LMFDB - Embedded newform 540.2.n.d.179.10

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			179.10
Character	$\chi$	$=$	540.179
Dual form			540.2.n.d.359.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.356046 - 1.36866i) q^{2} +(-1.74646 + 0.974612i) q^{4} +(0.493735 - 2.18088i) q^{5} +(1.65751 + 2.87089i) q^{7} +(1.95573 + 2.04331i) q^{8} +(-3.16067 + 0.100737i) q^{10} +(1.17952 + 2.04298i) q^{11} +(3.81058 + 2.20004i) q^{13} +(3.33912 - 3.29074i) q^{14} +(2.10026 - 3.40425i) q^{16} -0.889368 q^{17} -3.03537i q^{19} +(1.26322 + 4.29002i) q^{20} +(2.37619 - 2.34176i) q^{22} +(6.29952 + 3.63703i) q^{23} +(-4.51245 - 2.15355i) q^{25} +(1.65437 - 5.99870i) q^{26} +(-5.69278 - 3.39848i) q^{28} +(-1.03714 + 0.598791i) q^{29} +(-0.205172 - 0.118456i) q^{31} +(-5.40705 - 1.66248i) q^{32} +(0.316656 + 1.21724i) q^{34} +(7.07943 - 2.19737i) q^{35} -11.4975i q^{37} +(-4.15440 + 1.08073i) q^{38} +(5.42182 - 3.25636i) q^{40} +(-2.45213 - 1.41574i) q^{41} +(4.17637 + 7.23369i) q^{43} +(-4.05110 - 2.41842i) q^{44} +(2.73494 - 9.91686i) q^{46} +(6.55796 - 3.78624i) q^{47} +(-1.99467 + 3.45488i) q^{49} +(-1.34084 + 6.94278i) q^{50} +(-8.79922 - 0.128451i) q^{52} +0.772055 q^{53} +(5.03787 - 1.56369i) q^{55} +(-2.62447 + 9.00150i) q^{56} +(1.18881 + 1.20629i) q^{58} +(1.06446 - 1.84370i) q^{59} +(1.91303 + 3.31346i) q^{61} +(-0.0890754 + 0.322986i) q^{62} +(-0.350216 + 7.99233i) q^{64} +(6.67943 - 7.22417i) q^{65} +(3.17238 - 5.49472i) q^{67} +(1.55325 - 0.866788i) q^{68} +(-5.52805 - 8.90697i) q^{70} -11.7244 q^{71} +6.10889i q^{73} +(-15.7362 + 4.09365i) q^{74} +(2.95831 + 5.30117i) q^{76} +(-3.91012 + 6.77253i) q^{77} +(-8.94873 + 5.16655i) q^{79} +(-6.38727 - 6.26121i) q^{80} +(-1.06459 + 3.86020i) q^{82} +(2.25103 - 1.29963i) q^{83} +(-0.439112 + 1.93960i) q^{85} +(8.41349 - 8.29156i) q^{86} +(-1.86763 + 6.40565i) q^{88} +4.68130i q^{89} +14.5863i q^{91} +(-14.5466 - 0.212351i) q^{92} +(-7.51702 - 7.62755i) q^{94} +(-6.61978 - 1.49867i) q^{95} +(-5.34684 + 3.08700i) q^{97} +(5.43875 + 1.49994i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.356046	−	1.36866i	−0.251762	−	0.967789i
$2$	−0.356046	−	1.36866i	−0.251762	−	0.967789i
$3$		0			0
$3$		0			0
$4$	−1.74646	+	0.974612i	−0.873231	+	0.487306i
$5$	0.493735	−	2.18088i	0.220805	−	0.975318i
$5$	0.493735	−	2.18088i	0.220805	−	0.975318i
$6$		0			0
$7$	1.65751	+	2.87089i	0.626480	+	1.08509i	0.988253	+	0.152828i	$0.0488382\pi$
$7$	1.65751	+	2.87089i	0.626480	+	1.08509i	−0.361773	+	0.932266i	$0.617828\pi$
$8$	1.95573	+	2.04331i	0.691456	+	0.722418i
$9$		0			0
$10$	−3.16067	+	0.100737i	−0.999492	+	0.0318558i
$11$	1.17952	+	2.04298i	0.355638	+	0.615983i	0.987227	−	0.159320i	$-0.0509303\pi$
$11$	1.17952	+	2.04298i	0.355638	+	0.615983i	−0.631589	+	0.775303i	$0.717597\pi$
$12$		0			0
$13$	3.81058	+	2.20004i	1.05686	+	0.610181i	0.924563	−	0.381029i	$-0.124430\pi$
$13$	3.81058	+	2.20004i	1.05686	+	0.610181i	0.132301	+	0.991210i	$0.457763\pi$
$14$	3.33912	−	3.29074i	0.892419	−	0.879486i
$15$		0			0
$16$	2.10026	−	3.40425i	0.525066	−	0.851061i
$17$	−0.889368			−0.215703			−0.107852	−	0.994167i	$-0.534397\pi$
$17$	−0.889368			−0.215703			−0.107852	+	0.994167i	$0.534397\pi$
$18$		0			0
$19$		−	3.03537i		−	0.696363i	−0.937427	−	0.348181i	$-0.886799\pi$
$19$		−	3.03537i		−	0.696363i	0.937427	−	0.348181i	$-0.113201\pi$
$20$	1.26322	+	4.29002i	0.282464	+	0.959278i
$21$		0			0
$22$	2.37619	−	2.34176i	0.506605	−	0.499264i
$23$	6.29952	+	3.63703i	1.31354	+	0.758374i	0.982681	−	0.185306i	$-0.0593276\pi$
$23$	6.29952	+	3.63703i	1.31354	+	0.758374i	0.330861	+	0.943680i	$0.392661\pi$
$24$		0			0
$25$	−4.51245	−	2.15355i	−0.902490	−	0.430710i
$26$	1.65437	−	5.99870i	0.324448	−	1.17644i
$27$		0			0
$28$	−5.69278	−	3.39848i	−1.07583	−	0.642251i
$29$	−1.03714	+	0.598791i	−0.192592	+	0.111193i	−0.593195	−	0.805059i	$-0.702134\pi$
$29$	−1.03714	+	0.598791i	−0.192592	+	0.111193i	0.400604	+	0.916251i	$0.368800\pi$
$30$		0			0
$31$	−0.205172	−	0.118456i	−0.0368499	−	0.0212753i	0.481462	−	0.876467i	$-0.340106\pi$
$31$	−0.205172	−	0.118456i	−0.0368499	−	0.0212753i	−0.518312	+	0.855192i	$0.673439\pi$
$32$	−5.40705	−	1.66248i	−0.955840	−	0.293888i
$33$		0			0
$34$	0.316656	+	1.21724i	0.0543060	+	0.208755i
$35$	7.07943	−	2.19737i	1.19664	−	0.371423i
$36$		0			0
$37$		−	11.4975i		−	1.89018i	−0.326807	−	0.945091i	$-0.605973\pi$
$37$		−	11.4975i		−	1.89018i	0.326807	−	0.945091i	$-0.394027\pi$
$38$	−4.15440	+	1.08073i	−0.673932	+	0.175318i
$39$		0			0
$40$	5.42182	−	3.25636i	0.857265	−	0.514876i
$41$	−2.45213	−	1.41574i	−0.382958	−	0.221101i	0.296146	−	0.955143i	$-0.404298\pi$
$41$	−2.45213	−	1.41574i	−0.382958	−	0.221101i	−0.679105	+	0.734042i	$0.737632\pi$
$42$		0			0
$43$	4.17637	+	7.23369i	0.636891	+	1.10313i	0.986111	+	0.166087i	$0.0531132\pi$
$43$	4.17637	+	7.23369i	0.636891	+	1.10313i	−0.349220	+	0.937041i	$0.613553\pi$
$44$	−4.05110	−	2.41842i	−0.610726	−	0.364591i
$45$		0			0
$46$	2.73494	−	9.91686i	0.403245	−	1.46216i
$47$	6.55796	−	3.78624i	0.956577	−	0.552280i	0.0614594	−	0.998110i	$-0.480425\pi$
$47$	6.55796	−	3.78624i	0.956577	−	0.552280i	0.895118	+	0.445829i	$0.147091\pi$
$48$		0			0
$49$	−1.99467	+	3.45488i	−0.284954	+	0.493554i
$50$	−1.34084	+	6.94278i	−0.189623	+	0.981857i
$51$		0			0
$52$	−8.79922	−	0.128451i	−1.22023	−	0.0178130i
$53$	0.772055			0.106050			0.0530249	−	0.998593i	$-0.483114\pi$
$53$	0.772055			0.106050			0.0530249	+	0.998593i	$0.483114\pi$
$54$		0			0
$55$	5.03787	−	1.56369i	0.679306	−	0.210848i
$56$	−2.62447	+	9.00150i	−0.350709	+	1.20288i
$57$		0			0
$58$	1.18881	+	1.20629i	0.156098	+	0.158394i
$59$	1.06446	−	1.84370i	0.138581	−	0.240029i	−0.788379	−	0.615190i	$-0.789079\pi$
$59$	1.06446	−	1.84370i	0.138581	−	0.240029i	0.926960	+	0.375161i	$0.122413\pi$
$60$		0			0
$61$	1.91303	+	3.31346i	0.244938	+	0.424245i	0.962114	−	0.272647i	$-0.0878990\pi$
$61$	1.91303	+	3.31346i	0.244938	+	0.424245i	−0.717176	+	0.696892i	$0.754566\pi$
$62$	−0.0890754	+	0.322986i	−0.0113126	+	0.0410193i
$63$		0			0
$64$	−0.350216	+	7.99233i	−0.0437769	+	0.999041i
$65$	6.67943	−	7.22417i	0.828481	−	0.896048i
$66$		0			0
$67$	3.17238	−	5.49472i	0.387567	−	0.671287i	−0.604554	−	0.796564i	$-0.706649\pi$
$67$	3.17238	−	5.49472i	0.387567	−	0.671287i	0.992122	+	0.125277i	$0.0399821\pi$
$68$	1.55325	−	0.866788i	0.188359	−	0.105113i
$69$		0			0
$70$	−5.52805	−	8.90697i	−0.660728	−	1.06459i
$71$	−11.7244			−1.39143			−0.695717	−	0.718316i	$-0.744913\pi$
$71$	−11.7244			−1.39143			−0.695717	+	0.718316i	$0.744913\pi$
$72$		0			0
$73$			6.10889i			0.714992i	0.933915	+	0.357496i	$0.116369\pi$
$73$			6.10889i			0.714992i	−0.933915	+	0.357496i	$0.883631\pi$
$74$	−15.7362	+	4.09365i	−1.82930	+	0.475877i
$75$		0			0
$76$	2.95831	+	5.30117i	0.339342	+	0.608086i
$77$	−3.91012	+	6.77253i	−0.445600	+	0.771802i
$78$		0			0
$79$	−8.94873	+	5.16655i	−1.00681	+	0.581283i	−0.910256	−	0.414045i	$-0.864116\pi$
$79$	−8.94873	+	5.16655i	−1.00681	+	0.581283i	−0.0965546	+	0.995328i	$0.530782\pi$
$80$	−6.38727	−	6.26121i	−0.714118	−	0.700025i
$81$		0			0
$82$	−1.06459	+	3.86020i	−0.117565	+	0.426288i
$83$	2.25103	−	1.29963i	0.247083	−	0.142653i	−0.371345	−	0.928495i	$-0.621103\pi$
$83$	2.25103	−	1.29963i	0.247083	−	0.142653i	0.618428	+	0.785842i	$0.287770\pi$
$84$		0			0
$85$	−0.439112	+	1.93960i	−0.0476284	+	0.210379i
$86$	8.41349	−	8.29156i	0.907250	−	0.894102i
$87$		0			0
$88$	−1.86763	+	6.40565i	−0.199089	+	0.682845i
$89$			4.68130i			0.496217i	0.968732	+	0.248108i	$0.0798089\pi$
$89$			4.68130i			0.496217i	−0.968732	+	0.248108i	$0.920191\pi$
$90$		0			0
$91$			14.5863i			1.52906i
$92$	−14.5466	−	0.212351i	−1.51659	−	0.0221391i
$93$		0			0
$94$	−7.51702	−	7.62755i	−0.775321	−	0.786722i
$95$	−6.61978	−	1.49867i	−0.679175	−	0.153760i
$96$		0			0
$97$	−5.34684	+	3.08700i	−0.542890	+	0.313438i	−0.746249	−	0.665667i	$-0.768147\pi$
$97$	−5.34684	+	3.08700i	−0.542890	+	0.313438i	0.203360	+	0.979104i	$0.434814\pi$
$98$	5.43875	+	1.49994i	0.549397	+	0.151517i
$99$		0			0
$100$	9.97970	−	0.636793i	0.997970	−	0.0636793i
$101$	6.72336	−	3.88174i	0.669000	−	0.386247i	−0.126698	−	0.991941i	$-0.540438\pi$
$101$	6.72336	−	3.88174i	0.669000	−	0.386247i	0.795697	+	0.605694i	$0.207105\pi$
$102$		0			0
$103$	−6.58033	+	11.3975i	−0.648379	+	1.12302i	0.335131	+	0.942171i	$0.391219\pi$
$103$	−6.58033	+	11.3975i	−0.648379	+	1.12302i	−0.983510	+	0.180853i	$0.942114\pi$
$104$	2.95712	+	12.0889i	0.289969	+	1.18541i
$105$		0			0
$106$	−0.274887	−	1.05668i	−0.0266994	−	0.102634i
$107$			0.252175i			0.0243786i	0.999926	+	0.0121893i	$0.00388008\pi$
$107$			0.252175i			0.0243786i	−0.999926	+	0.0121893i	$0.996120\pi$
$108$		0			0
$109$	0.459068			0.0439708			0.0219854	−	0.999758i	$-0.493001\pi$
$109$	0.459068			0.0439708			0.0219854	+	0.999758i	$0.493001\pi$
$110$	−3.93387	−	6.33838i	−0.375080	−	0.604341i
$111$		0			0
$112$	13.2544	+	0.387059i	1.25243	+	0.0365736i
$113$	8.71557	−	15.0958i	0.819892	−	1.42009i	−0.0858696	−	0.996306i	$-0.527367\pi$
$113$	8.71557	−	15.0958i	0.819892	−	1.42009i	0.905761	−	0.423788i	$-0.139300\pi$
$114$		0			0
$115$	11.0422	−	11.9428i	1.02969	−	1.11367i
$116$	1.22773	−	2.05657i	0.113992	−	0.190948i
$117$		0			0
$118$	−2.90240	−	0.800444i	−0.267187	−	0.0736868i
$119$	−1.47414	−	2.55328i	−0.135134	−	0.234059i
$120$		0			0
$121$	2.71748	−	4.70681i	0.247043	−	0.427891i
$122$	3.85388	−	3.79803i	0.348914	−	0.343857i
$123$		0			0
$124$	0.473773	+	0.00691615i	0.0425461	+	0.000621089i
$125$	−6.92458	+	8.77782i	−0.619354	+	0.785112i
$126$		0			0
$127$	−10.5666			−0.937635			−0.468817	−	0.883295i	$-0.655320\pi$
$127$	−10.5666			−0.937635			−0.468817	+	0.883295i	$0.655320\pi$
$128$	11.0635	−	2.36631i	0.977883	−	0.209154i
$129$		0			0
$130$	−12.2656	−	6.56974i	−1.07577	−	0.576204i
$131$	−8.12900	+	14.0798i	−0.710234	+	1.23016i	0.254535	+	0.967064i	$0.418078\pi$
$131$	−8.12900	+	14.0798i	−0.710234	+	1.23016i	−0.964769	+	0.263098i	$0.915256\pi$
$132$		0			0
$133$	8.71423	−	5.03116i	0.755619	−	0.436257i
$134$	−8.64991	−	2.38554i	−0.747239	−	0.206079i
$135$		0			0
$136$	−1.73937	−	1.81725i	−0.149149	−	0.155828i
$137$	6.59587	+	11.4244i	0.563523	+	0.976051i	0.997185	+	0.0749753i	$0.0238878\pi$
$137$	6.59587	+	11.4244i	0.563523	+	0.976051i	−0.433662	+	0.901076i	$0.642779\pi$
$138$		0			0
$139$	5.61535	+	3.24202i	0.476288	+	0.274985i	0.718868	−	0.695146i	$-0.244660\pi$
$139$	5.61535	+	3.24202i	0.476288	+	0.274985i	−0.242580	+	0.970131i	$0.577994\pi$
$140$	−10.2224	+	10.7373i	−0.863949	+	0.907469i
$141$		0			0
$142$	4.17443	+	16.0468i	0.350311	+	1.34661i
$143$			10.3799i			0.868014i
$144$		0			0
$145$	0.793820	+	2.55751i	0.0659232	+	0.212390i
$146$	8.36100	−	2.17505i	0.691961	−	0.180008i
$147$		0			0
$148$	11.2056	+	20.0800i	0.921097	+	1.65057i
$149$	−7.25009	−	4.18584i	−0.593950	−	0.342917i	0.172708	−	0.984973i	$-0.444748\pi$
$149$	−7.25009	−	4.18584i	−0.593950	−	0.342917i	−0.766658	+	0.642056i	$0.778082\pi$
$150$		0			0
$151$	−14.2008	+	8.19886i	−1.15565	+	0.667214i	−0.950257	−	0.311466i	$-0.899180\pi$
$151$	−14.2008	+	8.19886i	−1.15565	+	0.667214i	−0.205391	+	0.978680i	$0.565847\pi$
$152$	6.20220	−	5.93638i	0.503065	−	0.481504i
$153$		0			0
$154$	10.6615	+	2.94030i	0.859127	+	0.236936i
$155$	−0.359638	+	0.388968i	−0.0288868	+	0.0312427i
$156$		0			0
$157$	9.27700	+	5.35608i	0.740386	+	0.427462i	0.822209	−	0.569185i	$-0.192741\pi$
$157$	9.27700	+	5.35608i	0.740386	+	0.427462i	−0.0818239	+	0.996647i	$0.526075\pi$
$158$	10.2574	+	10.4082i	0.816036	+	0.828036i
$159$		0			0
$160$	−6.29531	+	10.9713i	−0.497688	+	0.867356i
$161$			24.1137i			1.90042i
$162$		0			0
$163$	−1.33584			−0.104631			−0.0523153	−	0.998631i	$-0.516660\pi$
$163$	−1.33584			−0.104631			−0.0523153	+	0.998631i	$0.516660\pi$
$164$	5.66235	+	0.0826590i	0.442155	+	0.00645459i
$165$		0			0
$166$	−2.58023	−	2.61817i	−0.200265	−	0.203209i
$167$	−6.20942	−	3.58501i	−0.480500	−	0.277417i	0.240125	−	0.970742i	$-0.422812\pi$
$167$	−6.20942	−	3.58501i	−0.480500	−	0.277417i	−0.720625	+	0.693325i	$0.756145\pi$
$168$		0			0
$169$	3.18034	+	5.50851i	0.244641	+	0.423731i
$170$	2.81100	−	0.0895921i	0.215594	−	0.00687140i
$171$		0			0
$172$	−14.3439	−	8.56303i	−1.09371	−	0.652925i
$173$	−1.28765	−	2.23027i	−0.0978979	−	0.169564i	0.812916	−	0.582380i	$-0.197879\pi$
$173$	−1.28765	−	2.23027i	−0.0978979	−	0.169564i	−0.910814	+	0.412816i	$0.864545\pi$
$174$		0			0
$175$	−1.29682	−	16.5243i	−0.0980307	−	1.24912i
$176$	9.43212	+	0.275439i	0.710973	+	0.0207620i
$177$		0			0
$178$	6.40711	−	1.66676i	0.480233	−	0.124929i
$179$	10.1847			0.761243			0.380622	−	0.924731i	$-0.375710\pi$
$179$	10.1847			0.761243			0.380622	+	0.924731i	$0.375710\pi$
$180$		0			0
$181$	4.17537			0.310353			0.155176	−	0.987887i	$-0.450405\pi$
$181$	4.17537			0.310353			0.155176	+	0.987887i	$0.450405\pi$
$182$	19.9637	−	5.19340i	1.47981	−	0.384961i
$183$		0			0
$184$	4.88861	+	19.9849i	0.360393	+	1.47331i
$185$	−25.0747	−	5.67673i	−1.84353	−	0.417362i
$186$		0			0
$187$	−1.04902	−	1.81696i	−0.0767123	−	0.132870i
$188$	−7.76312	+	13.0040i	−0.566184	+	0.948414i
$189$		0			0
$190$	0.305774	+	9.59382i	0.0221832	+	0.696009i
$191$	−12.5152	−	21.6770i	−0.905570	−	1.56849i	−0.820151	−	0.572147i	$-0.806111\pi$
$191$	−12.5152	−	21.6770i	−0.905570	−	1.56849i	−0.0854186	−	0.996345i	$-0.527223\pi$
$192$		0			0
$193$	−16.3830	−	9.45871i	−1.17927	−	0.680853i	−0.223426	−	0.974721i	$-0.571724\pi$
$193$	−16.3830	−	9.45871i	−1.17927	−	0.680853i	−0.955846	+	0.293868i	$0.905057\pi$
$194$	6.12878	+	6.21890i	0.440021	+	0.446491i
$195$		0			0
$196$	0.116461	−	7.97785i	0.00831863	−	0.569846i
$197$	−5.25418			−0.374345			−0.187172	−	0.982327i	$-0.559932\pi$
$197$	−5.25418			−0.374345			−0.187172	+	0.982327i	$0.559932\pi$
$198$		0			0
$199$		−	18.8487i		−	1.33615i	−0.744095	−	0.668074i	$-0.767119\pi$
$199$		−	18.8487i		−	1.33615i	0.744095	−	0.668074i	$-0.232881\pi$
$200$	−4.42478	−	13.4321i	−0.312880	−	0.949793i
$201$		0			0
$202$	−7.70660	−	7.81993i	−0.542235	−	0.550208i
$203$	−3.43813	−	1.98500i	−0.241309	−	0.139320i
$204$		0			0
$205$	−4.29825	+	4.64879i	−0.300203	+	0.324686i
$206$	17.9421	+	4.94821i	1.25009	+	0.344758i
$207$		0			0
$208$	15.4927	−	8.35148i	1.07423	−	0.579071i
$209$	6.20122	−	3.58028i	0.428948	−	0.247653i
$210$		0			0
$211$	3.96081	+	2.28678i	0.272674	+	0.157428i	0.630102	−	0.776512i	$-0.283013\pi$
$211$	3.96081	+	2.28678i	0.272674	+	0.157428i	−0.357428	+	0.933941i	$0.616346\pi$
$212$	−1.34837	+	0.752454i	−0.0926061	+	0.0516787i
$213$		0			0
$214$	0.345141	−	0.0897857i	0.0235934	−	0.00613762i
$215$	17.8378	−	5.53663i	1.21653	−	0.377595i
$216$		0			0
$217$		−	0.785367i		−	0.0533142i
$218$	−0.163449	−	0.628309i	−0.0110702	−	0.0425544i
$219$		0			0
$220$	−7.27446	+	7.64089i	−0.490444	+	0.515149i
$221$	−3.38900	−	1.95664i	−0.227969	−	0.131618i
$222$		0			0
$223$	−11.8767	−	20.5711i	−0.795323	−	1.37754i	−0.922634	−	0.385677i	$-0.873968\pi$
$223$	−11.8767	−	20.5711i	−0.795323	−	1.37754i	0.127310	−	0.991863i	$-0.459366\pi$
$224$	−4.18943	−	18.2786i	−0.279918	−	1.22129i
$225$		0			0
$226$	−23.7642	−	6.55386i	−1.58077	−	0.435956i
$227$	−24.1252	+	13.9287i	−1.60124	+	0.924478i	−0.610005	+	0.792398i	$0.708832\pi$
$227$	−24.1252	+	13.9287i	−1.60124	+	0.924478i	−0.991239	+	0.132081i	$0.957834\pi$
$228$		0			0
$229$	8.35991	−	14.4798i	0.552439	−	0.956852i	−0.445659	−	0.895203i	$-0.647031\pi$
$229$	8.35991	−	14.4798i	0.552439	−	0.956852i	0.998098	−	0.0616492i	$-0.0196360\pi$
$230$	−20.2771	−	10.8609i	−1.33703	−	0.716145i
$231$		0			0
$232$	−3.25188	−	0.948115i	−0.213496	−	0.0622468i
$233$	1.67938			0.110020			0.0550101	−	0.998486i	$-0.482481\pi$
$233$	1.67938			0.110020			0.0550101	+	0.998486i	$0.482481\pi$
$234$		0			0
$235$	−5.01943	−	16.1715i	−0.327432	−	1.05491i
$236$	−0.0621495	+	4.25739i	−0.00404559	+	0.277133i
$237$		0			0
$238$	−2.96971	+	2.92667i	−0.192498	+	0.189708i
$239$	5.41085	−	9.37186i	0.349999	−	0.606215i	−0.636250	−	0.771483i	$-0.719515\pi$
$239$	5.41085	−	9.37186i	0.349999	−	0.606215i	0.986249	+	0.165267i	$0.0528487\pi$
$240$		0			0
$241$	−5.45657	−	9.45105i	−0.351488	−	0.608796i	0.635022	−	0.772494i	$-0.280991\pi$
$241$	−5.45657	−	9.45105i	−0.351488	−	0.608796i	−0.986510	+	0.163698i	$0.947658\pi$
$242$	−7.40957	−	2.04346i	−0.476305	−	0.131359i
$243$		0			0
$244$	−6.57037	−	3.92238i	−0.420625	−	0.251104i
$245$	6.54982	+	6.05593i	0.418453	+	0.386899i
$246$		0			0
$247$	6.67794	−	11.5665i	0.424907	−	0.735961i
$248$	−0.159219	−	0.650897i	−0.0101104	−	0.0413320i
$249$		0			0
$250$	14.4793	+	6.35210i	0.915753	+	0.401742i
$251$	−5.05766			−0.319237			−0.159618	−	0.987179i	$-0.551026\pi$
$251$	−5.05766			−0.319237			−0.159618	+	0.987179i	$0.551026\pi$
$252$		0			0
$253$			17.1598i			1.07883i
$254$	3.76220	+	14.4621i	0.236061	+	0.907433i
$255$		0			0
$256$	−7.17778	−	14.2996i	−0.448611	−	0.893727i
$257$	6.69541	−	11.5968i	0.417649	−	0.723388i	−0.578054	−	0.815999i	$-0.696188\pi$
$257$	6.69541	−	11.5968i	0.417649	−	0.723388i	0.995702	+	0.0926101i	$0.0295210\pi$
$258$		0			0
$259$	33.0081	−	19.0573i	2.05103	−	1.18416i
$260$	−4.62462	+	19.1266i	−0.286807	+	1.18618i
$261$		0			0
$262$	22.1648	+	6.11278i	1.36935	+	0.377649i
$263$	−9.43213	+	5.44564i	−0.581610	+	0.335793i	−0.761773	−	0.647844i	$-0.775671\pi$
$263$	−9.43213	+	5.44564i	−0.581610	+	0.335793i	0.180163	+	0.983637i	$0.442337\pi$
$264$		0			0
$265$	0.381190	−	1.68376i	0.0234163	−	0.103432i
$266$	−9.98862	−	10.1355i	−0.612441	−	0.621447i
$267$		0			0
$268$	−0.185222	+	12.6882i	−0.0113142	+	0.775052i
$269$		−	21.5020i		−	1.31100i	−0.755195	−	0.655500i	$-0.772458\pi$
$269$		−	21.5020i		−	1.31100i	0.755195	−	0.655500i	$-0.227542\pi$
$270$		0			0
$271$			18.9445i			1.15080i	0.817873	+	0.575399i	$0.195153\pi$
$271$			18.9445i			1.15080i	−0.817873	+	0.575399i	$0.804847\pi$
$272$	−1.86791	+	3.02763i	−0.113258	+	0.183577i
$273$		0			0
$274$	13.2877	−	13.0951i	0.802737	−	0.791105i
$275$	−0.922846	−	11.7590i	−0.0556497	−	0.709096i
$276$		0			0
$277$	−16.1616	+	9.33092i	−0.971058	+	0.560641i	−0.899559	−	0.436800i	$-0.856112\pi$
$277$	−16.1616	+	9.33092i	−0.971058	+	0.560641i	−0.0714994	+	0.997441i	$0.522778\pi$
$278$	2.43791	−	8.83982i	0.146216	−	0.530177i
$279$		0			0
$280$	18.3354	+	10.1680i	1.09575	+	0.607654i
$281$	5.84683	−	3.37567i	0.348792	−	0.201375i	−0.315361	−	0.948972i	$-0.602126\pi$
$281$	5.84683	−	3.37567i	0.348792	−	0.201375i	0.664153	+	0.747596i	$0.268792\pi$
$282$		0			0
$283$	−2.63488	+	4.56374i	−0.156627	+	0.271286i	−0.933650	−	0.358186i	$-0.883395\pi$
$283$	−2.63488	+	4.56374i	−0.156627	+	0.271286i	0.777023	+	0.629472i	$0.216729\pi$
$284$	20.4763	−	11.4268i	1.21504	−	0.678054i
$285$		0			0
$286$	14.2066	−	3.69573i	0.840054	−	0.218533i
$287$		−	9.38639i		−	0.554061i
$288$		0			0
$289$	−16.2090			−0.953472
$290$	3.21773	−	1.99706i	0.188952	−	0.117272i
$291$		0			0
$292$	−5.95380	−	10.6690i	−0.348420	−	0.624353i
$293$	−11.1453	+	19.3041i	−0.651113	+	1.12776i	0.331741	+	0.943371i	$0.392364\pi$
$293$	−11.1453	+	19.3041i	−0.651113	+	1.12776i	−0.982853	+	0.184390i	$0.940969\pi$
$294$		0			0
$295$	−3.49532	−	3.23176i	−0.203506	−	0.188160i
$296$	23.4930	−	22.4861i	1.36550	−	1.30698i
$297$		0			0
$298$	−3.14763	+	11.4133i	−0.182337	+	0.661153i
$299$	16.0032	+	27.7184i	0.925490	+	1.60300i
$300$		0			0
$301$	−13.8448	+	23.9798i	−0.797999	+	1.38217i
$302$	16.2776	+	16.5170i	0.936671	+	0.950444i
$303$		0			0
$304$	−10.3332	−	6.37509i	−0.592647	−	0.365636i
$305$	8.17078	−	2.53611i	0.467857	−	0.145217i
$306$		0			0
$307$	0.415414			0.0237089			0.0118545	−	0.999930i	$-0.496227\pi$
$307$	0.415414			0.0237089			0.0118545	+	0.999930i	$0.496227\pi$
$308$	0.228296	−	15.6388i	0.0130084	−	0.891105i
$309$		0			0
$310$	0.660413	+	0.353732i	0.0375090	+	0.0200906i
$311$	−0.284562	+	0.492876i	−0.0161360	+	0.0279484i	−0.873981	−	0.485961i	$-0.838470\pi$
$311$	−0.284562	+	0.492876i	−0.0161360	+	0.0279484i	0.857845	+	0.513909i	$0.171803\pi$
$312$		0			0
$313$	24.3028	−	14.0312i	1.37367	−	0.793091i	0.382285	−	0.924044i	$-0.375137\pi$
$313$	24.3028	−	14.0312i	1.37367	−	0.793091i	0.991388	+	0.130954i	$0.0418039\pi$
$314$	4.02762	−	14.6041i	0.227292	−	0.824156i
$315$		0			0
$316$	10.5932	−	17.7447i	0.595917	−	0.998219i
$317$	−6.63676	−	11.4952i	−0.372758	−	0.645635i	0.617231	−	0.786782i	$-0.288254\pi$
$317$	−6.63676	−	11.4952i	−0.372758	−	0.645635i	−0.989989	+	0.141147i	$0.954921\pi$
$318$		0			0
$319$	−2.44664	−	1.41257i	−0.136986	−	0.0790887i
$320$	17.2574	+	4.70987i	0.964717	+	0.263290i
$321$		0			0
$322$	33.0034	−	8.58557i	1.83921	−	0.478455i
$323$			2.69956i			0.150208i
$324$		0			0
$325$	−12.4572	−	18.1338i	−0.690999	−	1.00588i
$326$	0.475619	+	1.82830i	0.0263421	+	0.101260i
$327$		0			0
$328$	−1.90292	−	7.77926i	−0.105071	−	0.429538i
$329$	21.7398	+	12.5515i	1.19855	+	0.691985i
$330$		0			0
$331$	−7.43989	+	4.29542i	−0.408933	+	0.236098i	−0.690331	−	0.723493i	$-0.742535\pi$
$331$	−7.43989	+	4.29542i	−0.408933	+	0.236098i	0.281398	+	0.959591i	$0.409202\pi$
$332$	−2.66471	+	4.46364i	−0.146245	+	0.244974i
$333$		0			0
$334$	−2.69583	+	9.77502i	−0.147509	+	0.534865i
$335$	−10.4170	−	9.63150i	−0.569141	−	0.526225i
$336$		0			0
$337$	−0.914017	−	0.527708i	−0.0497897	−	0.0287461i	0.474899	−	0.880041i	$-0.342485\pi$
$337$	−0.914017	−	0.527708i	−0.0497897	−	0.0287461i	−0.524688	+	0.851294i	$0.675818\pi$
$338$	6.40693	−	6.31409i	0.348491	−	0.343441i
$339$		0			0
$340$	−1.12347	−	3.81541i	−0.0609285	−	0.206919i
$341$		−	0.558884i		−	0.0302652i
$342$		0			0
$343$	9.98036			0.538889
$344$	−6.61279	+	22.6808i	−0.356538	+	1.22287i
$345$		0			0
$346$	−2.59402	+	2.55643i	−0.139455	+	0.137434i
$347$	5.97844	+	3.45165i	0.320939	+	0.185294i	0.651811	−	0.758381i	$-0.274009\pi$
$347$	5.97844	+	3.45165i	0.320939	+	0.185294i	−0.330872	+	0.943676i	$0.607343\pi$
$348$		0			0
$349$	−15.5145	−	26.8719i	−0.830473	−	1.43842i	−0.897663	−	0.440682i	$-0.854737\pi$
$349$	−15.5145	−	26.8719i	−0.830473	−	1.43842i	0.0671899	−	0.997740i	$-0.478597\pi$
$350$	−22.1544	+	7.65831i	−1.18420	+	0.409354i
$351$		0			0
$352$	−2.98128	−	13.0074i	−0.158903	−	0.693299i
$353$	7.67847	+	13.2995i	0.408684	+	0.707861i	0.994743	−	0.102408i	$-0.0326546\pi$
$353$	7.67847	+	13.2995i	0.408684	+	0.707861i	−0.586059	+	0.810269i	$0.699321\pi$
$354$		0			0
$355$	−5.78876	+	25.5695i	−0.307235	+	1.35709i
$356$	−4.56245	−	8.17572i	−0.241809	−	0.433312i
$357$		0			0
$358$	−3.62623	−	13.9394i	−0.191652	−	0.736723i
$359$	−8.51196			−0.449244			−0.224622	−	0.974446i	$-0.572115\pi$
$359$	−8.51196			−0.449244			−0.224622	+	0.974446i	$0.572115\pi$
$360$		0			0
$361$	9.78650			0.515079
$362$	−1.48662	−	5.71466i	−0.0781352	−	0.300356i
$363$		0			0
$364$	−14.2160	−	25.4745i	−0.745122	−	1.33523i
$365$	13.3227	+	3.01617i	0.697344	+	0.157874i
$366$		0			0
$367$	0.646542	+	1.11984i	0.0337492	+	0.0584553i	0.882407	−	0.470488i	$-0.155922\pi$
$367$	0.646542	+	1.11984i	0.0337492	+	0.0584553i	−0.848657	+	0.528943i	$0.822589\pi$
$368$	25.6120	−	13.8064i	1.33512	−	0.719708i
$369$		0			0
$370$	1.15823	+	36.3399i	0.0602133	+	1.88922i
$371$	1.27969	+	2.21648i	0.0664381	+	0.115074i
$372$		0			0
$373$	−14.1837	−	8.18898i	−0.734406	−	0.424010i	0.0856259	−	0.996327i	$-0.472711\pi$
$373$	−14.1837	−	8.18898i	−0.734406	−	0.424010i	−0.820032	+	0.572318i	$0.806044\pi$
$374$	−2.11331	+	2.08268i	−0.109276	+	0.107693i
$375$		0			0
$376$	20.5621	+	5.99506i	1.06041	+	0.309172i
$377$	−5.26946			−0.271391
$378$		0			0
$379$			11.7940i			0.605818i	0.953020	+	0.302909i	$0.0979578\pi$
$379$			11.7940i			0.605818i	−0.953020	+	0.302909i	$0.902042\pi$
$380$	13.0218	−	3.83434i	0.668005	−	0.196698i
$381$		0			0
$382$	−25.2125	+	24.8471i	−1.28998	+	1.27129i
$383$	−9.75933	−	5.63455i	−0.498678	−	0.287912i	0.229489	−	0.973311i	$-0.426294\pi$
$383$	−9.75933	−	5.63455i	−0.498678	−	0.287912i	−0.728168	+	0.685399i	$0.759628\pi$
$384$		0			0
$385$	12.8395	+	11.8713i	0.654361	+	0.605019i
$386$	−7.11268	+	25.7905i	−0.362026	+	1.31270i
$387$		0			0
$388$	6.32944	−	10.6024i	0.321328	−	0.538257i
$389$	−17.4583	+	10.0796i	−0.885172	+	0.511054i	−0.872360	−	0.488864i	$-0.837411\pi$
$389$	−17.4583	+	10.0796i	−0.885172	+	0.511054i	−0.0128115	+	0.999918i	$0.504078\pi$
$390$		0			0
$391$	−5.60259	−	3.23466i	−0.283335	−	0.163584i
$392$	−10.9604	+	2.68108i	−0.553585	+	0.135415i
$393$		0			0
$394$	1.87073	+	7.19119i	0.0942460	+	0.362287i
$395$	6.84932	+	22.0670i	0.344627	+	1.11031i
$396$		0			0
$397$			5.11859i			0.256895i	0.991716	+	0.128447i	$0.0409993\pi$
$397$			5.11859i			0.256895i	−0.991716	+	0.128447i	$0.959001\pi$
$398$	−25.7975	+	6.71100i	−1.29311	+	0.336392i
$399$		0			0
$400$	−16.8086	+	10.8385i	−0.840428	+	0.541924i
$401$	−9.58291	−	5.53269i	−0.478548	−	0.276290i	0.241263	−	0.970460i	$-0.422438\pi$
$401$	−9.58291	−	5.53269i	−0.478548	−	0.276290i	−0.719811	+	0.694170i	$0.755772\pi$
$402$		0			0
$403$	−0.521215	−	0.902771i	−0.0259636	−	0.0449702i
$404$	−7.95892	+	13.3320i	−0.395971	+	0.663291i
$405$		0			0
$406$	−1.49267	+	5.41238i	−0.0740798	+	0.268612i
$407$	23.4893	−	13.5615i	1.16432	−	0.672221i
$408$		0			0
$409$	−8.08315	+	14.0004i	−0.399686	+	0.692276i	−0.993687	−	0.112188i	$-0.964214\pi$
$409$	−8.08315	+	14.0004i	−0.399686	+	0.692276i	0.594001	+	0.804464i	$0.297548\pi$
$410$	7.89300	+	4.22766i	0.389807	+	0.208789i
$411$		0			0
$412$	0.384198	−	26.3185i	0.0189281	−	1.29662i
$413$	7.05742			0.347273
$414$		0			0
$415$	−1.72293	−	5.55090i	−0.0845753	−	0.272483i
$416$	−16.9465	−	18.2307i	−0.830868	−	0.893835i
$417$		0			0
$418$	−7.10810	−	7.21263i	−0.347669	−	0.352781i
$419$	3.65564	−	6.33176i	0.178590	−	0.309327i	−0.762808	−	0.646625i	$-0.776180\pi$
$419$	3.65564	−	6.33176i	0.178590	−	0.309327i	0.941398	+	0.337298i	$0.109513\pi$
$420$		0			0
$421$	14.9731	+	25.9341i	0.729742	+	1.26395i	0.956992	+	0.290114i	$0.0936932\pi$
$421$	14.9731	+	25.9341i	0.729742	+	1.26395i	−0.227250	+	0.973836i	$0.572973\pi$
$422$	1.71959	−	6.23521i	0.0837083	−	0.303525i
$423$		0			0
$424$	1.50993	+	1.57755i	0.0733288	+	0.0766124i
$425$	4.01323	+	1.91530i	0.194670	+	0.0929056i
$426$		0			0
$427$	−6.34172	+	10.9842i	−0.306897	+	0.531562i
$428$	−0.245772	−	0.440413i	−0.0118798	−	0.0212882i
$429$		0			0
$430$	−13.9289	−	22.4426i	−0.671709	−	1.08228i
$431$	−30.7505			−1.48120			−0.740599	−	0.671947i	$-0.765458\pi$
$431$	−30.7505			−1.48120			−0.740599	+	0.671947i	$0.765458\pi$
$432$		0			0
$433$			29.3734i			1.41160i	0.708413	+	0.705798i	$0.249411\pi$
$433$			29.3734i			1.41160i	−0.708413	+	0.705798i	$0.750589\pi$
$434$	−1.07490	+	0.279627i	−0.0515969	+	0.0134225i
$435$		0			0
$436$	−0.801746	+	0.447413i	−0.0383967	+	0.0214272i
$437$	11.0398	−	19.1214i	0.528103	−	0.914701i
$438$		0			0
$439$	−6.77418	+	3.91108i	−0.323314	+	0.186665i	−0.652869	−	0.757471i	$-0.726435\pi$
$439$	−6.77418	+	3.91108i	−0.323314	+	0.186665i	0.329555	+	0.944136i	$0.393101\pi$
$440$	13.0478	+	7.23575i	0.622031	+	0.344951i
$441$		0			0
$442$	−1.47134	+	5.33505i	−0.0699844	+	0.253763i
$443$	23.1263	−	13.3520i	1.09876	−	0.634371i	0.162867	−	0.986648i	$-0.447926\pi$
$443$	23.1263	−	13.3520i	1.09876	−	0.634371i	0.935896	+	0.352277i	$0.114592\pi$
$444$		0			0
$445$	10.2093	+	2.31132i	0.483969	+	0.109567i
$446$	−23.9261	+	23.5794i	−1.13294	+	1.11652i
$447$		0			0
$448$	−23.5256	+	12.2419i	−1.11148	+	0.578377i
$449$		−	23.8441i		−	1.12527i	−0.826704	−	0.562637i	$-0.809787\pi$
$449$		−	23.8441i		−	1.12527i	0.826704	−	0.562637i	$-0.190213\pi$
$450$		0			0
$451$		−	6.67955i		−	0.314528i
$452$	−0.508866	+	34.8586i	−0.0239350	+	1.63961i
$453$		0			0
$454$	27.6533	+	28.0599i	1.29783	+	1.31692i
$455$	31.8110	+	7.20178i	1.49132	+	0.337625i
$456$		0			0
$457$	13.6451	−	7.87798i	0.638289	−	0.368516i	−0.145666	−	0.989334i	$-0.546532\pi$
$457$	13.6451	−	7.87798i	0.638289	−	0.368516i	0.783955	+	0.620817i	$0.213199\pi$
$458$	−22.7944	−	6.28641i	−1.06511	−	0.293745i
$459$		0			0
$460$	−7.64526	+	31.6195i	−0.356462	+	1.47426i
$461$	−9.24515	+	5.33769i	−0.430590	+	0.248601i	−0.699598	−	0.714537i	$-0.746637\pi$
$461$	−9.24515	+	5.33769i	−0.430590	+	0.248601i	0.269008	+	0.963138i	$0.413304\pi$
$462$		0			0
$463$	3.17644	−	5.50175i	0.147622	−	0.255688i	−0.782726	−	0.622366i	$-0.786172\pi$
$463$	3.17644	−	5.50175i	0.147622	−	0.255688i	0.930348	+	0.366678i	$0.119505\pi$
$464$	−0.139829	+	4.78829i	−0.00649139	+	0.222291i
$465$		0			0
$466$	−0.597938	−	2.29851i	−0.0276989	−	0.106476i
$467$			7.76191i			0.359179i	0.983742	+	0.179589i	$0.0574769\pi$
$467$			7.76191i			0.359179i	−0.983742	+	0.179589i	$0.942523\pi$
$468$		0			0
$469$	21.0330			0.971213
$470$	−20.3462	+	12.6277i	−0.938498	+	0.582472i
$471$		0			0
$472$	5.84905	−	1.43076i	0.269224	−	0.0658563i
$473$	−9.85221	+	17.0645i	−0.453005	+	0.784628i
$474$		0			0
$475$	−6.53683	+	13.6970i	−0.299930	+	0.628461i
$476$	5.06298	+	3.02249i	0.232061	+	0.138536i
$477$		0			0
$478$	−14.7534	−	4.06880i	−0.674805	−	0.186103i
$479$	−3.56565	−	6.17588i	−0.162919	−	0.282183i	0.772996	−	0.634411i	$-0.218757\pi$
$479$	−3.56565	−	6.17588i	−0.162919	−	0.282183i	−0.935914	+	0.352228i	$0.885424\pi$
$480$		0			0
$481$	25.2950	−	43.8122i	1.15335	−	1.99767i
$482$	−10.9925	+	10.8332i	−0.500694	+	0.493439i
$483$		0			0
$484$	−0.158662	+	10.8687i	−0.00721192	+	0.494034i
$485$	4.09245	+	13.1850i	0.185829	+	0.598699i
$486$		0			0
$487$	15.1089			0.684649			0.342325	−	0.939582i	$-0.388786\pi$
$487$	15.1089			0.684649			0.342325	+	0.939582i	$0.388786\pi$
$488$	−3.02905	+	10.3891i	−0.137119	+	0.470295i
$489$		0			0
$490$	5.95648	−	11.1207i	0.269086	−	0.502381i
$491$	−14.7215	+	25.4984i	−0.664372	+	1.15073i	0.315083	+	0.949064i	$0.397968\pi$
$491$	−14.7215	+	25.4984i	−0.664372	+	1.15073i	−0.979455	+	0.201662i	$0.935366\pi$
$492$		0			0
$493$	0.922396	−	0.532546i	0.0415426	−	0.0239847i
$494$	−18.2083	−	5.02162i	−0.819230	−	0.225933i
$495$		0			0
$496$	−0.834168	+	0.449666i	−0.0374552	+	0.0201906i
$497$	−19.4333	−	33.6595i	−0.871705	−	1.50984i
$498$		0			0
$499$	−18.0795	−	10.4382i	−0.809351	−	0.467279i	0.0373795	−	0.999301i	$-0.488099\pi$
$499$	−18.0795	−	10.4382i	−0.809351	−	0.467279i	−0.846730	+	0.532022i	$0.821432\pi$
$500$	3.53856	−	22.0789i	0.158249	−	0.987399i
$501$		0			0
$502$	1.80076	+	6.92222i	0.0803718	+	0.308954i
$503$		−	22.6713i		−	1.01086i	−0.862867	−	0.505431i	$-0.831333\pi$
$503$		−	22.6713i		−	1.01086i	0.862867	−	0.505431i	$-0.168667\pi$
$504$		0			0
$505$	−5.14603	−	16.5794i	−0.228995	−	0.737773i
$506$	23.4859	−	6.10967i	1.04408	−	0.271608i
$507$		0			0
$508$	18.4542	−	10.2983i	0.818772	−	0.456915i
$509$	23.5593	+	13.6020i	1.04425	+	0.602896i	0.921033	−	0.389484i	$-0.127347\pi$
$509$	23.5593	+	13.6020i	1.04425	+	0.602896i	0.123213	+	0.992380i	$0.460680\pi$
$510$		0			0
$511$	−17.5380	+	10.1255i	−0.775834	+	0.447928i
$512$	−17.0157	+	14.9153i	−0.751996	+	0.659168i
$513$		0			0
$514$	−18.2560	−	5.03476i	−0.805236	−	0.222074i
$515$	21.6075	+	19.9782i	0.952141	+	0.880345i
$516$		0			0
$517$	15.4705	+	8.93188i	0.680390	+	0.392824i
$518$	−37.8353	−	38.3917i	−1.66239	−	1.68683i
$519$		0			0
$520$	27.8244	−	0.480414i	1.22018	−	0.0210675i
$521$			2.18176i			0.0955847i	0.998857	+	0.0477924i	$0.0152186\pi$
$521$			2.18176i			0.0955847i	−0.998857	+	0.0477924i	$0.984781\pi$
$522$		0			0
$523$	28.8185			1.26014			0.630071	−	0.776537i	$-0.283026\pi$
$523$	28.8185			1.26014			0.630071	+	0.776537i	$0.283026\pi$
$524$	0.474619	−	32.5126i	0.0207338	−	1.42032i
$525$		0			0
$526$	10.8115	+	10.9705i	0.471404	+	0.478336i
$527$	0.182473	+	0.105351i	0.00794865	+	0.00458916i
$528$		0			0
$529$	14.9560	+	25.9046i	0.650261	+	1.12629i
$530$	−2.44021	+	0.0777744i	−0.105996	+	0.00337830i
$531$		0			0
$532$	−10.3156	+	17.2797i	−0.447240	+	0.749171i
$533$	−6.22935	−	10.7896i	−0.269823	−	0.467348i
$534$		0			0
$535$	0.549962	+	0.124507i	0.0237769	+	0.00538292i
$536$	17.4317	−	4.26406i	0.752936	−	0.184179i
$537$		0			0
$538$	−29.4290	+	7.65570i	−1.26877	+	0.330061i
$539$	−9.41102			−0.405361
$540$		0			0
$541$	3.32257			0.142848			0.0714242	−	0.997446i	$-0.477246\pi$
$541$	3.32257			0.142848			0.0714242	+	0.997446i	$0.477246\pi$
$542$	25.9286	−	6.74512i	1.11373	−	0.289728i
$543$		0			0
$544$	4.80885	+	1.47856i	0.206178	+	0.0633926i
$545$	0.226658	−	1.00117i	0.00970897	−	0.0428855i
$546$		0			0
$547$	13.8697	+	24.0231i	0.593027	+	1.02715i	0.993822	+	0.110986i	$0.0354008\pi$
$547$	13.8697	+	24.0231i	0.593027	+	1.02715i	−0.400795	+	0.916168i	$0.631266\pi$
$548$	−22.6538	−	13.5238i	−0.967721	−	0.577710i
$549$		0			0
$550$	−15.7655	+	5.44981i	−0.672244	+	0.232381i
$551$	1.81756	+	3.14810i	0.0774305	+	0.134114i
$552$		0			0
$553$	−29.6652	−	17.1272i	−1.26149	−	0.728323i
$554$	18.5251	+	18.7975i	0.787058	+	0.798631i
$555$		0			0
$556$	−12.9667	−	0.189288i	−0.549911	−	0.00802761i
$557$	30.0401			1.27284			0.636419	−	0.771344i	$-0.280415\pi$
$557$	30.0401			1.27284			0.636419	+	0.771344i	$0.280415\pi$
$558$		0			0
$559$			36.7527i			1.55447i
$560$	7.38830	−	28.7152i	0.312213	−	1.21344i
$561$		0			0
$562$	−6.70188	−	6.80043i	−0.282702	−	0.286859i
$563$	−1.52959	−	0.883109i	−0.0644645	−	0.0372186i	0.467421	−	0.884035i	$-0.345183\pi$
$563$	−1.52959	−	0.883109i	−0.0644645	−	0.0372186i	−0.531886	+	0.846816i	$0.678516\pi$
$564$		0			0
$565$	−28.6189	−	26.4609i	−1.20401	−	1.11322i
$566$	7.18435	+	1.98135i	0.301981	+	0.0832824i
$567$		0			0
$568$	−22.9298	−	23.9566i	−0.962115	−	1.00520i
$569$	−31.9951	+	18.4724i	−1.34131	+	0.774403i	−0.986999	−	0.160726i	$-0.948616\pi$
$569$	−31.9951	+	18.4724i	−1.34131	+	0.774403i	−0.354306	+	0.935129i	$0.615283\pi$
$570$		0			0
$571$	26.5164	+	15.3092i	1.10968	+	0.640672i	0.938745	−	0.344612i	$-0.111989\pi$
$571$	26.5164	+	15.3092i	1.10968	+	0.640672i	0.170930	+	0.985283i	$0.445323\pi$
$572$	−10.1164	−	18.1282i	−0.422988	−	0.757977i
$573$		0			0
$574$	−12.8468	+	3.34199i	−0.536214	+	0.139492i
$575$	−20.5938	−	29.9783i	−0.858819	−	1.25018i
$576$		0			0
$577$			23.6405i			0.984168i	0.870548	+	0.492084i	$0.163765\pi$
$577$			23.6405i			0.984168i	−0.870548	+	0.492084i	$0.836235\pi$
$578$	5.77116	+	22.1847i	0.240048	+	0.922760i
$579$		0			0
$580$	−3.87896	−	3.69294i	−0.161065	−	0.153341i
$581$	7.46221	+	4.30831i	0.309585	+	0.178739i
$582$		0			0
$583$	0.910652	+	1.57730i	0.0377154	+	0.0653249i
$584$	−12.4824	+	11.9474i	−0.516523	+	0.494385i
$585$		0			0
$586$	30.3890	+	8.38091i	1.25536	+	0.346212i
$587$	−0.0513568	+	0.0296509i	−0.00211972	+	0.00122382i	−0.501059	−	0.865413i	$-0.667056\pi$
$587$	−0.0513568	+	0.0296509i	−0.00211972	+	0.00122382i	0.498940	+	0.866637i	$0.333723\pi$
$588$		0			0
$589$	−0.359558	+	0.622773i	−0.0148153	+	0.0256609i
$590$	−3.17868	+	5.93456i	−0.130864	+	0.244322i
$591$		0			0
$592$	−39.1404	−	24.1478i	−1.60866	−	0.992471i
$593$	−44.6245			−1.83251			−0.916255	−	0.400596i	$-0.868803\pi$
$593$	−44.6245			−1.83251			−0.916255	+	0.400596i	$0.868803\pi$
$594$		0			0
$595$	−6.29622	+	1.95427i	−0.258120	+	0.0801171i
$596$	16.7416	+	0.244394i	0.685762	+	0.0100108i
$597$		0			0
$598$	32.2392	−	31.7720i	1.31836	−	1.29925i
$599$	11.5001	−	19.9187i	0.469881	−	0.813857i	−0.529526	−	0.848294i	$-0.677630\pi$
$599$	11.5001	−	19.9187i	0.469881	−	0.813857i	0.999407	+	0.0344362i	$0.0109636\pi$
$600$		0			0
$601$	0.981232	+	1.69954i	0.0400253	+	0.0693259i	0.885344	−	0.464936i	$-0.153923\pi$
$601$	0.981232	+	1.69954i	0.0400253	+	0.0693259i	−0.845319	+	0.534262i	$0.820589\pi$
$602$	37.7496	+	10.4109i	1.53856	+	0.424315i
$603$		0			0
$604$	16.8105	−	28.1593i	0.684011	−	1.14579i
$605$	−8.92325	−	8.25040i	−0.362782	−	0.335426i
$606$		0			0
$607$	−10.1049	+	17.5023i	−0.410146	+	0.710394i	−0.994905	−	0.100813i	$-0.967856\pi$
$607$	−10.1049	+	17.5023i	−0.410146	+	0.710394i	0.584759	+	0.811207i	$0.301189\pi$
$608$	−5.04625	+	16.4124i	−0.204653	+	0.665611i
$609$		0			0
$610$	−6.38024	−	10.2801i	−0.258328	−	0.416227i
$611$	33.3195			1.34796
$612$		0			0
$613$		−	24.8672i		−	1.00438i	−0.864758	−	0.502189i	$-0.832528\pi$
$613$		−	24.8672i		−	1.00438i	0.864758	−	0.502189i	$-0.167472\pi$
$614$	−0.147906	−	0.568560i	−0.00596901	−	0.0229452i
$615$		0			0
$616$	−21.4855	+	5.25568i	−0.865677	+	0.211757i
$617$	−16.3707	+	28.3549i	−0.659059	+	1.14152i	0.321800	+	0.946808i	$0.395712\pi$
$617$	−16.3707	+	28.3549i	−0.659059	+	1.14152i	−0.980860	+	0.194717i	$0.937621\pi$
$618$		0			0
$619$	−11.9754	+	6.91400i	−0.481332	+	0.277897i	−0.720971	−	0.692965i	$-0.756304\pi$
$619$	−11.9754	+	6.91400i	−0.481332	+	0.277897i	0.239640	+	0.970862i	$0.422971\pi$
$620$	0.249002	−	1.02983i	0.0100001	−	0.0413588i
$621$		0			0
$622$	0.775897	+	0.213982i	0.0311106	+	0.00857991i
$623$	−13.4395	+	7.75930i	−0.538442	+	0.310870i
$624$		0			0
$625$	15.7244	+	19.4356i	0.628978	+	0.777423i
$626$	−27.8569	−	28.2665i	−1.11338	−	1.12976i
$627$		0			0
$628$	−21.4220	−	0.312719i	−0.854833	−	0.0124789i
$629$			10.2255i			0.407719i
$630$		0			0
$631$		−	0.298908i		−	0.0118994i	−0.999982	−	0.00594968i	$-0.998106\pi$
$631$		−	0.298908i		−	0.0118994i	0.999982	−	0.00594968i	$-0.00189385\pi$
$632$	−28.0582	−	8.18062i	−1.11609	−	0.325407i
$633$		0			0
$634$	−13.3700	+	13.1763i	−0.530992	+	0.523297i
$635$	−5.21710	+	23.0445i	−0.207034	+	0.914492i
$636$		0			0
$637$	−15.2017	+	8.77672i	−0.602314	+	0.347746i
$638$	−1.06221	+	3.85156i	−0.0420534	+	0.152485i
$639$		0			0
$640$	0.301795	−	25.2964i	0.0119295	−	0.999929i
$641$	−12.2453	+	7.06982i	−0.483660	+	0.279241i	−0.721940	−	0.691955i	$-0.756750\pi$
$641$	−12.2453	+	7.06982i	−0.483660	+	0.279241i	0.238281	+	0.971196i	$0.423416\pi$
$642$		0			0
$643$	18.2808	−	31.6633i	0.720925	−	1.24868i	−0.239704	−	0.970846i	$-0.577050\pi$
$643$	18.2808	−	31.6633i	0.720925	−	1.24868i	0.960629	−	0.277833i	$-0.0896162\pi$
$644$	−23.5015	−	42.1136i	−0.926087	−	1.65951i
$645$		0			0
$646$	3.69479	−	0.961168i	0.145369	−	0.0378167i
$647$			25.4645i			1.00111i	0.865704	+	0.500556i	$0.166871\pi$
$647$			25.4645i			1.00111i	−0.865704	+	0.500556i	$0.833129\pi$
$648$		0			0
$649$	5.02220			0.197139
$650$	−20.3838	+	23.5061i	−0.799516	+	0.921985i
$651$		0			0
$652$	2.33299	−	1.30192i	0.0913668	−	0.0509871i
$653$	11.2123	−	19.4203i	0.438772	−	0.759976i	−0.558823	−	0.829287i	$-0.688747\pi$
$653$	11.2123	−	19.4203i	0.438772	−	0.759976i	0.997595	+	0.0693112i	$0.0220801\pi$
$654$		0			0
$655$	26.6929	+	24.6801i	1.04298	+	0.964330i
$656$	−9.96964	+	5.37423i	−0.389249	+	0.209828i
$657$		0			0
$658$	9.43834	−	34.2233i	0.367945	−	1.33416i
$659$	3.28193	+	5.68446i	0.127846	+	0.221435i	0.922842	−	0.385179i	$-0.125860\pi$
$659$	3.28193	+	5.68446i	0.127846	+	0.221435i	−0.794996	+	0.606615i	$0.792527\pi$
$660$		0			0
$661$	−9.44856	+	16.3654i	−0.367506	+	0.636540i	−0.989175	−	0.146741i	$-0.953122\pi$
$661$	−9.44856	+	16.3654i	−0.367506	+	0.636540i	0.621669	+	0.783280i	$0.286455\pi$
$662$	8.52792	+	8.65332i	0.331447	+	0.336321i
$663$		0			0
$664$	7.05797	+	2.05781i	0.273902	+	0.0798587i
$665$	−6.66983	−	21.4887i	−0.258645	−	0.833297i
$666$		0			0
$667$	−8.71129			−0.337303
$668$	14.3385	+	0.209314i	0.554774	+	0.00809860i
$669$		0			0
$670$	−9.47332	+	17.6866i	−0.365986	+	0.683292i
$671$	−4.51290	+	7.81657i	−0.174219	+	0.301755i
$672$		0			0
$673$	27.1258	−	15.6611i	1.04562	−	0.603690i	0.124201	−	0.992257i	$-0.460363\pi$
$673$	27.1258	−	15.6611i	1.04562	−	0.603690i	0.921420	+	0.388567i	$0.127030\pi$
$674$	−0.396821	+	1.43887i	−0.0152850	+	0.0554231i
$675$		0			0
$676$	−10.9230	−	6.52081i	−0.420115	−	0.250800i
$677$	20.4922	+	35.4936i	0.787580	+	1.36413i	0.927446	+	0.373958i	$0.122000\pi$
$677$	20.4922	+	35.4936i	0.787580	+	1.36413i	−0.139866	+	0.990171i	$0.544667\pi$
$678$		0			0
$679$	−17.7249	−	10.2335i	−0.680219	−	0.392724i
$680$	−4.82199	+	2.89610i	−0.184915	+	0.111060i
$681$		0			0
$682$	−0.764922	+	0.198988i	−0.0292904	+	0.00761965i
$683$		−	42.0703i		−	1.60978i	−0.593427	−	0.804888i	$-0.702225\pi$
$683$		−	42.0703i		−	1.60978i	0.593427	−	0.804888i	$-0.297775\pi$
$684$		0			0
$685$	28.1718	−	8.74417i	1.07639	−	0.334097i
$686$	−3.55347	−	13.6597i	−0.135672	−	0.521531i
$687$		0			0
$688$	33.3968	+	0.975261i	1.27324	+	0.0371815i
$689$	2.94198	+	1.69855i	0.112080	+	0.0647096i
$690$		0			0
$691$	30.3277	−	17.5097i	1.15372	−	0.666101i	0.203930	−	0.978986i	$-0.434629\pi$
$691$	30.3277	−	17.5097i	1.15372	−	0.666101i	0.949791	+	0.312885i	$0.101295\pi$
$692$	4.42247	+	2.64012i	0.168117	+	0.100362i
$693$		0			0
$694$	2.59554	−	9.41140i	0.0985255	−	0.357252i
$695$	9.84295	−	10.6457i	0.373364	−	0.403814i
$696$		0			0
$697$	2.18084	+	1.25911i	0.0826054	+	0.0476922i
$698$	−31.2547	+	30.8018i	−1.18301	+	1.16586i
$699$		0			0
$700$	18.3696	+	27.5951i	0.694306	+	1.04300i
$701$		−	41.5315i		−	1.56862i	−0.620366	−	0.784312i	$-0.713016\pi$
$701$		−	41.5315i		−	1.56862i	0.620366	−	0.784312i	$-0.286984\pi$
$702$		0			0
$703$	−34.8993			−1.31625
$704$	−16.7413	+	8.71161i	−0.630961	+	0.328331i
$705$		0			0
$706$	15.4686	−	15.2445i	0.582169	−	0.573732i
$707$	22.2881	+	12.8680i	0.838229	+	0.483952i
$708$		0			0
$709$	5.69139	+	9.85778i	0.213745	+	0.370217i	0.952883	−	0.303337i	$-0.0981006\pi$
$709$	5.69139	+	9.85778i	0.213745	+	0.370217i	−0.739139	+	0.673553i	$0.764767\pi$
$710$	37.0571	−	1.18108i	1.39073	−	0.0443252i
$711$		0			0
$712$	−9.56534	+	9.15538i	−0.358476	+	0.343112i
$713$	−0.861656	−	1.49243i	−0.0322693	−	0.0558920i
$714$		0			0
$715$	22.6374	+	5.12494i	0.846590	+	0.191662i
$716$	−17.7873	+	9.92616i	−0.664741	+	0.370958i
$717$		0			0
$718$	3.03065	+	11.6500i	0.113103	+	0.434774i
$719$	−24.0599			−0.897282			−0.448641	−	0.893712i	$-0.648092\pi$
$719$	−24.0599			−0.897282			−0.448641	+	0.893712i	$0.648092\pi$
$720$		0			0
$721$	−43.6278			−1.62478
$722$	−3.48444	−	13.3944i	−0.129678	−	0.498488i
$723$		0			0
$724$	−7.29213	+	4.06936i	−0.271010	+	0.151237i
$725$	5.96956	−	0.468490i	0.221704	−	0.0173993i
$726$		0			0
$727$	−2.85756	−	4.94944i	−0.105981	−	0.183565i	0.808158	−	0.588966i	$-0.200465\pi$
$727$	−2.85756	−	4.94944i	−0.105981	−	0.183565i	−0.914139	+	0.405402i	$0.867132\pi$
$728$	−29.8044	+	28.5270i	−1.10462	+	1.05728i
$729$		0			0
$730$	−0.615391	−	19.3082i	−0.0227766	−	0.714629i
$731$	−3.71433	−	6.43341i	−0.137380	−	0.237948i
$732$		0			0
$733$	−22.3900	−	12.9269i	−0.826994	−	0.477465i	0.0258286	−	0.999666i	$-0.491778\pi$
$733$	−22.3900	−	12.9269i	−0.826994	−	0.477465i	−0.852822	+	0.522201i	$0.825111\pi$
$734$	1.30249	−	1.28361i	0.0480756	−	0.0473790i
$735$		0			0
$736$	−28.0153	−	30.1384i	−1.03266	−	1.11092i
$737$	14.9675			0.551335
$738$		0			0
$739$		−	18.0774i		−	0.664989i	−0.943105	−	0.332495i	$-0.892110\pi$
$739$		−	18.0774i		−	0.664989i	0.943105	−	0.332495i	$-0.107890\pi$
$740$	49.3246	−	14.5239i	1.81321	−	0.533909i
$741$		0			0
$742$	2.57799	−	2.54063i	0.0946409	−	0.0932694i
$743$	15.5973	+	9.00512i	0.572210	+	0.330366i	0.758032	−	0.652218i	$-0.226161\pi$
$743$	15.5973	+	9.00512i	0.572210	+	0.330366i	−0.185821	+	0.982584i	$0.559495\pi$
$744$		0			0
$745$	−12.7084	+	13.7449i	−0.465601	+	0.503573i
$746$	−6.15788	+	22.3284i	−0.225456	+	0.817500i
$747$		0			0
$748$	3.60292	+	2.15087i	0.131736	+	0.0786435i
$749$	−0.723965	+	0.417982i	−0.0264531	+	0.0152727i
$750$		0			0
$751$	−35.2487	−	20.3509i	−1.28624	−	0.742613i	−0.308262	−	0.951302i	$-0.599747\pi$
$751$	−35.2487	−	20.3509i	−1.28624	−	0.742613i	−0.977982	+	0.208689i	$0.933081\pi$
$752$	0.884158	−	30.2770i	0.0322419	−	1.10409i
$753$		0			0
$754$	1.87617	+	7.21210i	0.0683260	+	0.262649i
$755$	10.8693	+	35.0184i	0.395573	+	1.27445i
$756$		0			0
$757$		−	35.4823i		−	1.28963i	−0.764340	−	0.644813i	$-0.776935\pi$
$757$		−	35.4823i		−	1.28963i	0.764340	−	0.644813i	$-0.223065\pi$
$758$	16.1420	−	4.19921i	0.586304	−	0.152522i
$759$		0			0
$760$	−9.88428	−	16.4572i	−0.358540	−	0.596967i
$761$	34.0009	+	19.6304i	1.23253	+	0.711602i	0.967557	−	0.252654i	$-0.0813033\pi$
$761$	34.0009	+	19.6304i	1.23253	+	0.711602i	0.264974	+	0.964256i	$0.414637\pi$
$762$		0			0
$763$	0.760910	+	1.31794i	0.0275468	+	0.0477125i
$764$	42.9840	+	25.6606i	1.55511	+	0.928367i
$765$		0			0
$766$	−4.23702	+	15.3634i	−0.153090	+	0.555101i
$767$	8.11242	−	4.68371i	0.292923	−	0.169119i
$768$		0			0
$769$	−3.27941	+	5.68011i	−0.118259	+	0.204830i	−0.919078	−	0.394076i	$-0.871065\pi$
$769$	−3.27941	+	5.68011i	−0.118259	+	0.204830i	0.800819	+	0.598906i	$0.204398\pi$
$770$	11.6764	−	21.7997i	0.420787	−	0.785605i
$771$		0			0
$772$	37.8308	+	0.552255i	1.36156	+	0.0198761i
$773$	34.2118			1.23051			0.615256	−	0.788327i	$-0.289053\pi$
$773$	34.2118			1.23051			0.615256	+	0.788327i	$0.289053\pi$
$774$		0			0
$775$	0.670727	+	0.976374i	0.0240932	+	0.0350724i
$776$	−16.7647	−	4.88790i	−0.601817	−	0.175465i
$777$		0			0
$778$	20.0115	+	20.3057i	0.717445	+	0.727995i
$779$	−4.29729	+	7.44313i	−0.153967	+	0.266678i
$780$		0			0
$781$	−13.8292	−	23.9528i	−0.494847	−	0.857099i
$782$	−2.43237	+	8.81973i	−0.0869813	+	0.315393i
$783$		0			0
$784$	7.57191	+	14.0465i	0.270425	+	0.501661i
$785$	16.2613	−	17.5875i	0.580392	−	0.627726i
$786$		0			0
$787$	−8.68943	+	15.0505i	−0.309745	+	0.536494i	−0.978306	−	0.207163i	$-0.933577\pi$
$787$	−8.68943	+	15.0505i	−0.309745	+	0.536494i	0.668562	+	0.743657i	$0.266910\pi$
$788$	9.17623	−	5.12079i	0.326890	−	0.182420i
$789$		0			0
$790$	27.7636	−	17.2312i	0.987783	−	0.613060i
$791$	57.7846			2.05458
$792$		0			0
$793$			16.8349i			0.597826i
$794$	7.00561	−	1.82245i	0.248620	−	0.0646764i
$795$		0			0
$796$	18.3702	+	32.9185i	0.651113	+	1.16677i
$797$	3.50633	−	6.07314i	0.124201	−	0.215122i	−0.797220	−	0.603689i	$-0.793697\pi$
$797$	3.50633	−	6.07314i	0.124201	−	0.215122i	0.921420	+	0.388568i	$0.127030\pi$
$798$		0			0
$799$	−5.83244	+	3.36736i	−0.206337	+	0.119129i
$800$	20.8188	+	19.1462i	0.736056	+	0.676921i
$801$		0			0
$802$	−4.16042	+	15.0856i	−0.146910	+	0.532692i
$803$	−12.4804	+	7.20555i	−0.440423	+	0.254278i
$804$		0			0
$805$	52.5889	+	11.9058i	1.85352	+	0.419623i
$806$	−1.05001	+	1.03479i	−0.0369851	+	0.0364491i
$807$		0			0
$808$	21.0807	+	6.14626i	0.741616	+	0.216225i
$809$		−	38.9234i		−	1.36847i	−0.729261	−	0.684236i	$-0.760136\pi$
$809$		−	38.9234i		−	1.36847i	0.729261	−	0.684236i	$-0.239864\pi$
$810$		0			0
$811$		−	35.7891i		−	1.25673i	−0.777920	−	0.628363i	$-0.783725\pi$
$811$		−	35.7891i		−	1.25673i	0.777920	−	0.628363i	$-0.216275\pi$
$812$	7.93917	+	0.115896i	0.278610	+	0.00406716i
$813$		0			0
$814$	−26.9244	−	27.3203i	−0.943700	−	0.957576i
$815$	−0.659548	+	2.91329i	−0.0231030	+	0.102048i
$816$		0			0
$817$	21.9570	−	12.6769i	0.768177	−	0.443507i
$818$	22.0398	+	6.07829i	0.770604	+	0.212523i
$819$		0			0
$820$	2.97597	−	12.3081i	0.103925	−	0.429817i
$821$	27.8765	−	16.0945i	0.972895	−	0.561701i	0.0727775	−	0.997348i	$-0.476814\pi$
$821$	27.8765	−	16.0945i	0.972895	−	0.561701i	0.900118	+	0.435647i	$0.143480\pi$
$822$		0			0
$823$	−8.65813	+	14.9963i	−0.301804	+	0.522739i	−0.976545	−	0.215315i	$-0.930922\pi$
$823$	−8.65813	+	14.9963i	−0.301804	+	0.522739i	0.674741	+	0.738055i	$0.264255\pi$
$824$	−36.1579	+	8.84475i	−1.25962	+	0.308122i
$825$		0			0
$826$	−2.51276	−	9.65921i	−0.0874302	−	0.336087i
$827$		−	15.5363i		−	0.540249i	−0.962825	−	0.270124i	$-0.912935\pi$
$827$		−	15.5363i		−	0.540249i	0.962825	−	0.270124i	$-0.0870648\pi$
$828$		0			0
$829$	−27.4645			−0.953882			−0.476941	−	0.878935i	$-0.658254\pi$
$829$	−27.4645			−0.953882			−0.476941	+	0.878935i	$0.658254\pi$
$830$	−6.98385	+	4.33448i	−0.242413	+	0.150452i
$831$		0			0
$832$	−18.9180	+	29.6849i	−0.655862	+	1.02914i
$833$	1.77400	−	3.07266i	0.0614654	−	0.106461i
$834$		0			0
$835$	−10.8843	+	11.7719i	−0.376666	+	0.407385i
$836$	−7.34082	+	12.2966i	−0.253888	+	0.425287i
$837$		0			0
$838$	−9.96761	−	2.74894i	−0.344325	−	0.0949605i
$839$	−6.91476	−	11.9767i	−0.238724	−	0.413482i	0.721624	−	0.692285i	$-0.243396\pi$
$839$	−6.91476	−	11.9767i	−0.238724	−	0.413482i	−0.960348	+	0.278803i	$0.910062\pi$
$840$		0			0
$841$	−13.7829	+	23.8727i	−0.475272	+	0.823196i
$842$	30.1639	−	29.7268i	1.03952	−	1.02445i
$843$		0			0
$844$	−9.14613	−	0.133515i	−0.314823	−	0.00459579i
$845$	13.5836	−	4.21619i	0.467291	−	0.145041i
$846$		0			0
$847$	18.0170			0.619070
$848$	1.62152	−	2.62826i	0.0556832	−	0.0902550i
$849$		0			0
$850$	1.19250	−	6.17468i	0.0409024	−	0.211790i
$851$	41.8169	−	72.4290i	1.43346	−	2.48283i
$852$		0			0
$853$	−31.2866	+	18.0633i	−1.07123	+	0.618476i	−0.928518	−	0.371288i	$-0.878916\pi$
$853$	−31.2866	+	18.0633i	−1.07123	+	0.618476i	−0.142714	+	0.989764i	$0.545583\pi$
$854$	17.2916	+	4.76879i	0.591705	+	0.163185i
$855$		0			0
$856$	−0.515270	+	0.493186i	−0.0176116	+	0.0168568i
$857$	3.70493	+	6.41713i	0.126558	+	0.219205i	0.922341	−	0.386377i	$-0.126274\pi$
$857$	3.70493	+	6.41713i	0.126558	+	0.219205i	−0.795783	+	0.605582i	$0.792940\pi$
$858$		0			0
$859$	35.7586	+	20.6452i	1.22007	+	0.704407i	0.964932	−	0.262499i	$-0.0845465\pi$
$859$	35.7586	+	20.6452i	1.22007	+	0.704407i	0.255136	+	0.966905i	$0.417880\pi$
$860$	−25.7570	+	27.0545i	−0.878307	+	0.922550i
$861$		0			0
$862$	10.9486	+	42.0870i	0.372910	+	1.43349i
$863$			46.7922i			1.59282i	0.604754	+	0.796412i	$0.293271\pi$
$863$			46.7922i			1.59282i	−0.604754	+	0.796412i	$0.706729\pi$
$864$		0			0
$865$	−5.49970	+	1.70704i	−0.186995	+	0.0580410i
$866$	40.2022	−	10.4583i	1.36613	−	0.355387i
$867$		0			0
$868$	0.765428	+	1.37161i	0.0259803	+	0.0465556i
$869$	−21.1104	−	12.1881i	−0.716120	−	0.413452i
$870$		0			0
$871$	24.1772	−	13.9587i	0.819213	−	0.472973i
$872$	0.897815	+	0.938018i	0.0304039	+	0.0317653i
$873$		0			0
$874$	−30.1014	−	8.30157i	−1.01819	−	0.280805i
$875$	−36.6777	−	5.33040i	−1.23993	−	0.180200i
$876$		0			0
$877$	12.2576	+	7.07692i	0.413909	+	0.238970i	0.692468	−	0.721449i	$-0.256523\pi$
$877$	12.2576	+	7.07692i	0.413909	+	0.238970i	−0.278559	+	0.960419i	$0.589857\pi$
$878$	7.76485	+	7.87903i	0.262051	+	0.265904i
$879$		0			0
$880$	5.25767	−	20.4343i	0.177236	−	0.688840i
$881$			13.5705i			0.457200i	0.973520	+	0.228600i	$0.0734148\pi$
$881$			13.5705i			0.457200i	−0.973520	+	0.228600i	$0.926585\pi$
$882$		0			0
$883$	46.0353			1.54921			0.774606	−	0.632444i	$-0.217948\pi$
$883$	46.0353			1.54921			0.774606	+	0.632444i	$0.217948\pi$
$884$	7.82574	+	0.114240i	0.263208	+	0.00384232i
$885$		0			0
$886$	−26.5083	−	26.8981i	−0.890565	−	0.903660i
$887$	−17.1621	−	9.90855i	−0.576247	−	0.332696i	0.183393	−	0.983040i	$-0.441292\pi$
$887$	−17.1621	−	9.90855i	−0.576247	−	0.332696i	−0.759641	+	0.650343i	$0.774625\pi$
$888$		0			0
$889$	−17.5143	−	30.3356i	−0.587409	−	1.01742i
$890$	−0.471580	−	14.7961i	−0.0158074	−	0.495965i
$891$		0			0
$892$	40.7910	+	24.3514i	1.36578	+	0.815346i
$893$	−11.4927	−	19.9059i	−0.384587	−	0.666125i
$894$		0			0
$895$	5.02856	−	22.2117i	0.168086	−	0.742454i
$896$	25.1312	+	27.8399i	0.839576	+	0.930064i
$897$		0			0
$898$	−32.6345	+	8.48960i	−1.08903	+	0.283302i
$899$	0.283722			0.00946265
$900$		0			0
$901$	−0.686641			−0.0228753
$902$	−9.14204	+	2.37823i	−0.304396	+	0.0791863i
$903$		0			0
$904$	47.8907	−	11.7148i	1.59282	−	0.389628i
$905$	2.06153	−	9.10597i	0.0685274	−	0.302693i
$906$		0			0
$907$	−24.4653	−	42.3752i	−0.812358	−	1.40705i	−0.911209	−	0.411943i	$-0.864850\pi$
$907$	−24.4653	−	42.3752i	−0.812358	−	1.40705i	0.0988513	−	0.995102i	$-0.468483\pi$
$908$	28.5587	−	47.8386i	0.947752	−	1.58758i
$909$		0			0
$910$	−1.46938	−	46.1026i	−0.0487095	−	1.52829i
$911$	16.0978	+	27.8822i	0.533343	+	0.923778i	0.999242	+	0.0389396i	$0.0123980\pi$
$911$	16.0978	+	27.8822i	0.533343	+	0.923778i	−0.465898	+	0.884838i	$0.654269\pi$
$912$		0			0
$913$	5.31026	+	3.06588i	0.175744	+	0.101466i
$914$	−15.6406	−	15.8705i	−0.517343	−	0.524951i
$915$		0			0
$916$	−0.488101	+	33.4361i	−0.0161273	+	1.10476i
$917$	−53.8956			−1.77979
$918$		0			0
$919$		−	37.8553i		−	1.24873i	−0.781133	−	0.624365i	$-0.785358\pi$
$919$		−	37.8553i		−	1.24873i	0.781133	−	0.624365i	$-0.214642\pi$
$920$	45.9984	−	0.794204i	1.51652	−	0.0261841i
$921$		0			0
$922$	10.5972	+	10.7530i	0.349000	+	0.354132i
$923$	−44.6768	−	25.7942i	−1.47056	−	0.849026i
$924$		0			0
$925$	−24.7605	+	51.8820i	−0.814121	+	1.70587i
$926$	−8.66098	−	2.38859i	−0.284618	−	0.0784939i
$927$		0			0
$928$	6.60333	−	1.51347i	0.216765	−	0.0496822i
$929$	−14.4535	+	8.34474i	−0.474205	+	0.273782i	−0.717998	−	0.696045i	$-0.754941\pi$
$929$	−14.4535	+	8.34474i	−0.474205	+	0.273782i	0.243794	+	0.969827i	$0.421608\pi$
$930$		0			0
$931$	10.4868	+	6.05458i	0.343693	+	0.198431i
$932$	−2.93298	+	1.63675i	−0.0960730	+	0.0536135i
$933$		0			0
$934$	10.6234	−	2.76360i	0.347609	−	0.0904277i
$935$	−4.48052	+	1.39070i	−0.146529	+	0.0454806i
$936$		0			0
$937$		−	41.7514i		−	1.36396i	−0.731372	−	0.681979i	$-0.761120\pi$
$937$		−	41.7514i		−	1.36396i	0.731372	−	0.681979i	$-0.238880\pi$
$938$	−7.48870	−	28.7870i	−0.244515	−	0.939929i
$939$		0			0
$940$	24.5272	+	23.3509i	0.799989	+	0.761624i
$941$	−9.78882	−	5.65158i	−0.319106	−	0.184236i	0.331888	−	0.943319i	$-0.392314\pi$
$941$	−9.78882	−	5.65158i	−0.319106	−	0.184236i	−0.650994	+	0.759083i	$0.725648\pi$
$942$		0			0
$943$	−10.2982	−	17.8369i	−0.335354	−	0.580851i
$944$	−4.04076	−	7.49595i	−0.131516	−	0.243972i
$945$		0			0
$946$	26.8634	+	7.40858i	0.873404	+	0.240874i
$947$	−4.45025	+	2.56935i	−0.144614	+	0.0834928i	−0.570561	−	0.821255i	$-0.693274\pi$
$947$	−4.45025	+	2.56935i	−0.144614	+	0.0834928i	0.425947	+	0.904748i	$0.359941\pi$
$948$		0			0
$949$	−13.4398	+	23.2784i	−0.436274	+	0.755649i
$950$	21.0739	+	4.06995i	0.683728	+	0.132047i
$951$		0			0
$952$	2.33412	−	8.00564i	0.0756491	−	0.259464i
$953$	22.9718			0.744131			0.372066	−	0.928206i	$-0.378650\pi$
$953$	22.9718			0.744131			0.372066	+	0.928206i	$0.378650\pi$
$954$		0			0
$955$	−53.4541	+	16.5915i	−1.72973	+	0.536887i
$956$	−0.315917	+	21.6411i	−0.0102175	+	0.699923i
$957$		0			0
$958$	−7.18315	+	7.07906i	−0.232077	+	0.228714i
$959$	−21.8654	+	37.8720i	−0.706072	+	1.22295i
$960$		0			0
$961$	−15.4719	−	26.7982i	−0.499095	−	0.864457i
$962$	−68.9703	−	19.0211i	−2.22369	−	0.613265i
$963$		0			0
$964$	18.7408	+	11.1879i	0.603601	+	0.360337i
$965$	−28.7171	+	31.0592i	−0.924437	+	0.999830i
$966$		0			0
$967$	21.0871	−	36.5239i	0.678115	−	1.17453i	−0.297433	−	0.954743i	$-0.596131\pi$
$967$	21.0871	−	36.5239i	0.678115	−	1.17453i	0.975548	−	0.219787i	$-0.0705361\pi$
$968$	14.9321	−	3.65262i	0.479936	−	0.117400i
$969$		0			0
$970$	16.5886	−	10.2956i	0.532629	−	0.330573i
$971$	−29.9678			−0.961712			−0.480856	−	0.876799i	$-0.659674\pi$
$971$	−29.9678			−0.961712			−0.480856	+	0.876799i	$0.659674\pi$
$972$		0			0
$973$			21.4947i			0.689090i
$974$	−5.37946	−	20.6789i	−0.172369	−	0.662596i
$975$		0			0
$976$	15.2977	+	0.446727i	0.489667	+	0.0142994i
$977$	−18.5590	+	32.1452i	−0.593756	+	1.02842i	0.399965	+	0.916530i	$0.369022\pi$
$977$	−18.5590	+	32.1452i	−0.593756	+	1.02842i	−0.993721	+	0.111885i	$0.964311\pi$
$978$		0			0
$979$	−9.56383	+	5.52168i	−0.305661	+	0.176474i
$980$	−17.3412	−	4.19293i	−0.553945	−	0.133938i
$981$		0			0
$982$	40.1402	+	11.0701i	1.28092	+	0.353262i
$983$	−24.8903	+	14.3704i	−0.793876	+	0.458345i	−0.841325	−	0.540529i	$-0.818224\pi$
$983$	−24.8903	+	14.3704i	−0.793876	+	0.458345i	0.0474493	+	0.998874i	$0.484891\pi$
$984$		0			0
$985$	−2.59417	+	11.4587i	−0.0826572	+	0.365105i
$986$	−1.05729	−	1.07284i	−0.0336710	−	0.0341661i
$987$		0			0
$988$	−0.389897	+	26.7089i	−0.0124043	+	0.849724i
$989$			60.7584i			1.93201i
$990$		0			0
$991$		−	5.20653i		−	0.165391i	−0.996575	−	0.0826954i	$-0.973647\pi$
$991$		−	5.20653i		−	0.165391i	0.996575	−	0.0826954i	$-0.0263529\pi$
$992$	0.912442	+	0.981591i	0.0289701	+	0.0311655i
$993$		0			0
$994$	−39.1493	+	38.5820i	−1.24174	+	1.22375i
$995$	−41.1067	−	9.30626i	−1.30317	−	0.295028i
$996$		0			0
$997$	−18.1724	+	10.4918i	−0.575525	+	0.332279i	−0.759353	−	0.650679i	$-0.774484\pi$
$997$	−18.1724	+	10.4918i	−0.575525	+	0.332279i	0.183828	+	0.982958i	$0.441151\pi$
$998$	−7.84924	+	28.4612i	−0.248463	+	0.900924i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	540.2.n.d.179.10		48
3.2	odd	2		180.2.n.d.59.15	yes	48
4.3	odd	2	inner	540.2.n.d.179.6		48
5.4	even	2	inner	540.2.n.d.179.15		48
9.2	odd	6	inner	540.2.n.d.359.19		48
9.7	even	3		180.2.n.d.119.6	yes	48
12.11	even	2		180.2.n.d.59.19	yes	48
15.2	even	4		900.2.r.g.851.3		48
15.8	even	4		900.2.r.g.851.22		48
15.14	odd	2		180.2.n.d.59.10	yes	48
20.19	odd	2	inner	540.2.n.d.179.19		48
36.7	odd	6		180.2.n.d.119.10	yes	48
36.11	even	6	inner	540.2.n.d.359.15		48
45.7	odd	12		900.2.r.g.551.7		48
45.29	odd	6	inner	540.2.n.d.359.6		48
45.34	even	6		180.2.n.d.119.19	yes	48
45.43	odd	12		900.2.r.g.551.18		48
60.23	odd	4		900.2.r.g.851.18		48
60.47	odd	4		900.2.r.g.851.7		48
60.59	even	2		180.2.n.d.59.6	✓	48
180.7	even	12		900.2.r.g.551.3		48
180.43	even	12		900.2.r.g.551.22		48
180.79	odd	6		180.2.n.d.119.15	yes	48
180.119	even	6	inner	540.2.n.d.359.10		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.n.d.59.6	✓	48	60.59	even	2
180.2.n.d.59.10	yes	48	15.14	odd	2
180.2.n.d.59.15	yes	48	3.2	odd	2
180.2.n.d.59.19	yes	48	12.11	even	2
180.2.n.d.119.6	yes	48	9.7	even	3
180.2.n.d.119.10	yes	48	36.7	odd	6
180.2.n.d.119.15	yes	48	180.79	odd	6
180.2.n.d.119.19	yes	48	45.34	even	6
540.2.n.d.179.6		48	4.3	odd	2	inner
540.2.n.d.179.10		48	1.1	even	1	trivial
540.2.n.d.179.15		48	5.4	even	2	inner
540.2.n.d.179.19		48	20.19	odd	2	inner
540.2.n.d.359.6		48	45.29	odd	6	inner
540.2.n.d.359.10		48	180.119	even	6	inner
540.2.n.d.359.15		48	36.11	even	6	inner
540.2.n.d.359.19		48	9.2	odd	6	inner
900.2.r.g.551.3		48	180.7	even	12
900.2.r.g.551.7		48	45.7	odd	12
900.2.r.g.551.18		48	45.43	odd	12
900.2.r.g.551.22		48	180.43	even	12
900.2.r.g.851.3		48	15.2	even	4
900.2.r.g.851.7		48	60.47	odd	4
900.2.r.g.851.18		48	60.23	odd	4
900.2.r.g.851.22		48	15.8	even	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)

\(f(q)\)	\(=\)	\(q+(-0.356046 - 1.36866i) q^{2} +(-1.74646 + 0.974612i) q^{4} +(0.493735 - 2.18088i) q^{5} +(1.65751 + 2.87089i) q^{7} +(1.95573 + 2.04331i) q^{8} +(-3.16067 + 0.100737i) q^{10} +(1.17952 + 2.04298i) q^{11} +(3.81058 + 2.20004i) q^{13} +(3.33912 - 3.29074i) q^{14} +(2.10026 - 3.40425i) q^{16} -0.889368 q^{17} -3.03537i q^{19} +(1.26322 + 4.29002i) q^{20} +(2.37619 - 2.34176i) q^{22} +(6.29952 + 3.63703i) q^{23} +(-4.51245 - 2.15355i) q^{25} +(1.65437 - 5.99870i) q^{26} +(-5.69278 - 3.39848i) q^{28} +(-1.03714 + 0.598791i) q^{29} +(-0.205172 - 0.118456i) q^{31} +(-5.40705 - 1.66248i) q^{32} +(0.316656 + 1.21724i) q^{34} +(7.07943 - 2.19737i) q^{35} -11.4975i q^{37} +(-4.15440 + 1.08073i) q^{38} +(5.42182 - 3.25636i) q^{40} +(-2.45213 - 1.41574i) q^{41} +(4.17637 + 7.23369i) q^{43} +(-4.05110 - 2.41842i) q^{44} +(2.73494 - 9.91686i) q^{46} +(6.55796 - 3.78624i) q^{47} +(-1.99467 + 3.45488i) q^{49} +(-1.34084 + 6.94278i) q^{50} +(-8.79922 - 0.128451i) q^{52} +0.772055 q^{53} +(5.03787 - 1.56369i) q^{55} +(-2.62447 + 9.00150i) q^{56} +(1.18881 + 1.20629i) q^{58} +(1.06446 - 1.84370i) q^{59} +(1.91303 + 3.31346i) q^{61} +(-0.0890754 + 0.322986i) q^{62} +(-0.350216 + 7.99233i) q^{64} +(6.67943 - 7.22417i) q^{65} +(3.17238 - 5.49472i) q^{67} +(1.55325 - 0.866788i) q^{68} +(-5.52805 - 8.90697i) q^{70} -11.7244 q^{71} +6.10889i q^{73} +(-15.7362 + 4.09365i) q^{74} +(2.95831 + 5.30117i) q^{76} +(-3.91012 + 6.77253i) q^{77} +(-8.94873 + 5.16655i) q^{79} +(-6.38727 - 6.26121i) q^{80} +(-1.06459 + 3.86020i) q^{82} +(2.25103 - 1.29963i) q^{83} +(-0.439112 + 1.93960i) q^{85} +(8.41349 - 8.29156i) q^{86} +(-1.86763 + 6.40565i) q^{88} +4.68130i q^{89} +14.5863i q^{91} +(-14.5466 - 0.212351i) q^{92} +(-7.51702 - 7.62755i) q^{94} +(-6.61978 - 1.49867i) q^{95} +(-5.34684 + 3.08700i) q^{97} +(5.43875 + 1.49994i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{4} + 18 q^{5} - 16 q^{10} + 42 q^{14} + 30 q^{16} - 26 q^{25} - 4 q^{34} + 10 q^{40} - 96 q^{41} + 4 q^{46} + 32 q^{49} + 90 q^{50} - 6 q^{56} + 8 q^{61} - 20 q^{64} + 6 q^{65} + 4 q^{70} - 72 q^{74}+ \cdots - 62 q^{94}+O(q^{100}) \) 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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