LMFDB - Embedded newform 276.2.k.a.5.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(5,276)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("276.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.k (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			5.6
Character	$\chi$	$=$	276.5
Dual form			276.2.k.a.221.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951673 + 1.44718i) q^{3} +(-0.185142 + 1.28769i) q^{5} +(-4.35485 + 1.98879i) q^{7} +(-1.18864 + 2.75448i) q^{9} +O(q^{10})$	\(q+(0.951673 + 1.44718i) q^{3} +(-0.185142 + 1.28769i) q^{5} +(-4.35485 + 1.98879i) q^{7} +(-1.18864 + 2.75448i) q^{9} +(0.951568 - 0.279406i) q^{11} +(-0.564722 + 1.23657i) q^{13} +(-2.03971 + 0.957526i) q^{15} +(4.94721 - 3.17938i) q^{17} +(-0.682840 + 1.06252i) q^{19} +(-7.02253 - 4.40956i) q^{21} +(3.50391 - 3.27454i) q^{23} +(3.17360 + 0.931853i) q^{25} +(-5.11741 + 0.901195i) q^{27} +(5.05992 + 7.87338i) q^{29} +(-0.896140 - 1.03420i) q^{31} +(1.30993 + 1.11118i) q^{33} +(-1.75468 - 5.97590i) q^{35} +(-4.20207 + 0.604167i) q^{37} +(-2.32696 + 0.359557i) q^{39} +(4.80804 + 0.691291i) q^{41} +(2.85232 + 2.47155i) q^{43} +(-3.32684 - 2.04056i) q^{45} +9.10570i q^{47} +(10.4254 - 12.0316i) q^{49} +(9.30924 + 4.13375i) q^{51} +(-4.41374 - 9.66473i) q^{53} +(0.183612 + 1.27705i) q^{55} +(-2.18749 + 0.0229818i) q^{57} +(-5.05009 - 2.30630i) q^{59} +(8.81714 - 7.64010i) q^{61} +(-0.301750 - 14.3593i) q^{63} +(-1.48776 - 0.956126i) q^{65} +(-0.532570 + 1.81377i) q^{67} +(8.07341 + 1.95449i) q^{69} +(0.175016 - 0.596050i) q^{71} +(-3.10347 - 1.99448i) q^{73} +(1.67168 + 5.47958i) q^{75} +(-3.58826 + 3.10924i) q^{77} +(-10.5050 - 4.79746i) q^{79} +(-6.17429 - 6.54815i) q^{81} +(0.410479 + 2.85495i) q^{83} +(3.17811 + 6.95909i) q^{85} +(-6.57878 + 14.8155i) q^{87} +(9.24637 - 10.6709i) q^{89} -6.50819i q^{91} +(0.643838 - 2.28109i) q^{93} +(-1.24177 - 1.07600i) q^{95} +(-9.60720 - 1.38131i) q^{97} +(-0.361453 + 2.95318i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{3} + 6 q^{9}+O(q^{10}) $ 80 * q - 2 * q^3 + 6 * q^9	$ 80 q - 2 q^{3} + 6 q^{9} - 4 q^{13} + 11 q^{15} + 33 q^{21} + 25 q^{27} + 20 q^{31} + 11 q^{33} - 44 q^{37} - 18 q^{39} - 44 q^{43} - 100 q^{49} - 98 q^{55} - 33 q^{57} - 44 q^{61} - 55 q^{63} - 22 q^{67} - 41 q^{69} - 26 q^{73} - 65 q^{75} - 44 q^{79} - 42 q^{81} + 2 q^{85} - 64 q^{87} - 46 q^{93} + 66 q^{97} - 66 q^{99}+O(q^{100}) $ 80 * q - 2 * q^3 + 6 * q^9 - 4 * q^13 + 11 * q^15 + 33 * q^21 + 25 * q^27 + 20 * q^31 + 11 * q^33 - 44 * q^37 - 18 * q^39 - 44 * q^43 - 100 * q^49 - 98 * q^55 - 33 * q^57 - 44 * q^61 - 55 * q^63 - 22 * q^67 - 41 * q^69 - 26 * q^73 - 65 * q^75 - 44 * q^79 - 42 * q^81 + 2 * q^85 - 64 * q^87 - 46 * q^93 + 66 * q^97 - 66 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{1}{22}\right)$	$1$	$-1$

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			0
$2$		0			0
$3$	0.951673	+	1.44718i	0.549449	+	0.835527i
$3$	0.951673	+	1.44718i	0.549449	+	0.835527i
$4$		0			0
$5$	−0.185142	+	1.28769i	−0.0827978	+	0.575872i	0.905617	+	0.424096i	$0.139408\pi$
$5$	−0.185142	+	1.28769i	−0.0827978	+	0.575872i	−0.988415	+	0.151775i	$0.951501\pi$
$6$		0			0
$7$	−4.35485	+	1.98879i	−1.64598	+	0.751694i	−0.999933	−	0.0116037i	$-0.996306\pi$
$7$	−4.35485	+	1.98879i	−1.64598	+	0.751694i	−0.646047	+	0.763298i	$0.723579\pi$
$8$		0			0
$9$	−1.18864	+	2.75448i	−0.396212	+	0.918159i
$10$		0			0
$11$	0.951568	−	0.279406i	0.286909	−	0.0842440i	−0.135112	−	0.990830i	$-0.543139\pi$
$11$	0.951568	−	0.279406i	0.286909	−	0.0842440i	0.422020	+	0.906586i	$0.361321\pi$
$12$		0			0
$13$	−0.564722	+	1.23657i	−0.156626	+	0.342962i	−0.971635	−	0.236485i	$-0.924004\pi$
$13$	−0.564722	+	1.23657i	−0.156626	+	0.342962i	0.815009	+	0.579448i	$0.196732\pi$
$14$		0			0
$15$	−2.03971	+	0.957526i	−0.526650	+	0.247232i
$16$		0			0
$17$	4.94721	−	3.17938i	1.19987	−	0.771112i	0.220939	−	0.975288i	$-0.429088\pi$
$17$	4.94721	−	3.17938i	1.19987	−	0.771112i	0.978934	+	0.204176i	$0.0654514\pi$
$18$		0			0
$19$	−0.682840	+	1.06252i	−0.156654	+	0.243759i	−0.910705	−	0.413057i	$-0.864461\pi$
$19$	−0.682840	+	1.06252i	−0.156654	+	0.243759i	0.754051	+	0.656816i	$0.228097\pi$
$20$		0			0
$21$	−7.02253	−	4.40956i	−1.53244	−	0.962244i
$22$		0			0
$23$	3.50391	−	3.27454i	0.730616	−	0.682788i
$23$	3.50391	−	3.27454i	0.730616	−	0.682788i
$24$		0			0
$25$	3.17360	+	0.931853i	0.634720	+	0.186371i
$26$		0			0
$27$	−5.11741	+	0.901195i	−0.984845	+	0.173435i
$28$		0			0
$29$	5.05992	+	7.87338i	0.939603	+	1.46205i	0.886106	+	0.463482i	$0.153400\pi$
$29$	5.05992	+	7.87338i	0.939603	+	1.46205i	0.0534965	+	0.998568i	$0.482963\pi$
$30$		0			0
$31$	−0.896140	−	1.03420i	−0.160951	−	0.185748i	0.669545	−	0.742771i	$-0.266489\pi$
$31$	−0.896140	−	1.03420i	−0.160951	−	0.185748i	−0.830497	+	0.557023i	$0.811943\pi$
$32$		0			0
$33$	1.30993	+	1.11118i	0.228030	+	0.193432i
$34$		0			0
$35$	−1.75468	−	5.97590i	−0.296596	−	1.01011i
$36$		0			0
$37$	−4.20207	+	0.604167i	−0.690817	+	0.0993245i	−0.478777	−	0.877937i	$-0.658920\pi$
$37$	−4.20207	+	0.604167i	−0.690817	+	0.0993245i	−0.212040	+	0.977261i	$0.568011\pi$
$38$		0			0
$39$	−2.32696	+	0.359557i	−0.372612	+	0.0575752i
$40$		0			0
$41$	4.80804	+	0.691291i	0.750889	+	0.107962i	0.507124	−	0.861873i	$-0.330708\pi$
$41$	4.80804	+	0.691291i	0.750889	+	0.107962i	0.243765	+	0.969834i	$0.421618\pi$
$42$		0			0
$43$	2.85232	+	2.47155i	0.434975	+	0.376908i	0.844646	−	0.535326i	$-0.179811\pi$
$43$	2.85232	+	2.47155i	0.434975	+	0.376908i	−0.409671	+	0.912233i	$0.634357\pi$
$44$		0			0
$45$	−3.32684	−	2.04056i	−0.495936	−	0.304189i
$46$		0			0
$47$			9.10570i			1.32820i	0.747643	+	0.664101i	$0.231186\pi$
$47$			9.10570i			1.32820i	−0.747643	+	0.664101i	$0.768814\pi$
$48$		0			0
$49$	10.4254	−	12.0316i	1.48935	−	1.71880i
$50$		0			0
$51$	9.30924	+	4.13375i	1.30355	+	0.578841i
$52$		0			0
$53$	−4.41374	−	9.66473i	−0.606273	−	1.32755i	−0.925094	−	0.379738i	$-0.876014\pi$
$53$	−4.41374	−	9.66473i	−0.606273	−	1.32755i	0.318821	−	0.947815i	$-0.396713\pi$
$54$		0			0
$55$	0.183612	+	1.27705i	0.0247583	+	0.172198i
$56$		0			0
$57$	−2.18749	+	0.0229818i	−0.289741	+	0.00304401i
$58$		0			0
$59$	−5.05009	−	2.30630i	−0.657466	−	0.300255i	0.0586057	−	0.998281i	$-0.481335\pi$
$59$	−5.05009	−	2.30630i	−0.657466	−	0.300255i	−0.716072	+	0.698026i	$0.754062\pi$
$60$		0			0
$61$	8.81714	−	7.64010i	1.12892	−	0.978214i	0.129009	−	0.991643i	$-0.458820\pi$
$61$	8.81714	−	7.64010i	1.12892	−	0.978214i	0.999910	+	0.0134292i	$0.00427478\pi$
$62$		0			0
$63$	−0.301750	−	14.3593i	−0.0380170	−	1.80910i
$64$		0			0
$65$	−1.48776	−	0.956126i	−0.184534	−	0.118593i
$66$		0			0
$67$	−0.532570	+	1.81377i	−0.0650638	+	0.221587i	−0.985607	−	0.169055i	$-0.945929\pi$
$67$	−0.532570	+	1.81377i	−0.0650638	+	0.221587i	0.920543	+	0.390641i	$0.127747\pi$
$68$		0			0
$69$	8.07341	+	1.95449i	0.971925	+	0.235293i
$70$		0			0
$71$	0.175016	−	0.596050i	0.0207706	−	0.0707381i	−0.948456	−	0.316910i	$-0.897355\pi$
$71$	0.175016	−	0.596050i	0.0207706	−	0.0707381i	0.969226	+	0.246172i	$0.0791728\pi$
$72$		0			0
$73$	−3.10347	−	1.99448i	−0.363234	−	0.233436i	0.346274	−	0.938133i	$-0.387447\pi$
$73$	−3.10347	−	1.99448i	−0.363234	−	0.233436i	−0.709508	+	0.704697i	$0.751083\pi$
$74$		0			0
$75$	1.67168	+	5.47958i	0.193028	+	0.632727i
$76$		0			0
$77$	−3.58826	+	3.10924i	−0.408920	+	0.354331i
$78$		0			0
$79$	−10.5050	−	4.79746i	−1.18190	−	0.539756i	−0.275142	−	0.961404i	$-0.588725\pi$
$79$	−10.5050	−	4.79746i	−1.18190	−	0.539756i	−0.906760	+	0.421647i	$0.861452\pi$
$80$		0			0
$81$	−6.17429	−	6.54815i	−0.686032	−	0.727572i
$82$		0			0
$83$	0.410479	+	2.85495i	0.0450559	+	0.313371i	0.999869	+	0.0161650i	$0.00514571\pi$
$83$	0.410479	+	2.85495i	0.0450559	+	0.313371i	−0.954813	+	0.297206i	$0.903945\pi$
$84$		0			0
$85$	3.17811	+	6.95909i	0.344715	+	0.754820i
$86$		0			0
$87$	−6.57878	+	14.8155i	−0.705320	+	1.58839i
$88$		0			0
$89$	9.24637	−	10.6709i	0.980114	−	1.13111i	−0.0112456	−	0.999937i	$-0.503580\pi$
$89$	9.24637	−	10.6709i	0.980114	−	1.13111i	0.991359	−	0.131175i	$-0.0418749\pi$
$90$		0			0
$91$		−	6.50819i		−	0.682244i
$92$		0			0
$93$	0.643838	−	2.28109i	0.0667629	−	0.236538i
$94$		0			0
$95$	−1.24177	−	1.07600i	−0.127403	−	0.110395i
$96$		0			0
$97$	−9.60720	−	1.38131i	−0.975463	−	0.140250i	−0.363893	−	0.931441i	$-0.618553\pi$
$97$	−9.60720	−	1.38131i	−0.975463	−	0.140250i	−0.611570	+	0.791190i	$0.709462\pi$
$98$		0			0
$99$	−0.361453	+	2.95318i	−0.0363273	+	0.296806i
$100$		0			0
$101$	14.8811	−	2.13958i	1.48072	−	0.212896i	0.645904	−	0.763419i	$-0.276481\pi$
$101$	14.8811	−	2.13958i	1.48072	−	0.212896i	0.834820	+	0.550523i	$0.185572\pi$
$102$		0			0
$103$	−0.679856	−	2.31538i	−0.0669882	−	0.228141i	0.919194	−	0.393805i	$-0.128841\pi$
$103$	−0.679856	−	2.31538i	−0.0669882	−	0.228141i	−0.986182	+	0.165664i	$0.947023\pi$
$104$		0			0
$105$	6.97830	−	8.22644i	0.681012	−	0.802818i
$106$		0			0
$107$	−1.14844	−	1.32538i	−0.111024	−	0.128129i	0.697517	−	0.716568i	$-0.254288\pi$
$107$	−1.14844	−	1.32538i	−0.111024	−	0.128129i	−0.808541	+	0.588439i	$0.799743\pi$
$108$		0			0
$109$	8.16742	+	12.7088i	0.782297	+	1.21728i	0.971895	+	0.235416i	$0.0756454\pi$
$109$	8.16742	+	12.7088i	0.782297	+	1.21728i	−0.189597	+	0.981862i	$0.560718\pi$
$110$		0			0
$111$	−4.87334	−	5.50617i	−0.462557	−	0.522623i
$112$		0			0
$113$	−10.4609	−	3.07160i	−0.984079	−	0.288952i	−0.250172	−	0.968201i	$-0.580487\pi$
$113$	−10.4609	−	3.07160i	−0.984079	−	0.288952i	−0.733907	+	0.679250i	$0.762305\pi$
$114$		0			0
$115$	3.56786	+	5.11820i	0.332705	+	0.477275i
$116$		0			0
$117$	−2.73485	−	3.02535i	−0.252837	−	0.279693i
$118$		0			0
$119$	−15.2212	+	23.6847i	−1.39533	+	2.17117i
$120$		0			0
$121$	−8.42637	+	5.41530i	−0.766034	+	0.492300i
$122$		0			0
$123$	3.57526	+	7.61596i	0.322370	+	0.686708i
$124$		0			0
$125$	−4.48963	+	9.83092i	−0.401565	+	0.879304i
$126$		0			0
$127$	−1.41705	+	0.416083i	−0.125743	+	0.0369214i	−0.343998	−	0.938970i	$-0.611781\pi$
$127$	−1.41705	+	0.416083i	−0.125743	+	0.0369214i	0.218256	+	0.975892i	$0.429963\pi$
$128$		0			0
$129$	−0.862291	+	6.47991i	−0.0759205	+	0.570525i
$130$		0			0
$131$	16.0382	−	7.32438i	1.40126	−	0.639934i	0.435695	−	0.900095i	$-0.356503\pi$
$131$	16.0382	−	7.32438i	1.40126	−	0.639934i	0.965565	+	0.260161i	$0.0837755\pi$
$132$		0			0
$133$	0.860535	−	5.98515i	0.0746178	−	0.518978i
$134$		0			0
$135$	−0.213013	−	6.75647i	−0.0183332	−	0.581505i
$136$		0			0
$137$	3.29596			0.281593			0.140797	−	0.990039i	$-0.455034\pi$
$137$	3.29596			0.281593			0.140797	+	0.990039i	$0.455034\pi$
$138$		0			0
$139$	11.7850			0.999590			0.499795	−	0.866144i	$-0.333409\pi$
$139$	11.7850			0.999590			0.499795	+	0.866144i	$0.333409\pi$
$140$		0			0
$141$	−13.1775	+	8.66565i	−1.10975	+	0.729779i
$142$		0			0
$143$	−0.191867	+	1.33447i	−0.0160447	+	0.111594i
$144$		0			0
$145$	−11.0753	+	5.05790i	−0.919750	+	0.420036i
$146$		0			0
$147$	27.3334	+	3.63729i	2.25442	+	0.299999i
$148$		0			0
$149$	−8.39744	+	2.46571i	−0.687945	+	0.201999i	−0.606979	−	0.794718i	$-0.707619\pi$
$149$	−8.39744	+	2.46571i	−0.687945	+	0.201999i	−0.0809662	+	0.996717i	$0.525801\pi$
$150$		0			0
$151$	−5.61205	+	12.2887i	−0.456702	+	1.00004i	0.531525	+	0.847042i	$0.321619\pi$
$151$	−5.61205	+	12.2887i	−0.456702	+	1.00004i	−0.988227	+	0.152995i	$0.951108\pi$
$152$		0			0
$153$	2.87709	+	17.4061i	0.232599	+	1.40720i
$154$		0			0
$155$	1.49764	−	0.962475i	0.120293	−	0.0773079i
$156$		0			0
$157$	−10.0006	+	15.5613i	−0.798138	+	1.24193i	0.168480	+	0.985705i	$0.446114\pi$
$157$	−10.0006	+	15.5613i	−0.798138	+	1.24193i	−0.966618	+	0.256222i	$0.917522\pi$
$158$		0			0
$159$	9.78614	−	15.5851i	0.776091	−	1.23598i
$160$		0			0
$161$	−8.74664	+	21.2287i	−0.689332	+	1.67306i
$162$		0			0
$163$	10.6289	+	3.12091i	0.832516	+	0.244449i	0.670097	−	0.742273i	$-0.266252\pi$
$163$	10.6289	+	3.12091i	0.832516	+	0.244449i	0.162419	+	0.986722i	$0.448071\pi$
$164$		0			0
$165$	−1.67338	+	1.48106i	−0.130273	+	0.115300i
$166$		0			0
$167$	−7.98537	−	12.4255i	−0.617927	−	0.961513i	−0.999312	−	0.0370966i	$-0.988189\pi$
$167$	−7.98537	−	12.4255i	−0.617927	−	0.961513i	0.381385	−	0.924416i	$-0.375447\pi$
$168$		0			0
$169$	7.30300	+	8.42811i	0.561769	+	0.648316i
$170$		0			0
$171$	−2.11504	−	3.14382i	−0.161741	−	0.240414i
$172$		0			0
$173$	0.376323	+	1.28164i	0.0286113	+	0.0974412i	0.972561	−	0.232649i	$-0.0747392\pi$
$173$	0.376323	+	1.28164i	0.0286113	+	0.0974412i	−0.943950	+	0.330090i	$0.892921\pi$
$174$		0			0
$175$	−15.6738	+	2.25356i	−1.18483	+	0.170353i
$176$		0			0
$177$	−1.46842	−	9.50322i	−0.110373	−	0.714306i
$178$		0			0
$179$	−20.4039	−	2.93364i	−1.52506	−	0.219271i	−0.671791	−	0.740741i	$-0.734475\pi$
$179$	−20.4039	−	2.93364i	−1.52506	−	0.219271i	−0.853270	+	0.521470i	$0.825384\pi$
$180$		0			0
$181$	−12.1658	−	10.5417i	−0.904274	−	0.783558i	0.0726026	−	0.997361i	$-0.476870\pi$
$181$	−12.1658	−	10.5417i	−0.904274	−	0.783558i	−0.976877	+	0.213803i	$0.931415\pi$
$182$		0			0
$183$	19.4476	+	5.48908i	1.43761	+	0.405765i
$184$		0			0
$185$		−	5.52282i		−	0.406046i
$186$		0			0
$187$	3.81927	−	4.40767i	0.279292	−	0.322321i
$188$		0			0
$189$	20.4933	−	14.1020i	1.49067	−	1.02577i
$190$		0			0
$191$	−2.59925	−	5.69155i	−0.188075	−	0.411826i	0.791982	−	0.610545i	$-0.209049\pi$
$191$	−2.59925	−	5.69155i	−0.188075	−	0.411826i	−0.980057	+	0.198718i	$0.936322\pi$
$192$		0			0
$193$	−2.42322	−	16.8539i	−0.174427	−	1.21317i	−0.869392	−	0.494124i	$-0.835489\pi$
$193$	−2.42322	−	16.8539i	−0.174427	−	1.21317i	0.694964	−	0.719044i	$-0.255420\pi$
$194$		0			0
$195$	−0.0321795	−	3.06297i	−0.00230443	−	0.219344i
$196$		0			0
$197$	12.0536	+	5.50469i	0.858782	+	0.392193i	0.795609	−	0.605810i	$-0.207151\pi$
$197$	12.0536	+	5.50469i	0.858782	+	0.392193i	0.0631727	+	0.998003i	$0.479878\pi$
$198$		0			0
$199$	12.9624	−	11.2319i	0.918877	−	0.796212i	−0.0605176	−	0.998167i	$-0.519275\pi$
$199$	12.9624	−	11.2319i	0.918877	−	0.796212i	0.979395	+	0.201956i	$0.0647297\pi$
$200$		0			0
$201$	−3.13167	+	0.955391i	−0.220891	+	0.0673881i
$202$		0			0
$203$	−37.6937	−	24.2243i	−2.64558	−	1.70021i
$204$		0			0
$205$	−1.78034	+	6.06326i	−0.124344	+	0.423477i
$206$		0			0
$207$	4.85476	+	13.5437i	0.337429	+	0.941351i
$208$		0			0
$209$	−0.352895	+	1.20185i	−0.0244103	+	0.0831337i
$210$		0			0
$211$	12.2658	+	7.88273i	0.844411	+	0.542670i	0.889827	−	0.456298i	$-0.150825\pi$
$211$	12.2658	+	7.88273i	0.844411	+	0.542670i	−0.0454162	+	0.998968i	$0.514461\pi$
$212$		0			0
$213$	1.02915	−	0.313966i	0.0705160	−	0.0215126i
$214$		0			0
$215$	−3.71067	+	3.21531i	−0.253065	+	0.219282i
$216$		0			0
$217$	5.95937	+	2.72155i	0.404548	+	0.184751i
$218$		0			0
$219$	−0.0671266	−	6.38936i	−0.00453599	−	0.431753i
$220$		0			0
$221$	1.13772	+	7.91302i	0.0765314	+	0.532288i
$222$		0			0
$223$	−7.34733	−	16.0884i	−0.492013	−	1.07736i	−0.978983	−	0.203940i	$-0.934625\pi$
$223$	−7.34733	−	16.0884i	−0.492013	−	1.07736i	0.486970	−	0.873419i	$-0.338102\pi$
$224$		0			0
$225$	−6.33903	+	7.63398i	−0.422602	+	0.508932i
$226$		0			0
$227$	3.28404	−	3.78998i	0.217969	−	0.251550i	−0.636226	−	0.771503i	$-0.719505\pi$
$227$	3.28404	−	3.78998i	0.217969	−	0.251550i	0.854195	+	0.519953i	$0.174051\pi$
$228$		0			0
$229$		−	16.1841i		−	1.06947i	−0.845019	−	0.534737i	$-0.820411\pi$
$229$		−	16.1841i		−	1.06947i	0.845019	−	0.534737i	$-0.179589\pi$
$230$		0			0
$231$	−7.91447	−	2.23386i	−0.520734	−	0.146977i
$232$		0			0
$233$	−6.93408	−	6.00841i	−0.454266	−	0.393624i	0.397453	−	0.917623i	$-0.369894\pi$
$233$	−6.93408	−	6.00841i	−0.454266	−	0.393624i	−0.851719	+	0.523999i	$0.824440\pi$
$234$		0			0
$235$	−11.7253	−	1.68584i	−0.764874	−	0.109972i
$236$		0			0
$237$	−3.05453	−	19.7682i	−0.198413	−	1.28408i
$238$		0			0
$239$	25.0967	−	3.60836i	1.62337	−	0.233405i	0.730235	−	0.683196i	$-0.239410\pi$
$239$	25.0967	−	3.60836i	1.62337	−	0.233405i	0.893134	+	0.449791i	$0.148501\pi$
$240$		0			0
$241$	6.62692	+	22.5692i	0.426877	+	1.45381i	0.839726	+	0.543010i	$0.182716\pi$
$241$	6.62692	+	22.5692i	0.426877	+	1.45381i	−0.412849	+	0.910800i	$0.635466\pi$
$242$		0			0
$243$	3.60042	−	15.1670i	0.230967	−	0.972962i
$244$		0			0
$245$	13.5627	+	15.6522i	0.866491	+	0.999984i
$246$		0			0
$247$	−0.928265	−	1.44441i	−0.0590641	−	0.0919055i
$248$		0			0
$249$	−3.74097	+	3.31101i	−0.237074	+	0.209827i
$250$		0			0
$251$	4.95506	+	1.45494i	0.312761	+	0.0918349i	0.434346	−	0.900746i	$-0.356980\pi$
$251$	4.95506	+	1.45494i	0.312761	+	0.0918349i	−0.121585	+	0.992581i	$0.538798\pi$
$252$		0			0
$253$	2.41929	−	4.09496i	0.152099	−	0.257448i
$254$		0			0
$255$	−7.04651	+	11.2221i	−0.441269	+	0.702753i
$256$		0			0
$257$	−8.44638	+	13.1428i	−0.526871	+	0.819827i	−0.998064	−	0.0622032i	$-0.980187\pi$
$257$	−8.44638	+	13.1428i	−0.526871	+	0.819827i	0.471193	+	0.882030i	$0.343824\pi$
$258$		0			0
$259$	17.0979	−	10.9881i	1.06241	−	0.682769i
$260$		0			0
$261$	−27.7015	+	4.57883i	−1.71468	+	0.283422i
$262$		0			0
$263$	−5.29632	+	11.5973i	−0.326585	+	0.715122i	−0.999702	−	0.0244143i	$-0.992228\pi$
$263$	−5.29632	+	11.5973i	−0.326585	+	0.715122i	0.673117	+	0.739536i	$0.264955\pi$
$264$		0			0
$265$	13.2623	−	3.89417i	0.814698	−	0.239217i
$266$		0			0
$267$	24.2422	+	3.22594i	1.48360	+	0.197424i
$268$		0			0
$269$	7.39685	−	3.37803i	0.450994	−	0.205962i	−0.176951	−	0.984220i	$-0.556624\pi$
$269$	7.39685	−	3.37803i	0.450994	−	0.205962i	0.627945	+	0.778258i	$0.283896\pi$
$270$		0			0
$271$	2.31867	−	16.1267i	0.140849	−	0.979630i	−0.789708	−	0.613483i	$-0.789768\pi$
$271$	2.31867	−	16.1267i	0.140849	−	0.979630i	0.930557	−	0.366146i	$-0.119323\pi$
$272$		0			0
$273$	9.41850	−	6.19367i	0.570034	−	0.374858i
$274$		0			0
$275$	3.28026			0.197807
$276$		0			0
$277$	−5.86011			−0.352100			−0.176050	−	0.984381i	$-0.556332\pi$
$277$	−5.86011			−0.352100			−0.176050	+	0.984381i	$0.556332\pi$
$278$		0			0
$279$	3.91387	−	1.23911i	0.234317	−	0.0741834i
$280$		0			0
$281$	0.0972735	−	0.676552i	0.00580285	−	0.0403597i	−0.986714	−	0.162465i	$-0.948056\pi$
$281$	0.0972735	−	0.676552i	0.00580285	−	0.0403597i	0.992517	+	0.122105i	$0.0389646\pi$
$282$		0			0
$283$	14.3871	−	6.57035i	0.855221	−	0.390567i	0.0609582	−	0.998140i	$-0.480584\pi$
$283$	14.3871	−	6.57035i	0.855221	−	0.390567i	0.794263	+	0.607574i	$0.207857\pi$
$284$		0			0
$285$	0.375403	−	2.82107i	0.0222369	−	0.167106i
$286$		0			0
$287$	−22.3131	+	6.55173i	−1.31710	+	0.386736i
$288$		0			0
$289$	7.30435	−	15.9943i	0.429668	−	0.940841i
$290$		0			0
$291$	−7.14392	−	15.2179i	−0.418784	−	0.892087i
$292$		0			0
$293$	18.1424	−	11.6594i	1.05989	−	0.681152i	0.110065	−	0.993924i	$-0.464894\pi$
$293$	18.1424	−	11.6594i	1.05989	−	0.681152i	0.949828	+	0.312773i	$0.101258\pi$
$294$		0			0
$295$	3.90478	−	6.07596i	0.227345	−	0.353756i
$296$		0			0
$297$	−4.61776	+	2.28738i	−0.267950	+	0.132727i
$298$		0			0
$299$	2.07045	+	6.18203i	0.119737	+	0.357516i
$300$		0			0
$301$	−17.3368	−	5.09055i	−0.999279	−	0.293415i
$302$		0			0
$303$	17.2583	+	19.4994i	0.991462	+	1.12021i
$304$		0			0
$305$	8.20564	+	12.7682i	0.469854	+	0.731107i
$306$		0			0
$307$	3.44223	+	3.97255i	0.196459	+	0.226725i	0.845428	−	0.534089i	$-0.179345\pi$
$307$	3.44223	+	3.97255i	0.196459	+	0.226725i	−0.648970	+	0.760814i	$0.724800\pi$
$308$		0			0
$309$	2.70376	−	3.18735i	0.153811	−	0.181322i
$310$		0			0
$311$	−6.93034	−	23.6026i	−0.392983	−	1.33838i	−0.884105	−	0.467288i	$-0.845231\pi$
$311$	−6.93034	−	23.6026i	−0.392983	−	1.33838i	0.491122	−	0.871091i	$-0.336587\pi$
$312$		0			0
$313$	3.13553	−	0.450821i	0.177231	−	0.0254819i	−0.0531281	−	0.998588i	$-0.516919\pi$
$313$	3.13553	−	0.450821i	0.177231	−	0.0254819i	0.230359	+	0.973106i	$0.426010\pi$
$314$		0			0
$315$	18.5462	+	2.26994i	1.04496	+	0.127897i
$316$		0			0
$317$	6.90218	+	0.992384i	0.387665	+	0.0557378i	0.333392	−	0.942788i	$-0.391807\pi$
$317$	6.90218	+	0.992384i	0.387665	+	0.0557378i	0.0542731	+	0.998526i	$0.482716\pi$
$318$		0			0
$319$	7.01472	+	6.07829i	0.392749	+	0.340319i
$320$		0			0
$321$	0.825108	−	2.92332i	0.0460530	−	0.163164i
$322$		0			0
$323$			7.42751i			0.413278i
$324$		0			0
$325$	−2.94450	+	3.39814i	−0.163332	+	0.188495i
$326$		0			0
$327$	−10.6191	+	23.9143i	−0.587237	+	1.32246i
$328$		0			0
$329$	−18.1094	−	39.6540i	−0.998402	−	2.18619i
$330$		0			0
$331$	−0.553887	−	3.85237i	−0.0304444	−	0.211745i	0.968921	−	0.247371i	$-0.0795666\pi$
$331$	−0.553887	−	3.85237i	−0.0304444	−	0.211745i	−0.999365	+	0.0356258i	$0.988658\pi$
$332$		0			0
$333$	3.33058	−	12.2927i	0.182514	−	0.673633i
$334$		0			0
$335$	−2.23697	−	1.02159i	−0.122218	−	0.0558153i
$336$		0			0
$337$	−25.3333	+	21.9514i	−1.37999	+	1.19577i	−0.422831	+	0.906209i	$0.638963\pi$
$337$	−25.3333	+	21.9514i	−1.37999	+	1.19577i	−0.957160	+	0.289560i	$0.906491\pi$
$338$		0			0
$339$	−5.51021	−	18.0619i	−0.299274	−	0.980989i
$340$		0			0
$341$	−1.14170	−	0.733726i	−0.0618265	−	0.0397335i
$342$		0			0
$343$	−12.0313	+	40.9748i	−0.649629	+	2.21243i
$344$		0			0
$345$	−4.01150	+	10.0342i	−0.215972	+	0.540222i
$346$		0			0
$347$	−0.364796	+	1.24238i	−0.0195833	+	0.0666944i	−0.968705	−	0.248215i	$-0.920156\pi$
$347$	−0.364796	+	1.24238i	−0.0195833	+	0.0666944i	0.949122	+	0.314910i	$0.101974\pi$
$348$		0			0
$349$	−13.6336	−	8.76179i	−0.729791	−	0.469008i	0.122240	−	0.992501i	$-0.460992\pi$
$349$	−13.6336	−	8.76179i	−0.729791	−	0.469008i	−0.852030	+	0.523493i	$0.824629\pi$
$350$		0			0
$351$	1.77552	−	6.83695i	0.0947704	−	0.364929i
$352$		0			0
$353$	−3.64971	+	3.16249i	−0.194254	+	0.168322i	−0.746557	−	0.665321i	$-0.768295\pi$
$353$	−3.64971	+	3.16249i	−0.194254	+	0.168322i	0.552303	+	0.833643i	$0.313749\pi$
$354$		0			0
$355$	0.735123	+	0.335720i	0.0390163	+	0.0178181i
$356$		0			0
$357$	−48.7615	+	0.512288i	−2.58073	+	0.0271132i
$358$		0			0
$359$	−3.47319	−	24.1566i	−0.183308	−	1.27494i	−0.848874	−	0.528596i	$-0.822719\pi$
$359$	−3.47319	−	24.1566i	−0.183308	−	1.27494i	0.665566	−	0.746339i	$-0.268190\pi$
$360$		0			0
$361$	7.23021	+	15.8319i	0.380537	+	0.833260i
$362$		0			0
$363$	−15.8560	−	7.04085i	−0.832227	−	0.369549i
$364$		0			0
$365$	3.14285	−	3.62704i	0.164504	−	0.189848i
$366$		0			0
$367$			9.38571i			0.489930i	0.969532	+	0.244965i	$0.0787765\pi$
$367$			9.38571i			0.489930i	−0.969532	+	0.244965i	$0.921223\pi$
$368$		0			0
$369$	−7.61915	+	12.4219i	−0.396637	+	0.646660i
$370$		0			0
$371$	38.4423	+	33.3105i	1.99583	+	1.72939i
$372$		0			0
$373$	−12.8495	−	1.84748i	−0.665323	−	0.0956589i	−0.198625	−	0.980076i	$-0.563647\pi$
$373$	−12.8495	−	1.84748i	−0.665323	−	0.0956589i	−0.466698	+	0.884417i	$0.654557\pi$
$374$		0			0
$375$	−18.4997	+	2.85854i	−0.955322	+	0.147614i
$376$		0			0
$377$	−12.5934	+	1.81066i	−0.648594	+	0.0932538i
$378$		0			0
$379$	4.94683	+	16.8474i	0.254102	+	0.865391i	0.983439	+	0.181237i	$0.0580102\pi$
$379$	4.94683	+	16.8474i	0.254102	+	0.865391i	−0.729338	+	0.684154i	$0.760172\pi$
$380$		0			0
$381$	−1.95071	−	1.65474i	−0.0999379	−	0.0847750i
$382$		0			0
$383$	13.8233	+	15.9530i	0.706340	+	0.815160i	0.989594	−	0.143885i	$-0.0459595\pi$
$383$	13.8233	+	15.9530i	0.706340	+	0.815160i	−0.283254	+	0.959045i	$0.591414\pi$
$384$		0			0
$385$	−3.33940	−	5.19621i	−0.170192	−	0.264823i
$386$		0			0
$387$	−10.1982	+	4.91887i	−0.518403	+	0.250040i
$388$		0			0
$389$	−13.0491	−	3.83155i	−0.661614	−	0.194267i	−0.0663485	−	0.997797i	$-0.521135\pi$
$389$	−13.0491	−	3.83155i	−0.661614	−	0.194267i	−0.595265	+	0.803529i	$0.702953\pi$
$390$		0			0
$391$	6.92359	−	27.3401i	0.350141	−	1.38265i
$392$		0			0
$393$	25.8627	+	16.2396i	1.30460	+	0.819180i
$394$		0			0
$395$	8.12254	−	12.6389i	0.408689	−	0.635933i
$396$		0			0
$397$	16.9899	−	10.9188i	0.852700	−	0.547997i	−0.0397159	−	0.999211i	$-0.512645\pi$
$397$	16.9899	−	10.9188i	0.852700	−	0.547997i	0.892416	+	0.451214i	$0.149009\pi$
$398$		0			0
$399$	9.48051	−	4.45056i	0.474619	−	0.222807i
$400$		0			0
$401$	8.88690	−	19.4596i	0.443790	−	0.971766i	−0.547097	−	0.837070i	$-0.684267\pi$
$401$	8.88690	−	19.4596i	0.443790	−	0.971766i	0.990887	−	0.134696i	$-0.0430058\pi$
$402$		0			0
$403$	1.78493	−	0.524103i	0.0889137	−	0.0261074i
$404$		0			0
$405$	9.57509	−	6.73822i	0.475790	−	0.334825i
$406$		0			0
$407$	−3.82975	+	1.74899i	−0.189834	+	0.0866942i
$408$		0			0
$409$	−1.59090	+	11.0649i	−0.0786649	+	0.547126i	0.911935	+	0.410335i	$0.134588\pi$
$409$	−1.59090	+	11.0649i	−0.0786649	+	0.547126i	−0.990600	+	0.136792i	$0.956321\pi$
$410$		0			0
$411$	3.13668	+	4.76984i	0.154721	+	0.235279i
$412$		0			0
$413$	26.5792			1.30788
$414$		0			0
$415$	−3.75228			−0.184192
$416$		0			0
$417$	11.2155	+	17.0550i	0.549223	+	0.835185i
$418$		0			0
$419$	−2.81881	+	19.6053i	−0.137708	+	0.957781i	0.797408	+	0.603440i	$0.206204\pi$
$419$	−2.81881	+	19.6053i	−0.137708	+	0.957781i	−0.935116	+	0.354341i	$0.884705\pi$
$420$		0			0
$421$	−2.10380	+	0.960773i	−0.102533	+	0.0468252i	−0.466021	−	0.884774i	$-0.654313\pi$
$421$	−2.10380	+	0.960773i	−0.102533	+	0.0468252i	0.363488	+	0.931599i	$0.381586\pi$
$422$		0			0
$423$	−25.0814	−	10.8234i	−1.21950	−	0.526250i
$424$		0			0
$425$	18.6632	−	5.48000i	0.905297	−	0.265819i
$426$		0			0
$427$	−23.2028	+	50.8070i	−1.12286	+	2.45872i
$428$		0			0
$429$	−2.11380	+	0.992310i	−0.102055	+	0.0479092i
$430$		0			0
$431$	27.2579	−	17.5176i	1.31297	−	0.843792i	0.318405	−	0.947955i	$-0.396853\pi$
$431$	27.2579	−	17.5176i	1.31297	−	0.843792i	0.994560	+	0.104163i	$0.0332164\pi$
$432$		0			0
$433$	7.31119	−	11.3764i	0.351354	−	0.546717i	−0.619925	−	0.784661i	$-0.712837\pi$
$433$	7.31119	−	11.3764i	0.351354	−	0.546717i	0.971279	+	0.237944i	$0.0764735\pi$
$434$		0			0
$435$	−17.8597	−	11.2144i	−0.856307	−	0.537689i
$436$		0			0
$437$	1.08665	+	5.95896i	0.0519815	+	0.285056i
$438$		0			0
$439$	−13.9564	−	4.09797i	−0.666103	−	0.195586i	−0.0688362	−	0.997628i	$-0.521929\pi$
$439$	−13.9564	−	4.09797i	−0.666103	−	0.195586i	−0.597267	+	0.802042i	$0.703747\pi$
$440$		0			0
$441$	20.7487	+	43.0177i	0.988031	+	2.04846i
$442$		0			0
$443$	21.3245	+	33.1815i	1.01316	+	1.57650i	0.800462	+	0.599384i	$0.204588\pi$
$443$	21.3245	+	33.1815i	1.01316	+	1.57650i	0.212695	+	0.977119i	$0.431776\pi$
$444$		0			0
$445$	12.0289	+	13.8821i	0.570224	+	0.658073i
$446$		0			0
$447$	−11.5599	−	9.80602i	−0.546766	−	0.463809i
$448$		0			0
$449$	−4.25279	−	14.4837i	−0.200701	−	0.683526i	−0.996913	−	0.0785087i	$-0.974984\pi$
$449$	−4.25279	−	14.4837i	−0.200701	−	0.683526i	0.796212	−	0.605018i	$-0.206834\pi$
$450$		0			0
$451$	4.76832	−	0.685582i	0.224532	−	0.0322828i
$452$		0			0
$453$	−23.1247	+	3.57317i	−1.08649	+	0.167882i
$454$		0			0
$455$	8.38052	+	1.20494i	0.392885	+	0.0564883i
$456$		0			0
$457$	−22.4058	−	19.4148i	−1.04810	−	0.908185i	−0.0522002	−	0.998637i	$-0.516623\pi$
$457$	−22.4058	−	19.4148i	−1.04810	−	0.908185i	−0.995901	+	0.0904519i	$0.971169\pi$
$458$		0			0
$459$	−22.4516	+	20.7286i	−1.04795	+	0.967526i
$460$		0			0
$461$			35.7273i			1.66398i	0.554787	+	0.831992i	$0.312800\pi$
$461$			35.7273i			1.66398i	−0.554787	+	0.831992i	$0.687200\pi$
$462$		0			0
$463$	−14.9256	+	17.2250i	−0.693650	+	0.800515i	−0.987880	−	0.155219i	$-0.950392\pi$
$463$	−14.9256	+	17.2250i	−0.693650	+	0.800515i	0.294230	+	0.955735i	$0.404937\pi$
$464$		0			0
$465$	2.81814	+	1.25139i	0.130688	+	0.0580317i
$466$		0			0
$467$	−0.784107	−	1.71695i	−0.0362841	−	0.0794512i	0.890622	−	0.454744i	$-0.150269\pi$
$467$	−0.784107	−	1.71695i	−0.0362841	−	0.0794512i	−0.926906	+	0.375293i	$0.877542\pi$
$468$		0			0
$469$	−1.28795	−	8.95786i	−0.0594718	−	0.413636i
$470$		0			0
$471$	−32.0373	+	0.336583i	−1.47620	+	0.0155089i
$472$		0			0
$473$	3.40474	+	1.55489i	0.156550	+	0.0714940i
$474$		0			0
$475$	−3.15718	+	2.73571i	−0.144861	+	0.125523i
$476$		0			0
$477$	31.8676	−	0.669675i	1.45912	−	0.0306623i
$478$		0			0
$479$	7.92285	+	5.09171i	0.362004	+	0.232646i	0.708981	−	0.705228i	$-0.249155\pi$
$479$	7.92285	+	5.09171i	0.362004	+	0.232646i	−0.346976	+	0.937874i	$0.612792\pi$
$480$		0			0
$481$	1.62591	−	5.53734i	0.0741351	−	0.252481i
$482$		0			0
$483$	−39.0456	+	7.54485i	−1.77664	+	0.343302i
$484$		0			0
$485$	3.55738	−	12.1153i	0.161533	−	0.550129i
$486$		0			0
$487$	−17.5816	−	11.2990i	−0.796697	−	0.512006i	0.0778397	−	0.996966i	$-0.475198\pi$
$487$	−17.5816	−	11.2990i	−0.796697	−	0.512006i	−0.874536	+	0.484960i	$0.838834\pi$
$488$		0			0
$489$	5.59868	+	18.3519i	0.253181	+	0.829902i
$490$		0			0
$491$	−10.1988	+	8.83732i	−0.460266	+	0.398823i	−0.853894	−	0.520447i	$-0.825765\pi$
$491$	−10.1988	+	8.83732i	−0.460266	+	0.398823i	0.393628	+	0.919270i	$0.371220\pi$
$492$		0			0
$493$	50.0649	+	22.8639i	2.25481	+	1.02974i
$494$		0			0
$495$	−3.73586	−	1.01220i	−0.167914	−	0.0454948i
$496$		0			0
$497$	0.423252	+	2.94378i	0.0189854	+	0.132047i
$498$		0			0
$499$	−17.4838	−	38.2841i	−0.782681	−	1.71383i	−0.696503	−	0.717554i	$-0.745262\pi$
$499$	−17.4838	−	38.2841i	−0.782681	−	1.71383i	−0.0861783	−	0.996280i	$-0.527465\pi$
$500$		0			0
$501$	10.3824	−	23.3812i	0.463851	−	1.04460i
$502$		0			0
$503$	21.5277	−	24.8442i	0.959871	−	1.10775i	−0.0342438	−	0.999414i	$-0.510902\pi$
$503$	21.5277	−	24.8442i	0.959871	−	1.10775i	0.994114	−	0.108336i	$-0.0345523\pi$
$504$		0			0
$505$			19.5583i			0.870334i
$506$		0			0
$507$	−5.24689	+	18.5895i	−0.233023	+	0.825590i
$508$		0			0
$509$	−6.32449	−	5.48020i	−0.280328	−	0.242906i	0.503336	−	0.864091i	$-0.332106\pi$
$509$	−6.32449	−	5.48020i	−0.280328	−	0.242906i	−0.783664	+	0.621185i	$0.786651\pi$
$510$		0			0
$511$	17.4818	+	2.51350i	0.773348	+	0.111191i
$512$		0			0
$513$	2.53683	−	6.05272i	0.112004	−	0.267234i
$514$		0			0
$515$	3.10735	−	0.446770i	0.136926	−	0.0196870i
$516$		0			0
$517$	2.54418	+	8.66469i	0.111893	+	0.381073i
$518$		0			0
$519$	−1.49662	+	1.76431i	−0.0656943	+	0.0774445i
$520$		0			0
$521$	−19.9505	−	23.0242i	−0.874049	−	1.00871i	−0.999861	−	0.0166527i	$-0.994699\pi$
$521$	−19.9505	−	23.0242i	−0.874049	−	1.00871i	0.125812	−	0.992054i	$-0.459846\pi$
$522$		0			0
$523$	−10.4824	−	16.3110i	−0.458364	−	0.713229i	0.532746	−	0.846275i	$-0.321160\pi$
$523$	−10.4824	−	16.3110i	−0.458364	−	0.713229i	−0.991110	+	0.133047i	$0.957524\pi$
$524$		0			0
$525$	−18.1777	−	20.5381i	−0.793338	−	0.896358i
$526$		0			0
$527$	−7.72150	−	2.26724i	−0.336354	−	0.0987624i
$528$		0			0
$529$	1.55481	−	22.9474i	0.0676003	−	0.997712i
$530$		0			0
$531$	12.3554	−	11.1690i	0.536178	−	0.484694i
$532$		0			0
$533$	−3.57003	+	5.55508i	−0.154635	+	0.240617i
$534$		0			0
$535$	1.91929	−	1.23346i	0.0829783	−	0.0533269i
$536$		0			0
$537$	−15.1724	−	32.3199i	−0.654736	−	1.39471i
$538$		0			0
$539$	6.55880	−	14.3618i	0.282508	−	0.618606i
$540$		0			0
$541$	16.6530	−	4.88977i	0.715969	−	0.210228i	0.0965953	−	0.995324i	$-0.469205\pi$
$541$	16.6530	−	4.88977i	0.715969	−	0.210228i	0.619374	+	0.785096i	$0.287387\pi$
$542$		0			0
$543$	3.67786	−	27.6383i	0.157832	−	1.18607i
$544$		0			0
$545$	−17.8770	+	8.16417i	−0.765769	+	0.349715i
$546$		0			0
$547$	0.335071	−	2.33047i	0.0143266	−	0.0996437i	−0.981403	−	0.191956i	$-0.938517\pi$
$547$	0.335071	−	2.33047i	0.0143266	−	0.0996437i	0.995730	+	0.0923126i	$0.0294259\pi$
$548$		0			0
$549$	10.5641	+	33.3679i	0.450864	+	1.42411i
$550$		0			0
$551$	−11.8207			−0.503581
$552$		0			0
$553$	55.2888			2.35112
$554$		0			0
$555$	7.99249	−	5.25592i	0.339262	−	0.223101i
$556$		0			0
$557$	−1.50216	+	10.4478i	−0.0636487	+	0.442686i	0.932931	+	0.360054i	$0.117242\pi$
$557$	−1.50216	+	10.4478i	−0.0636487	+	0.442686i	−0.996580	+	0.0826321i	$0.973667\pi$
$558$		0			0
$559$	−4.66701	+	2.13135i	−0.197393	+	0.0901465i
$560$		0			0
$561$	10.0134	+	1.33249i	0.422765	+	0.0562578i
$562$		0			0
$563$	17.4625	−	5.12746i	0.735958	−	0.216097i	0.107789	−	0.994174i	$-0.465623\pi$
$563$	17.4625	−	5.12746i	0.735958	−	0.216097i	0.628169	+	0.778077i	$0.283805\pi$
$564$		0			0
$565$	5.89201	−	12.9017i	0.247879	−	0.542778i
$566$		0			0
$567$	39.9110	+	16.2368i	1.67611	+	0.681883i
$568$		0			0
$569$	3.60236	−	2.31510i	0.151019	−	0.0970539i	−0.462949	−	0.886385i	$-0.653209\pi$
$569$	3.60236	−	2.31510i	0.151019	−	0.0970539i	0.613968	+	0.789331i	$0.289572\pi$
$570$		0			0
$571$	3.75571	−	5.84400i	0.157172	−	0.244564i	−0.753733	−	0.657181i	$-0.771749\pi$
$571$	3.75571	−	5.84400i	0.157172	−	0.244564i	0.910905	+	0.412617i	$0.135385\pi$
$572$		0			0
$573$	5.76305	−	9.17806i	0.240755	−	0.383419i
$574$		0			0
$575$	14.1714	−	7.12694i	0.590989	−	0.297214i
$576$		0			0
$577$	−41.6880	−	12.2407i	−1.73549	−	0.509587i	−0.747524	−	0.664235i	$-0.768757\pi$
$577$	−41.6880	−	12.2407i	−1.73549	−	0.509587i	−0.987970	+	0.154648i	$0.950576\pi$
$578$		0			0
$579$	22.0844	−	19.5462i	0.917796	−	0.812312i
$580$		0			0
$581$	−7.46548	−	11.6165i	−0.309720	−	0.481934i
$582$		0			0
$583$	−6.90035	−	7.96343i	−0.285783	−	0.329811i
$584$		0			0
$585$	4.40204	−	2.96152i	0.182002	−	0.122444i
$586$		0			0
$587$	−5.62063	−	19.1421i	−0.231988	−	0.790079i	−0.990391	−	0.138293i	$-0.955838\pi$
$587$	−5.62063	−	19.1421i	−0.231988	−	0.790079i	0.758403	−	0.651786i	$-0.225980\pi$
$588$		0			0
$589$	1.71078	−	0.245973i	0.0704914	−	0.0101351i
$590$		0			0
$591$	3.50482	+	22.6823i	0.144169	+	0.933026i
$592$		0			0
$593$	−46.4214	−	6.67439i	−1.90630	−	0.274085i	−0.914771	−	0.403973i	$-0.867629\pi$
$593$	−46.4214	−	6.67439i	−1.90630	−	0.274085i	−0.991529	+	0.129888i	$0.958538\pi$
$594$		0			0
$595$	−27.6804	−	23.9852i	−1.13479	−	0.983298i
$596$		0			0
$597$	28.5905	+	8.06967i	1.17013	+	0.330270i
$598$		0			0
$599$		−	16.2194i		−	0.662708i	−0.943507	−	0.331354i	$-0.892495\pi$
$599$		−	16.2194i		−	0.662708i	0.943507	−	0.331354i	$-0.107505\pi$
$600$		0			0
$601$	2.28182	−	2.63337i	0.0930776	−	0.107417i	−0.707300	−	0.706914i	$-0.750087\pi$
$601$	2.28182	−	2.63337i	0.0930776	−	0.107417i	0.800377	+	0.599496i	$0.204632\pi$
$602$		0			0
$603$	−4.36295	−	3.62286i	−0.177673	−	0.147534i
$604$		0			0
$605$	−5.41315	−	11.8531i	−0.220076	−	0.481899i
$606$		0			0
$607$	−0.897830	−	6.24454i	−0.0364418	−	0.253458i	0.963454	−	0.267873i	$-0.0863206\pi$
$607$	−0.897830	−	6.24454i	−0.0364418	−	0.253458i	−0.999896	+	0.0144145i	$0.995412\pi$
$608$		0			0
$609$	−0.815297	−	77.6031i	−0.0330375	−	3.14463i
$610$		0			0
$611$	−11.2598	−	5.14219i	−0.455524	−	0.208031i
$612$		0			0
$613$	13.8737	−	12.0216i	0.560352	−	0.485548i	−0.328021	−	0.944670i	$-0.606382\pi$
$613$	13.8737	−	12.0216i	0.560352	−	0.485548i	0.888373	+	0.459123i	$0.151836\pi$
$614$		0			0
$615$	−10.4689	+	3.19379i	−0.422147	+	0.128786i
$616$		0			0
$617$	9.60235	+	6.17105i	0.386576	+	0.248437i	0.719465	−	0.694529i	$-0.244387\pi$
$617$	9.60235	+	6.17105i	0.386576	+	0.248437i	−0.332889	+	0.942966i	$0.608023\pi$
$618$		0			0
$619$	−11.8382	+	40.3173i	−0.475818	+	1.62049i	0.276028	+	0.961150i	$0.410982\pi$
$619$	−11.8382	+	40.3173i	−0.475818	+	1.62049i	−0.751846	+	0.659338i	$0.770836\pi$
$620$		0			0
$621$	−14.9799	+	19.9148i	−0.601125	+	0.799155i
$622$		0			0
$623$	−19.0444	+	64.8593i	−0.762998	+	2.59853i
$624$		0			0
$625$	2.08463	+	1.33971i	0.0833853	+	0.0535885i
$626$		0			0
$627$	−2.07513	+	0.633067i	−0.0828727	+	0.0252823i
$628$		0			0
$629$	−18.8677	+	16.3489i	−0.752303	+	0.651874i
$630$		0			0
$631$	25.8134	+	11.7886i	1.02762	+	0.469296i	0.856605	−	0.515973i	$-0.172569\pi$
$631$	25.8134	+	11.7886i	1.02762	+	0.469296i	0.171011	+	0.985269i	$0.445297\pi$
$632$		0			0
$633$	0.265303	+	25.2525i	0.0105448	+	1.00370i
$634$		0			0
$635$	−0.273430	−	1.90175i	−0.0108507	−	0.0754686i
$636$		0			0
$637$	8.99040	+	19.6862i	0.356213	+	0.779997i
$638$		0			0
$639$	1.43377	+	1.19056i	0.0567193	+	0.0470980i
$640$		0			0
$641$	−4.34587	+	5.01540i	−0.171652	+	0.198097i	−0.835057	−	0.550164i	$-0.814565\pi$
$641$	−4.34587	+	5.01540i	−0.171652	+	0.198097i	0.663405	+	0.748260i	$0.269111\pi$
$642$		0			0
$643$		−	39.1587i		−	1.54427i	−0.635461	−	0.772133i	$-0.719190\pi$
$643$		−	39.1587i		−	1.54427i	0.635461	−	0.772133i	$-0.280810\pi$
$644$		0			0
$645$	−8.18446	−	2.31006i	−0.322263	−	0.0909586i
$646$		0			0
$647$	−13.2531	−	11.4839i	−0.521035	−	0.451479i	0.354205	−	0.935168i	$-0.384751\pi$
$647$	−13.2531	−	11.4839i	−0.521035	−	0.451479i	−0.875240	+	0.483688i	$0.839297\pi$
$648$		0			0
$649$	−5.44990	−	0.783578i	−0.213927	−	0.0307581i
$650$		0			0
$651$	1.73281	+	11.2143i	0.0679140	+	0.439523i
$652$		0			0
$653$	−21.5520	+	3.09870i	−0.843393	+	0.121262i	−0.550450	−	0.834868i	$-0.685544\pi$
$653$	−21.5520	+	3.09870i	−0.843393	+	0.121262i	−0.292943	+	0.956130i	$0.594635\pi$
$654$		0			0
$655$	6.46219	+	22.0082i	0.252499	+	0.859931i
$656$		0			0
$657$	9.18265	−	6.17773i	0.358249	−	0.241016i
$658$		0			0
$659$	12.8876	+	14.8731i	0.502031	+	0.579375i	0.949040	−	0.315154i	$-0.102056\pi$
$659$	12.8876	+	14.8731i	0.502031	+	0.579375i	−0.447009	+	0.894529i	$0.647511\pi$
$660$		0			0
$661$	−14.5176	−	22.5899i	−0.564670	−	0.878644i	0.435093	−	0.900385i	$-0.356715\pi$
$661$	−14.5176	−	22.5899i	−0.564670	−	0.878644i	−0.999764	+	0.0217414i	$0.993079\pi$
$662$		0			0
$663$	−10.3688	+	9.17709i	−0.402691	+	0.356409i
$664$		0			0
$665$	7.54769	+	2.21620i	0.292687	+	0.0859406i
$666$		0			0
$667$	43.5112	+	11.0188i	1.68476	+	0.426648i
$668$		0			0
$669$	16.2905	−	25.9438i	0.629827	−	1.00304i
$670$		0			0
$671$	6.25542	−	9.73363i	0.241488	−	0.375763i
$672$		0			0
$673$	−15.6421	+	10.0526i	−0.602960	+	0.387499i	−0.806211	−	0.591628i	$-0.798486\pi$
$673$	−15.6421	+	10.0526i	−0.602960	+	0.387499i	0.203251	+	0.979127i	$0.434849\pi$
$674$		0			0
$675$	−17.0804	−	1.90864i	−0.657425	−	0.0734636i
$676$		0			0
$677$	9.72425	−	21.2931i	0.373733	−	0.818361i	−0.625538	−	0.780194i	$-0.715121\pi$
$677$	9.72425	−	21.2931i	0.373733	−	0.818361i	0.999271	−	0.0381679i	$-0.0121522\pi$
$678$		0			0
$679$	44.5851	−	13.0914i	1.71102	−	0.502400i
$680$		0			0
$681$	8.61010	+	1.14576i	0.329940	+	0.0439055i
$682$		0			0
$683$	27.0833	−	12.3685i	1.03631	−	0.473269i	0.176728	−	0.984260i	$-0.443449\pi$
$683$	27.0833	−	12.3685i	1.03631	−	0.473269i	0.859586	+	0.510991i	$0.170721\pi$
$684$		0			0
$685$	−0.610220	+	4.24417i	−0.0233153	+	0.162161i
$686$		0			0
$687$	23.4212	−	15.4020i	0.893575	−	0.587621i
$688$		0			0
$689$	14.4436			0.550259
$690$		0			0
$691$	−5.42450			−0.206358			−0.103179	−	0.994663i	$-0.532901\pi$
$691$	−5.42450			−0.206358			−0.103179	+	0.994663i	$0.532901\pi$
$692$		0			0
$693$	−4.29920	−	13.5795i	−0.163313	−	0.515844i
$694$		0			0
$695$	−2.18189	+	15.1754i	−0.0827639	+	0.575636i
$696$		0			0
$697$	25.9842	−	11.8666i	0.984222	−	0.449479i
$698$		0			0
$699$	2.09625	−	15.7529i	0.0792876	−	0.595828i
$700$		0			0
$701$	2.49774	−	0.733403i	0.0943384	−	0.0277002i	−0.234223	−	0.972183i	$-0.575255\pi$
$701$	2.49774	−	0.733403i	0.0943384	−	0.0277002i	0.328561	+	0.944483i	$0.393436\pi$
$702$		0			0
$703$	2.22741	−	4.87734i	0.0840082	−	0.183952i
$704$		0			0
$705$	−8.71894	−	18.5729i	−0.328374	−	0.699498i
$706$		0			0
$707$	−60.5498	+	38.9130i	−2.27721	+	1.46347i
$708$		0			0
$709$	−4.61524	+	7.18145i	−0.173329	+	0.269705i	−0.917039	−	0.398797i	$-0.869428\pi$
$709$	−4.61524	+	7.18145i	−0.173329	+	0.269705i	0.743710	+	0.668502i	$0.233064\pi$
$710$		0			0
$711$	25.7011	−	23.2333i	0.963866	−	0.871315i
$712$		0			0
$713$	−6.52652	−	0.689305i	−0.244420	−	0.0258147i
$714$		0			0
$715$	−1.68285	−	0.494130i	−0.0629351	−	0.0184794i
$716$		0			0
$717$	29.1058	+	32.8853i	1.08697	+	1.22813i
$718$		0			0
$719$	−16.6118	−	25.8485i	−0.619516	−	0.963986i	−0.999244	−	0.0388877i	$-0.987619\pi$
$719$	−16.6118	−	25.8485i	−0.619516	−	0.963986i	0.379727	−	0.925098i	$-0.376018\pi$
$720$		0			0
$721$	7.56549	+	8.73104i	0.281753	+	0.325161i
$722$		0			0
$723$	−26.3549	+	31.0688i	−0.980151	+	1.15546i
$724$		0			0
$725$	8.72132	+	29.7021i	0.323902	+	1.10311i
$726$		0			0
$727$	−22.3349	+	3.21128i	−0.828356	+	0.119100i	−0.543435	−	0.839451i	$-0.682877\pi$
$727$	−22.3349	+	3.21128i	−0.828356	+	0.119100i	−0.284921	+	0.958551i	$0.591967\pi$
$728$		0			0
$729$	25.3757	−	9.22356i	0.939841	−	0.341613i
$730$		0			0
$731$	21.9690	+	3.15866i	0.812552	+	0.116827i
$732$		0			0
$733$	15.9425	+	13.8143i	0.588850	+	0.510242i	0.897547	−	0.440919i	$-0.145347\pi$
$733$	15.9425	+	13.8143i	0.588850	+	0.510242i	−0.308697	+	0.951161i	$0.599893\pi$
$734$		0			0
$735$	−9.74424	+	34.5235i	−0.359422	+	1.27342i
$736$		0			0
$737$			1.87473i			0.0690564i
$738$		0			0
$739$	−22.1885	+	25.6069i	−0.816216	+	0.941964i	−0.999153	−	0.0411609i	$-0.986894\pi$
$739$	−22.1885	+	25.6069i	−0.816216	+	0.941964i	0.182936	+	0.983125i	$0.441440\pi$
$740$		0			0
$741$	1.20691	−	2.71797i	0.0443369	−	0.0998470i
$742$		0			0
$743$	15.8333	+	34.6701i	0.580868	+	1.27192i	0.940806	+	0.338946i	$0.110071\pi$
$743$	15.8333	+	34.6701i	0.580868	+	1.27192i	−0.359938	+	0.932976i	$0.617202\pi$
$744$		0			0
$745$	−1.62035	−	11.2698i	−0.0593651	−	0.412893i
$746$		0			0
$747$	−8.35179	−	2.26284i	−0.305576	−	0.0827929i
$748$		0			0
$749$	7.63720	+	3.48779i	0.279057	+	0.127441i
$750$		0			0
$751$	−13.2080	+	11.4448i	−0.481967	+	0.417626i	−0.861660	−	0.507486i	$-0.830575\pi$
$751$	−13.2080	+	11.4448i	−0.481967	+	0.417626i	0.379693	+	0.925112i	$0.376029\pi$
$752$		0			0
$753$	2.61005	+	8.55548i	0.0951155	+	0.311779i
$754$		0			0
$755$	−14.7849	−	9.50171i	−0.538079	−	0.345803i
$756$		0			0
$757$	−4.20789	+	14.3308i	−0.152938	+	0.520860i	−0.999942	−	0.0107262i	$-0.996586\pi$
$757$	−4.20789	+	14.3308i	−0.152938	+	0.520860i	0.847004	+	0.531586i	$0.178404\pi$
$758$		0			0
$759$	8.22850	−	0.395927i	0.298675	−	0.0143712i
$760$		0			0
$761$	8.60223	−	29.2965i	0.311831	−	1.06200i	−0.643251	−	0.765655i	$-0.722415\pi$
$761$	8.60223	−	29.2965i	0.311831	−	1.06200i	0.955082	−	0.296342i	$-0.0957669\pi$
$762$		0			0
$763$	−60.8430	−	39.1014i	−2.20267	−	1.41557i
$764$		0			0
$765$	−22.9463	+	0.482200i	−0.829624	+	0.0174340i
$766$		0			0
$767$	5.70380	−	4.94237i	0.205952	−	0.178459i
$768$		0			0
$769$	−28.7457	−	13.1277i	−1.03660	−	0.473398i	−0.176914	−	0.984226i	$-0.556612\pi$
$769$	−28.7457	−	13.1277i	−1.03660	−	0.473398i	−0.859683	+	0.510828i	$0.829339\pi$
$770$		0			0
$771$	−27.0582	+	0.284273i	−0.974477	+	0.0102378i
$772$		0			0
$773$	4.86491	+	33.8362i	0.174979	+	1.21700i	0.868176	+	0.496256i	$0.165292\pi$
$773$	4.86491	+	33.8362i	0.174979	+	1.21700i	−0.693197	+	0.720748i	$0.743799\pi$
$774$		0			0
$775$	−1.88027	−	4.11721i	−0.0675412	−	0.147895i
$776$		0			0
$777$	32.1733	+	14.2865i	1.15421	+	0.512525i
$778$		0			0
$779$	−4.01763	+	4.63659i	−0.143947	+	0.166123i
$780$		0			0
$781$		−	0.616082i		−	0.0220452i
$782$		0			0
$783$	−32.9891	−	35.7313i	−1.17893	−	1.27693i
$784$		0			0
$785$	−18.1866	−	15.7588i	−0.649107	−	0.562454i
$786$		0			0
$787$	−17.0145	−	2.44631i	−0.606501	−	0.0872016i	−0.167779	−	0.985825i	$-0.553660\pi$
$787$	−17.0145	−	2.44631i	−0.606501	−	0.0872016i	−0.438722	+	0.898623i	$0.644569\pi$
$788$		0			0
$789$	−21.8237	+	3.37215i	−0.776946	+	0.120052i
$790$		0			0
$791$	51.6645	−	7.42823i	1.83698	−	0.264117i
$792$		0			0
$793$	4.46827	+	15.2175i	0.158673	+	0.540390i
$794$		0			0
$795$	18.2569	+	15.4869i	0.647507	+	0.549265i
$796$		0			0
$797$	−11.7030	−	13.5060i	−0.414541	−	0.478406i	0.509625	−	0.860397i	$-0.329784\pi$
$797$	−11.7030	−	13.5060i	−0.414541	−	0.478406i	−0.924166	+	0.381991i	$0.875239\pi$
$798$		0			0
$799$	28.9504	+	45.0478i	1.02419	+	1.59368i
$800$		0			0
$801$	18.4021	+	38.1527i	0.650207	+	1.34806i
$802$		0			0
$803$	−3.51043	−	1.03076i	−0.123881	−	0.0363746i
$804$		0			0
$805$	−25.7166	−	15.1933i	−0.906390	−	0.535492i
$806$		0			0
$807$	11.9280	+	7.48976i	0.419885	+	0.263652i
$808$		0			0
$809$	−14.3192	+	22.2811i	−0.503436	+	0.783362i	−0.996227	−	0.0867860i	$-0.972340\pi$
$809$	−14.3192	+	22.2811i	−0.503436	+	0.783362i	0.492791	+	0.870148i	$0.335977\pi$
$810$		0			0
$811$	−20.0570	+	12.8898i	−0.704296	+	0.452624i	−0.843142	−	0.537690i	$-0.819297\pi$
$811$	−20.0570	+	12.8898i	−0.704296	+	0.452624i	0.138846	+	0.990314i	$0.455661\pi$
$812$		0			0
$813$	25.5448	−	11.9919i	0.895897	−	0.420573i
$814$		0			0
$815$	−5.98661	+	13.1088i	−0.209702	+	0.459183i
$816$		0			0
$817$	−4.57375	+	1.34297i	−0.160015	+	0.0469847i
$818$		0			0
$819$	17.9267	+	7.73588i	0.626408	+	0.270313i
$820$		0			0
$821$	−23.2246	+	10.6063i	−0.810545	+	0.370163i	−0.777179	−	0.629280i	$-0.783350\pi$
$821$	−23.2246	+	10.6063i	−0.810545	+	0.370163i	−0.0333659	+	0.999443i	$0.510623\pi$
$822$		0			0
$823$	−6.38756	+	44.4265i	−0.222656	+	1.54861i	0.505275	+	0.862959i	$0.331391\pi$
$823$	−6.38756	+	44.4265i	−0.222656	+	1.54861i	−0.727931	+	0.685650i	$0.759518\pi$
$824$		0			0
$825$	3.12174	+	4.74712i	0.108685	+	0.165273i
$826$		0			0
$827$	−34.5550			−1.20160			−0.600798	−	0.799401i	$-0.705150\pi$
$827$	−34.5550			−1.20160			−0.600798	+	0.799401i	$0.705150\pi$
$828$		0			0
$829$	−14.9734			−0.520048			−0.260024	−	0.965602i	$-0.583731\pi$
$829$	−14.9734			−0.520048			−0.260024	+	0.965602i	$0.583731\pi$
$830$		0			0
$831$	−5.57691	−	8.48061i	−0.193461	−	0.294189i
$832$		0			0
$833$	13.3238	−	92.6690i	0.461642	−	3.21079i
$834$		0			0
$835$	17.4786	−	7.98220i	0.604871	−	0.276235i
$836$		0			0
$837$	5.51793	+	4.48483i	0.190728	+	0.155018i
$838$		0			0
$839$	−42.7769	+	12.5604i	−1.47682	+	0.433634i	−0.918310	−	0.395863i	$-0.870446\pi$
$839$	−42.7769	+	12.5604i	−1.47682	+	0.433634i	−0.558511	+	0.829497i	$0.688627\pi$
$840$		0			0
$841$	−24.3404	+	53.2980i	−0.839323	+	1.83786i
$842$		0			0
$843$	1.07166	−	0.503085i	0.0369100	−	0.0173272i
$844$		0			0
$845$	−12.2049	+	7.84359i	−0.419860	+	0.269828i
$846$		0			0
$847$	25.9257	−	40.3412i	0.890818	−	1.38614i
$848$		0			0
$849$	23.2002	+	14.5678i	0.796229	+	0.499965i
$850$		0			0
$851$	−12.7453	+	15.8768i	−0.436904	+	0.544250i
$852$		0			0
$853$	16.7257	+	4.91110i	0.572676	+	0.168153i	0.555233	−	0.831695i	$-0.312629\pi$
$853$	16.7257	+	4.91110i	0.572676	+	0.168153i	0.0174432	+	0.999848i	$0.494447\pi$
$854$		0			0
$855$	4.43984	−	2.14146i	0.151839	−	0.0732363i
$856$		0			0
$857$	−17.6555	−	27.4725i	−0.603101	−	0.938444i	−0.999790	−	0.0204906i	$-0.993477\pi$
$857$	−17.6555	−	27.4725i	−0.603101	−	0.938444i	0.396689	−	0.917953i	$-0.370159\pi$
$858$		0			0
$859$	10.0928	+	11.6477i	0.344361	+	0.397414i	0.901340	−	0.433113i	$-0.142585\pi$
$859$	10.0928	+	11.6477i	0.344361	+	0.397414i	−0.556978	+	0.830527i	$0.688039\pi$
$860$		0			0
$861$	−30.7163	−	26.0559i	−1.04681	−	0.887984i
$862$		0			0
$863$	9.60708	+	32.7187i	0.327029	+	1.11376i	0.944867	+	0.327453i	$0.106190\pi$
$863$	9.60708	+	32.7187i	0.327029	+	1.11376i	−0.617838	+	0.786305i	$0.711991\pi$
$864$		0			0
$865$	−1.72002	+	0.247302i	−0.0584826	+	0.00840852i
$866$		0			0
$867$	30.0979	−	4.65066i	1.02218	−	0.157945i
$868$		0			0
$869$	−11.3366	−	1.62996i	−0.384569	−	0.0552927i
$870$		0			0
$871$	−1.94209	−	1.68283i	−0.0658053	−	0.0570207i
$872$		0			0
$873$	15.2242	−	24.8209i	0.515263	−	0.840061i
$874$		0			0
$875$		−	51.7412i		−	1.74917i
$876$		0			0
$877$	19.1122	−	22.0567i	0.645374	−	0.744802i	−0.334941	−	0.942239i	$-0.608716\pi$
$877$	19.1122	−	22.0567i	0.645374	−	0.744802i	0.980316	+	0.197437i	$0.0632619\pi$
$878$		0			0
$879$	34.1389	+	15.1593i	1.15148	+	0.511311i
$880$		0			0
$881$	19.3731	+	42.4211i	0.652696	+	1.42920i	0.889175	+	0.457568i	$0.151279\pi$
$881$	19.3731	+	42.4211i	0.652696	+	1.42920i	−0.236479	+	0.971637i	$0.575993\pi$
$882$		0			0
$883$	3.98153	+	27.6922i	0.133989	+	0.931916i	0.940281	+	0.340398i	$0.110562\pi$
$883$	3.98153	+	27.6922i	0.133989	+	0.931916i	−0.806292	+	0.591517i	$0.798529\pi$
$884$		0			0
$885$	12.5090	−	0.131420i	0.420487	−	0.00441763i
$886$		0			0
$887$	−1.56262	−	0.713625i	−0.0524677	−	0.0239612i	0.389008	−	0.921234i	$-0.372818\pi$
$887$	−1.56262	−	0.713625i	−0.0524677	−	0.0239612i	−0.441476	+	0.897273i	$0.645545\pi$
$888$		0			0
$889$	5.34353	−	4.63019i	0.179216	−	0.155292i
$890$		0			0
$891$	−7.70484	−	4.50588i	−0.258122	−	0.150953i
$892$		0			0
$893$	−9.67499	−	6.21774i	−0.323761	−	0.208069i
$894$		0			0
$895$	7.55523	−	25.7307i	0.252543	−	0.860084i
$896$		0			0
$897$	−6.97609	+	8.87959i	−0.232925	+	0.296481i
$898$		0			0
$899$	3.60826	−	12.2886i	0.120342	−	0.409848i
$900$		0			0
$901$	−52.5635	−	33.7805i	−1.75114	−	1.12539i
$902$		0			0
$903$	−9.13207	−	29.9340i	−0.303896	−	0.996141i
$904$		0			0
$905$	15.8268	−	13.7140i	0.526101	−	0.455869i
$906$		0			0
$907$	0.887089	+	0.405120i	0.0294553	+	0.0134518i	0.430088	−	0.902787i	$-0.358482\pi$
$907$	0.887089	+	0.405120i	0.0294553	+	0.0134518i	−0.400633	+	0.916239i	$0.631210\pi$
$908$		0			0
$909$	−11.7948	+	43.5328i	−0.391209	+	1.44389i
$910$		0			0
$911$	−1.08794	−	7.56679i	−0.0360451	−	0.250699i	0.963830	−	0.266519i	$-0.0858734\pi$
$911$	−1.08794	−	7.56679i	−0.0360451	−	0.250699i	−0.999875	+	0.0158196i	$0.994964\pi$
$912$		0			0
$913$	1.18829	+	2.60198i	0.0393265	+	0.0861131i
$914$		0			0
$915$	−10.6688	+	24.0262i	−0.352699	+	0.794281i
$916$		0			0
$917$	−55.2771	+	63.7932i	−1.82541	+	2.10664i
$918$		0			0
$919$		−	3.89542i		−	0.128498i	−0.997934	−	0.0642489i	$-0.979535\pi$
$919$		−	3.89542i		−	0.128498i	0.997934	−	0.0642489i	$-0.0204652\pi$
$920$		0			0
$921$	−2.47310	+	8.76209i	−0.0814913	+	0.288721i
$922$		0			0
$923$	0.638221	+	0.553022i	0.0210073	+	0.0182029i
$924$		0			0
$925$	−13.8987	−	1.99833i	−0.456987	−	0.0657048i
$926$		0			0
$927$	7.18576	+	0.879495i	0.236011	+	0.0288864i
$928$		0			0
$929$	−28.3606	+	4.07765i	−0.930483	+	0.133783i	−0.590856	−	0.806777i	$-0.701210\pi$
$929$	−28.3606	+	4.07765i	−0.930483	+	0.133783i	−0.339627	+	0.940560i	$0.610301\pi$
$930$		0			0
$931$	5.66489	+	19.2929i	0.185659	+	0.632298i
$932$		0			0
$933$	27.5616	−	32.4913i	0.902328	−	1.06372i
$934$		0			0
$935$	4.96860	+	5.73407i	0.162491	+	0.187524i
$936$		0			0
$937$	17.6982	+	27.5390i	0.578176	+	0.899660i	0.999975	−	0.00702943i	$-0.00223756\pi$
$937$	17.6982	+	27.5390i	0.578176	+	0.899660i	−0.421799	+	0.906689i	$0.638601\pi$
$938$		0			0
$939$	3.63642	+	4.10863i	0.118670	+	0.134080i
$940$		0			0
$941$	39.8082	+	11.6887i	1.29771	+	0.381042i	0.856400	−	0.516312i	$-0.172696\pi$
$941$	39.8082	+	11.6887i	1.29771	+	0.381042i	0.441310	+	0.897354i	$0.354514\pi$
$942$		0			0
$943$	19.1106	−	13.3219i	0.622327	−	0.433820i
$944$		0			0
$945$	14.3649	+	28.9998i	0.467289	+	0.943364i
$946$		0			0
$947$	27.2404	−	42.3868i	0.885193	−	1.37739i	−0.0405277	−	0.999178i	$-0.512904\pi$
$947$	27.2404	−	42.3868i	0.885193	−	1.37739i	0.925720	−	0.378208i	$-0.123460\pi$
$948$		0			0
$949$	4.21891	−	2.71133i	0.136952	−	0.0880135i
$950$		0			0
$951$	5.13247	+	10.9331i	0.166432	+	0.354530i
$952$		0			0
$953$	−22.9637	+	50.2835i	−0.743867	+	1.62884i	0.0332205	+	0.999448i	$0.489424\pi$
$953$	−22.9637	+	50.2835i	−0.743867	+	1.62884i	−0.777087	+	0.629393i	$0.783304\pi$
$954$		0			0
$955$	7.81017	−	2.29327i	0.252731	−	0.0742086i
$956$		0			0
$957$	−2.12063	+	15.9361i	−0.0685504	+	0.515140i
$958$		0			0
$959$	−14.3534	+	6.55499i	−0.463497	+	0.211672i
$960$		0			0
$961$	4.14526	−	28.8309i	0.133718	−	0.930029i
$962$		0			0
$963$	5.01580	−	1.58797i	0.161632	−	0.0511717i
$964$		0			0
$965$	22.1512			0.713071
$966$		0			0
$967$	32.8235			1.05553			0.527766	−	0.849390i	$-0.323030\pi$
$967$	32.8235			1.05553			0.527766	+	0.849390i	$0.323030\pi$
$968$		0			0
$969$	−10.7489	+	7.06856i	−0.345305	+	0.227075i
$970$		0			0
$971$	−1.51808	+	10.5585i	−0.0487177	+	0.338839i	0.950856	+	0.309634i	$0.100207\pi$
$971$	−1.51808	+	10.5585i	−0.0487177	+	0.338839i	−0.999573	+	0.0292047i	$0.990703\pi$
$972$		0			0
$973$	−51.3219	+	23.4379i	−1.64531	+	0.751386i
$974$		0			0
$975$	−7.71991	−	1.02730i	−0.247235	−	0.0328999i
$976$		0			0
$977$	−12.1384	+	3.56415i	−0.388341	+	0.114027i	−0.470074	−	0.882627i	$-0.655773\pi$
$977$	−12.1384	+	3.56415i	−0.388341	+	0.114027i	0.0817330	+	0.996654i	$0.473955\pi$
$978$		0			0
$979$	5.81705	−	12.7376i	0.185914	−	0.407094i
$980$		0			0
$981$	−44.7141	+	7.39088i	−1.42761	+	0.235973i
$982$		0			0
$983$	13.6980	−	8.80317i	0.436898	−	0.280778i	−0.303646	−	0.952785i	$-0.598204\pi$
$983$	13.6980	−	8.80317i	0.436898	−	0.280778i	0.740544	+	0.672007i	$0.234568\pi$
$984$		0			0
$985$	−9.31994	+	14.5021i	−0.296958	+	0.462076i
$986$		0			0
$987$	40.1521	−	63.9451i	1.27806	−	2.03539i
$988$		0			0
$989$	18.0875	−	0.679936i	0.575148	−	0.0216207i
$990$		0			0
$991$	10.3322	+	3.03382i	0.328214	+	0.0963724i	0.441688	−	0.897169i	$-0.354380\pi$
$991$	10.3322	+	3.03382i	0.328214	+	0.0963724i	−0.113474	+	0.993541i	$0.536198\pi$
$992$		0			0
$993$	5.04793	−	4.46776i	0.160191	−	0.141780i
$994$		0			0
$995$	12.0634	+	18.7710i	0.382435	+	0.595080i
$996$		0			0
$997$	0.822309	+	0.948995i	0.0260428	+	0.0300550i	0.768622	−	0.639704i	$-0.220943\pi$
$997$	0.822309	+	0.948995i	0.0260428	+	0.0300550i	−0.742579	+	0.669759i	$0.766398\pi$
$998$		0			0
$999$	20.9593	−	6.87866i	0.663121	−	0.217631i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.k.a.5.6	yes	80
3.2	odd	2	inner	276.2.k.a.5.1	✓	80
23.14	odd	22	inner	276.2.k.a.221.1	yes	80
69.14	even	22	inner	276.2.k.a.221.6	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.k.a.5.1	✓	80	3.2	odd	2	inner
276.2.k.a.5.6	yes	80	1.1	even	1	trivial
276.2.k.a.221.1	yes	80	23.14	odd	22	inner
276.2.k.a.221.6	yes	80	69.14	even	22	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.k (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951673 + 1.44718i) q^{3} +(-0.185142 + 1.28769i) q^{5} +(-4.35485 + 1.98879i) q^{7} +(-1.18864 + 2.75448i) q^{9} +O(q^{10})\)	\(q+(0.951673 + 1.44718i) q^{3} +(-0.185142 + 1.28769i) q^{5} +(-4.35485 + 1.98879i) q^{7} +(-1.18864 + 2.75448i) q^{9} +(0.951568 - 0.279406i) q^{11} +(-0.564722 + 1.23657i) q^{13} +(-2.03971 + 0.957526i) q^{15} +(4.94721 - 3.17938i) q^{17} +(-0.682840 + 1.06252i) q^{19} +(-7.02253 - 4.40956i) q^{21} +(3.50391 - 3.27454i) q^{23} +(3.17360 + 0.931853i) q^{25} +(-5.11741 + 0.901195i) q^{27} +(5.05992 + 7.87338i) q^{29} +(-0.896140 - 1.03420i) q^{31} +(1.30993 + 1.11118i) q^{33} +(-1.75468 - 5.97590i) q^{35} +(-4.20207 + 0.604167i) q^{37} +(-2.32696 + 0.359557i) q^{39} +(4.80804 + 0.691291i) q^{41} +(2.85232 + 2.47155i) q^{43} +(-3.32684 - 2.04056i) q^{45} +9.10570i q^{47} +(10.4254 - 12.0316i) q^{49} +(9.30924 + 4.13375i) q^{51} +(-4.41374 - 9.66473i) q^{53} +(0.183612 + 1.27705i) q^{55} +(-2.18749 + 0.0229818i) q^{57} +(-5.05009 - 2.30630i) q^{59} +(8.81714 - 7.64010i) q^{61} +(-0.301750 - 14.3593i) q^{63} +(-1.48776 - 0.956126i) q^{65} +(-0.532570 + 1.81377i) q^{67} +(8.07341 + 1.95449i) q^{69} +(0.175016 - 0.596050i) q^{71} +(-3.10347 - 1.99448i) q^{73} +(1.67168 + 5.47958i) q^{75} +(-3.58826 + 3.10924i) q^{77} +(-10.5050 - 4.79746i) q^{79} +(-6.17429 - 6.54815i) q^{81} +(0.410479 + 2.85495i) q^{83} +(3.17811 + 6.95909i) q^{85} +(-6.57878 + 14.8155i) q^{87} +(9.24637 - 10.6709i) q^{89} -6.50819i q^{91} +(0.643838 - 2.28109i) q^{93} +(-1.24177 - 1.07600i) q^{95} +(-9.60720 - 1.38131i) q^{97} +(-0.361453 + 2.95318i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + 6 q^{9}+O(q^{10}) \) 80 * q - 2 * q^3 + 6 * q^9	\( 80 q - 2 q^{3} + 6 q^{9} - 4 q^{13} + 11 q^{15} + 33 q^{21} + 25 q^{27} + 20 q^{31} + 11 q^{33} - 44 q^{37} - 18 q^{39} - 44 q^{43} - 100 q^{49} - 98 q^{55} - 33 q^{57} - 44 q^{61} - 55 q^{63} - 22 q^{67} - 41 q^{69} - 26 q^{73} - 65 q^{75} - 44 q^{79} - 42 q^{81} + 2 q^{85} - 64 q^{87} - 46 q^{93} + 66 q^{97} - 66 q^{99}+O(q^{100}) \) 80 * q - 2 * q^3 + 6 * q^9 - 4 * q^13 + 11 * q^15 + 33 * q^21 + 25 * q^27 + 20 * q^31 + 11 * q^33 - 44 * q^37 - 18 * q^39 - 44 * q^43 - 100 * q^49 - 98 * q^55 - 33 * q^57 - 44 * q^61 - 55 * q^63 - 22 * q^67 - 41 * q^69 - 26 * q^73 - 65 * q^75 - 44 * q^79 - 42 * q^81 + 2 * q^85 - 64 * q^87 - 46 * q^93 + 66 * q^97 - 66 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more