LMFDB - Embedded newform 168.2.v.a.11.6

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			11.6
Character	$\chi$	$=$	168.11
Dual form			168.2.v.a.107.6

$q$-expansion

$f(q)$	$=$	$q+(-1.08135 + 0.911422i) q^{2} +(-0.316681 + 1.70285i) q^{3} +(0.338619 - 1.97113i) q^{4} +(1.86088 + 3.22314i) q^{5} +(-1.20958 - 2.13001i) q^{6} +(2.46429 - 0.962962i) q^{7} +(1.43036 + 2.44009i) q^{8} +(-2.79943 - 1.07852i) q^{9} +O(q^{10})$	\(q+(-1.08135 + 0.911422i) q^{2} +(-0.316681 + 1.70285i) q^{3} +(0.338619 - 1.97113i) q^{4} +(1.86088 + 3.22314i) q^{5} +(-1.20958 - 2.13001i) q^{6} +(2.46429 - 0.962962i) q^{7} +(1.43036 + 2.44009i) q^{8} +(-2.79943 - 1.07852i) q^{9} +(-4.94989 - 1.78928i) q^{10} +(-2.26958 - 1.31034i) q^{11} +(3.24931 + 1.20084i) q^{12} +3.57182i q^{13} +(-1.78708 + 3.28730i) q^{14} +(-6.07784 + 2.14810i) q^{15} +(-3.77067 - 1.33492i) q^{16} +(0.186192 + 0.107498i) q^{17} +(4.01014 - 1.38520i) q^{18} +(-1.14103 - 1.97631i) q^{19} +(6.98334 - 2.57661i) q^{20} +(0.859391 + 4.50127i) q^{21} +(3.64848 - 0.651612i) q^{22} +(-2.33586 - 4.04583i) q^{23} +(-4.60809 + 1.66297i) q^{24} +(-4.42574 + 7.66560i) q^{25} +(-3.25544 - 3.86238i) q^{26} +(2.72309 - 4.42547i) q^{27} +(-1.06366 - 5.18349i) q^{28} +2.57415 q^{29} +(4.61442 - 7.86231i) q^{30} +(4.26196 + 2.46064i) q^{31} +(5.29408 - 1.99316i) q^{32} +(2.95006 - 3.44980i) q^{33} +(-0.299314 + 0.0534570i) q^{34} +(7.68949 + 6.15077i) q^{35} +(-3.07384 + 5.15281i) q^{36} +(7.31104 - 4.22103i) q^{37} +(3.03510 + 1.09712i) q^{38} +(-6.08229 - 1.13113i) q^{39} +(-5.20302 + 9.15098i) q^{40} +0.909442i q^{41} +(-5.03186 - 4.08416i) q^{42} +3.73541 q^{43} +(-3.35137 + 4.02992i) q^{44} +(-1.73317 - 11.0299i) q^{45} +(6.21334 + 2.24599i) q^{46} +(-0.586728 - 1.01624i) q^{47} +(3.46728 - 5.99816i) q^{48} +(5.14541 - 4.74603i) q^{49} +(-2.20085 - 12.3229i) q^{50} +(-0.242017 + 0.283015i) q^{51} +(7.04051 + 1.20949i) q^{52} +(-1.06171 + 1.83894i) q^{53} +(1.08886 + 7.26735i) q^{54} -9.75355i q^{55} +(5.87454 + 4.63570i) q^{56} +(3.72672 - 1.31714i) q^{57} +(-2.78355 + 2.34614i) q^{58} +(-6.79199 - 3.92136i) q^{59} +(2.17610 + 12.7076i) q^{60} +(-0.301301 + 0.173956i) q^{61} +(-6.85134 + 1.22364i) q^{62} +(-7.93716 + 0.0379510i) q^{63} +(-3.90812 + 6.98044i) q^{64} +(-11.5125 + 6.64673i) q^{65} +(-0.0458036 + 6.41918i) q^{66} +(-4.98736 + 8.63836i) q^{67} +(0.274940 - 0.330607i) q^{68} +(7.62919 - 2.69640i) q^{69} +(-13.9210 + 0.357259i) q^{70} +10.0808 q^{71} +(-1.37250 - 8.37354i) q^{72} +(4.45173 - 7.71062i) q^{73} +(-4.05862 + 11.2278i) q^{74} +(-11.6519 - 9.96394i) q^{75} +(-4.28194 + 1.57989i) q^{76} +(-6.85470 - 1.04354i) q^{77} +(7.60800 - 4.32040i) q^{78} +(-9.70950 + 5.60578i) q^{79} +(-2.71413 - 14.6375i) q^{80} +(6.67358 + 6.03849i) q^{81} +(-0.828886 - 0.983422i) q^{82} -1.73937i q^{83} +(9.16358 - 0.169751i) q^{84} +0.800163i q^{85} +(-4.03927 + 3.40453i) q^{86} +(-0.815185 + 4.38341i) q^{87} +(-0.0489643 - 7.41226i) q^{88} +(15.4694 - 8.93127i) q^{89} +(11.9271 + 10.3475i) q^{90} +(3.43953 + 8.80199i) q^{91} +(-8.76581 + 3.23428i) q^{92} +(-5.53980 + 6.47826i) q^{93} +(1.56068 + 0.564153i) q^{94} +(4.24662 - 7.35536i) q^{95} +(1.71753 + 9.64625i) q^{96} -8.88553 q^{97} +(-1.23834 + 9.82174i) q^{98} +(4.94029 + 6.11600i) 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 $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−1.08135	+	0.911422i	−0.764627	+	0.644473i
$2$	−1.08135	+	0.911422i	−0.764627	+	0.644473i
$3$	−0.316681	+	1.70285i	−0.182836	+	0.983143i
$3$	−0.316681	+	1.70285i	−0.182836	+	0.983143i
$4$	0.338619	−	1.97113i	0.169310	−	0.985563i
$5$	1.86088	+	3.22314i	0.832210	+	1.44143i	0.896282	+	0.443485i	$0.146258\pi$
$5$	1.86088	+	3.22314i	0.832210	+	1.44143i	−0.0640716	+	0.997945i	$0.520409\pi$
$6$	−1.20958	−	2.13001i	−0.493808	−	0.869571i
$7$	2.46429	−	0.962962i	0.931412	−	0.363965i
$7$	2.46429	−	0.962962i	0.931412	−	0.363965i
$8$	1.43036	+	2.44009i	0.505710	+	0.862704i
$9$	−2.79943	−	1.07852i	−0.933142	−	0.359508i
$10$	−4.94989	−	1.78928i	−1.56529	−	0.565820i
$11$	−2.26958	−	1.31034i	−0.684304	−	0.395083i	0.117171	−	0.993112i	$-0.462618\pi$
$11$	−2.26958	−	1.31034i	−0.684304	−	0.395083i	−0.801475	+	0.598029i	$0.795951\pi$
$12$	3.24931	+	1.20084i	0.937994	+	0.346652i
$13$			3.57182i			0.990645i	0.868709	+	0.495323i	$0.164950\pi$
$13$			3.57182i			0.990645i	−0.868709	+	0.495323i	$0.835050\pi$
$14$	−1.78708	+	3.28730i	−0.477618	+	0.878568i
$15$	−6.07784	+	2.14810i	−1.56929	+	0.554637i
$16$	−3.77067	−	1.33492i	−0.942669	−	0.333730i
$17$	0.186192	+	0.107498i	0.0451582	+	0.0260721i	0.522409	−	0.852695i	$-0.325033\pi$
$17$	0.186192	+	0.107498i	0.0451582	+	0.0260721i	−0.477251	+	0.878767i	$0.658367\pi$
$18$	4.01014	−	1.38520i	0.945199	−	0.326495i
$19$	−1.14103	−	1.97631i	−0.261769	−	0.453398i	0.704943	−	0.709264i	$-0.250973\pi$
$19$	−1.14103	−	1.97631i	−0.261769	−	0.453398i	−0.966712	+	0.255866i	$0.917639\pi$
$20$	6.98334	−	2.57661i	1.56152	−	0.576148i
$21$	0.859391	+	4.50127i	0.187535	+	0.982258i
$22$	3.64848	−	0.651612i	0.777858	−	0.138924i
$23$	−2.33586	−	4.04583i	−0.487061	−	0.843615i	0.512828	−	0.858491i	$-0.328598\pi$
$23$	−2.33586	−	4.04583i	−0.487061	−	0.843615i	−0.999889	+	0.0148767i	$0.995264\pi$
$24$	−4.60809	+	1.66297i	−0.940623	+	0.339452i
$25$	−4.42574	+	7.66560i	−0.885148	+	1.53312i
$26$	−3.25544	−	3.86238i	−0.638444	−	0.757474i
$27$	2.72309	−	4.42547i	0.524060	−	0.851682i
$28$	−1.06366	−	5.18349i	−0.201014	−	0.979588i
$29$	2.57415			0.478008			0.239004	−	0.971019i	$-0.423179\pi$
$29$	2.57415			0.478008			0.239004	+	0.971019i	$0.423179\pi$
$30$	4.61442	−	7.86231i	0.842474	−	1.43546i
$31$	4.26196	+	2.46064i	0.765471	+	0.441945i	0.831257	−	0.555889i	$-0.187622\pi$
$31$	4.26196	+	2.46064i	0.765471	+	0.441945i	−0.0657857	+	0.997834i	$0.520955\pi$
$32$	5.29408	−	1.99316i	0.935870	−	0.352345i
$33$	2.95006	−	3.44980i	0.513539	−	0.600534i
$34$	−0.299314	+	0.0534570i	−0.0513319	+	0.00916779i
$35$	7.68949	+	6.15077i	1.29976	+	1.03967i
$36$	−3.07384	+	5.15281i	−0.512307	+	0.858802i
$37$	7.31104	−	4.22103i	1.20193	−	0.693933i	0.240944	−	0.970539i	$-0.422543\pi$
$37$	7.31104	−	4.22103i	1.20193	−	0.693933i	0.960983	+	0.276606i	$0.0892098\pi$
$38$	3.03510	+	1.09712i	0.492358	+	0.177977i
$39$	−6.08229	−	1.13113i	−0.973946	−	0.181125i
$40$	−5.20302	+	9.15098i	−0.822670	+	1.44690i
$41$			0.909442i			0.142031i	0.997475	+	0.0710155i	$0.0226240\pi$
$41$			0.909442i			0.142031i	−0.997475	+	0.0710155i	$0.977376\pi$
$42$	−5.03186	−	4.08416i	−0.776433	−	0.630200i
$43$	3.73541			0.569644			0.284822	−	0.958580i	$-0.408065\pi$
$43$	3.73541			0.569644			0.284822	+	0.958580i	$0.408065\pi$
$44$	−3.35137	+	4.02992i	−0.505239	+	0.607533i
$45$	−1.73317	−	11.0299i	−0.258365	−	1.64425i
$46$	6.21334	+	2.24599i	0.916107	+	0.331153i
$47$	−0.586728	−	1.01624i	−0.0855831	−	0.148234i	0.820056	−	0.572283i	$-0.193942\pi$
$47$	−0.586728	−	1.01624i	−0.0855831	−	0.148234i	−0.905640	+	0.424048i	$0.860609\pi$
$48$	3.46728	−	5.99816i	0.500459	−	0.865761i
$49$	5.14541	−	4.74603i	0.735058	−	0.678004i
$50$	−2.20085	−	12.3229i	−0.311247	−	1.74272i
$51$	−0.242017	+	0.283015i	−0.0338891	+	0.0396301i
$52$	7.04051	+	1.20949i	0.976343	+	0.167726i
$53$	−1.06171	+	1.83894i	−0.145837	+	0.252598i	−0.929685	−	0.368355i	$-0.879921\pi$
$53$	−1.06171	+	1.83894i	−0.145837	+	0.252598i	0.783848	+	0.620953i	$0.213254\pi$
$54$	1.08886	+	7.26735i	0.148176	+	0.988961i
$55$		−	9.75355i		−	1.31517i
$56$	5.87454	+	4.63570i	0.785019	+	0.619472i
$57$	3.72672	−	1.31714i	0.493616	−	0.174459i
$58$	−2.78355	+	2.34614i	−0.365498	+	0.308063i
$59$	−6.79199	−	3.92136i	−0.884242	−	0.510517i	−0.0121872	−	0.999926i	$-0.503879\pi$
$59$	−6.79199	−	3.92136i	−0.884242	−	0.510517i	−0.872055	+	0.489408i	$0.837213\pi$
$60$	2.17610	+	12.7076i	0.280934	+	1.64054i
$61$	−0.301301	+	0.173956i	−0.0385776	+	0.0222728i	−0.519165	−	0.854674i	$-0.673757\pi$
$61$	−0.301301	+	0.173956i	−0.0385776	+	0.0222728i	0.480587	+	0.876947i	$0.340424\pi$
$62$	−6.85134	+	1.22364i	−0.870121	+	0.155402i
$63$	−7.93716	+	0.0379510i	−0.999989	+	0.00478137i
$64$	−3.90812	+	6.98044i	−0.488515	+	0.872555i
$65$	−11.5125	+	6.64673i	−1.42795	+	0.824425i
$66$	−0.0458036	+	6.41918i	−0.00563803	+	0.790146i
$67$	−4.98736	+	8.63836i	−0.609303	+	1.05534i	0.382053	+	0.924140i	$0.375217\pi$
$67$	−4.98736	+	8.63836i	−0.609303	+	1.05534i	−0.991356	+	0.131203i	$0.958116\pi$
$68$	0.274940	−	0.330607i	0.0333414	−	0.0400920i
$69$	7.62919	−	2.69640i	0.918446	−	0.324608i
$70$	−13.9210	+	0.357259i	−1.66387	+	0.0427006i
$71$	10.0808			1.19637			0.598183	−	0.801359i	$-0.295889\pi$
$71$	10.0808			1.19637			0.598183	+	0.801359i	$0.295889\pi$
$72$	−1.37250	−	8.37354i	−0.161750	−	0.986832i
$73$	4.45173	−	7.71062i	0.521036	−	0.902460i	−0.478665	−	0.877998i	$-0.658879\pi$
$73$	4.45173	−	7.71062i	0.521036	−	0.902460i	0.999701	−	0.0244626i	$-0.00778746\pi$
$74$	−4.05862	+	11.2278i	−0.471805	+	1.30521i
$75$	−11.6519	−	9.96394i	−1.34544	−	1.15054i
$76$	−4.28194	+	1.57989i	−0.491172	+	0.181226i
$77$	−6.85470	−	1.04354i	−0.781166	−	0.118922i
$78$	7.60800	−	4.32040i	0.861436	−	0.489188i
$79$	−9.70950	+	5.60578i	−1.09240	+	0.630700i	−0.934216	−	0.356709i	$-0.883899\pi$
$79$	−9.70950	+	5.60578i	−1.09240	+	0.630700i	−0.158189	+	0.987409i	$0.550566\pi$
$80$	−2.71413	−	14.6375i	−0.303449	−	1.63652i
$81$	6.67358	+	6.03849i	0.741508	+	0.670944i
$82$	−0.828886	−	0.983422i	−0.0915351	−	0.108601i
$83$		−	1.73937i		−	0.190921i	−0.995433	−	0.0954603i	$-0.969568\pi$
$83$		−	1.73937i		−	0.190921i	0.995433	−	0.0954603i	$-0.0304323\pi$
$84$	9.16358	−	0.169751i	0.999828	−	0.0185214i
$85$			0.800163i			0.0867898i
$86$	−4.03927	+	3.40453i	−0.435566	+	0.367120i
$87$	−0.815185	+	4.38341i	−0.0873970	+	0.469950i
$88$	−0.0489643	−	7.41226i	−0.00521961	−	0.790149i
$89$	15.4694	−	8.93127i	1.63975	−	0.946712i	0.658837	−	0.752286i	$-0.271049\pi$
$89$	15.4694	−	8.93127i	1.63975	−	0.946712i	0.980917	−	0.194426i	$-0.0622845\pi$
$90$	11.9271	+	10.3475i	1.25722	+	1.09073i
$91$	3.43953	+	8.80199i	0.360560	+	0.922699i
$92$	−8.76581	+	3.23428i	−0.913899	+	0.337197i
$93$	−5.53980	+	6.47826i	−0.574451	+	0.671764i
$94$	1.56068	+	0.564153i	0.160972	+	0.0581880i
$95$	4.24662	−	7.35536i	0.435694	−	0.754644i
$96$	1.71753	+	9.64625i	0.175295	+	0.984516i
$97$	−8.88553			−0.902189			−0.451094	−	0.892476i	$-0.648966\pi$
$97$	−8.88553			−0.902189			−0.451094	+	0.892476i	$0.648966\pi$
$98$	−1.23834	+	9.82174i	−0.125091	+	0.992145i
$99$	4.94029	+	6.11600i	0.496518	+	0.614681i
$100$	13.6112	+	11.3194i	1.36112	+	1.13194i
$101$	−7.38721	+	12.7950i	−0.735055	+	1.27315i	0.219644	+	0.975580i	$0.429510\pi$
$101$	−7.38721	+	12.7950i	−0.735055	+	1.27315i	−0.954699	+	0.297573i	$0.903823\pi$
$102$	0.00375764	−	0.526617i	0.000372062	−	0.0521429i
$103$	6.50151	−	3.75365i	0.640613	−	0.369858i	−0.144238	−	0.989543i	$-0.546073\pi$
$103$	6.50151	−	3.75365i	0.640613	−	0.369858i	0.784851	+	0.619685i	$0.212740\pi$
$104$	−8.71558	+	5.10900i	−0.854633	+	0.500979i
$105$	−12.9090	+	11.1463i	−1.25979	+	1.08776i
$106$	−0.527972	−	2.95620i	−0.0512812	−	0.287131i
$107$	10.9396	−	6.31597i	1.05757	−	0.610588i	0.132810	−	0.991141i	$-0.457600\pi$
$107$	10.9396	−	6.31597i	1.05757	−	0.610588i	0.924759	+	0.380554i	$0.124267\pi$
$108$	−7.80106	−	6.86611i	−0.750658	−	0.660691i
$109$	−11.2275	−	6.48219i	−1.07540	−	0.620881i	−0.145747	−	0.989322i	$-0.546558\pi$
$109$	−11.2275	−	6.48219i	−1.07540	−	0.620881i	−0.929651	+	0.368441i	$0.879892\pi$
$110$	8.88961	+	10.5470i	0.847591	+	1.00561i
$111$	4.87253	+	13.7864i	0.462480	+	1.30854i
$112$	−10.5775	+	0.341386i	−0.999480	+	0.0322579i
$113$		−	7.10498i		−	0.668380i	−0.942506	−	0.334190i	$-0.891537\pi$
$113$		−	7.10498i		−	0.668380i	0.942506	−	0.334190i	$-0.108463\pi$
$114$	−2.82940	+	4.82090i	−0.264998	+	0.451518i
$115$	8.69351	−	15.0576i	0.810674	−	1.40413i
$116$	0.871657	−	5.07398i	0.0809313	−	0.471107i
$117$	3.85229	−	9.99905i	0.356145	−	0.924413i
$118$	10.9185	−	1.95003i	1.00513	−	0.179514i
$119$	0.562347	+	0.0856100i	0.0515502	+	0.00784786i
$120$	−13.9351	−	11.7579i	−1.27209	−	1.07335i
$121$	−2.06600	−	3.57842i	−0.187819	−	0.325311i
$122$	0.167263	−	0.462719i	0.0151433	−	0.0418926i
$123$	−1.54865	−	0.288003i	−0.139637	−	0.0259684i
$124$	6.29342	−	7.56764i	0.565166	−	0.679594i
$125$	−14.3343			−1.28210
$126$	8.54823	−	7.27514i	0.761537	−	0.648121i
$127$			2.53093i			0.224584i	0.993675	+	0.112292i	$0.0358192\pi$
$127$			2.53093i			0.224584i	−0.993675	+	0.112292i	$0.964181\pi$
$128$	−2.13610	−	11.1102i	−0.188806	−	0.982014i
$129$	−1.18293	+	6.36086i	−0.104151	+	0.560042i
$130$	6.39099	−	17.6801i	0.560527	−	1.55065i
$131$	−5.04824	+	2.91460i	−0.441067	+	0.254650i	−0.704050	−	0.710150i	$-0.748627\pi$
$131$	−5.04824	+	2.91460i	−0.441067	+	0.254650i	0.262983	+	0.964800i	$0.415294\pi$
$132$	−5.80105	−	6.98310i	−0.504917	−	0.607801i
$133$	−4.71493	−	3.77144i	−0.408836	−	0.327025i
$134$	−2.48013	−	13.8866i	−0.214251	−	1.19962i
$135$	19.3312	+	0.541642i	1.66377	+	0.0466171i
$136$	0.00401694	+	0.608087i	0.000344449	+	0.0521430i
$137$	−8.15158	−	4.70632i	−0.696437	−	0.402088i	0.109582	−	0.993978i	$-0.465049\pi$
$137$	−8.15158	−	4.70632i	−0.696437	−	0.402088i	−0.806019	+	0.591890i	$0.798382\pi$
$138$	−5.79224	+	9.86915i	−0.493068	+	0.840118i
$139$	−7.53929			−0.639474			−0.319737	−	0.947506i	$-0.603595\pi$
$139$	−7.53929			−0.639474			−0.319737	+	0.947506i	$0.603595\pi$
$140$	14.7278	−	13.0742i	1.24472	−	1.10497i
$141$	1.91632	−	0.677288i	0.161383	−	0.0570379i
$142$	−10.9008	+	9.18783i	−0.914774	+	0.771026i
$143$	4.68031	−	8.10654i	0.391387	−	0.677903i
$144$	9.11598	+	7.80378i	0.759665	+	0.650315i
$145$	4.79018	+	8.29684i	0.397803	+	0.689015i
$146$	2.21377	+	12.3953i	0.183213	+	1.02584i
$147$	6.45234	+	10.2649i	0.532180	+	0.846631i
$148$	−5.84452	−	15.8403i	−0.480417	−	1.30206i
$149$	−7.38721	−	12.7950i	−0.605184	−	1.04821i	−0.992022	−	0.126062i	$-0.959766\pi$
$149$	−7.38721	−	12.7950i	−0.605184	−	1.04821i	0.386838	−	0.922148i	$-0.373567\pi$
$150$	21.6810	+	0.154704i	1.77025	+	0.0126315i
$151$	3.18729	+	1.84018i	0.259378	+	0.149752i	0.624051	−	0.781384i	$-0.285486\pi$
$151$	3.18729	+	1.84018i	0.259378	+	0.149752i	−0.364673	+	0.931136i	$0.618819\pi$
$152$	3.19031	−	5.61106i	0.258769	−	0.455117i
$153$	−0.405292	−	0.501745i	−0.0327659	−	0.0405637i
$154$	8.36341	−	5.11910i	0.673943	−	0.412509i
$155$			18.3158i			1.47116i
$156$	−4.28918	+	11.6059i	−0.343409	+	0.929219i
$157$	18.5989	+	10.7381i	1.48436	+	0.856993i	0.999842	−	0.0177905i	$-0.00566318\pi$
$157$	18.5989	+	10.7381i	1.48436	+	0.856993i	0.484514	+	0.874784i	$0.338997\pi$
$158$	5.39010	−	14.9113i	0.428813	−	1.18628i
$159$	−2.79522	−	2.39030i	−0.221676	−	0.189563i
$160$	16.2759	+	13.3545i	1.28672	+	1.05577i
$161$	−9.65222	−	7.72074i	−0.760701	−	0.608480i
$162$	−12.7201	−	0.447256i	−0.999382	−	0.0351397i
$163$	−0.756294	−	1.30994i	−0.0592375	−	0.102602i	0.834886	−	0.550423i	$-0.185534\pi$
$163$	−0.756294	−	1.30994i	−0.0592375	−	0.102602i	−0.894123	+	0.447821i	$0.852200\pi$
$164$	1.79263	+	0.307955i	0.139981	+	0.0240472i
$165$	16.6089	+	3.08877i	1.29300	+	0.240460i
$166$	1.58530	+	1.88086i	0.123043	+	0.145983i
$167$	7.21687			0.558459			0.279229	−	0.960224i	$-0.409921\pi$
$167$	7.21687			0.558459			0.279229	+	0.960224i	$0.409921\pi$
$168$	−9.75429	+	8.53545i	−0.752560	+	0.658524i
$169$	0.242090			0.0186223
$170$	−0.729286	−	0.865253i	−0.0559337	−	0.0663619i
$171$	1.06272	+	6.76317i	0.0812680	+	0.517193i
$172$	1.26488	−	7.36296i	0.0964462	−	0.561420i
$173$	1.33696	+	2.31567i	0.101647	+	0.176057i	0.912363	−	0.409382i	$-0.134256\pi$
$173$	1.33696	+	2.31567i	0.101647	+	0.176057i	−0.810716	+	0.585439i	$0.800922\pi$
$174$	−3.11364	−	5.48296i	−0.236044	−	0.415662i
$175$	−3.52460	+	23.1521i	−0.266435	+	1.75013i
$176$	6.80864	+	7.97059i	0.513221	+	0.600806i
$177$	8.82840	−	10.3240i	0.663583	−	0.775996i
$178$	−8.58763	+	23.7569i	−0.643670	+	1.78066i
$179$	−7.29346	−	4.21088i	−0.545139	−	0.314736i	0.202020	−	0.979381i	$-0.435249\pi$
$179$	−7.29346	−	4.21088i	−0.545139	−	0.314736i	−0.747159	+	0.664645i	$0.768583\pi$
$180$	−22.3283	−	0.318660i	−1.66425	−	0.0237515i
$181$		−	6.12284i		−	0.455107i	−0.973766	−	0.227553i	$-0.926927\pi$
$181$		−	6.12284i		−	0.455107i	0.973766	−	0.227553i	$-0.0730726\pi$
$182$	−11.7416	−	6.38314i	−0.870349	−	0.473150i
$183$	−0.200806	−	0.568160i	−0.0148440	−	0.0419996i
$184$	6.53108	−	11.4867i	0.481478	−	0.846814i
$185$	27.2099	+	15.7096i	2.00051	+	1.15500i
$186$	0.0860129	−	12.0543i	0.00630677	−	0.883867i
$187$	−0.281718	−	0.487951i	−0.0206013	−	0.0356825i
$188$	−2.20182	+	0.812396i	−0.160584	+	0.0592500i
$189$	2.44892	−	13.5279i	0.178133	−	0.984006i
$190$	2.11177	+	11.8242i	0.153204	+	0.857815i
$191$	7.56478	+	13.1026i	0.547368	+	0.948069i	0.998454	+	0.0555887i	$0.0177036\pi$
$191$	7.56478	+	13.1026i	0.547368	+	0.948069i	−0.451086	+	0.892481i	$0.648963\pi$
$192$	−10.6491	−	8.86554i	−0.768529	−	0.639815i
$193$	−1.52962	+	2.64937i	−0.110104	+	0.190706i	−0.915812	−	0.401607i	$-0.868452\pi$
$193$	−1.52962	+	2.64937i	−0.110104	+	0.190706i	0.805708	+	0.592313i	$0.201785\pi$
$194$	9.60833	−	8.09847i	0.689838	−	0.581436i
$195$	−7.67263	−	21.7089i	−0.549448	−	1.55461i
$196$	−7.61268	−	11.7493i	−0.543763	−	0.839239i
$197$	−14.5736			−1.03833			−0.519163	−	0.854675i	$-0.673756\pi$
$197$	−14.5736			−1.03833			−0.519163	+	0.854675i	$0.673756\pi$
$198$	−10.9164	−	2.11083i	−0.775796	−	0.150010i
$199$	−15.0386	−	8.68255i	−1.06606	−	0.615490i	−0.138957	−	0.990298i	$-0.544375\pi$
$199$	−15.0386	−	8.68255i	−1.06606	−	0.615490i	−0.927102	+	0.374809i	$0.877708\pi$
$200$	−25.0352	+	0.165379i	−1.77026	+	0.0116941i
$201$	−13.1305	−	11.2283i	−0.926151	−	0.791987i
$202$	−3.67354	−	20.5687i	−0.258469	−	1.44721i
$203$	6.34345	−	2.47881i	0.445223	−	0.173978i
$204$	0.475907	+	0.572880i	0.0333202	+	0.0401096i
$205$	−2.93126	+	1.69236i	−0.204728	+	0.118200i
$206$	−3.60922	+	9.98462i	−0.251467	+	0.695661i
$207$	2.17555	+	13.8453i	0.151211	+	0.962314i
$208$	4.76810	−	13.4682i	0.330608	−	0.933850i
$209$			5.98054i			0.413683i
$210$	3.80014	−	23.8185i	0.262235	−	1.64363i
$211$	−21.2686			−1.46419			−0.732097	−	0.681201i	$-0.761458\pi$
$211$	−21.2686			−1.46419			−0.732097	+	0.681201i	$0.761458\pi$
$212$	3.26527	+	2.71547i	0.224259	+	0.186499i
$213$	−3.19239	+	17.1661i	−0.218739	+	1.17620i
$214$	−6.07296	+	16.8003i	−0.415139	+	1.14845i
$215$	6.95114	+	12.0397i	0.474064	+	0.821103i
$216$	14.6936	+	0.314577i	0.999771	+	0.0214043i
$217$	12.8722	+	1.95963i	0.873822	+	0.133028i
$218$	18.0488	−	3.22349i	1.22242	−	0.218322i
$219$	11.7203	+	10.0225i	0.791984	+	0.677255i
$220$	−19.2255	−	3.30274i	−1.29618	−	0.222671i
$221$	−0.383964	+	0.665045i	−0.0258282	+	0.0447357i
$222$	−17.8341	−	10.4669i	−1.19695	−	0.702491i
$223$			6.68788i			0.447854i	0.974606	+	0.223927i	$0.0718877\pi$
$223$			6.68788i			0.447854i	−0.974606	+	0.223927i	$0.928112\pi$
$224$	11.1268	−	10.0097i	0.743440	−	0.668803i
$225$	20.6571	−	16.6860i	1.37714	−	1.11240i
$226$	6.47563	+	7.68294i	0.430753	+	0.511062i
$227$	−20.7637	−	11.9879i	−1.37813	−	0.795666i	−0.386199	−	0.922415i	$-0.626212\pi$
$227$	−20.7637	−	11.9879i	−1.37813	−	0.795666i	−0.991935	+	0.126749i	$0.959546\pi$
$228$	−1.33431	−	7.79184i	−0.0883668	−	0.516027i
$229$	−14.3077	+	8.26054i	−0.945478	+	0.545872i	−0.891673	−	0.452680i	$-0.850468\pi$
$229$	−14.3077	+	8.26054i	−0.945478	+	0.545872i	−0.0538045	+	0.998551i	$0.517135\pi$
$230$	4.32314	+	24.2060i	0.285059	+	1.59609i
$231$	3.94775	−	11.3421i	0.259743	−	0.746255i
$232$	3.68197	+	6.28117i	0.241733	+	0.412379i
$233$	−13.4061	+	7.74002i	−0.878264	+	0.507066i	−0.870086	−	0.492901i	$-0.835937\pi$
$233$	−13.4061	+	7.74002i	−0.878264	+	0.507066i	−0.00817827	+	0.999967i	$0.502603\pi$
$234$	4.94770	+	14.3235i	0.323441	+	0.936357i
$235$	2.18366	−	3.78221i	0.142446	−	0.246724i
$236$	−10.0294	+	12.0600i	−0.652858	+	0.785041i
$237$	−6.47102	−	18.3091i	−0.420338	−	1.18930i
$238$	−0.686118	+	0.419961i	−0.0444744	+	0.0272220i
$239$	−20.5460			−1.32901			−0.664505	−	0.747284i	$-0.731358\pi$
$239$	−20.5460			−1.32901			−0.664505	+	0.747284i	$0.731358\pi$
$240$	25.7851	+	0.0136545i	1.66442	+	0.000881392i
$241$	−6.16667	+	10.6810i	−0.397230	+	0.688023i	−0.993383	−	0.114848i	$-0.963362\pi$
$241$	−6.16667	+	10.6810i	−0.397230	+	0.688023i	0.596153	+	0.802871i	$0.296695\pi$
$242$	5.49552	+	1.98651i	0.353266	+	0.127698i
$243$	−12.3961	+	9.45185i	−0.795208	+	0.606337i
$244$	0.240863	+	0.652807i	0.0154197	+	0.0417917i
$245$	24.8721	+	7.75258i	1.58902	+	0.495294i
$246$	1.93712	−	1.10004i	0.123506	−	0.0701361i
$247$	7.05904	−	4.07554i	0.449156	−	0.259320i
$248$	0.0919482	+	13.9192i	0.00583872	+	0.883870i
$249$	2.96189	+	0.550825i	0.187702	+	0.0349071i
$250$	15.5003	−	13.0646i	0.980325	−	0.826275i
$251$			21.2978i			1.34430i	0.740413	+	0.672152i	$0.234630\pi$
$251$			21.2978i			1.34430i	−0.740413	+	0.672152i	$0.765370\pi$
$252$	−2.61287	+	15.6580i	−0.164595	+	0.986361i
$253$			12.2431i			0.769719i
$254$	−2.30675	−	2.73681i	−0.144738	−	0.171723i
$255$	−1.36256	−	0.253396i	−0.0853269	−	0.0158683i
$256$	12.4360	+	10.0671i	0.777248	+	0.629194i
$257$	−13.2299	+	7.63828i	−0.825258	+	0.476463i	−0.852226	−	0.523173i	$-0.824748\pi$
$257$	−13.2299	+	7.63828i	−0.825258	+	0.476463i	0.0269684	+	0.999636i	$0.491415\pi$
$258$	−4.51827	−	7.95644i	−0.281295	−	0.495346i
$259$	13.9518	−	17.4421i	0.866922	−	1.08380i
$260$	9.20319	+	24.9432i	0.570758	+	1.54691i
$261$	−7.20615	−	2.77628i	−0.446049	−	0.171848i
$262$	2.80246	−	7.75278i	0.173137	−	0.478968i
$263$	0.249921	−	0.432876i	0.0154108	−	0.0266923i	−0.858217	−	0.513287i	$-0.828428\pi$
$263$	0.249921	−	0.432876i	0.0154108	−	0.0266923i	0.873628	+	0.486594i	$0.161761\pi$
$264$	12.6375	+	2.26394i	0.777784	+	0.139336i
$265$	−7.90287			−0.485470
$266$	8.53584	−	0.219059i	0.523366	−	0.0134314i
$267$	10.3098	+	29.1705i	0.630948	+	1.78521i
$268$	15.3385	+	12.7558i	0.936946	+	0.779186i
$269$	10.9207	−	18.9153i	0.665849	−	1.15328i	−0.313205	−	0.949685i	$-0.601403\pi$
$269$	10.9207	−	18.9153i	0.665849	−	1.15328i	0.979054	−	0.203599i	$-0.0652638\pi$
$270$	−21.3974	+	17.0332i	−1.30221	+	1.03661i
$271$	−13.6308	+	7.86975i	−0.828013	+	0.478053i	−0.853172	−	0.521630i	$-0.825324\pi$
$271$	−13.6308	+	7.86975i	−0.828013	+	0.478053i	0.0251590	+	0.999683i	$0.491991\pi$
$272$	−0.558568	−	0.653892i	−0.0338681	−	0.0396480i
$273$	−16.0777	+	3.06959i	−0.973069	+	0.185780i
$274$	13.1041	−	2.34037i	0.791649	−	0.141387i
$275$	20.0891	−	11.5985i	1.21142	−	0.699414i
$276$	−2.73155	−	15.9511i	−0.164420	−	0.960146i
$277$	−10.8672	−	6.27417i	−0.652945	−	0.376978i	0.136639	−	0.990621i	$-0.456370\pi$
$277$	−10.8672	−	6.27417i	−0.652945	−	0.376978i	−0.789584	+	0.613643i	$0.789703\pi$
$278$	8.15258	−	6.87148i	0.488959	−	0.412124i
$279$	−9.27718	−	11.4850i	−0.555411	−	0.687590i
$280$	−4.00970	+	27.5609i	−0.239625	+	1.64708i
$281$		−	22.7512i		−	1.35722i	−0.734498	−	0.678610i	$-0.762582\pi$
$281$		−	22.7512i		−	1.35722i	0.734498	−	0.678610i	$-0.237418\pi$
$282$	−1.45491	+	2.47896i	−0.0866386	+	0.147620i
$283$	0.440379	−	0.762759i	0.0261778	−	0.0453413i	−0.852640	−	0.522499i	$-0.825000\pi$
$283$	0.440379	−	0.762759i	0.0261778	−	0.0453413i	0.878818	+	0.477158i	$0.158333\pi$
$284$	3.41354	−	19.8705i	0.202556	−	1.17909i
$285$	11.1803	+	9.56068i	0.662263	+	0.566326i
$286$	2.32744	+	13.0317i	0.137624	+	0.770581i
$287$	0.875758	+	2.24113i	0.0516944	+	0.132289i
$288$	−16.9701	−	0.130076i	−0.999971	−	0.00766478i
$289$	−8.47689	−	14.6824i	−0.498640	−	0.863671i
$290$	−12.7418	−	4.60588i	−0.748223	−	0.270466i
$291$	2.81388	−	15.1308i	0.164952	−	0.886981i
$292$	−13.6912	−	11.3859i	−0.801215	−	0.666309i
$293$	22.1280			1.29273			0.646366	−	0.763028i	$-0.276288\pi$
$293$	22.1280			1.29273			0.646366	+	0.763028i	$0.276288\pi$
$294$	−16.3328	−	5.21906i	−0.952550	−	0.304382i
$295$		−	29.1887i		−	1.69943i
$296$	20.7571	+	11.8020i	1.20648	+	0.685978i
$297$	−11.9792	+	6.47577i	−0.695101	+	0.375762i
$298$	19.6498	+	7.10298i	1.13828	+	0.411465i
$299$	14.4510	−	8.34329i	0.835723	−	0.482505i
$300$	−23.5857	+	19.5933i	−1.36172	+	1.13122i
$301$	9.20511	−	3.59705i	0.530574	−	0.207331i
$302$	−5.12375	+	0.915093i	−0.294839	+	0.0526577i
$303$	−19.4487	−	16.6313i	−1.11730	−	0.955442i
$304$	1.66421	+	8.97522i	0.0954490	+	0.514764i
$305$	−1.12137	−	0.647422i	−0.0642094	−	0.0370713i
$306$	0.895562	+	0.173168i	0.0511959	+	0.00989937i
$307$	9.96754			0.568878			0.284439	−	0.958694i	$-0.408193\pi$
$307$	9.96754			0.568878			0.284439	+	0.958694i	$0.408193\pi$
$308$	−4.37808	+	13.1581i	−0.249464	+	0.749754i
$309$	4.33301	+	12.2598i	0.246496	+	0.697438i
$310$	−16.6935	−	19.8058i	−0.948125	−	1.12489i
$311$	5.87187	−	10.1704i	0.332963	−	0.576709i	−0.650128	−	0.759825i	$-0.725285\pi$
$311$	5.87187	−	10.1704i	0.332963	−	0.576709i	0.983091	+	0.183115i	$0.0586181\pi$
$312$	−5.93983	−	16.4593i	−0.336277	−	0.931824i
$313$	−0.343520	−	0.594993i	−0.0194169	−	0.0336310i	0.856154	−	0.516721i	$-0.172848\pi$
$313$	−0.343520	−	0.594993i	−0.0194169	−	0.0336310i	−0.875571	+	0.483090i	$0.839514\pi$
$314$	−29.8988	+	5.33988i	−1.68729	+	0.301347i
$315$	−14.8924	−	25.5119i	−0.839093	−	1.43743i
$316$	7.76188	+	21.0369i	0.436640	+	1.18342i
$317$	16.4535	+	28.4983i	0.924120	+	1.60062i	0.792970	+	0.609261i	$0.208534\pi$
$317$	16.4535	+	28.4983i	0.924120	+	1.60062i	0.131150	+	0.991363i	$0.458133\pi$
$318$	5.20118	+	0.0371126i	0.291667	+	0.00208117i
$319$	−5.84224	−	3.37302i	−0.327103	−	0.188853i
$320$	−29.7715	+	0.393349i	−1.66428	+	0.0219889i
$321$	7.29082	+	20.6287i	0.406934	+	1.15138i
$322$	17.4742	−	0.448448i	0.973802	−	0.0249911i
$323$		−	0.490632i		−	0.0272995i
$324$	14.1624	−	11.1097i	0.786802	−	0.617206i
$325$	−27.3802	−	15.8079i	−1.51878	−	0.876867i
$326$	2.01172	+	0.727195i	0.111419	+	0.0402756i
$327$	14.5938	−	17.0660i	0.807037	−	0.943751i
$328$	−2.21913	+	1.30083i	−0.122531	+	0.0718265i
$329$	−2.42447	−	1.93932i	−0.133665	−	0.106918i
$330$	−20.7751	+	11.7977i	−1.14363	+	0.649441i
$331$	−0.833276	−	1.44328i	−0.0458010	−	0.0793297i	0.842216	−	0.539140i	$-0.181251\pi$
$331$	−0.833276	−	1.44328i	−0.0458010	−	0.0793297i	−0.888017	+	0.459810i	$0.847917\pi$
$332$	−3.42852	−	0.588984i	−0.188164	−	0.0323247i
$333$	−25.0192	+	3.93134i	−1.37104	+	0.215436i
$334$	−7.80394	+	6.57762i	−0.427013	+	0.359911i
$335$	−37.1235			−2.02827
$336$	2.76836	−	18.1200i	0.151027	−	0.988530i
$337$	9.04814			0.492884			0.246442	−	0.969158i	$-0.420739\pi$
$337$	9.04814			0.492884			0.246442	+	0.969158i	$0.420739\pi$
$338$	−0.261783	+	0.220646i	−0.0142391	+	0.0120016i
$339$	12.0987	+	2.25001i	0.657113	+	0.122204i
$340$	1.57722	+	0.270950i	0.0855368	+	0.0146944i
$341$	−6.44858	−	11.1693i	−0.349210	−	0.604849i
$342$	−7.31327	−	6.34474i	−0.395456	−	0.343085i
$343$	8.10952	−	16.6504i	0.437873	−	0.899037i
$344$	5.34299	+	9.11475i	0.288075	+	0.491434i
$345$	22.8878	+	19.5722i	1.23224	+	1.05373i
$346$	−3.55627	−	1.28551i	−0.191186	−	0.0691097i
$347$	4.59168	+	2.65101i	0.246494	+	0.142313i	0.618158	−	0.786054i	$-0.287879\pi$
$347$	4.59168	+	2.65101i	0.246494	+	0.142313i	−0.371664	+	0.928367i	$0.621213\pi$
$348$	8.36421	+	3.09114i	0.448369	+	0.165702i
$349$			10.7938i			0.577779i	0.957362	+	0.288890i	$0.0932861\pi$
$349$			10.7938i			0.577779i	−0.957362	+	0.288890i	$0.906714\pi$
$350$	−17.2900	−	28.2478i	−0.924188	−	1.50991i
$351$	15.8070	+	9.72640i	0.843714	+	0.519157i
$352$	−14.6271	−	2.41342i	−0.779625	−	0.128636i
$353$	24.5717	+	14.1865i	1.30782	+	0.755071i	0.981732	−	0.190268i	$-0.0609357\pi$
$353$	24.5717	+	14.1865i	1.30782	+	0.755071i	0.326089	+	0.945339i	$0.394269\pi$
$354$	−0.137073	+	19.2102i	−0.00728533	+	1.02101i
$355$	18.7591	+	32.4917i	0.995628	+	1.72448i
$356$	−12.3664	−	33.5164i	−0.655418	−	1.77637i
$357$	−0.323866	+	0.930483i	−0.0171408	+	0.0492464i
$358$	11.7247	−	2.09400i	0.619667	−	0.110671i
$359$	−0.0586851	−	0.101646i	−0.00309728	−	0.00536465i	0.864473	−	0.502680i	$-0.167653\pi$
$359$	−0.0586851	−	0.101646i	−0.00309728	−	0.00536465i	−0.867570	+	0.497315i	$0.834319\pi$
$360$	24.4350	−	20.0059i	1.28784	−	1.05440i
$361$	6.89612	−	11.9444i	0.362954	−	0.628654i
$362$	5.58049	+	6.62091i	0.293304	+	0.347987i
$363$	6.74780	−	2.38489i	0.354168	−	0.125174i
$364$	18.5145	−	3.79922i	0.970424	−	0.199133i
$365$	33.1365			1.73444
$366$	0.734974	+	0.431359i	0.0384177	+	0.0225475i
$367$	7.31080	+	4.22089i	0.381621	+	0.220329i	0.678523	−	0.734579i	$-0.262620\pi$
$367$	7.31080	+	4.22089i	0.381621	+	0.220329i	−0.296902	+	0.954908i	$0.595954\pi$
$368$	3.40691	+	18.3737i	0.177597	+	0.957796i
$369$	0.980855	−	2.54592i	0.0510613	−	0.132535i
$370$	−43.7414	+	7.81215i	−2.27401	+	0.406134i
$371$	−0.845534	+	5.55406i	−0.0438980	+	0.288353i
$372$	10.8936	+	13.1133i	0.564806	+	0.679893i
$373$	0.0783826	−	0.0452542i	0.00405850	−	0.00234318i	−0.497969	−	0.867195i	$-0.665921\pi$
$373$	0.0783826	−	0.0452542i	0.00405850	−	0.00234318i	0.502028	+	0.864851i	$0.332587\pi$
$374$	0.749364	+	0.270879i	0.0387487	+	0.0140068i
$375$	4.53939	−	24.4092i	0.234413	−	1.26048i
$376$	1.64049	−	2.88527i	0.0846020	−	0.148796i
$377$			9.19441i			0.473536i
$378$	9.68145	+	16.8603i	0.497960	+	0.867200i
$379$	−19.7881			−1.01645			−0.508224	−	0.861225i	$-0.669698\pi$
$379$	−19.7881			−1.01645			−0.508224	+	0.861225i	$0.669698\pi$
$380$	−13.0604	−	10.8613i	−0.669982	−	0.557172i
$381$	−4.30981	−	0.801498i	−0.220798	−	0.0410620i
$382$	−20.1221	−	7.27372i	−1.02954	−	0.372156i
$383$	−12.4851	−	21.6249i	−0.637961	−	1.10498i	−0.985880	−	0.167456i	$-0.946445\pi$
$383$	−12.4851	−	21.6249i	−0.637961	−	1.10498i	0.347919	−	0.937525i	$-0.386888\pi$
$384$	19.5956	−	0.119068i	0.999982	−	0.00607617i
$385$	−9.39230	−	24.0355i	−0.478676	−	1.22496i
$386$	−0.760653	−	4.25902i	−0.0387162	−	0.216778i
$387$	−10.4570	−	4.02872i	−0.531559	−	0.204792i
$388$	−3.00881	+	17.5145i	−0.152749	+	0.889164i
$389$	15.0483	−	26.0644i	0.762979	−	1.32152i	−0.178329	−	0.983971i	$-0.557069\pi$
$389$	15.0483	−	26.0644i	0.762979	−	1.32152i	0.941308	−	0.337548i	$-0.109597\pi$
$390$	28.0828	+	16.4819i	1.42203	+	0.834593i
$391$		−	1.00440i		−	0.0507948i
$392$	18.9406	+	5.76674i	0.956643	+	0.291265i
$393$	−3.36446	−	9.51942i	−0.169715	−	0.480191i
$394$	15.7591	−	13.2827i	0.793932	−	0.669173i
$395$	−36.1364	−	20.8634i	−1.81822	−	1.04975i
$396$	13.7283	−	7.66693i	0.689872	−	0.385278i
$397$	4.91661	−	2.83861i	0.246758	−	0.142466i	−0.371521	−	0.928425i	$-0.621164\pi$
$397$	4.91661	−	2.83861i	0.246758	−	0.142466i	0.618279	+	0.785959i	$0.287830\pi$
$398$	24.1754	−	4.31769i	1.21180	−	0.216426i
$399$	7.91534	−	6.83449i	0.396263	−	0.342153i
$400$	26.9210	−	22.9965i	1.34605	−	1.14982i
$401$	−0.897563	+	0.518208i	−0.0448222	+	0.0258781i	−0.522244	−	0.852796i	$-0.674905\pi$
$401$	−0.897563	+	0.518208i	−0.0448222	+	0.0258781i	0.477421	+	0.878674i	$0.341572\pi$
$402$	24.4323	+	0.174335i	1.21857	+	0.00869505i
$403$	−8.78898	+	15.2230i	−0.437810	+	0.758310i
$404$	22.7192	+	18.8938i	1.13032	+	0.940000i
$405$	−7.04417	+	32.7467i	−0.350028	+	1.62720i
$406$	−4.60022	+	8.46201i	−0.228305	+	0.419962i
$407$	−22.1240			−1.09664
$408$	−1.03676	−	0.185729i	−0.0513271	−	0.00919497i
$409$	1.83983	−	3.18669i	0.0909739	−	0.157571i	−0.816947	−	0.576712i	$-0.804335\pi$
$409$	1.83983	−	3.18669i	0.0909739	−	0.157571i	0.907921	+	0.419141i	$0.137669\pi$
$410$	1.62725	−	4.50164i	0.0803640	−	0.222320i
$411$	10.5956	−	12.3906i	0.522644	−	0.611181i
$412$	−5.19738	−	14.0864i	−0.256056	−	0.693985i
$413$	−20.5135	−	3.12292i	−1.00940	−	0.153669i
$414$	−14.9714	−	12.9887i	−0.735806	−	0.638360i
$415$	5.60623	−	3.23676i	0.275199	−	0.158886i
$416$	7.11922	+	18.9095i	0.349049	+	0.927115i
$417$	2.38755	−	12.8383i	0.116919	−	0.628695i
$418$	−5.45080	−	6.46703i	−0.266607	−	0.316313i
$419$			9.81445i			0.479467i	0.970839	+	0.239734i	$0.0770601\pi$
$419$			9.81445i			0.479467i	−0.970839	+	0.239734i	$0.922940\pi$
$420$	17.5994	+	29.2196i	0.858765	+	1.42577i
$421$		−	33.0188i		−	1.60924i	−0.593790	−	0.804620i	$-0.702369\pi$
$421$		−	33.0188i		−	1.60924i	0.593790	−	0.804620i	$-0.297631\pi$
$422$	22.9988	−	19.3847i	1.11956	−	0.943633i
$423$	0.546461	+	3.47770i	0.0265698	+	0.169091i
$424$	−6.00582	+	0.0396736i	−0.291668	+	0.00192672i
$425$	−1.64807	+	0.951516i	−0.0799433	+	0.0461553i
$426$	−12.1935	−	21.4721i	−0.590775	−	1.04033i
$427$	−0.574978	+	0.718819i	−0.0278252	+	0.0347861i
$428$	−8.74522	−	23.7020i	−0.422716	−	1.14568i
$429$	12.3221	+	10.5371i	0.594916	+	0.508735i
$430$	−18.4899	−	6.68369i	−0.891660	−	0.322316i
$431$	−5.27304	+	9.13317i	−0.253993	+	0.439929i	−0.964622	−	0.263638i	$-0.915077\pi$
$431$	−5.27304	+	9.13317i	−0.253993	+	0.439929i	0.710628	+	0.703568i	$0.248411\pi$
$432$	−16.1756	+	13.0519i	−0.778247	+	0.627959i
$433$	13.7135			0.659026			0.329513	−	0.944151i	$-0.393115\pi$
$433$	13.7135			0.659026			0.329513	+	0.944151i	$0.393115\pi$
$434$	−15.7053	+	9.61297i	−0.753881	+	0.461437i
$435$	−15.6453	+	5.52953i	−0.750133	+	0.265121i
$436$	−16.5791	+	19.9358i	−0.793993	+	0.954751i
$437$	−5.33056	+	9.23280i	−0.254995	+	0.441665i
$438$	−21.8084	−	0.155612i	−1.04204	−	0.00743543i
$439$	−8.62149	+	4.97762i	−0.411481	+	0.237569i	−0.691426	−	0.722447i	$-0.743017\pi$
$439$	−8.62149	+	4.97762i	−0.411481	+	0.237569i	0.279945	+	0.960016i	$0.409684\pi$
$440$	23.7996	−	13.9511i	1.13460	−	0.665094i
$441$	−19.5229	+	7.73671i	−0.929662	+	0.368415i
$442$	−0.190939	−	1.06910i	−0.00908203	−	0.0508517i
$443$	−0.202164	+	0.116720i	−0.00960512	+	0.00554552i	−0.504795	−	0.863239i	$-0.668432\pi$
$443$	−0.202164	+	0.116720i	−0.00960512	+	0.00554552i	0.495190	+	0.868785i	$0.335099\pi$
$444$	28.8246	−	4.93605i	1.36795	−	0.234255i
$445$	57.5734	+	33.2400i	2.72924	+	1.57573i
$446$	−6.09548	−	7.23192i	−0.288630	−	0.342441i
$447$	24.1275	−	8.52740i	1.14119	−	0.403332i
$448$	−2.90883	+	20.9652i	−0.137429	+	0.990512i
$449$			5.83932i			0.275575i	0.990462	+	0.137787i	$0.0439990\pi$
$449$			5.83932i			0.275575i	−0.990462	+	0.137787i	$0.956001\pi$
$450$	−7.12941	+	36.8707i	−0.336084	+	1.73810i
$451$	1.19168	−	2.06405i	0.0561141	−	0.0971924i
$452$	−14.0048	−	2.40588i	−0.658731	−	0.113163i
$453$	−4.14292	+	4.84475i	−0.194651	+	0.227626i
$454$	33.3788	−	5.96139i	1.56654	−	0.279782i
$455$	−21.9695	+	27.4655i	−1.02994	+	1.28760i
$456$	8.54450	+	7.20955i	0.400133	+	0.337618i
$457$	8.93416	+	15.4744i	0.417923	+	0.723863i	0.995730	−	0.0923098i	$-0.0294250\pi$
$457$	8.93416	+	15.4744i	0.417923	+	0.723863i	−0.577808	+	0.816173i	$0.696092\pi$
$458$	7.94271	−	21.9728i	0.371138	−	1.02672i
$459$	0.982747	−	0.531260i	0.0458707	−	0.0247971i
$460$	−26.7367	−	22.2348i	−1.24660	−	1.03670i
$461$	−0.400330			−0.0186452			−0.00932262	−	0.999957i	$-0.502968\pi$
$461$	−0.400330			−0.0186452			−0.00932262	+	0.999957i	$0.502968\pi$
$462$	6.06855	+	15.8628i	0.282334	+	0.738004i
$463$			29.4293i			1.36769i	0.729626	+	0.683847i	$0.239694\pi$
$463$			29.4293i			1.36769i	−0.729626	+	0.683847i	$0.760306\pi$
$464$	−9.70629	−	3.43629i	−0.450603	−	0.159526i
$465$	−31.1892	−	5.80028i	−1.44637	−	0.268982i
$466$	7.44222	−	20.5883i	0.344754	−	0.953734i
$467$	−6.75074	+	3.89754i	−0.312387	+	0.180357i	−0.647994	−	0.761645i	$-0.724392\pi$
$467$	−6.75074	+	3.89754i	−0.312387	+	0.180357i	0.335607	+	0.942002i	$0.391059\pi$
$468$	−18.4049	−	10.9792i	−0.850768	−	0.507515i
$469$	−3.97187	+	26.0900i	−0.183404	+	1.20472i
$470$	1.08590	+	6.08011i	0.0500887	+	0.280455i
$471$	−24.1753	+	28.2707i	−1.11394	+	1.30265i
$472$	−0.146531	−	22.1821i	−0.00674466	−	1.02101i
$473$	−8.47781	−	4.89466i	−0.389810	−	0.225057i
$474$	23.6847	+	13.9007i	1.08788	+	0.638479i
$475$	20.1995			0.926818
$476$	0.359169	−	1.07947i	0.0164625	−	0.0494773i
$477$	4.95553	−	4.00290i	0.226898	−	0.183280i
$478$	22.2173	−	18.7261i	1.01620	−	0.856511i
$479$	−19.3422	+	33.5016i	−0.883765	+	1.53073i	−0.0366434	+	0.999328i	$0.511667\pi$
$479$	−19.3422	+	33.5016i	−0.883765	+	1.53073i	−0.847122	+	0.531398i	$0.821667\pi$
$480$	−27.8950	+	23.4863i	−1.27323	+	1.07200i
$481$	15.0768	+	26.1137i	0.687441	+	1.19068i
$482$	−3.06658	−	17.1703i	−0.139679	−	0.782085i
$483$	16.2040	−	13.9913i	0.737306	−	0.636627i
$484$	−7.75311	+	2.86063i	−0.352414	+	0.130029i
$485$	−16.5349	−	28.6393i	−0.750811	−	1.30044i
$486$	4.78981	−	21.5188i	0.217270	−	0.976111i
$487$	8.63096	+	4.98308i	0.391106	+	0.225805i	0.682639	−	0.730756i	$-0.260832\pi$
$487$	8.63096	+	4.98308i	0.391106	+	0.225805i	−0.291533	+	0.956561i	$0.594165\pi$
$488$	−0.855439	−	0.486382i	−0.0387239	−	0.0220175i
$489$	2.47014	−	0.873026i	0.111704	−	0.0394796i
$490$	−33.9612	+	14.2857i	−1.53421	+	0.645364i
$491$		−	15.5075i		−	0.699845i	−0.936779	−	0.349923i	$-0.886208\pi$
$491$		−	15.5075i		−	0.699845i	0.936779	−	0.349923i	$-0.113792\pi$
$492$	−1.09209	+	2.95506i	−0.0492353	+	0.133224i
$493$	0.479286	+	0.276716i	0.0215860	+	0.0124627i
$494$	−3.91873	+	10.8408i	−0.176312	+	0.487752i
$495$	−10.5194	+	27.3044i	−0.472813	+	1.22724i
$496$	−12.7857	−	14.9677i	−0.574095	−	0.672068i
$497$	24.8419	−	9.70739i	1.11431	−	0.435436i
$498$	−3.70487	+	2.10390i	−0.166019	+	0.0942781i
$499$	−0.275544	−	0.477256i	−0.0123350	−	0.0213649i	0.859792	−	0.510644i	$-0.170593\pi$
$499$	−0.275544	−	0.477256i	−0.0123350	−	0.0213649i	−0.872127	+	0.489279i	$0.837260\pi$
$500$	−4.85385	+	28.2546i	−0.217071	+	1.26359i
$501$	−2.28545	+	12.2893i	−0.102106	+	0.549045i
$502$	−19.4113	−	23.0303i	−0.866368	−	1.02789i
$503$	32.2097			1.43616			0.718079	−	0.695962i	$-0.245022\pi$
$503$	32.2097			1.43616			0.718079	+	0.695962i	$0.245022\pi$
$504$	−11.4456	−	19.3131i	−0.509829	−	0.860276i
$505$	−54.9868			−2.44688
$506$	−11.1587	−	13.2391i	−0.496063	−	0.588548i
$507$	−0.0766652	+	0.412243i	−0.00340482	+	0.0183084i
$508$	4.98879	+	0.857022i	0.221342	+	0.0380242i
$509$	−0.906135	−	1.56947i	−0.0401637	−	0.0695656i	0.845245	−	0.534379i	$-0.179455\pi$
$509$	−0.906135	−	1.56947i	−0.0401637	−	0.0695656i	−0.885408	+	0.464814i	$0.846121\pi$
$510$	1.70435	−	0.967859i	0.0754699	−	0.0428575i
$511$	3.54530	−	23.2880i	0.156835	−	1.03020i
$512$	−22.6230	+	0.448384i	−0.999804	+	0.0198160i
$513$	−11.8532	−	0.332116i	−0.523333	−	0.0146633i
$514$	7.34439	−	20.3176i	0.323947	−	0.896173i
$515$	24.1970	+	13.9702i	1.06625	+	0.615599i
$516$	12.1375	+	4.48562i	0.534323	+	0.197468i
$517$			3.07526i			0.135250i
$518$	0.810370	+	31.5769i	0.0356056	+	1.38741i
$519$	−4.36664	+	1.54331i	−0.191674	+	0.0677438i
$520$	−32.6857	−	18.5843i	−1.43336	−	0.814974i
$521$	6.65560	+	3.84261i	0.291587	+	0.168348i	0.638657	−	0.769491i	$-0.279490\pi$
$521$	6.65560	+	3.84261i	0.291587	+	0.168348i	−0.347070	+	0.937839i	$0.612823\pi$
$522$	10.3227	−	3.56572i	0.451813	−	0.156067i
$523$	−4.33611	−	7.51035i	−0.189605	−	0.328405i	0.755514	−	0.655133i	$-0.227387\pi$
$523$	−4.33611	−	7.51035i	−0.189605	−	0.328405i	−0.945118	+	0.326728i	$0.894054\pi$
$524$	4.03562	+	10.9377i	0.176297	+	0.477814i
$525$	−38.3084	−	13.3337i	−1.67192	−	0.581930i
$526$	0.124281	+	0.695872i	0.00541893	+	0.0303415i
$527$	0.529029	+	0.916305i	0.0230449	+	0.0399149i
$528$	−15.7289	+	9.06999i	−0.684513	+	0.394721i
$529$	0.587489	−	1.01756i	0.0255430	−	0.0442417i
$530$	8.54574	−	7.20285i	0.371203	−	0.312872i
$531$	14.7844	+	18.3029i	0.641588	+	0.794277i
$532$	−9.03055	+	8.01664i	−0.391524	+	0.347565i
$533$	−3.24837			−0.140702
$534$	−37.7351	−	22.1469i	−1.63296	−	0.958388i
$535$	40.7145	+	23.5065i	1.76024	+	1.01627i
$536$	−28.2121	+	0.186365i	−1.21858	+	0.00804975i
$537$	9.48022	−	11.0862i	0.409102	−	0.478405i
$538$	5.43070	+	30.4074i	0.234134	+	1.31095i
$539$	−17.8968	+	4.02924i	−0.770871	+	0.173551i
$540$	7.61357	−	37.9209i	0.327636	−	1.63185i
$541$	10.0751	−	5.81687i	0.433163	−	0.250087i	−0.267530	−	0.963549i	$-0.586208\pi$
$541$	10.0751	−	5.81687i	0.433163	−	0.250087i	0.700693	+	0.713463i	$0.252874\pi$
$542$	7.56696	−	20.9334i	0.325029	−	0.899164i
$543$	10.4263	+	1.93899i	0.447435	+	0.0832098i
$544$	1.19998	+	0.197992i	0.0514486	+	0.00848884i
$545$		−	48.2503i		−	2.06681i
$546$	14.5879	−	17.9729i	0.624305	−	0.769169i
$547$	−27.7574			−1.18682			−0.593410	−	0.804900i	$-0.702219\pi$
$547$	−27.7574			−1.18682			−0.593410	+	0.804900i	$0.702219\pi$
$548$	−12.0370	+	14.4741i	−0.514196	+	0.618305i
$549$	1.03109	−	0.162017i	0.0440056	−	0.00691473i
$550$	−11.1522	+	30.8516i	−0.475532	+	1.31552i
$551$	−2.93717	−	5.08733i	−0.125128	−	0.216728i
$552$	17.4920	+	14.7591i	0.744508	+	0.628190i
$553$	−18.5288	+	23.1641i	−0.787926	+	0.985039i
$554$	17.4696	−	3.12004i	0.742212	−	0.132558i
$555$	−35.3681	+	41.3596i	−1.50129	+	1.75562i
$556$	−2.55295	+	14.8609i	−0.108269	+	0.630242i
$557$	−7.71096	+	13.3558i	−0.326724	+	0.565902i	−0.981860	−	0.189609i	$-0.939278\pi$
$557$	−7.71096	+	13.3558i	−0.326724	+	0.565902i	0.655136	+	0.755511i	$0.272611\pi$
$558$	20.4995	+	3.96385i	0.867815	+	0.167803i
$559$			13.3422i			0.564315i
$560$	−20.7838	−	33.4574i	−0.878275	−	1.41383i
$561$	0.920124	−	0.325201i	0.0388476	−	0.0137300i
$562$	20.7359	+	24.6019i	0.874692	+	1.03777i
$563$	11.5626	+	6.67567i	0.487305	+	0.281346i	0.723456	−	0.690371i	$-0.242553\pi$
$563$	11.5626	+	6.67567i	0.487305	+	0.281346i	−0.236151	+	0.971716i	$0.575886\pi$
$564$	−0.686117	−	4.00665i	−0.0288907	−	0.168710i
$565$	22.9003	−	13.2215i	0.963423	−	0.556233i
$566$	0.218993	+	1.22618i	0.00920497	+	0.0515401i
$567$	22.2604	+	8.45417i	0.934850	+	0.355042i
$568$	14.4192	+	24.5980i	0.605014	+	1.03211i
$569$	−39.4279	+	22.7637i	−1.65290	+	0.954305i	−0.677034	+	0.735951i	$0.736735\pi$
$569$	−39.4279	+	22.7637i	−1.65290	+	0.954305i	−0.975870	+	0.218353i	$0.929931\pi$
$570$	−20.8036	−	0.148442i	−0.871366	−	0.00621757i
$571$	20.3243	−	35.2028i	0.850546	−	1.47319i	−0.0301698	−	0.999545i	$-0.509605\pi$
$571$	20.3243	−	35.2028i	0.850546	−	1.47319i	0.880716	−	0.473645i	$-0.157062\pi$
$572$	−14.3942	−	11.9705i	−0.601850	−	0.500512i
$573$	−24.7074	+	8.73238i	−1.03217	+	0.364800i
$574$	−2.98961	−	1.62525i	−0.124784	−	0.0678365i
$575$	41.3517			1.72448
$576$	18.4691	−	15.3262i	0.769545	−	0.638593i
$577$	−8.50680	+	14.7342i	−0.354143	+	0.613393i	−0.986971	−	0.160899i	$-0.948561\pi$
$577$	−8.50680	+	14.7342i	−0.354143	+	0.613393i	0.632828	+	0.774292i	$0.281894\pi$
$578$	22.5483	+	8.15073i	0.937886	+	0.339026i
$579$	−4.02710	−	3.44372i	−0.167360	−	0.143116i
$580$	17.9762	−	6.63259i	0.746420	−	0.275403i
$581$	−1.67495	−	4.28630i	−0.0694885	−	0.177826i
$582$	10.7477	+	18.9262i	0.445508	+	0.784517i
$583$	4.81928	−	2.78241i	0.199594	−	0.115236i
$584$	25.1822	−	0.166350i	1.04205	−	0.00688362i
$585$	39.3970	−	6.19056i	1.62886	−	0.255948i
$586$	−23.9280	+	20.1679i	−0.988458	+	0.833130i
$587$		−	28.5925i		−	1.18014i	−0.807352	−	0.590070i	$-0.799100\pi$
$587$		−	28.5925i		−	1.18014i	0.807352	−	0.590070i	$-0.200900\pi$
$588$	22.4182	−	9.24249i	0.924512	−	0.381154i
$589$		−	11.2306i		−	0.462750i
$590$	26.6032	+	31.5631i	1.09524	+	1.29943i
$591$	4.61518	−	24.8167i	0.189843	−	1.02082i
$592$	−33.2023	+	6.15646i	−1.36461	+	0.253029i
$593$	−4.49943	+	2.59775i	−0.184770	+	0.106677i	−0.589532	−	0.807745i	$-0.700688\pi$
$593$	−4.49943	+	2.59775i	−0.184770	+	0.106677i	0.404762	+	0.914422i	$0.367354\pi$
$594$	7.05146	−	17.9206i	0.289325	−	0.735292i
$595$	0.770526	+	1.97183i	0.0315885	+	0.0808371i
$596$	−27.7221	+	10.2285i	−1.13554	+	0.418975i
$597$	19.5476	−	22.8590i	0.800029	−	0.935556i
$598$	−8.02227	+	22.1929i	−0.328055	+	0.907537i
$599$	−22.7140	+	39.3418i	−0.928069	+	1.60746i	−0.141519	+	0.989936i	$0.545199\pi$
$599$	−22.7140	+	39.3418i	−0.928069	+	1.60746i	−0.786550	+	0.617527i	$0.788135\pi$
$600$	7.64656	−	42.6837i	0.312169	−	1.74255i
$601$	45.5994			1.86004			0.930019	−	0.367511i	$-0.119790\pi$
$601$	45.5994			1.86004			0.930019	+	0.367511i	$0.119790\pi$
$602$	−6.67548	+	12.2794i	−0.272072	+	0.500471i
$603$	23.2784	−	18.8035i	0.947970	−	0.765736i
$604$	4.70651	−	5.65944i	0.191505	−	0.230279i
$605$	7.68917	−	13.3180i	0.312609	−	0.541455i
$606$	36.1889	+	0.258223i	1.47007	+	0.0104896i
$607$	18.3382	−	10.5876i	0.744324	−	0.429736i	−0.0793155	−	0.996850i	$-0.525273\pi$
$607$	18.3382	−	10.5876i	0.744324	−	0.429736i	0.823639	+	0.567114i	$0.191940\pi$
$608$	−9.97980	−	8.18852i	−0.404734	−	0.332088i
$609$	2.21220	+	11.5870i	0.0896430	+	0.469527i
$610$	1.80266	−	0.321952i	0.0729877	−	0.0130355i
$611$	3.62984	−	2.09569i	0.146848	−	0.0847825i
$612$	−1.12624	+	0.628980i	−0.0455256	+	0.0254250i
$613$	−22.2592	−	12.8513i	−0.899039	−	0.519060i	−0.0221508	−	0.999755i	$-0.507051\pi$
$613$	−22.2592	−	12.8513i	−0.899039	−	0.519060i	−0.876888	+	0.480694i	$0.840385\pi$
$614$	−10.7784	+	9.08464i	−0.434979	+	0.366626i
$615$	−1.95357	−	5.52744i	−0.0787756	−	0.222888i
$616$	−7.25838	−	18.2188i	−0.292448	−	0.734055i
$617$			16.9888i			0.683941i	0.939711	+	0.341971i	$0.111094\pi$
$617$			16.9888i			0.683941i	−0.939711	+	0.341971i	$0.888906\pi$
$618$	−15.8594	−	9.30792i	−0.637958	−	0.374420i
$619$	−11.6456	+	20.1708i	−0.468076	+	0.810732i	−0.999334	−	0.0364781i	$-0.988386\pi$
$619$	−11.6456	+	20.1708i	−0.468076	+	0.810732i	0.531258	+	0.847210i	$0.321719\pi$
$620$	36.1028	+	6.20210i	1.44992	+	0.249082i
$621$	−24.2655	−	0.679895i	−0.973740	−	0.0272832i
$622$	2.91998	+	16.3495i	0.117081	+	0.655554i
$623$	29.5206	−	36.9056i	1.18272	−	1.47859i
$624$	21.4244	+	12.3845i	0.857661	+	0.495777i
$625$	−4.54562	−	7.87325i	−0.181825	−	0.314930i
$626$	0.913754	+	0.330302i	0.0365209	+	0.0132015i
$627$	−10.1840	−	1.89392i	−0.406709	−	0.0756360i
$628$	27.4641	−	33.0247i	1.09594	−	1.31783i
$629$	1.81501			0.0723691
$630$	39.3560	+	14.0140i	1.56798	+	0.558329i
$631$		−	15.0554i		−	0.599347i	−0.954042	−	0.299674i	$-0.903122\pi$
$631$		−	15.0554i		−	0.599347i	0.954042	−	0.299674i	$-0.0968778\pi$
$632$	−27.5668	−	15.6738i	−1.09655	−	0.623470i
$633$	6.73537	−	36.2174i	0.267707	−	1.43951i
$634$	−43.7659	−	15.8204i	−1.73817	−	0.628310i
$635$	−8.15754	+	4.70976i	−0.323722	+	0.186901i
$636$	−5.65810	+	4.70034i	−0.224358	+	0.186380i
$637$	16.9520	+	18.3785i	0.671661	+	0.728182i
$638$	9.39173	−	1.67735i	0.371822	−	0.0664068i
$639$	−28.2204	−	10.8723i	−1.11638	−	0.430103i
$640$	31.8347	−	27.5597i	1.25838	−	1.08939i
$641$	22.9318	+	13.2397i	0.905752	+	0.522936i	0.879062	−	0.476707i	$-0.158170\pi$
$641$	22.9318	+	13.2397i	0.905752	+	0.522936i	0.0266904	+	0.999644i	$0.491503\pi$
$642$	−26.6853	−	15.6617i	−1.05319	−	0.618118i
$643$	−29.9973			−1.18298			−0.591490	−	0.806312i	$-0.701460\pi$
$643$	−29.9973			−1.18298			−0.591490	+	0.806312i	$0.701460\pi$
$644$	−18.4870	+	16.4113i	−0.728489	+	0.646697i
$645$	−22.7032	+	8.02403i	−0.893937	+	0.315946i
$646$	0.447173	+	0.530543i	0.0175938	+	0.0208739i
$647$	9.22707	−	15.9817i	0.362753	−	0.628307i	−0.625659	−	0.780096i	$-0.715170\pi$
$647$	9.22707	−	15.9817i	0.362753	−	0.628307i	0.988413	+	0.151789i	$0.0485034\pi$
$648$	−5.18885	+	24.9214i	−0.203837	+	0.979005i
$649$	10.2766	+	17.7997i	0.403394	+	0.698698i
$650$	44.0152	−	7.86103i	1.72642	−	0.308335i
$651$	−7.41334	+	21.2989i	−0.290552	+	0.834770i
$652$	−2.83815	+	1.04718i	−0.111151	+	0.0410107i
$653$	−8.95898	−	15.5174i	−0.350592	−	0.607243i	0.635761	−	0.771886i	$-0.280686\pi$
$653$	−8.95898	−	15.5174i	−0.350592	−	0.607243i	−0.986353	+	0.164643i	$0.947353\pi$
$654$	−0.226588	+	31.7553i	−0.00886028	+	1.24173i
$655$	−18.7883	−	10.8474i	−0.734121	−	0.423845i
$656$	1.21403	−	3.42921i	0.0474001	−	0.133888i
$657$	−20.7784	+	16.7840i	−0.810642	+	0.654807i
$658$	4.38923	−	0.112642i	0.171110	−	0.00439126i
$659$		−	30.7250i		−	1.19687i	−0.801170	−	0.598437i	$-0.795789\pi$
$659$		−	30.7250i		−	1.19687i	0.801170	−	0.598437i	$-0.204211\pi$
$660$	11.7124	−	31.6923i	0.455906	−	1.23362i
$661$	−13.0311	−	7.52352i	−0.506852	−	0.292631i	0.224687	−	0.974431i	$-0.427864\pi$
$661$	−13.0311	−	7.52352i	−0.506852	−	0.292631i	−0.731539	+	0.681800i	$0.761197\pi$
$662$	2.21649	+	0.801215i	0.0861465	+	0.0311401i
$663$	−1.01088	−	0.864441i	−0.0392593	−	0.0335721i
$664$	4.24423	−	2.48793i	0.164708	−	0.0965504i
$665$	3.38195	−	22.2151i	0.131147	−	0.861463i
$666$	23.4713	−	27.0542i	0.909494	−	1.04833i
$667$	−6.01287	−	10.4146i	−0.232819	−	0.403254i
$668$	2.44377	−	14.2254i	0.0945524	−	0.550396i
$669$	−11.3885	−	2.11793i	−0.440304	−	0.0818837i
$670$	40.1433	−	33.8352i	1.55087	−	1.30717i
$671$	0.911768			0.0351984
$672$	13.5215	+	22.1172i	0.521602	+	0.853189i
$673$	20.6079			0.794376			0.397188	−	0.917737i	$-0.369986\pi$
$673$	20.6079			0.794376			0.397188	+	0.917737i	$0.369986\pi$
$674$	−9.78417	+	8.24667i	−0.376872	+	0.317650i
$675$	21.8722	+	40.4601i	0.841861	+	1.55731i
$676$	0.0819762	−	0.477189i	0.00315293	−	0.0183534i
$677$	5.13682	+	8.89723i	0.197424	+	0.341948i	0.947692	−	0.319185i	$-0.103409\pi$
$677$	5.13682	+	8.89723i	0.197424	+	0.341948i	−0.750268	+	0.661133i	$0.770076\pi$
$678$	−15.1336	+	8.59402i	−0.581204	+	0.330051i
$679$	−21.8965	+	8.55642i	−0.840310	+	0.328365i
$680$	−1.95247	+	1.14452i	−0.0748739	+	0.0438905i
$681$	26.9891	−	31.5612i	1.03423	−	1.20943i
$682$	17.1531	+	6.20046i	0.656824	+	0.237428i
$683$	30.7725	+	17.7665i	1.17748	+	0.679817i	0.955430	−	0.295218i	$-0.0953924\pi$
$683$	30.7725	+	17.7665i	1.17748	+	0.679817i	0.222048	+	0.975036i	$0.428726\pi$
$684$	13.6909	+	0.195391i	0.523485	+	0.00747096i
$685$		−	35.0316i		−	1.33849i
$686$	6.40634	+	25.3960i	0.244595	+	0.969625i
$687$	−9.53553	−	26.9798i	−0.363803	−	1.02935i
$688$	−14.0850	−	4.98648i	−0.536986	−	0.190108i
$689$	−6.56837	−	3.79225i	−0.250235	−	0.144473i
$690$	−42.5883	−	0.303886i	−1.62131	−	0.0115687i
$691$	17.0490	+	29.5298i	0.648576	+	1.12337i	0.983463	+	0.181109i	$0.0579685\pi$
$691$	17.0490	+	29.5298i	0.648576	+	1.12337i	−0.334887	+	0.942258i	$0.608698\pi$
$692$	5.01720	−	1.85118i	0.190725	−	0.0703711i
$693$	18.0638	+	10.3143i	0.686185	+	0.391807i
$694$	−7.38138	+	1.31830i	−0.280193	+	0.0500420i
$695$	−14.0297	−	24.3002i	−0.532177	−	0.921758i
$696$	−11.8619	+	4.28073i	−0.449625	+	0.162261i
$697$	−0.0977632	+	0.169331i	−0.00370305	+	0.00641386i
$698$	−9.83772	−	11.6718i	−0.372363	−	0.441786i
$699$	−8.93467	−	25.2798i	−0.337940	−	0.956169i
$700$	44.4421	+	14.7872i	1.67975	+	0.558902i
$701$	−42.6496			−1.61085			−0.805426	−	0.592696i	$-0.798063\pi$
$701$	−42.6496			−1.61085			−0.805426	+	0.592696i	$0.798063\pi$
$702$	−25.9577	+	3.88923i	−0.979709	+	0.146789i
$703$	−16.6842	−	9.63261i	−0.629255	−	0.363301i
$704$	18.0166	−	10.7217i	0.679025	−	0.404089i
$705$	5.74903	+	4.91621i	0.216521	+	0.185155i
$706$	−39.5004	+	7.05471i	−1.48662	+	0.265507i
$707$	−5.88308	+	38.6442i	−0.221256	+	1.45336i
$708$	−17.3603	−	20.8978i	−0.652442	−	0.785386i
$709$	−24.7114	+	14.2671i	−0.928054	+	0.535812i	−0.886196	−	0.463311i	$-0.846661\pi$
$709$	−24.7114	+	14.2671i	−0.928054	+	0.535812i	−0.0418586	+	0.999124i	$0.513328\pi$
$710$	−49.8987	−	18.0373i	−1.87266	−	0.676928i
$711$	33.2270	−	5.22106i	1.24611	−	0.195805i
$712$	43.9200	+	24.9719i	1.64597	+	0.935860i
$713$		−	22.9909i		−	0.861017i
$714$	−0.497852	−	1.30135i	−0.0186316	−	0.0487019i
$715$	34.8380			1.30287
$716$	−10.7699	+	12.9504i	−0.402490	+	0.483981i
$717$	6.50653	−	34.9869i	0.242991	−	1.30661i
$718$	0.156101	+	0.0564272i	0.00582564	+	0.00210584i
$719$	25.0072	+	43.3138i	0.932612	+	1.61533i	0.778837	+	0.627226i	$0.215810\pi$
$719$	25.0072	+	43.3138i	0.932612	+	1.61533i	0.153775	+	0.988106i	$0.450857\pi$
$720$	−8.18890	+	43.9039i	−0.305182	+	1.63620i
$721$	12.4070	−	15.5108i	0.462059	−	0.577651i
$722$	3.42933	+	19.2013i	0.127626	+	0.714600i
$723$	−16.2353	−	13.8834i	−0.603797	−	0.516329i
$724$	−12.0689	−	2.07331i	−0.448536	−	0.0770539i
$725$	−11.3925	+	19.7324i	−0.423108	+	0.732844i
$726$	−5.12307	+	8.72898i	−0.190135	+	0.323963i
$727$			27.7338i			1.02859i	0.857614	+	0.514295i	$0.171946\pi$
$727$			27.7338i			1.02859i	−0.857614	+	0.514295i	$0.828054\pi$
$728$	−16.5579	+	20.9828i	−0.613677	+	0.777675i
$729$	−12.1695	−	24.1019i	−0.450723	−	0.892664i
$730$	−35.8320	+	30.2014i	−1.32620	+	1.11780i
$731$	0.695503	+	0.401549i	0.0257241	+	0.0148518i
$732$	−1.18791	+	0.203423i	−0.0439065	+	0.00751875i
$733$	−24.4018	+	14.0884i	−0.901300	+	0.520366i	−0.877622	−	0.479354i	$-0.840871\pi$
$733$	−24.4018	+	14.0884i	−0.901300	+	0.520366i	−0.0236782	+	0.999720i	$0.507538\pi$
$734$	−11.7525	+	2.09898i	−0.433794	+	0.0774748i
$735$	−21.0780	+	39.8984i	−0.777475	+	1.47168i
$736$	−20.4303	−	16.7632i	−0.753069	−	0.617900i
$737$	22.6384	−	13.0703i	0.833897	−	0.481450i
$738$	1.25976	+	3.64699i	0.0463725	+	0.134248i
$739$	15.9133	−	27.5626i	0.585379	−	1.01391i	−0.409449	−	0.912333i	$-0.634279\pi$
$739$	15.9133	−	27.5626i	0.585379	−	1.01391i	0.994828	−	0.101573i	$-0.0323876\pi$
$740$	40.1795	−	48.3146i	1.47703	−	1.77608i
$741$	4.70459	+	13.3112i	0.172827	+	0.488998i
$742$	−4.14778	−	6.77650i	−0.152270	−	0.248773i
$743$	30.9943			1.13707			0.568535	−	0.822659i	$-0.307510\pi$
$743$	30.9943			1.13707			0.568535	+	0.822659i	$0.307510\pi$
$744$	−23.7315	−	4.25137i	−0.870039	−	0.155863i
$745$	27.4934	−	47.6200i	1.00728	−	1.74466i
$746$	−0.0435130	+	0.120375i	−0.00159313	+	0.00440725i
$747$	−1.87595	+	4.86924i	−0.0686375	+	0.178156i
$748$	−1.05721	+	0.390073i	−0.0386553	+	0.0142625i
$749$	20.8762	−	26.0988i	0.762800	−	0.953628i
$750$	17.3384	+	30.5320i	0.633109	+	1.11487i
$751$	32.0364	−	18.4962i	1.16902	−	0.674936i	0.215574	−	0.976488i	$-0.430838\pi$
$751$	32.0364	−	18.4962i	1.16902	−	0.674936i	0.953450	+	0.301551i	$0.0975045\pi$
$752$	0.855756	+	4.61516i	0.0312062	+	0.168297i
$753$	−36.2670	−	6.74460i	−1.32164	−	0.245787i
$754$	−8.37999	−	9.94234i	−0.305181	−	0.362079i
$755$			13.6974i			0.498501i
$756$	−25.8358	−	9.40793i	−0.939641	−	0.342163i
$757$		−	2.01191i		−	0.0731242i	−0.999331	−	0.0365621i	$-0.988359\pi$
$757$		−	2.01191i		−	0.0731242i	0.999331	−	0.0365621i	$-0.0116407\pi$
$758$	21.3978	−	18.0353i	0.777204	−	0.655073i
$759$	−20.8483	−	3.87716i	−0.756744	−	0.140732i
$760$	24.0220	−	0.158686i	0.871369	−	0.00575614i
$761$	−35.5006	+	20.4963i	−1.28689	+	0.742989i	−0.978099	−	0.208140i	$-0.933259\pi$
$761$	−35.5006	+	20.4963i	−1.28689	+	0.742989i	−0.308795	+	0.951129i	$0.599926\pi$
$762$	5.39090	−	3.06136i	0.195292	−	0.110901i
$763$	−33.9098	−	5.16233i	−1.22762	−	0.186889i
$764$	28.3884	−	10.4743i	1.02706	−	0.378948i
$765$	0.862994	−	2.24000i	0.0312016	−	0.0809873i
$766$	33.2102	+	12.0048i	1.19993	+	0.433750i
$767$	14.0064	−	24.2598i	0.505741	−	0.875970i
$768$	−21.0811	+	17.9886i	−0.760697	+	0.649107i
$769$	−46.8470			−1.68935			−0.844673	−	0.535282i	$-0.820205\pi$
$769$	−46.8470			−1.68935			−0.844673	+	0.535282i	$0.820205\pi$
$770$	32.0629	+	17.4304i	1.15547	+	0.628148i
$771$	−8.81723	−	24.9475i	−0.317545	−	0.898461i
$772$	4.70429	+	3.91219i	0.169311	+	0.140803i
$773$	−11.2358	+	19.4611i	−0.404125

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)

\(f(q)\)	\(=\)	\(q+(-1.08135 + 0.911422i) q^{2} +(-0.316681 + 1.70285i) q^{3} +(0.338619 - 1.97113i) q^{4} +(1.86088 + 3.22314i) q^{5} +(-1.20958 - 2.13001i) q^{6} +(2.46429 - 0.962962i) q^{7} +(1.43036 + 2.44009i) q^{8} +(-2.79943 - 1.07852i) q^{9} +O(q^{10})\)	\(q+(-1.08135 + 0.911422i) q^{2} +(-0.316681 + 1.70285i) q^{3} +(0.338619 - 1.97113i) q^{4} +(1.86088 + 3.22314i) q^{5} +(-1.20958 - 2.13001i) q^{6} +(2.46429 - 0.962962i) q^{7} +(1.43036 + 2.44009i) q^{8} +(-2.79943 - 1.07852i) q^{9} +(-4.94989 - 1.78928i) q^{10} +(-2.26958 - 1.31034i) q^{11} +(3.24931 + 1.20084i) q^{12} +3.57182i q^{13} +(-1.78708 + 3.28730i) q^{14} +(-6.07784 + 2.14810i) q^{15} +(-3.77067 - 1.33492i) q^{16} +(0.186192 + 0.107498i) q^{17} +(4.01014 - 1.38520i) q^{18} +(-1.14103 - 1.97631i) q^{19} +(6.98334 - 2.57661i) q^{20} +(0.859391 + 4.50127i) q^{21} +(3.64848 - 0.651612i) q^{22} +(-2.33586 - 4.04583i) q^{23} +(-4.60809 + 1.66297i) q^{24} +(-4.42574 + 7.66560i) q^{25} +(-3.25544 - 3.86238i) q^{26} +(2.72309 - 4.42547i) q^{27} +(-1.06366 - 5.18349i) q^{28} +2.57415 q^{29} +(4.61442 - 7.86231i) q^{30} +(4.26196 + 2.46064i) q^{31} +(5.29408 - 1.99316i) q^{32} +(2.95006 - 3.44980i) q^{33} +(-0.299314 + 0.0534570i) q^{34} +(7.68949 + 6.15077i) q^{35} +(-3.07384 + 5.15281i) q^{36} +(7.31104 - 4.22103i) q^{37} +(3.03510 + 1.09712i) q^{38} +(-6.08229 - 1.13113i) q^{39} +(-5.20302 + 9.15098i) q^{40} +0.909442i q^{41} +(-5.03186 - 4.08416i) q^{42} +3.73541 q^{43} +(-3.35137 + 4.02992i) q^{44} +(-1.73317 - 11.0299i) q^{45} +(6.21334 + 2.24599i) q^{46} +(-0.586728 - 1.01624i) q^{47} +(3.46728 - 5.99816i) q^{48} +(5.14541 - 4.74603i) q^{49} +(-2.20085 - 12.3229i) q^{50} +(-0.242017 + 0.283015i) q^{51} +(7.04051 + 1.20949i) q^{52} +(-1.06171 + 1.83894i) q^{53} +(1.08886 + 7.26735i) q^{54} -9.75355i q^{55} +(5.87454 + 4.63570i) q^{56} +(3.72672 - 1.31714i) q^{57} +(-2.78355 + 2.34614i) q^{58} +(-6.79199 - 3.92136i) q^{59} +(2.17610 + 12.7076i) q^{60} +(-0.301301 + 0.173956i) q^{61} +(-6.85134 + 1.22364i) q^{62} +(-7.93716 + 0.0379510i) q^{63} +(-3.90812 + 6.98044i) q^{64} +(-11.5125 + 6.64673i) q^{65} +(-0.0458036 + 6.41918i) q^{66} +(-4.98736 + 8.63836i) q^{67} +(0.274940 - 0.330607i) q^{68} +(7.62919 - 2.69640i) q^{69} +(-13.9210 + 0.357259i) q^{70} +10.0808 q^{71} +(-1.37250 - 8.37354i) q^{72} +(4.45173 - 7.71062i) q^{73} +(-4.05862 + 11.2278i) q^{74} +(-11.6519 - 9.96394i) q^{75} +(-4.28194 + 1.57989i) q^{76} +(-6.85470 - 1.04354i) q^{77} +(7.60800 - 4.32040i) q^{78} +(-9.70950 + 5.60578i) q^{79} +(-2.71413 - 14.6375i) q^{80} +(6.67358 + 6.03849i) q^{81} +(-0.828886 - 0.983422i) q^{82} -1.73937i q^{83} +(9.16358 - 0.169751i) q^{84} +0.800163i q^{85} +(-4.03927 + 3.40453i) q^{86} +(-0.815185 + 4.38341i) q^{87} +(-0.0489643 - 7.41226i) q^{88} +(15.4694 - 8.93127i) q^{89} +(11.9271 + 10.3475i) q^{90} +(3.43953 + 8.80199i) q^{91} +(-8.76581 + 3.23428i) q^{92} +(-5.53980 + 6.47826i) q^{93} +(1.56068 + 0.564153i) q^{94} +(4.24662 - 7.35536i) q^{95} +(1.71753 + 9.64625i) q^{96} -8.88553 q^{97} +(-1.23834 + 9.82174i) q^{98} +(4.94029 + 6.11600i) 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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