LMFDB - Embedded newform 161.4.c.b.160.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [161,4,Mod(160,161)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(161, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("161.160");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	161.c (of order $2$, degree $1$, 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:	$9.49930751092$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 16x^{6} - 2516x^{5} + 43236x^{4} + 20128x^{3} - 55968x^{2} - 6463604x + 23372755 $ x^8 - 16x^6 - 2516x^5 + 43236x^4 + 20128x^3 - 55968x^2 - 6463604x + 23372755
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{4}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			160.3
Root			$3.79050 + 1.54876i$ of defining polynomial
Character	$\chi$	$=$	161.160
Dual form			161.4.c.b.160.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} -5.83095i q^{3} -7.00000 q^{4} +7.58101 q^{5} +5.83095i q^{6} +(14.7738 - 11.1685i) q^{7} +15.0000 q^{8} -7.00000 q^{9} -7.58101 q^{10} -25.0705i q^{11} +40.8167i q^{12} -29.5884i q^{13} +(-14.7738 + 11.1685i) q^{14} -44.2045i q^{15} +41.0000 q^{16} -7.58101 q^{17} +7.00000 q^{18} -146.185 q^{19} -53.0670 q^{20} +(-65.1231 - 86.1451i) q^{21} +25.0705i q^{22} +(-110.264 + 2.96823i) q^{23} -87.4643i q^{24} -67.5284 q^{25} +29.5884i q^{26} -116.619i q^{27} +(-103.416 + 78.1796i) q^{28} +228.528 q^{29} +44.2045i q^{30} +282.921i q^{31} -161.000 q^{32} -146.185 q^{33} +7.58101 q^{34} +(112.000 - 84.6686i) q^{35} +49.0000 q^{36} -364.184i q^{37} +146.185 q^{38} -172.528 q^{39} +113.715 q^{40} -73.4403i q^{41} +(65.1231 + 86.1451i) q^{42} -370.121i q^{43} +175.493i q^{44} -53.0670 q^{45} +(110.264 - 2.96823i) q^{46} +446.188i q^{47} -239.069i q^{48} +(93.5284 - 330.002i) q^{49} +67.5284 q^{50} +44.2045i q^{51} +207.119i q^{52} -490.861i q^{53} +116.619i q^{54} -190.059i q^{55} +(221.606 - 167.528i) q^{56} +852.396i q^{57} -228.528 q^{58} -2.36207i q^{59} +309.431i q^{60} +421.246 q^{61} -282.921i q^{62} +(-103.416 + 78.1796i) q^{63} -167.000 q^{64} -224.310i q^{65} +146.185 q^{66} +478.988i q^{67} +53.0670 q^{68} +(17.3076 + 642.945i) q^{69} +(-112.000 + 84.6686i) q^{70} +620.528 q^{71} -105.000 q^{72} -134.351i q^{73} +364.184i q^{74} +393.755i q^{75} +1023.29 q^{76} +(-280.000 - 370.385i) q^{77} +172.528 q^{78} +1291.79i q^{79} +310.821 q^{80} -869.000 q^{81} +73.4403i q^{82} -821.896 q^{83} +(455.862 + 603.016i) q^{84} -57.4716 q^{85} +370.121i q^{86} -1332.54i q^{87} -376.057i q^{88} +97.4088 q^{89} +53.0670 q^{90} +(-330.458 - 437.132i) q^{91} +(771.849 - 20.7776i) q^{92} +1649.70 q^{93} -446.188i q^{94} -1108.23 q^{95} +938.783i q^{96} +1394.76 q^{97} +(-93.5284 + 330.002i) q^{98} +175.493i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 56 q^{4} + 120 q^{8} - 56 q^{9} + 328 q^{16} + 56 q^{18} - 124 q^{23} + 976 q^{25} + 312 q^{29} - 1288 q^{32} + 896 q^{35} + 392 q^{36} + 136 q^{39} + 124 q^{46} - 768 q^{49} - 976 q^{50}+ \cdots + 768 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 - 56 * q^4 + 120 * q^8 - 56 * q^9 + 328 * q^16 + 56 * q^18 - 124 * q^23 + 976 * q^25 + 312 * q^29 - 1288 * q^32 + 896 * q^35 + 392 * q^36 + 136 * q^39 + 124 * q^46 - 768 * q^49 - 976 * q^50 - 312 * q^58 - 1336 * q^64 - 896 * q^70 + 3448 * q^71 - 840 * q^72 - 2240 * q^77 - 136 * q^78 - 6952 * q^81 - 1976 * q^85 + 868 * q^92 + 2584 * q^93 + 3264 * q^95 + 768 * q^98

Character values

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

$n$	$24$	$120$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−1.00000			−0.353553			−0.176777	−	0.984251i	$-0.556567\pi$
$2$	−1.00000			−0.353553			−0.176777	+	0.984251i	$0.556567\pi$
$3$		−	5.83095i		−	1.12217i	−0.827759	−	0.561084i	$-0.810385\pi$
$3$		−	5.83095i		−	1.12217i	0.827759	−	0.561084i	$-0.189615\pi$
$4$	−7.00000			−0.875000
$5$	7.58101			0.678066			0.339033	−	0.940775i	$-0.389900\pi$
$5$	7.58101			0.678066			0.339033	+	0.940775i	$0.389900\pi$
$6$			5.83095i			0.396746i
$7$	14.7738	−	11.1685i	0.797708	−	0.603043i
$7$	14.7738	−	11.1685i	0.797708	−	0.603043i
$8$	15.0000			0.662913
$9$	−7.00000			−0.259259
$10$	−7.58101			−0.239732
$11$		−	25.0705i		−	0.687185i	−0.939119	−	0.343592i	$-0.888356\pi$
$11$		−	25.0705i		−	0.687185i	0.939119	−	0.343592i	$-0.111644\pi$
$12$			40.8167i			0.981896i
$13$		−	29.5884i		−	0.631257i	−0.948883	−	0.315628i	$-0.897785\pi$
$13$		−	29.5884i		−	0.631257i	0.948883	−	0.315628i	$-0.102215\pi$
$14$	−14.7738	+	11.1685i	−0.282033	+	0.213208i
$15$		−	44.2045i		−	0.760903i
$16$	41.0000			0.640625
$17$	−7.58101			−0.108157			−0.0540783	−	0.998537i	$-0.517222\pi$
$17$	−7.58101			−0.108157			−0.0540783	+	0.998537i	$0.517222\pi$
$18$	7.00000			0.0916620
$19$	−146.185			−1.76511			−0.882554	−	0.470210i	$-0.844178\pi$
$19$	−146.185			−1.76511			−0.882554	+	0.470210i	$0.844178\pi$
$20$	−53.0670			−0.593307
$21$	−65.1231	−	86.1451i	−0.676715	−	0.895162i
$22$			25.0705i			0.242956i
$23$	−110.264	+	2.96823i	−0.999638	+	0.0269095i
$23$	−110.264	+	2.96823i	−0.999638	+	0.0269095i
$24$		−	87.4643i		−	0.743899i
$25$	−67.5284			−0.540227
$26$			29.5884i			0.223183i
$27$		−	116.619i		−	0.831235i
$28$	−103.416	+	78.1796i	−0.697995	+	0.527663i
$29$	228.528			1.46333			0.731666	−	0.681663i	$-0.238743\pi$
$29$	228.528			1.46333			0.731666	+	0.681663i	$0.238743\pi$
$30$			44.2045i			0.269020i
$31$			282.921i			1.63916i	0.572961	+	0.819582i	$0.305794\pi$
$31$			282.921i			1.63916i	−0.572961	+	0.819582i	$0.694206\pi$
$32$	−161.000			−0.889408
$33$	−146.185			−0.771136
$34$	7.58101			0.0382392
$35$	112.000	−	84.6686i	0.540899	−	0.408903i
$36$	49.0000			0.226852
$37$		−	364.184i		−	1.61815i	−0.587706	−	0.809074i	$-0.699969\pi$
$37$		−	364.184i		−	1.61815i	0.587706	−	0.809074i	$-0.300031\pi$
$38$	146.185			0.624060
$39$	−172.528			−0.708376
$40$	113.715			0.449498
$41$		−	73.4403i		−	0.279743i	−0.990170	−	0.139871i	$-0.955331\pi$
$41$		−	73.4403i		−	0.279743i	0.990170	−	0.139871i	$-0.0446689\pi$
$42$	65.1231	+	86.1451i	0.239255	+	0.316488i
$43$		−	370.121i		−	1.31262i	−0.754489	−	0.656312i	$-0.772115\pi$
$43$		−	370.121i		−	1.31262i	0.754489	−	0.656312i	$-0.227885\pi$
$44$			175.493i			0.601287i
$45$	−53.0670			−0.175795
$46$	110.264	−	2.96823i	0.353425	−	0.00951395i
$47$			446.188i			1.38475i	0.721539	+	0.692374i	$0.243435\pi$
$47$			446.188i			1.38475i	−0.721539	+	0.692374i	$0.756565\pi$
$48$		−	239.069i		−	0.718888i
$49$	93.5284	−	330.002i	0.272677	−	0.962106i
$50$	67.5284			0.190999
$51$			44.2045i			0.121370i
$52$			207.119i			0.552350i
$53$		−	490.861i		−	1.27217i	−0.771619	−	0.636084i	$-0.780553\pi$
$53$		−	490.861i		−	1.27217i	0.771619	−	0.636084i	$-0.219447\pi$
$54$			116.619i			0.293886i
$55$		−	190.059i		−	0.465956i
$56$	221.606	−	167.528i	0.528811	−	0.399765i
$57$			852.396i			1.98075i
$58$	−228.528			−0.517366
$59$		−	2.36207i		−	0.00521212i	−0.999997	−	0.00260606i	$-0.999170\pi$
$59$		−	2.36207i		−	0.00521212i	0.999997	−	0.00260606i	$-0.000829535\pi$
$60$			309.431i			0.665790i
$61$	421.246			0.884182			0.442091	−	0.896970i	$-0.354237\pi$
$61$	421.246			0.884182			0.442091	+	0.896970i	$0.354237\pi$
$62$		−	282.921i		−	0.579532i
$63$	−103.416	+	78.1796i	−0.206813	+	0.156345i
$64$	−167.000			−0.326172
$65$		−	224.310i		−	0.428034i
$66$	146.185			0.272638
$67$			478.988i			0.873399i	0.899608	+	0.436699i	$0.143853\pi$
$67$			478.988i			0.873399i	−0.899608	+	0.436699i	$0.856147\pi$
$68$	53.0670			0.0946371
$69$	17.3076	+	642.945i	0.0301970	+	1.12176i
$70$	−112.000	+	84.6686i	−0.191237	+	0.144569i
$71$	620.528			1.03723			0.518614	−	0.855009i	$-0.326448\pi$
$71$	620.528			1.03723			0.518614	+	0.855009i	$0.326448\pi$
$72$	−105.000			−0.171866
$73$		−	134.351i		−	0.215406i	−0.994183	−	0.107703i	$-0.965650\pi$
$73$		−	134.351i		−	0.215406i	0.994183	−	0.107703i	$-0.0343496\pi$
$74$			364.184i			0.572102i
$75$			393.755i			0.606225i
$76$	1023.29			1.54447
$77$	−280.000	−	370.385i	−0.414402	−	0.548173i
$78$	172.528			0.250449
$79$			1291.79i			1.83972i	0.392247	+	0.919860i	$0.371698\pi$
$79$			1291.79i			1.83972i	−0.392247	+	0.919860i	$0.628302\pi$
$80$	310.821			0.434386
$81$	−869.000			−1.19204
$82$			73.4403i			0.0989040i
$83$	−821.896			−1.08692			−0.543462	−	0.839434i	$-0.682887\pi$
$83$	−821.896			−1.08692			−0.543462	+	0.839434i	$0.682887\pi$
$84$	455.862	+	603.016i	0.592126	+	0.783267i
$85$	−57.4716			−0.0733373
$86$			370.121i			0.464083i
$87$		−	1332.54i		−	1.64210i
$88$		−	376.057i		−	0.455543i
$89$	97.4088			0.116015			0.0580074	−	0.998316i	$-0.481525\pi$
$89$	97.4088			0.116015			0.0580074	+	0.998316i	$0.481525\pi$
$90$	53.0670			0.0621529
$91$	−330.458	−	437.132i	−0.380675	−	0.503559i
$92$	771.849	−	20.7776i	0.874683	−	0.0235458i
$93$	1649.70			1.83942
$94$		−	446.188i		−	0.489582i
$95$	−1108.23			−1.19686
$96$			938.783i			0.998064i
$97$	1394.76			1.45997			0.729983	−	0.683466i	$-0.239528\pi$
$97$	1394.76			1.45997			0.729983	+	0.683466i	$0.239528\pi$
$98$	−93.5284	+	330.002i	−0.0964060	+	0.340156i
$99$			175.493i			0.178159i
$100$	472.699			0.472699
$101$			1219.10i			1.20104i	0.799609	+	0.600521i	$0.205040\pi$
$101$			1219.10i			1.20104i	−0.799609	+	0.600521i	$0.794960\pi$
$102$		−	44.2045i		−	0.0429107i
$103$	66.0834			0.0632174			0.0316087	−	0.999500i	$-0.489937\pi$
$103$	66.0834			0.0632174			0.0316087	+	0.999500i	$0.489937\pi$
$104$		−	443.826i		−	0.418468i
$105$	−493.699	−	653.067i	−0.458858	−	0.606979i
$106$			490.861i			0.449780i
$107$		−	1177.67i		−	1.06402i	−0.846738	−	0.532010i	$-0.821437\pi$
$107$		−	1177.67i		−	1.06402i	0.846738	−	0.532010i	$-0.178563\pi$
$108$			816.333i			0.727331i
$109$			13.1975i			0.0115972i	0.999983	+	0.00579860i	$0.00184576\pi$
$109$			13.1975i			0.0115972i	−0.999983	+	0.00579860i	$0.998154\pi$
$110$			190.059i			0.164740i
$111$	−2123.54			−1.81583
$112$	605.724	−	457.909i	0.511032	−	0.386325i
$113$		−	2061.08i		−	1.71584i	−0.513784	−	0.857919i	$-0.671757\pi$
$113$		−	2061.08i		−	1.71584i	0.513784	−	0.857919i	$-0.328243\pi$
$114$		−	852.396i		−	0.700300i
$115$	−835.913	+	22.5022i	−0.677820	+	0.0182464i
$116$	−1599.70			−1.28042
$117$			207.119i			0.163659i
$118$			2.36207i			0.00184276i
$119$	−112.000	+	84.6686i	−0.0862775	+	0.0652232i
$120$		−	663.067i		−	0.504412i
$121$	702.472			0.527777
$122$	−421.246			−0.312605
$123$	−428.227			−0.313918
$124$		−	1980.45i		−	1.43427i
$125$	−1459.56			−1.04438
$126$	103.416	−	78.1796i	0.0731195	−	0.0552762i
$127$	1212.23			0.846990			0.423495	−	0.905898i	$-0.360803\pi$
$127$	1212.23			0.846990			0.423495	+	0.905898i	$0.360803\pi$
$128$	1455.00			1.00473
$129$	−2158.16			−1.47298
$130$			224.310i			0.151333i
$131$		−	2309.78i		−	1.54050i	−0.637740	−	0.770252i	$-0.720130\pi$
$131$		−	2309.78i		−	1.54050i	0.637740	−	0.770252i	$-0.279870\pi$
$132$	1023.29			0.674744
$133$	−2159.70	+	1632.67i	−1.40804	+	1.06444i
$134$		−	478.988i		−	0.308793i
$135$		−	884.090i		−	0.563632i
$136$	−113.715			−0.0716984
$137$		−	1802.42i		−	1.12403i	−0.827129	−	0.562013i	$-0.810027\pi$
$137$		−	1802.42i		−	1.12403i	0.827129	−	0.562013i	$-0.189973\pi$
$138$	−17.3076	−	642.945i	−0.0106762	−	0.396602i
$139$			1297.79i			0.791923i	0.918267	+	0.395961i	$0.129589\pi$
$139$			1297.79i			0.791923i	−0.918267	+	0.395961i	$0.870411\pi$
$140$	−784.000	+	592.680i	−0.473286	+	0.357790i
$141$	2601.70			1.55392
$142$	−620.528			−0.366715
$143$	−741.794			−0.433790
$144$	−287.000			−0.166088
$145$	1732.47			0.992236
$146$			134.351i			0.0761576i
$147$	−1924.23	−	545.359i	−1.07964	−	0.305990i
$148$			2549.29i			1.41588i
$149$			1467.28i			0.806743i	0.915036	+	0.403371i	$0.132162\pi$
$149$			1467.28i			0.806743i	−0.915036	+	0.403371i	$0.867838\pi$
$150$		−	393.755i		−	0.214333i
$151$	191.699			0.103313			0.0516563	−	0.998665i	$-0.483550\pi$
$151$	191.699			0.103313			0.0516563	+	0.998665i	$0.483550\pi$
$152$	−2192.77			−1.17011
$153$	53.0670			0.0280406
$154$	280.000	+	370.385i	0.146513	+	0.193808i
$155$			2144.83i			1.11146i
$156$	1207.70			0.619829
$157$	3067.73			1.55944			0.779719	−	0.626130i	$-0.215362\pi$
$157$	3067.73			1.55944			0.779719	+	0.626130i	$0.215362\pi$
$158$		−	1291.79i		−	0.650439i
$159$	−2862.19			−1.42759
$160$	−1220.54			−0.603077
$161$	−1595.87	+	1275.34i	−0.781192	+	0.624291i
$162$	869.000			0.421451
$163$	468.000			0.224887			0.112444	−	0.993658i	$-0.464132\pi$
$163$	468.000			0.224887			0.112444	+	0.993658i	$0.464132\pi$
$164$			514.082i			0.244775i
$165$	−1108.23			−0.522881
$166$	821.896			0.384286
$167$			1729.00i			0.801161i	0.916262	+	0.400580i	$0.131191\pi$
$167$			1729.00i			0.801161i	−0.916262	+	0.400580i	$0.868809\pi$
$168$	−976.846	−	1292.18i	−0.448603	−	0.593414i
$169$	1321.53			0.601515
$170$	57.4716			0.0259287
$171$	1023.29			0.457621
$172$			2590.84i			1.14855i
$173$		−	437.846i		−	0.192421i	−0.995361	−	0.0962105i	$-0.969328\pi$
$173$		−	437.846i		−	0.192421i	0.995361	−	0.0962105i	$-0.0306722\pi$
$174$			1332.54i			0.580571i
$175$	−997.648	+	754.192i	−0.430944	+	0.325780i
$176$		−	1027.89i		−	0.440228i
$177$	−13.7731			−0.00584887
$178$	−97.4088			−0.0410174
$179$	860.000			0.359103			0.179551	−	0.983749i	$-0.442535\pi$
$179$	860.000			0.359103			0.179551	+	0.983749i	$0.442535\pi$
$180$	371.469			0.153820
$181$	3139.25			1.28916			0.644582	−	0.764535i	$-0.277031\pi$
$181$	3139.25			1.28916			0.644582	+	0.764535i	$0.277031\pi$
$182$	330.458	+	437.132i	0.134589	+	0.178035i
$183$		−	2456.27i		−	0.992200i
$184$	−1653.96	+	44.5234i	−0.662673	+	0.0178387i
$185$		−	2760.88i		−	1.09721i
$186$	−1649.70			−0.650332
$187$			190.059i			0.0743236i
$188$		−	3123.31i		−	1.21165i
$189$	−1302.46	−	1722.90i	−0.501271	−	0.663083i
$190$	1108.23			0.423154
$191$		−	2048.57i		−	0.776068i	−0.921645	−	0.388034i	$-0.873154\pi$
$191$		−	2048.57i		−	0.776068i	0.921645	−	0.388034i	$-0.126846\pi$
$192$			973.769i			0.366019i
$193$	−1362.30			−0.508086			−0.254043	−	0.967193i	$-0.581760\pi$
$193$	−1362.30			−0.508086			−0.254043	+	0.967193i	$0.581760\pi$
$194$	−1394.76			−0.516176
$195$	−1307.94			−0.480325
$196$	−654.699	+	2310.02i	−0.238593	+	0.841842i
$197$	162.227			0.0586710			0.0293355	−	0.999570i	$-0.490661\pi$
$197$	162.227			0.0586710			0.0293355	+	0.999570i	$0.490661\pi$
$198$		−	175.493i		−	0.0629887i
$199$	3194.32			1.13789			0.568943	−	0.822377i	$-0.307352\pi$
$199$	3194.32			1.13789			0.568943	+	0.822377i	$0.307352\pi$
$200$	−1012.93			−0.358123
$201$	2792.96			0.980099
$202$		−	1219.10i		−	0.424632i
$203$	3376.22	−	2552.32i	1.16731	−	0.882453i
$204$		−	309.431i		−	0.106199i
$205$		−	556.751i		−	0.189684i
$206$	−66.0834			−0.0223507
$207$	771.849	−	20.7776i	0.259165	−	0.00697654i
$208$		−	1213.12i		−	0.404399i
$209$			3664.92i			1.21296i
$210$	493.699	+	653.067i	0.162231	+	0.214599i
$211$	611.397			0.199480			0.0997401	−	0.995014i	$-0.468199\pi$
$211$	611.397			0.199480			0.0997401	+	0.995014i	$0.468199\pi$
$212$			3436.03i			1.11315i
$213$		−	3618.27i		−	1.16394i
$214$			1177.67i			0.376188i
$215$		−	2805.89i		−	0.890046i
$216$		−	1749.29i		−	0.551036i
$217$	3159.81	+	4179.81i	0.988487	+	1.30758i
$218$		−	13.1975i		−	0.00410023i
$219$	−783.397			−0.241722
$220$			1330.42i			0.407712i
$221$			224.310i			0.0682746i
$222$	2123.54			0.641994
$223$			3794.11i			1.13934i	0.821874	+	0.569669i	$0.192929\pi$
$223$			3794.11i			1.13934i	−0.821874	+	0.569669i	$0.807071\pi$
$224$	−2378.58	+	1798.13i	−0.709488	+	0.536351i
$225$	472.699			0.140059
$226$			2061.08i			0.606641i
$227$	−1350.56			−0.394890			−0.197445	−	0.980314i	$-0.563264\pi$
$227$	−1350.56			−0.394890			−0.197445	+	0.980314i	$0.563264\pi$
$228$		−	5966.77i		−	1.73315i
$229$	−915.013			−0.264043			−0.132021	−	0.991247i	$-0.542147\pi$
$229$	−915.013			−0.264043			−0.132021	+	0.991247i	$0.542147\pi$
$230$	835.913	−	22.5022i	0.239646	−	0.00645108i
$231$	−2159.70	+	1632.67i	−0.615142	+	0.465028i
$232$	3427.93			0.970062
$233$	−2132.30			−0.599535			−0.299768	−	0.954012i	$-0.596909\pi$
$233$	−2132.30			−0.599535			−0.299768	+	0.954012i	$0.596909\pi$
$234$		−	207.119i		−	0.0578622i
$235$			3382.55i			0.938950i
$236$			16.5345i			0.00456060i
$237$	7532.37			2.06447
$238$	112.000	−	84.6686i	0.0305037	−	0.0230599i
$239$	6507.93			1.76135			0.880675	−	0.473721i	$-0.157089\pi$
$239$	6507.93			1.76135			0.880675	+	0.473721i	$0.157089\pi$
$240$		−	1812.38i		−	0.487454i
$241$	1227.98			0.328221			0.164110	−	0.986442i	$-0.447525\pi$
$241$	1227.98			0.328221			0.164110	+	0.986442i	$0.447525\pi$
$242$	−702.472			−0.186597
$243$			1918.38i			0.506438i
$244$	−2948.73			−0.773659
$245$	709.039	−	2501.75i	0.184893	−	0.652371i
$246$	428.227			0.110987
$247$			4325.37i			1.11424i
$248$			4243.81i			1.08662i
$249$			4792.43i			1.21971i
$250$	1459.56			0.369242
$251$	−5328.73			−1.34003			−0.670013	−	0.742349i	$-0.733712\pi$
$251$	−5328.73			−1.34003			−0.670013	+	0.742349i	$0.733712\pi$
$252$	723.915	−	547.257i	0.180962	−	0.136802i
$253$	74.4149	+	2764.37i	0.0184918	+	0.686936i
$254$	−1212.23			−0.299456
$255$			335.114i			0.0822968i
$256$	−119.000			−0.0290527
$257$			2865.15i			0.695422i	0.937602	+	0.347711i	$0.113041\pi$
$257$			2865.15i			0.695422i	−0.937602	+	0.347711i	$0.886959\pi$
$258$	2158.16			0.520779
$259$	−4067.40	−	5380.37i	−0.975814	−	1.29081i
$260$			1570.17i			0.374529i
$261$	−1599.70			−0.379383
$262$			2309.78i			0.544650i
$263$			2875.20i			0.674117i	0.941484	+	0.337058i	$0.109432\pi$
$263$			2875.20i			0.674117i	−0.941484	+	0.337058i	$0.890568\pi$
$264$	−2192.77			−0.511196
$265$		−	3721.22i		−	0.862614i
$266$	2159.70	−	1632.67i	0.497818	−	0.376335i
$267$		−	567.986i		−	0.130188i
$268$		−	3352.92i		−	0.764224i
$269$			474.863i			0.107632i	0.998551	+	0.0538158i	$0.0171384\pi$
$269$			474.863i			0.107632i	−0.998551	+	0.0538158i	$0.982862\pi$
$270$			884.090i			0.199274i
$271$		−	2582.92i		−	0.578971i	−0.957182	−	0.289485i	$-0.906516\pi$
$271$		−	2582.92i		−	0.578971i	0.957182	−	0.289485i	$-0.0934842\pi$
$272$	−310.821			−0.0692879
$273$	−2548.89	+	1926.89i	−0.565077	+	0.427181i
$274$			1802.42i			0.397403i
$275$			1692.97i			0.371236i
$276$	−121.153	−	4500.62i	−0.0264223	−	0.981541i
$277$	1703.70			0.369550			0.184775	−	0.982781i	$-0.440844\pi$
$277$	1703.70			0.369550			0.184775	+	0.982781i	$0.440844\pi$
$278$		−	1297.79i		−	0.279987i
$279$		−	1980.45i		−	0.424969i
$280$	1680.00	−	1270.03i	0.358569	−	0.271067i
$281$			2425.21i			0.514861i	0.966297	+	0.257431i	$0.0828759\pi$
$281$			2425.21i			0.514861i	−0.966297	+	0.257431i	$0.917124\pi$
$282$	−2601.70			−0.549393
$283$	3520.73			0.739526			0.369763	−	0.929126i	$-0.379439\pi$
$283$	3520.73			0.739526			0.369763	+	0.929126i	$0.379439\pi$
$284$	−4343.70			−0.907574
$285$			6462.02i			1.34308i
$286$	741.794			0.153368
$287$	−820.219	−	1084.99i	−0.168697	−	0.223153i
$288$	1127.00			0.230587
$289$	−4855.53			−0.988302
$290$	−1732.47			−0.350808
$291$		−	8132.79i		−	1.63833i
$292$			940.460i			0.188480i
$293$	3087.47			0.615604			0.307802	−	0.951450i	$-0.400407\pi$
$293$	3087.47			0.615604			0.307802	+	0.951450i	$0.400407\pi$
$294$	1924.23	+	545.359i	0.381712	+	0.108184i
$295$		−	17.9068i		−	0.00353416i
$296$		−	5462.76i		−	1.07269i
$297$	−2923.69			−0.571212
$298$		−	1467.28i		−	0.285227i
$299$	87.8251	+	3262.54i	0.0169868	+	0.631028i
$300$		−	2756.28i		−	0.530447i
$301$	−4133.70	−	5468.07i	−0.791570	−	1.04709i
$302$	−191.699			−0.0365265
$303$	7108.53			1.34777
$304$	−5993.57			−1.13077
$305$	3193.47			0.599533
$306$	−53.0670			−0.00991386
$307$			1207.49i			0.224478i	0.993681	+	0.112239i	$0.0358023\pi$
$307$			1207.49i			0.224478i	−0.993681	+	0.112239i	$0.964198\pi$
$308$	1960.00	+	2592.70i	0.362602	+	0.479651i
$309$		−	385.329i		−	0.0709405i
$310$		−	2144.83i		−	0.392961i
$311$			4470.50i			0.815109i	0.913181	+	0.407555i	$0.133618\pi$
$311$			4470.50i			0.815109i	−0.913181	+	0.407555i	$0.866382\pi$
$312$	−2587.93			−0.469591
$313$	−1780.39			−0.321513			−0.160757	−	0.986994i	$-0.551393\pi$
$313$	−1780.39			−0.321513			−0.160757	+	0.986994i	$0.551393\pi$
$314$	−3067.73			−0.551345
$315$	−784.000	+	592.680i	−0.140233	+	0.106012i
$316$		−	9042.54i		−	1.60976i
$317$	−3.92543			−0.000695502			−0.000347751	−	1.00000i	$-0.500111\pi$
$317$	−3.92543			−0.000695502			−0.000347751		1.00000i	$0.500111\pi$
$318$	2862.19			0.504728
$319$		−	5729.31i		−	1.00558i
$320$	−1266.03			−0.221166
$321$	−6866.96			−1.19401
$322$	1595.87	−	1275.34i	0.276193	−	0.220720i
$323$	1108.23			0.190908
$324$	6083.00			1.04304
$325$			1998.05i			0.341022i
$326$	−468.000			−0.0795096
$327$	76.9543			0.0130140
$328$		−	1101.60i		−	0.185445i
$329$	4983.25	+	6591.87i	0.835063	+	1.10463i
$330$	1108.23			0.184866
$331$	−3907.40			−0.648852			−0.324426	−	0.945911i	$-0.605171\pi$
$331$	−3907.40			−0.648852			−0.324426	+	0.945911i	$0.605171\pi$
$332$	5753.27			0.951059
$333$			2549.29i			0.419520i
$334$		−	1729.00i		−	0.283253i
$335$			3631.21i			0.592222i
$336$	−2670.05	−	3531.95i	−0.433521	−	0.573463i
$337$			5863.94i			0.947861i	0.880562	+	0.473930i	$0.157165\pi$
$337$			5863.94i			0.947861i	−0.880562	+	0.473930i	$0.842835\pi$
$338$	−1321.53			−0.212668
$339$	−12018.0			−1.92546
$340$	402.301			0.0641702
$341$	7092.96			1.12641
$342$	−1023.29			−0.161793
$343$	−2303.87	−	5919.95i	−0.362674	−	0.931916i
$344$		−	5551.81i		−	0.870155i
$345$	131.209	+	4874.17i	0.0204755	+	0.760628i
$346$			437.846i			0.0680311i
$347$	413.964			0.0640426			0.0320213	−	0.999487i	$-0.489806\pi$
$347$	413.964			0.0640426			0.0320213	+	0.999487i	$0.489806\pi$
$348$			9327.77i			1.43684i
$349$		−	1650.11i		−	0.253090i	−0.991961	−	0.126545i	$-0.959611\pi$
$349$		−	1650.11i		−	0.253090i	0.991961	−	0.126545i	$-0.0403889\pi$
$350$	997.648	−	754.192i	0.152362	−	0.115181i
$351$	−3450.57			−0.524723
$352$			4036.35i			0.611187i
$353$		−	10368.9i		−	1.56340i	−0.623656	−	0.781699i	$-0.714354\pi$
$353$		−	10368.9i		−	1.56340i	0.623656	−	0.781699i	$-0.285646\pi$
$354$	13.7731			0.00206789
$355$	4704.23			0.703309
$356$	−681.862			−0.101513
$357$	493.699	+	653.067i	0.0731913	+	0.0968178i
$358$	−860.000			−0.126962
$359$		−	13193.7i		−	1.93966i	−0.243777	−	0.969831i	$-0.578387\pi$
$359$		−	13193.7i		−	1.93966i	0.243777	−	0.969831i	$-0.421613\pi$
$360$	−796.006			−0.116537
$361$	14511.0			2.11561
$362$	−3139.25			−0.455788
$363$		−	4096.08i		−	0.592254i
$364$	2313.21	+	3059.92i	0.333091	+	0.440614i
$365$		−	1018.52i		−	0.146060i
$366$			2456.27i			0.350796i
$367$	880.826			0.125283			0.0626414	−	0.998036i	$-0.480048\pi$
$367$	880.826			0.125283			0.0626414	+	0.998036i	$0.480048\pi$
$368$	−4520.83	+	121.697i	−0.640393	+	0.0172389i
$369$			514.082i			0.0725259i
$370$			2760.88i			0.387923i
$371$	−5482.19	−	7251.87i	−0.767173	−	1.01482i
$372$	−11547.9			−1.60949
$373$		−	5673.82i		−	0.787613i	−0.919193	−	0.393806i	$-0.871158\pi$
$373$		−	5673.82i		−	0.787613i	0.919193	−	0.393806i	$-0.128842\pi$
$374$		−	190.059i		−	0.0262774i
$375$			8510.62i			1.17196i
$376$			6692.81i			0.917967i
$377$		−	6761.78i		−	0.923739i
$378$	1302.46	+	1722.90i	0.177226	+	0.234435i
$379$		−	4923.08i		−	0.667234i	−0.942709	−	0.333617i	$-0.891731\pi$
$379$		−	4923.08i		−	0.667234i	0.942709	−	0.333617i	$-0.108269\pi$
$380$	7757.59			1.04725
$381$		−	7068.44i		−	0.950465i
$382$			2048.57i			0.274382i
$383$	−7135.01			−0.951912			−0.475956	−	0.879469i	$-0.657898\pi$
$383$	−7135.01			−0.951912			−0.475956	+	0.879469i	$0.657898\pi$
$384$		−	8484.04i		−	1.12747i
$385$	−2122.68	−	2807.89i	−0.280992	−	0.371697i
$386$	1362.30			0.179636
$387$			2590.84i			0.340310i
$388$	−9763.33			−1.27747
$389$		−	944.681i		−	0.123129i	−0.998103	−	0.0615646i	$-0.980391\pi$
$389$		−	944.681i		−	0.123129i	0.998103	−	0.0615646i	$-0.0196090\pi$
$390$	1307.94			0.169821
$391$	835.913	−	22.5022i	0.108118	−	0.00291044i
$392$	1402.93	−	4950.03i	0.180761	−	0.637792i
$393$	−13468.2			−1.72870
$394$	−162.227			−0.0207433
$395$			9793.08i			1.24745i
$396$		−	1228.45i		−	0.155889i
$397$			11701.1i			1.47925i	0.673019	+	0.739625i	$0.264997\pi$
$397$			11701.1i			1.47925i	−0.673019	+	0.739625i	$0.735003\pi$
$398$	−3194.32			−0.402304
$399$	9520.00	+	12593.1i	1.19448	+	1.58006i
$400$	−2768.66			−0.346083
$401$			12453.4i			1.55086i	0.631436	+	0.775428i	$0.282466\pi$
$401$			12453.4i			1.55086i	−0.631436	+	0.775428i	$0.717534\pi$
$402$	−2792.96			−0.346517
$403$	8371.17			1.03473
$404$		−	8533.72i		−	1.05091i
$405$	−6587.89			−0.808284
$406$	−3376.22	+	2552.32i	−0.412707	+	0.311994i
$407$	−9130.27			−1.11197
$408$			663.067i			0.0804576i
$409$			8706.33i			1.05257i	0.850309	+	0.526284i	$0.176415\pi$
$409$			8706.33i			1.05257i	−0.850309	+	0.526284i	$0.823585\pi$
$410$			556.751i			0.0670634i
$411$	−10509.9			−1.26134
$412$	−462.584			−0.0553153
$413$	−26.3808	−	34.8966i	−0.00314313	−	0.00415775i
$414$	−771.849	+	20.7776i	−0.0916288	+	0.00246658i
$415$	−6230.79			−0.737006
$416$			4763.73i			0.561445i
$417$	7567.36			0.888670
$418$		−	3664.92i		−	0.428845i
$419$	5236.04			0.610495			0.305248	−	0.952273i	$-0.401261\pi$
$419$	5236.04			0.610495			0.305248	+	0.952273i	$0.401261\pi$
$420$	3455.89	+	4571.47i	0.401500	+	0.531106i
$421$			4164.30i			0.482080i	0.970515	+	0.241040i	$0.0774884\pi$
$421$			4164.30i			0.482080i	−0.970515	+	0.241040i	$0.922512\pi$
$422$	−611.397			−0.0705269
$423$		−	3123.31i		−	0.359009i
$424$		−	7362.92i		−	0.843337i
$425$	511.933			0.0584292
$426$			3618.27i			0.411516i
$427$	6223.40	−	4704.70i	0.705319	−	0.533200i
$428$			8243.72i			0.931017i
$429$			4325.37i			0.486785i
$430$			2805.89i			0.314679i
$431$		−	7842.44i		−	0.876467i	−0.898861	−	0.438233i	$-0.855604\pi$
$431$		−	7842.44i		−	0.876467i	0.898861	−	0.438233i	$-0.144396\pi$
$432$		−	4781.38i		−	0.532510i
$433$	11121.6			1.23434			0.617172	−	0.786828i	$-0.288278\pi$
$433$	11121.6			1.23434			0.617172	+	0.786828i	$0.288278\pi$
$434$	−3159.81	−	4179.81i	−0.349483	−	0.462298i
$435$		−	10102.0i		−	1.11345i
$436$		−	92.3828i		−	0.0101476i
$437$	16118.9	−	433.910i	1.76447	−	0.0474982i
$438$	783.397			0.0854616
$439$		−	12715.6i		−	1.38242i	−0.722652	−	0.691212i	$-0.757077\pi$
$439$		−	12715.6i		−	1.38242i	0.722652	−	0.691212i	$-0.242923\pi$
$440$		−	2850.89i		−	0.308888i
$441$	−654.699	+	2310.02i	−0.0706942	+	0.249435i
$442$		−	224.310i		−	0.0241387i
$443$	7266.19			0.779294			0.389647	−	0.920964i	$-0.372597\pi$
$443$	7266.19			0.779294			0.389647	+	0.920964i	$0.372597\pi$
$444$	14864.8			1.58885
$445$	738.457			0.0786657
$446$		−	3794.11i		−	0.402817i
$447$	8555.67			0.905300
$448$	−2467.22	+	1865.14i	−0.260190	+	0.196696i
$449$	−12977.6			−1.36403			−0.682016	−	0.731337i	$-0.738897\pi$
$449$	−12977.6			−1.36403			−0.682016	+	0.731337i	$0.738897\pi$
$450$	−472.699			−0.0495183
$451$	−1841.18			−0.192235
$452$			14427.5i			1.50136i
$453$		−	1117.78i		−	0.115934i
$454$	1350.56			0.139615
$455$	−2505.21	−	3313.90i	−0.258123	−	0.341446i
$456$			12785.9i			1.31306i
$457$			4692.25i			0.480294i	0.970737	+	0.240147i	$0.0771956\pi$
$457$			4692.25i			0.480294i	−0.970737	+	0.240147i	$0.922804\pi$
$458$	915.013			0.0933532
$459$			884.090i			0.0899036i
$460$	5851.39	−	157.515i	0.593093	−	0.0159656i
$461$			14205.6i			1.43519i	0.696463	+	0.717593i	$0.254756\pi$
$461$			14205.6i			1.43519i	−0.696463	+	0.717593i	$0.745244\pi$
$462$	2159.70	−	1632.67i	0.217485	−	0.164412i
$463$	−2991.10			−0.300233			−0.150117	−	0.988668i	$-0.547965\pi$
$463$	−2991.10			−0.300233			−0.150117	+	0.988668i	$0.547965\pi$
$464$	9369.66			0.937448
$465$	12506.4			1.24725
$466$	2132.30			0.211968
$467$	15997.6			1.58519			0.792594	−	0.609750i	$-0.208730\pi$
$467$	15997.6			1.58519			0.792594	+	0.609750i	$0.208730\pi$
$468$		−	1449.83i		−	0.143202i
$469$	5349.59	+	7076.46i	0.526697	+	0.696718i
$470$		−	3382.55i		−	0.331969i
$471$		−	17887.8i		−	1.74995i
$472$		−	35.4310i		−	0.00345518i
$473$	−9279.10			−0.902015
$474$	−7532.37			−0.729902
$475$	9871.61			0.953559
$476$	784.000	−	592.680i	0.0754928	−	0.0570703i
$477$			3436.03i			0.329822i
$478$	−6507.93			−0.622731
$479$	4369.81			0.416830			0.208415	−	0.978040i	$-0.433170\pi$
$479$	4369.81			0.416830			0.208415	+	0.978040i	$0.433170\pi$
$480$			7116.92i			0.676753i
$481$	−10775.6			−1.02147
$482$	−1227.98			−0.116043
$483$	7436.44	+	9305.42i	0.700559	+	0.876628i
$484$	−4917.30			−0.461805
$485$	10573.7			0.989952
$486$		−	1918.38i		−	0.179053i
$487$	1421.59			0.132276			0.0661379	−	0.997810i	$-0.478932\pi$
$487$	1421.59			0.132276			0.0661379	+	0.997810i	$0.478932\pi$
$488$	6318.70			0.586135
$489$		−	2728.89i		−	0.252361i
$490$	−709.039	+	2501.75i	−0.0653696	+	0.230648i
$491$	−398.567			−0.0366336			−0.0183168	−	0.999832i	$-0.505831\pi$
$491$	−398.567			−0.0366336			−0.0183168	+	0.999832i	$0.505831\pi$
$492$	2997.59			0.274678
$493$	−1732.47			−0.158269
$494$		−	4325.37i		−	0.393942i
$495$			1330.42i			0.120803i
$496$			11599.8i			1.05009i
$497$	9167.54	−	6930.38i	0.827405	−	0.625493i
$498$		−	4792.43i		−	0.431233i
$499$	−16817.0			−1.50868			−0.754340	−	0.656484i	$-0.772043\pi$
$499$	−16817.0			−1.50868			−0.754340	+	0.656484i	$0.772043\pi$
$500$	10216.9			0.913828
$501$	10081.7			0.899036
$502$	5328.73			0.473771
$503$	−16220.2			−1.43782			−0.718910	−	0.695103i	$-0.755359\pi$
$503$	−16220.2			−1.43782			−0.718910	+	0.695103i	$0.755359\pi$
$504$	−1551.25	+	1172.69i	−0.137099	+	0.103643i
$505$			9242.02i			0.814385i
$506$	−74.4149	−	2764.37i	−0.00653784	−	0.242868i
$507$		−	7705.77i		−	0.675000i
$508$	−8485.59			−0.741116
$509$		−	10924.1i		−	0.951280i	−0.879640	−	0.475640i	$-0.842216\pi$
$509$		−	10924.1i		−	0.951280i	0.879640	−	0.475640i	$-0.157784\pi$
$510$		−	335.114i		−	0.0290963i
$511$	−1500.51	−	1984.88i	−0.129899	−	0.171831i
$512$	−11521.0			−0.994455
$513$			17047.9i			1.46722i
$514$		−	2865.15i		−	0.245869i
$515$	500.979			0.0428656
$516$	15107.1			1.28886
$517$	11186.1			0.951577
$518$	4067.40	+	5380.37i	0.345002	+	0.456371i
$519$	−2553.06			−0.215929
$520$		−	3364.64i		−	0.283749i
$521$	−21961.9			−1.84677			−0.923386	−	0.383874i	$-0.874590\pi$
$521$	−21961.9			−1.84677			−0.923386	+	0.383874i	$0.874590\pi$
$522$	1599.70			0.134132
$523$	2025.70			0.169365			0.0846824	−	0.996408i	$-0.473012\pi$
$523$	2025.70			0.169365			0.0846824	+	0.996408i	$0.473012\pi$
$524$			16168.4i			1.34794i
$525$	4397.66	+	5817.24i	0.365580	+	0.483591i
$526$		−	2875.20i		−	0.238336i
$527$		−	2144.83i		−	0.177287i
$528$	−5993.57			−0.494009
$529$	12149.4	−	654.579i	0.998552	−	0.0537995i
$530$			3721.22i			0.304980i
$531$			16.5345i			0.00135129i
$532$	15117.9	−	11428.7i	1.23204	−	0.931383i
$533$	−2172.98			−0.176589
$534$			567.986i			0.0460284i
$535$		−	8927.95i		−	0.721475i
$536$			7184.82i			0.578987i
$537$		−	5014.62i		−	0.402973i
$538$		−	474.863i		−	0.0380535i
$539$	−8273.31	−	2344.80i	−0.661144	−	0.187380i
$540$			6188.63i			0.493178i
$541$	−2406.49			−0.191244			−0.0956222	−	0.995418i	$-0.530484\pi$
$541$	−2406.49			−0.191244			−0.0956222	+	0.995418i	$0.530484\pi$
$542$			2582.92i			0.204697i
$543$		−	18304.8i		−	1.44666i
$544$	1220.54			0.0961954
$545$			100.051i			0.00786367i
$546$	2548.89	−	1926.89i	0.199785	−	0.151031i
$547$	−5767.17			−0.450798			−0.225399	−	0.974267i	$-0.572369\pi$
$547$	−5767.17			−0.450798			−0.225399	+	0.974267i	$0.572369\pi$
$548$			12617.0i			0.983522i
$549$	−2948.73			−0.229232
$550$		−	1692.97i		−	0.131252i
$551$	−33407.3			−2.58294
$552$	259.614	+	9644.18i	0.0200180	+	0.743629i
$553$	14427.4	+	19084.6i	1.10943	+	1.46756i
$554$	−1703.70			−0.130656
$555$	−16098.6			−1.23125
$556$		−	9084.54i		−	0.692932i
$557$			4692.01i			0.356924i	0.983947	+	0.178462i	$0.0571122\pi$
$557$			4692.01i			0.356924i	−0.983947	+	0.178462i	$0.942888\pi$
$558$			1980.45i			0.150249i
$559$	−10951.3			−0.828603
$560$	4592.00	−	3471.41i	0.346513	−	0.261953i
$561$	1108.23			0.0834035
$562$		−	2425.21i		−	0.182031i
$563$	−8023.56			−0.600627			−0.300313	−	0.953841i	$-0.597091\pi$
$563$	−8023.56			−0.600627			−0.300313	+	0.953841i	$0.597091\pi$
$564$	−18211.9			−1.35968
$565$		−	15625.0i		−	1.16345i
$566$	−3520.73			−0.261462
$567$	−12838.4	+	9705.44i	−0.950903	+	0.718854i
$568$	9307.93			0.687591
$569$		−	14820.7i		−	1.09195i	−0.837803	−	0.545973i	$-0.816160\pi$
$569$		−	14820.7i		−	1.09195i	0.837803	−	0.545973i	$-0.183840\pi$
$570$		−	6462.02i		−	0.474849i
$571$			18211.0i			1.33469i	0.744751	+	0.667343i	$0.232568\pi$
$571$			18211.0i			1.33469i	−0.744751	+	0.667343i	$0.767432\pi$
$572$	5192.56			0.379566
$573$	−11945.1			−0.870878
$574$	820.219	+	1084.99i	0.0596434	+	0.0788965i
$575$	7445.96	−	200.440i	0.540031	−	0.0145372i
$576$	1169.00			0.0845631
$577$			6462.45i			0.466266i	0.972445	+	0.233133i	$0.0748977\pi$
$577$			6462.45i			0.466266i	−0.972445	+	0.233133i	$0.925102\pi$
$578$	4855.53			0.349418
$579$			7943.51i			0.570157i
$580$	−12127.3			−0.868206
$581$	−12142.5	+	9179.36i	−0.867049	+	0.655463i
$582$			8132.79i			0.579235i
$583$	−12306.1			−0.874215
$584$		−	2015.27i		−	0.142795i
$585$			1570.17i			0.110972i
$586$	−3087.47			−0.217649
$587$		−	10364.3i		−	0.728755i	−0.931251	−	0.364378i	$-0.881282\pi$
$587$		−	10364.3i		−	0.728755i	0.931251	−	0.364378i	$-0.118718\pi$
$588$	13469.6	+	3817.52i	0.944688	+	0.267741i
$589$		−	41358.7i		−	2.89330i
$590$			17.9068i			0.00124951i
$591$		−	945.937i		−	0.0658387i
$592$		−	14931.5i		−	1.03663i
$593$		−	10090.1i		−	0.698740i	−0.936985	−	0.349370i	$-0.886396\pi$
$593$		−	10090.1i		−	0.698740i	0.936985	−	0.349370i	$-0.113604\pi$
$594$	2923.69			0.201954
$595$	−849.073	+	641.873i	−0.0585018	+	0.0442256i
$596$		−	10271.0i		−	0.705900i
$597$		−	18625.9i		−	1.27690i
$598$	−87.8251	−	3262.54i	−0.00600574	−	0.223102i
$599$	14449.4			0.985618			0.492809	−	0.870138i	$-0.335970\pi$
$599$	14449.4			0.985618			0.492809	+	0.870138i	$0.335970\pi$
$600$			5906.32i			0.401874i
$601$			6654.20i			0.451631i	0.974170	+	0.225816i	$0.0725047\pi$
$601$			6654.20i			0.451631i	−0.974170	+	0.225816i	$0.927495\pi$
$602$	4133.70	+	5468.07i	0.279862	+	0.370203i
$603$		−	3352.92i		−	0.226437i
$604$	−1341.89			−0.0903985
$605$	5325.44			0.357868
$606$	−7108.53			−0.476509
$607$		−	9827.99i		−	0.657176i	−0.944473	−	0.328588i	$-0.893427\pi$
$607$		−	9827.99i		−	0.657176i	0.944473	−	0.328588i	$-0.106573\pi$
$608$	23535.7			1.56990
$609$	−14882.5	−	19686.6i	−0.990260	−	1.30992i
$610$	−3193.47			−0.211967
$611$	13202.0			0.874131
$612$	−371.469			−0.0245355
$613$			8922.39i			0.587882i	0.955824	+	0.293941i	$0.0949670\pi$
$613$			8922.39i			0.587882i	−0.955824	+	0.293941i	$0.905033\pi$
$614$		−	1207.49i		−	0.0793651i
$615$	−3246.39			−0.212857
$616$	−4200.00	−	5555.78i	−0.274712	−	0.363391i
$617$			4906.06i			0.320114i	0.987108	+	0.160057i	$0.0511678\pi$
$617$			4906.06i			0.320114i	−0.987108	+	0.160057i	$0.948832\pi$
$618$			385.329i			0.0250813i
$619$	−15023.8			−0.975540			−0.487770	−	0.872972i	$-0.662189\pi$
$619$	−15023.8			−0.975540			−0.487770	+	0.872972i	$0.662189\pi$
$620$		−	15013.8i		−	0.972529i
$621$	346.152	+	12858.9i	0.0223681	+	0.830934i
$622$		−	4470.50i		−	0.288185i
$623$	1439.10	−	1087.91i	0.0925460	−	0.0699620i
$624$	−7073.66			−0.453803
$625$	−2623.88			−0.167928
$626$	1780.39			0.113672
$627$	21370.0			1.36114
$628$	−21474.1			−1.36451
$629$			2760.88i			0.175014i
$630$	784.000	−	592.680i	0.0495799	−	0.0374809i
$631$			10274.9i			0.648235i	0.946017	+	0.324117i	$0.105067\pi$
$631$			10274.9i			0.648235i	−0.946017	+	0.324117i	$0.894933\pi$
$632$			19376.9i			1.21957i
$633$		−	3565.03i		−	0.223850i
$634$	3.92543			0.000245897
$635$	9189.90			0.574315
$636$	20035.3			1.24914
$637$	−9764.23	−	2767.35i	−0.607336	−	0.172129i
$638$			5729.31i			0.355526i
$639$	−4343.70			−0.268911
$640$	11030.4			0.681271
$641$		−	327.338i		−	0.0201702i	−0.999949	−	0.0100851i	$-0.996790\pi$
$641$		−	327.338i		−	0.0201702i	0.999949	−	0.0100851i	$-0.00321024\pi$
$642$	6866.96			0.422145
$643$	−29865.4			−1.83169			−0.915846	−	0.401529i	$-0.868479\pi$
$643$	−29865.4			−1.83169			−0.915846	+	0.401529i	$0.868479\pi$
$644$	11171.1	−	8927.38i	0.683543	−	0.546255i
$645$	−16361.0			−0.998780
$646$	−1108.23			−0.0674963
$647$			31588.3i			1.91942i	0.280998	+	0.959708i	$0.409335\pi$
$647$			31588.3i			1.91942i	−0.280998	+	0.959708i	$0.590665\pi$
$648$	−13035.0			−0.790221
$649$	−59.2181			−0.00358169
$650$		−	1998.05i		−	0.120569i
$651$	24372.3	−	18424.7i	1.46732	−	1.10925i
$652$	−3276.00			−0.196776
$653$	−15080.2			−0.903727			−0.451863	−	0.892087i	$-0.649241\pi$
$653$	−15080.2			−0.903727			−0.451863	+	0.892087i	$0.649241\pi$
$654$	−76.9543			−0.00460115
$655$		−	17510.4i		−	1.04456i
$656$		−	3011.05i		−	0.179210i
$657$			940.460i			0.0558461i
$658$	−4983.25	−	6591.87i	−0.295239	−	0.390544i
$659$			3803.45i			0.224828i	0.993661	+	0.112414i	$0.0358582\pi$
$659$			3803.45i			0.224828i	−0.993661	+	0.112414i	$0.964142\pi$
$660$	7757.59			0.457521
$661$	−4680.05			−0.275390			−0.137695	−	0.990475i	$-0.543969\pi$
$661$	−4680.05			−0.275390			−0.137695	+	0.990475i	$0.543969\pi$
$662$	3907.40			0.229404
$663$	1307.94			0.0766156
$664$	−12328.4			−0.720536
$665$	−16372.7	+	12377.3i	−0.954745	+	0.721758i
$666$		−	2549.29i		−	0.148323i
$667$	−25198.5	+	678.325i	−1.46280	+	0.0393776i
$668$		−	12103.0i		−	0.701015i
$669$	22123.3			1.27853
$670$		−	3631.21i		−	0.209382i
$671$		−	10560.8i		−	0.607596i
$672$	10484.8	+	13869.4i	0.601876	+	0.796164i
$673$	11137.4			0.637915			0.318957	−	0.947769i	$-0.396667\pi$
$673$	11137.4			0.637915			0.318957	+	0.947769i	$0.396667\pi$
$674$		−	5863.94i		−	0.335119i
$675$			7875.09i			0.449055i
$676$	−9250.70			−0.526326
$677$	12749.4			0.723780			0.361890	−	0.932221i	$-0.382132\pi$
$677$	12749.4			0.723780			0.361890	+	0.932221i	$0.382132\pi$
$678$	12018.0			0.680752
$679$	20605.9	−	15577.4i	1.16463	−	0.880422i
$680$	−862.075			−0.0486163
$681$			7875.07i			0.443133i
$682$	−7092.96			−0.398246
$683$	19985.6			1.11966			0.559830	−	0.828608i	$-0.310867\pi$
$683$	19985.6			1.11966			0.559830	+	0.828608i	$0.310867\pi$
$684$	−7163.05			−0.400418
$685$		−	13664.2i		−	0.762163i
$686$	2303.87	+	5919.95i	0.128225	+	0.329482i
$687$			5335.40i			0.296300i
$688$		−	15174.9i		−	0.840900i
$689$	−14523.8			−0.803065
$690$	−131.209	−	4874.17i	−0.00723919	−	0.268922i
$691$		−	8712.85i		−	0.479670i	−0.970814	−	0.239835i	$-0.922907\pi$
$691$		−	8712.85i		−	0.479670i	0.970814	−	0.239835i	$-0.0770934\pi$
$692$			3064.92i			0.168368i
$693$	1960.00	+	2592.70i	0.107438	+	0.142119i
$694$	−413.964			−0.0226425
$695$			9838.57i			0.536976i
$696$		−	19988.1i		−	1.08857i
$697$			556.751i			0.0302560i
$698$			1650.11i			0.0894810i
$699$			12433.3i			0.672779i
$700$	6983.54	−	5279.34i	0.377076	−	0.285058i
$701$		−	11693.5i		−	0.630038i	−0.949085	−	0.315019i	$-0.897989\pi$
$701$		−	11693.5i		−	0.630038i	0.949085	−	0.315019i	$-0.102011\pi$
$702$	3450.57			0.185517
$703$			53238.1i			2.85621i
$704$			4186.77i			0.224140i
$705$	19723.5			1.05366
$706$			10368.9i			0.552744i
$707$	13615.6	+	18010.7i	0.724280	+	0.958081i
$708$	96.4117			0.00511776
$709$		−	12250.5i		−	0.648911i	−0.945901	−	0.324456i	$-0.894819\pi$
$709$		−	12250.5i		−	0.648911i	0.945901	−	0.324456i	$-0.105181\pi$
$710$	−4704.23			−0.248657
$711$		−	9042.54i		−	0.476964i
$712$	1461.13			0.0769077
$713$	−839.774	−	31196.0i	−0.0441091	−	1.63857i
$714$	−493.699	−	653.067i	−0.0258770	−	0.0342303i
$715$	−5623.55			−0.294138
$716$	−6020.00			−0.314215
$717$		−	37947.4i		−	1.97653i
$718$			13193.7i			0.685774i
$719$			17012.4i			0.882416i	0.897405	+	0.441208i	$0.145450\pi$
$719$			17012.4i			0.882416i	−0.897405	+	0.441208i	$0.854550\pi$
$720$	−2175.75			−0.112619
$721$	976.301	−	738.054i	0.0504291	−	0.0381229i
$722$	−14511.0			−0.747981
$723$		−	7160.29i		−	0.368318i
$724$	−21974.8			−1.12802
$725$	−15432.1			−0.790532
$726$			4096.08i			0.209394i
$727$	−25516.2			−1.30171			−0.650856	−	0.759201i	$-0.725590\pi$
$727$	−25516.2			−1.30171			−0.650856	+	0.759201i	$0.725590\pi$
$728$	−4956.87	−	6556.98i	−0.252354	−	0.333815i
$729$	−12277.0			−0.623736
$730$			1018.52i			0.0516399i
$731$			2805.89i			0.141969i
$732$			17193.9i			0.868175i
$733$	−5141.78			−0.259094			−0.129547	−	0.991573i	$-0.541352\pi$
$733$	−5141.78			−0.259094			−0.129547	+	0.991573i	$0.541352\pi$
$734$	−880.826			−0.0442941
$735$	−14587.6	−	4134.37i	−0.732069	−	0.207481i
$736$	17752.5	−	477.885i	0.889086	−	0.0239335i
$737$	12008.5			0.600186
$738$		−	514.082i		−	0.0256418i
$739$	8901.81			0.443110			0.221555	−	0.975148i	$-0.428887\pi$
$739$	8901.81			0.443110			0.221555	+	0.975148i	$0.428887\pi$
$740$			19326.2i			0.960060i
$741$	25221.0			1.25036
$742$	5482.19	+	7251.87i	0.271237	+	0.358793i
$743$			21134.6i			1.04354i	0.853086	+	0.521771i	$0.174728\pi$
$743$			21134.6i			1.04354i	−0.853086	+	0.521771i	$0.825272\pi$
$744$	24745.5			1.21937
$745$			11123.5i			0.547024i
$746$			5673.82i			0.278463i
$747$	5753.27			0.281795
$748$		−	1330.42i		−	0.0650332i
$749$	−13152.9	−	17398.7i	−0.641650	−	0.848777i
$750$		−	8510.62i		−	0.414352i
$751$			25277.9i			1.22823i	0.789215	+	0.614117i	$0.210488\pi$
$751$			25277.9i			1.22823i	−0.789215	+	0.614117i	$0.789512\pi$
$752$			18293.7i			0.887104i
$753$			31071.6i			1.50373i
$754$			6761.78i			0.326591i
$755$	1453.27			0.0700527
$756$	9117.23	+	12060.3i	0.438612	+	0.580198i
$757$			18322.8i			0.879726i	0.898065	+	0.439863i	$0.144973\pi$
$757$			18322.8i			0.879726i	−0.898065	+	0.439863i	$0.855027\pi$
$758$			4923.08i			0.235903i
$759$	16118.9	−	433.910i	0.770857	−	0.0207509i
$760$	−16623.4			−0.793413
$761$			21176.6i			1.00874i	0.863488	+	0.504369i	$0.168275\pi$
$761$			21176.6i			1.00874i	−0.863488	+	0.504369i	$0.831725\pi$
$762$			7068.44i			0.336040i
$763$	147.397	+	194.977i	0.00699362	+	0.00925119i
$764$			14340.0i			0.679060i
$765$	402.301			0.0190134
$766$	7135.01			0.336552
$767$	−69.8897			−0.00329019
$768$			693.883i			0.0326020i
$769$	3297.17			0.154615			0.0773074	−	0.997007i	$-0.475368\pi$
$769$	3297.17			0.154615			0.0773074	+	0.997007i	$0.475368\pi$
$770$	2122.68	+	2807.89i	0.0993456	+	0.131415i
$771$	16706.6			0.780379
$772$	9536.11			0.444575
$773$	10213.9			0.475250			0.237625	−	0.971357i	$-0.423631\pi$
$773$	10213.9			0.475250			0.237625	+	0.971357i	$0.423631\pi$
$774$		−	2590.84i		−	0.120318i
$775$		−	19105.2i		−	0.885521i
$776$	20921.4			0.967829
$777$	−31372.7	+	23716.8i	−1.44851	+	1.09503i
$778$			944.681i			0.0435327i
$779$			10735.8i			0.493776i
$780$	9155.57			0.420285
$781$		−	15556.9i		−	0.712767i
$782$	−835.913	+	22.5022i	−0.0382253	+	0.00102900i
$783$		−	26650.8i		−	1.21637i
$784$	3834.66	−	13530.1i	0.174684	−	0.616349i
$785$	23256.5			1.05740
$786$	13468.2			0.611189
$787$	32488.8			1.47154			0.735768	−	0.677233i	$-0.236821\pi$
$787$	32488.8			1.47154			0.735768	+	0.677233i	$0.236821\pi$
$788$	−1135.59			−0.0513371
$789$	16765.2			0.756472
$790$		−	9793.08i		−	0.441041i
$791$	−23019.2	−	30449.9i	−1.03473	−	1.36874i
$792$			2632.40i			0.118104i
$793$		−	12464.0i		−	0.558146i
$794$		−	11701.1i		−	0.522994i
$795$	−21698.3			−0.967997
$796$	−22360.3			−0.995651
$797$	34071.5			1.51427			0.757135	−	0.653258i	$-0.226598\pi$
$797$	34071.5			1.51427			0.757135	+	0.653258i	$0.226598\pi$
$798$	−9520.00	−	12593.1i	−0.422311	−	0.558635i
$799$		−	3382.55i		−	0.149770i
$800$	10872.1			0.480482
$801$	−681.862			−0.0300779
$802$		−	12453.4i		−	0.548310i
$803$	−3368.25			−0.148024
$804$	−19550.7			−0.857587
$805$	−12098.3	+	9668.36i	−0.529699	+	0.423310i
$806$	−8371.17			−0.365834
$807$	2768.90			0.120781
$808$			18286.5i			0.796186i
$809$	−32073.7			−1.39388			−0.696942	−	0.717128i	$-0.745456\pi$
$809$	−32073.7			−1.39388			−0.696942	+	0.717128i	$0.745456\pi$
$810$	6587.89			0.285772
$811$		−	6172.70i		−	0.267266i	−0.991031	−	0.133633i	$-0.957336\pi$
$811$		−	6172.70i		−	0.267266i	0.991031	−	0.133633i	$-0.0426643\pi$
$812$	−23633.6	+	17866.3i	−1.02140	+	0.772146i
$813$	−15060.9			−0.649702
$814$	9130.27			0.393140
$815$	3547.91			0.152488
$816$			1812.38i			0.0777526i
$817$			54106.0i			2.31693i
$818$		−	8706.33i		−	0.372139i
$819$	2313.21	+	3059.92i	0.0986936	+	0.130552i
$820$			3897.26i			0.165973i
$821$	5920.46			0.251675			0.125838	−	0.992051i	$-0.459838\pi$
$821$	5920.46			0.251675			0.125838	+	0.992051i	$0.459838\pi$
$822$	10509.9			0.445953
$823$	24605.6			1.04216			0.521080	−	0.853508i	$-0.325529\pi$
$823$	24605.6			1.04216			0.521080	+	0.853508i	$0.325529\pi$
$824$	991.252			0.0419076
$825$	9871.61			0.416588
$826$	26.3808	+	34.8966i	0.00111127	+	0.00146999i
$827$		−	26331.2i		−	1.10716i	−0.832795	−	0.553582i	$-0.813261\pi$
$827$		−	26331.2i		−	1.10716i	0.832795	−	0.553582i	$-0.186739\pi$
$828$	−5402.94	+	145.443i	−0.226770	+	0.00610447i
$829$		−	25973.6i		−	1.08818i	−0.839027	−	0.544089i	$-0.816875\pi$
$829$		−	25973.6i		−	1.08818i	0.839027	−	0.544089i	$-0.183125\pi$
$830$	6230.79			0.260571
$831$		−	9934.18i		−	0.414697i
$832$			4941.26i			0.205898i
$833$	−709.039	+	2501.75i	−0.0294919	+	0.104058i
$834$	−7567.36			−0.314192
$835$			13107.5i			0.543239i
$836$		−	25654.4i		−	1.06134i
$837$	32994.0			1.36253
$838$	−5236.04			−0.215843
$839$	16769.5			0.690043			0.345022	−	0.938595i	$-0.387872\pi$
$839$	16769.5			0.690043			0.345022	+	0.938595i	$0.387872\pi$
$840$	−7405.48	−	9796.00i	−0.304182	−	0.402374i
$841$	27836.2			1.14134
$842$		−	4164.30i		−	0.170441i
$843$	14141.3			0.577761
$844$	−4279.78			−0.174545
$845$	10018.5			0.407867
$846$			3123.31i			0.126929i
$847$	10378.2	−	7845.57i	0.421012	−	0.318273i
$848$		−	20125.3i		−	0.814983i
$849$		−	20529.2i		−	0.829872i
$850$	−511.933			−0.0206578
$851$	1080.98	+	40156.5i	0.0435436	+	1.61756i
$852$			25327.9i			1.01845i
$853$		−	24892.5i		−	0.999182i	−0.866261	−	0.499591i	$-0.833484\pi$
$853$		−	24892.5i		−	0.999182i	0.866261	−	0.499591i	$-0.166516\pi$
$854$	−6223.40	+	4704.70i	−0.249368	+	0.188515i
$855$	7757.59			0.310297
$856$		−	17665.1i		−	0.705352i
$857$		−	33508.2i		−	1.33561i	−0.744337	−	0.667805i	$-0.767234\pi$
$857$		−	33508.2i		−	1.33561i	0.744337	−	0.667805i	$-0.232766\pi$
$858$		−	4325.37i		−	0.172104i
$859$			19113.9i			0.759208i	0.925149	+	0.379604i	$0.123940\pi$
$859$			19113.9i			0.759208i	−0.925149	+	0.379604i	$0.876060\pi$
$860$			19641.2i			0.778790i
$861$	−6326.52	+	4782.66i	−0.250415	+	0.189306i
$862$			7842.44i			0.309878i
$863$	−19584.8			−0.772507			−0.386253	−	0.922393i	$-0.626231\pi$
$863$	−19584.8			−0.772507			−0.386253	+	0.922393i	$0.626231\pi$
$864$			18775.7i			0.739307i
$865$		−	3319.31i		−	0.130474i
$866$	−11121.6			−0.436407
$867$			28312.4i			1.10904i
$868$	−22118.7	−	29258.7i	−0.864926	−	1.14413i
$869$	32385.8			1.26423
$870$			10102.0i			0.393666i
$871$	14172.5			0.551339
$872$			197.963i			0.00768794i
$873$	−9763.33			−0.378510
$874$	−16118.9	+	433.910i	−0.623834	+	0.0167932i
$875$	−21563.2	+	16301.1i	−0.833107	+	0.629803i
$876$	5483.78			0.211507
$877$	−34485.1			−1.32780			−0.663900	−	0.747822i	$-0.731100\pi$
$877$	−34485.1			−1.32780			−0.663900	+	0.747822i	$0.731100\pi$
$878$			12715.6i			0.488760i
$879$		−	18002.9i		−	0.690811i
$880$		−	7792.43i		−	0.298503i
$881$	−17772.3			−0.679642			−0.339821	−	0.940490i	$-0.610366\pi$
$881$	−17772.3			−0.679642			−0.339821	+	0.940490i	$0.610366\pi$
$882$	654.699	−	2310.02i	0.0249942	−	0.0881885i
$883$	22103.8			0.842414			0.421207	−	0.906965i	$-0.361607\pi$
$883$	22103.8			0.842414			0.421207	+	0.906965i	$0.361607\pi$
$884$		−	1570.17i		−	0.0597403i
$885$	−104.414			−0.00396592
$886$	−7266.19			−0.275522
$887$		−	28821.0i		−	1.09100i	−0.838111	−	0.545499i	$-0.816340\pi$
$887$		−	28821.0i		−	1.09100i	0.838111	−	0.545499i	$-0.183660\pi$
$888$	−31853.1			−1.20374
$889$	17909.2	−	13538.8i	0.675651	−	0.510772i
$890$	−738.457			−0.0278125
$891$			21786.2i			0.819154i
$892$		−	26558.8i		−	0.996921i
$893$		−	65225.8i		−	2.44423i
$894$	−8555.67			−0.320072
$895$	6519.66			0.243495
$896$	21495.8	−	16250.2i	0.801479	−	0.605894i
$897$	19023.7	−	512.104i	0.708119	−	0.0190620i
$898$	12977.6			0.482258
$899$			64655.5i			2.39864i
$900$	−3308.89			−0.122551
$901$			3721.22i			0.137594i
$902$	1841.18			0.0679653
$903$	−31884.1	+	24103.4i	−1.17501	+	0.888273i
$904$		−	30916.2i		−	1.13745i
$905$	23798.7			0.874138
$906$			1117.78i			0.0409889i
$907$			22509.0i			0.824033i	0.911176	+	0.412016i	$0.135175\pi$
$907$			22509.0i			0.824033i	−0.911176	+	0.412016i	$0.864825\pi$
$908$	9453.94			0.345529
$909$		−	8533.72i		−	0.311381i
$910$	2505.21	+	3313.90i	0.0912602	+	0.120719i
$911$			29325.6i			1.06652i	0.845951	+	0.533260i	$0.179033\pi$
$911$			29325.6i			1.06652i	−0.845951	+	0.533260i	$0.820967\pi$
$912$			34948.2i			1.26892i
$913$			20605.3i			0.746918i
$914$		−	4692.25i		−	0.169809i
$915$		−	18621.0i		−	0.672777i
$916$	6405.09			0.231037
$917$	−25796.8	−	34124.1i	−0.928991	−	1.22887i
$918$		−	884.090i		−	0.0317857i
$919$		−	14151.6i		−	0.507964i	−0.967209	−	0.253982i	$-0.918260\pi$
$919$		−	14151.6i		−	0.507964i	0.967209	−	0.253982i	$-0.0817404\pi$
$920$	−12538.7	+	337.532i	−0.449336	+	0.0120958i
$921$	7040.79			0.251902
$922$		−	14205.6i		−	0.507415i
$923$		−	18360.4i		−	0.654757i
$924$	15117.9	−	11428.7i	0.538249	−	0.406900i
$925$			24592.8i			0.874167i
$926$	2991.10			0.106148
$927$	−462.584			−0.0163897
$928$	−36793.1			−1.30150
$929$		−	8995.32i		−	0.317682i	−0.987304	−	0.158841i	$-0.949224\pi$
$929$		−	8995.32i		−	0.317682i	0.987304	−	0.158841i	$-0.0507758\pi$
$930$	−12506.4			−0.440968
$931$	−13672.4	+	48241.3i	−0.481305	+	1.69822i
$932$	14926.1			0.524593
$933$	26067.3			0.914689
$934$	−15997.6			−0.560448
$935$			1440.84i			0.0503963i
$936$			3106.78i			0.108492i
$937$	7536.52			0.262761			0.131381	−	0.991332i	$-0.458059\pi$
$937$	7536.52			0.262761			0.131381	+	0.991332i	$0.458059\pi$
$938$	−5349.59	−	7076.46i	−0.186216	−	0.246327i
$939$			10381.4i			0.360792i
$940$		−	23677.9i		−	0.821581i
$941$	−23466.9			−0.812965			−0.406483	−	0.913659i	$-0.633245\pi$
$941$	−23466.9			−0.812965			−0.406483	+	0.913659i	$0.633245\pi$
$942$			17887.8i			0.618701i
$943$	217.988	+	8097.84i	0.00752774	+	0.279641i
$944$		−	96.8448i		−	0.00333901i
$945$	−9873.97	−	13061.3i	−0.339894	−	0.449614i
$946$	9279.10			0.318911
$947$	24319.8			0.834516			0.417258	−	0.908788i	$-0.362991\pi$
$947$	24319.8			0.834516			0.417258	+	0.908788i	$0.362991\pi$
$948$	−52726.6			−1.80641
$949$	−3975.24			−0.135977
$950$	−9871.61			−0.337134
$951$			22.8890i			0.000780469i
$952$	−1680.00	+	1270.03i	−0.0571944	+	0.0432373i
$953$		−	6589.85i		−	0.223994i	−0.993709	−	0.111997i	$-0.964275\pi$
$953$		−	6589.85i		−	0.223994i	0.993709	−	0.111997i	$-0.0357247\pi$
$954$		−	3436.03i		−	0.116610i
$955$		−	15530.2i		−	0.526225i
$956$	−45555.5			−1.54118
$957$	−33407.3			−1.12843
$958$	−4369.81			−0.147372
$959$	−20130.4	−	26628.6i	−0.677836	−	0.896645i
$960$			7382.15i			0.248185i
$961$	−50253.3			−1.68686
$962$	10775.6			0.361143
$963$			8243.72i			0.275857i
$964$	−8595.86			−0.287193
$965$	−10327.6			−0.344516
$966$	−7436.44	−	9305.42i	−0.247685	−	0.309935i
$967$	20608.3			0.685335			0.342667	−	0.939457i	$-0.388670\pi$
$967$	20608.3			0.685335			0.342667	+	0.939457i	$0.388670\pi$
$968$	10537.1			0.349870
$969$		−	6462.02i		−	0.214231i
$970$	−10573.7			−0.350001
$971$	28456.8			0.940497			0.470248	−	0.882534i	$-0.344164\pi$
$971$	28456.8			0.940497			0.470248	+	0.882534i	$0.344164\pi$
$972$		−	13428.7i		−	0.443133i
$973$	14494.4	+	19173.3i	0.477564	+	0.631723i
$974$	−1421.59			−0.0467666
$975$	11650.6			0.382684
$976$	17271.1			0.566429
$977$			15554.4i			0.509344i	0.967028	+	0.254672i	$0.0819675\pi$
$977$			15554.4i			0.509344i	−0.967028	+	0.254672i	$0.918033\pi$
$978$			2728.89i			0.0892230i
$979$		−	2442.09i		−	0.0797236i
$980$	−4963.27	+	17512.2i	−0.161782	+	0.570824i
$981$		−	92.3828i		−	0.00300668i
$982$	398.567			0.0129519
$983$	−44671.9			−1.44945			−0.724726	−	0.689037i	$-0.758034\pi$
$983$	−44671.9			−1.44945			−0.724726	+	0.689037i	$0.758034\pi$
$984$	−6423.40			−0.208100
$985$	1229.84			0.0397828
$986$	1732.47			0.0559566
$987$	38436.9	−	29057.1i	1.23957	−	0.937080i
$988$		−	30277.6i		−	0.974957i
$989$	1098.60	+	40811.0i	0.0353221	+	1.31215i
$990$		−	1330.42i		−	0.0427105i
$991$	−59309.0			−1.90112			−0.950561	−	0.310537i	$-0.899491\pi$
$991$	−59309.0			−1.90112			−0.950561	+	0.310537i	$0.899491\pi$
$992$		−	45550.3i		−	1.45789i
$993$			22783.8i			0.728120i
$994$	−9167.54	+	6930.38i	−0.292532	+	0.221145i
$995$	24216.2			0.771562
$996$		−	33547.0i		−	1.06725i
$997$		−	23713.4i		−	0.753271i	−0.926362	−	0.376635i	$-0.877081\pi$
$997$		−	23713.4i		−	0.753271i	0.926362	−	0.376635i	$-0.122919\pi$
$998$	16817.0			0.533399
$999$	−42470.8			−1.34506

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.4.c.b.160.3	yes	8
7.6	odd	2	inner	161.4.c.b.160.6	yes	8
23.22	odd	2	inner	161.4.c.b.160.2	✓	8
161.160	even	2	inner	161.4.c.b.160.7	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.4.c.b.160.2	✓	8	23.22	odd	2	inner
161.4.c.b.160.3	yes	8	1.1	even	1	trivial
161.4.c.b.160.6	yes	8	7.6	odd	2	inner
161.4.c.b.160.7	yes	8	161.160	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	161.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -5.83095i q^{3} -7.00000 q^{4} +7.58101 q^{5} +5.83095i q^{6} +(14.7738 - 11.1685i) q^{7} +15.0000 q^{8} -7.00000 q^{9} -7.58101 q^{10} -25.0705i q^{11} +40.8167i q^{12} -29.5884i q^{13} +(-14.7738 + 11.1685i) q^{14} -44.2045i q^{15} +41.0000 q^{16} -7.58101 q^{17} +7.00000 q^{18} -146.185 q^{19} -53.0670 q^{20} +(-65.1231 - 86.1451i) q^{21} +25.0705i q^{22} +(-110.264 + 2.96823i) q^{23} -87.4643i q^{24} -67.5284 q^{25} +29.5884i q^{26} -116.619i q^{27} +(-103.416 + 78.1796i) q^{28} +228.528 q^{29} +44.2045i q^{30} +282.921i q^{31} -161.000 q^{32} -146.185 q^{33} +7.58101 q^{34} +(112.000 - 84.6686i) q^{35} +49.0000 q^{36} -364.184i q^{37} +146.185 q^{38} -172.528 q^{39} +113.715 q^{40} -73.4403i q^{41} +(65.1231 + 86.1451i) q^{42} -370.121i q^{43} +175.493i q^{44} -53.0670 q^{45} +(110.264 - 2.96823i) q^{46} +446.188i q^{47} -239.069i q^{48} +(93.5284 - 330.002i) q^{49} +67.5284 q^{50} +44.2045i q^{51} +207.119i q^{52} -490.861i q^{53} +116.619i q^{54} -190.059i q^{55} +(221.606 - 167.528i) q^{56} +852.396i q^{57} -228.528 q^{58} -2.36207i q^{59} +309.431i q^{60} +421.246 q^{61} -282.921i q^{62} +(-103.416 + 78.1796i) q^{63} -167.000 q^{64} -224.310i q^{65} +146.185 q^{66} +478.988i q^{67} +53.0670 q^{68} +(17.3076 + 642.945i) q^{69} +(-112.000 + 84.6686i) q^{70} +620.528 q^{71} -105.000 q^{72} -134.351i q^{73} +364.184i q^{74} +393.755i q^{75} +1023.29 q^{76} +(-280.000 - 370.385i) q^{77} +172.528 q^{78} +1291.79i q^{79} +310.821 q^{80} -869.000 q^{81} +73.4403i q^{82} -821.896 q^{83} +(455.862 + 603.016i) q^{84} -57.4716 q^{85} +370.121i q^{86} -1332.54i q^{87} -376.057i q^{88} +97.4088 q^{89} +53.0670 q^{90} +(-330.458 - 437.132i) q^{91} +(771.849 - 20.7776i) q^{92} +1649.70 q^{93} -446.188i q^{94} -1108.23 q^{95} +938.783i q^{96} +1394.76 q^{97} +(-93.5284 + 330.002i) q^{98} +175.493i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 56 q^{4} + 120 q^{8} - 56 q^{9} + 328 q^{16} + 56 q^{18} - 124 q^{23} + 976 q^{25} + 312 q^{29} - 1288 q^{32} + 896 q^{35} + 392 q^{36} + 136 q^{39} + 124 q^{46} - 768 q^{49} - 976 q^{50}+ \cdots + 768 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 - 56 * q^4 + 120 * q^8 - 56 * q^9 + 328 * q^16 + 56 * q^18 - 124 * q^23 + 976 * q^25 + 312 * q^29 - 1288 * q^32 + 896 * q^35 + 392 * q^36 + 136 * q^39 + 124 * q^46 - 768 * q^49 - 976 * q^50 - 312 * q^58 - 1336 * q^64 - 896 * q^70 + 3448 * q^71 - 840 * q^72 - 2240 * q^77 - 136 * q^78 - 6952 * q^81 - 1976 * q^85 + 868 * q^92 + 2584 * q^93 + 3264 * q^95 + 768 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more