LMFDB - Embedded newform 540.2.n.d.359.13

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			359.13
Character	$\chi$	$=$	540.359
Dual form			540.2.n.d.179.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0443404 + 1.41352i) q^{2} +(-1.99607 + 0.125352i) q^{4} +(2.11186 - 0.734875i) q^{5} +(0.667441 - 1.15604i) q^{7} +(-0.265693 - 2.81592i) q^{8} +(1.13240 + 2.95257i) q^{10} +(2.18799 - 3.78971i) q^{11} +(-3.56180 + 2.05641i) q^{13} +(1.66368 + 0.892181i) q^{14} +(3.96857 - 0.500421i) q^{16} +6.45392 q^{17} -5.84202i q^{19} +(-4.12330 + 1.73159i) q^{20} +(5.45385 + 2.92473i) q^{22} +(-0.0875178 + 0.0505284i) q^{23} +(3.91992 - 3.10391i) q^{25} +(-3.06470 - 4.94349i) q^{26} +(-1.18735 + 2.39120i) q^{28} +(4.53226 + 2.61670i) q^{29} +(-4.18262 + 2.41484i) q^{31} +(0.883323 + 5.58746i) q^{32} +(0.286169 + 9.12274i) q^{34} +(0.559997 - 2.93189i) q^{35} +3.24337i q^{37} +(8.25780 - 0.259037i) q^{38} +(-2.63046 - 5.75158i) q^{40} +(-3.50518 + 2.02372i) q^{41} +(-1.92364 + 3.33185i) q^{43} +(-3.89233 + 7.83880i) q^{44} +(-0.0753035 - 0.121468i) q^{46} +(3.00768 + 1.73649i) q^{47} +(2.60904 + 4.51900i) q^{49} +(4.56124 + 5.40325i) q^{50} +(6.85183 - 4.55121i) q^{52} -2.77476 q^{53} +(1.83577 - 9.61125i) q^{55} +(-3.43266 - 1.57231i) q^{56} +(-3.49779 + 6.52246i) q^{58} +(-1.37318 - 2.37841i) q^{59} +(1.04419 - 1.80858i) q^{61} +(-3.59888 - 5.80514i) q^{62} +(-7.85881 + 1.49634i) q^{64} +(-6.01084 + 6.96033i) q^{65} +(-0.216298 - 0.374638i) q^{67} +(-12.8825 + 0.809011i) q^{68} +(4.16911 + 0.661566i) q^{70} +8.41810 q^{71} -7.28163i q^{73} +(-4.58456 + 0.143812i) q^{74} +(0.732307 + 11.6611i) q^{76} +(-2.92071 - 5.05882i) q^{77} +(-2.58753 - 1.49391i) q^{79} +(8.01333 - 3.97323i) q^{80} +(-3.01598 - 4.86490i) q^{82} +(-11.6096 - 6.70282i) q^{83} +(13.6298 - 4.74283i) q^{85} +(-4.79492 - 2.57137i) q^{86} +(-11.2529 - 5.15431i) q^{88} +6.97377i q^{89} +5.49013i q^{91} +(0.168358 - 0.111829i) q^{92} +(-2.32119 + 4.32841i) q^{94} +(-4.29315 - 12.3375i) q^{95} +(-2.08608 - 1.20440i) q^{97} +(-6.27200 + 3.88831i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/540\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.0443404	+	1.41352i	0.0313534	+	0.999508i
$2$	0.0443404	+	1.41352i	0.0313534	+	0.999508i
$3$		0			0
$3$		0			0
$4$	−1.99607	+	0.125352i	−0.998034	+	0.0626759i
$5$	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	$-0.752157\pi$
$7$	0.667441	−	1.15604i	0.252269	−	0.436943i	0.964150	+	0.265357i	$0.0854898\pi$
$8$	−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	−0.320987	−	0.947083i	$-0.604015\pi$
$11$	2.18799	−	3.78971i	0.659705	−	1.14264i	0.980692	−	0.195558i	$-0.0626519\pi$
$12$		0			0
$13$	−3.56180	+	2.05641i	−0.987867	+	0.570345i	−0.904636	−	0.426185i	$-0.859857\pi$
$13$	−3.56180	+	2.05641i	−0.987867	+	0.570345i	−0.0832309	+	0.996530i	$0.526524\pi$
$14$	1.66368	+	0.892181i	0.444638	+	0.238445i
$15$		0			0
$16$	3.96857	−	0.500421i	0.992143	−	0.125105i
$17$	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	$-0.233760\pi$
$20$	−4.12330	+	1.73159i	−0.921998	+	0.387194i
$21$		0			0
$22$	5.45385	+	2.92473i	1.16276	+	0.623555i
$23$	−0.0875178	+	0.0505284i	−0.0182487	+	0.0105359i	−0.509097	−	0.860709i	$-0.670020\pi$
$23$	−0.0875178	+	0.0505284i	−0.0182487	+	0.0105359i	0.490848	+	0.871245i	$0.336687\pi$
$24$		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	0.857814	−	0.513960i	$-0.171822\pi$
$29$	4.53226	+	2.61670i	0.841620	+	0.485909i	−0.0161948	+	0.999869i	$0.505155\pi$
$30$		0			0
$31$	−4.18262	+	2.41484i	−0.751222	+	0.433718i	−0.826135	−	0.563472i	$-0.809465\pi$
$31$	−4.18262	+	2.41484i	−0.751222	+	0.433718i	0.0749136	+	0.997190i	$0.476132\pi$
$32$	0.883323	+	5.58746i	0.156151	+	0.987733i
$33$		0			0
$34$	0.286169	+	9.12274i	0.0490776	+	1.56454i
$35$	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	$0.914099\pi$
$38$	8.25780	−	0.259037i	1.33959	−	0.0420214i
$39$		0			0
$40$	−2.63046	−	5.75158i	−0.415912	−	0.909405i
$41$	−3.50518	+	2.02372i	−0.547417	+	0.316051i	−0.748079	−	0.663609i	$-0.769024\pi$
$41$	−3.50518	+	2.02372i	−0.547417	+	0.316051i	0.200663	+	0.979660i	$0.435690\pi$
$42$		0			0
$43$	−1.92364	+	3.33185i	−0.293353	+	0.508102i	−0.974600	−	0.223951i	$-0.928104\pi$
$43$	−1.92364	+	3.33185i	−0.293353	+	0.508102i	0.681248	+	0.732053i	$0.261438\pi$
$44$	−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	$-0.251820\pi$
$47$	3.00768	+	1.73649i	0.438715	+	0.253292i	−0.264337	+	0.964430i	$0.585153\pi$
$48$		0			0
$49$	2.60904	+	4.51900i	0.372721	+	0.645571i
$50$	4.56124	+	5.40325i	0.645057	+	0.764135i
$51$		0			0
$52$	6.85183	−	4.55121i	0.950178	−	0.631139i
$53$	−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
$56$	−3.43266	−	1.57231i	−0.458708	−	0.210109i
$57$		0			0
$58$	−3.49779	+	6.52246i	−0.459283	+	0.856441i
$59$	−1.37318	−	2.37841i	−0.178772	−	0.309642i	0.762688	−	0.646766i	$-0.223879\pi$
$59$	−1.37318	−	2.37841i	−0.178772	−	0.309642i	−0.941460	+	0.337124i	$0.890546\pi$
$60$		0			0
$61$	1.04419	−	1.80858i	0.133694	−	0.231566i	−0.791404	−	0.611294i	$-0.790649\pi$
$61$	1.04419	−	1.80858i	0.133694	−	0.231566i	0.925098	+	0.379729i	$0.123983\pi$
$62$	−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	$-0.175079\pi$
$67$	−0.216298	−	0.374638i	−0.0264250	−	0.0457694i	−0.878935	+	0.476941i	$0.841746\pi$
$68$	−12.8825	+	0.809011i	−1.56223	+	0.0981070i
$69$		0			0
$70$	4.16911	+	0.661566i	0.498304	+	0.0790722i
$71$	8.41810			0.999044			0.499522	−	0.866301i	$-0.333509\pi$
$71$	8.41810			0.999044			0.499522	+	0.866301i	$0.333509\pi$
$72$		0			0
$73$		−	7.28163i		−	0.852250i	−0.904664	−	0.426125i	$-0.859878\pi$
$73$		−	7.28163i		−	0.852250i	0.904664	−	0.426125i	$-0.140122\pi$
$74$	−4.58456	+	0.143812i	−0.532944	+	0.0167178i
$75$		0			0
$76$	0.732307	+	11.6611i	0.0840014	+	1.33762i
$77$	−2.92071	−	5.05882i	−0.332846	−	0.576507i
$78$		0			0
$79$	−2.58753	−	1.49391i	−0.291120	−	0.168078i	0.347327	−	0.937744i	$-0.387089\pi$
$79$	−2.58753	−	1.49391i	−0.291120	−	0.168078i	−0.638447	+	0.769666i	$0.720423\pi$
$80$	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	−0.298524	−	0.954402i	$-0.596494\pi$
$83$	−11.6096	−	6.70282i	−1.27432	−	0.735730i	−0.975798	+	0.218672i	$0.929828\pi$
$84$		0			0
$85$	13.6298	−	4.74283i	1.47836	−	0.514432i
$86$	−4.79492	−	2.57137i	−0.517049	−	0.277278i
$87$		0			0
$88$	−11.2529	−	5.15431i	−1.19956	−	0.549451i
$89$			6.97377i			0.739218i	0.929187	+	0.369609i	$0.120508\pi$
$89$			6.97377i			0.739218i	−0.929187	+	0.369609i	$0.879492\pi$
$90$		0			0
$91$			5.49013i			0.575522i
$92$	0.168358	−	0.111829i	0.0175525	−	0.0116590i
$93$		0			0
$94$	−2.32119	+	4.32841i	−0.239413	+	0.446441i
$95$	−4.29315	−	12.3375i	−0.440468	−	1.26580i
$96$		0			0
$97$	−2.08608	−	1.20440i	−0.211809	−	0.122288i	0.390343	−	0.920670i	$-0.372356\pi$
$97$	−2.08608	−	1.20440i	−0.211809	−	0.122288i	−0.602152	+	0.798382i	$0.705690\pi$
$98$	−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	0.682493	−	0.730892i	$-0.260896\pi$
$101$	3.92717	+	2.26735i	0.390768	+	0.225610i	−0.291725	+	0.956502i	$0.594229\pi$
$102$		0			0
$103$	1.95140	+	3.37992i	0.192277	+	0.333034i	0.946005	−	0.324153i	$-0.105079\pi$
$103$	1.95140	+	3.37992i	0.192277	+	0.333034i	−0.753727	+	0.657187i	$0.771746\pi$
$104$	6.73703	+	9.48338i	0.660620	+	0.929922i
$105$		0			0
$106$	−0.123034	−	3.92217i	−0.0119501	−	0.380955i
$107$			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	$0.576760\pi$
$110$	13.6671	+	2.16873i	1.30311	+	0.206780i
$111$		0			0
$112$	2.07028	−	4.92184i	0.195623	−	0.465070i
$113$	−10.2057	−	17.6768i	−0.960073	−	1.66290i	−0.722306	−	0.691574i	$-0.756918\pi$
$113$	−10.2057	−	17.6768i	−0.960073	−	1.66290i	−0.237767	−	0.971322i	$-0.576416\pi$
$114$		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
$122$	2.60277	+	1.39578i	0.235643	+	0.126368i
$123$		0			0
$124$	8.04610	−	5.34448i	0.722561	−	0.479949i
$125$	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	$0.824077\pi$
$128$	−2.46357	−	11.0422i	−0.217751	−	0.976004i
$129$		0			0
$130$	−10.1051	−	8.18780i	−0.886274	−	0.718118i
$131$	8.41433	+	14.5740i	0.735163	+	1.27334i	0.954652	+	0.297725i	$0.0962279\pi$
$131$	8.41433	+	14.5740i	0.735163	+	1.27334i	−0.219488	+	0.975615i	$0.570439\pi$
$132$		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	$-0.915767\pi$
$137$	−2.99744	+	5.19172i	−0.256089	+	0.443559i	0.709102	+	0.705106i	$0.249101\pi$
$138$		0			0
$139$	0.206175	−	0.119035i	0.0174875	−	0.0100964i	−0.491231	−	0.871029i	$-0.663453\pi$
$139$	0.206175	−	0.119035i	0.0174875	−	0.0100964i	0.508718	+	0.860933i	$0.330119\pi$
$140$	−0.750275	+	5.92244i	−0.0634098	+	0.500538i
$141$		0			0
$142$	0.373261	+	11.8991i	0.0313234	+	0.998553i
$143$			17.9976i			1.50504i
$144$		0			0
$145$	11.4945	+	2.19547i	0.954563	+	0.182324i
$146$	10.2927	−	0.322870i	0.851831	−	0.0267209i
$147$		0			0
$148$	−0.406562	−	6.47398i	−0.0334192	−	0.532158i
$149$	8.84885	−	5.10889i	0.724926	−	0.418536i	−0.0916368	−	0.995792i	$-0.529210\pi$
$149$	8.84885	−	5.10889i	0.724926	−	0.418536i	0.816563	+	0.577256i	$0.195877\pi$
$150$		0			0
$151$	13.0489	+	7.53379i	1.06190	+	0.613091i	0.925958	−	0.377625i	$-0.123259\pi$
$151$	13.0489	+	7.53379i	1.06190	+	0.613091i	0.135946	+	0.990716i	$0.456593\pi$
$152$	−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	−0.606611	−	0.794999i	$-0.707471\pi$
$157$	−2.77448	+	1.60184i	−0.221427	+	0.127841i	0.385184	+	0.922840i	$0.374138\pi$
$158$	1.99694	−	3.72376i	0.158868	−	0.296246i
$159$		0			0
$160$	5.97154	+	11.1508i	0.472092	+	0.881549i
$161$			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	$0.363487\pi$
$164$	6.74290	−	4.47885i	0.526532	−	0.349740i
$165$		0			0
$166$	8.95979	−	16.7076i	0.695414	−	1.29676i
$167$	10.9127	−	6.30046i	0.844451	−	0.487544i	−0.0143236	−	0.999897i	$-0.504560\pi$
$167$	10.9127	−	6.30046i	0.844451	−	0.487544i	0.858775	+	0.512353i	$0.171226\pi$
$168$		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	$-0.854116\pi$
$173$	−0.858165	+	1.48639i	−0.0652451	+	0.113008i	0.831558	+	0.555439i	$0.187450\pi$
$174$		0			0
$175$	−0.971933	−	6.60327i	−0.0734712	−	0.499160i
$176$	6.78676	−	16.1347i	0.511571	−	1.21620i
$177$		0			0
$178$	−9.85755	+	0.309220i	−0.738855	+	0.0231770i
$179$	−18.6630			−1.39494			−0.697468	−	0.716616i	$-0.745690\pi$
$179$	−18.6630			−1.39494			−0.697468	+	0.716616i	$0.745690\pi$
$180$		0			0
$181$	−19.9281			−1.48125			−0.740623	−	0.671920i	$-0.765470\pi$
$181$	−19.9281			−1.48125			−0.740623	+	0.671920i	$0.765470\pi$
$182$	−7.76040	+	0.243434i	−0.575239	+	0.0180445i
$183$		0			0
$184$	0.165537	+	0.233018i	0.0122035	+	0.0171783i
$185$	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
$190$	17.2490	−	6.61550i	1.25137	−	0.479939i
$191$	−10.8229	+	18.7459i	−0.783121	+	1.35641i	0.146994	+	0.989137i	$0.453040\pi$
$191$	−10.8229	+	18.7459i	−0.783121	+	1.35641i	−0.930115	+	0.367268i	$0.880293\pi$
$192$		0			0
$193$	−9.00614	+	5.19970i	−0.648276	+	0.374282i	−0.787795	−	0.615937i	$-0.788778\pi$
$193$	−9.00614	+	5.19970i	−0.648276	+	0.374282i	0.139519	+	0.990219i	$0.455444\pi$
$194$	1.60994	−	3.00211i	0.115587	−	0.215539i
$195$		0			0
$196$	−5.77429	−	8.69318i	−0.412450	−	0.620941i
$197$	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	$0.894488\pi$
$200$	−9.78185	−	10.2135i	−0.691681	−	0.722203i
$201$		0			0
$202$	−3.03081	+	5.65166i	−0.213247	+	0.397649i
$203$	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	$-0.781365\pi$
$211$	−8.87092	+	5.12163i	−0.610699	+	0.352587i	0.162540	+	0.986702i	$0.448031\pi$
$212$	5.53861	−	0.347821i	0.380393	−	0.0238885i
$213$		0			0
$214$	−7.05105	+	0.221183i	−0.482000	+	0.0151197i
$215$	−1.61398	+	8.45003i	−0.110072	+	0.576287i
$216$		0			0
$217$			6.44705i			0.437655i
$218$	−0.221111	−	7.04877i	−0.0149756	−	0.477403i
$219$		0			0
$220$	−2.45954	+	19.4148i	−0.165822	+	1.30895i
$221$	−22.9876	+	13.2719i	−1.54631	+	0.892765i
$222$		0			0
$223$	−11.6245	+	20.1343i	−0.778436	+	1.34829i	0.154407	+	0.988007i	$0.450653\pi$
$223$	−11.6245	+	20.1343i	−0.778436	+	1.34829i	−0.932843	+	0.360283i	$0.882680\pi$
$224$	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	$-0.524327\pi$
$227$	−14.7354	−	8.50750i	−0.978024	−	0.564663i	−0.901673	+	0.432418i	$0.857660\pi$
$228$		0			0
$229$	−0.750685	−	1.30022i	−0.0496066	−	0.0859212i	0.840156	−	0.542345i	$-0.182463\pi$
$229$	−0.750685	−	1.30022i	−0.0496066	−	0.0859212i	−0.889762	+	0.456424i	$0.849130\pi$
$230$	−0.248294	−	0.201184i	−0.0163720	−	0.0132657i
$231$		0			0
$232$	6.16423	−	13.4577i	0.404702	−	0.883543i
$233$	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
$236$	3.03909	+	4.57534i	0.197828	+	0.297829i
$237$		0			0
$238$	10.7373	+	5.75807i	0.695994	+	0.373240i
$239$	7.32324	+	12.6842i	0.473701	+	0.820474i	0.999547	−	0.0301057i	$-0.00958440\pi$
$239$	7.32324	+	12.6842i	0.473701	+	0.820474i	−0.525846	+	0.850580i	$0.676251\pi$
$240$		0			0
$241$	−12.2259	+	21.1758i	−0.787537	+	1.36405i	0.139934	+	0.990161i	$0.455311\pi$
$241$	−12.2259	+	21.1758i	−0.787537	+	1.36405i	−0.927472	+	0.373894i	$0.878022\pi$
$242$	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
$248$	7.91129	+	11.1363i	0.502367	+	0.707158i
$249$		0			0
$250$	13.6034	+	8.05897i	0.860356	+	0.509694i
$251$	13.1808			0.831965			0.415982	−	0.909373i	$-0.363438\pi$
$251$	13.1808			0.831965			0.415982	+	0.909373i	$0.363438\pi$
$252$		0			0
$253$			0.442223i			0.0278024i
$254$	−0.850595	−	27.1160i	−0.0533711	−	1.70141i
$255$		0			0
$256$	15.4992	−	3.97192i	0.968697	−	0.248245i
$257$	3.48508	+	6.03633i	0.217393	+	0.376536i	0.954010	−	0.299774i	$-0.0969113\pi$
$257$	3.48508	+	6.03633i	0.217393	+	0.376536i	−0.736617	+	0.676310i	$0.763578\pi$
$258$		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	0.864716	−	0.502262i	$-0.167499\pi$
$263$	13.9809	+	8.07190i	0.862102	+	0.497735i	−0.00261352	+	0.999997i	$0.500832\pi$
$264$		0			0
$265$	−5.85991	+	2.03910i	−0.359971	+	0.125261i
$266$	5.21214	−	9.71926i	0.319577	−	0.595926i
$267$		0			0
$268$	0.478706	+	0.720690i	0.0292416	+	0.0440232i
$269$		−	21.7634i		−	1.32694i	−0.748204	−	0.663468i	$-0.769084\pi$
$269$		−	21.7634i		−	1.32694i	0.748204	−	0.663468i	$-0.230916\pi$
$270$		0			0
$271$			30.1548i			1.83177i	0.401436	+	0.915887i	$0.368511\pi$
$271$			30.1548i			1.83177i	−0.401436	+	0.915887i	$0.631489\pi$
$272$	25.6129	−	3.22968i	1.55301	−	0.195828i
$273$		0			0
$274$	−7.47150	−	4.00674i	−0.451370	−	0.242056i
$275$	−3.18617	−	21.6467i	−0.192133	−	1.30535i
$276$		0			0
$277$	11.2614	+	6.50177i	0.676632	+	0.390654i	0.798585	−	0.601882i	$-0.205582\pi$
$277$	11.2614	+	6.50177i	0.676632	+	0.390654i	−0.121953	+	0.992536i	$0.538916\pi$
$278$	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	0.527679	−	0.849444i	$-0.323062\pi$
$281$	0.936692	+	0.540799i	0.0558784	+	0.0322614i	−0.471801	+	0.881705i	$0.656396\pi$
$282$		0			0
$283$	−14.6158	−	25.3154i	−0.868821	−	1.50484i	−0.863202	−	0.504858i	$-0.831545\pi$
$283$	−14.6158	−	25.3154i	−0.868821	−	1.50484i	−0.00561859	−	0.999984i	$-0.501788\pi$
$284$	−16.8031	+	1.05522i	−0.997080	+	0.0626160i
$285$		0			0
$286$	−25.4400	+	0.798021i	−1.50430	+	0.0471880i
$287$			5.40284i			0.318920i
$288$		0			0
$289$	24.6531			1.45019
$290$	−2.59367	+	16.3450i	−0.152305	+	0.959810i
$291$		0			0
$292$	0.912765	+	14.5346i	0.0534155	+	0.850575i
$293$	2.81552	+	4.87662i	0.164484	+	0.284895i	0.936472	−	0.350742i	$-0.114071\pi$
$293$	2.81552	+	4.87662i	0.164484	+	0.284895i	−0.771988	+	0.635637i	$0.780737\pi$
$294$		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
$302$	−10.0706	+	18.7789i	−0.579495	+	1.08060i
$303$		0			0
$304$	−2.92347	−	23.1845i	−0.167673	−	1.32972i
$305$	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	$0.356249\pi$
$308$	6.46408	+	9.73164i	0.368325	+	0.554512i
$309$		0			0
$310$	−11.8664	−	9.61493i	−0.673965	−	0.546091i
$311$	1.83417	+	3.17688i	0.104006	+	0.180144i	0.913332	−	0.407216i	$-0.133500\pi$
$311$	1.83417	+	3.17688i	0.104006	+	0.180144i	−0.809326	+	0.587360i	$0.800167\pi$
$312$		0			0
$313$	21.3301	+	12.3149i	1.20565	+	0.696081i	0.961805	−	0.273734i	$-0.0882588\pi$
$313$	21.3301	+	12.3149i	1.20565	+	0.696081i	0.243842	+	0.969815i	$0.421592\pi$
$314$	−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	$-0.930007\pi$
$317$	−5.32466	+	9.22258i	−0.299063	+	0.517992i	0.676859	+	0.736113i	$0.263341\pi$
$318$		0			0
$319$	19.8331	−	11.4506i	1.11044	−	0.641113i
$320$	−15.4971	+	8.93531i	−0.866314	+	0.499499i
$321$		0			0
$322$	−0.190682	+	0.00598147i	−0.0106263	+	0.000333334i
$323$		−	37.7039i		−	2.09790i
$324$		0			0
$325$	−7.57908	+	19.1165i	−0.420412	+	1.06039i
$326$	0.470816	+	15.0091i	0.0260761	+	0.831275i
$327$		0			0
$328$	6.62992	+	9.33261i	0.366076	+	0.515307i
$329$	4.01490	−	2.31800i	0.221349	−	0.127796i
$330$		0			0
$331$	−3.04582	−	1.75851i	−0.167414	−	0.0966563i	0.413952	−	0.910299i	$-0.364148\pi$
$331$	−3.04582	−	1.75851i	−0.167414	−	0.0966563i	−0.581366	+	0.813642i	$0.697481\pi$
$332$	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	0.171147	−	0.985245i	$-0.445253\pi$
$337$	20.3763	−	11.7643i	1.10997	−	0.640841i	0.938821	+	0.344405i	$0.111919\pi$
$338$	4.87965	+	2.61681i	0.265418	+	0.142336i
$339$		0			0
$340$	−26.6115	+	11.1755i	−1.44321	+	0.606078i
$341$			21.1346i			1.14450i
$342$		0			0
$343$	16.3097			0.880642
$344$	9.89331	+	4.53157i	0.533412	+	0.244326i
$345$		0			0
$346$	−2.13909	−	1.14713i	−0.114998	−	0.0616699i
$347$	−3.63147	+	2.09663i	−0.194947	+	0.112553i	−0.594297	−	0.804246i	$-0.702569\pi$
$347$	−3.63147	+	2.09663i	−0.194947	+	0.112553i	0.399349	+	0.916799i	$0.369236\pi$
$348$		0			0
$349$	2.78198	−	4.81854i	0.148916	−	0.257930i	−0.781911	−	0.623390i	$-0.785755\pi$
$349$	2.78198	−	4.81854i	0.148916	−	0.257930i	0.930827	+	0.365460i	$0.119088\pi$
$350$	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	$-0.928095\pi$
$353$	−5.51109	+	9.54549i	−0.293326	+	0.508055i	0.681268	+	0.732034i	$0.261429\pi$
$354$		0			0
$355$	17.7779	−	6.18625i	0.943550	−	0.328332i
$356$	−0.874175	−	13.9201i	−0.0463312	−	0.737765i
$357$		0			0
$358$	−0.827522	−	26.3804i	−0.0437359	−	1.39425i
$359$	−27.2920			−1.44042			−0.720209	−	0.693757i	$-0.755954\pi$
$359$	−27.2920			−1.44042			−0.720209	+	0.693757i	$0.755954\pi$
$360$		0			0
$361$	−15.1292			−0.796272
$362$	−0.883621	−	28.1688i	−0.0464421	−	1.48052i
$363$		0			0
$364$	−0.688198	−	10.9587i	−0.0360714	−	0.574390i
$365$	−5.35109	−	15.3778i	−0.280089	−	0.804910i
$366$		0			0
$367$	−15.7443	+	27.2699i	−0.821846	+	1.42348i	0.0824597	+	0.996594i	$0.473722\pi$
$367$	−15.7443	+	27.2699i	−0.821846	+	1.42348i	−0.904306	+	0.426885i	$0.859611\pi$
$368$	−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	$-0.874219\pi$
$373$	−20.2988	+	11.7195i	−1.05103	+	0.606812i	−0.128092	+	0.991762i	$0.540885\pi$
$374$	35.1987	+	18.8760i	1.82008	+	0.976054i
$375$		0			0
$376$	4.09068	−	8.93076i	0.210961	−	0.460569i
$377$	−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	$-0.0958918\pi$
$380$	10.1160	+	24.0884i	0.518937	+	1.23571i
$381$		0			0
$382$	−26.9776	−	14.4672i	−1.38029	−	0.740208i
$383$	−22.7016	+	13.1068i	−1.16000	+	0.669725i	−0.951304	−	0.308256i	$-0.900255\pi$
$383$	−22.7016	+	13.1068i	−1.16000	+	0.669725i	−0.208695	+	0.977981i	$0.566921\pi$
$384$		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	0.534711	−	0.845035i	$-0.320420\pi$
$389$	1.38545	+	0.799888i	0.0702449	+	0.0405559i	−0.464466	+	0.885591i	$0.653754\pi$
$390$		0			0
$391$	−0.564834	+	0.326107i	−0.0285649	+	0.0164919i
$392$	12.0319	−	8.54753i	0.607704	−	0.431715i
$393$		0			0
$394$	0.361691	+	11.5303i	0.0182217	+	0.580887i
$395$	−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	$-0.225599\pi$
$398$	−12.9785	+	0.407121i	−0.650555	+	0.0204071i
$399$		0			0
$400$	14.0032	−	14.2797i	0.700161	−	0.713985i
$401$	21.5383	−	12.4351i	1.07557	−	0.620980i	0.145872	−	0.989304i	$-0.453401\pi$
$401$	21.5383	−	12.4351i	1.07557	−	0.620980i	0.929698	+	0.368323i	$0.120068\pi$
$402$		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	−0.999450	−	0.0331484i	$-0.989447\pi$
$409$	−10.6869	−	18.5102i	−0.528433	−	0.915272i	0.471018	−	0.882124i	$-0.343887\pi$
$410$	−9.94442	−	8.05763i	−0.491120	−	0.397938i
$411$		0			0
$412$	−4.31881	−	6.50195i	−0.212772	−	0.320328i
$413$	−3.66606			−0.180395
$414$		0			0
$415$	−29.4437	−	5.62381i	−1.44533	−	0.276062i
$416$	−14.6363	−	18.0850i	−0.717605	−	0.886689i
$417$		0			0
$418$	17.0863	−	31.8615i	0.835719	−	1.55840i
$419$	3.12824	+	5.41826i	0.152824	+	0.264700i	0.932265	−	0.361777i	$-0.117830\pi$
$419$	3.12824	+	5.41826i	0.152824	+	0.264700i	−0.779440	+	0.626476i	$0.784496\pi$
$420$		0			0
$421$	15.3599	−	26.6041i	0.748596	−	1.29661i	−0.199900	−	0.979816i	$-0.564062\pi$
$421$	15.3599	−	26.6041i	0.748596	−	1.29661i	0.948496	−	0.316790i	$-0.102605\pi$
$422$	−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
$428$	−0.625292	−	9.95698i	−0.0302246	−	0.481289i
$429$		0			0
$430$	−12.0158	−	1.90671i	−0.579455	−	0.0919496i
$431$	35.1049			1.69094			0.845472	−	0.534020i	$-0.179319\pi$
$431$	35.1049			1.69094			0.845472	+	0.534020i	$0.179319\pi$
$432$		0			0
$433$		−	24.5043i		−	1.17760i	−0.808279	−	0.588800i	$-0.799601\pi$
$433$		−	24.5043i		−	1.17760i	0.808279	−	0.588800i	$-0.200399\pi$
$434$	−9.11303	+	0.285865i	−0.437439	+	0.0137219i
$435$		0			0
$436$	9.95376	−	0.625090i	0.476699	−	0.0299364i
$437$	0.295188	+	0.511281i	0.0141208	+	0.0244579i
$438$		0			0
$439$	−15.3741	−	8.87623i	−0.733765	−	0.423639i	0.0860332	−	0.996292i	$-0.472581\pi$
$439$	−15.3741	−	8.87623i	−0.733765	−	0.423639i	−0.819798	+	0.572653i	$0.805914\pi$
$440$	−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	0.637585	−	0.770380i	$-0.279933\pi$
$443$	6.08715	+	3.51442i	0.289209	+	0.166975i	−0.348376	+	0.937355i	$0.613267\pi$
$444$		0			0
$445$	5.12485	+	14.7276i	0.242941	+	0.698157i
$446$	−28.9756	−	15.5387i	−1.37203	−	0.735780i
$447$		0			0
$448$	−3.51546	+	10.0838i	−0.166090	+	0.476417i
$449$			16.6756i			0.786971i	0.919331	+	0.393485i	$0.128731\pi$
$449$			16.6756i			0.786971i	−0.919331	+	0.393485i	$0.871269\pi$
$450$		0			0
$451$			17.7115i			0.834002i
$452$	22.5871	+	34.0048i	1.06241	+	1.59945i
$453$		0			0
$454$	11.3721	−	21.2060i	0.533721	−	0.995248i
$455$	4.03456	+	11.5944i	0.189143	+	0.543554i
$456$		0			0
$457$	−25.7193	−	14.8490i	−1.20310	−	0.694608i	−0.241854	−	0.970313i	$-0.577756\pi$
$457$	−25.7193	−	14.8490i	−1.20310	−	0.694608i	−0.961242	+	0.275704i	$0.911089\pi$
$458$	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	0.186415	−	0.982471i	$-0.440313\pi$
$461$	−12.2647	−	7.08100i	−0.571222	−	0.329795i	−0.757637	+	0.652676i	$0.773646\pi$
$462$		0			0
$463$	2.85520	+	4.94535i	0.132692	+	0.229830i	0.924714	−	0.380664i	$-0.124304\pi$
$463$	2.85520	+	4.94535i	0.132692	+	0.229830i	−0.792021	+	0.610494i	$0.790971\pi$
$464$	19.2961	+	8.11653i	0.895797	+	0.376801i
$465$		0			0
$466$	0.600736	+	19.1508i	0.0278286	+	0.887142i
$467$		−	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
$470$	−1.72120	+	10.8468i	−0.0793930	+	0.500325i
$471$		0			0
$472$	−6.33257	+	4.49868i	−0.291480	+	0.207069i
$473$	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	−0.275471	−	0.961309i	$-0.588834\pi$
$479$	15.2061	−	26.3377i	0.694783	−	1.20340i	0.970254	−	0.242090i	$-0.0778329\pi$
$480$		0			0
$481$	−6.66969	−	11.5522i	−0.304112	−	0.526737i
$482$	−30.4745	−	16.3425i	−1.38808	−	0.744382i
$483$		0			0
$484$	9.01789	+	13.5764i	0.409904	+	0.617109i
$485$	−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	$0.526563\pi$
$488$	−5.37026	−	2.45982i	−0.243100	−	0.111351i
$489$		0			0
$490$	−10.3882	+	12.8207i	−0.469290	+	0.579180i
$491$	−9.05671	−	15.6867i	−0.408724	−	0.707930i	0.586023	−	0.810294i	$-0.300693\pi$
$491$	−9.05671	−	15.6867i	−0.408724	−	0.707930i	−0.994747	+	0.102364i	$0.967359\pi$
$492$		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	$-0.839095\pi$
$499$	−19.9488	+	11.5175i	−0.893032	+	0.515592i	−0.0180991	+	0.999836i	$0.505761\pi$
$500$	−10.7883	+	19.5860i	−0.482468	+	0.875913i
$501$		0			0
$502$	0.584441	+	18.6313i	0.0260849	+	0.831556i
$503$			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
$506$	−0.625091	+	0.0196083i	−0.0277887	+	0.000871697i
$507$		0			0
$508$	38.2912	−	2.40466i	1.69890	−	0.106690i
$509$	0.489681	−	0.282717i	0.0217047	−	0.0125312i	−0.489108	−	0.872223i	$-0.662678\pi$
$509$	0.489681	−	0.282717i	0.0217047	−	0.0125312i	0.510813	+	0.859692i	$0.329344\pi$
$510$		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
$518$	−2.89367	+	5.39593i	−0.127141	+	0.237083i
$519$		0			0
$520$	21.1968	+	15.0767i	0.929540	+	0.661158i
$521$		−	4.80678i		−	0.210589i	−0.994441	−	0.105294i	$-0.966422\pi$
$521$		−	4.80678i		−	0.210589i	0.994441	−	0.105294i	$-0.0335785\pi$
$522$		0			0
$523$	−19.6207			−0.857954			−0.428977	−	0.903315i	$-0.641126\pi$
$523$	−19.6207			−0.857954			−0.428977	+	0.903315i	$0.641126\pi$
$524$	−18.6225	−	28.0360i	−0.813526	−	1.22476i
$525$		0			0
$526$	−10.7899	+	20.1202i	−0.470460	+	0.877284i
$527$	−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
$535$	3.66577	+	10.5346i	0.158485	+	0.455450i
$536$	−0.997483	+	0.708616i	−0.0430847	+	0.0306075i
$537$		0			0
$538$	30.7629	−	0.964996i	1.32628	−	0.0416039i
$539$	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	$0.166392\pi$
$542$	−42.6244	+	1.33707i	−1.83087	+	0.0574323i
$543$		0			0
$544$	5.70090	+	36.0611i	0.244424	+	1.54611i
$545$	−10.5312	+	3.66459i	−0.451107	+	0.156974i
$546$		0			0
$547$	1.44201	−	2.49763i	0.0616557	−	0.106791i	−0.833550	−	0.552444i	$-0.813695\pi$
$547$	1.44201	−	2.49763i	0.0616557	−	0.106791i	0.895206	+	0.445653i	$0.147029\pi$
$548$	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
$554$	−8.69104	+	16.2065i	−0.369247	+	0.688547i
$555$		0			0
$556$	−0.396617	+	0.263446i	−0.0168203	+	0.0111726i
$557$	−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
$560$	0.755212	−	11.9156i	0.0319135	−	0.503528i
$561$		0			0
$562$	−0.722897	+	1.34801i	−0.0304935	+	0.0568624i
$563$	19.0842	−	11.0182i	0.804302	−	0.464364i	−0.0406715	−	0.999173i	$-0.512950\pi$
$563$	19.0842	−	11.0182i	0.804302	−	0.464364i	0.844973	+	0.534809i	$0.179616\pi$
$564$		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	0.912073	−	0.410029i	$-0.134481\pi$
$569$	24.1641	+	13.9512i	1.01301	+	0.584864i	0.100941	+	0.994892i	$0.467815\pi$
$570$		0			0
$571$	11.2510	−	6.49576i	0.470839	−	0.271839i	−0.245752	−	0.969333i	$-0.579035\pi$
$571$	11.2510	−	6.49576i	0.470839	−	0.271839i	0.716591	+	0.697494i	$0.245702\pi$
$572$	−2.25604	−	35.9245i	−0.0943296	−	1.50208i
$573$		0			0
$574$	−7.63702	+	0.239564i	−0.318763	+	0.00999921i
$575$	−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	$0.743807\pi$
$578$	1.09313	+	34.8477i	0.0454682	+	1.44947i
$579$		0			0
$580$	−23.2189	−	2.94145i	−0.964113	−	0.122137i
$581$	−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	$-0.405339\pi$
$587$	−9.41209	−	5.43407i	−0.388479	−	0.224288i	−0.681501	+	0.731817i	$0.738672\pi$
$588$		0			0
$589$	14.1075	+	24.4350i	0.581291	+	1.00683i
$590$	5.46744	−	6.74771i	0.225091	−	0.277799i
$591$		0			0
$592$	1.62305	+	12.8715i	0.0667069	+	0.529017i
$593$	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
$596$	−17.0225	+	11.3069i	−0.697269	+	0.463149i
$597$		0			0
$598$	0.518003	+	0.277789i	0.0211827	+	0.0113596i
$599$	−3.45192	−	5.97890i	−0.141042	−	0.244291i	0.786847	−	0.617148i	$-0.211712\pi$
$599$	−3.45192	−	5.97890i	−0.141042	−	0.244291i	−0.927889	+	0.372856i	$0.878379\pi$
$600$		0			0
$601$	−15.7058	+	27.2032i	−0.640653	+	1.10964i	0.344635	+	0.938737i	$0.388003\pi$
$601$	−15.7058	+	27.2032i	−0.640653	+	1.10964i	−0.985287	+	0.170906i	$0.945331\pi$
$602$	−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	$-0.297074\pi$
$607$	−9.81362	−	16.9977i	−0.398322	−	0.689915i	−0.993519	+	0.113665i	$0.963741\pi$
$608$	32.6421	−	5.16039i	1.32381	−	0.209281i
$609$		0			0
$610$	6.52241	+	1.03499i	0.264085	+	0.0419057i
$611$	−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	$-0.197647\pi$
$614$	0.678103	+	21.6171i	0.0273660	+	0.872396i
$615$		0			0
$616$	−13.4692	+	9.56859i	−0.542691	+	0.385530i
$617$	−8.02269	−	13.8957i	−0.322981	−	0.559420i	0.658120	−	0.752913i	$-0.271352\pi$
$617$	−8.02269	−	13.8957i	−0.322981	−	0.559420i	−0.981102	+	0.193493i	$0.938018\pi$
$618$		0			0
$619$	2.13387	+	1.23199i	0.0857674	+	0.0495178i	0.542270	−	0.840204i	$-0.317565\pi$
$619$	2.13387	+	1.23199i	0.0857674	+	0.0495178i	−0.456503	+	0.889722i	$0.650898\pi$
$620$	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
$625$	5.73152	−	24.3341i	0.229261	−	0.973365i
$626$	−16.4616	+	30.6965i	−0.657938	+	1.22688i
$627$		0			0
$628$	5.33725	−	3.54518i	0.212979	−	0.141468i
$629$			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	$-0.346003\pi$
$632$	−3.51924	+	7.68320i	−0.139988	+	0.305621i
$633$		0			0
$634$	−13.2724	−	7.11757i	−0.527114	−	0.282675i
$635$	−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
$640$	−13.3174	−	21.5092i	−0.526415	−	0.850227i
$641$	14.1935	+	8.19465i	0.560611	+	0.323669i	0.753391	−	0.657573i	$-0.228417\pi$
$641$	14.1935	+	8.19465i	0.560611	+	0.323669i	−0.192779	+	0.981242i	$0.561750\pi$
$642$		0			0
$643$	−17.5507	−	30.3987i	−0.692133	−	1.19881i	−0.971138	−	0.238520i	$-0.923338\pi$
$643$	−17.5507	−	30.3987i	−0.692133	−	1.19881i	0.279005	−	0.960290i	$-0.409995\pi$
$644$	−0.0169098	−	0.269268i	−0.000666341	−	0.0106106i
$645$		0			0
$646$	53.2952	−	1.67181i	2.09687	−	0.0657763i
$647$		−	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
$650$	−27.3575	−	9.86554i	−1.07305	−	0.386958i
$651$		0			0
$652$	−21.1947	+	1.33101i	−0.830049	+	0.0521265i
$653$	21.0708	+	36.4956i	0.824563	+	1.42818i	0.902253	+	0.431207i	$0.141912\pi$
$653$	21.0708	+	36.4956i	0.824563	+	1.42818i	−0.0776903	+	0.996978i	$0.524755\pi$
$654$		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	$-0.705028\pi$
$659$	10.0696	−	17.4410i	0.392256	−	0.679407i	0.992747	+	0.120225i	$0.0383616\pi$
$660$		0			0
$661$	3.54725	+	6.14402i	0.137972	+	0.238975i	0.926729	−	0.375731i	$-0.122608\pi$
$661$	3.54725	+	6.14402i	0.137972	+	0.238975i	−0.788757	+	0.614705i	$0.789275\pi$
$662$	2.35063	−	4.38330i	0.0913598	−	0.170362i
$663$		0			0
$664$	−15.7900	+	34.4727i	−0.612771	+	1.33780i
$665$	−17.1281	−	3.27151i	−0.664201	−	0.126864i
$666$		0			0
$667$	−0.528872			−0.0204780
$668$	−20.9927	+	13.9441i	−0.812234	+	0.539512i
$669$		0			0
$670$	0.861211	−	1.06287i	0.0332715	−	0.0410624i
$671$	−4.56935	−	7.91434i	−0.176398	−	0.305530i
$672$		0			0
$673$	19.8408	+	11.4551i	0.764806	+	0.441561i	0.831018	−	0.556245i	$-0.187758\pi$
$673$	19.8408	+	11.4551i	0.764806	+	0.441561i	−0.0662129	+	0.997806i	$0.521092\pi$
$674$	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	$-0.685934\pi$
$677$	11.6227	−	20.1311i	0.446696	−	0.773699i	0.998169	+	0.0604934i	$0.0192674\pi$
$678$		0			0
$679$	−2.78467	+	1.60773i	−0.106866	+	0.0616989i
$680$	−16.9768	−	37.1203i	−0.651029	−	1.42350i
$681$		0			0
$682$	−29.8741	+	0.937116i	−1.14394	+	0.0358840i
$683$		−	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
$686$	0.723178	+	23.0541i	0.0276111	+	0.880209i
$687$		0			0
$688$	−5.96679	+	14.1853i	−0.227482	+	0.540810i
$689$	9.88316	−	5.70604i	0.376518	−	0.217383i
$690$		0			0
$691$	−10.6015	−	6.12077i	−0.403299	−	0.232845i	0.284607	−	0.958644i	$-0.408137\pi$
$691$	−10.6015	−	6.12077i	−0.403299	−	0.232845i	−0.687907	+	0.725799i	$0.741470\pi$
$692$	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
$698$	6.93444	+	3.71873i	0.262473	+	0.140756i
$699$		0			0
$700$	2.76778	+	13.0587i	0.104612	+	0.493574i
$701$			0.0365464i			0.00138034i	1.00000		0.000690169i	$0.000219688\pi$
$701$			0.0365464i			0.00138034i	−1.00000		0.000690169i	$0.999780\pi$
$702$		0			0
$703$	18.9478			0.714630
$704$	−11.5243	+	33.0566i	−0.434339	+	1.24587i
$705$		0			0
$706$	−13.7371	−	7.36678i	−0.517002	−	0.277252i
$707$	5.24231	−	3.02665i	0.197157	−	0.113829i
$708$		0			0
$709$	13.6359	−	23.6181i	0.512109	−	0.886998i	−0.487793	−	0.872959i	$-0.662198\pi$
$709$	13.6359	−	23.6181i	0.512109	−	0.886998i	0.999901	−	0.0140387i	$-0.00446880\pi$
$710$	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
$715$	13.2260	+	38.0085i	0.494625	+	1.42144i
$716$	37.2525	−	2.33944i	1.39219	−	0.0874288i
$717$		0			0
$718$	−1.21014	−	38.5778i	−0.0451619	−	1.43971i
$719$	−7.73269			−0.288381			−0.144190	−	0.989550i	$-0.546058\pi$
$719$	−7.73269			−0.288381			−0.144190	+	0.989550i	$0.546058\pi$
$720$		0			0
$721$	5.20978			0.194022
$722$	−0.670832	−	21.3853i	−0.0249658	−	0.795880i
$723$		0			0
$724$	39.7779	−	2.49803i	1.47833	−	0.0928385i
$725$	25.8881	−	3.81046i	0.961460	−	0.141517i
$726$		0			0
$727$	8.24957	−	14.2887i	0.305960	−	0.529938i	−0.671515	−	0.740991i	$-0.734356\pi$
$727$	8.24957	−	14.2887i	0.305960	−	0.529938i	0.977475	+	0.211053i	$0.0676894\pi$
$728$	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	$-0.375703\pi$
$733$	37.1399	−	21.4427i	1.37179	−	0.792006i	0.991154	+	0.132717i	$0.0423702\pi$
$734$	−39.2447	−	21.0457i	−1.44855	−	0.776811i
$735$		0			0
$736$	−0.359632	−	0.444370i	−0.0132562	−	0.0163797i
$737$	−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	$-0.0178341\pi$
$740$	−5.61617	−	13.3734i	−0.206454	−	0.491615i
$741$		0			0
$742$	−4.61632	−	2.47559i	−0.169470	−	0.0908817i
$743$	35.0211	−	20.2194i	1.28480	−	0.741779i	0.307078	−	0.951684i	$-0.400649\pi$
$743$	35.0211	−	20.2194i	1.28480	−	0.741779i	0.977722	+	0.209905i	$0.0673155\pi$
$744$		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	$-0.748620\pi$
$751$	−12.0862	+	6.97795i	−0.441030	+	0.254629i	0.263004	+	0.964795i	$0.415287\pi$
$752$	12.8052	+	5.38626i	0.466957	+	0.196417i
$753$		0			0
$754$	−0.954383	−	30.4246i	−0.0347566	−	1.10800i
$755$	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	$0.803974\pi$
$758$	16.3303	−	0.512261i	0.593142	−	0.0186061i
$759$		0			0
$760$	−33.6008	+	15.3672i	−1.21883	+	0.557426i
$761$	21.6921	−	12.5240i	0.786339	−	0.453993i	−0.0523332	−	0.998630i	$-0.516666\pi$
$761$	21.6921	−	12.5240i	0.786339	−	0.453993i	0.838672	+	0.544637i	$0.183332\pi$
$762$		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	0.835772	−	0.549077i	$-0.185021\pi$
$769$	−1.59810	−	2.76799i	−0.0576290	−	0.0998164i	−0.893401	+	0.449261i	$0.851687\pi$
$770$	11.6291	−	14.3522i	0.419084	−	0.517218i
$771$		0			0
$772$	17.3251	−	11.5079i	0.623543	−	0.414178i
$773$	−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
$776$	−2.83723	+	6.19422i	−0.101851	+	0.222360i
$777$		0			0
$778$	−1.06923	+	1.99382i	−0.0383336	+	0.0714820i
$779$	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	0.992715	+	0.120488i	$0.0384461\pi$
$787$	16.8518	+	29.1883i	0.600703	+	1.04045i	−0.392011	+	0.919960i	$0.628221\pi$
$788$	−16.2822	+	1.02251i	−0.580030	+	0.0364255i
$789$		0			0
$790$	1.48076	−	9.33156i	0.0526830	−	0.332002i
$791$	−27.2469			−0.968787
$792$		0			0
$793$			8.58910i			0.305008i
$794$	36.6629	−	1.15007i	1.30112	−	0.0408145i
$795$		0			0
$796$	−1.15095	−	18.3273i	−0.0407942	−	0.649596i
$797$	14.4698	+	25.0624i	0.512546	+	0.887755i	0.999894	+	0.0145477i	$0.00463085\pi$
$797$	14.4698	+	25.0624i	0.512546	+	0.887755i	−0.487348	+	0.873208i	$0.662036\pi$
$798$		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
$805$	0.0991340	+	0.284888i	0.00349401	+	0.0100410i
$806$	24.7562	+	13.2760i	0.872002	+	0.467628i
$807$		0			0
$808$	5.34126	−	11.6610i	0.187905	−	0.410233i
$809$			14.9996i			0.527358i	0.964610	+	0.263679i	$0.0849360\pi$
$809$			14.9996i			0.527358i	−0.964610	+	0.263679i	$0.915064\pi$
$810$		0			0
$811$		−	17.4677i		−	0.613376i	−0.951810	−	0.306688i	$-0.900779\pi$
$811$		−	17.4677i		−	0.613376i	0.951810	−	0.306688i	$-0.0992207\pi$
$812$	−11.6384	+	7.73063i	−0.408429	+	0.271292i
$813$		0			0
$814$	−9.48597	+	17.6888i	−0.332483	+	0.619993i
$815$	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
$820$	10.9487	−	14.4139i	0.382344	−	0.503355i
$821$	−15.8290	−	9.13886i	−0.552435	−	0.318948i	0.197669	−	0.980269i	$-0.436663\pi$
$821$	−15.8290	−	9.13886i	−0.552435	−	0.318948i	−0.750103	+	0.661320i	$0.769996\pi$
$822$		0			0
$823$	14.6369	+	25.3518i	0.510210	+	0.883710i	0.999930	+	0.0118300i	$0.00376570\pi$
$823$	14.6369	+	25.3518i	0.510210	+	0.883710i	−0.489720	+	0.871880i	$0.662901\pi$
$824$	8.99912	−	6.39301i	0.313499	−	0.222711i
$825$		0			0
$826$	−0.162554	−	5.18204i	−0.00565598	−	0.180306i
$827$			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	$0.761879\pi$
$830$	6.64381	−	41.8685i	0.230610	−	1.45328i
$831$		0			0
$832$	24.9145	−	21.4906i	0.863754	−	0.745053i
$833$	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	0.358810	+	0.933411i	$0.383183\pi$
$839$	−18.2179	+	31.5544i	−0.628953	+	1.08938i	−0.987762	+	0.155967i	$0.950151\pi$
$840$		0			0
$841$	−0.805742	−	1.39559i	−0.0277842	−	0.0481237i
$842$	38.2865	+	20.5319i	1.31944	+	0.707575i
$843$		0			0
$844$	17.0650	−	11.3351i	0.587400	−	0.390170i
$845$	1.64250	−	8.59936i	0.0565036	−	0.295827i
$846$		0			0
$847$	−10.8783			−0.373783
$848$	−11.0118	+	1.38855i	−0.378148	+	0.0476830i
$849$		0			0
$850$	29.4379	+	34.8722i	1.00971	+	1.19610i
$851$	−0.163882	−	0.283852i	−0.00561781	−	0.00973033i
$852$		0			0
$853$	27.1128	+	15.6536i	0.928324	+	0.535968i	0.886281	−	0.463148i	$-0.153280\pi$
$853$	27.1128	+	15.6536i	0.928324	+	0.535968i	0.0420430	+	0.999116i	$0.486613\pi$
$854$	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	$-0.783090\pi$
$857$	4.60165	−	7.97029i	0.157189	−	0.272260i	0.933854	+	0.357654i	$0.116423\pi$
$858$		0			0
$859$	−4.62482	+	2.67014i	−0.157797	+	0.0911040i	−0.576819	−	0.816872i	$-0.695706\pi$
$859$	−4.62482	+	2.67014i	−0.157797	+	0.0911040i	0.419022	+	0.907976i	$0.362373\pi$
$860$	2.16238	−	17.0692i	0.0737365	−	0.582053i
$861$		0			0
$862$	1.55656	+	49.6214i	0.0530168	+	1.69011i
$863$			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
$866$	34.6372	−	1.08653i	1.17702	−	0.0369217i
$867$		0			0
$868$	−0.808150	−	12.8688i	−0.0274304	−	0.436794i
$869$	−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	−0.812135	−	0.583469i	$-0.801695\pi$
$877$	−21.1121	+	12.1891i	−0.712904	+	0.411595i	0.0992316	+	0.995064i	$0.468362\pi$
$878$	11.8650	−	22.1251i	0.400425	−	0.746686i
$879$		0			0
$880$	2.47572	−	39.0616i	0.0834565	−	1.31677i
$881$		−	42.8577i		−	1.44391i	−0.691939	−	0.721956i	$-0.743243\pi$
$881$		−	42.8577i		−	1.44391i	0.691939	−	0.721956i	$-0.256757\pi$
$882$		0			0
$883$	28.8663			0.971427			0.485713	−	0.874118i	$-0.338560\pi$
$883$	28.8663			0.971427			0.485713	+	0.874118i	$0.338560\pi$
$884$	44.2212	−	29.3732i	1.48732	−	0.987927i
$885$		0			0
$886$	−4.69779	+	8.76013i	−0.157825	+	0.294302i
$887$	13.1498	−	7.59206i	0.441528	−	0.254917i	−0.262717	−	0.964873i	$-0.584619\pi$
$887$	13.1498	−	7.59206i	0.441528	−	0.254917i	0.704246	+	0.709956i	$0.251285\pi$
$888$		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
$895$	−39.4136	+	13.7149i	−1.31745	+	0.458440i
$896$	−14.4096	−	4.52205i	−0.481390	−	0.151071i
$897$		0			0
$898$	−23.5713	+	0.739402i	−0.786584	+	0.0246742i
$899$	−25.2757			−0.842990
$900$		0			0
$901$	−17.9081			−0.596605
$902$	−25.0355	+	0.785334i	−0.833592	+	0.0261488i
$903$		0			0
$904$	−47.0649	+	33.4351i	−1.56536	+	1.11204i
$905$	−42.0855	+	14.6447i	−1.39897	+	0.486806i
$906$		0			0
$907$	−13.5599	+	23.4865i	−0.450250	+	0.779856i	−0.998401	−	0.0565230i	$-0.981999\pi$
$907$	−13.5599	+	23.4865i	−0.450250	+	0.779856i	0.548151	+	0.836379i	$0.315332\pi$
$908$	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	$-0.873291\pi$
$911$	−3.77888	+	6.54521i	−0.125200	+	0.216852i	0.796611	+	0.604492i	$0.206624\pi$
$912$		0			0
$913$	−50.8036	+	29.3315i	−1.68135	+	0.970729i
$914$	19.8490	−	37.0131i	0.656546	−	1.22428i
$915$		0			0
$916$	1.66140	+	2.50124i	0.0548943	+	0.0826431i
$917$	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	$0.811975\pi$
$920$	0.520830	+	0.370453i	0.0171713	+	0.0122135i
$921$		0			0
$922$	9.46531	−	17.6503i	0.311723	−	0.581281i
$923$	−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	−0.436622	−	0.899645i	$-0.643825\pi$
$929$	−43.7091	−	25.2355i	−1.43405	−	0.827949i	−0.997427	+	0.0716964i	$0.977159\pi$
$930$		0			0
$931$	26.4001	−	15.2421i	0.865227	−	0.499539i
$932$	−27.0433	+	1.69830i	−0.885833	+	0.0556298i
$933$		0			0
$934$	26.5697	−	0.833458i	0.869386	−	0.0272716i
$935$	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	$-0.253439\pi$
$938$	−0.0256049	−	0.816256i	−0.000836031	−	0.0266517i
$939$		0			0
$940$	−15.4084	−	1.95200i	−0.502568	−	0.0636671i
$941$	12.5420	−	7.24115i	0.408859	−	0.236055i	−0.281441	−	0.959579i	$-0.590812\pi$
$941$	12.5420	−	7.24115i	0.408859	−	0.236055i	0.690299	+	0.723524i	$0.257479\pi$
$942$		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	$-0.125445\pi$
$947$	32.3885	+	18.6995i	1.05249	+	0.607653i	0.129141	+	0.991626i	$0.458778\pi$
$948$		0			0
$949$	14.9740	+	25.9357i	0.486077	+	0.841910i
$950$	31.5659	−	26.6468i	1.02413	−	0.864538i
$951$		0			0
$952$	−22.1541	−	10.1476i	−0.718019	−	0.328884i
$953$	−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
$956$	−16.2077	−	24.4006i	−0.524194	−	0.789172i
$957$		0			0
$958$	37.9030	+	20.3262i	1.22459	+	0.656711i
$959$	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	−0.767625	−	0.640899i	$-0.778562\pi$
$967$	−29.1950	−	50.5672i	−0.938848	−	1.62613i	−0.171223	−	0.985232i	$-0.554772\pi$
$968$	−18.7906	+	13.3489i	−0.603954	+	0.429051i
$969$		0			0
$970$	1.19379	−	7.52314i	0.0383304	−	0.241553i
$971$	−35.2792			−1.13216			−0.566082	−	0.824349i	$-0.691541\pi$
$971$	−35.2792			−1.13216			−0.566082	+	0.824349i	$0.691541\pi$
$972$		0			0
$973$		−	0.317795i		−	0.0101881i
$974$	−0.163123	−	5.20018i	−0.00522680	−	0.166624i
$975$		0			0
$976$	3.23888	−	7.70004i	0.103674	−	0.246472i
$977$	4.78940	+	8.29548i	0.153226	+	0.265396i	0.932412	−	0.361398i	$-0.117700\pi$
$977$	4.78940	+	8.29548i	0.153226	+	0.265396i	−0.779185	+	0.626794i	$0.784367\pi$
$978$		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	0.867229	−	0.497910i	$-0.165899\pi$
$983$	27.2657	+	15.7419i	0.869641	+	0.502088i	0.00241215	+	0.999997i	$0.499232\pi$
$984$		0			0
$985$	17.2268	−	5.99448i	0.548890	−	0.191000i
$986$	−22.5745	+	42.0955i	−0.718919	+	1.34059i
$987$		0			0
$988$	−26.5882	−	40.0285i	−0.845885	−	1.27348i
$989$		−	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	$-0.162605\pi$
$992$	−17.1874	−	21.2372i	−0.545702	−	0.674281i
$993$		0			0
$994$	14.0050	+	7.51047i	0.444213	+	0.238218i
$995$	6.74742	+	19.3905i	0.213908	+	0.614721i
$996$		0			0
$997$	−29.1919	−	16.8539i	−0.924516	−	0.533770i	−0.0394432	−	0.999222i	$-0.512558\pi$
$997$	−29.1919	−	16.8539i	−0.924516	−	0.533770i	−0.885073	+	0.465452i	$0.845892\pi$
$998$	−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.359.13		48
3.2	odd	2		180.2.n.d.119.12	yes	48
4.3	odd	2	inner	540.2.n.d.359.5		48
5.4	even	2	inner	540.2.n.d.359.12		48
9.4	even	3		180.2.n.d.59.5	✓	48
9.5	odd	6	inner	540.2.n.d.179.20		48
12.11	even	2		180.2.n.d.119.20	yes	48
15.2	even	4		900.2.r.g.551.24		48
15.8	even	4		900.2.r.g.551.1		48
15.14	odd	2		180.2.n.d.119.13	yes	48
20.19	odd	2	inner	540.2.n.d.359.20		48
36.23	even	6	inner	540.2.n.d.179.12		48
36.31	odd	6		180.2.n.d.59.13	yes	48
45.4	even	6		180.2.n.d.59.20	yes	48
45.13	odd	12		900.2.r.g.851.8		48
45.14	odd	6	inner	540.2.n.d.179.5		48
45.22	odd	12		900.2.r.g.851.17		48
60.23	odd	4		900.2.r.g.551.8		48
60.47	odd	4		900.2.r.g.551.17		48
60.59	even	2		180.2.n.d.119.5	yes	48
180.59	even	6	inner	540.2.n.d.179.13		48
180.67	even	12		900.2.r.g.851.24		48
180.103	even	12		900.2.r.g.851.1		48
180.139	odd	6		180.2.n.d.59.12	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.n.d.59.5	✓	48	9.4	even	3
180.2.n.d.59.12	yes	48	180.139	odd	6
180.2.n.d.59.13	yes	48	36.31	odd	6
180.2.n.d.59.20	yes	48	45.4	even	6
180.2.n.d.119.5	yes	48	60.59	even	2
180.2.n.d.119.12	yes	48	3.2	odd	2
180.2.n.d.119.13	yes	48	15.14	odd	2
180.2.n.d.119.20	yes	48	12.11	even	2
540.2.n.d.179.5		48	45.14	odd	6	inner
540.2.n.d.179.12		48	36.23	even	6	inner
540.2.n.d.179.13		48	180.59	even	6	inner
540.2.n.d.179.20		48	9.5	odd	6	inner
540.2.n.d.359.5		48	4.3	odd	2	inner
540.2.n.d.359.12		48	5.4	even	2	inner
540.2.n.d.359.13		48	1.1	even	1	trivial
540.2.n.d.359.20		48	20.19	odd	2	inner
900.2.r.g.551.1		48	15.8	even	4
900.2.r.g.551.8		48	60.23	odd	4
900.2.r.g.551.17		48	60.47	odd	4
900.2.r.g.551.24		48	15.2	even	4
900.2.r.g.851.1		48	180.103	even	12
900.2.r.g.851.8		48	45.13	odd	12
900.2.r.g.851.17		48	45.22	odd	12
900.2.r.g.851.24		48	180.67	even	12

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)

\(f(q)\)	\(=\)	\(q+(0.0443404 + 1.41352i) q^{2} +(-1.99607 + 0.125352i) q^{4} +(2.11186 - 0.734875i) q^{5} +(0.667441 - 1.15604i) q^{7} +(-0.265693 - 2.81592i) q^{8} +(1.13240 + 2.95257i) q^{10} +(2.18799 - 3.78971i) q^{11} +(-3.56180 + 2.05641i) q^{13} +(1.66368 + 0.892181i) q^{14} +(3.96857 - 0.500421i) q^{16} +6.45392 q^{17} -5.84202i q^{19} +(-4.12330 + 1.73159i) q^{20} +(5.45385 + 2.92473i) q^{22} +(-0.0875178 + 0.0505284i) q^{23} +(3.91992 - 3.10391i) q^{25} +(-3.06470 - 4.94349i) q^{26} +(-1.18735 + 2.39120i) q^{28} +(4.53226 + 2.61670i) q^{29} +(-4.18262 + 2.41484i) q^{31} +(0.883323 + 5.58746i) q^{32} +(0.286169 + 9.12274i) q^{34} +(0.559997 - 2.93189i) q^{35} +3.24337i q^{37} +(8.25780 - 0.259037i) q^{38} +(-2.63046 - 5.75158i) q^{40} +(-3.50518 + 2.02372i) q^{41} +(-1.92364 + 3.33185i) q^{43} +(-3.89233 + 7.83880i) q^{44} +(-0.0753035 - 0.121468i) q^{46} +(3.00768 + 1.73649i) q^{47} +(2.60904 + 4.51900i) q^{49} +(4.56124 + 5.40325i) q^{50} +(6.85183 - 4.55121i) q^{52} -2.77476 q^{53} +(1.83577 - 9.61125i) q^{55} +(-3.43266 - 1.57231i) q^{56} +(-3.49779 + 6.52246i) q^{58} +(-1.37318 - 2.37841i) q^{59} +(1.04419 - 1.80858i) q^{61} +(-3.59888 - 5.80514i) q^{62} +(-7.85881 + 1.49634i) q^{64} +(-6.01084 + 6.96033i) q^{65} +(-0.216298 - 0.374638i) q^{67} +(-12.8825 + 0.809011i) q^{68} +(4.16911 + 0.661566i) q^{70} +8.41810 q^{71} -7.28163i q^{73} +(-4.58456 + 0.143812i) q^{74} +(0.732307 + 11.6611i) q^{76} +(-2.92071 - 5.05882i) q^{77} +(-2.58753 - 1.49391i) q^{79} +(8.01333 - 3.97323i) q^{80} +(-3.01598 - 4.86490i) q^{82} +(-11.6096 - 6.70282i) q^{83} +(13.6298 - 4.74283i) q^{85} +(-4.79492 - 2.57137i) q^{86} +(-11.2529 - 5.15431i) q^{88} +6.97377i q^{89} +5.49013i q^{91} +(0.168358 - 0.111829i) q^{92} +(-2.32119 + 4.32841i) q^{94} +(-4.29315 - 12.3375i) q^{95} +(-2.08608 - 1.20440i) q^{97} +(-6.27200 + 3.88831i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{4} + 18 q^{5} - 16 q^{10} + 42 q^{14} + 30 q^{16} - 26 q^{25} - 4 q^{34} + 10 q^{40} - 96 q^{41} + 4 q^{46} + 32 q^{49} + 90 q^{50} - 6 q^{56} + 8 q^{61} - 20 q^{64} + 6 q^{65} + 4 q^{70} - 72 q^{74}+ \cdots - 62 q^{94}+O(q^{100}) \) 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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