LMFDB - Embedded newform 161.2.g.a.68.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [161,2,Mod(45,161)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(161, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("161.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	161.g (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.28559147254$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			68.12
Character	$\chi$	$=$	161.68
Dual form			161.2.g.a.45.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.724735 - 1.25528i) q^{2} +(-2.07526 + 1.19815i) q^{3} +(-0.0504829 - 0.0874389i) q^{4} +(1.26781 - 2.19591i) q^{5} +3.47337i q^{6} +(1.91509 - 1.82550i) q^{7} +2.75259 q^{8} +(1.37113 - 2.37487i) q^{9} +(-1.83766 - 3.18291i) q^{10} +(0.954149 - 0.550878i) q^{11} +(0.209530 + 0.120972i) q^{12} +0.792485i q^{13} +(-0.903575 - 3.72697i) q^{14} +6.07612i q^{15} +(2.09587 - 3.63015i) q^{16} +(-1.96566 - 3.40463i) q^{17} +(-1.98742 - 3.44231i) q^{18} +(-3.54203 + 6.13498i) q^{19} -0.256011 q^{20} +(-1.78708 + 6.08294i) q^{21} -1.59696i q^{22} +(-0.0779482 + 4.79520i) q^{23} +(-5.71235 + 3.29803i) q^{24} +(-0.714694 - 1.23789i) q^{25} +(0.994790 + 0.574342i) q^{26} -0.617607i q^{27} +(-0.256299 - 0.0752969i) q^{28} +1.18102 q^{29} +(7.62723 + 4.40358i) q^{30} +(-4.22784 + 2.44094i) q^{31} +(-0.285306 - 0.494164i) q^{32} +(-1.32007 + 2.28643i) q^{33} -5.69834 q^{34} +(-1.58066 - 6.51976i) q^{35} -0.276875 q^{36} +(-9.91723 - 5.72572i) q^{37} +(5.13407 + 8.89247i) q^{38} +(-0.949517 - 1.64461i) q^{39} +(3.48977 - 6.04446i) q^{40} -0.854610i q^{41} +(6.34063 + 6.65181i) q^{42} +4.03573i q^{43} +(-0.0963363 - 0.0556198i) q^{44} +(-3.47668 - 6.02178i) q^{45} +(5.96282 + 3.57310i) q^{46} +(9.87089 + 5.69896i) q^{47} +10.0447i q^{48} +(0.335124 - 6.99197i) q^{49} -2.07186 q^{50} +(8.15852 + 4.71032i) q^{51} +(0.0692940 - 0.0400069i) q^{52} +(3.14173 - 1.81388i) q^{53} +(-0.775269 - 0.447602i) q^{54} -2.79364i q^{55} +(5.27146 - 5.02485i) q^{56} -16.9756i q^{57} +(0.855928 - 1.48251i) q^{58} +(-4.20283 + 2.42650i) q^{59} +(0.531289 - 0.306740i) q^{60} +(-5.00067 + 8.66142i) q^{61} +7.07616i q^{62} +(-1.70948 - 7.05109i) q^{63} +7.55639 q^{64} +(1.74023 + 1.00472i) q^{65} +(1.91340 + 3.31411i) q^{66} +(-4.47989 + 2.58647i) q^{67} +(-0.198465 + 0.343751i) q^{68} +(-5.58361 - 10.0447i) q^{69} +(-9.32967 - 2.74093i) q^{70} -10.5645 q^{71} +(3.77417 - 6.53706i) q^{72} +(8.12777 - 4.69257i) q^{73} +(-14.3747 + 8.29926i) q^{74} +(2.96635 + 1.71262i) q^{75} +0.715248 q^{76} +(0.821653 - 2.79677i) q^{77} -2.75259 q^{78} +(-5.61540 - 3.24205i) q^{79} +(-5.31433 - 9.20470i) q^{80} +(4.85339 + 8.40631i) q^{81} +(-1.07277 - 0.619366i) q^{82} -5.50430 q^{83} +(0.622103 - 0.150824i) q^{84} -9.96836 q^{85} +(5.06597 + 2.92484i) q^{86} +(-2.45092 + 1.41504i) q^{87} +(2.62638 - 1.51634i) q^{88} +(-0.261287 + 0.452563i) q^{89} -10.0787 q^{90} +(1.44668 + 1.51768i) q^{91} +(0.423222 - 0.235260i) q^{92} +(5.84924 - 10.1312i) q^{93} +(14.3076 - 8.26048i) q^{94} +(8.98126 + 15.5560i) q^{95} +(1.18417 + 0.683679i) q^{96} +11.9199 q^{97} +(-8.53400 - 5.48801i) q^{98} -3.02131i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{2} - 6 q^{3} - 12 q^{4} + 12 q^{8} + 4 q^{9} + 6 q^{12} + 22 q^{18} - 36 q^{24} - 22 q^{25} - 12 q^{26} - 44 q^{29} - 6 q^{32} - 10 q^{35} - 16 q^{39} + 18 q^{46} - 36 q^{47} + 28 q^{49} + 84 q^{50}+ \cdots - 146 q^{98}+O(q^{100}) $ 28 * q - 4 * q^2 - 6 * q^3 - 12 * q^4 + 12 * q^8 + 4 * q^9 + 6 * q^12 + 22 * q^18 - 36 * q^24 - 22 * q^25 - 12 * q^26 - 44 * q^29 - 6 * q^32 - 10 * q^35 - 16 * q^39 + 18 * q^46 - 36 * q^47 + 28 * q^49 + 84 * q^50 + 72 * q^52 - 30 * q^54 + 14 * q^58 - 54 * q^59 - 68 * q^64 + 38 * q^70 + 16 * q^71 - 4 * q^72 - 18 * q^73 + 96 * q^75 + 20 * q^77 - 12 * q^78 + 22 * q^81 - 52 * q^85 - 18 * q^87 - 28 * q^92 - 10 * q^93 + 84 * q^94 + 56 * q^95 - 84 * q^96 - 146 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/161\mathbb{Z}\right)^\times$.

$n$	$24$	$120$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.724735	−	1.25528i	0.512465	−	0.887616i	−0.487430	−	0.873162i	$-0.662066\pi$
$2$	0.724735	−	1.25528i	0.512465	−	0.887616i	0.999896	−	0.0144540i	$-0.00460102\pi$
$3$	−2.07526	+	1.19815i	−1.19815	+	0.691753i	−0.960143	−	0.279510i	$-0.909828\pi$
$3$	−2.07526	+	1.19815i	−1.19815	+	0.691753i	−0.238009	+	0.971263i	$0.576495\pi$
$4$	−0.0504829	−	0.0874389i	−0.0252414	−	0.0437195i
$5$	1.26781	−	2.19591i	0.566983	−	0.982043i	−0.429879	−	0.902886i	$-0.641444\pi$
$5$	1.26781	−	2.19591i	0.566983	−	0.982043i	0.996862	−	0.0791566i	$-0.0252227\pi$
$6$			3.47337i			1.41800i
$7$	1.91509	−	1.82550i	0.723835	−	0.689973i
$7$	1.91509	−	1.82550i	0.723835	−	0.689973i
$8$	2.75259			0.973189
$9$	1.37113	−	2.37487i	0.457044	−	0.791624i
$10$	−1.83766	−	3.18291i	−0.581118	−	1.00653i
$11$	0.954149	−	0.550878i	0.287687	−	0.166096i	−0.349211	−	0.937044i	$-0.613551\pi$
$11$	0.954149	−	0.550878i	0.287687	−	0.166096i	0.636898	+	0.770948i	$0.280217\pi$
$12$	0.209530	+	0.120972i	0.0604861	+	0.0349217i
$13$			0.792485i			0.219796i	0.993943	+	0.109898i	$0.0350524\pi$
$13$			0.792485i			0.219796i	−0.993943	+	0.109898i	$0.964948\pi$
$14$	−0.903575	−	3.72697i	−0.241490	−	0.996075i
$15$			6.07612i			1.56885i
$16$	2.09587	−	3.63015i	0.523967	−	0.907538i
$17$	−1.96566	−	3.40463i	−0.476743	−	0.825743i	0.522902	−	0.852393i	$-0.324849\pi$
$17$	−1.96566	−	3.40463i	−0.476743	−	0.825743i	−0.999645	+	0.0266497i	$0.991516\pi$
$18$	−1.98742	−	3.44231i	−0.468439	−	0.811360i
$19$	−3.54203	+	6.13498i	−0.812598	+	1.40746i	0.0984425	+	0.995143i	$0.468614\pi$
$19$	−3.54203	+	6.13498i	−0.812598	+	1.40746i	−0.911040	+	0.412318i	$0.864719\pi$
$20$	−0.256011			−0.0572458
$21$	−1.78708	+	6.08294i	−0.389973	+	1.32741i
$22$		−	1.59696i		−	0.340474i
$23$	−0.0779482	+	4.79520i	−0.0162533	+	0.999868i
$23$	−0.0779482	+	4.79520i	−0.0162533	+	0.999868i
$24$	−5.71235	+	3.29803i	−1.16603	+	0.673207i
$25$	−0.714694	−	1.23789i	−0.142939	−	0.247577i
$26$	0.994790	+	0.574342i	0.195094	+	0.112638i
$27$		−	0.617607i		−	0.118859i
$28$	−0.256299	−	0.0752969i	−0.0484359	−	0.0142298i
$29$	1.18102			0.219310			0.109655	−	0.993970i	$-0.465025\pi$
$29$	1.18102			0.219310			0.109655	+	0.993970i	$0.465025\pi$
$30$	7.62723	+	4.40358i	1.39253	+	0.803980i
$31$	−4.22784	+	2.44094i	−0.759342	+	0.438407i	−0.829060	−	0.559160i	$-0.811124\pi$
$31$	−4.22784	+	2.44094i	−0.759342	+	0.438407i	0.0697172	+	0.997567i	$0.477790\pi$
$32$	−0.285306	−	0.494164i	−0.0504354	−	0.0873567i
$33$	−1.32007	+	2.28643i	−0.229795	+	0.398016i
$34$	−5.69834			−0.977257
$35$	−1.58066	−	6.51976i	−0.267181	−	1.10204i
$36$	−0.276875			−0.0461458
$37$	−9.91723	−	5.72572i	−1.63038	−	0.941302i	−0.983974	−	0.178311i	$-0.942937\pi$
$37$	−9.91723	−	5.72572i	−1.63038	−	0.941302i	−0.646409	−	0.762991i	$-0.723730\pi$
$38$	5.13407	+	8.89247i	0.832856	+	1.44255i
$39$	−0.949517	−	1.64461i	−0.152044	−	0.263349i
$40$	3.48977	−	6.04446i	0.551781	−	0.955714i
$41$		−	0.854610i		−	0.133468i	−0.997771	−	0.0667338i	$-0.978742\pi$
$41$		−	0.854610i		−	0.133468i	0.997771	−	0.0667338i	$-0.0212578\pi$
$42$	6.34063	+	6.65181i	0.978380	+	1.02640i
$43$			4.03573i			0.615444i	0.951476	+	0.307722i	$0.0995666\pi$
$43$			4.03573i			0.615444i	−0.951476	+	0.307722i	$0.900433\pi$
$44$	−0.0963363	−	0.0556198i	−0.0145232	−	0.00838500i
$45$	−3.47668	−	6.02178i	−0.518273	−	0.897674i
$46$	5.96282	+	3.57310i	0.879169	+	0.526824i
$47$	9.87089	+	5.69896i	1.43982	+	0.831279i	0.997836	−	0.0657452i	$-0.0209425\pi$
$47$	9.87089	+	5.69896i	1.43982	+	0.831279i	0.441981	+	0.897024i	$0.354276\pi$
$48$			10.0447i			1.44982i
$49$	0.335124	−	6.99197i	0.0478749	−	0.998853i
$50$	−2.07186			−0.293005
$51$	8.15852	+	4.71032i	1.14242	+	0.659577i
$52$	0.0692940	−	0.0400069i	0.00960935	−	0.00554796i
$53$	3.14173	−	1.81388i	0.431550	−	0.249155i	−0.268457	−	0.963292i	$-0.586514\pi$
$53$	3.14173	−	1.81388i	0.431550	−	0.249155i	0.700007	+	0.714136i	$0.253180\pi$
$54$	−0.775269	−	0.447602i	−0.105501	−	0.0609109i
$55$		−	2.79364i		−	0.376694i
$56$	5.27146	−	5.02485i	0.704429	−	0.671474i
$57$		−	16.9756i		−	2.24847i
$58$	0.855928	−	1.48251i	0.112389	−	0.194663i
$59$	−4.20283	+	2.42650i	−0.547162	+	0.315904i	−0.747976	−	0.663725i	$-0.768974\pi$
$59$	−4.20283	+	2.42650i	−0.547162	+	0.315904i	0.200815	+	0.979629i	$0.435641\pi$
$60$	0.531289	−	0.306740i	0.0685892	−	0.0396000i
$61$	−5.00067	+	8.66142i	−0.640270	+	1.10898i	0.345102	+	0.938565i	$0.387844\pi$
$61$	−5.00067	+	8.66142i	−0.640270	+	1.10898i	−0.985372	+	0.170416i	$0.945489\pi$
$62$			7.07616i			0.898673i
$63$	−1.70948	−	7.05109i	−0.215374	−	0.888354i
$64$	7.55639			0.944549
$65$	1.74023	+	1.00472i	0.215849	+	0.124620i
$66$	1.91340	+	3.31411i	0.235524	+	0.407939i
$67$	−4.47989	+	2.58647i	−0.547306	+	0.315987i	−0.748035	−	0.663660i	$-0.769002\pi$
$67$	−4.47989	+	2.58647i	−0.547306	+	0.315987i	0.200729	+	0.979647i	$0.435669\pi$
$68$	−0.198465	+	0.343751i	−0.0240674	+	0.0416859i
$69$	−5.58361	−	10.0447i	−0.672188	−	1.20924i
$70$	−9.32967	−	2.74093i	−1.11511	−	0.327603i
$71$	−10.5645			−1.25378			−0.626888	−	0.779110i	$-0.715671\pi$
$71$	−10.5645			−1.25378			−0.626888	+	0.779110i	$0.715671\pi$
$72$	3.77417	−	6.53706i	0.444791	−	0.770400i
$73$	8.12777	−	4.69257i	0.951283	−	0.549224i	0.0578041	−	0.998328i	$-0.481590\pi$
$73$	8.12777	−	4.69257i	0.951283	−	0.549224i	0.893479	+	0.449104i	$0.148257\pi$
$74$	−14.3747	+	8.29926i	−1.67103	+	0.964769i
$75$	2.96635	+	1.71262i	0.342525	+	0.197757i
$76$	0.715248			0.0820445
$77$	0.821653	−	2.79677i	0.0936360	−	0.318722i
$78$	−2.75259			−0.311670
$79$	−5.61540	−	3.24205i	−0.631781	−	0.364759i	0.149660	−	0.988737i	$-0.452182\pi$
$79$	−5.61540	−	3.24205i	−0.631781	−	0.364759i	−0.781442	+	0.623978i	$0.785515\pi$
$80$	−5.31433	−	9.20470i	−0.594161	−	1.02912i
$81$	4.85339	+	8.40631i	0.539265	+	0.934035i
$82$	−1.07277	−	0.619366i	−0.118468	−	0.0683975i
$83$	−5.50430			−0.604175			−0.302087	−	0.953280i	$-0.597683\pi$
$83$	−5.50430			−0.604175			−0.302087	+	0.953280i	$0.597683\pi$
$84$	0.622103	−	0.150824i	0.0678770	−	0.0164562i
$85$	−9.96836			−1.08122
$86$	5.06597	+	2.92484i	0.546278	+	0.315394i
$87$	−2.45092	+	1.41504i	−0.262767	+	0.151708i
$88$	2.62638	−	1.51634i	0.279974	−	0.161643i
$89$	−0.261287	+	0.452563i	−0.0276964	+	0.0479716i	−0.879541	−	0.475822i	$-0.842151\pi$
$89$	−0.261287	+	0.452563i	−0.0276964	+	0.0479716i	0.851845	+	0.523794i	$0.175484\pi$
$90$	−10.0787			−1.06239
$91$	1.44668	+	1.51768i	0.151653	+	0.159096i
$92$	0.423222	−	0.235260i	0.0441239	−	0.0245275i
$93$	5.84924	−	10.1312i	0.606538	−	1.05055i
$94$	14.3076	−	8.26048i	1.47571	−	0.852003i
$95$	8.98126	+	15.5560i	0.921458	+	1.59601i
$96$	1.18417	+	0.683679i	0.120859	+	0.0697777i
$97$	11.9199			1.21028			0.605139	−	0.796120i	$-0.293118\pi$
$97$	11.9199			1.21028			0.605139	+	0.796120i	$0.293118\pi$
$98$	−8.53400	−	5.48801i	−0.862064	−	0.554372i
$99$		−	3.02131i		−	0.303653i
$100$	−0.0721596	+	0.124984i	−0.00721596	+	0.0124984i
$101$	−2.64903	+	1.52942i	−0.263588	+	0.152183i	−0.625970	−	0.779847i	$-0.715297\pi$
$101$	−2.64903	+	1.52942i	−0.263588	+	0.152183i	0.362382	+	0.932030i	$0.381963\pi$
$102$	11.8255	−	6.82747i	1.17090	−	0.676021i
$103$	7.66969	−	13.2843i	0.755717	−	1.30894i	−0.189299	−	0.981919i	$-0.560622\pi$
$103$	7.66969	−	13.2843i	0.755717	−	1.30894i	0.945017	−	0.327022i	$-0.106045\pi$
$104$			2.18139i			0.213903i
$105$	11.0919	+	11.6363i	1.08246	+	1.13559i
$106$		−	5.25833i		−	0.510734i
$107$	12.6702	+	7.31513i	1.22487	+	0.707181i	0.965953	−	0.258718i	$-0.0833001\pi$
$107$	12.6702	+	7.31513i	1.22487	+	0.707181i	0.258920	+	0.965899i	$0.416633\pi$
$108$	−0.0540029	+	0.0311786i	−0.00519643	+	0.00300016i
$109$	−12.1657	+	7.02387i	−1.16526	+	0.672764i	−0.952559	−	0.304353i	$-0.901560\pi$
$109$	−12.1657	+	7.02387i	−1.16526	+	0.672764i	−0.212703	+	0.977117i	$0.568227\pi$
$110$	−3.50679	−	2.02465i	−0.334360	−	0.193043i
$111$	27.4411			2.60459
$112$	−2.61306	−	10.7781i	−0.246911	−	1.01843i
$113$		−	7.95026i		−	0.747898i	−0.927449	−	0.373949i	$-0.878004\pi$
$113$		−	7.95026i		−	0.747898i	0.927449	−	0.373949i	$-0.121996\pi$
$114$	−21.3091	−	12.3028i	−1.99578	−	1.15226i
$115$	10.4310	+	6.25058i	0.972698	+	0.582869i
$116$	−0.0596213	−	0.103267i	−0.00553570	−	0.00958812i
$117$	1.88205	+	1.08660i	0.173996	+	0.100456i
$118$			7.03429i			0.647559i
$119$	−9.97955	−	2.93185i	−0.914824	−	0.268762i
$120$			16.7251i			1.52679i
$121$	−4.89307	+	8.47504i	−0.444824	+	0.770458i
$122$	7.24833	+	12.5545i	0.656233	+	1.13663i
$123$	1.02395	+	1.77354i	0.0923267	+	0.159914i
$124$	0.426867	+	0.246452i	0.0383338	+	0.0221320i
$125$	9.05373			0.809790
$126$	−10.0900	−	2.96430i	−0.898889	−	0.264081i
$127$	−6.22806			−0.552651			−0.276325	−	0.961064i	$-0.589117\pi$
$127$	−6.22806			−0.552651			−0.276325	+	0.961064i	$0.589117\pi$
$128$	6.04700	−	10.4737i	0.534484	−	0.925753i
$129$	−4.83542	−	8.37519i	−0.425735	−	0.737395i
$130$	2.52241	−	1.45632i	0.221230	−	0.127727i
$131$	13.0632	+	7.54205i	1.14134	+	0.658952i	0.946762	−	0.321936i	$-0.104334\pi$
$131$	13.0632	+	7.54205i	1.14134	+	0.658952i	0.194576	+	0.980887i	$0.437667\pi$
$132$	0.266564			0.0232014
$133$	4.41608	+	18.2150i	0.382923	+	1.57944i
$134$			7.49802i			0.647730i
$135$	−1.35621	−	0.783010i	−0.116724	−	0.0673908i
$136$	−5.41067	−	9.37156i	−0.463961	−	0.803604i
$137$	2.81361	−	1.62444i	0.240383	−	0.138785i	−0.374970	−	0.927037i	$-0.622347\pi$
$137$	2.81361	−	1.62444i	0.240383	−	0.138785i	0.615353	+	0.788252i	$0.289014\pi$
$138$	−16.6555	−	0.270743i	−1.41781	−	0.0230472i
$139$		−	15.7497i		−	1.33587i	−0.744220	−	0.667934i	$-0.767179\pi$
$139$		−	15.7497i		−	1.33587i	0.744220	−	0.667934i	$-0.232821\pi$
$140$	−0.490284	+	0.467348i	−0.0414366	+	0.0394981i
$141$	−27.3129			−2.30016
$142$	−7.65646	+	13.2614i	−0.642516	+	1.11287i
$143$	0.436563	+	0.756149i	0.0365072	+	0.0632323i
$144$	−5.74743	−	9.95484i	−0.478953	−	0.829570i
$145$	1.49731	−	2.59342i	0.124345	−	0.215372i
$146$		−	13.6035i		−	1.12583i
$147$	7.68197	+	14.9117i	0.633598	+	1.22990i
$148$			1.15620i			0.0950393i
$149$	5.41098	+	3.12403i	0.443285	+	0.255931i	0.704990	−	0.709217i	$-0.250951\pi$
$149$	5.41098	+	3.12403i	0.443285	+	0.255931i	−0.261705	+	0.965148i	$0.584285\pi$
$150$	4.29964	−	2.48240i	0.351064	−	0.202687i
$151$	−8.61081	−	14.9144i	−0.700738	−	1.21371i	−0.968208	−	0.250148i	$-0.919521\pi$
$151$	−8.61081	−	14.9144i	−0.700738	−	1.21371i	0.267470	−	0.963566i	$-0.413812\pi$
$152$	−9.74978	+	16.8871i	−0.790811	+	1.36973i
$153$	−10.7807			−0.871571
$154$	−2.91525	−	3.05833i	−0.234918	−	0.246447i
$155$			12.3786i			0.994276i
$156$	−0.0958687	+	0.166049i	−0.00767564	+	0.0132946i
$157$	2.92731	+	5.07024i	0.233624	+	0.404649i	0.958872	−	0.283839i	$-0.0916080\pi$
$157$	2.92731	+	5.07024i	0.233624	+	0.404649i	−0.725248	+	0.688488i	$0.758275\pi$
$158$	−8.13935	+	4.69926i	−0.647532	+	0.373853i
$159$	−4.34660	+	7.52853i	−0.344708	+	0.597051i
$160$	−1.44686			−0.114384
$161$	8.60434	+	9.32552i	0.678117	+	0.734954i
$162$	14.0697			1.10542
$163$	−2.38556	+	4.13192i	−0.186852	+	0.323637i	−0.944199	−	0.329376i	$-0.893162\pi$
$163$	−2.38556	+	4.13192i	−0.186852	+	0.323637i	0.757347	+	0.653012i	$0.226495\pi$
$164$	−0.0747262	+	0.0431432i	−0.00583513	+	0.00336892i
$165$	3.34720	+	5.79752i	0.260579	+	0.451337i
$166$	−3.98916	+	6.90942i	−0.309619	+	0.536275i
$167$		−	17.9409i		−	1.38831i	−0.719824	−	0.694156i	$-0.755778\pi$
$167$		−	17.9409i		−	1.38831i	0.719824	−	0.694156i	$-0.244222\pi$
$168$	−4.91911	+	16.7439i	−0.379518	+	1.29182i
$169$	12.3720			0.951690
$170$	−7.22442	+	12.5131i	−0.554088	+	0.959708i
$171$	9.71319	+	16.8237i	0.742786	+	1.28654i
$172$	0.352880	−	0.203735i	0.0269069	−	0.0155347i
$173$	−3.83381	−	2.21345i	−0.291479	−	0.168286i	0.347130	−	0.937817i	$-0.387156\pi$
$173$	−3.83381	−	2.21345i	−0.291479	−	0.168286i	−0.638609	+	0.769532i	$0.720490\pi$
$174$			4.10212i			0.310981i
$175$	−3.62846	−	1.06599i	−0.274286	−	0.0805813i
$176$		−	4.61827i		−	0.348115i
$177$	5.81464	−	10.0712i	0.437055	−	0.757001i
$178$	0.378729	+	0.655977i	0.0283869	+	0.0491676i
$179$	−6.72869	−	11.6544i	−0.502926	−	0.871093i	−0.999994	−	0.00338176i	$-0.998924\pi$
$179$	−6.72869	−	11.6544i	−0.502926	−	0.871093i	0.497068	−	0.867711i	$-0.334410\pi$
$180$	−0.351025	+	0.607994i	−0.0261639	+	0.0453172i
$181$	−12.4838			−0.927917			−0.463958	−	0.885857i	$-0.653571\pi$
$181$	−12.4838			−0.927917			−0.463958	+	0.885857i	$0.653571\pi$
$182$	2.95357	−	0.716069i	0.218933	−	0.0530786i
$183$		−	23.9662i		−	1.77164i
$184$	−0.214560	+	13.1992i	−0.0158176	+	0.973061i
$185$	−25.1464	+	14.5183i	−1.84880	+	1.06740i
$186$	−8.47830	−	14.6849i	−0.621659	−	1.07675i
$187$	−3.75107	−	2.16568i	−0.274305	−	0.158370i
$188$		−	1.15080i		−	0.0839307i
$189$	−1.12744	−	1.18277i	−0.0820092	−	0.0860340i
$190$	26.0361			1.88886
$191$	−9.37119	−	5.41046i	−0.678076	−	0.391487i	0.121054	−	0.992646i	$-0.461373\pi$
$191$	−9.37119	−	5.41046i	−0.678076	−	0.391487i	−0.799130	+	0.601159i	$0.794706\pi$
$192$	−15.6815	+	9.05370i	−1.13171	+	0.653394i
$193$	−3.58582	−	6.21083i	−0.258113	−	0.447065i	0.707623	−	0.706590i	$-0.249767\pi$
$193$	−3.58582	−	6.21083i	−0.258113	−	0.447065i	−0.965736	+	0.259525i	$0.916434\pi$
$194$	8.63874	−	14.9627i	0.620225	−	1.07426i
$195$	−4.81524			−0.344826
$196$	−0.628289	+	0.323672i	−0.0448778	+	0.0231194i
$197$	−4.56103			−0.324960			−0.162480	−	0.986712i	$-0.551949\pi$
$197$	−4.56103			−0.324960			−0.162480	+	0.986712i	$0.551949\pi$
$198$	−3.79258	−	2.18965i	−0.269527	−	0.155612i
$199$	−1.72033	−	2.97970i	−0.121951	−	0.211226i	0.798586	−	0.601881i	$-0.205582\pi$
$199$	−1.72033	−	2.97970i	−0.121951	−	0.211226i	−0.920537	+	0.390655i	$0.872248\pi$
$200$	−1.96726	−	3.40740i	−0.139107	−	0.240940i
$201$	6.19796	−	10.7352i	0.437170	−	0.757201i
$202$			4.43369i			0.311953i
$203$	2.26176	−	2.15595i	0.158744	−	0.151318i
$204$		−	0.951162i		−	0.0665947i
$205$	−1.87665	−	1.08348i	−0.131071	−	0.0756739i
$206$	−11.1170	−	19.2552i	−0.774558	−	1.34157i
$207$	11.2811	+	6.75997i	0.784091	+	0.469851i
$208$	2.87684	+	1.66094i	0.199473	+	0.115166i
$209$			7.80491i			0.539877i
$210$	22.6455	−	5.49023i	1.56269	−	0.378862i
$211$	9.49610			0.653739			0.326869	−	0.945070i	$-0.394006\pi$
$211$	9.49610			0.653739			0.326869	+	0.945070i	$0.394006\pi$
$212$	−0.317207	−	0.183140i	−0.0217859	−	0.0125781i
$213$	21.9241	−	12.6579i	1.50221	−	0.867303i
$214$	18.3651	−	10.6031i	1.25541	−	0.724811i
$215$	8.86213	+	5.11655i	0.604392	+	0.348946i
$216$		−	1.70002i		−	0.115672i
$217$	−3.64075	+	12.3925i	−0.247150	+	0.841260i
$218$			20.3618i			1.37907i
$219$	−11.2448	+	19.4766i	−0.759854	+	1.31611i
$220$	−0.244273	+	0.141031i	−0.0164689	+	0.00950830i
$221$	2.69812	−	1.55776i	0.181495	−	0.104786i
$222$	19.8875	−	34.4462i	1.33476	−	2.31188i
$223$			15.3821i			1.03006i	0.857171	+	0.515032i	$0.172220\pi$
$223$			15.3821i			1.03006i	−0.857171	+	0.515032i	$0.827780\pi$
$224$	−1.44848	−	0.425543i	−0.0967807	−	0.0284328i
$225$	−3.91976			−0.261318
$226$	−9.97979	−	5.76184i	−0.663846	−	0.383272i
$227$	−12.3428	−	21.3784i	−0.819222	−	1.41893i	−0.906256	−	0.422729i	$-0.861072\pi$
$227$	−12.3428	−	21.3784i	−0.819222	−	1.41893i	0.0870336	−	0.996205i	$-0.472261\pi$
$228$	−1.48432	+	0.856975i	−0.0983018	+	0.0567545i
$229$	−6.24731	+	10.8207i	−0.412834	+	0.715050i	−0.995198	−	0.0978783i	$-0.968794\pi$
$229$	−6.24731	+	10.8207i	−0.412834	+	0.715050i	0.582364	+	0.812928i	$0.302128\pi$
$230$	15.4059	−	8.56382i	1.01584	−	0.564682i
$231$	1.64582	+	6.78850i	0.108287	+	0.446650i
$232$	3.25087			0.213430
$233$	13.0198	−	22.5509i	0.852954	−	1.47736i	−0.0255758	−	0.999673i	$-0.508142\pi$
$233$	13.0198	−	22.5509i	0.852954	−	1.47736i	0.878530	−	0.477687i	$-0.158525\pi$
$234$	2.72798	−	1.57500i	0.178334	−	0.102961i
$235$	25.0289	−	14.4504i	1.63270	−	0.942642i
$236$	0.424342	+	0.244994i	0.0276223	+	0.0159477i
$237$	15.5379			1.00929
$238$	−10.9128	+	10.4023i	−0.707373	+	0.674281i
$239$	25.2986			1.63643			0.818215	−	0.574912i	$-0.194964\pi$
$239$	25.2986			1.63643			0.818215	+	0.574912i	$0.194964\pi$
$240$	22.0572	+	12.7348i	1.42379	+	0.822025i
$241$	14.4451	+	25.0196i	0.930490	+	1.61166i	0.782486	+	0.622668i	$0.213951\pi$
$241$	14.4451	+	25.0196i	0.930490	+	1.61166i	0.148004	+	0.988987i	$0.452715\pi$
$242$	7.09236	+	12.2843i	0.455914	+	0.789666i
$243$	−18.5395	−	10.7038i	−1.18931	−	0.686647i
$244$	1.00979			0.0646454
$245$	−14.9289	−	9.60041i	−0.953773	−	0.613348i
$246$	2.96838			0.189257
$247$	−4.86188	−	2.80701i	−0.309354	−	0.178606i
$248$	−11.6375	+	6.71893i	−0.738984	+	0.426653i
$249$	11.4228	−	6.59498i	0.723893	−	0.417940i
$250$	6.56156	−	11.3650i	0.414989	−	0.718783i
$251$	−2.54584			−0.160692			−0.0803459	−	0.996767i	$-0.525602\pi$
$251$	−2.54584			−0.160692			−0.0803459	+	0.996767i	$0.525602\pi$
$252$	−0.530240	+	0.505434i	−0.0334020	+	0.0318394i
$253$	2.56719	+	4.61827i	0.161398	+	0.290348i
$254$	−4.51370	+	7.81795i	−0.283214	+	0.490542i
$255$	20.6869	−	11.9436i	1.29547	−	0.747937i
$256$	−1.20855	−	2.09328i	−0.0755346	−	0.130830i
$257$	0.243730	+	0.140718i	0.0152035	+	0.00877774i	0.507582	−	0.861603i	$-0.330539\pi$
$257$	0.243730	+	0.140718i	0.0152035	+	0.00877774i	−0.492379	+	0.870381i	$0.663873\pi$
$258$	−14.0176			−0.872698
$259$	−29.4447	+	7.13862i	−1.82960	+	0.443572i
$260$		−	0.202885i		−	0.0125824i
$261$	1.61934	−	2.80477i	0.100234	−	0.173611i
$262$	18.9347	−	10.9320i	1.16979	−	0.675380i
$263$	−25.3650	+	14.6445i	−1.56407	+	0.903018i	−0.567235	+	0.823556i	$0.691987\pi$
$263$	−25.3650	+	14.6445i	−1.56407	+	0.903018i	−0.996838	+	0.0794624i	$0.974680\pi$
$264$	−3.63362	+	6.29361i	−0.223634	+	0.387345i
$265$		−	9.19862i		−	0.565067i
$266$	26.0654	+	7.65764i	1.59817	+	0.469520i
$267$		−	1.25225i		−	0.0766363i
$268$	0.452316	+	0.261145i	0.0276296	+	0.0159519i
$269$	−1.57794	+	0.911022i	−0.0962085	+	0.0555460i	−0.547332	−	0.836915i	$-0.684357\pi$
$269$	−1.57794	+	0.911022i	−0.0962085	+	0.0555460i	0.451124	+	0.892461i	$0.351023\pi$
$270$	−1.96579	+	1.13495i	−0.119634	+	0.0690709i
$271$	−2.06198	−	1.19048i	−0.125256	−	0.0723167i	0.436063	−	0.899916i	$-0.356373\pi$
$271$	−2.06198	−	1.19048i	−0.125256	−	0.0723167i	−0.561319	+	0.827600i	$0.689706\pi$
$272$	−16.4791			−0.999191
$273$	−4.82064	−	1.41624i	−0.291759	−	0.0857145i
$274$		−	4.70916i		−	0.284491i
$275$	−1.36385	−	0.787419i	−0.0822432	−	0.0474831i
$276$	−0.596418	+	0.995309i	−0.0359002	+	0.0599105i
$277$	−1.93244	−	3.34708i	−0.116109	−	0.201107i	0.802113	−	0.597172i	$-0.203709\pi$
$277$	−1.93244	−	3.34708i	−0.116109	−	0.201107i	−0.918223	+	0.396065i	$0.870376\pi$
$278$	−19.7702	−	11.4143i	−1.18574	−	0.684586i
$279$			13.3874i			0.801485i
$280$	−4.35093	−	17.9462i	−0.260018	−	1.07249i
$281$		−	21.8412i		−	1.30294i	−0.758675	−	0.651470i	$-0.774153\pi$
$281$		−	21.8412i		−	1.30294i	0.758675	−	0.651470i	$-0.225847\pi$
$282$	−19.7946	+	34.2853i	−1.17875	+	2.04166i
$283$	−7.71377	−	13.3606i	−0.458536	−	0.794208i	0.540348	−	0.841442i	$-0.318293\pi$
$283$	−7.71377	−	13.3606i	−0.458536	−	0.794208i	−0.998884	+	0.0472339i	$0.984959\pi$
$284$	0.533326	+	0.923748i	0.0316471	+	0.0548144i
$285$	−37.2769	−	21.5218i	−2.20809	−	1.27484i
$286$	1.26557			0.0748347
$287$	−1.56009	−	1.63665i	−0.0920891	−	0.0966086i
$288$	−1.56477			−0.0922049
$289$	0.772346	−	1.33774i	0.0454321	−	0.0786907i
$290$	−2.17031	−	3.75909i	−0.127445	−	0.220741i
$291$	−24.7368	+	14.2818i	−1.45010	+	0.837213i
$292$	−0.820626	−	0.473789i	−0.0480235	−	0.0277264i
$293$	7.77950			0.454484			0.227242	−	0.973838i	$-0.427029\pi$
$293$	7.77950			0.454484			0.227242	+	0.973838i	$0.427029\pi$
$294$	24.2857	+	1.16401i	1.41637	+	0.0678865i
$295$			12.3054i			0.716448i
$296$	−27.2981	−	15.7606i	−1.58667	−	0.916065i
$297$	−0.340226	−	0.589289i	−0.0197419	−	0.0341940i
$298$	7.84306	−	4.52819i	0.454336	−	0.262311i
$299$	−3.80012	−	0.0617728i	−0.219767	−	0.00357241i
$300$		−	0.345833i		−	0.0199667i
$301$	7.36722	+	7.72879i	0.424640	+	0.445480i
$302$	−24.9622			−1.43642
$303$	3.66494	−	6.34787i	0.210545	−	0.364675i
$304$	14.8473	+	25.7162i	0.851549	+	1.47493i
$305$	12.6798	+	21.9621i	0.726044	+	1.25755i
$306$	−7.81318	+	13.5328i	−0.446650	+	0.773620i
$307$		−	4.61716i		−	0.263515i	−0.991282	−	0.131758i	$-0.957938\pi$
$307$		−	4.61716i		−	0.263515i	0.991282	−	0.131758i	$-0.0420621\pi$
$308$	−0.286026	+	0.0693448i	−0.0162979	+	0.00395129i
$309$			36.7578i			2.09108i
$310$	15.5386	+	8.97123i	0.882535	+	0.509532i
$311$	20.4727	−	11.8199i	1.16090	−	0.670246i	0.209381	−	0.977834i	$-0.432855\pi$
$311$	20.4727	−	11.8199i	1.16090	−	0.670246i	0.951520	+	0.307588i	$0.0995217\pi$
$312$	−2.61364	−	4.52695i	−0.147968	−	0.256288i
$313$	5.35830	−	9.28084i	0.302869	−	0.524584i	−0.673916	−	0.738808i	$-0.735389\pi$
$313$	5.35830	−	9.28084i	0.302869	−	0.524584i	0.976785	+	0.214224i	$0.0687223\pi$
$314$	8.48609			0.478898
$315$	−17.6509	−	5.18558i	−0.994515	−	0.292174i
$316$			0.654672i			0.0368282i
$317$	5.84074	−	10.1165i	0.328049	−	0.568197i	−0.654076	−	0.756429i	$-0.726942\pi$
$317$	5.84074	−	10.1165i	0.328049	−	0.568197i	0.982125	+	0.188232i	$0.0602757\pi$
$318$	6.30027	+	10.9124i	0.353302	+	0.611936i
$319$	1.12687	−	0.650599i	0.0630926	−	0.0364265i
$320$	9.58008	−	16.5932i	0.535543	−	0.927587i
$321$	−35.0586			−1.95678
$322$	17.9420	−	4.04231i	0.999868	−	0.225269i
$323$	27.8497			1.54960
$324$	0.490026	−	0.848750i	0.0272237	−	0.0471528i
$325$	0.981007	−	0.566385i	0.0544165	−	0.0314174i
$326$	3.45780	+	5.98909i	0.191510	+	0.331705i
$327$	16.8313	−	29.1527i	0.930773	−	1.61215i
$328$		−	2.35239i		−	0.129889i
$329$	29.3071	−	7.10527i	1.61575	−	0.391726i
$330$	9.70334			0.534151
$331$	−13.9316	+	24.1303i	−0.765751	+	1.32632i	0.174098	+	0.984728i	$0.444299\pi$
$331$	−13.9316	+	24.1303i	−0.765751	+	1.32632i	−0.939849	+	0.341591i	$0.889034\pi$
$332$	0.277873	+	0.481290i	0.0152502	+	0.0264142i
$333$	−27.1957	+	15.7014i	−1.49032	+	0.860434i
$334$	−22.5209	−	13.0024i	−1.23229	−	0.711462i
$335$			13.1166i			0.716637i
$336$	18.3365	+	19.2364i	1.00034	+	1.04943i
$337$			3.40512i			0.185489i	0.995690	+	0.0927444i	$0.0295639\pi$
$337$			3.40512i			0.185489i	−0.995690	+	0.0927444i	$0.970436\pi$
$338$	8.96640	−	15.5303i	0.487708	−	0.844735i
$339$	9.52562	+	16.4989i	0.517360	+	0.896095i
$340$	0.503231	+	0.871622i	0.0272916	+	0.0472704i
$341$	−2.68932	+	4.65805i	−0.145635	+	0.252247i
$342$	28.1580			1.52261
$343$	−12.1220	−	14.0020i	−0.654528	−	0.756038i
$344$			11.1087i			0.598943i
$345$	−29.1362	−	0.473623i	−1.56864	−	0.0254990i
$346$	−5.55700	+	3.20833i	−0.298746	+	0.172481i
$347$	−3.25674	−	5.64083i	−0.174831	−	0.302816i	0.765272	−	0.643707i	$-0.222604\pi$
$347$	−3.25674	−	5.64083i	−0.174831	−	0.302816i	−0.940103	+	0.340891i	$0.889271\pi$
$348$	0.247459	+	0.142871i	0.0132652	+	0.00765868i
$349$			13.7110i			0.733931i	0.930234	+	0.366966i	$0.119603\pi$
$349$			13.7110i			0.733931i	−0.930234	+	0.366966i	$0.880397\pi$
$350$	−3.96779	+	3.78217i	−0.212087	+	0.202165i
$351$	0.489445			0.0261246
$352$	−0.544448	−	0.314337i	−0.0290192	−	0.0167542i
$353$	−10.4296	+	6.02155i	−0.555113	+	0.320495i	−0.751182	−	0.660096i	$-0.770516\pi$
$353$	−10.4296	+	6.02155i	−0.555113	+	0.320495i	0.196069	+	0.980590i	$0.437182\pi$
$354$	−8.42815	−	14.5980i	−0.447951	−	0.775874i
$355$	−13.3938	+	23.1987i	−0.710869	+	1.23126i
$356$	0.0527622			0.00279639
$357$	24.2230	−	5.87266i	1.28201	−	0.310814i
$358$	−19.5061			−1.03093
$359$	−13.1144	−	7.57162i	−0.692153	−	0.399615i	0.112265	−	0.993678i	$-0.464189\pi$
$359$	−13.1144	−	7.57162i	−0.692153	−	0.399615i	−0.804418	+	0.594064i	$0.797523\pi$
$360$	−9.56989	−	16.5755i	−0.504377	−	0.873607i
$361$	−15.5920	−	27.0061i	−0.820630	−	1.42137i
$362$	−9.04748	+	15.6707i	−0.475525	+	0.823634i
$363$		−	23.4505i		−	1.23083i
$364$	0.0596717	−	0.203113i	0.00312764	−	0.0106460i
$365$		−	23.7972i		−	1.24560i
$366$	−30.0843	−	17.3692i	−1.57253	−	0.907902i
$367$	15.2658	+	26.4412i	0.796870	+	1.38022i	0.921645	+	0.388034i	$0.126846\pi$
$367$	15.2658	+	26.4412i	0.796870	+	1.38022i	−0.124775	+	0.992185i	$0.539821\pi$
$368$	17.2439	+	10.3331i	0.898902	+	0.538648i
$369$	−2.02959	−	1.17178i	−0.105656	−	0.0610006i
$370$			42.0876i			2.18803i
$371$	2.70546	−	9.20895i	0.140460	−	0.478105i
$372$	−1.18115			−0.0612396
$373$	5.76974	+	3.33116i	0.298746	+	0.172481i	0.641879	−	0.766806i	$-0.278155\pi$
$373$	5.76974	+	3.33116i	0.298746	+	0.172481i	−0.343134	+	0.939287i	$0.611488\pi$
$374$	−5.43706	+	3.13909i	−0.281144	+	0.162318i
$375$	−18.7888	+	10.8477i	−0.970251	+	0.560175i
$376$	27.1706	+	15.6869i	1.40122	+	0.808992i
$377$			0.935942i			0.0482035i
$378$	−2.30180	+	0.558054i	−0.118392	+	0.0287032i
$379$			24.8693i			1.27745i	0.769434	+	0.638726i	$0.220538\pi$
$379$			24.8693i			1.27745i	−0.769434	+	0.638726i	$0.779462\pi$
$380$	0.906799	−	1.57062i	0.0465178	−	0.0805712i
$381$	12.9248	−	7.46216i	0.662159	−	0.382298i
$382$	−13.5833	+	7.84231i	−0.694981	+	0.401247i
$383$	5.34052	−	9.25006i	0.272888	−	0.472656i	−0.696712	−	0.717351i	$-0.745354\pi$
$383$	5.34052	−	9.25006i	0.272888	−	0.472656i	0.969600	+	0.244695i	$0.0786878\pi$
$384$			28.9809i			1.47892i
$385$	−5.09978	−	5.35006i	−0.259909	−	0.272665i
$386$	−10.3951			−0.529096
$387$	9.58436	+	5.53353i	0.487200	+	0.281285i
$388$	−0.601748	−	1.04226i	−0.0305491	−	0.0529127i
$389$	24.9946	−	14.4306i	1.26728	−	0.731663i	0.292805	−	0.956172i	$-0.405411\pi$
$389$	24.9946	−	14.4306i	1.26728	−	0.731663i	0.974472	+	0.224510i	$0.0720781\pi$
$390$	−3.48977	+	6.04446i	−0.176712	+	0.306073i
$391$	16.4791	−	9.16035i	0.833383	−	0.463259i
$392$	0.922461	−	19.2461i	0.0465913	−	0.972073i
$393$	−36.1461			−1.82333
$394$	−3.30554	+	5.72536i	−0.166531	+	0.288440i
$395$	−14.2385	+	8.22062i	−0.716418	+	0.413624i
$396$	−0.264180	+	0.152524i	−0.0132755	+	0.00766464i
$397$	−0.919722	−	0.531001i	−0.0461595	−	0.0266502i	0.476743	−	0.879043i	$-0.341817\pi$
$397$	−0.919722	−	0.531001i	−0.0461595	−	0.0266502i	−0.522902	+	0.852393i	$0.675151\pi$
$398$	−4.98714			−0.249983
$399$	−30.9888	−	32.5097i	−1.55138	−	1.62752i
$400$	−5.99162			−0.299581
$401$	21.0551	+	12.1562i	1.05144	+	0.607050i	0.923053	−	0.384674i	$-0.125686\pi$
$401$	21.0551	+	12.1562i	1.05144	+	0.607050i	0.128389	+	0.991724i	$0.459019\pi$
$402$	−8.98376	−	15.5603i	−0.448069	−	0.776079i
$403$	−1.93441	−	3.35050i	−0.0963599	−	0.166900i
$404$	0.267461	+	0.154419i	0.0133067	+	0.00768261i
$405$	24.6127			1.22302
$406$	−1.06714	−	4.40163i	−0.0529613	−	0.218449i
$407$	−12.6167			−0.625386
$408$	22.4571	+	12.9656i	1.11179	+	0.641893i
$409$	0.535872	−	0.309386i	0.0264972	−	0.0152981i	−0.486693	−	0.873573i	$-0.661797\pi$
$409$	0.535872	−	0.309386i	0.0264972	−	0.0152981i	0.513190	+	0.858275i	$0.328464\pi$
$410$	−2.72015	+	1.57048i	−0.134339	+	0.0775605i
$411$	−3.89265	+	6.74227i	−0.192010	+	0.332572i
$412$	−1.54875			−0.0763016
$413$	−3.61921	+	12.3192i	−0.178090	+	0.606189i
$414$	16.6615	−	9.26174i	0.818866	−	0.455190i
$415$	−6.97841	+	12.0870i	−0.342557	+	0.593326i
$416$	0.391618	−	0.226101i	0.0192006	−	0.0110855i
$417$	18.8705	+	32.6846i	0.924091	+	1.60057i
$418$	9.79733	+	5.65649i	0.479203	+	0.276668i
$419$	−13.8170			−0.675005			−0.337502	−	0.941325i	$-0.609582\pi$
$419$	−13.8170			−0.675005			−0.337502	+	0.941325i	$0.609582\pi$
$420$	0.457513	−	1.55730i	0.0223244	−	0.0759885i
$421$		−	1.48319i		−	0.0722863i	−0.999347	−	0.0361432i	$-0.988493\pi$
$421$		−	1.48319i		−	0.0722863i	0.999347	−	0.0361432i	$-0.0115072\pi$
$422$	6.88216	−	11.9203i	0.335018	−	0.580269i
$423$	27.0686	−	15.6281i	1.31612	−	0.759863i
$424$	8.64790	−	4.99287i	0.419979	−	0.242475i
$425$	−2.80969	+	4.86653i	−0.136290	+	0.236062i
$426$		−	36.6944i		−	1.77785i
$427$	6.23466	+	25.7161i	0.301716	+	1.24449i
$428$		−	1.47716i		−	0.0714010i
$429$	−1.81196	−	1.04614i	−0.0874823	−	0.0505079i
$430$	12.8454	−	7.41629i	0.619460	−	0.357645i
$431$	30.4482	−	17.5793i	1.46664	−	0.846763i	0.467333	−	0.884081i	$-0.345215\pi$
$431$	30.4482	−	17.5793i	1.46664	−	0.846763i	0.999303	+	0.0373185i	$0.0118816\pi$
$432$	−2.24201	−	1.29442i	−0.107869	−	0.0622780i
$433$	−12.5373			−0.602505			−0.301252	−	0.953544i	$-0.597405\pi$
$433$	−12.5373			−0.602505			−0.301252	+	0.953544i	$0.597405\pi$
$434$	12.9175	+	13.5515i	0.620060	+	0.650491i
$435$			7.17603i			0.344064i
$436$	1.22832	+	0.709170i	0.0588258	+	0.0339631i
$437$	−29.1423	−	17.4630i	−1.39407	−	0.835366i
$438$	16.2990	+	28.2308i	0.778798	+	1.34892i
$439$	21.8276	+	12.6022i	1.04177	+	0.601469i	0.920335	−	0.391130i	$-0.127916\pi$
$439$	21.8276	+	12.6022i	1.04177	+	0.601469i	0.121439	+	0.992599i	$0.461249\pi$
$440$		−	7.68976i		−	0.366595i
$441$	−16.1455	−	10.3828i	−0.768835	−	0.494419i
$442$		−	4.51585i		−	0.214797i
$443$	−4.17328	+	7.22834i	−0.198279	+	0.343429i	−0.947970	−	0.318359i	$-0.896868\pi$
$443$	−4.17328	+	7.22834i	−0.198279	+	0.343429i	0.749692	+	0.661787i	$0.230202\pi$
$444$	−1.38531	−	2.39942i	−0.0657437	−	0.113871i
$445$	0.662527	+	1.14753i	0.0314068	+	0.0543981i
$446$	19.3089	+	11.1480i	0.914302	+	0.527872i
$447$	−14.9723			−0.708163
$448$	14.4712	−	13.7942i	0.683698	−	0.651713i
$449$	4.40940			0.208092			0.104046	−	0.994572i	$-0.466821\pi$
$449$	4.40940			0.208092			0.104046	+	0.994572i	$0.466821\pi$
$450$	−2.84079	+	4.92040i	−0.133916	+	0.231950i
$451$	−0.470786	−	0.815425i	−0.0221684	−	0.0383969i
$452$	−0.695162	+	0.401352i	−0.0326977	+	0.0188780i
$453$	35.7393	+	20.6341i	1.67918	+	0.969475i
$454$	−35.7811			−1.67929
$455$	5.16681	−	1.25265i	0.242224	−	0.0587252i
$456$		−	46.7268i		−	2.18818i
$457$	27.4739	+	15.8620i	1.28517	+	0.741995i	0.977789	−	0.209590i	$-0.0672130\pi$
$457$	27.4739	+	15.8620i	1.28517	+	0.741995i	0.307384	+	0.951585i	$0.400546\pi$
$458$	9.05530	+	15.6842i	0.423126	+	0.732876i
$459$	−2.10272	+	1.21401i	−0.0981467	+	0.0566650i
$460$	0.0199556	−	1.22762i	0.000930435	−	0.0572383i
$461$		−	34.4607i		−	1.60500i	−0.596654	−	0.802498i	$-0.703504\pi$
$461$		−	34.4607i		−	1.60500i	0.596654	−	0.802498i	$-0.296496\pi$
$462$	9.71424	+	2.85390i	0.451947	+	0.132776i
$463$	−3.47708			−0.161594			−0.0807968	−	0.996731i	$-0.525746\pi$
$463$	−3.47708			−0.161594			−0.0807968	+	0.996731i	$0.525746\pi$
$464$	2.47527	−	4.28729i	0.114911	−	0.199032i
$465$	−14.8315	−	25.6889i	−0.687793	−	1.19129i
$466$	−18.8718	−	32.6869i	−0.874219	−	1.51419i
$467$	−11.4593	+	19.8481i	−0.530274	+	0.918461i	0.469103	+	0.883144i	$0.344577\pi$
$467$	−11.4593	+	19.8481i	−0.530274	+	0.918461i	−0.999376	+	0.0353171i	$0.988756\pi$
$468$		−	0.219419i		−	0.0101427i
$469$	−3.85780	+	13.1313i	−0.178137	+	0.606349i
$470$		−	41.8909i		−	1.93228i
$471$	−12.1498	−	7.01471i	−0.559835	−	0.323221i
$472$	−11.5687	+	6.67918i	−0.532492	+	0.307434i
$473$	2.22320	+	3.85069i	0.102223	+	0.177055i
$474$	11.2608	−	19.5044i	0.517228	−	0.895865i
$475$	10.1259			0.464607
$476$	0.247439	+	1.02061i	0.0113413	+	0.0467795i
$477$		−	9.94827i		−	0.455500i
$478$	18.3348	−	31.7568i	0.838614	−	1.45252i
$479$	−3.86417	−	6.69295i	−0.176559	−	0.305809i	0.764141	−	0.645049i	$-0.223163\pi$
$479$	−3.86417	−	6.69295i	−0.176559	−	0.305809i	−0.940700	+	0.339241i	$0.889830\pi$
$480$	3.00260	−	1.73355i	0.137049	−	0.0791255i
$481$	4.53755	−	7.85926i	0.206894	−	0.358351i
$482$	41.8755			1.90737
$483$	−29.0296	−	9.04357i	−1.32089	−	0.411497i
$484$	0.988064			0.0449120
$485$	15.1121	−	26.1750i	0.686207	−	1.18854i
$486$	−26.8724	+	15.5148i	−1.21896	+	0.703766i
$487$	−1.40999	−	2.44217i	−0.0638926	−	0.110665i	0.832310	−	0.554311i	$-0.187018\pi$
$487$	−1.40999	−	2.44217i	−0.0638926	−	0.110665i	−0.896202	+	0.443646i	$0.853685\pi$
$488$	−13.7648	+	23.8414i	−0.623104	+	1.07925i
$489$		−	11.4331i		−	0.517021i
$490$	−22.8707	+	11.7822i	−1.03319	+	0.532264i
$491$	−6.06047			−0.273505			−0.136753	−	0.990605i	$-0.543667\pi$
$491$	−6.06047			−0.273505			−0.136753	+	0.990605i	$0.543667\pi$
$492$	0.103384	−	0.179066i	0.00466091	−	0.00807294i
$493$	−2.32149	−	4.02094i	−0.104555	−	0.181094i
$494$	−7.04715	+	4.06867i	−0.317066	+	0.183058i
$495$	−6.63454	−	3.83045i	−0.298200	−	0.172166i
$496$			20.4636i			0.918843i
$497$	−20.2319	+	19.2855i	−0.907527	+	0.865071i
$498$		−	19.1185i		−	0.856719i
$499$	6.95553	−	12.0473i	0.311372	−	0.539313i	−0.667287	−	0.744800i	$-0.732545\pi$
$499$	6.95553	−	12.0473i	0.311372	−	0.539313i	0.978660	+	0.205488i	$0.0658780\pi$
$500$	−0.457058	−	0.791648i	−0.0204403	−	0.0354036i
$501$	21.4960	+	37.2321i	0.960369	+	1.66341i
$502$	−1.84506	+	3.19573i	−0.0823490	+	0.142633i
$503$	−18.7223			−0.834788			−0.417394	−	0.908726i	$-0.637056\pi$
$503$	−18.7223			−0.834788			−0.417394	+	0.908726i	$0.637056\pi$
$504$	−4.70551	−	19.4088i	−0.209600	−	0.864536i
$505$			7.75605i			0.345139i
$506$	7.65775	+	0.124480i	0.340429	+	0.00553383i
$507$	−25.6750	+	14.8235i	−1.14027	+	0.658334i
$508$	0.314410	+	0.544575i	0.0139497	+	0.0241616i
$509$	10.7975	+	6.23394i	0.478591	+	0.276315i	0.719829	−	0.694151i	$-0.244220\pi$
$509$	10.7975	+	6.23394i	0.478591	+	0.276315i	−0.241238	+	0.970466i	$0.577553\pi$
$510$		−	34.6238i		−	1.53317i
$511$	6.99912	−	23.8239i	0.309623	−	1.05391i
$512$	20.6845			0.914132
$513$	3.78901	+	2.18758i	0.167289	+	0.0965842i
$514$	0.353280	−	0.203966i	0.0155825	−	0.00899657i
$515$	−19.4475	−	33.6840i	−0.856957	−	1.48429i
$516$	−0.488212	+	0.845608i	−0.0214923	+	0.0372258i
$517$	12.5577			0.552288
$518$	−12.3786	+	42.1349i	−0.543885	+	1.85130i
$519$	10.6082			0.465648
$520$	4.79015	+	2.76559i	0.210062	+	0.121279i
$521$	−4.25588	−	7.37140i	−0.186453	−	0.322947i	0.757612	−	0.652705i	$-0.226366\pi$
$521$	−4.25588	−	7.37140i	−0.186453	−	0.322947i	−0.944065	+	0.329758i	$0.893033\pi$
$522$	−2.34718	−	4.06544i	−0.102733	−	0.177939i
$523$	2.22225	−	3.84905i	0.0971721	−	0.168307i	−0.813341	−	0.581787i	$-0.802354\pi$
$523$	2.22225	−	3.84905i	0.0971721	−	0.168307i	0.910513	+	0.413480i	$0.135687\pi$
$524$		−	1.52298i		−	0.0665315i
$525$	8.80721	−	2.13524i	0.384378	−	0.0931895i
$526$			42.4535i			1.85106i
$527$	16.6210	+	9.59614i	0.724022	+	0.418015i
$528$	5.53339	+	9.58411i	0.240810	+	0.417095i
$529$	−22.9878	−	0.747554i	−0.999472	−	0.0325024i
$530$	−11.5468	−	6.66657i	−0.501562	−	0.289577i
$531$			13.3082i			0.577528i
$532$	1.36976	−	1.30568i	0.0593867	−	0.0566085i
$533$	0.677266			0.0293356
$534$	−1.57192	−	0.907548i	−0.0680236	−	0.0392735i
$535$	32.1268	−	18.5484i	1.38896	−	0.801919i
$536$	−12.3313	+	7.11950i	−0.532632	+	0.307515i
$537$	27.9275	+	16.1240i	1.20516	+	0.695801i
$538$			2.64100i			0.113862i
$539$	−3.53197	−	6.85599i	−0.152133	−	0.295309i
$540$			0.158114i			0.00680416i
$541$	−14.0046	+	24.2567i	−0.602105	+	1.04288i	0.390396	+	0.920647i	$0.372338\pi$
$541$	−14.0046	+	24.2567i	−0.602105	+	1.04288i	−0.992502	+	0.122230i	$0.960995\pi$
$542$	−2.98878	+	1.72557i	−0.128379	+	0.0741196i
$543$	25.9072	−	14.9575i	1.11178	−	0.641889i
$544$	−1.12163	+	1.94272i	−0.0480895	+	0.0832934i
$545$			35.6198i			1.52578i
$546$	−5.27146	+	5.02485i	−0.225598	+	0.215044i
$547$	−15.7527			−0.673539			−0.336769	−	0.941587i	$-0.609334\pi$
$547$	−15.7527			−0.673539			−0.336769	+	0.941587i	$0.609334\pi$
$548$	−0.284079	−	0.164013i	−0.0121352	−	0.00700628i
$549$	13.7132	+	23.7519i	0.585264	+	1.01371i
$550$	−1.97686	+	1.14134i	−0.0842936	+	0.0486669i
$551$	−4.18321	+	7.24554i	−0.178211	+	0.308670i
$552$	−15.3694	−	27.6489i	−0.654166	−	1.17682i
$553$	−16.6723	+	4.04208i	−0.708980	+	0.171887i
$554$	−5.60203			−0.238007
$555$	34.7902	−	60.2583i	1.47676	−	2.55782i
$556$	−1.37713	+	0.795088i	−0.0584035	+	0.0337193i
$557$	−5.53273	+	3.19432i	−0.234429	+	0.135348i	−0.612614	−	0.790383i	$-0.709882\pi$
$557$	−5.53273	+	3.19432i	−0.234429	+	0.135348i	0.378185	+	0.925730i	$0.376548\pi$
$558$	16.8050	+	9.70235i	0.711411	+	0.410733i
$559$	−3.19826			−0.135272
$560$	−26.9806	−	7.92651i	−1.14014	−	0.334956i
$561$	10.3792			0.438212
$562$	−27.4168	−	15.8291i	−1.15651	−	0.667711i
$563$	1.50242	+	2.60227i	0.0633194	+	0.109672i	0.895947	−	0.444160i	$-0.146498\pi$
$563$	1.50242	+	2.60227i	0.0633194	+	0.109672i	−0.832628	+	0.553833i	$0.813165\pi$
$564$	1.37883	+	2.38821i	0.0580593	+	0.100562i
$565$	−17.4581	−	10.0794i	−0.734468	−	0.424045i
$566$	−22.3618			−0.939936
$567$	24.6404	+	7.23899i	1.03480	+	0.304009i
$568$	−29.0798			−1.22016
$569$	6.67438	+	3.85345i	0.279804	+	0.161545i	0.633335	−	0.773878i	$-0.281686\pi$
$569$	6.67438	+	3.85345i	0.279804	+	0.161545i	−0.353530	+	0.935423i	$0.615019\pi$
$570$	−54.0317	+	31.1952i	−2.26314	+	1.30662i
$571$	17.3049	−	9.99099i	0.724188	−	0.418110i	−0.0921042	−	0.995749i	$-0.529359\pi$
$571$	17.3049	−	9.99099i	0.724188	−	0.418110i	0.816292	+	0.577639i	$0.196026\pi$
$572$	0.0440779	−	0.0763451i	0.00184299	−	0.00319215i
$573$	25.9302			1.08325
$574$	−3.18511	+	0.772204i	−0.132944	+	0.0322312i
$575$	5.99162	−	3.33061i	0.249868	−	0.138896i
$576$	10.3608	−	17.9455i	0.431701	−	0.747728i
$577$	−18.0693	+	10.4323i	−0.752236	+	0.434304i	−0.826501	−	0.562935i	$-0.809672\pi$
$577$	−18.0693	+	10.4323i	−0.752236	+	0.434304i	0.0742654	+	0.997239i	$0.476339\pi$
$578$	−1.11949	−	1.93902i	−0.0465647	−	0.0806525i
$579$	14.8830	+	8.59272i	0.618517	+	0.357101i
$580$	−0.302355			−0.0125546
$581$	−10.5412	+	10.0481i	−0.437323	+	0.416864i
$582$			41.4021i			1.71617i
$583$	1.99845	−	3.46142i	0.0827674	−	0.143357i
$584$	22.3725	−	12.9167i	0.925779	−	0.534499i
$585$	4.77217	−	2.75522i	0.197305	−	0.113914i
$586$	5.63808	−	9.76545i	0.232907	−	0.403407i
$587$		−	6.07612i		−	0.250788i	−0.992107	−	0.125394i	$-0.959980\pi$
$587$		−	6.07612i		−	0.250788i	0.992107	−	0.125394i	$-0.0400196\pi$
$588$	0.916053	−	1.42449i	0.0377774	−	0.0587449i
$589$		−	34.5836i		−	1.42499i
$590$	15.4467	+	8.91816i	0.635931	+	0.367155i
$591$	9.46532	−	5.46480i	0.389351	−	0.224792i
$592$	−41.5704	+	24.0007i	−1.70853	+	0.986423i
$593$	−14.8284	−	8.56116i	−0.608928	−	0.351565i	0.163618	−	0.986524i	$-0.447684\pi$
$593$	−14.8284	−	8.56116i	−0.608928	−	0.351565i	−0.772546	+	0.634959i	$0.781017\pi$
$594$	−0.986296			−0.0404682
$595$	−19.0903	+	18.1972i	−0.782625	+	0.746013i
$596$		−	0.630840i		−	0.0258402i
$597$	7.14027	+	4.12244i	0.292232	+	0.168720i
$598$	−2.83163	+	4.72544i	−0.115794	+	0.193238i
$599$	12.6564	+	21.9216i	0.517128	+	0.895693i	0.999802	+	0.0198925i	$0.00633239\pi$
$599$	12.6564	+	21.9216i	0.517128	+	0.895693i	−0.482674	+	0.875800i	$0.660334\pi$
$600$	8.16516	+	4.71416i	0.333341	+	0.192455i
$601$			27.7769i			1.13304i	0.824047	+	0.566522i	$0.191711\pi$
$601$			27.7769i			1.13304i	−0.824047	+	0.566522i	$0.808289\pi$
$602$	15.0411	−	3.64659i	0.613028	−	0.148624i
$603$			14.1856i			0.577681i
$604$	−0.869397	+	1.50584i	−0.0353753	+	0.0612718i
$605$	12.4070	+	21.4895i	0.504415	+	0.873673i
$606$	−5.31223	−	9.20105i	−0.215795	−	0.373767i
$607$	11.2012	+	6.46699i	0.454641	+	0.262487i	0.709788	−	0.704415i	$-0.248791\pi$
$607$	11.2012	+	6.46699i	0.454641	+	0.262487i	−0.255147	+	0.966902i	$0.582124\pi$
$608$	4.04225			0.163935
$609$	−2.11058	+	7.18409i	−0.0855251	+	0.291114i
$610$	36.7581			1.48829
$611$	−4.51634	+	7.82254i	−0.182712	+	0.316466i
$612$	0.544243	+	0.942656i	0.0219997	+	0.0381046i
$613$	22.0172	−	12.7117i	0.889268	−	0.513419i	0.0155649	−	0.999879i	$-0.495045\pi$
$613$	22.0172	−	12.7117i	0.889268	−	0.513419i	0.873703	+	0.486460i	$0.161712\pi$
$614$	−5.79582	−	3.34622i	−0.233900	−	0.135042i
$615$	5.19271			0.209390
$616$	2.26168	−	7.69839i	0.0911256	−	0.310177i
$617$			23.3062i			0.938271i	0.883126	+	0.469135i	$0.155434\pi$
$617$			23.3062i			0.938271i	−0.883126	+	0.469135i	$0.844566\pi$
$618$	46.1413	+	26.6397i	1.85608	+	1.07161i
$619$	−6.18042	−	10.7048i	−0.248412	−	0.430262i	0.714673	−	0.699458i	$-0.246575\pi$
$619$	−6.18042	−	10.7048i	−0.248412	−	0.430262i	−0.963085	+	0.269196i	$0.913242\pi$
$620$	1.08237	−	0.624909i	0.0434692	−	0.0250969i
$621$	2.96155	+	0.0481414i	0.118843	+	0.00193185i
$622$		−	34.2653i		−	1.37391i
$623$	0.325764	+	1.34368i	0.0130515	+	0.0538333i
$624$	−7.96025			−0.318665
$625$	15.0519	−	26.0706i	0.602076	−	1.04283i
$626$	−7.76669	−	13.4523i	−0.310419	−	0.537662i
$627$	−9.35146	−	16.1972i	−0.373461	−	0.646854i
$628$	0.295558	−	0.511921i	0.0117940	−	0.0204279i
$629$			45.0193i			1.79504i
$630$	−19.3016	+	18.3986i	−0.768993	+	0.733018i
$631$		−	33.1168i		−	1.31836i	−0.751985	−	0.659180i	$-0.770903\pi$
$631$		−	33.1168i		−	1.31836i	0.751985	−	0.659180i	$-0.229097\pi$
$632$	−15.4569	−	8.92405i	−0.614843	−	0.354980i
$633$	−19.7069	+	11.3778i	−0.783278	+	0.452226i
$634$	−8.46598	−	14.6635i	−0.336227	−	0.582362i
$635$	−7.89601	+	13.6763i	−0.313344	+	0.542727i
$636$	0.877715			0.0348037
$637$	5.54103	+	0.265581i	0.219544	+	0.0105227i
$638$		−	1.88605i		−	0.0746693i
$639$	−14.4853	+	25.0893i	−0.573031	+	0.992519i
$640$	−15.3329	−	26.5574i	−0.606086	−	1.04977i
$641$	−16.6053	+	9.58710i	−0.655871	+	0.378668i	−0.790702	−	0.612201i	$-0.790284\pi$
$641$	−16.6053	+	9.58710i	−0.655871	+	0.378668i	0.134831	+	0.990869i	$0.456951\pi$
$642$	−25.4082	+	44.0082i	−1.00278	+	1.73687i
$643$	33.6042			1.32522			0.662610	−	0.748965i	$-0.269449\pi$
$643$	33.6042			1.32522			0.662610	+	0.748965i	$0.269449\pi$
$644$	0.381041	−	1.22313i	0.0150151	−	0.0481982i
$645$	−24.5216			−0.965538
$646$	20.1837	−	34.9592i	0.794117	−	1.37545i
$647$	−40.7198	+	23.5096i	−1.60086	+	0.924258i	−0.609546	+	0.792751i	$0.708648\pi$
$647$	−40.7198	+	23.5096i	−1.60086	+	0.924258i	−0.991315	+	0.131507i	$0.958019\pi$
$648$	13.3594	+	23.1392i	0.524807	+	0.908993i
$649$	−2.67341	+	4.63049i	−0.104941	+	0.181763i
$650$		−	1.64192i		−	0.0644012i
$651$	−7.29263	−	30.0799i	−0.285821	−	1.17892i
$652$	0.481720			0.0188656
$653$	−6.83605	+	11.8404i	−0.267515	+	0.463350i	−0.968220	−	0.250102i	$-0.919536\pi$
$653$	−6.83605	+	11.8404i	−0.267515	+	0.463350i	0.700704	+	0.713452i	$0.252869\pi$
$654$	−24.3965	−	42.2560i	−0.953978	−	1.65234i
$655$	33.1234	−	19.1238i	1.29424	−	0.747228i
$656$	−3.10236	−	1.79115i	−0.121127	−	0.0699327i
$657$		−	25.7366i		−	1.00408i
$658$	12.3208	−	41.9380i	0.480314	−	1.63491i
$659$			24.5743i			0.957280i	0.878011	+	0.478640i	$0.158870\pi$
$659$			24.5743i			0.957280i	−0.878011	+	0.478640i	$0.841130\pi$
$660$	0.337953	−	0.585351i	0.0131548	−	0.0227848i
$661$	−7.59564	−	13.1560i	−0.295436	−	0.511710i	0.679650	−	0.733536i	$-0.262132\pi$
$661$	−7.59564	−	13.1560i	−0.295436	−	0.511710i	−0.975086	+	0.221826i	$0.928798\pi$
$662$	20.1935	+	34.9761i	0.784841	+	1.35939i
$663$	−3.73286	+	6.46550i	−0.144972	+	0.251099i
$664$	−15.1511			−0.587977
$665$	45.5973	+	13.3958i	1.76819	+	0.519469i
$666$			45.5176i			1.76377i
$667$	−0.0920585	+	5.66323i	−0.00356452	+	0.219281i
$668$	−1.56874	+	0.905711i	−0.0606963	+	0.0350430i
$669$	−18.4301	−	31.9219i	−0.712550	−	1.23417i
$670$	16.4650	+	9.50608i	0.636099	+	0.367252i
$671$			11.0190i			0.425385i
$672$	3.51584	−	0.852387i	0.135626	−	0.0328815i
$673$	−0.379942			−0.0146457			−0.00732284	−	0.999973i	$-0.502331\pi$
$673$	−0.379942			−0.0146457			−0.00732284	+	0.999973i	$0.502331\pi$
$674$	4.27437	+	2.46781i	0.164643	+	0.0950565i
$675$	−0.764528	+	0.441400i	−0.0294267	+	0.0169895i
$676$	−0.624572	−	1.08179i	−0.0240220	−	0.0416074i
$677$	14.8652	−	25.7473i	0.571317	−	0.989550i	−0.425114	−	0.905140i	$-0.639766\pi$
$677$	14.8652	−	25.7473i	0.571317	−	0.989550i	0.996431	−	0.0844105i	$-0.0269007\pi$
$678$	27.6142			1.06052
$679$	22.8276	−	21.7597i	0.876042	−	0.835059i
$680$	−27.4389			−1.05223
$681$	51.2291	+	29.5772i	1.96310	+	1.13340i
$682$	3.89810	+	6.75170i	0.149266	+	0.258536i
$683$	−19.7761	−	34.2532i	−0.756710	−	1.31066i	−0.944520	−	0.328455i	$-0.893472\pi$
$683$	−19.7761	−	34.2532i	−0.756710	−	1.31066i	0.187809	−	0.982206i	$-0.439861\pi$
$684$	0.980700	−	1.69862i	0.0374980	−	0.0649484i
$685$		−	8.23794i		−	0.314756i
$686$	−26.3617	+	5.06877i	−1.00649	+	0.193527i
$687$		−	29.9409i		−	1.14232i
$688$	14.6503	+	8.45837i	0.558538	+	0.322472i
$689$	1.43747	+	2.48977i	0.0547633	+	0.0948528i
$690$	−21.7106	+	36.2308i	−0.826507	+	1.37928i
$691$	30.1036	+	17.3803i	1.14520	+	0.661180i	0.947712	−	0.319127i	$-0.103389\pi$
$691$	30.1036	+	17.3803i	1.14520	+	0.661180i	0.197484	+	0.980306i	$0.436723\pi$
$692$			0.446966i			0.0169911i
$693$	−5.51539	−	5.78607i	−0.209512	−	0.219795i
$694$	−9.44109			−0.358379
$695$	−34.5849	−	19.9676i	−1.31188	−	0.757415i
$696$	−6.74640	+	3.89504i	−0.255722	+	0.147641i
$697$	−2.90963	+	1.67987i	−0.110210	+	0.0636298i
$698$	17.2111	+	9.93683i	0.651449	+	0.376114i
$699$			62.3987i			2.36013i
$700$	0.0899661	+	0.371083i	0.00340040	+	0.0140256i
$701$			2.33382i			0.0881471i	0.999028	+	0.0440735i	$0.0140336\pi$
$701$			2.33382i			0.0881471i	−0.999028	+	0.0440735i	$0.985966\pi$
$702$	0.354718	−	0.614389i	0.0133880	−	0.0231886i
$703$	70.2543	−	40.5613i	2.64969	−	1.52980i
$704$	7.20992	−	4.16265i	0.271734	−	0.156886i
$705$	−34.6276	+	59.9768i	−1.30415	+	2.25886i
$706$			17.4561i			0.656970i
$707$	−2.28117	+	7.76475i	−0.0857924	+	0.292024i
$708$	−1.17416			−0.0441276
$709$	−23.0680	−	13.3183i	−0.866339	−	0.500181i	−0.000208831	−	1.00000i	$-0.500066\pi$
$709$	−23.0680	−	13.3183i	−0.866339	−	0.500181i	−0.866130	+	0.499819i	$0.833400\pi$
$710$	19.4139	+	33.6259i	0.728591	+	1.26196i
$711$	−15.3989	+	8.89057i	−0.577504	+	0.333422i
$712$	−0.719219	+	1.24572i	−0.0269539	+	0.0466854i
$713$	−11.3753	−	20.4636i	−0.426007	−	0.766368i
$714$	10.1834	−	34.6627i	0.381104	−	1.29722i
$715$	2.21392			0.0827958
$716$	−0.679367	+	1.17670i	−0.0253891	+	0.0439753i
$717$	−52.5012	+	30.3116i	−1.96069	+	1.13201i
$718$	−19.0090	+	10.9748i	−0.709409	+	0.409577i
$719$	−24.0839	−	13.9049i	−0.898179	−	0.518564i	−0.0215704	−	0.999767i	$-0.506867\pi$
$719$	−24.0839	−	13.9049i	−0.898179	−	0.518564i	−0.876609	+	0.481203i	$0.840200\pi$
$720$	−29.1466			−1.08623
$721$	−9.56231	−	39.4416i	−0.356119	−	1.46888i
$722$	−45.2002			−1.68218
$723$	−59.9546	−	34.6148i	−2.22973	−	1.28734i
$724$	0.630220	+	1.09157i	0.0234219	+	0.0405680i
$725$	−0.844069	−	1.46197i	−0.0313479	−	0.0542962i
$726$	−29.4370	−	16.9954i	−1.09251	−	0.630760i
$727$	−52.1718			−1.93494			−0.967472	−	0.252980i	$-0.918589\pi$
$727$	−52.1718			−1.93494			−0.967472	+	0.252980i	$0.918589\pi$
$728$	3.98212	+	4.17755i	0.147587	+	0.154830i
$729$	22.1786			0.821431
$730$	−29.8721	−	17.2467i	−1.10562	−	0.638328i
$731$	13.7402	−	7.93289i	0.508199	−	0.293409i
$732$	−2.09558	+	1.20988i	−0.0774549	+	0.0447186i
$733$	1.09544	−	1.89736i	0.0404610	−	0.0700806i	−0.845086	−	0.534631i	$-0.820451\pi$
$733$	1.09544	−	1.89736i	0.0404610	−	0.0700806i	0.885547	+	0.464550i	$0.153784\pi$
$734$	44.2548			1.63347
$735$	42.4841	+	2.03626i	1.56705	+	0.0751084i
$736$	2.39185	−	1.32958i	0.0881649	−	0.0490089i
$737$	−2.84966	+	4.93575i	−0.104968	+	0.181811i
$738$	−2.94183	+	1.69847i	−0.108290	+	0.0625214i
$739$	−18.1785	−	31.4861i	−0.668707	−	1.15823i	−0.978266	−	0.207354i	$-0.933515\pi$
$739$	−18.1785	−	31.4861i	−0.668707	−	1.15823i	0.309559	−	0.950880i	$-0.399819\pi$
$740$	2.53892	+	1.46585i	0.0933326	+	0.0538856i
$741$	13.4529			0.494204
$742$	−9.59906	−	10.0702i	−0.352392	−	0.369687i
$743$		−	9.56263i		−	0.350819i	−0.984496	−	0.175410i	$-0.943875\pi$
$743$		−	9.56263i		−	0.350819i	0.984496	−	0.175410i	$-0.0561249\pi$
$744$	16.1006	−	27.8870i	0.590276	−	1.02239i
$745$	13.7202	−	7.92137i	0.502670	−	0.290217i
$746$	8.36307	−	4.82842i	0.306194	−	0.176781i
$747$	−7.54712	+	13.0720i	−0.276135	+	0.478279i
$748$			0.437319i			0.0159900i
$749$	37.6183	−	9.12025i	1.37454	−	0.333247i
$750$			31.4470i			1.14828i
$751$	−17.9493	−	10.3630i	−0.654978	−	0.378152i	0.135383	−	0.990793i	$-0.456773\pi$
$751$	−17.9493	−	10.3630i	−0.654978	−	0.378152i	−0.790361	+	0.612642i	$0.790107\pi$
$752$	41.3762	−	23.8886i	1.50883	−	0.871126i
$753$	5.28327	−	3.05030i	0.192533	−	0.111159i
$754$	1.17487	+	0.678310i	0.0427862	+	0.0247026i
$755$	−43.6676			−1.58923
$756$	−0.0465039	+	0.158292i	−0.00169133	+	0.00575702i
$757$			30.8300i			1.12054i	0.828312	+	0.560268i	$0.189302\pi$
$757$			30.8300i			1.12054i	−0.828312	+	0.560268i	$0.810698\pi$
$758$	31.2179	+	18.0237i	1.13389	+	0.654650i
$759$	−10.8610	−	6.50822i	−0.394229	−	0.236233i
$760$	24.7218	+	42.8194i	0.896753	+	1.55322i
$761$	25.2474	+	14.5766i	0.915218	+	0.528402i	0.882106	−	0.471050i	$-0.156125\pi$
$761$	25.2474	+	14.5766i	0.915218	+	0.528402i	0.0331119	+	0.999452i	$0.489458\pi$
$762$		−	21.6324i		−	0.783658i
$763$	−10.4763	+	35.6598i	−0.379269	+	1.29097i
$764$			1.09254i			0.0395268i
$765$	−13.6679	+	23.6736i	−0.494166	+	0.855920i
$766$	−7.74093	−	13.4077i	−0.279691	−	0.484439i
$767$	−1.92297	−	3.33068i	−0.0694343	−	0.120264i
$768$	5.01612	+	2.89606i	0.181004	+	0.104503i
$769$	−1.49923			−0.0540637			−0.0270318	−	0.999635i	$-0.508606\pi$
$769$	−1.49923			−0.0540637			−0.0270318	+	0.999635i	$0.508606\pi$
$770$	−10.4118	+	2.52426i	−0.375216	+	0.0909681i
$771$	−0.674405			−0.0242881
$772$	−0.362045	+	0.627081i	−0.0130303	+	0.0225691i
$773$	6.31015	+	10.9295i	0.226960	+	0.393107i	0.956906	−	0.290399i	$-0.0937879\pi$
$773$	6.31015	+	10.9295i	0.226960	+	0.393107i	−0.729945	+	0.683505i	$0.760455\pi$
$774$	13.8922	−	8.02069i	0.499346	−	0.288298i
$775$	6.04322	+	3.48906i	0.217079	+	0.125331i
$776$	32.8105			1.17783
$777$	52.5521	−	50.0936i	1.88530	−	1.79710i
$778$		−	41.8336i		−	1.49981i
$779$	5.24301	+	3.02705i	0.187850	+	0.108456i
$780$	0.243087	+	0.421039i	0.00870391	+	0.0150756i
$781$	−10.0801	+	5.81975i	−0.360694	+	0.208247i
$782$	0.444175	−	27.3247i	0.0158837	−	0.977128i
$783$		−	0.729407i		−	0.0260669i
$784$	−24.6795	−	15.8708i	−0.881412	−	0.566815i
$785$	14.8451			0.529844
$786$	−26.1963	+	45.3734i	−0.934392	+	1.61841i
$787$	−5.38671	−	9.33005i	−0.192015	−	0.332580i	0.753903	−	0.656986i	$-0.228169\pi$
$787$	−5.38671	−	9.33005i	−0.192015	−	0.332580i	−0.945918	+	0.324406i	$0.894836\pi$
$788$	0.230254	+	0.398811i	0.00820245	+	0.0142071i
$789$	35.0926	−	60.7822i	1.24933	−	2.16390i
$790$			23.8311i			0.847873i
$791$	−14.5132	−	15.2254i	−0.516029	−	0.541355i
$792$		−	8.31644i		−	0.295512i
$793$	−6.86404	−	3.96296i	−0.243749	−	0.140729i
$794$	−1.33311	+	0.769671i	−0.0473103	+	0.0273146i
$795$	11.0213	+	19.0895i	0.390887	+	0.677036i
$796$	−0.173695	+	0.300848i	−0.00615644	+	0.0106633i
$797$	1.15594			0.0409457			0.0204728	−	0.999790i	$-0.493483\pi$
$797$	1.15594			0.0409457			0.0204728	+	0.999790i	$0.493483\pi$
$798$	−63.2674	+	15.3387i	−2.23964	+	0.542983i
$799$		−	44.8089i		−	1.58523i
$800$	−0.407813	+	0.706353i	−0.0144184	+	0.0249733i
$801$	0.716520	+	1.24105i	0.0253170	+	0.0438503i
$802$	30.5188	−	17.6200i	1.07765	−	0.622184i
$803$	5.17007	−	8.95482i	0.182448	−	0.316009i
$804$	−1.25156			−0.0441392
$805$	31.3867	−	7.07139i	1.10624	−	0.249234i
$806$	−5.60775			−0.197524
$807$	2.18309	−	3.78122i	0.0768483	−	0.133105i
$808$	−7.29169	+	4.20986i	−0.256521	+	0.148102i
$809$	−7.05670	−	12.2226i	−0.248100	−	0.429722i	0.714898	−	0.699228i	$-0.246473\pi$
$809$	−7.05670	−	12.2226i	−0.248100	−	0.429722i	−0.962999	+	0.269506i	$0.913140\pi$
$810$	17.8377	−	30.8958i	0.626753	−	1.08557i
$811$			36.0451i			1.26572i	0.774268	+	0.632858i	$0.218118\pi$
$811$			36.0451i			1.26572i	−0.774268	+	0.632858i	$0.781882\pi$
$812$	−0.302694	−	0.0889272i	−0.0106225	−	0.00312073i
$813$	5.70552			0.200101
$814$	−9.14376	+	15.8375i	−0.320489	+	0.555103i
$815$	6.04889	+	10.4770i	0.211883	+	0.366993i
$816$	34.1984	−	19.7444i	1.19718	−	0.691193i
$817$	−24.7591	−	14.2947i	−0.866213	−	0.500108i
$818$		−	0.896891i		−	0.0313591i
$819$	5.58788	−	1.35474i	0.195256	−	0.0473384i
$820$			0.218790i			0.00764047i
$821$	−11.4197	+	19.7796i	−0.398552	+	0.690312i	−0.993548	−	0.113417i	$-0.963820\pi$
$821$	−11.4197	+	19.7796i	−0.398552	+	0.690312i	0.594996	+	0.803729i	$0.297154\pi$
$822$	5.64229	+	9.77272i	0.196797	+	0.340863i
$823$	26.4562	+	45.8235i	0.922206	+	1.59731i	0.795995	+	0.605304i	$0.206948\pi$
$823$	26.4562	+	45.8235i	0.922206	+	1.59731i	0.126211	+	0.992003i	$0.459718\pi$
$824$	21.1116	−	36.5663i	0.735456	−	1.27385i
$825$	3.77379			0.131386
$826$	12.8411	+	13.4713i	0.446798	+	0.468726i
$827$		−	24.4927i		−	0.851694i	−0.904795	−	0.425847i	$-0.859976\pi$
$827$		−	24.4927i		−	0.851694i	0.904795	−	0.425847i	$-0.140024\pi$
$828$	0.0215819	−	1.32767i	0.000750023	−	0.0461397i
$829$	−1.46534	+	0.846013i	−0.0508933	+	0.0293833i	−0.525231	−	0.850960i	$-0.676021\pi$
$829$	−1.46534	+	0.846013i	−0.0508933	+	0.0293833i	0.474337	+	0.880343i	$0.342688\pi$
$830$	10.1150	+	17.5197i	0.351097	+	0.608118i
$831$	8.02063	+	4.63071i	0.278232	+	0.160638i
$832$			5.98833i			0.207608i
$833$	−24.4638	+	12.6029i	−0.847620	+	0.436664i
$834$	54.7044			1.89426
$835$	−39.3968	−	22.7457i	−1.36338	−	0.787149i
$836$	0.682453	−	0.394014i	0.0236031	−	0.0136273i
$837$	1.50755	+	2.61114i	0.0521084	+	0.0902544i
$838$	−10.0137	+	17.3442i	−0.345916	+	0.599145i
$839$	−35.3581			−1.22070			−0.610349	−	0.792133i	$-0.708971\pi$
$839$	−35.3581			−1.22070			−0.610349	+	0.792133i	$0.708971\pi$
$840$	30.5316	+	32.0300i	1.05344	+	1.10514i
$841$	−27.6052			−0.951903
$842$	−1.86182	−	1.07492i	−0.0641625	−	0.0370442i
$843$	26.1691	+	45.3262i	0.901312	+	1.56112i
$844$	−0.479391	−	0.830329i	−0.0165013	−	0.0285811i
$845$	15.6853	−	27.1678i	0.539592	−	0.934600i
$846$		−	45.3049i		−	1.55761i
$847$	6.10050	+	25.1627i	0.209616	+	0.864601i
$848$		−	15.2066i		−	0.522197i
$849$	32.0162	+	18.4845i	1.09879	+	0.634388i
$850$	4.07257	+	7.05390i	0.139688	+	0.241947i
$851$	28.2290	−	47.1088i	0.967677	−	1.61487i
$852$	−2.21358	−	1.27801i	−0.0758360	−	0.0437839i
$853$		−	22.6660i		−	0.776071i	−0.921645	−	0.388035i	$-0.873154\pi$
$853$		−	22.6660i		−	0.776071i	0.921645	−	0.388035i	$-0.126846\pi$
$854$	36.7993	+	10.8111i	1.25925	+	0.369949i
$855$	49.2580			1.68459
$856$	34.8759	+	20.1356i	1.19203	+	0.688221i
$857$	12.9065	−	7.45159i	0.440879	−	0.254542i	−0.263091	−	0.964771i	$-0.584742\pi$
$857$	12.9065	−	7.45159i	0.440879	−	0.254542i	0.703970	+	0.710229i	$0.251409\pi$
$858$	−2.62638	+	1.51634i	−0.0896633	+	0.0517671i
$859$	−6.14530	−	3.54799i	−0.209675	−	0.121056i	0.391485	−	0.920184i	$-0.371961\pi$
$859$	−6.14530	−	3.54799i	−0.209675	−	0.121056i	−0.601160	+	0.799128i	$0.705295\pi$
$860$		−	1.03319i		−	0.0352316i
$861$	5.19854	+	1.52726i	0.177166	+	0.0520488i
$862$		−	50.9612i		−	1.73575i
$863$	−11.0652	+	19.1655i	−0.376663	+	0.652400i	−0.990574	−	0.136975i	$-0.956262\pi$
$863$	−11.0652	+	19.1655i	−0.376663	+	0.652400i	0.613911	+	0.789375i	$0.289595\pi$
$864$	−0.305199	+	0.176207i	−0.0103831	+	0.00599468i
$865$	−9.72110	+	5.61248i	−0.330527	+	0.190830i
$866$	−9.08623	+	15.7378i	−0.308763	+	0.534793i
$867$			3.70155i			0.125711i
$868$	1.26738	−	0.307267i	0.0430178	−	0.0104293i
$869$	−7.14390			−0.242340
$870$	9.00792	+	5.20072i	0.305397	+	0.176321i
$871$	−2.04974	−	3.55025i	−0.0694527	−	0.120296i
$872$	−33.4872	+	19.3339i	−1.13402	+	0.654727i
$873$	16.3437	−	28.3081i	0.553151	−	0.958085i
$874$	−43.0414	+	23.9257i	−1.45590	+	0.809300i
$875$	17.3387	−	16.5275i	0.586155	−	0.558733i
$876$	2.27068			0.0767193
$877$	18.1869	−	31.5006i	0.614127	−	1.06370i	−0.376410	−	0.926453i	$-0.622842\pi$
$877$	18.1869	−	31.5006i	0.614127	−	1.06370i	0.990537	−	0.137245i	$-0.0438249\pi$
$878$	31.6385	−	18.2665i	1.06775	−	0.616464i
$879$	−16.1445	+	9.32102i	−0.544540	+	0.314390i
$880$	−10.1413	−	5.85510i	−0.341864	−	0.197375i
$881$	28.1227			0.947479			0.473739	−	0.880665i	$-0.342904\pi$
$881$	28.1227			0.947479			0.473739	+	0.880665i	$0.342904\pi$
$882$	−24.7346	+	12.7424i	−0.832856	+	0.429058i
$883$	40.3739			1.35869			0.679345	−	0.733819i	$-0.262264\pi$
$883$	40.3739			1.35869			0.679345	+	0.733819i	$0.262264\pi$
$884$	−0.272417	−	0.157280i	−0.00916238	−	0.00528991i
$885$	−14.7437	−	25.5369i	−0.495605	−	0.858413i
$886$	6.04905	+	10.4773i	0.203222	+	0.351990i
$887$	−40.6923	−	23.4937i	−1.36631	−	0.788842i	−0.375859	−	0.926677i	$-0.622652\pi$
$887$	−40.6923	−	23.4937i	−1.36631	−	0.788842i	−0.990455	+	0.137835i	$0.955986\pi$
$888$	75.5342			2.53476
$889$	−11.9273	+	11.3693i	−0.400028	+	0.381314i
$890$	1.92063			0.0643795
$891$	9.26171	+	5.34725i	0.310279	+	0.179140i
$892$	1.34500	−	0.776535i	0.0450339	−	0.0260003i
$893$	−69.9260	+	40.3718i	−2.33998	+	1.35099i
$894$	−10.8509	+	18.7943i	−0.362909	+	0.628577i
$895$	−34.1228			−1.14060
$896$	−7.53918	−	31.0968i	−0.251866	−	1.03887i
$897$	7.96025	−	4.42493i	0.265785	−	0.147744i
$898$	3.19564	−	5.53502i	0.106640	−	0.184706i
$899$	−4.99317	+	2.88281i	−0.166531	+	0.0961470i
$900$	0.197881	+	0.342740i	0.00659603	+	0.0114247i
$901$	−12.3512	−	7.13094i	−0.411477	−	0.237566i
$902$	−1.36478			−0.0454422
$903$	−24.5491	−	7.21219i	−0.816944	−	0.240007i
$904$		−	21.8838i		−	0.727846i
$905$	−15.8272	+	27.4134i	−0.526113	+	0.911254i
$906$	51.8031	−	29.9085i	1.72104	−	0.993645i
$907$	−14.0079	+	8.08749i	−0.465126	+	0.268541i	−0.714197	−	0.699945i	$-0.753208\pi$
$907$	−14.0079	+	8.08749i	−0.465126	+	0.268541i	0.249071	+	0.968485i	$0.419875\pi$
$908$	−1.24620	+	2.15849i	−0.0413567	+	0.0716319i
$909$			8.38813i			0.278217i
$910$	2.17214	−	7.39363i	0.0720058	−	0.245096i
$911$			54.7724i			1.81469i	0.420385	+	0.907346i	$0.361895\pi$
$911$			54.7724i			1.81469i	−0.420385	+	0.907346i	$0.638105\pi$
$912$	−61.6238	−	35.5785i	−2.04057	−	1.17812i
$913$	−5.25192	+	3.03220i	−0.173813	+	0.100351i
$914$	39.8226	−	22.9916i	1.31721	−	0.760494i
$915$	−52.6278	−	30.3847i	−1.73982	−	1.00449i
$916$	1.26153			0.0416821
$917$	38.7852	−	9.40316i	1.28080	−	0.310520i
$918$			3.51934i			0.116155i
$919$	44.2701	+	25.5594i	1.46034	+	0.843125i	0.999026	−	0.0441143i	$-0.0140466\pi$
$919$	44.2701	+	25.5594i	1.46034	+	0.843125i	0.461309	+	0.887239i	$0.347380\pi$
$920$	28.7124	+	17.2053i	0.946619	+	0.567242i
$921$	5.53206	+	9.58181i	0.182288	+	0.315731i
$922$	−43.2578	−	24.9749i	−1.42462	−	0.822505i
$923$		−	8.37221i		−	0.275575i
$924$	0.510493	−	0.486611i	0.0167940	−	0.0160083i
$925$			16.3685i			0.538195i
$926$	−2.51996	+	4.36471i	−0.0828112	+	0.143433i
$927$	−21.0323	−	36.4291i	−0.690793	−	1.19649i
$928$	−0.336952	−	0.583618i	−0.0110610	−	0.0191582i
$929$	−36.3178	−	20.9681i	−1.19155	−	0.687941i	−0.232891	−	0.972503i	$-0.574819\pi$
$929$	−36.3178	−	20.9681i	−1.19155	−	0.687941i	−0.958658	+	0.284562i	$0.908152\pi$
$930$	−42.9956			−1.40988
$931$	41.7086	+	26.8218i	1.36694	+	0.879048i
$932$	−2.62910			−0.0861192
$933$	−28.3241	+	49.0588i	−0.927290	+	1.60611i
$934$	16.6099	+	28.7693i	0.543494	+	0.941359i
$935$	−9.51130	+	5.49135i	−0.311053	+	0.179586i
$936$	5.18052	+	2.99098i	0.169331	+	0.0977631i
$937$	−35.9442			−1.17425			−0.587123	−	0.809498i	$-0.699739\pi$
$937$	−35.9442			−1.17425			−0.587123	+	0.809498i	$0.699739\pi$
$938$	13.6876	+	14.3594i	0.446916	+	0.468850i
$939$			25.6802i			0.838041i
$940$	−2.52706	−	1.45900i	−0.0824236	−	0.0475873i
$941$	14.9692	+	25.9274i	0.487981	+	0.845208i	0.999904	−	0.0138228i	$-0.00440007\pi$
$941$	14.9692	+	25.9274i	0.487981	+	0.845208i	−0.511923	+	0.859031i	$0.671067\pi$
$942$	−17.6108	+	10.1676i	−0.573792	+	0.331279i
$943$	4.09802	+	0.0666153i	0.133450	+	0.00216929i
$944$			20.3425i			0.662093i
$945$	−4.02665	+	0.976229i	−0.130987	+	0.0317567i
$946$	6.44492			0.209542
$947$	23.2755	−	40.3144i	0.756353	−	1.31004i	−0.188346	−	0.982103i	$-0.560313\pi$
$947$	23.2755	−	40.3144i	0.756353	−	1.31004i	0.944699	−	0.327939i	$-0.106354\pi$
$948$	−0.784396	−	1.35861i	−0.0254760	−	0.0441257i
$949$	3.71879	+	6.44114i	0.120717	+	0.209088i
$950$	7.33858	−	12.7108i	0.238095	−	0.412393i
$951$			27.9924i			0.907714i
$952$	−27.4697	−	8.07020i	−0.890297	−	0.261557i
$953$			46.6808i			1.51214i	0.654492	+	0.756069i	$0.272883\pi$
$953$			46.6808i			1.51214i	−0.654492	+	0.756069i	$0.727117\pi$
$954$	−12.4879	−	7.20987i	−0.404309	−	0.233428i
$955$	−23.7618	+	13.7189i	−0.768914	+	0.443933i
$956$	−1.27715	−	2.21208i	−0.0413059	−	0.0715439i
$957$	−1.55903	+	2.70032i	−0.0503963	+	0.0872890i
$958$	−11.2020			−0.361921
$959$	2.42291	−	8.24719i	0.0782398	−	0.266316i
$960$			45.9135i			1.48185i
$961$	−3.58358	+	6.20695i	−0.115599	+	0.200224i
$962$	−6.57704	−	11.3918i	−0.212052	−	0.367285i
$963$	34.7450	−	20.0600i	1.11964	−	0.646426i
$964$	1.45846	−	2.52612i	0.0469738	−	0.0813610i
$965$	−18.1846			−0.585383
$966$	−32.3910	+	29.8861i	−1.04216	+	0.961568i
$967$	−27.1443			−0.872902			−0.436451	−	0.899728i	$-0.643765\pi$
$967$	−27.1443			−0.872902			−0.436451	+	0.899728i	$0.643765\pi$
$968$	−13.4686	+	23.3284i	−0.432898	+	0.749802i
$969$	−57.7954	+	33.3682i	−1.85666	+	1.07194i
$970$	−21.9046	−	37.9399i	−0.703314	−	1.21818i
$971$	−8.26330	+	14.3125i	−0.265182	+	0.459309i	−0.967611	−	0.252445i	$-0.918765\pi$
$971$	−8.26330	+	14.3125i	−0.265182	+	0.459309i	0.702429	+	0.711754i	$0.252099\pi$
$972$			2.16143i			0.0693279i
$973$	−28.7510	−	30.1620i	−0.921713	−	0.966949i
$974$	−4.08747			−0.130971
$975$	−1.35723	+	2.35079i	−0.0434661	+	0.0752855i
$976$	20.9615	+	36.3064i	0.670961	+	1.16214i
$977$	−27.2815	+	15.7510i	−0.872813	+	0.503919i	−0.868282	−	0.496071i	$-0.834776\pi$
$977$	−27.2815	+	15.7510i	−0.872813	+	0.503919i	−0.00453074	+	0.999990i	$0.501442\pi$
$978$	−14.3517	−	8.28594i	−0.458916	−	0.264955i
$979$			0.575750i			0.0184011i
$980$	−0.0857956	+	1.79002i	−0.00274064	+	0.0571802i
$981$			38.5226i			1.22993i
$982$	−4.39224	+	7.60758i	−0.140162	+	0.242768i
$983$	−15.8593	−	27.4691i	−0.505833	−	0.876129i	−0.999977	−	0.00674862i	$-0.997852\pi$
$983$	−15.8593	−	27.4691i	−0.505833	−	0.876129i	0.494144	−	0.869380i	$-0.335482\pi$
$984$	2.81853	+	4.88183i	0.0898513	+	0.155627i
$985$	−5.78253	+	10.0156i	−0.184247	+	0.319124i
$986$	−6.72986			−0.214322
$987$	−52.3066	+	49.8596i	−1.66494	+	1.58705i
$988$			0.566823i			0.0180330i
$989$	−19.3521	−	0.314578i	−0.615362	−	0.0100030i
$990$	−9.61657	+	5.55213i	−0.305635	+	0.176458i
$991$	−7.74129	−	13.4083i	−0.245910	−	0.425929i	0.716477	−	0.697611i	$-0.245753\pi$
$991$	−7.74129	−	13.4083i	−0.245910	−	0.425929i	−0.962387	+	0.271682i	$0.912420\pi$
$992$	2.41245	+	1.39283i	0.0765955	+	0.0442224i
$993$		−	66.7687i		−	2.11884i
$994$	9.54581	+	39.3736i	0.302775	+	1.24885i
$995$	−8.72423			−0.276577
$996$	−1.15332	−	0.665867i	−0.0365442	−	0.0210988i
$997$	35.6689	−	20.5935i	1.12965	−	0.652202i	0.185800	−	0.982588i	$-0.440512\pi$
$997$	35.6689	−	20.5935i	1.12965	−	0.652202i	0.943846	+	0.330386i	$0.107179\pi$
$998$	−10.0818	−	17.4623i	−0.319135	−	0.552758i
$999$	−3.53624	+	6.12496i	−0.111882	+	0.193785i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.2.g.a.68.12	yes	28
7.2	even	3		1127.2.c.c.1126.8		28
7.3	odd	6	inner	161.2.g.a.45.11	✓	28
7.5	odd	6		1127.2.c.c.1126.6		28
23.22	odd	2	inner	161.2.g.a.68.11	yes	28
161.45	even	6	inner	161.2.g.a.45.12	yes	28
161.68	even	6		1127.2.c.c.1126.5		28
161.114	odd	6		1127.2.c.c.1126.7		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.2.g.a.45.11	✓	28	7.3	odd	6	inner
161.2.g.a.45.12	yes	28	161.45	even	6	inner
161.2.g.a.68.11	yes	28	23.22	odd	2	inner
161.2.g.a.68.12	yes	28	1.1	even	1	trivial
1127.2.c.c.1126.5		28	161.68	even	6
1127.2.c.c.1126.6		28	7.5	odd	6
1127.2.c.c.1126.7		28	161.114	odd	6
1127.2.c.c.1126.8		28	7.2	even	3

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:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	161.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.724735 - 1.25528i) q^{2} +(-2.07526 + 1.19815i) q^{3} +(-0.0504829 - 0.0874389i) q^{4} +(1.26781 - 2.19591i) q^{5} +3.47337i q^{6} +(1.91509 - 1.82550i) q^{7} +2.75259 q^{8} +(1.37113 - 2.37487i) q^{9} +(-1.83766 - 3.18291i) q^{10} +(0.954149 - 0.550878i) q^{11} +(0.209530 + 0.120972i) q^{12} +0.792485i q^{13} +(-0.903575 - 3.72697i) q^{14} +6.07612i q^{15} +(2.09587 - 3.63015i) q^{16} +(-1.96566 - 3.40463i) q^{17} +(-1.98742 - 3.44231i) q^{18} +(-3.54203 + 6.13498i) q^{19} -0.256011 q^{20} +(-1.78708 + 6.08294i) q^{21} -1.59696i q^{22} +(-0.0779482 + 4.79520i) q^{23} +(-5.71235 + 3.29803i) q^{24} +(-0.714694 - 1.23789i) q^{25} +(0.994790 + 0.574342i) q^{26} -0.617607i q^{27} +(-0.256299 - 0.0752969i) q^{28} +1.18102 q^{29} +(7.62723 + 4.40358i) q^{30} +(-4.22784 + 2.44094i) q^{31} +(-0.285306 - 0.494164i) q^{32} +(-1.32007 + 2.28643i) q^{33} -5.69834 q^{34} +(-1.58066 - 6.51976i) q^{35} -0.276875 q^{36} +(-9.91723 - 5.72572i) q^{37} +(5.13407 + 8.89247i) q^{38} +(-0.949517 - 1.64461i) q^{39} +(3.48977 - 6.04446i) q^{40} -0.854610i q^{41} +(6.34063 + 6.65181i) q^{42} +4.03573i q^{43} +(-0.0963363 - 0.0556198i) q^{44} +(-3.47668 - 6.02178i) q^{45} +(5.96282 + 3.57310i) q^{46} +(9.87089 + 5.69896i) q^{47} +10.0447i q^{48} +(0.335124 - 6.99197i) q^{49} -2.07186 q^{50} +(8.15852 + 4.71032i) q^{51} +(0.0692940 - 0.0400069i) q^{52} +(3.14173 - 1.81388i) q^{53} +(-0.775269 - 0.447602i) q^{54} -2.79364i q^{55} +(5.27146 - 5.02485i) q^{56} -16.9756i q^{57} +(0.855928 - 1.48251i) q^{58} +(-4.20283 + 2.42650i) q^{59} +(0.531289 - 0.306740i) q^{60} +(-5.00067 + 8.66142i) q^{61} +7.07616i q^{62} +(-1.70948 - 7.05109i) q^{63} +7.55639 q^{64} +(1.74023 + 1.00472i) q^{65} +(1.91340 + 3.31411i) q^{66} +(-4.47989 + 2.58647i) q^{67} +(-0.198465 + 0.343751i) q^{68} +(-5.58361 - 10.0447i) q^{69} +(-9.32967 - 2.74093i) q^{70} -10.5645 q^{71} +(3.77417 - 6.53706i) q^{72} +(8.12777 - 4.69257i) q^{73} +(-14.3747 + 8.29926i) q^{74} +(2.96635 + 1.71262i) q^{75} +0.715248 q^{76} +(0.821653 - 2.79677i) q^{77} -2.75259 q^{78} +(-5.61540 - 3.24205i) q^{79} +(-5.31433 - 9.20470i) q^{80} +(4.85339 + 8.40631i) q^{81} +(-1.07277 - 0.619366i) q^{82} -5.50430 q^{83} +(0.622103 - 0.150824i) q^{84} -9.96836 q^{85} +(5.06597 + 2.92484i) q^{86} +(-2.45092 + 1.41504i) q^{87} +(2.62638 - 1.51634i) q^{88} +(-0.261287 + 0.452563i) q^{89} -10.0787 q^{90} +(1.44668 + 1.51768i) q^{91} +(0.423222 - 0.235260i) q^{92} +(5.84924 - 10.1312i) q^{93} +(14.3076 - 8.26048i) q^{94} +(8.98126 + 15.5560i) q^{95} +(1.18417 + 0.683679i) q^{96} +11.9199 q^{97} +(-8.53400 - 5.48801i) q^{98} -3.02131i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{2} - 6 q^{3} - 12 q^{4} + 12 q^{8} + 4 q^{9} + 6 q^{12} + 22 q^{18} - 36 q^{24} - 22 q^{25} - 12 q^{26} - 44 q^{29} - 6 q^{32} - 10 q^{35} - 16 q^{39} + 18 q^{46} - 36 q^{47} + 28 q^{49} + 84 q^{50}+ \cdots - 146 q^{98}+O(q^{100}) \) 28 * q - 4 * q^2 - 6 * q^3 - 12 * q^4 + 12 * q^8 + 4 * q^9 + 6 * q^12 + 22 * q^18 - 36 * q^24 - 22 * q^25 - 12 * q^26 - 44 * q^29 - 6 * q^32 - 10 * q^35 - 16 * q^39 + 18 * q^46 - 36 * q^47 + 28 * q^49 + 84 * q^50 + 72 * q^52 - 30 * q^54 + 14 * q^58 - 54 * q^59 - 68 * q^64 + 38 * q^70 + 16 * q^71 - 4 * q^72 - 18 * q^73 + 96 * q^75 + 20 * q^77 - 12 * q^78 + 22 * q^81 - 52 * q^85 - 18 * q^87 - 28 * q^92 - 10 * q^93 + 84 * q^94 + 56 * q^95 - 84 * q^96 - 146 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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