LMFDB - Embedded newform 168.2.v.a.107.25

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			107.25
Character	$\chi$	$=$	168.107
Dual form			168.2.v.a.11.25

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.32990 - 0.481016i) q^{2} +(-1.64844 + 0.531631i) q^{3} +(1.53725 - 1.27940i) q^{4} +(0.646402 - 1.11960i) q^{5} +(-1.93654 + 1.49994i) q^{6} +(2.42742 + 1.05244i) q^{7} +(1.42896 - 2.44091i) q^{8} +(2.43474 - 1.75273i) q^{9} +(0.321101 - 1.79988i) q^{10} +(-1.60004 + 0.923782i) q^{11} +(-1.85389 + 2.92627i) q^{12} -2.25432i q^{13} +(3.73446 + 0.232013i) q^{14} +(-0.470342 + 2.18925i) q^{15} +(0.726254 - 3.93352i) q^{16} +(-3.89580 + 2.24924i) q^{17} +(2.39486 - 3.50209i) q^{18} +(-2.80851 + 4.86448i) q^{19} +(-0.438742 - 2.54811i) q^{20} +(-4.56098 - 0.444404i) q^{21} +(-1.68353 + 1.99818i) q^{22} +(-0.519880 + 0.900459i) q^{23} +(-1.05790 + 4.78339i) q^{24} +(1.66433 + 2.88270i) q^{25} +(-1.08436 - 2.99801i) q^{26} +(-3.08172 + 4.18366i) q^{27} +(5.07804 - 1.48778i) q^{28} +1.32085 q^{29} +(0.427556 + 3.13771i) q^{30} +(-3.69700 + 2.13446i) q^{31} +(-0.926243 - 5.58051i) q^{32} +(2.14646 - 2.37343i) q^{33} +(-4.09909 + 4.86521i) q^{34} +(2.74740 - 2.03744i) q^{35} +(1.50034 - 5.80939i) q^{36} +(-8.18394 - 4.72500i) q^{37} +(-1.39513 + 7.82020i) q^{38} +(1.19846 + 3.71611i) q^{39} +(-1.80916 - 3.17768i) q^{40} -1.39634i q^{41} +(-6.27939 + 1.60289i) q^{42} -6.02578 q^{43} +(-1.27776 + 3.46717i) q^{44} +(-0.388538 - 3.85890i) q^{45} +(-0.258251 + 1.44759i) q^{46} +(5.90249 - 10.2234i) q^{47} +(0.893991 + 6.87028i) q^{48} +(4.78472 + 5.10944i) q^{49} +(3.60001 + 3.03313i) q^{50} +(5.22625 - 5.77888i) q^{51} +(-2.88418 - 3.46544i) q^{52} +(6.02901 + 10.4425i) q^{53} +(-2.08596 + 7.04619i) q^{54} +2.38854i q^{55} +(6.03762 - 4.42122i) q^{56} +(2.04356 - 9.51192i) q^{57} +(1.75660 - 0.635353i) q^{58} +(9.57732 - 5.52947i) q^{59} +(2.07790 + 3.96717i) q^{60} +(7.65220 + 4.41800i) q^{61} +(-3.88991 + 4.61693i) q^{62} +(7.75477 - 1.69218i) q^{63} +(-3.91612 - 6.97596i) q^{64} +(-2.52393 - 1.45719i) q^{65} +(1.71291 - 4.18890i) q^{66} +(3.05545 + 5.29219i) q^{67} +(-3.11112 + 8.44195i) q^{68} +(0.378281 - 1.76074i) q^{69} +(2.67372 - 4.03113i) q^{70} -14.0121 q^{71} +(-0.799109 - 8.44757i) q^{72} +(-4.38664 - 7.59788i) q^{73} +(-13.1566 - 2.34715i) q^{74} +(-4.27609 - 3.86717i) q^{75} +(1.90626 + 11.0711i) q^{76} +(-4.85619 + 0.558456i) q^{77} +(3.38135 + 4.36556i) q^{78} +(2.37061 + 1.36867i) q^{79} +(-3.93451 - 3.35575i) q^{80} +(2.85588 - 8.53487i) q^{81} +(-0.671663 - 1.85699i) q^{82} -4.74366i q^{83} +(-7.57992 + 5.15217i) q^{84} +5.81566i q^{85} +(-8.01366 + 2.89850i) q^{86} +(-2.17736 + 0.702207i) q^{87} +(-0.0315236 + 5.22561i) q^{88} +(8.31219 + 4.79904i) q^{89} +(-2.37291 - 4.94504i) q^{90} +(2.37254 - 5.47217i) q^{91} +(0.352866 + 2.04936i) q^{92} +(4.95955 - 5.48398i) q^{93} +(2.93207 - 16.4353i) q^{94} +(3.63085 + 6.28882i) q^{95} +(4.49363 + 8.70674i) q^{96} -8.73466 q^{97} +(8.82091 + 4.49350i) q^{98} +(-2.27653 + 5.05360i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{3} - 2 q^{4} - 8 q^{6} - 2 q^{9} + 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 $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	1.32990	−	0.481016i	0.940378	−	0.340130i
$2$	1.32990	−	0.481016i	0.940378	−	0.340130i
$3$	−1.64844	+	0.531631i	−0.951730	+	0.306937i
$3$	−1.64844	+	0.531631i	−0.951730	+	0.306937i
$4$	1.53725	−	1.27940i	0.768623	−	0.639702i
$5$	0.646402	−	1.11960i	0.289080	−	0.500700i	−0.684511	−	0.729003i	$-0.739984\pi$
$5$	0.646402	−	1.11960i	0.289080	−	0.500700i	0.973590	+	0.228302i	$0.0733175\pi$
$6$	−1.93654	+	1.49994i	−0.790588	+	0.612349i
$7$	2.42742	+	1.05244i	0.917478	+	0.397786i
$7$	2.42742	+	1.05244i	0.917478	+	0.397786i
$8$	1.42896	−	2.44091i	0.505215	−	0.862993i
$9$	2.43474	−	1.75273i	0.811579	−	0.584243i
$10$	0.321101	−	1.79988i	0.101541	−	0.569173i
$11$	−1.60004	+	0.923782i	−0.482430	+	0.278531i	−0.721428	−	0.692489i	$-0.756514\pi$
$11$	−1.60004	+	0.923782i	−0.482430	+	0.278531i	0.238999	+	0.971020i	$0.423181\pi$
$12$	−1.85389	+	2.92627i	−0.535173	+	0.844742i
$13$		−	2.25432i		−	0.625235i	−0.949879	−	0.312617i	$-0.898794\pi$
$13$		−	2.25432i		−	0.625235i	0.949879	−	0.312617i	$-0.101206\pi$
$14$	3.73446	+	0.232013i	0.998076	+	0.0620081i
$15$	−0.470342	+	2.18925i	−0.121442	+	0.565261i
$16$	0.726254	−	3.93352i	0.181564	−	0.983379i
$17$	−3.89580	+	2.24924i	−0.944871	+	0.545522i	−0.891484	−	0.453052i	$-0.850335\pi$
$17$	−3.89580	+	2.24924i	−0.944871	+	0.545522i	−0.0533874	+	0.998574i	$0.517002\pi$
$18$	2.39486	−	3.50209i	0.564473	−	0.825452i
$19$	−2.80851	+	4.86448i	−0.644317	+	1.11599i	0.340142	+	0.940374i	$0.389525\pi$
$19$	−2.80851	+	4.86448i	−0.644317	+	1.11599i	−0.984459	+	0.175615i	$0.943809\pi$
$20$	−0.438742	−	2.54811i	−0.0981056	−	0.569775i
$21$	−4.56098	−	0.444404i	−0.995287	−	0.0969769i
$22$	−1.68353	+	1.99818i	−0.358930	+	0.426013i
$23$	−0.519880	+	0.900459i	−0.108402	+	0.187759i	−0.915123	−	0.403174i	$-0.867907\pi$
$23$	−0.519880	+	0.900459i	−0.108402	+	0.187759i	0.806721	+	0.590933i	$0.201240\pi$
$24$	−1.05790	+	4.78339i	−0.215943	+	0.976406i
$25$	1.66433	+	2.88270i	0.332866	+	0.576541i
$26$	−1.08436	−	2.99801i	−0.212661	−	0.587957i
$27$	−3.08172	+	4.18366i	−0.593078	+	0.805145i
$28$	5.07804	−	1.48778i	0.959660	−	0.281164i
$29$	1.32085			0.245277			0.122638	−	0.992451i	$-0.460865\pi$
$29$	1.32085			0.245277			0.122638	+	0.992451i	$0.460865\pi$
$30$	0.427556	+	3.13771i	0.0780608	+	0.572865i
$31$	−3.69700	+	2.13446i	−0.664000	+	0.383361i	−0.793800	−	0.608179i	$-0.791900\pi$
$31$	−3.69700	+	2.13446i	−0.664000	+	0.383361i	0.129799	+	0.991540i	$0.458567\pi$
$32$	−0.926243	−	5.58051i	−0.163738	−	0.986504i
$33$	2.14646	−	2.37343i	0.373651	−	0.413162i
$34$	−4.09909	+	4.86521i	−0.702988	+	0.834376i
$35$	2.74740	−	2.03744i	0.464396	−	0.344390i
$36$	1.50034	−	5.80939i	0.250057	−	0.968231i
$37$	−8.18394	−	4.72500i	−1.34543	−	0.776786i	−0.357834	−	0.933785i	$-0.616484\pi$
$37$	−8.18394	−	4.72500i	−1.34543	−	0.776786i	−0.987599	+	0.157000i	$0.949818\pi$
$38$	−1.39513	+	7.82020i	−0.226320	+	1.26860i
$39$	1.19846	+	3.71611i	0.191908	+	0.595055i
$40$	−1.80916	−	3.17768i	−0.286054	−	0.502435i
$41$		−	1.39634i		−	0.218072i	−0.994038	−	0.109036i	$-0.965224\pi$
$41$		−	1.39634i		−	0.218072i	0.994038	−	0.109036i	$-0.0347764\pi$
$42$	−6.27939	+	1.60289i	−0.968931	+	0.247332i
$43$	−6.02578			−0.918922			−0.459461	−	0.888198i	$-0.651957\pi$
$43$	−6.02578			−0.918922			−0.459461	+	0.888198i	$0.651957\pi$
$44$	−1.27776	+	3.46717i	−0.192630	+	0.522696i
$45$	−0.388538	−	3.85890i	−0.0579198	−	0.575251i
$46$	−0.258251	+	1.44759i	−0.0380770	+	0.213435i
$47$	5.90249	−	10.2234i	0.860966	−	1.49124i	−0.0100312	−	0.999950i	$-0.503193\pi$
$47$	5.90249	−	10.2234i	0.860966	−	1.49124i	0.870997	−	0.491288i	$-0.163474\pi$
$48$	0.893991	+	6.87028i	0.129036	+	0.991640i
$49$	4.78472	+	5.10944i	0.683532	+	0.729921i
$50$	3.60001	+	3.03313i	0.509119	+	0.428949i
$51$	5.22625	−	5.77888i	0.731821	−	0.809206i
$52$	−2.88418	−	3.46544i	−0.399964	−	0.480570i
$53$	6.02901	+	10.4425i	0.828148	+	1.43439i	0.899489	+	0.436943i	$0.143939\pi$
$53$	6.02901	+	10.4425i	0.828148	+	1.43439i	−0.0713414	+	0.997452i	$0.522728\pi$
$54$	−2.08596	+	7.04619i	−0.283864	+	0.958865i
$55$			2.38854i			0.322070i
$56$	6.03762	−	4.42122i	0.806811	−	0.590810i
$57$	2.04356	−	9.51192i	0.270676	−	1.25988i
$58$	1.75660	−	0.635353i	0.230653	−	0.0834259i
$59$	9.57732	−	5.52947i	1.24686	−	0.719875i	0.276378	−	0.961049i	$-0.410866\pi$
$59$	9.57732	−	5.52947i	1.24686	−	0.719875i	0.970482	+	0.241174i	$0.0775324\pi$
$60$	2.07790	+	3.96717i	0.268255	+	0.512159i
$61$	7.65220	+	4.41800i	0.979764	+	0.565667i	0.902199	−	0.431320i	$-0.141952\pi$
$61$	7.65220	+	4.41800i	0.979764	+	0.565667i	0.0775652	+	0.996987i	$0.475285\pi$
$62$	−3.88991	+	4.61693i	−0.494019	+	0.586351i
$63$	7.75477	−	1.69218i	0.977010	−	0.213195i
$64$	−3.91612	−	6.97596i	−0.489515	−	0.871995i
$65$	−2.52393	−	1.45719i	−0.313055	−	0.180743i
$66$	1.71291	−	4.18890i	0.210845	−	0.515618i
$67$	3.05545	+	5.29219i	0.373283	+	0.646544i	0.990068	−	0.140587i	$-0.0448989\pi$
$67$	3.05545	+	5.29219i	0.373283	+	0.646544i	−0.616786	+	0.787131i	$0.711566\pi$
$68$	−3.11112	+	8.44195i	−0.377279	+	1.02374i
$69$	0.378281	−	1.76074i	0.0455397	−	0.211968i
$70$	2.67372	−	4.03113i	0.319571	−	0.481812i
$71$	−14.0121			−1.66293			−0.831464	−	0.555578i	$-0.812497\pi$
$71$	−14.0121			−1.66293			−0.831464	+	0.555578i	$0.812497\pi$
$72$	−0.799109	−	8.44757i	−0.0941759	−	0.995556i
$73$	−4.38664	−	7.59788i	−0.513417	−	0.889264i	−0.999879	−	0.0155626i	$-0.995046\pi$
$73$	−4.38664	−	7.59788i	−0.513417	−	0.889264i	0.486462	−	0.873702i	$-0.338287\pi$
$74$	−13.1566	−	2.34715i	−1.52942	−	0.272851i
$75$	−4.27609	−	3.86717i	−0.493760	−	0.446542i
$76$	1.90626	+	11.0711i	0.218663	+	1.26995i
$77$	−4.85619	+	0.558456i	−0.553414	+	0.0636420i
$78$	3.38135	+	4.36556i	0.382862	+	0.494303i
$79$	2.37061	+	1.36867i	0.266714	+	0.153987i	0.627393	−	0.778702i	$-0.284122\pi$
$79$	2.37061	+	1.36867i	0.266714	+	0.153987i	−0.360679	+	0.932690i	$0.617455\pi$
$80$	−3.93451	−	3.35575i	−0.439892	−	0.375184i
$81$	2.85588	−	8.53487i	0.317320	−	0.948318i
$82$	−0.671663	−	1.85699i	−0.0741728	−	0.205070i
$83$		−	4.74366i		−	0.520685i	−0.965516	−	0.260342i	$-0.916165\pi$
$83$		−	4.74366i		−	0.520685i	0.965516	−	0.260342i	$-0.0838354\pi$
$84$	−7.57992	+	5.15217i	−0.827037	+	0.562148i
$85$			5.81566i			0.630797i
$86$	−8.01366	+	2.89850i	−0.864135	+	0.312553i
$87$	−2.17736	+	0.702207i	−0.233437	+	0.0752845i
$88$	−0.0315236	+	5.22561i	−0.00336043	+	0.557051i
$89$	8.31219	+	4.79904i	0.881090	+	0.508697i	0.871018	−	0.491252i	$-0.163461\pi$
$89$	8.31219	+	4.79904i	0.881090	+	0.508697i	0.0100723	+	0.999949i	$0.496794\pi$
$90$	−2.37291	−	4.94504i	−0.250126	−	0.521253i
$91$	2.37254	−	5.47217i	0.248710	−	0.573639i
$92$	0.352866	+	2.04936i	0.0367888	+	0.213661i
$93$	4.95955	−	5.48398i	0.514281	−	0.568662i
$94$	2.93207	−	16.4353i	0.302420	−	1.69517i
$95$	3.63085	+	6.28882i	0.372517	+	0.645219i
$96$	4.49363	+	8.70674i	0.458629	+	0.888628i
$97$	−8.73466			−0.886871			−0.443435	−	0.896306i	$-0.646240\pi$
$97$	−8.73466			−0.886871			−0.443435	+	0.896306i	$0.646240\pi$
$98$	8.82091	+	4.49350i	0.891046	+	0.453912i
$99$	−2.27653	+	5.05360i	−0.228800	+	0.507906i
$100$	6.24663	+	2.30208i	0.624663	+	0.230208i
$101$	−3.42033	−	5.92419i	−0.340336	−	0.589479i	0.644159	−	0.764891i	$-0.277207\pi$
$101$	−3.42033	−	5.92419i	−0.340336	−	0.589479i	−0.984495	+	0.175413i	$0.943874\pi$
$102$	4.17063	−	10.1992i	0.412954	−	1.00987i
$103$	−3.88733	−	2.24435i	−0.383030	−	0.221143i	0.296106	−	0.955155i	$-0.404312\pi$
$103$	−3.88733	−	2.24435i	−0.383030	−	0.221143i	−0.679136	+	0.734013i	$0.737645\pi$
$104$	−5.50259	−	3.22134i	−0.539574	−	0.315878i
$105$	−3.44578	+	4.81921i	−0.336273	+	0.470306i
$106$	13.0410	+	10.9875i	1.26665	+	1.06720i
$107$	−6.27888	−	3.62511i	−0.607002	−	0.350453i	0.164789	−	0.986329i	$-0.447306\pi$
$107$	−6.27888	−	3.62511i	−0.607002	−	0.350453i	−0.771791	+	0.635876i	$0.780639\pi$
$108$	0.615218	+	10.3741i	0.0591994	+	0.998246i
$109$	10.6680	−	6.15916i	1.02181	−	0.589941i	0.107180	−	0.994240i	$-0.465818\pi$
$109$	10.6680	−	6.15916i	1.02181	−	0.589941i	0.914627	+	0.404299i	$0.132484\pi$
$110$	1.14893	+	3.17651i	0.109546	+	0.302868i
$111$	16.0027	+	3.43806i	1.51891	+	0.326326i
$112$	5.90273	−	8.78395i	0.557756	−	0.830005i
$113$			7.27566i			0.684437i	0.939620	+	0.342218i	$0.111178\pi$
$113$			7.27566i			0.684437i	−0.939620	+	0.342218i	$0.888822\pi$
$114$	−1.85766	−	13.6329i	−0.173986	−	1.27683i
$115$	0.672102	+	1.16412i	0.0626739	+	0.108554i
$116$	2.03048	−	1.68991i	0.188525	−	0.156904i
$117$	−3.95120	−	5.48867i	−0.365289	−	0.507427i
$118$	10.0771	−	11.9605i	0.927669	−	1.10105i
$119$	−11.8240	+	1.35974i	−1.08390	+	0.124647i
$120$	4.67166	+	4.27642i	0.426462	+	0.390382i
$121$	−3.79325	+	6.57011i	−0.344841	+	0.597282i
$122$	12.3018	+	2.19465i	1.11375	+	0.198694i
$123$	0.742339	+	2.30179i	0.0669344	+	0.207546i
$124$	−2.95236	+	8.01115i	−0.265130	+	0.719422i
$125$	10.7673			0.963058
$126$	9.49908	−	5.98060i	0.846245	−	0.532794i
$127$		−	21.7722i		−	1.93197i	−0.258595	−	0.965986i	$-0.583260\pi$
$127$		−	21.7722i		−	1.93197i	0.258595	−	0.965986i	$-0.416740\pi$
$128$	−8.56359	−	7.39358i	−0.756921	−	0.653506i
$129$	9.93316	−	3.20349i	0.874566	−	0.282052i
$130$	−4.05750	−	0.723863i	−0.355866	−	0.0634870i
$131$	4.65916	+	2.68997i	0.407073	+	0.235024i	0.689531	−	0.724256i	$-0.257817\pi$
$131$	4.65916	+	2.68997i	0.407073	+	0.235024i	−0.282458	+	0.959280i	$0.591150\pi$
$132$	0.263062	−	6.39474i	0.0228966	−	0.556591i
$133$	−11.9370	+	8.85234i	−1.03507	+	0.767595i
$134$	6.60906	+	5.56835i	0.570936	+	0.481032i
$135$	2.69199	+	6.15462i	0.231690	+	0.529705i
$136$	−0.0767544	+	12.7234i	−0.00658163	+	1.09102i
$137$	−11.3713	+	6.56523i	−0.971517	+	0.560905i	−0.899698	−	0.436512i	$-0.856214\pi$
$137$	−11.3713	+	6.56523i	−0.971517	+	0.560905i	−0.0718185	+	0.997418i	$0.522880\pi$
$138$	−0.343870	−	2.52356i	−0.0292722	−	0.214820i
$139$	12.9760			1.10061			0.550307	−	0.834963i	$-0.314511\pi$
$139$	12.9760			1.10061			0.550307	+	0.834963i	$0.314511\pi$
$140$	1.61673	−	6.64708i	0.136639	−	0.561781i
$141$	−4.29484	+	19.9907i	−0.361691	+	1.68352i
$142$	−18.6346	+	6.74004i	−1.56378	+	0.565612i
$143$	2.08250	+	3.60699i	0.174147	+	0.301632i
$144$	−5.12615	−	10.8500i	−0.427179	−	0.904167i
$145$	0.853802	−	1.47883i	0.0709044	−	0.122810i
$146$	−9.48848	−	7.99434i	−0.785272	−	0.661617i
$147$	−10.6037	−	5.87893i	−0.874578	−	0.484886i
$148$	−18.6259	+	3.20707i	−1.53104	+	0.263620i
$149$	−3.42033	+	5.92419i	−0.280205	+	0.485328i	−0.971435	−	0.237306i	$-0.923736\pi$
$149$	−3.42033	+	5.92419i	−0.280205	+	0.485328i	0.691230	+	0.722634i	$0.257069\pi$
$150$	−7.54693	−	3.08606i	−0.616204	−	0.251976i
$151$	3.16245	−	1.82584i	0.257356	−	0.148585i	−0.365772	−	0.930705i	$-0.619195\pi$
$151$	3.16245	−	1.82584i	0.257356	−	0.148585i	0.623128	+	0.782120i	$0.285862\pi$
$152$	7.86052	+	13.8065i	0.637573	+	1.11986i
$153$	−5.54294	+	12.3046i	−0.448120	+	0.994768i
$154$	−6.18960	+	3.07860i	−0.498772	+	0.248080i
$155$			5.51888i			0.443287i
$156$	6.59674	+	4.17926i	0.528162	+	0.334609i
$157$	2.34584	−	1.35437i	0.187219	−	0.108091i	−0.403461	−	0.914997i	$-0.632193\pi$
$157$	2.34584	−	1.35437i	0.187219	−	0.108091i	0.590680	+	0.806906i	$0.298860\pi$
$158$	3.81101	+	0.679889i	0.303188	+	0.0540891i
$159$	−15.4901	−	14.0088i	−1.22844	−	1.11097i
$160$	−6.84666	−	2.57023i	−0.541276	−	0.203194i
$161$	−2.20965	+	1.63865i	−0.174145	+	0.129143i
$162$	−0.307381	−	12.7242i	−0.0241501	−	0.999708i
$163$	4.41842	−	7.65293i	0.346078	−	0.599424i	−0.639471	−	0.768815i	$-0.720847\pi$
$163$	4.41842	−	7.65293i	0.346078	−	0.599424i	0.985549	+	0.169391i	$0.0541801\pi$
$164$	−1.78648	−	2.14652i	−0.139501	−	0.167615i
$165$	−1.26982	−	3.93737i	−0.0988554	−	0.306524i
$166$	−2.28178	−	6.30858i	−0.177100	−	0.489641i
$167$	−11.8815			−0.919417			−0.459709	−	0.888070i	$-0.652046\pi$
$167$	−11.8815			−0.919417			−0.459709	+	0.888070i	$0.652046\pi$
$168$	−7.60222	+	10.4979i	−0.586524	+	0.809932i
$169$	7.91806			0.609081
$170$	2.79743	+	7.73422i	0.214553	+	0.593188i
$171$	1.68814	+	16.7663i	0.129095	+	1.28215i
$172$	−9.26310	+	7.70940i	−0.706305	+	0.587836i
$173$	3.12500	−	5.41265i	0.237589	−	0.411516i	−0.722433	−	0.691441i	$-0.756976\pi$
$173$	3.12500	−	5.41265i	0.237589	−	0.411516i	0.960022	+	0.279925i	$0.0903095\pi$
$174$	−2.55788	+	1.98121i	−0.193913	+	0.150195i
$175$	1.00614	+	8.74915i	0.0760571	+	0.661373i
$176$	2.47168	+	6.96468i	0.186310	+	0.524982i
$177$	−12.8480	+	14.2066i	−0.965717	+	1.06783i
$178$	13.3628	+	2.38393i	1.00158	+	0.178683i
$179$	−1.43978	+	0.831255i	−0.107614	+	0.0621309i	−0.552841	−	0.833287i	$-0.686456\pi$
$179$	−1.43978	+	0.831255i	−0.107614	+	0.0621309i	0.445227	+	0.895418i	$0.353123\pi$
$180$	−5.53437	−	5.43498i	−0.412507	−	0.405100i
$181$			4.46877i			0.332161i	0.986112	+	0.166081i	$0.0531112\pi$
$181$			4.46877i			0.332161i	−0.986112	+	0.166081i	$0.946889\pi$
$182$	0.523031	−	8.41865i	0.0387696	−	0.624032i
$183$	−14.9630	−	3.21468i	−1.10609	−	0.237636i
$184$	1.45505	+	2.55571i	0.107268	+	0.188409i
$185$	−10.5802	+	6.10850i	−0.777874	+	0.449106i
$186$	3.95780	−	9.67875i	0.290200	−	0.709680i
$187$	4.15562	−	7.19775i	0.303889	−	0.526352i
$188$	−4.00628	−	23.2676i	−0.292188	−	1.69696i
$189$	−11.8837	+	6.91215i	−0.864412	+	0.502785i
$190$	7.85368	+	6.61698i	0.569766	+	0.480046i
$191$	11.2771	−	19.5325i	0.815982	−	1.41332i	−0.0926380	−	0.995700i	$-0.529530\pi$
$191$	11.2771	−	19.5325i	0.815982	−	1.41332i	0.908620	−	0.417623i	$-0.137137\pi$
$192$	10.1641	+	9.41754i	0.733534	+	0.679653i
$193$	−2.90298	−	5.02810i	−0.208961	−	0.361931i	0.742427	−	0.669927i	$-0.233675\pi$
$193$	−2.90298	−	5.02810i	−0.208961	−	0.361931i	−0.951387	+	0.307997i	$0.900341\pi$
$194$	−11.6162	+	4.20152i	−0.833994	+	0.301651i
$195$	4.93525	+	1.06030i	0.353421	+	0.0759297i
$196$	13.8923	+	1.73289i	0.992310	+	0.123778i
$197$	−3.15873			−0.225050			−0.112525	−	0.993649i	$-0.535894\pi$
$197$	−3.15873			−0.225050			−0.112525	+	0.993649i	$0.535894\pi$
$198$	−0.596686	+	7.81581i	−0.0424046	+	0.555445i
$199$	−12.2352	+	7.06397i	−0.867327	+	0.500751i	−0.866459	−	0.499248i	$-0.833610\pi$
$199$	−12.2352	+	7.06397i	−0.867327	+	0.500751i	−0.000867851		1.00000i	$0.500276\pi$
$200$	9.41470	+	0.0567945i	0.665720	+	0.00401598i
$201$	−7.85023	−	7.09951i	−0.553713	−	0.500761i
$202$	−7.39832	−	6.23332i	−0.520544	−	0.438575i
$203$	3.20627	+	1.39013i	0.225036	+	0.0975677i
$204$	0.640509	−	15.5700i	0.0448446	−	1.09012i
$205$	−1.56334	−	0.902597i	−0.109189	−	0.0630401i
$206$	−6.24932	−	1.11488i	−0.435411	−	0.0776777i
$207$	0.312489	+	3.10359i	0.0217195	+	0.215714i
$208$	−8.86739	−	1.63721i	−0.614843	−	0.113520i
$209$		−	10.3778i		−	0.717848i
$210$	−2.26441	+	8.06652i	−0.156259	+	0.556643i
$211$	1.95410			0.134526			0.0672629	−	0.997735i	$-0.478573\pi$
$211$	1.95410			0.134526			0.0672629	+	0.997735i	$0.478573\pi$
$212$	22.6283	+	8.33924i	1.55412	+	0.572741i
$213$	23.0981	−	7.44926i	1.58266	−	0.510415i
$214$	−10.0940	−	1.80078i	−0.690011	−	0.123099i
$215$	−3.89507	+	6.74646i	−0.265642	+	0.460105i
$216$	5.80828	+	13.5005i	0.395203	+	0.918594i
$217$	−11.2206	+	1.29035i	−0.761702	+	0.0875948i
$218$	11.2246	−	13.3225i	0.760229	−	0.902315i
$219$	11.2704	+	10.1926i	0.761583	+	0.688753i
$220$	3.05590	+	3.67177i	0.206029	+	0.247551i
$221$	5.07051	+	8.78238i	0.341079	+	0.590766i
$222$	22.9357	−	3.12531i	1.53935	−	0.209757i
$223$		−	3.59985i		−	0.241064i	−0.992709	−	0.120532i	$-0.961540\pi$
$223$		−	3.59985i		−	0.241064i	0.992709	−	0.120532i	$-0.0384600\pi$
$224$	3.62479	−	14.5210i	0.242192	−	0.970228i
$225$	9.10480	+	4.10151i	0.606987	+	0.273434i
$226$	3.49971	+	9.67588i	0.232797	+	0.643630i
$227$	−5.05015	+	2.91571i	−0.335190	+	0.193522i	−0.658143	−	0.752893i	$-0.728658\pi$
$227$	−5.05015	+	2.91571i	−0.335190	+	0.193522i	0.322953	+	0.946415i	$0.395325\pi$
$228$	−9.02813	−	17.2367i	−0.597902	−	1.14153i
$229$	11.2803	+	6.51269i	0.745424	+	0.430371i	0.824038	−	0.566535i	$-0.191716\pi$
$229$	11.2803	+	6.51269i	0.745424	+	0.430371i	−0.0786144	+	0.996905i	$0.525050\pi$
$230$	1.45378	+	1.22486i	0.0958597	+	0.0807649i
$231$	7.70827	−	3.50229i	0.507167	−	0.230433i
$232$	1.88745	−	3.22409i	0.123917	−	0.211672i
$233$	13.6565	+	7.88458i	0.894667	+	0.516536i	0.875466	−	0.483279i	$-0.160554\pi$
$233$	13.6565	+	7.88458i	0.894667	+	0.516536i	0.0192009	+	0.999816i	$0.493888\pi$
$234$	−7.89483	−	5.39876i	−0.516101	−	0.352928i
$235$	−7.63075	−	13.2169i	−0.497775	−	0.862172i
$236$	7.64828	−	20.7534i	0.497861	−	1.35093i
$237$	−4.63544	−	0.995889i	−0.301104	−	0.0646899i
$238$	−15.0706	+	7.49583i	−0.976880	+	0.485882i
$239$	22.7458			1.47130			0.735651	−	0.677361i	$-0.236876\pi$
$239$	22.7458			1.47130			0.735651	+	0.677361i	$0.236876\pi$
$240$	8.26985	+	3.44005i	0.533816	+	0.222054i
$241$	−6.82067	−	11.8137i	−0.439358	−	0.760990i	0.558282	−	0.829651i	$-0.311461\pi$
$241$	−6.82067	−	11.8137i	−0.439358	−	0.760990i	−0.997640	+	0.0686608i	$0.978127\pi$
$242$	−1.88430	+	10.5622i	−0.121128	+	0.678962i
$243$	−0.170365	+	15.5875i	−0.0109289	+	0.999940i
$244$	17.4157	−	2.99870i	1.11493	−	0.191972i
$245$	8.81339	−	2.05422i	0.563067	−	0.131240i
$246$	2.09443	+	2.70407i	0.133536	+	0.172405i
$247$	10.9661	+	6.33127i	0.697755	+	0.402849i
$248$	−0.0728375	+	12.0741i	−0.00462519	+	0.766708i
$249$	2.52188	+	7.81966i	0.159818	+	0.495551i
$250$	14.3194	−	5.17926i	0.905639	−	0.327565i
$251$		−	5.33090i		−	0.336484i	−0.985746	−	0.168242i	$-0.946191\pi$
$251$		−	5.33090i		−	0.336484i	0.985746	−	0.168242i	$-0.0538089\pi$
$252$	9.75602	−	12.5228i	0.614571	−	0.788861i
$253$		−	1.92102i		−	0.120774i
$254$	−10.4728	−	28.9548i	−0.657121	−	1.81678i
$255$	−3.09179	−	9.58679i	−0.193615	−	0.600348i
$256$	−14.9451	−	5.71347i	−0.934069	−	0.357092i
$257$	−7.26678	−	4.19547i	−0.453289	−	0.261707i	0.255929	−	0.966696i	$-0.417619\pi$
$257$	−7.26678	−	4.19547i	−0.453289	−	0.261707i	−0.709218	+	0.704989i	$0.750952\pi$
$258$	11.6691	−	9.03832i	0.726488	−	0.562701i
$259$	−14.8931	−	20.0827i	−0.925410	−	1.24788i
$260$	−5.74425	+	0.989063i	−0.356243	+	0.0613391i
$261$	3.21593	−	2.31510i	0.199061	−	0.143301i
$262$	7.49012	+	1.33625i	0.462741	+	0.0825536i
$263$	−1.58410	−	2.74375i	−0.0976800	−	0.169187i	0.813044	−	0.582202i	$-0.197809\pi$
$263$	−1.58410	−	2.74375i	−0.0976800	−	0.169187i	−0.910724	+	0.413016i	$0.864475\pi$
$264$	−2.72613	−	8.63088i	−0.167782	−	0.531194i
$265$	15.5886			0.957603
$266$	−11.6169	+	17.5146i	−0.712277	+	1.07389i
$267$	−16.2535	−	3.49194i	−0.994698	−	0.213703i
$268$	11.4678	+	4.22625i	0.700509	+	0.258160i
$269$	−7.81827	−	13.5416i	−0.476689	−	0.825649i	0.522955	−	0.852361i	$-0.324830\pi$
$269$	−7.81827	−	13.5416i	−0.476689	−	0.825649i	−0.999643	+	0.0267117i	$0.991496\pi$
$270$	6.54054	+	6.89011i	0.398045	+	0.419319i
$271$	12.4371	+	7.18058i	0.755502	+	0.436189i	0.827678	−	0.561203i	$-0.189661\pi$
$271$	12.4371	+	7.18058i	0.755502	+	0.436189i	−0.0721766	+	0.997392i	$0.522995\pi$
$272$	6.01809	+	16.9577i	0.364901	+	1.02821i
$273$	−1.00183	+	10.2819i	−0.0606333	+	0.622288i
$274$	−11.9647	+	14.2009i	−0.722813	+	0.857905i
$275$	−5.32598	−	3.07496i	−0.321169	−	0.185427i
$276$	−1.67119	−	3.19067i	−0.100594	−	0.192056i
$277$	−3.23202	+	1.86601i	−0.194193	+	0.112117i	−0.593944	−	0.804506i	$-0.702430\pi$
$277$	−3.23202	+	1.86601i	−0.194193	+	0.112117i	0.399751	+	0.916624i	$0.369097\pi$
$278$	17.2568	−	6.24169i	1.03499	−	0.374351i
$279$	−5.26008	+	11.6767i	−0.314913	+	0.699065i
$280$	−1.04727	−	9.61760i	−0.0625862	−	0.574762i
$281$		−	18.8375i		−	1.12375i	−0.827223	−	0.561874i	$-0.810080\pi$
$281$		−	18.8375i		−	1.12375i	0.827223	−	0.561874i	$-0.189920\pi$
$282$	3.90415	+	28.6514i	0.232489	+	1.70617i
$283$	10.7726	+	18.6586i	0.640362	+	1.10914i	0.985352	+	0.170534i	$0.0545492\pi$
$283$	10.7726	+	18.6586i	0.640362	+	1.10914i	−0.344989	+	0.938607i	$0.612117\pi$
$284$	−21.5400	+	17.9271i	−1.27817	+	1.06378i
$285$	−9.32859	−	8.43649i	−0.552578	−	0.499735i
$286$	4.50453	+	3.79521i	0.266358	+	0.224415i
$287$	1.46957	−	3.38951i	0.0867460	−	0.200076i
$288$	−12.0363	−	11.9636i	−0.709244	−	0.704963i
$289$	1.61820	−	2.80280i	0.0951880	−	0.164870i
$290$	0.424127	−	2.37738i	0.0249056	−	0.139605i
$291$	14.3986	−	4.64362i	0.844061	−	0.272214i
$292$	−16.4641	−	6.06754i	−0.963488	−	0.355076i
$293$	−4.13814			−0.241753			−0.120876	−	0.992668i	$-0.538570\pi$
$293$	−4.13814			−0.241753			−0.120876	+	0.992668i	$0.538570\pi$
$294$	−16.9297	−	2.71781i	−0.987358	−	0.158506i
$295$		−	14.2970i		−	0.832405i
$296$	−23.2279	+	13.2244i	−1.35009	+	0.768655i
$297$	1.06608	−	9.54085i	0.0618604	−	0.553616i
$298$	−1.69905	+	9.52379i	−0.0984236	+	0.551698i
$299$	2.02992	+	1.17197i	0.117393	+	0.0677770i
$300$	−11.5211	−	0.473945i	−0.665169	−	0.0273632i
$301$	−14.6271	−	6.34179i	−0.843091	−	0.365535i
$302$	3.32747	−	3.94937i	0.191474	−	0.227260i
$303$	8.78771	+	7.94734i	0.504841	+	0.456563i
$304$	17.0948	+	14.5802i	0.980456	+	0.836230i
$305$	9.89279	−	5.71160i	0.566459	−	0.327046i
$306$	−1.45282	+	19.0301i	−0.0830523	+	1.08788i
$307$	−4.63154			−0.264336			−0.132168	−	0.991227i	$-0.542194\pi$
$307$	−4.63154			−0.264336			−0.132168	+	0.991227i	$0.542194\pi$
$308$	−6.75067	+	7.07151i	−0.384655	+	0.402937i
$309$	7.60122	+	1.63306i	0.432418	+	0.0929017i
$310$	2.65467	+	7.33954i	0.150775	+	0.416858i
$311$	7.04878	+	12.2088i	0.399700	+	0.692300i	0.993689	−	0.112173i	$-0.0357811\pi$
$311$	7.04878	+	12.2088i	0.399700	+	0.692300i	−0.593989	+	0.804473i	$0.702448\pi$
$312$	10.7833	+	2.38484i	0.610483	+	0.135015i
$313$	6.95418	−	12.0450i	0.393074	−	0.680824i	−0.599780	−	0.800165i	$-0.704745\pi$
$313$	6.95418	−	12.0450i	0.393074	−	0.680824i	0.992853	+	0.119342i	$0.0380784\pi$
$314$	2.46825	−	2.92956i	0.139292	−	0.165325i
$315$	3.11813	−	9.77608i	0.175687	−	0.550819i
$316$	5.39529	−	0.928978i	0.303509	−	0.0522591i
$317$	−8.34364	+	14.4516i	−0.468625	+	0.811683i	−0.999357	−	0.0358569i	$-0.988584\pi$
$317$	−8.34364	+	14.4516i	−0.468625	+	0.811683i	0.530731	+	0.847540i	$0.321917\pi$
$318$	−27.3386	−	11.1792i	−1.53307	−	0.626899i
$319$	−2.11342	+	1.22018i	−0.118329	+	0.0683171i
$320$	−10.3417	−	0.124777i	−0.578117	−	0.00697527i
$321$	12.2776	+	2.63775i	0.685269	+	0.147225i
$322$	−2.15039	+	3.24211i	−0.119836	+	0.180675i
$323$		−	25.2681i		−	1.40595i
$324$	−6.52934	−	16.7740i	−0.362741	−	0.931890i
$325$	6.49853	−	3.75193i	0.360473	−	0.208119i
$326$	2.19486	−	12.3029i	0.121562	−	0.681397i
$327$	−14.3112	+	15.8245i	−0.791410	+	0.875095i
$328$	−3.40835	−	1.99532i	−0.188195	−	0.110173i
$329$	25.0874	−	18.6045i	1.38311	−	1.02570i
$330$	−3.58267	−	4.62549i	−0.197219	−	0.254625i
$331$	−4.82148	+	8.35105i	−0.265012	+	0.459015i	−0.967567	−	0.252615i	$-0.918709\pi$
$331$	−4.82148	+	8.35105i	−0.265012	+	0.459015i	0.702554	+	0.711630i	$0.252043\pi$
$332$	−6.06906	−	7.29218i	−0.333083	−	0.400210i
$333$	−28.2074	+	2.84010i	−1.54576	+	0.155636i
$334$	−15.8011	+	5.71519i	−0.864600	+	0.312721i
$335$	7.90019			0.431633
$336$	−5.06050	+	17.6179i	−0.276073	+	0.961137i
$337$	29.4886			1.60635			0.803173	−	0.595746i	$-0.203144\pi$
$337$	29.4886			1.60635			0.803173	+	0.595746i	$0.203144\pi$
$338$	10.5302	−	3.80872i	0.572767	−	0.207167i
$339$	−3.86797	−	11.9935i	−0.210079	−	0.651399i
$340$	7.44057	+	8.94010i	0.403522	+	0.484845i
$341$	3.94356	−	6.83044i	0.213556	−	0.369889i
$342$	10.3099	+	21.4854i	0.557496	+	1.16180i
$343$	6.23712	+	17.4384i	0.336773	+	0.941586i
$344$	−8.61062	+	14.7084i	−0.464253	+	0.793024i
$345$	−1.72680	−	1.56167i	−0.0929680	−	0.0840774i
$346$	1.55235	−	8.70144i	0.0834547	−	0.467792i
$347$	−10.8911	+	6.28800i	−0.584667	+	0.337558i	−0.762986	−	0.646415i	$-0.776267\pi$
$347$	−10.8911	+	6.28800i	−0.584667	+	0.337558i	0.178319	+	0.983973i	$0.442934\pi$
$348$	−2.44873	+	3.86518i	−0.131265	+	0.207195i
$349$		−	34.5012i		−	1.84681i	−0.383830	−	0.923404i	$-0.625395\pi$
$349$		−	34.5012i		−	1.84681i	0.383830	−	0.923404i	$-0.374605\pi$
$350$	5.54654	+	11.1515i	0.296475	+	0.596072i
$351$	9.43129	+	6.94718i	0.503405	+	0.370813i
$352$	6.63720	+	8.07338i	0.353764	+	0.430312i
$353$	9.10737	−	5.25815i	0.484737	−	0.279863i	−0.237652	−	0.971350i	$-0.576378\pi$
$353$	9.10737	−	5.25815i	0.484737	−	0.279863i	0.722388	+	0.691488i	$0.243044\pi$
$354$	−10.2529	+	25.0734i	−0.544937	+	1.33264i
$355$	−9.05743	+	15.6879i	−0.480719	+	0.832629i
$356$	18.9178	−	3.25733i	1.00264	−	0.172638i
$357$	18.7682	−	8.52744i	0.993321	−	0.451320i
$358$	−1.51491	+	1.79804i	−0.0800652	+	0.0950293i
$359$	−8.02903	+	13.9067i	−0.423756	+	0.733967i	−0.996303	−	0.0859047i	$-0.972622\pi$
$359$	−8.02903	+	13.9067i	−0.423756	+	0.733967i	0.572547	+	0.819872i	$0.305955\pi$
$360$	−9.97445	−	4.56584i	−0.525699	−	0.240641i
$361$	−6.27547	−	10.8694i	−0.330288	−	0.572075i
$362$	2.14955	+	5.94300i	0.112978	+	0.312357i
$363$	2.76009	−	12.8471i	0.144867	−	0.674296i
$364$	−3.35393	−	11.4475i	−0.175794	−	0.600013i
$365$	−11.3421			−0.593673
$366$	−21.4455	+	2.92225i	−1.12097	+	0.152748i
$367$	−20.8250	+	12.0233i	−1.08706	+	0.627613i	−0.932791	−	0.360417i	$-0.882634\pi$
$367$	−20.8250	+	12.0233i	−1.08706	+	0.627613i	−0.154266	+	0.988029i	$0.549301\pi$
$368$	3.16440	+	2.69892i	0.164956	+	0.140691i
$369$	−2.44741	−	3.39972i	−0.127407	−	0.176983i
$370$	−11.1323	+	13.2129i	−0.578742	+	0.686907i
$371$	3.64473	+	31.6936i	0.189225	+	1.64545i
$372$	0.607823	−	14.7755i	0.0315142	−	0.766074i
$373$	−12.5120	−	7.22381i	−0.647847	−	0.374035i	0.139784	−	0.990182i	$-0.455359\pi$
$373$	−12.5120	−	7.22381i	−0.647847	−	0.374035i	−0.787631	+	0.616147i	$0.788693\pi$
$374$	2.06431	−	11.5712i	0.106743	−	0.598332i
$375$	−17.7493	+	5.72424i	−0.916571	+	0.295599i
$376$	−16.5200	−	29.0163i	−0.851955	−	1.49640i
$377$		−	2.97762i		−	0.153355i
$378$	−12.4792	+	14.9087i	−0.641862	+	0.766820i
$379$	−29.8048			−1.53097			−0.765485	−	0.643453i	$-0.777501\pi$
$379$	−29.8048			−1.53097			−0.765485	+	0.643453i	$0.777501\pi$
$380$	13.6274	+	5.02214i	0.699073	+	0.257630i
$381$	11.5748	+	35.8903i	0.592994	+	1.83871i
$382$	5.60191	−	31.4007i	0.286619	−	1.60660i
$383$	−5.62806	+	9.74809i	−0.287581	+	0.498104i	−0.973232	−	0.229826i	$-0.926184\pi$
$383$	−5.62806	+	9.74809i	−0.287581	+	0.498104i	0.685651	+	0.727930i	$0.259518\pi$
$384$	18.0472	+	7.63523i	0.920970	+	0.389634i
$385$	−2.51380	+	5.79798i	−0.128115	+	0.295492i
$386$	−6.27926	−	5.29048i	−0.319606	−	0.269278i
$387$	−14.6712	+	10.5616i	−0.745778	+	0.536874i
$388$	−13.4273	+	11.1752i	−0.681669	+	0.567333i
$389$	−13.4807	−	23.3492i	−0.683498	−	1.18385i	−0.973906	−	0.226950i	$-0.927124\pi$
$389$	−13.4807	−	23.3492i	−0.683498	−	1.18385i	0.290408	−	0.956903i	$-0.406209\pi$
$390$	7.07339	−	0.963847i	0.358175	−	0.0488063i
$391$		−	4.67735i		−	0.236544i
$392$	19.3089	−	4.37788i	0.975247	−	0.221117i
$393$	−9.11045	−	1.95731i	−0.459561	−	0.0987331i
$394$	−4.20078	+	1.51940i	−0.211632	+	0.0765463i
$395$	3.06473	−	1.76942i	0.154203	−	0.0890293i
$396$	2.96600	+	10.6812i	0.149047	+	0.536752i
$397$	6.75185	+	3.89818i	0.338866	+	0.195644i	0.659770	−	0.751467i	$-0.270654\pi$
$397$	6.75185	+	3.89818i	0.338866	+	0.195644i	−0.320905	+	0.947111i	$0.603987\pi$
$398$	−12.8736	+	15.2796i	−0.645295	+	0.765900i
$399$	14.9713	−	20.9387i	0.749505	−	1.04825i
$400$	12.5479	−	4.45309i	0.627395	−	0.222655i
$401$	2.98430	+	1.72299i	0.149029	+	0.0860420i	0.572660	−	0.819793i	$-0.305911\pi$
$401$	2.98430	+	1.72299i	0.149029	+	0.0860420i	−0.423631	+	0.905835i	$0.639245\pi$
$402$	−13.8550	−	5.66552i	−0.691023	−	0.282571i
$403$	4.81175	+	8.33420i	0.239691	+	0.415156i
$404$	−12.8373	−	4.73095i	−0.638681	−	0.235374i
$405$	−7.70959	−	8.71440i	−0.383093	−	0.433022i
$406$	4.93267	+	0.306456i	0.244805	+	0.0152091i
$407$	17.4595			0.865435
$408$	−6.63764	−	21.0146i	−0.328612	−	1.04038i
$409$	9.79039	+	16.9575i	0.484104	+	0.838492i	0.999833	−	0.0182590i	$-0.00581236\pi$
$409$	9.79039	+	16.9575i	0.484104	+	0.838492i	−0.515729	+	0.856752i	$0.672479\pi$
$410$	−2.51325	−	0.448366i	−0.124121	−	0.0221432i
$411$	15.2547	−	16.8678i	0.752459	−	0.832025i
$412$	−8.84722	+	1.52334i	−0.435871	+	0.0750497i
$413$	29.0676	−	3.34274i	1.43032	−	0.164485i
$414$	1.90845	+	3.97714i	0.0937954	+	0.195466i
$415$	−5.31101	−	3.06631i	−0.260707	−	0.150519i
$416$	−12.5802	+	2.08805i	−0.616797	+	0.102375i
$417$	−21.3903	+	6.89847i	−1.04749	+	0.337819i
$418$	−4.99190	−	13.8014i	−0.244162	−	0.675049i
$419$			27.6189i			1.34927i	0.738150	+	0.674637i	$0.235700\pi$
$419$			27.6189i			1.34927i	−0.738150	+	0.674637i	$0.764300\pi$
$420$	0.868701	+	11.8168i	0.0423883	+	0.576603i
$421$			9.36226i			0.456289i	0.973627	+	0.228144i	$0.0732658\pi$
$421$			9.36226i			0.456289i	−0.973627	+	0.228144i	$0.926734\pi$
$422$	2.59875	−	0.939954i	0.126505	−	0.0457563i
$423$	−3.54786	−	35.2368i	−0.172503	−	1.71327i
$424$	34.1046	+	0.205737i	1.65627	+	0.00999147i
$425$	−12.9678	−	7.48697i	−0.629031	−	0.363171i
$426$	27.1349	−	21.0173i	1.31469	−	1.01829i
$427$	13.9254	+	18.7779i	0.673897	+	0.908724i
$428$	−14.2902	+	2.46053i	−0.690741	+	0.118934i
$429$	−5.35047	−	4.83880i	−0.258323	−	0.233620i
$430$	−1.93488	+	10.8457i	−0.0933083	+	0.523025i
$431$	−4.22951	−	7.32573i	−0.203729	−	0.352868i	0.745998	−	0.665948i	$-0.231973\pi$
$431$	−4.22951	−	7.32573i	−0.203729	−	0.352868i	−0.949727	+	0.313080i	$0.898639\pi$
$432$	14.2184	+	15.1604i	0.684082	+	0.729405i
$433$	−10.9191			−0.524737			−0.262369	−	0.964968i	$-0.584504\pi$
$433$	−10.9191			−0.524737			−0.262369	+	0.964968i	$0.584504\pi$
$434$	−14.3015	+	7.11331i	−0.686494	+	0.341450i
$435$	−0.621254	+	2.89168i	−0.0297868	+	0.138645i
$436$	8.51927	−	23.1168i	0.407999	−	1.10709i
$437$	−2.92018	−	5.05790i	−0.139691	−	0.241952i
$438$	19.8913	+	8.13386i	0.950441	+	0.388651i
$439$	20.2600	+	11.6971i	0.966959	+	0.558274i	0.898308	−	0.439367i	$-0.144797\pi$
$439$	20.2600	+	11.6971i	0.966959	+	0.558274i	0.0686510	+	0.997641i	$0.478131\pi$
$440$	5.83021	+	3.41313i	0.277944	+	0.162715i
$441$	20.6050	+	4.05383i	0.981191	+	0.193040i
$442$	10.9677	+	9.24065i	0.521681	+	0.439533i
$443$	−5.31199	−	3.06688i	−0.252380	−	0.145712i	0.368473	−	0.929638i	$-0.379881\pi$
$443$	−5.31199	−	3.06688i	−0.252380	−	0.145712i	−0.620854	+	0.783926i	$0.713214\pi$
$444$	28.9988	−	15.1888i	1.37622	−	0.720829i
$445$	10.7460	−	6.20422i	0.509410	−	0.294108i
$446$	−1.73159	−	4.78743i	−0.0819931	−	0.226691i
$447$	2.48874	−	11.5840i	0.117713	−	0.547907i
$448$	−2.16426	−	21.0551i	−0.102252	−	0.994759i
$449$			35.8658i			1.69261i	0.532696	+	0.846307i	$0.321179\pi$
$449$			35.8658i			1.69261i	−0.532696	+	0.846307i	$0.678821\pi$
$450$	14.0813	+	1.07502i	0.663800	+	0.0506768i
$451$	1.28992	+	2.23420i	0.0607397	+	0.105204i
$452$	9.30851	+	11.1845i	0.437835	+	0.526074i
$453$	−4.24244	+	4.69105i	−0.199327	+	0.220405i
$454$	−5.31368	+	6.30679i	−0.249383	+	0.295992i
$455$	−4.59303	−	6.19352i	−0.215324	−	0.290357i
$456$	−20.2976	−	18.5804i	−0.950522	−	0.870105i
$457$	−1.51987	+	2.63249i	−0.0710964	+	0.123143i	−0.899382	−	0.437163i	$-0.855983\pi$
$457$	−1.51987	+	2.63249i	−0.0710964	+	0.123143i	0.828286	+	0.560306i	$0.189316\pi$
$458$	18.1343	+	3.23519i	0.847362	+	0.151170i
$459$	2.59572	−	23.2303i	0.121158	−	1.08430i
$460$	2.52256	+	0.929643i	0.117615	+	0.0433448i
$461$	−30.7564			−1.43247			−0.716233	−	0.697861i	$-0.754135\pi$
$461$	−30.7564			−1.43247			−0.716233	+	0.697861i	$0.754135\pi$
$462$	8.56654	−	8.36548i	0.398551	−	0.389197i
$463$		−	9.54146i		−	0.443429i	−0.975112	−	0.221715i	$-0.928835\pi$
$463$		−	9.54146i		−	0.443429i	0.975112	−	0.221715i	$-0.0711653\pi$
$464$	0.959276	−	5.19560i	0.0445333	−	0.241200i
$465$	−2.93401	−	9.09756i	−0.136061	−	0.421889i
$466$	21.9543	+	3.91668i	1.01702	+	0.181437i
$467$	−4.36437	−	2.51977i	−0.201959	−	0.116601i	0.395610	−	0.918419i	$-0.370533\pi$
$467$	−4.36437	−	2.51977i	−0.201959	−	0.116601i	−0.597569	+	0.801818i	$0.703867\pi$
$468$	−13.0962	−	3.38225i	−0.605372	−	0.156344i
$469$	1.84712	+	16.0621i	0.0852920	+	0.741677i
$470$	−16.5056	−	13.9065i	−0.761348	−	0.641460i
$471$	−3.14697	+	3.47973i	−0.145004	+	0.160338i
$472$	0.188690	−	31.2788i	0.00868518	−	1.43972i
$473$	9.64147	−	5.56650i	0.443315	−	0.255948i
$474$	−6.64369	+	0.905295i	−0.305155	+	0.0415816i
$475$	−18.6972			−0.857884
$476$	−16.4367	+	17.2179i	−0.753374	+	0.789179i
$477$	32.9820	+	14.8576i	1.51014	+	0.680285i
$478$	30.2495	−	10.9411i	1.38358	−	0.500434i
$479$	13.6307	+	23.6091i	0.622804	+	1.07873i	0.988961	+	0.148175i	$0.0473399\pi$
$479$	13.6307	+	23.6091i	0.622804	+	1.07873i	−0.366157	+	0.930553i	$0.619327\pi$
$480$	12.6528	+	0.596976i	0.577517	+	0.0272481i
$481$	−10.6516	+	18.4492i	−0.485673	+	0.841211i
$482$	−14.7534	−	12.4302i	−0.671998	−	0.566180i
$483$	2.77133	−	3.87593i	0.126100	−	0.176361i
$484$	2.57465	+	14.9530i	0.117030	+	0.679681i
$485$	−5.64610	+	9.77933i	−0.256376	+	0.444057i
$486$	7.27129	+	20.8117i	0.329832	+	0.944040i
$487$	0.905513	−	0.522798i	0.0410327	−	0.0236902i	−0.479343	−	0.877627i	$-0.659125\pi$
$487$	0.905513	−	0.522798i	0.0410327	−	0.0236902i	0.520376	+	0.853937i	$0.325792\pi$
$488$	21.7187	−	12.3652i	0.983159	−	0.559746i
$489$	−3.21499	+	14.9644i	−0.145387	+	0.676714i
$490$	10.7328	−	6.97129i	0.484857	−	0.314931i
$491$			29.3101i			1.32275i	0.750057	+	0.661373i	$0.230026\pi$
$491$			29.3101i			1.32275i	−0.750057	+	0.661373i	$0.769974\pi$
$492$	4.08608	+	2.58867i	0.184215	+	0.116706i
$493$	−5.14579	+	2.97092i	−0.231755	+	0.133804i
$494$	17.6292	+	3.14507i	0.793175	+	0.141503i
$495$	4.18646	+	5.81546i	0.188167	+	0.261385i
$496$	5.71098	+	16.0924i	0.256431	+	0.722569i
$497$	−34.0132	−	14.7469i	−1.52570	−	0.661490i
$498$	7.11522	+	9.18627i	0.318841	+	0.411647i
$499$	14.3749	−	24.8981i	0.643510	−	1.11459i	−0.341133	−	0.940015i	$-0.610811\pi$
$499$	14.3749	−	24.8981i	0.643510	−	1.11459i	0.984643	−	0.174578i	$-0.0558560\pi$
$500$	16.5520	−	13.7757i	0.740229	−	0.616070i
$501$	19.5860	−	6.31657i	0.875037	−	0.282204i
$502$	−2.56425	−	7.08955i	−0.114448	−	0.316422i
$503$	−19.8016			−0.882910			−0.441455	−	0.897283i	$-0.645538\pi$
$503$	−19.8016			−0.882910			−0.441455	+	0.897283i	$0.645538\pi$
$504$	6.95082	−	21.3468i	0.309614	−	0.950862i
$505$	−8.84363			−0.393536
$506$	−0.924044	−	2.55476i	−0.0410788	−	0.113573i
$507$	−13.0525	+	4.20949i	−0.579681	+	0.186950i
$508$	−27.8554	−	33.4693i	−1.23589	−	1.48496i
$509$	−14.1795	+	24.5596i	−0.628494	+	1.08858i	0.359360	+	0.933199i	$0.382995\pi$
$509$	−14.1795	+	24.5596i	−0.628494	+	1.08858i	−0.987854	+	0.155385i	$0.950338\pi$
$510$	−8.72315	−	11.2622i	−0.386268	−	0.498700i
$511$	−2.65186	−	23.0599i	−0.117312	−	1.02011i
$512$	−22.6237	−	0.409474i	−0.999836	−	0.0180964i
$513$	−11.6963	−	26.7408i	−0.516403	−	1.18064i
$514$	−11.6821	−	2.08411i	−0.515277	−	0.0919260i
$515$	−5.02555	+	2.90151i	−0.221452	+	0.127856i
$516$	11.1712	−	17.6331i	0.491783	−	0.776253i
$517$			21.8104i			0.959222i
$518$	−29.4663	−	19.5441i	−1.29468	−	0.858719i
$519$	−2.27385	+	10.5838i	−0.0998108	+	0.464577i
$520$	−7.16349	+	4.07843i	−0.314140	+	0.178851i
$521$	−27.4943	+	15.8738i	−1.20455	+	0.695445i	−0.961563	−	0.274585i	$-0.911460\pi$
$521$	−27.4943	+	15.8738i	−1.20455	+	0.695445i	−0.242984	+	0.970030i	$0.578126\pi$
$522$	3.16326	−	4.62576i	0.138452	−	0.202464i
$523$	3.11470	−	5.39482i	0.136196	−	0.235899i	−0.789858	−	0.613290i	$-0.789846\pi$
$523$	3.11470	−	5.39482i	0.136196	−	0.235899i	0.926054	+	0.377392i	$0.123179\pi$
$524$	10.6038	−	1.82580i	0.463231	−	0.0797606i
$525$	−6.30989	−	13.8876i	−0.275386	−	0.606104i
$526$	−3.42648	−	2.88692i	−0.149402	−	0.125876i
$527$	9.60185	−	16.6309i	0.418263	−	0.724453i
$528$	−7.77706	−	10.1669i	−0.338453	−	0.442456i
$529$	10.9594	+	18.9823i	0.476498	+	0.825318i
$530$	20.7313	−	7.49839i	0.900509	−	0.325709i
$531$	13.6266	−	30.2492i	0.591344	−	1.31270i
$532$	−7.02445	+	28.8805i	−0.304548	+	1.25213i
$533$	−3.14780			−0.136346
$534$	−23.2951	+	3.17428i	−1.00808	+	0.137365i
$535$	−8.11735	+	4.68656i	−0.350944	+	0.202618i
$536$	17.2839	+	0.104266i	0.746551	+	0.00450359i
$537$	1.93147	−	2.13571i	0.0833491	−	0.0921626i
$538$	−16.9112	−	14.2483i	−0.729096	−	0.614286i
$539$	−12.3758	−	3.75526i	−0.533061	−	0.161751i
$540$	12.0125	+	6.01702i	0.516936	+	0.258931i
$541$	1.99979	+	1.15458i	0.0859776	+	0.0496392i	0.542372	−	0.840138i	$-0.317526\pi$
$541$	1.99979	+	1.15458i	0.0859776	+	0.0496392i	−0.456395	+	0.889777i	$0.650860\pi$
$542$	19.9941	+	3.56696i	0.858819	+	0.153214i
$543$	−2.37574	−	7.36652i	−0.101953	−	0.316128i
$544$	16.1604	+	19.6572i	0.692871	+	0.842796i
$545$		−	15.9252i		−	0.682159i
$546$	3.61343	+	14.1557i	0.154640	+	0.605809i
$547$	32.5136			1.39018			0.695090	−	0.718922i	$-0.255364\pi$
$547$	32.5136			1.39018			0.695090	+	0.718922i	$0.255364\pi$
$548$	−9.08093	+	24.6409i	−0.387918	+	1.05261i
$549$	26.3747	−	2.65557i	1.12564	−	0.113337i
$550$	−8.56211	−	1.52749i	−0.365089	−	0.0651323i
$551$	−3.70963	+	6.42528i	−0.158036	+	0.273726i
$552$	−3.75726	−	3.43939i	−0.159920	−	0.146390i
$553$	4.31401	+	5.81727i	0.183450	+	0.247375i
$554$	−3.40067	+	4.03624i	−0.144480	+	0.171484i
$555$	14.1934	−	15.6943i	0.602478	−	0.666186i
$556$	19.9474	−	16.6016i	0.845957	−	0.704064i
$557$	−16.5711	−	28.7020i	−0.702140	−	1.21614i	−0.967714	−	0.252052i	$-0.918895\pi$
$557$	−16.5711	−	28.7020i	−0.702140	−	1.21614i	0.265574	−	0.964091i	$-0.414439\pi$
$558$	−1.37868	+	18.0590i	−0.0583643	+	0.764497i
$559$			13.5840i			0.574542i
$560$	−6.01898	−	12.2867i	−0.254348	−	0.519206i
$561$	−3.02376	+	14.0743i	−0.127663	+	0.594219i
$562$	−9.06112	−	25.0519i	−0.382220	−	1.05675i
$563$	13.6362	−	7.87286i	0.574697	−	0.331801i	−0.184326	−	0.982865i	$-0.559010\pi$
$563$	13.6362	−	7.87286i	0.574697	−	0.331801i	0.759023	+	0.651064i	$0.225677\pi$
$564$	18.9739	+	36.2254i	0.798945	+	1.52536i
$565$	8.14583	+	4.70300i	0.342698	+	0.197857i
$566$	23.3015	+	19.6323i	0.979435	+	0.825205i
$567$	15.9149	−	17.7120i	0.668363	−	0.743835i
$568$	−20.0228	+	34.2023i	−0.840137	+	1.43510i
$569$	20.1971	+	11.6608i	0.846706	+	0.488846i	0.859538	−	0.511072i	$-0.170751\pi$
$569$	20.1971	+	11.6608i	0.846706	+	0.488846i	−0.0128319	+	0.999918i	$0.504085\pi$
$570$	−16.4641	−	6.73246i	−0.689607	−	0.281992i
$571$	12.0030	+	20.7898i	0.502311	+	0.870027i	0.999996	+	0.00267009i	$0.000849917\pi$
$571$	12.0030	+	20.7898i	0.502311	+	0.870027i	−0.497686	+	0.867357i	$0.665817\pi$
$572$	7.81611	+	2.88048i	0.326808	+	0.120439i
$573$	−8.20558	+	38.1935i	−0.342793	+	1.59556i
$574$	0.323969	−	5.21458i	0.0135222	−	0.217652i
$575$	−3.46101			−0.144334
$576$	−21.7617	−	10.1207i	−0.906737	−	0.421697i
$577$	−2.69246	−	4.66349i	−0.112089	−	0.194143i	0.804523	−	0.593921i	$-0.202421\pi$
$577$	−2.69246	−	4.66349i	−0.112089	−	0.194143i	−0.916612	+	0.399777i	$0.869087\pi$
$578$	0.803841	−	4.50581i	0.0334354	−	0.187417i
$579$	7.45849	+	6.74524i	0.309964	+	0.280322i
$580$	−0.579514	−	3.36568i	−0.0240630	−	0.139752i
$581$	4.99244	−	11.5149i	0.207121	−	0.477717i
$582$	16.9150	−	13.1015i	0.701149	−	0.543074i
$583$	−19.2933	−	11.1390i	−0.799046	−	0.461329i
$584$	−24.8141	−	0.149692i	−1.02682	−	0.00619430i
$585$	−8.69918	+	0.875888i	−0.359667	+	0.0362135i
$586$	−5.50330	+	1.99051i	−0.227339	+	0.0822274i
$587$			20.8871i			0.862104i	0.902327	+	0.431052i	$0.141857\pi$
$587$			20.8871i			0.862104i	−0.902327	+	0.431052i	$0.858143\pi$
$588$	−23.8220	+	4.52904i	−0.982403	+	0.186774i
$589$		−	23.9786i		−	0.988023i
$590$	−6.87710	−	19.0135i	−0.283126	−	0.782775i
$591$	5.20699	−	1.67928i	0.214187	−	0.0690763i
$592$	−24.5295	+	28.7601i	−1.00816	+	1.18203i
$593$	31.7953	+	18.3570i	1.30567	+	0.753832i	0.981371	−	0.192122i	$-0.0615368\pi$
$593$	31.7953	+	18.3570i	1.30567	+	0.753832i	0.324303	+	0.945953i	$0.394870\pi$
$594$	−3.17152	−	13.2011i	−0.130129	−	0.541649i
$595$	−6.12065	+	14.1170i	−0.250922	+	0.578742i
$596$	2.32153	+	13.4829i	0.0950937	+	0.552282i
$597$	16.4135	−	18.1491i	0.671761	−	0.742795i
$598$	3.26332	+	0.582180i	0.133447	+	0.0238071i
$599$	−12.0639	−	20.8953i	−0.492918	−	0.853760i	0.507048	−	0.861918i	$-0.330737\pi$
$599$	−12.0639	−	20.8953i	−0.492918	−	0.853760i	−0.999967	+	0.00815783i	$0.997403\pi$
$600$	−15.5498	+	4.91153i	−0.634818	+	0.200512i
$601$	−30.7421			−1.25399			−0.626997	−	0.779021i	$-0.715716\pi$
$601$	−30.7421			−1.25399			−0.626997	+	0.779021i	$0.715716\pi$
$602$	−22.5030	−	1.39806i	−0.917154	−	0.0569806i
$603$	16.7150	+	7.52972i	0.680687	+	0.306634i
$604$	2.52548	−	6.85281i	0.102760	−	0.278837i
$605$	4.90393	+	8.49385i	0.199373	+	0.345324i
$606$	15.5095	+	6.34210i	0.630032	+	0.257630i
$607$	−3.75552	−	2.16825i	−0.152432	−	0.0880066i	0.421844	−	0.906668i	$-0.361383\pi$
$607$	−3.75552	−	2.16825i	−0.152432	−	0.0880066i	−0.574276	+	0.818662i	$0.694716\pi$
$608$	29.7477	+	11.1672i	1.20643	+	0.452891i
$609$	−6.02439	−	0.586993i	−0.244120	−	0.0237861i
$610$	10.4090	−	12.3544i	0.421448	−	0.500216i
$611$	−23.0468	−	13.3061i	−0.932373	−	0.538306i
$612$	7.22168	+	26.0069i	0.291919	+	1.05127i
$613$	−26.2945	+	15.1812i	−1.06203	+	0.613161i	−0.925992	−	0.377543i	$-0.876769\pi$
$613$	−26.2945	+	15.1812i	−1.06203	+	0.613161i	−0.136034	+	0.990704i	$0.543436\pi$
$614$	−6.15947	+	2.22785i	−0.248576	+	0.0899086i
$615$	3.05693	+	0.656759i	0.123268	+	0.0264831i
$616$	−5.57618	+	12.6516i	−0.224671	+	0.509746i
$617$		−	11.5709i		−	0.465827i	−0.972497	−	0.232913i	$-0.925174\pi$
$617$		−	11.5709i		−	0.465827i	0.972497	−	0.232913i	$-0.0748259\pi$
$618$	10.8944	−	1.48451i	0.438235	−	0.0597156i
$619$	−8.62076	−	14.9316i	−0.346497	−	0.600151i	0.639127	−	0.769101i	$-0.279296\pi$
$619$	−8.62076	−	14.9316i	−0.346497	−	0.600151i	−0.985625	+	0.168950i	$0.945962\pi$
$620$	7.06087	+	8.48388i	0.283571	+	0.340721i
$621$	−2.16508	−	4.94996i	−0.0868818	−	0.198635i
$622$	15.2468	+	12.8459i	0.611341	+	0.515074i
$623$	15.1264	+	20.3974i	0.606028	+	0.817204i
$624$	15.4878	−	2.01534i	0.620008	−	0.0806781i
$625$	−1.36164	+	2.35843i	−0.0544656	+	0.0943372i
$626$	3.45450	−	19.3637i	0.138070	−	0.773928i
$627$	5.51717	+	17.1072i	0.220334	+	0.683197i
$628$	1.87335	−	5.08329i	0.0747548	−	0.202845i
$629$	42.5107			1.69501
$630$	−0.555664	−	14.5010i	−0.0221382	−	0.577735i
$631$		−	4.91146i		−	0.195522i	−0.995210	−	0.0977611i	$-0.968832\pi$
$631$		−	4.91146i		−	0.195522i	0.995210	−	0.0977611i	$-0.0311681\pi$
$632$	6.72832	−	3.83067i	0.267638	−	0.152376i
$633$	−3.22123	+	1.03886i	−0.128032	+	0.0412910i
$634$	−4.14471	+	23.2326i	−0.164608	+	0.922683i
$635$	−24.3762	−	14.0736i	−0.967339	−	0.558493i
$636$	−41.7349	−	1.71686i	−1.65490	−	0.0680779i
$637$	11.5183	−	10.7863i	0.456372	−	0.427368i
$638$	−2.22370	+	2.63930i	−0.0880370	+	0.104491i
$639$	−34.1157	+	24.5594i	−1.34960	+	0.971554i
$640$	−13.8134	+	4.80857i	−0.546021	+	0.190075i
$641$	34.7916	−	20.0870i	1.37419	−	0.793387i	0.382735	−	0.923858i	$-0.374982\pi$
$641$	34.7916	−	20.0870i	1.37419	−	0.793387i	0.991452	+	0.130471i	$0.0416488\pi$
$642$	17.5967	−	2.39780i	0.694488	−	0.0946336i
$643$	12.5997			0.496884			0.248442	−	0.968647i	$-0.420081\pi$
$643$	12.5997			0.496884			0.248442	+	0.968647i	$0.420081\pi$
$644$	−1.30029	+	5.34603i	−0.0512385	+	0.210663i
$645$	2.83418	−	13.1919i	0.111596	−	0.519431i
$646$	−12.1544	−	33.6039i	−0.478207	−	1.32213i
$647$	9.55483	+	16.5495i	0.375639	+	0.650626i	0.990422	−	0.138070i	$-0.0440899\pi$
$647$	9.55483	+	16.5495i	0.375639	+	0.650626i	−0.614783	+	0.788696i	$0.710757\pi$
$648$	−16.7519	−	19.1670i	−0.658077	−	0.752950i
$649$	−10.2160	+	17.6947i	−0.401015	+	0.694578i
$650$	6.83763	−	8.11557i	0.268194	−	0.318319i
$651$	17.8105	−	8.09227i	0.698048	−	0.317161i
$652$	−2.99898	−	17.4174i	−0.117449	−	0.682118i
$653$	4.01546	−	6.95497i	0.157137	−	0.272169i	−0.776698	−	0.629873i	$-0.783107\pi$
$653$	4.01546	−	6.95497i	0.157137	−	0.272169i	0.933835	+	0.357704i	$0.116440\pi$
$654$	−11.4205	+	27.9288i	−0.446579	+	1.09210i
$655$	6.02338	−	3.47760i	0.235353	−	0.135881i
$656$	−5.49253	−	1.01410i	−0.214447	−	0.0395939i
$657$	−23.9973	−	10.8102i	−0.936225	−	0.421748i
$658$	24.4145	−	36.8094i	0.951778	−	1.43498i
$659$		−	5.21061i		−	0.202977i	−0.994837	−	0.101488i	$-0.967640\pi$
$659$		−	5.21061i		−	0.202977i	0.994837	−	0.101488i	$-0.0323604\pi$
$660$	−6.98951	−	4.42810i	−0.272066	−	0.172363i
$661$	−33.5498	+	19.3700i	−1.30494	+	0.753406i	−0.981246	−	0.192757i	$-0.938257\pi$
$661$	−33.5498	+	19.3700i	−1.30494	+	0.753406i	−0.323690	+	0.946163i	$0.604924\pi$
$662$	−2.39508	+	13.4252i	−0.0930873	+	0.521787i
$663$	−13.0274	−	11.7816i	−0.505944	−	0.457560i
$664$	−11.5789	−	6.77852i	−0.449347	−	0.263058i
$665$	2.19497	+	19.0869i	0.0851171	+	0.740157i
$666$	−36.1468	+	17.3453i	−1.40066	+	0.672115i
$667$	−0.686686	+	1.18937i	−0.0265886	+	0.0460528i
$668$	−18.2648	+	15.2012i	−0.706685	+	0.588153i
$669$	1.91379	+	5.93416i	0.0739915	+	0.229428i
$670$	10.5064	−	3.80012i	0.405899	−	0.146811i
$671$	−16.3251			−0.630223
$672$	1.74457	+	25.8642i	0.0672984	+	0.997733i
$673$	−33.1783			−1.27893			−0.639465	−	0.768821i	$-0.720844\pi$
$673$	−33.1783			−1.27893			−0.639465	+	0.768821i	$0.720844\pi$
$674$	39.2168	−	14.1845i	1.51057	−	0.546366i
$675$	−17.1893	−	1.92071i	−0.661615	−	0.0739280i
$676$	12.1720	−	10.1304i	0.468154	−	0.389630i
$677$	−15.7573	+	27.2925i	−0.605602	+	1.04893i	0.386354	+	0.922351i	$0.373734\pi$
$677$	−15.7573	+	27.2925i	−0.605602	+	1.04893i	−0.991956	+	0.126583i	$0.959599\pi$
$678$	−10.9131	−	14.0896i	−0.419114	−	0.541107i
$679$	−21.2027	−	9.19274i	−0.813684	−	0.352785i
$680$	14.1955	+	8.31037i	0.544373	+	0.318688i
$681$	6.77481	−	7.49120i	0.259611	−	0.287063i
$682$	1.95897	−	10.9807i	0.0750127	−	0.420472i
$683$	19.4038	−	11.2028i	0.742465	−	0.428663i	−0.0804996	−	0.996755i	$-0.525652\pi$
$683$	19.4038	−	11.2028i	0.742465	−	0.428663i	0.822965	+	0.568092i	$0.192318\pi$
$684$	24.0459	+	23.6141i	0.919419	+	0.902908i
$685$			16.9751i			0.648585i
$686$	16.6829	+	20.1911i	0.636956	+	0.770901i
$687$	−22.0573	−	4.73884i	−0.841539	−	0.180798i
$688$	−4.37625	+	23.7025i	−0.166843	+	0.903649i
$689$	23.5408	−	13.5913i	0.896833	−	0.517787i
$690$	−3.04766	−	1.24624i	−0.116022	−	0.0474434i
$691$	−7.24483	+	12.5484i	−0.275606	+	0.477364i	−0.970288	−	0.241953i	$-0.922212\pi$
$691$	−7.24483	+	12.5484i	−0.275606	+	0.477364i	0.694682	+	0.719317i	$0.255545\pi$
$692$	−2.12108	−	12.3187i	−0.0806312	−	0.468287i
$693$	−10.8447	+	9.87128i	−0.411957	+	0.374979i
$694$	−11.4594	+	13.6012i	−0.434995	+	0.516294i
$695$	8.38773	−	14.5280i	0.318165	−	0.551077i
$696$	−1.39733	+	6.31817i	−0.0529658	+	0.239489i
$697$	3.14071	+	5.43987i	0.118963	+	0.206050i
$698$	−16.5956	−	45.8830i	−0.628155	−	1.73670i
$699$	−26.7037	−	5.73708i	−1.01003	−	0.216996i
$700$	12.7404	+	12.1623i	0.481541	+	0.459693i
$701$	21.9950			0.830738			0.415369	−	0.909653i	$-0.363652\pi$
$701$	21.9950			0.830738			0.415369	+	0.909653i	$0.363652\pi$
$702$	15.8843	+	4.70242i	0.599516	+	0.177481i
$703$	45.9694	−	26.5404i	1.73377	−	1.00099i
$704$	12.7102	+	7.54415i	0.479034	+	0.284331i
$705$	19.6054	+	17.7305i	0.738381	+	0.667769i
$706$	9.58261	−	11.3736i	0.360646	−	0.428050i
$707$	−2.06770	−	17.9802i	−0.0777639	−	0.676215i
$708$	−1.57461	+	38.2769i	−0.0591773	+	1.43853i
$709$	17.2122	+	9.93745i	0.646416	+	0.373209i	0.787082	−	0.616849i	$-0.211591\pi$
$709$	17.2122	+	9.93745i	0.646416	+	0.373209i	−0.140666	+	0.990057i	$0.544924\pi$
$710$	−4.49929	+	25.2201i	−0.168855	+	0.946493i
$711$	8.17071	−	0.822679i	0.306426	−	0.0308529i
$712$	23.5919	−	13.4317i	0.884143	−	0.503373i
$713$		−	4.43866i		−	0.166229i
$714$	20.8580	−	20.3684i	0.780590	−	0.762270i
$715$	5.38452			0.201370
$716$	−1.14978	+	3.11990i	−0.0429693	+	0.116596i
$717$	−37.4951	+	12.0924i	−1.40028	+	0.451598i
$718$	−3.98843	+	22.3565i	−0.148847	+	0.834339i
$719$	−4.05138	+	7.01719i	−0.151091	+	0.261697i	−0.931629	−	0.363411i	$-0.881612\pi$
$719$	−4.05138	+	7.01719i	−0.151091	+	0.261697i	0.780538	+	0.625108i	$0.214945\pi$
$720$	−15.4612	−	1.27422i	−0.576206	−	0.0474874i
$721$	−7.07413	−	9.53918i	−0.263454	−	0.355258i
$722$	−13.5741	−	11.4366i	−0.505175	−	0.425626i
$723$	17.5241	+	15.8482i	0.651726	+	0.589402i
$724$	5.71736	+	6.86960i	0.212484	+	0.255307i
$725$	2.19834	+	3.80763i	0.0816442	+	0.141412i
$726$	−2.50901	−	18.4129i	−0.0931182	−	0.683367i
$727$			1.56460i			0.0580278i	0.999579	+	0.0290139i	$0.00923671\pi$
$727$			1.56460i			0.0580278i	−0.999579	+	0.0290139i	$0.990763\pi$
$728$	−9.96682	−	13.6107i	−0.369395	−	0.504446i
$729$	−8.00598	−	25.7857i	−0.296518	−	0.955027i
$730$	−15.0838	+	5.45574i	−0.558278	+	0.201926i
$731$	23.4752	−	13.5534i	0.868263	−	0.501292i
$732$	−27.1147	+	14.2019i	−1.00219	+	0.524918i
$733$	10.2679	+	5.92818i	0.379254	+	0.218962i	0.677493	−	0.735529i	$-0.263066\pi$
$733$	10.2679	+	5.92818i	0.379254	+	0.218962i	−0.298240	+	0.954491i	$0.596400\pi$
$734$	−21.9117	+	26.0069i	−0.808775	+	0.959934i
$735$	−13.4363	+	8.07175i	−0.495605	+	0.297731i
$736$	5.50655	+	2.06715i	0.202974	+	0.0761962i
$737$	−9.77767	−	5.64514i	−0.360165	−	0.207941i
$738$	−4.89012	−	3.34404i	−0.180008	−	0.123096i
$739$	−6.94639	−	12.0315i	−0.255527	−	0.442586i	0.709511	−	0.704694i	$-0.248916\pi$
$739$	−6.94639	−	12.0315i	−0.255527	−	0.442586i	−0.965039	+	0.262108i	$0.915582\pi$
$740$	−8.44919	+	22.9266i	−0.310598	+	0.842800i
$741$	−21.4429	−	4.60684i	−0.787724	−	0.169236i
$742$	20.0923	+	40.3961i	0.737610	+	1.48299i
$743$	25.3287			0.929221			0.464611	−	0.885515i	$-0.346194\pi$
$743$	25.3287			0.929221			0.464611	+	0.885515i	$0.346194\pi$
$744$	−6.29891	−	19.9422i	−0.230929	−	0.731118i
$745$	4.42182	+	7.65881i	0.162003	+	0.280597i
$746$	−20.1144	−	3.58844i	−0.736442	−	0.131382i
$747$	−8.31435	−	11.5496i	−0.304206	−	0.422577i
$748$	−2.82061	−	16.3814i	−0.103132	−	0.598965i
$749$	−11.4262	−	15.4078i	−0.417506	−	0.562990i
$750$	−20.8513	+	16.1504i	−0.761382	+	0.589728i
$751$	−10.4902	−	6.05653i	−0.382793	−	0.221006i	0.296240	−	0.955114i	$-0.404267\pi$
$751$	−10.4902	−	6.05653i	−0.382793	−	0.221006i	−0.679033	+	0.734108i	$0.737601\pi$
$752$	−35.9272	−	30.6423i	−1.31013	−	1.11741i
$753$	2.83407	+	8.78770i	0.103279	+	0.320241i
$754$	−1.43229	−	3.95993i	−0.0521608	−	0.144212i
$755$		−	4.72090i		−	0.171811i
$756$	−9.42474	+	25.8297i	−0.342775	+	0.939418i
$757$		−	21.6528i		−	0.786983i	−0.919328	−	0.393491i	$-0.871267\pi$
$757$		−	21.6528i		−	0.786983i	0.919328	−	0.393491i	$-0.128733\pi$
$758$	−39.6373	+	14.3366i	−1.43969	+	0.520729i
$759$	1.02128	+	3.16670i	0.0370700	+	0.114944i
$760$	20.5388	+	0.123901i	0.745021	+	0.00449436i
$761$	−33.4532	−	19.3142i	−1.21268	−	0.700141i	−0.249337	−	0.968417i	$-0.580213\pi$
$761$	−33.4532	−	19.3142i	−1.21268	−	0.700141i	−0.963342	+	0.268276i	$0.913546\pi$
$762$	32.6571	+	42.1627i	1.18304	+	1.52739i
$763$	32.3778	−	3.72341i	1.17216	−	0.134797i
$764$	−7.65428	−	44.4542i	−0.276922	−	1.60830i
$765$	10.1933	+	14.1596i	0.368539	+	0.511941i
$766$	−2.79575	+	15.6711i	−0.101014	+	0.566221i
$767$	−12.4652	−	21.5903i	−0.450091	−	0.779580i
$768$	27.6736	+	1.47304i	0.998586	+	0.0531539i
$769$	32.8604			1.18498			0.592489	−	0.805579i	$-0.298145\pi$
$769$	32.8604			1.18498			0.592489	+	0.805579i	$0.298145\pi$
$770$	−0.554172	+	8.91989i	−0.0199710	+	0.321450i
$771$	14.2093	+	3.05276i	0.511736	+	0.109943i
$772$	−10.8956	−	4.01536i	−0.392140	−	0.144516i
$773$	−14.2511	−	24.6836i	−0.512576	−	0.887808i	−0.999894	−	0.0145830i	$-0.995358\pi$
$773$	−14.2511	−	24.6836i	−0.512576	−	0.887808i	0.487318	−	0.873225i	$-0.337975\pi$
$774$	−14.4309	+	21.1028i	−0.518707	+	0.758526i
$775$	−12.3061	−	7.10490i	−0.442046	−	0.255216i
$776$	−12.4815	+	21.3206i	−0.448060	+	0.765364i
$777$	35.2270	+	25.1876i	1.26376	+	0.903600i
$778$	−29.1593	−	24.5676i	−1.04541	−	0.880792i
$779$	6.79248	+	3.92164i	0.243366	+	0.140507i
$780$	8.94325	−	4.68423i	0.320220	−	0.167723i
$781$	22.4199	−	12.9441i	0.802246	−	0.463177i
$782$	−2.24988	−	6.22039i	−0.0804556	−	0.222441i
$783$	−4.07051	+	5.52600i	−0.145468	+	0.197483i
$784$	23.5730	−	15.1100i	0.841893	−	0.539644i
$785$		−	3.50188i		−	0.124987i
$786$	−13.0574	+	1.77926i	−0.465744	+	0.0634640i
$787$	−18.8558	−	32.6593i	−0.672138	−	1.16418i	−0.977297	−	0.211875i	$-0.932043\pi$
$787$	−18.8558	−	32.6593i	−0.672138	−	1.16418i	0.305159	−	0.952301i	$-0.401290\pi$
$788$	−4.85575	+	4.04129i	−0.172979	+	0.143965i
$789$	4.06997	+	3.68076i	0.144895	+	0.131038i
$790$	3.22465	−	3.82733i	0.114728	−	0.136170i
$791$	−7.65723	+	17.6611i	−0.272260	+	0.627956i
$792$	9.08232	+	12.7782i	0.322726	+	0.454055i
$793$	9.95957	−	17.2505i	0.353675	−	0.612583i
$794$	10.8543	+	1.93643i	0.385206	+	0.0687212i
$795$	−25.6970	+	8.28741i	−0.911379	+	0.293924i
$796$	−9.77078	+	26.5128i	−0.346316	+	0.939720i
$797$	46.8382			1.65910			0.829548	−	0.558436i	$-0.188598\pi$
$797$	46.8382			1.65910			0.829548	+	0.558436i	$0.188598\pi$
$798$	9.83849	−	35.0477i	0.348279	−	1.24068i
$799$			53.1045i			1.87870i
$800$	14.5454	−	11.9579i	0.514257	−	0.422775i
$801$	28.6494	−	2.88460i	1.01228	−	0.101922i
$802$	4.79760	+	0.855897i	0.169409	+	0.0302228i
$803$	14.0376	+	8.10460i	0.495375	+	0.286005i
$804$	−21.1509	−	0.870089i	−0.745934	−	0.0306857i
$805$	0.406308	+	3.53315i	0.0143205	+	0.124527i
$806$	10.4080	+	8.76909i	0.366607	+	0.308878i
$807$	20.0872	+	18.1662i	0.707101	+	0.639481i
$808$	−19.3480	−	0.116717i	−0.680659	−	0.00410610i
$809$	−0.943718	+	0.544856i	−0.0331794	+	0.0191561i	−0.516498	−	0.856288i	$-0.672765\pi$
$809$	−0.943718	+	0.544856i	−0.0331794	+	0.0191561i	0.483319	+	0.875445i	$0.339431\pi$
$810$	−14.4447	−	7.88081i	−0.507536	−	0.276903i
$811$	−10.7828			−0.378634			−0.189317	−	0.981916i	$-0.560627\pi$
$811$	−10.7828			−0.378634			−0.189317	+	0.981916i	$0.560627\pi$
$812$	6.70735	−	1.96514i	0.235382	−	0.0689630i
$813$	−24.3193	−	5.22482i	−0.852916	−	0.183242i
$814$	23.2193	−	8.39830i	0.813836	−	0.294360i
$815$	−5.71215	−	9.89373i	−0.200088	−	0.346562i
$816$	−18.9358	−	24.7545i	−0.662884	−	0.866580i
$817$	16.9235	−	29.3123i	0.592077	−	1.02551i
$818$	21.1770	+	17.8423i	0.740437	+	0.623842i
$819$	−3.81471	−	17.4817i	−0.133297	−	0.610860i
$820$	−3.55803	+	0.612633i	−0.124252	+	0.0213941i
$821$	−8.63020	+	14.9479i	−0.301196	+	0.521687i	−0.976407	−	0.215938i	$-0.930719\pi$
$821$	−8.63020	+	14.9479i	−0.301196	+	0.521687i	0.675211	+	0.737625i	$0.264053\pi$
$822$	12.1735	−	29.7701i	0.424599	−	1.03835i
$823$	31.7271	−	18.3176i	1.10594	−	0.638513i	0.168163	−	0.985759i	$-0.446217\pi$
$823$	31.7271	−	18.3176i	1.10594	−	0.638513i	0.937774	+	0.347246i	$0.112883\pi$
$824$	−11.0331	+	6.28154i	−0.384357	+	0.218828i
$825$	10.4143	+	2.23744i	0.362580	+	0.0778976i
$826$	37.0490	−	18.4275i	1.28910	−	0.641174i
$827$		−	46.5193i		−	1.61764i	−0.588060	−	0.808818i	$-0.700108\pi$
$827$		−	46.5193i		−	1.61764i	0.588060	−	0.808818i	$-0.299892\pi$
$828$	4.45111	+	4.37118i	0.154687	+	0.151909i
$829$	29.9474	−	17.2901i	1.04011	−	0.600511i	0.120249	−	0.992744i	$-0.461631\pi$
$829$	29.9474	−	17.2901i	1.04011	−	0.600511i	0.919866	+	0.392233i	$0.128297\pi$
$830$	−8.53803	−	1.52319i	−0.296359	−	0.0528708i
$831$	4.33577	−	4.79425i	0.150406	−	0.166311i
$832$	−15.7260	+	8.82818i	−0.545201	+	0.306062i
$833$	−30.1327	−	9.14339i	−1.04404	−	0.316800i
$834$	−25.1286	+	19.4633i	−0.870131	+	0.673959i
$835$	−7.68021	+	13.3025i	−0.265785	+	0.460353i
$836$	−13.2774	−	15.9533i	−0.459209	−	0.551755i
$837$	2.46326	−	22.0448i	0.0851427	−	0.761980i
$838$	13.2852	+	36.7303i	0.458928	+	1.26883i
$839$	39.6383			1.36847			0.684233	−	0.729264i	$-0.260137\pi$
$839$	39.6383			1.36847			0.684233	+	0.729264i	$0.260137\pi$
$840$	6.83938	+	15.2973i	0.235981	+	0.527808i
$841$	−27.2553			−0.939839
$842$	4.50340	+	12.4508i	0.155197	+	0.429084i
$843$	10.0146	+	31.0525i	0.344920	+	1.06950i
$844$	3.00393	−	2.50008i	0.103400	−	0.0860564i
$845$	5.11825	−	8.86506i	0.176073	−	0.304967i
$846$	−21.6677	−	45.1547i	−0.744952	−	1.55245i
$847$	−16.1225	+	11.9562i	−0.553975	+	0.410820i
$848$	45.4545	−	16.1313i	1.56092	−	0.553950i
$849$	−27.6775	−	25.0307i	−0.949889	−	0.859051i
$850$	−20.8472	−	3.71916i	−0.715053	−	0.127566i
$851$	8.50934	−	4.91287i	0.291696	−	0.168411i
$852$	25.9769	−	41.0032i	0.889955	−	1.40475i
$853$			10.8810i			0.372557i	0.982497	+	0.186279i	$0.0596427\pi$
$853$			10.8810i			0.372557i	−0.982497	+	0.186279i	$0.940357\pi$
$854$	27.5518	+	18.2742i	0.942803	+	0.625332i
$855$	19.8628	+	8.94772i	0.679292	+	0.306006i
$856$	−17.8209	+	10.1460i	−0.609105	+	0.346785i
$857$	−39.8564	+	23.0111i	−1.36147	+	0.786045i	−0.989820	−	0.142328i	$-0.954541\pi$
$857$	−39.8564	+	23.0111i	−1.36147	+	0.786045i	−0.371650	+	0.928373i	$0.621208\pi$
$858$	−9.44311	−	3.86144i	−0.322382	−	0.131827i
$859$	11.4205	−	19.7808i	0.389661	−	0.674912i	−0.602743	−	0.797935i	$-0.705926\pi$
$859$	11.4205	−	19.7808i	0.389661	−	0.674912i	0.992404	+	0.123023i	$0.0392589\pi$
$860$	2.64376	+	15.3543i	0.0901515	+	0.523579i
$861$	−0.620539	+	6.36868i	−0.0211479	+	0.217044i
$862$	−9.14861	−	7.70800i	−0.311603	−	0.262535i
$863$	−2.49061	+	4.31386i	−0.0847813	+	0.146846i	−0.905298	−	0.424777i	$-0.860353\pi$
$863$	−2.49061	+	4.31386i	−0.0847813	+	0.146846i	0.820517	+	0.571623i	$0.193686\pi$
$864$	26.2014	+	13.3225i	0.891388	+	0.453240i
$865$	−4.04001	−	6.99750i	−0.137364	−	0.237922i
$866$	−14.5212	+	5.25225i	−0.493452	+	0.178479i
$867$	−1.17745	+	5.48054i	−0.0399883	+	0.186129i
$868$	−15.5979	+	16.3392i	−0.529427	+	0.554589i
$869$	−5.05741			−0.171561
$870$	0.564740	+	4.14446i	0.0191465	+	0.140510i
$871$	11.9303	−	6.88795i	0.404242	−	0.233389i
$872$	0.210178	−	34.8409i	0.00711754	−	1.17986i
$873$	−21.2666	+	15.3095i	−0.719765	+	0.518148i
$874$	−6.31646	−	5.32182i	−0.213658	−	0.180013i
$875$	26.1368	+	11.3320i	0.883585	+	0.383091i
$876$	30.3658	+	1.24917i	1.02597	+	0.0422054i
$877$	25.7564	+	14.8705i	0.869731	+	0.502139i	0.867259	−	0.497857i	$-0.165880\pi$
$877$	25.7564	+	14.8705i	0.869731	+	0.502139i	0.00247223	+	0.999997i	$0.499213\pi$
$878$	32.5703	+	5.81057i	1.09919	+	0.196097i
$879$	6.82150	−	2.19997i	0.230083	−	0.0742030i
$880$	9.39535	+	1.73468i	0.316717	+	0.0584762i
$881$			34.5022i			1.16241i	0.813757	+	0.581205i	$0.197419\pi$
$881$			34.5022i			1.16241i	−0.813757	+	0.581205i	$0.802581\pi$
$882$	29.3525	−	4.52017i	0.988349	−	0.152202i
$883$	34.9022			1.17455			0.587276	−	0.809387i	$-0.300200\pi$
$883$	34.9022			1.17455			0.587276	+	0.809387i	$0.300200\pi$
$884$	19.0308	+	7.01345i	0.640076	+	0.235888i
$885$	7.60074	+	23.5678i	0.255496	+	0.792224i
$886$	−8.53961	−	1.52348i	−0.286894	−	0.0511822i
$887$	20.1225	−	34.8531i	0.675646	−	1.17025i	−0.300634	−	0.953740i	$-0.597198\pi$
$887$	20.1225	−	34.8531i	0.675646	−	1.17025i	0.976280	−	0.216513i	$-0.0694685\pi$
$888$	31.2594	−	34.1484i	1.04900	−	1.14595i
$889$	22.9140	−	52.8503i	0.768512	−	1.77254i
$890$	11.3068	−	13.4200i	0.379003	−	0.449838i
$891$	3.31483	+	16.2943i	0.111051	+	0.545880i
$892$	−4.60566	−	5.53386i	−0.154209	−	0.185287i
$893$	33.1544	+	57.4251i	1.10947	+	1.92166i
$894$	−2.26235	−	16.6027i	−0.0756642	−	0.555278i
$895$			2.14930i			0.0718431i
$896$	−13.0061	−	26.9600i	−0.434503	−	0.900671i
$897$	−3.96926	−	0.852766i	−0.132530	−	0.0284730i
$898$	17.2521	+	47.6978i	0.575709	+	1.59170i
$899$	−4.88320	+	2.81931i	−0.162864	+	0.0940294i
$900$	19.2438	−	5.34369i	0.641460	−	0.178123i
$901$	−46.9757	−	27.1214i	−1.56499	−	0.903546i
$902$	2.79014	+	2.35078i	0.0929015	+	0.0782725i
$903$	27.4834	+	2.67788i	0.914591	+	0.0891142i
$904$	17.7593	+	10.3967i	0.590664	+	0.345788i
$905$	5.00324	+	2.88862i	0.166313	+	0.0960210i
$906$	−3.38554	+	8.27929i	−0.112477	+	0.275061i
$907$	−3.79336	−	6.57028i	−0.125956	−	0.218163i	0.796150	−	0.605099i	$-0.206867\pi$
$907$	−3.79336	−	6.57028i	−0.125956	−	0.218163i	−0.922106	+	0.386937i	$0.873533\pi$
$908$	−4.03297	+	10.9433i	−0.133839	+	0.363168i
$909$	−18.7111	−	8.42892i	−0.620608	−	0.279570i
$910$	−9.08743	−	6.02741i	−0.301245	−	0.199807i
$911$	−34.9091			−1.15659			−0.578294	−	0.815828i	$-0.696281\pi$
$911$	−34.9091			−1.15659			−0.578294	+	0.815828i	$0.696281\pi$
$912$	−35.9312	−	14.9465i	−1.18980	−	0.494927i
$913$	4.38211	+	7.59004i	0.145027	+	0.251194i
$914$	−0.754996	+	4.23201i	−0.0249730	+	0.139983i
$915$	−13.2712	+	14.6746i	−0.438734	+	0.485127i
$916$	25.6730	−	4.42045i	0.848259	−	0.146056i
$917$	8.47870	+	11.4332i	0.279991	+	0.377557i
$918$	−7.72209	−	32.1424i	−0.254867	−	1.06086i
$919$	−14.5134	−	8.37933i	−0.478754	−	0.276409i	0.241143	−	0.970490i	$-0.422478\pi$
$919$	−14.5134	−	8.37933i	−0.478754	−	0.276409i	−0.719897	+	0.694081i	$0.755811\pi$
$920$	3.80192	+	0.0229352i	0.125345	+	0.000756150i
$921$	7.63484	−	2.46227i	0.251577	−	0.0811347i
$922$	−40.9028	+	14.7943i	−1.34706	+	0.487225i
$923$			31.5877i			1.03972i
$924$	7.36867	−	15.2459i	0.242411	−	0.501552i
$925$		−	31.4559i		−	1.03426i
$926$	−4.58960	−	12.6891i	−0.150824	−	0.416991i
$927$	−13.3984	+	1.34903i	−0.440060	+	0.0443080i
$928$	−1.22343	−	7.37104i	−0.0401611	−	0.241966i
$929$	18.0406	+	10.4157i	0.591892	+	0.341729i	0.765845	−	0.643025i	$-0.222321\pi$
$929$	18.0406	+	10.4157i	0.591892	+	0.341729i	−0.173953	+	0.984754i	$0.555654\pi$
$930$	−8.27800	−	10.6875i	−0.271446	−	0.350457i
$931$	−38.2928	+	8.92528i	−1.25499	+	0.292514i
$932$	31.0810	−	5.35162i	1.01809	−	0.175298i
$933$	−18.1101	−	16.3782i	−0.592899	−	0.536200i
$934$	−7.01621	−	1.25170i	−0.229577	−	0.0409568i
$935$	−5.37240	−	9.30527i	−0.175696	−	0.304315i
$936$	−19.0435	+	1.80144i	−0.622456	+	0.0588820i
$937$	43.8738			1.43329			0.716647	−	0.697437i	$-0.245676\pi$
$937$	43.8738			1.43329			0.716647	+	0.697437i	$0.245676\pi$
$938$	10.1826	+	20.4724i	0.332473	+	0.668447i
$939$	−5.06009	+	23.5526i	−0.165130	+	0.768609i
$940$	−28.6400	−	10.5548i	−0.934135	−	0.344258i
$941$	−25.3064	−	43.8320i	−0.824966	−	1.42888i	−0.901945	−	0.431850i	$-0.857861\pi$
$941$	−25.3064	−	43.8320i	−0.824966	−	1.42888i	0.0769795	−	0.997033i	$-0.475472\pi$
$942$	−2.51133	+	6.14142i	−0.0818235	+	0.200098i
$943$	1.25735	+	0.725930i	0.0409449	+	0.0236395i
$944$	−14.7947	−	41.6883i	−0.481526	−	1.35684i
$945$	0.0572043	+	17.7730i	0.00186086	+	0.578156i
$946$	10.1446	−	12.0406i	0.329828	−	0.391473i
$947$	31.6220	+	18.2569i	1.02758	+	0.593271i	0.916289	−	0.400517i	$-0.131170\pi$
$947$	31.6220	+	18.2569i	1.02758	+	0.593271i	0.111286	+	0.993788i	$0.464503\pi$
$948$	−8.39996	+	4.39967i	−0.272818	+	0.142895i
$949$	−17.1280	+	9.88887i	−0.555999	+	0.321006i
$950$	−24.8653	+	8.99364i	−0.806736	+	0.291792i
$951$	6.07110	−	28.2584i	0.196869	−	0.916342i
$952$	−13.5770	+	30.8043i	−0.440033	+	0.998372i
$953$		−	19.5458i		−	0.633151i	−0.948567	−	0.316576i	$-0.897467\pi$
$953$		−	19.5458i		−	0.633151i	0.948567	−	0.316576i	$-0.102533\pi$
$954$	51.0094	+	3.89423i	1.65149	+	0.126080i
$955$	−14.5791	−	25.2517i	−0.471768	−	0.817125i
$956$	34.9659	−	29.1010i	1.13088	−	0.941194i
$957$	2.83516	−	3.13496i	0.0916478	−	0.101339i
$958$	29.4838	+	24.8411i	0.952579	+	0.802578i
$959$	−34.5125	+	3.96889i	−1.11447	+	0.128162i
$960$	17.1140	−	5.29227i	0.552352	−	0.170807i
$961$	−6.38814	+	11.0646i	−0.206069	+	0.356922i
$962$	−5.29122	+	29.6591i	−0.170596	+	0.956249i
$963$	−21.6413	+	2.17898i	−0.697380	+	0.0702166i
$964$	−25.5996	−	9.43425i	−0.824508	−	0.303857i
$965$	−7.50596			−0.241625
$966$	1.82119	−	6.48764i	0.0585958	−	0.208736i
$967$			43.0521i			1.38446i	0.721675	+	0.692232i	$0.243372\pi$
$967$			43.0521i			1.38446i	−0.721675	+	0.692232i	$0.756628\pi$
$968$	10.6166	+	18.6475i	0.341232	+	0.599352i
$969$	13.4333	+	41.6531i	0.431540	+	1.33809i
$970$	−2.80471	+	15.7214i	−0.0900537	+	0.504782i
$971$	−27.2617	−	15.7395i	−0.874868	−	0.505105i	−0.00590513	−	0.999983i	$-0.501880\pi$
$971$	−27.2617	−	15.7395i	−0.874868	−	0.505105i	−0.868963	+	0.494877i	$0.835213\pi$
$972$	19.6808	+	24.1798i	0.631263	+	0.775569i
$973$	31.4983	+	13.6566i	1.00979	+	0.437809i
$974$	0.952763	−	1.13083i	0.0305285	−	0.0362342i
$975$	−8.71782	+	9.63966i	−0.279194	+	0.308716i
$976$	22.9357	−	26.8915i	0.734155	−	0.860775i
$977$	−35.4465	+	20.4650i	−1.13403	+	0.654734i	−0.944946	−	0.327226i	$-0.893886\pi$
$977$	−35.4465	+	20.4650i	−1.13403	+	0.654734i	−0.189087	+	0.981960i	$0.560553\pi$
$978$	2.92253	+	21.4476i	0.0934521	+	0.685817i
$979$	−17.7331			−0.566752
$980$	10.9202	−	14.4337i	0.348832	−	0.461069i
$981$	15.1784	−	33.6940i	0.484609	−	1.07577i
$982$	14.0986	+	38.9794i	0.449906	+	1.24388i
$983$	4.13945	+	7.16974i	0.132028	+	0.228679i	0.924458	−	0.381283i	$-0.124518\pi$
$983$	4.13945	+	7.16974i	0.132028	+	0.228679i	−0.792430	+	0.609963i	$0.791184\pi$
$984$	6.67925	+	1.47719i	0.212927	+	0.0470912i
$985$	−2.04181	+	3.53652i	−0.0650574	+	0.112683i
$986$	−5.41430	+	6.42623i	−0.172427	+	0.204653i
$987$	−31.4644	+	44.0056i	−1.00152	+	1.40071i
$988$	24.9578	−	4.29732i	0.794014	−	0.136716i
$989$	3.13268	−	5.42596i	0.0996135	−	0.172536i
$990$	8.36488	+	5.72020i	0.265853	+	0.181800i
$991$	−27.2946	+	15.7586i	−0.867043	+	0.500587i	−0.866364	−	0.499412i	$-0.833549\pi$
$991$	−27.2946	+	15.7586i	−0.867043	+	0.500587i	−0.000678305		1.00000i	$0.500216\pi$
$992$	15.3357	+	18.6541i	0.486909	+	0.592268i
$993$	3.50826	−	16.3295i	0.111331	−	0.518201i
$994$	−52.3275	−	3.25099i	−1.65973	−	0.103115i
$995$			18.2646i			0.579028i
$996$	13.8813	+	8.79425i	0.439844	+	0.278657i
$997$	−46.6045	+	26.9071i	−1.47598	+	0.852157i	−0.999633	−	0.0271004i	$-0.991373\pi$
$997$	−46.6045	+	26.9071i	−1.47598	+	0.852157i	−0.476347	+	0.879258i	$0.658039\pi$
$998$	7.14077	−	40.0265i	0.226037	−	1.26702i
$999$	44.9884	−	19.6777i	1.42337	−	0.622574i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.v.a.107.25	yes	56
3.2	odd	2	inner	168.2.v.a.107.4	yes	56
4.3	odd	2		672.2.bd.a.527.26		56
7.4	even	3	inner	168.2.v.a.11.13	yes	56
8.3	odd	2	inner	168.2.v.a.107.16	yes	56
8.5	even	2		672.2.bd.a.527.25		56
12.11	even	2		672.2.bd.a.527.5		56
21.11	odd	6	inner	168.2.v.a.11.16	yes	56
24.5	odd	2		672.2.bd.a.527.6		56
24.11	even	2	inner	168.2.v.a.107.13	yes	56
28.11	odd	6		672.2.bd.a.431.6		56
56.11	odd	6	inner	168.2.v.a.11.4	✓	56
56.53	even	6		672.2.bd.a.431.5		56
84.11	even	6		672.2.bd.a.431.25		56
168.11	even	6	inner	168.2.v.a.11.25	yes	56
168.53	odd	6		672.2.bd.a.431.26		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.v.a.11.4	✓	56	56.11	odd	6	inner
168.2.v.a.11.13	yes	56	7.4	even	3	inner
168.2.v.a.11.16	yes	56	21.11	odd	6	inner
168.2.v.a.11.25	yes	56	168.11	even	6	inner
168.2.v.a.107.4	yes	56	3.2	odd	2	inner
168.2.v.a.107.13	yes	56	24.11	even	2	inner
168.2.v.a.107.16	yes	56	8.3	odd	2	inner
168.2.v.a.107.25	yes	56	1.1	even	1	trivial
672.2.bd.a.431.5		56	56.53	even	6
672.2.bd.a.431.6		56	28.11	odd	6
672.2.bd.a.431.25		56	84.11	even	6
672.2.bd.a.431.26		56	168.53	odd	6
672.2.bd.a.527.5		56	12.11	even	2
672.2.bd.a.527.6		56	24.5	odd	2
672.2.bd.a.527.25		56	8.5	even	2
672.2.bd.a.527.26		56	4.3	odd	2

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+(1.32990 - 0.481016i) q^{2} +(-1.64844 + 0.531631i) q^{3} +(1.53725 - 1.27940i) q^{4} +(0.646402 - 1.11960i) q^{5} +(-1.93654 + 1.49994i) q^{6} +(2.42742 + 1.05244i) q^{7} +(1.42896 - 2.44091i) q^{8} +(2.43474 - 1.75273i) q^{9} +(0.321101 - 1.79988i) q^{10} +(-1.60004 + 0.923782i) q^{11} +(-1.85389 + 2.92627i) q^{12} -2.25432i q^{13} +(3.73446 + 0.232013i) q^{14} +(-0.470342 + 2.18925i) q^{15} +(0.726254 - 3.93352i) q^{16} +(-3.89580 + 2.24924i) q^{17} +(2.39486 - 3.50209i) q^{18} +(-2.80851 + 4.86448i) q^{19} +(-0.438742 - 2.54811i) q^{20} +(-4.56098 - 0.444404i) q^{21} +(-1.68353 + 1.99818i) q^{22} +(-0.519880 + 0.900459i) q^{23} +(-1.05790 + 4.78339i) q^{24} +(1.66433 + 2.88270i) q^{25} +(-1.08436 - 2.99801i) q^{26} +(-3.08172 + 4.18366i) q^{27} +(5.07804 - 1.48778i) q^{28} +1.32085 q^{29} +(0.427556 + 3.13771i) q^{30} +(-3.69700 + 2.13446i) q^{31} +(-0.926243 - 5.58051i) q^{32} +(2.14646 - 2.37343i) q^{33} +(-4.09909 + 4.86521i) q^{34} +(2.74740 - 2.03744i) q^{35} +(1.50034 - 5.80939i) q^{36} +(-8.18394 - 4.72500i) q^{37} +(-1.39513 + 7.82020i) q^{38} +(1.19846 + 3.71611i) q^{39} +(-1.80916 - 3.17768i) q^{40} -1.39634i q^{41} +(-6.27939 + 1.60289i) q^{42} -6.02578 q^{43} +(-1.27776 + 3.46717i) q^{44} +(-0.388538 - 3.85890i) q^{45} +(-0.258251 + 1.44759i) q^{46} +(5.90249 - 10.2234i) q^{47} +(0.893991 + 6.87028i) q^{48} +(4.78472 + 5.10944i) q^{49} +(3.60001 + 3.03313i) q^{50} +(5.22625 - 5.77888i) q^{51} +(-2.88418 - 3.46544i) q^{52} +(6.02901 + 10.4425i) q^{53} +(-2.08596 + 7.04619i) q^{54} +2.38854i q^{55} +(6.03762 - 4.42122i) q^{56} +(2.04356 - 9.51192i) q^{57} +(1.75660 - 0.635353i) q^{58} +(9.57732 - 5.52947i) q^{59} +(2.07790 + 3.96717i) q^{60} +(7.65220 + 4.41800i) q^{61} +(-3.88991 + 4.61693i) q^{62} +(7.75477 - 1.69218i) q^{63} +(-3.91612 - 6.97596i) q^{64} +(-2.52393 - 1.45719i) q^{65} +(1.71291 - 4.18890i) q^{66} +(3.05545 + 5.29219i) q^{67} +(-3.11112 + 8.44195i) q^{68} +(0.378281 - 1.76074i) q^{69} +(2.67372 - 4.03113i) q^{70} -14.0121 q^{71} +(-0.799109 - 8.44757i) q^{72} +(-4.38664 - 7.59788i) q^{73} +(-13.1566 - 2.34715i) q^{74} +(-4.27609 - 3.86717i) q^{75} +(1.90626 + 11.0711i) q^{76} +(-4.85619 + 0.558456i) q^{77} +(3.38135 + 4.36556i) q^{78} +(2.37061 + 1.36867i) q^{79} +(-3.93451 - 3.35575i) q^{80} +(2.85588 - 8.53487i) q^{81} +(-0.671663 - 1.85699i) q^{82} -4.74366i q^{83} +(-7.57992 + 5.15217i) q^{84} +5.81566i q^{85} +(-8.01366 + 2.89850i) q^{86} +(-2.17736 + 0.702207i) q^{87} +(-0.0315236 + 5.22561i) q^{88} +(8.31219 + 4.79904i) q^{89} +(-2.37291 - 4.94504i) q^{90} +(2.37254 - 5.47217i) q^{91} +(0.352866 + 2.04936i) q^{92} +(4.95955 - 5.48398i) q^{93} +(2.93207 - 16.4353i) q^{94} +(3.63085 + 6.28882i) q^{95} +(4.49363 + 8.70674i) q^{96} -8.73466 q^{97} +(8.82091 + 4.49350i) q^{98} +(-2.27653 + 5.05360i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{3} - 2 q^{4} - 8 q^{6} - 2 q^{9} + 6 q^{10} + 10 q^{12} - 10 q^{16} - 10 q^{18} - 4 q^{19} - 20 q^{22} - 8 q^{24} - 16 q^{25} - 8 q^{27} - 22 q^{28} - 12 q^{30} - 14 q^{33} - 56 q^{34} + 4 q^{36}+ \cdots - 44 q^{99}+O(q^{100}) \) 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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