LMFDB - Embedded newform 605.2.m.e.282.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [605,2,Mod(112,605)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("605.112"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(605, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([5, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.m (of order $20$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,10,-4,0,-2,20,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.83094932229$
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			282.1
Character	$\chi$	$=$	605.282
Dual form			605.2.m.e.118.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50135 + 0.237790i) q^{2} +(-0.361933 - 0.710333i) q^{3} +(0.295389 - 0.0959778i) q^{4} +(-1.89470 + 1.18749i) q^{5} +(0.712297 + 0.980393i) q^{6} +(-0.170602 - 0.0869260i) q^{7} +(2.28811 - 1.16585i) q^{8} +(1.38978 - 1.91287i) q^{9} +(2.56223 - 2.23337i) q^{10} +(-0.175087 - 0.175087i) q^{12} +(0.484259 + 3.05749i) q^{13} +(0.276803 + 0.0899388i) q^{14} +(1.52926 + 0.916076i) q^{15} +(-3.66057 + 2.65956i) q^{16} +(-0.579827 + 3.66088i) q^{17} +(-1.63168 + 3.20235i) q^{18} +(0.229844 - 0.707388i) q^{19} +(-0.445701 + 0.532619i) q^{20} +0.152646i q^{21} +(-1.14886 + 1.14886i) q^{23} +(-1.65629 - 1.20336i) q^{24} +(2.17976 - 4.49985i) q^{25} +(-1.45408 - 4.47521i) q^{26} +(-4.22401 - 0.669017i) q^{27} +(-0.0587369 - 0.00930302i) q^{28} +(-2.95025 - 9.07993i) q^{29} +(-2.51379 - 1.01171i) q^{30} +(-0.283900 - 0.206266i) q^{31} +(1.23166 - 1.23166i) q^{32} -5.63413i q^{34} +(0.426463 - 0.0378887i) q^{35} +(0.226933 - 0.698428i) q^{36} +(2.45398 - 4.81621i) q^{37} +(-0.176866 + 1.11669i) q^{38} +(1.99657 - 1.45059i) q^{39} +(-2.95085 + 4.92603i) q^{40} +(-6.36824 - 2.06917i) q^{41} +(-0.0362976 - 0.229174i) q^{42} +(-3.72708 - 3.72708i) q^{43} +(-0.361710 + 5.27464i) q^{45} +(1.45165 - 1.99802i) q^{46} +(-11.0165 + 5.61318i) q^{47} +(3.21405 + 1.63764i) q^{48} +(-4.09295 - 5.63346i) q^{49} +(-2.20256 + 7.27417i) q^{50} +(2.81030 - 0.913123i) q^{51} +(0.436496 + 0.856672i) q^{52} +(-8.91914 + 1.41265i) q^{53} +6.50079 q^{54} -0.491699 q^{56} +(-0.585669 + 0.0927608i) q^{57} +(6.58847 + 12.9306i) q^{58} +(-9.15496 + 2.97463i) q^{59} +(0.539651 + 0.123824i) q^{60} +(3.46383 + 4.76756i) q^{61} +(0.475281 + 0.242168i) q^{62} +(-0.403377 + 0.205531i) q^{63} +(3.76284 - 5.17911i) q^{64} +(-4.54825 - 5.21797i) q^{65} +(4.13426 + 4.13426i) q^{67} +(0.180089 + 1.13704i) q^{68} +(1.23188 + 0.400262i) q^{69} +(-0.631259 + 0.158293i) q^{70} +(9.27272 - 6.73702i) q^{71} +(0.949851 - 5.99713i) q^{72} +(-1.09042 + 2.14008i) q^{73} +(-2.53903 + 7.81434i) q^{74} +(-3.98532 + 0.0802892i) q^{75} -0.231015i q^{76} +(-2.65261 + 2.65261i) q^{78} +(0.542434 + 0.394101i) q^{79} +(3.77749 - 9.38594i) q^{80} +(-1.13837 - 3.50353i) q^{81} +(10.0530 + 1.59224i) q^{82} +(-16.4776 - 2.60980i) q^{83} +(0.0146506 + 0.0450899i) q^{84} +(-3.24865 - 7.62480i) q^{85} +(6.48191 + 4.70938i) q^{86} +(-5.38198 + 5.38198i) q^{87} -7.92190i q^{89} +(-0.711206 - 8.00509i) q^{90} +(0.183160 - 0.563709i) q^{91} +(-0.229095 + 0.449625i) q^{92} +(-0.0437645 + 0.276318i) q^{93} +(15.2048 - 11.0469i) q^{94} +(0.404527 + 1.61322i) q^{95} +(-1.32067 - 0.429111i) q^{96} +(-0.215721 - 1.36201i) q^{97} +(7.48452 + 7.48452i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 10 q^{2} - 4 q^{3} - 2 q^{5} + 20 q^{6} + 10 q^{8} + 12 q^{12} + 10 q^{13} + 14 q^{15} - 8 q^{16} + 10 q^{18} + 16 q^{20} - 24 q^{23} + 16 q^{25} + 20 q^{26} - 16 q^{27} - 50 q^{28} - 30 q^{30} - 28 q^{31}+ \cdots - 8 q^{97}+O(q^{100}) $ 32 * q + 10 * q^2 - 4 * q^3 - 2 * q^5 + 20 * q^6 + 10 * q^8 + 12 * q^12 + 10 * q^13 + 14 * q^15 - 8 * q^16 + 10 * q^18 + 16 * q^20 - 24 * q^23 + 16 * q^25 + 20 * q^26 - 16 * q^27 - 50 * q^28 - 30 * q^30 - 28 * q^31 + 10 * q^35 + 24 * q^36 - 8 * q^37 + 10 * q^38 + 50 * q^40 - 40 * q^41 - 10 * q^42 - 28 * q^45 - 60 * q^46 - 28 * q^47 - 54 * q^48 + 50 * q^50 - 20 * q^51 + 50 * q^52 - 24 * q^53 - 80 * q^56 - 30 * q^57 - 50 * q^58 + 34 * q^60 + 60 * q^61 - 100 * q^62 + 30 * q^63 - 8 * q^67 + 30 * q^68 + 30 * q^70 + 24 * q^71 - 80 * q^72 - 50 * q^73 + 34 * q^75 + 60 * q^78 + 98 * q^80 - 12 * q^81 - 10 * q^82 - 90 * q^83 - 30 * q^85 + 100 * q^86 + 20 * q^90 + 20 * q^91 - 68 * q^92 - 8 * q^93 + 40 * q^95 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.50135	+	0.237790i	−1.06161	+	0.168143i	−0.662730	−	0.748859i	$-0.730602\pi$
$2$	−1.50135	+	0.237790i	−1.06161	+	0.168143i	−0.398884	+	0.917002i	$0.630602\pi$
$3$	−0.361933	−	0.710333i	−0.208962	−	0.410111i	0.762609	−	0.646860i	$-0.223918\pi$
$3$	−0.361933	−	0.710333i	−0.208962	−	0.410111i	−0.971571	+	0.236749i	$0.923918\pi$
$4$	0.295389	−	0.0959778i	0.147695	−	0.0479889i
$5$	−1.89470	+	1.18749i	−0.847335	+	0.531060i
$5$	−1.89470	+	1.18749i	−0.847335	+	0.531060i
$6$	0.712297	+	0.980393i	0.290794	+	0.400244i
$7$	−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	$0.661520\pi$
$8$	2.28811	−	1.16585i	0.808970	−	0.412191i
$9$	1.38978	−	1.91287i	0.463259	−	0.637622i
$10$	2.56223	−	2.23337i	0.810248	−	0.706253i
$11$		0			0
$11$		0			0
$12$	−0.175087	−	0.175087i	−0.0505433	−	0.0505433i
$13$	0.484259	+	3.05749i	0.134309	+	0.847995i	0.959205	+	0.282711i	$0.0912336\pi$
$13$	0.484259	+	3.05749i	0.134309	+	0.847995i	−0.824896	+	0.565285i	$0.808766\pi$
$14$	0.276803	+	0.0899388i	0.0739787	+	0.0240372i
$15$	1.52926	+	0.916076i	0.394854	+	0.236530i
$16$	−3.66057	+	2.65956i	−0.915143	+	0.664890i
$17$	−0.579827	+	3.66088i	−0.140629	+	0.887894i	0.811978	+	0.583688i	$0.198391\pi$
$17$	−0.579827	+	3.66088i	−0.140629	+	0.887894i	−0.952606	+	0.304206i	$0.901609\pi$
$18$	−1.63168	+	3.20235i	−0.384591	+	0.754802i
$19$	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	$0.0728091\pi$
$20$	−0.445701	+	0.532619i	−0.0996618	+	0.119097i
$21$			0.152646i			0.0333100i
$22$		0			0
$23$	−1.14886	+	1.14886i	−0.239553	+	0.239553i	−0.816665	−	0.577112i	$-0.804180\pi$
$23$	−1.14886	+	1.14886i	−0.239553	+	0.239553i	0.577112	+	0.816665i	$0.304180\pi$
$24$	−1.65629	−	1.20336i	−0.338088	−	0.245635i
$25$	2.17976	−	4.49985i	0.435952	−	0.899970i
$26$	−1.45408	−	4.47521i	−0.285169	−	0.877660i
$27$	−4.22401	−	0.669017i	−0.812911	−	0.128752i
$28$	−0.0587369	−	0.00930302i	−0.0111002	−	0.00175811i
$29$	−2.95025	−	9.07993i	−0.547847	−	1.68610i	−0.714122	−	0.700021i	$-0.753174\pi$
$29$	−2.95025	−	9.07993i	−0.547847	−	1.68610i	0.166275	−	0.986079i	$-0.446826\pi$
$30$	−2.51379	−	1.01171i	−0.458953	−	0.184711i
$31$	−0.283900	−	0.206266i	−0.0509900	−	0.0370464i	0.561998	−	0.827138i	$-0.310033\pi$
$31$	−0.283900	−	0.206266i	−0.0509900	−	0.0370464i	−0.612988	+	0.790092i	$0.710033\pi$
$32$	1.23166	−	1.23166i	0.217729	−	0.217729i
$33$		0			0
$34$		−	5.63413i		−	0.966246i
$35$	0.426463	−	0.0378887i	0.0720853	−	0.00640437i
$36$	0.226933	−	0.698428i	0.0378222	−	0.116405i
$37$	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	$0.00344622\pi$
$38$	−0.176866	+	1.11669i	−0.0286915	+	0.181151i
$39$	1.99657	−	1.45059i	0.319707	−	0.232280i
$40$	−2.95085	+	4.92603i	−0.466570	+	0.778874i
$41$	−6.36824	−	2.06917i	−0.994552	−	0.323150i	−0.233866	−	0.972269i	$-0.575138\pi$
$41$	−6.36824	−	2.06917i	−0.994552	−	0.323150i	−0.760687	+	0.649119i	$0.775138\pi$
$42$	−0.0362976	−	0.229174i	−0.00560084	−	0.0353623i
$43$	−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
$46$	1.45165	−	1.99802i	0.214034	−	0.294592i
$47$	−11.0165	+	5.61318i	−1.60692	+	0.818766i	−0.607213	+	0.794539i	$0.707713\pi$
$47$	−11.0165	+	5.61318i	−1.60692	+	0.818766i	−0.999706	+	0.0242272i	$0.992287\pi$
$48$	3.21405	+	1.63764i	0.463909	+	0.236373i
$49$	−4.09295	−	5.63346i	−0.584707	−	0.804780i
$50$	−2.20256	+	7.27417i	−0.311488	+	1.02872i
$51$	2.81030	−	0.913123i	0.393521	−	0.127863i
$52$	0.436496	+	0.856672i	0.0605311	+	0.118799i
$53$	−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	$0.662950\pi$
$54$	6.50079			0.884646
$55$		0			0
$56$	−0.491699			−0.0657061
$57$	−0.585669	+	0.0927608i	−0.0775737	+	0.0122865i
$58$	6.58847	+	12.9306i	0.865108	+	1.69787i
$59$	−9.15496	+	2.97463i	−1.19187	+	0.387263i	−0.836765	−	0.547562i	$-0.815556\pi$
$59$	−9.15496	+	2.97463i	−1.19187	+	0.387263i	−0.355108	+	0.934825i	$0.615556\pi$
$60$	0.539651	+	0.123824i	0.0696686	+	0.0159856i
$61$	3.46383	+	4.76756i	0.443498	+	0.610423i	0.970985	−	0.239140i	$-0.0768655\pi$
$61$	3.46383	+	4.76756i	0.443498	+	0.610423i	−0.527487	+	0.849563i	$0.676866\pi$
$62$	0.475281	+	0.242168i	0.0603608	+	0.0307554i
$63$	−0.403377	+	0.205531i	−0.0508207	+	0.0258944i
$64$	3.76284	−	5.17911i	0.470356	−	0.647389i
$65$	−4.54825	−	5.21797i	−0.564141	−	0.647209i
$66$		0			0
$67$	4.13426	+	4.13426i	0.505081	+	0.505081i	0.913012	−	0.407932i	$-0.133750\pi$
$67$	4.13426	+	4.13426i	0.505081	+	0.505081i	−0.407932	+	0.913012i	$0.633750\pi$
$68$	0.180089	+	1.13704i	0.0218390	+	0.137886i
$69$	1.23188	+	0.400262i	0.148301	+	0.0481859i
$70$	−0.631259	+	0.158293i	−0.0754499	+	0.0189196i
$71$	9.27272	−	6.73702i	1.10047	−	0.799538i	0.119333	−	0.992854i	$-0.461925\pi$
$71$	9.27272	−	6.73702i	1.10047	−	0.799538i	0.981136	+	0.193317i	$0.0619245\pi$
$72$	0.949851	−	5.99713i	0.111941	−	0.706768i
$73$	−1.09042	+	2.14008i	−0.127624	+	0.250477i	−0.945973	−	0.324245i	$-0.894890\pi$
$73$	−1.09042	+	2.14008i	−0.127624	+	0.250477i	0.818349	+	0.574722i	$0.194890\pi$
$74$	−2.53903	+	7.81434i	−0.295156	+	0.908398i
$75$	−3.98532	+	0.0802892i	−0.460185	+	0.00927099i
$76$		−	0.231015i		−	0.0264992i
$77$		0			0
$78$	−2.65261	+	2.65261i	−0.300348	+	0.300348i
$79$	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	$0.687991\pi$
$80$	3.77749	−	9.38594i	0.422336	−	1.04938i
$81$	−1.13837	−	3.50353i	−0.126485	−	0.389282i
$82$	10.0530	+	1.59224i	1.11017	+	0.175833i
$83$	−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	$0.918284\pi$
$84$	0.0146506	+	0.0450899i	0.00159851	+	0.00491971i
$85$	−3.24865	−	7.62480i	−0.352365	−	0.827025i
$86$	6.48191	+	4.70938i	0.698962	+	0.507826i
$87$	−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	$-0.137921\pi$
$90$	−0.711206	−	8.00509i	−0.0749677	−	0.843810i
$91$	0.183160	−	0.563709i	0.0192004	−	0.0590927i
$92$	−0.229095	+	0.449625i	−0.0238848	+	0.0468766i
$93$	−0.0437645	+	0.276318i	−0.00453817	+	0.0286528i
$94$	15.2048	−	11.0469i	1.56826	−	1.13941i
$95$	0.404527	+	1.61322i	0.0415036	+	0.165513i
$96$	−1.32067	−	0.429111i	−0.134790	−	0.0437960i
$97$	−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	$0.972302\pi$
$98$	7.48452	+	7.48452i	0.756051	+	0.756051i
$99$		0			0
$100$	0.211991	−	1.53842i	0.0211991	−	0.153842i
$101$	2.83633	−	3.90387i	0.282225	−	0.388449i	−0.644244	−	0.764820i	$-0.722828\pi$
$101$	2.83633	−	3.90387i	0.282225	−	0.388449i	0.926469	+	0.376370i	$0.122828\pi$
$102$	−4.00211	+	2.03918i	−0.396268	+	0.201909i
$103$	2.88449	+	1.46972i	0.284217	+	0.144816i	0.590287	−	0.807193i	$-0.299014\pi$
$103$	2.88449	+	1.46972i	0.284217	+	0.144816i	−0.306071	+	0.952009i	$0.599014\pi$
$104$	4.67262	+	6.43131i	0.458188	+	0.630641i
$105$	−0.181264	−	0.289217i	−0.0176896	−	0.0282247i
$106$	13.0548	−	4.24177i	1.26800	−	0.411997i
$107$	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	$0.670542\pi$
$108$	−1.31194	+	0.207790i	−0.126241	+	0.0199946i
$109$	−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
$112$	0.855686	−	0.135527i	0.0808547	−	0.0128061i
$113$	−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	$0.912500\pi$
$114$	0.857235	−	0.278533i	0.0802874	−	0.0260870i
$115$	0.812486	−	3.54099i	0.0757647	−	0.330199i
$116$	−1.74294	−	2.39895i	−0.161828	−	0.222737i
$117$	6.52158	+	3.32291i	0.602920	+	0.307203i
$118$	13.0374	−	6.64291i	1.20019	−	0.611529i
$119$	0.417145	−	0.574151i	0.0382397	−	0.0526324i
$120$	4.56713	+	0.313192i	0.416920	+	0.0285904i
$121$		0			0
$122$	−6.33410	−	6.33410i	−0.573462	−	0.573462i
$123$	0.835077	+	5.27247i	0.0752964	+	0.475403i
$124$	−0.103658	−	0.0336805i	−0.00930877	−	0.00302460i
$125$	1.21352	+	11.1143i	0.108541	+	0.994092i
$126$	0.556736	−	0.404492i	0.0495980	−	0.0360350i
$127$	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	$-0.173691\pi$
$128$	−5.99935	+	11.7744i	−0.530273	+	1.04072i
$129$	−1.29851	+	3.99642i	−0.114328	+	0.351865i
$130$	8.06929	+	6.75246i	0.707723	+	0.592230i
$131$			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
$134$	−7.19006	−	5.22388i	−0.621126	−	0.451275i
$135$	8.79767	−	3.74836i	0.757182	−	0.322608i
$136$	2.94133	+	9.05250i	0.252217	+	0.776245i
$137$	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	$0.490780\pi$
$138$	−1.94466	−	0.308004i	−0.165540	−	0.0262190i
$139$	−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	$-0.247062\pi$
$140$	0.122336	−	0.0521228i	0.0103393	−	0.00440518i
$141$	7.97445	+	5.79378i	0.671570	+	0.487924i
$142$	−12.3196	+	12.3196i	−1.03384	+	1.03384i
$143$		0			0
$144$			10.6984i			0.891532i
$145$	16.3721	+	13.7003i	1.35963	+	1.13775i
$146$	1.12822	−	3.47229i	0.0933719	−	0.287369i
$147$	−2.52026	+	4.94629i	−0.207868	+	0.407963i
$148$	0.262630	−	1.65818i	0.0215881	−	0.136302i
$149$	−4.66189	+	3.38706i	−0.381917	+	0.277479i	−0.762135	−	0.647418i	$-0.775849\pi$
$149$	−4.66189	+	3.38706i	−0.381917	+	0.277479i	0.380218	+	0.924897i	$0.375849\pi$
$150$	5.96426	−	1.06821i	0.486980	−	0.0872191i
$151$	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	$0.391617\pi$
$152$	−0.298800	−	1.88655i	−0.0242358	−	0.153019i
$153$	6.19694	+	6.19694i	0.500993	+	0.500993i
$154$		0			0
$155$	0.782843	+	0.0536836i	0.0628795	+	0.00431197i
$156$	0.450540	−	0.620115i	0.0360721	−	0.0496489i
$157$	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	$0.286733\pi$
$158$	−0.908095	−	0.462698i	−0.0722442	−	0.0368103i
$159$	4.23158	+	5.82427i	0.335586	+	0.461895i
$160$	−0.871047	+	3.79621i	−0.0688623	+	0.300117i
$161$	0.295863	−	0.0961317i	0.0233173	−	0.00757624i
$162$	2.54219	+	4.98933i	0.199733	+	0.391999i
$163$	−9.89335	+	1.56695i	−0.774907	+	0.122733i	−0.531349	−	0.847153i	$-0.678315\pi$
$163$	−9.89335	+	1.56695i	−0.774907	+	0.122733i	−0.243558	+	0.969886i	$0.578315\pi$
$164$	−2.07970			−0.162398
$165$		0			0
$166$	25.3592			1.96826
$167$	−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	$0.604558\pi$
$168$	0.177962	+	0.349270i	0.0137301	+	0.0269468i
$169$	3.24999	−	1.05599i	0.250000	−	0.0812298i
$170$	6.69045	+	10.6750i	0.513134	+	0.818734i
$171$	−1.03371	−	1.42277i	−0.0790494	−	0.108802i
$172$	−1.45866	−	0.743222i	−0.111221	−	0.0566702i
$173$	11.1065	−	5.65903i	0.844410	−	0.430248i	0.0224186	−	0.999749i	$-0.492863\pi$
$173$	11.1065	−	5.65903i	0.844410	−	0.430248i	0.821991	+	0.569501i	$0.192863\pi$
$174$	6.80045	−	9.36001i	0.515540	−	0.709581i
$175$	−0.763025	+	0.578206i	−0.0576793	+	0.0437082i
$176$		0			0
$177$	5.42645	+	5.42645i	0.407877	+	0.407877i
$178$	1.88375	+	11.8935i	0.141193	+	0.891458i
$179$	−19.1909	−	6.23551i	−1.43440	−	0.466064i	−0.514252	−	0.857639i	$-0.671930\pi$
$179$	−19.1909	−	6.23551i	−1.43440	−	0.466064i	−0.920146	+	0.391575i	$0.871930\pi$
$180$	0.399403	+	1.59279i	0.0297698	+	0.118719i
$181$	−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	$0.354803\pi$
$182$	−0.140943	+	0.889877i	−0.0104474	+	0.0659620i
$183$	2.13288	−	4.18601i	0.157667	−	0.309439i
$184$	−1.28932	+	3.96811i	−0.0950497	+	0.292533i
$185$	1.06962	+	12.0393i	0.0786403	+	0.885148i
$186$		−	0.425256i		−	0.0311813i
$187$		0			0
$188$	−2.71541	+	2.71541i	−0.198042	+	0.198042i
$189$	0.662469	+	0.481312i	0.0481875	+	0.0350103i
$190$	−0.990944	−	2.32582i	−0.0718907	−	0.168732i
$191$	1.95493	+	6.01667i	0.141454	+	0.435351i	0.996538	−	0.0831389i	$-0.0264945\pi$
$191$	1.95493	+	6.01667i	0.141454	+	0.435351i	−0.855084	+	0.518490i	$0.826495\pi$
$192$	−5.04079	−	0.798383i	−0.363788	−	0.0576183i
$193$	−5.85885	−	0.927951i	−0.421729	−	0.0667954i	−0.0580368	−	0.998314i	$-0.518484\pi$
$193$	−5.85885	−	0.927951i	−0.421729	−	0.0667954i	−0.363692	+	0.931519i	$0.618484\pi$
$194$	0.647745	+	1.99355i	0.0465054	+	0.143129i
$195$	−2.06034	+	5.11932i	−0.147544	+	0.366602i
$196$	−1.74970	−	1.27123i	−0.124979	−	0.0908022i
$197$	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	$-0.842687\pi$
$199$		−	13.3828i		−	0.948680i	0.880342	−	0.474340i	$-0.157313\pi$
$200$	−0.258626	−	12.8374i	−0.0182876	−	0.907744i
$201$	1.44038	−	4.43303i	0.101596	−	0.312682i
$202$	−3.33001	+	6.53551i	−0.234299	+	0.459837i
$203$	−0.285964	+	1.80551i	−0.0200708	+	0.126722i
$204$	0.742493	−	0.539453i	0.0519849	−	0.0377693i
$205$	14.5230	−	3.64175i	1.01433	−	0.254351i
$206$	−4.68010	−	1.52066i	−0.326078	−	0.105949i
$207$	0.600953	+	3.79427i	0.0417691	+	0.263720i
$208$	−9.90424	−	9.90424i	−0.686736	−	0.686736i
$209$		0			0
$210$	0.340914	+	0.391113i	0.0235253	+	0.0269893i
$211$	−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	$0.265460\pi$
$212$	−2.49903	+	1.27332i	−0.171634	+	0.0874521i
$213$	−8.14163	−	4.14837i	−0.557855	−	0.284241i
$214$	−9.87779	−	13.5956i	−0.675232	−	0.929377i
$215$	11.4875	+	2.63584i	0.783444	+	0.179763i
$216$	−10.4450	+	3.39378i	−0.710691	+	0.230917i
$217$	0.0305041	+	0.0598677i	0.00207075	+	0.00406408i
$218$	14.3260	−	2.26902i	0.970282	−	0.153678i
$219$	1.91483			0.129392
$220$		0			0
$221$	−11.4739			−0.771818
$222$	6.46974	−	1.02471i	0.434220	−	0.0687738i
$223$	9.64984	+	18.9389i	0.646201	+	1.26824i	0.949027	+	0.315195i	$0.102070\pi$
$223$	9.64984	+	18.9389i	0.646201	+	1.26824i	−0.302826	+	0.953046i	$0.597930\pi$
$224$	−0.317188	+	0.103060i	−0.0211930	+	0.00688602i
$225$	−5.57823	−	10.4234i	−0.371882	−	0.694892i
$226$	3.70584	+	5.10065i	0.246509	+	0.339290i
$227$	−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	$0.792809\pi$
$228$	−0.164097	+	0.0836117i	−0.0108676	+	0.00553732i
$229$	−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	$0.382673\pi$
$230$	−0.377812	+	5.50946i	−0.0249122	+	0.363283i
$231$		0			0
$232$	−17.3363	−	17.3363i	−1.13819	−	1.13819i
$233$	−2.44720	−	15.4510i	−0.160321	−	1.01223i	−0.928321	−	0.371779i	$-0.878748\pi$
$233$	−2.44720	−	15.4510i	−0.160321	−	1.01223i	0.768000	−	0.640450i	$-0.221252\pi$
$234$	−10.5813	−	3.43808i	−0.691722	−	0.224754i
$235$	14.2073	−	23.7172i	0.926785	−	1.54714i
$236$	−2.41878	+	1.75734i	−0.157449	+	0.114393i
$237$	0.0836185	−	0.527947i	0.00543161	−	0.0342938i
$238$	−0.489753	+	0.961194i	−0.0317460	+	0.0623050i
$239$	−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	$0.154643\pi$
$240$	−8.03434	+	0.713804i	−0.518614	+	0.0460759i
$241$		−	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
$244$	1.48076	+	1.07583i	0.0947959	+	0.0688732i
$245$	14.4445	+	5.81339i	0.922828	+	0.371404i
$246$	−2.50748	−	7.71724i	−0.159871	−	0.492033i
$247$	2.27413	+	0.360188i	0.144700	+	0.0229182i
$248$	−0.890071	−	0.140973i	−0.0565196	−	0.00895182i
$249$	4.10997	+	12.6492i	0.260458	+	0.801609i
$250$	−4.46479	−	16.3978i	−0.282378	−	1.03709i
$251$	−15.6486	−	11.3694i	−0.987729	−	0.717627i	−0.0283063	−	0.999599i	$-0.509011\pi$
$251$	−15.6486	−	11.3694i	−0.987729	−	0.717627i	−0.959423	+	0.281972i	$0.909011\pi$
$252$	−0.0994268	+	0.0994268i	−0.00626330	+	0.00626330i
$253$		0			0
$254$			22.1431i			1.38938i
$255$	−4.24035	+	5.06728i	−0.265541	+	0.317326i
$256$	2.25079	−	6.92722i	0.140674	−	0.432951i
$257$	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	$0.103109\pi$
$258$	0.999214	−	6.30879i	0.0622083	−	0.392768i
$259$	−0.837308	+	0.608340i	−0.0520278	+	0.0378004i
$260$	−1.84431	−	1.10480i	−0.114379	−	0.0685169i
$261$	−21.4689	−	6.97566i	−1.32889	−	0.431783i
$262$	−2.32303	−	14.6671i	−0.143517	−	0.906134i
$263$	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
$266$	0.127243	−	0.175135i	0.00780178	−	0.0107382i
$267$	−5.62719	+	2.86720i	−0.344378	+	0.175470i
$268$	1.61801	+	0.824419i	0.0988359	+	0.0503594i
$269$	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	$0.687925\pi$
$270$	−12.3170	+	7.71959i	−0.749591	+	0.469800i
$271$	−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	$0.582141\pi$
$272$	−7.61384	−	14.9430i	−0.461657	−	0.906052i
$273$	−0.466712	+	0.0739200i	−0.0282467	+	0.00447384i
$274$	−6.58205			−0.397636
$275$		0			0
$276$	0.402300			0.0242156
$277$	4.62395	−	0.732361i	0.277826	−	0.0440033i	−0.0159666	−	0.999873i	$-0.505083\pi$
$277$	4.62395	−	0.732361i	0.277826	−	0.0440033i	0.293793	+	0.955869i	$0.405083\pi$
$278$	7.25327	+	14.2353i	0.435022	+	0.853779i
$279$	−0.789117	+	0.256400i	−0.0472432	+	0.0153502i
$280$	0.931621	−	0.583886i	0.0556750	−	0.0348938i
$281$	7.75247	+	10.6704i	0.462474	+	0.636541i	0.975019	−	0.222119i	$-0.0712975\pi$
$281$	7.75247	+	10.6704i	0.462474	+	0.636541i	−0.512546	+	0.858660i	$0.671297\pi$
$282$	−13.3501	−	6.80223i	−0.794989	−	0.405067i
$283$	−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	$0.586832\pi$
$284$	2.09246	−	2.88002i	0.124164	−	0.170898i
$285$	0.999513	−	0.871227i	0.0592061	−	0.0516070i
$286$		0			0
$287$	0.906570	+	0.906570i	0.0535131	+	0.0535131i
$288$	−0.644267	−	4.06774i	−0.0379638	−	0.239694i
$289$	3.10211	+	1.00794i	0.182477	+	0.0592904i
$290$	−27.8380	−	16.6759i	−1.63471	−	0.979240i
$291$	−0.889404	+	0.646190i	−0.0521378	+	0.0378803i
$292$	−0.116700	+	0.736812i	−0.00682933	+	0.0431187i
$293$	3.28132	−	6.43996i	0.191697	−	0.376226i	−0.775074	−	0.631870i	$-0.782287\pi$
$293$	3.28132	−	6.43996i	0.191697	−	0.376226i	0.966771	+	0.255644i	$0.0822875\pi$
$294$	2.60761	−	8.02539i	0.152079	−	0.468051i
$295$	13.8135	−	16.5074i	0.804256	−	0.961097i
$296$		−	13.8810i		−	0.806817i
$297$		0			0
$298$	6.19371	−	6.19371i	0.358792	−	0.358792i
$299$	−4.06896	−	2.95628i	−0.235314	−	0.170966i
$300$	−1.16951	+	0.406218i	−0.0675219	+	0.0234530i
$301$	0.311867	+	0.959827i	0.0179757	+	0.0553235i
$302$	−22.4665	−	3.55834i	−1.29280	−	0.204759i
$303$	−3.79960	−	0.601798i	−0.218282	−	0.0345724i
$304$	1.03998	+	3.20073i	0.0596469	+	0.183574i
$305$	−12.2243	−	4.91983i	−0.699963	−	0.281709i
$306$	−10.7773	−	7.83020i	−0.616100	−	0.447623i
$307$	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
$310$	−1.18809	+	0.105555i	−0.0674787	+	0.00599509i
$311$	−2.32254	+	7.14803i	−0.131699	+	0.405328i	−0.995062	−	0.0992557i	$-0.968354\pi$
$311$	−2.32254	+	7.14803i	−0.131699	+	0.405328i	0.863363	+	0.504583i	$0.168354\pi$
$312$	2.87720	−	5.64681i	0.162889	−	0.319688i
$313$	−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	$0.0621122\pi$
$314$	−6.08499	+	4.42100i	−0.343396	+	0.249492i
$315$	0.520212	−	0.868422i	0.0293106	−	0.0489301i
$316$	0.198054	+	0.0643517i	0.0111414	+	0.00362006i
$317$	−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	$-0.153089\pi$
$318$	−7.73803	−	7.73803i	−0.433927	−	0.433927i
$319$		0			0
$320$	−0.979335	+	14.2812i	−0.0547465	+	0.798342i
$321$	5.18059	−	7.13047i	0.289152	−	0.397984i
$322$	−0.421334	+	0.214680i	−0.0234800	+	0.0119637i
$323$	2.45639	+	1.25159i	0.136677	+	0.0696406i
$324$	−0.672523	−	0.925648i	−0.0373624	−	0.0514249i
$325$	14.8138	+	4.48550i	0.821723	+	0.248811i
$326$	14.4808	−	4.70509i	0.802015	−	0.260591i
$327$	3.45360	+	6.77808i	0.190985	+	0.374829i
$328$	−16.9836	+	2.68994i	−0.937762	+	0.148527i
$329$	2.36737			0.130517
$330$		0			0
$331$	−17.7048			−0.973145			−0.486572	−	0.873640i	$-0.661753\pi$
$331$	−17.7048			−0.973145			−0.486572	+	0.873640i	$0.661753\pi$
$332$	−5.11780	+	0.810579i	−0.280876	+	0.0444863i
$333$	−5.80227	−	11.3876i	−0.317962	−	0.624036i
$334$	17.4380	−	5.66594i	0.954164	−	0.310027i
$335$	−12.7426	−	2.92380i	−0.696200	−	0.159744i
$336$	−0.405970	−	0.558770i	−0.0221475	−	0.0304834i
$337$	−6.78954	−	3.45945i	−0.369850	−	0.188448i	0.259180	−	0.965829i	$-0.416548\pi$
$337$	−6.78954	−	3.45945i	−0.369850	−	0.188448i	−0.629030	+	0.777381i	$0.716548\pi$
$338$	−4.62827	+	2.35822i	−0.251745	+	0.128270i
$339$	−1.94359	+	2.67513i	−0.105562	+	0.145293i
$340$	−1.69143	−	1.94049i	−0.0917305	−	0.105238i
$341$		0			0
$342$	1.89027	+	1.89027i	0.102214	+	0.102214i
$343$	0.418239	+	2.64066i	0.0225828	+	0.142582i
$344$	−12.8732	−	4.18275i	−0.694076	−	0.225519i
$345$	−2.80935	+	0.704464i	−0.151250	+	0.0379270i
$346$	−15.3290	+	11.1372i	−0.824093	+	0.598739i
$347$	−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	$0.969395\pi$
$348$	−1.07323	+	2.10633i	−0.0575311	+	0.112911i
$349$	0.464073	−	1.42827i	0.0248413	−	0.0764536i	−0.937867	−	0.346994i	$-0.887202\pi$
$349$	0.464073	−	1.42827i	0.0248413	−	0.0764536i	0.962709	+	0.270540i	$0.0872024\pi$
$350$	1.00807	−	1.04953i	0.0538839	−	0.0560996i
$351$		−	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	$0.197017\pi$
$354$	−9.43735	−	6.85664i	−0.501589	−	0.364426i
$355$	−9.56888	+	23.7758i	−0.507863	+	1.26189i
$356$	−0.760327	−	2.34004i	−0.0402972	−	0.124022i
$357$	−0.558817	−	0.0885080i	−0.0295757	−	0.00468434i
$358$	30.2950	+	4.79826i	1.60114	+	0.253596i
$359$	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	$0.655784\pi$
$360$	5.32182	+	12.4907i	0.280484	+	0.658316i
$361$	14.9238	+	10.8427i	0.785461	+	0.570671i
$362$	4.95475	−	4.95475i	0.260416	−	0.260416i
$363$		0			0
$364$		−	0.184093i		−	0.00964908i
$365$	−0.475287	−	5.34966i	−0.0248776	−	0.280014i
$366$	−2.20680	+	6.79184i	−0.115351	+	0.355015i
$367$	−3.70869	+	7.27872i	−0.193592	+	0.379946i	−0.967315	−	0.253579i	$-0.918392\pi$
$367$	−3.70869	+	7.27872i	−0.193592	+	0.379946i	0.773723	+	0.633524i	$0.218392\pi$
$368$	1.15002	−	7.26093i	0.0599488	−	0.378502i
$369$	−12.8085	+	9.30591i	−0.666783	+	0.484446i
$370$	−4.46871	−	17.8209i	−0.232317	−	0.926463i
$371$	1.64442	+	0.534304i	0.0853740	+	0.0277397i
$372$	0.0135928	+	0.0858218i	0.000704756	+	0.00444965i
$373$	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
$376$	−18.6628	+	25.6872i	−0.962461	+	1.32471i
$377$	26.3331	−	13.4174i	1.35622	−	0.691031i
$378$	−1.10905	−	0.565088i	−0.0570433	−	0.0290650i
$379$	0.363481	+	0.500288i	0.0186708	+	0.0256981i	0.818250	−	0.574862i	$-0.194944\pi$
$379$	0.363481	+	0.500288i	0.0186708	+	0.0256981i	−0.799580	+	0.600560i	$0.794944\pi$
$380$	0.274326	+	0.437703i	0.0140726	+	0.0224537i
$381$	−11.0449	+	3.58872i	−0.565849	+	0.183856i
$382$	−4.36574	−	8.56825i	−0.223371	−	0.438390i
$383$	10.2511	−	1.62362i	0.523807	−	0.0829629i	0.111069	−	0.993813i	$-0.464572\pi$
$383$	10.2511	−	1.62362i	0.523807	−	0.0829629i	0.412738	+	0.910850i	$0.364572\pi$
$384$	10.5351			0.537617
$385$		0			0
$386$	9.01683			0.458945
$387$	−12.3092	+	1.94959i	−0.625712	+	0.0991031i
$388$	−0.194444	−	0.381619i	−0.00987142	−	0.0193737i
$389$	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	$0.210245\pi$
$390$	1.87596	−	8.17582i	0.0949927	−	0.413999i
$391$	−3.53969	−	4.87197i	−0.179010	−	0.246386i
$392$	−15.9329	−	8.11822i	−0.804733	−	0.410032i
$393$	6.93942	−	3.53581i	0.350048	−	0.178358i
$394$	−12.5157	+	17.2264i	−0.630534	+	0.867855i
$395$	−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	$0.625078\pi$
$398$	3.18229	+	20.0922i	0.159514	+	1.00713i
$399$	0.107980	+	0.0350847i	0.00540574	+	0.00175643i
$400$	3.98847	+	22.2692i	0.199423	+	1.11346i
$401$	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	$0.265904\pi$
$402$	−1.10838	+	6.99803i	−0.0552809	+	0.349030i
$403$	0.493174	−	0.967909i	0.0245668	−	0.0482150i
$404$	0.463135	−	1.42538i	0.0230418	−	0.0709155i
$405$	6.31726	+	5.28634i	0.313907	+	0.262681i
$406$		−	2.77869i		−	0.137904i
$407$		0			0
$408$	5.36572	−	5.36572i	0.265643	−	0.265643i
$409$	3.47523	+	2.52490i	0.171839	+	0.124848i	0.670381	−	0.742017i	$-0.266131\pi$
$409$	3.47523	+	2.52490i	0.171839	+	0.124848i	−0.498541	+	0.866866i	$0.666131\pi$
$410$	−20.9381	+	8.92096i	−1.03406	+	0.440575i
$411$	−1.06675	−	3.28312i	−0.0526190	−	0.161945i
$412$	0.993106	+	0.157293i	0.0489268	+	0.00774925i
$413$	1.82043	+	0.288327i	0.0895773	+	0.0141877i
$414$	−1.80448	−	5.55361i	−0.0886853	−	0.272945i
$415$	34.3192	−	14.6222i	1.68466	−	0.717773i
$416$	4.36224	+	3.16935i	0.213876	+	0.155390i
$417$	−5.92504	+	5.92504i	−0.290151	+	0.290151i
$418$		0			0
$419$			1.20241i			0.0587414i	0.999569	+	0.0293707i	$0.00935032\pi$
$419$			1.20241i			0.0587414i	−0.999569	+	0.0293707i	$0.990650\pi$
$420$	−0.0813020	−	0.0680343i	−0.00396713	−	0.00331973i
$421$	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	$-0.176248\pi$
$422$	4.09390	−	8.03473i	0.199288	−	0.391124i
$423$	−4.57321	+	28.8741i	−0.222357	+	1.40391i
$424$	−18.7610	+	13.6307i	−0.911117	+	0.661965i
$425$	15.2095	+	10.5890i	0.737771	+	0.513640i
$426$	13.2099	+	4.29214i	0.640020	+	0.207955i
$427$	−0.176512	−	1.11445i	−0.00854201	−	0.0539321i
$428$	2.42802	+	2.42802i	0.117363	+	0.117363i
$429$		0			0
$430$	−17.8736	−	1.22568i	−0.861940	−	0.0591078i
$431$	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	$0.123435\pi$
$432$	17.2416	−	8.78502i	0.829536	−	0.422669i
$433$	−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	$0.874538\pi$
$434$	−0.0600332	−	0.0826286i	−0.00288169	−	0.00396630i
$435$	3.80620	−	16.5882i	0.182494	−	0.795346i
$436$	−2.81864	+	0.915831i	−0.134988	+	0.0438604i
$437$	0.548629	+	1.07675i	0.0262445	+	0.0515077i
$438$	−2.87482	+	0.455327i	−0.137364	+	0.0217564i
$439$	−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
$442$	17.2263	−	2.72838i	0.819372	−	0.129776i
$443$	−13.9816	−	27.4404i	−0.664286	−	1.30373i	−0.939565	−	0.342370i	$-0.888770\pi$
$443$	−13.9816	−	27.4404i	−0.664286	−	1.30373i	0.275279	−	0.961364i	$-0.411230\pi$
$444$	−1.27292	+	0.413596i	−0.0604099	+	0.0196284i
$445$	9.40714	+	15.0096i	0.445941	+	0.711524i
$446$	−18.9912	−	26.1392i	−0.899262	−	1.23773i
$447$	4.09323	+	2.08561i	0.193603	+	0.0986458i
$448$	−1.09215	+	0.556477i	−0.0515992	+	0.0262911i
$449$	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	$0.144707\pi$
$450$	10.8534	+	14.3227i	0.511636	+	0.675177i
$451$		0			0
$452$	−0.910918	−	0.910918i	−0.0428460	−	0.0428460i
$453$	−1.86624	−	11.7830i	−0.0876835	−	0.553612i
$454$	18.8951	+	6.13938i	0.886789	+	0.288135i
$455$	0.322363	+	1.28556i	0.0151126	+	0.0602678i
$456$	−1.23193	+	0.895050i	−0.0576904	+	0.0419146i
$457$	−1.05368	+	6.65265i	−0.0492889	+	0.311198i	0.950710	+	0.310080i	$0.100356\pi$
$457$	−1.05368	+	6.65265i	−0.0492889	+	0.311198i	−0.999999	+	0.00111791i	$0.999644\pi$
$458$	11.3390	−	22.2540i	0.529837	−	1.03986i
$459$	4.89838	−	15.0757i	0.228637	−	0.703672i
$460$	−0.0998565	−	1.12395i	−0.00465583	−	0.0524044i
$461$			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	−0.171256	−	0.985227i	$-0.554783\pi$
$463$	17.5146	−	17.5146i	0.813970	−	0.813970i	0.985227	+	0.171256i	$0.0547826\pi$
$464$	34.9482	+	25.3914i	1.62243	+	1.17876i
$465$	−0.245203	−	0.575509i	−0.0113710	−	0.0266886i
$466$	7.34819	+	22.6154i	0.340398	+	1.04764i
$467$	−26.1320	−	4.13890i	−1.20924	−	0.191525i	−0.480923	−	0.876763i	$-0.659698\pi$
$467$	−26.1320	−	4.13890i	−1.20924	−	0.191525i	−0.728320	+	0.685237i	$0.759698\pi$
$468$	2.24533	+	0.355625i	0.103790	+	0.0164388i
$469$	−0.345938	−	1.06469i	−0.0159739	−	0.0491627i
$470$	−15.6904	+	38.9861i	−0.723746	+	1.79830i
$471$	−3.19138	−	2.31868i	−0.147051	−	0.106839i
$472$	−17.4796	+	17.4796i	−0.804563	+	0.804563i
$473$		0			0
$474$			0.812515i			0.0373201i
$475$	−2.68213	−	2.57620i	−0.123065	−	0.118204i
$476$	0.0681145	−	0.209635i	0.00312202	−	0.00960860i
$477$	−9.69341	+	19.0244i	−0.443831	+	0.871067i
$478$	1.25594	−	7.92972i	0.0574455	−	0.362697i
$479$	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	$0.0952413\pi$
$480$	3.01183	−	0.755239i	0.137471	−	0.0344718i
$481$	15.9139	+	5.17073i	0.725610	+	0.235765i
$482$	3.84449	+	24.2731i	0.175112	+	1.10561i
$483$	−0.175368	−	0.175368i	−0.00797952	−	0.00797952i
$484$		0			0
$485$	2.02609	+	2.32443i	0.0920001	+	0.105547i
$486$	14.0872	−	19.3894i	0.639008	−	0.879519i
$487$	−20.7917	+	10.5939i	−0.942163	+	0.480056i	−0.856431	−	0.516262i	$-0.827323\pi$
$487$	−20.7917	+	10.5939i	−0.942163	+	0.480056i	−0.0857326	+	0.996318i	$0.527323\pi$
$488$	13.4839	+	6.87039i	0.610388	+	0.311008i
$489$	4.69379	+	6.46044i	0.212260	+	0.292151i
$490$	−23.0687	−	5.29315i	−1.04214	−	0.239120i
$491$	−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	$0.535872\pi$
$492$	0.752713	+	1.47728i	0.0339349	+	0.0666010i
$493$	34.9512	−	5.53572i	1.57412	−	0.249316i
$494$	−3.49992			−0.157469
$495$		0			0
$496$	1.58781			0.0712949
$497$	−2.16757	+	0.343309i	−0.0972286	+	0.0153995i
$498$	−9.17834	−	18.0135i	−0.411291	−	0.807204i
$499$	−11.1824	+	3.63339i	−0.500595	+	0.162653i	−0.548421	−	0.836203i	$-0.684771\pi$
$499$	−11.1824	+	3.63339i	−0.500595	+	0.162653i	0.0478260	+	0.998856i	$0.484771\pi$
$500$	1.42519	+	3.16657i	0.0637363	+	0.141613i
$501$	5.65234	+	7.77978i	0.252528	+	0.347575i
$502$	26.1975	+	13.3483i	1.16925	+	0.595763i
$503$	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	$0.312011\pi$
$504$	−0.683353	+	0.940555i	−0.0304390	+	0.0418956i
$505$	−0.738195	+	10.7647i	−0.0328492	+	0.479025i
$506$		0			0
$507$	−1.92638	−	1.92638i	−0.0855536	−	0.0855536i
$508$	−0.707777	−	4.46873i	−0.0314025	−	0.198268i
$509$	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	$0.457070\pi$
$510$	5.16130	−	8.61607i	0.228546	−	0.381526i
$511$	0.372057	−	0.270315i	0.0164588	−	0.0119580i
$512$	2.40248	−	15.1686i	0.106175	−	0.670365i
$513$	−1.44412	+	2.83424i	−0.0637594	+	0.125135i
$514$	−2.21058	+	6.80347i	−0.0975046	+	0.300088i
$515$	−7.21050	+	0.640611i	−0.317732	+	0.0282287i
$516$			1.30513i			0.0574550i
$517$		0			0
$518$	1.11243	−	1.11243i	0.0488775	−	0.0488775i
$519$	−8.03959	−	5.84110i	−0.352899	−	0.256396i
$520$	−16.4903	−	6.63672i	−0.723147	−	0.291039i
$521$	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	$0.765397\pi$
$522$	33.8910	+	5.36781i	1.48337	+	0.234943i
$523$	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	$0.532019\pi$
$524$	0.937631	+	2.88573i	0.0409606	+	0.126064i
$525$	0.686882	+	0.332730i	0.0299780	+	0.0145215i
$526$	−19.5162	−	14.1794i	−0.850948	−	0.618250i
$527$	0.919727	−	0.919727i	0.0400639	−	0.0400639i
$528$		0			0
$529$			20.3603i			0.885228i
$530$	−19.6979	+	23.5393i	−0.855622	+	1.02248i
$531$	−7.03330	+	21.6463i	−0.305219	+	0.939368i
$532$	−0.0200812	+	0.0394115i	−0.000870630	+	0.00170871i
$533$	3.24258	−	20.4729i	0.140452	−	0.886778i
$534$	7.76658	−	5.64275i	0.336093	−	0.244186i
$535$	−21.2071	−	12.7037i	−0.916862	−	0.549229i
$536$	14.2796	+	4.63972i	0.616784	+	0.200405i
$537$	2.51654	+	15.8888i	0.108597	+	0.685652i
$538$	−12.1591	−	12.1591i	−0.524216	−	0.524216i
$539$		0			0
$540$	2.23898	−	1.95161i	0.0963502	−	0.0839837i
$541$	−5.42829	+	7.47139i	−0.233380	+	0.321220i	−0.909604	−	0.415476i	$-0.863615\pi$
$541$	−5.42829	+	7.47139i	−0.233380	+	0.321220i	0.676224	+	0.736696i	$0.263615\pi$
$542$	24.1462	−	12.3031i	1.03717	−	0.528464i
$543$	3.27444	+	1.66841i	0.140520	+	0.0715983i
$544$	3.79482	+	5.22312i	0.162701	+	0.223939i
$545$	18.0794	−	11.3311i	0.774438	−	0.485372i
$546$	0.683120	−	0.221959i	0.0292348	−	0.00949898i
$547$	−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	$0.857289\pi$
$548$	1.32834	−	0.210388i	0.0567437	−	0.00898732i
$549$	13.9337			0.594674
$550$		0			0
$551$	−7.10113			−0.302518
$552$	3.28533	−	0.520344i	0.139833	−	0.0221473i
$553$	−0.0582826	−	0.114386i	−0.00247843	−	0.00486419i
$554$	−6.76800	+	2.19906i	−0.287545	+	0.0934290i
$555$	8.16479	−	5.11721i	0.346576	−	0.217214i
$556$	−1.91881	−	2.64102i	−0.0813758	−	0.112004i
$557$	38.3462	+	19.5384i	1.62478	+	0.827868i	0.998848	+	0.0479915i	$0.0152820\pi$
$557$	38.3462	+	19.5384i	1.62478	+	0.827868i	0.625934	+	0.779876i	$0.284718\pi$
$558$	1.12377	−	0.572590i	0.0475730	−	0.0242396i
$559$	9.59064	−	13.2004i	0.405641	−	0.558316i
$560$	−1.46033	+	1.27290i	−0.0617102	+	0.0537897i
$561$		0			0
$562$	−14.1765	−	14.1765i	−0.597998	−	0.597998i
$563$	−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	$-0.233464\pi$
$564$	2.91164	+	0.946049i	0.122602	+	0.0398359i
$565$	7.95622	+	4.76603i	0.334721	+	0.200508i
$566$	28.0219	−	20.3591i	1.17785	−	0.855756i
$567$	−0.110341	+	0.696664i	−0.00463387	+	0.0292571i
$568$	13.3626	−	26.2257i	0.560684	−	1.10040i
$569$	8.39651	−	25.8418i	0.352000	−	1.08334i	−0.605729	−	0.795671i	$-0.707118\pi$
$569$	8.39651	−	25.8418i	0.352000	−	1.08334i	0.957729	−	0.287673i	$-0.0928816\pi$
$570$	−1.29345	+	1.54569i	−0.0541766	+	0.0647418i
$571$			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
$574$	−1.57665	−	1.14550i	−0.0658081	−	0.0478124i
$575$	2.66546	+	7.67392i	0.111157	+	0.320024i
$576$	−4.67742	−	14.3956i	−0.194893	−	0.599818i
$577$	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	$0.301521\pi$
$578$	−4.89703	−	0.775613i	−0.203689	−	0.0322612i
$579$	1.46136	+	4.49759i	0.0607319	+	0.186913i
$580$	6.15107	+	2.47558i	0.255409	+	0.102793i
$581$	2.58426	+	1.87757i	0.107213	+	0.0778948i
$582$	1.18165	−	1.18165i	0.0489808	−	0.0489808i
$583$		0			0
$584$			6.16801i			0.255234i
$585$	−16.3023	+	1.44837i	−0.674018	+	0.0598826i
$586$	−3.39505	+	10.4489i	−0.140248	+	0.431640i
$587$	−4.39649	+	8.62859i	−0.181462	+	0.356140i	−0.963763	−	0.266762i	$-0.914046\pi$
$587$	−4.39649	+	8.62859i	−0.181462	+	0.356140i	0.782300	+	0.622902i	$0.214046\pi$
$588$	−0.269724	+	1.70297i	−0.0111232	+	0.0702293i
$589$	−0.211163	+	0.153419i	−0.00870081	+	0.00632151i
$590$	−16.8137	+	28.0681i	−0.692207	+	1.15554i
$591$	−10.6210	−	3.45096i	−0.436888	−	0.141953i
$592$	3.82603	+	24.1566i	0.157249	+	0.992829i
$593$	−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
$596$	−1.05199	+	1.44794i	−0.0430912	+	0.0593099i
$597$	−9.50623	+	4.84367i	−0.389064	+	0.198238i
$598$	6.81191	+	3.47084i	0.278560	+	0.141933i
$599$	−2.65433	−	3.65338i	−0.108453	−	0.149273i	0.751340	−	0.659915i	$-0.229408\pi$
$599$	−2.65433	−	3.65338i	−0.108453	−	0.149273i	−0.859793	+	0.510642i	$0.829408\pi$
$600$	−9.02525	+	4.83000i	−0.368454	+	0.197184i
$601$	7.96746	−	2.58878i	0.324999	−	0.105599i	−0.141973	−	0.989871i	$-0.545345\pi$
$601$	7.96746	−	2.58878i	0.324999	−	0.105599i	0.466973	+	0.884272i	$0.345345\pi$
$602$	−0.696458	−	1.36688i	−0.0283855	−	0.0557097i
$603$	13.6540	−	2.16258i	0.556034	−	0.0880671i
$604$	4.64774			0.189114
$605$		0			0
$606$	5.84763			0.237544
$607$	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	$0.400193\pi$
$608$	−0.588172	−	1.15435i	−0.0238535	−	0.0468152i
$609$	1.38601	−	0.450342i	0.0561640	−	0.0182488i
$610$	19.5229	+	4.47955i	0.790457	+	0.181372i
$611$	−22.4971	−	30.9646i	−0.910134	−	1.25269i
$612$	2.42528	+	1.23574i	0.0980361	+	0.0499519i
$613$	−38.2477	+	19.4882i	−1.54481	+	0.787120i	−0.998719	−	0.0506058i	$-0.983885\pi$
$613$	−38.2477	+	19.4882i	−1.54481	+	0.787120i	−0.546091	+	0.837726i	$0.683885\pi$
$614$	−25.4319	+	35.0041i	−1.02635	+	1.41265i
$615$	−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	$0.349067\pi$
$618$	0.613709	+	3.87481i	0.0246870	+	0.155868i
$619$	20.0674	+	6.52029i	0.806576	+	0.262073i	0.683147	−	0.730281i	$-0.260611\pi$
$619$	20.0674	+	6.52029i	0.806576	+	0.262073i	0.123429	+	0.992353i	$0.460611\pi$
$620$	0.236396	−	0.0592779i	0.00949388	−	0.00238066i
$621$	5.62139	−	4.08418i	0.225578	−	0.163892i
$622$	1.78720	−	11.2840i	0.0716603	−	0.452445i
$623$	−0.688620	+	1.35149i	−0.0275890	+	0.0541464i
$624$	−3.45064	+	10.6200i	−0.138136	+	0.425139i
$625$	−15.4973	−	19.6172i	−0.619892	−	0.784687i
$626$		−	2.04613i		−	0.0817798i
$627$		0			0
$628$	1.08671	−	1.08671i	0.0433645	−	0.0433645i
$629$	16.2087	+	11.7763i	0.646282	+	0.469552i
$630$	−0.574517	+	1.42751i	−0.0228893	+	0.0568732i
$631$	−8.72043	−	26.8387i	−0.347155	−	1.06843i	−0.960420	−	0.278555i	$-0.910144\pi$
$631$	−8.72043	−	26.8387i	−0.347155	−	1.06843i	0.613265	−	0.789877i	$-0.289856\pi$
$632$	1.70061	+	0.269351i	0.0676467	+	0.0107142i
$633$	4.67121	+	0.739847i	0.185664	+	0.0294063i
$634$	5.32290	+	16.3822i	0.211399	+	0.650621i
$635$	12.7677	+	29.9667i	0.506671	+	1.18919i
$636$	1.80896	+	1.31429i	0.0717301	+	0.0521150i
$637$	15.2422	−	15.2422i	0.603918	−	0.603918i
$638$		0			0
$639$		−	27.1004i		−	1.07208i
$640$	−2.61496	−	29.4330i	−0.103365	−	1.16344i
$641$	−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	$0.991426\pi$
$642$	−6.08232	+	11.9372i	−0.240050	+	0.471124i
$643$	0.981726	−	6.19838i	0.0387155	−	0.244440i	−0.960739	−	0.277452i	$-0.910510\pi$
$643$	0.981726	−	6.19838i	0.0387155	−	0.244440i	0.999455	+	0.0330121i	$0.0105100\pi$
$644$	0.0781682	−	0.0567925i	0.00308026	−	0.00223794i
$645$	−2.28539	−	9.11397i	−0.0899873	−	0.358862i
$646$	−3.98552	−	1.29497i	−0.156808	−	0.0509500i
$647$	−6.80289	−	42.9518i	−0.267449	−	1.68861i	−0.646247	−	0.763128i	$-0.723662\pi$
$647$	−6.80289	−	42.9518i	−0.267449	−	1.68861i	0.378798	−	0.925479i	$-0.376338\pi$
$648$	−6.68931	−	6.68931i	−0.262781	−	0.262781i
$649$		0			0
$650$	−23.3073	−	3.21171i	−0.914188	−	0.125974i
$651$	0.0314855	−	0.0433361i	0.00123402	−	0.00169848i
$652$	−2.77200	+	1.41240i	−0.108560	+	0.0553140i
$653$	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	$0.589021\pi$
$654$	−6.79682	−	9.35503i	−0.265777	−	0.365810i
$655$	−11.6008	−	18.5098i	−0.453283	−	0.723237i
$656$	28.8145	−	9.36239i	1.12502	−	0.365540i
$657$	2.57823	+	5.06007i	0.100586	+	0.197412i
$658$	−3.55424	+	0.562936i	−0.138559	+	0.0219455i
$659$	−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	$0.438137\pi$
$662$	26.5811	−	4.21003i	1.03310	−	0.163628i
$663$	4.15278	+	8.15028i	0.161280	+	0.316531i
$664$	−40.7453	+	13.2389i	−1.58122	+	0.513771i
$665$	0.0712179	−	0.310383i	0.00276171	−	0.0120361i
$666$	11.4191	+	15.7170i	0.442481	+	0.609022i
$667$	13.8210	+	7.04213i	0.535150	+	0.272672i
$668$	−3.33809	+	1.70084i	−0.129154	+	0.0658075i
$669$	9.96031	−	13.7092i	0.385088	−	0.530028i
$670$	19.8263	+	1.35959i	0.765955	+	0.0525256i
$671$		0			0
$672$	0.188008	+	0.188008i	0.00725256	+	0.00725256i
$673$	−5.98412	−	37.7823i	−0.230671	−	1.45640i	−0.782609	−	0.622514i	$-0.786111\pi$
$673$	−5.98412	−	37.7823i	−0.230671	−	1.45640i	0.551938	−	0.833885i	$-0.313889\pi$
$674$	11.0161	+	3.57935i	0.424324	+	0.137871i
$675$	−12.2178	+	17.5491i	−0.470263	+	0.675465i
$676$	0.858662	−	0.623855i	0.0330255	−	0.0239944i
$677$	−5.03592	+	31.7956i	−0.193546	+	1.22200i	0.679246	+	0.733911i	$0.262307\pi$
$677$	−5.03592	+	31.7956i	−0.193546	+	1.22200i	−0.872792	+	0.488092i	$0.837693\pi$
$678$	2.28189	−	4.47847i	0.0876356	−	0.171994i
$679$	−0.0815917	+	0.251113i	−0.00313120	+	0.00963684i
$680$	−16.3226	−	13.6590i	−0.625945	−	0.523797i
$681$			10.4198i			0.399289i
$682$		0			0
$683$	−28.7223	+	28.7223i	−1.09903	+	1.09903i	−0.104505	+	0.994524i	$0.533326\pi$
$683$	−28.7223	+	28.7223i	−1.09903	+	1.09903i	−0.994524	+	0.104505i	$0.966674\pi$
$684$	−0.441900	−	0.321059i	−0.0168965	−	0.0122760i
$685$	−8.90764	+	3.79522i	−0.340343	+	0.145008i
$686$	−1.25585	−	3.86510i	−0.0479484	−	0.147570i
$687$	12.9380	+	2.04918i	0.493616	+	0.0781811i
$688$	23.5556	+	3.73084i	0.898050	+	0.142237i
$689$	−8.63834	−	26.5861i	−0.329095	−	1.01285i
$690$	4.05029	−	1.72568i	0.154192	−	0.0656955i
$691$	20.4397	+	14.8503i	0.777564	+	0.564933i	0.904247	−	0.427010i	$-0.140433\pi$
$691$	20.4397	+	14.8503i	0.777564	+	0.564933i	−0.126683	+	0.991943i	$0.540433\pi$
$692$	2.73759	−	2.73759i	0.104068	−	0.104068i
$693$		0			0
$694$		−	14.1878i		−	0.538562i
$695$	18.0241	+	15.0828i	0.683694	+	0.572122i
$696$	−6.03999	+	18.5892i	−0.228945	+	0.704621i
$697$	11.2675	−	22.1136i	0.426785	−	0.837613i
$698$	−0.357107	+	2.25468i	−0.0135167	+	0.0853410i
$699$	−10.0896	+	7.33055i	−0.381625	+	0.277267i
$700$	−0.169895	+	0.244029i	−0.00642141	+	0.00922344i
$701$	−26.8458	−	8.72273i	−1.01395	−	0.329453i	−0.245525	−	0.969390i	$-0.578960\pi$
$701$	−26.8458	−	8.72273i	−1.01395	−	0.329453i	−0.768427	+	0.639937i	$0.778960\pi$
$702$	3.14807	+	19.8761i	0.118816	+	0.750175i
$703$	−2.84289	−	2.84289i	−0.107222	−	0.107222i
$704$		0			0
$705$	−21.9892	−	1.50791i	−0.828161	−	0.0567914i
$706$	−5.56255	+	7.65620i	−0.209349	+	0.288145i
$707$	−0.823230	+	0.419457i	−0.0309608	+	0.0157753i
$708$	2.12373	+	1.08210i	0.0798148	+	0.0406677i
$709$	−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	$0.848965\pi$
$710$	8.71256	−	37.9712i	0.326977	−	1.42503i
$711$	1.50773	−	0.489890i	0.0565441	−	0.0183723i
$712$	−9.23576	−	18.1262i	−0.346125	−	0.679308i
$713$	0.563131	−	0.0891912i	0.0210894	−	0.00334024i
$714$	0.860026			0.0321856
$715$		0			0
$716$	−6.26727			−0.234219
$717$	4.15889	−	0.658703i	0.155317	−	0.0245997i
$718$	−18.1524	−	35.6261i	−0.677441	−	1.32955i
$719$	−0.986856	+	0.320649i	−0.0368035	+	0.0119582i	−0.327361	−	0.944899i	$-0.606159\pi$
$719$	−0.986856	+	0.320649i	−0.0368035	+	0.0119582i	0.290557	+	0.956858i	$0.406159\pi$
$720$	−12.7042	−	20.2702i	−0.473456	−	0.755426i
$721$	−0.364342	−	0.501474i	−0.0135688	−	0.0186759i
$722$	−24.9840	−	12.7300i	−0.929810	−	0.473762i
$723$	−11.4843	+	5.85157i	−0.427107	+	0.217622i
$724$	−0.841554	+	1.15830i	−0.0312761	+	0.0430479i
$725$	−47.2892	−	6.51637i	−1.75627	−	0.242012i
$726$		0			0
$727$	−3.27903	−	3.27903i	−0.121612	−	0.121612i	0.643681	−	0.765294i	$-0.277406\pi$
$727$	−3.27903	−	3.27903i	−0.121612	−	0.121612i	−0.765294	+	0.643681i	$0.777406\pi$
$728$	−0.238110	−	1.50337i	−0.00882493	−	0.0557184i
$729$	1.44390	+	0.469153i	0.0534779	+	0.0173760i
$730$	1.98567	+	7.91869i	0.0734929	+	0.293084i
$731$	15.8055	−	11.4833i	0.584586	−	0.424726i
$732$	0.228265	−	1.44121i	0.00843693	−	0.0532687i
$733$	−20.7361	+	40.6968i	−0.765904	+	1.50317i	0.0956003	+	0.995420i	$0.469523\pi$
$733$	−20.7361	+	40.6968i	−0.765904	+	1.50317i	−0.861504	+	0.507751i	$0.830477\pi$
$734$	3.83723	−	11.8098i	0.141635	−	0.435907i
$735$	−1.09851	−	12.3645i	−0.0405193	−	0.456071i
$736$			2.83001i			0.104315i
$737$		0			0
$738$	17.0171	−	17.0171i	0.626410	−	0.626410i
$739$	−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	$0.722247\pi$
$740$	1.47146	+	3.45363i	0.0540920	+	0.126958i
$741$	−0.567231	−	1.74576i	−0.0208377	−	0.0641320i
$742$	−2.59590	−	0.411150i	−0.0952984	−	0.0150938i
$743$	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	$0.266090\pi$
$744$	0.222008	+	0.683270i	0.00813920	+	0.0250499i
$745$	4.81079	−	11.9534i	0.176254	−	0.437938i
$746$	−10.6517	−	7.73895i	−0.389988	−	0.283343i
$747$	−27.8924	+	27.8924i	−1.02053	+	1.02053i
$748$		0			0
$749$		−	2.11681i		−	0.0773467i
$750$	−10.0320	+	9.10640i	−0.366316	+	0.332519i
$751$	−3.08775	+	9.50312i	−0.112674	+	0.346774i	−0.991455	−	0.130451i	$-0.958357\pi$
$751$	−3.08775	+	9.50312i	−0.112674	+	0.346774i	0.878781	+	0.477225i	$0.158357\pi$
$752$	25.3980	−	49.8464i	0.926171	−	1.81771i
$753$	−2.41230	+	15.2306i	−0.0879089	+	0.555035i
$754$	−36.3446	+	26.4059i	−1.32359	+	0.961647i
$755$	−32.4561	+	8.13861i	−1.18120	+	0.296194i
$756$	0.241881	+	0.0785920i	0.00879714	+	0.00285837i
$757$	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	$0.770696\pi$
$758$	−0.664675	−	0.664675i	−0.0241421	−	0.0241421i
$759$		0			0
$760$	2.80638	+	3.21961i	0.101798	+	0.116788i
$761$	17.8404	−	24.5552i	0.646713	−	0.890124i	−0.352238	−	0.935910i	$-0.614579\pi$
$761$	17.8404	−	24.5552i	0.646713	−	0.890124i	0.998951	+	0.0457864i	$0.0145794\pi$
$762$	15.7289	−	8.01429i	0.569799	−	0.290327i
$763$	1.62790	+	0.829459i	0.0589341	+	0.0300284i
$764$	1.15493	+	1.58963i	0.0417840	+	0.0575107i
$765$	−19.1001	−	4.38256i	−0.690566	−	0.158452i
$766$	−15.0044	+	4.87523i	−0.542131	+	0.176149i
$767$	−13.5283	−	26.5507i	−0.488477	−	0.958690i
$768$	−5.73527	+	0.908377i	−0.206954	+	0.0327782i
$769$	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
$772$	−1.81970	+	0.288213i	−0.0654926	+	0.0103730i
$773$	−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	$-0.303663\pi$
$774$	18.0168	−	5.85402i	0.647601	−	0.210418i
$775$	−1.54700	+	0.827900i	−0.0555698	+	0.0297390i
$776$	−2.08149	−	2.86493i	−0.0747213	−	0.102845i
$777$	0.735173	+	0.374589i	0.0263742	+	0.0134383i
$778$	−29.9955	+	15.2835i	−1.07539	+	0.547939i
$779$	−2.92741	+	4.02923i	−0.104885	+	0.144362i
$780$	−0.117260	+	1.70994i	−0.00419856	+	0.0612257i
$781$		0			0
$782$	6.47282	+	6.47282i	0.231467	+	0.231467i
$783$	6.38724	+	40.3275i	0.228261	+	1.44119i
$784$	29.9651	+	9.73624i	1.07018	+	0.347723i
$785$	−5.68579	+	9.49165i	−0.202935	+	0.338771i
$786$	−9.57771	+	6.95861i	−0.341626	+	0.248206i
$787$	−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	$0.950375\pi$
$788$	1.97520	−	3.87655i	0.0703636	−	0.138096i
$789$	3.90967	−	12.0327i	0.139188	−	0.428376i
$790$	2.27001	−	0.201678i	0.0807634	−	0.00717537i
$791$			0.794162i			0.0282372i
$792$		0			0
$793$	−12.8994	+	12.8994i	−0.458070	+	0.458070i
$794$	−18.7425	−	13.6172i	−0.665145	−	0.483256i
$795$	−14.9338	−	6.01029i	−0.529647	−	0.213163i
$796$	−1.28445	−	3.95313i	−0.0455261	−	0.140115i
$797$	−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	$0.839586\pi$
$798$	−0.170458	−	0.0269979i	−0.00603414	−	0.000955714i
$799$	−14.1615	−	43.5847i	−0.500999	−	1.54192i
$800$	−2.85757	−	8.22702i	−0.101030	−	0.290869i
$801$	−15.1535	−	11.0097i	−0.535424	−	0.389008i
$802$	−4.60219	+	4.60219i	−0.162509	+	0.162509i
$803$		0			0
$804$		−	1.44771i		−	0.0510569i
$805$	−0.446416	+	0.533473i	−0.0157341	+	0.0188025i
$806$	−0.510267	+	1.57044i	−0.0179734	+	0.0553164i
$807$	4.09432	−	8.03556i	0.144127	−	0.282865i
$808$	1.93850	−	12.2392i	0.0681962	−	0.430574i
$809$	12.3255	−	8.95497i	0.433340	−	0.314840i	−0.349643	−	0.936883i	$-0.613697\pi$
$809$	12.3255	−	8.95497i	0.433340	−	0.314840i	0.782983	+	0.622043i	$0.213697\pi$
$810$	−10.7414	−	6.43446i	−0.377416	−	0.226084i
$811$	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	$0.304904\pi$
$812$	0.0888178	+	0.560774i	0.00311689	+	0.0196793i
$813$	10.0502	+	10.0502i	0.352475	+	0.352475i
$814$		0			0
$815$	16.8842	−	14.7171i	0.591427	−	0.515518i
$816$	−7.85881	+	10.8167i	−0.275113	+	0.378661i
$817$	−3.49314	+	1.77984i	−0.122209	+	0.0622688i
$818$	−5.81793	−	2.96438i	−0.203419	−	0.103647i
$819$	−0.823747	−	1.13379i	−0.0287840	−	0.0396178i
$820$	3.94041	−	2.46962i	0.137605	−	0.0862428i
$821$	27.3071	−	8.87260i	0.953023	−	0.309656i	0.209079	−	0.977899i	$-0.432953\pi$
$821$	27.3071	−	8.87260i	0.953023	−	0.309656i	0.743943	+	0.668243i	$0.232953\pi$
$822$	2.38226	+	4.67545i	0.0830909	+	0.163075i
$823$	−26.6252	+	4.21701i	−0.928095	+	0.146996i	−0.602141	−	0.798390i	$-0.705686\pi$
$823$	−26.6252	+	4.21701i	−0.928095	+	0.146996i	−0.325954	+	0.945386i	$0.605686\pi$
$824$	8.31350			0.289614
$825$		0			0
$826$	−2.80165			−0.0974820
$827$	−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	$0.692370\pi$
$828$	0.541680	+	1.06311i	0.0188247	+	0.0369455i
$829$	−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	$0.460433\pi$
$830$	−48.0481	+	30.1137i	−1.66777	+	1.04526i
$831$	−2.19378	−	3.01948i	−0.0761013	−	0.104744i
$832$	17.6573	+	8.99683i	0.612156	+	0.311909i
$833$	22.9966	−	11.7174i	0.796786	−	0.405983i
$834$	7.48663	−	10.3045i	0.259241	−	0.356815i
$835$	20.3322	−	17.7226i	0.703625	−	0.613316i
$836$		0			0
$837$	1.06120	+	1.06120i	0.0366805	+	0.0366805i
$838$	−0.285920	−	1.80523i	−0.00987695	−	0.0623606i
$839$	38.3426	+	12.4583i	1.32373	+	0.430107i	0.883775	−	0.467912i	$-0.154993\pi$
$839$	38.3426	+	12.4583i	1.32373	+	0.430107i	0.439958	+	0.898019i	$0.354993\pi$
$840$	−0.751937	−	0.450434i	−0.0259443	−	0.0155415i
$841$	−50.2797	+	36.5303i	−1.73378	+	1.25967i
$842$	−7.44491	+	47.0053i	−0.256569	+	1.61991i
$843$	4.77364	−	9.36879i	0.164413	−	0.322678i
$844$	−0.569376	+	1.75236i	−0.0195987	+	0.0603187i
$845$	−4.90379	+	5.86010i	−0.168695	+	0.201593i
$846$		−	44.4376i		−	1.52780i
$847$		0			0
$848$	28.8921	−	28.8921i	0.992159	−	0.992159i
$849$	14.6966	+	10.6777i	0.504386	+	0.366458i
$850$	−25.3528	−	12.2810i	−0.869593	−	0.421237i
$851$	2.71386	+	8.35241i	0.0930300	+	0.286317i
$852$	−2.80310	−	0.443967i	−0.0960326	−	0.0152101i
$853$	−13.7845	−	2.18326i	−0.471974	−	0.0747533i	−0.0840831	−	0.996459i	$-0.526796\pi$
$853$	−13.7845	−	2.18326i	−0.471974	−	0.0747533i	−0.387890	+	0.921705i	$0.626796\pi$
$854$	0.530012	+	1.63121i	0.0181366	+	0.0558188i
$855$	3.64808	+	1.46822i	0.124762	+	0.0502119i
$856$	22.9686	+	16.6876i	0.785049	+	0.570372i
$857$	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	$0.101178\pi$
$859$			18.3200i			0.625071i	−0.949906	+	0.312535i	$0.898822\pi$
$860$	3.64628	−	0.323951i	0.124337	−	0.0110466i
$861$	0.315849	−	0.972084i	0.0107641	−	0.0331285i
$862$	−6.82592	+	13.3966i	−0.232492	+	0.456291i
$863$	−1.90114	+	12.0033i	−0.0647154	+	0.408597i	0.933971	+	0.357350i	$0.116320\pi$
$863$	−1.90114	+	12.0033i	−0.0647154	+	0.408597i	−0.998686	+	0.0512472i	$0.983680\pi$
$864$	−6.02655	+	4.37855i	−0.205028	+	0.148961i
$865$	−14.3234	+	23.9109i	−0.487010	+	0.812996i
$866$	39.0074	+	12.6743i	1.32552	+	0.430689i
$867$	−0.406785	−	2.56834i	−0.0138151	−	0.0872253i
$868$	0.0147565	+	0.0147565i	0.000500870	+	0.000500870i
$869$		0			0
$870$	−1.76991	+	25.8098i	−0.0600057	+	0.875035i
$871$	−10.6384	+	14.6425i	−0.360469	+	0.496143i
$872$	−21.8334	+	11.1247i	−0.739374	+	0.376730i
$873$	−2.90515	−	1.48025i	−0.0983243	−	0.0500987i
$874$	−1.07972	−	1.48611i	−0.0365222	−	0.0502685i
$875$	0.759091	−	2.00161i	0.0256620	−	0.0676666i
$876$	0.565619	−	0.183781i	0.0191105	−	0.00620938i
$877$	5.82698	+	11.4361i	0.196763	+	0.386169i	0.968215	−	0.250118i	$-0.0804694\pi$
$877$	5.82698	+	11.4361i	0.196763	+	0.386169i	−0.771452	+	0.636287i	$0.780469\pi$
$878$	36.9125	−	5.84636i	1.24574	−	0.197305i
$879$	−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	$0.425110\pi$
$882$	24.7187	−	3.91506i	0.832322	−	0.131827i
$883$	−19.7888	−	38.8377i	−0.665947	−	1.30699i	−0.938642	−	0.344893i	$-0.887915\pi$
$883$	−19.7888	−	38.8377i	−0.665947	−	1.30699i	0.272695	−	0.962100i	$-0.412085\pi$
$884$	−3.38926	+	1.10124i	−0.113993	+	0.0370387i
$885$	−16.7253	−	3.83765i	−0.562215	−	0.129001i
$886$	27.5163	+	37.8730i	0.924429	+	1.27237i
$887$	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	$0.594141\pi$
$888$	−9.86013	+	5.02399i	−0.330884	+	0.168594i
$889$	−1.63945	+	2.25651i	−0.0549853	+	0.0756808i
$890$	−17.6925	−	20.2977i	−0.593055	−	0.680381i
$891$		0			0
$892$	4.66817	+	4.66817i	0.156302	+	0.156302i
$893$	1.43862	+	9.08308i	0.0481415	+	0.303954i
$894$	−6.64130	−	2.15789i	−0.222118	−	0.0721706i
$895$	43.7656	−	10.9745i	1.46292	−	0.366838i
$896$	2.04700	−	1.48723i	0.0683855	−	0.0496850i
$897$	−0.627249	+	3.96029i	−0.0209432	+	0.132230i
$898$	−5.05474	+	9.92048i	−0.168679	+	0.331051i
$899$	−1.03530	+	3.18633i	−0.0345292	+	0.106270i
$900$	−2.64816	−	2.54357i	−0.0882720	−	0.0847856i
$901$		−	33.4710i		−	1.11508i
$902$		0			0
$903$	0.568922	−	0.568922i	0.0189325	−	0.0189325i
$904$	−8.61708	−	6.26067i	−0.286600	−	0.208227i
$905$	3.84846	−	9.56228i	0.127927	−	0.317861i
$906$	5.60375	+	17.2466i	0.186172	+	0.572979i
$907$	16.1062	+	2.55097i	0.534798	+	0.0847036i	0.417991	−	0.908451i	$-0.362734\pi$
$907$	16.1062	+	2.55097i	0.534798	+	0.0847036i	0.116806	+	0.993155i	$0.462734\pi$
$908$	−4.00948	−	0.635040i	−0.133059	−	0.0210745i
$909$	−3.52571	−	10.8510i	−0.116940	−	0.359906i
$910$	−0.789672	−	1.85341i	−0.0261774	−	0.0614401i
$911$	14.3281	+	10.4099i	0.474710	+	0.344897i	0.799274	−	0.600967i	$-0.205218\pi$
$911$	14.3281	+	10.4099i	0.474710	+	0.344897i	−0.324564	+	0.945864i	$0.605218\pi$
$912$	1.89718	−	1.89718i	0.0628219	−	0.0628219i
$913$		0			0
$914$		−	10.2385i		−	0.338659i
$915$	0.929665	+	10.4640i	0.0307338	+	0.345929i
$916$	−1.57702	+	4.85357i	−0.0521062	+	0.160366i
$917$	0.849203	−	1.66665i	0.0280431	−	0.0550378i
$918$	−3.76933	+	23.7986i	−0.124406	+	0.785472i
$919$	−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	$0.348116\pi$
$920$	−2.26921	−	9.04942i	−0.0748135	−	0.298350i
$921$	−21.5818	−	7.01234i	−0.711143	−	0.231064i
$922$	−6.91497	−	43.6594i	−0.227732	−	1.43785i
$923$	25.0888	+	25.0888i	0.825807	+	0.825807i
$924$		0			0
$925$	−16.3231	−	21.5407i	−0.536701	−	0.708254i
$926$	−22.1307	+	30.4602i	−0.727259	+	1.00099i
$927$	6.82017	−	3.47505i	0.224004	−	0.114136i
$928$	−14.8171	−	7.54970i	−0.486396	−	0.247831i
$929$	−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	$0.809465\pi$
$930$	0.504986	+	0.805732i	0.0165591	+	0.0264210i
$931$	−4.92578	+	1.60048i	−0.161436	+	0.0524537i
$932$	−2.20583	−	4.32918i	−0.0722543	−	0.141807i
$933$	5.91808	−	0.937332i	0.193749	−	0.0306869i
$934$	40.2174			1.31595
$935$		0			0
$936$	18.7961			0.614371
$937$	−14.9726	+	2.37143i	−0.489133	+	0.0774711i	−0.396130	−	0.918195i	$-0.629647\pi$
$937$	−14.9726	+	2.37143i	−0.489133	+	0.0774711i	−0.0930039	+	0.995666i	$0.529647\pi$
$938$	0.772546	+	1.51621i	0.0252245	+	0.0495059i
$939$	1.02061	−	0.331616i	0.0333063	−	0.0108219i
$940$	1.92037	−	8.36939i	0.0626356	−	0.272979i
$941$	12.8308	+	17.6600i	0.418271	+	0.575701i	0.965211	−	0.261471i	$-0.0842075\pi$
$941$	12.8308	+	17.6600i	0.418271	+	0.575701i	−0.546940	+	0.837172i	$0.684208\pi$
$942$	5.34274	+	2.72226i	0.174076	+	0.0886961i
$943$	9.69338	−	4.93902i	0.315660	−	0.160837i
$944$	25.6012	−	35.2370i	0.833247	−	1.14687i
$945$	−1.82673	−	0.125268i	−0.0594235	−	0.00407498i
$946$		0			0
$947$	6.90662	+	6.90662i	0.224435	+	0.224435i	0.810363	−	0.585928i	$-0.199270\pi$
$947$	6.90662	+	6.90662i	0.224435	+	0.224435i	−0.585928	+	0.810363i	$0.699270\pi$
$948$	−0.0259711	−	0.163975i	−0.000843503	−	0.00532567i
$949$	−7.07131	−	2.29761i	−0.229545	−	0.0745835i
$950$	4.63941	+	3.22999i	0.150522	+	0.104795i
$951$	−7.30875	+	5.31012i	−0.237003	+	0.172192i
$952$	0.285100	−	1.80005i	0.00924015	−	0.0583400i
$953$	5.92153	−	11.6216i	0.191817	−	0.376462i	−0.774989	−	0.631975i	$-0.782244\pi$
$953$	5.92153	−	11.6216i	0.191817	−	0.376462i	0.966806	+	0.255513i	$0.0822444\pi$
$954$	10.0294	−	30.8672i	0.324713	−	0.999363i
$955$	−10.8487	−	9.07831i	−0.351056	−	0.293767i
$956$			1.64046i			0.0530561i
$957$		0			0
$958$	−28.2202	+	28.2202i	−0.911755	+	0.911755i
$959$	−0.670750	−	0.487328i	−0.0216596	−	0.0157367i
$960$	10.4988	−	4.47317i	0.338849	−	0.144371i
$961$	−9.54147	−	29.3656i	−0.307789	−	0.947279i
$962$	−25.1218	−	3.97890i	−0.809960	−	0.128285i
$963$	25.8182	+	4.08921i	0.831981	+	0.131773i
$964$	−1.55173	−	4.77572i	−0.0499777	−	0.153816i
$965$	12.2027	−	5.19911i	0.392818	−	0.167365i
$966$	0.304989	+	0.221588i	0.00981287	+	0.00712946i
$967$	−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
$970$	−3.59460	−	3.00800i	−0.115416	−	0.0965809i
$971$	1.26967	−	3.90765i	0.0407457	−	0.125403i	−0.928615	−	0.371046i	$-0.878999\pi$
$971$	1.26967	−	3.90765i	0.0407457	−	0.125403i	0.969360	+	0.245643i	$0.0789992\pi$
$972$	−2.22320	+	4.36328i	−0.0713093	+	0.139952i
$973$	−0.314819	+	1.98769i	−0.0100926	+	0.0637224i
$974$	28.6965	−	20.8492i	0.919495	−	0.668052i
$975$	−2.17541	−	12.1462i	−0.0696688	−	0.388989i
$976$	−25.3592	−	8.23971i	−0.811729	−	0.263747i
$977$	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	$0.786543\pi$
$978$	−8.58324	−	8.58324i	−0.274462	−	0.274462i
$979$		0			0
$980$	4.82472	+	0.330856i	0.154120	+	0.0105688i
$981$	−13.2614	+	18.2528i	−0.423405	+	0.582767i
$982$	24.8498	−	12.6616i	0.792990	−	0.404048i
$983$	24.7035	+	12.5871i	0.787919	+	0.401465i	0.801162	−	0.598447i	$-0.204215\pi$
$983$	24.7035	+	12.5871i	0.787919	+	0.401465i	−0.0132429	+	0.999912i	$0.504215\pi$
$984$	8.05767	+	11.0904i	0.256869	+	0.353550i
$985$	−7.00505	+	30.5295i	−0.223199	+	0.972750i
$986$	−51.1575	+	16.6221i	−1.62919	+	0.529355i
$987$	−0.856827	−	1.68162i	−0.0272731	−	0.0535265i
$988$	0.706325	−	0.111871i	0.0224712	−	0.00355909i
$989$	8.56376			0.272312
$990$		0			0
$991$	9.10087			0.289099			0.144549	−	0.989498i	$-0.453827\pi$
$991$	9.10087			0.289099			0.144549	+	0.989498i	$0.453827\pi$
$992$	−0.603719	+	0.0956197i	−0.0191681	+	0.00303593i
$993$	6.40795	+	12.5763i	0.203350	+	0.399097i
$994$	3.17264	−	1.03085i	0.100630	−	0.0326966i
$995$	15.8919	+	25.3563i	0.503806	+	0.803849i
$996$	2.42808	+	3.34196i	0.0769366	+	0.105894i
$997$	−25.7239	−	13.1070i	−0.814685	−	0.415103i	−0.00357282	−	0.999994i	$-0.501137\pi$
$997$	−25.7239	−	13.1070i	−0.814685	−	0.415103i	−0.811112	+	0.584891i	$0.801137\pi$
$998$	15.9247	−	8.11406i	0.504089	−	0.256846i
$999$	−13.5878	+	18.7019i	−0.429898	+	0.591703i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.m.e.282.1		32
5.3	odd	4	inner	605.2.m.e.403.4		32
11.2	odd	10		605.2.m.d.457.1		32
11.3	even	5		55.2.l.a.52.1	yes	32
11.4	even	5		605.2.m.d.112.1		32
11.5	even	5		605.2.e.b.362.14		32
11.6	odd	10		605.2.e.b.362.3		32
11.7	odd	10		605.2.m.c.112.4		32
11.8	odd	10	inner	605.2.m.e.602.4		32
11.9	even	5		605.2.m.c.457.4		32
11.10	odd	2		55.2.l.a.7.4	✓	32
33.14	odd	10		495.2.bj.a.217.4		32
33.32	even	2		495.2.bj.a.172.1		32
44.3	odd	10		880.2.cm.a.657.1		32
44.43	even	2		880.2.cm.a.337.4		32
55.3	odd	20		55.2.l.a.8.4	yes	32
55.8	even	20	inner	605.2.m.e.118.1		32
55.13	even	20		605.2.m.d.578.1		32
55.14	even	10		275.2.bm.b.107.4		32
55.18	even	20		605.2.m.c.233.4		32
55.28	even	20		605.2.e.b.483.14		32
55.32	even	4		275.2.bm.b.18.4		32
55.38	odd	20		605.2.e.b.483.3		32
55.43	even	4		55.2.l.a.18.1	yes	32
55.47	odd	20		275.2.bm.b.118.1		32
55.48	odd	20		605.2.m.d.233.1		32
55.53	odd	20		605.2.m.c.578.4		32
55.54	odd	2		275.2.bm.b.7.1		32
165.98	odd	4		495.2.bj.a.73.4		32
165.113	even	20		495.2.bj.a.118.1		32
220.3	even	20		880.2.cm.a.833.4		32
220.43	odd	4		880.2.cm.a.513.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.7.4	✓	32	11.10	odd	2
55.2.l.a.8.4	yes	32	55.3	odd	20
55.2.l.a.18.1	yes	32	55.43	even	4
55.2.l.a.52.1	yes	32	11.3	even	5
275.2.bm.b.7.1		32	55.54	odd	2
275.2.bm.b.18.4		32	55.32	even	4
275.2.bm.b.107.4		32	55.14	even	10
275.2.bm.b.118.1		32	55.47	odd	20
495.2.bj.a.73.4		32	165.98	odd	4
495.2.bj.a.118.1		32	165.113	even	20
495.2.bj.a.172.1		32	33.32	even	2
495.2.bj.a.217.4		32	33.14	odd	10
605.2.e.b.362.3		32	11.6	odd	10
605.2.e.b.362.14		32	11.5	even	5
605.2.e.b.483.3		32	55.38	odd	20
605.2.e.b.483.14		32	55.28	even	20
605.2.m.c.112.4		32	11.7	odd	10
605.2.m.c.233.4		32	55.18	even	20
605.2.m.c.457.4		32	11.9	even	5
605.2.m.c.578.4		32	55.53	odd	20
605.2.m.d.112.1		32	11.4	even	5
605.2.m.d.233.1		32	55.48	odd	20
605.2.m.d.457.1		32	11.2	odd	10
605.2.m.d.578.1		32	55.13	even	20
605.2.m.e.118.1		32	55.8	even	20	inner
605.2.m.e.282.1		32	1.1	even	1	trivial
605.2.m.e.403.4		32	5.3	odd	4	inner
605.2.m.e.602.4		32	11.8	odd	10	inner
880.2.cm.a.337.4		32	44.43	even	2
880.2.cm.a.513.1		32	220.43	odd	4
880.2.cm.a.657.1		32	44.3	odd	10
880.2.cm.a.833.4		32	220.3	even	20

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.m (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50135 + 0.237790i) q^{2} +(-0.361933 - 0.710333i) q^{3} +(0.295389 - 0.0959778i) q^{4} +(-1.89470 + 1.18749i) q^{5} +(0.712297 + 0.980393i) q^{6} +(-0.170602 - 0.0869260i) q^{7} +(2.28811 - 1.16585i) q^{8} +(1.38978 - 1.91287i) q^{9} +(2.56223 - 2.23337i) q^{10} +(-0.175087 - 0.175087i) q^{12} +(0.484259 + 3.05749i) q^{13} +(0.276803 + 0.0899388i) q^{14} +(1.52926 + 0.916076i) q^{15} +(-3.66057 + 2.65956i) q^{16} +(-0.579827 + 3.66088i) q^{17} +(-1.63168 + 3.20235i) q^{18} +(0.229844 - 0.707388i) q^{19} +(-0.445701 + 0.532619i) q^{20} +0.152646i q^{21} +(-1.14886 + 1.14886i) q^{23} +(-1.65629 - 1.20336i) q^{24} +(2.17976 - 4.49985i) q^{25} +(-1.45408 - 4.47521i) q^{26} +(-4.22401 - 0.669017i) q^{27} +(-0.0587369 - 0.00930302i) q^{28} +(-2.95025 - 9.07993i) q^{29} +(-2.51379 - 1.01171i) q^{30} +(-0.283900 - 0.206266i) q^{31} +(1.23166 - 1.23166i) q^{32} -5.63413i q^{34} +(0.426463 - 0.0378887i) q^{35} +(0.226933 - 0.698428i) q^{36} +(2.45398 - 4.81621i) q^{37} +(-0.176866 + 1.11669i) q^{38} +(1.99657 - 1.45059i) q^{39} +(-2.95085 + 4.92603i) q^{40} +(-6.36824 - 2.06917i) q^{41} +(-0.0362976 - 0.229174i) q^{42} +(-3.72708 - 3.72708i) q^{43} +(-0.361710 + 5.27464i) q^{45} +(1.45165 - 1.99802i) q^{46} +(-11.0165 + 5.61318i) q^{47} +(3.21405 + 1.63764i) q^{48} +(-4.09295 - 5.63346i) q^{49} +(-2.20256 + 7.27417i) q^{50} +(2.81030 - 0.913123i) q^{51} +(0.436496 + 0.856672i) q^{52} +(-8.91914 + 1.41265i) q^{53} +6.50079 q^{54} -0.491699 q^{56} +(-0.585669 + 0.0927608i) q^{57} +(6.58847 + 12.9306i) q^{58} +(-9.15496 + 2.97463i) q^{59} +(0.539651 + 0.123824i) q^{60} +(3.46383 + 4.76756i) q^{61} +(0.475281 + 0.242168i) q^{62} +(-0.403377 + 0.205531i) q^{63} +(3.76284 - 5.17911i) q^{64} +(-4.54825 - 5.21797i) q^{65} +(4.13426 + 4.13426i) q^{67} +(0.180089 + 1.13704i) q^{68} +(1.23188 + 0.400262i) q^{69} +(-0.631259 + 0.158293i) q^{70} +(9.27272 - 6.73702i) q^{71} +(0.949851 - 5.99713i) q^{72} +(-1.09042 + 2.14008i) q^{73} +(-2.53903 + 7.81434i) q^{74} +(-3.98532 + 0.0802892i) q^{75} -0.231015i q^{76} +(-2.65261 + 2.65261i) q^{78} +(0.542434 + 0.394101i) q^{79} +(3.77749 - 9.38594i) q^{80} +(-1.13837 - 3.50353i) q^{81} +(10.0530 + 1.59224i) q^{82} +(-16.4776 - 2.60980i) q^{83} +(0.0146506 + 0.0450899i) q^{84} +(-3.24865 - 7.62480i) q^{85} +(6.48191 + 4.70938i) q^{86} +(-5.38198 + 5.38198i) q^{87} -7.92190i q^{89} +(-0.711206 - 8.00509i) q^{90} +(0.183160 - 0.563709i) q^{91} +(-0.229095 + 0.449625i) q^{92} +(-0.0437645 + 0.276318i) q^{93} +(15.2048 - 11.0469i) q^{94} +(0.404527 + 1.61322i) q^{95} +(-1.32067 - 0.429111i) q^{96} +(-0.215721 - 1.36201i) q^{97} +(7.48452 + 7.48452i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 10 q^{2} - 4 q^{3} - 2 q^{5} + 20 q^{6} + 10 q^{8} + 12 q^{12} + 10 q^{13} + 14 q^{15} - 8 q^{16} + 10 q^{18} + 16 q^{20} - 24 q^{23} + 16 q^{25} + 20 q^{26} - 16 q^{27} - 50 q^{28} - 30 q^{30} - 28 q^{31}+ \cdots - 8 q^{97}+O(q^{100}) \) 32 * q + 10 * q^2 - 4 * q^3 - 2 * q^5 + 20 * q^6 + 10 * q^8 + 12 * q^12 + 10 * q^13 + 14 * q^15 - 8 * q^16 + 10 * q^18 + 16 * q^20 - 24 * q^23 + 16 * q^25 + 20 * q^26 - 16 * q^27 - 50 * q^28 - 30 * q^30 - 28 * q^31 + 10 * q^35 + 24 * q^36 - 8 * q^37 + 10 * q^38 + 50 * q^40 - 40 * q^41 - 10 * q^42 - 28 * q^45 - 60 * q^46 - 28 * q^47 - 54 * q^48 + 50 * q^50 - 20 * q^51 + 50 * q^52 - 24 * q^53 - 80 * q^56 - 30 * q^57 - 50 * q^58 + 34 * q^60 + 60 * q^61 - 100 * q^62 + 30 * q^63 - 8 * q^67 + 30 * q^68 + 30 * q^70 + 24 * q^71 - 80 * q^72 - 50 * q^73 + 34 * q^75 + 60 * q^78 + 98 * q^80 - 12 * q^81 - 10 * q^82 - 90 * q^83 - 30 * q^85 + 100 * q^86 + 20 * q^90 + 20 * q^91 - 68 * q^92 - 8 * q^93 + 40 * q^95 - 8 * q^97

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