LMFDB - Embedded newform 1008.2.cz.g.607.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(367,1008)]

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

lf = mfeigenbasis(mf)

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")

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

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			607.7
Character	$\chi$	$=$	1008.607
Dual form			1008.2.cz.g.367.7

$q$-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 $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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	0.168646	−	0.985677i	$-0.446061\pi$
$5$	2.47441	−	1.42860i	1.10659	−	0.638890i	0.937944	+	0.346787i	$0.112727\pi$
$6$		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	0.765317	−	0.643654i	$-0.222582\pi$
$11$	1.95865	+	1.13083i	0.590554	+	0.340957i	−0.174762	+	0.984611i	$0.555916\pi$
$12$		0			0
$13$	−5.59072	−	3.22780i	−1.55059	−	0.895232i	−0.998094	−	0.0617145i	$-0.980343\pi$
$13$	−5.59072	−	3.22780i	−1.55059	−	0.895232i	−0.552493	−	0.833517i	$-0.686323\pi$
$14$		0			0
$15$	0.842707	+	4.87654i	0.217586	+	1.25912i
$16$		0			0
$17$	−4.74820	+	2.74137i	−1.15161	+	0.664880i	−0.949278	−	0.314437i	$-0.898184\pi$
$17$	−4.74820	+	2.74137i	−1.15161	+	0.664880i	−0.202328	+	0.979318i	$0.564851\pi$
$18$		0			0
$19$	−1.59123	+	2.75609i	−0.365054	+	0.632292i	−0.988785	−	0.149347i	$-0.952283\pi$
$19$	−1.59123	+	2.75609i	−0.365054	+	0.632292i	0.623731	+	0.781639i	$0.285616\pi$
$20$		0			0
$21$	0.744104	−	4.52176i	0.162377	−	0.986729i
$22$		0			0
$23$	−5.17495	+	2.98776i	−1.07905	+	0.622990i	−0.930640	−	0.365936i	$-0.880749\pi$
$23$	−5.17495	+	2.98776i	−1.07905	+	0.622990i	−0.148411	+	0.988926i	$0.547416\pi$
$24$		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	0.948008	−	0.318247i	$-0.103094\pi$
$29$	1.06838	+	1.85049i	0.198394	+	0.343628i	−0.749614	+	0.661875i	$0.769761\pi$
$30$		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	0.0626906	+	0.998033i	$0.480032\pi$
$37$	−5.06680	+	8.77595i	−0.832977	+	1.44276i	−0.895667	+	0.444725i	$0.853301\pi$
$38$		0			0
$39$	8.58997	−	7.15800i	1.37550	−	1.14620i
$40$		0			0
$41$	9.02256	+	5.20918i	1.40909	+	0.813537i	0.995300	−	0.0968362i	$-0.0308723\pi$
$41$	9.02256	+	5.20918i	1.40909	+	0.813537i	0.413788	+	0.910373i	$0.364206\pi$
$42$		0			0
$43$	0.0397018	−	0.0229218i	0.00605446	−	0.00349555i	−0.496970	−	0.867768i	$-0.665554\pi$
$43$	0.0397018	−	0.0229218i	0.00605446	−	0.00349555i	0.503024	+	0.864272i	$0.332221\pi$
$44$		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	0.648529	−	0.761190i	$-0.275384\pi$
$53$	−2.43844	−	4.22350i	−0.334945	−	0.580142i	−0.983474	+	0.181048i	$0.942051\pi$
$54$		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	$-0.852360\pi$
$61$		−	6.98818i		−	0.894744i	0.894348	−	0.447372i	$-0.147640\pi$
$62$		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	$0.159908\pi$
$67$			7.88250i			0.963001i	−0.876446	+	0.481500i	$0.840092\pi$
$68$		0			0
$69$	−1.76243	−	10.1987i	−0.212171	−	1.22778i
$70$		0			0
$71$		−	15.5442i		−	1.84475i	−0.386291	−	0.922377i	$-0.626244\pi$
$71$		−	15.5442i		−	1.84475i	0.386291	−	0.922377i	$-0.373756\pi$
$72$		0			0
$73$	11.0585	−	6.38460i	1.29429	−	0.747261i	0.314882	−	0.949131i	$-0.398035\pi$
$73$	11.0585	−	6.38460i	1.29429	−	0.747261i	0.979412	+	0.201870i	$0.0647018\pi$
$74$		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	$0.236161\pi$
$79$			12.0116i			1.35141i	−0.737172	+	0.675706i	$0.763839\pi$
$80$		0			0
$81$	1.44163	+	8.88379i	0.160182	+	0.987088i
$82$		0			0
$83$	−1.88456	−	3.26415i	−0.206857	−	0.358287i	0.743866	−	0.668329i	$-0.232990\pi$
$83$	−1.88456	−	3.26415i	−0.206857	−	0.358287i	−0.950723	+	0.310042i	$0.899657\pi$
$84$		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	0.275727	−	0.961236i	$-0.411081\pi$
$89$	−3.95155	−	2.28143i	−0.418864	−	0.241831i	−0.694591	+	0.719405i	$0.744415\pi$
$90$		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	−0.246343	−	0.969183i	$-0.579229\pi$
$97$	4.62721	−	2.67152i	0.469822	−	0.271252i	0.716165	+	0.697931i	$0.245896\pi$
$98$		0			0
$99$	−2.27700	−	6.39147i	−0.228847	−	0.642367i
$100$		0			0
$101$	−5.16618	−	2.98270i	−0.514055	−	0.296790i	0.220444	−	0.975400i	$-0.429249\pi$
$101$	−5.16618	−	2.98270i	−0.514055	−	0.296790i	−0.734499	+	0.678610i	$0.762583\pi$
$102$		0			0
$103$	−4.43678	−	7.68473i	−0.437169	−	0.757199i	0.560301	−	0.828289i	$-0.310685\pi$
$103$	−4.43678	−	7.68473i	−0.437169	−	0.757199i	−0.997470	+	0.0710903i	$0.977352\pi$
$104$		0			0
$105$	−4.61857	−	12.2517i	−0.450726	−	1.19564i
$106$		0			0
$107$	−5.10984	−	2.95016i	−0.493986	−	0.285203i	0.232240	−	0.972658i	$-0.425394\pi$
$107$	−5.10984	−	2.95016i	−0.493986	−	0.285203i	−0.726227	+	0.687455i	$0.758728\pi$
$108$		0			0
$109$	−0.416247	−	0.720960i	−0.0398692	−	0.0690555i	0.845402	−	0.534130i	$-0.179361\pi$
$109$	−0.416247	−	0.720960i	−0.0398692	−	0.0690555i	−0.885271	+	0.465075i	$0.846027\pi$
$110$		0			0
$111$	−11.2362	−	13.4840i	−1.06649	−	1.27984i
$112$		0			0
$113$	−0.0601629	+	0.104205i	−0.00565965	+	0.00980279i	−0.868841	−	0.495091i	$-0.835135\pi$
$113$	−0.0601629	+	0.104205i	−0.00565965	+	0.00980279i	0.863182	+	0.504893i	$0.168468\pi$
$114$		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	$-0.920470\pi$
$127$		−	5.57295i		−	0.494520i	0.968949	−	0.247260i	$-0.0795301\pi$
$128$		0			0
$129$	0.0135212	+	0.0782438i	0.00119047	+	0.00688899i
$130$		0			0
$131$	−0.0314616	−	0.0544931i	−0.00274882	−	0.00476109i	0.864648	−	0.502379i	$-0.167542\pi$
$131$	−0.0314616	−	0.0544931i	−0.00274882	−	0.00476109i	−0.867397	+	0.497618i	$0.834208\pi$
$132$		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	−0.866787	−	0.498679i	$-0.833819\pi$
$137$	−0.0178475	+	0.0309127i	−0.00152481	+	0.00264105i	0.865262	+	0.501320i	$0.167152\pi$
$138$		0			0
$139$	−4.34888	+	7.53249i	−0.368868	+	0.638897i	−0.989389	−	0.145292i	$-0.953588\pi$
$139$	−4.34888	+	7.53249i	−0.368868	+	0.638897i	0.620521	+	0.784190i	$0.286921\pi$
$140$		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	0.988614	−	0.150471i	$-0.0480789\pi$
$149$	4.44314	+	7.69574i	0.363996	+	0.630459i	−0.624619	+	0.780930i	$0.714746\pi$
$150$		0			0
$151$	13.9709	+	8.06613i	1.13694	+	0.656412i	0.945671	−	0.325126i	$-0.105407\pi$
$151$	13.9709	+	8.06613i	1.13694	+	0.656412i	0.191268	+	0.981538i	$0.438740\pi$
$152$		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	$0.145764\pi$
$157$			11.0788i			0.884187i	−0.896969	+	0.442093i	$0.854236\pi$
$158$		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	0.727670	−	0.685928i	$-0.240603\pi$
$163$	6.35131	+	3.66693i	0.497473	+	0.287216i	−0.230196	+	0.973144i	$0.573937\pi$
$164$		0			0
$165$	−3.86395	+	10.5044i	−0.300808	+	0.817765i
$166$		0			0
$167$	12.6879	−	21.9760i	0.981816	−	1.70056i	0.326508	−	0.945194i	$-0.394128\pi$
$167$	12.6879	−	21.9760i	0.981816	−	1.70056i	0.655308	−	0.755362i	$-0.272539\pi$
$168$		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	$0.211529\pi$
$173$			16.2227i			1.23339i	−0.787202	+	0.616695i	$0.788471\pi$
$174$		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	−0.986855	−	0.161605i	$-0.948333\pi$
$179$	−17.9324	+	10.3533i	−1.34033	+	0.773839i	−0.353474	+	0.935445i	$0.615000\pi$
$180$		0			0
$181$		−	16.3983i		−	1.21888i	−0.792833	−	0.609439i	$-0.791395\pi$
$181$		−	16.3983i		−	1.21888i	0.792833	−	0.609439i	$-0.208605\pi$
$182$		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	$0.0629117\pi$
$191$			5.42747i			0.392718i	−0.980532	+	0.196359i	$0.937088\pi$
$192$		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	0.877487	−	0.479600i	$-0.159218\pi$
$199$	0.330072	+	0.571701i	0.0233982	+	0.0405268i	−0.854089	+	0.520127i	$0.825885\pi$
$200$		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	0.972341	−	0.233564i	$-0.0750389\pi$
$211$	18.2479	+	10.5354i	1.25624	+	0.725290i	0.283898	+	0.958854i	$0.408372\pi$
$212$		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	0.962335	−	0.271866i	$-0.0876407\pi$
$223$	3.66945	+	6.35568i	0.245725	+	0.425608i	−0.716610	+	0.697474i	$0.754307\pi$
$224$		0			0
$225$	−8.94040	+	3.18507i	−0.596027	+	0.212338i
$226$		0			0
$227$	1.70310	−	2.94986i	0.113039	−	0.195789i	−0.803955	−	0.594690i	$-0.797275\pi$
$227$	1.70310	−	2.94986i	0.113039	−	0.195789i	0.916994	+	0.398901i	$0.130608\pi$
$228$		0			0
$229$	16.5722	−	9.56799i	1.09512	−	0.632271i	0.160189	−	0.987086i	$-0.448790\pi$
$229$	16.5722	−	9.56799i	1.09512	−	0.632271i	0.934936	+	0.354816i	$0.115456\pi$
$230$		0			0
$231$	6.57076	−	8.01508i	0.432324	−	0.527353i
$232$		0			0
$233$	−0.734443	+	1.27209i	−0.0481150	+	0.0833376i	−0.889080	−	0.457752i	$-0.848655\pi$
$233$	−0.734443	+	1.27209i	−0.0481150	+	0.0833376i	0.840965	+	0.541090i	$0.181988\pi$
$234$		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	0.772232	−	0.635340i	$-0.219140\pi$
$239$	9.40142	+	5.42791i	0.608127	+	0.351103i	−0.164105	+	0.986443i	$0.552474\pi$
$240$		0			0
$241$	−5.39678	−	3.11583i	−0.347637	−	0.200708i	0.316007	−	0.948757i	$-0.397658\pi$
$241$	−5.39678	−	3.11583i	−0.347637	−	0.200708i	−0.663644	+	0.748048i	$0.730991\pi$
$242$		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	−0.507926	+	0.861401i	$0.669588\pi$
$257$	−24.1732	+	13.9564i	−1.50788	+	0.870577i	−0.999958	+	0.00917598i	$0.997079\pi$
$258$		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	0.623242	−	0.782029i	$-0.285815\pi$
$263$	4.17765	+	2.41197i	0.257605	+	0.148728i	−0.365637	+	0.930758i	$0.619149\pi$
$264$		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	−0.639879	−	0.768476i	$-0.721015\pi$
$269$	−4.82686	+	2.78679i	−0.294299	+	0.169913i	0.345580	+	0.938389i	$0.387682\pi$
$270$		0			0
$271$	10.8266	−	18.7521i	0.657666	−	1.13911i	−0.323552	−	0.946210i	$-0.604877\pi$
$271$	10.8266	−	18.7521i	0.657666	−	1.13911i	0.981218	−	0.192901i	$-0.0617896\pi$
$272$		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	−0.997214	−	0.0745949i	$-0.976234\pi$
$277$	−7.22330	+	12.5111i	−0.434006	+	0.751720i	0.563208	+	0.826315i	$0.309567\pi$
$278$		0			0
$279$	9.21621	+	7.84119i	0.551760	+	0.469440i
$280$		0			0
$281$	9.82235	+	17.0128i	0.585952	+	1.01490i	0.994756	+	0.102277i	$0.0326127\pi$
$281$	9.82235	+	17.0128i	0.585952	+	1.01490i	−0.408804	+	0.912622i	$0.634054\pi$
$282$		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	0.495466	−	0.868627i	$-0.334997\pi$
$293$	−0.154987	−	0.0894817i	−0.00905443	−	0.00522758i	−0.504520	+	0.863400i	$0.668331\pi$
$294$		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	$-0.953212\pi$
$313$		−	5.18230i		−	0.292921i	0.989217	−	0.146460i	$-0.0467881\pi$
$314$		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	$-0.857402\pi$
$331$		−	15.7609i		−	0.866300i	0.901322	−	0.433150i	$-0.142598\pi$
$332$		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	−0.866114	−	0.499846i	$-0.833390\pi$
$337$	−0.00326615	+	0.00565714i	−0.000177918	+	0.000308164i	0.865936	+	0.500154i	$0.166723\pi$
$338$		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	$0.0275035\pi$
$347$			3.21508i			0.172594i	−0.996269	+	0.0862972i	$0.972497\pi$
$348$		0			0
$349$	−29.6288	+	17.1062i	−1.58599	+	0.915674i	−0.592035	+	0.805912i	$0.701675\pi$
$349$	−29.6288	+	17.1062i	−1.58599	+	0.915674i	−0.993958	+	0.109762i	$0.964991\pi$
$350$		0			0
$351$	−33.5426	−	0.343615i	−1.79037	−	0.0183408i
$352$		0			0
$353$	−5.89661	−	3.40441i	−0.313845	−	0.181198i	0.334801	−	0.942289i	$-0.391331\pi$
$353$	−5.89661	−	3.40441i	−0.313845	−	0.181198i	−0.648646	+	0.761091i	$0.724664\pi$
$354$		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	0.917204	−	0.398417i	$-0.130440\pi$
$359$	19.5302	+	11.2758i	1.03077	+	0.595114i	0.113563	+	0.993531i	$0.463774\pi$
$360$		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	−0.389741	−	0.920925i	$-0.627435\pi$
$367$	11.5456	−	19.9975i	0.602674	−	1.04386i	0.992414	−	0.122937i	$-0.0392313\pi$
$368$		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	0.981062	−	0.193694i	$-0.0620468\pi$
$373$	6.23406	+	10.7977i	0.322787	+	0.559084i	−0.658275	+	0.752778i	$0.728713\pi$
$374$		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	$0.00707593\pi$
$379$			0.865461i			0.0444557i	−0.999753	+	0.0222279i	$0.992924\pi$
$380$		0			0
$381$	9.05919	+	3.33235i	0.464116	+	0.170721i
$382$		0			0
$383$	−5.77345	−	9.99991i	−0.295010	−	0.510971i	0.679978	−	0.733233i	$-0.261989\pi$
$383$	−5.77345	−	9.99991i	−0.295010	−	0.510971i	−0.974987	+	0.222261i	$0.928656\pi$
$384$		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	−0.802901	−	0.596112i	$-0.796711\pi$
$389$	2.26417	−	3.92165i	0.114798	−	0.198836i	0.917699	+	0.397277i	$0.130045\pi$
$390$		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	0.458576	−	0.888655i	$-0.348360\pi$
$397$	−1.62853	−	0.940235i	−0.0817338	−	0.0471890i	−0.540310	+	0.841466i	$0.681693\pi$
$398$		0			0
$399$	11.2784	+	9.24599i	0.564624	+	0.462879i
$400$		0			0
$401$	9.44812	+	16.3646i	0.471817	+	0.817210i	0.999480	−	0.0322433i	$-0.0102651\pi$
$401$	9.44812	+	16.3646i	0.471817	+	0.817210i	−0.527664	+	0.849453i	$0.676932\pi$
$402$		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	$0.269474\pi$
$409$			30.2959i			1.49803i	−0.662551	+	0.749017i	$0.730526\pi$
$410$		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	−0.786238	−	0.617924i	$-0.787974\pi$
$419$	2.90705	−	5.03516i	0.142019	−	0.245984i	0.928257	+	0.371940i	$0.121307\pi$
$420$		0			0
$421$	−7.49878	−	12.9883i	−0.365468	−	0.633009i	0.623383	−	0.781917i	$-0.285758\pi$
$421$	−7.49878	−	12.9883i	−0.365468	−	0.633009i	−0.988851	+	0.148907i	$0.952424\pi$
$422$		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	−0.897320	−	0.441381i	$-0.854489\pi$
$431$	−20.0076	+	11.5514i	−0.963732	+	0.556411i	−0.0664126	+	0.997792i	$0.521155\pi$
$432$		0			0
$433$			11.1544i			0.536045i	0.963413	+	0.268022i	$0.0863701\pi$
$433$			11.1544i			0.536045i	−0.963413	+	0.268022i	$0.913630\pi$
$434$		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	$-0.986934\pi$
$443$		−	1.72740i		−	0.0820712i	0.999158	−	0.0410356i	$-0.0130657\pi$
$444$		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	−0.999497	−	0.0317125i	$-0.989904\pi$
$461$	−31.6005	+	18.2446i	−1.47178	+	0.849734i	−0.472285	+	0.881446i	$0.656571\pi$
$462$		0			0
$463$	20.7706	+	11.9919i	0.965294	+	0.557313i	0.897798	−	0.440407i	$-0.145166\pi$
$463$	20.7706	+	11.9919i	0.965294	+	0.557313i	0.0674955	+	0.997720i	$0.478499\pi$
$464$		0			0
$465$	−3.39907	−	19.6696i	−0.157628	−	0.912155i
$466$		0			0
$467$	0.322176	−	0.558026i	0.0149085	−	0.0258224i	−0.858475	−	0.512856i	$-0.828588\pi$
$467$	0.322176	−	0.558026i	0.0149085	−	0.0258224i	0.873383	+	0.487033i	$0.161921\pi$
$468$		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	0.0829823	+	0.996551i	$0.473556\pi$
$479$	−17.9804	+	31.1430i	−0.821547	+	1.42296i	−0.904530	+	0.426411i	$0.859778\pi$
$480$		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	−0.938376	−	0.345617i	$-0.887670\pi$
$487$	−24.4569	+	14.1202i	−1.10825	+	0.639848i	−0.169874	+	0.985466i	$0.554336\pi$
$488$		0			0
$489$	−9.75860	+	8.13182i	−0.441299	+	0.367734i
$490$		0			0
$491$	−11.6928	−	6.75082i	−0.527687	−	0.304660i	0.212387	−	0.977186i	$-0.431876\pi$
$491$	−11.6928	−	6.75082i	−0.527687	−	0.304660i	−0.740074	+	0.672526i	$0.765210\pi$
$492$		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	−0.208210	−	0.978084i	$-0.566764\pi$
$499$	11.9450	−	6.89643i	0.534730	−	0.308727i	0.742941	+	0.669357i	$0.233430\pi$
$500$		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	−0.614222	−	0.789133i	$-0.710530\pi$
$509$	−5.36782	+	3.09911i	−0.237925	+	0.137366i	0.376298	+	0.926499i	$0.377197\pi$
$510$		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	0.478068	−	0.878323i	$-0.341337\pi$
$521$	33.7303	−	19.4742i	1.47775	−	0.853181i	0.999684	+	0.0251422i	$0.00800385\pi$
$522$		0			0
$523$	−4.02860	+	6.97774i	−0.176158	+	0.305115i	−0.940562	−	0.339623i	$-0.889700\pi$
$523$	−4.02860	+	6.97774i	−0.176158	+	0.305115i	0.764403	+	0.644739i	$0.223034\pi$
$524$		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	−0.984916	−	0.173035i	$-0.944643\pi$
$541$	−7.96878	+	13.8023i	−0.342605	+	0.593409i	0.642311	+	0.766444i	$0.277976\pi$
$542$		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	−0.598967	−	0.800773i	$-0.704422\pi$
$547$	−4.79363	+	2.76760i	−0.204961	+	0.118334i	0.394006	+	0.919108i	$0.371089\pi$
$548$		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	0.521151	−	0.853464i	$-0.325503\pi$
$557$	−11.2941	−	19.5619i	−0.478546	−	0.828866i	−0.999697	+	0.0245983i	$0.992169\pi$
$558$		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	$0.0663125\pi$
$571$			9.88433i			0.413646i	−0.978378	+	0.206823i	$0.933688\pi$
$572$		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	−0.0777451	−	0.996973i	$-0.524772\pi$
$577$	17.9384	−	10.3568i	0.746787	−	0.431157i	0.824532	+	0.565816i	$0.191439\pi$
$578$		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	0.527224	−	0.849726i	$-0.323233\pi$
$587$	−11.4423	−	19.8186i	−0.472272	−	0.818000i	−0.999497	+	0.0317264i	$0.989899\pi$
$588$		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	0.999847	+	0.0175029i	$0.00557163\pi$
$593$	36.8909	+	21.2990i	1.51493	+	0.874644i	0.515081	+	0.857141i	$0.327762\pi$
$594$		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	$-0.984105\pi$
$599$		−	2.44324i		−	0.0998283i	0.998754	−	0.0499141i	$-0.0158948\pi$
$600$		0			0
$601$	−11.6323	+	6.71589i	−0.474490	+	0.273947i	−0.718117	−	0.695922i	$-0.754996\pi$
$601$	−11.6323	+	6.71589i	−0.474490	+	0.273947i	0.243627	+	0.969869i	$0.421663\pi$
$602$		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	0.999342	−	0.0362583i	$-0.0115439\pi$
$607$	11.5370	+	19.9826i	0.468271	+	0.811068i	−0.531072	+	0.847327i	$0.678211\pi$
$608$		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	0.702187	−	0.711993i	$-0.252207\pi$
$613$	−6.57373	−	11.3860i	−0.265511	−	0.459878i	−0.967697	+	0.252115i	$0.918874\pi$
$614$		0			0
$615$	−17.7994	+	48.3887i	−0.717741	+	1.95122i
$616$		0			0
$617$	−3.44699	+	5.97036i	−0.138771	+	0.240358i	−0.927032	−	0.374983i	$-0.877648\pi$
$617$	−3.44699	+	5.97036i	−0.138771	+	0.240358i	0.788261	+	0.615341i	$0.210982\pi$
$618$		0			0
$619$	17.7739	−	30.7853i	0.714394	−	1.23737i	−0.248799	−	0.968555i	$-0.580036\pi$
$619$	17.7739	−	30.7853i	0.714394	−	1.23737i	0.963193	−	0.268811i	$-0.0866308\pi$
$620$		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	$-0.839690\pi$
$631$		−	24.2459i		−	0.965213i	0.875837	−	0.482607i	$-0.160310\pi$
$632$		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	−0.349480	−	0.936944i	$-0.613642\pi$
$641$	16.1194	−	27.9196i	0.636677	−	1.10276i	0.986157	−	0.165814i	$-0.0530250\pi$
$642$		0			0
$643$	7.26173	−	12.5777i	0.286375	−	0.496016i	−0.686567	−	0.727067i	$-0.740883\pi$
$643$	7.26173	−	12.5777i	0.286375	−	0.496016i	0.972942	+	0.231051i	$0.0742164\pi$
$644$		0			0
$645$	0.145236	+	0.174291i	0.00571867	+	0.00686270i
$646$		0			0
$647$	−11.5332	−	19.9760i	−0.453416	−	0.785339i	0.545180	−	0.838319i	$-0.316461\pi$
$647$	−11.5332	−	19.9760i	−0.453416	−	0.785339i	−0.998596	+	0.0529801i	$0.983128\pi$
$648$		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	−0.998212	−	0.0597655i	$-0.980965\pi$
$653$	−14.0767	−	24.3816i	−0.550865	−	0.954126i	0.447348	−	0.894360i	$-0.352369\pi$
$654$		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	−0.600047	−	0.799965i	$-0.704852\pi$
$659$	−5.32112	+	3.07215i	−0.207281	+	0.119674i	0.392766	+	0.919638i	$0.371518\pi$
$660$		0			0
$661$		−	1.66168i		−	0.0646317i	−0.999478	−	0.0323159i	$-0.989712\pi$
$661$		−	1.66168i		−	0.0646317i	0.999478	−	0.0323159i	$-0.0102882\pi$
$662$		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	0.750106	−	0.661318i	$-0.230003\pi$
$673$	−5.12788	−	8.88175i	−0.197665	−	0.342366i	−0.947771	+	0.318952i	$0.896669\pi$
$674$		0			0
$675$	0.168390	−	16.4377i	0.00648134	−	0.632687i
$676$		0			0
$677$			22.3830i			0.860247i	0.902770	+	0.430123i	$0.141530\pi$
$677$			22.3830i			0.860247i	−0.902770	+	0.430123i	$0.858470\pi$
$678$		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	0.124009	−	0.992281i	$-0.460425\pi$
$683$	27.3196	−	15.7730i	1.04535	−	0.603536i	0.921345	+	0.388745i	$0.127091\pi$
$684$		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	−0.881374	−	0.472419i	$-0.843381\pi$
$719$	−0.846263	+	1.46577i	−0.0315603	+	0.0546640i	0.849814	+	0.527083i	$0.176714\pi$
$720$		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	−0.992898	−	0.118965i	$-0.962042\pi$
$727$	−16.1636	−	27.9962i	−0.599476	−	1.03832i	0.393423	−	0.919358i	$-0.371291\pi$
$728$		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	−0.998900	−	0.0468850i	$-0.985071\pi$
$733$	−39.4670	+	22.7863i	−1.45775	+	0.841631i	−0.458847	+	0.888516i	$0.651737\pi$
$734$		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	−0.465394	−	0.885104i	$-0.654087\pi$
$739$	1.86030	−	1.07404i	0.0684321	−	0.0395093i	0.533826	+	0.845595i	$0.320754\pi$
$740$		0			0
$741$	6.05949	+	35.0648i	0.222601	+	1.28814i
$742$		0			0
$743$	38.9145	+	22.4673i	1.42763	+	0.824244i	0.996934	−	0.0782508i	$-0.0249335\pi$
$743$	38.9145	+	22.4673i	1.42763	+	0.824244i	0.430700	+	0.902495i	$0.358267\pi$
$744$		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	0.00639780	−	0.999980i	$-0.497964\pi$
$751$	23.9954	−	13.8537i	0.875604	−	0.505530i	0.869207	+	0.494449i	$0.164630\pi$
$752$		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	0.0733328	−	0.997308i	$-0.476636\pi$
$761$	26.8605	−	15.5079i	0.973693	−	0.562162i	0.900360	+	0.435146i	$0.143303\pi$
$762$		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	0.420008	−	0.907521i	$-0.362027\pi$
$769$	−4.32392	−	2.49641i	−0.155924	−	0.0900230i	−0.575932	+	0.817498i	$0.695361\pi$
$770$		0			0
$771$	−8.23264	−	47.6403i	−0.296491	−	1.71572i
$772$		0			0
$773$	−11.5944	+	6.69400i	−0.417020	+	0.240767i	−0.693802	−	0.720166i	$-0.744065\pi$
$773$	−11.5944	+	6.69400i	−0.417020	+	0.240767i	0.276782	+	0.960933i	$0.410732\pi$
$774$		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	0.978931	−	0.204193i	$-0.0654569\pi$
$797$	36.4623	+	21.0515i	1.29156	+	0.745682i	0.312629	+	0.949875i	$0.398790\pi$
$798$		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	0.884240	−	0.467032i	$-0.154677\pi$
$809$	1.07111	+	1.85521i	0.0376582	+	0.0652258i	−0.846582	+	0.532258i	$0.821344\pi$
$810$		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	$-0.828816\pi$
$823$		−	29.3902i		−	1.02448i	0.858843	−	0.512240i	$-0.171184\pi$
$824$		0			0
$825$	2.11029	+	12.2118i	0.0734710	+	0.425159i
$826$		0			0
$827$			22.6869i			0.788900i	0.918917	+	0.394450i	$0.129065\pi$
$827$			22.6869i			0.788900i	−0.918917	+	0.394450i	$0.870935\pi$
$828$		0			0
$829$	−19.3396	+	11.1657i	−0.671691	+	0.387801i	−0.796717	−	0.604353i	$-0.793432\pi$
$829$	−19.3396	+	11.1657i	−0.671691	+	0.387801i	0.125026	+	0.992153i	$0.460098\pi$
$830$		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	−0.880215	−	0.474574i	$-0.842602\pi$
$839$	−24.6526	−	42.6995i	−0.851101	−	1.47415i	0.0291142	−	0.999576i	$-0.490731\pi$
$840$		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	−0.540085	−	0.841611i	$-0.681608\pi$
$853$	−2.37362	+	1.37041i	−0.0812712	+	0.0469220i	0.458814	+	0.888533i	$0.348275\pi$
$854$		0			0
$855$	17.6768	−	20.7766i	0.604533	−	0.710543i
$856$		0			0
$857$	2.29909	+	1.32738i	0.0785355	+	0.0453425i	0.538753	−	0.842463i	$-0.318895\pi$
$857$	2.29909	+	1.32738i	0.0785355	+	0.0453425i	−0.460218	+	0.887806i	$0.652229\pi$
$858$		0			0
$859$	20.4410	+	35.4049i	0.697440	+	1.20800i	0.969351	+	0.245679i	$0.0790108\pi$
$859$	20.4410	+	35.4049i	0.697440	+	1.20800i	−0.271912	+	0.962322i	$0.587656\pi$
$860$		0			0
$861$	30.2684	−	36.9217i	1.03154	−	1.25829i
$862$		0			0
$863$	−36.5486	−	21.1013i	−1.24413	−	0.718298i	−0.274196	−	0.961674i	$-0.588412\pi$
$863$	−36.5486	−	21.1013i	−1.24413	−	0.718298i	−0.969932	+	0.243376i	$0.921745\pi$
$864$		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	0.760448	+	0.649399i	$0.224979\pi$
$877$	27.9149	+	48.3501i	0.942620	+	1.63267i	0.182171	+	0.983267i	$0.441687\pi$
$878$		0			0
$879$	0.238133	−	0.198435i	0.00803201	−	0.00669305i
$880$		0			0
$881$		−	49.2533i		−	1.65939i	−0.558219	−	0.829693i	$-0.688515\pi$
$881$		−	49.2533i		−	1.65939i	0.558219	−	0.829693i	$-0.311485\pi$
$882$		0			0
$883$		−	3.87310i		−	0.130340i	−0.997874	−	0.0651701i	$-0.979241\pi$
$883$		−	3.87310i		−	0.130340i	0.997874	−	0.0651701i	$-0.0207590\pi$
$884$		0			0
$885$	−5.23131	−	30.2723i	−0.175848	−	1.01759i
$886$		0			0
$887$	0.897157	+	1.55392i	0.0301236	+	0.0521756i	0.880694	−	0.473685i	$-0.157077\pi$
$887$	0.897157	+	1.55392i	0.0301236	+	0.0521756i	−0.850571	+	0.525861i	$0.823743\pi$
$888$		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	0.706156	−	0.708056i	$-0.250428\pi$
$907$	13.4331	+	7.75561i	0.446039	+	0.257521i	−0.260117	+	0.965577i	$0.583761\pi$
$908$		0			0
$909$	6.00587	+	16.8583i	0.199202	+	0.559155i
$910$		0			0
$911$	−38.1263	+	22.0122i	−1.26318	+	0.729297i	−0.973688	−	0.227883i	$-0.926819\pi$
$911$	−38.1263	+	22.0122i	−1.26318	+	0.729297i	−0.289491	+	0.957181i	$0.593486\pi$
$912$		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	0.909551	−	0.415591i	$-0.136425\pi$
$919$	30.4488	+	17.5796i	1.00441	+	0.579899i	0.0948631	+	0.995490i	$0.469759\pi$
$920$		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	$0.155578\pi$
$929$			28.6223i			0.939069i	−0.882914	+	0.469534i	$0.844422\pi$
$930$		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	$0.0126172\pi$
$937$			2.42605i			0.0792555i	−0.999215	+	0.0396277i	$0.987383\pi$
$938$		0			0
$939$	8.42415	+	3.09876i	0.274912	+	0.101124i
$940$		0			0
$941$		−	33.6961i		−	1.09846i	−0.835671	−	0.549231i	$-0.814921\pi$
$941$		−	33.6961i		−	1.09846i	0.835671	−	0.549231i	$-0.185079\pi$
$942$		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	$0.349322\pi$
$947$			54.7789i			1.78007i	−0.455888	+	0.890037i	$0.650678\pi$
$948$		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	0.648589	−	0.761139i	$-0.275360\pi$
$967$	9.75555	+	5.63237i	0.313717	+	0.181125i	−0.334871	+	0.942264i	$0.608693\pi$
$968$		0			0
$969$	28.3639	+	10.4334i	0.911178	+	0.335170i
$970$		0			0
$971$	−9.41975	+	16.3155i	−0.302294	+	0.523589i	−0.976655	−	0.214813i	$-0.931086\pi$
$971$	−9.41975	+	16.3155i	−0.302294	+	0.523589i	0.674361	+	0.738402i	$0.264419\pi$
$972$		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	−0.571285	−	0.820752i	$-0.693555\pi$
$983$	13.3296	−	23.0876i	0.425150	−	0.736381i	0.996434	+	0.0843710i	$0.0268881\pi$
$984$		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	−0.989089	−	0.147319i	$-0.952936\pi$
$991$	−42.6887	+	24.6463i	−1.35605	+	0.782917i	−0.366962	+	0.930236i	$0.619602\pi$
$992$		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	0.388762	−	0.921338i	$-0.372903\pi$
$997$	−6.78110	−	3.91507i	−0.214760	−	0.123992i	−0.603521	+	0.797347i	$0.706236\pi$
$998$		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.607.7	yes	24
3.2	odd	2		3024.2.cz.h.1279.2		24
4.3	odd	2		1008.2.cz.h.607.6	yes	24
7.3	odd	6		1008.2.bf.g.31.2	✓	24
9.2	odd	6		3024.2.bf.g.2287.2		24
9.7	even	3		1008.2.bf.h.943.11	yes	24
12.11	even	2		3024.2.cz.g.1279.2		24
21.17	even	6		3024.2.bf.h.1711.11		24
28.3	even	6		1008.2.bf.h.31.11	yes	24
36.7	odd	6		1008.2.bf.g.943.2	yes	24
36.11	even	6		3024.2.bf.h.2287.2		24
63.38	even	6		3024.2.cz.g.2719.2		24
63.52	odd	6		1008.2.cz.h.367.6	yes	24
84.59	odd	6		3024.2.bf.g.1711.11		24
252.115	even	6	inner	1008.2.cz.g.367.7	yes	24
252.227	odd	6		3024.2.cz.h.2719.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.g.31.2	✓	24	7.3	odd	6
1008.2.bf.g.943.2	yes	24	36.7	odd	6
1008.2.bf.h.31.11	yes	24	28.3	even	6
1008.2.bf.h.943.11	yes	24	9.7	even	3
1008.2.cz.g.367.7	yes	24	252.115	even	6	inner
1008.2.cz.g.607.7	yes	24	1.1	even	1	trivial
1008.2.cz.h.367.6	yes	24	63.52	odd	6
1008.2.cz.h.607.6	yes	24	4.3	odd	2
3024.2.bf.g.1711.11		24	84.59	odd	6
3024.2.bf.g.2287.2		24	9.2	odd	6
3024.2.bf.h.1711.11		24	21.17	even	6
3024.2.bf.h.2287.2		24	36.11	even	6
3024.2.cz.g.1279.2		24	12.11	even	2
3024.2.cz.g.2719.2		24	63.38	even	6
3024.2.cz.h.1279.2		24	3.2	odd	2
3024.2.cz.h.2719.2		24	252.227	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more