LMFDB - Embedded newform 819.2.dk.a.43.40

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(43,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 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("819.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.dk (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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$84$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.40
Character	$\chi$	$=$	819.43
Dual form			819.2.dk.a.400.40

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0786329 + 0.0453987i) q^{2} +(1.72806 - 0.117510i) q^{3} +(-0.995878 + 1.72491i) q^{4} +(0.215002 - 0.124132i) q^{5} +(-0.130548 + 0.0876919i) q^{6} -1.00000i q^{7} -0.362441i q^{8} +(2.97238 - 0.406129i) q^{9} +O(q^{10})$	\(q+(-0.0786329 + 0.0453987i) q^{2} +(1.72806 - 0.117510i) q^{3} +(-0.995878 + 1.72491i) q^{4} +(0.215002 - 0.124132i) q^{5} +(-0.130548 + 0.0876919i) q^{6} -1.00000i q^{7} -0.362441i q^{8} +(2.97238 - 0.406129i) q^{9} +(-0.0112708 + 0.0195217i) q^{10} +(3.63017 - 2.09588i) q^{11} +(-1.51824 + 3.09778i) q^{12} +(-1.61458 + 3.22384i) q^{13} +(0.0453987 + 0.0786329i) q^{14} +(0.356950 - 0.239772i) q^{15} +(-1.97530 - 3.42132i) q^{16} +(3.04852 + 5.28019i) q^{17} +(-0.215289 + 0.166878i) q^{18} +(4.13786 - 2.38900i) q^{19} +0.494480i q^{20} +(-0.117510 - 1.72806i) q^{21} +(-0.190301 + 0.329610i) q^{22} -1.30384 q^{23} +(-0.0425905 - 0.626321i) q^{24} +(-2.46918 + 4.27675i) q^{25} +(-0.0193993 - 0.326800i) q^{26} +(5.08873 - 1.05110i) q^{27} +(1.72491 + 0.995878i) q^{28} +(-0.828897 - 1.43569i) q^{29} +(-0.0171827 + 0.0350590i) q^{30} +(5.08430 - 2.93542i) q^{31} +(0.938415 + 0.541794i) q^{32} +(6.02686 - 4.04839i) q^{33} +(-0.479428 - 0.276798i) q^{34} +(-0.124132 - 0.215002i) q^{35} +(-2.25959 + 5.53155i) q^{36} +(-4.52192 - 2.61073i) q^{37} +(-0.216915 + 0.375708i) q^{38} +(-2.41125 + 5.76072i) q^{39} +(-0.0449904 - 0.0779257i) q^{40} +9.35757i q^{41} +(0.0876919 + 0.130548i) q^{42} +7.41985 q^{43} +8.34896i q^{44} +(0.588655 - 0.456285i) q^{45} +(0.102524 - 0.0591925i) q^{46} +(5.25270 + 3.03265i) q^{47} +(-3.81548 - 5.68013i) q^{48} -1.00000 q^{49} -0.448391i q^{50} +(5.88849 + 8.76625i) q^{51} +(-3.95291 - 5.99555i) q^{52} -10.8656 q^{53} +(-0.352423 + 0.313673i) q^{54} +(0.520330 - 0.901237i) q^{55} -0.362441 q^{56} +(6.86975 - 4.61457i) q^{57} +(0.130357 + 0.0752618i) q^{58} +(3.38619 + 1.95502i) q^{59} +(0.0581063 + 0.854490i) q^{60} -6.12360 q^{61} +(-0.266529 + 0.461642i) q^{62} +(-0.406129 - 2.97238i) q^{63} +7.80282 q^{64} +(0.0530427 + 0.893553i) q^{65} +(-0.290118 + 0.591949i) q^{66} +6.50443i q^{67} -12.1438 q^{68} +(-2.25311 + 0.153214i) q^{69} +(0.0195217 + 0.0112708i) q^{70} +(0.413219 - 0.238572i) q^{71} +(-0.147198 - 1.07731i) q^{72} -6.41037i q^{73} +0.474096 q^{74} +(-3.76433 + 7.68063i) q^{75} +9.51660i q^{76} +(-2.09588 - 3.63017i) q^{77} +(-0.0719255 - 0.562450i) q^{78} +(3.66713 - 6.35166i) q^{79} +(-0.849388 - 0.490395i) q^{80} +(8.67012 - 2.41434i) q^{81} +(-0.424822 - 0.735813i) q^{82} +(-13.9306 - 8.04285i) q^{83} +(3.09778 + 1.51824i) q^{84} +(1.31088 + 0.756834i) q^{85} +(-0.583445 + 0.336852i) q^{86} +(-1.60109 - 2.38356i) q^{87} +(-0.759634 - 1.31572i) q^{88} +(-3.63694 - 2.09979i) q^{89} +(-0.0255729 + 0.0626033i) q^{90} +(3.22384 + 1.61458i) q^{91} +(1.29846 - 2.24900i) q^{92} +(8.44104 - 5.67004i) q^{93} -0.550714 q^{94} +(0.593100 - 1.02728i) q^{95} +(1.68530 + 0.825979i) q^{96} -11.0898i q^{97} +(0.0786329 - 0.0453987i) q^{98} +(9.93906 - 7.70407i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q + 84 q^{4} - 2 q^{9}+O(q^{10}) $ 168 * q + 84 * q^4 - 2 * q^9	$ 168 q + 84 q^{4} - 2 q^{9} + 12 q^{12} + 8 q^{14} - 84 q^{16} + 12 q^{18} - 6 q^{21} + 40 q^{23} - 84 q^{24} + 84 q^{25} + 4 q^{26} - 24 q^{27} + 34 q^{29} + 44 q^{30} + 36 q^{32} + 18 q^{33} + 16 q^{35} + 4 q^{36} - 12 q^{38} - 6 q^{39} - 30 q^{45} - 30 q^{47} - 2 q^{48} - 168 q^{49} - 38 q^{51} + 18 q^{52} - 48 q^{53} + 114 q^{54} + 48 q^{56} - 54 q^{57} + 48 q^{59} + 24 q^{60} + 6 q^{62} - 12 q^{63} - 132 q^{64} - 16 q^{65} - 54 q^{66} - 156 q^{68} - 28 q^{69} + 24 q^{71} + 36 q^{72} - 84 q^{74} + 30 q^{75} - 16 q^{77} + 116 q^{78} - 6 q^{79} - 2 q^{81} - 6 q^{82} + 18 q^{83} - 24 q^{84} + 90 q^{85} - 24 q^{86} + 52 q^{87} + 24 q^{88} - 36 q^{89} - 44 q^{90} - 6 q^{91} + 8 q^{92} - 66 q^{93} + 120 q^{94} - 48 q^{95} - 24 q^{96} + 6 q^{99}+O(q^{100}) $ 168 * q + 84 * q^4 - 2 * q^9 + 12 * q^12 + 8 * q^14 - 84 * q^16 + 12 * q^18 - 6 * q^21 + 40 * q^23 - 84 * q^24 + 84 * q^25 + 4 * q^26 - 24 * q^27 + 34 * q^29 + 44 * q^30 + 36 * q^32 + 18 * q^33 + 16 * q^35 + 4 * q^36 - 12 * q^38 - 6 * q^39 - 30 * q^45 - 30 * q^47 - 2 * q^48 - 168 * q^49 - 38 * q^51 + 18 * q^52 - 48 * q^53 + 114 * q^54 + 48 * q^56 - 54 * q^57 + 48 * q^59 + 24 * q^60 + 6 * q^62 - 12 * q^63 - 132 * q^64 - 16 * q^65 - 54 * q^66 - 156 * q^68 - 28 * q^69 + 24 * q^71 + 36 * q^72 - 84 * q^74 + 30 * q^75 - 16 * q^77 + 116 * q^78 - 6 * q^79 - 2 * q^81 - 6 * q^82 + 18 * q^83 - 24 * q^84 + 90 * q^85 - 24 * q^86 + 52 * q^87 + 24 * q^88 - 36 * q^89 - 44 * q^90 - 6 * q^91 + 8 * q^92 - 66 * q^93 + 120 * q^94 - 48 * q^95 - 24 * q^96 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.0786329	+	0.0453987i	−0.0556019	+	0.0321018i	−0.527543	−	0.849528i	$-0.676887\pi$
$2$	−0.0786329	+	0.0453987i	−0.0556019	+	0.0321018i	0.471941	+	0.881630i	$0.343553\pi$
$3$	1.72806	−	0.117510i	0.997696	−	0.0678445i
$3$	1.72806	−	0.117510i	0.997696	−	0.0678445i
$4$	−0.995878	+	1.72491i	−0.497939	+	0.862456i
$5$	0.215002	−	0.124132i	0.0961519	−	0.0555133i	−0.451153	−	0.892447i	$-0.648987\pi$
$5$	0.215002	−	0.124132i	0.0961519	−	0.0555133i	0.547305	+	0.836933i	$0.315654\pi$
$6$	−0.130548	+	0.0876919i	−0.0532958	+	0.0358001i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		−	0.362441i		−	0.128142i
$9$	2.97238	−	0.406129i	0.990794	−	0.135376i
$10$	−0.0112708	+	0.0195217i	−0.00356415	+	0.00617329i
$11$	3.63017	−	2.09588i	1.09454	−	0.631931i	0.159757	−	0.987156i	$-0.448929\pi$
$11$	3.63017	−	2.09588i	1.09454	−	0.631931i	0.934781	+	0.355225i	$0.115596\pi$
$12$	−1.51824	+	3.09778i	−0.438279	+	0.894251i
$13$	−1.61458	+	3.22384i	−0.447803	+	0.894132i
$13$	−1.61458	+	3.22384i	−0.447803	+	0.894132i
$14$	0.0453987	+	0.0786329i	0.0121333	+	0.0210155i
$15$	0.356950	−	0.239772i	0.0921641	−	0.0619088i
$16$	−1.97530	−	3.42132i	−0.493825	−	0.855331i
$17$	3.04852	+	5.28019i	0.739374	+	1.28063i	0.952778	+	0.303669i	$0.0982117\pi$
$17$	3.04852	+	5.28019i	0.739374	+	1.28063i	−0.213404	+	0.976964i	$0.568455\pi$
$18$	−0.215289	+	0.166878i	−0.0507442	+	0.0393334i
$19$	4.13786	−	2.38900i	0.949291	−	0.548074i	0.0564306	−	0.998407i	$-0.482028\pi$
$19$	4.13786	−	2.38900i	0.949291	−	0.548074i	0.892861	+	0.450333i	$0.148695\pi$
$20$			0.494480i			0.110569i
$21$	−0.117510	−	1.72806i	−0.0256428	−	0.377094i
$22$	−0.190301	+	0.329610i	−0.0405722	+	0.0702732i
$23$	−1.30384			−0.271869			−0.135934	−	0.990718i	$-0.543404\pi$
$23$	−1.30384			−0.271869			−0.135934	+	0.990718i	$0.543404\pi$
$24$	−0.0425905	−	0.626321i	−0.00869375	−	0.127847i
$25$	−2.46918	+	4.27675i	−0.493837	+	0.855350i
$26$	−0.0193993	−	0.326800i	−0.00380452	−	0.0640907i
$27$	5.08873	−	1.05110i	0.979327	−	0.202284i
$28$	1.72491	+	0.995878i	0.325978	+	0.188203i
$29$	−0.828897	−	1.43569i	−0.153922	−	0.266601i	0.778744	−	0.627342i	$-0.215857\pi$
$29$	−0.828897	−	1.43569i	−0.153922	−	0.266601i	−0.932666	+	0.360741i	$0.882524\pi$
$30$	−0.0171827	+	0.0350590i	−0.00313712	+	0.00640088i
$31$	5.08430	−	2.93542i	0.913168	−	0.527218i	0.0317186	−	0.999497i	$-0.489902\pi$
$31$	5.08430	−	2.93542i	0.913168	−	0.527218i	0.881449	+	0.472279i	$0.156569\pi$
$32$	0.938415	+	0.541794i	0.165890	+	0.0957765i
$33$	6.02686	−	4.04839i	1.04914	−	0.704734i
$34$	−0.479428	−	0.276798i	−0.0822212	−	0.0474704i
$35$	−0.124132	−	0.215002i	−0.0209821	−	0.0363420i
$36$	−2.25959	+	5.53155i	−0.376599	+	0.921925i
$37$	−4.52192	−	2.61073i	−0.743399	−	0.429201i	0.0799050	−	0.996802i	$-0.474538\pi$
$37$	−4.52192	−	2.61073i	−0.743399	−	0.429201i	−0.823304	+	0.567601i	$0.807872\pi$
$38$	−0.216915	+	0.375708i	−0.0351883	+	0.0609478i
$39$	−2.41125	+	5.76072i	−0.386109	+	0.922453i
$40$	−0.0449904	−	0.0779257i	−0.00711361	−	0.0123211i
$41$			9.35757i			1.46141i	0.682695	+	0.730704i	$0.260808\pi$
$41$			9.35757i			1.46141i	−0.682695	+	0.730704i	$0.739192\pi$
$42$	0.0876919	+	0.130548i	0.0135312	+	0.0201439i
$43$	7.41985			1.13152			0.565758	−	0.824571i	$-0.308584\pi$
$43$	7.41985			1.13152			0.565758	+	0.824571i	$0.308584\pi$
$44$			8.34896i			1.25865i
$45$	0.588655	−	0.456285i	0.0877516	−	0.0680190i
$46$	0.102524	−	0.0591925i	0.0151164	−	0.00872746i
$47$	5.25270	+	3.03265i	0.766185	+	0.442357i	0.831512	−	0.555507i	$-0.187476\pi$
$47$	5.25270	+	3.03265i	0.766185	+	0.442357i	−0.0653270	+	0.997864i	$0.520809\pi$
$48$	−3.81548	−	5.68013i	−0.550717	−	0.819857i
$49$	−1.00000			−0.142857
$50$		−	0.448391i		−	0.0634121i
$51$	5.88849	+	8.76625i	0.824554	+	1.22752i
$52$	−3.95291	−	5.99555i	−0.548171	−	0.831434i
$53$	−10.8656			−1.49251			−0.746255	−	0.665660i	$-0.768150\pi$
$53$	−10.8656			−1.49251			−0.746255	+	0.665660i	$0.768150\pi$
$54$	−0.352423	+	0.313673i	−0.0479587	+	0.0426855i
$55$	0.520330	−	0.901237i	0.0701612	−	0.121523i
$56$	−0.362441			−0.0484333
$57$	6.86975	−	4.61457i	0.909920	−	0.611215i
$58$	0.130357	+	0.0752618i	0.0171167	+	0.00988236i
$59$	3.38619	+	1.95502i	0.440845	+	0.254522i	0.703956	−	0.710244i	$-0.251415\pi$
$59$	3.38619	+	1.95502i	0.440845	+	0.254522i	−0.263111	+	0.964766i	$0.584749\pi$
$60$	0.0581063	+	0.854490i	0.00750150	+	0.110314i
$61$	−6.12360			−0.784047			−0.392023	−	0.919955i	$-0.628225\pi$
$61$	−6.12360			−0.784047			−0.392023	+	0.919955i	$0.628225\pi$
$62$	−0.266529	+	0.461642i	−0.0338492	+	0.0586286i
$63$	−0.406129	−	2.97238i	−0.0511674	−	0.374485i
$64$	7.80282			0.975352
$65$	0.0530427	+	0.893553i	0.00657913	+	0.110832i
$66$	−0.290118	+	0.591949i	−0.0357111	+	0.0728638i
$67$			6.50443i			0.794643i	0.917679	+	0.397321i	$0.130060\pi$
$67$			6.50443i			0.794643i	−0.917679	+	0.397321i	$0.869940\pi$
$68$	−12.1438			−1.47265
$69$	−2.25311	+	0.153214i	−0.271242	+	0.0184448i
$70$	0.0195217	+	0.0112708i	0.00233328	+	0.00134712i
$71$	0.413219	−	0.238572i	0.0490401	−	0.0283133i	−0.475279	−	0.879835i	$-0.657653\pi$
$71$	0.413219	−	0.238572i	0.0490401	−	0.0283133i	0.524320	+	0.851522i	$0.324320\pi$
$72$	−0.147198	−	1.07731i	−0.0173474	−	0.126963i
$73$		−	6.41037i		−	0.750278i	−0.926969	−	0.375139i	$-0.877595\pi$
$73$		−	6.41037i		−	0.750278i	0.926969	−	0.375139i	$-0.122405\pi$
$74$	0.474096			0.0551125
$75$	−3.76433	+	7.68063i	−0.434668	+	0.886883i
$76$			9.51660i			1.09163i
$77$	−2.09588	−	3.63017i	−0.238848	−	0.413696i
$78$	−0.0719255	−	0.562450i	−0.00814396	−	0.0636849i
$79$	3.66713	−	6.35166i	0.412585	−	0.714618i	−0.582587	−	0.812768i	$-0.697959\pi$
$79$	3.66713	−	6.35166i	0.412585	−	0.714618i	0.995172	+	0.0981508i	$0.0312928\pi$
$80$	−0.849388	−	0.490395i	−0.0949645	−	0.0548278i
$81$	8.67012	−	2.41434i	0.963347	−	0.268260i
$82$	−0.424822	−	0.735813i	−0.0469137	−	0.0812570i
$83$	−13.9306	−	8.04285i	−1.52908	−	0.882818i	−0.999400	−	0.0346227i	$-0.988977\pi$
$83$	−13.9306	−	8.04285i	−1.52908	−	0.882818i	−0.529684	−	0.848195i	$-0.677690\pi$
$84$	3.09778	+	1.51824i	0.337995	+	0.165654i
$85$	1.31088	+	0.756834i	0.142184	+	0.0820902i
$86$	−0.583445	+	0.336852i	−0.0629145	+	0.0363237i
$87$	−1.60109	−	2.38356i	−0.171655	−	0.255544i
$88$	−0.759634	−	1.31572i	−0.0809772	−	0.140257i
$89$	−3.63694	−	2.09979i	−0.385515	−	0.222577i	0.294700	−	0.955590i	$-0.404780\pi$
$89$	−3.63694	−	2.09979i	−0.385515	−	0.222577i	−0.680215	+	0.733013i	$0.738114\pi$
$90$	−0.0255729	+	0.0626033i	−0.00269562	+	0.00659896i
$91$	3.22384	+	1.61458i	0.337950	+	0.169254i
$92$	1.29846	−	2.24900i	0.135374	−	0.234475i
$93$	8.44104	−	5.67004i	0.875295	−	0.587956i
$94$	−0.550714			−0.0568018
$95$	0.593100	−	1.02728i	0.0608508	−	0.105397i
$96$	1.68530	+	0.825979i	0.172005	+	0.0843011i
$97$		−	11.0898i		−	1.12600i	−0.826457	−	0.563000i	$-0.809647\pi$
$97$		−	11.0898i		−	1.12600i	0.826457	−	0.563000i	$-0.190353\pi$
$98$	0.0786329	−	0.0453987i	0.00794313	−	0.00458597i
$99$	9.93906	−	7.70407i	0.998913	−	0.774289i
$100$	−4.91801	−	8.51824i	−0.491801	−	0.851824i
$101$	−0.573753	−	0.993770i	−0.0570906	−	0.0988838i	0.836068	−	0.548626i	$-0.184849\pi$
$101$	−0.573753	−	0.993770i	−0.0570906	−	0.0988838i	−0.893158	+	0.449743i	$0.851516\pi$
$102$	−0.861006	−	0.421985i	−0.0852523	−	0.0417828i
$103$	−8.55696	−	14.8211i	−0.843143	−	1.46037i	−0.887225	−	0.461338i	$-0.847370\pi$
$103$	−8.55696	−	14.8211i	−0.843143	−	1.46037i	0.0440819	−	0.999028i	$-0.485964\pi$
$104$	1.16845	+	0.585190i	0.114576	+	0.0573826i
$105$	−0.239772	−	0.356950i	−0.0233993	−	0.0348348i
$106$	0.854398	−	0.493287i	0.0829864	−	0.0479122i
$107$	−3.39001	+	5.87167i	−0.327725	+	0.567636i	−0.982060	−	0.188569i	$-0.939615\pi$
$107$	−3.39001	+	5.87167i	−0.327725	+	0.567636i	0.654335	+	0.756205i	$0.272948\pi$
$108$	−3.25470	+	9.82438i	−0.313184	+	0.945351i
$109$			4.64711i			0.445112i	0.974920	+	0.222556i	$0.0714401\pi$
$109$			4.64711i			0.445112i	−0.974920	+	0.222556i	$0.928560\pi$
$110$			0.0944893i			0.00900920i
$111$	−8.12093	−	3.98013i	−0.770805	−	0.377777i
$112$	−3.42132	+	1.97530i	−0.323285	+	0.186648i
$113$	4.92021	−	8.52206i	0.462855	−	0.801688i	−0.536247	−	0.844061i	$-0.680158\pi$
$113$	4.92021	−	8.52206i	0.462855	−	0.801688i	0.999102	+	0.0423731i	$0.0134918\pi$
$114$	−0.330693	+	0.674735i	−0.0309722	+	0.0631947i
$115$	−0.280328	+	0.161847i	−0.0261407	+	0.0150923i
$116$	3.30192			0.306576
$117$	−3.48985	+	10.2382i	−0.322636	+	0.946523i
$118$	−0.355022			−0.0326824
$119$	5.28019	−	3.04852i	0.484034	−	0.279457i
$120$	−0.0869032	−	0.129373i	−0.00793314	−	0.0118101i
$121$	3.28542	−	5.69052i	0.298675	−	0.517320i
$122$	0.481517	−	0.278004i	0.0435945	−	0.0251693i
$123$	1.09961	+	16.1704i	0.0991484	+	1.45804i
$124$			11.6933i			1.05009i
$125$			2.46733i			0.220685i
$126$	0.166878	+	0.215289i	0.0148666	+	0.0191795i
$127$	3.18365	−	5.51424i	0.282503	−	0.489310i	−0.689497	−	0.724288i	$-0.742169\pi$
$127$	3.18365	−	5.51424i	0.282503	−	0.489310i	0.972001	+	0.234978i	$0.0755019\pi$
$128$	−2.49039	+	1.43783i	−0.220121	+	0.127087i
$129$	12.8219	−	0.871907i	1.12891	−	0.0767672i
$130$	−0.0447371	−	0.0678546i	−0.00392370	−	0.00595124i
$131$	−0.408486	−	0.707518i	−0.0356896	−	0.0618162i	0.847629	−	0.530590i	$-0.178029\pi$
$131$	−0.408486	−	0.707518i	−0.0356896	−	0.0618162i	−0.883318	+	0.468773i	$0.844696\pi$
$132$	0.981087	+	14.4275i	0.0853927	+	1.25575i
$133$	−2.38900	−	4.13786i	−0.207152	−	0.358798i
$134$	−0.295293	−	0.511463i	−0.0255094	−	0.0441836i
$135$	0.963614	−	0.857661i	0.0829347	−	0.0738157i
$136$	1.91376	−	1.10491i	0.164103	−	0.0947451i
$137$			17.4176i			1.48809i	0.668131	+	0.744044i	$0.267095\pi$
$137$			17.4176i			1.48809i	−0.668131	+	0.744044i	$0.732905\pi$
$138$	0.170213	−	0.114336i	0.0144895	−	0.00973291i
$139$	5.11812	−	8.86485i	0.434114	−	0.751907i	−0.563109	−	0.826382i	$-0.690395\pi$
$139$	5.11812	−	8.86485i	0.434114	−	0.751907i	0.997223	+	0.0744757i	$0.0237283\pi$
$140$	0.494480			0.0417912
$141$	9.43335	+	4.62335i	0.794431	+	0.389356i
$142$	−0.0216618	+	0.0375193i	−0.00181781	+	0.00314855i
$143$	0.895590	+	15.0870i	0.0748930	+	1.26164i
$144$	−7.26085	−	9.36725i	−0.605071	−	0.780604i
$145$	−0.356430	−	0.205785i	−0.0295999	−	0.0170895i
$146$	0.291023	+	0.504067i	0.0240852	+	0.0417168i
$147$	−1.72806	+	0.117510i	−0.142528	+	0.00969207i
$148$	9.00656	−	5.19994i	0.740334	−	0.427432i
$149$	2.22584	+	1.28509i	0.182348	+	0.105279i	0.588395	−	0.808573i	$-0.299760\pi$
$149$	2.22584	+	1.28509i	0.182348	+	0.105279i	−0.406047	+	0.913852i	$0.633093\pi$
$150$	−0.0526905	−	0.774847i	−0.00430216	−	0.0632660i
$151$	−8.85960	−	5.11509i	−0.720984	−	0.416261i	0.0941305	−	0.995560i	$-0.469993\pi$
$151$	−8.85960	−	5.11509i	−0.720984	−	0.416261i	−0.815115	+	0.579299i	$0.803326\pi$
$152$	−0.865872	−	1.49973i	−0.0702315	−	0.121644i
$153$	11.2058	+	14.4566i	0.905935	+	1.16875i
$154$	0.329610	+	0.190301i	0.0265608	+	0.0153349i
$155$	0.728757	−	1.26224i	0.0585352	−	0.101386i
$156$	−7.53541	−	9.89617i	−0.603316	−	0.792327i
$157$	−8.24495	−	14.2807i	−0.658018	−	1.13972i	−0.981128	−	0.193360i	$-0.938062\pi$
$157$	−8.24495	−	14.2807i	−0.658018	−	1.13972i	0.323110	−	0.946362i	$-0.395272\pi$
$158$			0.665933i			0.0529788i
$159$	−18.7765	+	1.27682i	−1.48907	+	0.101259i
$160$	0.269015			0.0212675
$161$			1.30384i			0.102757i
$162$	−0.572149	+	0.583459i	−0.0449523	+	0.0458409i
$163$	−5.81904	+	3.35963i	−0.455783	+	0.263146i	−0.710269	−	0.703930i	$-0.751427\pi$
$163$	−5.81904	+	3.35963i	−0.455783	+	0.263146i	0.254487	+	0.967076i	$0.418093\pi$
$164$	−16.1410	−	9.31900i	−1.26040	−	0.727691i
$165$	0.793256	−	1.61854i	0.0617549	−	0.126003i
$166$	1.46054			0.113360
$167$		−	21.9842i		−	1.70119i	−0.525822	−	0.850594i	$-0.676242\pi$
$167$		−	21.9842i		−	1.70119i	0.525822	−	0.850594i	$-0.323758\pi$
$168$	−0.626321	+	0.0425905i	−0.0483217	+	0.00328593i
$169$	−7.78628	−	10.4103i	−0.598945	−	0.800790i
$170$	−0.137437			−0.0105410
$171$	11.3291	−	8.78152i	0.866356	−	0.671540i
$172$	−7.38927	+	12.7986i	−0.563426	+	0.975883i
$173$	−25.4451			−1.93455			−0.967277	−	0.253723i	$-0.918345\pi$
$173$	−25.4451			−1.93455			−0.967277	+	0.253723i	$0.918345\pi$
$174$	0.234109	+	0.114739i	0.0177478	+	0.00869831i
$175$	4.27675	+	2.46918i	0.323292	+	0.186653i
$176$	−14.3414	−	8.27999i	−1.08102	−	0.624128i
$177$	6.08128	+	2.98048i	0.457097	+	0.224027i
$178$	0.381311			0.0285805
$179$	−10.7336	+	18.5911i	−0.802265	+	1.38956i	0.115858	+	0.993266i	$0.463038\pi$
$179$	−10.7336	+	18.5911i	−0.802265	+	1.38956i	−0.918122	+	0.396297i	$0.870295\pi$
$180$	0.200822	+	1.46978i	0.0149684	+	0.109551i
$181$	14.5711			1.08306			0.541532	−	0.840680i	$-0.317845\pi$
$181$	14.5711			1.08306			0.541532	+	0.840680i	$0.317845\pi$
$182$	−0.326800	+	0.0193993i	−0.0242240	+	0.00143797i
$183$	−10.5820	+	0.719585i	−0.782240	+	0.0531933i
$184$			0.472564i			0.0348379i
$185$	−1.29630			−0.0953056
$186$	−0.406331	+	0.829065i	−0.0297936	+	0.0607900i
$187$	22.1333	+	12.7786i	1.61854	+	0.934467i
$188$	−10.4621	+	6.04029i	−0.763027	+	0.440534i
$189$	−1.05110	−	5.08873i	−0.0764563	−	0.370151i
$190$			0.107704i			0.00781367i
$191$	−6.82420			−0.493782			−0.246891	−	0.969043i	$-0.579409\pi$
$191$	−6.82420			−0.493782			−0.246891	+	0.969043i	$0.579409\pi$
$192$	13.4837	−	0.916910i	0.973105	−	0.0661723i
$193$		−	8.37235i		−	0.602655i	−0.953521	−	0.301327i	$-0.902570\pi$
$193$		−	8.37235i		−	0.602655i	0.953521	−	0.301327i	$-0.0974297\pi$
$194$	0.503464	+	0.872025i	0.0361466	+	0.0626077i
$195$	0.196662	+	1.53788i	0.0140833	+	0.110130i
$196$	0.995878	−	1.72491i	0.0711341	−	0.123208i
$197$	4.82227	+	2.78414i	0.343573	+	0.198362i	0.661851	−	0.749636i	$-0.269771\pi$
$197$	4.82227	+	2.78414i	0.343573	+	0.198362i	−0.318278	+	0.947997i	$0.603105\pi$
$198$	−0.431782	+	1.05701i	−0.0306854	+	0.0751188i
$199$	−4.99237	−	8.64704i	−0.353900	−	0.612972i	0.633029	−	0.774128i	$-0.281811\pi$
$199$	−4.99237	−	8.64704i	−0.353900	−	0.612972i	−0.986929	+	0.161155i	$0.948478\pi$
$200$	1.55007	+	0.894934i	0.109607	+	0.0632814i
$201$	0.764336	+	11.2401i	0.0539121	+	0.792812i
$202$	0.0902318	+	0.0520954i	0.00634869	+	0.00366542i
$203$	−1.43569	+	0.828897i	−0.100766	+	0.0581772i
$204$	−20.9852	+	1.42702i	−1.46926	+	0.0999113i
$205$	1.16157	+	2.01190i	0.0811276	+	0.140517i
$206$	1.34572	+	0.776951i	0.0937606	+	0.0541327i
$207$	−3.87550	+	0.529525i	−0.269366	+	0.0368046i
$208$	14.2191	−	0.844066i	0.985915	−	0.0585254i
$209$	10.0141	−	17.3449i	0.692690	−	1.19977i
$210$	0.0350590	+	0.0171827i	0.00241930	+	0.00118572i
$211$	−18.6837			−1.28624			−0.643118	−	0.765767i	$-0.722359\pi$
$211$	−18.6837			−1.28624			−0.643118	+	0.765767i	$0.722359\pi$
$212$	10.8209	−	18.7423i	0.743179	−	1.28722i
$213$	0.686033	−	0.460825i	0.0470062	−	0.0315752i
$214$		−	0.615609i		−	0.0420822i
$215$	1.59528	−	0.921038i	0.108797	−	0.0628143i
$216$	−0.380962	−	1.84437i	−0.0259212	−	0.125493i
$217$	−2.93542	−	5.08430i	−0.199269	−	0.345145i
$218$	−0.210973	−	0.365416i	−0.0142889	−	0.0247491i
$219$	−0.753284	−	11.0775i	−0.0509022	−	0.748549i
$220$	1.03637	+	1.79505i	0.0698720	+	0.121022i
$221$	−21.9445	+	1.30266i	−1.47615	+	0.0876265i
$222$	0.819266	−	0.0557110i	0.0549855	−	0.00373908i
$223$	−13.3816	+	7.72586i	−0.896097	+	0.517362i	−0.875932	−	0.482435i	$-0.839753\pi$
$223$	−13.3816	+	7.72586i	−0.896097	+	0.517362i	−0.0201654	+	0.999797i	$0.506419\pi$
$224$	0.541794	−	0.938415i	0.0362001	−	0.0627005i
$225$	−5.60244	+	13.7149i	−0.373496	+	0.914330i
$226$			0.893486i			0.0594338i
$227$			13.3297i			0.884726i	0.896836	+	0.442363i	$0.145860\pi$
$227$			13.3297i			0.884726i	−0.896836	+	0.442363i	$0.854140\pi$
$228$	1.11830	+	16.4453i	0.0740610	+	1.08911i
$229$	20.4567	−	11.8107i	1.35182	−	0.780472i	0.363314	−	0.931667i	$-0.381645\pi$
$229$	20.4567	−	11.8107i	1.35182	−	0.780472i	0.988504	+	0.151195i	$0.0483121\pi$
$230$	0.0146953	−	0.0254530i	0.000968981	−	0.00167832i
$231$	−4.04839	−	6.02686i	−0.266364	−	0.396539i
$232$	−0.520354	+	0.300427i	−0.0341629	+	0.0197240i
$233$	−4.96236			−0.325095			−0.162548	−	0.986701i	$-0.551971\pi$
$233$	−4.96236			−0.325095			−0.162548	+	0.986701i	$0.551971\pi$
$234$	−0.190385	−	0.963495i	−0.0124459	−	0.0629857i
$235$	1.50579			0.0982269
$236$	−6.74447	+	3.89392i	−0.439028	+	0.253473i
$237$	5.59064	−	11.4070i	0.363151	−	0.740963i
$238$	−0.276798	+	0.479428i	−0.0179421	+	0.0310767i
$239$	9.88126	−	5.70495i	0.639165	−	0.369022i	−0.145128	−	0.989413i	$-0.546359\pi$
$239$	9.88126	−	5.70495i	0.639165	−	0.369022i	0.784293	+	0.620391i	$0.213026\pi$
$240$	−1.52542	−	0.747620i	−0.0984655	−	0.0482586i
$241$			1.76217i			0.113511i	0.998388	+	0.0567557i	$0.0180756\pi$
$241$			1.76217i			0.113511i	−0.998388	+	0.0567557i	$0.981924\pi$
$242$			0.596616i			0.0383520i
$243$	14.6988	−	5.19095i	0.942927	−	0.333000i
$244$	6.09836	−	10.5627i	0.390408	−	0.676206i
$245$	−0.215002	+	0.124132i	−0.0137360	+	0.00793048i
$246$	−0.820583	−	1.22161i	−0.0523185	−	0.0778869i
$247$	1.02084	+	17.1970i	0.0649546	+	1.09422i
$248$	−1.06392	−	1.84276i	−0.0675589	−	0.117015i
$249$	−25.0181	−	12.2615i	−1.58546	−	0.777043i
$250$	−0.112014	−	0.194013i	−0.00708437	−	0.0122705i
$251$	−3.29409	−	5.70554i	−0.207921	−	0.360130i	0.743138	−	0.669138i	$-0.233336\pi$
$251$	−3.29409	−	5.70554i	−0.207921	−	0.360130i	−0.951060	+	0.309008i	$0.900003\pi$
$252$	5.53155	+	2.25959i	0.348455	+	0.142341i
$253$	−4.73314	+	2.73268i	−0.297570	+	0.171802i
$254$			0.578135i			0.0362754i
$255$	2.35421	+	1.15381i	0.147426	+	0.0722546i
$256$	−7.67227	+	13.2888i	−0.479517	+	0.830547i
$257$	12.3642			0.771255			0.385627	−	0.922655i	$-0.373985\pi$
$257$	12.3642			0.771255			0.385627	+	0.922655i	$0.373985\pi$
$258$	−0.968644	+	0.650661i	−0.0603051	+	0.0405084i
$259$	−2.61073	+	4.52192i	−0.162223	+	0.280978i
$260$	−1.59412	−	0.798375i	−0.0988633	−	0.0495131i
$261$	−3.04688	−	3.93079i	−0.188597	−	0.243310i
$262$	0.0642409	+	0.0370895i	0.00396882	+	0.00229140i
$263$	8.72654	+	15.1148i	0.538102	+	0.932019i	0.999006	+	0.0445698i	$0.0141917\pi$
$263$	8.72654	+	15.1148i	0.538102	+	0.932019i	−0.460905	+	0.887450i	$0.652475\pi$
$264$	−1.46730	−	2.18439i	−0.0903063	−	0.134440i
$265$	−2.33614	+	1.34877i	−0.143508	+	0.0828543i
$266$	0.375708	+	0.216915i	0.0230361	+	0.0132999i
$267$	−6.53160	−	3.20118i	−0.399727	−	0.195909i
$268$	−11.2196	−	6.47762i	−0.685344	−	0.395684i
$269$	2.23646	+	3.87367i	0.136360	+	0.236182i	0.926116	−	0.377239i	$-0.123126\pi$
$269$	2.23646	+	3.87367i	0.136360	+	0.236182i	−0.789756	+	0.613421i	$0.789793\pi$
$270$	−0.0368350	+	0.111187i	−0.00224171	+	0.00676664i
$271$	−15.7347	−	9.08442i	−0.955814	−	0.551839i	−0.0609315	−	0.998142i	$-0.519407\pi$
$271$	−15.7347	−	9.08442i	−0.955814	−	0.551839i	−0.894882	+	0.446303i	$0.852740\pi$
$272$	12.0435	−	20.8599i	0.730243	−	1.26482i
$273$	5.76072	+	2.41125i	0.348654	+	0.145936i
$274$	−0.790738	−	1.36960i	−0.0477702	−	0.0827404i
$275$			20.7004i			1.24828i
$276$	1.97954	−	4.03899i	0.119154	−	0.243119i
$277$	0.0700777			0.00421056			0.00210528	−	0.999998i	$-0.499330\pi$
$277$	0.0700777			0.00421056			0.00210528	+	0.999998i	$0.499330\pi$
$278$			0.929426i			0.0557432i
$279$	13.9203	−	10.7901i	0.833388	−	0.645985i
$280$	−0.0779257	+	0.0449904i	−0.00465695	+	0.00268869i
$281$	−14.9845	−	8.65133i	−0.893903	−	0.516095i	−0.0186857	−	0.999825i	$-0.505948\pi$
$281$	−14.9845	−	8.65133i	−0.893903	−	0.516095i	−0.875217	+	0.483730i	$0.839282\pi$
$282$	−0.951666	+	0.0647144i	−0.0566709	+	0.00385369i
$283$	−33.6033			−1.99751			−0.998756	−	0.0498695i	$-0.984119\pi$
$283$	−33.6033			−1.99751			−0.998756	+	0.0498695i	$0.984119\pi$
$284$			0.950355i			0.0563932i
$285$	0.904197	−	1.84490i	0.0535600	−	0.109282i
$286$	−0.755356	−	1.14568i	−0.0446651	−	0.0677455i
$287$	9.35757			0.552360
$288$	3.00937	+	1.22930i	0.177329	+	0.0724373i
$289$	−10.0869	+	17.4710i	−0.593348	+	1.02771i
$290$	0.0373695			0.00219441
$291$	−1.30316	−	19.1639i	−0.0763929	−	1.12341i
$292$	11.0573	+	6.38395i	0.647081	+	0.373592i
$293$	20.6110	+	11.8998i	1.20411	+	0.695192i	0.961466	−	0.274924i	$-0.0886527\pi$
$293$	20.6110	+	11.8998i	1.20411	+	0.695192i	0.242642	+	0.970116i	$0.421986\pi$
$294$	0.130548	−	0.0876919i	0.00761369	−	0.00511430i
$295$	0.970719			0.0565175
$296$	−0.946237	+	1.63893i	−0.0549989	+	0.0952609i
$297$	16.2700	−	14.4810i	0.944080	−	0.840275i
$298$	−0.233366			−0.0135185
$299$	2.10514	−	4.20336i	0.121744	−	0.243086i
$300$	−9.49959	−	14.1421i	−0.548459	−	0.816495i
$301$		−	7.41985i		−	0.427673i
$302$	0.928876			0.0534508
$303$	−1.10826	−	1.64987i	−0.0636678	−	0.0947827i
$304$	−16.3471	−	9.43798i	−0.937568	−	0.541305i
$305$	−1.31659	+	0.760132i	−0.0753876	+	0.0435251i
$306$	−1.53746	−	0.628039i	−0.0878906	−	0.0359026i
$307$		−	0.710917i		−	0.0405742i	−0.999794	−	0.0202871i	$-0.993542\pi$
$307$		−	0.710917i		−	0.0405742i	0.999794	−	0.0202871i	$-0.00645802\pi$
$308$	8.34896			0.475726
$309$	−16.5286	−	24.6062i	−0.940278	−	1.39980i
$310$			0.132339i			0.00751633i
$311$	−3.55087	−	6.15029i	−0.201351	−	0.348751i	0.747613	−	0.664135i	$-0.231200\pi$
$311$	−3.55087	−	6.15029i	−0.201351	−	0.348751i	−0.948964	+	0.315384i	$0.897867\pi$
$312$	2.08792	+	0.873938i	0.118205	+	0.0494770i
$313$	−4.76973	+	8.26141i	−0.269601	+	0.466962i	−0.968759	−	0.248005i	$-0.920225\pi$
$313$	−4.76973	+	8.26141i	−0.269601	+	0.466962i	0.699158	+	0.714967i	$0.253558\pi$
$314$	1.29665	+	0.748621i	0.0731741	+	0.0422471i
$315$	−0.456285	−	0.588655i	−0.0257088	−	0.0331670i
$316$	7.30403	+	12.6510i	0.410884	+	0.711672i
$317$	14.6877	+	8.47996i	0.824945	+	0.476282i	0.852119	−	0.523348i	$-0.175317\pi$
$317$	14.6877	+	8.47996i	0.824945	+	0.476282i	−0.0271737	+	0.999631i	$0.508651\pi$
$318$	1.41848	−	0.952829i	0.0795446	−	0.0534320i
$319$	−6.01808	−	3.47454i	−0.336948	−	0.194537i
$320$	1.67762	−	0.968576i	0.0937820	−	0.0541451i
$321$	−5.16816	+	10.5450i	−0.288459	+	0.588562i
$322$	−0.0591925	−	0.102524i	−0.00329867	−	0.00571346i
$323$	25.2287	+	14.5658i	1.40376	+	0.810463i
$324$	−4.46986	+	17.3596i	−0.248325	+	0.964421i
$325$	−9.80087	−	14.8654i	−0.543654	−	0.824584i
$326$	0.305046	−	0.528355i	0.0168949	−	0.0292629i
$327$	0.546082	+	8.03048i	0.0301984	+	0.444087i
$328$	3.39157			0.187268
$329$	3.03265	−	5.25270i	0.167195	−	0.289591i
$330$	0.0111034	+	0.163283i	0.000611224	+	0.00898844i
$331$			0.459834i			0.0252748i	0.999920	+	0.0126374i	$0.00402271\pi$
$331$			0.459834i			0.0252748i	−0.999920	+	0.0126374i	$0.995977\pi$
$332$	27.7464	−	16.0194i	1.52278	−	0.879178i
$333$	−14.5012	−	5.92361i	−0.794659	−	0.324612i
$334$	0.998055	+	1.72868i	0.0546112	+	0.0945893i
$335$	0.807406	+	1.39847i	0.0441133	+	0.0764064i
$336$	−5.68013	+	3.81548i	−0.309877	+	0.208151i
$337$	14.9959	+	25.9736i	0.816877	+	1.41487i	0.907972	+	0.419030i	$0.137630\pi$
$337$	14.9959	+	25.9736i	0.816877	+	1.41487i	−0.0910958	+	0.995842i	$0.529037\pi$
$338$	1.08487	+	0.465103i	0.0590092	+	0.0252983i
$339$	7.50100	−	15.3048i	0.407398	−	0.831243i
$340$	−2.61094	+	1.50743i	−0.141598	+	0.0817518i
$341$	12.3046	−	21.3122i	0.666331	−	1.15412i
$342$	−0.492169	+	1.20484i	−0.0266134	+	0.0651504i
$343$			1.00000i			0.0539949i
$344$		−	2.68926i		−	0.144995i
$345$	−0.465404	+	0.312623i	−0.0250565	+	0.0168311i
$346$	2.00082	−	1.15518i	0.107565	−	0.0621026i
$347$	17.9348	−	31.0639i	0.962788	−	1.66760i	0.247344	−	0.968928i	$-0.420442\pi$
$347$	17.9348	−	31.0639i	0.962788	−	1.66760i	0.715444	−	0.698670i	$-0.246224\pi$
$348$	5.70592	−	0.388009i	0.305869	−	0.0207995i
$349$	26.3197	−	15.1957i	1.40886	−	0.813406i	0.413582	−	0.910467i	$-0.364277\pi$
$349$	26.3197	−	15.1957i	1.40886	−	0.813406i	0.995278	+	0.0970608i	$0.0309441\pi$
$350$	−0.448391			−0.0239675
$351$	−4.82757	+	18.1023i	−0.257677	+	0.966231i
$352$	4.54214			0.242097
$353$	−29.0215	+	16.7555i	−1.54466	+	0.891808i	−0.546121	+	0.837707i	$0.683896\pi$
$353$	−29.0215	+	16.7555i	−1.54466	+	0.891808i	−0.998535	+	0.0541011i	$0.982771\pi$
$354$	−0.613499	+	0.0417187i	−0.0326071	+	0.00221732i
$355$	0.0592287	−	0.102587i	0.00314353	−	0.00544476i
$356$	7.24390	−	4.18227i	0.383926	−	0.221660i
$357$	8.76625	−	5.88849i	0.463959	−	0.311652i
$358$		−	1.94916i		−	0.103016i
$359$			21.8569i			1.15356i	0.816898	+	0.576782i	$0.195692\pi$
$359$			21.8569i			1.15356i	−0.816898	+	0.576782i	$0.804308\pi$
$360$	−0.165377	−	0.213353i	−0.00871612	−	0.0112447i
$361$	1.91462	−	3.31621i	0.100769	−	0.174537i
$362$	−1.14577	+	0.661511i	−0.0602203	+	0.0347682i
$363$	5.00871	−	10.2196i	0.262889	−	0.536391i
$364$	−5.99555	+	3.95291i	−0.314252	+	0.207189i
$365$	−0.795730	−	1.37824i	−0.0416504	−	0.0721406i
$366$	0.799422	−	0.536990i	0.0417864	−	0.0280689i
$367$	−1.77629	−	3.07663i	−0.0927217	−	0.160599i	0.815934	−	0.578145i	$-0.196223\pi$
$367$	−1.77629	−	3.07663i	−0.0927217	−	0.160599i	−0.908655	+	0.417547i	$0.862890\pi$
$368$	2.57547	+	4.46084i	0.134256	+	0.232537i
$369$	3.80038	+	27.8143i	0.197840	+	1.44795i
$370$	0.101932	−	0.0588502i	0.00529917	−	0.00305948i
$371$			10.8656i			0.564116i
$372$	1.37408	+	20.2067i	0.0712427	+	1.04767i
$373$	−17.9062	+	31.0144i	−0.927146	+	1.60586i	−0.139073	+	0.990282i	$0.544412\pi$
$373$	−17.9062	+	31.0144i	−0.927146	+	1.60586i	−0.788073	+	0.615582i	$0.788921\pi$
$374$	−2.32054			−0.119992
$375$	0.289936	+	4.26369i	0.0149722	+	0.220176i
$376$	1.09916	−	1.90380i	0.0566847	−	0.0981808i
$377$	5.96676	−	0.354196i	0.307304	−	0.0182420i
$378$	0.313673	+	0.352423i	0.0161336	+	0.0181267i
$379$	−16.8619	−	9.73521i	−0.866136	−	0.500064i	−7.38628e−5	−	1.00000i	$-0.500024\pi$
$379$	−16.8619	−	9.73521i	−0.866136	−	0.500064i	−0.866062	+	0.499936i	$0.833357\pi$
$380$	1.18131	+	2.04609i	0.0605999	+	0.104962i
$381$	4.85356	−	9.90305i	0.248655	−	0.507349i
$382$	0.536607	−	0.309810i	0.0274552	−	0.0158513i
$383$	0.809753	+	0.467511i	0.0413764	+	0.0238887i	0.520546	−	0.853834i	$-0.325729\pi$
$383$	0.809753	+	0.467511i	0.0413764	+	0.0238887i	−0.479169	+	0.877723i	$0.659062\pi$
$384$	−4.13458	+	2.77730i	−0.210992	+	0.141728i
$385$	−0.901237	−	0.520330i	−0.0459313	−	0.0265185i
$386$	0.380094	+	0.658342i	0.0193463	+	0.0335087i
$387$	22.0546	−	3.01342i	1.12110	−	0.153181i
$388$	19.1289	+	11.0441i	0.971125	+	0.560679i
$389$	−6.81773	+	11.8087i	−0.345673	+	0.598723i	−0.985476	−	0.169816i	$-0.945683\pi$
$389$	−6.81773	+	11.8087i	−0.345673	+	0.598723i	0.639803	+	0.768539i	$0.279016\pi$
$390$	−0.0852819	−	0.112000i	−0.00431842	−	0.00567133i
$391$	−3.97476	−	6.88449i	−0.201012	−	0.348164i
$392$			0.362441i			0.0183061i
$393$	−0.789029	−	1.17463i	−0.0398012	−	0.0592524i
$394$	−0.505586			−0.0254710
$395$		−	1.82083i		−	0.0916158i
$396$	3.39075	+	24.8163i	0.170392	+	1.24707i
$397$	−18.5471	+	10.7082i	−0.930851	+	0.537427i	−0.887081	−	0.461615i	$-0.847270\pi$
$397$	−18.5471	+	10.7082i	−0.930851	+	0.537427i	−0.0437704	+	0.999042i	$0.513937\pi$
$398$	0.785130	+	0.453295i	0.0393550	+	0.0227216i
$399$	−4.61457	−	6.86975i	−0.231018	−	0.343918i
$400$	19.5095			0.975476
$401$			9.97613i			0.498184i	0.968480	+	0.249092i	$0.0801322\pi$
$401$			9.97613i			0.498184i	−0.968480	+	0.249092i	$0.919868\pi$
$402$	−0.570386	−	0.849138i	−0.0284483	−	0.0423512i
$403$	1.25434	+	21.1304i	0.0624829	+	1.05258i
$404$	2.28555			0.113711
$405$	1.56440	−	1.59532i	0.0777356	−	0.0792723i
$406$	0.0752618	−	0.130357i	0.00373518	−	0.00646952i
$407$	−21.8871			−1.08490
$408$	3.17725	−	2.13423i	0.157297	−	0.105660i
$409$	21.8042	+	12.5887i	1.07815	+	0.622469i	0.930396	−	0.366556i	$-0.119463\pi$
$409$	21.8042	+	12.5887i	1.07815	+	0.622469i	0.147752	+	0.989025i	$0.452796\pi$
$410$	−0.182675	−	0.105468i	−0.00902169	−	0.00520868i
$411$	2.04675	+	30.0987i	0.100958	+	1.48466i
$412$	34.0868			1.67933
$413$	1.95502	−	3.38619i	0.0962003	−	0.166624i
$414$	0.280702	−	0.217581i	0.0137958	−	0.0106935i
$415$	−3.99349			−0.196033
$416$	−3.26180	+	2.15053i	−0.159923	+	0.105438i
$417$	7.80271	−	15.9204i	0.382101	−	0.779626i
$418$			1.81851i			0.0889463i
$419$	3.51627			0.171781			0.0858905	−	0.996305i	$-0.472626\pi$
$419$	3.51627			0.171781			0.0858905	+	0.996305i	$0.472626\pi$
$420$	0.854490	−	0.0581063i	0.0416949	−	0.00283530i
$421$	10.2082	+	5.89371i	0.497518	+	0.287242i	0.727688	−	0.685908i	$-0.240595\pi$
$421$	10.2082	+	5.89371i	0.497518	+	0.287242i	−0.230170	+	0.973150i	$0.573928\pi$
$422$	1.46915	−	0.848214i	0.0715171	−	0.0412904i
$423$	16.8447	+	6.88092i	0.819016	+	0.334562i
$424$			3.93816i			0.191254i
$425$	−30.1094			−1.46052
$426$	−0.0330239	+	0.0673810i	−0.00160001	+	0.00326462i
$427$			6.12360i			0.296342i
$428$	−6.75207	−	11.6949i	−0.326374	−	0.565296i
$429$	3.32051	+	25.9661i	0.160316	+	1.25365i
$430$	−0.0836279	+	0.144848i	−0.00403290	+	0.00698518i
$431$	29.9512	+	17.2923i	1.44270	+	0.832942i	0.998029	−	0.0627527i	$-0.0199880\pi$
$431$	29.9512	+	17.2923i	1.44270	+	0.832942i	0.444669	+	0.895695i	$0.353321\pi$
$432$	−13.6479	−	15.3340i	−0.656636	−	0.737755i
$433$	7.61126	+	13.1831i	0.365774	+	0.633539i	0.988900	−	0.148582i	$-0.0474710\pi$
$433$	7.61126	+	13.1831i	0.365774	+	0.633539i	−0.623126	+	0.782121i	$0.714138\pi$
$434$	0.461642	+	0.266529i	0.0221595	+	0.0127938i
$435$	−0.640113	−	0.313724i	−0.0306911	−	0.0150419i
$436$	−8.01585	−	4.62795i	−0.383890	−	0.221639i
$437$	−5.39509	+	3.11486i	−0.258082	+	0.149004i
$438$	0.562138	+	0.836859i	0.0268600	+	0.0399867i
$439$	13.9594	+	24.1783i	0.666244	+	1.15397i	0.978946	+	0.204117i	$0.0654324\pi$
$439$	13.9594	+	24.1783i	0.666244	+	1.15397i	−0.312702	+	0.949851i	$0.601234\pi$
$440$	−0.326646	−	0.188589i	−0.0155722	−	0.00899063i
$441$	−2.97238	+	0.406129i	−0.141542	+	0.0193395i
$442$	1.66642	−	1.09869i	0.0792637	−	0.0522592i
$443$	10.1816	−	17.6351i	0.483745	−	0.837870i	−0.516081	−	0.856540i	$-0.672610\pi$
$443$	10.1816	−	17.6351i	0.483745	−	0.837870i	0.999826	+	0.0186696i	$0.00594305\pi$
$444$	14.9528	−	10.0442i	0.709630	−	0.476675i
$445$	−1.04260			−0.0494240
$446$	0.701489	−	1.21501i	0.0332165	−	0.0575326i
$447$	3.99740	+	1.95915i	0.189070	+	0.0926648i
$448$		−	7.80282i		−	0.368649i
$449$	20.5983	−	11.8924i	0.972094	−	0.561239i	0.0722199	−	0.997389i	$-0.476992\pi$
$449$	20.5983	−	11.8924i	0.972094	−	0.561239i	0.899874	+	0.436150i	$0.143658\pi$
$450$	−0.182105	−	1.33279i	−0.00858450	−	0.0628283i
$451$	19.6123	+	33.9696i	0.923509	+	1.59956i
$452$	9.79986	+	16.9739i	0.460947	+	0.798383i
$453$	−15.9110	−	7.79810i	−0.747564	−	0.366387i
$454$	−0.605153	−	1.04816i	−0.0284013	−	0.0491924i
$455$	0.893553	−	0.0530427i	0.0418904	−	0.00248668i
$456$	−1.67251	−	2.48988i	−0.0783225	−	0.116599i
$457$	12.5668	−	7.25547i	0.587852	−	0.339397i	−0.176396	−	0.984319i	$-0.556444\pi$
$457$	12.5668	−	7.25547i	0.587852	−	0.339397i	0.764248	+	0.644923i	$0.223110\pi$
$458$	−1.07238	+	1.85742i	−0.0501091	+	0.0867915i
$459$	21.0631	+	23.6652i	0.983141	+	1.10459i
$460$		−	0.644720i		−	0.0300602i
$461$		−	15.5111i		−	0.722423i	−0.932484	−	0.361211i	$-0.882363\pi$
$461$		−	15.5111i		−	0.722423i	0.932484	−	0.361211i	$-0.117637\pi$
$462$	0.591949	+	0.290118i	0.0275399	+	0.0134975i
$463$	8.86168	−	5.11629i	0.411837	−	0.237774i	−0.279742	−	0.960075i	$-0.590249\pi$
$463$	8.86168	−	5.11629i	0.411837	−	0.237774i	0.691579	+	0.722301i	$0.256916\pi$
$464$	−3.27464	+	5.67185i	−0.152022	+	0.263309i
$465$	1.11101	−	2.26687i	0.0515219	−	0.105124i
$466$	0.390205	−	0.225285i	0.0180759	−	0.0104361i
$467$	−10.9633			−0.507319			−0.253660	−	0.967294i	$-0.581634\pi$
$467$	−10.9633			−0.507319			−0.253660	+	0.967294i	$0.581634\pi$
$468$	−14.1845	−	16.2157i	−0.655681	−	0.749570i
$469$	6.50443			0.300347
$470$	−0.118405	+	0.0683610i	−0.00546160	+	0.00315326i
$471$	−15.9259	−	23.7090i	−0.733826	−	1.09245i
$472$	0.708580	−	1.22730i	0.0326151	−	0.0564909i
$473$	26.9353	−	15.5511i	1.23849	−	0.715041i
$474$	0.0782538	+	1.15077i	0.00359432	+	0.0528567i
$475$			23.5955i			1.08264i
$476$			12.1438i			0.556610i
$477$	−32.2969	+	4.41285i	−1.47877	+	0.202051i
$478$	−0.517995	+	0.897193i	−0.0236925	+	0.0410367i
$479$	13.9452	−	8.05126i	0.637172	−	0.367871i	−0.146352	−	0.989233i	$-0.546753\pi$
$479$	13.9452	−	8.05126i	0.637172	−	0.367871i	0.783524	+	0.621361i	$0.213420\pi$
$480$	0.464874	−	0.0316120i	0.0212185	−	0.00144288i
$481$	15.7176	−	10.3627i	0.716659	−	0.472499i
$482$	−0.0800004	−	0.138565i	−0.00364392	−	0.00631145i
$483$	0.153214	+	2.25311i	0.00697147	+	0.102520i
$484$	6.54376	+	11.3341i	0.297444	+	0.515187i
$485$	−1.37660	−	2.38433i	−0.0625080	−	0.108267i
$486$	−0.920145	+	1.07549i	−0.0417386	+	0.0487850i
$487$	−12.4030	+	7.16087i	−0.562033	+	0.324490i	−0.753961	−	0.656919i	$-0.771859\pi$
$487$	−12.4030	+	7.16087i	−0.562033	+	0.324490i	0.191928	+	0.981409i	$0.438526\pi$
$488$			2.21945i			0.100470i
$489$	−9.66087	+	6.48943i	−0.436879	+	0.293462i
$490$	0.0112708	−	0.0195217i	0.000509165	−	0.000881899i
$491$	32.0463			1.44623			0.723115	−	0.690728i	$-0.242710\pi$
$491$	32.0463			1.44623			0.723115	+	0.690728i	$0.242710\pi$
$492$	−28.9877	−	14.2071i	−1.30686	−	0.640504i
$493$	5.05381	−	8.75346i	0.227612	−	0.394236i
$494$	−0.860996	−	1.30591i	−0.0387380	−	0.0587556i
$495$	1.18060	−	2.89014i	0.0530640	−	0.129902i
$496$	−20.0861	−	11.5967i	−0.901891	−	0.520707i
$497$	−0.238572	−	0.413219i	−0.0107014	−	0.0185354i
$498$	2.52390	−	0.171628i	0.113099	−	0.00769085i
$499$	4.74072	−	2.73706i	0.212224	−	0.122528i	−0.390121	−	0.920764i	$-0.627567\pi$
$499$	4.74072	−	2.73706i	0.212224	−	0.122528i	0.602345	+	0.798236i	$0.294233\pi$
$500$	−4.25593	−	2.45716i	−0.190331	−	0.109888i
$501$	−2.58337	−	37.9900i	−0.115416	−	1.69727i
$502$	0.518049	+	0.299095i	0.0231216	+	0.0133493i
$503$	3.70097	+	6.41027i	0.165018	+	0.285820i	0.936662	−	0.350235i	$-0.113898\pi$
$503$	3.70097	+	6.41027i	0.165018	+	0.285820i	−0.771644	+	0.636055i	$0.780565\pi$
$504$	−1.07731	+	0.147198i	−0.0479874	+	0.00655672i
$505$	−0.246717	−	0.142442i	−0.0109787	−	0.00633858i
$506$	0.248121	−	0.429758i	0.0110303	−	0.0191051i
$507$	−14.6785	−	17.0746i	−0.651894	−	0.758310i
$508$	6.34105	+	10.9830i	0.281339	+	0.487293i
$509$			5.35400i			0.237312i	0.992935	+	0.118656i	$0.0378585\pi$
$509$			5.35400i			0.237312i	−0.992935	+	0.118656i	$0.962141\pi$
$510$	−0.237500	+	0.0161503i	−0.0105167	+	0.000715146i
$511$	−6.41037			−0.283578
$512$		−	7.14455i		−	0.315747i
$513$	18.5454	−	16.5063i	0.818800	−	0.728770i
$514$	−0.972230	+	0.561317i	−0.0428832	+	0.0247586i
$515$	−3.67953	−	2.12438i	−0.162140	−	0.0936113i
$516$	−11.2651	+	22.9850i	−0.495920	+	1.01186i
$517$	25.4243			1.11816
$518$		−	0.474096i		−	0.0208306i
$519$	−43.9706	+	2.99005i	−1.93010	+	0.131249i
$520$	0.323860	−	0.0192249i	0.0142022	−	0.000843066i
$521$	29.4381			1.28971			0.644854	−	0.764305i	$-0.276918\pi$
$521$	29.4381			1.28971			0.644854	+	0.764305i	$0.276918\pi$
$522$	0.418038	+	0.170765i	0.0182970	+	0.00747418i
$523$	−1.31103	+	2.27078i	−0.0573275	+	0.0992942i	−0.893265	−	0.449531i	$-0.851591\pi$
$523$	−1.31103	+	2.27078i	−0.0573275	+	0.0992942i	0.835937	+	0.548825i	$0.184925\pi$
$524$	1.62721			0.0710849
$525$	7.68063	+	3.76433i	0.335210	+	0.164289i
$526$	−1.37239	−	0.792348i	−0.0598389	−	0.0345480i
$527$	30.9992	+	17.8974i	1.35034	+	0.779622i
$528$	−25.7557	−	12.6231i	−1.12087	−	0.549348i
$529$	−21.3000			−0.926088
$530$	0.122465	−	0.212115i	0.00531954	−	0.00921371i
$531$	10.8591	+	4.43584i	0.471243	+	0.192499i
$532$	9.51660			0.412597
$533$	−30.1673	−	15.1085i	−1.30669	−	0.654423i
$534$	0.658929	−	0.0448079i	0.0285146	−	0.00193903i
$535$			1.68323i			0.0727723i
$536$	2.35748			0.101827
$537$	−16.3636	+	33.3878i	−0.706142	+	1.44079i
$538$	−0.351720	−	0.203065i	−0.0151637	−	0.00875477i
$539$	−3.63017	+	2.09588i	−0.156362	+	0.0902759i
$540$	0.519748	+	2.51627i	0.0223664	+	0.108283i
$541$		−	4.91202i		−	0.211184i	−0.994410	−	0.105592i	$-0.966326\pi$
$541$		−	4.91202i		−	0.211184i	0.994410	−	0.105592i	$-0.0336738\pi$
$542$	1.64969			0.0708600
$543$	25.1798	−	1.71225i	1.08057	−	0.0734798i
$544$			6.60667i			0.283259i
$545$	0.576853	+	0.999139i	0.0247097	+	0.0427984i
$546$	−0.562450	+	0.0719255i	−0.0240706	+	0.00307813i
$547$	4.36380	−	7.55832i	0.186583	−	0.323170i	−0.757526	−	0.652805i	$-0.773592\pi$
$547$	4.36380	−	7.55832i	0.186583	−	0.323170i	0.944109	+	0.329634i	$0.106925\pi$
$548$	−30.0438	−	17.3458i	−1.28341	−	0.740977i
$549$	−18.2017	+	2.48697i	−0.776829	+	0.106141i
$550$	−0.939774	−	1.62774i	−0.0400721	−	0.0694069i
$551$	−6.85973	−	3.96047i	−0.292234	−	0.168722i
$552$	0.0555310	+	0.816619i	0.00236356	+	0.0347576i
$553$	−6.35166	−	3.66713i	−0.270100	−	0.155942i
$554$	−0.00551042	+	0.00318144i	−0.000234115	+	0.000135167i
$555$	−2.24008	+	0.152328i	−0.0950860	+	0.00646596i
$556$	10.1941	+	17.6566i	0.432324	+	0.748807i
$557$	22.7689	+	13.1457i	0.964751	+	0.556999i	0.897632	−	0.440745i	$-0.145286\pi$
$557$	22.7689	+	13.1457i	0.964751	+	0.556999i	0.0671193	+	0.997745i	$0.478619\pi$
$558$	−0.604740	+	1.48042i	−0.0256007	+	0.0626712i
$559$	−11.9799	+	23.9204i	−0.506697	+	1.01173i
$560$	−0.490395	+	0.849388i	−0.0207230	+	0.0358932i
$561$	39.7492	+	19.4814i	1.67821	+	0.822505i
$562$	1.57104			0.0662702
$563$	5.57059	−	9.64854i	0.234772	−	0.406638i	−0.724434	−	0.689344i	$-0.757899\pi$
$563$	5.57059	−	9.64854i	0.234772	−	0.406638i	0.959206	+	0.282706i	$0.0912322\pi$
$564$	−17.3693	+	11.6674i	−0.731381	+	0.491286i
$565$		−	2.44302i		−	0.102778i
$566$	2.64233	−	1.52555i	0.111065	−	0.0641236i
$567$	−2.41434	−	8.67012i	−0.101393	−	0.364111i
$568$	−0.0864685	−	0.149768i	−0.00362814	−	0.00628412i
$569$	1.97632	+	3.42309i	0.0828518	+	0.143503i	0.904474	−	0.426529i	$-0.140264\pi$
$569$	1.97632	+	3.42309i	0.0828518	+	0.143503i	−0.821622	+	0.570033i	$0.806931\pi$
$570$	0.0126563	+	0.186119i	0.000530114	+	0.00779567i
$571$	−16.9637	−	29.3819i	−0.709907	−	1.22959i	−0.964891	−	0.262649i	$-0.915404\pi$
$571$	−16.9637	−	29.3819i	−0.709907	−	1.22959i	0.254985	−	0.966945i	$-0.417930\pi$
$572$	−26.9157	−	13.4800i	−1.12540	−	0.563629i
$573$	−11.7926	+	0.801913i	−0.492644	+	0.0335004i
$574$	−0.735813	+	0.424822i	−0.0307123	+	0.0177317i
$575$	3.21941	−	5.57618i	0.134259	−	0.232543i
$576$	23.1930	−	3.16895i	0.966373	−	0.132040i
$577$			3.83353i			0.159592i	0.996811	+	0.0797959i	$0.0254269\pi$
$577$			3.83353i			0.159592i	−0.996811	+	0.0797959i	$0.974573\pi$
$578$		−	1.83173i		−	0.0761900i
$579$	−0.983835	−	14.4679i	−0.0408868	−	0.601266i
$580$	0.709921	−	0.409873i	0.0294778	−	0.0170190i
$581$	−8.04285	+	13.9306i	−0.333674	+	0.577940i
$582$	0.972487	+	1.44775i	0.0403109	+	0.0600111i
$583$	−39.4441	+	22.7731i	−1.63361	+	0.943165i
$584$	−2.32339			−0.0961424
$585$	0.520561	+	2.63444i	0.0215225	+	0.108921i
$586$	−2.16094			−0.0892676
$587$	−28.0108	+	16.1721i	−1.15613	+	0.667492i	−0.950374	−	0.311111i	$-0.899299\pi$
$587$	−28.0108	+	16.1721i	−1.15613	+	0.667492i	−0.205757	+	0.978603i	$0.565966\pi$
$588$	1.51824	−	3.09778i	0.0626113	−	0.127750i
$589$	14.0254	−	24.2928i	0.577908	−	1.00097i
$590$	−0.0763305	+	0.0440694i	−0.00314248	+	0.00181431i
$591$	8.66034	+	4.24449i	0.356239	+	0.174595i
$592$			20.6279i			0.847802i
$593$		−	31.4950i		−	1.29335i	−0.762768	−	0.646673i	$-0.776160\pi$
$593$		−	31.4950i		−	1.29335i	0.762768	−	0.646673i	$-0.223840\pi$
$594$	−0.621935	+	1.87732i	−0.0255183	+	0.0770275i
$595$	0.756834	−	1.31088i	0.0310272	−	0.0537407i
$596$	−4.43333	+	2.55959i	−0.181596	+	0.104845i
$597$	−9.64323	−	14.3560i	−0.394671	−	0.587550i
$598$	0.0252935	+	0.426093i	0.00103433	+	0.0174242i
$599$	−6.76799	−	11.7225i	−0.276533	−	0.478968i	0.693988	−	0.719987i	$-0.255852\pi$
$599$	−6.76799	−	11.7225i	−0.276533	−	0.478968i	−0.970521	+	0.241018i	$0.922519\pi$
$600$	2.78378	+	1.36435i	0.113647	+	0.0556994i
$601$	−19.0294	−	32.9599i	−0.776225	−	1.34446i	−0.934103	−	0.357003i	$-0.883799\pi$
$601$	−19.0294	−	32.9599i	−0.776225	−	1.34446i	0.157878	−	0.987459i	$-0.449535\pi$
$602$	0.336852	+	0.583445i	0.0137291	+	0.0237794i
$603$	2.64164	+	19.3337i	0.107576	+	0.787328i
$604$	17.6462	−	10.1880i	0.718012	−	0.414545i
$605$		−	1.63130i		−	0.0663217i
$606$	0.162048	+	0.0794208i	0.00658274	+	0.00322625i
$607$	−0.210095	+	0.363895i	−0.00852748	+	0.0147700i	−0.870258	−	0.492597i	$-0.836048\pi$
$607$	−0.210095	+	0.363895i	−0.00852748	+	0.0147700i	0.861730	+	0.507367i	$0.169381\pi$
$608$	5.17738			0.209970
$609$	−2.38356	+	1.60109i	−0.0965867	+	0.0648795i
$610$	0.0690181	−	0.119543i	0.00279446	−	0.00484015i
$611$	−18.2577	+	12.0374i	−0.738626	+	0.486982i
$612$	−36.0960	+	4.93195i	−1.45910	+	0.199362i
$613$	−37.4075	−	21.5972i	−1.51087	−	0.872303i	−0.999919	−	0.0126955i	$-0.995959\pi$
$613$	−37.4075	−	21.5972i	−1.51087	−	0.872303i	−0.510954	−	0.859608i	$-0.670708\pi$
$614$	0.0322747	+	0.0559015i	0.00130250	+	0.00225600i
$615$	2.24368	+	3.34018i	0.0904740	+	0.134689i
$616$	−1.31572	+	0.759634i	−0.0530120	+	0.0306065i
$617$	−2.26975	−	1.31044i	−0.0913769	−	0.0527565i	0.453615	−	0.891198i	$-0.350134\pi$
$617$	−2.26975	−	1.31044i	−0.0913769	−	0.0527565i	−0.544992	+	0.838441i	$0.683467\pi$
$618$	2.41678	+	1.18448i	0.0972172	+	0.0476469i
$619$	7.21384	+	4.16492i	0.289949	+	0.167402i	0.637919	−	0.770104i	$-0.279796\pi$
$619$	7.21384	+	4.16492i	0.289949	+	0.167402i	−0.347970	+	0.937506i	$0.613129\pi$
$620$	1.45151	+	2.51408i	0.0582939	+	0.100968i
$621$	−6.63487	+	1.37046i	−0.266248	+	0.0549947i
$622$	0.558431	+	0.322410i	0.0223910	+	0.0129275i
$623$	−2.09979	+	3.63694i	−0.0841263	+	0.145711i
$624$	24.4722	−	3.12948i	0.979673	−	0.125279i
$625$	−12.0396	−	20.8533i	−0.481586	−	0.834131i
$626$		−	0.866158i		−	0.0346186i
$627$	15.2668	−	31.1498i	0.609696	−	1.24400i
$628$	32.8438			1.31061
$629$		−	31.8354i		−	1.26936i
$630$	0.0626033	+	0.0255729i	0.00249417	+	0.00101885i
$631$	23.9372	−	13.8201i	0.952925	−	0.550171i	0.0589364	−	0.998262i	$-0.481229\pi$
$631$	23.9372	−	13.8201i	0.952925	−	0.550171i	0.893988	+	0.448090i	$0.147896\pi$
$632$	−2.30210	−	1.32912i	−0.0915728	−	0.0528696i
$633$	−32.2865	+	2.19552i	−1.28327	+	0.0872640i
$634$	−1.53992			−0.0611580
$635$		−	1.58077i		−	0.0627308i
$636$	16.4967	−	33.6593i	0.654136	−	1.33468i
$637$	1.61458	−	3.22384i	0.0639719	−	0.127733i
$638$	0.630959			0.0249799
$639$	1.13135	−	0.876948i	0.0447557	−	0.0346915i
$640$	−0.356959	+	0.618272i	−0.0141101	+	0.0244393i
$641$	−36.5161			−1.44230			−0.721149	−	0.692780i	$-0.756386\pi$
$641$	−36.5161			−1.44230			−0.721149	+	0.692780i	$0.756386\pi$
$642$	−0.0723403	−	1.06381i	−0.00285504	−	0.0419852i
$643$	4.25878	+	2.45881i	0.167950	+	0.0969659i	0.581619	−	0.813461i	$-0.302420\pi$
$643$	4.25878	+	2.45881i	0.167950	+	0.0969659i	−0.413669	+	0.910427i	$0.635753\pi$
$644$	−2.24900	−	1.29846i	−0.0886230	−	0.0511665i
$645$	2.64852	−	1.77907i	0.104285	−	0.0700508i
$646$	−2.64508			−0.104069
$647$	11.9059	−	20.6216i	0.468068	−	0.810717i	−0.531266	−	0.847205i	$-0.678284\pi$
$647$	11.9059	−	20.6216i	0.468068	−	0.810717i	0.999334	+	0.0364875i	$0.0116169\pi$
$648$	−0.875057	−	3.14241i	−0.0343755	−	0.123446i
$649$	16.3900			0.643362
$650$	1.44554	+	0.723962i	0.0566988	+	0.0283961i
$651$	−5.67004	−	8.44104i	−0.222227	−	0.330830i
$652$		−	13.3831i		−	0.524123i
$653$	22.2338			0.870077			0.435038	−	0.900412i	$-0.356735\pi$
$653$	22.2338			0.870077			0.435038	+	0.900412i	$0.356735\pi$
$654$	−0.407514	−	0.606669i	−0.0159351	−	0.0237226i
$655$	−0.175651	−	0.101412i	−0.00686324	−	0.00396249i
$656$	32.0153	−	18.4840i	1.24999	−	0.721680i
$657$	−2.60344	−	19.0541i	−0.101570	−	0.743371i
$658$			0.550714i			0.0214691i
$659$	−22.5087			−0.876813			−0.438406	−	0.898777i	$-0.644457\pi$
$659$	−22.5087			−0.876813			−0.438406	+	0.898777i	$0.644457\pi$
$660$	2.00184	+	2.98016i	0.0779217	+	0.116003i
$661$		−	10.7965i		−	0.419934i	−0.977709	−	0.209967i	$-0.932664\pi$
$661$		−	10.7965i		−	0.419934i	0.977709	−	0.209967i	$-0.0673356\pi$
$662$	−0.0208759	−	0.0361581i	−0.000811365	−	0.00140532i
$663$	−37.7684	+	4.82978i	−1.46680	+	0.187573i
$664$	−2.91506	+	5.04904i	−0.113126	+	0.195941i
$665$	−1.02728	−	0.593100i	−0.0398362	−	0.0229994i
$666$	1.40919	−	0.192544i	0.0546051	−	0.00746093i
$667$	1.08075	+	1.87191i	0.0418466	+	0.0724805i
$668$	37.9208	+	21.8936i	1.46720	+	0.847088i
$669$	−22.2163	+	14.9232i	−0.858933	+	0.576965i
$670$	−0.126977	−	0.0733104i	−0.00490556	−	0.00283223i
$671$	−22.2297	+	12.8343i	−0.858169	+	0.495464i
$672$	0.825979	−	1.68530i	0.0318628	−	0.0650120i
$673$	8.03730	+	13.9210i	0.309815	+	0.536615i	0.978322	−	0.207091i	$-0.0663995\pi$
$673$	8.03730	+	13.9210i	0.309815	+	0.536615i	−0.668507	+	0.743706i	$0.733066\pi$
$674$	−2.35834	−	1.36159i	−0.0908398	−	0.0524464i
$675$	−8.06972	+	24.3586i	−0.310603	+	0.937563i
$676$	25.7110	−	3.06328i	0.988884	−	0.117819i
$677$	14.4424	−	25.0150i	0.555067	−	0.961405i	−0.442831	−	0.896605i	$-0.646026\pi$
$677$	14.4424	−	25.0150i	0.555067	−	0.961405i	0.997898	−	0.0647999i	$-0.0206409\pi$
$678$	0.104994	+	1.54400i	0.00403226	+	0.0592969i
$679$	−11.0898			−0.425588
$680$	0.274308	−	0.475116i	0.0105192	−	0.0182199i
$681$	1.56638	+	23.0346i	0.0600238	+	0.882687i
$682$			2.23445i			0.0855616i
$683$	−28.8556	+	16.6598i	−1.10413	+	0.637468i	−0.937302	−	0.348518i	$-0.886685\pi$
$683$	−28.8556	+	16.6598i	−1.10413	+	0.637468i	−0.166826	+	0.985986i	$0.553352\pi$
$684$	3.86497	+	28.2870i	0.147781	+	1.08158i
$685$	2.16208	+	3.74483i	0.0826087	+	0.143082i
$686$	−0.0453987	−	0.0786329i	−0.00173333	−	0.00300222i
$687$	33.9625	−	22.8134i	1.29575	−	0.870387i
$688$	−14.6564	−	25.3857i	−0.558772	−	0.967821i
$689$	17.5434	−	35.0291i	0.668351	−	1.33450i
$690$	0.0224034	−	0.0457112i	0.000852883	−	0.00174020i
$691$	−7.89841	+	4.56015i	−0.300470	+	0.173476i	−0.642654	−	0.766157i	$-0.722167\pi$
$691$	−7.89841	+	4.56015i	−0.300470	+	0.173476i	0.342184	+	0.939633i	$0.388833\pi$
$692$	25.3402	−	43.8905i	0.963290	−	1.66847i
$693$	−7.70407	−	9.93906i	−0.292654	−	0.377554i
$694$			3.25686i			0.123629i
$695$		−	2.54128i		−	0.0963964i
$696$	−0.863900	+	0.580302i	−0.0327461	+	0.0219963i
$697$	−49.4097	+	28.5267i	−1.87153	+	1.08053i
$698$	−1.37973	+	2.38976i	−0.0522235	+	0.0904538i
$699$	−8.57526	+	0.583128i	−0.324346	+	0.0220559i
$700$	−8.51824	+	4.91801i	−0.321959	+	0.185883i
$701$	−40.1282			−1.51562			−0.757811	−	0.652474i	$-0.773731\pi$
$701$	−40.1282			−1.51562			−0.757811	+	0.652474i	$0.773731\pi$
$702$	−0.442217	−	1.64261i	−0.0166904	−	0.0619962i
$703$	−24.9481			−0.940936
$704$	28.3256	−	16.3538i	1.06756	−	0.616356i
$705$	2.60209	−	0.176945i	0.0980005	−	0.00666415i
$706$	1.52136	−	2.63508i	0.0572572	−	0.0991724i
$707$	−0.993770	+	0.573753i	−0.0373746	+	0.0215782i
$708$	−11.1973	+	7.52148i	−0.420820	+	0.282674i
$709$			11.4936i			0.431652i	0.976432	+	0.215826i	$0.0692444\pi$
$709$			11.4936i			0.431652i	−0.976432	+	0.215826i	$0.930756\pi$
$710$			0.0107556i			0.000403652i
$711$	8.32053	−	20.3689i	0.312044	−	0.763893i
$712$	−0.761051	+	1.31818i	−0.0285216	+	0.0494008i
$713$	−6.62909	+	3.82731i	−0.248261	+	0.143334i
$714$	−0.421985	+	0.861006i	−0.0157924	+	0.0322224i
$715$	2.06533	+	3.13258i	0.0772391	+	0.117152i
$716$	−21.3786	−	37.0289i	−0.798958	−	1.38384i
$717$	16.4050	−	11.0196i	0.612657	−	0.411536i
$718$	−0.992277	−	1.71867i	−0.0370315	−	0.0641404i
$719$	−17.3069	−	29.9764i	−0.645438	−	1.11793i	−0.984200	−	0.177060i	$-0.943341\pi$
$719$	−17.3069	−	29.9764i	−0.645438	−	1.11793i	0.338762	−	0.940872i	$-0.389992\pi$
$720$	−2.72387	−	1.11268i	−0.101513	−	0.0414671i
$721$	−14.8211	+	8.55696i	−0.551966	+	0.318678i
$722$			0.347685i			0.0129395i
$723$	0.207073	+	3.04514i	0.00770112	+	0.113250i
$724$	−14.5111	+	25.1339i	−0.539299	+	0.934094i
$725$	8.18680			0.304050
$726$	0.0701084	+	1.03099i	0.00260197	+	0.0382636i
$727$	−6.38601	+	11.0609i	−0.236844	+	0.410226i	−0.959807	−	0.280661i	$-0.909446\pi$
$727$	−6.38601	+	11.0609i	−0.236844	+	0.410226i	0.722963	+	0.690887i	$0.242780\pi$
$728$	0.585190	−	1.16845i	0.0216886	−	0.0433058i
$729$	24.7904	−	10.6975i	0.918162	−	0.396205i
$730$	0.125141	+	0.0722503i	0.00463168	+	0.00267410i
$731$	22.6195	+	39.1782i	0.836614	+	1.44906i
$732$	9.29711	−	18.9695i	0.343631	−	0.701135i
$733$	44.6212	−	25.7621i	1.64812	−	0.951544i	0.670304	−	0.742086i	$-0.266164\pi$
$733$	44.6212	−	25.7621i	1.64812	−	0.951544i	0.977818	−	0.209457i	$-0.0671697\pi$
$734$	0.279350	+	0.161283i	0.0103110	+	0.00595306i
$735$	−0.356950	+	0.239772i	−0.0131663	+	0.00884411i
$736$	−1.22354	−	0.706410i	−0.0451002	−	0.0260386i
$737$	13.6325	+	23.6122i	0.502160	+	0.869766i
$738$	−1.56157	−	2.01459i	−0.0574821	−	0.0741579i
$739$	35.7221	+	20.6242i	1.31406	+	0.758673i	0.982766	−	0.184855i	$-0.0591814\pi$
$739$	35.7221	+	20.6242i	1.31406	+	0.758673i	0.331294	+	0.943528i	$0.392515\pi$
$740$	1.29095	−	2.23600i	0.0474564	−	0.0821969i
$741$	3.78490	+	29.5975i	0.139042	+	1.08729i
$742$	−0.493287	−	0.854398i	−0.0181091	−	0.0313659i
$743$			16.6004i			0.609011i	0.952511	+	0.304505i	$0.0984912\pi$
$743$			16.6004i			0.609011i	−0.952511	+	0.304505i	$0.901509\pi$
$744$	−2.05506	−	3.05938i	−0.0753421	−	0.112162i
$745$	0.638081			0.0233775
$746$		−	3.25167i		−	0.119052i
$747$	−44.6736	−	18.2488i	−1.63452	−	0.667689i
$748$	−44.0841	+	25.4519i	−1.61187	+	0.930615i
$749$	5.87167	+	3.39001i	0.214546	+	0.123868i
$750$	−0.216365	−	0.322104i	−0.00790053	−	0.0117616i
$751$	−21.5659			−0.786951			−0.393476	−	0.919335i	$-0.628727\pi$
$751$	−21.5659			−0.786951			−0.393476	+	0.919335i	$0.628727\pi$
$752$		−	23.9616i		−	0.873789i
$753$	−6.36285	−	9.47242i	−0.231875	−	0.345194i
$754$	−0.453104	+	0.298735i	−0.0165011	+	0.0108793i
$755$	−2.53978			−0.0924320
$756$	9.82438	+	3.25470i	0.357309	+	0.118372i
$757$	−24.5354	+	42.4966i	−0.891756	+	1.54457i	−0.0539865	+	0.998542i	$0.517193\pi$
$757$	−24.5354	+	42.4966i	−0.891756	+	1.54457i	−0.837769	+	0.546025i	$0.816141\pi$
$758$	1.76786			0.0642117
$759$	−7.85804	+	5.27843i	−0.285229	+	0.191595i
$760$	−0.372329	−	0.214964i	−0.0135058	−	0.00779756i
$761$	16.7628	+	9.67803i	0.607652	+	0.350828i	0.772046	−	0.635567i	$-0.219233\pi$
$761$	16.7628	+	9.67803i	0.607652	+	0.350828i	−0.164394	+	0.986395i	$0.552567\pi$
$762$	0.0679367	+	0.999052i	0.00246109	+	0.0361918i
$763$	4.64711			0.168237
$764$	6.79607	−	11.7711i	0.245873	−	0.425865i
$765$	4.20380	+	1.71722i	0.151989	+	0.0620861i
$766$	−0.0848977			−0.00306748
$767$	−11.7699	+	7.76002i	−0.424988	+	0.280198i
$768$	−11.6966	+	23.8653i	−0.422064	+	0.861166i
$769$		−	24.7761i		−	0.893447i	−0.894672	−	0.446724i	$-0.852591\pi$
$769$		−	24.7761i		−	0.893447i	0.894672	−	0.446724i	$-0.147409\pi$
$770$	0.0944893			0.00340516
$771$	21.3660	−	1.45291i	0.769478	−	0.0523254i
$772$	14.4416	+	8.33783i	0.519763	+	0.300085i
$773$	−43.4295	+	25.0740i	−1.56205	+	0.901849i	−0.564999	+	0.825092i	$0.691123\pi$
$773$	−43.4295	+	25.0740i	−1.56205	+	0.901849i	−0.997050	+	0.0767577i	$0.975543\pi$
$774$	−1.59742	+	1.23821i	−0.0574179	+	0.0445064i
$775$			28.9924i			1.04144i
$776$	−4.01941			−0.144288
$777$	−3.98013	+	8.12093i	−0.142786	+	0.291337i
$778$		−	1.23807i		−	0.0443868i
$779$	22.3552	+	38.7204i	0.800959	+	1.38730i
$780$	−2.84856	−	1.19232i	−0.101995	−	0.0426917i
$781$	1.00004	−	1.73212i	0.0357841	−	0.0619800i
$782$	0.625095	+	0.360899i	0.0223533	+	0.0129057i
$783$	−5.72709	−	6.43460i	−0.204670	−	0.229954i
$784$	1.97530	+	3.42132i	0.0705465	+	0.122190i
$785$	−3.54536	−	2.04692i	−0.126539	−	0.0730576i
$786$	0.115371	+	0.0565439i	0.00411513	+	0.00201685i
$787$	14.1104	+	8.14664i	0.502981	+	0.290396i	0.729944	−	0.683507i	$-0.239546\pi$
$787$	14.1104	+	8.14664i	0.502981	+	0.290396i	−0.226963	+	0.973903i	$0.572880\pi$
$788$	−9.60479	+	5.54533i	−0.342156	+	0.197544i
$789$	16.8561	+	25.0939i	0.600094	+	0.893365i
$790$	0.0826633	+	0.143177i	0.00294103	+	0.00509401i
$791$	−8.52206	−	4.92021i	−0.303010	−	0.174943i
$792$	−2.79228	−	3.60233i	−0.0992192	−	0.128003i
$793$	9.88703	−	19.7415i	0.351099	−	0.701042i
$794$	0.972274	−	1.68403i	0.0345047	−	0.0597639i
$795$	−3.87849	+	2.60527i	−0.137556	+	0.0923996i
$796$	19.8872			0.704882
$797$	−22.9236	+	39.7049i	−0.811997	+	1.40642i	0.0994681	+	0.995041i	$0.468286\pi$
$797$	−22.9236	+	39.7049i	−0.811997	+	1.40642i	−0.911465	+	0.411378i	$0.865047\pi$
$798$	0.674735	+	0.330693i	0.0238854	+	0.0117064i
$799$			36.9803i			1.30827i
$800$	−4.63423	+	2.67558i	−0.163845	+	0.0945959i
$801$	−11.6632	−	4.76431i	−0.412098	−	0.168339i
$802$	−0.452904	−	0.784452i	−0.0159926	−	0.0277000i
$803$	−13.4354	−	23.2707i	−0.474124	−	0.821207i
$804$	−20.1493	−	9.87531i	−0.710610	−	0.348275i
$805$	0.161847	+	0.280328i	0.00570436	+	0.00988025i
$806$	−1.05793	−	1.60460i	−0.0372639	−	0.0565197i
$807$	4.31994	+	6.43113i	0.152069	+	0.226386i
$808$	−0.360183	+	0.207952i	−0.0126712	+	0.00731573i
$809$	−3.31177	+	5.73616i	−0.116436	+	0.201673i	−0.918353	−	0.395763i	$-0.870480\pi$
$809$	−3.31177	+	5.73616i	−0.116436	+	0.201673i	0.801917	+	0.597435i	$0.203814\pi$
$810$	−0.0505875	+	0.196467i	−0.00177746	+	0.00690314i
$811$		−	49.7150i		−	1.74573i	−0.487962	−	0.872865i	$-0.662259\pi$
$811$		−	49.7150i		−	1.74573i	0.487962	−	0.872865i	$-0.337741\pi$
$812$		−	3.30192i		−	0.115875i
$813$	−28.2580	−	13.8494i	−0.991050	−	0.485721i
$814$	1.72105	−	0.993647i	0.0603227	−	0.0348273i
$815$	−0.834071	+	1.44465i	−0.0292162	+	0.0506040i
$816$	18.3606	−	37.4624i	0.642750	−	1.31145i
$817$	30.7023	−	17.7260i	1.07414	−	0.620154i
$818$	−2.28604			−0.0799294
$819$	10.2382	+	3.48985i	0.357752	+	0.121945i
$820$	−4.62713			−0.161586
$821$	31.9374	−	18.4391i	1.11462	−	0.643527i	0.174599	−	0.984640i	$-0.444137\pi$
$821$	31.9374	−	18.4391i	1.11462	−	0.643527i	0.940023	+	0.341112i	$0.110804\pi$
$822$	−1.52738	−	2.27383i	−0.0532736	−	0.0793089i
$823$	−0.505428	+	0.875428i	−0.0176181	+	0.0305155i	−0.874700	−	0.484665i	$-0.838942\pi$
$823$	−0.505428	+	0.875428i	−0.0176181	+	0.0305155i	0.857082	+	0.515180i	$0.172275\pi$
$824$	−5.37178	+	3.10140i	−0.187135	+	0.108042i
$825$	2.43251	+	35.7716i	0.0846891	+	1.24541i
$826$			0.355022i			0.0123528i
$827$			34.6870i			1.20619i	0.797671	+	0.603093i	$0.206065\pi$
$827$			34.6870i			1.20619i	−0.797671	+	0.603093i	$0.793935\pi$
$828$	2.94614	−	7.21223i	0.102385	−	0.250642i
$829$	0.528334	−	0.915101i	0.0183498	−	0.0317828i	−0.856705	−	0.515807i	$-0.827492\pi$
$829$	0.528334	−	0.915101i	0.0183498	−	0.0317828i	0.875054	+	0.484024i	$0.160825\pi$
$830$	0.314020	−	0.181299i	0.0108998	−	0.00629299i
$831$	0.121099	−	0.00823484i	0.00420086	−	0.000285664i
$832$	−12.5983	+	25.1550i	−0.436766	+	0.872094i
$833$	−3.04852	−	5.28019i	−0.105625	−	0.182948i
$834$	0.109217	+	1.60610i	0.00378187	+	0.0556148i
$835$	−2.72893	−	4.72665i	−0.0944387	−	0.163573i
$836$	19.9456	+	34.5469i	0.689835	+	1.19483i
$837$	22.7872	−	20.2817i	0.787642	−	0.701038i
$838$	−0.276495	+	0.159634i	−0.00955135	+	0.00551447i
$839$			19.9048i			0.687189i	0.939118	+	0.343594i	$0.111645\pi$
$839$			19.9048i			0.687189i	−0.939118	+	0.343594i	$0.888355\pi$
$840$	−0.129373	+	0.0869032i	−0.00446381	+	0.00299845i
$841$	13.1259	−	22.7347i	0.452616	−	0.783954i
$842$	−1.07027			−0.0368839
$843$	−26.9108	−	13.1892i	−0.926857	−	0.454260i
$844$	18.6066	−	32.2276i	0.640467	−	1.10932i
$845$	−2.96631	−	1.27171i	−0.102044	−	0.0437481i
$846$	−1.63693	+	0.223661i	−0.0562789	+	0.00768962i
$847$	−5.69052	−	3.28542i	−0.195529	−	0.112888i
$848$	21.4629	+	37.1749i	0.737040	+	1.27659i
$849$	−58.0686	+	3.94873i	−1.99291	+	0.135520i
$850$	2.36759	−	1.36693i	0.0812076	−	0.0468852i
$851$	5.89584	+	3.40396i	0.202107	+	0.116686i
$852$	0.111676	+	1.64227i	0.00382597	+	0.0562633i
$853$	2.74547	+	1.58510i	0.0940032	+	0.0542728i	0.546265	−	0.837613i	$-0.316049\pi$
$853$	2.74547	+	1.58510i	0.0940032	+	0.0542728i	−0.452261	+	0.891885i	$0.649383\pi$
$854$	−0.278004	−	0.481517i	−0.00951310	−	0.0164772i
$855$	1.34571	−	3.29434i	0.0460224	−	0.112664i
$856$	2.12814	+	1.22868i	0.0727382	+	0.0419954i
$857$	21.8402	−	37.8284i	0.746048	−	1.29219i	−0.203655	−	0.979043i	$-0.565282\pi$
$857$	21.8402	−	37.8284i	0.746048	−	1.29219i	0.949703	−	0.313151i	$-0.101385\pi$
$858$	−1.43993	−	1.89104i	−0.0491584	−	0.0645591i
$859$	17.6050	+	30.4928i	0.600675	+	1.04040i	0.992719	+	0.120453i	$0.0384347\pi$
$859$	17.6050	+	30.4928i	0.600675	+	1.04040i	−0.392044	+	0.919946i	$0.628232\pi$
$860$			3.66896i			0.125111i
$861$	16.1704	−	1.09961i	0.551087	−	0.0374746i
$862$	−3.14020			−0.106956
$863$			35.5346i			1.20961i	0.796372	+	0.604807i	$0.206750\pi$
$863$			35.5346i			1.20961i	−0.796372	+	0.604807i	$0.793250\pi$
$864$	5.34482	+	1.77068i	0.181834	+	0.0602396i
$865$	−5.47075	+	3.15854i	−0.186011	+	0.107394i
$866$	−1.19699	−	0.691084i	−0.0406755	−	0.0234840i
$867$	−15.3778	+	31.3763i	−0.522256	+	1.06560i
$868$	11.6933			0.396896
$869$		−	30.7435i		−	1.04290i
$870$	0.0645767	−	0.00439129i	0.00218935	−	0.000148879i
$871$	−20.9692	−	10.5019i	−0.710516	−	0.355844i
$872$	1.68430			0.0570378
$873$	−4.50389	−	32.9632i	−0.152434	−	1.11563i
$874$	0.282821	−	0.489861i	0.00956658	−	0.0165698i
$875$	2.46733			0.0834110
$876$	19.8579	+	9.73250i	0.670936	+	0.328831i
$877$	−10.5404	−	6.08550i	−0.355924	−	0.205493i	0.311367	−	0.950290i	$-0.399213\pi$
$877$	−10.5404	−	6.08550i	−0.355924	−	0.205493i	−0.667291	+	0.744797i	$0.732546\pi$
$878$	−2.19533	−	1.26748i	−0.0740888	−	0.0427752i
$879$	37.0154	+	18.1415i	1.24850	+	0.611898i
$880$	−4.11123			−0.138590
$881$	−22.5114	+	38.9910i	−0.758430	+	1.31364i	0.185221	+	0.982697i	$0.440700\pi$
$881$	−22.5114	+	38.9910i	−0.758430	+	1.31364i	−0.943651	+	0.330942i	$0.892633\pi$
$882$	0.215289	−	0.166878i	0.00724917	−	0.00561906i
$883$	−47.9950			−1.61516			−0.807580	−	0.589759i	$-0.799223\pi$
$883$	−47.9950			−1.61516			−0.807580	+	0.589759i	$0.799223\pi$
$884$	19.6071	−	39.1497i	0.659458	−	1.31675i
$885$	1.67746	−	0.114069i	0.0563872	−	0.00383440i
$886$			1.84894i			0.0621162i
$887$	−1.82237			−0.0611891			−0.0305946	−	0.999532i	$-0.509740\pi$
$887$	−1.82237			−0.0611891			−0.0305946	+	0.999532i	$0.509740\pi$
$888$	−1.44256	+	2.94336i	−0.0484093	+	0.0987728i
$889$	−5.51424	−	3.18365i	−0.184942	−	0.106776i
$890$	0.0819828	−	0.0473328i	0.00274807	−	0.00158660i
$891$	26.4138	−	26.9360i	0.884897	−	0.902390i
$892$		−	30.7761i		−	1.03046i
$893$	28.9799			0.969777
$894$	−0.403270	+	0.0274229i	−0.0134874	+	0.000917158i
$895$			5.32950i			0.178146i
$896$	1.43783	+	2.49039i	0.0480344	+	0.0831980i
$897$	3.14388	−	7.51103i	0.104971	−	0.250786i
$898$	−1.07980	+	1.87027i	−0.0360335	+	0.0624119i
$899$	−8.42873	−	4.86633i	−0.281114	−	0.162301i
$900$	−18.0777	−	23.3221i	−0.602590	−	0.777404i
$901$	−33.1241	−	57.3726i	−1.10352	−	1.91136i
$902$	−3.08435	−	1.78075i	−0.102698	−	0.0592925i
$903$	−0.871907	−	12.8219i	−0.0290153	−	0.426688i
$904$	−3.08875	−	1.78329i	−0.102730	−	0.0593113i
$905$	3.13282	−	1.80874i	0.104139	−	0.0601244i
$906$	1.60515	−	0.109152i	0.0533276	−	0.00362634i
$907$	−19.9257	−	34.5124i	−0.661623	−	1.14597i	−0.980189	−	0.198064i	$-0.936534\pi$
$907$	−19.9257	−	34.5124i	−0.661623	−	1.14597i	0.318566	−	0.947901i	$-0.396799\pi$
$908$	−22.9926	−	13.2748i	−0.763037	−	0.440539i
$909$	−2.10901	−	2.72085i	−0.0699516	−	0.0902448i
$910$	−0.0678546	+	0.0447371i	−0.00224936	+	0.00148302i
$911$	−13.8869	+	24.0528i	−0.460093	+	0.796905i	−0.998965	−	0.0454827i	$-0.985517\pi$
$911$	−13.8869	+	24.0528i	−0.460093	+	0.796905i	0.538872	+	0.842388i	$0.318851\pi$
$912$	−29.3578	−	14.3885i	−0.972133	−	0.476449i
$913$	−67.4274			−2.23152
$914$	−0.658779	+	1.14104i	−0.0217905	+	0.0377422i
$915$	−2.18582	+	1.46827i	−0.0722610	+	0.0485394i
$916$			47.0480i			1.55451i
$917$	−0.707518	+	0.408486i	−0.0233643	+	0.0134894i
$918$	−2.73062	−	0.904623i	−0.0901239	−	0.0298570i
$919$	20.0412	+	34.7124i	0.661098	+	1.14506i	0.980327	+	0.197378i	$0.0632426\pi$
$919$	20.0412	+	34.7124i	0.661098	+	1.14506i	−0.319229	+	0.947677i	$0.603424\pi$
$920$	0.0586601	+	0.101602i	0.00193397	+	0.00334973i
$921$	−0.0835399	−	1.22851i	−0.00275273	−	0.0404807i
$922$	0.704183	+	1.21968i	0.0231910	+	0.0401681i
$923$	0.101944	+	1.71735i	0.00335554	+	0.0565271i
$924$	14.4275	−	0.981087i	0.474630	−	0.0322754i
$925$	22.3309	−	12.8927i	0.734235	−	0.423911i
$926$	−0.464546	+	0.804618i	−0.0152659	+	0.0264414i
$927$	−31.4538	−	40.5787i	−1.03308	−	1.33278i
$928$		−	1.79637i		−	0.0589686i
$929$		−	51.0241i		−	1.67405i	−0.547168	−	0.837023i	$-0.684294\pi$
$929$		−	51.0241i		−	1.67405i	0.547168	−	0.837023i	$-0.315706\pi$
$930$	0.0155511	+	0.228689i	0.000509942	+	0.00749901i
$931$	−4.13786	+	2.38900i	−0.135613	+	0.0782962i
$932$	4.94191	−	8.55964i	0.161878	−	0.280380i
$933$	−6.85884	−	10.2108i	−0.224548	−	0.334287i
$934$	0.862073	−	0.497718i	0.0282079	−	0.0162858i
$935$	6.34494			0.207502
$936$	3.71075	+	1.26486i	0.121290	+	0.0413434i
$937$	46.1191			1.50664			0.753322	−	0.657651i	$-0.228450\pi$
$937$	46.1191			1.50664			0.753322	+	0.657651i	$0.228450\pi$
$938$	−0.511463	+	0.295293i	−0.0166998	+	0.00964166i
$939$	−7.27157	+	14.8367i	−0.237299	+	0.484177i
$940$	−1.49958	+	2.59735i	−0.0489110	+	0.0847163i
$941$	−30.1514	+	17.4079i	−0.982908	+	0.567482i	−0.903147	−	0.429332i	$-0.858749\pi$
$941$	−30.1514	+	17.4079i	−0.982908	+	0.567482i	−0.0797612	+	0.996814i	$0.525416\pi$
$942$	2.32866	+	1.14129i	0.0758718	+	0.0371853i
$943$		−	12.2007i		−	0.397311i
$944$		−	15.4470i		−	0.502758i
$945$	−0.857661	−	0.963614i	−0.0278997	−	0.0313464i
$946$	−1.41200	+	2.44566i	−0.0459082	+	0.0795153i
$947$	28.2929	−	16.3349i	0.919397	−	0.530814i	0.0359545	−	0.999353i	$-0.488553\pi$
$947$	28.2929	−	16.3349i	0.919397	−	0.530814i	0.883443	+	0.468539i	$0.155220\pi$
$948$	14.1084	+	21.0033i	0.458220	+	0.682156i
$949$	20.6660	+	10.3500i	0.670847	+	0.335977i
$950$	−1.07121	−	1.85538i	−0.0347545	−	0.0601965i
$951$	26.3778	+	12.9279i	0.855357	+	0.419217i
$952$	−1.10491	−	1.91376i	−0.0358103	−	0.0620253i
$953$	4.77841	+	8.27645i	0.154788	+	0.268101i	0.932982	−	0.359924i	$-0.117197\pi$
$953$	4.77841	+	8.27645i	0.154788	+	0.268101i	−0.778194	+	0.628024i	$0.783864\pi$
$954$	2.33926	−	1.81323i	0.0757363	−	0.0587056i
$955$	−1.46722	+	0.847099i	−0.0474781	+	0.0274115i
$956$			22.7257i			0.735002i
$957$	−10.8079	−	5.29703i	−0.349369	−	0.171229i
$958$	−0.731034	+	1.26619i	−0.0236186	+	0.0409087i
$959$	17.4176			0.562444
$960$	2.78522	−	1.87090i	0.0898925	−	0.0603829i
$961$	1.73342	−	3.00236i	0.0559166	−	0.0968505i
$962$	−0.765464	+	1.52841i	−0.0246795	+	0.0492779i
$963$	−7.69175	+	18.8296i	−0.247863	+	0.606776i
$964$	−3.03959	−	1.75491i	−0.0978986	−	0.0565218i
$965$	−1.03927	−	1.80007i	−0.0334554	−	0.0579464i
$966$	−0.114336	−	0.170213i	−0.00367870	−	0.00547650i
$967$	−15.0263	+	8.67545i	−0.483214	+	0.278984i	−0.721755	−	0.692149i	$-0.756664\pi$
$967$	−15.0263	+	8.67545i	−0.483214	+	0.278984i	0.238541	+	0.971132i	$0.423331\pi$
$968$	−2.06248	−	1.19077i	−0.0662906	−	0.0382729i
$969$	45.3083	+	22.2059i	1.45551	+	0.713358i
$970$	0.216492	+	0.124991i	0.00695113	+	0.00401323i
$971$	6.58186	+	11.4001i	0.211222	+	0.365847i	0.952097	−	0.305795i	$-0.0989224\pi$
$971$	6.58186	+	11.4001i	0.211222	+	0.365847i	−0.740875	+	0.671643i	$0.765589\pi$
$972$	−5.68425	+	30.5236i	−0.182322	+	0.979046i
$973$	−8.86485	−	5.11812i	−0.284194	−	0.164080i
$974$	0.650189	−	1.12616i	0.0208334	−	0.0360845i
$975$	−18.6833	−	24.5366i	−0.598345	−	0.785800i
$976$	12.0960	+	20.9508i	0.387182	+	0.670619i
$977$			56.2363i			1.79916i	0.436759	+	0.899579i	$0.356126\pi$
$977$			56.2363i			1.79916i	−0.436759	+	0.899579i	$0.643874\pi$
$978$	0.465050	−	0.948874i	0.0148707	−	0.0303417i
$979$	−17.6036			−0.562614
$980$		−	0.494480i		−	0.0157956i
$981$	1.88733	+	13.8130i	0.0602577	+	0.441015i
$982$	−2.51990	+	1.45486i	−0.0804131	+	0.0464265i
$983$	47.7301	+	27.5570i	1.52235	+	0.878932i	0.999651	+	0.0264178i	$0.00841003\pi$
$983$	47.7301	+	27.5570i	1.52235	+	0.878932i	0.522704	+	0.852514i	$0.324923\pi$
$984$	5.86084	−	0.398544i	0.186837	−	0.0127051i
$985$	1.38240			0.0440469
$986$			0.917747i			0.0292270i
$987$	4.62335	−	9.43335i	0.147163	−	0.300267i
$988$	−30.6800	−	15.3653i	−0.976060	−	0.488835i
$989$	−9.67427			−0.307624
$990$	0.0383748	+	0.280858i	0.00121963	+	0.00892626i
$991$	7.86399	−	13.6208i	0.249808	−	0.432680i	−0.713664	−	0.700488i	$-0.752966\pi$
$991$	7.86399	−	13.6208i	0.249808	−	0.432680i	0.963472	+	0.267808i	$0.0862992\pi$
$992$	6.36158			0.201980
$993$	0.0540351	+	0.794621i	0.00171475	+	0.0252165i
$994$	0.0375193	+	0.0216618i	0.00119004	+	0.000687069i
$995$	−2.14674	−	1.23942i	−0.0680563	−	0.0392923i
$996$	46.0650	−	30.9430i	1.45963	−	0.980465i
$997$	0.612224			0.0193893			0.00969466	−	0.999953i	$-0.496914\pi$
$997$	0.612224			0.0193893			0.00969466	+	0.999953i	$0.496914\pi$
$998$	−0.248518	+	0.430446i	−0.00786670	+	0.0136255i
$999$	−25.7550	−	8.53232i	−0.814851	−	0.269951i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.dk.a.43.40	yes	168
9.4	even	3		819.2.bh.a.589.40	✓	168
13.10	even	6		819.2.bh.a.673.45	yes	168
117.49	even	6	inner	819.2.dk.a.400.40	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.bh.a.589.40	✓	168	9.4	even	3
819.2.bh.a.673.45	yes	168	13.10	even	6
819.2.dk.a.43.40	yes	168	1.1	even	1	trivial
819.2.dk.a.400.40	yes	168	117.49	even	6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.dk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0786329 + 0.0453987i) q^{2} +(1.72806 - 0.117510i) q^{3} +(-0.995878 + 1.72491i) q^{4} +(0.215002 - 0.124132i) q^{5} +(-0.130548 + 0.0876919i) q^{6} -1.00000i q^{7} -0.362441i q^{8} +(2.97238 - 0.406129i) q^{9} +O(q^{10})\)	\(q+(-0.0786329 + 0.0453987i) q^{2} +(1.72806 - 0.117510i) q^{3} +(-0.995878 + 1.72491i) q^{4} +(0.215002 - 0.124132i) q^{5} +(-0.130548 + 0.0876919i) q^{6} -1.00000i q^{7} -0.362441i q^{8} +(2.97238 - 0.406129i) q^{9} +(-0.0112708 + 0.0195217i) q^{10} +(3.63017 - 2.09588i) q^{11} +(-1.51824 + 3.09778i) q^{12} +(-1.61458 + 3.22384i) q^{13} +(0.0453987 + 0.0786329i) q^{14} +(0.356950 - 0.239772i) q^{15} +(-1.97530 - 3.42132i) q^{16} +(3.04852 + 5.28019i) q^{17} +(-0.215289 + 0.166878i) q^{18} +(4.13786 - 2.38900i) q^{19} +0.494480i q^{20} +(-0.117510 - 1.72806i) q^{21} +(-0.190301 + 0.329610i) q^{22} -1.30384 q^{23} +(-0.0425905 - 0.626321i) q^{24} +(-2.46918 + 4.27675i) q^{25} +(-0.0193993 - 0.326800i) q^{26} +(5.08873 - 1.05110i) q^{27} +(1.72491 + 0.995878i) q^{28} +(-0.828897 - 1.43569i) q^{29} +(-0.0171827 + 0.0350590i) q^{30} +(5.08430 - 2.93542i) q^{31} +(0.938415 + 0.541794i) q^{32} +(6.02686 - 4.04839i) q^{33} +(-0.479428 - 0.276798i) q^{34} +(-0.124132 - 0.215002i) q^{35} +(-2.25959 + 5.53155i) q^{36} +(-4.52192 - 2.61073i) q^{37} +(-0.216915 + 0.375708i) q^{38} +(-2.41125 + 5.76072i) q^{39} +(-0.0449904 - 0.0779257i) q^{40} +9.35757i q^{41} +(0.0876919 + 0.130548i) q^{42} +7.41985 q^{43} +8.34896i q^{44} +(0.588655 - 0.456285i) q^{45} +(0.102524 - 0.0591925i) q^{46} +(5.25270 + 3.03265i) q^{47} +(-3.81548 - 5.68013i) q^{48} -1.00000 q^{49} -0.448391i q^{50} +(5.88849 + 8.76625i) q^{51} +(-3.95291 - 5.99555i) q^{52} -10.8656 q^{53} +(-0.352423 + 0.313673i) q^{54} +(0.520330 - 0.901237i) q^{55} -0.362441 q^{56} +(6.86975 - 4.61457i) q^{57} +(0.130357 + 0.0752618i) q^{58} +(3.38619 + 1.95502i) q^{59} +(0.0581063 + 0.854490i) q^{60} -6.12360 q^{61} +(-0.266529 + 0.461642i) q^{62} +(-0.406129 - 2.97238i) q^{63} +7.80282 q^{64} +(0.0530427 + 0.893553i) q^{65} +(-0.290118 + 0.591949i) q^{66} +6.50443i q^{67} -12.1438 q^{68} +(-2.25311 + 0.153214i) q^{69} +(0.0195217 + 0.0112708i) q^{70} +(0.413219 - 0.238572i) q^{71} +(-0.147198 - 1.07731i) q^{72} -6.41037i q^{73} +0.474096 q^{74} +(-3.76433 + 7.68063i) q^{75} +9.51660i q^{76} +(-2.09588 - 3.63017i) q^{77} +(-0.0719255 - 0.562450i) q^{78} +(3.66713 - 6.35166i) q^{79} +(-0.849388 - 0.490395i) q^{80} +(8.67012 - 2.41434i) q^{81} +(-0.424822 - 0.735813i) q^{82} +(-13.9306 - 8.04285i) q^{83} +(3.09778 + 1.51824i) q^{84} +(1.31088 + 0.756834i) q^{85} +(-0.583445 + 0.336852i) q^{86} +(-1.60109 - 2.38356i) q^{87} +(-0.759634 - 1.31572i) q^{88} +(-3.63694 - 2.09979i) q^{89} +(-0.0255729 + 0.0626033i) q^{90} +(3.22384 + 1.61458i) q^{91} +(1.29846 - 2.24900i) q^{92} +(8.44104 - 5.67004i) q^{93} -0.550714 q^{94} +(0.593100 - 1.02728i) q^{95} +(1.68530 + 0.825979i) q^{96} -11.0898i q^{97} +(0.0786329 - 0.0453987i) q^{98} +(9.93906 - 7.70407i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 84 q^{4} - 2 q^{9}+O(q^{10}) \) 168 * q + 84 * q^4 - 2 * q^9	\( 168 q + 84 q^{4} - 2 q^{9} + 12 q^{12} + 8 q^{14} - 84 q^{16} + 12 q^{18} - 6 q^{21} + 40 q^{23} - 84 q^{24} + 84 q^{25} + 4 q^{26} - 24 q^{27} + 34 q^{29} + 44 q^{30} + 36 q^{32} + 18 q^{33} + 16 q^{35} + 4 q^{36} - 12 q^{38} - 6 q^{39} - 30 q^{45} - 30 q^{47} - 2 q^{48} - 168 q^{49} - 38 q^{51} + 18 q^{52} - 48 q^{53} + 114 q^{54} + 48 q^{56} - 54 q^{57} + 48 q^{59} + 24 q^{60} + 6 q^{62} - 12 q^{63} - 132 q^{64} - 16 q^{65} - 54 q^{66} - 156 q^{68} - 28 q^{69} + 24 q^{71} + 36 q^{72} - 84 q^{74} + 30 q^{75} - 16 q^{77} + 116 q^{78} - 6 q^{79} - 2 q^{81} - 6 q^{82} + 18 q^{83} - 24 q^{84} + 90 q^{85} - 24 q^{86} + 52 q^{87} + 24 q^{88} - 36 q^{89} - 44 q^{90} - 6 q^{91} + 8 q^{92} - 66 q^{93} + 120 q^{94} - 48 q^{95} - 24 q^{96} + 6 q^{99}+O(q^{100}) \) 168 * q + 84 * q^4 - 2 * q^9 + 12 * q^12 + 8 * q^14 - 84 * q^16 + 12 * q^18 - 6 * q^21 + 40 * q^23 - 84 * q^24 + 84 * q^25 + 4 * q^26 - 24 * q^27 + 34 * q^29 + 44 * q^30 + 36 * q^32 + 18 * q^33 + 16 * q^35 + 4 * q^36 - 12 * q^38 - 6 * q^39 - 30 * q^45 - 30 * q^47 - 2 * q^48 - 168 * q^49 - 38 * q^51 + 18 * q^52 - 48 * q^53 + 114 * q^54 + 48 * q^56 - 54 * q^57 + 48 * q^59 + 24 * q^60 + 6 * q^62 - 12 * q^63 - 132 * q^64 - 16 * q^65 - 54 * q^66 - 156 * q^68 - 28 * q^69 + 24 * q^71 + 36 * q^72 - 84 * q^74 + 30 * q^75 - 16 * q^77 + 116 * q^78 - 6 * q^79 - 2 * q^81 - 6 * q^82 + 18 * q^83 - 24 * q^84 + 90 * q^85 - 24 * q^86 + 52 * q^87 + 24 * q^88 - 36 * q^89 - 44 * q^90 - 6 * q^91 + 8 * q^92 - 66 * q^93 + 120 * q^94 - 48 * q^95 - 24 * q^96 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more