LMFDB - Embedded newform 540.2.n.d.179.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [540,2,Mod(179,540)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(540, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("540.179"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 540 = 2^{2} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	540.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,-2,18,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.31192170915$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			179.20
Character	$\chi$	$=$	540.179
Dual form			540.2.n.d.359.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.24631 + 0.668359i) q^{2} +(1.10659 + 1.66597i) q^{4} +(1.69235 + 1.46149i) q^{5} +(0.667441 + 1.15604i) q^{7} +(0.265693 + 2.81592i) q^{8} +(1.13240 + 2.95257i) q^{10} +(-2.18799 - 3.78971i) q^{11} +(3.56180 + 2.05641i) q^{13} +(0.0591892 + 1.88688i) q^{14} +(-1.55091 + 3.68710i) q^{16} -6.45392 q^{17} -5.84202i q^{19} +(-0.562053 + 4.43668i) q^{20} +(-0.194033 - 6.18554i) q^{22} +(-0.0875178 - 0.0505284i) q^{23} +(0.728104 + 4.94670i) q^{25} +(3.06470 + 4.94349i) q^{26} +(-1.18735 + 2.39120i) q^{28} +(4.53226 - 2.61670i) q^{29} +(4.18262 + 2.41484i) q^{31} +(-4.39722 + 3.55871i) q^{32} +(-8.04361 - 4.31354i) q^{34} +(-0.559997 + 2.93189i) q^{35} +3.24337i q^{37} +(3.90457 - 7.28098i) q^{38} +(-3.66579 + 5.15383i) q^{40} +(-3.50518 - 2.02372i) q^{41} +(-1.92364 - 3.33185i) q^{43} +(3.89233 - 7.83880i) q^{44} +(-0.0753035 - 0.121468i) q^{46} +(3.00768 - 1.73649i) q^{47} +(2.60904 - 4.51900i) q^{49} +(-2.39873 + 6.65177i) q^{50} +(0.515549 + 8.20946i) q^{52} +2.77476 q^{53} +(1.83577 - 9.61125i) q^{55} +(-3.07799 + 2.18661i) q^{56} +(7.39751 - 0.232051i) q^{58} +(1.37318 - 2.37841i) q^{59} +(1.04419 + 1.80858i) q^{61} +(3.59888 + 5.80514i) q^{62} +(-7.85881 + 1.49634i) q^{64} +(3.02241 + 8.68570i) q^{65} +(-0.216298 + 0.374638i) q^{67} +(-7.14186 - 10.7520i) q^{68} +(-2.65749 + 3.27977i) q^{70} -8.41810 q^{71} -7.28163i q^{73} +(-2.16773 + 4.04225i) q^{74} +(9.73262 - 6.46473i) q^{76} +(2.92071 - 5.05882i) q^{77} +(2.58753 - 1.49391i) q^{79} +(-8.01333 + 3.97323i) q^{80} +(-3.01598 - 4.86490i) q^{82} +(-11.6096 + 6.70282i) q^{83} +(-10.9223 - 9.43234i) q^{85} +(-0.170590 - 5.43821i) q^{86} +(10.0902 - 7.16812i) q^{88} -6.97377i q^{89} +5.49013i q^{91} +(-0.0126677 - 0.201716i) q^{92} +(4.90911 - 0.153993i) q^{94} +(8.53804 - 9.88674i) q^{95} +(2.08608 - 1.20440i) q^{97} +(6.27200 - 3.88831i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{4} + 18 q^{5} - 16 q^{10} + 42 q^{14} + 30 q^{16} - 26 q^{25} - 4 q^{34} + 10 q^{40} - 96 q^{41} + 4 q^{46} + 32 q^{49} + 90 q^{50} - 6 q^{56} + 8 q^{61} - 20 q^{64} + 6 q^{65} + 4 q^{70} - 72 q^{74}+ \cdots - 62 q^{94}+O(q^{100}) $ 48 * q - 2 * q^4 + 18 * q^5 - 16 * q^10 + 42 * q^14 + 30 * q^16 - 26 * q^25 - 4 * q^34 + 10 * q^40 - 96 * q^41 + 4 * q^46 + 32 * q^49 + 90 * q^50 - 6 * q^56 + 8 * q^61 - 20 * q^64 + 6 * q^65 + 4 * q^70 - 72 * q^74 - 4 * q^85 - 108 * q^86 - 62 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/540\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$461$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.24631	+	0.668359i	0.881276	+	0.472601i
$2$	1.24631	+	0.668359i	0.881276	+	0.472601i
$3$		0			0
$3$		0			0
$4$	1.10659	+	1.66597i	0.553296	+	0.832985i
$5$	1.69235	+	1.46149i	0.756842	+	0.653597i
$5$	1.69235	+	1.46149i	0.756842	+	0.653597i
$6$		0			0
$7$	0.667441	+	1.15604i	0.252269	+	0.436943i	0.964150	−	0.265357i	$-0.0854898\pi$
$7$	0.667441	+	1.15604i	0.252269	+	0.436943i	−0.711881	+	0.702300i	$0.752157\pi$
$8$	0.265693	+	2.81592i	0.0939368	+	0.995578i
$9$		0			0
$10$	1.13240	+	2.95257i	0.358096	+	0.933685i
$11$	−2.18799	−	3.78971i	−0.659705	−	1.14264i	−0.980692	−	0.195558i	$-0.937348\pi$
$11$	−2.18799	−	3.78971i	−0.659705	−	1.14264i	0.320987	−	0.947083i	$-0.395985\pi$
$12$		0			0
$13$	3.56180	+	2.05641i	0.987867	+	0.570345i	0.904636	−	0.426185i	$-0.140143\pi$
$13$	3.56180	+	2.05641i	0.987867	+	0.570345i	0.0832309	+	0.996530i	$0.473476\pi$
$14$	0.0591892	+	1.88688i	0.0158190	+	0.504290i
$15$		0			0
$16$	−1.55091	+	3.68710i	−0.387727	+	0.921774i
$17$	−6.45392			−1.56531			−0.782653	−	0.622458i	$-0.786134\pi$
$17$	−6.45392			−1.56531			−0.782653	+	0.622458i	$0.786134\pi$
$18$		0			0
$19$		−	5.84202i		−	1.34025i	−0.742248	−	0.670125i	$-0.766240\pi$
$19$		−	5.84202i		−	1.34025i	0.742248	−	0.670125i	$-0.233760\pi$
$20$	−0.562053	+	4.43668i	−0.125679	+	0.992071i
$21$		0			0
$22$	−0.194033	−	6.18554i	−0.0413679	−	1.31876i
$23$	−0.0875178	−	0.0505284i	−0.0182487	−	0.0105359i	0.490848	−	0.871245i	$-0.336687\pi$
$23$	−0.0875178	−	0.0505284i	−0.0182487	−	0.0105359i	−0.509097	+	0.860709i	$0.670020\pi$
$24$		0			0
$25$	0.728104	+	4.94670i	0.145621	+	0.989340i
$26$	3.06470	+	4.94349i	0.601038	+	0.969499i
$27$		0			0
$28$	−1.18735	+	2.39120i	−0.224387	+	0.451895i
$29$	4.53226	−	2.61670i	0.841620	−	0.485909i	−0.0161948	−	0.999869i	$-0.505155\pi$
$29$	4.53226	−	2.61670i	0.841620	−	0.485909i	0.857814	+	0.513960i	$0.171822\pi$
$30$		0			0
$31$	4.18262	+	2.41484i	0.751222	+	0.433718i	0.826135	−	0.563472i	$-0.190535\pi$
$31$	4.18262	+	2.41484i	0.751222	+	0.433718i	−0.0749136	+	0.997190i	$0.523868\pi$
$32$	−4.39722	+	3.55871i	−0.777327	+	0.629097i
$33$		0			0
$34$	−8.04361	−	4.31354i	−1.37947	−	0.739766i
$35$	−0.559997	+	2.93189i	−0.0946568	+	0.495579i
$36$		0			0
$37$			3.24337i			0.533206i	0.963806	+	0.266603i	$0.0859013\pi$
$37$			3.24337i			0.533206i	−0.963806	+	0.266603i	$0.914099\pi$
$38$	3.90457	−	7.28098i	0.633404	−	1.18113i
$39$		0			0
$40$	−3.66579	+	5.15383i	−0.579612	+	0.814893i
$41$	−3.50518	−	2.02372i	−0.547417	−	0.316051i	0.200663	−	0.979660i	$-0.435690\pi$
$41$	−3.50518	−	2.02372i	−0.547417	−	0.316051i	−0.748079	+	0.663609i	$0.769024\pi$
$42$		0			0
$43$	−1.92364	−	3.33185i	−0.293353	−	0.508102i	0.681248	−	0.732053i	$-0.261438\pi$
$43$	−1.92364	−	3.33185i	−0.293353	−	0.508102i	−0.974600	+	0.223951i	$0.928104\pi$
$44$	3.89233	−	7.83880i	0.586792	−	1.18174i
$45$		0			0
$46$	−0.0753035	−	0.121468i	−0.0111029	−	0.0179094i
$47$	3.00768	−	1.73649i	0.438715	−	0.253292i	−0.264337	−	0.964430i	$-0.585153\pi$
$47$	3.00768	−	1.73649i	0.438715	−	0.253292i	0.703053	+	0.711138i	$0.251820\pi$
$48$		0			0
$49$	2.60904	−	4.51900i	0.372721	−	0.645571i
$50$	−2.39873	+	6.65177i	−0.339232	+	0.940703i
$51$		0			0
$52$	0.515549	+	8.20946i	0.0714938	+	1.13845i
$53$	2.77476			0.381143			0.190571	−	0.981673i	$-0.438966\pi$
$53$	2.77476			0.381143			0.190571	+	0.981673i	$0.438966\pi$
$54$		0			0
$55$	1.83577	−	9.61125i	0.247535	−	1.29598i
$56$	−3.07799	+	2.18661i	−0.411313	+	0.292199i
$57$		0			0
$58$	7.39751	−	0.232051i	0.971341	−	0.0304698i
$59$	1.37318	−	2.37841i	0.178772	−	0.309642i	−0.762688	−	0.646766i	$-0.776121\pi$
$59$	1.37318	−	2.37841i	0.178772	−	0.309642i	0.941460	+	0.337124i	$0.109454\pi$
$60$		0			0
$61$	1.04419	+	1.80858i	0.133694	+	0.231566i	0.925098	−	0.379729i	$-0.123983\pi$
$61$	1.04419	+	1.80858i	0.133694	+	0.231566i	−0.791404	+	0.611294i	$0.790649\pi$
$62$	3.59888	+	5.80514i	0.457058	+	0.737254i
$63$		0			0
$64$	−7.85881	+	1.49634i	−0.982352	+	0.187043i
$65$	3.02241	+	8.68570i	0.374883	+	1.07733i
$66$		0			0
$67$	−0.216298	+	0.374638i	−0.0264250	+	0.0457694i	−0.878935	−	0.476941i	$-0.841746\pi$
$67$	−0.216298	+	0.374638i	−0.0264250	+	0.0457694i	0.852511	+	0.522710i	$0.175079\pi$
$68$	−7.14186	−	10.7520i	−0.866078	−	1.30388i
$69$		0			0
$70$	−2.65749	+	3.27977i	−0.317630	+	0.392007i
$71$	−8.41810			−0.999044			−0.499522	−	0.866301i	$-0.666491\pi$
$71$	−8.41810			−0.999044			−0.499522	+	0.866301i	$0.666491\pi$
$72$		0			0
$73$		−	7.28163i		−	0.852250i	−0.904664	−	0.426125i	$-0.859878\pi$
$73$		−	7.28163i		−	0.852250i	0.904664	−	0.426125i	$-0.140122\pi$
$74$	−2.16773	+	4.04225i	−0.251994	+	0.469902i
$75$		0			0
$76$	9.73262	−	6.46473i	1.11641	−	0.741555i
$77$	2.92071	−	5.05882i	0.332846	−	0.576507i
$78$		0			0
$79$	2.58753	−	1.49391i	0.291120	−	0.168078i	−0.347327	−	0.937744i	$-0.612911\pi$
$79$	2.58753	−	1.49391i	0.291120	−	0.168078i	0.638447	+	0.769666i	$0.279577\pi$
$80$	−8.01333	+	3.97323i	−0.895918	+	0.444220i
$81$		0			0
$82$	−3.01598	−	4.86490i	−0.333059	−	0.537238i
$83$	−11.6096	+	6.70282i	−1.27432	+	0.735730i	−0.975798	−	0.218672i	$-0.929828\pi$
$83$	−11.6096	+	6.70282i	−1.27432	+	0.735730i	−0.298524	+	0.954402i	$0.596494\pi$
$84$		0			0
$85$	−10.9223	−	9.43234i	−1.18469	−	1.02308i
$86$	−0.170590	−	5.43821i	−0.0183952	−	0.586417i
$87$		0			0
$88$	10.0902	−	7.16812i	1.07562	−	0.764124i
$89$		−	6.97377i		−	0.739218i	−0.929187	−	0.369609i	$-0.879492\pi$
$89$		−	6.97377i		−	0.739218i	0.929187	−	0.369609i	$-0.120508\pi$
$90$		0			0
$91$			5.49013i			0.575522i
$92$	−0.0126677	−	0.201716i	−0.00132070	−	0.0210304i
$93$		0			0
$94$	4.90911	−	0.153993i	0.506336	−	0.0158831i
$95$	8.53804	−	9.88674i	0.875984	−	1.01436i
$96$		0			0
$97$	2.08608	−	1.20440i	0.211809	−	0.122288i	−0.390343	−	0.920670i	$-0.627644\pi$
$97$	2.08608	−	1.20440i	0.211809	−	0.122288i	0.602152	+	0.798382i	$0.294310\pi$
$98$	6.27200	−	3.88831i	0.633568	−	0.392778i
$99$		0			0
$100$	−7.43534	+	6.68698i	−0.743534	+	0.668698i
$101$	3.92717	−	2.26735i	0.390768	−	0.225610i	−0.291725	−	0.956502i	$-0.594229\pi$
$101$	3.92717	−	2.26735i	0.390768	−	0.225610i	0.682493	+	0.730892i	$0.260896\pi$
$102$		0			0
$103$	1.95140	−	3.37992i	0.192277	−	0.333034i	−0.753727	−	0.657187i	$-0.771746\pi$
$103$	1.95140	−	3.37992i	0.192277	−	0.333034i	0.946005	+	0.324153i	$0.105079\pi$
$104$	−4.84434	+	10.5761i	−0.475026	+	1.03708i
$105$		0			0
$106$	3.45822	+	1.85454i	0.335892	+	0.180129i
$107$		−	4.98830i		−	0.482237i	−0.970496	−	0.241118i	$-0.922486\pi$
$107$		−	4.98830i		−	0.482237i	0.970496	−	0.241118i	$-0.0775142\pi$
$108$		0			0
$109$	−4.98669			−0.477638			−0.238819	−	0.971064i	$-0.576760\pi$
$109$	−4.98669			−0.477638			−0.238819	+	0.971064i	$0.576760\pi$
$110$	8.71172	−	10.7517i	0.830630	−	1.02513i
$111$		0			0
$112$	−5.29758	+	0.668004i	−0.500574	+	0.0631204i
$113$	10.2057	−	17.6768i	0.960073	−	1.66290i	0.237767	−	0.971322i	$-0.423584\pi$
$113$	10.2057	−	17.6768i	0.960073	−	1.66290i	0.722306	−	0.691574i	$-0.243082\pi$
$114$		0			0
$115$	−0.0742642	−	0.213418i	−0.00692517	−	0.0199013i
$116$	9.37471	+	4.65499i	0.870420	+	0.432205i
$117$		0			0
$118$	3.30104	−	2.04647i	0.303885	−	0.188393i
$119$	−4.30762	−	7.46101i	−0.394879	−	0.683950i
$120$		0			0
$121$	−4.07462	+	7.05746i	−0.370420	+	0.641587i
$122$	0.0925992	+	2.95195i	0.00838354	+	0.267257i
$123$		0			0
$124$	0.605409	+	9.64037i	0.0543673	+	0.865730i
$125$	−5.99734	+	9.43567i	−0.536418	+	0.843952i
$126$		0			0
$127$	−19.1833			−1.70224			−0.851122	−	0.524968i	$-0.824077\pi$
$127$	−19.1833			−1.70224			−0.851122	+	0.524968i	$0.824077\pi$
$128$	−10.7946	−	3.38760i	−0.954120	−	0.299424i
$129$		0			0
$130$	−2.03831	+	12.8452i	−0.178771	+	1.12659i
$131$	−8.41433	+	14.5740i	−0.735163	+	1.27334i	0.219488	+	0.975615i	$0.429561\pi$
$131$	−8.41433	+	14.5740i	−0.735163	+	1.27334i	−0.954652	+	0.297725i	$0.903772\pi$
$132$		0			0
$133$	6.75362	−	3.89920i	0.585613	−	0.338104i
$134$	−0.519967	+	0.322352i	−0.0449183	+	0.0278470i
$135$		0			0
$136$	−1.71477	−	18.1737i	−0.147040	−	1.55839i
$137$	2.99744	+	5.19172i	0.256089	+	0.443559i	0.965191	−	0.261547i	$-0.0842327\pi$
$137$	2.99744	+	5.19172i	0.256089	+	0.443559i	−0.709102	+	0.705106i	$0.750899\pi$
$138$		0			0
$139$	−0.206175	−	0.119035i	−0.0174875	−	0.0100964i	0.491231	−	0.871029i	$-0.336547\pi$
$139$	−0.206175	−	0.119035i	−0.0174875	−	0.0100964i	−0.508718	+	0.860933i	$0.669881\pi$
$140$	−5.50412	+	2.31146i	−0.465183	+	0.195354i
$141$		0			0
$142$	−10.4916	−	5.62631i	−0.880434	−	0.472150i
$143$		−	17.9976i		−	1.50504i
$144$		0			0
$145$	11.4945	+	2.19547i	0.954563	+	0.182324i
$146$	4.86674	−	9.07519i	0.402775	−	0.751068i
$147$		0			0
$148$	−5.40335	+	3.58908i	−0.444153	+	0.295021i
$149$	8.84885	+	5.10889i	0.724926	+	0.418536i	0.816563	−	0.577256i	$-0.195877\pi$
$149$	8.84885	+	5.10889i	0.724926	+	0.418536i	−0.0916368	+	0.995792i	$0.529210\pi$
$150$		0			0
$151$	−13.0489	+	7.53379i	−1.06190	+	0.613091i	−0.925958	−	0.377625i	$-0.876741\pi$
$151$	−13.0489	+	7.53379i	−1.06190	+	0.613091i	−0.135946	+	0.990716i	$0.543407\pi$
$152$	16.4507	−	1.55219i	1.33432	−	0.125899i
$153$		0			0
$154$	7.02124	−	4.35279i	0.565787	−	0.350758i
$155$	3.54921	+	10.1996i	0.285079	+	0.819253i
$156$		0			0
$157$	2.77448	+	1.60184i	0.221427	+	0.127841i	0.606611	−	0.794999i	$-0.292529\pi$
$157$	2.77448	+	1.60184i	0.221427	+	0.127841i	−0.385184	+	0.922840i	$0.625862\pi$
$158$	4.22334	−	0.132481i	0.335991	−	0.0105396i
$159$		0			0
$160$	−12.6427	−	0.403902i	−0.999490	−	0.0319313i
$161$		−	0.134899i		−	0.0106315i
$162$		0			0
$163$	10.6182			0.831684			0.415842	−	0.909437i	$-0.363487\pi$
$163$	10.6182			0.831684			0.415842	+	0.909437i	$0.363487\pi$
$164$	−0.507353	−	8.07895i	−0.0396176	−	0.630860i
$165$		0			0
$166$	−18.9491	+	0.594411i	−1.47074	+	0.0461352i
$167$	10.9127	+	6.30046i	0.844451	+	0.487544i	0.858775	−	0.512353i	$-0.171226\pi$
$167$	10.9127	+	6.30046i	0.844451	+	0.487544i	−0.0143236	+	0.999897i	$0.504560\pi$
$168$		0			0
$169$	1.95764	+	3.39073i	0.150587	+	0.260825i
$170$	−7.30842	−	19.0557i	−0.560530	−	1.46150i
$171$		0			0
$172$	3.42207	−	6.89172i	0.260930	−	0.525489i
$173$	0.858165	+	1.48639i	0.0652451	+	0.113008i	0.896803	−	0.442431i	$-0.145884\pi$
$173$	0.858165	+	1.48639i	0.0652451	+	0.113008i	−0.831558	+	0.555439i	$0.812550\pi$
$174$		0			0
$175$	−5.23263	+	4.14335i	−0.395550	+	0.313208i
$176$	17.3664	−	2.18984i	1.30904	−	0.165065i
$177$		0			0
$178$	4.66099	−	8.69150i	0.349356	−	0.651456i
$179$	18.6630			1.39494			0.697468	−	0.716616i	$-0.254310\pi$
$179$	18.6630			1.39494			0.697468	+	0.716616i	$0.254310\pi$
$180$		0			0
$181$	−19.9281			−1.48125			−0.740623	−	0.671920i	$-0.765470\pi$
$181$	−19.9281			−1.48125			−0.740623	+	0.671920i	$0.765470\pi$
$182$	−3.66938	+	6.84242i	−0.271992	+	0.507194i
$183$		0			0
$184$	0.119031	−	0.259868i	0.00877509	−	0.0191577i
$185$	−4.74014	+	5.48891i	−0.348502	+	0.403553i
$186$		0			0
$187$	14.1211	+	24.4585i	1.03264	+	1.78859i
$188$	6.22121	+	3.08912i	0.453728	+	0.225298i
$189$		0			0
$190$	17.2490	−	6.61550i	1.25137	−	0.479939i
$191$	10.8229	+	18.7459i	0.783121	+	1.35641i	0.930115	+	0.367268i	$0.119707\pi$
$191$	10.8229	+	18.7459i	0.783121	+	1.35641i	−0.146994	+	0.989137i	$0.546960\pi$
$192$		0			0
$193$	9.00614	+	5.19970i	0.648276	+	0.374282i	0.787795	−	0.615937i	$-0.211222\pi$
$193$	9.00614	+	5.19970i	0.648276	+	0.374282i	−0.139519	+	0.990219i	$0.544556\pi$
$194$	3.40487	−	0.106807i	0.244456	−	0.00766827i
$195$		0			0
$196$	10.4157	−	0.654097i	0.743976	−	0.0467212i
$197$	−8.15715			−0.581173			−0.290586	−	0.956849i	$-0.593850\pi$
$197$	−8.15715			−0.581173			−0.290586	+	0.956849i	$0.593850\pi$
$198$		0			0
$199$			9.18172i			0.650875i	0.945564	+	0.325438i	$0.105512\pi$
$199$			9.18172i			0.650875i	−0.945564	+	0.325438i	$0.894488\pi$
$200$	−13.7361	+	3.36459i	−0.971287	+	0.237912i
$201$		0			0
$202$	6.40988	−	0.201070i	0.450998	−	0.0141473i
$203$	6.05004	+	3.49299i	0.424629	+	0.245160i
$204$		0			0
$205$	−2.97435	−	8.54761i	−0.207738	−	0.596991i
$206$	4.69106	−	2.90821i	0.326842	−	0.202624i
$207$		0			0
$208$	−13.1062	+	9.94341i	−0.908752	+	0.689452i
$209$	−22.1396	+	12.7823i	−1.53143	+	0.884170i
$210$		0			0
$211$	8.87092	+	5.12163i	0.610699	+	0.352587i	0.773239	−	0.634115i	$-0.218635\pi$
$211$	8.87092	+	5.12163i	0.610699	+	0.352587i	−0.162540	+	0.986702i	$0.551969\pi$
$212$	3.07053	+	4.62267i	0.210885	+	0.317486i
$213$		0			0
$214$	3.33397	−	6.21698i	0.227906	−	0.424984i
$215$	1.61398	−	8.45003i	0.110072	−	0.576287i
$216$		0			0
$217$			6.44705i			0.437655i
$218$	−6.21497	−	3.33290i	−0.420931	−	0.225732i
$219$		0			0
$220$	18.0435	−	7.57739i	1.21649	−	0.510868i
$221$	−22.9876	−	13.2719i	−1.54631	−	0.892765i
$222$		0			0
$223$	−11.6245	−	20.1343i	−0.778436	−	1.34829i	−0.932843	−	0.360283i	$-0.882680\pi$
$223$	−11.6245	−	20.1343i	−0.778436	−	1.34829i	0.154407	−	0.988007i	$-0.450653\pi$
$224$	−7.04891	−	2.70815i	−0.470975	−	0.180946i
$225$		0			0
$226$	24.5340	−	15.2098i	1.63198	−	1.01174i
$227$	−14.7354	+	8.50750i	−0.978024	+	0.564663i	−0.901673	−	0.432418i	$-0.857660\pi$
$227$	−14.7354	+	8.50750i	−0.978024	+	0.564663i	−0.0763513	+	0.997081i	$0.524327\pi$
$228$		0			0
$229$	−0.750685	+	1.30022i	−0.0496066	+	0.0859212i	−0.889762	−	0.456424i	$-0.849130\pi$
$229$	−0.750685	+	1.30022i	−0.0496066	+	0.0859212i	0.840156	+	0.542345i	$0.182463\pi$
$230$	0.0500836	−	0.315621i	0.00330242	−	0.0208114i
$231$		0			0
$232$	8.57262	+	12.0672i	0.562820	+	0.792253i
$233$	−13.5483			−0.887579			−0.443789	−	0.896131i	$-0.646366\pi$
$233$	−13.5483			−0.887579			−0.443789	+	0.896131i	$0.646366\pi$
$234$		0			0
$235$	7.62791	+	1.45695i	0.497590	+	0.0950408i
$236$	5.48190	−	0.344260i	0.356841	−	0.0224094i
$237$		0			0
$238$	−0.382002	−	12.1778i	−0.0247615	−	0.789369i
$239$	−7.32324	+	12.6842i	−0.473701	+	0.820474i	−0.999547	−	0.0301057i	$-0.990416\pi$
$239$	−7.32324	+	12.6842i	−0.473701	+	0.820474i	0.525846	+	0.850580i	$0.323749\pi$
$240$		0			0
$241$	−12.2259	−	21.1758i	−0.787537	−	1.36405i	−0.927472	−	0.373894i	$-0.878022\pi$
$241$	−12.2259	−	21.1758i	−0.787537	−	1.36405i	0.139934	−	0.990161i	$-0.455311\pi$
$242$	−9.79517	+	6.07249i	−0.629658	+	0.390354i
$243$		0			0
$244$	−1.85756	+	3.74095i	−0.118918	+	0.239490i
$245$	11.0199	−	3.83464i	0.704034	−	0.244986i
$246$		0			0
$247$	12.0136	−	20.8081i	0.764406	−	1.32399i
$248$	−5.68870	+	12.4195i	−0.361233	+	0.788642i
$249$		0			0
$250$	−13.7810	+	7.75142i	−0.871586	+	0.490243i
$251$	−13.1808			−0.831965			−0.415982	−	0.909373i	$-0.636562\pi$
$251$	−13.1808			−0.831965			−0.415982	+	0.909373i	$0.636562\pi$
$252$		0			0
$253$			0.442223i			0.0278024i
$254$	−23.9084	−	12.8214i	−1.50015	−	0.804483i
$255$		0			0
$256$	−11.1894	−	11.4367i	−0.699335	−	0.714794i
$257$	−3.48508	+	6.03633i	−0.217393	+	0.376536i	−0.954010	−	0.299774i	$-0.903089\pi$
$257$	−3.48508	+	6.03633i	−0.217393	+	0.376536i	0.736617	+	0.676310i	$0.236422\pi$
$258$		0			0
$259$	−3.74947	+	2.16476i	−0.232981	+	0.134511i
$260$	−11.1255	+	14.6468i	−0.689977	+	0.908354i
$261$		0			0
$262$	−20.2276	+	12.5400i	−1.24966	+	0.774725i
$263$	13.9809	−	8.07190i	0.862102	−	0.497735i	−0.00261352	−	0.999997i	$-0.500832\pi$
$263$	13.9809	−	8.07190i	0.862102	−	0.497735i	0.864716	+	0.502262i	$0.167499\pi$
$264$		0			0
$265$	4.69587	+	4.05528i	0.288465	+	0.249114i
$266$	11.0232	−	0.345784i	0.675875	−	0.0212014i
$267$		0			0
$268$	−0.863489	+	0.0542266i	−0.0527460	+	0.00331242i
$269$			21.7634i			1.32694i	0.748204	+	0.663468i	$0.230916\pi$
$269$			21.7634i			1.32694i	−0.748204	+	0.663468i	$0.769084\pi$
$270$		0			0
$271$			30.1548i			1.83177i	0.401436	+	0.915887i	$0.368511\pi$
$271$			30.1548i			1.83177i	−0.401436	+	0.915887i	$0.631489\pi$
$272$	10.0095	−	23.7962i	0.606912	−	1.44286i
$273$		0			0
$274$	0.265815	+	8.47388i	0.0160585	+	0.511926i
$275$	17.1535	−	13.5827i	1.03440	−	0.819065i
$276$		0			0
$277$	−11.2614	+	6.50177i	−0.676632	+	0.390654i	−0.798585	−	0.601882i	$-0.794418\pi$
$277$	−11.2614	+	6.50177i	−0.676632	+	0.390654i	0.121953	+	0.992536i	$0.461084\pi$
$278$	−0.177400	−	0.286153i	−0.0106397	−	0.0171623i
$279$		0			0
$280$	−8.40475	−	0.797925i	−0.502280	−	0.0476851i
$281$	0.936692	−	0.540799i	0.0558784	−	0.0322614i	−0.471801	−	0.881705i	$-0.656396\pi$
$281$	0.936692	−	0.540799i	0.0558784	−	0.0322614i	0.527679	+	0.849444i	$0.323062\pi$
$282$		0			0
$283$	−14.6158	+	25.3154i	−0.868821	+	1.50484i	−0.00561859	+	0.999984i	$0.501788\pi$
$283$	−14.6158	+	25.3154i	−0.868821	+	1.50484i	−0.863202	+	0.504858i	$0.831545\pi$
$284$	−9.31540	−	14.0243i	−0.552767	−	0.832189i
$285$		0			0
$286$	12.0289	−	22.4307i	0.711283	−	1.32635i
$287$		−	5.40284i		−	0.318920i
$288$		0			0
$289$	24.6531			1.45019
$290$	12.8583	+	10.4187i	0.755067	+	0.611805i
$291$		0			0
$292$	12.1310	−	8.05779i	0.709911	−	0.471547i
$293$	−2.81552	+	4.87662i	−0.164484	+	0.284895i	−0.936472	−	0.350742i	$-0.885929\pi$
$293$	−2.81552	+	4.87662i	−0.164484	+	0.284895i	0.771988	+	0.635637i	$0.219263\pi$
$294$		0			0
$295$	5.79991	−	2.01822i	0.337684	−	0.117506i
$296$	−9.13306	+	0.861741i	−0.530848	+	0.0500877i
$297$		0			0
$298$	7.61387	+	12.2815i	0.441060	+	0.711447i
$299$	−0.207814	−	0.359945i	−0.0120182	−	0.0208162i
$300$		0			0
$301$	2.56784	−	4.44762i	0.148008	−	0.256357i
$302$	−21.2983	+	0.668101i	−1.22558	+	0.0384449i
$303$		0			0
$304$	21.5401	+	9.06044i	1.23541	+	0.519652i
$305$	−0.876095	+	4.58683i	−0.0501650	+	0.262641i
$306$		0			0
$307$	15.2931			0.872826			0.436413	−	0.899747i	$-0.356249\pi$
$307$	15.2931			0.872826			0.436413	+	0.899747i	$0.356249\pi$
$308$	11.6599	−	0.732233i	0.664384	−	0.0417229i
$309$		0			0
$310$	−2.39358	+	15.0841i	−0.135946	+	0.856717i
$311$	−1.83417	+	3.17688i	−0.104006	+	0.180144i	−0.913332	−	0.407216i	$-0.866500\pi$
$311$	−1.83417	+	3.17688i	−0.104006	+	0.180144i	0.809326	+	0.587360i	$0.199833\pi$
$312$		0			0
$313$	−21.3301	+	12.3149i	−1.20565	+	0.696081i	−0.961805	−	0.273734i	$-0.911741\pi$
$313$	−21.3301	+	12.3149i	−1.20565	+	0.696081i	−0.243842	+	0.969815i	$0.578408\pi$
$314$	2.38726	+	3.85075i	0.134721	+	0.217310i
$315$		0			0
$316$	5.35215	+	2.65759i	0.301082	+	0.149501i
$317$	5.32466	+	9.22258i	0.299063	+	0.517992i	0.975922	−	0.218121i	$-0.0699927\pi$
$317$	5.32466	+	9.22258i	0.299063	+	0.517992i	−0.676859	+	0.736113i	$0.736659\pi$
$318$		0			0
$319$	−19.8331	−	11.4506i	−1.11044	−	0.641113i
$320$	−15.4868	−	8.95323i	−0.865736	−	0.500501i
$321$		0			0
$322$	0.0901611	−	0.168126i	0.00502448	−	0.00936932i
$323$			37.7039i			2.09790i
$324$		0			0
$325$	−7.57908	+	19.1165i	−0.420412	+	1.06039i
$326$	13.2336	+	7.09679i	0.732943	+	0.393055i
$327$		0			0
$328$	4.76732	−	10.4080i	0.263231	−	0.574685i
$329$	4.01490	+	2.31800i	0.221349	+	0.127796i
$330$		0			0
$331$	3.04582	−	1.75851i	0.167414	−	0.0966563i	−0.413952	−	0.910299i	$-0.635852\pi$
$331$	3.04582	−	1.75851i	0.167414	−	0.0966563i	0.581366	+	0.813642i	$0.302519\pi$
$332$	−24.0138	−	11.9240i	−1.31793	−	0.654415i
$333$		0			0
$334$	9.38969	+	15.1460i	0.513781	+	0.828750i
$335$	−0.913581	+	0.317903i	−0.0499143	+	0.0173689i
$336$		0			0
$337$	−20.3763	−	11.7643i	−1.10997	−	0.640841i	−0.171147	−	0.985245i	$-0.554747\pi$
$337$	−20.3763	−	11.7643i	−1.10997	−	0.640841i	−0.938821	+	0.344405i	$0.888081\pi$
$338$	0.173605	+	5.53431i	0.00944284	+	0.301027i
$339$		0			0
$340$	3.62745	−	28.6340i	0.196726	−	1.55290i
$341$		−	21.1346i		−	1.14450i
$342$		0			0
$343$	16.3097			0.880642
$344$	8.87111	−	6.30207i	0.478298	−	0.339785i
$345$		0			0
$346$	0.0761027	+	2.42607i	0.00409131	+	0.130426i
$347$	−3.63147	−	2.09663i	−0.194947	−	0.112553i	0.399349	−	0.916799i	$-0.369236\pi$
$347$	−3.63147	−	2.09663i	−0.194947	−	0.112553i	−0.594297	+	0.804246i	$0.702569\pi$
$348$		0			0
$349$	2.78198	+	4.81854i	0.148916	+	0.257930i	0.930827	−	0.365460i	$-0.119088\pi$
$349$	2.78198	+	4.81854i	0.148916	+	0.257930i	−0.781911	+	0.623390i	$0.785755\pi$
$350$	−9.29074	+	1.66664i	−0.496611	+	0.0890855i
$351$		0			0
$352$	23.1076	+	8.87779i	1.23164	+	0.473188i
$353$	5.51109	+	9.54549i	0.293326	+	0.508055i	0.974594	−	0.223979i	$-0.0719046\pi$
$353$	5.51109	+	9.54549i	0.293326	+	0.508055i	−0.681268	+	0.732034i	$0.738571\pi$
$354$		0			0
$355$	−14.2464	−	12.3029i	−0.756119	−	0.652973i
$356$	11.6181	−	7.71712i	0.615758	−	0.409006i
$357$		0			0
$358$	23.2599	+	12.4736i	1.22932	+	0.659248i
$359$	27.2920			1.44042			0.720209	−	0.693757i	$-0.244046\pi$
$359$	27.2920			1.44042			0.720209	+	0.693757i	$0.244046\pi$
$360$		0			0
$361$	−15.1292			−0.796272
$362$	−24.8367	−	13.3192i	−1.30539	−	0.700039i
$363$		0			0
$364$	−9.14639	+	6.07533i	−0.479401	+	0.318434i
$365$	10.6420	−	12.3231i	0.557029	−	0.645019i
$366$		0			0
$367$	−15.7443	−	27.2699i	−0.821846	−	1.42348i	−0.904306	−	0.426885i	$-0.859611\pi$
$367$	−15.7443	−	27.2699i	−0.821846	−	1.42348i	0.0824597	−	0.996594i	$-0.473722\pi$
$368$	0.322035	−	0.244322i	0.0167873	−	0.0127361i
$369$		0			0
$370$	−9.57627	+	3.67279i	−0.497846	+	0.190939i
$371$	1.85199	+	3.20774i	0.0961505	+	0.166538i
$372$		0			0
$373$	20.2988	+	11.7195i	1.05103	+	0.606812i	0.922937	−	0.384950i	$-0.125781\pi$
$373$	20.2988	+	11.7195i	1.05103	+	0.606812i	0.128092	+	0.991762i	$0.459115\pi$
$374$	1.25227	+	39.9210i	0.0647535	+	2.06426i
$375$		0			0
$376$	5.68893	+	8.00802i	0.293384	+	0.412982i
$377$	21.5240			1.10854
$378$		0			0
$379$		−	11.5529i		−	0.593434i	−0.954965	−	0.296717i	$-0.904108\pi$
$379$		−	11.5529i		−	0.593434i	0.954965	−	0.296717i	$-0.0958918\pi$
$380$	25.9191	+	3.28353i	1.32962	+	0.168441i
$381$		0			0
$382$	0.959787	+	30.5969i	0.0491070	+	1.56547i
$383$	−22.7016	−	13.1068i	−1.16000	−	0.669725i	−0.208695	−	0.977981i	$-0.566921\pi$
$383$	−22.7016	−	13.1068i	−1.16000	−	0.669725i	−0.951304	+	0.308256i	$0.900255\pi$
$384$		0			0
$385$	12.3363	−	4.29272i	0.628715	−	0.218777i
$386$	7.74920	+	12.4998i	0.394424	+	0.636222i
$387$		0			0
$388$	4.31492	+	2.14256i	0.219057	+	0.108772i
$389$	1.38545	−	0.799888i	0.0702449	−	0.0405559i	−0.464466	−	0.885591i	$-0.653754\pi$
$389$	1.38545	−	0.799888i	0.0702449	−	0.0405559i	0.534711	+	0.845035i	$0.320420\pi$
$390$		0			0
$391$	0.564834	+	0.326107i	0.0285649	+	0.0164919i
$392$	13.4183	+	6.14619i	0.677729	+	0.310430i
$393$		0			0
$394$	−10.1664	−	5.45190i	−0.512174	−	0.274663i
$395$	6.56234	+	1.25342i	0.330187	+	0.0630665i
$396$		0			0
$397$		−	25.9373i		−	1.30176i	−0.759182	−	0.650879i	$-0.774401\pi$
$397$		−	25.9373i		−	1.30176i	0.759182	−	0.650879i	$-0.225599\pi$
$398$	−6.13669	+	11.4433i	−0.307605	+	0.573601i
$399$		0			0
$400$	−19.3682	−	4.98730i	−0.968410	−	0.249365i
$401$	21.5383	+	12.4351i	1.07557	+	0.620980i	0.929698	−	0.368323i	$-0.120068\pi$
$401$	21.5383	+	12.4351i	1.07557	+	0.620980i	0.145872	+	0.989304i	$0.453401\pi$
$402$		0			0
$403$	9.93179	+	17.2024i	0.494738	+	0.856911i
$404$	8.12311	+	4.03351i	0.404140	+	0.200675i
$405$		0			0
$406$	5.20567	+	8.39696i	0.258353	+	0.416734i
$407$	12.2914	−	7.09646i	0.609264	−	0.351759i
$408$		0			0
$409$	−10.6869	+	18.5102i	−0.528433	+	0.915272i	0.471018	+	0.882124i	$0.343887\pi$
$409$	−10.6869	+	18.5102i	−0.528433	+	0.915272i	−0.999450	+	0.0331484i	$0.989447\pi$
$410$	2.00590	−	12.6409i	0.0990643	−	0.624291i
$411$		0			0
$412$	7.79025	−	0.489223i	0.383798	−	0.0241023i
$413$	3.66606			0.180395
$414$		0			0
$415$	−29.4437	−	5.62381i	−1.44533	−	0.276062i
$416$	−22.9802	+	3.63295i	−1.12670	+	0.178120i
$417$		0			0
$418$	−36.1360	+	1.13354i	−1.76747	+	0.0554434i
$419$	−3.12824	+	5.41826i	−0.152824	+	0.264700i	−0.932265	−	0.361777i	$-0.882170\pi$
$419$	−3.12824	+	5.41826i	−0.152824	+	0.264700i	0.779440	+	0.626476i	$0.215504\pi$
$420$		0			0
$421$	15.3599	+	26.6041i	0.748596	+	1.29661i	0.948496	+	0.316790i	$0.102605\pi$
$421$	15.3599	+	26.6041i	0.748596	+	1.29661i	−0.199900	+	0.979816i	$0.564062\pi$
$422$	7.63286	+	12.3121i	0.371562	+	0.599344i
$423$		0			0
$424$	0.737236	+	7.81350i	0.0358033	+	0.379457i
$425$	−4.69913	−	31.9256i	−0.227941	−	1.54862i
$426$		0			0
$427$	−1.39387	+	2.41425i	−0.0674540	+	0.116834i
$428$	8.31035	−	5.52001i	0.401696	−	0.266820i
$429$		0			0
$430$	7.65918	−	9.45267i	0.369358	−	0.455848i
$431$	−35.1049			−1.69094			−0.845472	−	0.534020i	$-0.820681\pi$
$431$	−35.1049			−1.69094			−0.845472	+	0.534020i	$0.820681\pi$
$432$		0			0
$433$		−	24.5043i		−	1.17760i	−0.808279	−	0.588800i	$-0.799601\pi$
$433$		−	24.5043i		−	1.17760i	0.808279	−	0.588800i	$-0.200399\pi$
$434$	−4.30895	+	8.03505i	−0.206836	+	0.385695i
$435$		0			0
$436$	−5.51823	−	8.30767i	−0.264275	−	0.397865i
$437$	−0.295188	+	0.511281i	−0.0141208	+	0.0244579i
$438$		0			0
$439$	15.3741	−	8.87623i	0.733765	−	0.423639i	−0.0860332	−	0.996292i	$-0.527419\pi$
$439$	15.3741	−	8.87623i	0.733765	−	0.423639i	0.819798	+	0.572653i	$0.194086\pi$
$440$	27.5523	+	2.61574i	1.31350	+	0.124701i
$441$		0			0
$442$	−19.7794	−	31.9049i	−0.940808	−	1.51756i
$443$	6.08715	−	3.51442i	0.289209	−	0.166975i	−0.348376	−	0.937355i	$-0.613267\pi$
$443$	6.08715	−	3.51442i	0.289209	−	0.166975i	0.637585	+	0.770380i	$0.279933\pi$
$444$		0			0
$445$	10.1921	−	11.8021i	0.483151	−	0.559472i
$446$	−1.03087	−	32.8630i	−0.0488132	−	1.55611i
$447$		0			0
$448$	−6.97513	−	8.08640i	−0.329544	−	0.382047i
$449$		−	16.6756i		−	0.786971i	−0.919331	−	0.393485i	$-0.871269\pi$
$449$		−	16.6756i		−	0.786971i	0.919331	−	0.393485i	$-0.128731\pi$
$450$		0			0
$451$			17.7115i			0.834002i
$452$	40.7426	−	2.55861i	1.91637	−	0.120347i
$453$		0			0
$454$	−24.0510	+	0.754451i	−1.12877	+	0.0354081i
$455$	−8.02376	+	9.29123i	−0.376160	+	0.435579i
$456$		0			0
$457$	25.7193	−	14.8490i	1.20310	−	0.694608i	0.241854	−	0.970313i	$-0.422244\pi$
$457$	25.7193	−	14.8490i	1.20310	−	0.694608i	0.961242	+	0.275704i	$0.0889111\pi$
$458$	−1.80460	+	1.11876i	−0.0843236	+	0.0522762i
$459$		0			0
$460$	0.273368	−	0.359889i	0.0127459	−	0.0167799i
$461$	−12.2647	+	7.08100i	−0.571222	+	0.329795i	−0.757637	−	0.652676i	$-0.773646\pi$
$461$	−12.2647	+	7.08100i	−0.571222	+	0.329795i	0.186415	+	0.982471i	$0.440313\pi$
$462$		0			0
$463$	2.85520	−	4.94535i	0.132692	−	0.229830i	−0.792021	−	0.610494i	$-0.790971\pi$
$463$	2.85520	−	4.94535i	0.132692	−	0.229830i	0.924714	+	0.380664i	$0.124304\pi$
$464$	2.61891	+	20.7691i	0.121580	+	0.964184i
$465$		0			0
$466$	−16.8854	−	9.05513i	−0.782202	−	0.419471i
$467$			18.7968i			0.869813i	0.900476	+	0.434907i	$0.143219\pi$
$467$			18.7968i			0.869813i	−0.900476	+	0.434907i	$0.856781\pi$
$468$		0			0
$469$	−0.577464			−0.0266648
$470$	8.53299	+	6.91399i	0.393598	+	0.318919i
$471$		0			0
$472$	7.06225	+	3.23482i	0.325067	+	0.148895i
$473$	−8.41783	+	14.5801i	−0.387052	+	0.670394i
$474$		0			0
$475$	28.8987	−	4.25359i	1.32596	−	0.195168i
$476$	7.66304	−	15.4327i	0.351235	−	0.707354i
$477$		0			0
$478$	−17.6047	+	10.9140i	−0.805219	+	0.499193i
$479$	−15.2061	−	26.3377i	−0.694783	−	1.20340i	−0.970254	−	0.242090i	$-0.922167\pi$
$479$	−15.2061	−	26.3377i	−0.694783	−	1.20340i	0.275471	−	0.961309i	$-0.411166\pi$
$480$		0			0
$481$	−6.66969	+	11.5522i	−0.304112	+	0.526737i
$482$	−1.08420	−	34.5630i	−0.0493839	−	1.57430i
$483$		0			0
$484$	−16.2665	+	1.02152i	−0.739384	+	0.0464329i
$485$	5.29058	+	1.01051i	0.240233	+	0.0458851i
$486$		0			0
$487$	−3.67889			−0.166706			−0.0833532	−	0.996520i	$-0.526563\pi$
$487$	−3.67889			−0.166706			−0.0833532	+	0.996520i	$0.526563\pi$
$488$	−4.81540	+	3.42088i	−0.217983	+	0.154856i
$489$		0			0
$490$	16.2971	+	2.58608i	0.736230	+	0.116827i
$491$	9.05671	−	15.6867i	0.408724	−	0.707930i	−0.586023	−	0.810294i	$-0.699307\pi$
$491$	9.05671	−	15.6867i	0.408724	−	0.707930i	0.994747	+	0.102364i	$0.0326406\pi$
$492$		0			0
$493$	−29.2509	+	16.8880i	−1.31739	+	0.760597i
$494$	28.8800	−	17.9040i	1.29937	−	0.805541i
$495$		0			0
$496$	−15.3906	+	11.6765i	−0.691059	+	0.524292i
$497$	−5.61859	−	9.73168i	−0.252028	−	0.436525i
$498$		0			0
$499$	19.9488	+	11.5175i	0.893032	+	0.515592i	0.874933	−	0.484244i	$-0.160905\pi$
$499$	19.9488	+	11.5175i	0.893032	+	0.515592i	0.0180991	+	0.999836i	$0.494239\pi$
$500$	−22.3562	+	0.450050i	−0.999797	+	0.0201268i
$501$		0			0
$502$	−16.4274	−	8.80951i	−0.733191	−	0.393188i
$503$		−	31.1266i		−	1.38787i	−0.720039	−	0.693934i	$-0.755876\pi$
$503$		−	31.1266i		−	1.38787i	0.720039	−	0.693934i	$-0.244124\pi$
$504$		0			0
$505$	9.95985	+	1.90235i	0.443208	+	0.0846537i
$506$	−0.295564	+	0.551149i	−0.0131394	+	0.0245016i
$507$		0			0
$508$	−21.2281	−	31.9588i	−0.941845	−	1.41794i
$509$	0.489681	+	0.282717i	0.0217047	+	0.0125312i	0.510813	−	0.859692i	$-0.329344\pi$
$509$	0.489681	+	0.282717i	0.0217047	+	0.0125312i	−0.489108	+	0.872223i	$0.662678\pi$
$510$		0			0
$511$	8.41787	−	4.86006i	0.372385	−	0.214996i
$512$	−6.30162	−	21.7322i	−0.278495	−	0.960438i
$513$		0			0
$514$	−8.37793	+	5.19387i	−0.369535	+	0.229092i
$515$	8.24217	−	2.86807i	0.363194	−	0.126382i
$516$		0			0
$517$	−13.1616	−	7.59884i	−0.578845	−	0.334196i
$518$	−6.11985	+	0.191972i	−0.268891	+	0.00843477i
$519$		0			0
$520$	−23.6552	+	10.8186i	−1.03735	+	0.474427i
$521$			4.80678i			0.210589i	0.994441	+	0.105294i	$0.0335785\pi$
$521$			4.80678i			0.210589i	−0.994441	+	0.105294i	$0.966422\pi$
$522$		0			0
$523$	−19.6207			−0.857954			−0.428977	−	0.903315i	$-0.641126\pi$
$523$	−19.6207			−0.857954			−0.428977	+	0.903315i	$0.641126\pi$
$524$	−33.5911	+	2.10950i	−1.46744	+	0.0921540i
$525$		0			0
$526$	22.8196	−	0.715822i	0.994980	−	0.0312113i
$527$	−26.9943	−	15.5852i	−1.17589	−	0.678902i
$528$		0			0
$529$	−11.4949	−	19.9097i	−0.499778	−	0.865641i
$530$	3.14214	+	8.19268i	0.136486	+	0.355867i
$531$		0			0
$532$	13.9695	+	6.93650i	0.605653	+	0.300735i
$533$	−8.32317	−	14.4162i	−0.360517	−	0.624433i
$534$		0			0
$535$	7.29034	−	8.44195i	0.315189	−	0.364977i
$536$	−1.11242	−	0.509538i	−0.0480493	−	0.0220087i
$537$		0			0
$538$	−14.5458	+	27.1240i	−0.627112	+	1.16940i
$539$	−22.8343			−0.983542
$540$		0			0
$541$	40.3065			1.73291			0.866457	−	0.499252i	$-0.166392\pi$
$541$	40.3065			1.73291			0.866457	+	0.499252i	$0.166392\pi$
$542$	−20.1542	+	37.5823i	−0.865699	+	1.61430i
$543$		0			0
$544$	28.3793	−	22.9677i	1.21675	−	0.984730i
$545$	−8.43922	−	7.28798i	−0.361497	−	0.312183i
$546$		0			0
$547$	1.44201	+	2.49763i	0.0616557	+	0.106791i	0.895206	−	0.445653i	$-0.147029\pi$
$547$	1.44201	+	2.49763i	0.0616557	+	0.106791i	−0.833550	+	0.552444i	$0.813695\pi$
$548$	−5.33231	+	10.7388i	−0.227785	+	0.458737i
$549$		0			0
$550$	30.4567	−	5.46353i	1.29868	−	0.232966i
$551$	−15.2868	−	26.4775i	−0.651240	−	1.12798i
$552$		0			0
$553$	3.45405	+	1.99419i	0.146881	+	0.0848018i
$554$	−18.3807	+	0.576582i	−0.780923	+	0.0244966i
$555$		0			0
$556$	−0.0298425	−	0.475204i	−0.00126560	−	0.0201531i
$557$	17.0510			0.722475			0.361237	−	0.932474i	$-0.382354\pi$
$557$	17.0510			0.722475			0.361237	+	0.932474i	$0.382354\pi$
$558$		0			0
$559$		−	15.8232i		−	0.669249i
$560$	−9.94165	−	6.61186i	−0.420111	−	0.279402i
$561$		0			0
$562$	1.52886	−	0.0479585i	0.0644910	−	0.00202301i
$563$	19.0842	+	11.0182i	0.804302	+	0.464364i	0.844973	−	0.534809i	$-0.179616\pi$
$563$	19.0842	+	11.0182i	0.804302	+	0.464364i	−0.0406715	+	0.999173i	$0.512950\pi$
$564$		0			0
$565$	43.1061	−	14.9999i	1.81349	−	0.631049i
$566$	−35.1357	+	21.7822i	−1.47686	+	0.915576i
$567$		0			0
$568$	−2.23663	−	23.7047i	−0.0938470	−	0.994627i
$569$	24.1641	−	13.9512i	1.01301	−	0.584864i	0.100941	−	0.994892i	$-0.467815\pi$
$569$	24.1641	−	13.9512i	1.01301	−	0.584864i	0.912073	+	0.410029i	$0.134481\pi$
$570$		0			0
$571$	−11.2510	−	6.49576i	−0.470839	−	0.271839i	0.245752	−	0.969333i	$-0.420965\pi$
$571$	−11.2510	−	6.49576i	−0.470839	−	0.271839i	−0.716591	+	0.697494i	$0.754298\pi$
$572$	29.9835	−	19.9160i	1.25367	−	0.832731i
$573$		0			0
$574$	3.61104	−	6.73364i	0.150722	−	0.281057i
$575$	0.186227	−	0.469715i	0.00776621	−	0.0195885i
$576$		0			0
$577$			34.6251i			1.44146i	0.693216	+	0.720730i	$0.256193\pi$
$577$			34.6251i			1.44146i	−0.693216	+	0.720730i	$0.743807\pi$
$578$	30.7255	+	16.4772i	1.27801	+	0.685359i
$579$		0			0
$580$	9.06209	+	21.5789i	0.376283	+	0.896015i
$581$	−15.4975	−	8.94748i	−0.642944	−	0.371204i
$582$		0			0
$583$	−6.07116	−	10.5156i	−0.251442	−	0.435510i
$584$	20.5045	−	1.93468i	0.848482	−	0.0800577i
$585$		0			0
$586$	−6.76835	+	4.19601i	−0.279598	+	0.173336i
$587$	−9.41209	+	5.43407i	−0.388479	+	0.224288i	−0.681501	−	0.731817i	$-0.738672\pi$
$587$	−9.41209	+	5.43407i	−0.388479	+	0.224288i	0.293022	+	0.956106i	$0.405339\pi$
$588$		0			0
$589$	14.1075	−	24.4350i	0.581291	−	1.00683i
$590$	8.57740	+	1.36109i	0.353126	+	0.0560350i
$591$		0			0
$592$	−11.9586	−	5.03017i	−0.491496	−	0.206739i
$593$	−4.49540			−0.184604			−0.0923019	−	0.995731i	$-0.529422\pi$
$593$	−4.49540			−0.184604			−0.0923019	+	0.995731i	$0.529422\pi$
$594$		0			0
$595$	3.61418	−	18.9222i	0.148167	−	0.775734i
$596$	1.28082	+	20.3954i	0.0524643	+	0.835427i
$597$		0			0
$598$	−0.0184291	−	0.587499i	−0.000753623	−	0.0240246i
$599$	3.45192	−	5.97890i	0.141042	−	0.244291i	−0.786847	−	0.617148i	$-0.788288\pi$
$599$	3.45192	−	5.97890i	0.141042	−	0.244291i	0.927889	+	0.372856i	$0.121621\pi$
$600$		0			0
$601$	−15.7058	−	27.2032i	−0.640653	−	1.10964i	−0.985287	−	0.170906i	$-0.945331\pi$
$601$	−15.7058	−	27.2032i	−0.640653	−	1.10964i	0.344635	−	0.938737i	$-0.388003\pi$
$602$	6.17294	−	3.82689i	0.251590	−	0.155973i
$603$		0			0
$604$	−26.9909	−	13.4022i	−1.09824	−	0.545330i
$605$	−17.2101	+	5.98868i	−0.699689	+	0.243474i
$606$		0			0
$607$	−9.81362	+	16.9977i	−0.398322	+	0.689915i	−0.993519	−	0.113665i	$-0.963741\pi$
$607$	−9.81362	+	16.9977i	−0.398322	+	0.689915i	0.595197	+	0.803580i	$0.297074\pi$
$608$	20.7901	+	25.6887i	0.843148	+	1.04181i
$609$		0			0
$610$	−4.15754	+	5.13108i	−0.168334	+	0.207751i
$611$	14.2837			0.577857
$612$		0			0
$613$		−	28.8088i		−	1.16358i	−0.813340	−	0.581788i	$-0.802353\pi$
$613$		−	28.8088i		−	1.16358i	0.813340	−	0.581788i	$-0.197647\pi$
$614$	19.0600	+	10.2213i	0.769200	+	0.412499i
$615$		0			0
$616$	15.0213	+	6.88040i	0.605224	+	0.277219i
$617$	8.02269	−	13.8957i	0.322981	−	0.559420i	−0.658120	−	0.752913i	$-0.728648\pi$
$617$	8.02269	−	13.8957i	0.322981	−	0.559420i	0.981102	+	0.193493i	$0.0619815\pi$
$618$		0			0
$619$	−2.13387	+	1.23199i	−0.0857674	+	0.0495178i	−0.542270	−	0.840204i	$-0.682435\pi$
$619$	−2.13387	+	1.23199i	−0.0857674	+	0.0495178i	0.456503	+	0.889722i	$0.349102\pi$
$620$	−13.0647	+	17.1997i	−0.524692	+	0.690756i
$621$		0			0
$622$	−4.40924	+	2.73350i	−0.176795	+	0.109603i
$623$	8.06198	−	4.65458i	0.322996	−	0.186482i
$624$		0			0
$625$	−23.9397	+	7.20343i	−0.957589	+	0.288137i
$626$	−34.8148	+	1.09210i	−1.39148	+	0.0436490i
$627$		0			0
$628$	0.401588	+	6.39478i	0.0160251	+	0.255179i
$629$		−	20.9324i		−	0.834631i
$630$		0			0
$631$		−	44.4737i		−	1.77047i	−0.465144	−	0.885235i	$-0.653997\pi$
$631$		−	44.4737i		−	1.77047i	0.465144	−	0.885235i	$-0.346003\pi$
$632$	4.89422	+	6.88935i	0.194682	+	0.274044i
$633$		0			0
$634$	0.472194	+	15.0530i	0.0187532	+	0.597831i
$635$	−32.4649	−	28.0362i	−1.28833	−	1.11258i
$636$		0			0
$637$	18.5858	−	10.7305i	0.736397	−	0.425159i
$638$	−17.0651	−	27.5267i	−0.675614	−	1.08979i
$639$		0			0
$640$	−13.3174	−	21.5092i	−0.526415	−	0.850227i
$641$	14.1935	−	8.19465i	0.560611	−	0.323669i	−0.192779	−	0.981242i	$-0.561750\pi$
$641$	14.1935	−	8.19465i	0.560611	−	0.323669i	0.753391	+	0.657573i	$0.228417\pi$
$642$		0			0
$643$	−17.5507	+	30.3987i	−0.692133	+	1.19881i	0.279005	+	0.960290i	$0.409995\pi$
$643$	−17.5507	+	30.3987i	−0.692133	+	1.19881i	−0.971138	+	0.238520i	$0.923338\pi$
$644$	0.224738	−	0.149278i	0.00885591	−	0.00588239i
$645$		0			0
$646$	−25.1998	+	46.9909i	−0.991472	+	1.84883i
$647$			19.0579i			0.749243i	0.927178	+	0.374621i	$0.122227\pi$
$647$			19.0579i			0.749243i	−0.927178	+	0.374621i	$0.877773\pi$
$648$		0			0
$649$	−12.0180			−0.471747
$650$	−22.2226	+	18.7596i	−0.871641	+	0.735810i
$651$		0			0
$652$	11.7500	+	17.6896i	0.460167	+	0.692780i
$653$	−21.0708	+	36.4956i	−0.824563	+	1.42818i	0.0776903	+	0.996978i	$0.475245\pi$
$653$	−21.0708	+	36.4956i	−0.824563	+	1.42818i	−0.902253	+	0.431207i	$0.858088\pi$
$654$		0			0
$655$	−35.5398	+	12.3670i	−1.38865	+	0.483217i
$656$	12.8978	−	9.78533i	0.503576	−	0.382053i
$657$		0			0
$658$	3.45456	+	5.57236i	0.134673	+	0.217233i
$659$	−10.0696	−	17.4410i	−0.392256	−	0.679407i	0.600491	−	0.799631i	$-0.294972\pi$
$659$	−10.0696	−	17.4410i	−0.392256	−	0.679407i	−0.992747	+	0.120225i	$0.961638\pi$
$660$		0			0
$661$	3.54725	−	6.14402i	0.137972	−	0.238975i	−0.788757	−	0.614705i	$-0.789275\pi$
$661$	3.54725	−	6.14402i	0.137972	−	0.238975i	0.926729	+	0.375731i	$0.122608\pi$
$662$	4.97136	−	0.155946i	0.193218	−	0.00606100i
$663$		0			0
$664$	−21.9592	−	30.9109i	−0.852183	−	1.19958i
$665$	17.1281	+	3.27151i	0.664201	+	0.126864i
$666$		0			0
$667$	−0.528872			−0.0204780
$668$	1.57955	+	25.1523i	0.0611145	+	0.973171i
$669$		0			0
$670$	−1.35108	−	0.214393i	−0.0521968	−	0.00828274i
$671$	4.56935	−	7.91434i	0.176398	−	0.305530i
$672$		0			0
$673$	−19.8408	+	11.4551i	−0.764806	+	0.441561i	−0.831018	−	0.556245i	$-0.812242\pi$
$673$	−19.8408	+	11.4551i	−0.764806	+	0.441561i	0.0662129	+	0.997806i	$0.478908\pi$
$674$	−17.5325	−	28.2807i	−0.675327	−	1.08933i
$675$		0			0
$676$	−3.48254	+	7.01351i	−0.133944	+	0.269750i
$677$	−11.6227	−	20.1311i	−0.446696	−	0.773699i	0.551473	−	0.834193i	$-0.314066\pi$
$677$	−11.6227	−	20.1311i	−0.446696	−	0.773699i	−0.998169	+	0.0604934i	$0.980733\pi$
$678$		0			0
$679$	2.78467	+	1.60773i	0.106866	+	0.0616989i
$680$	23.6587	−	33.2625i	0.907271	−	1.27556i
$681$		0			0
$682$	14.1255	−	26.3403i	0.540894	−	1.00862i
$683$			30.3578i			1.16161i	0.814043	+	0.580804i	$0.197262\pi$
$683$			30.3578i			1.16161i	−0.814043	+	0.580804i	$0.802738\pi$
$684$		0			0
$685$	−2.51492	+	13.1669i	−0.0960900	+	0.503083i
$686$	20.3270	+	10.9007i	0.776089	+	0.416193i
$687$		0			0
$688$	15.2682	−	1.92526i	0.582096	−	0.0734000i
$689$	9.88316	+	5.70604i	0.376518	+	0.217383i
$690$		0			0
$691$	10.6015	−	6.12077i	0.403299	−	0.232845i	−0.284607	−	0.958644i	$-0.591863\pi$
$691$	10.6015	−	6.12077i	0.403299	−	0.232845i	0.687907	+	0.725799i	$0.258530\pi$
$692$	−1.52664	+	3.07450i	−0.0580340	+	0.116875i
$693$		0			0
$694$	−3.12464	−	5.04018i	−0.118610	−	0.191323i
$695$	−0.174952	−	0.502771i	−0.00663629	−	0.0190712i
$696$		0			0
$697$	22.6222	+	13.0609i	0.856875	+	0.494717i
$698$	0.246708	+	7.86477i	0.00933804	+	0.297686i
$699$		0			0
$700$	−12.6931	−	4.13240i	−0.479754	−	0.156190i
$701$		−	0.0365464i		−	0.00138034i	−1.00000		0.000690169i	$-0.999780\pi$
$701$		−	0.0365464i		−	0.00138034i	1.00000		0.000690169i	$-0.000219688\pi$
$702$		0			0
$703$	18.9478			0.714630
$704$	22.8657	+	26.5087i	0.861785	+	0.999083i
$705$		0			0
$706$	0.488727	+	15.5801i	0.0183935	+	0.586363i
$707$	5.24231	+	3.02665i	0.197157	+	0.113829i
$708$		0			0
$709$	13.6359	+	23.6181i	0.512109	+	0.886998i	0.999901	+	0.0140387i	$0.00446880\pi$
$709$	13.6359	+	23.6181i	0.512109	+	0.886998i	−0.487793	+	0.872959i	$0.662198\pi$
$710$	−9.53265	−	24.8550i	−0.357754	−	0.932792i
$711$		0			0
$712$	19.6376	−	1.85289i	0.735950	−	0.0694398i
$713$	−0.244036	−	0.422683i	−0.00913923	−	0.0158296i
$714$		0			0
$715$	26.3033	−	30.4583i	0.983689	−	1.13908i
$716$	20.6523	+	31.0919i	0.771812	+	1.16196i
$717$		0			0
$718$	34.0144	+	18.2409i	1.26941	+	0.680743i
$719$	7.73269			0.288381			0.144190	−	0.989550i	$-0.453942\pi$
$719$	7.73269			0.288381			0.144190	+	0.989550i	$0.453942\pi$
$720$		0			0
$721$	5.20978			0.194022
$722$	−18.8557	−	10.1117i	−0.701735	−	0.376319i
$723$		0			0
$724$	−22.0523	−	33.1997i	−0.819568	−	1.23386i
$725$	16.2440	+	20.5145i	0.603287	+	0.761890i
$726$		0			0
$727$	8.24957	+	14.2887i	0.305960	+	0.529938i	0.977475	−	0.211053i	$-0.0676894\pi$
$727$	8.24957	+	14.2887i	0.305960	+	0.529938i	−0.671515	+	0.740991i	$0.734356\pi$
$728$	−15.4598	+	1.45869i	−0.572977	+	0.0540627i
$729$		0			0
$730$	21.4995	−	8.24571i	0.795733	−	0.305188i
$731$	12.4150	+	21.5035i	0.459187	+	0.795335i
$732$		0			0
$733$	−37.1399	−	21.4427i	−1.37179	−	0.792006i	−0.380641	−	0.924723i	$-0.624297\pi$
$733$	−37.1399	−	21.4427i	−1.37179	−	0.792006i	−0.991154	+	0.132717i	$0.957630\pi$
$734$	−1.39622	−	44.5097i	−0.0515353	−	1.64288i
$735$		0			0
$736$	0.564652	−	0.0892658i	0.0208133	−	0.00329038i
$737$	1.89303			0.0697307
$738$		0			0
$739$		−	3.04457i		−	0.111996i	−0.998431	−	0.0559981i	$-0.982166\pi$
$739$		−	3.04457i		−	0.111996i	0.998431	−	0.0559981i	$-0.0178341\pi$
$740$	−14.3898	−	1.82294i	−0.528978	−	0.0670128i
$741$		0			0
$742$	0.164236	+	5.23564i	0.00602928	+	0.192207i
$743$	35.0211	+	20.2194i	1.28480	+	0.741779i	0.977722	−	0.209905i	$-0.0673155\pi$
$743$	35.0211	+	20.2194i	1.28480	+	0.741779i	0.307078	+	0.951684i	$0.400649\pi$
$744$		0			0
$745$	7.50879	+	21.5785i	0.275101	+	0.790576i
$746$	17.4658	+	28.1730i	0.639467	+	1.03149i
$747$		0			0
$748$	−25.1208	+	50.5910i	−0.918509	+	1.84979i
$749$	5.76668	−	3.32940i	0.210710	−	0.121653i
$750$		0			0
$751$	12.0862	+	6.97795i	0.441030	+	0.254629i	0.704034	−	0.710166i	$-0.251380\pi$
$751$	12.0862	+	6.97795i	0.441030	+	0.254629i	−0.263004	+	0.964795i	$0.584713\pi$
$752$	1.73795	+	13.7827i	0.0633765	+	0.502605i
$753$		0			0
$754$	26.8257	+	14.3858i	0.976934	+	0.523900i
$755$	−33.0939	−	6.32101i	−1.20441	−	0.230045i
$756$		0			0
$757$			31.7859i			1.15528i	0.816293	+	0.577639i	$0.196026\pi$
$757$			31.7859i			1.15528i	−0.816293	+	0.577639i	$0.803974\pi$
$758$	7.72151	−	14.3986i	0.280458	−	0.522979i
$759$		0			0
$760$	30.1088	+	21.4156i	1.09216	+	0.776825i
$761$	21.6921	+	12.5240i	0.786339	+	0.453993i	0.838672	−	0.544637i	$-0.183332\pi$
$761$	21.6921	+	12.5240i	0.786339	+	0.453993i	−0.0523332	+	0.998630i	$0.516666\pi$
$762$		0			0
$763$	−3.32832	−	5.76482i	−0.120493	−	0.208700i
$764$	−19.2535	+	38.7748i	−0.696568	+	1.40282i
$765$		0			0
$766$	−19.5333	−	31.5080i	−0.705766	−	1.13843i
$767$	9.78196	−	5.64762i	0.353206	−	0.203924i
$768$		0			0
$769$	−1.59810	+	2.76799i	−0.0576290	+	0.0998164i	−0.893401	−	0.449261i	$-0.851687\pi$
$769$	−1.59810	+	2.76799i	−0.0576290	+	0.0998164i	0.835772	+	0.549077i	$0.185021\pi$
$770$	18.2440	+	2.89500i	0.657466	+	0.104329i
$771$		0			0
$772$	1.30358	+	20.7579i	0.0469170	+	0.747093i
$773$	26.8609			0.966121			0.483060	−	0.875587i	$-0.339525\pi$
$773$	26.8609			0.966121			0.483060	+	0.875587i	$0.339525\pi$
$774$		0			0
$775$	−8.90011	+	22.4485i	−0.319701	+	0.806372i
$776$	3.94574	+	5.55422i	0.141644	+	0.199385i
$777$		0			0
$778$	2.26131	−	0.0709346i	0.0810720	−	0.00254313i
$779$	−11.8226	+	20.4773i	−0.423588	+	0.733676i
$780$		0			0
$781$	18.4187	+	31.9022i	0.659074	+	1.14155i
$782$	0.486003	+	0.783943i	0.0173794	+	0.0280337i
$783$		0			0
$784$	12.6156	+	16.6284i	0.450557	+	0.593870i
$785$	2.35431	+	6.76575i	0.0840289	+	0.241480i
$786$		0			0
$787$	16.8518	−	29.1883i	0.600703	−	1.04045i	−0.392011	−	0.919960i	$-0.628221\pi$
$787$	16.8518	−	29.1883i	0.600703	−	1.04045i	0.992715	−	0.120488i	$-0.0384461\pi$
$788$	−9.02663	−	13.5896i	−0.321560	−	0.484108i
$789$		0			0
$790$	7.34099	+	5.94816i	0.261181	+	0.211626i
$791$	27.2469			0.968787
$792$		0			0
$793$			8.58910i			0.305008i
$794$	17.3355	−	32.3260i	0.615212	−	1.14721i
$795$		0			0
$796$	−15.2965	+	10.1604i	−0.542169	+	0.360127i
$797$	−14.4698	+	25.0624i	−0.512546	+	0.887755i	0.487348	+	0.873208i	$0.337964\pi$
$797$	−14.4698	+	25.0624i	−0.512546	+	0.887755i	−0.999894	+	0.0145477i	$0.995369\pi$
$798$		0			0
$799$	−19.4113	+	11.2071i	−0.686724	+	0.396480i
$800$	−20.8055	−	19.1606i	−0.735586	−	0.677431i
$801$		0			0
$802$	18.5323	+	29.8934i	0.654398	+	1.05557i
$803$	−27.5953	+	15.9322i	−0.973817	+	0.562233i
$804$		0			0
$805$	0.197153	−	0.228297i	0.00694875	−	0.00804640i
$806$	0.880759	+	28.0775i	0.0310234	+	0.988989i
$807$		0			0
$808$	7.42810	+	10.4562i	0.261320	+	0.367847i
$809$		−	14.9996i		−	0.527358i	−0.964610	−	0.263679i	$-0.915064\pi$
$809$		−	14.9996i		−	0.527358i	0.964610	−	0.263679i	$-0.0849360\pi$
$810$		0			0
$811$		−	17.4677i		−	0.613376i	−0.951810	−	0.306688i	$-0.900779\pi$
$811$		−	17.4677i		−	0.613376i	0.951810	−	0.306688i	$-0.0992207\pi$
$812$	0.875705	+	13.9445i	0.0307312	+	0.489356i
$813$		0			0
$814$	20.0620	−	0.629319i	0.703171	−	0.0220576i
$815$	17.9698	+	15.5184i	0.629454	+	0.543587i
$816$		0			0
$817$	−19.4647	+	11.2379i	−0.680984	+	0.393166i
$818$	−25.6907	+	15.9269i	−0.898254	+	0.556870i
$819$		0			0
$820$	10.9487	−	14.4139i	0.382344	−	0.503355i
$821$	−15.8290	+	9.13886i	−0.552435	+	0.318948i	−0.750103	−	0.661320i	$-0.769996\pi$
$821$	−15.8290	+	9.13886i	−0.552435	+	0.318948i	0.197669	+	0.980269i	$0.436663\pi$
$822$		0			0
$823$	14.6369	−	25.3518i	0.510210	−	0.883710i	−0.489720	−	0.871880i	$-0.662901\pi$
$823$	14.6369	−	25.3518i	0.510210	−	0.883710i	0.999930	−	0.0118300i	$-0.00376570\pi$
$824$	10.0361	+	4.59696i	0.349623	+	0.160143i
$825$		0			0
$826$	4.56905	+	2.45024i	0.158978	+	0.0852548i
$827$		−	24.5270i		−	0.852886i	−0.904514	−	0.426443i	$-0.859767\pi$
$827$		−	24.5270i		−	0.852886i	0.904514	−	0.426443i	$-0.140233\pi$
$828$		0			0
$829$	−42.2094			−1.46599			−0.732996	−	0.680233i	$-0.761879\pi$
$829$	−42.2094			−1.46599			−0.732996	+	0.680233i	$0.761879\pi$
$830$	−32.9373	−	26.6880i	−1.14327	−	0.926353i
$831$		0			0
$832$	−31.0687	−	10.8313i	−1.07711	−	0.375506i
$833$	−16.8386	+	29.1653i	−0.583422	+	1.01052i
$834$		0			0
$835$	9.26010	+	26.6114i	0.320459	+	0.920925i
$836$	−45.7944	−	22.7391i	−1.58383	−	0.786448i
$837$		0			0
$838$	−7.52011	+	4.66207i	−0.259778	+	0.161048i
$839$	18.2179	+	31.5544i	0.628953	+	1.08938i	0.987762	+	0.155967i	$0.0498494\pi$
$839$	18.2179	+	31.5544i	0.628953	+	1.08938i	−0.358810	+	0.933411i	$0.616817\pi$
$840$		0			0
$841$	−0.805742	+	1.39559i	−0.0277842	+	0.0481237i
$842$	1.36213	+	43.4230i	0.0469420	+	1.49646i
$843$		0			0
$844$	1.28401	+	20.4462i	0.0441975	+	0.703788i
$845$	−1.64250	+	8.59936i	−0.0565036	+	0.295827i
$846$		0			0
$847$	−10.8783			−0.373783
$848$	−4.30340	+	10.2308i	−0.147779	+	0.351327i
$849$		0			0
$850$	15.4812	−	42.9300i	0.531001	−	1.47249i
$851$	0.163882	−	0.283852i	0.00561781	−	0.00973033i
$852$		0			0
$853$	−27.1128	+	15.6536i	−0.928324	+	0.535968i	−0.886281	−	0.463148i	$-0.846720\pi$
$853$	−27.1128	+	15.6536i	−0.928324	+	0.535968i	−0.0420430	+	0.999116i	$0.513387\pi$
$854$	−3.35078	+	2.07731i	−0.114661	+	0.0710839i
$855$		0			0
$856$	14.0466	−	1.32536i	0.480104	−	0.0452998i
$857$	−4.60165	−	7.97029i	−0.157189	−	0.272260i	0.776665	−	0.629914i	$-0.216910\pi$
$857$	−4.60165	−	7.97029i	−0.157189	−	0.272260i	−0.933854	+	0.357654i	$0.883577\pi$
$858$		0			0
$859$	4.62482	+	2.67014i	0.157797	+	0.0911040i	0.576819	−	0.816872i	$-0.304294\pi$
$859$	4.62482	+	2.67014i	0.157797	+	0.0911040i	−0.419022	+	0.907976i	$0.637627\pi$
$860$	15.8635	−	6.66190i	0.540941	−	0.227169i
$861$		0			0
$862$	−43.7517	−	23.4627i	−1.49019	−	0.799142i
$863$		−	19.0360i		−	0.647992i	−0.946058	−	0.323996i	$-0.894974\pi$
$863$		−	19.0360i		−	0.647992i	0.946058	−	0.323996i	$-0.105026\pi$
$864$		0			0
$865$	−0.720019	+	3.76969i	−0.0244814	+	0.128173i
$866$	16.3776	−	30.5400i	0.556535	−	1.03779i
$867$		0			0
$868$	−10.7406	+	7.13426i	−0.364560	+	0.242152i
$869$	−11.3230	−	6.53733i	−0.384106	−	0.221764i
$870$		0			0
$871$	−1.54082	+	0.889593i	−0.0522087	+	0.0301427i
$872$	−1.32493	−	14.0421i	−0.0448678	−	0.475526i
$873$		0			0
$874$	−0.709616	+	0.439924i	−0.0240031	+	0.0148807i
$875$	−14.9109	−	0.635422i	−0.504081	−	0.0214812i
$876$		0			0
$877$	21.1121	+	12.1891i	0.712904	+	0.411595i	0.812135	−	0.583469i	$-0.198305\pi$
$877$	21.1121	+	12.1891i	0.712904	+	0.411595i	−0.0992316	+	0.995064i	$0.531638\pi$
$878$	25.0934	−	0.787150i	0.846862	−	0.0265650i
$879$		0			0
$880$	32.5905	+	21.6749i	1.09863	+	0.730659i
$881$			42.8577i			1.44391i	0.691939	+	0.721956i	$0.256757\pi$
$881$			42.8577i			1.44391i	−0.691939	+	0.721956i	$0.743243\pi$
$882$		0			0
$883$	28.8663			0.971427			0.485713	−	0.874118i	$-0.338560\pi$
$883$	28.8663			0.971427			0.485713	+	0.874118i	$0.338560\pi$
$884$	−3.32732	−	52.9833i	−0.111910	−	1.78202i
$885$		0			0
$886$	9.93539	−	0.311661i	0.333786	−	0.0104705i
$887$	13.1498	+	7.59206i	0.441528	+	0.254917i	0.704246	−	0.709956i	$-0.251285\pi$
$887$	13.1498	+	7.59206i	0.441528	+	0.254917i	−0.262717	+	0.964873i	$0.584619\pi$
$888$		0			0
$889$	−12.8037	−	22.1767i	−0.429424	−	0.743784i
$890$	20.5906	−	7.89710i	0.690197	−	0.264711i
$891$		0			0
$892$	20.6795	−	41.6465i	0.692400	−	1.39443i
$893$	−10.1446	−	17.5709i	−0.339475	−	0.587989i
$894$		0			0
$895$	31.5843	+	27.2757i	1.05575	+	0.911726i
$896$	−3.28858	−	14.7401i	−0.109864	−	0.492432i
$897$		0			0
$898$	11.1453	−	20.7830i	0.371923	−	0.693539i
$899$	25.2757			0.842990
$900$		0			0
$901$	−17.9081			−0.596605
$902$	−11.8376	+	22.0741i	−0.394150	+	0.734986i
$903$		0			0
$904$	52.4881	+	24.0419i	1.74573	+	0.799621i
$905$	−33.7254	−	29.1247i	−1.12107	−	0.968139i
$906$		0			0
$907$	−13.5599	−	23.4865i	−0.450250	−	0.779856i	0.548151	−	0.836379i	$-0.315332\pi$
$907$	−13.5599	−	23.4865i	−0.450250	−	0.779856i	−0.998401	+	0.0565230i	$0.981999\pi$
$908$	−30.4793	−	15.1344i	−1.01149	−	0.502254i
$909$		0			0
$910$	−16.2100	+	6.21702i	−0.537356	+	0.206092i
$911$	3.77888	+	6.54521i	0.125200	+	0.216852i	0.921811	−	0.387640i	$-0.126709\pi$
$911$	3.77888	+	6.54521i	0.125200	+	0.216852i	−0.796611	+	0.604492i	$0.793376\pi$
$912$		0			0
$913$	50.8036	+	29.3315i	1.68135	+	0.970729i
$914$	41.9787	−	1.31682i	1.38853	−	0.0435566i
$915$		0			0
$916$	−2.99683	+	0.188199i	−0.0990182	+	0.00621828i
$917$	−22.4643			−0.741836
$918$		0			0
$919$			33.7674i			1.11388i	0.830552	+	0.556942i	$0.188025\pi$
$919$			33.7674i			1.11388i	−0.830552	+	0.556942i	$0.811975\pi$
$920$	0.581237	−	0.265826i	0.0191628	−	0.00876402i
$921$		0			0
$922$	−20.0183	+	0.627948i	−0.659266	+	0.0206804i
$923$	−29.9836	−	17.3110i	−0.986923	−	0.569800i
$924$		0			0
$925$	−16.0440	+	2.36151i	−0.527522	+	0.0776459i
$926$	6.86375	−	4.25516i	0.225557	−	0.139833i
$927$		0			0
$928$	−10.6173	+	27.6352i	−0.348529	+	0.907171i
$929$	−43.7091	+	25.2355i	−1.43405	+	0.827949i	−0.997427	−	0.0716964i	$-0.977159\pi$
$929$	−43.7091	+	25.2355i	−1.43405	+	0.827949i	−0.436622	+	0.899645i	$0.643825\pi$
$930$		0			0
$931$	−26.4001	−	15.2421i	−0.865227	−	0.499539i
$932$	−14.9924	−	22.5711i	−0.491094	−	0.739339i
$933$		0			0
$934$	−12.5630	+	23.4267i	−0.411075	+	0.766546i
$935$	−11.8479	+	62.0303i	−0.387469	+	2.02861i
$936$		0			0
$937$		−	43.7549i		−	1.42941i	−0.699425	−	0.714706i	$-0.746561\pi$
$937$		−	43.7549i		−	1.42941i	0.699425	−	0.714706i	$-0.253439\pi$
$938$	−0.719701	−	0.385953i	−0.0234991	−	0.0126018i
$939$		0			0
$940$	6.01375	+	14.3201i	0.196147	+	0.467070i
$941$	12.5420	+	7.24115i	0.408859	+	0.236055i	0.690299	−	0.723524i	$-0.257479\pi$
$941$	12.5420	+	7.24115i	0.408859	+	0.236055i	−0.281441	+	0.959579i	$0.590812\pi$
$942$		0			0
$943$	0.204510	+	0.354222i	0.00665977	+	0.0115351i
$944$	6.63975	+	8.75173i	0.216106	+	0.284844i
$945$		0			0
$946$	−20.2360	+	12.5452i	−0.657929	+	0.407881i
$947$	32.3885	−	18.6995i	1.05249	−	0.607653i	0.129141	−	0.991626i	$-0.458778\pi$
$947$	32.3885	−	18.6995i	1.05249	−	0.607653i	0.923344	+	0.383973i	$0.125445\pi$
$948$		0			0
$949$	14.9740	−	25.9357i	0.486077	−	0.841910i
$950$	38.8598	+	14.0134i	1.26078	+	0.454655i
$951$		0			0
$952$	19.8651	−	14.1122i	0.643832	−	0.457381i
$953$	22.8733			0.740937			0.370469	−	0.928845i	$-0.379197\pi$
$953$	22.8733			0.740937			0.370469	+	0.928845i	$0.379197\pi$
$954$		0			0
$955$	−9.08068	+	47.5423i	−0.293844	+	1.53843i
$956$	−29.2354	+	1.83596i	−0.945539	+	0.0593793i
$957$		0			0
$958$	−1.34848	−	42.9881i	−0.0435676	−	1.38888i
$959$	−4.00123	+	6.93034i	−0.129207	+	0.223792i
$960$		0			0
$961$	−3.83710	−	6.64606i	−0.123777	−	0.214389i
$962$	−16.0336	+	9.93996i	−0.516943	+	0.320477i
$963$		0			0
$964$	21.7492	−	43.8009i	0.700496	−	1.41073i
$965$	7.64225	+	21.9621i	0.246013	+	0.706984i
$966$		0			0
$967$	−29.1950	+	50.5672i	−0.938848	+	1.62613i	−0.171223	+	0.985232i	$0.554772\pi$
$967$	−29.1950	+	50.5672i	−0.938848	+	1.62613i	−0.767625	+	0.640899i	$0.778562\pi$
$968$	−20.9558	−	9.59870i	−0.673546	−	0.308514i
$969$		0			0
$970$	5.91833	+	4.79543i	0.190026	+	0.153972i
$971$	35.2792			1.13216			0.566082	−	0.824349i	$-0.308459\pi$
$971$	35.2792			1.13216			0.566082	+	0.824349i	$0.308459\pi$
$972$		0			0
$973$		−	0.317795i		−	0.0101881i
$974$	−4.58505	−	2.45882i	−0.146914	−	0.0787856i
$975$		0			0
$976$	−8.28787	+	1.04507i	−0.265288	+	0.0334518i
$977$	−4.78940	+	8.29548i	−0.153226	+	0.265396i	−0.932412	−	0.361398i	$-0.882300\pi$
$977$	−4.78940	+	8.29548i	−0.153226	+	0.265396i	0.779185	+	0.626794i	$0.215633\pi$
$978$		0			0
$979$	−26.4286	+	15.2586i	−0.844662	+	0.487666i
$980$	18.5829	+	14.1154i	0.593609	+	0.450900i
$981$		0			0
$982$	21.7718	−	13.4974i	0.694767	−	0.430719i
$983$	27.2657	−	15.7419i	0.869641	−	0.502088i	0.00241215	−	0.999997i	$-0.499232\pi$
$983$	27.2657	−	15.7419i	0.869641	−	0.502088i	0.867229	+	0.497910i	$0.165899\pi$
$984$		0			0
$985$	−13.8048	−	11.9216i	−0.439856	−	0.379853i
$986$	−47.7430	+	1.49764i	−1.52045	+	0.0476946i
$987$		0			0
$988$	47.9598	−	3.01185i	1.52581	−	0.0958196i
$989$			0.388795i			0.0123629i
$990$		0			0
$991$		−	30.7819i		−	0.977818i	−0.872335	−	0.488909i	$-0.837395\pi$
$991$		−	30.7819i		−	0.977818i	0.872335	−	0.488909i	$-0.162605\pi$
$992$	−26.9857	+	4.26616i	−0.856795	+	0.135451i
$993$		0			0
$994$	−0.498260	−	15.8839i	−0.0158039	−	0.503808i
$995$	−13.4190	+	15.5387i	−0.425410	+	0.492610i
$996$		0			0
$997$	29.1919	−	16.8539i	0.924516	−	0.533770i	0.0394432	−	0.999222i	$-0.487442\pi$
$997$	29.1919	−	16.8539i	0.924516	−	0.533770i	0.885073	+	0.465452i	$0.154108\pi$
$998$	17.1647	+	27.6873i	0.543338	+	0.876428i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	540.2.n.d.179.20		48
3.2	odd	2		180.2.n.d.59.5	✓	48
4.3	odd	2	inner	540.2.n.d.179.12		48
5.4	even	2	inner	540.2.n.d.179.5		48
9.2	odd	6	inner	540.2.n.d.359.13		48
9.7	even	3		180.2.n.d.119.12	yes	48
12.11	even	2		180.2.n.d.59.13	yes	48
15.2	even	4		900.2.r.g.851.17		48
15.8	even	4		900.2.r.g.851.8		48
15.14	odd	2		180.2.n.d.59.20	yes	48
20.19	odd	2	inner	540.2.n.d.179.13		48
36.7	odd	6		180.2.n.d.119.20	yes	48
36.11	even	6	inner	540.2.n.d.359.5		48
45.7	odd	12		900.2.r.g.551.24		48
45.29	odd	6	inner	540.2.n.d.359.12		48
45.34	even	6		180.2.n.d.119.13	yes	48
45.43	odd	12		900.2.r.g.551.1		48
60.23	odd	4		900.2.r.g.851.1		48
60.47	odd	4		900.2.r.g.851.24		48
60.59	even	2		180.2.n.d.59.12	yes	48
180.7	even	12		900.2.r.g.551.17		48
180.43	even	12		900.2.r.g.551.8		48
180.79	odd	6		180.2.n.d.119.5	yes	48
180.119	even	6	inner	540.2.n.d.359.20		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.n.d.59.5	✓	48	3.2	odd	2
180.2.n.d.59.12	yes	48	60.59	even	2
180.2.n.d.59.13	yes	48	12.11	even	2
180.2.n.d.59.20	yes	48	15.14	odd	2
180.2.n.d.119.5	yes	48	180.79	odd	6
180.2.n.d.119.12	yes	48	9.7	even	3
180.2.n.d.119.13	yes	48	45.34	even	6
180.2.n.d.119.20	yes	48	36.7	odd	6
540.2.n.d.179.5		48	5.4	even	2	inner
540.2.n.d.179.12		48	4.3	odd	2	inner
540.2.n.d.179.13		48	20.19	odd	2	inner
540.2.n.d.179.20		48	1.1	even	1	trivial
540.2.n.d.359.5		48	36.11	even	6	inner
540.2.n.d.359.12		48	45.29	odd	6	inner
540.2.n.d.359.13		48	9.2	odd	6	inner
540.2.n.d.359.20		48	180.119	even	6	inner
900.2.r.g.551.1		48	45.43	odd	12
900.2.r.g.551.8		48	180.43	even	12
900.2.r.g.551.17		48	180.7	even	12
900.2.r.g.551.24		48	45.7	odd	12
900.2.r.g.851.1		48	60.23	odd	4
900.2.r.g.851.8		48	15.8	even	4
900.2.r.g.851.17		48	15.2	even	4
900.2.r.g.851.24		48	60.47	odd	4

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:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	540.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.24631 + 0.668359i) q^{2} +(1.10659 + 1.66597i) q^{4} +(1.69235 + 1.46149i) q^{5} +(0.667441 + 1.15604i) q^{7} +(0.265693 + 2.81592i) q^{8} +(1.13240 + 2.95257i) q^{10} +(-2.18799 - 3.78971i) q^{11} +(3.56180 + 2.05641i) q^{13} +(0.0591892 + 1.88688i) q^{14} +(-1.55091 + 3.68710i) q^{16} -6.45392 q^{17} -5.84202i q^{19} +(-0.562053 + 4.43668i) q^{20} +(-0.194033 - 6.18554i) q^{22} +(-0.0875178 - 0.0505284i) q^{23} +(0.728104 + 4.94670i) q^{25} +(3.06470 + 4.94349i) q^{26} +(-1.18735 + 2.39120i) q^{28} +(4.53226 - 2.61670i) q^{29} +(4.18262 + 2.41484i) q^{31} +(-4.39722 + 3.55871i) q^{32} +(-8.04361 - 4.31354i) q^{34} +(-0.559997 + 2.93189i) q^{35} +3.24337i q^{37} +(3.90457 - 7.28098i) q^{38} +(-3.66579 + 5.15383i) q^{40} +(-3.50518 - 2.02372i) q^{41} +(-1.92364 - 3.33185i) q^{43} +(3.89233 - 7.83880i) q^{44} +(-0.0753035 - 0.121468i) q^{46} +(3.00768 - 1.73649i) q^{47} +(2.60904 - 4.51900i) q^{49} +(-2.39873 + 6.65177i) q^{50} +(0.515549 + 8.20946i) q^{52} +2.77476 q^{53} +(1.83577 - 9.61125i) q^{55} +(-3.07799 + 2.18661i) q^{56} +(7.39751 - 0.232051i) q^{58} +(1.37318 - 2.37841i) q^{59} +(1.04419 + 1.80858i) q^{61} +(3.59888 + 5.80514i) q^{62} +(-7.85881 + 1.49634i) q^{64} +(3.02241 + 8.68570i) q^{65} +(-0.216298 + 0.374638i) q^{67} +(-7.14186 - 10.7520i) q^{68} +(-2.65749 + 3.27977i) q^{70} -8.41810 q^{71} -7.28163i q^{73} +(-2.16773 + 4.04225i) q^{74} +(9.73262 - 6.46473i) q^{76} +(2.92071 - 5.05882i) q^{77} +(2.58753 - 1.49391i) q^{79} +(-8.01333 + 3.97323i) q^{80} +(-3.01598 - 4.86490i) q^{82} +(-11.6096 + 6.70282i) q^{83} +(-10.9223 - 9.43234i) q^{85} +(-0.170590 - 5.43821i) q^{86} +(10.0902 - 7.16812i) q^{88} -6.97377i q^{89} +5.49013i q^{91} +(-0.0126677 - 0.201716i) q^{92} +(4.90911 - 0.153993i) q^{94} +(8.53804 - 9.88674i) q^{95} +(2.08608 - 1.20440i) q^{97} +(6.27200 - 3.88831i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{4} + 18 q^{5} - 16 q^{10} + 42 q^{14} + 30 q^{16} - 26 q^{25} - 4 q^{34} + 10 q^{40} - 96 q^{41} + 4 q^{46} + 32 q^{49} + 90 q^{50} - 6 q^{56} + 8 q^{61} - 20 q^{64} + 6 q^{65} + 4 q^{70} - 72 q^{74}+ \cdots - 62 q^{94}+O(q^{100}) \) 48 * q - 2 * q^4 + 18 * q^5 - 16 * q^10 + 42 * q^14 + 30 * q^16 - 26 * q^25 - 4 * q^34 + 10 * q^40 - 96 * q^41 + 4 * q^46 + 32 * q^49 + 90 * q^50 - 6 * q^56 + 8 * q^61 - 20 * q^64 + 6 * q^65 + 4 * q^70 - 72 * q^74 - 4 * q^85 - 108 * q^86 - 62 * q^94

Introduction

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