LMFDB - Embedded newform 168.2.v.a.11.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.23
Character	$\chi$	$=$	168.11
Dual form			168.2.v.a.107.23

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.08135 - 0.911422i) q^{2} +(-1.31637 + 1.12568i) q^{3} +(0.338619 - 1.97113i) q^{4} +(-1.86088 - 3.22314i) q^{5} +(-0.397486 + 2.41702i) q^{6} +(2.46429 - 0.962962i) q^{7} +(-1.43036 - 2.44009i) q^{8} +(0.465685 - 2.96364i) q^{9} +(-4.94989 - 1.78928i) q^{10} +(2.26958 + 1.31034i) q^{11} +(1.77311 + 2.97592i) 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} +(-2.19756 - 3.62915i) q^{18} +(-1.14103 - 1.97631i) q^{19} +(-6.98334 + 2.57661i) q^{20} +(-2.15994 + 4.04162i) q^{21} +(3.64848 - 0.651612i) q^{22} +(2.33586 + 4.04583i) q^{23} +(4.62966 + 1.60195i) 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} +(8.53007 - 3.21664i) q^{30} +(4.26196 + 2.46064i) q^{31} +(-5.29408 + 1.99316i) q^{32} +(-4.46265 + 0.829921i) q^{33} +(-0.299314 + 0.0534570i) q^{34} +(-7.68949 - 6.15077i) q^{35} +(-5.68401 - 1.92147i) q^{36} +(7.31104 - 4.22103i) q^{37} +(-3.03510 - 1.09712i) q^{38} +(-4.02073 - 4.70186i) q^{39} +(-5.20302 + 9.15098i) q^{40} -0.909442i q^{41} +(1.34798 + 6.33900i) q^{42} +3.73541 q^{43} +(3.35137 - 4.02992i) q^{44} +(-10.4188 + 4.01400i) q^{45} +(6.21334 + 2.24599i) q^{46} +(0.586728 + 1.01624i) q^{47} +(6.46632 - 2.48732i) q^{48} +(5.14541 - 4.74603i) q^{49} +(2.20085 + 12.3229i) q^{50} +(0.366107 - 0.0680851i) q^{51} +(7.04051 + 1.20949i) q^{52} +(1.06171 - 1.83894i) q^{53} +(6.97808 + 2.30358i) 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} +(6.29225 - 11.2528i) q^{60} +(-0.301301 + 0.173956i) q^{61} +(6.85134 - 1.22364i) q^{62} +(-1.70629 - 7.75168i) q^{63} +(-3.90812 + 6.98044i) q^{64} +(11.5125 - 6.64673i) q^{65} +(-4.06926 + 4.96479i) 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} +(-7.89765 + 3.10276i) q^{72} +(4.45173 - 7.71062i) q^{73} +(4.05862 - 11.2278i) q^{74} +(-2.80309 - 15.0728i) q^{75} +(-4.28194 + 1.57989i) q^{76} +(6.85470 + 1.04354i) q^{77} +(-8.63318 - 1.41975i) q^{78} +(-9.70950 + 5.60578i) q^{79} +(2.71413 + 14.6375i) q^{80} +(-8.56628 - 2.76024i) q^{81} +(-0.828886 - 0.983422i) q^{82} +1.73937i q^{83} +(7.23514 + 5.62607i) q^{84} +0.800163i q^{85} +(4.03927 - 3.40453i) q^{86} +(3.38855 - 2.89767i) q^{87} +(-0.0489643 - 7.41226i) q^{88} +(-15.4694 + 8.93127i) q^{89} +(-7.60786 + 13.8364i) q^{90} +(3.43953 + 8.80199i) q^{91} +(8.76581 - 3.23428i) q^{92} +(-8.38024 + 1.55848i) q^{93} +(1.56068 + 0.564153i) q^{94} +(-4.24662 + 7.35536i) q^{95} +(4.72533 - 8.58320i) 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} + 6 q^{10} + 10 q^{12} - 10 q^{16} - 10 q^{18} - 4 q^{19} - 20 q^{22} - 8 q^{24} - 16 q^{25} - 8 q^{27} - 22 q^{28} - 12 q^{30} - 14 q^{33} - 56 q^{34} + 4 q^{36}+ \cdots - 44 q^{99}+O(q^{100}) $ 56 * q - 2 * q^3 - 2 * q^4 - 8 * q^6 - 2 * q^9 + 6 * q^10 + 10 * q^12 - 10 * q^16 - 10 * q^18 - 4 * q^19 - 20 * q^22 - 8 * q^24 - 16 * q^25 - 8 * q^27 - 22 * q^28 - 12 * q^30 - 14 * q^33 - 56 * q^34 + 4 * q^36 + 14 * q^40 - 8 * q^42 - 16 * q^43 - 12 * q^46 + 64 * q^48 - 16 * q^49 - 34 * q^51 - 8 * q^52 + 32 * q^54 + 4 * q^57 - 18 * q^58 + 40 * q^60 + 4 * q^64 - 20 * q^66 - 36 * q^67 - 42 * q^70 + 22 * q^72 + 4 * q^73 + 104 * q^76 + 28 * q^78 - 10 * q^81 + 52 * q^82 + 4 * q^84 + 46 * q^88 + 140 * q^90 + 72 * q^91 - 46 * q^96 - 32 * q^97 - 44 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	1.08135	−	0.911422i	0.764627	−	0.644473i
$2$	1.08135	−	0.911422i	0.764627	−	0.644473i
$3$	−1.31637	+	1.12568i	−0.760009	+	0.649912i
$3$	−1.31637	+	1.12568i	−0.760009	+	0.649912i
$4$	0.338619	−	1.97113i	0.169310	−	0.985563i
$5$	−1.86088	−	3.22314i	−0.832210	−	1.44143i	−0.896282	−	0.443485i	$-0.853742\pi$
$5$	−1.86088	−	3.22314i	−0.832210	−	1.44143i	0.0640716	−	0.997945i	$-0.479591\pi$
$6$	−0.397486	+	2.41702i	−0.162273	+	0.986746i
$7$	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
$9$	0.465685	−	2.96364i	0.155228	−	0.987879i
$10$	−4.94989	−	1.78928i	−1.56529	−	0.565820i
$11$	2.26958	+	1.31034i	0.684304	+	0.395083i	0.801475	−	0.598029i	$-0.204049\pi$
$11$	2.26958	+	1.31034i	0.684304	+	0.395083i	−0.117171	+	0.993112i	$0.537382\pi$
$12$	1.77311	+	2.97592i	0.511853	+	0.859073i
$13$			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	0.477251	−	0.878767i	$-0.341633\pi$
$17$	−0.186192	−	0.107498i	−0.0451582	−	0.0260721i	−0.522409	+	0.852695i	$0.674967\pi$
$18$	−2.19756	−	3.62915i	−0.517969	−	0.855399i
$19$	−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
$21$	−2.15994	+	4.04162i	−0.471337	+	0.881953i
$22$	3.64848	−	0.651612i	0.777858	−	0.138924i
$23$	2.33586	+	4.04583i	0.487061	+	0.843615i	0.999889	−	0.0148767i	$-0.00473557\pi$
$23$	2.33586	+	4.04583i	0.487061	+	0.843615i	−0.512828	+	0.858491i	$0.671402\pi$
$24$	4.62966	+	1.60195i	0.945026	+	0.326996i
$25$	−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	$-0.576821\pi$
$29$	−2.57415			−0.478008			−0.239004	+	0.971019i	$0.576821\pi$
$30$	8.53007	−	3.21664i	1.55737	−	0.587275i
$31$	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
$33$	−4.46265	+	0.829921i	−0.776847	+	0.144471i
$34$	−0.299314	+	0.0534570i	−0.0513319	+	0.00916779i
$35$	−7.68949	−	6.15077i	−1.29976	−	1.03967i
$36$	−5.68401	−	1.92147i	−0.947335	−	0.320244i
$37$	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
$39$	−4.02073	−	4.70186i	−0.643832	−	0.752899i
$40$	−5.20302	+	9.15098i	−0.822670	+	1.44690i
$41$		−	0.909442i		−	0.142031i	−0.997475	−	0.0710155i	$-0.977376\pi$
$41$		−	0.909442i		−	0.142031i	0.997475	−	0.0710155i	$-0.0226240\pi$
$42$	1.34798	+	6.33900i	0.207998	+	0.978129i
$43$	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
$45$	−10.4188	+	4.01400i	−1.55314	+	0.598372i
$46$	6.21334	+	2.24599i	0.916107	+	0.331153i
$47$	0.586728	+	1.01624i	0.0855831	+	0.148234i	0.905640	−	0.424048i	$-0.139391\pi$
$47$	0.586728	+	1.01624i	0.0855831	+	0.148234i	−0.820056	+	0.572283i	$0.806058\pi$
$48$	6.46632	−	2.48732i	0.933332	−	0.359014i
$49$	5.14541	−	4.74603i	0.735058	−	0.678004i
$50$	2.20085	+	12.3229i	0.311247	+	1.74272i
$51$	0.366107	−	0.0680851i	0.0512652	−	0.00953383i
$52$	7.04051	+	1.20949i	0.976343	+	0.167726i
$53$	1.06171	−	1.83894i	0.145837	−	0.252598i	−0.783848	−	0.620953i	$-0.786746\pi$
$53$	1.06171	−	1.83894i	0.145837	−	0.252598i	0.929685	+	0.368355i	$0.120079\pi$
$54$	6.97808	+	2.30358i	0.949596	+	0.313477i
$55$		−	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	0.872055	−	0.489408i	$-0.162787\pi$
$59$	6.79199	+	3.92136i	0.884242	+	0.510517i	0.0121872	+	0.999926i	$0.496121\pi$
$60$	6.29225	−	11.2528i	0.812325	−	1.45273i
$61$	−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
$63$	−1.70629	−	7.75168i	−0.214972	−	0.976620i
$64$	−3.90812	+	6.98044i	−0.488515	+	0.872555i
$65$	11.5125	−	6.64673i	1.42795	−	0.824425i
$66$	−4.06926	+	4.96479i	−0.500891	+	0.611123i
$67$	−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	$-0.704111\pi$
$71$	−10.0808			−1.19637			−0.598183	+	0.801359i	$0.704111\pi$
$72$	−7.89765	+	3.10276i	−0.930747	+	0.365664i
$73$	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
$75$	−2.80309	−	15.0728i	−0.323673	−	1.74045i
$76$	−4.28194	+	1.57989i	−0.491172	+	0.181226i
$77$	6.85470	+	1.04354i	0.781166	+	0.118922i
$78$	−8.63318	−	1.41975i	−0.977515	−	0.160755i
$79$	−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
$81$	−8.56628	−	2.76024i	−0.951808	−	0.306693i
$82$	−0.828886	−	0.983422i	−0.0915351	−	0.108601i
$83$			1.73937i			0.190921i	0.995433	+	0.0954603i	$0.0304323\pi$
$83$			1.73937i			0.190921i	−0.995433	+	0.0954603i	$0.969568\pi$
$84$	7.23514	+	5.62607i	0.789419	+	0.613855i
$85$			0.800163i			0.0867898i
$86$	4.03927	−	3.40453i	0.435566	−	0.367120i
$87$	3.38855	−	2.89767i	0.363290	−	0.310663i
$88$	−0.0489643	−	7.41226i	−0.00521961	−	0.790149i
$89$	−15.4694	+	8.93127i	−1.63975	+	0.946712i	−0.658837	+	0.752286i	$0.728951\pi$
$89$	−15.4694	+	8.93127i	−1.63975	+	0.946712i	−0.980917	+	0.194426i	$0.937716\pi$
$90$	−7.60786	+	13.8364i	−0.801939	+	1.45849i
$91$	3.43953	+	8.80199i	0.360560	+	0.922699i
$92$	8.76581	−	3.23428i	0.913899	−	0.337197i
$93$	−8.38024	+	1.55848i	−0.868990	+	0.161607i
$94$	1.56068	+	0.564153i	0.160972	+	0.0581880i
$95$	−4.24662	+	7.35536i	−0.435694	+	0.754644i
$96$	4.72533	−	8.58320i	0.482277	−	0.876019i
$97$	−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	$-0.570490\pi$
$101$	7.38721	−	12.7950i	0.735055	−	1.27315i	0.954699	−	0.297573i	$-0.0961770\pi$
$102$	0.333834	−	0.407301i	0.0330545	−	0.0403289i
$103$	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
$105$	17.0461	−	0.559193i	1.66353	−	0.0545717i
$106$	−0.527972	−	2.95620i	−0.0512812	−	0.287131i
$107$	−10.9396	+	6.31597i	−1.05757	+	0.610588i	−0.924759	−	0.380554i	$-0.875733\pi$
$107$	−10.9396	+	6.31597i	−1.05757	+	0.610588i	−0.132810	+	0.991141i	$0.542400\pi$
$108$	9.64525	−	3.86901i	0.928114	−	0.372296i
$109$	−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	$0.108463\pi$
$113$			7.10498i			0.668380i	−0.942506	+	0.334190i	$0.891537\pi$
$114$	5.23034	−	1.97233i	0.489866	−	0.184726i
$115$	8.69351	−	15.0576i	0.810674	−	1.40413i
$116$	−0.871657	+	5.07398i	−0.0809313	+	0.471107i
$117$	10.5856	+	1.66334i	0.978637	+	0.153776i
$118$	10.9185	−	1.95003i	1.00513	−	0.179514i
$119$	−0.562347	−	0.0856100i	−0.0515502	−	0.00784786i
$120$	−3.45195	−	17.9031i	−0.315118	−	1.63432i
$121$	−2.06600	−	3.57842i	−0.187819	−	0.325311i
$122$	−0.167263	+	0.462719i	−0.0151433	+	0.0418926i
$123$	1.02374	+	1.19717i	0.0923077	+	0.107945i
$124$	6.29342	−	7.56764i	0.565166	−	0.679594i
$125$	14.3343			1.28210
$126$	−8.91014	−	6.82710i	−0.793779	−	0.608207i
$127$			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
$129$	−4.91720	+	4.20488i	−0.432935	+	0.370219i
$130$	6.39099	−	17.6801i	0.560527	−	1.55065i
$131$	5.04824	−	2.91460i	0.441067	−	0.254650i	−0.262983	−	0.964800i	$-0.584706\pi$
$131$	5.04824	−	2.91460i	0.441067	−	0.254650i	0.704050	+	0.710150i	$0.251373\pi$
$132$	0.124742	+	9.07746i	0.0108574	+	0.790092i
$133$	−4.71493	−	3.77144i	−0.408836	−	0.327025i
$134$	2.48013	+	13.8866i	0.214251	+	1.19962i
$135$	9.19654	−	17.0122i	0.791512	−	1.46417i
$136$	0.00401694	+	0.608087i	0.000344449	+	0.0521430i
$137$	8.15158	+	4.70632i	0.696437	+	0.402088i	0.806019	−	0.591890i	$-0.201618\pi$
$137$	8.15158	+	4.70632i	0.696437	+	0.402088i	−0.109582	+	0.993978i	$0.534951\pi$
$138$	−10.7073	+	4.03767i	−0.911470	+	0.343710i
$139$	−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
$144$	−5.71217	+	10.5533i	−0.476014	+	0.879438i
$145$	4.79018	+	8.29684i	0.397803	+	0.689015i
$146$	−2.21377	−	12.3953i	−0.183213	−	1.02584i
$147$	−1.43078	+	12.0396i	−0.118008	+	0.993013i
$148$	−5.84452	−	15.8403i	−0.480417	−	1.30206i
$149$	7.38721	+	12.7950i	0.605184	+	1.04821i	0.992022	+	0.126062i	$0.0402338\pi$
$149$	7.38721	+	12.7950i	0.605184	+	1.04821i	−0.386838	+	0.922148i	$0.626433\pi$
$150$	−16.7688	−	13.7441i	−1.36916	−	1.12220i
$151$	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
$156$	−10.6294	+	6.33323i	−0.851037	+	0.507064i
$157$	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
$159$	0.672448	+	3.61588i	0.0533286	+	0.286758i
$160$	16.2759	+	13.3545i	1.28672	+	1.05577i
$161$	9.65222	+	7.72074i	0.760701	+	0.608480i
$162$	−11.7789	+	4.82272i	−0.925434	+	0.378909i
$163$	−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
$165$	10.9794	+	12.8393i	0.854744	+	0.999541i
$166$	1.58530	+	1.88086i	0.123043	+	0.145983i
$167$	−7.21687			−0.558459			−0.279229	−	0.960224i	$-0.590079\pi$
$167$	−7.21687			−0.558459			−0.279229	+	0.960224i	$0.590079\pi$
$168$	12.9514	−	0.510535i	0.999224	−	0.0393886i
$169$	0.242090			0.0186223
$170$	0.729286	+	0.865253i	0.0559337	+	0.0663619i
$171$	−6.38844	+	2.46125i	−0.488536	+	0.188216i
$172$	1.26488	−	7.36296i	0.0964462	−	0.561420i
$173$	−1.33696	−	2.31567i	−0.101647	−	0.176057i	0.810716	−	0.585439i	$-0.199078\pi$
$173$	−1.33696	−	2.31567i	−0.101647	−	0.176057i	−0.912363	+	0.409382i	$0.865744\pi$
$174$	1.02319	−	6.22179i	0.0775678	−	0.471672i
$175$	−3.52460	+	23.1521i	−0.266435	+	1.75013i
$176$	−6.80864	−	7.97059i	−0.513221	−	0.600806i
$177$	−13.3550	+	2.48364i	−1.00382	+	0.186682i
$178$	−8.58763	+	23.7569i	−0.643670	+	1.78066i
$179$	7.29346	+	4.21088i	0.545139	+	0.314736i	0.747159	−	0.664645i	$-0.231417\pi$
$179$	7.29346	+	4.21088i	0.545139	+	0.314736i	−0.202020	+	0.979381i	$0.564751\pi$
$180$	4.38410	+	21.8960i	0.326772	+	1.63203i
$181$		−	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
$186$	−7.64151	+	9.32319i	−0.560303	+	0.683610i
$187$	−0.281718	−	0.487951i	−0.0206013	−	0.0356825i
$188$	2.20182	−	0.812396i	0.160584	−	0.0592500i
$189$	10.9720	+	8.28338i	0.798098	+	0.602527i
$190$	2.11177	+	11.8242i	0.153204	+	0.857815i
$191$	−7.56478	−	13.1026i	−0.547368	−	0.948069i	−0.998454	−	0.0555887i	$-0.982296\pi$
$191$	−7.56478	−	13.1026i	−0.547368	−	0.948069i	0.451086	−	0.892481i	$-0.351037\pi$
$192$	−2.71320	−	13.5882i	−0.195808	−	0.980642i
$193$	−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	$-0.326244\pi$
$197$	14.5736			1.03833			0.519163	+	0.854675i	$0.326244\pi$
$198$	−0.232100	−	11.1162i	−0.0164946	−	0.789994i
$199$	−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
$201$	−3.15880	−	16.9855i	−0.222805	−	1.19806i
$202$	−3.67354	−	20.5687i	−0.258469	−	1.44721i
$203$	−6.34345	+	2.47881i	−0.445223	+	0.173978i
$204$	−0.0102336	−	0.744698i	−0.000716494	−	0.0521393i
$205$	−2.93126	+	1.69236i	−0.204728	+	0.118200i
$206$	3.60922	−	9.98462i	0.251467	−	0.695661i
$207$	13.0782	−	5.03856i	0.908994	−	0.350204i
$208$	4.76810	−	13.4682i	0.330608	−	0.933850i
$209$		−	5.98054i		−	0.413683i
$210$	17.9230	−	16.1408i	1.23681	−	1.11382i
$211$	−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
$213$	13.2701	−	11.3477i	0.909250	−	0.777533i
$214$	−6.07296	+	16.8003i	−0.415139	+	1.14845i
$215$	−6.95114	−	12.0397i	−0.474064	−	0.821103i
$216$	6.90355	−	12.9746i	0.469727	−	0.882812i
$217$	12.8722	+	1.95963i	0.873822	+	0.133028i
$218$	−18.0488	+	3.22349i	−1.22242	+	0.218322i
$219$	2.81956	+	15.1613i	0.190528	+	1.02451i
$220$	−19.2255	−	3.30274i	−1.29618	−	0.222671i
$221$	0.383964	−	0.665045i	0.0258282	−	0.0447357i
$222$	7.29629	+	19.3488i	0.489695	+	1.29860i
$223$			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	0.991935	−	0.126749i	$-0.0404544\pi$
$227$	20.7637	+	11.9879i	1.37813	+	0.795666i	0.386199	+	0.922415i	$0.373788\pi$
$228$	3.85819	−	6.89982i	0.255515	−	0.456952i
$229$	−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
$231$	−10.1981	+	6.34252i	−0.670983	+	0.417307i
$232$	3.68197	+	6.28117i	0.241733	+	0.412379i
$233$	13.4061	−	7.74002i	0.878264	−	0.507066i	0.00817827	−	0.999967i	$-0.497397\pi$
$233$	13.4061	−	7.74002i	0.878264	−	0.507066i	0.870086	+	0.492901i	$0.164063\pi$
$234$	12.9627	−	7.84928i	0.847397	−	0.513124i
$235$	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	$-0.268642\pi$
$239$	20.5460			1.32901			0.664505	+	0.747284i	$0.268642\pi$
$240$	−20.0500	−	16.2132i	−1.29422	−	1.04656i
$241$	−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
$243$	14.3836	−	6.00938i	0.922707	−	0.385502i
$244$	0.240863	+	0.652807i	0.0154197	+	0.0417917i
$245$	−24.8721	−	7.75258i	−1.58902	−	0.495294i
$246$	2.19814	+	0.361491i	0.140149	+	0.0230478i
$247$	7.05904	−	4.07554i	0.449156	−	0.259320i
$248$	−0.0919482	−	13.9192i	−0.00583872	−	0.883870i
$249$	−1.95798	−	2.28966i	−0.124082	−	0.145101i
$250$	15.5003	−	13.0646i	0.980325	−	0.826275i
$251$		−	21.2978i		−	1.34430i	−0.740413	−	0.672152i	$-0.765370\pi$
$251$		−	21.2978i		−	1.34430i	0.740413	−	0.672152i	$-0.234630\pi$
$252$	−15.8573	+	0.738440i	−0.998917	+	0.0465173i
$253$			12.2431i			0.769719i
$254$	2.30675	+	2.73681i	0.144738	+	0.171723i
$255$	−0.900728	−	1.05331i	−0.0564058	−	0.0659611i
$256$	12.4360	+	10.0671i	0.777248	+	0.629194i
$257$	13.2299	−	7.63828i	0.825258	−	0.476463i	−0.0269684	−	0.999636i	$-0.508585\pi$
$257$	13.2299	−	7.63828i	0.825258	−	0.476463i	0.852226	+	0.523173i	$0.175252\pi$
$258$	−1.48477	+	9.02857i	−0.0924379	+	0.562094i
$259$	13.9518	−	17.4421i	0.866922	−	1.08380i
$260$	−9.20319	−	24.9432i	−0.570758	−	1.54691i
$261$	−1.19874	+	7.62885i	−0.0742003	+	0.472214i
$262$	2.80246	−	7.75278i	0.173137	−	0.478968i
$263$	−0.249921	+	0.432876i	−0.0154108	+	0.0266923i	−0.873628	−	0.486594i	$-0.838239\pi$
$263$	−0.249921	+	0.432876i	−0.0154108	+	0.0266923i	0.858217	+	0.513287i	$0.171572\pi$
$264$	8.40829	+	9.70219i	0.517494	+	0.597128i
$265$	−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	$0.398597\pi$
$269$	−10.9207	+	18.9153i	−0.665849	+	1.15328i	−0.979054	+	0.203599i	$0.934736\pi$
$270$	−5.56062	−	26.7780i	−0.338408	−	1.62965i
$271$	−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
$273$	−14.4359	−	7.71491i	−0.873703	−	0.466927i
$274$	13.1041	−	2.34037i	0.791649	−	0.141387i
$275$	−20.0891	+	11.5985i	−1.21142	+	0.699414i
$276$	−7.89833	+	14.1250i	−0.475423	+	0.850227i
$277$	−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	$0.237418\pi$
$281$			22.7512i			1.35722i	−0.734498	+	0.678610i	$0.762582\pi$
$282$	−2.68950	+	1.01419i	−0.160157	+	0.0603943i
$283$	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
$285$	−2.68965	−	14.4628i	−0.159321	−	0.856700i
$286$	2.32744	+	13.0317i	0.137624	+	0.770581i
$287$	−0.875758	−	2.24113i	−0.0516944	−	0.132289i
$288$	3.44164	+	16.6179i	0.202800	+	0.979220i
$289$	−8.47689	−	14.6824i	−0.498640	−	0.863671i
$290$	12.7418	+	4.60588i	0.748223	+	0.270466i
$291$	11.6967	−	10.0023i	0.685672	−	0.586343i
$292$	−13.6912	−	11.3859i	−0.801215	−	0.666309i
$293$	−22.1280			−1.29273			−0.646366	−	0.763028i	$-0.723712\pi$
$293$	−22.1280			−1.29273			−0.646366	+	0.763028i	$0.723712\pi$
$294$	9.42603	+	14.3231i	0.549737	+	0.835338i
$295$		−	29.1887i		−	1.69943i
$296$	−20.7571	−	11.8020i	−1.20648	−	0.685978i
$297$	0.381399	+	13.6121i	0.0221310	+	0.789856i
$298$	19.6498	+	7.10298i	1.13828	+	0.411465i
$299$	−14.4510	+	8.34329i	−0.835723	+	0.482505i
$300$	−30.6595	+	0.421321i	−1.77013	+	0.0243250i
$301$	9.20511	−	3.59705i	0.530574	−	0.207331i
$302$	5.12375	−	0.915093i	0.294839	−	0.0526577i
$303$	4.67878	+	25.1587i	0.268789	+	1.44533i
$304$	1.66421	+	8.97522i	0.0954490	+	0.514764i
$305$	1.12137	+	0.647422i	0.0642094	+	0.0370713i
$306$	0.0190410	+	0.911952i	0.00108850	+	0.0521328i
$307$	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	−0.983091	−	0.183115i	$-0.941382\pi$
$311$	−5.87187	+	10.1704i	−0.332963	+	0.576709i	0.650128	+	0.759825i	$0.274715\pi$
$312$	−5.72186	+	16.5363i	−0.323937	+	0.936185i
$313$	−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
$315$	−21.8095	+	19.9245i	−1.22883	+	1.12262i
$316$	7.76188	+	21.0369i	0.436640	+	1.18342i
$317$	−16.4535	−	28.4983i	−0.924120	−	1.60062i	−0.792970	−	0.609261i	$-0.791466\pi$
$317$	−16.4535	−	28.4983i	−0.924120	−	1.60062i	−0.131150	−	0.991363i	$-0.541867\pi$
$318$	4.02275	+	3.29714i	0.225584	+	0.184894i
$319$	−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
$324$	−8.34148	+	15.9505i	−0.463416	+	0.886141i
$325$	−27.3802	−	15.8079i	−1.51878	−	0.876867i
$326$	−2.01172	−	0.727195i	−0.111419	−	0.0402756i
$327$	22.0765	−	4.10557i	1.22083	−	0.227039i
$328$	−2.21913	+	1.30083i	−0.122531	+	0.0718265i
$329$	2.42447	+	1.93932i	0.133665	+	0.106918i
$330$	23.5746	+	3.87690i	1.29774	+	0.213416i
$331$	−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
$333$	−9.10496	−	23.6329i	−0.498948	−	1.29508i
$334$	−7.80394	+	6.57762i	−0.427013	+	0.359911i
$335$	37.1235			2.02827
$336$	13.5397	−	12.3563i	0.738649	−	0.674090i
$337$	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
$339$	−7.99794	−	9.35281i	−0.434388	−	0.507975i
$340$	1.57722	+	0.270950i	0.0855368	+	0.0146944i
$341$	6.44858	+	11.1693i	0.349210	+	0.604849i
$342$	−4.66488	+	8.48402i	−0.252248	+	0.458763i
$343$	8.10952	−	16.6504i	0.437873	−	0.899037i
$344$	−5.34299	−	9.11475i	−0.288075	−	0.491434i
$345$	5.50614	+	29.6076i	0.296441	+	1.59402i
$346$	−3.55627	−	1.28551i	−0.191186	−	0.0691097i
$347$	−4.59168	−	2.65101i	−0.246494	−	0.142313i	0.371664	−	0.928367i	$-0.378787\pi$
$347$	−4.59168	−	2.65101i	−0.246494	−	0.142313i	−0.618158	+	0.786054i	$0.712121\pi$
$348$	−4.56425	−	7.66046i	−0.244670	−	0.410644i
$349$			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	−0.326089	−	0.945339i	$-0.605731\pi$
$353$	−24.5717	−	14.1865i	−1.30782	−	0.755071i	−0.981732	+	0.190268i	$0.939064\pi$
$354$	−12.1777	+	14.8577i	−0.647239	+	0.789679i
$355$	18.7591	+	32.4917i	0.995628	+	1.72448i
$356$	12.3664	+	33.5164i	0.655418	+	1.77637i
$357$	0.836628	−	0.520328i	0.0442791	−	0.0275387i
$358$	11.7247	−	2.09400i	0.619667	−	0.110671i
$359$	0.0586851	+	0.101646i	0.00309728	+	0.00536465i	0.867570	−	0.497315i	$-0.165681\pi$
$359$	0.0586851	+	0.101646i	0.00309728	+	0.00536465i	−0.864473	+	0.502680i	$0.832347\pi$
$360$	24.6972	+	19.6813i	1.30166	+	1.03730i
$361$	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
$366$	−0.300693	−	0.797396i	−0.0157175	−	0.0416806i
$367$	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
$369$	−2.69526	−	0.423513i	−0.140309	−	0.0220472i
$370$	−43.7414	+	7.81215i	−2.27401	+	0.406134i
$371$	0.845534	−	5.55406i	0.0438980	−	0.288353i
$372$	0.234248	+	17.0462i	0.0121452	+	0.883806i
$373$	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
$375$	−18.8693	+	16.1358i	−0.974404	+	0.833249i
$376$	1.64049	−	2.88527i	0.0846020	−	0.148796i
$377$		−	9.19441i		−	0.473536i
$378$	19.4142	−	1.04295i	0.998560	−	0.0536437i
$379$	−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
$381$	−2.84902	−	3.33165i	−0.145960	−	0.170686i
$382$	−20.1221	−	7.27372i	−1.02954	−	0.372156i
$383$	12.4851	+	21.6249i	0.637961	+	1.10498i	0.985880	+	0.167456i	$0.0535551\pi$
$383$	12.4851	+	21.6249i	0.637961	+	1.10498i	−0.347919	+	0.937525i	$0.613112\pi$
$384$	−15.3185	−	12.2207i	−0.781718	−	0.623633i
$385$	−9.39230	−	24.0355i	−0.478676	−	1.22496i
$386$	0.760653	+	4.25902i	0.0387162	+	0.216778i
$387$	1.73952	−	11.0704i	0.0884249	−	0.562739i
$388$	−3.00881	+	17.5145i	−0.152749	+	0.889164i
$389$	−15.0483	+	26.0644i	−0.762979	+	1.32152i	0.178329	+	0.983971i	$0.442931\pi$
$389$	−15.0483	+	26.0644i	−0.762979	+	1.32152i	−0.941308	+	0.337548i	$0.890403\pi$
$390$	11.4893	+	30.4679i	0.581781	+	1.54280i
$391$		−	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
$396$	−10.3825	−	11.8089i	−0.521742	−	0.593421i
$397$	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
$399$	10.4521	−	0.342878i	0.523257	−	0.0171654i
$400$	26.9210	−	22.9965i	1.34605	−	1.14982i
$401$	0.897563	−	0.518208i	0.0448222	−	0.0258781i	−0.477421	−	0.878674i	$-0.658428\pi$
$401$	0.897563	−	0.518208i	0.0448222	−	0.0258781i	0.522244	+	0.852796i	$0.325095\pi$
$402$	−18.8967	−	15.4882i	−0.942482	−	0.772481i
$403$	−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
$408$	−0.689800	−	0.795949i	−0.0341502	−	0.0394053i
$409$	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
$411$	−16.0284	+	2.98080i	−0.790620	+	0.147032i
$412$	−5.19738	−	14.0864i	−0.256056	−	0.693985i
$413$	20.5135	+	3.12292i	1.00940	+	0.153669i
$414$	9.54975	−	17.3682i	0.469345	−	0.853598i
$415$	5.60623	−	3.23676i	0.275199	−	0.158886i
$416$	−7.11922	−	18.9095i	−0.349049	−	0.927115i
$417$	9.92453	−	8.48684i	0.486006	−	0.415602i
$418$	−5.45080	−	6.46703i	−0.266607	−	0.316313i
$419$		−	9.81445i		−	0.479467i	−0.970839	−	0.239734i	$-0.922940\pi$
$419$		−	9.81445i		−	0.479467i	0.970839	−	0.239734i	$-0.0770601\pi$
$420$	4.66988	−	33.7893i	0.227867	−	1.64875i
$421$		−	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
$423$	3.28500	−	1.26560i	0.159722	−	0.0615356i
$424$	−6.00582	+	0.0396736i	−0.291668	+	0.00192672i
$425$	1.64807	−	0.951516i	0.0799433	−	0.0461553i
$426$	4.00696	−	24.3654i	0.194138	−	1.18051i
$427$	−0.574978	+	0.718819i	−0.0278252	+	0.0347861i
$428$	8.74522	+	23.7020i	0.422716	+	1.14568i
$429$	−2.96433	−	15.9398i	−0.143119	−	0.769580i
$430$	−18.4899	−	6.68369i	−0.891660	−	0.322316i
$431$	5.27304	−	9.13317i	0.253993	−	0.439929i	−0.710628	−	0.703568i	$-0.751589\pi$
$431$	5.27304	−	9.13317i	0.253993	−	0.439929i	0.964622	+	0.263638i	$0.0849226\pi$
$432$	−4.36024	−	20.3221i	−0.209782	−	0.977748i
$433$	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
$438$	16.8673	+	13.8248i	0.805949	+	0.660575i
$439$	−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
$441$	−11.6694	−	17.4593i	−0.555684	−	0.831394i
$442$	−0.190939	−	1.06910i	−0.00908203	−	0.0508517i
$443$	0.202164	−	0.116720i	0.00960512	−	0.00554552i	−0.495190	−	0.868785i	$-0.664901\pi$
$443$	0.202164	−	0.116720i	0.00960512	−	0.00554552i	0.504795	+	0.863239i	$0.331568\pi$
$444$	25.5247	+	14.2727i	1.21135	+	0.677352i
$445$	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	$-0.956001\pi$
$449$		−	5.83932i		−	0.275575i	0.990462	−	0.137787i	$-0.0439990\pi$
$450$	37.5454	−	0.783927i	1.76991	−	0.0369547i
$451$	1.19168	−	2.06405i	0.0561141	−	0.0971924i
$452$	14.0048	+	2.40588i	0.658731	+	0.113163i
$453$	−6.26713	+	1.16550i	−0.294456	+	0.0547601i
$454$	33.3788	−	5.96139i	1.56654	−	0.279782i
$455$	21.9695	−	27.4655i	1.02994	−	1.28760i
$456$	−2.11661	−	10.9775i	−0.0991196	−	0.514070i
$457$	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
$459$	−0.0312892	−	1.11671i	−0.00146046	−	0.0521237i
$460$	−26.7367	−	22.2348i	−1.24660	−	1.03670i
$461$	0.400330			0.0186452			0.00932262	−	0.999957i	$-0.497032\pi$
$461$	0.400330			0.0186452			0.00932262	+	0.999957i	$0.497032\pi$
$462$	−5.24691	+	16.1532i	−0.244108	+	0.751514i
$463$			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
$465$	20.6178	+	24.1105i	0.956127	+	1.11810i
$466$	7.44222	−	20.5883i	0.344754	−	0.953734i
$467$	6.75074	−	3.89754i	0.312387	−	0.180357i	−0.335607	−	0.942002i	$-0.608941\pi$
$467$	6.75074	−	3.89754i	0.312387	−	0.180357i	0.647994	+	0.761645i	$0.275608\pi$
$468$	6.86314	−	20.3023i	0.317249	−	0.938473i
$469$	−3.97187	+	26.0900i	−0.183404	+	1.20472i
$470$	−1.08590	−	6.08011i	−0.0500887	−	0.280455i
$471$	−36.5708	+	6.80110i	−1.68509	+	0.313378i
$472$	−0.146531	−	22.1821i	−0.00674466	−	1.02101i
$473$	8.47781	+	4.89466i	0.389810	+	0.225057i
$474$	−9.68992	−	25.6963i	−0.445073	−	1.18027i
$475$	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	$-0.488333\pi$
$479$	19.3422	−	33.5016i	0.883765	−	1.53073i	0.847122	−	0.531398i	$-0.178333\pi$
$480$	−36.4581	+	0.741908i	−1.66408	+	0.0338633i
$481$	15.0768	+	26.1137i	0.687441	+	1.19068i
$482$	3.06658	+	17.1703i	0.139679	+	0.782085i
$483$	−21.3970	+	0.701926i	−0.973598	+	0.0319387i
$484$	−7.75311	+	2.86063i	−0.352414	+	0.130029i
$485$	16.5349	+	28.6393i	0.750811	+	1.30044i
$486$	10.0765	−	19.6077i	0.457081	−	0.889425i
$487$	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	$0.113792\pi$
$491$			15.5075i			0.699845i	−0.936779	+	0.349923i	$0.886208\pi$
$492$	2.70643	−	1.61254i	0.122015	−	0.0726989i
$493$	0.479286	+	0.276716i	0.0215860	+	0.0124627i
$494$	3.91873	−	10.8408i	0.176312	−	0.487752i
$495$	−28.9060	−	4.54208i	−1.29923	−	0.204151i
$496$	−12.7857	−	14.9677i	−0.574095	−	0.672068i
$497$	−24.8419	+	9.70739i	−1.11431	+	0.435436i
$498$	−4.20410	−	0.691375i	−0.188390	−	0.0309813i
$499$	−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
$501$	9.50011	−	8.12390i	0.424434	−	0.362949i
$502$	−19.4113	−	23.0303i	−0.866368	−	1.02789i
$503$	−32.2097			−1.43616			−0.718079	−	0.695962i	$-0.754978\pi$
$503$	−32.2097			−1.43616			−0.718079	+	0.695962i	$0.754978\pi$
$504$	−16.4742	+	15.2512i	−0.733820	+	0.679344i
$505$	−54.9868			−2.44688
$506$	11.1587	+	13.2391i	0.496063	+	0.588548i
$507$	−0.318681	+	0.272516i	−0.0141531	+	0.0121028i
$508$	4.98879	+	0.857022i	0.221342	+	0.0380242i
$509$	0.906135	+	1.56947i	0.0401637	+	0.0695656i	0.885408	−	0.464814i	$-0.153879\pi$
$509$	0.906135	+	1.56947i	0.0401637	+	0.0695656i	−0.845245	+	0.534379i	$0.820545\pi$
$510$	−1.93401	−	0.318054i	−0.0856395	−	0.0140836i
$511$	3.54530	−	23.2880i	0.156835	−	1.03020i
$512$	22.6230	−	0.448384i	0.999804	−	0.0198160i
$513$	5.63900	−	10.4313i	0.248968	−	0.460551i
$514$	7.34439	−	20.3176i	0.323947	−	0.896173i
$515$	−24.1970	−	13.9702i	−1.06625	−	0.615599i
$516$	6.62329	+	11.1163i	0.291574	+	0.489366i
$517$			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	0.347070	−	0.937839i	$-0.387177\pi$
$521$	−6.65560	−	3.84261i	−0.291587	−	0.168348i	−0.638657	+	0.769491i	$0.720510\pi$
$522$	5.65685	+	9.34199i	0.247593	+	0.408888i
$523$	−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
$525$	−21.4221	−	34.4444i	−0.934938	−	1.50327i
$526$	0.124281	+	0.695872i	0.00541893	+	0.0303415i
$527$	−0.529029	−	0.916305i	−0.0230449	−	0.0399149i
$528$	17.9351	+	2.82792i	0.780523	+	0.123069i
$529$	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
$534$	−15.4382	−	40.9400i	−0.668077	−	1.77165i
$535$	40.7145	+	23.5065i	1.76024	+	1.01627i
$536$	28.2121	−	0.186365i	1.21858	−	0.00804975i
$537$	−14.3410	+	2.66701i	−0.618862	+	0.115090i
$538$	5.43070	+	30.4074i	0.234134	+	1.31095i
$539$	17.8968	−	4.02924i	0.770871	−	0.173551i
$540$	−30.4190	−	23.8882i	−1.30902	−	1.02798i
$541$	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
$543$	6.89236	+	8.05995i	0.295779	+	0.345885i
$544$	1.19998	+	0.197992i	0.0514486	+	0.00848884i
$545$			48.2503i			2.06681i
$546$	−22.6418	+	4.81475i	−0.968979	+	0.206052i
$547$	−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
$549$	0.375231	+	0.973955i	0.0160145	+	0.0415674i
$550$	−11.1522	+	30.8516i	−0.475532	+	1.31552i
$551$	2.93717	+	5.08733i	0.125128	+	0.216728i
$552$	4.33305	+	22.4728i	0.184427	+	0.956504i
$553$	−18.5288	+	23.1641i	−0.787926	+	0.985039i
$554$	−17.4696	+	3.12004i	−0.742212	+	0.132558i
$555$	53.5025	−	9.94989i	2.27105	−	0.422349i
$556$	−2.55295	+	14.8609i	−0.108269	+	0.630242i
$557$	7.71096	−	13.3558i	0.326724	−	0.565902i	−0.655136	−	0.755511i	$-0.727389\pi$
$557$	7.71096	−	13.3558i	0.326724	−	0.565902i	0.981860	+	0.189609i	$0.0607220\pi$
$558$	−0.435852	−	20.8747i	−0.0184511	−	0.883697i
$559$			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	0.236151	−	0.971716i	$-0.424114\pi$
$563$	−11.5626	−	6.67567i	−0.487305	−	0.281346i	−0.723456	+	0.690371i	$0.757447\pi$
$564$	−1.98392	+	3.54796i	−0.0835382	+	0.149396i
$565$	22.9003	−	13.2215i	0.963423	−	0.556233i
$566$	−0.218993	−	1.22618i	−0.00920497	−	0.0515401i
$567$	−23.7678	+	1.44698i	−0.998152	+	0.0607673i
$568$	14.4192	+	24.5980i	0.605014	+	1.03211i
$569$	39.4279	−	22.7637i	1.65290	−	0.954305i	0.677034	−	0.735951i	$-0.263265\pi$
$569$	39.4279	−	22.7637i	1.65290	−	0.954305i	0.975870	−	0.218353i	$-0.0700685\pi$
$570$	−16.0901	−	13.1878i	−0.673941	−	0.552378i
$571$	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
$576$	18.8675	+	14.8329i	0.786147	+	0.618039i
$577$	−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
$579$	−0.968801	−	5.20943i	−0.0402620	−	0.216496i
$580$	17.9762	−	6.63259i	0.746420	−	0.275403i
$581$	1.67495	+	4.28630i	0.0694885	+	0.177826i
$582$	3.53187	−	21.4765i	0.146401	−	0.890231i
$583$	4.81928	−	2.78241i	0.199594	−	0.115236i
$584$	−25.1822	+	0.166350i	−1.04205	+	0.00688362i
$585$	−14.3373	−	37.2140i	−0.592774	−	1.53861i
$586$	−23.9280	+	20.1679i	−0.988458	+	0.833130i
$587$			28.5925i			1.18014i	0.807352	+	0.590070i	$0.200900\pi$
$587$			28.5925i			1.18014i	−0.807352	+	0.590070i	$0.799100\pi$
$588$	23.2472	+	6.89709i	0.958696	+	0.284431i
$589$		−	11.2306i		−	0.462750i
$590$	−26.6032	−	31.5631i	−1.09524	−	1.29943i
$591$	−19.1843	+	16.4052i	−0.789137	+	0.674821i
$592$	−33.2023	+	6.15646i	−1.36461	+	0.253029i
$593$	4.49943	−	2.59775i	0.184770	−	0.106677i	−0.404762	−	0.914422i	$-0.632646\pi$
$593$	4.49943	−	2.59775i	0.184770	−	0.106677i	0.589532	+	0.807745i	$0.299312\pi$
$594$	12.8188	+	14.3718i	0.525963	+	0.589683i
$595$	0.770526	+	1.97183i	0.0315885	+	0.0808371i
$596$	27.7221	−	10.2285i	1.13554	−	0.418975i
$597$	29.5702	−	5.49920i	1.21023	−	0.225067i
$598$	−8.02227	+	22.1929i	−0.328055	+	0.907537i
$599$	22.7140	−	39.3418i	0.928069	−	1.60746i	0.141519	−	0.989936i	$-0.454801\pi$
$599$	22.7140	−	39.3418i	0.928069	−	1.60746i	0.786550	−	0.617527i	$-0.211865\pi$
$600$	−32.7696	+	28.3994i	−1.33781	+	1.15940i
$601$	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
$606$	27.9896	+	22.9409i	1.13700	+	0.931911i
$607$	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
$609$	5.56000	−	10.4037i	0.225303	−	0.421581i
$610$	1.80266	−	0.321952i	0.0729877	−	0.0130355i
$611$	−3.62984	+	2.09569i	−0.146848	+	0.0847825i
$612$	0.851763	+	0.968781i	0.0344305	+	0.0391607i
$613$	−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	$-0.888906\pi$
$617$		−	16.9888i		−	0.683941i	0.939711	−	0.341971i	$-0.111094\pi$
$618$	6.48840	+	17.2063i	0.261002	+	0.692140i
$619$	−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
$621$	−11.5439	+	21.3545i	−0.463242	+	0.856925i
$622$	2.91998	+	16.3495i	0.117081	+	0.655554i
$623$	−29.5206	+	36.9056i	−1.18272	+	1.47859i
$624$	8.88426	+	23.0965i	0.355655	+	0.924601i
$625$	−4.54562	−	7.87325i	−0.181825	−	0.314930i
$626$	−0.913754	−	0.330302i	−0.0365209	−	0.0132015i
$627$	6.73218	+	7.87263i	0.268857	+	0.314403i
$628$	27.4641	−	33.0247i	1.09594	−	1.31783i
$629$	−1.81501			−0.0723691
$630$	−5.42399	+	41.4230i	−0.216097	+	1.65033i
$631$		−	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
$633$	27.9975	−	23.9417i	1.11280	−	0.951597i
$634$	−43.7659	−	15.8204i	−1.73817	−	0.628310i
$635$	8.15754	−	4.70976i	0.323722	−	0.186901i
$636$	7.35507	−	0.101073i	0.291647	−	0.00400780i
$637$	16.9520	+	18.3785i	0.671661	+	0.728182i
$638$	−9.39173	+	1.67735i	−0.371822	+	0.0664068i
$639$	−4.69446	+	29.8757i	−0.185710	+	1.18186i
$640$	31.8347	−	27.5597i	1.25838	−	1.08939i
$641$	−22.9318	−	13.2397i	−0.905752	−	0.522936i	−0.0266904	−	0.999644i	$-0.508497\pi$
$641$	−22.9318	−	13.2397i	−0.905752	−	0.522936i	−0.879062	+	0.476707i	$0.841830\pi$
$642$	−10.9175	−	28.9517i	−0.430880	−	1.14263i
$643$	−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	−0.988413	−	0.151789i	$-0.951497\pi$
$647$	−9.22707	+	15.9817i	−0.362753	+	0.628307i	0.625659	+	0.780096i	$0.284830\pi$
$648$	5.51764	+	24.8507i	0.216753	+	0.976226i
$649$	10.2766	+	17.7997i	0.403394	+	0.698698i
$650$	−44.0152	+	7.86103i	−1.72642	+	0.308335i
$651$	−19.1505	+	11.9104i	−0.750569	+	0.466805i
$652$	−2.83815	+	1.04718i	−0.111151	+	0.0410107i
$653$	8.95898	+	15.5174i	0.350592	+	0.607243i	0.986353	−	0.164643i	$-0.0526470\pi$
$653$	8.95898	+	15.5174i	0.350592	+	0.607243i	−0.635761	+	0.771886i	$0.719314\pi$
$654$	20.1304	−	24.5605i	0.787160	−	0.960392i
$655$	−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	$0.204211\pi$
$659$			30.7250i			1.19687i	−0.801170	+	0.598437i	$0.795789\pi$
$660$	29.0258	−	17.2941i	1.12983	−	0.673173i
$661$	−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
$663$	0.243188	+	1.30767i	0.00944464	+	0.0507856i
$664$	4.24423	−	2.48793i	0.164708	−	0.0965504i
$665$	−3.38195	+	22.2151i	−0.131147	+	0.861463i
$666$	−31.3852	−	17.2569i	−1.21615	−	0.668692i
$667$	−6.01287	−	10.4146i	−0.232819	−	0.403254i
$668$	−2.44377	+	14.2254i	−0.0945524	+	0.550396i
$669$	−7.52842	−	8.80376i	−0.291066	−	0.340373i
$670$	40.1433	−	33.8352i	1.55087	−	1.30717i
$671$	−0.911768			−0.0351984
$672$	3.37927	−	25.7018i	0.130358	−	0.991467i
$673$	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
$675$	−45.9756	+	1.28819i	−1.76960	+	0.0495825i
$676$	0.0819762	−	0.477189i	0.00315293	−	0.0183534i
$677$	−5.13682	−	8.89723i	−0.197424	−	0.341948i	0.750268	−	0.661133i	$-0.229924\pi$
$677$	−5.13682	−	8.89723i	−0.197424	−	0.341948i	−0.947692	+	0.319185i	$0.896591\pi$
$678$	−17.1729	−	2.82413i	−0.659521	−	0.108460i
$679$	−21.8965	+	8.55642i	−0.840310	+	0.328365i
$680$	1.95247	−	1.14452i	0.0748739	−	0.0438905i
$681$	−40.8274	+	7.59269i	−1.56451	+	0.290953i
$682$	17.1531	+	6.20046i	0.656824	+	0.237428i
$683$	−30.7725	−	17.7665i	−1.17748	−	0.679817i	−0.222048	−	0.975036i	$-0.571274\pi$
$683$	−30.7725	−	17.7665i	−1.17748	−	0.679817i	−0.955430	+	0.295218i	$0.904608\pi$
$684$	2.68818	+	13.4258i	0.102785	+	0.513350i
$685$		−	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
$690$	32.9391	+	26.9976i	1.25397	+	1.02778i
$691$	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
$693$	6.28480	−	19.8289i	0.238740	−	0.753237i
$694$	−7.38138	+	1.31830i	−0.280193	+	0.0500420i
$695$	14.0297	+	24.3002i	0.532177	+	0.921758i
$696$	−11.9175	−	4.12365i	−0.451730	−	0.156307i
$697$	−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	$-0.201937\pi$
$701$	42.6496			1.61085			0.805426	+	0.592696i	$0.201937\pi$
$702$	−8.22796	+	24.9244i	−0.310544	+	0.940712i
$703$	−16.6842	−	9.63261i	−0.629255	−	0.363301i
$704$	−18.0166	+	10.7217i	−0.679025	+	0.404089i
$705$	1.38305	+	7.43691i	0.0520886	+	0.280090i
$706$	−39.5004	+	7.05471i	−1.48662	+	0.265507i
$707$	5.88308	−	38.6442i	0.221256	−	1.45336i
$708$	0.373305	+	27.1654i	0.0140297	+	1.02094i
$709$	−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
$711$	12.0919	+	31.3860i	0.453483	+	1.17707i
$712$	43.9200	+	24.9719i	1.64597	+	0.935860i
$713$			22.9909i			0.861017i
$714$	0.430446	−	1.32518i	0.0161091	−	0.0495935i
$715$	34.8380			1.30287
$716$	10.7699	−	12.9504i	0.402490	−	0.483981i
$717$	−27.0462	+	23.1282i	−1.01006	+	0.863740i
$718$	0.156101	+	0.0564272i	0.00582564	+	0.00210584i
$719$	−25.0072	−	43.3138i	−0.932612	−	1.61533i	−0.778837	−	0.627226i	$-0.784190\pi$
$719$	−25.0072	−	43.3138i	−0.932612	−	1.61533i	−0.153775	−	0.988106i	$-0.549143\pi$
$720$	44.6442	−	1.22723i	1.66379	−	0.0457361i
$721$	12.4070	−	15.5108i	0.462059	−	0.577651i
$722$	−3.42933	−	19.2013i	−0.127626	−	0.714600i
$723$	−3.90573	−	21.0019i	−0.145256	−	0.781068i
$724$	−12.0689	−	2.07331i	−0.448536	−	0.0770539i
$725$	11.3925	−	19.7324i	0.423108	−	0.732844i
$726$	9.47035	−	3.57121i	0.351478	−	0.132540i
$727$			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
$732$	−1.05192	−	0.588203i	−0.0388800	−	0.0217406i
$733$	−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
$735$	41.4679	−	17.7927i	1.52957	−	0.656294i
$736$	−20.4303	−	16.7632i	−0.753069	−	0.617900i
$737$	−22.6384	+	13.0703i	−0.833897	+	0.481450i
$738$	−3.30050	+	1.99855i	−0.121493	+	0.0735677i
$739$	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	$-0.692490\pi$
$743$	−30.9943			−1.13707			−0.568535	+	0.822659i	$0.692490\pi$
$744$	15.7896	+	18.2194i	0.578876	+	0.667955i
$745$	27.4934	−	47.6200i	1.00728	−	1.74466i
$746$	0.0435130	−	0.120375i	0.00159313	−	0.00440725i
$747$	5.15486	+	0.809998i	0.188606	+	0.0296363i
$748$	−1.05721	+	0.390073i	−0.0386553	+	0.0142625i
$749$	−20.8762	+	26.0988i	−0.762800	+	0.953628i
$750$	−5.69767	+	34.6462i	−0.208049	+	1.26510i
$751$	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
$753$	23.9745	+	28.0359i	0.873680	+	1.02168i
$754$	−8.37999	−	9.94234i	−0.305181	−	0.362079i
$755$		−	13.6974i		−	0.498501i
$756$	20.0429	−	18.8224i	0.728954	−	0.684562i
$757$		−	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
$759$	−13.7819	−	16.1165i	−0.500249	−	0.584993i
$760$	24.0220	−	0.158686i	0.871369	−	0.00575614i
$761$	35.5006	−	20.4963i	1.28689	−	0.742989i	0.308795	−	0.951129i	$-0.400074\pi$
$761$	35.5006	−	20.4963i	1.28689	−	0.742989i	0.978099	+	0.208140i	$0.0667409\pi$
$762$	−6.11732	−	1.00601i	−0.221607	−	0.0364439i
$763$	−33.9098	−	5.16233i	−1.22762	−	0.186889i
$764$	−28.3884	+	10.4743i	−1.02706	+	0.378948i
$765$	2.37139	+	0.372624i	0.0857378	+	0.0134722i
$766$	33.2102	+	12.0048i	1.19993	+	0.433750i
$767$	−14.0064	+	24.2598i	−0.505741	+	0.875970i
$768$	−27.7027	+	0.746841i	−0.999637	+	0.0269493i
$769$	−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	−	0.699966i	−0.590094	−	0.807335i	$-0.700909\pi$
$773$	11.2358	−	19.4611i	0.404125	−	0.699966i	0.994219	+	0.107369i	$0.0342426\pi$
$774$	−8.20877	−	13.5564i	−0.295058	−	0.487273i
$775$	−37.7247	+	21.7803i	−1.35511	+	0.782373i
$776$	12.7095	+	21.6815i	0.456246	+	0.778322i
$777$	1.26842	+	38.6656i	0.0455042	+	1.38712i
$778$	7.48327	+	41.9000i	0.268288	+	1.50219i
$779$	−1.79734	+	1.03770i	−0.0643965	+	0.0371794i
$780$	40.1930	+	22.4748i	1.43914	+	0.804726i
$781$	−22.8791	−	13.2093i	−0.818679	−	0.472664i
$782$	−0.915434	−	1.08611i	−0.0327359	−	0.0388391i
$783$	−7.00965	−	11.3918i	−0.250505	−	0.407111i
$784$	−25.7372	+	11.0270i	−0.919187	+	0.393821i
$785$		−	79.9291i		−	2.85279i
$786$	5.03806	+	13.3602i	0.179702	+	0.476544i
$787$	11.3998	−	19.7450i	0.406358	−	0.703833i	−0.588120	−	0.808773i	$-0.700132\pi$
$787$	11.3998	−	19.7450i	0.406358	−	0.703833i	0.994479	+	0.104940i	$0.0334652\pi$
$788$	4.93490	−	28.7264i	0.175799	−	1.02334i
$789$	−0.158290	−	0.851158i	−0.00563529	−	0.0303020i
$790$	58.0913	−	10.3750i	2.06680	−	0.369126i
$791$	6.84182	+	17.5087i	0.243267	+	0.622538i
$792$	−21.9900	−	3.30666i	−0.781382	−	0.117497i
$793$	−0.621340	−	1.07619i	−0.0220644	−	0.0382167i
$794$	2.72939	−	7.55063i	0.0968625	−	0.267962i
$795$	10.4031	−	8.89611i	0.368961	−	0.315513i
$796$	−22.2068	+	26.7029i	−0.787098	+	0.946461i
$797$	−21.8746			−0.774837			−0.387419	−	0.921904i	$-0.626633\pi$
$797$	−21.8746			−0.774837			−0.387419	+	0.921904i	$0.626633\pi$
$798$	10.9898	−	9.89700i	0.389034	−	0.350350i
$799$		−	0.252288i		−	0.00892532i
$800$	8.15142	−	49.4035i	0.288196	−	1.74668i
$801$	19.2652	+	50.0048i	0.680701	+	1.76683i
$802$	0.498270	−	1.37842i	0.0175945	−	0.0486738i
$803$	20.2071	−	11.6666i	0.713094	−	0.411705i
$804$	−34.5502	+	0.474786i	−1.21849	+	0.0167444i
$805$	6.92340	−	45.4778i	0.244018	−	1.60288i
$806$	4.37062	+	24.4718i	0.153948	+	0.861981i
$807$	−6.91678	−	37.1928i	−0.243482	−	1.30925i
$808$	−41.7875	+	0.276042i	−1.47008	+	0.00971112i
$809$	−24.0416	−	13.8804i	−0.845258	−	0.488010i	0.0137900	−	0.999905i	$-0.495610\pi$
$809$	−24.0416	−	13.8804i	−0.845258	−	0.488010i	−0.859048	+	0.511895i	$0.828944\pi$
$810$	37.4633	+	28.9904i	1.31633	+	1.01862i
$811$	6.49133			0.227942			0.113971	−	0.993484i	$-0.463643\pi$
$811$	6.49133			0.227942			0.113971	+	0.993484i	$0.463643\pi$
$812$	2.73803	+	13.3431i	0.0960861	+	0.468251i
$813$	9.08442	−	25.7035i	0.318605	−	0.901461i
$814$	23.9237	−	20.1643i	0.838524	−	0.706758i
$815$	−2.81474	+	4.87528i	−0.0985962	+	0.170774i
$816$	−1.47136	−	0.231997i	−0.0515078	−	0.00812153i
$817$	−4.26220	−	7.38234i	−0.149115	−	0.258275i
$818$	−0.914919	−	5.12277i	−0.0319894	−	0.179114i
$819$	27.6876	−	6.09456i	0.967484	−	0.212961i
$820$	2.34328	+	6.35094i	0.0818308	+	0.221784i
$821$	−12.8884	−	22.3234i	−0.449810	−	0.779094i	0.548563	−	0.836109i	$-0.315175\pi$
$821$	−12.8884	−	22.3234i	−0.449810	−	0.779094i	−0.998373	+	0.0570153i	$0.981842\pi$
$822$	−14.6154	+	17.8319i	−0.509772	+	0.621958i
$823$	−18.5654	−	10.7188i	−0.647151	−	0.373633i	0.140213	−	0.990121i	$-0.455221\pi$
$823$	−18.5654	−	10.7188i	−0.647151	−	0.373633i	−0.787364	+	0.616489i	$0.788555\pi$
$824$	−18.4588	−	10.4952i	−0.643042	−	0.365618i
$825$	13.3887	−	37.8819i	0.466133	−	1.31888i
$826$	25.0285	−	15.3195i	0.870854	−	0.533034i
$827$		−	0.550214i		−	0.0191328i	−0.999954	−	0.00956640i	$-0.996955\pi$
$827$		−	0.550214i		−	0.0191328i	0.999954	−	0.00956640i	$-0.00304513\pi$
$828$	−5.50313	−	27.4848i	−0.191247	−	0.955164i
$829$	40.9798	+	23.6597i	1.42329	+	0.821735i	0.996578	−	0.0826545i	$-0.0263398\pi$
$829$	40.9798	+	23.6597i	1.42329	+	0.821735i	0.426708	+	0.904389i	$0.359673\pi$
$830$	3.11222	−	8.60969i	0.108027	−	0.298847i
$831$	21.3680	−	3.97382i	0.741247	−	0.137850i
$832$	−24.9329	−	13.9591i	−0.864393	−	0.483945i
$833$	−1.46822	+	0.330551i	−0.0508709	+	0.0114529i
$834$	2.99676	−	18.2226i	0.103769	−	0.630999i
$835$	13.4297	+	23.2610i	0.464755	+	0.804979i
$836$	−11.7884	−	2.02512i	−0.407710	−	0.0700404i
$837$	0.716215	+	25.5617i	0.0247560	+	0.883543i
$838$	−8.94511	−	10.6128i	−0.309004	−	0.366614i
$839$	13.0088			0.449114			0.224557	−	0.974461i	$-0.427906\pi$
$839$	13.0088			0.449114			0.224557	+	0.974461i	$0.427906\pi$
$840$	−25.7465	−	40.7942i	−0.888340	−	1.40753i
$841$	−22.3737			−0.771508
$842$	−30.0941	−	35.7048i	−1.03711	−	1.23047i
$843$	−25.6106	−	29.9491i	−0.882074	−	1.03150i
$844$	−7.20197	+	41.9232i	−0.247902	+	1.44305i
$845$	−0.450499	−	0.780288i	−0.0154977	−	0.0268427i
$846$	2.39873	−	4.36258i	0.0824701	−	0.149989i
$847$	−8.53711	−	6.82878i	−0.293339	−	0.234640i
$848$	−6.45821	+	5.51674i	−0.221776	+	0.189446i
$849$	0.278919	+	1.49980i	0.00957249	+	0.0514731i
$850$	0.914906	−	2.53101i	0.0313810	−	0.0868129i
$851$	34.1552	+	19.7195i	1.17082	+	0.675975i
$852$	−17.8743	−	29.9995i	−0.612363	−	1.02777i
$853$		−	30.6386i		−	1.04904i	−0.851397	−	0.524522i	$-0.824244\pi$
$853$		−	30.6386i		−	1.04904i	0.851397	−	0.524522i	$-0.175756\pi$
$854$	0.0333968	+	1.30134i	0.00114281	+	0.0445309i
$855$	19.8210	+	16.0107i	0.677865	+	0.547555i
$856$	31.0591	+	17.6595i	1.06158	+	0.603589i
$857$	37.8255	+	21.8385i	1.29209	+	0.745991i	0.979025	−	0.203740i	$-0.0653097\pi$
$857$	37.8255	+	21.8385i	1.29209	+	0.745991i	0.313069	+	0.949731i	$0.398643\pi$
$858$	−17.7333	−	14.5347i	−0.605406	−	0.496205i
$859$	−10.5500	−	18.2731i	−0.359961	−	0.623471i	0.627993	−	0.778219i	$-0.283877\pi$
$859$	−10.5500	−	18.2731i	−0.359961	−	0.623471i	−0.987954	+	0.154748i	$0.950543\pi$
$860$	−26.0856	+	9.62469i	−0.889512	+	0.328199i
$861$	3.67562	+	1.96434i	0.125265	+	0.0669444i
$862$	−2.62219	−	14.6821i	−0.0893123	−	0.500074i
$863$	−23.7379	−	41.1152i	−0.808047	−	1.39958i	−0.914215	−	0.405230i	$-0.867191\pi$
$863$	−23.7379	−	41.1152i	−0.808047	−	1.39958i	0.106168	−	0.994348i	$-0.466142\pi$
$864$	−23.2370	−	18.0012i	−0.790537	−	0.612414i
$865$	−4.97582	+	8.61838i	−0.169183	+	0.293034i
$866$	14.8290	−	12.4987i	0.503910	−	0.424725i
$867$	27.6865	+	9.78527i	0.940282	+	0.332325i
$868$	8.22144	−	24.7092i	0.279054	−	0.838683i
$869$	−29.3820			−0.996716
$870$	−21.9577	+	8.28011i	−0.744436	+	0.280722i
$871$	−30.8547	−	17.8140i	−1.04547	−	0.603603i
$872$	0.242224	+	36.6680i	0.00820272	+	1.24174i
$873$	−4.13785	+	26.3335i	−0.140045	+	0.891253i
$874$	−2.65080	−	14.8422i	−0.0896646	−	0.502046i
$875$	35.3237	−	13.8033i	1.19416	−	0.466638i
$876$	30.8396	−	0.423795i	1.04197	−	0.0143187i
$877$	−33.6478	+	19.4266i	−1.13621	+	0.655989i	−0.945488	−	0.325656i	$-0.894415\pi$
$877$	−33.6478	+	19.4266i	−1.13621	+	0.655989i	−0.190718	+	0.981645i	$0.561082\pi$
$878$	−4.78610	+	13.2403i	−0.161523	+	0.446840i
$879$	29.1287	−	24.9091i	0.982488	−	0.840162i
$880$	−13.0202	+	36.7775i	−0.438912	+	1.23977i
$881$			45.6144i			1.53679i	0.639978	+	0.768393i	$0.278944\pi$
$881$			45.6144i			1.53679i	−0.639978	+	0.768393i	$0.721056\pi$
$882$	−28.5314	−	8.24381i	−0.960702	−	0.277583i
$883$	56.6501			1.90643			0.953214	−	0.302295i	$-0.0977527\pi$
$883$	56.6501			1.90643			0.953214	+	0.302295i	$0.0977527\pi$
$884$	−1.18087	−	0.982037i	−0.0397169	−	0.0330295i
$885$	32.8571	+	38.4232i	1.10448	+	1.29158i
$886$	0.112229	−	0.310471i	0.00377040	−	0.0104305i
$887$	3.46905	+	6.00857i	0.116479	+	0.201748i	0.918370	−	0.395723i	$-0.129506\pi$
$887$	3.46905	+	6.00857i	0.116479	+	0.201748i	−0.801891	+	0.597471i	$0.796172\pi$
$888$	40.6095	−	7.83005i	1.36277	−	0.262759i
$889$	2.43719	+	6.23694i	0.0817407	+	0.209180i
$890$	92.5524	−	16.5297i	3.10236	−	0.554077i
$891$	−15.8250	−	17.4893i	−0.530157	−	0.585915i
$892$	13.1827	+	2.26465i	0.441388	+	0.0758259i
$893$	1.33894	−	2.31912i	0.0448060	−	0.0776064i
$894$	−33.8622	+	12.7692i	−1.13252	+	0.427067i
$895$		−	31.3438i		−	1.04771i
$896$	15.9627	+	25.3218i	0.533276	+	0.845942i
$897$	9.63105	−	27.2501i	0.321571	−	0.909854i
$898$	−5.32209	−	6.31433i	−0.177600	−	0.210712i
$899$	−10.9709	−	6.33407i	−0.365901	−	0.211253i
$900$	39.8851	−	35.0675i	1.32950	−	1.16892i
$901$	−0.395365	+	0.228264i	−0.0131715	+	0.00760457i
$902$	−0.592603	−	3.31808i	−0.0197315	−	0.110480i
$903$	−8.06824	+	15.0971i	−0.268494	+	0.502400i
$904$	17.3368	−	10.1627i	0.576614	−	0.338006i
$905$	−19.7347	+	11.3939i	−0.656005	+	0.378745i
$906$	−5.71468	+	6.97232i	−0.189857	+	0.231640i
$907$	−23.0866	+	39.9871i	−0.766577	+	1.32775i	0.172832	+	0.984951i	$0.444708\pi$
$907$	−23.0866	+	39.9871i	−0.766577	+	1.32775i	−0.939409	+	0.342799i	$0.888625\pi$
$908$	30.6607	−	36.8685i	1.01751	−	1.22352i
$909$	−34.4797	−	27.8515i	−1.14362	−	0.923774i
$910$	−1.27607	−	49.7232i	−0.0423012	−	1.64831i
$911$	33.7577			1.11844			0.559221	−	0.829018i	$-0.311100\pi$
$911$	33.7577			1.11844			0.559221	+	0.829018i	$0.311100\pi$
$912$	−12.2940	−	9.94138i	−0.407094	−	0.329192i
$913$	−2.27917	+	3.94764i	−0.0754295	+	0.130648i
$914$	23.7647	+	8.59042i	0.786065	+	0.284146i
$915$	−2.20493	+	0.410053i	−0.0728928	+	0.0135559i
$916$	11.4377	+	30.9994i	0.377913	+	1.02425i
$917$	9.63366	−	12.0437i	0.318131	−	0.397717i
$918$	−1.05163	−	1.17904i	−0.0347090	−	0.0389140i
$919$	1.09773	−	0.633774i	0.0362107	−	0.0209063i	−0.481785	−	0.876289i	$-0.660012\pi$
$919$	1.09773	−	0.633774i	0.0362107	−	0.0209063i	0.517996	+	0.855383i	$0.326678\pi$
$920$	−49.1769	+	0.324855i	−1.62131	+	0.0107102i
$921$	−13.1210	+	11.2203i	−0.432352	+	0.369721i
$922$	0.432896	−	0.364870i	0.0142567	−	0.0120164i
$923$		−	36.0067i		−	1.18517i
$924$	9.04865	+	22.2493i	0.297679	+	0.731950i
$925$			74.7247i			2.45693i
$926$	26.8225	+	31.8232i	0.881441	+	1.04578i
$927$	−8.09679	−	21.0161i	−0.265934	−	0.690260i
$928$	13.6278	−	5.13070i	0.447353	−	0.168424i
$929$	−28.9002	+	16.6855i	−0.948183	+	0.547434i	−0.892516	−	0.451015i	$-0.851062\pi$
$929$	−28.9002	+	16.6855i	−0.948183	+	0.547434i	−0.0556673	+	0.998449i	$0.517729\pi$
$930$	44.2698	+	7.28029i	1.45166	+	0.238730i
$931$	−15.2507	−	4.75361i	−0.499821	−	0.155793i
$932$	−10.7170	−	29.0461i	−0.351047	−	0.951435i
$933$	−3.71902	−	19.9979i	−0.121755	−	0.654702i
$934$	3.74758	−	10.3674i	0.122625	−	0.339231i
$935$	−1.04849	+	1.81603i	−0.0342892	+	0.0593906i
$936$	−11.0825	−	28.2090i	−0.362243	−	0.922040i
$937$	−9.31498			−0.304307			−0.152154	−	0.988357i	$-0.548621\pi$
$937$	−9.31498			−0.304307			−0.152154	+	0.988357i	$0.548621\pi$
$938$	19.4841	+	31.8324i	0.636177	+	1.03936i
$939$	1.12197	+	0.396541i	0.0366142	+	0.0129406i
$940$	−6.71578	−	5.58500i	−0.219045	−	0.182163i
$941$	20.0007	−	34.6422i	0.652003	−	1.12930i	−0.330633	−	0.943759i	$-0.607262\pi$
$941$	20.0007	−	34.6422i	0.652003	−	1.12930i	0.982636	−	0.185543i	$-0.0594043\pi$
$942$	−33.3470	+	40.6858i	−1.08651	+	1.32561i
$943$	3.67945	−	2.12433i	0.119819	−	0.0691778i
$944$	−20.3757	−	23.8529i	−0.663172	−	0.776347i
$945$	6.28085	−	50.7787i	0.204316	−	1.65183i
$946$	13.6285	−	2.43403i	0.443102	−	0.0791373i
$947$	−28.9295	+	16.7025i	−0.940083	+	0.542757i	−0.889986	−	0.455987i	$-0.849286\pi$
$947$	−28.9295	+	16.7025i	−0.940083	+	0.542757i	−0.0500965	+	0.998744i	$0.515953\pi$
$948$	−33.8984	−	18.9550i	−1.10097	−	0.615630i
$949$	27.5410	+	15.9008i	0.894018	+	0.516161i
$950$	21.8427	−	18.4103i	0.708670	−	0.597309i
$951$	53.7389	+	18.9930i	1.74260	+	0.615891i
$952$	0.595464	+	1.49463i	0.0192991	+	0.0484413i
$953$		−	35.4084i		−	1.14699i	−0.819209	−	0.573495i	$-0.805587\pi$
$953$		−	35.4084i		−	1.14699i	0.819209	−	0.573495i	$-0.194413\pi$
$954$	−9.00697	+	0.188060i	−0.291611	+	0.00608867i
$955$	−28.1543	+	48.7646i	−0.911051	+	1.57799i
$956$	6.95727	−	40.4988i	0.225014	−	1.30982i
$957$	11.4875	−	2.13634i	0.371339	−	0.0690582i
$958$	−9.61853	−	53.8557i	−0.310761	−	1.74000i
$959$	24.6198	+	3.74805i	0.795016	+	0.121031i
$960$	−38.7476	+	34.0310i	−1.25057	+	1.09834i
$961$	−3.39046	−	5.87244i	−0.109370	−	0.189434i
$962$	40.1038	+	14.4967i	1.29300	+	0.467392i
$963$	13.6238	+	35.3622i	0.439022	+	1.13953i
$964$	18.9654	+	15.7721i	0.610835	+	0.507984i
$965$	11.3857			0.366519
$966$	−22.4978	+	20.2608i	−0.723856	+	0.651879i
$967$			59.2726i			1.90608i	0.302849	+	0.953039i	$0.402062\pi$
$967$			59.2726i			1.90608i	−0.302849	+	0.953039i	$0.597938\pi$
$968$	−5.77656	+	10.1597i	−0.185666	+	0.326545i
$969$	−0.552295	−	0.645855i	−0.0177423	−	0.0207479i
$970$	43.9824	+	15.8987i	1.41219	+	0.510476i
$971$	−49.2281	+	28.4218i	−1.57980	+	0.912101i	−0.584919	+	0.811092i	$0.698874\pi$
$971$	−49.2281	+	28.4218i	−1.57980	+	0.912101i	−0.994886	+	0.101009i	$0.967793\pi$
$972$	−6.97470	−	30.3867i	−0.223714	−	0.974655i
$973$	−18.5790	+	7.26005i	−0.595614	+	0.232746i
$974$	13.8747	−	2.47801i	0.444576	−	0.0794004i
$975$	53.8373	−	10.0122i	1.72417	−	0.320645i
$976$	1.36833	−	0.253719i	0.0437990	−	0.00812134i
$977$	31.5116	+	18.1932i	1.00814	+	0.582052i	0.910648	−	0.413183i	$-0.135583\pi$
$977$	31.5116	+	18.1932i	1.00814	+	0.582052i	0.0974966	+	0.995236i	$0.468916\pi$
$978$	3.46677	−	1.30730i	0.110855	−	0.0418028i
$979$	−46.8121			−1.49612
$980$	−23.7035	+	46.4008i	−0.757179	+	1.48222i
$981$	−24.4393	+	30.2555i	−0.780287	+	0.965984i
$982$	14.1339	+	16.7690i	0.451031	+	0.535121i
$983$	−7.30275	+	12.6487i	−0.232921	+	0.403432i	−0.958667	−	0.284532i	$-0.908162\pi$
$983$	−7.30275	+	12.6487i	−0.232921	+	0.403432i	0.725745	+	0.687964i	$0.241495\pi$
$984$	1.45688	−	4.21041i	0.0464435	−	0.134223i
$985$	−27.1197	−	46.9727i	−0.864105	−	1.49667i
$986$	0.770480	−	0.137606i	0.0245371	−	0.00438228i
$987$	−5.37456	+	0.176312i	−0.171074	+	0.00561206i
$988$	−5.64308	−	15.2943i	−0.179530	−	0.486577i
$989$	8.72540	+	15.1128i	0.277452	+	0.480560i
$990$	−35.3971	+	21.4340i	−1.12499	+	0.681217i
$991$	36.4541	+	21.0468i	1.15800	+	0.668572i	0.950824	−	0.309731i	$-0.100239\pi$
$991$	36.4541	+	21.0468i	1.15800	+	0.668572i	0.207177	+	0.978303i	$0.433572\pi$
$992$	−27.4676	−	4.53207i	−0.872098	−	0.143893i
$993$	2.72157	+	0.961890i	0.0863665	+	0.0305246i
$994$	−18.0151	+	33.1385i	−0.571406	+	1.05109i
$995$			64.6287i			2.04887i
$996$	−5.17622	+	3.08409i	−0.164015	+	0.0977232i
$997$	11.0158	+	6.36000i	0.348875	+	0.201423i	0.664190	−	0.747564i	$-0.268777\pi$
$997$	11.0158	+	6.36000i	0.348875	+	0.201423i	−0.315315	+	0.948987i	$0.602110\pi$
$998$	−0.732941	−	0.264942i	−0.0232008	−	0.00838660i
$999$	38.5887	+	20.8605i	1.22089	+	0.659997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.v.a.11.23	yes	56
3.2	odd	2	inner	168.2.v.a.11.6	yes	56
4.3	odd	2		672.2.bd.a.431.21		56
7.2	even	3	inner	168.2.v.a.107.3	yes	56
8.3	odd	2	inner	168.2.v.a.11.26	yes	56
8.5	even	2		672.2.bd.a.431.22		56
12.11	even	2		672.2.bd.a.431.16		56
21.2	odd	6	inner	168.2.v.a.107.26	yes	56
24.5	odd	2		672.2.bd.a.431.15		56
24.11	even	2	inner	168.2.v.a.11.3	✓	56
28.23	odd	6		672.2.bd.a.527.15		56
56.37	even	6		672.2.bd.a.527.16		56
56.51	odd	6	inner	168.2.v.a.107.6	yes	56
84.23	even	6		672.2.bd.a.527.22		56
168.107	even	6	inner	168.2.v.a.107.23	yes	56
168.149	odd	6		672.2.bd.a.527.21		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.v.a.11.3	✓	56	24.11	even	2	inner
168.2.v.a.11.6	yes	56	3.2	odd	2	inner
168.2.v.a.11.23	yes	56	1.1	even	1	trivial
168.2.v.a.11.26	yes	56	8.3	odd	2	inner
168.2.v.a.107.3	yes	56	7.2	even	3	inner
168.2.v.a.107.6	yes	56	56.51	odd	6	inner
168.2.v.a.107.23	yes	56	168.107	even	6	inner
168.2.v.a.107.26	yes	56	21.2	odd	6	inner
672.2.bd.a.431.15		56	24.5	odd	2
672.2.bd.a.431.16		56	12.11	even	2
672.2.bd.a.431.21		56	4.3	odd	2
672.2.bd.a.431.22		56	8.5	even	2
672.2.bd.a.527.15		56	28.23	odd	6
672.2.bd.a.527.16		56	56.37	even	6
672.2.bd.a.527.21		56	168.149	odd	6
672.2.bd.a.527.22		56	84.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.08135 - 0.911422i) q^{2} +(-1.31637 + 1.12568i) q^{3} +(0.338619 - 1.97113i) q^{4} +(-1.86088 - 3.22314i) q^{5} +(-0.397486 + 2.41702i) q^{6} +(2.46429 - 0.962962i) q^{7} +(-1.43036 - 2.44009i) q^{8} +(0.465685 - 2.96364i) q^{9} +(-4.94989 - 1.78928i) q^{10} +(2.26958 + 1.31034i) q^{11} +(1.77311 + 2.97592i) 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} +(-2.19756 - 3.62915i) q^{18} +(-1.14103 - 1.97631i) q^{19} +(-6.98334 + 2.57661i) q^{20} +(-2.15994 + 4.04162i) q^{21} +(3.64848 - 0.651612i) q^{22} +(2.33586 + 4.04583i) q^{23} +(4.62966 + 1.60195i) 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} +(8.53007 - 3.21664i) q^{30} +(4.26196 + 2.46064i) q^{31} +(-5.29408 + 1.99316i) q^{32} +(-4.46265 + 0.829921i) q^{33} +(-0.299314 + 0.0534570i) q^{34} +(-7.68949 - 6.15077i) q^{35} +(-5.68401 - 1.92147i) q^{36} +(7.31104 - 4.22103i) q^{37} +(-3.03510 - 1.09712i) q^{38} +(-4.02073 - 4.70186i) q^{39} +(-5.20302 + 9.15098i) q^{40} -0.909442i q^{41} +(1.34798 + 6.33900i) q^{42} +3.73541 q^{43} +(3.35137 - 4.02992i) q^{44} +(-10.4188 + 4.01400i) q^{45} +(6.21334 + 2.24599i) q^{46} +(0.586728 + 1.01624i) q^{47} +(6.46632 - 2.48732i) q^{48} +(5.14541 - 4.74603i) q^{49} +(2.20085 + 12.3229i) q^{50} +(0.366107 - 0.0680851i) q^{51} +(7.04051 + 1.20949i) q^{52} +(1.06171 - 1.83894i) q^{53} +(6.97808 + 2.30358i) 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} +(6.29225 - 11.2528i) q^{60} +(-0.301301 + 0.173956i) q^{61} +(6.85134 - 1.22364i) q^{62} +(-1.70629 - 7.75168i) q^{63} +(-3.90812 + 6.98044i) q^{64} +(11.5125 - 6.64673i) q^{65} +(-4.06926 + 4.96479i) 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} +(-7.89765 + 3.10276i) q^{72} +(4.45173 - 7.71062i) q^{73} +(4.05862 - 11.2278i) q^{74} +(-2.80309 - 15.0728i) q^{75} +(-4.28194 + 1.57989i) q^{76} +(6.85470 + 1.04354i) q^{77} +(-8.63318 - 1.41975i) q^{78} +(-9.70950 + 5.60578i) q^{79} +(2.71413 + 14.6375i) q^{80} +(-8.56628 - 2.76024i) q^{81} +(-0.828886 - 0.983422i) q^{82} +1.73937i q^{83} +(7.23514 + 5.62607i) q^{84} +0.800163i q^{85} +(4.03927 - 3.40453i) q^{86} +(3.38855 - 2.89767i) q^{87} +(-0.0489643 - 7.41226i) q^{88} +(-15.4694 + 8.93127i) q^{89} +(-7.60786 + 13.8364i) q^{90} +(3.43953 + 8.80199i) q^{91} +(8.76581 - 3.23428i) q^{92} +(-8.38024 + 1.55848i) q^{93} +(1.56068 + 0.564153i) q^{94} +(-4.24662 + 7.35536i) q^{95} +(4.72533 - 8.58320i) q^{96} -8.88553 q^{97} +(1.23834 - 9.82174i) q^{98} +(4.94029 - 6.11600i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{3} - 2 q^{4} - 8 q^{6} - 2 q^{9} + 6 q^{10} + 10 q^{12} - 10 q^{16} - 10 q^{18} - 4 q^{19} - 20 q^{22} - 8 q^{24} - 16 q^{25} - 8 q^{27} - 22 q^{28} - 12 q^{30} - 14 q^{33} - 56 q^{34} + 4 q^{36}+ \cdots - 44 q^{99}+O(q^{100}) \) 56 * q - 2 * q^3 - 2 * q^4 - 8 * q^6 - 2 * q^9 + 6 * q^10 + 10 * q^12 - 10 * q^16 - 10 * q^18 - 4 * q^19 - 20 * q^22 - 8 * q^24 - 16 * q^25 - 8 * q^27 - 22 * q^28 - 12 * q^30 - 14 * q^33 - 56 * q^34 + 4 * q^36 + 14 * q^40 - 8 * q^42 - 16 * q^43 - 12 * q^46 + 64 * q^48 - 16 * q^49 - 34 * q^51 - 8 * q^52 + 32 * q^54 + 4 * q^57 - 18 * q^58 + 40 * q^60 + 4 * q^64 - 20 * q^66 - 36 * q^67 - 42 * q^70 + 22 * q^72 + 4 * q^73 + 104 * q^76 + 28 * q^78 - 10 * q^81 + 52 * q^82 + 4 * q^84 + 46 * q^88 + 140 * q^90 + 72 * q^91 - 46 * q^96 - 32 * q^97 - 44 * q^99

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