LMFDB - Embedded newform 140.2.o.a.131.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,2,Mod(31,140)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("140.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	140.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.16
Character	$\chi$	$=$	140.131
Dual form			140.2.o.a.31.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.38207 + 0.299797i) q^{2} +(-1.36859 - 2.37047i) q^{3} +(1.82024 + 0.828682i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-1.18083 - 3.68646i) q^{6} +(1.02440 - 2.43939i) q^{7} +(2.26727 + 1.69100i) q^{8} +(-2.24609 + 3.89033i) q^{9} +(-1.04701 - 0.950668i) q^{10} +(-0.0868131 + 0.0501216i) q^{11} +(-0.526805 - 5.44896i) q^{12} +4.11735i q^{13} +(2.14711 - 3.06430i) q^{14} +2.73718i q^{15} +(2.62657 + 3.01680i) q^{16} +(4.67424 - 2.69867i) q^{17} +(-4.27056 + 4.70335i) q^{18} +(-3.72967 + 6.45997i) q^{19} +(-1.16204 - 1.62778i) q^{20} +(-7.18448 + 0.910218i) q^{21} +(-0.135008 + 0.0432453i) q^{22} +(-1.30623 - 0.754151i) q^{23} +(0.905498 - 7.68879i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-1.23437 + 5.69048i) q^{26} +4.08434 q^{27} +(3.88613 - 3.59138i) q^{28} -2.37688 q^{29} +(-0.820599 + 3.78298i) q^{30} +(2.72129 + 4.71341i) q^{31} +(2.72568 + 4.95688i) q^{32} +(0.237623 + 0.137192i) q^{33} +(7.26919 - 2.32844i) q^{34} +(-2.10685 + 1.60037i) q^{35} +(-7.31227 + 5.22007i) q^{36} +(-0.519260 + 0.899386i) q^{37} +(-7.09135 + 7.81000i) q^{38} +(9.76007 - 5.63498i) q^{39} +(-1.11801 - 2.59808i) q^{40} -7.99125i q^{41} +(-10.2023 - 0.895897i) q^{42} -7.04778i q^{43} +(-0.199556 + 0.0192930i) q^{44} +(3.89033 - 2.24609i) q^{45} +(-1.57921 - 1.43389i) q^{46} +(-2.22188 + 3.84841i) q^{47} +(3.55654 - 10.3550i) q^{48} +(-4.90122 - 4.99781i) q^{49} +(0.431404 + 1.34681i) q^{50} +(-12.7943 - 7.38677i) q^{51} +(-3.41198 + 7.49459i) q^{52} +(-3.07131 - 5.31966i) q^{53} +(5.64485 + 1.22447i) q^{54} +0.100243 q^{55} +(6.44759 - 3.79849i) q^{56} +20.4176 q^{57} +(-3.28502 - 0.712582i) q^{58} +(-4.26148 - 7.38111i) q^{59} +(-2.26825 + 4.98234i) q^{60} +(6.84408 + 3.95143i) q^{61} +(2.34795 + 7.33010i) q^{62} +(7.18914 + 9.46432i) q^{63} +(2.28103 + 7.66791i) q^{64} +(2.05868 - 3.56573i) q^{65} +(0.287283 + 0.260848i) q^{66} +(0.0950895 - 0.0549000i) q^{67} +(10.7446 - 1.03879i) q^{68} +4.12850i q^{69} +(-3.39160 + 1.58020i) q^{70} +6.73221i q^{71} +(-11.6710 + 5.02231i) q^{72} +(-5.32344 + 3.07349i) q^{73} +(-0.987288 + 1.08734i) q^{74} +(1.36859 - 2.37047i) q^{75} +(-12.1422 + 8.66802i) q^{76} +(0.0333347 + 0.263115i) q^{77} +(15.1785 - 4.86190i) q^{78} +(-3.70178 - 2.13723i) q^{79} +(-0.766277 - 3.92592i) q^{80} +(1.14846 + 1.98919i) q^{81} +(2.39575 - 11.0445i) q^{82} +6.50159 q^{83} +(-13.8318 - 4.29682i) q^{84} -5.39735 q^{85} +(2.11290 - 9.74053i) q^{86} +(3.25298 + 5.63433i) q^{87} +(-0.281584 - 0.0331618i) q^{88} +(-2.76417 - 1.59589i) q^{89} +(6.05009 - 1.93794i) q^{90} +(10.0438 + 4.21781i) q^{91} +(-1.75270 - 2.45519i) q^{92} +(7.44866 - 12.9015i) q^{93} +(-4.22454 + 4.65267i) q^{94} +(6.45997 - 3.72967i) q^{95} +(8.01978 - 13.2451i) q^{96} -11.0691i q^{97} +(-5.27550 - 8.37670i) q^{98} -0.450309i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9} - 30 q^{12} + 2 q^{14} - 14 q^{16} - 12 q^{21} - 8 q^{22} + 36 q^{24} + 16 q^{25} + 30 q^{26} + 2 q^{28} - 40 q^{29} + 2 q^{32} + 60 q^{36} + 8 q^{37} - 60 q^{38}+ \cdots + 78 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9 - 30 * q^12 + 2 * q^14 - 14 * q^16 - 12 * q^21 - 8 * q^22 + 36 * q^24 + 16 * q^25 + 30 * q^26 + 2 * q^28 - 40 * q^29 + 2 * q^32 + 60 * q^36 + 8 * q^37 - 60 * q^38 - 62 * q^42 - 18 * q^44 + 12 * q^45 + 2 * q^46 - 16 * q^49 + 4 * q^50 - 36 * q^52 - 8 * q^53 + 12 * q^54 - 4 * q^56 + 48 * q^57 + 2 * q^58 + 14 * q^60 + 24 * q^61 + 4 * q^64 + 4 * q^65 + 24 * q^66 + 60 * q^68 - 4 * q^70 + 4 * q^72 - 72 * q^73 + 38 * q^74 - 40 * q^77 + 120 * q^78 - 36 * q^81 + 42 * q^82 - 20 * q^84 + 28 * q^86 + 4 * q^88 - 60 * q^89 - 4 * q^92 - 8 * q^93 + 18 * q^94 - 60 * q^96 + 78 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.38207	+	0.299797i	0.977272	+	0.211988i
$2$	1.38207	+	0.299797i	0.977272	+	0.211988i
$3$	−1.36859	−	2.37047i	−0.790157	−	1.36859i	−0.925870	−	0.377843i	$-0.876666\pi$
$3$	−1.36859	−	2.37047i	−0.790157	−	1.36859i	0.135713	−	0.990748i	$-0.456668\pi$
$4$	1.82024	+	0.828682i	0.910122	+	0.414341i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	−1.18083	−	3.68646i	−0.482073	−	1.50499i
$7$	1.02440	−	2.43939i	0.387186	−	0.922002i
$7$	1.02440	−	2.43939i	0.387186	−	0.922002i
$8$	2.26727	+	1.69100i	0.801601	+	0.597859i
$9$	−2.24609	+	3.89033i	−0.748695	+	1.29678i
$10$	−1.04701	−	0.950668i	−0.331094	−	0.300627i
$11$	−0.0868131	+	0.0501216i	−0.0261751	+	0.0151122i	−0.513030	−	0.858370i	$-0.671477\pi$
$11$	−0.0868131	+	0.0501216i	−0.0261751	+	0.0151122i	0.486855	+	0.873483i	$0.338144\pi$
$12$	−0.526805	−	5.44896i	−0.152076	−	1.57298i
$13$			4.11735i			1.14195i	0.820968	+	0.570974i	$0.193434\pi$
$13$			4.11735i			1.14195i	−0.820968	+	0.570974i	$0.806566\pi$
$14$	2.14711	−	3.06430i	0.573840	−	0.818967i
$15$			2.73718i			0.706738i
$16$	2.62657	+	3.01680i	0.656643	+	0.754201i
$17$	4.67424	−	2.69867i	1.13367	−	0.654525i	0.188815	−	0.982013i	$-0.439535\pi$
$17$	4.67424	−	2.69867i	1.13367	−	0.654525i	0.944855	+	0.327488i	$0.106202\pi$
$18$	−4.27056	+	4.70335i	−1.00658	+	1.10859i
$19$	−3.72967	+	6.45997i	−0.855645	+	1.48202i	0.0204012	+	0.999792i	$0.493506\pi$
$19$	−3.72967	+	6.45997i	−0.855645	+	1.48202i	−0.876046	+	0.482228i	$0.839828\pi$
$20$	−1.16204	−	1.62778i	−0.259839	−	0.363983i
$21$	−7.18448	+	0.910218i	−1.56778	+	0.198626i
$22$	−0.135008	+	0.0432453i	−0.0287838	+	0.00921993i
$23$	−1.30623	−	0.754151i	−0.272367	−	0.157251i	0.357596	−	0.933877i	$-0.383597\pi$
$23$	−1.30623	−	0.754151i	−0.272367	−	0.157251i	−0.629963	+	0.776625i	$0.716930\pi$
$24$	0.905498	−	7.68879i	0.184834	−	1.56947i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−1.23437	+	5.69048i	−0.242080	+	1.11599i
$27$	4.08434			0.786032
$28$	3.88613	−	3.59138i	0.734409	−	0.678707i
$29$	−2.37688			−0.441376			−0.220688	−	0.975344i	$-0.570830\pi$
$29$	−2.37688			−0.441376			−0.220688	+	0.975344i	$0.570830\pi$
$30$	−0.820599	+	3.78298i	−0.149820	+	0.690675i
$31$	2.72129	+	4.71341i	0.488758	+	0.846553i	0.999916	−	0.0129330i	$-0.00411682\pi$
$31$	2.72129	+	4.71341i	0.488758	+	0.846553i	−0.511159	+	0.859486i	$0.670783\pi$
$32$	2.72568	+	4.95688i	0.481837	+	0.876261i
$33$	0.237623	+	0.137192i	0.0413649	+	0.0238820i
$34$	7.26919	−	2.32844i	1.24666	−	0.399324i
$35$	−2.10685	+	1.60037i	−0.356122	+	0.270512i
$36$	−7.31227	+	5.22007i	−1.21871	+	0.870011i
$37$	−0.519260	+	0.899386i	−0.0853659	+	0.147858i	−0.905547	−	0.424246i	$-0.860539\pi$
$37$	−0.519260	+	0.899386i	−0.0853659	+	0.147858i	0.820181	+	0.572104i	$0.193873\pi$
$38$	−7.09135	+	7.81000i	−1.15037	+	1.26695i
$39$	9.76007	−	5.63498i	1.56286	−	0.902318i
$40$	−1.11801	−	2.59808i	−0.176774	−	0.410793i
$41$		−	7.99125i		−	1.24802i	−0.781415	−	0.624012i	$-0.785502\pi$
$41$		−	7.99125i		−	1.24802i	0.781415	−	0.624012i	$-0.214498\pi$
$42$	−10.2023	−	0.895897i	−1.57426	−	0.138240i
$43$		−	7.04778i		−	1.07478i	−0.843335	−	0.537388i	$-0.819411\pi$
$43$		−	7.04778i		−	1.07478i	0.843335	−	0.537388i	$-0.180589\pi$
$44$	−0.199556	+	0.0192930i	−0.0300842	+	0.00290854i
$45$	3.89033	−	2.24609i	0.579937	−	0.334827i
$46$	−1.57921	−	1.43389i	−0.232842	−	0.211416i
$47$	−2.22188	+	3.84841i	−0.324095	+	0.561348i	−0.981329	−	0.192338i	$-0.938393\pi$
$47$	−2.22188	+	3.84841i	−0.324095	+	0.561348i	0.657234	+	0.753686i	$0.271726\pi$
$48$	3.55654	−	10.3550i	0.513342	−	1.49461i
$49$	−4.90122	−	4.99781i	−0.700174	−	0.713973i
$50$	0.431404	+	1.34681i	0.0610097	+	0.190467i
$51$	−12.7943	−	7.38677i	−1.79155	−	1.03435i
$52$	−3.41198	+	7.49459i	−0.473156	+	1.03931i
$53$	−3.07131	−	5.31966i	−0.421876	−	0.730711i	0.574247	−	0.818682i	$-0.305295\pi$
$53$	−3.07131	−	5.31966i	−0.421876	−	0.730711i	−0.996123	+	0.0879710i	$0.971962\pi$
$54$	5.64485	+	1.22447i	0.768167	+	0.166630i
$55$	0.100243			0.0135168
$56$	6.44759	−	3.79849i	0.861596	−	0.507595i
$57$	20.4176			2.70437
$58$	−3.28502	−	0.712582i	−0.431344	−	0.0935666i
$59$	−4.26148	−	7.38111i	−0.554798	−	0.960938i	−0.997919	−	0.0644767i	$-0.979462\pi$
$59$	−4.26148	−	7.38111i	−0.554798	−	0.960938i	0.443121	−	0.896462i	$-0.353871\pi$
$60$	−2.26825	+	4.98234i	−0.292830	+	0.643217i
$61$	6.84408	+	3.95143i	0.876295	+	0.505929i	0.869435	−	0.494048i	$-0.164483\pi$
$61$	6.84408	+	3.95143i	0.876295	+	0.505929i	0.00685975	+	0.999976i	$0.497816\pi$
$62$	2.34795	+	7.33010i	0.298190	+	0.930924i
$63$	7.18914	+	9.46432i	0.905747	+	1.19239i
$64$	2.28103	+	7.66791i	0.285129	+	0.958489i
$65$	2.05868	−	3.56573i	0.255348	−	0.442275i
$66$	0.287283	+	0.260848i	0.0353621	+	0.0321081i
$67$	0.0950895	−	0.0549000i	0.0116170	−	0.00670710i	−0.494180	−	0.869359i	$-0.664532\pi$
$67$	0.0950895	−	0.0549000i	0.0116170	−	0.00670710i	0.505797	+	0.862652i	$0.331198\pi$
$68$	10.7446	−	1.03879i	1.30297	−	0.125972i
$69$			4.12850i			0.497013i
$70$	−3.39160	+	1.58020i	−0.405374	+	0.188870i
$71$			6.73221i			0.798967i	0.916740	+	0.399483i	$0.130810\pi$
$71$			6.73221i			0.798967i	−0.916740	+	0.399483i	$0.869190\pi$
$72$	−11.6710	+	5.02231i	−1.37545	+	0.591885i
$73$	−5.32344	+	3.07349i	−0.623062	+	0.359725i	−0.778060	−	0.628190i	$-0.783796\pi$
$73$	−5.32344	+	3.07349i	−0.623062	+	0.359725i	0.154998	+	0.987915i	$0.450463\pi$
$74$	−0.987288	+	1.08734i	−0.114770	+	0.126401i
$75$	1.36859	−	2.37047i	0.158031	−	0.273718i
$76$	−12.1422	+	8.66802i	−1.39280	+	0.994290i
$77$	0.0333347	+	0.263115i	0.00379884	+	0.0299848i
$78$	15.1785	−	4.86190i	1.71862	−	0.550502i
$79$	−3.70178	−	2.13723i	−0.416483	−	0.240457i	0.277088	−	0.960844i	$-0.410631\pi$
$79$	−3.70178	−	2.13723i	−0.416483	−	0.240457i	−0.693572	+	0.720388i	$0.743964\pi$
$80$	−0.766277	−	3.92592i	−0.0856724	−	0.438931i
$81$	1.14846	+	1.98919i	0.127607	+	0.221021i
$82$	2.39575	−	11.0445i	0.264566	−	1.21966i
$83$	6.50159			0.713642			0.356821	−	0.934173i	$-0.383861\pi$
$83$	6.50159			0.713642			0.356821	+	0.934173i	$0.383861\pi$
$84$	−13.8318	−	4.29682i	−1.50917	−	0.468822i
$85$	−5.39735			−0.585425
$86$	2.11290	−	9.74053i	0.227840	−	1.05035i
$87$	3.25298	+	5.63433i	0.348756	+	0.604063i
$88$	−0.281584	−	0.0331618i	−0.0300170	−	0.00353506i
$89$	−2.76417	−	1.59589i	−0.293001	−	0.169164i	0.346293	−	0.938126i	$-0.387440\pi$
$89$	−2.76417	−	1.59589i	−0.293001	−	0.169164i	−0.639294	+	0.768962i	$0.720774\pi$
$90$	6.05009	−	1.93794i	0.637735	−	0.204277i
$91$	10.0438	+	4.21781i	1.05288	+	0.442147i
$92$	−1.75270	−	2.45519i	−0.182732	−	0.255971i
$93$	7.44866	−	12.9015i	0.772391	−	1.33782i
$94$	−4.22454	+	4.65267i	−0.435728	+	0.479886i
$95$	6.45997	−	3.72967i	0.662779	−	0.382656i
$96$	8.01978	−	13.2451i	0.818516	−	1.35182i
$97$		−	11.0691i		−	1.12390i	−0.827173	−	0.561948i	$-0.810052\pi$
$97$		−	11.0691i		−	1.12390i	0.827173	−	0.561948i	$-0.189948\pi$
$98$	−5.27550	−	8.37670i	−0.532906	−	0.846174i
$99$		−	0.450309i		−	0.0452578i
$100$	0.192463	+	1.99072i	0.0192463	+	0.199072i
$101$	−6.20412	+	3.58195i	−0.617333	+	0.356418i	−0.775830	−	0.630942i	$-0.782669\pi$
$101$	−6.20412	+	3.58195i	−0.617333	+	0.356418i	0.158497	+	0.987359i	$0.449335\pi$
$102$	−15.4680	−	14.0447i	−1.53156	−	1.39063i
$103$	−2.44304	+	4.23147i	−0.240720	+	0.416939i	−0.960920	−	0.276828i	$-0.910717\pi$
$103$	−2.44304	+	4.23147i	−0.240720	+	0.416939i	0.720200	+	0.693767i	$0.244050\pi$
$104$	−6.96245	+	9.33516i	−0.682724	+	0.915388i
$105$	6.67705	+	2.80397i	0.651613	+	0.273639i
$106$	−2.64995	−	8.27292i	−0.257386	−	0.803537i
$107$	−6.55470	−	3.78436i	−0.633667	−	0.365848i	0.148504	−	0.988912i	$-0.452554\pi$
$107$	−6.55470	−	3.78436i	−0.633667	−	0.365848i	−0.782171	+	0.623064i	$0.785888\pi$
$108$	7.43450	+	3.38462i	0.715385	+	0.325685i
$109$	9.02662	+	15.6346i	0.864593	+	1.49752i	0.867451	+	0.497523i	$0.165757\pi$
$109$	9.02662	+	15.6346i	0.864593	+	1.49752i	−0.00285729	+	0.999996i	$0.500910\pi$
$110$	0.138543	+	0.0300526i	0.0132096	+	0.00286540i
$111$	2.84262			0.269810
$112$	10.0498	−	3.31682i	0.949618	−	0.313410i
$113$	−18.1432			−1.70677			−0.853384	−	0.521283i	$-0.825453\pi$
$113$	−18.1432			−1.70677			−0.853384	+	0.521283i	$0.825453\pi$
$114$	28.2185	+	6.12112i	2.64291	+	0.573296i
$115$	0.754151	+	1.30623i	0.0703250	+	0.121806i
$116$	−4.32651	−	1.96968i	−0.401706	−	0.182880i
$117$	−16.0179	−	9.24793i	−1.48085	−	0.854971i
$118$	−3.67684	−	11.4788i	−0.338481	−	1.05671i
$119$	−1.79483	−	14.1668i	−0.164531	−	1.29867i
$120$	−4.62858	+	6.20593i	−0.422529	+	0.566522i
$121$	−5.49498	+	9.51758i	−0.499543	+	0.865234i
$122$	8.27438	+	7.51299i	0.749127	+	0.680195i
$123$	−18.9430	+	10.9368i	−1.70803	+	0.986134i
$124$	1.04749	+	10.8346i	0.0940676	+	0.972979i
$125$		−	1.00000i		−	0.0894427i
$126$	7.09853	+	15.2357i	0.632388	+	1.35730i
$127$		−	4.37573i		−	0.388283i	−0.980974	−	0.194141i	$-0.937808\pi$
$127$		−	4.37573i		−	0.388283i	0.980974	−	0.194141i	$-0.0621921\pi$
$128$	0.853736	+	11.2815i	0.0754603	+	0.997149i
$129$	−16.7065	+	9.64553i	−1.47093	+	0.849241i
$130$	3.91424	−	4.31091i	0.343301	−	0.378092i
$131$	1.49073	−	2.58201i	0.130245	−	0.225592i	−0.793526	−	0.608537i	$-0.791757\pi$
$131$	1.49073	−	2.58201i	0.130245	−	0.225592i	0.923771	+	0.382945i	$0.125090\pi$
$132$	0.318844	+	0.446637i	0.0277518	+	0.0388747i
$133$	11.9377	+	15.7157i	1.03513	+	1.36272i
$134$	0.147879	−	0.0473681i	0.0127748	−	0.00409198i
$135$	−3.53714	−	2.04217i	−0.304429	−	0.175762i
$136$	15.1612	+	1.78552i	1.30007	+	0.153107i
$137$	0.762377	+	1.32048i	0.0651342	+	0.112816i	0.896754	−	0.442530i	$-0.145919\pi$
$137$	0.762377	+	1.32048i	0.0651342	+	0.112816i	−0.831619	+	0.555346i	$0.812586\pi$
$138$	−1.23771	+	5.70588i	−0.105361	+	0.485717i
$139$	−7.16082			−0.607373			−0.303686	−	0.952772i	$-0.598217\pi$
$139$	−7.16082			−0.607373			−0.303686	+	0.952772i	$0.598217\pi$
$140$	−5.16118	+	1.16716i	−0.436199	+	0.0986430i
$141$	12.1634			1.02434
$142$	−2.01830	+	9.30440i	−0.169372	+	0.780808i
$143$	−0.206368	−	0.357440i	−0.0172574	−	0.0298907i
$144$	−17.6359	+	3.44225i	−1.46966	+	0.286854i
$145$	2.05844	+	1.18844i	0.170944	+	0.0986947i
$146$	−8.27880	+	2.65183i	−0.685158	+	0.219467i
$147$	−5.13939	+	18.4581i	−0.423890	+	1.52240i
$148$	−1.69048	+	1.20680i	−0.138957	+	0.0991983i
$149$	10.5236	−	18.2275i	0.862129	−	1.49325i	−0.00774027	−	0.999970i	$-0.502464\pi$
$149$	10.5236	−	18.2275i	0.862129	−	1.49325i	0.869870	−	0.493282i	$-0.164203\pi$
$150$	2.60215	−	2.86586i	0.212465	−	0.233996i
$151$	3.31081	−	1.91150i	0.269430	−	0.155555i	−0.359199	−	0.933261i	$-0.616950\pi$
$151$	3.31081	−	1.91150i	0.269430	−	0.155555i	0.628628	+	0.777706i	$0.283617\pi$
$152$	−19.3800	+	8.33964i	−1.57192	+	0.676434i
$153$			24.2458i			1.96016i
$154$	−0.0328102	+	0.373638i	−0.00264392	+	0.0301086i
$155$		−	5.44258i		−	0.437158i
$156$	22.4353	−	2.16904i	1.79626	−	0.173663i
$157$	−1.11209	+	0.642065i	−0.0887543	+	0.0512423i	−0.543720	−	0.839266i	$-0.682985\pi$
$157$	−1.11209	+	0.642065i	−0.0887543	+	0.0512423i	0.454966	+	0.890509i	$0.349651\pi$
$158$	−4.47540	−	4.06358i	−0.356044	−	0.323281i
$159$	−8.40673	+	14.5609i	−0.666697	+	1.15475i
$160$	0.117927	−	5.65562i	0.00932296	−	0.447116i
$161$	−3.17776	+	2.41384i	−0.250443	+	0.190238i
$162$	0.990900	+	3.09351i	0.0778525	+	0.243049i
$163$	7.44875	+	4.30054i	0.583431	+	0.336844i	0.762496	−	0.646993i	$-0.223974\pi$
$163$	7.44875	+	4.30054i	0.583431	+	0.336844i	−0.179064	+	0.983837i	$0.557307\pi$
$164$	6.62220	−	14.5460i	0.517107	−	1.13585i
$165$	−0.137192	−	0.237623i	−0.0106804	−	0.0184989i
$166$	8.98566	+	1.94916i	0.697422	+	0.151284i
$167$	8.10448			0.627144			0.313572	−	0.949565i	$-0.398474\pi$
$167$	8.10448			0.627144			0.313572	+	0.949565i	$0.398474\pi$
$168$	−17.8283	−	10.0852i	−1.37549	−	0.778093i
$169$	−3.95261			−0.304047
$170$	−7.45952	−	1.61811i	−0.572119	−	0.124103i
$171$	−16.7543	−	29.0193i	−1.28123	−	2.21916i
$172$	5.84036	−	12.8287i	0.445323	−	0.978177i
$173$	−6.95744	−	4.01688i	−0.528964	−	0.305398i	0.211630	−	0.977350i	$-0.432123\pi$
$173$	−6.95744	−	4.01688i	−0.528964	−	0.305398i	−0.740595	+	0.671952i	$0.765456\pi$
$174$	2.80670	+	8.76228i	0.212775	+	0.664267i
$175$	2.62477	−	0.332538i	0.198414	−	0.0251375i
$176$	−0.379228	−	0.130250i	−0.0285854	−	0.00981797i
$177$	−11.6645	+	20.2034i	−0.876755	+	1.51858i
$178$	−3.34183	−	3.03433i	−0.250481	−	0.227432i
$179$	7.66309	−	4.42429i	0.572766	−	0.330687i	−0.185487	−	0.982647i	$-0.559386\pi$
$179$	7.66309	−	4.42429i	0.572766	−	0.330687i	0.758253	+	0.651960i	$0.226053\pi$
$180$	8.94264	−	0.864575i	0.666545	−	0.0644416i
$181$		−	21.3610i		−	1.58775i	−0.608082	−	0.793874i	$-0.708061\pi$
$181$		−	21.3610i		−	1.58775i	0.608082	−	0.793874i	$-0.291939\pi$
$182$	12.6168	+	8.84042i	0.935219	+	0.655296i
$183$		−	21.6316i		−	1.59905i
$184$	−1.68630	−	3.91870i	−0.124316	−	0.288890i
$185$	0.899386	−	0.519260i	0.0661241	−	0.0381768i
$186$	14.1624	−	15.5977i	1.03844	−	1.14368i
$187$	−0.270524	+	0.468561i	−0.0197826	+	0.0342645i
$188$	−7.23347	+	5.16381i	−0.527555	+	0.376610i
$189$	4.18399	−	9.96329i	0.304341	−	0.724723i
$190$	10.0463	−	3.21799i	0.728835	−	0.233457i
$191$	21.6710	+	12.5117i	1.56806	+	0.905317i	0.996396	+	0.0848269i	$0.0270337\pi$
$191$	21.6710	+	12.5117i	1.56806	+	0.905317i	0.571660	+	0.820491i	$0.306300\pi$
$192$	15.0548	−	15.9014i	1.08648	−	1.14758i
$193$	−4.08078	−	7.06813i	−0.293741	−	0.508775i	0.680950	−	0.732330i	$-0.261567\pi$
$193$	−4.08078	−	7.06813i	−0.293741	−	0.508775i	−0.974691	+	0.223555i	$0.928234\pi$
$194$	3.31848	−	15.2983i	0.238253	−	1.09835i
$195$	−11.2700			−0.807058
$196$	−4.77982	−	13.1588i	−0.341415	−	0.939913i
$197$	−12.4517			−0.887149			−0.443574	−	0.896238i	$-0.646290\pi$
$197$	−12.4517			−0.887149			−0.443574	+	0.896238i	$0.646290\pi$
$198$	0.135001	−	0.622359i	0.00959412	−	0.0442292i
$199$	11.5867	+	20.0687i	0.821358	+	1.42263i	0.904671	+	0.426110i	$0.140116\pi$
$199$	11.5867	+	20.0687i	0.821358	+	1.42263i	−0.0833132	+	0.996523i	$0.526550\pi$
$200$	−0.330814	+	2.80901i	−0.0233921	+	0.198627i
$201$	−0.260277	−	0.150271i	−0.0183586	−	0.0105993i
$202$	−9.64840	+	3.09054i	−0.678859	+	0.217449i
$203$	−2.43487	+	5.79814i	−0.170895	+	0.406949i
$204$	−17.1674	−	24.0481i	−1.20196	−	1.68370i
$205$	−3.99562	+	6.92062i	−0.279067	+	0.483357i
$206$	−4.64504	+	5.11578i	−0.323635	+	0.356433i
$207$	5.86780	−	3.38778i	0.407840	−	0.235467i
$208$	−12.4213	+	10.8145i	−0.861259	+	0.749853i
$209$		−	0.747747i		−	0.0517228i
$210$	8.38754	+	5.87704i	0.578795	+	0.405554i
$211$		−	10.9759i		−	0.755613i	−0.925885	−	0.377807i	$-0.876678\pi$
$211$		−	10.9759i		−	0.755613i	0.925885	−	0.377807i	$-0.123322\pi$
$212$	−1.18222	−	12.2282i	−0.0811954	−	0.839837i
$213$	15.9585	−	9.21365i	1.09346	−	0.631309i
$214$	−7.92453	−	7.19533i	−0.541710	−	0.491863i
$215$	−3.52389	+	6.10355i	−0.240327	+	0.416259i
$216$	9.26031	+	6.90663i	0.630084	+	0.469936i
$217$	14.2855	−	1.80987i	0.969764	−	0.122862i
$218$	7.78824	+	24.3142i	0.527486	+	1.64677i
$219$	14.5712	+	8.41270i	0.984633	+	0.568478i
$220$	0.182467	+	0.0830696i	0.0123019	+	0.00560055i
$221$	11.1114	+	19.2455i	0.747434	+	1.29459i
$222$	3.92871	+	0.852209i	0.263678	+	0.0571965i
$223$	−14.9798			−1.00312			−0.501559	−	0.865123i	$-0.667240\pi$
$223$	−14.9798			−1.00312			−0.501559	+	0.865123i	$0.667240\pi$
$224$	14.8839	−	1.57118i	0.994474	−	0.104979i
$225$	−4.49217			−0.299478
$226$	−25.0752	−	5.43927i	−1.66798	−	0.361815i
$227$	0.753708	+	1.30546i	0.0500254	+	0.0866465i	0.889954	−	0.456051i	$-0.150736\pi$
$227$	0.753708	+	1.30546i	0.0500254	+	0.0866465i	−0.839928	+	0.542697i	$0.817403\pi$
$228$	37.1649	+	16.9197i	2.46131	+	1.12053i
$229$	7.38329	+	4.26274i	0.487901	+	0.281690i	0.723703	−	0.690111i	$-0.242438\pi$
$229$	7.38329	+	4.26274i	0.487901	+	0.281690i	−0.235802	+	0.971801i	$0.575772\pi$
$230$	0.650688	+	2.03139i	0.0429051	+	0.133946i
$231$	0.578085	−	0.439116i	0.0380352	−	0.0288917i
$232$	−5.38904	−	4.01931i	−0.353808	−	0.263881i
$233$	10.6117	−	18.3799i	0.695193	−	1.20411i	−0.274922	−	0.961467i	$-0.588652\pi$
$233$	10.6117	−	18.3799i	0.695193	−	1.20411i	0.970115	−	0.242644i	$-0.0780146\pi$
$234$	−19.3654	−	17.5834i	−1.26595	−	1.14946i
$235$	3.84841	−	2.22188i	0.251043	−	0.144940i
$236$	−1.64035	−	16.9668i	−0.106778	−	1.10445i
$237$			11.7000i			0.759994i
$238$	1.76659	−	20.1176i	0.114511	−	1.30403i
$239$			10.1532i			0.656754i	0.944547	+	0.328377i	$0.106502\pi$
$239$			10.1532i			0.656754i	−0.944547	+	0.328377i	$0.893498\pi$
$240$	−8.25755	+	7.18941i	−0.533022	+	0.464075i
$241$	16.4985	−	9.52539i	1.06276	−	0.613584i	0.136565	−	0.990631i	$-0.456394\pi$
$241$	16.4985	−	9.52539i	1.06276	−	0.613584i	0.926194	+	0.377047i	$0.123060\pi$
$242$	−10.4478	+	11.5066i	−0.671609	+	0.739672i
$243$	9.27006	−	16.0562i	0.594674	−	1.03001i
$244$	9.18342	+	12.8641i	0.587908	+	0.823542i
$245$	1.74567	+	6.77884i	0.111527	+	0.433084i
$246$	−29.4594	+	9.43632i	−1.87826	+	0.601638i
$247$	−26.5980	−	15.3564i	−1.69239	−	0.977102i
$248$	−1.80048	+	15.2883i	−0.114331	+	0.970807i
$249$	−8.89801	−	15.4118i	−0.563889	−	0.976684i
$250$	0.299797	−	1.38207i	0.0189608	−	0.0874099i
$251$	9.46184			0.597226			0.298613	−	0.954374i	$-0.403476\pi$
$251$	9.46184			0.597226			0.298613	+	0.954374i	$0.403476\pi$
$252$	5.24308	+	23.1849i	0.330283	+	1.46051i
$253$	0.151197			0.00950567
$254$	1.31183	−	6.04757i	0.0823115	−	0.379458i
$255$	7.38677	+	12.7943i	0.462577	+	0.801207i
$256$	−2.20222	+	15.8477i	−0.137639	+	0.990483i
$257$	2.37760	+	1.37271i	0.148310	+	0.0856270i	0.572319	−	0.820031i	$-0.306044\pi$
$257$	2.37760	+	1.37271i	0.148310	+	0.0856270i	−0.424008	+	0.905658i	$0.639377\pi$
$258$	−25.9813	+	8.32224i	−1.61753	+	0.518120i
$259$	1.66202	+	2.18801i	0.103273	+	0.135956i
$260$	6.70215	−	4.78452i	0.415650	−	0.296723i
$261$	5.33868	−	9.24686i	0.330456	−	0.572367i
$262$	2.83437	−	3.12161i	0.175108	−	0.192854i
$263$	22.2367	−	12.8384i	1.37117	−	0.791648i	0.380098	−	0.924946i	$-0.375890\pi$
$263$	22.2367	−	12.8384i	1.37117	−	0.791648i	0.991076	+	0.133298i	$0.0425568\pi$
$264$	0.306765	+	0.712872i	0.0188801	+	0.0438743i
$265$			6.14261i			0.377338i
$266$	11.7873	+	25.2991i	0.722723	+	1.55119i
$267$			8.73650i			0.534665i
$268$	0.218581	−	0.0211324i	0.0133519	−	0.00129087i
$269$	7.10140	−	4.10000i	0.432980	−	0.249981i	−0.267635	−	0.963520i	$-0.586242\pi$
$269$	7.10140	−	4.10000i	0.432980	−	0.249981i	0.700615	+	0.713539i	$0.252909\pi$
$270$	−4.27635	−	3.88285i	−0.260250	−	0.236303i
$271$	−3.20364	+	5.54886i	−0.194607	+	0.337069i	−0.946772	−	0.321906i	$-0.895676\pi$
$271$	−3.20364	+	5.54886i	−0.194607	+	0.337069i	0.752165	+	0.658975i	$0.229010\pi$
$272$	20.4186	+	7.01301i	1.23806	+	0.425226i
$273$	−3.74769	−	29.5810i	−0.226821	−	1.79033i
$274$	0.657785	+	2.05355i	0.0397382	+	0.124059i
$275$	−0.0868131	−	0.0501216i	−0.00523503	−	0.00302244i
$276$	−3.42121	+	7.51488i	−0.205933	+	0.452342i
$277$	−7.98456	−	13.8297i	−0.479746	−	0.830944i	0.519984	−	0.854176i	$-0.325938\pi$
$277$	−7.98456	−	13.8297i	−0.479746	−	0.830944i	−0.999730	+	0.0232316i	$0.992604\pi$
$278$	−9.89676	−	2.14679i	−0.593568	−	0.128756i
$279$	−24.4490			−1.46372
$280$	−7.48303	+	0.0657943i	−0.447196	+	0.00393196i
$281$	−9.68409			−0.577704			−0.288852	−	0.957374i	$-0.593274\pi$
$281$	−9.68409			−0.577704			−0.288852	+	0.957374i	$0.593274\pi$
$282$	16.8107	+	3.64655i	1.00106	+	0.217149i
$283$	−13.0633	−	22.6264i	−0.776535	−	1.34500i	−0.933928	−	0.357462i	$-0.883642\pi$
$283$	−13.0633	−	22.6264i	−0.776535	−	1.34500i	0.157393	−	0.987536i	$-0.449691\pi$
$284$	−5.57886	+	12.2543i	−0.331044	+	0.727157i
$285$	−17.6821	−	10.2088i	−1.04740	−	0.604716i
$286$	−0.178056	−	0.555877i	−0.0105287	−	0.0328697i
$287$	−19.4937	−	8.18622i	−1.15068	−	0.483217i
$288$	−25.4060	−	0.529749i	−1.49706	−	0.0312158i
$289$	6.06569	−	10.5061i	0.356805	−	0.618005i
$290$	2.48862	+	2.25962i	0.146137	+	0.132690i
$291$	−26.2389	+	15.1491i	−1.53815	+	0.888053i
$292$	−12.2369	+	1.18306i	−0.716111	+	0.0692336i
$293$			16.2389i			0.948684i	0.880341	+	0.474342i	$0.157314\pi$
$293$			16.2389i			0.948684i	−0.880341	+	0.474342i	$0.842686\pi$
$294$	−12.6367	+	23.9697i	−0.736987	+	1.39794i
$295$			8.52297i			0.496226i
$296$	−2.69817	+	1.16108i	−0.156828	+	0.0674865i
$297$	−0.354574	+	0.204714i	−0.0205745	+	0.0118787i
$298$	20.0089	−	22.0367i	1.15909	−	1.27655i
$299$	3.10511	−	5.37821i	0.179573	−	0.311030i
$300$	4.45553	−	3.18071i	0.257240	−	0.183638i
$301$	−17.1923	−	7.21973i	−0.990945	−	0.416138i
$302$	5.14883	−	1.64925i	0.296282	−	0.0949039i
$303$	16.9818	+	9.80446i	0.975580	+	0.563251i
$304$	−29.2847	+	5.71592i	−1.67959	+	0.327831i
$305$	−3.95143	−	6.84408i	−0.226258	−	0.391891i
$306$	−7.26882	+	33.5094i	−0.415531	+	1.91561i
$307$	23.5437			1.34371			0.671854	−	0.740684i	$-0.265498\pi$
$307$	23.5437			1.34371			0.671854	+	0.740684i	$0.265498\pi$
$308$	−0.157361	+	0.506557i	−0.00896650	+	0.0288638i
$309$	13.3741			0.760825
$310$	1.63167	−	7.52203i	0.0926725	−	0.427223i
$311$	2.69773	+	4.67261i	0.152974	+	0.264959i	0.932320	−	0.361635i	$-0.117781\pi$
$311$	2.69773	+	4.67261i	0.152974	+	0.264959i	−0.779345	+	0.626595i	$0.784448\pi$
$312$	31.6575	+	3.72826i	1.79225	+	0.211071i
$313$	28.1990	+	16.2807i	1.59390	+	0.920240i	0.992629	+	0.121197i	$0.0386732\pi$
$313$	28.1990	+	16.2807i	1.59390	+	0.920240i	0.601274	+	0.799043i	$0.294660\pi$
$314$	−1.72948	+	0.553979i	−0.0975999	+	0.0312628i
$315$	−1.49382	−	11.7909i	−0.0841672	−	0.664343i
$316$	−4.96707	−	6.95787i	−0.279420	−	0.391411i
$317$	−6.85587	+	11.8747i	−0.385064	+	0.666951i	−0.991778	−	0.127970i	$-0.959154\pi$
$317$	−6.85587	+	11.8747i	−0.385064	+	0.666951i	0.606714	+	0.794920i	$0.292487\pi$
$318$	−15.9840	+	17.6039i	−0.896338	+	0.987176i
$319$	0.206344	−	0.119133i	0.0115531	−	0.00667017i
$320$	1.85852	−	7.78112i	0.103895	−	0.434978i
$321$			20.7170i			1.15631i
$322$	−5.11556	+	2.38342i	−0.285079	+	0.132823i
$323$			40.2606i			2.24016i
$324$	0.442071	+	4.57252i	0.0245595	+	0.254029i
$325$	−3.56573	+	2.05868i	−0.197791	+	0.114195i
$326$	9.00542	+	8.17677i	0.498764	+	0.452869i
$327$	24.7075	−	42.7947i	1.36633	−	2.36655i
$328$	13.5132	−	18.1183i	0.746142	−	1.00042i
$329$	7.11167	+	9.36233i	0.392079	+	0.516162i
$330$	−0.118370	−	0.369542i	−0.00651607	−	0.0203426i
$331$	4.92495	+	2.84342i	0.270700	+	0.156289i	0.629206	−	0.777239i	$-0.283380\pi$
$331$	4.92495	+	2.84342i	0.270700	+	0.156289i	−0.358506	+	0.933527i	$0.616714\pi$
$332$	11.8345	+	5.38774i	0.649501	+	0.295691i
$333$	−2.33261	−	4.04019i	−0.127826	−	0.221401i
$334$	11.2010	+	2.42970i	0.612890	+	0.132947i
$335$	−0.109800			−0.00599901
$336$	−21.6165	−	19.2834i	−1.17928	−	1.05200i
$337$	−14.7219			−0.801955			−0.400978	−	0.916088i	$-0.631330\pi$
$337$	−14.7219			−0.801955			−0.400978	+	0.916088i	$0.631330\pi$
$338$	−5.46279	−	1.18498i	−0.297137	−	0.0644544i
$339$	24.8306	+	43.0079i	1.34861	+	2.33587i
$340$	−9.82449	−	4.47268i	−0.532808	−	0.242565i
$341$	−0.472487	−	0.272790i	−0.0255866	−	0.0147724i
$342$	−14.4557	−	45.1296i	−0.781677	−	2.44033i
$343$	−17.2124	+	6.83621i	−0.929381	+	0.369121i
$344$	11.9178	−	15.9792i	0.642564	−	0.861542i
$345$	2.06425	−	3.57539i	0.111135	−	0.192492i
$346$	−8.41143	−	7.63743i	−0.452201	−	0.410591i
$347$	−13.3966	+	7.73454i	−0.719168	+	0.415212i	−0.814446	−	0.580239i	$-0.802959\pi$
$347$	−13.3966	+	7.73454i	−0.719168	+	0.415212i	0.0952784	+	0.995451i	$0.469626\pi$
$348$	1.25215	+	12.9515i	0.0671225	+	0.694275i
$349$		−	11.5290i		−	0.617132i	−0.951203	−	0.308566i	$-0.900151\pi$
$349$		−	11.5290i		−	0.617132i	0.951203	−	0.308566i	$-0.0998491\pi$
$350$	3.72731	+	0.327306i	0.199233	+	0.0174952i
$351$			16.8167i			0.897608i
$352$	−0.485072	−	0.293706i	−0.0258544	−	0.0156546i
$353$	17.6983	−	10.2181i	0.941985	−	0.543855i	0.0514030	−	0.998678i	$-0.483631\pi$
$353$	17.6983	−	10.2181i	0.941985	−	0.543855i	0.890582	+	0.454823i	$0.150297\pi$
$354$	−22.1781	+	24.4256i	−1.17875	+	1.29821i
$355$	3.36611	−	5.83027i	0.178654	−	0.309438i
$356$	−3.70897	−	5.19553i	−0.196575	−	0.275362i
$357$	−31.1256	+	23.6431i	−1.64734	+	1.25133i
$358$	11.9173	−	3.81731i	0.629850	−	0.201751i
$359$	−18.3761	−	10.6095i	−0.969856	−	0.559946i	−0.0706634	−	0.997500i	$-0.522512\pi$
$359$	−18.3761	−	10.6095i	−0.969856	−	0.559946i	−0.899192	+	0.437554i	$0.855845\pi$
$360$	12.6186	+	1.48607i	0.665057	+	0.0783229i
$361$	−18.3208	−	31.7326i	−0.964255	−	1.67014i
$362$	6.40395	−	29.5224i	0.336584	−	1.55166i
$363$	30.0815			1.57887
$364$	14.7870	+	16.0006i	0.775048	+	0.838658i
$365$	6.14698			0.321748
$366$	6.48508	−	29.8964i	0.338981	−	1.56271i
$367$	−3.82574	−	6.62637i	−0.199702	−	0.345894i	0.748730	−	0.662875i	$-0.230664\pi$
$367$	−3.82574	−	6.62637i	−0.199702	−	0.345894i	−0.948432	+	0.316982i	$0.897331\pi$
$368$	−1.15578	−	5.92147i	−0.0602491	−	0.308678i
$369$	31.0886	+	17.9490i	1.61841	+	0.934389i
$370$	1.39869	−	0.448022i	0.0727143	−	0.0232916i
$371$	−16.1229	+	2.04265i	−0.837062	+	0.106049i
$372$	24.2496	−	17.3112i	1.25728	−	0.897546i
$373$	−12.8172	+	22.2000i	−0.663647	+	1.14947i	0.316003	+	0.948758i	$0.397659\pi$
$373$	−12.8172	+	22.2000i	−0.663647	+	1.14947i	−0.979650	+	0.200713i	$0.935674\pi$
$374$	−0.514356	+	0.566482i	−0.0265967	+	0.0292921i
$375$	−2.37047	+	1.36859i	−0.122411	+	0.0706738i
$376$	−11.5453	+	4.96819i	−0.595402	+	0.256215i
$377$		−	9.78647i		−	0.504029i
$378$	8.76954	−	12.5156i	0.451057	−	0.643735i
$379$		−	29.1039i		−	1.49497i	−0.664279	−	0.747485i	$-0.731261\pi$
$379$		−	29.1039i		−	1.49497i	0.664279	−	0.747485i	$-0.268739\pi$
$380$	14.8494	−	1.43564i	0.761760	−	0.0736469i
$381$	−10.3725	+	5.98858i	−0.531401	+	0.306804i
$382$	26.1998	+	23.7890i	1.34050	+	1.21715i
$383$	−4.32161	+	7.48525i	−0.220824	+	0.382478i	−0.955058	−	0.296418i	$-0.904208\pi$
$383$	−4.32161	+	7.48525i	−0.220824	+	0.382478i	0.734234	+	0.678896i	$0.237541\pi$
$384$	25.5739	−	17.4635i	1.30506	−	0.891178i
$385$	0.102689	−	0.244532i	0.00523351	−	0.0124625i
$386$	−3.52093	−	10.9921i	−0.179211	−	0.559481i
$387$	27.4182	+	15.8299i	1.39375	+	0.804679i
$388$	9.17274	−	20.1484i	0.465676	−	1.02288i
$389$	7.08846	+	12.2776i	0.359399	+	0.622498i	0.987861	−	0.155343i	$-0.0496483\pi$
$389$	7.08846	+	12.2776i	0.359399	+	0.622498i	−0.628461	+	0.777841i	$0.716315\pi$
$390$	−15.5759	−	3.37870i	−0.788715	−	0.171087i
$391$	−8.14084			−0.411700
$392$	−2.66109	−	19.6193i	−0.134405	−	0.990926i
$393$	−8.16078			−0.411657
$394$	−17.2092	−	3.73299i	−0.866986	−	0.188065i
$395$	2.13723	+	3.70178i	0.107536	+	0.186257i
$396$	0.373163	−	0.819672i	0.0187521	−	0.0411901i
$397$	0.151559	+	0.0875029i	0.00760655	+	0.00439164i	0.503798	−	0.863821i	$-0.331935\pi$
$397$	0.151559	+	0.0875029i	0.00760655	+	0.00439164i	−0.496192	+	0.868213i	$0.665269\pi$
$398$	9.99708	+	31.2101i	0.501108	+	1.56442i
$399$	20.9157	−	49.8063i	1.04710	−	2.49344i
$400$	−1.29934	+	3.78308i	−0.0649671	+	0.189154i
$401$	−12.0285	+	20.8339i	−0.600674	+	1.04040i	0.392046	+	0.919946i	$0.371768\pi$
$401$	−12.0285	+	20.8339i	−0.600674	+	1.04040i	−0.992719	+	0.120452i	$0.961566\pi$
$402$	−0.314671	−	0.285716i	−0.0156944	−	0.0142502i
$403$	−19.4068	+	11.2045i	−0.966721	+	0.558136i
$404$	−14.2613	+	1.37878i	−0.709527	+	0.0685970i
$405$		−	2.29692i		−	0.114135i
$406$	−5.10343	+	7.28347i	−0.253279	+	0.361473i
$407$		−	0.104105i		−	0.00516027i
$408$	−16.5170	−	38.3829i	−0.817714	−	1.90024i
$409$	−10.3372	+	5.96818i	−0.511141	+	0.295108i	−0.733303	−	0.679902i	$-0.762022\pi$
$409$	−10.3372	+	5.96818i	−0.511141	+	0.295108i	0.222161	+	0.975010i	$0.428689\pi$
$410$	−7.59702	+	8.36692i	−0.375190	+	0.413213i
$411$	2.08676	−	3.61438i	0.102932	−	0.178284i
$412$	−7.95347	+	5.67780i	−0.391839	+	0.279725i
$413$	−22.3708	+	2.83421i	−1.10080	+	0.139463i
$414$	9.12536	−	2.92300i	0.448487	−	0.143658i
$415$	−5.63054	−	3.25079i	−0.276392	−	0.159575i
$416$	−20.4092	+	11.2226i	−1.00064	+	0.550234i
$417$	9.80023	+	16.9745i	0.479919	+	0.831245i
$418$	0.224172	−	1.03344i	0.0109646	−	0.0505472i
$419$	−30.1003			−1.47050			−0.735249	−	0.677798i	$-0.762935\pi$
$419$	−30.1003			−1.47050			−0.735249	+	0.677798i	$0.762935\pi$
$420$	9.83026	+	10.6370i	0.479668	+	0.519035i
$421$	6.78256			0.330562			0.165281	−	0.986247i	$-0.447147\pi$
$421$	6.78256			0.330562			0.165281	+	0.986247i	$0.447147\pi$
$422$	3.29055	−	15.1695i	0.160181	−	0.738440i
$423$	−9.98107	−	17.2877i	−0.485296	−	0.840557i
$424$	2.03206	−	17.2547i	0.0986857	−	0.837962i
$425$	4.67424	+	2.69867i	0.226734	+	0.130905i
$426$	24.8180	−	7.94961i	1.20244	−	0.385160i
$427$	16.6501	−	12.6475i	0.805756	−	0.612056i
$428$	−8.79513	−	12.3202i	−0.425128	−	0.595520i
$429$	−0.564868	+	0.978379i	−0.0272721	+	0.0472366i
$430$	−6.70009	+	7.37910i	−0.323107	+	0.355852i
$431$	−13.8010	+	7.96802i	−0.664772	+	0.383806i	−0.794093	−	0.607797i	$-0.792054\pi$
$431$	−13.8010	+	7.96802i	−0.664772	+	0.383806i	0.129321	+	0.991603i	$0.458720\pi$
$432$	10.7278	+	12.3217i	0.516143	+	0.592826i
$433$		−	15.1291i		−	0.727057i	−0.931583	−	0.363529i	$-0.881572\pi$
$433$		−	15.1291i		−	0.727057i	0.931583	−	0.363529i	$-0.118428\pi$
$434$	20.2862	+	1.78139i	0.973769	+	0.0855094i
$435$		−	6.50596i		−	0.311937i
$436$	3.47457	+	35.9389i	0.166402	+	1.72116i
$437$	9.74360	−	5.62547i	0.466099	−	0.269103i
$438$	17.6164	+	15.9954i	0.841743	+	0.764288i
$439$	2.18337	−	3.78171i	0.104207	−	0.180491i	−0.809207	−	0.587523i	$-0.800103\pi$
$439$	2.18337	−	3.78171i	0.104207	−	0.180491i	0.913414	+	0.407032i	$0.133436\pi$
$440$	0.227278	+	0.169511i	0.0108351	+	0.00808113i
$441$	30.4517	−	7.84186i	1.45008	−	0.373422i
$442$	9.58701	+	29.9298i	0.456007	+	1.42362i
$443$	12.2094	+	7.04909i	0.580086	+	0.334913i	0.761167	−	0.648555i	$-0.224627\pi$
$443$	12.2094	+	7.04909i	0.580086	+	0.334913i	−0.181082	+	0.983468i	$0.557960\pi$
$444$	5.17426	+	2.35563i	0.245560	+	0.111793i
$445$	1.59589	+	2.76417i	0.0756526	+	0.131034i
$446$	−20.7031	−	4.49088i	−0.980320	−	0.212650i
$447$	−57.6102			−2.72487
$448$	21.0417	+	2.29067i	0.994127	+	0.108224i
$449$	17.0120			0.802848			0.401424	−	0.915892i	$-0.368515\pi$
$449$	17.0120			0.802848			0.401424	+	0.915892i	$0.368515\pi$
$450$	−6.20850	−	1.34674i	−0.292672	−	0.0634859i
$451$	0.400534	+	0.693745i	0.0188604	+	0.0326672i
$452$	−33.0250	−	15.0349i	−1.55337	−	0.707183i
$453$	−9.06228	−	5.23211i	−0.425783	−	0.245826i
$454$	0.650306	+	2.03020i	0.0305204	+	0.0952820i
$455$	−6.58930	−	8.67464i	−0.308911	−	0.406674i
$456$	46.2922	+	34.5261i	2.16783	+	1.61683i
$457$	−5.83234	+	10.1019i	−0.272825	+	0.472548i	−0.969584	−	0.244758i	$-0.921291\pi$
$457$	−5.83234	+	10.1019i	−0.272825	+	0.472548i	0.696759	+	0.717306i	$0.254625\pi$
$458$	8.92627	+	8.10490i	0.417097	+	0.378717i
$459$	19.0912	−	11.0223i	0.891101	−	0.514477i
$460$	0.290292	+	3.00261i	0.0135349	+	0.139997i
$461$			26.4488i			1.23184i	0.787808	+	0.615921i	$0.211216\pi$
$461$			26.4488i			1.23184i	−0.787808	+	0.615921i	$0.788784\pi$
$462$	0.930600	−	0.433582i	0.0432954	−	0.0201720i
$463$		−	3.13685i		−	0.145782i	−0.997340	−	0.0728909i	$-0.976778\pi$
$463$		−	3.13685i		−	0.145782i	0.997340	−	0.0728909i	$-0.0232225\pi$
$464$	−6.24306	−	7.17059i	−0.289827	−	0.332886i
$465$	−12.9015	+	7.44866i	−0.598291	+	0.345424i
$466$	20.1763	−	22.2211i	0.934651	−	1.02937i
$467$	4.07057	−	7.05043i	0.188363	−	0.326255i	−0.756341	−	0.654177i	$-0.773015\pi$
$467$	4.07057	−	7.05043i	0.188363	−	0.326255i	0.944705	+	0.327922i	$0.106348\pi$
$468$	−21.4929	−	30.1072i	−0.993508	−	1.39171i
$469$	−0.0365127	−	0.288200i	−0.00168600	−	0.0133078i
$470$	5.98489	−	1.91706i	0.276062	−	0.0884272i
$471$	3.04399	+	1.75745i	0.140260	+	0.0809789i
$472$	2.81952	−	23.9411i	0.129779	−	1.10198i
$473$	0.353246	+	0.611839i	0.0162422	+	0.0281324i
$474$	−3.50761	+	16.1702i	−0.161110	+	0.742721i
$475$	−7.45934			−0.342258
$476$	8.47275	−	27.2744i	0.388348	−	1.25012i
$477$	27.5937			1.26343
$478$	−3.04389	+	14.0324i	−0.139224	+	0.641827i
$479$	−12.3904	−	21.4608i	−0.566131	−	0.980567i	−0.996944	−	0.0781258i	$-0.975106\pi$
$479$	−12.3904	−	21.4608i	−0.566131	−	0.980567i	0.430813	−	0.902441i	$-0.358227\pi$
$480$	−13.5679	+	7.46070i	−0.619286	+	0.340533i
$481$	−3.70309	−	2.13798i	−0.168846	−	0.0974835i
$482$	25.6577	−	8.21858i	1.16868	−	0.374346i
$483$	10.0710	+	4.22923i	0.458247	+	0.192437i
$484$	−17.8892	+	12.7707i	−0.813147	+	0.580487i
$485$	−5.53454	+	9.58611i	−0.251311	+	0.435283i
$486$	17.6255	−	19.4117i	0.799508	−	0.880532i
$487$	−10.9938	+	6.34726i	−0.498175	+	0.287622i	−0.727960	−	0.685620i	$-0.759531\pi$
$487$	−10.9938	+	6.34726i	−0.498175	+	0.287622i	0.229784	+	0.973242i	$0.426198\pi$
$488$	8.83551	+	20.5323i	0.399965	+	0.929454i
$489$		−	23.5427i		−	1.06464i
$490$	0.380371	+	9.89218i	0.0171834	+	0.446883i
$491$		−	9.51192i		−	0.429267i	−0.976695	−	0.214633i	$-0.931144\pi$
$491$		−	9.51192i		−	0.429267i	0.976695	−	0.214633i	$-0.0688557\pi$
$492$	−43.5440	+	4.20983i	−1.96311	+	0.189794i
$493$	−11.1101	+	6.41443i	−0.500375	+	0.288892i
$494$	−32.1566	−	29.1976i	−1.44679	−	1.31366i
$495$	−0.225155	+	0.389979i	−0.0101199	+	0.0175283i
$496$	−7.07177	+	20.5897i	−0.317532	+	0.924506i
$497$	16.4225	+	6.89647i	0.736649	+	0.309349i
$498$	−7.67728	−	23.9678i	−0.344027	−	1.07402i
$499$	7.35497	+	4.24639i	0.329254	+	0.190095i	0.655510	−	0.755187i	$-0.272454\pi$
$499$	7.35497	+	4.24639i	0.329254	+	0.190095i	−0.326256	+	0.945281i	$0.605787\pi$
$500$	0.828682	−	1.82024i	0.0370598	−	0.0814038i
$501$	−11.0917	−	19.2114i	−0.495542	−	0.858303i
$502$	13.0769	+	2.83663i	0.583653	+	0.126605i
$503$	10.4796			0.467261			0.233630	−	0.972325i	$-0.424939\pi$
$503$	10.4796			0.467261			0.233630	+	0.972325i	$0.424939\pi$
$504$	0.295559	+	33.6150i	0.0131652	+	1.49733i
$505$	7.16390			0.318790
$506$	0.208965	+	0.0453284i	0.00928963	+	0.00201509i
$507$	5.40951	+	9.36955i	0.240245	+	0.416116i
$508$	3.62608	−	7.96489i	0.160881	−	0.353385i
$509$	−19.7483	−	11.4017i	−0.875329	−	0.505371i	−0.00621337	−	0.999981i	$-0.501978\pi$
$509$	−19.7483	−	11.4017i	−0.875329	−	0.505371i	−0.869115	+	0.494609i	$0.835311\pi$
$510$	6.37336	+	19.8971i	0.282217	+	0.881059i
$511$	2.04411	+	16.1344i	0.0904259	+	0.713744i
$512$	−7.79472	+	21.2425i	−0.344481	+	0.938793i
$513$	−15.2332	+	26.3847i	−0.672564	+	1.16492i
$514$	2.87447	+	2.60997i	0.126788	+	0.115121i
$515$	4.23147	−	2.44304i	0.186461	−	0.107653i
$516$	−38.4031	+	3.71281i	−1.69060	+	0.163447i
$517$		−	0.445456i		−	0.0195912i
$518$	1.64107	+	3.52225i	0.0721046	+	0.154759i
$519$			21.9899i			0.965248i
$520$	10.6972	−	4.60326i	0.469105	−	0.201866i
$521$	−7.88048	+	4.54980i	−0.345250	+	0.199330i	−0.662591	−	0.748981i	$-0.730543\pi$
$521$	−7.88048	+	4.54980i	−0.345250	+	0.199330i	0.317341	+	0.948311i	$0.397210\pi$
$522$	10.1506	−	11.1793i	0.444281	−	0.489305i
$523$	−2.38048	+	4.12311i	−0.104091	+	0.180291i	−0.913366	−	0.407138i	$-0.866527\pi$
$523$	−2.38048	+	4.12311i	−0.104091	+	0.180291i	0.809275	+	0.587429i	$0.199860\pi$
$524$	4.85315	−	3.46456i	0.212011	−	0.151350i
$525$	−4.38051	−	5.76683i	−0.191181	−	0.251685i
$526$	34.5816	−	11.0771i	1.50783	−	0.482982i
$527$	25.4399	+	14.6877i	1.10818	+	0.639808i
$528$	0.210254	+	1.07721i	0.00915013	+	0.0468794i
$529$	−10.3625	−	17.9484i	−0.450544	−	0.780365i
$530$	−1.84154	+	8.48953i	−0.0799912	+	0.368762i
$531$	38.2866			1.66150
$532$	8.70624	+	38.4989i	0.377463	+	1.66914i
$533$	32.9028			1.42518
$534$	−2.61918	+	12.0745i	−0.113343	+	0.522513i
$535$	3.78436	+	6.55470i	0.163612	+	0.283384i
$536$	0.308430	+	0.0363234i	0.0133221	+	0.00156893i
$537$	−20.9753	−	12.1101i	−0.905150	−	0.522588i
$538$	11.0438	−	3.53751i	0.476133	−	0.152513i
$539$	0.675988	+	0.188219i	0.0291168	+	0.00810715i
$540$	−4.74615	−	6.64842i	−0.204242	−	0.286102i
$541$	11.2312	−	19.4530i	0.482867	−	0.836350i	−0.516939	−	0.856022i	$-0.672929\pi$
$541$	11.2312	−	19.4530i	0.482867	−	0.836350i	0.999806	+	0.0196717i	$0.00626211\pi$
$542$	−6.09118	+	6.70848i	−0.261639	+	0.288154i
$543$	−50.6355	+	29.2344i	−2.17298	+	1.25457i
$544$	26.1175	+	15.8139i	1.11978	+	0.678016i
$545$		−	18.0532i		−	0.773316i
$546$	3.68872	−	42.0067i	0.157863	−	1.79772i
$547$			24.4644i			1.04602i	0.852326	+	0.523012i	$0.175192\pi$
$547$			24.4644i			1.04602i	−0.852326	+	0.523012i	$0.824808\pi$
$548$	0.293458	+	3.03535i	0.0125359	+	0.129664i
$549$	−30.7448	+	17.7505i	−1.31215	+	0.757573i
$550$	−0.104956	−	0.0952979i	−0.00447532	−	0.00406352i
$551$	8.86498	−	15.3546i	0.377661	−	0.654128i
$552$	−6.98130	+	9.36043i	−0.297144	+	0.398406i
$553$	−9.00562	+	6.84071i	−0.382958	+	0.290897i
$554$	−6.88915	−	21.5073i	−0.292692	−	0.913759i
$555$	−2.46178	−	1.42131i	−0.104497	−	0.0603313i
$556$	−13.0344	−	5.93404i	−0.552783	−	0.251659i
$557$	4.21627	+	7.30280i	0.178649	+	0.309430i	0.941418	−	0.337242i	$-0.109494\pi$
$557$	4.21627	+	7.30280i	0.178649	+	0.309430i	−0.762769	+	0.646671i	$0.776161\pi$
$558$	−33.7902	−	7.32973i	−1.43046	−	0.310292i
$559$	29.0182			1.22734
$560$	−10.3618	−	2.15246i	−0.437866	−	0.0909578i
$561$	1.48095			0.0625255
$562$	−13.3841	−	2.90326i	−0.564574	−	0.122467i
$563$	−13.5833	−	23.5269i	−0.572467	−	0.991541i	−0.996312	−	0.0858067i	$-0.972653\pi$
$563$	−13.5833	−	23.5269i	−0.572467	−	0.991541i	0.423845	−	0.905735i	$-0.360680\pi$
$564$	22.1403	+	10.0796i	0.932276	+	0.424427i
$565$	15.7125	+	9.07159i	0.661028	+	0.381645i
$566$	−11.2712	−	35.1876i	−0.473762	−	1.47905i
$567$	6.02888	−	0.763813i	0.253189	−	0.0320771i
$568$	−11.3842	+	15.2638i	−0.477669	+	0.640453i
$569$	−7.11643	+	12.3260i	−0.298336	+	0.516733i	−0.975755	−	0.218864i	$-0.929765\pi$
$569$	−7.11643	+	12.3260i	−0.298336	+	0.516733i	0.677419	+	0.735597i	$0.263098\pi$
$570$	−21.3774	−	19.4103i	−0.895401	−	0.813009i
$571$	14.5870	−	8.42181i	0.610447	−	0.352442i	−0.162693	−	0.986677i	$-0.552018\pi$
$571$	14.5870	−	8.42181i	0.610447	−	0.352442i	0.773140	+	0.634235i	$0.218685\pi$
$572$	−0.0794363	−	0.821642i	−0.00332140	−	0.0343546i
$573$		−	68.4938i		−	2.86137i
$574$	−24.4875	−	17.1581i	−1.02209	−	0.716166i
$575$		−	1.50830i		−	0.0629006i
$576$	−34.9541	−	8.34880i	−1.45642	−	0.347867i
$577$	1.86487	−	1.07668i	0.0776356	−	0.0448230i	−0.460680	−	0.887566i	$-0.652394\pi$
$577$	1.86487	−	1.07668i	0.0776356	−	0.0448230i	0.538315	+	0.842744i	$0.319061\pi$
$578$	11.5329	−	12.7017i	0.479706	−	0.528321i
$579$	−11.1699	+	19.3468i	−0.464203	+	0.804024i
$580$	2.76202	+	3.86904i	0.114687	+	0.160653i
$581$	6.66021	−	15.8599i	0.276312	−	0.657979i
$582$	−40.8057	+	13.0707i	−1.69145	+	0.541799i
$583$	0.533259	+	0.307877i	0.0220853	+	0.0127510i
$584$	−17.2670	−	2.03351i	−0.714512	−	0.0841471i
$585$	9.24793	+	16.0179i	0.382355	+	0.662258i
$586$	−4.86836	+	22.4433i	−0.201110	+	0.927123i
$587$	11.3061			0.466652			0.233326	−	0.972399i	$-0.425039\pi$
$587$	11.3061			0.466652			0.233326	+	0.972399i	$0.425039\pi$
$588$	−24.6509	+	29.3394i	−1.01658	+	1.20994i
$589$	−40.5980			−1.67281
$590$	−2.55516	+	11.7794i	−0.105194	+	0.484948i
$591$	17.0413	+	29.5164i	0.700986	+	1.21414i
$592$	−4.07715	+	0.795795i	−0.167570	+	0.0327070i
$593$	14.7570	+	8.51993i	0.605996	+	0.349872i	0.771397	−	0.636355i	$-0.219558\pi$
$593$	14.7570	+	8.51993i	0.605996	+	0.349872i	−0.165401	+	0.986226i	$0.552892\pi$
$594$	−0.551420	+	0.176629i	−0.0226250	+	0.00724716i
$595$	−5.52904	+	13.1662i	−0.226668	+	0.539763i
$596$	34.2603	−	24.4577i	1.40336	−	1.00183i
$597$	31.7149	−	54.9318i	1.29800	−	2.24821i
$598$	5.90385	−	6.50216i	0.241426	−	0.265893i
$599$	−3.39864	+	1.96221i	−0.138865	+	0.0801736i	−0.567823	−	0.823151i	$-0.692214\pi$
$599$	−3.39864	+	1.96221i	−0.138865	+	0.0801736i	0.428958	+	0.903324i	$0.358881\pi$
$600$	7.11143	−	3.06021i	0.290323	−	0.124932i
$601$		−	8.98026i		−	0.366312i	−0.983084	−	0.183156i	$-0.941369\pi$
$601$		−	8.98026i		−	0.366312i	0.983084	−	0.183156i	$-0.0586314\pi$
$602$	−21.5965	−	15.1324i	−0.880207	−	0.616749i
$603$			0.493240i			0.0200863i
$604$	7.61050	−	0.735783i	0.309667	−	0.0299386i
$605$	9.51758	−	5.49498i	0.386945	−	0.223403i
$606$	20.5307	+	18.6416i	0.834004	+	0.757262i
$607$	−18.7895	+	32.5444i	−0.762644	+	1.32094i	0.178840	+	0.983878i	$0.442766\pi$
$607$	−18.7895	+	32.5444i	−0.762644	+	1.32094i	−0.941483	+	0.337059i	$0.890568\pi$
$608$	−42.1872	−	0.879659i	−1.71092	−	0.0356749i
$609$	17.0767	−	2.16348i	0.691981	−	0.0876687i
$610$	−3.40933	−	10.6436i	−0.138040	−	0.430948i
$611$	−15.8453	−	9.14827i	−0.641031	−	0.370099i
$612$	−20.0921	+	44.1333i	−0.812173	+	1.78398i
$613$	23.1299	+	40.0621i	0.934207	+	1.61809i	0.776042	+	0.630681i	$0.217224\pi$
$613$	23.1299	+	40.0621i	0.934207	+	1.61809i	0.158165	+	0.987413i	$0.449442\pi$
$614$	32.5390	+	7.05832i	1.31317	+	0.284850i
$615$	21.8735			0.882025
$616$	−0.369349	+	0.652922i	−0.0148815	+	0.0263070i
$617$	−42.8844			−1.72646			−0.863231	−	0.504809i	$-0.831563\pi$
$617$	−42.8844			−1.72646			−0.863231	+	0.504809i	$0.831563\pi$
$618$	18.4840	+	4.00951i	0.743534	+	0.161286i
$619$	14.7503	+	25.5483i	0.592865	+	1.02687i	0.993844	+	0.110785i	$0.0353364\pi$
$619$	14.7503	+	25.5483i	0.592865	+	1.02687i	−0.400980	+	0.916087i	$0.631330\pi$
$620$	4.51016	−	9.90682i	0.181133	−	0.397867i
$621$	−5.33508	−	3.08021i	−0.214090	−	0.123605i
$622$	2.32762	+	7.26665i	0.0933293	+	0.291366i
$623$	−6.72461	+	5.10804i	−0.269416	+	0.204649i
$624$	42.6352	+	14.6435i	1.70677	+	0.586210i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	34.0921	+	30.9551i	1.36260	+	1.23721i
$627$	−1.77251	+	1.02336i	−0.0707873	+	0.0408691i
$628$	−2.55634	+	0.247147i	−0.102009	+	0.00986223i
$629$			5.60526i			0.223496i
$630$	1.47031	−	16.7437i	0.0585787	−	0.667086i
$631$		−	20.5872i		−	0.819563i	−0.912184	−	0.409781i	$-0.865605\pi$
$631$		−	20.5872i		−	0.819563i	0.912184	−	0.409781i	$-0.134395\pi$
$632$	−4.77890	−	11.1054i	−0.190094	−	0.441749i
$633$	−26.0181	+	15.0215i	−1.03413	+	0.597053i
$634$	−13.0353	+	14.3563i	−0.517698	+	0.570163i
$635$	−2.18786	+	3.78949i	−0.0868227	+	0.150381i
$636$	−27.3686	+	19.5378i	−1.08524	+	0.774726i
$637$	20.5777	−	20.1800i	0.815320	−	0.799562i
$638$	0.320899	−	0.102789i	0.0127045	−	0.00406945i
$639$	−26.1906	−	15.1211i	−1.03608	−	0.598182i
$640$	4.90137	−	10.1969i	0.193744	−	0.403068i
$641$	18.4263	+	31.9153i	0.727795	+	1.26058i	0.957813	+	0.287392i	$0.0927883\pi$
$641$	18.4263	+	31.9153i	0.727795	+	1.26058i	−0.230018	+	0.973186i	$0.573878\pi$
$642$	−6.21088	+	28.6323i	−0.245124	+	1.13003i
$643$	48.4719			1.91154			0.955772	−	0.294108i	$-0.0950227\pi$
$643$	48.4719			1.91154			0.955772	+	0.294108i	$0.0950227\pi$
$644$	−7.78461	+	1.76043i	−0.306757	+	0.0693707i
$645$	19.2911			0.759585
$646$	−12.0700	+	55.6431i	−0.474888	+	2.18925i
$647$	−19.5933	−	33.9366i	−0.770292	−	1.33418i	−0.937403	−	0.348247i	$-0.886777\pi$
$647$	−19.5933	−	33.9366i	−0.770292	−	1.33418i	0.167111	−	0.985938i	$-0.446556\pi$
$648$	−0.759853	+	6.45208i	−0.0298498	+	0.253462i
$649$	0.739905	+	0.427185i	0.0290438	+	0.0167685i
$650$	−5.54528	+	1.77624i	−0.217504	+	0.0696700i
$651$	−23.8413	−	31.3864i	−0.934413	−	1.23013i
$652$	9.99477	+	14.0007i	0.391425	+	0.548309i
$653$	−3.44161	+	5.96105i	−0.134681	+	0.233274i	−0.925475	−	0.378808i	$-0.876334\pi$
$653$	−3.44161	+	5.96105i	−0.134681	+	0.233274i	0.790795	+	0.612082i	$0.209668\pi$
$654$	46.9772	−	51.7380i	1.83696	−	2.02312i
$655$	−2.58201	+	1.49073i	−0.100888	+	0.0582475i
$656$	24.1080	−	20.9896i	0.941261	−	0.819506i
$657$		−	27.6133i		−	1.07730i
$658$	7.02204	+	15.0715i	0.273748	+	0.587547i
$659$			40.9792i			1.59632i	0.602444	+	0.798161i	$0.294194\pi$
$659$			40.9792i			1.59632i	−0.602444	+	0.798161i	$0.705806\pi$
$660$	−0.0528086	−	0.546221i	−0.00205557	−	0.0212616i
$661$	10.4696	−	6.04460i	0.407219	−	0.235108i	−0.282375	−	0.959304i	$-0.591122\pi$
$661$	10.4696	−	6.04460i	0.407219	−	0.235108i	0.689594	+	0.724196i	$0.257789\pi$
$662$	5.95418	+	5.40630i	0.231416	+	0.210122i
$663$	30.4139	−	52.6785i	1.18118	−	2.04586i
$664$	14.7409	+	10.9942i	0.572056	+	0.426657i
$665$	−2.48052	−	19.5790i	−0.0961903	−	0.759243i
$666$	−2.01259	−	6.28314i	−0.0779863	−	0.243467i
$667$	3.10475	+	1.79253i	0.120216	+	0.0694070i
$668$	14.7521	+	6.71603i	0.570777	+	0.259851i
$669$	20.5012	+	35.5091i	0.792621	+	1.37286i
$670$	−0.151751	−	0.0329177i	−0.00586267	−	0.00127172i
$671$	−0.792208			−0.0305828
$672$	−24.0945	−	33.1316i	−0.929464	−	1.27808i
$673$	29.0006			1.11789			0.558945	−	0.829205i	$-0.311206\pi$
$673$	29.0006			1.11789			0.558945	+	0.829205i	$0.311206\pi$
$674$	−20.3468	−	4.41359i	−0.783729	−	0.170005i
$675$	2.04217	+	3.53714i	0.0786032	+	0.136145i
$676$	−7.19472	−	3.27546i	−0.276720	−	0.125979i
$677$	41.8361	+	24.1541i	1.60789	+	0.928317i	0.989841	+	0.142178i	$0.0454106\pi$
$677$	41.8361	+	24.1541i	1.60789	+	0.928317i	0.618051	+	0.786138i	$0.287923\pi$
$678$	21.4240	+	66.8841i	0.822786	+	2.56867i
$679$	−27.0018	−	11.3392i	−1.03623	−	0.435157i
$680$	−12.2373	−	9.12692i	−0.469277	−	0.350001i
$681$	2.06304	−	3.57329i	0.0790558	−	0.136929i
$682$	−0.571229	−	0.518666i	−0.0218735	−	0.0198607i
$683$	−11.4528	+	6.61231i	−0.438231	+	0.253013i	−0.702847	−	0.711341i	$-0.748088\pi$
$683$	−11.4528	+	6.61231i	−0.438231	+	0.253013i	0.264616	+	0.964354i	$0.414755\pi$
$684$	−6.44915	−	66.7062i	−0.246590	−	2.55057i
$685$		−	1.52475i		−	0.0582578i
$686$	−25.8382	+	4.28792i	−0.986508	+	0.163713i
$687$		−	23.3358i		−	0.890317i
$688$	21.2618	−	18.5115i	0.810597	−	0.705745i
$689$	21.9029	−	12.6457i	0.834435	−	0.481761i
$690$	3.92483	−	4.32258i	0.149416	−	0.164558i
$691$	19.9447	−	34.5453i	0.758733	−	1.31416i	−0.184763	−	0.982783i	$-0.559152\pi$
$691$	19.9447	−	34.5453i	0.758733	−	1.31416i	0.943497	−	0.331382i	$-0.107515\pi$
$692$	−9.33552	−	13.0772i	−0.354883	−	0.497121i
$693$	−1.09848	−	0.461296i	−0.0417277	−	0.0175232i
$694$	−20.8339	+	6.67342i	−0.790843	+	0.253320i
$695$	6.20145	+	3.58041i	0.235234	+	0.135813i
$696$	−2.15226	+	18.2753i	−0.0815813	+	0.692725i
$697$	−21.5658	−	37.3530i	−0.816862	−	1.41485i
$698$	3.45635	−	15.9339i	0.130825	−	0.603106i
$699$	−58.0921			−2.19725
$700$	5.05329	+	1.56980i	0.190996	+	0.0593328i
$701$	−5.82647			−0.220063			−0.110031	−	0.993928i	$-0.535095\pi$
$701$	−5.82647			−0.220063			−0.110031	+	0.993928i	$0.535095\pi$
$702$	−5.04159	+	23.2419i	−0.190283	+	0.877208i
$703$	−3.87334	−	6.70882i	−0.146086	−	0.253028i
$704$	−0.582351	−	0.551346i	−0.0219482	−	0.0207796i
$705$	−10.5338	−	6.08169i	−0.396726	−	0.229050i
$706$	27.5237	−	8.81627i	1.03587	−	0.331805i
$707$	2.38227	+	18.8036i	0.0895946	+	0.707182i
$708$	−37.9744	+	27.1091i	−1.42716	+	1.01882i
$709$	8.29615	−	14.3694i	0.311569	−	0.539653i	−0.667134	−	0.744938i	$-0.732479\pi$
$709$	8.29615	−	14.3694i	0.311569	−	0.539653i	0.978702	+	0.205286i	$0.0658123\pi$
$710$	6.40010	−	7.04870i	0.240191	−	0.264533i
$711$	16.6290	−	9.60078i	0.623638	−	0.360058i
$712$	−3.56846	−	8.29253i	−0.133734	−	0.310776i
$713$		−	8.20905i		−	0.307431i
$714$	−50.1059	+	23.3452i	−1.87517	+	0.873671i
$715$			0.412736i			0.0154355i
$716$	17.6150	−	1.70302i	0.658304	−	0.0636448i
$717$	24.0678	−	13.8955i	0.898828	−	0.518938i
$718$	−22.2165	−	20.1722i	−0.829111	−	0.752818i
$719$	−1.69923	+	2.94314i	−0.0633704	+	0.109761i	−0.895970	−	0.444115i	$-0.853518\pi$
$719$	−1.69923	+	2.94314i	−0.0633704	+	0.109761i	0.832600	+	0.553875i	$0.186852\pi$
$720$	16.9942	+	5.83687i	0.633338	+	0.217527i
$721$	7.81954	+	10.2942i	0.291215	+	0.383377i
$722$	−15.8074	−	49.3493i	−0.588290	−	1.83659i
$723$	−45.1593	−	26.0727i	−1.67949	−	0.969655i
$724$	17.7014	−	38.8822i	0.657869	−	1.44504i
$725$	−1.18844	−	2.05844i	−0.0441376	−	0.0764486i
$726$	41.5748	+	9.01834i	1.54299	+	0.334702i
$727$	14.3045			0.530526			0.265263	−	0.964176i	$-0.414541\pi$
$727$	14.3045			0.530526			0.265263	+	0.964176i	$0.414541\pi$
$728$	15.6397	+	26.5470i	0.579647	+	0.983898i
$729$	−43.8569			−1.62433
$730$	8.49557	+	1.84285i	0.314435	+	0.0682068i
$731$	−19.0197	−	32.9430i	−0.703468	−	1.21844i
$732$	17.9257	−	39.3747i	0.662553	−	1.45533i
$733$	−42.8607	−	24.7457i	−1.58310	−	0.914001i	−0.994404	−	0.105645i	$-0.966309\pi$
$733$	−42.8607	−	24.7457i	−1.58310	−	0.914001i	−0.588693	−	0.808357i	$-0.700357\pi$
$734$	−3.30088	−	10.3051i	−0.121838	−	0.380367i
$735$	13.6799	−	13.4155i	0.504591	−	0.494839i
$736$	0.177870	−	8.53039i	0.00655637	−	0.314434i
$737$	−0.00550334	+	0.00953207i	−0.000202718	+	0.000351118i
$738$	37.5856	+	34.1271i	1.38355	+	1.25624i
$739$	23.2184	−	13.4052i	0.854104	−	0.493117i	−0.00792968	−	0.999969i	$-0.502524\pi$
$739$	23.2184	−	13.4052i	0.854104	−	0.493117i	0.862033	+	0.506852i	$0.169191\pi$
$740$	2.06740	−	0.199876i	0.0759992	−	0.00734760i
$741$			84.0664i			3.08826i
$742$	−22.8954	−	2.01051i	−0.840518	−	0.0738083i
$743$		−	22.2896i		−	0.817727i	−0.912596	−	0.408863i	$-0.865925\pi$
$743$		−	22.2896i		−	0.817727i	0.912596	−	0.408863i	$-0.134075\pi$
$744$	38.7045	−	16.6554i	1.41898	−	0.610617i
$745$	−18.2275	+	10.5236i	−0.667803	+	0.385556i
$746$	−24.3697	+	26.8394i	−0.892238	+	0.982660i
$747$	−14.6031	+	25.2933i	−0.534300	+	0.925435i
$748$	−0.880706	+	0.628717i	−0.0322018	+	0.0229882i
$749$	−15.9461	+	12.1128i	−0.582659	+	0.442591i
$750$	−3.68646	+	1.18083i	−0.134610	+	0.0431179i
$751$	11.1427	+	6.43324i	0.406603	+	0.234752i	0.689329	−	0.724448i	$-0.257905\pi$
$751$	11.1427	+	6.43324i	0.406603	+	0.234752i	−0.282726	+	0.959201i	$0.591239\pi$
$752$	−17.4458	+	3.40515i	−0.636184	+	0.124173i
$753$	−12.9494	−	22.4290i	−0.471902	−	0.817359i
$754$	2.93395	−	13.5256i	0.106848	−	0.492573i
$755$	−3.82299			−0.139133
$756$	15.8723	−	14.6684i	0.577269	−	0.533485i
$757$	−3.66830			−0.133327			−0.0666633	−	0.997776i	$-0.521235\pi$
$757$	−3.66830			−0.133327			−0.0666633	+	0.997776i	$0.521235\pi$
$758$	8.72527	−	40.2237i	0.316916	−	1.46099i
$759$	−0.206927	−	0.358408i	−0.00751097	−	0.0130094i
$760$	20.9534	+	2.46765i	0.760059	+	0.0895112i
$761$	−2.56137	−	1.47880i	−0.0928494	−	0.0536066i	0.452856	−	0.891583i	$-0.350405\pi$
$761$	−2.56137	−	1.47880i	−0.0928494	−	0.0536066i	−0.545706	+	0.837977i	$0.683738\pi$
$762$	−16.1309	+	5.16700i	−0.584362	+	0.187181i
$763$	47.3856	−	6.00339i	1.71547	−	0.217337i
$764$	29.0782	+	40.7327i	1.05201	+	1.47366i
$765$	12.1229	−	20.9975i	0.438305	−	0.759166i
$766$	−8.21683	+	9.04954i	−0.296886	+	0.326973i
$767$	30.3906	−	17.5460i	1.09734	−	0.633551i
$768$	40.5805	−	16.4688i	1.46432	−	0.594265i
$769$			32.6324i			1.17676i	0.808586	+	0.588378i	$0.200233\pi$
$769$			32.6324i			1.17676i	−0.808586	+	0.588378i	$0.799767\pi$
$770$	0.215233	−	0.307175i	0.00775647	−	0.0110698i
$771$		−	7.51469i		−	0.270635i
$772$	−1.57080	−	16.2474i	−0.0565342	−	0.584756i
$773$	−4.76043	+	2.74844i	−0.171221	+	0.0988544i	−0.583161	−	0.812356i	$-0.698184\pi$
$773$	−4.76043	+	2.74844i	−0.171221	+	0.0988544i	0.411941	+	0.911211i	$0.364851\pi$
$774$	33.1482	+	30.0980i	1.19149	+	1.08185i
$775$	−2.72129	+	4.71341i	−0.0977516	+	0.169311i
$776$	18.7178	−	25.0966i	0.671931	−	0.900916i
$777$	2.91198	−	6.93425i	0.104467	−	0.248765i
$778$	6.11598	+	19.0936i	0.219269	+	0.684538i
$779$	51.6233	+	29.8047i	1.84960	+	1.06786i
$780$	−20.5141	−	9.33920i	−0.734521	−	0.334397i
$781$	−0.337429	−	0.584444i	−0.0120742	−	0.0209131i
$782$	−11.2512	−	2.44060i	−0.402343	−	0.0872756i
$783$	−9.70800			−0.346936
$784$	2.20400	−	27.9131i	0.0787144	−	0.996897i
$785$	1.28413			0.0458325
$786$	−11.2788	−	2.44658i	−0.402301	−	0.0872665i
$787$	15.7430	+	27.2677i	0.561177	+	0.971987i	0.997394	+	0.0721455i	$0.0229846\pi$
$787$	15.7430	+	27.2677i	0.561177	+	0.971987i	−0.436217	+	0.899841i	$0.643682\pi$
$788$	−22.6652	−	10.3185i	−0.807413	−	0.367582i
$789$	−60.8659	−	35.1410i	−2.16689	−	1.25105i
$790$	1.84402	+	5.75687i	0.0656072	+	0.204820i
$791$	−18.5858	+	44.2582i	−0.660837	+	1.57364i
$792$	0.761473	−	1.02097i	0.0270578	−	0.0362787i
$793$	−16.2694	+	28.1795i	−0.577745	+	1.00068i
$794$	0.183233	+	0.166372i	0.00650269	+	0.00590433i
$795$	14.5609	−	8.40673i	0.516421	−	0.298156i
$796$	4.46000	+	46.1316i	0.158081	+	1.63509i
$797$			20.2691i			0.717968i	0.933344	+	0.358984i	$0.116877\pi$
$797$			20.2691i			0.717968i	−0.933344	+	0.358984i	$0.883123\pi$
$798$	43.8388	−	62.5655i	1.55188	−	2.21479i
$799$			23.9845i			0.848512i
$800$	−2.92994	+	4.83895i	−0.103589	+	0.171083i
$801$	12.4171	−	7.16902i	0.438737	−	0.253305i
$802$	−22.8702	+	25.1879i	−0.807574	+	0.889416i
$803$	0.308096	−	0.533638i	0.0108725	−	0.0188317i
$804$	−0.349241	−	0.489217i	−0.0123168	−	0.0172534i
$805$	3.95895	−	0.501568i	0.139535	−	0.0176780i
$806$	−30.1806	+	9.66734i	−1.06307	+	0.340518i
$807$	−19.4378	−	11.2224i	−0.684244	−	0.395049i
$808$	−20.1235	−	2.36992i	−0.707943	−	0.0833735i
$809$	15.6376	+	27.0851i	0.549789	+	0.952262i	0.998289	+	0.0584790i	$0.0186251\pi$
$809$	15.6376	+	27.0851i	0.549789	+	0.952262i	−0.448500	+	0.893783i	$0.648042\pi$
$810$	0.688609	−	3.17451i	0.0241953	−	0.111541i
$811$	−51.4855			−1.80790			−0.903950	−	0.427638i	$-0.859346\pi$
$811$	−51.4855			−1.80790			−0.903950	+	0.427638i	$0.859346\pi$
$812$	−9.23687	+	8.53628i	−0.324151	+	0.299565i
$813$	17.5379			0.615080
$814$	0.0312102	−	0.143880i	0.00109392	−	0.00504299i
$815$	−4.30054	−	7.44875i	−0.150641	−	0.260918i
$816$	−11.3206	−	57.9997i	−0.396301	−	2.03039i
$817$	45.5285	+	26.2859i	1.59284	+	0.919626i
$818$	−16.0760	+	5.14940i	−0.562084	+	0.180044i
$819$	−38.9680	+	29.6002i	−1.36165	+	1.03432i
$820$	−13.0080	+	9.28612i	−0.454259	+	0.324285i
$821$	24.0601	−	41.6733i	0.839702	−	1.45441i	−0.0504413	−	0.998727i	$-0.516063\pi$
$821$	24.0601	−	41.6733i	0.839702	−	1.45441i	0.890144	−	0.455680i	$-0.150604\pi$
$822$	3.96764	−	4.36973i	0.138387	−	0.152412i
$823$	−21.3892	+	12.3490i	−0.745580	+	0.430461i	−0.824095	−	0.566452i	$-0.808316\pi$
$823$	−21.3892	+	12.3490i	−0.745580	+	0.430461i	0.0785148	+	0.996913i	$0.474982\pi$
$824$	−12.6944	+	5.46270i	−0.442232	+	0.190302i
$825$			0.274384i			0.00955282i
$826$	−31.7678	−	2.78962i	−1.10534	−	0.0970633i
$827$			19.9120i			0.692408i	0.938159	+	0.346204i	$0.112530\pi$
$827$			19.9120i			0.692408i	−0.938159	+	0.346204i	$0.887470\pi$
$828$	13.4882	−	1.30404i	0.468748	−	0.0453185i
$829$	−13.8257	+	7.98225i	−0.480185	+	0.277235i	−0.720494	−	0.693461i	$-0.756085\pi$
$829$	−13.8257	+	7.98225i	−0.480185	+	0.277235i	0.240308	+	0.970697i	$0.422751\pi$
$830$	−6.80723	−	6.18085i	−0.236282	−	0.214540i
$831$	−21.8552	+	37.8543i	−0.758149	+	1.31315i
$832$	−31.5715	+	9.39183i	−1.09455	+	0.325603i
$833$	−36.3969	−	10.1342i	−1.26108	−	0.351128i
$834$	8.45572	+	26.3981i	0.292798	+	0.914090i
$835$	−7.01869	−	4.05224i	−0.242892	−	0.140234i
$836$	0.619644	−	1.36108i	0.0214308	−	0.0470740i
$837$	11.1147	+	19.2512i	0.384179	+	0.665418i
$838$	−41.6008	−	9.02398i	−1.43708	−	0.311728i
$839$	14.5375			0.501889			0.250944	−	0.968002i	$-0.419259\pi$
$839$	14.5375			0.501889			0.250944	+	0.968002i	$0.419259\pi$
$840$	10.3972	+	17.6482i	0.358736	+	0.608922i
$841$	−23.3504			−0.805187
$842$	9.37398	+	2.03339i	0.323049	+	0.0700752i
$843$	13.2536	+	22.9558i	0.456477	+	0.790641i
$844$	9.09554	−	19.9788i	0.313081	−	0.687700i
$845$	3.42306	+	1.97631i	0.117757	+	0.0679870i
$846$	−8.61174	−	26.8851i	−0.296078	−	0.924330i
$847$	17.5880	+	23.1542i	0.604331	+	0.795586i
$848$	7.98136	−	23.2380i	0.274081	−	0.797996i
$849$	−35.7568	+	61.9325i	−1.22717	+	2.12552i
$850$	5.65108	+	5.13109i	0.193831	+	0.175995i
$851$	1.35655	−	0.783202i	0.0465018	−	0.0268478i
$852$	36.6836	−	3.54657i	1.25676	−	0.121503i
$853$			36.2299i			1.24049i	0.784408	+	0.620245i	$0.212967\pi$
$853$			36.2299i			1.24049i	−0.784408	+	0.620245i	$0.787033\pi$
$854$	26.8034	−	12.4881i	0.917192	−	0.427335i
$855$			33.5086i			1.14597i
$856$	−8.46193	−	19.6642i	−0.289223	−	0.672107i
$857$	−32.9576	+	19.0281i	−1.12581	+	0.649986i	−0.942878	−	0.333139i	$-0.891892\pi$
$857$	−32.9576	+	19.0281i	−1.12581	+	0.649986i	−0.182932	+	0.983126i	$0.558559\pi$
$858$	−1.07400	+	1.18284i	−0.0366658	+	0.0403817i
$859$	13.3104	−	23.0543i	0.454145	−	0.786602i	−0.544494	−	0.838765i	$-0.683278\pi$
$859$	13.3104	−	23.0543i	0.454145	−	0.786602i	0.998639	+	0.0521630i	$0.0166115\pi$
$860$	−11.4722	+	8.18977i	−0.391200	+	0.279269i
$861$	7.27378	+	57.4129i	0.247890	+	1.95663i
$862$	−21.4628	+	6.87487i	−0.731025	+	0.234159i
$863$	20.1195	+	11.6160i	0.684876	+	0.395413i	0.801690	−	0.597741i	$-0.203935\pi$
$863$	20.1195	+	11.6160i	0.684876	+	0.395413i	−0.116814	+	0.993154i	$0.537268\pi$
$864$	11.1326	+	20.2456i	0.378740	+	0.688769i
$865$	4.01688	+	6.95744i	0.136578	+	0.236560i
$866$	4.53565	−	20.9095i	0.154128	−	0.710533i
$867$	−33.2058			−1.12773
$868$	27.5029	+	8.54375i	0.933510	+	0.289994i
$869$	0.428484			0.0145353
$870$	1.95047	−	8.99170i	0.0661270	−	0.304847i
$871$	0.226043	+	0.391517i	0.00765916	+	0.0132661i
$872$	−5.97226	+	50.7118i	−0.202246	+	1.71732i
$873$	43.0624	+	24.8621i	1.45744	+	0.841455i
$874$	15.1528	−	4.85370i	0.512553	−	0.164179i
$875$	−2.43939	−	1.02440i	−0.0824663	−	0.0346310i
$876$	19.5517	+	27.3881i	0.660592	+	0.925358i
$877$	1.28202	−	2.22052i	0.0432907	−	0.0749817i	−0.843568	−	0.537022i	$-0.819549\pi$
$877$	1.28202	−	2.22052i	0.0432907	−	0.0749817i	0.886859	+	0.462040i	$0.152882\pi$
$878$	4.15132	−	4.57202i	0.140100	−	0.154298i
$879$	38.4937	−	22.2244i	1.29836	−	0.749609i
$880$	0.263296	+	0.302414i	0.00887570	+	0.0101944i
$881$		−	11.4074i		−	0.384324i	−0.981363	−	0.192162i	$-0.938450\pi$
$881$		−	11.4074i		−	0.384324i	0.981363	−	0.192162i	$-0.0615498\pi$
$882$	44.4374	−	1.70869i	1.49628	−	0.0575347i
$883$		−	15.8634i		−	0.533845i	−0.963718	−	0.266922i	$-0.913993\pi$
$883$		−	15.8634i		−	0.533845i	0.963718	−	0.266922i	$-0.0860068\pi$
$884$	4.27706	+	44.2393i	0.143853	+	1.48793i
$885$	20.2034	−	11.6645i	0.679131	−	0.392097i
$886$	14.7610	+	13.4027i	0.495904	+	0.450272i
$887$	−13.5260	+	23.4277i	−0.454159	+	0.786626i	−0.998639	−	0.0521471i	$-0.983394\pi$
$887$	−13.5260	+	23.4277i	−0.454159	+	0.786626i	0.544480	+	0.838774i	$0.316727\pi$
$888$	6.44499	+	4.80687i	0.216280	+	0.161308i
$889$	−10.6741	−	4.48249i	−0.357997	−	0.150338i
$890$	1.37695	+	4.29872i	0.0461554	+	0.144093i
$891$	−0.199403	−	0.115125i	−0.00668024	−	0.00385684i
$892$	−27.2668	−	12.4134i	−0.912960	−	0.415633i
$893$	−16.5738	−	28.7066i	−0.554620	−	0.960629i
$894$	−79.6214	−	17.2714i	−2.66294	−	0.577641i
$895$	−8.84857			−0.295775
$896$	28.3944	+	9.47411i	0.948590	+	0.316508i
$897$	−16.9985			−0.567563
$898$	23.5119	+	5.10016i	0.784601	+	0.170194i
$899$	−6.46818	−	11.2032i	−0.215726	−	0.373648i
$900$	−8.17684	−	3.72258i	−0.272561	−	0.124086i
$901$	−28.7121	−	16.5769i	−0.956537	−	0.552257i
$902$	0.345584	+	1.07888i	0.0115067	+	0.0359229i
$903$	6.41502	+	50.6346i	0.213478	+	1.68501i
$904$	−41.1355	−	30.6801i	−1.36815	−	1.02041i
$905$	−10.6805	+	18.4991i	−0.355031	+	0.614932i
$906$	−10.9562	−	9.94800i	−0.363994	−	0.330500i
$907$	9.02842	−	5.21256i	0.299784	−	0.173080i	−0.342562	−	0.939495i	$-0.611295\pi$
$907$	9.02842	−	5.21256i	0.299784	−	0.173080i	0.642346	+	0.766415i	$0.277961\pi$
$908$	0.290121	+	3.00084i	0.00962801	+	0.0995864i
$909$		−	32.1815i		−	1.06739i
$910$	−6.50625	−	13.9644i	−0.215680	−	0.462916i
$911$		−	43.7727i		−	1.45026i	−0.688614	−	0.725128i	$-0.741781\pi$
$911$		−	43.7727i		−	1.45026i	0.688614	−	0.725128i	$-0.258219\pi$
$912$	53.6283	+	61.5958i	1.77581	+	2.03964i
$913$	−0.564423	+	0.325870i	−0.0186797	+	0.0107847i
$914$	−11.0892	+	12.2130i	−0.366799	+	0.403972i
$915$	−10.8158	+	18.7335i	−0.357559	+	0.619310i
$916$	9.90692	+	13.8776i	0.327334	+	0.458529i
$917$	−4.77143	−	6.28147i	−0.157567	−	0.207432i
$918$	29.6899	−	9.51014i	0.979912	−	0.313881i
$919$	−43.5772	−	25.1593i	−1.43748	−	0.829929i	−0.439806	−	0.898093i	$-0.644953\pi$
$919$	−43.5772	−	25.1593i	−1.43748	−	0.829929i	−0.997674	+	0.0681637i	$0.978286\pi$
$920$	−0.498968	+	4.23684i	−0.0164505	+	0.139685i
$921$	−32.2216	−	55.8095i	−1.06174	−	1.83899i
$922$	−7.92926	+	36.5541i	−0.261136	+	1.20385i
$923$	−27.7189			−0.912379
$924$	1.41614	−	0.320250i	0.0465877	−	0.0105354i
$925$	−1.03852			−0.0341464
$926$	0.940418	−	4.33535i	0.0309041	−	0.142469i
$927$	−10.9745	−	19.0085i	−0.360451	−	0.624320i
$928$	−6.47863	−	11.7819i	−0.212671	−	0.386760i
$929$	−16.4494	−	9.49704i	−0.539686	−	0.311588i	0.205266	−	0.978706i	$-0.434194\pi$
$929$	−16.4494	−	9.49704i	−0.539686	−	0.311588i	−0.744952	+	0.667118i	$0.767527\pi$
$930$	−20.0638	+	6.42677i	−0.657919	+	0.210742i
$931$	50.5656	−	13.0216i	1.65722	−	0.426765i
$932$	34.5469	−	24.6623i	1.13162	−	0.807840i
$933$	7.38419	−	12.7898i	0.241747	−	0.418719i
$934$	7.73951	−	8.52385i	0.253244	−	0.278909i
$935$	0.468561	−	0.270524i	0.0153236	−	0.00884707i
$936$	−20.6786	−	48.0538i	−0.675902	−	1.57069i
$937$			44.7192i			1.46091i	0.682959	+	0.730457i	$0.260693\pi$
$937$			44.7192i			1.46091i	−0.682959	+	0.730457i	$0.739307\pi$
$938$	0.0359382	−	0.409259i	0.00117342	−	0.0133628i
$939$		−	89.1265i		−	2.90853i
$940$	8.84628	−	0.855258i	0.288534	−	0.0278954i
$941$	8.88040	−	5.12710i	0.289493	−	0.167139i	−0.348220	−	0.937413i	$-0.613214\pi$
$941$	8.88040	−	5.12710i	0.289493	−	0.167139i	0.637713	+	0.770274i	$0.279881\pi$
$942$	3.68013	+	3.34150i	0.119905	+	0.108872i
$943$	−6.02661	+	10.4384i	−0.196253	+	0.339921i
$944$	11.0743	−	32.2431i	0.360436	−	1.04942i
$945$	−8.60509	+	6.53647i	−0.279924	+	0.212631i
$946$	0.304783	+	0.951508i	0.00990936	+	0.0309362i
$947$	−21.6242	−	12.4847i	−0.702691	−	0.405699i	0.105658	−	0.994403i	$-0.466305\pi$
$947$	−21.6242	−	12.4847i	−0.702691	−	0.405699i	−0.808349	+	0.588704i	$0.799638\pi$
$948$	−9.69554	+	21.2968i	−0.314897	+	0.691687i
$949$	−12.6546	−	21.9185i	−0.410787	−	0.711504i
$950$	−10.3093	−	2.23629i	−0.334479	−	0.0725547i
$951$	37.5316			1.21704
$952$	19.8867	−	35.1550i	0.644532	−	1.13938i
$953$	26.3831			0.854633			0.427317	−	0.904102i	$-0.359459\pi$
$953$	26.3831			0.854633			0.427317	+	0.904102i	$0.359459\pi$
$954$	38.1364	+	8.27249i	1.23471	+	0.267832i
$955$	−12.5117	−	21.6710i	−0.404870	−	0.701256i
$956$	−8.41374	+	18.4812i	−0.272120	+	0.597726i
$957$	−0.564803	−	0.326089i	−0.0182575	−	0.0105410i
$958$	−10.6905	−	33.3749i	−0.345395	−	1.07829i
$959$	4.00213	−	0.507039i	0.129235	−	0.0163731i
$960$	−20.9885	+	6.24361i	−0.677400	+	0.201512i
$961$	0.689177	−	1.19369i	0.0222315	−	0.0385061i
$962$	−4.47697	−	4.06502i	−0.144343	−	0.131061i
$963$	29.4448	−	17.0000i	0.948846	−	0.547817i
$964$	37.9247	−	3.66656i	1.22147	−	0.118092i
$965$			8.16157i			0.262730i
$966$	12.6509	+	8.86435i	0.407037	+	0.285206i
$967$		−	47.1287i		−	1.51556i	−0.652512	−	0.757778i	$-0.726285\pi$
$967$		−	47.1287i		−	1.51556i	0.652512	−	0.757778i	$-0.273715\pi$
$968$	−28.5528	+	12.2869i	−0.917723	+	0.394917i
$969$	95.4367	−	55.1004i	3.06587	−	1.77008i
$970$	−10.5230	+	11.5894i	−0.337874	+	0.372115i
$971$	−27.6416	+	47.8767i	−0.887062	+	1.53644i	−0.0437306	+	0.999043i	$0.513924\pi$
$971$	−27.6416	+	47.8767i	−0.887062	+	1.53644i	−0.843332	+	0.537394i	$0.819409\pi$
$972$	30.1792	−	21.5443i	0.968000	−	0.691033i
$973$	−7.33553	+	17.4680i	−0.235166	+	0.559998i
$974$	−17.0971	+	5.47647i	−0.547826	+	0.175477i
$975$	9.76007	+	5.63498i	0.312572	+	0.180464i
$976$	6.05579	+	31.0260i	0.193841	+	0.993117i
$977$	−4.22669	−	7.32085i	−0.135224	−	0.234215i	0.790459	−	0.612515i	$-0.209842\pi$
$977$	−4.22669	−	7.32085i	−0.135224	−	0.234215i	−0.925683	+	0.378300i	$0.876509\pi$
$978$	7.05804	−	32.5377i	0.225691	−	1.04044i
$979$	0.319954			0.0102258
$980$	−2.43995	+	13.7857i	−0.0779412	+	0.440369i
$981$	−81.0982			−2.58927
$982$	2.85164	−	13.1461i	0.0909996	−	0.419510i
$983$	16.4461	+	28.4854i	0.524548	+	0.908543i	0.999591	+	0.0285811i	$0.00909888\pi$
$983$	16.4461	+	28.4854i	0.524548	+	0.908543i	−0.475044	+	0.879962i	$0.657568\pi$
$984$	−61.4430	−	7.23606i	−1.95873	−	0.230677i
$985$	10.7835	+	6.22586i	0.343591	+	0.198372i
$986$	−17.2780	+	5.53442i	−0.550244	+	0.176252i
$987$	12.4602	−	29.6712i	0.396611	−	0.944445i
$988$	−35.6893	−	49.9936i	−1.13543	−	1.59051i
$989$	−5.31509	+	9.20601i	−0.169010	+	0.292734i
$990$	−0.428094	+	0.471478i	−0.0136057	+	0.0149846i
$991$	−26.5344	+	15.3196i	−0.842893	+	0.486645i	−0.858247	−	0.513238i	$-0.828446\pi$
$991$	−26.5344	+	15.3196i	−0.842893	+	0.486645i	0.0153535	+	0.999882i	$0.495113\pi$
$992$	−15.9464	+	26.3364i	−0.506300	+	0.836180i
$993$		−	15.5659i		−	0.493970i
$994$	20.6295	+	14.4548i	0.654328	+	0.458479i
$995$		−	23.1734i		−	0.734645i
$996$	−3.42507	−	35.4269i	−0.108527	−	1.12254i
$997$	36.7799	−	21.2349i	1.16483	−	0.672516i	0.212374	−	0.977188i	$-0.431880\pi$
$997$	36.7799	−	21.2349i	1.16483	−	0.672516i	0.952457	+	0.304673i	$0.0985471\pi$
$998$	8.89204	+	8.07382i	0.281473	+	0.255572i
$999$	−2.12084	+	3.67340i	−0.0671003	+	0.116221i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.o.a.131.16	yes	32
4.3	odd	2	inner	140.2.o.a.131.4	yes	32
5.2	odd	4		700.2.t.d.299.8		32
5.3	odd	4		700.2.t.c.299.9		32
5.4	even	2		700.2.p.c.551.1		32
7.2	even	3		980.2.g.a.391.14		32
7.3	odd	6	inner	140.2.o.a.31.4	✓	32
7.4	even	3		980.2.o.f.31.4		32
7.5	odd	6		980.2.g.a.391.13		32
7.6	odd	2		980.2.o.f.411.16		32
20.3	even	4		700.2.t.c.299.5		32
20.7	even	4		700.2.t.d.299.12		32
20.19	odd	2		700.2.p.c.551.13		32
28.3	even	6	inner	140.2.o.a.31.16	yes	32
28.11	odd	6		980.2.o.f.31.16		32
28.19	even	6		980.2.g.a.391.16		32
28.23	odd	6		980.2.g.a.391.15		32
28.27	even	2		980.2.o.f.411.4		32
35.3	even	12		700.2.t.d.199.12		32
35.17	even	12		700.2.t.c.199.5		32
35.24	odd	6		700.2.p.c.451.13		32
140.3	odd	12		700.2.t.d.199.8		32
140.59	even	6		700.2.p.c.451.1		32
140.87	odd	12		700.2.t.c.199.9		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.o.a.31.4	✓	32	7.3	odd	6	inner
140.2.o.a.31.16	yes	32	28.3	even	6	inner
140.2.o.a.131.4	yes	32	4.3	odd	2	inner
140.2.o.a.131.16	yes	32	1.1	even	1	trivial
700.2.p.c.451.1		32	140.59	even	6
700.2.p.c.451.13		32	35.24	odd	6
700.2.p.c.551.1		32	5.4	even	2
700.2.p.c.551.13		32	20.19	odd	2
700.2.t.c.199.5		32	35.17	even	12
700.2.t.c.199.9		32	140.87	odd	12
700.2.t.c.299.5		32	20.3	even	4
700.2.t.c.299.9		32	5.3	odd	4
700.2.t.d.199.8		32	140.3	odd	12
700.2.t.d.199.12		32	35.3	even	12
700.2.t.d.299.8		32	5.2	odd	4
700.2.t.d.299.12		32	20.7	even	4
980.2.g.a.391.13		32	7.5	odd	6
980.2.g.a.391.14		32	7.2	even	3
980.2.g.a.391.15		32	28.23	odd	6
980.2.g.a.391.16		32	28.19	even	6
980.2.o.f.31.4		32	7.4	even	3
980.2.o.f.31.16		32	28.11	odd	6
980.2.o.f.411.4		32	28.27	even	2
980.2.o.f.411.16		32	7.6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38207 + 0.299797i) q^{2} +(-1.36859 - 2.37047i) q^{3} +(1.82024 + 0.828682i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-1.18083 - 3.68646i) q^{6} +(1.02440 - 2.43939i) q^{7} +(2.26727 + 1.69100i) q^{8} +(-2.24609 + 3.89033i) q^{9} +(-1.04701 - 0.950668i) q^{10} +(-0.0868131 + 0.0501216i) q^{11} +(-0.526805 - 5.44896i) q^{12} +4.11735i q^{13} +(2.14711 - 3.06430i) q^{14} +2.73718i q^{15} +(2.62657 + 3.01680i) q^{16} +(4.67424 - 2.69867i) q^{17} +(-4.27056 + 4.70335i) q^{18} +(-3.72967 + 6.45997i) q^{19} +(-1.16204 - 1.62778i) q^{20} +(-7.18448 + 0.910218i) q^{21} +(-0.135008 + 0.0432453i) q^{22} +(-1.30623 - 0.754151i) q^{23} +(0.905498 - 7.68879i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-1.23437 + 5.69048i) q^{26} +4.08434 q^{27} +(3.88613 - 3.59138i) q^{28} -2.37688 q^{29} +(-0.820599 + 3.78298i) q^{30} +(2.72129 + 4.71341i) q^{31} +(2.72568 + 4.95688i) q^{32} +(0.237623 + 0.137192i) q^{33} +(7.26919 - 2.32844i) q^{34} +(-2.10685 + 1.60037i) q^{35} +(-7.31227 + 5.22007i) q^{36} +(-0.519260 + 0.899386i) q^{37} +(-7.09135 + 7.81000i) q^{38} +(9.76007 - 5.63498i) q^{39} +(-1.11801 - 2.59808i) q^{40} -7.99125i q^{41} +(-10.2023 - 0.895897i) q^{42} -7.04778i q^{43} +(-0.199556 + 0.0192930i) q^{44} +(3.89033 - 2.24609i) q^{45} +(-1.57921 - 1.43389i) q^{46} +(-2.22188 + 3.84841i) q^{47} +(3.55654 - 10.3550i) q^{48} +(-4.90122 - 4.99781i) q^{49} +(0.431404 + 1.34681i) q^{50} +(-12.7943 - 7.38677i) q^{51} +(-3.41198 + 7.49459i) q^{52} +(-3.07131 - 5.31966i) q^{53} +(5.64485 + 1.22447i) q^{54} +0.100243 q^{55} +(6.44759 - 3.79849i) q^{56} +20.4176 q^{57} +(-3.28502 - 0.712582i) q^{58} +(-4.26148 - 7.38111i) q^{59} +(-2.26825 + 4.98234i) q^{60} +(6.84408 + 3.95143i) q^{61} +(2.34795 + 7.33010i) q^{62} +(7.18914 + 9.46432i) q^{63} +(2.28103 + 7.66791i) q^{64} +(2.05868 - 3.56573i) q^{65} +(0.287283 + 0.260848i) q^{66} +(0.0950895 - 0.0549000i) q^{67} +(10.7446 - 1.03879i) q^{68} +4.12850i q^{69} +(-3.39160 + 1.58020i) q^{70} +6.73221i q^{71} +(-11.6710 + 5.02231i) q^{72} +(-5.32344 + 3.07349i) q^{73} +(-0.987288 + 1.08734i) q^{74} +(1.36859 - 2.37047i) q^{75} +(-12.1422 + 8.66802i) q^{76} +(0.0333347 + 0.263115i) q^{77} +(15.1785 - 4.86190i) q^{78} +(-3.70178 - 2.13723i) q^{79} +(-0.766277 - 3.92592i) q^{80} +(1.14846 + 1.98919i) q^{81} +(2.39575 - 11.0445i) q^{82} +6.50159 q^{83} +(-13.8318 - 4.29682i) q^{84} -5.39735 q^{85} +(2.11290 - 9.74053i) q^{86} +(3.25298 + 5.63433i) q^{87} +(-0.281584 - 0.0331618i) q^{88} +(-2.76417 - 1.59589i) q^{89} +(6.05009 - 1.93794i) q^{90} +(10.0438 + 4.21781i) q^{91} +(-1.75270 - 2.45519i) q^{92} +(7.44866 - 12.9015i) q^{93} +(-4.22454 + 4.65267i) q^{94} +(6.45997 - 3.72967i) q^{95} +(8.01978 - 13.2451i) q^{96} -11.0691i q^{97} +(-5.27550 - 8.37670i) q^{98} -0.450309i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9} - 30 q^{12} + 2 q^{14} - 14 q^{16} - 12 q^{21} - 8 q^{22} + 36 q^{24} + 16 q^{25} + 30 q^{26} + 2 q^{28} - 40 q^{29} + 2 q^{32} + 60 q^{36} + 8 q^{37} - 60 q^{38}+ \cdots + 78 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9 - 30 * q^12 + 2 * q^14 - 14 * q^16 - 12 * q^21 - 8 * q^22 + 36 * q^24 + 16 * q^25 + 30 * q^26 + 2 * q^28 - 40 * q^29 + 2 * q^32 + 60 * q^36 + 8 * q^37 - 60 * q^38 - 62 * q^42 - 18 * q^44 + 12 * q^45 + 2 * q^46 - 16 * q^49 + 4 * q^50 - 36 * q^52 - 8 * q^53 + 12 * q^54 - 4 * q^56 + 48 * q^57 + 2 * q^58 + 14 * q^60 + 24 * q^61 + 4 * q^64 + 4 * q^65 + 24 * q^66 + 60 * q^68 - 4 * q^70 + 4 * q^72 - 72 * q^73 + 38 * q^74 - 40 * q^77 + 120 * q^78 - 36 * q^81 + 42 * q^82 - 20 * q^84 + 28 * q^86 + 4 * q^88 - 60 * q^89 - 4 * q^92 - 8 * q^93 + 18 * q^94 - 60 * q^96 + 78 * q^98

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