LMFDB - Embedded newform 936.2.dg.f.829.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(829,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.829"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.dg (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [56,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			829.10
Character	$\chi$	$=$	936.829
Dual form			936.2.dg.f.901.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.579236 + 1.29015i) q^{2} +(-1.32897 - 1.49460i) q^{4} -3.41501 q^{5} +(-1.18985 - 0.686961i) q^{7} +(2.69805 - 0.848845i) q^{8} +(1.97809 - 4.40587i) q^{10} +(-3.02491 - 5.23930i) q^{11} +(3.56588 + 0.533406i) q^{13} +(1.57549 - 1.13717i) q^{14} +(-0.467669 + 3.97257i) q^{16} +(-3.22892 + 5.59265i) q^{17} +(1.47915 - 2.56196i) q^{19} +(4.53845 + 5.10407i) q^{20} +(8.51161 - 0.867797i) q^{22} +(3.18261 + 5.51244i) q^{23} +6.66227 q^{25} +(-2.75366 + 4.29155i) q^{26} +(0.554545 + 2.69131i) q^{28} +(1.54870 - 0.894140i) q^{29} +4.78951i q^{31} +(-4.85431 - 2.90442i) q^{32} +(-5.34505 - 7.40526i) q^{34} +(4.06335 + 2.34598i) q^{35} +(2.52420 + 4.37205i) q^{37} +(2.44853 + 3.39230i) q^{38} +(-9.21385 + 2.89881i) q^{40} +(2.96921 - 1.71428i) q^{41} +(-3.92452 - 2.26583i) q^{43} +(-3.81064 + 11.4839i) q^{44} +(-8.95535 + 0.913038i) q^{46} -0.675737i q^{47} +(-2.55617 - 4.42742i) q^{49} +(-3.85902 + 8.59532i) q^{50} +(-3.94172 - 6.03845i) q^{52} +12.4101i q^{53} +(10.3301 + 17.8922i) q^{55} +(-3.79340 - 0.843454i) q^{56} +(0.256514 + 2.51597i) q^{58} +(2.78619 - 4.82582i) q^{59} +(-0.167415 - 0.0966574i) q^{61} +(-6.17919 - 2.77426i) q^{62} +(6.55892 - 4.58045i) q^{64} +(-12.1775 - 1.82158i) q^{65} +(4.90885 + 8.50237i) q^{67} +(12.6499 - 2.60653i) q^{68} +(-5.38030 + 3.88345i) q^{70} +(11.7740 + 6.79775i) q^{71} +1.97079i q^{73} +(-7.10270 + 0.724152i) q^{74} +(-5.79485 + 1.19403i) q^{76} +8.31198i q^{77} -1.01051 q^{79} +(1.59709 - 13.5663i) q^{80} +(0.491798 + 4.82370i) q^{82} -4.43962 q^{83} +(11.0268 - 19.0989i) q^{85} +(5.19648 - 3.75078i) q^{86} +(-12.6087 - 11.5682i) q^{88} +(11.3849 - 6.57306i) q^{89} +(-3.87643 - 3.08429i) q^{91} +(4.00931 - 12.0826i) q^{92} +(0.871802 + 0.391411i) q^{94} +(-5.05130 + 8.74910i) q^{95} +(15.0845 + 8.70903i) q^{97} +(7.19265 - 0.733323i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{10} - 4 q^{16} + 64 q^{25} - 48 q^{28} - 48 q^{40} + 20 q^{49} - 12 q^{52} + 16 q^{55} + 12 q^{58} - 72 q^{64} - 84 q^{76} + 80 q^{79} - 12 q^{82} - 12 q^{88} - 24 q^{94} + 24 q^{97}+O(q^{100}) $ 56 * q - 4 * q^10 - 4 * q^16 + 64 * q^25 - 48 * q^28 - 48 * q^40 + 20 * q^49 - 12 * q^52 + 16 * q^55 + 12 * q^58 - 72 * q^64 - 84 * q^76 + 80 * q^79 - 12 * q^82 - 12 * q^88 - 24 * q^94 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−0.579236	+	1.29015i	−0.409582	+	0.912273i
$2$	−0.579236	+	1.29015i	−0.409582	+	0.912273i
$3$		0			0
$3$		0			0
$4$	−1.32897	−	1.49460i	−0.664486	−	0.747301i
$5$	−3.41501			−1.52724			−0.763619	−	0.645668i	$-0.776579\pi$
$5$	−3.41501			−1.52724			−0.763619	+	0.645668i	$0.776579\pi$
$6$		0			0
$7$	−1.18985	−	0.686961i	−0.449721	−	0.259647i	0.257991	−	0.966147i	$-0.416939\pi$
$7$	−1.18985	−	0.686961i	−0.449721	−	0.259647i	−0.707713	+	0.706500i	$0.750273\pi$
$8$	2.69805	−	0.848845i	0.953904	−	0.300112i
$9$		0			0
$10$	1.97809	−	4.40587i	0.625528	−	1.39326i
$11$	−3.02491	−	5.23930i	−0.912044	−	1.57971i	−0.811172	−	0.584808i	$-0.801170\pi$
$11$	−3.02491	−	5.23930i	−0.912044	−	1.57971i	−0.100873	−	0.994899i	$-0.532163\pi$
$12$		0			0
$13$	3.56588	+	0.533406i	0.988996	+	0.147940i
$13$	3.56588	+	0.533406i	0.988996	+	0.147940i
$14$	1.57549	−	1.13717i	0.421067	−	0.303922i
$15$		0			0
$16$	−0.467669	+	3.97257i	−0.116917	+	0.993142i
$17$	−3.22892	+	5.59265i	−0.783128	+	1.35642i	0.146983	+	0.989139i	$0.453044\pi$
$17$	−3.22892	+	5.59265i	−0.783128	+	1.35642i	−0.930111	+	0.367279i	$0.880290\pi$
$18$		0			0
$19$	1.47915	−	2.56196i	0.339340	−	0.587753i	−0.644969	−	0.764209i	$-0.723130\pi$
$19$	1.47915	−	2.56196i	0.339340	−	0.587753i	0.984309	+	0.176455i	$0.0564631\pi$
$20$	4.53845	+	5.10407i	1.01483	+	1.14131i
$21$		0			0
$22$	8.51161	−	0.867797i	1.81468	−	0.185015i
$23$	3.18261	+	5.51244i	0.663620	+	1.14942i	0.979658	+	0.200677i	$0.0643141\pi$
$23$	3.18261	+	5.51244i	0.663620	+	1.14942i	−0.316038	+	0.948747i	$0.602353\pi$
$24$		0			0
$25$	6.66227			1.33245
$26$	−2.75366	+	4.29155i	−0.540037	+	0.841642i
$27$		0			0
$28$	0.554545	+	2.69131i	0.104799	+	0.508609i
$29$	1.54870	−	0.894140i	0.287586	−	0.166038i	−0.349267	−	0.937023i	$-0.613569\pi$
$29$	1.54870	−	0.894140i	0.287586	−	0.166038i	0.636853	+	0.770986i	$0.280236\pi$
$30$		0			0
$31$			4.78951i			0.860222i	0.902776	+	0.430111i	$0.141526\pi$
$31$			4.78951i			0.860222i	−0.902776	+	0.430111i	$0.858474\pi$
$32$	−4.85431	−	2.90442i	−0.858130	−	0.513433i
$33$		0			0
$34$	−5.34505	−	7.40526i	−0.916669	−	1.26999i
$35$	4.06335	+	2.34598i	0.686831	+	0.396542i
$36$		0			0
$37$	2.52420	+	4.37205i	0.414976	+	0.718760i	0.995426	−	0.0955362i	$-0.0304566\pi$
$37$	2.52420	+	4.37205i	0.414976	+	0.718760i	−0.580450	+	0.814296i	$0.697123\pi$
$38$	2.44853	+	3.39230i	0.397205	+	0.550304i
$39$		0			0
$40$	−9.21385	+	2.89881i	−1.45684	+	0.458342i
$41$	2.96921	−	1.71428i	0.463713	−	0.267725i	−0.249891	−	0.968274i	$-0.580395\pi$
$41$	2.96921	−	1.71428i	0.463713	−	0.267725i	0.713604	+	0.700549i	$0.247062\pi$
$42$		0			0
$43$	−3.92452	−	2.26583i	−0.598484	−	0.345535i	0.169961	−	0.985451i	$-0.445636\pi$
$43$	−3.92452	−	2.26583i	−0.598484	−	0.345535i	−0.768445	+	0.639916i	$0.778969\pi$
$44$	−3.81064	+	11.4839i	−0.574476	+	1.73126i
$45$		0			0
$46$	−8.95535	+	0.913038i	−1.32039	+	0.134620i
$47$		−	0.675737i		−	0.0985664i	−0.998785	−	0.0492832i	$-0.984306\pi$
$47$		−	0.675737i		−	0.0985664i	0.998785	−	0.0492832i	$-0.0156937\pi$
$48$		0			0
$49$	−2.55617	−	4.42742i	−0.365167	−	0.632488i
$50$	−3.85902	+	8.59532i	−0.545748	+	1.21556i
$51$		0			0
$52$	−3.94172	−	6.03845i	−0.546618	−	0.837382i
$53$			12.4101i			1.70466i	0.523002	+	0.852331i	$0.324812\pi$
$53$			12.4101i			1.70466i	−0.523002	+	0.852331i	$0.675188\pi$
$54$		0			0
$55$	10.3301	+	17.8922i	1.39291	+	2.41259i
$56$	−3.79340	−	0.843454i	−0.506914	−	0.112711i
$57$		0			0
$58$	0.256514	+	2.51597i	0.0336820	+	0.330363i
$59$	2.78619	−	4.82582i	0.362731	−	0.628268i	−0.625678	−	0.780081i	$-0.715178\pi$
$59$	2.78619	−	4.82582i	0.362731	−	0.628268i	0.988409	+	0.151813i	$0.0485111\pi$
$60$		0			0
$61$	−0.167415	−	0.0966574i	−0.0214354	−	0.0123757i	0.489244	−	0.872147i	$-0.337273\pi$
$61$	−0.167415	−	0.0966574i	−0.0214354	−	0.0123757i	−0.510679	+	0.859771i	$0.670606\pi$
$62$	−6.17919	−	2.77426i	−0.784758	−	0.352331i
$63$		0			0
$64$	6.55892	−	4.58045i	0.819865	−	0.572556i
$65$	−12.1775	−	1.82158i	−1.51043	−	0.225940i
$66$		0			0
$67$	4.90885	+	8.50237i	0.599711	+	1.03873i	0.992863	+	0.119256i	$0.0380511\pi$
$67$	4.90885	+	8.50237i	0.599711	+	1.03873i	−0.393153	+	0.919473i	$0.628616\pi$
$68$	12.6499	−	2.60653i	1.53403	−	0.316088i
$69$		0			0
$70$	−5.38030	+	3.88345i	−0.643068	+	0.464162i
$71$	11.7740	+	6.79775i	1.39732	+	0.806744i	0.994111	−	0.108363i	$-0.0345608\pi$
$71$	11.7740	+	6.79775i	1.39732	+	0.806744i	0.403211	+	0.915107i	$0.367894\pi$
$72$		0			0
$73$			1.97079i			0.230663i	0.993327	+	0.115332i	$0.0367930\pi$
$73$			1.97079i			0.230663i	−0.993327	+	0.115332i	$0.963207\pi$
$74$	−7.10270	+	0.724152i	−0.825672	+	0.0841810i
$75$		0			0
$76$	−5.79485	+	1.19403i	−0.664715	+	0.136965i
$77$			8.31198i			0.947238i
$78$		0			0
$79$	−1.01051			−0.113691			−0.0568455	−	0.998383i	$-0.518104\pi$
$79$	−1.01051			−0.113691			−0.0568455	+	0.998383i	$0.518104\pi$
$80$	1.59709	−	13.5663i	0.178560	−	1.51676i
$81$		0			0
$82$	0.491798	+	4.82370i	0.0543100	+	0.532688i
$83$	−4.43962			−0.487312			−0.243656	−	0.969862i	$-0.578347\pi$
$83$	−4.43962			−0.487312			−0.243656	+	0.969862i	$0.578347\pi$
$84$		0			0
$85$	11.0268	−	19.0989i	1.19602	−	2.07157i
$86$	5.19648	−	3.75078i	0.560351	−	0.404457i
$87$		0			0
$88$	−12.6087	−	11.5682i	−1.34409	−	1.23317i
$89$	11.3849	−	6.57306i	1.20679	−	0.696743i	0.244737	−	0.969589i	$-0.421298\pi$
$89$	11.3849	−	6.57306i	1.20679	−	0.696743i	0.962058	+	0.272846i	$0.0879650\pi$
$90$		0			0
$91$	−3.87643	−	3.08429i	−0.406361	−	0.323322i
$92$	4.00931	−	12.0826i	0.417999	−	1.25970i
$93$		0			0
$94$	0.871802	+	0.391411i	0.0899195	+	0.0403710i
$95$	−5.05130	+	8.74910i	−0.518252	+	0.897639i
$96$		0			0
$97$	15.0845	+	8.70903i	1.53160	+	0.884268i	0.999288	+	0.0377182i	$0.0120089\pi$
$97$	15.0845	+	8.70903i	1.53160	+	0.884268i	0.532309	+	0.846550i	$0.321324\pi$
$98$	7.19265	−	0.733323i	0.726568	−	0.0740768i
$99$		0			0
$100$	−8.85396	−	9.95743i	−0.885396	−	0.995743i
$101$	−4.57759	+	2.64287i	−0.455487	+	0.262976i	−0.710145	−	0.704056i	$-0.751371\pi$
$101$	−4.57759	+	2.64287i	−0.455487	+	0.262976i	0.254657	+	0.967031i	$0.418037\pi$
$102$		0			0
$103$	6.98106			0.687864			0.343932	−	0.938994i	$-0.388241\pi$
$103$	6.98106			0.687864			0.343932	+	0.938994i	$0.388241\pi$
$104$	10.0737	−	1.58772i	0.987806	−	0.155689i
$105$		0			0
$106$	−16.0109	−	7.18839i	−1.55512	−	0.698198i
$107$	9.02755	−	5.21206i	0.872726	−	0.503868i	0.00447271	−	0.999990i	$-0.498576\pi$
$107$	9.02755	−	5.21206i	0.872726	−	0.503868i	0.868253	+	0.496122i	$0.165243\pi$
$108$		0			0
$109$	−16.6956			−1.59915			−0.799575	−	0.600566i	$-0.794942\pi$
$109$	−16.6956			−1.59915			−0.799575	+	0.600566i	$0.794942\pi$
$110$	−29.0672	+	2.96353i	−2.77145	+	0.282562i
$111$		0			0
$112$	3.28545	−	4.40549i	0.310446	−	0.416280i
$113$	−5.81227	+	10.0672i	−0.546773	+	0.947038i	0.451720	+	0.892160i	$0.350810\pi$
$113$	−5.81227	+	10.0672i	−0.546773	+	0.947038i	−0.998493	+	0.0548783i	$0.982523\pi$
$114$		0			0
$115$	−10.8686	−	18.8250i	−1.01350	−	1.75544i
$116$	−3.39456	−	1.12640i	−0.315177	−	0.104583i
$117$		0			0
$118$	4.61217	+	6.38989i	0.424585	+	0.588237i
$119$	7.68387	−	4.43628i	0.704379	−	0.406673i
$120$		0			0
$121$	−12.8002	+	22.1705i	−1.16365	+	2.01550i
$122$	0.221676	−	0.160004i	0.0200696	−	0.0144860i
$123$		0			0
$124$	7.15841	−	6.36513i	0.642845	−	0.571605i
$125$	−5.67665			−0.507735
$126$		0			0
$127$	0.754501	+	1.30683i	0.0669511	+	0.115963i	0.897558	−	0.440897i	$-0.145340\pi$
$127$	0.754501	+	1.30683i	0.0669511	+	0.115963i	−0.830607	+	0.556859i	$0.812006\pi$
$128$	2.11030	+	11.1152i	0.186526	+	0.982450i
$129$		0			0
$130$	9.40376	−	14.6557i	0.824764	−	1.28539i
$131$		−	0.608733i		−	0.0531852i	−0.999646	−	0.0265926i	$-0.991534\pi$
$131$		−	0.608733i		−	0.0531852i	0.999646	−	0.0265926i	$-0.00846569\pi$
$132$		0			0
$133$	−3.51993	+	2.03223i	−0.305217	+	0.176217i
$134$	−13.8127	+	1.40827i	−1.19324	+	0.121656i
$135$		0			0
$136$	−3.96448	+	17.8301i	−0.339952	+	1.52892i
$137$	−9.96572	−	5.75371i	−0.851429	−	0.491573i	0.00970370	−	0.999953i	$-0.496911\pi$
$137$	−9.96572	−	5.75371i	−0.851429	−	0.491573i	−0.861133	+	0.508380i	$0.830245\pi$
$138$		0			0
$139$	13.4078	+	7.74102i	1.13724	+	0.656585i	0.945745	−	0.324909i	$-0.105334\pi$
$139$	13.4078	+	7.74102i	1.13724	+	0.656585i	0.191493	+	0.981494i	$0.438667\pi$
$140$	−1.89378	−	9.19082i	−0.160053	−	0.776766i
$141$		0			0
$142$	−15.5901	+	11.2528i	−1.30829	+	0.944312i
$143$	−7.99178	−	20.2962i	−0.668306	−	1.69725i
$144$		0			0
$145$	−5.28881	+	3.05349i	−0.439211	+	0.253579i
$146$	−2.54261	−	1.14155i	−0.210428	−	0.0944753i
$147$		0			0
$148$	3.17987	−	9.58300i	0.261384	−	0.787718i
$149$	0.454670	−	0.787511i	0.0372480	−	0.0645154i	−0.846800	−	0.531911i	$-0.821474\pi$
$149$	0.454670	−	0.787511i	0.0372480	−	0.0645154i	0.884048	+	0.467395i	$0.154808\pi$
$150$		0			0
$151$		−	21.8390i		−	1.77723i	−0.458650	−	0.888617i	$-0.651667\pi$
$151$		−	21.8390i		−	1.77723i	0.458650	−	0.888617i	$-0.348333\pi$
$152$	1.81610	−	8.16785i	0.147305	−	0.662500i
$153$		0			0
$154$	−10.7237	−	4.81459i	−0.864140	−	0.387971i
$155$		−	16.3562i		−	1.31376i
$156$		0			0
$157$			3.03910i			0.242547i	0.992619	+	0.121273i	$0.0386978\pi$
$157$			3.03910i			0.242547i	−0.992619	+	0.121273i	$0.961302\pi$
$158$	0.585322	−	1.30371i	0.0465657	−	0.103717i
$159$		0			0
$160$	16.5775	+	9.91860i	1.31057	+	0.784134i
$161$		−	8.74531i		−	0.689227i
$162$		0			0
$163$	−8.36620	+	14.4907i	−0.655291	+	1.13500i	0.326530	+	0.945187i	$0.394121\pi$
$163$	−8.36620	+	14.4907i	−0.655291	+	1.13500i	−0.981821	+	0.189811i	$0.939213\pi$
$164$	−6.50816	−	2.15957i	−0.508202	−	0.168634i
$165$		0			0
$166$	2.57159	−	5.72777i	0.199594	−	0.444562i
$167$	15.2052	−	8.77871i	1.17661	−	0.679317i	0.221383	−	0.975187i	$-0.428943\pi$
$167$	15.2052	−	8.77871i	1.17661	−	0.679317i	0.955228	+	0.295870i	$0.0956095\pi$
$168$		0			0
$169$	12.4310	+	3.80412i	0.956227	+	0.292625i
$170$	18.2534	+	25.2890i	1.39997	+	1.93958i
$171$		0			0
$172$	1.82908	+	8.87682i	0.139466	+	0.676851i
$173$	2.27946	+	1.31605i	0.173304	+	0.100057i	0.584143	−	0.811651i	$-0.301431\pi$
$173$	2.27946	+	1.31605i	0.173304	+	0.100057i	−0.410839	+	0.911708i	$0.634764\pi$
$174$		0			0
$175$	−7.92710	−	4.57672i	−0.599233	−	0.345967i
$176$	22.2281	−	9.56640i	1.67551	−	0.721094i
$177$		0			0
$178$	1.88570	+	18.4955i	0.141339	+	1.38630i
$179$	17.9329	−	10.3536i	1.34037	−	0.773863i	0.353509	−	0.935431i	$-0.384988\pi$
$179$	17.9329	−	10.3536i	1.34037	−	0.773863i	0.986862	+	0.161568i	$0.0516551\pi$
$180$		0			0
$181$			16.5473i			1.22995i	0.788547	+	0.614974i	$0.210834\pi$
$181$			16.5473i			1.22995i	−0.788547	+	0.614974i	$0.789166\pi$
$182$	6.22457	−	3.21465i	0.461396	−	0.238285i
$183$		0			0
$184$	13.2660	+	12.1713i	0.977985	+	0.897279i
$185$	−8.62016	−	14.9306i	−0.633767	−	1.09772i
$186$		0			0
$187$	39.0688			2.85699
$188$	−1.00996	+	0.898035i	−0.0736587	+	0.0654960i
$189$		0			0
$190$	−8.36176	−	11.5847i	−0.606626	−	0.840444i
$191$	−7.40658	+	12.8286i	−0.535921	+	0.928242i	0.463197	+	0.886255i	$0.346702\pi$
$191$	−7.40658	+	12.8286i	−0.535921	+	0.928242i	−0.999118	+	0.0419872i	$0.986631\pi$
$192$		0			0
$193$	−12.1754	+	7.02946i	−0.876403	+	0.505992i	−0.869471	−	0.493984i	$-0.835540\pi$
$193$	−12.1754	+	7.02946i	−0.876403	+	0.505992i	−0.00693238	+	0.999976i	$0.502207\pi$
$194$	−19.9734	+	14.4167i	−1.43401	+	1.03506i
$195$		0			0
$196$	−3.22015	+	9.70437i	−0.230010	+	0.693169i
$197$	−4.77917	−	8.27776i	−0.340501	−	0.589766i	0.644024	−	0.765005i	$-0.277264\pi$
$197$	−4.77917	−	8.27776i	−0.340501	−	0.589766i	−0.984526	+	0.175239i	$0.943930\pi$
$198$		0			0
$199$	1.90281	−	3.29576i	0.134887	−	0.233630i	−0.790668	−	0.612246i	$-0.790266\pi$
$199$	1.90281	−	3.29576i	0.134887	−	0.233630i	0.925554	+	0.378615i	$0.123600\pi$
$200$	17.9751	−	5.65523i	1.27103	−	0.399885i
$201$		0			0
$202$	−0.758197	−	7.43663i	−0.0533466	−	0.523239i
$203$	−2.45696			−0.172445
$204$		0			0
$205$	−10.1399	+	5.85426i	−0.708200	+	0.408879i
$206$	−4.04368	+	9.00661i	−0.281737	+	0.627520i
$207$		0			0
$208$	−3.78664	+	13.9162i	−0.262556	+	0.964917i
$209$	−17.8971			−1.23797
$210$		0			0
$211$	8.77615	−	5.06691i	0.604175	−	0.348821i	−0.166507	−	0.986040i	$-0.553249\pi$
$211$	8.77615	−	5.06691i	0.604175	−	0.348821i	0.770682	+	0.637220i	$0.219916\pi$
$212$	18.5482	−	16.4927i	1.27390	−	1.13272i
$213$		0			0
$214$	1.49525	+	14.6659i	0.102213	+	1.00254i
$215$	13.4023	+	7.73781i	0.914028	+	0.527714i
$216$		0			0
$217$	3.29021	−	5.69881i	0.223354	−	0.386860i
$218$	9.67070	−	21.5398i	0.654982	−	1.45886i
$219$		0			0
$220$	13.0134	−	39.2176i	0.877361	−	2.64405i
$221$	−14.4971	+	18.2204i	−0.975180	+	1.22564i
$222$		0			0
$223$	−1.88434	+	1.08792i	−0.126185	+	0.0728527i	−0.561764	−	0.827298i	$-0.689877\pi$
$223$	−1.88434	+	1.08792i	−0.126185	+	0.0728527i	0.435579	+	0.900150i	$0.356544\pi$
$224$	3.78069	+	6.79055i	0.252608	+	0.453712i
$225$		0			0
$226$	−9.62145	−	13.3300i	−0.640010	−	0.886695i
$227$	2.53742	−	4.39495i	0.168415	−	0.291703i	−0.769448	−	0.638710i	$-0.779469\pi$
$227$	2.53742	−	4.39495i	0.168415	−	0.291703i	0.937863	+	0.347007i	$0.112802\pi$
$228$		0			0
$229$	−12.7135			−0.840132			−0.420066	−	0.907493i	$-0.637993\pi$
$229$	−12.7135			−0.840132			−0.420066	+	0.907493i	$0.637993\pi$
$230$	30.5826	−	3.11803i	2.01656	−	0.205597i
$231$		0			0
$232$	3.41947	−	3.72704i	0.224499	−	0.244692i
$233$	0.408995			0.0267941			0.0133971	−	0.999910i	$-0.495735\pi$
$233$	0.408995			0.0267941			0.0133971	+	0.999910i	$0.495735\pi$
$234$		0			0
$235$			2.30765i			0.150534i
$236$	−10.9154	+	2.24914i	−0.710535	+	0.146406i
$237$		0			0
$238$	1.27270	+	12.4830i	0.0824967	+	0.809152i
$239$		−	13.2448i		−	0.856734i	−0.903605	−	0.428367i	$-0.859089\pi$
$239$		−	13.2448i		−	0.856734i	0.903605	−	0.428367i	$-0.140911\pi$
$240$		0			0
$241$	15.9642	+	9.21693i	1.02834	+	0.593715i	0.916510	−	0.400012i	$-0.130994\pi$
$241$	15.9642	+	9.21693i	1.02834	+	0.593715i	0.111834	+	0.993727i	$0.464328\pi$
$242$	−21.1890	−	29.3561i	−1.36208	−	1.88708i
$243$		0			0
$244$	0.0780261	+	0.378674i	0.00499511	+	0.0242421i
$245$	8.72933	+	15.1197i	0.557697	+	0.965959i
$246$		0			0
$247$	6.64102	−	8.34664i	0.422558	−	0.531084i
$248$	4.06555	+	12.9223i	0.258163	+	0.820569i
$249$		0			0
$250$	3.28812	−	7.32372i	0.207959	−	0.463193i
$251$	−10.4275	−	6.02030i	−0.658176	−	0.379998i	0.133406	−	0.991062i	$-0.457409\pi$
$251$	−10.4275	−	6.02030i	−0.658176	−	0.379998i	−0.791582	+	0.611063i	$0.790742\pi$
$252$		0			0
$253$	19.2542	−	33.3493i	1.21050	−	2.09665i
$254$	−2.12304	+	0.216454i	−0.133212	+	0.0135815i
$255$		0			0
$256$	−15.5626	−	3.71569i	−0.972661	−	0.232231i
$257$	−1.85401	−	3.21124i	−0.115650	−	0.200312i	0.802389	−	0.596801i	$-0.203562\pi$
$257$	−1.85401	−	3.21124i	−0.115650	−	0.200312i	−0.918039	+	0.396489i	$0.870228\pi$
$258$		0			0
$259$		−	6.93611i		−	0.430989i
$260$	13.4610	+	20.6213i	0.834816	+	1.27888i
$261$		0			0
$262$	0.785356	+	0.352600i	0.0485195	+	0.0217837i
$263$	6.78854	+	11.7581i	0.418599	+	0.725035i	0.995799	−	0.0915678i	$-0.0291878\pi$
$263$	6.78854	+	11.7581i	0.418599	+	0.725035i	−0.577199	+	0.816603i	$0.695855\pi$
$264$		0			0
$265$		−	42.3807i		−	2.60342i
$266$	−0.583014	−	5.71838i	−0.0357469	−	0.350616i
$267$		0			0
$268$	6.18394	−	18.6362i	0.377744	−	1.13839i
$269$	14.2966	+	8.25414i	0.871679	+	0.503264i	0.867906	−	0.496729i	$-0.165466\pi$
$269$	14.2966	+	8.25414i	0.871679	+	0.503264i	0.00377292	+	0.999993i	$0.498799\pi$
$270$		0			0
$271$	9.81144	−	5.66464i	0.596003	−	0.344102i	−0.171465	−	0.985190i	$-0.554850\pi$
$271$	9.81144	−	5.66464i	0.596003	−	0.344102i	0.767467	+	0.641088i	$0.221517\pi$
$272$	−20.7071	−	15.4426i	−1.25555	−	0.936346i
$273$		0			0
$274$	13.1957	−	9.52451i	0.797179	−	0.575397i
$275$	−20.1527	−	34.9056i	−1.21526	−	2.10489i
$276$		0			0
$277$	−0.350695	−	0.202474i	−0.0210712	−	0.0121655i	0.489427	−	0.872044i	$-0.337206\pi$
$277$	−0.350695	−	0.202474i	−0.0210712	−	0.0121655i	−0.510499	+	0.859879i	$0.670539\pi$
$278$	−17.7534	+	12.8142i	−1.06478	+	0.768547i
$279$		0			0
$280$	12.9545	+	2.88040i	0.774178	+	0.172137i
$281$		−	5.21840i		−	0.311304i	−0.987812	−	0.155652i	$-0.950252\pi$
$281$		−	5.21840i		−	0.311304i	0.987812	−	0.155652i	$-0.0497478\pi$
$282$		0			0
$283$	−19.4544	+	11.2320i	−1.15644	+	0.667673i	−0.950449	−	0.310880i	$-0.899376\pi$
$283$	−19.4544	+	11.2320i	−1.15644	+	0.667673i	−0.205995	+	0.978553i	$0.566043\pi$
$284$	−5.48745	−	26.6315i	−0.325620	−	1.58029i
$285$		0			0
$286$	30.8142	+	1.44569i	1.82208	+	0.0854853i
$287$	−4.71056			−0.278056
$288$		0			0
$289$	−12.3518	−	21.3940i	−0.726579	−	1.25847i
$290$	−0.875997	−	8.59204i	−0.0514403	−	0.504542i
$291$		0			0
$292$	2.94554	−	2.61912i	0.172375	−	0.153272i
$293$	−7.79411	+	13.4998i	−0.455337	+	0.788667i	−0.998708	−	0.0508261i	$-0.983815\pi$
$293$	−7.79411	+	13.4998i	−0.455337	+	0.788667i	0.543370	+	0.839493i	$0.317148\pi$
$294$		0			0
$295$	−9.51485	+	16.4802i	−0.553976	+	0.959515i
$296$	10.5216	+	9.65333i	0.611556	+	0.561088i
$297$		0			0
$298$	0.752646	+	1.04275i	0.0435996	+	0.0604047i
$299$	8.40842	+	21.3543i	0.486272	+	1.23495i
$300$		0			0
$301$	3.11307	+	5.39199i	0.179434	+	0.310789i
$302$	28.1756	+	12.6499i	1.62132	+	0.727922i
$303$		0			0
$304$	9.48580	+	7.07416i	0.544048	+	0.405731i
$305$	0.571725	+	0.330085i	0.0327369	+	0.0189006i
$306$		0			0
$307$	−28.8805			−1.64830			−0.824149	−	0.566373i	$-0.808346\pi$
$307$	−28.8805			−1.64830			−0.824149	+	0.566373i	$0.808346\pi$
$308$	12.4231	−	11.0464i	0.707872	−	0.629426i
$309$		0			0
$310$	21.1020	+	9.47411i	1.19851	+	0.538093i
$311$	7.65884			0.434293			0.217147	−	0.976139i	$-0.430325\pi$
$311$	7.65884			0.434293			0.217147	+	0.976139i	$0.430325\pi$
$312$		0			0
$313$	−14.6712			−0.829266			−0.414633	−	0.909989i	$-0.636090\pi$
$313$	−14.6712			−0.829266			−0.414633	+	0.909989i	$0.636090\pi$
$314$	−3.92090	−	1.76036i	−0.221269	−	0.0993427i
$315$		0			0
$316$	1.34294	+	1.51031i	0.0755461	+	0.0849614i
$317$	−12.7648			−0.716943			−0.358471	−	0.933541i	$-0.616702\pi$
$317$	−12.7648			−0.716943			−0.358471	+	0.933541i	$0.616702\pi$
$318$		0			0
$319$	−9.36933	−	5.40939i	−0.524582	−	0.302867i
$320$	−22.3988	+	15.6423i	−1.25213	+	0.874429i
$321$		0			0
$322$	11.2828	+	5.06560i	0.628764	+	0.282295i
$323$	9.55209	+	16.5447i	0.531493	+	0.920572i
$324$		0			0
$325$	23.7568	+	3.55369i	1.31779	+	0.197123i
$326$	−13.8491	−	19.1872i	−0.767033	−	1.06268i
$327$		0			0
$328$	6.55592	−	7.14560i	0.361990	−	0.394550i
$329$	−0.464205	+	0.804027i	−0.0255924	+	0.0443274i
$330$		0			0
$331$	0.0572169	−	0.0991026i	0.00314492	−	0.00544717i	−0.864449	−	0.502721i	$-0.832332\pi$
$331$	0.0572169	−	0.0991026i	0.00314492	−	0.00544717i	0.867594	+	0.497274i	$0.165666\pi$
$332$	5.90013	+	6.63547i	0.323812	+	0.364168i
$333$		0			0
$334$	2.51847	+	24.7019i	0.137804	+	1.35163i
$335$	−16.7637	−	29.0356i	−0.915901	−	1.58639i
$336$		0			0
$337$	−14.2820			−0.777992			−0.388996	−	0.921240i	$-0.627178\pi$
$337$	−14.2820			−0.777992			−0.388996	+	0.921240i	$0.627178\pi$
$338$	−12.1083	+	13.8343i	−0.658607	+	0.752487i
$339$		0			0
$340$	−43.1996	+	8.90131i	−2.34283	+	0.482741i
$341$	25.0937	−	14.4878i	1.35890	−	0.784561i
$342$		0			0
$343$			16.6414i			0.898551i
$344$	−12.5119	−	2.78199i	−0.674596	−	0.149995i
$345$		0			0
$346$	−3.01824	+	2.17854i	−0.162262	+	0.117119i
$347$	17.4058	+	10.0492i	0.934390	+	0.539470i	0.888197	−	0.459462i	$-0.151958\pi$
$347$	17.4058	+	10.0492i	0.934390	+	0.539470i	0.0461927	+	0.998933i	$0.485291\pi$
$348$		0			0
$349$	10.9808	+	19.0194i	0.587791	+	1.01808i	0.994521	+	0.104535i	$0.0333354\pi$
$349$	10.9808	+	19.0194i	0.587791	+	1.01808i	−0.406731	+	0.913548i	$0.633331\pi$
$350$	10.4963	−	7.57615i	0.561051	−	0.404962i
$351$		0			0
$352$	−0.533235	+	34.2188i	−0.0284215	+	1.82387i
$353$	24.8246	−	14.3325i	1.32128	−	0.762842i	0.337348	−	0.941380i	$-0.390470\pi$
$353$	24.8246	−	14.3325i	1.32128	−	0.762842i	0.983933	+	0.178538i	$0.0571368\pi$
$354$		0			0
$355$	−40.2084	−	23.2144i	−2.13404	−	1.23209i
$356$	−24.9543	−	8.28045i	−1.32257	−	0.438863i
$357$		0			0
$358$	2.97027	+	29.1333i	0.156984	+	1.53974i
$359$			32.1297i			1.69574i	0.530202	+	0.847872i	$0.322116\pi$
$359$			32.1297i			1.69574i	−0.530202	+	0.847872i	$0.677884\pi$
$360$		0			0
$361$	5.12425	+	8.87546i	0.269697	+	0.467129i
$362$	−21.3484	−	9.58477i	−1.12205	−	0.503764i
$363$		0			0
$364$	0.541883	+	9.89266i	0.0284024	+	0.518516i
$365$		−	6.73024i		−	0.352277i
$366$		0			0
$367$	−3.91198	−	6.77575i	−0.204204	−	0.353691i	0.745675	−	0.666310i	$-0.232127\pi$
$367$	−3.91198	−	6.77575i	−0.204204	−	0.353691i	−0.949879	+	0.312619i	$0.898794\pi$
$368$	−23.3869	+	10.0651i	−1.21913	+	0.524681i
$369$		0			0
$370$	24.2558	−	2.47298i	1.26100	−	0.128564i
$371$	8.52527	−	14.7662i	0.442610	−	0.766623i
$372$		0			0
$373$	11.4709	+	6.62274i	0.593942	+	0.342913i	0.766655	−	0.642060i	$-0.221920\pi$
$373$	11.4709	+	6.62274i	0.593942	+	0.342913i	−0.172713	+	0.984972i	$0.555253\pi$
$374$	−22.6300	+	50.4045i	−1.17017	+	2.60636i
$375$		0			0
$376$	−0.573596	−	1.82317i	−0.0295810	−	0.0940229i
$377$	5.99940	−	2.36231i	0.308985	−	0.121665i
$378$		0			0
$379$	15.1774	+	26.2881i	0.779611	+	1.35033i	0.932166	+	0.362032i	$0.117917\pi$
$379$	15.1774	+	26.2881i	0.779611	+	1.35033i	−0.152554	+	0.988295i	$0.548750\pi$
$380$	19.7895	−	4.07763i	1.01518	−	0.209178i
$381$		0			0
$382$	−12.2606	−	16.9864i	−0.627308	−	0.869098i
$383$	19.2691	+	11.1250i	0.984604	+	0.568462i	0.903657	−	0.428257i	$-0.140872\pi$
$383$	19.2691	+	11.1250i	0.984604	+	0.568462i	0.0809474	+	0.996718i	$0.474205\pi$
$384$		0			0
$385$		−	28.3854i		−	1.44666i
$386$	−2.01664	−	19.7798i	−0.102644	−	1.00676i
$387$		0			0
$388$	−7.03032	−	34.1194i	−0.356910	−	1.73215i
$389$			2.92168i			0.148135i	0.997253	+	0.0740674i	$0.0235980\pi$
$389$			2.92168i			0.148135i	−0.997253	+	0.0740674i	$0.976402\pi$
$390$		0			0
$391$	−41.1056			−2.07880
$392$	−10.6549	−	9.77559i	−0.538152	−	0.493742i
$393$		0			0
$394$	13.4478	−	1.37106i	0.677491	−	0.0690732i
$395$	3.45089			0.173633
$396$		0			0
$397$	3.13178	−	5.42441i	0.157180	−	0.272243i	−0.776671	−	0.629907i	$-0.783093\pi$
$397$	3.13178	−	5.42441i	0.157180	−	0.272243i	0.933851	+	0.357663i	$0.116426\pi$
$398$	3.14985	+	4.36393i	0.157888	+	0.218744i
$399$		0			0
$400$	−3.11573	+	26.4663i	−0.155787	+	1.32331i
$401$	−19.9809	+	11.5360i	−0.997798	+	0.576079i	−0.907596	−	0.419845i	$-0.862085\pi$
$401$	−19.9809	+	11.5360i	−0.997798	+	0.576079i	−0.0902020	+	0.995923i	$0.528751\pi$
$402$		0			0
$403$	−2.55475	+	17.0788i	−0.127261	+	0.850756i
$404$	10.0335	+	3.32937i	0.499187	+	0.165642i
$405$		0			0
$406$	1.42316	−	3.16984i	0.0706301	−	0.157317i
$407$	15.2710	−	26.4501i	0.756953	−	1.31108i
$408$		0			0
$409$	−31.9635	−	18.4541i	−1.58049	−	0.912497i	−0.994787	−	0.101972i	$-0.967485\pi$
$409$	−31.9635	−	18.4541i	−1.58049	−	0.912497i	−0.585704	−	0.810525i	$-0.699182\pi$
$410$	−1.67949	−	16.4730i	−0.0829442	−	0.813541i
$411$		0			0
$412$	−9.27763	−	10.4339i	−0.457076	−	0.514042i
$413$	−6.63030	+	3.82800i	−0.326256	+	0.188364i
$414$		0			0
$415$	15.1613			0.744240
$416$	−15.7607	−	12.9461i	−0.772730	−	0.634735i
$417$		0			0
$418$	10.3667	−	23.0900i	0.507050	−	1.12937i
$419$	−8.26881	+	4.77400i	−0.403958	+	0.233225i	−0.688190	−	0.725530i	$-0.741595\pi$
$419$	−8.26881	+	4.77400i	−0.403958	+	0.233225i	0.284232	+	0.958755i	$0.408261\pi$
$420$		0			0
$421$	−27.0280			−1.31726			−0.658632	−	0.752465i	$-0.728865\pi$
$421$	−27.0280			−1.31726			−0.658632	+	0.752465i	$0.728865\pi$
$422$	1.45361	+	14.2575i	0.0707608	+	0.694044i
$423$		0			0
$424$	10.5343	+	33.4831i	0.511590	+	1.62608i
$425$	−21.5119	+	37.2597i	−1.04348	+	1.80736i
$426$		0			0
$427$	0.132800	+	0.230016i	0.00642663	+	0.0111312i
$428$	−19.7873	−	6.56591i	−0.956455	−	0.317375i
$429$		0			0
$430$	−17.7460	+	12.8089i	−0.855788	+	0.617701i
$431$	−6.80703	+	3.93004i	−0.327883	+	0.189304i	−0.654901	−	0.755715i	$-0.727290\pi$
$431$	−6.80703	+	3.93004i	−0.327883	+	0.189304i	0.327018	+	0.945018i	$0.393956\pi$
$432$		0			0
$433$	7.72021	−	13.3718i	0.371009	−	0.642607i	−0.618712	−	0.785618i	$-0.712345\pi$
$433$	7.72021	−	13.3718i	0.371009	−	0.642607i	0.989721	+	0.143011i	$0.0456784\pi$
$434$	5.44651	+	7.54581i	0.261441	+	0.362211i
$435$		0			0
$436$	22.1880	+	24.9533i	1.06261	+	1.19505i
$437$	18.8302			0.900770
$438$		0			0
$439$	−10.8658	−	18.8200i	−0.518594	−	0.898231i	−0.999767	−	0.0216054i	$-0.993122\pi$
$439$	−10.8658	−	18.8200i	−0.518594	−	0.898231i	0.481172	−	0.876626i	$-0.340211\pi$
$440$	43.0588	+	39.5054i	2.05275	+	1.88335i
$441$		0			0
$442$	−15.1098	−	29.2573i	−0.718700	−	1.39163i
$443$			6.62675i			0.314846i	0.987531	+	0.157423i	$0.0503187\pi$
$443$			6.62675i			0.314846i	−0.987531	+	0.157423i	$0.949681\pi$
$444$		0			0
$445$	−38.8794	+	22.4470i	−1.84306	+	1.06409i
$446$	−0.312107	−	3.06124i	−0.0147787	−	0.144954i
$447$		0			0
$448$	−10.9507	+	0.944329i	−0.517373	+	0.0446154i
$449$	21.1222	+	12.1949i	0.996817	+	0.575513i	0.907305	−	0.420473i	$-0.138136\pi$
$449$	21.1222	+	12.1949i	0.996817	+	0.575513i	0.0895123	+	0.995986i	$0.471469\pi$
$450$		0			0
$451$	−17.9632	−	10.3711i	−0.845854	−	0.488354i
$452$	22.7707	−	4.69193i	1.07104	−	0.220690i
$453$		0			0
$454$	4.20037	+	5.81937i	0.197133	+	0.273116i
$455$	13.2380	+	10.5329i	0.620609	+	0.493789i
$456$		0			0
$457$	11.7699	−	6.79536i	0.550573	−	0.317874i	−0.198780	−	0.980044i	$-0.563698\pi$
$457$	11.7699	−	6.79536i	0.550573	−	0.317874i	0.749353	+	0.662170i	$0.230365\pi$
$458$	7.36412	−	16.4023i	0.344103	−	0.766431i
$459$		0			0
$460$	−13.6918	+	41.2622i	−0.638384	+	1.92386i
$461$	−7.43675	+	12.8808i	−0.346364	+	0.599920i	−0.985601	−	0.169090i	$-0.945917\pi$
$461$	−7.43675	+	12.8808i	−0.346364	+	0.599920i	0.639237	+	0.769010i	$0.279250\pi$
$462$		0			0
$463$			28.8166i			1.33922i	0.742712	+	0.669611i	$0.233539\pi$
$463$			28.8166i			1.33922i	−0.742712	+	0.669611i	$0.766461\pi$
$464$	2.82775	+	6.57046i	0.131275	+	0.305026i
$465$		0			0
$466$	−0.236904	+	0.527664i	−0.0109744	+	0.0244436i
$467$			14.1259i			0.653670i	0.945081	+	0.326835i	$0.105982\pi$
$467$			14.1259i			0.653670i	−0.945081	+	0.326835i	$0.894018\pi$
$468$		0			0
$469$		−	13.4887i		−	0.622852i
$470$	−2.97721	−	1.33667i	−0.137328	−	0.0616561i
$471$		0			0
$472$	3.42090	−	15.3853i	0.157459	−	0.708167i
$473$			27.4157i			1.26057i
$474$		0			0
$475$	9.85447	−	17.0684i	0.452154	−	0.783154i
$476$	−16.8421	−	5.58863i	−0.771957	−	0.256154i
$477$		0			0
$478$	17.0877	+	7.67185i	0.781575	+	0.350902i
$479$	−35.0552	+	20.2391i	−1.60171	+	0.924748i	−0.610566	+	0.791965i	$0.709058\pi$
$479$	−35.0552	+	20.2391i	−1.60171	+	0.924748i	−0.991145	+	0.132783i	$0.957609\pi$
$480$		0			0
$481$	6.66892	+	16.9366i	0.304076	+	0.772242i
$482$	−21.1382	+	15.2574i	−0.962821	+	0.694956i
$483$		0			0
$484$	50.1471	−	10.3329i	2.27941	−	0.469675i
$485$	−51.5136	−	29.7414i	−2.33911	−	1.35049i
$486$		0			0
$487$	−24.5598	−	14.1796i	−1.11291	−	0.642540i	−0.173330	−	0.984864i	$-0.555453\pi$
$487$	−24.5598	−	14.1796i	−1.11291	−	0.642540i	−0.939582	+	0.342324i	$0.888786\pi$
$488$	−0.533742	−	0.118676i	−0.0241614	−	0.00537223i
$489$		0			0
$490$	−24.5630	+	2.50430i	−1.10964	+	0.113133i
$491$	−13.5117	+	7.80101i	−0.609777	+	0.352055i	−0.772878	−	0.634555i	$-0.781184\pi$
$491$	−13.5117	+	7.80101i	−0.609777	+	0.352055i	0.163101	+	0.986609i	$0.447850\pi$
$492$		0			0
$493$			11.5484i			0.520115i
$494$	6.92170	+	13.4026i	0.311422	+	0.603011i
$495$		0			0
$496$	−19.0267	−	2.23991i	−0.854322	−	0.100575i
$497$	−9.33957	−	16.1766i	−0.418937	−	0.725620i
$498$		0			0
$499$	15.0705			0.674650			0.337325	−	0.941388i	$-0.390478\pi$
$499$	15.0705			0.674650			0.337325	+	0.941388i	$0.390478\pi$
$500$	7.54410	+	8.48432i	0.337382	+	0.379431i
$501$		0			0
$502$	13.8071	−	9.96582i	0.616239	−	0.444796i
$503$	−6.64251	+	11.5052i	−0.296175	+	0.512990i	−0.975258	−	0.221072i	$-0.929044\pi$
$503$	−6.64251	+	11.5052i	−0.296175	+	0.512990i	0.679083	+	0.734062i	$0.262378\pi$
$504$		0			0
$505$	15.6325	−	9.02543i	0.695637	−	0.401626i
$506$	31.8728	+	44.1579i	1.41692	+	1.96306i
$507$		0			0
$508$	0.950486	−	2.86442i	0.0421710	−	0.127088i
$509$	−2.67052	−	4.62548i	−0.118369	−	0.205021i	0.800753	−	0.598995i	$-0.204433\pi$
$509$	−2.67052	−	4.62548i	−0.118369	−	0.205021i	−0.919121	+	0.393974i	$0.871100\pi$
$510$		0			0
$511$	1.35385	−	2.34494i	0.0598909	−	0.103734i
$512$	13.8082	−	17.9258i	0.610242	−	0.792215i
$513$		0			0
$514$	5.21689	−	0.531886i	0.230107	−	0.0234605i
$515$	−23.8404			−1.05053
$516$		0			0
$517$	−3.54039	+	2.04404i	−0.155706	+	0.0898969i
$518$	8.94862	+	4.01764i	0.393180	+	0.176525i
$519$		0			0
$520$	−34.4017	+	5.42208i	−1.50861	+	0.237774i
$521$	2.03430			0.0891244			0.0445622	−	0.999007i	$-0.485811\pi$
$521$	2.03430			0.0891244			0.0445622	+	0.999007i	$0.485811\pi$
$522$		0			0
$523$	24.3054	−	14.0327i	1.06280	−	0.613608i	0.136594	−	0.990627i	$-0.456384\pi$
$523$	24.3054	−	14.0327i	1.06280	−	0.613608i	0.926205	+	0.377019i	$0.123051\pi$
$524$	−0.909813	+	0.808988i	−0.0397454	+	0.0353408i
$525$		0			0
$526$	−19.1019	+	1.94752i	−0.832881	+	0.0849159i
$527$	−26.7861	−	15.4650i	−1.16682	−	0.673664i
$528$		0			0
$529$	−8.75800	+	15.1693i	−0.380783	+	0.659535i
$530$	54.6774	+	24.5484i	2.37503	+	1.06631i
$531$		0			0
$532$	7.71526	+	2.56011i	0.334499	+	0.110995i
$533$	11.5023	−	4.52910i	0.498218	−	0.196177i
$534$		0			0
$535$	−30.8291	+	17.7992i	−1.33286	+	0.769527i
$536$	20.4615	+	18.7729i	0.883802	+	0.810868i
$537$		0			0
$538$	−18.9302	+	13.6636i	−0.816138	+	0.589082i
$539$	−15.4644	+	26.7851i	−0.666097	+	1.15371i
$540$		0			0
$541$	−29.6268			−1.27375			−0.636877	−	0.770965i	$-0.719774\pi$
$541$	−29.6268			−1.27375			−0.636877	+	0.770965i	$0.719774\pi$
$542$	1.62509	+	15.9394i	0.0698037	+	0.684655i
$543$		0			0
$544$	31.9176	−	17.7704i	1.36846	−	0.761898i
$545$	57.0156			2.44228
$546$		0			0
$547$		−	0.345795i		−	0.0147851i	−0.999973	−	0.00739257i	$-0.997647\pi$
$547$		−	0.345795i		−	0.0147851i	0.999973	−	0.00739257i	$-0.00235315\pi$
$548$	4.64465	+	22.5413i	0.198410	+	0.962917i
$549$		0			0
$550$	56.7066	−	5.78149i	2.41798	−	0.246524i
$551$		−	5.29026i		−	0.225373i
$552$		0			0
$553$	1.20235	+	0.694179i	0.0511293	+	0.0295195i
$554$	0.464357	−	0.335169i	0.0197286	−	0.0142400i
$555$		0			0
$556$	−6.24890	−	30.3270i	−0.265012	−	1.28615i
$557$	−7.15368	−	12.3905i	−0.303111	−	0.525004i	0.673728	−	0.738980i	$-0.264692\pi$
$557$	−7.15368	−	12.3905i	−0.303111	−	0.525004i	−0.976839	+	0.213976i	$0.931359\pi$
$558$		0			0
$559$	−12.7858	−	10.1730i	−0.540780	−	0.430273i
$560$	−11.2198	+	15.0448i	−0.474125	+	0.635758i
$561$		0			0
$562$	6.73252	+	3.02269i	0.283994	+	0.127504i
$563$	−5.57398	−	3.21814i	−0.234915	−	0.135628i	0.377922	−	0.925837i	$-0.376639\pi$
$563$	−5.57398	−	3.21814i	−0.234915	−	0.135628i	−0.612837	+	0.790209i	$0.709972\pi$
$564$		0			0
$565$	19.8489	−	34.3794i	0.835051	−	1.44635i
$566$	−3.22228	−	31.6051i	−0.135442	−	1.32846i
$567$		0			0
$568$	37.5372	+	8.34631i	1.57502	+	0.350203i
$569$	14.0501	+	24.3355i	0.589012	+	1.02020i	0.994362	+	0.106038i	$0.0338164\pi$
$569$	14.0501	+	24.3355i	0.589012	+	1.02020i	−0.405350	+	0.914162i	$0.632850\pi$
$570$		0			0
$571$		−	4.83071i		−	0.202159i	−0.994878	−	0.101079i	$-0.967770\pi$
$571$		−	4.83071i		−	0.202159i	0.994878	−	0.101079i	$-0.0322296\pi$
$572$	−19.7139	+	38.9176i	−0.824278	+	1.62723i
$573$		0			0
$574$	2.72853	−	6.07733i	0.113886	−	0.253663i
$575$	21.2034	+	36.7253i	0.884242	+	1.53155i
$576$		0			0
$577$			6.81392i			0.283667i	0.989891	+	0.141834i	$0.0452998\pi$
$577$			6.81392i			0.283667i	−0.989891	+	0.141834i	$0.954700\pi$
$578$	34.7561	−	3.54354i	1.44566	−	0.147392i
$579$		0			0
$580$	11.5924	+	3.84665i	0.481350	+	0.159724i
$581$	5.28249	+	3.04985i	0.219155	+	0.126529i
$582$		0			0
$583$	65.0203	−	37.5395i	2.69287	−	1.55473i
$584$	1.67289	+	5.31727i	0.0692248	+	0.220030i
$585$		0			0
$586$	−12.9021	−	17.8751i	−0.532982	−	0.738415i
$587$	−6.33027	−	10.9643i	−0.261278	−	0.452547i	0.705304	−	0.708905i	$-0.250811\pi$
$587$	−6.33027	−	10.9643i	−0.261278	−	0.452547i	−0.966582	+	0.256358i	$0.917477\pi$
$588$		0			0
$589$	12.2705	+	7.08439i	0.505598	+	0.291907i
$590$	−15.7506	−	21.8215i	−0.648441	−	0.898377i
$591$		0			0
$592$	−18.5487	+	7.98289i	−0.762348	+	0.328095i
$593$		−	7.20191i		−	0.295747i	−0.989006	−	0.147873i	$-0.952757\pi$
$593$		−	7.20191i		−	0.295747i	0.989006	−	0.147873i	$-0.0472428\pi$
$594$		0			0
$595$	−26.2405	+	15.1499i	−1.07575	+	0.621087i
$596$	−1.78126	+	0.367030i	−0.0729632	+	0.0150341i
$597$		0			0
$598$	−32.4207	−	1.52106i	−1.32578	−	0.0622007i
$599$	−9.36355			−0.382584			−0.191292	−	0.981533i	$-0.561268\pi$
$599$	−9.36355			−0.382584			−0.191292	+	0.981533i	$0.561268\pi$
$600$		0			0
$601$	15.3653	+	26.6135i	0.626765	+	1.08559i	0.988197	+	0.153190i	$0.0489545\pi$
$601$	15.3653	+	26.6135i	0.626765	+	1.08559i	−0.361432	+	0.932398i	$0.617712\pi$
$602$	−8.75967	+	0.893088i	−0.357018	+	0.0363995i
$603$		0			0
$604$	−32.6406	+	29.0234i	−1.32813	+	1.18095i
$605$	43.7126	−	75.7124i	1.77717	−	3.07815i
$606$		0			0
$607$	17.9472	−	31.0855i	0.728455	−	1.26172i	−0.229081	−	0.973407i	$-0.573572\pi$
$607$	17.9472	−	31.0855i	0.728455	−	1.26172i	0.957536	−	0.288313i	$-0.0930944\pi$
$608$	−14.6212	+	8.14049i	−0.592969	+	0.330140i
$609$		0			0
$610$	−0.757023	+	0.546413i	−0.0306510	+	0.0221236i
$611$	0.360442	−	2.40960i	0.0145819	−	0.0974818i
$612$		0			0
$613$	−2.48114	−	4.29747i	−0.100212	−	0.173573i	0.811560	−	0.584270i	$-0.198619\pi$
$613$	−2.48114	−	4.29747i	−0.100212	−	0.173573i	−0.911772	+	0.410697i	$0.865286\pi$
$614$	16.7286	−	37.2602i	0.675112	−	1.50370i
$615$		0			0
$616$	7.05558	+	22.4261i	0.284277	+	0.903574i
$617$	−18.3016	−	10.5665i	−0.736796	−	0.425389i	0.0841072	−	0.996457i	$-0.473196\pi$
$617$	−18.3016	−	10.5665i	−0.736796	−	0.425389i	−0.820903	+	0.571067i	$0.806530\pi$
$618$		0			0
$619$	−8.60082			−0.345696			−0.172848	−	0.984948i	$-0.555297\pi$
$619$	−8.60082			−0.345696			−0.172848	+	0.984948i	$0.555297\pi$
$620$	−24.4460	+	21.7369i	−0.981776	+	0.872977i
$621$		0			0
$622$	−4.43628	+	9.88105i	−0.177878	+	0.396194i
$623$	−18.0617			−0.723629
$624$		0			0
$625$	−13.9255			−0.557022
$626$	8.49809	−	18.9281i	0.339652	−	0.756517i
$627$		0			0
$628$	4.54225	−	4.03888i	0.181255	−	0.161169i
$629$	−32.6018			−1.29992
$630$		0			0
$631$	−1.51792	−	0.876372i	−0.0604275	−	0.0348878i	0.469482	−	0.882942i	$-0.344441\pi$
$631$	−1.51792	−	0.876372i	−0.0604275	−	0.0348878i	−0.529909	+	0.848054i	$0.677774\pi$
$632$	−2.72640	+	0.857765i	−0.108450	+	0.0341200i
$633$		0			0
$634$	7.39383	−	16.4685i	0.293647	−	0.654048i
$635$	−2.57662	−	4.46284i	−0.102250	−	0.177103i
$636$		0			0
$637$	−6.75338	−	17.1511i	−0.267579	−	0.679551i
$638$	12.4060	−	8.95453i	0.491157	−	0.354513i
$639$		0			0
$640$	−7.20669	−	37.9583i	−0.284869	−	1.50043i
$641$	13.1070	−	22.7019i	0.517694	−	0.896673i	−0.482094	−	0.876119i	$-0.660124\pi$
$641$	13.1070	−	22.7019i	0.517694	−	0.896673i	0.999789	−	0.0205536i	$-0.00654287\pi$
$642$		0			0
$643$	11.4912	−	19.9033i	0.453167	−	0.784908i	−0.545414	−	0.838167i	$-0.683627\pi$
$643$	11.4912	−	19.9033i	0.453167	−	0.784908i	0.998581	+	0.0532586i	$0.0169608\pi$
$644$	−13.0708	+	11.6223i	−0.515060	+	0.457982i
$645$		0			0
$646$	−26.8781	+	2.74034i	−1.05750	+	0.107817i
$647$	−4.81890	−	8.34657i	−0.189450	−	0.328138i	0.755617	−	0.655014i	$-0.227337\pi$
$647$	−4.81890	−	8.34657i	−0.189450	−	0.328138i	−0.945067	+	0.326876i	$0.894004\pi$
$648$		0			0
$649$	−33.7119			−1.32331
$650$	−18.3456	+	28.5914i	−0.719573	+	1.12145i
$651$		0			0
$652$	32.7762	−	6.75357i	1.28362	−	0.264490i
$653$	37.2110	−	21.4838i	1.45618	−	0.840725i	0.457358	−	0.889283i	$-0.348796\pi$
$653$	37.2110	−	21.4838i	1.45618	−	0.840725i	0.998820	+	0.0485577i	$0.0154625\pi$
$654$		0			0
$655$			2.07883i			0.0812264i
$656$	5.42147	+	12.5971i	0.211673	+	0.491834i
$657$		0			0
$658$	−0.768430	−	1.06461i	−0.0299565	−	0.0415030i
$659$	3.12326	+	1.80322i	0.121665	+	0.0702433i	0.559597	−	0.828765i	$-0.310956\pi$
$659$	3.12326	+	1.80322i	0.121665	+	0.0702433i	−0.437932	+	0.899008i	$0.644289\pi$
$660$		0			0
$661$	5.43287	+	9.41001i	0.211314	+	0.366007i	0.952126	−	0.305706i	$-0.0988924\pi$
$661$	5.43287	+	9.41001i	0.211314	+	0.366007i	−0.740812	+	0.671712i	$0.765559\pi$
$662$	0.0947150	+	0.131222i	0.00368120	+	0.00510009i
$663$		0			0
$664$	−11.9783	+	3.76855i	−0.464849	+	0.146248i
$665$	12.0206	−	6.94008i	0.466138	−	0.269125i
$666$		0			0
$667$	9.85779	+	5.69140i	0.381695	+	0.220372i
$668$	−33.3279	−	11.0590i	−1.28950	−	0.427886i
$669$		0			0
$670$	47.1705	−	4.80924i	1.82235	−	0.185797i
$671$			1.16952i			0.0451488i
$672$		0			0
$673$	2.90112	+	5.02489i	0.111830	+	0.193695i	0.916508	−	0.400016i	$-0.130995\pi$
$673$	2.90112	+	5.02489i	0.111830	+	0.193695i	−0.804678	+	0.593711i	$0.797662\pi$
$674$	8.27266	−	18.4260i	0.318651	−	0.709741i
$675$		0			0
$676$	−10.8347	−	23.6349i	−0.416721	−	0.909034i
$677$			27.4225i			1.05393i	0.849887	+	0.526966i	$0.176670\pi$
$677$			27.4225i			1.05393i	−0.849887	+	0.526966i	$0.823330\pi$
$678$		0			0
$679$	−11.9655	−	20.7249i	−0.459195	−	0.795349i
$680$	13.5387	−	60.8899i	0.519187	−	2.33502i
$681$		0			0
$682$	4.15632	+	40.7665i	0.159154	+	1.56103i
$683$	−13.3166	+	23.0650i	−0.509544	+	0.882556i	0.490395	+	0.871500i	$0.336853\pi$
$683$	−13.3166	+	23.0650i	−0.509544	+	0.882556i	−0.999939	+	0.0110559i	$0.996481\pi$
$684$		0			0
$685$	34.0330	+	19.6490i	1.30033	+	0.750748i
$686$	−21.4699	−	9.63930i	−0.819725	−	0.368030i
$687$		0			0
$688$	10.8365	−	14.5308i	0.413138	−	0.553981i
$689$	−6.61964	+	44.2530i	−0.252188	+	1.68590i
$690$		0			0
$691$	−0.313614	−	0.543196i	−0.0119305	−	0.0206642i	0.859999	−	0.510296i	$-0.170464\pi$
$691$	−0.313614	−	0.543196i	−0.0119305	−	0.0206642i	−0.871929	+	0.489632i	$0.837131\pi$
$692$	−1.06237	−	5.15587i	−0.0403853	−	0.195997i
$693$		0			0
$694$	−23.0470	+	16.6352i	−0.874853	+	0.631462i
$695$	−45.7879	−	26.4356i	−1.73683	−	1.00276i
$696$		0			0
$697$			22.1410i			0.838652i
$698$	−30.8983	+	3.15022i	−1.16952	+	0.119238i
$699$		0			0
$700$	3.69453	+	17.9302i	0.139640	+	0.677697i
$701$			25.5900i			0.966522i	0.875476	+	0.483261i	$0.160548\pi$
$701$			25.5900i			0.966522i	−0.875476	+	0.483261i	$0.839452\pi$
$702$		0			0
$703$	14.9347			0.563271
$704$	−43.8385	−	20.5087i	−1.65222	−	0.772951i
$705$		0			0
$706$	4.11176	+	40.3294i	0.154748	+	1.51782i
$707$	7.26220			0.273123
$708$		0			0
$709$	−13.9996	+	24.2481i	−0.525767	+	0.910655i	0.473783	+	0.880642i	$0.342888\pi$
$709$	−13.9996	+	24.2481i	−0.525767	+	0.910655i	−0.999550	+	0.0300132i	$0.990445\pi$
$710$	53.2402	−	38.4283i	1.99807	−	1.44219i
$711$		0			0
$712$	25.1374	−	27.3984i	0.942065	−	1.02680i
$713$	−26.4019	+	15.2431i	−0.988759	+	0.570860i
$714$		0			0
$715$	27.2920	+	69.3116i	1.02066	+	2.59211i
$716$	−39.3069	−	13.0430i	−1.46897	−	0.487439i
$717$		0			0
$718$	−41.4522	−	18.6107i	−1.54698	−	0.694545i
$719$	8.07202	−	13.9812i	0.301036	−	0.521409i	−0.675335	−	0.737511i	$-0.736001\pi$
$719$	8.07202	−	13.9812i	0.301036	−	0.521409i	0.976371	+	0.216102i	$0.0693344\pi$
$720$		0			0
$721$	−8.30642	−	4.79572i	−0.309347	−	0.178602i
$722$	−14.4188	+	1.47006i	−0.536613	+	0.0547101i
$723$		0			0
$724$	24.7316	−	21.9908i	0.919142	−	0.817283i
$725$	10.3178	−	5.95700i	0.383194	−	0.221237i
$726$		0			0
$727$	36.6341			1.35868			0.679342	−	0.733822i	$-0.262265\pi$
$727$	36.6341			1.35868			0.679342	+	0.733822i	$0.262265\pi$
$728$	−13.0769	−	5.03107i	−0.484662	−	0.186464i
$729$		0			0
$730$	8.68302	+	3.89840i	0.321373	+	0.144286i
$731$	25.3440	−	14.6323i	0.937380	−	0.541197i
$732$		0			0
$733$	39.0091			1.44083			0.720417	−	0.693541i	$-0.243950\pi$
$733$	39.0091			1.44083			0.720417	+	0.693541i	$0.243950\pi$
$734$	11.0077	−	1.12228i	0.406301	−	0.0414242i
$735$		0			0
$736$	0.561034	−	36.0027i	0.0206800	−	1.32708i
$737$	29.6976	−	51.4378i	1.09393	−	1.89474i
$738$		0			0
$739$	9.63783	+	16.6932i	0.354533	+	0.614069i	0.987038	−	0.160487i	$-0.0513065\pi$
$739$	9.63783	+	16.6932i	0.354533	+	0.614069i	−0.632505	+	0.774556i	$0.717973\pi$
$740$	−10.8593	+	32.7260i	−0.399195	+	1.20303i
$741$		0			0
$742$	14.1125	+	19.5520i	0.518085	+	0.717776i
$743$	−13.3110	+	7.68512i	−0.488334	+	0.281940i	−0.723883	−	0.689923i	$-0.757645\pi$
$743$	−13.3110	+	7.68512i	−0.488334	+	0.281940i	0.235549	+	0.971862i	$0.424311\pi$
$744$		0			0
$745$	−1.55270	+	2.68936i	−0.0568865	+	0.0985304i
$746$	−15.1887	+	10.9631i	−0.556098	+	0.401387i
$747$		0			0
$748$	−51.9213	−	58.3922i	−1.89843	−	2.13503i
$749$	−14.3219			−0.523311
$750$		0			0
$751$	5.84408	+	10.1222i	0.213254	+	0.369366i	0.952731	−	0.303815i	$-0.0982606\pi$
$751$	5.84408	+	10.1222i	0.213254	+	0.369366i	−0.739477	+	0.673181i	$0.764927\pi$
$752$	2.68441	+	0.316021i	0.0978904	+	0.0115241i
$753$		0			0
$754$	−0.427334	+	9.10846i	−0.0155626	+	0.331710i
$755$			74.5804i			2.71426i
$756$		0			0
$757$	−13.5679	+	7.83343i	−0.493134	+	0.284711i	−0.725874	−	0.687828i	$-0.758564\pi$
$757$	−13.5679	+	7.83343i	−0.493134	+	0.284711i	0.232740	+	0.972539i	$0.425231\pi$
$758$	−42.7068	+	4.35415i	−1.55118	+	0.158150i
$759$		0			0
$760$	−6.20201	+	27.8933i	−0.224970	+	1.01179i
$761$	−34.3924	−	19.8565i	−1.24672	−	0.719797i	−0.276270	−	0.961080i	$-0.589098\pi$
$761$	−34.3924	−	19.8565i	−1.24672	−	0.719797i	−0.970455	+	0.241283i	$0.922432\pi$
$762$		0			0
$763$	19.8653	+	11.4692i	0.719172	+	0.415214i
$764$	29.0167	−	5.97892i	1.04979	−	0.216310i
$765$		0			0
$766$	−25.5143	+	18.4160i	−0.921868	+	0.665397i
$767$	12.5093	−	15.7221i	0.451686	−	0.567692i
$768$		0			0
$769$	38.6620	−	22.3215i	1.39419	−	0.804935i	0.400412	−	0.916335i	$-0.368867\pi$
$769$	38.6620	−	22.3215i	1.39419	−	0.804935i	0.993776	+	0.111400i	$0.0355336\pi$
$770$	36.6215	+	16.4419i	1.31975	+	0.592524i
$771$		0			0
$772$	26.6870	+	8.85539i	0.960485	+	0.318713i
$773$	22.4489	−	38.8827i	0.807432	−	1.39851i	−0.107205	−	0.994237i	$-0.534190\pi$
$773$	22.4489	−	38.8827i	0.807432	−	1.39851i	0.914637	−	0.404276i	$-0.132476\pi$
$774$		0			0
$775$			31.9090i			1.14621i
$776$	48.0913	+	10.6930i	1.72638	+	0.383856i
$777$		0			0
$778$	−3.76940	−	1.69234i	−0.135139	−	0.0606733i
$779$		−	10.1427i		−	0.363399i
$780$		0			0
$781$		−	82.2503i		−	2.94315i
$782$	23.8098	−	53.0323i	0.851437	−	1.89643i
$783$		0			0
$784$	18.7836	−	8.08399i	0.670844	−	0.288714i
$785$		−	10.3785i		−	0.370426i
$786$		0			0
$787$	13.8178	−	23.9331i	0.492551	−	0.853124i	−0.507412	−	0.861704i	$-0.669398\pi$
$787$	13.8178	−	23.9331i	0.492551	−	0.853124i	0.999963	+	0.00857979i	$0.00273107\pi$
$788$	−6.02058	+	18.1439i	−0.214474	+	0.646348i
$789$		0			0
$790$	−1.99888	+	4.45216i	−0.0711169	+	0.158401i
$791$	13.8315	−	7.98561i	0.491791	−	0.283935i
$792$		0			0
$793$	−0.545425	−	0.433969i	−0.0193686	−	0.0154107i
$794$	5.18426	+	7.18248i	0.183982	+	0.254897i
$795$		0			0
$796$	−7.45463	+	1.53603i	−0.264222	+	0.0544432i
$797$	34.0592	+	19.6641i	1.20644	+	0.696539i	0.961980	−	0.273121i	$-0.0880559\pi$
$797$	34.0592	+	19.6641i	1.20644	+	0.696539i	0.244460	+	0.969659i	$0.421389\pi$
$798$		0			0
$799$	3.77916	+	2.18190i	0.133697	+	0.0771901i
$800$	−32.3407	−	19.3500i	−1.14342	−	0.684125i
$801$		0			0
$802$	−3.30948	−	32.4604i	−0.116862	−	1.14622i
$803$	10.3255	−	5.96145i	0.364380	−	0.210375i
$804$		0			0
$805$			29.8653i			1.05261i
$806$	−20.5544	−	13.1887i	−0.723998	−	0.464551i
$807$		0			0
$808$	−10.1072	+	11.0163i	−0.355569	+	0.387551i
$809$	23.1914	+	40.1687i	0.815366	+	1.41226i	0.909064	+	0.416655i	$0.136798\pi$
$809$	23.1914	+	40.1687i	0.815366	+	1.41226i	−0.0936981	+	0.995601i	$0.529869\pi$
$810$		0			0
$811$	25.2433			0.886411			0.443206	−	0.896420i	$-0.353841\pi$
$811$	25.2433			0.886411			0.443206	+	0.896420i	$0.353841\pi$
$812$	3.26523	+	3.67217i	0.114587	+	0.128868i
$813$		0			0
$814$	25.2791	+	35.0227i	0.886031	+	1.22754i
$815$	28.5706	−	49.4857i	1.00078	−	1.73341i
$816$		0			0
$817$	−11.6099	+	6.70298i	−0.406179	+	0.234507i
$818$	42.3229	−	30.5484i	1.47979	−	1.06810i
$819$		0			0
$820$	22.2254	+	7.37493i	0.776145	+	0.257544i
$821$	1.82456	+	3.16024i	0.0636777	+	0.110293i	0.896107	−	0.443839i	$-0.146384\pi$
$821$	1.82456	+	3.16024i	0.0636777	+	0.110293i	−0.832429	+	0.554132i	$0.813050\pi$
$822$		0			0
$823$	−16.0083	+	27.7272i	−0.558014	+	0.966509i	0.439648	+	0.898170i	$0.355103\pi$
$823$	−16.0083	+	27.7272i	−0.558014	+	0.966509i	−0.997662	+	0.0683386i	$0.978230\pi$
$824$	18.8352	−	5.92584i	0.656157	−	0.206436i
$825$		0			0
$826$	−1.09819	−	10.7714i	−0.0382110	−	0.374785i
$827$	−32.5482			−1.13181			−0.565906	−	0.824470i	$-0.691473\pi$
$827$	−32.5482			−1.13181			−0.565906	+	0.824470i	$0.691473\pi$
$828$		0			0
$829$	1.89091	−	1.09172i	0.0656739	−	0.0379168i	−0.466804	−	0.884361i	$-0.654594\pi$
$829$	1.89091	−	1.09172i	0.0656739	−	0.0379168i	0.532477	+	0.846444i	$0.321261\pi$
$830$	−8.78199	+	19.5604i	−0.304827	+	0.678951i
$831$		0			0
$832$	25.8316	−	12.8348i	0.895548	−	0.444965i
$833$	33.0147			1.14389
$834$		0			0
$835$	−51.9257	+	29.9793i	−1.79696	+	1.03748i
$836$	23.7848	+	26.7491i	0.822614	+	0.925137i
$837$		0			0
$838$	−1.36958	−	13.4333i	−0.0473114	−	0.464045i
$839$	33.5508	+	19.3706i	1.15830	+	0.668747i	0.950897	−	0.309508i	$-0.100164\pi$
$839$	33.5508	+	19.3706i	1.15830	+	0.668747i	0.207406	+	0.978255i	$0.433498\pi$
$840$		0			0
$841$	−12.9010	+	22.3452i	−0.444863	+	0.770525i
$842$	15.6556	−	34.8702i	0.539527	−	1.20171i
$843$		0			0
$844$	−19.2363	−	6.38307i	−0.662140	−	0.219714i
$845$	−42.4518	−	12.9911i	−1.46039	−	0.446907i
$846$		0			0
$847$	30.4605	−	17.5864i	1.04664	−	0.604276i
$848$	−49.3001	−	5.80383i	−1.69297	−	0.199304i
$849$		0			0
$850$	−35.6102	−	49.3358i	−1.22142	−	1.69220i
$851$	−16.0671	+	27.8290i	−0.550773	+	0.953967i
$852$		0			0
$853$	−32.6789			−1.11891			−0.559453	−	0.828862i	$-0.688989\pi$
$853$	−32.6789			−1.11891			−0.559453	+	0.828862i	$0.688989\pi$
$854$	−0.373677	+	0.0380980i	−0.0127870	+	0.00130369i
$855$		0			0
$856$	19.9325	−	21.7254i	0.681280	−	0.742558i
$857$	26.0253			0.889008			0.444504	−	0.895777i	$-0.353380\pi$
$857$	26.0253			0.889008			0.444504	+	0.895777i	$0.353380\pi$
$858$		0			0
$859$		−	15.4455i		−	0.526994i	−0.964660	−	0.263497i	$-0.915124\pi$
$859$		−	15.4455i		−	0.526994i	0.964660	−	0.263497i	$-0.0848759\pi$
$860$	−6.24630	−	30.3144i	−0.212997	−	1.03371i
$861$		0			0
$862$	−1.12746	−	11.0585i	−0.0384016	−	0.376654i
$863$		−	22.7498i		−	0.774411i	−0.921993	−	0.387206i	$-0.873440\pi$
$863$		−	22.7498i		−	0.774411i	0.921993	−	0.387206i	$-0.126560\pi$
$864$		0			0
$865$	−7.78436	−	4.49430i	−0.264676	−	0.152811i
$866$	12.7798	+	17.7056i	0.434275	+	0.601662i
$867$		0			0
$868$	−12.8900	+	2.65600i	−0.437516	+	0.0901506i
$869$	3.05669	+	5.29435i	0.103691	+	0.179599i
$870$		0			0
$871$	12.9691	+	32.9368i	0.439442	+	1.11602i
$872$	−45.0456	+	14.1720i	−1.52544	+	0.479924i
$873$		0			0
$874$	−10.9071	+	24.2938i	−0.368939	+	0.821749i
$875$	6.75436	+	3.89963i	0.228339	+	0.131832i
$876$		0			0
$877$	7.48245	−	12.9600i	0.252664	−	0.437628i	−0.711594	−	0.702591i	$-0.752026\pi$
$877$	7.48245	−	12.9600i	0.252664	−	0.437628i	0.964259	+	0.264963i	$0.0853598\pi$
$878$	30.5745	−	3.11721i	1.03184	−	0.105201i
$879$		0			0
$880$	−75.9091	+	32.6693i	−2.55890	+	1.10128i
$881$	17.2978	+	29.9607i	0.582779	+	1.00940i	0.995148	+	0.0983859i	$0.0313679\pi$
$881$	17.2978	+	29.9607i	0.582779	+	1.00940i	−0.412370	+	0.911017i	$0.635299\pi$
$882$		0			0
$883$		−	51.1608i		−	1.72170i	−0.508861	−	0.860849i	$-0.669933\pi$
$883$		−	51.1608i		−	1.72170i	0.508861	−	0.860849i	$-0.330067\pi$
$884$	46.4984	−	2.54701i	1.56391	−	0.0856652i
$885$		0			0
$886$	−8.54950	−	3.83845i	−0.287226	−	0.128955i
$887$	−20.7550	−	35.9488i	−0.696886	−	1.20704i	−0.969541	−	0.244930i	$-0.921235\pi$
$887$	−20.7550	−	35.9488i	−0.696886	−	1.20704i	0.272655	−	0.962112i	$-0.412098\pi$
$888$		0			0
$889$		−	2.07325i		−	0.0695346i
$890$	−6.43969	−	63.1624i	−0.215859	−	2.11721i
$891$		0			0
$892$	4.13024	+	1.37052i	0.138291	+	0.0458883i
$893$	−1.73121	−	0.999515i	−0.0579327	−	0.0334475i
$894$		0			0
$895$	−61.2411	+	35.3576i	−2.04706	+	1.18187i
$896$	5.12473	−	14.6751i	0.171205	−	0.490260i
$897$		0			0
$898$	−27.9680	+	20.1871i	−0.933303	+	0.673651i
$899$	4.28250	+	7.41750i	0.142829	+	0.247387i
$900$		0			0
$901$	−69.4056	−	40.0713i	−2.31223	−	1.33497i
$902$	23.7851	−	17.1679i	0.791959	−	0.571629i
$903$		0			0
$904$	−7.13634	+	32.0954i	−0.237351	+	1.06748i
$905$		−	56.5090i		−	1.87842i
$906$		0			0
$907$	35.1223	−	20.2779i	1.16622	−	0.673315i	0.213430	−	0.976958i	$-0.431536\pi$
$907$	35.1223	−	20.2779i	1.16622	−	0.673315i	0.952786	+	0.303643i	$0.0982031\pi$
$908$	−9.94086	+	2.04832i	−0.329899	+	0.0679759i
$909$		0			0
$910$	−21.2569	+	10.9780i	−0.704660	+	0.363918i
$911$	−8.86652			−0.293761			−0.146880	−	0.989154i	$-0.546923\pi$
$911$	−8.86652			−0.293761			−0.146880	+	0.989154i	$0.546923\pi$
$912$		0			0
$913$	13.4294	+	23.2605i	0.444450	+	0.769810i
$914$	1.94948	+	19.1211i	0.0644830	+	0.632469i
$915$		0			0
$916$	16.8959	+	19.0016i	0.558256	+	0.627832i
$917$	−0.418175	+	0.724301i	−0.0138094	+	0.0239185i
$918$		0			0
$919$	25.0399	−	43.3703i	0.825989	−	1.43065i	−0.0751721	−	0.997171i	$-0.523951\pi$
$919$	25.0399	−	43.3703i	0.825989	−	1.43065i	0.901161	−	0.433484i	$-0.142716\pi$
$920$	−45.3036	−	41.5650i	−1.49362	−	1.37036i
$921$		0			0
$922$	−12.3106	−	17.0556i	−0.405427	−	0.561695i
$923$	38.3588	+	30.5203i	1.26260	+	1.00459i
$924$		0			0
$925$	16.8169	+	29.1277i	0.552936	+	0.957714i
$926$	−37.1777	−	16.6916i	−1.22174	−	0.548520i
$927$		0			0
$928$	−10.1148	−	0.157620i	−0.332035	−	0.00517413i
$929$	−24.8897	−	14.3700i	−0.816603	−	0.471466i	0.0326406	−	0.999467i	$-0.489608\pi$
$929$	−24.8897	−	14.3700i	−0.816603	−	0.471466i	−0.849244	+	0.528001i	$0.822942\pi$
$930$		0			0
$931$	−15.1238			−0.495663
$932$	−0.543542	−	0.611284i	−0.0178043	−	0.0200233i
$933$		0			0
$934$	−18.2246	−	8.18224i	−0.596326	−	0.267731i
$935$	−133.420			−4.36330
$936$		0			0
$937$	49.4166			1.61437			0.807185	−	0.590298i	$-0.200990\pi$
$937$	49.4166			1.61437			0.807185	+	0.590298i	$0.200990\pi$
$938$	17.4025	+	7.81316i	0.568211	+	0.255109i
$939$		0			0
$940$	3.44901	−	3.06680i	0.112494	−	0.100028i
$941$	28.9013			0.942157			0.471078	−	0.882091i	$-0.343865\pi$
$941$	28.9013			0.942157			0.471078	+	0.882091i	$0.343865\pi$
$942$		0			0
$943$	18.8997	+	10.9117i	0.615458	+	0.355335i
$944$	17.8679	+	13.3252i	0.581550	+	0.433698i
$945$		0			0
$946$	−35.3703	−	15.8801i	−1.14999	−	0.516308i
$947$	23.6288	+	40.9262i	0.767831	+	1.32992i	0.938737	+	0.344636i	$0.111998\pi$
$947$	23.6288	+	40.9262i	0.767831	+	1.32992i	−0.170905	+	0.985288i	$0.554669\pi$
$948$		0			0
$949$	−1.05123	+	7.02758i	−0.0341243	+	0.228125i
$950$	16.3128	+	22.6004i	0.529256	+	0.733254i
$951$		0			0
$952$	16.9657	−	18.4917i	0.549862	−	0.599320i
$953$	5.28519	−	9.15421i	0.171204	−	0.296534i	−0.767637	−	0.640885i	$-0.778568\pi$
$953$	5.28519	−	9.15421i	0.171204	−	0.296534i	0.938841	+	0.344351i	$0.111901\pi$
$954$		0			0
$955$	25.2935	−	43.8096i	0.818478	−	1.41765i
$956$	−19.7957	+	17.6019i	−0.640238	+	0.569287i
$957$		0			0
$958$	−5.80627	−	56.9496i	−0.187592	−	1.83996i
$959$	7.90515	+	13.6921i	0.255271	+	0.442142i
$960$		0			0
$961$	8.06057			0.260018
$962$	−25.7136	−	1.20639i	−0.829040	−	0.0388954i
$963$		0			0
$964$	−7.44032	−	36.1091i	−0.239636	−	1.16300i
$965$	41.5790	−	24.0056i	1.33848	−	0.772769i
$966$		0			0
$967$			7.41489i			0.238447i	0.992867	+	0.119223i	$0.0380405\pi$
$967$			7.41489i			0.238447i	−0.992867	+	0.119223i	$0.961960\pi$
$968$	−15.7161	+	70.6824i	−0.505134	+	2.27182i
$969$		0			0
$970$	68.2094	−	49.2330i	2.19007	−	1.58078i
$971$	14.6011	+	8.42995i	0.468572	+	0.270530i	0.715642	−	0.698468i	$-0.246134\pi$
$971$	14.6011	+	8.42995i	0.468572	+	0.270530i	−0.247070	+	0.968998i	$0.579468\pi$
$972$		0			0
$973$	−10.6356	−	18.4213i	−0.340960	−	0.590561i
$974$	32.5198	−	23.4725i	1.04200	−	0.752107i
$975$		0			0
$976$	0.462273	−	0.619866i	0.0147970	−	0.0198414i
$977$	−32.1699	+	18.5733i	−1.02921	+	0.594213i	−0.916758	−	0.399444i	$-0.869203\pi$
$977$	−32.1699	+	18.5733i	−1.02921	+	0.594213i	−0.112450	+	0.993657i	$0.535870\pi$
$978$		0			0
$979$	−68.8764	−	39.7658i	−2.20130	−	1.27092i
$980$	10.9968	−	33.1405i	0.351280	−	1.05863i
$981$		0			0
$982$	−2.23798	−	21.9508i	−0.0714169	−	0.700478i
$983$		−	8.77688i		−	0.279939i	−0.990156	−	0.139969i	$-0.955300\pi$
$983$		−	8.77688i		−	0.279939i	0.990156	−	0.139969i	$-0.0447004\pi$
$984$		0			0
$985$	16.3209	+	28.2686i	0.520027	+	0.900712i
$986$	−14.8992	−	6.68926i	−0.474487	−	0.213030i
$987$		0			0
$988$	−21.3006	+	1.16677i	−0.677663	+	0.0371198i
$989$		−	28.8449i		−	0.917216i
$990$		0			0
$991$	14.4649	+	25.0539i	0.459492	+	0.795864i	0.998934	−	0.0461588i	$-0.0146980\pi$
$991$	14.4649	+	25.0539i	0.459492	+	0.795864i	−0.539442	+	0.842023i	$0.681365\pi$
$992$	13.9107	−	23.2498i	0.441666	−	0.738182i
$993$		0			0
$994$	26.2801	−	2.67937i	0.833553	−	0.0849845i
$995$	−6.49810	+	11.2550i	−0.206004	+	0.356809i
$996$		0			0
$997$	37.6297	+	21.7255i	1.19174	+	0.688054i	0.958702	−	0.284412i	$-0.0917984\pi$
$997$	37.6297	+	21.7255i	1.19174	+	0.688054i	0.233043	+	0.972466i	$0.425132\pi$
$998$	−8.72940	+	19.4433i	−0.276324	+	0.615466i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.dg.f.829.10	yes	56
3.2	odd	2	inner	936.2.dg.f.829.19	yes	56
8.5	even	2	inner	936.2.dg.f.829.1	✓	56
13.4	even	6	inner	936.2.dg.f.901.1	yes	56
24.5	odd	2	inner	936.2.dg.f.829.28	yes	56
39.17	odd	6	inner	936.2.dg.f.901.28	yes	56
104.69	even	6	inner	936.2.dg.f.901.10	yes	56
312.173	odd	6	inner	936.2.dg.f.901.19	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.dg.f.829.1	✓	56	8.5	even	2	inner
936.2.dg.f.829.10	yes	56	1.1	even	1	trivial
936.2.dg.f.829.19	yes	56	3.2	odd	2	inner
936.2.dg.f.829.28	yes	56	24.5	odd	2	inner
936.2.dg.f.901.1	yes	56	13.4	even	6	inner
936.2.dg.f.901.10	yes	56	104.69	even	6	inner
936.2.dg.f.901.19	yes	56	312.173	odd	6	inner
936.2.dg.f.901.28	yes	56	39.17	odd	6	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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.dg (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.579236 + 1.29015i) q^{2} +(-1.32897 - 1.49460i) q^{4} -3.41501 q^{5} +(-1.18985 - 0.686961i) q^{7} +(2.69805 - 0.848845i) q^{8} +(1.97809 - 4.40587i) q^{10} +(-3.02491 - 5.23930i) q^{11} +(3.56588 + 0.533406i) q^{13} +(1.57549 - 1.13717i) q^{14} +(-0.467669 + 3.97257i) q^{16} +(-3.22892 + 5.59265i) q^{17} +(1.47915 - 2.56196i) q^{19} +(4.53845 + 5.10407i) q^{20} +(8.51161 - 0.867797i) q^{22} +(3.18261 + 5.51244i) q^{23} +6.66227 q^{25} +(-2.75366 + 4.29155i) q^{26} +(0.554545 + 2.69131i) q^{28} +(1.54870 - 0.894140i) q^{29} +4.78951i q^{31} +(-4.85431 - 2.90442i) q^{32} +(-5.34505 - 7.40526i) q^{34} +(4.06335 + 2.34598i) q^{35} +(2.52420 + 4.37205i) q^{37} +(2.44853 + 3.39230i) q^{38} +(-9.21385 + 2.89881i) q^{40} +(2.96921 - 1.71428i) q^{41} +(-3.92452 - 2.26583i) q^{43} +(-3.81064 + 11.4839i) q^{44} +(-8.95535 + 0.913038i) q^{46} -0.675737i q^{47} +(-2.55617 - 4.42742i) q^{49} +(-3.85902 + 8.59532i) q^{50} +(-3.94172 - 6.03845i) q^{52} +12.4101i q^{53} +(10.3301 + 17.8922i) q^{55} +(-3.79340 - 0.843454i) q^{56} +(0.256514 + 2.51597i) q^{58} +(2.78619 - 4.82582i) q^{59} +(-0.167415 - 0.0966574i) q^{61} +(-6.17919 - 2.77426i) q^{62} +(6.55892 - 4.58045i) q^{64} +(-12.1775 - 1.82158i) q^{65} +(4.90885 + 8.50237i) q^{67} +(12.6499 - 2.60653i) q^{68} +(-5.38030 + 3.88345i) q^{70} +(11.7740 + 6.79775i) q^{71} +1.97079i q^{73} +(-7.10270 + 0.724152i) q^{74} +(-5.79485 + 1.19403i) q^{76} +8.31198i q^{77} -1.01051 q^{79} +(1.59709 - 13.5663i) q^{80} +(0.491798 + 4.82370i) q^{82} -4.43962 q^{83} +(11.0268 - 19.0989i) q^{85} +(5.19648 - 3.75078i) q^{86} +(-12.6087 - 11.5682i) q^{88} +(11.3849 - 6.57306i) q^{89} +(-3.87643 - 3.08429i) q^{91} +(4.00931 - 12.0826i) q^{92} +(0.871802 + 0.391411i) q^{94} +(-5.05130 + 8.74910i) q^{95} +(15.0845 + 8.70903i) q^{97} +(7.19265 - 0.733323i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{10} - 4 q^{16} + 64 q^{25} - 48 q^{28} - 48 q^{40} + 20 q^{49} - 12 q^{52} + 16 q^{55} + 12 q^{58} - 72 q^{64} - 84 q^{76} + 80 q^{79} - 12 q^{82} - 12 q^{88} - 24 q^{94} + 24 q^{97}+O(q^{100}) \) 56 * q - 4 * q^10 - 4 * q^16 + 64 * q^25 - 48 * q^28 - 48 * q^40 + 20 * q^49 - 12 * q^52 + 16 * q^55 + 12 * q^58 - 72 * q^64 - 84 * q^76 + 80 * q^79 - 12 * q^82 - 12 * q^88 - 24 * q^94 + 24 * q^97

Introduction

L-functions

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