LMFDB - Embedded newform 261.2.o.b.91.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [261,2,Mod(64,261)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(261, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("261.64"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$261 = 3^{2} \cdot 29$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	261.o (of order $14$ , degree $6$ , minimal)

Newform invariants

comment:select newform

sage:traces = [24] 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:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{14})$
Twist minimal:	no (minimal twist has level 87)
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			91.2
Character	$\chi$	$=$	261.91
Dual form			261.2.o.b.109.2

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26950 - 0.289755i) q^{2} +(-0.274272 - 0.132082i) q^{4} +(0.0725658 - 0.317931i) q^{5} +(0.994220 - 0.478791i) q^{7} +(2.34603 + 1.87090i) q^{8} +(-0.184244 + 0.382587i) q^{10} +(0.600556 - 0.478928i) q^{11} +(-2.99941 - 3.76114i) q^{13} +(-1.40089 + 0.319744i) q^{14} +(-2.05658 - 2.57887i) q^{16} -5.18289i q^{17} +(1.81600 - 3.77095i) q^{19} +(-0.0618958 + 0.0776149i) q^{20} +(-0.901176 + 0.433984i) q^{22} +(-0.314479 - 1.37782i) q^{23} +(4.40903 + 2.12328i) q^{25} +(2.71794 + 5.64386i) q^{26} -0.335926 q^{28} +(0.401521 - 5.37018i) q^{29} +(-4.40253 - 1.00485i) q^{31} +(-0.740318 - 1.53729i) q^{32} +(-1.50177 + 6.57967i) q^{34} +(-0.0800764 - 0.350838i) q^{35} +(1.40085 + 1.11714i) q^{37} +(-3.39805 + 4.26102i) q^{38} +(0.765059 - 0.610114i) q^{40} -1.34344i q^{41} +(7.02843 - 1.60419i) q^{43} +(-0.227973 + 0.0520334i) q^{44} +1.84026i q^{46} +(-0.354469 + 0.282680i) q^{47} +(-3.60520 + 4.52077i) q^{49} +(-4.98202 - 3.97303i) q^{50} +(0.325873 + 1.42774i) q^{52} +(-1.96455 + 8.60725i) q^{53} +(-0.108686 - 0.225689i) q^{55} +(3.22824 + 0.736825i) q^{56} +(-2.06576 + 6.70108i) q^{58} -3.67450 q^{59} +(3.83753 + 7.96872i) q^{61} +(5.29784 + 2.55131i) q^{62} +(1.96236 + 8.59768i) q^{64} +(-1.41344 + 0.680677i) q^{65} +(9.51550 - 11.9321i) q^{67} +(-0.684568 + 1.42152i) q^{68} +0.468590i q^{70} +(9.37723 + 11.7587i) q^{71} +(-13.3579 + 3.04884i) q^{73} +(-1.45468 - 1.82412i) q^{74} +(-0.996152 + 0.794405i) q^{76} +(0.367779 - 0.763701i) q^{77} +(-4.56304 - 3.63890i) q^{79} +(-0.969139 + 0.466713i) q^{80} +(-0.389269 + 1.70550i) q^{82} +(11.4666 + 5.52203i) q^{83} +(-1.64780 - 0.376101i) q^{85} -9.38739 q^{86} +2.30495 q^{88} +(8.07964 + 1.84412i) q^{89} +(-4.78288 - 2.30331i) q^{91} +(-0.0957331 + 0.419434i) q^{92} +(0.531905 - 0.256152i) q^{94} +(-1.06713 - 0.851004i) q^{95} +(-0.670747 + 1.39282i) q^{97} +(5.88670 - 4.69449i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$24 q - 2 q^{4} + 4 q^{5} + 8 q^{7} + 28 q^{11} - 10 q^{13} - 22 q^{16} + 20 q^{20} + 4 q^{22} - 18 q^{23} - 18 q^{25} - 28 q^{26} + 8 q^{28} - 28 q^{29} + 28 q^{31} + 14 q^{32} + 34 q^{34} - 28 q^{37} + 4 q^{38}+ \cdots + 42 q^{98}+O(q^{100})$ 24 * q - 2 * q^4 + 4 * q^5 + 8 * q^7 + 28 * q^11 - 10 * q^13 - 22 * q^16 + 20 * q^20 + 4 * q^22 - 18 * q^23 - 18 * q^25 - 28 * q^26 + 8 * q^28 - 28 * q^29 + 28 * q^31 + 14 * q^32 + 34 * q^34 - 28 * q^37 + 4 * q^38 - 14 * q^43 - 14 * q^44 + 20 * q^49 - 42 * q^50 - 68 * q^52 - 6 * q^53 - 14 * q^55 + 50 * q^58 - 28 * q^59 + 8 * q^62 - 20 * q^64 - 18 * q^65 + 8 * q^67 - 14 * q^68 + 42 * q^71 - 84 * q^73 - 10 * q^74 - 14 * q^76 + 70 * q^77 - 14 * q^79 - 36 * q^80 - 50 * q^82 + 32 * q^83 + 14 * q^85 + 128 * q^86 - 20 * q^88 + 14 * q^89 + 34 * q^91 + 58 * q^92 - 44 * q^94 + 56 * q^97 + 42 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$ .

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{1}{14}\right)$	$1$

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

)

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

$2$	−1.26950	−	0.289755i	−0.897670	−	0.204887i	−0.251298	−	0.967910i	$-0.580857\pi$
$2$	−1.26950	−	0.289755i	−0.897670	−	0.204887i	−0.646372	+	0.763022i	$0.723715\pi$
$3$		0			0
$3$		0			0
$4$	−0.274272	−	0.132082i	−0.137136	−	0.0660411i
$5$	0.0725658	−	0.317931i	0.0324524	−	0.142183i	−0.956106	−	0.293020i	$-0.905340\pi$
$5$	0.0725658	−	0.317931i	0.0324524	−	0.142183i	0.988559	+	0.150837i	$0.0481968\pi$
$6$		0			0
$7$	0.994220	−	0.478791i	0.375780	−	0.180966i	−0.236454	−	0.971643i	$-0.575985\pi$
$7$	0.994220	−	0.478791i	0.375780	−	0.180966i	0.612234	+	0.790677i	$0.290271\pi$
$8$	2.34603	+	1.87090i	0.829447	+	0.661462i
$9$		0			0
$10$	−0.184244	+	0.382587i	−0.0582631	+	0.120985i
$11$	0.600556	−	0.478928i	0.181075	−	0.144402i	−0.528758	−	0.848773i	$-0.677342\pi$
$11$	0.600556	−	0.478928i	0.181075	−	0.144402i	0.709832	+	0.704371i	$0.248771\pi$
$12$		0			0
$13$	−2.99941	−	3.76114i	−0.831887	−	1.04315i	−0.998368	−	0.0571090i	$-0.981812\pi$
$13$	−2.99941	−	3.76114i	−0.831887	−	1.04315i	0.166481	−	0.986045i	$-0.446760\pi$
$14$	−1.40089	+	0.319744i	−0.374404	+	0.0854553i
$15$		0			0
$16$	−2.05658	−	2.57887i	−0.514144	−	0.644716i
$17$		−	5.18289i		−	1.25704i	−0.777795	−	0.628518i	$-0.783662\pi$
$17$		−	5.18289i		−	1.25704i	0.777795	−	0.628518i	$-0.216338\pi$
$18$		0			0
$19$	1.81600	−	3.77095i	0.416618	−	0.865116i	−0.582032	−	0.813166i	$-0.697742\pi$
$19$	1.81600	−	3.77095i	0.416618	−	0.865116i	0.998650	−	0.0519502i	$-0.0165437\pi$
$20$	−0.0618958	+	0.0776149i	−0.0138403	+	0.0173552i
$21$		0			0
$22$	−0.901176	+	0.433984i	−0.192131	+	0.0925256i
$23$	−0.314479	−	1.37782i	−0.0655733	−	0.287295i	0.931501	−	0.363740i	$-0.118500\pi$
$23$	−0.314479	−	1.37782i	−0.0655733	−	0.287295i	−0.997074	+	0.0764445i	$0.975643\pi$
$24$		0			0
$25$	4.40903	+	2.12328i	0.881806	+	0.424655i
$26$	2.71794	+	5.64386i	0.533032	+	1.10685i
$27$		0			0
$28$	−0.335926			−0.0634841
$29$	0.401521	−	5.37018i	0.0745606	−	0.997216i
$29$	0.401521	−	5.37018i	0.0745606	−	0.997216i
$30$		0			0
$31$	−4.40253	−	1.00485i	−0.790718	−	0.180476i	−0.191956	−	0.981403i	$-0.561483\pi$
$31$	−4.40253	−	1.00485i	−0.790718	−	0.180476i	−0.598762	+	0.800927i	$0.704340\pi$
$32$	−0.740318	−	1.53729i	−0.130871	−	0.271756i
$33$		0			0
$34$	−1.50177	+	6.57967i	−0.257551	+	1.12840i
$35$	−0.0800764	−	0.350838i	−0.0135354	−	0.0593024i
$36$		0			0
$37$	1.40085	+	1.11714i	0.230299	+	0.183657i	0.731840	−	0.681477i	$-0.238662\pi$
$37$	1.40085	+	1.11714i	0.230299	+	0.183657i	−0.501541	+	0.865134i	$0.667233\pi$
$38$	−3.39805	+	4.26102i	−0.551237	+	0.691229i
$39$		0			0
$40$	0.765059	−	0.610114i	0.120966	−	0.0964675i
$41$		−	1.34344i		−	0.209811i	−0.994482	−	0.104905i	$-0.966546\pi$
$41$		−	1.34344i		−	0.209811i	0.994482	−	0.104905i	$-0.0334540\pi$
$42$		0			0
$43$	7.02843	−	1.60419i	1.07182	−	0.244637i	0.350026	−	0.936740i	$-0.386173\pi$
$43$	7.02843	−	1.60419i	1.07182	−	0.244637i	0.721799	+	0.692103i	$0.243316\pi$
$44$	−0.227973	+	0.0520334i	−0.0343683	+	0.00784433i
$45$		0			0
$46$			1.84026i			0.271332i
$47$	−0.354469	+	0.282680i	−0.0517046	+	0.0412331i	−0.649001	−	0.760787i	$-0.724813\pi$
$47$	−0.354469	+	0.282680i	−0.0517046	+	0.0412331i	0.597297	+	0.802020i	$0.296242\pi$
$48$		0			0
$49$	−3.60520	+	4.52077i	−0.515028	+	0.645825i
$50$	−4.98202	−	3.97303i	−0.704564	−	0.561871i
$51$		0			0
$52$	0.325873	+	1.42774i	0.0451905	+	0.197992i
$53$	−1.96455	+	8.60725i	−0.269851	+	1.18230i	0.640334	+	0.768096i	$0.278796\pi$
$53$	−1.96455	+	8.60725i	−0.269851	+	1.18230i	−0.910186	+	0.414200i	$0.864061\pi$
$54$		0			0
$55$	−0.108686	−	0.225689i	−0.0146553	−	0.0304320i
$56$	3.22824	+	0.736825i	0.431392	+	0.0984624i
$57$		0			0
$58$	−2.06576	+	6.70108i	−0.271248	+	0.879895i
$59$	−3.67450			−0.478379			−0.239190	−	0.970973i	$-0.576882\pi$
$59$	−3.67450			−0.478379			−0.239190	+	0.970973i	$0.576882\pi$
$60$		0			0
$61$	3.83753	+	7.96872i	0.491346	+	1.02029i	0.988301	+	0.152514i	$0.0487369\pi$
$61$	3.83753	+	7.96872i	0.491346	+	1.02029i	−0.496956	+	0.867776i	$0.665549\pi$
$62$	5.29784	+	2.55131i	0.672827	+	0.324016i
$63$		0			0
$64$	1.96236	+	8.59768i	0.245295	+	1.07471i
$65$	−1.41344	+	0.680677i	−0.175316	+	0.0844276i
$66$		0			0
$67$	9.51550	−	11.9321i	1.16250	−	1.45773i	0.298384	−	0.954446i	$-0.403552\pi$
$67$	9.51550	−	11.9321i	1.16250	−	1.45773i	0.864119	−	0.503287i	$-0.167876\pi$
$68$	−0.684568	+	1.42152i	−0.0830161	+	0.172385i
$69$		0			0
$70$			0.468590i			0.0560072i
$71$	9.37723	+	11.7587i	1.11287	+	1.39550i	0.909150	+	0.416469i	$0.136733\pi$
$71$	9.37723	+	11.7587i	1.11287	+	1.39550i	0.203722	+	0.979029i	$0.434696\pi$
$72$		0			0
$73$	−13.3579	+	3.04884i	−1.56342	+	0.356840i	−0.914683	−	0.404173i	$-0.867559\pi$
$73$	−13.3579	+	3.04884i	−1.56342	+	0.356840i	−0.648737	+	0.761013i	$0.724702\pi$
$74$	−1.45468	−	1.82412i	−0.169104	−	0.212049i
$75$		0			0
$76$	−0.996152	+	0.794405i	−0.114266	+	0.0911245i
$77$	0.367779	−	0.763701i	0.0419123	−	0.0870318i
$78$		0			0
$79$	−4.56304	−	3.63890i	−0.513382	−	0.409408i	0.332237	−	0.943196i	$-0.392197\pi$
$79$	−4.56304	−	3.63890i	−0.513382	−	0.409408i	−0.845619	+	0.533788i	$0.820768\pi$
$80$	−0.969139	+	0.466713i	−0.108353	+	0.0521801i
$81$		0			0
$82$	−0.389269	+	1.70550i	−0.0429876	+	0.188341i
$83$	11.4666	+	5.52203i	1.25862	+	0.606122i	0.939811	−	0.341695i	$-0.111001\pi$
$83$	11.4666	+	5.52203i	1.25862	+	0.606122i	0.318814	+	0.947817i	$0.396715\pi$
$84$		0			0
$85$	−1.64780	−	0.376101i	−0.178730	−	0.0407938i
$86$	−9.38739			−1.01227
$87$		0			0
$88$	2.30495			0.245708
$89$	8.07964	+	1.84412i	0.856440	+	0.195477i	0.628127	−	0.778111i	$-0.283822\pi$
$89$	8.07964	+	1.84412i	0.856440	+	0.195477i	0.228313	+	0.973588i	$0.426679\pi$
$90$		0			0
$91$	−4.78288	−	2.30331i	−0.501382	−	0.241453i
$92$	−0.0957331	+	0.419434i	−0.00998086	+	0.0437290i
$93$		0			0
$94$	0.531905	−	0.256152i	0.0548618	−	0.0264201i
$95$	−1.06713	−	0.851004i	−0.109485	−	0.0873112i
$96$		0			0
$97$	−0.670747	+	1.39282i	−0.0681040	+	0.141419i	−0.932242	−	0.361836i	$-0.882150\pi$
$97$	−0.670747	+	1.39282i	−0.0681040	+	0.141419i	0.864138	+	0.503255i	$0.167864\pi$
$98$	5.88670	−	4.69449i	0.594647	−	0.474215i
$99$		0			0
$100$	−0.928824	−	1.16471i	−0.0928824	−	0.116471i
$101$	−15.7570	+	3.59643i	−1.56788	+	0.357858i	−0.916226	−	0.400661i	$-0.868781\pi$
$101$	−15.7570	+	3.59643i	−1.56788	+	0.357858i	−0.651651	+	0.758519i	$0.725923\pi$
$102$		0			0
$103$	−6.82835	−	8.56248i	−0.672818	−	0.843687i	0.321853	−	0.946790i	$-0.395694\pi$
$103$	−6.82835	−	8.56248i	−0.672818	−	0.843687i	−0.994671	+	0.103103i	$0.967123\pi$
$104$		−	14.4354i		−	1.41550i
$105$		0			0
$106$	4.98798	−	10.3576i	0.484475	−	1.00602i
$107$	7.79954	−	9.78032i	0.754010	−	0.945499i	−0.245706	−	0.969345i	$-0.579020\pi$
$107$	7.79954	−	9.78032i	0.754010	−	0.945499i	0.999716	+	0.0238458i	$0.00759106\pi$
$108$		0			0
$109$	7.93042	−	3.81909i	0.759597	−	0.365802i	−0.0136509	−	0.999907i	$-0.504345\pi$
$109$	7.93042	−	3.81909i	0.759597	−	0.365802i	0.773247	+	0.634104i	$0.218631\pi$
$110$	0.0725825	+	0.318005i	0.00692047	+	0.0303205i
$111$		0			0
$112$	−3.27943	−	1.57929i	−0.309877	−	0.149229i
$113$	1.06799	+	2.21771i	0.100468	+	0.208624i	0.945144	−	0.326654i	$-0.105921\pi$
$113$	1.06799	+	2.21771i	0.100468	+	0.208624i	−0.844676	+	0.535278i	$0.820207\pi$
$114$		0			0
$115$	−0.460873			−0.0429766
$116$	−0.819430	+	1.41985i	−0.0760822	+	0.131830i
$117$		0			0
$118$	4.66477	+	1.06470i	0.429427	+	0.0980139i
$119$	−2.48152	−	5.15294i	−0.227481	−	0.472369i
$120$		0			0
$121$	−2.31643	+	10.1490i	−0.210585	+	0.922633i
$122$	−2.56277	−	11.2282i	−0.232022	−	1.01655i
$123$		0			0
$124$	1.07477	+	0.857097i	0.0965169	+	0.0769696i
$125$	2.01162	−	2.52250i	0.179925	−	0.225619i
$126$		0			0
$127$	11.9351	−	9.51790i	1.05907	−	0.844577i	0.0708265	−	0.997489i	$-0.477436\pi$
$127$	11.9351	−	9.51790i	1.05907	−	0.844577i	0.988240	+	0.152911i	$0.0488649\pi$
$128$		−	8.07081i		−	0.713366i
$129$		0			0
$130$	1.99159	−	0.454567i	0.174674	−	0.0398682i
$131$	−8.52336	+	1.94540i	−0.744689	+	0.169970i	−0.577997	−	0.816039i	$-0.696166\pi$
$131$	−8.52336	+	1.94540i	−0.744689	+	0.169970i	−0.166692	+	0.986009i	$0.553308\pi$
$132$		0			0
$133$		−	4.61864i		−	0.400487i
$134$	−15.5373	+	12.3906i	−1.34222	+	1.07038i
$135$		0			0
$136$	9.69667	−	12.1592i	0.831482	−	1.04265i
$137$	−18.2169	−	14.5275i	−1.55638	−	1.24117i	−0.838305	−	0.545202i	$-0.816453\pi$
$137$	−18.2169	−	14.5275i	−1.55638	−	1.24117i	−0.718073	−	0.695968i	$-0.754975\pi$
$138$		0			0
$139$	3.01052	+	13.1900i	0.255349	+	1.11876i	0.926160	+	0.377130i	$0.123089\pi$
$139$	3.01052	+	13.1900i	0.255349	+	1.11876i	−0.670811	+	0.741628i	$0.734054\pi$
$140$	−0.0243767	+	0.106801i	−0.00206021	+	0.00902637i
$141$		0			0
$142$	−8.49724	−	17.6447i	−0.713073	−	1.48071i
$143$	−3.60263	−	0.822277i	−0.301267	−	0.0687623i
$144$		0			0
$145$	−1.67821	−	0.517347i	−0.139368	−	0.0429633i
$146$	17.8412			1.47655
$147$		0			0
$148$	−0.236660	−	0.491429i	−0.0194533	−	0.0403952i
$149$	1.19555	+	0.575745i	0.0979430	+	0.0471668i	0.482214	−	0.876054i	$-0.339833\pi$
$149$	1.19555	+	0.575745i	0.0979430	+	0.0471668i	−0.384271	+	0.923220i	$0.625547\pi$
$150$		0			0
$151$	3.19768	+	14.0099i	0.260223	+	1.14011i	0.921010	+	0.389539i	$0.127366\pi$
$151$	3.19768	+	14.0099i	0.260223	+	1.14011i	−0.660787	+	0.750574i	$0.729777\pi$
$152$	11.3155	−	5.44924i	0.917805	−	0.441991i
$153$		0			0
$154$	−0.688180	+	0.862950i	−0.0554551	+	0.0695385i
$155$	−0.638946	+	1.32679i	−0.0513214	+	0.106570i
$156$		0			0
$157$		−	13.1931i		−	1.05292i	−0.850199	−	0.526462i	$-0.823518\pi$
$157$		−	13.1931i		−	1.05292i	0.850199	−	0.526462i	$-0.176482\pi$
$158$	4.73838	+	5.94174i	0.376965	+	0.472699i
$159$		0			0
$160$	−0.542473	+	0.123816i	−0.0428863	+	0.00978851i
$161$	−0.972350	−	1.21929i	−0.0766319	−	0.0960933i
$162$		0			0
$163$	2.35391	−	1.87718i	0.184373	−	0.147032i	−0.526954	−	0.849894i	$-0.676666\pi$
$163$	2.35391	−	1.87718i	0.184373	−	0.147032i	0.711327	+	0.702861i	$0.248095\pi$
$164$	−0.177445	+	0.368469i	−0.0138561	+	0.0287726i
$165$		0			0
$166$	−12.9568	−	10.3327i	−1.00564	−	0.801974i
$167$	1.23842	−	0.596394i	0.0958321	−	0.0461503i	−0.385354	−	0.922769i	$-0.625921\pi$
$167$	1.23842	−	0.596394i	0.0958321	−	0.0461503i	0.481186	+	0.876619i	$0.340206\pi$
$168$		0			0
$169$	−2.25696	+	9.88838i	−0.173612	+	0.760645i
$170$	1.98291	+	0.954918i	0.152082	+	0.0732389i
$171$		0			0
$172$	−2.13958	−	0.488346i	−0.163142	−	0.0372360i
$173$	13.2857			1.01009			0.505045	−	0.863093i	$-0.331476\pi$
$173$	13.2857			1.01009			0.505045	+	0.863093i	$0.331476\pi$
$174$		0			0
$175$	5.40015			0.408213
$176$	−2.47018	−	0.563802i	−0.186197	−	0.0424982i
$177$		0			0
$178$	−9.72273	−	4.68222i	−0.728750	−	0.350947i
$179$	−1.36940	+	5.99973i	−0.102354	+	0.448441i	0.897617	+	0.440777i	$0.145297\pi$
$179$	−1.36940	+	5.99973i	−0.102354	+	0.448441i	−0.999971	+	0.00766454i	$0.997560\pi$
$180$		0			0
$181$	−21.7247	+	10.4620i	−1.61478	+	0.777638i	−0.999939	−	0.0110120i	$-0.996495\pi$
$181$	−21.7247	+	10.4620i	−1.61478	+	0.777638i	−0.614842	+	0.788650i	$0.710780\pi$
$182$	5.40446	+	4.30991i	0.400605	+	0.319472i
$183$		0			0
$184$	1.83999	−	3.82077i	0.135645	−	0.281671i
$185$	0.456829	−	0.364309i	0.0335868	−	0.0267845i
$186$		0			0
$187$	−2.48223	−	3.11262i	−0.181519	−	0.227617i
$188$	0.134558	−	0.0307119i	0.00981363	−	0.00223990i
$189$		0			0
$190$	1.10813	+	1.38955i	0.0803923	+	0.100809i
$191$			5.15567i			0.373051i	0.982450	+	0.186526i	$0.0597228\pi$
$191$			5.15567i			0.373051i	−0.982450	+	0.186526i	$0.940277\pi$
$192$		0			0
$193$	−1.20357	+	2.49924i	−0.0866349	+	0.179899i	−0.939785	−	0.341766i	$-0.888975\pi$
$193$	−1.20357	+	2.49924i	−0.0866349	+	0.179899i	0.853150	+	0.521666i	$0.174689\pi$
$194$	1.25509	−	1.57383i	0.0901100	−	0.112994i
$195$		0			0
$196$	1.58592	−	0.763737i	0.113280	−	0.0545526i
$197$	5.49393	+	24.0705i	0.391426	+	1.71495i	0.659631	+	0.751589i	$0.270712\pi$
$197$	5.49393	+	24.0705i	0.391426	+	1.71495i	−0.268205	+	0.963362i	$0.586430\pi$
$198$		0			0
$199$	4.73656	+	2.28101i	0.335766	+	0.161696i	0.594168	−	0.804341i	$-0.297482\pi$
$199$	4.73656	+	2.28101i	0.335766	+	0.161696i	−0.258402	+	0.966038i	$0.583196\pi$
$200$	6.37129	+	13.2301i	0.450518	+	0.935511i
$201$		0			0
$202$	21.0455			1.48076
$203$	−2.17199	−	5.53138i	−0.152444	−	0.388227i
$204$		0			0
$205$	−0.427123	−	0.0974881i	−0.0298316	−	0.00680886i
$206$	6.18756	+	12.8486i	0.431108	+	0.895204i
$207$		0			0
$208$	−3.53096	+	15.4702i	−0.244828	+	1.07266i
$209$	−0.715407	−	3.13440i	−0.0494857	−	0.216811i
$210$		0			0
$211$	18.9222	+	15.0899i	1.30266	+	1.03883i	0.996213	+	0.0869434i	$0.0277099\pi$
$211$	18.9222	+	15.0899i	1.30266	+	1.03883i	0.306442	+	0.951889i	$0.400862\pi$
$212$	1.67568	−	2.10124i	0.115086	−	0.144314i
$213$		0			0
$214$	−12.7354	+	10.1561i	−0.870573	+	0.694259i
$215$		−	2.35097i		−	0.160335i
$216$		0			0
$217$	−4.85820	+	1.10885i	−0.329796	+	0.0752738i
$218$	−11.1742	+	2.55045i	−0.756816	+	0.172738i
$219$		0			0
$220$			0.0762557i			0.00514116i
$221$	−19.4936	+	15.5456i	−1.31128	+	1.04571i
$222$		0			0
$223$	0.757116	−	0.949394i	0.0507003	−	0.0635761i	−0.755835	−	0.654762i	$-0.772769\pi$
$223$	0.757116	−	0.949394i	0.0507003	−	0.0635761i	0.806535	+	0.591186i	$0.201340\pi$
$224$	−1.47208	−	1.17394i	−0.0983573	−	0.0784374i
$225$		0			0
$226$	−0.713222	−	3.12483i	−0.0474428	−	0.207861i
$227$	3.55503	−	15.5756i	0.235956	−	1.03379i	−0.708645	−	0.705566i	$-0.750693\pi$
$227$	3.55503	−	15.5756i	0.235956	−	1.03379i	0.944600	−	0.328223i	$-0.106450\pi$
$228$		0			0
$229$	6.65454	+	13.8183i	0.439745	+	0.913139i	0.996589	+	0.0825223i	$0.0262976\pi$
$229$	6.65454	+	13.8183i	0.439745	+	0.913139i	−0.556845	+	0.830617i	$0.687988\pi$
$230$	0.585077	+	0.133540i	0.0385788	+	0.00880537i
$231$		0			0
$232$	10.9890	−	11.8474i	0.721465	−	0.777820i
$233$	−12.9851			−0.850684			−0.425342	−	0.905033i	$-0.639846\pi$
$233$	−12.9851			−0.850684			−0.425342	+	0.905033i	$0.639846\pi$
$234$		0			0
$235$	0.0641504	+	0.133210i	0.00418471	+	0.00868964i
$236$	1.00781	+	0.485336i	0.0656029	+	0.0315927i
$237$		0			0
$238$	1.65720	+	7.26068i	0.107420	+	0.470640i
$239$	0.229801	−	0.110667i	0.0148646	−	0.00715842i	−0.426437	−	0.904517i	$-0.640231\pi$
$239$	0.229801	−	0.110667i	0.0148646	−	0.00715842i	0.441301	+	0.897359i	$0.354517\pi$
$240$		0			0
$241$	−5.23484	+	6.56429i	−0.337206	+	0.422843i	−0.921306	−	0.388839i	$-0.872876\pi$
$241$	−5.23484	+	6.56429i	−0.337206	+	0.422843i	0.584100	+	0.811682i	$0.301448\pi$
$242$	5.88141	−	12.2129i	0.378072	−	0.785074i
$243$		0			0
$244$		−	2.69246i		−	0.172367i
$245$	1.17568	+	1.47426i	0.0751115	+	0.0941869i
$246$		0			0
$247$	−19.6300	+	4.48043i	−1.24903	+	0.285083i
$248$	−8.44851	−	10.5941i	−0.536481	−	0.672726i
$249$		0			0
$250$	−3.28466	+	2.61943i	−0.207740	+	0.165667i
$251$	8.09013	−	16.7993i	0.510644	−	1.06036i	−0.473136	−	0.880989i	$-0.656878\pi$
$251$	8.09013	−	16.7993i	0.510644	−	1.06036i	0.983781	−	0.179375i	$-0.0574075\pi$
$252$		0			0
$253$	−0.848739	−	0.676846i	−0.0533597	−	0.0425530i
$254$	−17.9094	+	8.62471i	−1.12374	+	0.541163i
$255$		0			0
$256$	1.58617	−	6.94947i	0.0991357	−	0.434342i
$257$	22.1806	+	10.6816i	1.38359	+	0.666301i	0.969762	−	0.244054i	$-0.0784775\pi$
$257$	22.1806	+	10.6816i	1.38359	+	0.666301i	0.413827	+	0.910355i	$0.364192\pi$
$258$		0			0
$259$	1.92764	+	0.439971i	0.119778	+	0.0273384i
$260$	0.477572			0.0296177
$261$		0			0
$262$	11.3841			0.703310
$263$	−9.91282	−	2.26254i	−0.611251	−	0.139514i	−0.0943210	−	0.995542i	$-0.530068\pi$
$263$	−9.91282	−	2.26254i	−0.611251	−	0.139514i	−0.516930	+	0.856028i	$0.672925\pi$
$264$		0			0
$265$	2.59396	+	1.24918i	0.159345	+	0.0767367i
$266$	−1.33827	+	5.86336i	−0.0820548	+	0.359505i
$267$		0			0
$268$	−4.18584	+	2.01580i	−0.255691	+	0.123134i
$269$	−0.522286	−	0.416509i	−0.0318444	−	0.0253950i	0.607438	−	0.794367i	$-0.292197\pi$
$269$	−0.522286	−	0.416509i	−0.0318444	−	0.0253950i	−0.639283	+	0.768972i	$0.720769\pi$
$270$		0			0
$271$	−4.03127	+	8.37102i	−0.244882	+	0.508504i	−0.986791	−	0.161997i	$-0.948206\pi$
$271$	−4.03127	+	8.37102i	−0.244882	+	0.508504i	0.741909	+	0.670501i	$0.233921\pi$
$272$	−13.3660	+	10.6590i	−0.810432	+	0.646298i
$273$		0			0
$274$	18.9169	+	23.7211i	1.14281	+	1.43304i
$275$	3.66477	−	0.836459i	0.220994	−	0.0504404i
$276$		0			0
$277$	−9.19224	−	11.5267i	−0.552308	−	0.692572i	0.424807	−	0.905284i	$-0.360342\pi$
$277$	−9.19224	−	11.5267i	−0.552308	−	0.692572i	−0.977115	+	0.212712i	$0.931770\pi$
$278$		−	17.6169i		−	1.05659i
$279$		0			0
$280$	0.468520	−	0.972891i	0.0279994	−	0.0581414i
$281$	13.4220	−	16.8307i	0.800690	−	1.00403i	−0.199021	−	0.979995i	$-0.563776\pi$
$281$	13.4220	−	16.8307i	0.800690	−	1.00403i	0.999711	−	0.0240385i	$-0.00765244\pi$
$282$		0			0
$283$	9.29893	−	4.47813i	0.552764	−	0.266197i	−0.136583	−	0.990629i	$-0.543612\pi$
$283$	9.29893	−	4.47813i	0.552764	−	0.266197i	0.689347	+	0.724431i	$0.257898\pi$
$284$	−1.01880	−	4.46363i	−0.0604544	−	0.264868i
$285$		0			0
$286$	4.33527	+	2.08776i	0.256350	+	0.123452i
$287$	−0.643229	−	1.33568i	−0.0379686	−	0.0788427i
$288$		0			0
$289$	−9.86239			−0.580141
$290$	1.98058	+	1.14304i	0.116304	+	0.0671216i
$291$		0			0
$292$	4.06638	+	0.928124i	0.237967	+	0.0543144i
$293$	10.9372	+	22.7113i	0.638958	+	1.32681i	0.929101	+	0.369826i	$0.120583\pi$
$293$	10.9372	+	22.7113i	0.638958	+	1.32681i	−0.290143	+	0.956983i	$0.593703\pi$
$294$		0			0
$295$	−0.266643	+	1.16824i	−0.0155246	+	0.0680175i
$296$	1.19639	+	5.24171i	0.0695385	+	0.304668i
$297$		0			0
$298$	−1.35092	−	1.07732i	−0.0782566	−	0.0624075i
$299$	−4.23893	+	5.31545i	−0.245144	+	0.307401i
$300$		0			0
$301$	6.21973	−	4.96007i	0.358499	−	0.285894i
$302$		−	18.7121i		−	1.07676i
$303$		0			0
$304$	−13.4595	+	3.07205i	−0.771956	+	0.176194i
$305$	2.81198	−	0.641816i	0.161013	−	0.0367503i
$306$		0			0
$307$		−	17.7845i		−	1.01502i	−0.861647	−	0.507508i	$-0.830567\pi$
$307$		−	17.7845i		−	1.01502i	0.861647	−	0.507508i	$-0.169433\pi$
$308$	−0.201743	+	0.160884i	−0.0114953	+	0.00916723i
$309$		0			0
$310$	1.19558	−	1.49921i	0.0679045	−	0.0851496i
$311$	−6.56620	−	5.23637i	−0.372335	−	0.296927i	0.419388	−	0.907807i	$-0.362245\pi$
$311$	−6.56620	−	5.23637i	−0.372335	−	0.296927i	−0.791724	+	0.610880i	$0.790816\pi$
$312$		0			0
$313$	0.467343	+	2.04756i	0.0264158	+	0.115735i	0.986417	−	0.164261i	$-0.0525239\pi$
$313$	0.467343	+	2.04756i	0.0264158	+	0.115735i	−0.960001	+	0.279996i	$0.909667\pi$
$314$	−3.82276	+	16.7486i	−0.215731	+	0.945179i
$315$		0			0
$316$	0.770877	+	1.60074i	0.0433652	+	0.0900489i
$317$	−4.90180	−	1.11880i	−0.275312	−	0.0628382i	0.0826355	−	0.996580i	$-0.473666\pi$
$317$	−4.90180	−	1.11880i	−0.275312	−	0.0628382i	−0.357948	+	0.933742i	$0.616523\pi$
$318$		0			0
$319$	−2.33079	−	3.41739i	−0.130499	−	0.191337i
$320$	2.87587			0.160766
$321$		0			0
$322$	0.881101	+	1.82963i	0.0491018	+	0.101961i
$323$	−19.5445	−	9.41212i	−1.08748	−	0.523704i
$324$		0			0
$325$	−5.23855	−	22.9516i	−0.290582	−	1.27312i
$326$	−3.53221	+	1.70102i	−0.195631	+	0.0942108i
$327$		0			0
$328$	2.51345	−	3.15176i	0.138782	−	0.174027i
$329$	−0.217076	+	0.450762i	−0.0119678	+	0.0248513i
$330$		0			0
$331$		−	3.80922i		−	0.209374i	−0.994505	−	0.104687i	$-0.966616\pi$
$331$		−	3.80922i		−	0.209374i	0.994505	−	0.104687i	$-0.0333840\pi$
$332$	−2.41560	−	3.02907i	−0.132574	−	0.166242i
$333$		0			0
$334$	−1.74498	+	0.398281i	−0.0954813	+	0.0217930i
$335$	−3.10308	−	3.89113i	−0.169539	−	0.212595i
$336$		0			0
$337$	−1.18125	+	0.942012i	−0.0643466	+	0.0513147i	−0.655135	−	0.755512i	$-0.727388\pi$
$337$	−1.18125	+	0.942012i	−0.0643466	+	0.0513147i	0.590788	+	0.806827i	$0.298817\pi$
$338$	5.73041	−	11.8993i	0.311693	−	0.647237i
$339$		0			0
$340$	0.402270	+	0.320799i	0.0218161	+	0.0173978i
$341$	−3.12522	+	1.50503i	−0.169240	+	0.0815017i
$342$		0			0
$343$	−3.13872	+	13.7516i	−0.169475	+	0.742518i
$344$	19.4902	+	9.38598i	1.05084	+	0.506058i
$345$		0			0
$346$	−16.8661	−	3.84958i	−0.906729	−	0.206955i
$347$	23.3601			1.25404			0.627019	−	0.779004i	$-0.284275\pi$
$347$	23.3601			1.25404			0.627019	+	0.779004i	$0.284275\pi$
$348$		0			0
$349$	−15.0240			−0.804216			−0.402108	−	0.915592i	$-0.631722\pi$
$349$	−15.0240			−0.804216			−0.402108	+	0.915592i	$0.631722\pi$
$350$	−6.85548	−	1.56472i	−0.366441	−	0.0836377i
$351$		0			0
$352$	−1.18085	−	0.568668i	−0.0629396	−	0.0303101i
$353$	−3.57377	+	15.6577i	−0.190213	+	0.833377i	0.786288	+	0.617861i	$0.212000\pi$
$353$	−3.57377	+	15.6577i	−0.190213	+	0.833377i	−0.976500	+	0.215516i	$0.930857\pi$
$354$		0			0
$355$	4.41892	−	2.12804i	0.234532	−	0.112945i
$356$	−1.97244	−	1.57297i	−0.104539	−	0.0833671i
$357$		0			0
$358$	3.47690	−	7.21986i	0.183760	−	0.381581i
$359$	20.7505	−	16.5480i	1.09517	−	0.873370i	0.102562	−	0.994727i	$-0.467296\pi$
$359$	20.7505	−	16.5480i	1.09517	−	0.873370i	0.992609	+	0.121357i	$0.0387246\pi$
$360$		0			0
$361$	0.924048	+	1.15872i	0.0486341	+	0.0609852i
$362$	30.6108	−	6.98672i	1.60887	−	0.367214i
$363$		0			0
$364$	1.00758	+	1.26347i	0.0528116	+	0.0662236i
$365$			4.46812i			0.233872i
$366$		0			0
$367$	7.37679	−	15.3181i	0.385065	−	0.799597i	−0.614874	−	0.788625i	$-0.710793\pi$
$367$	7.37679	−	15.3181i	0.385065	−	0.799597i	0.999940	−	0.0109716i	$-0.00349242\pi$
$368$	−2.90646	+	3.64459i	−0.151510	+	0.189987i
$369$		0			0
$370$	−0.685504	+	0.330121i	−0.0356377	+	0.0171622i
$371$	2.16788	+	9.49811i	0.112551	+	0.493117i
$372$		0			0
$373$	10.5705	+	5.09050i	0.547322	+	0.263576i	0.687046	−	0.726614i	$-0.258907\pi$
$373$	10.5705	+	5.09050i	0.547322	+	0.263576i	−0.139724	+	0.990190i	$0.544622\pi$
$374$	2.24929	+	4.67070i	0.116308	+	0.241516i
$375$		0			0
$376$	−1.36046			−0.0701604
$377$	−21.4023	+	14.5972i	−1.10228	+	0.751794i
$378$		0			0
$379$	−7.51780	−	1.71589i	−0.386163	−	0.0881392i	0.0250318	−	0.999687i	$-0.492031\pi$
$379$	−7.51780	−	1.71589i	−0.386163	−	0.0881392i	−0.411195	+	0.911547i	$0.634888\pi$
$380$	0.180280	+	0.374355i	0.00924815	+	0.0192040i
$381$		0			0
$382$	1.49388	−	6.54511i	0.0764335	−	0.334877i
$383$	3.92927	+	17.2153i	0.200776	+	0.879659i	0.970466	+	0.241240i	$0.0775541\pi$
$383$	3.92927	+	17.2153i	0.200776	+	0.879659i	−0.769689	+	0.638419i	$0.779589\pi$
$384$		0			0
$385$	−0.216116	−	0.172347i	−0.0110143	−	0.00878361i
$386$	2.25210	−	2.82404i	0.114629	−	0.143740i
$387$		0			0
$388$	0.367933	−	0.293417i	0.0186790	−	0.0148960i
$389$		−	17.4066i		−	0.882550i	−0.897372	−	0.441275i	$-0.854526\pi$
$389$		−	17.4066i		−	0.882550i	0.897372	−	0.441275i	$-0.145474\pi$
$390$		0			0
$391$	−7.14110	+	1.62991i	−0.361141	+	0.0824281i
$392$	−16.9158	+	3.86092i	−0.854377	+	0.195006i
$393$		0			0
$394$		−	32.1493i		−	1.61966i
$395$	−1.48804	+	1.18667i	−0.0748715	+	0.0597080i
$396$		0			0
$397$	5.44605	−	6.82914i	0.273330	−	0.342744i	−0.626154	−	0.779700i	$-0.715372\pi$
$397$	5.44605	−	6.82914i	0.273330	−	0.342744i	0.899483	+	0.436955i	$0.143943\pi$
$398$	−5.35212	−	4.26817i	−0.268278	−	0.213944i
$399$		0			0
$400$	−3.59186	−	15.7370i	−0.179593	−	0.786849i
$401$	2.21564	−	9.70733i	0.110644	−	0.484761i	−0.888996	−	0.457915i	$-0.848596\pi$
$401$	2.21564	−	9.70733i	0.110644	−	0.484761i	0.999640	−	0.0268462i	$-0.00854643\pi$
$402$		0			0
$403$	9.42562	+	19.5725i	0.469524	+	0.974976i
$404$	4.79671	+	1.09482i	0.238645	+	0.0544693i
$405$		0			0
$406$	1.15460	+	7.65142i	0.0573016	+	0.379734i
$407$	1.37632			0.0682218
$408$		0			0
$409$	−8.84673	−	18.3704i	−0.437443	−	0.908359i	−0.996838	−	0.0794584i	$-0.974681\pi$
$409$	−8.84673	−	18.3704i	−0.437443	−	0.908359i	0.559395	−	0.828901i	$-0.311033\pi$
$410$	0.513984	+	0.247522i	0.0253839	+	0.0122242i
$411$		0			0
$412$	0.741871	+	3.25035i	0.0365494	+	0.160133i
$413$	−3.65326	+	1.75932i	−0.179765	+	0.0865704i
$414$		0			0
$415$	2.58771	−	3.24489i	0.127026	−	0.159285i
$416$	−3.56143	+	7.39540i	−0.174614	+	0.362589i
$417$		0			0
$418$			4.18641i			0.204764i
$419$	22.7123	+	28.4803i	1.10957	+	1.39135i	0.911567	+	0.411153i	$0.134874\pi$
$419$	22.7123	+	28.4803i	1.10957	+	1.39135i	0.198002	+	0.980202i	$0.436555\pi$
$420$		0			0
$421$	19.3547	−	4.41759i	0.943292	−	0.215300i	0.276897	−	0.960900i	$-0.410694\pi$
$421$	19.3547	−	4.41759i	0.943292	−	0.215300i	0.666394	+	0.745599i	$0.267837\pi$
$422$	−19.6493	−	24.6394i	−0.956511	−	1.19943i
$423$		0			0
$424$	−20.7122	+	16.5174i	−1.00587	+	0.802156i
$425$	11.0047	−	22.8515i	0.533807	−	1.10846i
$426$		0			0
$427$	7.63071	+	6.08528i	0.369276	+	0.294488i
$428$	−3.43100	+	1.65228i	−0.165844	+	0.0798660i
$429$		0			0
$430$	−0.681203	+	2.98455i	−0.0328505	+	0.143928i
$431$	−32.2188	−	15.5158i	−1.55193	−	0.747369i	−0.555475	−	0.831533i	$-0.687464\pi$
$431$	−32.2188	−	15.5158i	−1.55193	−	0.747369i	−0.996452	+	0.0841645i	$0.973178\pi$
$432$		0			0
$433$	36.6041	+	8.35464i	1.75908	+	0.401498i	0.975536	−	0.219839i	$-0.0705532\pi$
$433$	36.6041	+	8.35464i	1.75908	+	0.401498i	0.783543	+	0.621337i	$0.213410\pi$
$434$	6.48877			0.311471
$435$		0			0
$436$	−2.67952			−0.128326
$437$	−5.76679	−	1.31623i	−0.275863	−	0.0629639i
$438$		0			0
$439$	6.21349	+	2.99226i	0.296554	+	0.142813i	0.576244	−	0.817277i	$-0.304518\pi$
$439$	6.21349	+	2.99226i	0.296554	+	0.142813i	−0.279691	+	0.960090i	$0.590232\pi$
$440$	0.167260	−	0.732815i	0.00797382	−	0.0349356i
$441$		0			0
$442$	29.2515	−	14.0868i	1.39135	−	0.670040i
$443$	10.8106	+	8.62118i	0.513628	+	0.409605i	0.845707	−	0.533647i	$-0.179179\pi$
$443$	10.8106	+	8.62118i	0.513628	+	0.409605i	−0.332080	+	0.943251i	$0.607750\pi$
$444$		0			0
$445$	1.17261	−	2.43495i	0.0555870	−	0.115428i
$446$	−1.23625	+	0.985875i	−0.0585381	+	0.0466826i
$447$		0			0
$448$	6.06751	+	7.60842i	0.286663	+	0.359464i
$449$	−19.5253	+	4.45651i	−0.921454	+	0.210316i	−0.656833	−	0.754036i	$-0.728104\pi$
$449$	−19.5253	+	4.45651i	−0.921454	+	0.210316i	−0.264622	+	0.964352i	$0.585247\pi$
$450$		0			0
$451$	−0.643413	−	0.806814i	−0.0302971	−	0.0379914i
$452$		−	0.749317i		−	0.0352449i
$453$		0			0
$454$	−9.02620	+	18.7431i	−0.423621	+	0.879657i
$455$	−1.07937	+	1.35349i	−0.0506016	+	0.0634524i
$456$		0			0
$457$	−22.0357	+	10.6119i	−1.03079	+	0.496402i	−0.871276	−	0.490794i	$-0.836707\pi$
$457$	−22.0357	+	10.6119i	−1.03079	+	0.496402i	−0.159513	+	0.987196i	$0.550992\pi$
$458$	−4.44401	−	19.4705i	−0.207655	−	0.909796i
$459$		0			0
$460$	0.126404	+	0.0608731i	0.00589363	+	0.00283822i
$461$	−9.66512	−	20.0698i	−0.450150	−	0.934746i	−0.995339	−	0.0964329i	$-0.969257\pi$
$461$	−9.66512	−	20.0698i	−0.450150	−	0.934746i	0.545190	−	0.838313i	$-0.316458\pi$
$462$		0			0
$463$	−27.5102			−1.27851			−0.639254	−	0.768996i	$-0.720757\pi$
$463$	−27.5102			−1.27851			−0.639254	+	0.768996i	$0.720757\pi$
$464$	−14.6747	+	10.0087i	−0.681257	+	0.464643i
$465$		0			0
$466$	16.4846	+	3.76250i	0.763634	+	0.174294i
$467$	−10.3029	−	21.3941i	−0.476760	−	0.990002i	−0.991187	−	0.132468i	$-0.957710\pi$
$467$	−10.3029	−	21.3941i	−0.476760	−	0.990002i	0.514428	−	0.857534i	$-0.328004\pi$
$468$		0			0
$469$	3.74754	−	16.4190i	0.173045	−	0.758160i
$470$	−0.0428407	−	0.187697i	−0.00197609	−	0.00865783i
$471$		0			0
$472$	−8.62050	−	6.87462i	−0.396791	−	0.316430i
$473$	3.45267	−	4.32951i	0.158754	−	0.199071i
$474$		0			0
$475$	16.0136	−	12.7704i	0.734753	−	0.585946i
$476$			1.74107i			0.0798018i
$477$		0			0
$478$	−0.323798	+	0.0739049i	−0.0148102	+	0.00338033i
$479$	−25.5186	+	5.82446i	−1.16598	+	0.266126i	−0.761341	−	0.648352i	$-0.775459\pi$
$479$	−25.5186	+	5.82446i	−1.16598	+	0.266126i	−0.404635	+	0.914478i	$0.632601\pi$
$480$		0			0
$481$		−	8.61959i		−	0.393020i
$482$	8.54765	−	6.81652i	0.389335	−	0.310484i
$483$		0			0
$484$	1.97583	−	2.47761i	0.0898104	−	0.112619i
$485$	0.394148	+	0.314322i	0.0178973	+	0.0142726i
$486$		0			0
$487$	3.63049	+	15.9062i	0.164513	+	0.720780i	0.988128	+	0.153631i	$0.0490966\pi$
$487$	3.63049	+	15.9062i	0.164513	+	0.720780i	−0.823615	+	0.567149i	$0.808046\pi$
$488$	−5.90569	+	25.8745i	−0.267338	+	1.17128i
$489$		0			0
$490$	−1.06535	−	2.21223i	−0.0481277	−	0.0999382i
$491$	32.0763	+	7.32121i	1.44758	+	0.330402i	0.872870	−	0.487952i	$-0.162256\pi$
$491$	32.0763	+	7.32121i	1.44758	+	0.330402i	0.574714	+	0.818354i	$0.305113\pi$
$492$		0			0
$493$	−27.8331	−	2.08104i	−1.25354	−	0.0937254i
$494$	26.2185			1.17963
$495$		0			0
$496$	6.46277	+	13.4201i	0.290187	+	0.602580i
$497$	14.9530	+	7.20098i	0.670733	+	0.323008i
$498$		0			0
$499$	−4.93194	−	21.6082i	−0.220784	−	0.967317i	−0.956890	−	0.290451i	$-0.906195\pi$
$499$	−4.93194	−	21.6082i	−0.220784	−	0.967317i	0.736106	−	0.676866i	$-0.236662\pi$
$500$	−0.884908	+	0.426149i	−0.0395743	+	0.0190580i
$501$		0			0
$502$	−15.1381	+	18.9825i	−0.675645	+	0.847233i
$503$	17.2581	−	35.8369i	0.769503	−	1.59789i	−0.0317009	−	0.999497i	$-0.510092\pi$
$503$	17.2581	−	35.8369i	0.769503	−	1.59789i	0.801204	−	0.598392i	$-0.204193\pi$
$504$		0			0
$505$			5.27061i			0.234539i
$506$	0.881352	+	1.10518i	0.0391809	+	0.0491313i
$507$		0			0
$508$	−4.53060	+	1.03408i	−0.201013	+	0.0458798i
$509$	6.35541	+	7.96943i	0.281699	+	0.353239i	0.902470	−	0.430753i	$-0.141752\pi$
$509$	6.35541	+	7.96943i	0.281699	+	0.353239i	−0.620771	+	0.783992i	$0.713180\pi$
$510$		0			0
$511$	−11.8209	+	9.42685i	−0.522926	+	0.417019i
$512$	−11.0309	+	22.9058i	−0.487500	+	1.01230i
$513$		0			0
$514$	−25.0632	−	19.9872i	−1.10549	−	0.881599i
$515$	−3.21779	+	1.54960i	−0.141793	+	0.0682837i
$516$		0			0
$517$	−0.0774955	+	0.339530i	−0.00340825	+	0.0149325i
$518$	−2.31965	−	1.11708i	−0.101919	−	0.0490818i
$519$		0			0
$520$	−4.58945	−	1.04751i	−0.201261	−	0.0459365i
$521$	7.09229			0.310719			0.155359	−	0.987858i	$-0.450346\pi$
$521$	7.09229			0.310719			0.155359	+	0.987858i	$0.450346\pi$
$522$		0			0
$523$	10.9937			0.480723			0.240361	−	0.970683i	$-0.422734\pi$
$523$	10.9937			0.480723			0.240361	+	0.970683i	$0.422734\pi$
$524$	2.59467	+	0.592216i	0.113349	+	0.0258711i
$525$		0			0
$526$	11.9287	+	5.74457i	0.520117	+	0.250475i
$527$	−5.20803	+	22.8179i	−0.226865	+	0.993961i
$528$		0			0
$529$	18.9228	−	9.11274i	0.822730	−	0.396206i
$530$	−2.93106	−	2.33745i	−0.127317	−	0.101532i
$531$		0			0
$532$	−0.610041	+	1.26676i	−0.0264486	+	0.0549211i
$533$	−5.05289	+	4.02954i	−0.218865	+	0.174539i
$534$		0			0
$535$	−2.54349	−	3.18943i	−0.109965	−	0.137891i
$536$	44.6473	−	10.1905i	1.92847	−	0.440161i
$537$		0			0
$538$	0.542356	+	0.680093i	0.0233826	+	0.0293209i
$539$			4.44161i			0.191314i
$540$		0			0
$541$	−2.09471	+	4.34971i	−0.0900586	+	0.187009i	−0.941133	−	0.338037i	$-0.890237\pi$
$541$	−2.09471	+	4.34971i	−0.0900586	+	0.187009i	0.851074	+	0.525045i	$0.175952\pi$
$542$	7.54323	−	9.45892i	0.324010	−	0.406295i
$543$		0			0
$544$	−7.96759	+	3.83699i	−0.341608	+	0.164510i
$545$	−0.638731	−	2.79847i	−0.0273602	−	0.119873i
$546$		0			0
$547$	30.9219	+	14.8912i	1.32212	+	0.636701i	0.955864	−	0.293811i	$-0.0949236\pi$
$547$	30.9219	+	14.8912i	1.32212	+	0.636701i	0.366261	+	0.930512i	$0.380638\pi$
$548$	3.07756	+	6.39062i	0.131467	+	0.272994i
$549$		0			0
$550$	−4.89478			−0.208714
$551$	−19.5215	−	11.2663i	−0.831645	−	0.479962i
$552$		0			0
$553$	−6.27894	−	1.43313i	−0.267008	−	0.0609428i
$554$	8.32961	+	17.2966i	0.353891	+	0.734862i
$555$		0			0
$556$	0.916459	−	4.01527i	0.0388665	−	0.170285i
$557$	2.97941	+	13.0536i	0.126242	+	0.553101i	0.998003	+	0.0631697i	$0.0201209\pi$
$557$	2.97941	+	13.0536i	0.126242	+	0.553101i	−0.871761	+	0.489931i	$0.837022\pi$
$558$		0			0
$559$	−27.1147	−	21.6233i	−1.14683	−	0.914568i
$560$	−0.740080	+	0.928031i	−0.0312741	+	0.0392165i
$561$		0			0
$562$	−21.9160	+	17.4774i	−0.924470	+	0.737240i
$563$			1.89811i			0.0799960i	0.999200	+	0.0399980i	$0.0127352\pi$
$563$			1.89811i			0.0799960i	−0.999200	+	0.0399980i	$0.987265\pi$
$564$		0			0
$565$	0.782578	−	0.178618i	0.0329233	−	0.00751453i
$566$	−13.1025	+	2.99057i	−0.550741	+	0.125703i
$567$		0			0
$568$			45.1301i			1.89362i
$569$	8.72457	−	6.95761i	0.365753	−	0.291678i	−0.423317	−	0.905982i	$-0.639134\pi$
$569$	8.72457	−	6.95761i	0.365753	−	0.291678i	0.789070	+	0.614303i	$0.210563\pi$
$570$		0			0
$571$	−8.23671	+	10.3285i	−0.344696	+	0.432235i	−0.923716	−	0.383079i	$-0.874864\pi$
$571$	−8.23671	+	10.3285i	−0.344696	+	0.432235i	0.579020	+	0.815313i	$0.303435\pi$
$572$	0.879491	+	0.701371i	0.0367734	+	0.0293258i
$573$		0			0
$574$	0.429559	+	1.88202i	0.0179294	+	0.0785540i
$575$	1.53895	−	6.74258i	0.0641786	−	0.281185i
$576$		0			0
$577$	6.01524	+	12.4908i	0.250418	+	0.519998i	0.987848	−	0.155426i	$-0.0496750\pi$
$577$	6.01524	+	12.4908i	0.250418	+	0.519998i	−0.737430	+	0.675424i	$0.763961\pi$
$578$	12.5203	+	2.85767i	0.520775	+	0.118864i
$579$		0			0
$580$	0.391953	+	0.363555i	0.0162750	+	0.0150958i
$581$	14.0442			0.582653
$582$		0			0
$583$	2.94243	+	6.11001i	0.121863	+	0.253051i
$584$	−37.0420	−	17.8385i	−1.53281	−	0.738163i
$585$		0			0
$586$	−7.30403	−	32.0011i	−0.301727	−	1.32195i
$587$	−25.0371	+	12.0572i	−1.03339	+	0.497655i	−0.872139	−	0.489258i	$-0.837268\pi$
$587$	−25.0371	+	12.0572i	−1.03339	+	0.497655i	−0.161253	+	0.986913i	$0.551553\pi$
$588$		0			0
$589$	−11.7842	+	14.7769i	−0.485560	+	0.608873i
$590$	0.677005	−	1.40582i	0.0278719	−	0.0578765i
$591$		0			0
$592$		−	5.91011i		−	0.242904i
$593$	−5.03568	−	6.31455i	−0.206791	−	0.259307i	0.667611	−	0.744511i	$-0.267317\pi$
$593$	−5.03568	−	6.31455i	−0.206791	−	0.259307i	−0.874401	+	0.485203i	$0.838746\pi$
$594$		0			0
$595$	−1.81835	+	0.415028i	−0.0745453	+	0.0170145i
$596$	−0.251859	−	0.315821i	−0.0103165	−	0.0129365i
$597$		0			0
$598$	6.92149	−	5.51970i	0.283041	−	0.225717i
$599$	−8.35658	+	17.3526i	−0.341440	+	0.709008i	−0.999015	−	0.0443814i	$-0.985868\pi$
$599$	−8.35658	+	17.3526i	−0.341440	+	0.709008i	0.657574	+	0.753390i	$0.271583\pi$
$600$		0			0
$601$	17.3000	+	13.7963i	0.705681	+	0.562762i	0.909226	−	0.416304i	$-0.136675\pi$
$601$	17.3000	+	13.7963i	0.705681	+	0.562762i	−0.203544	+	0.979066i	$0.565246\pi$
$602$	−9.33313	+	4.49460i	−0.380390	+	0.183186i
$603$		0			0
$604$	0.973432	−	4.26488i	0.0396084	−	0.173536i
$605$	3.05858	+	1.47293i	0.124349	+	0.0598833i
$606$		0			0
$607$	11.5672	+	2.64014i	0.469499	+	0.107160i	0.450723	−	0.892664i	$-0.351166\pi$
$607$	11.5672	+	2.64014i	0.469499	+	0.107160i	0.0187755	+	0.999824i	$0.494023\pi$
$608$	−7.14145			−0.289624
$609$		0			0
$610$	−3.75577			−0.152067
$611$	2.12640	+	0.485336i	0.0860248	+	0.0196346i
$612$		0			0
$613$	30.4811	+	14.6789i	1.23112	+	0.592876i	0.932387	−	0.361461i	$-0.117722\pi$
$613$	30.4811	+	14.6789i	1.23112	+	0.592876i	0.298733	+	0.954337i	$0.403436\pi$
$614$	−5.15314	+	22.5774i	−0.207964	+	0.911150i
$615$		0			0
$616$	2.29163	−	1.10359i	0.0923323	−	0.0444649i
$617$	−1.32047	−	1.05304i	−0.0531601	−	0.0423938i	0.596549	−	0.802576i	$-0.296538\pi$
$617$	−1.32047	−	1.05304i	−0.0531601	−	0.0423938i	−0.649709	+	0.760183i	$0.725109\pi$
$618$		0			0
$619$	−6.73642	+	13.9883i	−0.270759	+	0.562238i	−0.991369	−	0.131104i	$-0.958148\pi$
$619$	−6.73642	+	13.9883i	−0.270759	+	0.562238i	0.720609	+	0.693341i	$0.243862\pi$
$620$	0.350489	−	0.279506i	0.0140760	−	0.0112252i
$621$		0			0
$622$	6.81851	+	8.55014i	0.273397	+	0.342830i
$623$	8.91589	−	2.03499i	0.357208	−	0.0815303i
$624$		0			0
$625$	14.5997	+	18.3075i	0.583988	+	0.732298i
$626$		−	2.73479i		−	0.109304i
$627$		0			0
$628$	−1.74257	+	3.61849i	−0.0695363	+	0.144394i
$629$	5.79004	−	7.26048i	0.230864	−	0.289494i
$630$		0			0
$631$	−16.5425	+	7.96642i	−0.658545	+	0.317138i	−0.733142	−	0.680075i	$-0.761947\pi$
$631$	−16.5425	+	7.96642i	−0.658545	+	0.317138i	0.0745977	+	0.997214i	$0.476233\pi$
$632$	−3.89702	−	17.0740i	−0.155015	−	0.679166i
$633$		0			0
$634$	5.89864	+	2.84064i	0.234265	+	0.112816i
$635$	−2.15996	−	4.48521i	−0.0857155	−	0.177990i
$636$		0			0
$637$	27.8167			1.10214
$638$	1.96873	+	5.01373i	0.0779426	+	0.198495i
$639$		0			0
$640$	−2.56597	−	0.585665i	−0.101429	−	0.0231504i
$641$	−2.23437	−	4.63971i	−0.0882522	−	0.183258i	0.852171	−	0.523263i	$-0.175285\pi$
$641$	−2.23437	−	4.63971i	−0.0882522	−	0.183258i	−0.940424	+	0.340005i	$0.889571\pi$
$642$		0			0
$643$	6.29062	−	27.5610i	0.248078	−	1.08690i	−0.685372	−	0.728193i	$-0.740361\pi$
$643$	6.29062	−	27.5610i	0.248078	−	1.08690i	0.933450	−	0.358707i	$-0.116782\pi$
$644$	0.105642	+	0.462846i	0.00416286	+	0.0182387i
$645$		0			0
$646$	22.0844	+	17.6118i	0.868901	+	0.692925i
$647$	−17.6767	+	22.1659i	−0.694943	+	0.871431i	−0.996634	−	0.0819746i	$-0.973877\pi$
$647$	−17.6767	+	22.1659i	−0.694943	+	0.871431i	0.301691	+	0.953406i	$0.402449\pi$
$648$		0			0
$649$	−2.20674	+	1.75982i	−0.0866223	+	0.0690790i
$650$			30.6549i			1.20238i
$651$		0			0
$652$	−0.893553	+	0.203948i	−0.0349942	+	0.00798721i
$653$	−39.3129	+	8.97291i	−1.53843	+	0.351137i	−0.905932	−	0.423424i	$-0.860828\pi$
$653$	−39.3129	+	8.97291i	−1.53843	+	0.351137i	−0.632500	+	0.774561i	$0.717971\pi$
$654$		0			0
$655$			2.85101i			0.111398i
$656$	−3.46456	+	2.76290i	−0.135268	+	0.107873i
$657$		0			0
$658$	0.406188	−	0.509343i	0.0158348	−	0.0198563i
$659$	38.6554	+	30.8267i	1.50580	+	1.20084i	0.920941	+	0.389701i	$0.127422\pi$
$659$	38.6554	+	30.8267i	1.50580	+	1.20084i	0.584859	+	0.811135i	$0.301150\pi$
$660$		0			0
$661$	−3.53346	−	15.4811i	−0.137436	−	0.602146i	−0.995993	−	0.0894282i	$-0.971496\pi$
$661$	−3.53346	−	15.4811i	−0.137436	−	0.602146i	0.858557	−	0.512717i	$-0.171361\pi$
$662$	−1.10374	+	4.83579i	−0.0428980	+	0.187949i
$663$		0			0
$664$	16.5699	+	34.4077i	0.643036	+	1.33528i
$665$	−1.46841	−	0.335155i	−0.0569426	−	0.0129968i
$666$		0			0
$667$	−7.52541	+	1.13558i	−0.291385	+	0.0439699i
$668$	−0.418437			−0.0161898
$669$		0			0
$670$	2.81187	+	5.83892i	0.108632	+	0.225577i
$671$	6.12109	+	2.94776i	0.236302	+	0.113797i
$672$		0			0
$673$	−2.60304	−	11.4047i	−0.100340	−	0.439617i	−0.999995	−	0.00301712i	$-0.999040\pi$
$673$	−2.60304	−	11.4047i	−0.100340	−	0.439617i	0.899656	−	0.436600i	$-0.143818\pi$
$674$	1.77254	−	0.853611i	0.0682757	−	0.0328799i
$675$		0			0
$676$	1.92510	−	2.41400i	0.0740423	−	0.0928461i
$677$	8.46222	−	17.5720i	0.325230	−	0.675346i	−0.672683	−	0.739931i	$-0.734858\pi$
$677$	8.46222	−	17.5720i	0.325230	−	0.675346i	0.997912	+	0.0645849i	$0.0205723\pi$
$678$		0			0
$679$			1.70592i			0.0654671i
$680$	−3.16216	−	3.96522i	−0.121263	−	0.152059i
$681$		0			0
$682$	4.40354	−	1.00508i	0.168620	−	0.0384865i
$683$	−15.4166	−	19.3318i	−0.589900	−	0.739711i	0.393866	−	0.919168i	$-0.371137\pi$
$683$	−15.4166	−	19.3318i	−0.589900	−	0.739711i	−0.983766	+	0.179457i	$0.942566\pi$
$684$		0			0
$685$	−5.94068	+	4.73753i	−0.226982	+	0.181012i
$686$	7.96919	−	16.5482i	0.304265	−	0.631813i
$687$		0			0
$688$	−18.5915	−	14.8262i	−0.708794	−	0.565244i
$689$	38.2656	−	18.4277i	1.45780	−	0.702041i
$690$		0			0
$691$	10.6279	−	46.5640i	0.404306	−	1.77138i	−0.205324	−	0.978694i	$-0.565825\pi$
$691$	10.6279	−	46.5640i	0.404306	−	1.77138i	0.609630	−	0.792686i	$-0.291318\pi$
$692$	−3.64388	−	1.75480i	−0.138520	−	0.0667075i
$693$		0			0
$694$	−29.6556	−	6.76870i	−1.12571	−	0.256936i
$695$	4.41197			0.167355
$696$		0			0
$697$	−6.96293			−0.263740
$698$	19.0729	+	4.35327i	0.721921	+	0.164774i
$699$		0			0
$700$	−1.48111	−	0.713264i	−0.0559806	−	0.0269588i
$701$	1.81198	−	7.93882i	0.0684377	−	0.299845i	−0.929113	−	0.369797i	$-0.879427\pi$
$701$	1.81198	−	7.93882i	0.0684377	−	0.299845i	0.997550	+	0.0699516i	$0.0222845\pi$
$702$		0			0
$703$	6.75665	−	3.25383i	0.254832	−	0.122721i
$704$	5.29617	+	4.22356i	0.199607	+	0.159181i
$705$		0			0
$706$	9.07379	−	18.8419i	0.341497	−	0.709125i
$707$	−13.9440	+	11.1199i	−0.524417	+	0.418208i
$708$		0			0
$709$	1.10726	+	1.38847i	0.0415842	+	0.0521449i	0.802189	−	0.597071i	$-0.203669\pi$
$709$	1.10726	+	1.38847i	0.0415842	+	0.0521449i	−0.760605	+	0.649215i	$0.775097\pi$
$710$	−6.22641	+	1.42114i	−0.233673	+	0.0533344i
$711$		0			0
$712$	15.5049	+	19.4425i	0.581071	+	0.728640i
$713$			6.38190i			0.239004i
$714$		0			0
$715$	−0.522855	+	1.08572i	−0.0195537	+	0.0406036i
$716$	1.16805	−	1.46468i	0.0436519	−	0.0547378i
$717$		0			0
$718$	−31.1376	+	14.9951i	−1.16204	+	0.559611i
$719$	6.25224	+	27.3929i	0.233169	+	1.02158i	0.946992	+	0.321256i	$0.104105\pi$
$719$	6.25224	+	27.3929i	0.233169	+	1.02158i	−0.713823	+	0.700326i	$0.753038\pi$
$720$		0			0
$721$	−10.8885	−	5.24364i	−0.405510	−	0.195283i
$722$	−0.837332	−	1.73874i	−0.0311623	−	0.0647091i
$723$		0			0
$724$	7.34031			0.272800
$725$	13.1727	−	22.8247i	0.489221	−	0.847689i
$726$		0			0
$727$	−45.8409	−	10.4629i	−1.70015	−	0.388047i	−0.741121	−	0.671372i	$-0.765705\pi$
$727$	−45.8409	−	10.4629i	−1.70015	−	0.388047i	−0.959024	+	0.283325i	$0.908563\pi$
$728$	−6.91152	−	14.3519i	−0.256158	−	0.531918i
$729$		0			0
$730$	1.29466	−	5.67227i	0.0479175	−	0.209940i
$731$	−8.31436	−	36.4276i	−0.307518	−	1.34732i
$732$		0			0
$733$	−24.3427	−	19.4127i	−0.899119	−	0.717023i	0.0605475	−	0.998165i	$-0.480715\pi$
$733$	−24.3427	−	19.4127i	−0.899119	−	0.717023i	−0.959666	+	0.281142i	$0.909287\pi$
$734$	−13.8033	+	17.3088i	−0.509489	+	0.638879i
$735$		0			0
$736$	−1.88529	+	1.50347i	−0.0694927	+	0.0554186i
$737$		−	11.7231i		−	0.431826i
$738$		0			0
$739$	12.3734	−	2.82414i	0.455161	−	0.103888i	0.0112072	−	0.999937i	$-0.496433\pi$
$739$	12.3734	−	2.82414i	0.455161	−	0.103888i	0.443954	+	0.896050i	$0.353575\pi$
$740$	−0.173414	+	0.0395806i	−0.00637483	+	0.00145501i
$741$		0			0
$742$		−	12.6860i		−	0.465717i
$743$	10.7328	−	8.55909i	0.393747	−	0.314002i	−0.406525	−	0.913639i	$-0.633260\pi$
$743$	10.7328	−	8.55909i	0.393747	−	0.314002i	0.800272	+	0.599637i	$0.204688\pi$
$744$		0			0
$745$	0.269803	−	0.338322i	0.00988482	−	0.0123952i
$746$	−11.9443	−	9.52524i	−0.437311	−	0.348744i
$747$		0			0
$748$	0.269684	+	1.18156i	0.00986061	+	0.0432022i
$749$	3.07173	−	13.4581i	0.112239	−	0.491750i
$750$		0			0
$751$	−2.11829	−	4.39867i	−0.0772973	−	0.160510i	0.858739	−	0.512414i	$-0.171249\pi$
$751$	−2.11829	−	4.39867i	−0.0772973	−	0.160510i	−0.936036	+	0.351904i	$0.885534\pi$
$752$	1.45799	+	0.332776i	0.0531672	+	0.0121351i
$753$		0			0
$754$	31.3998	−	12.3297i	1.14351	−	0.449020i
$755$	4.68624			0.170550
$756$		0			0
$757$	−8.84210	−	18.3608i	−0.321372	−	0.667335i	0.676220	−	0.736700i	$-0.263617\pi$
$757$	−8.84210	−	18.3608i	−0.321372	−	0.667335i	−0.997591	+	0.0693651i	$0.977903\pi$
$758$	9.04664	+	4.35663i	0.328589	+	0.158240i
$759$		0			0
$760$	−0.911368	−	3.99297i	−0.0330588	−	0.144840i
$761$	−32.2082	+	15.5107i	−1.16755	+	0.562261i	−0.914259	−	0.405130i	$-0.867226\pi$
$761$	−32.2082	+	15.5107i	−1.16755	+	0.562261i	−0.253288	+	0.967391i	$0.581512\pi$
$762$		0			0
$763$	6.05604	−	7.59403i	0.219243	−	0.274922i
$764$	0.680973	−	1.41405i	0.0246367	−	0.0511587i
$765$		0			0
$766$		−	22.9933i		−	0.830780i
$767$	11.0213	+	13.8203i	0.397958	+	0.499023i
$768$		0			0
$769$	22.6272	−	5.16452i	0.815959	−	0.186237i	0.205879	−	0.978577i	$-0.433995\pi$
$769$	22.6272	−	5.16452i	0.815959	−	0.186237i	0.610080	+	0.792340i	$0.291137\pi$
$770$	0.224421	+	0.281415i	0.00808756	+	0.0101415i
$771$		0			0
$772$	0.660210	−	0.526500i	0.0237615	−	0.0189492i
$773$	18.5344	−	38.4871i	0.666636	−	1.38428i	−0.243470	−	0.969908i	$-0.578286\pi$
$773$	18.5344	−	38.4871i	0.666636	−	1.38428i	0.910106	−	0.414375i	$-0.136000\pi$
$774$		0			0
$775$	−17.2773	−	13.7782i	−0.620620	−	0.494928i
$776$	−4.17942	+	2.01270i	−0.150032	+	0.0722517i
$777$		0			0
$778$	−5.04364	+	22.0977i	−0.180823	+	0.792239i
$779$	−5.06607	−	2.43969i	−0.181511	−	0.0874110i
$780$		0			0
$781$	11.2631	+	2.57073i	0.403026	+	0.0919880i
$782$	9.53788			0.341074
$783$		0			0
$784$	19.0728			0.681172
$785$	−4.19450	−	0.957368i	−0.149708	−	0.0341699i
$786$		0			0
$787$	−12.6203	−	6.07762i	−0.449866	−	0.216644i	0.195212	−	0.980761i	$-0.437461\pi$
$787$	−12.6203	−	6.07762i	−0.449866	−	0.216644i	−0.645077	+	0.764117i	$0.723175\pi$
$788$	1.67245	−	7.32750i	0.0595787	−	0.261031i
$789$		0			0
$790$	2.23291	−	1.07531i	0.0794433	−	0.0382579i
$791$	2.12364	+	1.69354i	0.0755079	+	0.0602155i
$792$		0			0
$793$	18.4612	−	38.3350i	0.655575	−	1.36132i
$794$	−8.89252	+	7.09155i	−0.315584	+	0.251670i
$795$		0			0
$796$	−0.997823	−	1.25123i	−0.0353669	−	0.0443487i
$797$	−8.94816	+	2.04236i	−0.316960	+	0.0723441i	−0.378041	−	0.925789i	$-0.623402\pi$
$797$	−8.94816	+	2.04236i	−0.316960	+	0.0723441i	0.0610812	+	0.998133i	$0.480545\pi$
$798$		0			0
$799$	1.46510	+	1.83718i	0.0518315	+	0.0649946i
$800$		−	8.34984i		−	0.295211i
$801$		0			0
$802$	−5.62549	+	11.6814i	−0.198643	+	0.412486i
$803$	−6.56197	+	8.22845i	−0.231567	+	0.290376i
$804$		0			0
$805$	−0.458209	+	0.220662i	−0.0161497	+	0.00777731i
$806$	−6.29458	−	27.5784i	−0.221717	−	0.971407i
$807$		0			0
$808$	−43.6949	−	21.0424i	−1.53718	−	0.740268i
$809$	5.06054	+	10.5083i	0.177919	+	0.369453i	0.970788	−	0.239940i	$-0.0771277\pi$
$809$	5.06054	+	10.5083i	0.177919	+	0.369453i	−0.792869	+	0.609392i	$0.791413\pi$
$810$		0			0
$811$	10.2506			0.359946			0.179973	−	0.983672i	$-0.442399\pi$
$811$	10.2506			0.359946			0.179973	+	0.983672i	$0.442399\pi$
$812$	−0.134881	+	1.80398i	−0.00473341	+	0.0633074i
$813$		0			0
$814$	−1.74724	−	0.398796i	−0.0612407	−	0.0139778i
$815$	−0.426002	−	0.884601i	−0.0149222	−	0.0309862i
$816$		0			0
$817$	6.71426	−	29.4171i	0.234902	−	1.02917i
$818$	5.90799	+	25.8846i	0.206568	+	0.905034i
$819$		0			0
$820$	0.104271	+	0.0831536i	0.00364131	+	0.00290385i
$821$	14.2411	−	17.8578i	0.497019	−	0.623242i	−0.468535	−	0.883445i	$-0.655218\pi$
$821$	14.2411	−	17.8578i	0.497019	−	0.623242i	0.965554	+	0.260203i	$0.0837894\pi$
$822$		0			0
$823$	0.386174	−	0.307963i	0.0134612	−	0.0107349i	−0.616736	−	0.787170i	$-0.711545\pi$
$823$	0.386174	−	0.307963i	0.0134612	−	0.0107349i	0.630197	+	0.776435i	$0.282974\pi$
$824$		−	32.8630i		−	1.14484i
$825$		0			0
$826$	5.14758	−	1.17490i	0.179107	−	0.0408801i
$827$	51.0365	−	11.6488i	1.77471	−	0.405067i	0.795185	−	0.606367i	$-0.207374\pi$
$827$	51.0365	−	11.6488i	1.77471	−	0.405067i	0.979530	+	0.201300i	$0.0645166\pi$
$828$		0			0
$829$			39.7417i			1.38029i	0.723673	+	0.690143i	$0.242452\pi$
$829$			39.7417i			1.38029i	−0.723673	+	0.690143i	$0.757548\pi$
$830$	−4.22531	+	3.36958i	−0.146663	+	0.116960i
$831$		0			0
$832$	26.4512	−	33.1687i	0.917029	−	1.14992i
$833$	23.4307	+	18.6853i	0.811825	+	0.647409i
$834$		0			0
$835$	−0.0997451	−	0.437012i	−0.00345182	−	0.0151234i
$836$	−0.217783	+	0.954170i	−0.00753218	+	0.0330006i
$837$		0			0
$838$	−20.5809	−	42.7367i	−0.710955	−	1.47631i
$839$	−31.1101	−	7.10068i	−1.07404	−	0.245143i	−0.351301	−	0.936263i	$-0.614260\pi$
$839$	−31.1101	−	7.10068i	−1.07404	−	0.245143i	−0.722740	+	0.691120i	$0.757118\pi$
$840$		0			0
$841$	−28.6776	−	4.31248i	−0.988881	−	0.148706i
$842$	−25.8508			−0.890877
$843$		0			0
$844$	−3.19670	−	6.63802i	−0.110035	−	0.228490i
$845$	2.98005	+	1.43512i	0.102517	+	0.0493695i
$846$		0			0
$847$	2.55619	+	11.1994i	0.0878317	+	0.384816i
$848$	26.2372	−	12.6352i	0.900988	−	0.433893i
$849$		0			0
$850$	−20.5918	+	25.8213i	−0.706293	+	0.885663i
$851$	1.09869	−	2.28144i	0.0376625	−	0.0782069i
$852$		0			0
$853$			12.8451i			0.439806i	0.975522	+	0.219903i	$0.0705741\pi$
$853$			12.8451i			0.439806i	−0.975522	+	0.219903i	$0.929426\pi$
$854$	−7.92392	−	9.93629i	−0.271151	−	0.340013i
$855$		0			0
$856$	36.5959	−	8.35278i	1.25082	−	0.285492i
$857$	−5.92373	−	7.42812i	−0.202351	−	0.253740i	0.670294	−	0.742096i	$-0.266168\pi$
$857$	−5.92373	−	7.42812i	−0.202351	−	0.253740i	−0.872644	+	0.488356i	$0.837597\pi$
$858$		0			0
$859$	−14.5414	+	11.5964i	−0.496146	+	0.395663i	−0.839344	−	0.543600i	$-0.817061\pi$
$859$	−14.5414	+	11.5964i	−0.496146	+	0.395663i	0.343199	+	0.939263i	$0.388489\pi$
$860$	−0.310521	+	0.644803i	−0.0105887	+	0.0219876i
$861$		0			0
$862$	36.4060	+	29.0328i	1.23999	+	0.988861i
$863$	−43.7868	+	21.0866i	−1.49052	+	0.717796i	−0.989078	−	0.147396i	$-0.952911\pi$
$863$	−43.7868	+	21.0866i	−1.49052	+	0.717796i	−0.501441	+	0.865192i	$0.667197\pi$
$864$		0			0
$865$	0.964085	−	4.22393i	0.0327799	−	0.143618i
$866$	−44.0480	−	21.2124i	−1.49681	−	0.720826i
$867$		0			0
$868$	1.47893	+	0.337555i	0.0501980	+	0.0114574i
$869$	−4.48313			−0.152080
$870$		0			0
$871$	−73.4191			−2.48771
$872$	25.7501	+	5.87730i	0.872010	+	0.199031i
$873$		0			0
$874$	6.93954	+	3.34191i	0.234734	+	0.113042i
$875$	0.792248	−	3.47107i	0.0267829	−	0.117343i
$876$		0			0
$877$	−11.3140	+	5.44854i	−0.382047	+	0.183984i	−0.615043	−	0.788493i	$-0.710861\pi$
$877$	−11.3140	+	5.44854i	−0.382047	+	0.183984i	0.232996	+	0.972478i	$0.425147\pi$
$878$	−7.02099	−	5.59905i	−0.236947	−	0.188959i
$879$		0			0
$880$	−0.358501	+	0.744435i	−0.0120851	+	0.0250949i
$881$	11.2267	−	8.95299i	0.378237	−	0.301634i	−0.415856	−	0.909431i	$-0.636518\pi$
$881$	11.2267	−	8.95299i	0.378237	−	0.301634i	0.794093	+	0.607797i	$0.207946\pi$
$882$		0			0
$883$	15.4326	+	19.3518i	0.519347	+	0.651241i	0.970470	−	0.241221i	$-0.0775478\pi$
$883$	15.4326	+	19.3518i	0.519347	+	0.651241i	−0.451123	+	0.892462i	$0.648976\pi$
$884$	7.39985	−	1.68897i	0.248884	−	0.0568061i
$885$		0			0
$886$	−11.2260	−	14.0770i	−0.377146	−	0.472926i
$887$			17.0877i			0.573749i	0.957968	+	0.286875i	$0.0926163\pi$
$887$			17.0877i			0.573749i	−0.957968	+	0.286875i	$0.907384\pi$
$888$		0			0
$889$	7.30900	−	15.1773i	0.245136	−	0.509030i
$890$	−2.19416	+	2.75139i	−0.0735485	+	0.0922269i
$891$		0			0
$892$	−0.333054	+	0.160390i	−0.0111515	+	0.00537026i
$893$	0.422258	+	1.85003i	0.0141303	+	0.0619089i
$894$		0			0
$895$	1.80813	+	0.870750i	0.0604392	+	0.0291060i
$896$	−3.86424	−	8.02417i	−0.129095	−	0.268069i
$897$		0			0
$898$	26.0786			0.870253
$899$	−7.16392	+	23.2389i	−0.238930	+	0.775061i
$900$		0			0
$901$	44.6105	+	10.1820i	1.48619	+	0.339213i
$902$	0.583033	+	1.21068i	0.0194129	+	0.0403112i
$903$		0			0
$904$	−1.64356	+	7.20091i	−0.0546641	+	0.239499i
$905$	1.74975	+	7.66614i	0.0581635	+	0.254831i
$906$		0			0
$907$	−4.05424	−	3.23315i	−0.134619	−	0.107355i	0.553865	−	0.832606i	$-0.313152\pi$
$907$	−4.05424	−	3.23315i	−0.134619	−	0.107355i	−0.688484	+	0.725251i	$0.741724\pi$
$908$	−3.03230	+	3.80239i	−0.100631	+	0.126187i
$909$		0			0
$910$	1.76243	−	1.40549i	0.0584241	−	0.0465917i
$911$			18.0436i			0.597811i	0.954283	+	0.298905i	$0.0966215\pi$
$911$			18.0436i			0.597811i	−0.954283	+	0.298905i	$0.903378\pi$
$912$		0			0
$913$	9.53100	−	2.17539i	0.315430	−	0.0719949i
$914$	31.0492	−	7.08677i	1.02701	−	0.234409i
$915$		0			0
$916$		−	4.66891i		−	0.154265i
$917$	−7.54265	+	6.01506i	−0.249080	+	0.198635i
$918$		0			0
$919$	−5.45496	+	6.84030i	−0.179943	+	0.225641i	−0.863620	−	0.504144i	$-0.831808\pi$
$919$	−5.45496	+	6.84030i	−0.179943	+	0.225641i	0.683677	+	0.729785i	$0.260380\pi$
$920$	−1.08122	−	0.862246i	−0.0356468	−	0.0284274i
$921$		0			0
$922$	6.45453	+	28.2791i	0.212568	+	0.931323i
$923$	16.0999	−	70.5382i	0.529934	−	2.32179i
$924$		0			0
$925$	3.80440	+	7.89992i	0.125088	+	0.259748i
$926$	34.9241	+	7.97121i	1.14768	+	0.261950i
$927$		0			0
$928$	−8.55275	+	3.35838i	−0.280758	+	0.110244i
$929$	−42.8899			−1.40717			−0.703587	−	0.710609i	$-0.748419\pi$
$929$	−42.8899			−1.40717			−0.703587	+	0.710609i	$0.748419\pi$
$930$		0			0
$931$	10.5006	+	21.8047i	0.344144	+	0.714621i
$932$	3.56145	+	1.71510i	0.116659	+	0.0561801i
$933$		0			0
$934$	6.88042	+	30.1451i	0.225134	+	0.986377i
$935$	−1.16972	+	0.563310i	−0.0382541	+	0.0184222i
$936$		0			0
$937$	−10.3965	+	13.0367i	−0.339637	+	0.425892i	−0.922092	−	0.386972i	$-0.873521\pi$
$937$	−10.3965	+	13.0367i	−0.339637	+	0.425892i	0.582454	+	0.812863i	$0.302093\pi$
$938$	−9.51498	+	19.7581i	−0.310675	+	0.645123i
$939$		0			0
$940$		−	0.0450088i		−	0.00146802i
$941$	10.3481	+	12.9761i	0.337337	+	0.423007i	0.921348	−	0.388738i	$-0.127089\pi$
$941$	10.3481	+	12.9761i	0.337337	+	0.423007i	−0.584011	+	0.811746i	$0.698518\pi$
$942$		0			0
$943$	−1.85103	+	0.422485i	−0.0602777	+	0.0137580i
$944$	7.55689	+	9.47604i	0.245956	+	0.308419i
$945$		0			0
$946$	−5.63766	+	4.49588i	−0.183296	+	0.146174i
$947$	−19.5444	+	40.5843i	−0.635107	+	1.31881i	0.296391	+	0.955067i	$0.404217\pi$
$947$	−19.5444	+	40.5843i	−0.635107	+	1.31881i	−0.931498	+	0.363746i	$0.881498\pi$
$948$		0			0
$949$	51.5329	+	41.0961i	1.67283	+	1.33404i
$950$	−24.0295	+	11.5720i	−0.779618	+	0.375444i
$951$		0			0
$952$	3.81889	−	16.7316i	0.123771	−	0.542275i
$953$	17.4621	+	8.40933i	0.565655	+	0.272405i	0.694779	−	0.719224i	$-0.255502\pi$
$953$	17.4621	+	8.40933i	0.565655	+	0.272405i	−0.129124	+	0.991628i	$0.541217\pi$
$954$		0			0
$955$	1.63915	+	0.374125i	0.0530417	+	0.0121064i
$956$	−0.0776451			−0.00251122
$957$		0			0
$958$	34.0835			1.10119
$959$	−25.0673	−	5.72145i	−0.809465	−	0.184755i
$960$		0			0
$961$	−9.55748	−	4.60264i	−0.308306	−	0.148472i
$962$	−2.49757	+	10.9426i	−0.0805248	+	0.352802i
$963$		0			0
$964$	2.30279	−	1.10897i	0.0741680	−	0.0357174i
$965$	0.707249	+	0.564012i	0.0227671	+	0.0181562i
$966$		0			0
$967$	−11.2078	+	23.2732i	−0.360417	+	0.748414i	−0.999790	−	0.0204826i	$-0.993480\pi$
$967$	−11.2078	+	23.2732i	−0.360417	+	0.748414i	0.639373	+	0.768897i	$0.279194\pi$
$968$	−24.4221	+	19.4760i	−0.784956	+	0.625981i
$969$		0			0
$970$	−0.409293	−	0.513238i	−0.0131416	−	0.0164791i
$971$	−27.5064	+	6.27816i	−0.882723	+	0.201476i	−0.639774	−	0.768563i	$-0.720972\pi$
$971$	−27.5064	+	6.27816i	−0.882723	+	0.201476i	−0.242949	+	0.970039i	$0.578115\pi$
$972$		0			0
$973$	9.30836	+	11.6723i	0.298412	+	0.374197i
$974$		−	21.2449i		−	0.680729i
$975$		0			0
$976$	12.6581	−	26.2848i	0.405175	−	0.841355i
$977$	−17.8073	+	22.3297i	−0.569707	+	0.714390i	−0.980319	−	0.197420i	$-0.936744\pi$
$977$	−17.8073	+	22.3297i	−0.569707	+	0.714390i	0.410612	+	0.911810i	$0.365315\pi$
$978$		0			0
$979$	5.73548	−	2.76206i	0.183307	−	0.0882758i
$980$	−0.127733	−	0.559634i	−0.00408027	−	0.0178768i
$981$		0			0
$982$	−38.5995	−	18.5885i	−1.23176	−	0.593184i
$983$	9.85199	+	20.4579i	0.314230	+	0.652505i	0.996939	−	0.0781854i	$-0.0249126\pi$
$983$	9.85199	+	20.4579i	0.314230	+	0.652505i	−0.682709	+	0.730690i	$0.739198\pi$
$984$		0			0
$985$	8.05143			0.256540
$986$	34.7310	+	10.7066i	1.10606	+	0.340969i
$987$		0			0
$988$	5.97574	+	1.36392i	0.190114	+	0.0433922i
$989$	−4.42058	−	9.17943i	−0.140566	−	0.291889i
$990$		0			0
$991$	−10.4378	+	45.7310i	−0.331568	+	1.45269i	0.484528	+	0.874776i	$0.338991\pi$
$991$	−10.4378	+	45.7310i	−0.331568	+	1.45269i	−0.816096	+	0.577917i	$0.803866\pi$
$992$	1.71453	+	7.51186i	0.0544364	+	0.238502i
$993$		0			0
$994$	−16.8963	−	13.4743i	−0.535917	−	0.427379i
$995$	1.06892	−	1.34038i	0.0338869	−	0.0424929i
$996$		0			0
$997$	−28.3877	+	22.6385i	−0.899048	+	0.716967i	−0.959651	−	0.281195i	$-0.909269\pi$
$997$	−28.3877	+	22.6385i	−0.899048	+	0.716967i	0.0606024	+	0.998162i	$0.480698\pi$
$998$			28.8606i			0.913567i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.o.b.91.2		24
3.2	odd	2		87.2.i.a.4.3	✓	24
29.14	odd	28		7569.2.a.bn.1.10		12
29.15	odd	28		7569.2.a.bt.1.3		12
29.22	even	14	inner	261.2.o.b.109.2		24
87.14	even	28		2523.2.a.v.1.3		12
87.44	even	28		2523.2.a.s.1.10		12
87.80	odd	14		87.2.i.a.22.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.i.a.4.3	✓	24	3.2	odd	2
87.2.i.a.22.3	yes	24	87.80	odd	14
261.2.o.b.91.2		24	1.1	even	1	trivial
261.2.o.b.109.2		24	29.22	even	14	inner
2523.2.a.s.1.10		12	87.44	even	28
2523.2.a.v.1.3		12	87.14	even	28
7569.2.a.bn.1.10		12	29.14	odd	28
7569.2.a.bt.1.3		12	29.15	odd	28

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Elliptic curves over $\Q$
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Higher genus families
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Newspace parameters

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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	261.2.o.b.91.2

Level	$261$
Weight	$2$
Character	261.91
Analytic conductor	$2.084$
Analytic rank	$0$
Dimension	$24$
Inner twists	$2$