LMFDB - Embedded newform 756.2.cf.a.659.87

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [756,2,Mod(155,756)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(756, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 7, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("756.155"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.cf (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$108$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			659.87
Character	$\chi$	$=$	756.659
Dual form			756.2.cf.a.491.87

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.16303 + 0.804587i) q^{2} +(1.27272 - 1.17481i) q^{3} +(0.705279 + 1.87152i) q^{4} +(-0.349585 + 0.960476i) q^{5} +(2.42545 - 0.342323i) q^{6} +(0.984808 + 0.173648i) q^{7} +(-0.685540 + 2.74409i) q^{8} +(0.239643 - 2.99041i) q^{9} +(-1.17936 + 0.835791i) q^{10} +(0.828551 - 0.301568i) q^{11} +(3.09630 + 1.55335i) q^{12} +(4.19087 - 3.51656i) q^{13} +(1.00565 + 0.994322i) q^{14} +(0.683453 + 1.63311i) q^{15} +(-3.00516 + 2.63988i) q^{16} +(-0.0129346 + 0.00746778i) q^{17} +(2.68476 - 3.28513i) q^{18} +(0.274082 + 0.158241i) q^{19} +(-2.04410 + 0.0231490i) q^{20} +(1.45739 - 0.935956i) q^{21} +(1.20627 + 0.315909i) q^{22} +(0.788442 + 4.47148i) q^{23} +(2.35128 + 4.29784i) q^{24} +(3.02992 + 2.54240i) q^{25} +(7.70349 - 0.717942i) q^{26} +(-3.20817 - 4.08750i) q^{27} +(0.369578 + 1.96556i) q^{28} +(-4.13426 + 4.92702i) q^{29} +(-0.519107 + 2.44926i) q^{30} +(-6.54564 + 1.15417i) q^{31} +(-5.61911 + 0.652349i) q^{32} +(0.700230 - 1.35720i) q^{33} +(-0.0210518 - 0.00172174i) q^{34} +(-0.511059 + 0.885180i) q^{35} +(5.76563 - 1.66058i) q^{36} +(2.31077 + 4.00238i) q^{37} +(0.191447 + 0.404563i) q^{38} +(1.20253 - 9.39908i) q^{39} +(-2.39598 - 1.61774i) q^{40} +(0.483722 + 0.576477i) q^{41} +(2.44805 + 0.0840524i) q^{42} +(-3.52530 - 9.68569i) q^{43} +(1.14875 + 1.33796i) q^{44} +(2.78845 + 1.27557i) q^{45} +(-2.68071 + 5.83483i) q^{46} +(0.489145 - 2.77408i) q^{47} +(-0.723376 + 6.89034i) q^{48} +(0.939693 + 0.342020i) q^{49} +(1.47830 + 5.39472i) q^{50} +(-0.00768890 + 0.0247001i) q^{51} +(9.53704 + 5.36314i) q^{52} -5.23795i q^{53} +(-0.442446 - 7.33514i) q^{54} +0.901226i q^{55} +(-1.15163 + 2.58336i) q^{56} +(0.534734 - 0.120597i) q^{57} +(-8.77250 + 2.40390i) q^{58} +(-4.40483 - 1.60323i) q^{59} +(-2.57438 + 2.43090i) q^{60} +(0.347795 - 1.97244i) q^{61} +(-8.54142 - 3.92420i) q^{62} +(0.755282 - 2.90337i) q^{63} +(-7.06007 - 3.76237i) q^{64} +(1.91251 + 5.25457i) q^{65} +(1.90638 - 1.01507i) q^{66} +(-7.70417 - 9.18147i) q^{67} +(-0.0230986 - 0.0189404i) q^{68} +(6.25660 + 4.76468i) q^{69} +(-1.30658 + 0.618299i) q^{70} +(-3.54433 - 6.13896i) q^{71} +(8.04168 + 2.70765i) q^{72} +(3.71226 - 6.42983i) q^{73} +(-0.532763 + 6.51411i) q^{74} +(6.84308 - 0.323805i) q^{75} +(-0.102847 + 0.624554i) q^{76} +(0.868330 - 0.153110i) q^{77} +(8.96095 - 9.96388i) q^{78} +(-2.61491 + 3.11633i) q^{79} +(-1.48499 - 3.80925i) q^{80} +(-8.88514 - 1.43326i) q^{81} +(0.0987568 + 1.05966i) q^{82} +(2.17499 + 1.82503i) q^{83} +(2.77953 + 2.06742i) q^{84} +(-0.00265090 - 0.0150340i) q^{85} +(3.69295 - 14.1012i) q^{86} +(0.526548 + 11.1277i) q^{87} +(0.259525 + 2.48035i) q^{88} +(-5.70033 - 3.29109i) q^{89} +(2.21674 + 3.72708i) q^{90} +(4.73785 - 2.73540i) q^{91} +(-7.81238 + 4.62922i) q^{92} +(-6.97485 + 9.15883i) q^{93} +(2.80088 - 2.83278i) q^{94} +(-0.247802 + 0.207931i) q^{95} +(-6.38518 + 7.43165i) q^{96} +(10.2642 - 3.73585i) q^{97} +(0.817706 + 1.15384i) q^{98} +(-0.703256 - 2.54998i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66}+ \cdots + 36 q^{97}+O(q^{100}) $ 648 * q + 18 * q^12 + 42 * q^18 + 42 * q^20 - 48 * q^30 - 30 * q^32 + 60 * q^33 + 60 * q^41 - 30 * q^42 - 144 * q^44 - 18 * q^48 - 156 * q^50 + 54 * q^52 - 12 * q^57 + 54 * q^58 - 186 * q^60 - 24 * q^65 - 186 * q^66 - 78 * q^68 - 42 * q^72 - 24 * q^81 - 30 * q^86 - 36 * q^89 + 198 * q^90 + 114 * q^92 - 144 * q^93 - 54 * q^94 + 156 * q^96 + 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.16303	+	0.804587i	0.822387	+	0.568929i
$2$	1.16303	+	0.804587i	0.822387	+	0.568929i
$3$	1.27272	−	1.17481i	0.734806	−	0.678277i
$3$	1.27272	−	1.17481i	0.734806	−	0.678277i
$4$	0.705279	+	1.87152i	0.352639	+	0.935759i
$5$	−0.349585	+	0.960476i	−0.156339	+	0.429538i	−0.992990	−	0.118198i	$-0.962288\pi$
$5$	−0.349585	+	0.960476i	−0.156339	+	0.429538i	0.836651	+	0.547736i	$0.184510\pi$
$6$	2.42545	−	0.342323i	0.990186	−	0.139753i
$7$	0.984808	+	0.173648i	0.372222	+	0.0656328i
$7$	0.984808	+	0.173648i	0.372222	+	0.0656328i
$8$	−0.685540	+	2.74409i	−0.242375	+	0.970183i
$9$	0.239643	−	2.99041i	0.0798811	−	0.996804i
$10$	−1.17936	+	0.835791i	−0.372948	+	0.264300i
$11$	0.828551	−	0.301568i	0.249817	−	0.0909261i	−0.214076	−	0.976817i	$-0.568674\pi$
$11$	0.828551	−	0.301568i	0.249817	−	0.0909261i	0.463894	+	0.885891i	$0.346452\pi$
$12$	3.09630	+	1.55335i	0.893826	+	0.448415i
$13$	4.19087	−	3.51656i	1.16234	−	0.975318i	0.162404	−	0.986724i	$-0.448075\pi$
$13$	4.19087	−	3.51656i	1.16234	−	0.975318i	0.999935	+	0.0114065i	$0.00363089\pi$
$14$	1.00565	+	0.994322i	0.268770	+	0.265744i
$15$	0.683453	+	1.63311i	0.176467	+	0.421668i
$16$	−3.00516	+	2.63988i	−0.751291	+	0.659971i
$17$	−0.0129346	+	0.00746778i	−0.00313710	+	0.00181120i	−0.501568	−	0.865118i	$-0.667243\pi$
$17$	−0.0129346	+	0.00746778i	−0.00313710	+	0.00181120i	0.498431	+	0.866930i	$0.333910\pi$
$18$	2.68476	−	3.28513i	0.632804	−	0.774312i
$19$	0.274082	+	0.158241i	0.0628788	+	0.0363031i	0.531110	−	0.847303i	$-0.321775\pi$
$19$	0.274082	+	0.158241i	0.0628788	+	0.0363031i	−0.468231	+	0.883606i	$0.655109\pi$
$20$	−2.04410	+	0.0231490i	−0.457075	+	0.00517627i
$21$	1.45739	−	0.935956i	0.318029	−	0.204242i
$22$	1.20627	+	0.315909i	0.257177	+	0.0673520i
$23$	0.788442	+	4.47148i	0.164402	+	0.932367i	0.949679	+	0.313224i	$0.101409\pi$
$23$	0.788442	+	4.47148i	0.164402	+	0.932367i	−0.785278	+	0.619144i	$0.787480\pi$
$24$	2.35128	+	4.29784i	0.479954	+	0.877294i
$25$	3.02992	+	2.54240i	0.605983	+	0.508480i
$26$	7.70349	−	0.717942i	1.51078	−	0.140800i
$27$	−3.20817	−	4.08750i	−0.617412	−	0.786640i
$28$	0.369578	+	1.96556i	0.0698437	+	0.371455i
$29$	−4.13426	+	4.92702i	−0.767714	+	0.914926i	−0.998309	−	0.0581241i	$-0.981488\pi$
$29$	−4.13426	+	4.92702i	−0.767714	+	0.914926i	0.230596	+	0.973050i	$0.425933\pi$
$30$	−0.519107	+	2.44926i	−0.0947756	+	0.447172i
$31$	−6.54564	+	1.15417i	−1.17563	+	0.207296i	−0.727139	−	0.686490i	$-0.759150\pi$
$31$	−6.54564	+	1.15417i	−1.17563	+	0.207296i	−0.448494	+	0.893786i	$0.648039\pi$
$32$	−5.61911	+	0.652349i	−0.993328	+	0.115320i
$33$	0.700230	−	1.35720i	0.121894	−	0.236258i
$34$	−0.0210518	−	0.00172174i	−0.00361035	−	0.000295276i
$35$	−0.511059	+	0.885180i	−0.0863847	+	0.149623i
$36$	5.76563	−	1.66058i	0.960938	−	0.276763i
$37$	2.31077	+	4.00238i	0.379889	+	0.657987i	0.991046	−	0.133522i	$-0.0426288\pi$
$37$	2.31077	+	4.00238i	0.379889	+	0.657987i	−0.611157	+	0.791510i	$0.709296\pi$
$38$	0.191447	+	0.404563i	0.0310568	+	0.0656287i
$39$	1.20253	−	9.39908i	0.192558	−	1.50506i
$40$	−2.39598	−	1.61774i	−0.378838	−	0.255787i
$41$	0.483722	+	0.576477i	0.0755446	+	0.0900306i	0.802493	−	0.596662i	$-0.203507\pi$
$41$	0.483722	+	0.576477i	0.0755446	+	0.0900306i	−0.726948	+	0.686692i	$0.759062\pi$
$42$	2.44805	+	0.0840524i	0.377742	+	0.0129696i
$43$	−3.52530	−	9.68569i	−0.537604	−	1.47705i	−0.849836	−	0.527048i	$-0.823299\pi$
$43$	−3.52530	−	9.68569i	−0.537604	−	1.47705i	0.312232	−	0.950006i	$-0.398923\pi$
$44$	1.14875	+	1.33796i	0.173180	+	0.201705i
$45$	2.78845	+	1.27557i	0.415677	+	0.190151i
$46$	−2.68071	+	5.83483i	−0.395249	+	0.860299i
$47$	0.489145	−	2.77408i	0.0713492	−	0.404641i	−0.928127	−	0.372265i	$-0.878581\pi$
$47$	0.489145	−	2.77408i	0.0713492	−	0.404641i	0.999476	−	0.0323765i	$-0.0103076\pi$
$48$	−0.723376	+	6.89034i	−0.104410	+	0.994534i
$49$	0.939693	+	0.342020i	0.134242	+	0.0488600i
$50$	1.47830	+	5.39472i	0.209063	+	0.762929i
$51$	−0.00768890	+	0.0247001i	−0.00107666	+	0.00345870i
$52$	9.53704	+	5.36314i	1.32255	+	0.743734i
$53$		−	5.23795i		−	0.719488i	−0.933051	−	0.359744i	$-0.882864\pi$
$53$		−	5.23795i		−	0.719488i	0.933051	−	0.359744i	$-0.117136\pi$
$54$	−0.442446	−	7.33514i	−0.0602093	−	0.998186i
$55$			0.901226i			0.121521i
$56$	−1.15163	+	2.58336i	−0.153893	+	0.345216i
$57$	0.534734	−	0.120597i	0.0708272	−	0.0159735i
$58$	−8.77250	+	2.40390i	−1.15189	+	0.315648i
$59$	−4.40483	−	1.60323i	−0.573459	−	0.208722i	0.0389796	−	0.999240i	$-0.487589\pi$
$59$	−4.40483	−	1.60323i	−0.573459	−	0.208722i	−0.612439	+	0.790518i	$0.709811\pi$
$60$	−2.57438	+	2.43090i	−0.332351	+	0.313827i
$61$	0.347795	−	1.97244i	0.0445306	−	0.252546i	−0.954413	−	0.298488i	$-0.903518\pi$
$61$	0.347795	−	1.97244i	0.0445306	−	0.252546i	0.998944	+	0.0459420i	$0.0146289\pi$
$62$	−8.54142	−	3.92420i	−1.08476	−	0.498374i
$63$	0.755282	−	2.90337i	0.0951566	−	0.365790i
$64$	−7.06007	−	3.76237i	−0.882509	−	0.470296i
$65$	1.91251	+	5.25457i	0.237217	+	0.651749i
$66$	1.90638	−	1.01507i	0.234659	−	0.124946i
$67$	−7.70417	−	9.18147i	−0.941214	−	1.12170i	−0.992406	−	0.123006i	$-0.960746\pi$
$67$	−7.70417	−	9.18147i	−0.941214	−	1.12170i	0.0511918	−	0.998689i	$-0.483698\pi$
$68$	−0.0230986	−	0.0189404i	−0.00280111	−	0.00229686i
$69$	6.25660	+	4.76468i	0.753207	+	0.573600i
$70$	−1.30658	+	0.618299i	−0.156166	+	0.0739009i
$71$	−3.54433	−	6.13896i	−0.420635	−	0.728561i	0.575367	−	0.817895i	$-0.304859\pi$
$71$	−3.54433	−	6.13896i	−0.420635	−	0.728561i	−0.996002	+	0.0893345i	$0.971526\pi$
$72$	8.04168	+	2.70765i	0.947721	+	0.319100i
$73$	3.71226	−	6.42983i	0.434488	−	0.752555i	−0.562766	−	0.826616i	$-0.690263\pi$
$73$	3.71226	−	6.42983i	0.434488	−	0.752555i	0.997254	+	0.0740616i	$0.0235962\pi$
$74$	−0.532763	+	6.51411i	−0.0619324	+	0.757250i
$75$	6.84308	−	0.323805i	0.790171	−	0.0373898i
$76$	−0.102847	+	0.624554i	−0.0117974	+	0.0716413i
$77$	0.868330	−	0.153110i	0.0989553	−	0.0174485i
$78$	8.96095	−	9.96388i	1.01463	−	1.12819i
$79$	−2.61491	+	3.11633i	−0.294201	+	0.350615i	−0.892816	−	0.450422i	$-0.851274\pi$
$79$	−2.61491	+	3.11633i	−0.294201	+	0.350615i	0.598615	+	0.801037i	$0.295718\pi$
$80$	−1.48499	−	3.80925i	−0.166027	−	0.425887i
$81$	−8.88514	−	1.43326i	−0.987238	−	0.159252i
$82$	0.0987568	+	1.05966i	0.0109059	+	0.117019i
$83$	2.17499	+	1.82503i	0.238736	+	0.200323i	0.754304	−	0.656525i	$-0.227975\pi$
$83$	2.17499	+	1.82503i	0.238736	+	0.200323i	−0.515568	+	0.856849i	$0.672419\pi$
$84$	2.77953	+	2.06742i	0.303271	+	0.225574i
$85$	−0.00265090	−	0.0150340i	−0.000287530	−	0.00163066i
$86$	3.69295	−	14.1012i	0.398221	−	1.52057i
$87$	0.526548	+	11.1277i	0.0564518	+	1.19302i
$88$	0.259525	+	2.48035i	0.0276655	+	0.264407i
$89$	−5.70033	−	3.29109i	−0.604234	−	0.348854i	0.166472	−	0.986046i	$-0.446763\pi$
$89$	−5.70033	−	3.29109i	−0.604234	−	0.348854i	−0.770705	+	0.637192i	$0.780096\pi$
$90$	2.21674	+	3.72708i	0.233664	+	0.392869i
$91$	4.73785	−	2.73540i	0.496661	−	0.286748i
$92$	−7.81238	+	4.62922i	−0.814497	+	0.482630i
$93$	−6.97485	+	9.15883i	−0.723258	+	0.949726i
$94$	2.80088	−	2.83278i	0.288889	−	0.292179i
$95$	−0.247802	+	0.207931i	−0.0254240	+	0.0213332i
$96$	−6.38518	+	7.43165i	−0.651685	+	0.758490i
$97$	10.2642	−	3.73585i	1.04217	−	0.379318i	0.236466	−	0.971640i	$-0.424011\pi$
$97$	10.2642	−	3.73585i	1.04217	−	0.379318i	0.805702	+	0.592322i	$0.201789\pi$
$98$	0.817706	+	1.15384i	0.0826008	+	0.116556i
$99$	−0.703256	−	2.54998i	−0.0706799	−	0.256282i
$100$	−2.62122	+	7.46365i	−0.262122	+	0.746365i
$101$	6.47210	+	1.14121i	0.643998	+	0.113554i	0.486103	−	0.873902i	$-0.338418\pi$
$101$	6.47210	+	1.14121i	0.643998	+	0.113554i	0.157895	+	0.987456i	$0.449529\pi$
$102$	−0.0288158	+	0.0225405i	−0.00285319	+	0.00223185i
$103$	2.37047	−	6.51282i	0.233569	−	0.641727i	−0.766430	−	0.642327i	$-0.777969\pi$
$103$	2.37047	−	6.51282i	0.233569	−	0.641727i	1.00000		0.000600606i	$0.000191179\pi$
$104$	6.77675	+	13.9109i	0.664515	+	1.36407i
$105$	0.389482	+	1.72698i	0.0380096	+	0.168536i
$106$	4.21439	−	6.09190i	0.409338	−	0.591698i
$107$	−19.6413			−1.89879			−0.949397	−	0.314079i	$-0.898304\pi$
$107$	−19.6413			−1.89879			−0.949397	+	0.314079i	$0.898304\pi$
$108$	5.38718	−	8.88697i	0.518382	−	0.855149i
$109$	−4.14089			−0.396625			−0.198312	−	0.980139i	$-0.563546\pi$
$109$	−4.14089			−0.396625			−0.198312	+	0.980139i	$0.563546\pi$
$110$	−0.725115	+	1.04815i	−0.0691370	+	0.0999375i
$111$	7.64301	+	2.37920i	0.725442	+	0.225823i
$112$	−3.41792	+	2.07794i	−0.322963	+	0.196347i
$113$	1.35342	−	3.71848i	0.127319	−	0.349805i	−0.859613	−	0.510946i	$-0.829295\pi$
$113$	1.35342	−	3.71848i	0.127319	−	0.349805i	0.986931	+	0.161141i	$0.0515174\pi$
$114$	0.718943	+	0.289982i	0.0673351	+	0.0271593i
$115$	−4.57037	−	0.805880i	−0.426190	−	0.0751487i
$116$	−12.1368	−	4.26243i	−1.12688	−	0.395756i
$117$	−9.51165	−	13.3752i	−0.879352	−	1.23653i
$118$	−3.83301	−	5.40867i	−0.352857	−	0.497908i
$119$	−0.0140348	+	0.00510826i	−0.00128657	+	0.000468274i
$120$	−4.94995	+	0.755891i	−0.451867	+	0.0690031i
$121$	−7.83094	+	6.57094i	−0.711903	+	0.597358i
$122$	1.99150	−	2.01418i	0.180302	−	0.182355i
$123$	1.29289	+	0.165414i	0.116576	+	0.0149149i
$124$	−6.77656	−	11.4363i	−0.608553	−	1.02701i
$125$	−7.92703	+	4.57667i	−0.709015	+	0.409350i
$126$	3.21443	−	2.76901i	0.286364	−	0.246683i
$127$	−11.2420	−	6.49056i	−0.997565	−	0.575944i	−0.0900379	−	0.995938i	$-0.528699\pi$
$127$	−11.2420	−	6.49056i	−0.997565	−	0.575944i	−0.907527	+	0.419994i	$0.862032\pi$
$128$	−5.18392	−	10.0562i	−0.458198	−	0.888850i
$129$	−15.8656	−	8.18563i	−1.39689	−	0.720705i
$130$	−2.00346	+	7.65000i	−0.175715	+	0.670949i
$131$	3.87374	+	21.9691i	0.338451	+	1.91945i	0.390078	+	0.920782i	$0.372448\pi$
$131$	3.87374	+	21.9691i	0.338451	+	1.91945i	−0.0516273	+	0.998666i	$0.516441\pi$
$132$	3.03388	+	0.353288i	0.264066	+	0.0307498i
$133$	0.242440	+	0.203431i	0.0210222	+	0.0176397i
$134$	−1.57289	−	16.8770i	−0.135877	−	1.45795i
$135$	5.04747	−	1.65244i	0.434417	−	0.142220i
$136$	−0.0116251	−	0.0406131i	−0.000996844	−	0.00348255i
$137$	−13.9492	+	16.6240i	−1.19176	+	1.42028i	−0.308610	+	0.951189i	$0.599864\pi$
$137$	−13.9492	+	16.6240i	−1.19176	+	1.42028i	−0.883149	+	0.469093i	$0.844581\pi$
$138$	3.44302	+	10.5754i	0.293089	+	0.900242i
$139$	5.30651	−	0.935681i	0.450092	−	0.0793634i	0.0559928	−	0.998431i	$-0.482168\pi$
$139$	5.30651	−	0.935681i	0.450092	−	0.0793634i	0.394100	+	0.919068i	$0.371057\pi$
$140$	−2.01707	−	0.332158i	−0.170473	−	0.0280724i
$141$	−2.63647	−	4.10529i	−0.222031	−	0.345728i
$142$	0.817166	−	9.99152i	0.0685751	−	0.838470i
$143$	2.41187	−	4.17748i	0.201691	−	0.349338i
$144$	7.17418	+	9.61931i	0.597848	+	0.801609i
$145$	−3.28701	−	5.69328i	−0.272972	−	0.472801i
$146$	9.49083	−	4.49125i	0.785467	−	0.371698i
$147$	1.59778	−	0.668664i	0.131782	−	0.0551504i
$148$	−5.86079	+	7.14745i	−0.481754	+	0.587517i
$149$	9.65113	+	11.5018i	0.790651	+	0.942261i	0.999362	−	0.0357160i	$-0.0113712\pi$
$149$	9.65113	+	11.5018i	0.790651	+	0.942261i	−0.208711	+	0.977977i	$0.566927\pi$
$150$	8.21924	+	5.12926i	0.671098	+	0.418802i
$151$	4.08652	+	11.2276i	0.332556	+	0.913690i	0.987445	+	0.157965i	$0.0504933\pi$
$151$	4.08652	+	11.2276i	0.332556	+	0.913690i	−0.654889	+	0.755725i	$0.727285\pi$
$152$	−0.622123	+	0.643626i	−0.0504608	+	0.0522049i
$153$	0.0192321	+	0.0404693i	0.00155482	+	0.00327175i
$154$	1.13308	+	0.520575i	0.0913065	+	0.0419492i
$155$	1.17970	−	6.69042i	0.0947559	−	0.537387i
$156$	18.4387	−	4.37842i	1.47627	−	0.350554i
$157$	19.5711	+	7.12330i	1.56194	+	0.568501i	0.971181	−	0.238344i	$-0.0766045\pi$
$157$	19.5711	+	7.12330i	1.56194	+	0.568501i	0.590763	+	0.806845i	$0.298827\pi$
$158$	−5.54858	+	1.52046i	−0.441422	+	0.120962i
$159$	−6.15360	−	6.66646i	−0.488012	−	0.528685i
$160$	1.33779	−	5.62508i	0.105762	−	0.444701i
$161$			4.54046i			0.357838i
$162$	−9.18050	−	8.81580i	−0.721288	−	0.692635i
$163$			1.88113i			0.147342i	0.997283	+	0.0736709i	$0.0234714\pi$
$163$			1.88113i			0.147342i	−0.997283	+	0.0736709i	$0.976529\pi$
$164$	−0.737729	+	1.31187i	−0.0576069	+	0.102440i
$165$	1.05877	+	1.14701i	0.0824251	+	0.0892947i
$166$	1.06118	+	3.87254i	0.0823635	+	0.300567i
$167$	−5.40110	−	1.96584i	−0.417949	−	0.152121i	0.124481	−	0.992222i	$-0.460273\pi$
$167$	−5.40110	−	1.96584i	−0.417949	−	0.152121i	−0.542430	+	0.840101i	$0.682496\pi$
$168$	1.56925	+	4.64085i	0.121070	+	0.358049i
$169$	2.93979	−	16.6724i	0.226138	−	1.28249i
$170$	0.00901307	−	0.0196178i	0.000691271	−	0.00150462i
$171$	0.538889	−	0.781697i	0.0412099	−	0.0597779i
$172$	15.6406	−	13.4288i	1.19259	−	1.02393i
$173$	3.22757	+	8.86767i	0.245387	+	0.674196i	0.999841	+	0.0178427i	$0.00567979\pi$
$173$	3.22757	+	8.86767i	0.245387	+	0.674196i	−0.754453	+	0.656354i	$0.772098\pi$
$174$	−8.34082	+	13.3655i	−0.632316	+	1.01324i
$175$	2.54240	+	3.02992i	0.192188	+	0.229040i
$176$	−1.69383	+	3.09354i	−0.127677	+	0.233184i
$177$	−7.48960	+	3.13437i	−0.562953	+	0.235594i
$178$	−3.98169	−	8.41404i	−0.298440	−	0.630659i
$179$	−7.52328	−	13.0307i	−0.562316	−	0.973961i	−0.997294	−	0.0735192i	$-0.976577\pi$
$179$	−7.52328	−	13.0307i	−0.562316	−	0.973961i	0.434977	−	0.900441i	$-0.356756\pi$
$180$	−0.420630	+	6.11826i	−0.0313519	+	0.456028i
$181$	−2.25687	+	3.90902i	−0.167752	+	0.290555i	−0.937629	−	0.347637i	$-0.886984\pi$
$181$	−2.25687	+	3.90902i	−0.167752	+	0.290555i	0.769877	+	0.638192i	$0.220318\pi$
$182$	7.71112	+	0.630662i	0.571587	+	0.0467477i
$183$	−1.87460	−	2.91897i	−0.138574	−	0.215776i
$184$	−12.8106	−	0.901818i	−0.944413	−	0.0664829i
$185$	−4.65200	+	0.820273i	−0.342022	+	0.0603077i
$186$	−15.4810	+	5.04012i	−1.13513	+	0.369560i
$187$	−0.00846491	+	0.0100881i	−0.000619015	+	0.000737714i
$188$	5.53673	−	1.04106i	0.403807	−	0.0759268i
$189$	−2.44964	−	4.58249i	−0.178185	−	0.333327i
$190$	−0.455500	+	0.0424512i	−0.0330454	+	0.00307973i
$191$	17.7152	+	14.8648i	1.28183	+	1.07558i	0.992989	+	0.118204i	$0.0377138\pi$
$191$	17.7152	+	14.8648i	1.28183	+	1.07558i	0.288839	+	0.957378i	$0.406731\pi$
$192$	−13.4056	+	3.50579i	−0.967464	+	0.253009i
$193$	−2.78704	−	15.8061i	−0.200615	−	1.13775i	−0.904192	−	0.427126i	$-0.859526\pi$
$193$	−2.78704	−	15.8061i	−0.200615	−	1.13775i	0.703577	−	0.710619i	$-0.251585\pi$
$194$	14.9433	+	3.91351i	1.07287	+	0.280974i
$195$	8.60721	+	4.44077i	0.616375	+	0.318010i
$196$	0.0226481	+	1.99987i	0.00161772	+	0.142848i
$197$	15.1905	+	8.77023i	1.08228	+	0.624853i	0.931510	−	0.363717i	$-0.118492\pi$
$197$	15.1905	+	8.77023i	1.08228	+	0.624853i	0.150767	+	0.988569i	$0.451826\pi$
$198$	1.23377	−	3.53153i	0.0876803	−	0.250975i
$199$	−8.71014	+	5.02880i	−0.617445	+	0.356482i	−0.775874	−	0.630888i	$-0.782691\pi$
$199$	−8.71014	+	5.02880i	−0.617445	+	0.356482i	0.158428	+	0.987370i	$0.449357\pi$
$200$	−9.05371	+	6.57145i	−0.640194	+	0.464672i
$201$	−20.5918	−	2.63453i	−1.45243	−	0.185825i
$202$	6.60905	+	6.53462i	0.465011	+	0.459775i
$203$	−4.92702	+	4.13426i	−0.345809	+	0.290168i
$204$	−0.0516495	+	0.00303052i	−0.00361619	+	0.000212179i
$205$	−0.722794	+	0.263075i	−0.0504821	+	0.0183740i
$206$	7.99706	−	5.66735i	0.557181	−	0.394863i
$207$	13.5605	−	1.28621i	0.942520	−	0.0893977i
$208$	−3.31095	+	21.6313i	−0.229573	+	1.49986i
$209$	0.274811	+	0.0484567i	0.0190091	+	0.00335182i
$210$	−0.936530	+	2.32191i	−0.0646267	+	0.160227i
$211$	4.30465	−	11.8269i	0.296344	−	0.814200i	−0.698759	−	0.715358i	$-0.746264\pi$
$211$	4.30465	−	11.8269i	0.296344	−	0.814200i	0.995103	−	0.0988423i	$-0.0315139\pi$
$212$	9.80293	−	3.69422i	0.673268	−	0.253720i
$213$	−11.7231	−	3.64928i	−0.803251	−	0.250044i
$214$	−22.8434	−	15.8031i	−1.56154	−	1.08028i
$215$	10.5353			0.718499
$216$	13.4158	−	6.00136i	0.912829	−	0.408341i
$217$	−6.64662			−0.451202
$218$	−4.81598	−	3.33170i	−0.326179	−	0.225652i
$219$	−2.82915	−	12.5446i	−0.191176	−	0.847685i
$220$	−1.68666	+	0.635616i	−0.113715	+	0.0428532i
$221$	−0.0279463	+	0.0767817i	−0.00187987	+	0.00516490i
$222$	6.97478	+	8.91654i	0.468117	+	0.598439i
$223$	14.6421	+	2.58180i	0.980510	+	0.172890i	0.640857	−	0.767661i	$-0.278579\pi$
$223$	14.6421	+	2.58180i	0.980510	+	0.172890i	0.339653	+	0.940551i	$0.389690\pi$
$224$	−5.64703	−	0.333311i	−0.377308	−	0.0222703i
$225$	8.32893	−	8.45144i	0.555262	−	0.563429i
$226$	4.56590	−	3.23576i	0.303719	−	0.215240i
$227$	−4.10424	+	1.49382i	−0.272408	+	0.0991485i	−0.474612	−	0.880195i	$-0.657412\pi$
$227$	−4.10424	+	1.49382i	−0.272408	+	0.0991485i	0.202204	+	0.979343i	$0.435190\pi$
$228$	0.602836	+	0.915710i	0.0399238	+	0.0606444i
$229$	18.1673	−	15.2442i	1.20053	−	1.00736i	0.200916	−	0.979608i	$-0.435608\pi$
$229$	18.1673	−	15.2442i	1.20053	−	1.00736i	0.999615	−	0.0277565i	$-0.00883629\pi$
$230$	−4.66708	−	4.61453i	−0.307738	−	0.304273i
$231$	0.925267	−	1.21499i	0.0608781	−	0.0799404i
$232$	−10.6860	−	14.7225i	−0.701570	−	0.966577i
$233$	1.67401	−	0.966493i	0.109668	−	0.0633171i	−0.444163	−	0.895946i	$-0.646499\pi$
$233$	1.67401	−	0.966493i	0.109668	−	0.0633171i	0.553831	+	0.832629i	$0.313165\pi$
$234$	−0.300856	−	23.2087i	−0.0196676	−	1.51720i
$235$	2.49344	+	1.43959i	0.162654	+	0.0939084i
$236$	−0.106163	−	9.37443i	−0.00691064	−	0.610224i
$237$	0.333040	+	7.03825i	0.0216333	+	0.457184i
$238$	−0.0204330	−	0.00535119i	−0.00132447	−	0.000346866i
$239$	2.67494	+	15.1703i	0.173027	+	0.981287i	0.940396	+	0.340081i	$0.110455\pi$
$239$	2.67494	+	15.1703i	0.173027	+	0.981287i	−0.767369	+	0.641206i	$0.778434\pi$
$240$	−6.36512	−	3.10354i	−0.410867	−	0.200333i
$241$	−14.9046	−	12.5065i	−0.960092	−	0.805613i	0.0208762	−	0.999782i	$-0.493354\pi$
$241$	−14.9046	−	12.5065i	−0.960092	−	0.805613i	−0.980968	+	0.194169i	$0.937799\pi$
$242$	−14.3945	+	1.34153i	−0.925314	+	0.0862365i
$243$	−12.9921	+	8.61421i	−0.833446	+	0.552602i
$244$	3.93676	−	0.740218i	0.252025	−	0.0473876i
$245$	−0.657004	+	0.782987i	−0.0419745	+	0.0500232i
$246$	1.37058	+	1.23263i	0.0873853	+	0.0785895i
$247$	1.70511	−	0.300657i	0.108493	−	0.0191303i
$248$	1.32014	−	18.7531i	0.0838290	−	1.19082i
$249$	4.91222	−	0.232440i	0.311299	−	0.0147303i
$250$	−12.9017	−	1.05518i	−0.815975	−	0.0667353i
$251$	7.64577	−	13.2429i	0.482597	−	0.835882i	−0.517203	−	0.855863i	$-0.673027\pi$
$251$	7.64577	−	13.2429i	0.482597	−	0.835882i	0.999800	+	0.0199800i	$0.00636026\pi$
$252$	5.96639	−	0.634159i	0.375847	−	0.0399483i
$253$	2.00172	+	3.46708i	0.125847	+	0.217973i
$254$	−7.85254	−	16.5939i	−0.492712	−	1.04119i
$255$	−0.0210359	−	0.0160198i	−0.00131732	−	0.00100320i
$256$	2.06202	−	15.8666i	0.128876	−	0.991661i
$257$	0.439713	+	0.524030i	0.0274286	+	0.0326881i	0.779584	−	0.626297i	$-0.215430\pi$
$257$	0.439713	+	0.524030i	0.0274286	+	0.0326881i	−0.752156	+	0.658985i	$0.770986\pi$
$258$	−11.8661	−	22.2854i	−0.738751	−	1.38743i
$259$	1.58066	+	4.34284i	0.0982176	+	0.269851i
$260$	−8.48517	+	7.28523i	−0.526228	+	0.451810i
$261$	13.7431	+	13.5439i	0.850676	+	0.838346i
$262$	−13.1708	+	28.6675i	−0.813693	+	1.77108i
$263$	−0.435362	+	2.46906i	−0.0268456	+	0.152249i	−0.995284	−	0.0970042i	$-0.969074\pi$
$263$	−0.435362	+	2.46906i	−0.0268456	+	0.152249i	0.968438	+	0.249253i	$0.0801851\pi$
$264$	3.24425	+	2.85191i	0.199670	+	0.175523i
$265$	5.03093	+	1.83111i	0.309048	+	0.112484i
$266$	0.118287	+	0.431661i	0.00725263	+	0.0264668i
$267$	−11.1213	+	2.50816i	−0.680615	+	0.153497i
$268$	11.7497	−	20.8940i	0.717728	−	1.27630i
$269$		−	30.6805i		−	1.87062i	−0.353827	−	0.935311i	$-0.615120\pi$
$269$		−	30.6805i		−	1.87062i	0.353827	−	0.935311i	$-0.384880\pi$
$270$	7.19990	+	2.13929i	0.438172	+	0.130193i
$271$		−	6.28136i		−	0.381566i	−0.981632	−	0.190783i	$-0.938897\pi$
$271$		−	6.28136i		−	0.381566i	0.981632	−	0.190783i	$-0.0611026\pi$
$272$	0.0191564	−	0.0565877i	0.00116153	−	0.00343113i
$273$	2.81639	−	9.04747i	0.170456	−	0.547578i
$274$	−29.5987	+	8.11086i	−1.78813	+	0.489995i
$275$	3.27715	+	1.19278i	0.197619	+	0.0719276i
$276$	−4.50454	+	15.0698i	−0.271141	+	0.907094i
$277$	3.84781	−	21.8220i	0.231193	−	1.31116i	−0.619293	−	0.785160i	$-0.712581\pi$
$277$	3.84781	−	21.8220i	0.231193	−	1.31116i	0.850485	−	0.525999i	$-0.176308\pi$
$278$	6.92447	+	3.18133i	0.415302	+	0.190803i
$279$	1.88284	+	19.8508i	0.112723	+	1.18843i
$280$	−2.07866	−	2.00922i	−0.124224	−	0.120074i
$281$	8.65451	+	23.7781i	0.516285	+	1.41848i	0.874584	+	0.484874i	$0.161135\pi$
$281$	8.65451	+	23.7781i	0.516285	+	1.41848i	−0.358299	+	0.933607i	$0.616643\pi$
$282$	0.236765	−	6.89584i	0.0140992	−	0.410642i
$283$	7.09245	+	8.45246i	0.421603	+	0.502446i	0.934480	−	0.356015i	$-0.115865\pi$
$283$	7.09245	+	8.45246i	0.421603	+	0.502446i	−0.512877	+	0.858462i	$0.671420\pi$
$284$	8.98944	−	10.9630i	0.533425	−	0.650532i
$285$	−0.0711042	+	0.555758i	−0.00421185	+	0.0329203i
$286$	6.16622	−	2.91797i	0.364616	−	0.172543i
$287$	0.376269	+	0.651716i	0.0222104	+	0.0384696i
$288$	0.604210	+	16.9598i	0.0356034	+	0.999366i
$289$	−8.49989	+	14.7222i	−0.499993	+	0.866014i
$290$	0.757840	−	9.26614i	0.0445019	−	0.544127i
$291$	8.67451	−	16.8131i	0.508509	−	0.985604i
$292$	14.6517	+	2.41275i	0.857427	+	0.141195i
$293$	18.4942	−	3.26102i	1.08044	−	0.190511i	0.395030	−	0.918668i	$-0.370734\pi$
$293$	18.4942	−	3.26102i	1.08044	−	0.190511i	0.685410	+	0.728157i	$0.259623\pi$
$294$	2.39626	+	0.507874i	0.139753	+	0.0296198i
$295$	3.07972	−	3.67027i	0.179308	−	0.213691i
$296$	−12.5670	+	3.59719i	−0.730443	+	0.209082i
$297$	−3.89079	−	2.41922i	−0.225766	−	0.140377i
$298$	1.97038	+	21.1421i	0.114141	+	1.22473i
$299$	19.0285	+	15.9668i	1.10044	+	0.923383i
$300$	5.43229	+	12.5786i	0.313633	+	0.726225i
$301$	−1.78984	−	10.1507i	−0.103165	−	0.585077i
$302$	−4.28085	+	16.3460i	−0.246335	+	0.940607i
$303$	9.57788	−	6.15105i	0.550235	−	0.353369i
$304$	−1.24140	+	0.248004i	−0.0711992	+	0.0142240i
$305$	1.77290	+	1.02359i	0.101516	+	0.0586103i
$306$	−0.0101936	+	0.0625409i	−0.000582731	+	0.00357523i
$307$	−20.8273	+	12.0247i	−1.18868	+	0.686284i	−0.958006	−	0.286747i	$-0.907426\pi$
$307$	−20.8273	+	12.0247i	−1.18868	+	0.686284i	−0.230673	+	0.973031i	$0.574093\pi$
$308$	0.898962	+	1.51711i	0.0512231	+	0.0864454i
$309$	−4.63437	−	11.0739i	−0.263640	−	0.629970i
$310$	6.75505	−	6.83198i	0.383661	−	0.388031i
$311$	−20.0768	+	16.8465i	−1.13845	+	0.955276i	−0.999387	−	0.0350070i	$-0.988855\pi$
$311$	−20.0768	+	16.8465i	−1.13845	+	0.955276i	−0.139067	+	0.990283i	$0.544410\pi$
$312$	24.9675	+	9.74328i	1.41351	+	0.551605i
$313$	−4.76677	+	1.73496i	−0.269434	+	0.0980660i	−0.473204	−	0.880953i	$-0.656903\pi$
$313$	−4.76677	+	1.73496i	−0.269434	+	0.0980660i	0.203770	+	0.979019i	$0.434680\pi$
$314$	17.0305	+	24.0313i	0.961085	+	1.35616i
$315$	2.52458	+	1.74040i	0.142244	+	0.0980607i
$316$	−7.67652	−	2.69598i	−0.431838	−	0.151661i
$317$	−2.72721	−	0.480882i	−0.153176	−	0.0270090i	0.0965344	−	0.995330i	$-0.469224\pi$
$317$	−2.72721	−	0.480882i	−0.153176	−	0.0270090i	−0.249710	+	0.968321i	$0.580335\pi$
$318$	−1.79307	−	12.7044i	−0.100551	−	0.712428i
$319$	−1.93962	+	5.32905i	−0.108598	+	0.298369i
$320$	6.08176	−	5.46576i	0.339981	−	0.305545i
$321$	−24.9979	+	23.0748i	−1.39525	+	1.28791i
$322$	−3.65319	+	5.28069i	−0.203585	+	0.294281i
$323$	−0.00472685			−0.000263009
$324$	−3.58412	−	17.6396i	−0.199118	−	0.979976i
$325$	21.6385			1.20029
$326$	−1.51354	+	2.18782i	−0.0838270	+	0.121172i
$327$	−5.27020	+	4.86475i	−0.291443	+	0.269022i
$328$	−1.91352	+	0.932178i	−0.105656	+	0.0514709i
$329$	0.963428	−	2.64700i	0.0531155	−	0.145934i
$330$	0.308511	+	2.18588i	0.0169830	+	0.120329i
$331$	27.0247	+	4.76518i	1.48541	+	0.261918i	0.856738	−	0.515751i	$-0.172487\pi$
$331$	27.0247	+	4.76518i	1.48541	+	0.261918i	0.628674	+	0.777669i	$0.283598\pi$
$332$	−1.88161	+	5.35769i	−0.103267	+	0.294041i
$333$	12.5225	−	5.95103i	0.686230	−	0.326114i
$334$	−4.69995	−	6.63198i	−0.257170	−	0.362886i
$335$	11.5118	−	4.18997i	0.628959	−	0.228922i
$336$	−1.90888	+	6.66004i	−0.104138	+	0.363335i
$337$	−9.65525	+	8.10171i	−0.525955	+	0.441328i	−0.866702	−	0.498827i	$-0.833764\pi$
$337$	−9.65525	+	8.10171i	−0.525955	+	0.441328i	0.340747	+	0.940155i	$0.389320\pi$
$338$	16.8335	−	17.0252i	0.915619	−	0.926047i
$339$	−2.64598	−	6.32260i	−0.143710	−	0.343396i
$340$	0.0262667	−	0.0155643i	0.00142451	−	0.000844095i
$341$	−5.07534	+	2.93025i	−0.274845	+	0.158682i
$342$	1.25569	−	0.475554i	0.0678998	−	0.0257150i
$343$	0.866025	+	0.500000i	0.0467610	+	0.0269975i
$344$	28.9952	−	3.03383i	1.56331	−	0.163573i
$345$	−6.76357	+	4.34366i	−0.364139	+	0.233855i
$346$	−3.38105	+	12.9102i	−0.181767	+	0.694058i
$347$	−2.00505	−	11.3712i	−0.107637	−	0.610438i	−0.990134	−	0.140121i	$-0.955251\pi$
$347$	−2.00505	−	11.3712i	−0.107637	−	0.610438i	0.882498	−	0.470317i	$-0.155860\pi$
$348$	−20.4544	+	8.83358i	−1.09647	+	0.473530i
$349$	−8.55608	−	7.17940i	−0.457997	−	0.384305i	0.384397	−	0.923168i	$-0.374409\pi$
$349$	−8.55608	−	7.17940i	−0.457997	−	0.384305i	−0.842393	+	0.538863i	$0.818854\pi$
$350$	0.519058	+	5.56947i	0.0277448	+	0.297701i
$351$	−27.8190	−	5.84848i	−1.48487	−	0.312169i
$352$	−4.45899	+	2.23505i	−0.237665	+	0.119128i
$353$	20.3258	−	24.2234i	1.08184	−	1.28928i	0.127079	−	0.991893i	$-0.459440\pi$
$353$	20.3258	−	24.2234i	1.08184	−	1.28928i	0.954756	−	0.297389i	$-0.0961158\pi$
$354$	−11.2325	−	2.38067i	−0.597001	−	0.126531i
$355$	7.13537	−	1.25816i	0.378706	−	0.0667761i
$356$	2.13901	−	12.9894i	0.113367	−	0.688437i
$357$	−0.0118612	+	0.0229897i	−0.000627762	+	0.00121674i
$358$	1.73454	−	21.2082i	0.0916731	−	1.12089i
$359$	−5.53672	+	9.58988i	−0.292217	+	0.506135i	−0.974334	−	0.225109i	$-0.927726\pi$
$359$	−5.53672	+	9.58988i	−0.292217	+	0.506135i	0.682117	+	0.731243i	$0.261060\pi$
$360$	−5.41188	+	6.77729i	−0.285231	+	0.357195i
$361$	−9.44992	−	16.3677i	−0.497364	−	0.861460i
$362$	−5.76996	+	2.73046i	−0.303263	+	0.143510i
$363$	−2.24700	+	17.5628i	−0.117937	+	0.921810i
$364$	8.46085	+	6.93775i	0.443469	+	0.363637i
$365$	4.87795	+	5.81331i	0.255323	+	0.304283i
$366$	0.168346	−	4.90313i	0.00879960	−	0.256291i
$367$	10.1502	+	27.8874i	0.529835	+	1.45571i	0.859265	+	0.511530i	$0.170921\pi$
$367$	10.1502	+	27.8874i	0.529835	+	1.45571i	−0.329430	+	0.944180i	$0.606857\pi$
$368$	−14.1736	−	11.3561i	−0.738849	−	0.591979i
$369$	1.83982	−	1.30838i	0.0957774	−	0.0681115i
$370$	−6.07040	−	2.78894i	−0.315585	−	0.144990i
$371$	0.909561	−	5.15838i	0.0472221	−	0.267810i
$372$	−22.0601	−	6.59404i	−1.14376	−	0.341885i
$373$	29.2697	+	10.6533i	1.51553	+	0.551606i	0.960026	−	0.279911i	$-0.0903050\pi$
$373$	29.2697	+	10.6533i	1.51553	+	0.551606i	0.555499	+	0.831517i	$0.312527\pi$
$374$	−0.0179617	+	0.00492199i	−0.000928777	+	0.000254510i
$375$	−4.71218	+	15.1376i	−0.243336	+	0.781701i
$376$	7.27700	+	3.24400i	0.375283	+	0.167297i
$377$			35.1869i			1.81222i
$378$	0.838009	−	7.30053i	0.0431025	−	0.375499i
$379$			0.759047i			0.0389896i	0.999810	+	0.0194948i	$0.00620578\pi$
$379$			0.759047i			0.0389896i	−0.999810	+	0.0194948i	$0.993794\pi$
$380$	−0.563915	−	0.317117i	−0.0289283	−	0.0162678i
$381$	−21.9331	+	4.94651i	−1.12367	+	0.253417i
$382$	8.64328	+	31.5417i	0.442229	+	1.61381i
$383$	9.42572	+	3.43068i	0.481632	+	0.175300i	0.571414	−	0.820662i	$-0.306395\pi$
$383$	9.42572	+	3.43068i	0.481632	+	0.175300i	−0.0897825	+	0.995961i	$0.528617\pi$
$384$	−18.4118	−	6.70861i	−0.939573	−	0.342347i
$385$	−0.156496	+	0.887535i	−0.00797579	+	0.0452330i
$386$	9.47595	−	20.6253i	0.482313	−	1.04980i
$387$	−29.8090	+	8.22100i	−1.51528	+	0.417897i
$388$	14.2308	+	16.5748i	0.722460	+	0.841456i
$389$	0.533185	+	1.46491i	0.0270336	+	0.0742741i	0.952475	−	0.304616i	$-0.0985281\pi$
$389$	0.533185	+	1.46491i	0.0270336	+	0.0742741i	−0.925442	+	0.378890i	$0.876306\pi$
$390$	6.43745	+	12.0900i	0.325973	+	0.612201i
$391$	−0.0435902	−	0.0519487i	−0.00220445	−	0.00262716i
$392$	−1.58273	+	2.34413i	−0.0799400	+	0.118397i
$393$	30.7397	+	23.4096i	1.55061	+	1.18086i
$394$	10.6106	+	22.4221i	0.534553	+	1.12961i
$395$	−2.07903	−	3.60098i	−0.104607	−	0.181185i
$396$	4.27634	−	3.11460i	0.214894	−	0.156515i
$397$	−10.5123	+	18.2078i	−0.527595	+	0.913822i	0.471888	+	0.881659i	$0.343573\pi$
$397$	−10.5123	+	18.2078i	−0.527595	+	0.913822i	−0.999483	+	0.0321628i	$0.989761\pi$
$398$	−14.1763	−	1.15942i	−0.710592	−	0.0581164i
$399$	0.547552	−	0.0259094i	0.0274119	−	0.00129709i
$400$	−15.8170	+	0.358295i	−0.790852	+	0.0179147i
$401$	12.8373	−	2.26357i	0.641065	−	0.113037i	0.156340	−	0.987703i	$-0.450031\pi$
$401$	12.8373	−	2.26357i	0.641065	−	0.113037i	0.484726	+	0.874666i	$0.338919\pi$
$402$	−21.8291	−	19.6319i	−1.08874	−	0.979150i
$403$	−23.3732	+	27.8551i	−1.16430	+	1.38756i
$404$	2.42885	+	12.9175i	0.120840	+	0.642671i
$405$	4.48273	−	8.03292i	0.222748	−	0.399159i
$406$	−9.05666	+	0.844053i	−0.449474	+	0.0418897i
$407$	3.12158	+	2.61932i	0.154731	+	0.129835i
$408$	−0.0625082	−	0.0380319i	−0.00309462	−	0.00188286i
$409$	3.66882	+	20.8069i	0.181412	+	1.02884i	0.930480	+	0.366343i	$0.119390\pi$
$409$	3.66882	+	20.8069i	0.181412	+	1.02884i	−0.749068	+	0.662493i	$0.769498\pi$
$410$	−1.05230	−	0.275586i	−0.0519693	−	0.0136102i
$411$	1.77659	+	37.5453i	0.0876328	+	1.85197i
$412$	13.8607	−	0.156969i	0.682868	−	0.00773332i
$413$	−4.05951	−	2.34376i	−0.199755	−	0.115329i
$414$	16.8061	+	9.41471i	0.825977	+	0.462708i
$415$	−2.51324	+	1.45102i	−0.123370	+	0.0712278i
$416$	−21.2550	+	22.4939i	−1.04211	+	1.10285i
$417$	5.65447	−	7.42500i	0.276900	−	0.363604i
$418$	0.280626	+	0.277466i	0.0137259	+	0.0135713i
$419$	5.78462	−	4.85388i	0.282597	−	0.237127i	−0.490460	−	0.871464i	$-0.663171\pi$
$419$	5.78462	−	4.85388i	0.282597	−	0.237127i	0.773057	+	0.634337i	$0.218727\pi$
$420$	−2.95739	+	1.94693i	−0.144306	+	0.0950004i
$421$	5.79891	−	2.11063i	0.282622	−	0.102866i	−0.196820	−	0.980440i	$-0.563061\pi$
$421$	5.79891	−	2.11063i	0.282622	−	0.102866i	0.479442	+	0.877574i	$0.340839\pi$
$422$	14.5222	−	10.2916i	0.706932	−	0.500988i
$423$	−8.17843	−	2.12754i	−0.397649	−	0.103444i
$424$	14.3734	+	3.59083i	0.698035	+	0.174386i
$425$	−0.0581768	−	0.0102581i	−0.00282199	−	0.000497593i
$426$	−10.6981	−	13.6764i	−0.518325	−	0.662626i
$427$	0.685023	−	1.88208i	0.0331506	−	0.0910805i
$428$	−13.8526	−	36.7590i	−0.669589	−	1.77681i
$429$	−1.83810	−	8.15026i	−0.0887445	−	0.393498i
$430$	12.2528	+	8.47654i	0.590884	+	0.408775i
$431$	−8.77170			−0.422518			−0.211259	−	0.977430i	$-0.567756\pi$
$431$	−8.77170			−0.422518			−0.211259	+	0.977430i	$0.567756\pi$
$432$	20.4316	+	3.81442i	0.983016	+	0.183521i
$433$	−2.14228			−0.102951			−0.0514757	−	0.998674i	$-0.516392\pi$
$433$	−2.14228			−0.102951			−0.0514757	+	0.998674i	$0.516392\pi$
$434$	−7.73022	−	5.34779i	−0.371063	−	0.256702i
$435$	−10.8720	−	3.38434i	−0.521271	−	0.162267i
$436$	−2.92048	−	7.74975i	−0.139866	−	0.371146i
$437$	−0.491475	+	1.35032i	−0.0235104	+	0.0645944i
$438$	6.80283	−	16.8660i	0.325052	−	0.805890i
$439$	−16.7254	−	2.94913i	−0.798258	−	0.140754i	−0.240382	−	0.970678i	$-0.577273\pi$
$439$	−16.7254	−	2.94913i	−0.798258	−	0.140754i	−0.557876	+	0.829924i	$0.688384\pi$
$440$	−2.47305	−	0.617827i	−0.117898	−	0.0294537i
$441$	1.24797	−	2.72811i	0.0594273	−	0.129910i
$442$	−0.0942799	+	0.0668142i	−0.00448444	+	0.00317803i
$443$	−4.43342	+	1.61363i	−0.210638	+	0.0766659i	−0.445184	−	0.895439i	$-0.646862\pi$
$443$	−4.43342	+	1.61363i	−0.210638	+	0.0766659i	0.234546	+	0.972105i	$0.424640\pi$
$444$	0.937743	+	15.9820i	0.0445033	+	0.758474i
$445$	5.15376	−	4.32452i	0.244312	−	0.205002i
$446$	14.9520	+	14.7836i	0.707996	+	0.700023i
$447$	25.7956	+	3.30031i	1.22009	+	0.156099i
$448$	−6.29948	−	4.93118i	−0.297623	−	0.232976i
$449$	−33.5906	+	19.3935i	−1.58524	+	0.915237i	−0.591160	+	0.806554i	$0.701330\pi$
$449$	−33.5906	+	19.3935i	−1.58524	+	0.915237i	−0.994077	+	0.108682i	$0.965337\pi$
$450$	16.4867	−	3.12792i	0.777191	−	0.147452i
$451$	0.574635	+	0.331765i	0.0270585	+	0.0156222i
$452$	7.91374	−	0.0896212i	0.372231	−	0.00421543i
$453$	18.3913	+	9.48875i	0.864099	+	0.445820i
$454$	−5.97527	−	1.56486i	−0.280433	−	0.0734426i
$455$	0.971005	+	5.50684i	0.0455214	+	0.258165i
$456$	−0.0356519	+	1.55003i	−0.00166955	+	0.0725869i
$457$	16.1766	+	13.5737i	0.756708	+	0.634953i	0.937268	−	0.348611i	$-0.113347\pi$
$457$	16.1766	+	13.5737i	0.756708	+	0.634953i	−0.180560	+	0.983564i	$0.557791\pi$
$458$	33.3944	−	3.11226i	1.56042	−	0.145426i
$459$	0.0720208	+	0.0289122i	0.00336165	+	0.00134951i
$460$	−1.71517	−	9.12191i	−0.0799701	−	0.425311i
$461$	−24.3520	+	29.0216i	−1.13418	+	1.35167i	−0.206437	+	0.978460i	$0.566187\pi$
$461$	−24.3520	+	29.0216i	−1.13418	+	1.35167i	−0.927747	+	0.373209i	$0.878258\pi$
$462$	2.05368	−	0.668610i	0.0955458	−	0.0311066i
$463$	10.5907	−	1.86743i	0.492192	−	0.0867867i	0.0779570	−	0.996957i	$-0.475160\pi$
$463$	10.5907	−	1.86743i	0.492192	−	0.0867867i	0.414235	+	0.910170i	$0.364049\pi$
$464$	−0.582632	−	25.7205i	−0.0270480	−	1.19404i
$465$	−6.35854	−	9.90097i	−0.294870	−	0.459146i
$466$	2.72456	+	0.222831i	0.126213	+	0.0103224i
$467$	5.84673	−	10.1268i	0.270555	−	0.468614i	−0.698449	−	0.715659i	$-0.746126\pi$
$467$	5.84673	−	10.1268i	0.270555	−	0.468614i	0.969004	+	0.247045i	$0.0794596\pi$
$468$	18.3235	−	27.2344i	0.847004	−	1.25891i
$469$	−5.99278	−	10.3798i	−0.276721	−	0.479295i
$470$	1.74167	+	3.68048i	0.0803374	+	0.169768i
$471$	33.2771	−	13.9263i	1.53333	−	0.641692i
$472$	7.41908	−	10.9882i	0.341491	−	0.505771i
$473$	−5.84178	−	6.96197i	−0.268605	−	0.320112i
$474$	−5.27555	+	8.45366i	−0.242314	+	0.388289i
$475$	0.428133	+	1.17629i	0.0196441	+	0.0539717i
$476$	−0.0194587	−	0.0226637i	−0.000891887	−	0.00103879i
$477$	−15.6636	−	1.25524i	−0.717189	−	0.0574735i
$478$	−9.09482	+	19.7958i	−0.415987	+	0.905438i
$479$	6.03555	−	34.2293i	0.275771	−	1.56398i	−0.460729	−	0.887541i	$-0.652412\pi$
$479$	6.03555	−	34.2293i	0.275771	−	1.56398i	0.736501	−	0.676437i	$-0.236477\pi$
$480$	−4.90576	−	8.73081i	−0.223916	−	0.398505i
$481$	23.7588	+	8.64748i	1.08331	+	0.394291i
$482$	−7.27199	−	26.5375i	−0.331230	−	1.20875i
$483$	5.33417	+	5.77874i	0.242713	+	0.262942i
$484$	−17.8206	−	10.0214i	−0.810028	−	0.455518i
$485$			11.1645i			0.506953i
$486$	−22.0411	−	0.434720i	−0.999806	−	0.0197193i
$487$			8.66789i			0.392779i	0.980526	+	0.196390i	$0.0629218\pi$
$487$			8.66789i			0.392779i	−0.980526	+	0.196390i	$0.937078\pi$
$488$	5.17414	+	2.30657i	0.234222	+	0.104414i
$489$	2.20997	+	2.39416i	0.0999385	+	0.108268i
$490$	−1.39410	+	0.382021i	−0.0629789	+	0.0172579i
$491$	−21.2299	−	7.72705i	−0.958091	−	0.348717i	−0.184806	−	0.982775i	$-0.559166\pi$
$491$	−21.2299	−	7.72705i	−0.958091	−	0.348717i	−0.773285	+	0.634058i	$0.781388\pi$
$492$	0.602275	+	2.53634i	0.0271527	+	0.114347i
$493$	0.0166810	−	0.0946027i	0.000751275	−	0.00426069i
$494$	2.22500	+	1.02224i	0.100107	+	0.0459926i
$495$	2.69504	+	0.215973i	0.121133	+	0.00970725i
$496$	16.6238	−	20.7482i	0.746433	−	0.931623i
$497$	−2.42447	−	6.66117i	−0.108752	−	0.298794i
$498$	5.90008	+	3.68198i	0.264389	+	0.164993i
$499$	21.1356	+	25.1884i	0.946160	+	1.12759i	0.991693	+	0.128626i	$0.0410568\pi$
$499$	21.1356	+	25.1884i	0.946160	+	1.12759i	−0.0455334	+	0.998963i	$0.514499\pi$
$500$	−14.1561	−	11.6078i	−0.633080	−	0.519114i
$501$	−9.18358	+	3.84330i	−0.410292	+	0.171706i
$502$	19.5473	−	9.25016i	0.872439	−	0.412855i
$503$	−14.3475	−	24.8506i	−0.639722	−	1.10803i	−0.985494	−	0.169713i	$-0.945716\pi$
$503$	−14.3475	−	24.8506i	−0.639722	−	1.10803i	0.345771	−	0.938319i	$-0.387617\pi$
$504$	7.44933	+	4.06294i	0.331820	+	0.180978i
$505$	−3.35865	+	5.81735i	−0.149458	+	0.258869i
$506$	−0.461507	+	5.64287i	−0.0205165	+	0.250856i
$507$	−15.8453	−	24.6730i	−0.703717	−	1.09577i
$508$	4.21848	−	25.6172i	0.187165	−	1.13658i
$509$	4.50348	−	0.794084i	0.199613	−	0.0351972i	−0.0729476	−	0.997336i	$-0.523241\pi$
$509$	4.50348	−	0.794084i	0.199613	−	0.0351972i	0.272561	+	0.962139i	$0.412129\pi$
$510$	−0.0115761	−	0.0355567i	−0.000512598	−	0.00157448i
$511$	4.77239	−	5.68752i	0.211118	−	0.251601i
$512$	15.1642	−	16.7942i	0.670171	−	0.742207i
$513$	−0.232490	−	1.62798i	−0.0102647	−	0.0718769i
$514$	0.0897721	+	0.963250i	0.00395968	+	0.0424872i
$515$	5.42672	+	4.55356i	0.239130	+	0.200654i
$516$	4.12991	−	35.4659i	0.181809	−	1.56130i
$517$	−0.431292	−	2.44598i	−0.0189682	−	0.107574i
$518$	−1.65583	+	6.32263i	−0.0727531	+	0.277800i
$519$	14.5256	+	7.49430i	0.637604	+	0.328963i
$520$	−15.7301	+	1.64588i	−0.689811	+	0.0721765i
$521$	−24.1730	−	13.9563i	−1.05904	−	0.611435i	−0.133871	−	0.990999i	$-0.542741\pi$
$521$	−24.1730	−	13.9563i	−1.05904	−	0.611435i	−0.925166	+	0.379564i	$0.876074\pi$
$522$	5.08639	+	26.8095i	0.222625	+	1.17342i
$523$	23.1614	−	13.3723i	1.01278	−	0.584728i	0.100775	−	0.994909i	$-0.467868\pi$
$523$	23.1614	−	13.3723i	1.01278	−	0.584728i	0.912004	+	0.410181i	$0.134534\pi$
$524$	−38.3835	+	22.7441i	−1.67679	+	0.993581i
$525$	6.79535	+	0.869403i	0.296573	+	0.0379439i
$526$	−2.49292	+	2.52131i	−0.108696	+	0.109934i
$527$	0.0760460	−	0.0638102i	0.00331262	−	0.00277962i
$528$	1.47855	+	5.92714i	0.0643456	+	0.257946i
$529$	2.24046	−	0.815463i	0.0974115	−	0.0354549i
$530$	4.37784	+	6.17746i	0.190161	+	0.268332i
$531$	−5.84989	+	12.7880i	−0.253864	+	0.554954i
$532$	−0.209738	+	0.597206i	−0.00909328	+	0.0258922i
$533$	4.05443	+	0.714905i	0.175617	+	0.0309660i
$534$	−14.9525	−	6.03101i	−0.647057	−	0.260987i
$535$	6.86629	−	18.8650i	0.296856	−	0.815604i
$536$	30.4763	−	14.8467i	1.31638	−	0.641279i
$537$	−24.8836	−	7.74604i	−1.07381	−	0.334266i
$538$	24.6851	−	35.6823i	1.06425	−	1.53837i
$539$	0.881725			0.0379786
$540$	6.65245	+	8.28101i	0.286276	+	0.356358i
$541$	21.0202			0.903727			0.451864	−	0.892087i	$-0.350759\pi$
$541$	21.0202			0.903727			0.451864	+	0.892087i	$0.350759\pi$
$542$	5.05390	−	7.30541i	0.217084	−	0.313794i
$543$	1.71998	+	7.62650i	0.0738115	+	0.327284i
$544$	0.0678093	−	0.0504002i	0.00290730	−	0.00216089i
$545$	1.44759	−	3.97722i	0.0620080	−	0.170366i
$546$	10.5550	−	8.25645i	0.451713	−	0.353343i
$547$	40.2324	+	7.09406i	1.72021	+	0.303320i	0.944682	−	0.327988i	$-0.106371\pi$
$547$	40.2324	+	7.09406i	1.72021	+	0.303320i	0.775532	+	0.631309i	$0.217482\pi$
$548$	−40.9501	−	14.3816i	−1.74930	−	0.614351i
$549$	−5.81508	−	1.51273i	−0.248181	−	0.0645619i
$550$	2.85172	+	4.02399i	0.121598	+	0.171584i
$551$	−1.91279	+	0.696198i	−0.0814875	+	0.0296590i
$552$	−17.3639	+	13.9023i	−0.739055	+	0.591722i
$553$	−3.11633	+	2.61491i	−0.132520	+	0.111197i
$554$	22.0329	−	22.2838i	0.936086	−	0.946747i
$555$	−4.95704	+	6.50920i	−0.210415	+	0.276300i
$556$	5.49371	+	9.27132i	0.232985	+	0.393191i
$557$	26.8048	−	15.4757i	1.13575	−	0.655728i	0.190378	−	0.981711i	$-0.439029\pi$
$557$	26.8048	−	15.4757i	1.13575	−	0.655728i	0.945376	+	0.325983i	$0.105695\pi$
$558$	−13.7819	+	24.6020i	−0.583434	+	1.04148i
$559$	−48.8344	−	28.1945i	−2.06547	−	1.19250i
$560$	−0.800957	−	4.00925i	−0.0338466	−	0.169422i
$561$	0.00107811	+	0.0227840i	4.55177e−5	+	0.000961941i
$562$	−9.06608	+	34.6179i	−0.382430	+	1.46027i
$563$	0.337353	+	1.91322i	0.0142177	+	0.0806328i	0.991091	−	0.133186i	$-0.0425208\pi$
$563$	0.337353	+	1.91322i	0.0142177	+	0.0806328i	−0.976873	+	0.213819i	$0.931410\pi$
$564$	5.82367	−	7.82958i	0.245221	−	0.329685i
$565$	3.09838	+	2.59985i	0.130350	+	0.109376i
$566$	1.44800	+	15.5370i	0.0608639	+	0.653067i
$567$	−8.50127	−	2.95438i	−0.357020	−	0.124072i
$568$	19.2757	−	5.51747i	0.808789	−	0.231508i
$569$	−1.38279	+	1.64795i	−0.0579698	+	0.0690857i	−0.794250	−	0.607591i	$-0.792136\pi$
$569$	−1.38279	+	1.64795i	−0.0579698	+	0.0690857i	0.736280	+	0.676677i	$0.236580\pi$
$570$	−0.529852	+	0.589154i	−0.0221931	+	0.0246769i
$571$	30.4775	−	5.37400i	1.27544	−	0.224895i	0.505398	−	0.862886i	$-0.331346\pi$
$571$	30.4775	−	5.37400i	1.27544	−	0.224895i	0.770043	+	0.637991i	$0.220234\pi$
$572$	9.51927	+	1.56757i	0.398021	+	0.0655434i
$573$	40.0099	−	1.89321i	1.67144	−	0.0790901i
$574$	−0.0867509	+	1.06071i	−0.00362091	+	0.0442730i
$575$	−8.97938	+	15.5527i	−0.374466	+	0.648594i
$576$	−12.9429	+	20.2109i	−0.539289	+	0.842121i
$577$	−3.55125	−	6.15094i	−0.147840	−	0.256067i	0.782589	−	0.622539i	$-0.213899\pi$
$577$	−3.55125	−	6.15094i	−0.147840	−	0.256067i	−0.930429	+	0.366472i	$0.880566\pi$
$578$	−21.7310	+	10.2835i	−0.903888	+	0.427737i
$579$	−22.1162	−	16.8425i	−0.919120	−	0.699950i
$580$	8.33681	−	10.1671i	0.346167	−	0.422164i
$581$	1.82503	+	2.17499i	0.0757151	+	0.0902337i
$582$	23.6164	−	12.5748i	0.978930	−	0.521242i
$583$	−1.57960	−	4.33991i	−0.0654203	−	0.179741i
$584$	15.0991	+	14.5947i	0.624807	+	0.603933i
$585$	16.1716	−	4.45996i	0.668615	−	0.184397i
$586$	24.1330	+	11.0875i	0.996927	+	0.458020i
$587$	8.38241	−	47.5390i	0.345979	−	1.96215i	0.0873000	−	0.996182i	$-0.472176\pi$
$587$	8.38241	−	47.5390i	0.345979	−	1.96215i	0.258679	−	0.965963i	$-0.416713\pi$
$588$	2.37829	+	2.51867i	0.0980792	+	0.103868i
$589$	−1.97668	−	0.719453i	−0.0814478	−	0.0296446i
$590$	6.53486	−	1.79073i	0.269036	−	0.0737231i
$591$	29.6366	−	6.68386i	1.21909	−	0.274937i
$592$	−17.5101	−	5.92763i	−0.719660	−	0.243624i
$593$		−	20.5858i		−	0.845359i	−0.906279	−	0.422680i	$-0.861090\pi$
$593$		−	20.5858i		−	0.845359i	0.906279	−	0.422680i	$-0.138910\pi$
$594$	−2.57863	−	5.94410i	−0.105802	−	0.243890i
$595$		−	0.0152659i		−	0.000625841i
$596$	−14.7190	+	26.1742i	−0.602915	+	1.07214i
$597$	−5.17770	+	16.6330i	−0.211909	+	0.680744i
$598$	9.28402	+	33.8799i	0.379652	+	1.38545i
$599$	3.51192	+	1.27824i	0.143493	+	0.0522273i	0.412768	−	0.910836i	$-0.364562\pi$
$599$	3.51192	+	1.27824i	0.143493	+	0.0522273i	−0.269275	+	0.963063i	$0.586784\pi$
$600$	−3.80265	+	19.0000i	−0.155243	+	0.775673i
$601$	−4.33097	+	24.5621i	−0.176664	+	1.00191i	0.759542	+	0.650458i	$0.225423\pi$
$601$	−4.33097	+	24.5621i	−0.176664	+	1.00191i	−0.936206	+	0.351452i	$0.885688\pi$
$602$	6.08549	−	13.2457i	0.248026	−	0.539853i
$603$	−29.3026	+	20.8384i	−1.19330	+	0.848604i
$604$	−18.1306	+	15.5666i	−0.737722	+	0.633395i
$605$	−3.57365	−	9.81853i	−0.145290	−	0.399180i
$606$	16.0884	+	0.552387i	0.653548	+	0.0224392i
$607$	−8.38769	−	9.99606i	−0.340446	−	0.405728i	0.568472	−	0.822703i	$-0.307535\pi$
$607$	−8.38769	−	9.99606i	−0.340446	−	0.405728i	−0.908918	+	0.416975i	$0.863090\pi$
$608$	−1.64333	−	0.710379i	−0.0666457	−	0.0288097i
$609$	−1.41376	+	11.0501i	−0.0572884	+	0.447772i
$610$	1.23837	+	2.61692i	0.0501403	+	0.105956i
$611$	−7.70527	−	13.3459i	−0.311722	−	0.539918i
$612$	−0.0621751	+	0.0645353i	−0.00251328	+	0.00260869i
$613$	−23.0194	+	39.8707i	−0.929744	+	1.61036i	−0.145995	+	0.989285i	$0.546638\pi$
$613$	−23.0194	+	39.8707i	−0.929744	+	1.61036i	−0.783749	+	0.621078i	$0.786695\pi$
$614$	−33.8977	−	2.77236i	−1.36800	−	0.111883i
$615$	−0.610852	+	1.18397i	−0.0246319	+	0.0477422i
$616$	−0.175127	+	2.48774i	−0.00705606	+	0.100234i
$617$	−25.8760	+	4.56263i	−1.04173	+	0.183685i	−0.668237	−	0.743949i	$-0.732951\pi$
$617$	−25.8760	+	4.56263i	−1.04173	+	0.183685i	−0.373491	+	0.927634i	$0.621839\pi$
$618$	3.51997	−	16.6080i	0.141594	−	0.668071i
$619$	15.4550	−	18.4185i	0.621188	−	0.740303i	−0.360087	−	0.932919i	$-0.617253\pi$
$619$	15.4550	−	18.4185i	0.621188	−	0.740303i	0.981274	+	0.192616i	$0.0616973\pi$
$620$	13.3533	−	2.51078i	0.536280	−	0.100835i
$621$	15.7477	−	17.5680i	0.631934	−	0.704980i
$622$	−36.9044	+	3.43938i	−1.47973	+	0.137907i
$623$	−5.04224	−	4.23094i	−0.202013	−	0.169509i
$624$	21.1987	+	31.4203i	0.848627	+	1.25782i
$625$	1.80952	+	10.2623i	0.0723806	+	0.410491i
$626$	−6.93983	−	1.81747i	−0.277371	−	0.0726407i
$627$	0.406686	−	0.261179i	0.0162415	−	0.0104305i
$628$	0.471695	+	41.6516i	0.0188227	+	1.66208i
$629$	−0.0597778	−	0.0345127i	−0.00238350	−	0.00137611i
$630$	1.53586	+	4.05539i	0.0611900	+	0.161571i
$631$	7.95830	−	4.59473i	0.316815	−	0.182913i	−0.333157	−	0.942871i	$-0.608114\pi$
$631$	7.95830	−	4.59473i	0.316815	−	0.182913i	0.649972	+	0.759958i	$0.274781\pi$
$632$	−6.75887	−	9.31193i	−0.268854	−	0.370409i
$633$	−8.41577	−	20.1096i	−0.334497	−	0.799283i
$634$	−2.78492	−	2.75356i	−0.110603	−	0.109358i
$635$	10.1641	−	8.52866i	0.403348	−	0.338449i
$636$	8.13640	−	16.2183i	0.322629	−	0.643097i
$637$	5.14086	−	1.87112i	0.203688	−	0.0741365i
$638$	−6.54352	+	4.63726i	−0.259060	+	0.183591i
$639$	−19.2074	+	9.12786i	−0.759834	+	0.361092i
$640$	11.4710	−	1.46355i	0.453429	−	0.0578517i
$641$	16.8296	+	2.96750i	0.664727	+	0.117209i	0.495824	−	0.868423i	$-0.334866\pi$
$641$	16.8296	+	2.96750i	0.664727	+	0.117209i	0.168904	+	0.985633i	$0.445977\pi$
$642$	−47.6390	+	6.72367i	−1.88016	+	0.265362i
$643$	−13.6386	+	37.4716i	−0.537852	+	1.47774i	0.311673	+	0.950190i	$0.399111\pi$
$643$	−13.6386	+	37.4716i	−0.537852	+	1.47774i	−0.849525	+	0.527548i	$0.823111\pi$
$644$	−8.49755	+	3.20229i	−0.334850	+	0.126188i
$645$	13.4085	−	12.3769i	0.527958	−	0.487341i
$646$	−0.00549747	−	0.00380316i	−0.000216295	−	0.000149633i
$647$	24.1632			0.949952			0.474976	−	0.879999i	$-0.342457\pi$
$647$	24.1632			0.949952			0.474976	+	0.879999i	$0.342457\pi$
$648$	10.0241	−	23.3991i	0.393785	−	0.919203i
$649$	−4.13310			−0.162238
$650$	25.1662	+	17.4101i	0.987101	+	0.682879i
$651$	−8.45930	+	7.80852i	−0.331546	+	0.306040i
$652$	−3.52058	+	1.32672i	−0.137876	+	0.0519585i
$653$	−1.56669	+	4.30445i	−0.0613094	+	0.168446i	−0.966565	−	0.256421i	$-0.917457\pi$
$653$	−1.56669	+	4.30445i	−0.0613094	+	0.168446i	0.905256	+	0.424867i	$0.139679\pi$
$654$	−10.0435	+	1.41752i	−0.392733	+	0.0554295i
$655$	−22.4550	−	3.95942i	−0.877389	−	0.154707i
$656$	−2.97549	−	0.455439i	−0.116174	−	0.0177819i
$657$	−18.3382	−	12.6421i	−0.715442	−	0.493214i
$658$	3.25024	−	2.30338i	0.126707	−	0.0897949i
$659$	8.36618	−	3.04504i	0.325900	−	0.118618i	−0.173889	−	0.984765i	$-0.555633\pi$
$659$	8.36618	−	3.04504i	0.325900	−	0.118618i	0.499789	+	0.866147i	$0.333411\pi$
$660$	−1.39992	+	2.79047i	−0.0544920	+	0.108619i
$661$	−33.1489	+	27.8152i	−1.28934	+	1.08189i	−0.297460	+	0.954734i	$0.596139\pi$
$661$	−33.1489	+	27.8152i	−1.28934	+	1.08189i	−0.991883	+	0.127153i	$0.959416\pi$
$662$	27.5965	+	27.2858i	1.07257	+	1.06049i
$663$	0.0546361	+	0.130553i	0.00212189	+	0.00507027i
$664$	−6.49910	+	4.71724i	−0.252214	+	0.183064i
$665$	−0.280144	+	0.161741i	−0.0108635	+	0.00627206i
$666$	19.3522	+	3.15424i	0.749883	+	0.122224i
$667$	−25.2907	−	14.6016i	−0.979260	−	0.565376i
$668$	−0.130175	−	11.4947i	−0.00503662	−	0.444744i
$669$	21.6685	−	13.9158i	0.837752	−	0.538016i
$670$	16.7598	+	4.38922i	0.647488	+	0.169570i
$671$	−0.306660	−	1.73915i	−0.0118385	−	0.0671393i
$672$	−7.57867	+	6.20997i	−0.292354	+	0.239555i
$673$	−36.5732	−	30.6886i	−1.40979	−	1.18296i	−0.956549	−	0.291571i	$-0.905822\pi$
$673$	−36.5732	−	30.6886i	−1.40979	−	1.18296i	−0.453244	−	0.891386i	$-0.649733\pi$
$674$	−17.7479	+	1.65405i	−0.683623	+	0.0637116i
$675$	0.671587	−	20.5412i	0.0258494	−	0.790633i
$676$	33.2761	−	6.25680i	1.27985	−	0.240646i
$677$	11.4819	−	13.6836i	0.441285	−	0.525902i	−0.498858	−	0.866684i	$-0.666247\pi$
$677$	11.4819	−	13.6836i	0.441285	−	0.525902i	0.940143	+	0.340781i	$0.110692\pi$
$678$	2.00972	−	9.48229i	0.0771829	−	0.364165i
$679$	10.7570	−	1.89674i	0.412814	−	0.0727902i
$680$	0.0430719	+	0.00303209i	0.00165173	+	0.000116275i
$681$	−3.46860	+	6.72293i	−0.132917	+	0.257623i
$682$	−8.26041	−	0.675585i	−0.316307	−	0.0258695i
$683$	15.7615	−	27.2998i	0.603098	−	1.04460i	−0.389251	−	0.921132i	$-0.627266\pi$
$683$	15.7615	−	27.2998i	0.603098	−	1.04460i	0.992349	−	0.123465i	$-0.0394007\pi$
$684$	1.84303	+	0.457226i	0.0704699	+	0.0174825i
$685$	−11.0905	−	19.2093i	−0.423747	−	0.733951i
$686$	0.604920	+	1.27831i	0.0230960	+	0.0488060i
$687$	5.21292	−	40.7448i	0.198885	−	1.55451i
$688$	36.1632	+	19.8007i	1.37871	+	0.754894i
$689$	−18.4196	−	21.9516i	−0.701730	−	0.836289i
$690$	−11.3611	−	0.390077i	−0.432509	−	0.0148500i
$691$	10.5392	+	28.9562i	0.400930	+	1.10155i	0.961826	+	0.273661i	$0.0882345\pi$
$691$	10.5392	+	28.9562i	0.400930	+	1.10155i	−0.560896	+	0.827886i	$0.689543\pi$
$692$	−14.3197	+	12.2946i	−0.544352	+	0.467372i
$693$	−0.249773	−	2.63336i	−0.00948808	−	0.100033i
$694$	6.81720	−	14.8383i	0.258777	−	0.563254i
$695$	−0.956376	+	5.42388i	−0.0362774	+	0.205739i
$696$	−30.8964	−	6.18359i	−1.17113	−	0.234388i
$697$	−0.0105617	−	0.00384416i	−0.000400054	−	0.000145608i
$698$	−4.17452	−	15.2340i	−0.158008	−	0.576615i
$699$	0.995110	−	3.19673i	0.0376385	−	0.120911i
$700$	−3.87744	+	6.89509i	−0.146554	+	0.260610i
$701$		−	43.3931i		−	1.63894i	−0.573126	−	0.819468i	$-0.694269\pi$
$701$		−	43.3931i		−	1.63894i	0.573126	−	0.819468i	$-0.305731\pi$
$702$	−27.6487	−	29.1847i	−1.04353	−	1.10151i
$703$			1.46264i			0.0551645i
$704$	−6.98423	−	0.988221i	−0.263228	−	0.0372450i
$705$	4.86470	−	1.09712i	0.183215	−	0.0413200i
$706$	43.1294	−	11.8186i	1.62320	−	0.444800i
$707$	6.17560	+	2.24774i	0.232258	+	0.0845348i
$708$	−11.1483	−	11.8063i	−0.418979	−	0.443709i
$709$	−5.46624	+	31.0006i	−0.205289	+	1.16425i	0.691695	+	0.722190i	$0.256864\pi$
$709$	−5.46624	+	31.0006i	−0.205289	+	1.16425i	−0.896984	+	0.442062i	$0.854247\pi$
$710$	9.31095	+	4.27775i	0.349434	+	0.160541i
$711$	8.69247	+	8.56648i	0.325993	+	0.321268i
$712$	12.9388	−	13.3860i	0.484904	−	0.501663i
$713$	−10.3217	−	28.3587i	−0.386552	−	1.06204i
$714$	−0.0322921	+	0.0171943i	−0.00120850	+	0.000643480i
$715$	3.16922	+	3.77692i	0.118522	+	0.141249i
$716$	19.0812	−	23.2702i	0.713098	−	0.869650i
$717$	21.2267	+	16.1651i	0.792726	+	0.603696i
$718$	−14.1553	+	6.69855i	−0.528270	+	0.249988i
$719$	−5.59834	−	9.69662i	−0.208783	−	0.361623i	0.742548	−	0.669792i	$-0.233617\pi$
$719$	−5.59834	−	9.69662i	−0.208783	−	0.361623i	−0.951331	+	0.308170i	$0.900284\pi$
$720$	−11.7471	+	3.52786i	−0.437789	+	0.131476i
$721$	3.46540	−	6.00224i	0.129058	−	0.223535i
$722$	2.17873	−	26.6395i	0.0810841	−	0.991418i
$723$	−33.6622	+	1.59285i	−1.25191	+	0.0592386i
$724$	−8.90753	−	1.46683i	−0.331046	−	0.0545144i
$725$	−25.0530	+	4.41751i	−0.930444	+	0.164062i
$726$	−16.7442	+	18.6182i	−0.621434	+	0.690986i
$727$	−31.3122	+	37.3164i	−1.16130	+	1.38399i	−0.252066	+	0.967710i	$0.581110\pi$
$727$	−31.3122	+	37.3164i	−1.16130	+	1.38399i	−0.909237	+	0.416278i	$0.863334\pi$
$728$	4.25820	+	14.8763i	0.157819	+	0.551353i
$729$	−6.41532	+	26.2268i	−0.237604	+	0.971362i
$730$	0.995884	+	10.6858i	0.0368593	+	0.395499i
$731$	0.117929	+	0.0989541i	0.00436176	+	0.00365995i
$732$	4.14079	−	5.56704i	0.153048	−	0.205764i
$733$	−6.48970	−	36.8049i	−0.239703	−	1.35942i	−0.832480	−	0.554055i	$-0.813080\pi$
$733$	−6.48970	−	36.8049i	−0.239703	−	1.35942i	0.592778	−	0.805366i	$-0.298031\pi$
$734$	−10.6329	+	40.6006i	−0.392467	+	1.49860i
$735$	0.0836773	+	1.76838i	0.00308648	+	0.0652277i
$736$	−7.34731	−	24.6114i	−0.270825	−	0.907188i
$737$	−9.15213	−	5.28398i	−0.337123	−	0.194638i
$738$	3.19248	−	0.0413843i	0.117517	−	0.00152338i
$739$	−10.5452	+	6.08825i	−0.387910	+	0.223960i	−0.681254	−	0.732047i	$-0.738565\pi$
$739$	−10.5452	+	6.08825i	−0.387910	+	0.223960i	0.293344	+	0.956007i	$0.405232\pi$
$740$	−4.81611	−	8.12779i	−0.177044	−	0.298783i
$741$	1.81691	−	2.38583i	0.0667460	−	0.0876457i
$742$	5.20821	−	5.26753i	0.191199	−	0.193377i
$743$	−16.5647	+	13.8994i	−0.607698	+	0.509919i	−0.893910	−	0.448247i	$-0.852048\pi$
$743$	−16.5647	+	13.8994i	−0.607698	+	0.509919i	0.286211	+	0.958166i	$0.407604\pi$
$744$	−20.3511	−	25.4184i	−0.746109	−	0.931883i
$745$	−14.4211	+	5.24884i	−0.528347	+	0.192302i
$746$	25.4700	+	35.9401i	0.932523	+	1.31586i
$747$	5.97882	−	6.06676i	0.218754	−	0.221971i
$748$	−0.0248502	−	0.00872732i	−0.000908612	−	0.000319102i
$749$	−19.3429	−	3.41067i	−0.706773	−	0.124623i
$750$	−17.6599	+	13.8141i	−0.644849	+	0.504420i
$751$	4.00293	−	10.9979i	0.146069	−	0.401321i	−0.844984	−	0.534792i	$-0.820390\pi$
$751$	4.00293	−	10.9979i	0.146069	−	0.401321i	0.991053	+	0.133471i	$0.0426123\pi$
$752$	5.85329	+	9.62786i	0.213448	+	0.351092i
$753$	−5.82691	−	25.8368i	−0.212344	−	0.941546i
$754$	−28.3109	+	40.9234i	−1.03102	+	1.49034i
$755$	−12.2124			−0.444456
$756$	6.84854	−	7.81649i	0.249079	−	0.284283i
$757$	32.2762			1.17310			0.586549	−	0.809914i	$-0.300486\pi$
$757$	32.2762			1.17310			0.586549	+	0.809914i	$0.300486\pi$
$758$	−0.610719	+	0.882794i	−0.0221823	+	0.0320645i
$759$	6.62078	+	2.06099i	0.240319	+	0.0748091i
$760$	−0.400702	−	0.822536i	−0.0145350	−	0.0298365i
$761$	15.0556	−	41.3650i	0.545766	−	1.49948i	−0.293609	−	0.955926i	$-0.594856\pi$
$761$	15.0556	−	41.3650i	0.545766	−	1.49948i	0.839375	−	0.543553i	$-0.182921\pi$
$762$	−29.4888	−	11.8941i	−1.06826	−	0.430880i
$763$	−4.07798	−	0.719057i	−0.147633	−	0.0260316i
$764$	−15.3257	+	43.6382i	−0.554463	+	1.57878i
$765$	−0.0455931	+	0.00432448i	−0.00164842	+	0.000156352i
$766$	8.20211	+	11.5738i	0.296354	+	0.418178i
$767$	−24.0979	+	8.77092i	−0.870124	+	0.316699i
$768$	−16.0158	−	22.6162i	−0.577921	−	0.816093i
$769$	−19.8705	+	16.6733i	−0.716547	+	0.601255i	−0.926428	−	0.376473i	$-0.877137\pi$
$769$	−19.8705	+	16.6733i	−0.716547	+	0.601255i	0.209881	+	0.977727i	$0.432692\pi$
$770$	−0.896109	+	0.906315i	−0.0322935	+	0.0326613i
$771$	1.17527	+	0.150365i	0.0423263	+	0.00541526i
$772$	27.6157	−	16.3637i	0.993911	−	0.588941i
$773$	18.3567	−	10.5982i	0.660244	−	0.381192i	−0.132126	−	0.991233i	$-0.542180\pi$
$773$	18.3567	−	10.5982i	0.660244	−	0.381192i	0.792370	+	0.610041i	$0.208847\pi$
$774$	−41.2833	−	14.4227i	−1.48390	−	0.518413i
$775$	−22.7671	−	13.1446i	−0.817820	−	0.472168i
$776$	3.21502	+	30.7269i	0.115413	+	1.10303i
$777$	7.11375	+	3.67024i	0.255204	+	0.131669i
$778$	−0.558541	+	2.13273i	−0.0200247	+	0.0764622i
$779$	0.0413569	+	0.234547i	0.00148177	+	0.00840351i
$780$	−2.24051	+	19.2405i	−0.0802231	+	0.688921i
$781$	−4.78797	−	4.01759i	−0.171327	−	0.143761i
$782$	−0.00889939	−	0.0954901i	−0.000318242	−	0.00341472i
$783$	33.4026	+	1.09208i	1.19371	+	0.0390279i
$784$	−3.72682	+	1.45285i	−0.133101	+	0.0518876i
$785$	−13.6835	+	16.3074i	−0.488386	+	0.582035i
$786$	16.9161	+	51.9589i	0.603378	+	1.85331i
$787$	31.0900	−	5.48200i	1.10824	−	0.195412i	0.410567	−	0.911831i	$-0.365331\pi$
$787$	31.0900	−	5.48200i	1.10824	−	0.195412i	0.697671	+	0.716418i	$0.254220\pi$
$788$	−5.70012	+	34.6147i	−0.203058	+	1.23310i
$789$	2.34658	+	3.65390i	0.0835406	+	0.130082i
$790$	0.479332	−	5.86081i	0.0170539	−	0.208518i
$791$	1.97856	−	3.42697i	0.0703495	−	0.121849i
$792$	7.47948	−	0.181687i	0.265772	−	0.00645597i
$793$	−5.47865	−	9.48930i	−0.194553	−	0.336975i
$794$	−26.8758	+	12.7182i	−0.953787	+	0.451350i
$795$	8.55418	−	3.57989i	0.303386	−	0.126966i
$796$	−15.5546	−	12.7545i	−0.551317	−	0.452071i
$797$	14.6599	+	17.4710i	0.519281	+	0.618855i	0.960411	−	0.278588i	$-0.0898664\pi$
$797$	14.6599	+	17.4710i	0.519281	+	0.618855i	−0.441129	+	0.897444i	$0.645422\pi$
$798$	0.657665	+	0.410420i	0.0232811	+	0.0145287i
$799$	0.0143893	+	0.0395344i	0.000509058	+	0.00139863i
$800$	−18.6840	−	12.3095i	−0.660579	−	0.435206i
$801$	−11.2078	+	16.2577i	−0.396006	+	0.574436i
$802$	16.7514	+	7.69615i	0.591513	+	0.271760i
$803$	1.13677	−	6.44694i	0.0401157	−	0.227507i
$804$	−9.59236	−	40.3959i	−0.338296	−	1.42465i
$805$	−4.36100	−	1.58727i	−0.153705	−	0.0559441i
$806$	−49.5957	+	13.5906i	−1.74693	+	0.478707i
$807$	−36.0437	−	39.0477i	−1.26880	−	1.37454i
$808$	−7.56845	+	16.9777i	−0.266257	+	0.597273i
$809$		−	7.37325i		−	0.259230i	−0.991564	−	0.129615i	$-0.958626\pi$
$809$		−	7.37325i		−	0.259230i	0.991564	−	0.129615i	$-0.0413741\pi$
$810$	11.6767	−	5.73578i	0.410279	−	0.201535i
$811$		−	24.5966i		−	0.863704i	−0.901944	−	0.431852i	$-0.857860\pi$
$811$		−	24.5966i		−	0.863704i	0.901944	−	0.431852i	$-0.142140\pi$
$812$	−11.2123	−	6.30521i	−0.393474	−	0.221269i
$813$	−7.37941	−	7.99443i	−0.258807	−	0.280377i
$814$	1.52302	+	5.55793i	0.0533820	+	0.194805i
$815$	−1.80678	−	0.657616i	−0.0632889	−	0.0230353i
$816$	−0.0420989	−	0.0945256i	−0.00147376	−	0.00330906i
$817$	0.566455	−	3.21252i	0.0198177	−	0.112392i
$818$	−12.4740	+	27.1510i	−0.436145	+	0.949312i
$819$	−7.04457	−	14.8236i	−0.246157	−	0.517980i
$820$	−1.00212	−	1.16718i	−0.0349956	−	0.0407597i
$821$	−1.24816	−	3.42929i	−0.0435611	−	0.119683i	0.916005	−	0.401168i	$-0.131395\pi$
$821$	−1.24816	−	3.42929i	−0.0435611	−	0.119683i	−0.959566	+	0.281484i	$0.909173\pi$
$822$	−28.1423	+	45.0958i	−0.981574	+	1.57290i
$823$	−14.7791	−	17.6130i	−0.515166	−	0.613951i	0.444265	−	0.895896i	$-0.353465\pi$
$823$	−14.7791	−	17.6130i	−0.515166	−	0.613951i	−0.959431	+	0.281945i	$0.909020\pi$
$824$	16.2467	+	10.9696i	0.565981	+	0.382143i
$825$	5.57219	−	2.33194i	0.193999	−	0.0811878i
$826$	−2.83557	−	5.99209i	−0.0986622	−	0.208492i
$827$	15.4297	+	26.7251i	0.536544	+	0.929321i	0.999087	+	0.0427245i	$0.0136038\pi$
$827$	15.4297	+	26.7251i	0.536544	+	0.929321i	−0.462543	+	0.886597i	$0.653063\pi$
$828$	11.9711	+	24.4716i	0.416025	+	0.850447i
$829$	3.73399	−	6.46746i	0.129687	−	0.224624i	−0.793868	−	0.608090i	$-0.791936\pi$
$829$	3.73399	−	6.46746i	0.129687	−	0.224624i	0.923555	+	0.383465i	$0.125269\pi$
$830$	−4.09045	−	0.334541i	−0.141982	−	0.0116121i
$831$	−20.7395	−	32.2938i	−0.719447	−	1.12026i
$832$	−42.8184	+	9.05956i	−1.48446	+	0.314084i
$833$	−0.0147087	+	0.00259353i	−0.000509625	+	8.98606e-5i
$834$	12.5504	−	4.08599i	0.434584	−	0.141486i
$835$	3.77628	−	4.50040i	0.130684	−	0.155743i
$836$	0.103131	+	0.548490i	0.00356686	+	0.0189699i
$837$	25.7172	+	23.0525i	0.888917	+	0.796812i
$838$	10.6331	−	0.990969i	0.367313	−	0.0342325i
$839$	18.9542	+	15.9045i	0.654372	+	0.549083i	0.908394	−	0.418115i	$-0.137309\pi$
$839$	18.9542	+	15.9045i	0.654372	+	0.549083i	−0.254022	+	0.967198i	$0.581754\pi$
$840$	−5.00601	−	0.115142i	−0.172724	−	0.00397278i
$841$	−2.14763	−	12.1798i	−0.0740562	−	0.419994i
$842$	8.44250	+	2.21100i	0.290948	+	0.0761962i
$843$	38.9495	+	20.0955i	1.34149	+	0.692125i
$844$	25.1703	−	0.285048i	0.866398	−	0.00981175i
$845$	14.9857	+	8.65201i	0.515525	+	0.297638i
$846$	−7.79997	−	9.05465i	−0.268169	−	0.311305i
$847$	−8.85300	+	5.11128i	−0.304193	+	0.175626i
$848$	13.8276	+	15.7409i	0.474841	+	0.540545i
$849$	18.9568	+	2.42534i	0.650594	+	0.0832376i
$850$	−0.0594078	−	0.0587388i	−0.00203767	−	0.00201473i
$851$	−16.0746	+	13.4882i	−0.551031	+	0.462370i
$852$	−1.43834	−	24.5137i	−0.0492766	−	0.839825i
$853$	−26.1594	+	9.52125i	−0.895682	+	0.326001i	−0.748521	−	0.663111i	$-0.769236\pi$
$853$	−26.1594	+	9.52125i	−0.895682	+	0.326001i	−0.147161	+	0.989113i	$0.547013\pi$
$854$	2.31100	−	1.63776i	0.0790809	−	0.0560430i
$855$	0.562414	+	0.790860i	0.0192342	+	0.0270468i
$856$	13.4649	−	53.8974i	0.460220	−	1.84218i
$857$	9.90846	+	1.74713i	0.338467	+	0.0596808i	0.340298	−	0.940318i	$-0.389472\pi$
$857$	9.90846	+	1.74713i	0.338467	+	0.0596808i	−0.00183176	+	0.999998i	$0.500583\pi$
$858$	4.41982	−	10.9579i	0.150890	−	0.374097i
$859$	17.6714	−	48.5517i	0.602939	−	1.65656i	−0.142346	−	0.989817i	$-0.545465\pi$
$859$	17.6714	−	48.5517i	0.602939	−	1.65656i	0.745286	−	0.666745i	$-0.232313\pi$
$860$	7.43030	+	19.7169i	0.253371	+	0.672342i
$861$	1.24453	+	0.387410i	0.0424134	+	0.0132029i
$862$	−10.2018	−	7.05760i	−0.347473	−	0.240383i
$863$	−10.1664			−0.346068			−0.173034	−	0.984916i	$-0.555357\pi$
$863$	−10.1664			−0.346068			−0.173034	+	0.984916i	$0.555357\pi$
$864$	20.6935	+	20.8753i	0.704008	+	0.710192i
$865$	−9.64549			−0.327957
$866$	−2.49154	−	1.72365i	−0.0846658	−	0.0585720i
$867$	6.47784	+	28.7231i	0.219999	+	0.975487i
$868$	−4.68772	−	12.4393i	−0.159112	−	0.422217i
$869$	−1.22680	+	3.37061i	−0.0416164	+	0.114340i
$870$	−9.92143	−	12.6835i	−0.336368	−	0.430012i
$871$	−64.5744	−	11.3862i	−2.18802	−	0.385807i
$872$	2.83874	−	11.3630i	0.0961319	−	0.384799i
$873$	−8.71200	−	31.5894i	−0.294856	−	1.06914i
$874$	−1.65805	+	1.17502i	−0.0560843	+	0.0397458i
$875$	−8.60133	+	3.13063i	−0.290778	+	0.105835i
$876$	21.4821	−	14.1422i	0.725813	−	0.477822i
$877$	−17.9177	+	15.0347i	−0.605036	+	0.507686i	−0.893060	−	0.449937i	$-0.851446\pi$
$877$	−17.9177	+	15.0347i	−0.605036	+	0.507686i	0.288024	+	0.957623i	$0.407002\pi$
$878$	−17.0793	−	16.8869i	−0.576397	−	0.569907i
$879$	19.7068	−	25.8775i	0.664695	−	0.872826i
$880$	−2.37913	−	2.70833i	−0.0802006	−	0.0912979i
$881$	−10.4724	+	6.04623i	−0.352823	+	0.203703i	−0.665928	−	0.746016i	$-0.731964\pi$
$881$	−10.4724	+	6.04623i	−0.352823	+	0.203703i	0.313105	+	0.949719i	$0.398631\pi$
$882$	3.64643	−	2.16877i	0.122782	−	0.0730262i
$883$	−1.99294	−	1.15062i	−0.0670677	−	0.0387215i	0.466091	−	0.884737i	$-0.345662\pi$
$883$	−1.99294	−	1.15062i	−0.0670677	−	0.0387215i	−0.533159	+	0.846015i	$0.678995\pi$
$884$	−0.163408	+	0.00185056i	−0.00549601	+	6.22411e-5i
$885$	−0.392239	−	8.28931i	−0.0131850	−	0.278642i
$886$	−6.45450	−	1.69037i	−0.216843	−	0.0567890i
$887$	−0.0778886	−	0.441728i	−0.00261524	−	0.0148318i	0.983472	−	0.181059i	$-0.0579525\pi$
$887$	−0.0778886	−	0.441728i	−0.00261524	−	0.0148318i	−0.986087	+	0.166227i	$0.946841\pi$
$888$	−11.7683	+	19.3421i	−0.394919	+	0.649078i
$889$	−9.94412	−	8.34411i	−0.333515	−	0.279852i
$890$	9.47343	−	0.882895i	0.317550	−	0.0295947i
$891$	−7.79402	+	1.49194i	−0.261109	+	0.0499819i
$892$	5.49489	+	29.2239i	0.183983	+	0.978489i
$893$	0.573040	−	0.682923i	0.0191761	−	0.0228531i
$894$	27.3457	+	24.5932i	0.914576	+	0.822519i
$895$	15.1457	−	2.67060i	0.506265	−	0.0892682i
$896$	−3.35893	−	10.8036i	−0.112214	−	0.360923i
$897$	42.9759	−	2.03356i	1.43492	−	0.0678986i
$898$	−54.6706	−	4.47129i	−1.82438	−	0.149209i
$899$	21.3748	−	37.0222i	0.712889	−	1.23476i
$900$	21.6912	+	9.62714i	0.723041	+	0.320905i
$901$	0.0391159	+	0.0677507i	0.00130314	+	0.00225710i
$902$	0.401383	+	0.848197i	0.0133646	+	0.0282419i
$903$	−14.2031	−	10.8163i	−0.472650	−	0.359944i
$904$	9.27602	+	6.26306i	0.308516	+	0.208306i
$905$	−2.96555	−	3.53421i	−0.0985783	−	0.117481i
$906$	13.7551	+	25.8331i	0.456983	+	0.858248i
$907$	11.0631	+	30.3957i	0.367345	+	1.00927i	0.976367	+	0.216119i	$0.0693398\pi$
$907$	11.0631	+	30.3957i	0.367345	+	1.00927i	−0.609022	+	0.793153i	$0.708438\pi$
$908$	−5.69035	−	6.62761i	−0.188841	−	0.219945i
$909$	4.96367	−	19.0808i	0.164635	−	0.632869i
$910$	−3.30143	+	7.18588i	−0.109441	+	0.238210i
$911$	−6.92343	+	39.2647i	−0.229384	+	1.30090i	0.624742	+	0.780831i	$0.285204\pi$
$911$	−6.92343	+	39.2647i	−0.229384	+	1.30090i	−0.854125	+	0.520067i	$0.825907\pi$
$912$	−1.28860	+	1.77405i	−0.0426698	+	0.0587447i
$913$	2.35246	+	0.856225i	0.0778550	+	0.0283369i
$914$	7.89257	+	28.8021i	0.261063	+	0.952690i
$915$	3.45893	−	0.780083i	0.114349	−	0.0257888i
$916$	41.3428	+	23.2491i	1.36601	+	0.768171i
$917$			22.3080i			0.736675i
$918$	0.0605000	+	0.0915728i	0.00199680	+	0.00302235i
$919$		−	49.1239i		−	1.62045i	−0.586121	−	0.810224i	$-0.699346\pi$
$919$		−	49.1239i		−	1.62045i	0.586121	−	0.810224i	$-0.300654\pi$
$920$	5.34458	−	11.9891i	0.176206	−	0.395268i
$921$	−12.3807	+	39.7722i	−0.407959	+	1.31054i
$922$	−51.6725	+	14.1597i	−1.70174	+	0.466323i
$923$	−36.4419	−	13.2638i	−1.19950	−	0.436582i
$924$	2.92645	+	0.874749i	0.0962730	+	0.0287771i
$925$	−3.17420	+	18.0018i	−0.104367	+	0.591895i
$926$	13.8198	+	6.34927i	0.454147	+	0.208650i
$927$	−18.9079	−	8.64944i	−0.621018	−	0.284085i
$928$	20.0168	−	30.3825i	0.657083	−	0.997354i
$929$	−8.24204	−	22.6448i	−0.270413	−	0.742953i	−0.998356	−	0.0573155i	$-0.981746\pi$
$929$	−8.24204	−	22.6448i	−0.270413	−	0.742953i	0.727943	−	0.685637i	$-0.240476\pi$
$930$	0.571021	−	16.6311i	0.0187245	−	0.545356i
$931$	0.203431	+	0.242440i	0.00666719	+	0.00794565i
$932$	2.98946	+	2.45130i	0.0979229	+	0.0802951i
$933$	−5.76084	+	45.0274i	−0.188601	+	1.47413i
$934$	14.9479	−	7.07361i	0.489109	−	0.231456i
$935$	−0.00673016	−	0.0116570i	−0.000220100	−	0.000381224i
$936$	43.2233	−	16.9316i	1.41280	−	0.553428i
$937$	6.52740	−	11.3058i	0.213241	−	0.369344i	−0.739486	−	0.673172i	$-0.764931\pi$
$937$	6.52740	−	11.3058i	0.213241	−	0.369344i	0.952727	+	0.303828i	$0.0982648\pi$
$938$	1.38167	−	16.8937i	0.0451131	−	0.551600i
$939$	−4.02853	+	7.80818i	−0.131466	+	0.254810i
$940$	−0.935647	+	5.68183i	−0.0305174	+	0.185321i
$941$	50.7898	−	8.95561i	1.65570	−	0.291944i	0.733797	−	0.679368i	$-0.237746\pi$
$941$	50.7898	−	8.95561i	1.65570	−	0.291944i	0.921902	+	0.387424i	$0.126635\pi$
$942$	49.9072	+	10.5776i	1.62607	+	0.344636i
$943$	−2.19632	+	2.61747i	−0.0715219	+	0.0852365i
$944$	17.4696	−	6.81027i	0.568586	−	0.221656i
$945$	5.25773	−	0.750852i	0.171034	−	0.0244252i
$946$	−1.19266	−	12.7972i	−0.0387768	−	0.416073i
$947$	24.9458	+	20.9320i	0.810630	+	0.680199i	0.950758	−	0.309934i	$-0.100307\pi$
$947$	24.9458	+	20.9320i	0.810630	+	0.680199i	−0.140128	+	0.990133i	$0.544751\pi$
$948$	−12.9373	+	5.58722i	−0.420185	+	0.181464i
$949$	−7.05325	−	40.0010i	−0.228958	−	1.29849i
$950$	−0.448493	+	1.71253i	−0.0145510	+	0.0555617i
$951$	−4.03593	+	2.59193i	−0.130874	+	0.0840491i
$952$	−0.00439610	−	0.0420148i	−0.000142478	−	0.00136171i
$953$	−2.16048	−	1.24735i	−0.0699848	−	0.0404058i	0.464599	−	0.885521i	$-0.346198\pi$
$953$	−2.16048	−	1.24735i	−0.0699848	−	0.0404058i	−0.534584	+	0.845115i	$0.679532\pi$
$954$	−17.2073	−	14.0627i	−0.557108	−	0.455295i
$955$	−20.4703	+	11.8185i	−0.662403	+	0.382439i
$956$	−26.5050	+	15.7055i	−0.857232	+	0.507952i
$957$	3.79203	+	9.06108i	0.122579	+	0.292903i
$958$	34.5600	−	34.9536i	1.11658	−	1.12930i
$959$	−16.6240	+	13.9492i	−0.536816	+	0.450442i
$960$	1.31915	−	14.1013i	0.0425754	−	0.455118i
$961$	12.3829	−	4.50700i	0.399447	−	0.145387i
$962$	20.6745	+	29.1733i	0.666573	+	0.940584i
$963$	−4.70690	+	58.7355i	−0.151678	+	1.89273i
$964$	12.8942	−	36.7148i	0.415293	−	1.18251i
$965$	16.1557	+	2.84868i	0.520069	+	0.0917022i
$966$	1.55430	+	11.0127i	0.0500089	+	0.354326i
$967$	0.263359	−	0.723573i	0.00846905	−	0.0232685i	−0.935386	−	0.353628i	$-0.884948\pi$
$967$	0.263359	−	0.723573i	0.00846905	−	0.0232685i	0.943855	+	0.330360i	$0.107170\pi$
$968$	−12.6628	−	25.9934i	−0.406999	−	0.835461i
$969$	−0.00601596	+	0.00555315i	−0.000193261	+	0.000178393i
$970$	−8.98280	+	12.9846i	−0.288420	+	0.416911i
$971$	−16.5107			−0.529855			−0.264927	−	0.964268i	$-0.585348\pi$
$971$	−16.5107			−0.529855			−0.264927	+	0.964268i	$0.585348\pi$
$972$	−25.2847	−	18.2396i	−0.811008	−	0.585035i
$973$	5.38837			0.172743
$974$	−6.97407	+	10.0810i	−0.223464	+	0.323016i
$975$	27.5398	−	25.4211i	0.881979	−	0.814128i
$976$	4.16184	+	6.84566i	0.133217	+	0.219124i
$977$	−15.2249	+	41.8301i	−0.487088	+	1.33826i	0.416217	+	0.909266i	$0.363356\pi$
$977$	−15.2249	+	41.8301i	−0.487088	+	1.33826i	−0.903305	+	0.428999i	$0.858866\pi$
$978$	0.643956	+	4.56260i	0.0205915	+	0.145896i
$979$	−5.71550	−	1.00780i	−0.182668	−	0.0322093i
$980$	−1.92875	−	0.677372i	−0.0616116	−	0.0216378i
$981$	−0.992335	+	12.3830i	−0.0316828	+	0.395358i
$982$	−18.4739	−	26.0681i	−0.589526	−	0.831866i
$983$	5.27392	−	1.91955i	0.168212	−	0.0612242i	−0.256541	−	0.966533i	$-0.582583\pi$
$983$	5.27392	−	1.91955i	0.168212	−	0.0612242i	0.424753	+	0.905309i	$0.360361\pi$
$984$	−1.34024	+	3.43442i	−0.0427253	+	0.109485i
$985$	−13.7340	+	11.5242i	−0.437600	+	0.367190i
$986$	0.0955167	−	0.0966045i	0.00304187	−	0.00307651i
$987$	−1.88354	−	4.50074i	−0.0599538	−	0.143260i
$988$	1.76526	+	2.97909i	0.0561604	+	0.0947776i
$989$	40.5298	−	23.3999i	1.28877	−	0.744074i
$990$	2.96064	+	2.41958i	0.0940954	+	0.0768992i
$991$	−1.19076	−	0.687487i	−0.0378258	−	0.0218387i	0.480968	−	0.876738i	$-0.340285\pi$
$991$	−1.19076	−	0.687487i	−0.0378258	−	0.0218387i	−0.518794	+	0.854899i	$0.673619\pi$
$992$	36.0278	−	10.7555i	1.14388	−	0.341487i
$993$	39.9931	−	25.6841i	1.26914	−	0.815061i
$994$	2.53976	−	9.69783i	0.0805564	−	0.307597i
$995$	−1.78511	−	10.1239i	−0.0565919	−	0.320948i
$996$	3.89950	+	9.02938i	0.123560	+	0.286107i
$997$	36.8191	+	30.8949i	1.16607	+	0.978450i	0.999971	−	0.00765857i	$-0.00243782\pi$
$997$	36.8191	+	30.8949i	1.16607	+	0.978450i	0.166101	+	0.986109i	$0.446882\pi$
$998$	4.31506	+	46.3004i	0.136591	+	1.46561i
$999$	8.94637	−	22.2856i	0.283051	−	0.705085i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.cf.a.659.87	yes	648
4.3	odd	2	inner	756.2.cf.a.659.26	yes	648
27.5	odd	18	inner	756.2.cf.a.491.26	✓	648
108.59	even	18	inner	756.2.cf.a.491.87	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.cf.a.491.26	✓	648	27.5	odd	18	inner
756.2.cf.a.491.87	yes	648	108.59	even	18	inner
756.2.cf.a.659.26	yes	648	4.3	odd	2	inner
756.2.cf.a.659.87	yes	648	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.cf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.16303 + 0.804587i) q^{2} +(1.27272 - 1.17481i) q^{3} +(0.705279 + 1.87152i) q^{4} +(-0.349585 + 0.960476i) q^{5} +(2.42545 - 0.342323i) q^{6} +(0.984808 + 0.173648i) q^{7} +(-0.685540 + 2.74409i) q^{8} +(0.239643 - 2.99041i) q^{9} +(-1.17936 + 0.835791i) q^{10} +(0.828551 - 0.301568i) q^{11} +(3.09630 + 1.55335i) q^{12} +(4.19087 - 3.51656i) q^{13} +(1.00565 + 0.994322i) q^{14} +(0.683453 + 1.63311i) q^{15} +(-3.00516 + 2.63988i) q^{16} +(-0.0129346 + 0.00746778i) q^{17} +(2.68476 - 3.28513i) q^{18} +(0.274082 + 0.158241i) q^{19} +(-2.04410 + 0.0231490i) q^{20} +(1.45739 - 0.935956i) q^{21} +(1.20627 + 0.315909i) q^{22} +(0.788442 + 4.47148i) q^{23} +(2.35128 + 4.29784i) q^{24} +(3.02992 + 2.54240i) q^{25} +(7.70349 - 0.717942i) q^{26} +(-3.20817 - 4.08750i) q^{27} +(0.369578 + 1.96556i) q^{28} +(-4.13426 + 4.92702i) q^{29} +(-0.519107 + 2.44926i) q^{30} +(-6.54564 + 1.15417i) q^{31} +(-5.61911 + 0.652349i) q^{32} +(0.700230 - 1.35720i) q^{33} +(-0.0210518 - 0.00172174i) q^{34} +(-0.511059 + 0.885180i) q^{35} +(5.76563 - 1.66058i) q^{36} +(2.31077 + 4.00238i) q^{37} +(0.191447 + 0.404563i) q^{38} +(1.20253 - 9.39908i) q^{39} +(-2.39598 - 1.61774i) q^{40} +(0.483722 + 0.576477i) q^{41} +(2.44805 + 0.0840524i) q^{42} +(-3.52530 - 9.68569i) q^{43} +(1.14875 + 1.33796i) q^{44} +(2.78845 + 1.27557i) q^{45} +(-2.68071 + 5.83483i) q^{46} +(0.489145 - 2.77408i) q^{47} +(-0.723376 + 6.89034i) q^{48} +(0.939693 + 0.342020i) q^{49} +(1.47830 + 5.39472i) q^{50} +(-0.00768890 + 0.0247001i) q^{51} +(9.53704 + 5.36314i) q^{52} -5.23795i q^{53} +(-0.442446 - 7.33514i) q^{54} +0.901226i q^{55} +(-1.15163 + 2.58336i) q^{56} +(0.534734 - 0.120597i) q^{57} +(-8.77250 + 2.40390i) q^{58} +(-4.40483 - 1.60323i) q^{59} +(-2.57438 + 2.43090i) q^{60} +(0.347795 - 1.97244i) q^{61} +(-8.54142 - 3.92420i) q^{62} +(0.755282 - 2.90337i) q^{63} +(-7.06007 - 3.76237i) q^{64} +(1.91251 + 5.25457i) q^{65} +(1.90638 - 1.01507i) q^{66} +(-7.70417 - 9.18147i) q^{67} +(-0.0230986 - 0.0189404i) q^{68} +(6.25660 + 4.76468i) q^{69} +(-1.30658 + 0.618299i) q^{70} +(-3.54433 - 6.13896i) q^{71} +(8.04168 + 2.70765i) q^{72} +(3.71226 - 6.42983i) q^{73} +(-0.532763 + 6.51411i) q^{74} +(6.84308 - 0.323805i) q^{75} +(-0.102847 + 0.624554i) q^{76} +(0.868330 - 0.153110i) q^{77} +(8.96095 - 9.96388i) q^{78} +(-2.61491 + 3.11633i) q^{79} +(-1.48499 - 3.80925i) q^{80} +(-8.88514 - 1.43326i) q^{81} +(0.0987568 + 1.05966i) q^{82} +(2.17499 + 1.82503i) q^{83} +(2.77953 + 2.06742i) q^{84} +(-0.00265090 - 0.0150340i) q^{85} +(3.69295 - 14.1012i) q^{86} +(0.526548 + 11.1277i) q^{87} +(0.259525 + 2.48035i) q^{88} +(-5.70033 - 3.29109i) q^{89} +(2.21674 + 3.72708i) q^{90} +(4.73785 - 2.73540i) q^{91} +(-7.81238 + 4.62922i) q^{92} +(-6.97485 + 9.15883i) q^{93} +(2.80088 - 2.83278i) q^{94} +(-0.247802 + 0.207931i) q^{95} +(-6.38518 + 7.43165i) q^{96} +(10.2642 - 3.73585i) q^{97} +(0.817706 + 1.15384i) q^{98} +(-0.703256 - 2.54998i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66}+ \cdots + 36 q^{97}+O(q^{100}) \) 648 * q + 18 * q^12 + 42 * q^18 + 42 * q^20 - 48 * q^30 - 30 * q^32 + 60 * q^33 + 60 * q^41 - 30 * q^42 - 144 * q^44 - 18 * q^48 - 156 * q^50 + 54 * q^52 - 12 * q^57 + 54 * q^58 - 186 * q^60 - 24 * q^65 - 186 * q^66 - 78 * q^68 - 42 * q^72 - 24 * q^81 - 30 * q^86 - 36 * q^89 + 198 * q^90 + 114 * q^92 - 144 * q^93 - 54 * q^94 + 156 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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