LMFDB - Embedded newform 276.2.k.a.5.1

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			5.1
Character	$\chi$	$=$	276.5
Dual form			276.2.k.a.221.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.56788 - 0.736032i) q^{3} +(0.185142 - 1.28769i) q^{5} +(-4.35485 + 1.98879i) q^{7} +(1.91651 + 2.30802i) q^{9} +O(q^{10})$	\(q+(-1.56788 - 0.736032i) q^{3} +(0.185142 - 1.28769i) q^{5} +(-4.35485 + 1.98879i) q^{7} +(1.91651 + 2.30802i) q^{9} +(-0.951568 + 0.279406i) q^{11} +(-0.564722 + 1.23657i) q^{13} +(-1.23806 + 1.88267i) q^{15} +(-4.94721 + 3.17938i) q^{17} +(-0.682840 + 1.06252i) q^{19} +(8.29172 + 0.0871127i) q^{21} +(-3.50391 + 3.27454i) q^{23} +(3.17360 + 0.931853i) q^{25} +(-1.30609 - 5.02933i) q^{27} +(-5.05992 - 7.87338i) q^{29} +(-0.896140 - 1.03420i) q^{31} +(1.69760 + 0.262309i) q^{33} +(1.75468 + 5.97590i) q^{35} +(-4.20207 + 0.604167i) q^{37} +(1.79557 - 1.52314i) q^{39} +(-4.80804 - 0.691291i) q^{41} +(2.85232 + 2.47155i) q^{43} +(3.32684 - 2.04056i) q^{45} -9.10570i q^{47} +(10.4254 - 12.0316i) q^{49} +(10.0968 - 1.34359i) q^{51} +(4.41374 + 9.66473i) q^{53} +(0.183612 + 1.27705i) q^{55} +(1.85266 - 1.16332i) q^{57} +(5.05009 + 2.30630i) q^{59} +(8.81714 - 7.64010i) q^{61} +(-12.9363 - 6.23955i) q^{63} +(1.48776 + 0.956126i) q^{65} +(-0.532570 + 1.81377i) q^{67} +(7.90389 - 2.55510i) q^{69} +(-0.175016 + 0.596050i) q^{71} +(-3.10347 - 1.99448i) q^{73} +(-4.28996 - 3.79691i) q^{75} +(3.58826 - 3.10924i) q^{77} +(-10.5050 - 4.79746i) q^{79} +(-1.65394 + 8.84672i) q^{81} +(-0.410479 - 2.85495i) q^{83} +(3.17811 + 6.95909i) q^{85} +(2.13830 + 16.0688i) q^{87} +(-9.24637 + 10.6709i) q^{89} -6.50819i q^{91} +(0.643838 + 2.28109i) q^{93} +(1.24177 + 1.07600i) q^{95} +(-9.60720 - 1.38131i) q^{97} +(-2.46857 - 1.66076i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.56788	−	0.736032i	−0.905218	−	0.424948i
$3$	−1.56788	−	0.736032i	−0.905218	−	0.424948i
$4$		0			0
$5$	0.185142	−	1.28769i	0.0827978	−	0.575872i	−0.905617	−	0.424096i	$-0.860592\pi$
$5$	0.185142	−	1.28769i	0.0827978	−	0.575872i	0.988415	−	0.151775i	$-0.0484991\pi$
$6$		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
$9$	1.91651	+	2.30802i	0.638838	+	0.769341i
$10$		0			0
$11$	−0.951568	+	0.279406i	−0.286909	+	0.0842440i	−0.422020	−	0.906586i	$-0.638679\pi$
$11$	−0.951568	+	0.279406i	−0.286909	+	0.0842440i	0.135112	+	0.990830i	$0.456861\pi$
$12$		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
$15$	−1.23806	+	1.88267i	−0.319666	+	0.486104i
$16$		0			0
$17$	−4.94721	+	3.17938i	−1.19987	+	0.771112i	−0.978934	−	0.204176i	$-0.934549\pi$
$17$	−4.94721	+	3.17938i	−1.19987	+	0.771112i	−0.220939	+	0.975288i	$0.570912\pi$
$18$		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
$21$	8.29172	+	0.0871127i	1.80940	+	0.0190095i
$22$		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
$27$	−1.30609	−	5.02933i	−0.251358	−	0.967894i
$28$		0			0
$29$	−5.05992	−	7.87338i	−0.939603	−	1.46205i	−0.886106	−	0.463482i	$-0.846600\pi$
$29$	−5.05992	−	7.87338i	−0.939603	−	1.46205i	−0.0534965	−	0.998568i	$-0.517037\pi$
$30$		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
$33$	1.69760	+	0.262309i	0.295514	+	0.0456621i
$34$		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
$39$	1.79557	−	1.52314i	0.287522	−	0.243898i
$40$		0			0
$41$	−4.80804	−	0.691291i	−0.750889	−	0.107962i	−0.243765	−	0.969834i	$-0.578382\pi$
$41$	−4.80804	−	0.691291i	−0.750889	−	0.107962i	−0.507124	+	0.861873i	$0.669292\pi$
$42$		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	$-0.768814\pi$
$47$		−	9.10570i		−	1.32820i	0.747643	−	0.664101i	$-0.231186\pi$
$48$		0			0
$49$	10.4254	−	12.0316i	1.48935	−	1.71880i
$50$		0			0
$51$	10.0968	−	1.34359i	1.41383	−	0.188140i
$52$		0			0
$53$	4.41374	+	9.66473i	0.606273	+	1.32755i	0.925094	+	0.379738i	$0.123986\pi$
$53$	4.41374	+	9.66473i	0.606273	+	1.32755i	−0.318821	+	0.947815i	$0.603287\pi$
$54$		0			0
$55$	0.183612	+	1.27705i	0.0247583	+	0.172198i
$56$		0			0
$57$	1.85266	−	1.16332i	0.245391	−	0.154085i
$58$		0			0
$59$	5.05009	+	2.30630i	0.657466	+	0.300255i	0.716072	−	0.698026i	$-0.245938\pi$
$59$	5.05009	+	2.30630i	0.657466	+	0.300255i	−0.0586057	+	0.998281i	$0.518665\pi$
$60$		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
$63$	−12.9363	−	6.23955i	−1.62982	−	0.786109i
$64$		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
$69$	7.90389	−	2.55510i	0.951516	−	0.307598i
$70$		0			0
$71$	−0.175016	+	0.596050i	−0.0207706	+	0.0707381i	−0.969226	−	0.246172i	$-0.920827\pi$
$71$	−0.175016	+	0.596050i	−0.0207706	+	0.0707381i	0.948456	+	0.316910i	$0.102645\pi$
$72$		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
$75$	−4.28996	−	3.79691i	−0.495362	−	0.438429i
$76$		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
$81$	−1.65394	+	8.84672i	−0.183772	+	0.982969i
$82$		0			0
$83$	−0.410479	−	2.85495i	−0.0450559	−	0.313371i	−0.999869	−	0.0161650i	$-0.994854\pi$
$83$	−0.410479	−	2.85495i	−0.0450559	−	0.313371i	0.954813	−	0.297206i	$-0.0960548\pi$
$84$		0			0
$85$	3.17811	+	6.95909i	0.344715	+	0.754820i
$86$		0			0
$87$	2.13830	+	16.0688i	0.229249	+	1.72276i
$88$		0			0
$89$	−9.24637	+	10.6709i	−0.980114	+	1.13111i	0.0112456	+	0.999937i	$0.496420\pi$
$89$	−9.24637	+	10.6709i	−0.980114	+	1.13111i	−0.991359	+	0.131175i	$0.958125\pi$
$90$		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
$99$	−2.46857	−	1.66076i	−0.248100	−	0.166912i
$100$		0			0
$101$	−14.8811	+	2.13958i	−1.48072	+	0.212896i	−0.834820	−	0.550523i	$-0.814428\pi$
$101$	−14.8811	+	2.13958i	−1.48072	+	0.212896i	−0.645904	+	0.763419i	$0.723519\pi$
$102$		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
$105$	1.64732	−	10.6610i	0.160762	−	1.04041i
$106$		0			0
$107$	1.14844	+	1.32538i	0.111024	+	0.128129i	0.808541	−	0.588439i	$-0.200257\pi$
$107$	1.14844	+	1.32538i	0.111024	+	0.128129i	−0.697517	+	0.716568i	$0.745712\pi$
$108$		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
$111$	7.03305	+	2.14560i	0.667547	+	0.203651i
$112$		0			0
$113$	10.4609	+	3.07160i	0.984079	+	0.288952i	0.733907	−	0.679250i	$-0.237695\pi$
$113$	10.4609	+	3.07160i	0.984079	+	0.288952i	0.250172	+	0.968201i	$0.419513\pi$
$114$		0			0
$115$	3.56786	+	5.11820i	0.332705	+	0.477275i
$116$		0			0
$117$	−3.93633	+	1.06651i	−0.363914	+	0.0985989i
$118$		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
$123$	7.02963	+	4.62273i	0.633840	+	0.416818i
$124$		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
$129$	−2.65296	−	5.97450i	−0.233581	−	0.526025i
$130$		0			0
$131$	−16.0382	+	7.32438i	−1.40126	+	0.639934i	−0.965565	−	0.260161i	$-0.916224\pi$
$131$	−16.0382	+	7.32438i	−1.40126	+	0.639934i	−0.435695	+	0.900095i	$0.643497\pi$
$132$		0			0
$133$	0.860535	−	5.98515i	0.0746178	−	0.518978i
$134$		0			0
$135$	−6.71802	+	0.750701i	−0.578195	+	0.0646101i
$136$		0			0
$137$	−3.29596			−0.281593			−0.140797	−	0.990039i	$-0.544966\pi$
$137$	−3.29596			−0.281593			−0.140797	+	0.990039i	$0.544966\pi$
$138$		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
$141$	−6.70208	+	14.2767i	−0.564417	+	1.20231i
$142$		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
$147$	−25.2015	+	11.1907i	−2.07858	+	0.922990i
$148$		0			0
$149$	8.39744	−	2.46571i	0.687945	−	0.201999i	0.0809662	−	0.996717i	$-0.474199\pi$
$149$	8.39744	−	2.46571i	0.687945	−	0.201999i	0.606979	+	0.794718i	$0.292381\pi$
$150$		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
$153$	−16.8195	−	5.32495i	−1.35977	−	0.430496i
$154$		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
$159$	0.193329	−	18.4018i	0.0153320	−	1.45936i
$160$		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
$165$	0.652068	−	2.13741i	0.0507635	−	0.166397i
$166$		0			0
$167$	7.98537	+	12.4255i	0.617927	+	0.961513i	0.999312	+	0.0370966i	$0.0118109\pi$
$167$	7.98537	+	12.4255i	0.617927	+	0.961513i	−0.381385	+	0.924416i	$0.624553\pi$
$168$		0			0
$169$	7.30300	+	8.42811i	0.561769	+	0.648316i
$170$		0			0
$171$	−3.76100	+	0.460324i	−0.287610	+	0.0352019i
$172$		0			0
$173$	−0.376323	−	1.28164i	−0.0286113	−	0.0974412i	0.943950	−	0.330090i	$-0.107079\pi$
$173$	−0.376323	−	1.28164i	−0.0286113	−	0.0974412i	−0.972561	+	0.232649i	$0.925261\pi$
$174$		0			0
$175$	−15.6738	+	2.25356i	−1.18483	+	0.170353i
$176$		0			0
$177$	−6.22045	−	7.33304i	−0.467557	−	0.551185i
$178$		0			0
$179$	20.4039	+	2.93364i	1.52506	+	0.219271i	0.853270	−	0.521470i	$-0.174616\pi$
$179$	20.4039	+	2.93364i	1.52506	+	0.219271i	0.671791	+	0.740741i	$0.265525\pi$
$180$		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
$189$	15.6901	+	19.3044i	1.14129	+	1.40419i
$190$		0			0
$191$	2.59925	+	5.69155i	0.188075	+	0.411826i	0.980057	−	0.198718i	$-0.0636779\pi$
$191$	2.59925	+	5.69155i	0.188075	+	0.411826i	−0.791982	+	0.610545i	$0.790951\pi$
$192$		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
$195$	−1.62890	−	2.59413i	−0.116648	−	0.185770i
$196$		0			0
$197$	−12.0536	−	5.50469i	−0.858782	−	0.392193i	−0.0631727	−	0.998003i	$-0.520122\pi$
$197$	−12.0536	−	5.50469i	−0.858782	−	0.392193i	−0.795609	+	0.605810i	$0.792849\pi$
$198$		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
$201$	2.17000	−	2.45179i	0.153060	−	0.172936i
$202$		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
$207$	−14.2730	−	1.81141i	−0.992043	−	0.125902i
$208$		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
$213$	0.713116	−	0.805719i	0.0488619	−	0.0552070i
$214$		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
$219$	3.39788	+	5.41137i	0.229608	+	0.365666i
$220$		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
$225$	3.93151	+	9.11066i	0.262101	+	0.607377i
$226$		0			0
$227$	−3.28404	+	3.78998i	−0.217969	+	0.251550i	−0.854195	−	0.519953i	$-0.825949\pi$
$227$	−3.28404	+	3.78998i	−0.217969	+	0.251550i	0.636226	+	0.771503i	$0.280495\pi$
$228$		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	0.851719	−	0.523999i	$-0.175560\pi$
$233$	6.93408	+	6.00841i	0.454266	+	0.393624i	−0.397453	+	0.917623i	$0.630106\pi$
$234$		0			0
$235$	−11.7253	−	1.68584i	−0.764874	−	0.109972i
$236$		0			0
$237$	12.9395	+	15.2538i	0.840510	+	0.990844i
$238$		0			0
$239$	−25.0967	+	3.60836i	−1.62337	+	0.233405i	−0.893134	−	0.449791i	$-0.851499\pi$
$239$	−25.0967	+	3.60836i	−1.62337	+	0.233405i	−0.730235	+	0.683196i	$0.760590\pi$
$240$		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
$243$	9.10466	−	12.6533i	0.584064	−	0.811707i
$244$		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
$249$	−1.45775	+	4.77835i	−0.0923810	+	0.302815i
$250$		0			0
$251$	−4.95506	−	1.45494i	−0.312761	−	0.0918349i	0.121585	−	0.992581i	$-0.461202\pi$
$251$	−4.95506	−	1.45494i	−0.312761	−	0.0918349i	−0.434346	+	0.900746i	$0.643020\pi$
$252$		0			0
$253$	2.41929	−	4.09496i	0.152099	−	0.257448i
$254$		0			0
$255$	0.139207	−	13.2502i	0.00871747	−	0.829762i
$256$		0			0
$257$	8.44638	−	13.1428i	0.526871	−	0.819827i	−0.471193	−	0.882030i	$-0.656176\pi$
$257$	8.44638	−	13.1428i	0.526871	−	0.819827i	0.998064	+	0.0622032i	$0.0198127\pi$
$258$		0			0
$259$	17.0979	−	10.9881i	1.06241	−	0.682769i
$260$		0			0
$261$	8.47455	−	26.7679i	0.524561	−	1.65689i
$262$		0			0
$263$	5.29632	−	11.5973i	0.326585	−	0.715122i	−0.673117	−	0.739536i	$-0.735045\pi$
$263$	5.29632	−	11.5973i	0.326585	−	0.715122i	0.999702	+	0.0244143i	$0.00777210\pi$
$264$		0			0
$265$	13.2623	−	3.89417i	0.814698	−	0.239217i
$266$		0			0
$267$	22.3513	−	9.92507i	1.36788	−	0.607405i
$268$		0			0
$269$	−7.39685	+	3.37803i	−0.450994	+	0.205962i	−0.627945	−	0.778258i	$-0.716104\pi$
$269$	−7.39685	+	3.37803i	−0.450994	+	0.205962i	0.176951	+	0.984220i	$0.443376\pi$
$270$		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
$273$	−4.79024	+	10.2041i	−0.289918	+	0.617579i
$274$		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
$279$	0.669494	−	4.05037i	0.0400816	−	0.242489i
$280$		0			0
$281$	−0.0972735	+	0.676552i	−0.00580285	+	0.0403597i	−0.992517	−	0.122105i	$-0.961035\pi$
$281$	−0.0972735	+	0.676552i	−0.00580285	+	0.0403597i	0.986714	+	0.162465i	$0.0519445\pi$
$282$		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
$285$	−1.15498	−	2.60103i	−0.0684153	−	0.154072i
$286$		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
$291$	14.0463	+	9.23693i	0.823407	+	0.541478i
$292$		0			0
$293$	−18.1424	+	11.6594i	−1.05989	+	0.681152i	−0.949828	−	0.312773i	$-0.898742\pi$
$293$	−18.1424	+	11.6594i	−1.05989	+	0.681152i	−0.110065	+	0.993924i	$0.535106\pi$
$294$		0			0
$295$	3.90478	−	6.07596i	0.227345	−	0.353756i
$296$		0			0
$297$	2.64806	+	4.42082i	0.153656	+	0.256522i
$298$		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
$303$	24.9066	+	7.59835i	1.43085	+	0.436514i
$304$		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
$309$	−0.638257	+	4.13064i	−0.0363091	+	0.234984i
$310$		0			0
$311$	6.93034	+	23.6026i	0.392983	+	1.33838i	0.884105	+	0.467288i	$0.154769\pi$
$311$	6.93034	+	23.6026i	0.392983	+	1.33838i	−0.491122	+	0.871091i	$0.663413\pi$
$312$		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
$315$	−10.4296	+	15.5028i	−0.587644	+	0.873481i
$316$		0			0
$317$	−6.90218	−	0.992384i	−0.387665	−	0.0557378i	−0.0542731	−	0.998526i	$-0.517284\pi$
$317$	−6.90218	−	0.992384i	−0.387665	−	0.0557378i	−0.333392	+	0.942788i	$0.608193\pi$
$318$		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
$327$	−3.45151	−	25.9373i	−0.190869	−	1.43434i
$328$		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
$333$	−9.44777	−	8.54059i	−0.517735	−	0.468022i
$334$		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
$339$	−14.1407	−	12.5155i	−0.768016	−	0.679746i
$340$		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
$345$	−1.82683	−	10.6508i	−0.0983535	−	0.573420i
$346$		0			0
$347$	0.364796	−	1.24238i	0.0195833	−	0.0666944i	−0.949122	−	0.314910i	$-0.898026\pi$
$347$	0.364796	−	1.24238i	0.0195833	−	0.0666944i	0.968705	+	0.248215i	$0.0798440\pi$
$348$		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
$351$	6.95669	+	1.22510i	0.371320	+	0.0653909i
$352$		0			0
$353$	3.64971	−	3.16249i	0.194254	−	0.168322i	−0.552303	−	0.833643i	$-0.686251\pi$
$353$	3.64971	−	3.16249i	0.194254	−	0.168322i	0.746557	+	0.665321i	$0.231705\pi$
$354$		0			0
$355$	0.735123	+	0.335720i	0.0390163	+	0.0178181i
$356$		0			0
$357$	−41.2978	+	25.9315i	−2.18571	+	1.37244i
$358$		0			0
$359$	3.47319	+	24.1566i	0.183308	+	1.27494i	0.848874	+	0.528596i	$0.177281\pi$
$359$	3.47319	+	24.1566i	0.183308	+	1.27494i	−0.665566	+	0.746339i	$0.731810\pi$
$360$		0			0
$361$	7.23021	+	15.8319i	0.380537	+	0.833260i
$362$		0			0
$363$	17.1974	−	2.28848i	0.902630	−	0.120114i
$364$		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
$375$	−14.2751	+	12.1092i	−0.737162	+	0.625318i
$376$		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
$381$	2.52801	+	0.390623i	0.129514	+	0.0200122i
$382$		0			0
$383$	−13.8233	−	15.9530i	−0.706340	−	0.815160i	0.283254	−	0.959045i	$-0.408586\pi$
$383$	−13.8233	−	15.9530i	−0.706340	−	0.815160i	−0.989594	+	0.143885i	$0.954040\pi$
$384$		0			0
$385$	−3.33940	−	5.19621i	−0.170192	−	0.264823i
$386$		0			0
$387$	−0.237881	+	11.3200i	−0.0120922	+	0.575427i
$388$		0			0
$389$	13.0491	+	3.83155i	0.661614	+	0.194267i	0.595265	−	0.803529i	$-0.297047\pi$
$389$	13.0491	+	3.83155i	0.661614	+	0.194267i	0.0663485	+	0.997797i	$0.478865\pi$
$390$		0			0
$391$	6.92359	−	27.3401i	0.350141	−	1.38265i
$392$		0			0
$393$	30.5369	+	0.320821i	1.54038	+	0.0161833i
$394$		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
$399$	−5.75448	+	8.75063i	−0.288084	+	0.438080i
$400$		0			0
$401$	−8.88690	+	19.4596i	−0.443790	+	0.971766i	0.547097	+	0.837070i	$0.315733\pi$
$401$	−8.88690	+	19.4596i	−0.443790	+	0.971766i	−0.990887	+	0.134696i	$0.956994\pi$
$402$		0			0
$403$	1.78493	−	0.524103i	0.0889137	−	0.0261074i
$404$		0			0
$405$	11.0856	+	3.76766i	0.550848	+	0.187217i
$406$		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
$411$	5.16768	+	2.42593i	0.254903	+	0.119662i
$412$		0			0
$413$	−26.5792			−1.30788
$414$		0			0
$415$	−3.75228			−0.184192
$416$		0			0
$417$	−18.4775	−	8.67413i	−0.904847	−	0.424774i
$418$		0			0
$419$	2.81881	−	19.6053i	0.137708	−	0.957781i	−0.797408	−	0.603440i	$-0.793796\pi$
$419$	2.81881	−	19.6053i	0.137708	−	0.957781i	0.935116	−	0.354341i	$-0.115295\pi$
$420$		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
$423$	21.0162	−	17.4512i	1.02184	−	0.848507i
$424$		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
$429$	−1.28303	+	1.95107i	−0.0619455	+	0.0941984i
$430$		0			0
$431$	−27.2579	+	17.5176i	−1.31297	+	0.843792i	−0.994560	−	0.104163i	$-0.966784\pi$
$431$	−27.2579	+	17.5176i	−1.31297	+	0.843792i	−0.318405	+	0.947955i	$0.603147\pi$
$432$		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
$435$	21.0875	+	0.221545i	1.01107	+	0.0106223i
$436$		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
$441$	47.7496	+	1.00342i	2.27379	+	0.0477821i
$442$		0			0
$443$	−21.3245	−	33.1815i	−1.01316	−	1.57650i	−0.800462	−	0.599384i	$-0.795412\pi$
$443$	−21.3245	−	33.1815i	−1.01316	−	1.57650i	−0.212695	−	0.977119i	$-0.568224\pi$
$444$		0			0
$445$	12.0289	+	13.8821i	0.570224	+	0.658073i
$446$		0			0
$447$	−14.9810	−	2.31484i	−0.708579	−	0.109488i
$448$		0			0
$449$	4.25279	+	14.4837i	0.200701	+	0.683526i	0.996913	+	0.0785087i	$0.0250158\pi$
$449$	4.25279	+	14.4837i	0.200701	+	0.683526i	−0.796212	+	0.605018i	$0.793166\pi$
$450$		0			0
$451$	4.76832	−	0.685582i	0.224532	−	0.0322828i
$452$		0			0
$453$	17.8439	−	15.1365i	0.838379	−	0.711177i
$454$		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	$-0.687200\pi$
$461$		−	35.7273i		−	1.66398i	0.554787	−	0.831992i	$-0.312800\pi$
$462$		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
$465$	3.05654	−	0.406737i	0.141744	−	0.0188620i
$466$		0			0
$467$	0.784107	+	1.71695i	0.0362841	+	0.0794512i	0.926906	−	0.375293i	$-0.122458\pi$
$467$	0.784107	+	1.71695i	0.0362841	+	0.0794512i	−0.890622	+	0.454744i	$0.849731\pi$
$468$		0			0
$469$	−1.28795	−	8.95786i	−0.0594718	−	0.413636i
$470$		0			0
$471$	27.1335	−	17.0375i	1.25024	−	0.785047i
$472$		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
$477$	−13.8474	+	28.7096i	−0.634031	+	1.31452i
$478$		0			0
$479$	−7.92285	−	5.09171i	−0.362004	−	0.232646i	0.346976	−	0.937874i	$-0.387208\pi$
$479$	−7.92285	−	5.09171i	−0.362004	−	0.232646i	−0.708981	+	0.705228i	$0.750845\pi$
$480$		0			0
$481$	1.62591	−	5.53734i	0.0741351	−	0.252481i
$482$		0			0
$483$	−29.3387	+	26.8463i	−1.33496	+	1.22155i
$484$		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
$489$	−14.3677	−	12.7164i	−0.649730	−	0.575055i
$490$		0			0
$491$	10.1988	−	8.83732i	0.460266	−	0.398823i	−0.393628	−	0.919270i	$-0.628780\pi$
$491$	10.1988	−	8.83732i	0.460266	−	0.398823i	0.853894	+	0.520447i	$0.174235\pi$
$492$		0			0
$493$	50.0649	+	22.8639i	2.25481	+	1.02974i
$494$		0			0
$495$	−2.59557	+	2.87127i	−0.116662	+	0.129054i
$496$		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
$501$	−3.37458	−	25.3592i	−0.150765	−	1.13297i
$502$		0			0
$503$	−21.5277	+	24.8442i	−0.959871	+	1.10775i	0.0342438	+	0.999414i	$0.489098\pi$
$503$	−21.5277	+	24.8442i	−0.959871	+	1.10775i	−0.994114	+	0.108336i	$0.965448\pi$
$504$		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	0.783664	−	0.621185i	$-0.213349\pi$
$509$	6.32449	+	5.48020i	0.280328	+	0.242906i	−0.503336	+	0.864091i	$0.667894\pi$
$510$		0			0
$511$	17.4818	+	2.51350i	0.773348	+	0.111191i
$512$		0			0
$513$	6.23561	+	2.04648i	0.275309	+	0.0903542i
$514$		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
$519$	−0.353296	+	2.28645i	−0.0155080	+	0.100364i
$520$		0			0
$521$	19.9505	+	23.0242i	0.874049	+	1.00871i	0.999861	+	0.0166527i	$0.00530095\pi$
$521$	19.9505	+	23.0242i	0.874049	+	1.00871i	−0.125812	+	0.992054i	$0.540154\pi$
$522$		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
$525$	26.2334	+	8.00313i	1.14492	+	0.349285i
$526$		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
$531$	4.35558	+	16.0758i	0.189016	+	0.697630i
$532$		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
$537$	−29.8317	−	19.6175i	−1.28733	−	0.846559i
$538$		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
$543$	11.3155	+	25.4825i	0.485593	+	1.09356i
$544$		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
$549$	34.5317	+	5.70781i	1.47378	+	0.243604i
$550$		0			0
$551$	11.8207			0.503581
$552$		0			0
$553$	55.2888			2.35112
$554$		0			0
$555$	4.06497	−	8.65913i	0.172548	−	0.367560i
$556$		0			0
$557$	1.50216	−	10.4478i	0.0636487	−	0.442686i	−0.932931	−	0.360054i	$-0.882758\pi$
$557$	1.50216	−	10.4478i	0.0636487	−	0.442686i	0.996580	−	0.0826321i	$-0.0263327\pi$
$558$		0			0
$559$	−4.66701	+	2.13135i	−0.197393	+	0.0901465i
$560$		0			0
$561$	−9.23235	+	4.09961i	−0.389790	+	0.173086i
$562$		0			0
$563$	−17.4625	+	5.12746i	−0.735958	+	0.216097i	−0.628169	−	0.778077i	$-0.716195\pi$
$563$	−17.4625	+	5.12746i	−0.735958	+	0.216097i	−0.107789	+	0.994174i	$0.534377\pi$
$564$		0			0
$565$	5.89201	−	12.9017i	0.247879	−	0.542778i
$566$		0			0
$567$	−10.3916	−	41.8155i	−0.436407	−	1.75609i
$568$		0			0
$569$	−3.60236	+	2.31510i	−0.151019	+	0.0970539i	−0.613968	−	0.789331i	$-0.710428\pi$
$569$	−3.60236	+	2.31510i	−0.151019	+	0.0970539i	0.462949	+	0.886385i	$0.346791\pi$
$570$		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
$573$	0.113851	−	10.8368i	0.00475621	−	0.452714i
$574$		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
$579$	−8.60566	+	28.2085i	−0.357639	+	1.17230i
$580$		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
$585$	0.644555	+	5.26622i	0.0266491	+	0.217731i
$586$		0			0
$587$	5.62063	+	19.1421i	0.231988	+	0.790079i	0.990391	+	0.138293i	$0.0441617\pi$
$587$	5.62063	+	19.1421i	0.231988	+	0.790079i	−0.758403	+	0.651786i	$0.774020\pi$
$588$		0			0
$589$	1.71078	−	0.245973i	0.0704914	−	0.0101351i
$590$		0			0
$591$	14.8470	+	17.5025i	0.610723	+	0.719958i
$592$		0			0
$593$	46.4214	+	6.67439i	1.90630	+	0.274085i	0.991529	−	0.129888i	$-0.0414619\pi$
$593$	46.4214	+	6.67439i	1.90630	+	0.274085i	0.914771	+	0.403973i	$0.132371\pi$
$594$		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	$0.107505\pi$
$599$			16.2194i			0.662708i	−0.943507	+	0.331354i	$0.892495\pi$
$600$		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
$603$	−5.20690	+	2.24693i	−0.212041	+	0.0915019i
$604$		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
$609$	−41.2695	−	65.7246i	−1.67233	−	2.66330i
$610$		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
$615$	7.25411	−	8.19611i	0.292514	−	0.330499i
$616$		0			0
$617$	−9.60235	−	6.17105i	−0.386576	−	0.248437i	0.332889	−	0.942966i	$-0.391977\pi$
$617$	−9.60235	−	6.17105i	−0.386576	−	0.248437i	−0.719465	+	0.694529i	$0.755613\pi$
$618$		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
$621$	21.0452	+	13.3455i	0.844513	+	0.535535i
$622$		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
$627$	−1.43790	+	1.62462i	−0.0574241	+	0.0648810i
$628$		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
$633$	−13.4294	−	21.3872i	−0.533769	−	0.850065i
$634$		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
$639$	−1.71112	+	0.738397i	−0.0676908	+	0.0292105i
$640$		0			0
$641$	4.34587	−	5.01540i	0.171652	−	0.198097i	−0.663405	−	0.748260i	$-0.730889\pi$
$641$	4.34587	−	5.01540i	0.171652	−	0.198097i	0.835057	+	0.550164i	$0.185435\pi$
$642$		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	0.875240	−	0.483688i	$-0.160703\pi$
$647$	13.2531	+	11.4839i	0.521035	+	0.451479i	−0.354205	+	0.935168i	$0.615249\pi$
$648$		0			0
$649$	−5.44990	−	0.783578i	−0.213927	−	0.0307581i
$650$		0			0
$651$	−7.34045	−	8.65336i	−0.287695	−	0.339152i
$652$		0			0
$653$	21.5520	−	3.09870i	0.843393	−	0.121262i	0.292943	−	0.956130i	$-0.405365\pi$
$653$	21.5520	−	3.09870i	0.843393	−	0.121262i	0.550450	+	0.834868i	$0.314456\pi$
$654$		0			0
$655$	6.46219	+	22.0082i	0.252499	+	0.859931i
$656$		0			0
$657$	−1.34454	−	10.9853i	−0.0524556	−	0.428579i
$658$		0			0
$659$	−12.8876	−	14.8731i	−0.502031	−	0.579375i	0.447009	−	0.894529i	$-0.352489\pi$
$659$	−12.8876	−	14.8731i	−0.502031	−	0.579375i	−0.949040	+	0.315154i	$0.897944\pi$
$660$		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
$663$	−4.04042	+	13.2441i	−0.156917	+	0.514358i
$664$		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
$669$	−0.321826	+	30.6326i	−0.0124425	+	1.18432i
$670$		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
$675$	0.541580	−	17.1782i	0.0208454	−	0.661188i
$676$		0			0
$677$	−9.72425	+	21.2931i	−0.373733	+	0.818361i	0.625538	+	0.780194i	$0.284879\pi$
$677$	−9.72425	+	21.2931i	−0.373733	+	0.818361i	−0.999271	+	0.0381679i	$0.987848\pi$
$678$		0			0
$679$	44.5851	−	13.0914i	1.71102	−	0.502400i
$680$		0			0
$681$	7.93853	−	3.52509i	0.304205	−	0.135082i
$682$		0			0
$683$	−27.0833	+	12.3685i	−1.03631	+	0.473269i	−0.859586	−	0.510991i	$-0.829279\pi$
$683$	−27.0833	+	12.3685i	−1.03631	+	0.473269i	−0.176728	+	0.984260i	$0.556551\pi$
$684$		0			0
$685$	−0.610220	+	4.24417i	−0.0233153	+	0.162161i
$686$		0			0
$687$	−11.9120	+	25.3747i	−0.454471	+	0.968107i
$688$		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
$693$	14.0532	+	2.32287i	0.533835	+	0.0882387i
$694$		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
$699$	−6.44944	−	14.5242i	−0.243940	−	0.549355i
$700$		0			0
$701$	−2.49774	+	0.733403i	−0.0943384	+	0.0277002i	−0.328561	−	0.944483i	$-0.606564\pi$
$701$	−2.49774	+	0.733403i	−0.0943384	+	0.0277002i	0.234223	+	0.972183i	$0.424745\pi$
$702$		0			0
$703$	2.22741	−	4.87734i	0.0840082	−	0.183952i
$704$		0			0
$705$	17.1431	+	11.2734i	0.645645	+	0.424581i
$706$		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
$711$	−9.06028	−	33.4401i	−0.339787	−	1.25410i
$712$		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
$717$	42.0045	+	12.8145i	1.56869	+	0.478565i
$718$		0			0
$719$	16.6118	+	25.8485i	0.619516	+	0.963986i	0.999244	+	0.0388877i	$0.0123814\pi$
$719$	16.6118	+	25.8485i	0.619516	+	0.963986i	−0.379727	+	0.925098i	$0.623982\pi$
$720$		0			0
$721$	7.56549	+	8.73104i	0.281753	+	0.325161i
$722$		0			0
$723$	6.22142	−	40.2635i	0.231377	−	1.49742i
$724$		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
$729$	−23.5882	+	13.1375i	−0.873639	+	0.486575i
$730$		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
$741$	0.392280	+	2.94789i	0.0144108	+	0.108294i
$742$		0			0
$743$	−15.8333	−	34.6701i	−0.580868	−	1.27192i	−0.940806	−	0.338946i	$-0.889929\pi$
$743$	−15.8333	−	34.6701i	−0.580868	−	1.27192i	0.359938	−	0.932976i	$-0.382798\pi$
$744$		0			0
$745$	−1.62035	−	11.2698i	−0.0593651	−	0.412893i
$746$		0			0
$747$	5.80259	−	6.41894i	0.212306	−	0.234857i
$748$		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
$753$	6.69808	+	5.92826i	0.244092	+	0.216038i
$754$		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
$759$	−6.80718	+	4.63974i	−0.247085	+	0.168412i
$760$		0			0
$761$	−8.60223	+	29.2965i	−0.311831	+	1.06200i	0.643251	+	0.765655i	$0.277585\pi$
$761$	−8.60223	+	29.2965i	−0.311831	+	1.06200i	−0.955082	+	0.296342i	$0.904233\pi$
$762$		0			0
$763$	−60.8430	−	39.1014i	−2.20267	−	1.41557i
$764$		0			0
$765$	−9.97085	+	20.6724i	−0.360497	+	0.747411i
$766$		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
$771$	−22.9165	+	14.3896i	−0.825317	+	0.518229i
$772$		0			0
$773$	−4.86491	−	33.8362i	−0.174979	−	1.21700i	−0.868176	−	0.496256i	$-0.834708\pi$
$773$	−4.86491	−	33.8362i	−0.174979	−	1.21700i	0.693197	−	0.720748i	$-0.256201\pi$
$774$		0			0
$775$	−1.88027	−	4.11721i	−0.0675412	−	0.147895i
$776$		0			0
$777$	−34.8950	+	4.64353i	−1.25185	+	0.166586i
$778$		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
$789$	−16.8400	+	14.2850i	−0.599521	+	0.508559i
$790$		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
$795$	−23.6600	−	3.65589i	−0.839134	−	0.129661i
$796$		0			0
$797$	11.7030	+	13.5060i	0.414541	+	0.478406i	0.924166	−	0.381991i	$-0.124761\pi$
$797$	11.7030	+	13.5060i	0.414541	+	0.478406i	−0.509625	+	0.860397i	$0.670216\pi$
$798$		0			0
$799$	28.9504	+	45.0478i	1.02419	+	1.59368i
$800$		0			0
$801$	−42.3495	−	0.889944i	−1.49634	−	0.0314446i
$802$		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
$807$	14.0837	+	0.147963i	0.495771	+	0.00520856i
$808$		0			0
$809$	14.3192	−	22.2811i	0.503436	−	0.783362i	−0.492791	−	0.870148i	$-0.664023\pi$
$809$	14.3192	−	22.2811i	0.503436	−	0.783362i	0.996227	+	0.0867860i	$0.0276596\pi$
$810$		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
$813$	−15.5052	+	23.5782i	−0.543791	+	0.826924i
$814$		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
$819$	15.0211	−	12.4730i	0.524878	−	0.435843i
$820$		0			0
$821$	23.2246	−	10.6063i	0.810545	−	0.370163i	0.0333659	−	0.999443i	$-0.489377\pi$
$821$	23.2246	−	10.6063i	0.810545	−	0.370163i	0.777179	+	0.629280i	$0.216650\pi$
$822$		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
$825$	5.14307	+	2.41438i	0.179059	+	0.0840578i
$826$		0			0
$827$	34.5550			1.20160			0.600798	−	0.799401i	$-0.294850\pi$
$827$	34.5550			1.20160			0.600798	+	0.799401i	$0.294850\pi$
$828$		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
$831$	9.18797	+	4.31323i	0.318727	+	0.149624i
$832$		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
$837$	−4.03089	+	5.85774i	−0.139328	+	0.202473i
$838$		0			0
$839$	42.7769	−	12.5604i	1.47682	−	0.433634i	0.558511	−	0.829497i	$-0.311373\pi$
$839$	42.7769	−	12.5604i	1.47682	−	0.433634i	0.918310	+	0.395863i	$0.129554\pi$
$840$		0			0
$841$	−24.3404	+	53.2980i	−0.839323	+	1.83786i
$842$		0			0
$843$	0.650477	−	0.989158i	0.0224036	−	0.0340684i
$844$		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
$849$	−27.3932	−	0.287793i	−0.940132	−	0.00987702i
$850$		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
$855$	−0.103563	+	4.92821i	−0.00354178	+	0.168541i
$856$		0			0
$857$	17.6555	+	27.4725i	0.603101	+	0.938444i	0.999790	+	0.0204906i	$0.00652280\pi$
$857$	17.6555	+	27.4725i	0.603101	+	0.938444i	−0.396689	+	0.917953i	$0.629841\pi$
$858$		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
$861$	−39.8067	−	6.15083i	−1.35661	−	0.209620i
$862$		0			0
$863$	−9.60708	−	32.7187i	−0.327029	−	1.11376i	−0.944867	−	0.327453i	$-0.893810\pi$
$863$	−9.60708	−	32.7187i	−0.327029	−	1.11376i	0.617838	−	0.786305i	$-0.288009\pi$
$864$		0			0
$865$	−1.72002	+	0.247302i	−0.0584826	+	0.00840852i
$866$		0			0
$867$	−23.2247	+	19.7010i	−0.788752	+	0.669080i
$868$		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
$879$	37.0269	−	4.92722i	1.24889	−	0.166191i
$880$		0			0
$881$	−19.3731	−	42.4211i	−0.652696	−	1.42920i	−0.889175	−	0.457568i	$-0.848721\pi$
$881$	−19.3731	−	42.4211i	−0.652696	−	1.42920i	0.236479	−	0.971637i	$-0.424007\pi$
$882$		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
$885$	−10.5943	+	6.65235i	−0.356125	+	0.223616i
$886$		0			0
$887$	1.56262	+	0.713625i	0.0524677	+	0.0239612i	0.441476	−	0.897273i	$-0.354455\pi$
$887$	1.56262	+	0.713625i	0.0524677	+	0.0239612i	−0.389008	+	0.921234i	$0.627182\pi$
$888$		0			0
$889$	5.34353	−	4.63019i	0.179216	−	0.155292i
$890$		0			0
$891$	−0.897982	−	8.88038i	−0.0300835	−	0.297504i
$892$		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
$897$	−1.30394	+	11.2166i	−0.0435374	+	0.374512i
$898$		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
$903$	23.4353	+	20.7419i	0.779879	+	0.690246i
$904$		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
$909$	−33.4580	−	30.2454i	−1.10973	−	1.00318i
$910$		0			0
$911$	1.08794	+	7.56679i	0.0360451	+	0.250699i	0.999875	−	0.0158196i	$-0.00503573\pi$
$911$	1.08794	+	7.56679i	0.0360451	+	0.250699i	−0.963830	+	0.266519i	$0.914127\pi$
$912$		0			0
$913$	1.18829	+	2.60198i	0.0393265	+	0.0861131i
$914$		0			0
$915$	3.46767	+	26.0587i	0.114637	+	0.861474i
$916$		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
$927$	4.04099	−	6.00658i	0.132724	−	0.197282i
$928$		0			0
$929$	28.3606	−	4.07765i	0.930483	−	0.133783i	0.339627	−	0.940560i	$-0.389699\pi$
$929$	28.3606	−	4.07765i	0.930483	−	0.133783i	0.590856	+	0.806777i	$0.298790\pi$
$930$		0			0
$931$	5.66489	+	19.2929i	0.185659	+	0.632298i
$932$		0			0
$933$	6.50628	−	42.1070i	0.213006	−	1.37852i
$934$		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
$939$	−5.24796	−	1.60101i	−0.171261	−	0.0522471i
$940$		0			0
$941$	−39.8082	−	11.6887i	−1.29771	−	0.381042i	−0.441310	−	0.897354i	$-0.645486\pi$
$941$	−39.8082	−	11.6887i	−1.29771	−	0.381042i	−0.856400	+	0.516312i	$0.827304\pi$
$942$		0			0
$943$	19.1106	−	13.3219i	0.622327	−	0.433820i
$944$		0			0
$945$	27.7630	−	16.6300i	0.903130	−	0.540972i
$946$		0			0
$947$	−27.2404	+	42.3868i	−0.885193	+	1.37739i	0.0405277	+	0.999178i	$0.487096\pi$
$947$	−27.2404	+	42.3868i	−0.885193	+	1.37739i	−0.925720	+	0.378208i	$0.876540\pi$
$948$		0			0
$949$	4.21891	−	2.71133i	0.136952	−	0.0880135i
$950$		0			0
$951$	10.0914	+	6.63617i	0.327236	+	0.215192i
$952$		0			0
$953$	22.9637	−	50.2835i	0.743867	−	1.62884i	−0.0332205	−	0.999448i	$-0.510576\pi$
$953$	22.9637	−	50.2835i	0.743867	−	1.62884i	0.777087	−	0.629393i	$-0.216696\pi$
$954$		0			0
$955$	7.81017	−	2.29327i	0.252731	−	0.0742086i
$956$		0			0
$957$	−6.52445	−	14.6931i	−0.210905	−	0.474961i
$958$		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
$963$	−0.857987	+	5.19074i	−0.0276483	+	0.167269i
$964$		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
$969$	−5.46688	+	11.6455i	−0.175622	+	0.374106i
$970$		0			0
$971$	1.51808	−	10.5585i	0.0487177	−	0.338839i	−0.950856	−	0.309634i	$-0.899793\pi$
$971$	1.51808	−	10.5585i	0.0487177	−	0.338839i	0.999573	−	0.0292047i	$-0.00929746\pi$
$972$		0			0
$973$	−51.3219	+	23.4379i	−1.64531	+	0.751386i
$974$		0			0
$975$	7.11778	−	3.16064i	0.227951	−	0.101221i
$976$		0			0
$977$	12.1384	−	3.56415i	0.388341	−	0.114027i	−0.0817330	−	0.996654i	$-0.526045\pi$
$977$	12.1384	−	3.56415i	0.388341	−	0.114027i	0.470074	+	0.882627i	$0.344227\pi$
$978$		0			0
$979$	5.81705	−	12.7376i	0.185914	−	0.407094i
$980$		0			0
$981$	−13.6791	+	43.2071i	−0.436741	+	1.37950i
$982$		0			0
$983$	−13.6980	+	8.80317i	−0.436898	+	0.280778i	−0.740544	−	0.672007i	$-0.765432\pi$
$983$	−13.6980	+	8.80317i	−0.436898	+	0.280778i	0.303646	+	0.952785i	$0.401796\pi$
$984$		0			0
$985$	−9.31994	+	14.5021i	−0.296958	+	0.462076i
$986$		0			0
$987$	0.793222	−	75.5019i	0.0252485	−	2.40325i
$988$		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
$993$	−1.96703	+	6.44774i	−0.0624219	+	0.204613i
$994$		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
$999$	8.52685	+	20.3445i	0.269778	+	0.643672i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.56788 - 0.736032i) q^{3} +(0.185142 - 1.28769i) q^{5} +(-4.35485 + 1.98879i) q^{7} +(1.91651 + 2.30802i) q^{9} +O(q^{10})\)	\(q+(-1.56788 - 0.736032i) q^{3} +(0.185142 - 1.28769i) q^{5} +(-4.35485 + 1.98879i) q^{7} +(1.91651 + 2.30802i) q^{9} +(-0.951568 + 0.279406i) q^{11} +(-0.564722 + 1.23657i) q^{13} +(-1.23806 + 1.88267i) q^{15} +(-4.94721 + 3.17938i) q^{17} +(-0.682840 + 1.06252i) q^{19} +(8.29172 + 0.0871127i) q^{21} +(-3.50391 + 3.27454i) q^{23} +(3.17360 + 0.931853i) q^{25} +(-1.30609 - 5.02933i) q^{27} +(-5.05992 - 7.87338i) q^{29} +(-0.896140 - 1.03420i) q^{31} +(1.69760 + 0.262309i) q^{33} +(1.75468 + 5.97590i) q^{35} +(-4.20207 + 0.604167i) q^{37} +(1.79557 - 1.52314i) q^{39} +(-4.80804 - 0.691291i) q^{41} +(2.85232 + 2.47155i) q^{43} +(3.32684 - 2.04056i) q^{45} -9.10570i q^{47} +(10.4254 - 12.0316i) q^{49} +(10.0968 - 1.34359i) q^{51} +(4.41374 + 9.66473i) q^{53} +(0.183612 + 1.27705i) q^{55} +(1.85266 - 1.16332i) q^{57} +(5.05009 + 2.30630i) q^{59} +(8.81714 - 7.64010i) q^{61} +(-12.9363 - 6.23955i) q^{63} +(1.48776 + 0.956126i) q^{65} +(-0.532570 + 1.81377i) q^{67} +(7.90389 - 2.55510i) q^{69} +(-0.175016 + 0.596050i) q^{71} +(-3.10347 - 1.99448i) q^{73} +(-4.28996 - 3.79691i) q^{75} +(3.58826 - 3.10924i) q^{77} +(-10.5050 - 4.79746i) q^{79} +(-1.65394 + 8.84672i) q^{81} +(-0.410479 - 2.85495i) q^{83} +(3.17811 + 6.95909i) q^{85} +(2.13830 + 16.0688i) q^{87} +(-9.24637 + 10.6709i) q^{89} -6.50819i q^{91} +(0.643838 + 2.28109i) q^{93} +(1.24177 + 1.07600i) q^{95} +(-9.60720 - 1.38131i) q^{97} +(-2.46857 - 1.66076i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + 6 q^{9}+O(q^{10}) \) 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

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