LMFDB - Embedded newform 768.2.s.a.431.24

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			431.24
Character	$\chi$	$=$	768.431
Dual form			768.2.s.a.335.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36847 + 1.06173i) q^{3} +(1.45822 - 2.18239i) q^{5} +(1.27779 + 3.08486i) q^{7} +(0.745444 + 2.90591i) q^{9} +(2.31748 - 0.460975i) q^{11} +(-5.55652 + 3.71275i) q^{13} +(4.31265 - 1.43829i) q^{15} +(3.42067 - 3.42067i) q^{17} +(1.23054 - 0.822221i) q^{19} +(-1.52668 + 5.57823i) q^{21} +(-1.87568 + 4.52828i) q^{23} +(-0.722975 - 1.74542i) q^{25} +(-2.06518 + 4.76813i) q^{27} +(0.760797 - 3.82478i) q^{29} +0.0497279 q^{31} +(3.66084 + 1.82971i) q^{33} +(8.59567 + 1.70978i) q^{35} +(5.53510 - 8.28386i) q^{37} +(-11.5459 - 0.818742i) q^{39} +(-2.28385 - 0.946002i) q^{41} +(0.522190 - 0.103870i) q^{43} +(7.42884 + 2.61062i) q^{45} +(-2.51930 - 2.51930i) q^{47} +(-2.93388 + 2.93388i) q^{49} +(8.31294 - 1.04926i) q^{51} +(-1.79038 - 9.00087i) q^{53} +(2.37338 - 5.72983i) q^{55} +(2.55694 + 0.181318i) q^{57} +(2.56739 + 1.71547i) q^{59} +(-0.935842 + 4.70479i) q^{61} +(-8.01181 + 6.01274i) q^{63} +17.5405i q^{65} +(3.65093 + 0.726215i) q^{67} +(-7.37464 + 4.20537i) q^{69} +(-12.6483 + 5.23910i) q^{71} +(13.6168 + 5.64025i) q^{73} +(0.863794 - 3.15617i) q^{75} +(4.38330 + 6.56007i) q^{77} +(1.69637 + 1.69637i) q^{79} +(-7.88863 + 4.33239i) q^{81} +(-5.63016 - 8.42612i) q^{83} +(-2.47712 - 12.4533i) q^{85} +(5.10203 - 4.42636i) q^{87} +(-8.26075 + 3.42172i) q^{89} +(-18.5534 - 12.3970i) q^{91} +(0.0680513 + 0.0527977i) q^{93} -3.88450i q^{95} -3.93119i q^{97} +(3.06710 + 6.39075i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{16}\right)$

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
$3$	1.36847	+	1.06173i	0.790089	+	0.612992i
$3$	1.36847	+	1.06173i	0.790089	+	0.612992i
$4$		0			0
$5$	1.45822	−	2.18239i	0.652138	−	0.975993i	−0.347133	−	0.937816i	$-0.612845\pi$
$5$	1.45822	−	2.18239i	0.652138	−	0.975993i	0.999271	−	0.0381770i	$-0.0121551\pi$
$6$		0			0
$7$	1.27779	+	3.08486i	0.482960	+	1.16597i	0.958197	+	0.286111i	$0.0923625\pi$
$7$	1.27779	+	3.08486i	0.482960	+	1.16597i	−0.475237	+	0.879858i	$0.657638\pi$
$8$		0			0
$9$	0.745444	+	2.90591i	0.248481	+	0.968637i
$10$		0			0
$11$	2.31748	−	0.460975i	0.698746	−	0.138989i	0.167080	−	0.985943i	$-0.446566\pi$
$11$	2.31748	−	0.460975i	0.698746	−	0.138989i	0.531666	+	0.846954i	$0.321566\pi$
$12$		0			0
$13$	−5.55652	+	3.71275i	−1.54110	+	1.02973i	−0.561811	+	0.827266i	$0.689895\pi$
$13$	−5.55652	+	3.71275i	−1.54110	+	1.02973i	−0.979289	+	0.202465i	$0.935105\pi$
$14$		0			0
$15$	4.31265	−	1.43829i	1.11352	−	0.371366i
$16$		0			0
$17$	3.42067	−	3.42067i	0.829634	−	0.829634i	−0.157832	−	0.987466i	$-0.550450\pi$
$17$	3.42067	−	3.42067i	0.829634	−	0.829634i	0.987466	+	0.157832i	$0.0504503\pi$
$18$		0			0
$19$	1.23054	−	0.822221i	0.282305	−	0.188630i	−0.406353	−	0.913716i	$-0.633200\pi$
$19$	1.23054	−	0.822221i	0.282305	−	0.188630i	0.688659	+	0.725086i	$0.258200\pi$
$20$		0			0
$21$	−1.52668	+	5.57823i	−0.333148	+	1.21727i
$22$		0			0
$23$	−1.87568	+	4.52828i	−0.391105	+	0.944212i	0.598594	+	0.801052i	$0.295726\pi$
$23$	−1.87568	+	4.52828i	−0.391105	+	0.944212i	−0.989700	+	0.143160i	$0.954274\pi$
$24$		0			0
$25$	−0.722975	−	1.74542i	−0.144595	−	0.349083i
$26$		0			0
$27$	−2.06518	+	4.76813i	−0.397444	+	0.917626i
$28$		0			0
$29$	0.760797	−	3.82478i	0.141276	−	0.710245i	−0.843598	−	0.536975i	$-0.819567\pi$
$29$	0.760797	−	3.82478i	0.141276	−	0.710245i	0.984874	−	0.173269i	$-0.0554331\pi$
$30$		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	−0.0221727	−	0.999754i	$-0.507058\pi$
$37$	5.53510	−	8.28386i	0.909965	−	1.36186i	0.932138	−	0.362104i	$-0.117942\pi$
$38$		0			0
$39$	−11.5459	−	0.818742i	−1.84882	−	0.131104i
$40$		0			0
$41$	−2.28385	−	0.946002i	−0.356678	−	0.147741i	0.197147	−	0.980374i	$-0.436832\pi$
$41$	−2.28385	−	0.946002i	−0.356678	−	0.147741i	−0.553825	+	0.832633i	$0.686832\pi$
$42$		0			0
$43$	0.522190	−	0.103870i	0.0796333	−	0.0158400i	−0.155113	−	0.987897i	$-0.549574\pi$
$43$	0.522190	−	0.103870i	0.0796333	−	0.0158400i	0.234746	+	0.972057i	$0.424574\pi$
$44$		0			0
$45$	7.42884	+	2.61062i	1.10743	+	0.389168i
$46$		0			0
$47$	−2.51930	−	2.51930i	−0.367477	−	0.367477i	0.499079	−	0.866556i	$-0.333672\pi$
$47$	−2.51930	−	2.51930i	−0.367477	−	0.367477i	−0.866556	+	0.499079i	$0.833672\pi$
$48$		0			0
$49$	−2.93388	+	2.93388i	−0.419126	+	0.419126i
$50$		0			0
$51$	8.31294	−	1.04926i	1.16404	−	0.146926i
$52$		0			0
$53$	−1.79038	−	9.00087i	−0.245928	−	1.23636i	−0.884404	−	0.466722i	$-0.845435\pi$
$53$	−1.79038	−	9.00087i	−0.245928	−	1.23636i	0.638476	−	0.769642i	$-0.279565\pi$
$54$		0			0
$55$	2.37338	−	5.72983i	0.320026	−	0.772611i
$56$		0			0
$57$	2.55694	+	0.181318i	0.338675	+	0.0240161i
$58$		0			0
$59$	2.56739	+	1.71547i	0.334245	+	0.223336i	0.711355	−	0.702833i	$-0.248082\pi$
$59$	2.56739	+	1.71547i	0.334245	+	0.223336i	−0.377109	+	0.926169i	$0.623082\pi$
$60$		0			0
$61$	−0.935842	+	4.70479i	−0.119822	+	0.602387i	0.873482	+	0.486857i	$0.161857\pi$
$61$	−0.935842	+	4.70479i	−0.119822	+	0.602387i	−0.993304	+	0.115530i	$0.963143\pi$
$62$		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	0.412996	−	0.910733i	$-0.364482\pi$
$67$	3.65093	+	0.726215i	0.446032	+	0.0887213i	0.0330361	+	0.999454i	$0.489482\pi$
$68$		0			0
$69$	−7.37464	+	4.20537i	−0.887803	+	0.506267i
$70$		0			0
$71$	−12.6483	+	5.23910i	−1.50108	+	0.621767i	−0.973694	−	0.227860i	$-0.926827\pi$
$71$	−12.6483	+	5.23910i	−1.50108	+	0.621767i	−0.527384	+	0.849627i	$0.676827\pi$
$72$		0			0
$73$	13.6168	+	5.64025i	1.59372	+	0.660142i	0.990510	−	0.137439i	$-0.0438870\pi$
$73$	13.6168	+	5.64025i	1.59372	+	0.660142i	0.603213	+	0.797580i	$0.293887\pi$
$74$		0			0
$75$	0.863794	−	3.15617i	0.0997424	−	0.364443i
$76$		0			0
$77$	4.38330	+	6.56007i	0.499523	+	0.747589i
$78$		0			0
$79$	1.69637	+	1.69637i	0.190856	+	0.190856i	0.796066	−	0.605210i	$-0.206911\pi$
$79$	1.69637	+	1.69637i	0.190856	+	0.190856i	−0.605210	+	0.796066i	$0.706911\pi$
$80$		0			0
$81$	−7.88863	+	4.33239i	−0.876514	+	0.481376i
$82$		0			0
$83$	−5.63016	−	8.42612i	−0.617990	−	0.924887i	−1.00000		0.000728896i	$-0.999768\pi$
$83$	−5.63016	−	8.42612i	−0.617990	−	0.924887i	0.382010	−	0.924158i	$-0.375232\pi$
$84$		0			0
$85$	−2.47712	−	12.4533i	−0.268681	−	1.35075i
$86$		0			0
$87$	5.10203	−	4.42636i	0.546995	−	0.474555i
$88$		0			0
$89$	−8.26075	+	3.42172i	−0.875638	+	0.362701i	−0.774804	−	0.632202i	$-0.782151\pi$
$89$	−8.26075	+	3.42172i	−0.875638	+	0.362701i	−0.100834	+	0.994903i	$0.532151\pi$
$90$		0			0
$91$	−18.5534	−	12.3970i	−1.94492	−	1.29956i
$92$		0			0
$93$	0.0680513	+	0.0527977i	0.00705659	+	0.00547487i
$94$		0			0
$95$		−	3.88450i		−	0.398541i
$96$		0			0
$97$		−	3.93119i		−	0.399152i	−0.979882	−	0.199576i	$-0.936044\pi$
$97$		−	3.93119i		−	0.399152i	0.979882	−	0.199576i	$-0.0639565\pi$
$98$		0			0
$99$	3.06710	+	6.39075i	0.308255	+	0.642294i
$100$		0			0
$101$	1.14688	+	0.766317i	0.114118	+	0.0762514i	0.611320	−	0.791384i	$-0.290639\pi$
$101$	1.14688	+	0.766317i	0.114118	+	0.0762514i	−0.497201	+	0.867635i	$0.665639\pi$
$102$		0			0
$103$	−3.42308	+	1.41789i	−0.337286	+	0.139708i	−0.544897	−	0.838503i	$-0.683431\pi$
$103$	−3.42308	+	1.41789i	−0.337286	+	0.139708i	0.207611	+	0.978212i	$0.433431\pi$
$104$		0			0
$105$	9.94762	+	11.4661i	0.970788	+	1.11898i
$106$		0			0
$107$	0.353820	+	1.77877i	0.0342051	+	0.171960i	0.994112	−	0.108359i	$-0.0345596\pi$
$107$	0.353820	+	1.77877i	0.0342051	+	0.171960i	−0.959907	+	0.280319i	$0.909560\pi$
$108$		0			0
$109$	−4.27438	−	6.39706i	−0.409411	−	0.612728i	0.568264	−	0.822846i	$-0.307615\pi$
$109$	−4.27438	−	6.39706i	−0.409411	−	0.612728i	−0.977676	+	0.210118i	$0.932615\pi$
$110$		0			0
$111$	16.3699	−	5.45945i	1.55376	−	0.518188i
$112$		0			0
$113$	−7.68145	−	7.68145i	−0.722610	−	0.722610i	0.246526	−	0.969136i	$-0.420711\pi$
$113$	−7.68145	−	7.68145i	−0.722610	−	0.722610i	−0.969136	+	0.246526i	$0.920711\pi$
$114$		0			0
$115$	7.14731	+	10.6967i	0.666490	+	0.997472i
$116$		0			0
$117$	−14.9310	−	13.3791i	−1.38037	−	1.23690i
$118$		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
$123$	−2.12099	−	3.71942i	−0.191243	−	0.335369i
$124$		0			0
$125$	8.00807	+	1.59290i	0.716263	+	0.142474i
$126$		0			0
$127$		−	2.11042i		−	0.187270i	−0.995607	−	0.0936348i	$-0.970151\pi$
$127$		−	2.11042i		−	0.187270i	0.995607	−	0.0936348i	$-0.0298486\pi$
$128$		0			0
$129$	0.824886	+	0.412283i	0.0726272	+	0.0362995i
$130$		0			0
$131$	2.13696	−	10.7432i	0.186707	−	0.938640i	−0.767854	−	0.640625i	$-0.778675\pi$
$131$	2.13696	−	10.7432i	0.186707	−	0.938640i	0.954561	−	0.298015i	$-0.0963246\pi$
$132$		0			0
$133$	4.10881	+	2.74542i	0.356279	+	0.238058i
$134$		0			0
$135$	7.39440	+	11.4600i	0.636408	+	0.986321i
$136$		0			0
$137$	1.35133	−	3.26240i	0.115452	−	0.278726i	−0.855582	−	0.517667i	$-0.826800\pi$
$137$	1.35133	−	3.26240i	0.115452	−	0.278726i	0.971034	+	0.238942i	$0.0768005\pi$
$138$		0			0
$139$	−2.25479	−	11.3356i	−0.191249	−	0.961475i	−0.950511	−	0.310690i	$-0.899440\pi$
$139$	−2.25479	−	11.3356i	−0.191249	−	0.961475i	0.759262	−	0.650785i	$-0.225560\pi$
$140$		0			0
$141$	−0.772771	−	6.12242i	−0.0650791	−	0.515600i
$142$		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
$147$	−7.12994	+	0.899941i	−0.588067	+	0.0742259i
$148$		0			0
$149$	9.41669	−	1.87310i	0.771445	−	0.153450i	0.206353	−	0.978478i	$-0.433841\pi$
$149$	9.41669	−	1.87310i	0.771445	−	0.153450i	0.565092	+	0.825028i	$0.308841\pi$
$150$		0			0
$151$	−15.4374	−	6.39437i	−1.25628	−	0.520367i	−0.347511	−	0.937676i	$-0.612973\pi$
$151$	−15.4374	−	6.39437i	−1.25628	−	0.520367i	−0.908765	+	0.417309i	$0.862973\pi$
$152$		0			0
$153$	12.4901	+	7.39024i	1.00976	+	0.597466i
$154$		0			0
$155$	0.0725144	−	0.108525i	0.00582449	−	0.00871697i
$156$		0			0
$157$	−1.10477	−	0.219752i	−0.0881699	−	0.0175381i	0.150808	−	0.988563i	$-0.451812\pi$
$157$	−1.10477	−	0.219752i	−0.0881699	−	0.0175381i	−0.238978	+	0.971025i	$0.576812\pi$
$158$		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	−0.440477	−	0.897764i	$-0.645191\pi$
$163$	3.95820	−	19.8992i	0.310030	−	1.55863i	0.750507	−	0.660862i	$-0.229809\pi$
$164$		0			0
$165$	9.33146	−	5.32124i	0.726453	−	0.414258i
$166$		0			0
$167$	−0.109882	−	0.265279i	−0.00850292	−	0.0205279i	0.919571	−	0.392924i	$-0.128536\pi$
$167$	−0.109882	−	0.265279i	−0.00850292	−	0.0205279i	−0.928074	+	0.372396i	$0.878536\pi$
$168$		0			0
$169$	12.1155	−	29.2494i	0.931963	−	2.24996i
$170$		0			0
$171$	3.30660	+	2.96292i	0.252862	+	0.226580i
$172$		0			0
$173$	11.1530	−	7.45221i	0.847948	−	0.566581i	−0.0539429	−	0.998544i	$-0.517179\pi$
$173$	11.1530	−	7.45221i	0.847948	−	0.566581i	0.901891	+	0.431963i	$0.142179\pi$
$174$		0			0
$175$	4.46056	−	4.46056i	0.337187	−	0.337187i
$176$		0			0
$177$	1.69203	+	5.07346i	0.127181	+	0.381345i
$178$		0			0
$179$	−13.7986	+	9.21991i	−1.03135	+	0.689128i	−0.951491	−	0.307677i	$-0.900448\pi$
$179$	−13.7986	+	9.21991i	−1.03135	+	0.689128i	−0.0798628	+	0.996806i	$0.525448\pi$
$180$		0			0
$181$	−0.368628	+	0.0733247i	−0.0273999	+	0.00545018i	−0.208771	−	0.977965i	$-0.566946\pi$
$181$	−0.368628	+	0.0733247i	−0.0273999	+	0.00545018i	0.181371	+	0.983415i	$0.441946\pi$
$182$		0			0
$183$	−6.27591	+	5.44478i	−0.463929	+	0.402489i
$184$		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
$189$	−17.3479	−	0.278125i	−1.26187	−	0.0202306i
$190$		0			0
$191$	−4.88024			−0.353122			−0.176561	−	0.984290i	$-0.556497\pi$
$191$	−4.88024			−0.353122			−0.176561	+	0.984290i	$0.556497\pi$
$192$		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
$195$	−18.6233	+	24.0037i	−1.33364	+	1.71894i
$196$		0			0
$197$	−8.61841	+	12.8984i	−0.614036	+	0.918970i	−0.999994	−	0.00354629i	$-0.998871\pi$
$197$	−8.61841	+	12.8984i	−0.614036	+	0.918970i	0.385957	+	0.922517i	$0.373871\pi$
$198$		0			0
$199$	−4.43073	−	10.6967i	−0.314086	−	0.758271i	−0.999545	−	0.0301595i	$-0.990398\pi$
$199$	−4.43073	−	10.6967i	−0.314086	−	0.758271i	0.685459	−	0.728111i	$-0.259602\pi$
$200$		0			0
$201$	4.22516	+	4.87012i	0.298020	+	0.343512i
$202$		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
$207$	−14.5570	−	2.07496i	−1.01178	−	0.144220i
$208$		0			0
$209$	2.47273	−	2.47273i	0.171042	−	0.171042i
$210$		0			0
$211$	−17.8899	+	11.9536i	−1.23159	+	0.822923i	−0.989102	−	0.147232i	$-0.952964\pi$
$211$	−17.8899	+	11.9536i	−1.23159	+	0.822923i	−0.242489	+	0.970154i	$0.577964\pi$
$212$		0			0
$213$	−22.8714	−	6.25956i	−1.56712	−	0.428898i
$214$		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
$219$	12.6458	+	22.1759i	0.854521	+	1.49851i
$220$		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	$-0.210019\pi$
$227$	19.3684	+	3.85261i	1.28552	+	0.255707i	0.495406	+	0.868662i	$0.335019\pi$
$228$		0			0
$229$	0.936069	−	1.40093i	0.0618572	−	0.0925758i	−0.799252	−	0.600997i	$-0.794771\pi$
$229$	0.936069	−	1.40093i	0.0618572	−	0.0925758i	0.861109	+	0.508421i	$0.169771\pi$
$230$		0			0
$231$	−0.966614	+	13.6312i	−0.0635985	+	0.896866i
$232$		0			0
$233$	14.4154	+	5.97104i	0.944382	+	0.391176i	0.801117	−	0.598508i	$-0.204240\pi$
$233$	14.4154	+	5.97104i	0.944382	+	0.391176i	0.143266	+	0.989684i	$0.454240\pi$
$234$		0			0
$235$	−9.17178	+	1.82438i	−0.598301	+	0.119009i
$236$		0			0
$237$	0.520345	+	4.12252i	0.0338000	+	0.267787i
$238$		0			0
$239$	0.690266	+	0.690266i	0.0446496	+	0.0446496i	0.729079	−	0.684429i	$-0.239949\pi$
$239$	0.690266	+	0.690266i	0.0446496	+	0.0446496i	−0.684429	+	0.729079i	$0.739949\pi$
$240$		0			0
$241$	−10.6103	+	10.6103i	−0.683472	+	0.683472i	−0.960781	−	0.277309i	$-0.910558\pi$
$241$	−10.6103	+	10.6103i	−0.683472	+	0.683472i	0.277309	+	0.960781i	$0.410558\pi$
$242$		0			0
$243$	−15.3952	−	2.44686i	−0.987604	−	0.156966i
$244$		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
$249$	1.24157	−	17.5087i	0.0786815	−	1.10957i
$250$		0			0
$251$	−22.7440	−	15.1971i	−1.43559	−	0.959232i	−0.998201	−	0.0599600i	$-0.980903\pi$
$251$	−22.7440	−	15.1971i	−1.43559	−	0.959232i	−0.437391	−	0.899272i	$-0.644097\pi$
$252$		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
$261$	11.6816	−	0.640356i	0.723074	−	0.0396370i
$262$		0			0
$263$	−2.04943	+	0.848904i	−0.126374	+	0.0523456i	−0.444974	−	0.895543i	$-0.646787\pi$
$263$	−2.04943	+	0.848904i	−0.126374	+	0.0523456i	0.318601	+	0.947889i	$0.396787\pi$
$264$		0			0
$265$	−22.2541	−	9.21797i	−1.36706	−	0.566255i
$266$		0			0
$267$	−14.9376	−	4.08819i	−0.914165	−	0.250193i
$268$		0			0
$269$	−12.8156	−	19.1799i	−0.781379	−	1.16942i	−0.981839	−	0.189715i	$-0.939244\pi$
$269$	−12.8156	−	19.1799i	−0.781379	−	1.16942i	0.200460	−	0.979702i	$-0.435756\pi$
$270$		0			0
$271$	4.68156	+	4.68156i	0.284384	+	0.284384i	0.834855	−	0.550470i	$-0.185552\pi$
$271$	4.68156	+	4.68156i	0.284384	+	0.284384i	−0.550470	+	0.834855i	$0.685552\pi$
$272$		0			0
$273$	−12.2275	−	36.6637i	−0.740045	−	2.21899i
$274$		0			0
$275$	−2.48007	−	3.71169i	−0.149554	−	0.223823i
$276$		0			0
$277$	0.351539	+	1.76730i	0.0211219	+	0.106187i	0.989908	−	0.141711i	$-0.0452603\pi$
$277$	0.351539	+	1.76730i	0.0211219	+	0.106187i	−0.968786	+	0.247898i	$0.920260\pi$
$278$		0			0
$279$	0.0370693	+	0.144505i	0.00221928	+	0.00865127i
$280$		0			0
$281$	−6.33662	+	2.62472i	−0.378011	+	0.156577i	−0.563595	−	0.826051i	$-0.690582\pi$
$281$	−6.33662	+	2.62472i	−0.378011	+	0.156577i	0.185584	+	0.982628i	$0.440582\pi$
$282$		0			0
$283$	19.0458	+	12.7260i	1.13215	+	0.756481i	0.973007	−	0.230774i	$-0.0741259\pi$
$283$	19.0458	+	12.7260i	1.13215	+	0.756481i	0.159146	+	0.987255i	$0.449126\pi$
$284$		0			0
$285$	4.12430	−	5.31583i	0.244302	−	0.314883i
$286$		0			0
$287$		−	8.25416i		−	0.487228i
$288$		0			0
$289$		−	6.40197i		−	0.376586i
$290$		0			0
$291$	4.17388	−	5.37973i	0.244677	−	0.315366i
$292$		0			0
$293$	10.4198	+	6.96228i	0.608731	+	0.406741i	0.821375	−	0.570389i	$-0.193207\pi$
$293$	10.4198	+	6.96228i	0.608731	+	0.406741i	−0.212644	+	0.977130i	$0.568207\pi$
$294$		0			0
$295$	7.48765	−	3.10149i	0.435948	−	0.180575i
$296$		0			0
$297$	−2.58802	+	12.0020i	−0.150172	+	0.696428i
$298$		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
$303$	0.755844	+	2.26636i	0.0434221	+	0.130199i
$304$		0			0
$305$	8.90301	+	8.90301i	0.509785	+	0.509785i
$306$		0			0
$307$	7.76821	+	11.6259i	0.443355	+	0.663528i	0.984091	−	0.177665i	$-0.0568542\pi$
$307$	7.76821	+	11.6259i	0.443355	+	0.663528i	−0.540736	+	0.841192i	$0.681854\pi$
$308$		0			0
$309$	−6.18982	−	1.69406i	−0.352126	−	0.0963716i
$310$		0			0
$311$	30.5106	+	12.6379i	1.73010	+	0.716630i	0.999425	+	0.0339024i	$0.0107935\pi$
$311$	30.5106	+	12.6379i	1.73010	+	0.716630i	0.730673	+	0.682728i	$0.239206\pi$
$312$		0			0
$313$	−0.773283	+	0.320305i	−0.0437086	+	0.0181047i	−0.404431	−	0.914569i	$-0.632530\pi$
$313$	−0.773283	+	0.320305i	−0.0437086	+	0.0181047i	0.360722	+	0.932673i	$0.382530\pi$
$314$		0			0
$315$	1.43911	+	26.2528i	0.0810847	+	1.47918i
$316$		0			0
$317$	−13.4190	−	2.66920i	−0.753685	−	0.149917i	−0.196728	−	0.980458i	$-0.563031\pi$
$317$	−13.4190	−	2.66920i	−0.753685	−	0.149917i	−0.556958	+	0.830541i	$0.688031\pi$
$318$		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
$327$	0.942595	−	13.2925i	0.0521256	−	0.735075i
$328$		0			0
$329$	4.55255	−	10.9908i	0.250990	−	0.605944i
$330$		0			0
$331$	−2.41877	−	12.1600i	−0.132947	−	0.668372i	−0.988569	−	0.150770i	$-0.951825\pi$
$331$	−2.41877	−	12.1600i	−0.132947	−	0.668372i	0.855621	−	0.517602i	$-0.173175\pi$
$332$		0			0
$333$	28.1983	+	9.90935i	1.54526	+	0.543029i
$334$		0			0
$335$	6.90875	−	6.90875i	0.377466	−	0.377466i
$336$		0			0
$337$	22.7974	+	22.7974i	1.24185	+	1.24185i	0.959231	+	0.282622i	$0.0912041\pi$
$337$	22.7974	+	22.7974i	1.24185	+	1.24185i	0.282622	+	0.959231i	$0.408796\pi$
$338$		0			0
$339$	−2.35622	−	18.6675i	−0.127972	−	1.01388i
$340$		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
$345$	−1.57614	+	22.2267i	−0.0848564	+	1.19664i
$346$		0			0
$347$	−15.3279	+	22.9398i	−0.822843	+	1.23147i	0.147338	+	0.989086i	$0.452930\pi$
$347$	−15.3279	+	22.9398i	−0.822843	+	1.23147i	−0.970180	+	0.242385i	$0.922070\pi$
$348$		0			0
$349$	8.15254	+	1.62164i	0.436395	+	0.0868044i	0.408399	−	0.912804i	$-0.366087\pi$
$349$	8.15254	+	1.62164i	0.436395	+	0.0868044i	0.0279965	+	0.999608i	$0.491087\pi$
$350$		0			0
$351$	−6.22763	−	34.1617i	−0.332406	−	1.82341i
$352$		0			0
$353$	−12.2210			−0.650460			−0.325230	−	0.945635i	$-0.605442\pi$
$353$	−12.2210			−0.650460			−0.325230	+	0.945635i	$0.605442\pi$
$354$		0			0
$355$	−7.01032	+	35.2433i	−0.372069	+	1.87052i
$356$		0			0
$357$	13.8590	+	24.3035i	0.733498	+	1.28628i
$358$		0			0
$359$	−3.41180	−	8.23682i	−0.180068	−	0.434723i	0.807912	−	0.589303i	$-0.200598\pi$
$359$	−3.41180	−	8.23682i	−0.180068	−	0.434723i	−0.987980	+	0.154580i	$0.950598\pi$
$360$		0			0
$361$	−6.43280	+	15.5302i	−0.338569	+	0.817377i
$362$		0			0
$363$	−9.04938	−	2.47668i	−0.474969	−	0.129992i
$364$		0			0
$365$	32.1655	−	21.4923i	1.68362	−	1.12496i
$366$		0			0
$367$	−11.6703	+	11.6703i	−0.609183	+	0.609183i	−0.942733	−	0.333550i	$-0.891754\pi$
$367$	−11.6703	+	11.6703i	−0.609183	+	0.609183i	0.333550	+	0.942733i	$0.391754\pi$
$368$		0			0
$369$	1.04651	−	7.34186i	0.0544793	−	0.382202i
$370$		0			0
$371$	25.4787	−	17.0243i	1.32279	−	0.883859i
$372$		0			0
$373$	30.2561	−	6.01831i	1.56660	−	0.311616i	0.665894	−	0.746046i	$-0.268050\pi$
$373$	30.2561	−	6.01831i	1.56660	−	0.311616i	0.900706	+	0.434430i	$0.143050\pi$
$374$		0			0
$375$	9.26759	+	10.6823i	0.478576	+	0.551630i
$376$		0			0
$377$	9.97307	+	24.0771i	0.513639	+	1.24004i
$378$		0			0
$379$	−12.8100	+	19.1715i	−0.658005	+	0.984774i	0.340995	+	0.940065i	$0.389236\pi$
$379$	−12.8100	+	19.1715i	−0.658005	+	0.984774i	−0.999000	+	0.0447089i	$0.985764\pi$
$380$		0			0
$381$	2.24070	−	2.88806i	0.114795	−	0.147960i
$382$		0			0
$383$	11.5359			0.589459			0.294729	−	0.955581i	$-0.404770\pi$
$383$	11.5359			0.589459			0.294729	+	0.955581i	$0.404770\pi$
$384$		0			0
$385$	20.7084			1.05540
$386$		0			0
$387$	0.691101	+	1.44001i	0.0351306	+	0.0731997i
$388$		0			0
$389$	−12.8942	+	19.2976i	−0.653764	+	0.978427i	0.345436	+	0.938442i	$0.387731\pi$
$389$	−12.8942	+	19.2976i	−0.653764	+	0.978427i	−0.999200	+	0.0399850i	$0.987269\pi$
$390$		0			0
$391$	9.07369	+	21.9058i	0.458876	+	1.10783i
$392$		0			0
$393$	14.3308	−	12.4329i	0.722894	−	0.627159i
$394$		0			0
$395$	6.17581	−	1.22844i	0.310739	−	0.0618097i
$396$		0			0
$397$	2.60492	−	1.74055i	0.130737	−	0.0873557i	−0.488482	−	0.872574i	$-0.662449\pi$
$397$	2.60492	−	1.74055i	0.130737	−	0.0873557i	0.619219	+	0.785218i	$0.287449\pi$
$398$		0			0
$399$	2.70790	+	8.11950i	0.135565	+	0.406483i
$400$		0			0
$401$	24.3210	−	24.3210i	1.21453	−	1.21453i	0.245012	−	0.969520i	$-0.421208\pi$
$401$	24.3210	−	24.3210i	1.21453	−	1.21453i	0.969520	−	0.245012i	$-0.0787918\pi$
$402$		0			0
$403$	−0.276314	+	0.184627i	−0.0137642	+	0.00919692i
$404$		0			0
$405$	−2.04844	+	23.5336i	−0.101788	+	1.16939i
$406$		0			0
$407$	9.00882	−	21.7492i	0.446550	−	1.07807i
$408$		0			0
$409$	3.24175	+	7.82629i	0.160294	+	0.386985i	0.983538	−	0.180704i	$-0.0578376\pi$
$409$	3.24175	+	7.82629i	0.160294	+	0.386985i	−0.823243	+	0.567689i	$0.807838\pi$
$410$		0			0
$411$	5.31306	−	3.02976i	0.262074	−	0.149447i
$412$		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	$-0.713246\pi$
$419$	−30.5931	−	6.08535i	−1.49457	−	0.297289i	−0.873639	+	0.486575i	$0.838246\pi$
$420$		0			0
$421$	−3.52363	+	5.27349i	−0.171731	+	0.257014i	−0.907345	−	0.420388i	$-0.861894\pi$
$421$	−3.52363	+	5.27349i	−0.171731	+	0.257014i	0.735613	+	0.677402i	$0.236894\pi$
$422$		0			0
$423$	5.44286	−	9.19885i	0.264641	−	0.447263i
$424$		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
$429$	−27.1348	+	3.42495i	−1.31008	+	0.165358i
$430$		0			0
$431$	25.0198	+	25.0198i	1.20516	+	1.20516i	0.972576	+	0.232586i	$0.0747186\pi$
$431$	25.0198	+	25.0198i	1.20516	+	1.20516i	0.232586	+	0.972576i	$0.425281\pi$
$432$		0			0
$433$	−0.182313	+	0.182313i	−0.00876139	+	0.00876139i	−0.711474	−	0.702713i	$-0.751972\pi$
$433$	−0.182313	+	0.182313i	−0.00876139	+	0.00876139i	0.702713	+	0.711474i	$0.251972\pi$
$434$		0			0
$435$	−2.22011	−	17.5892i	−0.106446	−	0.843339i
$436$		0			0
$437$	1.41515	+	7.11445i	0.0676959	+	0.340330i
$438$		0			0
$439$	15.4119	−	37.2076i	0.735570	−	1.77582i	0.112508	−	0.993651i	$-0.464112\pi$
$439$	15.4119	−	37.2076i	0.735570	−	1.77582i	0.623062	−	0.782172i	$-0.285888\pi$
$440$		0			0
$441$	−10.7126	−	6.33855i	−0.510125	−	0.301836i
$442$		0			0
$443$	−5.50223	−	3.67647i	−0.261419	−	0.174674i	0.417953	−	0.908469i	$-0.362748\pi$
$443$	−5.50223	−	3.67647i	−0.261419	−	0.174674i	−0.679372	+	0.733794i	$0.737748\pi$
$444$		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
$453$	−14.3365	−	25.1409i	−0.673589	−	1.18122i
$454$		0			0
$455$	−54.1100	+	22.4131i	−2.53672	+	1.05074i
$456$		0			0
$457$	−18.5018	−	7.66368i	−0.865476	−	0.358492i	−0.0946295	−	0.995513i	$-0.530167\pi$
$457$	−18.5018	−	7.66368i	−0.865476	−	0.358492i	−0.770847	+	0.637020i	$0.780167\pi$
$458$		0			0
$459$	9.24589	+	23.3745i	0.431561	+	1.09103i
$460$		0			0
$461$	19.4038	+	29.0398i	0.903724	+	1.35252i	0.935613	+	0.353027i	$0.114848\pi$
$461$	19.4038	+	29.0398i	0.903724	+	1.35252i	−0.0318892	+	0.999491i	$0.510152\pi$
$462$		0			0
$463$	26.4304	+	26.4304i	1.22833	+	1.22833i	0.964597	+	0.263728i	$0.0849522\pi$
$463$	26.4304	+	26.4304i	1.22833	+	1.22833i	0.263728	+	0.964597i	$0.415048\pi$
$464$		0			0
$465$	0.214459	−	0.0715233i	0.00994530	−	0.00331681i
$466$		0			0
$467$	6.62269	+	9.91156i	0.306462	+	0.458652i	0.952450	−	0.304695i	$-0.0985545\pi$
$467$	6.62269	+	9.91156i	0.306462	+	0.458652i	−0.645988	+	0.763347i	$0.723555\pi$
$468$		0			0
$469$	2.42485	+	12.1906i	0.111969	+	0.562908i
$470$		0			0
$471$	−1.27853	−	1.47369i	−0.0589114	−	0.0679041i
$472$		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
$477$	24.8211	−	11.9123i	1.13648	−	0.545428i
$478$		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
$483$	−22.3963	−	17.3762i	−1.01906	−	0.790643i
$484$		0			0
$485$	−8.57938	−	5.73256i	−0.389569	−	0.260302i
$486$		0			0
$487$	20.1298	−	8.33804i	0.912168	−	0.377833i	0.123282	−	0.992372i	$-0.460658\pi$
$487$	20.1298	−	8.33804i	0.912168	−	0.377833i	0.788886	+	0.614539i	$0.210658\pi$
$488$		0			0
$489$	26.5443	−	23.0290i	1.20038	−	1.04141i
$490$		0			0
$491$	3.99742	+	20.0964i	0.180401	+	0.906936i	0.959859	+	0.280482i	$0.0904944\pi$
$491$	3.99742	+	20.0964i	0.180401	+	0.906936i	−0.779458	+	0.626454i	$0.784506\pi$
$492$		0			0
$493$	−10.4809	−	15.6858i	−0.472036	−	0.706451i
$494$		0			0
$495$	18.4196	+	2.62554i	0.827900	+	0.118009i
$496$		0			0
$497$	−32.3238	−	32.3238i	−1.44992	−	1.44992i
$498$		0			0
$499$	−10.8139	−	16.1841i	−0.484095	−	0.724500i	0.506362	−	0.862321i	$-0.330990\pi$
$499$	−10.8139	−	16.1841i	−0.484095	−	0.724500i	−0.990457	+	0.137821i	$0.955990\pi$
$500$		0			0
$501$	0.131284	−	0.479692i	0.00586536	−	0.0214311i
$502$		0			0
$503$	−13.0766	−	5.41650i	−0.583056	−	0.241510i	0.0716041	−	0.997433i	$-0.477188\pi$
$503$	−13.0766	−	5.41650i	−0.583056	−	0.241510i	−0.654660	+	0.755923i	$0.727188\pi$
$504$		0			0
$505$	3.34480	−	1.38546i	0.148842	−	0.0616522i
$506$		0			0
$507$	47.6349	−	27.1637i	2.11554	−	1.20638i
$508$		0			0
$509$	−21.9603	−	4.36817i	−0.973371	−	0.193616i	−0.317309	−	0.948322i	$-0.602779\pi$
$509$	−21.9603	−	4.36817i	−0.973371	−	0.193616i	−0.656062	+	0.754707i	$0.727779\pi$
$510$		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
$519$	23.1749	+	1.64338i	1.01726	+	0.0721362i
$520$		0			0
$521$	0.213242	−	0.514813i	0.00934232	−	0.0225544i	−0.919140	−	0.393932i	$-0.871115\pi$
$521$	0.213242	−	0.514813i	0.00934232	−	0.0225544i	0.928482	+	0.371378i	$0.121115\pi$
$522$		0			0
$523$	0.636430	+	3.19955i	0.0278291	+	0.139907i	0.992202	−	0.124640i	$-0.0397777\pi$
$523$	0.636430	+	3.19955i	0.0278291	+	0.139907i	−0.964373	+	0.264547i	$0.914778\pi$
$524$		0			0
$525$	10.8401	−	1.36824i	0.473100	−	0.0597147i
$526$		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
$531$	−3.07117	+	8.73938i	−0.133277	+	0.379257i
$532$		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
$537$	−28.6721	−	2.03319i	−1.23729	−	0.0877388i
$538$		0			0
$539$	−5.44675	+	8.15164i	−0.234608	+	0.351116i
$540$		0			0
$541$	−18.6138	−	3.70251i	−0.800270	−	0.159184i	−0.222019	−	0.975042i	$-0.571265\pi$
$541$	−18.6138	−	3.70251i	−0.800270	−	0.159184i	−0.578251	+	0.815859i	$0.696265\pi$
$542$		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	−0.987052	−	0.160403i	$-0.948721\pi$
$547$	−0.321617	+	1.61688i	−0.0137513	+	0.0691327i	0.973300	+	0.229535i	$0.0737207\pi$
$548$		0			0
$549$	−14.3693	+	0.787689i	−0.613268	+	0.0336178i
$550$		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
$555$	11.9563	−	43.6865i	0.507518	−	1.85439i
$556$		0			0
$557$	7.81765	−	5.22359i	0.331245	−	0.221330i	−0.378815	−	0.925473i	$-0.623668\pi$
$557$	7.81765	−	5.22359i	0.331245	−	0.221330i	0.710059	+	0.704142i	$0.248668\pi$
$558$		0			0
$559$	−2.51592	+	2.51592i	−0.106412	+	0.106412i
$560$		0			0
$561$	18.7814	−	6.26369i	0.792950	−	0.264453i
$562$		0			0
$563$	−25.4030	+	16.9737i	−1.07061	+	0.715357i	−0.960420	−	0.278554i	$-0.910145\pi$
$563$	−25.4030	+	16.9737i	−1.07061	+	0.715357i	−0.110186	+	0.993911i	$0.535145\pi$
$564$		0			0
$565$	−27.9652	+	5.56262i	−1.17650	+	0.234021i
$566$		0			0
$567$	−23.4448	−	18.7994i	−0.984591	−	0.789502i
$568$		0			0
$569$	11.5727	+	27.9391i	0.485154	+	1.17127i	0.957131	+	0.289655i	$0.0935407\pi$
$569$	11.5727	+	27.9391i	0.485154	+	1.17127i	−0.471977	+	0.881611i	$0.656459\pi$
$570$		0			0
$571$	−7.03644	+	10.5308i	−0.294466	+	0.440700i	−0.948973	−	0.315356i	$-0.897876\pi$
$571$	−7.03644	+	10.5308i	−0.294466	+	0.440700i	0.654507	+	0.756056i	$0.272876\pi$
$572$		0			0
$573$	−6.67848	−	5.18151i	−0.278998	−	0.216461i
$574$		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
$579$	−10.3036	−	7.99410i	−0.428205	−	0.332223i
$580$		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
$585$	−50.9711	+	13.0754i	−2.10739	+	0.540603i
$586$		0			0
$587$	43.4391	−	8.64058i	1.79292	−	0.356635i	0.817322	−	0.576180i	$-0.195457\pi$
$587$	43.4391	−	8.64058i	1.79292	−	0.356635i	0.975602	+	0.219546i	$0.0704575\pi$
$588$		0			0
$589$	0.0611921	−	0.0408873i	0.00252138	−	0.00168473i
$590$		0			0
$591$	−25.4887	+	8.50062i	−1.04846	+	0.349669i
$592$		0			0
$593$	12.4091	−	12.4091i	0.509580	−	0.509580i	−0.404817	−	0.914398i	$-0.632665\pi$
$593$	12.4091	−	12.4091i	0.509580	−	0.509580i	0.914398	+	0.404817i	$0.132665\pi$
$594$		0			0
$595$	35.2516	−	23.5543i	1.44517	−	0.965634i
$596$		0			0
$597$	5.29373	−	19.3424i	0.216658	−	0.791633i
$598$		0			0
$599$	5.32882	−	12.8649i	0.217730	−	0.525646i	−0.776843	−	0.629695i	$-0.783180\pi$
$599$	5.32882	−	12.8649i	0.217730	−	0.525646i	0.994572	+	0.104049i	$0.0331799\pi$
$600$		0			0
$601$	−9.61422	−	23.2108i	−0.392172	−	0.946788i	−0.989466	−	0.144765i	$-0.953757\pi$
$601$	−9.61422	−	23.2108i	−0.392172	−	0.946788i	0.597294	−	0.802023i	$-0.296243\pi$
$602$		0			0
$603$	0.611248	+	11.1506i	0.0248920	+	0.454089i
$604$		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	−0.326009	−	0.945367i	$-0.605704\pi$
$613$	16.6418	−	24.9062i	0.672154	−	1.00595i	0.998163	−	0.0605835i	$-0.0192961\pi$
$614$		0			0
$615$	−11.2101	−	0.794930i	−0.452034	−	0.0320547i
$616$		0			0
$617$	−34.0519	−	14.1048i	−1.37088	−	0.567836i	−0.428852	−	0.903375i	$-0.641082\pi$
$617$	−34.0519	−	14.1048i	−1.37088	−	0.567836i	−0.942027	+	0.335538i	$0.891082\pi$
$618$		0			0
$619$	−29.7566	+	5.91895i	−1.19602	+	0.237903i	−0.752640	−	0.658433i	$-0.771220\pi$
$619$	−29.7566	+	5.91895i	−1.19602	+	0.237903i	−0.443377	+	0.896335i	$0.646220\pi$
$620$		0			0
$621$	−17.7178	−	18.2952i	−0.710991	−	0.734160i
$622$		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
$627$	6.00924	−	0.758486i	0.239986	−	0.0302910i
$628$		0			0
$629$	−9.40261	−	47.2701i	−0.374907	−	1.88478i
$630$		0			0
$631$	5.45257	−	13.1637i	0.217063	−	0.524037i	−0.777414	−	0.628989i	$-0.783469\pi$
$631$	5.45257	−	13.1637i	0.217063	−	0.524037i	0.994477	+	0.104952i	$0.0334689\pi$
$632$		0			0
$633$	−37.1734	−	2.63604i	−1.47751	−	0.104773i
$634$		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	−0.414318	−	0.910132i	$-0.635980\pi$
$643$	−29.0442	−	5.77725i	−1.14539	−	0.227832i	−0.731072	+	0.682300i	$0.760980\pi$
$644$		0			0
$645$	2.10263	−	1.19902i	0.0827910	−	0.0472113i
$646$		0			0
$647$	43.7051	−	18.1032i	1.71822	−	0.711711i	0.718352	−	0.695680i	$-0.244897\pi$
$647$	43.7051	−	18.1032i	1.71822	−	0.711711i	0.999871	−	0.0160315i	$-0.00510319\pi$
$648$		0			0
$649$	6.74065	+	2.79207i	0.264594	+	0.109598i
$650$		0			0
$651$	−0.0759184	+	0.277394i	−0.00297548	+	0.0108719i
$652$		0			0
$653$	−14.1402	−	21.1623i	−0.553348	−	0.828143i	0.444358	−	0.895849i	$-0.353432\pi$
$653$	−14.1402	−	21.1623i	−0.553348	−	0.828143i	−0.997705	+	0.0677063i	$0.978432\pi$
$654$		0			0
$655$	−20.3297	−	20.3297i	−0.794347	−	0.794347i
$656$		0			0
$657$	−6.23952	+	43.7736i	−0.243427	+	1.70777i
$658$		0			0
$659$	−18.1263	−	27.1279i	−0.706100	−	1.05675i	−0.995047	−	0.0994083i	$-0.968305\pi$
$659$	−18.1263	−	27.1279i	−0.706100	−	1.05675i	0.288947	−	0.957345i	$-0.406695\pi$
$660$		0			0
$661$	5.91065	+	29.7149i	0.229898	+	1.15577i	0.907405	+	0.420258i	$0.138060\pi$
$661$	5.91065	+	29.7149i	0.229898	+	1.15577i	−0.677507	+	0.735516i	$0.736940\pi$
$662$		0			0
$663$	−42.2954	+	36.6941i	−1.64262	+	1.42508i
$664$		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
$669$	1.99448	+	1.54742i	0.0771109	+	0.0598266i
$670$		0			0
$671$			11.3347i			0.437569i
$672$		0			0
$673$			11.0359i			0.425402i	0.977117	+	0.212701i	$0.0682259\pi$
$673$			11.0359i			0.425402i	−0.977117	+	0.212701i	$0.931774\pi$
$674$		0			0
$675$	9.81544	+	0.157363i	0.377797	+	0.00605692i
$676$		0			0
$677$	−16.1303	−	10.7779i	−0.619939	−	0.414230i	0.205551	−	0.978646i	$-0.434101\pi$
$677$	−16.1303	−	10.7779i	−0.619939	−	0.414230i	−0.825490	+	0.564416i	$0.809101\pi$
$678$		0			0
$679$	12.1272	−	5.02324i	0.465399	−	0.192774i
$680$		0			0
$681$	22.4147	+	25.8362i	0.858932	+	0.990047i
$682$		0			0
$683$	9.44062	+	47.4612i	0.361235	+	1.81605i	0.551331	+	0.834287i	$0.314120\pi$
$683$	9.44062	+	47.4612i	0.361235	+	1.81605i	−0.190095	+	0.981766i	$0.560880\pi$
$684$		0			0
$685$	−5.14927	−	7.70643i	−0.196744	−	0.294448i
$686$		0			0
$687$	2.76840	−	0.923276i	0.105621	−	0.0352252i
$688$		0			0
$689$	43.3662	+	43.3662i	1.65212	+	1.65212i
$690$		0			0
$691$	2.62103	+	3.92264i	0.0997085	+	0.149224i	0.877969	−	0.478717i	$-0.158898\pi$
$691$	2.62103	+	3.92264i	0.0997085	+	0.149224i	−0.778261	+	0.627941i	$0.783898\pi$
$692$		0			0
$693$	−15.7955	+	17.6276i	−0.600020	+	0.669619i
$694$		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
$699$	13.3874	+	23.4765i	0.506358	+	0.887963i
$700$		0			0
$701$	−0.420755	−	0.0836934i	−0.0158917	−	0.00316106i	0.187138	−	0.982334i	$-0.440079\pi$
$701$	−0.420755	−	0.0836934i	−0.0158917	−	0.00316106i	−0.203030	+	0.979173i	$0.565079\pi$
$702$		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	0.931847	−	0.362852i	$-0.118197\pi$
$709$	25.3814	+	16.9593i	0.953218	+	0.636920i	0.0213708	+	0.999772i	$0.493197\pi$
$710$		0			0
$711$	−3.66494	+	6.19403i	−0.137446	+	0.232294i
$712$		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
$717$	0.211733	+	1.67749i	0.00790731	+	0.0626470i
$718$		0			0
$719$	4.47853	−	4.47853i	0.167021	−	0.167021i	−0.618648	−	0.785669i	$-0.712319\pi$
$719$	4.47853	−	4.47853i	0.167021	−	0.167021i	0.785669	+	0.618648i	$0.212319\pi$
$720$		0			0
$721$	−8.74797	−	8.74797i	−0.325791	−	0.325791i
$722$		0			0
$723$	−25.7853	+	3.25463i	−0.958967	+	0.121041i
$724$		0			0
$725$	−7.22588	+	1.43732i	−0.268363	+	0.0533806i
$726$		0			0
$727$	3.41297	+	1.41370i	0.126580	+	0.0524311i	0.445074	−	0.895494i	$-0.353177\pi$
$727$	3.41297	+	1.41370i	0.126580	+	0.0524311i	−0.318494	+	0.947925i	$0.603177\pi$
$728$		0			0
$729$	−18.4701	−	19.6941i	−0.684076	−	0.729411i
$730$		0			0
$731$	1.43094	−	2.14155i	0.0529250	−	0.0792079i
$732$		0			0
$733$	−1.76647	−	0.351374i	−0.0652462	−	0.0129783i	0.162359	−	0.986732i	$-0.448090\pi$
$733$	−1.76647	−	0.351374i	−0.0652462	−	0.0129783i	−0.227605	+	0.973753i	$0.573090\pi$
$734$		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	−0.554636	−	0.832093i	$-0.687143\pi$
$739$	7.50862	−	37.7484i	0.276209	−	1.38860i	0.830845	−	0.556504i	$-0.187857\pi$
$740$		0			0
$741$	−14.8809	+	8.48578i	−0.546663	+	0.311733i
$742$		0			0
$743$	13.3142	+	32.1432i	0.488449	+	1.17922i	0.955500	+	0.294990i	$0.0953165\pi$
$743$	13.3142	+	32.1432i	0.488449	+	1.17922i	−0.467051	+	0.884230i	$0.654684\pi$
$744$		0			0
$745$	9.64382	−	23.2822i	0.353322	−	0.852995i
$746$		0			0
$747$	20.2886	−	22.6419i	0.742321	−	0.828425i
$748$		0			0
$749$	−5.03516	+	3.36439i	−0.183981	+	0.122932i
$750$		0			0
$751$	−30.0300	+	30.0300i	−1.09581	+	1.09581i	−0.100914	+	0.994895i	$0.532177\pi$
$751$	−30.0300	+	30.0300i	−1.09581	+	1.09581i	−0.994895	+	0.100914i	$0.967823\pi$
$752$		0			0
$753$	−14.9894	−	44.9449i	−0.546244	−	1.63788i
$754$		0			0
$755$	−36.4661	+	24.3659i	−1.32714	+	0.886766i
$756$		0			0
$757$	37.4839	−	7.45600i	1.36237	−	0.270993i	0.540827	−	0.841134i	$-0.318111\pi$
$757$	37.4839	−	7.45600i	1.36237	−	0.270993i	0.821547	+	0.570141i	$0.193111\pi$
$758$		0			0
$759$	−15.1520	+	13.1454i	−0.549983	+	0.477147i
$760$		0			0
$761$	5.61157	+	13.5475i	0.203419	+	0.491097i	0.992361	−	0.123371i	$-0.0393705\pi$
$761$	5.61157	+	13.5475i	0.203419	+	0.491097i	−0.788941	+	0.614468i	$0.789371\pi$
$762$		0			0
$763$	14.2723	−	21.3600i	0.516692	−	0.773284i
$764$		0			0
$765$	34.3417	−	16.4815i	1.24163	−	0.595892i
$766$		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
$771$	−4.79710	+	6.18301i	−0.172763	+	0.222676i
$772$		0			0
$773$	−9.82391	+	14.7025i	−0.353341	+	0.528813i	−0.964980	−	0.262325i	$-0.915511\pi$
$773$	−9.82391	+	14.7025i	−0.353341	+	0.528813i	0.611638	+	0.791138i	$0.290511\pi$
$774$		0			0
$775$	−0.0359520	−	0.0867959i	−0.00129144	−	0.00311780i
$776$		0			0
$777$	37.7590	+	43.5228i	1.35460	+	1.56137i
$778$		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
$783$	16.6659	+	11.5264i	0.595590	+	0.411922i
$784$		0			0
$785$	−2.09058	+	2.09058i	−0.0746160	+	0.0746160i
$786$		0			0
$787$	30.2625	−	20.2207i	1.07874	−	0.720791i	0.116554	−	0.993184i	$-0.462815\pi$
$787$	30.2625	−	20.2207i	1.07874	−	0.720791i	0.962186	+	0.272393i	$0.0878151\pi$
$788$		0			0
$789$	−3.70591	−	1.01425i	−0.131934	−	0.0361083i
$790$		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
$795$	−20.6672	−	36.2425i	−0.732990	−	1.28539i
$796$		0			0
$797$	4.54990	−	22.8739i	0.161166	−	0.810234i	−0.812625	−	0.582787i	$-0.801962\pi$
$797$	4.54990	−	22.8739i	0.161166	−	0.810234i	0.973790	−	0.227447i	$-0.0730378\pi$
$798$		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
$807$	2.82612	−	39.8539i	0.0994840	−	1.40292i
$808$		0			0
$809$	18.3664	+	7.60762i	0.645729	+	0.267470i	0.681419	−	0.731893i	$-0.261363\pi$
$809$	18.3664	+	7.60762i	0.645729	+	0.267470i	−0.0356905	+	0.999363i	$0.511363\pi$
$810$		0			0
$811$	46.0682	−	9.16353i	1.61767	−	0.321775i	0.698494	−	0.715616i	$-0.253854\pi$
$811$	46.0682	−	9.16353i	1.61767	−	0.321775i	0.919179	+	0.393840i	$0.128854\pi$
$812$		0			0
$813$	1.43603	+	11.3772i	0.0503636	+	0.399014i
$814$		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
$819$	22.1940	−	63.1557i	0.775521	−	2.20684i
$820$		0			0
$821$	7.82812	+	39.3546i	0.273203	+	1.37349i	0.836833	+	0.547458i	$0.184404\pi$
$821$	7.82812	+	39.3546i	0.273203	+	1.37349i	−0.563630	+	0.826028i	$0.690596\pi$
$822$		0			0
$823$	−10.4572	+	25.2460i	−0.364516	+	0.880019i	0.630112	+	0.776504i	$0.283009\pi$
$823$	−10.4572	+	25.2460i	−0.364516	+	0.880019i	−0.994628	+	0.103515i	$0.966991\pi$
$824$		0			0
$825$	0.546911	−	7.71253i	0.0190410	−	0.268516i
$826$		0			0
$827$	−13.3380	−	8.91218i	−0.463809	−	0.309907i	0.301620	−	0.953428i	$-0.402473\pi$
$827$	−13.3380	−	8.91218i	−0.463809	−	0.309907i	−0.765428	+	0.643521i	$0.777473\pi$
$828$		0			0
$829$	4.63371	−	23.2952i	0.160935	−	0.809077i	−0.813002	−	0.582261i	$-0.802168\pi$
$829$	4.63371	−	23.2952i	0.160935	−	0.809077i	0.973938	−	0.226816i	$-0.0728317\pi$
$830$		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
$837$	−0.102697	+	0.237109i	−0.00354973	+	0.00819568i
$838$		0			0
$839$	−27.5815	+	11.4246i	−0.952220	+	0.394423i	−0.804065	−	0.594542i	$-0.797334\pi$
$839$	−27.5815	+	11.4246i	−0.952220	+	0.394423i	−0.148155	+	0.988964i	$0.547334\pi$
$840$		0			0
$841$	12.7423	+	5.27805i	0.439391	+	0.182002i
$842$		0			0
$843$	−11.4583	−	3.13595i	−0.394643	−	0.108008i
$844$		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
$849$	12.5521	+	37.6367i	0.430785	+	1.29169i
$850$		0			0
$851$	27.1296	+	40.6023i	0.929991	+	1.39183i
$852$		0			0
$853$	0.300445	+	1.51044i	0.0102870	+	0.0517164i	0.985588	−	0.169164i	$-0.0541068\pi$
$853$	0.300445	+	1.51044i	0.0102870	+	0.0517164i	−0.975301	+	0.220881i	$0.929107\pi$
$854$		0			0
$855$	11.2880	−	2.89567i	0.386041	−	0.0990300i
$856$		0			0
$857$	−6.92900	+	2.87008i	−0.236690	+	0.0980402i	−0.497876	−	0.867248i	$-0.665886\pi$
$857$	−6.92900	+	2.87008i	−0.236690	+	0.0980402i	0.261186	+	0.965289i	$0.415886\pi$
$858$		0			0
$859$	−12.3876	−	8.27714i	−0.422660	−	0.282412i	0.325996	−	0.945371i	$-0.394300\pi$
$859$	−12.3876	−	8.27714i	−0.422660	−	0.282412i	−0.748656	+	0.662959i	$0.769300\pi$
$860$		0			0
$861$	8.76372	−	11.2956i	0.298667	−	0.384953i
$862$		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
$867$	6.79718	−	8.76093i	0.230844	−	0.297537i
$868$		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
$873$	11.4237	−	2.93048i	0.386633	−	0.0991818i
$874$		0			0
$875$	5.31875	+	26.7392i	0.179807	+	0.903949i
$876$		0			0
$877$	13.8663	+	20.7524i	0.468232	+	0.700759i	0.988156	−	0.153454i	$-0.0490397\pi$
$877$	13.8663	+	20.7524i	0.468232	+	0.700759i	−0.519924	+	0.854213i	$0.674040\pi$
$878$		0			0
$879$	6.86713	+	20.5907i	0.231623	+	0.694509i
$880$		0			0
$881$	22.9018	+	22.9018i	0.771582	+	0.771582i	0.978383	−	0.206801i	$-0.0663052\pi$
$881$	22.9018	+	22.9018i	0.771582	+	0.771582i	−0.206801	+	0.978383i	$0.566305\pi$
$882$		0			0
$883$	−10.2732	−	15.3750i	−0.345722	−	0.517409i	0.617338	−	0.786698i	$-0.288211\pi$
$883$	−10.2732	−	15.3750i	−0.345722	−	0.517409i	−0.963059	+	0.269289i	$0.913211\pi$
$884$		0			0
$885$	13.5396	+	3.70558i	0.455129	+	0.124562i
$886$		0			0
$887$	−9.52810	−	3.94667i	−0.319922	−	0.132516i	0.216943	−	0.976184i	$-0.430392\pi$
$887$	−9.52810	−	3.94667i	−0.319922	−	0.132516i	−0.536865	+	0.843668i	$0.680392\pi$
$888$		0			0
$889$	6.51036	−	2.69668i	0.218350	−	0.0904437i
$890$		0			0
$891$	−16.2846	+	13.6767i	−0.545554	+	0.458186i
$892$		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
$903$	−0.217804	+	3.07147i	−0.00724807	+	0.102212i
$904$		0			0
$905$	−0.377519	+	0.911413i	−0.0125492	+	0.0302964i
$906$		0			0
$907$	−6.38322	−	32.0906i	−0.211951	−	1.06555i	−0.929438	−	0.368979i	$-0.879708\pi$
$907$	−6.38322	−	32.0906i	−0.211951	−	1.06555i	0.717487	−	0.696572i	$-0.245292\pi$
$908$		0			0
$909$	−1.37192	+	3.90396i	−0.0455037	+	0.129486i
$910$		0			0
$911$	20.1753	−	20.1753i	0.668438	−	0.668438i	−0.288916	−	0.957354i	$-0.593295\pi$
$911$	20.1753	−	20.1753i	0.668438	−	0.668438i	0.957354	+	0.288916i	$0.0932950\pi$
$912$		0			0
$913$	−16.9320	−	16.9320i	−0.560367	−	0.560367i
$914$		0			0
$915$	2.73092	+	21.6362i	0.0902813	+	0.715270i
$916$		0			0
$917$	35.8720	−	7.13538i	1.18460	−	0.235631i
$918$		0			0
$919$	44.0591	+	18.2499i	1.45338	+	0.602008i	0.963000	−	0.269502i	$-0.0868591\pi$
$919$	44.0591	+	18.2499i	1.45338	+	0.602008i	0.490377	+	0.871510i	$0.336859\pi$
$920$		0			0
$921$	−1.71306	+	24.1576i	−0.0564473	+	0.796019i
$922$		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	$-0.347481\pi$
$929$	28.1038			0.922057			0.461028	+	0.887385i	$0.347481\pi$
$930$		0			0
$931$	−1.19796	+	6.02255i	−0.0392616	+	0.197381i
$932$		0			0
$933$	28.3349	+	49.6888i	0.927643	+	1.62674i
$934$		0			0
$935$	−11.4813	−	27.7184i	−0.375480	−	0.906489i
$936$		0			0
$937$	−7.86396	+	18.9853i	−0.256904	+	0.620222i	−0.998731	−	0.0503700i	$-0.983960\pi$
$937$	−7.86396	+	18.9853i	−0.256904	+	0.620222i	0.741826	+	0.670592i	$0.233960\pi$
$938$		0			0
$939$	−1.39830	−	0.382692i	−0.0456317	−	0.0124887i
$940$		0			0
$941$	−43.2971	+	28.9302i	−1.41145	+	0.943098i	−0.411955	+	0.911204i	$0.635154\pi$
$941$	−43.2971	+	28.9302i	−1.41145	+	0.943098i	−0.999491	+	0.0318944i	$0.989846\pi$
$942$		0			0
$943$	8.56753	−	8.56753i	0.278997	−	0.278997i
$944$		0			0
$945$	−25.9041	+	37.4542i	−0.842660	+	1.21839i
$946$		0			0
$947$	−13.0677	+	8.73155i	−0.424643	+	0.283737i	−0.749473	−	0.662035i	$-0.769693\pi$
$947$	−13.0677	+	8.73155i	−0.424643	+	0.283737i	0.324830	+	0.945772i	$0.394693\pi$
$948$		0			0
$949$	−96.6027	+	19.2155i	−3.13586	+	0.623760i
$950$		0			0
$951$	−15.5296	−	17.9001i	−0.503580	−	0.580451i
$952$		0			0
$953$	18.0842	+	43.6591i	0.585804	+	1.41426i	0.887480	+	0.460846i	$0.152454\pi$
$953$	18.0842	+	43.6591i	0.585804	+	1.41426i	−0.301676	+	0.953411i	$0.597546\pi$
$954$		0			0
$955$	−7.11648	+	10.6506i	−0.230284	+	0.344644i
$956$		0			0
$957$	9.78341	−	12.6099i	0.316253	−	0.407620i
$958$		0			0
$959$	11.7908			0.380744
$960$		0			0
$961$	−30.9975			−0.999920
$962$		0			0
$963$	−4.90520	+	2.35414i	−0.158068	+	0.0758612i
$964$		0			0
$965$	−10.9794	+	16.4318i	−0.353439	+	0.528959i
$966$		0			0
$967$	−7.60618	−	18.3629i	−0.244598	−	0.590512i	0.753131	−	0.657871i	$-0.228543\pi$
$967$	−7.60618	−	18.3629i	−0.244598	−	0.590512i	−0.997729	+	0.0673588i	$0.978543\pi$
$968$		0			0
$969$	9.36668	−	8.12623i	0.300901	−	0.261052i
$970$		0			0
$971$	−23.2362	+	4.62196i	−0.745685	+	0.148326i	−0.553286	−	0.832991i	$-0.686627\pi$
$971$	−23.2362	+	4.62196i	−0.745685	+	0.148326i	−0.192398	+	0.981317i	$0.561627\pi$
$972$		0			0
$973$	32.0877	−	21.4403i	1.02868	−	0.687344i
$974$		0			0
$975$	6.91835	+	20.7443i	0.221565	+	0.664351i
$976$		0			0
$977$	−18.8219	+	18.8219i	−0.602164	+	0.602164i	−0.940886	−	0.338722i	$-0.890005\pi$
$977$	−18.8219	+	18.8219i	−0.602164	+	0.602164i	0.338722	+	0.940886i	$0.390005\pi$
$978$		0			0
$979$	−17.5668	+	11.7377i	−0.561437	+	0.375140i
$980$		0			0
$981$	15.4030	−	17.1896i	0.491779	−	0.548822i
$982$		0			0
$983$	−13.8501	+	33.4371i	−0.441750	+	1.06648i	0.533585	+	0.845746i	$0.320844\pi$
$983$	−13.8501	+	33.4371i	−0.441750	+	1.06648i	−0.975335	+	0.220731i	$0.929156\pi$
$984$		0			0
$985$	15.5816	+	37.6174i	0.496472	+	1.19859i
$986$		0			0
$987$	17.8994	−	10.2071i	0.569743	−	0.324895i
$988$		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	−0.151764	−	0.988417i	$-0.548495\pi$
$997$	25.8757	−	38.7257i	0.819492	−	1.22646i	0.971256	−	0.238039i	$-0.0765047\pi$
$998$		0			0
$999$	28.0675	+	43.4997i	0.888017	+	1.37627i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.s.a.107.13	✓	240	192.149	odd	16
192.2.s.a.107.18	yes	240	64.21	even	16
192.2.s.a.131.13	yes	240	4.3	odd	2
192.2.s.a.131.18	yes	240	12.11	even	2
768.2.s.a.335.24		240	192.107	even	16	inner
768.2.s.a.335.28		240	64.43	odd	16	inner
768.2.s.a.431.24		240	1.1	even	1	trivial
768.2.s.a.431.28		240	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.36847 + 1.06173i) q^{3} +(1.45822 - 2.18239i) q^{5} +(1.27779 + 3.08486i) q^{7} +(0.745444 + 2.90591i) q^{9} +(2.31748 - 0.460975i) q^{11} +(-5.55652 + 3.71275i) q^{13} +(4.31265 - 1.43829i) q^{15} +(3.42067 - 3.42067i) q^{17} +(1.23054 - 0.822221i) q^{19} +(-1.52668 + 5.57823i) q^{21} +(-1.87568 + 4.52828i) q^{23} +(-0.722975 - 1.74542i) q^{25} +(-2.06518 + 4.76813i) q^{27} +(0.760797 - 3.82478i) q^{29} +0.0497279 q^{31} +(3.66084 + 1.82971i) q^{33} +(8.59567 + 1.70978i) q^{35} +(5.53510 - 8.28386i) q^{37} +(-11.5459 - 0.818742i) q^{39} +(-2.28385 - 0.946002i) q^{41} +(0.522190 - 0.103870i) q^{43} +(7.42884 + 2.61062i) q^{45} +(-2.51930 - 2.51930i) q^{47} +(-2.93388 + 2.93388i) q^{49} +(8.31294 - 1.04926i) q^{51} +(-1.79038 - 9.00087i) q^{53} +(2.37338 - 5.72983i) q^{55} +(2.55694 + 0.181318i) q^{57} +(2.56739 + 1.71547i) q^{59} +(-0.935842 + 4.70479i) q^{61} +(-8.01181 + 6.01274i) q^{63} +17.5405i q^{65} +(3.65093 + 0.726215i) q^{67} +(-7.37464 + 4.20537i) q^{69} +(-12.6483 + 5.23910i) q^{71} +(13.6168 + 5.64025i) q^{73} +(0.863794 - 3.15617i) q^{75} +(4.38330 + 6.56007i) q^{77} +(1.69637 + 1.69637i) q^{79} +(-7.88863 + 4.33239i) q^{81} +(-5.63016 - 8.42612i) q^{83} +(-2.47712 - 12.4533i) q^{85} +(5.10203 - 4.42636i) q^{87} +(-8.26075 + 3.42172i) q^{89} +(-18.5534 - 12.3970i) q^{91} +(0.0680513 + 0.0527977i) q^{93} -3.88450i q^{95} -3.93119i q^{97} +(3.06710 + 6.39075i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 8 q^{3} + 16 q^{7} - 8 q^{9} - 16 q^{13} + 8 q^{15} + 16 q^{19} - 8 q^{21} - 16 q^{25} + 8 q^{27} + 32 q^{31} - 16 q^{37} + 8 q^{39} + 16 q^{43} - 8 q^{45} - 16 q^{49} + 8 q^{51} + 80 q^{55} - 8 q^{57}+ \cdots + 8 q^{99}+O(q^{100}) \) 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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