LMFDB - Embedded newform 540.2.n.d.179.5

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			179.5
Character	$\chi$	$=$	540.179
Dual form			540.2.n.d.359.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.24631 - 0.668359i) q^{2} +(1.10659 + 1.66597i) q^{4} +(2.11186 + 0.734875i) q^{5} +(-0.667441 - 1.15604i) q^{7} +(-0.265693 - 2.81592i) q^{8} +(-2.14088 - 2.32737i) q^{10} +(-2.18799 - 3.78971i) q^{11} +(-3.56180 - 2.05641i) q^{13} +(0.0591892 + 1.88688i) q^{14} +(-1.55091 + 3.68710i) q^{16} +6.45392 q^{17} -5.84202i q^{19} +(1.11269 + 4.33150i) q^{20} +(0.194033 + 6.18554i) q^{22} +(0.0875178 + 0.0505284i) q^{23} +(3.91992 + 3.10391i) q^{25} +(3.06470 + 4.94349i) q^{26} +(1.18735 - 2.39120i) q^{28} +(4.53226 - 2.61670i) q^{29} +(4.18262 + 2.41484i) q^{31} +(4.39722 - 3.55871i) q^{32} +(-8.04361 - 4.31354i) q^{34} +(-0.559997 - 2.93189i) q^{35} -3.24337i q^{37} +(-3.90457 + 7.28098i) q^{38} +(1.50824 - 6.14209i) q^{40} +(-3.50518 - 2.02372i) q^{41} +(1.92364 + 3.33185i) q^{43} +(3.89233 - 7.83880i) q^{44} +(-0.0753035 - 0.121468i) q^{46} +(-3.00768 + 1.73649i) q^{47} +(2.60904 - 4.51900i) q^{49} +(-2.81092 - 6.48835i) q^{50} +(-0.515549 - 8.20946i) q^{52} -2.77476 q^{53} +(-1.83577 - 9.61125i) q^{55} +(-3.07799 + 2.18661i) q^{56} +(-7.39751 + 0.232051i) q^{58} +(1.37318 - 2.37841i) q^{59} +(1.04419 + 1.80858i) q^{61} +(-3.59888 - 5.80514i) q^{62} +(-7.85881 + 1.49634i) q^{64} +(-6.01084 - 6.96033i) q^{65} +(0.216298 - 0.374638i) q^{67} +(7.14186 + 10.7520i) q^{68} +(-1.26162 + 4.02833i) q^{70} -8.41810 q^{71} +7.28163i q^{73} +(-2.16773 + 4.04225i) q^{74} +(9.73262 - 6.46473i) q^{76} +(-2.92071 + 5.05882i) q^{77} +(2.58753 - 1.49391i) q^{79} +(-5.98486 + 6.64691i) q^{80} +(3.01598 + 4.86490i) q^{82} +(11.6096 - 6.70282i) q^{83} +(13.6298 + 4.74283i) q^{85} +(-0.170590 - 5.43821i) q^{86} +(-10.0902 + 7.16812i) q^{88} -6.97377i q^{89} +5.49013i q^{91} +(0.0126677 + 0.201716i) q^{92} +(4.90911 - 0.153993i) q^{94} +(4.29315 - 12.3375i) q^{95} +(-2.08608 + 1.20440i) q^{97} +(-6.27200 + 3.88831i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	2.11186	+	0.734875i	0.944453	+	0.328646i
$5$	2.11186	+	0.734875i	0.944453	+	0.328646i
$6$		0			0
$7$	−0.667441	−	1.15604i	−0.252269	−	0.436943i	0.711881	−	0.702300i	$-0.247843\pi$
$7$	−0.667441	−	1.15604i	−0.252269	−	0.436943i	−0.964150	+	0.265357i	$0.914510\pi$
$8$	−0.265693	−	2.81592i	−0.0939368	−	0.995578i
$9$		0			0
$10$	−2.14088	−	2.32737i	−0.677006	−	0.735978i
$11$	−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	−0.0832309	−	0.996530i	$-0.526524\pi$
$13$	−3.56180	−	2.05641i	−0.987867	−	0.570345i	−0.904636	+	0.426185i	$0.859857\pi$
$14$	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	$-0.213866\pi$
$17$	6.45392			1.56531			0.782653	+	0.622458i	$0.213866\pi$
$18$		0			0
$19$		−	5.84202i		−	1.34025i	−0.742248	−	0.670125i	$-0.766240\pi$
$19$		−	5.84202i		−	1.34025i	0.742248	−	0.670125i	$-0.233760\pi$
$20$	1.11269	+	4.33150i	0.248805	+	0.968554i
$21$		0			0
$22$	0.194033	+	6.18554i	0.0413679	+	1.31876i
$23$	0.0875178	+	0.0505284i	0.0182487	+	0.0105359i	0.509097	−	0.860709i	$-0.329980\pi$
$23$	0.0875178	+	0.0505284i	0.0182487	+	0.0105359i	−0.490848	+	0.871245i	$0.663313\pi$
$24$		0			0
$25$	3.91992	+	3.10391i	0.783984	+	0.620782i
$26$	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	$-0.914099\pi$
$37$		−	3.24337i		−	0.533206i	0.963806	−	0.266603i	$-0.0859013\pi$
$38$	−3.90457	+	7.28098i	−0.633404	+	1.18113i
$39$		0			0
$40$	1.50824	−	6.14209i	0.238474	−	0.971149i
$41$	−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	0.974600	−	0.223951i	$-0.0718957\pi$
$43$	1.92364	+	3.33185i	0.293353	+	0.508102i	−0.681248	+	0.732053i	$0.738562\pi$
$44$	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	−0.703053	−	0.711138i	$-0.748180\pi$
$47$	−3.00768	+	1.73649i	−0.438715	+	0.253292i	0.264337	+	0.964430i	$0.414847\pi$
$48$		0			0
$49$	2.60904	−	4.51900i	0.372721	−	0.645571i
$50$	−2.81092	−	6.48835i	−0.397524	−	0.917592i
$51$		0			0
$52$	−0.515549	−	8.20946i	−0.0714938	−	1.13845i
$53$	−2.77476			−0.381143			−0.190571	−	0.981673i	$-0.561034\pi$
$53$	−2.77476			−0.381143			−0.190571	+	0.981673i	$0.561034\pi$
$54$		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
$65$	−6.01084	−	6.96033i	−0.745552	−	0.863323i
$66$		0			0
$67$	0.216298	−	0.374638i	0.0264250	−	0.0457694i	−0.852511	−	0.522710i	$-0.824921\pi$
$67$	0.216298	−	0.374638i	0.0264250	−	0.0457694i	0.878935	+	0.476941i	$0.158254\pi$
$68$	7.14186	+	10.7520i	0.866078	+	1.30388i
$69$		0			0
$70$	−1.26162	+	4.02833i	−0.150793	+	0.481477i
$71$	−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	$0.140122\pi$
$73$			7.28163i			0.852250i	−0.904664	+	0.426125i	$0.859878\pi$
$74$	−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	$0.279577\pi$
$80$	−5.98486	+	6.64691i	−0.669128	+	0.743147i
$81$		0			0
$82$	3.01598	+	4.86490i	0.333059	+	0.537238i
$83$	11.6096	−	6.70282i	1.27432	−	0.735730i	0.298524	−	0.954402i	$-0.403506\pi$
$83$	11.6096	−	6.70282i	1.27432	−	0.735730i	0.975798	+	0.218672i	$0.0701724\pi$
$84$		0			0
$85$	13.6298	+	4.74283i	1.47836	+	0.514432i
$86$	−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
$95$	4.29315	−	12.3375i	0.440468	−	1.26580i
$96$		0			0
$97$	−2.08608	+	1.20440i	−0.211809	+	0.122288i	−0.602152	−	0.798382i	$-0.705690\pi$
$97$	−2.08608	+	1.20440i	−0.211809	+	0.122288i	0.390343	+	0.920670i	$0.372356\pi$
$98$	−6.27200	+	3.88831i	−0.633568	+	0.392778i
$99$		0			0
$100$	−0.833267	+	9.96522i	−0.0833267	+	0.996522i
$101$	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	−0.946005	−	0.324153i	$-0.894921\pi$
$103$	−1.95140	+	3.37992i	−0.192277	+	0.333034i	0.753727	+	0.657187i	$0.228254\pi$
$104$	−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	$0.0775142\pi$
$107$			4.98830i			0.482237i	−0.970496	+	0.241118i	$0.922486\pi$
$108$		0			0
$109$	−4.98669			−0.477638			−0.238819	−	0.971064i	$-0.576760\pi$
$109$	−4.98669			−0.477638			−0.238819	+	0.971064i	$0.576760\pi$
$110$	−4.13582	+	13.2056i	−0.394335	+	1.25910i
$111$		0			0
$112$	5.29758	−	0.668004i	0.500574	−	0.0631204i
$113$	−10.2057	+	17.6768i	−0.960073	+	1.66290i	−0.237767	+	0.971322i	$0.576416\pi$
$113$	−10.2057	+	17.6768i	−0.960073	+	1.66290i	−0.722306	+	0.691574i	$0.756918\pi$
$114$		0			0
$115$	0.147693	+	0.171024i	0.0137725	+	0.0159480i
$116$	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	$-0.175923\pi$
$127$	19.1833			1.70224			0.851122	+	0.524968i	$0.175923\pi$
$128$	10.7946	+	3.38760i	0.954120	+	0.299424i
$129$		0			0
$130$	2.83938	+	12.6921i	0.249030	+	1.11318i
$131$	−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	0.709102	−	0.705106i	$-0.249101\pi$
$137$	−2.99744	−	5.19172i	−0.256089	−	0.443559i	−0.965191	+	0.261547i	$0.915767\pi$
$138$		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	$0.669881\pi$
$140$	4.26475	−	4.17734i	0.360437	−	0.353050i
$141$		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
$155$	7.05852	+	8.17351i	0.566954	+	0.656512i
$156$		0			0
$157$	−2.77448	−	1.60184i	−0.221427	−	0.127841i	0.385184	−	0.922840i	$-0.374138\pi$
$157$	−2.77448	−	1.60184i	−0.221427	−	0.127841i	−0.606611	+	0.794999i	$0.707471\pi$
$158$	−4.22334	+	0.132481i	−0.335991	+	0.0105396i
$159$		0			0
$160$	11.9015	−	4.28410i	0.940899	−	0.338688i
$161$		−	0.134899i		−	0.0106315i
$162$		0			0
$163$	−10.6182			−0.831684			−0.415842	−	0.909437i	$-0.636513\pi$
$163$	−10.6182			−0.831684			−0.415842	+	0.909437i	$0.636513\pi$
$164$	−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	0.0143236	−	0.999897i	$-0.495440\pi$
$167$	−10.9127	−	6.30046i	−0.844451	−	0.487544i	−0.858775	+	0.512353i	$0.828774\pi$
$168$		0			0
$169$	1.95764	+	3.39073i	0.150587	+	0.260825i
$170$	−13.8171	−	15.0206i	−1.05972	−	1.15203i
$171$		0			0
$172$	−3.42207	+	6.89172i	−0.260930	+	0.525489i
$173$	−0.858165	−	1.48639i	−0.0652451	−	0.113008i	0.831558	−	0.555439i	$-0.187450\pi$
$173$	−0.858165	−	1.48639i	−0.0652451	−	0.113008i	−0.896803	+	0.442431i	$0.854116\pi$
$174$		0			0
$175$	0.971933	−	6.60327i	0.0734712	−	0.499160i
$176$	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
$185$	2.38347	−	6.84954i	0.175236	−	0.503588i
$186$		0			0
$187$	−14.1211	−	24.4585i	−1.03264	−	1.78859i
$188$	−6.22121	−	3.08912i	−0.453728	−	0.225298i
$189$		0			0
$190$	−13.5965	+	12.5071i	−0.986395	+	0.907357i
$191$	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	0.139519	−	0.990219i	$-0.455444\pi$
$193$	−9.00614	−	5.19970i	−0.648276	−	0.374282i	−0.787795	+	0.615937i	$0.788778\pi$
$194$	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	$-0.406150\pi$
$197$	8.15715			0.581173			0.290586	+	0.956849i	$0.406150\pi$
$198$		0			0
$199$			9.18172i			0.650875i	0.945564	+	0.325438i	$0.105512\pi$
$199$			9.18172i			0.650875i	−0.945564	+	0.325438i	$0.894488\pi$
$200$	7.69886	−	11.8629i	0.544392	−	0.838831i
$201$		0			0
$202$	−6.40988	+	0.201070i	−0.450998	+	0.0141473i
$203$	−6.05004	−	3.49299i	−0.424629	−	0.245160i
$204$		0			0
$205$	−5.91527	−	6.84967i	−0.413141	−	0.478402i
$206$	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
$220$	13.9806	−	13.6941i	0.942572	−	0.923254i
$221$	−22.9876	−	13.2719i	−1.54631	−	0.892765i
$222$		0			0
$223$	11.6245	+	20.1343i	0.778436	+	1.34829i	0.932843	+	0.360283i	$0.117320\pi$
$223$	11.6245	+	20.1343i	0.778436	+	1.34829i	−0.154407	+	0.988007i	$0.549347\pi$
$224$	−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	0.0763513	−	0.997081i	$-0.475673\pi$
$227$	14.7354	−	8.50750i	0.978024	−	0.564663i	0.901673	+	0.432418i	$0.142340\pi$
$228$		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	$0.182463\pi$
$230$	−0.0697670	−	0.311861i	−0.00460030	−	0.0205635i
$231$		0			0
$232$	−8.57262	−	12.0672i	−0.562820	−	0.792253i
$233$	13.5483			0.887579			0.443789	−	0.896131i	$-0.353634\pi$
$233$	13.5483			0.887579			0.443789	+	0.896131i	$0.353634\pi$
$234$		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
$245$	8.83084	−	7.62617i	0.564181	−	0.487218i
$246$		0			0
$247$	−12.0136	+	20.8081i	−0.764406	+	1.32399i
$248$	5.68870	−	12.4195i	0.361233	−	0.788642i
$249$		0			0
$250$	−1.16814	−	15.7682i	−0.0738799	−	0.997267i
$251$	−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	−0.736617	−	0.676310i	$-0.763578\pi$
$257$	3.48508	−	6.03633i	0.217393	−	0.376536i	0.954010	+	0.299774i	$0.0969113\pi$
$258$		0			0
$259$	−3.74947	+	2.16476i	−0.232981	+	0.134511i
$260$	4.94416	−	17.7161i	0.306624	−	1.09871i
$261$		0			0
$262$	20.2276	−	12.5400i	1.24966	−	0.774725i
$263$	−13.9809	+	8.07190i	−0.862102	+	0.497735i	−0.864716	−	0.502262i	$-0.832501\pi$
$263$	−13.9809	+	8.07190i	−0.862102	+	0.497735i	0.00261352	+	0.999997i	$0.499168\pi$
$264$		0			0
$265$	−5.85991	−	2.03910i	−0.359971	−	0.125261i
$266$	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
$275$	3.18617	−	21.6467i	0.192133	−	1.30535i
$276$		0			0
$277$	11.2614	−	6.50177i	0.676632	−	0.390654i	−0.121953	−	0.992536i	$-0.538916\pi$
$277$	11.2614	−	6.50177i	0.676632	−	0.390654i	0.798585	+	0.601882i	$0.205582\pi$
$278$	0.177400	+	0.286153i	0.0106397	+	0.0171623i
$279$		0			0
$280$	−8.10717	+	2.35589i	−0.484496	+	0.140791i
$281$	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	$-0.498212\pi$
$283$	14.6158	−	25.3154i	0.868821	−	1.50484i	0.863202	−	0.504858i	$-0.168455\pi$
$284$	−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
$290$	−15.7930	−	4.94619i	−0.927400	−	0.290450i
$291$		0			0
$292$	−12.1310	+	8.05779i	−0.709911	+	0.471547i
$293$	2.81552	−	4.87662i	0.164484	−	0.284895i	−0.771988	−	0.635637i	$-0.780737\pi$
$293$	2.81552	−	4.87662i	0.164484	−	0.284895i	0.936472	+	0.350742i	$0.114071\pi$
$294$		0			0
$295$	4.64779	−	4.01376i	0.270605	−	0.233690i
$296$	−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	$-0.643751\pi$
$307$	−15.2931			−0.872826			−0.436413	+	0.899747i	$0.643751\pi$
$308$	−11.6599	+	0.732233i	−0.664384	+	0.0417229i
$309$		0			0
$310$	−3.33428	−	14.9044i	−0.189374	−	0.846512i
$311$	−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	0.243842	−	0.969815i	$-0.421592\pi$
$313$	21.3301	−	12.3149i	1.20565	−	0.696081i	0.961805	+	0.273734i	$0.0882588\pi$
$314$	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	0.676859	−	0.736113i	$-0.263341\pi$
$317$	−5.32466	−	9.22258i	−0.299063	−	0.517992i	−0.975922	+	0.218121i	$0.930007\pi$
$318$		0			0
$319$	−19.8331	−	11.4506i	−1.11044	−	0.641113i
$320$	−17.6964	−	2.61518i	−0.989256	−	0.146193i
$321$		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
$335$	0.732103	−	0.632233i	0.0399990	−	0.0345426i
$336$		0			0
$337$	20.3763	+	11.7643i	1.10997	+	0.640841i	0.938821	−	0.344405i	$-0.111919\pi$
$337$	20.3763	+	11.7643i	1.10997	+	0.640841i	0.171147	+	0.985245i	$0.445253\pi$
$338$	−0.173605	−	5.53431i	−0.00944284	−	0.301027i
$339$		0			0
$340$	7.18121	+	27.9552i	0.389456	+	1.51608i
$341$		−	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	0.594297	−	0.804246i	$-0.297431\pi$
$347$	3.63147	+	2.09663i	0.194947	+	0.112553i	−0.399349	+	0.916799i	$0.630764\pi$
$348$		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	$0.785755\pi$
$350$	−5.62469	+	7.58014i	−0.300652	+	0.405175i
$351$		0			0
$352$	−23.1076	−	8.87779i	−1.23164	−	0.473188i
$353$	−5.51109	−	9.54549i	−0.293326	−	0.508055i	0.681268	−	0.732034i	$-0.261429\pi$
$353$	−5.51109	−	9.54549i	−0.293326	−	0.508055i	−0.974594	+	0.223979i	$0.928095\pi$
$354$		0			0
$355$	−17.7779	−	6.18625i	−0.943550	−	0.328332i
$356$	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
$365$	−5.35109	+	15.3778i	−0.280089	+	0.804910i
$366$		0			0
$367$	15.7443	+	27.2699i	0.821846	+	1.42348i	0.904306	+	0.426885i	$0.140389\pi$
$367$	15.7443	+	27.2699i	0.821846	+	1.42348i	−0.0824597	+	0.996594i	$0.526278\pi$
$368$	−0.322035	+	0.244322i	−0.0167873	+	0.0127361i
$369$		0			0
$370$	−7.54850	+	6.94366i	−0.392428	+	0.360984i
$371$	1.85199	+	3.20774i	0.0961505	+	0.166538i
$372$		0			0
$373$	−20.2988	−	11.7195i	−1.05103	−	0.606812i	−0.128092	−	0.991762i	$-0.540885\pi$
$373$	−20.2988	−	11.7195i	−1.05103	−	0.606812i	−0.922937	+	0.384950i	$0.874219\pi$
$374$	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	$-0.0958918\pi$
$380$	25.3047	−	6.50035i	1.29810	−	0.333461i
$381$		0			0
$382$	−0.959787	−	30.5969i	−0.0491070	−	1.56547i
$383$	22.7016	+	13.1068i	1.16000	+	0.669725i	0.951304	−	0.308256i	$-0.0997452\pi$
$383$	22.7016	+	13.1068i	1.16000	+	0.669725i	0.208695	+	0.977981i	$0.433079\pi$
$384$		0			0
$385$	−9.88575	+	8.53718i	−0.503824	+	0.435095i
$386$	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	$0.225599\pi$
$397$			25.9373i			1.30176i	−0.759182	+	0.650879i	$0.774401\pi$
$398$	6.13669	−	11.4433i	0.307605	−	0.573601i
$399$		0			0
$400$	−17.5238	+	9.63924i	−0.876192	+	0.481962i
$401$	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	$0.989447\pi$
$410$	2.79424	+	12.4904i	0.137998	+	0.616855i
$411$		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
$425$	25.2989	+	20.0324i	1.22717	+	0.971713i
$426$		0			0
$427$	1.39387	−	2.41425i	0.0674540	−	0.116834i
$428$	−8.31035	+	5.52001i	−0.401696	+	0.266820i
$429$		0			0
$430$	3.63614	−	11.6101i	0.175350	−	0.559889i
$431$	−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	$0.200399\pi$
$433$			24.5043i			1.17760i	−0.808279	+	0.588800i	$0.799601\pi$
$434$	−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	$0.194086\pi$
$440$	−26.5768	+	7.72303i	−1.26700	+	0.368181i
$441$		0			0
$442$	19.7794	+	31.9049i	0.940808	+	1.51756i
$443$	−6.08715	+	3.51442i	−0.289209	+	0.166975i	−0.637585	−	0.770380i	$-0.720067\pi$
$443$	−6.08715	+	3.51442i	−0.289209	+	0.166975i	0.348376	+	0.937355i	$0.386733\pi$
$444$		0			0
$445$	5.12485	−	14.7276i	0.242941	−	0.698157i
$446$	−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
$455$	−4.03456	+	11.5944i	−0.189143	+	0.543554i
$456$		0			0
$457$	−25.7193	+	14.8490i	−1.20310	+	0.694608i	−0.961242	−	0.275704i	$-0.911089\pi$
$457$	−25.7193	+	14.8490i	−1.20310	+	0.694608i	−0.241854	+	0.970313i	$0.577756\pi$
$458$	1.80460	−	1.11876i	0.0843236	−	0.0522762i
$459$		0			0
$460$	−0.121484	+	0.435306i	−0.00566422	+	0.0202963i
$461$	−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	−0.924714	−	0.380664i	$-0.875696\pi$
$463$	−2.85520	+	4.94535i	−0.132692	+	0.229830i	0.792021	+	0.610494i	$0.209029\pi$
$464$	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	$-0.856781\pi$
$467$		−	18.7968i		−	0.869813i	0.900476	−	0.434907i	$-0.143219\pi$
$468$		0			0
$469$	−0.577464			−0.0266648
$470$	10.4805	+	3.28237i	0.483430	+	0.151404i
$471$		0			0
$472$	−7.06225	−	3.23482i	−0.325067	−	0.148895i
$473$	8.41783	−	14.5801i	0.387052	−	0.670394i
$474$		0			0
$475$	18.1331	−	22.9002i	0.832003	−	1.05073i
$476$	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	$-0.473437\pi$
$487$	3.67889			0.166706			0.0833532	+	0.996520i	$0.473437\pi$
$488$	4.81540	−	3.42088i	0.217983	−	0.154856i
$489$		0			0
$490$	−16.1030	+	3.60243i	−0.727460	+	0.162741i
$491$	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	$0.494239\pi$
$500$	−9.08293	+	20.4328i	−0.406201	+	0.913784i
$501$		0			0
$502$	16.4274	+	8.80951i	0.733191	+	0.393188i
$503$			31.1266i			1.38787i	0.720039	+	0.693934i	$0.244124\pi$
$503$			31.1266i			1.38787i	−0.720039	+	0.693934i	$0.755876\pi$
$504$		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
$515$	−6.60491	+	5.70390i	−0.291047	+	0.251344i
$516$		0			0
$517$	13.1616	+	7.59884i	0.578845	+	0.334196i
$518$	6.11985	−	0.191972i	0.268891	−	0.00843477i
$519$		0			0
$520$	−18.0027	+	18.7753i	−0.789471	+	0.823353i
$521$			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	$-0.358874\pi$
$523$	19.6207			0.857954			0.428977	+	0.903315i	$0.358874\pi$
$524$	−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
$530$	5.94043	+	6.45788i	0.258036	+	0.280513i
$531$		0			0
$532$	−13.9695	−	6.93650i	−0.605653	−	0.300735i
$533$	8.32317	+	14.4162i	0.360517	+	0.624433i
$534$		0			0
$535$	−3.66577	+	10.5346i	−0.158485	+	0.455450i
$536$	−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
$545$	−10.5312	−	3.66459i	−0.451107	−	0.156974i
$546$		0			0
$547$	−1.44201	−	2.49763i	−0.0616557	−	0.106791i	0.833550	−	0.552444i	$-0.186305\pi$
$547$	−1.44201	−	2.49763i	−0.0616557	−	0.106791i	−0.895206	+	0.445653i	$0.852971\pi$
$548$	5.33231	−	10.7388i	0.227785	−	0.458737i
$549$		0			0
$550$	−18.4387	+	24.8491i	−0.786230	+	1.05957i
$551$	−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	$-0.617646\pi$
$557$	−17.0510			−0.722475			−0.361237	+	0.932474i	$0.617646\pi$
$558$		0			0
$559$		−	15.8232i		−	0.669249i
$560$	11.6787	+	2.48233i	0.493513	+	0.104897i
$561$		0			0
$562$	−1.52886	+	0.0479585i	−0.0644910	+	0.00202301i
$563$	−19.0842	−	11.0182i	−0.804302	−	0.464364i	0.0406715	−	0.999173i	$-0.487050\pi$
$563$	−19.0842	−	11.0182i	−0.804302	−	0.464364i	−0.844973	+	0.534809i	$0.820384\pi$
$564$		0			0
$565$	−34.5433	+	29.8311i	−1.45325	+	1.25500i
$566$	−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	$-0.743807\pi$
$577$		−	34.6251i		−	1.44146i	0.693216	−	0.720730i	$-0.256193\pi$
$578$	−30.7255	−	16.4772i	−1.27801	−	0.685359i
$579$		0			0
$580$	16.3773	+	16.7199i	0.680028	+	0.694257i
$581$	−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	−0.293022	−	0.956106i	$-0.594661\pi$
$587$	9.41209	−	5.43407i	0.388479	−	0.224288i	0.681501	+	0.731817i	$0.261328\pi$
$588$		0			0
$589$	14.1075	−	24.4350i	0.581291	−	1.00683i
$590$	−8.47523	+	1.89601i	−0.348920	+	0.0780574i
$591$		0			0
$592$	11.9586	+	5.03017i	0.491496	+	0.206739i
$593$	4.49540			0.184604			0.0923019	−	0.995731i	$-0.470578\pi$
$593$	4.49540			0.184604			0.0923019	+	0.995731i	$0.470578\pi$
$594$		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
$605$	−13.7914	+	11.9100i	−0.560700	+	0.484212i
$606$		0			0
$607$	9.81362	−	16.9977i	0.398322	−	0.689915i	−0.595197	−	0.803580i	$-0.702926\pi$
$607$	9.81362	−	16.9977i	0.398322	−	0.689915i	0.993519	+	0.113665i	$0.0362592\pi$
$608$	−20.7901	−	25.6887i	−0.843148	−	1.04181i
$609$		0			0
$610$	1.97376	−	6.30217i	0.0799152	−	0.255167i
$611$	14.2837			0.577857
$612$		0			0
$613$			28.8088i			1.16358i	0.813340	+	0.581788i	$0.197647\pi$
$613$			28.8088i			1.16358i	−0.813340	+	0.581788i	$0.802353\pi$
$614$	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	−0.981102	−	0.193493i	$-0.938018\pi$
$617$	−8.02269	+	13.8957i	−0.322981	+	0.559420i	0.658120	+	0.752913i	$0.271352\pi$
$618$		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	$0.349102\pi$
$620$	−5.80592	+	20.8040i	−0.233171	+	0.835509i
$621$		0			0
$622$	4.40924	−	2.73350i	0.176795	−	0.109603i
$623$	−8.06198	+	4.65458i	−0.322996	+	0.186482i
$624$		0			0
$625$	5.73152	+	24.3341i	0.229261	+	0.973365i
$626$	−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
$635$	40.5125	+	14.0973i	1.60769	+	0.559436i
$636$		0			0
$637$	−18.5858	+	10.7305i	−0.736397	+	0.425159i
$638$	17.0651	+	27.5267i	0.675614	+	1.08979i
$639$		0			0
$640$	20.3073	+	15.0868i	0.802717	+	0.596360i
$641$	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	$-0.590005\pi$
$643$	17.5507	−	30.3987i	0.692133	−	1.19881i	0.971138	−	0.238520i	$-0.0766621\pi$
$644$	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	$-0.877773\pi$
$647$		−	19.0579i		−	0.749243i	0.927178	−	0.374621i	$-0.122227\pi$
$648$		0			0
$649$	−12.0180			−0.471747
$650$	−3.33076	+	28.8906i	−0.130643	+	1.13318i
$651$		0			0
$652$	−11.7500	−	17.6896i	−0.460167	−	0.692780i
$653$	21.0708	−	36.4956i	0.824563	−	1.42818i	−0.0776903	−	0.996978i	$-0.524755\pi$
$653$	21.0708	−	36.4956i	0.824563	−	1.42818i	0.902253	−	0.431207i	$-0.141912\pi$
$654$		0			0
$655$	−28.4800	+	24.5949i	−1.11281	+	0.961002i
$656$	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
$670$	−1.33499	+	0.298652i	−0.0515751	+	0.0115379i
$671$	4.56935	−	7.91434i	0.176398	−	0.305530i
$672$		0			0
$673$	19.8408	−	11.4551i	0.764806	−	0.441561i	−0.0662129	−	0.997806i	$-0.521092\pi$
$673$	19.8408	−	11.4551i	0.764806	−	0.441561i	0.831018	+	0.556245i	$0.187758\pi$
$674$	−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	0.998169	−	0.0604934i	$-0.0192674\pi$
$677$	11.6227	+	20.1311i	0.446696	+	0.773699i	−0.551473	+	0.834193i	$0.685934\pi$
$678$		0			0
$679$	2.78467	+	1.60773i	0.106866	+	0.0616989i
$680$	9.73408	−	39.6406i	0.373285	−	1.52015i
$681$		0			0
$682$	−14.1255	+	26.3403i	−0.540894	+	1.00862i
$683$		−	30.3578i		−	1.16161i	−0.814043	−	0.580804i	$-0.802738\pi$
$683$		−	30.3578i		−	1.16161i	0.814043	−	0.580804i	$-0.197262\pi$
$684$		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
$695$	−0.347936	−	0.402898i	−0.0131980	−	0.0152828i
$696$		0			0
$697$	−22.6222	−	13.0609i	−0.856875	−	0.494717i
$698$	−0.246708	−	7.86477i	−0.00933804	−	0.297686i
$699$		0			0
$700$	12.0764	−	5.68791i	0.456444	−	0.214983i
$701$		−	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	$0.662198\pi$
$710$	18.0221	+	19.5920i	0.676359	+	0.735274i
$711$		0			0
$712$	−19.6376	+	1.85289i	−0.735950	+	0.0694398i
$713$	0.244036	+	0.422683i	0.00913923	+	0.0158296i
$714$		0			0
$715$	−13.2260	+	38.0085i	−0.494625	+	1.42144i
$716$	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
$725$	25.8881	+	3.81046i	0.961460	+	0.141517i
$726$		0			0
$727$	−8.24957	−	14.2887i	−0.305960	−	0.529938i	0.671515	−	0.740991i	$-0.265644\pi$
$727$	−8.24957	−	14.2887i	−0.305960	−	0.529938i	−0.977475	+	0.211053i	$0.932311\pi$
$728$	15.4598	−	1.45869i	0.572977	−	0.0540627i
$729$		0			0
$730$	16.9470	−	15.5891i	0.627237	−	0.576978i
$731$	12.4150	+	21.5035i	0.459187	+	0.795335i
$732$		0			0
$733$	37.1399	+	21.4427i	1.37179	+	0.792006i	0.991154	−	0.132717i	$-0.0423702\pi$
$733$	37.1399	+	21.4427i	1.37179	+	0.792006i	0.380641	+	0.924723i	$0.375703\pi$
$734$	−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	$-0.0178341\pi$
$740$	14.0487	−	3.60886i	0.516439	−	0.132664i
$741$		0			0
$742$	−0.164236	−	5.23564i	−0.00602928	−	0.192207i
$743$	−35.0211	−	20.2194i	−1.28480	−	0.741779i	−0.307078	−	0.951684i	$-0.599351\pi$
$743$	−35.0211	−	20.2194i	−1.28480	−	0.741779i	−0.977722	+	0.209905i	$0.932684\pi$
$744$		0			0
$745$	14.9332	+	17.2921i	0.547109	+	0.633532i
$746$	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	$-0.803974\pi$
$757$		−	31.7859i		−	1.15528i	0.816293	−	0.577639i	$-0.196026\pi$
$758$	−7.72151	+	14.3986i	−0.280458	+	0.522979i
$759$		0			0
$760$	−35.8822	−	8.81117i	−1.30158	−	0.319615i
$761$	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	$0.185021\pi$
$770$	18.0266	−	4.03277i	0.649635	−	0.145331i
$771$		0			0
$772$	−1.30358	−	20.7579i	−0.0469170	−	0.747093i
$773$	−26.8609			−0.966121			−0.483060	−	0.875587i	$-0.660475\pi$
$773$	−26.8609			−0.966121			−0.483060	+	0.875587i	$0.660475\pi$
$774$		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
$785$	−4.68215	−	5.42177i	−0.167113	−	0.193511i
$786$		0			0
$787$	−16.8518	+	29.1883i	−0.600703	+	1.04045i	0.392011	+	0.919960i	$0.371779\pi$
$787$	−16.8518	+	29.1883i	−0.600703	+	1.04045i	−0.992715	+	0.120488i	$0.961554\pi$
$788$	9.02663	+	13.5896i	0.321560	+	0.484108i
$789$		0			0
$790$	−9.01646	−	2.82384i	−0.320791	−	0.100468i
$791$	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	$-0.662036\pi$
$797$	14.4698	−	25.0624i	0.512546	−	0.887755i	0.999894	−	0.0145477i	$-0.00463085\pi$
$798$		0			0
$799$	−19.4113	+	11.2071i	−0.686724	+	0.396480i
$800$	28.2827	−	0.301282i	0.999943	−	0.0106519i
$801$		0			0
$802$	−18.5323	−	29.8934i	−0.654398	−	1.05557i
$803$	27.5953	−	15.9322i	0.973817	−	0.562233i
$804$		0			0
$805$	0.0991340	−	0.284888i	0.00349401	−	0.0100410i
$806$	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
$815$	−22.4242	−	7.80307i	−0.785487	−	0.273330i
$816$		0			0
$817$	19.4647	−	11.2379i	0.680984	−	0.393166i
$818$	25.6907	−	15.9269i	0.898254	−	0.556870i
$819$		0			0
$820$	4.86555	−	17.4345i	0.169913	−	0.608838i
$821$	−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	$0.337099\pi$
$823$	−14.6369	+	25.3518i	−0.510210	+	0.883710i	−0.999930	+	0.0118300i	$0.996234\pi$
$824$	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	$0.140233\pi$
$827$			24.5270i			0.852886i	−0.904514	+	0.426443i	$0.859767\pi$
$828$		0			0
$829$	−42.2094			−1.46599			−0.732996	−	0.680233i	$-0.761879\pi$
$829$	−42.2094			−1.46599			−0.732996	+	0.680233i	$0.761879\pi$
$830$	−40.4547	−	12.6699i	−1.40420	−	0.439779i
$831$		0			0
$832$	31.0687	+	10.8313i	1.07711	+	0.375506i
$833$	16.8386	−	29.1653i	0.583422	−	1.01052i
$834$		0			0
$835$	−18.4161	−	21.3252i	−0.637315	−	0.737988i
$836$	−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
$850$	−18.1415	−	41.8753i	−0.622247	−	1.43631i
$851$	0.163882	−	0.283852i	0.00561781	−	0.00973033i
$852$		0			0
$853$	27.1128	−	15.6536i	0.928324	−	0.535968i	0.0420430	−	0.999116i	$-0.486613\pi$
$853$	27.1128	−	15.6536i	0.928324	−	0.535968i	0.886281	+	0.463148i	$0.153280\pi$
$854$	−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	0.933854	−	0.357654i	$-0.116423\pi$
$857$	4.60165	+	7.97029i	0.157189	+	0.272260i	−0.776665	+	0.629914i	$0.783090\pi$
$858$		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	$0.637627\pi$
$860$	−12.2915	+	12.0396i	−0.419136	+	0.410546i
$861$		0			0
$862$	43.7517	+	23.4627i	1.49019	+	0.799142i
$863$			19.0360i			0.647992i	0.946058	+	0.323996i	$0.105026\pi$
$863$			19.0360i			0.647992i	−0.946058	+	0.323996i	$0.894974\pi$
$864$		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
$875$	6.90516	−	13.2309i	0.233437	−	0.447287i
$876$		0			0
$877$	−21.1121	−	12.1891i	−0.712904	−	0.411595i	0.0992316	−	0.995064i	$-0.468362\pi$
$877$	−21.1121	−	12.1891i	−0.712904	−	0.411595i	−0.812135	+	0.583469i	$0.801695\pi$
$878$	−25.0934	+	0.787150i	−0.846862	+	0.0265650i
$879$		0			0
$880$	38.2847	+	8.13751i	1.29058	+	0.274316i
$881$			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	$-0.661440\pi$
$883$	−28.8663			−0.971427			−0.485713	+	0.874118i	$0.661440\pi$
$884$	−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	0.262717	−	0.964873i	$-0.415381\pi$
$887$	−13.1498	−	7.59206i	−0.441528	−	0.254917i	−0.704246	+	0.709956i	$0.748715\pi$
$888$		0			0
$889$	−12.8037	−	22.1767i	−0.429424	−	0.743784i
$890$	−16.2305	+	14.9300i	−0.544048	+	0.500455i
$891$		0			0
$892$	−20.6795	+	41.6465i	−0.692400	+	1.39443i
$893$	10.1446	+	17.5709i	0.339475	+	0.587989i
$894$		0			0
$895$	39.4136	+	13.7149i	1.31745	+	0.458440i
$896$	−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
$905$	−42.0855	−	14.6447i	−1.39897	−	0.486806i
$906$		0			0
$907$	13.5599	+	23.4865i	0.450250	+	0.779856i	0.998401	−	0.0565230i	$-0.0180014\pi$
$907$	13.5599	+	23.4865i	0.450250	+	0.779856i	−0.548151	+	0.836379i	$0.684668\pi$
$908$	30.4793	+	15.1344i	1.01149	+	0.502254i
$909$		0			0
$910$	12.7775	−	11.7537i	0.423571	−	0.389632i
$911$	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	$0.811975\pi$
$920$	0.442348	−	0.461333i	0.0145838	−	0.0152097i
$921$		0			0
$922$	20.0183	−	0.627948i	0.659266	−	0.0206804i
$923$	29.9836	+	17.3110i	0.986923	+	0.569800i
$924$		0			0
$925$	10.0671	−	12.7137i	0.331005	−	0.418025i
$926$	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	$0.253439\pi$
$937$			43.7549i			1.42941i	−0.699425	+	0.714706i	$0.746561\pi$
$938$	0.719701	+	0.385953i	0.0234991	+	0.0126018i
$939$		0			0
$940$	−10.8682	−	11.0956i	−0.354482	−	0.361899i
$941$	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	−0.923344	−	0.383973i	$-0.874555\pi$
$947$	−32.3885	+	18.6995i	−1.05249	+	0.607653i	−0.129141	+	0.991626i	$0.541222\pi$
$948$		0			0
$949$	14.9740	−	25.9357i	0.486077	−	0.841910i
$950$	−37.9051	+	16.4214i	−1.22980	+	0.532782i
$951$		0			0
$952$	−19.8651	+	14.1122i	−0.643832	+	0.457381i
$953$	−22.8733			−0.740937			−0.370469	−	0.928845i	$-0.620803\pi$
$953$	−22.8733			−0.740937			−0.370469	+	0.928845i	$0.620803\pi$
$954$		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
$965$	−15.1986	−	17.5994i	−0.489260	−	0.566545i
$966$		0			0
$967$	29.1950	−	50.5672i	0.938848	−	1.62613i	0.171223	−	0.985232i	$-0.445228\pi$
$967$	29.1950	−	50.5672i	0.938848	−	1.62613i	0.767625	−	0.640899i	$-0.221438\pi$
$968$	20.9558	+	9.59870i	0.673546	+	0.308514i
$969$		0			0
$970$	7.26911	+	2.27659i	0.233397	+	0.0730970i
$971$	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	−0.779185	−	0.626794i	$-0.784367\pi$
$977$	4.78940	−	8.29548i	0.153226	−	0.265396i	0.932412	+	0.361398i	$0.117700\pi$
$978$		0			0
$979$	−26.4286	+	15.2586i	−0.844662	+	0.487666i
$980$	22.4771	+	6.27284i	0.718005	+	0.200379i
$981$		0			0
$982$	−21.7718	+	13.4974i	−0.694767	+	0.430719i
$983$	−27.2657	+	15.7419i	−0.869641	+	0.502088i	−0.867229	−	0.497910i	$-0.834101\pi$
$983$	−27.2657	+	15.7419i	−0.869641	+	0.502088i	−0.00241215	+	0.999997i	$0.500768\pi$
$984$		0			0
$985$	17.2268	+	5.99448i	0.548890	+	0.191000i
$986$	−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
$995$	−6.74742	+	19.3905i	−0.213908	+	0.614721i
$996$		0			0
$997$	−29.1919	+	16.8539i	−0.924516	+	0.533770i	−0.885073	−	0.465452i	$-0.845892\pi$
$997$	−29.1919	+	16.8539i	−0.924516	+	0.533770i	−0.0394432	+	0.999222i	$0.512558\pi$
$998$	−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.179.5		48
3.2	odd	2		180.2.n.d.59.20	yes	48
4.3	odd	2	inner	540.2.n.d.179.13		48
5.4	even	2	inner	540.2.n.d.179.20		48
9.2	odd	6	inner	540.2.n.d.359.12		48
9.7	even	3		180.2.n.d.119.13	yes	48
12.11	even	2		180.2.n.d.59.12	yes	48
15.2	even	4		900.2.r.g.851.8		48
15.8	even	4		900.2.r.g.851.17		48
15.14	odd	2		180.2.n.d.59.5	✓	48
20.19	odd	2	inner	540.2.n.d.179.12		48
36.7	odd	6		180.2.n.d.119.5	yes	48
36.11	even	6	inner	540.2.n.d.359.20		48
45.7	odd	12		900.2.r.g.551.1		48
45.29	odd	6	inner	540.2.n.d.359.13		48
45.34	even	6		180.2.n.d.119.12	yes	48
45.43	odd	12		900.2.r.g.551.24		48
60.23	odd	4		900.2.r.g.851.24		48
60.47	odd	4		900.2.r.g.851.1		48
60.59	even	2		180.2.n.d.59.13	yes	48
180.7	even	12		900.2.r.g.551.8		48
180.43	even	12		900.2.r.g.551.17		48
180.79	odd	6		180.2.n.d.119.20	yes	48
180.119	even	6	inner	540.2.n.d.359.5		48

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

\(f(q)\)	\(=\)	\(q+(-1.24631 - 0.668359i) q^{2} +(1.10659 + 1.66597i) q^{4} +(2.11186 + 0.734875i) q^{5} +(-0.667441 - 1.15604i) q^{7} +(-0.265693 - 2.81592i) q^{8} +(-2.14088 - 2.32737i) q^{10} +(-2.18799 - 3.78971i) q^{11} +(-3.56180 - 2.05641i) q^{13} +(0.0591892 + 1.88688i) q^{14} +(-1.55091 + 3.68710i) q^{16} +6.45392 q^{17} -5.84202i q^{19} +(1.11269 + 4.33150i) q^{20} +(0.194033 + 6.18554i) q^{22} +(0.0875178 + 0.0505284i) q^{23} +(3.91992 + 3.10391i) q^{25} +(3.06470 + 4.94349i) q^{26} +(1.18735 - 2.39120i) q^{28} +(4.53226 - 2.61670i) q^{29} +(4.18262 + 2.41484i) q^{31} +(4.39722 - 3.55871i) q^{32} +(-8.04361 - 4.31354i) q^{34} +(-0.559997 - 2.93189i) q^{35} -3.24337i q^{37} +(-3.90457 + 7.28098i) q^{38} +(1.50824 - 6.14209i) q^{40} +(-3.50518 - 2.02372i) q^{41} +(1.92364 + 3.33185i) q^{43} +(3.89233 - 7.83880i) q^{44} +(-0.0753035 - 0.121468i) q^{46} +(-3.00768 + 1.73649i) q^{47} +(2.60904 - 4.51900i) q^{49} +(-2.81092 - 6.48835i) q^{50} +(-0.515549 - 8.20946i) q^{52} -2.77476 q^{53} +(-1.83577 - 9.61125i) q^{55} +(-3.07799 + 2.18661i) q^{56} +(-7.39751 + 0.232051i) q^{58} +(1.37318 - 2.37841i) q^{59} +(1.04419 + 1.80858i) q^{61} +(-3.59888 - 5.80514i) q^{62} +(-7.85881 + 1.49634i) q^{64} +(-6.01084 - 6.96033i) q^{65} +(0.216298 - 0.374638i) q^{67} +(7.14186 + 10.7520i) q^{68} +(-1.26162 + 4.02833i) q^{70} -8.41810 q^{71} +7.28163i q^{73} +(-2.16773 + 4.04225i) q^{74} +(9.73262 - 6.46473i) q^{76} +(-2.92071 + 5.05882i) q^{77} +(2.58753 - 1.49391i) q^{79} +(-5.98486 + 6.64691i) q^{80} +(3.01598 + 4.86490i) q^{82} +(11.6096 - 6.70282i) q^{83} +(13.6298 + 4.74283i) q^{85} +(-0.170590 - 5.43821i) q^{86} +(-10.0902 + 7.16812i) q^{88} -6.97377i q^{89} +5.49013i q^{91} +(0.0126677 + 0.201716i) q^{92} +(4.90911 - 0.153993i) q^{94} +(4.29315 - 12.3375i) q^{95} +(-2.08608 + 1.20440i) q^{97} +(-6.27200 + 3.88831i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{4} + 18 q^{5} - 16 q^{10} + 42 q^{14} + 30 q^{16} - 26 q^{25} - 4 q^{34} + 10 q^{40} - 96 q^{41} + 4 q^{46} + 32 q^{49} + 90 q^{50} - 6 q^{56} + 8 q^{61} - 20 q^{64} + 6 q^{65} + 4 q^{70} - 72 q^{74}+ \cdots - 62 q^{94}+O(q^{100}) \) 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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