LMFDB - Embedded newform 945.2.cs.b.104.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(104,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([11, 9, 9]))

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

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

chi := DirichletCharacter("945.104");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.cs (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$816$
Relative dimension:	$136$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			104.20
Character	$\chi$	$=$	945.104
Dual form			945.2.cs.b.209.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.96750 - 0.716110i) q^{2} +(1.00171 - 1.41301i) q^{3} +(1.82614 + 1.53231i) q^{4} +(1.23328 - 1.86521i) q^{5} +(-2.98272 + 2.06275i) q^{6} +(1.53873 - 2.15228i) q^{7} +(-0.401851 - 0.696026i) q^{8} +(-0.993173 - 2.83083i) q^{9} +O(q^{10})$	\(q+(-1.96750 - 0.716110i) q^{2} +(1.00171 - 1.41301i) q^{3} +(1.82614 + 1.53231i) q^{4} +(1.23328 - 1.86521i) q^{5} +(-2.98272 + 2.06275i) q^{6} +(1.53873 - 2.15228i) q^{7} +(-0.401851 - 0.696026i) q^{8} +(-0.993173 - 2.83083i) q^{9} +(-3.76217 + 2.78664i) q^{10} +(-4.44627 + 0.783998i) q^{11} +(3.99442 - 1.04542i) q^{12} +(3.46319 - 1.26050i) q^{13} +(-4.56871 + 3.13271i) q^{14} +(-1.40017 - 3.61103i) q^{15} +(-0.535695 - 3.03808i) q^{16} +(1.90720 + 1.10112i) q^{17} +(-0.0731236 + 6.28087i) q^{18} +(-4.91222 + 2.83607i) q^{19} +(5.11023 - 1.51637i) q^{20} +(-1.49984 - 4.33018i) q^{21} +(9.30946 + 1.64151i) q^{22} +(-5.48722 - 4.60432i) q^{23} +(-1.38602 - 0.129395i) q^{24} +(-1.95804 - 4.60066i) q^{25} -7.71647 q^{26} +(-4.99485 - 1.43230i) q^{27} +(6.10790 - 1.57255i) q^{28} +(-2.81698 + 7.73958i) q^{29} +(0.168946 + 8.10736i) q^{30} +(4.05814 - 4.83631i) q^{31} +(-1.40074 + 7.94401i) q^{32} +(-3.34606 + 7.06795i) q^{33} +(-2.96388 - 3.53222i) q^{34} +(-2.11678 - 5.52442i) q^{35} +(2.52405 - 6.69134i) q^{36} +(1.79890 + 1.03859i) q^{37} +(11.6957 - 2.06227i) q^{38} +(1.68800 - 6.15616i) q^{39} +(-1.79383 - 0.108857i) q^{40} +(6.31954 - 2.30012i) q^{41} +(-0.149968 + 9.59367i) q^{42} +(4.69546 - 0.827937i) q^{43} +(-9.32084 - 5.38139i) q^{44} +(-6.50496 - 1.63873i) q^{45} +(7.49887 + 12.9884i) q^{46} +(-6.25944 - 7.45971i) q^{47} +(-4.82943 - 2.28632i) q^{48} +(-2.26463 - 6.62355i) q^{49} +(0.557859 + 10.4540i) q^{50} +(3.46634 - 1.59188i) q^{51} +(8.25574 + 3.00484i) q^{52} +2.90976 q^{53} +(8.80166 + 6.39491i) q^{54} +(-4.02118 + 9.26014i) q^{55} +(-2.11638 - 0.206098i) q^{56} +(-0.913211 + 9.78191i) q^{57} +(11.0848 - 13.2103i) q^{58} +(1.44006 - 8.16701i) q^{59} +(2.97631 - 8.73974i) q^{60} +(0.318741 + 0.379861i) q^{61} +(-11.4477 + 6.60934i) q^{62} +(-7.62097 - 2.21829i) q^{63} +(5.35979 - 9.28344i) q^{64} +(1.91999 - 8.01414i) q^{65} +(11.6448 - 11.5100i) q^{66} +(2.04359 + 5.61471i) q^{67} +(1.79555 + 4.93323i) q^{68} +(-12.0025 + 3.14130i) q^{69} +(0.208667 + 12.3851i) q^{70} +(-6.10717 - 3.52597i) q^{71} +(-1.57122 + 1.82885i) q^{72} +(-0.632890 - 1.09620i) q^{73} +(-2.79558 - 3.33164i) q^{74} +(-8.46214 - 1.84178i) q^{75} +(-13.3161 - 2.34799i) q^{76} +(-5.15422 + 10.7760i) q^{77} +(-7.72963 + 10.9034i) q^{78} +(8.96547 + 3.26316i) q^{79} +(-6.32733 - 2.74762i) q^{80} +(-7.02722 + 5.62301i) q^{81} -14.0808 q^{82} +(0.743273 - 2.04213i) q^{83} +(3.89629 - 10.2057i) q^{84} +(4.40594 - 2.19934i) q^{85} +(-9.83120 - 1.73351i) q^{86} +(8.11430 + 11.7332i) q^{87} +(2.33242 + 2.77967i) q^{88} +(5.99817 + 10.3891i) q^{89} +(11.6250 + 7.88246i) q^{90} +(2.61596 - 9.39332i) q^{91} +(-2.96516 - 16.8163i) q^{92} +(-2.76867 - 10.5787i) q^{93} +(6.97345 + 19.1594i) q^{94} +(-0.768264 + 12.6600i) q^{95} +(9.82180 + 9.93682i) q^{96} +(2.37599 + 13.4749i) q^{97} +(-0.287534 + 14.6535i) q^{98} +(6.63528 + 11.8080i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 816 q - 24 q^{4} - 24 q^{9}+O(q^{10}) $ 816 * q - 24 * q^4 - 24 * q^9	$ 816 q - 24 q^{4} - 24 q^{9} - 12 q^{11} - 6 q^{14} + 24 q^{21} - 12 q^{25} + 12 q^{29} + 78 q^{30} - 36 q^{35} + 12 q^{36} - 84 q^{39} - 36 q^{44} - 12 q^{46} + 6 q^{49} + 24 q^{50} - 60 q^{51} + 120 q^{56} - 150 q^{60} - 444 q^{64} + 162 q^{65} + 21 q^{70} - 36 q^{71} - 48 q^{74} - 48 q^{79} - 48 q^{81} + 66 q^{84} - 102 q^{85} - 192 q^{86} - 6 q^{91} - 210 q^{95} - 216 q^{99}+O(q^{100}) $ 816 * q - 24 * q^4 - 24 * q^9 - 12 * q^11 - 6 * q^14 + 24 * q^21 - 12 * q^25 + 12 * q^29 + 78 * q^30 - 36 * q^35 + 12 * q^36 - 84 * q^39 - 36 * q^44 - 12 * q^46 + 6 * q^49 + 24 * q^50 - 60 * q^51 + 120 * q^56 - 150 * q^60 - 444 * q^64 + 162 * q^65 + 21 * q^70 - 36 * q^71 - 48 * q^74 - 48 * q^79 - 48 * q^81 + 66 * q^84 - 102 * q^85 - 192 * q^86 - 6 * q^91 - 210 * q^95 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.96750	−	0.716110i	−1.39123	−	0.506366i	−0.465667	−	0.884960i	$-0.654186\pi$
$2$	−1.96750	−	0.716110i	−1.39123	−	0.506366i	−0.925563	+	0.378594i	$0.876408\pi$
$3$	1.00171	−	1.41301i	0.578335	−	0.815799i
$3$	1.00171	−	1.41301i	0.578335	−	0.815799i
$4$	1.82614	+	1.53231i	0.913069	+	0.766156i
$5$	1.23328	−	1.86521i	0.551540	−	0.834149i
$5$	1.23328	−	1.86521i	0.551540	−	0.834149i
$6$	−2.98272	+	2.06275i	−1.21769	+	0.842115i
$7$	1.53873	−	2.15228i	0.581584	−	0.813486i
$7$	1.53873	−	2.15228i	0.581584	−	0.813486i
$8$	−0.401851	−	0.696026i	−0.142076	−	0.246082i
$9$	−0.993173	−	2.83083i	−0.331058	−	0.943611i
$10$	−3.76217	+	2.78664i	−1.18970	+	0.881212i
$11$	−4.44627	+	0.783998i	−1.34060	+	0.236384i	−0.797519	−	0.603294i	$-0.793854\pi$
$11$	−4.44627	+	0.783998i	−1.34060	+	0.236384i	−0.543084	+	0.839679i	$0.682743\pi$
$12$	3.99442	−	1.04542i	1.15309	−	0.301787i
$13$	3.46319	−	1.26050i	0.960516	−	0.349599i	0.186280	−	0.982497i	$-0.440357\pi$
$13$	3.46319	−	1.26050i	0.960516	−	0.349599i	0.774236	+	0.632897i	$0.218134\pi$
$14$	−4.56871	+	3.13271i	−1.22104	+	0.837251i
$15$	−1.40017	−	3.61103i	−0.361524	−	0.932363i
$16$	−0.535695	−	3.03808i	−0.133924	−	0.759520i
$17$	1.90720	+	1.10112i	0.462564	+	0.267061i	0.713122	−	0.701040i	$-0.247281\pi$
$17$	1.90720	+	1.10112i	0.462564	+	0.267061i	−0.250558	+	0.968102i	$0.580614\pi$
$18$	−0.0731236	+	6.28087i	−0.0172354	+	1.48042i
$19$	−4.91222	+	2.83607i	−1.12694	+	0.650639i	−0.943164	−	0.332329i	$-0.892166\pi$
$19$	−4.91222	+	2.83607i	−1.12694	+	0.650639i	−0.183777	+	0.982968i	$0.558832\pi$
$20$	5.11023	−	1.51637i	1.14268	−	0.339070i
$21$	−1.49984	−	4.33018i	−0.327291	−	0.944924i
$22$	9.30946	+	1.64151i	1.98478	+	0.349971i
$23$	−5.48722	−	4.60432i	−1.14416	−	0.960067i	−0.144596	−	0.989491i	$-0.546188\pi$
$23$	−5.48722	−	4.60432i	−1.14416	−	0.960067i	−0.999567	+	0.0294235i	$0.990633\pi$
$24$	−1.38602	−	0.129395i	−0.282921	−	0.0264127i
$25$	−1.95804	−	4.60066i	−0.391608	−	0.920132i
$26$	−7.71647			−1.51332
$27$	−4.99485	−	1.43230i	−0.961259	−	0.275646i
$28$	6.10790	−	1.57255i	1.15428	−	0.297185i
$29$	−2.81698	+	7.73958i	−0.523100	+	1.43720i	0.343952	+	0.938987i	$0.388234\pi$
$29$	−2.81698	+	7.73958i	−0.523100	+	1.43720i	−0.867052	+	0.498217i	$0.833988\pi$
$30$	0.168946	+	8.10736i	0.0308452	+	1.48019i
$31$	4.05814	−	4.83631i	0.728864	−	0.868626i	−0.266596	−	0.963808i	$-0.585899\pi$
$31$	4.05814	−	4.83631i	0.728864	−	0.868626i	0.995460	+	0.0951822i	$0.0303434\pi$
$32$	−1.40074	+	7.94401i	−0.247619	+	1.40432i
$33$	−3.34606	+	7.06795i	−0.582475	+	1.23037i
$34$	−2.96388	−	3.53222i	−0.508302	−	0.605770i
$35$	−2.11678	−	5.52442i	−0.357802	−	0.933798i
$36$	2.52405	−	6.69134i	0.420674	−	1.11522i
$37$	1.79890	+	1.03859i	0.295737	+	0.170744i	0.640526	−	0.767936i	$-0.278716\pi$
$37$	1.79890	+	1.03859i	0.295737	+	0.170744i	−0.344789	+	0.938680i	$0.612050\pi$
$38$	11.6957	−	2.06227i	1.89730	−	0.334544i
$39$	1.68800	−	6.15616i	0.270297	−	0.985774i
$40$	−1.79383	−	0.108857i	−0.283630	−	0.0172119i
$41$	6.31954	−	2.30012i	0.986946	−	0.359219i	0.202409	−	0.979301i	$-0.435123\pi$
$41$	6.31954	−	2.30012i	0.986946	−	0.359219i	0.784537	+	0.620082i	$0.212901\pi$
$42$	−0.149968	+	9.59367i	−0.0231405	+	1.48034i
$43$	4.69546	−	0.827937i	0.716051	−	0.126259i	0.196259	−	0.980552i	$-0.437121\pi$
$43$	4.69546	−	0.827937i	0.716051	−	0.126259i	0.519792	+	0.854293i	$0.326009\pi$
$44$	−9.32084	−	5.38139i	−1.40517	−	0.811275i
$45$	−6.50496	−	1.63873i	−0.969703	−	0.244287i
$46$	7.49887	+	12.9884i	1.10565	+	1.91504i
$47$	−6.25944	−	7.45971i	−0.913034	−	1.08811i	−0.995801	−	0.0915423i	$-0.970820\pi$
$47$	−6.25944	−	7.45971i	−0.913034	−	1.08811i	0.0827675	−	0.996569i	$-0.473624\pi$
$48$	−4.82943	−	2.28632i	−0.697069	−	0.330002i
$49$	−2.26463	−	6.62355i	−0.323519	−	0.946222i
$50$	0.557859	+	10.4540i	0.0788932	+	1.47841i
$51$	3.46634	−	1.59188i	0.485385	−	0.222908i
$52$	8.25574	+	3.00484i	1.14487	+	0.416697i
$53$	2.90976			0.399686			0.199843	−	0.979828i	$-0.435957\pi$
$53$	2.90976			0.399686			0.199843	+	0.979828i	$0.435957\pi$
$54$	8.80166	+	6.39491i	1.19775	+	0.870237i
$55$	−4.02118	+	9.26014i	−0.542215	+	1.24864i
$56$	−2.11638	−	0.206098i	−0.282813	−	0.0275410i
$57$	−0.913211	+	9.78191i	−0.120958	+	1.29564i
$58$	11.0848	−	13.2103i	1.45550	−	1.73460i
$59$	1.44006	−	8.16701i	0.187480	−	1.06325i	−0.735246	−	0.677800i	$-0.762934\pi$
$59$	1.44006	−	8.16701i	0.187480	−	1.06325i	0.922727	−	0.385455i	$-0.125955\pi$
$60$	2.97631	−	8.73974i	0.384240	−	1.12830i
$61$	0.318741	+	0.379861i	0.0408106	+	0.0486362i	0.786064	−	0.618146i	$-0.212116\pi$
$61$	0.318741	+	0.379861i	0.0408106	+	0.0486362i	−0.745253	+	0.666782i	$0.767671\pi$
$62$	−11.4477	+	6.60934i	−1.45386	+	0.839387i
$63$	−7.62097	−	2.21829i	−0.960152	−	0.279479i
$64$	5.35979	−	9.28344i	0.669974	−	1.16043i
$65$	1.91999	−	8.01414i	0.238145	−	0.994031i
$66$	11.6448	−	11.5100i	1.43338	−	1.41678i
$67$	2.04359	+	5.61471i	0.249664	+	0.685946i	0.999699	+	0.0245475i	$0.00781449\pi$
$67$	2.04359	+	5.61471i	0.249664	+	0.685946i	−0.750035	+	0.661398i	$0.769963\pi$
$68$	1.79555	+	4.93323i	0.217742	+	0.598242i
$69$	−12.0025	+	3.14130i	−1.44493	+	0.378168i
$70$	0.208667	+	12.3851i	0.0249405	+	1.48031i
$71$	−6.10717	−	3.52597i	−0.724787	−	0.418456i	0.0917247	−	0.995784i	$-0.470762\pi$
$71$	−6.10717	−	3.52597i	−0.724787	−	0.418456i	−0.816512	+	0.577328i	$0.804095\pi$
$72$	−1.57122	+	1.82885i	−0.185171	+	0.215531i
$73$	−0.632890	−	1.09620i	−0.0740742	−	0.128300i	0.826609	−	0.562776i	$-0.190267\pi$
$73$	−0.632890	−	1.09620i	−0.0740742	−	0.128300i	−0.900683	+	0.434476i	$0.856933\pi$
$74$	−2.79558	−	3.33164i	−0.324979	−	0.387295i
$75$	−8.46214	−	1.84178i	−0.977124	−	0.212671i
$76$	−13.3161	−	2.34799i	−1.52747	−	0.269333i
$77$	−5.15422	+	10.7760i	−0.587378	+	1.22804i
$78$	−7.72963	+	10.9034i	−0.875208	+	1.23457i
$79$	8.96547	+	3.26316i	1.00869	+	0.367135i	0.792931	−	0.609311i	$-0.208554\pi$
$79$	8.96547	+	3.26316i	1.00869	+	0.367135i	0.215763	+	0.976446i	$0.430776\pi$
$80$	−6.32733	−	2.74762i	−0.707417	−	0.307193i
$81$	−7.02722	+	5.62301i	−0.780802	+	0.624779i
$82$	−14.0808			−1.55497
$83$	0.743273	−	2.04213i	0.0815848	−	0.224152i	−0.892193	−	0.451655i	$-0.850834\pi$
$83$	0.743273	−	2.04213i	0.0815848	−	0.224152i	0.973777	+	0.227503i	$0.0730560\pi$
$84$	3.89629	−	10.2057i	0.425120	−	1.11354i
$85$	4.40594	−	2.19934i	0.477891	−	0.238552i
$86$	−9.83120	−	1.73351i	−1.06013	−	0.186929i
$87$	8.11430	+	11.7332i	0.869944	+	1.25793i
$88$	2.33242	+	2.77967i	0.248637	+	0.296314i
$89$	5.99817	+	10.3891i	0.635805	+	1.10125i	0.986344	+	0.164699i	$0.0526652\pi$
$89$	5.99817	+	10.3891i	0.635805	+	1.10125i	−0.350539	+	0.936548i	$0.614001\pi$
$90$	11.6250	+	7.88246i	1.22538	+	0.830885i
$91$	2.61596	−	9.39332i	0.274227	−	0.984688i
$92$	−2.96516	−	16.8163i	−0.309139	−	1.75322i
$93$	−2.76867	−	10.5787i	−0.287097	−	1.09696i
$94$	6.97345	+	19.1594i	0.719257	+	1.97614i
$95$	−0.768264	+	12.6600i	−0.0788223	+	1.29889i
$96$	9.82180	+	9.93682i	1.00243	+	1.01417i
$97$	2.37599	+	13.4749i	0.241245	+	1.36817i	0.829054	+	0.559169i	$0.188880\pi$
$97$	2.37599	+	13.4749i	0.241245	+	1.36817i	−0.587809	+	0.809000i	$0.700009\pi$
$98$	−0.287534	+	14.6535i	−0.0290453	+	1.48023i
$99$	6.63528	+	11.8080i	0.666871	+	1.18675i
$100$	3.47399	−	11.4018i	0.347399	−	1.14018i
$101$	−12.6510	+	10.6155i	−1.25882	+	1.05628i	−0.263019	+	0.964791i	$0.584718\pi$
$101$	−12.6510	+	10.6155i	−1.25882	+	1.05628i	−0.995806	+	0.0914885i	$0.970838\pi$
$102$	−7.95998	+	0.649743i	−0.788156	+	0.0643341i
$103$	1.18283	−	6.70816i	0.116548	−	0.660975i	−0.869425	−	0.494066i	$-0.835510\pi$
$103$	1.18283	−	6.70816i	0.116548	−	0.660975i	0.985972	−	0.166909i	$-0.0533786\pi$
$104$	−2.26902	−	1.90394i	−0.222496	−	0.186696i
$105$	−9.92643	−	2.54282i	−0.968721	−	0.248153i
$106$	−5.72493	−	2.08371i	−0.556055	−	0.202387i
$107$	1.61281			0.155916			0.0779579	−	0.996957i	$-0.475160\pi$
$107$	1.61281			0.155916			0.0779579	+	0.996957i	$0.475160\pi$
$108$	−6.92655	−	10.2692i	−0.666508	−	0.988159i
$109$	−11.0718			−1.06048			−0.530241	−	0.847847i	$-0.677899\pi$
$109$	−11.0718			−1.06048			−0.530241	+	0.847847i	$0.677899\pi$
$110$	14.5429	−	15.3397i	1.38661	−	1.46258i
$111$	3.26951	−	1.50149i	0.310328	−	0.142515i
$112$	−7.36309	−	3.52181i	−0.695747	−	0.332780i
$113$	1.99228	−	11.2988i	0.187418	−	1.06290i	−0.735391	−	0.677643i	$-0.763001\pi$
$113$	1.99228	−	11.2988i	0.187418	−	1.06290i	0.922809	−	0.385258i	$-0.125888\pi$
$114$	8.80166	−	18.5919i	0.824351	−	1.74129i
$115$	−15.3553	+	4.55641i	−1.43189	+	0.424887i
$116$	−17.0036	+	9.81706i	−1.57875	+	0.911491i
$117$	−7.00780	−	8.55182i	−0.647872	−	0.790616i
$118$	−8.68180	+	15.0373i	−0.799225	+	1.38430i
$119$	5.30459	−	2.41050i	0.486271	−	0.220970i
$120$	−1.95071	+	2.42565i	−0.178074	+	0.221431i
$121$	8.81808	−	3.20952i	0.801644	−	0.291775i
$122$	−0.355100	−	0.975628i	−0.0321492	−	0.0883292i
$123$	3.08023	−	11.2336i	0.277735	−	1.01290i
$124$	14.8215	−	2.61342i	1.33101	−	0.234692i
$125$	−10.9960	−	2.02174i	−0.983514	−	0.180830i
$126$	13.4057	+	9.82193i	1.19427	+	0.875007i
$127$	−7.94667	+	4.58801i	−0.705153	+	0.407120i	−0.809264	−	0.587446i	$-0.800134\pi$
$127$	−7.94667	+	4.58801i	−0.705153	+	0.407120i	0.104111	+	0.994566i	$0.466800\pi$
$128$	−4.83465	+	4.05675i	−0.427327	+	0.358570i
$129$	3.53359	−	7.46407i	0.311115	−	0.657174i
$130$	−9.51657	+	14.3929i	−0.834658	+	1.26234i
$131$	−7.10311	−	5.96022i	−0.620602	−	0.520747i	0.277391	−	0.960757i	$-0.410530\pi$
$131$	−7.10311	−	5.96022i	−0.620602	−	0.520747i	−0.897993	+	0.440010i	$0.854975\pi$
$132$	−16.9407	+	7.77984i	−1.47450	+	0.677148i
$133$	−1.45454	+	14.9364i	−0.126125	+	1.29515i
$134$		−	12.5104i		−	1.08073i
$135$	−8.83159	+	7.55003i	−0.760102	+	0.649803i
$136$		−	1.76995i		−	0.151772i
$137$	18.3118	+	6.66493i	1.56448	+	0.569424i	0.971757	−	0.235983i	$-0.0758311\pi$
$137$	18.3118	+	6.66493i	1.56448	+	0.569424i	0.592722	+	0.805407i	$0.298053\pi$
$138$	25.8644	+	2.41463i	2.20172	+	0.205547i
$139$	−4.02795	+	4.80032i	−0.341646	+	0.407158i	−0.909321	−	0.416095i	$-0.863398\pi$
$139$	−4.02795	+	4.80032i	−0.341646	+	0.407158i	0.567675	+	0.823253i	$0.307843\pi$
$140$	4.59960	−	13.3319i	0.388737	−	1.12675i
$141$	−16.8107	+	1.37220i	−1.41572	+	0.115560i
$142$	9.49084	+	11.3107i	0.796454	+	0.949177i
$143$	−14.4101	+	8.31966i	−1.20503	+	0.695725i
$144$	−8.06825	+	4.53380i	−0.672355	+	0.377817i
$145$	10.9619	+	14.7993i	0.910332	+	1.22902i
$146$	0.460210	+	2.60998i	0.0380873	+	0.216004i
$147$	−11.6276	−	3.43491i	−0.959029	−	0.283306i
$148$	1.69359	+	4.65309i	0.139212	+	0.382482i
$149$	−5.26471	−	14.4647i	−0.431302	−	1.18499i	−0.945014	−	0.327029i	$-0.893953\pi$
$149$	−5.26471	−	14.4647i	−0.431302	−	1.18499i	0.513713	−	0.857962i	$-0.328270\pi$
$150$	15.3303	+	9.68352i	1.25171	+	0.790656i
$151$	1.40527	+	7.96969i	0.114359	+	0.648564i	0.987065	+	0.160318i	$0.0512520\pi$
$151$	1.40527	+	7.96969i	0.114359	+	0.648564i	−0.872706	+	0.488246i	$0.837637\pi$
$152$	3.94796	+	2.27935i	0.320222	+	0.184880i
$153$	1.22291	−	6.49256i	0.0988667	−	0.524893i
$154$	17.8577	−	17.5107i	1.43902	−	1.41106i
$155$	−4.01592	−	13.5338i	−0.322566	−	1.08706i
$156$	12.5157	−	8.65544i	1.00206	−	0.692990i
$157$	0.754737	−	4.28032i	0.0602345	−	0.341607i	−0.939765	−	0.341820i	$-0.888957\pi$
$157$	0.754737	−	4.28032i	0.0602345	−	0.341607i	1.00000		0.000212988i	$6.77962e-5\pi$
$158$	−15.3027	−	12.8405i	−1.21742	−	1.02154i
$159$	2.91472	−	4.11150i	0.231152	−	0.326063i
$160$	13.0898	+	12.4099i	1.03484	+	0.981087i
$161$	−18.3531	+	4.72524i	−1.44643	+	0.372401i
$162$	17.8527	−	6.03099i	1.40264	−	0.473839i
$163$		−	7.67621i		−	0.601247i	−0.953743	−	0.300624i	$-0.902805\pi$
$163$		−	7.67621i		−	0.601247i	0.953743	−	0.300624i	$-0.0971948\pi$
$164$	15.0649	+	5.48316i	1.17637	+	0.428163i
$165$	9.05660	+	14.9579i	0.705055	+	1.16447i
$166$	−2.92477	+	3.48561i	−0.227006	+	0.270536i
$167$	8.58297	+	1.51341i	0.664170	+	0.117111i	0.495563	−	0.868572i	$-0.334962\pi$
$167$	8.58297	+	1.51341i	0.664170	+	0.117111i	0.168608	+	0.985683i	$0.446073\pi$
$168$	−2.41121	+	2.78401i	−0.186029	+	0.214791i
$169$	0.446254	−	0.374451i	0.0343272	−	0.0288039i
$170$	−10.2436	+	1.17206i	−0.785651	+	0.0898929i
$171$	12.9071	+	11.0890i	0.987032	+	0.847994i
$172$	9.84322	+	5.68299i	0.750539	+	0.433324i
$173$	15.4779	−	2.72917i	1.17676	−	0.207495i	0.449132	−	0.893465i	$-0.351733\pi$
$173$	15.4779	−	2.72917i	1.17676	−	0.207495i	0.727630	+	0.685970i	$0.240622\pi$
$174$	−7.56259	−	28.8957i	−0.573319	−	2.19058i
$175$	−12.9148	−	2.86491i	−0.976268	−	0.216567i
$176$	4.76370	+	13.0882i	0.359077	+	0.986557i
$177$	−10.0975	−	10.2158i	−0.758976	−	0.767864i
$178$	−4.36162	−	24.7360i	−0.326917	−	1.85404i
$179$	21.0864	+	12.1743i	1.57607	+	0.909947i	0.995399	+	0.0958117i	$0.0305447\pi$
$179$	21.0864	+	12.1743i	1.57607	+	0.909947i	0.580675	+	0.814135i	$0.302789\pi$
$180$	−9.36792	−	12.9602i	−0.698244	−	0.965995i
$181$	2.40999	−	1.39141i	0.179133	−	0.103423i	−0.407752	−	0.913093i	$-0.633687\pi$
$181$	2.40999	−	1.39141i	0.179133	−	0.103423i	0.586885	+	0.809670i	$0.300354\pi$
$182$	−11.8735	+	16.6080i	−0.880126	+	1.23107i
$183$	0.856030	−	0.0698744i	0.0632796	−	0.00516527i
$184$	−0.999684	+	5.66949i	−0.0736977	+	0.417960i
$185$	4.15575	−	2.07445i	0.305537	−	0.152517i
$186$	−2.12820	+	22.7963i	−0.156047	+	1.67150i
$187$	−9.34321	−	3.40065i	−0.683243	−	0.248680i
$188$		−	23.2139i		−	1.69305i
$189$	−10.7684	+	8.54640i	−0.783288	+	0.621659i
$190$	10.5775	−	24.3584i	0.767374	−	1.76714i
$191$	−0.575587	+	1.58141i	−0.0416480	+	0.114427i	−0.958773	−	0.284172i	$-0.908281\pi$
$191$	−0.575587	+	1.58141i	−0.0416480	+	0.114427i	0.917125	+	0.398599i	$0.130503\pi$
$192$	−7.74862	−	16.8727i	−0.559208	−	1.21768i
$193$	7.11343	−	8.47746i	0.512036	−	0.610221i	−0.446642	−	0.894713i	$-0.647380\pi$
$193$	7.11343	−	8.47746i	0.512036	−	0.610221i	0.958679	+	0.284492i	$0.0918248\pi$
$194$	4.97476	−	28.2133i	0.357167	−	2.02559i
$195$	−9.40076	−	10.7408i	−0.673203	−	0.769161i
$196$	6.01381	−	15.5656i	0.429558	−	1.11183i
$197$	−4.17651	−	7.23392i	−0.297564	−	0.515396i	0.678014	−	0.735049i	$-0.262841\pi$
$197$	−4.17651	−	7.23392i	−0.297564	−	0.515396i	−0.975578	+	0.219653i	$0.929507\pi$
$198$	−4.59906	−	27.9838i	−0.326841	−	1.98872i
$199$	−7.22720	−	4.17262i	−0.512322	−	0.295790i	0.221465	−	0.975168i	$-0.428916\pi$
$199$	−7.22720	−	4.17262i	−0.512322	−	0.295790i	−0.733788	+	0.679379i	$0.762249\pi$
$200$	−2.41534	+	3.21162i	−0.170790	+	0.227096i
$201$	9.98069	+	2.73668i	0.703984	+	0.193031i
$202$	32.4927	−	11.8264i	2.28618	−	0.832101i
$203$	12.3232	+	17.9720i	0.864919	+	1.26139i
$204$	8.76929	+	2.40452i	0.613973	+	0.168350i
$205$	3.50354	−	14.6240i	0.244698	−	1.02138i
$206$	−7.13099	+	12.3512i	−0.496840	+	0.860552i
$207$	−7.58430	+	20.1063i	−0.527146	+	1.39748i
$208$	−5.68471	−	9.84620i	−0.394164	−	0.682711i
$209$	19.6176	−	16.4611i	1.35698	−	1.13864i
$210$	17.7093	+	12.1114i	1.22206	+	0.835766i
$211$	1.31065	−	7.43306i	0.0902288	−	0.511713i	−0.905877	−	0.423542i	$-0.860787\pi$
$211$	1.31065	−	7.43306i	0.0902288	−	0.511713i	0.996105	−	0.0881712i	$-0.0281022\pi$
$212$	5.31362	+	4.45865i	0.364941	+	0.306222i
$213$	−11.0998	+	5.09748i	−0.760546	+	0.349273i
$214$	−3.17319	−	1.15495i	−0.216915	−	0.0789505i
$215$	4.24654	−	9.77912i	0.289612	−	0.666930i
$216$	1.01027	+	4.05211i	0.0687398	+	0.275711i
$217$	−4.16472	−	16.1760i	−0.282719	−	1.09810i
$218$	21.7837	+	7.92860i	1.47538	+	0.536993i
$219$	−2.18290	−	0.203790i	−0.147507	−	0.0137708i
$220$	−21.5326	+	10.7486i	−1.45173	+	0.724670i
$221$	7.99296	+	1.40937i	0.537664	+	0.0948047i
$222$	−7.50797	+	0.612847i	−0.503902	+	0.0411316i
$223$	18.6222	−	15.6259i	1.24703	−	1.04639i	0.250093	−	0.968222i	$-0.419539\pi$
$223$	18.6222	−	15.6259i	1.24703	−	1.04639i	0.996941	−	0.0781635i	$-0.0249056\pi$
$224$	14.9424	+	15.2385i	0.998380	+	1.01816i
$225$	−11.0790	+	10.1121i	−0.738601	+	0.674142i
$226$	−12.0110	+	20.8036i	−0.798959	+	1.38384i
$227$	11.8463	−	2.08883i	0.786268	−	0.138640i	0.233922	−	0.972255i	$-0.424844\pi$
$227$	11.8463	−	2.08883i	0.786268	−	0.138640i	0.552346	+	0.833615i	$0.313733\pi$
$228$	−16.6566	+	16.4638i	−1.10311	+	1.09034i
$229$	−0.436253	−	1.19860i	−0.0288284	−	0.0792054i	0.924444	−	0.381319i	$-0.124530\pi$
$229$	−0.436253	−	1.19860i	−0.0288284	−	0.0792054i	−0.953272	+	0.302114i	$0.902308\pi$
$230$	33.4744	+	2.03137i	2.20724	+	0.133945i
$231$	10.0635	+	18.0773i	0.662132	+	1.18940i
$232$	6.51895	−	1.14947i	0.427990	−	0.0754662i
$233$	8.77621	−	15.2008i	0.574949	−	0.995841i	−0.421098	−	0.907015i	$-0.638355\pi$
$233$	8.77621	−	15.2008i	0.574949	−	0.995841i	0.996047	−	0.0888257i	$-0.0283114\pi$
$234$	7.66379	+	21.8440i	0.500997	+	1.42799i
$235$	−21.6336	+	2.47528i	−1.41122	+	0.161470i
$236$	15.1442	−	12.7075i	0.985802	−	0.827186i
$237$	13.5916	−	9.39954i	0.882871	−	0.610566i
$238$	−12.1629	+	0.943989i	−0.788406	+	0.0611897i
$239$	−3.48022	+	4.14756i	−0.225116	+	0.268283i	−0.866766	−	0.498714i	$-0.833806\pi$
$239$	−3.48022	+	4.14756i	−0.225116	+	0.268283i	0.641650	+	0.766998i	$0.278250\pi$
$240$	−10.2205	+	6.18825i	−0.659732	+	0.399450i
$241$	9.89061	−	27.1742i	0.637110	−	1.75045i	−0.0235067	−	0.999724i	$-0.507483\pi$
$241$	9.89061	−	27.1742i	0.637110	−	1.75045i	0.660617	−	0.750723i	$-0.270295\pi$
$242$	−19.6479			−1.26302
$243$	0.906146	+	15.5621i	0.0581293	+	0.998309i
$244$			1.18209i			0.0756755i
$245$	−15.1473	−	3.94467i	−0.967723	−	0.252016i
$246$	−14.1048	+	19.8963i	−0.899291	+	1.26854i
$247$	−13.4371	+	16.0137i	−0.854982	+	1.01893i
$248$	−4.99696	−	0.881099i	−0.317307	−	0.0559498i
$249$	−2.14100	−	3.09586i	−0.135680	−	0.196192i
$250$	20.1869	+	11.8521i	1.27673	+	0.749594i
$251$	8.93455	+	15.4751i	0.563944	+	0.976780i	0.997147	+	0.0754833i	$0.0240499\pi$
$251$	8.93455	+	15.4751i	0.563944	+	0.976780i	−0.433203	+	0.901296i	$0.642617\pi$
$252$	−10.5178	−	15.7286i	−0.662561	−	0.990809i
$253$	28.0074	+	16.1701i	1.76081	+	1.01661i
$254$	18.9206	−	3.33620i	1.18718	−	0.209332i
$255$	1.30577	−	8.42871i	0.0817704	−	0.527826i
$256$	−7.72900	+	2.81312i	−0.483062	+	0.175820i
$257$	2.61908	+	7.19585i	0.163374	+	0.448865i	0.994185	−	0.107690i	$-0.0343452\pi$
$257$	2.61908	+	7.19585i	0.163374	+	0.448865i	−0.830811	+	0.556555i	$0.812123\pi$
$258$	−12.2974	+	12.1551i	−0.765604	+	0.756742i
$259$	5.00336	−	2.27362i	0.310894	−	0.141276i
$260$	15.7863	−	11.6929i	0.979026	−	0.725163i
$261$	24.7072	+	0.287648i	1.52934	+	0.0178050i
$262$	9.70717	+	16.8133i	0.599711	+	1.03873i
$263$	8.78731	−	7.37343i	0.541849	−	0.454665i	−0.330321	−	0.943869i	$-0.607157\pi$
$263$	8.78731	−	7.37343i	0.541849	−	0.454665i	0.872170	+	0.489203i	$0.162712\pi$
$264$	6.26409	−	0.511314i	0.385528	−	0.0314692i
$265$	3.58854	−	5.42732i	0.220443	−	0.333397i
$266$	13.5579	−	28.3457i	0.831290	−	1.73799i
$267$	20.6883	+	1.93140i	1.26610	+	0.118200i
$268$	−4.87161	+	13.3846i	−0.297581	+	0.817597i
$269$	12.4690			0.760248			0.380124	−	0.924935i	$-0.375881\pi$
$269$	12.4690			0.760248			0.380124	+	0.924935i	$0.375881\pi$
$270$	22.7828	−	8.53026i	1.38652	−	0.519135i
$271$		−	17.0770i		−	1.03735i	−0.854970	−	0.518677i	$-0.826425\pi$
$271$		−	17.0770i		−	1.03735i	0.854970	−	0.518677i	$-0.173575\pi$
$272$	2.32362	−	6.38409i	0.140890	−	0.387092i
$273$	−10.6524	−	13.1057i	−0.644713	−	0.793194i
$274$	−31.2555	−	26.2265i	−1.88821	−	1.58440i
$275$	12.3129	+	18.9207i	0.742496	+	1.14096i
$276$	−26.7317	−	12.6551i	−1.60906	−	0.761750i
$277$	2.63866	+	3.14464i	0.158542	+	0.188943i	0.839468	−	0.543409i	$-0.182867\pi$
$277$	2.63866	+	3.14464i	0.158542	+	0.188943i	−0.680926	+	0.732352i	$0.738422\pi$
$278$	11.3625	−	6.56016i	0.681479	−	0.393452i
$279$	−17.7212	−	6.68463i	−1.06094	−	0.400198i
$280$	−2.99451	+	3.69333i	−0.178956	+	0.220718i
$281$	27.8803	−	4.91605i	1.66320	−	0.293267i	0.738582	−	0.674164i	$-0.235496\pi$
$281$	27.8803	−	4.91605i	1.66320	−	0.293267i	0.924618	+	0.380897i	$0.124385\pi$
$282$	34.0577	+	9.33855i	2.02811	+	0.556102i
$283$	2.02830	−	0.738240i	0.120570	−	0.0438838i	−0.281031	−	0.959699i	$-0.590676\pi$
$283$	2.02830	−	0.738240i	0.120570	−	0.0438838i	0.401600	+	0.915815i	$0.368454\pi$
$284$	−5.74964	−	15.7970i	−0.341178	−	0.937380i
$285$	17.1191	+	13.7672i	1.01405	+	0.815496i
$286$	34.3095	−	6.04970i	2.02877	−	0.357726i
$287$	4.77354	−	17.1407i	0.281773	−	1.01178i
$288$	23.8793	−	3.92450i	1.40710	−	0.231254i
$289$	−6.07506	−	10.5223i	−0.357356	−	0.618960i
$290$	−10.9694	−	36.9675i	−0.644148	−	2.17081i
$291$	21.4201	+	10.1406i	1.25567	+	0.594452i
$292$	0.523972	−	2.97159i	0.0306631	−	0.173899i
$293$	−13.2899	+	15.8383i	−0.776405	+	0.925283i	−0.998765	−	0.0496814i	$-0.984179\pi$
$293$	−13.2899	+	15.8383i	−0.776405	+	0.925283i	0.222360	+	0.974965i	$0.428624\pi$
$294$	20.4175	+	15.0848i	1.19077	+	0.879764i
$295$	−13.4572	−	12.7582i	−0.783510	−	0.742814i
$296$		−	1.66944i		−	0.0970342i
$297$	23.3314	+	2.45245i	1.35382	+	0.142305i
$298$			32.2293i			1.86699i
$299$	−24.8070	−	9.02901i	−1.43463	−	0.522161i
$300$	−12.6309	−	16.3300i	−0.729243	−	0.942812i
$301$	5.44309	−	11.3799i	0.313734	−	0.655928i
$302$	2.94231	−	16.6867i	0.169311	−	0.960209i
$303$	2.32713	+	28.5096i	0.133690	+	1.63783i
$304$	11.2477	+	13.4044i	0.645098	+	0.768798i
$305$	1.10162	−	0.126045i	0.0630785	−	0.00721733i
$306$	−7.05547	+	11.8984i	−0.403334	+	0.680184i
$307$	2.89678	−	5.01737i	0.165328	−	0.286356i	−0.771444	−	0.636297i	$-0.780465\pi$
$307$	2.89678	−	5.01737i	0.165328	−	0.286356i	0.936772	+	0.349941i	$0.113798\pi$
$308$	−25.9245	+	11.7806i	−1.47719	+	0.671261i
$309$	−8.29382	−	8.39094i	−0.471819	−	0.477344i
$310$	−1.79041	+	29.5036i	−0.101688	+	1.67569i
$311$	−12.4442	+	4.52931i	−0.705645	+	0.256834i	−0.669819	−	0.742524i	$-0.733628\pi$
$311$	−12.4442	+	4.52931i	−0.705645	+	0.256834i	−0.0358257	+	0.999358i	$0.511406\pi$
$312$	−4.96317	+	1.29896i	−0.280984	+	0.0735392i
$313$	4.72350	+	26.7883i	0.266988	+	1.51417i	0.763313	+	0.646029i	$0.223571\pi$
$313$	4.72350	+	26.7883i	0.266988	+	1.51417i	−0.496325	+	0.868137i	$0.665318\pi$
$314$	−4.55012	+	7.88105i	−0.256778	+	0.444753i
$315$	−13.5364	+	11.4790i	−0.762688	+	0.646766i
$316$	11.3720	+	19.6969i	0.639725	+	1.10804i
$317$	−19.2423	+	16.1462i	−1.08076	+	0.906862i	−0.995983	−	0.0895379i	$-0.971461\pi$
$317$	−19.2423	+	16.1462i	−1.08076	+	0.906862i	−0.0847731	+	0.996400i	$0.527017\pi$
$318$	−8.67899	+	6.00211i	−0.486693	+	0.336581i
$319$	6.45724	−	36.6208i	0.361536	−	2.05037i
$320$	−10.7055	−	21.4462i	−0.598453	−	1.19888i
$321$	1.61556	−	2.27890i	0.0901716	−	0.127196i
$322$	39.4935	+	3.84597i	2.20089	+	0.214328i
$323$	−12.4914			−0.695043
$324$	−21.4489	−	0.499495i	−1.19160	−	0.0277497i
$325$	−12.5802	−	13.4649i	−0.697824	−	0.746896i
$326$	−5.49701	+	15.1029i	−0.304451	+	0.836473i
$327$	−11.0906	+	15.6445i	−0.613314	+	0.865141i
$328$	−4.14046	−	3.47426i	−0.228618	−	0.191834i
$329$	−25.6870	+	1.99362i	−1.41617	+	0.109912i
$330$	−7.10733	−	35.9151i	−0.391246	−	1.97706i
$331$	8.38165	−	7.03304i	0.460697	−	0.386571i	−0.382690	−	0.923877i	$-0.625002\pi$
$331$	8.38165	−	7.03304i	0.460697	−	0.386571i	0.843387	+	0.537306i	$0.180558\pi$
$332$	4.48649	−	2.59028i	0.246228	−	0.142160i
$333$	1.15347	−	6.12388i	0.0632097	−	0.335587i
$334$	−15.8032	−	9.12398i	−0.864713	−	0.499242i
$335$	12.9929	+	3.11278i	0.709880	+	0.170069i
$336$	−12.3520	+	6.87628i	−0.673856	+	0.375132i
$337$	3.38123	+	9.28985i	0.184187	+	0.506050i	0.997080	−	0.0763631i	$-0.0243308\pi$
$337$	3.38123	+	9.28985i	0.184187	+	0.506050i	−0.812893	+	0.582413i	$0.802109\pi$
$338$	−1.14615	+	0.417165i	−0.0623424	+	0.0226908i
$339$	−13.9696	−	14.1332i	−0.758724	−	0.767609i
$340$	11.4159	+	2.73497i	0.619116	+	0.148325i
$341$	−14.2520	+	24.6851i	−0.771787	+	1.33677i
$342$	−17.4538	−	31.0604i	−0.943793	−	1.67955i
$343$	−17.7404	−	5.31771i	−0.957892	−	0.287130i
$344$	−2.46314	−	2.93546i	−0.132804	−	0.158269i
$345$	−8.94326	+	26.2613i	−0.481489	+	1.41386i
$346$	−32.4071	−	5.71424i	−1.74221	−	0.307199i
$347$	−19.5786	−	16.4284i	−1.05103	−	0.881921i	−0.0578309	−	0.998326i	$-0.518418\pi$
$347$	−19.5786	−	16.4284i	−1.05103	−	0.881921i	−0.993202	+	0.116405i	$0.962863\pi$
$348$	−3.16108	+	33.8601i	−0.169452	+	1.81509i
$349$	−6.51740	+	17.9064i	−0.348868	+	0.958508i	0.633859	+	0.773448i	$0.281470\pi$
$349$	−6.51740	+	17.9064i	−0.348868	+	0.958508i	−0.982727	+	0.185059i	$0.940752\pi$
$350$	23.3582	+	14.8851i	1.24855	+	0.795643i
$351$	−19.1035	+	1.33567i	−1.01967	+	0.0712928i
$352$		−	36.4194i		−	1.94116i
$353$	5.80576	−	15.9512i	0.309009	−	0.848996i	−0.683841	−	0.729631i	$-0.739692\pi$
$353$	5.80576	−	15.9512i	0.309009	−	0.848996i	0.992850	−	0.119365i	$-0.0380860\pi$
$354$	12.5512	+	27.3304i	0.667090	+	1.45259i
$355$	−14.1085	+	7.04266i	−0.748804	+	0.373785i
$356$	−4.96591	+	28.1631i	−0.263193	+	1.49264i
$357$	1.90758	−	9.91003i	0.100960	−	0.524494i
$358$	−32.7694	−	39.0530i	−1.73192	−	2.06402i
$359$	28.1244	−	16.2376i	1.48435	−	0.856989i	0.484507	−	0.874787i	$-0.338999\pi$
$359$	28.1244	−	16.2376i	1.48435	−	0.856989i	0.999842	+	0.0177981i	$0.00566560\pi$
$360$	1.47343	+	5.18615i	0.0776564	+	0.273334i
$361$	6.58660	−	11.4083i	0.346663	−	0.600439i
$362$	−5.73805	+	1.01177i	−0.301585	+	0.0531776i
$363$	4.29805	−	15.6750i	0.225589	−	0.822724i
$364$	19.1706	−	13.1450i	1.00481	−	0.688988i
$365$	−2.82517	−	0.171444i	−0.147876	−	0.00897377i
$366$	−1.73427	−	0.475534i	−0.0906519	−	0.0248566i
$367$	2.19754	+	12.4629i	0.114711	+	0.650556i	0.986893	+	0.161375i	$0.0515930\pi$
$367$	2.19754	+	12.4629i	0.114711	+	0.650556i	−0.872183	+	0.489180i	$0.837296\pi$
$368$	−11.0488	+	19.1371i	−0.575959	+	0.997591i
$369$	−12.7877	−	15.6051i	−0.665699	−	0.812371i
$370$	−9.66195	+	1.10550i	−0.502301	+	0.0574724i
$371$	4.47732	−	6.26262i	0.232451	−	0.325139i
$372$	11.1540	−	23.5607i	0.578306	−	1.22157i
$373$	−10.5128	−	1.85370i	−0.544334	−	0.0959807i	−0.105282	−	0.994442i	$-0.533574\pi$
$373$	−10.5128	−	1.85370i	−0.544334	−	0.0959807i	−0.439052	+	0.898462i	$0.644686\pi$
$374$	15.9475	+	13.3815i	0.824625	+	0.691943i
$375$	−13.8715	+	13.5123i	−0.716322	+	0.697770i
$376$	−2.67679	+	7.35442i	−0.138045	+	0.379275i
$377$			30.3544i			1.56333i
$378$	27.3070	−	9.10363i	1.40452	−	0.468240i
$379$	−18.0645			−0.927910			−0.463955	−	0.885859i	$-0.653570\pi$
$379$	−18.0645			−0.927910			−0.463955	+	0.885859i	$0.653570\pi$
$380$	−20.8020	+	21.9417i	−1.06712	+	1.12559i
$381$	−1.47733	+	15.8245i	−0.0756860	+	0.810715i
$382$	2.26493	−	2.69924i	0.115884	−	0.138105i
$383$	1.57647	+	0.277975i	0.0805540	+	0.0142038i	0.213780	−	0.976882i	$-0.431422\pi$
$383$	1.57647	+	0.277975i	0.0805540	+	0.0142038i	−0.133226	+	0.991086i	$0.542534\pi$
$384$	0.889322	+	10.8951i	0.0453830	+	0.555986i
$385$	13.7429	+	22.9035i	0.700405	+	1.16727i
$386$	−20.0664	+	11.5854i	−1.02136	+	0.589680i
$387$	−7.00716	−	12.4698i	−0.356194	−	0.633875i
$388$	−16.3089	+	28.2478i	−0.827957	+	1.43406i
$389$	4.32725	−	0.763010i	0.219400	−	0.0386861i	−0.0628675	−	0.998022i	$-0.520025\pi$
$389$	4.32725	−	0.763010i	0.219400	−	0.0386861i	0.282267	+	0.959336i	$0.408913\pi$
$390$	10.8044	+	27.8644i	0.547102	+	1.41097i
$391$	−5.39529	−	14.8235i	−0.272852	−	0.749654i
$392$	−3.70012	+	4.23792i	−0.186884	+	0.214047i
$393$	−15.5371	+	4.06636i	−0.783741	+	0.205121i
$394$	3.03698	+	17.2235i	0.153001	+	0.867710i
$395$	17.1434	−	12.6981i	0.862580	−	0.638912i
$396$	−5.97661	+	31.7304i	−0.300336	+	1.59451i
$397$	−10.1088	−	17.5090i	−0.507348	−	0.878752i	−0.999964	−	0.00850506i	$-0.997293\pi$
$397$	−10.1088	−	17.5090i	−0.507348	−	0.878752i	0.492616	−	0.870247i	$-0.336041\pi$
$398$	11.2314	+	13.3851i	0.562980	+	0.670934i
$399$	19.6482	+	17.0172i	0.983642	+	0.851924i
$400$	−12.9283	+	8.41324i	−0.646413	+	0.420662i
$401$	15.3228	−	18.2610i	0.765186	−	0.911913i	−0.232978	−	0.972482i	$-0.574847\pi$
$401$	15.3228	−	18.2610i	0.765186	−	0.911913i	0.998164	+	0.0605693i	$0.0192916\pi$
$402$	−17.6772	−	12.5317i	−0.881659	−	0.625024i
$403$	7.95796	−	21.8643i	0.396414	−	1.08914i
$404$	−39.3688			−1.95867
$405$	1.82159	+	20.0420i	0.0905154	+	0.995895i
$406$	−11.3759	−	44.1847i	−0.564576	−	2.19285i
$407$	−8.81265	−	3.20754i	−0.436827	−	0.158992i
$408$	−2.50094	−	1.77296i	−0.123815	−	0.0877748i
$409$	−12.2108	+	14.5523i	−0.603787	+	0.719565i	−0.978193	−	0.207700i	$-0.933402\pi$
$409$	−12.2108	+	14.5523i	−0.603787	+	0.719565i	0.374406	+	0.927265i	$0.377847\pi$
$410$	−17.3656	+	26.2637i	−0.857625	+	1.29707i
$411$	27.7606	−	19.1983i	1.36933	−	0.946984i
$412$	12.4390	−	10.4376i	0.612826	−	0.514222i
$413$	−15.3618	−	15.6662i	−0.755907	−	0.770885i
$414$	29.3204	−	34.1278i	1.44102	−	1.67729i
$415$	−2.89234	−	3.90487i	−0.141979	−	0.191683i
$416$	5.16237	+	29.2772i	0.253106	+	1.43544i
$417$	2.74806	+	10.5000i	0.134573	+	0.514188i
$418$	−50.3855	+	18.3388i	−2.46444	+	0.896982i
$419$	−4.06130	+	1.47819i	−0.198407	+	0.0722144i	−0.439313	−	0.898334i	$-0.644778\pi$
$419$	−4.06130	+	1.47819i	−0.198407	+	0.0722144i	0.240905	+	0.970549i	$0.422556\pi$
$420$	−14.2307	−	19.8539i	−0.694385	−	0.968773i
$421$	−5.27236	−	29.9011i	−0.256959	−	1.45729i	−0.790993	−	0.611825i	$-0.790436\pi$
$421$	−5.27236	−	29.9011i	−0.256959	−	1.45729i	0.534034	−	0.845463i	$-0.320675\pi$
$422$	−7.90159	+	13.6859i	−0.384643	+	0.666222i
$423$	−14.9005	+	25.1282i	−0.724486	+	1.22178i
$424$	−1.16929	−	2.02526i	−0.0567856	−	0.0983556i
$425$	1.33151	−	10.9304i	0.0645879	−	0.530203i
$426$	25.4892	−	2.08058i	1.23495	−	0.100805i
$427$	1.30802	−	0.101518i	0.0632997	−	0.00491281i
$428$	2.94521	+	2.47132i	0.142362	+	0.119456i
$429$	−2.67892	+	28.6954i	−0.129339	+	1.38542i
$430$	−15.3580	+	16.1994i	−0.740628	+	0.781204i
$431$			8.71009i			0.419551i	0.977750	+	0.209775i	$0.0672732\pi$
$431$			8.71009i			0.419551i	−0.977750	+	0.209775i	$0.932727\pi$
$432$	−1.67572	+	15.9420i	−0.0806233	+	0.767011i
$433$	4.19676			0.201683			0.100842	−	0.994902i	$-0.467846\pi$
$433$	4.19676			0.201683			0.100842	+	0.994902i	$0.467846\pi$
$434$	−3.38975	+	34.8087i	−0.162713	+	1.67087i
$435$	31.8921	−	0.664586i	1.52911	−	0.0318645i
$436$	−20.2186	−	16.9654i	−0.968294	−	0.812495i
$437$	40.0126	+	7.05530i	1.91406	+	0.337501i
$438$	4.14892	+	1.96415i	0.198243	+	0.0938509i
$439$	13.4488	+	16.0277i	0.641878	+	0.764960i	0.984666	−	0.174453i	$-0.0558156\pi$
$439$	13.4488	+	16.0277i	0.641878	+	0.764960i	−0.342788	+	0.939413i	$0.611371\pi$
$440$	8.06121	−	0.922350i	0.384303	−	0.0439713i
$441$	−16.5010	+	12.9891i	−0.785761	+	0.618530i
$442$	−14.7168	−	8.49677i	−0.700009	−	0.404150i
$443$	−2.89508	−	16.4188i	−0.137549	−	0.780080i	−0.973051	−	0.230592i	$-0.925934\pi$
$443$	−2.89508	−	16.4188i	−0.137549	−	0.780080i	0.835501	−	0.549488i	$-0.185177\pi$
$444$	8.27132	+	2.26798i	0.392540	+	0.107633i
$445$	26.7754	+	1.62485i	1.26928	+	0.0770252i
$446$	−47.8289	+	17.4083i	−2.26476	+	0.824307i
$447$	−25.7123	−	7.05027i	−1.21615	−	0.333466i
$448$	−11.7333	−	25.8205i	−0.554347	−	1.21990i
$449$	−32.8568	−	18.9699i	−1.55061	−	0.895245i	−0.998092	−	0.0617431i	$-0.980334\pi$
$449$	−32.8568	−	18.9699i	−1.55061	−	0.895245i	−0.552517	−	0.833502i	$-0.686333\pi$
$450$	29.0393	−	11.9618i	1.36893	−	0.563884i
$451$	−26.2951	+	15.1815i	−1.23819	+	0.714869i
$452$	20.9515	−	17.5804i	0.985474	−	0.826911i
$453$	12.6689	+	5.99762i	0.595236	+	0.281793i
$454$	−24.8034	−	4.37351i	−1.16408	−	0.205259i
$455$	−14.2943	−	16.4639i	−0.670129	−	0.771841i
$456$	7.17543	−	3.29525i	0.336020	−	0.154314i
$457$	−6.45144	+	17.7252i	−0.301786	+	0.829149i	0.692404	+	0.721510i	$0.256551\pi$
$457$	−6.45144	+	17.7252i	−0.301786	+	0.829149i	−0.994190	+	0.107640i	$0.965671\pi$
$458$			2.67064i			0.124791i
$459$	−7.94904	−	8.23162i	−0.371029	−	0.384219i
$460$	−35.0228	−	15.2085i	−1.63295	−	0.709100i
$461$	5.36766	+	1.95367i	0.249997	+	0.0909915i	0.463979	−	0.885846i	$-0.346421\pi$
$461$	5.36766	+	1.95367i	0.249997	+	0.0909915i	−0.213982	+	0.976838i	$0.568643\pi$
$462$	−6.85462	−	42.7737i	−0.318906	−	1.99001i
$463$	18.4686	−	22.0100i	0.858308	−	1.02289i	−0.141151	−	0.989988i	$-0.545080\pi$
$463$	18.4686	−	22.0100i	0.858308	−	1.02289i	0.999459	−	0.0329035i	$-0.0104754\pi$
$464$	25.0225	+	4.41214i	1.16164	+	0.204829i
$465$	−23.1461	−	7.88239i	−1.07338	−	0.365537i
$466$	−28.1526	+	23.6229i	−1.30415	+	1.09431i
$467$	14.3300	−	8.27343i	0.663113	−	0.382848i	−0.130349	−	0.991468i	$-0.541610\pi$
$467$	14.3300	−	8.27343i	0.663113	−	0.382848i	0.793462	+	0.608620i	$0.208276\pi$
$468$	0.306831	−	26.3549i	0.0141833	−	1.21826i
$469$	15.2290	+	4.24113i	0.703208	+	0.195837i
$470$	44.3366	+	10.6219i	2.04510	+	0.489953i
$471$	−5.29210	−	5.35407i	−0.243847	−	0.246703i
$472$	−6.26314	+	2.27960i	−0.288284	+	0.104927i
$473$	−20.2282	+	7.36247i	−0.930094	+	0.338527i
$474$	−33.4726	+	8.76045i	−1.53745	+	0.402381i
$475$	22.6661	+	17.0463i	1.03999	+	0.782138i
$476$	13.3806	+	3.72637i	0.613297	+	0.170798i
$477$	−2.88989	−	8.23703i	−0.132319	−	0.377148i
$478$	9.81742	−	5.66809i	0.449038	−	0.259252i
$479$	8.40305	−	7.05099i	0.383945	−	0.322168i	−0.430304	−	0.902684i	$-0.641594\pi$
$479$	8.40305	−	7.05099i	0.383945	−	0.322168i	0.814249	+	0.580516i	$0.197149\pi$
$480$	30.6473	−	6.06488i	1.39885	−	0.276823i
$481$	7.53907	+	1.32934i	0.343752	+	0.0606128i
$482$	−38.9195	+	46.3824i	−1.77273	+	2.11266i
$483$	−11.7076	+	30.6664i	−0.532716	+	1.39537i
$484$	21.0210	+	7.65103i	0.955501	+	0.347774i
$485$	28.0638	+	12.1866i	1.27431	+	0.553365i
$486$	9.36134	−	31.2673i	0.424639	−	1.41831i
$487$			12.6066i			0.571259i	0.958340	+	0.285630i	$0.0922027\pi$
$487$			12.6066i			0.571259i	−0.958340	+	0.285630i	$0.907797\pi$
$488$	0.136307	−	0.374499i	0.00617031	−	0.0169528i
$489$	−10.8465	−	7.68930i	−0.490497	−	0.347722i
$490$	26.9774	+	18.6082i	1.21871	+	0.840634i
$491$	33.0592	+	5.82924i	1.49194	+	0.263070i	0.859339	−	0.511406i	$-0.170875\pi$
$491$	33.0592	+	5.82924i	1.49194	+	0.263070i	0.632603	+	0.774476i	$0.281986\pi$
$492$	22.8383	−	15.7942i	1.02963	−	0.712059i
$493$	−13.8948	+	11.6591i	−0.625789	+	0.525099i
$494$	37.9050	−	21.8845i	1.70543	−	0.984628i
$495$	30.2076	+	2.18636i	1.35773	+	0.0982696i
$496$	−16.8670	−	9.73817i	−0.757351	−	0.437257i
$497$	−16.9862	+	7.71883i	−0.761933	+	0.346237i
$498$	1.99543	+	7.62428i	0.0894172	+	0.341652i
$499$	−3.61055	+	1.31413i	−0.161630	+	0.0588286i	−0.421568	−	0.906797i	$-0.638520\pi$
$499$	−3.61055	+	1.31413i	−0.161630	+	0.0588286i	0.259938	+	0.965625i	$0.416298\pi$
$500$	−16.9823	−	20.5413i	−0.759473	−	0.918636i
$501$	10.7361	−	10.6118i	0.479652	−	0.474100i
$502$	−6.49682	−	36.8453i	−0.289967	−	1.64449i
$503$	−18.6458	−	10.7652i	−0.831376	−	0.479995i	0.0229475	−	0.999737i	$-0.492695\pi$
$503$	−18.6458	−	10.7652i	−0.831376	−	0.479995i	−0.854324	+	0.519741i	$0.826028\pi$
$504$	1.51850	+	6.19581i	0.0676395	+	0.275983i
$505$	4.19786	+	36.6887i	0.186802	+	1.63263i
$506$	−43.5250	−	51.8710i	−1.93492	−	2.30595i
$507$	−0.0820872	−	1.00565i	−0.00364562	−	0.0446624i
$508$	−21.5420	−	3.79843i	−0.955771	−	0.168528i
$509$	5.32142	+	4.46520i	0.235868	+	0.197917i	0.753058	−	0.657954i	$-0.228578\pi$
$509$	5.32142	+	4.46520i	0.235868	+	0.197917i	−0.517191	+	0.855870i	$0.673022\pi$
$510$	−8.60498	+	15.6484i	−0.381035	+	0.692922i
$511$	−3.33317	−	0.324592i	−0.147451	−	0.0143591i
$512$	29.8437			1.31892
$513$	28.5979	−	7.12997i	1.26263	−	0.314796i
$514$		−	16.0334i		−	0.707201i
$515$	−11.0534	−	10.4793i	−0.487070	−	0.461772i
$516$	17.8901	−	8.21586i	0.787568	−	0.361683i
$517$	33.6796	+	28.2605i	1.48123	+	1.24290i
$518$	−11.4723	+	0.890384i	−0.504062	+	0.0391212i
$519$	11.6480	−	24.6042i	0.511288	−	1.08000i
$520$	−6.34959	+	1.88413i	−0.278448	+	0.0826244i
$521$	7.63869	+	13.2306i	0.334657	+	0.579643i	0.983419	−	0.181349i	$-0.0580462\pi$
$521$	7.63869	+	13.2306i	0.334657	+	0.579643i	−0.648762	+	0.760991i	$0.724713\pi$
$522$	−48.4053	−	18.2590i	−2.11864	−	0.799176i
$523$	−11.4024	+	19.7495i	−0.498592	+	0.863587i	−0.999999	−	0.00162509i	$-0.999483\pi$
$523$	−11.4024	+	19.7495i	−0.498592	+	0.863587i	0.501407	+	0.865212i	$0.332816\pi$
$524$	−3.83835	−	21.7684i	−0.167679	−	0.950956i
$525$	−16.9850	+	15.3789i	−0.741285	+	0.671191i
$526$	−22.5692	+	8.21451i	−0.984064	+	0.358170i
$527$	13.0650	−	4.75529i	0.569123	−	0.207144i
$528$	23.2655	+	6.37934i	1.01250	+	0.277625i
$529$	4.91586	+	27.8792i	0.213733	+	1.21214i
$530$	−10.9470	+	8.10843i	−0.475507	+	0.352208i
$531$	−24.5497	+	4.03467i	−1.06537	+	0.175090i
$532$	−25.5435	+	25.0472i	−1.10745	+	1.08593i
$533$	18.9865	−	15.9315i	0.822395	−	0.690072i
$534$	−39.3211	−	18.6151i	−1.70159	−	0.805556i
$535$	1.98904	−	3.00823i	0.0859937	−	0.130057i
$536$	3.08676	−	3.67866i	0.133328	−	0.158894i
$537$	38.3247	−	17.6002i	1.65383	−	0.759507i
$538$	−24.5327	−	8.92917i	−1.05768	−	0.384964i
$539$	15.2620	+	27.6747i	0.657382	+	1.19203i
$540$	−27.6967	+	0.254646i	−1.19188	+	0.0109582i
$541$	34.3030			1.47480			0.737400	−	0.675457i	$-0.236054\pi$
$541$	34.3030			1.47480			0.737400	+	0.675457i	$0.236054\pi$
$542$	−12.2290	+	33.5989i	−0.525281	+	1.44320i
$543$	0.448032	−	4.79912i	0.0192269	−	0.205950i
$544$	−11.4188	+	13.6084i	−0.489578	+	0.583456i
$545$	−13.6546	+	20.6512i	−0.584898	+	0.884600i
$546$	11.5734	+	33.4137i	0.495297	+	1.42998i
$547$	−5.91721	−	7.05186i	−0.253002	−	0.301516i	0.624563	−	0.780975i	$-0.285277\pi$
$547$	−5.91721	−	7.05186i	−0.253002	−	0.301516i	−0.877564	+	0.479459i	$0.840833\pi$
$548$	23.2270	+	40.2304i	0.992210	+	1.71856i
$549$	0.758757	−	1.27957i	0.0323830	−	0.0546107i
$550$	−10.6763	−	46.0438i	−0.455238	−	1.96331i
$551$	−8.11240	−	46.0077i	−0.345600	−	1.95999i
$552$	7.00964	+	7.09172i	0.298350	+	0.301844i
$553$	20.8187	−	14.2751i	0.885300	−	0.607039i
$554$	−2.93965	−	8.07663i	−0.124894	−	0.343143i
$555$	1.23162	−	7.95008i	0.0522794	−	0.337462i
$556$	−14.7112	+	2.59398i	−0.623893	+	0.110009i
$557$	16.6747	−	28.8815i	0.706531	−	1.22375i	−0.259605	−	0.965715i	$-0.583592\pi$
$557$	16.6747	−	28.8815i	0.706531	−	1.22375i	0.966136	−	0.258033i	$-0.0830744\pi$
$558$	30.0795	+	25.8423i	1.27337	+	1.09399i
$559$	15.2177	−	8.78593i	0.643639	−	0.371605i
$560$	−15.6497	+	9.39036i	−0.661320	+	0.396815i
$561$	−14.1643	+	9.79556i	−0.598016	+	0.413569i
$562$	−58.3748	−	10.2931i	−2.46239	−	0.434186i
$563$	16.6369	−	19.8271i	0.701163	−	0.835614i	−0.291494	−	0.956573i	$-0.594152\pi$
$563$	16.6369	−	19.8271i	0.701163	−	0.835614i	0.992658	+	0.120959i	$0.0385969\pi$
$564$	−32.8014	−	23.2535i	−1.38119	−	0.979148i
$565$	−18.6176	−	17.6506i	−0.783249	−	0.742567i
$566$	−4.51933			−0.189962
$567$	1.28933	+	23.7768i	0.0541467	+	0.998533i
$568$			5.66766i			0.237810i
$569$	−15.3291	+	42.1163i	−0.642628	+	1.76561i	0.000682401		1.00000i	$0.499783\pi$
$569$	−15.3291	+	42.1163i	−0.642628	+	1.76561i	−0.643310	+	0.765606i	$0.722439\pi$
$570$	−23.8230	−	39.3460i	−0.997834	−	1.64802i
$571$	−2.04055	−	1.71223i	−0.0853944	−	0.0716544i	0.599091	−	0.800681i	$-0.295529\pi$
$571$	−2.04055	−	1.71223i	−0.0853944	−	0.0716544i	−0.684486	+	0.729026i	$0.739973\pi$
$572$	−39.0631	−	6.88788i	−1.63331	−	0.287997i
$573$	1.65798	+	2.39742i	0.0692629	+	0.100154i
$574$	−21.6665	+	30.3059i	−0.904344	+	1.26494i
$575$	−10.4387	+	34.2603i	−0.435325	+	1.42875i
$576$	−31.6030	−	5.95262i	−1.31679	−	0.248026i
$577$	14.5617	−	25.2217i	0.606213	−	1.04999i	−0.385646	−	0.922647i	$-0.626021\pi$
$577$	14.5617	−	25.2217i	0.606213	−	1.04999i	0.991859	−	0.127345i	$-0.0406454\pi$
$578$	4.41752	+	25.0530i	0.183745	+	1.04207i
$579$	−4.85314	−	18.5432i	−0.201690	−	0.770631i
$580$	−2.65935	+	43.8226i	−0.110423	+	1.81963i
$581$	−3.25153	−	4.74201i	−0.134896	−	0.196732i
$582$	−34.8823	−	35.2908i	−1.44592	−	1.46285i
$583$	−12.9376	+	2.28124i	−0.535820	+	0.0944794i
$584$	−0.508654	+	0.881015i	−0.0210483	+	0.0364567i
$585$	−24.5935	+	2.52427i	−1.01682	+	0.104366i
$586$	37.4898	−	21.6447i	1.54869	−	0.894136i
$587$	−9.87308	−	11.7663i	−0.407506	−	0.485647i	0.522787	−	0.852463i	$-0.324892\pi$
$587$	−9.87308	−	11.7663i	−0.407506	−	0.485647i	−0.930293	+	0.366817i	$0.880448\pi$
$588$	−15.9703	−	24.0897i	−0.658603	−	0.993444i
$589$	−6.21838	+	35.2662i	−0.256224	+	1.45312i
$590$	17.3407	+	34.7386i	0.713906	+	1.43017i
$591$	−14.4052	−	1.34483i	−0.592551	−	0.0553189i
$592$	2.19167	−	6.02157i	0.0900771	−	0.247485i
$593$		−	34.6784i		−	1.42407i	−0.702143	−	0.712036i	$-0.747773\pi$
$593$		−	34.6784i		−	1.42407i	0.702143	−	0.712036i	$-0.252227\pi$
$594$	−44.1482	−	21.5330i	−1.81142	−	0.883511i
$595$	2.04594	−	12.8670i	0.0838752	−	0.527496i
$596$	12.5503	−	34.4816i	0.514080	−	1.41242i
$597$	−13.1355	+	6.03233i	−0.537599	+	0.246887i
$598$	42.3419	+	35.5291i	1.73149	+	1.45289i
$599$	−14.1986	−	2.50360i	−0.580140	−	0.102294i	−0.124125	−	0.992267i	$-0.539613\pi$
$599$	−14.1986	−	2.50360i	−0.580140	−	0.102294i	−0.456015	+	0.889972i	$0.650724\pi$
$600$	2.11859	+	6.62999i	0.0864910	+	0.270668i
$601$	21.0441	+	25.0794i	0.858407	+	1.02301i	0.999455	+	0.0330066i	$0.0105082\pi$
$601$	21.0441	+	25.0794i	0.858407	+	1.02301i	−0.141048	+	0.990003i	$0.545047\pi$
$602$	−18.8585	+	18.4921i	−0.768616	+	0.753682i
$603$	13.8647	−	11.3614i	0.564613	−	0.462673i
$604$	−9.64583	+	16.7071i	−0.392483	+	0.679801i
$605$	4.88873	−	20.4058i	0.198755	−	0.829615i
$606$	15.8374	−	57.7589i	0.643349	−	2.34630i
$607$	1.55390	−	0.565575i	0.0630710	−	0.0229560i	−0.310292	−	0.950641i	$-0.600427\pi$
$607$	1.55390	−	0.565575i	0.0630710	−	0.0229560i	0.373363	+	0.927685i	$0.378205\pi$
$608$	−15.6490	−	42.9953i	−0.634652	−	1.74369i
$609$	37.7388	+	0.589932i	1.52925	+	0.0239052i
$610$	−2.25769	−	0.540886i	−0.0914113	−	0.0218998i
$611$	−31.0806	−	17.9444i	−1.25739	−	0.725952i
$612$	12.1818	−	9.98244i	0.492422	−	0.403516i
$613$	0.0468704	−	0.0270606i	0.00189308	−	0.00109297i	−0.499053	−	0.866571i	$-0.666319\pi$
$613$	0.0468704	−	0.0270606i	0.00189308	−	0.00109297i	0.500946	+	0.865478i	$0.332985\pi$
$614$	−9.29238	+	7.79724i	−0.375010	+	0.314671i
$615$	−17.1543	−	19.5995i	−0.691727	−	0.790326i
$616$	9.57160	−	0.742870i	0.385651	−	0.0299311i
$617$	14.6348	+	12.2801i	0.589175	+	0.494377i	0.887946	−	0.459948i	$-0.152132\pi$
$617$	14.6348	+	12.2801i	0.589175	+	0.494377i	−0.298770	+	0.954325i	$0.596576\pi$
$618$	10.3092	+	22.4484i	0.414698	+	0.903009i
$619$	−12.2042	+	33.5306i	−0.490526	+	1.34771i	0.409673	+	0.912232i	$0.365643\pi$
$619$	−12.2042	+	33.5306i	−0.490526	+	1.34771i	−0.900200	+	0.435478i	$0.856579\pi$
$620$	13.4044	−	30.8683i	0.538334	−	1.23970i
$621$	20.8130	+	30.8572i	0.835199	+	1.23826i
$622$	27.7274			1.11177
$623$	31.5899	+	3.07630i	1.26562	+	0.123249i
$624$	−19.6072	−	1.83047i	−0.784914	−	0.0732774i
$625$	−17.3322	+	18.0166i	−0.693286	+	0.720663i
$626$	9.88991	−	56.0885i	0.395280	−	2.24175i
$627$	−3.60861	−	44.2090i	−0.144114	−	1.76554i
$628$	7.93704	−	6.65997i	0.316723	−	0.265762i
$629$	2.28724	+	3.96161i	0.0911982	+	0.157960i
$630$	34.8530	−	12.8913i	1.38858	−	0.513601i
$631$	−4.85472	+	8.40861i	−0.193263	+	0.334742i	−0.946330	−	0.323203i	$-0.895240\pi$
$631$	−4.85472	+	8.40861i	−0.193263	+	0.334742i	0.753067	+	0.657944i	$0.228574\pi$
$632$	−1.33153	−	7.55150i	−0.0529656	−	0.300383i
$633$	−9.19008	−	9.29769i	−0.365273	−	0.369550i
$634$	49.4217	−	17.9880i	1.96279	−	0.714395i
$635$	−1.24285	+	20.4805i	−0.0493209	+	0.812745i
$636$	11.6228	−	3.04192i	0.460873	−	0.120620i
$637$	−16.1918	−	20.0841i	−0.641544	−	0.795759i
$638$	−38.9291	+	67.4272i	−1.54122	+	2.66947i
$639$	−3.91597	+	20.7903i	−0.154913	+	0.822450i
$640$	1.60423	+	14.0208i	0.0634129	+	0.554220i
$641$	−29.7726	−	35.4815i	−1.17595	−	1.40144i	−0.897517	−	0.440980i	$-0.854631\pi$
$641$	−29.7726	−	35.4815i	−1.17595	−	1.40144i	−0.278428	−	0.960457i	$-0.589813\pi$
$642$	−4.81055	+	3.32682i	−0.189857	+	0.131299i
$643$	−3.12370	+	17.7154i	−0.123187	+	0.698626i	0.859182	+	0.511670i	$0.170973\pi$
$643$	−3.12370	+	17.7154i	−0.123187	+	0.698626i	−0.982368	+	0.186955i	$0.940138\pi$
$644$	−40.7559	−	19.4938i	−1.60601	−	0.768162i
$645$	−9.56417	−	15.7962i	−0.376589	−	0.621974i
$646$	24.5769	+	8.94525i	0.966964	+	0.351946i
$647$		−	2.57630i		−	0.101285i	−0.998717	−	0.0506424i	$-0.983873\pi$
$647$		−	2.57630i		−	0.101285i	0.998717	−	0.0506424i	$-0.0161269\pi$
$648$	6.73765	+	2.63151i	0.264680	+	0.103376i
$649$			37.4418i			1.46972i
$650$	15.1092	+	35.5009i	0.592630	+	1.39246i
$651$	−27.0286	−	10.3188i	−1.05934	−	0.404427i
$652$	11.7624	−	14.0178i	0.460649	−	0.548981i
$653$	6.21509	−	35.2475i	0.243215	−	1.37934i	−0.581386	−	0.813628i	$-0.697489\pi$
$653$	6.21509	−	35.2475i	0.243215	−	1.37934i	0.824601	−	0.565714i	$-0.191399\pi$
$654$	33.0240	−	22.8383i	1.29134	−	0.893049i
$655$	−19.8772	+	5.89820i	−0.776667	+	0.230462i
$656$	−10.3733	−	17.9671i	−0.405010	−	0.701497i
$657$	−2.47458	+	2.88032i	−0.0965426	+	0.112372i
$658$	51.9667	+	14.4723i	2.02587	+	0.564188i
$659$	18.6704	−	3.29210i	0.727297	−	0.128242i	0.202273	−	0.979329i	$-0.435167\pi$
$659$	18.6704	−	3.29210i	0.727297	−	0.128242i	0.525024	+	0.851087i	$0.324056\pi$
$660$	−6.38154	+	41.1927i	−0.248401	+	1.60342i
$661$	1.71768	+	4.71928i	0.0668099	+	0.183559i	0.968605	−	0.248606i	$-0.0799723\pi$
$661$	1.71768	+	4.71928i	0.0668099	+	0.183559i	−0.901795	+	0.432164i	$0.857750\pi$
$662$	−21.5273	+	7.83529i	−0.836682	+	0.304527i
$663$	9.99804	−	9.88232i	0.388292	−	0.383797i
$664$	−1.72006	+	0.303292i	−0.0667511	+	0.0117700i
$665$	26.0658	+	21.1338i	1.01079	+	0.819535i
$666$	−6.65482	+	11.2227i	−0.257869	+	0.434871i
$667$	51.0929	−	29.4985i	1.97832	−	1.14219i
$668$	13.3547	+	15.9155i	0.516708	+	0.615789i
$669$	−3.42550	−	41.9658i	−0.132438	−	1.62249i
$670$	−23.3345	−	15.4288i	−0.901489	−	0.596065i
$671$	−1.71502	−	1.43907i	−0.0662076	−	0.0555548i
$672$	36.4999	−	5.84923i	1.40801	−	0.225639i
$673$	−10.9530	+	30.0930i	−0.422205	+	1.16000i	0.528237	+	0.849097i	$0.322853\pi$
$673$	−10.9530	+	30.0930i	−0.422205	+	1.16000i	−0.950442	+	0.310902i	$0.899369\pi$
$674$		−	20.6991i		−	0.797298i
$675$	3.19059	+	25.7841i	0.122806	+	0.992431i
$676$	1.38870			0.0534114
$677$	1.82703	−	5.01973i	0.0702185	−	0.192924i	−0.899619	−	0.436675i	$-0.856156\pi$
$677$	1.82703	−	5.01973i	0.0702185	−	0.192924i	0.969838	+	0.243751i	$0.0783781\pi$
$678$	17.3642	+	37.8107i	0.666868	+	1.45211i
$679$	32.6578	+	15.6204i	1.25329	+	0.599456i
$680$	−3.30133	−	2.18284i	−0.126600	−	0.0837081i
$681$	8.91500	−	18.8313i	0.341623	−	0.721617i
$682$	45.7179	−	38.3619i	1.75063	−	1.46895i
$683$	25.1727	+	43.6004i	0.963207	+	1.66832i	0.714358	+	0.699781i	$0.246719\pi$
$683$	25.1727	+	43.6004i	0.963207	+	1.66832i	0.248849	+	0.968542i	$0.419948\pi$
$684$	6.57845	+	40.0277i	0.251533	+	1.53050i
$685$	35.0150	−	25.9356i	1.33786	−	0.990948i
$686$	31.0961	+	23.1667i	1.18725	+	0.884507i
$687$	−2.13062	−	0.584211i	−0.0812882	−	0.0222890i
$688$	−5.03068	−	13.8217i	−0.191793	−	0.526946i
$689$	10.0770	−	3.66774i	0.383905	−	0.139730i
$690$	36.4018	−	45.2647i	1.38579	−	1.72320i
$691$	−36.5482	+	6.44444i	−1.39036	+	0.245158i	−0.818176	−	0.574968i	$-0.805015\pi$
$691$	−36.5482	+	6.44444i	−1.39036	+	0.245158i	−0.572183	+	0.820126i	$0.693903\pi$
$692$	32.4467	+	18.7331i	1.23344	+	0.712126i
$693$	35.6241	+	3.88831i	1.35325	+	0.147705i
$694$	26.7562	+	46.3432i	1.01565	+	1.75916i
$695$	3.98603	+	13.4331i	0.151199	+	0.509547i
$696$	4.90587	−	10.3627i	0.185956	−	0.392799i
$697$	14.5853	+	2.57179i	0.552459	+	0.0974135i
$698$	25.6459	−	30.5636i	0.970712	−	1.15685i
$699$	−12.6877	−	27.6276i	−0.479893	−	1.04497i
$700$	−19.1943	−	25.0212i	−0.725476	−	0.945714i
$701$			4.36553i			0.164884i	0.996596	+	0.0824419i	$0.0262719\pi$
$701$			4.36553i			0.164884i	−0.996596	+	0.0824419i	$0.973728\pi$
$702$	38.5426	+	11.0523i	1.45470	+	0.417142i
$703$	−11.7821			−0.444371
$704$	−16.5529	+	45.4788i	−0.623862	+	1.71405i
$705$	−18.1729	+	33.0479i	−0.684431	+	1.24466i
$706$	−22.8456	+	27.2263i	−0.859806	+	1.02468i
$707$	3.38100	+	43.5629i	0.127156	+	1.63835i
$708$	−2.78573	−	34.1280i	−0.104694	−	1.28261i
$709$	2.58861	−	2.17210i	0.0972174	−	0.0815751i	−0.592884	−	0.805288i	$-0.702011\pi$
$709$	2.58861	−	2.17210i	0.0972174	−	0.0815751i	0.690101	+	0.723713i	$0.257566\pi$
$710$	32.8018	−	3.75313i	1.23103	−	0.140852i
$711$	0.333209	−	28.6206i	0.0124963	−	1.07336i
$712$	4.82074	−	8.34977i	0.180665	−	0.312921i
$713$	−44.5358	+	7.85286i	−1.66788	+	0.294092i
$714$	−10.8498	+	18.1319i	−0.406044	+	0.678569i
$715$	−2.25371	+	37.1383i	−0.0842841	+	1.38889i
$716$	19.8520	+	54.5429i	0.741904	+	2.03836i
$717$	2.37438	+	9.07220i	0.0886727	+	0.338808i
$718$	−66.9626	+	11.8073i	−2.49902	+	0.440645i
$719$	15.1075	−	26.1669i	0.563413	−	0.975860i	−0.433782	−	0.901018i	$-0.642821\pi$
$719$	15.1075	−	26.1669i	0.563413	−	0.975860i	0.997195	−	0.0748424i	$-0.0238454\pi$
$720$	−1.49391	+	20.6405i	−0.0556747	+	0.769225i
$721$	−12.6178	−	12.8678i	−0.469911	−	0.479222i
$722$	−21.1287	+	17.7291i	−0.786330	+	0.659809i
$723$	−28.4899	−	41.1961i	−1.05955	−	1.53210i
$724$	6.53305	+	1.15195i	0.242799	+	0.0428120i
$725$	41.1229	−	2.19446i	1.52727	−	0.0815003i
$726$	−19.6814	+	27.7626i	−0.730446	+	1.03037i
$727$	9.33068	+	3.39609i	0.346056	+	0.125954i	0.509200	−	0.860648i	$-0.329941\pi$
$727$	9.33068	+	3.39609i	0.346056	+	0.125954i	−0.163144	+	0.986602i	$0.552164\pi$
$728$	−7.58922	+	1.95394i	−0.281275	+	0.0724178i
$729$	22.8970	+	14.3082i	0.848038	+	0.529935i
$730$	5.43574	+	2.36045i	0.201186	+	0.0873641i
$731$	9.86684	+	3.59124i	0.364938	+	0.132827i
$732$	1.67030	+	1.18410i	0.0617360	+	0.0437658i
$733$	15.4420	+	12.9574i	0.570363	+	0.478592i	0.881766	−	0.471686i	$-0.156354\pi$
$733$	15.4420	+	12.9574i	0.570363	+	0.478592i	−0.311403	+	0.950278i	$0.600799\pi$
$734$	4.60113	−	26.0943i	0.169831	−	0.963158i
$735$	−20.7469	+	17.4518i	−0.765262	+	0.643719i
$736$	44.2629	−	37.1410i	1.63155	−	1.36904i
$737$	−13.4883	−	23.3624i	−0.496847	−	0.860564i
$738$	13.9847	+	39.8604i	0.514783	+	1.46728i
$739$	−3.19346	+	5.53123i	−0.117473	+	0.203470i	−0.918766	−	0.394803i	$-0.870813\pi$
$739$	−3.19346	+	5.53123i	−0.117473	+	0.203470i	0.801292	+	0.598273i	$0.204146\pi$
$740$	10.7677	+	2.57966i	0.395828	+	0.0948303i
$741$	9.16745	+	35.0277i	0.336775	+	1.28677i
$742$	−13.2938	+	9.11542i	−0.488032	+	0.334637i
$743$	17.5737	−	6.39631i	0.644717	−	0.234658i	0.00109279	−	0.999999i	$-0.499652\pi$
$743$	17.5737	−	6.39631i	0.644717	−	0.234658i	0.643624	+	0.765342i	$0.277430\pi$
$744$	−6.25048	+	6.17813i	−0.229154	+	0.226501i
$745$	−33.4725	−	8.01918i	−1.22634	−	0.293800i
$746$	19.3565	+	11.1755i	0.708692	+	0.409164i
$747$	−6.51911	−	0.0758973i	−0.238522	−	0.00277694i
$748$	−11.8511	−	20.5268i	−0.433320	−	0.750533i
$749$	2.48167	−	3.47121i	0.0906782	−	0.126835i
$750$	36.9684	−	16.6518i	1.34990	−	0.608038i
$751$	−7.00662	+	39.7365i	−0.255675	+	1.45001i	0.538659	+	0.842524i	$0.318931\pi$
$751$	−7.00662	+	39.7365i	−0.255675	+	1.45001i	−0.794334	+	0.607482i	$0.792180\pi$
$752$	−19.3101	+	23.0128i	−0.704165	+	0.839191i
$753$	30.8162	+	2.87691i	1.12300	+	0.104841i
$754$	21.7371	−	59.7222i	0.791619	−	2.17496i
$755$	16.5983	+	7.20773i	0.604072	+	0.262316i
$756$	−32.7604	−	0.893677i	−1.19148	−	0.0325027i
$757$			27.5160i			1.00009i	0.866000	+	0.500044i	$0.166683\pi$
$757$			27.5160i			1.00009i	−0.866000	+	0.500044i	$0.833317\pi$
$758$	35.5418	+	12.9362i	1.29094	+	0.469862i
$759$	50.9037	−	23.3770i	1.84769	−	0.848532i
$760$	9.12042	−	4.55270i	0.330832	−	0.165144i
$761$	−6.08100	+	34.4870i	−0.220436	+	1.25015i	0.650785	+	0.759262i	$0.274440\pi$
$761$	−6.08100	+	34.4870i	−0.220436	+	1.25015i	−0.871221	+	0.490892i	$0.836671\pi$
$762$	14.2387	−	30.0768i	0.515815	−	1.08957i
$763$	−17.0364	+	23.8296i	−0.616760	+	0.862688i
$764$	−3.47432	+	2.00590i	−0.125696	+	0.0725708i
$765$	−10.6018	−	10.2881i	−0.383310	−	0.371969i
$766$	−2.90264	−	1.67584i	−0.104877	−	0.0605506i
$767$	−5.30729	−	30.0991i	−0.191635	−	1.08682i
$768$	−3.76722	+	13.7390i	−0.135938	+	0.495765i
$769$	−15.8244	−	43.4773i	−0.570644	−	1.56783i	−0.803490	−	0.595318i	$-0.797026\pi$
$769$	−15.8244	−	43.4773i	−0.570644	−	1.56783i	0.232847	−	0.972513i	$-0.425196\pi$
$770$	−10.6377	−	54.9041i	−0.383356	−	1.97861i
$771$	12.7913	+	3.50735i	0.460669	+	0.126314i
$772$	25.9802	−	4.58102i	0.935049	−	0.164874i
$773$	15.4782	+	8.93634i	0.556712	+	0.321418i	0.751825	−	0.659363i	$-0.229174\pi$
$773$	15.4782	+	8.93634i	0.556712	+	0.321418i	−0.195113	+	0.980781i	$0.562507\pi$
$774$	4.85682	+	29.5521i	0.174575	+	1.06223i
$775$	−30.1962	−	9.20045i	−1.08468	−	0.330490i
$776$	8.42408	−	7.06864i	0.302407	−	0.253749i
$777$	1.79925	−	9.34728i	0.0645479	−	0.335332i
$778$	−9.06024	−	1.59756i	−0.324825	−	0.0572755i
$779$	−24.5197	+	29.2214i	−0.878508	+	1.04696i
$780$	−0.708908	−	34.0190i	−0.0253830	−	1.21808i
$781$	29.9185	+	10.8894i	1.07057	+	0.389655i
$782$			33.0287i			1.18110i
$783$	25.1558	−	34.6233i	0.898994	−	1.23734i
$784$	−18.9097	+	10.4283i	−0.675347	+	0.372441i
$785$	−7.05291	−	6.68658i	−0.251729	−	0.238654i
$786$	33.4811	+	3.12570i	1.19423	+	0.111490i
$787$	−5.71659	−	4.79679i	−0.203774	−	0.170987i	0.535190	−	0.844732i	$-0.320240\pi$
$787$	−5.71659	−	4.79679i	−0.203774	−	0.170987i	−0.738964	+	0.673745i	$0.764685\pi$
$788$	3.45775	−	19.6099i	0.123177	−	0.698572i
$789$	−1.61640	−	19.8025i	−0.0575455	−	0.704989i
$790$	−42.8229	+	12.7069i	−1.52357	+	0.452092i
$791$	−21.2526	−	21.6737i	−0.755656	−	0.770629i
$792$	5.55228	−	9.36338i	0.197292	−	0.332713i
$793$	1.58267	+	0.913757i	0.0562024	+	0.0324485i
$794$	7.35071	+	41.6879i	0.260867	+	1.47945i
$795$	−4.07417	−	10.5072i	−0.144496	−	0.372652i
$796$	−6.80410	−	18.6941i	−0.241165	−	0.662595i
$797$	4.32804	+	11.8912i	0.153307	+	0.421207i	0.992442	−	0.122716i	$-0.0391604\pi$
$797$	4.32804	+	11.8912i	0.153307	+	0.421207i	−0.839135	+	0.543923i	$0.816938\pi$
$798$	−26.4717	−	47.5515i	−0.937086	−	1.68331i
$799$	−3.72395	−	21.1196i	−0.131744	−	0.747157i
$800$	39.2904	−	9.11035i	1.38913	−	0.322100i
$801$	23.4527	−	27.2980i	0.828660	−	0.964529i
$802$	−43.2245	+	24.9557i	−1.52631	+	0.881216i
$803$	3.67342	+	4.37781i	0.129632	+	0.154490i
$804$	14.0327	+	20.2911i	0.494894	+	0.715612i
$805$	−13.8210	+	40.0600i	−0.487125	+	1.41193i
$806$	−31.3145	+	37.3192i	−1.10301	+	1.31451i
$807$	12.4903	−	17.6188i	0.439678	−	0.620210i
$808$	12.4725	+	4.53961i	0.438780	+	0.159703i
$809$			18.8468i			0.662618i	0.943522	+	0.331309i	$0.107490\pi$
$809$			18.8468i			0.662618i	−0.943522	+	0.331309i	$0.892510\pi$
$810$	10.7683	−	40.7370i	0.378360	−	1.43135i
$811$		−	31.0285i		−	1.08956i	−0.838579	−	0.544779i	$-0.816613\pi$
$811$		−	31.0285i		−	1.08956i	0.838579	−	0.544779i	$-0.183387\pi$
$812$	−5.03491	+	51.7024i	−0.176691	+	1.81440i
$813$	−24.1299	−	17.1061i	−0.846273	−	0.599938i
$814$	15.0419	+	12.6217i	0.527219	+	0.442389i
$815$	−14.3178	−	9.46692i	−0.501530	−	0.331612i
$816$	−6.69318	−	9.67826i	−0.234308	−	0.338807i
$817$	−20.7171	+	17.3837i	−0.724798	+	0.608178i
$818$	34.4458	−	19.8873i	1.20437	−	0.695343i
$819$	−29.1890	+	1.92385i	−1.01995	+	0.0672248i
$820$	28.8065	−	21.3369i	1.00597	−	0.745117i
$821$	4.74489	−	0.836651i	0.165598	−	0.0291993i	−0.0902345	−	0.995921i	$-0.528762\pi$
$821$	4.74489	−	0.836651i	0.165598	−	0.0291993i	0.255832	+	0.966721i	$0.417651\pi$
$822$	−68.3669	+	17.8930i	−2.38457	+	0.624090i
$823$	−6.86958	−	18.8740i	−0.239458	−	0.657906i	−0.999963	−	0.00857426i	$-0.997271\pi$
$823$	−6.86958	−	18.8740i	−0.239458	−	0.657906i	0.760505	−	0.649332i	$-0.224952\pi$
$824$	−5.14437	+	1.87240i	−0.179213	+	0.0652281i
$825$	39.0690	+	1.55477i	1.36021	+	0.0541300i
$826$	19.0056	+	41.8240i	0.661290	+	1.45524i
$827$	−20.4523	+	35.4245i	−0.711197	+	1.23183i	0.253211	+	0.967411i	$0.418513\pi$
$827$	−20.4523	+	35.4245i	−0.711197	+	1.23183i	−0.964408	+	0.264418i	$0.914820\pi$
$828$	−44.6591	+	25.0953i	−1.55201	+	0.872122i
$829$	4.07579	−	2.35316i	0.141558	−	0.0817285i	−0.427548	−	0.903992i	$-0.640623\pi$
$829$	4.07579	−	2.35316i	0.141558	−	0.0817285i	0.569106	+	0.822264i	$0.307289\pi$
$830$	2.89434	+	9.75406i	0.100464	+	0.338568i
$831$	7.08655	−	0.578448i	0.245830	−	0.0200661i
$832$	6.86023	−	38.9063i	0.237836	−	1.34883i
$833$	2.97423	−	15.1261i	0.103051	−	0.524087i
$834$	2.11236	−	22.6267i	0.0731451	−	0.783497i
$835$	13.4080	−	14.1426i	0.464004	−	0.489425i
$836$	61.0480			2.11139
$837$	−27.1969	+	18.3441i	−0.940061	+	0.634066i
$838$	9.04914			0.312597
$839$	−3.64095	−	1.32520i	−0.125700	−	0.0457509i	0.278405	−	0.960464i	$-0.410194\pi$
$839$	−3.64095	−	1.32520i	−0.125700	−	0.0457509i	−0.404104	+	0.914713i	$0.632417\pi$
$840$	2.21908	+	7.93088i	0.0765655	+	0.273642i
$841$	−29.7505	−	24.9636i	−1.02588	−	0.860815i
$842$	−11.0391	+	62.6058i	−0.380432	+	2.15754i
$843$	20.9814	−	44.3195i	0.722639	−	1.52644i
$844$	13.7832	−	11.5655i	0.474437	−	0.398100i
$845$	−0.148076	−	1.29416i	−0.00509396	−	0.0445205i
$846$	47.3112	−	38.7693i	1.62659	−	1.33292i
$847$	6.66084	−	23.9176i	0.228869	−	0.821818i
$848$	−1.55874	−	8.84007i	−0.0535275	−	0.303569i
$849$	0.988619	−	3.60550i	0.0339293	−	0.123740i
$850$	−10.4471	+	20.5520i	−0.358334	+	0.704929i
$851$	−5.08892	−	13.9817i	−0.174446	−	0.479286i
$852$	−28.0807	−	7.69967i	−0.962029	−	0.263786i
$853$	1.91732	+	10.8736i	0.0656477	+	0.372307i	0.999878	+	0.0156356i	$0.00497717\pi$
$853$	1.91732	+	10.8736i	0.0656477	+	0.372307i	−0.934230	+	0.356671i	$0.883912\pi$
$854$	−2.64623	−	0.736952i	−0.0905521	−	0.0252180i
$855$	36.6014	−	10.3987i	1.25174	−	0.355630i
$856$	−0.648107	−	1.12255i	−0.0221518	−	0.0383681i
$857$	−18.2665	−	21.7692i	−0.623973	−	0.743622i	0.357775	−	0.933808i	$-0.383535\pi$
$857$	−18.2665	−	21.7692i	−0.623973	−	0.743622i	−0.981748	+	0.190186i	$0.939091\pi$
$858$	25.8198	−	54.5396i	0.881473	−	1.86195i
$859$	27.4050	+	4.83224i	0.935047	+	0.164874i	0.620356	−	0.784320i	$-0.286988\pi$
$859$	27.4050	+	4.83224i	0.935047	+	0.164874i	0.314691	+	0.949194i	$0.398099\pi$
$860$	22.7394	−	11.3510i	0.775408	−	0.387066i
$861$	−19.4382	−	23.9150i	−0.662453	−	0.815020i
$862$	6.23739	−	17.1371i	0.212446	−	0.583691i
$863$	−22.1229			−0.753074			−0.376537	−	0.926402i	$-0.622885\pi$
$863$	−22.1229			−0.753074			−0.376537	+	0.926402i	$0.622885\pi$
$864$	18.3747	−	37.6728i	0.625120	−	1.28166i
$865$	13.9981	−	32.2354i	0.475949	−	1.09604i
$866$	−8.25711	−	3.00534i	−0.280588	−	0.102126i
$867$	−20.9535	−	1.95616i	−0.711619	−	0.0664347i
$868$	17.1814	−	35.9213i	0.583174	−	1.21925i
$869$	−42.4213	−	7.48001i	−1.43904	−	0.253742i
$870$	−63.2235	−	21.5307i	−2.14348	−	0.729958i
$871$	14.1547	+	16.8689i	0.479612	+	0.571580i
$872$	4.44920	+	7.70623i	0.150669	+	0.260966i
$873$	35.7854	−	20.1089i	1.21115	−	0.680584i
$874$	−73.6722	−	42.5347i	−2.49200	−	1.43876i
$875$	−21.2712	+	20.5556i	−0.719099	+	0.694907i
$876$	−3.67401	−	3.71704i	−0.124133	−	0.125587i
$877$	−5.67982	−	15.6052i	−0.191794	−	0.526949i	0.806103	−	0.591776i	$-0.201573\pi$
$877$	−5.67982	−	15.6052i	−0.191794	−	0.526949i	−0.997897	+	0.0648263i	$0.979351\pi$
$878$	−14.9829	−	41.1653i	−0.505649	−	1.38926i
$879$	9.06704	+	34.6440i	0.305824	+	1.16851i
$880$	30.2872	+	7.25604i	1.02098	+	0.244601i
$881$	−7.35278	+	12.7354i	−0.247721	+	0.429066i	−0.962893	−	0.269883i	$-0.913015\pi$
$881$	−7.35278	+	12.7354i	−0.247721	+	0.429066i	0.715172	+	0.698949i	$0.246348\pi$
$882$	41.7673	−	13.7395i	1.40638	−	0.462634i
$883$	18.8685	−	10.8938i	0.634977	−	0.366604i	−0.147700	−	0.989032i	$-0.547187\pi$
$883$	18.8685	−	10.8938i	0.634977	−	0.366604i	0.782677	+	0.622428i	$0.213854\pi$
$884$	12.4366	+	14.8214i	0.418290	+	0.498498i
$885$	−31.5076	+	6.23513i	−1.05912	+	0.209592i
$886$	−6.06161	+	34.3771i	−0.203644	+	1.15492i
$887$	−2.87146	+	3.42207i	−0.0964142	+	0.114902i	−0.812094	−	0.583526i	$-0.801672\pi$
$887$	−2.87146	+	3.42207i	−0.0964142	+	0.114902i	0.715680	+	0.698428i	$0.246117\pi$
$888$	−2.35893	−	1.67229i	−0.0791604	−	0.0561183i
$889$	−2.35307	+	24.1632i	−0.0789193	+	0.810406i
$890$	−51.5169	−	22.3710i	−1.72685	−	0.749878i
$891$	26.8365	−	30.5108i	0.899057	−	1.02215i
$892$	57.9504			1.94032
$893$	51.9040	+	18.8915i	1.73690	+	0.632181i
$894$	45.5402	+	32.2842i	1.52309	+	1.07975i
$895$	48.7131	−	24.3164i	1.62830	−	0.812809i
$896$	1.29207	+	16.6478i	0.0431649	+	0.556163i
$897$	−37.6074	+	26.0080i	−1.25567	+	0.868383i
$898$	51.0611	+	60.8523i	1.70393	+	2.03067i
$899$	25.9993	+	45.0321i	0.867125	+	1.50190i
$900$	−35.7268	+	1.48964i	−1.19089	+	0.0496546i
$901$	5.54949	+	3.20400i	0.184880	+	0.106741i
$902$	62.6072	−	11.0393i	2.08459	−	0.367570i
$903$	−10.6275	−	19.0905i	−0.353662	−	0.635290i
$904$	−8.66485	+	3.15375i	−0.288189	+	0.104892i
$905$	0.376919	−	6.21115i	0.0125292	−	0.206466i
$906$	−20.6310	−	20.8726i	−0.685420	−	0.693446i
$907$	35.9614	−	6.34096i	1.19408	−	0.210548i	0.458941	−	0.888467i	$-0.348229\pi$
$907$	35.9614	−	6.34096i	1.19408	−	0.210548i	0.735137	+	0.677919i	$0.237118\pi$
$908$	24.8338	+	14.3378i	0.824137	+	0.475816i
$909$	42.6153	+	25.2699i	1.41346	+	0.838151i
$910$	16.3341	+	42.6290i	0.541470	+	1.41314i
$911$	−15.7057	−	18.7173i	−0.520353	−	0.620133i	0.440311	−	0.897845i	$-0.354868\pi$
$911$	−15.7057	−	18.7173i	−0.520353	−	0.620133i	−0.960664	+	0.277712i	$0.910424\pi$
$912$	30.2074	−	2.46571i	1.00027	−	0.0816480i
$913$	−1.70377	+	9.66257i	−0.0563866	+	0.319785i
$914$	25.3864	−	30.2543i	0.839707	−	1.00072i
$915$	0.925394	−	1.68285i	0.0305926	−	0.0556334i
$916$	1.03996	−	2.85728i	0.0343614	−	0.0944071i
$917$	−23.7578	+	6.11675i	−0.784553	+	0.201993i
$918$	9.74495	+	21.8881i	0.321631	+	0.722414i
$919$	7.21074			0.237860			0.118930	−	0.992903i	$-0.462054\pi$
$919$	7.21074			0.237860			0.118930	+	0.992903i	$0.462054\pi$
$920$	9.34192	+	8.85669i	0.307994	+	0.291997i
$921$	−4.18785	−	9.11909i	−0.137994	−	0.300484i
$922$	−9.16182	−	7.68768i	−0.301728	−	0.253180i
$923$	−25.5948	−	4.51305i	−0.842462	−	0.148549i
$924$	−9.32268	+	48.4322i	−0.306694	+	1.59330i
$925$	1.25590	−	10.3097i	0.0412939	−	0.338982i
$926$	−52.0985	+	30.0791i	−1.71206	+	0.988459i
$927$	−20.1644	+	3.31397i	−0.662287	+	0.108845i
$928$	−57.5375	−	33.2193i	−1.88876	−	1.09048i
$929$	8.22788	+	46.6626i	0.269948	+	1.53095i	0.754565	+	0.656225i	$0.227848\pi$
$929$	8.22788	+	46.6626i	0.269948	+	1.53095i	−0.484617	+	0.874726i	$0.661041\pi$
$930$	39.8953	+	32.0837i	1.30822	+	1.05207i
$931$	29.9092	+	26.1137i	0.980236	+	0.855841i
$932$	39.3190	−	14.3110i	1.28794	−	0.468771i
$933$	−6.06546	+	22.1207i	−0.198574	+	0.724200i
$934$	−34.1189	+	6.01608i	−1.11640	+	0.196852i
$935$	−17.8657	+	13.2331i	−0.584272	+	0.432769i
$936$	−3.13619	+	8.31416i	−0.102510	+	0.271757i
$937$	7.66648	+	13.2787i	0.250453	+	0.433797i	0.963651	−	0.267166i	$-0.0860871\pi$
$937$	7.66648	+	13.2787i	0.250453	+	0.433797i	−0.713198	+	0.700963i	$0.752754\pi$
$938$	−26.9258	−	19.2500i	−0.879158	−	0.628536i
$939$	42.5836	+	20.1597i	1.38966	+	0.657886i
$940$	−43.2989	−	28.6292i	−1.41225	−	0.933782i
$941$	−2.32465	−	1.95061i	−0.0757814	−	0.0635881i	0.604110	−	0.796901i	$-0.293529\pi$
$941$	−2.32465	−	1.95061i	−0.0757814	−	0.0635881i	−0.679892	+	0.733313i	$0.737973\pi$
$942$	6.57808	+	14.3238i	0.214325	+	0.466696i
$943$	−45.2672	−	16.4759i	−1.47410	−	0.536529i
$944$	−25.5835			−0.832671
$945$	2.66038	+	30.6255i	0.0865421	+	0.996248i
$946$	45.0713			1.46539
$947$	−17.5905	−	6.40240i	−0.571613	−	0.208050i	0.0400102	−	0.999199i	$-0.487261\pi$
$947$	−17.5905	−	6.40240i	−0.571613	−	0.208050i	−0.611623	+	0.791149i	$0.709483\pi$
$948$	39.2232	+	3.66177i	1.27391	+	0.118929i
$949$	−3.57357	−	2.99858i	−0.116003	−	0.0973381i
$950$	−32.3885	−	49.7700i	−1.05082	−	1.61475i
$951$	3.53958	+	43.3633i	0.114779	+	1.40615i
$952$	−3.80942	−	2.72347i	−0.123464	−	0.0882680i
$953$	−12.5736	−	21.7781i	−0.407298	−	0.705461i	0.587288	−	0.809378i	$-0.300196\pi$
$953$	−12.5736	−	21.7781i	−0.407298	−	0.705461i	−0.994586	+	0.103917i	$0.966862\pi$
$954$	−0.212772	+	18.2758i	−0.00688874	+	0.591701i
$955$	2.23981	+	3.02392i	0.0724786	+	0.0978516i
$956$	−12.7107	+	2.24124i	−0.411094	+	0.0724869i
$957$	−45.2772	−	45.8074i	−1.46360	−	1.48074i
$958$	−21.5822	+	7.85530i	−0.697291	+	0.253793i
$959$	42.5216	−	29.1565i	1.37309	−	0.941514i
$960$	−41.0274	−	6.35593i	−1.32415	−	0.205137i
$961$	−1.53824	−	8.72380i	−0.0496207	−	0.281413i
$962$	−13.8811	−	8.01428i	−0.447546	−	0.258391i
$963$	−1.60179	−	4.56558i	−0.0516171	−	0.147124i
$964$	59.7010	−	34.4684i	1.92284	−	1.11015i
$965$	−7.03942	−	23.7232i	−0.226607	−	0.763675i
$966$	44.9952	−	51.9520i	1.44770	−	1.67153i
$967$	16.6675	+	2.93893i	0.535991	+	0.0945097i	0.435090	−	0.900387i	$-0.356716\pi$
$967$	16.6675	+	2.93893i	0.535991	+	0.0945097i	0.100901	+	0.994897i	$0.467828\pi$
$968$	−5.77746	−	4.84786i	−0.185695	−	0.155816i
$969$	−12.5127	+	17.6505i	−0.401967	+	0.567015i
$970$	−46.4885	−	44.0739i	−1.49266	−	1.41513i
$971$	5.47368			0.175659			0.0878294	−	0.996136i	$-0.472007\pi$
$971$	5.47368			0.175659			0.0878294	+	0.996136i	$0.472007\pi$
$972$	−22.1912	+	29.8070i	−0.711784	+	0.956061i
$973$	4.13373	+	16.0557i	0.132521	+	0.514721i
$974$	9.02771	−	24.8034i	0.289266	−	0.794753i
$975$	−31.6276	+	4.28807i	−1.01289	+	0.137328i
$976$	0.983299	−	1.17185i	0.0314746	−	0.0375100i
$977$	9.52464	−	54.0169i	0.304720	−	1.72815i	−0.320099	−	0.947384i	$-0.603716\pi$
$977$	9.52464	−	54.0169i	0.304720	−	1.72815i	0.624819	−	0.780770i	$-0.285173\pi$
$978$	15.8341	+	22.8960i	0.506320	+	0.732133i
$979$	−34.8146	−	41.4904i	−1.11268	−	1.32604i
$980$	−21.6165	−	30.4138i	−0.690515	−	0.971535i
$981$	10.9962	+	31.3423i	0.351081	+	1.00068i
$982$	−60.8695	−	35.1430i	−1.94243	−	1.12146i
$983$	−39.3717	+	6.94230i	−1.25576	+	0.221425i	−0.761659	−	0.647978i	$-0.775615\pi$
$983$	−39.3717	+	6.94230i	−1.25576	+	0.221425i	−0.494104	+	0.869403i	$0.664504\pi$
$984$	−9.05666	+	2.37031i	−0.288716	+	0.0755627i
$985$	−18.6436	−	1.13138i	−0.594035	−	0.0360486i
$986$	35.6871	−	12.9890i	1.13651	−	0.413655i
$987$	−22.9138	+	38.2929i	−0.729354	+	1.21888i
$988$	−49.0760	+	8.65342i	−1.56131	+	0.275302i
$989$	−29.5771	−	17.0763i	−0.940497	−	0.542996i
$990$	−57.8677	−	25.9336i	−1.83916	−	0.824225i
$991$	−12.1277	−	21.0058i	−0.385249	−	0.667271i	0.606555	−	0.795042i	$-0.292551\pi$
$991$	−12.1277	−	21.0058i	−0.385249	−	0.667271i	−0.991804	+	0.127771i	$0.959218\pi$
$992$	32.7352	+	39.0123i	1.03934	+	1.23864i
$993$	−1.54178	−	18.8883i	−0.0489270	−	0.599404i
$994$	38.9477	−	3.02281i	1.23535	−	0.0958777i
$995$	−16.6960	+	8.33425i	−0.529299	+	0.264214i
$996$	0.834066	−	8.93414i	0.0264284	−	0.283089i
$997$	−46.0475	−	16.7599i	−1.45834	−	0.530792i	−0.513433	−	0.858130i	$-0.671626\pi$
$997$	−46.0475	−	16.7599i	−1.45834	−	0.530792i	−0.944908	+	0.327337i	$0.893849\pi$
$998$	8.04480			0.254654
$999$	−7.49765	−	7.76419i	−0.237215	−	0.245648i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.cs.b.104.20	yes	816
5.4	even	2	inner	945.2.cs.b.104.117	yes	816
7.6	odd	2	inner	945.2.cs.b.104.19	✓	816
27.20	odd	18	inner	945.2.cs.b.209.118	yes	816
35.34	odd	2	inner	945.2.cs.b.104.118	yes	816
135.74	odd	18	inner	945.2.cs.b.209.19	yes	816
189.20	even	18	inner	945.2.cs.b.209.117	yes	816
945.209	even	18	inner	945.2.cs.b.209.20	yes	816

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.cs.b.104.19	✓	816	7.6	odd	2	inner
945.2.cs.b.104.20	yes	816	1.1	even	1	trivial
945.2.cs.b.104.117	yes	816	5.4	even	2	inner
945.2.cs.b.104.118	yes	816	35.34	odd	2	inner
945.2.cs.b.209.19	yes	816	135.74	odd	18	inner
945.2.cs.b.209.20	yes	816	945.209	even	18	inner
945.2.cs.b.209.117	yes	816	189.20	even	18	inner
945.2.cs.b.209.118	yes	816	27.20	odd	18	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.cs (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.96750 - 0.716110i) q^{2} +(1.00171 - 1.41301i) q^{3} +(1.82614 + 1.53231i) q^{4} +(1.23328 - 1.86521i) q^{5} +(-2.98272 + 2.06275i) q^{6} +(1.53873 - 2.15228i) q^{7} +(-0.401851 - 0.696026i) q^{8} +(-0.993173 - 2.83083i) q^{9} +O(q^{10})\)	\(q+(-1.96750 - 0.716110i) q^{2} +(1.00171 - 1.41301i) q^{3} +(1.82614 + 1.53231i) q^{4} +(1.23328 - 1.86521i) q^{5} +(-2.98272 + 2.06275i) q^{6} +(1.53873 - 2.15228i) q^{7} +(-0.401851 - 0.696026i) q^{8} +(-0.993173 - 2.83083i) q^{9} +(-3.76217 + 2.78664i) q^{10} +(-4.44627 + 0.783998i) q^{11} +(3.99442 - 1.04542i) q^{12} +(3.46319 - 1.26050i) q^{13} +(-4.56871 + 3.13271i) q^{14} +(-1.40017 - 3.61103i) q^{15} +(-0.535695 - 3.03808i) q^{16} +(1.90720 + 1.10112i) q^{17} +(-0.0731236 + 6.28087i) q^{18} +(-4.91222 + 2.83607i) q^{19} +(5.11023 - 1.51637i) q^{20} +(-1.49984 - 4.33018i) q^{21} +(9.30946 + 1.64151i) q^{22} +(-5.48722 - 4.60432i) q^{23} +(-1.38602 - 0.129395i) q^{24} +(-1.95804 - 4.60066i) q^{25} -7.71647 q^{26} +(-4.99485 - 1.43230i) q^{27} +(6.10790 - 1.57255i) q^{28} +(-2.81698 + 7.73958i) q^{29} +(0.168946 + 8.10736i) q^{30} +(4.05814 - 4.83631i) q^{31} +(-1.40074 + 7.94401i) q^{32} +(-3.34606 + 7.06795i) q^{33} +(-2.96388 - 3.53222i) q^{34} +(-2.11678 - 5.52442i) q^{35} +(2.52405 - 6.69134i) q^{36} +(1.79890 + 1.03859i) q^{37} +(11.6957 - 2.06227i) q^{38} +(1.68800 - 6.15616i) q^{39} +(-1.79383 - 0.108857i) q^{40} +(6.31954 - 2.30012i) q^{41} +(-0.149968 + 9.59367i) q^{42} +(4.69546 - 0.827937i) q^{43} +(-9.32084 - 5.38139i) q^{44} +(-6.50496 - 1.63873i) q^{45} +(7.49887 + 12.9884i) q^{46} +(-6.25944 - 7.45971i) q^{47} +(-4.82943 - 2.28632i) q^{48} +(-2.26463 - 6.62355i) q^{49} +(0.557859 + 10.4540i) q^{50} +(3.46634 - 1.59188i) q^{51} +(8.25574 + 3.00484i) q^{52} +2.90976 q^{53} +(8.80166 + 6.39491i) q^{54} +(-4.02118 + 9.26014i) q^{55} +(-2.11638 - 0.206098i) q^{56} +(-0.913211 + 9.78191i) q^{57} +(11.0848 - 13.2103i) q^{58} +(1.44006 - 8.16701i) q^{59} +(2.97631 - 8.73974i) q^{60} +(0.318741 + 0.379861i) q^{61} +(-11.4477 + 6.60934i) q^{62} +(-7.62097 - 2.21829i) q^{63} +(5.35979 - 9.28344i) q^{64} +(1.91999 - 8.01414i) q^{65} +(11.6448 - 11.5100i) q^{66} +(2.04359 + 5.61471i) q^{67} +(1.79555 + 4.93323i) q^{68} +(-12.0025 + 3.14130i) q^{69} +(0.208667 + 12.3851i) q^{70} +(-6.10717 - 3.52597i) q^{71} +(-1.57122 + 1.82885i) q^{72} +(-0.632890 - 1.09620i) q^{73} +(-2.79558 - 3.33164i) q^{74} +(-8.46214 - 1.84178i) q^{75} +(-13.3161 - 2.34799i) q^{76} +(-5.15422 + 10.7760i) q^{77} +(-7.72963 + 10.9034i) q^{78} +(8.96547 + 3.26316i) q^{79} +(-6.32733 - 2.74762i) q^{80} +(-7.02722 + 5.62301i) q^{81} -14.0808 q^{82} +(0.743273 - 2.04213i) q^{83} +(3.89629 - 10.2057i) q^{84} +(4.40594 - 2.19934i) q^{85} +(-9.83120 - 1.73351i) q^{86} +(8.11430 + 11.7332i) q^{87} +(2.33242 + 2.77967i) q^{88} +(5.99817 + 10.3891i) q^{89} +(11.6250 + 7.88246i) q^{90} +(2.61596 - 9.39332i) q^{91} +(-2.96516 - 16.8163i) q^{92} +(-2.76867 - 10.5787i) q^{93} +(6.97345 + 19.1594i) q^{94} +(-0.768264 + 12.6600i) q^{95} +(9.82180 + 9.93682i) q^{96} +(2.37599 + 13.4749i) q^{97} +(-0.287534 + 14.6535i) q^{98} +(6.63528 + 11.8080i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 816 q - 24 q^{4} - 24 q^{9}+O(q^{10}) \) 816 * q - 24 * q^4 - 24 * q^9	\( 816 q - 24 q^{4} - 24 q^{9} - 12 q^{11} - 6 q^{14} + 24 q^{21} - 12 q^{25} + 12 q^{29} + 78 q^{30} - 36 q^{35} + 12 q^{36} - 84 q^{39} - 36 q^{44} - 12 q^{46} + 6 q^{49} + 24 q^{50} - 60 q^{51} + 120 q^{56} - 150 q^{60} - 444 q^{64} + 162 q^{65} + 21 q^{70} - 36 q^{71} - 48 q^{74} - 48 q^{79} - 48 q^{81} + 66 q^{84} - 102 q^{85} - 192 q^{86} - 6 q^{91} - 210 q^{95} - 216 q^{99}+O(q^{100}) \) 816 * q - 24 * q^4 - 24 * q^9 - 12 * q^11 - 6 * q^14 + 24 * q^21 - 12 * q^25 + 12 * q^29 + 78 * q^30 - 36 * q^35 + 12 * q^36 - 84 * q^39 - 36 * q^44 - 12 * q^46 + 6 * q^49 + 24 * q^50 - 60 * q^51 + 120 * q^56 - 150 * q^60 - 444 * q^64 + 162 * q^65 + 21 * q^70 - 36 * q^71 - 48 * q^74 - 48 * q^79 - 48 * q^81 + 66 * q^84 - 102 * q^85 - 192 * q^86 - 6 * q^91 - 210 * q^95 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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