LMFDB - Embedded newform 168.2.v.a.107.16

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			107.16
Character	$\chi$	$=$	168.107
Dual form			168.2.v.a.11.16

$q$-expansion

$f(q)$	$=$	$q+(0.248376 + 1.39223i) q^{2} +(-1.64844 + 0.531631i) q^{3} +(-1.87662 + 0.691593i) q^{4} +(-0.646402 + 1.11960i) q^{5} +(-1.14959 - 2.16297i) q^{6} +(-2.42742 - 1.05244i) q^{7} +(-1.42896 - 2.44091i) q^{8} +(2.43474 - 1.75273i) q^{9} +O(q^{10})$	\(q+(0.248376 + 1.39223i) q^{2} +(-1.64844 + 0.531631i) q^{3} +(-1.87662 + 0.691593i) q^{4} +(-0.646402 + 1.11960i) q^{5} +(-1.14959 - 2.16297i) q^{6} +(-2.42742 - 1.05244i) q^{7} +(-1.42896 - 2.44091i) q^{8} +(2.43474 - 1.75273i) q^{9} +(-1.71929 - 0.621859i) q^{10} +(-1.60004 + 0.923782i) q^{11} +(2.72583 - 2.13772i) q^{12} +2.25432i q^{13} +(0.862334 - 3.64093i) q^{14} +(0.470342 - 2.18925i) q^{15} +(3.04340 - 2.59571i) q^{16} +(-3.89580 + 2.24924i) q^{17} +(3.04493 + 2.95438i) q^{18} +(-2.80851 + 4.86448i) q^{19} +(0.438742 - 2.54811i) q^{20} +(4.56098 + 0.444404i) q^{21} +(-1.68353 - 1.99818i) q^{22} +(0.519880 - 0.900459i) q^{23} +(3.65323 + 3.26403i) q^{24} +(1.66433 + 2.88270i) q^{25} +(-3.13853 + 0.559917i) q^{26} +(-3.08172 + 4.18366i) q^{27} +(5.28320 + 0.296251i) q^{28} -1.32085 q^{29} +(3.16476 + 0.111070i) q^{30} +(3.69700 - 2.13446i) q^{31} +(4.36974 + 3.59240i) q^{32} +(2.14646 - 2.37343i) q^{33} +(-4.09909 - 4.86521i) q^{34} +(2.74740 - 2.03744i) q^{35} +(-3.35690 + 4.97305i) q^{36} +(8.18394 + 4.72500i) q^{37} +(-7.47005 - 2.70188i) q^{38} +(-1.19846 - 3.71611i) q^{39} +(3.65653 - 0.0220581i) q^{40} -1.39634i q^{41} +(0.514122 + 6.46032i) q^{42} -6.02578 q^{43} +(2.36378 - 2.84016i) q^{44} +(0.388538 + 3.85890i) q^{45} +(1.38277 + 0.500142i) q^{46} +(-5.90249 + 10.2234i) q^{47} +(-3.63691 + 5.89685i) q^{48} +(4.78472 + 5.10944i) q^{49} +(-3.60001 + 3.03313i) q^{50} +(5.22625 - 5.77888i) q^{51} +(-1.55907 - 4.23049i) q^{52} +(-6.02901 - 10.4425i) q^{53} +(-6.59005 - 3.25135i) q^{54} -2.38854i q^{55} +(0.899769 + 7.42903i) q^{56} +(2.04356 - 9.51192i) q^{57} +(-0.328068 - 1.83894i) q^{58} +(9.57732 - 5.52947i) q^{59} +(0.631413 + 4.43367i) q^{60} +(-7.65220 - 4.41800i) q^{61} +(3.88991 + 4.61693i) q^{62} +(-7.75477 + 1.69218i) q^{63} +(-3.91612 + 6.97596i) q^{64} +(-2.52393 - 1.45719i) q^{65} +(3.83750 + 2.39887i) q^{66} +(3.05545 + 5.29219i) q^{67} +(5.75538 - 6.91528i) q^{68} +(-0.378281 + 1.76074i) q^{69} +(3.51897 + 3.31897i) q^{70} +14.0121 q^{71} +(-7.75741 - 3.43840i) q^{72} +(-4.38664 - 7.59788i) q^{73} +(-4.54561 + 12.5675i) q^{74} +(-4.27609 - 3.86717i) q^{75} +(1.90626 - 11.0711i) q^{76} +(4.85619 - 0.558456i) q^{77} +(4.87602 - 2.59153i) q^{78} +(-2.37061 - 1.36867i) q^{79} +(0.938904 + 5.08526i) q^{80} +(2.85588 - 8.53487i) q^{81} +(1.94403 - 0.346817i) q^{82} -4.74366i q^{83} +(-8.86656 + 2.32036i) q^{84} -5.81566i q^{85} +(-1.49666 - 8.38928i) q^{86} +(2.17736 - 0.702207i) q^{87} +(4.54127 + 2.58550i) q^{88} +(8.31219 + 4.79904i) q^{89} +(-5.27598 + 1.49939i) q^{90} +(2.37254 - 5.47217i) q^{91} +(-0.352866 + 2.04936i) q^{92} +(-4.95955 + 5.48398i) q^{93} +(-15.6994 - 5.67839i) q^{94} +(-3.63085 - 6.28882i) q^{95} +(-9.11311 - 3.59879i) q^{96} -8.73466 q^{97} +(-5.92512 + 7.93051i) q^{98} +(-2.27653 + 5.05360i) 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 $

$2$	0.248376	+	1.39223i	0.175628	+	0.984457i
$2$	0.248376	+	1.39223i	0.175628	+	0.984457i
$3$	−1.64844	+	0.531631i	−0.951730	+	0.306937i
$3$	−1.64844	+	0.531631i	−0.951730	+	0.306937i
$4$	−1.87662	+	0.691593i	−0.938310	+	0.345796i
$5$	−0.646402	+	1.11960i	−0.289080	+	0.500700i	−0.973590	−	0.228302i	$-0.926683\pi$
$5$	−0.646402	+	1.11960i	−0.289080	+	0.500700i	0.684511	+	0.729003i	$0.260016\pi$
$6$	−1.14959	−	2.16297i	−0.469317	−	0.883030i
$7$	−2.42742	−	1.05244i	−0.917478	−	0.397786i
$7$	−2.42742	−	1.05244i	−0.917478	−	0.397786i
$8$	−1.42896	−	2.44091i	−0.505215	−	0.862993i
$9$	2.43474	−	1.75273i	0.811579	−	0.584243i
$10$	−1.71929	−	0.621859i	−0.543688	−	0.196649i
$11$	−1.60004	+	0.923782i	−0.482430	+	0.278531i	−0.721428	−	0.692489i	$-0.756514\pi$
$11$	−1.60004	+	0.923782i	−0.482430	+	0.278531i	0.238999	+	0.971020i	$0.423181\pi$
$12$	2.72583	−	2.13772i	0.786879	−	0.617107i
$13$			2.25432i			0.625235i	0.949879	+	0.312617i	$0.101206\pi$
$13$			2.25432i			0.625235i	−0.949879	+	0.312617i	$0.898794\pi$
$14$	0.862334	−	3.64093i	0.230469	−	0.973080i
$15$	0.470342	−	2.18925i	0.121442	−	0.565261i
$16$	3.04340	−	2.59571i	0.760850	−	0.648928i
$17$	−3.89580	+	2.24924i	−0.944871	+	0.545522i	−0.891484	−	0.453052i	$-0.850335\pi$
$17$	−3.89580	+	2.24924i	−0.944871	+	0.545522i	−0.0533874	+	0.998574i	$0.517002\pi$
$18$	3.04493	+	2.95438i	0.717698	+	0.696355i
$19$	−2.80851	+	4.86448i	−0.644317	+	1.11599i	0.340142	+	0.940374i	$0.389525\pi$
$19$	−2.80851	+	4.86448i	−0.644317	+	1.11599i	−0.984459	+	0.175615i	$0.943809\pi$
$20$	0.438742	−	2.54811i	0.0981056	−	0.569775i
$21$	4.56098	+	0.444404i	0.995287	+	0.0969769i
$22$	−1.68353	−	1.99818i	−0.358930	−	0.426013i
$23$	0.519880	−	0.900459i	0.108402	−	0.187759i	−0.806721	−	0.590933i	$-0.798760\pi$
$23$	0.519880	−	0.900459i	0.108402	−	0.187759i	0.915123	+	0.403174i	$0.132093\pi$
$24$	3.65323	+	3.26403i	0.745713	+	0.666267i
$25$	1.66433	+	2.88270i	0.332866	+	0.576541i
$26$	−3.13853	+	0.559917i	−0.615517	+	0.109809i
$27$	−3.08172	+	4.18366i	−0.593078	+	0.805145i
$28$	5.28320	+	0.296251i	0.998432	+	0.0559862i
$29$	−1.32085			−0.245277			−0.122638	−	0.992451i	$-0.539135\pi$
$29$	−1.32085			−0.245277			−0.122638	+	0.992451i	$0.539135\pi$
$30$	3.16476	+	0.111070i	0.577803	+	0.0202786i
$31$	3.69700	−	2.13446i	0.664000	−	0.383361i	−0.129799	−	0.991540i	$-0.541433\pi$
$31$	3.69700	−	2.13446i	0.664000	−	0.383361i	0.793800	+	0.608179i	$0.208100\pi$
$32$	4.36974	+	3.59240i	0.772468	+	0.635053i
$33$	2.14646	−	2.37343i	0.373651	−	0.413162i
$34$	−4.09909	−	4.86521i	−0.702988	−	0.834376i
$35$	2.74740	−	2.03744i	0.464396	−	0.344390i
$36$	−3.35690	+	4.97305i	−0.559483	+	0.828842i
$37$	8.18394	+	4.72500i	1.34543	+	0.776786i	0.987599	−	0.157000i	$-0.0501822\pi$
$37$	8.18394	+	4.72500i	1.34543	+	0.776786i	0.357834	+	0.933785i	$0.383516\pi$
$38$	−7.47005	−	2.70188i	−1.21180	−	0.438303i
$39$	−1.19846	−	3.71611i	−0.191908	−	0.595055i
$40$	3.65653	−	0.0220581i	0.578149	−	0.00348770i
$41$		−	1.39634i		−	0.218072i	−0.994038	−	0.109036i	$-0.965224\pi$
$41$		−	1.39634i		−	0.218072i	0.994038	−	0.109036i	$-0.0347764\pi$
$42$	0.514122	+	6.46032i	0.0793308	+	0.996848i
$43$	−6.02578			−0.918922			−0.459461	−	0.888198i	$-0.651957\pi$
$43$	−6.02578			−0.918922			−0.459461	+	0.888198i	$0.651957\pi$
$44$	2.36378	−	2.84016i	0.356353	−	0.428171i
$45$	0.388538	+	3.85890i	0.0579198	+	0.575251i
$46$	1.38277	+	0.500142i	0.203879	+	0.0737418i
$47$	−5.90249	+	10.2234i	−0.860966	+	1.49124i	0.0100312	+	0.999950i	$0.496807\pi$
$47$	−5.90249	+	10.2234i	−0.860966	+	1.49124i	−0.870997	+	0.491288i	$0.836526\pi$
$48$	−3.63691	+	5.89685i	−0.524943	+	0.851138i
$49$	4.78472	+	5.10944i	0.683532	+	0.729921i
$50$	−3.60001	+	3.03313i	−0.509119	+	0.428949i
$51$	5.22625	−	5.77888i	0.731821	−	0.809206i
$52$	−1.55907	−	4.23049i	−0.216204	−	0.586664i
$53$	−6.02901	−	10.4425i	−0.828148	−	1.43439i	−0.899489	−	0.436943i	$-0.856061\pi$
$53$	−6.02901	−	10.4425i	−0.828148	−	1.43439i	0.0713414	−	0.997452i	$-0.477272\pi$
$54$	−6.59005	−	3.25135i	−0.896792	−	0.442453i
$55$		−	2.38854i		−	0.322070i
$56$	0.899769	+	7.42903i	0.120237	+	0.992745i
$57$	2.04356	−	9.51192i	0.270676	−	1.25988i
$58$	−0.328068	−	1.83894i	−0.0430775	−	0.241464i
$59$	9.57732	−	5.52947i	1.24686	−	0.719875i	0.276378	−	0.961049i	$-0.410866\pi$
$59$	9.57732	−	5.52947i	1.24686	−	0.719875i	0.970482	+	0.241174i	$0.0775324\pi$
$60$	0.631413	+	4.43367i	0.0815151	+	0.572384i
$61$	−7.65220	−	4.41800i	−0.979764	−	0.565667i	−0.0775652	−	0.996987i	$-0.524715\pi$
$61$	−7.65220	−	4.41800i	−0.979764	−	0.565667i	−0.902199	+	0.431320i	$0.858048\pi$
$62$	3.88991	+	4.61693i	0.494019	+	0.586351i
$63$	−7.75477	+	1.69218i	−0.977010	+	0.213195i
$64$	−3.91612	+	6.97596i	−0.489515	+	0.871995i
$65$	−2.52393	−	1.45719i	−0.313055	−	0.180743i
$66$	3.83750	+	2.39887i	0.472363	+	0.295280i
$67$	3.05545	+	5.29219i	0.373283	+	0.646544i	0.990068	−	0.140587i	$-0.0448989\pi$
$67$	3.05545	+	5.29219i	0.373283	+	0.646544i	−0.616786	+	0.787131i	$0.711566\pi$
$68$	5.75538	−	6.91528i	0.697942	−	0.838601i
$69$	−0.378281	+	1.76074i	−0.0455397	+	0.211968i
$70$	3.51897	+	3.31897i	0.420598	+	0.396693i
$71$	14.0121			1.66293			0.831464	−	0.555578i	$-0.187503\pi$
$71$	14.0121			1.66293			0.831464	+	0.555578i	$0.187503\pi$
$72$	−7.75741	−	3.43840i	−0.914220	−	0.405219i
$73$	−4.38664	−	7.59788i	−0.513417	−	0.889264i	−0.999879	−	0.0155626i	$-0.995046\pi$
$73$	−4.38664	−	7.59788i	−0.513417	−	0.889264i	0.486462	−	0.873702i	$-0.338287\pi$
$74$	−4.54561	+	12.5675i	−0.528416	+	1.46095i
$75$	−4.27609	−	3.86717i	−0.493760	−	0.446542i
$76$	1.90626	−	11.0711i	0.218663	−	1.26995i
$77$	4.85619	−	0.558456i	0.553414	−	0.0636420i
$78$	4.87602	−	2.59153i	0.552101	−	0.293433i
$79$	−2.37061	−	1.36867i	−0.266714	−	0.153987i	0.360679	−	0.932690i	$-0.382545\pi$
$79$	−2.37061	−	1.36867i	−0.266714	−	0.153987i	−0.627393	+	0.778702i	$0.715878\pi$
$80$	0.938904	+	5.08526i	0.104973	+	0.568550i
$81$	2.85588	−	8.53487i	0.317320	−	0.948318i
$82$	1.94403	−	0.346817i	0.214682	−	0.0382996i
$83$		−	4.74366i		−	0.520685i	−0.965516	−	0.260342i	$-0.916165\pi$
$83$		−	4.74366i		−	0.520685i	0.965516	−	0.260342i	$-0.0838354\pi$
$84$	−8.86656	+	2.32036i	−0.967421	+	0.253172i
$85$		−	5.81566i		−	0.630797i
$86$	−1.49666	−	8.38928i	−0.161389	−	0.904639i
$87$	2.17736	−	0.702207i	0.233437	−	0.0752845i
$88$	4.54127	+	2.58550i	0.484101	+	0.275616i
$89$	8.31219	+	4.79904i	0.881090	+	0.508697i	0.871018	−	0.491252i	$-0.163461\pi$
$89$	8.31219	+	4.79904i	0.881090	+	0.508697i	0.0100723	+	0.999949i	$0.496794\pi$
$90$	−5.27598	+	1.49939i	−0.556137	+	0.158050i
$91$	2.37254	−	5.47217i	0.248710	−	0.573639i
$92$	−0.352866	+	2.04936i	−0.0367888	+	0.213661i
$93$	−4.95955	+	5.48398i	−0.514281	+	0.568662i
$94$	−15.6994	−	5.67839i	−1.61927	−	0.585681i
$95$	−3.63085	−	6.28882i	−0.372517	−	0.645219i
$96$	−9.11311	−	3.59879i	−0.930103	−	0.367300i
$97$	−8.73466			−0.886871			−0.443435	−	0.896306i	$-0.646240\pi$
$97$	−8.73466			−0.886871			−0.443435	+	0.896306i	$0.646240\pi$
$98$	−5.92512	+	7.93051i	−0.598528	+	0.801102i
$99$	−2.27653	+	5.05360i	−0.228800	+	0.507906i
$100$	−5.11697	−	4.25870i	−0.511697	−	0.425870i
$101$	3.42033	+	5.92419i	0.340336	+	0.589479i	0.984495	−	0.175413i	$-0.0561259\pi$
$101$	3.42033	+	5.92419i	0.340336	+	0.589479i	−0.644159	+	0.764891i	$0.722793\pi$
$102$	9.34362	+	5.84082i	0.925156	+	0.578327i
$103$	3.88733	+	2.24435i	0.383030	+	0.221143i	0.679136	−	0.734013i	$-0.262355\pi$
$103$	3.88733	+	2.24435i	0.383030	+	0.221143i	−0.296106	+	0.955155i	$0.595688\pi$
$104$	5.50259	−	3.22134i	0.539574	−	0.315878i
$105$	−3.44578	+	4.81921i	−0.336273	+	0.470306i
$106$	13.0410	−	10.9875i	1.26665	−	1.06720i
$107$	−6.27888	−	3.62511i	−0.607002	−	0.350453i	0.164789	−	0.986329i	$-0.447306\pi$
$107$	−6.27888	−	3.62511i	−0.607002	−	0.350453i	−0.771791	+	0.635876i	$0.780639\pi$
$108$	2.88983	−	9.98243i	0.278074	−	0.960560i
$109$	−10.6680	+	6.15916i	−1.02181	+	0.589941i	−0.914627	−	0.404299i	$-0.867516\pi$
$109$	−10.6680	+	6.15916i	−1.02181	+	0.589941i	−0.107180	+	0.994240i	$0.534182\pi$
$110$	3.32540	−	0.593254i	0.317064	−	0.0565646i
$111$	−16.0027	−	3.43806i	−1.51891	−	0.326326i
$112$	−10.1194	+	3.09788i	−0.956198	+	0.292722i
$113$			7.27566i			0.684437i	0.939620	+	0.342218i	$0.111178\pi$
$113$			7.27566i			0.684437i	−0.939620	+	0.342218i	$0.888822\pi$
$114$	13.7504	+	0.482583i	1.28784	+	0.0451980i
$115$	0.672102	+	1.16412i	0.0626739	+	0.108554i
$116$	2.47874	−	0.913494i	0.230145	−	0.0848158i
$117$	3.95120	+	5.48867i	0.365289	+	0.507427i
$118$	10.0771	+	11.9605i	0.927669	+	1.10105i
$119$	11.8240	−	1.35974i	1.08390	−	0.124647i
$120$	−6.01586	+	1.98029i	−0.549171	+	0.180775i
$121$	−3.79325	+	6.57011i	−0.344841	+	0.597282i
$122$	4.25026	−	11.7510i	0.384801	−	1.06388i
$123$	0.742339	+	2.30179i	0.0669344	+	0.207546i
$124$	−5.46168	+	6.56239i	−0.490473	+	0.589320i
$125$	−10.7673			−0.963058
$126$	−4.28201	−	10.3761i	−0.381472	−	0.924381i
$127$			21.7722i			1.93197i	0.258595	+	0.965986i	$0.416740\pi$
$127$			21.7722i			1.93197i	−0.258595	+	0.965986i	$0.583260\pi$
$128$	−10.6848	−	3.71949i	−0.944414	−	0.328760i
$129$	9.93316	−	3.20349i	0.874566	−	0.282052i
$130$	1.40187	−	3.87583i	0.122952	−	0.339933i
$131$	4.65916	+	2.68997i	0.407073	+	0.235024i	0.689531	−	0.724256i	$-0.257817\pi$
$131$	4.65916	+	2.68997i	0.407073	+	0.235024i	−0.282458	+	0.959280i	$0.591150\pi$
$132$	−2.38664	+	5.93851i	−0.207730	+	0.516881i
$133$	11.9370	−	8.85234i	1.03507	−	0.767595i
$134$	−6.60906	+	5.56835i	−0.570936	+	0.481032i
$135$	−2.69199	−	6.15462i	−0.231690	−	0.529705i
$136$	11.0572	+	6.29524i	0.948145	+	0.539812i
$137$	−11.3713	+	6.56523i	−0.971517	+	0.560905i	−0.899698	−	0.436512i	$-0.856214\pi$
$137$	−11.3713	+	6.56523i	−0.971517	+	0.560905i	−0.0718185	+	0.997418i	$0.522880\pi$
$138$	−2.54531	−	0.0893303i	−0.216672	−	0.00760430i
$139$	12.9760			1.10061			0.550307	−	0.834963i	$-0.314511\pi$
$139$	12.9760			1.10061			0.550307	+	0.834963i	$0.314511\pi$
$140$	−3.74675	+	5.72358i	−0.316658	+	0.483731i
$141$	4.29484	−	19.9907i	0.361691	−	1.68352i
$142$	3.48026	+	19.5081i	0.292057	+	1.63708i
$143$	−2.08250	−	3.60699i	−0.174147	−	0.301632i
$144$	2.86029	−	11.6541i	0.238358	−	0.971177i
$145$	0.853802	−	1.47883i	0.0709044	−	0.122810i
$146$	9.48848	−	7.99434i	0.785272	−	0.661617i
$147$	−10.6037	−	5.87893i	−0.874578	−	0.484886i
$148$	−18.6259	−	3.20707i	−1.53104	−	0.263620i
$149$	3.42033	−	5.92419i	0.280205	−	0.485328i	−0.691230	−	0.722634i	$-0.742931\pi$
$149$	3.42033	−	5.92419i	0.280205	−	0.485328i	0.971435	+	0.237306i	$0.0762644\pi$
$150$	4.32192	−	6.91382i	0.352883	−	0.564511i
$151$	−3.16245	+	1.82584i	−0.257356	+	0.148585i	−0.623128	−	0.782120i	$-0.714138\pi$
$151$	−3.16245	+	1.82584i	−0.257356	+	0.148585i	0.365772	+	0.930705i	$0.380805\pi$
$152$	15.8870	−	0.0958391i	1.28861	−	0.00777358i
$153$	−5.54294	+	12.3046i	−0.448120	+	0.994768i
$154$	1.98366	+	6.62224i	0.159848	+	0.533635i
$155$			5.51888i			0.443287i
$156$	4.81910	+	6.14488i	0.385837	+	0.491984i
$157$	−2.34584	+	1.35437i	−0.187219	+	0.108091i	−0.590680	−	0.806906i	$-0.701140\pi$
$157$	−2.34584	+	1.35437i	−0.187219	+	0.108091i	0.403461	+	0.914997i	$0.367807\pi$
$158$	1.31671	−	3.64038i	0.104751	−	0.289613i
$159$	15.4901	+	14.0088i	1.22844	+	1.11097i
$160$	−6.84666	+	2.57023i	−0.541276	+	0.203194i
$161$	−2.20965	+	1.63865i	−0.174145	+	0.129143i
$162$	12.5918	+	1.85620i	0.989309	+	0.145837i
$163$	4.41842	−	7.65293i	0.346078	−	0.599424i	−0.639471	−	0.768815i	$-0.720847\pi$
$163$	4.41842	−	7.65293i	0.346078	−	0.599424i	0.985549	+	0.169391i	$0.0541801\pi$
$164$	0.965700	+	2.62040i	0.0754085	+	0.204619i
$165$	1.26982	+	3.93737i	0.0988554	+	0.306524i
$166$	6.60428	−	1.17821i	0.512591	−	0.0914469i
$167$	11.8815			0.919417			0.459709	−	0.888070i	$-0.347954\pi$
$167$	11.8815			0.919417			0.459709	+	0.888070i	$0.347954\pi$
$168$	−5.43272	−	11.7680i	−0.419143	−	0.907920i
$169$	7.91806			0.609081
$170$	8.09674	−	1.44447i	0.620992	−	0.110786i
$171$	1.68814	+	16.7663i	0.129095	+	1.28215i
$172$	11.3081	−	4.16738i	0.862234	−	0.317760i
$173$	−3.12500	+	5.41265i	−0.237589	+	0.411516i	−0.960022	−	0.279925i	$-0.909691\pi$
$173$	−3.12500	+	5.41265i	−0.237589	+	0.411516i	0.722433	+	0.691441i	$0.243024\pi$
$174$	1.51844	+	2.85697i	0.115112	+	0.216586i
$175$	−1.00614	−	8.74915i	−0.0760571	−	0.661373i
$176$	−2.47168	+	6.96468i	−0.186310	+	0.524982i
$177$	−12.8480	+	14.2066i	−0.965717	+	1.06783i
$178$	−4.61684	+	12.7645i	−0.346046	+	0.956736i
$179$	−1.43978	+	0.831255i	−0.107614	+	0.0621309i	−0.552841	−	0.833287i	$-0.686456\pi$
$179$	−1.43978	+	0.831255i	−0.107614	+	0.0621309i	0.445227	+	0.895418i	$0.353123\pi$
$180$	−3.39792	−	6.97297i	−0.253266	−	0.519735i
$181$		−	4.46877i		−	0.332161i	−0.986112	−	0.166081i	$-0.946889\pi$
$181$		−	4.46877i		−	0.332161i	0.986112	−	0.166081i	$-0.0531112\pi$
$182$	8.20781	+	1.94397i	0.608403	+	0.144097i
$183$	14.9630	+	3.21468i	1.10609	+	0.237636i
$184$	−2.94083	+	0.0177407i	−0.216801	+	0.00130786i
$185$	−10.5802	+	6.10850i	−0.777874	+	0.449106i
$186$	−8.86681	−	5.54275i	−0.650146	−	0.406414i
$187$	4.15562	−	7.19775i	0.303889	−	0.526352i
$188$	4.00628	−	23.2676i	0.292188	−	1.69696i
$189$	11.8837	−	6.91215i	0.864412	−	0.502785i
$190$	7.85368	−	6.61698i	0.569766	−	0.480046i
$191$	−11.2771	+	19.5325i	−0.815982	+	1.41332i	0.0926380	+	0.995700i	$0.470470\pi$
$191$	−11.2771	+	19.5325i	−0.815982	+	1.41332i	−0.908620	+	0.417623i	$0.862863\pi$
$192$	2.74687	−	13.5814i	0.198238	−	0.980154i
$193$	−2.90298	−	5.02810i	−0.208961	−	0.361931i	0.742427	−	0.669927i	$-0.233675\pi$
$193$	−2.90298	−	5.02810i	−0.208961	−	0.361931i	−0.951387	+	0.307997i	$0.900341\pi$
$194$	−2.16948	−	12.1607i	−0.155759	−	0.873086i
$195$	4.93525	+	1.06030i	0.353421	+	0.0759297i
$196$	−12.5128	−	6.27940i	−0.893768	−	0.448529i
$197$	3.15873			0.225050			0.112525	−	0.993649i	$-0.464106\pi$
$197$	3.15873			0.225050			0.112525	+	0.993649i	$0.464106\pi$
$198$	−7.60122	−	1.91427i	−0.540195	−	0.136041i
$199$	12.2352	−	7.06397i	0.867327	−	0.500751i	0.000867851	−	1.00000i	$-0.499724\pi$
$199$	12.2352	−	7.06397i	0.867327	−	0.500751i	0.866459	+	0.499248i	$0.166390\pi$
$200$	4.65817	−	8.18177i	0.329382	−	0.578538i
$201$	−7.85023	−	7.09951i	−0.553713	−	0.500761i
$202$	−7.39832	+	6.23332i	−0.520544	+	0.438575i
$203$	3.20627	+	1.39013i	0.225036	+	0.0975677i
$204$	−5.81104	+	14.4592i	−0.406854	+	1.01235i
$205$	1.56334	+	0.902597i	0.109189	+	0.0630401i
$206$	−2.15914	+	5.96951i	−0.150434	+	0.415915i
$207$	−0.312489	−	3.10359i	−0.0217195	−	0.215714i
$208$	5.85156	+	6.86078i	0.405733	+	0.475710i
$209$		−	10.3778i		−	0.717848i
$210$	−7.56530	−	3.60035i	−0.522055	−	0.248447i
$211$	1.95410			0.134526			0.0672629	−	0.997735i	$-0.478573\pi$
$211$	1.95410			0.134526			0.0672629	+	0.997735i	$0.478573\pi$
$212$	18.5361	+	15.4271i	1.27307	+	1.05954i
$213$	−23.0981	+	7.44926i	−1.58266	+	0.510415i
$214$	3.48748	−	9.64205i	0.238399	−	0.659117i
$215$	3.89507	−	6.74646i	0.265642	−	0.460105i
$216$	14.6156	+	1.54392i	0.994467	+	0.105051i
$217$	−11.2206	+	1.29035i	−0.761702	+	0.0875948i
$218$	−11.2246	−	13.3225i	−0.760229	−	0.902315i
$219$	11.2704	+	10.1926i	0.761583	+	0.688753i
$220$	1.65190	+	4.48237i	0.111371	+	0.302202i
$221$	−5.07051	−	8.78238i	−0.341079	−	0.590766i
$222$	0.811891	−	23.1334i	0.0544906	−	1.55262i
$223$			3.59985i			0.241064i	0.992709	+	0.120532i	$0.0384600\pi$
$223$			3.59985i			0.241064i	−0.992709	+	0.120532i	$0.961540\pi$
$224$	−6.82638	−	13.3192i	−0.456107	−	0.889925i
$225$	9.10480	+	4.10151i	0.606987	+	0.273434i
$226$	−10.1294	+	1.80710i	−0.673798	+	0.120206i
$227$	−5.05015	+	2.91571i	−0.335190	+	0.193522i	−0.658143	−	0.752893i	$-0.728658\pi$
$227$	−5.05015	+	2.91571i	−0.335190	+	0.193522i	0.322953	+	0.946415i	$0.395325\pi$
$228$	2.74339	+	19.2636i	0.181685	+	1.27576i
$229$	−11.2803	−	6.51269i	−0.745424	−	0.430371i	0.0786144	−	0.996905i	$-0.474950\pi$
$229$	−11.2803	−	6.51269i	−0.745424	−	0.430371i	−0.824038	+	0.566535i	$0.808284\pi$
$230$	−1.45378	+	1.22486i	−0.0958597	+	0.0807649i
$231$	−7.70827	+	3.50229i	−0.507167	+	0.230433i
$232$	1.88745	+	3.22409i	0.123917	+	0.211672i
$233$	13.6565	+	7.88458i	0.894667	+	0.516536i	0.875466	−	0.483279i	$-0.160554\pi$
$233$	13.6565	+	7.88458i	0.894667	+	0.516536i	0.0192009	+	0.999816i	$0.493888\pi$
$234$	−6.66011	+	6.86424i	−0.435385	+	0.448730i
$235$	−7.63075	−	13.2169i	−0.497775	−	0.862172i
$236$	−14.1488	+	17.0003i	−0.921011	+	1.10663i
$237$	4.63544	+	0.995889i	0.301104	+	0.0646899i
$238$	4.82986	+	16.1240i	0.313073	+	1.04516i
$239$	−22.7458			−1.47130			−0.735651	−	0.677361i	$-0.763124\pi$
$239$	−22.7458			−1.47130			−0.735651	+	0.677361i	$0.763124\pi$
$240$	−4.25121	−	7.88362i	−0.274415	−	0.508886i
$241$	−6.82067	−	11.8137i	−0.439358	−	0.760990i	0.558282	−	0.829651i	$-0.311461\pi$
$241$	−6.82067	−	11.8137i	−0.439358	−	0.760990i	−0.997640	+	0.0686608i	$0.978127\pi$
$242$	−10.0893	−	3.64923i	−0.648562	−	0.234582i
$243$	−0.170365	+	15.5875i	−0.0109289	+	0.999940i
$244$	17.4157	+	2.99870i	1.11493	+	0.191972i
$245$	−8.81339	+	2.05422i	−0.563067	+	0.131240i
$246$	−3.02025	+	1.60522i	−0.192564	+	0.102345i
$247$	−10.9661	−	6.33127i	−0.697755	−	0.402849i
$248$	−10.4929	−	5.97398i	−0.666301	−	0.379348i
$249$	2.52188	+	7.81966i	0.159818	+	0.495551i
$250$	−2.67434	−	14.9906i	−0.169140	−	0.948089i
$251$		−	5.33090i		−	0.336484i	−0.985746	−	0.168242i	$-0.946191\pi$
$251$		−	5.33090i		−	0.336484i	0.985746	−	0.168242i	$-0.0538089\pi$
$252$	13.3825	−	8.53873i	0.843015	−	0.537889i
$253$			1.92102i			0.120774i
$254$	−30.3120	+	5.40769i	−1.90194	+	0.339308i
$255$	3.09179	+	9.58679i	0.193615	+	0.600348i
$256$	2.52455	−	15.7996i	0.157784	−	0.987474i
$257$	−7.26678	−	4.19547i	−0.453289	−	0.261707i	0.255929	−	0.966696i	$-0.417619\pi$
$257$	−7.26678	−	4.19547i	−0.453289	−	0.261707i	−0.709218	+	0.704989i	$0.750952\pi$
$258$	6.92716	+	13.0336i	0.431266	+	0.811436i
$259$	−14.8931	−	20.0827i	−0.925410	−	1.24788i
$260$	5.74425	+	0.989063i	0.356243	+	0.0613391i
$261$	−3.21593	+	2.31510i	−0.199061	+	0.143301i
$262$	−2.58784	+	7.15476i	−0.159877	+	0.442023i
$263$	1.58410	+	2.74375i	0.0976800	+	0.169187i	0.910724	−	0.413016i	$-0.135525\pi$
$263$	1.58410	+	2.74375i	0.0976800	+	0.169187i	−0.813044	+	0.582202i	$0.802191\pi$
$264$	−8.86056	−	1.84778i	−0.545330	−	0.113723i
$265$	15.5886			0.957603
$266$	15.2894	+	14.4204i	0.937452	+	0.884172i
$267$	−16.2535	−	3.49194i	−0.994698	−	0.213703i
$268$	−9.39396	−	7.81830i	−0.573827	−	0.477579i
$269$	7.81827	+	13.5416i	0.476689	+	0.825649i	0.999643	−	0.0267117i	$-0.00850361\pi$
$269$	7.81827	+	13.5416i	0.476689	+	0.825649i	−0.522955	+	0.852361i	$0.675170\pi$
$270$	7.90003	−	5.27654i	0.480781	−	0.321120i
$271$	−12.4371	−	7.18058i	−0.755502	−	0.436189i	0.0721766	−	0.997392i	$-0.477005\pi$
$271$	−12.4371	−	7.18058i	−0.755502	−	0.436189i	−0.827678	+	0.561203i	$0.810339\pi$
$272$	−6.01809	+	16.9577i	−0.364901	+	1.02821i
$273$	−1.00183	+	10.2819i	−0.0606333	+	0.622288i
$274$	−11.9647	−	14.2009i	−0.722813	−	0.857905i
$275$	−5.32598	−	3.07496i	−0.321169	−	0.185427i
$276$	−0.507826	−	3.56586i	−0.0305675	−	0.214639i
$277$	3.23202	−	1.86601i	0.194193	−	0.112117i	−0.399751	−	0.916624i	$-0.630903\pi$
$277$	3.23202	−	1.86601i	0.194193	−	0.112117i	0.593944	+	0.804506i	$0.297570\pi$
$278$	3.22293	+	18.0657i	0.193299	+	1.08351i
$279$	5.26008	−	11.6767i	0.314913	−	0.699065i
$280$	−8.89915	−	3.79475i	−0.531826	−	0.226780i
$281$		−	18.8375i		−	1.12375i	−0.827223	−	0.561874i	$-0.810080\pi$
$281$		−	18.8375i		−	1.12375i	0.827223	−	0.561874i	$-0.189920\pi$
$282$	28.8984	+	1.01422i	1.72087	+	0.0603957i
$283$	10.7726	+	18.6586i	0.640362	+	1.10914i	0.985352	+	0.170534i	$0.0545492\pi$
$283$	10.7726	+	18.6586i	0.640362	+	1.10914i	−0.344989	+	0.938607i	$0.612117\pi$
$284$	−26.2953	+	9.69066i	−1.56034	+	0.575035i
$285$	9.32859	+	8.43649i	0.552578	+	0.499735i
$286$	4.50453	−	3.79521i	0.266358	−	0.224415i
$287$	−1.46957	+	3.38951i	−0.0867460	+	0.200076i
$288$	16.9357	+	1.08759i	0.997944	+	0.0640868i
$289$	1.61820	−	2.80280i	0.0951880	−	0.164870i
$290$	2.27094	+	0.821386i	0.133354	+	0.0482334i
$291$	14.3986	−	4.64362i	0.844061	−	0.272214i
$292$	13.4867	+	11.2246i	0.789249	+	0.656868i
$293$	4.13814			0.241753			0.120876	−	0.992668i	$-0.461430\pi$
$293$	4.13814			0.241753			0.120876	+	0.992668i	$0.461430\pi$
$294$	5.55113	−	16.2230i	0.323749	−	0.946143i
$295$			14.2970i			0.832405i
$296$	−0.161238	−	26.7282i	−0.00937180	−	1.55354i
$297$	1.06608	−	9.54085i	0.0618604	−	0.553616i
$298$	9.09737	+	3.29047i	0.526997	+	0.190612i
$299$	2.02992	+	1.17197i	0.117393	+	0.0677770i
$300$	10.6991	+	4.29989i	0.617713	+	0.248254i
$301$	14.6271	+	6.34179i	0.843091	+	0.365535i
$302$	−3.32747	−	3.94937i	−0.191474	−	0.227260i
$303$	−8.78771	−	7.94734i	−0.504841	−	0.456563i
$304$	4.07939	+	22.0946i	0.233969	+	1.26722i
$305$	9.89279	−	5.71160i	0.566459	−	0.327046i
$306$	−18.5076	−	4.66090i	−1.05801	−	0.266446i
$307$	−4.63154			−0.264336			−0.132168	−	0.991227i	$-0.542194\pi$
$307$	−4.63154			−0.264336			−0.132168	+	0.991227i	$0.542194\pi$
$308$	−8.72700	+	4.40652i	−0.497267	+	0.251085i
$309$	−7.60122	−	1.63306i	−0.432418	−	0.0929017i
$310$	−7.68356	+	1.37076i	−0.436397	+	0.0778537i
$311$	−7.04878	−	12.2088i	−0.399700	−	0.692300i	0.593989	−	0.804473i	$-0.297552\pi$
$311$	−7.04878	−	12.2088i	−0.399700	−	0.692300i	−0.993689	+	0.112173i	$0.964219\pi$
$312$	−7.35815	+	8.23554i	−0.416573	+	0.466246i
$313$	6.95418	−	12.0450i	0.393074	−	0.680824i	−0.599780	−	0.800165i	$-0.704745\pi$
$313$	6.95418	−	12.0450i	0.393074	−	0.680824i	0.992853	+	0.119342i	$0.0380784\pi$
$314$	−2.46825	−	2.92956i	−0.139292	−	0.165325i
$315$	3.11813	−	9.77608i	0.175687	−	0.550819i
$316$	5.39529	+	0.928978i	0.303509	+	0.0522591i
$317$	8.34364	−	14.4516i	0.468625	−	0.811683i	−0.530731	−	0.847540i	$-0.678083\pi$
$317$	8.34364	−	14.4516i	0.468625	−	0.811683i	0.999357	+	0.0358569i	$0.0114161\pi$
$318$	−15.6561	+	25.0452i	−0.877949	+	1.40447i
$319$	2.11342	−	1.22018i	0.118329	−	0.0683171i
$320$	−5.27890	−	8.89376i	−0.295099	−	0.497176i
$321$	12.2776	+	2.63775i	0.685269	+	0.147225i
$322$	−2.83020	−	2.66934i	−0.157721	−	0.148757i
$323$		−	25.2681i		−	1.40595i
$324$	0.543246	+	17.9918i	0.0301803	+	0.999544i
$325$	−6.49853	+	3.75193i	−0.360473	+	0.208119i
$326$	11.7521	+	4.25067i	0.650888	+	0.235423i
$327$	14.3112	−	15.8245i	0.791410	−	0.875095i
$328$	−3.40835	+	1.99532i	−0.188195	+	0.110173i
$329$	25.0874	−	18.6045i	1.38311	−	1.02570i
$330$	−5.16634	+	2.74583i	−0.284398	+	0.151153i
$331$	−4.82148	+	8.35105i	−0.265012	+	0.459015i	−0.967567	−	0.252615i	$-0.918709\pi$
$331$	−4.82148	+	8.35105i	−0.265012	+	0.459015i	0.702554	+	0.711630i	$0.252043\pi$
$332$	3.28068	+	8.90205i	0.180051	+	0.488563i
$333$	28.2074	−	2.84010i	1.54576	−	0.155636i
$334$	2.95107	+	16.5418i	0.161475	+	0.905126i
$335$	−7.90019			−0.431633
$336$	15.0344	−	10.4865i	0.820194	−	0.572085i
$337$	29.4886			1.60635			0.803173	−	0.595746i	$-0.203144\pi$
$337$	29.4886			1.60635			0.803173	+	0.595746i	$0.203144\pi$
$338$	1.96665	+	11.0238i	0.106972	+	0.599614i
$339$	−3.86797	−	11.9935i	−0.210079	−	0.651399i
$340$	4.02207	+	10.9138i	0.218127	+	0.591883i
$341$	−3.94356	+	6.83044i	−0.213556	+	0.369889i
$342$	−22.9233	+	6.51462i	−1.23955	+	0.352270i
$343$	−6.23712	−	17.4384i	−0.336773	−	0.941586i
$344$	8.61062	+	14.7084i	0.464253	+	0.793024i
$345$	−1.72680	−	1.56167i	−0.0929680	−	0.0840774i
$346$	−8.31184	−	3.00635i	−0.446847	−	0.161622i
$347$	−10.8911	+	6.28800i	−0.584667	+	0.337558i	−0.762986	−	0.646415i	$-0.776267\pi$
$347$	−10.8911	+	6.28800i	−0.584667	+	0.337558i	0.178319	+	0.983973i	$0.442934\pi$
$348$	−3.60042	+	2.82362i	−0.193003	+	0.151362i
$349$			34.5012i			1.84681i	0.383830	+	0.923404i	$0.374605\pi$
$349$			34.5012i			1.84681i	−0.383830	+	0.923404i	$0.625395\pi$
$350$	11.9309	−	3.57386i	0.637735	−	0.191031i
$351$	−9.43129	−	6.94718i	−0.503405	−	0.370813i
$352$	−10.3103	−	1.71129i	−0.549543	−	0.0912123i
$353$	9.10737	−	5.25815i	0.484737	−	0.279863i	−0.237652	−	0.971350i	$-0.576378\pi$
$353$	9.10737	−	5.25815i	0.484737	−	0.279863i	0.722388	+	0.691488i	$0.243044\pi$
$354$	−22.9700	−	14.3589i	−1.22084	−	0.763165i
$355$	−9.05743	+	15.6879i	−0.480719	+	0.832629i
$356$	−18.9178	−	3.25733i	−1.00264	−	0.172638i
$357$	−18.7682	+	8.52744i	−0.993321	+	0.451320i
$358$	−1.51491	−	1.79804i	−0.0800652	−	0.0950293i
$359$	8.02903	−	13.9067i	0.423756	−	0.733967i	−0.572547	−	0.819872i	$-0.694045\pi$
$359$	8.02903	−	13.9067i	0.423756	−	0.733967i	0.996303	+	0.0859047i	$0.0273780\pi$
$360$	8.86403	−	6.46262i	0.467175	−	0.340610i
$361$	−6.27547	−	10.8694i	−0.330288	−	0.572075i
$362$	6.22156	−	1.10993i	0.326998	−	0.0583368i
$363$	2.76009	−	12.8471i	0.144867	−	0.674296i
$364$	−0.667843	+	11.9100i	−0.0350045	+	0.624254i
$365$	11.3421			0.593673
$366$	−0.759140	+	21.6304i	−0.0396809	+	1.13064i
$367$	20.8250	−	12.0233i	1.08706	−	0.627613i	0.154266	−	0.988029i	$-0.450699\pi$
$367$	20.8250	−	12.0233i	1.08706	−	0.627613i	0.932791	+	0.360417i	$0.117366\pi$
$368$	−0.755130	−	4.08991i	−0.0393639	−	0.213201i
$369$	−2.44741	−	3.39972i	−0.127407	−	0.176983i
$370$	−11.1323	−	13.2129i	−0.578742	−	0.686907i
$371$	3.64473	+	31.6936i	0.189225	+	1.64545i
$372$	5.51450	−	13.7213i	0.285913	−	0.711418i
$373$	12.5120	+	7.22381i	0.647847	+	0.374035i	0.787631	−	0.616147i	$-0.211307\pi$
$373$	12.5120	+	7.22381i	0.647847	+	0.374035i	−0.139784	+	0.990182i	$0.544641\pi$
$374$	11.0531	+	3.99784i	0.571542	+	0.206724i
$375$	17.7493	−	5.72424i	0.916571	−	0.295599i
$376$	33.3889	−	0.201420i	1.72190	−	0.0103874i
$377$		−	2.97762i		−	0.153355i
$378$	12.5749	+	14.8280i	0.646785	+	0.762673i
$379$	−29.8048			−1.53097			−0.765485	−	0.643453i	$-0.777501\pi$
$379$	−29.8048			−1.53097			−0.765485	+	0.643453i	$0.777501\pi$
$380$	11.1630	+	9.29065i	0.572651	+	0.476600i
$381$	−11.5748	−	35.8903i	−0.592994	−	1.83871i
$382$	−29.9947	−	10.8489i	−1.53466	−	0.555080i
$383$	5.62806	−	9.74809i	0.287581	−	0.498104i	−0.685651	−	0.727930i	$-0.740482\pi$
$383$	5.62806	−	9.74809i	0.287581	−	0.498104i	0.973232	+	0.229826i	$0.0738158\pi$
$384$	19.5907	+	0.450993i	0.999735	+	0.0230146i
$385$	−2.51380	+	5.79798i	−0.128115	+	0.295492i
$386$	6.27926	−	5.29048i	0.319606	−	0.269278i
$387$	−14.6712	+	10.5616i	−0.745778	+	0.536874i
$388$	16.3916	−	6.04083i	0.832159	−	0.306677i
$389$	13.4807	+	23.3492i	0.683498	+	1.18385i	0.973906	+	0.226950i	$0.0728755\pi$
$389$	13.4807	+	23.3492i	0.683498	+	1.18385i	−0.290408	+	0.956903i	$0.593791\pi$
$390$	−0.250388	+	7.13437i	−0.0126789	+	0.361263i
$391$			4.67735i			0.236544i
$392$	5.63452	−	18.9803i	0.284586	−	0.958650i
$393$	−9.11045	−	1.95731i	−0.459561	−	0.0987331i
$394$	0.784552	+	4.39769i	0.0395252	+	0.221552i
$395$	3.06473	−	1.76942i	0.154203	−	0.0890293i
$396$	0.777148	−	11.0581i	0.0390532	−	0.555691i
$397$	−6.75185	−	3.89818i	−0.338866	−	0.195644i	0.320905	−	0.947111i	$-0.396013\pi$
$397$	−6.75185	−	3.89818i	−0.338866	−	0.195644i	−0.659770	+	0.751467i	$0.729346\pi$
$398$	12.8736	+	15.2796i	0.645295	+	0.765900i
$399$	−14.9713	+	20.9387i	−0.749505	+	1.04825i
$400$	12.5479	+	4.45309i	0.627395	+	0.222655i
$401$	2.98430	+	1.72299i	0.149029	+	0.0860420i	0.572660	−	0.819793i	$-0.305911\pi$
$401$	2.98430	+	1.72299i	0.149029	+	0.0860420i	−0.423631	+	0.905835i	$0.639245\pi$
$402$	7.93436	−	12.6927i	0.395730	−	0.633054i
$403$	4.81175	+	8.33420i	0.239691	+	0.415156i
$404$	−10.5158	−	8.75197i	−0.523180	−	0.435427i
$405$	7.70959	+	8.71440i	0.383093	+	0.433022i
$406$	−1.13902	+	4.80914i	−0.0565285	+	0.238674i
$407$	−17.4595			−0.865435
$408$	−21.5739	−	4.49900i	−1.06807	−	0.222734i
$409$	9.79039	+	16.9575i	0.484104	+	0.838492i	0.999833	−	0.0182590i	$-0.00581236\pi$
$409$	9.79039	+	16.9575i	0.484104	+	0.838492i	−0.515729	+	0.856752i	$0.672479\pi$
$410$	−0.868328	+	2.40072i	−0.0428837	+	0.118563i
$411$	15.2547	−	16.8678i	0.752459	−	0.832025i
$412$	−8.84722	−	1.52334i	−0.435871	−	0.0750497i
$413$	−29.0676	+	3.34274i	−1.43032	+	0.164485i
$414$	4.24330	−	1.20591i	0.208547	−	0.0592674i
$415$	5.31101	+	3.06631i	0.260707	+	0.150519i
$416$	−8.09842	+	9.85078i	−0.397057	+	0.482974i
$417$	−21.3903	+	6.89847i	−1.04749	+	0.337819i
$418$	14.4483	−	2.57759i	0.706690	−	0.126074i
$419$			27.6189i			1.34927i	0.738150	+	0.674637i	$0.235700\pi$
$419$			27.6189i			1.34927i	−0.738150	+	0.674637i	$0.764300\pi$
$420$	3.13348	−	11.4269i	0.152898	−	0.557575i
$421$		−	9.36226i		−	0.456289i	−0.973627	−	0.228144i	$-0.926734\pi$
$421$		−	9.36226i		−	0.456289i	0.973627	−	0.228144i	$-0.0732658\pi$
$422$	0.485351	+	2.72056i	0.0236265	+	0.132435i
$423$	3.54786	+	35.2368i	0.172503	+	1.71327i
$424$	−16.8741	+	29.6383i	−0.819480	+	1.43936i
$425$	−12.9678	−	7.48697i	−0.629031	−	0.363171i
$426$	−16.1081	−	30.3078i	−0.780441	−	1.46842i
$427$	13.9254	+	18.7779i	0.673897	+	0.908724i
$428$	14.2902	+	2.46053i	0.690741	+	0.118934i
$429$	5.35047	+	4.83880i	0.258323	+	0.233620i
$430$	10.3601	+	3.74719i	0.499607	+	0.180705i
$431$	4.22951	+	7.32573i	0.203729	+	0.352868i	0.949727	−	0.313080i	$-0.101361\pi$
$431$	4.22951	+	7.32573i	0.203729	+	0.352868i	−0.745998	+	0.665948i	$0.768027\pi$
$432$	1.48067	+	20.7318i	0.0712386	+	0.997459i
$433$	−10.9191			−0.524737			−0.262369	−	0.964968i	$-0.584504\pi$
$433$	−10.9191			−0.524737			−0.262369	+	0.964968i	$0.584504\pi$
$434$	−4.58338	−	15.3011i	−0.220009	−	0.734478i
$435$	−0.621254	+	2.89168i	−0.0297868	+	0.138645i
$436$	15.7601	−	18.9363i	0.754772	−	0.906884i
$437$	2.92018	+	5.05790i	0.139691	+	0.241952i
$438$	−11.3912	+	18.2226i	−0.544292	+	0.870710i
$439$	−20.2600	−	11.6971i	−0.966959	−	0.558274i	−0.0686510	−	0.997641i	$-0.521869\pi$
$439$	−20.2600	−	11.6971i	−0.966959	−	0.558274i	−0.898308	+	0.439367i	$0.855203\pi$
$440$	−5.83021	+	3.41313i	−0.277944	+	0.162715i
$441$	20.6050	+	4.05383i	0.981191	+	0.193040i
$442$	10.9677	−	9.24065i	0.521681	−	0.439533i
$443$	−5.31199	−	3.06688i	−0.252380	−	0.145712i	0.368473	−	0.929638i	$-0.379881\pi$
$443$	−5.31199	−	3.06688i	−0.252380	−	0.145712i	−0.620854	+	0.783926i	$0.713214\pi$
$444$	32.4088	−	4.61544i	1.53805	−	0.219039i
$445$	−10.7460	+	6.20422i	−0.509410	+	0.294108i
$446$	−5.01183	+	0.894116i	−0.237317	+	0.0423376i
$447$	−2.48874	+	11.5840i	−0.117713	+	0.547907i
$448$	16.8479	−	12.8121i	0.795987	−	0.605313i
$449$			35.8658i			1.69261i	0.532696	+	0.846307i	$0.321179\pi$
$449$			35.8658i			1.69261i	−0.532696	+	0.846307i	$0.678821\pi$
$450$	−3.44884	+	13.6947i	−0.162580	+	0.645575i
$451$	1.28992	+	2.23420i	0.0607397	+	0.105204i
$452$	−5.03180	−	13.6536i	−0.236676	−	0.642214i
$453$	4.24244	−	4.69105i	0.199327	−	0.220405i
$454$	−5.31368	−	6.30679i	−0.249383	−	0.295992i
$455$	4.59303	+	6.19352i	0.215324	+	0.290357i
$456$	−26.1380	+	8.60404i	−1.22402	+	0.402921i
$457$	−1.51987	+	2.63249i	−0.0710964	+	0.123143i	−0.899382	−	0.437163i	$-0.855983\pi$
$457$	−1.51987	+	2.63249i	−0.0710964	+	0.123143i	0.828286	+	0.560306i	$0.189316\pi$
$458$	6.26542	−	17.3224i	0.292764	−	0.809422i
$459$	2.59572	−	23.2303i	0.121158	−	1.08430i
$460$	−2.06637	−	1.71978i	−0.0963452	−	0.0801852i
$461$	30.7564			1.43247			0.716233	−	0.697861i	$-0.245865\pi$
$461$	30.7564			1.43247			0.716233	+	0.697861i	$0.245865\pi$
$462$	−6.79054	−	9.86181i	−0.315924	−	0.458813i
$463$			9.54146i			0.443429i	0.975112	+	0.221715i	$0.0711653\pi$
$463$			9.54146i			0.443429i	−0.975112	+	0.221715i	$0.928835\pi$
$464$	−4.01989	+	3.42856i	−0.186619	+	0.159167i
$465$	−2.93401	−	9.09756i	−0.136061	−	0.421889i
$466$	−7.58523	+	20.9714i	−0.351379	+	0.971479i
$467$	−4.36437	−	2.51977i	−0.201959	−	0.116601i	0.395610	−	0.918419i	$-0.370533\pi$
$467$	−4.36437	−	2.51977i	−0.201959	−	0.116601i	−0.597569	+	0.801818i	$0.703867\pi$
$468$	−11.2108	−	7.56751i	−0.518221	−	0.349808i
$469$	−1.84712	−	16.0621i	−0.0852920	−	0.741677i
$470$	16.5056	−	13.9065i	0.761348	−	0.641460i
$471$	3.14697	−	3.47973i	0.145004	−	0.160338i
$472$	−27.1826	−	15.4760i	−1.25118	−	0.712340i
$473$	9.64147	−	5.56650i	0.443315	−	0.255948i
$474$	−0.235177	+	6.70096i	−0.0108020	+	0.307785i
$475$	−18.6972			−0.857884
$476$	−21.2487	+	10.7291i	−0.973931	+	0.491766i
$477$	−32.9820	−	14.8576i	−1.51014	−	0.680285i
$478$	−5.64950	−	31.6674i	−0.258402	−	1.44843i
$479$	−13.6307	−	23.6091i	−0.622804	−	1.07873i	−0.988961	−	0.148175i	$-0.952660\pi$
$479$	−13.6307	−	23.6091i	−0.622804	−	1.07873i	0.366157	−	0.930553i	$-0.380673\pi$
$480$	9.91993	−	7.87678i	0.452781	−	0.359524i
$481$	−10.6516	+	18.4492i	−0.485673	+	0.841211i
$482$	14.7534	−	12.4302i	0.671998	−	0.566180i
$483$	2.77133	−	3.87593i	0.126100	−	0.176361i
$484$	2.57465	−	14.9530i	0.117030	−	0.679681i
$485$	5.64610	−	9.77933i	0.256376	−	0.444057i
$486$	−21.7438	+	3.63437i	−0.986317	+	0.164859i
$487$	−0.905513	+	0.522798i	−0.0410327	+	0.0236902i	−0.520376	−	0.853937i	$-0.674208\pi$
$487$	−0.905513	+	0.522798i	−0.0410327	+	0.0236902i	0.479343	+	0.877627i	$0.340875\pi$
$488$	0.150762	+	24.9915i	0.00682468	+	1.13131i
$489$	−3.21499	+	14.9644i	−0.145387	+	0.676714i
$490$	−5.04899	−	11.7601i	−0.228090	−	0.531265i
$491$			29.3101i			1.32275i	0.750057	+	0.661373i	$0.230026\pi$
$491$			29.3101i			1.32275i	−0.750057	+	0.661373i	$0.769974\pi$
$492$	−2.98499	−	3.80619i	−0.134574	−	0.171596i
$493$	5.14579	−	2.97092i	0.231755	−	0.133804i
$494$	6.09089	−	16.8399i	0.274042	−	0.757661i
$495$	−4.18646	−	5.81546i	−0.188167	−	0.261385i
$496$	5.71098	−	16.0924i	0.256431	−	0.722569i
$497$	−34.0132	−	14.7469i	−1.52570	−	0.661490i
$498$	−10.2604	+	5.45325i	−0.459780	+	0.244366i
$499$	14.3749	−	24.8981i	0.643510	−	1.11459i	−0.341133	−	0.940015i	$-0.610811\pi$
$499$	14.3749	−	24.8981i	0.643510	−	1.11459i	0.984643	−	0.174578i	$-0.0558560\pi$
$500$	20.2062	−	7.44660i	0.903647	−	0.333022i
$501$	−19.5860	+	6.31657i	−0.875037	+	0.282204i
$502$	7.42185	−	1.32407i	0.331253	−	0.0590960i
$503$	19.8016			0.882910			0.441455	−	0.897283i	$-0.354462\pi$
$503$	19.8016			0.882910			0.441455	+	0.897283i	$0.354462\pi$
$504$	15.2118	+	16.5107i	0.677586	+	0.735444i
$505$	−8.84363			−0.393536
$506$	−2.67451	+	0.477135i	−0.118896	+	0.0212113i
$507$	−13.0525	+	4.20949i	−0.579681	+	0.186950i
$508$	−15.0575	−	40.8582i	−0.668069	−	1.81279i
$509$	14.1795	−	24.5596i	0.628494	−	1.08858i	−0.359360	−	0.933199i	$-0.617005\pi$
$509$	14.1795	−	24.5596i	0.628494	−	1.08858i	0.987854	−	0.155385i	$-0.0496618\pi$
$510$	−12.5791	+	6.68561i	−0.557012	+	0.296044i
$511$	2.65186	+	23.0599i	0.117312	+	1.02011i
$512$	22.6237	−	0.409474i	0.999836	−	0.0180964i
$513$	−11.6963	−	26.7408i	−0.516403	−	1.18064i
$514$	4.03618	−	11.1591i	0.178028	−	0.492206i
$515$	−5.02555	+	2.90151i	−0.221452	+	0.127856i
$516$	−16.4252	+	12.8814i	−0.723081	+	0.567073i
$517$		−	21.8104i		−	0.959222i
$518$	24.2607	−	25.7226i	1.06595	−	1.13019i
$519$	2.27385	−	10.5838i	0.0998108	−	0.464577i
$520$	0.0497260	+	8.24298i	0.00218063	+	0.361479i
$521$	−27.4943	+	15.8738i	−1.20455	+	0.695445i	−0.961563	−	0.274585i	$-0.911460\pi$
$521$	−27.4943	+	15.8738i	−1.20455	+	0.695445i	−0.242984	+	0.970030i	$0.578126\pi$
$522$	−4.02191	−	3.90231i	−0.176034	−	0.170799i
$523$	3.11470	−	5.39482i	0.136196	−	0.235899i	−0.789858	−	0.613290i	$-0.789846\pi$
$523$	3.11470	−	5.39482i	0.136196	−	0.235899i	0.926054	+	0.377392i	$0.123179\pi$
$524$	−10.6038	−	1.82580i	−0.463231	−	0.0797606i
$525$	6.30989	+	13.8876i	0.275386	+	0.606104i
$526$	−3.42648	+	2.88692i	−0.149402	+	0.125876i
$527$	−9.60185	+	16.6309i	−0.418263	+	0.724453i
$528$	0.371785	−	12.7949i	0.0161799	−	0.556827i
$529$	10.9594	+	18.9823i	0.476498	+	0.825318i
$530$	3.87184	+	21.7030i	0.168182	+	0.942718i
$531$	13.6266	−	30.2492i	0.591344	−	1.31270i
$532$	−16.2790	+	24.8680i	−0.705786	+	1.07817i
$533$	3.14780			0.136346
$534$	0.824614	−	23.4959i	0.0356845	−	1.01677i
$535$	8.11735	−	4.68656i	0.350944	−	0.202618i
$536$	8.55166	−	15.0204i	0.369376	−	0.648784i
$537$	1.93147	−	2.13571i	0.0833491	−	0.0921626i
$538$	−16.9112	+	14.2483i	−0.729096	+	0.614286i
$539$	−12.3758	−	3.75526i	−0.533061	−	0.161751i
$540$	9.30834	+	9.68811i	0.400567	+	0.416910i
$541$	−1.99979	−	1.15458i	−0.0859776	−	0.0496392i	0.456395	−	0.889777i	$-0.349140\pi$
$541$	−1.99979	−	1.15458i	−0.0859776	−	0.0496392i	−0.542372	+	0.840138i	$0.682474\pi$
$542$	6.90795	−	19.0988i	0.296722	−	0.820366i
$543$	2.37574	+	7.36652i	0.101953	+	0.316128i
$544$	−25.1038	−	4.16669i	−1.07632	−	0.178646i
$545$		−	15.9252i		−	0.682159i
$546$	−14.5636	+	1.15899i	−0.623264	+	0.0496004i
$547$	32.5136			1.39018			0.695090	−	0.718922i	$-0.255364\pi$
$547$	32.5136			1.39018			0.695090	+	0.718922i	$0.255364\pi$
$548$	16.7992	−	20.1848i	0.717624	−	0.862250i
$549$	−26.3747	+	2.65557i	−1.12564	+	0.113337i
$550$	2.95821	−	8.17875i	0.126138	−	0.348743i
$551$	3.70963	−	6.42528i	0.158036	−	0.273726i
$552$	4.83837	−	1.59268i	0.205935	−	0.0677891i
$553$	4.31401	+	5.81727i	0.183450	+	0.247375i
$554$	3.40067	+	4.03624i	0.144480	+	0.171484i
$555$	14.1934	−	15.6943i	0.602478	−	0.666186i
$556$	−24.3511	+	8.97414i	−1.03272	+	0.380588i
$557$	16.5711	+	28.7020i	0.702140	+	1.21614i	0.967714	+	0.252052i	$0.0811053\pi$
$557$	16.5711	+	28.7020i	0.702140	+	1.21614i	−0.265574	+	0.964091i	$0.585561\pi$
$558$	17.5631	+	4.42305i	0.743507	+	0.187243i
$559$		−	13.5840i		−	0.574542i
$560$	3.07284	−	13.3322i	0.129851	−	0.563388i
$561$	−3.02376	+	14.0743i	−0.127663	+	0.594219i
$562$	26.2261	−	4.67877i	1.10628	−	0.197362i
$563$	13.6362	−	7.87286i	0.574697	−	0.331801i	−0.184326	−	0.982865i	$-0.559010\pi$
$563$	13.6362	−	7.87286i	0.574697	−	0.331801i	0.759023	+	0.651064i	$0.225677\pi$
$564$	5.76563	+	40.4851i	0.242777	+	1.70473i
$565$	−8.14583	−	4.70300i	−0.342698	−	0.197857i
$566$	−23.3015	+	19.6323i	−0.979435	+	0.825205i
$567$	−15.9149	+	17.7120i	−0.668363	+	0.743835i
$568$	−20.0228	−	34.2023i	−0.840137	−	1.43510i
$569$	20.1971	+	11.6608i	0.846706	+	0.488846i	0.859538	−	0.511072i	$-0.170751\pi$
$569$	20.1971	+	11.6608i	0.846706	+	0.488846i	−0.0128319	+	0.999918i	$0.504085\pi$
$570$	−9.42856	+	15.0830i	−0.394919	+	0.631756i
$571$	12.0030	+	20.7898i	0.502311	+	0.870027i	0.999996	+	0.00267009i	$0.000849917\pi$
$571$	12.0030	+	20.7898i	0.502311	+	0.870027i	−0.497686	+	0.867357i	$0.665817\pi$
$572$	6.40262	+	5.32871i	0.267707	+	0.222804i
$573$	8.20558	−	38.1935i	0.342793	−	1.59556i
$574$	−5.08398	−	1.20411i	−0.212201	−	0.0502587i
$575$	3.46101			0.144334
$576$	2.69223	+	23.8485i	0.112176	+	0.993688i
$577$	−2.69246	−	4.66349i	−0.112089	−	0.194143i	0.804523	−	0.593921i	$-0.202421\pi$
$577$	−2.69246	−	4.66349i	−0.112089	−	0.194143i	−0.916612	+	0.399777i	$0.869087\pi$
$578$	4.30406	+	1.55676i	0.179025	+	0.0647526i
$579$	7.45849	+	6.74524i	0.309964	+	0.280322i
$580$	−0.579514	+	3.36568i	−0.0240630	+	0.139752i
$581$	−4.99244	+	11.5149i	−0.207121	+	0.477717i
$582$	10.0413	+	18.8928i	0.416223	+	0.783133i
$583$	19.2933	+	11.1390i	0.799046	+	0.461329i
$584$	−12.2774	+	21.5645i	−0.508043	+	0.892345i
$585$	−8.69918	+	0.875888i	−0.359667	+	0.0362135i
$586$	1.02781	+	5.76125i	0.0424586	+	0.237995i
$587$			20.8871i			0.862104i	0.902327	+	0.431052i	$0.141857\pi$
$587$			20.8871i			0.862104i	−0.902327	+	0.431052i	$0.858143\pi$
$588$	23.9649	+	3.69907i	0.988296	+	0.152547i
$589$			23.9786i			0.988023i
$590$	−19.9048	+	3.55103i	−0.819466	+	0.146194i
$591$	−5.20699	+	1.67928i	−0.214187	+	0.0690763i
$592$	37.1718	−	6.86311i	1.52775	−	0.282072i
$593$	31.7953	+	18.3570i	1.30567	+	0.753832i	0.981371	−	0.192122i	$-0.0615368\pi$
$593$	31.7953	+	18.3570i	1.30567	+	0.753832i	0.324303	+	0.945953i	$0.394870\pi$
$594$	13.5479	−	0.885479i	0.555876	−	0.0363317i
$595$	−6.12065	+	14.1170i	−0.250922	+	0.578742i
$596$	−2.32153	+	13.4829i	−0.0950937	+	0.552282i
$597$	−16.4135	+	18.1491i	−0.671761	+	0.742795i
$598$	−1.12748	+	3.11721i	−0.0461060	+	0.127472i
$599$	12.0639	+	20.8953i	0.492918	+	0.853760i	0.999967	−	0.00815783i	$-0.00259675\pi$
$599$	12.0639	+	20.8953i	0.492918	+	0.853760i	−0.507048	+	0.861918i	$0.669263\pi$
$600$	−3.32904	+	15.9636i	−0.135908	+	0.651712i
$601$	−30.7421			−1.25399			−0.626997	−	0.779021i	$-0.715716\pi$
$601$	−30.7421			−1.25399			−0.626997	+	0.779021i	$0.715716\pi$
$602$	−5.19623	+	21.9394i	−0.211783	+	0.894185i
$603$	16.7150	+	7.52972i	0.680687	+	0.306634i
$604$	4.67197	−	5.61353i	0.190100	−	0.228411i
$605$	−4.90393	−	8.49385i	−0.199373	−	0.345324i
$606$	8.88189	−	14.2085i	0.360802	−	0.577179i
$607$	3.75552	+	2.16825i	0.152432	+	0.0880066i	0.574276	−	0.818662i	$-0.305284\pi$
$607$	3.75552	+	2.16825i	0.152432	+	0.0880066i	−0.421844	+	0.906668i	$0.638617\pi$
$608$	−29.7477	+	11.1672i	−1.20643	+	0.452891i
$609$	−6.02439	−	0.586993i	−0.244120	−	0.0237861i
$610$	10.4090	+	12.3544i	0.421448	+	0.500216i
$611$	−23.0468	−	13.3061i	−0.932373	−	0.538306i
$612$	1.89222	−	26.9245i	0.0764883	−	1.08836i
$613$	26.2945	−	15.1812i	1.06203	−	0.613161i	0.136034	−	0.990704i	$-0.456564\pi$
$613$	26.2945	−	15.1812i	1.06203	−	0.613161i	0.925992	+	0.377543i	$0.123231\pi$
$614$	−1.15036	−	6.44818i	−0.0464249	−	0.260228i
$615$	−3.05693	−	0.656759i	−0.123268	−	0.0264831i
$616$	−8.30247	−	11.0555i	−0.334516	−	0.445440i
$617$		−	11.5709i		−	0.465827i	−0.972497	−	0.232913i	$-0.925174\pi$
$617$		−	11.5709i		−	0.465827i	0.972497	−	0.232913i	$-0.0748259\pi$
$618$	0.385644	−	10.9883i	0.0155129	−	0.442013i
$619$	−8.62076	−	14.9316i	−0.346497	−	0.600151i	0.639127	−	0.769101i	$-0.279296\pi$
$619$	−8.62076	−	14.9316i	−0.346497	−	0.600151i	−0.985625	+	0.168950i	$0.945962\pi$
$620$	−3.81682	−	10.3568i	−0.153287	−	0.415940i
$621$	2.16508	+	4.94996i	0.0868818	+	0.198635i
$622$	15.2468	−	12.8459i	0.611341	−	0.515074i
$623$	−15.1264	−	20.3974i	−0.606028	−	0.817204i
$624$	−13.2934	−	8.19875i	−0.532161	−	0.328213i
$625$	−1.36164	+	2.35843i	−0.0544656	+	0.0943372i
$626$	18.4967	+	6.69015i	0.739276	+	0.267392i
$627$	5.51717	+	17.1072i	0.220334	+	0.683197i
$628$	3.46558	−	4.16401i	0.138292	−	0.166162i
$629$	−42.5107			−1.69501
$630$	14.3850	+	1.91302i	0.573113	+	0.0762166i
$631$			4.91146i			0.195522i	0.995210	+	0.0977611i	$0.0311681\pi$
$631$			4.91146i			0.195522i	−0.995210	+	0.0977611i	$0.968832\pi$
$632$	0.0467052	+	7.74223i	0.00185783	+	0.307969i
$633$	−3.22123	+	1.03886i	−0.128032	+	0.0412910i
$634$	22.1923	+	8.02685i	0.881371	+	0.318787i
$635$	−24.3762	−	14.0736i	−0.967339	−	0.558493i
$636$	−38.7573	−	15.5763i	−1.53683	−	0.617639i
$637$	−11.5183	+	10.7863i	−0.456372	+	0.427368i
$638$	2.22370	+	2.63930i	0.0880370	+	0.104491i
$639$	34.1157	−	24.5594i	1.34960	−	0.971554i
$640$	11.0710	−	9.55844i	0.437621	−	0.377831i
$641$	34.7916	−	20.0870i	1.37419	−	0.793387i	0.382735	−	0.923858i	$-0.374982\pi$
$641$	34.7916	−	20.0870i	1.37419	−	0.793387i	0.991452	+	0.130471i	$0.0416488\pi$
$642$	−0.622899	+	17.7484i	−0.0245838	+	0.700475i
$643$	12.5997			0.496884			0.248442	−	0.968647i	$-0.420081\pi$
$643$	12.5997			0.496884			0.248442	+	0.968647i	$0.420081\pi$
$644$	3.01339	−	4.60329i	0.118744	−	0.181395i
$645$	−2.83418	+	13.1919i	−0.111596	+	0.519431i
$646$	35.1791	−	6.27598i	1.38410	−	0.246925i
$647$	−9.55483	−	16.5495i	−0.375639	−	0.650626i	0.614783	−	0.788696i	$-0.289243\pi$
$647$	−9.55483	−	16.5495i	−0.375639	−	0.650626i	−0.990422	+	0.138070i	$0.955910\pi$
$648$	−24.9138	+	5.22505i	−0.978708	+	0.205259i
$649$	−10.2160	+	17.6947i	−0.401015	+	0.694578i
$650$	−6.83763	−	8.11557i	−0.268194	−	0.318319i
$651$	17.8105	−	8.09227i	0.698048	−	0.317161i
$652$	−2.99898	+	17.4174i	−0.117449	+	0.682118i
$653$	−4.01546	+	6.95497i	−0.157137	+	0.272169i	−0.933835	−	0.357704i	$-0.883560\pi$
$653$	−4.01546	+	6.95497i	−0.157137	+	0.272169i	0.776698	+	0.629873i	$0.216893\pi$
$654$	25.5859	+	15.9941i	1.00049	+	0.625417i
$655$	−6.02338	+	3.47760i	−0.235353	+	0.135881i
$656$	−3.62450	−	4.24962i	−0.141513	−	0.165920i
$657$	−23.9973	−	10.8102i	−0.936225	−	0.421748i
$658$	32.1328	+	30.3065i	1.25267	+	1.18147i
$659$		−	5.21061i		−	0.202977i	−0.994837	−	0.101488i	$-0.967640\pi$
$659$		−	5.21061i		−	0.202977i	0.994837	−	0.101488i	$-0.0323604\pi$
$660$	−5.10603	−	6.51074i	−0.198752	−	0.253430i
$661$	33.5498	−	19.3700i	1.30494	−	0.753406i	0.323690	−	0.946163i	$-0.395076\pi$
$661$	33.5498	−	19.3700i	1.30494	−	0.753406i	0.981246	+	0.192757i	$0.0617431\pi$
$662$	−12.8241	−	4.63842i	−0.498424	−	0.180277i
$663$	13.0274	+	11.7816i	0.505944	+	0.457560i
$664$	−11.5789	+	6.77852i	−0.449347	+	0.263058i
$665$	2.19497	+	19.0869i	0.0851171	+	0.740157i
$666$	10.9601	+	38.5658i	0.424695	+	1.49440i
$667$	−0.686686	+	1.18937i	−0.0265886	+	0.0460528i
$668$	−22.2970	+	8.21715i	−0.862698	+	0.317931i
$669$	−1.91379	−	5.93416i	−0.0739915	−	0.229428i
$670$	−1.96221	−	10.9989i	−0.0758069	−	0.424924i
$671$	16.3251			0.630223
$672$	18.3338	+	18.3268i	0.707242	+	0.706972i
$673$	−33.1783			−1.27893			−0.639465	−	0.768821i	$-0.720844\pi$
$673$	−33.1783			−1.27893			−0.639465	+	0.768821i	$0.720844\pi$
$674$	7.32425	+	41.0550i	0.282119	+	1.58138i
$675$	−17.1893	−	1.92071i	−0.661615	−	0.0739280i
$676$	−14.8592	+	5.47607i	−0.571507	+	0.210618i
$677$	15.7573	−	27.2925i	0.605602	−	1.04893i	−0.386354	−	0.922351i	$-0.626266\pi$
$677$	15.7573	−	27.2925i	0.605602	−	1.04893i	0.991956	−	0.126583i	$-0.0404011\pi$
$678$	15.7371	−	8.36401i	0.604378	−	0.321218i
$679$	21.2027	+	9.19274i	0.813684	+	0.352785i
$680$	−14.1955	+	8.31037i	−0.544373	+	0.318688i
$681$	6.77481	−	7.49120i	0.259611	−	0.287063i
$682$	−10.4890	−	3.79383i	−0.401646	−	0.145273i
$683$	19.4038	−	11.2028i	0.742465	−	0.428663i	−0.0804996	−	0.996755i	$-0.525652\pi$
$683$	19.4038	−	11.2028i	0.742465	−	0.428663i	0.822965	+	0.568092i	$0.192318\pi$
$684$	−14.7634	−	30.2964i	−0.564494	−	1.15841i
$685$		−	16.9751i		−	0.648585i
$686$	22.7292	−	13.0148i	0.867804	−	0.496907i
$687$	22.0573	+	4.73884i	0.841539	+	0.180798i
$688$	−18.3388	+	15.6412i	−0.699162	+	0.596315i
$689$	23.5408	−	13.5913i	0.896833	−	0.517787i
$690$	1.74531	−	2.79199i	0.0664428	−	0.106289i
$691$	−7.24483	+	12.5484i	−0.275606	+	0.477364i	−0.970288	−	0.241953i	$-0.922212\pi$
$691$	−7.24483	+	12.5484i	−0.275606	+	0.477364i	0.694682	+	0.719317i	$0.255545\pi$
$692$	2.12108	−	12.3187i	0.0806312	−	0.468287i
$693$	10.8447	−	9.87128i	0.411957	−	0.374979i
$694$	−11.4594	−	13.6012i	−0.434995	−	0.516294i
$695$	−8.38773	+	14.5280i	−0.318165	+	0.551077i
$696$	−4.82539	−	4.31131i	−0.182906	−	0.163420i
$697$	3.14071	+	5.43987i	0.118963	+	0.206050i
$698$	−48.0337	+	8.56926i	−1.81810	+	0.324351i
$699$	−26.7037	−	5.73708i	−1.01003	−	0.216996i
$700$	7.93899	+	15.7230i	0.300066	+	0.594273i
$701$	−21.9950			−0.830738			−0.415369	−	0.909653i	$-0.636348\pi$
$701$	−21.9950			−0.830738			−0.415369	+	0.909653i	$0.636348\pi$
$702$	7.32958	−	14.8560i	0.276637	−	0.560705i
$703$	−45.9694	+	26.5404i	−1.73377	+	1.00099i
$704$	−0.178321	−	14.7794i	−0.00672074	−	0.557021i
$705$	19.6054	+	17.7305i	0.738381	+	0.667769i
$706$	9.58261	+	11.3736i	0.360646	+	0.428050i
$707$	−2.06770	−	17.9802i	−0.0777639	−	0.676215i
$708$	14.2857	−	35.5460i	0.536888	−	1.33590i
$709$	−17.2122	−	9.93745i	−0.646416	−	0.373209i	0.140666	−	0.990057i	$-0.455076\pi$
$709$	−17.2122	−	9.93745i	−0.646416	−	0.373209i	−0.787082	+	0.616849i	$0.788409\pi$
$710$	−24.0909	−	8.71355i	−0.904115	−	0.327014i
$711$	−8.17071	+	0.822679i	−0.306426	+	0.0308529i
$712$	−0.163765	−	27.1470i	−0.00613735	−	1.01738i
$713$		−	4.43866i		−	0.166229i
$714$	−16.5337	−	24.0117i	−0.618760	−	0.898617i
$715$	5.38452			0.201370
$716$	2.12702	−	2.55569i	0.0794905	−	0.0955106i
$717$	37.4951	−	12.0924i	1.40028	−	0.451598i
$718$	21.3556	+	7.72419i	0.796982	+	0.288264i
$719$	4.05138	−	7.01719i	0.151091	−	0.261697i	−0.780538	−	0.625108i	$-0.785055\pi$
$719$	4.05138	−	7.01719i	0.151091	−	0.261697i	0.931629	+	0.363411i	$0.118388\pi$
$720$	11.1991	+	10.7356i	0.417365	+	0.400093i
$721$	−7.07413	−	9.53918i	−0.263454	−	0.355258i
$722$	13.5741	−	11.4366i	0.505175	−	0.425626i
$723$	17.5241	+	15.8482i	0.651726	+	0.589402i
$724$	3.09057	+	8.38618i	0.114860	+	0.311670i
$725$	−2.19834	−	3.80763i	−0.0816442	−	0.141412i
$726$	18.5716	+	0.651790i	0.689258	+	0.0241902i
$727$		−	1.56460i		−	0.0580278i	−0.999579	−	0.0290139i	$-0.990763\pi$
$727$		−	1.56460i		−	0.0580278i	0.999579	−	0.0290139i	$-0.00923671\pi$
$728$	−16.7474	+	2.02836i	−0.620699	+	0.0751762i
$729$	−8.00598	−	25.7857i	−0.296518	−	0.955027i
$730$	2.81711	+	15.7909i	0.104266	+	0.584446i
$731$	23.4752	−	13.5534i	0.868263	−	0.501292i
$732$	−30.3031	+	4.31556i	−1.12003	+	0.159508i
$733$	−10.2679	−	5.92818i	−0.379254	−	0.218962i	0.298240	−	0.954491i	$-0.403600\pi$
$733$	−10.2679	−	5.92818i	−0.379254	−	0.218962i	−0.677493	+	0.735529i	$0.736934\pi$
$734$	21.9117	+	26.0069i	0.808775	+	0.959934i
$735$	13.4363	−	8.07175i	0.495605	−	0.297731i
$736$	5.50655	−	2.06715i	0.202974	−	0.0761962i
$737$	−9.77767	−	5.64514i	−0.360165	−	0.207941i
$738$	4.12533	−	4.25177i	0.151855	−	0.156510i
$739$	−6.94639	−	12.0315i	−0.255527	−	0.442586i	0.709511	−	0.704694i	$-0.248916\pi$
$739$	−6.94639	−	12.0315i	−0.255527	−	0.442586i	−0.965039	+	0.262108i	$0.915582\pi$
$740$	15.6305	−	18.7805i	0.574587	−	0.690386i
$741$	21.4429	+	4.60684i	0.787724	+	0.169236i
$742$	−43.2196	+	12.9462i	−1.58664	+	0.475271i
$743$	−25.3287			−0.929221			−0.464611	−	0.885515i	$-0.653806\pi$
$743$	−25.3287			−0.929221			−0.464611	+	0.885515i	$0.653806\pi$
$744$	20.4729	+	4.26942i	0.750575	+	0.156524i
$745$	4.42182	+	7.65881i	0.162003	+	0.280597i
$746$	−6.94954	+	19.2138i	−0.254441	+	0.703468i
$747$	−8.31435	−	11.5496i	−0.304206	−	0.422577i
$748$	−2.82061	+	16.3814i	−0.103132	+	0.598965i
$749$	11.4262	+	15.4078i	0.417506	+	0.562990i
$750$	12.3780	+	23.2894i	0.451980	+	0.850409i
$751$	10.4902	+	6.05653i	0.382793	+	0.221006i	0.679033	−	0.734108i	$-0.262399\pi$
$751$	10.4902	+	6.05653i	0.382793	+	0.221006i	−0.296240	+	0.955114i	$0.595733\pi$
$752$	8.57341	+	46.4351i	0.312640	+	1.69331i
$753$	2.83407	+	8.78770i	0.103279	+	0.320241i
$754$	4.14554	−	0.739569i	0.150972	−	0.0269335i
$755$		−	4.72090i		−	0.171811i
$756$	−17.5208	+	21.1901i	−0.637224	+	0.770678i
$757$			21.6528i			0.786983i	0.919328	+	0.393491i	$0.128733\pi$
$757$			21.6528i			0.786983i	−0.919328	+	0.393491i	$0.871267\pi$
$758$	−7.40279	−	41.4952i	−0.268881	−	1.50717i
$759$	−1.02128	−	3.16670i	−0.0370700	−	0.114944i
$760$	−10.1621	+	17.8491i	−0.368618	+	0.647455i
$761$	−33.4532	−	19.3142i	−1.21268	−	0.700141i	−0.249337	−	0.968417i	$-0.580213\pi$
$761$	−33.4532	−	19.3142i	−1.21268	−	0.700141i	−0.963342	+	0.268276i	$0.913546\pi$
$762$	47.0927	−	25.0291i	1.70599	−	0.906707i
$763$	32.3778	−	3.72341i	1.17216	−	0.134797i
$764$	7.65428	−	44.4542i	0.276922	−	1.60830i
$765$	−10.1933	−	14.1596i	−0.368539	−	0.511941i
$766$	14.9695	+	5.41438i	0.540869	+	0.195629i
$767$	12.4652	+	21.5903i	0.450091	+	0.779580i
$768$	4.23797	+	27.3869i	0.152925	+	0.988238i
$769$	32.8604			1.18498			0.592489	−	0.805579i	$-0.298145\pi$
$769$	32.8604			1.18498			0.592489	+	0.805579i	$0.298145\pi$
$770$	−8.69650	−	2.05972i	−0.313400	−	0.0742271i
$771$	14.2093	+	3.05276i	0.511736	+	0.109943i
$772$	8.92518	+	7.42816i	0.321224	+	0.267345i
$773$	14.2511	+	24.6836i	0.512576	+	0.887808i	0.999894	+	0.0145830i<

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)

\(f(q)\)	\(=\)	\(q+(0.248376 + 1.39223i) q^{2} +(-1.64844 + 0.531631i) q^{3} +(-1.87662 + 0.691593i) q^{4} +(-0.646402 + 1.11960i) q^{5} +(-1.14959 - 2.16297i) q^{6} +(-2.42742 - 1.05244i) q^{7} +(-1.42896 - 2.44091i) q^{8} +(2.43474 - 1.75273i) q^{9} +O(q^{10})\)	\(q+(0.248376 + 1.39223i) q^{2} +(-1.64844 + 0.531631i) q^{3} +(-1.87662 + 0.691593i) q^{4} +(-0.646402 + 1.11960i) q^{5} +(-1.14959 - 2.16297i) q^{6} +(-2.42742 - 1.05244i) q^{7} +(-1.42896 - 2.44091i) q^{8} +(2.43474 - 1.75273i) q^{9} +(-1.71929 - 0.621859i) q^{10} +(-1.60004 + 0.923782i) q^{11} +(2.72583 - 2.13772i) q^{12} +2.25432i q^{13} +(0.862334 - 3.64093i) q^{14} +(0.470342 - 2.18925i) q^{15} +(3.04340 - 2.59571i) q^{16} +(-3.89580 + 2.24924i) q^{17} +(3.04493 + 2.95438i) q^{18} +(-2.80851 + 4.86448i) q^{19} +(0.438742 - 2.54811i) q^{20} +(4.56098 + 0.444404i) q^{21} +(-1.68353 - 1.99818i) q^{22} +(0.519880 - 0.900459i) q^{23} +(3.65323 + 3.26403i) q^{24} +(1.66433 + 2.88270i) q^{25} +(-3.13853 + 0.559917i) q^{26} +(-3.08172 + 4.18366i) q^{27} +(5.28320 + 0.296251i) q^{28} -1.32085 q^{29} +(3.16476 + 0.111070i) q^{30} +(3.69700 - 2.13446i) q^{31} +(4.36974 + 3.59240i) q^{32} +(2.14646 - 2.37343i) q^{33} +(-4.09909 - 4.86521i) q^{34} +(2.74740 - 2.03744i) q^{35} +(-3.35690 + 4.97305i) q^{36} +(8.18394 + 4.72500i) q^{37} +(-7.47005 - 2.70188i) q^{38} +(-1.19846 - 3.71611i) q^{39} +(3.65653 - 0.0220581i) q^{40} -1.39634i q^{41} +(0.514122 + 6.46032i) q^{42} -6.02578 q^{43} +(2.36378 - 2.84016i) q^{44} +(0.388538 + 3.85890i) q^{45} +(1.38277 + 0.500142i) q^{46} +(-5.90249 + 10.2234i) q^{47} +(-3.63691 + 5.89685i) q^{48} +(4.78472 + 5.10944i) q^{49} +(-3.60001 + 3.03313i) q^{50} +(5.22625 - 5.77888i) q^{51} +(-1.55907 - 4.23049i) q^{52} +(-6.02901 - 10.4425i) q^{53} +(-6.59005 - 3.25135i) q^{54} -2.38854i q^{55} +(0.899769 + 7.42903i) q^{56} +(2.04356 - 9.51192i) q^{57} +(-0.328068 - 1.83894i) q^{58} +(9.57732 - 5.52947i) q^{59} +(0.631413 + 4.43367i) q^{60} +(-7.65220 - 4.41800i) q^{61} +(3.88991 + 4.61693i) q^{62} +(-7.75477 + 1.69218i) q^{63} +(-3.91612 + 6.97596i) q^{64} +(-2.52393 - 1.45719i) q^{65} +(3.83750 + 2.39887i) q^{66} +(3.05545 + 5.29219i) q^{67} +(5.75538 - 6.91528i) q^{68} +(-0.378281 + 1.76074i) q^{69} +(3.51897 + 3.31897i) q^{70} +14.0121 q^{71} +(-7.75741 - 3.43840i) q^{72} +(-4.38664 - 7.59788i) q^{73} +(-4.54561 + 12.5675i) q^{74} +(-4.27609 - 3.86717i) q^{75} +(1.90626 - 11.0711i) q^{76} +(4.85619 - 0.558456i) q^{77} +(4.87602 - 2.59153i) q^{78} +(-2.37061 - 1.36867i) q^{79} +(0.938904 + 5.08526i) q^{80} +(2.85588 - 8.53487i) q^{81} +(1.94403 - 0.346817i) q^{82} -4.74366i q^{83} +(-8.86656 + 2.32036i) q^{84} -5.81566i q^{85} +(-1.49666 - 8.38928i) q^{86} +(2.17736 - 0.702207i) q^{87} +(4.54127 + 2.58550i) q^{88} +(8.31219 + 4.79904i) q^{89} +(-5.27598 + 1.49939i) q^{90} +(2.37254 - 5.47217i) q^{91} +(-0.352866 + 2.04936i) q^{92} +(-4.95955 + 5.48398i) q^{93} +(-15.6994 - 5.67839i) q^{94} +(-3.63085 - 6.28882i) q^{95} +(-9.11311 - 3.59879i) q^{96} -8.73466 q^{97} +(-5.92512 + 7.93051i) q^{98} +(-2.27653 + 5.05360i) 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

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