LMFDB - Embedded newform 864.2.y.d.193.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(97,864)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("864.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.y (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			193.6
Character	$\chi$	$=$	864.193
Dual form			864.2.y.d.385.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.141380 - 1.72627i) q^{3} +(0.298268 - 1.69156i) q^{5} +(0.0848018 - 0.0711572i) q^{7} +(-2.96002 - 0.488119i) q^{9} +O(q^{10})$	\(q+(0.141380 - 1.72627i) q^{3} +(0.298268 - 1.69156i) q^{5} +(0.0848018 - 0.0711572i) q^{7} +(-2.96002 - 0.488119i) q^{9} +(-0.107979 - 0.612378i) q^{11} +(4.44975 - 1.61957i) q^{13} +(-2.87792 - 0.754043i) q^{15} +(0.373528 - 0.646970i) q^{17} +(-1.50580 - 2.60813i) q^{19} +(-0.110847 - 0.156451i) q^{21} +(-5.03088 - 4.22141i) q^{23} +(1.92605 + 0.701026i) q^{25} +(-1.26111 + 5.04079i) q^{27} +(-0.518433 - 0.188694i) q^{29} +(-6.23218 - 5.22942i) q^{31} +(-1.07240 + 0.0998228i) q^{33} +(-0.0950730 - 0.164671i) q^{35} +(1.23214 - 2.13412i) q^{37} +(-2.16672 - 7.91044i) q^{39} +(-3.38996 + 1.23385i) q^{41} +(1.06938 + 6.06474i) q^{43} +(-1.70856 + 4.86147i) q^{45} +(-1.70861 + 1.43370i) q^{47} +(-1.21341 + 6.88159i) q^{49} +(-1.06404 - 0.736279i) q^{51} -1.81090 q^{53} -1.06808 q^{55} +(-4.71522 + 2.23069i) q^{57} +(-1.00265 + 5.68630i) q^{59} +(5.68347 - 4.76900i) q^{61} +(-0.285749 + 0.169234i) q^{63} +(-1.41239 - 8.01008i) q^{65} +(2.65969 - 0.968049i) q^{67} +(-7.99856 + 8.08784i) q^{69} +(5.81993 - 10.0804i) q^{71} +(4.32111 + 7.48439i) q^{73} +(1.48246 - 3.22578i) q^{75} +(-0.0527319 - 0.0442473i) q^{77} +(-3.14112 - 1.14327i) q^{79} +(8.52348 + 2.88969i) q^{81} +(-9.62391 - 3.50282i) q^{83} +(-0.982977 - 0.824816i) q^{85} +(-0.399033 + 0.868278i) q^{87} +(-7.11921 - 12.3308i) q^{89} +(0.262102 - 0.453974i) q^{91} +(-9.90850 + 10.0191i) q^{93} +(-4.86093 + 1.76924i) q^{95} +(2.11406 + 11.9895i) q^{97} +(0.0207061 + 1.86536i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 12 q^{9}+O(q^{10}) $ 60 * q + 12 * q^9	$ 60 q + 12 q^{9} - 12 q^{17} + 24 q^{21} - 24 q^{25} + 6 q^{29} - 12 q^{33} - 30 q^{37} - 30 q^{41} - 90 q^{45} + 42 q^{49} - 36 q^{53} - 60 q^{57} + 48 q^{61} + 12 q^{65} + 78 q^{69} - 48 q^{73} - 12 q^{77} + 12 q^{81} - 102 q^{85} - 12 q^{89} - 36 q^{93} + 12 q^{97}+O(q^{100}) $ 60 * q + 12 * q^9 - 12 * q^17 + 24 * q^21 - 24 * q^25 + 6 * q^29 - 12 * q^33 - 30 * q^37 - 30 * q^41 - 90 * q^45 + 42 * q^49 - 36 * q^53 - 60 * q^57 + 48 * q^61 + 12 * q^65 + 78 * q^69 - 48 * q^73 - 12 * q^77 + 12 * q^81 - 102 * q^85 - 12 * q^89 - 36 * q^93 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$	$1$

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
$3$	0.141380	−	1.72627i	0.0816256	−	0.996663i
$3$	0.141380	−	1.72627i	0.0816256	−	0.996663i
$4$		0			0
$5$	0.298268	−	1.69156i	0.133389	−	0.756489i	−0.842578	−	0.538574i	$-0.818963\pi$
$5$	0.298268	−	1.69156i	0.133389	−	0.756489i	0.975968	−	0.217915i	$-0.0699255\pi$
$6$		0			0
$7$	0.0848018	−	0.0711572i	0.0320521	−	0.0268949i	−0.626621	−	0.779324i	$-0.715563\pi$
$7$	0.0848018	−	0.0711572i	0.0320521	−	0.0268949i	0.658673	+	0.752429i	$0.271118\pi$
$8$		0			0
$9$	−2.96002	−	0.488119i	−0.986675	−	0.162706i
$10$		0			0
$11$	−0.107979	−	0.612378i	−0.0325568	−	0.184639i	0.964193	−	0.265203i	$-0.0854390\pi$
$11$	−0.107979	−	0.612378i	−0.0325568	−	0.184639i	−0.996749	+	0.0805640i	$0.974328\pi$
$12$		0			0
$13$	4.44975	−	1.61957i	1.23414	−	0.449189i	0.359125	−	0.933290i	$-0.383075\pi$
$13$	4.44975	−	1.61957i	1.23414	−	0.449189i	0.875013	+	0.484100i	$0.160853\pi$
$14$		0			0
$15$	−2.87792	−	0.754043i	−0.743076	−	0.194693i
$16$		0			0
$17$	0.373528	−	0.646970i	0.0905939	−	0.156913i	−0.817167	−	0.576401i	$-0.804457\pi$
$17$	0.373528	−	0.646970i	0.0905939	−	0.156913i	0.907761	+	0.419487i	$0.137790\pi$
$18$		0			0
$19$	−1.50580	−	2.60813i	−0.345455	−	0.598345i	0.639982	−	0.768390i	$-0.278942\pi$
$19$	−1.50580	−	2.60813i	−0.345455	−	0.598345i	−0.985436	+	0.170045i	$0.945609\pi$
$20$		0			0
$21$	−0.110847	−	0.156451i	−0.0241889	−	0.0341404i
$22$		0			0
$23$	−5.03088	−	4.22141i	−1.04901	−	0.880225i	−0.0560217	−	0.998430i	$-0.517842\pi$
$23$	−5.03088	−	4.22141i	−1.04901	−	0.880225i	−0.992989	+	0.118205i	$0.962286\pi$
$24$		0			0
$25$	1.92605	+	0.701026i	0.385210	+	0.140205i
$26$		0			0
$27$	−1.26111	+	5.04079i	−0.242701	+	0.970101i
$28$		0			0
$29$	−0.518433	−	0.188694i	−0.0962705	−	0.0350396i	0.293436	−	0.955979i	$-0.405201\pi$
$29$	−0.518433	−	0.188694i	−0.0962705	−	0.0350396i	−0.389706	+	0.920939i	$0.627424\pi$
$30$		0			0
$31$	−6.23218	−	5.22942i	−1.11933	−	0.939232i	−0.120762	−	0.992681i	$-0.538534\pi$
$31$	−6.23218	−	5.22942i	−1.11933	−	0.939232i	−0.998571	+	0.0534499i	$0.982978\pi$
$32$		0			0
$33$	−1.07240	+	0.0998228i	−0.186680	+	0.0173769i
$34$		0			0
$35$	−0.0950730	−	0.164671i	−0.0160703	−	0.0278345i
$36$		0			0
$37$	1.23214	−	2.13412i	0.202562	−	0.350848i	−0.746791	−	0.665058i	$-0.768407\pi$
$37$	1.23214	−	2.13412i	0.202562	−	0.350848i	0.949353	+	0.314211i	$0.101740\pi$
$38$		0			0
$39$	−2.16672	−	7.91044i	−0.346953	−	1.26668i
$40$		0			0
$41$	−3.38996	+	1.23385i	−0.529424	+	0.192694i	−0.592881	−	0.805290i	$-0.702010\pi$
$41$	−3.38996	+	1.23385i	−0.529424	+	0.192694i	0.0634574	+	0.997985i	$0.479787\pi$
$42$		0			0
$43$	1.06938	+	6.06474i	0.163079	+	0.924864i	0.951023	+	0.309119i	$0.100034\pi$
$43$	1.06938	+	6.06474i	0.163079	+	0.924864i	−0.787945	+	0.615746i	$0.788855\pi$
$44$		0			0
$45$	−1.70856	+	4.86147i	−0.254697	+	0.724705i
$46$		0			0
$47$	−1.70861	+	1.43370i	−0.249227	+	0.209126i	−0.758839	−	0.651278i	$-0.774233\pi$
$47$	−1.70861	+	1.43370i	−0.249227	+	0.209126i	0.509612	+	0.860404i	$0.329789\pi$
$48$		0			0
$49$	−1.21341	+	6.88159i	−0.173344	+	0.983084i
$50$		0			0
$51$	−1.06404	−	0.736279i	−0.148995	−	0.103100i
$52$		0			0
$53$	−1.81090			−0.248746			−0.124373	−	0.992236i	$-0.539692\pi$
$53$	−1.81090			−0.248746			−0.124373	+	0.992236i	$0.539692\pi$
$54$		0			0
$55$	−1.06808			−0.144020
$56$		0			0
$57$	−4.71522	+	2.23069i	−0.624547	+	0.295462i
$58$		0			0
$59$	−1.00265	+	5.68630i	−0.130534	+	0.740294i	0.847333	+	0.531063i	$0.178207\pi$
$59$	−1.00265	+	5.68630i	−0.130534	+	0.740294i	−0.977866	+	0.209231i	$0.932904\pi$
$60$		0			0
$61$	5.68347	−	4.76900i	0.727694	−	0.610607i	−0.201808	−	0.979425i	$-0.564682\pi$
$61$	5.68347	−	4.76900i	0.727694	−	0.610607i	0.929502	+	0.368818i	$0.120237\pi$
$62$		0			0
$63$	−0.285749	+	0.169234i	−0.0360009	+	0.0213214i
$64$		0			0
$65$	−1.41239	−	8.01008i	−0.175186	−	0.993528i
$66$		0			0
$67$	2.65969	−	0.968049i	0.324933	−	0.118266i	−0.174403	−	0.984674i	$-0.555800\pi$
$67$	2.65969	−	0.968049i	0.324933	−	0.118266i	0.499336	+	0.866408i	$0.333577\pi$
$68$		0			0
$69$	−7.99856	+	8.08784i	−0.962914	+	0.973662i
$70$		0			0
$71$	5.81993	−	10.0804i	0.690699	−	1.19633i	−0.280910	−	0.959734i	$-0.590636\pi$
$71$	5.81993	−	10.0804i	0.690699	−	1.19633i	0.971609	−	0.236592i	$-0.0760303\pi$
$72$		0			0
$73$	4.32111	+	7.48439i	0.505748	+	0.875982i	0.999978	+	0.00665026i	$0.00211686\pi$
$73$	4.32111	+	7.48439i	0.505748	+	0.875982i	−0.494230	+	0.869331i	$0.664550\pi$
$74$		0			0
$75$	1.48246	−	3.22578i	0.171180	−	0.372481i
$76$		0			0
$77$	−0.0527319	−	0.0442473i	−0.00600936	−	0.00504245i
$78$		0			0
$79$	−3.14112	−	1.14327i	−0.353404	−	0.128628i	0.159217	−	0.987244i	$-0.449103\pi$
$79$	−3.14112	−	1.14327i	−0.353404	−	0.128628i	−0.512621	+	0.858615i	$0.671325\pi$
$80$		0			0
$81$	8.52348	+	2.88969i	0.947053	+	0.321077i
$82$		0			0
$83$	−9.62391	−	3.50282i	−1.05636	−	0.384484i	−0.245301	−	0.969447i	$-0.578887\pi$
$83$	−9.62391	−	3.50282i	−1.05636	−	0.384484i	−0.811060	+	0.584963i	$0.801109\pi$
$84$		0			0
$85$	−0.982977	−	0.824816i	−0.106619	−	0.0894638i
$86$		0			0
$87$	−0.399033	+	0.868278i	−0.0427808	+	0.0930892i
$88$		0			0
$89$	−7.11921	−	12.3308i	−0.754635	−	1.30707i	−0.945556	−	0.325461i	$-0.894481\pi$
$89$	−7.11921	−	12.3308i	−0.754635	−	1.30707i	0.190921	−	0.981605i	$-0.438853\pi$
$90$		0			0
$91$	0.262102	−	0.453974i	0.0274758	−	0.0475894i
$92$		0			0
$93$	−9.90850	+	10.0191i	−1.02746	+	1.03893i
$94$		0			0
$95$	−4.86093	+	1.76924i	−0.498721	+	0.181520i
$96$		0			0
$97$	2.11406	+	11.9895i	0.214651	+	1.21734i	0.881512	+	0.472162i	$0.156526\pi$
$97$	2.11406	+	11.9895i	0.214651	+	1.21734i	−0.666861	+	0.745182i	$0.732363\pi$
$98$		0			0
$99$	0.0207061	+	1.86536i	0.00208104	+	0.187476i
$100$		0			0
$101$	3.58086	−	3.00470i	0.356309	−	0.298979i	−0.447009	−	0.894530i	$-0.647511\pi$
$101$	3.58086	−	3.00470i	0.356309	−	0.298979i	0.803318	+	0.595551i	$0.203066\pi$
$102$		0			0
$103$	3.29738	−	18.7004i	0.324900	−	1.84260i	−0.185474	−	0.982649i	$-0.559382\pi$
$103$	3.29738	−	18.7004i	0.324900	−	1.84260i	0.510375	−	0.859952i	$-0.329507\pi$
$104$		0			0
$105$	−0.297709	+	0.140841i	−0.0290534	+	0.0137446i
$106$		0			0
$107$	14.2347			1.37612			0.688059	−	0.725655i	$-0.258463\pi$
$107$	14.2347			1.37612			0.688059	+	0.725655i	$0.258463\pi$
$108$		0			0
$109$	9.50622			0.910530			0.455265	−	0.890356i	$-0.349544\pi$
$109$	9.50622			0.910530			0.455265	+	0.890356i	$0.349544\pi$
$110$		0			0
$111$	−3.50987	−	2.42872i	−0.333143	−	0.230524i
$112$		0			0
$113$	3.33882	−	18.9354i	0.314090	−	1.78129i	−0.263187	−	0.964745i	$-0.584774\pi$
$113$	3.33882	−	18.9354i	0.314090	−	1.78129i	0.577277	−	0.816548i	$-0.304115\pi$
$114$		0			0
$115$	−8.64132	+	7.25092i	−0.805807	+	0.676152i
$116$		0			0
$117$	−13.9619	+	2.62197i	−1.29078	+	0.242401i
$118$		0			0
$119$	−0.0143607	−	0.0814434i	−0.00131644	−	0.00746591i
$120$		0			0
$121$	9.97327	−	3.62997i	0.906661	−	0.329998i
$122$		0			0
$123$	1.65068	+	6.02644i	0.148837	+	0.543386i
$124$		0			0
$125$	6.05444	−	10.4866i	0.541526	−	0.937950i
$126$		0			0
$127$	9.06851	+	15.7071i	0.804700	+	1.39378i	0.916493	+	0.400050i	$0.131007\pi$
$127$	9.06851	+	15.7071i	0.804700	+	1.39378i	−0.111793	+	0.993732i	$0.535659\pi$
$128$		0			0
$129$	10.6206	−	0.988604i	0.935089	−	0.0870417i
$130$		0			0
$131$	14.1204	+	11.8485i	1.23371	+	1.03520i	0.997989	+	0.0633828i	$0.0201889\pi$
$131$	14.1204	+	11.8485i	1.23371	+	1.03520i	0.235719	+	0.971821i	$0.424256\pi$
$132$		0			0
$133$	−0.313282	−	0.114025i	−0.0271650	−	0.00988724i
$134$		0			0
$135$	8.15065	+	3.63675i	0.701497	+	0.313002i
$136$		0			0
$137$	−10.3291	−	3.75948i	−0.882474	−	0.321194i	−0.139266	−	0.990255i	$-0.544474\pi$
$137$	−10.3291	−	3.75948i	−0.882474	−	0.321194i	−0.743208	+	0.669061i	$0.766697\pi$
$138$		0			0
$139$	2.74189	+	2.30072i	0.232564	+	0.195145i	0.751621	−	0.659595i	$-0.229272\pi$
$139$	2.74189	+	2.30072i	0.232564	+	0.195145i	−0.519057	+	0.854740i	$0.673717\pi$
$140$		0			0
$141$	2.23339	+	3.15223i	0.188085	+	0.265465i
$142$		0			0
$143$	−1.47227	−	2.55005i	−0.123117	−	0.213246i
$144$		0			0
$145$	−0.473819	+	0.820679i	−0.0393485	+	0.0681536i
$146$		0			0
$147$	11.7079	+	3.06759i	0.965654	+	0.253011i
$148$		0			0
$149$	0.917496	−	0.333941i	0.0751642	−	0.0273575i	−0.304164	−	0.952620i	$-0.598377\pi$
$149$	0.917496	−	0.333941i	0.0751642	−	0.0273575i	0.379329	+	0.925262i	$0.376155\pi$
$150$		0			0
$151$	1.61495	+	9.15886i	0.131423	+	0.745337i	0.977284	+	0.211934i	$0.0679761\pi$
$151$	1.61495	+	9.15886i	0.131423	+	0.745337i	−0.845861	+	0.533403i	$0.820913\pi$
$152$		0			0
$153$	−1.42145	+	1.73272i	−0.114917	+	0.140082i
$154$		0			0
$155$	−10.7047	+	8.98234i	−0.859825	+	0.721479i
$156$		0			0
$157$	0.449618	−	2.54991i	0.0358835	−	0.203505i	−0.961595	−	0.274471i	$-0.911497\pi$
$157$	0.449618	−	2.54991i	0.0358835	−	0.203505i	0.997479	+	0.0709662i	$0.0226082\pi$
$158$		0			0
$159$	−0.256024	+	3.12610i	−0.0203041	+	0.247916i
$160$		0			0
$161$	−0.727011			−0.0572965
$162$		0			0
$163$	18.7294			1.46700			0.733500	−	0.679689i	$-0.237885\pi$
$163$	18.7294			1.46700			0.733500	+	0.679689i	$0.237885\pi$
$164$		0			0
$165$	−0.151005	+	1.84380i	−0.0117557	+	0.143539i
$166$		0			0
$167$	−2.64060	+	14.9756i	−0.204336	+	1.15885i	0.694145	+	0.719835i	$0.255783\pi$
$167$	−2.64060	+	14.9756i	−0.204336	+	1.15885i	−0.898481	+	0.439012i	$0.855328\pi$
$168$		0			0
$169$	7.21863	−	6.05715i	0.555279	−	0.465935i
$170$		0			0
$171$	3.18413	+	8.45513i	0.243497	+	0.646580i
$172$		0			0
$173$	−0.701626	−	3.97912i	−0.0533436	−	0.302527i	0.946450	−	0.322851i	$-0.104641\pi$
$173$	−0.701626	−	3.97912i	−0.0533436	−	0.302527i	−0.999793	+	0.0203242i	$0.993530\pi$
$174$		0			0
$175$	0.213216	−	0.0776042i	0.0161176	−	0.00586632i
$176$		0			0
$177$	9.67435	+	2.53477i	0.727168	+	0.190525i
$178$		0			0
$179$	5.97034	−	10.3409i	0.446244	−	0.772917i	−0.551894	−	0.833914i	$-0.686095\pi$
$179$	5.97034	−	10.3409i	0.446244	−	0.772917i	0.998138	+	0.0609970i	$0.0194280\pi$
$180$		0			0
$181$	−4.69722	−	8.13582i	−0.349141	−	0.604730i	0.636956	−	0.770900i	$-0.280193\pi$
$181$	−4.69722	−	8.13582i	−0.349141	−	0.604730i	−0.986097	+	0.166170i	$0.946860\pi$
$182$		0			0
$183$	−7.42905	−	10.4854i	−0.549171	−	0.775106i
$184$		0			0
$185$	−3.24249	−	2.72077i	−0.238393	−	0.200035i
$186$		0			0
$187$	−0.436523	−	0.158881i	−0.0319217	−	0.0116186i
$188$		0			0
$189$	0.251744	+	0.517206i	0.0183117	+	0.0376212i
$190$		0			0
$191$	−1.23764	−	0.450464i	−0.0895524	−	0.0325944i	0.296855	−	0.954922i	$-0.404062\pi$
$191$	−1.23764	−	0.450464i	−0.0895524	−	0.0325944i	−0.386408	+	0.922328i	$0.626284\pi$
$192$		0			0
$193$	7.59865	+	6.37603i	0.546963	+	0.458956i	0.873911	−	0.486086i	$-0.161576\pi$
$193$	7.59865	+	6.37603i	0.546963	+	0.458956i	−0.326948	+	0.945042i	$0.606020\pi$
$194$		0			0
$195$	−14.0272	+	1.30571i	−1.00451	+	0.0935039i
$196$		0			0
$197$	7.19945	+	12.4698i	0.512939	+	0.888437i	0.999887	+	0.0150060i	$0.00477672\pi$
$197$	7.19945	+	12.4698i	0.512939	+	0.888437i	−0.486948	+	0.873431i	$0.661890\pi$
$198$		0			0
$199$	−0.629103	+	1.08964i	−0.0445959	+	0.0772424i	−0.887462	−	0.460881i	$-0.847533\pi$
$199$	−0.629103	+	1.08964i	−0.0445959	+	0.0772424i	0.842866	+	0.538124i	$0.180867\pi$
$200$		0			0
$201$	−1.29509	−	4.72821i	−0.0913485	−	0.333502i
$202$		0			0
$203$	−0.0573910	+	0.0208886i	−0.00402806	+	0.00146609i
$204$		0			0
$205$	1.07601	+	6.10234i	0.0751517	+	0.426206i
$206$		0			0
$207$	12.8310	+	14.9511i	0.891814	+	1.03918i
$208$		0			0
$209$	−1.43456	+	1.20374i	−0.0992309	+	0.0832646i
$210$		0			0
$211$	0.371353	−	2.10605i	0.0255650	−	0.144986i	−0.969353	−	0.245670i	$-0.920992\pi$
$211$	0.371353	−	2.10605i	0.0255650	−	0.144986i	0.994918	+	0.100684i	$0.0321031\pi$
$212$		0			0
$213$	−16.5787	−	11.4719i	−1.13595	−	0.786045i
$214$		0			0
$215$	10.5778			0.721402
$216$		0			0
$217$	−0.900611			−0.0611375
$218$		0			0
$219$	13.5310	−	6.40127i	0.914341	−	0.432558i
$220$		0			0
$221$	0.614289	−	3.48381i	0.0413216	−	0.234346i
$222$		0			0
$223$	−11.6335	+	9.76164i	−0.779035	+	0.653688i	−0.943005	−	0.332777i	$-0.892014\pi$
$223$	−11.6335	+	9.76164i	−0.779035	+	0.653688i	0.163970	+	0.986465i	$0.447570\pi$
$224$		0			0
$225$	−5.35897	−	3.01520i	−0.357265	−	0.201013i
$226$		0			0
$227$	−3.13115	−	17.7576i	−0.207821	−	1.17861i	−0.892938	−	0.450180i	$-0.851360\pi$
$227$	−3.13115	−	17.7576i	−0.207821	−	1.17861i	0.685116	−	0.728434i	$-0.259751\pi$
$228$		0			0
$229$	4.87272	−	1.77352i	0.321998	−	0.117198i	−0.175964	−	0.984397i	$-0.556304\pi$
$229$	4.87272	−	1.77352i	0.321998	−	0.117198i	0.497962	+	0.867199i	$0.334082\pi$
$230$		0			0
$231$	−0.0838381	+	0.0847739i	−0.00551614	+	0.00557771i
$232$		0			0
$233$	−5.11944	+	8.86712i	−0.335385	+	0.580905i	−0.983559	−	0.180588i	$-0.942200\pi$
$233$	−5.11944	+	8.86712i	−0.335385	+	0.580905i	0.648173	+	0.761493i	$0.275533\pi$
$234$		0			0
$235$	1.91556	+	3.31785i	0.124957	+	0.216433i
$236$		0			0
$237$	−2.41769	+	5.26079i	−0.157046	+	0.341725i
$238$		0			0
$239$	17.1926	+	14.4263i	1.11210	+	0.933162i	0.998179	−	0.0603274i	$-0.0192145\pi$
$239$	17.1926	+	14.4263i	1.11210	+	0.933162i	0.113921	+	0.993490i	$0.463659\pi$
$240$		0			0
$241$	−7.39742	−	2.69244i	−0.476510	−	0.173435i	0.0925892	−	0.995704i	$-0.470486\pi$
$241$	−7.39742	−	2.69244i	−0.476510	−	0.173435i	−0.569099	+	0.822269i	$0.692708\pi$
$242$		0			0
$243$	6.19343	−	14.3053i	0.397309	−	0.917685i
$244$		0			0
$245$	11.2787	+	4.10511i	0.720569	+	0.262266i
$246$		0			0
$247$	−10.9245	−	9.16674i	−0.695109	−	0.583266i
$248$		0			0
$249$	−7.40744	+	16.1183i	−0.469427	+	1.02145i
$250$		0			0
$251$	9.63730	+	16.6923i	0.608301	+	1.05361i	0.991520	+	0.129951i	$0.0414819\pi$
$251$	9.63730	+	16.6923i	0.608301	+	1.05361i	−0.383220	+	0.923657i	$0.625185\pi$
$252$		0			0
$253$	−2.04187	+	3.53662i	−0.128371	+	0.222346i
$254$		0			0
$255$	−1.56283	+	1.58027i	−0.0978681	+	0.0989605i
$256$		0			0
$257$	−26.0752	+	9.49060i	−1.62653	+	0.592008i	−0.984610	−	0.174766i	$-0.944083\pi$
$257$	−26.0752	+	9.49060i	−1.62653	+	0.592008i	−0.641918	+	0.766774i	$0.721861\pi$
$258$		0			0
$259$	−0.0473707	−	0.268653i	−0.00294347	−	0.0166933i
$260$		0			0
$261$	1.44247	+	0.811596i	0.0892865	+	0.0502365i
$262$		0			0
$263$	12.4016	−	10.4062i	0.764717	−	0.641674i	−0.174633	−	0.984634i	$-0.555874\pi$
$263$	12.4016	−	10.4062i	0.764717	−	0.641674i	0.939350	+	0.342960i	$0.111429\pi$
$264$		0			0
$265$	−0.540133	+	3.06324i	−0.0331801	+	0.188174i
$266$		0			0
$267$	−22.2929	+	10.5464i	−1.36430	+	0.645427i
$268$		0			0
$269$	−0.692446			−0.0422192			−0.0211096	−	0.999777i	$-0.506720\pi$
$269$	−0.692446			−0.0422192			−0.0211096	+	0.999777i	$0.506720\pi$
$270$		0			0
$271$	28.6325			1.73930			0.869651	−	0.493668i	$-0.164344\pi$
$271$	28.6325			1.73930			0.869651	+	0.493668i	$0.164344\pi$
$272$		0			0
$273$	−0.746627	−	0.516642i	−0.0451879	−	0.0312686i
$274$		0			0
$275$	0.221320	−	1.25517i	0.0133461	−	0.0756895i
$276$		0			0
$277$	17.0838	−	14.3350i	1.02647	−	0.861308i	0.0360404	−	0.999350i	$-0.488526\pi$
$277$	17.0838	−	14.3350i	1.02647	−	0.861308i	0.990426	+	0.138043i	$0.0440811\pi$
$278$		0			0
$279$	15.8948	+	18.5213i	0.951598	+	1.10884i
$280$		0			0
$281$	−0.0501172	−	0.284229i	−0.00298974	−	0.0169557i	0.983276	−	0.182120i	$-0.0582958\pi$
$281$	−0.0501172	−	0.284229i	−0.00298974	−	0.0169557i	−0.986266	+	0.165164i	$0.947185\pi$
$282$		0			0
$283$	−12.3273	+	4.48679i	−0.732785	+	0.266712i	−0.681343	−	0.731964i	$-0.738604\pi$
$283$	−12.3273	+	4.48679i	−0.732785	+	0.266712i	−0.0514416	+	0.998676i	$0.516382\pi$
$284$		0			0
$285$	2.36694	+	8.64142i	0.140206	+	0.511874i
$286$		0			0
$287$	−0.199678	+	0.345853i	−0.0117866	+	0.0204150i
$288$		0			0
$289$	8.22095	+	14.2391i	0.483585	+	0.837595i
$290$		0			0
$291$	20.9959	−	1.95438i	1.23080	−	0.114568i
$292$		0			0
$293$	16.9886	+	14.2551i	0.992482	+	0.832792i	0.985925	−	0.167187i	$-0.0534683\pi$
$293$	16.9886	+	14.2551i	0.992482	+	0.832792i	0.00655718	+	0.999979i	$0.497913\pi$
$294$		0			0
$295$	9.31967	+	3.39208i	0.542612	+	0.197495i
$296$		0			0
$297$	3.22304	+	0.227980i	0.187020	+	0.0132287i
$298$		0			0
$299$	−29.2230	−	10.6363i	−1.69001	−	0.615114i
$300$		0			0
$301$	0.522235	+	0.438207i	0.0301011	+	0.0252578i
$302$		0			0
$303$	−4.68066	−	6.60634i	−0.268897	−	0.379524i
$304$		0			0
$305$	−6.37185	−	11.0364i	−0.364851	−	0.631940i
$306$		0			0
$307$	16.2041	−	28.0663i	0.924817	−	1.60183i	0.132962	−	0.991121i	$-0.457551\pi$
$307$	16.2041	−	28.0663i	0.924817	−	1.60183i	0.791855	−	0.610709i	$-0.209115\pi$
$308$		0			0
$309$	−31.8157	−	8.33602i	−1.80993	−	0.474220i
$310$		0			0
$311$	−18.7965	+	6.84135i	−1.06585	+	0.387938i	−0.814623	−	0.579991i	$-0.803056\pi$
$311$	−18.7965	+	6.84135i	−1.06585	+	0.387938i	−0.251227	+	0.967928i	$0.580834\pi$
$312$		0			0
$313$	3.10652	+	17.6180i	0.175591	+	0.995826i	0.937460	+	0.348094i	$0.113171\pi$
$313$	3.10652	+	17.6180i	0.175591	+	0.995826i	−0.761869	+	0.647732i	$0.775718\pi$
$314$		0			0
$315$	0.201039	+	0.533838i	0.0113273	+	0.0300784i
$316$		0			0
$317$	1.17418	−	0.985253i	0.0659484	−	0.0553373i	−0.609218	−	0.793003i	$-0.708516\pi$
$317$	1.17418	−	0.985253i	0.0659484	−	0.0553373i	0.675166	+	0.737666i	$0.264072\pi$
$318$		0			0
$319$	−0.0595724	+	0.337852i	−0.00333541	+	0.0189161i
$320$		0			0
$321$	2.01249	−	24.5729i	0.112326	−	1.37153i
$322$		0			0
$323$	−2.24984			−0.125184
$324$		0			0
$325$	9.70580			0.538381
$326$		0			0
$327$	1.34399	−	16.4103i	0.0743226	−	0.907492i
$328$		0			0
$329$	−0.0428757	+	0.243160i	−0.00236382	+	0.0134059i
$330$		0			0
$331$	−17.8251	+	14.9571i	−0.979758	+	0.822114i	−0.984053	−	0.177876i	$-0.943077\pi$
$331$	−17.8251	+	14.9571i	−0.979758	+	0.822114i	0.00429514	+	0.999991i	$0.498633\pi$
$332$		0			0
$333$	−4.68886	+	5.71562i	−0.256948	+	0.313214i
$334$		0			0
$335$	−0.844212	−	4.78777i	−0.0461243	−	0.261584i
$336$		0			0
$337$	−28.3282	+	10.3106i	−1.54314	+	0.561656i	−0.966795	−	0.255553i	$-0.917743\pi$
$337$	−28.3282	+	10.3106i	−1.54314	+	0.561656i	−0.576342	+	0.817209i	$0.695520\pi$
$338$		0			0
$339$	−32.2156	−	8.44080i	−1.74971	−	0.458441i
$340$		0			0
$341$	−2.52944	+	4.38112i	−0.136977	+	0.237251i
$342$		0			0
$343$	0.774228	+	1.34100i	0.0418044	+	0.0724073i
$344$		0			0
$345$	11.2954	+	15.9424i	0.608121	+	0.858309i
$346$		0			0
$347$	0.304694	+	0.255669i	0.0163568	+	0.0137250i	0.650929	−	0.759138i	$-0.274379\pi$
$347$	0.304694	+	0.255669i	0.0163568	+	0.0137250i	−0.634573	+	0.772863i	$0.718824\pi$
$348$		0			0
$349$	−26.6427	−	9.69715i	−1.42615	−	0.519076i	−0.490325	−	0.871540i	$-0.663122\pi$
$349$	−26.6427	−	9.69715i	−1.42615	−	0.519076i	−0.935826	+	0.352463i	$0.885344\pi$
$350$		0			0
$351$	2.55231	+	24.4727i	0.136232	+	1.30626i
$352$		0			0
$353$	−5.58062	−	2.03118i	−0.297026	−	0.108109i	0.189209	−	0.981937i	$-0.439408\pi$
$353$	−5.58062	−	2.03118i	−0.297026	−	0.108109i	−0.486235	+	0.873828i	$0.661630\pi$
$354$		0			0
$355$	−15.3157	−	12.8514i	−0.812875	−	0.682083i
$356$		0			0
$357$	−0.142624	+	0.0132760i	−0.00754845	+	0.000702639i
$358$		0			0
$359$	−9.64495	−	16.7055i	−0.509041	−	0.881685i	−0.999945	−	0.0104714i	$-0.996667\pi$
$359$	−9.64495	−	16.7055i	−0.509041	−	0.881685i	0.490904	−	0.871214i	$-0.336667\pi$
$360$		0			0
$361$	4.96512	−	8.59984i	0.261322	−	0.452623i
$362$		0			0
$363$	−4.85630	−	17.7298i	−0.254890	−	0.930572i
$364$		0			0
$365$	13.9491	−	5.07707i	0.730132	−	0.265746i
$366$		0			0
$367$	1.46830	+	8.32715i	0.0766447	+	0.434674i	0.998849	+	0.0479701i	$0.0152752\pi$
$367$	1.46830	+	8.32715i	0.0766447	+	0.434674i	−0.922204	+	0.386704i	$0.873614\pi$
$368$		0			0
$369$	10.6366	−	1.99751i	0.553721	−	0.103986i
$370$		0			0
$371$	−0.153568	+	0.128858i	−0.00797283	+	0.00669000i
$372$		0			0
$373$	4.63555	−	26.2895i	0.240020	−	1.36122i	−0.591760	−	0.806114i	$-0.701567\pi$
$373$	4.63555	−	26.2895i	0.240020	−	1.36122i	0.831780	−	0.555105i	$-0.187322\pi$
$374$		0			0
$375$	−17.2467	−	11.9342i	−0.890618	−	0.616280i
$376$		0			0
$377$	−2.61250			−0.134550
$378$		0			0
$379$	8.54090			0.438717			0.219358	−	0.975644i	$-0.429604\pi$
$379$	8.54090			0.438717			0.219358	+	0.975644i	$0.429604\pi$
$380$		0			0
$381$	28.3969	−	13.4340i	1.45482	−	0.688247i
$382$		0			0
$383$	−4.58050	+	25.9773i	−0.234052	+	1.32738i	0.610548	+	0.791979i	$0.290949\pi$
$383$	−4.58050	+	25.9773i	−0.234052	+	1.32738i	−0.844600	+	0.535398i	$0.820162\pi$
$384$		0			0
$385$	−0.0905752	+	0.0760016i	−0.00461614	+	0.00387340i
$386$		0			0
$387$	−0.205065	−	18.4738i	−0.0104240	−	0.939074i
$388$		0			0
$389$	4.71986	+	26.7676i	0.239306	+	1.35717i	0.833352	+	0.552742i	$0.186418\pi$
$389$	4.71986	+	26.7676i	0.239306	+	1.35717i	−0.594046	+	0.804431i	$0.702470\pi$
$390$		0			0
$391$	−4.61030	+	1.67801i	−0.233153	+	0.0848607i
$392$		0			0
$393$	22.4500	−	22.7006i	1.13245	−	1.14509i
$394$		0			0
$395$	−2.87081	+	4.97239i	−0.144446	+	0.250188i
$396$		0			0
$397$	−9.92582	−	17.1920i	−0.498163	−	0.862843i	0.501835	−	0.864963i	$-0.332658\pi$
$397$	−9.92582	−	17.1920i	−0.498163	−	0.862843i	−0.999998	+	0.00212029i	$0.999325\pi$
$398$		0			0
$399$	−0.241130	+	0.524688i	−0.0120716	+	0.0262673i
$400$		0			0
$401$	15.7102	+	13.1824i	0.784531	+	0.658300i	0.944385	−	0.328841i	$-0.106658\pi$
$401$	15.7102	+	13.1824i	0.784531	+	0.658300i	−0.159854	+	0.987141i	$0.551102\pi$
$402$		0			0
$403$	−36.2011	−	13.1761i	−1.80330	−	0.656349i
$404$		0			0
$405$	7.43036	−	13.5561i	0.369218	−	0.673607i
$406$		0			0
$407$	−1.43993	−	0.524093i	−0.0713749	−	0.0259783i
$408$		0			0
$409$	2.01694	+	1.69242i	0.0997315	+	0.0836846i	0.691290	−	0.722577i	$-0.257043\pi$
$409$	2.01694	+	1.69242i	0.0997315	+	0.0836846i	−0.591559	+	0.806262i	$0.701487\pi$
$410$		0			0
$411$	−7.95021	+	17.2993i	−0.392155	+	0.853311i
$412$		0			0
$413$	0.319595	+	0.553555i	0.0157262	+	0.0272386i
$414$		0			0
$415$	−8.79573	+	15.2346i	−0.431765	+	0.747839i
$416$		0			0
$417$	4.35932	−	4.40798i	0.213477	−	0.215860i
$418$		0			0
$419$	17.0806	−	6.21684i	0.834443	−	0.303712i	0.110762	−	0.993847i	$-0.464671\pi$
$419$	17.0806	−	6.21684i	0.834443	−	0.303712i	0.723681	+	0.690135i	$0.242449\pi$
$420$		0			0
$421$	0.723939	+	4.10566i	0.0352826	+	0.200098i	0.997354	−	0.0727009i	$-0.0231618\pi$
$421$	0.723939	+	4.10566i	0.0352826	+	0.200098i	−0.962071	+	0.272799i	$0.912051\pi$
$422$		0			0
$423$	5.75735	−	3.40977i	0.279932	−	0.165789i
$424$		0			0
$425$	1.17298	−	0.984245i	0.0568977	−	0.0477429i
$426$		0			0
$427$	0.142620	−	0.808839i	0.00690187	−	0.0391425i
$428$		0			0
$429$	−4.61022	+	2.18101i	−0.222584	+	0.105300i
$430$		0			0
$431$	13.6524			0.657614			0.328807	−	0.944397i	$-0.393353\pi$
$431$	13.6524			0.657614			0.328807	+	0.944397i	$0.393353\pi$
$432$		0			0
$433$	−30.2325			−1.45288			−0.726441	−	0.687229i	$-0.758827\pi$
$433$	−30.2325			−1.45288			−0.726441	+	0.687229i	$0.758827\pi$
$434$		0			0
$435$	1.34973	+	0.933967i	0.0647144	+	0.0447803i
$436$		0			0
$437$	−3.43446	+	19.4778i	−0.164292	+	0.931748i
$438$		0			0
$439$	5.46671	−	4.58712i	0.260912	−	0.218931i	−0.502942	−	0.864320i	$-0.667749\pi$
$439$	5.46671	−	4.58712i	0.260912	−	0.218931i	0.763854	+	0.645389i	$0.223305\pi$
$440$		0			0
$441$	6.95076	−	19.7774i	0.330988	−	0.941779i
$442$		0			0
$443$	−6.18594	−	35.0822i	−0.293903	−	1.66681i	−0.671629	−	0.740888i	$-0.734405\pi$
$443$	−6.18594	−	35.0822i	−0.293903	−	1.66681i	0.377726	−	0.925917i	$-0.376706\pi$
$444$		0			0
$445$	−22.9818	+	8.36468i	−1.08944	+	0.396524i
$446$		0			0
$447$	−0.446758	−	1.63106i	−0.0211309	−	0.0771465i
$448$		0			0
$449$	4.92409	−	8.52878i	0.232382	−	0.402498i	−0.726126	−	0.687561i	$-0.758681\pi$
$449$	4.92409	−	8.52878i	0.232382	−	0.402498i	0.958509	+	0.285063i	$0.0920146\pi$
$450$		0			0
$451$	1.12162	+	1.94271i	0.0528152	+	0.0914787i
$452$		0			0
$453$	16.0390	−	1.49297i	0.753577	−	0.0701459i
$454$		0			0
$455$	−0.689748	−	0.578767i	−0.0323359	−	0.0271330i
$456$		0			0
$457$	−24.7288	−	9.00055i	−1.15676	−	0.421028i	−0.308824	−	0.951119i	$-0.599935\pi$
$457$	−24.7288	−	9.00055i	−1.15676	−	0.421028i	−0.847940	+	0.530092i	$0.822158\pi$
$458$		0			0
$459$	2.79018	+	2.69878i	0.130234	+	0.125968i
$460$		0			0
$461$	0.744335	+	0.270916i	0.0346671	+	0.0126178i	0.359296	−	0.933224i	$-0.383017\pi$
$461$	0.744335	+	0.270916i	0.0346671	+	0.0126178i	−0.324628	+	0.945842i	$0.605239\pi$
$462$		0			0
$463$	−28.5448	−	23.9519i	−1.32659	−	1.11314i	−0.984862	−	0.173341i	$-0.944544\pi$
$463$	−28.5448	−	23.9519i	−1.32659	−	1.11314i	−0.341727	−	0.939799i	$-0.611012\pi$
$464$		0			0
$465$	13.9925	+	19.7492i	0.648888	+	0.915847i
$466$		0			0
$467$	−6.24595	−	10.8183i	−0.289028	−	0.500611i	0.684550	−	0.728966i	$-0.259999\pi$
$467$	−6.24595	−	10.8183i	−0.289028	−	0.500611i	−0.973578	+	0.228355i	$0.926665\pi$
$468$		0			0
$469$	0.156663	−	0.271349i	0.00723403	−	0.0125297i
$470$		0			0
$471$	−4.33827	−	1.13667i	−0.199897	−	0.0523750i
$472$		0			0
$473$	3.59844	−	1.30973i	0.165457	−	0.0602213i
$474$		0			0
$475$	−1.07189	−	6.07899i	−0.0491817	−	0.278923i
$476$		0			0
$477$	5.36030	+	0.883935i	0.245431	+	0.0404726i
$478$		0			0
$479$	−20.4517	+	17.1610i	−0.934462	+	0.784107i	−0.976613	−	0.215005i	$-0.931023\pi$
$479$	−20.4517	+	17.1610i	−0.934462	+	0.784107i	0.0421513	+	0.999111i	$0.486579\pi$
$480$		0			0
$481$	2.02632	−	11.4918i	0.0923923	−	0.523983i
$482$		0			0
$483$	−0.102785	+	1.25502i	−0.00467686	+	0.0571053i
$484$		0			0
$485$	20.9114			0.949539
$486$		0			0
$487$	0.761007			0.0344845			0.0172423	−	0.999851i	$-0.494511\pi$
$487$	0.761007			0.0344845			0.0172423	+	0.999851i	$0.494511\pi$
$488$		0			0
$489$	2.64796	−	32.3320i	0.119745	−	1.46210i
$490$		0			0
$491$	−2.12288	+	12.0395i	−0.0958044	+	0.543334i	0.898693	+	0.438577i	$0.144517\pi$
$491$	−2.12288	+	12.0395i	−0.0958044	+	0.543334i	−0.994498	+	0.104757i	$0.966594\pi$
$492$		0			0
$493$	−0.315729	+	0.264928i	−0.0142197	+	0.0119317i
$494$		0			0
$495$	3.16154	+	0.521351i	0.142101	+	0.0234330i
$496$		0			0
$497$	−0.223753	−	1.26897i	−0.0100367	−	0.0569210i
$498$		0			0
$499$	31.5849	−	11.4960i	1.41393	−	0.514630i	0.481652	−	0.876362i	$-0.340037\pi$
$499$	31.5849	−	11.4960i	1.41393	−	0.514630i	0.932282	+	0.361733i	$0.117815\pi$
$500$		0			0
$501$	25.4786	+	6.67565i	1.13830	+	0.298246i
$502$		0			0
$503$	19.6004	−	33.9489i	0.873939	−	1.51371i	0.0160501	−	0.999871i	$-0.494891\pi$
$503$	19.6004	−	33.9489i	0.873939	−	1.51371i	0.857889	−	0.513835i	$-0.171776\pi$
$504$		0			0
$505$	−4.01457	−	6.95344i	−0.178646	−	0.309424i
$506$		0			0
$507$	−9.43572	−	13.3177i	−0.419055	−	0.591459i
$508$		0			0
$509$	−28.0375	−	23.5262i	−1.24274	−	1.04278i	−0.997305	−	0.0733695i	$-0.976625\pi$
$509$	−28.0375	−	23.5262i	−1.24274	−	1.04278i	−0.245435	−	0.969413i	$-0.578931\pi$
$510$		0			0
$511$	0.899007	+	0.327212i	0.0397697	+	0.0144750i
$512$		0			0
$513$	15.0460	−	4.30129i	0.664298	−	0.189907i
$514$		0			0
$515$	−30.6493	−	11.1554i	−1.35057	−	0.491567i
$516$		0			0
$517$	1.06246	+	0.891509i	0.0467269	+	0.0392085i
$518$		0			0
$519$	−6.96823	+	0.648630i	−0.305872	+	0.0284717i
$520$		0			0
$521$	21.7365	+	37.6487i	0.952292	+	1.64942i	0.740447	+	0.672115i	$0.234614\pi$
$521$	21.7365	+	37.6487i	0.952292	+	1.64942i	0.211846	+	0.977303i	$0.432053\pi$
$522$		0			0
$523$	13.4858	−	23.3581i	0.589692	−	1.02138i	−0.404580	−	0.914503i	$-0.632582\pi$
$523$	13.4858	−	23.3581i	0.589692	−	1.02138i	0.994273	−	0.106875i	$-0.0340843\pi$
$524$		0			0
$525$	−0.103821	−	0.379040i	−0.00453114	−	0.0165427i
$526$		0			0
$527$	−5.71117	+	2.07870i	−0.248783	+	0.0905495i
$528$		0			0
$529$	3.49555	+	19.8242i	0.151980	+	0.861923i
$530$		0			0
$531$	5.74346	−	16.3422i	0.249245	−	0.709190i
$532$		0			0
$533$	−13.0862	+	10.9806i	−0.566825	+	0.475623i
$534$		0			0
$535$	4.24574	−	24.0788i	0.183559	−	1.04102i
$536$		0			0
$537$	−17.0072	−	11.7684i	−0.733913	−	0.507845i
$538$		0			0
$539$	4.34515			0.187159
$540$		0			0
$541$	−25.5928			−1.10032			−0.550161	−	0.835059i	$-0.685434\pi$
$541$	−25.5928			−1.10032			−0.550161	+	0.835059i	$0.685434\pi$
$542$		0			0
$543$	−14.7087	+	6.95843i	−0.631211	+	0.298615i
$544$		0			0
$545$	2.83540	−	16.0803i	0.121455	−	0.688806i
$546$		0			0
$547$	−29.7003	+	24.9215i	−1.26989	+	1.06557i	−0.275340	+	0.961347i	$0.588791\pi$
$547$	−29.7003	+	24.9215i	−1.26989	+	1.06557i	−0.994554	+	0.104221i	$0.966765\pi$
$548$		0			0
$549$	−19.1510	+	11.3421i	−0.817346	+	0.484070i
$550$		0			0
$551$	0.288519	+	1.63627i	0.0122913	+	0.0697076i
$552$		0			0
$553$	−0.347725	+	0.126562i	−0.0147868	+	0.00538195i
$554$		0			0
$555$	−5.15521	+	5.21275i	−0.218827	+	0.221269i
$556$		0			0
$557$	−11.8428	+	20.5123i	−0.501796	+	0.869135i	0.498202	+	0.867061i	$0.333994\pi$
$557$	−11.8428	+	20.5123i	−0.501796	+	0.869135i	−0.999998	+	0.00207455i	$0.999340\pi$
$558$		0			0
$559$	14.5808	+	25.2546i	0.616700	+	1.06816i
$560$		0			0
$561$	−0.335988	+	0.731095i	−0.0141854	+	0.0308668i
$562$		0			0
$563$	−1.64424	−	1.37968i	−0.0692966	−	0.0581468i	0.607481	−	0.794334i	$-0.292180\pi$
$563$	−1.64424	−	1.37968i	−0.0692966	−	0.0581468i	−0.676778	+	0.736187i	$0.736624\pi$
$564$		0			0
$565$	−31.0345	−	11.2956i	−1.30563	−	0.475211i
$566$		0			0
$567$	0.928429	−	0.361456i	0.0389903	−	0.0151797i
$568$		0			0
$569$	24.6232	+	8.96212i	1.03226	+	0.375712i	0.801941	−	0.597404i	$-0.203801\pi$
$569$	24.6232	+	8.96212i	1.03226	+	0.375712i	0.230318	+	0.973115i	$0.426023\pi$
$570$		0			0
$571$	17.5657	+	14.7394i	0.735103	+	0.616825i	0.931518	−	0.363696i	$-0.118485\pi$
$571$	17.5657	+	14.7394i	0.735103	+	0.616825i	−0.196414	+	0.980521i	$0.562930\pi$
$572$		0			0
$573$	−0.952600	+	2.07281i	−0.0397954	+	0.0865931i
$574$		0			0
$575$	−6.73042	−	11.6574i	−0.280678	−	0.486148i
$576$		0			0
$577$	−9.78899	+	16.9550i	−0.407521	+	0.705847i	−0.994611	−	0.103674i	$-0.966940\pi$
$577$	−9.78899	+	16.9550i	−0.407521	+	0.705847i	0.587090	+	0.809521i	$0.300273\pi$
$578$		0			0
$579$	12.0810	−	12.2159i	0.502071	−	0.507675i
$580$		0			0
$581$	−1.06538	+	0.387765i	−0.0441992	+	0.0160872i
$582$		0			0
$583$	0.195539	+	1.10895i	0.00809838	+	0.0459282i
$584$		0			0
$585$	0.270842	+	24.3994i	0.0111979	+	1.00879i
$586$		0			0
$587$	−4.30667	+	3.61372i	−0.177755	+	0.149154i	−0.727324	−	0.686294i	$-0.759236\pi$
$587$	−4.30667	+	3.61372i	−0.177755	+	0.149154i	0.549569	+	0.835448i	$0.314792\pi$
$588$		0			0
$589$	−4.25456	+	24.1288i	−0.175306	+	0.994209i
$590$		0			0
$591$	22.5441	−	10.6652i	0.927341	−	0.438708i
$592$		0			0
$593$	−10.8726			−0.446485			−0.223242	−	0.974763i	$-0.571664\pi$
$593$	−10.8726			−0.446485			−0.223242	+	0.974763i	$0.571664\pi$
$594$		0			0
$595$	−0.142050			−0.00582347
$596$		0			0
$597$	1.79207	+	1.24005i	0.0733445	+	0.0507521i
$598$		0			0
$599$	−5.35724	+	30.3824i	−0.218891	+	1.24139i	0.655135	+	0.755512i	$0.272612\pi$
$599$	−5.35724	+	30.3824i	−0.218891	+	1.24139i	−0.874026	+	0.485880i	$0.838499\pi$
$600$		0			0
$601$	23.1145	−	19.3954i	0.942859	−	0.791153i	−0.0352212	−	0.999380i	$-0.511214\pi$
$601$	23.1145	−	19.3954i	0.942859	−	0.791153i	0.978081	+	0.208227i	$0.0667691\pi$
$602$		0			0
$603$	−8.34528	+	1.56720i	−0.339846	+	0.0638213i
$604$		0			0
$605$	−3.16561	−	17.9531i	−0.128701	−	0.729897i
$606$		0			0
$607$	−22.6270	+	8.23554i	−0.918400	+	0.334270i	−0.757602	−	0.652717i	$-0.773629\pi$
$607$	−22.6270	+	8.23554i	−0.918400	+	0.334270i	−0.160798	+	0.986987i	$0.551407\pi$
$608$		0			0
$609$	0.0279455	+	0.102026i	0.00113241	+	0.00413429i
$610$		0			0
$611$	−5.28092	+	9.14682i	−0.213643	+	0.370041i
$612$		0			0
$613$	−2.40618	−	4.16763i	−0.0971848	−	0.168329i	0.813334	−	0.581798i	$-0.197650\pi$
$613$	−2.40618	−	4.16763i	−0.0971848	−	0.168329i	−0.910518	+	0.413469i	$0.864317\pi$
$614$		0			0
$615$	10.6864	−	0.994734i	0.430918	−	0.0401115i
$616$		0			0
$617$	22.6131	+	18.9746i	0.910368	+	0.763890i	0.972189	−	0.234198i	$-0.0752463\pi$
$617$	22.6131	+	18.9746i	0.910368	+	0.763890i	−0.0618207	+	0.998087i	$0.519691\pi$
$618$		0			0
$619$	−25.4127	−	9.24948i	−1.02142	−	0.371768i	−0.223614	−	0.974678i	$-0.571786\pi$
$619$	−25.4127	−	9.24948i	−1.02142	−	0.371768i	−0.797809	+	0.602910i	$0.794008\pi$
$620$		0			0
$621$	27.6238	−	20.0359i	1.10850	−	0.804015i
$622$		0			0
$623$	−1.48115	−	0.539095i	−0.0593410	−	0.0215984i
$624$		0			0
$625$	−8.08221	−	6.78178i	−0.323289	−	0.271271i
$626$		0			0
$627$	1.87517	+	2.64663i	0.0748870	+	0.105696i
$628$		0			0
$629$	−0.920475	−	1.59431i	−0.0367017	−	0.0635693i
$630$		0			0
$631$	−10.8466	+	18.7868i	−0.431795	+	0.747890i	−0.997028	−	0.0770409i	$-0.975453\pi$
$631$	−10.8466	+	18.7868i	−0.431795	+	0.747890i	0.565233	+	0.824931i	$0.308786\pi$
$632$		0			0
$633$	−3.58311	−	0.938809i	−0.142416	−	0.0373143i
$634$		0			0
$635$	29.2744	−	10.6550i	1.16172	−	0.422831i
$636$		0			0
$637$	5.74588	+	32.5865i	0.227660	+	1.29112i
$638$		0			0
$639$	−22.1476	+	26.9975i	−0.876145	+	1.06800i
$640$		0			0
$641$	−1.76584	+	1.48172i	−0.0697465	+	0.0585242i	−0.676994	−	0.735988i	$-0.736718\pi$
$641$	−1.76584	+	1.48172i	−0.0697465	+	0.0585242i	0.607248	+	0.794512i	$0.292273\pi$
$642$		0			0
$643$	4.07742	−	23.1242i	0.160798	−	0.911929i	−0.792495	−	0.609879i	$-0.791218\pi$
$643$	4.07742	−	23.1242i	0.160798	−	0.911929i	0.953292	−	0.302050i	$-0.0976708\pi$
$644$		0			0
$645$	1.49549	−	18.2602i	0.0588849	−	0.718995i
$646$		0			0
$647$	17.6845			0.695249			0.347625	−	0.937634i	$-0.386988\pi$
$647$	17.6845			0.695249			0.347625	+	0.937634i	$0.386988\pi$
$648$		0			0
$649$	3.59043			0.140937
$650$		0			0
$651$	−0.127328	+	1.55470i	−0.00499038	+	0.0609335i
$652$		0			0
$653$	−8.38632	+	47.5612i	−0.328182	+	1.86121i	0.158116	+	0.987421i	$0.449458\pi$
$653$	−8.38632	+	47.5612i	−0.328182	+	1.86121i	−0.486298	+	0.873793i	$0.661653\pi$
$654$		0			0
$655$	24.2540	−	20.3516i	0.947684	−	0.795201i
$656$		0			0
$657$	−9.13733	−	24.2632i	−0.356481	−	0.946597i
$658$		0			0
$659$	3.39217	+	19.2379i	0.132140	+	0.749403i	0.976809	+	0.214114i	$0.0686863\pi$
$659$	3.39217	+	19.2379i	0.132140	+	0.749403i	−0.844669	+	0.535289i	$0.820203\pi$
$660$		0			0
$661$	0.962869	−	0.350456i	0.0374513	−	0.0136311i	−0.323227	−	0.946322i	$-0.604768\pi$
$661$	0.962869	−	0.350456i	0.0374513	−	0.0136311i	0.360678	+	0.932690i	$0.382545\pi$
$662$		0			0
$663$	−5.92715	−	1.55297i	−0.230191	−	0.0603123i
$664$		0			0
$665$	−0.286322	+	0.495925i	−0.0111031	+	0.0192311i
$666$		0			0
$667$	1.81162	+	3.13781i	0.0701461	+	0.121497i
$668$		0			0
$669$	15.2065	+	21.4626i	0.587917	+	0.829793i
$670$		0			0
$671$	−3.53412	−	2.96548i	−0.136433	−	0.114481i
$672$		0			0
$673$	−46.6520	−	16.9799i	−1.79830	−	0.654529i	−0.998529	−	0.0542270i	$-0.982731\pi$
$673$	−46.6520	−	16.9799i	−1.79830	−	0.654529i	−0.799774	−	0.600302i	$-0.795047\pi$
$674$		0			0
$675$	−5.96269	+	8.82476i	−0.229504	+	0.339665i
$676$		0			0
$677$	−1.37819	−	0.501621i	−0.0529682	−	0.0192788i	0.315400	−	0.948959i	$-0.397861\pi$
$677$	−1.37819	−	0.501621i	−0.0529682	−	0.0192788i	−0.368368	+	0.929680i	$0.620083\pi$
$678$		0			0
$679$	1.03241	+	0.866297i	0.0396203	+	0.0332454i
$680$		0			0
$681$	−31.0971	+	2.89464i	−1.19164	+	0.110923i
$682$		0			0
$683$	18.2547	+	31.6181i	0.698498	+	1.20983i	0.968987	+	0.247111i	$0.0794813\pi$
$683$	18.2547	+	31.6181i	0.698498	+	1.20983i	−0.270489	+	0.962723i	$0.587185\pi$
$684$		0			0
$685$	−9.44022	+	16.3509i	−0.360692	+	0.624737i
$686$		0			0
$687$	−2.37268	−	8.66237i	−0.0905234	−	0.330490i
$688$		0			0
$689$	−8.05804	+	2.93289i	−0.306987	+	0.111734i
$690$		0			0
$691$	8.32578	+	47.2178i	0.316728	+	1.79625i	0.562365	+	0.826889i	$0.309892\pi$
$691$	8.32578	+	47.2178i	0.316728	+	1.79625i	−0.245637	+	0.969362i	$0.578997\pi$
$692$		0			0
$693$	0.134490	+	0.156713i	0.00510884	+	0.00595302i
$694$		0			0
$695$	4.70963	−	3.95185i	0.178646	−	0.149902i
$696$		0			0
$697$	−0.467986	+	2.65408i	−0.0177262	+	0.100530i
$698$		0			0
$699$	14.5833	+	10.0912i	0.551590	+	0.381683i
$700$		0			0
$701$	−6.02917			−0.227719			−0.113859	−	0.993497i	$-0.536321\pi$
$701$	−6.02917			−0.227719			−0.113859	+	0.993497i	$0.536321\pi$
$702$		0			0
$703$	−7.42141			−0.279904
$704$		0			0
$705$	5.99833	−	2.83770i	0.225910	−	0.106874i
$706$		0			0
$707$	0.0898576	−	0.509608i	0.00337944	−	0.0191658i
$708$		0			0
$709$	26.2161	−	21.9979i	0.984567	−	0.826150i	−0.000205004	−	1.00000i	$-0.500065\pi$
$709$	26.2161	−	21.9979i	0.984567	−	0.826150i	0.984772	+	0.173850i	$0.0556208\pi$
$710$		0			0
$711$	8.73974	+	4.91736i	0.327766	+	0.184416i
$712$		0			0
$713$	9.27783	+	52.6172i	0.347457	+	1.97053i
$714$		0			0
$715$	−4.75269	+	1.72984i	−0.177740	+	0.0646922i
$716$		0			0
$717$	27.3345	−	27.6396i	1.02082	−	1.03222i
$718$		0			0
$719$	22.0922	−	38.2649i	0.823902	−	1.42704i	−0.0788539	−	0.996886i	$-0.525126\pi$
$719$	22.0922	−	38.2649i	0.823902	−	1.42704i	0.902756	−	0.430154i	$-0.141541\pi$
$720$		0			0
$721$	−1.05104	−	1.82046i	−0.0391428	−	0.0677974i
$722$		0			0
$723$	−5.69373	+	12.3893i	−0.211752	+	0.460763i
$724$		0			0
$725$	−0.866249	−	0.726869i	−0.0321717	−	0.0269952i
$726$		0			0
$727$	35.8200	+	13.0374i	1.32849	+	0.483531i	0.906169	−	0.422915i	$-0.138993\pi$
$727$	35.8200	+	13.0374i	1.32849	+	0.483531i	0.422321	+	0.906446i	$0.361215\pi$
$728$		0			0
$729$	−23.8192	−	12.7140i	−0.882192	−	0.470890i
$730$		0			0
$731$	4.32315	+	1.57350i	0.159897	+	0.0581979i
$732$		0			0
$733$	−31.6649	−	26.5700i	−1.16957	−	0.981386i	−0.169579	−	0.985517i	$-0.554241\pi$
$733$	−31.6649	−	26.5700i	−1.16957	−	0.981386i	−0.999991	+	0.00413034i	$0.998685\pi$
$734$		0			0
$735$	8.68111	−	18.8897i	0.320208	−	0.696757i
$736$		0			0
$737$	−0.880002	−	1.52421i	−0.0324153	−	0.0561449i
$738$		0			0
$739$	−5.57182	+	9.65067i	−0.204963	+	0.355006i	−0.950121	−	0.311882i	$-0.899041\pi$
$739$	−5.57182	+	9.65067i	−0.204963	+	0.355006i	0.745158	+	0.666888i	$0.232374\pi$
$740$		0			0
$741$	−17.3688	+	17.5626i	−0.638058	+	0.645180i
$742$		0			0
$743$	−38.9528	+	14.1777i	−1.42904	+	0.520128i	−0.936656	−	0.350250i	$-0.886097\pi$
$743$	−38.9528	+	14.1777i	−1.42904	+	0.520128i	−0.492384	+	0.870378i	$0.663875\pi$
$744$		0			0
$745$	−0.291222	−	1.65160i	−0.0106696	−	0.0605101i
$746$		0			0
$747$	26.7772	+	15.0660i	0.979727	+	0.551238i
$748$		0			0
$749$	1.20713	−	1.01290i	0.0441074	−	0.0370105i
$750$		0			0
$751$	3.57094	−	20.2518i	0.130306	−	0.738999i	−0.847709	−	0.530462i	$-0.822019\pi$
$751$	3.57094	−	20.2518i	0.130306	−	0.738999i	0.978014	−	0.208537i	$-0.0668703\pi$
$752$		0			0
$753$	30.1779	−	14.2766i	1.09975	−	0.520270i
$754$		0			0
$755$	15.9744			0.581369
$756$		0			0
$757$	20.6622			0.750982			0.375491	−	0.926826i	$-0.377474\pi$
$757$	20.6622			0.750982			0.375491	+	0.926826i	$0.377474\pi$
$758$		0			0
$759$	5.81649	+	4.02483i	0.211125	+	0.146092i
$760$		0			0
$761$	−3.18914	+	18.0865i	−0.115606	+	0.655636i	0.870842	+	0.491563i	$0.163574\pi$
$761$	−3.18914	+	18.0865i	−0.115606	+	0.655636i	−0.986448	+	0.164073i	$0.947537\pi$
$762$		0			0
$763$	0.806145	−	0.676436i	0.0291844	−	0.0244886i
$764$		0			0
$765$	2.50703	+	2.92128i	0.0906417	+	0.105619i
$766$		0			0
$767$	4.74786	+	26.9265i	0.171435	+	0.972258i
$768$		0			0
$769$	10.2361	−	3.72563i	0.369123	−	0.134350i	−0.150797	−	0.988565i	$-0.548184\pi$
$769$	10.2361	−	3.72563i	0.369123	−	0.134350i	0.519920	+	0.854215i	$0.325962\pi$
$770$		0			0
$771$	12.6968	+	46.3547i	0.457266	+	1.66942i
$772$		0			0
$773$	−10.3426	+	17.9139i	−0.371998	+	0.644320i	−0.989873	−	0.141957i	$-0.954661\pi$
$773$	−10.3426	+	17.9139i	−0.371998	+	0.644320i	0.617875	+	0.786277i	$0.287994\pi$
$774$		0			0
$775$	−8.33755	−	14.4411i	−0.299493	−	0.518738i
$776$		0			0
$777$	−0.470465	+	0.0437927i	−0.0168778	+	0.00157105i
$778$		0			0
$779$	8.32264	+	6.98353i	0.298190	+	0.250211i
$780$		0			0
$781$	−6.80146	−	2.47553i	−0.243375	−	0.0885813i
$782$		0			0
$783$	1.60497	−	2.37535i	0.0573570	−	0.0848880i
$784$		0			0
$785$	−4.17922	−	1.52111i	−0.149163	−	0.0542909i
$786$		0			0
$787$	23.6833	+	19.8726i	0.844217	+	0.708382i	0.958508	−	0.285065i	$-0.0920153\pi$
$787$	23.6833	+	19.8726i	0.844217	+	0.708382i	−0.114291	+	0.993447i	$0.536460\pi$
$788$		0			0
$789$	−16.2106	−	22.8798i	−0.577112	−	0.814543i
$790$		0			0
$791$	−1.06425	−	1.84334i	−0.0378404	−	0.0655416i
$792$		0			0
$793$	17.5662	−	30.4256i	0.623795	−	1.08045i
$794$		0			0
$795$	5.21163	+	1.36550i	0.184837	+	0.0484291i
$796$		0			0
$797$	44.9010	−	16.3426i	1.59047	−	0.578885i	0.613026	−	0.790063i	$-0.289952\pi$
$797$	44.9010	−	16.3426i	1.59047	−	0.578885i	0.977448	+	0.211178i	$0.0677300\pi$
$798$		0			0
$799$	0.289343	+	1.64095i	0.0102362	+	0.0580526i
$800$		0			0
$801$	15.0541	+	39.9746i	0.531911	+	1.41243i
$802$		0			0
$803$	4.11669	−	3.45431i	0.145275	−	0.121900i
$804$		0			0
$805$	−0.216844	+	1.22978i	−0.00764275	+	0.0433442i
$806$		0			0
$807$	−0.0978978	+	1.19535i	−0.00344617	+	0.0420783i
$808$		0			0
$809$	13.0291			0.458078			0.229039	−	0.973417i	$-0.426442\pi$
$809$	13.0291			0.458078			0.229039	+	0.973417i	$0.426442\pi$
$810$		0			0
$811$	35.1935			1.23581			0.617905	−	0.786253i	$-0.287982\pi$
$811$	35.1935			1.23581			0.617905	+	0.786253i	$0.287982\pi$
$812$		0			0
$813$	4.04806	−	49.4275i	0.141972	−	1.73350i
$814$		0			0
$815$	5.58637	−	31.6819i	0.195682	−	1.10977i
$816$		0			0
$817$	14.2073	−	11.9214i	0.497052	−	0.417076i
$818$		0			0
$819$	−0.997422	+	1.21584i	−0.0348528	+	0.0424848i
$820$		0			0
$821$	0.376951	+	2.13779i	0.0131557	+	0.0746095i	0.990679	−	0.136219i	$-0.0434950\pi$
$821$	0.376951	+	2.13779i	0.0131557	+	0.0746095i	−0.977523	+	0.210828i	$0.932384\pi$
$822$		0			0
$823$	−0.757409	+	0.275674i	−0.0264016	+	0.00960941i	−0.355187	−	0.934795i	$-0.615583\pi$
$823$	−0.757409	+	0.275674i	−0.0264016	+	0.00960941i	0.328786	+	0.944405i	$0.393361\pi$
$824$		0			0
$825$	−2.13547	−	0.559513i	−0.0743475	−	0.0194798i
$826$		0			0
$827$	−24.8277	+	43.0029i	−0.863344	+	1.49536i	0.00533726	+	0.999986i	$0.498301\pi$
$827$	−24.8277	+	43.0029i	−0.863344	+	1.49536i	−0.868682	+	0.495371i	$0.835032\pi$
$828$		0			0
$829$	6.98084	+	12.0912i	0.242455	+	0.419944i	0.961413	−	0.275109i	$-0.0887141\pi$
$829$	6.98084	+	12.0912i	0.242455	+	0.419944i	−0.718958	+	0.695053i	$0.755381\pi$
$830$		0			0
$831$	−22.3308	−	31.5180i	−0.774648	−	1.09335i
$832$		0			0
$833$	3.99894	+	3.35551i	0.138555	+	0.116261i
$834$		0			0
$835$	24.5445	+	8.93348i	0.849399	+	0.309156i
$836$		0			0
$837$	34.2199	−	24.8202i	1.18281	−	0.857913i
$838$		0			0
$839$	30.6122	+	11.1419i	1.05685	+	0.384662i	0.811244	−	0.584708i	$-0.198791\pi$
$839$	30.6122	+	11.1419i	1.05685	+	0.384662i	0.245606	+	0.969370i	$0.421013\pi$
$840$		0			0
$841$	−21.9821	−	18.4452i	−0.758004	−	0.636041i
$842$		0			0
$843$	−0.497741	+	0.0463317i	−0.0171431	+	0.00159575i
$844$		0			0
$845$	−8.09295	−	14.0174i	−0.278406	−	0.482213i
$846$		0			0
$847$	0.587453	−	1.01750i	0.0201851	−	0.0349617i
$848$		0			0
$849$	6.00257	+	21.9147i	0.206008	+	0.752110i
$850$		0			0
$851$	−15.2077	+	5.53516i	−0.521314	+	0.189743i
$852$		0			0
$853$	2.93012	+	16.6175i	0.100325	+	0.568974i	0.992985	+	0.118242i	$0.0377258\pi$
$853$	2.93012	+	16.6175i	0.100325	+	0.568974i	−0.892659	+	0.450732i	$0.851163\pi$
$854$		0			0
$855$	15.2521	−	2.86426i	0.521610	−	0.0979557i
$856$		0			0
$857$	−8.44797	+	7.08869i	−0.288577	+	0.242145i	−0.775571	−	0.631261i	$-0.782538\pi$
$857$	−8.44797	+	7.08869i	−0.288577	+	0.242145i	0.486994	+	0.873405i	$0.338093\pi$
$858$		0			0
$859$	−5.61388	+	31.8379i	−0.191543	+	1.08629i	0.725713	+	0.687997i	$0.241510\pi$
$859$	−5.61388	+	31.8379i	−0.191543	+	1.08629i	−0.917256	+	0.398297i	$0.869601\pi$
$860$		0			0
$861$	0.568805	+	0.393595i	0.0193848	+	0.0134137i
$862$		0			0
$863$	−8.00690			−0.272558			−0.136279	−	0.990670i	$-0.543514\pi$
$863$	−8.00690			−0.272558			−0.136279	+	0.990670i	$0.543514\pi$
$864$		0			0
$865$	−6.94019			−0.235974
$866$		0			0
$867$	25.7428	−	12.1785i	0.874273	−	0.413603i
$868$		0			0
$869$	−0.360942	+	2.04700i	−0.0122441	+	0.0694398i
$870$		0			0
$871$	10.2671	−	8.61514i	0.347888	−	0.291913i
$872$		0			0
$873$	−0.405395	−	36.5210i	−0.0137205	−	1.23605i
$874$		0			0
$875$	−0.232769	−	1.32010i	−0.00786904	−	0.0446275i
$876$		0			0
$877$	25.0105	−	9.10306i	0.844543	−	0.307389i	0.116730	−	0.993164i	$-0.462759\pi$
$877$	25.0105	−	9.10306i	0.844543	−	0.307389i	0.727814	+	0.685775i	$0.240537\pi$
$878$		0			0
$879$	27.0100	−	27.3115i	0.911025	−	0.921193i
$880$		0			0
$881$	4.62649	−	8.01331i	0.155870	−	0.269975i	−0.777505	−	0.628876i	$-0.783515\pi$
$881$	4.62649	−	8.01331i	0.155870	−	0.269975i	0.933376	+	0.358901i	$0.116848\pi$
$882$		0			0
$883$	−12.6630	−	21.9330i	−0.426145	−	0.738104i	0.570382	−	0.821380i	$-0.306795\pi$
$883$	−12.6630	−	21.9330i	−0.426145	−	0.738104i	−0.996527	+	0.0832755i	$0.973462\pi$
$884$		0			0
$885$	7.17326	−	15.6087i	0.241127	−	0.524681i
$886$		0			0
$887$	−0.931036	−	0.781232i	−0.0312611	−	0.0262312i	0.627023	−	0.779001i	$-0.284273\pi$
$887$	−0.931036	−	0.781232i	−0.0312611	−	0.0262312i	−0.658284	+	0.752769i	$0.728718\pi$
$888$		0			0
$889$	1.88670	+	0.686703i	0.0632779	+	0.0230313i
$890$		0			0
$891$	0.849228	−	5.53162i	0.0284502	−	0.185316i
$892$		0			0
$893$	6.31210	+	2.29742i	0.211226	+	0.0768801i
$894$		0			0
$895$	−15.7115	−	13.1835i	−0.525179	−	0.440677i
$896$		0			0
$897$	−22.4927	+	48.9431i	−0.751009	+	1.63416i
$898$		0			0
$899$	2.24421	+	3.88708i	0.0748484	+	0.129641i
$900$		0			0
$901$	−0.676422	+	1.17160i	−0.0225349	+	0.0390316i
$902$		0			0
$903$	0.830298	−	0.839566i	0.0276306	−	0.0279390i
$904$		0			0
$905$	−15.1632	+	5.51897i	−0.504043	+	0.183457i
$906$		0			0
$907$	−0.833391	−	4.72640i	−0.0276723	−	0.156937i	0.967840	−	0.251565i	$-0.0809452\pi$
$907$	−0.833391	−	4.72640i	−0.0276723	−	0.156937i	−0.995513	+	0.0946274i	$0.969834\pi$
$908$		0			0
$909$	−12.0661	+	7.14609i	−0.400207	+	0.237021i
$910$		0			0
$911$	1.33780	−	1.12255i	0.0443235	−	0.0371918i	−0.620357	−	0.784320i	$-0.713012\pi$
$911$	1.33780	−	1.12255i	0.0443235	−	0.0371918i	0.664680	+	0.747128i	$0.268568\pi$
$912$		0			0
$913$	−1.10587	+	6.27170i	−0.0365990	+	0.207563i
$914$		0			0
$915$	−19.9526	+	9.43922i	−0.659613	+	0.312051i
$916$		0			0
$917$	2.04054			0.0673846
$918$		0			0
$919$	−43.0678			−1.42067			−0.710337	−	0.703862i	$-0.751458\pi$
$919$	−43.0678			−1.42067			−0.710337	+	0.703862i	$0.751458\pi$
$920$		0			0
$921$	−46.1592	−	31.9407i	−1.52100	−	1.05248i
$922$		0			0
$923$	9.57122	−	54.2811i	0.315041	−	1.78668i
$924$		0			0
$925$	3.86923	−	3.24667i	0.127220	−	0.106750i
$926$		0			0
$927$	−18.8883	+	53.7440i	−0.620374	+	1.76518i
$928$		0			0
$929$	−8.09519	−	45.9101i	−0.265595	−	1.50626i	−0.767336	−	0.641245i	$-0.778418\pi$
$929$	−8.09519	−	45.9101i	−0.265595	−	1.50626i	0.501742	−	0.865018i	$-0.332693\pi$
$930$		0			0
$931$	19.7752	−	7.19758i	0.648106	−	0.235891i
$932$		0			0
$933$	9.15259	+	33.4150i	0.299642	+	1.09396i
$934$		0			0
$935$	−0.398958	+	0.691016i	−0.0130473	+	0.0225986i
$936$		0			0
$937$	−8.86081	−	15.3474i	−0.289470	−	0.501377i	0.684213	−	0.729282i	$-0.260146\pi$
$937$	−8.86081	−	15.3474i	−0.289470	−	0.501377i	−0.973683	+	0.227905i	$0.926812\pi$
$938$		0			0
$939$	30.8526	−	2.87188i	1.00684	−	0.0937201i
$940$		0			0
$941$	−40.9818	−	34.3878i	−1.33597	−	1.12101i	−0.982642	−	0.185509i	$-0.940606\pi$
$941$	−40.9818	−	34.3878i	−1.33597	−	1.12101i	−0.353325	−	0.935501i	$-0.614949\pi$
$942$		0			0
$943$	22.2631	+	8.10310i	0.724985	+	0.263873i
$944$		0			0
$945$	0.949972	−	0.271574i	0.0309026	−	0.00883431i
$946$		0			0
$947$	50.5523	+	18.3995i	1.64273	+	0.597905i	0.987513	−	0.157537i	$-0.0503552\pi$
$947$	50.5523	+	18.3995i	1.64273	+	0.597905i	0.655216	+	0.755441i	$0.272577\pi$
$948$		0			0
$949$	31.3494	+	26.3053i	1.01764	+	0.853905i
$950$		0			0
$951$	−1.53481	−	2.16625i	−0.0497696	−	0.0702453i
$952$		0			0
$953$	11.5960	+	20.0848i	0.375630	+	0.650611i	0.990421	−	0.138079i	$-0.0440929\pi$
$953$	11.5960	+	20.0848i	0.375630	+	0.650611i	−0.614791	+	0.788690i	$0.710760\pi$
$954$		0			0
$955$	−1.13113	+	1.95918i	−0.0366027	+	0.0633977i
$956$		0			0
$957$	0.574801	+	0.150603i	0.0185807	+	0.00486832i
$958$		0			0
$959$	−1.14344	+	0.416178i	−0.0369236	+	0.0134391i
$960$		0			0
$961$	6.11014	+	34.6523i	0.197101	+	1.11782i
$962$		0			0
$963$	−42.1349	−	6.94822i	−1.35778	−	0.223903i
$964$		0			0
$965$	13.0519	−	10.9518i	0.420154	−	0.352551i
$966$		0			0
$967$	−4.02407	+	22.8216i	−0.129405	+	0.733894i	0.849188	+	0.528091i	$0.177092\pi$
$967$	−4.02407	+	22.8216i	−0.129405	+	0.733894i	−0.978593	+	0.205803i	$0.934019\pi$
$968$		0			0
$969$	−0.318082	+	3.88383i	−0.0102183	+	0.124767i
$970$		0			0
$971$	6.85324			0.219931			0.109965	−	0.993935i	$-0.464926\pi$
$971$	6.85324			0.219931			0.109965	+	0.993935i	$0.464926\pi$
$972$		0			0
$973$	0.396231			0.0127026
$974$		0			0
$975$	1.37220	−	16.7548i	0.0439457	−	0.536585i
$976$		0			0
$977$	4.62627	−	26.2369i	0.148008	−	0.839393i	−0.816895	−	0.576786i	$-0.804307\pi$
$977$	4.62627	−	26.2369i	0.148008	−	0.839393i	0.964903	−	0.262607i	$-0.0845822\pi$
$978$		0			0
$979$	−6.78241	+	5.69112i	−0.216767	+	0.181889i
$980$		0			0
$981$	−28.1386	−	4.64017i	−0.898397	−	0.148149i
$982$		0			0
$983$	0.287621	+	1.63118i	0.00917367	+	0.0520265i	0.989051	−	0.147574i	$-0.0471466\pi$
$983$	0.287621	+	1.63118i	0.00917367	+	0.0520265i	−0.979877	+	0.199601i	$0.936035\pi$
$984$		0			0
$985$	23.2408	−	8.45895i	0.740513	−	0.269525i
$986$		0			0
$987$	0.413699	+	0.108393i	0.0131682	+	0.00345019i
$988$		0			0
$989$	20.2218	−	35.0253i	0.643017	−	1.11374i
$990$		0			0
$991$	4.05179	+	7.01790i	0.128709	+	0.222931i	0.923177	−	0.384376i	$-0.125583\pi$
$991$	4.05179	+	7.01790i	0.128709	+	0.222931i	−0.794468	+	0.607307i	$0.792250\pi$
$992$		0			0
$993$	23.2998	+	32.8856i	0.739398	+	1.04359i
$994$		0			0
$995$	1.65555	+	1.38917i	0.0524844	+	0.0440396i
$996$		0			0
$997$	−15.6478	−	5.69532i	−0.495570	−	0.180373i	0.0821306	−	0.996622i	$-0.473828\pi$
$997$	−15.6478	−	5.69532i	−0.495570	−	0.180373i	−0.577700	+	0.816249i	$0.696050\pi$
$998$		0			0
$999$	9.20380	+	8.90231i	0.291195	+	0.281657i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.y.d.193.6	yes	60
4.3	odd	2	inner	864.2.y.d.193.5	✓	60
27.7	even	9	inner	864.2.y.d.385.6	yes	60
108.7	odd	18	inner	864.2.y.d.385.5	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.y.d.193.5	✓	60	4.3	odd	2	inner
864.2.y.d.193.6	yes	60	1.1	even	1	trivial
864.2.y.d.385.5	yes	60	108.7	odd	18	inner
864.2.y.d.385.6	yes	60	27.7	even	9	inner

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.y (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.141380 - 1.72627i) q^{3} +(0.298268 - 1.69156i) q^{5} +(0.0848018 - 0.0711572i) q^{7} +(-2.96002 - 0.488119i) q^{9} +O(q^{10})\)	\(q+(0.141380 - 1.72627i) q^{3} +(0.298268 - 1.69156i) q^{5} +(0.0848018 - 0.0711572i) q^{7} +(-2.96002 - 0.488119i) q^{9} +(-0.107979 - 0.612378i) q^{11} +(4.44975 - 1.61957i) q^{13} +(-2.87792 - 0.754043i) q^{15} +(0.373528 - 0.646970i) q^{17} +(-1.50580 - 2.60813i) q^{19} +(-0.110847 - 0.156451i) q^{21} +(-5.03088 - 4.22141i) q^{23} +(1.92605 + 0.701026i) q^{25} +(-1.26111 + 5.04079i) q^{27} +(-0.518433 - 0.188694i) q^{29} +(-6.23218 - 5.22942i) q^{31} +(-1.07240 + 0.0998228i) q^{33} +(-0.0950730 - 0.164671i) q^{35} +(1.23214 - 2.13412i) q^{37} +(-2.16672 - 7.91044i) q^{39} +(-3.38996 + 1.23385i) q^{41} +(1.06938 + 6.06474i) q^{43} +(-1.70856 + 4.86147i) q^{45} +(-1.70861 + 1.43370i) q^{47} +(-1.21341 + 6.88159i) q^{49} +(-1.06404 - 0.736279i) q^{51} -1.81090 q^{53} -1.06808 q^{55} +(-4.71522 + 2.23069i) q^{57} +(-1.00265 + 5.68630i) q^{59} +(5.68347 - 4.76900i) q^{61} +(-0.285749 + 0.169234i) q^{63} +(-1.41239 - 8.01008i) q^{65} +(2.65969 - 0.968049i) q^{67} +(-7.99856 + 8.08784i) q^{69} +(5.81993 - 10.0804i) q^{71} +(4.32111 + 7.48439i) q^{73} +(1.48246 - 3.22578i) q^{75} +(-0.0527319 - 0.0442473i) q^{77} +(-3.14112 - 1.14327i) q^{79} +(8.52348 + 2.88969i) q^{81} +(-9.62391 - 3.50282i) q^{83} +(-0.982977 - 0.824816i) q^{85} +(-0.399033 + 0.868278i) q^{87} +(-7.11921 - 12.3308i) q^{89} +(0.262102 - 0.453974i) q^{91} +(-9.90850 + 10.0191i) q^{93} +(-4.86093 + 1.76924i) q^{95} +(2.11406 + 11.9895i) q^{97} +(0.0207061 + 1.86536i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 12 q^{9}+O(q^{10}) \) 60 * q + 12 * q^9	\( 60 q + 12 q^{9} - 12 q^{17} + 24 q^{21} - 24 q^{25} + 6 q^{29} - 12 q^{33} - 30 q^{37} - 30 q^{41} - 90 q^{45} + 42 q^{49} - 36 q^{53} - 60 q^{57} + 48 q^{61} + 12 q^{65} + 78 q^{69} - 48 q^{73} - 12 q^{77} + 12 q^{81} - 102 q^{85} - 12 q^{89} - 36 q^{93} + 12 q^{97}+O(q^{100}) \) 60 * q + 12 * q^9 - 12 * q^17 + 24 * q^21 - 24 * q^25 + 6 * q^29 - 12 * q^33 - 30 * q^37 - 30 * q^41 - 90 * q^45 + 42 * q^49 - 36 * q^53 - 60 * q^57 + 48 * q^61 + 12 * q^65 + 78 * q^69 - 48 * q^73 - 12 * q^77 + 12 * q^81 - 102 * q^85 - 12 * q^89 - 36 * q^93 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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