LMFDB - Embedded newform 168.2.v.a.11.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [168,2,Mod(11,168)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(168, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 3, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("168.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.v (of order $6$, degree $2$, 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:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.19
Character	$\chi$	$=$	168.11
Dual form			168.2.v.a.107.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.819527 - 1.15255i) q^{2} +(1.03943 + 1.38549i) q^{3} +(-0.656749 - 1.88910i) q^{4} +(0.692094 + 1.19874i) q^{5} +(2.44869 - 0.0625523i) q^{6} +(2.08863 + 1.62408i) q^{7} +(-2.71550 - 0.791228i) q^{8} +(-0.839162 + 2.88024i) q^{9} +(1.94880 + 0.184728i) q^{10} +(-3.82316 - 2.20731i) q^{11} +(1.93467 - 2.87351i) q^{12} -6.43609i q^{13} +(3.58352 - 1.07627i) q^{14} +(-0.941460 + 2.20490i) q^{15} +(-3.13736 + 2.48132i) q^{16} +(-2.52866 - 1.45992i) q^{17} +(2.63191 + 3.32762i) q^{18} +(1.58928 + 2.75271i) q^{19} +(1.81001 - 2.09470i) q^{20} +(-0.0791630 + 4.58189i) q^{21} +(-5.67722 + 2.59745i) q^{22} +(1.84696 + 3.19902i) q^{23} +(-1.72634 - 4.58473i) q^{24} +(1.54201 - 2.67084i) q^{25} +(-7.41792 - 5.27455i) q^{26} +(-4.86280 + 1.83117i) q^{27} +(1.69634 - 5.01223i) q^{28} -6.67884 q^{29} +(1.76971 + 2.89206i) q^{30} +(2.17580 + 1.25620i) q^{31} +(0.288700 + 5.64948i) q^{32} +(-0.915722 - 7.59130i) q^{33} +(-3.75494 + 1.71796i) q^{34} +(-0.501330 + 3.62774i) q^{35} +(5.99217 - 0.306343i) q^{36} +(-5.00149 + 2.88761i) q^{37} +(4.47510 + 0.424197i) q^{38} +(8.91713 - 6.68987i) q^{39} +(-0.930905 - 3.80279i) q^{40} +0.497427i q^{41} +(5.21599 + 3.84623i) q^{42} +0.865898 q^{43} +(-1.65895 + 8.67197i) q^{44} +(-4.03345 + 0.987462i) q^{45} +(5.20067 + 0.492975i) q^{46} +(1.59001 + 2.75398i) q^{47} +(-6.69892 - 1.76761i) q^{48} +(1.72472 + 6.78420i) q^{49} +(-1.81456 - 3.96608i) q^{50} +(-0.605663 - 5.02092i) q^{51} +(-12.1584 + 4.22690i) q^{52} +(4.12906 - 7.15175i) q^{53} +(-1.87468 + 7.10532i) q^{54} -6.11065i q^{55} +(-4.38665 - 6.06278i) q^{56} +(-2.16191 + 5.06319i) q^{57} +(-5.47350 + 7.69771i) q^{58} +(6.62279 + 3.82367i) q^{59} +(4.78357 + 0.330440i) q^{60} +(2.99321 - 1.72813i) q^{61} +(3.23096 - 1.47823i) q^{62} +(-6.43045 + 4.65289i) q^{63} +(6.74792 + 4.29716i) q^{64} +(7.71521 - 4.45438i) q^{65} +(-9.49982 - 5.16586i) q^{66} +(-3.36806 + 5.83364i) q^{67} +(-1.09724 + 5.73567i) q^{68} +(-2.51243 + 5.88411i) q^{69} +(3.77030 + 3.55084i) q^{70} +1.90437 q^{71} +(4.55768 - 7.15735i) q^{72} +(3.23515 - 5.60345i) q^{73} +(-0.770738 + 8.13095i) q^{74} +(5.30324 - 0.639719i) q^{75} +(4.15638 - 4.81014i) q^{76} +(-4.40032 - 10.8194i) q^{77} +(-0.402592 - 15.7600i) q^{78} +(1.65073 - 0.953048i) q^{79} +(-5.14582 - 2.04358i) q^{80} +(-7.59162 - 4.83398i) q^{81} +(0.573310 + 0.407655i) q^{82} -7.00064i q^{83} +(8.70762 - 2.85961i) q^{84} -4.04161i q^{85} +(0.709627 - 0.997992i) q^{86} +(-6.94220 - 9.25347i) q^{87} +(8.63533 + 9.01894i) q^{88} +(8.22776 - 4.75030i) q^{89} +(-2.16742 + 5.45801i) q^{90} +(10.4527 - 13.4426i) q^{91} +(4.83027 - 5.59004i) q^{92} +(0.521147 + 4.32029i) q^{93} +(4.47717 + 0.424393i) q^{94} +(-2.19986 + 3.81027i) q^{95} +(-7.52721 + 6.27224i) q^{96} +1.19214 q^{97} +(9.23259 + 3.57201i) q^{98} +(9.56583 - 9.15936i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{3} - 2 q^{4} - 8 q^{6} - 2 q^{9} + 6 q^{10} + 10 q^{12} - 10 q^{16} - 10 q^{18} - 4 q^{19} - 20 q^{22} - 8 q^{24} - 16 q^{25} - 8 q^{27} - 22 q^{28} - 12 q^{30} - 14 q^{33} - 56 q^{34} + 4 q^{36}+ \cdots - 44 q^{99}+O(q^{100}) $ 56 * q - 2 * q^3 - 2 * q^4 - 8 * q^6 - 2 * q^9 + 6 * q^10 + 10 * q^12 - 10 * q^16 - 10 * q^18 - 4 * q^19 - 20 * q^22 - 8 * q^24 - 16 * q^25 - 8 * q^27 - 22 * q^28 - 12 * q^30 - 14 * q^33 - 56 * q^34 + 4 * q^36 + 14 * q^40 - 8 * q^42 - 16 * q^43 - 12 * q^46 + 64 * q^48 - 16 * q^49 - 34 * q^51 - 8 * q^52 + 32 * q^54 + 4 * q^57 - 18 * q^58 + 40 * q^60 + 4 * q^64 - 20 * q^66 - 36 * q^67 - 42 * q^70 + 22 * q^72 + 4 * q^73 + 104 * q^76 + 28 * q^78 - 10 * q^81 + 52 * q^82 + 4 * q^84 + 46 * q^88 + 140 * q^90 + 72 * q^91 - 46 * q^96 - 32 * q^97 - 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$	$-1$

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 $

$2$	0.819527	−	1.15255i	0.579493	−	0.814977i
$2$	0.819527	−	1.15255i	0.579493	−	0.814977i
$3$	1.03943	+	1.38549i	0.600116	+	0.799913i
$3$	1.03943	+	1.38549i	0.600116	+	0.799913i
$4$	−0.656749	−	1.88910i	−0.328375	−	0.944548i
$5$	0.692094	+	1.19874i	0.309514	+	0.536094i	0.978256	−	0.207401i	$-0.0665004\pi$
$5$	0.692094	+	1.19874i	0.309514	+	0.536094i	−0.668742	+	0.743494i	$0.733167\pi$
$6$	2.44869	−	0.0625523i	0.999674	−	0.0255369i
$7$	2.08863	+	1.62408i	0.789426	+	0.613845i
$7$	2.08863	+	1.62408i	0.789426	+	0.613845i
$8$	−2.71550	−	0.791228i	−0.960075	−	0.279741i
$9$	−0.839162	+	2.88024i	−0.279721	+	0.960081i
$10$	1.94880	+	0.184728i	0.616265	+	0.0584162i
$11$	−3.82316	−	2.20731i	−1.15273	−	0.665528i	−0.203177	−	0.979142i	$-0.565127\pi$
$11$	−3.82316	−	2.20731i	−1.15273	−	0.665528i	−0.949550	+	0.313614i	$0.898460\pi$
$12$	1.93467	−	2.87351i	0.558492	−	0.829510i
$13$		−	6.43609i		−	1.78505i	−0.450999	−	0.892525i	$-0.648932\pi$
$13$		−	6.43609i		−	1.78505i	0.450999	−	0.892525i	$-0.351068\pi$
$14$	3.58352	−	1.07627i	0.957737	−	0.287645i
$15$	−0.941460	+	2.20490i	−0.243084	+	0.569303i
$16$	−3.13736	+	2.48132i	−0.784340	+	0.620331i
$17$	−2.52866	−	1.45992i	−0.613289	−	0.354083i	0.160962	−	0.986961i	$-0.448540\pi$
$17$	−2.52866	−	1.45992i	−0.613289	−	0.354083i	−0.774252	+	0.632878i	$0.781874\pi$
$18$	2.63191	+	3.32762i	0.620348	+	0.784327i
$19$	1.58928	+	2.75271i	0.364606	+	0.631515i	0.988713	−	0.149823i	$-0.0478705\pi$
$19$	1.58928	+	2.75271i	0.364606	+	0.631515i	−0.624107	+	0.781339i	$0.714537\pi$
$20$	1.81001	−	2.09470i	0.404730	−	0.468390i
$21$	−0.0791630	+	4.58189i	−0.0172748	+	0.999851i
$22$	−5.67722	+	2.59745i	−1.21039	+	0.553777i
$23$	1.84696	+	3.19902i	0.385117	+	0.667043i	0.991785	−	0.127912i	$-0.0408277\pi$
$23$	1.84696	+	3.19902i	0.385117	+	0.667043i	−0.606668	+	0.794955i	$0.707494\pi$
$24$	−1.72634	−	4.58473i	−0.352388	−	0.935854i
$25$	1.54201	−	2.67084i	0.308402	−	0.534169i
$26$	−7.41792	−	5.27455i	−1.45477	−	1.03442i
$27$	−4.86280	+	1.83117i	−0.935846	+	0.352409i
$28$	1.69634	−	5.01223i	0.320578	−	0.947222i
$29$	−6.67884			−1.24023			−0.620115	−	0.784511i	$-0.712914\pi$
$29$	−6.67884			−1.24023			−0.620115	+	0.784511i	$0.712914\pi$
$30$	1.76971	+	2.89206i	0.323103	+	0.528015i
$31$	2.17580	+	1.25620i	0.390786	+	0.225620i	0.682500	−	0.730885i	$-0.260893\pi$
$31$	2.17580	+	1.25620i	0.390786	+	0.225620i	−0.291715	+	0.956505i	$0.594226\pi$
$32$	0.288700	+	5.64948i	0.0510355	+	0.998697i
$33$	−0.915722	−	7.59130i	−0.159407	−	1.32148i
$34$	−3.75494	+	1.71796i	−0.643966	+	0.294628i
$35$	−0.501330	+	3.62774i	−0.0847402	+	0.613200i
$36$	5.99217	−	0.306343i	0.998696	−	0.0510571i
$37$	−5.00149	+	2.88761i	−0.822240	+	0.474720i	−0.851188	−	0.524861i	$-0.824117\pi$
$37$	−5.00149	+	2.88761i	−0.822240	+	0.474720i	0.0289485	+	0.999581i	$0.490784\pi$
$38$	4.47510	+	0.424197i	0.725957	+	0.0688139i
$39$	8.91713	−	6.68987i	1.42788	−	1.07124i
$40$	−0.930905	−	3.80279i	−0.147189	−	0.601274i
$41$			0.497427i			0.0776850i	0.999245	+	0.0388425i	$0.0123671\pi$
$41$			0.497427i			0.0776850i	−0.999245	+	0.0388425i	$0.987633\pi$
$42$	5.21599	+	3.84623i	0.804845	+	0.593486i
$43$	0.865898			0.132048			0.0660241	−	0.997818i	$-0.478969\pi$
$43$	0.865898			0.132048			0.0660241	+	0.997818i	$0.478969\pi$
$44$	−1.65895	+	8.67197i	−0.250096	+	1.30735i
$45$	−4.03345	+	0.987462i	−0.601271	+	0.147202i
$46$	5.20067	+	0.492975i	0.766797	+	0.0726852i
$47$	1.59001	+	2.75398i	0.231927	+	0.401710i	0.958375	−	0.285512i	$-0.0921635\pi$
$47$	1.59001	+	2.75398i	0.231927	+	0.401710i	−0.726448	+	0.687221i	$0.758830\pi$
$48$	−6.69892	−	1.76761i	−0.966906	−	0.255133i
$49$	1.72472	+	6.78420i	0.246388	+	0.969171i
$50$	−1.81456	−	3.96608i	−0.256618	−	0.560888i
$51$	−0.605663	−	5.02092i	−0.0848097	−	0.703069i
$52$	−12.1584	+	4.22690i	−1.68606	+	0.586165i
$53$	4.12906	−	7.15175i	0.567171	−	0.982368i	−0.429673	−	0.902984i	$-0.641371\pi$
$53$	4.12906	−	7.15175i	0.567171	−	0.982368i	0.996844	−	0.0793841i	$-0.0252954\pi$
$54$	−1.87468	+	7.10532i	−0.255112	+	0.966912i
$55$		−	6.11065i		−	0.823960i
$56$	−4.38665	−	6.06278i	−0.586191	−	0.810173i
$57$	−2.16191	+	5.06319i	−0.286351	+	0.670635i
$58$	−5.47350	+	7.69771i	−0.718705	+	1.01076i
$59$	6.62279	+	3.82367i	0.862214	+	0.497799i	0.864753	−	0.502197i	$-0.167475\pi$
$59$	6.62279	+	3.82367i	0.862214	+	0.497799i	−0.00253919	+	0.999997i	$0.500808\pi$
$60$	4.78357	+	0.330440i	0.617556	+	0.0426596i
$61$	2.99321	−	1.72813i	0.383241	−	0.221265i	−0.295986	−	0.955192i	$-0.595648\pi$
$61$	2.99321	−	1.72813i	0.383241	−	0.221265i	0.679228	+	0.733928i	$0.262315\pi$
$62$	3.23096	−	1.47823i	0.410333	−	0.187736i
$63$	−6.43045	+	4.65289i	−0.810160	+	0.586209i
$64$	6.74792	+	4.29716i	0.843490	+	0.537146i
$65$	7.71521	−	4.45438i	0.956954	−	0.552497i
$66$	−9.49982	−	5.16586i	−1.16935	−	0.635873i
$67$	−3.36806	+	5.83364i	−0.411473	+	0.712693i	−0.995051	−	0.0993644i	$-0.968319\pi$
$67$	−3.36806	+	5.83364i	−0.411473	+	0.712693i	0.583578	+	0.812057i	$0.301652\pi$
$68$	−1.09724	+	5.73567i	−0.133059	+	0.695553i
$69$	−2.51243	+	5.88411i	−0.302461	+	0.708363i
$70$	3.77030	+	3.55084i	0.450638	+	0.424407i
$71$	1.90437			0.226007			0.113004	−	0.993595i	$-0.463953\pi$
$71$	1.90437			0.226007			0.113004	+	0.993595i	$0.463953\pi$
$72$	4.55768	−	7.15735i	0.537127	−	0.843501i
$73$	3.23515	−	5.60345i	0.378646	−	0.655834i	−0.612219	−	0.790688i	$-0.709723\pi$
$73$	3.23515	−	5.60345i	0.378646	−	0.655834i	0.990866	+	0.134854i	$0.0430564\pi$
$74$	−0.770738	+	8.13095i	−0.0895964	+	0.945204i
$75$	5.30324	−	0.639719i	0.612365	−	0.0738684i
$76$	4.15638	−	4.81014i	0.476769	−	0.551761i
$77$	−4.40032	−	10.8194i	−0.501463	−	1.23298i
$78$	−0.402592	−	15.7600i	−0.0455846	−	1.78447i
$79$	1.65073	−	0.953048i	0.185721	−	0.107226i	−0.404257	−	0.914646i	$-0.632470\pi$
$79$	1.65073	−	0.953048i	0.185721	−	0.107226i	0.589978	+	0.807419i	$0.299136\pi$
$80$	−5.14582	−	2.04358i	−0.575320	−	0.228479i
$81$	−7.59162	−	4.83398i	−0.843513	−	0.537109i
$82$	0.573310	+	0.407655i	0.0633115	+	0.0450179i
$83$		−	7.00064i		−	0.768420i	−0.923246	−	0.384210i	$-0.874474\pi$
$83$		−	7.00064i		−	0.768420i	0.923246	−	0.384210i	$-0.125526\pi$
$84$	8.70762	−	2.85961i	0.950079	−	0.312009i
$85$		−	4.04161i		−	0.438374i
$86$	0.709627	−	0.997992i	0.0765210	−	0.107616i
$87$	−6.94220	−	9.25347i	−0.744282	−	0.992076i
$88$	8.63533	+	9.01894i	0.920530	+	0.961422i
$89$	8.22776	−	4.75030i	0.872141	−	0.503531i	0.00408165	−	0.999992i	$-0.498701\pi$
$89$	8.22776	−	4.75030i	0.872141	−	0.503531i	0.868059	+	0.496461i	$0.165367\pi$
$90$	−2.16742	+	5.45801i	−0.228466	+	0.575325i
$91$	10.4527	−	13.4426i	1.09574	−	1.40916i
$92$	4.83027	−	5.59004i	0.503591	−	0.582801i
$93$	0.521147	+	4.32029i	0.0540404	+	0.447993i
$94$	4.47717	+	0.424393i	0.461785	+	0.0437728i
$95$	−2.19986	+	3.81027i	−0.225701	+	0.390926i
$96$	−7.52721	+	6.27224i	−0.768243	+	0.640158i
$97$	1.19214			0.121044			0.0605218	−	0.998167i	$-0.480724\pi$
$97$	1.19214			0.121044			0.0605218	+	0.998167i	$0.480724\pi$
$98$	9.23259	+	3.57201i	0.932632	+	0.360828i
$99$	9.56583	−	9.15936i	0.961402	−	0.920551i
$100$	−6.05819	−	1.15893i	−0.605819	−	0.115893i
$101$	1.03566	−	1.79382i	0.103052	−	0.178491i	−0.809889	−	0.586584i	$-0.800473\pi$
$101$	1.03566	−	1.79382i	0.103052	−	0.178491i	0.912941	+	0.408092i	$0.133806\pi$
$102$	−6.28322	−	3.41672i	−0.622131	−	0.338306i
$103$	−4.80043	+	2.77153i	−0.473000	+	0.273087i	−0.717495	−	0.696564i	$-0.754711\pi$
$103$	−4.80043	+	2.77153i	−0.473000	+	0.273087i	0.244495	+	0.969651i	$0.421378\pi$
$104$	−5.09241	+	17.4772i	−0.499352	+	1.71378i
$105$	−5.54729	+	3.07620i	−0.541361	+	0.300207i
$106$	−4.85888	−	10.6200i	−0.471936	−	1.03151i
$107$	−5.17522	+	2.98792i	−0.500308	+	0.288853i	−0.728841	−	0.684683i	$-0.759940\pi$
$107$	−5.17522	+	2.98792i	−0.500308	+	0.288853i	0.228533	+	0.973536i	$0.426607\pi$
$108$	6.65289	+	7.98367i	0.640175	+	0.768229i
$109$	1.43595	+	0.829048i	0.137539	+	0.0794084i	0.567191	−	0.823586i	$-0.308030\pi$
$109$	1.43595	+	0.829048i	0.137539	+	0.0794084i	−0.429651	+	0.902995i	$0.641364\pi$
$110$	−7.04284	−	5.00785i	−0.671508	−	0.477479i
$111$	−9.19946	−	3.92803i	−0.873174	−	0.372832i
$112$	−10.5826	+	0.0872278i	−0.999966	+	0.00824226i
$113$			16.4545i			1.54791i	0.633241	+	0.773955i	$0.281724\pi$
$113$			16.4545i			1.54791i	−0.633241	+	0.773955i	$0.718276\pi$
$114$	4.06384	+	6.64113i	0.380614	+	0.621999i
$115$	−2.55654	+	4.42805i	−0.238398	+	0.412918i
$116$	4.38633	+	12.6170i	0.407260	+	1.17146i
$117$	18.5375	+	5.40092i	1.71379	+	0.499315i
$118$	9.83453	−	4.49950i	0.905342	−	0.414213i
$119$	−2.91039	−	7.15597i	−0.266795	−	0.655987i
$120$	4.30112	−	5.24250i	0.392636	−	0.478573i
$121$	4.24439	+	7.35150i	0.385854	+	0.668318i
$122$	0.461259	−	4.86608i	0.0417604	−	0.440554i
$123$	−0.689179	+	0.517041i	−0.0621412	+	0.0466200i
$124$	0.944124	−	4.93531i	0.0847849	−	0.443204i
$125$	11.1898			1.00085
$126$	0.0927622	+	11.2246i	0.00826392	+	0.999966i
$127$			2.31360i			0.205299i	0.994718	+	0.102649i	$0.0327319\pi$
$127$			2.31360i			0.205299i	−0.994718	+	0.102649i	$0.967268\pi$
$128$	10.4828	−	4.25568i	0.926558	−	0.376152i
$129$	0.900042	+	1.19969i	0.0792443	+	0.105627i
$130$	1.18893	−	12.5427i	0.104276	−	1.10006i
$131$	−4.11383	+	2.37512i	−0.359427	+	0.207515i	−0.668830	−	0.743416i	$-0.733204\pi$
$131$	−4.11383	+	2.37512i	−0.359427	+	0.207515i	0.309402	+	0.950931i	$0.399871\pi$
$132$	−13.7393	+	6.71547i	−1.19585	+	0.584506i
$133$	−1.15122	+	8.33050i	−0.0998234	+	0.722346i
$134$	3.96336	+	8.66269i	0.342382	+	0.748342i
$135$	−5.56061	−	4.56190i	−0.478581	−	0.392626i
$136$	5.71145	+	5.96516i	0.489752	+	0.511508i
$137$	−0.290760	−	0.167870i	−0.0248413	−	0.0143421i	0.487528	−	0.873107i	$-0.337899\pi$
$137$	−0.290760	−	0.167870i	−0.0248413	−	0.0143421i	−0.512369	+	0.858765i	$0.671232\pi$
$138$	4.72273	+	7.71789i	0.402026	+	0.656990i
$139$	−9.35410			−0.793405			−0.396702	−	0.917947i	$-0.629845\pi$
$139$	−9.35410			−0.793405			−0.396702	+	0.917947i	$0.629845\pi$
$140$	7.18240	−	1.43546i	0.607023	−	0.121318i
$141$	−2.16290	+	5.06553i	−0.182149	+	0.426594i
$142$	1.56069	−	2.19489i	0.130970	−	0.184191i
$143$	−14.2064	+	24.6062i	−1.18800	+	2.05768i
$144$	−4.51407	−	11.1186i	−0.376172	−	0.926550i
$145$	−4.62239	−	8.00621i	−0.383868	−	0.664880i
$146$	−3.80697	−	8.32086i	−0.315067	−	0.688639i
$147$	−7.60671	+	9.44129i	−0.627391	+	0.778705i
$148$	8.73970	+	7.55185i	0.718399	+	0.620758i
$149$	1.03566	+	1.79382i	0.0848446	+	0.146955i	0.905325	−	0.424720i	$-0.139627\pi$
$149$	1.03566	+	1.79382i	0.0848446	+	0.146955i	−0.820480	+	0.571675i	$0.806294\pi$
$150$	3.60884	−	6.63652i	0.294661	−	0.541870i
$151$	−20.2661	−	11.7007i	−1.64923	−	0.952186i	−0.977377	−	0.211506i	$-0.932163\pi$
$151$	−20.2661	−	11.7007i	−1.64923	−	0.952186i	−0.671858	−	0.740680i	$-0.734504\pi$
$152$	−2.13767	−	8.73248i	−0.173388	−	0.708298i
$153$	6.32688	−	6.05804i	0.511498	−	0.489763i
$154$	−16.0761	−	3.79518i	−1.29545	−	0.305824i
$155$			3.47763i			0.279330i
$156$	−18.4941	−	12.4517i	−1.48072	−	0.996936i
$157$	19.3264	+	11.1581i	1.54241	+	0.890511i	0.998686	+	0.0512477i	$0.0163198\pi$
$157$	19.3264	+	11.1581i	1.54241	+	0.890511i	0.543725	+	0.839264i	$0.317014\pi$
$158$	0.254380	−	2.68360i	0.0202374	−	0.213496i
$159$	14.2006	−	1.71298i	1.12618	−	0.135848i
$160$	−6.57246	+	4.25605i	−0.519599	+	0.336470i
$161$	−1.33787	+	9.68118i	−0.105439	+	0.762983i
$162$	−11.7929	+	4.78815i	−0.926542	+	0.376192i
$163$	−8.50029	−	14.7229i	−0.665794	−	1.15319i	−0.979069	−	0.203526i	$-0.934760\pi$
$163$	−8.50029	−	14.7229i	−0.665794	−	1.15319i	0.313276	−	0.949662i	$-0.398574\pi$
$164$	0.939686	−	0.326685i	0.0733772	−	0.0255098i
$165$	8.46624	−	6.35161i	0.659096	−	0.494472i
$166$	−8.06859	−	5.73721i	−0.626244	−	0.445294i
$167$	23.9142			1.85054			0.925269	−	0.379311i	$-0.123839\pi$
$167$	23.9142			1.85054			0.925269	+	0.379311i	$0.123839\pi$
$168$	3.84029	−	12.3795i	0.296285	−	0.955100i
$169$	−28.4232			−2.18640
$170$	−4.65816	−	3.31221i	−0.357265	−	0.254035i
$171$	−9.26215	+	2.26754i	−0.708294	+	0.173403i
$172$	−0.568678	−	1.63576i	−0.0433613	−	0.124726i
$173$	−4.38442	−	7.59404i	−0.333341	−	0.577364i	0.649824	−	0.760085i	$-0.274843\pi$
$173$	−4.38442	−	7.59404i	−0.333341	−	0.577364i	−0.983165	+	0.182721i	$0.941509\pi$
$174$	−16.3544	+	0.417777i	−1.23983	+	0.0316716i
$175$	7.55835	−	3.07404i	0.571358	−	0.232375i
$176$	17.4717	−	2.56140i	1.31698	−	0.193073i
$177$	1.58629	+	13.1503i	0.119233	+	0.988433i
$178$	1.26791	−	13.3759i	0.0950340	−	1.00257i
$179$	−5.26665	−	3.04070i	−0.393648	−	0.227273i	0.290092	−	0.956999i	$-0.406314\pi$
$179$	−5.26665	−	3.04070i	−0.393648	−	0.227273i	−0.683740	+	0.729726i	$0.739648\pi$
$180$	4.51437	+	6.97105i	0.336482	+	0.519592i
$181$			11.5816i			0.860857i	0.902625	+	0.430429i	$0.141638\pi$
$181$			11.5816i			0.860857i	−0.902625	+	0.430429i	$0.858362\pi$
$182$	−6.92696	−	23.0639i	−0.513460	−	1.70961i
$183$	5.50555	+	2.35079i	0.406982	+	0.173775i
$184$	−2.48426	−	10.1483i	−0.183142	−	0.748144i
$185$	−6.92300	−	3.99700i	−0.508989	−	0.293865i
$186$	5.40645	+	2.93994i	0.396420	+	0.215567i
$187$	6.44498	+	11.1630i	0.471304	+	0.816322i
$188$	4.15830	−	4.81236i	0.303275	−	0.350978i
$189$	−13.1305	−	4.07296i	−0.955106	−	0.296264i
$190$	2.58869	+	5.65807i	0.187803	+	0.410480i
$191$	0.757053	+	1.31125i	0.0547784	+	0.0948790i	0.892114	−	0.451810i	$-0.149221\pi$
$191$	0.757053	+	1.31125i	0.0547784	+	0.0948790i	−0.837336	+	0.546689i	$0.815888\pi$
$192$	1.06033	+	13.8158i	0.0765224	+	0.997068i
$193$	−7.97806	+	13.8184i	−0.574273	+	0.994670i	0.421847	+	0.906667i	$0.361382\pi$
$193$	−7.97806	+	13.8184i	−0.574273	+	0.994670i	−0.996120	+	0.0880034i	$0.971951\pi$
$194$	0.976993	−	1.37401i	0.0701440	−	0.0986478i
$195$	14.1909	+	6.05931i	1.01623	+	0.433917i
$196$	11.6833	−	7.71367i	0.834521	−	0.550977i
$197$	0.963016			0.0686121			0.0343060	−	0.999411i	$-0.489078\pi$
$197$	0.963016			0.0686121			0.0343060	+	0.999411i	$0.489078\pi$
$198$	−2.71717	−	18.5315i	−0.193101	−	1.31697i
$199$	1.72593	+	0.996469i	0.122348	+	0.0706378i	0.559925	−	0.828543i	$-0.310830\pi$
$199$	1.72593	+	0.996469i	0.122348	+	0.0706378i	−0.437577	+	0.899181i	$0.644163\pi$
$200$	−6.30058	+	6.03260i	−0.445519	+	0.426569i
$201$	−11.5833	+	1.39727i	−0.817024	+	0.0985559i
$202$	−1.21871	−	2.66373i	−0.0857484	−	0.187420i
$203$	−13.9496	−	10.8470i	−0.979070	−	0.761309i
$204$	−9.08722	+	4.44164i	−0.636232	+	0.310977i
$205$	−0.596286	+	0.344266i	−0.0416464	+	0.0240446i
$206$	−0.739754	+	7.80408i	−0.0515411	+	0.543736i
$207$	−10.7639	+	2.63519i	−0.748141	+	0.183158i
$208$	15.9700	+	20.1923i	1.10732	+	1.40009i
$209$		−	14.0321i		−	0.970620i
$210$	−1.00068	+	8.91458i	−0.0690533	+	0.615164i
$211$	21.4567			1.47714			0.738569	−	0.674178i	$-0.235502\pi$
$211$	21.4567			1.47714			0.738569	+	0.674178i	$0.235502\pi$
$212$	−16.2221	−	3.10329i	−1.11414	−	0.213135i
$213$	1.97947	+	2.63849i	0.135631	+	0.180786i
$214$	−0.797511	+	8.41339i	−0.0545167	+	0.575128i
$215$	0.599283	+	1.03799i	0.0408707	+	0.0707902i
$216$	14.6538	−	1.12496i	0.997066	−	0.0765440i
$217$	2.50427	+	6.15741i	0.170001	+	0.417992i
$218$	2.13232	−	0.975582i	0.144419	−	0.0660747i
$219$	11.1262	−	1.34214i	0.751842	−	0.0906931i
$220$	−11.5436	+	4.01317i	−0.778269	+	0.270568i
$221$	−9.39617	+	16.2747i	−0.632055	+	1.09475i
$222$	−12.0665	+	7.38372i	−0.809849	+	0.495563i
$223$			12.1938i			0.816559i	0.912857	+	0.408279i	$0.133871\pi$
$223$			12.1938i			0.816559i	−0.912857	+	0.408279i	$0.866129\pi$
$224$	−8.57223	+	12.2685i	−0.572757	+	0.819726i
$225$	6.39868	+	6.68264i	0.426579	+	0.445509i
$226$	18.9647	+	13.4849i	1.26151	+	0.897004i
$227$	13.5954	+	7.84932i	0.902360	+	0.520978i	0.877965	−	0.478724i	$-0.158901\pi$
$227$	13.5954	+	7.84932i	0.902360	+	0.520978i	0.0243951	+	0.999702i	$0.492234\pi$
$228$	10.9847	+	0.758800i	0.727478	+	0.0502528i
$229$	−10.4894	+	6.05608i	−0.693161	+	0.400197i	−0.804795	−	0.593553i	$-0.797725\pi$
$229$	−10.4894	+	6.05608i	−0.693161	+	0.400197i	0.111634	+	0.993749i	$0.464392\pi$
$230$	3.00840	+	6.57545i	0.198368	+	0.433572i
$231$	10.4163	−	17.3426i	0.685341	−	1.14106i
$232$	18.1364	+	5.28449i	1.19071	+	0.346944i
$233$	5.05877	−	2.92068i	0.331411	−	0.191340i	−0.325056	−	0.945695i	$-0.605383\pi$
$233$	5.05877	−	2.92068i	0.331411	−	0.191340i	0.656468	+	0.754354i	$0.272050\pi$
$234$	21.4168	−	16.9392i	1.40006	−	1.10735i
$235$	−2.20088	+	3.81203i	−0.143569	+	0.248670i
$236$	2.87376	−	15.0223i	0.187066	−	0.977867i
$237$	3.03626	+	1.29644i	0.197226	+	0.0842126i
$238$	−10.6328	−	2.51015i	−0.689220	−	0.162709i
$239$	−22.6171			−1.46298			−0.731490	−	0.681852i	$-0.761175\pi$
$239$	−22.6171			−1.46298			−0.731490	+	0.681852i	$0.761175\pi$
$240$	−2.51737	−	9.25363i	−0.162496	−	0.597319i
$241$	12.7459	−	22.0766i	0.821038	−	1.42208i	−0.0838714	−	0.996477i	$-0.526729\pi$
$241$	12.7459	−	22.0766i	0.821038	−	1.42208i	0.904910	−	0.425604i	$-0.139938\pi$
$242$	11.9514	+	1.13288i	0.768264	+	0.0728242i
$243$	−1.19354	−	15.5427i	−0.0765656	−	0.997065i
$244$	−5.23039	−	4.51951i	−0.334842	−	0.289332i
$245$	−6.93884	+	6.76279i	−0.443306	+	0.432059i
$246$	0.0311152	+	1.21804i	0.00198383	+	0.0776596i
$247$	17.7167	−	10.2287i	1.12729	−	0.650839i
$248$	−4.91446	−	5.13277i	−0.312068	−	0.325931i
$249$	9.69931	−	7.27669i	0.614669	−	0.461141i
$250$	9.17036	−	12.8968i	0.579984	−	0.815667i
$251$		−	1.11008i		−	0.0700675i	−0.999386	−	0.0350338i	$-0.988846\pi$
$251$		−	1.11008i		−	0.0700675i	0.999386	−	0.0350338i	$-0.0111539\pi$
$252$	13.0129	+	9.09195i	0.819738	+	0.572739i
$253$		−	16.3072i		−	1.02522i
$254$	2.66654	+	1.89606i	0.167314	+	0.118969i
$255$	5.59961	−	4.20098i	0.350661	−	0.263075i
$256$	3.68606	−	15.5696i	0.230379	−	0.973101i
$257$	−12.0906	+	6.98049i	−0.754188	+	0.435431i	−0.827205	−	0.561900i	$-0.810071\pi$
$257$	−12.0906	+	6.98049i	−0.754188	+	0.435431i	0.0730169	+	0.997331i	$0.476737\pi$
$258$	2.12032	−	0.0541639i	0.132005	−	0.00337210i
$259$	−15.1360	−	2.09169i	−0.940503	−	0.129971i
$260$	−13.4817	−	11.6494i	−0.836099	−	0.722462i
$261$	5.60463	−	19.2367i	0.346918	−	1.19072i
$262$	−0.633949	+	6.68788i	−0.0391655	+	0.413179i
$263$	7.08483	−	12.2713i	0.436870	−	0.756680i	−0.560577	−	0.828103i	$-0.689420\pi$
$263$	7.08483	−	12.2713i	0.436870	−	0.756680i	0.997446	+	0.0714223i	$0.0227538\pi$
$264$	−3.51980	+	21.3387i	−0.216629	+	1.31331i
$265$	11.4308			0.702189
$266$	8.65788	+	8.15392i	0.530849	+	0.499949i
$267$	15.1337	+	6.46186i	0.926166	+	0.395459i
$268$	13.2323	+	2.53134i	0.808290	+	0.154626i
$269$	9.11023	−	15.7794i	0.555461	−	0.962086i	−0.442407	−	0.896814i	$-0.645875\pi$
$269$	9.11023	−	15.7794i	0.555461	−	0.962086i	0.997868	−	0.0652716i	$-0.0207914\pi$
$270$	−9.81490	+	2.67029i	−0.597316	+	0.162509i
$271$	−21.9278	+	12.6600i	−1.33202	+	0.769041i	−0.985609	−	0.169042i	$-0.945933\pi$
$271$	−21.9278	+	12.6600i	−1.33202	+	0.769041i	−0.346410	+	0.938083i	$0.612599\pi$
$272$	11.5558	−	1.69412i	0.700676	−	0.102721i
$273$	29.4894	+	0.509500i	1.78478	+	0.0308363i
$274$	−0.431765	+	0.197542i	−0.0260839	+	0.0119339i
$275$	−11.7907	+	6.80738i	−0.711008	+	0.410500i
$276$	12.7657	+	0.881829i	0.768403	+	0.0530799i
$277$	−16.2822	−	9.40051i	−0.978300	−	0.564822i	−0.0765434	−	0.997066i	$-0.524388\pi$
$277$	−16.2822	−	9.40051i	−0.978300	−	0.564822i	−0.901756	+	0.432245i	$0.857722\pi$
$278$	−7.66594	+	10.7811i	−0.459773	+	0.646606i
$279$	−5.44401	+	5.21269i	−0.325924	+	0.312075i
$280$	4.23173	−	9.45448i	0.252894	−	0.565013i
$281$		−	25.4910i		−	1.52067i	−0.649533	−	0.760333i	$-0.725036\pi$
$281$		−	25.4910i		−	1.52067i	0.649533	−	0.760333i	$-0.274964\pi$
$282$	4.06572	+	6.64420i	0.242110	+	0.395656i
$283$	−6.01848	+	10.4243i	−0.357761	+	0.619661i	−0.987586	−	0.157076i	$-0.949793\pi$
$283$	−6.01848	+	10.4243i	−0.357761	+	0.619661i	0.629825	+	0.776737i	$0.283126\pi$
$284$	−1.25070	−	3.59754i	−0.0742151	−	0.213475i
$285$	−7.56570	+	0.912634i	−0.448153	+	0.0540598i
$286$	16.7174	+	36.5391i	0.988520	+	2.16060i
$287$	−0.807861	+	1.03894i	−0.0476865	+	0.0613266i
$288$	−16.5142	−	3.90930i	−0.973106	−	0.230358i
$289$	−4.23726	−	7.33916i	−0.249251	−	0.431715i
$290$	−13.0157	−	1.23377i	−0.764311	−	0.0724495i
$291$	1.23915	+	1.65170i	0.0726403	+	0.0968244i
$292$	−12.7101	−	2.43145i	−0.743804	−	0.142290i
$293$	−3.90464			−0.228111			−0.114056	−	0.993474i	$-0.536384\pi$
$293$	−3.90464			−0.228111			−0.114056	+	0.993474i	$0.536384\pi$
$294$	4.64767	+	16.5045i	0.271057	+	0.962563i
$295$			10.5854i			0.616303i
$296$	15.8663	−	3.88400i	0.922211	−	0.225753i
$297$	22.6332	+	3.73282i	1.31331	+	0.216600i
$298$	2.91622	+	0.276430i	0.168932	+	0.0160132i
$299$	20.5892	−	11.8872i	1.19070	−	0.687453i
$300$	−4.69139	−	9.59819i	−0.270858	−	0.554152i
$301$	1.80854	+	1.40629i	0.104242	+	0.0810571i
$302$	−30.0943	+	13.7688i	−1.73173	+	0.792303i
$303$	3.56181	−	0.429654i	0.204621	−	0.0246830i
$304$	−11.8165	−	4.69273i	−0.677723	−	0.269147i
$305$	4.14317	+	2.39206i	0.237237	+	0.136969i
$306$	−1.79715	−	12.2568i	−0.102736	−	0.700674i
$307$	−11.0339			−0.629740			−0.314870	−	0.949135i	$-0.601961\pi$
$307$	−11.0339			−0.629740			−0.314870	+	0.949135i	$0.601961\pi$
$308$	−17.5489	+	15.4182i	−0.999942	+	0.878535i
$309$	−8.82964	−	3.77013i	−0.502301	−	0.214475i
$310$	4.00815	+	2.85002i	0.227648	+	0.161870i
$311$	15.6553	−	27.1158i	0.887732	−	1.53760i	0.0451815	−	0.998979i	$-0.485613\pi$
$311$	15.6553	−	27.1158i	0.887732	−	1.53760i	0.842550	−	0.538618i	$-0.181053\pi$
$312$	−29.5077	+	11.1109i	−1.67055	+	0.629031i
$313$	6.53063	+	11.3114i	0.369133	+	0.639357i	0.989430	−	0.145010i	$-0.0463213\pi$
$313$	6.53063	+	11.3114i	0.369133	+	0.639357i	−0.620297	+	0.784367i	$0.712988\pi$
$314$	28.6987	−	13.1303i	1.61956	−	0.740984i
$315$	−10.0281	−	4.48821i	−0.565019	−	0.252882i
$316$	−2.88451	−	2.49247i	−0.162267	−	0.140212i
$317$	12.2315	+	21.1856i	0.686990	+	1.18990i	0.972807	+	0.231618i	$0.0744018\pi$
$317$	12.2315	+	21.1856i	0.686990	+	1.18990i	−0.285817	+	0.958284i	$0.592265\pi$
$318$	9.66345	−	17.7707i	0.541899	−	0.996532i
$319$	25.5343	+	14.7422i	1.42965	+	0.825407i
$320$	−0.480999	+	11.0631i	−0.0268886	+	0.618443i
$321$	−9.51902	−	4.06448i	−0.531300	−	0.226857i
$322$	10.0616	+	9.47596i	0.560713	+	0.528074i
$323$		−	9.28088i		−	0.516402i
$324$	−4.14606	+	17.5160i	−0.230337	+	0.973111i
$325$	−17.1898	−	9.92452i	−0.953517	−	0.550513i
$326$	−23.9352	−	2.26883i	−1.32565	−	0.125659i
$327$	0.343939	+	2.85124i	0.0190198	+	0.157674i
$328$	0.393578	−	1.35076i	0.0217317	−	0.0745834i
$329$	−1.15175	+	8.33435i	−0.0634981	+	0.459488i
$330$	−0.382236	−	14.9631i	−0.0210414	−	0.823691i
$331$	−7.26267	−	12.5793i	−0.399192	−	0.691422i	0.594434	−	0.804144i	$-0.297376\pi$
$331$	−7.26267	−	12.5793i	−0.399192	−	0.691422i	−0.993626	+	0.112723i	$0.964043\pi$
$332$	−13.2249	+	4.59766i	−0.725809	+	0.252330i
$333$	−4.11997	−	16.8287i	−0.225773	−	0.922206i
$334$	19.5984	−	27.5624i	1.07237	−	1.50815i
$335$	−9.32404			−0.509427
$336$	−11.1208	−	14.5715i	−0.606689	−	0.794939i
$337$	−18.7954			−1.02385			−0.511924	−	0.859030i	$-0.671067\pi$
$337$	−18.7954			−1.02385			−0.511924	+	0.859030i	$0.671067\pi$
$338$	−23.2936	+	32.7592i	−1.26700	+	1.78187i
$339$	−22.7975	+	17.1033i	−1.23819	+	0.928926i
$340$	−7.63498	+	2.65432i	−0.414065	+	0.143951i
$341$	−5.54563	−	9.60532i	−0.300313	−	0.520157i
$342$	−4.97712	+	12.5334i	−0.269132	+	0.677729i
$343$	−7.41581	+	16.9707i	−0.400416	+	0.916334i
$344$	−2.35135	−	0.685122i	−0.126776	−	0.0369393i
$345$	−8.79236	+	1.06060i	−0.473365	+	0.0571010i
$346$	−12.3457	−	1.17025i	−0.663707	−	0.0629132i
$347$	20.7411	+	11.9749i	1.11344	+	0.642846i	0.939719	−	0.341949i	$-0.111087\pi$
$347$	20.7411	+	11.9749i	1.11344	+	0.642846i	0.173723	+	0.984795i	$0.444420\pi$
$348$	−12.9214	+	19.1917i	−0.692659	+	1.02878i
$349$			3.59423i			0.192395i	0.995362	+	0.0961974i	$0.0306680\pi$
$349$			3.59423i			0.192395i	−0.995362	+	0.0961974i	$0.969332\pi$
$350$	2.65129	−	11.2306i	0.141717	−	0.600303i
$351$	11.7856	+	31.2974i	0.629067	+	1.67053i
$352$	11.3664	−	22.2362i	0.605830	−	1.18519i
$353$	−22.4603	−	12.9675i	−1.19544	−	0.690189i	−0.235907	−	0.971776i	$-0.575806\pi$
$353$	−22.4603	−	12.9675i	−1.19544	−	0.690189i	−0.959536	+	0.281587i	$0.909139\pi$
$354$	16.4563	+	8.94871i	0.874645	+	0.475619i
$355$	1.31800	+	2.28285i	0.0699524	+	0.121161i
$356$	−14.3773	−	12.4233i	−0.761998	−	0.658432i
$357$	6.88937	−	11.4705i	0.364624	−	0.607081i
$358$	−7.82073	+	3.57815i	−0.413338	+	0.189111i
$359$	−14.1756	−	24.5529i	−0.748162	−	1.29585i	−0.948703	−	0.316169i	$-0.897603\pi$
$359$	−14.1756	−	24.5529i	−0.748162	−	1.29585i	0.200541	−	0.979685i	$-0.435730\pi$
$360$	11.7342	+	0.509922i	0.618444	+	0.0268752i
$361$	4.44838	−	7.70483i	0.234126	−	0.405517i
$362$	13.3484	+	9.49148i	0.701579	+	0.498861i
$363$	−5.77367	+	13.5219i	−0.303039	+	0.709718i
$364$	−32.2591	−	10.9178i	−1.69084	−	0.572248i
$365$	8.95612			0.468785
$366$	7.22135	−	4.41889i	0.377466	−	0.230979i
$367$	−3.10999	−	1.79556i	−0.162340	−	0.0937272i	0.416629	−	0.909077i	$-0.363211\pi$
$367$	−3.10999	−	1.79556i	−0.162340	−	0.0937272i	−0.578969	+	0.815349i	$0.696545\pi$
$368$	−13.7324	−	5.45359i	−0.715850	−	0.284288i
$369$	−1.43271	−	0.417421i	−0.0745839	−	0.0217301i
$370$	−10.2803	+	4.70347i	−0.534449	+	0.244522i
$371$	20.2391	−	8.23139i	1.05076	−	0.427353i
$372$	7.81917	−	3.82184i	0.405405	−	0.198153i
$373$	13.4339	−	7.75604i	0.695579	−	0.401593i	−0.110120	−	0.993918i	$-0.535123\pi$
$373$	13.4339	−	7.75604i	0.695579	−	0.401593i	0.805699	+	0.592326i	$0.201790\pi$
$374$	18.1478	+	1.72024i	0.938401	+	0.0889516i
$375$	11.6310	+	15.5034i	0.600625	+	0.800590i
$376$	−2.13866	−	8.73652i	−0.110293	−	0.450551i
$377$			42.9856i			2.21387i
$378$	−15.4551	+	11.7957i	−0.794926	+	0.606706i
$379$	−14.5848			−0.749171			−0.374586	−	0.927192i	$-0.622215\pi$
$379$	−14.5848			−0.749171			−0.374586	+	0.927192i	$0.622215\pi$
$380$	8.64272	+	1.65335i	0.443362	+	0.0848152i
$381$	−3.20547	+	2.40483i	−0.164221	+	0.123203i
$382$	2.13171	+	0.202066i	0.109068	+	0.0103386i
$383$	−5.47353	−	9.48043i	−0.279684	−	0.484427i	0.691622	−	0.722260i	$-0.256896\pi$
$383$	−5.47353	−	9.48043i	−0.279684	−	0.484427i	−0.971306	+	0.237832i	$0.923563\pi$
$384$	16.7924	+	10.1003i	0.856932	+	0.515430i
$385$	9.92420	−	12.7629i	0.505784	−	0.650456i
$386$	9.38818	+	20.5197i	0.477846	+	1.04442i
$387$	−0.726628	+	2.49400i	−0.0369366	+	0.126777i
$388$	−0.782939	−	2.25207i	−0.0397477	−	0.114332i
$389$	−9.51835	+	16.4863i	−0.482600	+	0.835887i	−0.999800	−	0.0199769i	$-0.993641\pi$
$389$	−9.51835	+	16.4863i	−0.482600	+	0.835887i	0.517201	+	0.855864i	$0.326974\pi$
$390$	18.6135	−	11.3900i	0.942532	−	0.576755i
$391$		−	10.7856i		−	0.545453i
$392$	0.684373	−	19.7872i	0.0345661	−	0.999402i
$393$	−7.56676	−	3.23089i	−0.381692	−	0.162977i
$394$	0.789218	−	1.10993i	0.0397602	−	0.0559172i
$395$	2.28492	+	1.31920i	0.114967	+	0.0663760i
$396$	−23.5853	−	12.0554i	−1.18520	−	0.605805i
$397$	−6.49649	+	3.75075i	−0.326050	+	0.188245i	−0.654086	−	0.756420i	$-0.726947\pi$
$397$	−6.49649	+	3.75075i	−0.326050	+	0.188245i	0.328036	+	0.944665i	$0.393613\pi$
$398$	2.56293	−	1.17259i	0.128468	−	0.0587768i
$399$	−12.7384	+	7.06399i	−0.637720	+	0.353642i
$400$	1.78938	+	12.2056i	0.0894690	+	0.610281i
$401$	24.3528	−	14.0601i	1.21612	−	0.702128i	0.252035	−	0.967718i	$-0.418900\pi$
$401$	24.3528	−	14.0601i	1.21612	−	0.702128i	0.964086	+	0.265591i	$0.0855670\pi$
$402$	−7.88242	+	14.4955i	−0.393139	+	0.722968i
$403$	8.08501	−	14.0036i	0.402743	−	0.697571i
$404$	−4.06886	−	0.778373i	−0.202433	−	0.0387255i
$405$	0.540584	−	12.4460i	0.0268618	−	0.618445i
$406$	−23.9338	+	7.18823i	−1.18781	+	0.356746i
$407$	25.4954			1.26376
$408$	−2.32801	+	14.1135i	−0.115254	+	0.698724i
$409$	6.57782	−	11.3931i	0.325252	−	0.563353i	−0.656311	−	0.754490i	$-0.727884\pi$
$409$	6.57782	−	11.3931i	0.325252	−	0.563353i	0.981563	+	0.191137i	$0.0612175\pi$
$410$	−0.0918887	+	0.969386i	−0.00453806	+	0.0478746i
$411$	−0.0696427	−	0.577335i	−0.00343522	−	0.0284778i
$412$	8.38836	+	7.24827i	0.413265	+	0.357096i
$413$	7.62258	+	18.7422i	0.375083	+	0.922242i
$414$	−5.78409	+	14.5655i	−0.284273	+	0.715856i
$415$	8.39196	−	4.84510i	0.411945	−	0.237837i
$416$	36.3606	−	1.85810i	1.78272	−	0.0911008i
$417$	−9.72296	−	12.9600i	−0.476135	−	0.634654i
$418$	−16.1727	−	11.4997i	−0.791033	−	0.562468i
$419$		−	4.42222i		−	0.216040i	−0.994149	−	0.108020i	$-0.965549\pi$
$419$		−	4.42222i		−	0.216040i	0.994149	−	0.108020i	$-0.0344510\pi$
$420$	9.45442	+	8.45907i	0.461329	+	0.412760i
$421$		−	22.2013i		−	1.08203i	−0.841014	−	0.541014i	$-0.818041\pi$
$421$		−	22.2013i		−	1.08203i	0.841014	−	0.541014i	$-0.181959\pi$
$422$	17.5843	−	24.7299i	0.855992	−	1.20383i
$423$	−9.26642	+	2.26859i	−0.450549	+	0.110303i
$424$	−16.8712	+	16.1536i	−0.819336	+	0.784487i
$425$	−7.79844	+	4.50243i	−0.378280	+	0.218400i
$426$	4.66322	−	0.119123i	0.225934	−	0.00577153i
$427$	9.05832	+	1.25180i	0.438363	+	0.0605788i
$428$	9.04328	+	7.81418i	0.437124	+	0.377713i
$429$	−48.8582	+	5.89367i	−2.35890	+	0.284549i
$430$	1.68746	+	0.159956i	0.0813767	+	0.00771375i
$431$	−8.76759	+	15.1859i	−0.422320	+	0.731479i	−0.996166	−	0.0874837i	$-0.972117\pi$
$431$	−8.76759	+	15.1859i	−0.422320	+	0.731479i	0.573846	+	0.818963i	$0.305451\pi$
$432$	10.7126	−	17.8112i	0.515412	−	0.856943i
$433$	0.852347			0.0409612			0.0204806	−	0.999790i	$-0.493480\pi$
$433$	0.852347			0.0409612			0.0204806	+	0.999790i	$0.493480\pi$
$434$	9.14905	+	2.15987i	0.439168	+	0.103677i
$435$	6.28786	−	14.7262i	0.301480	−	0.706066i
$436$	0.623089	−	3.25713i	0.0298405	−	0.155988i
$437$	−5.87066	+	10.1683i	−0.280832	+	0.486415i
$438$	7.57138	−	13.9235i	0.361775	−	0.665290i
$439$	14.5943	−	8.42604i	0.696549	−	0.402153i	−0.109512	−	0.993986i	$-0.534929\pi$
$439$	14.5943	−	8.42604i	0.696549	−	0.402153i	0.806061	+	0.591833i	$0.201595\pi$
$440$	−4.83492	+	16.5935i	−0.230496	+	0.791064i
$441$	−20.9875	−	0.725433i	−0.999403	−	0.0345444i
$442$	11.0569	+	24.1671i	0.525925	+	1.14951i
$443$	−24.9578	+	14.4094i	−1.18578	+	0.684611i	−0.957345	−	0.288948i	$-0.906695\pi$
$443$	−24.9578	+	14.4094i	−1.18578	+	0.684611i	−0.228436	+	0.973559i	$0.573361\pi$
$444$	−1.37869	+	19.9584i	−0.0654297	+	0.947183i
$445$	11.3888	+	6.57531i	0.539879	+	0.311699i
$446$	14.0540	+	9.99317i	0.665477	+	0.473190i
$447$	−1.40881	+	3.29945i	−0.0666347	+	0.156058i
$448$	7.11493	+	19.9343i	0.336149	+	0.941809i
$449$		−	1.27217i		−	0.0600373i	−0.999549	−	0.0300186i	$-0.990443\pi$
$449$		−	1.27217i		−	0.0600373i	0.999549	−	0.0300186i	$-0.00955666\pi$
$450$	12.9460	−	1.89820i	0.610279	−	0.0894822i
$451$	1.09797	−	1.90174i	0.0517015	−	0.0895496i
$452$	31.0841	−	10.8065i	1.46207	−	0.508294i
$453$	−4.85413	−	40.2406i	−0.228067	−	1.89067i
$454$	20.1886	−	9.23669i	0.947497	−	0.433499i
$455$	23.3485	+	3.22660i	1.09459	+	0.151265i
$456$	9.87680	−	12.0385i	0.462523	−	0.563756i
$457$	7.46471	+	12.9293i	0.349185	+	0.604805i	0.986105	−	0.166124i	$-0.0531253\pi$
$457$	7.46471	+	12.9293i	0.349185	+	0.604805i	−0.636920	+	0.770930i	$0.719792\pi$
$458$	−1.61644	+	17.0527i	−0.0755312	+	0.796822i
$459$	14.9697	+	2.46890i	0.698726	+	0.115239i
$460$	10.0440	+	1.92142i	0.468305	+	0.0895867i
$461$	−27.1371			−1.26390			−0.631950	−	0.775009i	$-0.717745\pi$
$461$	−27.1371			−1.26390			−0.631950	+	0.775009i	$0.717745\pi$
$462$	−11.4518	−	26.2180i	−0.532786	−	1.21977i
$463$		−	24.3062i		−	1.12960i	−0.825227	−	0.564801i	$-0.808953\pi$
$463$		−	24.3062i		−	1.12960i	0.825227	−	0.564801i	$-0.191047\pi$
$464$	20.9539	−	16.5724i	0.972762	−	0.769353i
$465$	−4.81822	+	3.61476i	−0.223440	+	0.167631i
$466$	0.779565	−	8.22408i	0.0361127	−	0.380973i
$467$	−22.2686	+	12.8568i	−1.03047	+	0.594940i	−0.917118	−	0.398615i	$-0.869491\pi$
$467$	−22.2686	+	12.8568i	−1.03047	+	0.594940i	−0.113349	+	0.993555i	$0.536158\pi$
$468$	−1.97165	−	38.5661i	−0.0911395	−	1.78272i
$469$	−16.5089	+	6.71430i	−0.762311	+	0.310038i
$470$	2.58988	+	5.66069i	0.119462	+	0.261108i
$471$	4.62904	+	38.3745i	0.213295	+	1.76820i
$472$	−14.9588	−	15.6233i	−0.688535	−	0.719122i
$473$	−3.31047	−	1.91130i	−0.152216	−	0.0878817i
$474$	3.98251	−	2.43698i	0.182923	−	0.111934i
$475$	9.80275			0.449781
$476$	−11.6069	+	10.1977i	−0.532002	+	0.467410i
$477$	17.1338	+	17.8942i	0.784504	+	0.819319i
$478$	−18.5353	+	26.0674i	−0.847787	+	1.19229i
$479$	4.48448	−	7.76735i	0.204901	−	0.354899i	−0.745200	−	0.666841i	$-0.767646\pi$
$479$	4.48448	−	7.76735i	0.204901	−	0.354899i	0.950101	+	0.311942i	$0.100979\pi$
$480$	−12.7283	−	4.68220i	−0.580967	−	0.213712i
$481$	18.5849	+	32.1900i	0.847399	+	1.46774i
$482$	−14.9988	−	32.7828i	−0.683176	−	1.49321i
$483$	−14.8038	+	8.20932i	−0.673596	+	0.373537i
$484$	11.1002	−	12.8462i	0.504554	−	0.583916i
$485$	0.825074	+	1.42907i	0.0374647	+	0.0648908i
$486$	−18.8919	−	11.3621i	−0.856954	−	0.515393i
$487$	−5.02256	−	2.89978i	−0.227594	−	0.131401i	0.381868	−	0.924217i	$-0.375281\pi$
$487$	−5.02256	−	2.89978i	−0.227594	−	0.131401i	−0.609462	+	0.792816i	$0.708614\pi$
$488$	−9.49542	+	2.32443i	−0.429837	+	0.105222i
$489$	11.5630	−	27.0805i	0.522896	−	1.22462i
$490$	2.10790	+	13.5397i	0.0952252	+	0.611660i
$491$			13.5893i			0.613275i	0.951826	+	0.306637i	$0.0992039\pi$
$491$			13.5893i			0.613275i	−0.951826	+	0.306637i	$0.900796\pi$
$492$	1.42936	+	0.962359i	0.0644404	+	0.0433865i
$493$	16.8885	+	9.75058i	0.760620	+	0.439144i
$494$	2.73017	−	28.8021i	0.122836	−	1.29587i
$495$	17.6002	+	5.12782i	0.791069	+	0.230479i
$496$	−9.94331	+	1.45772i	−0.446468	+	0.0654535i
$497$	3.97752	+	3.09286i	0.178416	+	0.138734i
$498$	−0.437906	−	17.1424i	−0.0196230	−	0.768169i
$499$	18.6144	+	32.2411i	0.833294	+	1.44331i	0.895412	+	0.445239i	$0.146881\pi$
$499$	18.6144	+	32.2411i	0.833294	+	1.44331i	−0.0621178	+	0.998069i	$0.519785\pi$
$500$	−7.34890	−	21.1386i	−0.328653	−	0.945348i
$501$	24.8572	+	33.1329i	1.11054	+	1.48027i
$502$	−1.27942	−	0.909740i	−0.0571034	−	0.0406037i
$503$	−24.5224			−1.09340			−0.546699	−	0.837329i	$-0.684116\pi$
$503$	−24.5224			−1.09340			−0.546699	+	0.837329i	$0.684116\pi$
$504$	21.1434	−	7.54698i	0.941802	−	0.336169i
$505$	2.86710			0.127584
$506$	−18.7949	−	13.3642i	−0.835534	−	0.594111i
$507$	−29.5440	−	39.3800i	−1.31209	−	1.74893i
$508$	4.37061	−	1.51945i	0.193914	−	0.0674149i
$509$	21.4381	+	37.1319i	0.950226	+	1.64584i	0.744932	+	0.667140i	$0.232482\pi$
$509$	21.4381	+	37.1319i	0.950226	+	1.64584i	0.205294	+	0.978700i	$0.434185\pi$
$510$	−0.252812	−	9.89665i	−0.0111947	−	0.438231i
$511$	15.8575	−	6.44936i	0.701494	−	0.285303i
$512$	−14.9240	−	17.0081i	−0.659552	−	0.751659i
$513$	−12.7690	−	10.4756i	−0.563766	−	0.462511i
$514$	−1.86317	+	19.6557i	−0.0821811	+	0.866975i
$515$	−6.64470	−	3.83632i	−0.292800	−	0.169048i
$516$	1.67523	−	2.48816i	0.0737479	−	0.109535i
$517$		−	14.0386i		−	0.617416i
$518$	−14.8151	+	15.7308i	−0.650939	+	0.691170i
$519$	5.96415	−	13.9681i	0.261797	−	0.613129i
$520$	−24.4751	+	5.99139i	−1.07330	+	0.262740i
$521$	1.58214	+	0.913450i	0.0693149	+	0.0400190i	0.534257	−	0.845322i	$-0.320591\pi$
$521$	1.58214	+	0.913450i	0.0693149	+	0.0400190i	−0.464942	+	0.885341i	$0.653925\pi$
$522$	−17.5781	−	22.2246i	−0.769374	−	0.972746i
$523$	12.7145	+	22.0222i	0.555966	+	0.962962i	0.997828	+	0.0658788i	$0.0209851\pi$
$523$	12.7145	+	22.0222i	0.555966	+	0.962962i	−0.441861	+	0.897083i	$0.645682\pi$
$524$	7.18859	+	6.21156i	0.314035	+	0.271353i
$525$	12.1154	+	7.27676i	0.528761	+	0.317584i
$526$	−8.33708	−	18.2223i	−0.363514	−	0.794530i
$527$	−3.66790	−	6.35300i	−0.159776	−	0.276741i
$528$	21.7094	+	21.5444i	0.944781	+	0.937601i
$529$	4.67750	−	8.10166i	0.203369	−	0.352246i
$530$	9.36786	−	13.1746i	0.406914	−	0.572268i
$531$	−16.5707	+	15.8666i	−0.719107	+	0.688551i
$532$	16.4932	−	3.29629i	0.715070	−	0.142912i
$533$	3.20148			0.138671
$534$	19.8501	−	12.1467i	0.858998	−	0.525638i
$535$	−7.16348	−	4.13584i	−0.309704	−	0.178808i
$536$	13.7617	−	13.1764i	0.594415	−	0.569133i
$537$	−1.26147	−	10.4575i	−0.0544362	−	0.451274i
$538$	−10.7205	−	23.4317i	−0.462192	−	1.01021i
$539$	8.38092	−	29.7441i	0.360992	−	1.28117i
$540$	−4.96593	+	13.5006i	−0.213700	+	0.580971i
$541$	16.3531	−	9.44148i	0.703076	−	0.405921i	−0.105416	−	0.994428i	$-0.533618\pi$
$541$	16.3531	−	9.44148i	0.703076	−	0.405921i	0.808492	+	0.588507i	$0.200284\pi$
$542$	−3.37911	+	35.6481i	−0.145145	+	1.53122i
$543$	−16.0463	+	12.0383i	−0.688611	+	0.516615i
$544$	7.51777	−	14.7071i	0.322322	−	0.630561i
$545$			2.29512i			0.0983119i
$546$	24.7546	−	33.5706i	1.05940	−	1.43669i
$547$	13.0624			0.558509			0.279254	−	0.960217i	$-0.409913\pi$
$547$	13.0624			0.558509			0.279254	+	0.960217i	$0.409913\pi$
$548$	−0.126167	+	0.659522i	−0.00538957	+	0.0281734i
$549$	2.46565	+	10.0714i	0.105231	+	0.429835i
$550$	−1.81697	+	19.1683i	−0.0774759	+	0.817337i
$551$	−10.6145	−	18.3849i	−0.452195	−	0.783224i
$552$	11.4782	−	13.9904i	0.488544	−	0.595472i
$553$	4.99558	+	0.690356i	0.212434	+	0.0293569i
$554$	−24.1782	+	11.0620i	−1.02723	+	0.469981i
$555$	−1.65819	−	13.7464i	−0.0703864	−	0.583500i
$556$	6.14330	+	17.6708i	0.260534	+	0.749408i
$557$	15.9928	−	27.7003i	0.677635	−	1.17370i	−0.298056	−	0.954549i	$-0.596338\pi$
$557$	15.9928	−	27.7003i	0.677635	−	1.17370i	0.975691	−	0.219151i	$-0.0703286\pi$
$558$	1.54637	+	10.5464i	0.0654631	+	0.446467i
$559$		−	5.57299i		−	0.235712i
$560$	−7.42875	−	12.6255i	−0.313922	−	0.533524i
$561$	−8.76714	+	20.5327i	−0.370149	+	0.866890i
$562$	−29.3797	−	20.8906i	−1.23931	−	0.881216i
$563$	31.2546	+	18.0449i	1.31723	+	0.760501i	0.983281	−	0.182092i	$-0.0582870\pi$
$563$	31.2546	+	18.0449i	1.31723	+	0.760501i	0.333944	+	0.942593i	$0.391620\pi$
$564$	10.9897	+	0.759151i	0.462752	+	0.0319660i
$565$	−19.7247	+	11.3881i	−0.829825	+	0.479100i
$566$	7.08224	+	15.4796i	0.297689	+	0.650656i
$567$	−8.00527	−	22.4258i	−0.336190	−	0.941794i
$568$	−5.17133	−	1.50679i	−0.216984	−	0.0632236i
$569$	−23.5336	+	13.5871i	−0.986579	+	0.569601i	−0.904250	−	0.427004i	$-0.859569\pi$
$569$	−23.5336	+	13.5871i	−0.986579	+	0.569601i	−0.0823288	+	0.996605i	$0.526236\pi$
$570$	−5.14844	+	9.46778i	−0.215644	+	0.396562i
$571$	−7.45448	+	12.9115i	−0.311960	+	0.540331i	−0.978787	−	0.204882i	$-0.934319\pi$
$571$	−7.45448	+	12.9115i	−0.311960	+	0.540331i	0.666826	+	0.745213i	$0.267652\pi$
$572$	55.8135	+	10.6771i	2.33368	+	0.446433i
$573$	−1.02982	+	2.41185i	−0.0430215	+	0.100756i
$574$	0.535365	+	1.78254i	0.0223457	+	0.0744018i
$575$	11.3921			0.475084
$576$	−18.0395	+	15.8296i	−0.751645	+	0.659568i
$577$	−19.1659	+	33.1963i	−0.797886	+	1.38198i	0.123104	+	0.992394i	$0.460715\pi$
$577$	−19.1659	+	33.1963i	−0.797886	+	1.38198i	−0.920990	+	0.389585i	$0.872618\pi$
$578$	−11.9313	−	1.13098i	−0.496277	−	0.0470424i
$579$	−27.4379	+	3.30978i	−1.14028	+	0.137550i
$580$	−12.0887	+	13.9902i	−0.501958	+	0.580912i
$581$	11.3696	−	14.6217i	0.471691	−	0.606611i
$582$	2.91919	−	0.0745713i	0.121004	−	0.00309108i
$583$	−31.5722	+	18.2282i	−1.30759	+	0.754935i
$584$	−13.2187	+	12.6564i	−0.546993	+	0.523727i
$585$	6.35539	+	25.9596i	0.262763	+	1.07330i
$586$	−3.19996	+	4.50029i	−0.132189	+	0.185905i
$587$		−	0.964880i		−	0.0398249i	−0.999802	−	0.0199124i	$-0.993661\pi$
$587$		−	0.964880i		−	0.0398249i	0.999802	−	0.0199124i	$-0.00633874\pi$
$588$	22.8312	+	8.16923i	0.941543	+	0.336894i
$589$			7.98581i			0.329050i
$590$	12.2002	+	8.67499i	0.502273	+	0.357144i
$591$	1.00099	+	1.33425i	0.0411752	+	0.0548837i
$592$	8.52637	−	21.4698i	0.350432	−	0.882403i
$593$	−14.9519	+	8.63251i	−0.614003	+	0.354495i	−0.774530	−	0.632537i	$-0.782014\pi$
$593$	−14.9519	+	8.63251i	−0.614003	+	0.354495i	0.160528	+	0.987031i	$0.448680\pi$
$594$	22.8508	−	23.0268i	0.937581	−	0.944802i
$595$	6.56390	−	8.44141i	0.269094	−	0.346064i
$596$	2.70852	−	3.13455i	0.110945	−	0.128396i
$597$	0.413395	+	3.42702i	0.0169191	+	0.140259i
$598$	3.17283	−	33.4720i	0.129747	−	1.36877i
$599$	−6.22127	+	10.7756i	−0.254194	+	0.440277i	−0.964676	−	0.263438i	$-0.915144\pi$
$599$	−6.22127	+	10.7756i	−0.254194	+	0.440277i	0.710482	+	0.703715i	$0.248477\pi$
$600$	−14.9071	−	2.45891i	−0.608581	−	0.100385i
$601$	−27.7052			−1.13012			−0.565059	−	0.825051i	$-0.691147\pi$
$601$	−27.7052			−1.13012			−0.565059	+	0.825051i	$0.691147\pi$
$602$	3.10297	−	0.931939i	0.126467	−	0.0379830i
$603$	−13.9760	−	14.5962i	−0.569146	−	0.594403i
$604$	−8.79389	+	45.9691i	−0.357818	+	1.87045i
$605$	−5.87504	+	10.1759i	−0.238854	+	0.413708i
$606$	2.42380	−	4.45729i	0.0984603	−	0.181065i
$607$	−5.43950	+	3.14050i	−0.220783	+	0.127469i	−0.606313	−	0.795226i	$-0.707352\pi$
$607$	−5.43950	+	3.14050i	−0.220783	+	0.127469i	0.385530	+	0.922695i	$0.374019\pi$
$608$	−15.0926	+	9.77331i	−0.612085	+	0.396360i
$609$	0.528717	−	30.6017i	0.0214247	−	1.24004i
$610$	6.15241	−	2.81486i	0.249104	−	0.113970i
$611$	17.7249	−	10.2335i	0.717072	−	0.414002i
$612$	−15.5994	−	7.97346i	−0.630568	−	0.322308i
$613$	17.0190	+	9.82590i	0.687389	+	0.396864i	0.802633	−	0.596473i	$-0.203432\pi$
$613$	17.0190	+	9.82590i	0.687389	+	0.396864i	−0.115244	+	0.993337i	$0.536765\pi$
$614$	−9.04262	+	12.7172i	−0.364930	+	0.513224i
$615$	−1.09678	−	0.468307i	−0.0442263	−	0.0188840i
$616$	3.38849	+	32.8617i	0.136526	+	1.32403i
$617$		−	32.2579i		−	1.29865i	−0.760509	−	0.649327i	$-0.775051\pi$
$617$		−	32.2579i		−	1.29865i	0.760509	−	0.649327i	$-0.224949\pi$
$618$	−11.5814	+	7.08689i	−0.465872	+	0.285077i
$619$	13.3846	−	23.1828i	0.537973	−	0.931797i	−0.461040	−	0.887379i	$-0.652524\pi$
$619$	13.3846	−	23.1828i	0.537973	−	0.931797i	0.999013	−	0.0444173i	$-0.0141431\pi$
$620$	6.56958	−	2.28393i	0.263841	−	0.0917250i
$621$	−14.8393	−	12.1741i	−0.595482	−	0.488531i
$622$	−18.4224	−	40.2657i	−0.738671	−	1.61451i
$623$	24.8996	+	3.44096i	0.997581	+	0.137859i
$624$	−11.3765	+	43.1148i	−0.455424	+	1.72597i
$625$	0.0343418	+	0.0594818i	0.00137367	+	0.00237927i
$626$	18.3890	+	1.74310i	0.734972	+	0.0696684i
$627$	19.4413	−	14.5854i	0.776411	−	0.582485i
$628$	8.38609	−	43.8374i	0.334642	−	1.74930i
$629$	16.8627			0.672361
$630$	−13.3912	+	7.87967i	−0.533518	+	0.313934i
$631$		−	29.4363i		−	1.17184i	−0.810369	−	0.585920i	$-0.800733\pi$
$631$		−	29.4363i		−	1.17184i	0.810369	−	0.585920i	$-0.199267\pi$
$632$	−5.23663	+	1.28190i	−0.208302	+	0.0509914i
$633$	22.3027	+	29.7280i	0.886455	+	1.18158i
$634$	34.4416	+	3.26474i	1.36785	+	0.129659i
$635$	−2.77341	+	1.60123i	−0.110059	+	0.0635428i
$636$	−12.5622	−	25.7012i	−0.498123	−	1.01912i
$637$	43.6637	−	11.1004i	1.73002	−	0.439815i
$638$	37.9173	−	17.3479i	1.50116	−	0.686811i
$639$	−1.59808	+	5.48506i	−0.0632189	+	0.216986i
$640$	12.3565	+	9.62085i	0.488435	+	0.380298i
$641$	34.2214	+	19.7578i	1.35167	+	0.780384i	0.988483	−	0.151334i	$-0.0483568\pi$
$641$	34.2214	+	19.7578i	1.35167	+	0.780384i	0.363183	+	0.931718i	$0.381690\pi$
$642$	−12.4856	+	7.64021i	−0.492768	+	0.301535i
$643$	17.3857			0.685626			0.342813	−	0.939404i	$-0.388620\pi$
$643$	17.3857			0.685626			0.342813	+	0.939404i	$0.388620\pi$
$644$	19.1673	−	3.83074i	0.755298	−	0.150952i
$645$	−0.815208	+	1.90922i	−0.0320988	+	0.0751754i
$646$	−10.6967	−	7.60594i	−0.420856	−	0.299252i
$647$	−23.6414	+	40.9480i	−0.929438	+	1.60983i	−0.145174	+	0.989406i	$0.546374\pi$
$647$	−23.6414	+	40.9480i	−0.929438	+	1.60983i	−0.784264	+	0.620427i	$0.786959\pi$
$648$	16.7903	+	19.1334i	0.659584	+	0.751631i
$649$	−16.8800	−	29.2370i	−0.662598	−	1.14765i
$650$	−25.5260	+	11.6787i	−1.00121	+	0.458075i
$651$	−5.92802	+	9.86985i	−0.232337	+	0.386830i
$652$	−22.2305	+	25.7271i	−0.870612	+	1.00755i
$653$	−14.1939	−	24.5845i	−0.555449	−	0.962067i	−0.997868	−	0.0652581i	$-0.979213\pi$
$653$	−14.1939	−	24.5845i	−0.555449	−	0.962067i	0.442419	−	0.896808i	$-0.354120\pi$
$654$	3.56806	+	1.94026i	0.139522	+	0.0758701i
$655$	−5.69432	−	3.28762i	−0.222495	−	0.128458i
$656$	−1.23428	−	1.56061i	−0.0481904	−	0.0609314i
$657$	13.4245	+	14.0202i	0.523739	+	0.546981i
$658$	8.66188	+	8.15769i	0.337675	+	0.318020i
$659$			3.58703i			0.139731i	0.997556	+	0.0698654i	$0.0222570\pi$
$659$			3.58703i			0.139731i	−0.997556	+	0.0698654i	$0.977743\pi$
$660$	−17.5590	−	11.8221i	−0.683483	−	0.460175i
$661$	1.09189	+	0.630403i	0.0424696	+	0.0245198i	0.521084	−	0.853505i	$-0.325528\pi$
$661$	1.09189	+	0.630403i	0.0424696	+	0.0245198i	−0.478615	+	0.878025i	$0.658861\pi$
$662$	−20.4503	−	1.93849i	−0.794822	−	0.0753417i
$663$	−32.3150	+	3.89810i	−1.25501	+	0.151390i
$664$	−5.53910	+	19.0103i	−0.214959	+	0.737741i
$665$	−10.7829	+	4.38548i	−0.418142	+	0.170062i
$666$	−22.7723	−	9.04309i	−0.882411	−	0.350413i
$667$	−12.3355	−	21.3658i	−0.477634	−	0.827286i
$668$	−15.7057	−	45.1762i	−0.607670	−	1.74792i
$669$	−16.8944	+	12.6747i	−0.653176	+	0.490030i
$670$	−7.64131	+	10.7464i	−0.295210	+	0.415171i
$671$	−15.2581			−0.589031
$672$	−25.9082	+	0.875563i	−0.999429	+	0.0337756i
$673$	34.9662			1.34785			0.673925	−	0.738800i	$-0.264607\pi$
$673$	34.9662			1.34785			0.673925	+	0.738800i	$0.264607\pi$
$674$	−15.4033	+	21.6626i	−0.593314	+	0.834413i
$675$	−2.60773	+	15.8115i	−0.100372	+	0.608583i
$676$	18.6669	+	53.6941i	0.717958	+	2.06516i
$677$	−2.84885	−	4.93435i	−0.109490	−	0.189642i	0.806074	−	0.591815i	$-0.201588\pi$
$677$	−2.84885	−	4.93435i	−0.109490	−	0.189642i	−0.915564	+	0.402173i	$0.868255\pi$
$678$	1.02927	+	40.2920i	0.0395288	+	1.54741i
$679$	2.48994	+	1.93614i	0.0955551	+	0.0743021i
$680$	−3.19783	+	10.9750i	−0.122631	+	0.420872i
$681$	3.25637	+	26.9952i	0.124784	+	1.03446i
$682$	−15.6154	−	1.48020i	−0.597945	−	0.0566796i
$683$	−19.9548	−	11.5209i	−0.763551	−	0.440836i	0.0670183	−	0.997752i	$-0.478651\pi$
$683$	−19.9548	−	11.5209i	−0.763551	−	0.440836i	−0.830569	+	0.556915i	$0.811985\pi$
$684$	10.3665	+	16.0079i	0.396373	+	0.612076i
$685$		−	0.464729i		−	0.0177564i
$686$	13.4822	+	22.4551i	0.514752	+	0.857339i
$687$	−19.2937	−	8.23812i	−0.736100	−	0.314304i
$688$	−2.71663	+	2.14857i	−0.103571	+	0.0819136i
$689$	−46.0293	−	26.5750i	−1.75358	−	1.01243i
$690$	−5.98318	+	11.0028i	−0.227776	+	0.418871i
$691$	−18.0614	−	31.2833i	−0.687090	−	1.19007i	−0.972775	−	0.231751i	$-0.925555\pi$
$691$	−18.0614	−	31.2833i	−0.687090	−	1.19007i	0.285686	−	0.958323i	$-0.407779\pi$
$692$	−11.4664	+	13.2700i	−0.435887	+	0.504448i
$693$	34.8550	−	3.59479i	1.32403	−	0.136555i
$694$	30.7996	−	14.0915i	1.16914	−	0.534904i
$695$	−6.47392	−	11.2132i	−0.245570	−	0.425339i
$696$	11.5300	+	30.6207i	0.437043	+	1.16067i
$697$	0.726203	−	1.25782i	0.0275069	−	0.0476434i
$698$	4.14254	+	2.94557i	0.156797	+	0.111492i
$699$	9.30483	+	3.97302i	0.351941	+	0.150274i
$700$	−10.7711	−	12.2596i	−0.407109	−	0.463368i
$701$	29.8672			1.12807			0.564035	−	0.825751i	$-0.309248\pi$
$701$	29.8672			1.12807			0.564035	+	0.825751i	$0.309248\pi$
$702$	45.7304	+	12.0656i	1.72598	+	0.455387i
$703$	−15.8975	−	9.17844i	−0.599586	−	0.346171i
$704$	−16.3132	−	31.3235i	−0.614829	−	1.18055i
$705$	−7.56919	+	0.913056i	−0.285072	+	0.0343877i
$706$	−33.3525	+	15.2595i	−1.25524	+	0.574298i
$707$	5.07641	−	2.06461i	0.190918	−	0.0776478i
$708$	23.8003	−	11.6331i	0.894469	−	0.437197i
$709$	−42.5302	+	24.5548i	−1.59725	+	0.922175i	−0.605240	+	0.796043i	$0.706923\pi$
$709$	−42.5302	+	24.5548i	−1.59725	+	0.922175i	−0.992013	+	0.126132i	$0.959744\pi$
$710$	3.71124	+	0.351791i	0.139281	+	0.0132025i
$711$	1.35978	+	5.55426i	0.0509959	+	0.208301i
$712$	−26.1011	+	6.38942i	−0.978179	+	0.239454i
$713$			9.28059i			0.347561i
$714$	−7.57426	−	17.3407i	−0.283460	−	0.648960i
$715$	−39.3287			−1.47081
$716$	−2.28531	+	11.9462i	−0.0854059	+	0.446450i
$717$	−23.5090	−	31.3358i	−0.877958	−	1.17026i
$718$	−39.9158	−	3.78365i	−1.48965	−	0.141204i
$719$	−8.31324	−	14.3990i	−0.310032	−	0.536991i	0.668337	−	0.743858i	$-0.267006\pi$
$719$	−8.31324	−	14.3990i	−0.310032	−	0.536991i	−0.978369	+	0.206868i	$0.933673\pi$
$720$	10.2042	−	13.1063i	0.380287	−	0.488444i
$721$	−14.5275	−	2.00760i	−0.541032	−	0.0747670i
$722$	−5.23464	−	11.4413i	−0.194813	−	0.425801i
$723$	43.8355	−	5.28778i	1.63026	−	0.196655i
$724$	21.8788	−	7.60624i	0.813121	−	0.282684i
$725$	−10.2989	+	17.8381i	−0.382490	+	0.662492i
$726$	10.8531	+	17.7361i	0.402795	+	0.658247i
$727$		−	6.37182i		−	0.236318i	−0.992995	−	0.118159i	$-0.962301\pi$
$727$		−	6.37182i		−	0.236318i	0.992995	−	0.118159i	$-0.0376992\pi$
$728$	−39.0206	+	28.2329i	−1.44620	+	1.04638i
$729$	20.2936	−	17.8092i	0.751616	−	0.659601i
$730$	7.33979	−	10.3224i	0.271658	−	0.382049i
$731$	−2.18956	−	1.26414i	−0.0809837	−	0.0467560i
$732$	0.825095	−	11.9444i	0.0304964	−	0.441477i
$733$	33.2648	−	19.2054i	1.22866	−	0.709369i	0.261912	−	0.965092i	$-0.415647\pi$
$733$	33.2648	−	19.2054i	1.22866	−	0.709369i	0.966750	+	0.255723i	$0.0823135\pi$
$734$	−4.61819	+	2.11292i	−0.170461	+	0.0779893i
$735$	−16.5822	−	2.58422i	−0.611645	−	0.0953204i
$736$	−17.5396	+	11.3579i	−0.646519	+	0.418658i
$737$	25.7533	−	14.8687i	0.948634	−	0.547694i
$738$	−1.65524	+	1.30918i	−0.0609304	+	0.0481917i
$739$	0.546366	−	0.946333i	0.0200984	−	0.0348114i	−0.855801	−	0.517305i	$-0.826935\pi$
$739$	0.546366	−	0.946333i	0.0200984	−	0.0348114i	0.875900	+	0.482493i	$0.160269\pi$
$740$	−3.00403	+	15.7032i	−0.110430	+	0.577262i
$741$	32.5871	+	13.9142i	1.19712	+	0.511151i
$742$	7.09940	−	30.0725i	0.260627	−	1.10399i
$743$	−26.5914			−0.975545			−0.487772	−	0.872971i	$-0.662190\pi$
$743$	−26.5914			−0.975545			−0.487772	+	0.872971i	$0.662190\pi$
$744$	2.00315	−	12.1441i	0.0734392	−	0.445224i
$745$	−1.43355	+	2.48298i	−0.0525212	+	0.0909693i
$746$	2.07018	−	21.8395i	0.0757947	−	0.799601i
$747$	20.1635	+	5.87467i	0.737746	+	0.214943i
$748$	16.8553	−	19.5065i	0.616291	−	0.713228i
$749$	−15.6617	−	2.16435i	−0.572267	−	0.0790835i
$750$	27.4004	−	0.699949i	1.00052	−	0.0255585i
$751$	−24.4781	+	14.1324i	−0.893217	+	0.515699i	−0.874993	−	0.484135i	$-0.839134\pi$
$751$	−24.4781	+	14.1324i	−0.893217	+	0.515699i	−0.0182235	+	0.999834i	$0.505801\pi$
$752$	−11.8220	−	4.69490i	−0.431103	−	0.171205i
$753$	1.53800	−	1.15385i	0.0560479	−	0.0420487i
$754$	49.5431	+	35.2279i	1.80425	+	1.28292i
$755$		−	32.3918i		−	1.17886i
$756$	0.929270	+	27.4797i	0.0337972	+	0.999429i
$757$			26.8780i			0.976898i	0.872592	+	0.488449i	$0.162437\pi$
$757$			26.8780i			0.976898i	−0.872592	+	0.488449i	$0.837563\pi$
$758$	−11.9526	+	16.8097i	−0.434140	+	0.610557i
$759$	22.5934	−	16.9502i	0.820090	−	0.615254i
$760$	8.98852	−	8.60621i	0.326048	−	0.312180i
$761$	46.8523	−	27.0502i	1.69840	−	0.980569i	0.751111	−	0.660176i	$-0.229518\pi$
$761$	46.8523	−	27.0502i	1.69840	−	0.980569i	0.947285	−	0.320393i	$-0.103815\pi$
$762$	0.144721	+	5.66529i	0.00524269	+	0.205232i
$763$	1.65273	+	4.06367i	0.0598327	+	0.147115i
$764$	1.97989	−	2.29131i	0.0716299	−	0.0828967i
$765$	11.6408	+	3.39156i	0.420875	+	0.122622i
$766$	−15.4124	−	1.46095i	−0.556872	−	0.0527863i
$767$	24.6095	−	42.6248i	0.888596	−	1.53909i
$768$	25.4029	−	11.0766i	0.916650	−	0.399691i
$769$	−9.44304			−0.340525			−0.170262	−	0.985399i	$-0.554462\pi$
$769$	−9.44304			−0.340525			−0.170262	+	0.985399i	$0.554462\pi$
$770$	−6.57670	−	21.8977i	−0.237008	−	0.789137i
$771$	−22.2387	−	9.49560i	−0.800907	−	0.341976i
$772$	31.3439	+	5.99608i	1.12809	+	0.215804i
$773$	18.7073	−	32.4020i	0.672856	−	1.16542i	−0.304235	−	0.952597i	$-0.598401\pi$
$773$	18.7073	−	32.4020i	0.672856	−	1.16542i	0.977091	−	0.212823i	$-0.0682659\pi$
$774$	2.27897	+	2.88138i	0.0819158	+	0.103569i
$775$	6.71022	−	3.87415i	0.241038	−	0.139164i
$776$	−3.23727	−	0.943256i	−0.116211	−	0.0338609i
$777$	−12.8348	−	23.1449i	−0.460445	−	0.830318i
$778$	11.2007	+	24.4813i	0.401565	+	0.877699i
$779$	−1.36927	+	0.790550i	−0.0490593	+	0.0283244i
$780$	2.12674	−	30.7875i	0.0761495	−	1.10237i
$781$	−7.28073	−	4.20353i	−0.260525	−	0.150414i
$782$	−12.4310	−	8.83913i	−0.444532	−	0.316087i
$783$	32.4779	−	12.2301i	1.16066	−	0.437068i
$784$	−22.2449	−	17.0049i	−0.794459	−	0.607318i
$785$			30.8897i			1.10250i
$786$	−9.92494	+	6.07327i	−0.354011	+	0.216626i
$787$	6.80641	−	11.7890i	0.242622	−	0.420234i	−0.718838	−	0.695178i	$-0.755326\pi$
$787$	6.80641	−	11.7890i	0.242622	−	0.420234i	0.961460	+	0.274943i	$0.0886591\pi$
$788$	−0.632460	−	1.81923i	−0.0225305	−	0.0648073i
$789$	24.3659	−	2.93921i	0.867451	−	0.104639i
$790$	3.39300	−	1.55237i	0.120717	−	0.0552307i
$791$	−26.7235	+	34.3673i	−0.950177	+	1.22196i
$792$	−33.2232	+	17.3035i	−1.18053	+	0.614854i
$793$	−11.1224	−	19.2646i	−0.394968	−	0.684105i
$794$	−1.00112	+	10.5614i	−0.0355284	+	0.374810i
$795$	11.8815	+	15.8373i	0.421395	+	0.561690i
$796$	0.748918	−	3.91488i	0.0265447	−	0.138759i
$797$	−45.9884			−1.62899			−0.814496	−	0.580169i	$-0.802987\pi$
$797$	−45.9884			−1.62899			−0.814496	+	0.580169i	$0.802987\pi$
$798$	−2.29789	+	20.4708i	−0.0813444	+	0.724660i
$799$		−	9.28517i		−	0.328486i
$800$	15.5341	+	7.94049i	0.549212	+	0.280739i
$801$	6.77760	+	27.6842i	0.239475	+	0.978174i
$802$	3.75281	−	39.5905i	0.132516	−	1.39799i
$803$	−24.7370	+	14.2819i	−0.872951	+	0.503999i
$804$	10.2469	+	20.9643i	0.361381	+	0.739355i
$805$	−12.5312	+	5.09652i	−0.441666	+	0.179629i
$806$	−9.51404	−	20.7948i	−0.335118	−	0.732464i
$807$	31.3316	−	3.77947i	1.10293	−	0.133044i
$808$	−4.23166	+	4.05167i	−0.148869	+	0.142537i
$809$	16.1190	+	9.30630i	0.566713	+	0.327192i	0.755836	−	0.654762i	$-0.227231\pi$
$809$	16.1190	+	9.30630i	0.566713	+	0.327192i	−0.189122	+	0.981954i	$0.560564\pi$
$810$	−13.9016	−	10.8229i	−0.488452	−	0.380276i
$811$	33.9178			1.19101			0.595507	−	0.803350i	$-0.296951\pi$
$811$	33.9178			1.19101			0.595507	+	0.803350i	$0.296951\pi$
$812$	−11.3296	+	33.4759i	−0.397591	+	1.17477i
$813$	−40.3328	−	17.2215i	−1.41453	−	0.603984i
$814$	20.8941	−	29.3847i	0.732339	−	1.02993i
$815$	11.7660	−	20.3793i	0.412145	−	0.713856i
$816$	14.3587	+	14.2496i	0.502655	+	0.498835i
$817$	1.37615	+	2.38357i	0.0481455	+	0.0833904i
$818$	−7.74045	−	16.9182i	−0.270638	−	0.591533i
$819$	29.9464	+	41.3869i	1.04641	+	1.44618i
$820$	1.04196	+	0.900345i	0.0363869	+	0.0314414i
$821$	14.0972	+	24.4171i	0.491996	+	0.852162i	0.999958	−	0.00921774i	$-0.00293414\pi$
$821$	14.0972	+	24.4171i	0.491996	+	0.852162i	−0.507962	+	0.861380i	$0.669601\pi$
$822$	−0.722482	−	0.392875i	−0.0251995	−	0.0137031i
$823$	16.0158	+	9.24672i	0.558275	+	0.322320i	0.752453	−	0.658646i	$-0.228871\pi$
$823$	16.0158	+	9.24672i	0.558275	+	0.322320i	−0.194178	+	0.980966i	$0.562204\pi$
$824$	15.2285	−	3.72786i	0.530510	−	0.129866i
$825$	−21.6872	−	9.26012i	−0.755052	−	0.322396i
$826$	27.8482	+	6.57431i	0.968964	+	0.228749i
$827$			14.5655i			0.506491i	0.967402	+	0.253245i	$0.0814980\pi$
$827$			14.5655i			0.506491i	−0.967402	+	0.253245i	$0.918502\pi$
$828$	12.0473	+	18.6033i	0.418672	+	0.646510i
$829$	−17.0346	−	9.83492i	−0.591635	−	0.341581i	0.174108	−	0.984726i	$-0.444296\pi$
$829$	−17.0346	−	9.83492i	−0.591635	−	0.341581i	−0.765744	+	0.643146i	$0.777629\pi$
$830$	1.29321	−	13.6429i	0.0448881	−	0.473550i
$831$	−3.89989	−	32.3299i	−0.135286	−	1.12151i
$832$	27.6569	−	43.4302i	0.958831	−	1.50567i
$833$	5.54317	−	19.6729i	0.192060	−	0.681624i
$834$	−22.9053	+	0.585121i	−0.793146	+	0.0202611i
$835$	16.5509	+	28.6670i	0.572767	+	0.992062i
$836$	−26.5080	+	9.21557i	−0.916797	+	0.318727i
$837$	−12.8808	−	2.12439i	−0.445226	−	0.0734295i
$838$	−5.09684	−	3.62413i	−0.176067	−	0.125194i
$839$	26.2321			0.905631			0.452816	−	0.891604i	$-0.350420\pi$
$839$	26.2321			0.905631			0.452816	+	0.891604i	$0.350420\pi$
$840$	17.4977	−	3.96427i	0.603727	−	0.136780i
$841$	15.6069			0.538171
$842$	−25.5882	−	18.1946i	−0.881827	−	0.627028i
$843$	35.3175	−	26.4962i	1.21640	−	0.912577i
$844$	−14.0917	−	40.5337i	−0.485055	−	1.39523i
$845$	−19.6715	−	34.0721i	−0.676721	−	1.17212i
$846$	−4.97942	+	12.5392i	−0.171196	+	0.431107i
$847$	−3.07449	+	22.2478i	−0.105641	+	0.764443i
$848$	4.79144	+	32.6832i	0.164539	+	1.12234i
$849$	−20.6986	+	2.49682i	−0.710373	+	0.0856908i
$850$	−1.20175	+	12.6780i	−0.0412197	+	0.434851i
$851$	−18.4751	−	10.6666i	−0.633317	−	0.365646i
$852$	3.68434	−	5.47222i	0.126223	−	0.187475i
$853$			21.5548i			0.738022i	0.929425	+	0.369011i	$0.120304\pi$
$853$			21.5548i			0.738022i	−0.929425	+	0.369011i	$0.879696\pi$
$854$	8.86631	−	9.41430i	0.303399	−	0.322151i
$855$	−9.12847	−	9.53357i	−0.312187	−	0.326041i
$856$	16.4175	−	4.01892i	0.561137	−	0.137364i
$857$	15.7399	+	9.08742i	0.537664	+	0.310420i	0.744132	−	0.668033i	$-0.232864\pi$
$857$	15.7399	+	9.08742i	0.537664	+	0.310420i	−0.206468	+	0.978453i	$0.566197\pi$
$858$	−33.2479	+	61.1417i	−1.13507	+	2.08734i
$859$	3.84011	+	6.65127i	0.131023	+	0.226938i	0.924071	−	0.382220i	$-0.124840\pi$
$859$	3.84011	+	6.65127i	0.131023	+	0.226938i	−0.793048	+	0.609159i	$0.791507\pi$
$860$	1.56728	−	1.81380i	0.0534438	−	0.0618501i
$861$	−2.27915	−	0.0393778i	−0.0776734	−	0.00134199i
$862$	10.3173	+	22.5504i	0.351407	+	0.768068i
$863$	16.7613	+	29.0314i	0.570562	+	0.988242i	0.996508	+	0.0834933i	$0.0266077\pi$
$863$	16.7613	+	29.0314i	0.570562	+	0.988242i	−0.425947	+	0.904748i	$0.640059\pi$
$864$	−11.7490	−	26.9436i	−0.399711	−	0.916641i
$865$	6.06886	−	10.5116i	0.206347	−	0.357404i
$866$	0.698521	−	0.982373i	0.0237367	−	0.0333824i
$867$	5.76398	−	13.4992i	0.195755	−	0.458458i
$868$	9.98726	−	8.77467i	0.338990	−	0.297832i
$869$	−8.41467			−0.285448
$870$	−11.8196	−	19.3156i	−0.400722	−	0.654860i
$871$	37.5458	+	21.6771i	1.27219	+	0.734500i
$872$	−3.24337	−	3.38745i	−0.109834	−	0.114713i
$873$	−1.00040	+	3.43366i	−0.0338584	+	0.116212i
$874$	6.90830	+	15.0994i	0.233677	+	0.510746i
$875$	23.3713	+	18.1732i	0.790095	+	0.614365i
$876$	−9.84257	−	20.1371i	−0.332550	−	0.680369i
$877$	22.4823	−	12.9802i	0.759174	−	0.438309i	−0.0698251	−	0.997559i	$-0.522244\pi$
$877$	22.4823	−	12.9802i	0.759174	−	0.438309i	0.828999	+	0.559250i	$0.188911\pi$
$878$	2.24901	−	23.7261i	0.0759004	−	0.800717i
$879$	−4.05861	−	5.40983i	−0.136893	−	0.182469i
$880$	15.1625	+	19.1713i	0.511128	+	0.646265i
$881$		−	0.0231379i		−	0.000779536i	−1.00000		0.000389768i	$-0.999876\pi$
$881$		−	0.0231379i		−	0.000779536i	1.00000		0.000389768i	$-0.000124067\pi$
$882$	−18.0359	+	23.5946i	−0.607300	+	0.794472i
$883$	−50.1245			−1.68682			−0.843412	−	0.537268i	$-0.819457\pi$
$883$	−50.1245			−1.68682			−0.843412	+	0.537268i	$0.819457\pi$
$884$	36.9153	+	7.06190i	1.24160	+	0.237517i
$885$	−14.6659	+	11.0028i	−0.492989	+	0.369854i
$886$	−3.84604	+	40.5740i	−0.129210	+	1.36311i
$887$	23.4706	+	40.6522i	0.788064	+	1.36497i	0.927151	+	0.374687i	$0.122250\pi$
$887$	23.4706	+	40.6522i	0.788064	+	1.36497i	−0.139087	+	0.990280i	$0.544417\pi$
$888$	21.8732	+	17.9455i	0.734017	+	0.602210i
$889$	−3.75747	+	4.83224i	−0.126022	+	0.162068i
$890$	16.9118	−	7.73749i	0.566884	−	0.259361i
$891$	18.3539	+	35.2381i	0.614880	+	1.18052i
$892$	23.0353	−	8.00829i	0.771279	−	0.268137i
$893$	−5.05395	+	8.75370i	−0.169124	+	0.292931i
$894$	2.64822	+	4.32772i	0.0885697	+	0.144741i
$895$		−	8.41781i		−	0.281376i
$896$	28.8062	+	8.13642i	0.962348	+	0.271819i
$897$	37.8706	+	16.1702i	1.26446	+	0.539907i
$898$	−1.46624	−	1.04258i	−0.0489290	−	0.0347912i
$899$	−14.5318	−	8.38996i	−0.484664	−	0.279821i
$900$	8.42181	−	16.4765i	0.280727	−	0.549218i
$901$	−20.8820	+	12.0562i	−0.695679	+	0.401651i
$902$	−1.29204	−	2.82400i	−0.0430202	−	0.0940289i
$903$	−0.0685471	+	3.96745i	−0.00228110	+	0.132028i
$904$	13.0193	−	44.6823i	0.433014	−	1.48611i
$905$	−13.8834	+	8.01559i	−0.461500	+	0.266447i
$906$	−50.3574	−	27.3836i	−1.67301	−	0.909759i
$907$	−7.24598	+	12.5504i	−0.240599	+	0.416729i	−0.960885	−	0.276948i	$-0.910677\pi$
$907$	−7.24598	+	12.5504i	−0.240599	+	0.416729i	0.720286	+	0.693677i	$0.244010\pi$
$908$	5.89933	−	30.8381i	0.195776	−	1.02340i
$909$	4.29754	+	4.48826i	0.142541	+	0.148866i
$910$	22.8535	−	24.2660i	0.757587	−	0.804410i
$911$	28.7559			0.952726			0.476363	−	0.879249i	$-0.341955\pi$
$911$	28.7559			0.952726			0.476363	+	0.879249i	$0.341955\pi$
$912$	−5.78073	−	21.2494i	−0.191419	−	0.703639i
$913$	−15.4525	+	26.7646i	−0.511404	+	0.885779i
$914$	21.0192	+	1.99242i	0.695253	+	0.0659034i
$915$	0.992369	+	8.22670i	0.0328067	+	0.271966i
$916$	18.3294	+	15.8382i	0.605622	+	0.523309i
$917$	−12.4497	−	1.72046i	−0.411124	−	0.0568146i
$918$	15.1136	−	15.2300i	0.498824	−	0.502666i
$919$	14.3049	−	8.25895i	0.471876	−	0.272438i	−0.245149	−	0.969485i	$-0.578837\pi$
$919$	14.3049	−	8.25895i	0.471876	−	0.272438i	0.717025	+	0.697048i	$0.245503\pi$
$920$	10.4459	−	10.0016i	0.344391	−	0.329742i
$921$	−11.4690	−	15.2874i	−0.377918	−	0.503737i
$922$	−22.2396	+	31.2769i	−0.732422	+	1.03005i
$923$		−	12.2567i		−	0.403434i
$924$	−39.6027	−	8.28762i	−1.30283	−	0.272643i
$925$			17.8109i			0.585619i
$926$	−28.0141	−	19.9196i	−0.920600	−	0.654597i
$927$	−3.95434	−	16.1522i	−0.129878	−	0.530507i
$928$	−1.92818	−	37.7320i	−0.0632957	−	1.23861i
$929$	−2.55192	+	1.47335i	−0.0837258	+	0.0483391i	−0.541278	−	0.840843i	$-0.682059\pi$
$929$	−2.55192	+	1.47335i	−0.0837258	+	0.0483391i	0.457553	+	0.889183i	$0.348726\pi$
$930$	0.217534	+	8.51565i	0.00713323	+	0.279239i
$931$	−15.9339	+	15.5296i	−0.522212	+	0.508963i
$932$	−8.83980	−	7.63835i	−0.289557	−	0.250202i
$933$	53.8413	−	6.49476i	1.76269	−	0.212629i
$934$	−3.43163	+	36.2022i	−0.112286	+	1.18457i
$935$	−8.92106	+	15.4517i	−0.291750	+	0.505326i
$936$	−46.0653	−	29.3336i	−1.50569	−	0.958799i
$937$	31.6130			1.03275			0.516375	−	0.856362i	$-0.327281\pi$
$937$	31.6130			1.03275			0.516375	+	0.856362i	$0.327281\pi$
$938$	−5.79094	+	24.5299i	−0.189081	+	0.800931i
$939$	−8.88366	+	20.8055i	−0.289907	+	0.678963i
$940$	8.64672	+	1.65412i	0.282025	+	0.0539514i
$941$	16.1958	−	28.0519i	0.527966	−	0.914465i	−0.471502	−	0.881865i	$-0.656288\pi$
$941$	16.1958	−	28.0519i	0.527966	−	0.914465i	0.999468	−	0.0325998i	$-0.0103787\pi$
$942$	48.0222	+	26.1138i	1.56465	+	0.850832i
$943$	−1.59128	+	0.918726i	−0.0518192	+	0.0299178i
$944$	−30.2658	+	4.43706i	−0.985069	+	0.144414i
$945$	−4.20514	−	18.5590i	−0.136793	−	0.603724i
$946$	−4.91589	+	2.24912i	−0.159829	+	0.0731253i
$947$	−18.1295	+	10.4671i	−0.589129	+	0.340134i	−0.764753	−	0.644324i	$-0.777139\pi$
$947$	−18.1295	+	10.4671i	−0.589129	+	0.340134i	0.175624	+	0.984457i	$0.443806\pi$
$948$	0.455032	−	6.58721i	0.0147788	−	0.213943i
$949$	−36.0643	−	20.8217i	−1.17070	−	0.675902i
$950$	8.03362	−	11.2982i	0.260645	−	0.366561i
$951$	−16.6386	+	38.9676i	−0.539543	+	1.26361i
$952$	2.24116	+	21.7348i	0.0726364	+	0.704430i
$953$		−	34.4190i		−	1.11494i	−0.830197	−	0.557470i	$-0.811772\pi$
$953$		−	34.4190i		−	1.11494i	0.830197	−	0.557470i	$-0.188228\pi$
$954$	34.6656	−	5.08285i	1.12234	−	0.164563i
$955$	−1.04790	+	1.81502i	−0.0339094	+	0.0587328i
$956$	14.8538	+	42.7259i	0.480405	+	1.38185i
$957$	6.11597	+	50.7011i	0.197701	+	1.63893i
$958$	−5.27711	−	11.5341i	−0.170496	−	0.372651i
$959$	−0.334654	−	0.822837i	−0.0108065	−	0.0265708i
$960$	−15.8277	+	10.8329i	−0.510837	+	0.349630i
$961$	−12.3439	−	21.3803i	−0.398191	−	0.689687i
$962$	52.3315	+	4.96053i	1.68723	+	0.159934i
$963$	−4.26308	−	17.4133i	−0.137376	−	0.561134i
$964$	−50.0757	−	9.57949i	−1.61283	−	0.308535i
$965$	−22.0863			−0.710982
$966$	−2.67046	+	23.7899i	−0.0859206	+	0.765427i
$967$			52.5582i			1.69016i	0.534643	+	0.845078i	$0.320446\pi$
$967$			52.5582i			1.69016i	−0.534643	+	0.845078i	$0.679554\pi$
$968$	−5.70895	−	23.3213i	−0.183492	−	0.749575i
$969$	12.8586	−	9.64685i	0.413077	−	0.309901i
$970$	2.32325	+	0.220222i	0.0745950	+	0.00707091i
$971$	−0.310281	+	0.179141i	−0.00995738	+	0.00574890i	−0.504970	−	0.863137i	$-0.668497\pi$
$971$	−0.310281	+	0.179141i	−0.00995738	+	0.00574890i	0.495013	+	0.868886i	$0.335163\pi$
$972$	−28.5778	+	12.4624i	−0.916633	+	0.399731i
$973$	−19.5372	−	15.1918i	−0.626335	−	0.487028i
$974$	−7.45827	+	3.41231i	−0.238978	+	0.109338i
$975$	−4.11729	−	34.1321i	−0.131859	−	1.09310i
$976$	−5.10273	+	12.8489i	−0.163334	+	0.411283i
$977$	−34.5190	−	19.9296i	−1.10436	−	0.637603i	−0.166998	−	0.985957i	$-0.553407\pi$
$977$	−34.5190	−	19.9296i	−1.10436	−	0.637603i	−0.937363	+	0.348354i	$0.886741\pi$
$978$	−21.7355	−	35.5202i	−0.695026	−	1.13581i
$979$	−41.9414			−1.34045
$980$	17.3326	+	8.66666i	0.553671	+	0.276846i
$981$	−3.59286	+	3.44019i	−0.114711	+	0.109837i
$982$	15.6623	+	11.1368i	0.499805	+	0.355389i
$983$	−14.8055	+	25.6439i	−0.472223	+	0.817914i	−0.999495	−	0.0317825i	$-0.989882\pi$
$983$	−14.8055	+	25.6439i	−0.472223	+	0.817914i	0.527272	+	0.849697i	$0.323215\pi$
$984$	2.28057	−	0.858729i	0.0727018	−	0.0273753i
$985$	0.666498	+	1.15441i	0.0212364	+	0.0367825i
$986$	25.0786	−	11.4740i	0.798666	−	0.365406i
$987$	−12.7443	+	7.06726i	−0.405656	+	0.224953i
$988$	−30.9585	−	26.7508i	−0.984920	−	0.851056i
$989$	1.59928	+	2.77003i	0.0508540	+	0.0880818i
$990$	20.3339	−	16.0827i	0.646254	−	0.511142i
$991$	−19.2020	−	11.0863i	−0.609970	−	0.352167i	0.162983	−	0.986629i	$-0.447888\pi$
$991$	−19.2020	−	11.0863i	−0.609970	−	0.352167i	−0.772954	+	0.634462i	$0.781222\pi$
$992$	−6.46872	+	12.6548i	−0.205382	+	0.401791i
$993$	9.87945	−	23.1377i	0.313515	−	0.734253i
$994$	6.82436	−	2.04962i	0.216456	−	0.0650099i
$995$			2.75860i			0.0874535i
$996$	−20.1164	−	13.5440i	−0.637412	−	0.429157i
$997$	−19.4291	−	11.2174i	−0.615324	−	0.355258i	0.159722	−	0.987162i	$-0.448940\pi$
$997$	−19.4291	−	11.2174i	−0.615324	−	0.355258i	−0.775046	+	0.631904i	$0.782274\pi$
$998$	52.4145	+	4.96840i	1.65915	+	0.157272i
$999$	19.0335	−	23.2004i	0.602194	−	0.734030i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.v.a.11.19	yes	56
3.2	odd	2	inner	168.2.v.a.11.10	yes	56
4.3	odd	2		672.2.bd.a.431.8		56
7.2	even	3	inner	168.2.v.a.107.1	yes	56
8.3	odd	2	inner	168.2.v.a.11.28	yes	56
8.5	even	2		672.2.bd.a.431.7		56
12.11	even	2		672.2.bd.a.431.27		56
21.2	odd	6	inner	168.2.v.a.107.28	yes	56
24.5	odd	2		672.2.bd.a.431.28		56
24.11	even	2	inner	168.2.v.a.11.1	✓	56
28.23	odd	6		672.2.bd.a.527.28		56
56.37	even	6		672.2.bd.a.527.27		56
56.51	odd	6	inner	168.2.v.a.107.10	yes	56
84.23	even	6		672.2.bd.a.527.7		56
168.107	even	6	inner	168.2.v.a.107.19	yes	56
168.149	odd	6		672.2.bd.a.527.8		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.v.a.11.1	✓	56	24.11	even	2	inner
168.2.v.a.11.10	yes	56	3.2	odd	2	inner
168.2.v.a.11.19	yes	56	1.1	even	1	trivial
168.2.v.a.11.28	yes	56	8.3	odd	2	inner
168.2.v.a.107.1	yes	56	7.2	even	3	inner
168.2.v.a.107.10	yes	56	56.51	odd	6	inner
168.2.v.a.107.19	yes	56	168.107	even	6	inner
168.2.v.a.107.28	yes	56	21.2	odd	6	inner
672.2.bd.a.431.7		56	8.5	even	2
672.2.bd.a.431.8		56	4.3	odd	2
672.2.bd.a.431.27		56	12.11	even	2
672.2.bd.a.431.28		56	24.5	odd	2
672.2.bd.a.527.7		56	84.23	even	6
672.2.bd.a.527.8		56	168.149	odd	6
672.2.bd.a.527.27		56	56.37	even	6
672.2.bd.a.527.28		56	28.23	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.v (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.819527 - 1.15255i) q^{2} +(1.03943 + 1.38549i) q^{3} +(-0.656749 - 1.88910i) q^{4} +(0.692094 + 1.19874i) q^{5} +(2.44869 - 0.0625523i) q^{6} +(2.08863 + 1.62408i) q^{7} +(-2.71550 - 0.791228i) q^{8} +(-0.839162 + 2.88024i) q^{9} +(1.94880 + 0.184728i) q^{10} +(-3.82316 - 2.20731i) q^{11} +(1.93467 - 2.87351i) q^{12} -6.43609i q^{13} +(3.58352 - 1.07627i) q^{14} +(-0.941460 + 2.20490i) q^{15} +(-3.13736 + 2.48132i) q^{16} +(-2.52866 - 1.45992i) q^{17} +(2.63191 + 3.32762i) q^{18} +(1.58928 + 2.75271i) q^{19} +(1.81001 - 2.09470i) q^{20} +(-0.0791630 + 4.58189i) q^{21} +(-5.67722 + 2.59745i) q^{22} +(1.84696 + 3.19902i) q^{23} +(-1.72634 - 4.58473i) q^{24} +(1.54201 - 2.67084i) q^{25} +(-7.41792 - 5.27455i) q^{26} +(-4.86280 + 1.83117i) q^{27} +(1.69634 - 5.01223i) q^{28} -6.67884 q^{29} +(1.76971 + 2.89206i) q^{30} +(2.17580 + 1.25620i) q^{31} +(0.288700 + 5.64948i) q^{32} +(-0.915722 - 7.59130i) q^{33} +(-3.75494 + 1.71796i) q^{34} +(-0.501330 + 3.62774i) q^{35} +(5.99217 - 0.306343i) q^{36} +(-5.00149 + 2.88761i) q^{37} +(4.47510 + 0.424197i) q^{38} +(8.91713 - 6.68987i) q^{39} +(-0.930905 - 3.80279i) q^{40} +0.497427i q^{41} +(5.21599 + 3.84623i) q^{42} +0.865898 q^{43} +(-1.65895 + 8.67197i) q^{44} +(-4.03345 + 0.987462i) q^{45} +(5.20067 + 0.492975i) q^{46} +(1.59001 + 2.75398i) q^{47} +(-6.69892 - 1.76761i) q^{48} +(1.72472 + 6.78420i) q^{49} +(-1.81456 - 3.96608i) q^{50} +(-0.605663 - 5.02092i) q^{51} +(-12.1584 + 4.22690i) q^{52} +(4.12906 - 7.15175i) q^{53} +(-1.87468 + 7.10532i) q^{54} -6.11065i q^{55} +(-4.38665 - 6.06278i) q^{56} +(-2.16191 + 5.06319i) q^{57} +(-5.47350 + 7.69771i) q^{58} +(6.62279 + 3.82367i) q^{59} +(4.78357 + 0.330440i) q^{60} +(2.99321 - 1.72813i) q^{61} +(3.23096 - 1.47823i) q^{62} +(-6.43045 + 4.65289i) q^{63} +(6.74792 + 4.29716i) q^{64} +(7.71521 - 4.45438i) q^{65} +(-9.49982 - 5.16586i) q^{66} +(-3.36806 + 5.83364i) q^{67} +(-1.09724 + 5.73567i) q^{68} +(-2.51243 + 5.88411i) q^{69} +(3.77030 + 3.55084i) q^{70} +1.90437 q^{71} +(4.55768 - 7.15735i) q^{72} +(3.23515 - 5.60345i) q^{73} +(-0.770738 + 8.13095i) q^{74} +(5.30324 - 0.639719i) q^{75} +(4.15638 - 4.81014i) q^{76} +(-4.40032 - 10.8194i) q^{77} +(-0.402592 - 15.7600i) q^{78} +(1.65073 - 0.953048i) q^{79} +(-5.14582 - 2.04358i) q^{80} +(-7.59162 - 4.83398i) q^{81} +(0.573310 + 0.407655i) q^{82} -7.00064i q^{83} +(8.70762 - 2.85961i) q^{84} -4.04161i q^{85} +(0.709627 - 0.997992i) q^{86} +(-6.94220 - 9.25347i) q^{87} +(8.63533 + 9.01894i) q^{88} +(8.22776 - 4.75030i) q^{89} +(-2.16742 + 5.45801i) q^{90} +(10.4527 - 13.4426i) q^{91} +(4.83027 - 5.59004i) q^{92} +(0.521147 + 4.32029i) q^{93} +(4.47717 + 0.424393i) q^{94} +(-2.19986 + 3.81027i) q^{95} +(-7.52721 + 6.27224i) q^{96} +1.19214 q^{97} +(9.23259 + 3.57201i) q^{98} +(9.56583 - 9.15936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{3} - 2 q^{4} - 8 q^{6} - 2 q^{9} + 6 q^{10} + 10 q^{12} - 10 q^{16} - 10 q^{18} - 4 q^{19} - 20 q^{22} - 8 q^{24} - 16 q^{25} - 8 q^{27} - 22 q^{28} - 12 q^{30} - 14 q^{33} - 56 q^{34} + 4 q^{36}+ \cdots - 44 q^{99}+O(q^{100}) \) 56 * q - 2 * q^3 - 2 * q^4 - 8 * q^6 - 2 * q^9 + 6 * q^10 + 10 * q^12 - 10 * q^16 - 10 * q^18 - 4 * q^19 - 20 * q^22 - 8 * q^24 - 16 * q^25 - 8 * q^27 - 22 * q^28 - 12 * q^30 - 14 * q^33 - 56 * q^34 + 4 * q^36 + 14 * q^40 - 8 * q^42 - 16 * q^43 - 12 * q^46 + 64 * q^48 - 16 * q^49 - 34 * q^51 - 8 * q^52 + 32 * q^54 + 4 * q^57 - 18 * q^58 + 40 * q^60 + 4 * q^64 - 20 * q^66 - 36 * q^67 - 42 * q^70 + 22 * q^72 + 4 * q^73 + 104 * q^76 + 28 * q^78 - 10 * q^81 + 52 * q^82 + 4 * q^84 + 46 * q^88 + 140 * q^90 + 72 * q^91 - 46 * q^96 - 32 * q^97 - 44 * q^99

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