LMFDB - Embedded newform 1008.2.cz.g.367.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(367,1008)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1008, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 4, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1008.367"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.cz (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,-3,0,-3,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			367.7
Character	$\chi$	$=$	1008.367
Dual form			1008.2.cz.g.607.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.597950 - 1.62556i) q^{3} +(2.47441 + 1.42860i) q^{5} +(-2.59845 - 0.498066i) q^{7} +(-2.28491 + 1.94401i) q^{9} +(1.95865 - 1.13083i) q^{11} +(-5.59072 + 3.22780i) q^{13} +(0.842707 - 4.87654i) q^{15} +(-4.74820 - 2.74137i) q^{17} +(-1.59123 - 2.75609i) q^{19} +(0.744104 + 4.52176i) q^{21} +(-5.17495 - 2.98776i) q^{23} +(1.58180 + 2.73976i) q^{25} +(4.52638 + 2.55184i) q^{27} +(1.06838 - 1.85049i) q^{29} -4.03351 q^{31} +(-3.00940 - 2.50773i) q^{33} +(-5.71808 - 4.94456i) q^{35} +(-5.06680 - 8.77595i) q^{37} +(8.58997 + 7.15800i) q^{39} +(9.02256 - 5.20918i) q^{41} +(0.0397018 + 0.0229218i) q^{43} +(-8.43102 + 1.54606i) q^{45} -5.74706 q^{47} +(6.50386 + 2.58840i) q^{49} +(-1.61709 + 9.35770i) q^{51} +(-2.43844 + 4.22350i) q^{53} +6.46199 q^{55} +(-3.52873 + 4.23466i) q^{57} -6.20774 q^{59} +6.98818i q^{61} +(6.90547 - 3.91338i) q^{63} -18.4450 q^{65} -7.88250i q^{67} +(-1.76243 + 10.1987i) q^{69} +15.5442i q^{71} +(11.0585 + 6.38460i) q^{73} +(3.50781 - 4.20956i) q^{75} +(-5.65267 + 1.96285i) q^{77} -12.0116i q^{79} +(1.44163 - 8.88379i) q^{81} +(-1.88456 + 3.26415i) q^{83} +(-7.83265 - 13.5666i) q^{85} +(-3.64693 - 0.630220i) q^{87} +(-3.95155 + 2.28143i) q^{89} +(16.1349 - 5.60273i) q^{91} +(2.41184 + 6.55672i) q^{93} -9.09294i q^{95} +(4.62721 + 2.67152i) q^{97} +(-2.27700 + 6.39147i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{3} - 3 q^{5} + 4 q^{7} + 17 q^{9} - 9 q^{11} - 3 q^{13} - 6 q^{15} - 3 q^{17} - 4 q^{19} + 13 q^{21} - 6 q^{23} + 15 q^{25} + 9 q^{27} + 18 q^{29} + 34 q^{31} - 21 q^{33} - 42 q^{35} - 3 q^{37}+ \cdots + 30 q^{99}+O(q^{100}) $ 24 * q - 3 * q^3 - 3 * q^5 + 4 * q^7 + 17 * q^9 - 9 * q^11 - 3 * q^13 - 6 * q^15 - 3 * q^17 - 4 * q^19 + 13 * q^21 - 6 * q^23 + 15 * q^25 + 9 * q^27 + 18 * q^29 + 34 * q^31 - 21 * q^33 - 42 * q^35 - 3 * q^37 + 27 * q^39 + 36 * q^41 + 24 * q^43 + 21 * q^45 - 42 * q^47 + 30 * q^49 - 6 * q^51 - 12 * q^53 - 30 * q^55 - 13 * q^57 - 12 * q^59 - 3 * q^63 + 6 * q^69 + 48 * q^73 + 36 * q^75 - 48 * q^77 - 31 * q^81 - 48 * q^83 - 21 * q^85 + 15 * q^87 + 39 * q^89 + 9 * q^91 + 10 * q^93 + 3 * q^97 + 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.597950	−	1.62556i	−0.345227	−	0.938519i
$3$	−0.597950	−	1.62556i	−0.345227	−	0.938519i
$4$		0			0
$5$	2.47441	+	1.42860i	1.10659	+	0.638890i	0.937944	−	0.346787i	$-0.112727\pi$
$5$	2.47441	+	1.42860i	1.10659	+	0.638890i	0.168646	+	0.985677i	$0.446061\pi$
$6$		0			0
$7$	−2.59845	−	0.498066i	−0.982121	−	0.188251i
$7$	−2.59845	−	0.498066i	−0.982121	−	0.188251i
$8$		0			0
$9$	−2.28491	+	1.94401i	−0.761637	+	0.648004i
$10$		0			0
$11$	1.95865	−	1.13083i	0.590554	−	0.340957i	−0.174762	−	0.984611i	$-0.555916\pi$
$11$	1.95865	−	1.13083i	0.590554	−	0.340957i	0.765317	+	0.643654i	$0.222582\pi$
$12$		0			0
$13$	−5.59072	+	3.22780i	−1.55059	+	0.895232i	−0.552493	+	0.833517i	$0.686323\pi$
$13$	−5.59072	+	3.22780i	−1.55059	+	0.895232i	−0.998094	+	0.0617145i	$0.980343\pi$
$14$		0			0
$15$	0.842707	−	4.87654i	0.217586	−	1.25912i
$16$		0			0
$17$	−4.74820	−	2.74137i	−1.15161	−	0.664880i	−0.202328	−	0.979318i	$-0.564851\pi$
$17$	−4.74820	−	2.74137i	−1.15161	−	0.664880i	−0.949278	+	0.314437i	$0.898184\pi$
$18$		0			0
$19$	−1.59123	−	2.75609i	−0.365054	−	0.632292i	0.623731	−	0.781639i	$-0.285616\pi$
$19$	−1.59123	−	2.75609i	−0.365054	−	0.632292i	−0.988785	+	0.149347i	$0.952283\pi$
$20$		0			0
$21$	0.744104	+	4.52176i	0.162377	+	0.986729i
$22$		0			0
$23$	−5.17495	−	2.98776i	−1.07905	−	0.622990i	−0.148411	−	0.988926i	$-0.547416\pi$
$23$	−5.17495	−	2.98776i	−1.07905	−	0.622990i	−0.930640	+	0.365936i	$0.880749\pi$
$24$		0			0
$25$	1.58180	+	2.73976i	0.316360	+	0.547952i
$26$		0			0
$27$	4.52638	+	2.55184i	0.871102	+	0.491103i
$28$		0			0
$29$	1.06838	−	1.85049i	0.198394	−	0.343628i	−0.749614	−	0.661875i	$-0.769761\pi$
$29$	1.06838	−	1.85049i	0.198394	−	0.343628i	0.948008	+	0.318247i	$0.103094\pi$
$30$		0			0
$31$	−4.03351			−0.724440			−0.362220	−	0.932093i	$-0.617981\pi$
$31$	−4.03351			−0.724440			−0.362220	+	0.932093i	$0.617981\pi$
$32$		0			0
$33$	−3.00940	−	2.50773i	−0.523870	−	0.436539i
$34$		0			0
$35$	−5.71808	−	4.94456i	−0.966533	−	0.835784i
$36$		0			0
$37$	−5.06680	−	8.77595i	−0.832977	−	1.44276i	−0.895667	−	0.444725i	$-0.853301\pi$
$37$	−5.06680	−	8.77595i	−0.832977	−	1.44276i	0.0626906	−	0.998033i	$-0.480032\pi$
$38$		0			0
$39$	8.58997	+	7.15800i	1.37550	+	1.14620i
$40$		0			0
$41$	9.02256	−	5.20918i	1.40909	−	0.813537i	0.413788	−	0.910373i	$-0.364206\pi$
$41$	9.02256	−	5.20918i	1.40909	−	0.813537i	0.995300	+	0.0968362i	$0.0308723\pi$
$42$		0			0
$43$	0.0397018	+	0.0229218i	0.00605446	+	0.00349555i	0.503024	−	0.864272i	$-0.332221\pi$
$43$	0.0397018	+	0.0229218i	0.00605446	+	0.00349555i	−0.496970	+	0.867768i	$0.665554\pi$
$44$		0			0
$45$	−8.43102	+	1.54606i	−1.25682	+	0.230472i
$46$		0			0
$47$	−5.74706			−0.838295			−0.419147	−	0.907918i	$-0.637671\pi$
$47$	−5.74706			−0.838295			−0.419147	+	0.907918i	$0.637671\pi$
$48$		0			0
$49$	6.50386	+	2.58840i	0.929123	+	0.369771i
$50$		0			0
$51$	−1.61709	+	9.35770i	−0.226438	+	1.31034i
$52$		0			0
$53$	−2.43844	+	4.22350i	−0.334945	+	0.580142i	−0.983474	−	0.181048i	$-0.942051\pi$
$53$	−2.43844	+	4.22350i	−0.334945	+	0.580142i	0.648529	+	0.761190i	$0.275384\pi$
$54$		0			0
$55$	6.46199			0.871335
$56$		0			0
$57$	−3.52873	+	4.23466i	−0.467391	+	0.560894i
$58$		0			0
$59$	−6.20774			−0.808179			−0.404090	−	0.914719i	$-0.632412\pi$
$59$	−6.20774			−0.808179			−0.404090	+	0.914719i	$0.632412\pi$
$60$		0			0
$61$			6.98818i			0.894744i	0.894348	+	0.447372i	$0.147640\pi$
$61$			6.98818i			0.894744i	−0.894348	+	0.447372i	$0.852360\pi$
$62$		0			0
$63$	6.90547	−	3.91338i	0.870007	−	0.493039i
$64$		0			0
$65$	−18.4450			−2.28782
$66$		0			0
$67$		−	7.88250i		−	0.963001i	−0.876446	−	0.481500i	$-0.840092\pi$
$67$		−	7.88250i		−	0.963001i	0.876446	−	0.481500i	$-0.159908\pi$
$68$		0			0
$69$	−1.76243	+	10.1987i	−0.212171	+	1.22778i
$70$		0			0
$71$			15.5442i			1.84475i	0.386291	+	0.922377i	$0.373756\pi$
$71$			15.5442i			1.84475i	−0.386291	+	0.922377i	$0.626244\pi$
$72$		0			0
$73$	11.0585	+	6.38460i	1.29429	+	0.747261i	0.979412	−	0.201870i	$-0.0647018\pi$
$73$	11.0585	+	6.38460i	1.29429	+	0.747261i	0.314882	+	0.949131i	$0.398035\pi$
$74$		0			0
$75$	3.50781	−	4.20956i	0.405047	−	0.486078i
$76$		0			0
$77$	−5.65267	+	1.96285i	−0.644181	+	0.223688i
$78$		0			0
$79$		−	12.0116i		−	1.35141i	−0.737172	−	0.675706i	$-0.763839\pi$
$79$		−	12.0116i		−	1.35141i	0.737172	−	0.675706i	$-0.236161\pi$
$80$		0			0
$81$	1.44163	−	8.88379i	0.160182	−	0.987088i
$82$		0			0
$83$	−1.88456	+	3.26415i	−0.206857	+	0.358287i	−0.950723	−	0.310042i	$-0.899657\pi$
$83$	−1.88456	+	3.26415i	−0.206857	+	0.358287i	0.743866	+	0.668329i	$0.232990\pi$
$84$		0			0
$85$	−7.83265	−	13.5666i	−0.849571	−	1.47150i
$86$		0			0
$87$	−3.64693	−	0.630220i	−0.390992	−	0.0675667i
$88$		0			0
$89$	−3.95155	+	2.28143i	−0.418864	+	0.241831i	−0.694591	−	0.719405i	$-0.744415\pi$
$89$	−3.95155	+	2.28143i	−0.418864	+	0.241831i	0.275727	+	0.961236i	$0.411081\pi$
$90$		0			0
$91$	16.1349	−	5.60273i	1.69139	−	0.587326i
$92$		0			0
$93$	2.41184	+	6.55672i	0.250096	+	0.679901i
$94$		0			0
$95$		−	9.09294i		−	0.932916i
$96$		0			0
$97$	4.62721	+	2.67152i	0.469822	+	0.271252i	0.716165	−	0.697931i	$-0.245896\pi$
$97$	4.62721	+	2.67152i	0.469822	+	0.271252i	−0.246343	+	0.969183i	$0.579229\pi$
$98$		0			0
$99$	−2.27700	+	6.39147i	−0.228847	+	0.642367i
$100$		0			0
$101$	−5.16618	+	2.98270i	−0.514055	+	0.296790i	−0.734499	−	0.678610i	$-0.762583\pi$
$101$	−5.16618	+	2.98270i	−0.514055	+	0.296790i	0.220444	+	0.975400i	$0.429249\pi$
$102$		0			0
$103$	−4.43678	+	7.68473i	−0.437169	+	0.757199i	−0.997470	−	0.0710903i	$-0.977352\pi$
$103$	−4.43678	+	7.68473i	−0.437169	+	0.757199i	0.560301	+	0.828289i	$0.310685\pi$
$104$		0			0
$105$	−4.61857	+	12.2517i	−0.450726	+	1.19564i
$106$		0			0
$107$	−5.10984	+	2.95016i	−0.493986	+	0.285203i	−0.726227	−	0.687455i	$-0.758728\pi$
$107$	−5.10984	+	2.95016i	−0.493986	+	0.285203i	0.232240	+	0.972658i	$0.425394\pi$
$108$		0			0
$109$	−0.416247	+	0.720960i	−0.0398692	+	0.0690555i	−0.885271	−	0.465075i	$-0.846027\pi$
$109$	−0.416247	+	0.720960i	−0.0398692	+	0.0690555i	0.845402	+	0.534130i	$0.179361\pi$
$110$		0			0
$111$	−11.2362	+	13.4840i	−1.06649	+	1.27984i
$112$		0			0
$113$	−0.0601629	−	0.104205i	−0.00565965	−	0.00980279i	0.863182	−	0.504893i	$-0.168468\pi$
$113$	−0.0601629	−	0.104205i	−0.00565965	−	0.00980279i	−0.868841	+	0.495091i	$0.835135\pi$
$114$		0			0
$115$	−8.53662	−	14.7859i	−0.796044	−	1.37879i
$116$		0			0
$117$	6.49941	−	18.2437i	0.600870	−	1.68663i
$118$		0			0
$119$	10.9726	+	9.48823i	1.00585	+	0.869784i
$120$		0			0
$121$	−2.94247	+	5.09650i	−0.267497	+	0.463319i
$122$		0			0
$123$	−13.8629	−	11.5519i	−1.24998	−	1.04160i
$124$		0			0
$125$		−	5.24696i		−	0.469302i
$126$		0			0
$127$			5.57295i			0.494520i	0.968949	+	0.247260i	$0.0795301\pi$
$127$			5.57295i			0.494520i	−0.968949	+	0.247260i	$0.920470\pi$
$128$		0			0
$129$	0.0135212	−	0.0782438i	0.00119047	−	0.00688899i
$130$		0			0
$131$	−0.0314616	+	0.0544931i	−0.00274882	+	0.00476109i	−0.867397	−	0.497618i	$-0.834208\pi$
$131$	−0.0314616	+	0.0544931i	−0.00274882	+	0.00476109i	0.864648	+	0.502379i	$0.167542\pi$
$132$		0			0
$133$	2.76202	+	7.95411i	0.239497	+	0.689709i
$134$		0			0
$135$	7.55454	+	12.7807i	0.650192	+	1.09999i
$136$		0			0
$137$	−0.0178475	−	0.0309127i	−0.00152481	−	0.00264105i	0.865262	−	0.501320i	$-0.167152\pi$
$137$	−0.0178475	−	0.0309127i	−0.00152481	−	0.00264105i	−0.866787	+	0.498679i	$0.833819\pi$
$138$		0			0
$139$	−4.34888	−	7.53249i	−0.368868	−	0.638897i	0.620521	−	0.784190i	$-0.286921\pi$
$139$	−4.34888	−	7.53249i	−0.368868	−	0.638897i	−0.989389	+	0.145292i	$0.953588\pi$
$140$		0			0
$141$	3.43646	+	9.34221i	0.289402	+	0.786756i
$142$		0			0
$143$	−7.30017	+	12.6443i	−0.610471	+	1.05737i
$144$		0			0
$145$	5.28723	−	3.05258i	0.439080	−	0.253503i
$146$		0			0
$147$	0.318620	−	12.1202i	0.0262793	−	0.999655i
$148$		0			0
$149$	4.44314	−	7.69574i	0.363996	−	0.630459i	−0.624619	−	0.780930i	$-0.714746\pi$
$149$	4.44314	−	7.69574i	0.363996	−	0.630459i	0.988614	+	0.150471i	$0.0480789\pi$
$150$		0			0
$151$	13.9709	−	8.06613i	1.13694	−	0.656412i	0.191268	−	0.981538i	$-0.438740\pi$
$151$	13.9709	−	8.06613i	1.13694	−	0.656412i	0.945671	+	0.325126i	$0.105407\pi$
$152$		0			0
$153$	16.1785	−	2.96676i	1.30795	−	0.239848i
$154$		0			0
$155$	−9.98055	−	5.76227i	−0.801657	−	0.462837i
$156$		0			0
$157$		−	11.0788i		−	0.884187i	−0.896969	−	0.442093i	$-0.854236\pi$
$157$		−	11.0788i		−	0.884187i	0.896969	−	0.442093i	$-0.145764\pi$
$158$		0			0
$159$	8.32363	+	1.43839i	0.660107	+	0.114072i
$160$		0			0
$161$	11.9587	+	10.3410i	0.942479	+	0.814984i
$162$		0			0
$163$	6.35131	−	3.66693i	0.497473	−	0.287216i	−0.230196	−	0.973144i	$-0.573937\pi$
$163$	6.35131	−	3.66693i	0.497473	−	0.287216i	0.727670	+	0.685928i	$0.240603\pi$
$164$		0			0
$165$	−3.86395	−	10.5044i	−0.300808	−	0.817765i
$166$		0			0
$167$	12.6879	+	21.9760i	0.981816	+	1.70056i	0.655308	+	0.755362i	$0.272539\pi$
$167$	12.6879	+	21.9760i	0.981816	+	1.70056i	0.326508	+	0.945194i	$0.394128\pi$
$168$		0			0
$169$	14.3374	−	24.8332i	1.10288	−	1.91024i
$170$		0			0
$171$	8.99371	+	3.20406i	0.687766	+	0.245020i
$172$		0			0
$173$		−	16.2227i		−	1.23339i	−0.787202	−	0.616695i	$-0.788471\pi$
$173$		−	16.2227i		−	1.23339i	0.787202	−	0.616695i	$-0.211529\pi$
$174$		0			0
$175$	−2.74565	−	7.90696i	−0.207551	−	0.597710i
$176$		0			0
$177$	3.71192	+	10.0911i	0.279005	+	0.758492i
$178$		0			0
$179$	−17.9324	−	10.3533i	−1.34033	−	0.773839i	−0.353474	−	0.935445i	$-0.615000\pi$
$179$	−17.9324	−	10.3533i	−1.34033	−	0.773839i	−0.986855	+	0.161605i	$0.948333\pi$
$180$		0			0
$181$			16.3983i			1.21888i	0.792833	+	0.609439i	$0.208605\pi$
$181$			16.3983i			1.21888i	−0.792833	+	0.609439i	$0.791395\pi$
$182$		0			0
$183$	11.3597	−	4.17858i	0.839735	−	0.308890i
$184$		0			0
$185$		−	28.9537i		−	2.12872i
$186$		0			0
$187$	−12.4001			−0.906782
$188$		0			0
$189$	−10.4906	−	8.88527i	−0.763077	−	0.646308i
$190$		0			0
$191$		−	5.42747i		−	0.392718i	−0.980532	−	0.196359i	$-0.937088\pi$
$191$		−	5.42747i		−	0.392718i	0.980532	−	0.196359i	$-0.0629117\pi$
$192$		0			0
$193$	5.60988			0.403808			0.201904	−	0.979405i	$-0.435287\pi$
$193$	5.60988			0.403808			0.201904	+	0.979405i	$0.435287\pi$
$194$		0			0
$195$	11.0292	+	29.9835i	0.789816	+	2.14716i
$196$		0			0
$197$	9.09436			0.647946			0.323973	−	0.946066i	$-0.394981\pi$
$197$	9.09436			0.647946			0.323973	+	0.946066i	$0.394981\pi$
$198$		0			0
$199$	0.330072	−	0.571701i	0.0233982	−	0.0405268i	−0.854089	−	0.520127i	$-0.825885\pi$
$199$	0.330072	−	0.571701i	0.0233982	−	0.0405268i	0.877487	+	0.479600i	$0.159218\pi$
$200$		0			0
$201$	−12.8135	+	4.71335i	−0.903795	+	0.332454i
$202$		0			0
$203$	−3.69780	+	4.27628i	−0.259535	+	0.300136i
$204$		0			0
$205$	29.7674			2.07904
$206$		0			0
$207$	17.6325	−	3.23340i	1.22554	−	0.224737i
$208$		0			0
$209$	−6.23332	−	3.59881i	−0.431168	−	0.248935i
$210$		0			0
$211$	18.2479	−	10.5354i	1.25624	−	0.725290i	0.283898	−	0.958854i	$-0.408372\pi$
$211$	18.2479	−	10.5354i	1.25624	−	0.725290i	0.972341	+	0.233564i	$0.0750389\pi$
$212$		0			0
$213$	25.2680	−	9.29465i	1.73134	−	0.636859i
$214$		0			0
$215$	0.0654923	+	0.113436i	0.00446654	+	0.00773627i
$216$		0			0
$217$	10.4809	+	2.00896i	0.711487	+	0.136377i
$218$		0			0
$219$	3.76617	−	21.7939i	0.254494	−	1.47269i
$220$		0			0
$221$	35.3945			2.38089
$222$		0			0
$223$	3.66945	−	6.35568i	0.245725	−	0.425608i	−0.716610	−	0.697474i	$-0.754307\pi$
$223$	3.66945	−	6.35568i	0.245725	−	0.425608i	0.962335	+	0.271866i	$0.0876407\pi$
$224$		0			0
$225$	−8.94040	−	3.18507i	−0.596027	−	0.212338i
$226$		0			0
$227$	1.70310	+	2.94986i	0.113039	+	0.195789i	0.916994	−	0.398901i	$-0.130608\pi$
$227$	1.70310	+	2.94986i	0.113039	+	0.195789i	−0.803955	+	0.594690i	$0.797275\pi$
$228$		0			0
$229$	16.5722	+	9.56799i	1.09512	+	0.632271i	0.934936	−	0.354816i	$-0.115456\pi$
$229$	16.5722	+	9.56799i	1.09512	+	0.632271i	0.160189	+	0.987086i	$0.448790\pi$
$230$		0			0
$231$	6.57076	+	8.01508i	0.432324	+	0.527353i
$232$		0			0
$233$	−0.734443	−	1.27209i	−0.0481150	−	0.0833376i	0.840965	−	0.541090i	$-0.181988\pi$
$233$	−0.734443	−	1.27209i	−0.0481150	−	0.0833376i	−0.889080	+	0.457752i	$0.848655\pi$
$234$		0			0
$235$	−14.2206	−	8.21025i	−0.927648	−	0.535578i
$236$		0			0
$237$	−19.5256	+	7.18234i	−1.26833	+	0.466543i
$238$		0			0
$239$	9.40142	−	5.42791i	0.608127	−	0.351103i	−0.164105	−	0.986443i	$-0.552474\pi$
$239$	9.40142	−	5.42791i	0.608127	−	0.351103i	0.772232	+	0.635340i	$0.219140\pi$
$240$		0			0
$241$	−5.39678	+	3.11583i	−0.347637	+	0.200708i	−0.663644	−	0.748048i	$-0.730991\pi$
$241$	−5.39678	+	3.11583i	−0.347637	+	0.200708i	0.316007	+	0.948757i	$0.397658\pi$
$242$		0			0
$243$	−15.3032	+	2.96860i	−0.981700	+	0.190436i
$244$		0			0
$245$	12.3954	+	15.6962i	0.791915	+	1.00279i
$246$		0			0
$247$	17.7923	+	10.2724i	1.13210	+	0.653615i
$248$		0			0
$249$	6.43296	+	1.11167i	0.407672	+	0.0704491i
$250$		0			0
$251$	−20.2337			−1.27714			−0.638569	−	0.769565i	$-0.720473\pi$
$251$	−20.2337			−1.27714			−0.638569	+	0.769565i	$0.720473\pi$
$252$		0			0
$253$	−13.5145			−0.849651
$254$		0			0
$255$	−17.3697	+	20.8446i	−1.08774	+	1.30534i
$256$		0			0
$257$	−24.1732	−	13.9564i	−1.50788	−	0.870577i	−0.999958	−	0.00917598i	$-0.997079\pi$
$257$	−24.1732	−	13.9564i	−1.50788	−	0.870577i	−0.507926	−	0.861401i	$-0.669588\pi$
$258$		0			0
$259$	8.79481	+	25.3275i	0.546483	+	1.57377i
$260$		0			0
$261$	1.15622	+	6.30516i	0.0715683	+	0.390279i
$262$		0			0
$263$	4.17765	−	2.41197i	0.257605	−	0.148728i	−0.365637	−	0.930758i	$-0.619149\pi$
$263$	4.17765	−	2.41197i	0.257605	−	0.148728i	0.623242	+	0.782029i	$0.285815\pi$
$264$		0			0
$265$	−12.0674	+	6.96711i	−0.741294	+	0.427986i
$266$		0			0
$267$	6.07144	+	5.05932i	0.371566	+	0.309625i
$268$		0			0
$269$	−4.82686	−	2.78679i	−0.294299	−	0.169913i	0.345580	−	0.938389i	$-0.387682\pi$
$269$	−4.82686	−	2.78679i	−0.294299	−	0.169913i	−0.639879	+	0.768476i	$0.721015\pi$
$270$		0			0
$271$	10.8266	+	18.7521i	0.657666	+	1.13911i	0.981218	+	0.192901i	$0.0617896\pi$
$271$	10.8266	+	18.7521i	0.657666	+	1.13911i	−0.323552	+	0.946210i	$0.604877\pi$
$272$		0			0
$273$	−18.7554	−	22.8781i	−1.13513	−	1.38464i
$274$		0			0
$275$	6.19638	+	3.57748i	0.373656	+	0.215730i
$276$		0			0
$277$	−7.22330	−	12.5111i	−0.434006	−	0.751720i	0.563208	−	0.826315i	$-0.309567\pi$
$277$	−7.22330	−	12.5111i	−0.434006	−	0.751720i	−0.997214	+	0.0745949i	$0.976234\pi$
$278$		0			0
$279$	9.21621	−	7.84119i	0.551760	−	0.469440i
$280$		0			0
$281$	9.82235	−	17.0128i	0.585952	−	1.01490i	−0.408804	−	0.912622i	$-0.634054\pi$
$281$	9.82235	−	17.0128i	0.585952	−	1.01490i	0.994756	−	0.102277i	$-0.0326127\pi$
$282$		0			0
$283$	−30.9384			−1.83910			−0.919549	−	0.392976i	$-0.871446\pi$
$283$	−30.9384			−1.83910			−0.919549	+	0.392976i	$0.871446\pi$
$284$		0			0
$285$	−14.7812	+	5.43713i	−0.875560	+	0.322068i
$286$		0			0
$287$	−26.0392	+	9.04195i	−1.53704	+	0.533729i
$288$		0			0
$289$	6.53024	+	11.3107i	0.384132	+	0.665336i
$290$		0			0
$291$	1.57588	−	9.11927i	0.0923800	−	0.534581i
$292$		0			0
$293$	−0.154987	+	0.0894817i	−0.00905443	+	0.00522758i	−0.504520	−	0.863400i	$-0.668331\pi$
$293$	−0.154987	+	0.0894817i	−0.00905443	+	0.00522758i	0.495466	+	0.868627i	$0.334997\pi$
$294$		0			0
$295$	−15.3605	−	8.86839i	−0.894323	−	0.516337i
$296$		0			0
$297$	11.7513	−	0.120382i	0.681878	−	0.00698526i
$298$		0			0
$299$	38.5756			2.23088
$300$		0			0
$301$	−0.0917464	−	0.0793353i	−0.00528817	−	0.00457281i
$302$		0			0
$303$	7.93769	+	6.61445i	0.456008	+	0.379990i
$304$		0			0
$305$	−9.98331	+	17.2916i	−0.571643	+	0.990115i
$306$		0			0
$307$	−9.20787			−0.525521			−0.262760	−	0.964861i	$-0.584633\pi$
$307$	−9.20787			−0.525521			−0.262760	+	0.964861i	$0.584633\pi$
$308$		0			0
$309$	15.1450	+	2.61718i	0.861568	+	0.148886i
$310$		0			0
$311$	−31.4074			−1.78095			−0.890476	−	0.455030i	$-0.849629\pi$
$311$	−31.4074			−1.78095			−0.890476	+	0.455030i	$0.849629\pi$
$312$		0			0
$313$			5.18230i			0.292921i	0.989217	+	0.146460i	$0.0467881\pi$
$313$			5.18230i			0.292921i	−0.989217	+	0.146460i	$0.953212\pi$
$314$		0			0
$315$	22.6776	+	0.181862i	1.27774	+	0.0102467i
$316$		0			0
$317$	−19.3977			−1.08949			−0.544743	−	0.838603i	$-0.683373\pi$
$317$	−19.3977			−1.08949			−0.544743	+	0.838603i	$0.683373\pi$
$318$		0			0
$319$		−	4.83261i		−	0.270574i
$320$		0			0
$321$	7.85111	+	6.54231i	0.438206	+	0.365156i
$322$		0			0
$323$			17.4486i			0.970868i
$324$		0			0
$325$	−17.6868	−	10.2115i	−0.981088	−	0.566431i
$326$		0			0
$327$	1.42086	+	0.245537i	0.0785738	+	0.0135782i
$328$		0			0
$329$	14.9334	+	2.86242i	0.823307	+	0.157810i
$330$		0			0
$331$			15.7609i			0.866300i	0.901322	+	0.433150i	$0.142598\pi$
$331$			15.7609i			0.866300i	−0.901322	+	0.433150i	$0.857402\pi$
$332$		0			0
$333$	28.6377	+	10.2024i	1.56934	+	0.559085i
$334$		0			0
$335$	11.2610	−	19.5045i	0.615251	−	1.06565i
$336$		0			0
$337$	−0.00326615	−	0.00565714i	−0.000177918	−	0.000308164i	0.865936	−	0.500154i	$-0.166723\pi$
$337$	−0.00326615	−	0.00565714i	−0.000177918	−	0.000308164i	−0.866114	+	0.499846i	$0.833390\pi$
$338$		0			0
$339$	−0.133418	+	0.160108i	−0.00724625	+	0.00869587i
$340$		0			0
$341$	−7.90022	+	4.56119i	−0.427821	+	0.247003i
$342$		0			0
$343$	−15.6107	−	9.96517i	−0.842901	−	0.538069i
$344$		0			0
$345$	−18.9309	+	22.7180i	−1.01920	+	1.22310i
$346$		0			0
$347$		−	3.21508i		−	0.172594i	−0.996269	−	0.0862972i	$-0.972497\pi$
$347$		−	3.21508i		−	0.172594i	0.996269	−	0.0862972i	$-0.0275035\pi$
$348$		0			0
$349$	−29.6288	−	17.1062i	−1.58599	−	0.915674i	−0.993958	−	0.109762i	$-0.964991\pi$
$349$	−29.6288	−	17.1062i	−1.58599	−	0.915674i	−0.592035	−	0.805912i	$-0.701675\pi$
$350$		0			0
$351$	−33.5426	+	0.343615i	−1.79037	+	0.0183408i
$352$		0			0
$353$	−5.89661	+	3.40441i	−0.313845	+	0.181198i	−0.648646	−	0.761091i	$-0.724664\pi$
$353$	−5.89661	+	3.40441i	−0.313845	+	0.181198i	0.334801	+	0.942289i	$0.391331\pi$
$354$		0			0
$355$	−22.2064	+	38.4627i	−1.17859	+	2.04139i
$356$		0			0
$357$	8.86267	−	23.5101i	0.469062	−	1.24428i
$358$		0			0
$359$	19.5302	−	11.2758i	1.03077	−	0.595114i	0.113563	−	0.993531i	$-0.463774\pi$
$359$	19.5302	−	11.2758i	1.03077	−	0.595114i	0.917204	+	0.398417i	$0.130440\pi$
$360$		0			0
$361$	4.43596	−	7.68331i	0.233472	−	0.404385i
$362$		0			0
$363$	10.0441	+	1.73571i	0.527181	+	0.0911012i
$364$		0			0
$365$	18.2421	+	31.5962i	0.954835	+	1.65382i
$366$		0			0
$367$	11.5456	+	19.9975i	0.602674	+	1.04386i	0.992414	+	0.122937i	$0.0392313\pi$
$367$	11.5456	+	19.9975i	0.602674	+	1.04386i	−0.389741	+	0.920925i	$0.627435\pi$
$368$		0			0
$369$	−10.4890	+	29.4425i	−0.546038	+	1.53271i
$370$		0			0
$371$	8.43974	−	9.76004i	0.438169	−	0.506716i
$372$		0			0
$373$	6.23406	−	10.7977i	0.322787	−	0.559084i	−0.658275	−	0.752778i	$-0.728713\pi$
$373$	6.23406	−	10.7977i	0.322787	−	0.559084i	0.981062	+	0.193694i	$0.0620468\pi$
$374$		0			0
$375$	−8.52926	+	3.13742i	−0.440449	+	0.162016i
$376$		0			0
$377$			13.7941i			0.710433i
$378$		0			0
$379$		−	0.865461i		−	0.0444557i	−0.999753	−	0.0222279i	$-0.992924\pi$
$379$		−	0.865461i		−	0.0444557i	0.999753	−	0.0222279i	$-0.00707593\pi$
$380$		0			0
$381$	9.05919	−	3.33235i	0.464116	−	0.170721i
$382$		0			0
$383$	−5.77345	+	9.99991i	−0.295010	+	0.510971i	−0.974987	−	0.222261i	$-0.928656\pi$
$383$	−5.77345	+	9.99991i	−0.295010	+	0.510971i	0.679978	+	0.733233i	$0.261989\pi$
$384$		0			0
$385$	−16.7911	−	3.21850i	−0.855756	−	0.164030i
$386$		0			0
$387$	−0.135275	+	0.0248064i	−0.00687643	+	0.00126098i
$388$		0			0
$389$	2.26417	+	3.92165i	0.114798	+	0.198836i	0.917699	−	0.397277i	$-0.130045\pi$
$389$	2.26417	+	3.92165i	0.114798	+	0.198836i	−0.802901	+	0.596112i	$0.796711\pi$
$390$		0			0
$391$	16.3811	+	28.3729i	0.828428	+	1.43488i
$392$		0			0
$393$	0.107395	+	0.0185587i	0.00541734	+	0.000936161i
$394$		0			0
$395$	17.1598	−	29.7216i	0.863403	−	1.49546i
$396$		0			0
$397$	−1.62853	+	0.940235i	−0.0817338	+	0.0471890i	−0.540310	−	0.841466i	$-0.681693\pi$
$397$	−1.62853	+	0.940235i	−0.0817338	+	0.0471890i	0.458576	+	0.888655i	$0.348360\pi$
$398$		0			0
$399$	11.2784	−	9.24599i	0.564624	−	0.462879i
$400$		0			0
$401$	9.44812	−	16.3646i	0.471817	−	0.817210i	−0.527664	−	0.849453i	$-0.676932\pi$
$401$	9.44812	−	16.3646i	0.471817	−	0.817210i	0.999480	+	0.0322433i	$0.0102651\pi$
$402$		0			0
$403$	22.5502	−	13.0194i	1.12331	−	0.648541i
$404$		0			0
$405$	16.2586	−	19.9226i	0.807895	−	0.989962i
$406$		0			0
$407$	−19.8481	−	11.4593i	−0.983836	−	0.568018i
$408$		0			0
$409$		−	30.2959i		−	1.49803i	−0.662551	−	0.749017i	$-0.730526\pi$
$409$		−	30.2959i		−	1.49803i	0.662551	−	0.749017i	$-0.269474\pi$
$410$		0			0
$411$	−0.0395787	+	0.0474964i	−0.00195227	+	0.00234283i
$412$		0			0
$413$	16.1305	+	3.09187i	0.793730	+	0.152141i
$414$		0			0
$415$	−9.32634	+	5.38456i	−0.457812	+	0.264318i
$416$		0			0
$417$	−9.64412	+	11.5734i	−0.472275	+	0.566754i
$418$		0			0
$419$	2.90705	+	5.03516i	0.142019	+	0.245984i	0.928257	−	0.371940i	$-0.121307\pi$
$419$	2.90705	+	5.03516i	0.142019	+	0.245984i	−0.786238	+	0.617924i	$0.787974\pi$
$420$		0			0
$421$	−7.49878	+	12.9883i	−0.365468	+	0.633009i	−0.988851	−	0.148907i	$-0.952424\pi$
$421$	−7.49878	+	12.9883i	−0.365468	+	0.633009i	0.623383	+	0.781917i	$0.285758\pi$
$422$		0			0
$423$	13.1315	−	11.1724i	0.638476	−	0.543218i
$424$		0			0
$425$		−	17.3452i		−	0.841367i
$426$		0			0
$427$	3.48058	−	18.1584i	0.168437	−	0.878747i
$428$		0			0
$429$	24.9192	+	4.30624i	1.20311	+	0.207907i
$430$		0			0
$431$	−20.0076	−	11.5514i	−0.963732	−	0.556411i	−0.0664126	−	0.997792i	$-0.521155\pi$
$431$	−20.0076	−	11.5514i	−0.963732	−	0.556411i	−0.897320	+	0.441381i	$0.854489\pi$
$432$		0			0
$433$		−	11.1544i		−	0.536045i	−0.963413	−	0.268022i	$-0.913630\pi$
$433$		−	11.1544i		−	0.536045i	0.963413	−	0.268022i	$-0.0863701\pi$
$434$		0			0
$435$	−8.12367	−	6.76943i	−0.389500	−	0.324569i
$436$		0			0
$437$			19.0169i			0.909699i
$438$		0			0
$439$	7.38929			0.352672			0.176336	−	0.984330i	$-0.443576\pi$
$439$	7.38929			0.352672			0.176336	+	0.984330i	$0.443576\pi$
$440$		0			0
$441$	−19.8926	+	6.72932i	−0.947267	+	0.320444i
$442$		0			0
$443$			1.72740i			0.0820712i	0.999158	+	0.0410356i	$0.0130657\pi$
$443$			1.72740i			0.0820712i	−0.999158	+	0.0410356i	$0.986934\pi$
$444$		0			0
$445$	−13.0370			−0.618014
$446$		0			0
$447$	−15.1667	−	2.62093i	−0.717359	−	0.123966i
$448$		0			0
$449$	−37.3078			−1.76067			−0.880333	−	0.474357i	$-0.842681\pi$
$449$	−37.3078			−1.76067			−0.880333	+	0.474357i	$0.842681\pi$
$450$		0			0
$451$	11.7813	−	20.4059i	0.554762	−	0.960876i
$452$		0			0
$453$	−21.4659	−	17.8875i	−1.00856	−	0.840428i
$454$		0			0
$455$	47.9283	+	9.18682i	2.24691	+	0.430685i
$456$		0			0
$457$	−11.2540			−0.526441			−0.263220	−	0.964736i	$-0.584785\pi$
$457$	−11.2540			−0.526441			−0.263220	+	0.964736i	$0.584785\pi$
$458$		0			0
$459$	−14.4966	−	24.5251i	−0.676642	−	1.14474i
$460$		0			0
$461$	−31.6005	−	18.2446i	−1.47178	−	0.849734i	−0.472285	−	0.881446i	$-0.656571\pi$
$461$	−31.6005	−	18.2446i	−1.47178	−	0.849734i	−0.999497	+	0.0317125i	$0.989904\pi$
$462$		0			0
$463$	20.7706	−	11.9919i	0.965294	−	0.557313i	0.0674955	−	0.997720i	$-0.478499\pi$
$463$	20.7706	−	11.9919i	0.965294	−	0.557313i	0.897798	+	0.440407i	$0.145166\pi$
$464$		0			0
$465$	−3.39907	+	19.6696i	−0.157628	+	0.912155i
$466$		0			0
$467$	0.322176	+	0.558026i	0.0149085	+	0.0258224i	0.873383	−	0.487033i	$-0.161921\pi$
$467$	0.322176	+	0.558026i	0.0149085	+	0.0258224i	−0.858475	+	0.512856i	$0.828588\pi$
$468$		0			0
$469$	−3.92601	+	20.4823i	−0.181286	+	0.945783i
$470$		0			0
$471$	−18.0093	+	6.62459i	−0.829826	+	0.305245i
$472$		0			0
$473$	0.103682			0.00476732
$474$		0			0
$475$	5.03403	−	8.71919i	0.230977	−	0.400064i
$476$		0			0
$477$	−2.63892	−	14.3907i	−0.120828	−	0.658904i
$478$		0			0
$479$	−17.9804	−	31.1430i	−0.821547	−	1.42296i	−0.904530	−	0.426411i	$-0.859778\pi$
$479$	−17.9804	−	31.1430i	−0.821547	−	1.42296i	0.0829823	−	0.996551i	$-0.473556\pi$
$480$		0			0
$481$	56.6541	+	32.7093i	2.58321	+	1.49141i
$482$		0			0
$483$	9.65921	−	25.6231i	0.439509	−	1.16589i
$484$		0			0
$485$	7.63308	+	13.2209i	0.346600	+	0.600329i
$486$		0			0
$487$	−24.4569	−	14.1202i	−1.10825	−	0.639848i	−0.169874	−	0.985466i	$-0.554336\pi$
$487$	−24.4569	−	14.1202i	−1.10825	−	0.639848i	−0.938376	+	0.345617i	$0.887670\pi$
$488$		0			0
$489$	−9.75860	−	8.13182i	−0.441299	−	0.367734i
$490$		0			0
$491$	−11.6928	+	6.75082i	−0.527687	+	0.304660i	−0.740074	−	0.672526i	$-0.765210\pi$
$491$	−11.6928	+	6.75082i	−0.527687	+	0.304660i	0.212387	+	0.977186i	$0.431876\pi$
$492$		0			0
$493$	−10.1458	+	5.85767i	−0.456943	+	0.263816i
$494$		0			0
$495$	−14.7651	+	12.5622i	−0.663641	+	0.564629i
$496$		0			0
$497$	7.74203	−	40.3907i	0.347278	−	1.81177i
$498$		0			0
$499$	11.9450	+	6.89643i	0.534730	+	0.308727i	0.742941	−	0.669357i	$-0.233430\pi$
$499$	11.9450	+	6.89643i	0.534730	+	0.308727i	−0.208210	+	0.978084i	$0.566764\pi$
$500$		0			0
$501$	28.1367	−	33.7655i	1.25706	−	1.50853i
$502$		0			0
$503$	22.6371			1.00934			0.504669	−	0.863313i	$-0.331615\pi$
$503$	22.6371			1.00934			0.504669	+	0.863313i	$0.331615\pi$
$504$		0			0
$505$	−17.0443			−0.758463
$506$		0			0
$507$	−48.9410	−	8.45741i	−2.17355	−	0.375607i
$508$		0			0
$509$	−5.36782	−	3.09911i	−0.237925	−	0.137366i	0.376298	−	0.926499i	$-0.377197\pi$
$509$	−5.36782	−	3.09911i	−0.237925	−	0.137366i	−0.614222	+	0.789133i	$0.710530\pi$
$510$		0			0
$511$	−25.5549	−	22.0979i	−1.13048	−	0.977553i
$512$		0			0
$513$	−0.169394	−	16.5357i	−0.00747894	−	0.730069i
$514$		0			0
$515$	−21.9568	+	12.6768i	−0.967533	+	0.558605i
$516$		0			0
$517$	−11.2565	+	6.49892i	−0.495059	+	0.285822i
$518$		0			0
$519$	−26.3710	+	9.70038i	−1.15756	+	0.425799i
$520$		0			0
$521$	33.7303	+	19.4742i	1.47775	+	0.853181i	0.999684	−	0.0251422i	$-0.00800385\pi$
$521$	33.7303	+	19.4742i	1.47775	+	0.853181i	0.478068	+	0.878323i	$0.341337\pi$
$522$		0			0
$523$	−4.02860	−	6.97774i	−0.176158	−	0.305115i	0.764403	−	0.644739i	$-0.223034\pi$
$523$	−4.02860	−	6.97774i	−0.176158	−	0.305115i	−0.940562	+	0.339623i	$0.889700\pi$
$524$		0			0
$525$	−11.2115	+	9.19119i	−0.489310	+	0.401136i
$526$		0			0
$527$	19.1519	+	11.0573i	0.834269	+	0.481666i
$528$		0			0
$529$	6.35337	+	11.0044i	0.276234	+	0.478451i
$530$		0			0
$531$	14.1841	−	12.0679i	0.615539	−	0.523703i
$532$		0			0
$533$	−33.6284	+	58.2461i	−1.45661	+	2.52292i
$534$		0			0
$535$	−16.8584			−0.728854
$536$		0			0
$537$	−6.10721	+	35.3410i	−0.263546	+	1.52507i
$538$		0			0
$539$	15.6658	−	2.28497i	0.674773	−	0.0984207i
$540$		0			0
$541$	−7.96878	−	13.8023i	−0.342605	−	0.593409i	0.642311	−	0.766444i	$-0.277976\pi$
$541$	−7.96878	−	13.8023i	−0.342605	−	0.593409i	−0.984916	+	0.173035i	$0.944643\pi$
$542$		0			0
$543$	26.6565	−	9.80538i	1.14394	−	0.420789i
$544$		0			0
$545$	−2.05993	+	1.18930i	−0.0882377	+	0.0509440i
$546$		0			0
$547$	−4.79363	−	2.76760i	−0.204961	−	0.118334i	0.394006	−	0.919108i	$-0.371089\pi$
$547$	−4.79363	−	2.76760i	−0.204961	−	0.118334i	−0.598967	+	0.800773i	$0.704422\pi$
$548$		0			0
$549$	−13.5851	−	15.9674i	−0.579798	−	0.681470i
$550$		0			0
$551$	−6.80018			−0.289697
$552$		0			0
$553$	−5.98258	+	31.2115i	−0.254405	+	1.32725i
$554$		0			0
$555$	−47.0661	+	17.3129i	−1.99785	+	0.734892i
$556$		0			0
$557$	−11.2941	+	19.5619i	−0.478546	+	0.828866i	−0.999697	−	0.0245983i	$-0.992169\pi$
$557$	−11.2941	+	19.5619i	−0.478546	+	0.828866i	0.521151	+	0.853464i	$0.325503\pi$
$558$		0			0
$559$	−0.295949			−0.0125173
$560$		0			0
$561$	7.41462	+	20.1571i	0.313045	+	0.851032i
$562$		0			0
$563$	19.9543			0.840975			0.420488	−	0.907298i	$-0.361859\pi$
$563$	19.9543			0.840975			0.420488	+	0.907298i	$0.361859\pi$
$564$		0			0
$565$		−	0.343795i		−	0.0144636i
$566$		0			0
$567$	−8.17073	+	22.3660i	−0.343138	+	0.939285i
$568$		0			0
$569$	−31.5615			−1.32313			−0.661563	−	0.749889i	$-0.730107\pi$
$569$	−31.5615			−1.32313			−0.661563	+	0.749889i	$0.730107\pi$
$570$		0			0
$571$		−	9.88433i		−	0.413646i	−0.978378	−	0.206823i	$-0.933688\pi$
$571$		−	9.88433i		−	0.413646i	0.978378	−	0.206823i	$-0.0663125\pi$
$572$		0			0
$573$	−8.82269	+	3.24536i	−0.368573	+	0.135577i
$574$		0			0
$575$		−	18.9041i		−	0.788357i
$576$		0			0
$577$	17.9384	+	10.3568i	0.746787	+	0.431157i	0.824532	−	0.565816i	$-0.191439\pi$
$577$	17.9384	+	10.3568i	0.746787	+	0.431157i	−0.0777451	+	0.996973i	$0.524772\pi$
$578$		0			0
$579$	−3.35443	−	9.11922i	−0.139405	−	0.378982i
$580$		0			0
$581$	6.52269	−	7.54309i	0.270607	−	0.312940i
$582$		0			0
$583$			11.0298i			0.456807i
$584$		0			0
$585$	42.1451	−	35.8573i	1.74249	−	1.48252i
$586$		0			0
$587$	−11.4423	+	19.8186i	−0.472272	+	0.818000i	−0.999497	−	0.0317264i	$-0.989899\pi$
$587$	−11.4423	+	19.8186i	−0.472272	+	0.818000i	0.527224	+	0.849726i	$0.323233\pi$
$588$		0			0
$589$	6.41825	+	11.1167i	0.264459	+	0.458057i
$590$		0			0
$591$	−5.43797	−	14.7835i	−0.223688	−	0.608110i
$592$		0			0
$593$	36.8909	−	21.2990i	1.51493	−	0.874644i	0.515081	−	0.857141i	$-0.327762\pi$
$593$	36.8909	−	21.2990i	1.51493	−	0.874644i	0.999847	−	0.0175029i	$-0.00557163\pi$
$594$		0			0
$595$	13.5957	+	39.1532i	0.557369	+	1.60512i
$596$		0			0
$597$	−1.12670	−	0.194704i	−0.0461129	−	0.00796869i
$598$		0			0
$599$			2.44324i			0.0998283i	0.998754	+	0.0499141i	$0.0158948\pi$
$599$			2.44324i			0.0998283i	−0.998754	+	0.0499141i	$0.984105\pi$
$600$		0			0
$601$	−11.6323	−	6.71589i	−0.474490	−	0.273947i	0.243627	−	0.969869i	$-0.421663\pi$
$601$	−11.6323	−	6.71589i	−0.474490	−	0.273947i	−0.718117	+	0.695922i	$0.754996\pi$
$602$		0			0
$603$	15.3237	+	18.0108i	0.624029	+	0.733457i
$604$		0			0
$605$	−14.5617	+	8.40722i	−0.592019	+	0.341802i
$606$		0			0
$607$	11.5370	−	19.9826i	0.468271	−	0.811068i	−0.531072	−	0.847327i	$-0.678211\pi$
$607$	11.5370	−	19.9826i	0.468271	−	0.811068i	0.999342	+	0.0362583i	$0.0115439\pi$
$608$		0			0
$609$	9.16247	+	3.45401i	0.371282	+	0.139963i
$610$		0			0
$611$	32.1302	−	18.5504i	1.29985	−	0.750468i
$612$		0			0
$613$	−6.57373	+	11.3860i	−0.265511	+	0.459878i	−0.967697	−	0.252115i	$-0.918874\pi$
$613$	−6.57373	+	11.3860i	−0.265511	+	0.459878i	0.702187	+	0.711993i	$0.252207\pi$
$614$		0			0
$615$	−17.7994	−	48.3887i	−0.717741	−	1.95122i
$616$		0			0
$617$	−3.44699	−	5.97036i	−0.138771	−	0.240358i	0.788261	−	0.615341i	$-0.210982\pi$
$617$	−3.44699	−	5.97036i	−0.138771	−	0.240358i	−0.927032	+	0.374983i	$0.877648\pi$
$618$		0			0
$619$	17.7739	+	30.7853i	0.714394	+	1.23737i	0.963193	+	0.268811i	$0.0866308\pi$
$619$	17.7739	+	30.7853i	0.714394	+	1.23737i	−0.248799	+	0.968555i	$0.580036\pi$
$620$		0			0
$621$	−15.7995	−	26.7294i	−0.634011	−	1.07261i
$622$		0			0
$623$	11.4042	−	3.96004i	0.456900	−	0.158656i
$624$		0			0
$625$	15.4048	−	26.6819i	0.616193	−	1.06728i
$626$		0			0
$627$	−2.12288	+	12.2846i	−0.0847795	+	0.490599i
$628$		0			0
$629$			55.5599i			2.21532i
$630$		0			0
$631$			24.2459i			0.965213i	0.875837	+	0.482607i	$0.160310\pi$
$631$			24.2459i			0.965213i	−0.875837	+	0.482607i	$0.839690\pi$
$632$		0			0
$633$	−28.0374	−	23.3635i	−1.11439	−	0.928615i
$634$		0			0
$635$	−7.96153	+	13.7898i	−0.315944	+	0.547230i
$636$		0			0
$637$	−44.7161	+	6.52217i	−1.77172	+	0.258418i
$638$		0			0
$639$	−30.2181	−	35.5171i	−1.19541	−	1.40503i
$640$		0			0
$641$	16.1194	+	27.9196i	0.636677	+	1.10276i	0.986157	+	0.165814i	$0.0530250\pi$
$641$	16.1194	+	27.9196i	0.636677	+	1.10276i	−0.349480	+	0.936944i	$0.613642\pi$
$642$		0			0
$643$	7.26173	+	12.5777i	0.286375	+	0.496016i	0.972942	−	0.231051i	$-0.0742164\pi$
$643$	7.26173	+	12.5777i	0.286375	+	0.496016i	−0.686567	+	0.727067i	$0.740883\pi$
$644$		0			0
$645$	0.145236	−	0.174291i	0.00571867	−	0.00686270i
$646$		0			0
$647$	−11.5332	+	19.9760i	−0.453416	+	0.785339i	−0.998596	−	0.0529801i	$-0.983128\pi$
$647$	−11.5332	+	19.9760i	−0.453416	+	0.785339i	0.545180	+	0.838319i	$0.316461\pi$
$648$		0			0
$649$	−12.1588	+	7.01987i	−0.477274	+	0.275554i
$650$		0			0
$651$	−3.00135	−	18.2386i	−0.117632	−	0.714825i
$652$		0			0
$653$	−14.0767	+	24.3816i	−0.550865	+	0.954126i	0.447348	+	0.894360i	$0.352369\pi$
$653$	−14.0767	+	24.3816i	−0.550865	+	0.954126i	−0.998212	+	0.0597655i	$0.980965\pi$
$654$		0			0
$655$	−0.155698	+	0.0898922i	−0.00608362	+	0.00351238i
$656$		0			0
$657$	−37.6793	+	6.90953i	−1.47001	+	0.269566i
$658$		0			0
$659$	−5.32112	−	3.07215i	−0.207281	−	0.119674i	0.392766	−	0.919638i	$-0.371518\pi$
$659$	−5.32112	−	3.07215i	−0.207281	−	0.119674i	−0.600047	+	0.799965i	$0.704852\pi$
$660$		0			0
$661$			1.66168i			0.0646317i	0.999478	+	0.0323159i	$0.0102882\pi$
$661$			1.66168i			0.0646317i	−0.999478	+	0.0323159i	$0.989712\pi$
$662$		0			0
$663$	−21.1641	−	57.5359i	−0.821947	−	2.23451i
$664$		0			0
$665$	−4.52889	+	23.6275i	−0.175623	+	0.916237i
$666$		0			0
$667$	−11.0576	+	6.38413i	−0.428153	+	0.247194i
$668$		0			0
$669$	−12.5257	−	2.16455i	−0.484272	−	0.0836862i
$670$		0			0
$671$	7.90241	+	13.6874i	0.305069	+	0.528395i
$672$		0			0
$673$	−5.12788	+	8.88175i	−0.197665	+	0.342366i	−0.947771	−	0.318952i	$-0.896669\pi$
$673$	−5.12788	+	8.88175i	−0.197665	+	0.342366i	0.750106	+	0.661318i	$0.230003\pi$
$674$		0			0
$675$	0.168390	+	16.4377i	0.00648134	+	0.632687i
$676$		0			0
$677$		−	22.3830i		−	0.860247i	−0.902770	−	0.430123i	$-0.858470\pi$
$677$		−	22.3830i		−	0.860247i	0.902770	−	0.430123i	$-0.141530\pi$
$678$		0			0
$679$	−10.6930	−	9.24647i	−0.410359	−	0.354847i
$680$		0			0
$681$	3.77681	−	4.53237i	0.144728	−	0.173681i
$682$		0			0
$683$	27.3196	+	15.7730i	1.04535	+	0.603536i	0.921345	−	0.388745i	$-0.127091\pi$
$683$	27.3196	+	15.7730i	1.04535	+	0.603536i	0.124009	+	0.992281i	$0.460425\pi$
$684$		0			0
$685$		−	0.101988i		−	0.00389675i
$686$		0			0
$687$	5.64399	−	32.6604i	0.215332	−	1.24607i
$688$		0			0
$689$		−	31.4832i		−	1.19941i
$690$		0			0
$691$	−26.3023			−1.00059			−0.500294	−	0.865856i	$-0.666775\pi$
$691$	−26.3023			−1.00059			−0.500294	+	0.865856i	$0.666775\pi$
$692$		0			0
$693$	9.10003	−	15.4738i	0.345681	−	0.587801i
$694$		0			0
$695$		−	24.8513i		−	0.942663i
$696$		0			0
$697$	−57.1212			−2.16362
$698$		0			0
$699$	−1.62871	+	1.95453i	−0.0616033	+	0.0739272i
$700$		0			0
$701$	−5.62320			−0.212385			−0.106193	−	0.994346i	$-0.533866\pi$
$701$	−5.62320			−0.212385			−0.106193	+	0.994346i	$0.533866\pi$
$702$		0			0
$703$	−16.1249	+	27.9292i	−0.608162	+	1.05337i
$704$		0			0
$705$	−4.84309	+	28.0258i	−0.182401	+	1.05551i
$706$		0			0
$707$	14.9096	−	5.17728i	0.560735	−	0.194712i
$708$		0			0
$709$	25.1226			0.943500			0.471750	−	0.881732i	$-0.343622\pi$
$709$	25.1226			0.943500			0.471750	+	0.881732i	$0.343622\pi$
$710$		0			0
$711$	23.3507	+	27.4454i	0.875720	+	1.02928i
$712$		0			0
$713$	20.8732	+	12.0511i	0.781707	+	0.451319i
$714$		0			0
$715$	−36.1272	+	20.8580i	−1.35108	+	0.780047i
$716$		0			0
$717$	−14.4450	−	12.0370i	−0.539458	−	0.449529i
$718$		0			0
$719$	−0.846263	−	1.46577i	−0.0315603	−	0.0546640i	0.849814	−	0.527083i	$-0.176714\pi$
$719$	−0.846263	−	1.46577i	−0.0315603	−	0.0546640i	−0.881374	+	0.472419i	$0.843381\pi$
$720$		0			0
$721$	15.3562	−	17.7586i	0.571896	−	0.661363i
$722$		0			0
$723$	8.29199	+	6.90969i	0.308382	+	0.256974i
$724$		0			0
$725$	6.75987			0.251055
$726$		0			0
$727$	−16.1636	+	27.9962i	−0.599476	+	1.03832i	0.393423	+	0.919358i	$0.371291\pi$
$727$	−16.1636	+	27.9962i	−0.599476	+	1.03832i	−0.992898	+	0.118965i	$0.962042\pi$
$728$		0			0
$729$	13.9762	+	23.1012i	0.517637	+	0.855601i
$730$		0			0
$731$	−0.125674	−	0.217675i	−0.00464824	−	0.00805099i
$732$		0			0
$733$	−39.4670	−	22.7863i	−1.45775	−	0.841631i	−0.458847	−	0.888516i	$-0.651737\pi$
$733$	−39.4670	−	22.7863i	−1.45775	−	0.841631i	−0.998900	+	0.0468850i	$0.985071\pi$
$734$		0			0
$735$	18.1033	−	29.5351i	0.667749	−	1.08942i
$736$		0			0
$737$	−8.91373	−	15.4390i	−0.328342	−	0.568704i
$738$		0			0
$739$	1.86030	+	1.07404i	0.0684321	+	0.0395093i	0.533826	−	0.845595i	$-0.320754\pi$
$739$	1.86030	+	1.07404i	0.0684321	+	0.0395093i	−0.465394	+	0.885104i	$0.654087\pi$
$740$		0			0
$741$	6.05949	−	35.0648i	0.222601	−	1.28814i
$742$		0			0
$743$	38.9145	−	22.4673i	1.42763	−	0.824244i	0.430700	−	0.902495i	$-0.358267\pi$
$743$	38.9145	−	22.4673i	1.42763	−	0.824244i	0.996934	+	0.0782508i	$0.0249335\pi$
$744$		0			0
$745$	21.9883	−	12.6949i	0.805588	−	0.465107i
$746$		0			0
$747$	−2.03950	−	11.1219i	−0.0746215	−	0.406929i
$748$		0			0
$749$	14.7470	−	5.12081i	0.538844	−	0.187110i
$750$		0			0
$751$	23.9954	+	13.8537i	0.875604	+	0.505530i	0.869207	−	0.494449i	$-0.164630\pi$
$751$	23.9954	+	13.8537i	0.875604	+	0.505530i	0.00639780	+	0.999980i	$0.497964\pi$
$752$		0			0
$753$	12.0987	+	32.8911i	0.440902	+	1.19862i
$754$		0			0
$755$	46.0931			1.67750
$756$		0			0
$757$	−8.18716			−0.297568			−0.148784	−	0.988870i	$-0.547536\pi$
$757$	−8.18716			−0.297568			−0.148784	+	0.988870i	$0.547536\pi$
$758$		0			0
$759$	8.08101	+	21.9687i	0.293322	+	0.797414i
$760$		0			0
$761$	26.8605	+	15.5079i	0.973693	+	0.562162i	0.900360	−	0.435146i	$-0.143303\pi$
$761$	26.8605	+	15.5079i	0.973693	+	0.562162i	0.0733328	+	0.997308i	$0.476636\pi$
$762$		0			0
$763$	1.44068	−	1.66606i	0.0521562	−	0.0603154i
$764$		0			0
$765$	44.2705	+	15.7716i	1.60060	+	0.570223i
$766$		0			0
$767$	34.7058	−	20.0374i	1.25315	−	0.723508i
$768$		0			0
$769$	−4.32392	+	2.49641i	−0.155924	+	0.0900230i	−0.575932	−	0.817498i	$-0.695361\pi$
$769$	−4.32392	+	2.49641i	−0.155924	+	0.0900230i	0.420008	+	0.907521i	$0.362027\pi$
$770$		0			0
$771$	−8.23264	+	47.6403i	−0.296491	+	1.71572i
$772$		0			0
$773$	−11.5944	−	6.69400i	−0.417020	−	0.240767i	0.276782	−	0.960933i	$-0.410732\pi$
$773$	−11.5944	−	6.69400i	−0.417020	−	0.240767i	−0.693802	+	0.720166i	$0.744065\pi$
$774$		0			0
$775$	−6.38021	−	11.0508i	−0.229184	−	0.396958i
$776$		0			0
$777$	35.9125	−	29.4411i	1.28835	−	1.05619i
$778$		0			0
$779$	−28.7140	−	16.5780i	−1.02879	−	0.593970i
$780$		0			0
$781$	17.5777	+	30.4456i	0.628981	+	1.08943i
$782$		0			0
$783$	9.55807	−	5.64968i	0.341577	−	0.201903i
$784$		0			0
$785$	15.8272	−	27.4136i	0.564898	−	0.978432i
$786$		0			0
$787$	24.2635			0.864900			0.432450	−	0.901658i	$-0.357649\pi$
$787$	24.2635			0.864900			0.432450	+	0.901658i	$0.357649\pi$
$788$		0			0
$789$	−6.41883	−	5.34880i	−0.228516	−	0.190422i
$790$		0			0
$791$	0.104429	+	0.300737i	0.00371307	+	0.0106930i
$792$		0			0
$793$	−22.5565	−	39.0689i	−0.801004	−	1.38738i
$794$		0			0
$795$	18.5412	+	15.4503i	0.657588	+	0.547966i
$796$		0			0
$797$	36.4623	−	21.0515i	1.29156	−	0.745682i	0.312629	−	0.949875i	$-0.398790\pi$
$797$	36.4623	−	21.0515i	1.29156	−	0.745682i	0.978931	+	0.204193i	$0.0654569\pi$
$798$		0			0
$799$	27.2882	+	15.7548i	0.965386	+	0.557366i
$800$		0			0
$801$	4.59382	−	12.8947i	0.162315	−	0.455613i
$802$		0			0
$803$	28.8795			1.01913
$804$		0			0
$805$	14.8176	+	42.6721i	0.522253	+	1.50399i
$806$		0			0
$807$	−1.64388	+	9.51272i	−0.0578672	+	0.334864i
$808$		0			0
$809$	1.07111	−	1.85521i	0.0376582	−	0.0652258i	−0.846582	−	0.532258i	$-0.821344\pi$
$809$	1.07111	−	1.85521i	0.0376582	−	0.0652258i	0.884240	+	0.467032i	$0.154677\pi$
$810$		0			0
$811$	−11.5213			−0.404566			−0.202283	−	0.979327i	$-0.564836\pi$
$811$	−11.5213			−0.404566			−0.202283	+	0.979327i	$0.564836\pi$
$812$		0			0
$813$	24.0090	−	28.8121i	0.842034	−	1.01048i
$814$		0			0
$815$	20.9543			0.733998
$816$		0			0
$817$		−	0.145896i		−	0.00510425i
$818$		0			0
$819$	−25.9749	+	44.1681i	−0.907638	+	1.54336i
$820$		0			0
$821$	−18.8542			−0.658018			−0.329009	−	0.944327i	$-0.606715\pi$
$821$	−18.8542			−0.658018			−0.329009	+	0.944327i	$0.606715\pi$
$822$		0			0
$823$			29.3902i			1.02448i	0.858843	+	0.512240i	$0.171184\pi$
$823$			29.3902i			1.02448i	−0.858843	+	0.512240i	$0.828816\pi$
$824$		0			0
$825$	2.11029	−	12.2118i	0.0734710	−	0.425159i
$826$		0			0
$827$		−	22.6869i		−	0.788900i	−0.918917	−	0.394450i	$-0.870935\pi$
$827$		−	22.6869i		−	0.788900i	0.918917	−	0.394450i	$-0.129065\pi$
$828$		0			0
$829$	−19.3396	−	11.1657i	−0.671691	−	0.387801i	0.125026	−	0.992153i	$-0.460098\pi$
$829$	−19.3396	−	11.1657i	−0.671691	−	0.387801i	−0.796717	+	0.604353i	$0.793432\pi$
$830$		0			0
$831$	−16.0184	+	19.2230i	−0.555673	+	0.666837i
$832$		0			0
$833$	−23.7858	−	30.1197i	−0.824130	−	1.04359i
$834$		0			0
$835$			72.5036i			2.50909i
$836$		0			0
$837$	−18.2572	−	10.2929i	−0.631061	−	0.355774i
$838$		0			0
$839$	−24.6526	+	42.6995i	−0.851101	+	1.47415i	0.0291142	+	0.999576i	$0.490731\pi$
$839$	−24.6526	+	42.6995i	−0.851101	+	1.47415i	−0.880215	+	0.474574i	$0.842602\pi$
$840$		0			0
$841$	12.2171	+	21.1607i	0.421280	+	0.729678i
$842$		0			0
$843$	−33.5287	−	5.79403i	−1.15479	−	0.199557i
$844$		0			0
$845$	70.9534	−	40.9650i	2.44087	−	1.40924i
$846$		0			0
$847$	10.1842	−	11.7775i	0.349935	−	0.404678i
$848$		0			0
$849$	18.4996	+	50.2923i	0.634906	+	1.72603i
$850$		0			0
$851$			60.5534i			2.07575i
$852$		0			0
$853$	−2.37362	−	1.37041i	−0.0812712	−	0.0469220i	0.458814	−	0.888533i	$-0.348275\pi$
$853$	−2.37362	−	1.37041i	−0.0812712	−	0.0469220i	−0.540085	+	0.841611i	$0.681608\pi$
$854$		0			0
$855$	17.6768	+	20.7766i	0.604533	+	0.710543i
$856$		0			0
$857$	2.29909	−	1.32738i	0.0785355	−	0.0453425i	−0.460218	−	0.887806i	$-0.652229\pi$
$857$	2.29909	−	1.32738i	0.0785355	−	0.0453425i	0.538753	+	0.842463i	$0.318895\pi$
$858$		0			0
$859$	20.4410	−	35.4049i	0.697440	−	1.20800i	−0.271912	−	0.962322i	$-0.587656\pi$
$859$	20.4410	−	35.4049i	0.697440	−	1.20800i	0.969351	−	0.245679i	$-0.0790108\pi$
$860$		0			0
$861$	30.2684	+	36.9217i	1.03154	+	1.25829i
$862$		0			0
$863$	−36.5486	+	21.1013i	−1.24413	+	0.718298i	−0.969932	−	0.243376i	$-0.921745\pi$
$863$	−36.5486	+	21.1013i	−1.24413	+	0.718298i	−0.274196	+	0.961674i	$0.588412\pi$
$864$		0			0
$865$	23.1758	−	40.1416i	0.788000	−	1.36486i
$866$		0			0
$867$	14.4815	−	17.3786i	0.491818	−	0.590207i
$868$		0			0
$869$	−13.5830	−	23.5265i	−0.460773	−	0.798082i
$870$		0			0
$871$	25.4432	+	44.0689i	0.862109	+	1.49322i
$872$		0			0
$873$	−15.7662	+	2.89117i	−0.533606	+	0.0978512i
$874$		0			0
$875$	−2.61333	+	13.6339i	−0.0883468	+	0.460912i
$876$		0			0
$877$	27.9149	−	48.3501i	0.942620	−	1.63267i	0.182171	−	0.983267i	$-0.441687\pi$
$877$	27.9149	−	48.3501i	0.942620	−	1.63267i	0.760448	−	0.649399i	$-0.224979\pi$
$878$		0			0
$879$	0.238133	+	0.198435i	0.00803201	+	0.00669305i
$880$		0			0
$881$			49.2533i			1.65939i	0.558219	+	0.829693i	$0.311485\pi$
$881$			49.2533i			1.65939i	−0.558219	+	0.829693i	$0.688515\pi$
$882$		0			0
$883$			3.87310i			0.130340i	0.997874	+	0.0651701i	$0.0207590\pi$
$883$			3.87310i			0.130340i	−0.997874	+	0.0651701i	$0.979241\pi$
$884$		0			0
$885$	−5.23131	+	30.2723i	−0.175848	+	1.01759i
$886$		0			0
$887$	0.897157	−	1.55392i	0.0301236	−	0.0521756i	−0.850571	−	0.525861i	$-0.823743\pi$
$887$	0.897157	−	1.55392i	0.0301236	−	0.0521756i	0.880694	+	0.473685i	$0.157077\pi$
$888$		0			0
$889$	2.77570	−	14.4810i	0.0930940	−	0.485678i
$890$		0			0
$891$	−7.22236	−	19.0304i	−0.241958	−	0.637544i
$892$		0			0
$893$	9.14491	+	15.8394i	0.306023	+	0.530047i
$894$		0			0
$895$	−29.5814	−	51.2364i	−0.988796	−	1.71265i
$896$		0			0
$897$	−23.0663	−	62.7070i	−0.770161	−	2.09373i
$898$		0			0
$899$	−4.30933	+	7.46398i	−0.143724	+	0.248938i
$900$		0			0
$901$	23.1564	−	13.3693i	0.771450	−	0.445397i
$902$		0			0
$903$	−0.0741047	+	0.196578i	−0.00246605	+	0.00654171i
$904$		0			0
$905$	−23.4267	+	40.5761i	−0.778728	+	1.34880i
$906$		0			0
$907$	13.4331	−	7.75561i	0.446039	−	0.257521i	−0.260117	−	0.965577i	$-0.583761\pi$
$907$	13.4331	−	7.75561i	0.446039	−	0.257521i	0.706156	+	0.708056i	$0.250428\pi$
$908$		0			0
$909$	6.00587	−	16.8583i	0.199202	−	0.559155i
$910$		0			0
$911$	−38.1263	−	22.0122i	−1.26318	−	0.729297i	−0.289491	−	0.957181i	$-0.593486\pi$
$911$	−38.1263	−	22.0122i	−1.26318	−	0.729297i	−0.973688	+	0.227883i	$0.926819\pi$
$912$		0			0
$913$			8.52443i			0.282117i
$914$		0			0
$915$	34.0781	+	5.88898i	1.12659	+	0.194684i
$916$		0			0
$917$	0.108893	−	0.125928i	0.00359595	−	0.00415850i
$918$		0			0
$919$	30.4488	−	17.5796i	1.00441	−	0.579899i	0.0948631	−	0.995490i	$-0.469759\pi$
$919$	30.4488	−	17.5796i	1.00441	−	0.579899i	0.909551	+	0.415591i	$0.136425\pi$
$920$		0			0
$921$	5.50585	+	14.9680i	0.181424	+	0.493211i
$922$		0			0
$923$	−50.1736	−	86.9032i	−1.65148	−	2.86045i
$924$		0			0
$925$	16.0293	−	27.7636i	0.527041	−	0.912862i
$926$		0			0
$927$	−4.80156	−	26.1841i	−0.157704	−	0.859998i
$928$		0			0
$929$		−	28.6223i		−	0.939069i	−0.882914	−	0.469534i	$-0.844422\pi$
$929$		−	28.6223i		−	0.939069i	0.882914	−	0.469534i	$-0.155578\pi$
$930$		0			0
$931$	−3.21528	−	22.0440i	−0.105377	−	0.722463i
$932$		0			0
$933$	18.7801	+	51.0548i	0.614832	+	1.67146i
$934$		0			0
$935$	−30.6828	−	17.7147i	−1.00344	−	0.579334i
$936$		0			0
$937$		−	2.42605i		−	0.0792555i	−0.999215	−	0.0396277i	$-0.987383\pi$
$937$		−	2.42605i		−	0.0792555i	0.999215	−	0.0396277i	$-0.0126172\pi$
$938$		0			0
$939$	8.42415	−	3.09876i	0.274912	−	0.101124i
$940$		0			0
$941$			33.6961i			1.09846i	0.835671	+	0.549231i	$0.185079\pi$
$941$			33.6961i			1.09846i	−0.835671	+	0.549231i	$0.814921\pi$
$942$		0			0
$943$	−62.2550			−2.02730
$944$		0			0
$945$	−13.2645	−	36.9726i	−0.431493	−	1.20272i
$946$		0			0
$947$		−	54.7789i		−	1.78007i	−0.455888	−	0.890037i	$-0.650678\pi$
$947$		−	54.7789i		−	1.78007i	0.455888	−	0.890037i	$-0.349322\pi$
$948$		0			0
$949$	−82.4330			−2.67589
$950$		0			0
$951$	11.5989	+	31.5322i	0.376119	+	1.02250i
$952$		0			0
$953$	−34.7473			−1.12558			−0.562789	−	0.826601i	$-0.690271\pi$
$953$	−34.7473			−1.12558			−0.562789	+	0.826601i	$0.690271\pi$
$954$		0			0
$955$	7.75368	−	13.4298i	0.250903	−	0.434577i
$956$		0			0
$957$	−7.85572	+	2.88966i	−0.253939	+	0.0934096i
$958$		0			0
$959$	0.0309791	+	0.0892143i	0.00100037	+	0.00288088i
$960$		0			0
$961$	−14.7308			−0.475187
$962$		0			0
$963$	5.94036	−	16.6744i	0.191425	−	0.537326i
$964$		0			0
$965$	13.8811	+	8.01428i	0.446850	+	0.257989i
$966$		0			0
$967$	9.75555	−	5.63237i	0.313717	−	0.181125i	−0.334871	−	0.942264i	$-0.608693\pi$
$967$	9.75555	−	5.63237i	0.313717	−	0.181125i	0.648589	+	0.761139i	$0.275360\pi$
$968$		0			0
$969$	28.3639	−	10.4334i	0.911178	−	0.335170i
$970$		0			0
$971$	−9.41975	−	16.3155i	−0.302294	−	0.523589i	0.674361	−	0.738402i	$-0.264419\pi$
$971$	−9.41975	−	16.3155i	−0.302294	−	0.523589i	−0.976655	+	0.214813i	$0.931086\pi$
$972$		0			0
$973$	7.54867	+	21.7388i	0.241999	+	0.696914i
$974$		0			0
$975$	−6.02358	+	34.8570i	−0.192909	+	1.11632i
$976$		0			0
$977$	−6.17446			−0.197538			−0.0987692	−	0.995110i	$-0.531491\pi$
$977$	−6.17446			−0.197538			−0.0987692	+	0.995110i	$0.531491\pi$
$978$		0			0
$979$	−5.15980	+	8.93704i	−0.164908	+	0.285629i
$980$		0			0
$981$	−0.450469	−	2.45652i	−0.0143824	−	0.0784306i
$982$		0			0
$983$	13.3296	+	23.0876i	0.425150	+	0.736381i	0.996434	−	0.0843710i	$-0.0268881\pi$
$983$	13.3296	+	23.0876i	0.425150	+	0.736381i	−0.571285	+	0.820752i	$0.693555\pi$
$984$		0			0
$985$	22.5032	+	12.9922i	0.717010	+	0.413966i
$986$		0			0
$987$	−4.27641	−	25.9868i	−0.136120	−	0.827170i
$988$		0			0
$989$	−0.136970	−	0.237238i	−0.00435538	−	0.00754374i
$990$		0			0
$991$	−42.6887	−	24.6463i	−1.35605	−	0.782917i	−0.366962	−	0.930236i	$-0.619602\pi$
$991$	−42.6887	−	24.6463i	−1.35605	−	0.782917i	−0.989089	+	0.147319i	$0.952936\pi$
$992$		0			0
$993$	25.6204	−	9.42426i	0.813039	−	0.299070i
$994$		0			0
$995$	1.63347	−	0.943082i	0.0517844	−	0.0298977i
$996$		0			0
$997$	−6.78110	+	3.91507i	−0.214760	+	0.123992i	−0.603521	−	0.797347i	$-0.706236\pi$
$997$	−6.78110	+	3.91507i	−0.214760	+	0.123992i	0.388762	+	0.921338i	$0.372903\pi$
$998$		0			0
$999$	−0.539385	−	52.6530i	−0.0170654	−	1.66587i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cz.g.367.7	yes	24
3.2	odd	2		3024.2.cz.h.2719.2		24
4.3	odd	2		1008.2.cz.h.367.6	yes	24
7.5	odd	6		1008.2.bf.g.943.2	yes	24
9.4	even	3		1008.2.bf.h.31.11	yes	24
9.5	odd	6		3024.2.bf.g.1711.11		24
12.11	even	2		3024.2.cz.g.2719.2		24
21.5	even	6		3024.2.bf.h.2287.2		24
28.19	even	6		1008.2.bf.h.943.11	yes	24
36.23	even	6		3024.2.bf.h.1711.11		24
36.31	odd	6		1008.2.bf.g.31.2	✓	24
63.5	even	6		3024.2.cz.g.1279.2		24
63.40	odd	6		1008.2.cz.h.607.6	yes	24
84.47	odd	6		3024.2.bf.g.2287.2		24
252.103	even	6	inner	1008.2.cz.g.607.7	yes	24
252.131	odd	6		3024.2.cz.h.1279.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.g.31.2	✓	24	36.31	odd	6
1008.2.bf.g.943.2	yes	24	7.5	odd	6
1008.2.bf.h.31.11	yes	24	9.4	even	3
1008.2.bf.h.943.11	yes	24	28.19	even	6
1008.2.cz.g.367.7	yes	24	1.1	even	1	trivial
1008.2.cz.g.607.7	yes	24	252.103	even	6	inner
1008.2.cz.h.367.6	yes	24	4.3	odd	2
1008.2.cz.h.607.6	yes	24	63.40	odd	6
3024.2.bf.g.1711.11		24	9.5	odd	6
3024.2.bf.g.2287.2		24	84.47	odd	6
3024.2.bf.h.1711.11		24	36.23	even	6
3024.2.bf.h.2287.2		24	21.5	even	6
3024.2.cz.g.1279.2		24	63.5	even	6
3024.2.cz.g.2719.2		24	12.11	even	2
3024.2.cz.h.1279.2		24	252.131	odd	6
3024.2.cz.h.2719.2		24	3.2	odd	2

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.cz (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.597950 - 1.62556i) q^{3} +(2.47441 + 1.42860i) q^{5} +(-2.59845 - 0.498066i) q^{7} +(-2.28491 + 1.94401i) q^{9} +(1.95865 - 1.13083i) q^{11} +(-5.59072 + 3.22780i) q^{13} +(0.842707 - 4.87654i) q^{15} +(-4.74820 - 2.74137i) q^{17} +(-1.59123 - 2.75609i) q^{19} +(0.744104 + 4.52176i) q^{21} +(-5.17495 - 2.98776i) q^{23} +(1.58180 + 2.73976i) q^{25} +(4.52638 + 2.55184i) q^{27} +(1.06838 - 1.85049i) q^{29} -4.03351 q^{31} +(-3.00940 - 2.50773i) q^{33} +(-5.71808 - 4.94456i) q^{35} +(-5.06680 - 8.77595i) q^{37} +(8.58997 + 7.15800i) q^{39} +(9.02256 - 5.20918i) q^{41} +(0.0397018 + 0.0229218i) q^{43} +(-8.43102 + 1.54606i) q^{45} -5.74706 q^{47} +(6.50386 + 2.58840i) q^{49} +(-1.61709 + 9.35770i) q^{51} +(-2.43844 + 4.22350i) q^{53} +6.46199 q^{55} +(-3.52873 + 4.23466i) q^{57} -6.20774 q^{59} +6.98818i q^{61} +(6.90547 - 3.91338i) q^{63} -18.4450 q^{65} -7.88250i q^{67} +(-1.76243 + 10.1987i) q^{69} +15.5442i q^{71} +(11.0585 + 6.38460i) q^{73} +(3.50781 - 4.20956i) q^{75} +(-5.65267 + 1.96285i) q^{77} -12.0116i q^{79} +(1.44163 - 8.88379i) q^{81} +(-1.88456 + 3.26415i) q^{83} +(-7.83265 - 13.5666i) q^{85} +(-3.64693 - 0.630220i) q^{87} +(-3.95155 + 2.28143i) q^{89} +(16.1349 - 5.60273i) q^{91} +(2.41184 + 6.55672i) q^{93} -9.09294i q^{95} +(4.62721 + 2.67152i) q^{97} +(-2.27700 + 6.39147i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{3} - 3 q^{5} + 4 q^{7} + 17 q^{9} - 9 q^{11} - 3 q^{13} - 6 q^{15} - 3 q^{17} - 4 q^{19} + 13 q^{21} - 6 q^{23} + 15 q^{25} + 9 q^{27} + 18 q^{29} + 34 q^{31} - 21 q^{33} - 42 q^{35} - 3 q^{37}+ \cdots + 30 q^{99}+O(q^{100}) \) 24 * q - 3 * q^3 - 3 * q^5 + 4 * q^7 + 17 * q^9 - 9 * q^11 - 3 * q^13 - 6 * q^15 - 3 * q^17 - 4 * q^19 + 13 * q^21 - 6 * q^23 + 15 * q^25 + 9 * q^27 + 18 * q^29 + 34 * q^31 - 21 * q^33 - 42 * q^35 - 3 * q^37 + 27 * q^39 + 36 * q^41 + 24 * q^43 + 21 * q^45 - 42 * q^47 + 30 * q^49 - 6 * q^51 - 12 * q^53 - 30 * q^55 - 13 * q^57 - 12 * q^59 - 3 * q^63 + 6 * q^69 + 48 * q^73 + 36 * q^75 - 48 * q^77 - 31 * q^81 - 48 * q^83 - 21 * q^85 + 15 * q^87 + 39 * q^89 + 9 * q^91 + 10 * q^93 + 3 * q^97 + 30 * q^99

Introduction

L-functions

Modular forms

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Database

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