LMFDB - Embedded newform 513.2.k.a.8.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [513,2,Mod(8,513)] 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([1, 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("513.8"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 513 = 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	513.k (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			8.13
Character	$\chi$	$=$	513.8
Dual form			513.2.k.a.449.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.775454 + 1.34313i) q^{2} +(-0.202658 + 0.351014i) q^{4} -1.88474i q^{5} +(-2.41078 + 4.17560i) q^{7} +2.47321 q^{8} +(2.53144 - 1.46153i) q^{10} +(2.70914 + 1.56412i) q^{11} +(2.92553 + 1.68905i) q^{13} -7.47781 q^{14} +(2.32318 + 4.02386i) q^{16} +(-3.06986 - 1.77238i) q^{17} +(4.35881 - 0.0276906i) q^{19} +(0.661569 + 0.381957i) q^{20} +4.85162i q^{22} +(3.74666 + 2.16313i) q^{23} +1.44777 q^{25} +5.23914i q^{26} +(-0.977130 - 1.69244i) q^{28} -2.27211 q^{29} +(-1.96133 + 1.13238i) q^{31} +(-1.12982 + 1.95691i) q^{32} -5.49760i q^{34} +(7.86990 + 4.54369i) q^{35} +4.36294i q^{37} +(3.41725 + 5.83296i) q^{38} -4.66135i q^{40} -5.63929 q^{41} +(-4.51773 - 7.82493i) q^{43} +(-1.09806 + 0.633964i) q^{44} +6.70964i q^{46} -9.51469i q^{47} +(-8.12375 - 14.0707i) q^{49} +(1.12268 + 1.94453i) q^{50} +(-1.18576 + 0.684601i) q^{52} +(-4.04616 - 7.00816i) q^{53} +(2.94796 - 5.10601i) q^{55} +(-5.96237 + 10.3271i) q^{56} +(-1.76192 - 3.05174i) q^{58} -2.28754 q^{59} -10.6751 q^{61} +(-3.04185 - 1.75621i) q^{62} +5.78820 q^{64} +(3.18342 - 5.51385i) q^{65} +(7.42268 + 4.28548i) q^{67} +(1.24426 - 0.718375i) q^{68} +14.0937i q^{70} +(-0.454871 + 0.787860i) q^{71} +(-1.23937 + 2.14665i) q^{73} +(-5.85998 + 3.38326i) q^{74} +(-0.873629 + 1.53562i) q^{76} +(-13.0623 + 7.54152i) q^{77} +(-0.455556 + 0.263015i) q^{79} +(7.58391 - 4.37857i) q^{80} +(-4.37301 - 7.57427i) q^{82} +(-1.65409 - 0.954990i) q^{83} +(-3.34047 + 5.78587i) q^{85} +(7.00658 - 12.1358i) q^{86} +(6.70026 + 3.86840i) q^{88} +(-7.48128 - 12.9580i) q^{89} +(-14.1056 + 8.14389i) q^{91} +(-1.51858 + 0.876753i) q^{92} +(12.7794 - 7.37820i) q^{94} +(-0.0521894 - 8.21521i) q^{95} +(11.6719 - 6.73877i) q^{97} +(12.5992 - 21.8224i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{2} - 15 q^{4} - q^{7} - 12 q^{8} - 6 q^{10} + 9 q^{11} - 6 q^{13} + 6 q^{14} - 9 q^{16} + 27 q^{17} + q^{19} - 9 q^{20} - 9 q^{23} - 22 q^{25} + 2 q^{28} + 24 q^{29} + 12 q^{31} + 15 q^{32}+ \cdots + 84 q^{98}+O(q^{100}) $ 36 * q + 3 * q^2 - 15 * q^4 - q^7 - 12 * q^8 - 6 * q^10 + 9 * q^11 - 6 * q^13 + 6 * q^14 - 9 * q^16 + 27 * q^17 + q^19 - 9 * q^20 - 9 * q^23 - 22 * q^25 + 2 * q^28 + 24 * q^29 + 12 * q^31 + 15 * q^32 - 15 * q^35 + 18 * q^38 - 36 * q^41 + 3 * q^43 - 66 * q^44 - 9 * q^49 - 3 * q^50 + 15 * q^52 + 12 * q^53 - 7 * q^55 - 6 * q^56 - 6 * q^58 + 18 * q^59 - 16 * q^61 + 12 * q^62 + 12 * q^64 + 18 * q^65 + 27 * q^67 - 60 * q^68 - 9 * q^71 - 18 * q^73 - 90 * q^74 - 23 * q^76 + 6 * q^77 - 6 * q^79 + 12 * q^80 - 9 * q^82 + 9 * q^83 + 11 * q^85 - 51 * q^86 + 3 * q^88 + 18 * q^89 + 27 * q^91 + 93 * q^92 + 12 * q^94 + 24 * q^97 + 84 * q^98

Character values

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

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

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 $

$2$	0.775454	+	1.34313i	0.548329	+	0.949733i	0.998389	+	0.0567353i	$0.0180691\pi$
$2$	0.775454	+	1.34313i	0.548329	+	0.949733i	−0.450060	+	0.892998i	$0.648598\pi$
$3$		0			0
$3$		0			0
$4$	−0.202658	+	0.351014i	−0.101329	+	0.175507i
$5$		−	1.88474i		−	0.842880i	−0.906856	−	0.421440i	$-0.861525\pi$
$5$		−	1.88474i		−	0.842880i	0.906856	−	0.421440i	$-0.138475\pi$
$6$		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
$13$	2.92553	+	1.68905i	0.811396	+	0.468460i	0.847440	−	0.530891i	$-0.178143\pi$
$13$	2.92553	+	1.68905i	0.811396	+	0.468460i	−0.0360446	+	0.999350i	$0.511476\pi$
$14$	−7.47781			−1.99853
$15$		0			0
$16$	2.32318	+	4.02386i	0.580794	+	1.00596i
$17$	−3.06986	−	1.77238i	−0.744549	−	0.429866i	0.0791717	−	0.996861i	$-0.474772\pi$
$17$	−3.06986	−	1.77238i	−0.744549	−	0.429866i	−0.823721	+	0.566995i	$0.808106\pi$
$18$		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
$22$			4.85162i			1.03437i
$23$	3.74666	+	2.16313i	0.781232	+	0.451044i	0.836867	−	0.547407i	$-0.184385\pi$
$23$	3.74666	+	2.16313i	0.781232	+	0.451044i	−0.0556348	+	0.998451i	$0.517718\pi$
$24$		0			0
$25$	1.44777			0.289553
$26$			5.23914i			1.02748i
$27$		0			0
$28$	−0.977130	−	1.69244i	−0.184660	−	0.319841i
$29$	−2.27211			−0.421921			−0.210961	−	0.977495i	$-0.567659\pi$
$29$	−2.27211			−0.421921			−0.210961	+	0.977495i	$0.567659\pi$
$30$		0			0
$31$	−1.96133	+	1.13238i	−0.352266	+	0.203381i	−0.665683	−	0.746235i	$-0.731860\pi$
$31$	−1.96133	+	1.13238i	−0.352266	+	0.203381i	0.313417	+	0.949616i	$0.398526\pi$
$32$	−1.12982	+	1.95691i	−0.199727	+	0.345937i
$33$		0			0
$34$		−	5.49760i		−	0.942831i
$35$	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	$0.883244\pi$
$38$	3.41725	+	5.83296i	0.554351	+	0.946231i
$39$		0			0
$40$		−	4.66135i		−	0.737024i
$41$	−5.63929			−0.880708			−0.440354	−	0.897824i	$-0.645147\pi$
$41$	−5.63929			−0.880708			−0.440354	+	0.897824i	$0.645147\pi$
$42$		0			0
$43$	−4.51773	−	7.82493i	−0.688947	−	1.19329i	−0.972179	−	0.234240i	$-0.924740\pi$
$43$	−4.51773	−	7.82493i	−0.688947	−	1.19329i	0.283232	−	0.959051i	$-0.408593\pi$
$44$	−1.09806	+	0.633964i	−0.165538	+	0.0955737i
$45$		0			0
$46$			6.70964i			0.989283i
$47$		−	9.51469i		−	1.38786i	−0.720042	−	0.693930i	$-0.755878\pi$
$47$		−	9.51469i		−	1.38786i	0.720042	−	0.693930i	$-0.244122\pi$
$48$		0			0
$49$	−8.12375	−	14.0707i	−1.16054	−	2.01011i
$50$	1.12268	+	1.94453i	0.158771	+	0.274999i
$51$		0			0
$52$	−1.18576	+	0.684601i	−0.164436	+	0.0949371i
$53$	−4.04616	−	7.00816i	−0.555783	−	0.962644i	−0.997842	−	0.0656585i	$-0.979085\pi$
$53$	−4.04616	−	7.00816i	−0.555783	−	0.962644i	0.442059	−	0.896986i	$-0.354248\pi$
$54$		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
$59$	−2.28754			−0.297812			−0.148906	−	0.988851i	$-0.547575\pi$
$59$	−2.28754			−0.297812			−0.148906	+	0.988851i	$0.547575\pi$
$60$		0			0
$61$	−10.6751			−1.36681			−0.683406	−	0.730039i	$-0.739502\pi$
$61$	−10.6751			−1.36681			−0.683406	+	0.730039i	$0.739502\pi$
$62$	−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
$67$	7.42268	+	4.28548i	0.906824	+	0.523555i	0.879408	−	0.476069i	$-0.157939\pi$
$67$	7.42268	+	4.28548i	0.906824	+	0.523555i	0.0274163	+	0.999624i	$0.491272\pi$
$68$	1.24426	−	0.718375i	0.150889	−	0.0871158i
$69$		0			0
$70$			14.0937i			1.68452i
$71$	−0.454871	+	0.787860i	−0.0539833	+	0.0935018i	−0.891754	−	0.452520i	$-0.850525\pi$
$71$	−0.454871	+	0.787860i	−0.0539833	+	0.0935018i	0.837771	+	0.546022i	$0.183858\pi$
$72$		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	$0.213003\pi$
$74$	−5.85998	+	3.38326i	−0.681208	+	0.393296i
$75$		0			0
$76$	−0.873629	+	1.53562i	−0.100212	+	0.176147i
$77$	−13.0623	+	7.54152i	−1.48859	+	0.859436i
$78$		0			0
$79$	−0.455556	+	0.263015i	−0.0512540	+	0.0295915i	−0.525408	−	0.850850i	$-0.676087\pi$
$79$	−0.455556	+	0.263015i	−0.0512540	+	0.0295915i	0.474154	+	0.880442i	$0.342754\pi$
$80$	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
$85$	−3.34047	+	5.78587i	−0.362325	+	0.627566i
$86$	7.00658	−	12.1358i	0.755539	−	1.30863i
$87$		0			0
$88$	6.70026	+	3.86840i	0.714250	+	0.412373i
$89$	−7.48128	−	12.9580i	−0.793014	−	1.37354i	−0.924093	−	0.382169i	$-0.875177\pi$
$89$	−7.48128	−	12.9580i	−0.793014	−	1.37354i	0.131079	−	0.991372i	$-0.458156\pi$
$90$		0			0
$91$	−14.1056	+	8.14389i	−1.47867	+	0.853712i
$92$	−1.51858	+	0.876753i	−0.158323	+	0.0914078i
$93$		0			0
$94$	12.7794	−	7.37820i	1.31810	−	0.761004i
$95$	−0.0521894	−	8.21521i	−0.00535452	−	0.842863i
$96$		0			0
$97$	11.6719	−	6.73877i	1.18510	−	0.684219i	0.227912	−	0.973682i	$-0.426810\pi$
$97$	11.6719	−	6.73877i	1.18510	−	0.684219i	0.957189	+	0.289463i	$0.0934767\pi$
$98$	12.5992	−	21.8224i	1.27271	−	2.20440i
$99$		0			0
$100$	−0.293402	+	0.508187i	−0.0293402	+	0.0508187i
$101$			14.7915i			1.47181i	0.677086	+	0.735904i	$0.263243\pi$
$101$			14.7915i			1.47181i	−0.677086	+	0.735904i	$0.736757\pi$
$102$		0			0
$103$	6.03192	−	3.48253i	0.594343	−	0.343144i	−0.172470	−	0.985015i	$-0.555175\pi$
$103$	6.03192	−	3.48253i	0.594343	−	0.343144i	0.766813	+	0.641871i	$0.221841\pi$
$104$	7.23544	+	4.17738i	0.709493	+	0.409626i
$105$		0			0
$106$	6.27523	−	10.8690i	0.609504	−	1.05569i
$107$	6.21001			0.600344			0.300172	−	0.953885i	$-0.402956\pi$
$107$	6.21001			0.600344			0.300172	+	0.953885i	$0.402956\pi$
$108$		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	$0.713334\pi$
$110$	9.14402			0.871849
$111$		0			0
$112$	−22.4027			−2.11685
$113$	6.17578	+	10.6968i	0.580969	+	1.00627i	0.995365	+	0.0961706i	$0.0306594\pi$
$113$	6.17578	+	10.6968i	0.580969	+	1.00627i	−0.414396	+	0.910097i	$0.636007\pi$
$114$		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
$119$	14.8015	−	8.54566i	1.35685	−	0.783379i
$120$		0			0
$121$	−0.607046	−	1.05143i	−0.0551860	−	0.0955849i
$122$	−8.27808	−	14.3381i	−0.749462	−	1.29811i
$123$		0			0
$124$		−	0.917941i		−	0.0824335i
$125$		−	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	$0.278420\pi$
$128$	6.74813	+	11.6881i	0.596456	+	1.03309i
$129$		0			0
$130$	9.87440			0.866042
$131$		−	13.0672i		−	1.14169i	−0.821059	−	0.570843i	$-0.806616\pi$
$131$		−	13.0672i		−	1.14169i	0.821059	−	0.570843i	$-0.193384\pi$
$132$		0			0
$133$	−10.3925	+	18.2674i	−0.901146	+	1.58398i
$134$			13.2928i			1.14832i
$135$		0			0
$136$	−7.59239	−	4.38347i	−0.651042	−	0.375879i
$137$		−	0.901415i		−	0.0770131i	−0.999258	−	0.0385065i	$-0.987740\pi$
$137$		−	0.901415i		−	0.0770131i	0.999258	−	0.0385065i	$-0.0122600\pi$
$138$		0			0
$139$	−9.68285	+	16.7712i	−0.821289	+	1.42251i	0.0834342	+	0.996513i	$0.473411\pi$
$139$	−9.68285	+	16.7712i	−0.821289	+	1.42251i	−0.904723	+	0.426001i	$0.859922\pi$
$140$	−3.18980	+	1.84163i	−0.269587	+	0.155646i
$141$		0			0
$142$	−1.41093			−0.118402
$143$	5.28378	+	9.15177i	0.441851	+	0.765309i
$144$		0			0
$145$			4.28234i			0.355629i
$146$	−3.84429			−0.318156
$147$		0			0
$148$	−1.53145	−	0.884185i	−0.125885	−	0.0726796i
$149$			1.89950i			0.155613i	0.996968	+	0.0778065i	$0.0247917\pi$
$149$			1.89950i			0.155613i	−0.996968	+	0.0778065i	$0.975208\pi$
$150$		0			0
$151$	−3.36348	−	1.94190i	−0.273716	−	0.158030i	0.356859	−	0.934158i	$-0.383848\pi$
$151$	−3.36348	−	1.94190i	−0.273716	−	0.158030i	−0.630575	+	0.776128i	$0.717181\pi$
$152$	10.7802	−	0.0684845i	0.874393	−	0.00555483i
$153$		0			0
$154$	−20.2584	−	11.6962i	−1.63247	−	0.942507i
$155$	2.13423	+	3.69660i	0.171426	+	0.296918i
$156$		0			0
$157$	16.5454			1.32047			0.660235	−	0.751059i	$-0.270457\pi$
$157$	16.5454			1.32047			0.660235	+	0.751059i	$0.270457\pi$
$158$	−0.706525	−	0.407913i	−0.0562081	−	0.0324518i
$159$		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
$166$		−	2.96220i		−	0.229912i
$167$	−3.53401	+	6.12109i	−0.273470	+	0.473664i	−0.969748	−	0.244108i	$-0.921505\pi$
$167$	−3.53401	+	6.12109i	−0.273470	+	0.473664i	0.696278	+	0.717772i	$0.254838\pi$
$168$		0			0
$169$	−0.794187	−	1.37557i	−0.0610913	−	0.105813i
$170$	−10.3615			−0.794693
$171$		0			0
$172$	3.66222			0.279241
$173$	−6.49992	−	11.2582i	−0.494179	−	0.855944i	0.505798	−	0.862652i	$-0.331198\pi$
$173$	−6.49992	−	11.2582i	−0.494179	−	0.855944i	−0.999978	+	0.00670798i	$0.997865\pi$
$174$		0			0
$175$	−3.49025	+	6.04529i	−0.263838	+	0.456981i
$176$			14.5349i			1.09561i
$177$		0			0
$178$	11.6028	−	20.0966i	0.869665	−	1.50630i
$179$	−8.63956			−0.645751			−0.322875	−	0.946442i	$-0.604649\pi$
$179$	−8.63956			−0.645751			−0.322875	+	0.946442i	$0.604649\pi$
$180$		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
$184$	9.26626	+	5.34988i	0.683118	+	0.394398i
$185$	8.22299			0.604566
$186$		0			0
$187$	−5.54444	−	9.60326i	−0.405450	−	0.702260i
$188$	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
$193$		−	8.01692i		−	0.577071i	−0.957469	−	0.288535i	$-0.906832\pi$
$193$		−	8.01692i		−	0.577071i	0.957469	−	0.288535i	$-0.0931683\pi$
$194$	18.1020	+	10.4512i	1.29965	+	0.750354i
$195$		0			0
$196$	6.58537			0.470384
$197$			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	0.932867	−	0.360221i	$-0.117299\pi$
$199$	2.17911	+	3.77433i	0.154473	+	0.267555i	−0.778394	+	0.627776i	$0.783965\pi$
$200$	3.58063			0.253189
$201$		0			0
$202$	−19.8668	+	11.4701i	−1.39783	+	0.807035i
$203$	5.47758	−	9.48744i	0.384450	−	0.665888i
$204$		0			0
$205$			10.6286i			0.742331i
$206$	9.35496	+	5.40109i	0.651791	+	0.376312i
$207$		0			0
$208$			15.6959i			1.08831i
$209$	11.8519	+	6.74269i	0.819815	+	0.466402i
$210$		0			0
$211$		−	13.2577i		−	0.912700i	−0.889800	−	0.456350i	$-0.849157\pi$
$211$		−	13.2577i		−	0.912700i	0.889800	−	0.456350i	$-0.150843\pi$
$212$	3.27995			0.225268
$213$		0			0
$214$	4.81557	+	8.34082i	0.329186	+	0.570167i
$215$	−14.7479	+	8.51473i	−1.00580	+	0.580700i
$216$		0			0
$217$		−	10.9197i		−	0.741274i
$218$		−	4.73077i		−	0.320408i
$219$		0			0
$220$	1.19486	+	2.06955i	0.0805571	+	0.139529i
$221$	−5.98730	−	10.3703i	−0.402749	−	0.697582i
$222$		0			0
$223$	3.13409	−	1.80947i	0.209874	−	0.121171i	−0.391379	−	0.920230i	$-0.628002\pi$
$223$	3.13409	−	1.80947i	0.209874	−	0.121171i	0.601253	+	0.799059i	$0.294668\pi$
$224$	−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	$-0.596718\pi$
$227$	10.1964	−	17.6606i	0.676757	−	1.17218i	0.975952	−	0.217985i	$-0.0699484\pi$
$228$		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	$0.890958\pi$
$230$	12.6459			0.833847
$231$		0			0
$232$	−5.61941			−0.368933
$233$	22.2854	+	12.8665i	1.45996	+	0.842910i	0.999009	−	0.0445134i	$-0.0141737\pi$
$233$	22.2854	+	12.8665i	1.45996	+	0.842910i	0.460955	+	0.887424i	$0.347507\pi$
$234$		0			0
$235$	−17.9327			−1.16980
$236$	0.463589	−	0.802959i	0.0301771	−	0.0522682i
$237$		0			0
$238$	22.9558	+	13.2535i	1.48800	+	0.859099i
$239$	−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
$241$		−	19.0538i		−	1.22736i	−0.789553	−	0.613682i	$-0.789688\pi$
$241$		−	19.0538i		−	1.22736i	0.789553	−	0.613682i	$-0.210312\pi$
$242$	0.941472	−	1.63068i	0.0605201	−	0.104824i
$243$		0			0
$244$	2.16340	−	3.74712i	0.138498	−	0.239885i
$245$	−26.5196	+	15.3111i	−1.69428	+	0.978192i
$246$		0			0
$247$	12.7986	+	7.28126i	0.814355	+	0.463296i
$248$	−4.85079	+	2.80060i	−0.308025	+	0.177838i
$249$		0			0
$250$	16.3221	−	9.42359i	1.03230	−	0.596000i
$251$	−7.74070	+	4.46909i	−0.488589	+	0.282087i	−0.723989	−	0.689812i	$-0.757693\pi$
$251$	−7.74070	+	4.46909i	−0.488589	+	0.282087i	0.235400	+	0.971899i	$0.424360\pi$
$252$		0			0
$253$	6.76681	+	11.7205i	0.425426	+	0.736859i
$254$	5.19659	+	3.00025i	0.326063	+	0.188253i
$255$		0			0
$256$	−4.67753	+	8.10172i	−0.292346	+	0.506358i
$257$	−2.93041	+	5.07563i	−0.182794	+	0.316609i	−0.942831	−	0.333271i	$-0.891848\pi$
$257$	−2.93041	+	5.07563i	−0.182794	+	0.316609i	0.760037	+	0.649880i	$0.225181\pi$
$258$		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
$263$	−5.16520	+	2.98213i	−0.318500	+	0.183886i	−0.650724	−	0.759315i	$-0.725534\pi$
$263$	−5.16520	+	2.98213i	−0.318500	+	0.183886i	0.332224	+	0.943201i	$0.392201\pi$
$264$		0			0
$265$	−13.2085	+	7.62595i	−0.811394	+	0.468458i
$266$	−32.5943	+	0.207065i	−1.99849	+	0.0126960i
$267$		0			0
$268$	−3.00853	+	1.73698i	−0.183775	+	0.106103i
$269$	−4.25123	+	7.36335i	−0.259202	+	0.448951i	−0.966028	−	0.258436i	$-0.916793\pi$
$269$	−4.25123	+	7.36335i	−0.259202	+	0.448951i	0.706826	+	0.707387i	$0.250126\pi$
$270$		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	$0.0916485\pi$
$272$		−	16.4702i		−	0.998654i
$273$		0			0
$274$	1.21071	−	0.699006i	0.0731419	−	0.0422285i
$275$	3.92220	+	2.26448i	0.236518	+	0.136554i
$276$		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
$281$	−29.6481			−1.76866			−0.884329	−	0.466864i	$-0.845384\pi$
$281$	−29.6481			−1.76866			−0.884329	+	0.466864i	$0.845384\pi$
$282$		0			0
$283$	−22.5195			−1.33864			−0.669322	−	0.742972i	$-0.733415\pi$
$283$	−22.5195			−1.33864			−0.669322	+	0.742972i	$0.733415\pi$
$284$	−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
$290$	−5.75172	+	3.32076i	−0.337753	+	0.195002i
$291$		0			0
$292$	−0.502336	−	0.870072i	−0.0293970	−	0.0509171i
$293$	1.43273	+	2.48156i	0.0837010	+	0.144974i	0.904837	−	0.425758i	$-0.139993\pi$
$293$	1.43273	+	2.48156i	0.0837010	+	0.144974i	−0.821136	+	0.570733i	$0.806659\pi$
$294$		0			0
$295$			4.31141i			0.251020i
$296$			10.7905i			0.627183i
$297$		0			0
$298$	−2.55127	+	1.47297i	−0.147791	+	0.0853271i
$299$	7.30730	+	12.6566i	0.422592	+	0.731951i
$300$		0			0
$301$	43.5650			2.51105
$302$		−	6.02343i		−	0.346609i
$303$		0			0
$304$	10.2377	+	17.4749i	0.587173	+	1.00225i
$305$			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	$0.839132\pi$
$308$		−	6.11340i		−	0.348343i
$309$		0			0
$310$	−3.31000	+	5.73308i	−0.187995	+	0.325617i
$311$	−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
$313$	1.47819			0.0835525			0.0417762	−	0.999127i	$-0.486698\pi$
$313$	1.47819			0.0835525			0.0417762	+	0.999127i	$0.486698\pi$
$314$	12.8302	+	22.2226i	0.724052	+	1.25409i
$315$		0			0
$316$		−	0.213209i		−	0.0119939i
$317$	18.2349			1.02417			0.512087	−	0.858934i	$-0.328872\pi$
$317$	18.2349			1.02417			0.512087	+	0.858934i	$0.328872\pi$
$318$		0			0
$319$	−6.15547	−	3.55386i	−0.344640	−	0.198978i
$320$		−	10.9092i		−	0.609844i
$321$		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
$326$	7.92806	+	13.7318i	0.439095	+	0.760534i
$327$		0			0
$328$	−13.9471			−0.770101
$329$	39.7295	+	22.9378i	2.19036	+	1.26460i
$330$		0			0
$331$	26.0644	+	15.0483i	1.43263	+	0.827128i	0.997321	−	0.0731549i	$-0.0233067\pi$
$331$	26.0644	+	15.0483i	1.43263	+	0.827128i	0.435306	+	0.900282i	$0.356640\pi$
$332$	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
$337$		−	3.64508i		−	0.198560i	−0.995060	−	0.0992802i	$-0.968346\pi$
$337$		−	3.64508i		−	0.198560i	0.995060	−	0.0992802i	$-0.0316540\pi$
$338$	1.23171	−	2.13339i	0.0669963	−	0.116041i
$339$		0			0
$340$	−1.35395	−	2.34511i	−0.0734282	−	0.127181i
$341$	−7.08470			−0.383658
$342$		0			0
$343$	44.5874			2.40749
$344$	−11.1733	−	19.3527i	−0.602423	−	1.04343i
$345$		0			0
$346$	10.0808	−	17.4604i	0.541946	−	0.938678i
$347$			7.64224i			0.410257i	0.978735	+	0.205128i	$0.0657612\pi$
$347$			7.64224i			0.410257i	−0.978735	+	0.205128i	$0.934239\pi$
$348$		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
$355$	1.48491	+	0.857313i	0.0788108	+	0.0455014i
$356$	6.06457			0.321422
$357$		0			0
$358$	−6.69958	−	11.6040i	−0.354084	−	0.613291i
$359$	0.986080	+	0.569313i	0.0520433	+	0.0300472i	0.525796	−	0.850611i	$-0.323768\pi$
$359$	0.986080	+	0.569313i	0.0520433	+	0.0300472i	−0.473753	+	0.880658i	$0.657101\pi$
$360$		0			0
$361$	18.9985	−	0.241396i	0.999919	−	0.0127050i
$362$	−3.20248	−	1.84895i	−0.168319	−	0.0971788i
$363$		0			0
$364$		−	6.60170i		−	0.346023i
$365$	4.04587	+	2.33588i	0.211770	+	0.122266i
$366$		0			0
$367$	0.702648			0.0366779			0.0183390	−	0.999832i	$-0.494162\pi$
$367$	0.702648			0.0366779			0.0183390	+	0.999832i	$0.494162\pi$
$368$			20.1014i			1.04786i
$369$		0			0
$370$	6.37655	+	11.0445i	0.331501	+	0.574177i
$371$	39.0177			2.02570
$372$		0			0
$373$	−8.13834	+	4.69867i	−0.421387	+	0.243288i	−0.695671	−	0.718361i	$-0.744893\pi$
$373$	−8.13834	+	4.69867i	−0.421387	+	0.243288i	0.274283	+	0.961649i	$0.411559\pi$
$374$	8.59892	−	14.8938i	0.444640	−	0.770138i
$375$		0			0
$376$		−	23.5318i		−	1.21356i
$377$	−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	$-0.212796\pi$
$380$	2.89423	+	1.64656i	0.148471	+	0.0844668i
$381$		0			0
$382$		−	11.5780i		−	0.592382i
$383$	28.8797			1.47568			0.737841	−	0.674975i	$-0.235846\pi$
$383$	28.8797			1.47568			0.737841	+	0.674975i	$0.235846\pi$
$384$		0			0
$385$	14.2138	+	24.6190i	0.724401	+	1.25470i
$386$	10.7677	−	6.21676i	0.548063	−	0.316425i
$387$		0			0
$388$			5.46267i			0.277325i
$389$		−	38.7316i		−	1.96377i	−0.189473	−	0.981886i	$-0.560678\pi$
$389$		−	38.7316i		−	1.96377i	0.189473	−	0.981886i	$-0.439322\pi$
$390$		0			0
$391$	−7.66780	−	13.2810i	−0.387777	−	0.671650i
$392$	−20.0917	−	34.7999i	−1.01478	−	1.75766i
$393$		0			0
$394$	−11.0053	+	6.35392i	−0.554439	+	0.320106i
$395$	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
$401$	4.64123			0.231772			0.115886	−	0.993263i	$-0.463029\pi$
$401$	4.64123			0.231772			0.115886	+	0.993263i	$0.463029\pi$
$402$		0			0
$403$	−7.65058			−0.381103
$404$	−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
$409$	−16.6379	−	9.60588i	−0.822690	−	0.474980i	0.0286534	−	0.999589i	$-0.490878\pi$
$409$	−16.6379	−	9.60588i	−0.822690	−	0.474980i	−0.851343	+	0.524609i	$0.824211\pi$
$410$	−14.2755	+	8.24197i	−0.705017	+	0.407042i
$411$		0			0
$412$			2.82305i			0.139082i
$413$	5.51476	−	9.55185i	0.271364	−	0.470016i
$414$		0			0
$415$	−1.79990	+	3.11753i	−0.0883538	+	0.153033i
$416$	−6.61067	+	3.81667i	−0.324115	+	0.187128i
$417$		0			0
$418$	0.134344	+	21.1473i	0.00657099	+	1.03435i
$419$	−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
$421$	14.2147	−	8.20685i	0.692782	−	0.399978i	−0.111872	−	0.993723i	$-0.535685\pi$
$421$	14.2147	−	8.20685i	0.692782	−	0.399978i	0.804653	+	0.593745i	$0.202351\pi$
$422$	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
$427$	25.7354	−	44.5751i	1.24542	−	2.15714i
$428$	−1.25851	+	2.17980i	−0.0608323	+	0.105365i
$429$		0			0
$430$	−22.8727	−	13.2056i	−1.10302	−	0.636829i
$431$	17.2912	+	29.9492i	0.832888	+	1.44260i	0.895738	+	0.444581i	$0.146648\pi$
$431$	17.2912	+	29.9492i	0.832888	+	1.44260i	−0.0628504	+	0.998023i	$0.520019\pi$
$432$		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	$0.469616\pi$
$434$	14.6665	−	8.46769i	0.704013	−	0.406462i
$435$		0			0
$436$	1.07071	−	0.618172i	0.0512775	−	0.0296051i
$437$	16.3909	+	9.32494i	0.784081	+	0.446072i
$438$		0			0
$439$	25.2618	−	14.5849i	1.20568	−	0.696099i	0.243867	−	0.969809i	$-0.421584\pi$
$439$	25.2618	−	14.5849i	1.20568	−	0.696099i	0.961812	+	0.273710i	$0.0882507\pi$
$440$	7.29091	−	12.6282i	0.347581	−	0.602027i
$441$		0			0
$442$	9.28575	−	16.0834i	0.441678	−	0.765009i
$443$			7.75203i			0.368310i	0.982897	+	0.184155i	$0.0589549\pi$
$443$			7.75203i			0.368310i	−0.982897	+	0.184155i	$0.941045\pi$
$444$		0			0
$445$	−24.4223	+	14.1002i	−1.15773	+	0.668416i
$446$	4.86069	+	2.80632i	0.230160	+	0.132883i
$447$		0			0
$448$	−13.9541	+	24.1692i	−0.659268	+	1.14189i
$449$	−21.5509			−1.01705			−0.508526	−	0.861047i	$-0.669809\pi$
$449$	−21.5509			−1.01705			−0.508526	+	0.861047i	$0.669809\pi$
$450$		0			0
$451$	−15.2776	−	8.82053i	−0.719394	−	0.415343i
$452$	−5.00629			−0.235476
$453$		0			0
$454$	31.6273			1.48434
$455$	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
$461$	−22.4385	+	12.9549i	−1.04507	+	0.603370i	−0.921264	−	0.388937i	$-0.872842\pi$
$461$	−22.4385	+	12.9549i	−1.04507	+	0.603370i	−0.123803	+	0.992307i	$0.539509\pi$
$462$		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
$466$			39.9094i			1.84877i
$467$		−	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
$470$	−13.9060	−	24.0859i	−0.641435	−	1.11100i
$471$		0			0
$472$	−5.65756			−0.260410
$473$		−	28.2651i		−	1.29963i
$474$		0			0
$475$	6.31054	−	0.0400895i	0.289548	−	0.00183943i
$476$			6.92739i			0.317516i
$477$		0			0
$478$	−16.3048	−	9.41355i	−0.745762	−	0.430566i
$479$		−	14.7307i		−	0.673065i	−0.941672	−	0.336532i	$-0.890746\pi$
$479$		−	14.7307i		−	0.673065i	0.941672	−	0.336532i	$-0.109254\pi$
$480$		0			0
$481$	−7.36924	+	12.7639i	−0.336009	+	0.581984i
$482$	25.5917	−	14.7754i	1.16567	−	0.673000i
$483$		0			0
$484$	0.492091			0.0223678
$485$	−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	$0.896878\pi$
$488$	−26.4018			−1.19515
$489$		0			0
$490$	−41.1295	−	23.7461i	−1.85804	−	1.07274i
$491$			16.6102i			0.749608i	0.927104	+	0.374804i	$0.122290\pi$
$491$			16.6102i			0.749608i	−0.927104	+	0.374804i	$0.877710\pi$
$492$		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
$497$	−2.19319	−	3.79872i	−0.0983781	−	0.170396i
$498$		0			0
$499$	−22.5746			−1.01058			−0.505288	−	0.862951i	$-0.668614\pi$
$499$	−22.5746			−1.01058			−0.505288	+	0.862951i	$0.668614\pi$
$500$	4.26565	+	2.46277i	0.190765	+	0.110138i
$501$		0			0
$502$	−12.0051	−	6.93116i	−0.535814	−	0.309353i
$503$	−25.4796	+	14.7107i	−1.13608	+	0.655917i	−0.945457	−	0.325746i	$-0.894384\pi$
$503$	−25.4796	+	14.7107i	−1.13608	+	0.655917i	−0.190624	+	0.981663i	$0.561051\pi$
$504$		0			0
$505$	27.8781			1.24056
$506$	−10.4947	+	18.1774i	−0.466546	+	0.808082i
$507$		0			0
$508$			1.56818i			0.0695767i
$509$	15.6211	−	27.0565i	0.692391	−	1.19926i	−0.278661	−	0.960389i	$-0.589891\pi$
$509$	15.6211	−	27.0565i	0.692391	−	1.19926i	0.971052	−	0.238867i	$-0.0767760\pi$
$510$		0			0
$511$	−5.97569	−	10.3502i	−0.264349	−	0.457866i
$512$	12.4837			0.551705
$513$		0			0
$514$	−9.08961			−0.400925
$515$	−6.56366	−	11.3686i	−0.289229	−	0.500960i
$516$		0			0
$517$	14.8821	−	25.7766i	0.654515	−	1.13365i
$518$		−	32.6252i		−	1.43347i
$519$		0			0
$520$	7.87327	−	13.6369i	0.345266	−	0.598018i
$521$	−0.424924			−0.0186163			−0.00930814	−	0.999957i	$-0.502963\pi$
$521$	−0.424924			−0.0186163			−0.00930814	+	0.999957i	$0.502963\pi$
$522$		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
$526$	−8.01075	−	4.62501i	−0.349285	−	0.201660i
$527$	8.02801			0.349706
$528$		0			0
$529$	−2.14171	−	3.70955i	−0.0931178	−	0.161285i
$530$	−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
$535$		−	11.7042i		−	0.506018i
$536$	18.3578	+	10.5989i	0.792937	+	0.457803i
$537$		0			0
$538$	−13.1865			−0.568512
$539$		−	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	$0.693065\pi$
$542$	11.9231			0.512141
$543$		0			0
$544$	6.93679	−	4.00496i	0.297413	−	0.171711i
$545$	−2.87452	+	4.97882i	−0.123131	+	0.213269i
$546$		0			0
$547$			20.5955i			0.880600i	0.897851	+	0.440300i	$0.145128\pi$
$547$			20.5955i			0.880600i	−0.897851	+	0.440300i	$0.854872\pi$
$548$	0.316409	+	0.182679i	0.0135163	+	0.00780366i
$549$		0			0
$550$			7.02401i			0.299505i
$551$	−9.90372	+	0.0629162i	−0.421913	+	0.00268032i
$552$		0			0
$553$		−	2.53629i		−	0.107854i
$554$	−47.6623			−2.02498
$555$		0			0
$556$	−3.92462	−	6.79764i	−0.166441	−	0.288284i
$557$	−9.85951	+	5.69239i	−0.417761	+	0.241194i	−0.694119	−	0.719860i	$-0.744206\pi$
$557$	−9.85951	+	5.69239i	−0.417761	+	0.241194i	0.276358	+	0.961055i	$0.410872\pi$
$558$		0			0
$559$		−	30.5228i		−	1.29098i
$560$			42.2232i			1.78425i
$561$		0			0
$562$	−22.9907	−	39.8211i	−0.969806	−	1.67975i
$563$	22.3588	+	38.7266i	0.942311	+	1.63213i	0.761048	+	0.648695i	$0.224685\pi$
$563$	22.3588	+	38.7266i	0.942311	+	1.63213i	0.181263	+	0.983435i	$0.441982\pi$
$564$		0			0
$565$	20.1606	−	11.6397i	0.848162	−	0.489687i
$566$	−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	$-0.825850\pi$
$569$	0.560747	−	0.971242i	0.0235077	−	0.0407166i	0.877540	+	0.479504i	$0.159183\pi$
$570$		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	$0.704619\pi$
$572$	−4.28320			−0.179090
$573$		0			0
$574$	42.1695			1.76012
$575$	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
$580$	−1.50316	−	0.867851i	−0.0624154	−	0.0360355i
$581$	7.97531	−	4.60455i	0.330872	−	0.191029i
$582$		0			0
$583$		−	25.3148i		−	1.04843i
$584$	−3.06521	+	5.30911i	−0.126839	+	0.219692i
$585$		0			0
$586$	−2.22203	+	3.84867i	−0.0917913	+	0.158987i
$587$	−5.63608	+	3.25400i	−0.232626	+	0.134307i	−0.611783	−	0.791026i	$-0.709547\pi$
$587$	−5.63608	+	3.25400i	−0.232626	+	0.134307i	0.379157	+	0.925332i	$0.376214\pi$
$588$		0			0
$589$	−8.51772	+	4.99012i	−0.350967	+	0.205615i
$590$	−5.79077	+	3.34330i	−0.238402	+	0.137642i
$591$		0			0
$592$	−17.5558	+	10.1359i	−0.721541	+	0.416582i
$593$	8.23530	−	4.75465i	0.338183	−	0.195250i	−0.321285	−	0.946983i	$-0.604115\pi$
$593$	8.23530	−	4.75465i	0.338183	−	0.195250i	0.659468	+	0.751732i	$0.270781\pi$
$594$		0			0
$595$	−16.1063	−	27.8970i	−0.660294	−	1.14366i
$596$	−0.666751	−	0.384949i	−0.0273112	−	0.0157681i
$597$		0			0
$598$	−11.3330	+	19.6293i	−0.463439	+	0.802700i
$599$	−18.2911	+	31.6812i	−0.747355	+	1.29446i	0.201731	+	0.979441i	$0.435343\pi$
$599$	−18.2911	+	31.6812i	−0.747355	+	1.29446i	−0.949086	+	0.315017i	$0.897990\pi$
$600$		0			0
$601$	39.1747	+	22.6175i	1.59797	+	0.922587i	0.991878	+	0.127190i	$0.0405960\pi$
$601$	39.1747	+	22.6175i	1.59797	+	0.922587i	0.606089	+	0.795397i	$0.292737\pi$
$602$	33.7827	+	58.5133i	1.37688	+	2.38483i
$603$		0			0
$604$	1.36327	−	0.787085i	0.0554707	−	0.0320261i
$605$	−1.98168	+	1.14412i	−0.0805666	+	0.0465151i
$606$		0			0
$607$	29.9152	−	17.2715i	1.21422	−	0.701030i	0.250544	−	0.968105i	$-0.419391\pi$
$607$	29.9152	−	17.2715i	1.21422	−	0.701030i	0.963676	+	0.267075i	$0.0860573\pi$
$608$	−4.87050	+	8.56110i	−0.197525	+	0.347198i
$609$		0			0
$610$	−27.0235	+	15.6020i	−1.09415	+	0.631706i
$611$	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	$0.241695\pi$
$614$		−	28.0270i		−	1.13108i
$615$		0			0
$616$	−32.3058	+	18.6517i	−1.30164	+	0.751500i
$617$	−30.1196	−	17.3895i	−1.21257	−	0.700077i	−0.249251	−	0.968439i	$-0.580184\pi$
$617$	−30.1196	−	17.3895i	−1.21257	−	0.700077i	−0.963318	+	0.268362i	$0.913518\pi$
$618$		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
$623$	72.1430			2.89035
$624$		0			0
$625$	−15.6651			−0.626605
$626$	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	$0.634146\pi$
$632$	−1.12668	+	0.650491i	−0.0448171	+	0.0258752i
$633$		0			0
$634$	14.1403	+	24.4918i	0.561584	+	0.972693i
$635$	−3.64605	−	6.31514i	−0.144689	−	0.250609i
$636$		0			0
$637$		−	54.8858i		−	2.17466i
$638$		−	11.0234i		−	0.436422i
$639$		0			0
$640$	22.0290	−	12.7184i	0.870772	−	0.502741i
$641$	−14.9336	−	25.8657i	−0.589840	−	1.02163i	−0.994253	−	0.107057i	$-0.965857\pi$
$641$	−14.9336	−	25.8657i	−0.589840	−	1.02163i	0.404413	−	0.914577i	$-0.367476\pi$
$642$		0			0
$643$	19.8648			0.783391			0.391696	−	0.920095i	$-0.371889\pi$
$643$	19.8648			0.783391			0.391696	+	0.920095i	$0.371889\pi$
$644$		−	8.45465i		−	0.333160i
$645$		0			0
$646$	−0.152232	−	23.9630i	−0.00598948	−	0.942812i
$647$			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
$650$			7.58505i			0.297510i
$651$		0			0
$652$	−2.07193	+	3.58869i	−0.0811430	+	0.140544i
$653$	−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
$655$	−24.6282			−0.962305
$656$	−13.1011	−	22.6917i	−0.511510	−	0.885962i
$657$		0			0
$658$			71.1490i			2.77368i
$659$	−21.8705			−0.851953			−0.425977	−	0.904734i	$-0.640069\pi$
$659$	−21.8705			−0.851953			−0.425977	+	0.904734i	$0.640069\pi$
$660$		0			0
$661$	−3.54829	−	2.04861i	−0.138013	−	0.0796816i	0.429404	−	0.903113i	$-0.358724\pi$
$661$	−3.54829	−	2.04861i	−0.138013	−	0.0796816i	−0.567416	+	0.823431i	$0.692057\pi$
$662$			46.6770i			1.81415i
$663$		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
$668$	−1.43239	−	2.48098i	−0.0554210	−	0.0959919i
$669$		0			0
$670$	25.0534			0.967897
$671$	−28.9204	−	16.6972i	−1.11646	−	0.644589i
$672$		0			0
$673$	−20.9877	−	12.1172i	−0.809015	−	0.467085i	0.0375989	−	0.999293i	$-0.488029\pi$
$673$	−20.9877	−	12.1172i	−0.809015	−	0.467085i	−0.846614	+	0.532208i	$0.821362\pi$
$674$	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	$-0.961817\pi$
$677$	−10.2196	+	17.7009i	−0.392773	+	0.680302i	0.600041	+	0.799969i	$0.295151\pi$
$678$		0			0
$679$			64.9829i			2.49381i
$680$	−8.26169	+	14.3097i	−0.316821	+	0.548750i
$681$		0			0
$682$	−5.49386	−	9.51564i	−0.210371	−	0.364373i
$683$	26.3929			1.00990			0.504949	−	0.863149i	$-0.331511\pi$
$683$	26.3929			1.00990			0.504949	+	0.863149i	$0.331511\pi$
$684$		0			0
$685$	−1.69893			−0.0649128
$686$	34.5755	+	59.8865i	1.32010	+	2.28648i
$687$		0			0
$688$	20.9909	−	36.3574i	0.800272	−	1.38611i
$689$		−	27.3368i		−	1.04145i
$690$		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
$697$	17.3118	+	9.99497i	0.655731	+	0.378586i
$698$	−11.9573			−0.452589
$699$		0			0
$700$	−1.41466	−	2.45026i	−0.0534690	−	0.0926110i
$701$	17.9358	+	10.3552i	0.677424	+	0.391111i	0.798884	−	0.601485i	$-0.205424\pi$
$701$	17.9358	+	10.3552i	0.677424	+	0.391111i	−0.121460	+	0.992596i	$0.538758\pi$
$702$		0			0
$703$	0.120812	+	19.0172i	0.00455652	+	0.717248i
$704$	15.6810	+	9.05344i	0.591001	+	0.341214i
$705$		0			0
$706$			26.6790i			1.00408i
$707$	−61.7633	−	35.6591i	−2.32285	−	1.34110i
$708$		0			0
$709$	12.0940			0.454199			0.227099	−	0.973872i	$-0.427076\pi$
$709$	12.0940			0.454199			0.227099	+	0.973872i	$0.427076\pi$
$710$			2.65923i			0.0997990i
$711$		0			0
$712$	−18.5028	−	32.0477i	−0.693420	−	1.20104i
$713$	−9.79792			−0.366935
$714$		0			0
$715$	17.2487	−	9.95853i	0.645064	−	0.372428i
$716$	1.75088	−	3.03261i	0.0654333	−	0.113334i
$717$		0			0
$718$			1.76591i			0.0659030i
$719$	19.5960	+	11.3137i	0.730807	+	0.421932i	0.818717	−	0.574197i	$-0.194686\pi$
$719$	19.5960	+	11.3137i	0.730807	+	0.421932i	−0.0879104	+	0.996128i	$0.528019\pi$
$720$		0			0
$721$			33.5825i			1.25068i
$722$	15.0567	+	25.3301i	0.560351	+	0.942690i
$723$		0			0
$724$		−	0.966416i		−	0.0359166i
$725$	−3.28949			−0.122169
$726$		0			0
$727$	19.3469	+	33.5098i	0.717536	+	1.24281i	0.961973	+	0.273143i	$0.0880634\pi$
$727$	19.3469	+	33.5098i	0.717536	+	1.24281i	−0.244437	+	0.969665i	$0.578603\pi$
$728$	−34.8862	+	20.1415i	−1.29297	+	0.746495i
$729$		0			0
$730$			7.24548i			0.268167i
$731$			32.0286i			1.18462i
$732$		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
$736$	−8.46613	+	4.88792i	−0.312066	+	0.180171i
$737$	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
$743$	13.4091			0.491931			0.245966	−	0.969279i	$-0.420895\pi$
$743$	13.4091			0.491931			0.245966	+	0.969279i	$0.420895\pi$
$744$		0			0
$745$	3.58006			0.131163
$746$	−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
$751$	37.2232	+	21.4909i	1.35830	+	0.784212i	0.989394	−	0.145256i	$-0.0464006\pi$
$751$	37.2232	+	21.4909i	1.35830	+	0.784212i	0.368901	+	0.929469i	$0.379734\pi$
$752$	38.2858	−	22.1043i	1.39614	−	0.806061i
$753$		0			0
$754$		−	11.9039i		−	0.433515i
$755$	−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	$0.0557141\pi$
$758$	32.4142	−	18.7143i	1.17734	−	0.679735i
$759$		0			0
$760$	−0.129075	−	20.3179i	−0.00468205	−	0.737009i
$761$	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
$763$	12.7369	−	7.35366i	0.461107	−	0.266220i
$764$	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
$769$	−25.1694	+	43.5947i	−0.907632	+	1.57206i	−0.0902873	+	0.995916i	$0.528779\pi$
$769$	−25.1694	+	43.5947i	−0.907632	+	1.57206i	−0.817345	+	0.576149i	$0.804555\pi$
$770$	−22.0443	+	38.1818i	−0.794420	+	1.37598i
$771$		0			0
$772$	2.81405	+	1.62469i	0.101280	+	0.0584740i
$773$	−15.2092	−	26.3432i	−0.547039	−	0.947499i	−0.998476	−	0.0551956i	$-0.982422\pi$
$773$	−15.2092	−	26.3432i	−0.547039	−	0.947499i	0.451437	−	0.892303i	$-0.350912\pi$
$774$		0			0
$775$	−2.83955	+	1.63942i	−0.102000	+	0.0588896i
$776$	28.8670	−	16.6664i	1.03627	−	0.598288i
$777$		0			0
$778$	52.0215	−	30.0346i	1.86506	−	1.07679i
$779$	−24.5806	+	0.156155i	−0.880691	+	0.00559484i
$780$		0			0
$781$	−2.46462	+	1.42295i	−0.0881910	+	0.0509171i
$782$	11.8920	−	20.5976i	0.425259	−	0.736570i
$783$		0			0
$784$	37.7458	−	65.3776i	1.34806	−	2.33491i
$785$		−	31.1838i		−	1.11300i
$786$		0			0
$787$	−21.5905	+	12.4653i	−0.769619	+	0.444340i	−0.832739	−	0.553666i	$-0.813228\pi$
$787$	−21.5905	+	12.4653i	−0.769619	+	0.444340i	0.0631196	+	0.998006i	$0.479895\pi$
$788$	−2.87614	−	1.66054i	−0.102458	−	0.0591543i
$789$		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
$794$	−34.7988			−1.23496
$795$		0			0
$796$	−1.76646			−0.0626105
$797$	−22.8991	−	39.6625i	−0.811129	−	1.40492i	−0.912074	−	0.410025i	$-0.865520\pi$
$797$	−22.8991	−	39.6625i	−0.811129	−	1.40492i	0.100945	−	0.994892i	$-0.467813\pi$
$798$		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
$803$	−6.71524	+	3.87705i	−0.236976	+	0.136818i
$804$		0			0
$805$	19.6572	+	34.0473i	0.692826	+	1.20001i
$806$	−5.93268	−	10.2757i	−0.208970	−	0.361946i
$807$		0			0
$808$			36.5824i			1.28697i
$809$			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	−0.342563	−	0.939495i	$-0.611295\pi$
$811$	8.53722	−	4.92896i	0.299782	−	0.173079i	0.642345	+	0.766416i	$0.277962\pi$
$812$	2.22015	+	3.84541i	0.0779120	+	0.134948i
$813$		0			0
$814$	−21.1673			−0.741914
$815$		−	19.2691i		−	0.674967i
$816$		0			0
$817$	−19.9086	−	33.9823i	−0.696514	−	1.18889i
$818$		−	29.7957i		−	1.04178i
$819$		0			0
$820$	−3.73078	−	2.15397i	−0.130284	−	0.0752198i
$821$			40.8423i			1.42541i	0.701466	+	0.712703i	$0.252529\pi$
$821$			40.8423i			1.42541i	−0.701466	+	0.712703i	$0.747471\pi$
$822$		0			0
$823$	18.3096	−	31.7131i	0.638231	−	1.10545i	−0.347590	−	0.937647i	$-0.613000\pi$
$823$	18.3096	−	31.7131i	0.638231	−	1.10545i	0.985821	−	0.167802i	$-0.0536669\pi$
$824$	14.9182	−	8.61303i	0.519700	−	0.300049i
$825$		0			0
$826$	17.1058			0.595186
$827$	−19.3427	−	33.5025i	−0.672611	−	1.16500i	−0.977161	−	0.212500i	$-0.931839\pi$
$827$	−19.3427	−	33.5025i	−0.672611	−	1.16500i	0.304550	−	0.952496i	$-0.401494\pi$
$828$		0			0
$829$		−	19.0627i		−	0.662076i	−0.943617	−	0.331038i	$-0.892601\pi$
$829$		−	19.0627i		−	0.662076i	0.943617	−	0.331038i	$-0.107399\pi$
$830$	−5.58297			−0.193788
$831$		0			0
$832$	16.9335	+	9.77658i	0.587065	+	0.338942i
$833$			57.5935i			1.99550i
$834$		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
$839$	3.38323	+	5.85993i	0.116802	+	0.202307i	0.918499	−	0.395424i	$-0.129402\pi$
$839$	3.38323	+	5.85993i	0.116802	+	0.202307i	−0.801697	+	0.597731i	$0.796069\pi$
$840$		0			0
$841$	−23.8375			−0.821983
$842$	22.0457	+	12.7281i	0.759744	+	0.438639i
$843$		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
$850$		−	7.95925i		−	0.273000i
$851$	−9.43762	+	16.3464i	−0.323517	+	0.560349i
$852$		0			0
$853$	−2.01369	−	3.48781i	−0.0689473	−	0.119420i	0.829491	−	0.558520i	$-0.188631\pi$
$853$	−2.01369	−	3.48781i	−0.0689473	−	0.119420i	−0.898438	+	0.439100i	$0.855297\pi$
$854$	79.8266			2.73161
$855$		0			0
$856$	15.3586			0.524947
$857$	9.30815	+	16.1222i	0.317960	+	0.550724i	0.980062	−	0.198690i	$-0.0636688\pi$
$857$	9.30815	+	16.1222i	0.317960	+	0.550724i	−0.662102	+	0.749414i	$0.730335\pi$
$858$		0			0
$859$	−17.5081	+	30.3249i	−0.597369	+	1.03467i	0.395839	+	0.918320i	$0.370454\pi$
$859$	−17.5081	+	30.3249i	−0.597369	+	1.03467i	−0.993208	+	0.116353i	$0.962880\pi$
$860$		−	6.90232i		−	0.235367i
$861$		0			0
$862$	−26.8171	+	46.4485i	−0.913393	+	1.58204i
$863$	7.92119			0.269640			0.134820	−	0.990870i	$-0.456954\pi$
$863$	7.92119			0.269640			0.134820	+	0.990870i	$0.456954\pi$
$864$		0			0
$865$	−21.2187	+	12.2506i	−0.721458	+	0.416534i
$866$	−23.2077	−	13.3990i	−0.788630	−	0.455315i
$867$		0			0
$868$	3.83295	+	2.21296i	0.130099	+	0.0751126i
$869$	−1.64555			−0.0558215
$870$		0			0
$871$	14.4768	+	25.0746i	0.490529	+	0.849621i
$872$	−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
$877$			42.1542i			1.42345i	0.702460	+	0.711723i	$0.252085\pi$
$877$			42.1542i			1.42345i	−0.702460	+	0.711723i	$0.747915\pi$
$878$	39.1787	+	22.6198i	1.32222	+	0.763383i
$879$		0			0
$880$	27.3945			0.923468
$881$			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	0.978562	−	0.205952i	$-0.0660292\pi$
$883$	9.23912	+	16.0026i	0.310921	+	0.538531i	−0.667641	+	0.744483i	$0.732696\pi$
$884$	4.85350			0.163241
$885$		0			0
$886$	−10.4120	+	6.01134i	−0.349796	+	0.201955i
$887$	−3.22067	+	5.57836i	−0.108139	+	0.187303i	−0.915016	−	0.403416i	$-0.867823\pi$
$887$	−3.22067	+	5.57836i	−0.108139	+	0.187303i	0.806877	+	0.590719i	$0.201156\pi$
$888$		0			0
$889$			18.6548i			0.625661i
$890$	−37.8768	−	21.8682i	−1.26963	−	0.733023i
$891$		0			0
$892$			1.46681i			0.0491126i
$893$	−0.263467	−	41.4727i	−0.00881659	−	1.38783i
$894$		0			0
$895$			16.2833i			0.544290i
$896$	−65.0731			−2.17394
$897$		0			0
$898$	−16.7118	−	28.9456i	−0.557679	−	0.965928i
$899$	4.45637	−	2.57289i	0.148628	−	0.0858106i
$900$		0			0
$901$			28.6854i			0.955648i
$902$		−	27.3597i		−	0.910977i
$903$		0			0
$904$	15.2740	+	26.4553i	0.508005	+	0.879891i
$905$	2.24694	+	3.89181i	0.0746907	+	0.129368i
$906$		0			0
$907$	−4.05181	+	2.33932i	−0.134538	+	0.0776757i	−0.565758	−	0.824571i	$-0.691417\pi$
$907$	−4.05181	+	2.33932i	−0.134538	+	0.0776757i	0.431220	+	0.902247i	$0.358083\pi$
$908$	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	$-0.827388\pi$
$911$	0.563718	−	0.976388i	0.0186768	−	0.0323492i	0.875213	+	0.483738i	$0.160721\pi$
$912$		0			0
$913$	−2.98744	−	5.17440i	−0.0988699	−	0.171248i
$914$	−3.25811			−0.107769
$915$		0			0
$916$	2.20864			0.0729756
$917$	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
$922$	−34.8001	−	20.0919i	−1.14608	−	0.661690i
$923$	−2.66148	+	1.53661i	−0.0876037	+	0.0505780i
$924$		0			0
$925$			6.31652i			0.207686i
$926$	−14.3258	+	24.8130i	−0.470774	+	0.815404i
$927$		0			0
$928$	2.56709	−	4.44633i	0.0842689	−	0.145958i
$929$	−25.0993	+	14.4911i	−0.823481	+	0.475437i	−0.851615	−	0.524167i	$-0.824377\pi$
$929$	−25.0993	+	14.4911i	−0.823481	+	0.475437i	0.0281347	+	0.999604i	$0.491043\pi$
$930$		0			0
$931$	−35.7995	−	61.1068i	−1.17328	−	2.00269i
$932$	−9.03263	+	5.21499i	−0.295873	+	0.170823i
$933$		0			0
$934$	39.9912	−	23.0889i	1.30855	−	0.755493i
$935$	−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
$940$	3.63420	−	6.29463i	0.118535	−	0.205308i
$941$	12.2375	−	21.1960i	0.398931	−	0.690969i	−0.594663	−	0.803975i	$-0.702715\pi$
$941$	12.2375	−	21.1960i	0.398931	−	0.690969i	0.993594	+	0.113006i	$0.0360479\pi$
$942$		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
$947$	16.4596	−	9.50294i	0.534864	−	0.308804i	−0.208131	−	0.978101i	$-0.566738\pi$
$947$	16.4596	−	9.50294i	0.534864	−	0.308804i	0.742995	+	0.669297i	$0.233405\pi$
$948$		0			0
$949$	−7.25161	+	4.18672i	−0.235397	+	0.135907i
$950$	4.94738	+	8.44477i	0.160514	+	0.273984i
$951$		0			0
$952$	36.6072	−	21.1352i	1.18645	−	0.684995i
$953$	0.925412	−	1.60286i	0.0299770	−	0.0519217i	−0.850648	−	0.525736i	$-0.823790\pi$
$953$	0.925412	−	1.60286i	0.0299770	−	0.0519217i	0.880625	+	0.473814i	$0.157123\pi$
$954$		0			0
$955$	−7.03506	+	12.1851i	−0.227649	+	0.394300i
$956$		−	4.92030i		−	0.159134i
$957$		0			0
$958$	19.7852	−	11.4230i	0.639232	−	0.369061i
$959$	3.76395	+	2.17312i	0.121544	+	0.0701736i
$960$		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
$965$	−15.1098			−0.486401
$966$		0			0
$967$	−43.2041			−1.38935			−0.694674	−	0.719324i	$-0.744452\pi$
$967$	−43.2041			−1.38935			−0.694674	+	0.719324i	$0.744452\pi$
$968$	−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	$-0.674405\pi$
$971$	14.9198	−	25.8419i	0.478801	−	0.829307i	0.999705	+	0.0243082i	$0.00773832\pi$
$972$		0			0
$973$	−46.6865	−	80.8634i	−1.49670	−	2.59236i
$974$	−18.8707	+	10.8950i	−0.604655	+	0.349098i
$975$		0			0
$976$	−24.8002	−	42.9552i	−0.793836	−	1.37496i
$977$	9.91018	+	17.1649i	0.317055	+	0.549155i	0.979872	−	0.199626i	$-0.0639728\pi$
$977$	9.91018	+	17.1649i	0.317055	+	0.549155i	−0.662817	+	0.748781i	$0.730639\pi$
$978$		0			0
$979$		−	46.8065i		−	1.49594i
$980$		−	12.4117i		−	0.396477i
$981$		0			0
$982$	−22.3096	+	12.8805i	−0.711928	+	0.411032i
$983$	−0.500857	−	0.867510i	−0.0159749	−	0.0276693i	0.857927	−	0.513771i	$-0.171752\pi$
$983$	−0.500857	−	0.867510i	−0.0159749	−	0.0276693i	−0.873902	+	0.486102i	$0.838419\pi$
$984$		0			0
$985$	15.4432			0.492060
$986$			12.4912i			0.397800i
$987$		0			0
$988$	−5.14957	+	3.01688i	−0.163830	+	0.0959798i
$989$		−	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	$0.800532\pi$
$992$		−	5.11754i		−	0.162482i
$993$		0			0
$994$	3.40144	−	5.89147i	0.107887	−	0.186866i
$995$	7.11362	−	4.10705i	0.225517	−	0.130202i
$996$		0			0
$997$	15.3547			0.486288			0.243144	−	0.969990i	$-0.421821\pi$
$997$	15.3547			0.486288			0.243144	+	0.969990i	$0.421821\pi$
$998$	−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.k.a.8.13		36
3.2	odd	2		171.2.k.a.65.6	yes	36
9.4	even	3		171.2.t.a.122.6	yes	36
9.5	odd	6		513.2.t.a.179.13		36
19.12	odd	6		513.2.t.a.278.13		36
57.50	even	6		171.2.t.a.164.6	yes	36
171.31	odd	6		171.2.k.a.50.6	✓	36
171.50	even	6	inner	513.2.k.a.449.13		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.k.a.50.6	✓	36	171.31	odd	6
171.2.k.a.65.6	yes	36	3.2	odd	2
171.2.t.a.122.6	yes	36	9.4	even	3
171.2.t.a.164.6	yes	36	57.50	even	6
513.2.k.a.8.13		36	1.1	even	1	trivial
513.2.k.a.449.13		36	171.50	even	6	inner
513.2.t.a.179.13		36	9.5	odd	6
513.2.t.a.278.13		36	19.12	odd	6

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.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.775454 + 1.34313i) q^{2} +(-0.202658 + 0.351014i) q^{4} -1.88474i q^{5} +(-2.41078 + 4.17560i) q^{7} +2.47321 q^{8} +(2.53144 - 1.46153i) q^{10} +(2.70914 + 1.56412i) q^{11} +(2.92553 + 1.68905i) q^{13} -7.47781 q^{14} +(2.32318 + 4.02386i) q^{16} +(-3.06986 - 1.77238i) q^{17} +(4.35881 - 0.0276906i) q^{19} +(0.661569 + 0.381957i) q^{20} +4.85162i q^{22} +(3.74666 + 2.16313i) q^{23} +1.44777 q^{25} +5.23914i q^{26} +(-0.977130 - 1.69244i) q^{28} -2.27211 q^{29} +(-1.96133 + 1.13238i) q^{31} +(-1.12982 + 1.95691i) q^{32} -5.49760i q^{34} +(7.86990 + 4.54369i) q^{35} +4.36294i q^{37} +(3.41725 + 5.83296i) q^{38} -4.66135i q^{40} -5.63929 q^{41} +(-4.51773 - 7.82493i) q^{43} +(-1.09806 + 0.633964i) q^{44} +6.70964i q^{46} -9.51469i q^{47} +(-8.12375 - 14.0707i) q^{49} +(1.12268 + 1.94453i) q^{50} +(-1.18576 + 0.684601i) q^{52} +(-4.04616 - 7.00816i) q^{53} +(2.94796 - 5.10601i) q^{55} +(-5.96237 + 10.3271i) q^{56} +(-1.76192 - 3.05174i) q^{58} -2.28754 q^{59} -10.6751 q^{61} +(-3.04185 - 1.75621i) q^{62} +5.78820 q^{64} +(3.18342 - 5.51385i) q^{65} +(7.42268 + 4.28548i) q^{67} +(1.24426 - 0.718375i) q^{68} +14.0937i q^{70} +(-0.454871 + 0.787860i) q^{71} +(-1.23937 + 2.14665i) q^{73} +(-5.85998 + 3.38326i) q^{74} +(-0.873629 + 1.53562i) q^{76} +(-13.0623 + 7.54152i) q^{77} +(-0.455556 + 0.263015i) q^{79} +(7.58391 - 4.37857i) q^{80} +(-4.37301 - 7.57427i) q^{82} +(-1.65409 - 0.954990i) q^{83} +(-3.34047 + 5.78587i) q^{85} +(7.00658 - 12.1358i) q^{86} +(6.70026 + 3.86840i) q^{88} +(-7.48128 - 12.9580i) q^{89} +(-14.1056 + 8.14389i) q^{91} +(-1.51858 + 0.876753i) q^{92} +(12.7794 - 7.37820i) q^{94} +(-0.0521894 - 8.21521i) q^{95} +(11.6719 - 6.73877i) q^{97} +(12.5992 - 21.8224i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{2} - 15 q^{4} - q^{7} - 12 q^{8} - 6 q^{10} + 9 q^{11} - 6 q^{13} + 6 q^{14} - 9 q^{16} + 27 q^{17} + q^{19} - 9 q^{20} - 9 q^{23} - 22 q^{25} + 2 q^{28} + 24 q^{29} + 12 q^{31} + 15 q^{32}+ \cdots + 84 q^{98}+O(q^{100}) \) 36 * q + 3 * q^2 - 15 * q^4 - q^7 - 12 * q^8 - 6 * q^10 + 9 * q^11 - 6 * q^13 + 6 * q^14 - 9 * q^16 + 27 * q^17 + q^19 - 9 * q^20 - 9 * q^23 - 22 * q^25 + 2 * q^28 + 24 * q^29 + 12 * q^31 + 15 * q^32 - 15 * q^35 + 18 * q^38 - 36 * q^41 + 3 * q^43 - 66 * q^44 - 9 * q^49 - 3 * q^50 + 15 * q^52 + 12 * q^53 - 7 * q^55 - 6 * q^56 - 6 * q^58 + 18 * q^59 - 16 * q^61 + 12 * q^62 + 12 * q^64 + 18 * q^65 + 27 * q^67 - 60 * q^68 - 9 * q^71 - 18 * q^73 - 90 * q^74 - 23 * q^76 + 6 * q^77 - 6 * q^79 + 12 * q^80 - 9 * q^82 + 9 * q^83 + 11 * q^85 - 51 * q^86 + 3 * q^88 + 18 * q^89 + 27 * q^91 + 93 * q^92 + 12 * q^94 + 24 * q^97 + 84 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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