LMFDB - Embedded newform 187.3.q.a.2.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [187,3,Mod(2,187)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("187.2"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(187, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([4, 35])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	187.q (of order $40$, degree $16$, 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:	$5.09538094354$
Analytic rank:	$0$
Dimension:	$544$
Relative dimension:	$34$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			2.17
Character	$\chi$	$=$	187.2
Dual form			187.3.q.a.94.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0206482 - 0.0405244i) q^{2} +(0.427119 - 0.696996i) q^{3} +(2.34993 - 3.23439i) q^{4} +(-1.14178 + 0.975172i) q^{5} +(-0.0370646 - 0.00291705i) q^{6} +(6.06168 + 9.89176i) q^{7} +(-0.359280 - 0.0569044i) q^{8} +(3.78254 + 7.42366i) q^{9} +(0.0630940 + 0.0261344i) q^{10} +(5.26541 - 9.65792i) q^{11} +(-1.25066 - 3.01936i) q^{12} +(2.00739 - 6.17812i) q^{13} +(0.275695 - 0.449894i) q^{14} +(0.192014 + 1.21233i) q^{15} +(-4.93660 - 15.1933i) q^{16} +(14.1913 - 9.35983i) q^{17} +(0.222737 - 0.306571i) q^{18} +(2.39622 - 15.1291i) q^{19} +(0.470994 + 5.98455i) q^{20} +9.48358 q^{21} +(-0.500103 - 0.0139588i) q^{22} +(-11.3595 - 4.70526i) q^{23} +(-0.193118 + 0.226112i) q^{24} +(-3.55816 + 22.4653i) q^{25} +(-0.291814 + 0.0462188i) q^{26} +(14.1243 + 1.11160i) q^{27} +(46.2384 + 3.63904i) q^{28} +(-34.4313 - 8.26623i) q^{29} +(0.0451642 - 0.0328137i) q^{30} +(3.88274 + 49.3348i) q^{31} +(-1.54263 + 1.54263i) q^{32} +(-4.48257 - 7.79506i) q^{33} +(-0.672327 - 0.381831i) q^{34} +(-16.5673 - 5.38303i) q^{35} +(32.8997 + 5.21081i) q^{36} +(31.9119 + 7.66137i) q^{37} +(-0.662578 + 0.215285i) q^{38} +(-3.44873 - 4.03794i) q^{39} +(0.465711 - 0.285388i) q^{40} +(-16.0712 + 3.85835i) q^{41} +(-0.195819 - 0.384317i) q^{42} +(-23.9713 - 23.9713i) q^{43} +(-18.8642 - 39.7258i) q^{44} +(-11.5582 - 4.78755i) q^{45} +(0.0438756 + 0.557492i) q^{46} +(-7.12664 - 9.80897i) q^{47} +(-12.6982 - 3.04856i) q^{48} +(-38.8575 + 76.2621i) q^{49} +(0.983865 - 0.319677i) q^{50} +(-0.462373 - 13.8891i) q^{51} +(-15.2653 - 21.0108i) q^{52} +(29.5974 - 15.0806i) q^{53} +(-0.246594 - 0.595331i) q^{54} +(3.40619 + 16.1619i) q^{55} +(-1.61496 - 3.89885i) q^{56} +(-9.52148 - 8.13211i) q^{57} +(0.375962 + 1.56599i) q^{58} +(-46.7219 + 7.40001i) q^{59} +(4.37237 + 2.22784i) q^{60} +(-3.20895 + 40.7736i) q^{61} +(1.91909 - 1.17602i) q^{62} +(-50.5045 + 82.4159i) q^{63} +(-60.6788 - 19.7157i) q^{64} +(3.73273 + 9.01161i) q^{65} +(-0.223333 + 0.342608i) q^{66} -52.4148 q^{67} +(3.07515 - 67.8952i) q^{68} +(-8.13141 + 5.90781i) q^{69} +(0.123940 + 0.782529i) q^{70} +(9.72067 + 11.3814i) q^{71} +(-0.936555 - 2.88242i) q^{72} +(-80.1304 - 19.2376i) q^{73} +(-0.348451 - 1.45140i) q^{74} +(14.1385 + 12.0754i) q^{75} +(-43.3027 - 43.3027i) q^{76} +(127.451 - 6.45903i) q^{77} +(-0.0924251 + 0.223134i) q^{78} +(62.8671 + 53.6936i) q^{79} +(20.4526 + 12.5334i) q^{80} +(-37.2681 + 51.2951i) q^{81} +(0.488199 + 0.571607i) q^{82} +(-33.0768 - 16.8535i) q^{83} +(22.2857 - 30.6736i) q^{84} +(-7.07591 + 24.5258i) q^{85} +(-0.476458 + 1.46639i) q^{86} +(-20.4678 + 20.4678i) q^{87} +(-2.44134 + 3.17028i) q^{88} -62.3451i q^{89} +(0.0446430 + 0.567243i) q^{90} +(73.2807 - 17.5931i) q^{91} +(-41.9126 + 25.6841i) q^{92} +(36.0446 + 18.3656i) q^{93} +(-0.250351 + 0.491341i) q^{94} +(12.0176 + 19.6109i) q^{95} +(0.416320 + 1.73410i) q^{96} +(154.977 - 12.1970i) q^{97} +3.89282 q^{98} +(91.6137 + 2.55712i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 544 q - 20 q^{2} - 12 q^{3} - 20 q^{5} - 20 q^{6} - 20 q^{7} - 20 q^{8} + 36 q^{9} + 28 q^{11} - 200 q^{12} + 36 q^{14} + 108 q^{15} + 424 q^{16} - 180 q^{17} - 40 q^{18} - 20 q^{19} - 140 q^{20} + 32 q^{22}+ \cdots - 72 q^{99}+O(q^{100}) $ 544 * q - 20 * q^2 - 12 * q^3 - 20 * q^5 - 20 * q^6 - 20 * q^7 - 20 * q^8 + 36 * q^9 + 28 * q^11 - 200 * q^12 + 36 * q^14 + 108 * q^15 + 424 * q^16 - 180 * q^17 - 40 * q^18 - 20 * q^19 - 140 * q^20 + 32 * q^22 - 48 * q^23 + 460 * q^24 - 84 * q^25 + 132 * q^26 - 228 * q^27 - 20 * q^28 - 20 * q^29 - 100 * q^31 + 24 * q^33 + 96 * q^34 - 40 * q^35 + 164 * q^36 - 332 * q^37 - 20 * q^39 - 760 * q^40 - 560 * q^41 + 276 * q^42 - 240 * q^44 - 32 * q^45 - 20 * q^46 + 252 * q^48 - 472 * q^49 - 40 * q^50 - 20 * q^51 + 280 * q^52 + 92 * q^53 - 160 * q^56 + 1060 * q^57 - 1348 * q^58 - 260 * q^59 - 748 * q^60 - 320 * q^61 - 20 * q^62 + 580 * q^63 + 292 * q^66 + 160 * q^67 - 20 * q^68 - 192 * q^69 - 628 * q^70 - 268 * q^71 - 20 * q^73 - 20 * q^74 + 1116 * q^75 + 732 * q^77 + 1232 * q^78 - 20 * q^79 - 936 * q^80 - 684 * q^82 - 380 * q^83 + 1240 * q^84 - 1320 * q^85 - 632 * q^86 - 412 * q^88 - 20 * q^90 + 1204 * q^91 + 540 * q^92 + 1108 * q^93 - 3800 * q^94 + 360 * q^95 - 20 * q^96 + 652 * q^97 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{8}\right)$

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 $

$2$	−0.0206482	−	0.0405244i	−0.0103241	−	0.0202622i	0.885787	−	0.464092i	$-0.153619\pi$
$2$	−0.0206482	−	0.0405244i	−0.0103241	−	0.0202622i	−0.896111	+	0.443830i	$0.853619\pi$
$3$	0.427119	−	0.696996i	0.142373	−	0.232332i	−0.773503	−	0.633792i	$-0.781497\pi$
$3$	0.427119	−	0.696996i	0.142373	−	0.232332i	0.915876	+	0.401461i	$0.131497\pi$
$4$	2.34993	−	3.23439i	0.587481	−	0.808599i
$5$	−1.14178	+	0.975172i	−0.228356	+	0.195034i	−0.756263	−	0.654268i	$-0.772977\pi$
$5$	−1.14178	+	0.975172i	−0.228356	+	0.195034i	0.527907	+	0.849302i	$0.322977\pi$
$6$	−0.0370646	−	0.00291705i	−0.00617743	−	0.000486175i
$7$	6.06168	+	9.89176i	0.865954	+	1.41311i	0.910236	+	0.414090i	$0.135900\pi$
$7$	6.06168	+	9.89176i	0.865954	+	1.41311i	−0.0442815	+	0.999019i	$0.514100\pi$
$8$	−0.359280	−	0.0569044i	−0.0449101	−	0.00711305i
$9$	3.78254	+	7.42366i	0.420283	+	0.824851i
$10$	0.0630940	+	0.0261344i	0.00630940	+	0.00261344i
$11$	5.26541	−	9.65792i	0.478674	−	0.877993i
$11$	5.26541	−	9.65792i	0.478674	−	0.877993i
$12$	−1.25066	−	3.01936i	−0.104222	−	0.251613i
$13$	2.00739	−	6.17812i	0.154415	−	0.475240i	−0.843686	−	0.536837i	$-0.819619\pi$
$13$	2.00739	−	6.17812i	0.154415	−	0.475240i	0.998101	+	0.0615964i	$0.0196192\pi$
$14$	0.275695	−	0.449894i	0.0196925	−	0.0321353i
$15$	0.192014	+	1.21233i	0.0128010	+	0.0808220i
$16$	−4.93660	−	15.1933i	−0.308538	−	0.949581i
$17$	14.1913	−	9.35983i	0.834783	−	0.550578i
$17$	14.1913	−	9.35983i	0.834783	−	0.550578i
$18$	0.222737	−	0.306571i	0.0123743	−	0.0170317i
$19$	2.39622	−	15.1291i	0.126117	−	0.796271i	−0.840831	−	0.541297i	$-0.817933\pi$
$19$	2.39622	−	15.1291i	0.126117	−	0.796271i	0.966948	−	0.254973i	$-0.0820667\pi$
$20$	0.470994	+	5.98455i	0.0235497	+	0.299227i
$21$	9.48358			0.451599
$22$	−0.500103	−	0.0139588i	−0.0227320	−	0.000634493i
$23$	−11.3595	−	4.70526i	−0.493891	−	0.204576i	0.121814	−	0.992553i	$-0.461129\pi$
$23$	−11.3595	−	4.70526i	−0.493891	−	0.204576i	−0.615705	+	0.787976i	$0.711129\pi$
$24$	−0.193118	+	0.226112i	−0.00804658	+	0.00942133i
$25$	−3.55816	+	22.4653i	−0.142326	+	0.898614i
$26$	−0.291814	+	0.0462188i	−0.0112236	+	0.00177765i
$27$	14.1243	+	1.11160i	0.523121	+	0.0411705i
$28$	46.2384	+	3.63904i	1.65137	+	0.129966i
$29$	−34.4313	−	8.26623i	−1.18729	−	0.285043i	−0.408754	−	0.912645i	$-0.634036\pi$
$29$	−34.4313	−	8.26623i	−1.18729	−	0.285043i	−0.778534	+	0.627602i	$0.784036\pi$
$30$	0.0451642	−	0.0328137i	0.00150547	−	0.00109379i
$31$	3.88274	+	49.3348i	0.125250	+	1.59145i	0.663182	+	0.748458i	$0.269206\pi$
$31$	3.88274	+	49.3348i	0.125250	+	1.59145i	−0.537932	+	0.842988i	$0.680794\pi$
$32$	−1.54263	+	1.54263i	−0.0482073	+	0.0482073i
$33$	−4.48257	−	7.79506i	−0.135835	−	0.236214i
$34$	−0.672327	−	0.381831i	−0.0197743	−	0.0112303i
$35$	−16.5673	−	5.38303i	−0.473351	−	0.153801i
$36$	32.8997	+	5.21081i	0.913881	+	0.144745i
$37$	31.9119	+	7.66137i	0.862483	+	0.207064i	0.640473	−	0.767980i	$-0.278738\pi$
$37$	31.9119	+	7.66137i	0.862483	+	0.207064i	0.222010	+	0.975044i	$0.428738\pi$
$38$	−0.662578	+	0.215285i	−0.0174363	+	0.00566538i
$39$	−3.44873	−	4.03794i	−0.0884289	−	0.103537i
$40$	0.465711	−	0.285388i	0.0116428	−	0.00713470i
$41$	−16.0712	+	3.85835i	−0.391980	+	0.0941061i	−0.424644	−	0.905360i	$-0.639601\pi$
$41$	−16.0712	+	3.85835i	−0.391980	+	0.0941061i	0.0326643	+	0.999466i	$0.489601\pi$
$42$	−0.195819	−	0.384317i	−0.00466236	−	0.00915040i
$43$	−23.9713	−	23.9713i	−0.557472	−	0.557472i	0.371115	−	0.928587i	$-0.378976\pi$
$43$	−23.9713	−	23.9713i	−0.557472	−	0.557472i	−0.928587	+	0.371115i	$0.878976\pi$
$44$	−18.8642	−	39.7258i	−0.428732	−	0.902859i
$45$	−11.5582	−	4.78755i	−0.256848	−	0.106390i
$46$	0.0438756	+	0.557492i	0.000953817	+	0.0121194i
$47$	−7.12664	−	9.80897i	−0.151631	−	0.208702i	0.726444	−	0.687226i	$-0.241172\pi$
$47$	−7.12664	−	9.80897i	−0.151631	−	0.208702i	−0.878074	+	0.478524i	$0.841172\pi$
$48$	−12.6982	−	3.04856i	−0.264545	−	0.0635118i
$49$	−38.8575	+	76.2621i	−0.793010	+	1.55637i
$50$	0.983865	−	0.319677i	0.0196773	−	0.00639354i
$51$	−0.462373	−	13.8891i	−0.00906614	−	0.272334i
$52$	−15.2653	−	21.0108i	−0.293563	−	0.404054i
$53$	29.5974	−	15.0806i	0.558442	−	0.284540i	−0.151901	−	0.988396i	$-0.548540\pi$
$53$	29.5974	−	15.0806i	0.558442	−	0.284540i	0.710343	+	0.703855i	$0.248540\pi$
$54$	−0.246594	−	0.595331i	−0.00456656	−	0.0110246i
$55$	3.40619	+	16.1619i	0.0619308	+	0.293853i
$56$	−1.61496	−	3.89885i	−0.0288385	−	0.0696224i
$57$	−9.52148	−	8.13211i	−0.167043	−	0.142669i
$58$	0.375962	+	1.56599i	0.00648210	+	0.0269999i
$59$	−46.7219	+	7.40001i	−0.791896	+	0.125424i	−0.539262	−	0.842138i	$-0.681297\pi$
$59$	−46.7219	+	7.40001i	−0.791896	+	0.125424i	−0.252634	+	0.967562i	$0.581297\pi$
$60$	4.37237	+	2.22784i	0.0728729	+	0.0371306i
$61$	−3.20895	+	40.7736i	−0.0526057	+	0.668419i	0.912925	+	0.408128i	$0.133818\pi$
$61$	−3.20895	+	40.7736i	−0.0526057	+	0.668419i	−0.965530	+	0.260291i	$0.916182\pi$
$62$	1.91909	−	1.17602i	0.0309531	−	0.0189681i
$63$	−50.5045	+	82.4159i	−0.801659	+	1.30819i
$64$	−60.6788	−	19.7157i	−0.948107	−	0.308059i
$65$	3.73273	+	9.01161i	0.0574266	+	0.138640i
$66$	−0.223333	+	0.342608i	−0.00338383	+	0.00519102i
$67$	−52.4148			−0.782310			−0.391155	−	0.920325i	$-0.627924\pi$
$67$	−52.4148			−0.782310			−0.391155	+	0.920325i	$0.627924\pi$
$68$	3.07515	−	67.8952i	0.0452228	−	0.998459i
$69$	−8.13141	+	5.90781i	−0.117846	+	0.0856205i
$70$	0.123940	+	0.782529i	0.00177058	+	0.0111790i
$71$	9.72067	+	11.3814i	0.136911	+	0.160302i	0.824625	−	0.565679i	$-0.191386\pi$
$71$	9.72067	+	11.3814i	0.136911	+	0.160302i	−0.687715	+	0.725981i	$0.741386\pi$
$72$	−0.936555	−	2.88242i	−0.0130077	−	0.0400336i
$73$	−80.1304	−	19.2376i	−1.09768	−	0.263529i	−0.356134	−	0.934435i	$-0.615905\pi$
$73$	−80.1304	−	19.2376i	−1.09768	−	0.263529i	−0.741542	+	0.670906i	$0.765905\pi$
$74$	−0.348451	−	1.45140i	−0.00470880	−	0.0196136i
$75$	14.1385	+	12.0754i	0.188513	+	0.161005i
$76$	−43.3027	−	43.3027i	−0.569772	−	0.569772i
$77$	127.451	−	6.45903i	1.65521	−	0.0838835i
$78$	−0.0924251	+	0.223134i	−0.00118494	+	0.00286069i
$79$	62.8671	+	53.6936i	0.795786	+	0.679665i	0.951334	−	0.308163i	$-0.0997142\pi$
$79$	62.8671	+	53.6936i	0.795786	+	0.679665i	−0.155548	+	0.987828i	$0.549714\pi$
$80$	20.4526	+	12.5334i	0.255657	+	0.156667i
$81$	−37.2681	+	51.2951i	−0.460100	+	0.633273i
$82$	0.488199	+	0.571607i	0.00595364	+	0.00697082i
$83$	−33.0768	−	16.8535i	−0.398515	−	0.203054i	0.243235	−	0.969967i	$-0.421791\pi$
$83$	−33.0768	−	16.8535i	−0.398515	−	0.203054i	−0.641750	+	0.766914i	$0.721791\pi$
$84$	22.2857	−	30.6736i	0.265306	−	0.365162i
$85$	−7.07591	+	24.5258i	−0.0832460	+	0.288539i
$86$	−0.476458	+	1.46639i	−0.00554021	+	0.0170510i
$87$	−20.4678	+	20.4678i	−0.235262	+	0.235262i
$88$	−2.44134	+	3.17028i	−0.0277425	+	0.0360259i
$89$		−	62.3451i		−	0.700506i	−0.936655	−	0.350253i	$-0.886096\pi$
$89$		−	62.3451i		−	0.700506i	0.936655	−	0.350253i	$-0.113904\pi$
$90$	0.0446430	+	0.567243i	0.000496033	+	0.00630270i
$91$	73.2807	−	17.5931i	0.805282	−	0.193331i
$92$	−41.9126	+	25.6841i	−0.455572	+	0.279175i
$93$	36.0446	+	18.3656i	0.387576	+	0.197480i
$94$	−0.250351	+	0.491341i	−0.00266330	+	0.00522703i
$95$	12.0176	+	19.6109i	0.126501	+	0.206430i
$96$	0.416320	+	1.73410i	0.00433667	+	0.0180635i
$97$	154.977	−	12.1970i	1.59770	−	0.125742i	0.751914	−	0.659262i	$-0.229131\pi$
$97$	154.977	−	12.1970i	1.59770	−	0.125742i	0.845788	+	0.533520i	$0.179131\pi$
$98$	3.89282			0.0397226
$99$	91.6137	+	2.55712i	0.925391	+	0.0258294i
$100$	64.3004	+	64.3004i	0.643004	+	0.643004i
$101$	−145.922	−	47.4131i	−1.44478	−	0.469437i	−0.521394	−	0.853316i	$-0.674588\pi$
$101$	−145.922	−	47.4131i	−1.44478	−	0.469437i	−0.923383	+	0.383880i	$0.874588\pi$
$102$	−0.553299	+	0.305522i	−0.00542450	+	0.00299531i
$103$	−25.8101	−	18.7521i	−0.250583	−	0.182059i	0.455402	−	0.890286i	$-0.349496\pi$
$103$	−25.8101	−	18.7521i	−0.250583	−	0.182059i	−0.705985	+	0.708227i	$0.749496\pi$
$104$	−1.07278	+	2.10545i	−0.0103152	+	0.0202447i
$105$	−10.8282	+	9.24812i	−0.103125	+	0.0880773i
$106$	−1.22227	−	0.888030i	−0.0115308	−	0.00837764i
$107$	31.6896	−	51.7128i	0.296165	−	0.483297i	−0.669598	−	0.742724i	$-0.733534\pi$
$107$	31.6896	−	51.7128i	0.296165	−	0.483297i	0.965763	+	0.259427i	$0.0835336\pi$
$108$	36.7864	−	43.0713i	0.340614	−	0.398808i
$109$	−94.3023	−	39.0613i	−0.865158	−	0.358360i	−0.0944357	−	0.995531i	$-0.530105\pi$
$109$	−94.3023	−	39.0613i	−0.865158	−	0.358360i	−0.770723	+	0.637171i	$0.780105\pi$
$110$	0.584620	−	0.471749i	0.00531473	−	0.00428862i
$111$	18.9701	−	18.9701i	0.170902	−	0.170902i
$112$	120.364	−	140.929i	1.07468	−	1.25829i
$113$	−187.095	+	44.9176i	−1.65571	+	0.397501i	−0.950310	−	0.311306i	$-0.899234\pi$
$113$	−187.095	+	44.9176i	−1.65571	+	0.397501i	−0.705402	+	0.708807i	$0.749234\pi$
$114$	−0.132947	+	0.553766i	−0.00116621	+	0.00485760i
$115$	17.5585	−	5.70510i	0.152682	−	0.0496095i
$116$	−107.647	+	91.9395i	−0.927994	+	0.792582i
$117$	53.4573	−	8.46681i	0.456900	−	0.0723659i
$118$	1.26460	+	1.74058i	0.0107170	+	0.0147507i
$119$	178.609	+	83.6409i	1.50091	+	0.702864i
$120$		−	0.446493i		−	0.00372078i
$121$	−65.5509	−	101.706i	−0.541743	−	0.840544i
$122$	1.71858	−	0.711861i	0.0140868	−	0.00583493i
$123$	−4.17506	+	12.8495i	−0.0339436	+	0.104468i
$124$	168.692	+	103.375i	1.36042	+	0.833668i
$125$	−37.4587	−	61.1271i	−0.299670	−	0.489017i
$126$	4.38268	+	0.344925i	0.0347832	+	0.00273750i
$127$	−61.9844	+	121.651i	−0.488066	+	0.957883i	0.507304	+	0.861767i	$0.330642\pi$
$127$	−61.9844	+	121.651i	−0.488066	+	0.957883i	−0.995370	+	0.0961160i	$0.969358\pi$
$128$	1.81906	+	11.4851i	0.0142114	+	0.0897272i
$129$	−26.9465	+	6.46928i	−0.208888	+	0.0501495i
$130$	0.288116	−	0.337340i	0.00221628	−	0.00259493i
$131$	122.144	−	50.5939i	0.932400	−	0.386213i	0.135812	−	0.990735i	$-0.456636\pi$
$131$	122.144	−	50.5939i	0.932400	−	0.386213i	0.796589	+	0.604522i	$0.206636\pi$
$132$	−35.7460	−	3.81940i	−0.270803	−	0.0289348i
$133$	164.179	−	68.0052i	1.23443	−	0.511317i
$134$	1.08227	+	2.12408i	0.00807666	+	0.0158513i
$135$	−17.2108	+	12.5044i	−0.127488	+	0.0926251i
$136$	−5.63128	+	2.55526i	−0.0414065	+	0.0187886i
$137$	−25.6455	−	78.9288i	−0.187194	−	0.576123i	0.812786	−	0.582563i	$-0.197950\pi$
$137$	−25.6455	−	78.9288i	−0.187194	−	0.576123i	−0.999979	+	0.00644010i	$0.997950\pi$
$138$	0.407310	+	0.207535i	0.00295152	+	0.00150388i
$139$	15.9188	−	66.3067i	0.114524	−	0.477027i	−0.885402	−	0.464827i	$-0.846117\pi$
$139$	15.9188	−	66.3067i	0.114524	−	0.477027i	0.999926	−	0.0121998i	$-0.00388343\pi$
$140$	−56.3427	+	40.9354i	−0.402448	+	0.292396i
$141$	−9.88074	+	0.777631i	−0.0700761	+	0.00551511i
$142$	0.260512	−	0.628931i	0.00183459	−	0.00442909i
$143$	−49.0981	−	51.9176i	−0.343343	−	0.363060i
$144$	94.1170	−	94.1170i	0.653590	−	0.653590i
$145$	47.3740	−	24.1383i	0.326717	−	0.166471i
$146$	0.874958	+	3.64446i	0.00599286	+	0.0249621i
$147$	36.5576	+	59.6565i	0.248691	+	0.405827i
$148$	99.7704	−	85.2120i	0.674124	−	0.575757i
$149$	9.33605	+	28.7334i	0.0626580	+	0.192842i	0.977485	−	0.211004i	$-0.0676733\pi$
$149$	9.33605	+	28.7334i	0.0626580	+	0.192842i	−0.914827	+	0.403846i	$0.867673\pi$
$150$	0.197414	−	0.822290i	0.00131610	−	0.00548193i
$151$	−18.0181	+	113.762i	−0.119325	+	0.753388i	0.853371	+	0.521304i	$0.174554\pi$
$151$	−18.0181	+	113.762i	−0.119325	+	0.753388i	−0.972696	+	0.232084i	$0.925446\pi$
$152$	−1.72183	+	5.29925i	−0.0113278	+	0.0348635i
$153$	123.163	+	69.9475i	0.804990	+	0.457173i
$154$	−2.89339	−	5.03152i	−0.0187882	−	0.0326722i
$155$	−52.5432	−	52.5432i	−0.338988	−	0.338988i
$156$	−21.1645	+	1.66569i	−0.135670	+	0.0106775i
$157$	−58.2325	−	80.1502i	−0.370908	−	0.510511i	0.582240	−	0.813017i	$-0.302177\pi$
$157$	−58.2325	−	80.1502i	−0.370908	−	0.510511i	−0.953147	+	0.302507i	$0.902177\pi$
$158$	0.877807	−	3.65633i	0.00555574	−	0.0231413i
$159$	2.13050	−	27.0705i	0.0133993	−	0.170255i
$160$	0.257015	−	3.26568i	0.00160634	−	0.0204105i
$161$	−22.3143	−	140.887i	−0.138598	−	0.875076i
$162$	2.84822	+	0.451114i	0.0175816	+	0.00278466i
$163$	176.951	+	151.130i	1.08559	+	0.927180i	0.997621	−	0.0689434i	$-0.0219628\pi$
$163$	176.951	+	151.130i	1.08559	+	0.927180i	0.0879677	+	0.996123i	$0.471963\pi$
$164$	−25.2866	+	61.0474i	−0.154187	+	0.372240i
$165$	12.7196	+	4.52896i	0.0770886	+	0.0274482i
$166$			1.68841i			0.0101712i
$167$	248.397	−	19.5492i	1.48741	−	0.117061i	0.691454	−	0.722421i	$-0.256971\pi$
$167$	248.397	−	19.5492i	1.48741	−	0.117061i	0.795952	+	0.605360i	$0.206971\pi$
$168$	−3.40726	−	0.539658i	−0.0202813	−	0.00321225i
$169$	102.584	+	74.5319i	0.607008	+	0.441017i
$170$	1.14000	−	0.219668i	0.00670589	−	0.00129216i
$171$	121.377	−	39.4379i	0.709809	−	0.230631i
$172$	−133.863	+	21.2019i	−0.778275	+	0.123267i
$173$	−183.867	−	112.674i	−1.06282	−	0.651295i	−0.122803	−	0.992431i	$-0.539188\pi$
$173$	−183.867	−	112.674i	−1.06282	−	0.651295i	−0.940014	+	0.341136i	$0.889188\pi$
$174$	1.25207	+	0.406823i	0.00719581	+	0.00233806i
$175$	−243.790	+	100.981i	−1.39309	+	0.577036i
$176$	−172.729	−	32.3217i	−0.981414	−	0.183646i
$177$	−14.7980	+	35.7256i	−0.0836047	+	0.201840i
$178$	−2.52650	+	1.28732i	−0.0141938	+	0.00723211i
$179$	−38.6516	+	244.037i	−0.215931	+	1.36333i	0.606779	+	0.794871i	$0.292461\pi$
$179$	−38.6516	+	244.037i	−0.215931	+	1.36333i	−0.822709	+	0.568462i	$0.807539\pi$
$180$	−42.6457	+	26.1333i	−0.236920	+	0.145185i
$181$	5.35258	−	68.0110i	0.0295723	−	0.375751i	−0.964268	−	0.264929i	$-0.914652\pi$
$181$	5.35258	−	68.0110i	0.0295723	−	0.375751i	0.993840	−	0.110822i	$-0.0353485\pi$
$182$	−2.22607	−	2.60639i	−0.0122311	−	0.0143208i
$183$	27.0484	+	19.6518i	0.147805	+	0.107387i
$184$	3.81350	+	2.33691i	0.0207255	+	0.0127006i
$185$	−43.9075	+	22.3720i	−0.237338	+	0.120930i
$186$		−	1.83990i		−	0.00989195i
$187$	−15.6734	−	186.342i	−0.0838149	−	0.996481i
$188$	−48.4731			−0.257836
$189$	74.6211	+	146.452i	0.394821	+	0.774879i
$190$	0.546578	−	0.891935i	0.00287673	−	0.00469439i
$191$	−179.252	+	246.719i	−0.938492	+	1.29172i	0.0179612	+	0.999839i	$0.494282\pi$
$191$	−179.252	+	246.719i	−0.938492	+	1.29172i	−0.956453	+	0.291885i	$0.905718\pi$
$192$	−39.6589	+	33.8719i	−0.206557	+	0.176416i
$193$	19.7247	+	1.55236i	0.102200	+	0.00804334i	0.129456	−	0.991585i	$-0.458677\pi$
$193$	19.7247	+	1.55236i	0.102200	+	0.00804334i	−0.0272558	+	0.999628i	$0.508677\pi$
$194$	−3.69428	−	6.02851i	−0.0190427	−	0.0310748i
$195$	7.87537	+	1.24734i	0.0403865	+	0.00639660i
$196$	155.350	+	304.891i	0.792600	+	1.55556i
$197$	−75.0893	−	31.1030i	−0.381164	−	0.157883i	0.183871	−	0.982950i	$-0.441137\pi$
$197$	−75.0893	−	31.1030i	−0.381164	−	0.157883i	−0.565035	+	0.825067i	$0.691137\pi$
$198$	−1.78804	−	3.76539i	−0.00903048	−	0.0190171i
$199$	−60.0029	−	144.860i	−0.301522	−	0.727939i	−0.999925	−	0.0122340i	$-0.996106\pi$
$199$	−60.0029	−	144.860i	−0.301522	−	0.727939i	0.698403	−	0.715705i	$-0.253894\pi$
$200$	2.55676	−	7.86888i	0.0127838	−	0.0393444i
$201$	−22.3874	+	36.5329i	−0.111380	+	0.181756i
$202$	1.09165	+	6.89242i	0.00540422	+	0.0341209i
$203$	−126.944	−	390.694i	−0.625341	−	1.92460i
$204$	−46.0092	−	31.1427i	−0.225535	−	0.152661i
$205$	14.5872	−	20.0775i	0.0711570	−	0.0979392i
$206$	−0.226987	+	1.43314i	−0.00110188	+	0.00695697i
$207$	−8.03756	−	102.127i	−0.0388288	−	0.493367i
$208$	−103.776			−0.498922
$209$	−133.499	−	102.804i	−0.638751	−	0.491884i
$210$	0.598357	+	0.247848i	0.00284932	+	0.00118023i
$211$	127.497	−	149.280i	0.604250	−	0.707486i	−0.370989	−	0.928637i	$-0.620981\pi$
$211$	127.497	−	149.280i	0.604250	−	0.707486i	0.975240	+	0.221151i	$0.0709813\pi$
$212$	20.7750	−	131.168i	0.0979952	−	0.618718i
$213$	12.0847	−	1.91403i	0.0567357	−	0.00898605i
$214$	−2.74997	−	0.216427i	−0.0128503	−	0.00101134i
$215$	50.7461	+	3.99380i	0.236028	+	0.0185758i
$216$	−5.01132	−	1.20311i	−0.0232006	−	0.00556996i
$217$	−464.473	+	337.459i	−2.14043	+	1.55511i
$218$	0.364239	+	4.62809i	0.00167082	+	0.0212298i
$219$	−47.6338	+	47.6338i	−0.217506	+	0.217506i
$220$	60.2783	+	26.9623i	0.273992	+	0.122556i
$221$	−29.3386	−	106.465i	−0.132754	−	0.481740i
$222$	−1.16045	−	0.377054i	−0.00522727	−	0.00169844i
$223$	110.748	+	17.5408i	0.496628	+	0.0786582i	0.399724	−	0.916636i	$-0.369106\pi$
$223$	110.748	+	17.5408i	0.496628	+	0.0786582i	0.0969041	+	0.995294i	$0.469106\pi$
$224$	−24.6103	−	5.90841i	−0.109867	−	0.0263768i
$225$	−180.234	+	58.5616i	−0.801040	+	0.260274i
$226$	5.68345	+	6.65447i	0.0251480	+	0.0294445i
$227$	−55.8697	+	34.2370i	−0.246122	+	0.150824i	−0.640089	−	0.768301i	$-0.721102\pi$
$227$	−55.8697	+	34.2370i	−0.246122	+	0.150824i	0.393967	+	0.919125i	$0.371102\pi$
$228$	−48.6772	+	11.6864i	−0.213496	+	0.0512560i
$229$	64.0286	+	125.663i	0.279601	+	0.548748i	0.987510	−	0.157556i	$-0.0503614\pi$
$229$	64.0286	+	125.663i	0.279601	+	0.548748i	−0.707909	+	0.706304i	$0.750361\pi$
$230$	−0.593747	−	0.593747i	−0.00258151	−	0.00258151i
$231$	49.9349	−	91.5917i	0.216169	−	0.396501i
$232$	11.9001	+	4.92919i	0.0512936	+	0.0212465i
$233$	−25.0374	−	318.130i	−0.107457	−	1.36537i	−0.780219	−	0.625507i	$-0.784892\pi$
$233$	−25.0374	−	318.130i	−0.107457	−	1.36537i	0.672762	−	0.739859i	$-0.265108\pi$
$234$	−1.44691	−	1.99150i	−0.00618338	−	0.00851069i
$235$	17.7025	+	4.24999i	0.0753297	+	0.0180851i
$236$	−85.8583	+	168.506i	−0.363806	+	0.714010i
$237$	64.2759	−	20.8845i	0.271207	−	0.0881203i
$238$	−0.298450	−	8.96504i	−0.00125399	−	0.0376682i
$239$	118.683	+	163.352i	0.496580	+	0.683483i	0.981585	−	0.191028i	$-0.0611822\pi$
$239$	118.683	+	163.352i	0.496580	+	0.683483i	−0.485005	+	0.874511i	$0.661182\pi$
$240$	17.4714	−	8.90212i	0.0727975	−	0.0370922i
$241$	−96.9723	−	234.112i	−0.402374	−	0.971418i	−0.987088	−	0.160178i	$-0.948793\pi$
$241$	−96.9723	−	234.112i	−0.402374	−	0.971418i	0.584714	−	0.811240i	$-0.301207\pi$
$242$	−2.76806	+	4.75646i	−0.0114383	+	0.0196548i
$243$	68.6311	+	165.690i	0.282433	+	0.681852i
$244$	124.337	+	106.194i	0.509578	+	0.435221i
$245$	−30.0020	−	124.967i	−0.122457	−	0.510070i
$246$	0.606927	−	0.0961278i	0.00246718	−	0.000390763i
$247$	−88.6595	−	45.1743i	−0.358946	−	0.182892i
$248$	1.41238	−	17.9460i	0.00569508	−	0.0723628i
$249$	−25.8745	+	15.8559i	−0.103914	+	0.0636784i
$250$	−1.70368	+	2.78016i	−0.00681474	+	0.0111206i
$251$	22.1944	+	7.21140i	0.0884239	+	0.0287307i	0.352895	−	0.935663i	$-0.385197\pi$
$251$	22.1944	+	7.21140i	0.0884239	+	0.0287307i	−0.264471	+	0.964394i	$0.585197\pi$
$252$	147.884	+	357.023i	0.586840	+	1.41676i
$253$	−105.255	+	84.9340i	−0.416029	+	0.335708i
$254$	6.20971			0.0244477
$255$	14.0721	+	15.4073i	0.0551849	+	0.0604210i
$256$	−206.038	+	149.695i	−0.804836	+	0.584748i
$257$	−12.4553	−	78.6397i	−0.0484642	−	0.305991i	0.951535	−	0.307542i	$-0.0995064\pi$
$257$	−12.4553	−	78.6397i	−0.0484642	−	0.305991i	−0.999999	+	0.00155067i	$0.999506\pi$
$258$	0.818561	+	0.958412i	0.00317272	+	0.00371477i
$259$	117.655	+	362.106i	0.454267	+	1.39809i
$260$	37.9187	+	9.10348i	0.145841	+	0.0350134i
$261$	−68.8723	−	286.874i	−0.263879	−	1.09913i
$262$	−4.57235	−	3.90516i	−0.0174517	−	0.0149052i
$263$	208.830	+	208.830i	0.794030	+	0.794030i	0.982147	−	0.188116i	$-0.0602382\pi$
$263$	208.830	+	208.830i	0.794030	+	0.794030i	−0.188116	+	0.982147i	$0.560238\pi$
$264$	1.16693	+	3.05569i	0.00442018	+	0.0115746i
$265$	−19.0875	+	46.0814i	−0.0720284	+	0.173892i
$266$	−6.14588	−	5.24908i	−0.0231048	−	0.0197334i
$267$	−43.4542	−	26.6288i	−0.162750	−	0.0997333i
$268$	−123.171	+	169.530i	−0.459592	+	0.632575i
$269$	343.152	+	401.779i	1.27566	+	1.49360i	0.781023	+	0.624503i	$0.214698\pi$
$269$	343.152	+	401.779i	1.27566	+	1.49360i	0.494635	+	0.869101i	$0.335302\pi$
$270$	0.862106	+	0.439265i	0.00319299	+	0.00162691i
$271$	158.735	−	218.480i	0.585739	−	0.806200i	−0.408571	−	0.912727i	$-0.633973\pi$
$271$	158.735	−	218.480i	0.585739	−	0.806200i	0.994310	+	0.106526i	$0.0339728\pi$
$272$	−212.264	−	169.407i	−0.780381	−	0.622821i
$273$	19.0373	−	58.5907i	0.0697336	−	0.214618i
$274$	−2.66901	+	2.66901i	−0.00974091	+	0.00974091i
$275$	198.233	+	152.654i	0.720849	+	0.555104i
$276$			40.1831i			0.145591i
$277$	−15.0077	−	190.690i	−0.0541793	−	0.688413i	−0.962700	−	0.270572i	$-0.912787\pi$
$277$	−15.0077	−	190.690i	−0.0541793	−	0.688413i	0.908520	−	0.417841i	$-0.137213\pi$
$278$	−3.01574	+	0.724014i	−0.0108480	+	0.00260437i
$279$	−351.558	+	215.435i	−1.26007	+	0.772169i
$280$	5.64598	+	2.87677i	0.0201642	+	0.0102742i
$281$	222.069	−	435.835i	0.790280	−	1.55101i	−0.0435880	−	0.999050i	$-0.513879\pi$
$281$	222.069	−	435.835i	0.790280	−	1.55101i	0.833868	−	0.551963i	$-0.186121\pi$
$282$	0.235533	+	0.384354i	0.000835222	+	0.00136296i
$283$	17.9630	+	74.8212i	0.0634734	+	0.264386i	0.995079	−	0.0990851i	$-0.0315916\pi$
$283$	17.9630	+	74.8212i	0.0634734	+	0.264386i	−0.931606	+	0.363471i	$0.881592\pi$
$284$	59.6549	−	4.69494i	0.210052	−	0.0165315i
$285$	18.8016			0.0659706
$286$	−1.09014	+	3.06168i	−0.00381169	+	0.0107052i
$287$	−135.584	−	135.584i	−0.472419	−	0.472419i
$288$	−17.2871	−	5.61691i	−0.0600245	−	0.0195031i
$289$	113.787	−	265.657i	0.393727	−	0.919227i
$290$	−1.95638	−	1.42139i	−0.00674613	−	0.00490135i
$291$	57.6925	−	113.228i	0.198256	−	0.389099i
$292$	−250.522	+	213.966i	−0.857953	+	0.732761i
$293$	−321.475	−	233.565i	−1.09718	−	0.797152i	−0.116587	−	0.993180i	$-0.537195\pi$
$293$	−321.475	−	233.565i	−1.09718	−	0.797152i	−0.980598	+	0.196029i	$0.937195\pi$
$294$	1.66270	−	2.71328i	0.00565544	−	0.00922883i
$295$	46.1298	−	54.0110i	0.156372	−	0.183088i
$296$	−11.0293	−	4.56851i	−0.0372613	−	0.0154341i
$297$	85.1059	−	130.558i	0.286552	−	0.439590i
$298$	0.971632	−	0.971632i	0.00326051	−	0.00326051i
$299$	−51.8726	+	60.7351i	−0.173487	+	0.203127i
$300$	72.2810	−	17.3531i	0.240937	−	0.0578438i
$301$	91.8120	−	382.425i	0.305023	−	1.27051i
$302$	4.98216	−	1.61880i	0.0164972	−	0.00536028i
$303$	−95.3731	+	81.4563i	−0.314763	+	0.268833i
$304$	−241.691	+	38.2801i	−0.795036	+	0.125921i
$305$	−36.0973	−	49.6837i	−0.118352	−	0.162897i
$306$	0.291477	−	6.43542i	0.000952539	−	0.0210308i
$307$		−	530.430i		−	1.72778i	−0.503677	−	0.863892i	$-0.668020\pi$
$307$		−	530.430i		−	1.72778i	0.503677	−	0.863892i	$-0.331980\pi$
$308$	278.610	−	427.405i	0.904576	−	1.38768i
$309$	−24.0941	+	9.98012i	−0.0779745	+	0.0322981i
$310$	−1.04436	+	3.21420i	−0.00336890	+	0.0103684i
$311$	462.141	+	283.201i	1.48599	+	0.910613i	0.999314	+	0.0370274i	$0.0117889\pi$
$311$	462.141	+	283.201i	1.48599	+	0.910613i	0.486671	+	0.873585i	$0.338211\pi$
$312$	1.00928	+	1.64700i	0.00323488	+	0.00527885i
$313$	545.069	+	42.8979i	1.74143	+	0.137054i	0.908926	−	0.416958i	$-0.136904\pi$
$313$	545.069	+	42.8979i	1.74143	+	0.137054i	0.832509	+	0.554012i	$0.186904\pi$
$314$	−2.04564	+	4.01480i	−0.00651478	+	0.0127860i
$315$	−22.7046	−	143.351i	−0.0720782	−	0.455084i
$316$	321.399	−	77.1611i	1.01709	−	0.244181i
$317$	58.8821	−	68.9420i	0.185748	−	0.217483i	−0.659717	−	0.751514i	$-0.729324\pi$
$317$	58.8821	−	68.9420i	0.185748	−	0.217483i	0.845464	+	0.534032i	$0.179324\pi$
$318$	−1.14101	+	0.472621i	−0.00358808	+	0.00148623i
$319$	−261.130	+	289.010i	−0.818589	+	0.905988i
$320$	88.5081	−	36.6613i	0.276588	−	0.114566i
$321$	−22.5083	−	44.1751i	−0.0701194	−	0.137617i
$322$	−5.24862	+	3.81335i	−0.0163001	+	0.0118427i
$323$	−107.601	−	237.131i	−0.333129	−	0.734151i
$324$	78.3314	+	241.079i	0.241764	+	0.744072i
$325$	131.651	+	67.0795i	0.405080	+	0.206399i
$326$	2.47075	−	10.2914i	0.00757898	−	0.0315687i
$327$	−67.5039	+	49.0444i	−0.206434	+	0.149983i
$328$	5.99362	−	0.471708i	0.0182732	−	0.00143813i
$329$	53.8287	−	129.954i	0.163613	−	0.394997i
$330$	−0.0791042	−	0.608971i	−0.000239710	−	0.00184537i
$331$	−119.780	+	119.780i	−0.361872	+	0.361872i	−0.864502	−	0.502630i	$-0.832366\pi$
$331$	−119.780	+	119.780i	−0.361872	+	0.361872i	0.502630	+	0.864502i	$0.332366\pi$
$332$	−132.239	+	67.3790i	−0.398309	+	0.202949i
$333$	63.8327	+	265.882i	0.191690	+	0.798445i
$334$	−5.92117	−	9.66248i	−0.0177281	−	0.0289296i
$335$	59.8461	−	51.1134i	0.178645	−	0.152577i
$336$	−46.8167	−	144.087i	−0.139335	−	0.428830i
$337$	−121.755	+	507.145i	−0.361290	+	1.50488i	0.435258	+	0.900306i	$0.356657\pi$
$337$	−121.755	+	507.145i	−0.361290	+	1.50488i	−0.796548	+	0.604575i	$0.793343\pi$
$338$	0.902177	−	5.69612i	0.00266916	−	0.0168524i
$339$	−48.6047	+	149.590i	−0.143377	+	0.441268i
$340$	62.6984	+	80.5202i	0.184407	+	0.236824i
$341$	496.916	+	222.269i	1.45723	+	0.651815i
$342$	−4.10443	−	4.10443i	−0.0120012	−	0.0120012i
$343$	−423.196	+	33.3062i	−1.23381	+	0.0971027i
$344$	7.24834	+	9.97649i	0.0210708	+	0.0290014i
$345$	3.52314	−	14.6749i	0.0102120	−	0.0425361i
$346$	−0.769517	+	9.77764i	−0.00222404	+	0.0282591i
$347$	−49.4683	+	628.555i	−0.142560	+	1.81140i	0.345319	+	0.938485i	$0.387771\pi$
$347$	−49.4683	+	628.555i	−0.142560	+	1.81140i	−0.487879	+	0.872911i	$0.662229\pi$
$348$	18.1032	+	114.299i	0.0520206	+	0.328445i
$349$	286.932	+	45.4456i	0.822156	+	0.130217i	0.553319	−	0.832969i	$-0.313361\pi$
$349$	286.932	+	45.4456i	0.822156	+	0.130217i	0.268836	+	0.963186i	$0.413361\pi$
$350$	9.12605	+	7.79438i	0.0260744	+	0.0222697i
$351$	35.2206	−	85.0301i	0.100344	−	0.242251i
$352$	6.77603	+	23.0212i	0.0192501	+	0.0654012i
$353$		−	414.444i		−	1.17406i	−0.809565	−	0.587031i	$-0.800297\pi$
$353$		−	414.444i		−	1.17406i	0.809565	−	0.587031i	$-0.199703\pi$
$354$	1.75331	−	0.137989i	0.00495286	−	0.000389799i
$355$	−22.1977	−	3.51577i	−0.0625288	−	0.00990359i
$356$	−201.649	−	146.506i	−0.566428	−	0.411534i
$357$	134.584	−	88.7647i	0.376987	−	0.248641i
$358$	10.6875	−	3.47259i	0.0298534	−	0.00969997i
$359$	333.382	−	52.8025i	0.928640	−	0.147082i	0.326249	−	0.945284i	$-0.394215\pi$
$359$	333.382	−	52.8025i	0.928640	−	0.147082i	0.602390	+	0.798202i	$0.294215\pi$
$360$	3.88019	+	2.37779i	0.0107783	+	0.00660496i
$361$	120.182	+	39.0496i	0.332915	+	0.108171i
$362$	−2.86663	+	1.18740i	−0.00791886	+	0.00328010i
$363$	−98.8866	+	2.24813i	−0.272415	+	0.00619319i
$364$	115.301	−	278.361i	0.316761	−	0.764729i
$365$	110.251	−	56.1758i	0.302058	−	0.153906i
$366$	0.237877	−	1.50190i	0.000649937	−	0.00410354i
$367$	474.021	−	290.480i	1.29161	−	0.791500i	0.304650	−	0.952464i	$-0.401460\pi$
$367$	474.021	−	290.480i	1.29161	−	0.791500i	0.986960	+	0.160965i	$0.0514605\pi$
$368$	−15.4111	+	195.816i	−0.0418779	+	0.532109i
$369$	−89.4330	−	104.713i	−0.242366	−	0.283774i
$370$	1.81322	+	1.31738i	0.00490060	+	0.00356050i
$371$	328.584	+	201.357i	0.885672	+	0.542741i
$372$	144.104	−	73.4245i	0.387375	−	0.197378i
$373$		−	633.544i		−	1.69851i	−0.527984	−	0.849255i	$-0.677052\pi$
$373$		−	633.544i		−	1.69851i	0.527984	−	0.849255i	$-0.322948\pi$
$374$	−7.22778	+	4.48279i	−0.0193256	+	0.0119861i
$375$	−58.6047			−0.156279
$376$	2.00229	+	3.92971i	0.00532523	+	0.0104514i
$377$	−120.187	+	196.127i	−0.318799	+	0.520232i
$378$	4.39410	−	6.04796i	0.0116246	−	0.0159999i
$379$	−551.701	+	471.197i	−1.45567	+	1.24326i	−0.539803	+	0.841791i	$0.681501\pi$
$379$	−551.701	+	471.197i	−1.45567	+	1.24326i	−0.915871	+	0.401472i	$0.868499\pi$
$380$	91.6697	+	7.21456i	0.241236	+	0.0189857i
$381$	58.3156	+	95.1624i	0.153059	+	0.249770i
$382$	13.6994	+	2.16977i	0.0358623	+	0.00568003i
$383$	−34.3297	−	67.3758i	−0.0896336	−	0.175916i	0.841838	−	0.539731i	$-0.181474\pi$
$383$	−34.3297	−	67.3758i	−0.0896336	−	0.175916i	−0.931471	+	0.363815i	$0.881474\pi$
$384$	8.78201	+	3.63763i	0.0228698	+	0.00947299i
$385$	−139.222	+	131.662i	−0.361617	+	0.341978i
$386$	−0.344371	−	0.831384i	−0.000892152	−	0.00215384i
$387$	87.2822	−	268.627i	0.225535	−	0.694127i
$388$	324.735	−	529.919i	0.836945	−	1.36577i
$389$	118.212	+	746.364i	0.303888	+	1.91867i	0.386895	+	0.922124i	$0.373547\pi$
$389$	118.212	+	746.364i	0.303888	+	1.91867i	−0.0830075	+	0.996549i	$0.526453\pi$
$390$	−0.112065	−	0.344900i	−0.000287346	−	0.000884360i
$391$	−205.247	+	39.5492i	−0.524928	+	0.101149i
$392$	18.3004	−	25.1883i	0.0466847	−	0.0642559i
$393$	16.9066	−	106.744i	0.0430192	−	0.271613i
$394$	0.290029	+	3.68517i	0.000736115	+	0.00935323i
$395$	−124.141			−0.314281
$396$	223.556	−	290.306i	0.564536	−	0.733096i
$397$	349.948	+	144.953i	0.881480	+	0.365121i	0.777071	−	0.629413i	$-0.216705\pi$
$397$	349.948	+	144.953i	0.881480	+	0.365121i	0.104410	+	0.994534i	$0.466705\pi$
$398$	−4.63141	+	5.42268i	−0.0116367	+	0.0136248i
$399$	22.7248	−	143.478i	0.0569543	−	0.359595i
$400$	358.888	−	56.8423i	0.897220	−	0.142106i
$401$	−299.068	−	23.5372i	−0.745806	−	0.0586962i	−0.300139	−	0.953895i	$-0.597033\pi$
$401$	−299.068	−	23.5372i	−0.745806	−	0.0586962i	−0.445666	+	0.895199i	$0.647033\pi$
$402$	1.94273	+	0.152896i	0.00483267	+	0.000380339i
$403$	312.591	+	75.0464i	0.775659	+	0.186219i
$404$	−496.260	+	360.554i	−1.22837	+	0.892460i
$405$	−7.46962	−	94.9105i	−0.0184435	−	0.234347i
$406$	−13.2115	+	13.2115i	−0.0325406	+	0.0325406i
$407$	242.022	−	267.862i	0.594649	−	0.658138i
$408$	−0.624227	+	5.01638i	−0.00152997	+	0.0122950i
$409$	−580.871	−	188.736i	−1.42022	−	0.461458i	−0.504549	−	0.863383i	$-0.668341\pi$
$409$	−580.871	−	188.736i	−1.42022	−	0.461458i	−0.915673	+	0.401925i	$0.868341\pi$
$410$	−1.11483	−	0.176572i	−0.00271910	−	0.000430663i
$411$	−65.9668	−	15.8372i	−0.160503	−	0.0385334i
$412$	−121.303	+	39.4139i	−0.294426	+	0.0956648i
$413$	−356.412	−	417.305i	−0.862984	−	1.01042i
$414$	−3.97267	+	2.43446i	−0.00959582	+	0.00588033i
$415$	54.2014	−	13.0126i	0.130606	−	0.0313557i
$416$	6.43390	+	12.6272i	0.0154661	+	0.0303540i
$417$	−39.4162	−	39.4162i	−0.0945234	−	0.0945234i
$418$	−1.40954	+	7.53268i	−0.00337211	+	0.0180208i
$419$	212.574	+	88.0511i	0.507337	+	0.210146i	0.621644	−	0.783300i	$-0.286465\pi$
$419$	212.574	+	88.0511i	0.507337	+	0.210146i	−0.114307	+	0.993445i	$0.536465\pi$
$420$	4.46671	+	56.7549i	0.0106350	+	0.135131i
$421$	−76.4462	−	105.219i	−0.181582	−	0.249927i	0.708516	−	0.705694i	$-0.249365\pi$
$421$	−76.4462	−	105.219i	−0.181582	−	0.249927i	−0.890099	+	0.455768i	$0.849365\pi$
$422$	−8.68205	−	2.08438i	−0.0205736	−	0.00493928i
$423$	45.8617	−	90.0086i	0.108420	−	0.212786i
$424$	−11.4919	+	3.73396i	−0.0271036	+	0.00880650i
$425$	159.777	+	352.117i	0.375946	+	0.828510i
$426$	−0.327092	−	0.450204i	−0.000767823	−	0.00105682i
$427$	−422.774	+	215.414i	−0.990103	+	0.504483i
$428$	−92.7913	−	224.018i	−0.216802	−	0.523407i
$429$	−57.1571	+	12.0461i	−0.133233	+	0.0280795i
$430$	−0.885970	−	2.13892i	−0.00206039	−	0.00497423i
$431$	−39.2018	−	33.4815i	−0.0909555	−	0.0776833i	0.602808	−	0.797886i	$-0.294049\pi$
$431$	−39.2018	−	33.4815i	−0.0909555	−	0.0776833i	−0.693763	+	0.720203i	$0.744049\pi$
$432$	−52.8370	−	220.082i	−0.122308	−	0.509449i
$433$	−298.380	+	47.2588i	−0.689100	+	0.109143i	−0.491157	−	0.871071i	$-0.663426\pi$
$433$	−298.380	+	47.2588i	−0.689100	+	0.109143i	−0.197943	+	0.980214i	$0.563426\pi$
$434$	23.2659	+	11.8546i	0.0536080	+	0.0273146i
$435$	3.41010	−	43.3294i	0.00783931	−	0.0996078i
$436$	−347.943	+	213.220i	−0.798034	+	0.489036i
$437$	−98.4064	+	160.585i	−0.225186	+	0.367471i
$438$	2.91388	+	0.946778i	0.00665270	+	0.00216159i
$439$	144.203	+	348.136i	0.328480	+	0.793022i	0.998706	+	0.0508639i	$0.0161975\pi$
$439$	144.203	+	348.136i	0.328480	+	0.793022i	−0.670225	+	0.742158i	$0.733803\pi$
$440$	−0.304095	−	6.00048i	−0.000691125	−	0.0136375i
$441$	−713.124			−1.61706
$442$	−3.70863	+	3.38724i	−0.00839055	+	0.00766343i
$443$	−445.097	+	323.382i	−1.00473	+	0.729982i	−0.963098	−	0.269151i	$-0.913257\pi$
$443$	−445.097	+	323.382i	−1.00473	+	0.729982i	−0.0416357	+	0.999133i	$0.513257\pi$
$444$	−16.7785	−	105.935i	−0.0377894	−	0.238593i
$445$	60.7972	+	71.1843i	0.136623	+	0.159965i
$446$	−1.57592	−	4.85019i	−0.00353346	−	0.0108749i
$447$	24.0147	+	5.76541i	0.0537241	+	0.0128980i
$448$	−172.792	−	719.731i	−0.385697	−	1.60654i
$449$	−328.991	−	280.985i	−0.732719	−	0.625801i	0.202741	−	0.979232i	$-0.435015\pi$
$449$	−328.991	−	280.985i	−0.732719	−	0.625801i	−0.935461	+	0.353431i	$0.885015\pi$
$450$	6.09468	+	6.09468i	0.0135437	+	0.0135437i
$451$	−47.3577	+	175.530i	−0.105006	+	0.389202i
$452$	−294.379	+	710.694i	−0.651281	+	1.57233i
$453$	71.5955	+	61.1483i	0.158047	+	0.134985i
$454$	2.54105	+	1.55715i	0.00559702	+	0.00342986i
$455$	−66.5141	+	91.5488i	−0.146185	+	0.201206i
$456$	2.95813	+	3.46352i	0.00648712	+	0.00759544i
$457$	351.575	+	179.136i	0.769311	+	0.391984i	0.794161	−	0.607708i	$-0.207911\pi$
$457$	351.575	+	179.136i	0.769311	+	0.391984i	−0.0248498	+	0.999691i	$0.507911\pi$
$458$	3.77035	−	5.18945i	0.00823221	−	0.0113307i
$459$	210.847	−	116.426i	0.459361	−	0.253651i
$460$	22.8086	−	70.1976i	0.0495839	−	0.152603i
$461$	−558.031	+	558.031i	−1.21048	+	1.21048i	−0.239610	+	0.970869i	$0.577020\pi$
$461$	−558.031	+	558.031i	−1.21048	+	1.21048i	−0.970869	+	0.239610i	$0.922980\pi$
$462$	−4.74277	−	0.132380i	−0.0102657	−	0.000286536i
$463$			105.336i			0.227508i	0.993509	+	0.113754i	$0.0362875\pi$
$463$			105.336i			0.227508i	−0.993509	+	0.113754i	$0.963712\pi$
$464$	44.3825	+	563.933i	0.0956519	+	1.21537i
$465$	−59.0646	+	14.1801i	−0.127021	+	0.0304949i
$466$	−12.3751	+	7.58345i	−0.0265559	+	0.0162735i
$467$	−161.153	−	82.1117i	−0.345082	−	0.175828i	0.272856	−	0.962055i	$-0.412032\pi$
$467$	−161.153	−	82.1117i	−0.345082	−	0.175828i	−0.617938	+	0.786227i	$0.712032\pi$
$468$	98.2357	−	192.798i	0.209905	−	0.411962i
$469$	−317.722	−	518.474i	−0.677445	−	1.10549i
$470$	−0.193296	−	0.805138i	−0.000411269	−	0.00171306i
$471$	−80.7366	+	6.35410i	−0.171415	+	0.0134907i
$472$	17.2073			0.0364562
$473$	−357.732	+	105.294i	−0.756303	+	0.222609i
$474$	−2.17352	−	2.17352i	−0.00458548	−	0.00458548i
$475$	331.355	+	107.664i	0.697590	+	0.226661i
$476$	690.244	−	381.141i	1.45009	−	0.800715i
$477$	223.907	+	162.678i	0.469407	+	0.341044i
$478$	4.16918	−	8.18248i	0.00872214	−	0.0171182i
$479$	583.438	−	498.304i	1.21803	−	1.04030i	0.220138	−	0.975469i	$-0.429349\pi$
$479$	583.438	−	498.304i	1.21803	−	1.04030i	0.997896	−	0.0648309i	$-0.0206508\pi$
$480$	−2.16639	−	1.57397i	−0.00451331	−	0.00327911i
$481$	111.393	−	181.776i	0.231585	−	0.377913i
$482$	−7.48494	+	8.76374i	−0.0155289	+	0.0181820i
$483$	−107.729	−	44.6227i	−0.223041	−	0.0923865i
$484$	−482.997	−	26.9837i	−0.997927	−	0.0557515i
$485$	−165.055	+	165.055i	−0.340321	+	0.340321i
$486$	5.29739	−	6.20244i	0.0109000	−	0.0127622i
$487$	−504.064	+	121.015i	−1.03504	+	0.248491i	−0.715155	−	0.698966i	$-0.753644\pi$
$487$	−504.064	+	121.015i	−1.03504	+	0.248491i	−0.319884	+	0.947457i	$0.603644\pi$
$488$	3.47311	−	14.4665i	0.00711703	−	0.0296445i
$489$	180.916	−	58.7833i	0.369972	−	0.120211i
$490$	−4.44474	+	3.79617i	−0.00907090	+	0.00774728i
$491$	−169.419	+	26.8334i	−0.345050	+	0.0546505i	−0.326554	−	0.945178i	$-0.605888\pi$
$491$	−169.419	+	26.8334i	−0.345050	+	0.0546505i	−0.0184955	+	0.999829i	$0.505888\pi$
$492$	31.7493	+	43.6992i	0.0645311	+	0.0888195i
$493$	−565.997	+	204.963i	−1.14807	+	0.415746i
$494$			4.52565i			0.00916123i
$495$	−107.096	+	86.4195i	−0.216356	+	0.174585i
$496$	730.391	−	302.538i	1.47256	−	0.609956i
$497$	−53.6589	+	165.145i	−0.107966	+	0.332284i
$498$	1.17682	+	0.721153i	0.00236308	+	0.00144810i
$499$	187.640	+	306.200i	0.376031	+	0.613627i	0.983541	−	0.180685i	$-0.0578315\pi$
$499$	187.640	+	306.200i	0.376031	+	0.613627i	−0.607510	+	0.794312i	$0.707831\pi$
$500$	−285.734	−	22.4878i	−0.571469	−	0.0449756i
$501$	92.4693	−	181.481i	0.184570	−	0.362238i
$502$	−0.166037	−	1.04832i	−0.000330751	−	0.00208828i
$503$	753.898	−	180.995i	1.49880	−	0.359831i	0.600649	−	0.799513i	$-0.294909\pi$
$503$	753.898	−	180.995i	1.49880	−	0.359831i	0.898154	+	0.439682i	$0.144909\pi$
$504$	22.8351	−	26.7365i	0.0453078	−	0.0530486i
$505$	212.847	−	88.1642i	0.421480	−	0.174583i
$506$	5.61524	+	2.51168i	0.0110973	+	0.00496379i
$507$	95.7641	−	39.6668i	0.188884	−	0.0782383i
$508$	247.809	+	486.353i	0.487813	+	0.957388i
$509$	−583.297	+	423.790i	−1.14597	+	0.832594i	−0.987939	−	0.154841i	$-0.950514\pi$
$509$	−583.297	+	423.790i	−1.14597	+	0.832594i	−0.158028	+	0.987435i	$0.550514\pi$
$510$	0.333809	−	0.888400i	0.000654528	−	0.00174196i
$511$	−295.431	−	909.243i	−0.578143	−	1.77934i
$512$	51.7640	+	26.3751i	0.101102	+	0.0515138i
$513$	50.6625	−	211.025i	0.0987574	−	0.411354i
$514$	−2.92965	+	2.12852i	−0.00569971	+	0.00414108i
$515$	47.7560	−	3.75848i	0.0927300	−	0.00729801i
$516$	−42.3980	+	102.358i	−0.0821667	+	0.198368i
$517$	−132.259	+	17.1802i	−0.255820	+	0.0332306i
$518$	12.2447	−	12.2447i	0.0236385	−	0.0236385i
$519$	−157.067	+	80.0294i	−0.302633	+	0.154199i
$520$	−0.828297	−	3.45010i	−0.00159288	−	0.00663481i
$521$	229.267	+	374.129i	0.440051	+	0.718098i	0.993381	−	0.114864i	$-0.0366433\pi$
$521$	229.267	+	374.129i	0.440051	+	0.718098i	−0.553330	+	0.832962i	$0.686643\pi$
$522$	−10.2033	+	8.71445i	−0.0195466	+	0.0166943i
$523$	−109.593	−	337.293i	−0.209547	−	0.644920i	−0.999496	−	0.0317471i	$-0.989893\pi$
$523$	−109.593	−	337.293i	−0.209547	−	0.644920i	0.789949	−	0.613173i	$-0.210107\pi$
$524$	123.390	−	513.955i	0.235477	−	0.980830i
$525$	−33.7441	+	213.052i	−0.0642745	+	0.405813i
$526$	4.15075	−	12.7747i	0.00789115	−	0.0242865i
$527$	516.867	+	663.785i	0.980772	+	1.25955i
$528$	−96.3040	+	106.586i	−0.182394	+	0.201868i
$529$	−267.161	−	267.161i	−0.505030	−	0.505030i
$530$	2.26154	−	0.177987i	0.00426706	−	0.000335825i
$531$	−231.663	−	318.856i	−0.436276	−	0.600482i
$532$	165.853	−	690.827i	0.311754	−	1.29855i
$533$	−8.42383	+	107.035i	−0.0158046	+	0.200816i
$534$	−0.181864	+	2.31080i	−0.000340568	+	0.00432733i
$535$	14.2463	+	89.9475i	0.0266286	+	0.168126i
$536$	18.8316	+	2.98263i	0.0351336	+	0.00556461i
$537$	153.584	+	131.173i	0.286003	+	0.244270i
$538$	9.19640	−	22.2021i	0.0170937	−	0.0412678i
$539$	531.933	+	776.834i	0.986888	+	1.44125i
$540$			85.0510i			0.157502i
$541$	−172.311	+	13.5611i	−0.318504	+	0.0250668i	−0.236703	−	0.971582i	$-0.576067\pi$
$541$	−172.311	+	13.5611i	−0.318504	+	0.0250668i	−0.0818003	+	0.996649i	$0.526067\pi$
$542$	−12.1314	−	1.92142i	−0.0223826	−	0.00354506i
$543$	−45.1172	−	32.7795i	−0.0830887	−	0.0603675i
$544$	−7.45321	+	36.3308i	−0.0137008	+	0.0667845i
$545$	145.764	−	47.3616i	0.267457	−	0.0869019i
$546$	−2.76744	+	0.438320i	−0.00506857	+	0.000802783i
$547$	54.9705	+	33.6859i	0.100494	+	0.0615831i	0.571838	−	0.820367i	$-0.306231\pi$
$547$	54.9705	+	33.6859i	0.100494	+	0.0615831i	−0.471343	+	0.881950i	$0.656231\pi$
$548$	−315.552	−	102.529i	−0.575825	−	0.187097i
$549$	−314.827	+	130.406i	−0.573455	+	0.237533i
$550$	2.09304	−	11.1853i	0.00380552	−	0.0203369i
$551$	−207.566	+	501.109i	−0.376708	+	0.909454i
$552$	3.25764	−	1.65985i	0.00590152	−	0.00300697i
$553$	−150.044	+	947.340i	−0.271327	+	1.71309i
$554$	−7.41774	+	4.54559i	−0.0133894	+	0.00820504i
$555$	−3.16057	+	40.1588i	−0.00569472	+	0.0723583i
$556$	−177.054	−	207.304i	−0.318442	−	0.372848i
$557$	730.622	+	530.828i	1.31171	+	0.953012i	0.999996	+	0.00283575i	$0.000902648\pi$
$557$	730.622	+	530.828i	1.31171	+	0.953012i	0.311713	+	0.950176i	$0.399097\pi$
$558$	15.9894	+	9.79834i	0.0286549	+	0.0175598i
$559$	−196.217	+	99.9777i	−0.351015	+	0.178851i
$560$			278.285i			0.496938i
$561$	−136.574	−	68.6660i	−0.243447	−	0.122399i
$562$	−22.2473			−0.0395859
$563$	86.1413	+	169.062i	0.153004	+	0.300287i	0.954767	−	0.297355i	$-0.0961044\pi$
$563$	86.1413	+	169.062i	0.153004	+	0.300287i	−0.801763	+	0.597642i	$0.796104\pi$
$564$	−20.7038	+	33.7856i	−0.0367089	+	0.0599035i
$565$	169.819	−	233.736i	0.300565	−	0.413693i
$566$	2.66118	−	2.27286i	0.00470173	−	0.00401566i
$567$	−733.306	−	57.7124i	−1.29331	−	0.101786i
$568$	−2.84479	−	4.64228i	−0.00500843	−	0.00817302i
$569$	67.6934	+	10.7216i	0.118969	+	0.0188429i	0.215635	−	0.976474i	$-0.430818\pi$
$569$	67.6934	+	10.7216i	0.118969	+	0.0188429i	−0.0966659	+	0.995317i	$0.530818\pi$
$570$	−0.388220	−	0.761925i	−0.000681088	−	0.00133671i
$571$	38.7596	+	16.0547i	0.0678801	+	0.0281169i	0.416365	−	0.909197i	$-0.363304\pi$
$571$	38.7596	+	16.0547i	0.0678801	+	0.0281169i	−0.348485	+	0.937314i	$0.613304\pi$
$572$	−283.299	+	36.8000i	−0.495278	+	0.0643357i
$573$	95.4002	+	230.316i	0.166493	+	0.401948i
$574$	−2.69490	+	8.29405i	−0.00469495	+	0.0144496i
$575$	146.124	−	238.453i	0.254129	−	0.414701i
$576$	−83.1573	−	525.035i	−0.144370	−	0.911518i
$577$	−231.706	−	713.118i	−0.401570	−	1.23591i	−0.923725	−	0.383056i	$-0.874872\pi$
$577$	−231.706	−	713.118i	−0.401570	−	1.23591i	0.522155	−	0.852851i	$-0.325128\pi$
$578$	−13.1151	+	0.874184i	−0.0226905	+	0.00151243i
$579$	9.50678	−	13.0850i	0.0164193	−	0.0225992i
$580$	33.2527	−	209.949i	0.0573323	−	0.361982i
$581$	−33.7904	−	429.348i	−0.0581591	−	0.738981i
$582$	−5.77974			−0.00993083
$583$	10.1950	−	365.255i	0.0174871	−	0.626510i
$584$	27.6946	+	11.4715i	0.0474222	+	0.0196429i
$585$	−52.7799	+	61.7973i	−0.0902220	+	0.105636i
$586$	−2.82721	+	17.8503i	−0.00482459	+	0.0304613i
$587$	874.644	−	138.530i	1.49002	−	0.235997i	0.642308	−	0.766447i	$-0.277977\pi$
$587$	874.644	−	138.530i	1.49002	−	0.235997i	0.847716	+	0.530450i	$0.177977\pi$
$588$	278.860	+	21.9468i	0.474252	+	0.0373245i
$589$	755.698	+	59.4747i	1.28302	+	0.100976i
$590$	−3.14126	−	0.754151i	−0.00532418	−	0.00127822i
$591$	−53.7508	+	39.0522i	−0.0909489	+	0.0660782i
$592$	−41.1349	−	522.668i	−0.0694846	−	0.882885i
$593$	515.110	−	515.110i	0.868651	−	0.868651i	−0.123672	−	0.992323i	$-0.539467\pi$
$593$	515.110	−	515.110i	0.868651	−	0.868651i	0.992323	+	0.123672i	$0.0394670\pi$
$594$	−7.04808	−	0.753076i	−0.0118655	−	0.00126780i
$595$	−285.496	+	78.6746i	−0.479825	+	0.132226i
$596$	114.874	+	37.3249i	0.192742	+	0.0626256i
$597$	−126.595	−	20.0507i	−0.212052	−	0.0335857i
$598$	3.53233	+	0.848038i	0.00590691	+	0.00141812i
$599$	636.244	−	206.728i	1.06218	−	0.345122i	0.274741	−	0.961518i	$-0.411408\pi$
$599$	636.244	−	206.728i	1.06218	−	0.345122i	0.787436	+	0.616396i	$0.211408\pi$
$600$	−4.39254	−	5.14300i	−0.00732090	−	0.00857167i
$601$	−337.378	+	206.745i	−0.561360	+	0.344002i	−0.774057	−	0.633116i	$-0.781775\pi$
$601$	−337.378	+	206.745i	−0.561360	+	0.344002i	0.212696	+	0.977118i	$0.431775\pi$
$602$	−17.3933	+	4.17576i	−0.0288925	+	0.00693648i
$603$	−198.261	−	389.109i	−0.328791	−	0.645289i
$604$	325.609	+	325.609i	0.539087	+	0.539087i
$605$	174.025	+	52.2023i	0.287645	+	0.0862848i
$606$	5.27025	+	2.18301i	0.00869679	+	0.00360233i
$607$	8.91460	+	113.271i	0.0146863	+	0.186608i	0.999885	+	0.0151891i	$0.00483502\pi$
$607$	8.91460	+	113.271i	0.0146863	+	0.186608i	−0.985198	+	0.171418i	$0.945165\pi$
$608$	19.6422	+	27.0352i	0.0323063	+	0.0444658i
$609$	−326.532	−	78.3935i	−0.536178	−	0.128725i
$610$	−1.26806	+	2.48870i	−0.00207878	+	0.00407984i
$611$	−74.9070	+	24.3388i	−0.122597	+	0.0398343i
$612$	515.663	−	233.988i	0.842586	−	0.382333i
$613$	72.4365	+	99.7003i	0.118167	+	0.162643i	0.864003	−	0.503487i	$-0.167950\pi$
$613$	72.4365	+	99.7003i	0.118167	+	0.162643i	−0.745836	+	0.666130i	$0.767950\pi$
$614$	−21.4954	+	10.9524i	−0.0350087	+	0.0178378i
$615$	−7.76349	−	18.7427i	−0.0126236	−	0.0304760i
$616$	−46.1582	−	4.93193i	−0.0749322	−	0.00800638i
$617$	170.847	+	412.461i	0.276899	+	0.668494i	0.999747	−	0.0225139i	$-0.00716699\pi$
$617$	170.847	+	412.461i	0.276899	+	0.668494i	−0.722847	+	0.691008i	$0.757167\pi$
$618$	0.901939	+	0.770329i	0.00145945	+	0.00124649i
$619$	−101.806	−	424.054i	−0.164469	−	0.685064i	−0.992276	−	0.124050i	$-0.960412\pi$
$619$	−101.806	−	424.054i	−0.164469	−	0.685064i	0.827807	−	0.561013i	$-0.189588\pi$
$620$	−293.418	+	46.4728i	−0.473255	+	0.0749562i
$621$	−155.214	−	79.0856i	−0.249943	−	0.127352i
$622$	1.93414	−	24.5756i	0.00310955	−	0.0395106i
$623$	616.703	−	377.916i	0.989892	−	0.606607i
$624$	−44.3247	+	72.3313i	−0.0710331	+	0.115915i
$625$	−438.424	−	142.453i	−0.701479	−	0.227924i
$626$	−9.51630	−	22.9744i	−0.0152018	−	0.0367003i
$627$	−128.674	+	49.1388i	−0.205221	+	0.0783712i
$628$	−396.079			−0.630699
$629$	524.581	−	189.965i	0.833992	−	0.302011i
$630$	−5.34042	+	3.88004i	−0.00847686	+	0.00615880i
$631$	−104.916	−	662.413i	−0.166269	−	1.04978i	−0.919805	−	0.392375i	$-0.871653\pi$
$631$	−104.916	−	662.413i	−0.166269	−	1.04978i	0.753536	−	0.657407i	$-0.228347\pi$
$632$	−19.5315	−	22.8685i	−0.0309043	−	0.0361843i
$633$	−49.5909	−	152.625i	−0.0783426	−	0.241114i
$634$	−4.00965	−	0.962631i	−0.00632436	−	0.00151835i
$635$	−47.8583	−	199.344i	−0.0753674	−	0.313928i
$636$	−82.5502	−	70.5046i	−0.129796	−	0.110856i
$637$	393.154	+	393.154i	0.617197	+	0.617197i
$638$	17.1038	+	4.61459i	0.0268085	+	0.00723290i
$639$	−47.7231	+	115.214i	−0.0746840	+	0.180303i
$640$	−13.2769	−	11.3395i	−0.0207452	−	0.0177180i
$641$	−156.165	−	95.6979i	−0.243627	−	0.149295i	0.395325	−	0.918541i	$-0.370632\pi$
$641$	−156.165	−	95.6979i	−0.243627	−	0.149295i	−0.638952	+	0.769246i	$0.720632\pi$
$642$	−1.32541	+	1.82427i	−0.00206451	+	0.00284155i
$643$	−40.3071	−	47.1936i	−0.0626861	−	0.0733959i	0.728177	−	0.685389i	$-0.240368\pi$
$643$	−40.3071	−	47.1936i	−0.0626861	−	0.0733959i	−0.790863	+	0.611993i	$0.790368\pi$
$644$	−508.122	−	258.901i	−0.789009	−	0.402020i
$645$	24.4583	−	33.6640i	0.0379198	−	0.0521922i
$646$	−7.38782	+	9.25679i	−0.0114363	+	0.0143294i
$647$	74.1413	−	228.183i	0.114592	−	0.352679i	−0.877269	−	0.479998i	$-0.840637\pi$
$647$	74.1413	−	228.183i	0.114592	−	0.352679i	0.991862	+	0.127319i	$0.0406373\pi$
$648$	16.3086	−	16.3086i	0.0251676	−	0.0251676i
$649$	−174.541	+	490.200i	−0.268938	+	0.755316i
$650$		−	6.72016i		−	0.0103387i
$651$	36.8222	+	467.871i	0.0565626	+	0.718695i
$652$	904.636	−	217.184i	1.38748	−	0.333104i
$653$	788.650	−	483.285i	1.20773	−	0.740100i	0.234993	−	0.971997i	$-0.424493\pi$
$653$	788.650	−	483.285i	1.20773	−	0.740100i	0.972740	+	0.231897i	$0.0744932\pi$
$654$	3.38133	+	1.72288i	0.00517023	+	0.00263437i
$655$	−90.1243	+	176.879i	−0.137594	+	0.270044i
$656$	137.958	+	225.127i	0.210302	+	0.343182i
$657$	−160.283	−	667.628i	−0.243962	−	1.01618i
$658$	−6.37777	+	0.501942i	−0.00969266	+	0.000762829i
$659$	479.023			0.726893			0.363447	−	0.931615i	$-0.381600\pi$
$659$	479.023			0.726893			0.363447	+	0.931615i	$0.381600\pi$
$660$	44.5386	−	30.4976i	0.0674827	−	0.0462084i
$661$	428.351	+	428.351i	0.648035	+	0.648035i	0.952518	−	0.304482i	$-0.0984835\pi$
$661$	428.351	+	428.351i	0.648035	+	0.648035i	−0.304482	+	0.952518i	$0.598484\pi$
$662$	7.32723	+	2.38076i	0.0110683	+	0.00359632i
$663$	−86.7364	−	25.0242i	−0.130824	−	0.0377439i
$664$	10.9248	+	7.93733i	0.0164530	+	0.0119538i
$665$	−121.140	+	237.750i	−0.182165	+	0.357518i
$666$	9.45670	−	8.07678i	0.0141992	−	0.0121273i
$667$	352.228	+	255.909i	0.528078	+	0.383671i
$668$	520.484	−	849.352i	0.779167	−	1.27149i
$669$	59.5285	−	69.6989i	0.0889813	−	0.104184i
$670$	−3.30706	−	1.36983i	−0.00493591	−	0.00204452i
$671$	376.891	+	245.681i	0.561686	+	0.366142i
$672$	−14.6297	+	14.6297i	−0.0217704	+	0.0217704i
$673$	−375.775	+	439.976i	−0.558358	+	0.653754i	−0.965742	−	0.259503i	$-0.916441\pi$
$673$	−375.775	+	439.976i	−0.558358	+	0.653754i	0.407384	+	0.913257i	$0.366441\pi$
$674$	23.0658	−	5.53760i	0.0342222	−	0.00821603i
$675$	−75.2290	+	313.352i	−0.111450	+	0.464224i
$676$	482.131	−	156.654i	0.713211	−	0.231736i
$677$	−399.734	+	341.405i	−0.590449	+	0.504291i	−0.893727	−	0.448611i	$-0.851919\pi$
$677$	−399.734	+	341.405i	−0.590449	+	0.504291i	0.303278	+	0.952902i	$0.401919\pi$
$678$	7.06565	−	1.11909i	0.0104213	−	0.00165057i
$679$	1060.07	+	1459.06i	1.56122	+	2.14884i
$680$	3.93787	−	8.40900i	0.00579098	−	0.0123662i
$681$			53.5642i			0.0786553i
$682$	−1.25311	−	24.7267i	−0.00183741	−	0.0362562i
$683$	−108.396	+	44.8990i	−0.158706	+	0.0657380i	−0.460622	−	0.887596i	$-0.652374\pi$
$683$	−108.396	+	44.8990i	−0.158706	+	0.0657380i	0.301916	+	0.953334i	$0.402374\pi$
$684$	157.670	−	485.259i	0.230512	−	0.709442i
$685$	106.251	+	65.1105i	0.155111	+	0.0950519i
$686$	10.0880	+	16.4620i	0.0147055	+	0.0239972i
$687$	114.935	+	9.04555i	0.167299	+	0.0131667i
$688$	−245.866	+	482.540i	−0.357364	+	0.701366i
$689$	−33.7564	−	213.129i	−0.0489933	−	0.309331i
$690$	−0.667440	+	0.160238i	−0.000967305	+	0.000232229i
$691$	−395.203	+	462.723i	−0.571929	+	0.669643i	−0.968688	−	0.248280i	$-0.920135\pi$
$691$	−395.203	+	462.723i	−0.571929	+	0.669643i	0.396759	+	0.917923i	$0.370135\pi$
$692$	−796.507	+	329.924i	−1.15102	+	0.476769i
$693$	530.039	+	921.722i	0.764847	+	1.33005i
$694$	26.4933	−	10.9739i	0.0381747	−	0.0158125i
$695$	46.4846	+	91.2312i	0.0668844	+	0.131268i
$696$	8.51840	−	6.18898i	0.0122391	−	0.00889221i
$697$	−191.958	+	205.179i	−0.275406	+	0.294374i
$698$	−4.08299	−	12.5661i	−0.00584955	−	0.0180031i
$699$	−232.429	−	118.429i	−0.332517	−	0.169426i
$700$	−246.276	+	1025.81i	−0.351823	+	1.46545i
$701$	834.397	−	606.225i	1.19029	−	0.864800i	0.196999	−	0.980404i	$-0.436880\pi$
$701$	834.397	−	606.225i	1.19029	−	0.864800i	0.993295	+	0.115604i	$0.0368804\pi$
$702$	−4.17304	+	0.328425i	−0.00594450	+	0.000467842i
$703$	192.378	−	464.441i	0.273653	−	0.660656i
$704$	−509.912	+	482.220i	−0.724307	+	0.684971i
$705$	10.5233	−	10.5233i	0.0149267	−	0.0149267i
$706$	−16.7951	+	8.55753i	−0.0237891	+	0.0121211i
$707$	−415.536	−	1730.83i	−0.587746	−	2.44814i
$708$	80.7765	+	131.815i	0.114091	+	0.186180i
$709$	420.135	−	358.829i	0.592574	−	0.506106i	−0.301832	−	0.953361i	$-0.597598\pi$
$709$	420.135	−	358.829i	0.592574	−	0.506106i	0.894407	+	0.447255i	$0.147598\pi$
$710$	0.315869	+	0.972144i	0.000444886	+	0.00136922i
$711$	−160.805	+	669.802i	−0.226168	+	0.942056i
$712$	−3.54771	+	22.3994i	−0.00498274	+	0.0314598i
$713$	188.027	−	578.688i	0.263713	−	0.811624i
$714$	−6.37607	−	3.62113i	−0.00893007	−	0.00507160i
$715$	106.688	+	11.3994i	0.149214	+	0.0159432i
$716$	698.482	+	698.482i	0.975534	+	0.975534i
$717$	164.548	−	12.9502i	0.229495	−	0.0180616i
$718$	−9.02353	−	12.4198i	−0.0125676	−	0.0172978i
$719$	−116.411	+	484.886i	−0.161907	+	0.674390i	0.831079	+	0.556155i	$0.187724\pi$
$719$	−116.411	+	484.886i	−0.161907	+	0.674390i	−0.992986	+	0.118235i	$0.962276\pi$
$720$	−15.6806	+	199.241i	−0.0217786	+	0.276724i
$721$	29.0391	−	368.977i	0.0402761	−	0.511757i
$722$	−0.899089	−	5.67662i	−0.00124527	−	0.00786236i
$723$	−204.594	−	32.4044i	−0.282979	−	0.0448194i
$724$	−207.396	−	177.133i	−0.286459	−	0.244659i
$725$	308.216	−	744.099i	0.425126	−	1.02634i
$726$	2.13294	+	3.96090i	0.00293793	+	0.00545579i
$727$		−	1409.71i		−	1.93907i	−0.244945	−	0.969537i	$-0.578770\pi$
$727$		−	1409.71i		−	1.93907i	0.244945	−	0.969537i	$-0.421230\pi$
$728$	−27.3295	+	2.15087i	−0.0375405	+	0.00295450i
$729$	−418.813	−	66.3335i	−0.574504	−	0.0909925i
$730$	−4.55298	−	3.30794i	−0.00623696	−	0.00453142i
$731$	−564.551	−	115.817i	−0.772300	−	0.158436i
$732$	127.123	−	41.3049i	0.173666	−	0.0564274i
$733$	−21.0296	+	3.33075i	−0.0286897	+	0.00454400i	−0.170763	−	0.985312i	$-0.554623\pi$
$733$	−21.0296	+	3.33075i	−0.0286897	+	0.00454400i	0.142073	+	0.989856i	$0.454623\pi$
$734$	−21.5592	−	13.2115i	−0.0293723	−	0.0179993i
$735$	−99.9161	−	32.4647i	−0.135940	−	0.0441697i
$736$	24.7820	−	10.2651i	0.0336712	−	0.0139471i
$737$	−275.985	+	506.218i	−0.374471	+	0.686862i
$738$	−2.39678	+	5.78635i	−0.00324767	+	0.00784058i
$739$	−1280.48	+	652.435i	−1.73271	+	0.882862i	−0.760310	+	0.649560i	$0.774953\pi$
$739$	−1280.48	+	652.435i	−1.73271	+	0.882862i	−0.972404	+	0.233302i	$0.925047\pi$
$740$	−30.8195	+	194.587i	−0.0416480	+	0.262955i
$741$	−69.3545	+	42.5005i	−0.0935958	+	0.0573556i
$742$	1.37518	−	17.4734i	0.00185335	−	0.0235490i
$743$	−224.174	−	262.475i	−0.301715	−	0.353263i	0.588749	−	0.808316i	$-0.299621\pi$
$743$	−224.174	−	262.475i	−0.301715	−	0.353263i	−0.890465	+	0.455052i	$0.849621\pi$
$744$	−11.9050	−	8.64950i	−0.0160014	−	0.0116257i
$745$	−38.6797	−	23.7030i	−0.0519191	−	0.0318160i
$746$	−25.6740	+	13.0816i	−0.0344156	+	0.0175356i
$747$		−	309.300i		−	0.414056i
$748$	−639.535	−	387.196i	−0.854993	−	0.517642i
$749$	703.623			0.939417
$750$	1.21008	+	2.37492i	0.00161344	+	0.00316656i
$751$	−387.359	+	632.113i	−0.515791	+	0.841694i	−0.999436	−	0.0335696i	$-0.989312\pi$
$751$	−387.359	+	632.113i	−0.515791	+	0.841694i	0.483645	+	0.875264i	$0.339312\pi$
$752$	−113.849	+	156.700i	−0.151395	+	0.208378i
$753$	14.5060	−	12.3893i	0.0192642	−	0.0164532i
$754$	10.4296	+	0.820828i	0.0138324	+	0.00108863i
$755$	−90.3645	−	147.461i	−0.119688	−	0.195313i
$756$	649.038	+	102.798i	0.858516	+	0.135976i
$757$	−614.954	−	1206.92i	−0.812357	−	1.59434i	−0.804189	−	0.594374i	$-0.797400\pi$
$757$	−614.954	−	1206.92i	−0.812357	−	1.59434i	−0.00816855	−	0.999967i	$-0.502600\pi$
$758$	30.4866	+	12.6280i	0.0402198	+	0.0166596i
$759$	14.2420	+	109.640i	0.0187641	+	0.144453i
$760$	−3.20173	−	7.72966i	−0.00421280	−	0.0101706i
$761$	−227.419	+	699.924i	−0.298843	+	0.919743i	0.683061	+	0.730361i	$0.260648\pi$
$761$	−227.419	+	699.924i	−0.298843	+	0.919743i	−0.981904	+	0.189381i	$0.939352\pi$
$762$	2.65229	−	4.32814i	0.00348069	−	0.00567997i
$763$	−185.245	−	1169.59i	−0.242785	−	1.53289i
$764$	376.758	+	1159.54i	0.493139	+	1.51773i
$765$	−208.836	+	40.2409i	−0.272989	+	0.0526025i
$766$	−2.02152	+	2.78238i	−0.00263906	+	0.00363235i
$767$	−48.0710	+	303.508i	−0.0626740	+	0.395708i
$768$	16.3342	+	207.546i	0.0212685	+	0.270242i
$769$	629.693			0.818846			0.409423	−	0.912345i	$-0.365730\pi$
$769$	629.693			0.818846			0.409423	+	0.912345i	$0.365730\pi$
$770$	8.21020	+	2.92333i	0.0106626	+	0.00379653i
$771$	−60.1315	−	24.9073i	−0.0779915	−	0.0323051i
$772$	51.3724	−	60.1494i	0.0665446	−	0.0779137i
$773$	156.653	−	989.071i	0.202656	−	1.27952i	−0.651157	−	0.758943i	$-0.725716\pi$
$773$	156.653	−	989.071i	0.202656	−	1.27952i	0.853813	−	0.520579i	$-0.174284\pi$
$774$	−12.6882	+	2.00961i	−0.0163930	+	0.00259640i
$775$	−1122.14	−	88.3143i	−1.44792	−	0.113954i
$776$	−56.3743	−	4.43675i	−0.0726473	−	0.00571746i
$777$	302.639	+	72.6572i	0.389497	+	0.0935099i
$778$	27.8051	−	20.2016i	0.0357392	−	0.0259660i
$779$	19.8634	+	252.389i	0.0254986	+	0.323991i
$780$	22.5409	−	22.5409i	0.0288986	−	0.0288986i
$781$	161.104	−	33.9535i	0.206280	−	0.0434744i
$782$	5.84069	+	7.50088i	0.00746891	+	0.00959192i
$783$	−477.129	−	155.029i	−0.609360	−	0.197993i
$784$	1350.50	+	213.898i	1.72257	+	0.272829i
$785$	144.649	+	34.7271i	0.184266	+	0.0442384i
$786$	−4.67482	+	1.51894i	−0.00594761	+	0.00193250i
$787$	−62.9728	−	73.7317i	−0.0800163	−	0.0936870i	0.718954	−	0.695058i	$-0.244621\pi$
$787$	−62.9728	−	73.7317i	−0.0800163	−	0.0936870i	−0.798970	+	0.601371i	$0.794621\pi$
$788$	−277.054	+	169.779i	−0.351591	+	0.215455i
$789$	234.749	−	56.3582i	0.297527	−	0.0714300i
$790$	2.56329	+	5.03074i	0.00324467	+	0.00636802i
$791$	−1578.43	−	1578.43i	−1.99548	−	1.99548i
$792$	−32.7695	−	6.13195i	−0.0413757	−	0.00774236i
$793$	245.462	+	101.674i	0.309536	+	0.128214i
$794$	−1.35166	−	17.1745i	−0.00170234	−	0.0216303i
$795$	23.9659	+	32.9862i	0.0301457	+	0.0414920i
$796$	−609.536	−	146.337i	−0.765749	−	0.183840i
$797$	−340.765	+	668.788i	−0.427559	+	0.839132i	0.572259	+	0.820073i	$0.306067\pi$
$797$	−340.765	+	668.788i	−0.427559	+	0.839132i	−0.999818	+	0.0190593i	$0.993933\pi$
$798$	−6.28361	+	2.04167i	−0.00787419	+	0.00255848i
$799$	−192.947	−	72.4981i	−0.241485	−	0.0907361i
$800$	−29.1669	−	40.1447i	−0.0364586	−	0.0501809i
$801$	462.828	−	235.823i	0.577813	−	0.294411i
$802$	5.22140	+	12.6056i	0.00651047	+	0.0157177i
$803$	−607.715	+	672.599i	−0.756805	+	0.837608i
$804$	65.5530	+	158.259i	0.0815336	+	0.196840i
$805$	162.867	+	139.102i	0.202320	+	0.172797i
$806$	−3.41323	−	14.2171i	−0.00423478	−	0.0176391i
$807$	426.605	−	67.5676i	0.528631	−	0.0837269i
$808$	49.7291	+	25.3382i	0.0615459	+	0.0313592i
$809$	−79.2433	+	1006.88i	−0.0979522	+	1.24460i	0.729861	+	0.683596i	$0.239585\pi$
$809$	−79.2433	+	1006.88i	−0.0979522	+	1.24460i	−0.827813	+	0.561004i	$0.810415\pi$
$810$	−3.69196	+	2.26243i	−0.00455797	+	0.00279313i
$811$	−431.191	+	703.639i	−0.531678	+	0.867619i	−0.999872	−	0.0160064i	$-0.994905\pi$
$811$	−431.191	+	703.639i	−0.531678	+	0.867619i	0.468194	+	0.883626i	$0.344905\pi$
$812$	−1561.97	−	507.514i	−1.92361	−	0.625017i
$813$	−84.4809	−	203.955i	−0.103913	−	0.250867i
$814$	−15.8523	−	4.27693i	−0.0194746	−	0.00525421i
$815$	−349.417			−0.428732
$816$	−208.738	+	75.5897i	−0.255806	+	0.0926345i
$817$	−420.106	+	305.225i	−0.514205	+	0.373592i
$818$	4.34552	+	27.4365i	0.00531237	+	0.0335410i
$819$	407.793	+	477.464i	0.497916	+	0.582984i
$820$	−30.6599	−	94.3614i	−0.0373901	−	0.115075i
$821$	−521.303	−	125.154i	−0.634961	−	0.152441i	−0.0968285	−	0.995301i	$-0.530870\pi$
$821$	−521.303	−	125.154i	−0.634961	−	0.152441i	−0.538132	+	0.842861i	$0.680870\pi$
$822$	0.720302	+	3.00028i	0.000876280	+	0.00364997i
$823$	477.617	+	407.924i	0.580337	+	0.495654i	0.890472	−	0.455038i	$-0.150374\pi$
$823$	477.617	+	407.924i	0.580337	+	0.495654i	−0.310135	+	0.950692i	$0.600374\pi$
$824$	8.20598	+	8.20598i	0.00995871	+	0.00995871i
$825$	191.068	−	72.9664i	0.231598	−	0.0884441i
$826$	−9.55177	+	23.0600i	−0.0115639	+	0.0279177i
$827$	−639.999	−	546.610i	−0.773880	−	0.660956i	0.172137	−	0.985073i	$-0.444933\pi$
$827$	−639.999	−	546.610i	−0.773880	−	0.660956i	−0.946017	+	0.324117i	$0.894933\pi$
$828$	−349.206	−	213.994i	−0.421747	−	0.258447i
$829$	472.756	−	650.693i	0.570272	−	0.784913i	−0.422315	−	0.906449i	$-0.638782\pi$
$829$	472.756	−	650.693i	0.570272	−	0.784913i	0.992587	+	0.121537i	$0.0387822\pi$
$830$	−1.64649	−	1.92779i	−0.00198372	−	0.00232264i
$831$	−139.320	−	70.9873i	−0.167654	−	0.0854239i
$832$	−243.613	+	335.304i	−0.292804	+	0.403010i
$833$	162.362	+	1445.96i	0.194912	+	1.73585i
$834$	−0.783445	+	2.41120i	−0.000939383	+	0.00289112i
$835$	−264.550	+	264.550i	−0.316827	+	0.316827i
$836$	−646.220	+	190.207i	−0.772991	+	0.227521i
$837$			701.135i			0.837676i
$838$	−0.821059	−	10.4325i	−0.000979784	−	0.0124493i
$839$	−513.617	+	123.308i	−0.612177	+	0.146971i	−0.527666	−	0.849452i	$-0.676933\pi$
$839$	−513.617	+	123.308i	−0.612177	+	0.146971i	−0.0845110	+	0.996423i	$0.526933\pi$
$840$	4.41660	−	2.70650i	0.00525786	−	0.00322202i
$841$	367.850	+	187.429i	0.437396	+	0.222865i
$842$	−2.68547	+	5.27053i	−0.00318939	+	0.00625953i
$843$	−208.925	−	340.934i	−0.247835	−	0.404430i
$844$	−183.221	−	763.171i	−0.217087	−	0.904231i
$845$	−189.810	+	14.9384i	−0.224627	+	0.0176786i
$846$	−4.59451			−0.00543086
$847$	608.702	−	1264.92i	0.718656	−	1.49341i
$848$	−375.235	−	375.235i	−0.442495	−	0.442495i
$849$	59.8224	+	19.4375i	0.0704622	+	0.0228945i
$850$	10.9702	−	13.7455i	0.0129061	−	0.0161711i
$851$	−326.454	−	237.183i	−0.383613	−	0.278711i
$852$	22.2074	−	43.5845i	0.0260650	−	0.0511555i
$853$	432.841	−	369.681i	0.507434	−	0.433389i	−0.358514	−	0.933524i	$-0.616716\pi$
$853$	432.841	−	369.681i	0.507434	−	0.433389i	0.865947	+	0.500135i	$0.166716\pi$
$854$	17.4591	+	12.6848i	0.0204439	+	0.0148533i
$855$	−100.128	+	163.393i	−0.117108	+	0.191103i
$856$	−14.3282	+	16.7761i	−0.0167385	+	0.0195983i
$857$	873.086	+	361.644i	1.01877	+	0.421988i	0.828647	−	0.559772i	$-0.189111\pi$
$857$	873.086	+	361.644i	1.01877	+	0.421988i	0.190123	+	0.981760i	$0.439111\pi$
$858$	1.66835	+	2.06753i	0.00194447	+	0.00240971i
$859$	69.2229	−	69.2229i	0.0805854	−	0.0805854i	−0.665665	−	0.746251i	$-0.731852\pi$
$859$	69.2229	−	69.2229i	0.0805854	−	0.0805854i	0.746251	+	0.665665i	$0.231852\pi$
$860$	132.167	−	154.748i	0.153683	−	0.179939i
$861$	−152.412	+	36.5909i	−0.177018	+	0.0424982i
$862$	−0.547371	+	2.27996i	−0.000635001	+	0.00264497i
$863$	241.133	−	78.3489i	0.279413	−	0.0907867i	−0.165958	−	0.986133i	$-0.553072\pi$
$863$	241.133	−	78.3489i	0.279413	−	0.0907867i	0.445371	+	0.895346i	$0.353072\pi$
$864$	−23.5034	+	20.0738i	−0.0272030	+	0.0232335i
$865$	319.812	−	50.6533i	0.369725	−	0.0585588i
$866$	8.07616	+	11.1159i	0.00932582	+	0.0128359i
$867$	−136.561	−	192.776i	−0.157510	−	0.222349i
$868$			2295.29i			2.64434i
$869$	849.589	−	324.447i	0.977663	−	0.373356i
$870$	−1.82631	+	0.756483i	−0.00209921	+	0.000869521i
$871$	−105.217	+	323.825i	−0.120800	+	0.371785i
$872$	31.6582	+	19.4002i	0.0363053	+	0.0222479i
$873$	676.753	+	1104.36i	0.775204	+	1.26502i
$874$	8.53952	+	0.672075i	0.00977062	+	0.000768964i
$875$	377.592	−	741.066i	0.431534	−	0.846933i
$876$	42.1306	+	266.002i	0.0480943	+	0.303656i
$877$	−645.530	+	154.978i	−0.736067	+	0.176714i	−0.584112	−	0.811673i	$-0.698557\pi$
$877$	−645.530	+	154.978i	−0.736067	+	0.176714i	−0.151955	+	0.988387i	$0.548557\pi$
$878$	11.1305	−	13.0321i	0.0126771	−	0.0148430i
$879$	−300.102	+	124.306i	−0.341413	+	0.141418i
$880$	228.738	−	131.536i	0.259929	−	0.149473i
$881$	−678.624	+	281.095i	−0.770288	+	0.319064i	−0.732989	−	0.680240i	$-0.761875\pi$
$881$	−678.624	+	281.095i	−0.770288	+	0.319064i	−0.0372988	+	0.999304i	$0.511875\pi$
$882$	14.7247	+	28.8989i	0.0166947	+	0.0327652i
$883$	1022.40	−	742.819i	1.15787	−	0.841245i	0.168367	−	0.985724i	$-0.446151\pi$
$883$	1022.40	−	742.819i	1.15787	−	0.841245i	0.989508	+	0.144479i	$0.0461507\pi$
$884$	−413.292	−	155.291i	−0.467525	−	0.175669i
$885$	−17.9425	−	55.2214i	−0.0202740	−	0.0623971i
$886$	22.2953	+	11.3600i	0.0251640	+	0.0128217i
$887$	−25.2351	+	105.112i	−0.0284499	+	0.118502i	−0.984788	−	0.173760i	$-0.944408\pi$
$887$	−25.2351	+	105.112i	−0.0284499	+	0.118502i	0.956338	+	0.292263i	$0.0944082\pi$
$888$	−7.89508	+	5.73611i	−0.00889086	+	0.00645958i
$889$	−1579.07	+	124.276i	−1.77624	+	0.139793i
$890$	1.62935	−	3.93360i	0.00183073	−	0.00441978i
$891$	299.172	+	630.022i	0.335771	+	0.707095i
$892$	316.983	−	316.983i	0.355363	−	0.355363i
$893$	−165.478	+	84.3154i	−0.185306	+	0.0944182i
$894$	−0.262220	−	1.09223i	−0.000293311	−	0.00122173i
$895$	−193.846	−	316.328i	−0.216588	−	0.353439i
$896$	−102.581	+	87.6126i	−0.114488	+	0.0977819i
$897$	20.1763	+	62.0961i	0.0224930	+	0.0692265i
$898$	−4.59367	+	19.1340i	−0.00511544	+	0.0213074i
$899$	274.125	−	1730.76i	0.304923	−	1.92521i
$900$	−234.125	+	720.563i	−0.260139	+	0.800625i
$901$	278.874	−	491.041i	0.309516	−	0.544996i
$902$	8.09110	−	1.70524i	0.00897018	−	0.00189051i
$903$	−227.334	−	227.334i	−0.251754	−	0.251754i
$904$	69.7757	−	5.49147i	0.0771856	−	0.00607464i
$905$	60.2109	+	82.8733i	0.0665314	+	0.0915727i
$906$	0.999681	−	4.16397i	0.00110340	−	0.00459599i
$907$	−81.6157	+	1037.03i	−0.0899842	+	1.14336i	0.771725	+	0.635956i	$0.219394\pi$
$907$	−81.6157	+	1037.03i	−0.0899842	+	1.14336i	−0.861710	+	0.507402i	$0.830606\pi$
$908$	−20.5537	+	261.159i	−0.0226362	+	0.287620i
$909$	−199.979	−	1262.62i	−0.219999	−	1.38902i
$910$	5.08336	+	0.805125i	0.00558611	+	0.000884753i
$911$	278.152	+	237.565i	0.305326	+	0.260773i	0.788888	−	0.614537i	$-0.210657\pi$
$911$	278.152	+	237.565i	0.305326	+	0.260773i	−0.483562	+	0.875310i	$0.660657\pi$
$912$	−76.5498	+	184.808i	−0.0839362	+	0.202640i
$913$	−336.932	+	230.713i	−0.369039	+	0.252697i
$914$		−	17.9462i		−	0.0196348i
$915$	−50.0472	+	3.93880i	−0.0546964	+	0.00430470i
$916$	556.907	+	88.2054i	0.607977	+	0.0962941i
$917$	1240.86	+	901.540i	1.35318	+	0.983141i
$918$	−9.07169	−	6.14045i	−0.00988202	−	0.00668895i
$919$	983.153	−	319.446i	1.06981	−	0.347601i	0.279395	−	0.960176i	$-0.409866\pi$
$919$	983.153	−	319.446i	1.06981	−	0.347601i	0.790412	+	0.612575i	$0.209866\pi$
$920$	−6.63306	+	1.05057i	−0.00720985	+	0.00114193i
$921$	−369.707	−	226.557i	−0.401419	−	0.245990i
$922$	34.1362	+	11.0915i	0.0370241	+	0.0120299i
$923$	89.8291	−	37.2084i	0.0973230	−	0.0403125i
$924$	−178.900	−	376.743i	−0.193615	−	0.407730i
$925$	−285.663	+	689.651i	−0.308825	+	0.745569i
$926$	4.26868	−	2.17500i	0.00460981	−	0.00234882i
$927$	41.5816	−	262.536i	0.0448561	−	0.283210i
$928$	65.8667	−	40.3632i	0.0709771	−	0.0434948i
$929$	66.3720	−	843.337i	0.0714446	−	0.907790i	−0.851872	−	0.523750i	$-0.824533\pi$
$929$	66.3720	−	843.337i	0.0714446	−	0.907790i	0.923317	−	0.384040i	$-0.125467\pi$
$930$	1.79422	+	2.10076i	0.00192927	+	0.00225888i
$931$	1060.67	+	770.622i	1.13928	+	0.827735i
$932$	−1087.79	−	666.602i	−1.16716	−	0.715238i
$933$	394.779	−	201.150i	0.423129	−	0.215595i
$934$			8.22610i			0.00880739i
$935$	199.611	+	197.477i	0.213488	+	0.211206i
$936$	−19.6880			−0.0210342
$937$	152.682	+	299.654i	0.162947	+	0.319802i	0.958015	−	0.286719i	$-0.0925646\pi$
$937$	152.682	+	299.654i	0.162947	+	0.319802i	−0.795067	+	0.606521i	$0.792565\pi$
$938$	−14.4505	+	23.5811i	−0.0154056	+	0.0251397i
$939$	262.709	−	361.588i	0.279776	−	0.385078i
$940$	55.3456	−	47.2696i	0.0588783	−	0.0502869i
$941$	1185.28	+	93.2836i	1.25960	+	0.0991325i	0.690618	−	0.723220i	$-0.257339\pi$
$941$	1185.28	+	93.2836i	1.25960	+	0.0991325i	0.568979	+	0.822352i	$0.307339\pi$
$942$	1.92456	+	3.14060i	0.00204306	+	0.00333397i
$943$	200.715	+	31.7901i	0.212847	+	0.0337117i
$944$	343.078	+	673.328i	0.363430	+	0.713271i
$945$	−228.017	−	94.4477i	−0.241288	−	0.0999447i
$946$	11.6535	+	12.3227i	0.0123187	+	0.0130261i
$947$	−334.037	−	806.437i	−0.352732	−	0.851570i	−0.996281	−	0.0861651i	$-0.972539\pi$
$947$	−334.037	−	806.437i	−0.352732	−	0.851570i	0.643549	−	0.765405i	$-0.277461\pi$
$948$	83.4949	−	256.971i	0.0880748	−	0.271066i
$949$	−279.705	+	456.438i	−0.294737	+	0.480967i
$950$	−2.47888	−	15.6511i	−0.00260935	−	0.0164748i
$951$	−22.9026	−	70.4870i	−0.0240827	−	0.0741188i
$952$	−59.4110	−	40.2141i	−0.0624065	−	0.0422418i
$953$	−266.471	+	366.766i	−0.279613	+	0.384855i	−0.925606	−	0.378489i	$-0.876444\pi$
$953$	−266.471	+	366.766i	−0.279613	+	0.384855i	0.645992	+	0.763344i	$0.276444\pi$
$954$	1.96915	−	12.4327i	0.00206410	−	0.0130322i
$955$	−35.9274	−	456.501i	−0.0376203	−	0.478011i
$956$	807.241			0.844395
$957$	89.9051	+	305.448i	0.0939448	+	0.319173i
$958$	−32.2404	−	13.3544i	−0.0336539	−	0.0139399i
$959$	625.290	−	732.121i	0.652023	−	0.763421i
$960$	12.2508	−	77.3485i	0.0127612	−	0.0805714i
$961$	−1469.68	+	232.775i	−1.52932	+	0.242221i
$962$	−9.66643	−	0.760765i	−0.0100483	−	0.000790816i
$963$	503.765	+	39.6472i	0.523121	+	0.0411705i
$964$	−985.087	−	236.499i	−1.02187	−	0.245330i
$965$	−24.0350	+	17.4625i	−0.0249068	+	0.0180958i
$966$	0.416098	+	5.28702i	0.000430743	+	0.00547311i
$967$	595.058	−	595.058i	0.615365	−	0.615365i	−0.328974	−	0.944339i	$-0.606703\pi$
$967$	595.058	−	595.058i	0.615365	−	0.615365i	0.944339	+	0.328974i	$0.106703\pi$
$968$	17.7636	+	40.2711i	0.0183509	+	0.0416023i
$969$	−211.237	−	26.2859i	−0.217995	−	0.0271269i
$970$	10.0969	+	3.28068i	0.0104092	+	0.00338214i
$971$	−967.028	−	153.162i	−0.995909	−	0.157737i	−0.362856	−	0.931845i	$-0.618198\pi$
$971$	−967.028	−	153.162i	−0.995909	−	0.157737i	−0.633053	+	0.774108i	$0.718198\pi$
$972$	697.185	+	167.379i	0.717269	+	0.172201i
$973$	752.385	−	244.465i	0.773263	−	0.251248i
$974$	15.3121	+	17.9282i	0.0157208	+	0.0184067i
$975$	102.985	−	63.1092i	0.105626	−	0.0647274i
$976$	635.326	−	152.528i	0.650949	−	0.156279i
$977$	567.303	+	1113.39i	0.580658	+	1.13961i	0.975323	+	0.220781i	$0.0708605\pi$
$977$	567.303	+	1113.39i	0.580658	+	1.13961i	−0.394665	+	0.918825i	$0.629139\pi$
$978$	−6.11776	−	6.11776i	−0.00625538	−	0.00625538i
$979$	−602.124	−	328.272i	−0.615040	−	0.335314i
$980$	−474.696	−	196.625i	−0.484384	−	0.200638i
$981$	−66.7248	−	847.819i	−0.0680171	−	0.864239i
$982$	4.58562	+	6.31157i	0.00466967	+	0.00642726i
$983$	−498.821	−	119.756i	−0.507448	−	0.121827i	−0.0283658	−	0.999598i	$-0.509030\pi$
$983$	−498.821	−	119.756i	−0.507448	−	0.121827i	−0.479082	+	0.877770i	$0.659030\pi$
$984$	2.23121	−	4.37900i	0.00226749	−	0.00445020i
$985$	116.066	−	37.7122i	0.117834	−	0.0382865i
$986$	19.9928	+	18.7046i	0.0202767	+	0.0189702i
$987$	−67.5860	−	93.0242i	−0.0684762	−	0.0942494i
$988$	−354.455	+	180.604i	−0.358760	+	0.182797i
$989$	159.511	+	385.093i	0.161285	+	0.389376i
$990$	5.71345	+	2.55561i	0.00577116	+	0.00258142i
$991$	−295.014	−	712.227i	−0.297693	−	0.718695i	−0.999977	−	0.00679805i	$-0.997836\pi$
$991$	−295.014	−	712.227i	−0.297693	−	0.718695i	0.702283	−	0.711897i	$-0.252164\pi$
$992$	−82.0952	−	70.1159i	−0.0827572	−	0.0706814i
$993$	32.3257	+	134.646i	0.0325535	+	0.135595i
$994$	7.80037	−	1.23546i	0.00784746	−	0.00124292i
$995$	209.773	+	106.885i	0.210827	+	0.107422i
$996$	−9.51887	+	120.949i	−0.00955710	+	0.121434i
$997$	−413.606	+	253.458i	−0.414850	+	0.254221i	−0.714227	−	0.699914i	$-0.753221\pi$
$997$	−413.606	+	253.458i	−0.414850	+	0.254221i	0.299376	+	0.954135i	$0.403221\pi$
$998$	8.53415	−	13.9265i	0.00855126	−	0.0139544i
$999$	442.216	+	143.685i	0.442659	+	0.143828i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.3.q.a.2.17	✓	544
11.6	odd	10	inner	187.3.q.a.138.17	yes	544
17.9	even	8	inner	187.3.q.a.145.17	yes	544
187.94	odd	40	inner	187.3.q.a.94.17	yes	544

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.3.q.a.2.17	✓	544	1.1	even	1	trivial
187.3.q.a.94.17	yes	544	187.94	odd	40	inner
187.3.q.a.138.17	yes	544	11.6	odd	10	inner
187.3.q.a.145.17	yes	544	17.9	even	8	inner

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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	187.q (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0206482 - 0.0405244i) q^{2} +(0.427119 - 0.696996i) q^{3} +(2.34993 - 3.23439i) q^{4} +(-1.14178 + 0.975172i) q^{5} +(-0.0370646 - 0.00291705i) q^{6} +(6.06168 + 9.89176i) q^{7} +(-0.359280 - 0.0569044i) q^{8} +(3.78254 + 7.42366i) q^{9} +(0.0630940 + 0.0261344i) q^{10} +(5.26541 - 9.65792i) q^{11} +(-1.25066 - 3.01936i) q^{12} +(2.00739 - 6.17812i) q^{13} +(0.275695 - 0.449894i) q^{14} +(0.192014 + 1.21233i) q^{15} +(-4.93660 - 15.1933i) q^{16} +(14.1913 - 9.35983i) q^{17} +(0.222737 - 0.306571i) q^{18} +(2.39622 - 15.1291i) q^{19} +(0.470994 + 5.98455i) q^{20} +9.48358 q^{21} +(-0.500103 - 0.0139588i) q^{22} +(-11.3595 - 4.70526i) q^{23} +(-0.193118 + 0.226112i) q^{24} +(-3.55816 + 22.4653i) q^{25} +(-0.291814 + 0.0462188i) q^{26} +(14.1243 + 1.11160i) q^{27} +(46.2384 + 3.63904i) q^{28} +(-34.4313 - 8.26623i) q^{29} +(0.0451642 - 0.0328137i) q^{30} +(3.88274 + 49.3348i) q^{31} +(-1.54263 + 1.54263i) q^{32} +(-4.48257 - 7.79506i) q^{33} +(-0.672327 - 0.381831i) q^{34} +(-16.5673 - 5.38303i) q^{35} +(32.8997 + 5.21081i) q^{36} +(31.9119 + 7.66137i) q^{37} +(-0.662578 + 0.215285i) q^{38} +(-3.44873 - 4.03794i) q^{39} +(0.465711 - 0.285388i) q^{40} +(-16.0712 + 3.85835i) q^{41} +(-0.195819 - 0.384317i) q^{42} +(-23.9713 - 23.9713i) q^{43} +(-18.8642 - 39.7258i) q^{44} +(-11.5582 - 4.78755i) q^{45} +(0.0438756 + 0.557492i) q^{46} +(-7.12664 - 9.80897i) q^{47} +(-12.6982 - 3.04856i) q^{48} +(-38.8575 + 76.2621i) q^{49} +(0.983865 - 0.319677i) q^{50} +(-0.462373 - 13.8891i) q^{51} +(-15.2653 - 21.0108i) q^{52} +(29.5974 - 15.0806i) q^{53} +(-0.246594 - 0.595331i) q^{54} +(3.40619 + 16.1619i) q^{55} +(-1.61496 - 3.89885i) q^{56} +(-9.52148 - 8.13211i) q^{57} +(0.375962 + 1.56599i) q^{58} +(-46.7219 + 7.40001i) q^{59} +(4.37237 + 2.22784i) q^{60} +(-3.20895 + 40.7736i) q^{61} +(1.91909 - 1.17602i) q^{62} +(-50.5045 + 82.4159i) q^{63} +(-60.6788 - 19.7157i) q^{64} +(3.73273 + 9.01161i) q^{65} +(-0.223333 + 0.342608i) q^{66} -52.4148 q^{67} +(3.07515 - 67.8952i) q^{68} +(-8.13141 + 5.90781i) q^{69} +(0.123940 + 0.782529i) q^{70} +(9.72067 + 11.3814i) q^{71} +(-0.936555 - 2.88242i) q^{72} +(-80.1304 - 19.2376i) q^{73} +(-0.348451 - 1.45140i) q^{74} +(14.1385 + 12.0754i) q^{75} +(-43.3027 - 43.3027i) q^{76} +(127.451 - 6.45903i) q^{77} +(-0.0924251 + 0.223134i) q^{78} +(62.8671 + 53.6936i) q^{79} +(20.4526 + 12.5334i) q^{80} +(-37.2681 + 51.2951i) q^{81} +(0.488199 + 0.571607i) q^{82} +(-33.0768 - 16.8535i) q^{83} +(22.2857 - 30.6736i) q^{84} +(-7.07591 + 24.5258i) q^{85} +(-0.476458 + 1.46639i) q^{86} +(-20.4678 + 20.4678i) q^{87} +(-2.44134 + 3.17028i) q^{88} -62.3451i q^{89} +(0.0446430 + 0.567243i) q^{90} +(73.2807 - 17.5931i) q^{91} +(-41.9126 + 25.6841i) q^{92} +(36.0446 + 18.3656i) q^{93} +(-0.250351 + 0.491341i) q^{94} +(12.0176 + 19.6109i) q^{95} +(0.416320 + 1.73410i) q^{96} +(154.977 - 12.1970i) q^{97} +3.89282 q^{98} +(91.6137 + 2.55712i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 544 q - 20 q^{2} - 12 q^{3} - 20 q^{5} - 20 q^{6} - 20 q^{7} - 20 q^{8} + 36 q^{9} + 28 q^{11} - 200 q^{12} + 36 q^{14} + 108 q^{15} + 424 q^{16} - 180 q^{17} - 40 q^{18} - 20 q^{19} - 140 q^{20} + 32 q^{22}+ \cdots - 72 q^{99}+O(q^{100}) \) 544 * q - 20 * q^2 - 12 * q^3 - 20 * q^5 - 20 * q^6 - 20 * q^7 - 20 * q^8 + 36 * q^9 + 28 * q^11 - 200 * q^12 + 36 * q^14 + 108 * q^15 + 424 * q^16 - 180 * q^17 - 40 * q^18 - 20 * q^19 - 140 * q^20 + 32 * q^22 - 48 * q^23 + 460 * q^24 - 84 * q^25 + 132 * q^26 - 228 * q^27 - 20 * q^28 - 20 * q^29 - 100 * q^31 + 24 * q^33 + 96 * q^34 - 40 * q^35 + 164 * q^36 - 332 * q^37 - 20 * q^39 - 760 * q^40 - 560 * q^41 + 276 * q^42 - 240 * q^44 - 32 * q^45 - 20 * q^46 + 252 * q^48 - 472 * q^49 - 40 * q^50 - 20 * q^51 + 280 * q^52 + 92 * q^53 - 160 * q^56 + 1060 * q^57 - 1348 * q^58 - 260 * q^59 - 748 * q^60 - 320 * q^61 - 20 * q^62 + 580 * q^63 + 292 * q^66 + 160 * q^67 - 20 * q^68 - 192 * q^69 - 628 * q^70 - 268 * q^71 - 20 * q^73 - 20 * q^74 + 1116 * q^75 + 732 * q^77 + 1232 * q^78 - 20 * q^79 - 936 * q^80 - 684 * q^82 - 380 * q^83 + 1240 * q^84 - 1320 * q^85 - 632 * q^86 - 412 * q^88 - 20 * q^90 + 1204 * q^91 + 540 * q^92 + 1108 * q^93 - 3800 * q^94 + 360 * q^95 - 20 * q^96 + 652 * q^97 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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