LMFDB - Embedded newform 161.2.g.a.45.11

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			45.11
Character	$\chi$	$=$	161.45
Dual form			161.2.g.a.68.11

$q$-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} +(-4.11379 - 2.46510i) 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} +(0.112984 - 6.95050i) 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 $\left(\mathbb{Z}/161\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.724735	+	1.25528i	0.512465	+	0.887616i	0.999896	+	0.0144540i	$0.00460102\pi$
$2$	0.724735	+	1.25528i	0.512465	+	0.887616i	−0.487430	+	0.873162i	$0.662066\pi$
$3$	−2.07526	−	1.19815i	−1.19815	−	0.691753i	−0.238009	−	0.971263i	$-0.576495\pi$
$3$	−2.07526	−	1.19815i	−1.19815	−	0.691753i	−0.960143	+	0.279510i	$0.909828\pi$
$4$	−0.0504829	+	0.0874389i	−0.0252414	+	0.0437195i
$5$	−1.26781	−	2.19591i	−0.566983	−	0.982043i	−0.996862	−	0.0791566i	$-0.974777\pi$
$5$	−1.26781	−	2.19591i	−0.566983	−	0.982043i	0.429879	−	0.902886i	$-0.358556\pi$
$6$		−	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	$-0.386449\pi$
$11$	−0.954149	−	0.550878i	−0.287687	−	0.166096i	−0.636898	+	0.770948i	$0.719783\pi$
$12$	0.209530	−	0.120972i	0.0604861	−	0.0349217i
$13$		−	0.792485i		−	0.219796i	−0.993943	−	0.109898i	$-0.964948\pi$
$13$		−	0.792485i		−	0.219796i	0.993943	−	0.109898i	$-0.0350524\pi$
$14$	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	$-0.675151\pi$
$17$	1.96566	−	3.40463i	0.476743	−	0.825743i	0.999645	+	0.0266497i	$0.00848388\pi$
$18$	−1.98742	+	3.44231i	−0.468439	+	0.811360i
$19$	3.54203	+	6.13498i	0.812598	+	1.40746i	0.911040	+	0.412318i	$0.135281\pi$
$19$	3.54203	+	6.13498i	0.812598	+	1.40746i	−0.0984425	+	0.995143i	$0.531386\pi$
$20$	0.256011			0.0572458
$21$	1.78708	+	6.08294i	0.389973	+	1.32741i
$22$		−	1.59696i		−	0.340474i
$23$	−4.11379	−	2.46510i	−0.857784	−	0.514010i
$23$	−4.11379	−	2.46510i	−0.857784	−	0.514010i
$24$	−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	0.0697172	−	0.997567i	$-0.477790\pi$
$31$	−4.22784	−	2.44094i	−0.759342	−	0.438407i	−0.829060	+	0.559160i	$0.811124\pi$
$32$	−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	0.646409	−	0.762991i	$-0.276270\pi$
$37$	9.91723	−	5.72572i	1.63038	−	0.941302i	0.983974	−	0.178311i	$-0.0570633\pi$
$38$	−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	$0.0212578\pi$
$41$			0.854610i			0.133468i	−0.997771	+	0.0667338i	$0.978742\pi$
$42$	−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
$46$	0.112984	−	6.95050i	0.0166585	−	1.02480i
$47$	9.87089	−	5.69896i	1.43982	−	0.831279i	0.441981	−	0.897024i	$-0.354276\pi$
$47$	9.87089	−	5.69896i	1.43982	−	0.831279i	0.997836	+	0.0657452i	$0.0209425\pi$
$48$		−	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	$-0.413486\pi$
$53$	−3.14173	−	1.81388i	−0.431550	−	0.249155i	−0.700007	+	0.714136i	$0.746820\pi$
$54$	−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	0.200815	−	0.979629i	$-0.435641\pi$
$59$	−4.20283	−	2.42650i	−0.547162	−	0.315904i	−0.747976	+	0.663725i	$0.768974\pi$
$60$	−0.531289	−	0.306740i	−0.0685892	−	0.0396000i
$61$	5.00067	+	8.66142i	0.640270	+	1.10898i	0.985372	+	0.170416i	$0.0545110\pi$
$61$	5.00067	+	8.66142i	0.640270	+	1.10898i	−0.345102	+	0.938565i	$0.612156\pi$
$62$		−	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	$-0.230998\pi$
$67$	4.47989	+	2.58647i	0.547306	+	0.315987i	−0.200729	+	0.979647i	$0.564331\pi$
$68$	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	0.893479	−	0.449104i	$-0.148257\pi$
$73$	8.12777	+	4.69257i	0.951283	+	0.549224i	0.0578041	+	0.998328i	$0.481590\pi$
$74$	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	$-0.547818\pi$
$79$	5.61540	−	3.24205i	0.631781	−	0.364759i	0.781442	+	0.623978i	$0.214485\pi$
$80$	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	$-0.402317\pi$
$83$	5.50430			0.604175			0.302087	+	0.953280i	$0.402317\pi$
$84$	−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	$-0.157849\pi$
$89$	0.261287	+	0.452563i	0.0276964	+	0.0479716i	−0.851845	+	0.523794i	$0.824516\pi$
$90$	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	$-0.706882\pi$
$97$	−11.9199			−1.21028			−0.605139	+	0.796120i	$0.706882\pi$
$98$	−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	0.362382	−	0.932030i	$-0.381963\pi$
$101$	−2.64903	−	1.52942i	−0.263588	−	0.152183i	−0.625970	+	0.779847i	$0.715297\pi$
$102$	−11.8255	−	6.82747i	−1.17090	−	0.676021i
$103$	−7.66969	−	13.2843i	−0.755717	−	1.30894i	−0.945017	−	0.327022i	$-0.893955\pi$
$103$	−7.66969	−	13.2843i	−0.755717	−	1.30894i	0.189299	−	0.981919i	$-0.439378\pi$
$104$		−	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	$-0.916700\pi$
$107$	−12.6702	+	7.31513i	−1.22487	+	0.707181i	−0.258920	+	0.965899i	$0.583367\pi$
$108$	−0.0540029	−	0.0311786i	−0.00519643	−	0.00300016i
$109$	12.1657	+	7.02387i	1.16526	+	0.672764i	0.952559	−	0.304353i	$-0.0984401\pi$
$109$	12.1657	+	7.02387i	1.16526	+	0.672764i	0.212703	+	0.977117i	$0.431773\pi$
$110$	−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
$115$	−0.197647	+	12.1588i	−0.0184307	+	1.13382i
$116$	−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	0.194576	−	0.980887i	$-0.437667\pi$
$131$	13.0632	−	7.54205i	1.14134	−	0.658952i	0.946762	+	0.321936i	$0.104334\pi$
$132$	−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	$-0.377653\pi$
$137$	−2.81361	−	1.62444i	−0.240383	−	0.138785i	−0.615353	+	0.788252i	$0.710986\pi$
$138$	−8.56222	+	14.2887i	−0.728865	+	1.21634i
$139$			15.7497i			1.33587i	0.744220	+	0.667934i	$0.232821\pi$
$139$			15.7497i			1.33587i	−0.744220	+	0.667934i	$0.767179\pi$
$140$	−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	$-0.749049\pi$
$149$	−5.41098	+	3.12403i	−0.443285	+	0.255931i	0.261705	+	0.965148i	$0.415715\pi$
$150$	4.29964	+	2.48240i	0.351064	+	0.202687i
$151$	−8.61081	+	14.9144i	−0.700738	+	1.21371i	0.267470	+	0.963566i	$0.413812\pi$
$151$	−8.61081	+	14.9144i	−0.700738	+	1.21371i	−0.968208	+	0.250148i	$0.919521\pi$
$152$	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	$-0.908392\pi$
$157$	−2.92731	+	5.07024i	−0.233624	+	0.404649i	0.725248	+	0.688488i	$0.241725\pi$
$158$	8.13935	+	4.69926i	0.647532	+	0.373853i
$159$	4.34660	+	7.52853i	0.344708	+	0.597051i
$160$	1.44686			0.114384
$161$	3.37823	+	12.2306i	0.266242	+	0.963906i
$162$	14.0697			1.10542
$163$	−2.38556	−	4.13192i	−0.186852	−	0.323637i	0.757347	−	0.653012i	$-0.226495\pi$
$163$	−2.38556	−	4.13192i	−0.186852	−	0.323637i	−0.944199	+	0.329376i	$0.893162\pi$
$164$	−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	$0.244222\pi$
$167$			17.9409i			1.38831i	−0.719824	+	0.694156i	$0.755778\pi$
$168$	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	−0.638609	−	0.769532i	$-0.720490\pi$
$173$	−3.83381	+	2.21345i	−0.291479	+	0.168286i	0.347130	+	0.937817i	$0.387156\pi$
$174$		−	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	0.497068	+	0.867711i	$0.334410\pi$
$179$	−6.72869	+	11.6544i	−0.502926	+	0.871093i	−0.999994	+	0.00338176i	$0.998924\pi$
$180$	0.351025	+	0.607994i	0.0261639	+	0.0453172i
$181$	12.4838			0.927917			0.463958	−	0.885857i	$-0.346429\pi$
$181$	12.4838			0.927917			0.463958	+	0.885857i	$0.346429\pi$
$182$	−2.95357	−	0.716069i	−0.218933	−	0.0530786i
$183$		−	23.9662i		−	1.77164i
$184$	−11.3236	−	6.78543i	−0.834786	−	0.500229i
$185$	−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	$-0.538627\pi$
$191$	9.37119	−	5.41046i	0.678076	−	0.391487i	0.799130	+	0.601159i	$0.205294\pi$
$192$	−15.6815	−	9.05370i	−1.13171	−	0.653394i
$193$	−3.58582	+	6.21083i	−0.258113	+	0.447065i	−0.965736	−	0.259525i	$-0.916434\pi$
$193$	−3.58582	+	6.21083i	−0.258113	+	0.447065i	0.707623	+	0.706590i	$0.249767\pi$
$194$	−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	$-0.794418\pi$
$199$	1.72033	−	2.97970i	0.121951	−	0.211226i	0.920537	+	0.390655i	$0.127752\pi$
$200$	−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
$207$	0.213755	−	13.1497i	0.0148570	−	0.913968i
$208$	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	$-0.827780\pi$
$223$		−	15.3821i		−	1.03006i	0.857171	−	0.515032i	$-0.172220\pi$
$224$	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	−0.0870336	−	0.996205i	$-0.527739\pi$
$227$	12.3428	−	21.3784i	0.819222	−	1.41893i	0.906256	−	0.422729i	$-0.138928\pi$
$228$	1.48432	+	0.856975i	0.0983018	+	0.0567545i
$229$	6.24731	+	10.8207i	0.412834	+	0.715050i	0.995198	−	0.0978783i	$-0.0312056\pi$
$229$	6.24731	+	10.8207i	0.412834	+	0.715050i	−0.582364	+	0.812928i	$0.697872\pi$
$230$	−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	0.878530	+	0.477687i	$0.158525\pi$
$233$	13.0198	+	22.5509i	0.852954	+	1.47736i	−0.0255758	+	0.999673i	$0.508142\pi$
$234$	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	−0.148004	+	0.988987i	$0.547285\pi$
$241$	−14.4451	+	25.0196i	−0.930490	+	1.61166i	−0.782486	+	0.622668i	$0.786049\pi$
$242$	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	$-0.474398\pi$
$251$	2.54584			0.160692			0.0803459	+	0.996767i	$0.474398\pi$
$252$	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	−0.492379	−	0.870381i	$-0.663873\pi$
$257$	0.243730	−	0.140718i	0.0152035	−	0.00877774i	0.507582	+	0.861603i	$0.330539\pi$
$258$	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	0.996838	+	0.0794624i	$0.0253204\pi$
$263$	25.3650	+	14.6445i	1.56407	+	0.903018i	0.567235	+	0.823556i	$0.308013\pi$
$264$	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	0.451124	−	0.892461i	$-0.351023\pi$
$269$	−1.57794	−	0.911022i	−0.0962085	−	0.0555460i	−0.547332	+	0.836915i	$0.684357\pi$
$270$	1.96579	+	1.13495i	0.119634	+	0.0690709i
$271$	−2.06198	+	1.19048i	−0.125256	+	0.0723167i	−0.561319	−	0.827600i	$-0.689706\pi$
$271$	−2.06198	+	1.19048i	−0.125256	+	0.0723167i	0.436063	+	0.899916i	$0.356373\pi$
$272$	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
$276$	−1.16017	−	0.0188591i	−0.0698341	−	0.00113519i
$277$	−1.93244	+	3.34708i	−0.116109	+	0.201107i	−0.918223	−	0.396065i	$-0.870376\pi$
$277$	−1.93244	+	3.34708i	−0.116109	+	0.201107i	0.802113	+	0.597172i	$0.203709\pi$
$278$	−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	$-0.681707\pi$
$283$	7.71377	−	13.3606i	0.458536	−	0.794208i	0.998884	+	0.0472339i	$0.0150406\pi$
$284$	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	$-0.572971\pi$
$293$	−7.77950			−0.454484			−0.227242	+	0.973838i	$0.572971\pi$
$294$	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
$299$	−1.95356	+	3.26012i	−0.112977	+	0.188537i
$300$			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	$0.0420621\pi$
$307$			4.61716i			0.263515i	−0.991282	+	0.131758i	$0.957938\pi$
$308$	−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	0.951520	−	0.307588i	$-0.0995217\pi$
$311$	20.4727	+	11.8199i	1.16090	+	0.670246i	0.209381	+	0.977834i	$0.432855\pi$
$312$	−2.61364	+	4.52695i	−0.147968	+	0.256288i
$313$	−5.35830	−	9.28084i	−0.302869	−	0.524584i	0.673916	−	0.738808i	$-0.264611\pi$
$313$	−5.35830	−	9.28084i	−0.302869	−	0.524584i	−0.976785	+	0.214224i	$0.931278\pi$
$314$	−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	0.982125	−	0.188232i	$-0.0602757\pi$
$317$	5.84074	+	10.1165i	0.328049	+	0.568197i	−0.654076	+	0.756429i	$0.726942\pi$
$318$	−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
$322$	−12.9045	+	13.1046i	−0.719139	+	0.730289i
$323$	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	−0.939849	−	0.341591i	$-0.889034\pi$
$331$	−13.9316	−	24.1303i	−0.765751	−	1.32632i	0.174098	−	0.984728i	$-0.444299\pi$
$332$	−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
$345$	14.9783	−	24.9959i	0.806403	−	1.34573i
$346$	−5.55700	−	3.20833i	−0.298746	−	0.172481i
$347$	−3.25674	+	5.64083i	−0.174831	+	0.302816i	−0.940103	−	0.340891i	$-0.889271\pi$
$347$	−3.25674	+	5.64083i	−0.174831	+	0.302816i	0.765272	+	0.643707i	$0.222604\pi$
$348$	0.247459	−	0.142871i	0.0132652	−	0.00765868i
$349$		−	13.7110i		−	0.733931i	−0.930234	−	0.366966i	$-0.880397\pi$
$349$		−	13.7110i		−	0.733931i	0.930234	−	0.366966i	$-0.119603\pi$
$350$	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	0.196069	−	0.980590i	$-0.437182\pi$
$353$	−10.4296	−	6.02155i	−0.555113	−	0.320495i	−0.751182	+	0.660096i	$0.770516\pi$
$354$	−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	$-0.535811\pi$
$359$	13.1144	−	7.57162i	0.692153	−	0.399615i	0.804418	+	0.594064i	$0.202477\pi$
$360$	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	0.124775	+	0.992185i	$0.460179\pi$
$367$	−15.2658	+	26.4412i	−0.796870	+	1.38022i	−0.921645	+	0.388034i	$0.873154\pi$
$368$	0.326738	−	20.1002i	0.0170324	−	1.04780i
$369$	−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	$-0.721845\pi$
$373$	−5.76974	+	3.33116i	−0.298746	+	0.172481i	0.343134	+	0.939287i	$0.388512\pi$
$374$	−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	$-0.254646\pi$
$383$	−5.34052	−	9.25006i	−0.272888	−	0.472656i	−0.969600	+	0.244695i	$0.921312\pi$
$384$		−	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	$-0.594589\pi$
$389$	−24.9946	−	14.4306i	−1.26728	−	0.731663i	−0.974472	+	0.224510i	$0.927922\pi$
$390$	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	−0.522902	−	0.852393i	$-0.675151\pi$
$397$	−0.919722	+	0.531001i	−0.0461595	+	0.0266502i	0.476743	+	0.879043i	$0.341817\pi$
$398$	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	$-0.874314\pi$
$401$	−21.0551	+	12.1562i	−1.05144	+	0.607050i	−0.128389	+	0.991724i	$0.540981\pi$
$402$	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	0.513190	−	0.858275i	$-0.328464\pi$
$409$	0.535872	+	0.309386i	0.0264972	+	0.0152981i	−0.486693	+	0.873573i	$0.661797\pi$
$410$	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	$-0.390418\pi$
$419$	13.8170			0.675005			0.337502	+	0.941325i	$0.390418\pi$
$420$	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	$-0.654785\pi$
$431$	−30.4482	−	17.5793i	−1.46664	−	0.846763i	−0.999303	+	0.0373185i	$0.988118\pi$
$432$	−2.24201	+	1.29442i	−0.107869	+	0.0622780i
$433$	12.5373			0.602505			0.301252	−	0.953544i	$-0.402595\pi$
$433$	12.5373			0.602505			0.301252	+	0.953544i	$0.402595\pi$
$434$	−12.9175	+	13.5515i	−0.620060	+	0.650491i
$435$			7.17603i			0.344064i
$436$	−1.22832	+	0.709170i	−0.0588258	+	0.0339631i
$437$	0.552190	−	33.9695i	0.0264148	−	1.62498i
$438$	16.2990	−	28.2308i	0.778798	−	1.34892i
$439$	21.8276	−	12.6022i	1.04177	−	0.601469i	0.121439	−	0.992599i	$-0.461249\pi$
$439$	21.8276	−	12.6022i	1.04177	−	0.601469i	0.920335	+	0.391130i	$0.127916\pi$
$440$			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	0.749692	−	0.661787i	$-0.230202\pi$
$443$	−4.17328	−	7.22834i	−0.198279	−	0.343429i	−0.947970	+	0.318359i	$0.896868\pi$
$444$	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	$-0.932787\pi$
$457$	−27.4739	+	15.8620i	−1.28517	+	0.741995i	−0.307384	+	0.951585i	$0.599454\pi$
$458$	−9.05530	+	15.6842i	−0.423126	+	0.732876i
$459$	2.10272	+	1.21401i	0.0981467	+	0.0566650i
$460$	−1.05318	−	0.631094i	−0.0491046	−	0.0294249i
$461$			34.4607i			1.60500i	0.596654	+	0.802498i	$0.296496\pi$
$461$			34.4607i			1.60500i	−0.596654	+	0.802498i	$0.703504\pi$
$462$	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	0.999376	+	0.0353171i	$0.0112441\pi$
$467$	11.4593	+	19.8481i	0.530274	+	0.918461i	−0.469103	+	0.883144i	$0.655423\pi$
$468$			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	$-0.776837\pi$
$479$	3.86417	−	6.69295i	0.176559	−	0.305809i	0.940700	+	0.339241i	$0.110170\pi$
$480$	−3.00260	−	1.73355i	−0.137049	−	0.0791255i
$481$	−4.53755	−	7.85926i	−0.206894	−	0.358351i
$482$	−41.8755			−1.90737
$483$	7.64341	−	29.4293i	0.347787	−	1.33908i
$484$	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	−0.896202	−	0.443646i	$-0.853685\pi$
$487$	−1.40999	+	2.44217i	−0.0638926	+	0.110665i	0.832310	+	0.554311i	$0.187018\pi$
$488$	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	0.978660	−	0.205488i	$-0.0658780\pi$
$499$	6.95553	+	12.0473i	0.311372	+	0.539313i	−0.667287	+	0.744800i	$0.732545\pi$
$500$	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	$-0.362944\pi$
$503$	18.7223			0.834788			0.417394	+	0.908726i	$0.362944\pi$
$504$	4.70551	−	19.4088i	0.209600	−	0.864536i
$505$			7.75605i			0.345139i
$506$	−3.93668	+	6.56957i	−0.175007	+	0.292053i
$507$	−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	−0.241238	−	0.970466i	$-0.577553\pi$
$509$	10.7975	−	6.23394i	0.478591	−	0.276315i	0.719829	+	0.694151i	$0.244220\pi$
$510$			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	$-0.773634\pi$
$521$	4.25588	−	7.37140i	0.186453	−	0.322947i	0.944065	+	0.329758i	$0.106967\pi$
$522$	−2.34718	+	4.06544i	−0.102733	+	0.177939i
$523$	−2.22225	−	3.84905i	−0.0971721	−	0.168307i	0.813341	−	0.581787i	$-0.197646\pi$
$523$	−2.22225	−	3.84905i	−0.0971721	−	0.168307i	−0.910513	+	0.413480i	$0.864313\pi$
$524$			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
$529$	10.8465	+	20.2818i	0.471588	+	0.881819i
$530$	−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	−0.992502	−	0.122230i	$-0.960995\pi$
$541$	−14.0046	−	24.2567i	−0.602105	−	1.04288i	0.390396	−	0.920647i	$-0.372338\pi$
$542$	−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	$-0.290118\pi$
$557$	5.53273	+	3.19432i	0.234429	+	0.135348i	−0.378185	+	0.925730i	$0.623452\pi$
$558$	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	$-0.853502\pi$
$563$	−1.50242	+	2.60227i	−0.0633194	+	0.109672i	0.832628	+	0.553833i	$0.186835\pi$
$564$	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	$-0.718314\pi$
$569$	−6.67438	+	3.85345i	−0.279804	+	0.161545i	0.353530	+	0.935423i	$0.384981\pi$
$570$	−54.0317	−	31.1952i	−2.26314	−	1.30662i
$571$	−17.3049	−	9.99099i	−0.724188	−	0.418110i	0.0921042	−	0.995749i	$-0.470641\pi$
$571$	−17.3049	−	9.99099i	−0.724188	−	0.418110i	−0.816292	+	0.577639i	$0.803974\pi$
$572$	−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	0.0742654	−	0.997239i	$-0.476339\pi$
$577$	−18.0693	−	10.4323i	−0.752236	−	0.434304i	−0.826501	+	0.562935i	$0.809672\pi$
$578$	−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	$0.0400196\pi$
$587$			6.07612i			0.250788i	−0.992107	+	0.125394i	$0.959980\pi$
$588$	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	−0.772546	−	0.634959i	$-0.781017\pi$
$593$	−14.8284	+	8.56116i	−0.608928	+	0.351565i	0.163618	+	0.986524i	$0.447684\pi$
$594$	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
$598$	−5.50817	−	0.0895379i	−0.225246	−	0.00366148i
$599$	12.6564	−	21.9216i	0.517128	−	0.895693i	−0.482674	−	0.875800i	$-0.660334\pi$
$599$	12.6564	−	21.9216i	0.517128	−	0.895693i	0.999802	−	0.0198925i	$-0.00633239\pi$
$600$	8.16516	−	4.71416i	0.333341	−	0.192455i
$601$		−	27.7769i		−	1.13304i	−0.824047	−	0.566522i	$-0.808289\pi$
$601$		−	27.7769i		−	1.13304i	0.824047	−	0.566522i	$-0.191711\pi$
$602$	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	−0.255147	−	0.966902i	$-0.582124\pi$
$607$	11.2012	−	6.46699i	0.454641	−	0.262487i	0.709788	+	0.704415i	$0.248791\pi$
$608$	−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	$-0.504955\pi$
$613$	−22.0172	−	12.7117i	−0.889268	−	0.513419i	−0.873703	+	0.486460i	$0.838288\pi$
$614$	−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	$-0.753425\pi$
$619$	6.18042	−	10.7048i	0.248412	−	0.430262i	0.963085	+	0.269196i	$0.0867579\pi$
$620$	−1.08237	−	0.624909i	−0.0434692	−	0.0250969i
$621$	1.52247	−	2.54071i	0.0610945	−	0.101955i
$622$			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	$-0.209716\pi$
$641$	16.6053	+	9.58710i	0.655871	+	0.378668i	−0.134831	+	0.990869i	$0.543049\pi$
$642$	25.4082	+	44.0082i	1.00278	+	1.73687i
$643$	−33.6042			−1.32522			−0.662610	−	0.748965i	$-0.730551\pi$
$643$	−33.6042			−1.32522			−0.662610	+	0.748965i	$0.730551\pi$
$644$	−1.23997	−	0.322047i	−0.0488618	−	0.0126904i
$645$	−24.5216			−0.965538
$646$	20.1837	+	34.9592i	0.794117	+	1.37545i
$647$	−40.7198	−	23.5096i	−1.60086	−	0.924258i	−0.991315	−	0.131507i	$-0.958019\pi$
$647$	−40.7198	−	23.5096i	−1.60086	−	0.924258i	−0.609546	−	0.792751i	$-0.708648\pi$
$648$	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	0.700704	−	0.713452i	$-0.252869\pi$
$653$	−6.83605	−	11.8404i	−0.267515	−	0.463350i	−0.968220	+	0.250102i	$0.919536\pi$
$654$	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	$-0.737868\pi$
$661$	7.59564	−	13.1560i	0.295436	−	0.511710i	0.975086	+	0.221826i	$0.0712017\pi$
$662$	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
$667$	−4.85847	−	2.91134i	−0.188121	−	0.112728i
$668$	−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	−0.996431	−	0.0844105i	$-0.973099\pi$
$677$	−14.8652	−	25.7473i	−0.571317	−	0.989550i	0.425114	−	0.905140i	$-0.360234\pi$
$678$	−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	0.187809	+	0.982206i	$0.439861\pi$
$683$	−19.7761	+	34.2532i	−0.756710	+	1.31066i	−0.944520	+	0.328455i	$0.893472\pi$
$684$	−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
$690$	42.2321	+	0.686503i	1.60775	+	0.0261347i
$691$	30.1036	−	17.3803i	1.14520	−	0.661180i	0.197484	−	0.980306i	$-0.436723\pi$
$691$	30.1036	−	17.3803i	1.14520	−	0.661180i	0.947712	+	0.319127i	$0.103389\pi$
$692$		−	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	$-0.499934\pi$
$709$	23.0680	−	13.3183i	0.866339	−	0.500181i	0.866130	+	0.499819i	$0.166600\pi$
$710$	−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	−0.876609	−	0.481203i	$-0.840200\pi$
$719$	−24.0839	+	13.9049i	−0.898179	+	0.518564i	−0.0215704	+	0.999767i	$0.506867\pi$
$720$	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	$-0.0814106\pi$
$727$	52.1718			1.93494			0.967472	+	0.252980i	$0.0814106\pi$
$728$	−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	$-0.179549\pi$
$733$	−1.09544	−	1.89736i	−0.0404610	−	0.0700806i	−0.885547	+	0.464550i	$0.846216\pi$
$734$	−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	0.309559	+	0.950880i	$0.399819\pi$
$739$	−18.1785	+	31.4861i	−0.668707	+	1.15823i	−0.978266	+	0.207354i	$0.933515\pi$
$740$	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	$-0.543227\pi$
$751$	17.9493	−	10.3630i	0.654978	−	0.378152i	0.790361	+	0.612642i	$0.209893\pi$
$752$	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
$759$	0.205794	−	12.6600i	0.00746986	−	0.459529i
$760$	24.7218	−	42.8194i	0.896753	−	1.55322i
$761$	25.2474	−	14.5766i	0.915218	−	0.528402i	0.0331119	−	0.999452i	$-0.489458\pi$
$761$	25.2474	−	14.5766i	0.915218	−	0.528402i	0.882106	+	0.471050i	$0.156125\pi$
$762$			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	$-0.491394\pi$
$769$	1.49923			0.0540637			0.0270318	+	0.999635i	$0.491394\pi$
$770$	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	$-0.906212\pi$
$773$	−6.31015	+	10.9295i	−0.226960	+	0.393107i	0.729945	+	0.683505i	$0.239545\pi$
$774$	−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
$782$	−23.4418	−	14.0470i	−0.838276	−	0.502320i
$783$			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	$-0.771831\pi$
$787$	5.38671	−	9.33005i	0.192015	−	0.332580i	0.945918	+	0.324406i	$0.105164\pi$
$788$	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	$-0.506517\pi$
$797$	−1.15594			−0.0409457			−0.0204728	+	0.999790i	$0.506517\pi$
$798$	−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
$805$	22.5744	−	22.9244i	0.795643	−	0.807979i
$806$	−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	−0.962999	−	0.269506i	$-0.913140\pi$
$809$	−7.05670	+	12.2226i	−0.248100	+	0.429722i	0.714898	+	0.699228i	$0.246473\pi$
$810$	−17.8377	−	30.8958i	−0.626753	−	1.08557i
$811$		−	36.0451i		−	1.26572i	−0.774268	−	0.632858i	$-0.781882\pi$
$811$		−	36.0451i		−	1.26572i	0.774268	−	0.632858i	$-0.218118\pi$
$812$	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	0.594996	−	0.803729i	$-0.297154\pi$
$821$	−11.4197	−	19.7796i	−0.398552	−	0.690312i	−0.993548	+	0.113417i	$0.963820\pi$
$822$	−5.64229	+	9.77272i	−0.196797	+	0.340863i
$823$	26.4562	−	45.8235i	0.922206	−	1.59731i	0.126211	−	0.992003i	$-0.459718\pi$
$823$	26.4562	−	45.8235i	0.922206	−	1.59731i	0.795995	−	0.605304i	$-0.206948\pi$
$824$	−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	$-0.140024\pi$
$828$	1.13901	+	0.682526i	0.0395832	+	0.0237194i
$829$	−1.46534	−	0.846013i	−0.0508933	−	0.0293833i	0.474337	−	0.880343i	$-0.342688\pi$
$829$	−1.46534	−	0.846013i	−0.0508933	−	0.0293833i	−0.525231	+	0.850960i	$0.676021\pi$
$830$	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	$-0.291029\pi$
$839$	35.3581			1.22070			0.610349	+	0.792133i	$0.291029\pi$
$840$	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
$851$	−54.9119	−	0.892619i	−1.88236	−	0.0305986i
$852$	−2.21358	+	1.27801i	−0.0758360	+	0.0437839i
$853$			22.6660i			0.776071i	0.921645	+	0.388035i	$0.126846\pi$
$853$			22.6660i			0.776071i	−0.921645	+	0.388035i	$0.873154\pi$
$854$	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	0.703970	−	0.710229i	$-0.251409\pi$
$857$	12.9065	+	7.45159i	0.440879	+	0.254542i	−0.263091	+	0.964771i	$0.584742\pi$
$858$	2.62638	+	1.51634i	0.0896633	+	0.0517671i
$859$	−6.14530	+	3.54799i	−0.209675	+	0.121056i	−0.601160	−	0.799128i	$-0.705295\pi$
$859$	−6.14530	+	3.54799i	−0.209675	+	0.121056i	0.391485	+	0.920184i	$0.371961\pi$
$860$			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	0.613911	−	0.789375i	$-0.289595\pi$
$863$	−11.0652	−	19.1655i	−0.376663	−	0.652400i	−0.990574	+	0.136975i	$0.956262\pi$
$864$	−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	0.990537	+	0.137245i	$0.0438249\pi$
$877$	18.1869	+	31.5006i	0.614127	+	1.06370i	−0.376410	+	0.926453i	$0.622842\pi$
$878$	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	$-0.657096\pi$
$881$	−28.1227			−0.947479			−0.473739	+	0.880665i	$0.657096\pi$
$882$	−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	−0.990455	−	0.137835i	$-0.955986\pi$
$887$	−40.6923	+	23.4937i	−1.36631	+	0.788842i	−0.375859	+	0.926677i	$0.622652\pi$
$888$	−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	$-0.246792\pi$
$907$	14.0079	+	8.08749i	0.465126	+	0.268541i	−0.249071	+	0.968485i	$0.580125\pi$
$908$	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	$-0.985953\pi$
$919$	−44.2701	+	25.5594i	−1.46034	+	0.843125i	−0.461309	+	0.887239i	$0.652620\pi$
$920$	−0.544043	+	33.4683i	−0.0179366	+	1.10342i
$921$	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	−0.958658	−	0.284562i	$-0.908152\pi$
$929$	−36.3178	+	20.9681i	−1.19155	+	0.687941i	−0.232891	+	0.972503i	$0.574819\pi$
$930$	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	$-0.300261\pi$
$937$	35.9442			1.17425			0.587123	+	0.809498i	$0.300261\pi$
$938$	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	$-0.995600\pi$
$941$	−14.9692	+	25.9274i	−0.487981	+	0.845208i	0.511923	+	0.859031i	$0.328933\pi$
$942$	17.6108	+	10.1676i	0.573792	+	0.331279i
$943$	2.10670	−	3.51569i	0.0686037	−	0.114486i
$944$		−	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	0.944699	+	0.327939i	$0.106354\pi$
$947$	23.2755	+	40.3144i	0.756353	+	1.31004i	−0.188346	+	0.982103i	$0.560313\pi$
$948$	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
$966$	42.4814	−	11.7338i	1.36682	−	0.377530i
$967$	−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	$-0.0812346\pi$
$971$	8.26330	+	14.3125i	0.265182	+	0.459309i	−0.702429	+	0.711754i	$0.747901\pi$
$972$		−	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	$-0.165224\pi$
$977$	27.2815	+	15.7510i	0.872813	+	0.503919i	0.00453074	+	0.999990i	$0.498558\pi$
$978$	−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	−0.494144	−	0.869380i	$-0.664518\pi$
$983$	15.8593	−	27.4691i	0.505833	−	0.876129i	0.999977	−	0.00674862i	$-0.00214817\pi$
$984$	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
$989$	9.94851	−	16.6022i	0.316344	−	0.527918i
$990$	−9.61657	−	5.55213i	−0.305635	−	0.176458i
$991$	−7.74129	+	13.4083i	−0.245910	+	0.425929i	−0.962387	−	0.271682i	$-0.912420\pi$
$991$	−7.74129	+	13.4083i	−0.245910	+	0.425929i	0.716477	+	0.697611i	$0.245753\pi$
$992$	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	0.943846	−	0.330386i	$-0.107179\pi$
$997$	35.6689	+	20.5935i	1.12965	+	0.652202i	0.185800	+	0.982588i	$0.440512\pi$
$998$	−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.45.11	✓	28
7.3	odd	6		1127.2.c.c.1126.8		28
7.4	even	3		1127.2.c.c.1126.6		28
7.5	odd	6	inner	161.2.g.a.68.12	yes	28
23.22	odd	2	inner	161.2.g.a.45.12	yes	28
161.45	even	6		1127.2.c.c.1126.7		28
161.68	even	6	inner	161.2.g.a.68.11	yes	28
161.137	odd	6		1127.2.c.c.1126.5		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.2.g.a.45.11	✓	28	1.1	even	1	trivial
161.2.g.a.45.12	yes	28	23.22	odd	2	inner
161.2.g.a.68.11	yes	28	161.68	even	6	inner
161.2.g.a.68.12	yes	28	7.5	odd	6	inner
1127.2.c.c.1126.5		28	161.137	odd	6
1127.2.c.c.1126.6		28	7.4	even	3
1127.2.c.c.1126.7		28	161.45	even	6
1127.2.c.c.1126.8		28	7.3	odd	6

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} +(-4.11379 - 2.46510i) 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} +(0.112984 - 6.95050i) 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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