LMFDB - Embedded newform 261.2.e.a.88.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [261,2,Mod(88,261)] 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("261.88"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(261, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			88.4
Character	$\chi$	$=$	261.88
Dual form			261.2.e.a.175.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.540070 + 0.935429i) q^{2} +(1.44567 - 0.953961i) q^{3} +(0.416648 + 0.721656i) q^{4} +(-1.91815 - 3.32233i) q^{5} +(0.111600 + 1.86753i) q^{6} +(1.07867 - 1.86831i) q^{7} -3.06036 q^{8} +(1.17992 - 2.75822i) q^{9} +4.14374 q^{10} +(1.42920 - 2.47544i) q^{11} +(1.29077 + 0.645809i) q^{12} +(0.862163 + 1.49331i) q^{13} +(1.16511 + 2.01804i) q^{14} +(-5.94238 - 2.97315i) q^{15} +(0.819512 - 1.41944i) q^{16} +1.10776 q^{17} +(1.94288 + 2.59336i) q^{18} -2.98771 q^{19} +(1.59839 - 2.76849i) q^{20} +(-0.222896 - 3.72996i) q^{21} +(1.54374 + 2.67383i) q^{22} +(4.05735 + 7.02753i) q^{23} +(-4.42426 + 2.91946i) q^{24} +(-4.85859 + 8.41533i) q^{25} -1.86251 q^{26} +(-0.925468 - 5.11307i) q^{27} +1.79770 q^{28} +(0.500000 - 0.866025i) q^{29} +(5.99048 - 3.95297i) q^{30} +(1.57902 + 2.73494i) q^{31} +(-2.17517 - 3.76750i) q^{32} +(-0.295330 - 4.94207i) q^{33} +(-0.598267 + 1.03623i) q^{34} -8.27619 q^{35} +(2.48210 - 0.297715i) q^{36} +6.10228 q^{37} +(1.61357 - 2.79479i) q^{38} +(2.67096 + 1.33636i) q^{39} +(5.87022 + 10.1675i) q^{40} +(4.70802 + 8.15454i) q^{41} +(3.60950 + 1.80594i) q^{42} +(3.66422 - 6.34662i) q^{43} +2.38189 q^{44} +(-11.4270 + 1.37061i) q^{45} -8.76501 q^{46} +(-0.381479 + 0.660741i) q^{47} +(-0.169344 - 2.83382i) q^{48} +(1.17295 + 2.03161i) q^{49} +(-5.24796 - 9.08973i) q^{50} +(1.60145 - 1.05676i) q^{51} +(-0.718437 + 1.24437i) q^{52} -10.4826 q^{53} +(5.28274 + 1.89571i) q^{54} -10.9657 q^{55} +(-3.30111 + 5.71769i) q^{56} +(-4.31924 + 2.85016i) q^{57} +(0.540070 + 0.935429i) q^{58} +(0.153307 + 0.265536i) q^{59} +(-0.330291 - 5.52711i) q^{60} +(-3.35396 + 5.80923i) q^{61} -3.41112 q^{62} +(-3.88047 - 5.17966i) q^{63} +7.97703 q^{64} +(3.30751 - 5.72878i) q^{65} +(4.78246 + 2.39281i) q^{66} +(-5.53084 - 9.57969i) q^{67} +(0.461545 + 0.799419i) q^{68} +(12.5696 + 6.28893i) q^{69} +(4.46972 - 7.74179i) q^{70} -10.0525 q^{71} +(-3.61097 + 8.44115i) q^{72} -3.16319 q^{73} +(-3.29566 + 5.70825i) q^{74} +(1.00398 + 16.8007i) q^{75} +(-1.24482 - 2.15610i) q^{76} +(-3.08326 - 5.34037i) q^{77} +(-2.69258 + 1.77677i) q^{78} +(1.18767 - 2.05710i) q^{79} -6.28779 q^{80} +(-6.21559 - 6.50895i) q^{81} -10.1707 q^{82} +(-5.09219 + 8.81993i) q^{83} +(2.59888 - 1.71494i) q^{84} +(-2.12484 - 3.68034i) q^{85} +(3.95787 + 6.85524i) q^{86} +(-0.103320 - 1.72897i) q^{87} +(-4.37386 + 7.57575i) q^{88} +17.6849 q^{89} +(4.88927 - 11.4294i) q^{90} +3.71995 q^{91} +(-3.38097 + 5.85602i) q^{92} +(4.89176 + 2.44749i) q^{93} +(-0.412051 - 0.713693i) q^{94} +(5.73087 + 9.92615i) q^{95} +(-6.73863 - 3.37154i) q^{96} +(8.44064 - 14.6196i) q^{97} -2.53390 q^{98} +(-5.14149 - 6.86287i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - q^{2} - 2 q^{3} - 5 q^{4} + q^{5} - q^{6} + 7 q^{7} + 6 q^{8} - 2 q^{9} - 20 q^{10} - 3 q^{11} + 10 q^{12} + 7 q^{13} + 10 q^{14} - 8 q^{15} + 7 q^{16} + 2 q^{17} + 2 q^{18} - 56 q^{19} + 4 q^{20}+ \cdots - 40 q^{99}+O(q^{100}) $ 22 * q - q^2 - 2 * q^3 - 5 * q^4 + q^5 - q^6 + 7 * q^7 + 6 * q^8 - 2 * q^9 - 20 * q^10 - 3 * q^11 + 10 * q^12 + 7 * q^13 + 10 * q^14 - 8 * q^15 + 7 * q^16 + 2 * q^17 + 2 * q^18 - 56 * q^19 + 4 * q^20 + 16 * q^21 + 13 * q^22 - 4 * q^23 - 33 * q^24 + 4 * q^25 - 12 * q^26 + 13 * q^27 - 32 * q^28 + 11 * q^29 + 46 * q^30 + 27 * q^31 - 7 * q^32 - 10 * q^33 + 19 * q^34 - 22 * q^35 + 19 * q^36 - 28 * q^37 + 5 * q^38 + 17 * q^39 + 24 * q^40 + 9 * q^41 - 50 * q^42 + 25 * q^43 + 46 * q^44 - 56 * q^45 - 20 * q^46 - 6 * q^47 + 33 * q^48 + 12 * q^49 - 41 * q^50 - 15 * q^51 + 20 * q^52 - 12 * q^53 + 5 * q^54 - 70 * q^55 + 10 * q^56 + 25 * q^57 + q^58 - 48 * q^60 + 25 * q^61 - 12 * q^62 - 11 * q^63 - 50 * q^64 - 5 * q^65 + 29 * q^66 + 29 * q^67 + 50 * q^68 + 20 * q^69 + 7 * q^70 - 2 * q^71 + 30 * q^72 - 26 * q^73 - 14 * q^74 + 46 * q^75 + 38 * q^76 - 9 * q^77 - 39 * q^78 + 27 * q^79 - 74 * q^80 - 38 * q^81 - 34 * q^82 + 12 * q^83 + 60 * q^84 + 7 * q^85 - q^86 - q^87 - 5 * q^88 + 46 * q^89 - 35 * q^90 - 86 * q^91 - 19 * q^92 + 78 * q^93 - 10 * q^94 - 8 * q^95 - 75 * q^96 + 36 * q^97 + 86 * q^98 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.540070	+	0.935429i	−0.381887	+	0.661448i	−0.991332	−	0.131380i	$-0.958059\pi$
$2$	−0.540070	+	0.935429i	−0.381887	+	0.661448i	0.609445	+	0.792829i	$0.291392\pi$
$3$	1.44567	−	0.953961i	0.834657	−	0.550770i
$3$	1.44567	−	0.953961i	0.834657	−	0.550770i
$4$	0.416648	+	0.721656i	0.208324	+	0.360828i
$5$	−1.91815	−	3.32233i	−0.857822	−	1.48579i	−0.874002	−	0.485923i	$-0.838484\pi$
$5$	−1.91815	−	3.32233i	−0.857822	−	1.48579i	0.0161795	−	0.999869i	$-0.494850\pi$
$6$	0.111600	+	1.86753i	0.0455606	+	0.762415i
$7$	1.07867	−	1.86831i	0.407698	−	0.706154i	−0.586933	−	0.809635i	$-0.699665\pi$
$7$	1.07867	−	1.86831i	0.407698	−	0.706154i	0.994631	+	0.103481i	$0.0329982\pi$
$8$	−3.06036			−1.08200
$9$	1.17992	−	2.75822i	0.393306	−	0.919408i
$10$	4.14374			1.31037
$11$	1.42920	−	2.47544i	0.430920	−	0.746375i	−0.566033	−	0.824382i	$-0.691523\pi$
$11$	1.42920	−	2.47544i	0.430920	−	0.746375i	0.996953	+	0.0780079i	$0.0248559\pi$
$12$	1.29077	+	0.645809i	0.372612	+	0.186429i
$13$	0.862163	+	1.49331i	0.239121	+	0.414170i	0.960462	−	0.278410i	$-0.0898074\pi$
$13$	0.862163	+	1.49331i	0.239121	+	0.414170i	−0.721341	+	0.692580i	$0.756474\pi$
$14$	1.16511	+	2.01804i	0.311390	+	0.539343i
$15$	−5.94238	−	2.97315i	−1.53432	−	0.767665i
$16$	0.819512	−	1.41944i	0.204878	−	0.354859i
$17$	1.10776			0.268671			0.134335	−	0.990936i	$-0.457110\pi$
$17$	1.10776			0.268671			0.134335	+	0.990936i	$0.457110\pi$
$18$	1.94288	+	2.59336i	0.457942	+	0.611262i
$19$	−2.98771			−0.685427			−0.342714	−	0.939440i	$-0.611346\pi$
$19$	−2.98771			−0.685427			−0.342714	+	0.939440i	$0.611346\pi$
$20$	1.59839	−	2.76849i	0.357410	−	0.619052i
$21$	−0.222896	−	3.72996i	−0.0486399	−	0.813945i
$22$	1.54374	+	2.67383i	0.329125	+	0.570062i
$23$	4.05735	+	7.02753i	0.846016	+	1.46534i	0.884736	+	0.466092i	$0.154338\pi$
$23$	4.05735	+	7.02753i	0.846016	+	1.46534i	−0.0387207	+	0.999250i	$0.512328\pi$
$24$	−4.42426	+	2.91946i	−0.903099	+	0.595933i
$25$	−4.85859	+	8.41533i	−0.971718	+	1.68307i
$26$	−1.86251			−0.365269
$27$	−0.925468	−	5.11307i	−0.178106	−	0.984011i
$28$	1.79770			0.339733
$29$	0.500000	−	0.866025i	0.0928477	−	0.160817i
$29$	0.500000	−	0.866025i	0.0928477	−	0.160817i
$30$	5.99048	−	3.95297i	1.09371	−	0.721710i
$31$	1.57902	+	2.73494i	0.283600	+	0.491209i	0.972269	−	0.233867i	$-0.0751379\pi$
$31$	1.57902	+	2.73494i	0.283600	+	0.491209i	−0.688669	+	0.725076i	$0.741805\pi$
$32$	−2.17517	−	3.76750i	−0.384519	−	0.666007i
$33$	−0.295330	−	4.94207i	−0.0514103	−	0.860304i
$34$	−0.598267	+	1.03623i	−0.102602	+	0.177712i
$35$	−8.27619			−1.39893
$36$	2.48210	−	0.297715i	0.413683	−	0.0496191i
$37$	6.10228			1.00321			0.501604	−	0.865097i	$-0.332743\pi$
$37$	6.10228			1.00321			0.501604	+	0.865097i	$0.332743\pi$
$38$	1.61357	−	2.79479i	0.261756	−	0.453375i
$39$	2.67096	+	1.33636i	0.427696	+	0.213989i
$40$	5.87022	+	10.1675i	0.928164	+	1.60763i
$41$	4.70802	+	8.15454i	0.735270	+	1.27352i	0.954605	+	0.297875i	$0.0962778\pi$
$41$	4.70802	+	8.15454i	0.735270	+	1.27352i	−0.219335	+	0.975650i	$0.570389\pi$
$42$	3.60950	+	1.80594i	0.556957	+	0.278662i
$43$	3.66422	−	6.34662i	0.558788	−	0.967850i	−0.438810	−	0.898580i	$-0.644600\pi$
$43$	3.66422	−	6.34662i	0.558788	−	0.967850i	0.997598	−	0.0692698i	$-0.0220669\pi$
$44$	2.38189			0.359084
$45$	−11.4270	+	1.37061i	−1.70343	+	0.204318i
$46$	−8.76501			−1.29233
$47$	−0.381479	+	0.660741i	−0.0556444	+	0.0963789i	−0.892506	−	0.451036i	$-0.851055\pi$
$47$	−0.381479	+	0.660741i	−0.0556444	+	0.0963789i	0.836861	+	0.547415i	$0.184388\pi$
$48$	−0.169344	−	2.83382i	−0.0244427	−	0.409027i
$49$	1.17295	+	2.03161i	0.167564	+	0.290230i
$50$	−5.24796	−	9.08973i	−0.742174	−	1.28548i
$51$	1.60145	−	1.05676i	0.224248	−	0.147976i
$52$	−0.718437	+	1.24437i	−0.0996293	+	0.172563i
$53$	−10.4826			−1.43990			−0.719950	−	0.694026i	$-0.755835\pi$
$53$	−10.4826			−1.43990			−0.719950	+	0.694026i	$0.755835\pi$
$54$	5.28274	+	1.89571i	0.718889	+	0.257973i
$55$	−10.9657			−1.47861
$56$	−3.30111	+	5.71769i	−0.441130	+	0.764059i
$57$	−4.31924	+	2.85016i	−0.572097	+	0.377512i
$58$	0.540070	+	0.935429i	0.0709147	+	0.122828i
$59$	0.153307	+	0.265536i	0.0199589	+	0.0345698i	0.875832	−	0.482615i	$-0.160313\pi$
$59$	0.153307	+	0.265536i	0.0199589	+	0.0345698i	−0.855873	+	0.517185i	$0.826980\pi$
$60$	−0.330291	−	5.52711i	−0.0426403	−	0.713547i
$61$	−3.35396	+	5.80923i	−0.429431	+	0.743796i	−0.996823	−	0.0796519i	$-0.974619\pi$
$61$	−3.35396	+	5.80923i	−0.429431	+	0.743796i	0.567392	+	0.823448i	$0.307952\pi$
$62$	−3.41112			−0.433213
$63$	−3.88047	−	5.17966i	−0.488894	−	0.652575i
$64$	7.97703			0.997128
$65$	3.30751	−	5.72878i	0.410246	−	0.710568i
$66$	4.78246	+	2.39281i	0.588680	+	0.294534i
$67$	−5.53084	−	9.57969i	−0.675699	−	1.17035i	−0.976264	−	0.216584i	$-0.930508\pi$
$67$	−5.53084	−	9.57969i	−0.675699	−	1.17035i	0.300565	−	0.953761i	$-0.402825\pi$
$68$	0.461545	+	0.799419i	0.0559705	+	0.0969438i
$69$	12.5696	+	6.28893i	1.51320	+	0.757099i
$70$	4.46972	−	7.74179i	0.534234	−	0.925320i
$71$	−10.0525			−1.19301			−0.596507	−	0.802608i	$-0.703445\pi$
$71$	−10.0525			−1.19301			−0.596507	+	0.802608i	$0.703445\pi$
$72$	−3.61097	+	8.44115i	−0.425557	+	0.994799i
$73$	−3.16319			−0.370224			−0.185112	−	0.982717i	$-0.559265\pi$
$73$	−3.16319			−0.370224			−0.185112	+	0.982717i	$0.559265\pi$
$74$	−3.29566	+	5.70825i	−0.383113	+	0.663571i
$75$	1.00398	+	16.8007i	0.115930	+	1.93998i
$76$	−1.24482	−	2.15610i	−0.142791	−	0.247321i
$77$	−3.08326	−	5.34037i	−0.351370	−	0.608591i
$78$	−2.69258	+	1.77677i	−0.304874	+	0.201179i
$79$	1.18767	−	2.05710i	0.133623	−	0.231442i	−0.791448	−	0.611237i	$-0.790672\pi$
$79$	1.18767	−	2.05710i	0.133623	−	0.231442i	0.925071	+	0.379795i	$0.124006\pi$
$80$	−6.28779			−0.702996
$81$	−6.21559	−	6.50895i	−0.690621	−	0.723217i
$82$	−10.1707			−1.12316
$83$	−5.09219	+	8.81993i	−0.558940	+	0.968113i	0.438645	+	0.898660i	$0.355459\pi$
$83$	−5.09219	+	8.81993i	−0.558940	+	0.968113i	−0.997585	+	0.0694526i	$0.977875\pi$
$84$	2.59888	−	1.71494i	0.283561	−	0.187115i
$85$	−2.12484	−	3.68034i	−0.230472	−	0.399189i
$86$	3.95787	+	6.85524i	0.426788	+	0.739219i
$87$	−0.103320	−	1.72897i	−0.0110771	−	0.185365i
$88$	−4.37386	+	7.57575i	−0.466255	+	0.807577i
$89$	17.6849			1.87460			0.937298	−	0.348529i	$-0.113319\pi$
$89$	17.6849			1.87460			0.937298	+	0.348529i	$0.113319\pi$
$90$	4.88927	−	11.4294i	0.515374	−	1.20476i
$91$	3.71995			0.389957
$92$	−3.38097	+	5.85602i	−0.352491	+	0.610532i
$93$	4.89176	+	2.44749i	0.507252	+	0.253793i
$94$	−0.412051	−	0.713693i	−0.0424998	−	0.0736118i
$95$	5.73087	+	9.92615i	0.587975	+	1.01840i
$96$	−6.73863	−	3.37154i	−0.687758	−	0.344106i
$97$	8.44064	−	14.6196i	0.857017	−	1.48440i	−0.0177443	−	0.999843i	$-0.505648\pi$
$97$	8.44064	−	14.6196i	0.857017	−	1.48440i	0.874761	−	0.484554i	$-0.161018\pi$
$98$	−2.53390			−0.255963
$99$	−5.14149	−	6.86287i	−0.516739	−	0.689744i
$100$	−8.09729			−0.809729
$101$	−7.54970	+	13.0765i	−0.751224	+	1.30116i	0.196006	+	0.980603i	$0.437203\pi$
$101$	−7.54970	+	13.0765i	−0.751224	+	1.30116i	−0.947230	+	0.320555i	$0.896131\pi$
$102$	0.123626	+	2.06877i	0.0122408	+	0.204838i
$103$	5.89195	+	10.2052i	0.580551	+	1.00554i	0.995414	+	0.0956600i	$0.0304962\pi$
$103$	5.89195	+	10.2052i	0.580551	+	1.00554i	−0.414863	+	0.909884i	$0.636170\pi$
$104$	−2.63853	−	4.57006i	−0.258729	−	0.448131i
$105$	−11.9646	+	7.89516i	−1.16763	+	0.770489i
$106$	5.66136	−	9.80576i	0.549880	−	0.952419i
$107$	9.62158			0.930153			0.465076	−	0.885271i	$-0.346027\pi$
$107$	9.62158			0.930153			0.465076	+	0.885271i	$0.346027\pi$
$108$	3.30428	−	2.79822i	0.317955	−	0.269259i
$109$	−3.41480			−0.327079			−0.163539	−	0.986537i	$-0.552291\pi$
$109$	−3.41480			−0.327079			−0.163539	+	0.986537i	$0.552291\pi$
$110$	5.92223	−	10.2576i	0.564662	−	0.978024i
$111$	8.82187	−	5.82134i	0.837335	−	0.552537i
$112$	−1.76796	−	3.06220i	−0.167057	−	0.289351i
$113$	−4.62319	−	8.00760i	−0.434913	−	0.753291i	0.562376	−	0.826882i	$-0.309888\pi$
$113$	−4.62319	−	8.00760i	−0.434913	−	0.753291i	−0.997289	+	0.0735905i	$0.976554\pi$
$114$	−0.333428	−	5.57962i	−0.0312284	−	0.522580i
$115$	15.5652	−	26.9597i	1.45146	−	2.51401i
$116$	0.833296			0.0773696
$117$	5.13616	−	0.616056i	0.474838	−	0.0569544i
$118$	−0.331187			−0.0304882
$119$	1.19490	−	2.06963i	0.109537	−	0.189723i
$120$	18.1858	+	9.09891i	1.66013	+	0.830613i
$121$	1.41478	+	2.45048i	0.128617	+	0.222771i
$122$	−3.62275	−	6.27479i	−0.327988	−	0.568093i
$123$	14.5854	+	7.29749i	1.31512	+	0.657992i
$124$	−1.31579	+	2.27901i	−0.118161	+	0.204661i
$125$	18.0965			1.61860
$126$	6.94093	−	0.832529i	0.618347	−	0.0741675i
$127$	−4.12328			−0.365882			−0.182941	−	0.983124i	$-0.558562\pi$
$127$	−4.12328			−0.365882			−0.182941	+	0.983124i	$0.558562\pi$
$128$	0.0421835	−	0.0730640i	0.00372853	−	0.00645801i
$129$	−0.757174	−	12.6706i	−0.0666655	−	1.11559i
$130$	3.57258	+	6.18789i	0.313336	+	0.542714i
$131$	11.2127	+	19.4210i	0.979659	+	1.69682i	0.663613	+	0.748076i	$0.269022\pi$
$131$	11.2127	+	19.4210i	0.979659	+	1.69682i	0.316047	+	0.948744i	$0.397644\pi$
$132$	3.44343	−	2.27223i	0.299712	−	0.197772i
$133$	−3.22275	+	5.58196i	−0.279447	+	0.484017i
$134$	11.9482			1.03216
$135$	−15.2121	+	12.8823i	−1.30925	+	1.10874i
$136$	−3.39013			−0.290702
$137$	8.03996	−	13.9256i	0.686900	−	1.18975i	−0.285935	−	0.958249i	$-0.592304\pi$
$137$	8.03996	−	13.9256i	0.686900	−	1.18975i	0.972836	−	0.231497i	$-0.0743624\pi$
$138$	−12.6713	+	8.36148i	−1.07865	+	0.711776i
$139$	6.97636	+	12.0834i	0.591727	+	1.02490i	0.994000	+	0.109382i	$0.0348871\pi$
$139$	6.97636	+	12.0834i	0.591727	+	1.02490i	−0.402272	+	0.915520i	$0.631780\pi$
$140$	−3.44826	−	5.97256i	−0.291431	−	0.504773i
$141$	0.0788288	+	1.31913i	0.00663858	+	0.111091i
$142$	5.42907	−	9.40342i	0.455597	−	0.789117i
$143$	4.92881			0.412167
$144$	−2.94817	−	3.93522i	−0.245681	−	0.327935i
$145$	−3.83630			−0.318587
$146$	1.70835	−	2.95894i	0.141384	−	0.244884i
$147$	3.63377	+	1.81808i	0.299708	+	0.149953i
$148$	2.54250	+	4.40374i	0.208992	+	0.361986i
$149$	−9.40018	−	16.2816i	−0.770093	−	1.33384i	−0.937512	−	0.347954i	$-0.886877\pi$
$149$	−9.40018	−	16.2816i	−0.770093	−	1.33384i	0.167419	−	0.985886i	$-0.446457\pi$
$150$	−16.2581	−	8.13440i	−1.32747	−	0.664171i
$151$	−6.71040	+	11.6228i	−0.546084	+	0.945846i	0.452453	+	0.891788i	$0.350549\pi$
$151$	−6.71040	+	11.6228i	−0.546084	+	0.945846i	−0.998538	+	0.0540579i	$0.982784\pi$
$152$	9.14346			0.741632
$153$	1.30706	−	3.05544i	0.105670	−	0.247018i
$154$	6.66071			0.536736
$155$	6.05758	−	10.4920i	0.486556	−	0.842740i
$156$	0.148458	+	2.48431i	0.0118861	+	0.198904i
$157$	−3.53679	−	6.12590i	−0.282267	−	0.488900i	0.689676	−	0.724118i	$-0.257753\pi$
$157$	−3.53679	−	6.12590i	−0.282267	−	0.488900i	−0.971943	+	0.235218i	$0.924420\pi$
$158$	1.28285	+	2.22195i	0.102058	+	0.176769i
$159$	−15.1544	+	10.0000i	−1.20182	+	0.793053i
$160$	−8.34460	+	14.4533i	−0.659698	+	1.14263i
$161$	17.5061			1.37968
$162$	9.44552	−	2.29896i	0.742110	−	0.180623i
$163$	0.494773			0.0387536			0.0193768	−	0.999812i	$-0.493832\pi$
$163$	0.494773			0.0387536			0.0193768	+	0.999812i	$0.493832\pi$
$164$	−3.92318	+	6.79514i	−0.306349	+	0.530612i
$165$	−15.8527	+	10.4608i	−1.23413	+	0.814373i
$166$	−5.50028	−	9.52676i	−0.426905	−	0.739420i
$167$	4.47485	+	7.75066i	0.346274	+	0.599764i	0.985584	−	0.169185i	$-0.0541134\pi$
$167$	4.47485	+	7.75066i	0.346274	+	0.599764i	−0.639310	+	0.768949i	$0.720780\pi$
$168$	0.682142	+	11.4150i	0.0526284	+	0.880688i
$169$	5.01335	−	8.68338i	0.385642	−	0.667952i
$170$	4.59026			0.352057
$171$	−3.52525	+	8.24076i	−0.269582	+	0.630187i
$172$	6.10676			0.465636
$173$	2.06857	−	3.58287i	0.157271	−	0.272401i	−0.776613	−	0.629978i	$-0.783064\pi$
$173$	2.06857	−	3.58287i	0.157271	−	0.272401i	0.933883	+	0.357577i	$0.116397\pi$
$174$	1.67313	+	0.837115i	0.126839	+	0.0634615i
$175$	10.4816	+	18.1547i	0.792336	+	1.37237i
$176$	−2.34249	−	4.05731i	−0.176572	−	0.305832i
$177$	0.474942	+	0.237628i	0.0356988	+	0.0178612i
$178$	−9.55109	+	16.5430i	−0.715884	+	1.23995i
$179$	8.18598			0.611849			0.305925	−	0.952056i	$-0.401034\pi$
$179$	8.18598			0.611849			0.305925	+	0.952056i	$0.401034\pi$
$180$	−5.75014	−	7.67529i	−0.428590	−	0.572082i
$181$	−19.3485			−1.43816			−0.719080	−	0.694927i	$-0.755437\pi$
$181$	−19.3485			−1.43816			−0.719080	+	0.694927i	$0.755437\pi$
$182$	−2.00903	+	3.47975i	−0.148920	+	0.257936i
$183$	0.693063	+	11.5978i	0.0512327	+	0.857332i
$184$	−12.4169	−	21.5068i	−0.915389	−	1.58550i
$185$	−11.7051	−	20.2738i	−0.860575	−	1.49056i
$186$	−4.93135	+	3.25408i	−0.361584	+	0.238600i
$187$	1.58320	−	2.74219i	0.115775	−	0.200529i
$188$	−0.635770			−0.0463683
$189$	−10.5511	−	3.78625i	−0.767477	−	0.275409i
$190$	−12.3803			−0.898160
$191$	0.593880	−	1.02863i	0.0429716	−	0.0744290i	−0.843740	−	0.536753i	$-0.819651\pi$
$191$	0.593880	−	1.02863i	0.0429716	−	0.0744290i	0.886711	+	0.462324i	$0.152984\pi$
$192$	11.5321	−	7.60977i	0.832261	−	0.549188i
$193$	−3.53894	−	6.12963i	−0.254739	−	0.441220i	0.710086	−	0.704115i	$-0.248656\pi$
$193$	−3.53894	−	6.12963i	−0.254739	−	0.441220i	−0.964825	+	0.262895i	$0.915323\pi$
$194$	9.11708	+	15.7912i	0.654568	+	1.13374i
$195$	−0.683464	−	11.4372i	−0.0489439	−	0.819032i
$196$	−0.977414	+	1.69293i	−0.0698153	+	0.120924i
$197$	−5.26692			−0.375252			−0.187626	−	0.982241i	$-0.560079\pi$
$197$	−5.26692			−0.375252			−0.187626	+	0.982241i	$0.560079\pi$
$198$	9.19649	−	1.10307i	0.653566	−	0.0783919i
$199$	−3.04425			−0.215801			−0.107900	−	0.994162i	$-0.534413\pi$
$199$	−3.04425			−0.215801			−0.107900	+	0.994162i	$0.534413\pi$
$200$	14.8690	−	25.7539i	1.05140	−	1.82108i
$201$	−17.1344	−	8.57286i	−1.20857	−	0.604683i
$202$	−8.15474	−	14.1244i	−0.573766	−	0.993791i
$203$	−1.07867	−	1.86831i	−0.0757077	−	0.131130i
$204$	1.42986	+	0.715400i	0.100110	+	0.0500880i
$205$	18.0614	−	31.2832i	1.26146	−	2.18492i
$206$	−12.7283			−0.886820
$207$	24.1708	−	2.89917i	1.67999	−	0.201506i
$208$	2.82621			0.195963
$209$	−4.27003	+	7.39590i	−0.295364	+	0.511585i
$210$	−0.923623	−	15.4560i	−0.0637361	−	1.06657i
$211$	−6.13180	−	10.6206i	−0.422131	−	0.731152i	0.574017	−	0.818843i	$-0.305384\pi$
$211$	−6.13180	−	10.6206i	−0.422131	−	0.731152i	−0.996148	+	0.0876916i	$0.972051\pi$
$212$	−4.36757	−	7.56485i	−0.299966	−	0.519556i
$213$	−14.5326	+	9.58971i	−0.995758	+	0.657076i
$214$	−5.19633	+	9.00030i	−0.355214	+	0.615248i
$215$	−28.1141			−1.91736
$216$	2.83226	+	15.6478i	0.192711	+	1.06470i
$217$	6.81294			0.462493
$218$	1.84423	−	3.19431i	0.124907	−	0.216346i
$219$	−4.57293	+	3.01756i	−0.309010	+	0.203908i
$220$	−4.56882	−	7.91343i	−0.308030	−	0.533524i
$221$	0.955067	+	1.65422i	0.0642447	+	0.111275i
$222$	0.681015	+	11.3962i	0.0457067	+	0.764861i
$223$	−4.90904	+	8.50271i	−0.328734	+	0.569383i	−0.982261	−	0.187520i	$-0.939955\pi$
$223$	−4.90904	+	8.50271i	−0.328734	+	0.569383i	0.653527	+	0.756903i	$0.273289\pi$
$224$	−9.38515			−0.627072
$225$	17.4786	+	23.3305i	1.16524	+	1.55536i
$226$	9.98739			0.664351
$227$	−6.80019	+	11.7783i	−0.451344	+	0.781752i	−0.998470	−	0.0552991i	$-0.982389\pi$
$227$	−6.80019	+	11.7783i	−0.451344	+	0.781752i	0.547125	+	0.837051i	$0.315722\pi$
$228$	−3.85643	−	1.92949i	−0.255399	−	0.127784i
$229$	−1.42351	−	2.46559i	−0.0940681	−	0.162931i	0.815151	−	0.579248i	$-0.196654\pi$
$229$	−1.42351	−	2.46559i	−0.0940681	−	0.162931i	−0.909219	+	0.416317i	$0.863320\pi$
$230$	16.8126	+	29.1203i	1.10859	+	1.92013i
$231$	−9.55188	−	4.77909i	−0.628467	−	0.314441i
$232$	−1.53018	+	2.65035i	−0.100461	+	0.174004i
$233$	−12.6232			−0.826972			−0.413486	−	0.910511i	$-0.635689\pi$
$233$	−12.6232			−0.826972			−0.413486	+	0.910511i	$0.635689\pi$
$234$	−2.19761	+	5.13723i	−0.143662	+	0.335831i
$235$	2.92693			0.190932
$236$	−0.127750	+	0.221270i	−0.00831583	+	0.0144034i
$237$	−0.245419	−	4.10687i	−0.0159417	−	0.266770i
$238$	1.29066	+	2.23549i	0.0836612	+	0.144906i
$239$	6.27728	+	10.8726i	0.406044	+	0.703288i	0.994442	−	0.105283i	$-0.0335747\pi$
$239$	6.27728	+	10.8726i	0.406044	+	0.703288i	−0.588399	+	0.808571i	$0.700241\pi$
$240$	−9.09006	+	5.99830i	−0.586761	+	0.387189i
$241$	−7.59619	+	13.1570i	−0.489313	+	0.847516i	−0.999924	−	0.0122961i	$-0.996086\pi$
$241$	−7.59619	+	13.1570i	−0.489313	+	0.847516i	0.510611	+	0.859812i	$0.329419\pi$
$242$	−3.05633			−0.196468
$243$	−15.1950	−	3.48035i	−0.974758	−	0.223265i
$244$	−5.58969			−0.357843
$245$	4.49978	−	7.79385i	0.287481	−	0.497931i
$246$	−14.7034	+	9.70241i	−0.937454	+	0.618603i
$247$	−2.57589	−	4.46157i	−0.163900	−	0.283883i
$248$	−4.83236	−	8.36989i	−0.306855	−	0.531488i
$249$	1.05225	+	17.6084i	0.0666836	+	1.11589i
$250$	−9.77339	+	16.9280i	−0.618123	+	1.07062i
$251$	5.75737			0.363402			0.181701	−	0.983354i	$-0.441840\pi$
$251$	5.75737			0.363402			0.181701	+	0.983354i	$0.441840\pi$
$252$	2.12114	−	4.95846i	0.133619	−	0.312354i
$253$	23.1950			1.45826
$254$	2.22686	−	3.85703i	0.139726	−	0.242012i
$255$	−6.58272	−	3.29353i	−0.412226	−	0.206249i
$256$	8.02259	+	13.8955i	0.501412	+	0.868471i
$257$	−0.660494	−	1.14401i	−0.0412005	−	0.0713614i	0.844690	−	0.535256i	$-0.179785\pi$
$257$	−0.660494	−	1.14401i	−0.0412005	−	0.0713614i	−0.885890	+	0.463895i	$0.846452\pi$
$258$	12.2614	+	6.13475i	0.763362	+	0.381933i
$259$	6.58234	−	11.4009i	0.409006	−	0.708420i
$260$	5.51228			0.341857
$261$	−1.79873	−	2.40095i	−0.111339	−	0.148615i
$262$	−24.2226			−1.49648
$263$	−7.82926	+	13.5607i	−0.482773	+	0.836187i	−0.999804	−	0.0197791i	$-0.993704\pi$
$263$	−7.82926	+	13.5607i	−0.482773	+	0.836187i	0.517031	+	0.855966i	$0.327037\pi$
$264$	0.903814	+	15.1245i	0.0556259	+	0.930849i
$265$	20.1072	+	34.8268i	1.23518	+	2.13939i
$266$	−3.48102	−	6.02930i	−0.213435	−	0.369680i
$267$	25.5665	−	16.8707i	1.56465	−	1.03247i
$268$	4.60883	−	7.98272i	0.281529	−	0.487622i
$269$	9.10901			0.555386			0.277693	−	0.960670i	$-0.410430\pi$
$269$	9.10901			0.555386			0.277693	+	0.960670i	$0.410430\pi$
$270$	−3.83490	−	21.1872i	−0.233385	−	1.28941i
$271$	14.8503			0.902091			0.451046	−	0.892501i	$-0.351051\pi$
$271$	14.8503			0.902091			0.451046	+	0.892501i	$0.351051\pi$
$272$	0.907821	−	1.57239i	0.0550447	−	0.0953402i
$273$	5.37782	−	3.54869i	0.325480	−	0.214776i
$274$	8.68429	+	15.0416i	0.524637	+	0.908698i
$275$	13.8878	+	24.0543i	0.837465	+	1.45053i
$276$	0.698644	+	11.6912i	0.0420534	+	0.703726i
$277$	10.4412	−	18.0847i	0.627352	−	1.08661i	−0.360729	−	0.932671i	$-0.617472\pi$
$277$	10.4412	−	18.0847i	0.627352	−	1.08661i	0.988081	−	0.153935i	$-0.0491946\pi$
$278$	−15.0709			−0.903893
$279$	9.40668	−	1.12828i	0.563163	−	0.0675485i
$280$	25.3281			1.51364
$281$	−8.37487	+	14.5057i	−0.499603	+	0.865337i	−1.00000		0.000458759i	$-0.999854\pi$
$281$	−8.37487	+	14.5057i	−0.499603	+	0.865337i	0.500397	+	0.865796i	$0.333187\pi$
$282$	−1.27652	−	0.638683i	−0.0760159	−	0.0380330i
$283$	−7.71129	−	13.3564i	−0.458389	−	0.793953i	0.540487	−	0.841352i	$-0.318240\pi$
$283$	−7.71129	−	13.3564i	−0.458389	−	0.793953i	−0.998876	+	0.0473996i	$0.984907\pi$
$284$	−4.18836	−	7.25446i	−0.248534	−	0.430473i
$285$	17.7541	+	8.88291i	1.05166	+	0.526178i
$286$	−2.66190	+	4.61055i	−0.157402	+	0.272627i
$287$	20.3136			1.19907
$288$	−12.9581	+	1.55426i	−0.763566	+	0.0915857i
$289$	−15.7729			−0.927816
$290$	2.07187	−	3.58859i	0.121664	−	0.210729i
$291$	−1.74417	−	29.1872i	−0.102245	−	1.71098i
$292$	−1.31794	−	2.28274i	−0.0771266	−	0.133587i
$293$	−3.78792	−	6.56087i	−0.221293	−	0.383290i	0.733908	−	0.679249i	$-0.237694\pi$
$293$	−3.78792	−	6.56087i	−0.221293	−	0.383290i	−0.955201	+	0.295959i	$0.904361\pi$
$294$	−3.66318	+	2.41724i	−0.213641	+	0.140976i
$295$	0.588132	−	1.01867i	0.0342424	−	0.0593095i
$296$	−18.6752			−1.08547
$297$	−13.9798	−	5.01665i	−0.811190	−	0.291096i
$298$	20.3070			1.17635
$299$	−6.99619	+	12.1178i	−0.404600	+	0.700788i
$300$	−11.7060	+	7.72450i	−0.675846	+	0.445974i
$301$	−7.90496	−	13.6918i	−0.455634	−	0.789182i
$302$	−7.24817	−	12.5542i	−0.417086	−	0.722413i
$303$	1.56007	+	26.1064i	0.0896237	+	1.49977i
$304$	−2.44846	+	4.24086i	−0.140429	+	0.243230i
$305$	25.7336			1.47350
$306$	2.15224	+	2.87282i	0.123036	+	0.164228i
$307$	−20.6263			−1.17721			−0.588603	−	0.808422i	$-0.700322\pi$
$307$	−20.6263			−1.17721			−0.588603	+	0.808422i	$0.700322\pi$
$308$	2.56927	−	4.45011i	0.146398	−	0.253568i
$309$	18.2531	+	9.13259i	1.03838	+	0.519535i
$310$	6.54304	+	11.3329i	0.371620	+	0.643664i
$311$	−2.05340	−	3.55660i	−0.116438	−	0.201676i	0.801916	−	0.597437i	$-0.203814\pi$
$311$	−2.05340	−	3.55660i	−0.116438	−	0.201676i	−0.918354	+	0.395761i	$0.870481\pi$
$312$	−8.17410	−	4.08975i	−0.462767	−	0.231536i
$313$	−0.490020	+	0.848739i	−0.0276976	+	0.0479736i	−0.879542	−	0.475821i	$-0.842151\pi$
$313$	−0.490020	+	0.848739i	−0.0276976	+	0.0479736i	0.851844	+	0.523795i	$0.175484\pi$
$314$	7.64046			0.431176
$315$	−9.76521	+	22.8276i	−0.550207	+	1.28619i
$316$	1.97936			0.111347
$317$	14.3911	−	24.9260i	0.808282	−	1.39999i	−0.105770	−	0.994391i	$-0.533731\pi$
$317$	14.3911	−	24.9260i	0.808282	−	1.39999i	0.914053	−	0.405596i	$-0.132936\pi$
$318$	−1.16986	−	19.5766i	−0.0656026	−	1.09780i
$319$	−1.42920	−	2.47544i	−0.0800198	−	0.138598i
$320$	−15.3011	−	26.5023i	−0.855359	−	1.48153i
$321$	13.9096	−	9.17861i	0.776359	−	0.512300i
$322$	−9.45454	+	16.3757i	−0.526881	+	0.912585i
$323$	−3.30965			−0.184154
$324$	2.10751	−	7.19746i	0.117084	−	0.399859i
$325$	−16.7556			−0.929432
$326$	−0.267212	+	0.462825i	−0.0147995	+	0.0256335i
$327$	−4.93667	+	3.25759i	−0.272999	+	0.180145i
$328$	−14.4082	−	24.9558i	−0.795562	−	1.37795i
$329$	0.822978	+	1.42544i	0.0453723	+	0.0785871i
$330$	−1.22377	−	20.4787i	−0.0673663	−	1.12731i
$331$	9.95768	−	17.2472i	0.547324	−	0.947993i	−0.451133	−	0.892457i	$-0.648980\pi$
$331$	9.95768	−	17.2472i	0.547324	−	0.947993i	0.998457	−	0.0555359i	$-0.0176867\pi$
$332$	−8.48660			−0.465763
$333$	7.20018	−	16.8314i	0.394568	−	0.922358i
$334$	−9.66693			−0.528951
$335$	−21.2179	+	36.7505i	−1.15926	+	2.00790i
$336$	−5.47711	−	2.74036i	−0.298801	−	0.149499i
$337$	−2.56806	−	4.44801i	−0.139891	−	0.242299i	0.787564	−	0.616233i	$-0.211342\pi$
$337$	−2.56806	−	4.44801i	−0.139891	−	0.242299i	−0.927455	+	0.373934i	$0.878009\pi$
$338$	5.41512	+	9.37927i	0.294544	+	0.510165i
$339$	−14.3225	−	7.16599i	−0.777893	−	0.389203i
$340$	1.77062	−	3.06681i	0.0960256	−	0.166321i
$341$	9.02691			0.488835
$342$	−5.80477	−	7.74821i	−0.313886	−	0.418975i
$343$	20.1622			1.08866
$344$	−11.2138	+	19.4229i	−0.604609	+	1.04721i
$345$	−3.21639	−	53.8234i	−0.173165	−	2.89775i
$346$	2.23435	+	3.87000i	0.120119	+	0.208053i
$347$	−2.95607	−	5.12006i	−0.158690	−	0.274859i	0.775706	−	0.631094i	$-0.217394\pi$
$347$	−2.95607	−	5.12006i	−0.158690	−	0.274859i	−0.934397	+	0.356235i	$0.884060\pi$
$348$	1.20467	−	0.794932i	0.0645771	−	0.0426128i
$349$	−9.25123	+	16.0236i	−0.495207	+	0.857724i	−0.999985	−	0.00552570i	$-0.998241\pi$
$349$	−9.25123	+	16.0236i	−0.495207	+	0.857724i	0.504778	+	0.863249i	$0.331574\pi$
$350$	−22.6432			−1.21033
$351$	6.83750	−	5.79031i	0.364958	−	0.309064i
$352$	−12.4350			−0.662788
$353$	13.9240	−	24.1171i	0.741100	−	1.28362i	−0.210894	−	0.977509i	$-0.567638\pi$
$353$	13.9240	−	24.1171i	0.741100	−	1.28362i	0.951995	−	0.306115i	$-0.0990291\pi$
$354$	−0.478786	+	0.315939i	−0.0254472	+	0.0167920i
$355$	19.2822	+	33.3978i	1.02339	+	1.77257i
$356$	7.36838	+	12.7624i	0.390523	+	0.676406i
$357$	−0.246915	−	4.13189i	−0.0130681	−	0.218683i
$358$	−4.42101	+	7.65741i	−0.233657	+	0.404707i
$359$	−15.8603			−0.837074			−0.418537	−	0.908200i	$-0.637457\pi$
$359$	−15.8603			−0.837074			−0.418537	+	0.908200i	$0.637457\pi$
$360$	34.9707	−	4.19455i	1.84312	−	0.221072i
$361$	−10.0736			−0.530190
$362$	10.4495	−	18.0991i	0.549216	−	0.951269i
$363$	4.38297	+	2.19293i	0.230046	+	0.115099i
$364$	1.54991	+	2.68452i	0.0812374	+	0.140707i
$365$	6.06748	+	10.5092i	0.317586	+	0.550076i
$366$	−11.2232	−	5.61530i	−0.586646	−	0.293517i
$367$	−11.4363	+	19.8083i	−0.596971	+	1.03398i	0.396294	+	0.918124i	$0.370296\pi$
$367$	−11.4363	+	19.8083i	−0.596971	+	1.03398i	−0.993265	+	0.115861i	$0.963037\pi$
$368$	13.3002			0.693320
$369$	28.0471	−	3.36410i	1.46007	−	0.175128i
$370$	25.2863			1.31457
$371$	−11.3073	+	19.5848i	−0.587045	+	1.01679i
$372$	0.271895	+	4.54991i	0.0140971	+	0.235902i
$373$	−6.67563	−	11.5625i	−0.345651	−	0.598685i	0.639821	−	0.768524i	$-0.279009\pi$
$373$	−6.67563	−	11.5625i	−0.345651	−	0.598685i	−0.985472	+	0.169839i	$0.945675\pi$
$374$	1.71008	+	2.96195i	0.0884263	+	0.153159i
$375$	26.1616	−	17.2634i	1.35098	−	0.891476i
$376$	1.16746	−	2.02210i	0.0602073	−	0.104282i
$377$	1.72433			0.0888073
$378$	9.24009	−	7.82494i	0.475259	−	0.402471i
$379$	−26.0228			−1.33670			−0.668352	−	0.743845i	$-0.733000\pi$
$379$	−26.0228			−1.33670			−0.668352	+	0.743845i	$0.733000\pi$
$380$	−4.77551	+	8.27143i	−0.244979	+	0.424315i
$381$	−5.96089	+	3.93344i	−0.305386	+	0.201516i
$382$	0.641474	+	1.11106i	0.0328206	+	0.0568470i
$383$	−12.6399	−	21.8929i	−0.645867	−	1.11867i	−0.984101	−	0.177612i	$-0.943163\pi$
$383$	−12.6399	−	21.8929i	−0.645867	−	1.11867i	0.338234	−	0.941062i	$-0.390170\pi$
$384$	−0.00871681	−	0.145868i	−0.000444828	−	0.00744379i
$385$	−11.8283	+	20.4872i	−0.602827	+	1.04413i
$386$	7.64511			0.389126
$387$	−13.1819	−	17.5952i	−0.670074	−	0.894415i
$388$	14.0671			0.714149
$389$	−15.3122	+	26.5215i	−0.776358	+	1.34469i	0.157670	+	0.987492i	$0.449602\pi$
$389$	−15.3122	+	26.5215i	−0.776358	+	1.34469i	−0.934028	+	0.357200i	$0.883732\pi$
$390$	11.0678	+	5.53754i	0.560438	+	0.280404i
$391$	4.49456	+	7.78480i	0.227299	+	0.393694i
$392$	−3.58964	−	6.21745i	−0.181304	−	0.314028i
$393$	34.7367	+	17.3798i	1.75224	+	0.876696i
$394$	2.84451	−	4.92683i	0.143304	−	0.248210i
$395$	−9.11248			−0.458499
$396$	2.81043	−	6.56979i	0.141230	−	0.330144i
$397$	11.6965			0.587031			0.293515	−	0.955954i	$-0.405175\pi$
$397$	11.6965			0.587031			0.293515	+	0.955954i	$0.405175\pi$
$398$	1.64411	−	2.84768i	0.0824116	−	0.142741i
$399$	0.665948	+	11.1440i	0.0333391	+	0.557900i
$400$	7.96335	+	13.7929i	0.398168	+	0.689646i
$401$	−1.07915	−	1.86915i	−0.0538903	−	0.0933407i	0.837822	−	0.545944i	$-0.183829\pi$
$401$	−1.07915	−	1.86915i	−0.0538903	−	0.0933407i	−0.891712	+	0.452603i	$0.850495\pi$
$402$	17.2731	−	11.3981i	0.861503	−	0.568485i
$403$	−2.72274	+	4.71592i	−0.135629	+	0.234917i
$404$	−12.5823			−0.625992
$405$	−9.70246	+	33.1354i	−0.482119	+	1.64651i
$406$	2.33023			0.115647
$407$	8.72137	−	15.1059i	0.432302	−	0.748769i
$408$	−4.90101	+	3.23406i	−0.242636	+	0.160110i
$409$	−9.98826	−	17.3002i	−0.493888	−	0.855438i	0.506088	−	0.862482i	$-0.331091\pi$
$409$	−9.98826	−	17.3002i	−0.493888	−	0.855438i	−0.999975	+	0.00704370i	$0.997758\pi$
$410$	19.5088	+	33.7903i	0.963472	+	1.66878i
$411$	−1.66138	−	27.8016i	−0.0819497	−	1.37135i
$412$	−4.90974	+	8.50392i	−0.241886	+	0.418958i
$413$	0.661470			0.0325488
$414$	−10.3420	+	24.1759i	−0.508281	+	1.18818i
$415$	39.0703			1.91789
$416$	3.75070	−	6.49640i	0.183893	−	0.318512i
$417$	21.6126	+	10.8134i	1.05837	+	0.529536i
$418$	−4.61223	−	7.98862i	−0.225592	−	0.390736i
$419$	−6.15943	−	10.6684i	−0.300908	−	0.521187i	0.675434	−	0.737420i	$-0.263956\pi$
$419$	−6.15943	−	10.6684i	−0.300908	−	0.521187i	−0.976342	+	0.216233i	$0.930623\pi$
$420$	−10.6826	−	5.34484i	−0.521259	−	0.260801i
$421$	13.1455	−	22.7686i	0.640671	−	1.10968i	−0.344612	−	0.938745i	$-0.611989\pi$
$421$	13.1455	−	22.7686i	0.640671	−	1.10968i	0.985283	−	0.170930i	$-0.0546772\pi$
$422$	13.2464			0.644826
$423$	1.37236	+	1.83182i	0.0667263	+	0.0890663i
$424$	32.0806			1.55797
$425$	−5.38214	+	9.32214i	−0.261072	+	0.452190i
$426$	−1.12186	−	18.7733i	−0.0543544	−	0.909571i
$427$	7.23563	+	12.5325i	0.350156	+	0.606489i
$428$	4.00881	+	6.94347i	0.193773	+	0.335625i
$429$	7.12542	−	4.70189i	0.344019	−	0.227009i
$430$	15.1836	−	26.2987i	0.732217	−	1.26824i
$431$	−33.2790			−1.60299			−0.801496	−	0.598001i	$-0.795962\pi$
$431$	−33.2790			−1.60299			−0.801496	+	0.598001i	$0.795962\pi$
$432$	−8.01612	−	2.87658i	−0.385676	−	0.138400i
$433$	−18.4333			−0.885849			−0.442924	−	0.896559i	$-0.646059\pi$
$433$	−18.4333			−0.885849			−0.442924	+	0.896559i	$0.646059\pi$
$434$	−3.67947	+	6.37303i	−0.176620	+	0.305915i
$435$	−5.54602	+	3.65968i	−0.265911	+	0.175468i
$436$	−1.42277	−	2.46431i	−0.0681384	−	0.118019i
$437$	−12.1222	−	20.9962i	−0.579882	−	1.00439i
$438$	−0.353013	−	5.90735i	−0.0168676	−	0.282264i
$439$	−2.83242	+	4.90590i	−0.135184	+	0.234146i	−0.925668	−	0.378337i	$-0.876496\pi$
$439$	−2.83242	+	4.90590i	−0.135184	+	0.234146i	0.790484	+	0.612483i	$0.209829\pi$
$440$	33.5589			1.59986
$441$	6.98761	−	0.838127i	0.332743	−	0.0399108i
$442$	−2.06321			−0.0981370
$443$	−10.1167	+	17.5227i	−0.480660	+	0.832527i	−0.999754	−	0.0221903i	$-0.992936\pi$
$443$	−10.1167	+	17.5227i	−0.480660	+	0.832527i	0.519094	+	0.854717i	$0.326269\pi$
$444$	7.87662	+	3.94091i	0.373808	+	0.187027i
$445$	−33.9223	−	58.7551i	−1.60807	−	2.78526i
$446$	−5.30245	−	9.18412i	−0.251078	−	0.434881i
$447$	−29.1215	−	14.5704i	−1.37740	−	0.689155i
$448$	8.60457	−	14.9035i	0.406528	−	0.704126i
$449$	2.42977			0.114668			0.0573339	−	0.998355i	$-0.481740\pi$
$449$	2.42977			0.114668			0.0573339	+	0.998355i	$0.481740\pi$
$450$	−31.2637	+	3.74992i	−1.47378	+	0.176773i
$451$	26.9148			1.26737
$452$	3.85249	−	6.67270i	0.181206	−	0.313857i
$453$	1.38664	+	23.2041i	0.0651499	+	1.09022i
$454$	−7.34516	−	12.7222i	−0.344726	−	0.597082i
$455$	−7.13542	−	12.3589i	−0.334514	−	0.579395i
$456$	13.2184	−	8.72250i	0.619009	−	0.408468i
$457$	−18.8081	+	32.5765i	−0.879805	+	1.52387i	−0.0282501	+	0.999601i	$0.508993\pi$
$457$	−18.8081	+	32.5765i	−0.879805	+	1.52387i	−0.851555	+	0.524266i	$0.824340\pi$
$458$	3.07518			0.143694
$459$	−1.02519	−	5.66404i	−0.0478520	−	0.264375i
$460$	25.9408			1.20950
$461$	−6.64785	+	11.5144i	−0.309621	+	0.536280i	−0.978280	−	0.207290i	$-0.933536\pi$
$461$	−6.64785	+	11.5144i	−0.309621	+	0.536280i	0.668658	+	0.743570i	$0.266869\pi$
$462$	9.62919	−	6.35406i	0.447990	−	0.295618i
$463$	10.0206	+	17.3563i	0.465699	+	0.806614i	0.999233	−	0.0391645i	$-0.0124696\pi$
$463$	10.0206	+	17.3563i	0.465699	+	0.806614i	−0.533534	+	0.845779i	$0.679136\pi$
$464$	−0.819512	−	1.41944i	−0.0380449	−	0.0658957i
$465$	−1.25174	−	20.9467i	−0.0580480	−	0.971380i
$466$	6.81740	−	11.8081i	0.315810	−	0.546999i
$467$	24.7703			1.14623			0.573115	−	0.819475i	$-0.305735\pi$
$467$	24.7703			1.14623			0.573115	+	0.819475i	$0.305735\pi$
$468$	2.58455	+	3.44986i	0.119471	+	0.159470i
$469$	−23.8638			−1.10193
$470$	−1.58075	+	2.73794i	−0.0729145	+	0.126292i
$471$	−10.9569	−	5.48206i	−0.504867	−	0.252600i
$472$	−0.469175	−	0.812635i	−0.0215955	−	0.0374045i
$473$	−10.4738	−	18.1411i	−0.481586	−	0.834131i
$474$	3.97423	+	1.98843i	0.182542	+	0.0913314i
$475$	14.5160	−	25.1425i	0.666042	−	1.15362i
$476$	1.99142			0.0912764
$477$	−12.3686	+	28.9134i	−0.566321	+	1.32386i
$478$	−13.5607			−0.620252
$479$	4.81471	−	8.33932i	0.219990	−	0.381033i	−0.734815	−	0.678268i	$-0.762731\pi$
$479$	4.81471	−	8.33932i	0.219990	−	0.381033i	0.954804	+	0.297235i	$0.0960643\pi$
$480$	1.72433	+	28.8551i	0.0787044	+	1.31705i
$481$	5.26116	+	9.11259i	0.239888	+	0.415498i
$482$	−8.20495	−	14.2114i	−0.373725	−	0.647311i
$483$	25.3081	−	16.7002i	1.15156	−	0.759884i
$484$	−1.17893	+	2.04197i	−0.0535879	+	0.0928170i
$485$	−64.7616			−2.94067
$486$	11.4620	−	12.3342i	0.519926	−	0.559490i
$487$	−31.1756			−1.41270			−0.706351	−	0.707861i	$-0.749660\pi$
$487$	−31.1756			−1.41270			−0.706351	+	0.707861i	$0.749660\pi$
$488$	10.2643	−	17.7783i	0.464644	−	0.804787i
$489$	0.715277	−	0.471994i	0.0323460	−	0.0213443i
$490$	4.86040	+	8.41845i	0.219570	+	0.380307i
$491$	−16.7143	−	28.9500i	−0.754305	−	1.30649i	−0.945719	−	0.324985i	$-0.894641\pi$
$491$	−16.7143	−	28.9500i	−0.754305	−	1.30649i	0.191415	−	0.981509i	$-0.438693\pi$
$492$	0.810685	+	13.5661i	0.0365485	+	0.611606i
$493$	0.553879	−	0.959346i	0.0249454	−	0.0432068i
$494$	5.56465			0.250365
$495$	−12.9386	+	30.2457i	−0.581546	+	1.35945i
$496$	5.17610			0.232414
$497$	−10.8433	+	18.7812i	−0.486390	+	0.842452i
$498$	−17.0397	−	8.52549i	−0.763569	−	0.382037i
$499$	20.6223	+	35.7189i	0.923181	+	1.59900i	0.794460	+	0.607316i	$0.207754\pi$
$499$	20.6223	+	35.7189i	0.923181	+	1.59900i	0.128721	+	0.991681i	$0.458913\pi$
$500$	7.53988	+	13.0595i	0.337194	+	0.584036i
$501$	13.8630	+	6.93606i	0.619352	+	0.309880i
$502$	−3.10939	+	5.38561i	−0.138779	+	0.240372i
$503$	25.5727			1.14023			0.570115	−	0.821565i	$-0.306899\pi$
$503$	25.5727			1.14023			0.570115	+	0.821565i	$0.306899\pi$
$504$	11.8756	+	15.8516i	0.528983	+	0.706087i
$505$	57.9258			2.57767
$506$	−12.5269	+	21.6973i	−0.556891	+	0.964563i
$507$	−1.03596	−	17.3358i	−0.0460085	−	0.769911i
$508$	−1.71796	−	2.97559i	−0.0762219	−	0.132020i
$509$	−2.23394	−	3.86929i	−0.0990175	−	0.171503i	0.812261	−	0.583295i	$-0.198237\pi$
$509$	−2.23394	−	3.86929i	−0.0990175	−	0.171503i	−0.911278	+	0.411791i	$0.864903\pi$
$510$	6.63599	−	4.37893i	0.293847	−	0.193902i
$511$	−3.41204	+	5.90982i	−0.150940	+	0.261435i
$512$	−17.1623			−0.758475
$513$	2.76503	+	15.2764i	0.122079	+	0.674468i
$514$	1.42685			0.0629358
$515$	22.6033	−	39.1500i	0.996019	−	1.72516i
$516$	8.82836	−	5.82561i	0.388647	−	0.256458i
$517$	1.09042	+	1.88866i	0.0479565	+	0.0830631i
$518$	7.10985	+	12.3146i	0.312389	+	0.541073i
$519$	−0.427449	−	7.15298i	−0.0187629	−	0.313981i
$520$	−10.1222	+	17.5321i	−0.443887	+	0.768834i
$521$	1.99483			0.0873952			0.0436976	−	0.999045i	$-0.486086\pi$
$521$	1.99483			0.0873952			0.0436976	+	0.999045i	$0.486086\pi$
$522$	3.21736	−	0.385906i	0.140820	−	0.0168906i
$523$	32.4353			1.41830			0.709148	−	0.705059i	$-0.249080\pi$
$523$	32.4353			1.41830			0.709148	+	0.705059i	$0.249080\pi$
$524$	−9.34351	+	16.1834i	−0.408173	+	0.706977i
$525$	32.4718	+	16.2466i	1.41719	+	0.709061i
$526$	−8.45670	−	14.6474i	−0.368730	−	0.638659i
$527$	1.74917	+	3.02965i	0.0761949	+	0.131973i
$528$	−7.25699	−	3.63089i	−0.315820	−	0.158014i
$529$	−21.4242	+	37.1077i	−0.931485	+	1.61338i
$530$	−43.4373			−1.88680
$531$	0.913297	−	0.109545i	0.0396337	−	0.00475386i
$532$	−5.37100			−0.232863
$533$	−8.11816	+	14.0611i	−0.351637	+	0.609053i
$534$	1.97364	+	33.0270i	0.0854076	+	1.42922i
$535$	−18.4556	−	31.9661i	−0.797906	−	1.38201i
$536$	16.9263	+	29.3173i	0.731107	+	1.26631i
$537$	11.8342	−	7.80911i	0.510684	−	0.336988i
$538$	−4.91951	+	8.52083i	−0.212095	+	0.367359i
$539$	6.70551			0.288827
$540$	−15.6347	−	5.61052i	−0.672811	−	0.241438i
$541$	2.33676			0.100465			0.0502326	−	0.998738i	$-0.484004\pi$
$541$	2.33676			0.100465			0.0502326	+	0.998738i	$0.484004\pi$
$542$	−8.02021	+	13.8914i	−0.344497	+	0.596687i
$543$	−27.9715	+	18.4577i	−1.20037	+	0.792095i
$544$	−2.40956	−	4.17348i	−0.103309	−	0.178936i
$545$	6.55010	+	11.3451i	0.280575	+	0.485971i
$546$	0.415147	+	6.94711i	0.0177666	+	0.297309i
$547$	−5.43167	+	9.40793i	−0.232242	+	0.402254i	−0.958467	−	0.285202i	$-0.907939\pi$
$547$	−5.43167	+	9.40793i	−0.232242	+	0.402254i	0.726226	+	0.687456i	$0.241273\pi$
$548$	13.3993			0.572391
$549$	12.0658	+	16.1054i	0.514954	+	0.687361i
$550$	−30.0015			−1.27927
$551$	−1.49385	+	2.58743i	−0.0636403	+	0.110228i
$552$	−38.4674	−	19.2464i	−1.63728	−	0.819181i
$553$	−2.56220	−	4.43785i	−0.108956	−	0.188717i
$554$	11.2780	+	19.5340i	0.479156	+	0.829922i
$555$	−36.2621	−	18.1430i	−1.53924	−	0.770128i
$556$	−5.81338	+	10.0691i	−0.246542	+	0.427023i
$557$	22.0642			0.934892			0.467446	−	0.884022i	$-0.345174\pi$
$557$	22.0642			0.934892			0.467446	+	0.884022i	$0.345174\pi$
$558$	−4.02484	+	9.40863i	−0.170385	+	0.398299i
$559$	12.6366			0.534472
$560$	−6.78244	+	11.7475i	−0.286610	+	0.496424i
$561$	−0.327153	−	5.47462i	−0.0138124	−	0.231138i
$562$	−9.04603	−	15.6682i	−0.381584	−	0.660923i
$563$	−15.6295	−	27.0712i	−0.658707	−	1.14091i	−0.980951	−	0.194257i	$-0.937770\pi$
$563$	−15.6295	−	27.0712i	−0.658707	−	1.14091i	0.322244	−	0.946657i	$-0.395563\pi$
$564$	−0.919113	+	0.606500i	−0.0387016	+	0.0255382i
$565$	−17.7359	+	30.7195i	−0.746156	+	1.29238i
$566$	16.6586			0.700212
$567$	−18.8653	+	4.59165i	−0.792268	+	0.192831i
$568$	30.7643			1.29084
$569$	11.4167	−	19.7743i	0.478613	−	0.828983i	−0.521086	−	0.853504i	$-0.674473\pi$
$569$	11.4167	−	19.7743i	0.478613	−	0.828983i	0.999699	+	0.0245216i	$0.00780625\pi$
$570$	−17.8978	+	11.8103i	−0.749656	+	0.494679i
$571$	17.7840	+	30.8028i	0.744238	+	1.28906i	0.950550	+	0.310572i	$0.100521\pi$
$571$	17.7840	+	30.8028i	0.744238	+	1.28906i	−0.206311	+	0.978486i	$0.566146\pi$
$572$	2.05358	+	3.55690i	0.0858644	+	0.148722i
$573$	−0.122719	−	2.05360i	−0.00512667	−	0.0857902i
$574$	−10.9708	+	19.0019i	−0.457911	+	0.793125i
$575$	−78.8520			−3.28835
$576$	9.41223	−	22.0024i	0.392176	−	0.916768i
$577$	−27.0200			−1.12486			−0.562430	−	0.826845i	$-0.690133\pi$
$577$	−27.0200			−1.12486			−0.562430	+	0.826845i	$0.690133\pi$
$578$	8.51846	−	14.7544i	0.354321	−	0.613702i
$579$	−10.9636	−	5.48540i	−0.455630	−	0.227966i
$580$	−1.59839	−	2.76849i	−0.0663694	−	0.114955i
$581$	10.9856	+	19.0276i	0.455758	+	0.789396i
$582$	28.2445	+	14.1316i	1.17077	+	0.585772i
$583$	−14.9818	+	25.9492i	−0.620481	+	1.07470i
$584$	9.68051			0.400582
$585$	−11.8987	−	15.8823i	−0.491949	−	0.656654i
$586$	8.18298			0.338036
$587$	8.09364	−	14.0186i	0.334060	−	0.578610i	−0.649243	−	0.760581i	$-0.724914\pi$
$587$	8.09364	−	14.0186i	0.334060	−	0.578610i	0.983304	+	0.181971i	$0.0582477\pi$
$588$	0.201973	+	3.37983i	0.00832922	+	0.139382i
$589$	−4.71764	−	8.17119i	−0.194387	−	0.336688i
$590$	0.635265	+	1.10031i	0.0261534	+	0.0452991i
$591$	−7.61422	+	5.02443i	−0.313207	+	0.206678i
$592$	5.00089	−	8.66180i	0.205535	−	0.355998i
$593$	11.5743			0.475300			0.237650	−	0.971351i	$-0.423623\pi$
$593$	11.5743			0.475300			0.237650	+	0.971351i	$0.423623\pi$
$594$	12.2428	−	10.3678i	0.502328	−	0.425395i
$595$	−9.16800			−0.375852
$596$	7.83313	−	13.5674i	0.320858	−	0.555742i
$597$	−4.40097	+	2.90409i	−0.180120	+	0.118857i
$598$	−7.55687	−	13.0889i	−0.309023	−	0.535244i
$599$	−1.87626	−	3.24978i	−0.0766619	−	0.132782i	0.825146	−	0.564920i	$-0.191093\pi$
$599$	−1.87626	−	3.24978i	−0.0766619	−	0.132782i	−0.901808	+	0.432137i	$0.857760\pi$
$600$	−3.07254	−	51.4161i	−0.125436	−	2.09905i
$601$	4.35337	−	7.54026i	0.177578	−	0.307574i	−0.763473	−	0.645840i	$-0.776507\pi$
$601$	4.35337	−	7.54026i	0.177578	−	0.307574i	0.941050	+	0.338267i	$0.109841\pi$
$602$	17.0769			0.696004
$603$	−32.9489	+	3.95204i	−1.34178	+	0.160940i
$604$	−11.1835			−0.455050
$605$	5.42753	−	9.40076i	0.220660	−	0.382195i
$606$	−25.2632	−	12.6399i	−1.02625	−	0.513462i
$607$	3.00340	+	5.20204i	0.121904	+	0.211144i	0.920519	−	0.390699i	$-0.127767\pi$
$607$	3.00340	+	5.20204i	0.121904	+	0.211144i	−0.798614	+	0.601843i	$0.794433\pi$
$608$	6.49877	+	11.2562i	0.263560	+	0.456499i
$609$	−3.34169	−	1.67195i	−0.135412	−	0.0677507i
$610$	−13.8979	+	24.0720i	−0.562712	+	0.974645i
$611$	−1.31559			−0.0532230
$612$	2.74956	−	0.329796i	0.111144	−	0.0133312i
$613$	−7.37324			−0.297802			−0.148901	−	0.988852i	$-0.547574\pi$
$613$	−7.37324			−0.297802			−0.148901	+	0.988852i	$0.547574\pi$
$614$	11.1397	−	19.2945i	0.449560	−	0.778661i
$615$	−3.73220	−	62.4550i	−0.150497	−	2.51843i
$616$	9.43589	+	16.3434i	0.380183	+	0.658496i
$617$	−7.63391	−	13.2223i	−0.307330	−	0.532311i	0.670448	−	0.741957i	$-0.266102\pi$
$617$	−7.63391	−	13.2223i	−0.307330	−	0.532311i	−0.977777	+	0.209646i	$0.932769\pi$
$618$	−18.4009	+	12.1423i	−0.740191	+	0.488434i
$619$	−12.1315	+	21.0124i	−0.487607	+	0.844559i	−0.999898	−	0.0142521i	$-0.995463\pi$
$619$	−12.1315	+	21.0124i	−0.487607	+	0.844559i	0.512292	+	0.858811i	$0.328797\pi$
$620$	10.0955			0.405446
$621$	32.1773	−	27.2493i	1.29123	−	1.09348i
$622$	4.43593			0.177865
$623$	19.0761	−	33.0409i	0.764270	−	1.32375i
$624$	4.08577	−	2.69610i	0.163562	−	0.107930i
$625$	−10.4189	−	18.0460i	−0.416754	−	0.721839i
$626$	−0.529290	−	0.916758i	−0.0211547	−	0.0366410i
$627$	0.882358	+	14.7655i	0.0352380	+	0.589676i
$628$	2.94719	−	5.10469i	0.117606	−	0.203699i
$629$	6.75984			0.269533
$630$	−16.0797	−	21.4632i	−0.640630	−	0.855113i
$631$	−11.6760			−0.464815			−0.232407	−	0.972619i	$-0.574660\pi$
$631$	−11.6760			−0.464815			−0.232407	+	0.972619i	$0.574660\pi$
$632$	−3.63468	+	6.29546i	−0.144580	+	0.250420i
$633$	−18.9962	−	9.50436i	−0.755031	−	0.377764i
$634$	15.5444	+	26.9236i	0.617346	+	1.06927i
$635$	7.90906	+	13.6989i	0.313861	+	0.543624i
$636$	−13.5306	−	6.76978i	−0.536524	−	0.268439i
$637$	−2.02255	+	3.50315i	−0.0801362	+	0.138800i
$638$	3.08747			0.122234
$639$	−11.8611	+	27.7271i	−0.469219	+	1.09687i
$640$	−0.323657			−0.0127937
$641$	16.9157	−	29.2988i	0.668128	−	1.15723i	−0.310299	−	0.950639i	$-0.600429\pi$
$641$	16.9157	−	29.2988i	0.668128	−	1.15723i	0.978427	−	0.206593i	$-0.0662376\pi$
$642$	1.07377	+	17.9686i	0.0423783	+	0.709162i
$643$	10.9360	+	18.9418i	0.431275	+	0.746990i	0.996983	−	0.0776152i	$-0.0247306\pi$
$643$	10.9360	+	18.9418i	0.431275	+	0.746990i	−0.565708	+	0.824605i	$0.691397\pi$
$644$	7.29390	+	12.6334i	0.287420	+	0.497826i
$645$	−40.6437	+	26.8197i	−1.60034	+	1.05603i
$646$	1.78745	−	3.09595i	0.0703261	−	0.121808i
$647$	−10.6531			−0.418815			−0.209407	−	0.977828i	$-0.567153\pi$
$647$	−10.6531			−0.418815			−0.209407	+	0.977828i	$0.567153\pi$
$648$	19.0219	+	19.9197i	0.747252	+	0.782520i
$649$	0.876425			0.0344027
$650$	9.04919	−	15.6737i	0.354938	−	0.614771i
$651$	9.84926	−	6.49928i	0.386023	−	0.254727i
$652$	0.206146	+	0.357056i	0.00807330	+	0.0139834i
$653$	11.5268	+	19.9650i	0.451079	+	0.781292i	0.998453	−	0.0555962i	$-0.0177060\pi$
$653$	11.5268	+	19.9650i	0.451079	+	0.781292i	−0.547374	+	0.836888i	$0.684373\pi$
$654$	−0.381092	−	6.37723i	−0.0149019	−	0.249370i
$655$	43.0153	−	74.5047i	1.68075	−	2.91114i
$656$	15.4331			0.602563
$657$	−3.73231	+	8.72480i	−0.145611	+	0.340387i
$658$	−1.77786			−0.0693084
$659$	−2.60639	+	4.51440i	−0.101531	+	0.175856i	−0.912315	−	0.409488i	$-0.865707\pi$
$659$	−2.60639	+	4.51440i	−0.101531	+	0.175856i	0.810785	+	0.585344i	$0.199041\pi$
$660$	−14.1541	−	7.08173i	−0.550948	−	0.275656i
$661$	19.8857	+	34.4431i	0.773465	+	1.33968i	0.935653	+	0.352920i	$0.114811\pi$
$661$	19.8857	+	34.4431i	0.773465	+	1.33968i	−0.162189	+	0.986760i	$0.551855\pi$
$662$	10.7557	+	18.6294i	0.418032	+	0.724053i
$663$	2.95878	+	1.48036i	0.114909	+	0.0574926i
$664$	15.5839	−	26.9921i	0.604773	−	1.04750i
$665$	24.7268			0.958865
$666$	11.8560	+	15.8254i	0.459412	+	0.613223i
$667$	8.11470			0.314202
$668$	−3.72887	+	6.45860i	−0.144274	+	0.249891i
$669$	1.01440	+	16.9751i	0.0392191	+	0.656297i
$670$	−22.9184	−	39.6958i	−0.885413	−	1.53358i
$671$	9.58695	+	16.6051i	0.370100	+	0.641032i
$672$	−13.5678	+	8.95306i	−0.523390	+	0.345372i
$673$	15.7029	−	27.1982i	0.605301	−	1.04841i	−0.386702	−	0.922205i	$-0.626386\pi$
$673$	15.7029	−	27.1982i	0.605301	−	1.04841i	0.992004	−	0.126208i	$-0.0402808\pi$
$674$	5.54773			0.213691
$675$	47.5246	+	17.0542i	1.82922	+	0.656417i
$676$	8.35521			0.321354
$677$	2.73739	−	4.74130i	0.105206	−	0.182223i	−0.808616	−	0.588337i	$-0.799783\pi$
$677$	2.73739	−	4.74130i	0.105206	−	0.182223i	0.913823	+	0.406114i	$0.133116\pi$
$678$	14.4385	−	9.52758i	0.554506	−	0.365904i
$679$	−18.2093	−	31.5394i	−0.698809	−	1.21037i
$680$	6.50278	+	11.2631i	0.249370	+	0.431922i
$681$	1.40519	+	23.5146i	0.0538470	+	0.901081i
$682$	−4.87517	+	8.44404i	−0.186680	+	0.323339i
$683$	−39.1823			−1.49927			−0.749635	−	0.661852i	$-0.769771\pi$
$683$	−39.1823			−1.49927			−0.749635	+	0.661852i	$0.769771\pi$
$684$	−7.41578	+	0.889485i	−0.283550	+	0.0340103i
$685$	−61.6874			−2.35695
$686$	−10.8890	+	18.8604i	−0.415745	+	0.720092i
$687$	−4.41000	−	2.20645i	−0.168252	−	0.0841815i
$688$	−6.00575	−	10.4023i	−0.228967	−	0.396582i
$689$	−9.03773	−	15.6538i	−0.344310	−	0.596363i
$690$	52.0851	+	26.0597i	1.98284	+	0.992076i
$691$	15.9532	−	27.6318i	0.606890	−	1.05116i	−0.384859	−	0.922975i	$-0.625750\pi$
$691$	15.9532	−	27.6318i	0.606890	−	1.05116i	0.991750	−	0.128190i	$-0.0409166\pi$
$692$	3.44747			0.131053
$693$	−18.3679	+	2.20314i	−0.697740	+	0.0836902i
$694$	6.38594			0.242407
$695$	26.7634	−	46.3556i	1.01519	−	1.75837i
$696$	0.316196	+	5.29126i	0.0119854	+	0.200565i
$697$	5.21535	+	9.03324i	0.197545	+	0.342159i
$698$	−9.99263	−	17.3077i	−0.378227	−	0.655108i
$699$	−18.2489	+	12.0420i	−0.690238	+	0.455471i
$700$	−8.73429	+	15.1282i	−0.330125	+	0.571794i
$701$	7.07204			0.267107			0.133554	−	0.991042i	$-0.457361\pi$
$701$	7.07204			0.267107			0.133554	+	0.991042i	$0.457361\pi$
$702$	1.72370	+	9.52317i	0.0650568	+	0.359429i
$703$	−18.2318			−0.687626
$704$	11.4008	−	19.7467i	0.429682	−	0.744231i
$705$	4.23138	−	2.79218i	0.159363	−	0.105160i
$706$	15.0399	+	26.0499i	0.566034	+	0.980399i
$707$	16.2873	+	28.2104i	0.612545	+	1.06096i
$708$	0.0263983	+	0.441752i	0.000992109	+	0.0166020i
$709$	20.6257	−	35.7247i	0.774613	−	1.34167i	−0.160399	−	0.987052i	$-0.551278\pi$
$709$	20.6257	−	35.7247i	0.774613	−	1.34167i	0.935012	−	0.354616i	$-0.115388\pi$
$710$	−41.6550			−1.56329
$711$	−4.27259	−	5.70305i	−0.160235	−	0.213881i
$712$	−54.1221			−2.02831
$713$	−12.8132	+	22.1932i	−0.479860	+	0.831141i
$714$	3.99844	+	2.00054i	0.149638	+	0.0748684i
$715$	−9.45418	−	16.3751i	−0.353566	−	0.612395i
$716$	3.41067	+	5.90746i	0.127463	+	0.220772i
$717$	19.4469	+	9.72986i	0.726257	+	0.363368i
$718$	8.56567	−	14.8362i	0.319668	−	0.553681i
$719$	28.3020			1.05549			0.527743	−	0.849404i	$-0.323038\pi$
$719$	28.3020			1.05549			0.527743	+	0.849404i	$0.323038\pi$
$720$	−7.41907	+	17.3431i	−0.276492	+	0.646340i
$721$	25.4218			0.946759
$722$	5.44045	−	9.42314i	0.202473	−	0.350693i
$723$	1.56968	+	26.2671i	0.0583769	+	0.976884i
$724$	−8.06151	−	13.9629i	−0.299604	−	0.518929i
$725$	4.85859	+	8.41533i	0.180444	+	0.312537i
$726$	−4.41844	+	2.91562i	−0.163984	+	0.108209i
$727$	12.6616	−	21.9305i	0.469593	−	0.813359i	−0.529803	−	0.848121i	$-0.677734\pi$
$727$	12.6616	−	21.9305i	0.469593	−	0.813359i	0.999396	+	0.0347620i	$0.0110673\pi$
$728$	−11.3844			−0.421933
$729$	−25.2870	+	9.46397i	−0.936556	+	0.350517i
$730$	−13.1075			−0.485129
$731$	4.05907	−	7.03051i	0.150130	−	0.260033i
$732$	−8.08084	+	5.33234i	−0.298676	+	0.197089i
$733$	−2.08659	−	3.61408i	−0.0770700	−	0.133489i	0.824915	−	0.565257i	$-0.191223\pi$
$733$	−2.08659	−	3.61408i	−0.0770700	−	0.133489i	−0.901985	+	0.431768i	$0.857890\pi$
$734$	−12.3528	−	21.3957i	−0.455952	−	0.789731i
$735$	−0.929835	−	15.5599i	−0.0342975	−	0.573937i
$736$	17.6508	−	30.5722i	0.650619	−	1.12690i
$737$	−31.6187			−1.16469
$738$	−12.0005	+	28.0529i	−0.441746	+	1.03264i
$739$	18.7700			0.690467			0.345234	−	0.938517i	$-0.387800\pi$
$739$	18.7700			0.690467			0.345234	+	0.938517i	$0.387800\pi$
$740$	9.75380	−	16.8941i	0.358557	−	0.621039i
$741$	−7.98005	−	3.99266i	−0.293154	−	0.146674i
$742$	−12.2135	−	21.1543i	−0.448370	−	0.776600i
$743$	22.8903	+	39.6471i	0.839762	+	1.45451i	0.890093	+	0.455778i	$0.150639\pi$
$743$	22.8903	+	39.6471i	0.839762	+	1.45451i	−0.0503311	+	0.998733i	$0.516028\pi$
$744$	−14.9705	−	7.49021i	−0.548846	−	0.274604i
$745$	−36.0619	+	62.4610i	−1.32121	+	2.28839i
$746$	14.4212			0.527999
$747$	18.3190	+	24.4522i	0.670256	+	0.894658i
$748$	2.63856			0.0964752
$749$	10.3785	−	17.9761i	0.379222	−	0.656831i
$750$	2.01957	+	33.7957i	0.0737444	+	1.23405i
$751$	−7.98847	−	13.8364i	−0.291504	−	0.504899i	0.682662	−	0.730734i	$-0.260822\pi$
$751$	−7.98847	−	13.8364i	−0.291504	−	0.504899i	−0.974165	+	0.225835i	$0.927489\pi$
$752$	0.625253	+	1.08297i	0.0228006	+	0.0394919i
$753$	8.32325	−	5.49231i	0.303316	−	0.200151i
$754$	−0.931257	+	1.61298i	−0.0339144	+	0.0587414i
$755$	51.4862			1.87377
$756$	−1.66371	−	9.19177i	−0.0605087	−	0.334302i
$757$	27.5114			0.999917			0.499959	−	0.866049i	$-0.333349\pi$
$757$	27.5114			0.999917			0.499959	+	0.866049i	$0.333349\pi$
$758$	14.0542	−	24.3425i	0.510470	−	0.884160i
$759$	33.5323	−	22.1271i	1.21715	−	0.803165i
$760$	−17.5385	−	30.3776i	−0.636189	−	1.10191i
$761$	12.5942	+	21.8138i	0.456539	+	0.790749i	0.998775	−	0.0494769i	$-0.0157554\pi$
$761$	12.5942	+	21.8138i	0.456539	+	0.790749i	−0.542236	+	0.840226i	$0.682422\pi$
$762$	−0.460158	−	7.70033i	−0.0166698	−	0.278953i
$763$	−3.68344	+	6.37990i	−0.133349	+	0.230968i
$764$	0.989755			0.0358081
$765$	−12.6583	+	1.51830i	−0.457663	+	0.0548943i
$766$	27.3057			0.986593
$767$	−0.264351	+	0.457870i	−0.00954517	+	0.0165327i
$768$	24.8538	+	12.4351i	0.896835	+	0.448713i
$769$	14.8296	+	25.6856i	0.534770	+	0.926248i	0.999174	+	0.0406252i	$0.0129349\pi$
$769$	14.8296	+	25.6856i	0.534770	+	0.926248i	−0.464405	+	0.885623i	$0.653732\pi$
$770$	−12.7762	−	22.1291i	−0.460424	−	0.797477i
$771$	−2.04620	−	1.02377i	−0.0736920	−	0.0368703i
$772$	2.94899	−	5.10780i	0.106136	−	0.183834i
$773$	−20.8183			−0.748783			−0.374392	−	0.927271i	$-0.622148\pi$
$773$	−20.8183			−0.748783			−0.374392	+	0.927271i	$0.622148\pi$
$774$	23.5782	−	2.82809i	0.847502	−	0.101653i
$775$	−30.6872			−1.10232
$776$	−25.8314	+	44.7413i	−0.927292	+	1.60612i
$777$	−1.36017	−	22.7613i	−0.0487960	−	0.816556i
$778$	−16.5393	−	28.6469i	−0.592963	−	1.02704i
$779$	−14.0662	−	24.3634i	−0.503974	−	0.872908i
$780$	7.96893	−	5.25850i	0.285333	−	0.188284i
$781$	−14.3670	+	24.8844i	−0.514093	+	0.890435i
$782$	−9.70951			−0.347211
$783$	−4.89078	−	1.75506i	−0.174782	−	0.0627206i
$784$	3.84499			0.137321
$785$	−13.5682	+	23.5008i	−0.484269	+	0.838779i
$786$	−35.0179	+	23.1074i	−1.24905	+	0.824215i
$787$	8.51043	+	14.7405i	0.303364	+	0.525442i	0.976896	−	0.213716i	$-0.0685568\pi$
$787$	8.51043	+	14.7405i	0.303364	+	0.525442i	−0.673532	+	0.739158i	$0.735223\pi$
$788$	−2.19445	−	3.80090i	−0.0781741	−	0.135402i
$789$	1.61784	+	27.0731i	0.0575966	+	0.963827i
$790$	4.92138	−	8.52408i	0.175095	−	0.303273i
$791$	−19.9476			−0.709253
$792$	15.7348	+	21.0028i	0.559112	+	0.746303i
$793$	−11.5666			−0.410744
$794$	−6.31694	+	10.9413i	−0.224180	+	0.388291i
$795$	62.2918	+	31.1664i	2.20926	+	1.10536i
$796$	−1.26838	−	2.19690i	−0.0449565	−	0.0778670i
$797$	−10.7313	−	18.5872i	−0.380124	−	0.658393i	0.610956	−	0.791665i	$-0.290785\pi$
$797$	−10.7313	−	18.5872i	−0.380124	−	0.658393i	−0.991080	+	0.133271i	$0.957452\pi$
$798$	−10.7841	−	5.39562i	−0.381754	−	0.191003i
$799$	−0.422586	+	0.731940i	−0.0149500	+	0.0258942i
$800$	42.2730			1.49458
$801$	20.8667	−	48.7789i	0.737289	−	1.72352i
$802$	2.33127			0.0823201
$803$	−4.52083	+	7.83031i	−0.159537	+	0.276326i
$804$	−0.952368	−	15.9370i	−0.0335874	−	0.562055i
$805$	−33.5794	−	58.1612i	−1.18352	−	2.04991i
$806$	−2.94094	−	5.09386i	−0.103590	−	0.179424i
$807$	13.1686	−	8.68964i	0.463557	−	0.305890i
$808$	23.1048	−	40.0187i	0.812824	−	1.40785i
$809$	−26.2479			−0.922828			−0.461414	−	0.887185i	$-0.652658\pi$
$809$	−26.2479			−0.922828			−0.461414	+	0.887185i	$0.652658\pi$
$810$	−25.7558	−	26.9714i	−0.904967	−	0.947678i
$811$	17.3539			0.609379			0.304690	−	0.952452i	$-0.401447\pi$
$811$	17.3539			0.609379			0.304690	+	0.952452i	$0.401447\pi$
$812$	0.898850	−	1.55685i	0.0315435	−	0.0546349i
$813$	21.4686	−	14.1666i	0.752937	−	0.496845i
$814$	9.42030	+	16.3164i	0.330181	+	0.571891i
$815$	−0.949048	−	1.64380i	−0.0332437	−	0.0575798i
$816$	−0.187592	−	3.13918i	−0.00656703	−	0.109893i
$817$	−10.9476	+	18.9618i	−0.383009	+	0.663391i
$818$	21.5774			0.754438
$819$	4.38923	−	10.2605i	0.153372	−	0.358529i
$820$	30.1010			1.05117
$821$	8.98403	−	15.5608i	0.313545	−	0.543075i	−0.665582	−	0.746324i	$-0.731817\pi$
$821$	8.98403	−	15.5608i	0.313545	−	0.543075i	0.979127	+	0.203249i	$0.0651501\pi$
$822$	26.9037	+	13.4607i	0.938375	+	0.469497i
$823$	14.4046	+	24.9494i	0.502111	+	0.869682i	0.999997	+	0.00243953i	$0.000776528\pi$
$823$	14.4046	+	24.9494i	0.502111	+	0.869682i	−0.497886	+	0.867243i	$0.665890\pi$
$824$	−18.0315	−	31.2314i	−0.628156	−	1.08800i
$825$	43.0240	+	21.5262i	1.49790	+	0.749447i
$826$	−0.357240	+	0.618759i	−0.0124300	+	0.0215294i
$827$	36.0302			1.25289			0.626446	−	0.779465i	$-0.284509\pi$
$827$	36.0302			1.25289			0.626446	+	0.779465i	$0.284509\pi$
$828$	12.1629	+	16.2351i	0.422691	+	0.564208i
$829$	2.29705			0.0797798			0.0398899	−	0.999204i	$-0.487299\pi$
$829$	2.29705			0.0797798			0.0398899	+	0.999204i	$0.487299\pi$
$830$	−21.1007	+	36.5475i	−0.732416	+	1.26858i
$831$	−2.15757	−	36.1050i	−0.0748454	−	1.25247i
$832$	6.87750	+	11.9122i	0.238434	+	0.412980i
$833$	1.29934	+	2.25053i	0.0450196	+	0.0779762i
$834$	−21.7875	+	14.3771i	−0.754441	+	0.497837i
$835$	17.1668	−	29.7338i	0.594083	−	1.02898i
$836$	−7.11639			−0.246126
$837$	12.5226	−	10.6047i	0.432844	−	0.366553i
$838$	13.3061			0.459651
$839$	4.05509	−	7.02363i	0.139997	−	0.242483i	−0.787498	−	0.616317i	$-0.788624\pi$
$839$	4.05509	−	7.02363i	0.139997	−	0.242483i	0.927495	+	0.373835i	$0.121957\pi$
$840$	36.6160	−	24.1620i	1.26337	−	0.833669i
$841$	−0.500000	−	0.866025i	−0.0172414	−	0.0298629i
$842$	14.1990	+	24.5933i	0.489329	+	0.847542i
$843$	1.73058	+	28.9597i	0.0596044	+	0.997426i
$844$	5.10961	−	8.85010i	0.175880	−	0.304633i
$845$	−38.4654			−1.32325
$846$	−2.45471	+	0.294430i	−0.0843947	+	0.0101227i
$847$	6.10433			0.209747
$848$	−8.59064	+	14.8794i	−0.295004	+	0.510962i
$849$	−23.8894	−	11.9526i	−0.819883	−	0.410212i
$850$	−5.81347	−	10.0692i	−0.199400	−	0.345371i
$851$	24.7591	+	42.8840i	0.848730	+	1.47004i
$852$	−12.9755	−	6.49201i	−0.444532	−	0.222412i
$853$	−18.0699	+	31.2981i	−0.618703	+	1.07163i	0.371020	+	0.928625i	$0.379008\pi$
$853$	−18.0699	+	31.2981i	−0.618703	+	1.07163i	−0.989723	+	0.143000i	$0.954325\pi$
$854$	−15.6310			−0.534881
$855$	34.1405	−	4.09498i	1.16758	−	0.140045i
$856$	−29.4455			−1.00643
$857$	16.3017	−	28.2354i	0.556856	−	0.964503i	−0.440900	−	0.897556i	$-0.645341\pi$
$857$	16.3017	−	28.2354i	0.556856	−	0.964503i	0.997757	−	0.0669473i	$-0.0213259\pi$
$858$	0.550055	+	9.20468i	0.0187786	+	0.314243i
$859$	−12.2701	−	21.2524i	−0.418650	−	0.725122i	0.577154	−	0.816635i	$-0.304163\pi$
$859$	−12.2701	−	21.2524i	−0.418650	−	0.725122i	−0.995804	+	0.0915127i	$0.970830\pi$
$860$	−11.7137	−	20.2887i	−0.399433	−	0.691839i
$861$	29.3667	−	19.3784i	1.00081	−	0.660413i
$862$	17.9730	−	31.1301i	0.612162	−	1.06030i
$863$	6.99463			0.238100			0.119050	−	0.992888i	$-0.462015\pi$
$863$	6.99463			0.238100			0.119050	+	0.992888i	$0.462015\pi$
$864$	−17.2505	+	14.6085i	−0.586873	+	0.496991i
$865$	−15.8713			−0.539641
$866$	9.95529	−	17.2431i	0.338294	−	0.585943i
$867$	−22.8024	+	15.0467i	−0.774409	+	0.511013i
$868$	2.83860	+	4.91660i	0.0963483	+	0.166880i
$869$	−3.39482	−	5.88000i	−0.115161	−	0.199465i
$870$	−0.428131	−	7.16439i	−0.0145150	−	0.242896i
$871$	9.53696	−	16.5185i	0.323148	−	0.559708i
$872$	10.4505			0.353899
$873$	−30.3649	−	40.5311i	−1.02770	−	1.37177i
$874$	26.1873			0.885798
$875$	19.5201	−	33.8099i	0.659901	−	1.14298i
$876$	−4.08295	−	2.04282i	−0.137950	−	0.0690205i
$877$	0.113890	+	0.197264i	0.00384581	+	0.00666114i	0.867942	−	0.496666i	$-0.165443\pi$
$877$	0.113890	+	0.197264i	0.00384581	+	0.00666114i	−0.864096	+	0.503327i	$0.832109\pi$
$878$	−3.05942	−	5.29906i	−0.103250	−	0.178835i
$879$	−11.7349	−	5.87132i	−0.395808	−	0.198035i
$880$	−8.98650	+	15.5651i	−0.302935	+	0.524698i
$881$	10.6537			0.358932			0.179466	−	0.983764i	$-0.442563\pi$
$881$	10.6537			0.358932			0.179466	+	0.983764i	$0.442563\pi$
$882$	−2.98979	+	6.98906i	−0.100672	+	0.235334i
$883$	−18.9241			−0.636848			−0.318424	−	0.947948i	$-0.603153\pi$
$883$	−18.9241			−0.636848			−0.318424	+	0.947948i	$0.603153\pi$
$884$	−0.795854	+	1.37846i	−0.0267675	+	0.0463626i
$885$	−0.121532	−	2.03372i	−0.00408524	−	0.0683628i
$886$	−10.9275	−	18.9269i	−0.367116	−	0.635863i
$887$	5.00827	+	8.67457i	0.168161	+	0.291264i	0.937773	−	0.347248i	$-0.112884\pi$
$887$	5.00827	+	8.67457i	0.168161	+	0.291264i	−0.769612	+	0.638512i	$0.779550\pi$
$888$	−26.9981	+	17.8154i	−0.905997	+	0.597845i
$889$	−4.44765	+	7.70355i	−0.149169	+	0.258369i
$890$	73.2817			2.45641
$891$	−24.9959	+	6.08377i	−0.837393	+	0.203814i
$892$	−8.18137			−0.273933
$893$	1.13975	−	1.97410i	0.0381402	−	0.0660607i
$894$	29.3572	−	19.3721i	0.981853	−	0.647900i
$895$	−15.7019	−	27.1966i	−0.524858	−	0.909080i
$896$	−0.0910041	−	0.157624i	−0.00304023	−	0.00526584i
$897$	1.44569	+	24.1923i	0.0482703	+	0.807759i
$898$	−1.31225	+	2.27288i	−0.0437902	+	0.0758468i
$899$	3.15803			0.105326
$900$	−9.55413	+	22.3341i	−0.318471	+	0.744471i
$901$	−11.6122			−0.386859
$902$	−14.5359	+	25.1769i	−0.483992	+	0.838299i
$903$	−24.4894	−	12.2528i	−0.814956	−	0.407747i
$904$	14.1486	+	24.5061i	0.470576	+	0.815061i
$905$	37.1133	+	64.2821i	1.23369	+	2.13681i
$906$	−22.4547	−	11.2347i	−0.746007	−	0.373250i
$907$	−12.3257	+	21.3487i	−0.409268	+	0.708872i	−0.994808	−	0.101771i	$-0.967549\pi$
$907$	−12.3257	+	21.3487i	−0.409268	+	0.708872i	0.585540	+	0.810643i	$0.300882\pi$
$908$	−11.3331			−0.376104
$909$	27.1598	+	36.2529i	0.900834	+	1.20243i
$910$	15.4145			0.510986
$911$	−24.5004	+	42.4359i	−0.811734	+	1.40596i	0.0999152	+	0.994996i	$0.468143\pi$
$911$	−24.5004	+	42.4359i	−0.811734	+	1.40596i	−0.911649	+	0.410969i	$0.865190\pi$
$912$	0.505950	+	8.46662i	0.0167537	+	0.280358i
$913$	14.5555	+	25.2109i	0.481717	+	0.834358i
$914$	−20.3154	−	35.1873i	−0.671973	−	1.16389i
$915$	37.2023	−	24.5488i	1.22987	−	0.811560i
$916$	1.18620	−	2.05457i	0.0391933	−	0.0678848i
$917$	48.3792			1.59762
$918$	5.85199	+	2.09998i	0.193144	+	0.0693098i
$919$	−43.3109			−1.42870			−0.714348	−	0.699791i	$-0.753276\pi$
$919$	−43.3109			−1.42870			−0.714348	+	0.699791i	$0.753276\pi$
$920$	−47.6351	+	82.5064i	−1.57048	+	2.72015i
$921$	−29.8188	+	19.6767i	−0.982564	+	0.648370i
$922$	−7.18061	−	12.4372i	−0.236481	−	0.409597i
$923$	−8.66690	−	15.0115i	−0.285275	−	0.494110i
$924$	−0.530914	−	8.88437i	−0.0174658	−	0.292274i
$925$	−29.6485	+	51.3527i	−0.974836	+	1.68847i
$926$	−21.6474			−0.711378
$927$	35.1001	−	4.21008i	1.15284	−	0.138277i
$928$	−4.35034			−0.142807
$929$	−4.42854	+	7.67045i	−0.145296	+	0.251659i	−0.929483	−	0.368864i	$-0.879747\pi$
$929$	−4.42854	+	7.67045i	−0.145296	+	0.251659i	0.784188	+	0.620524i	$0.213080\pi$
$930$	20.2702	+	10.1418i	0.664685	+	0.332562i
$931$	−3.50443	−	6.06985i	−0.114853	−	0.198931i
$932$	−5.25942	−	9.10959i	−0.172278	−	0.298394i
$933$	−6.36140	−	3.18280i	−0.208263	−	0.104200i
$934$	−13.3777	+	23.1708i	−0.437731	+	0.758172i
$935$	−12.1473			−0.397259
$936$	−15.7185	+	1.88535i	−0.513775	+	0.0616246i
$937$	−28.7603			−0.939558			−0.469779	−	0.882784i	$-0.655666\pi$
$937$	−28.7603			−0.939558			−0.469779	+	0.882784i	$0.655666\pi$
$938$	12.8881	−	22.3229i	0.420812	−	0.728867i
$939$	0.101258	+	1.69446i	0.00330442	+	0.0552965i
$940$	1.21950	+	2.11224i	0.0397757	+	0.0688936i
$941$	−12.4277	−	21.5255i	−0.405133	−	0.701710i	0.589204	−	0.807984i	$-0.299441\pi$
$941$	−12.4277	−	21.5255i	−0.405133	−	0.701710i	−0.994337	+	0.106274i	$0.966108\pi$
$942$	11.0456	−	7.28870i	0.359884	−	0.237479i
$943$	−38.2042	+	66.1716i	−1.24410	+	2.15484i
$944$	0.502548			0.0163566
$945$	7.65935	+	42.3167i	0.249159	+	1.37656i
$946$	22.6263			0.735646
$947$	8.78613	−	15.2180i	0.285511	−	0.494519i	−0.687222	−	0.726447i	$-0.741170\pi$
$947$	8.78613	−	15.2180i	0.285511	−	0.494519i	0.972733	+	0.231928i	$0.0745034\pi$
$948$	2.86149	−	1.88823i	0.0929370	−	0.0613268i
$949$	−2.72719	−	4.72363i	−0.0885283	−	0.153335i
$950$	15.6794	+	27.1575i	0.508706	+	0.881105i
$951$	−2.97377	−	49.7633i	−0.0964310	−	1.61369i
$952$	−3.65683	+	6.33382i	−0.118519	+	0.205280i
$953$	24.6134			0.797307			0.398654	−	0.917102i	$-0.369478\pi$
$953$	24.6134			0.797307			0.398654	+	0.917102i	$0.369478\pi$
$954$	−20.3665	−	27.1853i	−0.659391	−	0.880156i
$955$	−4.55660			−0.147448
$956$	−5.23084	+	9.06007i	−0.169177	+	0.293024i
$957$	−4.42763	−	2.21527i	−0.143125	−	0.0716096i
$958$	5.20056	+	9.00763i	0.168022	+	0.291023i
$959$	−17.3449	−	30.0423i	−0.560096	−	0.970115i
$960$	−47.4026	−	23.7169i	−1.52991	−	0.765460i
$961$	10.5134	−	18.2098i	0.339142	−	0.587412i
$962$	−11.3656			−0.366441
$963$	11.3527	−	26.5385i	0.365834	−	0.855190i
$964$	−12.6597			−0.407743
$965$	−13.5764	+	23.5151i	−0.437041	+	0.756978i
$966$	1.95369	+	32.6932i	0.0628588	+	1.05189i
$967$	5.49376	+	9.51546i	0.176667	+	0.305997i	0.940737	−	0.339137i	$-0.110135\pi$
$967$	5.49376	+	9.51546i	0.176667	+	0.305997i	−0.764070	+	0.645134i	$0.776802\pi$
$968$	−4.32974	−	7.49934i	−0.139163	−	0.241038i
$969$	−4.78466	+	3.15728i	−0.153706	+	0.101426i
$970$	34.9758	−	60.5799i	1.12301	−	1.94510i
$971$	20.9373			0.671911			0.335956	−	0.941878i	$-0.390941\pi$
$971$	20.9373			0.671911			0.335956	+	0.941878i	$0.390941\pi$
$972$	−3.81934	−	12.4156i	−0.122505	−	0.398231i
$973$	30.1007			0.964985
$974$	16.8370	−	29.1626i	0.539493	−	0.934430i
$975$	−24.2230	+	15.9842i	−0.775758	+	0.511903i
$976$	5.49723	+	9.52148i	0.175962	+	0.304775i
$977$	−14.3968	−	24.9360i	−0.460594	−	0.797772i	0.538397	−	0.842691i	$-0.319030\pi$
$977$	−14.3968	−	24.9360i	−0.460594	−	0.797772i	−0.998991	+	0.0449196i	$0.985697\pi$
$978$	0.0552167	+	0.924001i	0.00176563	+	0.0295463i
$979$	25.2752	−	43.7780i	0.807800	−	1.39915i
$980$	7.49930			0.239556
$981$	−4.02918	+	9.41879i	−0.128642	+	0.300719i
$982$	36.1075			1.15224
$983$	10.9092	−	18.8954i	0.347951	−	0.602668i	−0.637935	−	0.770091i	$-0.720211\pi$
$983$	10.9092	−	18.8954i	0.347951	−	0.602668i	0.985885	+	0.167422i	$0.0535443\pi$
$984$	−44.6364	−	22.3329i	−1.42296	−	0.711948i
$985$	10.1027	+	17.4984i	0.321900	+	0.557547i
$986$	0.598267	+	1.03623i	0.0190527	+	0.0330002i
$987$	2.54957	+	1.27563i	0.0811537	+	0.0406036i
$988$	2.14648	−	3.71781i	0.0682886	−	0.118279i
$989$	59.4681			1.89097
$990$	−21.3050	−	28.4379i	−0.677118	−	0.903817i
$991$	−12.7745			−0.405796			−0.202898	−	0.979200i	$-0.565036\pi$
$991$	−12.7745			−0.405796			−0.202898	+	0.979200i	$0.565036\pi$
$992$	6.86926	−	11.8979i	0.218099	−	0.377759i
$993$	−2.05766	−	34.4330i	−0.0652977	−	1.09270i
$994$	−11.7123	−	20.2863i	−0.371492	−	0.643444i
$995$	5.83932	+	10.1140i	0.185119	+	0.320635i
$996$	−12.2688	+	8.09589i	−0.388752	+	0.256528i
$997$	8.83118	−	15.2960i	0.279686	−	0.484431i	−0.691621	−	0.722261i	$-0.743103\pi$
$997$	8.83118	−	15.2960i	0.279686	−	0.484431i	0.971307	+	0.237830i	$0.0764362\pi$
$998$	−44.5500			−1.41021
$999$	−5.64746	−	31.2014i	−0.178678	−	0.987168i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.e.a.88.4	✓	22
3.2	odd	2		783.2.e.a.262.8		22
9.2	odd	6		2349.2.a.e.1.4		11
9.4	even	3	inner	261.2.e.a.175.4	yes	22
9.5	odd	6		783.2.e.a.523.8		22
9.7	even	3		2349.2.a.f.1.8		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.e.a.88.4	✓	22	1.1	even	1	trivial
261.2.e.a.175.4	yes	22	9.4	even	3	inner
783.2.e.a.262.8		22	3.2	odd	2
783.2.e.a.523.8		22	9.5	odd	6
2349.2.a.e.1.4		11	9.2	odd	6
2349.2.a.f.1.8		11	9.7	even	3

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.540070 + 0.935429i) q^{2} +(1.44567 - 0.953961i) q^{3} +(0.416648 + 0.721656i) q^{4} +(-1.91815 - 3.32233i) q^{5} +(0.111600 + 1.86753i) q^{6} +(1.07867 - 1.86831i) q^{7} -3.06036 q^{8} +(1.17992 - 2.75822i) q^{9} +4.14374 q^{10} +(1.42920 - 2.47544i) q^{11} +(1.29077 + 0.645809i) q^{12} +(0.862163 + 1.49331i) q^{13} +(1.16511 + 2.01804i) q^{14} +(-5.94238 - 2.97315i) q^{15} +(0.819512 - 1.41944i) q^{16} +1.10776 q^{17} +(1.94288 + 2.59336i) q^{18} -2.98771 q^{19} +(1.59839 - 2.76849i) q^{20} +(-0.222896 - 3.72996i) q^{21} +(1.54374 + 2.67383i) q^{22} +(4.05735 + 7.02753i) q^{23} +(-4.42426 + 2.91946i) q^{24} +(-4.85859 + 8.41533i) q^{25} -1.86251 q^{26} +(-0.925468 - 5.11307i) q^{27} +1.79770 q^{28} +(0.500000 - 0.866025i) q^{29} +(5.99048 - 3.95297i) q^{30} +(1.57902 + 2.73494i) q^{31} +(-2.17517 - 3.76750i) q^{32} +(-0.295330 - 4.94207i) q^{33} +(-0.598267 + 1.03623i) q^{34} -8.27619 q^{35} +(2.48210 - 0.297715i) q^{36} +6.10228 q^{37} +(1.61357 - 2.79479i) q^{38} +(2.67096 + 1.33636i) q^{39} +(5.87022 + 10.1675i) q^{40} +(4.70802 + 8.15454i) q^{41} +(3.60950 + 1.80594i) q^{42} +(3.66422 - 6.34662i) q^{43} +2.38189 q^{44} +(-11.4270 + 1.37061i) q^{45} -8.76501 q^{46} +(-0.381479 + 0.660741i) q^{47} +(-0.169344 - 2.83382i) q^{48} +(1.17295 + 2.03161i) q^{49} +(-5.24796 - 9.08973i) q^{50} +(1.60145 - 1.05676i) q^{51} +(-0.718437 + 1.24437i) q^{52} -10.4826 q^{53} +(5.28274 + 1.89571i) q^{54} -10.9657 q^{55} +(-3.30111 + 5.71769i) q^{56} +(-4.31924 + 2.85016i) q^{57} +(0.540070 + 0.935429i) q^{58} +(0.153307 + 0.265536i) q^{59} +(-0.330291 - 5.52711i) q^{60} +(-3.35396 + 5.80923i) q^{61} -3.41112 q^{62} +(-3.88047 - 5.17966i) q^{63} +7.97703 q^{64} +(3.30751 - 5.72878i) q^{65} +(4.78246 + 2.39281i) q^{66} +(-5.53084 - 9.57969i) q^{67} +(0.461545 + 0.799419i) q^{68} +(12.5696 + 6.28893i) q^{69} +(4.46972 - 7.74179i) q^{70} -10.0525 q^{71} +(-3.61097 + 8.44115i) q^{72} -3.16319 q^{73} +(-3.29566 + 5.70825i) q^{74} +(1.00398 + 16.8007i) q^{75} +(-1.24482 - 2.15610i) q^{76} +(-3.08326 - 5.34037i) q^{77} +(-2.69258 + 1.77677i) q^{78} +(1.18767 - 2.05710i) q^{79} -6.28779 q^{80} +(-6.21559 - 6.50895i) q^{81} -10.1707 q^{82} +(-5.09219 + 8.81993i) q^{83} +(2.59888 - 1.71494i) q^{84} +(-2.12484 - 3.68034i) q^{85} +(3.95787 + 6.85524i) q^{86} +(-0.103320 - 1.72897i) q^{87} +(-4.37386 + 7.57575i) q^{88} +17.6849 q^{89} +(4.88927 - 11.4294i) q^{90} +3.71995 q^{91} +(-3.38097 + 5.85602i) q^{92} +(4.89176 + 2.44749i) q^{93} +(-0.412051 - 0.713693i) q^{94} +(5.73087 + 9.92615i) q^{95} +(-6.73863 - 3.37154i) q^{96} +(8.44064 - 14.6196i) q^{97} -2.53390 q^{98} +(-5.14149 - 6.86287i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - q^{2} - 2 q^{3} - 5 q^{4} + q^{5} - q^{6} + 7 q^{7} + 6 q^{8} - 2 q^{9} - 20 q^{10} - 3 q^{11} + 10 q^{12} + 7 q^{13} + 10 q^{14} - 8 q^{15} + 7 q^{16} + 2 q^{17} + 2 q^{18} - 56 q^{19} + 4 q^{20}+ \cdots - 40 q^{99}+O(q^{100}) \) 22 * q - q^2 - 2 * q^3 - 5 * q^4 + q^5 - q^6 + 7 * q^7 + 6 * q^8 - 2 * q^9 - 20 * q^10 - 3 * q^11 + 10 * q^12 + 7 * q^13 + 10 * q^14 - 8 * q^15 + 7 * q^16 + 2 * q^17 + 2 * q^18 - 56 * q^19 + 4 * q^20 + 16 * q^21 + 13 * q^22 - 4 * q^23 - 33 * q^24 + 4 * q^25 - 12 * q^26 + 13 * q^27 - 32 * q^28 + 11 * q^29 + 46 * q^30 + 27 * q^31 - 7 * q^32 - 10 * q^33 + 19 * q^34 - 22 * q^35 + 19 * q^36 - 28 * q^37 + 5 * q^38 + 17 * q^39 + 24 * q^40 + 9 * q^41 - 50 * q^42 + 25 * q^43 + 46 * q^44 - 56 * q^45 - 20 * q^46 - 6 * q^47 + 33 * q^48 + 12 * q^49 - 41 * q^50 - 15 * q^51 + 20 * q^52 - 12 * q^53 + 5 * q^54 - 70 * q^55 + 10 * q^56 + 25 * q^57 + q^58 - 48 * q^60 + 25 * q^61 - 12 * q^62 - 11 * q^63 - 50 * q^64 - 5 * q^65 + 29 * q^66 + 29 * q^67 + 50 * q^68 + 20 * q^69 + 7 * q^70 - 2 * q^71 + 30 * q^72 - 26 * q^73 - 14 * q^74 + 46 * q^75 + 38 * q^76 - 9 * q^77 - 39 * q^78 + 27 * q^79 - 74 * q^80 - 38 * q^81 - 34 * q^82 + 12 * q^83 + 60 * q^84 + 7 * q^85 - q^86 - q^87 - 5 * q^88 + 46 * q^89 - 35 * q^90 - 86 * q^91 - 19 * q^92 + 78 * q^93 - 10 * q^94 - 8 * q^95 - 75 * q^96 + 36 * q^97 + 86 * q^98 - 40 * q^99

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