LMFDB - Embedded newform 880.2.cm.a.337.4

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			337.4
Character	$\chi$	$=$	880.337
Dual form			880.2.cm.a.833.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.361933 + 0.710333i) q^{3} +(-1.89470 + 1.18749i) q^{5} +(-0.170602 - 0.0869260i) q^{7} +(1.38978 - 1.91287i) q^{9} +(-1.77694 - 2.80044i) q^{11} +(-0.484259 - 3.05749i) q^{13} +(-1.52926 - 0.916076i) q^{15} +(0.579827 - 3.66088i) q^{17} +(0.229844 - 0.707388i) q^{19} -0.152646i q^{21} +(1.14886 - 1.14886i) q^{23} +(2.17976 - 4.49985i) q^{25} +(4.22401 + 0.669017i) q^{27} +(2.95025 + 9.07993i) q^{29} +(0.283900 + 0.206266i) q^{31} +(1.34611 - 2.27579i) q^{33} +(0.426463 - 0.0378887i) q^{35} +(2.45398 - 4.81621i) q^{37} +(1.99657 - 1.45059i) q^{39} +(6.36824 + 2.06917i) q^{41} +(-3.72708 - 3.72708i) q^{43} +(-0.361710 + 5.27464i) q^{45} +(11.0165 - 5.61318i) q^{47} +(-4.09295 - 5.63346i) q^{49} +(2.81030 - 0.913123i) q^{51} +(-8.91914 + 1.41265i) q^{53} +(6.69225 + 3.19590i) q^{55} +(0.585669 - 0.0927608i) q^{57} +(9.15496 - 2.97463i) q^{59} +(-3.46383 - 4.76756i) q^{61} +(-0.403377 + 0.205531i) q^{63} +(4.54825 + 5.21797i) q^{65} +(-4.13426 - 4.13426i) q^{67} +(1.23188 + 0.400262i) q^{69} +(-9.27272 + 6.73702i) q^{71} +(1.09042 - 2.14008i) q^{73} +(3.98532 - 0.0802892i) q^{75} +(0.0597184 + 0.632224i) q^{77} +(0.542434 + 0.394101i) q^{79} +(-1.13837 - 3.50353i) q^{81} +(-16.4776 - 2.60980i) q^{83} +(3.24865 + 7.62480i) q^{85} +(-5.38198 + 5.38198i) q^{87} -7.92190i q^{89} +(-0.183160 + 0.563709i) q^{91} +(-0.0437645 + 0.276318i) q^{93} +(0.404527 + 1.61322i) q^{95} +(-0.215721 - 1.36201i) q^{97} +(-7.82643 - 0.492943i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{10}\right)$	$1$

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
$3$	0.361933	+	0.710333i	0.208962	+	0.410111i	0.971571	−	0.236749i	$-0.0760819\pi$
$3$	0.361933	+	0.710333i	0.208962	+	0.410111i	−0.762609	+	0.646860i	$0.776082\pi$
$4$		0			0
$5$	−1.89470	+	1.18749i	−0.847335	+	0.531060i
$5$	−1.89470	+	1.18749i	−0.847335	+	0.531060i
$6$		0			0
$7$	−0.170602	−	0.0869260i	−0.0644815	−	0.0328550i	0.421452	−	0.906851i	$-0.361520\pi$
$7$	−0.170602	−	0.0869260i	−0.0644815	−	0.0328550i	−0.485934	+	0.873996i	$0.661520\pi$
$8$		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
$13$	−0.484259	−	3.05749i	−0.134309	−	0.847995i	−0.959205	−	0.282711i	$-0.908766\pi$
$13$	−0.484259	−	3.05749i	−0.134309	−	0.847995i	0.824896	−	0.565285i	$-0.191234\pi$
$14$		0			0
$15$	−1.52926	−	0.916076i	−0.394854	−	0.236530i
$16$		0			0
$17$	0.579827	−	3.66088i	0.140629	−	0.887894i	−0.811978	−	0.583688i	$-0.801609\pi$
$17$	0.579827	−	3.66088i	0.140629	−	0.887894i	0.952606	−	0.304206i	$-0.0983910\pi$
$18$		0			0
$19$	0.229844	−	0.707388i	0.0527299	−	0.162286i	−0.921224	−	0.389033i	$-0.872809\pi$
$19$	0.229844	−	0.707388i	0.0527299	−	0.162286i	0.973954	+	0.226747i	$0.0728091\pi$
$20$		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
$25$	2.17976	−	4.49985i	0.435952	−	0.899970i
$26$		0			0
$27$	4.22401	+	0.669017i	0.812911	+	0.128752i
$28$		0			0
$29$	2.95025	+	9.07993i	0.547847	+	1.68610i	0.714122	+	0.700021i	$0.246826\pi$
$29$	2.95025	+	9.07993i	0.547847	+	1.68610i	−0.166275	+	0.986079i	$0.553174\pi$
$30$		0			0
$31$	0.283900	+	0.206266i	0.0509900	+	0.0370464i	0.612988	−	0.790092i	$-0.289967\pi$
$31$	0.283900	+	0.206266i	0.0509900	+	0.0370464i	−0.561998	+	0.827138i	$0.689967\pi$
$32$		0			0
$33$	1.34611	−	2.27579i	0.234328	−	0.396165i
$34$		0			0
$35$	0.426463	−	0.0378887i	0.0720853	−	0.00640437i
$36$		0			0
$37$	2.45398	−	4.81621i	0.403432	−	0.791780i	−0.596510	−	0.802606i	$-0.703446\pi$
$37$	2.45398	−	4.81621i	0.403432	−	0.791780i	0.999941	+	0.0108264i	$0.00344622\pi$
$38$		0			0
$39$	1.99657	−	1.45059i	0.319707	−	0.232280i
$40$		0			0
$41$	6.36824	+	2.06917i	0.994552	+	0.323150i	0.760687	−	0.649119i	$-0.224862\pi$
$41$	6.36824	+	2.06917i	0.994552	+	0.323150i	0.233866	+	0.972269i	$0.424862\pi$
$42$		0			0
$43$	−3.72708	−	3.72708i	−0.568374	−	0.568374i	0.363299	−	0.931673i	$-0.381650\pi$
$43$	−3.72708	−	3.72708i	−0.568374	−	0.568374i	−0.931673	+	0.363299i	$0.881650\pi$
$44$		0			0
$45$	−0.361710	+	5.27464i	−0.0539205	+	0.786297i
$46$		0			0
$47$	11.0165	−	5.61318i	1.60692	−	0.818766i	0.607213	−	0.794539i	$-0.292287\pi$
$47$	11.0165	−	5.61318i	1.60692	−	0.818766i	0.999706	−	0.0242272i	$-0.00771250\pi$
$48$		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
$53$	−8.91914	+	1.41265i	−1.22514	+	0.194043i	−0.735282	−	0.677761i	$-0.762950\pi$
$53$	−8.91914	+	1.41265i	−1.22514	+	0.194043i	−0.489855	+	0.871804i	$0.662950\pi$
$54$		0			0
$55$	6.69225	+	3.19590i	0.902383	+	0.430935i
$56$		0			0
$57$	0.585669	−	0.0927608i	0.0775737	−	0.0122865i
$58$		0			0
$59$	9.15496	−	2.97463i	1.19187	−	0.387263i	0.355108	−	0.934825i	$-0.384444\pi$
$59$	9.15496	−	2.97463i	1.19187	−	0.387263i	0.836765	+	0.547562i	$0.184444\pi$
$60$		0			0
$61$	−3.46383	−	4.76756i	−0.443498	−	0.610423i	0.527487	−	0.849563i	$-0.323134\pi$
$61$	−3.46383	−	4.76756i	−0.443498	−	0.610423i	−0.970985	+	0.239140i	$0.923134\pi$
$62$		0			0
$63$	−0.403377	+	0.205531i	−0.0508207	+	0.0258944i
$64$		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	−0.981136	−	0.193317i	$-0.938075\pi$
$71$	−9.27272	+	6.73702i	−1.10047	+	0.799538i	−0.119333	+	0.992854i	$0.538075\pi$
$72$		0			0
$73$	1.09042	−	2.14008i	0.127624	−	0.250477i	−0.818349	−	0.574722i	$-0.805110\pi$
$73$	1.09042	−	2.14008i	0.127624	−	0.250477i	0.945973	+	0.324245i	$0.105110\pi$
$74$		0			0
$75$	3.98532	−	0.0802892i	0.460185	−	0.00927099i
$76$		0			0
$77$	0.0597184	+	0.632224i	0.00680554	+	0.0720486i
$78$		0			0
$79$	0.542434	+	0.394101i	0.0610286	+	0.0443399i	0.617881	−	0.786271i	$-0.287991\pi$
$79$	0.542434	+	0.394101i	0.0610286	+	0.0443399i	−0.556853	+	0.830611i	$0.687991\pi$
$80$		0			0
$81$	−1.13837	−	3.50353i	−0.126485	−	0.389282i
$82$		0			0
$83$	−16.4776	−	2.60980i	−1.80865	−	0.286463i	−0.841426	−	0.540372i	$-0.818284\pi$
$83$	−16.4776	−	2.60980i	−1.80865	−	0.286463i	−0.967228	+	0.253909i	$0.918284\pi$
$84$		0			0
$85$	3.24865	+	7.62480i	0.352365	+	0.827025i
$86$		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
$93$	−0.0437645	+	0.276318i	−0.00453817	+	0.0286528i
$94$		0			0
$95$	0.404527	+	1.61322i	0.0415036	+	0.165513i
$96$		0			0
$97$	−0.215721	−	1.36201i	−0.0219032	−	0.138291i	0.974313	−	0.225196i	$-0.0723023\pi$
$97$	−0.215721	−	1.36201i	−0.0219032	−	0.138291i	−0.996217	+	0.0869051i	$0.972302\pi$
$98$		0			0
$99$	−7.82643	−	0.492943i	−0.786585	−	0.0495427i
$100$		0			0
$101$	−2.83633	+	3.90387i	−0.282225	+	0.388449i	−0.926469	−	0.376370i	$-0.877172\pi$
$101$	−2.83633	+	3.90387i	−0.282225	+	0.388449i	0.644244	+	0.764820i	$0.277172\pi$
$102$		0			0
$103$	−2.88449	−	1.46972i	−0.284217	−	0.144816i	0.306071	−	0.952009i	$-0.400986\pi$
$103$	−2.88449	−	1.46972i	−0.284217	−	0.144816i	−0.590287	+	0.807193i	$0.700986\pi$
$104$		0			0
$105$	0.181264	+	0.289217i	0.0176896	+	0.0282247i
$106$		0			0
$107$	5.01911	+	9.85055i	0.485215	+	0.952289i	0.995721	+	0.0924142i	$0.0294584\pi$
$107$	5.01911	+	9.85055i	0.485215	+	0.952289i	−0.510505	+	0.859875i	$0.670542\pi$
$108$		0			0
$109$	9.54212			0.913969			0.456985	−	0.889475i	$-0.348929\pi$
$109$	9.54212			0.913969			0.456985	+	0.889475i	$0.348929\pi$
$110$		0			0
$111$	4.30929			0.409019
$112$		0			0
$113$	−1.88301	−	3.69562i	−0.177139	−	0.347654i	0.785317	−	0.619094i	$-0.212500\pi$
$113$	−1.88301	−	3.69562i	−0.177139	−	0.347654i	−0.962455	+	0.271440i	$0.912500\pi$
$114$		0			0
$115$	−0.812486	+	3.54099i	−0.0757647	+	0.330199i
$116$		0			0
$117$	−6.52158	−	3.32291i	−0.602920	−	0.307203i
$118$		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
$123$	0.835077	+	5.27247i	0.0752964	+	0.475403i
$124$		0			0
$125$	1.21352	+	11.1143i	0.108541	+	0.994092i
$126$		0			0
$127$	2.27881	−	14.3879i	0.202212	−	1.27672i	−0.652570	−	0.757728i	$-0.726309\pi$
$127$	2.27881	−	14.3879i	0.202212	−	1.27672i	0.854782	−	0.518987i	$-0.173691\pi$
$128$		0			0
$129$	1.29851	−	3.99642i	0.114328	−	0.351865i
$130$		0			0
$131$			9.76926i			0.853544i	0.904359	+	0.426772i	$0.140349\pi$
$131$			9.76926i			0.853544i	−0.904359	+	0.426772i	$0.859651\pi$
$132$		0			0
$133$	−0.100702	+	0.100702i	−0.00873200	+	0.00873200i
$134$		0			0
$135$	−8.79767	+	3.74836i	−0.757182	+	0.322608i
$136$		0			0
$137$	4.27681	+	0.677380i	0.365392	+	0.0578725i	0.336431	−	0.941708i	$-0.390780\pi$
$137$	4.27681	+	0.677380i	0.365392	+	0.0578725i	0.0289612	+	0.999581i	$0.490780\pi$
$138$		0			0
$139$	−3.24794	−	9.99613i	−0.275487	−	0.847860i	−0.989090	−	0.147311i	$-0.952938\pi$
$139$	−3.24794	−	9.99613i	−0.275487	−	0.847860i	0.713604	−	0.700550i	$-0.247062\pi$
$140$		0			0
$141$	7.97445	+	5.79378i	0.671570	+	0.487924i
$142$		0			0
$143$	−7.70183	+	6.78912i	−0.644059	+	0.567735i
$144$		0			0
$145$	−16.3721	−	13.7003i	−1.35963	−	1.13775i
$146$		0			0
$147$	2.52026	−	4.94629i	0.207868	−	0.407963i
$148$		0			0
$149$	4.66189	−	3.38706i	0.381917	−	0.277479i	−0.380218	−	0.924897i	$-0.624151\pi$
$149$	4.66189	−	3.38706i	0.381917	−	0.277479i	0.762135	+	0.647418i	$0.224151\pi$
$150$		0			0
$151$	14.2318	+	4.62419i	1.15817	+	0.376311i	0.824214	−	0.566278i	$-0.191617\pi$
$151$	14.2318	+	4.62419i	1.15817	+	0.376311i	0.333953	+	0.942590i	$0.391617\pi$
$152$		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
$157$	4.40881	−	2.24640i	0.351861	−	0.179282i	−0.269122	−	0.963106i	$-0.586733\pi$
$157$	4.40881	−	2.24640i	0.351861	−	0.179282i	0.620983	+	0.783824i	$0.286733\pi$
$158$		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
$163$	9.89335	−	1.56695i	0.774907	−	0.122733i	0.243558	−	0.969886i	$-0.421685\pi$
$163$	9.89335	−	1.56695i	0.774907	−	0.122733i	0.531349	+	0.847153i	$0.321685\pi$
$164$		0			0
$165$	0.151992	+	5.91043i	0.0118325	+	0.460126i
$166$		0			0
$167$	−11.9137	+	1.88695i	−0.921913	+	0.146017i	−0.599310	−	0.800517i	$-0.704558\pi$
$167$	−11.9137	+	1.88695i	−0.921913	+	0.146017i	−0.322604	+	0.946534i	$0.604558\pi$
$168$		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
$173$	−11.1065	+	5.65903i	−0.844410	+	0.430248i	−0.821991	−	0.569501i	$-0.807137\pi$
$173$	−11.1065	+	5.65903i	−0.844410	+	0.430248i	−0.0224186	+	0.999749i	$0.507137\pi$
$174$		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	$-0.128070\pi$
$179$	19.1909	+	6.23551i	1.43440	+	0.466064i	0.514252	+	0.857639i	$0.328070\pi$
$180$		0			0
$181$	−3.72935	+	2.70953i	−0.277200	+	0.201398i	−0.717695	−	0.696357i	$-0.754803\pi$
$181$	−3.72935	+	2.70953i	−0.277200	+	0.201398i	0.440495	+	0.897755i	$0.354803\pi$
$182$		0			0
$183$	2.13288	−	4.18601i	0.157667	−	0.309439i
$184$		0			0
$185$	1.06962	+	12.0393i	0.0786403	+	0.885148i
$186$		0			0
$187$	−11.2824	+	4.88140i	−0.825051	+	0.356963i
$188$		0			0
$189$	−0.662469	−	0.481312i	−0.0481875	−	0.0350103i
$190$		0			0
$191$	−1.95493	−	6.01667i	−0.141454	−	0.435351i	0.855084	−	0.518490i	$-0.173505\pi$
$191$	−1.95493	−	6.01667i	−0.141454	−	0.435351i	−0.996538	+	0.0831389i	$0.973505\pi$
$192$		0			0
$193$	5.85885	+	0.927951i	0.421729	+	0.0667954i	0.363692	−	0.931519i	$-0.381516\pi$
$193$	5.85885	+	0.927951i	0.421729	+	0.0667954i	0.0580368	+	0.998314i	$0.481516\pi$
$194$		0			0
$195$	−2.06034	+	5.11932i	−0.147544	+	0.366602i
$196$		0			0
$197$	−9.90515	+	9.90515i	−0.705713	+	0.705713i	−0.965631	−	0.259918i	$-0.916304\pi$
$197$	−9.90515	+	9.90515i	−0.705713	+	0.705713i	0.259918	+	0.965631i	$0.416304\pi$
$198$		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
$203$	0.285964	−	1.80551i	0.0200708	−	0.126722i
$204$		0			0
$205$	−14.5230	+	3.64175i	−1.01433	+	0.254351i
$206$		0			0
$207$	−0.600953	−	3.79427i	−0.0417691	−	0.263720i
$208$		0			0
$209$	−2.38942	+	0.613321i	−0.165280	+	0.0424243i
$210$		0			0
$211$	−3.48696	+	4.79939i	−0.240052	+	0.330404i	−0.911996	−	0.410198i	$-0.865460\pi$
$211$	−3.48696	+	4.79939i	−0.240052	+	0.330404i	0.671944	+	0.740602i	$0.265460\pi$
$212$		0			0
$213$	−8.14163	−	4.14837i	−0.557855	−	0.284241i
$214$		0			0
$215$	11.4875	+	2.63584i	0.783444	+	0.179763i
$216$		0			0
$217$	−0.0305041	−	0.0598677i	−0.00207075	−	0.00406408i
$218$		0			0
$219$	1.91483			0.129392
$220$		0			0
$221$	−11.4739			−0.771818
$222$		0			0
$223$	−9.64984	−	18.9389i	−0.646201	−	1.26824i	−0.949027	−	0.315195i	$-0.897930\pi$
$223$	−9.64984	−	18.9389i	−0.646201	−	1.26824i	0.302826	−	0.953046i	$-0.402070\pi$
$224$		0			0
$225$	−5.57823	−	10.4234i	−0.371882	−	0.694892i
$226$		0			0
$227$	−11.6456	−	5.93372i	−0.772944	−	0.393835i	0.0225888	−	0.999745i	$-0.492809\pi$
$227$	−11.6456	−	5.93372i	−0.772944	−	0.393835i	−0.795533	+	0.605910i	$0.792809\pi$
$228$		0			0
$229$	−9.65796	+	13.2930i	−0.638216	+	0.878429i	−0.998519	−	0.0544066i	$-0.982673\pi$
$229$	−9.65796	+	13.2930i	−0.638216	+	0.878429i	0.360303	+	0.932835i	$0.382673\pi$
$230$		0			0
$231$	−0.427475	+	0.271242i	−0.0281258	+	0.0178464i
$232$		0			0
$233$	2.44720	+	15.4510i	0.160321	+	1.01223i	0.928321	+	0.371779i	$0.121252\pi$
$233$	2.44720	+	15.4510i	0.160321	+	1.01223i	−0.768000	+	0.640450i	$0.778748\pi$
$234$		0			0
$235$	−14.2073	+	23.7172i	−0.926785	+	1.54714i
$236$		0			0
$237$	−0.0836185	+	0.527947i	−0.00543161	+	0.0342938i
$238$		0			0
$239$	−1.63214	+	5.02322i	−0.105575	+	0.324925i	−0.989865	−	0.142012i	$-0.954643\pi$
$239$	−1.63214	+	5.02322i	−0.105575	+	0.324925i	0.884290	+	0.466938i	$0.154643\pi$
$240$		0			0
$241$			16.1676i			1.04144i	0.853726	+	0.520722i	$0.174337\pi$
$241$			16.1676i			1.04144i	−0.853726	+	0.520722i	$0.825663\pi$
$242$		0			0
$243$	11.1488	−	11.1488i	0.715198	−	0.715198i
$244$		0			0
$245$	14.4445	+	5.81339i	0.922828	+	0.371404i
$246$		0			0
$247$	−2.27413	−	0.360188i	−0.144700	−	0.0229182i
$248$		0			0
$249$	−4.10997	−	12.6492i	−0.260458	−	0.801609i
$250$		0			0
$251$	15.6486	+	11.3694i	0.987729	+	0.717627i	0.959423	−	0.281972i	$-0.0909886\pi$
$251$	15.6486	+	11.3694i	0.987729	+	0.717627i	0.0283063	+	0.999599i	$0.490989\pi$
$252$		0			0
$253$	−5.25876	−	1.17586i	−0.330615	−	0.0739254i
$254$		0			0
$255$	−4.24035	+	5.06728i	−0.265541	+	0.317326i
$256$		0			0
$257$	2.13653	−	4.19318i	0.133273	−	0.261563i	−0.814720	−	0.579855i	$-0.803109\pi$
$257$	2.13653	−	4.19318i	0.133273	−	0.261563i	0.947993	+	0.318292i	$0.103109\pi$
$258$		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	0.962664	−	0.270700i	$-0.0872550\pi$
$263$	11.2218	+	11.2218i	0.691964	+	0.691964i	−0.270700	+	0.962664i	$0.587255\pi$
$264$		0			0
$265$	15.2216	−	13.2679i	0.935053	−	0.815040i
$266$		0			0
$267$	5.62719	−	2.86720i	0.344378	−	0.175470i
$268$		0			0
$269$	6.64926	+	9.15192i	0.405412	+	0.558002i	0.962092	−	0.272725i	$-0.0879249\pi$
$269$	6.64926	+	9.15192i	0.405412	+	0.558002i	−0.556680	+	0.830727i	$0.687925\pi$
$270$		0			0
$271$	−16.9556	+	5.50921i	−1.02998	+	0.334661i	−0.774782	−	0.632228i	$-0.782141\pi$
$271$	−16.9556	+	5.50921i	−1.02998	+	0.334661i	−0.255198	+	0.966889i	$0.582141\pi$
$272$		0			0
$273$	−0.466712	+	0.0739200i	−0.0282467	+	0.00447384i
$274$		0			0
$275$	−16.4749	+	1.89169i	−0.993472	+	0.114073i
$276$		0			0
$277$	−4.62395	+	0.732361i	−0.277826	+	0.0440033i	−0.293793	−	0.955869i	$-0.594917\pi$
$277$	−4.62395	+	0.732361i	−0.277826	+	0.0440033i	0.0159666	+	0.999873i	$0.494917\pi$
$278$		0			0
$279$	0.789117	−	0.256400i	0.0472432	−	0.0153502i
$280$		0			0
$281$	−7.75247	−	10.6704i	−0.462474	−	0.636541i	0.512546	−	0.858660i	$-0.328703\pi$
$281$	−7.75247	−	10.6704i	−0.462474	−	0.636541i	−0.975019	+	0.222119i	$0.928703\pi$
$282$		0			0
$283$	−20.3029	+	10.3449i	−1.20688	+	0.614938i	−0.937463	−	0.348084i	$-0.886832\pi$
$283$	−20.3029	+	10.3449i	−1.20688	+	0.614938i	−0.269421	+	0.963022i	$0.586832\pi$
$284$		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
$293$	−3.28132	+	6.43996i	−0.191697	+	0.376226i	−0.966771	−	0.255644i	$-0.917713\pi$
$293$	−3.28132	+	6.43996i	−0.191697	+	0.376226i	0.775074	+	0.631870i	$0.217713\pi$
$294$		0			0
$295$	−13.8135	+	16.5074i	−0.804256	+	0.961097i
$296$		0			0
$297$	−5.63227	−	13.0179i	−0.326818	−	0.755375i
$298$		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
$303$	−3.79960	−	0.601798i	−0.218282	−	0.0345724i
$304$		0			0
$305$	12.2243	+	4.91983i	0.699963	+	0.281709i
$306$		0			0
$307$	20.1272	−	20.1272i	1.14872	−	1.14872i	0.161918	−	0.986804i	$-0.448232\pi$
$307$	20.1272	−	20.1272i	1.14872	−	1.14872i	0.986804	−	0.161918i	$-0.0517681\pi$
$308$		0			0
$309$		−	2.58088i		−	0.146821i
$310$		0			0
$311$	2.32254	−	7.14803i	0.131699	−	0.405328i	−0.863363	−	0.504583i	$-0.831646\pi$
$311$	2.32254	−	7.14803i	0.131699	−	0.405328i	0.995062	+	0.0992557i	$0.0316462\pi$
$312$		0			0
$313$	−0.210574	+	1.32951i	−0.0119023	+	0.0751483i	−0.992925	−	0.118747i	$-0.962112\pi$
$313$	−0.210574	+	1.32951i	−0.0119023	+	0.0751483i	0.981022	+	0.193895i	$0.0621122\pi$
$314$		0			0
$315$	0.520212	−	0.868422i	0.0293106	−	0.0489301i
$316$		0			0
$317$	−1.77271	−	11.1924i	−0.0995652	−	0.628630i	−0.986124	−	0.166013i	$-0.946911\pi$
$317$	−1.77271	−	11.1924i	−0.0995652	−	0.628630i	0.886558	−	0.462617i	$-0.153089\pi$
$318$		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
$323$	−2.45639	−	1.25159i	−0.136677	−	0.0696406i
$324$		0			0
$325$	−14.8138	−	4.48550i	−0.821723	−	0.248811i
$326$		0			0
$327$	3.45360	+	6.77808i	0.190985	+	0.374829i
$328$		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
$333$	−5.80227	−	11.3876i	−0.317962	−	0.624036i
$334$		0			0
$335$	12.7426	+	2.92380i	0.696200	+	0.159744i
$336$		0			0
$337$	6.78954	+	3.45945i	0.369850	+	0.188448i	0.629030	−	0.777381i	$-0.283452\pi$
$337$	6.78954	+	3.45945i	0.369850	+	0.188448i	−0.259180	+	0.965829i	$0.583452\pi$
$338$		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
$343$	0.418239	+	2.64066i	0.0225828	+	0.142582i
$344$		0			0
$345$	−2.80935	+	0.704464i	−0.151250	+	0.0379270i
$346$		0			0
$347$	−1.46011	+	9.21879i	−0.0783830	+	0.494891i	0.916998	+	0.398891i	$0.130605\pi$
$347$	−1.46011	+	9.21879i	−0.0783830	+	0.494891i	−0.995381	+	0.0959998i	$0.969395\pi$
$348$		0			0
$349$	−0.464073	+	1.42827i	−0.0248413	+	0.0764536i	−0.962709	−	0.270540i	$-0.912798\pi$
$349$	−0.464073	+	1.42827i	−0.0248413	+	0.0764536i	0.937867	+	0.346994i	$0.112798\pi$
$350$		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
$355$	9.56888	−	23.7758i	0.507863	−	1.26189i
$356$		0			0
$357$	−0.558817	−	0.0885080i	−0.0295757	−	0.00468434i
$358$		0			0
$359$	8.12845	+	25.0168i	0.429003	+	1.32034i	0.899108	+	0.437726i	$0.144216\pi$
$359$	8.12845	+	25.0168i	0.429003	+	1.32034i	−0.470105	+	0.882611i	$0.655784\pi$
$360$		0			0
$361$	14.9238	+	10.8427i	0.785461	+	0.570671i
$362$		0			0
$363$	−8.76519	+	0.274237i	−0.460053	+	0.0143937i
$364$		0			0
$365$	0.475287	+	5.34966i	0.0248776	+	0.280014i
$366$		0			0
$367$	3.70869	−	7.27872i	0.193592	−	0.379946i	−0.773723	−	0.633524i	$-0.781608\pi$
$367$	3.70869	−	7.27872i	0.193592	−	0.379946i	0.967315	+	0.253579i	$0.0816076\pi$
$368$		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	0.530536	−	0.847662i	$-0.321991\pi$
$373$	−6.12473	−	6.12473i	−0.317126	−	0.317126i	−0.847662	+	0.530536i	$0.821991\pi$
$374$		0			0
$375$	−7.45563	+	4.88463i	−0.385007	+	0.252241i
$376$		0			0
$377$	26.3331	−	13.4174i	1.35622	−	0.691031i
$378$		0			0
$379$	−0.363481	−	0.500288i	−0.0186708	−	0.0256981i	0.799580	−	0.600560i	$-0.205056\pi$
$379$	−0.363481	−	0.500288i	−0.0186708	−	0.0256981i	−0.818250	+	0.574862i	$0.805056\pi$
$380$		0			0
$381$	11.0449	−	3.58872i	0.565849	−	0.183856i
$382$		0			0
$383$	−10.2511	+	1.62362i	−0.523807	+	0.0829629i	−0.412738	−	0.910850i	$-0.635428\pi$
$383$	−10.2511	+	1.62362i	−0.523807	+	0.0829629i	−0.111069	+	0.993813i	$0.535428\pi$
$384$		0			0
$385$	−0.863904	−	1.12696i	−0.0440286	−	0.0574351i
$386$		0			0
$387$	−12.3092	+	1.94959i	−0.625712	+	0.0991031i
$388$		0			0
$389$	21.0630	−	6.84378i	1.06794	−	0.346993i	0.278252	−	0.960508i	$-0.410245\pi$
$389$	21.0630	−	6.84378i	1.06794	−	0.346993i	0.789683	+	0.613515i	$0.210245\pi$
$390$		0			0
$391$	−3.53969	−	4.87197i	−0.179010	−	0.246386i
$392$		0			0
$393$	−6.93942	+	3.53581i	−0.350048	+	0.178358i
$394$		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	−0.497925	−	0.867220i	$-0.665904\pi$
$401$	3.46399	−	2.51673i	0.172983	−	0.125680i	0.670908	+	0.741540i	$0.265904\pi$
$402$		0			0
$403$	0.493174	−	0.967909i	0.0245668	−	0.0482150i
$404$		0			0
$405$	6.31726	+	5.28634i	0.313907	+	0.262681i
$406$		0			0
$407$	−17.8481	+	1.68589i	−0.884697	+	0.0835664i
$408$		0			0
$409$	−3.47523	−	2.52490i	−0.171839	−	0.124848i	0.498541	−	0.866866i	$-0.333869\pi$
$409$	−3.47523	−	2.52490i	−0.171839	−	0.124848i	−0.670381	+	0.742017i	$0.733869\pi$
$410$		0			0
$411$	1.06675	+	3.28312i	0.0526190	+	0.161945i
$412$		0			0
$413$	−1.82043	−	0.288327i	−0.0895773	−	0.0141877i
$414$		0			0
$415$	34.3192	−	14.6222i	1.68466	−	0.717773i
$416$		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	−0.379057	−	0.925373i	$-0.623752\pi$
$421$	9.67493	−	29.7764i	0.471527	−	1.45121i	0.850584	−	0.525839i	$-0.176248\pi$
$422$		0			0
$423$	4.57321	−	28.8741i	0.222357	−	1.40391i
$424$		0			0
$425$	−15.2095	−	10.5890i	−0.737771	−	0.513640i
$426$		0			0
$427$	0.176512	+	1.11445i	0.00854201	+	0.0539321i
$428$		0			0
$429$	−7.61008	−	3.01366i	−0.367418	−	0.145501i
$430$		0			0
$431$	5.81395	−	8.00222i	0.280048	−	0.385453i	−0.645702	−	0.763590i	$-0.723435\pi$
$431$	5.81395	−	8.00222i	0.280048	−	0.385453i	0.925750	+	0.378137i	$0.123435\pi$
$432$		0			0
$433$	−24.0414	−	12.2497i	−1.15536	−	0.588683i	−0.232033	−	0.972708i	$-0.574538\pi$
$433$	−24.0414	−	12.2497i	−1.15536	−	0.588683i	−0.923323	+	0.384025i	$0.874538\pi$
$434$		0			0
$435$	3.80620	−	16.5882i	0.182494	−	0.795346i
$436$		0			0
$437$	−0.548629	−	1.07675i	−0.0262445	−	0.0515077i
$438$		0			0
$439$	−24.5862			−1.17344			−0.586718	−	0.809791i	$-0.699580\pi$
$439$	−24.5862			−1.17344			−0.586718	+	0.809791i	$0.699580\pi$
$440$		0			0
$441$	−16.4643			−0.784016
$442$		0			0
$443$	13.9816	+	27.4404i	0.664286	+	1.30373i	0.939565	+	0.342370i	$0.111230\pi$
$443$	13.9816	+	27.4404i	0.664286	+	1.30373i	−0.275279	+	0.961364i	$0.588770\pi$
$444$		0			0
$445$	9.40714	+	15.0096i	0.445941	+	0.711524i
$446$		0			0
$447$	4.09323	+	2.08561i	0.193603	+	0.0986458i
$448$		0			0
$449$	4.30536	−	5.92582i	0.203182	−	0.279657i	−0.695250	−	0.718768i	$-0.744707\pi$
$449$	4.30536	−	5.92582i	0.203182	−	0.279657i	0.898433	+	0.439111i	$0.144707\pi$
$450$		0			0
$451$	−5.52141	−	21.5107i	−0.259993	−	1.01290i
$452$		0			0
$453$	1.86624	+	11.7830i	0.0876835	+	0.553612i
$454$		0			0
$455$	−0.322363	−	1.28556i	−0.0151126	−	0.0602678i
$456$		0			0
$457$	1.05368	−	6.65265i	0.0492889	−	0.311198i	−0.950710	−	0.310080i	$-0.899644\pi$
$457$	1.05368	−	6.65265i	0.0492889	−	0.311198i	0.999999	−	0.00111791i	$-0.000355842\pi$
$458$		0			0
$459$	4.89838	−	15.0757i	0.228637	−	0.703672i
$460$		0			0
$461$		−	29.0801i		−	1.35440i	−0.735801	−	0.677198i	$-0.763194\pi$
$461$		−	29.0801i		−	1.35440i	0.735801	−	0.677198i	$-0.236806\pi$
$462$		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
$465$	−0.245203	−	0.575509i	−0.0113710	−	0.0266886i
$466$		0			0
$467$	26.1320	+	4.13890i	1.20924	+	0.191525i	0.728320	−	0.685237i	$-0.240302\pi$
$467$	26.1320	+	4.13890i	1.20924	+	0.191525i	0.480923	+	0.876763i	$0.340302\pi$
$468$		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
$473$	−3.81467	+	17.0603i	−0.175399	+	0.784432i
$474$		0			0
$475$	−2.68213	−	2.57620i	−0.123065	−	0.118204i
$476$		0			0
$477$	−9.69341	+	19.0244i	−0.443831	+	0.871067i
$478$		0			0
$479$	21.2408	−	15.4324i	0.970519	−	0.705123i	0.0149492	−	0.999888i	$-0.495241\pi$
$479$	21.2408	−	15.4324i	0.970519	−	0.705123i	0.955570	+	0.294765i	$0.0952413\pi$
$480$		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
$487$	20.7917	−	10.5939i	0.942163	−	0.480056i	0.0857326	−	0.996318i	$-0.472677\pi$
$487$	20.7917	−	10.5939i	0.942163	−	0.480056i	0.856431	+	0.516262i	$0.172677\pi$
$488$		0			0
$489$	4.69379	+	6.46044i	0.212260	+	0.292151i
$490$		0			0
$491$	−17.4497	+	5.66974i	−0.787493	+	0.255872i	−0.675036	−	0.737785i	$-0.735872\pi$
$491$	−17.4497	+	5.66974i	−0.787493	+	0.255872i	−0.112457	+	0.993657i	$0.535872\pi$
$492$		0			0
$493$	34.9512	−	5.53572i	1.57412	−	0.249316i
$494$		0			0
$495$	15.4141	−	8.35979i	0.692811	−	0.375744i
$496$		0			0
$497$	2.16757	−	0.343309i	0.0972286	−	0.0153995i
$498$		0			0
$499$	11.1824	−	3.63339i	0.500595	−	0.162653i	−0.0478260	−	0.998856i	$-0.515229\pi$
$499$	11.1824	−	3.63339i	0.500595	−	0.162653i	0.548421	+	0.836203i	$0.315229\pi$
$500$		0			0
$501$	−5.65234	−	7.77978i	−0.252528	−	0.347575i
$502$		0			0
$503$	4.75855	−	2.42460i	0.212173	−	0.108108i	−0.344674	−	0.938722i	$-0.612011\pi$
$503$	4.75855	−	2.42460i	0.212173	−	0.108108i	0.556848	+	0.830615i	$0.312011\pi$
$504$		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	$-0.257070\pi$
$509$	18.6283	+	6.05272i	0.825687	+	0.268282i	0.134459	+	0.990919i	$0.457070\pi$
$510$		0			0
$511$	−0.372057	+	0.270315i	−0.0164588	+	0.0119580i
$512$		0			0
$513$	1.44412	−	2.83424i	0.0637594	−	0.125135i
$514$		0			0
$515$	7.21050	−	0.640611i	0.317732	−	0.0282287i
$516$		0			0
$517$	−35.2950	−	20.8767i	−1.55227	−	0.918158i
$518$		0			0
$519$	−8.03959	−	5.84110i	−0.352899	−	0.256396i
$520$		0			0
$521$	5.78913	+	17.8171i	0.253626	+	0.780582i	0.994097	+	0.108493i	$0.0346026\pi$
$521$	5.78913	+	17.8171i	0.253626	+	0.780582i	−0.740471	+	0.672089i	$0.765397\pi$
$522$		0			0
$523$	2.55051	+	0.403961i	0.111526	+	0.0176640i	0.211948	−	0.977281i	$-0.432019\pi$
$523$	2.55051	+	0.403961i	0.111526	+	0.0176640i	−0.100422	+	0.994945i	$0.532019\pi$
$524$		0			0
$525$	−0.686882	−	0.332730i	−0.0299780	−	0.0145215i
$526$		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
$533$	3.24258	−	20.4729i	0.140452	−	0.886778i
$534$		0			0
$535$	−21.2071	−	12.7037i	−0.916862	−	0.549229i
$536$		0			0
$537$	2.51654	+	15.8888i	0.108597	+	0.685652i
$538$		0			0
$539$	−8.50325	+	21.4724i	−0.366261	+	0.924881i
$540$		0			0
$541$	5.42829	−	7.47139i	0.233380	−	0.321220i	−0.676224	−	0.736696i	$-0.736385\pi$
$541$	5.42829	−	7.47139i	0.233380	−	0.321220i	0.909604	+	0.415476i	$0.136385\pi$
$542$		0			0
$543$	−3.27444	−	1.66841i	−0.140520	−	0.0715983i
$544$		0			0
$545$	−18.0794	+	11.3311i	−0.774438	+	0.485372i
$546$		0			0
$547$	−0.486237	−	0.954295i	−0.0207900	−	0.0408027i	0.880378	−	0.474273i	$-0.157289\pi$
$547$	−0.486237	−	0.954295i	−0.0207900	−	0.0408027i	−0.901168	+	0.433470i	$0.857289\pi$
$548$		0			0
$549$	−13.9337			−0.594674
$550$		0			0
$551$	7.10113			0.302518
$552$		0			0
$553$	−0.0582826	−	0.114386i	−0.00247843	−	0.00486419i
$554$		0			0
$555$	−8.16479	+	5.11721i	−0.346576	+	0.217214i
$556$		0			0
$557$	−38.3462	−	19.5384i	−1.62478	−	0.827868i	−0.998848	−	0.0479915i	$-0.984718\pi$
$557$	−38.3462	−	19.5384i	−1.62478	−	0.827868i	−0.625934	−	0.779876i	$-0.715282\pi$
$558$		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
$563$	−4.04575	−	25.5439i	−0.170508	−	1.07655i	−0.913379	−	0.407111i	$-0.866536\pi$
$563$	−4.04575	−	25.5439i	−0.170508	−	1.07655i	0.742871	−	0.669435i	$-0.233464\pi$
$564$		0			0
$565$	7.95622	+	4.76603i	0.334721	+	0.200508i
$566$		0			0
$567$	−0.110341	+	0.696664i	−0.00463387	+	0.0292571i
$568$		0			0
$569$	−8.39651	+	25.8418i	−0.352000	+	1.08334i	0.605729	+	0.795671i	$0.292882\pi$
$569$	−8.39651	+	25.8418i	−0.352000	+	1.08334i	−0.957729	+	0.287673i	$0.907118\pi$
$570$		0			0
$571$			40.5475i			1.69686i	0.529308	+	0.848430i	$0.322451\pi$
$571$			40.5475i			1.69686i	−0.529308	+	0.848430i	$0.677549\pi$
$572$		0			0
$573$	3.56628	−	3.56628i	0.148984	−	0.148984i
$574$		0			0
$575$	−2.66546	−	7.67392i	−0.111157	−	0.320024i
$576$		0			0
$577$	33.3917	+	5.28872i	1.39011	+	0.220172i	0.806200	−	0.591643i	$-0.201521\pi$
$577$	33.3917	+	5.28872i	1.39011	+	0.220172i	0.583914	+	0.811815i	$0.301521\pi$
$578$		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
$583$	19.8048	+	22.4673i	0.820233	+	0.930502i
$584$		0			0
$585$	16.3023	−	1.44837i	0.674018	−	0.0598826i
$586$		0			0
$587$	4.39649	−	8.62859i	0.181462	−	0.356140i	−0.782300	−	0.622902i	$-0.785954\pi$
$587$	4.39649	−	8.62859i	0.181462	−	0.356140i	0.963763	+	0.266762i	$0.0859536\pi$
$588$		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	0.934012	−	0.357243i	$-0.116283\pi$
$593$	14.0452	+	14.0452i	0.576769	+	0.576769i	−0.357243	+	0.934012i	$0.616283\pi$
$594$		0			0
$595$	0.108568	−	1.58320i	0.00445086	−	0.0649048i
$596$		0			0
$597$	−9.50623	+	4.84367i	−0.389064	+	0.198238i
$598$		0			0
$599$	2.65433	+	3.65338i	0.108453	+	0.149273i	0.859793	−	0.510642i	$-0.170592\pi$
$599$	2.65433	+	3.65338i	0.108453	+	0.149273i	−0.751340	+	0.659915i	$0.770592\pi$
$600$		0			0
$601$	−7.96746	+	2.58878i	−0.324999	+	0.105599i	−0.466973	−	0.884272i	$-0.654655\pi$
$601$	−7.96746	+	2.58878i	−0.324999	+	0.105599i	0.141973	+	0.989871i	$0.454655\pi$
$602$		0			0
$603$	−13.6540	+	2.16258i	−0.556034	+	0.0880671i
$604$		0			0
$605$	−2.94181	−	24.4202i	−0.119601	−	0.992822i
$606$		0			0
$607$	7.58425	−	1.20123i	0.307835	−	0.0487563i	−0.000605683	−	1.00000i	$-0.500193\pi$
$607$	7.58425	−	1.20123i	0.307835	−	0.0487563i	0.308441	+	0.951244i	$0.400193\pi$
$608$		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
$613$	38.2477	−	19.4882i	1.54481	−	0.787120i	0.546091	−	0.837726i	$-0.316115\pi$
$613$	38.2477	−	19.4882i	1.54481	−	0.787120i	0.998719	+	0.0506058i	$0.0161152\pi$
$614$		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	$-0.539389\pi$
$619$	−20.0674	−	6.52029i	−0.806576	−	0.262073i	−0.683147	+	0.730281i	$0.739389\pi$
$620$		0			0
$621$	5.62139	−	4.08418i	0.225578	−	0.163892i
$622$		0			0
$623$	−0.688620	+	1.35149i	−0.0275890	+	0.0541464i
$624$		0			0
$625$	−15.4973	−	19.6172i	−0.619892	−	0.784687i
$626$		0			0
$627$	−1.30047	−	1.47530i	−0.0519358	−	0.0589179i
$628$		0			0
$629$	−16.2087	−	11.7763i	−0.646282	−	0.469552i
$630$		0			0
$631$	8.72043	+	26.8387i	0.347155	+	1.06843i	0.960420	+	0.278555i	$0.0898556\pi$
$631$	8.72043	+	26.8387i	0.347155	+	1.06843i	−0.613265	+	0.789877i	$0.710144\pi$
$632$		0			0
$633$	−4.67121	−	0.739847i	−0.185664	−	0.0294063i
$634$		0			0
$635$	12.7677	+	29.9667i	0.506671	+	1.18919i
$636$		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	0.792893	+	0.609362i	$0.208574\pi$
$641$	−5.23436	+	16.1097i	−0.206745	+	0.636295i	−0.999637	+	0.0269333i	$0.991426\pi$
$642$		0			0
$643$	−0.981726	+	6.19838i	−0.0387155	+	0.244440i	−0.999455	−	0.0330121i	$-0.989490\pi$
$643$	−0.981726	+	6.19838i	−0.0387155	+	0.244440i	0.960739	+	0.277452i	$0.0894900\pi$
$644$		0			0
$645$	2.28539	+	9.11397i	0.0899873	+	0.358862i
$646$		0			0
$647$	6.80289	+	42.9518i	0.267449	+	1.68861i	0.646247	+	0.763128i	$0.276338\pi$
$647$	6.80289	+	42.9518i	0.267449	+	1.68861i	−0.378798	+	0.925479i	$0.623662\pi$
$648$		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
$653$	8.67042	+	4.41780i	0.339300	+	0.172882i	0.615335	−	0.788266i	$-0.289021\pi$
$653$	8.67042	+	4.41780i	0.339300	+	0.172882i	−0.276035	+	0.961147i	$0.589021\pi$
$654$		0			0
$655$	−11.6008	−	18.5098i	−0.453283	−	0.723237i
$656$		0			0
$657$	−2.57823	−	5.06007i	−0.100586	−	0.197412i
$658$		0			0
$659$	−3.37375			−0.131423			−0.0657113	−	0.997839i	$-0.520932\pi$
$659$	−3.37375			−0.131423			−0.0657113	+	0.997839i	$0.520932\pi$
$660$		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
$663$	−4.15278	−	8.15028i	−0.161280	−	0.316531i
$664$		0			0
$665$	0.0712179	−	0.310383i	0.00276171	−	0.0120361i
$666$		0			0
$667$	13.8210	+	7.04213i	0.535150	+	0.272672i
$668$		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
$673$	5.98412	+	37.7823i	0.230671	+	1.45640i	0.782609	+	0.622514i	$0.213889\pi$
$673$	5.98412	+	37.7823i	0.230671	+	1.45640i	−0.551938	+	0.833885i	$0.686111\pi$
$674$		0			0
$675$	12.2178	−	17.5491i	0.470263	−	0.675465i
$676$		0			0
$677$	5.03592	−	31.7956i	0.193546	−	1.22200i	−0.679246	−	0.733911i	$-0.737693\pi$
$677$	5.03592	−	31.7956i	0.193546	−	1.22200i	0.872792	−	0.488092i	$-0.162307\pi$
$678$		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
$685$	−8.90764	+	3.79522i	−0.340343	+	0.145008i
$686$		0			0
$687$	−12.9380	−	2.04918i	−0.493616	−	0.0781811i
$688$		0			0
$689$	8.63834	+	26.5861i	0.329095	+	1.01285i
$690$		0			0
$691$	−20.4397	−	14.8503i	−0.777564	−	0.564933i	0.126683	−	0.991943i	$-0.459567\pi$
$691$	−20.4397	−	14.8503i	−0.777564	−	0.564933i	−0.904247	+	0.427010i	$0.859567\pi$
$692$		0			0
$693$	1.29235	+	0.764417i	0.0490925	+	0.0290378i
$694$		0			0
$695$	18.0241	+	15.0828i	0.683694	+	0.572122i
$696$		0			0
$697$	11.2675	−	22.1136i	0.426785	−	0.837613i
$698$		0			0
$699$	−10.0896	+	7.33055i	−0.381625	+	0.277267i
$700$		0			0
$701$	26.8458	+	8.72273i	1.01395	+	0.329453i	0.768427	−	0.639937i	$-0.221040\pi$
$701$	26.8458	+	8.72273i	1.01395	+	0.329453i	0.245525	+	0.969390i	$0.421040\pi$
$702$		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
$707$	0.823230	−	0.419457i	0.0309608	−	0.0157753i
$708$		0			0
$709$	−4.79615	−	6.60134i	−0.180123	−	0.247918i	0.709402	−	0.704804i	$-0.248965\pi$
$709$	−4.79615	−	6.60134i	−0.180123	−	0.247918i	−0.889526	+	0.456885i	$0.848965\pi$
$710$		0			0
$711$	1.50773	−	0.489890i	0.0565441	−	0.0183723i
$712$		0			0
$713$	0.563131	−	0.0891912i	0.0210894	−	0.00334024i
$714$		0			0
$715$	6.53065	−	22.0091i	0.244232	−	0.823095i
$716$		0			0
$717$	−4.15889	+	0.658703i	−0.155317	+	0.0245997i
$718$		0			0
$719$	0.986856	−	0.320649i	0.0368035	−	0.0119582i	−0.290557	−	0.956858i	$-0.593841\pi$
$719$	0.986856	−	0.320649i	0.0368035	−	0.0119582i	0.327361	+	0.944899i	$0.393841\pi$
$720$		0			0
$721$	0.364342	+	0.501474i	0.0135688	+	0.0186759i
$722$		0			0
$723$	−11.4843	+	5.85157i	−0.427107	+	0.217622i
$724$		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
$733$	20.7361	−	40.6968i	0.765904	−	1.50317i	−0.0956003	−	0.995420i	$-0.530477\pi$
$733$	20.7361	−	40.6968i	0.765904	−	1.50317i	0.861504	−	0.507751i	$-0.169523\pi$
$734$		0			0
$735$	1.09851	+	12.3645i	0.0405193	+	0.456071i
$736$		0			0
$737$	−4.23142	+	18.9241i	−0.155866	+	0.697079i
$738$		0			0
$739$	−3.07164	−	2.23167i	−0.112992	−	0.0820934i	0.529854	−	0.848089i	$-0.322247\pi$
$739$	−3.07164	−	2.23167i	−0.112992	−	0.0820934i	−0.642846	+	0.765995i	$0.722247\pi$
$740$		0			0
$741$	−0.567231	−	1.74576i	−0.0208377	−	0.0641320i
$742$		0			0
$743$	41.9067	+	6.63736i	1.53741	+	0.243501i	0.866930	−	0.498430i	$-0.166090\pi$
$743$	41.9067	+	6.63736i	1.53741	+	0.243501i	0.670476	+	0.741931i	$0.266090\pi$
$744$		0			0
$745$	−4.81079	+	11.9534i	−0.176254	+	0.437938i
$746$		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	−0.878781	−	0.477225i	$-0.841643\pi$
$751$	3.08775	−	9.50312i	0.112674	−	0.346774i	0.991455	+	0.130451i	$0.0416427\pi$
$752$		0			0
$753$	−2.41230	+	15.2306i	−0.0879089	+	0.555035i
$754$		0			0
$755$	−32.4561	+	8.13861i	−1.18120	+	0.296194i
$756$		0			0
$757$	4.59658	+	29.0217i	0.167065	+	1.05481i	0.918621	+	0.395140i	$0.129304\pi$
$757$	4.59658	+	29.0217i	0.167065	+	1.05481i	−0.751555	+	0.659670i	$0.770696\pi$
$758$		0			0
$759$	−1.06807	−	4.16105i	−0.0387684	−	0.151037i
$760$		0			0
$761$	−17.8404	+	24.5552i	−0.646713	+	0.890124i	−0.998951	−	0.0457864i	$-0.985421\pi$
$761$	−17.8404	+	24.5552i	−0.646713	+	0.890124i	0.352238	+	0.935910i	$0.385421\pi$
$762$		0			0
$763$	−1.62790	−	0.829459i	−0.0589341	−	0.0300284i
$764$		0			0
$765$	19.1001	+	4.38256i	0.690566	+	0.158452i
$766$		0			0
$767$	−13.5283	−	26.5507i	−0.488477	−	0.958690i
$768$		0			0
$769$	−37.6421			−1.35741			−0.678705	−	0.734411i	$-0.737458\pi$
$769$	−37.6421			−1.35741			−0.678705	+	0.734411i	$0.737458\pi$
$770$		0			0
$771$	3.75184			0.135119
$772$		0			0
$773$	−11.7188	−	22.9995i	−0.421497	−	0.827234i	−0.999934	−	0.0115072i	$-0.996337\pi$
$773$	−11.7188	−	22.9995i	−0.421497	−	0.827234i	0.578437	−	0.815727i	$-0.303663\pi$
$774$		0			0
$775$	1.54700	−	0.827900i	0.0555698	−	0.0297390i
$776$		0			0
$777$	−0.735173	−	0.374589i	−0.0263742	−	0.0134383i
$778$		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
$783$	6.38724	+	40.3275i	0.228261	+	1.44119i
$784$		0			0
$785$	−5.68579	+	9.49165i	−0.202935	+	0.338771i
$786$		0			0
$787$	−2.70244	+	17.0625i	−0.0963315	+	0.608213i	0.891540	+	0.452942i	$0.149625\pi$
$787$	−2.70244	+	17.0625i	−0.0963315	+	0.608213i	−0.987872	+	0.155272i	$0.950375\pi$
$788$		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
$795$	14.9338	+	6.01029i	0.529647	+	0.213163i
$796$		0			0
$797$	−44.0203	−	6.97213i	−1.55928	−	0.246965i	−0.683599	−	0.729858i	$-0.739586\pi$
$797$	−44.0203	−	6.97213i	−1.55928	−	0.246965i	−0.875680	+	0.482892i	$0.839586\pi$
$798$		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
$803$	−7.93078	+	0.749124i	−0.279871	+	0.0264360i
$804$		0			0
$805$	0.446416	−	0.533473i	0.0157341	−	0.0188025i
$806$		0			0
$807$	−4.09432	+	8.03556i	−0.144127	+	0.282865i
$808$		0			0
$809$	−12.3255	+	8.95497i	−0.433340	+	0.314840i	−0.782983	−	0.622043i	$-0.786303\pi$
$809$	−12.3255	+	8.95497i	−0.433340	+	0.314840i	0.349643	+	0.936883i	$0.386303\pi$
$810$		0			0
$811$	43.3276	+	14.0780i	1.52144	+	0.494345i	0.946183	−	0.323631i	$-0.104904\pi$
$811$	43.3276	+	14.0780i	1.52144	+	0.494345i	0.575253	+	0.817976i	$0.304904\pi$
$812$		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
$817$	−3.49314	+	1.77984i	−0.122209	+	0.0622688i
$818$		0			0
$819$	0.823747	+	1.13379i	0.0287840	+	0.0396178i
$820$		0			0
$821$	−27.3071	+	8.87260i	−0.953023	+	0.309656i	−0.743943	−	0.668243i	$-0.767047\pi$
$821$	−27.3071	+	8.87260i	−0.953023	+	0.309656i	−0.209079	+	0.977899i	$0.567047\pi$
$822$		0			0
$823$	26.6252	−	4.21701i	0.928095	−	0.146996i	0.325954	−	0.945386i	$-0.394314\pi$
$823$	26.6252	−	4.21701i	0.928095	−	0.146996i	0.602141	+	0.798390i	$0.294314\pi$
$824$		0			0
$825$	−7.30652	−	11.0180i	−0.254380	−	0.383597i
$826$		0			0
$827$	−39.1944	+	6.20779i	−1.36292	+	0.215866i	−0.794697	−	0.607006i	$-0.792370\pi$
$827$	−39.1944	+	6.20779i	−1.36292	+	0.215866i	−0.568227	+	0.822872i	$0.692370\pi$
$828$		0			0
$829$	−10.3353	+	3.35814i	−0.358959	+	0.116633i	−0.482944	−	0.875651i	$-0.660433\pi$
$829$	−10.3353	+	3.35814i	−0.358959	+	0.116633i	0.123985	+	0.992284i	$0.460433\pi$
$830$		0			0
$831$	−2.19378	−	3.01948i	−0.0761013	−	0.104744i
$832$		0			0
$833$	−22.9966	+	11.7174i	−0.796786	+	0.405983i
$834$		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	$-0.645007\pi$
$839$	−38.3426	−	12.4583i	−1.32373	−	0.430107i	−0.883775	+	0.467912i	$0.845007\pi$
$840$		0			0
$841$	−50.2797	+	36.5303i	−1.73378	+	1.25967i
$842$		0			0
$843$	4.77364	−	9.36879i	0.164413	−	0.322678i
$844$		0			0
$845$	−4.90379	+	5.86010i	−0.168695	+	0.201593i
$846$		0			0
$847$	1.66439	−	1.29066i	0.0571891	−	0.0443477i
$848$		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
$853$	13.7845	+	2.18326i	0.471974	+	0.0747533i	0.387890	−	0.921705i	$-0.373204\pi$
$853$	13.7845	+	2.18326i	0.471974	+	0.0747533i	0.0840831	+	0.996459i	$0.473204\pi$
$854$		0			0
$855$	3.64808	+	1.46822i	0.124762	+	0.0502119i
$856$		0			0
$857$	−26.9229	+	26.9229i	−0.919668	+	0.919668i	−0.997005	−	0.0773373i	$-0.975358\pi$
$857$	−26.9229	+	26.9229i	−0.919668	+	0.919668i	0.0773373	+	0.997005i	$0.475358\pi$
$858$		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
$863$	1.90114	−	12.0033i	0.0647154	−	0.408597i	−0.933971	−	0.357350i	$-0.883680\pi$
$863$	1.90114	−	12.0033i	0.0647154	−	0.408597i	0.998686	−	0.0512472i	$-0.0163196\pi$
$864$		0			0
$865$	14.3234	−	23.9109i	0.487010	−	0.812996i
$866$		0			0
$867$	0.406785	+	2.56834i	0.0138151	+	0.0872253i
$868$		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
$873$	−2.90515	−	1.48025i	−0.0983243	−	0.0500987i
$874$		0			0
$875$	0.759091	−	2.00161i	0.0256620	−	0.0676666i
$876$		0			0
$877$	−5.82698	−	11.4361i	−0.196763	−	0.386169i	0.771452	−	0.636287i	$-0.219531\pi$
$877$	−5.82698	−	11.4361i	−0.196763	−	0.386169i	−0.968215	+	0.250118i	$0.919531\pi$
$878$		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
$883$	19.7888	+	38.8377i	0.665947	+	1.30699i	0.938642	+	0.344893i	$0.112085\pi$
$883$	19.7888	+	38.8377i	0.665947	+	1.30699i	−0.272695	+	0.962100i	$0.587915\pi$
$884$		0			0
$885$	−16.7253	−	3.83765i	−0.562215	−	0.129001i
$886$		0			0
$887$	9.26576	+	4.72114i	0.311114	+	0.158520i	0.602575	−	0.798062i	$-0.294141\pi$
$887$	9.26576	+	4.72114i	0.311114	+	0.158520i	−0.291461	+	0.956583i	$0.594141\pi$
$888$		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
$893$	−1.43862	−	9.08308i	−0.0481415	−	0.303954i
$894$		0			0
$895$	−43.7656	+	10.9745i	−1.46292	+	0.366838i
$896$		0			0
$897$	0.627249	−	3.96029i	0.0209432	−	0.132230i
$898$		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
$905$	3.84846	−	9.56228i	0.127927	−	0.317861i
$906$		0			0
$907$	−16.1062	−	2.55097i	−0.534798	−	0.0847036i	−0.116806	−	0.993155i	$-0.537266\pi$
$907$	−16.1062	−	2.55097i	−0.534798	−	0.0847036i	−0.417991	+	0.908451i	$0.637266\pi$
$908$		0			0
$909$	3.52571	+	10.8510i	0.116940	+	0.359906i
$910$		0			0
$911$	−14.3281	−	10.4099i	−0.474710	−	0.344897i	0.324564	−	0.945864i	$-0.394782\pi$
$911$	−14.3281	−	10.4099i	−0.474710	−	0.344897i	−0.799274	+	0.600967i	$0.794782\pi$
$912$		0			0
$913$	21.9712	+	50.7821i	0.727140	+	1.68064i
$914$		0			0
$915$	0.929665	+	10.4640i	0.0307338	+	0.345929i
$916$		0			0
$917$	0.849203	−	1.66665i	0.0280431	−	0.0550378i
$918$		0			0
$919$	−7.38632	+	5.36648i	−0.243652	+	0.177024i	−0.702909	−	0.711280i	$-0.748116\pi$
$919$	−7.38632	+	5.36648i	−0.243652	+	0.177024i	0.459257	+	0.888304i	$0.348116\pi$
$920$		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
$927$	−6.82017	+	3.47505i	−0.224004	+	0.114136i
$928$		0			0
$929$	−1.06529	−	1.46625i	−0.0349511	−	0.0481061i	0.791184	−	0.611578i	$-0.209465\pi$
$929$	−1.06529	−	1.46625i	−0.0349511	−	0.0481061i	−0.826135	+	0.563472i	$0.809465\pi$
$930$		0			0
$931$	−4.92578	+	1.60048i	−0.161436	+	0.0524537i
$932$		0			0
$933$	5.91808	−	0.937332i	0.193749	−	0.0306869i
$934$		0			0
$935$	15.5802	−	22.6465i	0.509525	−	0.740619i
$936$		0			0
$937$	14.9726	−	2.37143i	0.489133	−	0.0774711i	0.0930039	−	0.995666i	$-0.470353\pi$
$937$	14.9726	−	2.37143i	0.489133	−	0.0774711i	0.396130	+	0.918195i	$0.370353\pi$
$938$		0			0
$939$	−1.02061	+	0.331616i	−0.0333063	+	0.0108219i
$940$		0			0
$941$	−12.8308	−	17.6600i	−0.418271	−	0.575701i	0.546940	−	0.837172i	$-0.315792\pi$
$941$	−12.8308	−	17.6600i	−0.418271	−	0.575701i	−0.965211	+	0.261471i	$0.915792\pi$
$942$		0			0
$943$	9.69338	−	4.93902i	0.315660	−	0.160837i
$944$		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
$953$	−5.92153	+	11.6216i	−0.191817	+	0.376462i	−0.966806	−	0.255513i	$-0.917756\pi$
$953$	−5.92153	+	11.6216i	−0.191817	+	0.376462i	0.774989	+	0.631975i	$0.217756\pi$
$954$		0			0
$955$	10.8487	+	9.07831i	0.351056	+	0.293767i
$956$		0			0
$957$	24.6354	+	5.50846i	0.796349	+	0.178063i
$958$		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
$963$	25.8182	+	4.08921i	0.831981	+	0.131773i
$964$		0			0
$965$	−12.2027	+	5.19911i	−0.392818	+	0.167365i
$966$		0			0
$967$	−13.6319	+	13.6319i	−0.438372	+	0.438372i	−0.891464	−	0.453092i	$-0.850321\pi$
$967$	−13.6319	+	13.6319i	−0.438372	+	0.438372i	0.453092	+	0.891464i	$0.350321\pi$
$968$		0			0
$969$		−	2.19785i		−	0.0706051i
$970$		0			0
$971$	−1.26967	+	3.90765i	−0.0407457	+	0.125403i	−0.969360	−	0.245643i	$-0.921001\pi$
$971$	−1.26967	+	3.90765i	−0.0407457	+	0.125403i	0.928615	+	0.371046i	$0.121001\pi$
$972$		0			0
$973$	−0.314819	+	1.98769i	−0.0100926	+	0.0637224i
$974$		0			0
$975$	−2.17541	−	12.1462i	−0.0696688	−	0.388989i
$976$		0			0
$977$	4.80402	+	30.3314i	0.153694	+	0.970386i	0.937147	+	0.348935i	$0.113457\pi$
$977$	4.80402	+	30.3314i	0.153694	+	0.970386i	−0.783453	+	0.621451i	$0.786543\pi$
$978$		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
$983$	−24.7035	−	12.5871i	−0.787919	−	0.401465i	0.0132429	−	0.999912i	$-0.495785\pi$
$983$	−24.7035	−	12.5871i	−0.787919	−	0.401465i	−0.801162	+	0.598447i	$0.795785\pi$
$984$		0			0
$985$	7.00505	−	30.5295i	0.223199	−	0.972750i
$986$		0			0
$987$	−0.856827	−	1.68162i	−0.0272731	−	0.0535265i
$988$		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
$993$	6.40795	+	12.5763i	0.203350	+	0.399097i
$994$		0			0
$995$	−15.8919	−	25.3563i	−0.503806	−	0.803849i
$996$		0			0
$997$	25.7239	+	13.1070i	0.814685	+	0.415103i	0.811112	−	0.584891i	$-0.198863\pi$
$997$	25.7239	+	13.1070i	0.814685	+	0.415103i	0.00357282	+	0.999994i	$0.498863\pi$
$998$		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.337.4		32
4.3	odd	2		55.2.l.a.7.4	✓	32
5.3	odd	4	inner	880.2.cm.a.513.1		32
11.8	odd	10	inner	880.2.cm.a.657.1		32
12.11	even	2		495.2.bj.a.172.1		32
20.3	even	4		55.2.l.a.18.1	yes	32
20.7	even	4		275.2.bm.b.18.4		32
20.19	odd	2		275.2.bm.b.7.1		32
44.3	odd	10		605.2.m.e.602.4		32
44.7	even	10		605.2.m.d.112.1		32
44.15	odd	10		605.2.m.c.112.4		32
44.19	even	10		55.2.l.a.52.1	yes	32
44.27	odd	10		605.2.e.b.362.3		32
44.31	odd	10		605.2.m.d.457.1		32
44.35	even	10		605.2.m.c.457.4		32
44.39	even	10		605.2.e.b.362.14		32
44.43	even	2		605.2.m.e.282.1		32
55.8	even	20	inner	880.2.cm.a.833.4		32
60.23	odd	4		495.2.bj.a.73.4		32
132.107	odd	10		495.2.bj.a.217.4		32
220.3	even	20		605.2.m.e.118.1		32
220.19	even	10		275.2.bm.b.107.4		32
220.43	odd	4		605.2.m.e.403.4		32
220.63	odd	20		55.2.l.a.8.4	yes	32
220.83	odd	20		605.2.e.b.483.3		32
220.103	even	20		605.2.m.c.233.4		32
220.107	odd	20		275.2.bm.b.118.1		32
220.123	odd	20		605.2.m.c.578.4		32
220.163	even	20		605.2.m.d.578.1		32
220.183	odd	20		605.2.m.d.233.1		32
220.203	even	20		605.2.e.b.483.14		32
660.503	even	20		495.2.bj.a.118.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.7.4	✓	32	4.3	odd	2
55.2.l.a.8.4	yes	32	220.63	odd	20
55.2.l.a.18.1	yes	32	20.3	even	4
55.2.l.a.52.1	yes	32	44.19	even	10
275.2.bm.b.7.1		32	20.19	odd	2
275.2.bm.b.18.4		32	20.7	even	4
275.2.bm.b.107.4		32	220.19	even	10
275.2.bm.b.118.1		32	220.107	odd	20
495.2.bj.a.73.4		32	60.23	odd	4
495.2.bj.a.118.1		32	660.503	even	20
495.2.bj.a.172.1		32	12.11	even	2
495.2.bj.a.217.4		32	132.107	odd	10
605.2.e.b.362.3		32	44.27	odd	10
605.2.e.b.362.14		32	44.39	even	10
605.2.e.b.483.3		32	220.83	odd	20
605.2.e.b.483.14		32	220.203	even	20
605.2.m.c.112.4		32	44.15	odd	10
605.2.m.c.233.4		32	220.103	even	20
605.2.m.c.457.4		32	44.35	even	10
605.2.m.c.578.4		32	220.123	odd	20
605.2.m.d.112.1		32	44.7	even	10
605.2.m.d.233.1		32	220.183	odd	20
605.2.m.d.457.1		32	44.31	odd	10
605.2.m.d.578.1		32	220.163	even	20
605.2.m.e.118.1		32	220.3	even	20
605.2.m.e.282.1		32	44.43	even	2
605.2.m.e.403.4		32	220.43	odd	4
605.2.m.e.602.4		32	44.3	odd	10
880.2.cm.a.337.4		32	1.1	even	1	trivial
880.2.cm.a.513.1		32	5.3	odd	4	inner
880.2.cm.a.657.1		32	11.8	odd	10	inner
880.2.cm.a.833.4		32	55.8	even	20	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)

\(f(q)\)	\(=\)	\(q+(0.361933 + 0.710333i) q^{3} +(-1.89470 + 1.18749i) q^{5} +(-0.170602 - 0.0869260i) q^{7} +(1.38978 - 1.91287i) q^{9} +(-1.77694 - 2.80044i) q^{11} +(-0.484259 - 3.05749i) q^{13} +(-1.52926 - 0.916076i) q^{15} +(0.579827 - 3.66088i) q^{17} +(0.229844 - 0.707388i) q^{19} -0.152646i q^{21} +(1.14886 - 1.14886i) q^{23} +(2.17976 - 4.49985i) q^{25} +(4.22401 + 0.669017i) q^{27} +(2.95025 + 9.07993i) q^{29} +(0.283900 + 0.206266i) q^{31} +(1.34611 - 2.27579i) q^{33} +(0.426463 - 0.0378887i) q^{35} +(2.45398 - 4.81621i) q^{37} +(1.99657 - 1.45059i) q^{39} +(6.36824 + 2.06917i) q^{41} +(-3.72708 - 3.72708i) q^{43} +(-0.361710 + 5.27464i) q^{45} +(11.0165 - 5.61318i) q^{47} +(-4.09295 - 5.63346i) q^{49} +(2.81030 - 0.913123i) q^{51} +(-8.91914 + 1.41265i) q^{53} +(6.69225 + 3.19590i) q^{55} +(0.585669 - 0.0927608i) q^{57} +(9.15496 - 2.97463i) q^{59} +(-3.46383 - 4.76756i) q^{61} +(-0.403377 + 0.205531i) q^{63} +(4.54825 + 5.21797i) q^{65} +(-4.13426 - 4.13426i) q^{67} +(1.23188 + 0.400262i) q^{69} +(-9.27272 + 6.73702i) q^{71} +(1.09042 - 2.14008i) q^{73} +(3.98532 - 0.0802892i) q^{75} +(0.0597184 + 0.632224i) q^{77} +(0.542434 + 0.394101i) q^{79} +(-1.13837 - 3.50353i) q^{81} +(-16.4776 - 2.60980i) q^{83} +(3.24865 + 7.62480i) q^{85} +(-5.38198 + 5.38198i) q^{87} -7.92190i q^{89} +(-0.183160 + 0.563709i) q^{91} +(-0.0437645 + 0.276318i) q^{93} +(0.404527 + 1.61322i) q^{95} +(-0.215721 - 1.36201i) q^{97} +(-7.82643 - 0.492943i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} - 2 q^{5} + 24 q^{11} - 10 q^{13} - 14 q^{15} + 24 q^{23} + 16 q^{25} + 16 q^{27} + 28 q^{31} + 66 q^{33} + 10 q^{35} - 8 q^{37} + 40 q^{41} - 28 q^{45} + 28 q^{47} - 20 q^{51} - 24 q^{53}+ \cdots - 8 q^{97}+O(q^{100}) \) 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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