LMFDB - Embedded newform 168.2.v.a.107.19

Newspace parameters

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

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			107.19
Character	$\chi$	$=$	168.107
Dual form			168.2.v.a.11.19

$q$-expansion

$f(q)$	$=$	$q+(0.819527 + 1.15255i) q^{2} +(1.03943 - 1.38549i) q^{3} +(-0.656749 + 1.88910i) q^{4} +(0.692094 - 1.19874i) q^{5} +(2.44869 + 0.0625523i) q^{6} +(2.08863 - 1.62408i) q^{7} +(-2.71550 + 0.791228i) q^{8} +(-0.839162 - 2.88024i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 56 * q - 2 * q^3 - 2 * q^4 - 8 * q^6 - 2 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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	−0.668742	−	0.743494i	$-0.733167\pi$
$5$	0.692094	−	1.19874i	0.309514	−	0.536094i	0.978256	+	0.207401i	$0.0665004\pi$
$6$	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	−0.949550	−	0.313614i	$-0.898460\pi$
$11$	−3.82316	+	2.20731i	−1.15273	+	0.665528i	−0.203177	+	0.979142i	$0.565127\pi$
$12$	1.93467	+	2.87351i	0.558492	+	0.829510i
$13$			6.43609i			1.78505i	0.450999	+	0.892525i	$0.351068\pi$
$13$			6.43609i			1.78505i	−0.450999	+	0.892525i	$0.648932\pi$
$14$	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	−0.774252	−	0.632878i	$-0.781874\pi$
$17$	−2.52866	+	1.45992i	−0.613289	+	0.354083i	0.160962	+	0.986961i	$0.448540\pi$
$18$	2.63191	−	3.32762i	0.620348	−	0.784327i
$19$	1.58928	−	2.75271i	0.364606	−	0.631515i	−0.624107	−	0.781339i	$-0.714537\pi$
$19$	1.58928	−	2.75271i	0.364606	−	0.631515i	0.988713	+	0.149823i	$0.0478705\pi$
$20$	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	−0.606668	−	0.794955i	$-0.707494\pi$
$23$	1.84696	−	3.19902i	0.385117	−	0.667043i	0.991785	+	0.127912i	$0.0408277\pi$
$24$	−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	−0.291715	−	0.956505i	$-0.594226\pi$
$31$	2.17580	−	1.25620i	0.390786	−	0.225620i	0.682500	+	0.730885i	$0.260893\pi$
$32$	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	0.0289485	−	0.999581i	$-0.490784\pi$
$37$	−5.00149	−	2.88761i	−0.822240	−	0.474720i	−0.851188	+	0.524861i	$0.824117\pi$
$38$	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	$-0.987633\pi$
$41$		−	0.497427i		−	0.0776850i	0.999245	−	0.0388425i	$-0.0123671\pi$
$42$	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	−0.726448	−	0.687221i	$-0.758830\pi$
$47$	1.59001	−	2.75398i	0.231927	−	0.401710i	0.958375	+	0.285512i	$0.0921635\pi$
$48$	−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	0.996844	+	0.0793841i	$0.0252954\pi$
$53$	4.12906	+	7.15175i	0.567171	+	0.982368i	−0.429673	+	0.902984i	$0.641371\pi$
$54$	−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	−0.00253919	−	0.999997i	$-0.500808\pi$
$59$	6.62279	−	3.82367i	0.862214	−	0.497799i	0.864753	+	0.502197i	$0.167475\pi$
$60$	4.78357	−	0.330440i	0.617556	−	0.0426596i
$61$	2.99321	+	1.72813i	0.383241	+	0.221265i	0.679228	−	0.733928i	$-0.262315\pi$
$61$	2.99321	+	1.72813i	0.383241	+	0.221265i	−0.295986	+	0.955192i	$0.595648\pi$
$62$	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	0.583578	−	0.812057i	$-0.301652\pi$
$67$	−3.36806	−	5.83364i	−0.411473	−	0.712693i	−0.995051	+	0.0993644i	$0.968319\pi$
$68$	−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	0.990866	−	0.134854i	$-0.0430564\pi$
$73$	3.23515	+	5.60345i	0.378646	+	0.655834i	−0.612219	+	0.790688i	$0.709723\pi$
$74$	−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	0.589978	−	0.807419i	$-0.299136\pi$
$79$	1.65073	+	0.953048i	0.185721	+	0.107226i	−0.404257	+	0.914646i	$0.632470\pi$
$80$	−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	$0.125526\pi$
$83$			7.00064i			0.768420i	−0.923246	+	0.384210i	$0.874474\pi$
$84$	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	0.868059	−	0.496461i	$-0.165367\pi$
$89$	8.22776	+	4.75030i	0.872141	+	0.503531i	0.00408165	+	0.999992i	$0.498701\pi$
$90$	−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	0.912941	−	0.408092i	$-0.133806\pi$
$101$	1.03566	+	1.79382i	0.103052	+	0.178491i	−0.809889	+	0.586584i	$0.800473\pi$
$102$	−6.28322	+	3.41672i	−0.622131	+	0.338306i
$103$	−4.80043	−	2.77153i	−0.473000	−	0.273087i	0.244495	−	0.969651i	$-0.421378\pi$
$103$	−4.80043	−	2.77153i	−0.473000	−	0.273087i	−0.717495	+	0.696564i	$0.754711\pi$
$104$	−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	0.228533	−	0.973536i	$-0.426607\pi$
$107$	−5.17522	−	2.98792i	−0.500308	−	0.288853i	−0.728841	+	0.684683i	$0.759940\pi$
$108$	6.65289	−	7.98367i	0.640175	−	0.768229i
$109$	1.43595	−	0.829048i	0.137539	−	0.0794084i	−0.429651	−	0.902995i	$-0.641364\pi$
$109$	1.43595	−	0.829048i	0.137539	−	0.0794084i	0.567191	+	0.823586i	$0.308030\pi$
$110$	−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	$-0.718276\pi$
$113$		−	16.4545i		−	1.54791i	0.633241	−	0.773955i	$-0.281724\pi$
$114$	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	$-0.967268\pi$
$127$		−	2.31360i		−	0.205299i	0.994718	−	0.102649i	$-0.0327319\pi$
$128$	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	0.309402	−	0.950931i	$-0.399871\pi$
$131$	−4.11383	−	2.37512i	−0.359427	−	0.207515i	−0.668830	+	0.743416i	$0.733204\pi$
$132$	−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	−0.512369	−	0.858765i	$-0.671232\pi$
$137$	−0.290760	+	0.167870i	−0.0248413	+	0.0143421i	0.487528	+	0.873107i	$0.337899\pi$
$138$	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	−0.820480	−	0.571675i	$-0.806294\pi$
$149$	1.03566	−	1.79382i	0.0848446	−	0.146955i	0.905325	+	0.424720i	$0.139627\pi$
$150$	3.60884	+	6.63652i	0.294661	+	0.541870i
$151$	−20.2661	+	11.7007i	−1.64923	+	0.952186i	−0.671858	+	0.740680i	$0.734504\pi$
$151$	−20.2661	+	11.7007i	−1.64923	+	0.952186i	−0.977377	+	0.211506i	$0.932163\pi$
$152$	−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	0.543725	−	0.839264i	$-0.317014\pi$
$157$	19.3264	−	11.1581i	1.54241	−	0.890511i	0.998686	−	0.0512477i	$-0.0163198\pi$
$158$	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	0.313276	+	0.949662i	$0.398574\pi$
$163$	−8.50029	+	14.7229i	−0.665794	+	1.15319i	−0.979069	+	0.203526i	$0.934760\pi$
$164$	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	−0.983165	−	0.182721i	$-0.941509\pi$
$173$	−4.38442	+	7.59404i	−0.333341	+	0.577364i	0.649824	+	0.760085i	$0.274843\pi$
$174$	−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	−0.683740	−	0.729726i	$-0.739648\pi$
$179$	−5.26665	+	3.04070i	−0.393648	+	0.227273i	0.290092	+	0.956999i	$0.406314\pi$
$180$	4.51437	−	6.97105i	0.336482	−	0.519592i
$181$		−	11.5816i		−	0.860857i	−0.902625	−	0.430429i	$-0.858362\pi$
$181$		−	11.5816i		−	0.860857i	0.902625	−	0.430429i	$-0.141638\pi$
$182$	−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	−0.837336	−	0.546689i	$-0.815888\pi$
$191$	0.757053	−	1.31125i	0.0547784	−	0.0948790i	0.892114	+	0.451810i	$0.149221\pi$
$192$	1.06033	−	13.8158i	0.0765224	−	0.997068i
$193$	−7.97806	−	13.8184i	−0.574273	−	0.994670i	−0.996120	−	0.0880034i	$-0.971951\pi$
$193$	−7.97806	−	13.8184i	−0.574273	−	0.994670i	0.421847	−	0.906667i	$-0.361382\pi$
$194$	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	−0.437577	−	0.899181i	$-0.644163\pi$
$199$	1.72593	−	0.996469i	0.122348	−	0.0706378i	0.559925	+	0.828543i	$0.310830\pi$
$200$	−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	$-0.866129\pi$
$223$		−	12.1938i		−	0.816559i	0.912857	−	0.408279i	$-0.133871\pi$
$224$	−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	0.0243951	−	0.999702i	$-0.492234\pi$
$227$	13.5954	−	7.84932i	0.902360	−	0.520978i	0.877965	+	0.478724i	$0.158901\pi$
$228$	10.9847	−	0.758800i	0.727478	−	0.0502528i
$229$	−10.4894	−	6.05608i	−0.693161	−	0.400197i	0.111634	−	0.993749i	$-0.464392\pi$
$229$	−10.4894	−	6.05608i	−0.693161	−	0.400197i	−0.804795	+	0.593553i	$0.797725\pi$
$230$	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	0.656468	−	0.754354i	$-0.272050\pi$
$233$	5.05877	+	2.92068i	0.331411	+	0.191340i	−0.325056	+	0.945695i	$0.605383\pi$
$234$	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	0.904910	+	0.425604i	$0.139938\pi$
$241$	12.7459	+	22.0766i	0.821038	+	1.42208i	−0.0838714	+	0.996477i	$0.526729\pi$
$242$	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	$0.0111539\pi$
$251$			1.11008i			0.0700675i	−0.999386	+	0.0350338i	$0.988846\pi$
$252$	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	0.0730169	−	0.997331i	$-0.476737\pi$
$257$	−12.0906	−	6.98049i	−0.754188	−	0.435431i	−0.827205	+	0.561900i	$0.810071\pi$
$258$	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	0.997446	−	0.0714223i	$-0.0227538\pi$
$263$	7.08483	+	12.2713i	0.436870	+	0.756680i	−0.560577	+	0.828103i	$0.689420\pi$
$264$	−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	0.997868	+	0.0652716i	$0.0207914\pi$
$269$	9.11023	+	15.7794i	0.555461	+	0.962086i	−0.442407	+	0.896814i	$0.645875\pi$
$270$	−9.81490	−	2.67029i	−0.597316	−	0.162509i
$271$	−21.9278	−	12.6600i	−1.33202	−	0.769041i	−0.346410	−	0.938083i	$-0.612599\pi$
$271$	−21.9278	−	12.6600i	−1.33202	−	0.769041i	−0.985609	+	0.169042i	$0.945933\pi$
$272$	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	−0.901756	−	0.432245i	$-0.857722\pi$
$277$	−16.2822	+	9.40051i	−0.978300	+	0.564822i	−0.0765434	+	0.997066i	$0.524388\pi$
$278$	−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	$0.274964\pi$
$281$			25.4910i			1.52067i	−0.649533	+	0.760333i	$0.725036\pi$
$282$	4.06572	−	6.64420i	0.242110	−	0.395656i
$283$	−6.01848	−	10.4243i	−0.357761	−	0.619661i	0.629825	−	0.776737i	$-0.283126\pi$
$283$	−6.01848	−	10.4243i	−0.357761	−	0.619661i	−0.987586	+	0.157076i	$0.949793\pi$
$284$	−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	0.842550	+	0.538618i	$0.181053\pi$
$311$	15.6553	+	27.1158i	0.887732	+	1.53760i	0.0451815	+	0.998979i	$0.485613\pi$
$312$	−29.5077	−	11.1109i	−1.67055	−	0.629031i
$313$	6.53063	−	11.3114i	0.369133	−	0.639357i	−0.620297	−	0.784367i	$-0.712988\pi$
$313$	6.53063	−	11.3114i	0.369133	−	0.639357i	0.989430	+	0.145010i	$0.0463213\pi$
$314$	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	−0.285817	−	0.958284i	$-0.592265\pi$
$317$	12.2315	−	21.1856i	0.686990	−	1.18990i	0.972807	−	0.231618i	$-0.0744018\pi$
$318$	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	−0.993626	−	0.112723i	$-0.964043\pi$
$331$	−7.26267	+	12.5793i	−0.399192	+	0.691422i	0.594434	+	0.804144i	$0.297376\pi$
$332$	−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	0.173723	−	0.984795i	$-0.444420\pi$
$347$	20.7411	−	11.9749i	1.11344	−	0.642846i	0.939719	+	0.341949i	$0.111087\pi$
$348$	−12.9214	−	19.1917i	−0.692659	−	1.02878i
$349$		−	3.59423i		−	0.192395i	−0.995362	−	0.0961974i	$-0.969332\pi$
$349$		−	3.59423i		−	0.192395i	0.995362	−	0.0961974i	$-0.0306680\pi$
$350$	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	−0.959536	−	0.281587i	$-0.909139\pi$
$353$	−22.4603	+	12.9675i	−1.19544	+	0.690189i	−0.235907	+	0.971776i	$0.575806\pi$
$354$	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	0.200541	+	0.979685i	$0.435730\pi$
$359$	−14.1756	+	24.5529i	−0.748162	+	1.29585i	−0.948703	+	0.316169i	$0.897603\pi$
$360$	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	−0.578969	−	0.815349i	$-0.696545\pi$
$367$	−3.10999	+	1.79556i	−0.162340	+	0.0937272i	0.416629	+	0.909077i	$0.363211\pi$
$368$	−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	0.805699	−	0.592326i	$-0.201790\pi$
$373$	13.4339	+	7.75604i	0.695579	+	0.401593i	−0.110120	+	0.993918i	$0.535123\pi$
$374$	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	−0.971306	−	0.237832i	$-0.923563\pi$
$383$	−5.47353	+	9.48043i	−0.279684	+	0.484427i	0.691622	+	0.722260i	$0.256896\pi$
$384$	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	0.517201	−	0.855864i	$-0.326974\pi$
$389$	−9.51835	−	16.4863i	−0.482600	−	0.835887i	−0.999800	+	0.0199769i	$0.993641\pi$
$390$	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	0.328036	−	0.944665i	$-0.393613\pi$
$397$	−6.49649	−	3.75075i	−0.326050	−	0.188245i	−0.654086	+	0.756420i	$0.726947\pi$
$398$	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	0.964086	−	0.265591i	$-0.0855670\pi$
$401$	24.3528	+	14.0601i	1.21612	+	0.702128i	0.252035	+	0.967718i	$0.418900\pi$
$402$	−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	0.981563	−	0.191137i	$-0.0612175\pi$
$409$	6.57782	+	11.3931i	0.325252	+	0.563353i	−0.656311	+	0.754490i	$0.727884\pi$
$410$	−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	$0.0344510\pi$
$419$			4.42222i			0.216040i	−0.994149	+	0.108020i	$0.965549\pi$
$420$	9.45442	−	8.45907i	0.461329	−	0.412760i
$421$			22.2013i			1.08203i	0.841014	+	0.541014i	$0.181959\pi$
$421$			22.2013i			1.08203i	−0.841014	+	0.541014i	$0.818041\pi$
$422$	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	0.573846	−	0.818963i	$-0.305451\pi$
$431$	−8.76759	−	15.1859i	−0.422320	−	0.731479i	−0.996166	+	0.0874837i	$0.972117\pi$
$432$	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	0.806061	−	0.591833i	$-0.201595\pi$
$439$	14.5943	+	8.42604i	0.696549	+	0.402153i	−0.109512	+	0.993986i	$0.534929\pi$
$440$	−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	−0.228436	−	0.973559i	$-0.573361\pi$
$443$	−24.9578	−	14.4094i	−1.18578	−	0.684611i	−0.957345	+	0.288948i	$0.906695\pi$
$444$	−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	$0.00955666\pi$
$449$			1.27217i			0.0600373i	−0.999549	+	0.0300186i	$0.990443\pi$
$450$	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	−0.636920	−	0.770930i	$-0.719792\pi$
$457$	7.46471	−	12.9293i	0.349185	−	0.604805i	0.986105	+	0.166124i	$0.0531253\pi$
$458$	−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	$0.191047\pi$
$463$			24.3062i			1.12960i	−0.825227	+	0.564801i	$0.808953\pi$
$464$	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	−0.113349	−	0.993555i	$-0.536158\pi$
$467$	−22.2686	−	12.8568i	−1.03047	−	0.594940i	−0.917118	+	0.398615i	$0.869491\pi$
$468$	−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	0.950101	−	0.311942i	$-0.100979\pi$
$479$	4.48448	+	7.76735i	0.204901	+	0.354899i	−0.745200	+	0.666841i	$0.767646\pi$
$480$	−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	−0.609462	−	0.792816i	$-0.708614\pi$
$487$	−5.02256	+	2.89978i	−0.227594	+	0.131401i	0.381868	+	0.924217i	$0.375281\pi$
$488$	−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	$-0.900796\pi$
$491$		−	13.5893i		−	0.613275i	0.951826	−	0.306637i	$-0.0992039\pi$
$492$	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	−0.0621178	−	0.998069i	$-0.519785\pi$
$499$	18.6144	−	32.2411i	0.833294	−	1.44331i	0.895412	−	0.445239i	$-0.146881\pi$
$500$	−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	0.205294	−	0.978700i	$-0.434185\pi$
$509$	21.4381	−	37.1319i	0.950226	−	1.64584i	0.744932	−	0.667140i	$-0.232482\pi$
$510$	−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	−0.464942	−	0.885341i	$-0.653925\pi$
$521$	1.58214	−	0.913450i	0.0693149	−	0.0400190i	0.534257	+	0.845322i	$0.320591\pi$
$522$	−17.5781	+	22.2246i	−0.769374	+	0.972746i
$523$	12.7145	−	22.0222i	0.555966	−	0.962962i	−0.441861	−	0.897083i	$-0.645682\pi$
$523$	12.7145	−	22.0222i	0.555966	−	0.962962i	0.997828	−	0.0658788i	$-0.0209851\pi$
$524$	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	0.808492	−	0.588507i	$-0.200284\pi$
$541$	16.3531	+	9.44148i	0.703076	+	0.405921i	−0.105416	+	0.994428i	$0.533618\pi$
$542$	−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	0.975691	+	0.219151i	$0.0703286\pi$
$557$	15.9928	+	27.7003i	0.677635	+	1.17370i	−0.298056	+	0.954549i	$0.596338\pi$
$558$	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	0.333944	−	0.942593i	$-0.391620\pi$
$563$	31.2546	−	18.0449i	1.31723	−	0.760501i	0.983281	+	0.182092i	$0.0582870\pi$
$564$	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	−0.0823288	−	0.996605i	$-0.526236\pi$
$569$	−23.5336	−	13.5871i	−0.986579	−	0.569601i	−0.904250	+	0.427004i	$0.859569\pi$
$570$	−5.14844	−	9.46778i	−0.215644	−	0.396562i
$571$	−7.45448	−	12.9115i	−0.311960	−	0.540331i	0.666826	−	0.745213i	$-0.267652\pi$
$571$	−7.45448	−	12.9115i	−0.311960	−	0.540331i	−0.978787	+	0.204882i	$0.934319\pi$
$572$	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	−0.920990	−	0.389585i	$-0.872618\pi$
$577$	−19.1659	−	33.1963i	−0.797886	−	1.38198i	0.123104	−	0.992394i	$-0.460715\pi$
$578$	−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	$0.00633874\pi$
$587$			0.964880i			0.0398249i	−0.999802	+	0.0199124i	$0.993661\pi$
$588$	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	0.160528	−	0.987031i	$-0.448680\pi$
$593$	−14.9519	−	8.63251i	−0.614003	−	0.354495i	−0.774530	+	0.632537i	$0.782014\pi$
$594$	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	0.710482	−	0.703715i	$-0.248477\pi$
$599$	−6.22127	−	10.7756i	−0.254194	−	0.440277i	−0.964676	+	0.263438i	$0.915144\pi$
$600$	−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	0.385530	−	0.922695i	$-0.374019\pi$
$607$	−5.43950	−	3.14050i	−0.220783	−	0.127469i	−0.606313	+	0.795226i	$0.707352\pi$
$608$	−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	−0.115244	−	0.993337i	$-0.536765\pi$
$613$	17.0190	−	9.82590i	0.687389	−	0.396864i	0.802633	+	0.596473i	$0.203432\pi$
$614$	−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	$0.224949\pi$
$617$			32.2579i			1.29865i	−0.760509	+	0.649327i	$0.775051\pi$
$618$	−11.5814	−	7.08689i	−0.465872	−	0.285077i
$619$	13.3846	+	23.1828i	0.537973	+	0.931797i	0.999013	+	0.0444173i	$0.0141431\pi$
$619$	13.3846	+	23.1828i	0.537973	+	0.931797i	−0.461040	+	0.887379i	$0.652524\pi$
$620$	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	$0.199267\pi$
$631$			29.4363i			1.17184i	−0.810369	+	0.585920i	$0.800733\pi$
$632$	−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	0.363183	−	0.931718i	$-0.381690\pi$
$641$	34.2214	−	19.7578i	1.35167	−	0.780384i	0.988483	+	0.151334i	$0.0483568\pi$
$642$	−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	−0.784264	−	0.620427i	$-0.786959\pi$
$647$	−23.6414	−	40.9480i	−0.929438	−	1.60983i	−0.145174	−	0.989406i	$-0.546374\pi$
$648$	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	0.442419	+	0.896808i	$0.354120\pi$
$653$	−14.1939	+	24.5845i	−0.555449	+	0.962067i	−0.997868	+	0.0652581i	$0.979213\pi$
$654$	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	$-0.977743\pi$
$659$		−	3.58703i		−	0.139731i	0.997556	−	0.0698654i	$-0.0222570\pi$
$660$	−17.5590	+	11.8221i	−0.683483	+	0.460175i
$661$	1.09189	−	0.630403i	0.0424696	−	0.0245198i	−0.478615	−	0.878025i	$-0.658861\pi$
$661$	1.09189	−	0.630403i	0.0424696	−	0.0245198i	0.521084	+	0.853505i	$0.325528\pi$
$662$	−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	−0.915564	−	0.402173i	$-0.868255\pi$
$677$	−2.84885	+	4.93435i	−0.109490	+	0.189642i	0.806074	+	0.591815i	$0.201588\pi$
$678$	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	−0.830569	−	0.556915i	$-0.811985\pi$
$683$	−19.9548	+	11.5209i	−0.763551	+	0.440836i	0.0670183	+	0.997752i	$0.478651\pi$
$684$	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	0.285686	+	0.958323i	$0.407779\pi$
$691$	−18.0614	+	31.2833i	−0.687090	+	1.19007i	−0.972775	+	0.231751i	$0.925555\pi$
$692$	−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	−0.992013	−	0.126132i	$-0.959744\pi$
$709$	−42.5302	−	24.5548i	−1.59725	−	0.922175i	−0.605240	−	0.796043i	$-0.706923\pi$
$710$	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	−0.978369	−	0.206868i	$-0.933673\pi$
$719$	−8.31324	+	14.3990i	−0.310032	+	0.536991i	0.668337	+	0.743858i	$0.267006\pi$
$720$	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	$0.0376992\pi$
$727$			6.37182i			0.236318i	−0.992995	+	0.118159i	$0.962301\pi$
$728$	−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	0.966750	−	0.255723i	$-0.0823135\pi$
$733$	33.2648	+	19.2054i	1.22866	+	0.709369i	0.261912	+	0.965092i	$0.415647\pi$
$734$	−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	0.875900	−	0.482493i	$-0.160269\pi$
$739$	0.546366	+	0.946333i	0.0200984	+	0.0348114i	−0.855801	+	0.517305i	$0.826935\pi$
$740$	−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	−0.0182235	−	0.999834i	$-0.505801\pi$
$751$	−24.4781	−	14.1324i	−0.893217	−	0.515699i	−0.874993	+	0.484135i	$0.839134\pi$
$752$	−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	$-0.837563\pi$
$757$		−	26.8780i		−	0.976898i	0.872592	−	0.488449i	$-0.162437\pi$
$758$	−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	0.947285	+	0.320393i	$0.103815\pi$
$761$	46.8523	+	27.0502i	1.69840	+	0.980569i	0.751111	+	0.660176i	$0.229518\pi$
$762$	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	+

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.819527 + 1.15255i) q^{2} +(1.03943 - 1.38549i) q^{3} +(-0.656749 + 1.88910i) q^{4} +(0.692094 - 1.19874i) q^{5} +(2.44869 + 0.0625523i) q^{6} +(2.08863 - 1.62408i) q^{7} +(-2.71550 + 0.791228i) q^{8} +(-0.839162 - 2.88024i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{3} - 2 q^{4} - 8 q^{6} - 2 q^{9}+O(q^{10}) \) 56 * q - 2 * q^3 - 2 * q^4 - 8 * q^6 - 2 * q^9	\( 56 q - 2 q^{3} - 2 q^{4} - 8 q^{6} - 2 q^{9} + 6 q^{10} + 10 q^{12} - 10 q^{16} - 10 q^{18} - 4 q^{19} - 20 q^{22} - 8 q^{24} - 16 q^{25} - 8 q^{27} - 22 q^{28} - 12 q^{30} - 14 q^{33} - 56 q^{34} + 4 q^{36} + 14 q^{40} - 8 q^{42} - 16 q^{43} - 12 q^{46} + 64 q^{48} - 16 q^{49} - 34 q^{51} - 8 q^{52} + 32 q^{54} + 4 q^{57} - 18 q^{58} + 40 q^{60} + 4 q^{64} - 20 q^{66} - 36 q^{67} - 42 q^{70} + 22 q^{72} + 4 q^{73} + 104 q^{76} + 28 q^{78} - 10 q^{81} + 52 q^{82} + 4 q^{84} + 46 q^{88} + 140 q^{90} + 72 q^{91} - 46 q^{96} - 32 q^{97} - 44 q^{99}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more