LMFDB - Embedded newform 513.2.t.a.179.13

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			179.13
Character	$\chi$	$=$	513.179
Dual form			513.2.t.a.278.13

$q$-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 $\left(\mathbb{Z}/513\mathbb{Z}\right)^\times$.

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

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	−0.0884504	−	0.996081i	$-0.528191\pi$
$5$	1.63223	−	0.942368i	0.729955	−	0.421440i	0.818406	+	0.574641i	$0.194858\pi$
$6$		0			0
$7$	−2.41078	−	4.17560i	−0.911190	−	1.57823i	−0.812385	−	0.583121i	$-0.801831\pi$
$7$	−2.41078	−	4.17560i	−0.911190	−	1.57823i	−0.0988049	−	0.995107i	$-0.531502\pi$
$8$	−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	−0.0324882	−	0.999472i	$-0.510343\pi$
$11$	2.70914	−	1.56412i	0.816836	−	0.471600i	0.849324	+	0.527872i	$0.177010\pi$
$12$		0			0
$13$		−	3.37811i		−	0.936919i	−0.883485	−	0.468460i	$-0.844809\pi$
$13$		−	3.37811i		−	0.936919i	0.883485	−	0.468460i	$-0.155191\pi$
$14$	−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	0.823721	−	0.566995i	$-0.191894\pi$
$17$	3.06986	+	1.77238i	0.744549	+	0.429866i	−0.0791717	+	0.996861i	$0.525228\pi$
$18$		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	$0.148948\pi$
$23$			4.32627i			0.902089i	−0.892501	+	0.451044i	$0.851052\pi$
$24$		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	−0.952015	−	0.306050i	$-0.900992\pi$
$29$	−1.13606	+	1.96771i	−0.210961	+	0.365394i	0.741055	+	0.671444i	$0.234326\pi$
$30$		0			0
$31$	1.96133	+	1.13238i	0.352266	+	0.203381i	0.665683	−	0.746235i	$-0.268140\pi$
$31$	1.96133	+	1.13238i	0.352266	+	0.203381i	−0.313417	+	0.949616i	$0.601474\pi$
$32$	−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	$0.116756\pi$
$37$			4.36294i			0.717263i	−0.933479	+	0.358631i	$0.883244\pi$
$38$	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	0.557361	−	0.830270i	$-0.311814\pi$
$41$	−2.81964	−	4.88376i	−0.440354	−	0.762716i	−0.997716	+	0.0675541i	$0.978480\pi$
$42$		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	−0.240940	−	0.970540i	$-0.577456\pi$
$47$	−8.23996	−	4.75734i	−1.20192	−	0.693930i	−0.960982	+	0.276610i	$0.910789\pi$
$48$		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	0.997842	+	0.0656585i	$0.0209148\pi$
$53$	4.04616	+	7.00816i	0.555783	+	0.962644i	−0.442059	+	0.896986i	$0.645752\pi$
$54$		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	0.781917	−	0.623382i	$-0.214242\pi$
$59$	−1.14377	−	1.98107i	−0.148906	−	0.257913i	−0.930823	+	0.365469i	$0.880909\pi$
$60$		0			0
$61$	5.33757	−	9.24494i	0.683406	−	1.18369i	−0.290529	−	0.956866i	$-0.593831\pi$
$61$	5.33757	−	9.24494i	0.683406	−	1.18369i	0.973935	−	0.226827i	$-0.0728352\pi$
$62$	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	$-0.824605\pi$
$67$		−	8.57097i		−	1.04711i	0.851992	−	0.523555i	$-0.175395\pi$
$68$	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	−0.837771	−	0.546022i	$-0.816142\pi$
$71$	0.454871	−	0.787860i	0.0539833	−	0.0935018i	0.891754	+	0.452520i	$0.149475\pi$
$72$		0			0
$73$	−1.23937	+	2.14665i	−0.145057	+	0.251246i	−0.929394	−	0.369089i	$-0.879670\pi$
$73$	−1.23937	+	2.14665i	−0.145057	+	0.251246i	0.784337	+	0.620335i	$0.213003\pi$
$74$			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	$-0.990579\pi$
$79$		−	0.526031i		−	0.0591831i	0.999562	−	0.0295915i	$-0.00942065\pi$
$80$	−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	−0.588025	−	0.808842i	$-0.700095\pi$
$83$	−1.65409	+	0.954990i	−0.181560	+	0.104824i	0.406465	+	0.913666i	$0.366761\pi$
$84$		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	0.924093	+	0.382169i	$0.124823\pi$
$89$	7.48128	+	12.9580i	0.793014	+	1.37354i	−0.131079	+	0.991372i	$0.541844\pi$
$90$		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	$0.239857\pi$
$97$			13.4775i			1.36844i	−0.729277	+	0.684219i	$0.760143\pi$
$98$	−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	0.975855	−	0.218421i	$-0.0700907\pi$
$101$	12.8098	+	7.39575i	1.27462	+	0.735904i	0.298769	+	0.954325i	$0.403424\pi$
$102$		0			0
$103$	−6.03192	−	3.48253i	−0.594343	−	0.343144i	0.172470	−	0.985015i	$-0.444825\pi$
$103$	−6.03192	−	3.48253i	−0.594343	−	0.343144i	−0.766813	+	0.641871i	$0.778159\pi$
$104$			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	0.368124	−	0.929777i	$-0.380000\pi$
$109$	−2.64165	−	1.52516i	−0.253025	−	0.146084i	−0.621148	+	0.783693i	$0.713334\pi$
$110$	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	0.414396	+	0.910097i	$0.363993\pi$
$113$	−6.17578	+	10.6968i	−0.580969	+	1.00627i	−0.995365	+	0.0961706i	$0.969341\pi$
$114$		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	−0.343916	−	0.939000i	$-0.611754\pi$
$127$	3.35067	−	1.93451i	0.297324	−	0.171660i	0.641240	+	0.767340i	$0.278420\pi$
$128$	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	0.0838353	−	0.996480i	$-0.473283\pi$
$131$	11.3165	−	6.53360i	0.988730	−	0.570843i	0.904894	+	0.425636i	$0.139950\pi$
$132$		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	0.466282	−	0.884636i	$-0.345593\pi$
$137$	−0.780648	−	0.450707i	−0.0666953	−	0.0385065i	−0.532977	+	0.846130i	$0.678927\pi$
$138$		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	−0.565867	−	0.824497i	$-0.691458\pi$
$149$	−1.64502	+	0.949750i	−0.134765	+	0.0778065i	0.431102	+	0.902303i	$0.358125\pi$
$150$		0			0
$151$	3.36348	−	1.94190i	0.273716	−	0.158030i	−0.356859	−	0.934158i	$-0.616152\pi$
$151$	3.36348	−	1.94190i	0.273716	−	0.158030i	0.630575	+	0.776128i	$0.282819\pi$
$152$	−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	−0.980554	−	0.196251i	$-0.937123\pi$
$157$	−8.27272	−	14.3288i	−0.660235	−	1.14356i	0.320319	−	0.947310i	$-0.396210\pi$
$158$		−	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	−0.574775	−	0.818312i	$-0.694910\pi$
$181$	−2.06491	+	1.19217i	−0.153483	+	0.0886137i	0.421291	+	0.906925i	$0.361577\pi$
$182$	−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	−0.715319	−	0.698798i	$-0.753718\pi$
$191$	−6.46514	+	3.73265i	−0.467801	+	0.270085i	0.247518	+	0.968883i	$0.420385\pi$
$192$		0			0
$193$	−6.94286	+	4.00846i	−0.499758	+	0.288535i	−0.728614	−	0.684925i	$-0.759835\pi$
$193$	−6.94286	+	4.00846i	−0.499758	+	0.288535i	0.228856	+	0.973460i	$0.426502\pi$
$194$			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	$-0.905715\pi$
$197$		−	8.19380i		−	0.583784i	0.956451	−	0.291892i	$-0.0942848\pi$
$198$		0			0
$199$	2.17911	+	3.77433i	0.154473	+	0.267555i	0.932867	−	0.360221i	$-0.117299\pi$
$199$	2.17911	+	3.77433i	0.154473	+	0.267555i	−0.778394	+	0.627776i	$0.783965\pi$
$200$	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	−0.840111	−	0.542415i	$-0.817510\pi$
$211$	−11.4815	+	6.62887i	−0.790421	+	0.456350i	0.0496895	+	0.998765i	$0.484177\pi$
$212$	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	$0.0386649\pi$
$223$			3.61894i			0.242342i	−0.992632	+	0.121171i	$0.961335\pi$
$224$	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	−0.975952	−	0.217985i	$-0.930052\pi$
$227$	−10.1964	−	17.6606i	−0.676757	−	1.17218i	0.299196	−	0.954192i	$-0.403282\pi$
$228$		0			0
$229$	−2.72459	+	4.71913i	−0.180046	+	0.311849i	−0.941896	−	0.335905i	$-0.890958\pi$
$229$	−2.72459	+	4.71913i	−0.180046	+	0.311849i	0.761850	+	0.647754i	$0.224291\pi$
$230$	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	−0.460955	−	0.887424i	$-0.652493\pi$
$233$	−22.2854	−	12.8665i	−1.45996	−	0.842910i	−0.999009	+	0.0445134i	$0.985826\pi$
$234$		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	0.119835	−	0.992794i	$-0.461763\pi$
$239$	−10.5130	−	6.06970i	−0.680032	−	0.392616i	−0.799867	+	0.600177i	$0.795097\pi$
$240$		0			0
$241$	16.5011	+	9.52691i	1.06293	+	0.613682i	0.926241	−	0.376932i	$-0.123021\pi$
$241$	16.5011	+	9.52691i	1.06293	+	0.613682i	0.136688	+	0.990614i	$0.456354\pi$
$242$	−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	−0.235400	−	0.971899i	$-0.575640\pi$
$251$	7.74070	−	4.46909i	0.488589	−	0.282087i	0.723989	+	0.689812i	$0.242307\pi$
$252$		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	$0.0588677\pi$
$263$			5.96426i			0.367772i	−0.982948	+	0.183886i	$0.941132\pi$
$264$		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	−0.706826	−	0.707387i	$-0.749874\pi$
$269$	4.25123	−	7.36335i	0.259202	−	0.448951i	0.966028	+	0.258436i	$0.0832071\pi$
$270$		0			0
$271$	3.84391	−	6.65785i	0.233501	−	0.404436i	−0.725335	−	0.688396i	$-0.758315\pi$
$271$	3.84391	−	6.65785i	0.233501	−	0.404436i	0.958836	+	0.283960i	$0.0916485\pi$
$272$	−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	−0.794353	−	0.607456i	$-0.792190\pi$
$277$	−15.3659	−	26.6146i	−0.923249	−	1.59911i	−0.128895	−	0.991658i	$-0.541143\pi$
$278$	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	−0.0378481	+	0.999284i	$0.512050\pi$
$281$	−14.8241	+	25.6760i	−0.884329	+	1.53170i	−0.846481	+	0.532419i	$0.821283\pi$
$282$		0			0
$283$	11.2597	+	19.5024i	0.669322	+	1.15930i	0.978094	+	0.208164i	$0.0667486\pi$
$283$	11.2597	+	19.5024i	0.669322	+	1.15930i	−0.308772	+	0.951136i	$0.599918\pi$
$284$	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	−0.904837	−	0.425758i	$-0.860007\pi$
$293$	−1.43273	+	2.48156i	−0.0837010	+	0.144974i	0.821136	+	0.570733i	$0.193341\pi$
$294$		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	−0.0182175	−	0.999834i	$-0.505799\pi$
$307$	−15.6503	−	9.03569i	−0.893208	−	0.515694i	−0.874990	+	0.484140i	$0.839132\pi$
$308$	−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	0.195470	−	0.980710i	$-0.437377\pi$
$311$	−9.80717	−	5.66217i	−0.556114	−	0.321072i	−0.751584	+	0.659637i	$0.770710\pi$
$312$		0			0
$313$	−0.739097	+	1.28015i	−0.0417762	+	0.0723586i	−0.886157	−	0.463384i	$-0.846635\pi$
$313$	−0.739097	+	1.28015i	−0.0417762	+	0.0723586i	0.844381	+	0.535743i	$0.179968\pi$
$314$	−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	−0.487815	−	0.872947i	$-0.662206\pi$
$317$	9.11745	−	15.7919i	0.512087	−	0.886961i	0.999902	−	0.0140137i	$-0.00446084\pi$
$318$		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	−0.997321	−	0.0731549i	$-0.976693\pi$
$331$	−26.0644	+	15.0483i	−1.43263	+	0.827128i	−0.435306	+	0.900282i	$0.643360\pi$
$332$	−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	−0.583509	−	0.812107i	$-0.698321\pi$
$337$	−3.15674	+	1.82254i	−0.171958	+	0.0992802i	0.411551	+	0.911387i	$0.364987\pi$
$338$	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	−0.667014	−	0.745045i	$-0.732428\pi$
$347$	−6.61837	+	3.82112i	−0.355293	+	0.205128i	0.311721	+	0.950174i	$0.399095\pi$
$348$		0			0
$349$	−3.85492	−	6.67692i	−0.206349	−	0.357407i	0.744212	−	0.667943i	$-0.232825\pi$
$349$	−3.85492	−	6.67692i	−0.206349	−	0.357407i	−0.950562	+	0.310535i	$0.899492\pi$
$350$	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	−0.0480728	−	0.998844i	$-0.515308\pi$
$353$	14.8975	−	8.60109i	0.792915	−	0.457790i	0.840988	+	0.541054i	$0.181975\pi$
$354$		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	0.473753	−	0.880658i	$-0.342899\pi$
$359$	−0.986080	−	0.569313i	−0.0520433	−	0.0300472i	−0.525796	+	0.850611i	$0.676232\pi$
$360$		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	−0.875049	−	0.484034i	$-0.839171\pi$
$367$	−0.351324	+	0.608511i	−0.0183390	+	0.0317640i	0.856710	+	0.515798i	$0.172504\pi$
$368$		−	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	0.695671	−	0.718361i	$-0.255107\pi$
$373$	8.13834	+	4.69867i	0.421387	+	0.243288i	−0.274283	+	0.961649i	$0.588441\pi$
$374$	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	$-0.787204\pi$
$379$		−	24.1334i		−	1.23965i	0.784740	−	0.619825i	$-0.212796\pi$
$380$	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	0.953466	+	0.301501i	$0.0974878\pi$
$383$	14.4398	+	25.0105i	0.737841	+	1.27798i	−0.215625	+	0.976476i	$0.569179\pi$
$384$		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	−0.945075	−	0.326855i	$-0.894011\pi$
$389$	−33.5426	−	19.3658i	−1.70068	−	0.981886i	−0.755602	−	0.655031i	$-0.772655\pi$
$390$		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	0.434169	+	0.900831i	$0.357042\pi$
$397$	−11.2189	+	19.4316i	−0.563058	+	0.975246i	−0.997227	+	0.0744143i	$0.976291\pi$
$398$	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	0.918134	−	0.396271i	$-0.129696\pi$
$401$	2.32062	+	4.01943i	0.115886	+	0.200721i	−0.802248	+	0.596992i	$0.796363\pi$
$402$		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	$0.157545\pi$
$409$			19.2118i			0.949960i	−0.879997	+	0.474980i	$0.842455\pi$
$410$	−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	0.244680	−	0.969604i	$-0.421317\pi$
$419$	−9.67554	−	5.58618i	−0.472681	−	0.272903i	−0.717361	+	0.696701i	$0.754650\pi$
$420$		0			0
$421$			16.4137i			0.799955i	0.916525	+	0.399978i	$0.130982\pi$
$421$			16.4137i			0.799955i	−0.916525	+	0.399978i	$0.869018\pi$
$422$	−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	−0.895738	−	0.444581i	$-0.853352\pi$
$431$	−17.2912	−	29.9492i	−0.832888	−	1.44260i	0.0628504	−	0.998023i	$-0.479981\pi$
$432$		0			0
$433$	−14.9639	+	8.63943i	−0.719121	+	0.415185i	−0.814429	−	0.580263i	$-0.802950\pi$
$433$	−14.9639	+	8.63943i	−0.719121	+	0.415185i	0.0953081	+	0.995448i	$0.469616\pi$
$434$		−	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	$0.245083\pi$
$439$			29.1698i			1.39220i	−0.717946	+	0.696099i	$0.754917\pi$
$440$	−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	0.650932	−	0.759136i	$-0.274378\pi$
$443$	6.71346	+	3.87602i	0.318966	+	0.184155i	−0.331966	+	0.943291i	$0.607712\pi$
$444$		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	0.840412	−	0.541948i	$-0.182313\pi$
$457$	−1.05039	−	1.81932i	−0.0491350	−	0.0851044i	−0.889547	+	0.456844i	$0.848980\pi$
$458$	−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	$0.206176\pi$
$461$			25.9098i			1.20674i	−0.797461	+	0.603370i	$0.793824\pi$
$462$		0			0
$463$	9.23702	−	15.9990i	0.429281	−	0.743536i	−0.567529	−	0.823354i	$-0.692100\pi$
$463$	9.23702	−	15.9990i	0.429281	−	0.743536i	0.996809	+	0.0798177i	$0.0254338\pi$
$464$	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	$0.241908\pi$
$467$			29.7747i			1.37781i	−0.724852	+	0.688905i	$0.758092\pi$
$468$		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	0.179390	−	0.983778i	$-0.442587\pi$
$479$	−12.7572	−	7.36537i	−0.582891	−	0.336532i	−0.762282	+	0.647246i	$0.775921\pi$
$480$		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	$0.103122\pi$
$487$			14.0498i			0.636658i	−0.947980	+	0.318329i	$0.896878\pi$
$488$	−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	−0.788142	−	0.615494i	$-0.788957\pi$
$491$	−14.3849	+	8.30510i	−0.649180	+	0.374804i	0.138962	+	0.990298i	$0.455623\pi$
$492$		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	0.999981	+	0.00611735i	$0.00194723\pi$
$499$	11.2873	+	19.5502i	0.505288	+	0.875185i	−0.494693	+	0.869068i	$0.664719\pi$
$500$			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	0.190624	−	0.981663i	$-0.438949\pi$
$503$	25.4796	−	14.7107i	1.13608	−	0.655917i	0.945457	+	0.325746i	$0.105616\pi$
$504$		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	0.368530	−	0.929616i	$-0.379861\pi$
$523$	31.0533	−	17.9286i	1.35787	−	0.783964i	0.989336	+	0.145652i	$0.0465278\pi$
$524$	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	0.996563	−	0.0828391i	$-0.0263988\pi$
$541$	9.92108	+	17.1838i	0.426541	+	0.738790i	−0.570022	+	0.821629i	$0.693065\pi$
$542$	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	0.0676143	−	0.997712i	$-0.478461\pi$
$547$	−17.8362	−	10.2978i	−0.762622	−	0.440300i	−0.830236	+	0.557411i	$0.811795\pi$
$548$	−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	−0.276358	−	0.961055i	$-0.589128\pi$
$557$	9.85951	−	5.69239i	0.417761	−	0.241194i	0.694119	+	0.719860i	$0.255794\pi$
$558$		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	−0.181263	+	0.983435i	$0.558018\pi$
$563$	−22.3588	+	38.7266i	−0.942311	+	1.63213i	−0.761048	+	0.648695i	$0.775315\pi$
$564$		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	0.854032	−	0.520220i	$-0.174150\pi$
$569$	−0.560747	−	0.971242i	−0.0235077	−	0.0407166i	−0.877540	+	0.479504i	$0.840817\pi$
$570$		0			0
$571$	9.40145	−	16.2838i	0.393438	−	0.681455i	−0.599462	−	0.800403i	$-0.704619\pi$
$571$	9.40145	−	16.2838i	0.393438	−	0.681455i	0.992900	+	0.118948i	$0.0379522\pi$
$572$	−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	$0.0428807\pi$
$587$			6.50799i			0.268613i	−0.990940	+	0.134307i	$0.957119\pi$
$588$		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	−0.659468	−	0.751732i	$-0.729219\pi$
$593$	−8.23530	+	4.75465i	−0.338183	+	0.195250i	0.321285	+	0.946983i	$0.395885\pi$
$594$		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	−0.606089	+	0.795397i	$0.707263\pi$
$601$	−39.1747	+	22.6175i	−1.59797	+	0.922587i	−0.991878	+	0.127190i	$0.959404\pi$
$602$	−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	−0.250544	−	0.968105i	$-0.580609\pi$
$607$	−29.9152	−	17.2715i	−1.21422	−	0.701030i	−0.963676	+	0.267075i	$0.913943\pi$
$608$	−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	−0.958845	−	0.283930i	$-0.908362\pi$
$613$	−5.78197	+	10.0147i	−0.233531	+	0.404488i	0.725313	+	0.688419i	$0.241695\pi$
$614$	−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	$-0.753149\pi$
$617$		−	34.7791i		−	1.40015i	0.714067	−	0.700077i	$-0.246851\pi$
$618$		0			0
$619$	8.34985	+	14.4624i	0.335609	+	0.581291i	0.983602	−	0.180355i	$-0.0577247\pi$
$619$	8.34985	+	14.4624i	0.335609	+	0.581291i	−0.647993	+	0.761646i	$0.724391\pi$
$620$	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	0.994786	+	0.101988i	$0.0325202\pi$
$631$	14.7130	+	25.4837i	0.585717	+	1.01449i	−0.409069	+	0.912503i	$0.634146\pi$
$632$			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	0.600978	−	0.799266i	$-0.294778\pi$
$643$	−9.93240	−	17.2034i	−0.391696	−	0.678437i	−0.992673	+	0.120829i	$0.961445\pi$
$644$	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	$-0.804865\pi$
$647$		−	29.2696i		−	1.15071i	0.817905	−	0.575353i	$-0.195135\pi$
$648$		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	0.165160	−	0.986267i	$-0.447186\pi$
$653$	−15.4957	−	8.94643i	−0.606393	−	0.350101i	−0.771552	+	0.636166i	$0.780519\pi$
$654$		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	−0.996511	−	0.0834604i	$-0.973403\pi$
$659$	−10.9352	+	18.9404i	−0.425977	+	0.737813i	0.570534	+	0.821274i	$0.306736\pi$
$660$		0			0
$661$			4.09721i			0.159363i	0.996820	+	0.0796816i	$0.0253903\pi$
$661$			4.09721i			0.159363i	−0.996820	+	0.0796816i	$0.974610\pi$
$662$	−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	−0.0375989	−	0.999293i	$-0.511971\pi$
$673$	20.9877	−	12.1172i	0.809015	−	0.467085i	0.846614	+	0.532208i	$0.178638\pi$
$674$	−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	0.992814	−	0.119667i	$-0.0381826\pi$
$677$	10.2196	+	17.7009i	0.392773	+	0.680302i	−0.600041	+	0.799969i	$0.704849\pi$
$678$		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	0.902459	−	0.430775i	$-0.141760\pi$
$691$	2.05478	+	3.55898i	0.0781674	+	0.135390i	−0.824292	+	0.566165i	$0.808426\pi$
$692$	−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	0.121460	−	0.992596i	$-0.461242\pi$
$701$	−17.9358	−	10.3552i	−0.677424	−	0.391111i	−0.798884	+	0.601485i	$0.794576\pi$
$702$		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	−0.956947	−	0.290262i	$-0.906258\pi$
$709$	−6.04698	+	10.4737i	−0.227099	+	0.393347i	0.729848	+	0.683610i	$0.239591\pi$
$710$		−	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	0.0879104	−	0.996128i	$-0.471981\pi$
$719$	−19.5960	−	11.3137i	−0.730807	−	0.421932i	−0.818717	+	0.574197i	$0.805314\pi$
$720$		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	−0.999491	−	0.0319066i	$-0.989842\pi$
$733$	−12.7820	+	22.1391i	−0.472114	+	0.817725i	0.527377	+	0.849631i	$0.323175\pi$
$734$	−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	−0.321681	−	0.946848i	$-0.604248\pi$
$739$	17.9188	−	31.0363i	0.659154	−	1.14169i	0.980835	−	0.194840i	$-0.0624187\pi$
$740$	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	0.962403	−	0.271627i	$-0.0875617\pi$
$743$	6.70454	+	11.6126i	0.245966	+	0.426025i	−0.716437	+	0.697652i	$0.754228\pi$
$744$		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	$-0.713067\pi$
$751$		−	42.9817i		−	1.56842i	0.620493	−	0.784212i	$-0.286933\pi$
$752$	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	−0.643169	−	0.765724i	$-0.722381\pi$
$757$	9.39734	−	16.2767i	0.341552	−	0.591586i	0.984721	+	0.174139i	$0.0557141\pi$
$758$		−	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	0.938340	−	0.345715i	$-0.112363\pi$
$761$	30.5686	+	17.6488i	1.10811	+	0.639769i	0.169772	+	0.985483i	$0.445697\pi$
$762$		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	0.998476	+	0.0551956i	$0.0175782\pi$
$773$	15.2092	+	26.3432i	0.547039	+	0.947499i	−0.451437	+	0.892303i	$0.649088\pi$
$774$		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	0.832739	−	0.553666i	$-0.186772\pi$
$787$	21.5905	+	12.4653i	0.769619	+	0.444340i	−0.0631196	+	0.998006i	$0.520105\pi$
$788$		−	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	−0.100945	−	0.994892i	$-0.532187\pi$
$797$	22.8991	−	39.6625i	0.811129	−	1.40492i	0.912074	−	0.410025i	$-0.134480\pi$
$798$		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	$-0.834314\pi$
$809$		−	28.2911i		−	0.994662i	0.867561	−	0.497331i	$-0.165686\pi$
$810$		0			0
$811$	8.53722	−	4.92896i	0.299782	−	0.173079i	−0.342563	−	0.939495i	$-0.611295\pi$
$811$	8.53722	−	4.92896i	0.299782	−	0.173079i	0.642345	+	0.766416i	$0.277962\pi$
$812$	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	0.967952	−	0.251136i	$-0.0808041\pi$
$821$	35.3705	+	20.4211i	1.23444	+	0.712703i	0.266486	+	0.963839i	$0.414137\pi$
$822$		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	0.977161	+	0.212500i	$0.0681606\pi$
$827$	19.3427	+	33.5025i	0.672611	+	1.16500i	−0.304550	+	0.952496i	$0.598506\pi$
$828$		0			0
$829$		−	19.0627i		−	0.662076i	−0.943617	−	0.331038i	$-0.892601\pi$
$829$		−	19.0627i		−	0.662076i	0.943617	−	0.331038i	$-0.107399\pi$
$830$	−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	0.265140	−	0.964210i	$-0.414582\pi$
$877$	36.5066	−	21.0771i	1.23274	−	0.711723i	0.967600	+	0.252487i	$0.0812485\pi$
$878$			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	$-0.722509\pi$
$881$		−	45.4405i		−	1.53093i	0.643478	−	0.765464i	$-0.277491\pi$
$882$		0			0
$883$	9.23912	+	16.0026i	0.310921	+	0.538531i	0.978562	−	0.205952i	$-0.0660292\pi$
$883$	9.23912	+	16.0026i	0.310921	+	0.538531i	−0.667641	+	0.744483i	$0.732696\pi$
$884$	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	$-0.975250\pi$
$907$		−	4.67863i		−	0.155351i	0.996979	−	0.0776757i	$-0.0247499\pi$
$908$	−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	0.856536	−	0.516087i	$-0.172612\pi$
$911$	−0.563718	−	0.976388i	−0.0186768	−	0.0323492i	−0.875213	+	0.483738i	$0.839279\pi$
$912$		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	$0.157710\pi$
$929$			28.9821i			0.950873i	−0.879750	+	0.475437i	$0.842290\pi$
$930$		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	0.508869	−	0.860844i	$-0.330064\pi$
$937$	−15.0321	−	26.0364i	−0.491079	−	0.850573i	−0.999947	+	0.0102711i	$0.996731\pi$
$938$	−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	$-0.900071\pi$
$947$		−	19.0059i		−	0.617608i	0.951126	−	0.308804i	$-0.0999287\pi$
$948$		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	−0.880625	−	0.473814i	$-0.842877\pi$
$953$	−0.925412	+	1.60286i	−0.0299770	+	0.0519217i	0.850648	+	0.525736i	$0.176210\pi$
$954$		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	0.970290	+	0.241943i	$0.0777848\pi$
$967$	21.6020	+	37.4158i	0.694674	+	1.20321i	−0.275616	+	0.961268i	$0.588882\pi$
$968$	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	−0.999705	−	0.0243082i	$-0.992262\pi$
$971$	−14.9198	+	25.8419i	−0.478801	+	0.829307i	0.520904	+	0.853615i	$0.325595\pi$
$972$		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	−0.979872	−	0.199626i	$-0.936027\pi$
$977$	−9.91018	+	17.1649i	−0.317055	+	0.549155i	0.662817	+	0.748781i	$0.269361\pi$
$978$		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	0.102865	−	0.994695i	$-0.467199\pi$
$991$	−22.2607	−	12.8522i	−0.707133	−	0.408264i	−0.809999	+	0.586432i	$0.800532\pi$
$992$	−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	−0.961608	−	0.274426i	$-0.911512\pi$
$997$	−7.67734	+	13.2975i	−0.243144	+	0.421137i	0.718464	+	0.695564i	$0.244845\pi$
$998$	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.179.13		36
3.2	odd	2		171.2.t.a.122.6	yes	36
9.2	odd	6		513.2.k.a.8.13		36
9.7	even	3		171.2.k.a.65.6	yes	36
19.12	odd	6		513.2.k.a.449.13		36
57.50	even	6		171.2.k.a.50.6	✓	36
171.88	odd	6		171.2.t.a.164.6	yes	36
171.164	even	6	inner	513.2.t.a.278.13		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.k.a.50.6	✓	36	57.50	even	6
171.2.k.a.65.6	yes	36	9.7	even	3
171.2.t.a.122.6	yes	36	3.2	odd	2
171.2.t.a.164.6	yes	36	171.88	odd	6
513.2.k.a.8.13		36	9.2	odd	6
513.2.k.a.449.13		36	19.12	odd	6
513.2.t.a.179.13		36	1.1	even	1	trivial
513.2.t.a.278.13		36	171.164	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 513 = 3^{3} \cdot 19 \)
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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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