i	0.536217	+	0.844080i	$0.319853\pi$
$594$	−2.36875	−	4.10280i	−0.0971910	−	0.168340i
$595$	−15.8155	−	27.3932i	−0.648372	−	1.12301i
$596$	3.99258	+	6.91535i	0.163542	+	0.283264i
$597$	−0.216180	−	0.374435i	−0.00884767	−	0.0153246i
$598$	−10.4241	+	18.0550i	−0.426272	+	0.738325i
$599$	−7.64298	−	13.2380i	−0.312284	−	0.540891i	0.666573	−	0.745440i	$-0.267761\pi$
$599$	−7.64298	−	13.2380i	−0.312284	−	0.540891i	−0.978856	+	0.204549i	$0.934427\pi$
$600$	−0.925541	−	1.60308i	−0.0377850	−	0.0654456i
$601$	32.9991			1.34606			0.673031	−	0.739614i	$-0.264992\pi$
$601$	32.9991			1.34606			0.673031	+	0.739614i	$0.264992\pi$
$602$	−11.7873	+	20.4162i	−0.480414	+	0.832101i
$603$	4.41308			0.179714
$604$	−5.95146	−	10.3082i	−0.242161	−	0.419436i
$605$	−20.3074			−0.825615
$606$	−9.00074	−	15.5897i	−0.365630	−	0.633290i
$607$	−7.42845	+	12.8665i	−0.301512	+	0.522233i	−0.976479	−	0.215615i	$-0.930825\pi$
$607$	−7.42845	+	12.8665i	−0.301512	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$608$	1.21405	−	2.10279i	0.0492361	−	0.0852794i
$609$	−10.2543			−0.415524
$610$	−9.88797			−0.400352
$611$	12.6705	+	21.9460i	0.512595	+	0.887841i
$612$	−2.37931	−	4.12109i	−0.0961780	−	0.166585i
$613$	38.6867			1.56254			0.781270	−	0.624193i	$-0.214572\pi$
$613$	38.6867			1.56254			0.781270	+	0.624193i	$0.214572\pi$
$614$	−1.57486	+	2.72774i	−0.0635563	+	0.110083i
$615$	−1.12229			−0.0452551
$616$	−8.87298	−	15.3685i	−0.357503	−	0.619213i
$617$	37.4266			1.50674			0.753369	−	0.657598i	$-0.228428\pi$
$617$	37.4266			1.50674			0.753369	+	0.657598i	$0.228428\pi$
$618$	−1.15402	+	1.99882i	−0.0464214	+	0.0804043i
$619$	14.2259	−	24.6400i	0.571787	−	0.990363i	−0.424596	−	0.905383i	$-0.639584\pi$
$619$	14.2259	−	24.6400i	0.571787	−	0.990363i	0.996383	−	0.0849805i	$-0.0270828\pi$
$620$	10.3020			0.413740
$621$	4.36080	−	7.55313i	0.174993	−	0.303097i
$622$	−6.93960	−	12.0197i	−0.278253	−	0.481948i
$623$	26.3930	−	45.7140i	1.05741	−	1.83149i
$624$	1.19520	−	2.07015i	0.0478463	−	0.0828723i
$625$	6.15905	+	10.6678i	0.246362	+	0.426711i
$626$	−15.3020	+	26.5038i	−0.611591	+	1.05931i
$627$	5.75155	−	9.96197i	0.229695	−	0.397843i
$628$	3.63665			0.145118
$629$	23.0268	+	39.8836i	0.918139	+	1.59026i
$630$	−3.32354	+	5.75654i	−0.132413	+	0.229346i
$631$	18.8264	−	32.6083i	0.749467	−	1.29811i	−0.198611	−	0.980078i	$-0.563643\pi$
$631$	18.8264	−	32.6083i	0.749467	−	1.29811i	0.948078	−	0.318037i	$-0.103024\pi$
$632$	−6.71908	−	11.6378i	−0.267271	−	0.462926i
$633$	−2.78934	−	4.83127i	−0.110866	−	0.192026i
$634$	−3.77596	−	6.54015i	−0.149962	−	0.259743i
$635$	−34.4458			−1.36694
$636$	−0.803992			−0.0318804
$637$	16.8078			0.665950
$638$	−6.48446	+	11.2314i	−0.256722	+	0.444656i
$639$	−1.93179			−0.0764202
$640$	0.887260	+	1.53678i	0.0350720	+	0.0607465i
$641$	20.6698			0.816408			0.408204	−	0.912891i	$-0.366155\pi$
$641$	20.6698			0.816408			0.408204	+	0.912891i	$0.366155\pi$
$642$	1.90502			0.0751850
$643$	20.8863			0.823674			0.411837	−	0.911257i	$-0.364887\pi$
$643$	20.8863			0.823674			0.411837	+	0.911257i	$0.364887\pi$
$644$	16.3349	−	28.2929i	0.643686	−	1.11490i
$645$	5.58398	−	9.67174i	0.219869	−	0.380824i
$646$	5.77719	−	10.0064i	0.227301	−	0.393696i
$647$	−22.0383	−	38.1715i	−0.866417	−	1.50068i	−0.865634	−	0.500678i	$-0.833084\pi$
$647$	−22.0383	−	38.1715i	−0.866417	−	1.50068i	−0.000782807	−	1.00000i	$-0.500249\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−1.83097	−	3.17133i	−0.0718719	−	0.124486i
$650$	2.21241	−	3.83201i	0.0867780	−	0.150304i
$651$	10.8733	+	18.8332i	0.426159	+	0.738130i
$652$	6.95712			0.272462
$653$	−38.2211			−1.49571			−0.747853	−	0.663864i	$-0.768915\pi$
$653$	−38.2211			−1.49571			−0.747853	+	0.663864i	$0.768915\pi$
$654$	11.1600			0.436389
$655$	−2.62949			−0.102743
$656$	−0.632448			−0.0246929
$657$	−8.22631	+	14.2484i	−0.320939	+	0.555883i
$658$	−19.8552	−	34.3902i	−0.774037	−	1.34067i
$659$	−18.3569	−	31.7950i	−0.715082	−	1.23856i	−0.962928	−	0.269759i	$-0.913056\pi$
$659$	−18.3569	−	31.7950i	−0.715082	−	1.23856i	0.247846	−	0.968800i	$-0.420277\pi$
$660$	4.20339	+	7.28049i	0.163617	+	0.283393i
$661$	−10.2281			−0.397826			−0.198913	−	0.980017i	$-0.563741\pi$
$661$	−10.2281			−0.397826			−0.198913	+	0.980017i	$0.563741\pi$
$662$	6.63419			0.257845
$663$	5.68752	−	9.85107i	0.220885	−	0.382584i
$664$	−8.19331	−	14.1912i	−0.317962	−	0.550727i
$665$	−16.1397			−0.625872
$666$	4.83896	−	8.38133i	0.187506	−	0.324770i
$667$	−23.8754			−0.924460
$668$	−18.8502			−0.729337
$669$	13.1015	+	7.16600i	0.506532	+	0.277054i
$670$	−7.83109			−0.302542
$671$	−26.3983			−1.01909
$672$	−1.87292	+	3.24400i	−0.0722496	+	0.125140i
$673$	9.20822			0.354951			0.177475	−	0.984125i	$-0.443207\pi$
$673$	9.20822			0.354951			0.177475	+	0.984125i	$0.443207\pi$
$674$	10.5094	+	18.2029i	0.404808	+	0.701149i
$675$	−0.925541	+	1.60308i	−0.0356241	+	0.0617027i
$676$	−7.28598			−0.280230
$677$	−34.2790			−1.31745			−0.658725	−	0.752384i	$-0.728904\pi$
$677$	−34.2790			−1.31745			−0.658725	+	0.752384i	$0.728904\pi$
$678$	−0.0278961	−	0.0483175i	−0.00107134	−	0.00185562i
$679$	25.6729	+	44.4668i	0.985236	+	1.70648i
$680$	4.22214	+	7.31296i	0.161912	+	0.280439i
$681$	−3.49947	+	6.06127i	−0.134100	+	0.232268i
$682$	27.5037			1.05317
$683$	20.2071			0.773205			0.386602	−	0.922246i	$-0.373649\pi$
$683$	20.2071			0.773205			0.386602	+	0.922246i	$0.373649\pi$
$684$	−2.42809			−0.0928404
$685$	27.6206			1.05533
$686$	−0.117532			−0.00448738
$687$	−10.9526	−	18.9705i	−0.417868	−	0.723769i
$688$	3.14676	−	5.45034i	0.119969	−	0.207792i
$689$	−0.960932	−	1.66438i	−0.0366086	−	0.0634080i
$690$	−7.73833	+	13.4032i	−0.294593	+	0.510250i
$691$	−0.915276	−	1.58531i	−0.0348188	−	0.0603079i	0.848091	−	0.529851i	$-0.177752\pi$
$691$	−0.915276	−	1.58531i	−0.0348188	−	0.0603079i	−0.882910	+	0.469543i	$0.844419\pi$
$692$	9.13704	−	15.8258i	0.347338	−	0.601607i
$693$	−8.87298	+	15.3685i	−0.337057	+	0.583799i
$694$	1.71558	−	2.97147i	0.0651224	−	0.112795i
$695$	−17.6071			−0.667875
$696$	2.73750			0.103765
$697$	−3.00958			−0.113996
$698$	2.22641	+	3.85625i	0.0842708	+	0.145961i
$699$	17.3170			0.654989
$700$	−3.46693	+	6.00491i	−0.131038	+	0.226964i
$701$	−42.3788			−1.60063			−0.800313	−	0.599583i	$-0.795333\pi$
$701$	−42.3788			−1.60063			−0.800313	+	0.599583i	$0.795333\pi$
$702$	−2.39040			−0.0902199
$703$	23.4989			0.886278
$704$	2.36875	+	4.10280i	0.0892756	+	0.154630i
$705$	9.40600	+	16.2917i	0.354250	+	0.613580i
$706$	−4.81975	−	8.34806i	−0.181394	−	0.314183i
$707$	−33.7154	+	58.3968i	−1.26800	+	2.19624i
$708$	−0.386484	+	0.669411i	−0.0145250	+	0.0251580i
$709$	4.93668	+	8.55057i	0.185401	+	0.321123i	0.943711	−	0.330770i	$-0.107308\pi$
$709$	4.93668	+	8.55057i	0.185401	+	0.321123i	−0.758311	+	0.651893i	$0.773975\pi$
$710$	3.42799			0.128650
$711$	−6.71908	+	11.6378i	−0.251985	+	0.436451i
$712$	−7.04593	+	12.2039i	−0.264058	+	0.457361i
$713$	25.3168	+	43.8500i	0.948122	+	1.64220i
$714$	−8.91255	+	15.4370i	−0.333544	+	0.577715i
$715$	−10.0478	+	17.4033i	−0.375766	+	0.650847i
$716$	1.31142	+	2.27145i	0.0490101	+	0.0848879i
$717$	−9.20014	+	15.9351i	−0.343586	+	0.595108i
$718$	30.0913			1.12300
$719$	−23.4704	+	40.6519i	−0.875298	+	1.51606i	−0.0188537	+	0.999822i	$0.506002\pi$
$719$	−23.4704	+	40.6519i	−0.875298	+	1.51606i	−0.856445	+	0.516239i	$0.827332\pi$
$720$	0.887260	−	1.53678i	0.0330662	−	0.0572724i
$721$	8.64556			0.321977
$722$	6.55218	+	11.3487i	0.243847	+	0.422355i
$723$	3.14939			0.117127
$724$	9.83095	−	17.0277i	0.365364	−	0.632829i
$725$	5.06734			0.188196
$726$	5.72196	+	9.91072i	0.212362	+	0.367821i
$727$	−2.16168	−	3.74414i	−0.0801722	−	0.138862i	0.823152	−	0.567822i	$-0.192214\pi$
$727$	−2.16168	−	3.74414i	−0.0801722	−	0.138862i	−0.903324	+	0.428959i	$0.858880\pi$
$728$	−8.95408			−0.331860
$729$	1.00000			0.0370370
$730$	14.5977	−	25.2840i	0.540287	−	0.935804i
$731$	14.9742	−	25.9362i	0.553843	−	0.959283i
$732$	2.78610	+	4.82566i	0.102977	+	0.178362i
$733$	43.6477			1.61216			0.806082	−	0.591804i	$-0.201584\pi$
$733$	43.6477			1.61216			0.806082	+	0.591804i	$0.201584\pi$
$734$	4.75430	+	8.23468i	0.175484	+	0.303948i
$735$	12.4773			0.460233
$736$	−4.36080	+	7.55313i	−0.160741	+	0.278412i
$737$	−20.9070			−0.770118
$738$	0.316224	+	0.547716i	0.0116404	+	0.0201617i
$739$	6.36864	+	11.0308i	0.234274	+	0.405775i	0.959062	−	0.283198i	$-0.0913953\pi$
$739$	6.36864	+	11.0308i	0.234274	+	0.405775i	−0.724787	+	0.688973i	$0.758062\pi$
$740$	−8.58683	+	14.8728i	−0.315658	+	0.546736i
$741$	−2.90206	−	5.02651i	−0.106610	−	0.184654i
$742$	1.50582	+	2.60815i	0.0552802	+	0.0957482i
$743$	4.83008	+	8.36594i	0.177198	+	0.306916i	0.940920	−	0.338629i	$-0.109963\pi$
$743$	4.83008	+	8.36594i	0.177198	+	0.306916i	−0.763722	+	0.645546i	$0.776630\pi$
$744$	−2.90277	−	5.02774i	−0.106421	−	0.184326i
$745$	−7.08491	+	12.2714i	−0.259571	+	0.449590i
$746$	−9.70475	−	16.8091i	−0.355316	−	0.615426i
$747$	−8.19331	+	14.1912i	−0.299778	+	0.519230i
$748$	11.2720	+	19.5237i	0.412145	+	0.713856i
$749$	−3.56795	−	6.17988i	−0.130370	−	0.225808i
$750$	6.07869	−	10.5286i	0.221962	−	0.384450i
$751$	5.93306			0.216500			0.108250	−	0.994124i	$-0.465475\pi$
$751$	5.93306			0.216500			0.108250	+	0.994124i	$0.465475\pi$
$752$	5.30059	+	9.18089i	0.193293	+	0.334793i
$753$	−8.73195	+	15.1242i	−0.318210	+	0.551156i
$754$	3.27186	+	5.66703i	0.119154	+	0.206381i
$755$	10.5610	−	18.2921i	0.384353	−	0.665719i
$756$	3.74585			0.136235
$757$	−2.17945	−	3.77492i	−0.0792136	−	0.137202i	0.823697	−	0.567030i	$-0.191908\pi$
$757$	−2.17945	−	3.77492i	−0.0792136	−	0.137202i	−0.902911	+	0.429828i	$0.858574\pi$
$758$	0.939270	−	1.62686i	0.0341158	−	0.0590904i
$759$	−20.6593	+	35.7830i	−0.749886	+	1.29884i
$760$	4.30870			0.156293
$761$	−0.582387	+	1.00872i	−0.0211115	+	0.0365662i	−0.876388	−	0.481605i	$-0.840054\pi$
$761$	−0.582387	+	1.00872i	−0.0211115	+	0.0365662i	0.855277	+	0.518172i	$0.173387\pi$
$762$	9.70566	+	16.8107i	0.351599	+	0.608988i
$763$	−20.9017	−	36.2029i	−0.756694	−	1.31063i
$764$	−8.84394			−0.319963
$765$	4.22214	−	7.31296i	0.152652	−	0.264401i
$766$	−2.17888	−	3.77392i	−0.0787260	−	0.136357i
$767$	−1.84771			−0.0667168
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	19.5163	−	33.8032i	0.703775	−	1.21897i	−0.263357	−	0.964699i	$-0.584830\pi$
$769$	19.5163	−	33.8032i	0.703775	−	1.21897i	0.967132	−	0.254276i	$-0.0818370\pi$
$770$	15.7453	−	27.2716i	0.567420	−	0.982801i
$771$	0.597066	−	1.03415i	0.0215028	−	0.0372440i
$772$	−10.4172			−0.374922
$773$	29.2240			1.05112			0.525558	−	0.850758i	$-0.323857\pi$
$773$	29.2240			1.05112			0.525558	+	0.850758i	$0.323857\pi$
$774$	−6.29352			−0.226216
$775$	−5.37326	−	9.30676i	−0.193013	−	0.334309i
$776$	−6.85370	−	11.8710i	−0.246033	−	0.426142i
$777$	−36.2520			−1.30053
$778$	12.8343	+	22.2297i	0.460132	+	0.796973i
$779$	−0.767821	+	1.32990i	−0.0275100	+	0.0476488i
$780$	4.24181			0.151881
$781$	9.15183			0.327478
$782$	−20.7514	+	35.9425i	−0.742070	+	1.28530i
$783$	−1.36875	−	2.37075i	−0.0489152	−	0.0847235i
$784$	7.03138			0.251121
$785$	3.22665	+	5.58873i	0.115164	+	0.199470i
$786$	0.740902	+	1.28328i	0.0264271	+	0.0457731i
$787$	15.1530			0.540147			0.270074	−	0.962840i	$-0.412952\pi$
$787$	15.1530			0.540147			0.270074	+	0.962840i	$0.412952\pi$
$788$	10.6771			0.380356
$789$	−20.4267			−0.727210
$790$	11.9231	−	20.6515i	0.424206	−	0.734747i
$791$	−0.104495	+	0.180990i	−0.00371540	+	0.00643526i
$792$	2.36875	−	4.10280i	0.0841699	−	0.145787i
$793$	−6.65990	+	11.5353i	−0.236500	+	0.409630i
$794$	21.8495			0.775409
$795$	−0.713350	−	1.23556i	−0.0252999	−	0.0438207i
$796$	0.216180	−	0.374435i	0.00766231	−	0.0132715i
$797$	−11.7684			−0.416857			−0.208429	−	0.978038i	$-0.566835\pi$
$797$	−11.7684			−0.416857			−0.208429	+	0.978038i	$0.566835\pi$
$798$	4.54763	+	7.87673i	0.160984	+	0.278833i
$799$	25.2235	+	43.6884i	0.892344	+	1.54559i
$800$	0.925541	−	1.60308i	0.0327228	−	0.0566776i
$801$	14.0919			0.497912
$802$	7.09149	−	12.2828i	0.250409	−	0.433722i
$803$	38.9722	−	67.5018i	1.37530	−	2.38209i
$804$	2.20654	+	3.82184i	0.0778186	+	0.134786i
$805$	57.9732			2.04329
$806$	6.93878	−	12.0183i	0.244408	−	0.423327i
$807$	2.79455	+	4.84030i	0.0983727	+	0.170387i
$808$	9.00074	−	15.5897i	0.316645	−	0.548445i
$809$	6.26129	+	10.8449i	0.220135	+	0.381285i	0.954849	−	0.297092i	$-0.0960168\pi$
$809$	6.26129	+	10.8449i	0.220135	+	0.381285i	−0.734714	+	0.678377i	$0.762683\pi$
$810$	−1.77452			−0.0623503
$811$	−0.447852	+	0.775703i	−0.0157262	+	0.0272386i	−0.873781	−	0.486319i	$-0.838339\pi$
$811$	−0.447852	+	0.775703i	−0.0157262	+	0.0272386i	0.858055	+	0.513557i	$0.171673\pi$
$812$	−5.12713	−	8.88045i	−0.179927	−	0.311643i
$813$	−11.4081	−	19.7594i	−0.400099	−	0.692992i
$814$	−22.9246	+	39.7065i	−0.803506	+	1.39171i
$815$	6.17277	+	10.6915i	0.216223	+	0.374509i
$816$	2.37931	−	4.12109i	0.0832926	−	0.144267i
$817$	−7.64062	−	13.2339i	−0.267311	−	0.462997i
$818$	−18.2433	−	31.5984i	−0.637863	−	1.10481i
$819$	4.47704	+	7.75446i	0.156440	+	0.270963i
$820$	−0.561145	−	0.971932i	−0.0195960	−	0.0339413i
$821$	−12.6526	+	21.9149i	−0.441578	+	0.764836i	−0.997807	−	0.0661936i	$-0.978915\pi$
$821$	−12.6526	+	21.9149i	−0.441578	+	0.764836i	0.556229	+	0.831029i	$0.312248\pi$
$822$	−7.78257	−	13.4798i	−0.271448	−	0.470162i
$823$	8.14345	+	14.1049i	0.283863	+	0.491665i	0.972333	−	0.233600i	$-0.0750506\pi$
$823$	8.14345	+	14.1049i	0.283863	+	0.491665i	−0.688470	+	0.725265i	$0.741717\pi$
$824$	−2.30804			−0.0804043
$825$	4.38475	−	7.59461i	0.152657	−	0.264410i
$826$	2.89542			0.100745
$827$	−2.87638	−	4.98203i	−0.100021	−	0.173242i	0.811672	−	0.584114i	$-0.198558\pi$
$827$	−2.87638	−	4.98203i	−0.100021	−	0.173242i	−0.911693	+	0.410871i	$0.865224\pi$
$828$	8.72161			0.303097
$829$	25.8829	+	44.8304i	0.898949	+	1.55703i	0.828840	+	0.559486i	$0.189002\pi$
$829$	25.8829	+	44.8304i	0.898949	+	1.55703i	0.0701095	+	0.997539i	$0.477665\pi$
$830$	14.5392	−	25.1826i	0.504663	−	0.874101i
$831$	−7.20031	+	12.4713i	−0.249776	+	0.432624i
$832$	2.39040			0.0828723
$833$	33.4597			1.15931
$834$	4.96109	+	8.59286i	0.171788	+	0.297546i
$835$	−16.7250	−	28.9686i	−0.578794	−	1.00250i
$836$	11.5031			0.397843
$837$	−2.90277	+	5.02774i	−0.100334	+	0.173784i
$838$	3.27422			0.113106
$839$	3.02749	+	5.24377i	0.104521	+	0.181035i	0.913542	−	0.406744i	$-0.133336\pi$
$839$	3.02749	+	5.24377i	0.104521	+	0.181035i	−0.809022	+	0.587779i	$0.800003\pi$
$840$	−6.64708			−0.229346
$841$	10.7530	−	18.6248i	0.370795	−	0.642235i
$842$	7.43351	−	12.8752i	0.256176	−	0.443709i
$843$	−31.5652			−1.08716
$844$	2.78934	−	4.83127i	0.0960129	−	0.166299i
$845$	−6.46455	−	11.1969i	−0.222387	−	0.385186i
$846$	5.30059	−	9.18089i	0.182238	−	0.315646i
$847$	21.4336	−	37.1241i	0.736467	−	1.27560i
$848$	−0.401996	−	0.696278i	−0.0138046	−	0.0239103i
$849$	6.90026	−	11.9516i	0.236816	−	0.410178i
$850$	4.40430	−	7.62848i	0.151066	−	0.261655i
$851$	−84.4071			−2.89344
$852$	−0.965893	−	1.67297i	−0.0330909	−	0.0573152i
$853$	−8.17654	+	14.1622i	−0.279959	+	0.484904i	−0.971374	−	0.237554i	$-0.923654\pi$
$853$	−8.17654	+	14.1622i	−0.279959	+	0.484904i	0.691415	+	0.722458i	$0.256988\pi$
$854$	10.4363	−	18.0762i	0.357123	−	0.618555i
$855$	−2.15435	−	3.73144i	−0.0736772	−	0.127613i
$856$	0.952509	+	1.64979i	0.0325561	+	0.0563888i
$857$	1.65485	+	2.86628i	0.0565284	+	0.0979101i	0.892905	−	0.450245i	$-0.148664\pi$
$857$	1.65485	+	2.86628i	0.0565284	+	0.0979101i	−0.836376	+	0.548156i	$0.815330\pi$
$858$	11.3245			0.386613
$859$	−14.7019			−0.501624			−0.250812	−	0.968036i	$-0.580698\pi$
$859$	−14.7019			−0.501624			−0.250812	+	0.968036i	$0.580698\pi$
$860$	11.1680			0.380824
$861$	1.18453	−	2.05166i	0.0403685	−	0.0699204i
$862$	18.7446			0.638445
$863$	3.75274	+	6.49994i	0.127745	+	0.221261i	0.922803	−	0.385273i	$-0.125893\pi$
$863$	3.75274	+	6.49994i	0.127745	+	0.221261i	−0.795058	+	0.606534i	$0.792559\pi$
$864$	−1.00000			−0.0340207
$865$	32.4277			1.10257
$866$	−36.0021			−1.22340
$867$	2.82226	−	4.88831i	0.0958491	−	0.166016i
$868$	−10.8733	+	18.8332i	−0.369065	+	0.639239i
$869$	31.8317	−	55.1340i	1.07981	−	1.87029i
$870$	2.42887	+	4.20693i	0.0823465	+	0.142628i
$871$	−5.27452	+	9.13573i	−0.178720	+	0.309552i
$872$	5.57998	+	9.66480i	0.188962	+	0.327291i
$873$	−6.85370	+	11.8710i	−0.231963	+	0.401771i
$874$	10.5884	+	18.3397i	0.358159	+	0.620350i
$875$	−45.5397			−1.53952
$876$	−16.4526			−0.555883
$877$	−11.9881			−0.404811			−0.202406	−	0.979302i	$-0.564876\pi$
$877$	−11.9881			−0.404811			−0.202406	+	0.979302i	$0.564876\pi$
$878$	1.35629			0.0457726
$879$	19.1980			0.647533
$880$	−4.20339	+	7.28049i	−0.141696	+	0.245425i
$881$	18.9921	+	32.8952i	0.639858	+	1.10827i	0.985464	+	0.169887i	$0.0543404\pi$
$881$	18.9921	+	32.8952i	0.639858	+	1.10827i	−0.345605	+	0.938380i	$0.612326\pi$
$882$	−3.51569	−	6.08935i	−0.118379	−	0.205039i
$883$	−5.53499	−	9.58688i	−0.186267	−	0.322624i	0.757736	−	0.652562i	$-0.226306\pi$
$883$	−5.53499	−	9.58688i	−0.186267	−	0.322624i	−0.944003	+	0.329937i	$0.892972\pi$
$884$	11.3750			0.382584
$885$	−1.37165			−0.0461074
$886$	−13.9058	+	24.0855i	−0.467174	+	0.809169i
$887$	17.4174	+	30.1678i	0.584819	+	1.01294i	0.994898	+	0.100887i	$0.0321680\pi$
$887$	17.4174	+	30.1678i	0.584819	+	1.01294i	−0.410078	+	0.912050i	$0.634499\pi$
$888$	9.67792			0.324770
$889$	36.3559	−	62.9703i	1.21934	−	2.11196i
$890$	−25.0063			−0.838213
$891$	−4.73750			−0.158712
$892$	0.344793	+	14.9292i	0.0115445	+	0.499867i
$893$	25.7407			0.861378
$894$	7.98516			0.267064
$895$	−2.32714	+	4.03073i	−0.0777877	+	0.134732i
$896$	−3.74585			−0.125140
$897$	10.4241	+	18.0550i	0.348050	+	0.602840i
$898$	1.51834	−	2.62983i	0.0506675	−	0.0877587i
$899$	15.8927			0.530050
$900$	−1.85108			−0.0617027
$901$	−1.91295	−	3.31333i	−0.0637296	−	0.110383i
$902$	−1.49811	−	2.59480i	−0.0498816	−	0.0863975i
$903$	11.7873	+	20.4162i	0.392256	+	0.679407i
$904$	0.0278961	−	0.0483175i	0.000927811	−	0.00160702i
$905$	34.8904			1.15980
$906$	−11.9029			−0.395448
$907$	−29.2846			−0.972380			−0.486190	−	0.873853i	$-0.661614\pi$
$907$	−29.2846			−0.972380			−0.486190	+	0.873853i	$0.661614\pi$
$908$	−6.99895			−0.232268
$909$	−18.0015			−0.597071
$910$	−7.94460	−	13.7604i	−0.263361	−	0.456154i
$911$	14.8163	−	25.6626i	0.490887	−	0.850241i	−0.509058	−	0.860732i	$-0.670006\pi$
$911$	14.8163	−	25.6626i	0.490887	−	0.850241i	0.999945	+	0.0104913i	$0.00333954\pi$
$912$	−1.21405	−	2.10279i	−0.0402011	−	0.0696303i
$913$	38.8158	−	67.2310i	1.28462	−	2.22502i
$914$	6.67371	+	11.5592i	0.220747	+	0.382344i
$915$	−4.94399	+	8.56323i	−0.163443	+	0.283092i
$916$	10.9526	−	18.9705i	0.361885	−	0.626803i
$917$	2.77531	−	4.80697i	0.0916487	−	0.158740i
$918$	−4.75863			−0.157058
$919$	−34.8554			−1.14977			−0.574887	−	0.818233i	$-0.694954\pi$
$919$	−34.8554			−1.14977			−0.574887	+	0.818233i	$0.694954\pi$
$920$	−15.4767			−0.510250
$921$	1.57486	+	2.72774i	0.0518935	+	0.0898822i
$922$	29.6966			0.978006
$923$	2.30887	−	3.99908i	0.0759974	−	0.131631i
$924$	−17.7460			−0.583799
$925$	17.9146			0.589029
$926$	−2.66639			−0.0876232
$927$	1.15402	+	1.99882i	0.0379029	+	0.0656498i
$928$	1.36875	+	2.37075i	0.0449314	+	0.0778235i
$929$	−13.2761	−	22.9949i	−0.435575	−	0.754437i	0.561768	−	0.827295i	$-0.310121\pi$
$929$	−13.2761	−	22.9949i	−0.435575	−	0.754437i	−0.997342	+	0.0728577i	$0.976788\pi$
$930$	5.15102	−	8.92182i	0.168909	−	0.292558i
$931$	8.53642	−	14.7855i	0.279770	−	0.484575i
$932$	8.65849	+	14.9970i	0.283618	+	0.491241i
$933$	−13.8792			−0.454385
$934$	18.0945	−	31.3406i	0.592071	−	1.02550i
$935$	−20.0024	+	34.6451i	−0.654148	+	1.13302i
$936$	−1.19520	−	2.07015i	−0.0390664	−	0.0676649i
$937$	−11.1051	+	19.2345i	−0.362787	+	0.628365i	−0.988418	−	0.151754i	$-0.951508\pi$
$937$	−11.1051	+	19.2345i	−0.362787	+	0.628365i	0.625632	+	0.780119i	$0.284841\pi$
$938$	8.26536	−	14.3160i	0.269874	−	0.467435i
$939$	15.3020	+	26.5038i	0.499362	+	0.864920i
$940$	−9.40600	+	16.2917i	−0.306790	+	0.531376i
$941$	37.5964			1.22561			0.612804	−	0.790235i	$-0.290041\pi$
$941$	37.5964			1.22561			0.612804	+	0.790235i	$0.290041\pi$
$942$	1.81832	−	3.14943i	0.0592442	−	0.102614i
$943$	2.75798	−	4.77696i	0.0898122	−	0.155559i
$944$	−0.772969			−0.0251580
$945$	3.32354	+	5.75654i	0.108115	+	0.187260i
$946$	29.8155			0.969387
$947$	−12.9061	+	22.3540i	−0.419391	+	0.726407i	−0.995878	−	0.0906996i	$-0.971090\pi$
$947$	−12.9061	+	22.3540i	−0.419391	+	0.726407i	0.576487	+	0.817106i	$0.304423\pi$
$948$	−13.4382			−0.436451
$949$	−19.6642	−	34.0594i	−0.638327	−	1.10561i
$950$	−2.24730	−	3.89244i	−0.0729120	−	0.126287i
$951$	−7.55192			−0.244888
$952$	−17.8251			−0.577715
$953$	16.1766	−	28.0187i	0.524011	−	0.907613i	−0.475599	−	0.879662i	$-0.657768\pi$
$953$	16.1766	−	28.0187i	0.524011	−	0.907613i	0.999609	−	0.0279508i	$-0.00889818\pi$
$954$	−0.401996	+	0.696278i	−0.0130151	+	0.0225428i
$955$	−7.84687	−	13.5912i	−0.253919	−	0.439800i
$956$	−18.4003			−0.595108
$957$	6.48446	+	11.2314i	0.209613	+	0.363060i
$958$	1.35910			0.0439104
$959$	−29.1523	+	50.4933i	−0.941378	+	1.63051i
$960$	1.77452			0.0572724
$961$	−1.35212	−	2.34195i	−0.0436169	−	0.0755467i
$962$	11.5671	+	20.0347i	0.372937	+	0.645946i
$963$	0.952509	−	1.64979i	0.0306942	−	0.0531638i
$964$	1.57469	+	2.72745i	0.0507175	+	0.0878453i
$965$	−9.24273	−	16.0089i	−0.297534	−	0.515344i
$966$	−16.3349	−	28.2929i	−0.525567	−	0.910309i
$967$	−1.15026	−	1.99232i	−0.0369900	−	0.0640685i	0.846938	−	0.531692i	$-0.178444\pi$
$967$	−1.15026	−	1.99232i	−0.0369900	−	0.0640685i	−0.883928	+	0.467624i	$0.845110\pi$
$968$	−5.72196	+	9.91072i	−0.183911	+	0.318543i
$969$	−5.77719	−	10.0064i	−0.185590	−	0.321452i
$970$	12.1620	−	21.0652i	0.390499	−	0.676364i
$971$	24.8744	+	43.0837i	0.798256	+	1.38262i	0.920751	+	0.390151i	$0.127577\pi$
$971$	24.8744	+	43.0837i	0.798256	+	1.38262i	−0.122494	+	0.992469i	$0.539089\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	18.5835	−	32.1875i	0.595759	−	1.03189i
$974$	−35.1048			−1.12483
$975$	−2.21241	−	3.83201i	−0.0708540	−	0.122723i
$976$	−2.78610	+	4.82566i	−0.0891808	+	0.154466i
$977$	−16.2977	−	28.2285i	−0.521410	−	0.903109i	−0.999690	−	0.0249012i	$-0.992073\pi$
$977$	−16.2977	−	28.2285i	−0.521410	−	0.903109i	0.478280	−	0.878207i	$-0.341260\pi$
$978$	3.47856	−	6.02504i	0.111232	−	0.192660i
$979$	−66.7602			−2.13367
$980$	6.23866	+	10.8057i	0.199287	+	0.345174i
$981$	5.57998	−	9.66480i	0.178155	−	0.308573i
$982$	17.5638	−	30.4214i	0.560483	−	0.970785i
$983$	−33.3075			−1.06234			−0.531172	−	0.847264i	$-0.678248\pi$
$983$	−33.3075			−1.06234			−0.531172	+	0.847264i	$0.678248\pi$
$984$	−0.316224	+	0.547716i	−0.0100808	+	0.0174605i
$985$	9.47337	+	16.4084i	0.301847	+	0.522814i
$986$	6.51337	+	11.2815i	0.207428	+	0.359276i
$987$	−39.7104			−1.26400
$988$	2.90206	−	5.02651i	0.0923268	−	0.159915i
$989$	27.4448	+	47.5358i	0.872694	+	1.51155i
$990$	8.40679			0.267185
$991$	8.35781	−	14.4762i	0.265495	−	0.459850i	−0.702198	−	0.711981i	$-0.747798\pi$
$991$	8.35781	−	14.4762i	0.265495	−	0.459850i	0.967693	+	0.252131i	$0.0811314\pi$
$992$	2.90277	−	5.02774i	0.0921630	−	0.159631i
$993$	3.31710	−	5.74538i	0.105265	−	0.182324i
$994$	−3.61809	+	6.26671i	−0.114759	+	0.198768i
$995$	0.767232			0.0243229
$996$	−16.3866			−0.519230
$997$	−47.2364			−1.49599			−0.747995	−	0.663704i	$-0.768983\pi$
$997$	−47.2364			−1.49599			−0.747995	+	0.663704i	$0.768983\pi$
$998$	−18.0271	−	31.2239i	−0.570639	−	0.988376i
$999$	−4.83896	−	8.38133i	−0.153098	−	0.265173i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1338.2.e.i.931.5	✓	14
223.183	even	3	inner	1338.2.e.i.1075.5	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1338.2.e.i.931.5	✓	14	1.1	even	1	trivial
1338.2.e.i.1075.5	yes	14	223.183	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1338 = 2 \cdot 3 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1338.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(0.887260 + 1.53678i) q^{5} +(0.500000 - 0.866025i) q^{6} -3.74585 q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.887260 + 1.53678i) q^{10} +(2.36875 + 4.10280i) q^{11} +(0.500000 - 0.866025i) q^{12} +2.39040 q^{13} -3.74585 q^{14} +1.77452 q^{15} +1.00000 q^{16} +4.75863 q^{17} +(-0.500000 - 0.866025i) q^{18} +(1.21405 - 2.10279i) q^{19} +(0.887260 + 1.53678i) q^{20} +(-1.87292 + 3.24400i) q^{21} +(2.36875 + 4.10280i) q^{22} +(-4.36080 + 7.55313i) q^{23} +(0.500000 - 0.866025i) q^{24} +(0.925541 - 1.60308i) q^{25} +2.39040 q^{26} -1.00000 q^{27} -3.74585 q^{28} +(1.36875 + 2.37075i) q^{29} +1.77452 q^{30} +(2.90277 - 5.02774i) q^{31} +1.00000 q^{32} +4.73750 q^{33} +4.75863 q^{34} +(-3.32354 - 5.75654i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(4.83896 + 8.38133i) q^{37} +(1.21405 - 2.10279i) q^{38} +(1.19520 - 2.07015i) q^{39} +(0.887260 + 1.53678i) q^{40} -0.632448 q^{41} +(-1.87292 + 3.24400i) q^{42} +(3.14676 - 5.45034i) q^{43} +(2.36875 + 4.10280i) q^{44} +(0.887260 - 1.53678i) q^{45} +(-4.36080 + 7.55313i) q^{46} +(5.30059 + 9.18089i) q^{47} +(0.500000 - 0.866025i) q^{48} +7.03138 q^{49} +(0.925541 - 1.60308i) q^{50} +(2.37931 - 4.12109i) q^{51} +2.39040 q^{52} +(-0.401996 - 0.696278i) q^{53} -1.00000 q^{54} +(-4.20339 + 7.28049i) q^{55} -3.74585 q^{56} +(-1.21405 - 2.10279i) q^{57} +(1.36875 + 2.37075i) q^{58} -0.772969 q^{59} +1.77452 q^{60} +(-2.78610 + 4.82566i) q^{61} +(2.90277 - 5.02774i) q^{62} +(1.87292 + 3.24400i) q^{63} +1.00000 q^{64} +(2.12091 + 3.67352i) q^{65} +4.73750 q^{66} +(-2.20654 + 3.82184i) q^{67} +4.75863 q^{68} +(4.36080 + 7.55313i) q^{69} +(-3.32354 - 5.75654i) q^{70} +(0.965893 - 1.67297i) q^{71} +(-0.500000 - 0.866025i) q^{72} +(-8.22631 - 14.2484i) q^{73} +(4.83896 + 8.38133i) q^{74} +(-0.925541 - 1.60308i) q^{75} +(1.21405 - 2.10279i) q^{76} +(-8.87298 - 15.3685i) q^{77} +(1.19520 - 2.07015i) q^{78} +(-6.71908 - 11.6378i) q^{79} +(0.887260 + 1.53678i) q^{80} +(-0.500000 + 0.866025i) q^{81} -0.632448 q^{82} +(-8.19331 - 14.1912i) q^{83} +(-1.87292 + 3.24400i) q^{84} +(4.22214 + 7.31296i) q^{85} +(3.14676 - 5.45034i) q^{86} +2.73750 q^{87} +(2.36875 + 4.10280i) q^{88} +(-7.04593 + 12.2039i) q^{89} +(0.887260 - 1.53678i) q^{90} -8.95408 q^{91} +(-4.36080 + 7.55313i) q^{92} +(-2.90277 - 5.02774i) q^{93} +(5.30059 + 9.18089i) q^{94} +4.30870 q^{95} +(0.500000 - 0.866025i) q^{96} +(-6.85370 - 11.8710i) q^{97} +7.03138 q^{98} +(2.36875 - 4.10280i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 14 q^{2} + 7 q^{3} + 14 q^{4} + 3 q^{5} + 7 q^{6} + 4 q^{7} + 14 q^{8} - 7 q^{9} + 3 q^{10} + 7 q^{11} + 7 q^{12} - 12 q^{13} + 4 q^{14} + 6 q^{15} + 14 q^{16} + 6 q^{17} - 7 q^{18} - 6 q^{19} + 3 q^{20}+ \cdots + 7 q^{99}+O(q^{100}) \) 14 * q + 14 * q^2 + 7 * q^3 + 14 * q^4 + 3 * q^5 + 7 * q^6 + 4 * q^7 + 14 * q^8 - 7 * q^9 + 3 * q^10 + 7 * q^11 + 7 * q^12 - 12 * q^13 + 4 * q^14 + 6 * q^15 + 14 * q^16 + 6 * q^17 - 7 * q^18 - 6 * q^19 + 3 * q^20 + 2 * q^21 + 7 * q^22 - 14 * q^23 + 7 * q^24 - 16 * q^25 - 12 * q^26 - 14 * q^27 + 4 * q^28 - 7 * q^29 + 6 * q^30 - 19 * q^31 + 14 * q^32 + 14 * q^33 + 6 * q^34 + q^35 - 7 * q^36 - 9 * q^37 - 6 * q^38 - 6 * q^39 + 3 * q^40 + 10 * q^41 + 2 * q^42 + 20 * q^43 + 7 * q^44 + 3 * q^45 - 14 * q^46 + q^47 + 7 * q^48 + 62 * q^49 - 16 * q^50 + 3 * q^51 - 12 * q^52 + 10 * q^53 - 14 * q^54 - 24 * q^55 + 4 * q^56 + 6 * q^57 - 7 * q^58 - 6 * q^59 + 6 * q^60 + 4 * q^61 - 19 * q^62 - 2 * q^63 + 14 * q^64 + 3 * q^65 + 14 * q^66 + 3 * q^67 + 6 * q^68 + 14 * q^69 + q^70 + 31 * q^71 - 7 * q^72 - 45 * q^73 - 9 * q^74 + 16 * q^75 - 6 * q^76 - 14 * q^77 - 6 * q^78 - 41 * q^79 + 3 * q^80 - 7 * q^81 + 10 * q^82 - q^83 + 2 * q^84 - 9 * q^85 + 20 * q^86 - 14 * q^87 + 7 * q^88 - 24 * q^89 + 3 * q^90 + 74 * q^91 - 14 * q^92 + 19 * q^93 + q^94 - 8 * q^95 + 7 * q^96 - 13 * q^97 + 62 * q^98 + 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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