LMFDB - Embedded newform 288.4.p.b.47.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [288,4,Mod(47,288)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("288.47"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(288, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 4, names="a")

Level:	$N$	$=$	$288 = 2^{5} \cdot 3^{2}$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	288.p (of order $6$ , degree $2$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [64] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$16.9925500817$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.7
Character	$\chi$	$=$	288.47
Dual form			288.4.p.b.239.7

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.10749 - 3.18254i) q^{3} +(-1.46312 - 2.53420i) q^{5} +(4.48829 + 2.59132i) q^{7} +(6.74292 + 26.1445i) q^{9} +(13.6440 + 7.87738i) q^{11} +(-37.3474 + 21.5625i) q^{13} +(-2.05543 + 15.0656i) q^{15} +3.31600i q^{17} +15.0818 q^{19} +(-10.1886 - 24.9279i) q^{21} +(61.7219 + 106.905i) q^{23} +(58.2185 - 100.837i) q^{25} +(55.5092 - 128.848i) q^{27} +(11.7175 - 20.2953i) q^{29} +(274.752 - 158.628i) q^{31} +(-30.9726 - 75.7788i) q^{33} -15.1657i q^{35} +286.660i q^{37} +(222.028 + 30.2916i) q^{39} +(284.954 - 164.518i) q^{41} +(175.008 - 303.123i) q^{43} +(56.3896 - 55.3405i) q^{45} +(-165.936 + 287.410i) q^{47} +(-158.070 - 273.786i) q^{49} +(10.5533 - 13.6204i) q^{51} +521.214 q^{53} -46.1023i q^{55} +(-61.9484 - 47.9984i) q^{57} +(130.749 - 75.4878i) q^{59} +(650.051 + 375.307i) q^{61} +(-37.4844 + 134.817i) q^{63} +(109.288 + 63.0972i) q^{65} +(-126.364 - 218.868i) q^{67} +(86.7085 - 635.545i) q^{69} -1083.28 q^{71} +678.405 q^{73} +(-560.051 + 228.906i) q^{75} +(40.8256 + 70.7119i) q^{77} +(-97.5980 - 56.3482i) q^{79} +(-638.066 + 352.580i) q^{81} +(857.418 + 495.030i) q^{83} +(8.40342 - 4.85171i) q^{85} +(-112.720 + 46.0714i) q^{87} +566.656i q^{89} -223.501 q^{91} +(-1633.38 - 222.845i) q^{93} +(-22.0666 - 38.2204i) q^{95} +(73.8806 - 127.965i) q^{97} +(-113.949 + 409.832i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$64 q - 6 q^{3} + 42 q^{9} - 48 q^{11} + 220 q^{19} - 902 q^{25} + 252 q^{27} - 660 q^{33} + 1620 q^{41} + 292 q^{43} + 1762 q^{49} + 1794 q^{51} - 294 q^{57} - 5592 q^{59} - 6 q^{65} - 68 q^{67} - 868 q^{73}+ \cdots + 2118 q^{99}+O(q^{100})$ 64 * q - 6 * q^3 + 42 * q^9 - 48 * q^11 + 220 * q^19 - 902 * q^25 + 252 * q^27 - 660 * q^33 + 1620 * q^41 + 292 * q^43 + 1762 * q^49 + 1794 * q^51 - 294 * q^57 - 5592 * q^59 - 6 * q^65 - 68 * q^67 - 868 * q^73 + 4254 * q^75 + 498 * q^81 - 3654 * q^83 + 1380 * q^91 - 1912 * q^97 + 2118 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$ .

$n$	$37$	$65$	$127$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

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			0
$2$		0			0
$3$	−4.10749	−	3.18254i	−0.790487	−	0.612479i
$3$	−4.10749	−	3.18254i	−0.790487	−	0.612479i
$4$		0			0
$5$	−1.46312	−	2.53420i	−0.130866	−	0.226666i	0.793145	−	0.609033i	$-0.208442\pi$
$5$	−1.46312	−	2.53420i	−0.130866	−	0.226666i	−0.924011	+	0.382367i	$0.875109\pi$
$6$		0			0
$7$	4.48829	+	2.59132i	0.242345	+	0.139918i	0.616254	−	0.787547i	$-0.288649\pi$
$7$	4.48829	+	2.59132i	0.242345	+	0.139918i	−0.373909	+	0.927465i	$0.621983\pi$
$8$		0			0
$9$	6.74292	+	26.1445i	0.249738	+	0.968313i
$10$		0			0
$11$	13.6440	+	7.87738i	0.373984	+	0.215920i	0.675198	−	0.737637i	$-0.264058\pi$
$11$	13.6440	+	7.87738i	0.373984	+	0.215920i	−0.301213	+	0.953557i	$0.597392\pi$
$12$		0			0
$13$	−37.3474	+	21.5625i	−0.796793	+	0.460028i	−0.842348	−	0.538933i	$-0.818827\pi$
$13$	−37.3474	+	21.5625i	−0.796793	+	0.460028i	0.0455558	+	0.998962i	$0.485494\pi$
$14$		0			0
$15$	−2.05543	+	15.0656i	−0.0353807	+	0.259329i
$16$		0			0
$17$			3.31600i			0.0473087i	0.999720	+	0.0236544i	$0.00753012\pi$
$17$			3.31600i			0.0473087i	−0.999720	+	0.0236544i	$0.992470\pi$
$18$		0			0
$19$	15.0818			0.182106			0.0910528	−	0.995846i	$-0.470977\pi$
$19$	15.0818			0.182106			0.0910528	+	0.995846i	$0.470977\pi$
$20$		0			0
$21$	−10.1886	−	24.9279i	−0.105874	−	0.259034i
$22$		0			0
$23$	61.7219	+	106.905i	0.559561	+	0.969188i	0.997533	+	0.0701991i	$0.0223635\pi$
$23$	61.7219	+	106.905i	0.559561	+	0.969188i	−0.437972	+	0.898988i	$0.644303\pi$
$24$		0			0
$25$	58.2185	−	100.837i	0.465748	−	0.806700i
$26$		0			0
$27$	55.5092	−	128.848i	0.395658	−	0.918398i
$28$		0			0
$29$	11.7175	−	20.2953i	0.0750306	−	0.129957i	−0.826069	−	0.563569i	$-0.809428\pi$
$29$	11.7175	−	20.2953i	0.0750306	−	0.129957i	0.901100	+	0.433612i	$0.142761\pi$
$30$		0			0
$31$	274.752	−	158.628i	1.59184	−	0.919048i	0.598846	−	0.800865i	$-0.295626\pi$
$31$	274.752	−	158.628i	1.59184	−	0.919048i	0.992992	−	0.118183i	$-0.0377070\pi$
$32$		0			0
$33$	−30.9726	−	75.7788i	−0.163383	−	0.399739i
$34$		0			0
$35$		−	15.1657i		−	0.0732418i
$36$		0			0
$37$			286.660i			1.27369i	0.770991	+	0.636846i	$0.219761\pi$
$37$			286.660i			1.27369i	−0.770991	+	0.636846i	$0.780239\pi$
$38$		0			0
$39$	222.028	+	30.2916i	0.911612	+	0.124373i
$40$		0			0
$41$	284.954	−	164.518i	1.08542	−	0.626669i	0.153068	−	0.988216i	$-0.451085\pi$
$41$	284.954	−	164.518i	1.08542	−	0.626669i	0.932354	+	0.361547i	$0.117751\pi$
$42$		0			0
$43$	175.008	−	303.123i	0.620663	−	1.07502i	−0.368700	−	0.929548i	$-0.620197\pi$
$43$	175.008	−	303.123i	0.620663	−	1.07502i	0.989363	−	0.145471i	$-0.0464697\pi$
$44$		0			0
$45$	56.3896	−	55.3405i	0.186802	−	0.183326i
$46$		0			0
$47$	−165.936	+	287.410i	−0.514984	+	0.891979i	0.484864	+	0.874589i	$0.338869\pi$
$47$	−165.936	+	287.410i	−0.514984	+	0.891979i	−0.999849	+	0.0173897i	$0.994464\pi$
$48$		0			0
$49$	−158.070	−	273.786i	−0.460846	−	0.798209i
$50$		0			0
$51$	10.5533	−	13.6204i	0.0289756	−	0.0373969i
$52$		0			0
$53$	521.214			1.35083			0.675417	−	0.737436i	$-0.263964\pi$
$53$	521.214			1.35083			0.675417	+	0.737436i	$0.263964\pi$
$54$		0			0
$55$		−	46.1023i		−	0.113026i
$56$		0			0
$57$	−61.9484	−	47.9984i	−0.143952	−	0.111536i
$58$		0			0
$59$	130.749	−	75.4878i	0.288509	−	0.166571i	−0.348760	−	0.937212i	$-0.613397\pi$
$59$	130.749	−	75.4878i	0.288509	−	0.166571i	0.637269	+	0.770641i	$0.280064\pi$
$60$		0			0
$61$	650.051	+	375.307i	1.36443	+	0.787756i	0.990210	−	0.139582i	$-0.0445760\pi$
$61$	650.051	+	375.307i	1.36443	+	0.787756i	0.374223	+	0.927339i	$0.377909\pi$
$62$		0			0
$63$	−37.4844	+	134.817i	−0.0749617	+	0.269609i
$64$		0			0
$65$	109.288	+	63.0972i	0.208546	+	0.120404i
$66$		0			0
$67$	−126.364	−	218.868i	−0.230415	−	0.399090i	0.727515	−	0.686091i	$-0.240675\pi$
$67$	−126.364	−	218.868i	−0.230415	−	0.399090i	−0.957930	+	0.287001i	$0.907342\pi$
$68$		0			0
$69$	86.7085	−	635.545i	0.151282	−	1.10885i
$70$		0			0
$71$	−1083.28			−1.81072			−0.905362	−	0.424640i	$-0.860401\pi$
$71$	−1083.28			−1.81072			−0.905362	+	0.424640i	$0.860401\pi$
$72$		0			0
$73$	678.405			1.08769			0.543845	−	0.839186i	$-0.316968\pi$
$73$	678.405			1.08769			0.543845	+	0.839186i	$0.316968\pi$
$74$		0			0
$75$	−560.051	+	228.906i	−0.862255	+	0.352424i
$76$		0			0
$77$	40.8256	+	70.7119i	0.0604221	+	0.104654i
$78$		0			0
$79$	−97.5980	−	56.3482i	−0.138995	−	0.0802490i	0.428890	−	0.903357i	$-0.358905\pi$
$79$	−97.5980	−	56.3482i	−0.138995	−	0.0802490i	−0.567885	+	0.823108i	$0.692238\pi$
$80$		0			0
$81$	−638.066	+	352.580i	−0.875262	+	0.483649i
$82$		0			0
$83$	857.418	+	495.030i	1.13390	+	0.654658i	0.944913	−	0.327321i	$-0.106146\pi$
$83$	857.418	+	495.030i	1.13390	+	0.654658i	0.188988	+	0.981979i	$0.439479\pi$
$84$		0			0
$85$	8.40342	−	4.85171i	0.0107233	−	0.00619109i
$86$		0			0
$87$	−112.720	+	46.0714i	−0.138907	+	0.0567744i
$88$		0			0
$89$			566.656i			0.674893i	0.941345	+	0.337446i	$0.109563\pi$
$89$			566.656i			0.674893i	−0.941345	+	0.337446i	$0.890437\pi$
$90$		0			0
$91$	−223.501			−0.257465
$92$		0			0
$93$	−1633.38	−	222.845i	−1.82122	−	0.248473i
$94$		0			0
$95$	−22.0666	−	38.2204i	−0.0238314	−	0.0412771i
$96$		0			0
$97$	73.8806	−	127.965i	0.0773344	−	0.133947i	−0.824765	−	0.565476i	$-0.808692\pi$
$97$	73.8806	−	127.965i	0.0773344	−	0.133947i	0.902099	+	0.431529i	$0.142026\pi$
$98$		0			0
$99$	−113.949	+	409.832i	−0.115680	+	0.416057i
$100$		0			0
$101$	−733.536	+	1270.52i	−0.722669	+	1.25170i	0.237258	+	0.971447i	$0.423751\pi$
$101$	−733.536	+	1270.52i	−0.722669	+	1.25170i	−0.959926	+	0.280252i	$0.909582\pi$
$102$		0			0
$103$	1005.07	−	580.278i	0.961482	−	0.555112i	0.0648531	−	0.997895i	$-0.479342\pi$
$103$	1005.07	−	580.278i	0.961482	−	0.555112i	0.896629	+	0.442783i	$0.146009\pi$
$104$		0			0
$105$	−48.2652	+	62.2927i	−0.0448591	+	0.0578967i
$106$		0			0
$107$			1244.09i			1.12402i	0.827130	+	0.562011i	$0.189972\pi$
$107$			1244.09i			1.12402i	−0.827130	+	0.562011i	$0.810028\pi$
$108$		0			0
$109$		−	569.937i		−	0.500826i	−0.968139	−	0.250413i	$-0.919434\pi$
$109$		−	569.937i		−	0.500826i	0.968139	−	0.250413i	$-0.0805664\pi$
$110$		0			0
$111$	912.306	−	1177.45i	0.780110	−	1.00684i
$112$		0			0
$113$	−824.716	+	476.150i	−0.686573	+	0.396393i	−0.802327	−	0.596885i	$-0.796405\pi$
$113$	−824.716	+	476.150i	−0.686573	+	0.396393i	0.115754	+	0.993278i	$0.463072\pi$
$114$		0			0
$115$	180.613	−	312.831i	0.146455	−	0.253667i
$116$		0			0
$117$	−815.571	−	831.033i	−0.644441	−	0.656658i
$118$		0			0
$119$	−8.59280	+	14.8832i	−0.00661934	+	0.0114650i
$120$		0			0
$121$	−541.394	−	937.722i	−0.406757	−	0.704524i
$122$		0			0
$123$	−1694.03	−	231.119i	−1.24183	−	0.169426i
$124$		0			0
$125$	−706.504			−0.505533
$126$		0			0
$127$			1274.79i			0.890701i	0.895356	+	0.445350i	$0.146921\pi$
$127$			1274.79i			0.890701i	−0.895356	+	0.445350i	$0.853079\pi$
$128$		0			0
$129$	−1683.54	+	688.104i	−1.14905	+	0.469645i
$130$		0			0
$131$	470.494	−	271.640i	0.313796	−	0.181170i	−0.334828	−	0.942279i	$-0.608678\pi$
$131$	470.494	−	271.640i	0.313796	−	0.181170i	0.648624	+	0.761109i	$0.275345\pi$
$132$		0			0
$133$	67.6916	+	39.0818i	0.0441324	+	0.0254798i
$134$		0			0
$135$	−407.743	+	47.8483i	−0.259948	+	0.0305047i
$136$		0			0
$137$	2185.39	+	1261.73i	1.36285	+	0.786840i	0.990002	−	0.141053i	$-0.0450488\pi$
$137$	2185.39	+	1261.73i	1.36285	+	0.786840i	0.372846	+	0.927893i	$0.378382\pi$
$138$		0			0
$139$	−937.946	−	1624.57i	−0.572342	−	0.991326i	−0.996325	−	0.0856555i	$-0.972702\pi$
$139$	−937.946	−	1624.57i	−0.572342	−	0.991326i	0.423983	−	0.905670i	$-0.360632\pi$
$140$		0			0
$141$	1596.27	−	652.434i	0.953407	−	0.389680i
$142$		0			0
$143$	−679.425			−0.397317
$144$		0			0
$145$	−68.5766			−0.0392757
$146$		0			0
$147$	−222.061	+	1627.64i	−0.124594	+	0.913232i
$148$		0			0
$149$	−998.646	−	1729.71i	−0.549076	−	0.951027i	−0.998338	−	0.0576270i	$-0.981647\pi$
$149$	−998.646	−	1729.71i	−0.549076	−	0.951027i	0.449263	−	0.893400i	$-0.351687\pi$
$150$		0			0
$151$	35.3646	+	20.4177i	0.0190591	+	0.0110038i	0.509499	−	0.860471i	$-0.329831\pi$
$151$	35.3646	+	20.4177i	0.0190591	+	0.0110038i	−0.490440	+	0.871475i	$0.663164\pi$
$152$		0			0
$153$	−86.6950	+	22.3595i	−0.0458097	+	0.0118148i
$154$		0			0
$155$	−803.992	−	464.185i	−0.416634	−	0.240544i
$156$		0			0
$157$	1170.05	−	675.530i	0.594779	−	0.343396i	−0.172206	−	0.985061i	$-0.555089\pi$
$157$	1170.05	−	675.530i	0.594779	−	0.343396i	0.766985	+	0.641665i	$0.221756\pi$
$158$		0			0
$159$	−2140.88	−	1658.78i	−1.06782	−	0.827358i
$160$		0			0
$161$			639.763i			0.313170i
$162$		0			0
$163$	1922.43			0.923779			0.461890	−	0.886937i	$-0.347172\pi$
$163$	1922.43			0.923779			0.461890	+	0.886937i	$0.347172\pi$
$164$		0			0
$165$	−146.722	+	189.365i	−0.0692261	+	0.0893455i
$166$		0			0
$167$	1311.20	+	2271.06i	0.607566	+	1.05234i	0.991640	+	0.129033i	$0.0411873\pi$
$167$	1311.20	+	2271.06i	0.607566	+	1.05234i	−0.384074	+	0.923302i	$0.625479\pi$
$168$		0			0
$169$	−168.615	+	292.049i	−0.0767477	+	0.132931i
$170$		0			0
$171$	101.696	+	394.306i	0.0454787	+	0.176335i
$172$		0			0
$173$	−1385.77	+	2400.23i	−0.609008	+	1.05483i	0.382396	+	0.923998i	$0.375099\pi$
$173$	−1385.77	+	2400.23i	−0.609008	+	1.05483i	−0.991404	+	0.130834i	$0.958234\pi$
$174$		0			0
$175$	522.603	−	301.725i	0.225743	−	0.130333i
$176$		0			0
$177$	−777.291	−	106.047i	−0.330084	−	0.0450339i
$178$		0			0
$179$			2108.40i			0.880389i	0.897903	+	0.440194i	$0.145090\pi$
$179$			2108.40i			0.880389i	−0.897903	+	0.440194i	$0.854910\pi$
$180$		0			0
$181$			583.190i			0.239493i	0.992805	+	0.119746i	$0.0382081\pi$
$181$			583.190i			0.239493i	−0.992805	+	0.119746i	$0.961792\pi$
$182$		0			0
$183$	−1475.65	−	3610.38i	−0.596082	−	1.45840i
$184$		0			0
$185$	726.455	−	419.419i	0.288703	−	0.166683i
$186$		0			0
$187$	−26.1214	+	45.2436i	−0.0102149	+	0.0176927i
$188$		0			0
$189$	583.027	−	434.464i	0.224386	−	0.167210i
$190$		0			0
$191$	622.663	−	1078.48i	0.235886	−	0.408567i	−0.723644	−	0.690174i	$-0.757534\pi$
$191$	622.663	−	1078.48i	0.235886	−	0.408567i	0.959530	+	0.281607i	$0.0908674\pi$
$192$		0			0
$193$	−1316.15	−	2279.63i	−0.490872	−	0.850215i	0.509073	−	0.860723i	$-0.329988\pi$
$193$	−1316.15	−	2279.63i	−0.490872	−	0.850215i	−0.999945	+	0.0105083i	$0.996655\pi$
$194$		0			0
$195$	−248.088	−	606.983i	−0.0911076	−	0.222907i
$196$		0			0
$197$	−1210.94			−0.437948			−0.218974	−	0.975731i	$-0.570271\pi$
$197$	−1210.94			−0.437948			−0.218974	+	0.975731i	$0.570271\pi$
$198$		0			0
$199$			2015.72i			0.718043i	0.933329	+	0.359021i	$0.116890\pi$
$199$			2015.72i			0.718043i	−0.933329	+	0.359021i	$0.883110\pi$
$200$		0			0
$201$	−177.519	+	1301.16i	−0.0622947	+	0.456600i
$202$		0			0
$203$	105.183	−	60.7275i	0.0363666	−	0.0209962i
$204$		0			0
$205$	−833.845	−	481.421i	−0.284089	−	0.164019i
$206$		0			0
$207$	−2378.80	+	2334.54i	−0.798734	+	0.783873i
$208$		0			0
$209$	205.777	+	118.805i	0.0681046	+	0.0393202i
$210$		0			0
$211$	601.260	+	1041.41i	0.196173	+	0.339781i	0.947284	−	0.320394i	$-0.103815\pi$
$211$	601.260	+	1041.41i	0.196173	+	0.339781i	−0.751112	+	0.660175i	$0.770482\pi$
$212$		0			0
$213$	4449.55	+	3447.57i	1.43135	+	1.10903i
$214$		0			0
$215$	−1024.23			−0.324894
$216$		0			0
$217$	1644.22			0.514365
$218$		0			0
$219$	−2786.54	−	2159.05i	−0.859804	−	0.666188i
$220$		0			0
$221$	−71.5013	−	123.844i	−0.0217634	−	0.0376952i
$222$		0			0
$223$	1135.80	+	655.752i	0.341070	+	0.196917i	0.660745	−	0.750611i	$-0.270241\pi$
$223$	1135.80	+	655.752i	0.341070	+	0.196917i	−0.319675	+	0.947527i	$0.603574\pi$
$224$		0			0
$225$	3028.90	+	842.153i	0.897453	+	0.249527i
$226$		0			0
$227$	2494.70	+	1440.32i	0.729423	+	0.421133i	0.818211	−	0.574918i	$-0.194966\pi$
$227$	2494.70	+	1440.32i	0.729423	+	0.421133i	−0.0887881	+	0.996051i	$0.528299\pi$
$228$		0			0
$229$	3858.07	−	2227.46i	1.11331	−	0.642771i	0.173627	−	0.984812i	$-0.444451\pi$
$229$	3858.07	−	2227.46i	1.11331	−	0.642771i	0.939685	+	0.342040i	$0.111118\pi$
$230$		0			0
$231$	57.3528	−	420.377i	0.0163357	−	0.119735i
$232$		0			0
$233$		−	1085.86i		−	0.305309i	−0.988280	−	0.152654i	$-0.951218\pi$
$233$		−	1085.86i		−	0.305309i	0.988280	−	0.152654i	$-0.0487821\pi$
$234$		0			0
$235$	971.139			0.269575
$236$		0			0
$237$	221.552	+	542.059i	0.0607231	+	0.148568i
$238$		0			0
$239$	1617.59	+	2801.74i	0.437795	+	0.758283i	0.997519	−	0.0703960i	$-0.0224263\pi$
$239$	1617.59	+	2801.74i	0.437795	+	0.758283i	−0.559724	+	0.828679i	$0.689093\pi$
$240$		0			0
$241$	715.242	−	1238.84i	0.191173	−	0.331122i	−0.754466	−	0.656339i	$-0.772104\pi$
$241$	715.242	−	1238.84i	0.191173	−	0.331122i	0.945639	+	0.325217i	$0.105437\pi$
$242$		0			0
$243$	3742.95	+	582.449i	0.988108	+	0.153762i
$244$		0			0
$245$	−462.552	+	801.164i	−0.120618	+	0.208916i
$246$		0			0
$247$	−563.267	+	325.202i	−0.145100	+	0.0837738i
$248$		0			0
$249$	−1946.38	−	4762.09i	−0.495369	−	1.21199i
$250$		0			0
$251$		−	5903.80i		−	1.48464i	−0.670046	−	0.742320i	$-0.733725\pi$
$251$		−	5903.80i		−	1.48464i	0.670046	−	0.742320i	$-0.266275\pi$
$252$		0			0
$253$			1944.83i			0.483281i
$254$		0			0
$255$	−49.9577	−	6.81582i	−0.0122685	−	0.00167382i
$256$		0			0
$257$	1225.66	−	707.636i	0.297489	−	0.171755i	−0.343825	−	0.939034i	$-0.611723\pi$
$257$	1225.66	−	707.636i	0.297489	−	0.171755i	0.641314	+	0.767278i	$0.278389\pi$
$258$		0			0
$259$	−742.827	+	1286.61i	−0.178212	+	0.308673i
$260$		0			0
$261$	609.621	+	169.498i	0.144577	+	0.0401980i
$262$		0			0
$263$	2793.50	−	4838.48i	0.654959	−	1.13442i	−0.326945	−	0.945043i	$-0.606019\pi$
$263$	2793.50	−	4838.48i	0.654959	−	1.13442i	0.981904	−	0.189379i	$-0.0606476\pi$
$264$		0			0
$265$	−762.599	−	1320.86i	−0.176778	−	0.306188i
$266$		0			0
$267$	1803.40	−	2327.53i	0.413358	−	0.533494i
$268$		0			0
$269$	5030.52			1.14021			0.570105	−	0.821572i	$-0.306903\pi$
$269$	5030.52			1.14021			0.570105	+	0.821572i	$0.306903\pi$
$270$		0			0
$271$			1317.52i			0.295328i	0.989038	+	0.147664i	$0.0471754\pi$
$271$			1317.52i			0.295328i	−0.989038	+	0.147664i	$0.952825\pi$
$272$		0			0
$273$	918.029	+	711.301i	0.203522	+	0.157692i
$274$		0			0
$275$	1588.67	−	917.219i	0.348365	−	0.201129i
$276$		0			0
$277$	−2626.49	−	1516.41i	−0.569714	−	0.328924i	0.187321	−	0.982299i	$-0.440019\pi$
$277$	−2626.49	−	1516.41i	−0.569714	−	0.328924i	−0.757035	+	0.653374i	$0.773353\pi$
$278$		0			0
$279$	5999.88	+	6113.63i	1.28747	+	1.31188i
$280$		0			0
$281$	−2118.05	−	1222.86i	−0.449653	−	0.259607i	0.258031	−	0.966137i	$-0.416926\pi$
$281$	−2118.05	−	1222.86i	−0.449653	−	0.259607i	−0.707683	+	0.706530i	$0.750260\pi$
$282$		0			0
$283$	−4229.51	−	7325.72i	−0.888403	−	1.53876i	−0.841763	−	0.539847i	$-0.818482\pi$
$283$	−4229.51	−	7325.72i	−0.888403	−	1.53876i	−0.0466401	−	0.998912i	$-0.514851\pi$
$284$		0			0
$285$	−30.9997	+	227.217i	−0.00644302	+	0.0472253i
$286$		0			0
$287$	1705.27			0.350729
$288$		0			0
$289$	4902.00			0.997762
$290$		0			0
$291$	−710.717	+	290.487i	−0.143172	+	0.0585177i
$292$		0			0
$293$	−219.370	−	379.960i	−0.0437397	−	0.0757593i	0.843327	−	0.537401i	$-0.180594\pi$
$293$	−219.370	−	379.960i	−0.0437397	−	0.0757593i	−0.887066	+	0.461642i	$0.847261\pi$
$294$		0			0
$295$	−382.603	−	220.896i	−0.0755118	−	0.0435968i
$296$		0			0
$297$	1772.35	−	1320.73i	0.346270	−	0.258036i
$298$		0			0
$299$	−4610.30	−	2661.76i	−0.891708	−	0.514828i
$300$		0			0
$301$	1570.97	−	907.003i	0.300829	−	0.173684i
$302$		0			0
$303$	7056.47	−	2884.15i	1.33790	−	0.546832i
$304$		0			0
$305$		−	2196.48i		−	0.412361i
$306$		0			0
$307$	7875.21			1.46405			0.732023	−	0.681280i	$-0.238577\pi$
$307$	7875.21			1.46405			0.732023	+	0.681280i	$0.238577\pi$
$308$		0			0
$309$	−5975.08	−	815.190i	−1.10003	−	0.150079i
$310$		0			0
$311$	−532.946	−	923.090i	−0.0971724	−	0.168308i	0.813341	−	0.581788i	$-0.197646\pi$
$311$	−532.946	−	923.090i	−0.0971724	−	0.168308i	−0.910513	+	0.413480i	$0.864313\pi$
$312$		0			0
$313$	−4954.30	+	8581.10i	−0.894676	+	1.54962i	−0.0604700	+	0.998170i	$0.519260\pi$
$313$	−4954.30	+	8581.10i	−0.894676	+	1.54962i	−0.834206	+	0.551454i	$0.814073\pi$
$314$		0			0
$315$	396.498	−	102.261i	0.0709210	−	0.0182913i
$316$		0			0
$317$	35.1444	−	60.8718i	0.00622683	−	0.0107852i	−0.862895	−	0.505383i	$-0.831351\pi$
$317$	35.1444	−	60.8718i	0.00622683	−	0.0107852i	0.869122	+	0.494598i	$0.164685\pi$
$318$		0			0
$319$	319.748	−	184.607i	0.0561205	−	0.0324012i
$320$		0			0
$321$	3959.35	−	5110.07i	0.688440	−	0.888524i
$322$		0			0
$323$			50.0113i			0.00861518i
$324$		0			0
$325$			5021.36i			0.857030i
$326$		0			0
$327$	−1813.84	+	2341.01i	−0.306746	+	0.395896i
$328$		0			0
$329$	−1489.54	+	859.986i	−0.249608	+	0.144111i
$330$		0			0
$331$	−4684.34	+	8113.51i	−0.777868	+	1.34731i	0.155300	+	0.987867i	$0.450366\pi$
$331$	−4684.34	+	8113.51i	−0.777868	+	1.34731i	−0.933168	+	0.359440i	$0.882968\pi$
$332$		0			0
$333$	−7494.57	+	1932.93i	−1.23333	+	0.318089i
$334$		0			0
$335$	−369.771	+	640.463i	−0.0603067	+	0.104454i
$336$		0			0
$337$	3086.72	+	5346.35i	0.498944	+	0.864197i	0.999999	−	0.00121842i	$-0.000387836\pi$
$337$	3086.72	+	5346.35i	0.498944	+	0.864197i	−0.501055	+	0.865416i	$0.667055\pi$
$338$		0			0
$339$	4902.87	+	668.908i	0.785509	+	0.107168i
$340$		0			0
$341$	4998.30			0.793763
$342$		0			0
$343$		−	3416.08i		−	0.537758i
$344$		0			0
$345$	−1737.46	+	710.143i	−0.271136	+	0.110820i
$346$		0			0
$347$	−5102.09	+	2945.69i	−0.789321	+	0.455715i	−0.839724	−	0.543014i	$-0.817283\pi$
$347$	−5102.09	+	2945.69i	−0.789321	+	0.455715i	0.0504023	+	0.998729i	$0.483950\pi$
$348$		0			0
$349$	−8150.29	−	4705.57i	−1.25007	−	0.721729i	−0.278948	−	0.960306i	$-0.589986\pi$
$349$	−8150.29	−	4705.57i	−1.25007	−	0.721729i	−0.971123	+	0.238577i	$0.923319\pi$
$350$		0			0
$351$	705.157	+	6009.04i	0.107232	+	0.913787i
$352$		0			0
$353$	−6050.47	−	3493.24i	−0.912278	−	0.526704i	−0.0311148	−	0.999516i	$-0.509906\pi$
$353$	−6050.47	−	3493.24i	−0.912278	−	0.526704i	−0.881163	+	0.472812i	$0.843239\pi$
$354$		0			0
$355$	1584.97	+	2745.25i	0.236962	+	0.410430i
$356$		0			0
$357$	82.6611	−	33.7855i	0.0122546	−	0.00500874i
$358$		0			0
$359$	−3844.64			−0.565215			−0.282607	−	0.959236i	$-0.591199\pi$
$359$	−3844.64			−0.565215			−0.282607	+	0.959236i	$0.591199\pi$
$360$		0			0
$361$	−6631.54			−0.966838
$362$		0			0
$363$	−760.564	+	5574.69i	−0.109970	+	0.806047i
$364$		0			0
$365$	−992.590	−	1719.22i	−0.142341	−	0.246542i
$366$		0			0
$367$	−11663.0	−	6733.63i	−1.65886	−	0.957746i	−0.973240	−	0.229789i	$-0.926196\pi$
$367$	−11663.0	−	6733.63i	−1.65886	−	0.957746i	−0.685624	−	0.727956i	$-0.740470\pi$
$368$		0			0
$369$	6222.66	+	6340.63i	0.877883	+	0.894526i
$370$		0			0
$371$	2339.36	+	1350.63i	0.327368	+	0.189006i
$372$		0			0
$373$	−5361.43	+	3095.42i	−0.744248	+	0.429692i	−0.823612	−	0.567154i	$-0.808044\pi$
$373$	−5361.43	+	3095.42i	−0.744248	+	0.429692i	0.0793639	+	0.996846i	$0.474711\pi$
$374$		0			0
$375$	2901.96	+	2248.47i	0.399617	+	0.309629i
$376$		0			0
$377$			1010.64i			0.138065i
$378$		0			0
$379$	−7854.31			−1.06451			−0.532255	−	0.846584i	$-0.678655\pi$
$379$	−7854.31			−1.06451			−0.532255	+	0.846584i	$0.678655\pi$
$380$		0			0
$381$	4057.05	−	5236.17i	0.545536	−	0.704087i
$382$		0			0
$383$	−5216.45	−	9035.15i	−0.695948	−	1.20542i	−0.969860	−	0.243662i	$-0.921651\pi$
$383$	−5216.45	−	9035.15i	−0.695948	−	1.20542i	0.273912	−	0.961755i	$-0.411682\pi$
$384$		0			0
$385$	119.466	−	206.920i	0.0158144	−	0.0273913i
$386$		0			0
$387$	9105.06	+	2531.56i	1.19596	+	0.332523i
$388$		0			0
$389$	5731.82	−	9927.81i	0.747082	−	1.29398i	−0.202133	−	0.979358i	$-0.564787\pi$
$389$	5731.82	−	9927.81i	0.747082	−	1.29398i	0.949216	−	0.314626i	$-0.101879\pi$
$390$		0			0
$391$	−354.498	+	204.670i	−0.0458510	+	0.0264721i
$392$		0			0
$393$	−2797.05	−	381.606i	−0.359014	−	0.0489809i
$394$		0			0
$395$			329.777i			0.0420074i
$396$		0			0
$397$			8809.54i			1.11370i	0.830614	+	0.556849i	$0.187990\pi$
$397$			8809.54i			1.11370i	−0.830614	+	0.556849i	$0.812010\pi$
$398$		0			0
$399$	−153.663	−	375.959i	−0.0192802	−	0.0471716i
$400$		0			0
$401$	−6817.45	+	3936.06i	−0.848996	+	0.490168i	−0.860312	−	0.509768i	$-0.829731\pi$
$401$	−6817.45	+	3936.06i	−0.848996	+	0.490168i	0.0113159	+	0.999936i	$0.496398\pi$
$402$		0			0
$403$	−6840.85	+	11848.7i	−0.845576	+	1.46458i
$404$		0			0
$405$	1827.08	+	1101.12i	0.224169	+	0.135099i
$406$		0			0
$407$	−2258.13	+	3911.20i	−0.275016	+	0.476341i
$408$		0			0
$409$	170.965	+	296.120i	0.0206691	+	0.0358000i	0.876175	−	0.481993i	$-0.160087\pi$
$409$	170.965	+	296.120i	0.0206691	+	0.0358000i	−0.855506	+	0.517793i	$0.826754\pi$
$410$		0			0
$411$	−4960.94	−	12137.6i	−0.595389	−	1.45670i
$412$		0			0
$413$	782.451			0.0932249
$414$		0			0
$415$		−	2897.16i		−	0.342689i
$416$		0			0
$417$	−1317.65	+	9657.95i	−0.154738	+	1.13418i
$418$		0			0
$419$	−1154.35	+	666.463i	−0.134591	+	0.0777060i	−0.565784	−	0.824554i	$-0.691426\pi$
$419$	−1154.35	+	666.463i	−0.134591	+	0.0777060i	0.431193	+	0.902260i	$0.358093\pi$
$420$		0			0
$421$	−5457.42	−	3150.84i	−0.631777	−	0.364757i	0.149663	−	0.988737i	$-0.452181\pi$
$421$	−5457.42	−	3150.84i	−0.631777	−	0.364757i	−0.781440	+	0.623980i	$0.785515\pi$
$422$		0			0
$423$	−8633.07	−	2400.33i	−0.992326	−	0.275905i
$424$		0			0
$425$	334.377	+	193.053i	0.0381639	+	0.0220340i
$426$		0			0
$427$	1945.08	+	3368.97i	0.220442	+	0.381817i
$428$		0			0
$429$	2790.73	+	2162.29i	0.314074	+	0.243349i
$430$		0			0
$431$	−1791.33			−0.200198			−0.100099	−	0.994977i	$-0.531916\pi$
$431$	−1791.33			−0.200198			−0.100099	+	0.994977i	$0.531916\pi$
$432$		0			0
$433$	7947.77			0.882092			0.441046	−	0.897485i	$-0.354608\pi$
$433$	7947.77			0.882092			0.441046	+	0.897485i	$0.354608\pi$
$434$		0			0
$435$	281.678	+	218.248i	0.0310469	+	0.0240556i
$436$		0			0
$437$	930.878	+	1612.33i	0.101899	+	0.176495i
$438$		0			0
$439$	−10066.8	−	5812.07i	−1.09445	−	0.631879i	−0.159690	−	0.987167i	$-0.551049\pi$
$439$	−10066.8	−	5812.07i	−1.09445	−	0.631879i	−0.934757	+	0.355288i	$0.884383\pi$
$440$		0			0
$441$	6092.12	−	5978.77i	0.657825	−	0.645586i
$442$		0			0
$443$	−12771.4	−	7373.55i	−1.36972	−	0.790808i	−0.378827	−	0.925467i	$-0.623672\pi$
$443$	−12771.4	−	7373.55i	−1.36972	−	0.790808i	−0.990892	+	0.134660i	$0.957006\pi$
$444$		0			0
$445$	1436.02	−	829.088i	0.152975	−	0.0883203i
$446$		0			0
$447$	−1402.92	+	10283.0i	−0.148447	+	1.08807i
$448$		0			0
$449$		−	8413.52i		−	0.884317i	−0.896937	−	0.442159i	$-0.854213\pi$
$449$		−	8413.52i		−	0.884317i	0.896937	−	0.442159i	$-0.145787\pi$
$450$		0			0
$451$	5183.89			0.541241
$452$		0			0
$453$	−80.2794	−	196.415i	−0.00832639	−	0.0203717i
$454$		0			0
$455$	327.010	+	566.398i	0.0336933	+	0.0583585i
$456$		0			0
$457$	−9060.70	+	15693.6i	−0.927443	+	1.60638i	−0.139860	+	0.990171i	$0.544665\pi$
$457$	−9060.70	+	15693.6i	−0.927443	+	1.60638i	−0.787584	+	0.616208i	$0.788668\pi$
$458$		0			0
$459$	427.259	+	184.069i	0.0434482	+	0.0187181i
$460$		0			0
$461$	8300.14	−	14376.3i	0.838560	−	1.45243i	−0.0525393	−	0.998619i	$-0.516731\pi$
$461$	8300.14	−	14376.3i	0.838560	−	1.45243i	0.891099	−	0.453809i	$-0.149935\pi$
$462$		0			0
$463$	9006.61	−	5199.97i	0.904045	−	0.521950i	0.0255344	−	0.999674i	$-0.491871\pi$
$463$	9006.61	−	5199.97i	0.904045	−	0.521950i	0.878510	+	0.477724i	$0.158538\pi$
$464$		0			0
$465$	1825.10	+	4465.37i	0.182015	+	0.445326i
$466$		0			0
$467$			4926.33i			0.488144i	0.969757	+	0.244072i	$0.0784833\pi$
$467$			4926.33i			0.488144i	−0.969757	+	0.244072i	$0.921517\pi$
$468$		0			0
$469$		−	1309.79i		−	0.128957i
$470$		0			0
$471$	−6955.87	−	949.002i	−0.680488	−	0.0928401i
$472$		0			0
$473$	4775.63	−	2757.21i	0.464236	−	0.268027i
$474$		0			0
$475$	878.042	−	1520.81i	0.0848154	−	0.146905i
$476$		0			0
$477$	3514.50	+	13626.9i	0.337354	+	1.30803i
$478$		0			0
$479$	−934.274	+	1618.21i	−0.0891191	+	0.154359i	−0.907139	−	0.420831i	$-0.861739\pi$
$479$	−934.274	+	1618.21i	−0.0891191	+	0.154359i	0.818020	+	0.575190i	$0.195072\pi$
$480$		0			0
$481$	−6181.12	−	10706.0i	−0.585935	−	1.01487i
$482$		0			0
$483$	2036.07	−	2627.82i	0.191810	−	0.247557i
$484$		0			0
$485$	−432.385			−0.0404817
$486$		0			0
$487$			3289.20i			0.306053i	0.988222	+	0.153026i	$0.0489020\pi$
$487$			3289.20i			0.306053i	−0.988222	+	0.153026i	$0.951098\pi$
$488$		0			0
$489$	−7896.34	−	6118.19i	−0.730235	−	0.565796i
$490$		0			0
$491$	1189.49	−	686.750i	0.109329	−	0.0631214i	−0.444338	−	0.895859i	$-0.646561\pi$
$491$	1189.49	−	686.750i	0.109329	−	0.0631214i	0.553668	+	0.832738i	$0.313228\pi$
$492$		0			0
$493$	67.2993	+	38.8553i	0.00614809	+	0.00354960i
$494$		0			0
$495$	1205.32	−	310.864i	0.109445	−	0.0282269i
$496$		0			0
$497$	−4862.07	−	2807.11i	−0.438820	−	0.253353i
$498$		0			0
$499$	925.039	+	1602.21i	0.0829868	+	0.143737i	0.904532	−	0.426407i	$-0.140221\pi$
$499$	925.039	+	1602.21i	0.0829868	+	0.143737i	−0.821545	+	0.570144i	$0.806887\pi$
$500$		0			0
$501$	1842.00	−	13501.3i	0.164261	−	1.20398i
$502$		0			0
$503$	17948.3			1.59100			0.795502	−	0.605951i	$-0.207207\pi$
$503$	17948.3			1.59100			0.795502	+	0.605951i	$0.207207\pi$
$504$		0			0
$505$	4293.01			0.378290
$506$		0			0
$507$	1622.04	−	662.966i	0.142085	−	0.0580737i
$508$		0			0
$509$	131.163	+	227.180i	0.0114218	+	0.0197831i	0.871680	−	0.490076i	$-0.163031\pi$
$509$	131.163	+	227.180i	0.0114218	+	0.0197831i	−0.860258	+	0.509859i	$0.829698\pi$
$510$		0			0
$511$	3044.88	+	1757.96i	0.263596	+	0.152187i
$512$		0			0
$513$	837.180	−	1943.26i	0.0720515	−	0.167245i
$514$		0			0
$515$	−2941.09	−	1698.04i	−0.251650	−	0.145290i
$516$		0			0
$517$	−4528.07	+	2614.28i	−0.385192	+	0.222391i
$518$		0			0
$519$	13330.9	−	5448.64i	1.12748	−	0.460826i
$520$		0			0
$521$			938.595i			0.0789263i	0.999221	+	0.0394631i	$0.0125648\pi$
$521$			938.595i			0.0789263i	−0.999221	+	0.0394631i	$0.987435\pi$
$522$		0			0
$523$	7118.07			0.595127			0.297563	−	0.954702i	$-0.403826\pi$
$523$	7118.07			0.595127			0.297563	+	0.954702i	$0.403826\pi$
$524$		0			0
$525$	−3106.84	−	423.872i	−0.258274	−	0.0352367i
$526$		0			0
$527$	526.011	+	911.078i	0.0434790	+	0.0753078i
$528$		0			0
$529$	−1535.67	+	2659.87i	−0.126216	+	0.218613i
$530$		0			0
$531$	2855.22	+	2909.35i	0.233344	+	0.237768i
$532$		0			0
$533$	−7094.86	+	12288.7i	−0.576571	+	0.998650i
$534$		0			0
$535$	3152.77	−	1820.25i	0.254777	−	0.147096i
$536$		0			0
$537$	6710.07	−	8660.25i	0.539220	−	0.695935i
$538$		0			0
$539$		−	4980.71i		−	0.398023i
$540$		0			0
$541$		−	6529.45i		−	0.518896i	−0.965757	−	0.259448i	$-0.916459\pi$
$541$		−	6529.45i		−	0.518896i	0.965757	−	0.259448i	$-0.0835407\pi$
$542$		0			0
$543$	1856.02	−	2395.45i	0.146684	−	0.189316i
$544$		0			0
$545$	−1444.33	+	833.887i	−0.113520	+	0.0655409i
$546$		0			0
$547$	902.529	−	1563.23i	0.0705473	−	0.122192i	−0.828594	−	0.559850i	$-0.810859\pi$
$547$	902.529	−	1563.23i	0.0705473	−	0.122192i	0.899141	+	0.437658i	$0.144192\pi$
$548$		0			0
$549$	−5428.96	+	19525.9i	−0.422044	+	1.51793i
$550$		0			0
$551$	176.721	−	306.090i	0.0136635	−	0.0236659i
$552$		0			0
$553$	−292.032	−	505.814i	−0.0224565	−	0.0388959i
$554$		0			0
$555$	−4318.72	−	589.210i	−0.330305	−	0.0450641i
$556$		0			0
$557$	−25569.6			−1.94510			−0.972550	−	0.232694i	$-0.925246\pi$
$557$	−25569.6			−1.94510			−0.972550	+	0.232694i	$0.925246\pi$
$558$		0			0
$559$			15094.5i			1.14209i
$560$		0			0
$561$	251.283	−	102.705i	0.0189112	−	0.00772944i
$562$		0			0
$563$	4254.07	−	2456.09i	0.318451	−	0.183858i	−0.332251	−	0.943191i	$-0.607808\pi$
$563$	4254.07	−	2456.09i	0.318451	−	0.183858i	0.650702	+	0.759333i	$0.274475\pi$
$564$		0			0
$565$	2413.32	+	1393.33i	0.179698	+	0.103748i
$566$		0			0
$567$	−3777.47	−	70.9477i	−0.279786	−	0.00525489i
$568$		0			0
$569$	13142.2	+	7587.64i	0.968275	+	0.559034i	0.898710	−	0.438544i	$-0.144506\pi$
$569$	13142.2	+	7587.64i	0.968275	+	0.559034i	0.0695650	+	0.997577i	$0.477839\pi$
$570$		0			0
$571$	−6558.52	−	11359.7i	−0.480675	−	0.832554i	0.519079	−	0.854726i	$-0.326275\pi$
$571$	−6558.52	−	11359.7i	−0.480675	−	0.832554i	−0.999754	+	0.0221726i	$0.992942\pi$
$572$		0			0
$573$	−5989.89	+	2448.21i	−0.436704	+	0.178491i
$574$		0			0
$575$	14373.4			1.04246
$576$		0			0
$577$	9122.28			0.658173			0.329086	−	0.944300i	$-0.393259\pi$
$577$	9122.28			0.658173			0.329086	+	0.944300i	$0.393259\pi$
$578$		0			0
$579$	−1848.96	+	13552.2i	−0.132712	+	0.972733i
$580$		0			0
$581$	2565.56	+	4443.68i	0.183197	+	0.317306i
$582$		0			0
$583$	7111.45	+	4105.80i	0.505191	+	0.291672i
$584$		0			0
$585$	−912.725	+	3282.73i	−0.0645069	+	0.232007i
$586$		0			0
$587$	13405.1	+	7739.45i	0.942570	+	0.544193i	0.890765	−	0.454464i	$-0.150169\pi$
$587$	13405.1	+	7739.45i	0.942570	+	0.544193i	0.0518051	+	0.998657i	$0.483503\pi$
$588$		0			0
$589$	4143.76	−	2392.40i	0.289883	−	0.167364i
$590$		0			0
$591$	4973.91	+	3853.85i	0.346192	+	0.268234i
$592$		0			0
$593$			13499.3i			0.934824i	0.884040	+	0.467412i	$0.154813\pi$
$593$			13499.3i			0.934824i	−0.884040	+	0.467412i	$0.845187\pi$
$594$		0			0
$595$	50.2893			0.00346498
$596$		0			0
$597$	6415.10	−	8279.54i	0.439787	−	0.567603i
$598$		0			0
$599$	−7097.54	−	12293.3i	−0.484136	−	0.838548i	0.515698	−	0.856771i	$-0.327533\pi$
$599$	−7097.54	−	12293.3i	−0.484136	−	0.838548i	−0.999834	+	0.0182222i	$0.994199\pi$
$600$		0			0
$601$	505.327	−	875.253i	0.0342974	−	0.0594048i	−0.848367	−	0.529408i	$-0.822414\pi$
$601$	505.327	−	875.253i	0.0342974	−	0.0594048i	0.882665	+	0.470003i	$0.155747\pi$
$602$		0			0
$603$	4870.14	−	4779.52i	0.328901	−	0.322782i
$604$		0			0
$605$	−1584.25	+	2744.00i	−0.106461	+	0.184396i
$606$		0			0
$607$	−7769.04	+	4485.46i	−0.519498	+	0.299933i	−0.736729	−	0.676188i	$-0.763631\pi$
$607$	−7769.04	+	4485.46i	−0.519498	+	0.299933i	0.217231	+	0.976120i	$0.430298\pi$
$608$		0			0
$609$	−625.306	−	85.3116i	−0.0416070	−	0.00567652i
$610$		0			0
$611$		−	14312.0i		−	0.947630i
$612$		0			0
$613$		−	14462.3i		−	0.952897i	−0.879202	−	0.476449i	$-0.841924\pi$
$613$		−	14462.3i		−	0.952897i	0.879202	−	0.476449i	$-0.158076\pi$
$614$		0			0
$615$	1892.87	+	4631.17i	0.124110	+	0.303653i
$616$		0			0
$617$	18159.9	−	10484.6i	1.18491	−	0.684108i	0.227764	−	0.973716i	$-0.426858\pi$
$617$	18159.9	−	10484.6i	1.18491	−	0.684108i	0.957145	+	0.289608i	$0.0935251\pi$
$618$		0			0
$619$	3168.60	−	5488.18i	0.205746	−	0.356363i	−0.744624	−	0.667484i	$-0.767371\pi$
$619$	3168.60	−	5488.18i	0.205746	−	0.356363i	0.950370	+	0.311121i	$0.100705\pi$
$620$		0			0
$621$	17200.6	−	2018.48i	1.11149	−	0.130433i
$622$		0			0
$623$	−1468.39	+	2543.32i	−0.0944296	+	0.163557i
$624$		0			0
$625$	−6243.62	−	10814.3i	−0.399591	−	0.692113i
$626$		0			0
$627$	−467.123	−	1142.88i	−0.0297530	−	0.0727948i
$628$		0			0
$629$	−950.565			−0.0602568
$630$		0			0
$631$			26190.2i			1.65232i	0.563436	+	0.826160i	$0.309479\pi$
$631$			26190.2i			1.65232i	−0.563436	+	0.826160i	$0.690521\pi$
$632$		0			0
$633$	844.666	−	6191.13i	0.0530371	−	0.388744i
$634$		0			0
$635$	3230.57	−	1865.17i	0.201892	−	0.116562i
$636$		0			0
$637$	11807.0	+	6816.79i	0.734397	+	0.424004i
$638$		0			0
$639$	−7304.46	−	28321.7i	−0.452207	−	1.75335i
$640$		0			0
$641$	−21831.2	−	12604.3i	−1.34521	−	0.776660i	−0.357647	−	0.933857i	$-0.616421\pi$
$641$	−21831.2	−	12604.3i	−1.34521	−	0.776660i	−0.987567	+	0.157197i	$0.949754\pi$
$642$		0			0
$643$	−3931.26	−	6809.13i	−0.241110	−	0.417614i	0.719921	−	0.694056i	$-0.244178\pi$
$643$	−3931.26	−	6809.13i	−0.241110	−	0.417614i	−0.961031	+	0.276442i	$0.910845\pi$
$644$		0			0
$645$	4207.03	+	3259.66i	0.256824	+	0.198991i
$646$		0			0
$647$	−188.733			−0.0114681			−0.00573404	−	0.999984i	$-0.501825\pi$
$647$	−188.733			−0.0114681			−0.00573404	+	0.999984i	$0.501825\pi$
$648$		0			0
$649$	2378.58			0.143864
$650$		0			0
$651$	−6753.63	−	5232.80i	−0.406599	−	0.315038i
$652$		0			0
$653$	15259.4	+	26430.1i	0.914468	+	1.58390i	0.807678	+	0.589623i	$0.200724\pi$
$653$	15259.4	+	26430.1i	0.914468	+	1.58390i	0.106790	+	0.994282i	$0.465943\pi$
$654$		0			0
$655$	−1376.78	−	794.884i	−0.0821301	−	0.0474178i
$656$		0			0
$657$	4574.44	+	17736.5i	0.271637	+	1.05322i
$658$		0			0
$659$	16805.7	+	9702.80i	0.993412	+	0.573547i	0.906292	−	0.422651i	$-0.138900\pi$
$659$	16805.7	+	9702.80i	0.993412	+	0.573547i	0.0871197	+	0.996198i	$0.472234\pi$
$660$		0			0
$661$	26953.4	−	15561.6i	1.58603	−	0.915696i	0.592079	−	0.805880i	$-0.298307\pi$
$661$	26953.4	−	15561.6i	1.58603	−	0.915696i	0.993952	−	0.109816i	$-0.0350262\pi$
$662$		0			0
$663$	−100.447	+	736.243i	−0.00588392	+	0.0431272i
$664$		0			0
$665$		−	228.726i		−	0.0133377i
$666$		0			0
$667$	2892.91			0.167937
$668$		0			0
$669$	−2578.31	−	6308.21i	−0.149004	−	0.364558i
$670$		0			0
$671$	5912.87	+	10241.4i	0.340185	+	0.589217i
$672$		0			0
$673$	16571.1	−	28701.9i	0.949134	−	1.64395i	0.201880	−	0.979410i	$-0.435295\pi$
$673$	16571.1	−	28701.9i	0.949134	−	1.64395i	0.747254	−	0.664539i	$-0.231372\pi$
$674$		0			0
$675$	−9761.01	−	13098.7i	−0.556595	−	0.746919i
$676$		0			0
$677$	−3831.16	+	6635.77i	−0.217494	+	0.376711i	−0.954041	−	0.299675i	$-0.903122\pi$
$677$	−3831.16	+	6635.77i	−0.217494	+	0.376711i	0.736547	+	0.676386i	$0.236455\pi$
$678$		0			0
$679$	663.195	−	382.896i	0.0374832	−	0.0216409i
$680$		0			0
$681$	−5663.09	−	13855.5i	−0.318664	−	0.779656i
$682$		0			0
$683$			8233.45i			0.461265i	0.973041	+	0.230633i	$0.0740795\pi$
$683$			8233.45i			0.461265i	−0.973041	+	0.230633i	$0.925920\pi$
$684$		0			0
$685$		−	7384.28i		−	0.411882i
$686$		0			0
$687$	−22935.9	−	3129.19i	−1.27374	−	0.173779i
$688$		0			0
$689$	−19466.0	+	11238.7i	−1.07633	+	0.621422i
$690$		0			0
$691$	9201.53	−	15937.5i	0.506574	−	0.877412i	−0.493397	−	0.869804i	$-0.664245\pi$
$691$	9201.53	−	15937.5i	0.506574	−	0.877412i	0.999971	−	0.00760808i	$-0.00242175\pi$
$692$		0			0
$693$	−1573.44	+	1544.17i	−0.0862484	+	0.0846437i
$694$		0			0
$695$	−2744.66	+	4753.89i	−0.149800	+	0.259461i
$696$		0			0
$697$	545.542	+	944.907i	0.0296469	+	0.0513499i
$698$		0			0
$699$	−3455.78	+	4460.15i	−0.186995	+	0.241342i
$700$		0			0
$701$	2617.11			0.141008			0.0705041	−	0.997511i	$-0.477539\pi$
$701$	2617.11			0.141008			0.0705041	+	0.997511i	$0.477539\pi$
$702$		0			0
$703$			4323.36i			0.231947i
$704$		0			0
$705$	−3988.94	−	3090.69i	−0.213095	−	0.165109i
$706$		0			0
$707$	−6584.64	+	3801.65i	−0.350270	+	0.202229i
$708$		0			0
$709$	15311.9	+	8840.30i	0.811070	+	0.468271i	0.847327	−	0.531071i	$-0.178210\pi$
$709$	15311.9	+	8840.30i	0.811070	+	0.468271i	−0.0362573	+	0.999342i	$0.511544\pi$
$710$		0			0
$711$	815.098	−	2931.60i	0.0429938	−	0.154632i
$712$		0			0
$713$	33916.4	+	19581.7i	1.78146	+	1.02853i
$714$		0			0
$715$	994.082	+	1721.80i	0.0519952	+	0.0900583i
$716$		0			0
$717$	2272.43	−	16656.2i	0.118362	−	0.867553i
$718$		0			0
$719$	−7767.21			−0.402876			−0.201438	−	0.979501i	$-0.564562\pi$
$719$	−7767.21			−0.402876			−0.201438	+	0.979501i	$0.564562\pi$
$720$		0			0
$721$	6014.74			0.310680
$722$		0			0
$723$	−6880.49	+	2812.22i	−0.353926	+	0.144658i
$724$		0			0
$725$	−1364.35	−	2363.13i	−0.0698907	−	0.121054i
$726$		0			0
$727$	9187.03	+	5304.13i	0.468677	+	0.270591i	0.715686	−	0.698423i	$-0.246114\pi$
$727$	9187.03	+	5304.13i	0.468677	+	0.270591i	−0.247009	+	0.969013i	$0.579448\pi$
$728$		0			0
$729$	−13520.5	−	14304.5i	−0.686910	−	0.726742i
$730$		0			0
$731$	1005.16	+	580.327i	0.0508578	+	0.0293628i
$732$		0			0
$733$	−7738.67	+	4467.92i	−0.389951	+	0.225138i	−0.682139	−	0.731223i	$-0.738950\pi$
$733$	−7738.67	+	4467.92i	−0.389951	+	0.225138i	0.292188	+	0.956361i	$0.405617\pi$
$734$		0			0
$735$	4449.66	−	1818.68i	0.223304	−	0.0912695i
$736$		0			0
$737$		−	3981.66i		−	0.199005i
$738$		0			0
$739$	−5767.08			−0.287071			−0.143535	−	0.989645i	$-0.545847\pi$
$739$	−5767.08			−0.287071			−0.143535	+	0.989645i	$0.545847\pi$
$740$		0			0
$741$	3348.58	+	456.853i	0.166010	+	0.0226490i
$742$		0			0
$743$	−711.865	−	1232.99i	−0.0351491	−	0.0608801i	0.847916	−	0.530131i	$-0.177857\pi$
$743$	−711.865	−	1232.99i	−0.0351491	−	0.0608801i	−0.883065	+	0.469251i	$0.844524\pi$
$744$		0			0
$745$	−2922.28	+	5061.54i	−0.143710	+	0.248913i
$746$		0			0
$747$	−7160.80	+	25754.7i	−0.350736	+	1.26147i
$748$		0			0
$749$	−3223.82	+	5583.82i	−0.157271	+	0.272401i
$750$		0			0
$751$	16310.8	−	9417.02i	0.792527	−	0.457566i	−0.0483243	−	0.998832i	$-0.515388\pi$
$751$	16310.8	−	9417.02i	0.792527	−	0.457566i	0.840851	+	0.541266i	$0.182055\pi$
$752$		0			0
$753$	−18789.1	+	24249.8i	−0.909311	+	1.17359i
$754$		0			0
$755$		−	119.495i		−	0.00576007i
$756$		0			0
$757$			21381.1i			1.02657i	0.858219	+	0.513283i	$0.171571\pi$
$757$			21381.1i			1.02657i	−0.858219	+	0.513283i	$0.828429\pi$
$758$		0			0
$759$	6189.48	−	7988.35i	0.296000	−	0.382027i
$760$		0			0
$761$	15809.6	−	9127.66i	0.753083	−	0.434793i	−0.0737237	−	0.997279i	$-0.523488\pi$
$761$	15809.6	−	9127.66i	0.753083	−	0.434793i	0.826807	+	0.562486i	$0.190155\pi$
$762$		0			0
$763$	1476.89	−	2558.04i	0.0700745	−	0.121373i
$764$		0			0
$765$	183.509	+	186.988i	0.00867292	+	0.00883734i
$766$		0			0
$767$	−3255.42	+	5638.55i	−0.153255	+	0.265445i
$768$		0			0
$769$	−7996.45	−	13850.3i	−0.374980	−	0.649484i	0.615344	−	0.788259i	$-0.289017\pi$
$769$	−7996.45	−	13850.3i	−0.374980	−	0.649484i	−0.990324	+	0.138774i	$0.955684\pi$
$770$		0			0
$771$	−7286.47	−	994.106i	−0.340358	−	0.0464356i
$772$		0			0
$773$	−23733.1			−1.10429			−0.552147	−	0.833747i	$-0.686191\pi$
$773$	−23733.1			−1.10429			−0.552147	+	0.833747i	$0.686191\pi$
$774$		0			0
$775$		−	36940.4i		−	1.71218i
$776$		0			0
$777$	7145.85	−	2920.68i	0.329930	−	0.134850i
$778$		0			0
$779$	4297.62	−	2481.23i	0.197662	−	0.114120i
$780$		0			0
$781$	−14780.3	−	8533.39i	−0.677182	−	0.390971i
$782$		0			0
$783$	−1964.58	−	2636.35i	−0.0896657	−	0.120326i
$784$		0			0
$785$	−3423.86	−	1976.77i	−0.155672	−	0.0898775i
$786$		0			0
$787$	−3774.80	−	6538.15i	−0.170975	−	0.296137i	0.767786	−	0.640706i	$-0.221358\pi$
$787$	−3774.80	−	6538.15i	−0.170975	−	0.296137i	−0.938761	+	0.344569i	$0.888025\pi$
$788$		0			0
$789$	−26872.9	+	10983.6i	−1.21255	+	0.495597i
$790$		0			0
$791$	−4935.42			−0.221850
$792$		0			0
$793$	−32370.3			−1.44956
$794$		0			0
$795$	−1071.32	+	7852.42i	−0.0477935	+	0.350310i
$796$		0			0
$797$	−13480.4	−	23348.7i	−0.599120	−	1.03771i	−0.992951	−	0.118524i	$-0.962184\pi$
$797$	−13480.4	−	23348.7i	−0.599120	−	1.03771i	0.393831	−	0.919183i	$-0.371149\pi$
$798$		0			0
$799$	−953.051	−	550.244i	−0.0421984	−	0.0243632i
$800$		0			0
$801$	−14814.9	+	3820.92i	−0.653508	+	0.168546i
$802$		0			0
$803$	9256.18	+	5344.06i	0.406779	+	0.234854i
$804$		0			0
$805$	1621.29	−	936.052i	0.0709850	−	0.0409832i
$806$		0			0
$807$	−20662.8	−	16009.8i	−0.901320	−	0.698355i
$808$		0			0
$809$			33739.1i			1.46626i	0.680090	+	0.733129i	$0.261941\pi$
$809$			33739.1i			1.46626i	−0.680090	+	0.733129i	$0.738059\pi$
$810$		0			0
$811$	9809.12			0.424716			0.212358	−	0.977192i	$-0.431886\pi$
$811$	9809.12			0.424716			0.212358	+	0.977192i	$0.431886\pi$
$812$		0			0
$813$	4193.07	−	5411.71i	0.180882	−	0.233453i
$814$		0			0
$815$	−2812.74	−	4871.82i	−0.120891	−	0.209389i
$816$		0			0
$817$	2639.44	−	4571.65i	0.113026	−	0.195767i
$818$		0			0
$819$	−1507.05	−	5843.32i	−0.0642987	−	0.249307i
$820$		0			0
$821$	9274.38	−	16063.7i	0.394248	−	0.682858i	−0.598756	−	0.800931i	$-0.704338\pi$
$821$	9274.38	−	16063.7i	0.394248	−	0.682858i	0.993005	+	0.118073i	$0.0376716\pi$
$822$		0			0
$823$	1262.62	−	728.972i	0.0534775	−	0.0308753i	−0.473023	−	0.881050i	$-0.656837\pi$
$823$	1262.62	−	728.972i	0.0534775	−	0.0308753i	0.526500	+	0.850175i	$0.323504\pi$
$824$		0			0
$825$	−9444.53	−	1288.53i	−0.398565	−	0.0543769i
$826$		0			0
$827$			42187.5i			1.77388i	0.461881	+	0.886942i	$0.347175\pi$
$827$			42187.5i			1.77388i	−0.461881	+	0.886942i	$0.652825\pi$
$828$		0			0
$829$			22370.3i			0.937218i	0.883406	+	0.468609i	$0.155245\pi$
$829$			22370.3i			0.937218i	−0.883406	+	0.468609i	$0.844755\pi$
$830$		0			0
$831$	5962.27	+	14587.5i	0.248892	+	0.608948i
$832$		0			0
$833$	907.873	−	524.161i	0.0377622	−	0.0218020i
$834$		0			0
$835$	3836.89	−	6645.68i	0.159019	−	0.275429i
$836$		0			0
$837$	−5187.60	−	44206.5i	−0.214229	−	1.82557i
$838$		0			0
$839$	−24035.3	+	41630.3i	−0.989023	+	1.71304i	−0.366548	+	0.930399i	$0.619460\pi$
$839$	−24035.3	+	41630.3i	−0.989023	+	1.71304i	−0.622476	+	0.782639i	$0.713873\pi$
$840$		0			0
$841$	11919.9	+	20645.9i	0.488741	+	0.846524i
$842$		0			0
$843$	4808.08	+	11763.7i	0.196440	+	0.480619i
$844$		0			0
$845$	986.816			0.0401745
$846$		0			0
$847$		−	5611.69i		−	0.227650i
$848$		0			0
$849$	−5941.72	+	43550.9i	−0.240188	+	1.76050i
$850$		0			0
$851$	−30645.5	+	17693.2i	−1.23445	+	0.712708i
$852$		0			0
$853$	−14708.0	−	8491.65i	−0.590377	−	0.340854i	0.174870	−	0.984592i	$-0.444050\pi$
$853$	−14708.0	−	8491.65i	−0.590377	−	0.340854i	−0.765246	+	0.643737i	$0.777383\pi$
$854$		0			0
$855$	850.458	−	834.635i	0.0340176	−	0.0333847i
$856$		0			0
$857$	22340.4	+	12898.3i	0.890473	+	0.514115i	0.874097	−	0.485751i	$-0.161454\pi$
$857$	22340.4	+	12898.3i	0.890473	+	0.514115i	0.0163755	+	0.999866i	$0.494787\pi$
$858$		0			0
$859$	9914.38	+	17172.2i	0.393800	+	0.682082i	0.992947	−	0.118557i	$-0.0378269\pi$
$859$	9914.38	+	17172.2i	0.393800	+	0.682082i	−0.599147	+	0.800639i	$0.704494\pi$
$860$		0			0
$861$	−7004.40	−	5427.10i	−0.277246	−	0.214814i
$862$		0			0
$863$	−42561.4			−1.67880			−0.839401	−	0.543513i	$-0.817094\pi$
$863$	−42561.4			−1.67880			−0.839401	+	0.543513i	$0.817094\pi$
$864$		0			0
$865$	8110.22			0.318793
$866$		0			0
$867$	−20134.9	−	15600.8i	−0.788717	−	0.611109i
$868$		0			0
$869$	−887.753	−	1537.63i	−0.0346547	−	0.0600237i
$870$		0			0
$871$	9438.71	+	5449.44i	0.367185	+	0.211995i
$872$		0			0
$873$	3843.75	+	1068.71i	0.149016	+	0.0414323i
$874$		0			0
$875$	−3171.00	−	1830.78i	−0.122513	−	0.0707331i
$876$		0			0
$877$	−13338.6	+	7701.03i	−0.513582	+	0.296517i	−0.734305	−	0.678820i	$-0.762492\pi$
$877$	−13338.6	+	7701.03i	−0.513582	+	0.296517i	0.220723	+	0.975337i	$0.429158\pi$
$878$		0			0
$879$	−308.177	+	2258.83i	−0.0118254	+	0.0866764i
$880$		0			0
$881$			408.896i			0.0156368i	0.999969	+	0.00781842i	$0.00248871\pi$
$881$			408.896i			0.0156368i	−0.999969	+	0.00781842i	$0.997511\pi$
$882$		0			0
$883$	−24945.2			−0.950704			−0.475352	−	0.879796i	$-0.657679\pi$
$883$	−24945.2			−0.950704			−0.475352	+	0.879796i	$0.657679\pi$
$884$		0			0
$885$	868.527	+	2124.97i	0.0329890	+	0.0807121i
$886$		0			0
$887$	5014.93	+	8686.11i	0.189836	+	0.328806i	0.945196	−	0.326505i	$-0.105871\pi$
$887$	5014.93	+	8686.11i	0.189836	+	0.328806i	−0.755359	+	0.655311i	$0.772538\pi$
$888$		0			0
$889$	−3303.37	+	5721.61i	−0.124625	+	0.215857i
$890$		0			0
$891$	−11483.2	−	215.675i	−0.431764	−	0.00810929i
$892$		0			0
$893$	−2502.62	+	4334.66i	−0.0937815	+	0.162434i
$894$		0			0
$895$	5343.12	−	3084.85i	0.199554	−	0.115213i
$896$		0			0
$897$	10465.6	+	25605.6i	0.389562	+	0.953117i
$898$		0			0
$899$		−	7434.91i		−	0.275827i
$900$		0			0
$901$			1728.34i			0.0639062i
$902$		0			0
$903$	−9339.33	−	1274.18i	−0.344179	−	0.0469569i
$904$		0			0
$905$	1477.92	−	853.278i	0.0542848	−	0.0313413i
$906$		0			0
$907$	−3767.44	+	6525.40i	−0.137923	+	0.238889i	−0.926710	−	0.375777i	$-0.877376\pi$
$907$	−3767.44	+	6525.40i	−0.137923	+	0.238889i	0.788788	+	0.614666i	$0.210709\pi$
$908$		0			0
$909$	−38163.3	−	10610.9i	−1.39251	−	0.387173i
$910$		0			0
$911$	11159.9	−	19329.6i	0.405867	−	0.702983i	−0.588555	−	0.808457i	$-0.700303\pi$
$911$	11159.9	−	19329.6i	0.405867	−	0.702983i	0.994422	+	0.105475i	$0.0336362\pi$
$912$		0			0
$913$	7799.08	+	13508.4i	0.282708	+	0.489664i
$914$		0			0
$915$	−6990.38	+	9022.02i	−0.252563	+	0.325966i
$916$		0			0
$917$	2815.62			0.101396
$918$		0			0
$919$		−	40992.7i		−	1.47141i	−0.677303	−	0.735704i	$-0.736851\pi$
$919$		−	40992.7i		−	1.47141i	0.677303	−	0.735704i	$-0.263149\pi$
$920$		0			0
$921$	−32347.3	−	25063.1i	−1.15731	−	0.896698i
$922$		0			0
$923$	40457.6	−	23358.2i	1.44277	−	0.832985i
$924$		0			0
$925$	28906.1	+	16688.9i	1.02749	+	0.593220i
$926$		0			0
$927$	21948.2	+	22364.3i	0.777641	+	0.792383i
$928$		0			0
$929$	−20199.6	−	11662.2i	−0.713376	−	0.411868i	0.0989336	−	0.995094i	$-0.468457\pi$
$929$	−20199.6	−	11662.2i	−0.713376	−	0.411868i	−0.812310	+	0.583226i	$0.801790\pi$
$930$		0			0
$931$	−2383.99	−	4129.18i	−0.0839226	−	0.145358i
$932$		0			0
$933$	−748.697	+	5487.70i	−0.0262714	+	0.192561i
$934$		0			0
$935$	152.875			0.00534712
$936$		0			0
$937$	−29355.3			−1.02348			−0.511738	−	0.859142i	$-0.670998\pi$
$937$	−29355.3			−1.02348			−0.511738	+	0.859142i	$0.670998\pi$
$938$		0			0
$939$	47659.4	−	19479.5i	1.65634	−	0.676986i
$940$		0			0
$941$	−1391.16	−	2409.56i	−0.0481939	−	0.0834743i	0.840922	−	0.541156i	$-0.182013\pi$
$941$	−1391.16	−	2409.56i	−0.0481939	−	0.0834743i	−0.889116	+	0.457682i	$0.848680\pi$
$942$		0			0
$943$	35175.8	+	20308.7i	1.21472	+	0.701319i
$944$		0			0
$945$	−1954.06	−	841.833i	−0.0672651	−	0.0289787i
$946$		0			0
$947$	−15438.1	−	8913.16i	−0.529746	−	0.305849i	0.211167	−	0.977450i	$-0.432274\pi$
$947$	−15438.1	−	8913.16i	−0.529746	−	0.305849i	−0.740913	+	0.671601i	$0.765607\pi$
$948$		0			0
$949$	−25336.7	+	14628.1i	−0.866663	+	0.500368i
$950$		0			0
$951$	−338.082	+	138.182i	−0.0115279	+	0.00471174i
$952$		0			0
$953$		−	21508.9i		−	0.731104i	−0.930791	−	0.365552i	$-0.880880\pi$
$953$		−	21508.9i		−	0.731104i	0.930791	−	0.365552i	$-0.119120\pi$
$954$		0			0
$955$	−3644.13			−0.123478
$956$		0			0
$957$	−1900.88	−	259.340i	−0.0642076	−	0.00875995i
$958$		0			0
$959$	6539.10	+	11326.1i	0.220186	+	0.381374i
$960$		0			0
$961$	35430.4	−	61367.2i	1.18930	−	2.05992i
$962$		0			0
$963$	−32526.0	+	8388.78i	−1.08841	+	0.280711i
$964$		0			0
$965$	−3851.37	+	6670.76i	−0.128477	+	0.222528i
$966$		0			0
$967$	−8410.42	+	4855.76i	−0.279691	+	0.161479i	−0.633283	−	0.773920i	$-0.718293\pi$
$967$	−8410.42	+	4855.76i	−0.279691	+	0.161479i	0.353593	+	0.935399i	$0.384960\pi$
$968$		0			0
$969$	159.163	−	205.421i	0.00527662	−	0.00681019i
$970$		0			0
$971$			1908.56i			0.0630777i	0.999503	+	0.0315389i	$0.0100408\pi$
$971$			1908.56i			0.0630777i	−0.999503	+	0.0315389i	$0.989959\pi$
$972$		0			0
$973$		−	9722.06i		−	0.320324i
$974$		0			0
$975$	15980.6	−	20625.2i	0.524913	−	0.677471i
$976$		0			0
$977$	−40899.7	+	23613.4i	−1.33930	+	0.773245i	−0.986704	−	0.162531i	$-0.948034\pi$
$977$	−40899.7	+	23613.4i	−1.33930	+	0.773245i	−0.352596	+	0.935776i	$0.614701\pi$
$978$		0			0
$979$	−4463.77	+	7731.47i	−0.145723	+	0.252399i
$980$		0			0
$981$	14900.7	−	3843.04i	0.484956	−	0.125075i
$982$		0			0
$983$	11777.7	−	20399.5i	0.382146	−	0.661895i	−0.609223	−	0.792999i	$-0.708519\pi$
$983$	11777.7	−	20399.5i	0.382146	−	0.661895i	0.991369	+	0.131103i	$0.0418520\pi$
$984$		0			0
$985$	1771.75	+	3068.76i	0.0573123	+	0.0992678i
$986$		0			0
$987$	8855.20	+	1208.13i	0.285577	+	0.0389617i
$988$		0			0
$989$	43207.3			1.38919
$990$		0			0
$991$		−	31768.2i		−	1.01831i	−0.860673	−	0.509157i	$-0.829957\pi$
$991$		−	31768.2i		−	1.01831i	0.860673	−	0.509157i	$-0.170043\pi$
$992$		0			0
$993$	45062.4	−	18418.1i	1.44009	−	0.588600i
$994$		0			0
$995$	5108.24	−	2949.24i	0.162756	−	0.0939672i
$996$		0			0
$997$	3600.15	+	2078.55i	0.114361	+	0.0660263i	0.556089	−	0.831122i	$-0.312301\pi$
$997$	3600.15	+	2078.55i	0.114361	+	0.0660263i	−0.441729	+	0.897149i	$0.645635\pi$
$998$		0			0
$999$	36935.5	+	15912.3i	1.16976	+	0.503946i

Display

a_p

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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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.4.p.b.47.7		64
3.2	odd	2		864.4.p.b.143.18		64
4.3	odd	2		72.4.l.b.11.30	yes	64
8.3	odd	2	inner	288.4.p.b.47.8		64
8.5	even	2		72.4.l.b.11.20	✓	64
9.4	even	3		864.4.p.b.719.15		64
9.5	odd	6	inner	288.4.p.b.239.8		64
12.11	even	2		216.4.l.b.35.3		64
24.5	odd	2		216.4.l.b.35.13		64
24.11	even	2		864.4.p.b.143.15		64
36.23	even	6		72.4.l.b.59.20	yes	64
36.31	odd	6		216.4.l.b.179.13		64
72.5	odd	6		72.4.l.b.59.30	yes	64
72.13	even	6		216.4.l.b.179.3		64
72.59	even	6	inner	288.4.p.b.239.7		64
72.67	odd	6		864.4.p.b.719.18		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.4.l.b.11.20	✓	64	8.5	even	2
72.4.l.b.11.30	yes	64	4.3	odd	2
72.4.l.b.59.20	yes	64	36.23	even	6
72.4.l.b.59.30	yes	64	72.5	odd	6
216.4.l.b.35.3		64	12.11	even	2
216.4.l.b.35.13		64	24.5	odd	2
216.4.l.b.179.3		64	72.13	even	6
216.4.l.b.179.13		64	36.31	odd	6
288.4.p.b.47.7		64	1.1	even	1	trivial
288.4.p.b.47.8		64	8.3	odd	2	inner
288.4.p.b.239.7		64	72.59	even	6	inner
288.4.p.b.239.8		64	9.5	odd	6	inner
864.4.p.b.143.15		64	24.11	even	2
864.4.p.b.143.18		64	3.2	odd	2
864.4.p.b.719.15		64	9.4	even	3
864.4.p.b.719.18		64	72.67	odd	6

Overview	Random
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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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	288.4.p.b.47.7

Level	$288$
Weight	$4$
Character	288.47
Analytic conductor	$16.993$
Analytic rank	$0$
Dimension	$64$
Inner twists	$4$