LMFDB - Embedded newform 936.2.dg.f.829.1

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			829.1
Character	$\chi$	$=$	936.829
Dual form			936.2.dg.f.901.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40692 - 0.143442i) q^{2} +(1.95885 + 0.403622i) q^{4} +3.41501 q^{5} +(-1.18985 - 0.686961i) q^{7} +(-2.69805 - 0.848845i) q^{8} +(-4.80464 - 0.489855i) q^{10} +(3.02491 + 5.23930i) q^{11} +(-3.56588 - 0.533406i) q^{13} +(1.57549 + 1.13717i) q^{14} +(3.67418 + 1.58127i) q^{16} +(-3.22892 + 5.59265i) q^{17} +(-1.47915 + 2.56196i) q^{19} +(6.68948 + 1.37837i) q^{20} +(-3.50427 - 7.80517i) q^{22} +(3.18261 + 5.51244i) q^{23} +6.66227 q^{25} +(4.94039 + 1.26196i) q^{26} +(-2.05347 - 1.82590i) q^{28} +(-1.54870 + 0.894140i) q^{29} +4.78951i q^{31} +(-4.94246 - 2.75175i) q^{32} +(5.34505 - 7.40526i) q^{34} +(-4.06335 - 2.34598i) q^{35} +(-2.52420 - 4.37205i) q^{37} +(2.44853 - 3.39230i) q^{38} +(-9.21385 - 2.89881i) q^{40} +(2.96921 - 1.71428i) q^{41} +(3.92452 + 2.26583i) q^{43} +(3.81064 + 11.4839i) q^{44} +(-3.68696 - 8.21208i) q^{46} -0.675737i q^{47} +(-2.55617 - 4.42742i) q^{49} +(-9.37328 - 0.955647i) q^{50} +(-6.76972 - 2.48413i) q^{52} -12.4101i q^{53} +(10.3301 + 17.8922i) q^{55} +(2.62715 + 2.86345i) q^{56} +(2.30715 - 1.03584i) q^{58} +(-2.78619 + 4.82582i) q^{59} +(0.167415 + 0.0966574i) q^{61} +(0.687016 - 6.73846i) q^{62} +(6.55892 + 4.58045i) q^{64} +(-12.1775 - 1.82158i) q^{65} +(-4.90885 - 8.50237i) q^{67} +(-8.58229 + 9.65190i) q^{68} +(5.38030 + 3.88345i) q^{70} +(11.7740 + 6.79775i) q^{71} +1.97079i q^{73} +(2.92422 + 6.51319i) q^{74} +(-3.93149 + 4.42147i) q^{76} -8.31198i q^{77} -1.01051 q^{79} +(12.5473 + 5.40005i) q^{80} +(-4.42334 + 1.98594i) q^{82} +4.43962 q^{83} +(-11.0268 + 19.0989i) q^{85} +(-5.19648 - 3.75078i) q^{86} +(-3.71400 - 16.7036i) q^{88} +(11.3849 - 6.57306i) q^{89} +(3.87643 + 3.08429i) q^{91} +(4.00931 + 12.0826i) q^{92} +(-0.0969289 + 0.950708i) q^{94} +(-5.05130 + 8.74910i) q^{95} +(15.0845 + 8.70903i) q^{97} +(2.96125 + 6.59568i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.40692	−	0.143442i	−0.994843	−	0.101429i
$2$	−1.40692	−	0.143442i	−0.994843	−	0.101429i
$3$		0			0
$3$		0			0
$4$	1.95885	+	0.403622i	0.979424	+	0.201811i
$5$	3.41501			1.52724			0.763619	−	0.645668i	$-0.223421\pi$
$5$	3.41501			1.52724			0.763619	+	0.645668i	$0.223421\pi$
$6$		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
$10$	−4.80464	−	0.489855i	−1.51936	−	0.154906i
$11$	3.02491	+	5.23930i	0.912044	+	1.57971i	0.811172	+	0.584808i	$0.198830\pi$
$11$	3.02491	+	5.23930i	0.912044	+	1.57971i	0.100873	+	0.994899i	$0.467837\pi$
$12$		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
$16$	3.67418	+	1.58127i	0.918545	+	0.395318i
$17$	−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	−0.984309	−	0.176455i	$-0.943537\pi$
$19$	−1.47915	+	2.56196i	−0.339340	+	0.587753i	0.644969	+	0.764209i	$0.276870\pi$
$20$	6.68948	+	1.37837i	1.49581	+	0.308213i
$21$		0			0
$22$	−3.50427	−	7.80517i	−0.747113	−	1.66407i
$23$	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
$26$	4.94039	+	1.26196i	0.968890	+	0.247490i
$27$		0			0
$28$	−2.05347	−	1.82590i	−0.388069	−	0.345063i
$29$	−1.54870	+	0.894140i	−0.287586	+	0.166038i	−0.636853	−	0.770986i	$-0.719764\pi$
$29$	−1.54870	+	0.894140i	−0.287586	+	0.166038i	0.349267	+	0.937023i	$0.386431\pi$
$30$		0			0
$31$			4.78951i			0.860222i	0.902776	+	0.430111i	$0.141526\pi$
$31$			4.78951i			0.860222i	−0.902776	+	0.430111i	$0.858474\pi$
$32$	−4.94246	−	2.75175i	−0.873711	−	0.486446i
$33$		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	0.580450	−	0.814296i	$-0.302877\pi$
$37$	−2.52420	−	4.37205i	−0.414976	−	0.718760i	−0.995426	+	0.0955362i	$0.969543\pi$
$38$	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	0.768445	−	0.639916i	$-0.221031\pi$
$43$	3.92452	+	2.26583i	0.598484	+	0.345535i	−0.169961	+	0.985451i	$0.554364\pi$
$44$	3.81064	+	11.4839i	0.574476	+	1.73126i
$45$		0			0
$46$	−3.68696	−	8.21208i	−0.543613	−	1.21081i
$47$		−	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
$50$	−9.37328	−	0.955647i	−1.32558	−	0.135149i
$51$		0			0
$52$	−6.76972	−	2.48413i	−0.938791	−	0.344487i
$53$		−	12.4101i		−	1.70466i	−0.523002	−	0.852331i	$-0.675188\pi$
$53$		−	12.4101i		−	1.70466i	0.523002	−	0.852331i	$-0.324812\pi$
$54$		0			0
$55$	10.3301	+	17.8922i	1.39291	+	2.41259i
$56$	2.62715	+	2.86345i	0.351068	+	0.382645i
$57$		0			0
$58$	2.30715	−	1.03584i	0.302944	−	0.136012i
$59$	−2.78619	+	4.82582i	−0.362731	+	0.628268i	−0.988409	−	0.151813i	$-0.951489\pi$
$59$	−2.78619	+	4.82582i	−0.362731	+	0.628268i	0.625678	+	0.780081i	$0.284822\pi$
$60$		0			0
$61$	0.167415	+	0.0966574i	0.0214354	+	0.0123757i	0.510679	−	0.859771i	$-0.329394\pi$
$61$	0.167415	+	0.0966574i	0.0214354	+	0.0123757i	−0.489244	+	0.872147i	$0.662727\pi$
$62$	0.687016	−	6.73846i	0.0872512	−	0.855786i
$63$		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	$-0.961949\pi$
$67$	−4.90885	−	8.50237i	−0.599711	−	1.03873i	0.393153	−	0.919473i	$-0.371384\pi$
$68$	−8.58229	+	9.65190i	−1.04076	+	1.17046i
$69$		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	$0.963207\pi$
$74$	2.92422	+	6.51319i	0.339933	+	0.757144i
$75$		0			0
$76$	−3.93149	+	4.42147i	−0.450973	+	0.507178i
$77$		−	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	$0.518104\pi$
$80$	12.5473	+	5.40005i	1.40284	+	0.603744i
$81$		0			0
$82$	−4.42334	+	1.98594i	−0.488477	+	0.219310i
$83$	4.43962			0.487312			0.243656	−	0.969862i	$-0.421653\pi$
$83$	4.43962			0.487312			0.243656	+	0.969862i	$0.421653\pi$
$84$		0			0
$85$	−11.0268	+	19.0989i	−1.19602	+	2.07157i
$86$	−5.19648	−	3.75078i	−0.560351	−	0.404457i
$87$		0			0
$88$	−3.71400	−	16.7036i	−0.395914	−	1.78060i
$89$	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
$94$	−0.0969289	+	0.950708i	−0.00999746	+	0.0980581i
$95$	−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	$0.321324\pi$
$98$	2.96125	+	6.59568i	0.299131	+	0.666264i
$99$		0			0
$100$	13.0504	+	2.68904i	1.30504	+	0.268904i
$101$	4.57759	−	2.64287i	0.455487	−	0.262976i	−0.254657	−	0.967031i	$-0.581963\pi$
$101$	4.57759	−	2.64287i	0.455487	−	0.262976i	0.710145	+	0.704056i	$0.248629\pi$
$102$		0			0
$103$	6.98106			0.687864			0.343932	−	0.938994i	$-0.388241\pi$
$103$	6.98106			0.687864			0.343932	+	0.938994i	$0.388241\pi$
$104$	9.16813	+	4.46603i	0.899009	+	0.437930i
$105$		0			0
$106$	−1.78013	+	17.4601i	−0.172902	+	1.69587i
$107$	−9.02755	+	5.21206i	−0.872726	+	0.503868i	−0.868253	−	0.496122i	$-0.834757\pi$
$107$	−9.02755	+	5.21206i	−0.872726	+	0.503868i	−0.00447271	+	0.999990i	$0.501424\pi$
$108$		0			0
$109$	16.6956			1.59915			0.799575	−	0.600566i	$-0.205058\pi$
$109$	16.6956			1.59915			0.799575	+	0.600566i	$0.205058\pi$
$110$	−11.9671	−	26.6547i	−1.14102	−	2.54143i
$111$		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
$124$	−1.93315	+	9.38193i	−0.173602	+	0.842522i
$125$	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	$0.812006\pi$
$128$	−8.57085	−	7.38515i	−0.757564	−	0.652761i
$129$		0			0
$130$	16.8715	+	4.30959i	1.47973	+	0.377976i
$131$			0.608733i			0.0531852i	0.999646	+	0.0265926i	$0.00846569\pi$
$131$			0.608733i			0.0531852i	−0.999646	+	0.0265926i	$0.991534\pi$
$132$		0			0
$133$	3.51993	−	2.03223i	0.305217	−	0.176217i
$134$	5.68676	+	12.6663i	0.491261	+	1.09420i
$135$		0			0
$136$	13.4591	−	12.3484i	1.15411	−	1.05887i
$137$	−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	−0.191493	−	0.981494i	$-0.561333\pi$
$139$	−13.4078	−	7.74102i	−1.13724	−	0.656585i	−0.945745	+	0.324909i	$0.894666\pi$
$140$	−7.01260	−	6.23547i	−0.592673	−	0.526993i
$141$		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
$146$	0.282693	−	2.77274i	0.0233958	−	0.229473i
$147$		0			0
$148$	−3.17987	−	9.58300i	−0.261384	−	0.787718i
$149$	−0.454670	+	0.787511i	−0.0372480	+	0.0645154i	−0.884048	−	0.467395i	$-0.845192\pi$
$149$	−0.454670	+	0.787511i	−0.0372480	+	0.0645154i	0.846800	+	0.531911i	$0.178526\pi$
$150$		0			0
$151$		−	21.8390i		−	1.77723i	−0.458650	−	0.888617i	$-0.651667\pi$
$151$		−	21.8390i		−	1.77723i	0.458650	−	0.888617i	$-0.348333\pi$
$152$	6.16551	−	5.65672i	0.500089	−	0.458820i
$153$		0			0
$154$	−1.19228	+	11.6943i	−0.0960770	+	0.942353i
$155$			16.3562i			1.31376i
$156$		0			0
$157$		−	3.03910i		−	0.242547i	−0.992619	−	0.121273i	$-0.961302\pi$
$157$		−	3.03910i		−	0.242547i	0.992619	−	0.121273i	$-0.0386978\pi$
$158$	1.42170	+	0.144949i	0.113105	+	0.0115315i
$159$		0			0
$160$	−16.8785	−	9.39725i	−1.33436	−	0.742918i
$161$		−	8.74531i		−	0.689227i
$162$		0			0
$163$	8.36620	−	14.4907i	0.655291	−	1.13500i	−0.326530	−	0.945187i	$-0.605879\pi$
$163$	8.36620	−	14.4907i	0.655291	−	1.13500i	0.981821	−	0.189811i	$-0.0607874\pi$
$164$	6.50816	−	2.15957i	0.508202	−	0.168634i
$165$		0			0
$166$	−6.24619	−	0.636827i	−0.484799	−	0.0494274i
$167$	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
$172$	6.77301	+	6.02243i	0.516437	+	0.459206i
$173$	−2.27946	−	1.31605i	−0.173304	−	0.100057i	0.410839	−	0.911708i	$-0.365236\pi$
$173$	−2.27946	−	1.31605i	−0.173304	−	0.100057i	−0.584143	+	0.811651i	$0.698569\pi$
$174$		0			0
$175$	−7.92710	−	4.57672i	−0.599233	−	0.345967i
$176$	2.82931	+	24.0333i	0.213267	+	1.81158i
$177$		0			0
$178$	−16.9605	+	7.61471i	−1.27124	+	0.570746i
$179$	−17.9329	+	10.3536i	−1.34037	+	0.773863i	−0.986862	−	0.161568i	$-0.948345\pi$
$179$	−17.9329	+	10.3536i	−1.34037	+	0.773863i	−0.353509	+	0.935431i	$0.615012\pi$
$180$		0			0
$181$		−	16.5473i		−	1.22995i	−0.788547	−	0.614974i	$-0.789166\pi$
$181$		−	16.5473i		−	1.22995i	0.788547	−	0.614974i	$-0.210834\pi$
$182$	−5.01142	−	4.89539i	−0.371471	−	0.362871i
$183$		0			0
$184$	−3.90762	−	17.5744i	−0.288074	−	1.29560i
$185$	−8.62016	−	14.9306i	−0.633767	−	1.09772i
$186$		0			0
$187$	−39.0688			−2.85699
$188$	0.272743	−	1.32367i	0.0198918	−	0.0965383i
$189$		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	0.984526	−	0.175239i	$-0.0560698\pi$
$197$	4.77917	+	8.27776i	0.340501	+	0.589766i	−0.644024	+	0.765005i	$0.722736\pi$
$198$		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
$202$	−6.81941	+	3.06169i	−0.479812	+	0.215420i
$203$	2.45696			0.172445
$204$		0			0
$205$	10.1399	−	5.85426i	0.708200	−	0.408879i
$206$	−9.82180	−	1.00138i	−0.684317	−	0.0697692i
$207$		0			0
$208$	−12.2582	−	7.59844i	−0.849954	−	0.526857i
$209$	−17.8971			−1.23797
$210$		0			0
$211$	−8.77615	+	5.06691i	−0.604175	+	0.348821i	−0.770682	−	0.637220i	$-0.780084\pi$
$211$	−8.77615	+	5.06691i	−0.604175	+	0.348821i	0.166507	+	0.986040i	$0.446751\pi$
$212$	5.00901	−	24.3096i	0.344020	−	1.66959i
$213$		0			0
$214$	13.4487	−	6.03802i	0.919332	−	0.412751i
$215$	13.4023	+	7.73781i	0.914028	+	0.527714i
$216$		0			0
$217$	3.29021	−	5.69881i	0.223354	−	0.386860i
$218$	−23.4894	−	2.39485i	−1.59090	−	0.162200i
$219$		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	$0.356544\pi$
$224$	3.99044	+	6.66945i	0.266622	+	0.445621i
$225$		0			0
$226$	9.62145	−	13.3300i	0.640010	−	0.886695i
$227$	−2.53742	+	4.39495i	−0.168415	+	0.291703i	−0.937863	−	0.347007i	$-0.887198\pi$
$227$	−2.53742	+	4.39495i	−0.168415	+	0.291703i	0.769448	+	0.638710i	$0.220531\pi$
$228$		0			0
$229$	12.7135			0.840132			0.420066	−	0.907493i	$-0.362007\pi$
$229$	12.7135			0.840132			0.420066	+	0.907493i	$0.362007\pi$
$230$	−12.5910	−	28.0443i	−0.830226	−	1.84919i
$231$		0			0
$232$	4.93744	−	1.09783i	0.324159	−	0.0720760i
$233$	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
$236$	−7.40553	+	8.32848i	−0.482059	+	0.542138i
$237$		0			0
$238$	−11.4469	+	5.13931i	−0.741995	+	0.333132i
$239$		−	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
$244$	0.288929	+	0.256910i	0.0184968	+	0.0164470i
$245$	−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
$250$	−7.98659	−	0.814268i	−0.505116	−	0.0514988i
$251$	10.4275	+	6.02030i	0.658176	+	0.379998i	0.791582	−	0.611063i	$-0.209258\pi$
$251$	10.4275	+	6.02030i	0.658176	+	0.379998i	−0.133406	+	0.991062i	$0.542591\pi$
$252$		0			0
$253$	−19.2542	+	33.3493i	−1.21050	+	2.09665i
$254$	−0.874068	−	1.94684i	−0.0548439	−	0.122155i
$255$		0			0
$256$	10.9992	+	11.6197i	0.687448	+	0.726234i
$257$	−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
$260$	−23.1186	−	8.48332i	−1.43376	−	0.526113i
$261$		0			0
$262$	0.0873177	−	0.856438i	0.00539450	−	0.0529109i
$263$	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
$266$	−5.24377	+	2.35428i	−0.321516	+	0.144350i
$267$		0			0
$268$	−6.18394	−	18.6362i	−0.377744	−	1.13839i
$269$	−14.2966	−	8.25414i	−0.871679	−	0.503264i	−0.00377292	−	0.999993i	$-0.501201\pi$
$269$	−14.2966	−	8.25414i	−0.871679	−	0.503264i	−0.867906	+	0.496729i	$0.834534\pi$
$270$		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	0.510499	−	0.859879i	$-0.329461\pi$
$277$	0.350695	+	0.202474i	0.0210712	+	0.0121655i	−0.489427	+	0.872044i	$0.662794\pi$
$278$	17.7534	+	12.8142i	1.06478	+	0.768547i
$279$		0			0
$280$	8.97174	+	9.77871i	0.536164	+	0.584390i
$281$		−	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	0.205995	−	0.978553i	$-0.433957\pi$
$283$	19.4544	−	11.2320i	1.15644	−	0.667673i	0.950449	+	0.310880i	$0.100624\pi$
$284$	20.3199	+	18.0680i	1.20576	+	1.07214i
$285$		0			0
$286$	8.33248	+	29.7015i	0.492710	+	1.75629i
$287$	−4.71056			−0.278056
$288$		0			0
$289$	−12.3518	−	21.3940i	−0.726579	−	1.25847i
$290$	7.87893	−	3.53739i	0.462667	−	0.207722i
$291$		0			0
$292$	−0.795453	+	3.86047i	−0.0465504	+	0.225917i
$293$	7.79411	−	13.4998i	0.455337	−	0.788667i	−0.543370	−	0.839493i	$-0.682852\pi$
$293$	7.79411	−	13.4998i	0.455337	−	0.788667i	0.998708	+	0.0508261i	$0.0161854\pi$
$294$		0			0
$295$	−9.51485	+	16.4802i	−0.553976	+	0.959515i
$296$	3.09923	+	13.9386i	0.180139	+	0.810167i
$297$		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
$302$	−3.13263	+	30.7258i	−0.180262	+	1.76807i
$303$		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	$-0.191654\pi$
$307$	28.8805			1.64830			0.824149	+	0.566373i	$0.191654\pi$
$308$	3.35490	−	16.2819i	0.191163	−	0.927748i
$309$		0			0
$310$	2.34616	−	23.0119i	0.133253	−	1.30699i
$311$	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	$0.636090\pi$
$314$	−0.435934	+	4.27577i	−0.0246012	+	0.241296i
$315$		0			0
$316$	−1.97943	−	0.407864i	−0.111352	−	0.0229441i
$317$	12.7648			0.716943			0.358471	−	0.933541i	$-0.383298\pi$
$317$	12.7648			0.716943			0.358471	+	0.933541i	$0.383298\pi$
$318$		0			0
$319$	−9.36933	−	5.40939i	−0.524582	−	0.302867i
$320$	22.3988	+	15.6423i	1.25213	+	0.874429i
$321$		0			0
$322$	−1.25444	+	12.3040i	−0.0699074	+	0.685673i
$323$	−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
$328$	−9.46623	+	2.10480i	−0.522685	+	0.116218i
$329$	−0.464205	+	0.804027i	−0.0255924	+	0.0443274i
$330$		0			0
$331$	−0.0572169	+	0.0991026i	−0.00314492	+	0.00544717i	−0.867594	−	0.497274i	$-0.834334\pi$
$331$	−0.0572169	+	0.0991026i	−0.00314492	+	0.00544717i	0.864449	+	0.502721i	$0.167668\pi$
$332$	8.69655	+	1.79193i	0.477285	+	0.0983449i
$333$		0			0
$334$	−22.6517	+	10.1699i	−1.23945	+	0.556471i
$335$	−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	$0.627178\pi$
$338$	−16.9437	−	7.13521i	−0.921615	−	0.388104i
$339$		0			0
$340$	−29.3086	+	32.9613i	−1.58948	+	1.78758i
$341$	−25.0937	+	14.4878i	−1.35890	+	0.784561i
$342$		0			0
$343$			16.6414i			0.898551i
$344$	−8.66522	−	9.44462i	−0.467197	−	0.509220i
$345$		0			0
$346$	3.01824	+	2.17854i	0.162262	+	0.117119i
$347$	−17.4058	−	10.0492i	−0.934390	−	0.539470i	−0.0461927	−	0.998933i	$-0.514709\pi$
$347$	−17.4058	−	10.0492i	−0.934390	−	0.539470i	−0.888197	+	0.459462i	$0.848042\pi$
$348$		0			0
$349$	−10.9808	−	19.0194i	−0.587791	−	1.01808i	−0.994521	−	0.104535i	$-0.966665\pi$
$349$	−10.9808	−	19.0194i	−0.587791	−	1.01808i	0.406731	−	0.913548i	$-0.366669\pi$
$350$	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
$358$	26.7153	−	11.9943i	1.41195	−	0.633920i
$359$			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
$362$	−2.37357	+	23.2807i	−0.124752	+	1.22361i
$363$		0			0
$364$	6.34846	+	7.60628i	0.332750	+	0.398677i
$365$			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	$0.898794\pi$
$368$	2.97681	+	25.2863i	0.155177	+	1.31814i
$369$		0			0
$370$	9.98622	+	22.2426i	0.519159	+	1.15634i
$371$	−8.52527	+	14.7662i	−0.442610	+	0.766623i
$372$		0			0
$373$	−11.4709	−	6.62274i	−0.593942	−	0.342913i	0.172713	−	0.984972i	$-0.444747\pi$
$373$	−11.4709	−	6.62274i	−0.593942	−	0.342913i	−0.766655	+	0.642060i	$0.778080\pi$
$374$	54.9666	+	5.60409i	2.84226	+	0.289781i
$375$		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	$-0.882083\pi$
$379$	−15.1774	−	26.2881i	−0.779611	−	1.35033i	0.152554	−	0.988295i	$-0.451250\pi$
$380$	−13.4261	+	15.0994i	−0.688742	+	0.774580i
$381$		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
$386$	18.1381	−	8.14343i	0.923205	−	0.414490i
$387$		0			0
$388$	26.0331	+	23.1481i	1.32163	+	1.17517i
$389$		−	2.92168i		−	0.148135i	−0.997253	−	0.0740674i	$-0.976402\pi$
$389$		−	2.92168i		−	0.148135i	0.997253	−	0.0740674i	$-0.0235980\pi$
$390$		0			0
$391$	−41.1056			−2.07880
$392$	3.13848	+	14.1152i	0.158517	+	0.712924i
$393$		0			0
$394$	−5.53653	−	12.3317i	−0.278926	−	0.621261i
$395$	−3.45089			−0.173633
$396$		0			0
$397$	−3.13178	+	5.42441i	−0.157180	+	0.272243i	−0.933851	−	0.357663i	$-0.883574\pi$
$397$	−3.13178	+	5.42441i	−0.157180	+	0.272243i	0.776671	+	0.629907i	$0.216907\pi$
$398$	−3.14985	+	4.36393i	−0.157888	+	0.218744i
$399$		0			0
$400$	24.4783	+	10.5348i	1.22392	+	0.526742i
$401$	−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
$406$	−3.45674	−	0.352430i	−0.171555	−	0.0174908i
$407$	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	$-0.699182\pi$
$410$	−15.1057	+	6.78200i	−0.746020	+	0.334939i
$411$		0			0
$412$	13.6748	+	2.81771i	0.673711	+	0.138819i
$413$	6.63030	−	3.82800i	0.326256	−	0.188364i
$414$		0			0
$415$	15.1613			0.744240
$416$	16.1564	+	12.4487i	0.792132	+	0.610350i
$417$		0			0
$418$	25.1798	+	2.56720i	1.23159	+	0.125566i
$419$	8.26881	−	4.77400i	0.403958	−	0.233225i	−0.284232	−	0.958755i	$-0.591739\pi$
$419$	8.26881	−	4.77400i	0.403958	−	0.233225i	0.688190	+	0.725530i	$0.258405\pi$
$420$		0			0
$421$	27.0280			1.31726			0.658632	−	0.752465i	$-0.271135\pi$
$421$	27.0280			1.31726			0.658632	+	0.752465i	$0.271135\pi$
$422$	13.0742	−	5.86988i	0.636440	−	0.285741i
$423$		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
$436$	32.7042	+	6.73872i	1.56625	+	0.322726i
$437$	−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	$-0.340211\pi$
$440$	−12.6833	−	57.0427i	−0.604654	−	2.71941i
$441$		0			0
$442$	−23.0098	+	23.5551i	−1.09446	+	1.12040i
$443$		−	6.62675i		−	0.314846i	−0.987531	−	0.157423i	$-0.949681\pi$
$443$		−	6.62675i		−	0.314846i	0.987531	−	0.157423i	$-0.0503187\pi$
$444$		0			0
$445$	38.8794	−	22.4470i	1.84306	−	1.06409i
$446$	2.80717	−	1.26033i	0.132923	−	0.0596783i
$447$		0			0
$448$	−4.65755	−	9.95578i	−0.220049	−	0.470366i
$449$	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
$452$	−15.4487	+	17.3741i	−0.726645	+	0.817207i
$453$		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	$0.230365\pi$
$458$	−17.8869	−	1.82365i	−0.835800	−	0.0852135i
$459$		0			0
$460$	13.6918	+	41.2622i	0.638384	+	1.92386i
$461$	7.43675	−	12.8808i	0.346364	−	0.599920i	−0.639237	−	0.769010i	$-0.720750\pi$
$461$	7.43675	−	12.8808i	0.346364	−	0.599920i	0.985601	+	0.169090i	$0.0540829\pi$
$462$		0			0
$463$			28.8166i			1.33922i	0.742712	+	0.669611i	$0.233539\pi$
$463$			28.8166i			1.33922i	−0.742712	+	0.669611i	$0.766461\pi$
$464$	−7.10406	+	0.836323i	−0.329798	+	0.0388253i
$465$		0			0
$466$	−0.575423	−	0.0586669i	−0.0266560	−	0.00271769i
$467$		−	14.1259i		−	0.653670i	−0.945081	−	0.326835i	$-0.894018\pi$
$467$		−	14.1259i		−	0.653670i	0.945081	−	0.326835i	$-0.105982\pi$
$468$		0			0
$469$			13.4887i			0.622852i
$470$	−0.331013	+	3.24667i	−0.0152685	+	0.149758i
$471$		0			0
$472$	11.6136	−	10.6553i	0.534561	−	0.490448i
$473$			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
$478$	−1.89985	+	18.6343i	−0.0868973	+	0.852315i
$479$	−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
$484$	−34.0221	+	38.2623i	−1.54646	+	1.73919i
$485$	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	$0.888786\pi$
$488$	−0.369648	−	0.402896i	−0.0167332	−	0.0182382i
$489$		0			0
$490$	10.1127	+	22.5243i	0.456845	+	1.01754i
$491$	13.5117	−	7.80101i	0.609777	−	0.352055i	−0.163101	−	0.986609i	$-0.552150\pi$
$491$	13.5117	−	7.80101i	0.609777	−	0.352055i	0.772878	+	0.634555i	$0.218816\pi$
$492$		0			0
$493$		−	11.5484i		−	0.520115i
$494$	−10.5406	+	10.7905i	−0.474246	+	0.485486i
$495$		0			0
$496$	−7.57351	+	17.5975i	−0.340061	+	0.790152i
$497$	−9.33957	−	16.1766i	−0.418937	−	0.725620i
$498$		0			0
$499$	−15.0705			−0.674650			−0.337325	−	0.941388i	$-0.609522\pi$
$499$	−15.0705			−0.674650			−0.337325	+	0.941388i	$0.609522\pi$
$500$	11.1197	+	2.29122i	0.497288	+	0.102467i
$501$		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	0.919121	−	0.393974i	$-0.128900\pi$
$509$	2.67052	+	4.62548i	0.118369	+	0.205021i	−0.800753	+	0.598995i	$0.795567\pi$
$510$		0			0
$511$	1.35385	−	2.34494i	0.0598909	−	0.103734i
$512$	−13.8082	−	17.9258i	−0.610242	−	0.792215i
$513$		0			0
$514$	2.14782	+	4.78390i	0.0947363	+	0.211009i
$515$	23.8404			1.05053
$516$		0			0
$517$	3.54039	−	2.04404i	0.155706	−	0.0898969i
$518$	0.994928	−	9.75855i	0.0437146	−	0.428766i
$519$		0			0
$520$	31.3092	+	15.2515i	1.37300	+	0.668824i
$521$	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	−0.926205	−	0.377019i	$-0.876949\pi$
$523$	−24.3054	+	14.0327i	−1.06280	+	0.613608i	−0.136594	+	0.990627i	$0.543616\pi$
$524$	−0.245698	+	1.19242i	−0.0107334	+	0.0520909i
$525$		0			0
$526$	−7.86433	−	17.5165i	−0.342901	−	0.763754i
$527$	−26.7861	−	15.4650i	−1.16682	−	0.673664i
$528$		0			0
$529$	−8.75800	+	15.1693i	−0.380783	+	0.659535i
$530$	−6.07916	+	59.6262i	−0.264062	+	2.59000i
$531$		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
$536$	6.02710	+	27.1066i	0.260331	+	1.17083i
$537$		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	$-0.280226\pi$
$541$	29.6268			1.27375			0.636877	+	0.770965i	$0.280226\pi$
$542$	−14.6165	+	6.56232i	−0.627831	+	0.281876i
$543$		0			0
$544$	31.3484	−	18.7563i	1.34405	−	0.804168i
$545$	57.0156			2.44228
$546$		0			0
$547$			0.345795i			0.0147851i	0.999973	+	0.00739257i	$0.00235315\pi$
$547$			0.345795i			0.0147851i	−0.999973	+	0.00739257i	$0.997647\pi$
$548$	−17.1990	−	15.2930i	−0.734706	−	0.653286i
$549$		0			0
$550$	−23.3464	−	52.0001i	−0.995493	−	2.21729i
$551$		−	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
$556$	−23.1395	−	20.5752i	−0.981333	−	0.872583i
$557$	7.15368	+	12.3905i	0.303111	+	0.525004i	0.976839	−	0.213976i	$-0.0686413\pi$
$557$	7.15368	+	12.3905i	0.303111	+	0.525004i	−0.673728	+	0.738980i	$0.735308\pi$
$558$		0			0
$559$	−12.7858	−	10.1730i	−0.540780	−	0.430273i
$560$	−11.2198	−	15.0448i	−0.474125	−	0.635758i
$561$		0			0
$562$	−0.748537	+	7.34187i	−0.0315751	+	0.309698i
$563$	5.57398	+	3.21814i	0.234915	+	0.135628i	0.612837	−	0.790209i	$-0.290028\pi$
$563$	5.57398	+	3.21814i	0.234915	+	0.135628i	−0.377922	+	0.925837i	$0.623361\pi$
$564$		0			0
$565$	−19.8489	+	34.3794i	−0.835051	+	1.44635i
$566$	−28.9819	+	13.0120i	−1.21820	+	0.546933i
$567$		0			0
$568$	−25.9967	−	28.3350i	−1.09080	−	1.18891i
$569$	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	$0.0322296\pi$
$571$			4.83071i			0.202159i	−0.994878	+	0.101079i	$0.967770\pi$
$572$	−7.46270	−	42.9828i	−0.312031	−	1.79720i
$573$		0			0
$574$	6.62738	+	0.675691i	0.276622	+	0.0282028i
$575$	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	$0.954700\pi$
$578$	14.3093	+	31.8715i	0.595187	+	1.32568i
$579$		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	0.966582	−	0.256358i	$-0.0825227\pi$
$587$	6.33027	+	10.9643i	0.261278	+	0.452547i	−0.705304	+	0.708905i	$0.749189\pi$
$588$		0			0
$589$	−12.2705	−	7.08439i	−0.505598	−	0.291907i
$590$	15.7506	−	21.8215i	0.648441	−	0.898377i
$591$		0			0
$592$	−2.36098	−	20.0551i	−0.0970357	−	0.824260i
$593$		−	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
$596$	−1.20849	+	1.35910i	−0.0495015	+	0.0556709i
$597$		0			0
$598$	8.76688	+	31.2499i	0.358504	+	1.27790i
$599$	−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	$0.617712\pi$
$602$	3.60640	+	8.03264i	0.146986	+	0.327386i
$603$		0			0
$604$	8.81472	−	42.7793i	0.358666	−	1.74067i
$605$	−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	$-0.0930944\pi$
$608$	14.3605	−	8.59212i	0.582395	−	0.348456i
$609$		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	0.911772	−	0.410697i	$-0.134714\pi$
$613$	2.48114	+	4.29747i	0.100212	+	0.173573i	−0.811560	+	0.584270i	$0.801381\pi$
$614$	−40.6326	−	4.14267i	−1.63980	−	0.167185i
$615$		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	$-0.444703\pi$
$619$	8.60082			0.345696			0.172848	+	0.984948i	$0.444703\pi$
$620$	−6.60173	+	32.0394i	−0.265132	+	1.28673i
$621$		0			0
$622$	−10.7754	−	1.09860i	−0.432053	−	0.0440498i
$623$	−18.0617			−0.723629
$624$		0			0
$625$	−13.9255			−0.557022
$626$	20.6412	+	2.10446i	0.824989	+	0.0841113i
$627$		0			0
$628$	1.22665	−	5.95314i	0.0489486	−	0.237556i
$629$	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
$634$	−17.9591	−	1.83101i	−0.713245	−	0.0727185i
$635$	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
$640$	−29.2695	−	25.2203i	−1.15698	−	0.996921i
$641$	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	−0.998581	−	0.0532586i	$-0.983039\pi$
$643$	−11.4912	+	19.9033i	−0.453167	+	0.784908i	0.545414	+	0.838167i	$0.316373\pi$
$644$	3.52980	−	17.1307i	0.139094	−	0.675046i
$645$		0			0
$646$	11.0658	+	24.6473i	0.435379	+	0.969734i
$647$	−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
$650$	32.9142	+	8.40748i	1.29100	+	0.329769i
$651$		0			0
$652$	22.2369	−	25.0083i	0.870863	−	0.979399i
$653$	−37.2110	+	21.4838i	−1.45618	+	0.840725i	−0.998820	−	0.0485577i	$-0.984538\pi$
$653$	−37.2110	+	21.4838i	−1.45618	+	0.840725i	−0.457358	+	0.889283i	$0.651204\pi$
$654$		0			0
$655$			2.07883i			0.0812264i
$656$	13.6201	−	1.60343i	0.531777	−	0.0626033i
$657$		0			0
$658$	0.768430	−	1.06461i	0.0299565	−	0.0415030i
$659$	−3.12326	−	1.80322i	−0.121665	−	0.0702433i	0.437932	−	0.899008i	$-0.355711\pi$
$659$	−3.12326	−	1.80322i	−0.121665	−	0.0702433i	−0.559597	+	0.828765i	$0.689044\pi$
$660$		0			0
$661$	−5.43287	−	9.41001i	−0.211314	−	0.366007i	0.740812	−	0.671712i	$-0.234441\pi$
$661$	−5.43287	−	9.41001i	−0.211314	−	0.366007i	−0.952126	+	0.305706i	$0.901108\pi$
$662$	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
$670$	19.4203	+	43.2554i	0.750272	+	1.67110i
$671$			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	$0.797662\pi$
$674$	20.0937	+	2.04864i	0.773979	+	0.0789107i
$675$		0			0
$676$	22.8149	+	12.4691i	0.877498	+	0.479581i
$677$		−	27.4225i		−	1.05393i	−0.849887	−	0.526966i	$-0.823330\pi$
$677$		−	27.4225i		−	1.05393i	0.849887	−	0.526966i	$-0.176670\pi$
$678$		0			0
$679$	−11.9655	−	20.7249i	−0.459195	−	0.795349i
$680$	45.9628	−	42.1698i	1.76259	−	1.61714i
$681$		0			0
$682$	37.3830	−	16.7838i	1.43147	−	0.642683i
$683$	13.3166	−	23.0650i	0.509544	−	0.882556i	−0.490395	−	0.871500i	$-0.663147\pi$
$683$	13.3166	−	23.0650i	0.509544	−	0.882556i	0.999939	−	0.0110559i	$-0.00351928\pi$
$684$		0			0
$685$	−34.0330	−	19.6490i	−1.30033	−	0.750748i
$686$	2.38707	−	23.4131i	0.0911389	−	0.893917i
$687$		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	0.871929	−	0.489632i	$-0.162869\pi$
$691$	0.313614	+	0.543196i	0.0119305	+	0.0206642i	−0.859999	+	0.510296i	$0.829536\pi$
$692$	−3.93393	−	3.49798i	−0.149546	−	0.132973i
$693$		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
$698$	12.7210	+	28.3338i	0.481496	+	1.07245i
$699$		0			0
$700$	−13.6807	−	12.1646i	−0.517083	−	0.459781i
$701$		−	25.5900i		−	0.966522i	−0.875476	−	0.483261i	$-0.839452\pi$
$701$		−	25.5900i		−	0.966522i	0.875476	−	0.483261i	$-0.160548\pi$
$702$		0			0
$703$	14.9347			0.563271
$704$	−4.15819	+	48.2196i	−0.156718	+	1.81734i
$705$		0			0
$706$	−36.9821	+	16.6038i	−1.39184	+	0.624892i
$707$	−7.26220			−0.273123
$708$		0			0
$709$	13.9996	−	24.2481i	0.525767	−	0.910655i	−0.473783	−	0.880642i	$-0.657112\pi$
$709$	13.9996	−	24.2481i	0.525767	−	0.910655i	0.999550	−	0.0300132i	$-0.00955495\pi$
$710$	−53.2402	−	38.4283i	−1.99807	−	1.44219i
$711$		0			0
$712$	−36.2965	+	8.07044i	−1.36027	+	0.302452i
$713$	−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
$718$	4.60875	−	45.2040i	0.171997	−	1.68700i
$719$	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
$722$	−5.93630	−	13.2221i	−0.220926	−	0.492075i
$723$		0			0
$724$	6.67885	−	32.4136i	0.248217	−	1.20464i
$725$	−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	$0.262265\pi$
$728$	−7.84072	−	11.6121i	−0.290596	−	0.430371i
$729$		0			0
$730$	0.965398	−	9.46892i	0.0357310	−	0.350460i
$731$	−25.3440	+	14.6323i	−0.937380	+	0.541197i
$732$		0			0
$733$	−39.0091			−1.44083			−0.720417	−	0.693541i	$-0.756050\pi$
$733$	−39.0091			−1.44083			−0.720417	+	0.693541i	$0.756050\pi$
$734$	4.53192	+	10.0941i	0.167276	+	0.372579i
$735$		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	0.632505	−	0.774556i	$-0.282027\pi$
$739$	−9.63783	−	16.6932i	−0.354533	−	0.614069i	−0.987038	+	0.160487i	$0.948694\pi$
$740$	−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
$748$	−76.5298	−	15.7690i	−2.79821	−	0.576573i
$749$	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	$0.764927\pi$
$752$	1.06852	−	2.48278i	0.0389650	−	0.0905376i
$753$		0			0
$754$	−8.77953	+	2.46302i	−0.319732	+	0.0896978i
$755$		−	74.5804i		−	2.71426i
$756$		0			0
$757$	13.5679	−	7.83343i	0.493134	−	0.284711i	−0.232740	−	0.972539i	$-0.574769\pi$
$757$	13.5679	−	7.83343i	0.493134	−	0.284711i	0.725874	+	0.687828i	$0.241436\pi$
$758$	17.5826	+	39.1623i	0.638629	+	1.42244i
$759$		0			0
$760$	21.0553	−	19.3177i	0.763755	−	0.700728i
$761$	−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
$764$	−19.6863	+	22.1398i	−0.712224	+	0.800989i
$765$		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	$0.0355336\pi$
$770$	−4.07166	+	39.9361i	−0.146732	+	1.43920i
$771$		0			0
$772$	−26.6870	+	8.85539i	−0.960485	+	0.318713i
$773$	−22.4489	+	38.8827i	−0.807432	+	1.39851i	0.107205	+	0.994237i	$0.465810\pi$
$773$	−22.4489	+	38.8827i	−0.807432	+	1.39851i	−0.914637	+	0.404276i	$0.867524\pi$
$774$		0			0
$775$			31.9090i			1.14621i
$776$	−33.3060	−	36.3018i	−1.19562	−	1.30316i
$777$		0			0
$778$	−0.419090	+	4.11056i	−0.0150251	+	0.147371i
$779$			10.1427i			0.363399i
$780$		0			0
$781$			82.2503i			2.94315i
$782$	57.8322	+	5.89626i	2.06808	+	0.210850i
$783$		0			0
$784$	−2.39088	−	20.3091i	−0.0853886	−	0.725325i
$785$		−	10.3785i		−	0.370426i
$786$		0			0
$787$	−13.8178	+	23.9331i	−0.492551	+	0.853124i	−0.999963	−	0.00857979i	$-0.997269\pi$
$787$	−13.8178	+	23.9331i	−0.492551	+	0.853124i	0.507412	+	0.861704i	$0.330602\pi$
$788$	6.02058	+	18.1439i	0.214474	+	0.646348i
$789$		0			0
$790$	4.85513	+	0.495002i	0.172738	+	0.0176114i
$791$	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
$796$	5.05756	−	5.68788i	0.179260	−	0.201602i
$797$	−34.0592	−	19.6641i	−1.20644	−	0.696539i	−0.244460	−	0.969659i	$-0.578611\pi$
$797$	−34.0592	−	19.6641i	−1.20644	−	0.696539i	−0.961980	+	0.273121i	$0.911944\pi$
$798$		0			0
$799$	3.77916	+	2.18190i	0.133697	+	0.0771901i
$800$	−32.9279	−	18.3329i	−1.16418	−	0.648166i
$801$		0			0
$802$	29.7663	−	13.3641i	1.05108	−	0.471903i
$803$	−10.3255	+	5.96145i	−0.364380	+	0.210375i
$804$		0			0
$805$		−	29.8653i		−	1.05261i
$806$	−6.04415	+	23.6621i	−0.212896	+	0.833461i
$807$		0			0
$808$	−14.5940	+	3.24493i	−0.513413	+	0.114156i
$809$	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	$-0.646159\pi$
$811$	−25.2433			−0.886411			−0.443206	+	0.896420i	$0.646159\pi$
$812$	4.81281	+	0.991683i	0.168896	+	0.0348012i
$813$		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	0.832429	−	0.554132i	$-0.186950\pi$
$821$	−1.82456	−	3.16024i	−0.0636777	−	0.110293i	−0.896107	+	0.443839i	$0.853616\pi$
$822$		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
$826$	−9.87740	+	4.43464i	−0.343679	+	0.154301i
$827$	32.5482			1.13181			0.565906	−	0.824470i	$-0.308527\pi$
$827$	32.5482			1.13181			0.565906	+	0.824470i	$0.308527\pi$
$828$		0			0
$829$	−1.89091	+	1.09172i	−0.0656739	+	0.0379168i	−0.532477	−	0.846444i	$-0.678739\pi$
$829$	−1.89091	+	1.09172i	−0.0656739	+	0.0379168i	0.466804	+	0.884361i	$0.345406\pi$
$830$	−21.3308	−	2.17477i	−0.740402	−	0.0754873i
$831$		0			0
$832$	−20.9451	−	19.8319i	−0.726140	−	0.687547i
$833$	33.0147			1.14389
$834$		0			0
$835$	51.9257	−	29.9793i	1.79696	−	1.03748i
$836$	−35.0578	−	7.22369i	−1.21250	−	0.249836i
$837$		0			0
$838$	−12.3183	+	5.53054i	−0.425530	+	0.191049i
$839$	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
$842$	−38.0262	−	3.87694i	−1.31047	−	0.133608i
$843$		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
$848$	19.6238	−	45.5970i	0.673883	−	1.56581i
$849$		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	$-0.311011\pi$
$853$	32.6789			1.11891			0.559453	+	0.828862i	$0.311011\pi$
$854$	0.153845	+	0.342663i	0.00526446	+	0.0117257i
$855$		0			0
$856$	28.7810	−	6.39939i	0.983714	−	0.218727i
$857$	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	$0.0848759\pi$
$859$			15.4455i			0.526994i	−0.964660	+	0.263497i	$0.915124\pi$
$860$	23.1299	+	20.5667i	0.788722	+	0.701317i
$861$		0			0
$862$	10.1407	−	4.55284i	0.345393	−	0.155070i
$863$		−	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
$868$	8.74519	−	9.83510i	0.296831	−	0.333825i
$869$	−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
$874$	26.4926	+	2.70104i	0.896125	+	0.0913639i
$875$	−6.75436	−	3.89963i	−0.228339	−	0.131832i
$876$		0			0
$877$	−7.48245	+	12.9600i	−0.252664	+	0.437628i	−0.964259	−	0.264963i	$-0.914640\pi$
$877$	−7.48245	+	12.9600i	−0.252664	+	0.437628i	0.711594	+	0.702591i	$0.247974\pi$
$878$	12.5877	+	28.0369i	0.424813	+	0.946199i
$879$		0			0
$880$	9.66211	+	82.0739i	0.325710	+	2.76671i
$881$	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	$0.330067\pi$
$883$			51.1608i			1.72170i	−0.508861	+	0.860849i	$0.669933\pi$
$884$	35.7518	−	29.8396i	1.20246	−	1.00362i
$885$		0			0
$886$	−0.950553	+	9.32331i	−0.0319345	+	0.313223i
$887$	−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
$890$	−57.9201	+	26.0043i	−1.94149	+	0.871665i
$891$		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
$904$	24.2272	−	22.2279i	0.805786	−	0.739290i
$905$		−	56.5090i		−	1.87842i
$906$		0			0
$907$	−35.1223	+	20.2779i	−1.16622	+	0.673315i	−0.952786	−	0.303643i	$-0.901797\pi$
$907$	−35.1223	+	20.2779i	−1.16622	+	0.673315i	−0.213430	+	0.976958i	$0.568464\pi$
$908$	−6.74433	+	7.58488i	−0.223818	+	0.251713i
$909$		0			0
$910$	−17.1140	−	16.7178i	−0.567324	−	0.554190i
$911$	−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
$914$	−17.5341	+	7.87224i	−0.579975	+	0.260390i
$915$		0			0
$916$	24.9038	+	5.13146i	0.822846	+	0.169548i
$917$	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	$-0.142716\pi$
$920$	−13.3446	−	60.0166i	−0.439957	−	1.97869i
$921$		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
$926$	4.13351	−	40.5427i	0.135835	−	1.33231i
$927$		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
$932$	0.801159	+	0.165079i	0.0262428	+	0.00540736i
$933$		0			0
$934$	−2.02625	+	19.8740i	−0.0663009	+	0.650299i
$935$	−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	$0.200990\pi$
$938$	1.93485	−	18.9776i	0.0631750	−	0.619640i
$939$		0			0
$940$	0.931418	−	4.52033i	0.0303795	−	0.147437i
$941$	−28.9013			−0.942157			−0.471078	−	0.882091i	$-0.656135\pi$
$941$	−28.9013			−0.942157			−0.471078	+	0.882091i	$0.656135\pi$
$942$		0			0
$943$	18.8997	+	10.9117i	0.615458	+	0.355335i
$944$	−17.8679	+	13.3252i	−0.581550	+	0.433698i
$945$		0			0
$946$	3.93255	−	38.5716i	0.127858	−	1.25407i
$947$	−23.6288	−	40.9262i	−0.767831	−	1.32992i	−0.938737	−	0.344636i	$-0.888002\pi$
$947$	−23.6288	−	40.9262i	−0.767831	−	1.32992i	0.170905	−	0.985288i	$-0.445331\pi$
$948$		0			0
$949$	1.05123	−	7.02758i	0.0341243	−	0.228125i
$950$	16.3128	−	22.6004i	0.529256	−	0.733254i
$951$		0			0
$952$	−24.4972	+	5.44689i	−0.793958	+	0.176535i
$953$	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
$956$	5.34589	−	25.9445i	0.172898	−	0.839106i
$957$		0			0
$958$	52.2229	−	23.4464i	1.68725	−	0.757520i
$959$	7.90515	+	13.6921i	0.255271	+	0.442142i
$960$		0			0
$961$	8.06057			0.260018
$962$	−6.95322	−	24.7850i	−0.224181	−	0.799102i
$963$		0			0
$964$	27.5513	+	24.4981i	0.887367	+	0.789030i
$965$	−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	$0.961960\pi$
$968$	53.3547	−	48.9518i	1.71489	−	1.57337i
$969$		0			0
$970$	−68.2094	−	49.2330i	−2.19007	−	1.58078i
$971$	−14.6011	−	8.42995i	−0.468572	−	0.270530i	0.247070	−	0.968998i	$-0.420532\pi$
$971$	−14.6011	−	8.42995i	−0.468572	−	0.270530i	−0.715642	+	0.698468i	$0.753866\pi$
$972$		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
$982$	−20.1289	+	9.03725i	−0.642340	+	0.288390i
$983$		−	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
$986$	−1.65653	+	16.2477i	−0.0527546	+	0.517433i
$987$		0			0
$988$	16.3776	−	13.6693i	0.521042	−	0.434880i
$989$			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	$0.681365\pi$
$992$	13.1796	−	23.6720i	0.418451	−	0.751585i
$993$		0			0
$994$	10.8196	+	24.0989i	0.343178	+	0.764371i
$995$	6.49810	−	11.2550i	0.206004	−	0.356809i
$996$		0			0
$997$	−37.6297	−	21.7255i	−1.19174	−	0.688054i	−0.233043	−	0.972466i	$-0.574868\pi$
$997$	−37.6297	−	21.7255i	−1.19174	−	0.688054i	−0.958702	+	0.284412i	$0.908202\pi$
$998$	21.2031	+	2.16175i	0.671171	+	0.0684289i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.40692 - 0.143442i) q^{2} +(1.95885 + 0.403622i) q^{4} +3.41501 q^{5} +(-1.18985 - 0.686961i) q^{7} +(-2.69805 - 0.848845i) q^{8} +(-4.80464 - 0.489855i) q^{10} +(3.02491 + 5.23930i) q^{11} +(-3.56588 - 0.533406i) q^{13} +(1.57549 + 1.13717i) q^{14} +(3.67418 + 1.58127i) q^{16} +(-3.22892 + 5.59265i) q^{17} +(-1.47915 + 2.56196i) q^{19} +(6.68948 + 1.37837i) q^{20} +(-3.50427 - 7.80517i) q^{22} +(3.18261 + 5.51244i) q^{23} +6.66227 q^{25} +(4.94039 + 1.26196i) q^{26} +(-2.05347 - 1.82590i) q^{28} +(-1.54870 + 0.894140i) q^{29} +4.78951i q^{31} +(-4.94246 - 2.75175i) q^{32} +(5.34505 - 7.40526i) q^{34} +(-4.06335 - 2.34598i) q^{35} +(-2.52420 - 4.37205i) q^{37} +(2.44853 - 3.39230i) q^{38} +(-9.21385 - 2.89881i) q^{40} +(2.96921 - 1.71428i) q^{41} +(3.92452 + 2.26583i) q^{43} +(3.81064 + 11.4839i) q^{44} +(-3.68696 - 8.21208i) q^{46} -0.675737i q^{47} +(-2.55617 - 4.42742i) q^{49} +(-9.37328 - 0.955647i) q^{50} +(-6.76972 - 2.48413i) q^{52} -12.4101i q^{53} +(10.3301 + 17.8922i) q^{55} +(2.62715 + 2.86345i) q^{56} +(2.30715 - 1.03584i) q^{58} +(-2.78619 + 4.82582i) q^{59} +(0.167415 + 0.0966574i) q^{61} +(0.687016 - 6.73846i) q^{62} +(6.55892 + 4.58045i) q^{64} +(-12.1775 - 1.82158i) q^{65} +(-4.90885 - 8.50237i) q^{67} +(-8.58229 + 9.65190i) q^{68} +(5.38030 + 3.88345i) q^{70} +(11.7740 + 6.79775i) q^{71} +1.97079i q^{73} +(2.92422 + 6.51319i) q^{74} +(-3.93149 + 4.42147i) q^{76} -8.31198i q^{77} -1.01051 q^{79} +(12.5473 + 5.40005i) q^{80} +(-4.42334 + 1.98594i) q^{82} +4.43962 q^{83} +(-11.0268 + 19.0989i) q^{85} +(-5.19648 - 3.75078i) q^{86} +(-3.71400 - 16.7036i) q^{88} +(11.3849 - 6.57306i) q^{89} +(3.87643 + 3.08429i) q^{91} +(4.00931 + 12.0826i) q^{92} +(-0.0969289 + 0.950708i) q^{94} +(-5.05130 + 8.74910i) q^{95} +(15.0845 + 8.70903i) q^{97} +(2.96125 + 6.59568i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{10} - 4 q^{16} + 64 q^{25} - 48 q^{28} - 48 q^{40} + 20 q^{49} - 12 q^{52} + 16 q^{55} + 12 q^{58} - 72 q^{64} - 84 q^{76} + 80 q^{79} - 12 q^{82} - 12 q^{88} - 24 q^{94} + 24 q^{97}+O(q^{100}) \) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more