LMFDB - Embedded newform 1184.2.y.a.1137.32

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1184,2,Mod(529,1184)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1184, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1184.529"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1184 = 2^{5} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1184.y (of order $6$, degree $2$, not 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:	$9.45428759932$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 296)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1137.32
Character	$\chi$	$=$	1184.1137
Dual form			1184.2.y.a.529.32

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.16163 - 1.24802i) q^{3} +(-0.890777 - 1.54287i) q^{5} +(1.76150 + 3.05101i) q^{7} +(1.61510 - 2.79744i) q^{9} -4.13321i q^{11} +(-0.0436485 - 0.0756014i) q^{13} +(-3.85106 - 2.22341i) q^{15} +(6.70855 + 3.87318i) q^{17} +(-2.34289 - 4.05801i) q^{19} +(7.61542 + 4.39677i) q^{21} -4.36925i q^{23} +(0.913033 - 1.58142i) q^{25} -0.574592i q^{27} -3.98156 q^{29} -1.77678i q^{31} +(-5.15832 - 8.93447i) q^{33} +(3.13820 - 5.43553i) q^{35} +(3.42531 - 5.02666i) q^{37} +(-0.188704 - 0.108948i) q^{39} +(4.07638 + 7.06049i) q^{41} -5.20812 q^{43} -5.75478 q^{45} +4.78830 q^{47} +(-2.70576 + 4.68651i) q^{49} +19.3352 q^{51} +(8.84851 + 5.10869i) q^{53} +(-6.37700 + 3.68176i) q^{55} +(-10.1289 - 5.84795i) q^{57} +(-1.80578 + 3.12770i) q^{59} +(0.507638 + 0.879255i) q^{61} +11.3800 q^{63} +(-0.0777621 + 0.134688i) q^{65} +(-2.90651 + 1.67808i) q^{67} +(-5.45291 - 9.44471i) q^{69} +(-7.96677 - 13.7988i) q^{71} -14.8336 q^{73} -4.55793i q^{75} +(12.6104 - 7.28064i) q^{77} +(-3.90643 + 2.25538i) q^{79} +(4.12820 + 7.15025i) q^{81} +(7.49112 + 4.32500i) q^{83} -13.8006i q^{85} +(-8.60666 + 4.96906i) q^{87} +(-7.29943 - 4.21433i) q^{89} +(0.153773 - 0.266343i) q^{91} +(-2.21745 - 3.84074i) q^{93} +(-4.17399 + 7.22956i) q^{95} +9.43247i q^{97} +(-11.5624 - 6.67555i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 2 q^{7} + 30 q^{9} + 6 q^{15} - 12 q^{17} - 32 q^{25} + 4 q^{33} + 6 q^{39} - 32 q^{47} - 18 q^{49} - 24 q^{55} - 6 q^{57} - 8 q^{63} + 6 q^{65} - 18 q^{71} - 64 q^{73} - 54 q^{79} - 16 q^{81} + 108 q^{87}+ \cdots - 50 q^{95}+O(q^{100}) $ 72 * q - 2 * q^7 + 30 * q^9 + 6 * q^15 - 12 * q^17 - 32 * q^25 + 4 * q^33 + 6 * q^39 - 32 * q^47 - 18 * q^49 - 24 * q^55 - 6 * q^57 - 8 * q^63 + 6 * q^65 - 18 * q^71 - 64 * q^73 - 54 * q^79 - 16 * q^81 + 108 * q^87 - 36 * q^89 - 50 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1184\mathbb{Z}\right)^\times$.

$n$	$223$	$705$	$741$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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
$3$	2.16163	−	1.24802i	1.24802	−	0.720544i	0.277305	−	0.960782i	$-0.410559\pi$
$3$	2.16163	−	1.24802i	1.24802	−	0.720544i	0.970714	+	0.240238i	$0.0772255\pi$
$4$		0			0
$5$	−0.890777	−	1.54287i	−0.398368	−	0.689993i	0.595157	−	0.803609i	$-0.297090\pi$
$5$	−0.890777	−	1.54287i	−0.398368	−	0.689993i	−0.993525	+	0.113617i	$0.963756\pi$
$6$		0			0
$7$	1.76150	+	3.05101i	0.665784	+	1.15317i	0.979072	+	0.203514i	$0.0652361\pi$
$7$	1.76150	+	3.05101i	0.665784	+	1.15317i	−0.313288	+	0.949658i	$0.601431\pi$
$8$		0			0
$9$	1.61510	−	2.79744i	0.538367	−	0.932479i
$10$		0			0
$11$		−	4.13321i		−	1.24621i	−0.782139	−	0.623104i	$-0.785871\pi$
$11$		−	4.13321i		−	1.24621i	0.782139	−	0.623104i	$-0.214129\pi$
$12$		0			0
$13$	−0.0436485	−	0.0756014i	−0.0121059	−	0.0209680i	0.859909	−	0.510447i	$-0.170520\pi$
$13$	−0.0436485	−	0.0756014i	−0.0121059	−	0.0209680i	−0.872015	+	0.489479i	$0.837187\pi$
$14$		0			0
$15$	−3.85106	−	2.22341i	−0.994340	−	0.574083i
$16$		0			0
$17$	6.70855	+	3.87318i	1.62706	+	0.939384i	0.984964	+	0.172761i	$0.0552689\pi$
$17$	6.70855	+	3.87318i	1.62706	+	0.939384i	0.642097	+	0.766623i	$0.278064\pi$
$18$		0			0
$19$	−2.34289	−	4.05801i	−0.537497	−	0.930972i	−0.999038	−	0.0438529i	$-0.986037\pi$
$19$	−2.34289	−	4.05801i	−0.537497	−	0.930972i	0.461541	−	0.887119i	$-0.347297\pi$
$20$		0			0
$21$	7.61542	+	4.39677i	1.66182	+	0.959453i
$22$		0			0
$23$		−	4.36925i		−	0.911052i	−0.890222	−	0.455526i	$-0.849451\pi$
$23$		−	4.36925i		−	0.911052i	0.890222	−	0.455526i	$-0.150549\pi$
$24$		0			0
$25$	0.913033	−	1.58142i	0.182607	−	0.316284i
$26$		0			0
$27$		−	0.574592i		−	0.110580i
$28$		0			0
$29$	−3.98156			−0.739357			−0.369678	−	0.929160i	$-0.620532\pi$
$29$	−3.98156			−0.739357			−0.369678	+	0.929160i	$0.620532\pi$
$30$		0			0
$31$		−	1.77678i		−	0.319119i	−0.987188	−	0.159559i	$-0.948993\pi$
$31$		−	1.77678i		−	0.319119i	0.987188	−	0.159559i	$-0.0510074\pi$
$32$		0			0
$33$	−5.15832	−	8.93447i	−0.897948	−	1.55529i
$34$		0			0
$35$	3.13820	−	5.43553i	0.530453	−	0.918772i
$36$		0			0
$37$	3.42531	−	5.02666i	0.563117	−	0.826377i
$37$	3.42531	−	5.02666i	0.563117	−	0.826377i
$38$		0			0
$39$	−0.188704	−	0.108948i	−0.0302168	−	0.0174457i
$40$		0			0
$41$	4.07638	+	7.06049i	0.636623	+	1.10266i	0.986169	+	0.165745i	$0.0530027\pi$
$41$	4.07638	+	7.06049i	0.636623	+	1.10266i	−0.349545	+	0.936919i	$0.613664\pi$
$42$		0			0
$43$	−5.20812			−0.794230			−0.397115	−	0.917769i	$-0.629989\pi$
$43$	−5.20812			−0.794230			−0.397115	+	0.917769i	$0.629989\pi$
$44$		0			0
$45$	−5.75478			−0.857872
$46$		0			0
$47$	4.78830			0.698446			0.349223	−	0.937040i	$-0.386446\pi$
$47$	4.78830			0.698446			0.349223	+	0.937040i	$0.386446\pi$
$48$		0			0
$49$	−2.70576	+	4.68651i	−0.386537	+	0.669501i
$50$		0			0
$51$	19.3352			2.70747
$52$		0			0
$53$	8.84851	+	5.10869i	1.21544	+	0.701733i	0.963938	−	0.266125i	$-0.0857435\pi$
$53$	8.84851	+	5.10869i	1.21544	+	0.701733i	0.251498	+	0.967858i	$0.419077\pi$
$54$		0			0
$55$	−6.37700	+	3.68176i	−0.859875	+	0.496449i
$56$		0			0
$57$	−10.1289	−	5.84795i	−1.34161	−	0.774580i
$58$		0			0
$59$	−1.80578	+	3.12770i	−0.235092	+	0.407192i	−0.959300	−	0.282391i	$-0.908873\pi$
$59$	−1.80578	+	3.12770i	−0.235092	+	0.407192i	0.724207	+	0.689582i	$0.242206\pi$
$60$		0			0
$61$	0.507638	+	0.879255i	0.0649964	+	0.112577i	0.896692	−	0.442654i	$-0.145963\pi$
$61$	0.507638	+	0.879255i	0.0649964	+	0.112577i	−0.831696	+	0.555231i	$0.812630\pi$
$62$		0			0
$63$	11.3800			1.43374
$64$		0			0
$65$	−0.0777621	+	0.134688i	−0.00964520	+	0.0167060i
$66$		0			0
$67$	−2.90651	+	1.67808i	−0.355087	+	0.205010i	−0.666923	−	0.745126i	$-0.732389\pi$
$67$	−2.90651	+	1.67808i	−0.355087	+	0.205010i	0.311837	+	0.950136i	$0.399056\pi$
$68$		0			0
$69$	−5.45291	−	9.44471i	−0.656453	−	1.13701i
$70$		0			0
$71$	−7.96677	−	13.7988i	−0.945481	−	1.63762i	−0.754785	−	0.655972i	$-0.772259\pi$
$71$	−7.96677	−	13.7988i	−0.945481	−	1.63762i	−0.190696	−	0.981649i	$-0.561074\pi$
$72$		0			0
$73$	−14.8336			−1.73614			−0.868068	−	0.496445i	$-0.834639\pi$
$73$	−14.8336			−1.73614			−0.868068	+	0.496445i	$0.834639\pi$
$74$		0			0
$75$		−	4.55793i		−	0.526304i
$76$		0			0
$77$	12.6104	−	7.28064i	1.43709	−	0.829706i
$78$		0			0
$79$	−3.90643	+	2.25538i	−0.439508	+	0.253750i	−0.703389	−	0.710805i	$-0.748331\pi$
$79$	−3.90643	+	2.25538i	−0.439508	+	0.253750i	0.263881	+	0.964555i	$0.414997\pi$
$80$		0			0
$81$	4.12820	+	7.15025i	0.458689	+	0.794473i
$82$		0			0
$83$	7.49112	+	4.32500i	0.822257	+	0.474731i	0.851194	−	0.524851i	$-0.175879\pi$
$83$	7.49112	+	4.32500i	0.822257	+	0.474731i	−0.0289369	+	0.999581i	$0.509212\pi$
$84$		0			0
$85$		−	13.8006i		−	1.49688i
$86$		0			0
$87$	−8.60666	+	4.96906i	−0.922731	+	0.532739i
$88$		0			0
$89$	−7.29943	−	4.21433i	−0.773739	−	0.446718i	0.0604681	−	0.998170i	$-0.480741\pi$
$89$	−7.29943	−	4.21433i	−0.773739	−	0.446718i	−0.834207	+	0.551452i	$0.814074\pi$
$90$		0			0
$91$	0.153773	−	0.266343i	0.0161198	−	0.0279204i
$92$		0			0
$93$	−2.21745	−	3.84074i	−0.229939	−	0.398266i
$94$		0			0
$95$	−4.17399	+	7.22956i	−0.428242	+	0.741738i
$96$		0			0
$97$			9.43247i			0.957722i	0.877891	+	0.478861i	$0.158950\pi$
$97$			9.43247i			0.957722i	−0.877891	+	0.478861i	$0.841050\pi$
$98$		0			0
$99$	−11.5624	−	6.67555i	−1.16206	−	0.670918i
$100$		0			0
$101$		−	0.346589i		−	0.0344869i	−0.999851	−	0.0172435i	$-0.994511\pi$
$101$		−	0.346589i		−	0.0344869i	0.999851	−	0.0172435i	$-0.00548904\pi$
$102$		0			0
$103$			1.49463i			0.147270i	0.997285	+	0.0736352i	$0.0234600\pi$
$103$			1.49463i			0.147270i	−0.997285	+	0.0736352i	$0.976540\pi$
$104$		0			0
$105$		−	15.6662i		−	1.52886i
$106$		0			0
$107$	5.13282	−	2.96344i	0.496208	−	0.286486i	−0.230938	−	0.972968i	$-0.574179\pi$
$107$	5.13282	−	2.96344i	0.496208	−	0.286486i	0.727146	+	0.686482i	$0.240846\pi$
$108$		0			0
$109$	−6.33750	+	10.9769i	−0.607022	+	1.05139i	0.384706	+	0.923039i	$0.374303\pi$
$109$	−6.33750	+	10.9769i	−0.607022	+	1.05139i	−0.991728	+	0.128354i	$0.959031\pi$
$110$		0			0
$111$	1.13089	−	15.1406i	0.107340	−	1.43708i
$112$		0			0
$113$	9.40525	+	5.43012i	0.884771	+	0.510823i	0.872229	−	0.489098i	$-0.162674\pi$
$113$	9.40525	+	5.43012i	0.884771	+	0.510823i	0.0125427	+	0.999921i	$0.496007\pi$
$114$		0			0
$115$	−6.74119	+	3.89203i	−0.628619	+	0.362934i
$116$		0			0
$117$	−0.281987			−0.0260697
$118$		0			0
$119$			27.2904i			2.50171i
$120$		0			0
$121$	−6.08340			−0.553036
$122$		0			0
$123$	17.6233	+	10.1748i	1.58904	+	0.917430i
$124$		0			0
$125$	−12.1610			−1.08771
$126$		0			0
$127$	−5.48594	+	9.50192i	−0.486798	+	0.843159i	−0.999885	−	0.0151778i	$-0.995169\pi$
$127$	−5.48594	+	9.50192i	−0.486798	+	0.843159i	0.513087	+	0.858337i	$0.328502\pi$
$128$		0			0
$129$	−11.2580	+	6.49983i	−0.991214	+	0.572278i
$130$		0			0
$131$	−8.39271	+	14.5366i	−0.733274	+	1.27007i	0.222202	+	0.975001i	$0.428676\pi$
$131$	−8.39271	+	14.5366i	−0.733274	+	1.27007i	−0.955476	+	0.295068i	$0.904658\pi$
$132$		0			0
$133$	8.25401	−	14.2964i	0.715713	−	1.23965i
$134$		0			0
$135$	−0.886521	+	0.511833i	−0.0762996	+	0.0440516i
$136$		0			0
$137$	4.38663			0.374775			0.187388	−	0.982286i	$-0.439998\pi$
$137$	4.38663			0.374775			0.187388	+	0.982286i	$0.439998\pi$
$138$		0			0
$139$	−9.76556	−	5.63815i	−0.828304	−	0.478222i	0.0249674	−	0.999688i	$-0.492052\pi$
$139$	−9.76556	−	5.63815i	−0.828304	−	0.478222i	−0.853272	+	0.521467i	$0.825385\pi$
$140$		0			0
$141$	10.3505	−	5.97589i	0.871673	−	0.503261i
$142$		0			0
$143$	−0.312476	+	0.180408i	−0.0261306	+	0.0150865i
$144$		0			0
$145$	3.54668	+	6.14303i	0.294536	+	0.510151i
$146$		0			0
$147$			13.5073i			1.11407i
$148$		0			0
$149$			15.3551i			1.25794i	0.777432	+	0.628968i	$0.216522\pi$
$149$			15.3551i			1.25794i	−0.777432	+	0.628968i	$0.783478\pi$
$150$		0			0
$151$	−3.99423	−	6.91822i	−0.325046	−	0.562996i	0.656476	−	0.754347i	$-0.272046\pi$
$151$	−3.99423	−	6.91822i	−0.325046	−	0.562996i	−0.981522	+	0.191351i	$0.938713\pi$
$152$		0			0
$153$	21.6700	−	12.5112i	1.75191	−	1.01147i
$154$		0			0
$155$	−2.74134	+	1.58271i	−0.220190	+	0.127127i
$156$		0			0
$157$	1.26284	+	0.729102i	0.100786	+	0.0581887i	0.549546	−	0.835464i	$-0.314801\pi$
$157$	1.26284	+	0.729102i	0.100786	+	0.0581887i	−0.448760	+	0.893652i	$0.648134\pi$
$158$		0			0
$159$	25.5030			2.02252
$160$		0			0
$161$	13.3306	−	7.69643i	1.05060	−	0.606564i
$162$		0			0
$163$	0.315274	−	0.546071i	0.0246942	−	0.0427716i	−0.853414	−	0.521233i	$-0.825472\pi$
$163$	0.315274	−	0.546071i	0.0246942	−	0.0427716i	0.878108	+	0.478462i	$0.158805\pi$
$164$		0			0
$165$	−9.18982	+	15.9172i	−0.715427	+	1.23916i
$166$		0			0
$167$	17.6690	−	10.2012i	1.36727	−	0.789393i	0.376690	−	0.926339i	$-0.377062\pi$
$167$	17.6690	−	10.2012i	1.36727	−	0.789393i	0.990578	+	0.136947i	$0.0437289\pi$
$168$		0			0
$169$	6.49619	−	11.2517i	0.499707	−	0.865518i
$170$		0			0
$171$	−15.1360			−1.15748
$172$		0			0
$173$	16.1422	+	9.31968i	1.22727	+	0.708562i	0.966457	−	0.256828i	$-0.0826775\pi$
$173$	16.1422	+	9.31968i	1.22727	+	0.708562i	0.260809	+	0.965390i	$0.416011\pi$
$174$		0			0
$175$	6.43323			0.486306
$176$		0			0
$177$			9.01458i			0.677577i
$178$		0			0
$179$	5.95491			0.445091			0.222545	−	0.974922i	$-0.428563\pi$
$179$	5.95491			0.445091			0.222545	+	0.974922i	$0.428563\pi$
$180$		0			0
$181$	−17.4288	+	10.0625i	−1.29548	+	0.747943i	−0.979619	−	0.200864i	$-0.935625\pi$
$181$	−17.4288	+	10.0625i	−1.29548	+	0.747943i	−0.315856	+	0.948807i	$0.602292\pi$
$182$		0			0
$183$	2.19465	+	1.26708i	0.162233	+	0.0936656i
$184$		0			0
$185$	−10.8067	−	0.807179i	−0.794522	−	0.0593450i
$186$		0			0
$187$	16.0087	−	27.7278i	1.17067	−	2.02766i
$188$		0			0
$189$	1.75308	−	1.01214i	0.127518	−	0.0736226i
$190$		0			0
$191$		−	2.63141i		−	0.190402i	−0.995458	−	0.0952010i	$-0.969651\pi$
$191$		−	2.63141i		−	0.190402i	0.995458	−	0.0952010i	$-0.0303494\pi$
$192$		0			0
$193$			6.45381i			0.464556i	0.972649	+	0.232278i	$0.0746179\pi$
$193$			6.45381i			0.464556i	−0.972649	+	0.232278i	$0.925382\pi$
$194$		0			0
$195$			0.388194i			0.0277992i
$196$		0			0
$197$	21.1982	+	12.2388i	1.51031	+	0.871979i	0.999928	+	0.0120325i	$0.00383015\pi$
$197$	21.1982	+	12.2388i	1.51031	+	0.871979i	0.510384	+	0.859946i	$0.329503\pi$
$198$		0			0
$199$		−	6.26164i		−	0.443876i	−0.975061	−	0.221938i	$-0.928762\pi$
$199$		−	6.26164i		−	0.443876i	0.975061	−	0.221938i	$-0.0712382\pi$
$200$		0			0
$201$	−4.18854	+	7.25476i	−0.295437	+	0.511711i
$202$		0			0
$203$	−7.01351	−	12.1478i	−0.492252	−	0.852605i
$204$		0			0
$205$	7.26229	−	12.5787i	0.507220	−	0.878531i
$206$		0			0
$207$	−12.2227	−	7.05678i	−0.849537	−	0.490480i
$208$		0			0
$209$	−16.7726	+	9.68366i	−1.16018	+	0.669833i
$210$		0			0
$211$			12.8294i			0.883210i	0.897210	+	0.441605i	$0.145591\pi$
$211$			12.8294i			0.883210i	−0.897210	+	0.441605i	$0.854409\pi$
$212$		0			0
$213$	−34.4424	−	19.8853i	−2.35996	−	1.36252i
$214$		0			0
$215$	4.63927	+	8.03545i	0.316396	+	0.548013i
$216$		0			0
$217$	5.42096	−	3.12979i	0.367999	−	0.212464i
$218$		0			0
$219$	−32.0647	+	18.5126i	−2.16673	+	1.25096i
$220$		0			0
$221$		−	0.676234i		−	0.0454884i
$222$		0			0
$223$	8.43355			0.564753			0.282376	−	0.959304i	$-0.408877\pi$
$223$	8.43355			0.564753			0.282376	+	0.959304i	$0.408877\pi$
$224$		0			0
$225$	−2.94928	−	5.10830i	−0.196619	−	0.340554i
$226$		0			0
$227$	5.90252	+	10.2235i	0.391764	+	0.678555i	0.992682	−	0.120755i	$-0.0385316\pi$
$227$	5.90252	+	10.2235i	0.391764	+	0.678555i	−0.600918	+	0.799310i	$0.705198\pi$
$228$		0			0
$229$	−5.42518	+	3.13223i	−0.358506	+	0.206984i	−0.668425	−	0.743779i	$-0.733031\pi$
$229$	−5.42518	+	3.13223i	−0.358506	+	0.206984i	0.309919	+	0.950763i	$0.399698\pi$
$230$		0			0
$231$	18.1727	−	31.4761i	1.19568	−	2.07098i
$232$		0			0
$233$	8.15339			0.534147			0.267073	−	0.963676i	$-0.413943\pi$
$233$	8.15339			0.534147			0.267073	+	0.963676i	$0.413943\pi$
$234$		0			0
$235$	−4.26531	−	7.38773i	−0.278238	−	0.481922i
$236$		0			0
$237$	−5.62951	+	9.75060i	−0.365676	+	0.633370i
$238$		0			0
$239$	−4.06018	−	2.34415i	−0.262631	−	0.151630i	0.362903	−	0.931827i	$-0.381786\pi$
$239$	−4.06018	−	2.34415i	−0.262631	−	0.151630i	−0.625534	+	0.780197i	$0.715119\pi$
$240$		0			0
$241$	6.90674	−	3.98761i	0.444902	−	0.256864i	−0.260773	−	0.965400i	$-0.583977\pi$
$241$	6.90674	−	3.98761i	0.444902	−	0.256864i	0.705675	+	0.708536i	$0.250644\pi$
$242$		0			0
$243$	19.3401	+	11.1660i	1.24067	+	0.716301i
$244$		0			0
$245$	9.64090			0.615934
$246$		0			0
$247$	−0.204527	+	0.354252i	−0.0130138	+	0.0225405i
$248$		0			0
$249$	21.5907			1.36826
$250$		0			0
$251$	−29.2064			−1.84349			−0.921745	−	0.387796i	$-0.873237\pi$
$251$	−29.2064			−1.84349			−0.921745	+	0.387796i	$0.873237\pi$
$252$		0			0
$253$	−18.0590			−1.13536
$254$		0			0
$255$	−17.2234	−	29.8317i	−1.07857	−	1.86813i
$256$		0			0
$257$	−4.50523	−	2.60110i	−0.281029	−	0.162252i	0.352860	−	0.935676i	$-0.385209\pi$
$257$	−4.50523	−	2.60110i	−0.281029	−	0.162252i	−0.633889	+	0.773424i	$0.718542\pi$
$258$		0			0
$259$	21.3700	+	1.59619i	1.32787	+	0.0991821i
$260$		0			0
$261$	−6.43062	+	11.1382i	−0.398045	+	0.689435i
$262$		0			0
$263$	11.8342	+	20.4975i	0.729730	+	1.26393i	0.956997	+	0.290096i	$0.0936874\pi$
$263$	11.8342	+	20.4975i	0.729730	+	1.26393i	−0.227268	+	0.973832i	$0.572979\pi$
$264$		0			0
$265$		−	18.2028i		−	1.11819i
$266$		0			0
$267$	−21.0383			−1.28752
$268$		0			0
$269$			0.924335i			0.0563577i	0.999603	+	0.0281789i	$0.00897079\pi$
$269$			0.924335i			0.0563577i	−0.999603	+	0.0281789i	$0.991029\pi$
$270$		0			0
$271$	−12.6708	+	21.9465i	−0.769697	+	1.33316i	0.168030	+	0.985782i	$0.446260\pi$
$271$	−12.6708	+	21.9465i	−0.769697	+	1.33316i	−0.937727	+	0.347373i	$0.887074\pi$
$272$		0			0
$273$		−	0.767649i		−	0.0464602i
$274$		0			0
$275$	−6.53633	−	3.77375i	−0.394156	−	0.227566i
$276$		0			0
$277$	−6.88276	−	11.9213i	−0.413545	−	0.716281i	0.581730	−	0.813382i	$-0.302376\pi$
$277$	−6.88276	−	11.9213i	−0.413545	−	0.716281i	−0.995274	+	0.0971016i	$0.969043\pi$
$278$		0			0
$279$	−4.97043	−	2.86968i	−0.297572	−	0.171803i
$280$		0			0
$281$	−15.0819	−	8.70754i	−0.899710	−	0.519448i	−0.0226042	−	0.999744i	$-0.507196\pi$
$281$	−15.0819	−	8.70754i	−0.899710	−	0.519448i	−0.877106	+	0.480296i	$0.840529\pi$
$282$		0			0
$283$	6.29225	+	10.8985i	0.374036	+	0.647849i	0.990182	−	0.139783i	$-0.0446404\pi$
$283$	6.29225	+	10.8985i	0.374036	+	0.647849i	−0.616147	+	0.787632i	$0.711307\pi$
$284$		0			0
$285$			20.8369i			1.23427i
$286$		0			0
$287$	−14.3611	+	24.8741i	−0.847707	+	1.46827i
$288$		0			0
$289$	21.5031	+	37.2444i	1.26489	+	2.19085i
$290$		0			0
$291$	11.7719	+	20.3895i	0.690081	+	1.19525i
$292$		0			0
$293$	−28.4577	+	16.4300i	−1.66251	+	0.959853i	−0.691006	+	0.722849i	$0.742832\pi$
$293$	−28.4577	+	16.4300i	−1.66251	+	0.959853i	−0.971509	+	0.237004i	$0.923834\pi$
$294$		0			0
$295$	6.43418			0.374613
$296$		0			0
$297$	−2.37491			−0.137806
$298$		0			0
$299$	−0.330321	+	0.190711i	−0.0191030	+	0.0110291i
$300$		0			0
$301$	−9.17409	−	15.8900i	−0.528786	−	0.915884i
$302$		0			0
$303$	−0.432550	−	0.749198i	−0.0248493	−	0.0430403i
$304$		0			0
$305$	0.904385	−	1.56644i	0.0517849	−	0.0896941i
$306$		0			0
$307$			3.45170i			0.196999i	0.995137	+	0.0984996i	$0.0314043\pi$
$307$			3.45170i			0.196999i	−0.995137	+	0.0984996i	$0.968596\pi$
$308$		0			0
$309$	1.86533	+	3.23084i	0.106115	+	0.183796i
$310$		0			0
$311$	−5.86851	−	3.38818i	−0.332773	−	0.192126i	0.324299	−	0.945955i	$-0.394872\pi$
$311$	−5.86851	−	3.38818i	−0.332773	−	0.192126i	−0.657071	+	0.753828i	$0.728205\pi$
$312$		0			0
$313$	−6.98349	−	4.03192i	−0.394730	−	0.227898i	0.289477	−	0.957185i	$-0.406518\pi$
$313$	−6.98349	−	4.03192i	−0.394730	−	0.227898i	−0.684208	+	0.729287i	$0.739852\pi$
$314$		0			0
$315$	−10.1370	−	17.5579i	−0.571157	−	0.989273i
$316$		0			0
$317$	−5.18482	−	2.99346i	−0.291209	−	0.168129i	0.347278	−	0.937762i	$-0.387106\pi$
$317$	−5.18482	−	2.99346i	−0.291209	−	0.168129i	−0.638487	+	0.769633i	$0.720439\pi$
$318$		0			0
$319$			16.4566i			0.921393i
$320$		0			0
$321$	7.39684	−	12.8117i	0.412852	−	0.715080i
$322$		0			0
$323$		−	36.2978i		−	2.01966i
$324$		0			0
$325$	−0.159410			−0.00884248
$326$		0			0
$327$			31.6373i			1.74954i
$328$		0			0
$329$	8.43459	+	14.6091i	0.465014	+	0.805428i
$330$		0			0
$331$	16.2890	−	28.2133i	0.895322	−	1.55074i	0.0619171	−	0.998081i	$-0.480279\pi$
$331$	16.2890	−	28.2133i	0.895322	−	1.55074i	0.833405	−	0.552662i	$-0.186388\pi$
$332$		0			0
$333$	−8.52953	−	17.7006i	−0.467416	−	0.969989i
$334$		0			0
$335$	5.17811	+	2.98958i	0.282910	+	0.163338i
$336$		0			0
$337$	1.67917	+	2.90840i	0.0914701	+	0.158431i	0.908130	−	0.418688i	$-0.137510\pi$
$337$	1.67917	+	2.90840i	0.0914701	+	0.158431i	−0.816660	+	0.577119i	$0.804177\pi$
$338$		0			0
$339$	27.1076			1.47228
$340$		0			0
$341$	−7.34379			−0.397689
$342$		0			0
$343$	5.59624			0.302169
$344$		0			0
$345$	−9.71465	+	16.8263i	−0.523019	+	0.905896i
$346$		0			0
$347$	0.803040			0.0431094			0.0215547	−	0.999768i	$-0.493138\pi$
$347$	0.803040			0.0431094			0.0215547	+	0.999768i	$0.493138\pi$
$348$		0			0
$349$	25.3543	+	14.6383i	1.35719	+	0.783572i	0.989244	−	0.146276i	$-0.0467289\pi$
$349$	25.3543	+	14.6383i	1.35719	+	0.783572i	0.367943	+	0.929848i	$0.380062\pi$
$350$		0			0
$351$	−0.0434399	+	0.0250801i	−0.00231865	+	0.00133867i
$352$		0			0
$353$	−15.7659	−	9.10247i	−0.839137	−	0.484476i	0.0178340	−	0.999841i	$-0.494323\pi$
$353$	−15.7659	−	9.10247i	−0.839137	−	0.484476i	−0.856971	+	0.515365i	$0.827656\pi$
$354$		0			0
$355$	−14.1932	+	24.5834i	−0.753298	+	1.30475i
$356$		0			0
$357$	34.0589	+	58.9918i	1.80259	+	3.12218i
$358$		0			0
$359$	−25.1427			−1.32698			−0.663491	−	0.748184i	$-0.730926\pi$
$359$	−25.1427			−1.32698			−0.663491	+	0.748184i	$0.730926\pi$
$360$		0			0
$361$	−1.47830	+	2.56049i	−0.0778054	+	0.134763i
$362$		0			0
$363$	−13.1501	+	7.59219i	−0.690199	+	0.398487i
$364$		0			0
$365$	13.2134	+	22.8863i	0.691621	+	1.19792i
$366$		0			0
$367$	7.64346	+	13.2389i	0.398985	+	0.691063i	0.993601	−	0.112947i	$-0.0360291\pi$
$367$	7.64346	+	13.2389i	0.398985	+	0.691063i	−0.594616	+	0.804010i	$0.702696\pi$
$368$		0			0
$369$	26.3351			1.37095
$370$		0			0
$371$			35.9958i			1.86881i
$372$		0			0
$373$	26.2790	−	15.1722i	1.36067	−	0.785586i	0.370961	−	0.928649i	$-0.379029\pi$
$373$	26.2790	−	15.1722i	1.36067	−	0.785586i	0.989714	+	0.143063i	$0.0456952\pi$
$374$		0			0
$375$	−26.2876	+	15.1772i	−1.35749	+	0.783745i
$376$		0			0
$377$	0.173789	+	0.301011i	0.00895059	+	0.0155029i
$378$		0			0
$379$	−6.46320	−	3.73153i	−0.331992	−	0.191676i	0.324733	−	0.945806i	$-0.394726\pi$
$379$	−6.46320	−	3.73153i	−0.331992	−	0.191676i	−0.656725	+	0.754130i	$0.728059\pi$
$380$		0			0
$381$			27.3862i			1.40304i
$382$		0			0
$383$	−13.7878	+	7.96037i	−0.704522	+	0.406756i	−0.809029	−	0.587768i	$-0.800007\pi$
$383$	−13.7878	+	7.96037i	−0.704522	+	0.406756i	0.104507	+	0.994524i	$0.466673\pi$
$384$		0			0
$385$	−22.4662	−	12.9708i	−1.14498	−	0.661056i
$386$		0			0
$387$	−8.41163	+	14.5694i	−0.427587	+	0.740603i
$388$		0			0
$389$	−0.882710	−	1.52890i	−0.0447552	−	0.0775182i	0.842780	−	0.538258i	$-0.180917\pi$
$389$	−0.882710	−	1.52890i	−0.0447552	−	0.0775182i	−0.887535	+	0.460740i	$0.847584\pi$
$390$		0			0
$391$	16.9229	−	29.3113i	0.855828	−	1.48234i
$392$		0			0
$393$			41.8970i			2.11343i
$394$		0			0
$395$	6.95952	+	4.01808i	0.350171	+	0.202172i
$396$		0			0
$397$		−	18.2297i		−	0.914923i	−0.889229	−	0.457462i	$-0.848759\pi$
$397$		−	18.2297i		−	0.914923i	0.889229	−	0.457462i	$-0.151241\pi$
$398$		0			0
$399$		−	41.2046i		−	2.06281i
$400$		0			0
$401$		−	11.5455i		−	0.576555i	−0.957547	−	0.288278i	$-0.906917\pi$
$401$		−	11.5455i		−	0.576555i	0.957547	−	0.288278i	$-0.0930826\pi$
$402$		0			0
$403$	−0.134327	+	0.0775537i	−0.00669130	+	0.00386322i
$404$		0			0
$405$	7.35461	−	12.7386i	0.365454	−	0.632984i
$406$		0			0
$407$	−20.7762	−	14.1575i	−1.02984	−	0.701762i
$408$		0			0
$409$	−16.2567	−	9.38584i	−0.803844	−	0.464100i	0.0409693	−	0.999160i	$-0.486955\pi$
$409$	−16.2567	−	9.38584i	−0.803844	−	0.464100i	−0.844814	+	0.535061i	$0.820289\pi$
$410$		0			0
$411$	9.48228	−	5.47460i	0.467727	−	0.270042i
$412$		0			0
$413$	−12.7235			−0.626083
$414$		0			0
$415$		−	15.4104i		−	0.756469i
$416$		0			0
$417$	−28.1461			−1.37832
$418$		0			0
$419$	−12.8243	−	7.40413i	−0.626509	−	0.361715i	0.152890	−	0.988243i	$-0.451142\pi$
$419$	−12.8243	−	7.40413i	−0.626509	−	0.361715i	−0.779399	+	0.626528i	$0.784475\pi$
$420$		0			0
$421$	−5.67693			−0.276676			−0.138338	−	0.990385i	$-0.544176\pi$
$421$	−5.67693			−0.276676			−0.138338	+	0.990385i	$0.544176\pi$
$422$		0			0
$423$	7.73359	−	13.3950i	0.376020	−	0.651286i
$424$		0			0
$425$	12.2502	−	7.07268i	0.594224	−	0.343076i
$426$		0			0
$427$	−1.78841	+	3.09761i	−0.0865472	+	0.149904i
$428$		0			0
$429$	−0.450305	+	0.779952i	−0.0217410	+	0.0376564i
$430$		0			0
$431$	25.4858	−	14.7142i	1.22761	−	0.708759i	0.261077	−	0.965318i	$-0.415922\pi$
$431$	25.4858	−	14.7142i	1.22761	−	0.708759i	0.966528	+	0.256559i	$0.0825889\pi$
$432$		0			0
$433$	−12.2227			−0.587385			−0.293692	−	0.955900i	$-0.594884\pi$
$433$	−12.2227			−0.587385			−0.293692	+	0.955900i	$0.594884\pi$
$434$		0			0
$435$	15.3332	+	8.85265i	0.735172	+	0.424452i
$436$		0			0
$437$	−17.7305	+	10.2367i	−0.848164	+	0.489687i
$438$		0			0
$439$	−6.92570	+	3.99855i	−0.330546	+	0.190841i	−0.656083	−	0.754688i	$-0.727788\pi$
$439$	−6.92570	+	3.99855i	−0.330546	+	0.190841i	0.325538	+	0.945529i	$0.394455\pi$
$440$		0			0
$441$	8.74014	+	15.1384i	0.416197	+	0.720874i
$442$		0			0
$443$		−	20.5052i		−	0.974232i	−0.873337	−	0.487116i	$-0.838049\pi$
$443$		−	20.5052i		−	0.974232i	0.873337	−	0.487116i	$-0.161951\pi$
$444$		0			0
$445$			15.0161i			0.711832i
$446$		0			0
$447$	19.1634	+	33.1920i	0.906397	+	1.56993i
$448$		0			0
$449$	9.98129	−	5.76270i	0.471046	−	0.271959i	−0.245631	−	0.969363i	$-0.578995\pi$
$449$	9.98129	−	5.76270i	0.471046	−	0.271959i	0.716678	+	0.697405i	$0.245662\pi$
$450$		0			0
$451$	29.1825	−	16.8485i	1.37415	−	0.793366i
$452$		0			0
$453$	−17.2681	−	9.96975i	−0.811327	−	0.468420i
$454$		0			0
$455$	−0.547911			−0.0256865
$456$		0			0
$457$	−26.1478	+	15.0965i	−1.22314	+	0.706183i	−0.965587	−	0.260080i	$-0.916251\pi$
$457$	−26.1478	+	15.0965i	−1.22314	+	0.706183i	−0.257557	+	0.966263i	$0.582918\pi$
$458$		0			0
$459$	2.22550	−	3.85468i	0.103877	−	0.179921i
$460$		0			0
$461$	5.91311	−	10.2418i	0.275401	−	0.477008i	−0.694835	−	0.719169i	$-0.744523\pi$
$461$	5.91311	−	10.2418i	0.275401	−	0.477008i	0.970236	+	0.242161i	$0.0778561\pi$
$462$		0			0
$463$	−22.2850	+	12.8663i	−1.03567	+	0.597946i	−0.918605	−	0.395177i	$-0.870683\pi$
$463$	−22.2850	+	12.8663i	−1.03567	+	0.597946i	−0.117069	+	0.993124i	$0.537350\pi$
$464$		0			0
$465$	−3.95051	+	6.84249i	−0.183201	+	0.317313i
$466$		0			0
$467$	−27.7201			−1.28273			−0.641367	−	0.767234i	$-0.721632\pi$
$467$	−27.7201			−1.28273			−0.641367	+	0.767234i	$0.721632\pi$
$468$		0			0
$469$	−10.2396	−	5.91186i	−0.472822	−	0.272984i
$470$		0			0
$471$	3.63973			0.167710
$472$		0			0
$473$			21.5262i			0.989777i
$474$		0			0
$475$	−8.55656			−0.392602
$476$		0			0
$477$	28.5825	−	16.5021i	1.30870	−	0.755579i
$478$		0			0
$479$	−11.9902	−	6.92257i	−0.547848	−	0.316300i	0.200406	−	0.979713i	$-0.435774\pi$
$479$	−11.9902	−	6.92257i	−0.547848	−	0.316300i	−0.748254	+	0.663413i	$0.769107\pi$
$480$		0			0
$481$	−0.529532	−	0.0395521i	−0.0241446	−	0.00180342i
$482$		0			0
$483$	19.2106	−	33.2737i	0.874112	−	1.51401i
$484$		0			0
$485$	14.5531	−	8.40222i	0.660821	−	0.381525i
$486$		0			0
$487$		−	1.30951i		−	0.0593398i	−0.999560	−	0.0296699i	$-0.990554\pi$
$487$		−	1.30951i		−	0.0593398i	0.999560	−	0.0296699i	$-0.00944560\pi$
$488$		0			0
$489$		−	1.57387i		−	0.0711730i
$490$		0			0
$491$			38.6573i			1.74458i	0.488990	+	0.872290i	$0.337366\pi$
$491$			38.6573i			1.74458i	−0.488990	+	0.872290i	$0.662634\pi$
$492$		0			0
$493$	−26.7105	−	15.4213i	−1.20298	−	0.694540i
$494$		0			0
$495$			23.7857i			1.06909i
$496$		0			0
$497$	28.0669	−	48.6133i	1.25897	−	2.18060i
$498$		0			0
$499$	−17.8061	−	30.8411i	−0.797111	−	1.38064i	−0.921490	−	0.388402i	$-0.873027\pi$
$499$	−17.8061	−	30.8411i	−0.797111	−	1.38064i	0.124379	−	0.992235i	$-0.460306\pi$
$500$		0			0
$501$	25.4626	−	44.1025i	1.13758	−	1.97035i
$502$		0			0
$503$	5.95414	+	3.43763i	0.265482	+	0.153276i	0.626833	−	0.779154i	$-0.284351\pi$
$503$	5.95414	+	3.43763i	0.265482	+	0.153276i	−0.361351	+	0.932430i	$0.617684\pi$
$504$		0			0
$505$	−0.534742	+	0.308734i	−0.0237957	+	0.0137385i
$506$		0			0
$507$		−	32.4295i		−	1.44024i
$508$		0			0
$509$	−8.34851	−	4.82001i	−0.370041	−	0.213643i	0.303435	−	0.952852i	$-0.401866\pi$
$509$	−8.34851	−	4.82001i	−0.370041	−	0.213643i	−0.673476	+	0.739209i	$0.735200\pi$
$510$		0			0
$511$	−26.1293	−	45.2573i	−1.15589	−	2.00206i
$512$		0			0
$513$	−2.33170	+	1.34621i	−0.102947	+	0.0594365i
$514$		0			0
$515$	2.30602	−	1.33138i	0.101615	−	0.0586677i
$516$		0			0
$517$		−	19.7910i		−	0.870409i
$518$		0			0
$519$	46.5245			2.04220
$520$		0			0
$521$	−4.26089	−	7.38007i	−0.186673	−	0.323327i	0.757466	−	0.652874i	$-0.226437\pi$
$521$	−4.26089	−	7.38007i	−0.186673	−	0.323327i	−0.944139	+	0.329548i	$0.893104\pi$
$522$		0			0
$523$	−9.42406	−	16.3229i	−0.412085	−	0.713753i	0.583032	−	0.812449i	$-0.301866\pi$
$523$	−9.42406	−	16.3229i	−0.412085	−	0.713753i	−0.995118	+	0.0986964i	$0.968533\pi$
$524$		0			0
$525$	13.9063	−	8.02879i	0.606919	−	0.350405i
$526$		0			0
$527$	6.88178	−	11.9196i	0.299775	−	0.519226i
$528$		0			0
$529$	3.90963			0.169984
$530$		0			0
$531$	5.83303	+	10.1031i	0.253132	+	0.438437i
$532$		0			0
$533$	0.355855	−	0.616360i	0.0154138	−	0.0266975i
$534$		0			0
$535$	−9.14439	−	5.27952i	−0.395347	−	0.228254i
$536$		0			0
$537$	12.8723	−	7.43184i	0.555481	−	0.320707i
$538$		0			0
$539$	19.3703	+	11.1834i	0.834338	+	0.481705i
$540$		0			0
$541$	−8.96967			−0.385636			−0.192818	−	0.981234i	$-0.561763\pi$
$541$	−8.96967			−0.385636			−0.192818	+	0.981234i	$0.561763\pi$
$542$		0			0
$543$	−25.1165	+	43.5030i	−1.07785	+	1.86689i
$544$		0			0
$545$	22.5812			0.967272
$546$		0			0
$547$	−25.6286			−1.09580			−0.547900	−	0.836544i	$-0.684573\pi$
$547$	−25.6286			−1.09580			−0.547900	+	0.836544i	$0.684573\pi$
$548$		0			0
$549$	3.27955			0.139968
$550$		0			0
$551$	9.32837	+	16.1572i	0.397402	+	0.688320i
$552$		0			0
$553$	−13.7624	−	7.94570i	−0.585235	−	0.337886i
$554$		0			0
$555$	−24.3674	+	11.7421i	−1.03434	+	0.498424i
$556$		0			0
$557$	20.4554	−	35.4298i	0.866723	−	1.50121i	0.00139745	−	0.999999i	$-0.499555\pi$
$557$	20.4554	−	35.4298i	0.866723	−	1.50121i	0.865326	−	0.501210i	$-0.167111\pi$
$558$		0			0
$559$	0.227326	+	0.393741i	0.00961488	+	0.0166535i
$560$		0			0
$561$		−	79.9164i		−	3.37407i
$562$		0			0
$563$	28.6566			1.20773			0.603867	−	0.797085i	$-0.293626\pi$
$563$	28.6566			1.20773			0.603867	+	0.797085i	$0.293626\pi$
$564$		0			0
$565$		−	19.3481i		−	0.813981i
$566$		0			0
$567$	−14.5436	+	25.1903i	−0.610776	+	1.05789i
$568$		0			0
$569$			2.98363i			0.125080i	0.998042	+	0.0625402i	$0.0199202\pi$
$569$			2.98363i			0.125080i	−0.998042	+	0.0625402i	$0.980080\pi$
$570$		0			0
$571$	−24.2093	−	13.9772i	−1.01313	−	0.584929i	−0.101021	−	0.994884i	$-0.532211\pi$
$571$	−24.2093	−	13.9772i	−1.01313	−	0.584929i	−0.912106	+	0.409955i	$0.865544\pi$
$572$		0			0
$573$	−3.28405	−	5.68813i	−0.137193	−	0.237625i
$574$		0			0
$575$	−6.90962	−	3.98927i	−0.288151	−	0.166364i
$576$		0			0
$577$	32.1667	+	18.5714i	1.33912	+	0.773139i	0.986676	−	0.162695i	$-0.0520187\pi$
$577$	32.1667	+	18.5714i	1.33912	+	0.773139i	0.352440	+	0.935834i	$0.385352\pi$
$578$		0			0
$579$	8.05448	+	13.9508i	0.334733	+	0.579774i
$580$		0			0
$581$			30.4739i			1.26427i
$582$		0			0
$583$	21.1153	−	36.5727i	0.874505	−	1.51469i
$584$		0			0
$585$	0.251187	+	0.435069i	0.0103853	+	0.0179879i
$586$		0			0
$587$	16.4048	+	28.4140i	0.677100	+	1.17277i	0.975850	+	0.218440i	$0.0700969\pi$
$587$	16.4048	+	28.4140i	0.677100	+	1.17277i	−0.298750	+	0.954331i	$0.596570\pi$
$588$		0			0
$589$	−7.21019	+	4.16280i	−0.297091	+	0.171525i
$590$		0			0
$591$	61.0970			2.51320
$592$		0			0
$593$	−18.4707			−0.758502			−0.379251	−	0.925294i	$-0.623818\pi$
$593$	−18.4707			−0.758502			−0.379251	+	0.925294i	$0.623818\pi$
$594$		0			0
$595$	42.1056	−	24.3097i	1.72616	−	0.996599i
$596$		0			0
$597$	−7.81464	−	13.5354i	−0.319832	−	0.553965i
$598$		0			0
$599$	8.58765	+	14.8743i	0.350882	+	0.607746i	0.986404	−	0.164337i	$-0.0525485\pi$
$599$	8.58765	+	14.8743i	0.350882	+	0.607746i	−0.635522	+	0.772083i	$0.719215\pi$
$600$		0			0
$601$	6.94512	−	12.0293i	0.283297	−	0.490685i	−0.688898	−	0.724859i	$-0.741905\pi$
$601$	6.94512	−	12.0293i	0.283297	−	0.490685i	0.972195	+	0.234173i	$0.0752384\pi$
$602$		0			0
$603$			10.8410i			0.441481i
$604$		0			0
$605$	5.41895	+	9.38590i	0.220312	+	0.381591i
$606$		0			0
$607$	20.3273	+	11.7360i	0.825061	+	0.476349i	0.852159	−	0.523284i	$-0.175293\pi$
$607$	20.3273	+	11.7360i	0.825061	+	0.476349i	−0.0270977	+	0.999633i	$0.508627\pi$
$608$		0			0
$609$	−30.3213	−	17.5060i	−1.22868	−	0.709378i
$610$		0			0
$611$	−0.209002	−	0.362002i	−0.00845532	−	0.0146450i
$612$		0			0
$613$	−25.6964	−	14.8359i	−1.03787	−	0.599214i	−0.118641	−	0.992937i	$-0.537854\pi$
$613$	−25.6964	−	14.8359i	−1.03787	−	0.599214i	−0.919229	+	0.393723i	$0.871187\pi$
$614$		0			0
$615$		−	36.2539i		−	1.46190i
$616$		0			0
$617$	3.78696	−	6.55921i	0.152457	−	0.264064i	−0.779673	−	0.626187i	$-0.784615\pi$
$617$	3.78696	−	6.55921i	0.152457	−	0.264064i	0.932130	+	0.362123i	$0.117948\pi$
$618$		0			0
$619$			8.67027i			0.348487i	0.984703	+	0.174244i	$0.0557481\pi$
$619$			8.67027i			0.348487i	−0.984703	+	0.174244i	$0.944252\pi$
$620$		0			0
$621$	−2.51054			−0.100744
$622$		0			0
$623$		−	29.6942i		−	1.18967i
$624$		0			0
$625$	6.26758	+	10.8558i	0.250703	+	0.434230i
$626$		0			0
$627$	−24.1708	+	41.8650i	−0.965288	+	1.67193i
$628$		0			0
$629$	42.4480	−	20.4547i	1.69251	−	0.815583i
$630$		0			0
$631$	13.7075	+	7.91403i	0.545687	+	0.315052i	0.747381	−	0.664396i	$-0.231311\pi$
$631$	13.7075	+	7.91403i	0.545687	+	0.315052i	−0.201694	+	0.979449i	$0.564645\pi$
$632$		0			0
$633$	16.0113	+	27.7324i	0.636392	+	1.10226i
$634$		0			0
$635$	19.5470			0.775698
$636$		0			0
$637$	0.472408			0.0187175
$638$		0			0
$639$	−51.4685			−2.03606
$640$		0			0
$641$	7.17964	−	12.4355i	0.283579	−	0.491172i	−0.688685	−	0.725061i	$-0.741812\pi$
$641$	7.17964	−	12.4355i	0.283579	−	0.491172i	0.972263	+	0.233888i	$0.0751450\pi$
$642$		0			0
$643$	23.8158			0.939203			0.469602	−	0.882878i	$-0.344398\pi$
$643$	23.8158			0.939203			0.469602	+	0.882878i	$0.344398\pi$
$644$		0			0
$645$	20.0568	+	11.5798i	0.789735	+	0.455954i
$646$		0			0
$647$	41.9603	−	24.2258i	1.64963	−	0.952415i	0.672414	−	0.740175i	$-0.265258\pi$
$647$	41.9603	−	24.2258i	1.64963	−	0.952415i	0.977218	−	0.212240i	$-0.0680758\pi$
$648$		0			0
$649$	12.9274	+	7.46366i	0.507446	+	0.292974i
$650$		0			0
$651$	7.81208	−	13.5309i	0.306180	−	0.530319i
$652$		0			0
$653$	3.61083	+	6.25415i	0.141303	+	0.244744i	0.927988	−	0.372611i	$-0.121538\pi$
$653$	3.61083	+	6.25415i	0.141303	+	0.244744i	−0.786685	+	0.617355i	$0.788204\pi$
$654$		0			0
$655$	29.9041			1.16845
$656$		0			0
$657$	−23.9577	+	41.4959i	−0.934679	+	1.61891i
$658$		0			0
$659$	15.8560	−	9.15444i	0.617660	−	0.356606i	−0.158297	−	0.987392i	$-0.550600\pi$
$659$	15.8560	−	9.15444i	0.617660	−	0.356606i	0.775958	+	0.630785i	$0.217267\pi$
$660$		0			0
$661$	−3.03719	−	5.26057i	−0.118133	−	0.204613i	0.800895	−	0.598805i	$-0.204358\pi$
$661$	−3.03719	−	5.26057i	−0.118133	−	0.204613i	−0.919028	+	0.394193i	$0.871024\pi$
$662$		0			0
$663$	−0.843952	−	1.46177i	−0.0327764	−	0.0567704i
$664$		0			0
$665$	−29.4099			−1.14047
$666$		0			0
$667$			17.3964i			0.673593i
$668$		0			0
$669$	18.2302	−	10.5252i	0.704822	−	0.406929i
$670$		0			0
$671$	3.63414	−	2.09817i	0.140295	−	0.0809991i
$672$		0			0
$673$	−24.9903	−	43.2845i	−0.963305	−	1.66849i	−0.714101	−	0.700043i	$-0.753164\pi$
$673$	−24.9903	−	43.2845i	−0.963305	−	1.66849i	−0.249205	−	0.968451i	$-0.580169\pi$
$674$		0			0
$675$	−0.908671	−	0.524621i	−0.0349748	−	0.0201927i
$676$		0			0
$677$			39.6165i			1.52259i	0.648409	+	0.761293i	$0.275435\pi$
$677$			39.6165i			1.52259i	−0.648409	+	0.761293i	$0.724565\pi$
$678$		0			0
$679$	−28.7785	+	16.6153i	−1.10442	+	0.637636i
$680$		0			0
$681$	25.5182	+	14.7329i	0.977858	+	0.564566i
$682$		0			0
$683$	6.90066	−	11.9523i	0.264046	−	0.457342i	−0.703267	−	0.710926i	$-0.748276\pi$
$683$	6.90066	−	11.9523i	0.264046	−	0.457342i	0.967313	+	0.253584i	$0.0816095\pi$
$684$		0			0
$685$	−3.90751	−	6.76801i	−0.149298	−	0.258592i
$686$		0			0
$687$	−7.81816	+	13.5415i	−0.298282	+	0.516639i
$688$		0			0
$689$		−	0.891946i		−	0.0339804i
$690$		0			0
$691$	25.3492	+	14.6353i	0.964328	+	0.556755i	0.897502	−	0.441010i	$-0.145380\pi$
$691$	25.3492	+	14.6353i	0.964328	+	0.556755i	0.0668253	+	0.997765i	$0.478713\pi$
$692$		0			0
$693$		−	47.0359i		−	1.78674i
$694$		0			0
$695$			20.0893i			0.762032i
$696$		0			0
$697$			63.1542i			2.39214i
$698$		0			0
$699$	17.6246	−	10.1756i	0.666625	−	0.384876i
$700$		0			0
$701$	19.1123	−	33.1035i	0.721861	−	1.25030i	−0.238392	−	0.971169i	$-0.576620\pi$
$701$	19.1123	−	33.1035i	0.721861	−	1.25030i	0.960253	−	0.279131i	$-0.0900464\pi$
$702$		0			0
$703$	−28.4234	−	2.12302i	−1.07201	−	0.0800711i
$704$		0			0
$705$	−18.4400	−	10.6464i	−0.694492	−	0.400965i
$706$		0			0
$707$	1.05745	−	0.610517i	0.0397693	−	0.0229608i
$708$		0			0
$709$	−1.38765			−0.0521142			−0.0260571	−	0.999660i	$-0.508295\pi$
$709$	−1.38765			−0.0521142			−0.0260571	+	0.999660i	$0.508295\pi$
$710$		0			0
$711$			14.5707i			0.546443i
$712$		0			0
$713$	−7.76319			−0.290734
$714$		0			0
$715$	0.556693	+	0.321407i	0.0208191	+	0.0120199i
$716$		0			0
$717$	−11.7022			−0.437025
$718$		0			0
$719$	14.2789	−	24.7318i	0.532514	−	0.922341i	−0.466765	−	0.884381i	$-0.654581\pi$
$719$	14.2789	−	24.7318i	0.532514	−	0.922341i	0.999279	−	0.0379602i	$-0.0120860\pi$
$720$		0			0
$721$	−4.56013	+	2.63279i	−0.169828	+	0.0980502i
$722$		0			0
$723$	9.95321	−	17.2395i	0.370164	−	0.641143i
$724$		0			0
$725$	−3.63530	+	6.29652i	−0.135011	+	0.233847i
$726$		0			0
$727$	5.84591	−	3.37514i	0.216813	−	0.125177i	−0.387661	−	0.921802i	$-0.626717\pi$
$727$	5.84591	−	3.37514i	0.216813	−	0.125177i	0.604474	+	0.796625i	$0.293384\pi$
$728$		0			0
$729$	30.9725			1.14713
$730$		0			0
$731$	−34.9389	−	20.1720i	−1.29226	−	0.746088i
$732$		0			0
$733$	27.6648	−	15.9723i	1.02182	−	0.589949i	0.107191	−	0.994238i	$-0.465814\pi$
$733$	27.6648	−	15.9723i	1.02182	−	0.589949i	0.914631	+	0.404289i	$0.132481\pi$
$734$		0			0
$735$	20.8401	−	12.0320i	0.768698	−	0.443808i
$736$		0			0
$737$	6.93583	+	12.0132i	0.255485	+	0.442512i
$738$		0			0
$739$		−	14.9757i		−	0.550890i	−0.961317	−	0.275445i	$-0.911175\pi$
$739$		−	14.9757i		−	0.550890i	0.961317	−	0.275445i	$-0.0888252\pi$
$740$		0			0
$741$			1.02102i			0.0375080i
$742$		0			0
$743$	−23.6302	−	40.9287i	−0.866909	−	1.50153i	−0.865139	−	0.501532i	$-0.832770\pi$
$743$	−23.6302	−	40.9287i	−0.866909	−	1.50153i	−0.00176941	−	0.999998i	$-0.500563\pi$
$744$		0			0
$745$	23.6909	−	13.6779i	0.867966	−	0.501120i
$746$		0			0
$747$	24.1978	−	13.9706i	0.885352	−	0.511158i
$748$		0			0
$749$	18.0829	+	10.4402i	0.660735	+	0.381476i
$750$		0			0
$751$	−12.6722			−0.462414			−0.231207	−	0.972905i	$-0.574267\pi$
$751$	−12.6722			−0.462414			−0.231207	+	0.972905i	$0.574267\pi$
$752$		0			0
$753$	−63.1335	+	36.4501i	−2.30071	+	1.32832i
$754$		0			0
$755$	−7.11594	+	12.3252i	−0.258976	+	0.448559i
$756$		0			0
$757$	−3.24429	+	5.61927i	−0.117916	+	0.204236i	−0.918941	−	0.394394i	$-0.870955\pi$
$757$	−3.24429	+	5.61927i	−0.117916	+	0.204236i	0.801026	+	0.598630i	$0.204288\pi$
$758$		0			0
$759$	−39.0370	+	22.5380i	−1.41695	+	0.818077i
$760$		0			0
$761$	11.5291	−	19.9690i	0.417931	−	0.723877i	−0.577800	−	0.816178i	$-0.696089\pi$
$761$	11.5291	−	19.9690i	0.417931	−	0.723877i	0.995731	+	0.0923007i	$0.0294221\pi$
$762$		0			0
$763$	−44.6540			−1.61658
$764$		0			0
$765$	−38.6062	−	22.2893i	−1.39581	−	0.805871i
$766$		0			0
$767$	0.315278			0.0113840
$768$		0			0
$769$		−	25.3546i		−	0.914308i	−0.889387	−	0.457154i	$-0.848869\pi$
$769$		−	25.3546i		−	0.914308i	0.889387	−	0.457154i	$-0.151131\pi$
$770$		0			0
$771$	−12.9849			−0.467639
$772$		0			0
$773$	5.23763	−	3.02395i	0.188384	−	0.108764i	−0.402842	−	0.915270i	$-0.631977\pi$
$773$	5.23763	−	3.02395i	0.188384	−	0.108764i	0.591226	+	0.806506i	$0.298644\pi$
$774$		0			0
$775$	−2.80983	−	1.62226i	−0.100932	−	0.0582732i
$776$		0			0
$777$	48.1862	−	23.2198i	1.72867	−	0.833007i
$778$		0			0
$779$	19.1010	−	33.0840i	0.684366	−	1.18536i
$780$		0			0
$781$	−57.0335	+	32.9283i	−2.04082	+	1.17827i
$782$		0			0
$783$			2.28777i			0.0817583i
$784$		0			0
$785$		−	2.59787i		−	0.0927219i
$786$		0			0
$787$		−	34.4150i		−	1.22676i	−0.789786	−	0.613382i	$-0.789809\pi$
$787$		−	34.4150i		−	1.22676i	0.789786	−	0.613382i	$-0.210191\pi$
$788$		0			0
$789$	51.1625	+	29.5387i	1.82143	+	1.05160i
$790$		0			0
$791$			38.2606i			1.36039i
$792$		0			0
$793$	0.0443153	−	0.0767563i	0.00157368	−	0.00272570i
$794$		0			0
$795$	−22.7174	−	39.3478i	−0.805705	−	1.39552i
$796$		0			0
$797$	−14.2093	+	24.6113i	−0.503321	+	0.871777i	0.496672	+	0.867938i	$0.334555\pi$
$797$	−14.2093	+	24.6113i	−0.503321	+	0.871777i	−0.999993	+	0.00383867i	$0.998778\pi$
$798$		0			0
$799$	32.1225	+	18.5460i	1.13641	+	0.656109i
$800$		0			0
$801$	−23.5786	+	13.6131i	−0.833110	+	0.480997i
$802$		0			0
$803$			61.3102i			2.16359i
$804$		0			0
$805$	−23.7492	−	13.7116i	−0.837049	−	0.483271i
$806$		0			0
$807$	1.15359	+	1.99807i	0.0406082	+	0.0703355i
$808$		0			0
$809$	−31.5871	+	18.2368i	−1.11054	+	0.641172i	−0.938970	−	0.344000i	$-0.888218\pi$
$809$	−31.5871	+	18.2368i	−1.11054	+	0.641172i	−0.171572	+	0.985172i	$0.554885\pi$
$810$		0			0
$811$	0.462912	−	0.267262i	0.0162550	−	0.00938485i	−0.491850	−	0.870680i	$-0.663679\pi$
$811$	0.462912	−	0.267262i	0.0162550	−	0.00938485i	0.508106	+	0.861295i	$0.330346\pi$
$812$		0			0
$813$			63.2537i			2.21840i
$814$		0			0
$815$	−1.12336			−0.0393494
$816$		0			0
$817$	12.2021	+	21.1346i	0.426896	+	0.739406i
$818$		0			0
$819$	−0.496719	−	0.860343i	−0.0173568	−	0.0300628i
$820$		0			0
$821$	18.3763	−	10.6096i	0.641337	−	0.370276i	−0.143792	−	0.989608i	$-0.545930\pi$
$821$	18.3763	−	10.6096i	0.641337	−	0.370276i	0.785129	+	0.619332i	$0.212596\pi$
$822$		0			0
$823$	0.842414	−	1.45910i	0.0293647	−	0.0508611i	−0.850970	−	0.525215i	$-0.823985\pi$
$823$	0.842414	−	1.45910i	0.0293647	−	0.0508611i	0.880334	+	0.474354i	$0.157318\pi$
$824$		0			0
$825$	−18.8389			−0.655885
$826$		0			0
$827$	10.2285	+	17.7164i	0.355681	+	0.616058i	0.987234	−	0.159275i	$-0.0509155\pi$
$827$	10.2285	+	17.7164i	0.355681	+	0.616058i	−0.631553	+	0.775333i	$0.717582\pi$
$828$		0			0
$829$	2.65709	−	4.60221i	0.0922844	−	0.159841i	−0.816188	−	0.577787i	$-0.803916\pi$
$829$	2.65709	−	4.60221i	0.0922844	−	0.159841i	0.908472	+	0.417946i	$0.137250\pi$
$830$		0			0
$831$	−29.7560	−	17.1796i	−1.03222	−	0.595954i
$832$		0			0
$833$	−36.3034	+	20.9598i	−1.25784	+	0.726213i
$834$		0			0
$835$	−31.4783	−	18.1740i	−1.08935	−	0.628937i
$836$		0			0
$837$	−1.02092			−0.0352882
$838$		0			0
$839$	6.99642	−	12.1182i	0.241543	−	0.418365i	−0.719611	−	0.694378i	$-0.755680\pi$
$839$	6.99642	−	12.1182i	0.241543	−	0.418365i	0.961154	+	0.276012i	$0.0890131\pi$
$840$		0			0
$841$	−13.1472			−0.453351
$842$		0			0
$843$	−43.4687			−1.49714
$844$		0			0
$845$	−23.1466			−0.796268
$846$		0			0
$847$	−10.7159	−	18.5605i	−0.368203	−	0.637746i
$848$		0			0
$849$	27.2031	+	15.7057i	0.933607	+	0.539018i
$850$		0			0
$851$	−21.9627	−	14.9660i	−0.752873	−	0.513029i
$852$		0			0
$853$	20.1421	−	34.8872i	0.689654	−	1.19452i	−0.282296	−	0.959327i	$-0.591096\pi$
$853$	20.1421	−	34.8872i	0.689654	−	1.19452i	0.971950	−	0.235188i	$-0.0755707\pi$
$854$		0			0
$855$	13.4828	+	23.3530i	0.461103	+	0.798654i
$856$		0			0
$857$		−	5.85118i		−	0.199872i	−0.994994	−	0.0999362i	$-0.968136\pi$
$857$		−	5.85118i		−	0.199872i	0.994994	−	0.0999362i	$-0.0318639\pi$
$858$		0			0
$859$	−22.6563			−0.773024			−0.386512	−	0.922284i	$-0.626320\pi$
$859$	−22.6563			−0.773024			−0.386512	+	0.922284i	$0.626320\pi$
$860$		0			0
$861$			71.6915i			2.44324i
$862$		0			0
$863$	−0.840900	+	1.45648i	−0.0286246	+	0.0495792i	−0.879983	−	0.475005i	$-0.842446\pi$
$863$	−0.840900	+	1.45648i	−0.0286246	+	0.0495792i	0.851358	+	0.524585i	$0.175779\pi$
$864$		0			0
$865$		−	33.2070i		−	1.12907i
$866$		0			0
$867$	92.9634	+	53.6724i	3.15720	+	1.82281i
$868$		0			0
$869$	9.32195	+	16.1461i	0.316226	+	0.547719i
$870$		0			0
$871$	0.253730	+	0.146491i	0.00859730	+	0.00496365i
$872$		0			0
$873$	26.3867	+	15.2344i	0.893055	+	0.515606i
$874$		0			0
$875$	−21.4216	−	37.1033i	−0.724182	−	1.25432i
$876$		0			0
$877$			2.87786i			0.0971785i	0.998819	+	0.0485893i	$0.0154725\pi$
$877$			2.87786i			0.0971785i	−0.998819	+	0.0485893i	$0.984527\pi$
$878$		0			0
$879$	−41.0100	+	71.0314i	−1.38323	+	2.39583i
$880$		0			0
$881$	10.3403	+	17.9100i	0.348375	+	0.603403i	0.985961	−	0.166976i	$-0.0534004\pi$
$881$	10.3403	+	17.9100i	0.348375	+	0.603403i	−0.637586	+	0.770379i	$0.720067\pi$
$882$		0			0
$883$	−17.3621	−	30.0720i	−0.584280	−	1.01200i	−0.994965	−	0.100225i	$-0.968044\pi$
$883$	−17.3621	−	30.0720i	−0.584280	−	1.01200i	0.410685	−	0.911777i	$-0.365290\pi$
$884$		0			0
$885$	13.9083	−	8.02998i	0.467523	−	0.269925i
$886$		0			0
$887$	−41.8321			−1.40459			−0.702293	−	0.711888i	$-0.747840\pi$
$887$	−41.8321			−1.40459			−0.702293	+	0.711888i	$0.747840\pi$
$888$		0			0
$889$	−38.6539			−1.29641
$890$		0			0
$891$	29.5535	−	17.0627i	0.990079	−	0.571622i
$892$		0			0
$893$	−11.2185	−	19.4310i	−0.375412	−	0.650233i
$894$		0			0
$895$	−5.30449	−	9.18765i	−0.177310	−	0.307109i
$896$		0			0
$897$	−0.476022	+	0.824495i	−0.0158939	+	0.0275291i
$898$		0			0
$899$			7.07435i			0.235943i
$900$		0			0
$901$	39.5738	+	68.5438i	1.31839	+	2.28352i
$902$		0			0
$903$	−39.6620	−	22.8989i	−1.31987	−	0.762027i
$904$		0			0
$905$	31.0504	+	17.9270i	1.03215	+	0.595912i
$906$		0			0
$907$	−5.48500	−	9.50029i	−0.182126	−	0.315452i	0.760478	−	0.649364i	$-0.224965\pi$
$907$	−5.48500	−	9.50029i	−0.182126	−	0.315452i	−0.942604	+	0.333912i	$0.891631\pi$
$908$		0			0
$909$	−0.969561	−	0.559777i	−0.0321583	−	0.0185666i
$910$		0			0
$911$		−	18.7503i		−	0.621225i	−0.950537	−	0.310612i	$-0.899466\pi$
$911$		−	18.7503i		−	0.621225i	0.950537	−	0.310612i	$-0.100534\pi$
$912$		0			0
$913$	17.8761	−	30.9624i	0.591613	−	1.02470i
$914$		0			0
$915$		−	4.51476i		−	0.149253i
$916$		0			0
$917$	−59.1350			−1.95281
$918$		0			0
$919$		−	14.7395i		−	0.486211i	−0.970000	−	0.243106i	$-0.921834\pi$
$919$		−	14.7395i		−	0.486211i	0.970000	−	0.243106i	$-0.0781662\pi$
$920$		0			0
$921$	4.30779	+	7.46131i	0.141947	+	0.245859i
$922$		0			0
$923$	−0.695474	+	1.20460i	−0.0228918	+	0.0396498i
$924$		0			0
$925$	−4.82183	−	10.0064i	−0.158541	−	0.329007i
$926$		0			0
$927$	4.18114	+	2.41398i	0.137326	+	0.0792855i
$928$		0			0
$929$	7.89990	+	13.6830i	0.259187	+	0.448926i	0.966024	−	0.258451i	$-0.0832119\pi$
$929$	7.89990	+	13.6830i	0.259187	+	0.448926i	−0.706837	+	0.707376i	$0.749879\pi$
$930$		0			0
$931$	25.3572			0.831049
$932$		0			0
$933$	−16.9141			−0.553742
$934$		0			0
$935$	−57.0406			−1.86543
$936$		0			0
$937$	−7.48297	+	12.9609i	−0.244458	+	0.423414i	−0.961979	−	0.273123i	$-0.911943\pi$
$937$	−7.48297	+	12.9609i	−0.244458	+	0.423414i	0.717521	+	0.696537i	$0.245277\pi$
$938$		0			0
$939$	−20.1276			−0.656841
$940$		0			0
$941$	−42.0222	−	24.2615i	−1.36988	−	0.790903i	−0.378971	−	0.925409i	$-0.623722\pi$
$941$	−42.0222	−	24.2615i	−1.36988	−	0.790903i	−0.990913	+	0.134506i	$0.957055\pi$
$942$		0			0
$943$	30.8491	−	17.8107i	1.00458	−	0.579997i
$944$		0			0
$945$	−3.12321	−	1.80319i	−0.101598	−	0.0586577i
$946$		0			0
$947$	1.45263	−	2.51603i	0.0472042	−	0.0817600i	−0.841458	−	0.540323i	$-0.818302\pi$
$947$	1.45263	−	2.51603i	0.0472042	−	0.0817600i	0.888662	+	0.458563i	$0.151636\pi$
$948$		0			0
$949$	0.647462	+	1.12144i	0.0210175	+	0.0364034i
$950$		0			0
$951$	−14.9436			−0.484579
$952$		0			0
$953$	−1.21050	+	2.09665i	−0.0392119	+	0.0679171i	−0.884965	−	0.465657i	$-0.845818\pi$
$953$	−1.21050	+	2.09665i	−0.0392119	+	0.0679171i	0.845753	+	0.533574i	$0.179151\pi$
$954$		0			0
$955$	−4.05992	+	2.34400i	−0.131376	+	0.0758500i
$956$		0			0
$957$	20.5381	+	35.5731i	0.663904	+	1.14992i
$958$		0			0
$959$	7.72705	+	13.3836i	0.249519	+	0.432180i
$960$		0			0
$961$	27.8431			0.898163
$962$		0			0
$963$		−	19.1450i		−	0.616939i
$964$		0			0
$965$	9.95740	−	5.74891i	0.320540	−	0.185064i
$966$		0			0
$967$	−47.0633	+	27.1720i	−1.51345	+	0.873793i	−0.513579	+	0.858042i	$0.671681\pi$
$967$	−47.0633	+	27.1720i	−1.51345	+	0.873793i	−0.999876	+	0.0157510i	$0.994986\pi$
$968$		0			0
$969$	−45.3003	−	78.4625i	−1.45526	−	2.52058i
$970$		0			0
$971$	35.3477	+	20.4080i	1.13436	+	0.654925i	0.945029	−	0.326988i	$-0.106034\pi$
$971$	35.3477	+	20.4080i	1.13436	+	0.654925i	0.189335	+	0.981913i	$0.439367\pi$
$972$		0			0
$973$		−	39.7264i		−	1.27357i
$974$		0			0
$975$	−0.344586	+	0.198947i	−0.0110356	+	0.00637139i
$976$		0			0
$977$	−17.1810	−	9.91943i	−0.549667	−	0.317351i	0.199320	−	0.979934i	$-0.436127\pi$
$977$	−17.1810	−	9.91943i	−0.549667	−	0.317351i	−0.748988	+	0.662584i	$0.769460\pi$
$978$		0			0
$979$	−17.4187	+	30.1701i	−0.556704	+	0.964240i
$980$		0			0
$981$	20.4714	+	35.4575i	0.653601	+	1.13207i
$982$		0			0
$983$	11.1646	−	19.3376i	0.356095	−	0.616775i	−0.631209	−	0.775612i	$-0.717441\pi$
$983$	11.1646	−	19.3376i	0.356095	−	0.616775i	0.987305	+	0.158837i	$0.0507745\pi$
$984$		0			0
$985$		−	43.6082i		−	1.38947i
$986$		0			0
$987$	36.4649	+	21.0530i	1.16069	+	0.670126i
$988$		0			0
$989$			22.7556i			0.723585i
$990$		0			0
$991$			43.0109i			1.36629i	0.730285	+	0.683143i	$0.239387\pi$
$991$			43.0109i			1.36629i	−0.730285	+	0.683143i	$0.760613\pi$
$992$		0			0
$993$		−	81.3157i		−	2.58048i
$994$		0			0
$995$	−9.66090	+	5.57772i	−0.306271	+	0.176826i
$996$		0			0
$997$	−12.6617	+	21.9308i	−0.401001	+	0.694554i	−0.993847	−	0.110762i	$-0.964671\pi$
$997$	−12.6617	+	21.9308i	−0.401001	+	0.694554i	0.592846	+	0.805316i	$0.298004\pi$
$998$		0			0
$999$	−2.88828	−	1.96815i	−0.0913810	−	0.0622696i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1184.2.y.a.1137.32		72
4.3	odd	2		296.2.q.a.101.11	yes	72
8.3	odd	2		296.2.q.a.101.3	yes	72
8.5	even	2	inner	1184.2.y.a.1137.5		72
37.11	even	6	inner	1184.2.y.a.529.5		72
148.11	odd	6		296.2.q.a.85.3	✓	72
296.11	odd	6		296.2.q.a.85.11	yes	72
296.85	even	6	inner	1184.2.y.a.529.32		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
296.2.q.a.85.3	✓	72	148.11	odd	6
296.2.q.a.85.11	yes	72	296.11	odd	6
296.2.q.a.101.3	yes	72	8.3	odd	2
296.2.q.a.101.11	yes	72	4.3	odd	2
1184.2.y.a.529.5		72	37.11	even	6	inner
1184.2.y.a.529.32		72	296.85	even	6	inner
1184.2.y.a.1137.5		72	8.5	even	2	inner
1184.2.y.a.1137.32		72	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:	\( N \)	\(=\)	\( 1184 = 2^{5} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1184.y (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.16163 - 1.24802i) q^{3} +(-0.890777 - 1.54287i) q^{5} +(1.76150 + 3.05101i) q^{7} +(1.61510 - 2.79744i) q^{9} -4.13321i q^{11} +(-0.0436485 - 0.0756014i) q^{13} +(-3.85106 - 2.22341i) q^{15} +(6.70855 + 3.87318i) q^{17} +(-2.34289 - 4.05801i) q^{19} +(7.61542 + 4.39677i) q^{21} -4.36925i q^{23} +(0.913033 - 1.58142i) q^{25} -0.574592i q^{27} -3.98156 q^{29} -1.77678i q^{31} +(-5.15832 - 8.93447i) q^{33} +(3.13820 - 5.43553i) q^{35} +(3.42531 - 5.02666i) q^{37} +(-0.188704 - 0.108948i) q^{39} +(4.07638 + 7.06049i) q^{41} -5.20812 q^{43} -5.75478 q^{45} +4.78830 q^{47} +(-2.70576 + 4.68651i) q^{49} +19.3352 q^{51} +(8.84851 + 5.10869i) q^{53} +(-6.37700 + 3.68176i) q^{55} +(-10.1289 - 5.84795i) q^{57} +(-1.80578 + 3.12770i) q^{59} +(0.507638 + 0.879255i) q^{61} +11.3800 q^{63} +(-0.0777621 + 0.134688i) q^{65} +(-2.90651 + 1.67808i) q^{67} +(-5.45291 - 9.44471i) q^{69} +(-7.96677 - 13.7988i) q^{71} -14.8336 q^{73} -4.55793i q^{75} +(12.6104 - 7.28064i) q^{77} +(-3.90643 + 2.25538i) q^{79} +(4.12820 + 7.15025i) q^{81} +(7.49112 + 4.32500i) q^{83} -13.8006i q^{85} +(-8.60666 + 4.96906i) q^{87} +(-7.29943 - 4.21433i) q^{89} +(0.153773 - 0.266343i) q^{91} +(-2.21745 - 3.84074i) q^{93} +(-4.17399 + 7.22956i) q^{95} +9.43247i q^{97} +(-11.5624 - 6.67555i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 2 q^{7} + 30 q^{9} + 6 q^{15} - 12 q^{17} - 32 q^{25} + 4 q^{33} + 6 q^{39} - 32 q^{47} - 18 q^{49} - 24 q^{55} - 6 q^{57} - 8 q^{63} + 6 q^{65} - 18 q^{71} - 64 q^{73} - 54 q^{79} - 16 q^{81} + 108 q^{87}+ \cdots - 50 q^{95}+O(q^{100}) \) 72 * q - 2 * q^7 + 30 * q^9 + 6 * q^15 - 12 * q^17 - 32 * q^25 + 4 * q^33 + 6 * q^39 - 32 * q^47 - 18 * q^49 - 24 * q^55 - 6 * q^57 - 8 * q^63 + 6 * q^65 - 18 * q^71 - 64 * q^73 - 54 * q^79 - 16 * q^81 + 108 * q^87 - 36 * q^89 - 50 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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