LMFDB - Embedded newform 460.2.x.a.333.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [460,2,Mod(17,460)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("460.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(460, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([0, 11, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.x (of order $44$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			333.10
Character	$\chi$	$=$	460.333
Dual form			460.2.x.a.297.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.82681 - 1.36753i) q^{3} +(-2.23541 + 0.0541276i) q^{5} +(0.160652 - 2.24620i) q^{7} +(0.621887 - 2.11795i) q^{9} +(2.67936 - 4.16917i) q^{11} +(-4.18667 + 0.299436i) q^{13} +(-4.00965 + 3.15588i) q^{15} +(0.285455 - 0.765335i) q^{17} +(1.10212 - 2.41330i) q^{19} +(-2.77827 - 4.32308i) q^{21} +(4.21324 - 2.29099i) q^{23} +(4.99414 - 0.241995i) q^{25} +(0.632098 + 1.69472i) q^{27} +(-4.75502 + 2.17155i) q^{29} +(-1.00269 - 6.97383i) q^{31} +(-0.806789 - 11.2804i) q^{33} +(-0.237541 + 5.02989i) q^{35} +(5.71348 + 10.4634i) q^{37} +(-7.23874 + 6.27241i) q^{39} +(-4.11047 + 1.20694i) q^{41} +(4.06707 + 5.43297i) q^{43} +(-1.27553 + 4.76816i) q^{45} +(-1.70451 + 1.70451i) q^{47} +(1.90913 + 0.274491i) q^{49} +(-0.525148 - 1.78849i) q^{51} +(-7.08796 - 0.506941i) q^{53} +(-5.76382 + 9.46485i) q^{55} +(-1.28690 - 5.91580i) q^{57} +(-3.37081 - 2.92082i) q^{59} +(12.5608 - 1.80597i) q^{61} +(-4.65745 - 1.73714i) q^{63} +(9.34272 - 0.895978i) q^{65} +(14.3461 + 3.12079i) q^{67} +(4.56377 - 9.94693i) q^{69} +(0.135232 - 0.0869081i) q^{71} +(-1.10528 + 0.412247i) q^{73} +(8.79240 - 7.27172i) q^{75} +(-8.93436 - 6.68818i) q^{77} +(-1.01147 + 1.16730i) q^{79} +(9.04317 + 5.81169i) q^{81} +(-10.7627 + 5.87690i) q^{83} +(-0.596685 + 1.72629i) q^{85} +(-5.71686 + 10.4696i) q^{87} +(1.44190 - 10.0287i) q^{89} +9.45221i q^{91} +(-11.3686 - 11.3686i) q^{93} +(-2.33306 + 5.45437i) q^{95} +(2.32366 + 1.26881i) q^{97} +(-7.16385 - 8.26752i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75}+ \cdots - 66 q^{97}+O(q^{100}) $ 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{9}{22}\right)$

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			0
$2$		0			0
$3$	1.82681	−	1.36753i	1.05471	−	0.789544i	0.0764785	−	0.997071i	$-0.475632\pi$
$3$	1.82681	−	1.36753i	1.05471	−	0.789544i	0.978229	+	0.207527i	$0.0665414\pi$
$4$		0			0
$5$	−2.23541	+	0.0541276i	−0.999707	+	0.0242066i
$5$	−2.23541	+	0.0541276i	−0.999707	+	0.0242066i
$6$		0			0
$7$	0.160652	−	2.24620i	0.0607206	−	0.848985i	−0.872256	−	0.489049i	$-0.837344\pi$
$7$	0.160652	−	2.24620i	0.0607206	−	0.848985i	0.932977	−	0.359936i	$-0.117202\pi$
$8$		0			0
$9$	0.621887	−	2.11795i	0.207296	−	0.705984i
$10$		0			0
$11$	2.67936	−	4.16917i	0.807858	−	1.25705i	−0.155233	−	0.987878i	$-0.549613\pi$
$11$	2.67936	−	4.16917i	0.807858	−	1.25705i	0.963091	−	0.269174i	$-0.0867508\pi$
$12$		0			0
$13$	−4.18667	+	0.299436i	−1.16117	+	0.0830487i	−0.638595	−	0.769543i	$-0.720484\pi$
$13$	−4.18667	+	0.299436i	−1.16117	+	0.0830487i	−0.522577	+	0.852592i	$0.675029\pi$
$14$		0			0
$15$	−4.00965	+	3.15588i	−1.03529	+	0.814844i
$16$		0			0
$17$	0.285455	−	0.765335i	0.0692331	−	0.185621i	−0.897725	−	0.440556i	$-0.854781\pi$
$17$	0.285455	−	0.765335i	0.0692331	−	0.185621i	0.966958	+	0.254935i	$0.0820541\pi$
$18$		0			0
$19$	1.10212	−	2.41330i	0.252843	−	0.553648i	−0.740065	−	0.672535i	$-0.765205\pi$
$19$	1.10212	−	2.41330i	0.252843	−	0.553648i	0.992908	+	0.118887i	$0.0379326\pi$
$20$		0			0
$21$	−2.77827	−	4.32308i	−0.606269	−	0.943373i
$22$		0			0
$23$	4.21324	−	2.29099i	0.878520	−	0.477705i
$23$	4.21324	−	2.29099i	0.878520	−	0.477705i
$24$		0			0
$25$	4.99414	−	0.241995i	0.998828	−	0.0483990i
$26$		0			0
$27$	0.632098	+	1.69472i	0.121647	+	0.326149i
$28$		0			0
$29$	−4.75502	+	2.17155i	−0.882986	+	0.403246i	−0.804698	−	0.593685i	$-0.797673\pi$
$29$	−4.75502	+	2.17155i	−0.882986	+	0.403246i	−0.0782881	+	0.996931i	$0.524945\pi$
$30$		0			0
$31$	−1.00269	−	6.97383i	−0.180088	−	1.25254i	−0.856552	−	0.516061i	$-0.827398\pi$
$31$	−1.00269	−	6.97383i	−0.180088	−	1.25254i	0.676464	−	0.736476i	$-0.263511\pi$
$32$		0			0
$33$	−0.806789	−	11.2804i	−0.140444	−	1.96366i
$34$		0			0
$35$	−0.237541	+	5.02989i	−0.0401518	+	0.850206i
$36$		0			0
$37$	5.71348	+	10.4634i	0.939290	+	1.72018i	0.644474	+	0.764626i	$0.277076\pi$
$37$	5.71348	+	10.4634i	0.939290	+	1.72018i	0.294816	+	0.955554i	$0.404742\pi$
$38$		0			0
$39$	−7.23874	+	6.27241i	−1.15913	+	1.00439i
$40$		0			0
$41$	−4.11047	+	1.20694i	−0.641947	+	0.188493i	−0.586475	−	0.809968i	$-0.699485\pi$
$41$	−4.11047	+	1.20694i	−0.641947	+	0.188493i	−0.0554724	+	0.998460i	$0.517666\pi$
$42$		0			0
$43$	4.06707	+	5.43297i	0.620223	+	0.828521i	0.995133	−	0.0985404i	$-0.0314174\pi$
$43$	4.06707	+	5.43297i	0.620223	+	0.828521i	−0.374910	+	0.927061i	$0.622326\pi$
$44$		0			0
$45$	−1.27553	+	4.76816i	−0.190145	+	0.710795i
$46$		0			0
$47$	−1.70451	+	1.70451i	−0.248628	+	0.248628i	−0.820408	−	0.571779i	$-0.806253\pi$
$47$	−1.70451	+	1.70451i	−0.248628	+	0.248628i	0.571779	+	0.820408i	$0.306253\pi$
$48$		0			0
$49$	1.90913	+	0.274491i	0.272732	+	0.0392130i
$50$		0			0
$51$	−0.525148	−	1.78849i	−0.0735354	−	0.250439i
$52$		0			0
$53$	−7.08796	−	0.506941i	−0.973606	−	0.0696337i	−0.424537	−	0.905411i	$-0.639563\pi$
$53$	−7.08796	−	0.506941i	−0.973606	−	0.0696337i	−0.549069	+	0.835777i	$0.685018\pi$
$54$		0			0
$55$	−5.76382	+	9.46485i	−0.777193	+	1.27624i
$56$		0			0
$57$	−1.28690	−	5.91580i	−0.170455	−	0.783567i
$58$		0			0
$59$	−3.37081	−	2.92082i	−0.438842	−	0.380259i	0.407231	−	0.913325i	$-0.366494\pi$
$59$	−3.37081	−	2.92082i	−0.438842	−	0.380259i	−0.846074	+	0.533066i	$0.821040\pi$
$60$		0			0
$61$	12.5608	−	1.80597i	1.60824	−	0.231231i	0.721137	−	0.692793i	$-0.243620\pi$
$61$	12.5608	−	1.80597i	1.60824	−	0.231231i	0.887108	+	0.461562i	$0.152711\pi$
$62$		0			0
$63$	−4.65745	−	1.73714i	−0.586783	−	0.218859i
$64$		0			0
$65$	9.34272	−	0.895978i	1.15882	−	0.111132i
$66$		0			0
$67$	14.3461	+	3.12079i	1.75265	+	0.381265i	0.970363	−	0.241653i	$-0.0776897\pi$
$67$	14.3461	+	3.12079i	1.75265	+	0.381265i	0.782286	+	0.622919i	$0.214053\pi$
$68$		0			0
$69$	4.56377	−	9.94693i	0.549413	−	1.19747i
$70$		0			0
$71$	0.135232	−	0.0869081i	0.0160490	−	0.0103141i	−0.532592	−	0.846372i	$-0.678782\pi$
$71$	0.135232	−	0.0869081i	0.0160490	−	0.0103141i	0.548641	+	0.836058i	$0.315145\pi$
$72$		0			0
$73$	−1.10528	+	0.412247i	−0.129363	+	0.0482498i	−0.413312	−	0.910590i	$-0.635628\pi$
$73$	−1.10528	+	0.412247i	−0.129363	+	0.0482498i	0.283949	+	0.958839i	$0.408355\pi$
$74$		0			0
$75$	8.79240	−	7.27172i	1.01526	−	0.839666i
$76$		0			0
$77$	−8.93436	−	6.68818i	−1.01817	−	0.762189i
$78$		0			0
$79$	−1.01147	+	1.16730i	−0.113800	+	0.131332i	−0.809791	−	0.586718i	$-0.800420\pi$
$79$	−1.01147	+	1.16730i	−0.113800	+	0.131332i	0.695992	+	0.718050i	$0.254965\pi$
$80$		0			0
$81$	9.04317	+	5.81169i	1.00480	+	0.645743i
$82$		0			0
$83$	−10.7627	+	5.87690i	−1.18136	+	0.645073i	−0.945153	−	0.326628i	$-0.894087\pi$
$83$	−10.7627	+	5.87690i	−1.18136	+	0.645073i	−0.236211	+	0.971702i	$0.575906\pi$
$84$		0			0
$85$	−0.596685	+	1.72629i	−0.0647195	+	0.187243i
$86$		0			0
$87$	−5.71686	+	10.4696i	−0.612911	+	1.12246i
$88$		0			0
$89$	1.44190	−	10.0287i	0.152841	−	1.06304i	−0.758586	−	0.651573i	$-0.774109\pi$
$89$	1.44190	−	10.0287i	0.152841	−	1.06304i	0.911427	−	0.411462i	$-0.134982\pi$
$90$		0			0
$91$			9.45221i			0.990861i
$92$		0			0
$93$	−11.3686	−	11.3686i	−1.17887	−	1.17887i
$94$		0			0
$95$	−2.33306	+	5.45437i	−0.239367	+	0.559606i
$96$		0			0
$97$	2.32366	+	1.26881i	0.235931	+	0.128828i	0.592866	−	0.805301i	$-0.297996\pi$
$97$	2.32366	+	1.26881i	0.235931	+	0.128828i	−0.356935	+	0.934129i	$0.616178\pi$
$98$		0			0
$99$	−7.16385	−	8.26752i	−0.719994	−	0.830917i
$100$		0			0
$101$	13.9519	+	4.09665i	1.38827	+	0.407632i	0.888639	−	0.458607i	$-0.151652\pi$
$101$	13.9519	+	4.09665i	1.38827	+	0.407632i	0.499629	+	0.866240i	$0.333470\pi$
$102$		0			0
$103$	12.0229	−	2.61541i	1.18465	−	0.257704i	0.423264	−	0.906006i	$-0.360884\pi$
$103$	12.0229	−	2.61541i	1.18465	−	0.257704i	0.761383	+	0.648302i	$0.224521\pi$
$104$		0			0
$105$	6.44459	+	9.51348i	0.628927	+	0.928421i
$106$		0			0
$107$	−5.35749	+	7.15677i	−0.517928	+	0.691871i	−0.980902	−	0.194501i	$-0.937691\pi$
$107$	−5.35749	+	7.15677i	−0.517928	+	0.691871i	0.462974	+	0.886372i	$0.346782\pi$
$108$		0			0
$109$	0.923834	+	2.02291i	0.0884872	+	0.193760i	0.948702	−	0.316172i	$-0.102398\pi$
$109$	0.923834	+	2.02291i	0.0884872	+	0.193760i	−0.860215	+	0.509932i	$0.829670\pi$
$110$		0			0
$111$	24.7465	+	11.3014i	2.34883	+	1.07268i
$112$		0			0
$113$	−1.32746	+	6.10222i	−0.124877	+	0.574048i	0.871603	+	0.490212i	$0.163081\pi$
$113$	−1.32746	+	6.10222i	−0.124877	+	0.574048i	−0.996480	+	0.0838360i	$0.973283\pi$
$114$		0			0
$115$	−9.29432	+	5.34936i	−0.866699	+	0.498831i
$116$		0			0
$117$	−1.96944	+	9.05338i	−0.182075	+	0.836985i
$118$		0			0
$119$	−1.67324	−	0.764143i	−0.153386	−	0.0700489i
$120$		0			0
$121$	−5.63343	−	12.3355i	−0.512130	−	1.12141i
$122$		0			0
$123$	−5.85850	+	7.82604i	−0.528243	+	0.705650i
$124$		0			0
$125$	−11.1509	+	0.811279i	−0.997364	+	0.0725630i
$126$		0			0
$127$	−9.20425	+	2.00226i	−0.816745	+	0.177672i	−0.601484	−	0.798885i	$-0.705424\pi$
$127$	−9.20425	+	2.00226i	−0.816745	+	0.177672i	−0.215261	+	0.976557i	$0.569060\pi$
$128$		0			0
$129$	14.8595	+	4.36315i	1.30831	+	0.384154i
$130$		0			0
$131$	1.35051	+	1.55857i	0.117994	+	0.136173i	0.811673	−	0.584111i	$-0.198557\pi$
$131$	1.35051	+	1.55857i	0.117994	+	0.136173i	−0.693679	+	0.720284i	$0.744011\pi$
$132$		0			0
$133$	−5.24370	−	2.86328i	−0.454686	−	0.248278i
$134$		0			0
$135$	−1.50473	−	3.75418i	−0.129507	−	0.323109i
$136$		0			0
$137$	−7.55228	−	7.55228i	−0.645234	−	0.645234i	0.306603	−	0.951837i	$-0.400808\pi$
$137$	−7.55228	−	7.55228i	−0.645234	−	0.645234i	−0.951837	+	0.306603i	$0.900808\pi$
$138$		0			0
$139$		−	5.84304i		−	0.495600i	−0.968811	−	0.247800i	$-0.920292\pi$
$139$		−	5.84304i		−	0.495600i	0.968811	−	0.247800i	$-0.0797076\pi$
$140$		0			0
$141$	−0.782841	+	5.44478i	−0.0659271	+	0.458533i
$142$		0			0
$143$	−9.96920	+	18.2572i	−0.833666	+	1.52675i
$144$		0			0
$145$	10.5119	−	5.11168i	0.872966	−	0.424502i
$146$		0			0
$147$	3.86298	−	2.10935i	0.318613	−	0.173976i
$148$		0			0
$149$	11.4383	+	7.35095i	0.937062	+	0.602213i	0.917560	−	0.397597i	$-0.130156\pi$
$149$	11.4383	+	7.35095i	0.937062	+	0.602213i	0.0195014	+	0.999810i	$0.493792\pi$
$150$		0			0
$151$	−13.7360	+	15.8522i	−1.11782	+	1.29003i	−0.165071	+	0.986282i	$0.552785\pi$
$151$	−13.7360	+	15.8522i	−1.11782	+	1.29003i	−0.952751	+	0.303753i	$0.901760\pi$
$152$		0			0
$153$	−1.44342	−	1.08053i	−0.116694	−	0.0873559i
$154$		0			0
$155$	2.61889	+	15.5351i	0.210355	+	1.24781i
$156$		0			0
$157$	8.75024	−	3.26367i	0.698345	−	0.260469i	0.0248824	−	0.999690i	$-0.492079\pi$
$157$	8.75024	−	3.26367i	0.698345	−	0.260469i	0.673463	+	0.739221i	$0.264806\pi$
$158$		0			0
$159$	−13.6416	+	8.76692i	−1.08185	+	0.695262i
$160$		0			0
$161$	−4.46917	−	9.83184i	−0.352220	−	0.774857i
$162$		0			0
$163$	−7.56248	−	1.64512i	−0.592339	−	0.128856i	−0.0936034	−	0.995610i	$-0.529839\pi$
$163$	−7.56248	−	1.64512i	−0.592339	−	0.128856i	−0.498736	+	0.866754i	$0.666202\pi$
$164$		0			0
$165$	2.41409	+	25.1726i	0.187936	+	1.95969i
$166$		0			0
$167$	−0.434454	−	0.162043i	−0.0336191	−	0.0125393i	0.332598	−	0.943069i	$-0.392075\pi$
$167$	−0.434454	−	0.162043i	−0.0336191	−	0.0125393i	−0.366217	+	0.930529i	$0.619347\pi$
$168$		0			0
$169$	4.57083	−	0.657186i	0.351602	−	0.0505527i
$170$		0			0
$171$	−4.42586	−	3.83503i	−0.338454	−	0.293272i
$172$		0			0
$173$	0.510110	+	2.34494i	0.0387829	+	0.178282i	0.992464	−	0.122538i	$-0.0391033\pi$
$173$	0.510110	+	2.34494i	0.0387829	+	0.178282i	−0.953681	+	0.300820i	$0.902740\pi$
$174$		0			0
$175$	0.258747	−	11.2567i	0.0195594	−	0.850929i
$176$		0			0
$177$	−10.1521	−	0.726096i	−0.763082	−	0.0545767i
$178$		0			0
$179$	0.655305	+	2.23176i	0.0489798	+	0.166810i	0.980351	−	0.197261i	$-0.0632047\pi$
$179$	0.655305	+	2.23176i	0.0489798	+	0.166810i	−0.931371	+	0.364071i	$0.881387\pi$
$180$		0			0
$181$	−14.1162	−	2.02960i	−1.04925	−	0.150859i	−0.403942	−	0.914785i	$-0.632360\pi$
$181$	−14.1162	−	2.02960i	−1.04925	−	0.150859i	−0.645304	+	0.763926i	$0.723269\pi$
$182$		0			0
$183$	20.4764	−	20.4764i	1.51366	−	1.51366i
$184$		0			0
$185$	−13.3383	−	23.0809i	−0.980654	−	1.69694i
$186$		0			0
$187$	−2.42598	−	3.24072i	−0.177405	−	0.236985i
$188$		0			0
$189$	3.90823	−	1.14756i	0.284282	−	0.0834728i
$190$		0			0
$191$	11.7814	−	10.2087i	0.852475	−	0.738674i	−0.114533	−	0.993419i	$-0.536537\pi$
$191$	11.7814	−	10.2087i	0.852475	−	0.738674i	0.967008	+	0.254745i	$0.0819916\pi$
$192$		0			0
$193$	4.28381	+	7.84522i	0.308356	+	0.564711i	0.985199	−	0.171416i	$-0.0548342\pi$
$193$	4.28381	+	7.84522i	0.308356	+	0.564711i	−0.676843	+	0.736127i	$0.736652\pi$
$194$		0			0
$195$	15.8421	−	14.4132i	1.13447	−	1.03215i
$196$		0			0
$197$	−0.406708	−	5.68653i	−0.0289768	−	0.405148i	−0.991153	−	0.132722i	$-0.957628\pi$
$197$	−0.406708	−	5.68653i	−0.0289768	−	0.405148i	0.962177	−	0.272427i	$-0.0878262\pi$
$198$		0			0
$199$	−3.42463	−	23.8188i	−0.242766	−	1.68847i	−0.638115	−	0.769941i	$-0.720286\pi$
$199$	−3.42463	−	23.8188i	−0.242766	−	1.68847i	0.395350	−	0.918531i	$-0.370623\pi$
$200$		0			0
$201$	30.4753	−	13.9176i	2.14956	−	0.981671i
$202$		0			0
$203$	4.11383	+	11.0296i	0.288735	+	0.774127i
$204$		0			0
$205$	9.12326	−	2.92050i	0.637196	−	0.203977i
$206$		0			0
$207$	−2.23206	−	10.3482i	−0.155139	−	0.719248i
$208$		0			0
$209$	−7.10848	−	11.0610i	−0.491704	−	0.765106i
$210$		0			0
$211$	4.14085	−	9.06719i	0.285068	−	0.624211i	−0.711878	−	0.702303i	$-0.752155\pi$
$211$	4.14085	−	9.06719i	0.285068	−	0.624211i	0.996946	+	0.0780913i	$0.0248826\pi$
$212$		0			0
$213$	0.128193	−	0.343698i	0.00878361	−	0.0235498i
$214$		0			0
$215$	−9.38566	−	11.9248i	−0.640097	−	0.813265i
$216$		0			0
$217$	−15.8257	+	1.13188i	−1.07432	+	0.0768369i
$218$		0			0
$219$	−1.45537	+	2.26459i	−0.0983445	+	0.153027i
$220$		0			0
$221$	−0.965937	+	3.28968i	−0.0649759	+	0.221288i
$222$		0			0
$223$	−0.372450	+	5.20753i	−0.0249411	+	0.348722i	0.969624	+	0.244602i	$0.0786572\pi$
$223$	−0.372450	+	5.20753i	−0.0249411	+	0.348722i	−0.994565	+	0.104120i	$0.966797\pi$
$224$		0			0
$225$	2.59326	−	10.7278i	0.172884	−	0.715190i
$226$		0			0
$227$	13.7895	−	10.3227i	0.915239	−	0.685140i	−0.0340912	−	0.999419i	$-0.510854\pi$
$227$	13.7895	−	10.3227i	0.915239	−	0.685140i	0.949331	+	0.314279i	$0.101763\pi$
$228$		0			0
$229$	−1.77819			−0.117506			−0.0587532	−	0.998273i	$-0.518712\pi$
$229$	−1.77819			−0.117506			−0.0587532	+	0.998273i	$0.518712\pi$
$230$		0			0
$231$	−25.4677			−1.67565
$232$		0			0
$233$	−18.7847	+	14.0621i	−1.23063	+	0.921236i	−0.998673	−	0.0514904i	$-0.983603\pi$
$233$	−18.7847	+	14.0621i	−1.23063	+	0.921236i	−0.231954	+	0.972727i	$0.574512\pi$
$234$		0			0
$235$	3.71802	−	3.90254i	0.242537	−	0.254574i
$236$		0			0
$237$	−0.251445	+	3.51566i	−0.0163331	+	0.228367i
$238$		0			0
$239$	8.21154	−	27.9659i	0.531160	−	1.80897i	−0.0546335	−	0.998506i	$-0.517399\pi$
$239$	8.21154	−	27.9659i	0.531160	−	1.80897i	0.585794	−	0.810460i	$-0.300783\pi$
$240$		0			0
$241$	9.39831	−	14.6241i	0.605398	−	0.942018i	−0.394336	−	0.918966i	$-0.629025\pi$
$241$	9.39831	−	14.6241i	0.605398	−	0.942018i	0.999734	−	0.0230517i	$-0.00733823\pi$
$242$		0			0
$243$	19.0553	−	1.36286i	1.22240	−	0.0874278i
$244$		0			0
$245$	−4.28254	−	0.510264i	−0.273602	−	0.0325996i
$246$		0			0
$247$	−3.89156	+	10.4337i	−0.247614	+	0.663879i
$248$		0			0
$249$	−11.6246	+	25.4543i	−0.736679	+	1.61310i
$250$		0			0
$251$	8.91333	+	13.8694i	0.562604	+	0.875430i	0.999712	−	0.0239794i	$-0.00763362\pi$
$251$	8.91333	+	13.8694i	0.562604	+	0.875430i	−0.437108	+	0.899409i	$0.643997\pi$
$252$		0			0
$253$	1.73725	−	23.7041i	0.109220	−	1.49026i
$254$		0			0
$255$	1.27073	+	3.96959i	0.0795761	+	0.248585i
$256$		0			0
$257$	−2.28011	−	6.11321i	−0.142229	−	0.381332i	0.846230	−	0.532818i	$-0.178867\pi$
$257$	−2.28011	−	6.11321i	−0.142229	−	0.381332i	−0.988459	+	0.151486i	$0.951594\pi$
$258$		0			0
$259$	24.4209	−	11.1527i	1.51744	−	0.692993i
$260$		0			0
$261$	1.64215	+	11.4214i	0.101646	+	0.706965i
$262$		0			0
$263$	−1.21174	−	16.9423i	−0.0747189	−	1.04471i	−0.887099	−	0.461578i	$-0.847283\pi$
$263$	−1.21174	−	16.9423i	−0.0747189	−	1.04471i	0.812381	−	0.583128i	$-0.198171\pi$
$264$		0			0
$265$	15.8720	+	0.749568i	0.975006	+	0.0460456i
$266$		0			0
$267$	−11.0804	−	20.2923i	−0.678110	−	1.24187i
$268$		0			0
$269$	−22.9193	+	19.8597i	−1.39742	+	1.21087i	−0.449122	+	0.893470i	$0.648263\pi$
$269$	−22.9193	+	19.8597i	−1.39742	+	1.21087i	−0.948293	+	0.317397i	$0.897191\pi$
$270$		0			0
$271$	−22.5228	+	6.61330i	−1.36816	+	0.401729i	−0.881634	−	0.471934i	$-0.843556\pi$
$271$	−22.5228	+	6.61330i	−1.36816	+	0.401729i	−0.486531	+	0.873664i	$0.661738\pi$
$272$		0			0
$273$	12.9262	+	17.2674i	0.782329	+	1.04507i
$274$		0			0
$275$	12.3722	−	21.4698i	0.746072	−	1.29468i
$276$		0			0
$277$	−18.6996	+	18.6996i	−1.12355	+	1.12355i	−0.132343	+	0.991204i	$0.542250\pi$
$277$	−18.6996	+	18.6996i	−1.12355	+	1.12355i	−0.991204	+	0.132343i	$0.957750\pi$
$278$		0			0
$279$	−15.3938	−	2.21329i	−0.921603	−	0.132506i
$280$		0			0
$281$	−5.51507	−	18.7826i	−0.329002	−	1.12048i	−0.943449	−	0.331518i	$-0.892439\pi$
$281$	−5.51507	−	18.7826i	−0.329002	−	1.12048i	0.614447	−	0.788958i	$-0.289379\pi$
$282$		0			0
$283$	−8.74649	−	0.625561i	−0.519925	−	0.0371858i	−0.191089	−	0.981573i	$-0.561202\pi$
$283$	−8.74649	−	0.625561i	−0.519925	−	0.0371858i	−0.328836	+	0.944387i	$0.606656\pi$
$284$		0			0
$285$	3.19697	+	13.1546i	0.189372	+	0.779212i
$286$		0			0
$287$	2.05068	+	9.42685i	0.121048	+	0.556449i
$288$		0			0
$289$	12.3435	+	10.6957i	0.726088	+	0.629158i
$290$		0			0
$291$	5.98001	−	0.859796i	0.350554	−	0.0504021i
$292$		0			0
$293$	−22.4878	−	8.38752i	−1.31375	−	0.490004i	−0.407678	−	0.913126i	$-0.633662\pi$
$293$	−22.4878	−	8.38752i	−1.31375	−	0.490004i	−0.906073	+	0.423122i	$0.860934\pi$
$294$		0			0
$295$	7.69325	+	6.34680i	0.447918	+	0.369525i
$296$		0			0
$297$	8.75919	+	1.90545i	0.508260	+	0.110565i
$298$		0			0
$299$	−16.9534	+	10.8532i	−0.980441	+	0.627657i
$300$		0			0
$301$	12.8570	−	8.26266i	0.741062	−	0.476252i
$302$		0			0
$303$	31.0898	−	11.5959i	1.78606	−	0.666166i
$304$		0			0
$305$	−27.9808	+	4.71697i	−1.60218	+	0.270093i
$306$		0			0
$307$	1.88338	+	1.40988i	0.107490	+	0.0804660i	0.651671	−	0.758502i	$-0.274068\pi$
$307$	1.88338	+	1.40988i	0.107490	+	0.0804660i	−0.544181	+	0.838968i	$0.683159\pi$
$308$		0			0
$309$	18.3868	−	21.2195i	1.04599	−	1.20713i
$310$		0			0
$311$	11.3186	+	7.27405i	0.641821	+	0.412473i	0.820669	−	0.571403i	$-0.193601\pi$
$311$	11.3186	+	7.27405i	0.641821	+	0.412473i	−0.178848	+	0.983877i	$0.557237\pi$
$312$		0			0
$313$	−1.27738	+	0.697500i	−0.0722015	+	0.0394250i	−0.514944	−	0.857224i	$-0.672187\pi$
$313$	−1.27738	+	0.697500i	−0.0722015	+	0.0394250i	0.442743	+	0.896649i	$0.354006\pi$
$314$		0			0
$315$	10.5053	+	3.63112i	0.591909	+	0.204591i
$316$		0			0
$317$	1.69968	−	3.11273i	0.0954635	−	0.174828i	−0.825583	−	0.564280i	$-0.809154\pi$
$317$	1.69968	−	3.11273i	0.0954635	−	0.174828i	0.921047	+	0.389452i	$0.127336\pi$
$318$		0			0
$319$	−3.68689	+	25.6429i	−0.206426	+	1.43573i
$320$		0			0
$321$			20.4006i			1.13865i
$322$		0			0
$323$	−1.53238	−	1.53238i	−0.0852637	−	0.0852637i
$324$		0			0
$325$	−20.8363	+	2.50858i	−1.15579	+	0.139151i
$326$		0			0
$327$	4.45406	+	2.43210i	0.246310	+	0.134496i
$328$		0			0
$329$	3.55484	+	4.10251i	0.195985	+	0.226179i
$330$		0			0
$331$	−14.5585	−	4.27476i	−0.800207	−	0.234962i	−0.144034	−	0.989573i	$-0.546007\pi$
$331$	−14.5585	−	4.27476i	−0.800207	−	0.234962i	−0.656173	+	0.754611i	$0.727826\pi$
$332$		0			0
$333$	25.7142	−	5.59379i	1.40913	−	0.306538i
$334$		0			0
$335$	−32.2383	−	6.19974i	−1.76136	−	0.338728i
$336$		0			0
$337$	1.78721	−	2.38743i	0.0973555	−	0.130052i	−0.749218	−	0.662323i	$-0.769571\pi$
$337$	1.78721	−	2.38743i	0.0973555	−	0.130052i	0.846574	+	0.532272i	$0.178661\pi$
$338$		0			0
$339$	5.91997	+	12.9629i	0.321528	+	0.704049i
$340$		0			0
$341$	−31.7617	−	14.5051i	−1.71999	−	0.785493i
$342$		0			0
$343$	4.27406	−	19.6475i	0.230778	−	1.06087i
$344$		0			0
$345$	−9.66350	+	22.4825i	−0.520265	+	1.21042i
$346$		0			0
$347$	−1.72651	+	7.93664i	−0.0926839	+	0.426061i	0.907301	+	0.420483i	$0.138139\pi$
$347$	−1.72651	+	7.93664i	−0.0926839	+	0.426061i	−0.999984	+	0.00557826i	$0.998224\pi$
$348$		0			0
$349$	7.41674	+	3.38711i	0.397009	+	0.181308i	0.603907	−	0.797055i	$-0.293610\pi$
$349$	7.41674	+	3.38711i	0.397009	+	0.181308i	−0.206898	+	0.978362i	$0.566337\pi$
$350$		0			0
$351$	−3.15384	−	6.90595i	−0.168340	−	0.368612i
$352$		0			0
$353$	10.3467	−	13.8216i	0.550701	−	0.735651i	−0.435684	−	0.900100i	$-0.643494\pi$
$353$	10.3467	−	13.8216i	0.550701	−	0.735651i	0.986386	+	0.164449i	$0.0525845\pi$
$354$		0			0
$355$	−0.297594	+	0.201595i	−0.0157947	+	0.0106996i
$356$		0			0
$357$	−4.10168	+	0.892265i	−0.217084	+	0.0472237i
$358$		0			0
$359$	18.2942	+	5.37166i	0.965531	+	0.283506i	0.726239	−	0.687442i	$-0.241266\pi$
$359$	18.2942	+	5.37166i	0.965531	+	0.283506i	0.239292	+	0.970948i	$0.423085\pi$
$360$		0			0
$361$	7.83301	+	9.03978i	0.412264	+	0.475778i
$362$		0			0
$363$	−27.1604	−	14.8307i	−1.42555	−	0.778409i
$364$		0			0
$365$	2.44843	−	0.981367i	0.128157	−	0.0513671i
$366$		0			0
$367$	16.0672	+	16.0672i	0.838702	+	0.838702i	0.988688	−	0.149986i	$-0.0479230\pi$
$367$	16.0672	+	16.0672i	0.838702	+	0.838702i	−0.149986	+	0.988688i	$0.547923\pi$
$368$		0			0
$369$			9.45636i			0.492278i
$370$		0			0
$371$	−2.27738	+	15.8396i	−0.118236	+	0.822349i
$372$		0			0
$373$	−13.7308	+	25.1460i	−0.710953	+	1.30201i	0.233176	+	0.972435i	$0.425088\pi$
$373$	−13.7308	+	25.1460i	−0.710953	+	1.30201i	−0.944128	+	0.329578i	$0.893094\pi$
$374$		0			0
$375$	−19.2610	+	16.7312i	−0.994636	+	0.863996i
$376$		0			0
$377$	19.2575	−	10.5154i	0.991810	−	0.541569i
$378$		0			0
$379$	7.89749	+	5.07541i	0.405667	+	0.260706i	0.727524	−	0.686082i	$-0.240671\pi$
$379$	7.89749	+	5.07541i	0.405667	+	0.260706i	−0.321857	+	0.946788i	$0.604307\pi$
$380$		0			0
$381$	−14.0762	+	16.2448i	−0.721148	+	0.832249i
$382$		0			0
$383$	−13.5105	−	10.1138i	−0.690354	−	0.516793i	0.195531	−	0.980698i	$-0.437357\pi$
$383$	−13.5105	−	10.1138i	−0.690354	−	0.516793i	−0.885885	+	0.463905i	$0.846448\pi$
$384$		0			0
$385$	20.3340	+	14.4673i	1.03632	+	0.737319i
$386$		0			0
$387$	14.0360	−	5.23517i	0.713492	−	0.266119i
$388$		0			0
$389$	3.03544	−	1.95076i	0.153903	−	0.0989074i	−0.461423	−	0.887180i	$-0.652661\pi$
$389$	3.03544	−	1.95076i	0.153903	−	0.0989074i	0.615326	+	0.788273i	$0.289024\pi$
$390$		0			0
$391$	−0.550687	−	3.87851i	−0.0278494	−	0.196145i
$392$		0			0
$393$	4.59850	+	1.00034i	0.231964	+	0.0504606i
$394$		0			0
$395$	2.19788	−	2.66415i	0.110587	−	0.134048i
$396$		0			0
$397$	13.9174	+	5.19091i	0.698493	+	0.260524i	0.673526	−	0.739164i	$-0.264779\pi$
$397$	13.9174	+	5.19091i	0.698493	+	0.260524i	0.0249673	+	0.999688i	$0.492052\pi$
$398$		0			0
$399$	−13.4948	+	1.94027i	−0.675587	+	0.0971348i
$400$		0			0
$401$	−12.0312	−	10.4251i	−0.600810	−	0.520605i	0.300499	−	0.953782i	$-0.402847\pi$
$401$	−12.0312	−	10.4251i	−0.600810	−	0.520605i	−0.901309	+	0.433177i	$0.857392\pi$
$402$		0			0
$403$	6.28613	+	28.8969i	0.313134	+	1.43946i
$404$		0			0
$405$	−20.5298	−	12.5020i	−1.02013	−	0.621231i
$406$		0			0
$407$	58.9324	+	4.21493i	2.92117	+	0.208926i
$408$		0			0
$409$	−9.43695	−	32.1393i	−0.466627	−	1.58919i	−0.771132	−	0.636676i	$-0.780309\pi$
$409$	−9.43695	−	32.1393i	−0.466627	−	1.58919i	0.304504	−	0.952511i	$-0.401509\pi$
$410$		0			0
$411$	−24.1245	−	3.46858i	−1.18998	−	0.171093i
$412$		0			0
$413$	−7.10230	+	7.10230i	−0.349481	+	0.349481i
$414$		0			0
$415$	23.7411	−	13.7199i	1.16540	−	0.673481i
$416$		0			0
$417$	−7.99054	−	10.6741i	−0.391298	−	0.522713i
$418$		0			0
$419$	−30.7331	+	9.02404i	−1.50141	+	0.440853i	−0.926162	−	0.377127i	$-0.876912\pi$
$419$	−30.7331	+	9.02404i	−1.50141	+	0.440853i	−0.575247	+	0.817980i	$0.695094\pi$
$420$		0			0
$421$	−21.1377	+	18.3159i	−1.03019	+	0.892663i	−0.994292	−	0.106692i	$-0.965974\pi$
$421$	−21.1377	+	18.3159i	−1.03019	+	0.892663i	−0.0358963	+	0.999356i	$0.511429\pi$
$422$		0			0
$423$	2.55006	+	4.67008i	0.123988	+	0.227067i
$424$		0			0
$425$	1.24040	−	3.89127i	0.0601681	−	0.188754i
$426$		0			0
$427$	−2.03866	−	28.5042i	−0.0986578	−	1.37942i
$428$		0			0
$429$	6.75551	+	46.9856i	0.326159	+	2.26849i
$430$		0			0
$431$	17.1603	−	7.83687i	0.826585	−	0.377489i	0.0432313	−	0.999065i	$-0.486235\pi$
$431$	17.1603	−	7.83687i	0.826585	−	0.377489i	0.783354	+	0.621576i	$0.213507\pi$
$432$		0			0
$433$	10.7015	+	28.6917i	0.514279	+	1.37884i	0.891630	+	0.452765i	$0.149562\pi$
$433$	10.7015	+	28.6917i	0.514279	+	1.37884i	−0.377351	+	0.926070i	$0.623165\pi$
$434$		0			0
$435$	12.2128	−	23.7134i	0.585561	−	1.13697i
$436$		0			0
$437$	−0.885370	−	12.6927i	−0.0423530	−	0.607175i
$438$		0			0
$439$	−8.34246	−	12.9811i	−0.398164	−	0.619555i	0.583060	−	0.812429i	$-0.301855\pi$
$439$	−8.34246	−	12.9811i	−0.398164	−	0.619555i	−0.981223	+	0.192874i	$0.938219\pi$
$440$		0			0
$441$	1.76862	−	3.87274i	0.0842200	−	0.184416i
$442$		0			0
$443$	3.60914	−	9.67648i	0.171475	−	0.459743i	−0.822576	−	0.568655i	$-0.807464\pi$
$443$	3.60914	−	9.67648i	0.171475	−	0.459743i	0.994051	+	0.108912i	$0.0347366\pi$
$444$		0			0
$445$	−2.68042	+	22.4962i	−0.127064	+	1.06642i
$446$		0			0
$447$	30.9482	−	2.21346i	1.46380	−	0.104693i
$448$		0			0
$449$	−12.2092	+	18.9979i	−0.576187	+	0.896564i	−0.999958	−	0.00920527i	$-0.997070\pi$
$449$	−12.2092	+	18.9979i	−0.576187	+	0.896564i	0.423771	+	0.905769i	$0.360706\pi$
$450$		0			0
$451$	−5.98149	+	20.3711i	−0.281657	+	0.959237i
$452$		0			0
$453$	−3.41467	+	47.7434i	−0.160435	+	2.24318i
$454$		0			0
$455$	−0.511625	−	21.1296i	−0.0239854	−	0.990570i
$456$		0			0
$457$	−2.01234	+	1.50642i	−0.0941332	+	0.0704672i	−0.645308	−	0.763923i	$-0.723271\pi$
$457$	−2.01234	+	1.50642i	−0.0941332	+	0.0704672i	0.551174	+	0.834390i	$0.314180\pi$
$458$		0			0
$459$	1.47746			0.0689621
$460$		0			0
$461$	−6.20403			−0.288951			−0.144475	−	0.989508i	$-0.546149\pi$
$461$	−6.20403			−0.288951			−0.144475	+	0.989508i	$0.546149\pi$
$462$		0			0
$463$	27.8106	−	20.8188i	1.29247	−	0.967531i	0.292534	−	0.956255i	$-0.405502\pi$
$463$	27.8106	−	20.8188i	1.29247	−	0.967531i	0.999936	−	0.0112760i	$-0.00358933\pi$
$464$		0			0
$465$	26.0290	+	24.7983i	1.20706	+	1.14999i
$466$		0			0
$467$	−0.527570	+	7.37639i	−0.0244130	+	0.341339i	0.970536	+	0.240956i	$0.0774611\pi$
$467$	−0.527570	+	7.37639i	−0.0244130	+	0.341339i	−0.994949	+	0.100382i	$0.967993\pi$
$468$		0			0
$469$	9.31465	−	31.7228i	0.430111	−	1.46482i
$470$		0			0
$471$	11.5218	−	17.9283i	0.530898	−	0.826094i
$472$		0			0
$473$	33.5482	−	2.39941i	1.54255	−	0.110325i
$474$		0			0
$475$	4.92011	−	12.3190i	0.225750	−	0.565237i
$476$		0			0
$477$	−5.48159	+	14.6967i	−0.250985	+	0.672916i
$478$		0			0
$479$	−10.1480	+	22.2211i	−0.463676	+	1.01531i	0.522958	+	0.852358i	$0.324828\pi$
$479$	−10.1480	+	22.2211i	−0.463676	+	1.01531i	−0.986634	+	0.162950i	$0.947899\pi$
$480$		0			0
$481$	−27.0535	−	42.0961i	−1.23354	−	1.91942i
$482$		0			0
$483$	−21.6097	−	11.8491i	−0.983274	−	0.539155i
$484$		0			0
$485$	−5.26301	−	2.71054i	−0.238981	−	0.123079i
$486$		0			0
$487$	3.52969	+	9.46348i	0.159946	+	0.428831i	0.992059	−	0.125775i	$-0.0401417\pi$
$487$	3.52969	+	9.46348i	0.159946	+	0.428831i	−0.832113	+	0.554606i	$0.812869\pi$
$488$		0			0
$489$	−16.0649	+	7.33662i	−0.726482	+	0.331773i
$490$		0			0
$491$	6.08541	+	42.3250i	0.274631	+	1.91010i	0.397368	+	0.917659i	$0.369924\pi$
$491$	6.08541	+	42.3250i	0.274631	+	1.91010i	−0.122737	+	0.992439i	$0.539167\pi$
$492$		0			0
$493$	0.304615	+	4.25907i	0.0137191	+	0.191819i
$494$		0			0
$495$	16.4617	+	18.0936i	0.739896	+	0.813245i
$496$		0			0
$497$	−0.173488	−	0.317720i	−0.00778200	−	0.0142517i
$498$		0			0
$499$	7.92815	−	6.86978i	0.354913	−	0.307534i	−0.459096	−	0.888387i	$-0.651826\pi$
$499$	7.92815	−	6.86978i	0.354913	−	0.307534i	0.814008	+	0.580853i	$0.197281\pi$
$500$		0			0
$501$	−1.01526	+	0.298108i	−0.0453586	+	0.0133185i
$502$		0			0
$503$	14.3716	+	19.1982i	0.640798	+	0.856006i	0.996919	−	0.0784334i	$-0.0249918\pi$
$503$	14.3716	+	19.1982i	0.640798	+	0.856006i	−0.356121	+	0.934440i	$0.615901\pi$
$504$		0			0
$505$	−31.4100	−	8.40253i	−1.39773	−	0.373908i
$506$		0			0
$507$	7.45130	−	7.45130i	0.330924	−	0.330924i
$508$		0			0
$509$	39.4523	+	5.67239i	1.74869	+	0.251424i	0.941055	−	0.338254i	$-0.109836\pi$
$509$	39.4523	+	5.67239i	1.74869	+	0.251424i	0.807638	+	0.589678i	$0.200745\pi$
$510$		0			0
$511$	0.748426	+	2.54890i	0.0331084	+	0.112757i
$512$		0			0
$513$	4.78650	+	0.342337i	0.211329	+	0.0151146i
$514$		0			0
$515$	−26.7345	+	6.49729i	−1.17806	+	0.286305i
$516$		0			0
$517$	2.53939	+	11.6734i	0.111682	+	0.513395i
$518$		0			0
$519$	4.13865	+	3.58616i	0.181666	+	0.157415i
$520$		0			0
$521$	−35.3347	+	5.08036i	−1.54804	+	0.222575i	−0.862726	−	0.505672i	$-0.831245\pi$
$521$	−35.3347	+	5.08036i	−1.54804	+	0.222575i	−0.685315	+	0.728247i	$0.740335\pi$
$522$		0			0
$523$	3.91979	+	1.46201i	0.171401	+	0.0639291i	0.433700	−	0.901058i	$-0.357208\pi$
$523$	3.91979	+	1.46201i	0.171401	+	0.0639291i	−0.262299	+	0.964987i	$0.584481\pi$
$524$		0			0
$525$	−14.9213	−	20.9177i	−0.651217	−	0.912925i
$526$		0			0
$527$	−5.62354	−	1.22333i	−0.244965	−	0.0532889i
$528$		0			0
$529$	12.5027	−	19.3050i	0.543596	−	0.839347i
$530$		0			0
$531$	−8.28243	+	5.32280i	−0.359427	+	0.230990i
$532$		0			0
$533$	16.8477	−	6.28389i	0.729757	−	0.272185i
$534$		0			0
$535$	11.5888	−	16.2883i	0.501029	−	0.704206i
$536$		0			0
$537$	4.24912	+	3.18085i	0.183363	+	0.137264i
$538$		0			0
$539$	6.25964	−	7.22401i	0.269622	−	0.311160i
$540$		0			0
$541$	27.7382	+	17.8262i	1.19256	+	0.766409i	0.977653	−	0.210226i	$-0.0674199\pi$
$541$	27.7382	+	17.8262i	1.19256	+	0.766409i	0.214904	+	0.976635i	$0.431056\pi$
$542$		0			0
$543$	−28.5630	+	15.5966i	−1.22576	+	0.669314i
$544$		0			0
$545$	−2.17464	−	4.47204i	−0.0931515	−	0.191561i
$546$		0			0
$547$	−5.85700	+	10.7263i	−0.250427	+	0.458623i	−0.972407	−	0.233291i	$-0.925051\pi$
$547$	−5.85700	+	10.7263i	−0.250427	+	0.458623i	0.721980	+	0.691914i	$0.243232\pi$
$548$		0			0
$549$	3.98644	−	27.7263i	0.170137	−	1.18333i
$550$		0			0
$551$			13.8686i			0.590821i
$552$		0			0
$553$	2.45951	+	2.45951i	0.104589	+	0.104589i
$554$		0			0
$555$	−55.9304	−	23.9237i	−2.37411	−	1.01551i
$556$		0			0
$557$	9.56518	+	5.22298i	0.405290	+	0.221305i	0.668945	−	0.743312i	$-0.266746\pi$
$557$	9.56518	+	5.22298i	0.405290	+	0.221305i	−0.263655	+	0.964617i	$0.584928\pi$
$558$		0			0
$559$	−18.6543	−	21.5282i	−0.788993	−	0.910547i
$560$		0			0
$561$	−8.86358	−	2.60258i	−0.374221	−	0.109881i
$562$		0			0
$563$	4.35388	−	0.947129i	0.183494	−	0.0399167i	−0.119879	−	0.992788i	$-0.538251\pi$
$563$	4.35388	−	0.947129i	0.183494	−	0.0399167i	0.303373	+	0.952872i	$0.401887\pi$
$564$		0			0
$565$	2.63711	−	13.7128i	0.110944	−	0.576903i
$566$		0			0
$567$	14.5070	−	19.3791i	0.609238	−	0.813847i
$568$		0			0
$569$	15.4465	+	33.8231i	0.647552	+	1.41794i	0.893681	+	0.448703i	$0.148114\pi$
$569$	15.4465	+	33.8231i	0.647552	+	1.41794i	−0.246129	+	0.969237i	$0.579159\pi$
$570$		0			0
$571$	−38.9151	−	17.7719i	−1.62855	−	0.743732i	−0.629110	−	0.777317i	$-0.716580\pi$
$571$	−38.9151	−	17.7719i	−1.62855	−	0.743732i	−0.999436	+	0.0335847i	$0.989308\pi$
$572$		0			0
$573$	7.56175	−	34.7608i	0.315896	−	1.45215i
$574$		0			0
$575$	20.4871	−	12.4611i	0.854370	−	0.519665i
$576$		0			0
$577$	6.03172	−	27.7274i	0.251104	−	1.15431i	−0.662934	−	0.748678i	$-0.730689\pi$
$577$	6.03172	−	27.7274i	0.251104	−	1.15431i	0.914038	−	0.405629i	$-0.132947\pi$
$578$		0			0
$579$	18.5543	+	8.47346i	0.771090	+	0.352145i
$580$		0			0
$581$	11.4717	+	25.1194i	0.475925	+	1.04213i
$582$		0			0
$583$	−21.1047	+	28.1926i	−0.874069	+	1.16762i
$584$		0			0
$585$	3.91248	−	20.3446i	0.161761	−	0.841147i
$586$		0			0
$587$	−45.7605	+	9.95459i	−1.88874	+	0.410870i	−0.998963	−	0.0455282i	$-0.985503\pi$
$587$	−45.7605	+	9.95459i	−1.88874	+	0.410870i	−0.889776	+	0.456398i	$0.849139\pi$
$588$		0			0
$589$	−17.9350	−	5.26619i	−0.738999	−	0.216990i
$590$		0			0
$591$	−8.51948	−	9.83200i	−0.350444	−	0.404435i
$592$		0			0
$593$	38.0122	+	20.7562i	1.56097	+	0.852356i	0.999694	+	0.0247300i	$0.00787260\pi$
$593$	38.0122	+	20.7562i	1.56097	+	0.852356i	0.561280	+	0.827626i	$0.310309\pi$
$594$		0			0
$595$	3.78174	+	1.61761i	0.155036	+	0.0663154i
$596$		0			0
$597$	−38.8291	−	38.8291i	−1.58917	−	1.58917i
$598$		0			0
$599$			17.4126i			0.711461i	0.934589	+	0.355730i	$0.115768\pi$
$599$			17.4126i			0.711461i	−0.934589	+	0.355730i	$0.884232\pi$
$600$		0			0
$601$	−5.42058	+	37.7010i	−0.221110	+	1.53786i	0.512740	+	0.858544i	$0.328631\pi$
$601$	−5.42058	+	37.7010i	−0.221110	+	1.53786i	−0.733850	+	0.679312i	$0.762279\pi$
$602$		0			0
$603$	15.5313	−	28.4435i	0.632484	−	1.15831i
$604$		0			0
$605$	13.2607	+	27.2700i	0.539126	+	1.10868i
$606$		0			0
$607$	−40.9196	+	22.3438i	−1.66087	+	0.906906i	−0.675325	+	0.737520i	$0.735997\pi$
$607$	−40.9196	+	22.3438i	−1.66087	+	0.906906i	−0.985550	+	0.169386i	$0.945822\pi$
$608$		0			0
$609$	22.5985	+	14.5232i	0.915739	+	0.588509i
$610$		0			0
$611$	6.62582	−	7.64661i	0.268052	−	0.309349i
$612$		0			0
$613$	9.36728	+	7.01226i	0.378341	+	0.283222i	0.771476	−	0.636258i	$-0.219519\pi$
$613$	9.36728	+	7.01226i	0.378341	+	0.283222i	−0.393135	+	0.919481i	$0.628610\pi$
$614$		0			0
$615$	12.6726	−	17.8115i	0.511007	−	0.718231i
$616$		0			0
$617$	−3.12211	+	1.16449i	−0.125691	+	0.0468805i	−0.411523	−	0.911399i	$-0.635003\pi$
$617$	−3.12211	+	1.16449i	−0.125691	+	0.0468805i	0.285831	+	0.958280i	$0.407730\pi$
$618$		0			0
$619$	−25.6628	+	16.4925i	−1.03148	+	0.662889i	−0.942864	−	0.333177i	$-0.891879\pi$
$619$	−25.6628	+	16.4925i	−1.03148	+	0.662889i	−0.0886112	+	0.996066i	$0.528243\pi$
$620$		0			0
$621$	6.54576	+	5.69212i	0.262672	+	0.228417i
$622$		0			0
$623$	−22.2948	−	4.84993i	−0.893221	−	0.194308i
$624$		0			0
$625$	24.8829	−	2.41711i	0.995315	−	0.0966845i
$626$		0			0
$627$	−28.1121	−	10.4853i	−1.12269	−	0.418741i
$628$		0			0
$629$	9.63899	−	1.38588i	0.384332	−	0.0552586i
$630$		0			0
$631$	15.2741	+	13.2350i	0.608050	+	0.526879i	0.903560	−	0.428461i	$-0.140944\pi$
$631$	15.2741	+	13.2350i	0.608050	+	0.526879i	−0.295510	+	0.955340i	$0.595489\pi$
$632$		0			0
$633$	−4.83514	−	22.2268i	−0.192179	−	0.883434i
$634$		0			0
$635$	20.4669	−	4.97409i	0.812205	−	0.197391i
$636$		0			0
$637$	−8.07507	−	0.577540i	−0.319946	−	0.0228830i
$638$		0			0
$639$	−0.0999684	−	0.340461i	−0.00395469	−	0.0134684i
$640$		0			0
$641$	−8.35997	−	1.20198i	−0.330199	−	0.0474754i	−0.0247783	−	0.999693i	$-0.507888\pi$
$641$	−8.35997	−	1.20198i	−0.330199	−	0.0474754i	−0.305421	+	0.952218i	$0.598797\pi$
$642$		0			0
$643$	12.9773	−	12.9773i	0.511774	−	0.511774i	−0.403296	−	0.915070i	$-0.632135\pi$
$643$	12.9773	−	12.9773i	0.511774	−	0.511774i	0.915070	+	0.403296i	$0.132135\pi$
$644$		0			0
$645$	−33.4533	−	8.94913i	−1.31722	−	0.352372i
$646$		0			0
$647$	12.5824	+	16.8082i	0.494667	+	0.660797i	0.976513	−	0.215458i	$-0.0691245\pi$
$647$	12.5824	+	16.8082i	0.494667	+	0.660797i	−0.481846	+	0.876256i	$0.660034\pi$
$648$		0			0
$649$	−21.2090	+	6.22754i	−0.832528	+	0.244452i
$650$		0			0
$651$	−27.3627	+	23.7099i	−1.07243	+	0.929264i
$652$		0			0
$653$	−16.4502	−	30.1262i	−0.643745	−	1.17893i	−0.972142	−	0.234392i	$-0.924690\pi$
$653$	−16.4502	−	30.1262i	−0.643745	−	1.17893i	0.328397	−	0.944540i	$-0.393492\pi$
$654$		0			0
$655$	−3.10330	−	3.41094i	−0.121256	−	0.133276i
$656$		0			0
$657$	0.185762	+	2.59729i	0.00724727	+	0.101330i
$658$		0			0
$659$	−3.99665	−	27.7973i	−0.155687	−	1.08283i	−0.906467	−	0.422276i	$-0.861231\pi$
$659$	−3.99665	−	27.7973i	−0.155687	−	1.08283i	0.750780	−	0.660552i	$-0.229678\pi$
$660$		0			0
$661$	13.0132	−	5.94293i	0.506155	−	0.231153i	−0.145936	−	0.989294i	$-0.546619\pi$
$661$	13.0132	−	5.94293i	0.506155	−	0.231153i	0.652091	+	0.758141i	$0.273892\pi$
$662$		0			0
$663$	2.73416	+	7.33056i	0.106186	+	0.284695i
$664$		0			0
$665$	11.8768	+	6.11678i	0.460563	+	0.237198i
$666$		0			0
$667$	−15.0590	+	20.0430i	−0.583088	+	0.776067i
$668$		0			0
$669$	6.44106	+	10.0225i	0.249026	+	0.387492i
$670$		0			0
$671$	26.1255	−	57.2069i	1.00857	−	2.20845i
$672$		0			0
$673$	−1.98008	+	5.30881i	−0.0763266	+	0.204640i	−0.969509	−	0.245054i	$-0.921194\pi$
$673$	−1.98008	+	5.30881i	−0.0763266	+	0.204640i	0.893183	+	0.449694i	$0.148467\pi$
$674$		0			0
$675$	3.56690	+	8.31070i	0.137290	+	0.319879i
$676$		0			0
$677$	−6.72951	+	0.481304i	−0.258636	+	0.0184980i	−0.200055	−	0.979785i	$-0.564112\pi$
$677$	−6.72951	+	0.481304i	−0.258636	+	0.0184980i	−0.0585809	+	0.998283i	$0.518658\pi$
$678$		0			0
$679$	3.22331	−	5.01557i	0.123699	−	0.192480i
$680$		0			0
$681$	11.0741	−	37.7151i	0.424362	−	1.44524i
$682$		0			0
$683$	−3.25956	+	45.5746i	−0.124723	+	1.74386i	0.422042	+	0.906576i	$0.361313\pi$
$683$	−3.25956	+	45.5746i	−0.124723	+	1.74386i	−0.546765	+	0.837286i	$0.684141\pi$
$684$		0			0
$685$	17.2912	+	16.4737i	0.660664	+	0.629427i
$686$		0			0
$687$	−3.24842	+	2.43173i	−0.123935	+	0.0927764i
$688$		0			0
$689$	29.8267			1.13631
$690$		0			0
$691$	−2.85704			−0.108687			−0.0543434	−	0.998522i	$-0.517307\pi$
$691$	−2.85704			−0.108687			−0.0543434	+	0.998522i	$0.517307\pi$
$692$		0			0
$693$	−19.7214	+	14.7633i	−0.749155	+	0.560810i
$694$		0			0
$695$	0.316269	+	13.0616i	0.0119968	+	0.495455i
$696$		0			0
$697$	−0.249639	+	3.49041i	−0.00945576	+	0.132209i
$698$		0			0
$699$	−15.0858	+	51.3774i	−0.570596	+	1.94327i
$700$		0			0
$701$	15.1275	−	23.5389i	0.571359	−	0.889052i	−0.428536	−	0.903525i	$-0.640971\pi$
$701$	15.1275	−	23.5389i	0.571359	−	0.889052i	0.999895	+	0.0144725i	$0.00460691\pi$
$702$		0			0
$703$	31.5483	−	2.25638i	1.18987	−	0.0851010i
$704$		0			0
$705$	1.45526	−	12.2137i	0.0548083	−	0.459995i
$706$		0			0
$707$	11.4433	−	30.6807i	0.430370	−	1.15387i
$708$		0			0
$709$	2.10131	−	4.60122i	0.0789163	−	0.172803i	−0.866061	−	0.499938i	$-0.833356\pi$
$709$	2.10131	−	4.60122i	0.0789163	−	0.172803i	0.944977	+	0.327136i	$0.106083\pi$
$710$		0			0
$711$	1.84327	+	2.86818i	0.0691280	+	0.107565i
$712$		0			0
$713$	−20.2015	−	27.0853i	−0.756554	−	1.01435i
$714$		0			0
$715$	21.2971	−	41.3520i	0.796465	−	1.54648i
$716$		0			0
$717$	−23.2434	−	62.3179i	−0.868040	−	2.32731i
$718$		0			0
$719$	2.89486	−	1.32204i	0.107960	−	0.0493037i	−0.360703	−	0.932681i	$-0.617463\pi$
$719$	2.89486	−	1.32204i	0.107960	−	0.0493037i	0.468663	+	0.883377i	$0.344736\pi$
$720$		0			0
$721$	−3.94326	−	27.4260i	−0.146855	−	1.02140i
$722$		0			0
$723$	−2.82995	−	39.5678i	−0.105247	−	1.47154i
$724$		0			0
$725$	−23.2218	+	11.9957i	−0.862434	+	0.445509i
$726$		0			0
$727$	0.976412	+	1.78817i	0.0362131	+	0.0663194i	0.895159	−	0.445747i	$-0.147062\pi$
$727$	0.976412	+	1.78817i	0.0362131	+	0.0663194i	−0.858946	+	0.512067i	$0.828880\pi$
$728$		0			0
$729$	8.57457	−	7.42991i	0.317577	−	0.275182i
$730$		0			0
$731$	5.31901	−	1.56180i	0.196731	−	0.0577654i
$732$		0			0
$733$	18.0301	+	24.0854i	0.665958	+	0.889616i	0.998571	−	0.0534476i	$-0.0170210\pi$
$733$	18.0301	+	24.0854i	0.665958	+	0.889616i	−0.332612	+	0.943064i	$0.607930\pi$
$734$		0			0
$735$	−8.52118	+	4.92436i	−0.314309	+	0.181638i
$736$		0			0
$737$	51.4494	−	51.4494i	1.89516	−	1.89516i
$738$		0			0
$739$	30.0329	+	4.31808i	1.10478	+	0.158843i	0.670481	−	0.741926i	$-0.266088\pi$
$739$	30.0329	+	4.31808i	1.10478	+	0.158843i	0.434297	+	0.900770i	$0.356997\pi$
$740$		0			0
$741$	7.15924	+	24.3821i	0.263001	+	0.895701i
$742$		0			0
$743$	−13.3538	−	0.955081i	−0.489902	−	0.0350385i	−0.175797	−	0.984427i	$-0.556250\pi$
$743$	−13.3538	−	0.955081i	−0.489902	−	0.0350385i	−0.314106	+	0.949388i	$0.601705\pi$
$744$		0			0
$745$	−25.9672	−	15.8133i	−0.951365	−	0.579353i
$746$		0			0
$747$	5.75379	+	26.4497i	0.210520	+	0.967745i
$748$		0			0
$749$	15.2149	+	13.1838i	0.555940	+	0.481724i
$750$		0			0
$751$	23.7384	−	3.41307i	0.866228	−	0.124545i	0.305146	−	0.952305i	$-0.401295\pi$
$751$	23.7384	−	3.41307i	0.866228	−	0.124545i	0.561081	+	0.827761i	$0.310385\pi$
$752$		0			0
$753$	35.2498	+	13.1475i	1.28457	+	0.479121i
$754$		0			0
$755$	29.8476	−	36.1797i	1.08627	−	1.31672i
$756$		0			0
$757$	−31.9349	−	6.94701i	−1.16069	−	0.252494i	−0.409333	−	0.912385i	$-0.634239\pi$
$757$	−31.9349	−	6.94701i	−1.16069	−	0.252494i	−0.751361	+	0.659891i	$0.770602\pi$
$758$		0			0
$759$	−29.2425	−	45.6786i	−1.06143	−	1.65803i
$760$		0			0
$761$	−23.0743	+	14.8289i	−0.836442	+	0.537549i	−0.887319	−	0.461156i	$-0.847435\pi$
$761$	−23.0743	+	14.8289i	−0.836442	+	0.537549i	0.0508770	+	0.998705i	$0.483798\pi$
$762$		0			0
$763$	4.69229	−	1.75013i	0.169872	−	0.0633591i
$764$		0			0
$765$	3.28513	+	2.33731i	0.118774	+	0.0845056i
$766$		0			0
$767$	14.9871	+	11.2192i	0.541151	+	0.405101i
$768$		0			0
$769$	0.286317	−	0.330427i	0.0103248	−	0.0119155i	−0.750564	−	0.660798i	$-0.770218\pi$
$769$	0.286317	−	0.330427i	0.0103248	−	0.0119155i	0.760889	+	0.648883i	$0.224763\pi$
$770$		0			0
$771$	−12.5253	−	8.04954i	−0.451089	−	0.289897i
$772$		0			0
$773$	36.0939	−	19.7088i	1.29821	−	0.708875i	0.326531	−	0.945186i	$-0.394120\pi$
$773$	36.0939	−	19.7088i	1.29821	−	0.708875i	0.971677	+	0.236311i	$0.0759384\pi$
$774$		0			0
$775$	−6.69518	−	34.5856i	−0.240498	−	1.24235i
$776$		0			0
$777$	29.3607	−	53.7701i	1.05331	−	1.92899i
$778$		0			0
$779$	−1.61750	+	11.2500i	−0.0579530	+	0.403072i
$780$		0			0
$781$		−	0.796662i		−	0.0285068i
$782$		0			0
$783$	−6.68580	−	6.68580i	−0.238931	−	0.238931i
$784$		0			0
$785$	−19.3837	+	7.76928i	−0.691836	+	0.277298i
$786$		0			0
$787$	−45.5324	−	24.8626i	−1.62306	−	0.886255i	−0.994058	−	0.108847i	$-0.965284\pi$
$787$	−45.5324	−	24.8626i	−1.62306	−	0.886255i	−0.628997	−	0.777408i	$-0.716534\pi$
$788$		0			0
$789$	−25.3827	−	29.2932i	−0.903648	−	1.04287i
$790$		0			0
$791$	13.4936	+	3.96207i	0.479776	+	0.140875i
$792$		0			0
$793$	−52.0471	+	11.3221i	−1.84825	+	0.402061i
$794$		0			0
$795$	30.0201	−	20.3361i	1.06470	−	0.721246i
$796$		0			0
$797$	−26.6170	+	35.5561i	−0.942822	+	1.25946i	0.0228613	+	0.999739i	$0.492722\pi$
$797$	−26.6170	+	35.5561i	−0.942822	+	1.25946i	−0.965683	+	0.259724i	$0.916369\pi$
$798$		0			0
$799$	0.817960	+	1.79108i	0.0289374	+	0.0633640i
$800$		0			0
$801$	−20.3435	−	9.29057i	−0.718803	−	0.328266i
$802$		0			0
$803$	−1.24271	+	5.71264i	−0.0438543	+	0.201595i
$804$		0			0
$805$	10.5226	+	21.7363i	0.370874	+	0.766104i
$806$		0			0
$807$	−14.7104	+	67.6227i	−0.517831	+	2.38043i
$808$		0			0
$809$	−24.7150	−	11.2869i	−0.868932	−	0.396828i	−0.0694983	−	0.997582i	$-0.522140\pi$
$809$	−24.7150	−	11.2869i	−0.868932	−	0.396828i	−0.799434	+	0.600754i	$0.794867\pi$
$810$		0			0
$811$	13.7063	+	30.0127i	0.481294	+	1.05389i	0.982106	+	0.188331i	$0.0603077\pi$
$811$	13.7063	+	30.0127i	0.481294	+	1.05389i	−0.500812	+	0.865556i	$0.666965\pi$
$812$		0			0
$813$	−32.1010	+	42.8819i	−1.12583	+	1.50393i
$814$		0			0
$815$	16.9943	+	3.26818i	0.595285	+	0.114479i
$816$		0			0
$817$	17.5938	−	3.82729i	0.615528	−	0.133900i
$818$		0			0
$819$	20.0193	+	5.87821i	0.699532	+	0.205401i
$820$		0			0
$821$	−16.0161	−	18.4836i	−0.558967	−	0.645083i	0.403981	−	0.914767i	$-0.367626\pi$
$821$	−16.0161	−	18.4836i	−0.558967	−	0.645083i	−0.962949	+	0.269684i	$0.913081\pi$
$822$		0			0
$823$	28.5442	+	15.5863i	0.994989	+	0.543305i	0.892317	−	0.451410i	$-0.149079\pi$
$823$	28.5442	+	15.5863i	0.994989	+	0.543305i	0.102672	+	0.994715i	$0.467261\pi$
$824$		0			0
$825$	−6.75901	−	56.1406i	−0.235319	−	1.95456i
$826$		0			0
$827$	−8.61030	−	8.61030i	−0.299410	−	0.299410i	0.541373	−	0.840783i	$-0.317905\pi$
$827$	−8.61030	−	8.61030i	−0.299410	−	0.299410i	−0.840783	+	0.541373i	$0.817905\pi$
$828$		0			0
$829$		−	40.6516i		−	1.41189i	−0.708268	−	0.705944i	$-0.750523\pi$
$829$		−	40.6516i		−	1.41189i	0.708268	−	0.705944i	$-0.249477\pi$
$830$		0			0
$831$	−8.58827	+	59.7327i	−0.297924	+	2.07210i
$832$		0			0
$833$	0.755048	−	1.38277i	0.0261609	−	0.0479100i
$834$		0			0
$835$	0.979956	+	0.338717i	0.0339128	+	0.0117218i
$836$		0			0
$837$	11.1849	−	6.10741i	0.386606	−	0.211103i
$838$		0			0
$839$	32.1754	+	20.6779i	1.11082	+	0.713880i	0.961471	−	0.274905i	$-0.0886464\pi$
$839$	32.1754	+	20.6779i	1.11082	+	0.713880i	0.149347	+	0.988785i	$0.452283\pi$
$840$		0			0
$841$	−1.09632	+	1.26522i	−0.0378041	+	0.0436282i
$842$		0			0
$843$	−35.7608	−	26.7702i	−1.23167	−	0.922014i
$844$		0			0
$845$	−10.1821	+	1.71649i	−0.350275	+	0.0590490i
$846$		0			0
$847$	−28.6131	+	10.6721i	−0.983157	+	0.366698i
$848$		0			0
$849$	−16.8336	+	10.8183i	−0.577729	+	0.371284i
$850$		0			0
$851$	48.0439	+	30.9955i	1.64692	+	1.06251i
$852$		0			0
$853$	−37.9031	−	8.24531i	−1.29778	−	0.282314i	−0.489959	−	0.871746i	$-0.662988\pi$
$853$	−37.9031	−	8.24531i	−1.29778	−	0.282314i	−0.807818	+	0.589431i	$0.799352\pi$
$854$		0			0
$855$	10.1012	+	8.33330i	0.345454	+	0.284993i
$856$		0			0
$857$	0.159267	+	0.0594035i	0.00544045	+	0.00202918i	0.352183	−	0.935931i	$-0.385439\pi$
$857$	0.159267	+	0.0594035i	0.00544045	+	0.00202918i	−0.346742	+	0.937960i	$0.612712\pi$
$858$		0			0
$859$	−1.78757	+	0.257014i	−0.0609912	+	0.00876921i	−0.172743	−	0.984967i	$-0.555263\pi$
$859$	−1.78757	+	0.257014i	−0.0609912	+	0.00876921i	0.111752	+	0.993736i	$0.464354\pi$
$860$		0			0
$861$	16.6377	+	14.4167i	0.567012	+	0.491318i
$862$		0			0
$863$	−1.07203	−	4.92804i	−0.0364923	−	0.167752i	0.955294	−	0.295657i	$-0.0955385\pi$
$863$	−1.07203	−	4.92804i	−0.0364923	−	0.167752i	−0.991786	+	0.127905i	$0.959175\pi$
$864$		0			0
$865$	−1.26723	−	5.21429i	−0.0430872	−	0.177291i
$866$		0			0
$867$	37.1759	+	2.65887i	1.26256	+	0.0903000i
$868$		0			0
$869$	2.15658	+	7.34464i	0.0731569	+	0.249150i
$870$		0			0
$871$	−60.9966	−	8.76999i	−2.06679	−	0.297160i
$872$		0			0
$873$	4.13234	−	4.13234i	0.139858	−	0.139858i
$874$		0			0
$875$	0.0308935	+	25.1775i	0.00104439	+	0.851153i
$876$		0			0
$877$	−11.0966	−	14.8233i	−0.374706	−	0.500548i	0.573061	−	0.819513i	$-0.305756\pi$
$877$	−11.0966	−	14.8233i	−0.374706	−	0.500548i	−0.947767	+	0.318965i	$0.896665\pi$
$878$		0			0
$879$	−52.5511	+	15.4304i	−1.77250	+	0.520454i
$880$		0			0
$881$	15.4649	−	13.4004i	0.521026	−	0.451472i	−0.354211	−	0.935165i	$-0.615251\pi$
$881$	15.4649	−	13.4004i	0.521026	−	0.451472i	0.875237	+	0.483694i	$0.160705\pi$
$882$		0			0
$883$	11.7510	+	21.5204i	0.395453	+	0.724218i	0.997225	−	0.0744500i	$-0.0237201\pi$
$883$	11.7510	+	21.5204i	0.395453	+	0.724218i	−0.601772	+	0.798668i	$0.705538\pi$
$884$		0			0
$885$	22.7335	+	1.07361i	0.764179	+	0.0360891i
$886$		0			0
$887$	−1.06064	−	14.8297i	−0.0356128	−	0.497932i	−0.983688	−	0.179885i	$-0.942427\pi$
$887$	−1.06064	−	14.8297i	−0.0356128	−	0.497932i	0.948075	−	0.318047i	$-0.103027\pi$
$888$		0			0
$889$	3.01881	+	20.9963i	0.101248	+	0.704193i
$890$		0			0
$891$	48.4599	−	22.1309i	1.62347	−	0.741412i
$892$		0			0
$893$	2.23492	+	5.99205i	0.0747888	+	0.200516i
$894$		0			0
$895$	−1.58568	−	4.95344i	−0.0530033	−	0.165575i
$896$		0			0
$897$	−16.1285	+	43.0110i	−0.538515	+	1.43610i
$898$		0			0
$899$	19.9118	+	30.9834i	0.664096	+	1.03335i
$900$		0			0
$901$	−2.41128	+	5.27996i	−0.0803312	+	0.175901i
$902$		0			0
$903$	12.1877	−	32.6766i	0.405582	−	1.08741i
$904$		0			0
$905$	31.6653	+	3.77291i	1.05259	+	0.125416i
$906$		0			0
$907$	−27.5031	+	1.96706i	−0.913224	+	0.0653151i	−0.520037	−	0.854144i	$-0.674082\pi$
$907$	−27.5031	+	1.96706i	−0.913224	+	0.0653151i	−0.393187	+	0.919459i	$0.628627\pi$
$908$		0			0
$909$	17.3530	−	27.0018i	0.575564	−	0.895595i
$910$		0			0
$911$	12.7763	−	43.5120i	0.423296	−	1.44162i	−0.421647	−	0.906760i	$-0.638548\pi$
$911$	12.7763	−	43.5120i	0.423296	−	1.44162i	0.844944	−	0.534855i	$-0.179634\pi$
$912$		0			0
$913$	−4.33549	+	60.6180i	−0.143484	+	2.00616i
$914$		0			0
$915$	−44.6649	+	46.8816i	−1.47658	+	1.54986i
$916$		0			0
$917$	3.71782	−	2.78313i	0.122773	−	0.0919069i
$918$		0			0
$919$	37.5077			1.23726			0.618632	−	0.785681i	$-0.287687\pi$
$919$	37.5077			1.23726			0.618632	+	0.785681i	$0.287687\pi$
$920$		0			0
$921$	5.36862			0.176902
$922$		0			0
$923$	−0.540146	+	0.404348i	−0.0177791	+	0.0133093i
$924$		0			0
$925$	31.0660	+	50.8733i	1.02144	+	1.67270i
$926$		0			0
$927$	1.93754	−	27.0903i	0.0636371	−	0.889763i
$928$		0			0
$929$	15.7532	−	53.6505i	0.516846	−	1.76022i	−0.123723	−	0.992317i	$-0.539483\pi$
$929$	15.7532	−	53.6505i	0.516846	−	1.76022i	0.640569	−	0.767901i	$-0.278699\pi$
$930$		0			0
$931$	2.76651	−	4.30477i	0.0906686	−	0.141083i
$932$		0			0
$933$	30.6245	−	2.19030i	1.00260	−	0.0717074i
$934$		0			0
$935$	5.59847	+	7.11304i	0.183090	+	0.232621i
$936$		0			0
$937$	−9.25531	+	24.8144i	−0.302358	+	0.810652i	0.693561	+	0.720398i	$0.256041\pi$
$937$	−9.25531	+	24.8144i	−0.302358	+	0.810652i	−0.995919	+	0.0902544i	$0.971232\pi$
$938$		0			0
$939$	−1.37967	+	3.02105i	−0.0450237	+	0.0985882i
$940$		0			0
$941$	−8.05363	−	12.5317i	−0.262541	−	0.408521i	0.684809	−	0.728723i	$-0.259886\pi$
$941$	−8.05363	−	12.5317i	−0.262541	−	0.408521i	−0.947349	+	0.320201i	$0.896249\pi$
$942$		0			0
$943$	−14.5533	+	14.5022i	−0.473920	+	0.472256i
$944$		0			0
$945$	−8.67440	+	2.77681i	−0.282178	+	0.0903298i
$946$		0			0
$947$	13.8500	+	37.1333i	0.450065	+	1.20667i	0.941873	+	0.335968i	$0.109063\pi$
$947$	13.8500	+	37.1333i	0.450065	+	1.20667i	−0.491808	+	0.870704i	$0.663664\pi$
$948$		0			0
$949$	4.50398	−	2.05690i	0.146205	−	0.0667697i
$950$		0			0
$951$	−1.15177	−	8.01072i	−0.0373486	−	0.259765i
$952$		0			0
$953$	0.951129	+	13.2985i	0.0308101	+	0.430782i	0.989324	+	0.145735i	$0.0465546\pi$
$953$	0.951129	+	13.2985i	0.0308101	+	0.430782i	−0.958514	+	0.285047i	$0.907991\pi$
$954$		0			0
$955$	−25.7838	+	23.4583i	−0.834345	+	0.759093i
$956$		0			0
$957$	28.3322	+	51.8865i	0.915850	+	1.67725i
$958$		0			0
$959$	−18.1772	+	15.7507i	−0.586974	+	0.508616i
$960$		0			0
$961$	−17.8847	+	5.25141i	−0.576925	+	0.169400i
$962$		0			0
$963$	11.8259	+	15.7976i	0.381086	+	0.509071i
$964$		0			0
$965$	−10.0007	−	17.3054i	−0.321935	−	0.557082i
$966$		0			0
$967$	−2.17661	+	2.17661i	−0.0699950	+	0.0699950i	−0.741238	−	0.671243i	$-0.765761\pi$
$967$	−2.17661	+	2.17661i	−0.0699950	+	0.0699950i	0.671243	+	0.741238i	$0.265761\pi$
$968$		0			0
$969$	−4.89493	−	0.703784i	−0.157248	−	0.0226088i
$970$		0			0
$971$	9.94381	+	33.8655i	0.319112	+	1.08680i	0.950344	+	0.311202i	$0.100731\pi$
$971$	9.94381	+	33.8655i	0.319112	+	1.08680i	−0.631232	+	0.775594i	$0.717450\pi$
$972$		0			0
$973$	−13.1247	−	0.938694i	−0.420757	−	0.0300931i
$974$		0			0
$975$	−34.6334	+	33.0770i	−1.10916	+	1.05931i
$976$		0			0
$977$	4.96097	+	22.8052i	0.158715	+	0.729603i	0.985854	+	0.167605i	$0.0536033\pi$
$977$	4.96097	+	22.8052i	0.158715	+	0.729603i	−0.827139	+	0.561998i	$0.810033\pi$
$978$		0			0
$979$	−37.9478	−	32.8819i	−1.21282	−	1.05091i
$980$		0			0
$981$	4.85896	−	0.698612i	0.155134	−	0.0223050i
$982$		0			0
$983$	22.9720	+	8.56813i	0.732694	+	0.273281i	0.687991	−	0.725720i	$-0.258493\pi$
$983$	22.9720	+	8.56813i	0.732694	+	0.273281i	0.0447034	+	0.999000i	$0.485766\pi$
$984$		0			0
$985$	1.21696	+	12.6897i	0.0387755	+	0.404328i
$986$		0			0
$987$	12.1043	+	2.63314i	0.385285	+	0.0838136i
$988$		0			0
$989$	29.5824	+	13.5728i	0.940667	+	0.431589i
$990$		0			0
$991$	−26.2842	+	16.8918i	−0.834944	+	0.536586i	−0.886845	−	0.462067i	$-0.847108\pi$
$991$	−26.2842	+	16.8918i	−0.834944	+	0.536586i	0.0519017	+	0.998652i	$0.483472\pi$
$992$		0			0
$993$	−32.4414	+	12.1000i	−1.02950	+	0.383983i
$994$		0			0
$995$	8.94472	+	53.0595i	0.283567	+	1.68210i
$996$		0			0
$997$	44.5742	+	33.3678i	1.41168	+	1.05677i	0.988582	+	0.150684i	$0.0481475\pi$
$997$	44.5742	+	33.3678i	1.41168	+	1.05677i	0.423096	+	0.906085i	$0.360943\pi$
$998$		0			0
$999$	−14.1211	+	16.2967i	−0.446773	+	0.515603i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.x.a.333.10	yes	240
5.2	odd	4	inner	460.2.x.a.57.3	✓	240
23.21	odd	22	inner	460.2.x.a.113.3	yes	240
115.67	even	44	inner	460.2.x.a.297.10	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.x.a.57.3	✓	240	5.2	odd	4	inner
460.2.x.a.113.3	yes	240	23.21	odd	22	inner
460.2.x.a.297.10	yes	240	115.67	even	44	inner
460.2.x.a.333.10	yes	240	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.x (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(1.82681 - 1.36753i) q^{3} +(-2.23541 + 0.0541276i) q^{5} +(0.160652 - 2.24620i) q^{7} +(0.621887 - 2.11795i) q^{9} +(2.67936 - 4.16917i) q^{11} +(-4.18667 + 0.299436i) q^{13} +(-4.00965 + 3.15588i) q^{15} +(0.285455 - 0.765335i) q^{17} +(1.10212 - 2.41330i) q^{19} +(-2.77827 - 4.32308i) q^{21} +(4.21324 - 2.29099i) q^{23} +(4.99414 - 0.241995i) q^{25} +(0.632098 + 1.69472i) q^{27} +(-4.75502 + 2.17155i) q^{29} +(-1.00269 - 6.97383i) q^{31} +(-0.806789 - 11.2804i) q^{33} +(-0.237541 + 5.02989i) q^{35} +(5.71348 + 10.4634i) q^{37} +(-7.23874 + 6.27241i) q^{39} +(-4.11047 + 1.20694i) q^{41} +(4.06707 + 5.43297i) q^{43} +(-1.27553 + 4.76816i) q^{45} +(-1.70451 + 1.70451i) q^{47} +(1.90913 + 0.274491i) q^{49} +(-0.525148 - 1.78849i) q^{51} +(-7.08796 - 0.506941i) q^{53} +(-5.76382 + 9.46485i) q^{55} +(-1.28690 - 5.91580i) q^{57} +(-3.37081 - 2.92082i) q^{59} +(12.5608 - 1.80597i) q^{61} +(-4.65745 - 1.73714i) q^{63} +(9.34272 - 0.895978i) q^{65} +(14.3461 + 3.12079i) q^{67} +(4.56377 - 9.94693i) q^{69} +(0.135232 - 0.0869081i) q^{71} +(-1.10528 + 0.412247i) q^{73} +(8.79240 - 7.27172i) q^{75} +(-8.93436 - 6.68818i) q^{77} +(-1.01147 + 1.16730i) q^{79} +(9.04317 + 5.81169i) q^{81} +(-10.7627 + 5.87690i) q^{83} +(-0.596685 + 1.72629i) q^{85} +(-5.71686 + 10.4696i) q^{87} +(1.44190 - 10.0287i) q^{89} +9.45221i q^{91} +(-11.3686 - 11.3686i) q^{93} +(-2.33306 + 5.45437i) q^{95} +(2.32366 + 1.26881i) q^{97} +(-7.16385 - 8.26752i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75}+ \cdots - 66 q^{97}+O(q^{100}) \) 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

Properties

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