LMFDB - Embedded newform 513.2.t.a.278.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [513,2,Mod(179,513)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(513, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("513.179"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 513 = 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	513.t (of order $6$, degree $2$, 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:	$4.09632562369$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 171)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			278.13
Character	$\chi$	$=$	513.278
Dual form			513.2.t.a.179.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.55091 q^{2} +0.405316 q^{4} +(1.63223 + 0.942368i) q^{5} +(-2.41078 + 4.17560i) q^{7} -2.47321 q^{8} +(2.53144 + 1.46153i) q^{10} +(2.70914 + 1.56412i) q^{11} +3.37811i q^{13} +(-3.73890 + 6.47597i) q^{14} -4.64635 q^{16} +(3.06986 - 1.77238i) q^{17} +(4.35881 + 0.0276906i) q^{19} +(0.661569 + 0.381957i) q^{20} +(4.20163 + 2.42581i) q^{22} -4.32627i q^{23} +(-0.723884 - 1.25380i) q^{25} +5.23914i q^{26} +(-0.977130 + 1.69244i) q^{28} +(-1.13606 - 1.96771i) q^{29} +(1.96133 - 1.13238i) q^{31} -2.25965 q^{32} +(4.76106 - 2.74880i) q^{34} +(-7.86990 + 4.54369i) q^{35} -4.36294i q^{37} +(6.76012 + 0.0429455i) q^{38} +(-4.03684 - 2.33067i) q^{40} +(-2.81964 + 4.88376i) q^{41} +9.03545 q^{43} +(1.09806 + 0.633964i) q^{44} -6.70964i q^{46} +(-8.23996 + 4.75734i) q^{47} +(-8.12375 - 14.0707i) q^{49} +(-1.12268 - 1.94453i) q^{50} +1.36920i q^{52} +(4.04616 - 7.00816i) q^{53} +(2.94796 + 5.10601i) q^{55} +(5.96237 - 10.3271i) q^{56} +(-1.76192 - 3.05174i) q^{58} +(-1.14377 + 1.98107i) q^{59} +(5.33757 + 9.24494i) q^{61} +(3.04185 - 1.75621i) q^{62} +5.78820 q^{64} +(-3.18342 + 5.51385i) q^{65} +8.57097i q^{67} +(1.24426 - 0.718375i) q^{68} +(-12.2055 + 7.04685i) q^{70} +(0.454871 + 0.787860i) q^{71} +(-1.23937 - 2.14665i) q^{73} -6.76652i q^{74} +(1.76670 + 0.0112234i) q^{76} +(-13.0623 + 7.54152i) q^{77} +0.526031i q^{79} +(-7.58391 - 4.37857i) q^{80} +(-4.37301 + 7.57427i) q^{82} +(-1.65409 - 0.954990i) q^{83} +6.68095 q^{85} +14.0132 q^{86} +(-6.70026 - 3.86840i) q^{88} +(7.48128 - 12.9580i) q^{89} +(-14.1056 - 8.14389i) q^{91} -1.75351i q^{92} +(-12.7794 + 7.37820i) q^{94} +(7.08849 + 4.15280i) q^{95} -13.4775i q^{97} +(-12.5992 - 21.8224i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{2} + 30 q^{4} + 3 q^{5} - q^{7} + 12 q^{8} - 6 q^{10} + 9 q^{11} + 3 q^{14} + 18 q^{16} - 27 q^{17} + q^{19} - 9 q^{20} - 6 q^{22} + 11 q^{25} + 2 q^{28} + 12 q^{29} - 12 q^{31} + 30 q^{32}+ \cdots - 84 q^{98}+O(q^{100}) $ 36 * q + 6 * q^2 + 30 * q^4 + 3 * q^5 - q^7 + 12 * q^8 - 6 * q^10 + 9 * q^11 + 3 * q^14 + 18 * q^16 - 27 * q^17 + q^19 - 9 * q^20 - 6 * q^22 + 11 * q^25 + 2 * q^28 + 12 * q^29 - 12 * q^31 + 30 * q^32 - 21 * q^34 + 15 * q^35 + 36 * q^38 - 30 * q^40 - 18 * q^41 - 6 * q^43 + 66 * q^44 - 45 * q^47 - 9 * q^49 + 3 * q^50 - 12 * q^53 - 7 * q^55 + 6 * q^56 - 6 * q^58 + 9 * q^59 + 8 * q^61 - 12 * q^62 + 12 * q^64 - 18 * q^65 - 60 * q^68 - 24 * q^70 + 9 * q^71 - 18 * q^73 + 10 * q^76 + 6 * q^77 - 12 * q^80 - 9 * q^82 + 9 * q^83 - 22 * q^85 - 102 * q^86 - 3 * q^88 - 18 * q^89 + 27 * q^91 - 12 * q^94 + 21 * q^95 - 84 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/513\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.55091			1.09666			0.548329	−	0.836263i	$-0.315264\pi$
$2$	1.55091			1.09666			0.548329	+	0.836263i	$0.315264\pi$
$3$		0			0
$3$		0			0
$4$	0.405316			0.202658
$5$	1.63223	+	0.942368i	0.729955	+	0.421440i	0.818406	−	0.574641i	$-0.194858\pi$
$5$	1.63223	+	0.942368i	0.729955	+	0.421440i	−0.0884504	+	0.996081i	$0.528191\pi$
$6$		0			0
$7$	−2.41078	+	4.17560i	−0.911190	+	1.57823i	−0.0988049	+	0.995107i	$0.531502\pi$
$7$	−2.41078	+	4.17560i	−0.911190	+	1.57823i	−0.812385	+	0.583121i	$0.801831\pi$
$8$	−2.47321			−0.874411
$9$		0			0
$10$	2.53144	+	1.46153i	0.800511	+	0.462175i
$11$	2.70914	+	1.56412i	0.816836	+	0.471600i	0.849324	−	0.527872i	$-0.177010\pi$
$11$	2.70914	+	1.56412i	0.816836	+	0.471600i	−0.0324882	+	0.999472i	$0.510343\pi$
$12$		0			0
$13$			3.37811i			0.936919i	0.883485	+	0.468460i	$0.155191\pi$
$13$			3.37811i			0.936919i	−0.883485	+	0.468460i	$0.844809\pi$
$14$	−3.73890	+	6.47597i	−0.999264	+	1.73078i
$15$		0			0
$16$	−4.64635			−1.16159
$17$	3.06986	−	1.77238i	0.744549	−	0.429866i	−0.0791717	−	0.996861i	$-0.525228\pi$
$17$	3.06986	−	1.77238i	0.744549	−	0.429866i	0.823721	+	0.566995i	$0.191894\pi$
$18$		0			0
$19$	4.35881	+	0.0276906i	0.999980	+	0.00635265i
$19$	4.35881	+	0.0276906i	0.999980	+	0.00635265i
$20$	0.661569	+	0.381957i	0.147931	+	0.0854082i
$21$		0			0
$22$	4.20163	+	2.42581i	0.895790	+	0.517184i
$23$		−	4.32627i		−	0.902089i	−0.892501	−	0.451044i	$-0.851052\pi$
$23$		−	4.32627i		−	0.902089i	0.892501	−	0.451044i	$-0.148948\pi$
$24$		0			0
$25$	−0.723884	−	1.25380i	−0.144777	−	0.250761i
$26$			5.23914i			1.02748i
$27$		0			0
$28$	−0.977130	+	1.69244i	−0.184660	+	0.319841i
$29$	−1.13606	−	1.96771i	−0.210961	−	0.365394i	0.741055	−	0.671444i	$-0.234326\pi$
$29$	−1.13606	−	1.96771i	−0.210961	−	0.365394i	−0.952015	+	0.306050i	$0.900992\pi$
$30$		0			0
$31$	1.96133	−	1.13238i	0.352266	−	0.203381i	−0.313417	−	0.949616i	$-0.601474\pi$
$31$	1.96133	−	1.13238i	0.352266	−	0.203381i	0.665683	+	0.746235i	$0.268140\pi$
$32$	−2.25965			−0.399453
$33$		0			0
$34$	4.76106	−	2.74880i	0.816516	−	0.471416i
$35$	−7.86990	+	4.54369i	−1.33026	+	0.768024i
$36$		0			0
$37$		−	4.36294i		−	0.717263i	−0.933479	−	0.358631i	$-0.883244\pi$
$37$		−	4.36294i		−	0.717263i	0.933479	−	0.358631i	$-0.116756\pi$
$38$	6.76012	+	0.0429455i	1.09664	+	0.00696669i
$39$		0			0
$40$	−4.03684	−	2.33067i	−0.638281	−	0.368512i
$41$	−2.81964	+	4.88376i	−0.440354	+	0.762716i	−0.997716	−	0.0675541i	$-0.978480\pi$
$41$	−2.81964	+	4.88376i	−0.440354	+	0.762716i	0.557361	+	0.830270i	$0.311814\pi$
$42$		0			0
$43$	9.03545			1.37789			0.688947	−	0.724812i	$-0.258073\pi$
$43$	9.03545			1.37789			0.688947	+	0.724812i	$0.258073\pi$
$44$	1.09806	+	0.633964i	0.165538	+	0.0955737i
$45$		0			0
$46$		−	6.70964i		−	0.989283i
$47$	−8.23996	+	4.75734i	−1.20192	+	0.693930i	−0.960982	−	0.276610i	$-0.910789\pi$
$47$	−8.23996	+	4.75734i	−1.20192	+	0.693930i	−0.240940	+	0.970540i	$0.577456\pi$
$48$		0			0
$49$	−8.12375	−	14.0707i	−1.16054	−	2.01011i
$50$	−1.12268	−	1.94453i	−0.158771	−	0.274999i
$51$		0			0
$52$			1.36920i			0.189874i
$53$	4.04616	−	7.00816i	0.555783	−	0.962644i	−0.442059	−	0.896986i	$-0.645752\pi$
$53$	4.04616	−	7.00816i	0.555783	−	0.962644i	0.997842	−	0.0656585i	$-0.0209148\pi$
$54$		0			0
$55$	2.94796	+	5.10601i	0.397503	+	0.688495i
$56$	5.96237	−	10.3271i	0.796755	−	1.38002i
$57$		0			0
$58$	−1.76192	−	3.05174i	−0.231352	−	0.400713i
$59$	−1.14377	+	1.98107i	−0.148906	+	0.257913i	−0.930823	−	0.365469i	$-0.880909\pi$
$59$	−1.14377	+	1.98107i	−0.148906	+	0.257913i	0.781917	+	0.623382i	$0.214242\pi$
$60$		0			0
$61$	5.33757	+	9.24494i	0.683406	+	1.18369i	0.973935	+	0.226827i	$0.0728352\pi$
$61$	5.33757	+	9.24494i	0.683406	+	1.18369i	−0.290529	+	0.956866i	$0.593831\pi$
$62$	3.04185	−	1.75621i	0.386315	−	0.223039i
$63$		0			0
$64$	5.78820			0.723524
$65$	−3.18342	+	5.51385i	−0.394855	+	0.683909i
$66$		0			0
$67$			8.57097i			1.04711i	0.851992	+	0.523555i	$0.175395\pi$
$67$			8.57097i			1.04711i	−0.851992	+	0.523555i	$0.824605\pi$
$68$	1.24426	−	0.718375i	0.150889	−	0.0871158i
$69$		0			0
$70$	−12.2055	+	7.04685i	−1.45884	+	0.842259i
$71$	0.454871	+	0.787860i	0.0539833	+	0.0935018i	0.891754	−	0.452520i	$-0.149475\pi$
$71$	0.454871	+	0.787860i	0.0539833	+	0.0935018i	−0.837771	+	0.546022i	$0.816142\pi$
$72$		0			0
$73$	−1.23937	−	2.14665i	−0.145057	−	0.251246i	0.784337	−	0.620335i	$-0.213003\pi$
$73$	−1.23937	−	2.14665i	−0.145057	−	0.251246i	−0.929394	+	0.369089i	$0.879670\pi$
$74$		−	6.76652i		−	0.786592i
$75$		0			0
$76$	1.76670	+	0.0112234i	0.202654	+	0.00128742i
$77$	−13.0623	+	7.54152i	−1.48859	+	0.859436i
$78$		0			0
$79$			0.526031i			0.0591831i	0.999562	+	0.0295915i	$0.00942065\pi$
$79$			0.526031i			0.0591831i	−0.999562	+	0.0295915i	$0.990579\pi$
$80$	−7.58391	−	4.37857i	−0.847907	−	0.489540i
$81$		0			0
$82$	−4.37301	+	7.57427i	−0.482918	+	0.836438i
$83$	−1.65409	−	0.954990i	−0.181560	−	0.104824i	0.406465	−	0.913666i	$-0.366761\pi$
$83$	−1.65409	−	0.954990i	−0.181560	−	0.104824i	−0.588025	+	0.808842i	$0.700095\pi$
$84$		0			0
$85$	6.68095			0.724650
$86$	14.0132			1.51108
$87$		0			0
$88$	−6.70026	−	3.86840i	−0.714250	−	0.412373i
$89$	7.48128	−	12.9580i	0.793014	−	1.37354i	−0.131079	−	0.991372i	$-0.541844\pi$
$89$	7.48128	−	12.9580i	0.793014	−	1.37354i	0.924093	−	0.382169i	$-0.124823\pi$
$90$		0			0
$91$	−14.1056	−	8.14389i	−1.47867	−	0.853712i
$92$		−	1.75351i		−	0.182816i
$93$		0			0
$94$	−12.7794	+	7.37820i	−1.31810	+	0.761004i
$95$	7.08849	+	4.15280i	0.727263	+	0.426069i
$96$		0			0
$97$		−	13.4775i		−	1.36844i	−0.729277	−	0.684219i	$-0.760143\pi$
$97$		−	13.4775i		−	1.36844i	0.729277	−	0.684219i	$-0.239857\pi$
$98$	−12.5992	−	21.8224i	−1.27271	−	2.20440i
$99$		0			0
$100$	−0.293402	−	0.508187i	−0.0293402	−	0.0508187i
$101$	12.8098	−	7.39575i	1.27462	−	0.735904i	0.298769	−	0.954325i	$-0.403424\pi$
$101$	12.8098	−	7.39575i	1.27462	−	0.735904i	0.975855	+	0.218421i	$0.0700907\pi$
$102$		0			0
$103$	−6.03192	+	3.48253i	−0.594343	+	0.343144i	−0.766813	−	0.641871i	$-0.778159\pi$
$103$	−6.03192	+	3.48253i	−0.594343	+	0.343144i	0.172470	+	0.985015i	$0.444825\pi$
$104$		−	8.35477i		−	0.819252i
$105$		0			0
$106$	6.27523	−	10.8690i	0.609504	−	1.05569i
$107$	−6.21001			−0.600344			−0.300172	−	0.953885i	$-0.597044\pi$
$107$	−6.21001			−0.600344			−0.300172	+	0.953885i	$0.597044\pi$
$108$		0			0
$109$	−2.64165	+	1.52516i	−0.253025	+	0.146084i	−0.621148	−	0.783693i	$-0.713334\pi$
$109$	−2.64165	+	1.52516i	−0.253025	+	0.146084i	0.368124	+	0.929777i	$0.380000\pi$
$110$	4.57201	+	7.91896i	0.435924	+	0.755043i
$111$		0			0
$112$	11.2013	−	19.4013i	1.05843	−	1.83325i
$113$	−6.17578	−	10.6968i	−0.580969	−	1.00627i	−0.995365	−	0.0961706i	$-0.969341\pi$
$113$	−6.17578	−	10.6968i	−0.580969	−	1.00627i	0.414396	−	0.910097i	$-0.363993\pi$
$114$		0			0
$115$	4.07694	−	7.06146i	0.380176	−	0.658485i
$116$	−0.460463	−	0.797545i	−0.0427529	−	0.0740502i
$117$		0			0
$118$	−1.77388	+	3.07245i	−0.163299	+	0.282842i
$119$			17.0913i			1.56676i
$120$		0			0
$121$	−0.607046	−	1.05143i	−0.0551860	−	0.0955849i
$122$	8.27808	+	14.3381i	0.749462	+	1.29811i
$123$		0			0
$124$	0.794960	−	0.458971i	0.0713895	−	0.0412168i
$125$		−	12.1523i		−	1.08694i
$126$		0			0
$127$	3.35067	+	1.93451i	0.297324	+	0.171660i	0.641240	−	0.767340i	$-0.278420\pi$
$127$	3.35067	+	1.93451i	0.297324	+	0.171660i	−0.343916	+	0.939000i	$0.611754\pi$
$128$	13.4963			1.19291
$129$		0			0
$130$	−4.93720	+	8.55148i	−0.433021	+	0.750014i
$131$	11.3165	+	6.53360i	0.988730	+	0.570843i	0.904894	−	0.425636i	$-0.139950\pi$
$131$	11.3165	+	6.53360i	0.988730	+	0.570843i	0.0838353	+	0.996480i	$0.473283\pi$
$132$		0			0
$133$	−10.6238	+	18.1339i	−0.921198	+	1.57241i
$134$			13.2928i			1.14832i
$135$		0			0
$136$	−7.59239	+	4.38347i	−0.651042	+	0.375879i
$137$	−0.780648	+	0.450707i	−0.0666953	+	0.0385065i	−0.532977	−	0.846130i	$-0.678927\pi$
$137$	−0.780648	+	0.450707i	−0.0666953	+	0.0385065i	0.466282	+	0.884636i	$0.345593\pi$
$138$		0			0
$139$	19.3657			1.64258			0.821289	−	0.570513i	$-0.193256\pi$
$139$	19.3657			1.64258			0.821289	+	0.570513i	$0.193256\pi$
$140$	−3.18980	+	1.84163i	−0.269587	+	0.155646i
$141$		0			0
$142$	0.705464	+	1.22190i	0.0592012	+	0.102540i
$143$	−5.28378	+	9.15177i	−0.441851	+	0.765309i
$144$		0			0
$145$		−	4.28234i		−	0.355629i
$146$	−1.92215	−	3.32925i	−0.159078	−	0.275531i
$147$		0			0
$148$		−	1.76837i		−	0.145359i
$149$	−1.64502	−	0.949750i	−0.134765	−	0.0778065i	0.431102	−	0.902303i	$-0.358125\pi$
$149$	−1.64502	−	0.949750i	−0.134765	−	0.0778065i	−0.565867	+	0.824497i	$0.691458\pi$
$150$		0			0
$151$	3.36348	+	1.94190i	0.273716	+	0.158030i	0.630575	−	0.776128i	$-0.282819\pi$
$151$	3.36348	+	1.94190i	0.273716	+	0.158030i	−0.356859	+	0.934158i	$0.616152\pi$
$152$	−10.7802	−	0.0684845i	−0.874393	−	0.00555483i
$153$		0			0
$154$	−20.2584	+	11.6962i	−1.63247	+	0.942507i
$155$	4.26846			0.342851
$156$		0			0
$157$	−8.27272	+	14.3288i	−0.660235	+	1.14356i	0.320319	+	0.947310i	$0.396210\pi$
$157$	−8.27272	+	14.3288i	−0.660235	+	1.14356i	−0.980554	+	0.196251i	$0.937123\pi$
$158$			0.815825i			0.0649036i
$159$		0			0
$160$	−3.68827	−	2.12942i	−0.291583	−	0.168346i
$161$	18.0648	+	10.4297i	1.42370	+	0.821975i
$162$		0			0
$163$	10.2238			0.800787			0.400394	−	0.916343i	$-0.368873\pi$
$163$	10.2238			0.800787			0.400394	+	0.916343i	$0.368873\pi$
$164$	−1.14285	+	1.97947i	−0.0892414	+	0.154571i
$165$		0			0
$166$	−2.56534	−	1.48110i	−0.199109	−	0.114956i
$167$	−7.06803			−0.546940			−0.273470	−	0.961880i	$-0.588171\pi$
$167$	−7.06803			−0.546940			−0.273470	+	0.961880i	$0.588171\pi$
$168$		0			0
$169$	1.58837			0.122183
$170$	10.3615			0.794693
$171$		0			0
$172$	3.66222			0.279241
$173$	−12.9998			−0.988359			−0.494179	−	0.869360i	$-0.664531\pi$
$173$	−12.9998			−0.988359			−0.494179	+	0.869360i	$0.664531\pi$
$174$		0			0
$175$	6.98050			0.527677
$176$	−12.5876	−	7.26746i	−0.948827	−	0.547805i
$177$		0			0
$178$	11.6028	−	20.0966i	0.869665	−	1.50630i
$179$	8.63956			0.645751			0.322875	−	0.946442i	$-0.395351\pi$
$179$	8.63956			0.645751			0.322875	+	0.946442i	$0.395351\pi$
$180$		0			0
$181$	−2.06491	−	1.19217i	−0.153483	−	0.0886137i	0.421291	−	0.906925i	$-0.361577\pi$
$181$	−2.06491	−	1.19217i	−0.153483	−	0.0886137i	−0.574775	+	0.818312i	$0.694910\pi$
$182$	−21.8765	−	12.6304i	−1.62160	−	0.936229i
$183$		0			0
$184$			10.6998i			0.788797i
$185$	4.11150	−	7.12132i	0.302283	−	0.523570i
$186$		0			0
$187$	11.0889			0.810900
$188$	−3.33979	+	1.92823i	−0.243579	+	0.140631i
$189$		0			0
$190$	10.9936	+	6.44062i	0.797559	+	0.467251i
$191$	−6.46514	−	3.73265i	−0.467801	−	0.270085i	0.247518	−	0.968883i	$-0.420385\pi$
$191$	−6.46514	−	3.73265i	−0.467801	−	0.270085i	−0.715319	+	0.698798i	$0.753718\pi$
$192$		0			0
$193$	−6.94286	−	4.00846i	−0.499758	−	0.288535i	0.228856	−	0.973460i	$-0.426502\pi$
$193$	−6.94286	−	4.00846i	−0.499758	−	0.288535i	−0.728614	+	0.684925i	$0.759835\pi$
$194$		−	20.9024i		−	1.50071i
$195$		0			0
$196$	−3.29269	−	5.70310i	−0.235192	−	0.407364i
$197$			8.19380i			0.583784i	0.956451	+	0.291892i	$0.0942848\pi$
$197$			8.19380i			0.583784i	−0.956451	+	0.291892i	$0.905715\pi$
$198$		0			0
$199$	2.17911	−	3.77433i	0.154473	−	0.267555i	−0.778394	−	0.627776i	$-0.783965\pi$
$199$	2.17911	−	3.77433i	0.154473	−	0.267555i	0.932867	+	0.360221i	$0.117299\pi$
$200$	1.79031	+	3.10092i	0.126594	+	0.219268i
$201$		0			0
$202$	19.8668	−	11.4701i	1.39783	−	0.807035i
$203$	10.9552			0.768901
$204$		0			0
$205$	−9.20461	+	5.31428i	−0.642878	+	0.371166i
$206$	−9.35496	+	5.40109i	−0.651791	+	0.376312i
$207$		0			0
$208$		−	15.6959i		−	1.08831i
$209$	11.7653	+	6.89273i	0.813824	+	0.476780i
$210$		0			0
$211$	−11.4815	−	6.62887i	−0.790421	−	0.456350i	0.0496895	−	0.998765i	$-0.484177\pi$
$211$	−11.4815	−	6.62887i	−0.790421	−	0.456350i	−0.840111	+	0.542415i	$0.817510\pi$
$212$	1.63998	−	2.84052i	0.112634	−	0.195088i
$213$		0			0
$214$	−9.63115			−0.658372
$215$	14.7479	+	8.51473i	1.00580	+	0.580700i
$216$		0			0
$217$			10.9197i			0.741274i
$218$	−4.09696	+	2.36538i	−0.277481	+	0.160204i
$219$		0			0
$220$	1.19486	+	2.06955i	0.0805571	+	0.139529i
$221$	5.98730	+	10.3703i	0.402749	+	0.697582i
$222$		0			0
$223$		−	3.61894i		−	0.242342i	−0.992632	−	0.121171i	$-0.961335\pi$
$223$		−	3.61894i		−	0.242342i	0.992632	−	0.121171i	$-0.0386649\pi$
$224$	5.44752	−	9.43538i	0.363978	−	0.630428i
$225$		0			0
$226$	−9.57807	−	16.5897i	−0.637124	−	1.10353i
$227$	−10.1964	+	17.6606i	−0.676757	+	1.17218i	0.299196	+	0.954192i	$0.403282\pi$
$227$	−10.1964	+	17.6606i	−0.676757	+	1.17218i	−0.975952	+	0.217985i	$0.930052\pi$
$228$		0			0
$229$	−2.72459	−	4.71913i	−0.180046	−	0.311849i	0.761850	−	0.647754i	$-0.224291\pi$
$229$	−2.72459	−	4.71913i	−0.180046	−	0.311849i	−0.941896	+	0.335905i	$0.890958\pi$
$230$	6.32295	−	10.9517i	0.416923	−	0.722132i
$231$		0			0
$232$	2.80971	+	4.86655i	0.184466	+	0.319505i
$233$	−22.2854	+	12.8665i	−1.45996	+	0.842910i	−0.999009	−	0.0445134i	$-0.985826\pi$
$233$	−22.2854	+	12.8665i	−1.45996	+	0.842910i	−0.460955	+	0.887424i	$0.652493\pi$
$234$		0			0
$235$	−17.9327			−1.16980
$236$	−0.463589	+	0.802959i	−0.0301771	+	0.0522682i
$237$		0			0
$238$			26.5071i			1.71820i
$239$	−10.5130	+	6.06970i	−0.680032	+	0.392616i	−0.799867	−	0.600177i	$-0.795097\pi$
$239$	−10.5130	+	6.06970i	−0.680032	+	0.392616i	0.119835	+	0.992794i	$0.461763\pi$
$240$		0			0
$241$	16.5011	−	9.52691i	1.06293	−	0.613682i	0.136688	−	0.990614i	$-0.456354\pi$
$241$	16.5011	−	9.52691i	1.06293	−	0.613682i	0.926241	+	0.376932i	$0.123021\pi$
$242$	−0.941472	−	1.63068i	−0.0605201	−	0.104824i
$243$		0			0
$244$	2.16340	+	3.74712i	0.138498	+	0.239885i
$245$		−	30.6223i		−	1.95638i
$246$		0			0
$247$	−0.0935418	+	14.7245i	−0.00595192	+	0.936900i
$248$	−4.85079	+	2.80060i	−0.308025	+	0.177838i
$249$		0			0
$250$		−	18.8472i		−	1.19200i
$251$	7.74070	+	4.46909i	0.488589	+	0.282087i	0.723989	−	0.689812i	$-0.242307\pi$
$251$	7.74070	+	4.46909i	0.488589	+	0.282087i	−0.235400	+	0.971899i	$0.575640\pi$
$252$		0			0
$253$	6.76681	−	11.7205i	0.425426	−	0.736859i
$254$	5.19659	+	3.00025i	0.326063	+	0.188253i
$255$		0			0
$256$	9.35506			0.584692
$257$	−5.86083			−0.365588			−0.182794	−	0.983151i	$-0.558514\pi$
$257$	−5.86083			−0.365588			−0.182794	+	0.983151i	$0.558514\pi$
$258$		0			0
$259$	18.2179	+	10.5181i	1.13200	+	0.653563i
$260$	−1.29029	+	2.23485i	−0.0800206	+	0.138600i
$261$		0			0
$262$	17.5509	+	10.1330i	1.08430	+	0.626020i
$263$		−	5.96426i		−	0.367772i	−0.982948	−	0.183886i	$-0.941132\pi$
$263$		−	5.96426i		−	0.367772i	0.982948	−	0.183886i	$-0.0588677\pi$
$264$		0			0
$265$	13.2085	−	7.62595i	0.811394	−	0.468458i
$266$	−16.4765	+	28.1240i	−1.01024	+	1.72439i
$267$		0			0
$268$			3.47395i			0.212205i
$269$	4.25123	+	7.36335i	0.259202	+	0.448951i	0.966028	−	0.258436i	$-0.0832071\pi$
$269$	4.25123	+	7.36335i	0.259202	+	0.448951i	−0.706826	+	0.707387i	$0.749874\pi$
$270$		0			0
$271$	3.84391	+	6.65785i	0.233501	+	0.404436i	0.958836	−	0.283960i	$-0.0916485\pi$
$271$	3.84391	+	6.65785i	0.233501	+	0.404436i	−0.725335	+	0.688396i	$0.758315\pi$
$272$	−14.2636	+	8.23511i	−0.864859	+	0.499327i
$273$		0			0
$274$	−1.21071	+	0.699006i	−0.0731419	+	0.0422285i
$275$		−	4.52897i		−	0.273107i
$276$		0			0
$277$	−15.3659	+	26.6146i	−0.923249	+	1.59911i	−0.128895	+	0.991658i	$0.541143\pi$
$277$	−15.3659	+	26.6146i	−0.923249	+	1.59911i	−0.794353	+	0.607456i	$0.792190\pi$
$278$	30.0344			1.80135
$279$		0			0
$280$	19.4639	−	11.2375i	1.16319	−	0.671569i
$281$	−14.8241	−	25.6760i	−0.884329	−	1.53170i	−0.846481	−	0.532419i	$-0.821283\pi$
$281$	−14.8241	−	25.6760i	−0.884329	−	1.53170i	−0.0378481	−	0.999284i	$-0.512050\pi$
$282$		0			0
$283$	11.2597	−	19.5024i	0.669322	−	1.15930i	−0.308772	−	0.951136i	$-0.599918\pi$
$283$	11.2597	−	19.5024i	0.669322	−	1.15930i	0.978094	−	0.208164i	$-0.0667486\pi$
$284$	0.184367	+	0.319333i	0.0109402	+	0.0189489i
$285$		0			0
$286$	−8.19465	+	14.1936i	−0.484560	+	0.839282i
$287$	−13.5951	−	23.5474i	−0.802493	−	1.38996i
$288$		0			0
$289$	−2.21732	+	3.84052i	−0.130431	+	0.225913i
$290$		−	6.64151i		−	0.390003i
$291$		0			0
$292$	−0.502336	−	0.870072i	−0.0293970	−	0.0509171i
$293$	−1.43273	−	2.48156i	−0.0837010	−	0.144974i	0.821136	−	0.570733i	$-0.193341\pi$
$293$	−1.43273	−	2.48156i	−0.0837010	−	0.144974i	−0.904837	+	0.425758i	$0.860007\pi$
$294$		0			0
$295$	−3.73379	+	2.15571i	−0.217390	+	0.125510i
$296$			10.7905i			0.627183i
$297$		0			0
$298$	−2.55127	−	1.47297i	−0.147791	−	0.0853271i
$299$	14.6146			0.845184
$300$		0			0
$301$	−21.7825	+	37.7284i	−1.25552	+	2.17463i
$302$	5.21644	+	3.01172i	0.300173	+	0.173305i
$303$		0			0
$304$	−20.2526	−	0.128660i	−1.16156	−	0.00737916i
$305$			20.1198i			1.15206i
$306$		0			0
$307$	−15.6503	+	9.03569i	−0.893208	+	0.515694i	−0.874990	−	0.484140i	$-0.839132\pi$
$307$	−15.6503	+	9.03569i	−0.893208	+	0.515694i	−0.0182175	+	0.999834i	$0.505799\pi$
$308$	−5.29436	+	3.05670i	−0.301674	+	0.174172i
$309$		0			0
$310$	6.61999			0.375990
$311$	−9.80717	+	5.66217i	−0.556114	+	0.321072i	−0.751584	−	0.659637i	$-0.770710\pi$
$311$	−9.80717	+	5.66217i	−0.556114	+	0.321072i	0.195470	+	0.980710i	$0.437377\pi$
$312$		0			0
$313$	−0.739097	−	1.28015i	−0.0417762	−	0.0723586i	0.844381	−	0.535743i	$-0.179968\pi$
$313$	−0.739097	−	1.28015i	−0.0417762	−	0.0723586i	−0.886157	+	0.463384i	$0.846635\pi$
$314$	−12.8302	+	22.2226i	−0.724052	+	1.25409i
$315$		0			0
$316$			0.213209i			0.0119939i
$317$	9.11745	+	15.7919i	0.512087	+	0.886961i	0.999902	+	0.0140137i	$0.00446084\pi$
$317$	9.11745	+	15.7919i	0.512087	+	0.886961i	−0.487815	+	0.872947i	$0.662206\pi$
$318$		0			0
$319$		−	7.10773i		−	0.397956i
$320$	9.44767	+	5.45461i	0.528141	+	0.304922i
$321$		0			0
$322$	28.0168	+	16.1755i	1.56131	+	0.901425i
$323$	13.4300	−	7.64047i	0.747265	−	0.425127i
$324$		0			0
$325$	4.23548	−	2.44536i	0.234942	−	0.135644i
$326$	15.8561			0.878190
$327$		0			0
$328$	6.97356	−	12.0786i	0.385051	−	0.666927i
$329$		−	45.8757i		−	2.52921i
$330$		0			0
$331$	−26.0644	−	15.0483i	−1.43263	−	0.827128i	−0.435306	−	0.900282i	$-0.643360\pi$
$331$	−26.0644	−	15.0483i	−1.43263	−	0.827128i	−0.997321	+	0.0731549i	$0.976693\pi$
$332$	−0.670430	−	0.387073i	−0.0367946	−	0.0212434i
$333$		0			0
$334$	−10.9619			−0.599806
$335$	−8.07701	+	13.9898i	−0.441294	+	0.764344i
$336$		0			0
$337$	−3.15674	−	1.82254i	−0.171958	−	0.0992802i	0.411551	−	0.911387i	$-0.364987\pi$
$337$	−3.15674	−	1.82254i	−0.171958	−	0.0992802i	−0.583509	+	0.812107i	$0.698321\pi$
$338$	2.46342			0.133993
$339$		0			0
$340$	2.70790			0.146856
$341$	7.08470			0.383658
$342$		0			0
$343$	44.5874			2.40749
$344$	−22.3466			−1.20485
$345$		0			0
$346$	−20.1615			−1.08389
$347$	−6.61837	−	3.82112i	−0.355293	−	0.205128i	0.311721	−	0.950174i	$-0.399095\pi$
$347$	−6.61837	−	3.82112i	−0.355293	−	0.205128i	−0.667014	+	0.745045i	$0.732428\pi$
$348$		0			0
$349$	−3.85492	+	6.67692i	−0.206349	+	0.357407i	−0.950562	−	0.310535i	$-0.899492\pi$
$349$	−3.85492	+	6.67692i	−0.206349	+	0.357407i	0.744212	+	0.667943i	$0.232825\pi$
$350$	10.8261			0.578681
$351$		0			0
$352$	−6.12170	−	3.53437i	−0.326288	−	0.188382i
$353$	14.8975	+	8.60109i	0.792915	+	0.457790i	0.840988	−	0.541054i	$-0.181975\pi$
$353$	14.8975	+	8.60109i	0.792915	+	0.457790i	−0.0480728	+	0.998844i	$0.515308\pi$
$354$		0			0
$355$			1.71463i			0.0910029i
$356$	3.03228	−	5.25207i	0.160711	−	0.278359i
$357$		0			0
$358$	13.3992			0.708167
$359$	−0.986080	+	0.569313i	−0.0520433	+	0.0300472i	−0.525796	−	0.850611i	$-0.676232\pi$
$359$	−0.986080	+	0.569313i	−0.0520433	+	0.0300472i	0.473753	+	0.880658i	$0.342899\pi$
$360$		0			0
$361$	18.9985	+	0.241396i	0.999919	+	0.0127050i
$362$	−3.20248	−	1.84895i	−0.168319	−	0.0971788i
$363$		0			0
$364$	−5.71724	−	3.30085i	−0.299665	−	0.173012i
$365$		−	4.67176i		−	0.244531i
$366$		0			0
$367$	−0.351324	−	0.608511i	−0.0183390	−	0.0317640i	0.856710	−	0.515798i	$-0.172504\pi$
$367$	−0.351324	−	0.608511i	−0.0183390	−	0.0317640i	−0.875049	+	0.484034i	$0.839171\pi$
$368$			20.1014i			1.04786i
$369$		0			0
$370$	6.37655	−	11.0445i	0.331501	−	0.574177i
$371$	19.5088	+	33.7903i	1.01285	+	1.75430i
$372$		0			0
$373$	8.13834	−	4.69867i	0.421387	−	0.243288i	−0.274283	−	0.961649i	$-0.588441\pi$
$373$	8.13834	−	4.69867i	0.421387	−	0.243288i	0.695671	+	0.718361i	$0.255107\pi$
$374$	17.1978			0.889279
$375$		0			0
$376$	20.3791	−	11.7659i	1.05097	−	0.606780i
$377$	6.64714	−	3.83773i	0.342345	−	0.197653i
$378$		0			0
$379$			24.1334i			1.23965i	0.784740	+	0.619825i	$0.212796\pi$
$379$			24.1334i			1.23965i	−0.784740	+	0.619825i	$0.787204\pi$
$380$	2.87308	+	1.68320i	0.147386	+	0.0863463i
$381$		0			0
$382$	−10.0268	−	5.78900i	−0.513018	−	0.296191i
$383$	14.4398	−	25.0105i	0.737841	−	1.27798i	−0.215625	−	0.976476i	$-0.569179\pi$
$383$	14.4398	−	25.0105i	0.737841	−	1.27798i	0.953466	−	0.301501i	$-0.0974878\pi$
$384$		0			0
$385$	−28.4275			−1.44880
$386$	−10.7677	−	6.21676i	−0.548063	−	0.316425i
$387$		0			0
$388$		−	5.46267i		−	0.277325i
$389$	−33.5426	+	19.3658i	−1.70068	+	0.981886i	−0.755602	+	0.655031i	$0.772655\pi$
$389$	−33.5426	+	19.3658i	−1.70068	+	0.981886i	−0.945075	+	0.326855i	$0.894011\pi$
$390$		0			0
$391$	−7.66780	−	13.2810i	−0.387777	−	0.671650i
$392$	20.0917	+	34.7999i	1.01478	+	1.75766i
$393$		0			0
$394$			12.7078i			0.640211i
$395$	−0.495715	+	0.858603i	−0.0249421	+	0.0432010i
$396$		0			0
$397$	−11.2189	−	19.4316i	−0.563058	−	0.975246i	−0.997227	−	0.0744143i	$-0.976291\pi$
$397$	−11.2189	−	19.4316i	−0.563058	−	0.975246i	0.434169	−	0.900831i	$-0.357042\pi$
$398$	3.37960	−	5.85364i	0.169404	−	0.293416i
$399$		0			0
$400$	3.36342	+	5.82561i	0.168171	+	0.291280i
$401$	2.32062	−	4.01943i	0.115886	−	0.200721i	−0.802248	−	0.596992i	$-0.796363\pi$
$401$	2.32062	−	4.01943i	0.115886	−	0.200721i	0.918134	+	0.396271i	$0.129696\pi$
$402$		0			0
$403$	3.82529	+	6.62560i	0.190551	+	0.330045i
$404$	5.19202	−	2.99762i	0.258313	−	0.149137i
$405$		0			0
$406$	16.9904			0.843221
$407$	6.82417	−	11.8198i	0.338261	−	0.585886i
$408$		0			0
$409$		−	19.2118i		−	0.949960i	−0.879997	−	0.474980i	$-0.842455\pi$
$409$		−	19.2118i		−	0.949960i	0.879997	−	0.474980i	$-0.157545\pi$
$410$	−14.2755	+	8.24197i	−0.705017	+	0.407042i
$411$		0			0
$412$	−2.44484	+	1.41153i	−0.120448	+	0.0695410i
$413$	−5.51476	−	9.55185i	−0.271364	−	0.470016i
$414$		0			0
$415$	−1.79990	−	3.11753i	−0.0883538	−	0.153033i
$416$		−	7.63334i		−	0.374255i
$417$		0			0
$418$	18.2469	+	10.6900i	0.892486	+	0.522865i
$419$	−9.67554	+	5.58618i	−0.472681	+	0.272903i	−0.717361	−	0.696701i	$-0.754650\pi$
$419$	−9.67554	+	5.58618i	−0.472681	+	0.272903i	0.244680	+	0.969604i	$0.421317\pi$
$420$		0			0
$421$		−	16.4137i		−	0.799955i	−0.916525	−	0.399978i	$-0.869018\pi$
$421$		−	16.4137i		−	0.799955i	0.916525	−	0.399978i	$-0.130982\pi$
$422$	−17.8068	−	10.2808i	−0.866822	−	0.500460i
$423$		0			0
$424$	−10.0070	+	17.3326i	−0.485983	+	0.841747i
$425$	−4.44444	−	2.56600i	−0.215587	−	0.124469i
$426$		0			0
$427$	−51.4709			−2.49085
$428$	−2.51702			−0.121665
$429$		0			0
$430$	22.8727	+	13.2056i	1.10302	+	0.636829i
$431$	−17.2912	+	29.9492i	−0.832888	+	1.44260i	0.0628504	+	0.998023i	$0.479981\pi$
$431$	−17.2912	+	29.9492i	−0.832888	+	1.44260i	−0.895738	+	0.444581i	$0.853352\pi$
$432$		0			0
$433$	−14.9639	−	8.63943i	−0.719121	−	0.415185i	0.0953081	−	0.995448i	$-0.469616\pi$
$433$	−14.9639	−	8.63943i	−0.719121	−	0.415185i	−0.814429	+	0.580263i	$0.802950\pi$
$434$			16.9354i			0.812924i
$435$		0			0
$436$	−1.07071	+	0.618172i	−0.0512775	+	0.0296051i
$437$	0.119797	−	18.8574i	0.00573066	−	0.902071i
$438$		0			0
$439$		−	29.1698i		−	1.39220i	−0.717946	−	0.696099i	$-0.754917\pi$
$439$		−	29.1698i		−	1.39220i	0.717946	−	0.696099i	$-0.245083\pi$
$440$	−7.29091	−	12.6282i	−0.347581	−	0.602027i
$441$		0			0
$442$	9.28575	+	16.0834i	0.441678	+	0.765009i
$443$	6.71346	−	3.87602i	0.318966	−	0.184155i	−0.331966	−	0.943291i	$-0.607712\pi$
$443$	6.71346	−	3.87602i	0.318966	−	0.184155i	0.650932	+	0.759136i	$0.274378\pi$
$444$		0			0
$445$	24.4223	−	14.1002i	1.15773	−	0.668416i
$446$		−	5.61264i		−	0.265766i
$447$		0			0
$448$	−13.9541	+	24.1692i	−0.659268	+	1.14189i
$449$	21.5509			1.01705			0.508526	−	0.861047i	$-0.330191\pi$
$449$	21.5509			1.01705			0.508526	+	0.861047i	$0.330191\pi$
$450$		0			0
$451$	−15.2776	+	8.82053i	−0.719394	+	0.415343i
$452$	−2.50314	−	4.33557i	−0.117738	−	0.203928i
$453$		0			0
$454$	−15.8136	+	27.3900i	−0.742170	+	1.28548i
$455$	−15.3491	−	26.5854i	−0.719576	−	1.24634i
$456$		0			0
$457$	−1.05039	+	1.81932i	−0.0491350	+	0.0851044i	−0.889547	−	0.456844i	$-0.848980\pi$
$457$	−1.05039	+	1.81932i	−0.0491350	+	0.0851044i	0.840412	+	0.541948i	$0.182313\pi$
$458$	−4.22559	−	7.31894i	−0.197449	−	0.341992i
$459$		0			0
$460$	1.65245	−	2.86213i	0.0770458	−	0.133447i
$461$		−	25.9098i		−	1.20674i	−0.797461	−	0.603370i	$-0.793824\pi$
$461$		−	25.9098i		−	1.20674i	0.797461	−	0.603370i	$-0.206176\pi$
$462$		0			0
$463$	9.23702	+	15.9990i	0.429281	+	0.743536i	0.996809	−	0.0798177i	$-0.0254338\pi$
$463$	9.23702	+	15.9990i	0.429281	+	0.743536i	−0.567529	+	0.823354i	$0.692100\pi$
$464$	5.27852	+	9.14267i	0.245049	+	0.424438i
$465$		0			0
$466$	−34.5626	+	19.9547i	−1.60108	+	0.924384i
$467$		−	29.7747i		−	1.37781i	−0.724852	−	0.688905i	$-0.758092\pi$
$467$		−	29.7747i		−	1.37781i	0.724852	−	0.688905i	$-0.241908\pi$
$468$		0			0
$469$	−35.7889	−	20.6627i	−1.65258	−	0.954117i
$470$	−27.8119			−1.28287
$471$		0			0
$472$	2.82878	−	4.89959i	0.130205	−	0.225522i
$473$	24.4783	+	14.1326i	1.12551	+	0.649815i
$474$		0			0
$475$	−3.12055	−	5.48514i	−0.143181	−	0.251675i
$476$			6.92739i			0.317516i
$477$		0			0
$478$	−16.3048	+	9.41355i	−0.745762	+	0.430566i
$479$	−12.7572	+	7.36537i	−0.582891	+	0.336532i	−0.762282	−	0.647246i	$-0.775921\pi$
$479$	−12.7572	+	7.36537i	−0.582891	+	0.336532i	0.179390	+	0.983778i	$0.442587\pi$
$480$		0			0
$481$	14.7385			0.672017
$482$	25.5917	−	14.7754i	1.16567	−	0.673000i
$483$		0			0
$484$	−0.246045	−	0.426163i	−0.0111839	−	0.0193711i
$485$	12.7008	−	21.9985i	0.576714	−	0.998898i
$486$		0			0
$487$		−	14.0498i		−	0.636658i	−0.947980	−	0.318329i	$-0.896878\pi$
$487$		−	14.0498i		−	0.636658i	0.947980	−	0.318329i	$-0.103122\pi$
$488$	−13.2009	−	22.8647i	−0.597577	−	1.03503i
$489$		0			0
$490$		−	47.4923i		−	2.14548i
$491$	−14.3849	−	8.30510i	−0.649180	−	0.374804i	0.138962	−	0.990298i	$-0.455623\pi$
$491$	−14.3849	−	8.30510i	−0.649180	−	0.374804i	−0.788142	+	0.615494i	$0.788957\pi$
$492$		0			0
$493$	−6.97506	−	4.02706i	−0.314141	−	0.181369i
$494$	−0.145075	+	22.8364i	−0.00652722	+	1.02746i
$495$		0			0
$496$	−9.11304	+	5.26142i	−0.409188	+	0.236245i
$497$	−4.38638			−0.196756
$498$		0			0
$499$	11.2873	−	19.5502i	0.505288	−	0.875185i	−0.494693	−	0.869068i	$-0.664719\pi$
$499$	11.2873	−	19.5502i	0.505288	−	0.875185i	0.999981	−	0.00611735i	$-0.00194723\pi$
$500$		−	4.92554i		−	0.220277i
$501$		0			0
$502$	12.0051	+	6.93116i	0.535814	+	0.309353i
$503$	25.4796	+	14.7107i	1.13608	+	0.655917i	0.945457	−	0.325746i	$-0.105616\pi$
$503$	25.4796	+	14.7107i	1.13608	+	0.655917i	0.190624	+	0.981663i	$0.438949\pi$
$504$		0			0
$505$	27.8781			1.24056
$506$	10.4947	−	18.1774i	0.466546	−	0.808082i
$507$		0			0
$508$	1.35808	+	0.784090i	0.0602552	+	0.0347883i
$509$	31.2421			1.38478			0.692391	−	0.721522i	$-0.256557\pi$
$509$	31.2421			1.38478			0.692391	+	0.721522i	$0.256557\pi$
$510$		0			0
$511$	11.9514			0.528698
$512$	−12.4837			−0.551705
$513$		0			0
$514$	−9.08961			−0.400925
$515$	−13.1273			−0.578459
$516$		0			0
$517$	−29.7643			−1.30903
$518$	28.2543	+	16.3126i	1.24142	+	0.716735i
$519$		0			0
$520$	7.87327	−	13.6369i	0.345266	−	0.598018i
$521$	0.424924			0.0186163			0.00930814	−	0.999957i	$-0.497037\pi$
$521$	0.424924			0.0186163			0.00930814	+	0.999957i	$0.497037\pi$
$522$		0			0
$523$	31.0533	+	17.9286i	1.35787	+	0.783964i	0.989336	−	0.145652i	$-0.0465278\pi$
$523$	31.0533	+	17.9286i	1.35787	+	0.783964i	0.368530	+	0.929616i	$0.379861\pi$
$524$	4.58677	+	2.64817i	0.200374	+	0.115686i
$525$		0			0
$526$		−	9.25002i		−	0.403320i
$527$	4.01401	−	6.95246i	0.174853	−	0.302854i
$528$		0			0
$529$	4.28342			0.186236
$530$	20.4852	−	11.8271i	0.889821	−	0.513738i
$531$		0			0
$532$	−4.30599	+	7.34996i	−0.186688	+	0.318661i
$533$	−16.4979	−	9.52506i	−0.714603	−	0.412576i
$534$		0			0
$535$	−10.1362	−	5.85211i	−0.438224	−	0.253009i
$536$		−	21.1978i		−	0.915605i
$537$		0			0
$538$	6.59327	+	11.4199i	0.284256	+	0.492346i
$539$		−	50.8261i		−	2.18924i
$540$		0			0
$541$	9.92108	−	17.1838i	0.426541	−	0.738790i	−0.570022	−	0.821629i	$-0.693065\pi$
$541$	9.92108	−	17.1838i	0.426541	−	0.738790i	0.996563	+	0.0828391i	$0.0263988\pi$
$542$	5.96155	+	10.3257i	0.256071	+	0.443527i
$543$		0			0
$544$	−6.93679	+	4.00496i	−0.297413	+	0.171711i
$545$	−5.74905			−0.246262
$546$		0			0
$547$	−17.8362	+	10.2978i	−0.762622	+	0.440300i	−0.830236	−	0.557411i	$-0.811795\pi$
$547$	−17.8362	+	10.2978i	−0.762622	+	0.440300i	0.0676143	+	0.997712i	$0.478461\pi$
$548$	−0.316409	+	0.182679i	−0.0135163	+	0.00780366i
$549$		0			0
$550$		−	7.02401i		−	0.299505i
$551$	−4.89737	−	8.60833i	−0.208635	−	0.366727i
$552$		0			0
$553$	−2.19649	−	1.26815i	−0.0934043	−	0.0539270i
$554$	−23.8311	+	41.2767i	−1.01249	+	1.75368i
$555$		0			0
$556$	7.84923			0.332882
$557$	9.85951	+	5.69239i	0.417761	+	0.241194i	0.694119	−	0.719860i	$-0.255794\pi$
$557$	9.85951	+	5.69239i	0.417761	+	0.241194i	−0.276358	+	0.961055i	$0.589128\pi$
$558$		0			0
$559$			30.5228i			1.29098i
$560$	36.5663	−	21.1116i	1.54521	−	0.892127i
$561$		0			0
$562$	−22.9907	−	39.8211i	−0.969806	−	1.67975i
$563$	−22.3588	−	38.7266i	−0.942311	−	1.63213i	−0.761048	−	0.648695i	$-0.775315\pi$
$563$	−22.3588	−	38.7266i	−0.942311	−	1.63213i	−0.181263	−	0.983435i	$-0.558018\pi$
$564$		0			0
$565$		−	23.2794i		−	0.979374i
$566$	17.4628	−	30.2465i	0.734017	−	1.27135i
$567$		0			0
$568$	−1.12499	−	1.94854i	−0.0472036	−	0.0817590i
$569$	−0.560747	+	0.971242i	−0.0235077	+	0.0407166i	−0.877540	−	0.479504i	$-0.840817\pi$
$569$	−0.560747	+	0.971242i	−0.0235077	+	0.0407166i	0.854032	+	0.520220i	$0.174150\pi$
$570$		0			0
$571$	9.40145	+	16.2838i	0.393438	+	0.681455i	0.992900	−	0.118948i	$-0.0379522\pi$
$571$	9.40145	+	16.2838i	0.393438	+	0.681455i	−0.599462	+	0.800403i	$0.704619\pi$
$572$	−2.14160	+	3.70936i	−0.0895448	+	0.155096i
$573$		0			0
$574$	−21.0847	−	36.5198i	−0.880060	−	1.52431i
$575$	−5.42429	+	3.13171i	−0.226208	+	0.130601i
$576$		0			0
$577$	−23.2617			−0.968397			−0.484199	−	0.874958i	$-0.660889\pi$
$577$	−23.2617			−0.968397			−0.484199	+	0.874958i	$0.660889\pi$
$578$	−3.43887	+	5.95629i	−0.143038	+	0.247749i
$579$		0			0
$580$		−	1.73570i		−	0.0720711i
$581$	7.97531	−	4.60455i	0.330872	−	0.191029i
$582$		0			0
$583$	21.9232	−	12.6574i	0.907967	−	0.524215i
$584$	3.06521	+	5.30911i	0.126839	+	0.219692i
$585$		0			0
$586$	−2.22203	−	3.84867i	−0.0917913	−	0.158987i
$587$		−	6.50799i		−	0.268613i	−0.990940	−	0.134307i	$-0.957119\pi$
$587$		−	6.50799i		−	0.268613i	0.990940	−	0.134307i	$-0.0428807\pi$
$588$		0			0
$589$	8.58044	−	4.88150i	0.353551	−	0.201139i
$590$	−5.79077	+	3.34330i	−0.238402	+	0.137642i
$591$		0			0
$592$			20.2717i			0.833164i
$593$	−8.23530	−	4.75465i	−0.338183	−	0.195250i	0.321285	−	0.946983i	$-0.395885\pi$
$593$	−8.23530	−	4.75465i	−0.338183	−	0.195250i	−0.659468	+	0.751732i	$0.729219\pi$
$594$		0			0
$595$	−16.1063	+	27.8970i	−0.660294	+	1.14366i
$596$	−0.666751	−	0.384949i	−0.0273112	−	0.0157681i
$597$		0			0
$598$	22.6659			0.926878
$599$	−36.5823			−1.49471			−0.747355	−	0.664424i	$-0.768677\pi$
$599$	−36.5823			−1.49471			−0.747355	+	0.664424i	$0.768677\pi$
$600$		0			0
$601$	−39.1747	−	22.6175i	−1.59797	−	0.922587i	−0.991878	−	0.127190i	$-0.959404\pi$
$601$	−39.1747	−	22.6175i	−1.59797	−	0.922587i	−0.606089	−	0.795397i	$-0.707263\pi$
$602$	−33.7827	+	58.5133i	−1.37688	+	2.38483i
$603$		0			0
$604$	1.36327	+	0.787085i	0.0554707	+	0.0320261i
$605$		−	2.28824i		−	0.0930303i
$606$		0			0
$607$	−29.9152	+	17.2715i	−1.21422	+	0.701030i	−0.963676	−	0.267075i	$-0.913943\pi$
$607$	−29.9152	+	17.2715i	−1.21422	+	0.701030i	−0.250544	+	0.968105i	$0.580609\pi$
$608$	−9.84938	−	0.0625710i	−0.399445	−	0.00253759i
$609$		0			0
$610$			31.2040i			1.26341i
$611$	−16.0708	−	27.8355i	−0.650156	−	1.12610i
$612$		0			0
$613$	−5.78197	−	10.0147i	−0.233531	−	0.404488i	0.725313	−	0.688419i	$-0.241695\pi$
$613$	−5.78197	−	10.0147i	−0.233531	−	0.404488i	−0.958845	+	0.283930i	$0.908362\pi$
$614$	−24.2721	+	14.0135i	−0.979543	+	0.565540i
$615$		0			0
$616$	32.3058	−	18.6517i	1.30164	−	0.751500i
$617$			34.7791i			1.40015i	0.714067	+	0.700077i	$0.246851\pi$
$617$			34.7791i			1.40015i	−0.714067	+	0.700077i	$0.753149\pi$
$618$		0			0
$619$	8.34985	−	14.4624i	0.335609	−	0.581291i	−0.647993	−	0.761646i	$-0.724391\pi$
$619$	8.34985	−	14.4624i	0.335609	−	0.581291i	0.983602	+	0.180355i	$0.0577247\pi$
$620$	1.73008			0.0694816
$621$		0			0
$622$	−15.2100	+	8.78151i	−0.609866	+	0.352107i
$623$	36.0715	+	62.4776i	1.44517	+	2.50311i
$624$		0			0
$625$	7.83257	−	13.5664i	0.313303	−	0.542656i
$626$	−1.14627	−	1.98540i	−0.0458142	−	0.0793526i
$627$		0			0
$628$	−3.35307	+	5.80768i	−0.133802	+	0.231752i
$629$	−7.73279	−	13.3936i	−0.308327	−	0.534038i
$630$		0			0
$631$	14.7130	−	25.4837i	0.585717	−	1.01449i	−0.409069	−	0.912503i	$-0.634146\pi$
$631$	14.7130	−	25.4837i	0.585717	−	1.01449i	0.994786	−	0.101988i	$-0.0325202\pi$
$632$		−	1.30098i		−	0.0517503i
$633$		0			0
$634$	14.1403	+	24.4918i	0.561584	+	0.972693i
$635$	3.64605	+	6.31514i	0.144689	+	0.250609i
$636$		0			0
$637$	47.5325	−	27.4429i	1.88331	−	1.08733i
$638$		−	11.0234i		−	0.436422i
$639$		0			0
$640$	22.0290	+	12.7184i	0.870772	+	0.502741i
$641$	−29.8671			−1.17968			−0.589840	−	0.807520i	$-0.700809\pi$
$641$	−29.8671			−1.17968			−0.589840	+	0.807520i	$0.700809\pi$
$642$		0			0
$643$	−9.93240	+	17.2034i	−0.391696	+	0.678437i	−0.992673	−	0.120829i	$-0.961445\pi$
$643$	−9.93240	+	17.2034i	−0.391696	+	0.678437i	0.600978	+	0.799266i	$0.294778\pi$
$644$	7.32194	+	4.22732i	0.288525	+	0.166580i
$645$		0			0
$646$	20.8287	−	11.8497i	0.819494	−	0.466219i
$647$			29.2696i			1.15071i	0.817905	+	0.575353i	$0.195135\pi$
$647$			29.2696i			1.15071i	−0.817905	+	0.575353i	$0.804865\pi$
$648$		0			0
$649$	−6.19726	+	3.57799i	−0.243264	+	0.140448i
$650$	6.56885	−	3.79253i	0.257651	−	0.148755i
$651$		0			0
$652$	4.14386			0.162286
$653$	−15.4957	+	8.94643i	−0.606393	+	0.350101i	−0.771552	−	0.636166i	$-0.780519\pi$
$653$	−15.4957	+	8.94643i	−0.606393	+	0.350101i	0.165160	+	0.986267i	$0.447186\pi$
$654$		0			0
$655$	12.3141	+	21.3287i	0.481152	+	0.833380i
$656$	13.1011	−	22.6917i	0.511510	−	0.885962i
$657$		0			0
$658$		−	71.1490i		−	2.77368i
$659$	−10.9352	−	18.9404i	−0.425977	−	0.737813i	0.570534	−	0.821274i	$-0.306736\pi$
$659$	−10.9352	−	18.9404i	−0.425977	−	0.737813i	−0.996511	+	0.0834604i	$0.973403\pi$
$660$		0			0
$661$		−	4.09721i		−	0.159363i	−0.996820	−	0.0796816i	$-0.974610\pi$
$661$		−	4.09721i		−	0.159363i	0.996820	−	0.0796816i	$-0.0253903\pi$
$662$	−40.4234	−	23.3385i	−1.57110	−	0.907076i
$663$		0			0
$664$	4.09091	+	2.36189i	0.158758	+	0.0916591i
$665$	−34.4292	+	19.5872i	−1.33511	+	0.759558i
$666$		0			0
$667$	−8.51283	+	4.91489i	−0.329618	+	0.190305i
$668$	−2.86479			−0.110842
$669$		0			0
$670$	−12.5267	+	21.6969i	−0.483949	+	0.838224i
$671$			33.3944i			1.28918i
$672$		0			0
$673$	20.9877	+	12.1172i	0.809015	+	0.467085i	0.846614	−	0.532208i	$-0.178638\pi$
$673$	20.9877	+	12.1172i	0.809015	+	0.467085i	−0.0375989	+	0.999293i	$0.511971\pi$
$674$	−4.89581	−	2.82660i	−0.188579	−	0.108876i
$675$		0			0
$676$	0.643794			0.0247613
$677$	10.2196	−	17.7009i	0.392773	−	0.680302i	−0.600041	−	0.799969i	$-0.704849\pi$
$677$	10.2196	−	17.7009i	0.392773	−	0.680302i	0.992814	+	0.119667i	$0.0381826\pi$
$678$		0			0
$679$	56.2768	+	32.4914i	2.15971	+	1.24691i
$680$	−16.5234			−0.633642
$681$		0			0
$682$	10.9877			0.420741
$683$	−26.3929			−1.00990			−0.504949	−	0.863149i	$-0.668489\pi$
$683$	−26.3929			−1.00990			−0.504949	+	0.863149i	$0.668489\pi$
$684$		0			0
$685$	−1.69893			−0.0649128
$686$	69.1510			2.64020
$687$		0			0
$688$	−41.9819			−1.60054
$689$	23.6743	+	13.6684i	0.901920	+	0.520724i
$690$		0			0
$691$	2.05478	−	3.55898i	0.0781674	−	0.135390i	−0.824292	−	0.566165i	$-0.808426\pi$
$691$	2.05478	−	3.55898i	0.0781674	−	0.135390i	0.902459	+	0.430775i	$0.141760\pi$
$692$	−5.26904			−0.200299
$693$		0			0
$694$	−10.2645	−	5.92621i	−0.389635	−	0.224956i
$695$	31.6093	+	18.2496i	1.19901	+	0.692248i
$696$		0			0
$697$			19.9899i			0.757173i
$698$	−5.97863	+	10.3553i	−0.226295	+	0.391954i
$699$		0			0
$700$	2.82931			0.106938
$701$	−17.9358	+	10.3552i	−0.677424	+	0.391111i	−0.798884	−	0.601485i	$-0.794576\pi$
$701$	−17.9358	+	10.3552i	−0.677424	+	0.391111i	0.121460	+	0.992596i	$0.461242\pi$
$702$		0			0
$703$	0.120812	−	19.0172i	0.00455652	−	0.717248i
$704$	15.6810	+	9.05344i	0.591001	+	0.341214i
$705$		0			0
$706$	23.1047	+	13.3395i	0.869556	+	0.502039i
$707$			71.3181i			2.68220i
$708$		0			0
$709$	−6.04698	−	10.4737i	−0.227099	−	0.393347i	0.729848	−	0.683610i	$-0.239591\pi$
$709$	−6.04698	−	10.4737i	−0.227099	−	0.393347i	−0.956947	+	0.290262i	$0.906258\pi$
$710$			2.65923i			0.0997990i
$711$		0			0
$712$	−18.5028	+	32.0477i	−0.693420	+	1.20104i
$713$	−4.89896	−	8.48525i	−0.183468	−	0.317775i
$714$		0			0
$715$	−17.2487	+	9.95853i	−0.645064	+	0.372428i
$716$	3.50175			0.130867
$717$		0			0
$718$	−1.52932	+	0.882953i	−0.0570737	+	0.0329515i
$719$	−19.5960	+	11.3137i	−0.730807	+	0.421932i	−0.818717	−	0.574197i	$-0.805314\pi$
$719$	−19.5960	+	11.3137i	−0.730807	+	0.421932i	0.0879104	+	0.996128i	$0.471981\pi$
$720$		0			0
$721$		−	33.5825i		−	1.25068i
$722$	29.4649	+	0.374383i	1.09657	+	0.0139331i
$723$		0			0
$724$	−0.836941	−	0.483208i	−0.0311047	−	0.0179583i
$725$	−1.64475	+	2.84878i	−0.0610844	+	0.105801i
$726$		0			0
$727$	−38.6937			−1.43507			−0.717536	−	0.696522i	$-0.754730\pi$
$727$	−38.6937			−1.43507			−0.717536	+	0.696522i	$0.754730\pi$
$728$	34.8862	+	20.1415i	1.29297	+	0.746495i
$729$		0			0
$730$		−	7.24548i		−	0.268167i
$731$	27.7375	−	16.0143i	1.02591	−	0.592309i
$732$		0			0
$733$	−12.7820	−	22.1391i	−0.472114	−	0.817725i	0.527377	−	0.849631i	$-0.323175\pi$
$733$	−12.7820	−	22.1391i	−0.472114	−	0.817725i	−0.999491	+	0.0319066i	$0.989842\pi$
$734$	−0.544871	−	0.943745i	−0.0201116	−	0.0348343i
$735$		0			0
$736$			9.77584i			0.360342i
$737$	−13.4060	+	23.2199i	−0.493818	+	0.855318i
$738$		0			0
$739$	17.9188	+	31.0363i	0.659154	+	1.14169i	0.980835	+	0.194840i	$0.0624187\pi$
$739$	17.9188	+	31.0363i	0.659154	+	1.14169i	−0.321681	+	0.946848i	$0.604248\pi$
$740$	1.66646	−	2.88639i	0.0612602	−	0.106106i
$741$		0			0
$742$	30.2564	+	52.4056i	1.11075	+	1.92387i
$743$	6.70454	−	11.6126i	0.245966	−	0.426025i	−0.716437	−	0.697652i	$-0.754228\pi$
$743$	6.70454	−	11.6126i	0.245966	−	0.426025i	0.962403	+	0.271627i	$0.0875617\pi$
$744$		0			0
$745$	−1.79003	−	3.10042i	−0.0655816	−	0.113591i
$746$	12.6218	−	7.28721i	0.462118	−	0.266804i
$747$		0			0
$748$	4.49451			0.164335
$749$	14.9710	−	25.9305i	0.547028	−	0.947480i
$750$		0			0
$751$			42.9817i			1.56842i	0.620493	+	0.784212i	$0.286933\pi$
$751$			42.9817i			1.56842i	−0.620493	+	0.784212i	$0.713067\pi$
$752$	38.2858	−	22.1043i	1.39614	−	0.806061i
$753$		0			0
$754$	10.3091	−	5.95196i	0.375435	−	0.216758i
$755$	3.65998	+	6.33927i	0.133200	+	0.230710i
$756$		0			0
$757$	9.39734	+	16.2767i	0.341552	+	0.591586i	0.984721	−	0.174139i	$-0.0557141\pi$
$757$	9.39734	+	16.2767i	0.341552	+	0.591586i	−0.643169	+	0.765724i	$0.722381\pi$
$758$			37.4287i			1.35947i
$759$		0			0
$760$	−17.5313	−	10.2707i	−0.635927	−	0.372559i
$761$	30.5686	−	17.6488i	1.10811	−	0.639769i	0.169772	−	0.985483i	$-0.445697\pi$
$761$	30.5686	−	17.6488i	1.10811	−	0.639769i	0.938340	+	0.345715i	$0.112363\pi$
$762$		0			0
$763$		−	14.7073i		−	0.532441i
$764$	−2.62043	−	1.51290i	−0.0948037	−	0.0547349i
$765$		0			0
$766$	22.3948	−	38.7890i	0.809159	−	1.40150i
$767$	−6.69227	−	3.86378i	−0.241644	−	0.139513i
$768$		0			0
$769$	50.3388			1.81526			0.907632	−	0.419767i	$-0.137888\pi$
$769$	50.3388			1.81526			0.907632	+	0.419767i	$0.137888\pi$
$770$	−44.0885			−1.58884
$771$		0			0
$772$	−2.81405	−	1.62469i	−0.101280	−	0.0584740i
$773$	15.2092	−	26.3432i	0.547039	−	0.947499i	−0.451437	−	0.892303i	$-0.649088\pi$
$773$	15.2092	−	26.3432i	0.547039	−	0.947499i	0.998476	−	0.0551956i	$-0.0175782\pi$
$774$		0			0
$775$	−2.83955	−	1.63942i	−0.102000	−	0.0588896i
$776$			33.3328i			1.19658i
$777$		0			0
$778$	−52.0215	+	30.0346i	−1.86506	+	1.07679i
$779$	−12.4255	+	21.2093i	−0.445191	+	0.759903i
$780$		0			0
$781$			2.84590i			0.101834i
$782$	−11.8920	−	20.5976i	−0.425259	−	0.736570i
$783$		0			0
$784$	37.7458	+	65.3776i	1.34806	+	2.33491i
$785$	−27.0060	+	15.5919i	−0.963884	+	0.556499i
$786$		0			0
$787$	21.5905	−	12.4653i	0.769619	−	0.444340i	−0.0631196	−	0.998006i	$-0.520105\pi$
$787$	21.5905	−	12.4653i	0.769619	−	0.444340i	0.832739	+	0.553666i	$0.186772\pi$
$788$			3.32108i			0.118309i
$789$		0			0
$790$	−0.768808	+	1.33161i	−0.0273530	+	0.0473767i
$791$	59.5539			2.11749
$792$		0			0
$793$	−31.2304	+	18.0309i	−1.10902	+	0.640296i
$794$	−17.3994	−	30.1367i	−0.617482	−	1.06951i
$795$		0			0
$796$	0.883229	−	1.52980i	0.0313052	−	0.0542222i
$797$	22.8991	+	39.6625i	0.811129	+	1.40492i	0.912074	+	0.410025i	$0.134480\pi$
$797$	22.8991	+	39.6625i	0.811129	+	1.40492i	−0.100945	+	0.994892i	$0.532187\pi$
$798$		0			0
$799$	−16.8637	+	29.2087i	−0.596594	+	1.03333i
$800$	1.63572	+	2.83315i	0.0578315	+	0.100167i
$801$		0			0
$802$	3.59906	−	6.23376i	0.127087	−	0.220122i
$803$		−	7.75409i		−	0.273636i
$804$		0			0
$805$	19.6572	+	34.0473i	0.692826	+	1.20001i
$806$	5.93268	+	10.2757i	0.208970	+	0.361946i
$807$		0			0
$808$	−31.6813	+	18.2912i	−1.11454	+	0.643483i
$809$			28.2911i			0.994662i	0.867561	+	0.497331i	$0.165686\pi$
$809$			28.2911i			0.994662i	−0.867561	+	0.497331i	$0.834314\pi$
$810$		0			0
$811$	8.53722	+	4.92896i	0.299782	+	0.173079i	0.642345	−	0.766416i	$-0.277962\pi$
$811$	8.53722	+	4.92896i	0.299782	+	0.173079i	−0.342563	+	0.939495i	$0.611295\pi$
$812$	4.44030			0.155824
$813$		0			0
$814$	10.5837	−	18.3314i	0.370957	−	0.642517i
$815$	16.6875	+	9.63456i	0.584539	+	0.337484i
$816$		0			0
$817$	39.3838	+	0.250197i	1.37787	+	0.00875328i
$818$		−	29.7957i		−	1.04178i
$819$		0			0
$820$	−3.73078	+	2.15397i	−0.130284	+	0.0752198i
$821$	35.3705	−	20.4211i	1.23444	−	0.712703i	0.266486	−	0.963839i	$-0.414137\pi$
$821$	35.3705	−	20.4211i	1.23444	−	0.712703i	0.967952	+	0.251136i	$0.0808041\pi$
$822$		0			0
$823$	−36.6191			−1.27646			−0.638231	−	0.769845i	$-0.720334\pi$
$823$	−36.6191			−1.27646			−0.638231	+	0.769845i	$0.720334\pi$
$824$	14.9182	−	8.61303i	0.519700	−	0.300049i
$825$		0			0
$826$	−8.55289	−	14.8140i	−0.297593	−	0.515446i
$827$	19.3427	−	33.5025i	0.672611	−	1.16500i	−0.304550	−	0.952496i	$-0.598506\pi$
$827$	19.3427	−	33.5025i	0.672611	−	1.16500i	0.977161	−	0.212500i	$-0.0681606\pi$
$828$		0			0
$829$			19.0627i			0.662076i	0.943617	+	0.331038i	$0.107399\pi$
$829$			19.0627i			0.662076i	−0.943617	+	0.331038i	$0.892601\pi$
$830$	−2.79149	−	4.83500i	−0.0968939	−	0.167825i
$831$		0			0
$832$			19.5532i			0.677884i
$833$	−49.8775	−	28.7968i	−1.72815	−	0.997749i
$834$		0			0
$835$	−11.5366	−	6.66068i	−0.399242	−	0.230502i
$836$	4.76867	+	2.79374i	0.164928	+	0.0966234i
$837$		0			0
$838$	−15.0059	+	8.66365i	−0.518370	+	0.299281i
$839$	6.76647			0.233604			0.116802	−	0.993155i	$-0.462736\pi$
$839$	6.76647			0.233604			0.116802	+	0.993155i	$0.462736\pi$
$840$		0			0
$841$	11.9187	−	20.6439i	0.410991	−	0.711858i
$842$		−	25.4562i		−	0.877277i
$843$		0			0
$844$	−4.65365	−	2.68679i	−0.160185	−	0.0924830i
$845$	2.59259	+	1.49683i	0.0891879	+	0.0514927i
$846$		0			0
$847$	5.85382			0.201140
$848$	−18.7999	+	32.5624i	−0.645591	+	1.11820i
$849$		0			0
$850$	−6.89291	−	3.97962i	−0.236425	−	0.136500i
$851$	−18.8752			−0.647035
$852$		0			0
$853$	4.02737			0.137895			0.0689473	−	0.997620i	$-0.478036\pi$
$853$	4.02737			0.137895			0.0689473	+	0.997620i	$0.478036\pi$
$854$	−79.8266			−2.73161
$855$		0			0
$856$	15.3586			0.524947
$857$	18.6163			0.635921			0.317960	−	0.948104i	$-0.397002\pi$
$857$	18.6163			0.635921			0.317960	+	0.948104i	$0.397002\pi$
$858$		0			0
$859$	35.0162			1.19474			0.597369	−	0.801967i	$-0.296213\pi$
$859$	35.0162			1.19474			0.597369	+	0.801967i	$0.296213\pi$
$860$	5.97758	+	3.45116i	0.203834	+	0.117683i
$861$		0			0
$862$	−26.8171	+	46.4485i	−0.913393	+	1.58204i
$863$	−7.92119			−0.269640			−0.134820	−	0.990870i	$-0.543046\pi$
$863$	−7.92119			−0.269640			−0.134820	+	0.990870i	$0.543046\pi$
$864$		0			0
$865$	−21.2187	−	12.2506i	−0.721458	−	0.416534i
$866$	−23.2077	−	13.3990i	−0.788630	−	0.455315i
$867$		0			0
$868$			4.42591i			0.150225i
$869$	−0.822776	+	1.42509i	−0.0279108	+	0.0483429i
$870$		0			0
$871$	−28.9537			−0.981058
$872$	6.53336	−	3.77204i	0.221248	−	0.127737i
$873$		0			0
$874$	0.185794	−	29.2461i	0.00628457	−	0.989263i
$875$	50.7433	+	29.2967i	1.71544	+	0.990408i
$876$		0			0
$877$	36.5066	+	21.0771i	1.23274	+	0.711723i	0.967600	−	0.252487i	$-0.0812485\pi$
$877$	36.5066	+	21.0771i	1.23274	+	0.711723i	0.265140	+	0.964210i	$0.414582\pi$
$878$		−	45.2397i		−	1.52677i
$879$		0			0
$880$	−13.6972	−	23.7243i	−0.461734	−	0.799747i
$881$			45.4405i			1.53093i	0.643478	+	0.765464i	$0.277491\pi$
$881$			45.4405i			1.53093i	−0.643478	+	0.765464i	$0.722509\pi$
$882$		0			0
$883$	9.23912	−	16.0026i	0.310921	−	0.538531i	−0.667641	−	0.744483i	$-0.732696\pi$
$883$	9.23912	−	16.0026i	0.310921	−	0.538531i	0.978562	+	0.205952i	$0.0660292\pi$
$884$	2.42675	+	4.20326i	0.0816205	+	0.141371i
$885$		0			0
$886$	10.4120	−	6.01134i	0.349796	−	0.201955i
$887$	−6.44133			−0.216279			−0.108139	−	0.994136i	$-0.534489\pi$
$887$	−6.44133			−0.216279			−0.108139	+	0.994136i	$0.534489\pi$
$888$		0			0
$889$	−16.1555	+	9.32738i	−0.541838	+	0.312830i
$890$	37.8768	−	21.8682i	1.26963	−	0.733023i
$891$		0			0
$892$		−	1.46681i		−	0.0491126i
$893$	−36.0482	+	20.5082i	−1.20631	+	0.686281i
$894$		0			0
$895$	14.1017	+	8.14164i	0.471369	+	0.272145i
$896$	−32.5365	+	56.3549i	−1.08697	+	1.88269i
$897$		0			0
$898$	33.4235			1.11536
$899$	−4.45637	−	2.57289i	−0.148628	−	0.0858106i
$900$		0			0
$901$		−	28.6854i		−	0.955648i
$902$	−23.6942	+	13.6798i	−0.788929	+	0.455489i
$903$		0			0
$904$	15.2740	+	26.4553i	0.508005	+	0.879891i
$905$	−2.24694	−	3.89181i	−0.0746907	−	0.129368i
$906$		0			0
$907$			4.67863i			0.155351i	0.996979	+	0.0776757i	$0.0247499\pi$
$907$			4.67863i			0.155351i	−0.996979	+	0.0776757i	$0.975250\pi$
$908$	−4.13275	+	7.15814i	−0.137150	+	0.237551i
$909$		0			0
$910$	−23.8050	−	41.2315i	−0.789129	−	1.36681i
$911$	−0.563718	+	0.976388i	−0.0186768	+	0.0323492i	−0.875213	−	0.483738i	$-0.839279\pi$
$911$	−0.563718	+	0.976388i	−0.0186768	+	0.0323492i	0.856536	+	0.516087i	$0.172612\pi$
$912$		0			0
$913$	−2.98744	−	5.17440i	−0.0988699	−	0.171248i
$914$	−1.62905	+	2.82160i	−0.0538843	+	0.0933304i
$915$		0			0
$916$	−1.10432	−	1.91274i	−0.0364878	−	0.0631987i
$917$	−54.5634	+	31.5022i	−1.80184	+	1.04029i
$918$		0			0
$919$	5.71119			0.188395			0.0941974	−	0.995554i	$-0.469972\pi$
$919$	5.71119			0.188395			0.0941974	+	0.995554i	$0.469972\pi$
$920$	−10.0831	+	17.4645i	−0.332430	+	0.575786i
$921$		0			0
$922$		−	40.1837i		−	1.32338i
$923$	−2.66148	+	1.53661i	−0.0876037	+	0.0505780i
$924$		0			0
$925$	−5.47027	+	3.15826i	−0.179861	+	0.103843i
$926$	14.3258	+	24.8130i	0.470774	+	0.815404i
$927$		0			0
$928$	2.56709	+	4.44633i	0.0842689	+	0.145958i
$929$		−	28.9821i		−	0.950873i	−0.879750	−	0.475437i	$-0.842290\pi$
$929$		−	28.9821i		−	0.950873i	0.879750	−	0.475437i	$-0.157710\pi$
$930$		0			0
$931$	−35.0203	−	61.5567i	−1.14774	−	2.01744i
$932$	−9.03263	+	5.21499i	−0.295873	+	0.170823i
$933$		0			0
$934$		−	46.1779i		−	1.51099i
$935$	18.0996	+	10.4498i	0.591921	+	0.341745i
$936$		0			0
$937$	−15.0321	+	26.0364i	−0.491079	+	0.850573i	−0.999947	−	0.0102711i	$-0.996731\pi$
$937$	−15.0321	+	26.0364i	−0.491079	+	0.850573i	0.508869	+	0.860844i	$0.330064\pi$
$938$	−55.5053	−	32.0460i	−1.81231	−	1.04634i
$939$		0			0
$940$	−7.26841			−0.237069
$941$	24.4750			0.797862			0.398931	−	0.916981i	$-0.369381\pi$
$941$	24.4750			0.797862			0.398931	+	0.916981i	$0.369381\pi$
$942$		0			0
$943$	21.1285	+	12.1985i	0.688038	+	0.397239i
$944$	5.31436	−	9.20474i	0.172968	−	0.299589i
$945$		0			0
$946$	37.9636	+	21.9183i	1.23430	+	0.712625i
$947$			19.0059i			0.617608i	0.951126	+	0.308804i	$0.0999287\pi$
$947$			19.0059i			0.617608i	−0.951126	+	0.308804i	$0.900071\pi$
$948$		0			0
$949$	7.25161	−	4.18672i	0.235397	−	0.135907i
$950$	−4.83969	−	8.50694i	−0.157020	−	0.276002i
$951$		0			0
$952$		−	42.2704i		−	1.36999i
$953$	−0.925412	−	1.60286i	−0.0299770	−	0.0519217i	0.850648	−	0.525736i	$-0.176210\pi$
$953$	−0.925412	−	1.60286i	−0.0299770	−	0.0519217i	−0.880625	+	0.473814i	$0.842877\pi$
$954$		0			0
$955$	−7.03506	−	12.1851i	−0.227649	−	0.394300i
$956$	−4.26110	+	2.46015i	−0.137814	+	0.0795669i
$957$		0			0
$958$	−19.7852	+	11.4230i	−0.639232	+	0.369061i
$959$		−	4.34623i		−	0.140347i
$960$		0			0
$961$	−12.9354	+	22.4049i	−0.417273	+	0.722737i
$962$	22.8580			0.736973
$963$		0			0
$964$	6.68816	−	3.86141i	0.215411	−	0.124368i
$965$	−7.55489	−	13.0855i	−0.243201	−	0.421236i
$966$		0			0
$967$	21.6020	−	37.4158i	0.694674	−	1.20321i	−0.275616	−	0.961268i	$-0.588882\pi$
$967$	21.6020	−	37.4158i	0.694674	−	1.20321i	0.970290	−	0.241943i	$-0.0777848\pi$
$968$	1.50135	+	2.60041i	0.0482552	+	0.0835805i
$969$		0			0
$970$	19.6978	−	34.1176i	0.632458	−	1.09545i
$971$	−14.9198	−	25.8419i	−0.478801	−	0.829307i	0.520904	−	0.853615i	$-0.325595\pi$
$971$	−14.9198	−	25.8419i	−0.478801	−	0.829307i	−0.999705	+	0.0243082i	$0.992262\pi$
$972$		0			0
$973$	−46.6865	+	80.8634i	−1.49670	+	2.59236i
$974$		−	21.7900i		−	0.698196i
$975$		0			0
$976$	−24.8002	−	42.9552i	−0.793836	−	1.37496i
$977$	−9.91018	−	17.1649i	−0.317055	−	0.549155i	0.662817	−	0.748781i	$-0.269361\pi$
$977$	−9.91018	−	17.1649i	−0.317055	−	0.549155i	−0.979872	+	0.199626i	$0.936027\pi$
$978$		0			0
$979$	40.5356	−	23.4033i	1.29552	−	0.747972i
$980$		−	12.4117i		−	0.396477i
$981$		0			0
$982$	−22.3096	−	12.8805i	−0.711928	−	0.411032i
$983$	−1.00171			−0.0319497			−0.0159749	−	0.999872i	$-0.505085\pi$
$983$	−1.00171			−0.0319497			−0.0159749	+	0.999872i	$0.505085\pi$
$984$		0			0
$985$	−7.72158	+	13.3742i	−0.246030	+	0.426136i
$986$	−10.8177	−	6.24559i	−0.344505	−	0.198900i
$987$		0			0
$988$	−0.0379140	+	5.96810i	−0.00120621	+	0.189870i
$989$		−	39.0898i		−	1.24298i
$990$		0			0
$991$	−22.2607	+	12.8522i	−0.707133	+	0.408264i	−0.809999	−	0.586432i	$-0.800532\pi$
$991$	−22.2607	+	12.8522i	−0.707133	+	0.408264i	0.102865	+	0.994695i	$0.467199\pi$
$992$	−4.43192	+	2.55877i	−0.140714	+	0.0812411i
$993$		0			0
$994$	−6.80288			−0.215774
$995$	7.11362	−	4.10705i	0.225517	−	0.130202i
$996$		0			0
$997$	−7.67734	−	13.2975i	−0.243144	−	0.421137i	0.718464	−	0.695564i	$-0.244845\pi$
$997$	−7.67734	−	13.2975i	−0.243144	−	0.421137i	−0.961608	+	0.274426i	$0.911512\pi$
$998$	17.5055	−	30.3205i	0.554128	−	0.959779i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	513.2.t.a.278.13		36
3.2	odd	2		171.2.t.a.164.6	yes	36
9.4	even	3		171.2.k.a.50.6	✓	36
9.5	odd	6		513.2.k.a.449.13		36
19.8	odd	6		513.2.k.a.8.13		36
57.8	even	6		171.2.k.a.65.6	yes	36
171.103	odd	6		171.2.t.a.122.6	yes	36
171.122	even	6	inner	513.2.t.a.179.13		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.k.a.50.6	✓	36	9.4	even	3
171.2.k.a.65.6	yes	36	57.8	even	6
171.2.t.a.122.6	yes	36	171.103	odd	6
171.2.t.a.164.6	yes	36	3.2	odd	2
513.2.k.a.8.13		36	19.8	odd	6
513.2.k.a.449.13		36	9.5	odd	6
513.2.t.a.179.13		36	171.122	even	6	inner
513.2.t.a.278.13		36	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:	\( N \)	\(=\)	\( 513 = 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	513.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.55091 q^{2} +0.405316 q^{4} +(1.63223 + 0.942368i) q^{5} +(-2.41078 + 4.17560i) q^{7} -2.47321 q^{8} +(2.53144 + 1.46153i) q^{10} +(2.70914 + 1.56412i) q^{11} +3.37811i q^{13} +(-3.73890 + 6.47597i) q^{14} -4.64635 q^{16} +(3.06986 - 1.77238i) q^{17} +(4.35881 + 0.0276906i) q^{19} +(0.661569 + 0.381957i) q^{20} +(4.20163 + 2.42581i) q^{22} -4.32627i q^{23} +(-0.723884 - 1.25380i) q^{25} +5.23914i q^{26} +(-0.977130 + 1.69244i) q^{28} +(-1.13606 - 1.96771i) q^{29} +(1.96133 - 1.13238i) q^{31} -2.25965 q^{32} +(4.76106 - 2.74880i) q^{34} +(-7.86990 + 4.54369i) q^{35} -4.36294i q^{37} +(6.76012 + 0.0429455i) q^{38} +(-4.03684 - 2.33067i) q^{40} +(-2.81964 + 4.88376i) q^{41} +9.03545 q^{43} +(1.09806 + 0.633964i) q^{44} -6.70964i q^{46} +(-8.23996 + 4.75734i) q^{47} +(-8.12375 - 14.0707i) q^{49} +(-1.12268 - 1.94453i) q^{50} +1.36920i q^{52} +(4.04616 - 7.00816i) q^{53} +(2.94796 + 5.10601i) q^{55} +(5.96237 - 10.3271i) q^{56} +(-1.76192 - 3.05174i) q^{58} +(-1.14377 + 1.98107i) q^{59} +(5.33757 + 9.24494i) q^{61} +(3.04185 - 1.75621i) q^{62} +5.78820 q^{64} +(-3.18342 + 5.51385i) q^{65} +8.57097i q^{67} +(1.24426 - 0.718375i) q^{68} +(-12.2055 + 7.04685i) q^{70} +(0.454871 + 0.787860i) q^{71} +(-1.23937 - 2.14665i) q^{73} -6.76652i q^{74} +(1.76670 + 0.0112234i) q^{76} +(-13.0623 + 7.54152i) q^{77} +0.526031i q^{79} +(-7.58391 - 4.37857i) q^{80} +(-4.37301 + 7.57427i) q^{82} +(-1.65409 - 0.954990i) q^{83} +6.68095 q^{85} +14.0132 q^{86} +(-6.70026 - 3.86840i) q^{88} +(7.48128 - 12.9580i) q^{89} +(-14.1056 - 8.14389i) q^{91} -1.75351i q^{92} +(-12.7794 + 7.37820i) q^{94} +(7.08849 + 4.15280i) q^{95} -13.4775i q^{97} +(-12.5992 - 21.8224i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{2} + 30 q^{4} + 3 q^{5} - q^{7} + 12 q^{8} - 6 q^{10} + 9 q^{11} + 3 q^{14} + 18 q^{16} - 27 q^{17} + q^{19} - 9 q^{20} - 6 q^{22} + 11 q^{25} + 2 q^{28} + 12 q^{29} - 12 q^{31} + 30 q^{32}+ \cdots - 84 q^{98}+O(q^{100}) \) 36 * q + 6 * q^2 + 30 * q^4 + 3 * q^5 - q^7 + 12 * q^8 - 6 * q^10 + 9 * q^11 + 3 * q^14 + 18 * q^16 - 27 * q^17 + q^19 - 9 * q^20 - 6 * q^22 + 11 * q^25 + 2 * q^28 + 12 * q^29 - 12 * q^31 + 30 * q^32 - 21 * q^34 + 15 * q^35 + 36 * q^38 - 30 * q^40 - 18 * q^41 - 6 * q^43 + 66 * q^44 - 45 * q^47 - 9 * q^49 + 3 * q^50 - 12 * q^53 - 7 * q^55 + 6 * q^56 - 6 * q^58 + 9 * q^59 + 8 * q^61 - 12 * q^62 + 12 * q^64 - 18 * q^65 - 60 * q^68 - 24 * q^70 + 9 * q^71 - 18 * q^73 + 10 * q^76 + 6 * q^77 - 12 * q^80 - 9 * q^82 + 9 * q^83 - 22 * q^85 - 102 * q^86 - 3 * q^88 - 18 * q^89 + 27 * q^91 - 12 * q^94 + 21 * q^95 - 84 * q^98

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