LMFDB - Embedded newform 768.2.s.a.335.28

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [768,2,Mod(47,768)] 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("768.47"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(768, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 11, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.s (of order $16$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 192)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			335.28
Character	$\chi$	$=$	768.335
Dual form			768.2.s.a.431.28

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.67061 + 0.457221i) q^{3} +(-1.45822 - 2.18239i) q^{5} +(1.27779 - 3.08486i) q^{7} +(2.58190 + 1.52768i) q^{9} +(-2.31748 - 0.460975i) q^{11} +(-5.55652 - 3.71275i) q^{13} +(-1.43829 - 4.31265i) q^{15} +(-3.42067 - 3.42067i) q^{17} +(1.23054 + 0.822221i) q^{19} +(3.54516 - 4.56938i) q^{21} +(1.87568 + 4.52828i) q^{23} +(-0.722975 + 1.74542i) q^{25} +(3.61486 + 3.73266i) q^{27} +(-0.760797 - 3.82478i) q^{29} +0.0497279 q^{31} +(-3.66084 - 1.82971i) q^{33} +(-8.59567 + 1.70978i) q^{35} +(5.53510 + 8.28386i) q^{37} +(-7.58524 - 8.74312i) q^{39} +(2.28385 - 0.946002i) q^{41} +(0.522190 + 0.103870i) q^{43} +(-0.430996 - 7.86240i) q^{45} +(2.51930 - 2.51930i) q^{47} +(-2.93388 - 2.93388i) q^{49} +(-4.15061 - 7.27862i) q^{51} +(1.79038 - 9.00087i) q^{53} +(2.37338 + 5.72983i) q^{55} +(1.67982 + 1.93624i) q^{57} +(-2.56739 + 1.71547i) q^{59} +(-0.935842 - 4.70479i) q^{61} +(8.01181 - 6.01274i) q^{63} +17.5405i q^{65} +(3.65093 - 0.726215i) q^{67} +(1.06310 + 8.42261i) q^{69} +(12.6483 + 5.23910i) q^{71} +(13.6168 - 5.64025i) q^{73} +(-2.00585 + 2.58536i) q^{75} +(-4.38330 + 6.56007i) q^{77} +(1.69637 - 1.69637i) q^{79} +(4.33239 + 7.88863i) q^{81} +(5.63016 - 8.42612i) q^{83} +(-2.47712 + 12.4533i) q^{85} +(0.477776 - 6.73759i) q^{87} +(8.26075 + 3.42172i) q^{89} +(-18.5534 + 12.3970i) q^{91} +(0.0830760 + 0.0227366i) q^{93} -3.88450i q^{95} +3.93119i q^{97} +(-5.27927 - 4.73055i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 8 q^{3} + 16 q^{7} - 8 q^{9} - 16 q^{13} + 8 q^{15} + 16 q^{19} - 8 q^{21} - 16 q^{25} + 8 q^{27} + 32 q^{31} - 16 q^{37} + 8 q^{39} + 16 q^{43} - 8 q^{45} - 16 q^{49} + 8 q^{51} + 80 q^{55} - 8 q^{57}+ \cdots + 8 q^{99}+O(q^{100}) $ 240 * q + 8 * q^3 + 16 * q^7 - 8 * q^9 - 16 * q^13 + 8 * q^15 + 16 * q^19 - 8 * q^21 - 16 * q^25 + 8 * q^27 + 32 * q^31 - 16 * q^37 + 8 * q^39 + 16 * q^43 - 8 * q^45 - 16 * q^49 + 8 * q^51 + 80 * q^55 - 8 * q^57 - 16 * q^61 + 144 * q^67 - 8 * q^69 - 16 * q^73 + 8 * q^75 + 48 * q^79 - 8 * q^81 - 16 * q^85 + 8 * q^87 + 16 * q^91 - 32 * q^93 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{16}\right)$

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
$3$	1.67061	+	0.457221i	0.964529	+	0.263977i
$3$	1.67061	+	0.457221i	0.964529	+	0.263977i
$4$		0			0
$5$	−1.45822	−	2.18239i	−0.652138	−	0.975993i	−0.999271	−	0.0381770i	$-0.987845\pi$
$5$	−1.45822	−	2.18239i	−0.652138	−	0.975993i	0.347133	−	0.937816i	$-0.387155\pi$
$6$		0			0
$7$	1.27779	−	3.08486i	0.482960	−	1.16597i	−0.475237	−	0.879858i	$-0.657638\pi$
$7$	1.27779	−	3.08486i	0.482960	−	1.16597i	0.958197	−	0.286111i	$-0.0923625\pi$
$8$		0			0
$9$	2.58190	+	1.52768i	0.860632	+	0.509227i
$10$		0			0
$11$	−2.31748	−	0.460975i	−0.698746	−	0.138989i	−0.167080	−	0.985943i	$-0.553434\pi$
$11$	−2.31748	−	0.460975i	−0.698746	−	0.138989i	−0.531666	+	0.846954i	$0.678434\pi$
$12$		0			0
$13$	−5.55652	−	3.71275i	−1.54110	−	1.02973i	−0.979289	−	0.202465i	$-0.935105\pi$
$13$	−5.55652	−	3.71275i	−1.54110	−	1.02973i	−0.561811	−	0.827266i	$-0.689895\pi$
$14$		0			0
$15$	−1.43829	−	4.31265i	−0.371366	−	1.11352i
$16$		0			0
$17$	−3.42067	−	3.42067i	−0.829634	−	0.829634i	0.157832	−	0.987466i	$-0.449550\pi$
$17$	−3.42067	−	3.42067i	−0.829634	−	0.829634i	−0.987466	+	0.157832i	$0.949550\pi$
$18$		0			0
$19$	1.23054	+	0.822221i	0.282305	+	0.188630i	0.688659	−	0.725086i	$-0.258200\pi$
$19$	1.23054	+	0.822221i	0.282305	+	0.188630i	−0.406353	+	0.913716i	$0.633200\pi$
$20$		0			0
$21$	3.54516	−	4.56938i	0.773618	−	0.997120i
$22$		0			0
$23$	1.87568	+	4.52828i	0.391105	+	0.944212i	0.989700	+	0.143160i	$0.0457263\pi$
$23$	1.87568	+	4.52828i	0.391105	+	0.944212i	−0.598594	+	0.801052i	$0.704274\pi$
$24$		0			0
$25$	−0.722975	+	1.74542i	−0.144595	+	0.349083i
$26$		0			0
$27$	3.61486	+	3.73266i	0.695681	+	0.718351i
$28$		0			0
$29$	−0.760797	−	3.82478i	−0.141276	−	0.710245i	−0.984874	−	0.173269i	$-0.944567\pi$
$29$	−0.760797	−	3.82478i	−0.141276	−	0.710245i	0.843598	−	0.536975i	$-0.180433\pi$
$30$		0			0
$31$	0.0497279			0.00893139			0.00446569	−	0.999990i	$-0.498579\pi$
$31$	0.0497279			0.00893139			0.00446569	+	0.999990i	$0.498579\pi$
$32$		0			0
$33$	−3.66084	−	1.82971i	−0.637271	−	0.318512i
$34$		0			0
$35$	−8.59567	+	1.70978i	−1.45293	+	0.289006i
$36$		0			0
$37$	5.53510	+	8.28386i	0.909965	+	1.36186i	0.932138	+	0.362104i	$0.117942\pi$
$37$	5.53510	+	8.28386i	0.909965	+	1.36186i	−0.0221727	+	0.999754i	$0.507058\pi$
$38$		0			0
$39$	−7.58524	−	8.74312i	−1.21461	−	1.40002i
$40$		0			0
$41$	2.28385	−	0.946002i	0.356678	−	0.147741i	−0.197147	−	0.980374i	$-0.563168\pi$
$41$	2.28385	−	0.946002i	0.356678	−	0.147741i	0.553825	+	0.832633i	$0.313168\pi$
$42$		0			0
$43$	0.522190	+	0.103870i	0.0796333	+	0.0158400i	0.234746	−	0.972057i	$-0.424574\pi$
$43$	0.522190	+	0.103870i	0.0796333	+	0.0158400i	−0.155113	+	0.987897i	$0.549574\pi$
$44$		0			0
$45$	−0.430996	−	7.86240i	−0.0642491	−	1.17206i
$46$		0			0
$47$	2.51930	−	2.51930i	0.367477	−	0.367477i	−0.499079	−	0.866556i	$-0.666328\pi$
$47$	2.51930	−	2.51930i	0.367477	−	0.367477i	0.866556	+	0.499079i	$0.166328\pi$
$48$		0			0
$49$	−2.93388	−	2.93388i	−0.419126	−	0.419126i
$50$		0			0
$51$	−4.15061	−	7.27862i	−0.581202	−	1.01921i
$52$		0			0
$53$	1.79038	−	9.00087i	0.245928	−	1.23636i	−0.638476	−	0.769642i	$-0.720435\pi$
$53$	1.79038	−	9.00087i	0.245928	−	1.23636i	0.884404	−	0.466722i	$-0.154565\pi$
$54$		0			0
$55$	2.37338	+	5.72983i	0.320026	+	0.772611i
$56$		0			0
$57$	1.67982	+	1.93624i	0.222498	+	0.256461i
$58$		0			0
$59$	−2.56739	+	1.71547i	−0.334245	+	0.223336i	−0.711355	−	0.702833i	$-0.751918\pi$
$59$	−2.56739	+	1.71547i	−0.334245	+	0.223336i	0.377109	+	0.926169i	$0.376918\pi$
$60$		0			0
$61$	−0.935842	−	4.70479i	−0.119822	−	0.602387i	−0.993304	−	0.115530i	$-0.963143\pi$
$61$	−0.935842	−	4.70479i	−0.119822	−	0.602387i	0.873482	−	0.486857i	$-0.161857\pi$
$62$		0			0
$63$	8.01181	−	6.01274i	1.00939	−	0.757534i
$64$		0			0
$65$			17.5405i			2.17563i
$66$		0			0
$67$	3.65093	−	0.726215i	0.446032	−	0.0887213i	0.0330361	−	0.999454i	$-0.489482\pi$
$67$	3.65093	−	0.726215i	0.446032	−	0.0887213i	0.412996	+	0.910733i	$0.364482\pi$
$68$		0			0
$69$	1.06310	+	8.42261i	0.127982	+	1.01396i
$70$		0			0
$71$	12.6483	+	5.23910i	1.50108	+	0.621767i	0.973694	−	0.227860i	$-0.0731728\pi$
$71$	12.6483	+	5.23910i	1.50108	+	0.621767i	0.527384	+	0.849627i	$0.323173\pi$
$72$		0			0
$73$	13.6168	−	5.64025i	1.59372	−	0.660142i	0.603213	−	0.797580i	$-0.293887\pi$
$73$	13.6168	−	5.64025i	1.59372	−	0.660142i	0.990510	+	0.137439i	$0.0438870\pi$
$74$		0			0
$75$	−2.00585	+	2.58536i	−0.231616	+	0.298531i
$76$		0			0
$77$	−4.38330	+	6.56007i	−0.499523	+	0.747589i
$78$		0			0
$79$	1.69637	−	1.69637i	0.190856	−	0.190856i	−0.605210	−	0.796066i	$-0.706911\pi$
$79$	1.69637	−	1.69637i	0.190856	−	0.190856i	0.796066	+	0.605210i	$0.206911\pi$
$80$		0			0
$81$	4.33239	+	7.88863i	0.481376	+	0.876514i
$82$		0			0
$83$	5.63016	−	8.42612i	0.617990	−	0.924887i	−0.382010	−	0.924158i	$-0.624768\pi$
$83$	5.63016	−	8.42612i	0.617990	−	0.924887i	1.00000		0.000728896i	$-0.000232015\pi$
$84$		0			0
$85$	−2.47712	+	12.4533i	−0.268681	+	1.35075i
$86$		0			0
$87$	0.477776	−	6.73759i	0.0512229	−	0.722345i
$88$		0			0
$89$	8.26075	+	3.42172i	0.875638	+	0.362701i	0.774804	−	0.632202i	$-0.217849\pi$
$89$	8.26075	+	3.42172i	0.875638	+	0.362701i	0.100834	+	0.994903i	$0.467849\pi$
$90$		0			0
$91$	−18.5534	+	12.3970i	−1.94492	+	1.29956i
$92$		0			0
$93$	0.0830760	+	0.0227366i	0.00861458	+	0.00235768i
$94$		0			0
$95$		−	3.88450i		−	0.398541i
$96$		0			0
$97$			3.93119i			0.399152i	0.979882	+	0.199576i	$0.0639565\pi$
$97$			3.93119i			0.399152i	−0.979882	+	0.199576i	$0.936044\pi$
$98$		0			0
$99$	−5.27927	−	4.73055i	−0.530586	−	0.475439i
$100$		0			0
$101$	−1.14688	+	0.766317i	−0.114118	+	0.0762514i	−0.611320	−	0.791384i	$-0.709361\pi$
$101$	−1.14688	+	0.766317i	−0.114118	+	0.0762514i	0.497201	+	0.867635i	$0.334361\pi$
$102$		0			0
$103$	−3.42308	−	1.41789i	−0.337286	−	0.139708i	0.207611	−	0.978212i	$-0.433431\pi$
$103$	−3.42308	−	1.41789i	−0.337286	−	0.139708i	−0.544897	+	0.838503i	$0.683431\pi$
$104$		0			0
$105$	−15.1418	−	1.07373i	−1.47769	−	0.104786i
$106$		0			0
$107$	−0.353820	+	1.77877i	−0.0342051	+	0.171960i	−0.994112	−	0.108359i	$-0.965440\pi$
$107$	−0.353820	+	1.77877i	−0.0342051	+	0.171960i	0.959907	+	0.280319i	$0.0904404\pi$
$108$		0			0
$109$	−4.27438	+	6.39706i	−0.409411	+	0.612728i	−0.977676	−	0.210118i	$-0.932615\pi$
$109$	−4.27438	+	6.39706i	−0.409411	+	0.612728i	0.568264	+	0.822846i	$0.307615\pi$
$110$		0			0
$111$	5.45945	+	16.3699i	0.518188	+	1.55376i
$112$		0			0
$113$	7.68145	−	7.68145i	0.722610	−	0.722610i	−0.246526	−	0.969136i	$-0.579289\pi$
$113$	7.68145	−	7.68145i	0.722610	−	0.722610i	0.969136	+	0.246526i	$0.0792891\pi$
$114$		0			0
$115$	7.14731	−	10.6967i	0.666490	−	0.997472i
$116$		0			0
$117$	−8.67447	−	18.0745i	−0.801955	−	1.67099i
$118$		0			0
$119$	−14.9232	+	6.18139i	−1.36801	+	0.566647i
$120$		0			0
$121$	−5.00447	−	2.07292i	−0.454952	−	0.188447i
$122$		0			0
$123$	4.24796	−	0.536178i	0.383026	−	0.0483456i
$124$		0			0
$125$	−8.00807	+	1.59290i	−0.716263	+	0.142474i
$126$		0			0
$127$			2.11042i			0.187270i	0.995607	+	0.0936348i	$0.0298486\pi$
$127$			2.11042i			0.187270i	−0.995607	+	0.0936348i	$0.970151\pi$
$128$		0			0
$129$	0.824886	+	0.412283i	0.0726272	+	0.0362995i
$130$		0			0
$131$	−2.13696	−	10.7432i	−0.186707	−	0.938640i	−0.954561	−	0.298015i	$-0.903675\pi$
$131$	−2.13696	−	10.7432i	−0.186707	−	0.938640i	0.767854	−	0.640625i	$-0.221325\pi$
$132$		0			0
$133$	4.10881	−	2.74542i	0.356279	−	0.238058i
$134$		0			0
$135$	2.87483	−	13.3321i	0.247426	−	1.14744i
$136$		0			0
$137$	−1.35133	−	3.26240i	−0.115452	−	0.278726i	0.855582	−	0.517667i	$-0.173200\pi$
$137$	−1.35133	−	3.26240i	−0.115452	−	0.278726i	−0.971034	+	0.238942i	$0.923200\pi$
$138$		0			0
$139$	−2.25479	+	11.3356i	−0.191249	+	0.961475i	0.759262	+	0.650785i	$0.225560\pi$
$139$	−2.25479	+	11.3356i	−0.191249	+	0.961475i	−0.950511	+	0.310690i	$0.899440\pi$
$140$		0			0
$141$	5.36065	−	3.05689i	0.451448	−	0.257437i
$142$		0			0
$143$	11.1656	+	11.1656i	0.933716	+	0.933716i
$144$		0			0
$145$	−7.23774	+	7.23774i	−0.601062	+	0.601062i
$146$		0			0
$147$	−3.55995	−	6.24281i	−0.293619	−	0.514898i
$148$		0			0
$149$	−9.41669	−	1.87310i	−0.771445	−	0.153450i	−0.206353	−	0.978478i	$-0.566159\pi$
$149$	−9.41669	−	1.87310i	−0.771445	−	0.153450i	−0.565092	+	0.825028i	$0.691159\pi$
$150$		0			0
$151$	−15.4374	+	6.39437i	−1.25628	+	0.520367i	−0.908765	−	0.417309i	$-0.862973\pi$
$151$	−15.4374	+	6.39437i	−1.25628	+	0.520367i	−0.347511	+	0.937676i	$0.612973\pi$
$152$		0			0
$153$	−3.60613	−	14.0575i	−0.291538	−	1.13648i
$154$		0			0
$155$	−0.0725144	−	0.108525i	−0.00582449	−	0.00871697i
$156$		0			0
$157$	−1.10477	+	0.219752i	−0.0881699	+	0.0175381i	−0.238978	−	0.971025i	$-0.576812\pi$
$157$	−1.10477	+	0.219752i	−0.0881699	+	0.0175381i	0.150808	+	0.988563i	$0.451812\pi$
$158$		0			0
$159$	7.10643	−	14.2184i	0.563576	−	1.12759i
$160$		0			0
$161$	16.3659			1.28981
$162$		0			0
$163$	3.95820	+	19.8992i	0.310030	+	1.55863i	0.750507	+	0.660862i	$0.229809\pi$
$163$	3.95820	+	19.8992i	0.310030	+	1.55863i	−0.440477	+	0.897764i	$0.645191\pi$
$164$		0			0
$165$	1.34519	+	10.6575i	0.104723	+	0.829685i
$166$		0			0
$167$	0.109882	−	0.265279i	0.00850292	−	0.0205279i	−0.919571	−	0.392924i	$-0.871464\pi$
$167$	0.109882	−	0.265279i	0.00850292	−	0.0205279i	0.928074	+	0.372396i	$0.121464\pi$
$168$		0			0
$169$	12.1155	+	29.2494i	0.931963	+	2.24996i
$170$		0			0
$171$	1.92104	+	4.00276i	0.146905	+	0.306099i
$172$		0			0
$173$	−11.1530	−	7.45221i	−0.847948	−	0.566581i	0.0539429	−	0.998544i	$-0.482821\pi$
$173$	−11.1530	−	7.45221i	−0.847948	−	0.566581i	−0.901891	+	0.431963i	$0.857821\pi$
$174$		0			0
$175$	4.46056	+	4.46056i	0.337187	+	0.337187i
$176$		0			0
$177$	−5.07346	+	1.69203i	−0.381345	+	0.127181i
$178$		0			0
$179$	13.7986	+	9.21991i	1.03135	+	0.689128i	0.951491	−	0.307677i	$-0.0995518\pi$
$179$	13.7986	+	9.21991i	1.03135	+	0.689128i	0.0798628	+	0.996806i	$0.474552\pi$
$180$		0			0
$181$	−0.368628	−	0.0733247i	−0.0273999	−	0.00545018i	0.181371	−	0.983415i	$-0.441946\pi$
$181$	−0.368628	−	0.0733247i	−0.0273999	−	0.00545018i	−0.208771	+	0.977965i	$0.566946\pi$
$182$		0			0
$183$	0.587703	−	8.28778i	0.0434442	−	0.612650i
$184$		0			0
$185$	10.0072	−	24.1595i	0.735742	−	1.77624i
$186$		0			0
$187$	6.35048	+	9.50417i	0.464393	+	0.695014i
$188$		0			0
$189$	16.1338	−	6.38180i	1.17356	−	0.464207i
$190$		0			0
$191$	4.88024			0.353122			0.176561	−	0.984290i	$-0.443503\pi$
$191$	4.88024			0.353122			0.176561	+	0.984290i	$0.443503\pi$
$192$		0			0
$193$	−7.52929			−0.541970			−0.270985	−	0.962584i	$-0.587349\pi$
$193$	−7.52929			−0.541970			−0.270985	+	0.962584i	$0.587349\pi$
$194$		0			0
$195$	−8.01988	+	29.3034i	−0.574316	+	2.09846i
$196$		0			0
$197$	8.61841	+	12.8984i	0.614036	+	0.918970i	0.999994	−	0.00354629i	$-0.00112882\pi$
$197$	8.61841	+	12.8984i	0.614036	+	0.918970i	−0.385957	+	0.922517i	$0.626129\pi$
$198$		0			0
$199$	−4.43073	+	10.6967i	−0.314086	+	0.758271i	0.685459	+	0.728111i	$0.259602\pi$
$199$	−4.43073	+	10.6967i	−0.314086	+	0.758271i	−0.999545	+	0.0301595i	$0.990398\pi$
$200$		0			0
$201$	6.43133	+	0.456058i	0.453631	+	0.0321679i
$202$		0			0
$203$	−12.7711	−	2.54032i	−0.896354	−	0.178296i
$204$		0			0
$205$	−5.39491	−	3.60476i	−0.376797	−	0.251768i
$206$		0			0
$207$	−2.07496	+	14.5570i	−0.144220	+	1.01178i
$208$		0			0
$209$	−2.47273	−	2.47273i	−0.171042	−	0.171042i
$210$		0			0
$211$	−17.8899	−	11.9536i	−1.23159	−	0.822923i	−0.242489	−	0.970154i	$-0.577964\pi$
$211$	−17.8899	−	11.9536i	−1.23159	−	0.822923i	−0.989102	+	0.147232i	$0.952964\pi$
$212$		0			0
$213$	18.7350	+	14.5356i	1.28370	+	0.995962i
$214$		0			0
$215$	−0.534786	−	1.29109i	−0.0364721	−	0.0880514i
$216$		0			0
$217$	0.0635419	−	0.153404i	0.00431350	−	0.0104137i
$218$		0			0
$219$	25.3272	−	3.19680i	1.71145	−	0.216020i
$220$		0			0
$221$	6.30693	+	31.7071i	0.424250	+	2.13285i
$222$		0			0
$223$	1.45744			0.0975977			0.0487989	−	0.998809i	$-0.484461\pi$
$223$	1.45744			0.0975977			0.0487989	+	0.998809i	$0.484461\pi$
$224$		0			0
$225$	−4.53309	+	3.40201i	−0.302206	+	0.226801i
$226$		0			0
$227$	−19.3684	+	3.85261i	−1.28552	+	0.255707i	−0.790118	−	0.612955i	$-0.789981\pi$
$227$	−19.3684	+	3.85261i	−1.28552	+	0.255707i	−0.495406	+	0.868662i	$0.664981\pi$
$228$		0			0
$229$	0.936069	+	1.40093i	0.0618572	+	0.0925758i	0.861109	−	0.508421i	$-0.169771\pi$
$229$	0.936069	+	1.40093i	0.0618572	+	0.0925758i	−0.799252	+	0.600997i	$0.794771\pi$
$230$		0			0
$231$	−10.3222	+	8.95520i	−0.679151	+	0.589209i
$232$		0			0
$233$	−14.4154	+	5.97104i	−0.944382	+	0.391176i	−0.801117	−	0.598508i	$-0.795760\pi$
$233$	−14.4154	+	5.97104i	−0.944382	+	0.391176i	−0.143266	+	0.989684i	$0.545760\pi$
$234$		0			0
$235$	−9.17178	−	1.82438i	−0.598301	−	0.119009i
$236$		0			0
$237$	3.60959	−	2.05836i	0.234468	−	0.133705i
$238$		0			0
$239$	−0.690266	+	0.690266i	−0.0446496	+	0.0446496i	−0.729079	−	0.684429i	$-0.760051\pi$
$239$	−0.690266	+	0.690266i	−0.0446496	+	0.0446496i	0.684429	+	0.729079i	$0.260051\pi$
$240$		0			0
$241$	−10.6103	−	10.6103i	−0.683472	−	0.683472i	0.277309	−	0.960781i	$-0.410558\pi$
$241$	−10.6103	−	10.6103i	−0.683472	−	0.683472i	−0.960781	+	0.277309i	$0.910558\pi$
$242$		0			0
$243$	3.63090	+	15.1597i	0.232922	+	0.972495i
$244$		0			0
$245$	−2.12461	+	10.6811i	−0.135736	+	0.682391i
$246$		0			0
$247$	−3.78482	−	9.13737i	−0.240822	−	0.581397i
$248$		0			0
$249$	13.2584	−	11.5026i	0.840218	−	0.728945i
$250$		0			0
$251$	22.7440	−	15.1971i	1.43559	−	0.959232i	0.437391	−	0.899272i	$-0.355903\pi$
$251$	22.7440	−	15.1971i	1.43559	−	0.959232i	0.998201	−	0.0599600i	$-0.0190973\pi$
$252$		0			0
$253$	−2.25941	−	11.3588i	−0.142048	−	0.714124i
$254$		0			0
$255$	−9.83224	+	19.6721i	−0.615719	+	1.23191i
$256$		0			0
$257$			4.51818i			0.281836i	0.990021	+	0.140918i	$0.0450054\pi$
$257$			4.51818i			0.281836i	−0.990021	+	0.140918i	$0.954995\pi$
$258$		0			0
$259$	32.6273	−	6.48997i	2.02736	−	0.403267i
$260$		0			0
$261$	3.87875	−	11.0375i	0.240088	−	0.683201i
$262$		0			0
$263$	2.04943	+	0.848904i	0.126374	+	0.0523456i	0.444974	−	0.895543i	$-0.353213\pi$
$263$	2.04943	+	0.848904i	0.126374	+	0.0523456i	−0.318601	+	0.947889i	$0.603213\pi$
$264$		0			0
$265$	−22.2541	+	9.21797i	−1.36706	+	0.566255i
$266$		0			0
$267$	12.2360	+	9.49335i	0.748833	+	0.580984i
$268$		0			0
$269$	12.8156	−	19.1799i	0.781379	−	1.16942i	−0.200460	−	0.979702i	$-0.564244\pi$
$269$	12.8156	−	19.1799i	0.781379	−	1.16942i	0.981839	−	0.189715i	$-0.0607564\pi$
$270$		0			0
$271$	4.68156	−	4.68156i	0.284384	−	0.284384i	−0.550470	−	0.834855i	$-0.685552\pi$
$271$	4.68156	−	4.68156i	0.284384	−	0.284384i	0.834855	+	0.550470i	$0.185552\pi$
$272$		0			0
$273$	−36.6637	+	12.2275i	−2.21899	+	0.740045i
$274$		0			0
$275$	2.48007	−	3.71169i	0.149554	−	0.223823i
$276$		0			0
$277$	0.351539	−	1.76730i	0.0211219	−	0.106187i	−0.968786	−	0.247898i	$-0.920260\pi$
$277$	0.351539	−	1.76730i	0.0211219	−	0.106187i	0.989908	+	0.141711i	$0.0452603\pi$
$278$		0			0
$279$	0.128392	+	0.0759683i	0.00768664	+	0.00454810i
$280$		0			0
$281$	6.33662	+	2.62472i	0.378011	+	0.156577i	0.563595	−	0.826051i	$-0.309418\pi$
$281$	6.33662	+	2.62472i	0.378011	+	0.156577i	−0.185584	+	0.982628i	$0.559418\pi$
$282$		0			0
$283$	19.0458	−	12.7260i	1.13215	−	0.756481i	0.159146	−	0.987255i	$-0.449126\pi$
$283$	19.0458	−	12.7260i	1.13215	−	0.756481i	0.973007	+	0.230774i	$0.0741259\pi$
$284$		0			0
$285$	1.77607	−	6.48949i	0.105206	−	0.384404i
$286$		0			0
$287$		−	8.25416i		−	0.487228i
$288$		0			0
$289$			6.40197i			0.376586i
$290$		0			0
$291$	−1.79742	+	6.56750i	−0.105367	+	0.384994i
$292$		0			0
$293$	−10.4198	+	6.96228i	−0.608731	+	0.406741i	−0.821375	−	0.570389i	$-0.806793\pi$
$293$	−10.4198	+	6.96228i	−0.608731	+	0.406741i	0.212644	+	0.977130i	$0.431793\pi$
$294$		0			0
$295$	7.48765	+	3.10149i	0.435948	+	0.180575i
$296$		0			0
$297$	−6.65670	−	10.3167i	−0.386261	−	0.598637i
$298$		0			0
$299$	6.39014	−	32.1254i	0.369551	−	1.85786i
$300$		0			0
$301$	0.987675	−	1.47816i	0.0569287	−	0.0851998i
$302$		0			0
$303$	−2.26636	+	0.755844i	−0.130199	+	0.0434221i
$304$		0			0
$305$	−8.90301	+	8.90301i	−0.509785	+	0.509785i
$306$		0			0
$307$	7.76821	−	11.6259i	0.443355	−	0.663528i	−0.540736	−	0.841192i	$-0.681854\pi$
$307$	7.76821	−	11.6259i	0.443355	−	0.663528i	0.984091	+	0.177665i	$0.0568542\pi$
$308$		0			0
$309$	−5.07036	−	3.93385i	−0.288442	−	0.223789i
$310$		0			0
$311$	−30.5106	+	12.6379i	−1.73010	+	0.716630i	−0.730673	+	0.682728i	$0.760794\pi$
$311$	−30.5106	+	12.6379i	−1.73010	+	0.716630i	−0.999425	+	0.0339024i	$0.989206\pi$
$312$		0			0
$313$	−0.773283	−	0.320305i	−0.0437086	−	0.0181047i	0.360722	−	0.932673i	$-0.382530\pi$
$313$	−0.773283	−	0.320305i	−0.0437086	−	0.0181047i	−0.404431	+	0.914569i	$0.632530\pi$
$314$		0			0
$315$	−24.8051	−	8.71694i	−1.39761	−	0.491144i
$316$		0			0
$317$	13.4190	−	2.66920i	0.753685	−	0.149917i	0.196728	−	0.980458i	$-0.436969\pi$
$317$	13.4190	−	2.66920i	0.753685	−	0.149917i	0.556958	+	0.830541i	$0.311969\pi$
$318$		0			0
$319$			9.21456i			0.515916i
$320$		0			0
$321$	−1.40439	+	2.80987i	−0.0783853	+	0.156831i
$322$		0			0
$323$	−1.39673	−	7.02182i	−0.0777159	−	0.390704i
$324$		0			0
$325$	10.4975	−	7.01422i	0.582297	−	0.389079i
$326$		0			0
$327$	−10.0657	+	8.73268i	−0.556635	+	0.482918i
$328$		0			0
$329$	−4.55255	−	10.9908i	−0.250990	−	0.605944i
$330$		0			0
$331$	−2.41877	+	12.1600i	−0.132947	+	0.668372i	0.855621	+	0.517602i	$0.173175\pi$
$331$	−2.41877	+	12.1600i	−0.132947	+	0.668372i	−0.988569	+	0.150770i	$0.951825\pi$
$332$		0			0
$333$	1.63597	+	29.8439i	0.0896505	+	1.63544i
$334$		0			0
$335$	−6.90875	−	6.90875i	−0.377466	−	0.377466i
$336$		0			0
$337$	22.7974	−	22.7974i	1.24185	−	1.24185i	0.282622	−	0.959231i	$-0.408796\pi$
$337$	22.7974	−	22.7974i	1.24185	−	1.24185i	0.959231	−	0.282622i	$-0.0912041\pi$
$338$		0			0
$339$	16.3449	−	9.32061i	0.887731	−	0.506226i
$340$		0			0
$341$	−0.115243	−	0.0229233i	−0.00624077	−	0.00124137i
$342$		0			0
$343$	8.79454	−	3.64282i	0.474860	−	0.196694i
$344$		0			0
$345$	16.8311	−	14.6021i	0.906158	−	0.786153i
$346$		0			0
$347$	15.3279	+	22.9398i	0.822843	+	1.23147i	0.970180	+	0.242385i	$0.0779296\pi$
$347$	15.3279	+	22.9398i	0.822843	+	1.23147i	−0.147338	+	0.989086i	$0.547070\pi$
$348$		0			0
$349$	8.15254	−	1.62164i	0.436395	−	0.0868044i	0.0279965	−	0.999608i	$-0.491087\pi$
$349$	8.15254	−	1.62164i	0.436395	−	0.0868044i	0.408399	+	0.912804i	$0.366087\pi$
$350$		0			0
$351$	−6.22763	−	34.1617i	−0.332406	−	1.82341i
$352$		0			0
$353$	12.2210			0.650460			0.325230	−	0.945635i	$-0.394558\pi$
$353$	12.2210			0.650460			0.325230	+	0.945635i	$0.394558\pi$
$354$		0			0
$355$	−7.01032	−	35.2433i	−0.372069	−	1.87052i
$356$		0			0
$357$	−27.7572	+	3.50351i	−1.46907	+	0.185425i
$358$		0			0
$359$	3.41180	−	8.23682i	0.180068	−	0.434723i	−0.807912	−	0.589303i	$-0.799402\pi$
$359$	3.41180	−	8.23682i	0.180068	−	0.434723i	0.987980	+	0.154580i	$0.0494025\pi$
$360$		0			0
$361$	−6.43280	−	15.5302i	−0.338569	−	0.817377i
$362$		0			0
$363$	−7.41275	−	5.75120i	−0.389069	−	0.301860i
$364$		0			0
$365$	−32.1655	−	21.4923i	−1.68362	−	1.12496i
$366$		0			0
$367$	−11.6703	−	11.6703i	−0.609183	−	0.609183i	0.333550	−	0.942733i	$-0.391754\pi$
$367$	−11.6703	−	11.6703i	−0.609183	−	0.609183i	−0.942733	+	0.333550i	$0.891754\pi$
$368$		0			0
$369$	7.34186	+	1.04651i	0.382202	+	0.0544793i
$370$		0			0
$371$	−25.4787	−	17.0243i	−1.32279	−	0.883859i
$372$		0			0
$373$	30.2561	+	6.01831i	1.56660	+	0.311616i	0.900706	−	0.434430i	$-0.143050\pi$
$373$	30.2561	+	6.01831i	1.56660	+	0.311616i	0.665894	+	0.746046i	$0.268050\pi$
$374$		0			0
$375$	−14.1067	−	1.00033i	−0.728466	−	0.0516570i
$376$		0			0
$377$	−9.97307	+	24.0771i	−0.513639	+	1.24004i
$378$		0			0
$379$	−12.8100	−	19.1715i	−0.658005	−	0.984774i	−0.999000	−	0.0447089i	$-0.985764\pi$
$379$	−12.8100	−	19.1715i	−0.658005	−	0.984774i	0.340995	−	0.940065i	$-0.389236\pi$
$380$		0			0
$381$	−0.964929	+	3.52570i	−0.0494348	+	0.180627i
$382$		0			0
$383$	−11.5359			−0.589459			−0.294729	−	0.955581i	$-0.595230\pi$
$383$	−11.5359			−0.589459			−0.294729	+	0.955581i	$0.595230\pi$
$384$		0			0
$385$	20.7084			1.05540
$386$		0			0
$387$	1.18956	+	1.06592i	0.0604688	+	0.0541838i
$388$		0			0
$389$	12.8942	+	19.2976i	0.653764	+	0.978427i	0.999200	+	0.0399850i	$0.0127310\pi$
$389$	12.8942	+	19.2976i	0.653764	+	0.978427i	−0.345436	+	0.938442i	$0.612269\pi$
$390$		0			0
$391$	9.07369	−	21.9058i	0.458876	−	1.10783i
$392$		0			0
$393$	1.34200	−	18.9248i	0.0676948	−	0.954632i
$394$		0			0
$395$	−6.17581	−	1.22844i	−0.310739	−	0.0618097i
$396$		0			0
$397$	2.60492	+	1.74055i	0.130737	+	0.0873557i	0.619219	−	0.785218i	$-0.287449\pi$
$397$	2.60492	+	1.74055i	0.130737	+	0.0873557i	−0.488482	+	0.872574i	$0.662449\pi$
$398$		0			0
$399$	8.11950	−	2.70790i	0.406483	−	0.135565i
$400$		0			0
$401$	−24.3210	−	24.3210i	−1.21453	−	1.21453i	−0.969520	−	0.245012i	$-0.921208\pi$
$401$	−24.3210	−	24.3210i	−1.21453	−	1.21453i	−0.245012	−	0.969520i	$-0.578792\pi$
$402$		0			0
$403$	−0.276314	−	0.184627i	−0.0137642	−	0.00919692i
$404$		0			0
$405$	10.8984	−	20.9583i	0.541548	−	1.04143i
$406$		0			0
$407$	−9.00882	−	21.7492i	−0.446550	−	1.07807i
$408$		0			0
$409$	3.24175	−	7.82629i	0.160294	−	0.386985i	−0.823243	−	0.567689i	$-0.807838\pi$
$409$	3.24175	−	7.82629i	0.160294	−	0.386985i	0.983538	+	0.180704i	$0.0578376\pi$
$410$		0			0
$411$	−0.765911	−	6.06807i	−0.0377796	−	0.299316i
$412$		0			0
$413$	2.01141	+	10.1121i	0.0989751	+	0.497582i
$414$		0			0
$415$	−26.5991			−1.30570
$416$		0			0
$417$	−8.94978	+	17.9065i	−0.438272	+	0.876885i
$418$		0			0
$419$	30.5931	−	6.08535i	1.49457	−	0.297289i	0.620933	−	0.783864i	$-0.286754\pi$
$419$	30.5931	−	6.08535i	1.49457	−	0.297289i	0.873639	+	0.486575i	$0.161754\pi$
$420$		0			0
$421$	−3.52363	−	5.27349i	−0.171731	−	0.257014i	0.735613	−	0.677402i	$-0.236894\pi$
$421$	−3.52363	−	5.27349i	−0.171731	−	0.257014i	−0.907345	+	0.420388i	$0.861894\pi$
$422$		0			0
$423$	10.3532	−	2.65589i	0.503392	−	0.129134i
$424$		0			0
$425$	8.44356	−	3.49744i	0.409573	−	0.169651i
$426$		0			0
$427$	−15.7095	−	3.12481i	−0.760234	−	0.151220i
$428$		0			0
$429$	13.5483	+	23.7586i	0.654117	+	1.14708i
$430$		0			0
$431$	−25.0198	+	25.0198i	−1.20516	+	1.20516i	−0.232586	+	0.972576i	$0.574719\pi$
$431$	−25.0198	+	25.0198i	−1.20516	+	1.20516i	−0.972576	+	0.232586i	$0.925281\pi$
$432$		0			0
$433$	−0.182313	−	0.182313i	−0.00876139	−	0.00876139i	0.702713	−	0.711474i	$-0.251972\pi$
$433$	−0.182313	−	0.182313i	−0.00876139	−	0.00876139i	−0.711474	+	0.702713i	$0.751972\pi$
$434$		0			0
$435$	−15.4007	+	8.78222i	−0.738408	+	0.421075i
$436$		0			0
$437$	−1.41515	+	7.11445i	−0.0676959	+	0.340330i
$438$		0			0
$439$	15.4119	+	37.2076i	0.735570	+	1.77582i	0.623062	+	0.782172i	$0.285888\pi$
$439$	15.4119	+	37.2076i	0.735570	+	1.77582i	0.112508	+	0.993651i	$0.464112\pi$
$440$		0			0
$441$	−3.09295	−	12.0570i	−0.147283	−	0.574143i
$442$		0			0
$443$	5.50223	−	3.67647i	0.261419	−	0.174674i	−0.417953	−	0.908469i	$-0.637252\pi$
$443$	5.50223	−	3.67647i	0.261419	−	0.174674i	0.679372	+	0.733794i	$0.262252\pi$
$444$		0			0
$445$	−4.57852	−	23.0178i	−0.217043	−	1.09115i
$446$		0			0
$447$	−14.8752	−	7.43473i	−0.703574	−	0.351651i
$448$		0			0
$449$		−	13.3291i		−	0.629041i	−0.949251	−	0.314520i	$-0.898156\pi$
$449$		−	13.3291i		−	0.629041i	0.949251	−	0.314520i	$-0.101844\pi$
$450$		0			0
$451$	−5.72886	+	1.13954i	−0.269761	+	0.0536589i
$452$		0			0
$453$	−28.7135	+	3.62422i	−1.34908	+	0.170281i
$454$		0			0
$455$	54.1100	+	22.4131i	2.53672	+	1.05074i
$456$		0			0
$457$	−18.5018	+	7.66368i	−0.865476	+	0.358492i	−0.770847	−	0.637020i	$-0.780167\pi$
$457$	−18.5018	+	7.66368i	−0.865476	+	0.358492i	−0.0946295	+	0.995513i	$0.530167\pi$
$458$		0			0
$459$	0.402945	−	25.1335i	0.0188079	−	1.17313i
$460$		0			0
$461$	−19.4038	+	29.0398i	−0.903724	+	1.35252i	0.0318892	+	0.999491i	$0.489848\pi$
$461$	−19.4038	+	29.0398i	−0.903724	+	1.35252i	−0.935613	+	0.353027i	$0.885152\pi$
$462$		0			0
$463$	26.4304	−	26.4304i	1.22833	−	1.22833i	0.263728	−	0.964597i	$-0.415048\pi$
$463$	26.4304	−	26.4304i	1.22833	−	1.22833i	0.964597	−	0.263728i	$-0.0849522\pi$
$464$		0			0
$465$	−0.0715233	−	0.214459i	−0.00331681	−	0.00994530i
$466$		0			0
$467$	−6.62269	+	9.91156i	−0.306462	+	0.458652i	−0.952450	−	0.304695i	$-0.901445\pi$
$467$	−6.62269	+	9.91156i	−0.306462	+	0.458652i	0.645988	+	0.763347i	$0.276445\pi$
$468$		0			0
$469$	2.42485	−	12.1906i	0.111969	−	0.562908i
$470$		0			0
$471$	−1.94611	−	0.138003i	−0.0896721	−	0.00635882i
$472$		0			0
$473$	−1.16228	−	0.481433i	−0.0534418	−	0.0221363i
$474$		0			0
$475$	−2.32477	+	1.55336i	−0.106668	+	0.0712731i
$476$		0			0
$477$	18.3730	−	20.5042i	0.841243	−	0.938822i
$478$		0			0
$479$			37.9382i			1.73344i	0.498795	+	0.866720i	$0.333776\pi$
$479$			37.9382i			1.73344i	−0.498795	+	0.866720i	$0.666224\pi$
$480$		0			0
$481$		−	66.5798i		−	3.03578i
$482$		0			0
$483$	27.3410	+	7.48282i	1.24406	+	0.340480i
$484$		0			0
$485$	8.57938	−	5.73256i	0.389569	−	0.260302i
$486$		0			0
$487$	20.1298	+	8.33804i	0.912168	+	0.377833i	0.788886	−	0.614539i	$-0.210658\pi$
$487$	20.1298	+	8.33804i	0.912168	+	0.377833i	0.123282	+	0.992372i	$0.460658\pi$
$488$		0			0
$489$	−2.48572	+	35.0536i	−0.112408	+	1.58518i
$490$		0			0
$491$	−3.99742	+	20.0964i	−0.180401	+	0.906936i	0.779458	+	0.626454i	$0.215494\pi$
$491$	−3.99742	+	20.0964i	−0.180401	+	0.906936i	−0.959859	+	0.280482i	$0.909506\pi$
$492$		0			0
$493$	−10.4809	+	15.6858i	−0.472036	+	0.706451i
$494$		0			0
$495$	−2.62554	+	18.4196i	−0.118009	+	0.827900i
$496$		0			0
$497$	32.3238	−	32.3238i	1.44992	−	1.44992i
$498$		0			0
$499$	−10.8139	+	16.1841i	−0.484095	+	0.724500i	−0.990457	−	0.137821i	$-0.955990\pi$
$499$	−10.8139	+	16.1841i	−0.484095	+	0.724500i	0.506362	+	0.862321i	$0.330990\pi$
$500$		0			0
$501$	0.304861	−	0.392937i	0.0136202	−	0.0175551i
$502$		0			0
$503$	13.0766	−	5.41650i	0.583056	−	0.241510i	−0.0716041	−	0.997433i	$-0.522812\pi$
$503$	13.0766	−	5.41650i	0.583056	−	0.241510i	0.654660	+	0.755923i	$0.272812\pi$
$504$		0			0
$505$	3.34480	+	1.38546i	0.148842	+	0.0616522i
$506$		0			0
$507$	6.86687	+	54.4040i	0.304969	+	2.41617i
$508$		0			0
$509$	21.9603	−	4.36817i	0.973371	−	0.193616i	0.317309	−	0.948322i	$-0.397221\pi$
$509$	21.9603	−	4.36817i	0.973371	−	0.193616i	0.656062	+	0.754707i	$0.272221\pi$
$510$		0			0
$511$		−	49.2130i		−	2.17705i
$512$		0			0
$513$	1.37916	+	7.56540i	0.0608916	+	0.334021i
$514$		0			0
$515$	1.89724	+	9.53808i	0.0836025	+	0.420298i
$516$		0			0
$517$	−6.99975	+	4.67708i	−0.307848	+	0.205698i
$518$		0			0
$519$	−15.2251	−	17.5492i	−0.668307	−	0.770323i
$520$		0			0
$521$	−0.213242	−	0.514813i	−0.00934232	−	0.0225544i	0.919140	−	0.393932i	$-0.128885\pi$
$521$	−0.213242	−	0.514813i	−0.00934232	−	0.0225544i	−0.928482	+	0.371378i	$0.878885\pi$
$522$		0			0
$523$	0.636430	−	3.19955i	0.0278291	−	0.139907i	−0.964373	−	0.264547i	$-0.914778\pi$
$523$	0.636430	−	3.19955i	0.0278291	−	0.139907i	0.992202	+	0.124640i	$0.0397777\pi$
$524$		0			0
$525$	5.41241	+	9.49134i	0.236217	+	0.414236i
$526$		0			0
$527$	−0.170103	−	0.170103i	−0.00740979	−	0.00740979i
$528$		0			0
$529$	−0.723726	+	0.723726i	−0.0314664	+	0.0314664i
$530$		0			0
$531$	−9.24942	+	0.507029i	−0.401391	+	0.0220032i
$532$		0			0
$533$	−16.2025	−	3.22288i	−0.701809	−	0.139599i
$534$		0			0
$535$	4.39792	−	1.82168i	0.190139	−	0.0787580i
$536$		0			0
$537$	18.8365	+	21.7119i	0.812856	+	0.936938i
$538$		0			0
$539$	5.44675	+	8.15164i	0.234608	+	0.351116i
$540$		0			0
$541$	−18.6138	+	3.70251i	−0.800270	+	0.159184i	−0.578251	−	0.815859i	$-0.696265\pi$
$541$	−18.6138	+	3.70251i	−0.800270	+	0.159184i	−0.222019	+	0.975042i	$0.571265\pi$
$542$		0			0
$543$	−0.582309	−	0.291042i	−0.0249893	−	0.0124898i
$544$		0			0
$545$	20.1939			0.865010
$546$		0			0
$547$	−0.321617	−	1.61688i	−0.0137513	−	0.0691327i	0.973300	−	0.229535i	$-0.0737207\pi$
$547$	−0.321617	−	1.61688i	−0.0137513	−	0.0691327i	−0.987052	+	0.160403i	$0.948721\pi$
$548$		0			0
$549$	4.77117	−	13.5770i	0.203629	−	0.579451i
$550$		0			0
$551$	2.20863	−	5.33209i	0.0940906	−	0.227155i
$552$		0			0
$553$	−3.06545	−	7.40066i	−0.130356	−	0.314708i
$554$		0			0
$555$	27.7643	−	35.7856i	1.17853	−	1.51901i
$556$		0			0
$557$	−7.81765	−	5.22359i	−0.331245	−	0.221330i	0.378815	−	0.925473i	$-0.376332\pi$
$557$	−7.81765	−	5.22359i	−0.331245	−	0.221330i	−0.710059	+	0.704142i	$0.751332\pi$
$558$		0			0
$559$	−2.51592	−	2.51592i	−0.106412	−	0.106412i
$560$		0			0
$561$	6.26369	+	18.7814i	0.264453	+	0.792950i
$562$		0			0
$563$	25.4030	+	16.9737i	1.07061	+	0.715357i	0.960420	−	0.278554i	$-0.0898552\pi$
$563$	25.4030	+	16.9737i	1.07061	+	0.715357i	0.110186	+	0.993911i	$0.464855\pi$
$564$		0			0
$565$	−27.9652	−	5.56262i	−1.17650	−	0.234021i
$566$		0			0
$567$	29.8712	−	3.28480i	1.25447	−	0.137949i
$568$		0			0
$569$	−11.5727	+	27.9391i	−0.485154	+	1.17127i	0.471977	+	0.881611i	$0.343541\pi$
$569$	−11.5727	+	27.9391i	−0.485154	+	1.17127i	−0.957131	+	0.289655i	$0.906459\pi$
$570$		0			0
$571$	−7.03644	−	10.5308i	−0.294466	−	0.440700i	0.654507	−	0.756056i	$-0.272876\pi$
$571$	−7.03644	−	10.5308i	−0.294466	−	0.440700i	−0.948973	+	0.315356i	$0.897876\pi$
$572$		0			0
$573$	8.15299	+	2.23135i	0.340596	+	0.0932160i
$574$		0			0
$575$	−9.25981			−0.386161
$576$		0			0
$577$	9.10864			0.379198			0.189599	−	0.981862i	$-0.439281\pi$
$577$	9.10864			0.379198			0.189599	+	0.981862i	$0.439281\pi$
$578$		0			0
$579$	−12.5785	−	3.44255i	−0.522746	−	0.143068i
$580$		0			0
$581$	−18.7993	−	28.1351i	−0.779925	−	1.16724i
$582$		0			0
$583$	−8.29835	+	20.0340i	−0.343682	+	0.829723i
$584$		0			0
$585$	−26.7962	+	45.2877i	−1.10789	+	1.87242i
$586$		0			0
$587$	−43.4391	−	8.64058i	−1.79292	−	0.356635i	−0.817322	−	0.576180i	$-0.804543\pi$
$587$	−43.4391	−	8.64058i	−1.79292	−	0.356635i	−0.975602	+	0.219546i	$0.929543\pi$
$588$		0			0
$589$	0.0611921	+	0.0408873i	0.00252138	+	0.00168473i
$590$		0			0
$591$	8.50062	+	25.4887i	0.349669	+	1.04846i
$592$		0			0
$593$	−12.4091	−	12.4091i	−0.509580	−	0.509580i	0.404817	−	0.914398i	$-0.367335\pi$
$593$	−12.4091	−	12.4091i	−0.509580	−	0.509580i	−0.914398	+	0.404817i	$0.867335\pi$
$594$		0			0
$595$	35.2516	+	23.5543i	1.44517	+	0.965634i
$596$		0			0
$597$	−12.2928	+	15.8443i	−0.503111	+	0.648463i
$598$		0			0
$599$	−5.32882	−	12.8649i	−0.217730	−	0.525646i	0.776843	−	0.629695i	$-0.216820\pi$
$599$	−5.32882	−	12.8649i	−0.217730	−	0.525646i	−0.994572	+	0.104049i	$0.966820\pi$
$600$		0			0
$601$	−9.61422	+	23.2108i	−0.392172	+	0.946788i	0.597294	+	0.802023i	$0.296243\pi$
$601$	−9.61422	+	23.2108i	−0.392172	+	0.946788i	−0.989466	+	0.144765i	$0.953757\pi$
$602$		0			0
$603$	10.5357	+	3.70244i	0.429049	+	0.150775i
$604$		0			0
$605$	2.77373	+	13.9445i	0.112768	+	0.566923i
$606$		0			0
$607$	−7.83446			−0.317991			−0.158995	−	0.987279i	$-0.550825\pi$
$607$	−7.83446			−0.317991			−0.158995	+	0.987279i	$0.550825\pi$
$608$		0			0
$609$	−20.1740	−	10.0831i	−0.817493	−	0.408588i
$610$		0			0
$611$	−23.3520	+	4.64501i	−0.944722	+	0.187917i
$612$		0			0
$613$	16.6418	+	24.9062i	0.672154	+	1.00595i	0.998163	+	0.0605835i	$0.0192961\pi$
$613$	16.6418	+	24.9062i	0.672154	+	1.00595i	−0.326009	+	0.945367i	$0.605704\pi$
$614$		0			0
$615$	−7.36463	−	8.48883i	−0.296971	−	0.342303i
$616$		0			0
$617$	34.0519	−	14.1048i	1.37088	−	0.567836i	0.428852	−	0.903375i	$-0.358918\pi$
$617$	34.0519	−	14.1048i	1.37088	−	0.567836i	0.942027	+	0.335538i	$0.108918\pi$
$618$		0			0
$619$	−29.7566	−	5.91895i	−1.19602	−	0.237903i	−0.443377	−	0.896335i	$-0.646220\pi$
$619$	−29.7566	−	5.91895i	−1.19602	−	0.237903i	−0.752640	+	0.658433i	$0.771220\pi$
$620$		0			0
$621$	−10.1222	+	23.3704i	−0.406191	+	0.937821i
$622$		0			0
$623$	21.1110	−	21.1110i	0.845796	−	0.845796i
$624$		0			0
$625$	21.8333	+	21.8333i	0.873332	+	0.873332i
$626$		0			0
$627$	−3.00038	−	5.26155i	−0.119824	−	0.210126i
$628$		0			0
$629$	9.40261	−	47.2701i	0.374907	−	1.88478i
$630$		0			0
$631$	5.45257	+	13.1637i	0.217063	+	0.524037i	0.994477	−	0.104952i	$-0.0334689\pi$
$631$	5.45257	+	13.1637i	0.217063	+	0.524037i	−0.777414	+	0.628989i	$0.783469\pi$
$632$		0			0
$633$	−24.4216	−	28.1496i	−0.970672	−	1.11884i
$634$		0			0
$635$	4.60575	−	3.07747i	0.182774	−	0.122126i
$636$		0			0
$637$	5.40940	+	27.1949i	0.214328	+	1.07750i
$638$		0			0
$639$	24.6530	+	32.8494i	0.975256	+	1.29950i
$640$		0			0
$641$			7.05243i			0.278554i	0.990253	+	0.139277i	$0.0444779\pi$
$641$			7.05243i			0.278554i	−0.990253	+	0.139277i	$0.955522\pi$
$642$		0			0
$643$	−29.0442	+	5.77725i	−1.14539	+	0.227832i	−0.731072	−	0.682300i	$-0.760980\pi$
$643$	−29.0442	+	5.77725i	−1.14539	+	0.227832i	−0.414318	+	0.910132i	$0.635980\pi$
$644$		0			0
$645$	−0.303107	−	2.40142i	−0.0119348	−	0.0945559i
$646$		0			0
$647$	−43.7051	−	18.1032i	−1.71822	−	0.711711i	−0.999871	−	0.0160315i	$-0.994897\pi$
$647$	−43.7051	−	18.1032i	−1.71822	−	0.711711i	−0.718352	−	0.695680i	$-0.755103\pi$
$648$		0			0
$649$	6.74065	−	2.79207i	0.264594	−	0.109598i
$650$		0			0
$651$	0.176293	−	0.227225i	0.00690948	−	0.00890567i
$652$		0			0
$653$	14.1402	−	21.1623i	0.553348	−	0.828143i	−0.444358	−	0.895849i	$-0.646568\pi$
$653$	14.1402	−	21.1623i	0.553348	−	0.828143i	0.997705	+	0.0677063i	$0.0215681\pi$
$654$		0			0
$655$	−20.3297	+	20.3297i	−0.794347	+	0.794347i
$656$		0			0
$657$	43.7736	+	6.23952i	1.70777	+	0.243427i
$658$		0			0
$659$	18.1263	−	27.1279i	0.706100	−	1.05675i	−0.288947	−	0.957345i	$-0.593305\pi$
$659$	18.1263	−	27.1279i	0.706100	−	1.05675i	0.995047	−	0.0994083i	$-0.0316950\pi$
$660$		0			0
$661$	5.91065	−	29.7149i	0.229898	−	1.15577i	−0.677507	−	0.735516i	$-0.736940\pi$
$661$	5.91065	−	29.7149i	0.229898	−	1.15577i	0.907405	−	0.420258i	$-0.138060\pi$
$662$		0			0
$663$	−3.96071	+	55.8540i	−0.153821	+	2.16919i
$664$		0			0
$665$	−11.9831	−	4.96358i	−0.464686	−	0.192479i
$666$		0			0
$667$	15.8927	−	10.6192i	0.615368	−	0.411176i
$668$		0			0
$669$	2.43483	+	0.666375i	0.0941358	+	0.0257635i
$670$		0			0
$671$			11.3347i			0.437569i
$672$		0			0
$673$		−	11.0359i		−	0.425402i	−0.977117	−	0.212701i	$-0.931774\pi$
$673$		−	11.0359i		−	0.425402i	0.977117	−	0.212701i	$-0.0682259\pi$
$674$		0			0
$675$	−9.12851	+	3.61082i	−0.351356	+	0.138981i
$676$		0			0
$677$	16.1303	−	10.7779i	0.619939	−	0.414230i	−0.205551	−	0.978646i	$-0.565899\pi$
$677$	16.1303	−	10.7779i	0.619939	−	0.414230i	0.825490	+	0.564416i	$0.190899\pi$
$678$		0			0
$679$	12.1272	+	5.02324i	0.465399	+	0.192774i
$680$		0			0
$681$	−34.1185	−	2.41941i	−1.30743	−	0.0927121i
$682$		0			0
$683$	−9.44062	+	47.4612i	−0.361235	+	1.81605i	0.190095	+	0.981766i	$0.439120\pi$
$683$	−9.44062	+	47.4612i	−0.361235	+	1.81605i	−0.551331	+	0.834287i	$0.685880\pi$
$684$		0			0
$685$	−5.14927	+	7.70643i	−0.196744	+	0.294448i
$686$		0			0
$687$	0.923276	+	2.76840i	0.0352252	+	0.105621i
$688$		0			0
$689$	−43.3662	+	43.3662i	−1.65212	+	1.65212i
$690$		0			0
$691$	2.62103	−	3.92264i	0.0997085	−	0.149224i	−0.778261	−	0.627941i	$-0.783898\pi$
$691$	2.62103	−	3.92264i	0.0997085	−	0.149224i	0.877969	+	0.478717i	$0.158898\pi$
$692$		0			0
$693$	−21.3389	+	10.2411i	−0.810598	+	0.389029i
$694$		0			0
$695$	28.0267	−	11.6090i	1.06311	−	0.440356i
$696$		0			0
$697$	−11.0483	−	4.57634i	−0.418483	−	0.173341i
$698$		0			0
$699$	−26.8126	+	3.38429i	−1.01415	+	0.128005i
$700$		0			0
$701$	0.420755	−	0.0836934i	0.0158917	−	0.00316106i	−0.187138	−	0.982334i	$-0.559921\pi$
$701$	0.420755	−	0.0836934i	0.0158917	−	0.00316106i	0.203030	+	0.979173i	$0.434921\pi$
$702$		0			0
$703$			14.7447i			0.556107i
$704$		0			0
$705$	−14.4883	−	7.24137i	−0.545663	−	0.272726i
$706$		0			0
$707$	0.898516	+	4.51715i	0.0337922	+	0.169885i
$708$		0			0
$709$	25.3814	−	16.9593i	0.953218	−	0.636920i	0.0213708	−	0.999772i	$-0.493197\pi$
$709$	25.3814	−	16.9593i	0.953218	−	0.636920i	0.931847	+	0.362852i	$0.118197\pi$
$710$		0			0
$711$	6.97135	−	1.78834i	0.261446	−	0.0670679i
$712$		0			0
$713$	0.0932734	+	0.225182i	0.00349312	+	0.00843313i
$714$		0			0
$715$	8.08572	−	40.6497i	0.302389	−	1.52021i
$716$		0			0
$717$	−1.46877	+	0.837563i	−0.0548523	+	0.0312794i
$718$		0			0
$719$	−4.47853	−	4.47853i	−0.167021	−	0.167021i	0.618648	−	0.785669i	$-0.287681\pi$
$719$	−4.47853	−	4.47853i	−0.167021	−	0.167021i	−0.785669	+	0.618648i	$0.787681\pi$
$720$		0			0
$721$	−8.74797	+	8.74797i	−0.325791	+	0.325791i
$722$		0			0
$723$	−12.8745	−	22.5770i	−0.478808	−	0.839649i
$724$		0			0
$725$	7.22588	+	1.43732i	0.268363	+	0.0533806i
$726$		0			0
$727$	3.41297	−	1.41370i	0.126580	−	0.0524311i	−0.318494	−	0.947925i	$-0.603177\pi$
$727$	3.41297	−	1.41370i	0.126580	−	0.0524311i	0.445074	+	0.895494i	$0.353177\pi$
$728$		0			0
$729$	−0.865518	+	26.9861i	−0.0320562	+	0.999486i
$730$		0			0
$731$	−1.43094	−	2.14155i	−0.0529250	−	0.0792079i
$732$		0			0
$733$	−1.76647	+	0.351374i	−0.0652462	+	0.0129783i	−0.227605	−	0.973753i	$-0.573090\pi$
$733$	−1.76647	+	0.351374i	−0.0652462	+	0.0129783i	0.162359	+	0.986732i	$0.448090\pi$
$734$		0			0
$735$	−8.43303	+	16.8726i	−0.311057	+	0.622355i
$736$		0			0
$737$	−8.79571			−0.323994
$738$		0			0
$739$	7.50862	+	37.7484i	0.276209	+	1.38860i	0.830845	+	0.556504i	$0.187857\pi$
$739$	7.50862	+	37.7484i	0.276209	+	1.38860i	−0.554636	+	0.832093i	$0.687143\pi$
$740$		0			0
$741$	−2.14517	−	16.9955i	−0.0788049	−	0.624345i
$742$		0			0
$743$	−13.3142	+	32.1432i	−0.488449	+	1.17922i	0.467051	+	0.884230i	$0.345316\pi$
$743$	−13.3142	+	32.1432i	−0.488449	+	1.17922i	−0.955500	+	0.294990i	$0.904684\pi$
$744$		0			0
$745$	9.64382	+	23.2822i	0.353322	+	0.852995i
$746$		0			0
$747$	27.4089	−	13.1543i	1.00284	−	0.481291i
$748$		0			0
$749$	5.03516	+	3.36439i	0.183981	+	0.122932i
$750$		0			0
$751$	−30.0300	−	30.0300i	−1.09581	−	1.09581i	−0.994895	−	0.100914i	$-0.967823\pi$
$751$	−30.0300	−	30.0300i	−1.09581	−	1.09581i	−0.100914	−	0.994895i	$-0.532177\pi$
$752$		0			0
$753$	44.9449	−	14.9894i	1.63788	−	0.546244i
$754$		0			0
$755$	36.4661	+	24.3659i	1.32714	+	0.886766i
$756$		0			0
$757$	37.4839	+	7.45600i	1.36237	+	0.270993i	0.821547	−	0.570141i	$-0.193111\pi$
$757$	37.4839	+	7.45600i	1.36237	+	0.270993i	0.540827	+	0.841134i	$0.318111\pi$
$758$		0			0
$759$	1.41890	−	20.0093i	0.0515027	−	0.726290i
$760$		0			0
$761$	−5.61157	+	13.5475i	−0.203419	+	0.491097i	−0.992361	−	0.123371i	$-0.960629\pi$
$761$	−5.61157	+	13.5475i	−0.203419	+	0.491097i	0.788941	+	0.614468i	$0.210629\pi$
$762$		0			0
$763$	14.2723	+	21.3600i	0.516692	+	0.773284i
$764$		0			0
$765$	−25.4204	+	28.3690i	−0.919075	+	1.02568i
$766$		0			0
$767$	20.6348			0.745081
$768$		0			0
$769$	17.9581			0.647587			0.323793	−	0.946128i	$-0.395042\pi$
$769$	17.9581			0.647587			0.323793	+	0.946128i	$0.395042\pi$
$770$		0			0
$771$	−2.06581	+	7.54813i	−0.0743982	+	0.271839i
$772$		0			0
$773$	9.82391	+	14.7025i	0.353341	+	0.528813i	0.964980	−	0.262325i	$-0.0844892\pi$
$773$	9.82391	+	14.7025i	0.353341	+	0.528813i	−0.611638	+	0.791138i	$0.709489\pi$
$774$		0			0
$775$	−0.0359520	+	0.0867959i	−0.00129144	+	0.00311780i
$776$		0			0
$777$	57.4749	+	4.07566i	2.06190	+	0.146214i
$778$		0			0
$779$	3.58819	+	0.713736i	0.128560	+	0.0255722i
$780$		0			0
$781$	−26.8971	−	17.9721i	−0.962453	−	0.643091i
$782$		0			0
$783$	11.5264	−	16.6659i	0.411922	−	0.595590i
$784$		0			0
$785$	2.09058	+	2.09058i	0.0746160	+	0.0746160i
$786$		0			0
$787$	30.2625	+	20.2207i	1.07874	+	0.720791i	0.962186	−	0.272393i	$-0.0878151\pi$
$787$	30.2625	+	20.2207i	1.07874	+	0.720791i	0.116554	+	0.993184i	$0.462815\pi$
$788$		0			0
$789$	3.03568	+	2.35523i	0.108073	+	0.0838486i
$790$		0			0
$791$	−13.8809	−	33.5115i	−0.493549	−	1.19153i
$792$		0			0
$793$	−12.2677	+	29.6168i	−0.435638	+	1.05172i
$794$		0			0
$795$	−41.3927	+	5.22459i	−1.46805	+	0.185297i
$796$		0			0
$797$	−4.54990	−	22.8739i	−0.161166	−	0.810234i	−0.973790	−	0.227447i	$-0.926962\pi$
$797$	−4.54990	−	22.8739i	−0.161166	−	0.810234i	0.812625	−	0.582787i	$-0.198038\pi$
$798$		0			0
$799$	−17.2354			−0.609744
$800$		0			0
$801$	16.1011	+	21.4543i	0.568905	+	0.758051i
$802$		0			0
$803$	−34.1566	+	6.79417i	−1.20536	+	0.239761i
$804$		0			0
$805$	−23.8651	−	35.7166i	−0.841134	−	1.25885i
$806$		0			0
$807$	30.1793	−	26.1826i	1.06236	−	0.921671i
$808$		0			0
$809$	−18.3664	+	7.60762i	−0.645729	+	0.267470i	−0.681419	−	0.731893i	$-0.738637\pi$
$809$	−18.3664	+	7.60762i	−0.645729	+	0.267470i	0.0356905	+	0.999363i	$0.488637\pi$
$810$		0			0
$811$	46.0682	+	9.16353i	1.61767	+	0.321775i	0.919179	−	0.393840i	$-0.128854\pi$
$811$	46.0682	+	9.16353i	1.61767	+	0.321775i	0.698494	+	0.715616i	$0.253854\pi$
$812$		0			0
$813$	9.96158	−	5.68056i	0.349368	−	0.199226i
$814$		0			0
$815$	37.6558	−	37.6558i	1.31903	−	1.31903i
$816$		0			0
$817$	0.557172	+	0.557172i	0.0194930	+	0.0194930i
$818$		0			0
$819$	−66.8416	+	3.66408i	−2.33563	+	0.128033i
$820$		0			0
$821$	−7.82812	+	39.3546i	−0.273203	+	1.37349i	0.563630	+	0.826028i	$0.309404\pi$
$821$	−7.82812	+	39.3546i	−0.273203	+	1.37349i	−0.836833	+	0.547458i	$0.815596\pi$
$822$		0			0
$823$	−10.4572	−	25.2460i	−0.364516	−	0.880019i	−0.994628	−	0.103515i	$-0.966991\pi$
$823$	−10.4572	−	25.2460i	−0.364516	−	0.880019i	0.630112	−	0.776504i	$-0.283009\pi$
$824$		0			0
$825$	5.84031	−	5.06686i	0.203333	−	0.176405i
$826$		0			0
$827$	13.3380	−	8.91218i	0.463809	−	0.309907i	−0.301620	−	0.953428i	$-0.597527\pi$
$827$	13.3380	−	8.91218i	0.463809	−	0.309907i	0.765428	+	0.643521i	$0.222527\pi$
$828$		0			0
$829$	4.63371	+	23.2952i	0.160935	+	0.809077i	0.973938	+	0.226816i	$0.0728317\pi$
$829$	4.63371	+	23.2952i	0.160935	+	0.809077i	−0.813002	+	0.582261i	$0.802168\pi$
$830$		0			0
$831$	1.39533	−	2.79175i	0.0484036	−	0.0968448i
$832$		0			0
$833$			20.0717i			0.695442i
$834$		0			0
$835$	−0.739173	+	0.147031i	−0.0255801	+	0.00508820i
$836$		0			0
$837$	0.179759	+	0.185617i	0.00621340	+	0.00641587i
$838$		0			0
$839$	27.5815	+	11.4246i	0.952220	+	0.394423i	0.804065	−	0.594542i	$-0.202666\pi$
$839$	27.5815	+	11.4246i	0.952220	+	0.394423i	0.148155	+	0.988964i	$0.452666\pi$
$840$		0			0
$841$	12.7423	−	5.27805i	0.439391	−	0.182002i
$842$		0			0
$843$	9.38597	+	7.28212i	0.323270	+	0.250810i
$844$		0			0
$845$	46.1664	−	69.0930i	1.58817	−	2.37687i
$846$		0			0
$847$	−12.7894	+	12.7894i	−0.439447	+	0.439447i
$848$		0			0
$849$	37.6367	−	12.5521i	1.29169	−	0.430785i
$850$		0			0
$851$	−27.1296	+	40.6023i	−0.929991	+	1.39183i
$852$		0			0
$853$	0.300445	−	1.51044i	0.0102870	−	0.0517164i	−0.975301	−	0.220881i	$-0.929107\pi$
$853$	0.300445	−	1.51044i	0.0102870	−	0.0517164i	0.985588	+	0.169164i	$0.0541068\pi$
$854$		0			0
$855$	5.93427	−	10.0294i	0.202948	−	0.342997i
$856$		0			0
$857$	6.92900	+	2.87008i	0.236690	+	0.0980402i	0.497876	−	0.867248i	$-0.334114\pi$
$857$	6.92900	+	2.87008i	0.236690	+	0.0980402i	−0.261186	+	0.965289i	$0.584114\pi$
$858$		0			0
$859$	−12.3876	+	8.27714i	−0.422660	+	0.282412i	−0.748656	−	0.662959i	$-0.769300\pi$
$859$	−12.3876	+	8.27714i	−0.422660	+	0.282412i	0.325996	+	0.945371i	$0.394300\pi$
$860$		0			0
$861$	3.77398	−	13.7895i	0.128617	−	0.469945i
$862$		0			0
$863$		−	31.0444i		−	1.05676i	−0.849007	−	0.528382i	$-0.822799\pi$
$863$		−	31.0444i		−	1.05676i	0.849007	−	0.528382i	$-0.177201\pi$
$864$		0			0
$865$			35.2072i			1.19708i
$866$		0			0
$867$	−2.92712	+	10.6952i	−0.0994101	+	0.363228i
$868$		0			0
$869$	−4.71327	+	3.14931i	−0.159887	+	0.106833i
$870$		0			0
$871$	−22.9827	−	9.51975i	−0.778739	−	0.322564i
$872$		0			0
$873$	−6.00560	+	10.1499i	−0.203259	+	0.343523i
$874$		0			0
$875$	−5.31875	+	26.7392i	−0.179807	+	0.903949i
$876$		0			0
$877$	13.8663	−	20.7524i	0.468232	−	0.700759i	−0.519924	−	0.854213i	$-0.674040\pi$
$877$	13.8663	−	20.7524i	0.468232	−	0.700759i	0.988156	+	0.153454i	$0.0490397\pi$
$878$		0			0
$879$	−20.5907	+	6.86713i	−0.694509	+	0.231623i
$880$		0			0
$881$	−22.9018	+	22.9018i	−0.771582	+	0.771582i	−0.978383	−	0.206801i	$-0.933695\pi$
$881$	−22.9018	+	22.9018i	−0.771582	+	0.771582i	0.206801	+	0.978383i	$0.433695\pi$
$882$		0			0
$883$	−10.2732	+	15.3750i	−0.345722	+	0.517409i	−0.963059	−	0.269289i	$-0.913211\pi$
$883$	−10.2732	+	15.3750i	−0.345722	+	0.517409i	0.617338	+	0.786698i	$0.288211\pi$
$884$		0			0
$885$	11.0909	+	8.60490i	0.372817	+	0.289250i
$886$		0			0
$887$	9.52810	−	3.94667i	0.319922	−	0.132516i	−0.216943	−	0.976184i	$-0.569608\pi$
$887$	9.52810	−	3.94667i	0.319922	−	0.132516i	0.536865	+	0.843668i	$0.319608\pi$
$888$		0			0
$889$	6.51036	+	2.69668i	0.218350	+	0.0904437i
$890$		0			0
$891$	−6.40375	−	20.2788i	−0.214534	−	0.679366i
$892$		0			0
$893$	5.17151	−	1.02868i	0.173058	−	0.0344234i
$894$		0			0
$895$		−	43.5585i		−	1.45600i
$896$		0			0
$897$	25.3639	−	50.7474i	0.846875	−	1.69441i
$898$		0			0
$899$	−0.0378328	−	0.190198i	−0.00126179	−	0.00634347i
$900$		0			0
$901$	−36.9133	+	24.6647i	−1.22976	+	0.821700i
$902$		0			0
$903$	2.32587	−	2.01785i	0.0774001	−	0.0671498i
$904$		0			0
$905$	0.377519	+	0.911413i	0.0125492	+	0.0302964i
$906$		0			0
$907$	−6.38322	+	32.0906i	−0.211951	+	1.06555i	0.717487	+	0.696572i	$0.245292\pi$
$907$	−6.38322	+	32.0906i	−0.211951	+	1.06555i	−0.929438	+	0.368979i	$0.879708\pi$
$908$		0			0
$909$	−4.13180	+	0.226495i	−0.137043	+	0.00751235i
$910$		0			0
$911$	−20.1753	−	20.1753i	−0.668438	−	0.668438i	0.288916	−	0.957354i	$-0.406705\pi$
$911$	−20.1753	−	20.1753i	−0.668438	−	0.668438i	−0.957354	+	0.288916i	$0.906705\pi$
$912$		0			0
$913$	−16.9320	+	16.9320i	−0.560367	+	0.560367i
$914$		0			0
$915$	−18.9441	+	10.8028i	−0.626274	+	0.357131i
$916$		0			0
$917$	−35.8720	−	7.13538i	−1.18460	−	0.235631i
$918$		0			0
$919$	44.0591	−	18.2499i	1.45338	−	0.602008i	0.490377	−	0.871510i	$-0.336859\pi$
$919$	44.0591	−	18.2499i	1.45338	−	0.602008i	0.963000	+	0.269502i	$0.0868591\pi$
$920$		0			0
$921$	18.2933	−	15.8707i	0.602785	−	0.522956i
$922$		0			0
$923$	−50.8291	−	76.0711i	−1.67306	−	2.50391i
$924$		0			0
$925$	−18.4605	+	3.67203i	−0.606979	+	0.120736i
$926$		0			0
$927$	−6.67197	−	8.89021i	−0.219136	−	0.291993i
$928$		0			0
$929$	−28.1038			−0.922057			−0.461028	−	0.887385i	$-0.652519\pi$
$929$	−28.1038			−0.922057			−0.461028	+	0.887385i	$0.652519\pi$
$930$		0			0
$931$	−1.19796	−	6.02255i	−0.0392616	−	0.197381i
$932$		0			0
$933$	−56.7498	+	7.16296i	−1.85790	+	0.234505i
$934$		0			0
$935$	11.4813	−	27.7184i	0.375480	−	0.906489i
$936$		0			0
$937$	−7.86396	−	18.9853i	−0.256904	−	0.620222i	0.741826	−	0.670592i	$-0.233960\pi$
$937$	−7.86396	−	18.9853i	−0.256904	−	0.620222i	−0.998731	+	0.0503700i	$0.983960\pi$
$938$		0			0
$939$	−1.14541	−	0.888667i	−0.0373790	−	0.0290005i
$940$		0			0
$941$	43.2971	+	28.9302i	1.41145	+	0.943098i	0.999491	+	0.0318944i	$0.0101540\pi$
$941$	43.2971	+	28.9302i	1.41145	+	0.943098i	0.411955	+	0.911204i	$0.364846\pi$
$942$		0			0
$943$	8.56753	+	8.56753i	0.278997	+	0.278997i
$944$		0			0
$945$	−37.4542	−	25.9041i	−1.21839	−	0.842660i
$946$		0			0
$947$	13.0677	+	8.73155i	0.424643	+	0.283737i	0.749473	−	0.662035i	$-0.230307\pi$
$947$	13.0677	+	8.73155i	0.424643	+	0.283737i	−0.324830	+	0.945772i	$0.605307\pi$
$948$		0			0
$949$	−96.6027	−	19.2155i	−3.13586	−	0.623760i
$950$		0			0
$951$	23.6384	+	1.67624i	0.766526	+	0.0543559i
$952$		0			0
$953$	−18.0842	+	43.6591i	−0.585804	+	1.41426i	0.301676	+	0.953411i	$0.402454\pi$
$953$	−18.0842	+	43.6591i	−0.585804	+	1.41426i	−0.887480	+	0.460846i	$0.847546\pi$
$954$		0			0
$955$	−7.11648	−	10.6506i	−0.230284	−	0.344644i
$956$		0			0
$957$	−4.21309	+	15.3940i	−0.136190	+	0.497616i
$958$		0			0
$959$	−11.7908			−0.380744
$960$		0			0
$961$	−30.9975			−0.999920
$962$		0			0
$963$	−3.63092	+	4.05208i	−0.117005	+	0.130577i
$964$		0			0
$965$	10.9794	+	16.4318i	0.353439	+	0.528959i
$966$		0			0
$967$	−7.60618	+	18.3629i	−0.244598	+	0.590512i	−0.997729	−	0.0673588i	$-0.978543\pi$
$967$	−7.60618	+	18.3629i	−0.244598	+	0.590512i	0.753131	+	0.657871i	$0.228543\pi$
$968$		0			0
$969$	0.877135	−	12.3694i	0.0281776	−	0.397361i
$970$		0			0
$971$	23.2362	+	4.62196i	0.745685	+	0.148326i	0.553286	−	0.832991i	$-0.313373\pi$
$971$	23.2362	+	4.62196i	0.745685	+	0.148326i	0.192398	+	0.981317i	$0.438373\pi$
$972$		0			0
$973$	32.0877	+	21.4403i	1.02868	+	0.687344i
$974$		0			0
$975$	20.7443	−	6.91835i	0.664351	−	0.221565i
$976$		0			0
$977$	18.8219	+	18.8219i	0.602164	+	0.602164i	0.940886	−	0.338722i	$-0.109995\pi$
$977$	18.8219	+	18.8219i	0.602164	+	0.602164i	−0.338722	+	0.940886i	$0.609995\pi$
$978$		0			0
$979$	−17.5668	−	11.7377i	−0.561437	−	0.375140i
$980$		0			0
$981$	−20.8087	+	9.98667i	−0.664370	+	0.318850i
$982$		0			0
$983$	13.8501	+	33.4371i	0.441750	+	1.06648i	0.975335	+	0.220731i	$0.0708444\pi$
$983$	13.8501	+	33.4371i	0.441750	+	1.06648i	−0.533585	+	0.845746i	$0.679156\pi$
$984$		0			0
$985$	15.5816	−	37.6174i	0.496472	−	1.19859i
$986$		0			0
$987$	−2.58031	−	20.4429i	−0.0821321	−	0.650706i
$988$		0			0
$989$	0.509107	+	2.55945i	0.0161886	+	0.0813858i
$990$		0			0
$991$	−3.20062			−0.101671			−0.0508356	−	0.998707i	$-0.516188\pi$
$991$	−3.20062			−0.101671			−0.0508356	+	0.998707i	$0.516188\pi$
$992$		0			0
$993$	−9.60062	+	19.2087i	−0.304667	+	0.609569i
$994$		0			0
$995$	29.8054	−	5.92866i	0.944894	−	0.187951i
$996$		0			0
$997$	25.8757	+	38.7257i	0.819492	+	1.22646i	0.971256	+	0.238039i	$0.0765047\pi$
$997$	25.8757	+	38.7257i	0.819492	+	1.22646i	−0.151764	+	0.988417i	$0.548495\pi$
$998$		0			0
$999$	−10.9122	+	50.6057i	−0.345247	+	1.60109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.s.a.335.28		240
3.2	odd	2	inner	768.2.s.a.335.24		240
4.3	odd	2		192.2.s.a.107.18	yes	240
12.11	even	2		192.2.s.a.107.13	✓	240
64.3	odd	16	inner	768.2.s.a.431.24		240
64.61	even	16		192.2.s.a.131.13	yes	240
192.125	odd	16		192.2.s.a.131.18	yes	240
192.131	even	16	inner	768.2.s.a.431.28		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.s.a.107.13	✓	240	12.11	even	2
192.2.s.a.107.18	yes	240	4.3	odd	2
192.2.s.a.131.13	yes	240	64.61	even	16
192.2.s.a.131.18	yes	240	192.125	odd	16
768.2.s.a.335.24		240	3.2	odd	2	inner
768.2.s.a.335.28		240	1.1	even	1	trivial
768.2.s.a.431.24		240	64.3	odd	16	inner
768.2.s.a.431.28		240	192.131	even	16	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.s (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.67061 + 0.457221i) q^{3} +(-1.45822 - 2.18239i) q^{5} +(1.27779 - 3.08486i) q^{7} +(2.58190 + 1.52768i) q^{9} +(-2.31748 - 0.460975i) q^{11} +(-5.55652 - 3.71275i) q^{13} +(-1.43829 - 4.31265i) q^{15} +(-3.42067 - 3.42067i) q^{17} +(1.23054 + 0.822221i) q^{19} +(3.54516 - 4.56938i) q^{21} +(1.87568 + 4.52828i) q^{23} +(-0.722975 + 1.74542i) q^{25} +(3.61486 + 3.73266i) q^{27} +(-0.760797 - 3.82478i) q^{29} +0.0497279 q^{31} +(-3.66084 - 1.82971i) q^{33} +(-8.59567 + 1.70978i) q^{35} +(5.53510 + 8.28386i) q^{37} +(-7.58524 - 8.74312i) q^{39} +(2.28385 - 0.946002i) q^{41} +(0.522190 + 0.103870i) q^{43} +(-0.430996 - 7.86240i) q^{45} +(2.51930 - 2.51930i) q^{47} +(-2.93388 - 2.93388i) q^{49} +(-4.15061 - 7.27862i) q^{51} +(1.79038 - 9.00087i) q^{53} +(2.37338 + 5.72983i) q^{55} +(1.67982 + 1.93624i) q^{57} +(-2.56739 + 1.71547i) q^{59} +(-0.935842 - 4.70479i) q^{61} +(8.01181 - 6.01274i) q^{63} +17.5405i q^{65} +(3.65093 - 0.726215i) q^{67} +(1.06310 + 8.42261i) q^{69} +(12.6483 + 5.23910i) q^{71} +(13.6168 - 5.64025i) q^{73} +(-2.00585 + 2.58536i) q^{75} +(-4.38330 + 6.56007i) q^{77} +(1.69637 - 1.69637i) q^{79} +(4.33239 + 7.88863i) q^{81} +(5.63016 - 8.42612i) q^{83} +(-2.47712 + 12.4533i) q^{85} +(0.477776 - 6.73759i) q^{87} +(8.26075 + 3.42172i) q^{89} +(-18.5534 + 12.3970i) q^{91} +(0.0830760 + 0.0227366i) q^{93} -3.88450i q^{95} +3.93119i q^{97} +(-5.27927 - 4.73055i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 8 q^{3} + 16 q^{7} - 8 q^{9} - 16 q^{13} + 8 q^{15} + 16 q^{19} - 8 q^{21} - 16 q^{25} + 8 q^{27} + 32 q^{31} - 16 q^{37} + 8 q^{39} + 16 q^{43} - 8 q^{45} - 16 q^{49} + 8 q^{51} + 80 q^{55} - 8 q^{57}+ \cdots + 8 q^{99}+O(q^{100}) \) 240 * q + 8 * q^3 + 16 * q^7 - 8 * q^9 - 16 * q^13 + 8 * q^15 + 16 * q^19 - 8 * q^21 - 16 * q^25 + 8 * q^27 + 32 * q^31 - 16 * q^37 + 8 * q^39 + 16 * q^43 - 8 * q^45 - 16 * q^49 + 8 * q^51 + 80 * q^55 - 8 * q^57 - 16 * q^61 + 144 * q^67 - 8 * q^69 - 16 * q^73 + 8 * q^75 + 48 * q^79 - 8 * q^81 - 16 * q^85 + 8 * q^87 + 16 * q^91 - 32 * q^93 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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