LMFDB - Embedded newform 880.2.cm.a.657.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [880,2,Mod(17,880)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(880, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 0, 5, 18])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("880.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.cm (of order $20$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			657.1
Character	$\chi$	$=$	880.657
Dual form			880.2.cm.a.513.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.710333 - 0.361933i) q^{3} +(-1.71486 - 1.43501i) q^{5} +(-0.0869260 - 0.170602i) q^{7} +(-1.38978 - 1.91287i) q^{9} +(-1.77694 + 2.80044i) q^{11} +(3.05749 + 0.484259i) q^{13} +(0.698743 + 1.64000i) q^{15} +(-3.66088 + 0.579827i) q^{17} +(-0.229844 - 0.707388i) q^{19} +0.152646i q^{21} +(1.14886 - 1.14886i) q^{23} +(0.881484 + 4.92169i) q^{25} +(0.669017 + 4.22401i) q^{27} +(-2.95025 + 9.07993i) q^{29} +(0.283900 - 0.206266i) q^{31} +(2.27579 - 1.34611i) q^{33} +(-0.0957498 + 0.417298i) q^{35} +(-4.81621 + 2.45398i) q^{37} +(-1.99657 - 1.45059i) q^{39} +(6.36824 - 2.06917i) q^{41} +(3.72708 + 3.72708i) q^{43} +(-0.361710 + 5.27464i) q^{45} +(-5.61318 + 11.0165i) q^{47} +(4.09295 - 5.63346i) q^{49} +(2.81030 + 0.913123i) q^{51} +(-1.41265 + 8.91914i) q^{53} +(7.06587 - 2.25243i) q^{55} +(-0.0927608 + 0.585669i) q^{57} +(-9.15496 - 2.97463i) q^{59} +(-3.46383 + 4.76756i) q^{61} +(-0.205531 + 0.403377i) q^{63} +(-4.54825 - 5.21797i) q^{65} +(-4.13426 - 4.13426i) q^{67} +(-1.23188 + 0.400262i) q^{69} +(-9.27272 - 6.73702i) q^{71} +(2.14008 - 1.09042i) q^{73} +(1.15517 - 3.81507i) q^{75} +(0.632224 + 0.0597184i) q^{77} +(-0.542434 + 0.394101i) q^{79} +(-1.13837 + 3.50353i) q^{81} +(2.60980 + 16.4776i) q^{83} +(7.10995 + 4.25908i) q^{85} +(5.38198 - 5.38198i) q^{87} -7.92190i q^{89} +(-0.183160 - 0.563709i) q^{91} +(-0.276318 + 0.0437645i) q^{93} +(-0.620959 + 1.54290i) q^{95} +(-1.36201 - 0.215721i) q^{97} +(7.82643 - 0.492943i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} - 2 q^{5} + 24 q^{11} - 10 q^{13} - 14 q^{15} + 24 q^{23} + 16 q^{25} + 16 q^{27} + 28 q^{31} + 66 q^{33} + 10 q^{35} - 8 q^{37} + 40 q^{41} - 28 q^{45} + 28 q^{47} - 20 q^{51} - 24 q^{53}+ \cdots - 8 q^{97}+O(q^{100}) $ 32 * q + 4 * q^3 - 2 * q^5 + 24 * q^11 - 10 * q^13 - 14 * q^15 + 24 * q^23 + 16 * q^25 + 16 * q^27 + 28 * q^31 + 66 * q^33 + 10 * q^35 - 8 * q^37 + 40 * q^41 - 28 * q^45 + 28 * q^47 - 20 * q^51 - 24 * q^53 + 64 * q^55 + 30 * q^57 - 60 * q^61 + 30 * q^63 + 8 * q^67 - 24 * q^71 + 50 * q^73 - 34 * q^75 + 70 * q^77 - 12 * q^81 - 90 * q^83 + 30 * q^85 - 20 * q^91 - 8 * q^93 + 40 * q^95 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{10}\right)$	$1$

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
$3$	−0.710333	−	0.361933i	−0.410111	−	0.208962i	0.236749	−	0.971571i	$-0.423918\pi$
$3$	−0.710333	−	0.361933i	−0.410111	−	0.208962i	−0.646860	+	0.762609i	$0.723918\pi$
$4$		0			0
$5$	−1.71486	−	1.43501i	−0.766908	−	0.641757i
$5$	−1.71486	−	1.43501i	−0.766908	−	0.641757i
$6$		0			0
$7$	−0.0869260	−	0.170602i	−0.0328550	−	0.0644815i	0.873996	−	0.485934i	$-0.161520\pi$
$7$	−0.0869260	−	0.170602i	−0.0328550	−	0.0644815i	−0.906851	+	0.421452i	$0.861520\pi$
$8$		0			0
$9$	−1.38978	−	1.91287i	−0.463259	−	0.637622i
$10$		0			0
$11$	−1.77694	+	2.80044i	−0.535768	+	0.844365i
$11$	−1.77694	+	2.80044i	−0.535768	+	0.844365i
$12$		0			0
$13$	3.05749	+	0.484259i	0.847995	+	0.134309i	0.565285	−	0.824896i	$-0.308766\pi$
$13$	3.05749	+	0.484259i	0.847995	+	0.134309i	0.282711	+	0.959205i	$0.408766\pi$
$14$		0			0
$15$	0.698743	+	1.64000i	0.180415	+	0.423446i
$16$		0			0
$17$	−3.66088	+	0.579827i	−0.887894	+	0.140629i	−0.583688	−	0.811978i	$-0.698391\pi$
$17$	−3.66088	+	0.579827i	−0.887894	+	0.140629i	−0.304206	+	0.952606i	$0.598391\pi$
$18$		0			0
$19$	−0.229844	−	0.707388i	−0.0527299	−	0.162286i	0.921224	−	0.389033i	$-0.127191\pi$
$19$	−0.229844	−	0.707388i	−0.0527299	−	0.162286i	−0.973954	+	0.226747i	$0.927191\pi$
$20$		0			0
$21$			0.152646i			0.0333100i
$22$		0			0
$23$	1.14886	−	1.14886i	0.239553	−	0.239553i	−0.577112	−	0.816665i	$-0.695820\pi$
$23$	1.14886	−	1.14886i	0.239553	−	0.239553i	0.816665	+	0.577112i	$0.195820\pi$
$24$		0			0
$25$	0.881484	+	4.92169i	0.176297	+	0.984337i
$26$		0			0
$27$	0.669017	+	4.22401i	0.128752	+	0.812911i
$28$		0			0
$29$	−2.95025	+	9.07993i	−0.547847	+	1.68610i	0.166275	+	0.986079i	$0.446826\pi$
$29$	−2.95025	+	9.07993i	−0.547847	+	1.68610i	−0.714122	+	0.700021i	$0.753174\pi$
$30$		0			0
$31$	0.283900	−	0.206266i	0.0509900	−	0.0370464i	−0.561998	−	0.827138i	$-0.689967\pi$
$31$	0.283900	−	0.206266i	0.0509900	−	0.0370464i	0.612988	+	0.790092i	$0.289967\pi$
$32$		0			0
$33$	2.27579	−	1.34611i	0.396165	−	0.234328i
$34$		0			0
$35$	−0.0957498	+	0.417298i	−0.0161847	+	0.0705363i
$36$		0			0
$37$	−4.81621	+	2.45398i	−0.791780	+	0.403432i	−0.802606	−	0.596510i	$-0.796554\pi$
$37$	−4.81621	+	2.45398i	−0.791780	+	0.403432i	0.0108264	+	0.999941i	$0.496554\pi$
$38$		0			0
$39$	−1.99657	−	1.45059i	−0.319707	−	0.232280i
$40$		0			0
$41$	6.36824	−	2.06917i	0.994552	−	0.323150i	0.233866	−	0.972269i	$-0.424862\pi$
$41$	6.36824	−	2.06917i	0.994552	−	0.323150i	0.760687	+	0.649119i	$0.224862\pi$
$42$		0			0
$43$	3.72708	+	3.72708i	0.568374	+	0.568374i	0.931673	−	0.363299i	$-0.118350\pi$
$43$	3.72708	+	3.72708i	0.568374	+	0.568374i	−0.363299	+	0.931673i	$0.618350\pi$
$44$		0			0
$45$	−0.361710	+	5.27464i	−0.0539205	+	0.786297i
$46$		0			0
$47$	−5.61318	+	11.0165i	−0.818766	+	1.60692i	−0.0242272	+	0.999706i	$0.507713\pi$
$47$	−5.61318	+	11.0165i	−0.818766	+	1.60692i	−0.794539	+	0.607213i	$0.792287\pi$
$48$		0			0
$49$	4.09295	−	5.63346i	0.584707	−	0.804780i
$50$		0			0
$51$	2.81030	+	0.913123i	0.393521	+	0.127863i
$52$		0			0
$53$	−1.41265	+	8.91914i	−0.194043	+	1.22514i	0.677761	+	0.735282i	$0.262950\pi$
$53$	−1.41265	+	8.91914i	−0.194043	+	1.22514i	−0.871804	+	0.489855i	$0.837050\pi$
$54$		0			0
$55$	7.06587	−	2.25243i	0.952762	−	0.303718i
$56$		0			0
$57$	−0.0927608	+	0.585669i	−0.0122865	+	0.0775737i
$58$		0			0
$59$	−9.15496	−	2.97463i	−1.19187	−	0.387263i	−0.355108	−	0.934825i	$-0.615556\pi$
$59$	−9.15496	−	2.97463i	−1.19187	−	0.387263i	−0.836765	+	0.547562i	$0.815556\pi$
$60$		0			0
$61$	−3.46383	+	4.76756i	−0.443498	+	0.610423i	−0.970985	−	0.239140i	$-0.923134\pi$
$61$	−3.46383	+	4.76756i	−0.443498	+	0.610423i	0.527487	+	0.849563i	$0.323134\pi$
$62$		0			0
$63$	−0.205531	+	0.403377i	−0.0258944	+	0.0508207i
$64$		0			0
$65$	−4.54825	−	5.21797i	−0.564141	−	0.647209i
$66$		0			0
$67$	−4.13426	−	4.13426i	−0.505081	−	0.505081i	0.407932	−	0.913012i	$-0.366250\pi$
$67$	−4.13426	−	4.13426i	−0.505081	−	0.505081i	−0.913012	+	0.407932i	$0.866250\pi$
$68$		0			0
$69$	−1.23188	+	0.400262i	−0.148301	+	0.0481859i
$70$		0			0
$71$	−9.27272	−	6.73702i	−1.10047	−	0.799538i	−0.119333	−	0.992854i	$-0.538075\pi$
$71$	−9.27272	−	6.73702i	−1.10047	−	0.799538i	−0.981136	+	0.193317i	$0.938075\pi$
$72$		0			0
$73$	2.14008	−	1.09042i	0.250477	−	0.127624i	−0.324245	−	0.945973i	$-0.605110\pi$
$73$	2.14008	−	1.09042i	0.250477	−	0.127624i	0.574722	+	0.818349i	$0.305110\pi$
$74$		0			0
$75$	1.15517	−	3.81507i	0.133388	−	0.440527i
$76$		0			0
$77$	0.632224	+	0.0597184i	0.0720486	+	0.00680554i
$78$		0			0
$79$	−0.542434	+	0.394101i	−0.0610286	+	0.0443399i	−0.617881	−	0.786271i	$-0.712009\pi$
$79$	−0.542434	+	0.394101i	−0.0610286	+	0.0443399i	0.556853	+	0.830611i	$0.312009\pi$
$80$		0			0
$81$	−1.13837	+	3.50353i	−0.126485	+	0.389282i
$82$		0			0
$83$	2.60980	+	16.4776i	0.286463	+	1.80865i	0.540372	+	0.841426i	$0.318284\pi$
$83$	2.60980	+	16.4776i	0.286463	+	1.80865i	−0.253909	+	0.967228i	$0.581716\pi$
$84$		0			0
$85$	7.10995	+	4.25908i	0.771183	+	0.461963i
$86$		0			0
$87$	5.38198	−	5.38198i	0.577009	−	0.577009i
$88$		0			0
$89$		−	7.92190i		−	0.839720i	−0.907589	−	0.419860i	$-0.862079\pi$
$89$		−	7.92190i		−	0.839720i	0.907589	−	0.419860i	$-0.137921\pi$
$90$		0			0
$91$	−0.183160	−	0.563709i	−0.0192004	−	0.0590927i
$92$		0			0
$93$	−0.276318	+	0.0437645i	−0.0286528	+	0.00453817i
$94$		0			0
$95$	−0.620959	+	1.54290i	−0.0637090	+	0.158298i
$96$		0			0
$97$	−1.36201	−	0.215721i	−0.138291	−	0.0219032i	0.0869051	−	0.996217i	$-0.472302\pi$
$97$	−1.36201	−	0.215721i	−0.138291	−	0.0219032i	−0.225196	+	0.974313i	$0.572302\pi$
$98$		0			0
$99$	7.82643	−	0.492943i	0.786585	−	0.0495427i
$100$		0			0
$101$	−2.83633	−	3.90387i	−0.282225	−	0.388449i	0.644244	−	0.764820i	$-0.277172\pi$
$101$	−2.83633	−	3.90387i	−0.282225	−	0.388449i	−0.926469	+	0.376370i	$0.877172\pi$
$102$		0			0
$103$	1.46972	+	2.88449i	0.144816	+	0.284217i	0.952009	−	0.306071i	$-0.0990144\pi$
$103$	1.46972	+	2.88449i	0.144816	+	0.284217i	−0.807193	+	0.590287i	$0.799014\pi$
$104$		0			0
$105$	0.219048	−	0.261766i	0.0213769	−	0.0255457i
$106$		0			0
$107$	9.85055	+	5.01911i	0.952289	+	0.485215i	0.859875	−	0.510505i	$-0.170542\pi$
$107$	9.85055	+	5.01911i	0.952289	+	0.485215i	0.0924142	+	0.995721i	$0.470542\pi$
$108$		0			0
$109$	−9.54212			−0.913969			−0.456985	−	0.889475i	$-0.651071\pi$
$109$	−9.54212			−0.913969			−0.456985	+	0.889475i	$0.651071\pi$
$110$		0			0
$111$	4.30929			0.409019
$112$		0			0
$113$	3.69562	+	1.88301i	0.347654	+	0.177139i	0.619094	−	0.785317i	$-0.287500\pi$
$113$	3.69562	+	1.88301i	0.347654	+	0.177139i	−0.271440	+	0.962455i	$0.587500\pi$
$114$		0			0
$115$	−3.61875	+	0.321505i	−0.337450	+	0.0299805i
$116$		0			0
$117$	−3.32291	−	6.52158i	−0.307203	−	0.602920i
$118$		0			0
$119$	0.417145	+	0.574151i	0.0382397	+	0.0526324i
$120$		0			0
$121$	−4.68496	−	9.95245i	−0.425905	−	0.904768i
$122$		0			0
$123$	−5.27247	−	0.835077i	−0.475403	−	0.0752964i
$124$		0			0
$125$	5.55105	−	9.70494i	0.496501	−	0.868036i
$126$		0			0
$127$	−14.3879	+	2.27881i	−1.27672	+	0.202212i	−0.757728	−	0.652570i	$-0.773691\pi$
$127$	−14.3879	+	2.27881i	−1.27672	+	0.202212i	−0.518987	+	0.854782i	$0.673691\pi$
$128$		0			0
$129$	−1.29851	−	3.99642i	−0.114328	−	0.351865i
$130$		0			0
$131$		−	9.76926i		−	0.853544i	−0.904359	−	0.426772i	$-0.859651\pi$
$131$		−	9.76926i		−	0.853544i	0.904359	−	0.426772i	$-0.140349\pi$
$132$		0			0
$133$	−0.100702	+	0.100702i	−0.00873200	+	0.00873200i
$134$		0			0
$135$	4.91423	−	8.20363i	0.422949	−	0.706056i
$136$		0			0
$137$	0.677380	+	4.27681i	0.0578725	+	0.365392i	0.999581	+	0.0289612i	$0.00921994\pi$
$137$	0.677380	+	4.27681i	0.0578725	+	0.365392i	−0.941708	+	0.336431i	$0.890780\pi$
$138$		0			0
$139$	3.24794	−	9.99613i	0.275487	−	0.847860i	−0.713604	−	0.700550i	$-0.752938\pi$
$139$	3.24794	−	9.99613i	0.275487	−	0.847860i	0.989090	−	0.147311i	$-0.0470618\pi$
$140$		0			0
$141$	7.97445	−	5.79378i	0.671570	−	0.487924i
$142$		0			0
$143$	−6.78912	+	7.70183i	−0.567735	+	0.644059i
$144$		0			0
$145$	18.0891	−	11.3372i	1.50221	−	0.941500i
$146$		0			0
$147$	−4.94629	+	2.52026i	−0.407963	+	0.207868i
$148$		0			0
$149$	−4.66189	−	3.38706i	−0.381917	−	0.277479i	0.380218	−	0.924897i	$-0.375849\pi$
$149$	−4.66189	−	3.38706i	−0.381917	−	0.277479i	−0.762135	+	0.647418i	$0.775849\pi$
$150$		0			0
$151$	14.2318	−	4.62419i	1.15817	−	0.376311i	0.333953	−	0.942590i	$-0.391617\pi$
$151$	14.2318	−	4.62419i	1.15817	−	0.376311i	0.824214	+	0.566278i	$0.191617\pi$
$152$		0			0
$153$	6.19694	+	6.19694i	0.500993	+	0.500993i
$154$		0			0
$155$	−0.782843	−	0.0536836i	−0.0628795	−	0.00431197i
$156$		0			0
$157$	−2.24640	+	4.40881i	−0.179282	+	0.351861i	−0.963106	−	0.269122i	$-0.913267\pi$
$157$	−2.24640	+	4.40881i	−0.179282	+	0.351861i	0.783824	+	0.620983i	$0.213267\pi$
$158$		0			0
$159$	4.23158	−	5.82427i	0.335586	−	0.461895i
$160$		0			0
$161$	−0.295863	−	0.0961317i	−0.0233173	−	0.00757624i
$162$		0			0
$163$	1.56695	−	9.89335i	0.122733	−	0.774907i	−0.847153	−	0.531349i	$-0.821685\pi$
$163$	1.56695	−	9.89335i	0.122733	−	0.774907i	0.969886	−	0.243558i	$-0.0783147\pi$
$164$		0			0
$165$	−5.83435	−	0.957393i	−0.454204	−	0.0745329i
$166$		0			0
$167$	1.88695	−	11.9137i	0.146017	−	0.921913i	−0.800517	−	0.599310i	$-0.795442\pi$
$167$	1.88695	−	11.9137i	0.146017	−	0.921913i	0.946534	−	0.322604i	$-0.104558\pi$
$168$		0			0
$169$	−3.24999	−	1.05599i	−0.250000	−	0.0812298i
$170$		0			0
$171$	−1.03371	+	1.42277i	−0.0790494	+	0.108802i
$172$		0			0
$173$	−5.65903	+	11.1065i	−0.430248	+	0.844410i	0.569501	+	0.821991i	$0.307137\pi$
$173$	−5.65903	+	11.1065i	−0.430248	+	0.844410i	−0.999749	+	0.0224186i	$0.992863\pi$
$174$		0			0
$175$	0.763025	−	0.578206i	0.0576793	−	0.0437082i
$176$		0			0
$177$	5.42645	+	5.42645i	0.407877	+	0.407877i
$178$		0			0
$179$	−19.1909	+	6.23551i	−1.43440	+	0.466064i	−0.920146	−	0.391575i	$-0.871930\pi$
$179$	−19.1909	+	6.23551i	−1.43440	+	0.466064i	−0.514252	+	0.857639i	$0.671930\pi$
$180$		0			0
$181$	−3.72935	−	2.70953i	−0.277200	−	0.201398i	0.440495	−	0.897755i	$-0.354803\pi$
$181$	−3.72935	−	2.70953i	−0.277200	−	0.201398i	−0.717695	+	0.696357i	$0.754803\pi$
$182$		0			0
$183$	4.18601	−	2.13288i	0.309439	−	0.157667i
$184$		0			0
$185$	11.7806	+	2.70308i	0.866127	+	0.198735i
$186$		0			0
$187$	4.88140	−	11.2824i	0.356963	−	0.825051i
$188$		0			0
$189$	0.662469	−	0.481312i	0.0481875	−	0.0350103i
$190$		0			0
$191$	−1.95493	+	6.01667i	−0.141454	+	0.435351i	−0.996538	−	0.0831389i	$-0.973505\pi$
$191$	−1.95493	+	6.01667i	−0.141454	+	0.435351i	0.855084	+	0.518490i	$0.173505\pi$
$192$		0			0
$193$	−0.927951	−	5.85885i	−0.0667954	−	0.421729i	−0.998314	−	0.0580368i	$-0.981516\pi$
$193$	−0.927951	−	5.85885i	−0.0667954	−	0.421729i	0.931519	−	0.363692i	$-0.118484\pi$
$194$		0			0
$195$	1.34222	+	5.35265i	0.0961181	+	0.383312i
$196$		0			0
$197$	9.90515	−	9.90515i	0.705713	−	0.705713i	−0.259918	−	0.965631i	$-0.583696\pi$
$197$	9.90515	−	9.90515i	0.705713	−	0.705713i	0.965631	+	0.259918i	$0.0836955\pi$
$198$		0			0
$199$			13.3828i			0.948680i	0.880342	+	0.474340i	$0.157313\pi$
$199$			13.3828i			0.948680i	−0.880342	+	0.474340i	$0.842687\pi$
$200$		0			0
$201$	1.44038	+	4.43303i	0.101596	+	0.312682i
$202$		0			0
$203$	1.80551	−	0.285964i	0.126722	−	0.0200708i
$204$		0			0
$205$	−13.8899	−	5.59017i	−0.970114	−	0.390434i
$206$		0			0
$207$	−3.79427	−	0.600953i	−0.263720	−	0.0417691i
$208$		0			0
$209$	2.38942	+	0.613321i	0.165280	+	0.0424243i
$210$		0			0
$211$	−3.48696	−	4.79939i	−0.240052	−	0.330404i	0.671944	−	0.740602i	$-0.265460\pi$
$211$	−3.48696	−	4.79939i	−0.240052	−	0.330404i	−0.911996	+	0.410198i	$0.865460\pi$
$212$		0			0
$213$	4.14837	+	8.14163i	0.284241	+	0.557855i
$214$		0			0
$215$	−1.04301	−	11.7398i	−0.0711330	−	0.800649i
$216$		0			0
$217$	−0.0598677	−	0.0305041i	−0.00406408	−	0.00207075i
$218$		0			0
$219$	−1.91483			−0.129392
$220$		0			0
$221$	−11.4739			−0.771818
$222$		0			0
$223$	18.9389	+	9.64984i	1.26824	+	0.646201i	0.953046	−	0.302826i	$-0.0979300\pi$
$223$	18.9389	+	9.64984i	1.26824	+	0.646201i	0.315195	+	0.949027i	$0.397930\pi$
$224$		0			0
$225$	8.18945	−	8.52621i	0.545964	−	0.568414i
$226$		0			0
$227$	−5.93372	−	11.6456i	−0.393835	−	0.772944i	0.605910	−	0.795533i	$-0.292809\pi$
$227$	−5.93372	−	11.6456i	−0.393835	−	0.772944i	−0.999745	+	0.0225888i	$0.992809\pi$
$228$		0			0
$229$	9.65796	+	13.2930i	0.638216	+	0.878429i	0.998519	−	0.0544066i	$-0.0173267\pi$
$229$	9.65796	+	13.2930i	0.638216	+	0.878429i	−0.360303	+	0.932835i	$0.617327\pi$
$230$		0			0
$231$	−0.427475	−	0.271242i	−0.0281258	−	0.0178464i
$232$		0			0
$233$	−15.4510	−	2.44720i	−1.01223	−	0.160321i	−0.371779	−	0.928321i	$-0.621252\pi$
$233$	−15.4510	−	2.44720i	−1.01223	−	0.160321i	−0.640450	+	0.768000i	$0.721252\pi$
$234$		0			0
$235$	25.4346	−	10.8367i	1.65917	−	0.706911i
$236$		0			0
$237$	0.527947	−	0.0836185i	0.0342938	−	0.00543161i
$238$		0			0
$239$	1.63214	+	5.02322i	0.105575	+	0.324925i	0.989865	−	0.142012i	$-0.0453572\pi$
$239$	1.63214	+	5.02322i	0.105575	+	0.324925i	−0.884290	+	0.466938i	$0.845357\pi$
$240$		0			0
$241$		−	16.1676i		−	1.04144i	−0.853726	−	0.520722i	$-0.825663\pi$
$241$		−	16.1676i		−	1.04144i	0.853726	−	0.520722i	$-0.174337\pi$
$242$		0			0
$243$	11.1488	−	11.1488i	0.715198	−	0.715198i
$244$		0			0
$245$	−15.1029	+	3.78716i	−0.964889	+	0.241953i
$246$		0			0
$247$	−0.360188	−	2.27413i	−0.0229182	−	0.144700i
$248$		0			0
$249$	4.10997	−	12.6492i	0.260458	−	0.801609i
$250$		0			0
$251$	15.6486	−	11.3694i	0.987729	−	0.717627i	0.0283063	−	0.999599i	$-0.490989\pi$
$251$	15.6486	−	11.3694i	0.987729	−	0.717627i	0.959423	+	0.281972i	$0.0909886\pi$
$252$		0			0
$253$	1.17586	+	5.25876i	0.0739254	+	0.330615i
$254$		0			0
$255$	−3.50893	−	5.59869i	−0.219738	−	0.350604i
$256$		0			0
$257$	−4.19318	+	2.13653i	−0.261563	+	0.133273i	−0.579855	−	0.814720i	$-0.696891\pi$
$257$	−4.19318	+	2.13653i	−0.261563	+	0.133273i	0.318292	+	0.947993i	$0.396891\pi$
$258$		0			0
$259$	0.837308	+	0.608340i	0.0520278	+	0.0378004i
$260$		0			0
$261$	21.4689	−	6.97566i	1.32889	−	0.431783i
$262$		0			0
$263$	−11.2218	−	11.2218i	−0.691964	−	0.691964i	0.270700	−	0.962664i	$-0.412745\pi$
$263$	−11.2218	−	11.2218i	−0.691964	−	0.691964i	−0.962664	+	0.270700i	$0.912745\pi$
$264$		0			0
$265$	15.2216	−	13.2679i	0.935053	−	0.815040i
$266$		0			0
$267$	−2.86720	+	5.62719i	−0.175470	+	0.344378i
$268$		0			0
$269$	−6.64926	+	9.15192i	−0.405412	+	0.558002i	−0.962092	−	0.272725i	$-0.912075\pi$
$269$	−6.64926	+	9.15192i	−0.405412	+	0.558002i	0.556680	+	0.830727i	$0.312075\pi$
$270$		0			0
$271$	−16.9556	−	5.50921i	−1.02998	−	0.334661i	−0.255198	−	0.966889i	$-0.582141\pi$
$271$	−16.9556	−	5.50921i	−1.02998	−	0.334661i	−0.774782	+	0.632228i	$0.782141\pi$
$272$		0			0
$273$	−0.0739200	+	0.466712i	−0.00447384	+	0.0282467i
$274$		0			0
$275$	−15.3492	−	6.27700i	−0.925594	−	0.378517i
$276$		0			0
$277$	0.732361	−	4.62395i	0.0440033	−	0.277826i	−0.955869	−	0.293793i	$-0.905083\pi$
$277$	0.732361	−	4.62395i	0.0440033	−	0.277826i	0.999873	+	0.0159666i	$0.00508253\pi$
$278$		0			0
$279$	−0.789117	−	0.256400i	−0.0472432	−	0.0153502i
$280$		0			0
$281$	−7.75247	+	10.6704i	−0.462474	+	0.636541i	−0.975019	−	0.222119i	$-0.928703\pi$
$281$	−7.75247	+	10.6704i	−0.462474	+	0.636541i	0.512546	+	0.858660i	$0.328703\pi$
$282$		0			0
$283$	−10.3449	+	20.3029i	−0.614938	+	1.20688i	0.348084	+	0.937463i	$0.386832\pi$
$283$	−10.3449	+	20.3029i	−0.614938	+	1.20688i	−0.963022	+	0.269421i	$0.913168\pi$
$284$		0			0
$285$	0.999513	−	0.871227i	0.0592061	−	0.0516070i
$286$		0			0
$287$	−0.906570	−	0.906570i	−0.0535131	−	0.0535131i
$288$		0			0
$289$	−3.10211	+	1.00794i	−0.182477	+	0.0592904i
$290$		0			0
$291$	0.889404	+	0.646190i	0.0521378	+	0.0378803i
$292$		0			0
$293$	−6.43996	+	3.28132i	−0.376226	+	0.191697i	−0.631870	−	0.775074i	$-0.717713\pi$
$293$	−6.43996	+	3.28132i	−0.376226	+	0.191697i	0.255644	+	0.966771i	$0.417713\pi$
$294$		0			0
$295$	11.4308	+	18.2385i	0.665529	+	1.06189i
$296$		0			0
$297$	−13.0179	−	5.63227i	−0.755375	−	0.326818i
$298$		0			0
$299$	4.06896	−	2.95628i	0.235314	−	0.170966i
$300$		0			0
$301$	0.311867	−	0.959827i	0.0179757	−	0.0553235i
$302$		0			0
$303$	0.601798	+	3.79960i	0.0345724	+	0.218282i
$304$		0			0
$305$	12.7815	−	3.20505i	0.731866	−	0.183521i
$306$		0			0
$307$	−20.1272	+	20.1272i	−1.14872	+	1.14872i	−0.161918	+	0.986804i	$0.551768\pi$
$307$	−20.1272	+	20.1272i	−1.14872	+	1.14872i	−0.986804	+	0.161918i	$0.948232\pi$
$308$		0			0
$309$		−	2.58088i		−	0.146821i
$310$		0			0
$311$	2.32254	+	7.14803i	0.131699	+	0.405328i	0.995062	−	0.0992557i	$-0.0316462\pi$
$311$	2.32254	+	7.14803i	0.131699	+	0.405328i	−0.863363	+	0.504583i	$0.831646\pi$
$312$		0			0
$313$	−1.32951	+	0.210574i	−0.0751483	+	0.0119023i	−0.193895	−	0.981022i	$-0.562112\pi$
$313$	−1.32951	+	0.210574i	−0.0751483	+	0.0119023i	0.118747	+	0.992925i	$0.462112\pi$
$314$		0			0
$315$	0.931306	−	0.396795i	0.0524732	−	0.0223569i
$316$		0			0
$317$	−11.1924	−	1.77271i	−0.628630	−	0.0995652i	−0.166013	−	0.986124i	$-0.553089\pi$
$317$	−11.1924	−	1.77271i	−0.628630	−	0.0995652i	−0.462617	+	0.886558i	$0.653089\pi$
$318$		0			0
$319$	−20.1854	−	24.3965i	−1.13017	−	1.36594i
$320$		0			0
$321$	−5.18059	−	7.13047i	−0.289152	−	0.397984i
$322$		0			0
$323$	1.25159	+	2.45639i	0.0696406	+	0.136677i
$324$		0			0
$325$	0.311760	+	15.4749i	0.0172934	+	0.858391i
$326$		0			0
$327$	6.77808	+	3.45360i	0.374829	+	0.190985i
$328$		0			0
$329$	2.36737			0.130517
$330$		0			0
$331$	17.7048			0.973145			0.486572	−	0.873640i	$-0.338247\pi$
$331$	17.7048			0.973145			0.486572	+	0.873640i	$0.338247\pi$
$332$		0			0
$333$	11.3876	+	5.80227i	0.624036	+	0.317962i
$334$		0			0
$335$	1.15696	+	13.0224i	0.0632117	+	0.711489i
$336$		0			0
$337$	3.45945	+	6.78954i	0.188448	+	0.369850i	0.965829	−	0.259180i	$-0.0834523\pi$
$337$	3.45945	+	6.78954i	0.188448	+	0.369850i	−0.777381	+	0.629030i	$0.783452\pi$
$338$		0			0
$339$	−1.94359	−	2.67513i	−0.105562	−	0.145293i
$340$		0			0
$341$	0.0731608	+	1.16157i	0.00396188	+	0.0629025i
$342$		0			0
$343$	−2.64066	−	0.418239i	−0.142582	−	0.0225828i
$344$		0			0
$345$	2.68688	+	1.08137i	0.144657	+	0.0582189i
$346$		0			0
$347$	9.21879	−	1.46011i	0.494891	−	0.0783830i	0.0959998	−	0.995381i	$-0.469395\pi$
$347$	9.21879	−	1.46011i	0.494891	−	0.0783830i	0.398891	+	0.916998i	$0.369395\pi$
$348$		0			0
$349$	0.464073	+	1.42827i	0.0248413	+	0.0764536i	0.962709	−	0.270540i	$-0.0872024\pi$
$349$	0.464073	+	1.42827i	0.0248413	+	0.0764536i	−0.937867	+	0.346994i	$0.887202\pi$
$350$		0			0
$351$			13.2388i			0.706637i
$352$		0			0
$353$	4.40229	−	4.40229i	0.234310	−	0.234310i	−0.580179	−	0.814489i	$-0.697017\pi$
$353$	4.40229	−	4.40229i	0.234310	−	0.234310i	0.814489	+	0.580179i	$0.197017\pi$
$354$		0			0
$355$	6.23370	+	24.8595i	0.330850	+	1.31941i
$356$		0			0
$357$	−0.0885080	−	0.558817i	−0.00468434	−	0.0295757i
$358$		0			0
$359$	−8.12845	+	25.0168i	−0.429003	+	1.32034i	0.470105	+	0.882611i	$0.344216\pi$
$359$	−8.12845	+	25.0168i	−0.429003	+	1.32034i	−0.899108	+	0.437726i	$0.855784\pi$
$360$		0			0
$361$	14.9238	−	10.8427i	0.785461	−	0.570671i
$362$		0			0
$363$	−0.274237	+	8.76519i	−0.0143937	+	0.460053i
$364$		0			0
$365$	−5.23470	−	1.20111i	−0.273997	−	0.0628691i
$366$		0			0
$367$	−7.27872	+	3.70869i	−0.379946	+	0.193592i	−0.633524	−	0.773723i	$-0.718392\pi$
$367$	−7.27872	+	3.70869i	−0.379946	+	0.193592i	0.253579	+	0.967315i	$0.418392\pi$
$368$		0			0
$369$	−12.8085	−	9.30591i	−0.666783	−	0.484446i
$370$		0			0
$371$	1.64442	−	0.534304i	0.0853740	−	0.0277397i
$372$		0			0
$373$	6.12473	+	6.12473i	0.317126	+	0.317126i	0.847662	−	0.530536i	$-0.178009\pi$
$373$	6.12473	+	6.12473i	0.317126	+	0.317126i	−0.530536	+	0.847662i	$0.678009\pi$
$374$		0			0
$375$	−7.45563	+	4.88463i	−0.385007	+	0.252241i
$376$		0			0
$377$	−13.4174	+	26.3331i	−0.691031	+	1.35622i
$378$		0			0
$379$	0.363481	−	0.500288i	0.0186708	−	0.0256981i	−0.799580	−	0.600560i	$-0.794944\pi$
$379$	0.363481	−	0.500288i	0.0186708	−	0.0256981i	0.818250	+	0.574862i	$0.194944\pi$
$380$		0			0
$381$	11.0449	+	3.58872i	0.565849	+	0.183856i
$382$		0			0
$383$	−1.62362	+	10.2511i	−0.0829629	+	0.523807i	0.910850	+	0.412738i	$0.135428\pi$
$383$	−1.62362	+	10.2511i	−0.0829629	+	0.523807i	−0.993813	+	0.111069i	$0.964572\pi$
$384$		0			0
$385$	−0.998478	−	1.00966i	−0.0508871	−	0.0514569i
$386$		0			0
$387$	1.94959	−	12.3092i	0.0991031	−	0.625712i
$388$		0			0
$389$	−21.0630	−	6.84378i	−1.06794	−	0.346993i	−0.278252	−	0.960508i	$-0.589755\pi$
$389$	−21.0630	−	6.84378i	−1.06794	−	0.346993i	−0.789683	+	0.613515i	$0.789755\pi$
$390$		0			0
$391$	−3.53969	+	4.87197i	−0.179010	+	0.246386i
$392$		0			0
$393$	−3.53581	+	6.93942i	−0.178358	+	0.350048i
$394$		0			0
$395$	1.49574	+	0.102571i	0.0752587	+	0.00516089i
$396$		0			0
$397$	10.7769	+	10.7769i	0.540876	+	0.540876i	0.923786	−	0.382910i	$-0.125078\pi$
$397$	10.7769	+	10.7769i	0.540876	+	0.540876i	−0.382910	+	0.923786i	$0.625078\pi$
$398$		0			0
$399$	0.107980	−	0.0350847i	0.00540574	−	0.00175643i
$400$		0			0
$401$	3.46399	+	2.51673i	0.172983	+	0.125680i	0.670908	−	0.741540i	$-0.265904\pi$
$401$	3.46399	+	2.51673i	0.172983	+	0.125680i	−0.497925	+	0.867220i	$0.665904\pi$
$402$		0			0
$403$	0.967909	−	0.493174i	0.0482150	−	0.0245668i
$404$		0			0
$405$	6.97975	−	4.37450i	0.346827	−	0.217371i
$406$		0			0
$407$	1.68589	−	17.8481i	0.0835664	−	0.884697i
$408$		0			0
$409$	3.47523	−	2.52490i	0.171839	−	0.124848i	−0.498541	−	0.866866i	$-0.666131\pi$
$409$	3.47523	−	2.52490i	0.171839	−	0.124848i	0.670381	+	0.742017i	$0.266131\pi$
$410$		0			0
$411$	1.06675	−	3.28312i	0.0526190	−	0.161945i
$412$		0			0
$413$	0.288327	+	1.82043i	0.0141877	+	0.0895773i
$414$		0			0
$415$	19.1701	−	32.0019i	0.941025	−	1.57091i
$416$		0			0
$417$	−5.92504	+	5.92504i	−0.290151	+	0.290151i
$418$		0			0
$419$		−	1.20241i		−	0.0587414i	−0.999569	−	0.0293707i	$-0.990650\pi$
$419$		−	1.20241i		−	0.0587414i	0.999569	−	0.0293707i	$-0.00935032\pi$
$420$		0			0
$421$	9.67493	+	29.7764i	0.471527	+	1.45121i	0.850584	+	0.525839i	$0.176248\pi$
$421$	9.67493	+	29.7764i	0.471527	+	1.45121i	−0.379057	+	0.925373i	$0.623752\pi$
$422$		0			0
$423$	28.8741	−	4.57321i	1.40391	−	0.222357i
$424$		0			0
$425$	−6.08073	−	17.5066i	−0.294959	−	0.849195i
$426$		0			0
$427$	1.11445	+	0.176512i	0.0539321	+	0.00854201i
$428$		0			0
$429$	7.61008	−	3.01366i	0.367418	−	0.145501i
$430$		0			0
$431$	5.81395	+	8.00222i	0.280048	+	0.385453i	0.925750	−	0.378137i	$-0.123435\pi$
$431$	5.81395	+	8.00222i	0.280048	+	0.385453i	−0.645702	+	0.763590i	$0.723435\pi$
$432$		0			0
$433$	12.2497	+	24.0414i	0.588683	+	1.15536i	0.972708	+	0.232033i	$0.0745378\pi$
$433$	12.2497	+	24.0414i	0.588683	+	1.15536i	−0.384025	+	0.923323i	$0.625462\pi$
$434$		0			0
$435$	−16.9525	+	1.50614i	−0.812812	+	0.0722137i
$436$		0			0
$437$	−1.07675	−	0.548629i	−0.0515077	−	0.0262445i
$438$		0			0
$439$	24.5862			1.17344			0.586718	−	0.809791i	$-0.300420\pi$
$439$	24.5862			1.17344			0.586718	+	0.809791i	$0.300420\pi$
$440$		0			0
$441$	−16.4643			−0.784016
$442$		0			0
$443$	−27.4404	−	13.9816i	−1.30373	−	0.664286i	−0.342370	−	0.939565i	$-0.611230\pi$
$443$	−27.4404	−	13.9816i	−1.30373	−	0.664286i	−0.961364	+	0.275279i	$0.911230\pi$
$444$		0			0
$445$	−11.3680	+	13.5849i	−0.538896	+	0.643988i
$446$		0			0
$447$	2.08561	+	4.09323i	0.0986458	+	0.193603i
$448$		0			0
$449$	−4.30536	−	5.92582i	−0.203182	−	0.279657i	0.695250	−	0.718768i	$-0.255293\pi$
$449$	−4.30536	−	5.92582i	−0.203182	−	0.279657i	−0.898433	+	0.439111i	$0.855293\pi$
$450$		0			0
$451$	−5.52141	+	21.5107i	−0.259993	+	1.01290i
$452$		0			0
$453$	−11.7830	−	1.86624i	−0.553612	−	0.0876835i
$454$		0			0
$455$	−0.494835	+	1.22952i	−0.0231982	+	0.0576407i
$456$		0			0
$457$	−6.65265	+	1.05368i	−0.311198	+	0.0492889i	−0.310080	−	0.950710i	$-0.600356\pi$
$457$	−6.65265	+	1.05368i	−0.311198	+	0.0492889i	−0.00111791	+	0.999999i	$0.500356\pi$
$458$		0			0
$459$	−4.89838	−	15.0757i	−0.228637	−	0.703672i
$460$		0			0
$461$			29.0801i			1.35440i	0.735801	+	0.677198i	$0.236806\pi$
$461$			29.0801i			1.35440i	−0.735801	+	0.677198i	$0.763194\pi$
$462$		0			0
$463$	−17.5146	+	17.5146i	−0.813970	+	0.813970i	−0.985227	−	0.171256i	$-0.945217\pi$
$463$	−17.5146	+	17.5146i	−0.813970	+	0.813970i	0.171256	+	0.985227i	$0.445217\pi$
$464$		0			0
$465$	0.536649	+	0.321470i	0.0248865	+	0.0149078i
$466$		0			0
$467$	4.13890	+	26.1320i	0.191525	+	1.20924i	0.876763	+	0.480923i	$0.159698\pi$
$467$	4.13890	+	26.1320i	0.191525	+	1.20924i	−0.685237	+	0.728320i	$0.740302\pi$
$468$		0			0
$469$	−0.345938	+	1.06469i	−0.0159739	+	0.0491627i
$470$		0			0
$471$	3.19138	−	2.31868i	0.147051	−	0.106839i
$472$		0			0
$473$	−17.0603	+	3.81467i	−0.784432	+	0.175399i
$474$		0			0
$475$	3.27894	−	1.75477i	0.150448	−	0.0805145i
$476$		0			0
$477$	19.0244	−	9.69341i	0.871067	−	0.443831i
$478$		0			0
$479$	−21.2408	−	15.4324i	−0.970519	−	0.705123i	−0.0149492	−	0.999888i	$-0.504759\pi$
$479$	−21.2408	−	15.4324i	−0.970519	−	0.705123i	−0.955570	+	0.294765i	$0.904759\pi$
$480$		0			0
$481$	−15.9139	+	5.17073i	−0.725610	+	0.235765i
$482$		0			0
$483$	0.175368	+	0.175368i	0.00797952	+	0.00797952i
$484$		0			0
$485$	2.02609	+	2.32443i	0.0920001	+	0.105547i
$486$		0			0
$487$	−10.5939	+	20.7917i	−0.480056	+	0.942163i	0.516262	+	0.856431i	$0.327323\pi$
$487$	−10.5939	+	20.7917i	−0.480056	+	0.942163i	−0.996318	+	0.0857326i	$0.972677\pi$
$488$		0			0
$489$	−4.69379	+	6.46044i	−0.212260	+	0.292151i
$490$		0			0
$491$	−17.4497	−	5.66974i	−0.787493	−	0.255872i	−0.112457	−	0.993657i	$-0.535872\pi$
$491$	−17.4497	−	5.66974i	−0.787493	−	0.255872i	−0.675036	+	0.737785i	$0.735872\pi$
$492$		0			0
$493$	5.53572	−	34.9512i	0.249316	−	1.57412i
$494$		0			0
$495$	−14.1286	−	10.3857i	−0.635033	−	0.466802i
$496$		0			0
$497$	−0.343309	+	2.16757i	−0.0153995	+	0.0972286i
$498$		0			0
$499$	−11.1824	−	3.63339i	−0.500595	−	0.162653i	0.0478260	−	0.998856i	$-0.484771\pi$
$499$	−11.1824	−	3.63339i	−0.500595	−	0.162653i	−0.548421	+	0.836203i	$0.684771\pi$
$500$		0			0
$501$	−5.65234	+	7.77978i	−0.252528	+	0.347575i
$502$		0			0
$503$	2.42460	−	4.75855i	0.108108	−	0.212173i	−0.830615	−	0.556848i	$-0.812011\pi$
$503$	2.42460	−	4.75855i	0.108108	−	0.212173i	0.938722	+	0.344674i	$0.112011\pi$
$504$		0			0
$505$	−0.738195	+	10.7647i	−0.0328492	+	0.479025i
$506$		0			0
$507$	1.92638	+	1.92638i	0.0855536	+	0.0855536i
$508$		0			0
$509$	−18.6283	+	6.05272i	−0.825687	+	0.268282i	−0.691228	−	0.722637i	$-0.742930\pi$
$509$	−18.6283	+	6.05272i	−0.825687	+	0.268282i	−0.134459	+	0.990919i	$0.542930\pi$
$510$		0			0
$511$	−0.372057	−	0.270315i	−0.0164588	−	0.0119580i
$512$		0			0
$513$	2.83424	−	1.44412i	0.125135	−	0.0637594i
$514$		0			0
$515$	1.61891	−	7.05555i	0.0713376	−	0.310905i
$516$		0			0
$517$	−20.8767	−	35.2950i	−0.918158	−	1.55227i
$518$		0			0
$519$	8.03959	−	5.84110i	0.352899	−	0.256396i
$520$		0			0
$521$	5.78913	−	17.8171i	0.253626	−	0.780582i	−0.740471	−	0.672089i	$-0.765397\pi$
$521$	5.78913	−	17.8171i	0.253626	−	0.780582i	0.994097	−	0.108493i	$-0.0346026\pi$
$522$		0			0
$523$	−0.403961	−	2.55051i	−0.0176640	−	0.111526i	0.977281	−	0.211948i	$-0.0679807\pi$
$523$	−0.403961	−	2.55051i	−0.0176640	−	0.111526i	−0.994945	+	0.100422i	$0.967981\pi$
$524$		0			0
$525$	−0.751273	+	0.134555i	−0.0327883	+	0.00587245i
$526$		0			0
$527$	−0.919727	+	0.919727i	−0.0400639	+	0.0400639i
$528$		0			0
$529$			20.3603i			0.885228i
$530$		0			0
$531$	7.03330	+	21.6463i	0.305219	+	0.939368i
$532$		0			0
$533$	20.4729	−	3.24258i	0.886778	−	0.140452i
$534$		0			0
$535$	−9.68984	−	22.7427i	−0.418928	−	0.983253i
$536$		0			0
$537$	15.8888	+	2.51654i	0.685652	+	0.108597i
$538$		0			0
$539$	8.50325	+	21.4724i	0.366261	+	0.924881i
$540$		0			0
$541$	5.42829	+	7.47139i	0.233380	+	0.321220i	0.909604	−	0.415476i	$-0.136385\pi$
$541$	5.42829	+	7.47139i	0.233380	+	0.321220i	−0.676224	+	0.736696i	$0.736385\pi$
$542$		0			0
$543$	1.66841	+	3.27444i	0.0715983	+	0.140520i
$544$		0			0
$545$	16.3634	+	13.6931i	0.700931	+	0.586546i
$546$		0			0
$547$	−0.954295	−	0.486237i	−0.0408027	−	0.0207900i	0.433470	−	0.901168i	$-0.357289\pi$
$547$	−0.954295	−	0.486237i	−0.0408027	−	0.0207900i	−0.474273	+	0.880378i	$0.657289\pi$
$548$		0			0
$549$	13.9337			0.594674
$550$		0			0
$551$	7.10113			0.302518
$552$		0			0
$553$	0.114386	+	0.0582826i	0.00486419	+	0.00247843i
$554$		0			0
$555$	−7.38982	−	6.18387i	−0.313680	−	0.262491i
$556$		0			0
$557$	−19.5384	−	38.3462i	−0.827868	−	1.62478i	−0.779876	−	0.625934i	$-0.784718\pi$
$557$	−19.5384	−	38.3462i	−0.827868	−	1.62478i	−0.0479915	−	0.998848i	$-0.515282\pi$
$558$		0			0
$559$	9.59064	+	13.2004i	0.405641	+	0.558316i
$560$		0			0
$561$	−7.55089	+	6.24752i	−0.318799	+	0.263771i
$562$		0			0
$563$	25.5439	+	4.04575i	1.07655	+	0.170508i	0.669435	−	0.742871i	$-0.266536\pi$
$563$	25.5439	+	4.04575i	1.07655	+	0.170508i	0.407111	+	0.913379i	$0.366536\pi$
$564$		0			0
$565$	−3.63532	−	8.53235i	−0.152939	−	0.358959i
$566$		0			0
$567$	0.696664	−	0.110341i	0.0292571	−	0.00463387i
$568$		0			0
$569$	8.39651	+	25.8418i	0.352000	+	1.08334i	0.957729	+	0.287673i	$0.0928816\pi$
$569$	8.39651	+	25.8418i	0.352000	+	1.08334i	−0.605729	+	0.795671i	$0.707118\pi$
$570$		0			0
$571$		−	40.5475i		−	1.69686i	−0.529308	−	0.848430i	$-0.677549\pi$
$571$		−	40.5475i		−	1.69686i	0.529308	−	0.848430i	$-0.322451\pi$
$572$		0			0
$573$	3.56628	−	3.56628i	0.148984	−	0.148984i
$574$		0			0
$575$	6.66701	+	4.64161i	0.278034	+	0.193569i
$576$		0			0
$577$	5.28872	+	33.3917i	0.220172	+	1.39011i	0.811815	+	0.583914i	$0.198479\pi$
$577$	5.28872	+	33.3917i	0.220172	+	1.39011i	−0.591643	+	0.806200i	$0.701521\pi$
$578$		0			0
$579$	−1.46136	+	4.49759i	−0.0607319	+	0.186913i
$580$		0			0
$581$	2.58426	−	1.87757i	0.107213	−	0.0778948i
$582$		0			0
$583$	−22.4673	−	19.8048i	−0.930502	−	0.820233i
$584$		0			0
$585$	−3.66022	+	15.9520i	−0.151331	+	0.659534i
$586$		0			0
$587$	−8.62859	+	4.39649i	−0.356140	+	0.181462i	−0.622902	−	0.782300i	$-0.714046\pi$
$587$	−8.62859	+	4.39649i	−0.356140	+	0.181462i	0.266762	+	0.963763i	$0.414046\pi$
$588$		0			0
$589$	−0.211163	−	0.153419i	−0.00870081	−	0.00632151i
$590$		0			0
$591$	−10.6210	+	3.45096i	−0.436888	+	0.141953i
$592$		0			0
$593$	−14.0452	−	14.0452i	−0.576769	−	0.576769i	0.357243	−	0.934012i	$-0.383717\pi$
$593$	−14.0452	−	14.0452i	−0.576769	−	0.576769i	−0.934012	+	0.357243i	$0.883717\pi$
$594$		0			0
$595$	0.108568	−	1.58320i	0.00445086	−	0.0649048i
$596$		0			0
$597$	4.84367	−	9.50623i	0.198238	−	0.389064i
$598$		0			0
$599$	−2.65433	+	3.65338i	−0.108453	+	0.149273i	−0.859793	−	0.510642i	$-0.829408\pi$
$599$	−2.65433	+	3.65338i	−0.108453	+	0.149273i	0.751340	+	0.659915i	$0.229408\pi$
$600$		0			0
$601$	−7.96746	−	2.58878i	−0.324999	−	0.105599i	0.141973	−	0.989871i	$-0.454655\pi$
$601$	−7.96746	−	2.58878i	−0.324999	−	0.105599i	−0.466973	+	0.884272i	$0.654655\pi$
$602$		0			0
$603$	−2.16258	+	13.6540i	−0.0880671	+	0.556034i
$604$		0			0
$605$	−6.24783	+	23.7900i	−0.254011	+	0.967201i
$606$		0			0
$607$	−1.20123	+	7.58425i	−0.0487563	+	0.307835i	−1.00000		0.000605683i	$-0.999807\pi$
$607$	−1.20123	+	7.58425i	−0.0487563	+	0.307835i	0.951244	+	0.308441i	$0.0998072\pi$
$608$		0			0
$609$	−1.38601	−	0.450342i	−0.0561640	−	0.0182488i
$610$		0			0
$611$	−22.4971	+	30.9646i	−0.910134	+	1.25269i
$612$		0			0
$613$	19.4882	−	38.2477i	0.787120	−	1.54481i	−0.0506058	−	0.998719i	$-0.516115\pi$
$613$	19.4882	−	38.2477i	0.787120	−	1.54481i	0.837726	−	0.546091i	$-0.183885\pi$
$614$		0			0
$615$	7.84320	+	8.99810i	0.316268	+	0.362838i
$616$		0			0
$617$	33.4407	+	33.4407i	1.34627	+	1.34627i	0.889671	+	0.456601i	$0.150933\pi$
$617$	33.4407	+	33.4407i	1.34627	+	1.34627i	0.456601	+	0.889671i	$0.349067\pi$
$618$		0			0
$619$	20.0674	−	6.52029i	0.806576	−	0.262073i	0.123429	−	0.992353i	$-0.460611\pi$
$619$	20.0674	−	6.52029i	0.806576	−	0.262073i	0.683147	+	0.730281i	$0.260611\pi$
$620$		0			0
$621$	5.62139	+	4.08418i	0.225578	+	0.163892i
$622$		0			0
$623$	−1.35149	+	0.688620i	−0.0541464	+	0.0275890i
$624$		0			0
$625$	−23.4460	+	8.67678i	−0.937839	+	0.347071i
$626$		0			0
$627$	−1.47530	−	1.30047i	−0.0589179	−	0.0519358i
$628$		0			0
$629$	16.2087	−	11.7763i	0.646282	−	0.469552i
$630$		0			0
$631$	8.72043	−	26.8387i	0.347155	−	1.06843i	−0.613265	−	0.789877i	$-0.710144\pi$
$631$	8.72043	−	26.8387i	0.347155	−	1.06843i	0.960420	−	0.278555i	$-0.0898556\pi$
$632$		0			0
$633$	0.739847	+	4.67121i	0.0294063	+	0.185664i
$634$		0			0
$635$	27.9433	+	16.7389i	1.10889	+	0.664263i
$636$		0			0
$637$	15.2422	−	15.2422i	0.603918	−	0.603918i
$638$		0			0
$639$			27.1004i			1.07208i
$640$		0			0
$641$	−5.23436	−	16.1097i	−0.206745	−	0.636295i	−0.999637	−	0.0269333i	$-0.991426\pi$
$641$	−5.23436	−	16.1097i	−0.206745	−	0.636295i	0.792893	−	0.609362i	$-0.208574\pi$
$642$		0			0
$643$	−6.19838	+	0.981726i	−0.244440	+	0.0387155i	−0.277452	−	0.960739i	$-0.589490\pi$
$643$	−6.19838	+	0.981726i	−0.244440	+	0.0387155i	0.0330121	+	0.999455i	$0.489490\pi$
$644$		0			0
$645$	−3.50814	+	8.71668i	−0.138133	+	0.343219i
$646$		0			0
$647$	42.9518	+	6.80289i	1.68861	+	0.267449i	0.925479	−	0.378798i	$-0.123662\pi$
$647$	42.9518	+	6.80289i	1.68861	+	0.267449i	0.763128	+	0.646247i	$0.223662\pi$
$648$		0			0
$649$	24.5981	−	20.3522i	0.965559	−	0.798893i
$650$		0			0
$651$	0.0314855	+	0.0433361i	0.00123402	+	0.00169848i
$652$		0			0
$653$	−4.41780	−	8.67042i	−0.172882	−	0.339300i	0.788266	−	0.615335i	$-0.210979\pi$
$653$	−4.41780	−	8.67042i	−0.172882	−	0.339300i	−0.961147	+	0.276035i	$0.910979\pi$
$654$		0			0
$655$	−14.0190	+	16.7529i	−0.547767	+	0.654590i
$656$		0			0
$657$	−5.06007	−	2.57823i	−0.197412	−	0.100586i
$658$		0			0
$659$	3.37375			0.131423			0.0657113	−	0.997839i	$-0.479068\pi$
$659$	3.37375			0.131423			0.0657113	+	0.997839i	$0.479068\pi$
$660$		0			0
$661$	9.93056			0.386254			0.193127	−	0.981174i	$-0.438137\pi$
$661$	9.93056			0.386254			0.193127	+	0.981174i	$0.438137\pi$
$662$		0			0
$663$	8.15028	+	4.15278i	0.316531	+	0.161280i
$664$		0			0
$665$	0.317199	−	0.0281813i	0.0123005	−	0.00109282i
$666$		0			0
$667$	7.04213	+	13.8210i	0.272672	+	0.535150i
$668$		0			0
$669$	−9.96031	−	13.7092i	−0.385088	−	0.530028i
$670$		0			0
$671$	−7.19624	−	18.1719i	−0.277808	−	0.701520i
$672$		0			0
$673$	−37.7823	−	5.98412i	−1.45640	−	0.230671i	−0.622514	−	0.782609i	$-0.713889\pi$
$673$	−37.7823	−	5.98412i	−1.45640	−	0.230671i	−0.833885	+	0.551938i	$0.813889\pi$
$674$		0			0
$675$	−20.1995	+	7.01609i	−0.777479	+	0.270049i
$676$		0			0
$677$	−31.7956	+	5.03592i	−1.22200	+	0.193546i	−0.733911	−	0.679246i	$-0.762307\pi$
$677$	−31.7956	+	5.03592i	−1.22200	+	0.193546i	−0.488092	+	0.872792i	$0.662307\pi$
$678$		0			0
$679$	0.0815917	+	0.251113i	0.00313120	+	0.00963684i
$680$		0			0
$681$			10.4198i			0.399289i
$682$		0			0
$683$	28.7223	−	28.7223i	1.09903	−	1.09903i	0.104505	−	0.994524i	$-0.466674\pi$
$683$	28.7223	−	28.7223i	1.09903	−	1.09903i	0.994524	−	0.104505i	$-0.0333260\pi$
$684$		0			0
$685$	4.97566	−	8.30617i	0.190110	−	0.317363i
$686$		0			0
$687$	−2.04918	−	12.9380i	−0.0781811	−	0.493616i
$688$		0			0
$689$	−8.63834	+	26.5861i	−0.329095	+	1.01285i
$690$		0			0
$691$	−20.4397	+	14.8503i	−0.777564	+	0.564933i	−0.904247	−	0.427010i	$-0.859567\pi$
$691$	−20.4397	+	14.8503i	−0.777564	+	0.564933i	0.126683	+	0.991943i	$0.459567\pi$
$692$		0			0
$693$	−0.764417	−	1.29235i	−0.0290378	−	0.0490925i
$694$		0			0
$695$	−19.9143	+	12.4811i	−0.755393	+	0.473436i
$696$		0			0
$697$	−22.1136	+	11.2675i	−0.837613	+	0.426785i
$698$		0			0
$699$	10.0896	+	7.33055i	0.381625	+	0.277267i
$700$		0			0
$701$	26.8458	−	8.72273i	1.01395	−	0.329453i	0.245525	−	0.969390i	$-0.421040\pi$
$701$	26.8458	−	8.72273i	1.01395	−	0.329453i	0.768427	+	0.639937i	$0.221040\pi$
$702$		0			0
$703$	2.84289	+	2.84289i	0.107222	+	0.107222i
$704$		0			0
$705$	−21.9892	−	1.50791i	−0.828161	−	0.0567914i
$706$		0			0
$707$	−0.419457	+	0.823230i	−0.0157753	+	0.0309608i
$708$		0			0
$709$	4.79615	−	6.60134i	0.180123	−	0.247918i	−0.709402	−	0.704804i	$-0.751035\pi$
$709$	4.79615	−	6.60134i	0.180123	−	0.247918i	0.889526	+	0.456885i	$0.151035\pi$
$710$		0			0
$711$	1.50773	+	0.489890i	0.0565441	+	0.0183723i
$712$		0			0
$713$	0.0891912	−	0.563131i	0.00334024	−	0.0210894i
$714$		0			0
$715$	22.6946	−	3.46508i	0.848730	−	0.129587i
$716$		0			0
$717$	0.658703	−	4.15889i	0.0245997	−	0.155317i
$718$		0			0
$719$	−0.986856	−	0.320649i	−0.0368035	−	0.0119582i	0.290557	−	0.956858i	$-0.406159\pi$
$719$	−0.986856	−	0.320649i	−0.0368035	−	0.0119582i	−0.327361	+	0.944899i	$0.606159\pi$
$720$		0			0
$721$	0.364342	−	0.501474i	0.0135688	−	0.0186759i
$722$		0			0
$723$	−5.85157	+	11.4843i	−0.217622	+	0.427107i
$724$		0			0
$725$	−47.2892	−	6.51637i	−1.75627	−	0.242012i
$726$		0			0
$727$	3.27903	+	3.27903i	0.121612	+	0.121612i	0.765294	−	0.643681i	$-0.222594\pi$
$727$	3.27903	+	3.27903i	0.121612	+	0.121612i	−0.643681	+	0.765294i	$0.722594\pi$
$728$		0			0
$729$	−1.44390	+	0.469153i	−0.0534779	+	0.0173760i
$730$		0			0
$731$	−15.8055	−	11.4833i	−0.584586	−	0.424726i
$732$		0			0
$733$	40.6968	−	20.7361i	1.50317	−	0.765904i	0.507751	−	0.861504i	$-0.330477\pi$
$733$	40.6968	−	20.7361i	1.50317	−	0.765904i	0.995420	+	0.0956003i	$0.0304771\pi$
$734$		0			0
$735$	12.0988	+	2.77609i	0.446271	+	0.102398i
$736$		0			0
$737$	18.9241	−	4.23142i	0.697079	−	0.155866i
$738$		0			0
$739$	3.07164	−	2.23167i	0.112992	−	0.0820934i	−0.529854	−	0.848089i	$-0.677753\pi$
$739$	3.07164	−	2.23167i	0.112992	−	0.0820934i	0.642846	+	0.765995i	$0.277753\pi$
$740$		0			0
$741$	−0.567231	+	1.74576i	−0.0208377	+	0.0641320i
$742$		0			0
$743$	−6.63736	−	41.9067i	−0.243501	−	1.53741i	−0.741931	−	0.670476i	$-0.766090\pi$
$743$	−6.63736	−	41.9067i	−0.243501	−	1.53741i	0.498430	−	0.866930i	$-0.333910\pi$
$744$		0			0
$745$	3.13401	+	12.4982i	0.114821	+	0.457899i
$746$		0			0
$747$	27.8924	−	27.8924i	1.02053	−	1.02053i
$748$		0			0
$749$		−	2.11681i		−	0.0773467i
$750$		0			0
$751$	3.08775	+	9.50312i	0.112674	+	0.346774i	0.991455	−	0.130451i	$-0.0416427\pi$
$751$	3.08775	+	9.50312i	0.112674	+	0.346774i	−0.878781	+	0.477225i	$0.841643\pi$
$752$		0			0
$753$	−15.2306	+	2.41230i	−0.555035	+	0.0879089i
$754$		0			0
$755$	−31.0413	−	12.4930i	−1.12971	−	0.454665i
$756$		0			0
$757$	29.0217	+	4.59658i	1.05481	+	0.167065i	0.659670	−	0.751555i	$-0.270696\pi$
$757$	29.0217	+	4.59658i	1.05481	+	0.167065i	0.395140	+	0.918621i	$0.370696\pi$
$758$		0			0
$759$	1.06807	−	4.16105i	0.0387684	−	0.151037i
$760$		0			0
$761$	−17.8404	−	24.5552i	−0.646713	−	0.890124i	0.352238	−	0.935910i	$-0.385421\pi$
$761$	−17.8404	−	24.5552i	−0.646713	−	0.890124i	−0.998951	+	0.0457864i	$0.985421\pi$
$762$		0			0
$763$	0.829459	+	1.62790i	0.0300284	+	0.0589341i
$764$		0			0
$765$	−1.73420	−	19.5196i	−0.0627002	−	0.705731i
$766$		0			0
$767$	−26.5507	−	13.5283i	−0.958690	−	0.488477i
$768$		0			0
$769$	37.6421			1.35741			0.678705	−	0.734411i	$-0.262542\pi$
$769$	37.6421			1.35741			0.678705	+	0.734411i	$0.262542\pi$
$770$		0			0
$771$	3.75184			0.135119
$772$		0			0
$773$	22.9995	+	11.7188i	0.827234	+	0.421497i	0.815727	−	0.578437i	$-0.196337\pi$
$773$	22.9995	+	11.7188i	0.827234	+	0.421497i	0.0115072	+	0.999934i	$0.496337\pi$
$774$		0			0
$775$	1.26543	+	1.21545i	0.0454555	+	0.0436602i
$776$		0			0
$777$	−0.374589	−	0.735173i	−0.0134383	−	0.0263742i
$778$		0			0
$779$	−2.92741	−	4.02923i	−0.104885	−	0.144362i
$780$		0			0
$781$	35.3437	−	13.9964i	1.26470	−	0.500831i
$782$		0			0
$783$	−40.3275	−	6.38724i	−1.44119	−	0.228261i
$784$		0			0
$785$	10.1790	−	4.33688i	0.363302	−	0.154790i
$786$		0			0
$787$	17.0625	−	2.70244i	0.608213	−	0.0963315i	0.155272	−	0.987872i	$-0.450375\pi$
$787$	17.0625	−	2.70244i	0.608213	−	0.0963315i	0.452942	+	0.891540i	$0.350375\pi$
$788$		0			0
$789$	3.90967	+	12.0327i	0.139188	+	0.428376i
$790$		0			0
$791$		−	0.794162i		−	0.0282372i
$792$		0			0
$793$	−12.8994	+	12.8994i	−0.458070	+	0.458070i
$794$		0			0
$795$	−15.6145	+	3.91544i	−0.553788	+	0.138866i
$796$		0			0
$797$	−6.97213	−	44.0203i	−0.246965	−	1.55928i	−0.729858	−	0.683599i	$-0.760414\pi$
$797$	−6.97213	−	44.0203i	−0.246965	−	1.55928i	0.482892	−	0.875680i	$-0.339586\pi$
$798$		0			0
$799$	14.1615	−	43.5847i	0.500999	−	1.54192i
$800$		0			0
$801$	−15.1535	+	11.0097i	−0.535424	+	0.389008i
$802$		0			0
$803$	−0.749124	+	7.93078i	−0.0264360	+	0.279871i
$804$		0			0
$805$	0.369413	+	0.589419i	0.0130201	+	0.0207743i
$806$		0			0
$807$	8.03556	−	4.09432i	0.282865	−	0.144127i
$808$		0			0
$809$	12.3255	+	8.95497i	0.433340	+	0.314840i	0.782983	−	0.622043i	$-0.213697\pi$
$809$	12.3255	+	8.95497i	0.433340	+	0.314840i	−0.349643	+	0.936883i	$0.613697\pi$
$810$		0			0
$811$	43.3276	−	14.0780i	1.52144	−	0.494345i	0.575253	−	0.817976i	$-0.304904\pi$
$811$	43.3276	−	14.0780i	1.52144	−	0.494345i	0.946183	+	0.323631i	$0.104904\pi$
$812$		0			0
$813$	10.0502	+	10.0502i	0.352475	+	0.352475i
$814$		0			0
$815$	−16.8842	+	14.7171i	−0.591427	+	0.515518i
$816$		0			0
$817$	1.77984	−	3.49314i	0.0622688	−	0.122209i
$818$		0			0
$819$	−0.823747	+	1.13379i	−0.0287840	+	0.0396178i
$820$		0			0
$821$	−27.3071	−	8.87260i	−0.953023	−	0.309656i	−0.209079	−	0.977899i	$-0.567047\pi$
$821$	−27.3071	−	8.87260i	−0.953023	−	0.309656i	−0.743943	+	0.668243i	$0.767047\pi$
$822$		0			0
$823$	4.21701	−	26.6252i	0.146996	−	0.928095i	−0.798390	−	0.602141i	$-0.794314\pi$
$823$	4.21701	−	26.6252i	0.146996	−	0.928095i	0.945386	−	0.325954i	$-0.105686\pi$
$824$		0			0
$825$	8.63122	+	10.0142i	0.300501	+	0.348648i
$826$		0			0
$827$	6.20779	−	39.1944i	0.215866	−	1.36292i	−0.607006	−	0.794697i	$-0.707630\pi$
$827$	6.20779	−	39.1944i	0.215866	−	1.36292i	0.822872	−	0.568227i	$-0.192370\pi$
$828$		0			0
$829$	10.3353	+	3.35814i	0.358959	+	0.116633i	0.482944	−	0.875651i	$-0.339567\pi$
$829$	10.3353	+	3.35814i	0.358959	+	0.116633i	−0.123985	+	0.992284i	$0.539567\pi$
$830$		0			0
$831$	−2.19378	+	3.01948i	−0.0761013	+	0.104744i
$832$		0			0
$833$	−11.7174	+	22.9966i	−0.405983	+	0.796786i
$834$		0			0
$835$	−20.3322	+	17.7226i	−0.703625	+	0.613316i
$836$		0			0
$837$	1.06120	+	1.06120i	0.0366805	+	0.0366805i
$838$		0			0
$839$	38.3426	−	12.4583i	1.32373	−	0.430107i	0.439958	−	0.898019i	$-0.354993\pi$
$839$	38.3426	−	12.4583i	1.32373	−	0.430107i	0.883775	+	0.467912i	$0.154993\pi$
$840$		0			0
$841$	−50.2797	−	36.5303i	−1.73378	−	1.25967i
$842$		0			0
$843$	9.36879	−	4.77364i	0.322678	−	0.164413i
$844$		0			0
$845$	4.05793	+	6.47465i	0.139597	+	0.222735i
$846$		0			0
$847$	−1.29066	+	1.66439i	−0.0443477	+	0.0571891i
$848$		0			0
$849$	14.6966	−	10.6777i	0.504386	−	0.366458i
$850$		0			0
$851$	−2.71386	+	8.35241i	−0.0930300	+	0.286317i
$852$		0			0
$853$	−2.18326	−	13.7845i	−0.0747533	−	0.471974i	−0.996459	−	0.0840831i	$-0.973204\pi$
$853$	−2.18326	−	13.7845i	−0.0747533	−	0.471974i	0.921705	−	0.387890i	$-0.126796\pi$
$854$		0			0
$855$	3.81435	−	0.956477i	0.130448	−	0.0327108i
$856$		0			0
$857$	26.9229	−	26.9229i	0.919668	−	0.919668i	−0.0773373	−	0.997005i	$-0.524642\pi$
$857$	26.9229	−	26.9229i	0.919668	−	0.919668i	0.997005	+	0.0773373i	$0.0246418\pi$
$858$		0			0
$859$		−	18.3200i		−	0.625071i	−0.949906	−	0.312535i	$-0.898822\pi$
$859$		−	18.3200i		−	0.625071i	0.949906	−	0.312535i	$-0.101178\pi$
$860$		0			0
$861$	0.315849	+	0.972084i	0.0107641	+	0.0331285i
$862$		0			0
$863$	12.0033	−	1.90114i	0.408597	−	0.0647154i	0.0512472	−	0.998686i	$-0.483680\pi$
$863$	12.0033	−	1.90114i	0.408597	−	0.0647154i	0.357350	+	0.933971i	$0.383680\pi$
$864$		0			0
$865$	25.6424	−	10.9253i	0.871866	−	0.371470i
$866$		0			0
$867$	2.56834	+	0.406785i	0.0872253	+	0.0138151i
$868$		0			0
$869$	−0.139785	−	2.21935i	−0.00474187	−	0.0752863i
$870$		0			0
$871$	−10.6384	−	14.6425i	−0.360469	−	0.496143i
$872$		0			0
$873$	1.48025	+	2.90515i	0.0500987	+	0.0983243i
$874$		0			0
$875$	−2.13821	−	0.103409i	−0.0722848	−	0.00349585i
$876$		0			0
$877$	−11.4361	−	5.82698i	−0.386169	−	0.196763i	0.250118	−	0.968215i	$-0.419531\pi$
$877$	−11.4361	−	5.82698i	−0.386169	−	0.196763i	−0.636287	+	0.771452i	$0.719531\pi$
$878$		0			0
$879$	5.76213			0.194352
$880$		0			0
$881$	13.8380			0.466216			0.233108	−	0.972451i	$-0.425110\pi$
$881$	13.8380			0.466216			0.233108	+	0.972451i	$0.425110\pi$
$882$		0			0
$883$	−38.8377	−	19.7888i	−1.30699	−	0.665947i	−0.344893	−	0.938642i	$-0.612085\pi$
$883$	−38.8377	−	19.7888i	−1.30699	−	0.665947i	−0.962100	+	0.272695i	$0.912085\pi$
$884$		0			0
$885$	−1.51858	−	17.0926i	−0.0510465	−	0.574562i
$886$		0			0
$887$	4.72114	+	9.26576i	0.158520	+	0.311114i	0.956583	−	0.291461i	$-0.0941414\pi$
$887$	4.72114	+	9.26576i	0.158520	+	0.311114i	−0.798062	+	0.602575i	$0.794141\pi$
$888$		0			0
$889$	1.63945	+	2.25651i	0.0549853	+	0.0756808i
$890$		0			0
$891$	−7.78863	−	9.41351i	−0.260929	−	0.315364i
$892$		0			0
$893$	9.08308	+	1.43862i	0.303954	+	0.0481415i
$894$		0			0
$895$	41.8578	+	16.8462i	1.39915	+	0.563106i
$896$		0			0
$897$	−3.96029	+	0.627249i	−0.132230	+	0.0209432i
$898$		0			0
$899$	1.03530	+	3.18633i	0.0345292	+	0.106270i
$900$		0			0
$901$		−	33.4710i		−	1.11508i
$902$		0			0
$903$	−0.568922	+	0.568922i	−0.0189325	+	0.0189325i
$904$		0			0
$905$	2.50710	+	9.99811i	0.0833388	+	0.332349i
$906$		0			0
$907$	−2.55097	−	16.1062i	−0.0847036	−	0.534798i	−0.993155	−	0.116806i	$-0.962734\pi$
$907$	−2.55097	−	16.1062i	−0.0847036	−	0.534798i	0.908451	−	0.417991i	$-0.137266\pi$
$908$		0			0
$909$	−3.52571	+	10.8510i	−0.116940	+	0.359906i
$910$		0			0
$911$	−14.3281	+	10.4099i	−0.474710	+	0.344897i	−0.799274	−	0.600967i	$-0.794782\pi$
$911$	−14.3281	+	10.4099i	−0.474710	+	0.344897i	0.324564	+	0.945864i	$0.394782\pi$
$912$		0			0
$913$	−50.7821	−	21.9712i	−1.68064	−	0.727140i
$914$		0			0
$915$	−10.2391	−	2.34939i	−0.338495	−	0.0776683i
$916$		0			0
$917$	−1.66665	+	0.849203i	−0.0550378	+	0.0280431i
$918$		0			0
$919$	7.38632	+	5.36648i	0.243652	+	0.177024i	0.702909	−	0.711280i	$-0.251884\pi$
$919$	7.38632	+	5.36648i	0.243652	+	0.177024i	−0.459257	+	0.888304i	$0.651884\pi$
$920$		0			0
$921$	21.5818	−	7.01234i	0.711143	−	0.231064i
$922$		0			0
$923$	−25.0888	−	25.0888i	−0.825807	−	0.825807i
$924$		0			0
$925$	−16.3231	−	21.5407i	−0.536701	−	0.708254i
$926$		0			0
$927$	3.47505	−	6.82017i	0.114136	−	0.224004i
$928$		0			0
$929$	1.06529	−	1.46625i	0.0349511	−	0.0481061i	−0.791184	−	0.611578i	$-0.790535\pi$
$929$	1.06529	−	1.46625i	0.0349511	−	0.0481061i	0.826135	+	0.563472i	$0.190535\pi$
$930$		0			0
$931$	−4.92578	−	1.60048i	−0.161436	−	0.0524537i
$932$		0			0
$933$	0.937332	−	5.91808i	0.0306869	−	0.193749i
$934$		0			0
$935$	−24.5613	+	12.3429i	−0.803240	+	0.403655i
$936$		0			0
$937$	−2.37143	+	14.9726i	−0.0774711	+	0.489133i	0.918195	+	0.396130i	$0.129647\pi$
$937$	−2.37143	+	14.9726i	−0.0774711	+	0.489133i	−0.995666	+	0.0930039i	$0.970353\pi$
$938$		0			0
$939$	1.02061	+	0.331616i	0.0333063	+	0.0108219i
$940$		0			0
$941$	−12.8308	+	17.6600i	−0.418271	+	0.575701i	−0.965211	−	0.261471i	$-0.915792\pi$
$941$	−12.8308	+	17.6600i	−0.418271	+	0.575701i	0.546940	+	0.837172i	$0.315792\pi$
$942$		0			0
$943$	4.93902	−	9.69338i	0.160837	−	0.315660i
$944$		0			0
$945$	−1.82673	−	0.125268i	−0.0594235	−	0.00407498i
$946$		0			0
$947$	−6.90662	−	6.90662i	−0.224435	−	0.224435i	0.585928	−	0.810363i	$-0.300730\pi$
$947$	−6.90662	−	6.90662i	−0.224435	−	0.224435i	−0.810363	+	0.585928i	$0.800730\pi$
$948$		0			0
$949$	7.07131	−	2.29761i	0.229545	−	0.0745835i
$950$		0			0
$951$	7.30875	+	5.31012i	0.237003	+	0.172192i
$952$		0			0
$953$	−11.6216	+	5.92153i	−0.376462	+	0.191817i	−0.631975	−	0.774989i	$-0.717756\pi$
$953$	−11.6216	+	5.92153i	−0.376462	+	0.191817i	0.255513	+	0.966806i	$0.417756\pi$
$954$		0			0
$955$	11.9864	−	7.51238i	0.387871	−	0.243095i
$956$		0			0
$957$	5.50846	+	24.6354i	0.178063	+	0.796349i
$958$		0			0
$959$	0.670750	−	0.487328i	0.0216596	−	0.0157367i
$960$		0			0
$961$	−9.54147	+	29.3656i	−0.307789	+	0.947279i
$962$		0			0
$963$	−4.08921	−	25.8182i	−0.131773	−	0.831981i
$964$		0			0
$965$	−6.81621	+	11.3787i	−0.219422	+	0.366294i
$966$		0			0
$967$	13.6319	−	13.6319i	0.438372	−	0.438372i	−0.453092	−	0.891464i	$-0.649679\pi$
$967$	13.6319	−	13.6319i	0.438372	−	0.438372i	0.891464	+	0.453092i	$0.149679\pi$
$968$		0			0
$969$		−	2.19785i		−	0.0706051i
$970$		0			0
$971$	−1.26967	−	3.90765i	−0.0407457	−	0.125403i	0.928615	−	0.371046i	$-0.121001\pi$
$971$	−1.26967	−	3.90765i	−0.0407457	−	0.125403i	−0.969360	+	0.245643i	$0.921001\pi$
$972$		0			0
$973$	−1.98769	+	0.314819i	−0.0637224	+	0.0100926i
$974$		0			0
$975$	5.37941	−	11.1051i	0.172279	−	0.355649i
$976$		0			0
$977$	30.3314	+	4.80402i	0.970386	+	0.153694i	0.621451	−	0.783453i	$-0.286543\pi$
$977$	30.3314	+	4.80402i	0.970386	+	0.153694i	0.348935	+	0.937147i	$0.386543\pi$
$978$		0			0
$979$	22.1848	+	14.0768i	0.709030	+	0.449895i
$980$		0			0
$981$	13.2614	+	18.2528i	0.423405	+	0.582767i
$982$		0			0
$983$	12.5871	+	24.7035i	0.401465	+	0.787919i	0.999912	−	0.0132429i	$-0.00421546\pi$
$983$	12.5871	+	24.7035i	0.401465	+	0.787919i	−0.598447	+	0.801162i	$0.704215\pi$
$984$		0			0
$985$	−31.1999	+	2.77194i	−0.994113	+	0.0883212i
$986$		0			0
$987$	−1.68162	−	0.856827i	−0.0535265	−	0.0272731i
$988$		0			0
$989$	8.56376			0.272312
$990$		0			0
$991$	−9.10087			−0.289099			−0.144549	−	0.989498i	$-0.546173\pi$
$991$	−9.10087			−0.289099			−0.144549	+	0.989498i	$0.546173\pi$
$992$		0			0
$993$	−12.5763	−	6.40795i	−0.399097	−	0.203350i
$994$		0			0
$995$	19.2044	−	22.9496i	0.608822	−	0.727551i
$996$		0			0
$997$	13.1070	+	25.7239i	0.415103	+	0.814685i	0.999994	+	0.00357282i	$0.00113727\pi$
$997$	13.1070	+	25.7239i	0.415103	+	0.814685i	−0.584891	+	0.811112i	$0.698863\pi$
$998$		0			0
$999$	−13.5878	−	18.7019i	−0.429898	−	0.591703i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.cm.a.657.1		32
4.3	odd	2		55.2.l.a.52.1	yes	32
5.3	odd	4	inner	880.2.cm.a.833.4		32
11.7	odd	10	inner	880.2.cm.a.337.4		32
12.11	even	2		495.2.bj.a.217.4		32
20.3	even	4		55.2.l.a.8.4	yes	32
20.7	even	4		275.2.bm.b.118.1		32
20.19	odd	2		275.2.bm.b.107.4		32
44.3	odd	10		605.2.m.c.457.4		32
44.7	even	10		55.2.l.a.7.4	✓	32
44.15	odd	10		605.2.m.e.282.1		32
44.19	even	10		605.2.m.d.457.1		32
44.27	odd	10		605.2.m.d.112.1		32
44.31	odd	10		605.2.e.b.362.14		32
44.35	even	10		605.2.e.b.362.3		32
44.39	even	10		605.2.m.c.112.4		32
44.43	even	2		605.2.m.e.602.4		32
55.18	even	20	inner	880.2.cm.a.513.1		32
60.23	odd	4		495.2.bj.a.118.1		32
132.95	odd	10		495.2.bj.a.172.1		32
220.3	even	20		605.2.m.c.578.4		32
220.7	odd	20		275.2.bm.b.18.4		32
220.43	odd	4		605.2.m.e.118.1		32
220.63	odd	20		605.2.m.d.578.1		32
220.83	odd	20		605.2.m.c.233.4		32
220.103	even	20		605.2.m.e.403.4		32
220.123	odd	20		605.2.e.b.483.14		32
220.139	even	10		275.2.bm.b.7.1		32
220.163	even	20		605.2.e.b.483.3		32
220.183	odd	20		55.2.l.a.18.1	yes	32
220.203	even	20		605.2.m.d.233.1		32
660.623	even	20		495.2.bj.a.73.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.7.4	✓	32	44.7	even	10
55.2.l.a.8.4	yes	32	20.3	even	4
55.2.l.a.18.1	yes	32	220.183	odd	20
55.2.l.a.52.1	yes	32	4.3	odd	2
275.2.bm.b.7.1		32	220.139	even	10
275.2.bm.b.18.4		32	220.7	odd	20
275.2.bm.b.107.4		32	20.19	odd	2
275.2.bm.b.118.1		32	20.7	even	4
495.2.bj.a.73.4		32	660.623	even	20
495.2.bj.a.118.1		32	60.23	odd	4
495.2.bj.a.172.1		32	132.95	odd	10
495.2.bj.a.217.4		32	12.11	even	2
605.2.e.b.362.3		32	44.35	even	10
605.2.e.b.362.14		32	44.31	odd	10
605.2.e.b.483.3		32	220.163	even	20
605.2.e.b.483.14		32	220.123	odd	20
605.2.m.c.112.4		32	44.39	even	10
605.2.m.c.233.4		32	220.83	odd	20
605.2.m.c.457.4		32	44.3	odd	10
605.2.m.c.578.4		32	220.3	even	20
605.2.m.d.112.1		32	44.27	odd	10
605.2.m.d.233.1		32	220.203	even	20
605.2.m.d.457.1		32	44.19	even	10
605.2.m.d.578.1		32	220.63	odd	20
605.2.m.e.118.1		32	220.43	odd	4
605.2.m.e.282.1		32	44.15	odd	10
605.2.m.e.403.4		32	220.103	even	20
605.2.m.e.602.4		32	44.43	even	2
880.2.cm.a.337.4		32	11.7	odd	10	inner
880.2.cm.a.513.1		32	55.18	even	20	inner
880.2.cm.a.657.1		32	1.1	even	1	trivial
880.2.cm.a.833.4		32	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.cm (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.710333 - 0.361933i) q^{3} +(-1.71486 - 1.43501i) q^{5} +(-0.0869260 - 0.170602i) q^{7} +(-1.38978 - 1.91287i) q^{9} +(-1.77694 + 2.80044i) q^{11} +(3.05749 + 0.484259i) q^{13} +(0.698743 + 1.64000i) q^{15} +(-3.66088 + 0.579827i) q^{17} +(-0.229844 - 0.707388i) q^{19} +0.152646i q^{21} +(1.14886 - 1.14886i) q^{23} +(0.881484 + 4.92169i) q^{25} +(0.669017 + 4.22401i) q^{27} +(-2.95025 + 9.07993i) q^{29} +(0.283900 - 0.206266i) q^{31} +(2.27579 - 1.34611i) q^{33} +(-0.0957498 + 0.417298i) q^{35} +(-4.81621 + 2.45398i) q^{37} +(-1.99657 - 1.45059i) q^{39} +(6.36824 - 2.06917i) q^{41} +(3.72708 + 3.72708i) q^{43} +(-0.361710 + 5.27464i) q^{45} +(-5.61318 + 11.0165i) q^{47} +(4.09295 - 5.63346i) q^{49} +(2.81030 + 0.913123i) q^{51} +(-1.41265 + 8.91914i) q^{53} +(7.06587 - 2.25243i) q^{55} +(-0.0927608 + 0.585669i) q^{57} +(-9.15496 - 2.97463i) q^{59} +(-3.46383 + 4.76756i) q^{61} +(-0.205531 + 0.403377i) q^{63} +(-4.54825 - 5.21797i) q^{65} +(-4.13426 - 4.13426i) q^{67} +(-1.23188 + 0.400262i) q^{69} +(-9.27272 - 6.73702i) q^{71} +(2.14008 - 1.09042i) q^{73} +(1.15517 - 3.81507i) q^{75} +(0.632224 + 0.0597184i) q^{77} +(-0.542434 + 0.394101i) q^{79} +(-1.13837 + 3.50353i) q^{81} +(2.60980 + 16.4776i) q^{83} +(7.10995 + 4.25908i) q^{85} +(5.38198 - 5.38198i) q^{87} -7.92190i q^{89} +(-0.183160 - 0.563709i) q^{91} +(-0.276318 + 0.0437645i) q^{93} +(-0.620959 + 1.54290i) q^{95} +(-1.36201 - 0.215721i) q^{97} +(7.82643 - 0.492943i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} - 2 q^{5} + 24 q^{11} - 10 q^{13} - 14 q^{15} + 24 q^{23} + 16 q^{25} + 16 q^{27} + 28 q^{31} + 66 q^{33} + 10 q^{35} - 8 q^{37} + 40 q^{41} - 28 q^{45} + 28 q^{47} - 20 q^{51} - 24 q^{53}+ \cdots - 8 q^{97}+O(q^{100}) \) 32 * q + 4 * q^3 - 2 * q^5 + 24 * q^11 - 10 * q^13 - 14 * q^15 + 24 * q^23 + 16 * q^25 + 16 * q^27 + 28 * q^31 + 66 * q^33 + 10 * q^35 - 8 * q^37 + 40 * q^41 - 28 * q^45 + 28 * q^47 - 20 * q^51 - 24 * q^53 + 64 * q^55 + 30 * q^57 - 60 * q^61 + 30 * q^63 + 8 * q^67 - 24 * q^71 + 50 * q^73 - 34 * q^75 + 70 * q^77 - 12 * q^81 - 90 * q^83 + 30 * q^85 - 20 * q^91 - 8 * q^93 + 40 * q^95 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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