LMFDB - Embedded newform 512.2.k.a.497.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [512,2,Mod(17,512)] 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("512.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(512, base_ring=CyclotomicField(32)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.k (of order $32$, degree $16$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$15$ over $\Q(\zeta_{32})$
Twist minimal:	no (minimal twist has level 128)
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			497.1
Character	$\chi$	$=$	512.497
Dual form			512.2.k.a.273.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.73660 + 1.46274i) q^{3} +(1.64287 + 2.00184i) q^{5} +(1.75623 - 1.17347i) q^{7} +(3.68265 - 5.51147i) q^{9} +(5.12430 - 1.55444i) q^{11} +(-0.540375 - 0.443474i) q^{13} +(-7.42405 - 3.07514i) q^{15} +(-0.278638 + 0.115416i) q^{17} +(0.517663 + 5.25592i) q^{19} +(-3.08960 + 5.78024i) q^{21} +(1.02260 - 0.203407i) q^{23} +(-0.332898 + 1.67359i) q^{25} +(-1.10362 + 11.2053i) q^{27} +(-0.356648 + 1.17571i) q^{29} +(5.90439 + 5.90439i) q^{31} +(-11.7494 + 11.7494i) q^{33} +(5.23436 + 1.58783i) q^{35} +(2.43658 + 0.239983i) q^{37} +(2.12748 + 0.423182i) q^{39} +(0.736357 + 3.70191i) q^{41} +(-8.55004 - 4.57009i) q^{43} +(17.0832 - 1.68255i) q^{45} +(-3.97444 - 9.59514i) q^{47} +(-0.971486 + 2.34538i) q^{49} +(0.593698 - 0.723423i) q^{51} +(-0.603962 - 1.99100i) q^{53} +(11.5303 + 7.70429i) q^{55} +(-9.10470 - 13.6261i) q^{57} +(-3.15067 + 2.58569i) q^{59} +(3.44200 + 6.43952i) q^{61} -14.0009i q^{63} -1.81031i q^{65} +(0.810030 + 1.51546i) q^{67} +(-2.50091 + 2.05244i) q^{69} +(4.34102 + 6.49679i) q^{71} +(3.85781 + 2.57771i) q^{73} +(-1.53702 - 5.06689i) q^{75} +(7.17535 - 8.74319i) q^{77} +(0.889548 - 2.14756i) q^{79} +(-5.76031 - 13.9066i) q^{81} +(-6.11293 + 0.602071i) q^{83} +(-0.688810 - 0.368177i) q^{85} +(-0.743761 - 3.73914i) q^{87} +(-5.90894 - 1.17536i) q^{89} +(-1.46943 - 0.144726i) q^{91} +(-24.7945 - 7.52134i) q^{93} +(-9.67106 + 9.67106i) q^{95} +(9.61317 + 9.61317i) q^{97} +(10.3037 - 33.9669i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35}+ \cdots + 16 q^{99}+O(q^{100}) $ 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{9}{32}\right)$	$1$

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
$3$	−2.73660	+	1.46274i	−1.57998	+	0.844515i	−0.580432	+	0.814308i	$0.697116\pi$
$3$	−2.73660	+	1.46274i	−1.57998	+	0.844515i	−0.999544	+	0.0302064i	$0.990384\pi$
$4$		0			0
$5$	1.64287	+	2.00184i	0.734713	+	0.895250i	0.997576	−	0.0695830i	$-0.0221669\pi$
$5$	1.64287	+	2.00184i	0.734713	+	0.895250i	−0.262863	+	0.964833i	$0.584667\pi$
$6$		0			0
$7$	1.75623	−	1.17347i	0.663792	−	0.443532i	−0.177494	−	0.984122i	$-0.556799\pi$
$7$	1.75623	−	1.17347i	0.663792	−	0.443532i	0.841286	+	0.540590i	$0.181799\pi$
$8$		0			0
$9$	3.68265	−	5.51147i	1.22755	−	1.83716i
$10$		0			0
$11$	5.12430	−	1.55444i	1.54503	−	0.468681i	0.601199	−	0.799099i	$-0.294690\pi$
$11$	5.12430	−	1.55444i	1.54503	−	0.468681i	0.943835	+	0.330418i	$0.107190\pi$
$12$		0			0
$13$	−0.540375	−	0.443474i	−0.149873	−	0.122998i	0.556469	−	0.830868i	$-0.312156\pi$
$13$	−0.540375	−	0.443474i	−0.149873	−	0.122998i	−0.706342	+	0.707871i	$0.749656\pi$
$14$		0			0
$15$	−7.42405	−	3.07514i	−1.91688	−	0.793998i
$16$		0			0
$17$	−0.278638	+	0.115416i	−0.0675797	+	0.0279924i	−0.416217	−	0.909265i	$-0.636644\pi$
$17$	−0.278638	+	0.115416i	−0.0675797	+	0.0279924i	0.348638	+	0.937258i	$0.386644\pi$
$18$		0			0
$19$	0.517663	+	5.25592i	0.118760	+	1.20579i	0.851156	+	0.524912i	$0.175902\pi$
$19$	0.517663	+	5.25592i	0.118760	+	1.20579i	−0.732396	+	0.680879i	$0.761598\pi$
$20$		0			0
$21$	−3.08960	+	5.78024i	−0.674207	+	1.26135i
$22$		0			0
$23$	1.02260	−	0.203407i	0.213227	−	0.0424134i	−0.0873210	−	0.996180i	$-0.527831\pi$
$23$	1.02260	−	0.203407i	0.213227	−	0.0424134i	0.300548	+	0.953767i	$0.402831\pi$
$24$		0			0
$25$	−0.332898	+	1.67359i	−0.0665795	+	0.334718i
$26$		0			0
$27$	−1.10362	+	11.2053i	−0.212393	+	2.15646i
$28$		0			0
$29$	−0.356648	+	1.17571i	−0.0662280	+	0.218324i	−0.983808	−	0.179228i	$-0.942640\pi$
$29$	−0.356648	+	1.17571i	−0.0662280	+	0.218324i	0.917580	+	0.397552i	$0.130140\pi$
$30$		0			0
$31$	5.90439	+	5.90439i	1.06046	+	1.06046i	0.998051	+	0.0624088i	$0.0198783\pi$
$31$	5.90439	+	5.90439i	1.06046	+	1.06046i	0.0624088	+	0.998051i	$0.480122\pi$
$32$		0			0
$33$	−11.7494	+	11.7494i	−2.04531	+	2.04531i
$34$		0			0
$35$	5.23436	+	1.58783i	0.884768	+	0.268392i
$36$		0			0
$37$	2.43658	+	0.239983i	0.400572	+	0.0394529i	0.296298	−	0.955096i	$-0.404248\pi$
$37$	2.43658	+	0.239983i	0.400572	+	0.0394529i	0.104274	+	0.994549i	$0.466748\pi$
$38$		0			0
$39$	2.12748	+	0.423182i	0.340669	+	0.0677633i
$40$		0			0
$41$	0.736357	+	3.70191i	0.115000	+	0.578142i	0.994718	+	0.102647i	$0.0327311\pi$
$41$	0.736357	+	3.70191i	0.115000	+	0.578142i	−0.879718	+	0.475495i	$0.842269\pi$
$42$		0			0
$43$	−8.55004	−	4.57009i	−1.30387	−	0.696933i	−0.334467	−	0.942408i	$-0.608556\pi$
$43$	−8.55004	−	4.57009i	−1.30387	−	0.696933i	−0.969403	+	0.245475i	$0.921056\pi$
$44$		0			0
$45$	17.0832	−	1.68255i	2.54661	−	0.250819i
$46$		0			0
$47$	−3.97444	−	9.59514i	−0.579731	−	1.39959i	−0.893055	−	0.449948i	$-0.851442\pi$
$47$	−3.97444	−	9.59514i	−0.579731	−	1.39959i	0.313324	−	0.949646i	$-0.398558\pi$
$48$		0			0
$49$	−0.971486	+	2.34538i	−0.138784	+	0.335054i
$50$		0			0
$51$	0.593698	−	0.723423i	0.0831343	−	0.101299i
$52$		0			0
$53$	−0.603962	−	1.99100i	−0.0829606	−	0.273484i	0.905640	−	0.424048i	$-0.139391\pi$
$53$	−0.603962	−	1.99100i	−0.0829606	−	0.273484i	−0.988600	+	0.150564i	$0.951891\pi$
$54$		0			0
$55$	11.5303	+	7.70429i	1.55474	+	1.03885i
$56$		0			0
$57$	−9.10470	−	13.6261i	−1.20595	−	1.80483i
$58$		0			0
$59$	−3.15067	+	2.58569i	−0.410183	+	0.336628i	−0.816749	−	0.576993i	$-0.804226\pi$
$59$	−3.15067	+	2.58569i	−0.410183	+	0.336628i	0.406566	+	0.913621i	$0.366726\pi$
$60$		0			0
$61$	3.44200	+	6.43952i	0.440702	+	0.824496i	0.999990	−	0.00447749i	$-0.00142524\pi$
$61$	3.44200	+	6.43952i	0.440702	+	0.824496i	−0.559288	+	0.828974i	$0.688925\pi$
$62$		0			0
$63$		−	14.0009i		−	1.76395i
$64$		0			0
$65$		−	1.81031i		−	0.224542i
$66$		0			0
$67$	0.810030	+	1.51546i	0.0989609	+	0.185143i	0.926530	−	0.376221i	$-0.122777\pi$
$67$	0.810030	+	1.51546i	0.0989609	+	0.185143i	−0.827569	+	0.561364i	$0.810277\pi$
$68$		0			0
$69$	−2.50091	+	2.05244i	−0.301074	+	0.247085i
$70$		0			0
$71$	4.34102	+	6.49679i	0.515184	+	0.771028i	0.994288	−	0.106731i	$-0.0340382\pi$
$71$	4.34102	+	6.49679i	0.515184	+	0.771028i	−0.479104	+	0.877758i	$0.659038\pi$
$72$		0			0
$73$	3.85781	+	2.57771i	0.451523	+	0.301698i	0.760460	−	0.649385i	$-0.224973\pi$
$73$	3.85781	+	2.57771i	0.451523	+	0.301698i	−0.308938	+	0.951082i	$0.599973\pi$
$74$		0			0
$75$	−1.53702	−	5.06689i	−0.177480	−	0.585074i
$76$		0			0
$77$	7.17535	−	8.74319i	0.817707	−	0.996379i
$78$		0			0
$79$	0.889548	−	2.14756i	0.100082	−	0.241619i	−0.865906	−	0.500207i	$-0.833257\pi$
$79$	0.889548	−	2.14756i	0.100082	−	0.241619i	0.965988	+	0.258588i	$0.0832572\pi$
$80$		0			0
$81$	−5.76031	−	13.9066i	−0.640035	−	1.54518i
$82$		0			0
$83$	−6.11293	+	0.602071i	−0.670981	+	0.0660859i	−0.427770	−	0.903887i	$-0.640701\pi$
$83$	−6.11293	+	0.602071i	−0.670981	+	0.0660859i	−0.243211	+	0.969973i	$0.578201\pi$
$84$		0			0
$85$	−0.688810	−	0.368177i	−0.0747119	−	0.0399344i
$86$		0			0
$87$	−0.743761	−	3.73914i	−0.0797395	−	0.400878i
$88$		0			0
$89$	−5.90894	−	1.17536i	−0.626346	−	0.124588i	−0.128295	−	0.991736i	$-0.540951\pi$
$89$	−5.90894	−	1.17536i	−0.626346	−	0.124588i	−0.498050	+	0.867148i	$0.665951\pi$
$90$		0			0
$91$	−1.46943	−	0.144726i	−0.154038	−	0.0151714i
$92$		0			0
$93$	−24.7945	−	7.52134i	−2.57107	−	0.779927i
$94$		0			0
$95$	−9.67106	+	9.67106i	−0.992230	+	0.992230i
$96$		0			0
$97$	9.61317	+	9.61317i	0.976070	+	0.976070i	0.999720	−	0.0236504i	$-0.00752886\pi$
$97$	9.61317	+	9.61317i	0.976070	+	0.976070i	−0.0236504	+	0.999720i	$0.507529\pi$
$98$		0			0
$99$	10.3037	−	33.9669i	1.03556	−	3.41380i
$100$		0			0
$101$	1.44283	−	14.6493i	0.143567	−	1.45766i	−0.605859	−	0.795572i	$-0.707171\pi$
$101$	1.44283	−	14.6493i	0.143567	−	1.45766i	0.749426	−	0.662088i	$-0.230329\pi$
$102$		0			0
$103$	3.58430	−	18.0195i	0.353171	−	1.77551i	−0.240342	−	0.970688i	$-0.577260\pi$
$103$	3.58430	−	18.0195i	0.353171	−	1.77551i	0.593513	−	0.804824i	$-0.297740\pi$
$104$		0			0
$105$	−16.6469	+	3.31128i	−1.62457	+	0.323148i
$106$		0			0
$107$	−5.24919	+	9.82054i	−0.507458	+	0.949387i	0.489541	+	0.871980i	$0.337164\pi$
$107$	−5.24919	+	9.82054i	−0.507458	+	0.949387i	−0.997000	+	0.0774073i	$0.975336\pi$
$108$		0			0
$109$	−0.835148	−	8.47940i	−0.0799927	−	0.812179i	−0.948558	−	0.316604i	$-0.897457\pi$
$109$	−0.835148	−	8.47940i	−0.0799927	−	0.812179i	0.868565	−	0.495575i	$-0.165043\pi$
$110$		0			0
$111$	−7.01898	+	2.90736i	−0.666212	+	0.275954i
$112$		0			0
$113$	−3.62481	−	1.50145i	−0.340994	−	0.141244i	0.205614	−	0.978633i	$-0.434081\pi$
$113$	−3.62481	−	1.50145i	−0.340994	−	0.141244i	−0.546607	+	0.837389i	$0.684081\pi$
$114$		0			0
$115$	2.08718	+	1.71291i	0.194631	+	0.159729i
$116$		0			0
$117$	−4.43421	+	1.34510i	−0.409943	+	0.124355i
$118$		0			0
$119$	−0.353915	+	0.529672i	−0.0324434	+	0.0485549i
$120$		0			0
$121$	14.6960	−	9.81955i	1.33600	−	0.892686i
$122$		0			0
$123$	−7.43006	−	9.05356i	−0.669946	−	0.816332i
$124$		0			0
$125$	7.52225	−	4.02073i	0.672810	−	0.359625i
$126$		0			0
$127$	17.4733			1.55051			0.775254	−	0.631649i	$-0.217622\pi$
$127$	17.4733			1.55051			0.775254	+	0.631649i	$0.217622\pi$
$128$		0			0
$129$	30.0829			2.64865
$130$		0			0
$131$	−1.98551	+	1.06128i	−0.173475	+	0.0927243i	−0.555849	−	0.831283i	$-0.687607\pi$
$131$	−1.98551	+	1.06128i	−0.173475	+	0.0927243i	0.382374	+	0.924008i	$0.375107\pi$
$132$		0			0
$133$	7.07683	+	8.62314i	0.613639	+	0.747721i
$134$		0			0
$135$	−24.2443	+	16.1995i	−2.08662	+	1.39423i
$136$		0			0
$137$	−4.33193	+	6.48318i	−0.370101	+	0.553896i	−0.969041	−	0.246898i	$-0.920589\pi$
$137$	−4.33193	+	6.48318i	−0.370101	+	0.553896i	0.598940	+	0.800794i	$0.295589\pi$
$138$		0			0
$139$	−4.37497	+	1.32713i	−0.371080	+	0.112566i	−0.470316	−	0.882498i	$-0.655860\pi$
$139$	−4.37497	+	1.32713i	−0.371080	+	0.112566i	0.0992360	+	0.995064i	$0.468360\pi$
$140$		0			0
$141$	24.9117	+	20.4445i	2.09794	+	1.72173i
$142$		0			0
$143$	−3.45840	−	1.43252i	−0.289206	−	0.119793i
$144$		0			0
$145$	−2.93951	+	1.21759i	−0.244113	+	0.101115i
$146$		0			0
$147$	−0.772112	−	7.83939i	−0.0636827	−	0.646582i
$148$		0			0
$149$	1.62668	−	3.04330i	0.133263	−	0.249317i	−0.806435	−	0.591322i	$-0.798606\pi$
$149$	1.62668	−	3.04330i	0.133263	−	0.249317i	0.939698	+	0.342005i	$0.111106\pi$
$150$		0			0
$151$	−8.99371	+	1.78896i	−0.731897	+	0.145583i	−0.546950	−	0.837165i	$-0.684211\pi$
$151$	−8.99371	+	1.78896i	−0.731897	+	0.145583i	−0.184947	+	0.982748i	$0.559211\pi$
$152$		0			0
$153$	−0.390016	+	1.96074i	−0.0315309	+	0.158517i
$154$		0			0
$155$	−2.11951	+	21.5198i	−0.170243	+	1.72851i
$156$		0			0
$157$	−1.20802	+	3.98230i	−0.0964103	+	0.317822i	−0.991859	−	0.127343i	$-0.959355\pi$
$157$	−1.20802	+	3.98230i	−0.0964103	+	0.317822i	0.895448	+	0.445165i	$0.146855\pi$
$158$		0			0
$159$	4.56512	+	4.56512i	0.362037	+	0.362037i
$160$		0			0
$161$	1.55722	−	1.55722i	0.122726	−	0.122726i
$162$		0			0
$163$	−5.12150	−	1.55359i	−0.401147	−	0.121687i	0.0832631	−	0.996528i	$-0.473466\pi$
$163$	−5.12150	−	1.55359i	−0.401147	−	0.121687i	−0.484410	+	0.874841i	$0.660966\pi$
$164$		0			0
$165$	−42.8231	−	4.21771i	−3.33378	−	0.328348i
$166$		0			0
$167$	13.4931	+	2.68394i	1.04413	+	0.207689i	0.687219	−	0.726451i	$-0.258831\pi$
$167$	13.4931	+	2.68394i	1.04413	+	0.207689i	0.356907	+	0.934140i	$0.383831\pi$
$168$		0			0
$169$	−2.44084	−	12.2709i	−0.187757	−	0.943917i
$170$		0			0
$171$	30.8742	+	16.5026i	2.36101	+	1.26199i
$172$		0			0
$173$	−24.3620	+	2.39945i	−1.85221	+	0.182427i	−0.961986	−	0.273100i	$-0.911951\pi$
$173$	−24.3620	+	2.39945i	−1.85221	+	0.182427i	−0.890222	+	0.455526i	$0.849451\pi$
$174$		0			0
$175$	1.37927	+	3.32985i	0.104263	+	0.251713i
$176$		0			0
$177$	4.83993	−	11.6846i	0.363791	−	0.878270i
$178$		0			0
$179$	−1.72733	+	2.10476i	−0.129107	+	0.157317i	−0.833551	−	0.552442i	$-0.813696\pi$
$179$	−1.72733	+	2.10476i	−0.129107	+	0.157317i	0.704445	+	0.709759i	$0.251196\pi$
$180$		0			0
$181$	1.43312	+	4.72437i	0.106523	+	0.351160i	0.993956	−	0.109777i	$-0.0350136\pi$
$181$	1.43312	+	4.72437i	0.106523	+	0.351160i	−0.887433	+	0.460937i	$0.847514\pi$
$182$		0			0
$183$	−18.8387	−	12.5876i	−1.39260	−	0.930505i
$184$		0			0
$185$	3.52258	+	5.27191i	0.258985	+	0.387598i
$186$		0			0
$187$	−1.24842	+	1.02455i	−0.0912935	+	0.0749226i
$188$		0			0
$189$	11.2109	+	20.9741i	0.815473	+	1.52564i
$190$		0			0
$191$		−	9.05650i		−	0.655305i	−0.944798	−	0.327653i	$-0.893742\pi$
$191$		−	9.05650i		−	0.655305i	0.944798	−	0.327653i	$-0.106258\pi$
$192$		0			0
$193$			2.23638i			0.160978i	0.996755	+	0.0804891i	$0.0256482\pi$
$193$			2.23638i			0.160978i	−0.996755	+	0.0804891i	$0.974352\pi$
$194$		0			0
$195$	2.64802	+	4.95410i	0.189629	+	0.354771i
$196$		0			0
$197$	13.1308	−	10.7762i	0.935531	−	0.767770i	−0.0372960	−	0.999304i	$-0.511874\pi$
$197$	13.1308	−	10.7762i	0.935531	−	0.767770i	0.972827	+	0.231534i	$0.0743744\pi$
$198$		0			0
$199$	5.52315	+	8.26597i	0.391526	+	0.585959i	0.973905	−	0.226958i	$-0.0728780\pi$
$199$	5.52315	+	8.26597i	0.391526	+	0.585959i	−0.582379	+	0.812917i	$0.697878\pi$
$200$		0			0
$201$	−4.43345	−	2.96234i	−0.312712	−	0.208947i
$202$		0			0
$203$	0.753312	+	2.48334i	0.0528722	+	0.174296i
$204$		0			0
$205$	−6.20090	+	7.55582i	−0.433090	+	0.527722i
$206$		0			0
$207$	2.64479	−	6.38510i	0.183826	−	0.443795i
$208$		0			0
$209$	10.8227	+	26.1282i	0.748620	+	1.80733i
$210$		0			0
$211$	25.8095	−	2.54202i	1.77680	−	0.175000i	0.844230	−	0.535982i	$-0.180058\pi$
$211$	25.8095	−	2.54202i	1.77680	−	0.175000i	0.932573	+	0.360982i	$0.117558\pi$
$212$		0			0
$213$	−21.3828	−	11.4293i	−1.46512	−	0.783125i
$214$		0			0
$215$	−4.89799	−	24.6239i	−0.334040	−	1.67933i
$216$		0			0
$217$	17.2981	+	3.44081i	1.17427	+	0.233577i
$218$		0			0
$219$	−14.3278	−	1.41117i	−0.968183	−	0.0953577i
$220$		0			0
$221$	0.201753	+	0.0612012i	0.0135714	+	0.00411684i
$222$		0			0
$223$	−7.17173	+	7.17173i	−0.480255	+	0.480255i	−0.905213	−	0.424958i	$-0.860289\pi$
$223$	−7.17173	+	7.17173i	−0.480255	+	0.480255i	0.424958	+	0.905213i	$0.360289\pi$
$224$		0			0
$225$	7.99800	+	7.99800i	0.533200	+	0.533200i
$226$		0			0
$227$	1.19680	−	3.94531i	0.0794342	−	0.261859i	−0.908224	−	0.418484i	$-0.862561\pi$
$227$	1.19680	−	3.94531i	0.0794342	−	0.261859i	0.987658	+	0.156625i	$0.0500614\pi$
$228$		0			0
$229$	1.64560	−	16.7081i	0.108745	−	1.10410i	−0.773657	−	0.633605i	$-0.781574\pi$
$229$	1.64560	−	16.7081i	0.108745	−	1.10410i	0.882401	−	0.470498i	$-0.155926\pi$
$230$		0			0
$231$	−6.84702	+	34.4223i	−0.450501	+	2.26482i
$232$		0			0
$233$	−1.62572	+	0.323375i	−0.106504	+	0.0211850i	−0.248055	−	0.968746i	$-0.579791\pi$
$233$	−1.62572	+	0.323375i	−0.106504	+	0.0211850i	0.141550	+	0.989931i	$0.454791\pi$
$234$		0			0
$235$	12.6785	−	23.7197i	0.827051	−	1.54730i
$236$		0			0
$237$	0.706990	+	7.17819i	0.0459239	+	0.466274i
$238$		0			0
$239$	−19.6109	+	8.12312i	−1.26853	+	0.525441i	−0.912516	−	0.409041i	$-0.865863\pi$
$239$	−19.6109	+	8.12312i	−1.26853	+	0.525441i	−0.356010	+	0.934482i	$0.615863\pi$
$240$		0			0
$241$	−12.6243	−	5.22917i	−0.813205	−	0.336840i	−0.0629728	−	0.998015i	$-0.520058\pi$
$241$	−12.6243	−	5.22917i	−0.813205	−	0.336840i	−0.750232	+	0.661175i	$0.770058\pi$
$242$		0			0
$243$	9.99435	+	8.20215i	0.641138	+	0.526168i
$244$		0			0
$245$	−6.29109	+	1.90838i	−0.401923	+	0.121922i
$246$		0			0
$247$	2.05113	−	3.06974i	0.130511	−	0.195323i
$248$		0			0
$249$	15.8480	−	10.5893i	1.00432	−	0.671068i
$250$		0			0
$251$	−11.0077	−	13.4129i	−0.694800	−	0.846616i	0.299404	−	0.954126i	$-0.403212\pi$
$251$	−11.0077	−	13.4129i	−0.694800	−	0.846616i	−0.994204	+	0.107510i	$0.965712\pi$
$252$		0			0
$253$	4.92392	−	2.63189i	0.309564	−	0.165465i
$254$		0			0
$255$	2.42354			0.151768
$256$		0			0
$257$	−18.7308			−1.16840			−0.584198	−	0.811611i	$-0.698591\pi$
$257$	−18.7308			−1.16840			−0.584198	+	0.811611i	$0.698591\pi$
$258$		0			0
$259$	4.56081	−	2.43780i	0.283395	−	0.151478i
$260$		0			0
$261$	5.16649	+	6.29539i	0.319798	+	0.389675i
$262$		0			0
$263$	−7.70403	+	5.14767i	−0.475051	+	0.317419i	−0.769944	−	0.638111i	$-0.779716\pi$
$263$	−7.70403	+	5.14767i	−0.475051	+	0.317419i	0.294893	+	0.955530i	$0.404716\pi$
$264$		0			0
$265$	2.99343	−	4.47998i	0.183885	−	0.275203i
$266$		0			0
$267$	17.8896	−	5.42676i	1.09483	−	0.332112i
$268$		0			0
$269$	−14.8668	−	12.2009i	−0.906446	−	0.743901i	0.0606908	−	0.998157i	$-0.480670\pi$
$269$	−14.8668	−	12.2009i	−0.906446	−	0.743901i	−0.967137	+	0.254255i	$0.918170\pi$
$270$		0			0
$271$	8.81859	+	3.65278i	0.535691	+	0.221890i	0.634094	−	0.773256i	$-0.281373\pi$
$271$	8.81859	+	3.65278i	0.535691	+	0.221890i	−0.0984027	+	0.995147i	$0.531373\pi$
$272$		0			0
$273$	4.23293	−	1.75334i	0.256189	−	0.106117i
$274$		0			0
$275$	0.895626	+	9.09344i	0.0540083	+	0.548355i
$276$		0			0
$277$	−4.32889	+	8.09879i	−0.260098	+	0.486609i	−0.977745	−	0.209798i	$-0.932719\pi$
$277$	−4.32889	+	8.09879i	−0.260098	+	0.486609i	0.717647	+	0.696407i	$0.245219\pi$
$278$		0			0
$279$	54.2856	−	10.7981i	3.25000	−	0.646464i
$280$		0			0
$281$	1.79910	−	9.04470i	0.107325	−	0.539561i	−0.889289	−	0.457345i	$-0.848800\pi$
$281$	1.79910	−	9.04470i	0.107325	−	0.539561i	0.996615	−	0.0822159i	$-0.0261997\pi$
$282$		0			0
$283$	1.62016	−	16.4498i	0.0963087	−	0.977838i	−0.818651	−	0.574292i	$-0.805277\pi$
$283$	1.62016	−	16.4498i	0.0963087	−	0.977838i	0.914959	−	0.403546i	$-0.132223\pi$
$284$		0			0
$285$	12.3195	−	40.6121i	0.729747	−	2.40565i
$286$		0			0
$287$	5.63731	+	5.63731i	0.332760	+	0.332760i
$288$		0			0
$289$	−11.9565	+	11.9565i	−0.703323	+	0.703323i
$290$		0			0
$291$	−40.3690	−	12.2458i	−2.36647	−	0.717862i
$292$		0			0
$293$	7.93021	+	0.781057i	0.463288	+	0.0456299i	0.326969	−	0.945035i	$-0.393973\pi$
$293$	7.93021	+	0.781057i	0.463288	+	0.0456299i	0.136319	+	0.990665i	$0.456473\pi$
$294$		0			0
$295$	−10.3523	−	2.05920i	−0.602733	−	0.119891i
$296$		0			0
$297$	11.7626	+	59.1347i	0.682537	+	3.43134i
$298$		0			0
$299$	−0.642793	−	0.343580i	−0.0371737	−	0.0198697i
$300$		0			0
$301$	−20.3787	+	2.00713i	−1.17461	+	0.115689i
$302$		0			0
$303$	17.4797	+	42.1997i	1.00418	+	2.42431i
$304$		0			0
$305$	−7.23615	+	17.4696i	−0.414341	+	1.00031i
$306$		0			0
$307$	−13.9486	+	16.9964i	−0.796088	+	0.970036i	−0.999960	−	0.00896176i	$-0.997147\pi$
$307$	−13.9486	+	16.9964i	−0.796088	+	0.970036i	0.203872	+	0.978998i	$0.434647\pi$
$308$		0			0
$309$	16.5491	+	54.5550i	0.941444	+	3.10353i
$310$		0			0
$311$	1.80607	+	1.20678i	0.102413	+	0.0684302i	0.605722	−	0.795676i	$-0.292884\pi$
$311$	1.80607	+	1.20678i	0.102413	+	0.0684302i	−0.503309	+	0.864106i	$0.667884\pi$
$312$		0			0
$313$	15.7480	+	23.5686i	0.890131	+	1.33218i	0.942729	+	0.333560i	$0.108250\pi$
$313$	15.7480	+	23.5686i	0.890131	+	1.33218i	−0.0525977	+	0.998616i	$0.516750\pi$
$314$		0			0
$315$	28.0276	−	23.0016i	1.57917	−	1.29599i
$316$		0			0
$317$	−11.7237	−	21.9336i	−0.658471	−	1.23191i	−0.960411	−	0.278586i	$-0.910134\pi$
$317$	−11.7237	−	21.9336i	−0.658471	−	1.23191i	0.301940	−	0.953327i	$-0.402366\pi$
$318$		0			0
$319$			6.57909i			0.368358i
$320$		0			0
$321$		−	34.5531i		−	1.92857i
$322$		0			0
$323$	−0.750857	−	1.40475i	−0.0417788	−	0.0781627i
$324$		0			0
$325$	0.922084	−	0.756735i	0.0511480	−	0.0419761i
$326$		0			0
$327$	14.6886	+	21.9831i	0.812284	+	1.21567i
$328$		0			0
$329$	−18.2397	−	12.1874i	−1.00559	−	0.671911i
$330$		0			0
$331$	−8.50861	−	28.0491i	−0.467675	−	1.54172i	−0.800856	−	0.598856i	$-0.795622\pi$
$331$	−8.50861	−	28.0491i	−0.467675	−	1.54172i	0.333181	−	0.942863i	$-0.391878\pi$
$332$		0			0
$333$	10.2957	−	12.5454i	0.564203	−	0.687483i
$334$		0			0
$335$	−1.70293	+	4.11125i	−0.0930413	+	0.224621i
$336$		0			0
$337$	−6.29152	−	15.1891i	−0.342721	−	0.827402i	−0.997439	−	0.0715281i	$-0.977212\pi$
$337$	−6.29152	−	15.1891i	−0.342721	−	0.827402i	0.654718	−	0.755874i	$-0.272788\pi$
$338$		0			0
$339$	12.1159	−	1.19331i	0.658045	−	0.0648118i
$340$		0			0
$341$	39.4339	+	21.0778i	2.13546	+	1.14143i
$342$		0			0
$343$	3.93057	+	19.7603i	0.212231	+	1.06696i
$344$		0			0
$345$	−8.21732	−	1.63453i	−0.442406	−	0.0880000i
$346$		0			0
$347$	−21.2570	−	2.09363i	−1.14113	−	0.112392i	−0.490258	−	0.871577i	$-0.663098\pi$
$347$	−21.2570	−	2.09363i	−1.14113	−	0.112392i	−0.650875	+	0.759185i	$0.725598\pi$
$348$		0			0
$349$	1.83902	+	0.557861i	0.0984406	+	0.0298616i	0.339121	−	0.940743i	$-0.389870\pi$
$349$	1.83902	+	0.557861i	0.0984406	+	0.0298616i	−0.240680	+	0.970604i	$0.577370\pi$
$350$		0			0
$351$	5.56563	−	5.56563i	0.297071	−	0.297071i
$352$		0			0
$353$	−17.4349	−	17.4349i	−0.927965	−	0.927965i	0.0696094	−	0.997574i	$-0.477825\pi$
$353$	−17.4349	−	17.4349i	−0.927965	−	0.927965i	−0.997574	+	0.0696094i	$0.977825\pi$
$354$		0			0
$355$	−5.87382	+	19.3634i	−0.311750	+	1.02770i
$356$		0			0
$357$	0.193751	−	1.96719i	0.0102544	−	0.104115i
$358$		0			0
$359$	6.74207	−	33.8947i	0.355833	−	1.78889i	−0.224458	−	0.974484i	$-0.572061\pi$
$359$	6.74207	−	33.8947i	0.355833	−	1.78889i	0.580291	−	0.814409i	$-0.302939\pi$
$360$		0			0
$361$	−8.72181	+	1.73488i	−0.459043	+	0.0913092i
$362$		0			0
$363$	−25.8536	+	48.3686i	−1.35696	+	2.53869i
$364$		0			0
$365$	1.17772	+	11.9576i	0.0616445	+	0.625887i
$366$		0			0
$367$	15.0403	−	6.22992i	0.785100	−	0.325199i	0.0461281	−	0.998936i	$-0.485312\pi$
$367$	15.0403	−	6.22992i	0.785100	−	0.325199i	0.738972	+	0.673737i	$0.235312\pi$
$368$		0			0
$369$	23.1147	+	9.57444i	1.20331	+	0.498425i
$370$		0			0
$371$	−3.39708	−	2.78791i	−0.176368	−	0.144741i
$372$		0			0
$373$	27.2585	−	8.26878i	1.41139	−	0.428141i	0.509638	−	0.860389i	$-0.329779\pi$
$373$	27.2585	−	8.26878i	1.41139	−	0.428141i	0.901755	+	0.432247i	$0.142279\pi$
$374$		0			0
$375$	−14.7041	+	22.0062i	−0.759316	+	1.13640i
$376$		0			0
$377$	0.714122	−	0.477161i	0.0367792	−	0.0245751i
$378$		0			0
$379$	10.3343	+	12.5924i	0.530840	+	0.646830i	0.967522	−	0.252786i	$-0.0813467\pi$
$379$	10.3343	+	12.5924i	0.530840	+	0.646830i	−0.436683	+	0.899616i	$0.643847\pi$
$380$		0			0
$381$	−47.8175	+	25.5590i	−2.44977	+	1.30943i
$382$		0			0
$383$	−22.2235			−1.13557			−0.567784	−	0.823177i	$-0.692199\pi$
$383$	−22.2235			−1.13557			−0.567784	+	0.823177i	$0.692199\pi$
$384$		0			0
$385$	29.2906			1.49279
$386$		0			0
$387$	−56.6747	+	30.2933i	−2.88094	+	1.53989i
$388$		0			0
$389$	−8.68522	−	10.5830i	−0.440358	−	0.536578i	0.504780	−	0.863248i	$-0.331574\pi$
$389$	−8.68522	−	10.5830i	−0.440358	−	0.536578i	−0.945139	+	0.326670i	$0.894074\pi$
$390$		0			0
$391$	−0.261459	+	0.174701i	−0.0132225	+	0.00883502i
$392$		0			0
$393$	3.88117	−	5.80859i	0.195779	−	0.293004i
$394$		0			0
$395$	5.76048	−	1.74742i	0.289841	−	0.0879224i
$396$		0			0
$397$	3.79912	+	3.11786i	0.190672	+	0.156481i	0.724886	−	0.688869i	$-0.241892\pi$
$397$	3.79912	+	3.11786i	0.190672	+	0.156481i	−0.534214	+	0.845349i	$0.679392\pi$
$398$		0			0
$399$	−31.9799	−	13.2465i	−1.60100	−	0.663154i
$400$		0			0
$401$	−19.8407	+	8.21829i	−0.990798	+	0.410402i	−0.818415	−	0.574628i	$-0.805147\pi$
$401$	−19.8407	+	8.21829i	−0.990798	+	0.410402i	−0.172383	+	0.985030i	$0.555147\pi$
$402$		0			0
$403$	−0.572139	−	5.80903i	−0.0285003	−	0.289368i
$404$		0			0
$405$	18.3754	−	34.3780i	0.913081	−	1.70826i
$406$		0			0
$407$	12.8588	−	2.55778i	0.637388	−	0.126784i
$408$		0			0
$409$	−1.76659	+	8.88124i	−0.0873522	+	0.439149i	0.912214	+	0.409713i	$0.134371\pi$
$409$	−1.76659	+	8.88124i	−0.0873522	+	0.439149i	−0.999567	+	0.0294361i	$0.990629\pi$
$410$		0			0
$411$	2.37151	−	24.0784i	0.116978	−	1.18770i
$412$		0			0
$413$	−2.49906	+	8.23830i	−0.122971	+	0.405380i
$414$		0			0
$415$	−11.2480	−	11.2480i	−0.552142	−	0.552142i
$416$		0			0
$417$	10.0313	−	10.0313i	0.491234	−	0.491234i
$418$		0			0
$419$	27.9730	+	8.48552i	1.36657	+	0.414545i	0.886518	−	0.462695i	$-0.153117\pi$
$419$	27.9730	+	8.48552i	1.36657	+	0.414545i	0.480053	+	0.877239i	$0.340617\pi$
$420$		0			0
$421$	5.97709	+	0.588692i	0.291306	+	0.0286911i	0.242614	−	0.970123i	$-0.421995\pi$
$421$	5.97709	+	0.588692i	0.291306	+	0.0286911i	0.0486912	+	0.998814i	$0.484495\pi$
$422$		0			0
$423$	−67.5198	−	13.4305i	−3.28292	−	0.653014i
$424$		0			0
$425$	−0.100401	−	0.504748i	−0.00487015	−	0.0244839i
$426$		0			0
$427$	13.6015	+	7.27018i	0.658225	+	0.351829i
$428$		0			0
$429$	11.5596	−	1.13853i	0.558105	−	0.0549685i
$430$		0			0
$431$	−13.3953	−	32.3391i	−0.645228	−	1.55772i	−0.819536	−	0.573028i	$-0.805769\pi$
$431$	−13.3953	−	32.3391i	−0.645228	−	1.55772i	0.174307	−	0.984691i	$-0.444231\pi$
$432$		0			0
$433$	−1.75476	+	4.23636i	−0.0843282	+	0.203586i	−0.960419	−	0.278560i	$-0.910143\pi$
$433$	−1.75476	+	4.23636i	−0.0843282	+	0.203586i	0.876090	+	0.482147i	$0.160143\pi$
$434$		0			0
$435$	6.26326	−	7.63180i	0.300300	−	0.365917i
$436$		0			0
$437$	1.59846	+	5.26940i	0.0764645	+	0.252070i
$438$		0			0
$439$	−14.8312	−	9.90986i	−0.707853	−	0.472972i	0.148799	−	0.988867i	$-0.452459\pi$
$439$	−14.8312	−	9.90986i	−0.707853	−	0.472972i	−0.856652	+	0.515896i	$0.827459\pi$
$440$		0			0
$441$	9.34883	+	13.9915i	0.445182	+	0.666262i
$442$		0			0
$443$	14.7609	−	12.1139i	0.701310	−	0.575550i	−0.214713	−	0.976677i	$-0.568881\pi$
$443$	14.7609	−	12.1139i	0.701310	−	0.575550i	0.916022	+	0.401127i	$0.131381\pi$
$444$		0			0
$445$	−7.35472	−	13.7597i	−0.348647	−	0.652273i
$446$		0			0
$447$			10.7077i			0.506458i
$448$		0			0
$449$			17.5534i			0.828396i	0.910187	+	0.414198i	$0.135938\pi$
$449$			17.5534i			0.828396i	−0.910187	+	0.414198i	$0.864062\pi$
$450$		0			0
$451$	9.52771	+	17.8251i	0.448642	+	0.839351i
$452$		0			0
$453$	21.9954	−	18.0511i	1.03343	−	0.848117i
$454$		0			0
$455$	−2.12436	−	3.17933i	−0.0995914	−	0.149049i
$456$		0			0
$457$	−7.57863	−	5.06388i	−0.354514	−	0.236878i	0.365542	−	0.930795i	$-0.380884\pi$
$457$	−7.57863	−	5.06388i	−0.354514	−	0.236878i	−0.720055	+	0.693916i	$0.755884\pi$
$458$		0			0
$459$	−0.985755	−	3.24960i	−0.0460111	−	0.151678i
$460$		0			0
$461$	15.3442	−	18.6970i	0.714652	−	0.870806i	−0.281399	−	0.959591i	$-0.590798\pi$
$461$	15.3442	−	18.6970i	0.714652	−	0.870806i	0.996051	+	0.0887853i	$0.0282985\pi$
$462$		0			0
$463$	6.62310	−	15.9896i	0.307801	−	0.743098i	−0.691974	−	0.721922i	$-0.743259\pi$
$463$	6.62310	−	15.9896i	0.307801	−	0.743098i	0.999776	−	0.0211762i	$-0.00674109\pi$
$464$		0			0
$465$	−25.6776	−	61.9913i	−1.19077	−	2.87478i
$466$		0			0
$467$	−5.73074	+	0.564429i	−0.265187	+	0.0261187i	−0.229737	−	0.973253i	$-0.573787\pi$
$467$	−5.73074	+	0.564429i	−0.265187	+	0.0261187i	−0.0354503	+	0.999371i	$0.511287\pi$
$468$		0			0
$469$	3.20095	+	1.71094i	0.147806	+	0.0790040i
$470$		0			0
$471$	−2.51922	−	12.6650i	−0.116080	−	0.583571i
$472$		0			0
$473$	−50.9169	−	10.1280i	−2.34116	−	0.465686i
$474$		0			0
$475$	−8.96858	−	0.883328i	−0.411507	−	0.0405299i
$476$		0			0
$477$	−13.1975	−	4.00342i	−0.604272	−	0.183304i
$478$		0			0
$479$	6.43746	−	6.43746i	0.294135	−	0.294135i	−0.544576	−	0.838711i	$-0.683310\pi$
$479$	6.43746	−	6.43746i	0.294135	−	0.294135i	0.838711	+	0.544576i	$0.183310\pi$
$480$		0			0
$481$	−1.21024	−	1.21024i	−0.0551823	−	0.0551823i
$482$		0			0
$483$	−1.98368	+	6.53931i	−0.0902605	+	0.297549i
$484$		0			0
$485$	−3.45086	+	35.0372i	−0.156696	+	1.59096i
$486$		0			0
$487$	−0.941291	+	4.73219i	−0.0426540	+	0.214436i	−0.996234	−	0.0867031i	$-0.972367\pi$
$487$	−0.941291	+	4.73219i	−0.0426540	+	0.214436i	0.953580	+	0.301139i	$0.0973668\pi$
$488$		0			0
$489$	16.2880	−	3.23989i	0.736569	−	0.146513i
$490$		0			0
$491$	14.9500	−	27.9695i	0.674683	−	1.26224i	−0.278670	−	0.960387i	$-0.589894\pi$
$491$	14.9500	−	27.9695i	0.674683	−	1.26224i	0.953353	−	0.301857i	$-0.0976065\pi$
$492$		0			0
$493$	−0.0363198	−	0.368761i	−0.00163576	−	0.0166082i
$494$		0			0
$495$	84.9239	−	35.1766i	3.81705	−	1.58107i
$496$		0			0
$497$	15.2476	+	6.31578i	0.683951	+	0.283302i
$498$		0			0
$499$	−9.04864	−	7.42603i	−0.405073	−	0.332435i	0.409694	−	0.912223i	$-0.365635\pi$
$499$	−9.04864	−	7.42603i	−0.405073	−	0.332435i	−0.814767	+	0.579788i	$0.803135\pi$
$500$		0			0
$501$	−40.8510	+	12.3920i	−1.82509	+	0.553635i
$502$		0			0
$503$	14.1510	−	21.1785i	0.630963	−	0.944303i	−0.368927	−	0.929459i	$-0.620275\pi$
$503$	14.1510	−	21.1785i	0.630963	−	0.944303i	0.999890	−	0.0148447i	$-0.00472539\pi$
$504$		0			0
$505$	31.6959	−	21.1785i	1.41045	−	0.942433i
$506$		0			0
$507$	24.6288	+	30.0103i	1.09380	+	1.33280i
$508$		0			0
$509$	11.1824	−	5.97713i	0.495652	−	0.264931i	−0.204576	−	0.978851i	$-0.565582\pi$
$509$	11.1824	−	5.97713i	0.495652	−	0.264931i	0.700228	+	0.713919i	$0.253082\pi$
$510$		0			0
$511$	9.80007			0.433530
$512$		0			0
$513$	−59.4654			−2.62546
$514$		0			0
$515$	41.9606	−	22.4284i	1.84901	−	0.988315i
$516$		0			0
$517$	−35.2813	−	42.9903i	−1.55167	−	1.89071i
$518$		0			0
$519$	63.1592	−	42.2016i	2.77238	−	1.85245i
$520$		0			0
$521$	15.1820	−	22.7214i	0.665134	−	0.995443i	−0.333477	−	0.942758i	$-0.608222\pi$
$521$	15.1820	−	22.7214i	0.665134	−	0.995443i	0.998611	−	0.0526849i	$-0.0167779\pi$
$522$		0			0
$523$	−18.4732	+	5.60379i	−0.807777	+	0.245036i	−0.667051	−	0.745012i	$-0.732444\pi$
$523$	−18.4732	+	5.60379i	−0.807777	+	0.245036i	−0.140726	+	0.990049i	$0.544944\pi$
$524$		0			0
$525$	−8.64523	−	7.09496i	−0.377309	−	0.309649i
$526$		0			0
$527$	−2.32665	−	0.963730i	−0.101350	−	0.0419807i
$528$		0			0
$529$	−20.2449	+	8.38571i	−0.880213	+	0.364596i
$530$		0			0
$531$	2.64814	+	26.8870i	0.114920	+	1.16680i
$532$		0			0
$533$	1.24380	−	2.32698i	0.0538748	−	0.100793i
$534$		0			0
$535$	−28.2829	+	5.62581i	−1.22278	+	0.243225i
$536$		0			0
$537$	1.64829	−	8.28651i	0.0711290	−	0.357589i
$538$		0			0
$539$	−1.33244	+	13.5285i	−0.0573924	+	0.582715i
$540$		0			0
$541$	−10.7233	+	35.3499i	−0.461029	+	1.51981i	0.351104	+	0.936336i	$0.385806\pi$
$541$	−10.7233	+	35.3499i	−0.461029	+	1.51981i	−0.812133	+	0.583472i	$0.801694\pi$
$542$		0			0
$543$	−10.8324	−	10.8324i	−0.464864	−	0.464864i
$544$		0			0
$545$	15.6024	−	15.6024i	0.668332	−	0.668332i
$546$		0			0
$547$	13.5385	+	4.10687i	0.578866	+	0.175597i	0.566122	−	0.824322i	$-0.308443\pi$
$547$	13.5385	+	4.10687i	0.578866	+	0.175597i	0.0127444	+	0.999919i	$0.495943\pi$
$548$		0			0
$549$	48.1669	+	4.74402i	2.05571	+	0.202470i
$550$		0			0
$551$	−6.36407	−	1.26589i	−0.271119	−	0.0539289i
$552$		0			0
$553$	−0.957856	−	4.81547i	−0.0407322	−	0.204775i
$554$		0			0
$555$	−17.3513	−	9.27448i	−0.736523	−	0.393680i
$556$		0			0
$557$	−0.613564	+	0.0604308i	−0.0259975	+	0.00256053i	−0.111008	−	0.993820i	$-0.535408\pi$
$557$	−0.613564	+	0.0604308i	−0.0259975	+	0.00256053i	0.0850100	+	0.996380i	$0.472908\pi$
$558$		0			0
$559$	2.59351	+	6.26129i	0.109694	+	0.264824i
$560$		0			0
$561$	1.91777	−	4.62990i	0.0809683	−	0.195475i
$562$		0			0
$563$	−14.3760	+	17.5173i	−0.605878	+	0.738265i	−0.982120	−	0.188257i	$-0.939716\pi$
$563$	−14.3760	+	17.5173i	−0.605878	+	0.738265i	0.376242	+	0.926522i	$0.377216\pi$
$564$		0			0
$565$	−2.94943	−	9.72298i	−0.124084	−	0.409049i
$566$		0			0
$567$	−26.4355	−	17.6636i	−1.11019	−	0.741803i
$568$		0			0
$569$	9.17842	+	13.7365i	0.384780	+	0.575863i	0.972414	−	0.233264i	$-0.0749405\pi$
$569$	9.17842	+	13.7365i	0.384780	+	0.575863i	−0.587634	+	0.809127i	$0.699941\pi$
$570$		0			0
$571$	−25.0731	+	20.5770i	−1.04928	+	0.861120i	−0.990550	−	0.137154i	$-0.956204\pi$
$571$	−25.0731	+	20.5770i	−1.04928	+	0.861120i	−0.0587279	+	0.998274i	$0.518704\pi$
$572$		0			0
$573$	13.2473	+	24.7840i	0.553415	+	1.03537i
$574$		0			0
$575$			1.77912i			0.0741946i
$576$		0			0
$577$		−	43.7581i		−	1.82168i	−0.412765	−	0.910838i	$-0.635437\pi$
$577$		−	43.7581i		−	1.82168i	0.412765	−	0.910838i	$-0.364563\pi$
$578$		0			0
$579$	−3.27125	−	6.12008i	−0.135948	−	0.254342i
$580$		0			0
$581$	−10.0292	+	8.23075i	−0.416081	+	0.341469i
$582$		0			0
$583$	−6.18977	−	9.26364i	−0.256354	−	0.383661i
$584$		0			0
$585$	−9.97749	−	6.66675i	−0.412519	−	0.275636i
$586$		0			0
$587$	−2.05366	−	6.77000i	−0.0847634	−	0.279428i	0.904305	−	0.426888i	$-0.140390\pi$
$587$	−2.05366	−	6.77000i	−0.0847634	−	0.279428i	−0.989068	+	0.147460i	$0.952890\pi$
$588$		0			0
$589$	−27.9765	+	34.0895i	−1.15275	+	1.40463i
$590$		0			0
$591$	−20.1710	+	48.6970i	−0.829723	+	2.00313i
$592$		0			0
$593$	2.16497	+	5.22670i	0.0889046	+	0.214635i	0.962078	−	0.272775i	$-0.0879416\pi$
$593$	2.16497	+	5.22670i	0.0889046	+	0.214635i	−0.873173	+	0.487410i	$0.837942\pi$
$594$		0			0
$595$	−1.64175	+	0.161699i	−0.0673054	+	0.00662900i
$596$		0			0
$597$	−27.2056	−	14.5417i	−1.11345	−	0.595153i
$598$		0			0
$599$	−1.45339	−	7.30670i	−0.0593840	−	0.298544i	0.939667	−	0.342089i	$-0.111135\pi$
$599$	−1.45339	−	7.30670i	−0.0593840	−	0.298544i	−0.999051	+	0.0435457i	$0.986135\pi$
$600$		0			0
$601$	−23.9713	−	4.76820i	−0.977812	−	0.194499i	−0.319782	−	0.947491i	$-0.603610\pi$
$601$	−23.9713	−	4.76820i	−0.977812	−	0.194499i	−0.658029	+	0.752992i	$0.728610\pi$
$602$		0			0
$603$	11.3355	+	1.11645i	0.461616	+	0.0454652i
$604$		0			0
$605$	43.8007	+	13.2868i	1.78075	+	0.540185i
$606$		0			0
$607$	−15.4335	+	15.4335i	−0.626428	+	0.626428i	−0.947167	−	0.320740i	$-0.896069\pi$
$607$	−15.4335	+	15.4335i	−0.626428	+	0.626428i	0.320740	+	0.947167i	$0.396069\pi$
$608$		0			0
$609$	−5.69400	−	5.69400i	−0.230732	−	0.230732i
$610$		0			0
$611$	−2.10751	+	6.94753i	−0.0852608	+	0.281067i
$612$		0			0
$613$	−2.54267	+	25.8161i	−0.102697	+	1.04270i	0.796345	+	0.604843i	$0.206764\pi$
$613$	−2.54267	+	25.8161i	−0.102697	+	1.04270i	−0.899042	+	0.437862i	$0.855736\pi$
$614$		0			0
$615$	5.91716	−	29.7476i	0.238603	−	1.19954i
$616$		0			0
$617$	14.5314	−	2.89047i	0.585011	−	0.116366i	0.106293	−	0.994335i	$-0.466102\pi$
$617$	14.5314	−	2.89047i	0.585011	−	0.116366i	0.478718	+	0.877969i	$0.341102\pi$
$618$		0			0
$619$	20.0427	−	37.4972i	0.805582	−	1.50714i	−0.0553773	−	0.998466i	$-0.517636\pi$
$619$	20.0427	−	37.4972i	0.805582	−	1.50714i	0.860960	−	0.508673i	$-0.169864\pi$
$620$		0			0
$621$	1.15067	+	11.6830i	0.0461750	+	0.468822i
$622$		0			0
$623$	−11.7567	+	4.86979i	−0.471022	+	0.195104i
$624$		0			0
$625$	28.2893	+	11.7178i	1.13157	+	0.468713i
$626$		0			0
$627$	−67.8362	−	55.6717i	−2.70912	−	2.22331i
$628$		0			0
$629$	−0.706623	+	0.214352i	−0.0281749	+	0.00854677i
$630$		0			0
$631$	−14.4570	+	21.6365i	−0.575525	+	0.861335i	−0.999006	−	0.0445704i	$-0.985808\pi$
$631$	−14.4570	+	21.6365i	−0.575525	+	0.861335i	0.423481	+	0.905905i	$0.360808\pi$
$632$		0			0
$633$	−66.9121	+	44.7092i	−2.65952	+	1.77703i
$634$		0			0
$635$	28.7064	+	34.9788i	1.13918	+	1.38809i
$636$		0			0
$637$	1.56508	−	0.836553i	0.0620108	−	0.0331455i
$638$		0			0
$639$	51.7933			2.04891
$640$		0			0
$641$	33.9931			1.34265			0.671323	−	0.741165i	$-0.265726\pi$
$641$	33.9931			1.34265			0.671323	+	0.741165i	$0.265726\pi$
$642$		0			0
$643$	7.68829	−	4.10948i	0.303197	−	0.162062i	−0.312782	−	0.949825i	$-0.601261\pi$
$643$	7.68829	−	4.10948i	0.303197	−	0.162062i	0.615978	+	0.787763i	$0.288761\pi$
$644$		0			0
$645$	49.4222	+	60.2212i	1.94600	+	2.37121i
$646$		0			0
$647$	−22.3267	+	14.9182i	−0.877753	+	0.586496i	−0.910749	−	0.412959i	$-0.864495\pi$
$647$	−22.3267	+	14.9182i	−0.877753	+	0.586496i	0.0329961	+	0.999455i	$0.489495\pi$
$648$		0			0
$649$	−12.1257	+	18.1474i	−0.475975	+	0.712347i
$650$		0			0
$651$	−52.3710	+	15.8866i	−2.05258	+	0.622644i
$652$		0			0
$653$	−5.58967	−	4.58733i	−0.218741	−	0.179516i	0.518641	−	0.854992i	$-0.326438\pi$
$653$	−5.58967	−	4.58733i	−0.218741	−	0.179516i	−0.737382	+	0.675476i	$0.763938\pi$
$654$		0			0
$655$	−5.38644	−	2.23114i	−0.210466	−	0.0871778i
$656$		0			0
$657$	28.4139	−	11.7694i	1.10853	−	0.459169i
$658$		0			0
$659$	3.69383	+	37.5041i	0.143891	+	1.46095i	0.747813	+	0.663909i	$0.231104\pi$
$659$	3.69383	+	37.5041i	0.143891	+	1.46095i	−0.603922	+	0.797043i	$0.706396\pi$
$660$		0			0
$661$	21.7875	−	40.7616i	0.847437	−	1.58544i	0.0372245	−	0.999307i	$-0.488148\pi$
$661$	21.7875	−	40.7616i	0.847437	−	1.58544i	0.810213	−	0.586136i	$-0.199352\pi$
$662$		0			0
$663$	−0.641639	+	0.127630i	−0.0249192	+	0.00495674i
$664$		0			0
$665$	−5.63585	+	28.3333i	−0.218549	+	1.09872i
$666$		0			0
$667$	−0.125559	+	1.27483i	−0.00486168	+	0.0493615i
$668$		0			0
$669$	9.13575	−	30.1165i	0.353209	−	1.16437i
$670$		0			0
$671$	27.6477	+	27.6477i	1.06733	+	1.06733i
$672$		0			0
$673$	−5.92084	+	5.92084i	−0.228232	+	0.228232i	−0.811954	−	0.583722i	$-0.801596\pi$
$673$	−5.92084	+	5.92084i	−0.228232	+	0.228232i	0.583722	+	0.811954i	$0.301596\pi$
$674$		0			0
$675$	−18.3857	−	5.57723i	−0.707664	−	0.214668i
$676$		0			0
$677$	−40.7980	−	4.01825i	−1.56799	−	0.154434i	−0.723624	−	0.690194i	$-0.757525\pi$
$677$	−40.7980	−	4.01825i	−1.56799	−	0.154434i	−0.844370	+	0.535760i	$0.820025\pi$
$678$		0			0
$679$	28.1638	+	5.60212i	1.08083	+	0.214990i
$680$		0			0
$681$	2.49582	+	12.5473i	0.0956400	+	0.480815i
$682$		0			0
$683$	43.9241	+	23.4779i	1.68071	+	0.898358i	0.983369	+	0.181617i	$0.0581330\pi$
$683$	43.9241	+	23.4779i	1.68071	+	0.898358i	0.697339	+	0.716741i	$0.254367\pi$
$684$		0			0
$685$	−20.0951	+	1.97919i	−0.767793	+	0.0756210i
$686$		0			0
$687$	19.9363	+	48.1305i	0.760617	+	1.83629i
$688$		0			0
$689$	−0.556590	+	1.34373i	−0.0212044	+	0.0511919i
$690$		0			0
$691$	−2.15330	+	2.62381i	−0.0819155	+	0.0998143i	−0.812355	−	0.583163i	$-0.801815\pi$
$691$	−2.15330	+	2.62381i	−0.0819155	+	0.0998143i	0.730440	+	0.682977i	$0.239315\pi$
$692$		0			0
$693$	−21.7635	−	71.7448i	−0.826729	−	2.72536i
$694$		0			0
$695$	−9.84421	−	6.57769i	−0.373412	−	0.249506i
$696$		0			0
$697$	−0.632437	−	0.946508i	−0.0239552	−	0.0358516i
$698$		0			0
$699$	3.97592	−	3.26295i	0.150383	−	0.123416i
$700$		0			0
$701$	17.0945	+	31.9815i	0.645650	+	1.20793i	0.965487	+	0.260453i	$0.0838719\pi$
$701$	17.0945	+	31.9815i	0.645650	+	1.20793i	−0.319837	+	0.947473i	$0.603628\pi$
$702$		0			0
$703$			12.9307i			0.487691i
$704$		0			0
$705$			83.4567i			3.14316i
$706$		0			0
$707$	−14.6566	−	27.4206i	−0.551220	−	1.03126i
$708$		0			0
$709$	34.5715	−	28.3721i	1.29836	−	1.06554i	0.304780	−	0.952423i	$-0.401417\pi$
$709$	34.5715	−	28.3721i	1.29836	−	1.06554i	0.993582	−	0.113115i	$-0.0360829\pi$
$710$		0			0
$711$	−8.56032	−	12.8114i	−0.321037	−	0.480466i
$712$		0			0
$713$	7.23882	+	4.83682i	0.271096	+	0.181140i
$714$		0			0
$715$	−2.81402	−	9.27659i	−0.105238	−	0.346925i
$716$		0			0
$717$	41.7852	−	50.9155i	1.56050	−	1.90147i
$718$		0			0
$719$	−0.233522	+	0.563773i	−0.00870891	+	0.0210252i	−0.928174	−	0.372146i	$-0.878622\pi$
$719$	−0.233522	+	0.563773i	−0.00870891	+	0.0210252i	0.919465	+	0.393171i	$0.128622\pi$
$720$		0			0
$721$	−14.8506	−	35.8524i	−0.553064	−	1.33521i
$722$		0			0
$723$	42.1967	−	4.15601i	1.56931	−	0.154564i
$724$		0			0
$725$	−1.84893	−	0.988275i	−0.0686676	−	0.0367036i
$726$		0			0
$727$	6.22143	+	31.2772i	0.230740	+	1.16001i	0.906278	+	0.422683i	$0.138912\pi$
$727$	6.22143	+	31.2772i	0.230740	+	1.16001i	−0.675538	+	0.737325i	$0.736088\pi$
$728$		0			0
$729$	4.94143	+	0.982912i	0.183016	+	0.0364041i
$730$		0			0
$731$	2.90983	+	0.286593i	0.107624	+	0.0106000i
$732$		0			0
$733$	10.3027	+	3.12528i	0.380538	+	0.115435i	0.474758	−	0.880116i	$-0.342536\pi$
$733$	10.3027	+	3.12528i	0.380538	+	0.115435i	−0.0942197	+	0.995551i	$0.530036\pi$
$734$		0			0
$735$	14.4247	−	14.4247i	0.532064	−	0.532064i
$736$		0			0
$737$	6.50652	+	6.50652i	0.239671	+	0.239671i
$738$		0			0
$739$	−9.34596	+	30.8095i	−0.343797	+	1.13335i	0.599216	+	0.800588i	$0.295479\pi$
$739$	−9.34596	+	30.8095i	−0.343797	+	1.13335i	−0.943012	+	0.332758i	$0.892021\pi$
$740$		0			0
$741$	−1.12289	+	11.4009i	−0.0412505	+	0.418823i
$742$		0			0
$743$	−0.781208	+	3.92740i	−0.0286597	+	0.144082i	−0.992466	−	0.122522i	$-0.960902\pi$
$743$	−0.781208	+	3.92740i	−0.0286597	+	0.144082i	0.963806	+	0.266604i	$0.0859017\pi$
$744$		0			0
$745$	8.76463	−	1.74339i	0.321111	−	0.0638730i
$746$		0			0
$747$	−19.1935	+	35.9085i	−0.702252	+	1.31382i
$748$		0			0
$749$	2.30538	+	23.4069i	0.0842367	+	0.855270i
$750$		0			0
$751$	−20.4012	+	8.45044i	−0.744449	+	0.308361i	−0.722474	−	0.691398i	$-0.756995\pi$
$751$	−20.4012	+	8.45044i	−0.744449	+	0.308361i	−0.0219745	+	0.999759i	$0.506995\pi$
$752$		0			0
$753$	49.7433	+	20.6044i	1.81275	+	0.750864i
$754$		0			0
$755$	−18.3567	−	15.0649i	−0.668068	−	0.548269i
$756$		0			0
$757$	−34.9543	+	10.6033i	−1.27044	+	0.385383i	−0.852325	−	0.523013i	$-0.824808\pi$
$757$	−34.9543	+	10.6033i	−1.27044	+	0.385383i	−0.418112	+	0.908396i	$0.637308\pi$
$758$		0			0
$759$	−9.62501	+	14.4048i	−0.349366	+	0.522863i
$760$		0			0
$761$	−34.3626	+	22.9604i	−1.24564	+	0.832313i	−0.990888	−	0.134692i	$-0.956996\pi$
$761$	−34.3626	+	22.9604i	−1.24564	+	0.832313i	−0.254757	+	0.967005i	$0.581996\pi$
$762$		0			0
$763$	−11.4171	−	13.9117i	−0.413326	−	0.503639i
$764$		0			0
$765$	−4.56584	+	2.44049i	−0.165078	+	0.0882362i
$766$		0			0
$767$	2.84923			0.102880
$768$		0			0
$769$	−10.7200			−0.386572			−0.193286	−	0.981142i	$-0.561914\pi$
$769$	−10.7200			−0.386572			−0.193286	+	0.981142i	$0.561914\pi$
$770$		0			0
$771$	51.2587	−	27.3984i	1.84604	−	0.986728i
$772$		0			0
$773$	28.1934	+	34.3538i	1.01405	+	1.23562i	0.971627	+	0.236520i	$0.0760068\pi$
$773$	28.1934	+	34.3538i	1.01405	+	1.23562i	0.0424202	+	0.999100i	$0.486493\pi$
$774$		0			0
$775$	−11.8471	+	7.91597i	−0.425560	+	0.284350i
$776$		0			0
$777$	−8.91523	+	13.3426i	−0.319832	+	0.478663i
$778$		0			0
$779$	−19.0758	+	5.78658i	−0.683461	+	0.207326i
$780$		0			0
$781$	32.3436	+	26.5437i	1.15734	+	0.949807i
$782$		0			0
$783$	−12.7806	−	5.29389i	−0.456741	−	0.189188i
$784$		0			0
$785$	−9.95654	+	4.12413i	−0.355364	+	0.147197i
$786$		0			0
$787$	−2.35525	−	23.9133i	−0.0839557	−	0.852417i	−0.941277	−	0.337635i	$-0.890373\pi$
$787$	−2.35525	−	23.9133i	−0.0839557	−	0.852417i	0.857321	−	0.514782i	$-0.172127\pi$
$788$		0			0
$789$	13.5531	−	25.3561i	0.482504	−	0.902702i
$790$		0			0
$791$	−8.12791	+	1.61674i	−0.288995	+	0.0574847i
$792$		0			0
$793$	0.995794	−	5.00619i	0.0353617	−	0.177775i
$794$		0			0
$795$	−1.63875	+	16.6385i	−0.0581205	+	0.590107i
$796$		0			0
$797$	2.13349	−	7.03317i	0.0755720	−	0.249128i	−0.911013	−	0.412379i	$-0.864698\pi$
$797$	2.13349	−	7.03317i	0.0755720	−	0.249128i	0.986585	+	0.163251i	$0.0521981\pi$
$798$		0			0
$799$	2.21486	+	2.21486i	0.0783562	+	0.0783562i
$800$		0			0
$801$	−28.2385	+	28.2385i	−0.997758	+	0.997758i
$802$		0			0
$803$	23.7755	+	7.21221i	0.839018	+	0.254513i
$804$		0			0
$805$	5.67562	+	0.559000i	0.200039	+	0.0197022i
$806$		0			0
$807$	58.5313	+	11.6426i	2.06040	+	0.409839i
$808$		0			0
$809$	−7.52025	−	37.8069i	−0.264398	−	1.32922i	−0.853472	−	0.521139i	$-0.825507\pi$
$809$	−7.52025	−	37.8069i	−0.264398	−	1.32922i	0.589074	−	0.808079i	$-0.299493\pi$
$810$		0			0
$811$	−8.43221	−	4.50711i	−0.296095	−	0.158266i	0.316660	−	0.948539i	$-0.397439\pi$
$811$	−8.43221	−	4.50711i	−0.296095	−	0.158266i	−0.612755	+	0.790273i	$0.709939\pi$
$812$		0			0
$813$	−29.4760	+	2.90313i	−1.03377	+	0.101817i
$814$		0			0
$815$	−5.30391	−	12.8048i	−0.185788	−	0.448532i
$816$		0			0
$817$	19.5940	−	47.3041i	0.685508	−	1.65496i
$818$		0			0
$819$	−6.20904	+	7.56574i	−0.216961	+	0.264368i
$820$		0			0
$821$	−4.65795	−	15.3552i	−0.162563	−	0.535900i	0.837379	−	0.546623i	$-0.184087\pi$
$821$	−4.65795	−	15.3552i	−0.162563	−	0.535900i	−0.999943	+	0.0107227i	$0.996587\pi$
$822$		0			0
$823$	−8.73225	−	5.83470i	−0.304387	−	0.203385i	0.393990	−	0.919115i	$-0.371094\pi$
$823$	−8.73225	−	5.83470i	−0.304387	−	0.203385i	−0.698377	+	0.715730i	$0.746094\pi$
$824$		0			0
$825$	−15.7523	−	23.5750i	−0.548426	−	0.820777i
$826$		0			0
$827$	2.18269	−	1.79129i	0.0758995	−	0.0622891i	−0.595679	−	0.803223i	$-0.703117\pi$
$827$	2.18269	−	1.79129i	0.0758995	−	0.0622891i	0.671578	+	0.740934i	$0.265617\pi$
$828$		0			0
$829$	−6.13756	−	11.4826i	−0.213166	−	0.398806i	0.752500	−	0.658592i	$-0.228848\pi$
$829$	−6.13756	−	11.4826i	−0.213166	−	0.398806i	−0.965666	+	0.259786i	$0.916348\pi$
$830$		0			0
$831$		−	28.4952i		−	0.988487i
$832$		0			0
$833$		−	0.765637i		−	0.0265277i
$834$		0			0
$835$	16.7945	+	31.4203i	0.581198	+	1.08735i
$836$		0			0
$837$	−72.6766	+	59.6441i	−2.51207	+	2.06160i
$838$		0			0
$839$	−14.2102	−	21.2671i	−0.490591	−	0.734221i	0.500742	−	0.865597i	$-0.333061\pi$
$839$	−14.2102	−	21.2671i	−0.490591	−	0.734221i	−0.991333	+	0.131376i	$0.958061\pi$
$840$		0			0
$841$	22.8575	+	15.2729i	0.788190	+	0.526652i
$842$		0			0
$843$	8.30664	+	27.3833i	0.286096	+	0.943132i
$844$		0			0
$845$	20.5545	−	25.0457i	0.707095	−	0.861597i
$846$		0			0
$847$	14.2865	−	34.4907i	0.490891	−	1.18512i
$848$		0			0
$849$	19.6281	+	47.3863i	0.673633	+	1.62630i
$850$		0			0
$851$	2.54046	−	0.250214i	0.0870859	−	0.00857721i
$852$		0			0
$853$	40.2418	+	21.5097i	1.37785	+	0.736477i	0.983231	−	0.182367i	$-0.0583759\pi$
$853$	40.2418	+	21.5097i	1.37785	+	0.736477i	0.394621	+	0.918844i	$0.370876\pi$
$854$		0			0
$855$	17.6867	+	88.9169i	0.604871	+	3.04089i
$856$		0			0
$857$	15.7391	+	3.13070i	0.537636	+	0.106943i	0.456438	−	0.889755i	$-0.349125\pi$
$857$	15.7391	+	3.13070i	0.537636	+	0.106943i	0.0811987	+	0.996698i	$0.474125\pi$
$858$		0			0
$859$	16.6895	+	1.64377i	0.569438	+	0.0560847i	0.378639	−	0.925544i	$-0.376392\pi$
$859$	16.6895	+	1.64377i	0.569438	+	0.0560847i	0.190799	+	0.981629i	$0.438892\pi$
$860$		0			0
$861$	−23.6730	−	7.18113i	−0.806774	−	0.244732i
$862$		0			0
$863$	1.10918	−	1.10918i	0.0377569	−	0.0377569i	−0.687976	−	0.725733i	$-0.741501\pi$
$863$	1.10918	−	1.10918i	0.0377569	−	0.0377569i	0.725733	+	0.687976i	$0.241501\pi$
$864$		0			0
$865$	−44.8268	−	44.8268i	−1.52416	−	1.52416i
$866$		0			0
$867$	15.2309	−	50.2094i	0.517267	−	1.70520i
$868$		0			0
$869$	1.22006	−	12.3875i	0.0413877	−	0.420217i
$870$		0			0
$871$	0.234347	−	1.17814i	0.00794056	−	0.0399199i
$872$		0			0
$873$	88.3846	−	17.5808i	2.99137	−	0.595020i
$874$		0			0
$875$	8.49257	−	15.8885i	0.287101	−	0.537129i
$876$		0			0
$877$	2.58500	+	26.2459i	0.0872893	+	0.886263i	0.934727	+	0.355367i	$0.115644\pi$
$877$	2.58500	+	26.2459i	0.0872893	+	0.886263i	−0.847437	+	0.530895i	$0.821856\pi$
$878$		0			0
$879$	−22.8443	+	9.46241i	−0.770519	+	0.319159i
$880$		0			0
$881$	−28.8316	−	11.9424i	−0.971362	−	0.402351i	−0.160143	−	0.987094i	$-0.551195\pi$
$881$	−28.8316	−	11.9424i	−0.971362	−	0.402351i	−0.811219	+	0.584743i	$0.801195\pi$
$882$		0			0
$883$	6.03304	+	4.95119i	0.203028	+	0.166621i	0.730413	−	0.683005i	$-0.239328\pi$
$883$	6.03304	+	4.95119i	0.203028	+	0.166621i	−0.527385	+	0.849626i	$0.676828\pi$
$884$		0			0
$885$	31.3421	−	9.50752i	1.05355	−	0.319592i
$886$		0			0
$887$	−15.7692	+	23.6002i	−0.529477	+	0.792418i	−0.995738	−	0.0922294i	$-0.970601\pi$
$887$	−15.7692	+	23.6002i	−0.529477	+	0.792418i	0.466261	+	0.884647i	$0.345601\pi$
$888$		0			0
$889$	30.6872	−	20.5045i	1.02922	−	0.687700i
$890$		0			0
$891$	−51.1346	−	62.3077i	−1.71307	−	2.08738i
$892$		0			0
$893$	48.3739	−	25.8564i	1.61877	−	0.865250i
$894$		0			0
$895$	−7.05116			−0.235694
$896$		0			0
$897$	2.26163			0.0755138
$898$		0			0
$899$	−9.04765	+	4.83607i	−0.301756	+	0.161292i
$900$		0			0
$901$	0.398080	+	0.485061i	0.0132620	+	0.0161597i
$902$		0			0
$903$	52.8325	−	35.3015i	1.75816	−	1.17476i
$904$		0			0
$905$	−7.10301	+	10.6304i	−0.236112	+	0.353366i
$906$		0			0
$907$	−13.2716	+	4.02589i	−0.440676	+	0.133678i	−0.502823	−	0.864389i	$-0.667705\pi$
$907$	−13.2716	+	4.02589i	−0.440676	+	0.133678i	0.0621470	+	0.998067i	$0.480205\pi$
$908$		0			0
$909$	−75.4257	−	61.9003i	−2.50171	−	2.05310i
$910$		0			0
$911$	−18.3236	−	7.58990i	−0.607089	−	0.251464i	0.0578944	−	0.998323i	$-0.481561\pi$
$911$	−18.3236	−	7.58990i	−0.607089	−	0.251464i	−0.664983	+	0.746858i	$0.731561\pi$
$912$		0			0
$913$	−30.3886	+	12.5874i	−1.00572	+	0.416581i
$914$		0			0
$915$	−5.75110	−	58.3919i	−0.190126	−	1.93038i
$916$		0			0
$917$	−2.24163	+	4.19380i	−0.0740252	+	0.138491i
$918$		0			0
$919$	−13.3548	+	2.65644i	−0.440535	+	0.0876279i	−0.410374	−	0.911917i	$-0.634602\pi$
$919$	−13.3548	+	2.65644i	−0.440535	+	0.0876279i	−0.0301608	+	0.999545i	$0.509602\pi$
$920$		0			0
$921$	13.3103	−	66.9155i	0.438590	−	2.20494i
$922$		0			0
$923$	0.535383	−	5.43584i	0.0176224	−	0.178923i
$924$		0			0
$925$	−1.21277	+	3.99795i	−0.0398755	+	0.131452i
$926$		0			0
$927$	−86.1141	−	86.1141i	−2.82836	−	2.82836i
$928$		0			0
$929$	30.5681	−	30.5681i	1.00291	−	1.00291i	0.00290990	−	0.999996i	$-0.499074\pi$
$929$	30.5681	−	30.5681i	1.00291	−	1.00291i	0.999996	−	0.00290990i	$-0.000926250\pi$
$930$		0			0
$931$	−12.8300	−	3.89194i	−0.420487	−	0.127553i
$932$		0			0
$933$	−6.70771	−	0.660652i	−0.219600	−	0.0216288i
$934$		0			0
$935$	−4.10198	−	0.815934i	−0.134149	−	0.0266839i
$936$		0			0
$937$	−0.690123	−	3.46948i	−0.0225453	−	0.113343i	0.967874	−	0.251436i	$-0.0809028\pi$
$937$	−0.690123	−	3.46948i	−0.0225453	−	0.113343i	−0.990419	+	0.138093i	$0.955903\pi$
$938$		0			0
$939$	−77.5708	−	41.4625i	−2.53143	−	1.35308i
$940$		0			0
$941$	−7.76006	+	0.764299i	−0.252971	+	0.0249154i	−0.223708	−	0.974656i	$-0.571816\pi$
$941$	−7.76006	+	0.764299i	−0.252971	+	0.0249154i	−0.0292631	+	0.999572i	$0.509316\pi$
$942$		0			0
$943$	1.50599	+	3.63579i	0.0490419	+	0.118398i
$944$		0			0
$945$	−23.5688	+	56.9001i	−0.766693	+	1.85096i
$946$		0			0
$947$	16.6613	−	20.3019i	0.541420	−	0.659722i	−0.428387	−	0.903595i	$-0.640918\pi$
$947$	16.6613	−	20.3019i	0.541420	−	0.659722i	0.969807	+	0.243873i	$0.0784180\pi$
$948$		0			0
$949$	−0.941518	−	3.10377i	−0.0305630	−	0.100753i
$950$		0			0
$951$	64.1664	+	42.8746i	2.08074	+	1.39030i
$952$		0			0
$953$	−11.5124	−	17.2295i	−0.372923	−	0.558119i	0.596780	−	0.802405i	$-0.296446\pi$
$953$	−11.5124	−	17.2295i	−0.372923	−	0.558119i	−0.969703	+	0.244286i	$0.921446\pi$
$954$		0			0
$955$	18.1297	−	14.8786i	0.586662	−	0.481461i
$956$		0			0
$957$	−9.62351	−	18.0043i	−0.311084	−	0.581997i
$958$		0			0
$959$			16.4694i			0.531823i
$960$		0			0
$961$			38.7236i			1.24915i
$962$		0			0
$963$	34.7947	+	65.0963i	1.12124	+	2.09770i
$964$		0			0
$965$	−4.47688	+	3.67408i	−0.144116	+	0.118273i
$966$		0			0
$967$	6.67306	+	9.98694i	0.214591	+	0.321158i	0.923112	−	0.384532i	$-0.125637\pi$
$967$	6.67306	+	9.98694i	0.214591	+	0.321158i	−0.708521	+	0.705690i	$0.750637\pi$
$968$		0			0
$969$	4.10959	+	2.74594i	0.132019	+	0.0882123i
$970$		0			0
$971$	5.31186	+	17.5109i	0.170466	+	0.561950i	0.999994	+	0.00348541i	$0.00110944\pi$
$971$	5.31186	+	17.5109i	0.170466	+	0.561950i	−0.829528	+	0.558465i	$0.811391\pi$
$972$		0			0
$973$	−6.12609	+	7.46467i	−0.196394	+	0.239306i
$974$		0			0
$975$	−1.41647	+	3.41965i	−0.0453632	+	0.109516i
$976$		0			0
$977$	19.2413	+	46.4525i	0.615583	+	1.48615i	0.856785	+	0.515673i	$0.172458\pi$
$977$	19.2413	+	46.4525i	0.615583	+	1.48615i	−0.241203	+	0.970475i	$0.577542\pi$
$978$		0			0
$979$	−32.1062	+	3.16218i	−1.02612	+	0.101064i
$980$		0			0
$981$	−49.8095	−	26.6237i	−1.59030	−	0.850031i
$982$		0			0
$983$	7.98363	+	40.1364i	0.254638	+	1.28015i	0.870449	+	0.492259i	$0.163829\pi$
$983$	7.98363	+	40.1364i	0.254638	+	1.28015i	−0.615810	+	0.787894i	$0.711171\pi$
$984$		0			0
$985$	43.1443	+	8.58194i	1.37469	+	0.273443i
$986$		0			0
$987$	67.7416	+	6.67197i	2.15624	+	0.212371i
$988$		0			0
$989$	−9.67285	−	2.93423i	−0.307579	−	0.0933030i
$990$		0			0
$991$	1.22257	−	1.22257i	0.0388361	−	0.0388361i	−0.687422	−	0.726258i	$-0.741258\pi$
$991$	1.22257	−	1.22257i	0.0388361	−	0.0388361i	0.726258	+	0.687422i	$0.241258\pi$
$992$		0			0
$993$	64.3133	+	64.3133i	2.04092	+	2.04092i
$994$		0			0
$995$	−7.47336	+	24.6364i	−0.236921	+	0.781025i
$996$		0			0
$997$	−2.60395	+	26.4384i	−0.0824679	+	0.837311i	0.861606	+	0.507578i	$0.169459\pi$
$997$	−2.60395	+	26.4384i	−0.0824679	+	0.837311i	−0.944074	+	0.329734i	$0.893041\pi$
$998$		0			0
$999$	−5.37814	+	27.0378i	−0.170157	+	0.855437i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.k.a.497.1		240
4.3	odd	2		128.2.k.a.101.1	✓	240
128.19	odd	32		128.2.k.a.109.1	yes	240
128.109	even	32	inner	512.2.k.a.273.1		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.2.k.a.101.1	✓	240	4.3	odd	2
128.2.k.a.109.1	yes	240	128.19	odd	32
512.2.k.a.273.1		240	128.109	even	32	inner
512.2.k.a.497.1		240	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.k (of order \(32\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.73660 + 1.46274i) q^{3} +(1.64287 + 2.00184i) q^{5} +(1.75623 - 1.17347i) q^{7} +(3.68265 - 5.51147i) q^{9} +(5.12430 - 1.55444i) q^{11} +(-0.540375 - 0.443474i) q^{13} +(-7.42405 - 3.07514i) q^{15} +(-0.278638 + 0.115416i) q^{17} +(0.517663 + 5.25592i) q^{19} +(-3.08960 + 5.78024i) q^{21} +(1.02260 - 0.203407i) q^{23} +(-0.332898 + 1.67359i) q^{25} +(-1.10362 + 11.2053i) q^{27} +(-0.356648 + 1.17571i) q^{29} +(5.90439 + 5.90439i) q^{31} +(-11.7494 + 11.7494i) q^{33} +(5.23436 + 1.58783i) q^{35} +(2.43658 + 0.239983i) q^{37} +(2.12748 + 0.423182i) q^{39} +(0.736357 + 3.70191i) q^{41} +(-8.55004 - 4.57009i) q^{43} +(17.0832 - 1.68255i) q^{45} +(-3.97444 - 9.59514i) q^{47} +(-0.971486 + 2.34538i) q^{49} +(0.593698 - 0.723423i) q^{51} +(-0.603962 - 1.99100i) q^{53} +(11.5303 + 7.70429i) q^{55} +(-9.10470 - 13.6261i) q^{57} +(-3.15067 + 2.58569i) q^{59} +(3.44200 + 6.43952i) q^{61} -14.0009i q^{63} -1.81031i q^{65} +(0.810030 + 1.51546i) q^{67} +(-2.50091 + 2.05244i) q^{69} +(4.34102 + 6.49679i) q^{71} +(3.85781 + 2.57771i) q^{73} +(-1.53702 - 5.06689i) q^{75} +(7.17535 - 8.74319i) q^{77} +(0.889548 - 2.14756i) q^{79} +(-5.76031 - 13.9066i) q^{81} +(-6.11293 + 0.602071i) q^{83} +(-0.688810 - 0.368177i) q^{85} +(-0.743761 - 3.73914i) q^{87} +(-5.90894 - 1.17536i) q^{89} +(-1.46943 - 0.144726i) q^{91} +(-24.7945 - 7.52134i) q^{93} +(-9.67106 + 9.67106i) q^{95} +(9.61317 + 9.61317i) q^{97} +(10.3037 - 33.9669i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35}+ \cdots + 16 q^{99}+O(q^{100}) \) 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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