LMFDB - Embedded newform 280.2.bo.a.17.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(17,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))

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

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

chi := DirichletCharacter("280.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bo (of order $12$, degree $4$, 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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			17.3
Character	$\chi$	$=$	280.17
Dual form			280.2.bo.a.33.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00047 + 0.536025i) q^{3} +(1.38383 + 1.75642i) q^{5} +(1.24986 - 2.33192i) q^{7} +(1.11649 - 0.644605i) q^{9} +O(q^{10})$	\(q+(-2.00047 + 0.536025i) q^{3} +(1.38383 + 1.75642i) q^{5} +(1.24986 - 2.33192i) q^{7} +(1.11649 - 0.644605i) q^{9} +(-3.09606 + 5.36253i) q^{11} +(0.782930 + 0.782930i) q^{13} +(-3.70979 - 2.77191i) q^{15} +(1.18027 + 4.40483i) q^{17} +(2.37523 + 4.11401i) q^{19} +(-1.25033 + 5.33490i) q^{21} +(-6.52089 - 1.74727i) q^{23} +(-1.17005 + 4.86117i) q^{25} +(2.50536 - 2.50536i) q^{27} +5.30715i q^{29} +(2.16657 + 1.25087i) q^{31} +(3.31913 - 12.3871i) q^{33} +(5.82543 - 1.03170i) q^{35} +(1.77376 - 6.61976i) q^{37} +(-1.98590 - 1.14656i) q^{39} -2.51428i q^{41} +(0.404551 - 0.404551i) q^{43} +(2.67723 + 1.06901i) q^{45} +(8.63838 + 2.31465i) q^{47} +(-3.87572 - 5.82913i) q^{49} +(-4.72220 - 8.17909i) q^{51} +(-2.66008 - 9.92755i) q^{53} +(-13.7033 + 1.98282i) q^{55} +(-6.95679 - 6.95679i) q^{57} +(0.0710796 - 0.123113i) q^{59} +(2.67752 - 1.54587i) q^{61} +(-0.107719 - 3.40923i) q^{63} +(-0.291718 + 2.45860i) q^{65} +(-4.34482 + 1.16419i) q^{67} +13.9814 q^{69} +10.3517 q^{71} +(-1.80614 + 0.483952i) q^{73} +(-0.265056 - 10.3518i) q^{75} +(8.63537 + 13.9221i) q^{77} +(5.42390 - 3.13149i) q^{79} +(-5.60278 + 9.70431i) q^{81} +(5.82768 + 5.82768i) q^{83} +(-6.10346 + 8.16858i) q^{85} +(-2.84477 - 10.6168i) q^{87} +(-4.58578 - 7.94281i) q^{89} +(2.80428 - 0.847183i) q^{91} +(-5.00466 - 1.34100i) q^{93} +(-3.93905 + 9.86498i) q^{95} +(2.64580 - 2.64580i) q^{97} +7.98294i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{7}+O(q^{10}) $ 48 * q - 4 * q^7	$ 48 q - 4 q^{7} + 4 q^{11} + 8 q^{15} - 4 q^{21} - 4 q^{23} - 8 q^{25} - 36 q^{33} + 24 q^{35} + 8 q^{37} - 16 q^{43} + 48 q^{45} + 24 q^{51} + 16 q^{53} - 96 q^{57} - 36 q^{61} - 68 q^{63} + 12 q^{65} - 16 q^{67} - 64 q^{71} - 48 q^{73} - 48 q^{75} + 4 q^{77} - 40 q^{85} - 12 q^{87} - 80 q^{91} + 24 q^{95}+O(q^{100}) $ 48 * q - 4 * q^7 + 4 * q^11 + 8 * q^15 - 4 * q^21 - 4 * q^23 - 8 * q^25 - 36 * q^33 + 24 * q^35 + 8 * q^37 - 16 * q^43 + 48 * q^45 + 24 * q^51 + 16 * q^53 - 96 * q^57 - 36 * q^61 - 68 * q^63 + 12 * q^65 - 16 * q^67 - 64 * q^71 - 48 * q^73 - 48 * q^75 + 4 * q^77 - 40 * q^85 - 12 * q^87 - 80 * q^91 + 24 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	−2.00047	+	0.536025i	−1.15497	+	0.309474i	−0.784956	−	0.619551i	$-0.787315\pi$
$3$	−2.00047	+	0.536025i	−1.15497	+	0.309474i	−0.370017	+	0.929025i	$0.620648\pi$
$4$		0			0
$5$	1.38383	+	1.75642i	0.618866	+	0.785497i
$5$	1.38383	+	1.75642i	0.618866	+	0.785497i
$6$		0			0
$7$	1.24986	−	2.33192i	0.472401	−	0.881384i
$7$	1.24986	−	2.33192i	0.472401	−	0.881384i
$8$		0			0
$9$	1.11649	−	0.644605i	0.372163	−	0.214868i
$10$		0			0
$11$	−3.09606	+	5.36253i	−0.933496	+	1.61686i	−0.156202	+	0.987725i	$0.549925\pi$
$11$	−3.09606	+	5.36253i	−0.933496	+	1.61686i	−0.777294	+	0.629138i	$0.783408\pi$
$12$		0			0
$13$	0.782930	+	0.782930i	0.217146	+	0.217146i	0.807294	−	0.590149i	$-0.200931\pi$
$13$	0.782930	+	0.782930i	0.217146	+	0.217146i	−0.590149	+	0.807294i	$0.700931\pi$
$14$		0			0
$15$	−3.70979	−	2.77191i	−0.957864	−	0.715705i
$16$		0			0
$17$	1.18027	+	4.40483i	0.286258	+	1.06833i	0.947915	+	0.318522i	$0.103187\pi$
$17$	1.18027	+	4.40483i	0.286258	+	1.06833i	−0.661658	+	0.749806i	$0.730147\pi$
$18$		0			0
$19$	2.37523	+	4.11401i	0.544914	+	0.943819i	0.998612	+	0.0526638i	$0.0167712\pi$
$19$	2.37523	+	4.11401i	0.544914	+	0.943819i	−0.453698	+	0.891156i	$0.649895\pi$
$20$		0			0
$21$	−1.25033	+	5.33490i	−0.272845	+	1.16417i
$22$		0			0
$23$	−6.52089	−	1.74727i	−1.35970	−	0.364330i	−0.495993	−	0.868326i	$-0.665196\pi$
$23$	−6.52089	−	1.74727i	−1.35970	−	0.364330i	−0.863706	+	0.503996i	$0.831863\pi$
$24$		0			0
$25$	−1.17005	+	4.86117i	−0.234010	+	0.972234i
$26$		0			0
$27$	2.50536	−	2.50536i	0.482157	−	0.482157i
$28$		0			0
$29$			5.30715i			0.985514i	0.870167	+	0.492757i	$0.164011\pi$
$29$			5.30715i			0.985514i	−0.870167	+	0.492757i	$0.835989\pi$
$30$		0			0
$31$	2.16657	+	1.25087i	0.389128	+	0.224663i	0.681782	−	0.731555i	$-0.261205\pi$
$31$	2.16657	+	1.25087i	0.389128	+	0.224663i	−0.292654	+	0.956218i	$0.594539\pi$
$32$		0			0
$33$	3.31913	−	12.3871i	0.577786	−	2.15633i
$34$		0			0
$35$	5.82543	−	1.03170i	0.984677	−	0.174389i
$36$		0			0
$37$	1.77376	−	6.61976i	0.291604	−	1.08828i	−0.652273	−	0.757984i	$-0.726184\pi$
$37$	1.77376	−	6.61976i	0.291604	−	1.08828i	0.943877	−	0.330298i	$-0.107149\pi$
$38$		0			0
$39$	−1.98590	−	1.14656i	−0.317998	−	0.183596i
$40$		0			0
$41$		−	2.51428i		−	0.392665i	−0.980537	−	0.196333i	$-0.937097\pi$
$41$		−	2.51428i		−	0.392665i	0.980537	−	0.196333i	$-0.0629032\pi$
$42$		0			0
$43$	0.404551	−	0.404551i	0.0616934	−	0.0616934i	−0.675587	−	0.737280i	$-0.736110\pi$
$43$	0.404551	−	0.404551i	0.0616934	−	0.0616934i	0.737280	+	0.675587i	$0.236110\pi$
$44$		0			0
$45$	2.67723	+	1.06901i	0.399097	+	0.159358i
$46$		0			0
$47$	8.63838	+	2.31465i	1.26004	+	0.337626i	0.826206	−	0.563368i	$-0.190495\pi$
$47$	8.63838	+	2.31465i	1.26004	+	0.337626i	0.433832	+	0.900994i	$0.357161\pi$
$48$		0			0
$49$	−3.87572	−	5.82913i	−0.553675	−	0.832733i
$50$		0			0
$51$	−4.72220	−	8.17909i	−0.661240	−	1.14530i
$52$		0			0
$53$	−2.66008	−	9.92755i	−0.365390	−	1.36365i	−0.866892	−	0.498497i	$-0.833886\pi$
$53$	−2.66008	−	9.92755i	−0.365390	−	1.36365i	0.501502	−	0.865157i	$-0.332781\pi$
$54$		0			0
$55$	−13.7033	+	1.98282i	−1.84775	+	0.267363i
$56$		0			0
$57$	−6.95679	−	6.95679i	−0.921449	−	0.921449i
$58$		0			0
$59$	0.0710796	−	0.123113i	0.00925377	−	0.0160280i	−0.861361	−	0.507993i	$-0.830388\pi$
$59$	0.0710796	−	0.123113i	0.00925377	−	0.0160280i	0.870615	+	0.491965i	$0.163721\pi$
$60$		0			0
$61$	2.67752	−	1.54587i	0.342822	−	0.197928i	−0.318697	−	0.947856i	$-0.603245\pi$
$61$	2.67752	−	1.54587i	0.342822	−	0.197928i	0.661519	+	0.749928i	$0.269912\pi$
$62$		0			0
$63$	−0.107719	−	3.40923i	−0.0135714	−	0.429523i
$64$		0			0
$65$	−0.291718	+	2.45860i	−0.0361832	+	0.304951i
$66$		0			0
$67$	−4.34482	+	1.16419i	−0.530804	+	0.142228i	−0.514259	−	0.857635i	$-0.671933\pi$
$67$	−4.34482	+	1.16419i	−0.530804	+	0.142228i	−0.0165444	+	0.999863i	$0.505266\pi$
$68$		0			0
$69$	13.9814			1.68317
$70$		0			0
$71$	10.3517			1.22852			0.614258	−	0.789105i	$-0.289455\pi$
$71$	10.3517			1.22852			0.614258	+	0.789105i	$0.289455\pi$
$72$		0			0
$73$	−1.80614	+	0.483952i	−0.211392	+	0.0566424i	−0.362961	−	0.931804i	$-0.618234\pi$
$73$	−1.80614	+	0.483952i	−0.211392	+	0.0566424i	0.151569	+	0.988447i	$0.451567\pi$
$74$		0			0
$75$	−0.265056	−	10.3518i	−0.0306060	−	1.19532i
$76$		0			0
$77$	8.63537	+	13.9221i	0.984092	+	1.58658i
$78$		0			0
$79$	5.42390	−	3.13149i	0.610236	−	0.352320i	−0.162822	−	0.986655i	$-0.552060\pi$
$79$	5.42390	−	3.13149i	0.610236	−	0.352320i	0.773058	+	0.634336i	$0.218726\pi$
$80$		0			0
$81$	−5.60278	+	9.70431i	−0.622532	+	1.07826i
$82$		0			0
$83$	5.82768	+	5.82768i	0.639671	+	0.639671i	0.950474	−	0.310803i	$-0.100598\pi$
$83$	5.82768	+	5.82768i	0.639671	+	0.639671i	−0.310803	+	0.950474i	$0.600598\pi$
$84$		0			0
$85$	−6.10346	+	8.16858i	−0.662013	+	0.886007i
$86$		0			0
$87$	−2.84477	−	10.6168i	−0.304991	−	1.13824i
$88$		0			0
$89$	−4.58578	−	7.94281i	−0.486092	−	0.841936i	0.513780	−	0.857922i	$-0.328245\pi$
$89$	−4.58578	−	7.94281i	−0.486092	−	0.841936i	−0.999872	+	0.0159859i	$0.994911\pi$
$90$		0			0
$91$	2.80428	−	0.847183i	0.293969	−	0.0888089i
$92$		0			0
$93$	−5.00466	−	1.34100i	−0.518960	−	0.139055i
$94$		0			0
$95$	−3.93905	+	9.86498i	−0.404138	+	1.01213i
$96$		0			0
$97$	2.64580	−	2.64580i	0.268641	−	0.268641i	−0.559912	−	0.828552i	$-0.689165\pi$
$97$	2.64580	−	2.64580i	0.268641	−	0.268641i	0.828552	+	0.559912i	$0.189165\pi$
$98$		0			0
$99$			7.98294i			0.802315i
$100$		0			0
$101$	−4.36323	−	2.51911i	−0.434157	−	0.250661i	0.266959	−	0.963708i	$-0.413981\pi$
$101$	−4.36323	−	2.51911i	−0.434157	−	0.250661i	−0.701116	+	0.713047i	$0.747315\pi$
$102$		0			0
$103$	0.710053	−	2.64995i	0.0699636	−	0.261108i	−0.922081	−	0.386998i	$-0.873512\pi$
$103$	0.710053	−	2.64995i	0.0699636	−	0.261108i	0.992044	+	0.125890i	$0.0401787\pi$
$104$		0			0
$105$	−11.1006	+	5.18646i	−1.08331	+	0.506147i
$106$		0			0
$107$	−3.79590	+	14.1665i	−0.366963	+	1.36953i	0.497776	+	0.867306i	$0.334150\pi$
$107$	−3.79590	+	14.1665i	−0.366963	+	1.36953i	−0.864740	+	0.502221i	$0.832517\pi$
$108$		0			0
$109$	13.0388	+	7.52797i	1.24889	+	0.721049i	0.970889	−	0.239531i	$-0.0769936\pi$
$109$	13.0388	+	7.52797i	1.24889	+	0.721049i	0.278005	+	0.960580i	$0.410327\pi$
$110$		0			0
$111$			14.1934i			1.34718i
$112$		0			0
$113$	1.41309	−	1.41309i	0.132932	−	0.132932i	−0.637510	−	0.770442i	$-0.720035\pi$
$113$	1.41309	−	1.41309i	0.132932	−	0.132932i	0.770442	+	0.637510i	$0.220035\pi$
$114$		0			0
$115$	−5.95483	−	13.8714i	−0.555291	−	1.29351i
$116$		0			0
$117$	1.37881	+	0.369452i	0.127471	+	0.0341558i
$118$		0			0
$119$	11.7469	+	2.75310i	1.07684	+	0.252376i
$120$		0			0
$121$	−13.6711	−	23.6791i	−1.24283	−	2.15264i
$122$		0			0
$123$	1.34772	+	5.02976i	0.121520	+	0.453518i
$124$		0			0
$125$	−10.1574	+	4.67191i	−0.908508	+	0.417868i
$126$		0			0
$127$	−4.61249	−	4.61249i	−0.409292	−	0.409292i	0.472200	−	0.881492i	$-0.343460\pi$
$127$	−4.61249	−	4.61249i	−0.409292	−	0.409292i	−0.881492	+	0.472200i	$0.843460\pi$
$128$		0			0
$129$	−0.592443	+	1.02614i	−0.0521617	+	0.0903467i
$130$		0			0
$131$	17.5930	−	10.1573i	1.53711	−	0.887448i	0.538099	−	0.842882i	$-0.319143\pi$
$131$	17.5930	−	10.1573i	1.53711	−	0.887448i	0.999006	−	0.0445661i	$-0.0141905\pi$
$132$		0			0
$133$	12.5622	−	0.396922i	1.08929	−	0.0344175i
$134$		0			0
$135$	7.86746	+	0.933492i	0.677123	+	0.0803422i
$136$		0			0
$137$	6.84734	−	1.83474i	0.585008	−	0.156752i	0.0458371	−	0.998949i	$-0.485404\pi$
$137$	6.84734	−	1.83474i	0.585008	−	0.156752i	0.539171	+	0.842197i	$0.318738\pi$
$138$		0			0
$139$	−7.94314			−0.673728			−0.336864	−	0.941553i	$-0.609366\pi$
$139$	−7.94314			−0.673728			−0.336864	+	0.941553i	$0.609366\pi$
$140$		0			0
$141$	−18.5216			−1.55980
$142$		0			0
$143$	−6.62248	+	1.77449i	−0.553799	+	0.148390i
$144$		0			0
$145$	−9.32161	+	7.34418i	−0.774118	+	0.609901i
$146$		0			0
$147$	10.8778	+	9.58353i	0.897189	+	0.790436i
$148$		0			0
$149$	−2.61568	+	1.51016i	−0.214285	+	0.123717i	−0.603301	−	0.797514i	$-0.706148\pi$
$149$	−2.61568	+	1.51016i	−0.214285	+	0.123717i	0.389016	+	0.921231i	$0.372815\pi$
$150$		0			0
$151$	2.00848	−	3.47878i	0.163447	−	0.283099i	−0.772655	−	0.634826i	$-0.781072\pi$
$151$	2.00848	−	3.47878i	0.163447	−	0.283099i	0.936103	+	0.351726i	$0.114405\pi$
$152$		0			0
$153$	4.15714	+	4.15714i	0.336085	+	0.336085i
$154$		0			0
$155$	0.801099	+	5.53641i	0.0643459	+	0.444695i
$156$		0			0
$157$	0.989145	+	3.69154i	0.0789424	+	0.294617i	0.994098	−	0.108483i	$-0.0345993\pi$
$157$	0.989145	+	3.69154i	0.0789424	+	0.294617i	−0.915156	+	0.403100i	$0.867933\pi$
$158$		0			0
$159$	10.6428	+	18.4339i	0.844031	+	1.46190i
$160$		0			0
$161$	−12.2247	+	13.0224i	−0.963438	+	1.02631i
$162$		0			0
$163$	−8.52498	−	2.28426i	−0.667728	−	0.178917i	−0.0909967	−	0.995851i	$-0.529005\pi$
$163$	−8.52498	−	2.28426i	−0.667728	−	0.178917i	−0.576731	+	0.816934i	$0.695672\pi$
$164$		0			0
$165$	26.3502	−	11.3119i	2.05136	−	0.880628i
$166$		0			0
$167$	5.91156	−	5.91156i	0.457450	−	0.457450i	−0.440367	−	0.897818i	$-0.645152\pi$
$167$	5.91156	−	5.91156i	0.457450	−	0.457450i	0.897818	+	0.440367i	$0.145152\pi$
$168$		0			0
$169$		−	11.7740i		−	0.905695i
$170$		0			0
$171$	5.30383	+	3.06217i	0.405594	+	0.234170i
$172$		0			0
$173$	−5.80426	+	21.6618i	−0.441290	+	1.64692i	0.284260	+	0.958747i	$0.408252\pi$
$173$	−5.80426	+	21.6618i	−0.441290	+	1.64692i	−0.725550	+	0.688170i	$0.758414\pi$
$174$		0			0
$175$	9.87348	+	8.80423i	0.746365	+	0.665537i
$176$		0			0
$177$	−0.0762008	+	0.284385i	−0.00572760	+	0.0213757i
$178$		0			0
$179$	−9.81825	−	5.66857i	−0.733850	−	0.423689i	0.0859789	−	0.996297i	$-0.472598\pi$
$179$	−9.81825	−	5.66857i	−0.733850	−	0.423689i	−0.819829	+	0.572608i	$0.805932\pi$
$180$		0			0
$181$			8.90901i			0.662201i	0.943595	+	0.331101i	$0.107420\pi$
$181$			8.90901i			0.662201i	−0.943595	+	0.331101i	$0.892580\pi$
$182$		0			0
$183$	−4.52768	+	4.52768i	−0.334696	+	0.334696i
$184$		0			0
$185$	14.0817	−	6.04512i	1.03531	−	0.444446i
$186$		0			0
$187$	−27.2752	−	7.30837i	−1.99456	−	0.534441i
$188$		0			0
$189$	−2.71097	−	8.97364i	−0.197194	−	0.652737i
$190$		0			0
$191$	8.07475	+	13.9859i	0.584268	+	1.01198i	0.994966	+	0.100211i	$0.0319517\pi$
$191$	8.07475	+	13.9859i	0.584268	+	1.01198i	−0.410698	+	0.911771i	$0.634715\pi$
$192$		0			0
$193$	−0.102134	−	0.381168i	−0.00735174	−	0.0274371i	0.962153	−	0.272511i	$-0.0878543\pi$
$193$	−0.102134	−	0.381168i	−0.00735174	−	0.0274371i	−0.969504	+	0.245074i	$0.921188\pi$
$194$		0			0
$195$	−0.734295	−	5.07472i	−0.0525839	−	0.363408i
$196$		0			0
$197$	−8.65729	−	8.65729i	−0.616806	−	0.616806i	0.327904	−	0.944711i	$-0.393658\pi$
$197$	−8.65729	−	8.65729i	−0.616806	−	0.616806i	−0.944711	+	0.327904i	$0.893658\pi$
$198$		0			0
$199$	−4.96288	+	8.59596i	−0.351809	+	0.609351i	−0.986566	−	0.163360i	$-0.947767\pi$
$199$	−4.96288	+	8.59596i	−0.351809	+	0.609351i	0.634757	+	0.772711i	$0.281100\pi$
$200$		0			0
$201$	8.06765	−	4.65786i	0.569048	−	0.328540i
$202$		0			0
$203$	12.3759	+	6.63318i	0.868616	+	0.465558i
$204$		0			0
$205$	4.41615	−	3.47933i	0.308437	−	0.243007i
$206$		0			0
$207$	−8.40680	+	2.25259i	−0.584313	+	0.156566i
$208$		0			0
$209$	−29.4153			−2.03470
$210$		0			0
$211$	9.25891			0.637410			0.318705	−	0.947854i	$-0.396752\pi$
$211$	9.25891			0.637410			0.318705	+	0.947854i	$0.396752\pi$
$212$		0			0
$213$	−20.7082	+	5.54875i	−1.41890	+	0.380194i
$214$		0			0
$215$	1.27039	+	0.150735i	0.0866399	+	0.0102800i
$216$		0			0
$217$	5.62484	−	3.48887i	0.381839	−	0.236840i
$218$		0			0
$219$	3.35371	−	1.93627i	0.226623	−	0.130841i
$220$		0			0
$221$	−2.52461	+	4.37274i	−0.169823	+	0.294143i
$222$		0			0
$223$	2.26542	+	2.26542i	0.151703	+	0.151703i	0.778878	−	0.627175i	$-0.215789\pi$
$223$	2.26542	+	2.26542i	0.151703	+	0.151703i	−0.627175	+	0.778878i	$0.715789\pi$
$224$		0			0
$225$	1.82719	+	6.18167i	0.121813	+	0.412111i
$226$		0			0
$227$	−5.72434	−	21.3635i	−0.379938	−	1.41795i	−0.845994	−	0.533192i	$-0.820992\pi$
$227$	−5.72434	−	21.3635i	−0.379938	−	1.41795i	0.466057	−	0.884755i	$-0.345674\pi$
$228$		0			0
$229$	−3.16366	−	5.47963i	−0.209061	−	0.362104i	0.742358	−	0.670003i	$-0.233707\pi$
$229$	−3.16366	−	5.47963i	−0.209061	−	0.362104i	−0.951419	+	0.307899i	$0.900374\pi$
$230$		0			0
$231$	−24.7374	−	23.2221i	−1.62760	−	1.52790i
$232$		0			0
$233$	10.1387	+	2.71667i	0.664211	+	0.177975i	0.575145	−	0.818051i	$-0.304945\pi$
$233$	10.1387	+	2.71667i	0.664211	+	0.177975i	0.0890650	+	0.996026i	$0.471612\pi$
$234$		0			0
$235$	7.88852	+	18.3757i	0.514590	+	1.19870i
$236$		0			0
$237$	−9.17180	+	9.17180i	−0.595772	+	0.595772i
$238$		0			0
$239$		−	2.87268i		−	0.185818i	−0.995675	−	0.0929091i	$-0.970383\pi$
$239$		−	2.87268i		−	0.185818i	0.995675	−	0.0929091i	$-0.0296166\pi$
$240$		0			0
$241$	25.6935	+	14.8342i	1.65507	+	0.955553i	0.974943	+	0.222456i	$0.0714074\pi$
$241$	25.6935	+	14.8342i	1.65507	+	0.955553i	0.680124	+	0.733097i	$0.261926\pi$
$242$		0			0
$243$	3.25539	−	12.1493i	0.208833	−	0.779376i
$244$		0			0
$245$	4.87510	−	14.8739i	0.311459	−	0.950260i
$246$		0			0
$247$	−1.36135	+	5.08062i	−0.0866205	+	0.323272i
$248$		0			0
$249$	−14.7819	−	8.53433i	−0.936764	−	0.540841i
$250$		0			0
$251$		−	15.0696i		−	0.951182i	−0.879667	−	0.475591i	$-0.842234\pi$
$251$		−	15.0696i		−	0.951182i	0.879667	−	0.475591i	$-0.157766\pi$
$252$		0			0
$253$	29.5588	−	29.5588i	1.85835	−	1.85835i
$254$		0			0
$255$	7.83124	−	19.6126i	0.490412	−	1.22819i
$256$		0			0
$257$	22.7927	+	6.10728i	1.42177	+	0.380962i	0.886111	−	0.463474i	$-0.153397\pi$
$257$	22.7927	+	6.10728i	1.42177	+	0.380962i	0.535658	+	0.844435i	$0.320064\pi$
$258$		0			0
$259$	−13.2198	−	12.4100i	−0.821440	−	0.771121i
$260$		0			0
$261$	3.42102	+	5.92538i	0.211756	+	0.366772i
$262$		0			0
$263$	−5.21774	−	19.4729i	−0.321739	−	1.20075i	−0.917549	−	0.397622i	$-0.869835\pi$
$263$	−5.21774	−	19.4729i	−0.321739	−	1.20075i	0.595810	−	0.803126i	$-0.296831\pi$
$264$		0			0
$265$	13.7559	−	18.4102i	0.845018	−	1.13093i
$266$		0			0
$267$	13.4313	+	13.4313i	0.821980	+	0.821980i
$268$		0			0
$269$	−6.41634	+	11.1134i	−0.391211	+	0.677597i	−0.992610	−	0.121352i	$-0.961277\pi$
$269$	−6.41634	+	11.1134i	−0.391211	+	0.677597i	0.601399	+	0.798949i	$0.294610\pi$
$270$		0			0
$271$	1.51548	−	0.874961i	0.0920587	−	0.0531501i	−0.453264	−	0.891376i	$-0.649740\pi$
$271$	1.51548	−	0.874961i	0.0920587	−	0.0531501i	0.545323	+	0.838226i	$0.316407\pi$
$272$		0			0
$273$	−5.15577	+	3.19793i	−0.312042	+	0.193547i
$274$		0			0
$275$	−22.4456	−	21.3249i	−1.35352	−	1.28594i
$276$		0			0
$277$	5.44886	−	1.46002i	0.327390	−	0.0877240i	−0.0913802	−	0.995816i	$-0.529128\pi$
$277$	5.44886	−	1.46002i	0.327390	−	0.0877240i	0.418770	+	0.908092i	$0.362461\pi$
$278$		0			0
$279$	3.22527			0.193092
$280$		0			0
$281$	18.7713			1.11980			0.559901	−	0.828560i	$-0.310839\pi$
$281$	18.7713			1.11980			0.559901	+	0.828560i	$0.310839\pi$
$282$		0			0
$283$	−12.0479	+	3.22822i	−0.716172	+	0.191898i	−0.598463	−	0.801150i	$-0.704222\pi$
$283$	−12.0479	+	3.22822i	−0.716172	+	0.191898i	−0.117709	+	0.993048i	$0.537555\pi$
$284$		0			0
$285$	2.59208	−	21.8461i	0.153542	−	1.29405i
$286$		0			0
$287$	−5.86312	−	3.14249i	−0.346089	−	0.185495i
$288$		0			0
$289$	−3.28707	+	1.89779i	−0.193357	+	0.111635i
$290$		0			0
$291$	−3.87464	+	6.71107i	−0.227135	+	0.393410i
$292$		0			0
$293$	0.810657	+	0.810657i	0.0473591	+	0.0473591i	0.730390	−	0.683031i	$-0.239338\pi$
$293$	0.810657	+	0.810657i	0.0473591	+	0.0473591i	−0.683031	+	0.730390i	$0.739338\pi$
$294$		0			0
$295$	0.314601	−	0.0455217i	0.0183168	−	0.00265038i
$296$		0			0
$297$	5.67833	+	21.1918i	0.329490	+	1.22967i
$298$		0			0
$299$	−3.73741	−	6.47339i	−0.216140	−	0.374366i
$300$		0			0
$301$	−0.437751	−	1.44901i	−0.0252315	−	0.0835196i
$302$		0			0
$303$	10.0788	+	2.70061i	0.579013	+	0.155146i
$304$		0			0
$305$	6.42042	+	2.56365i	0.367632	+	0.146794i
$306$		0			0
$307$	4.68380	−	4.68380i	0.267319	−	0.267319i	−0.560700	−	0.828019i	$-0.689468\pi$
$307$	4.68380	−	4.68380i	0.267319	−	0.267319i	0.828019	+	0.560700i	$0.189468\pi$
$308$		0			0
$309$			5.68177i			0.323224i
$310$		0			0
$311$	5.90190	+	3.40747i	0.334666	+	0.193220i	0.657911	−	0.753096i	$-0.271440\pi$
$311$	5.90190	+	3.40747i	0.334666	+	0.193220i	−0.323245	+	0.946315i	$0.604774\pi$
$312$		0			0
$313$	−6.97836	+	26.0436i	−0.394440	+	1.47207i	0.428291	+	0.903641i	$0.359116\pi$
$313$	−6.97836	+	26.0436i	−0.394440	+	1.47207i	−0.822731	+	0.568430i	$0.807551\pi$
$314$		0			0
$315$	5.83899	−	4.90698i	0.328990	−	0.276477i
$316$		0			0
$317$	−4.81685	+	17.9767i	−0.270541	+	1.00967i	0.688230	+	0.725493i	$0.258388\pi$
$317$	−4.81685	+	17.9767i	−0.270541	+	1.00967i	−0.958771	+	0.284180i	$0.908279\pi$
$318$		0			0
$319$	−28.4598	−	16.4313i	−1.59344	−	0.919973i
$320$		0			0
$321$		−	30.3744i		−	1.69533i
$322$		0			0
$323$	−15.3181	+	15.3181i	−0.852323	+	0.852323i
$324$		0			0
$325$	−4.72202	+	2.88989i	−0.261931	+	0.160302i
$326$		0			0
$327$	−30.1190	−	8.07036i	−1.66558	−	0.446292i
$328$		0			0
$329$	16.1943	−	17.2511i	0.892821	−	0.951082i
$330$		0			0
$331$	7.03546	+	12.1858i	0.386704	+	0.669791i	0.992004	−	0.126206i	$-0.0402802\pi$
$331$	7.03546	+	12.1858i	0.386704	+	0.669791i	−0.605300	+	0.795997i	$0.706947\pi$
$332$		0			0
$333$	−2.28675	−	8.53427i	−0.125313	−	0.467675i
$334$		0			0
$335$	−8.05728	−	6.02030i	−0.440216	−	0.328924i
$336$		0			0
$337$	−21.1500	−	21.1500i	−1.15212	−	1.15212i	−0.986128	−	0.165988i	$-0.946919\pi$
$337$	−21.1500	−	21.1500i	−1.15212	−	1.15212i	−0.165988	−	0.986128i	$-0.553081\pi$
$338$		0			0
$339$	−2.06940	+	3.58430i	−0.112394	+	0.194673i
$340$		0			0
$341$	−13.4157	+	7.74553i	−0.726499	+	0.419444i
$342$		0			0
$343$	−18.4372	+	1.75231i	−0.995514	+	0.0946160i
$344$		0			0
$345$	19.3479	+	24.5573i	1.04165	+	1.32212i
$346$		0			0
$347$	−4.07182	+	1.09104i	−0.218587	+	0.0585701i	−0.366450	−	0.930438i	$-0.619427\pi$
$347$	−4.07182	+	1.09104i	−0.218587	+	0.0585701i	0.147864	+	0.989008i	$0.452760\pi$
$348$		0			0
$349$	37.0391			1.98266			0.991329	−	0.131407i	$-0.0419495\pi$
$349$	37.0391			1.98266			0.991329	+	0.131407i	$0.0419495\pi$
$350$		0			0
$351$	3.92304			0.209397
$352$		0			0
$353$	22.7295	−	6.09034i	1.20977	−	0.324156i	0.403096	−	0.915157i	$-0.367934\pi$
$353$	22.7295	−	6.09034i	1.20977	−	0.324156i	0.806671	+	0.591001i	$0.201267\pi$
$354$		0			0
$355$	14.3249	+	18.1819i	0.760287	+	0.964995i
$356$		0			0
$357$	−24.9751	+	0.789123i	−1.32182	+	0.0417648i
$358$		0			0
$359$	17.5695	−	10.1437i	0.927281	−	0.535366i	0.0413304	−	0.999146i	$-0.486840\pi$
$359$	17.5695	−	10.1437i	0.927281	−	0.535366i	0.885951	+	0.463780i	$0.153507\pi$
$360$		0			0
$361$	−1.78340	+	3.08894i	−0.0938633	+	0.162576i
$362$		0			0
$363$	40.0413	+	40.0413i	2.10162	+	2.10162i
$364$		0			0
$365$	−3.34940	−	2.50263i	−0.175316	−	0.130994i
$366$		0			0
$367$	2.92561	+	10.9185i	0.152715	+	0.569942i	0.999290	+	0.0376718i	$0.0119941\pi$
$367$	2.92561	+	10.9185i	0.152715	+	0.569942i	−0.846575	+	0.532270i	$0.821339\pi$
$368$		0			0
$369$	−1.62072	−	2.80717i	−0.0843714	−	0.146136i
$370$		0			0
$371$	−26.4750	−	6.20490i	−1.37451	−	0.322142i
$372$		0			0
$373$	12.8568	+	3.44497i	0.665700	+	0.178374i	0.575817	−	0.817579i	$-0.304684\pi$
$373$	12.8568	+	3.44497i	0.665700	+	0.178374i	0.0898828	+	0.995952i	$0.471351\pi$
$374$		0			0
$375$	17.8154	−	14.7907i	0.919982	−	0.763786i
$376$		0			0
$377$	−4.15513	+	4.15513i	−0.214000	+	0.214000i
$378$		0			0
$379$			11.7429i			0.603191i	0.953436	+	0.301595i	$0.0975191\pi$
$379$			11.7429i			0.603191i	−0.953436	+	0.301595i	$0.902481\pi$
$380$		0			0
$381$	11.6996	+	6.75474i	0.599387	+	0.346056i
$382$		0			0
$383$	−8.49569	+	31.7063i	−0.434109	+	1.62012i	0.309079	+	0.951036i	$0.399979\pi$
$383$	−8.49569	+	31.7063i	−0.434109	+	1.62012i	−0.743188	+	0.669082i	$0.766687\pi$
$384$		0			0
$385$	−12.5033	+	34.4332i	−0.637229	+	1.75488i
$386$		0			0
$387$	0.190901	−	0.712452i	0.00970404	−	0.0362160i
$388$		0			0
$389$	−14.7903	−	8.53916i	−0.749895	−	0.432952i	0.0757607	−	0.997126i	$-0.475862\pi$
$389$	−14.7903	−	8.53916i	−0.749895	−	0.432952i	−0.825656	+	0.564174i	$0.809195\pi$
$390$		0			0
$391$		−	30.7857i		−	1.55690i
$392$		0			0
$393$	−29.7497	+	29.7497i	−1.50067	+	1.50067i
$394$		0			0
$395$	13.0060	+	5.19323i	0.654400	+	0.261300i
$396$		0			0
$397$	−11.6115	−	3.11129i	−0.582764	−	0.156151i	−0.0446201	−	0.999004i	$-0.514208\pi$
$397$	−11.6115	−	3.11129i	−0.582764	−	0.156151i	−0.538144	+	0.842853i	$0.680874\pi$
$398$		0			0
$399$	−24.9177	+	7.52771i	−1.24744	+	0.376857i
$400$		0			0
$401$	−12.4166	−	21.5062i	−0.620055	−	1.07397i	−0.989475	−	0.144704i	$-0.953777\pi$
$401$	−12.4166	−	21.5062i	−0.620055	−	1.07397i	0.369420	−	0.929263i	$-0.379556\pi$
$402$		0			0
$403$	0.716930	+	2.67562i	0.0357128	+	0.133282i
$404$		0			0
$405$	−24.7982	+	3.58821i	−1.23223	+	0.178300i
$406$		0			0
$407$	30.0070	+	30.0070i	1.48739	+	1.48739i
$408$		0			0
$409$	−15.8290	+	27.4166i	−0.782692	+	1.35566i	0.147676	+	0.989036i	$0.452821\pi$
$409$	−15.8290	+	27.4166i	−0.782692	+	1.35566i	−0.930368	+	0.366626i	$0.880513\pi$
$410$		0			0
$411$	−12.7144	+	7.34069i	−0.627157	+	0.362089i
$412$		0			0
$413$	−0.198252	−	0.319626i	−0.00975533	−	0.0157278i
$414$		0			0
$415$	−2.17138	+	18.3004i	−0.106589	+	0.898330i
$416$		0			0
$417$	15.8900	−	4.25772i	0.778138	−	0.208501i
$418$		0			0
$419$	6.53217			0.319118			0.159559	−	0.987188i	$-0.448993\pi$
$419$	6.53217			0.319118			0.159559	+	0.987188i	$0.448993\pi$
$420$		0			0
$421$	23.0995			1.12580			0.562899	−	0.826525i	$-0.309686\pi$
$421$	23.0995			1.12580			0.562899	+	0.826525i	$0.309686\pi$
$422$		0			0
$423$	11.1367	−	2.98407i	0.541485	−	0.145090i
$424$		0			0
$425$	−22.7936	+	0.583625i	−1.10565	+	0.0283100i
$426$		0			0
$427$	−0.258329	−	8.17588i	−0.0125014	−	0.395659i
$428$		0			0
$429$	12.2969	−	7.09963i	0.593701	−	0.342773i
$430$		0			0
$431$	−5.53350	+	9.58430i	−0.266539	+	0.461660i	−0.967966	−	0.251082i	$-0.919214\pi$
$431$	−5.53350	+	9.58430i	−0.266539	+	0.461660i	0.701427	+	0.712742i	$0.252547\pi$
$432$		0			0
$433$	4.53425	+	4.53425i	0.217902	+	0.217902i	0.807614	−	0.589712i	$-0.200759\pi$
$433$	4.53425	+	4.53425i	0.217902	+	0.217902i	−0.589712	+	0.807614i	$0.700759\pi$
$434$		0			0
$435$	14.7110	−	19.6884i	0.705337	−	0.943989i
$436$		0			0
$437$	−8.30031	−	30.9772i	−0.397058	−	1.48184i
$438$		0			0
$439$	9.10949	+	15.7781i	0.434772	+	0.753047i	0.997277	−	0.0737466i	$-0.0234956\pi$
$439$	9.10949	+	15.7781i	0.434772	+	0.753047i	−0.562505	+	0.826794i	$0.690162\pi$
$440$		0			0
$441$	−8.08469	−	4.00985i	−0.384985	−	0.190945i
$442$		0			0
$443$	17.9720	+	4.81558i	0.853875	+	0.228795i	0.659102	−	0.752053i	$-0.270936\pi$
$443$	17.9720	+	4.81558i	0.853875	+	0.228795i	0.194773	+	0.980848i	$0.437603\pi$
$444$		0			0
$445$	7.60501	−	19.0460i	0.360512	−	0.902869i
$446$		0			0
$447$	4.42311	−	4.42311i	0.209206	−	0.209206i
$448$		0			0
$449$			32.4548i			1.53164i	0.643056	+	0.765819i	$0.277666\pi$
$449$			32.4548i			1.53164i	−0.643056	+	0.765819i	$0.722334\pi$
$450$		0			0
$451$	13.4829	+	7.78437i	0.634886	+	0.366552i
$452$		0			0
$453$	−2.15319	+	8.03580i	−0.101165	+	0.377555i
$454$		0			0
$455$	5.36865	+	3.75315i	0.251686	+	0.175951i
$456$		0			0
$457$	−2.40043	+	8.95853i	−0.112287	+	0.419062i	−0.999070	−	0.0431250i	$-0.986269\pi$
$457$	−2.40043	+	8.95853i	−0.112287	+	0.419062i	0.886782	+	0.462187i	$0.152935\pi$
$458$		0			0
$459$	13.9927	+	8.07869i	0.653123	+	0.377081i
$460$		0			0
$461$		−	36.2380i		−	1.68777i	−0.536521	−	0.843887i	$-0.680262\pi$
$461$		−	36.2380i		−	1.68777i	0.536521	−	0.843887i	$-0.319738\pi$
$462$		0			0
$463$	6.39137	−	6.39137i	0.297032	−	0.297032i	−0.542818	−	0.839850i	$-0.682643\pi$
$463$	6.39137	−	6.39137i	0.297032	−	0.297032i	0.839850	+	0.542818i	$0.182643\pi$
$464$		0			0
$465$	−4.57023	−	10.6460i	−0.211939	−	0.493697i
$466$		0			0
$467$	−3.18040	−	0.852186i	−0.147171	−	0.0394345i	0.184481	−	0.982836i	$-0.440940\pi$
$467$	−3.18040	−	0.852186i	−0.147171	−	0.0394345i	−0.331653	+	0.943402i	$0.607606\pi$
$468$		0			0
$469$	−2.71559	+	11.5868i	−0.125394	+	0.535031i
$470$		0			0
$471$	−3.95752	−	6.85462i	−0.182353	−	0.315844i
$472$		0			0
$473$	0.916902	+	3.42193i	0.0421592	+	0.157340i
$474$		0			0
$475$	−22.7781	+	6.73278i	−1.04513	+	0.308921i
$476$		0			0
$477$	−9.36930	−	9.36930i	−0.428991	−	0.428991i
$478$		0			0
$479$	15.1734	−	26.2811i	0.693292	−	1.20082i	−0.277462	−	0.960737i	$-0.589493\pi$
$479$	15.1734	−	26.2811i	0.693292	−	1.20082i	0.970753	−	0.240079i	$-0.0771735\pi$
$480$		0			0
$481$	6.57154	−	3.79408i	0.299636	−	0.172995i
$482$		0			0
$483$	17.4748	−	32.6036i	0.795129	−	1.48352i
$484$		0			0
$485$	8.30848	+	0.985820i	0.377269	+	0.0447638i
$486$		0			0
$487$	28.1791	−	7.55058i	1.27692	−	0.342149i	0.444241	−	0.895907i	$-0.353473\pi$
$487$	28.1791	−	7.55058i	1.27692	−	0.342149i	0.832678	+	0.553758i	$0.186807\pi$
$488$		0			0
$489$	18.2784			0.826578
$490$		0			0
$491$	−25.5532			−1.15320			−0.576600	−	0.817027i	$-0.695621\pi$
$491$	−25.5532			−1.15320			−0.576600	+	0.817027i	$0.695621\pi$
$492$		0			0
$493$	−23.3771	+	6.26388i	−1.05285	+	0.282111i
$494$		0			0
$495$	−14.0214	+	11.0470i	−0.630216	+	0.496526i
$496$		0			0
$497$	12.9381	−	24.1393i	0.580352	−	1.08279i
$498$		0			0
$499$	−25.9209	+	14.9655i	−1.16038	+	0.669946i	−0.951395	−	0.307973i	$-0.900349\pi$
$499$	−25.9209	+	14.9655i	−1.16038	+	0.669946i	−0.208985	+	0.977919i	$0.567016\pi$
$500$		0			0
$501$	−8.65717	+	14.9947i	−0.386774	+	0.669912i
$502$		0			0
$503$	−10.5316	−	10.5316i	−0.469582	−	0.469582i	0.432197	−	0.901779i	$-0.357738\pi$
$503$	−10.5316	−	10.5316i	−0.469582	−	0.469582i	−0.901779	+	0.432197i	$0.857738\pi$
$504$		0			0
$505$	−1.61332	−	11.1497i	−0.0717919	−	0.496154i
$506$		0			0
$507$	6.31118	+	23.5536i	0.280289	+	1.04605i
$508$		0			0
$509$	−7.10159	−	12.3003i	−0.314772	−	0.545202i	0.664617	−	0.747184i	$-0.268595\pi$
$509$	−7.10159	−	12.3003i	−0.314772	−	0.545202i	−0.979389	+	0.201983i	$0.935261\pi$
$510$		0			0
$511$	−1.12887	+	4.81664i	−0.0499382	+	0.213075i
$512$		0			0
$513$	16.2579	+	4.35629i	0.717803	+	0.192335i
$514$		0			0
$515$	5.63703	−	2.41992i	0.248397	−	0.106635i
$516$		0			0
$517$	−39.1573	+	39.1573i	−1.72214	+	1.72214i
$518$		0			0
$519$		−	46.4451i		−	2.03871i
$520$		0			0
$521$	−21.2944	−	12.2943i	−0.932924	−	0.538624i	−0.0451888	−	0.998978i	$-0.514389\pi$
$521$	−21.2944	−	12.2943i	−0.932924	−	0.538624i	−0.887735	+	0.460355i	$0.847722\pi$
$522$		0			0
$523$	8.19527	−	30.5852i	0.358354	−	1.33740i	−0.517856	−	0.855468i	$-0.673270\pi$
$523$	8.19527	−	30.5852i	0.358354	−	1.33740i	0.876211	−	0.481929i	$-0.160064\pi$
$524$		0			0
$525$	−24.4709	−	12.3202i	−1.06800	−	0.537697i
$526$		0			0
$527$	−2.95273	+	11.0198i	−0.128623	+	0.480028i
$528$		0			0
$529$	19.5505	+	11.2875i	0.850020	+	0.490759i
$530$		0			0
$531$		−	0.183273i		−	0.00795337i
$532$		0			0
$533$	1.96851	−	1.96851i	0.0852656	−	0.0852656i
$534$		0			0
$535$	−30.1352	+	12.9367i	−1.30286	+	0.559304i
$536$		0			0
$537$	22.6796	+	6.07699i	0.978698	+	0.262241i
$538$		0			0
$539$	43.2583	−	2.73635i	1.86327	−	0.117863i
$540$		0			0
$541$	10.8368	+	18.7700i	0.465912	+	0.806984i	0.999242	−	0.0389236i	$-0.0123929\pi$
$541$	10.8368	+	18.7700i	0.465912	+	0.806984i	−0.533330	+	0.845907i	$0.679060\pi$
$542$		0			0
$543$	−4.77545	−	17.8222i	−0.204934	−	0.764824i
$544$		0			0
$545$	4.82116	+	33.3191i	0.206516	+	1.42723i
$546$		0			0
$547$	−7.94707	−	7.94707i	−0.339792	−	0.339792i	0.516497	−	0.856289i	$-0.327236\pi$
$547$	−7.94707	−	7.94707i	−0.339792	−	0.339792i	−0.856289	+	0.516497i	$0.827236\pi$
$548$		0			0
$549$	1.99295	−	3.45189i	0.0850570	−	0.147323i
$550$		0			0
$551$	−21.8337	+	12.6057i	−0.930147	+	0.537021i
$552$		0			0
$553$	−0.523300	−	16.5620i	−0.0222530	−	0.704288i
$554$		0			0
$555$	−24.9297	+	19.6412i	−1.05821	+	0.833724i
$556$		0			0
$557$	−14.1578	+	3.79358i	−0.599886	+	0.160739i	−0.545968	−	0.837806i	$-0.683838\pi$
$557$	−14.1578	+	3.79358i	−0.599886	+	0.160739i	−0.0539186	+	0.998545i	$0.517171\pi$
$558$		0			0
$559$	0.633470			0.0267929
$560$		0			0
$561$	58.4808			2.46906
$562$		0			0
$563$	−22.8910	+	6.13364i	−0.964742	+	0.258502i	−0.706607	−	0.707607i	$-0.749775\pi$
$563$	−22.8910	+	6.13364i	−0.964742	+	0.258502i	−0.258136	+	0.966109i	$0.583108\pi$
$564$		0			0
$565$	4.43746	+	0.526515i	0.186685	+	0.0221506i
$566$		0			0
$567$	15.6270	+	25.1942i	0.656273	+	1.05806i
$568$		0			0
$569$	−20.3034	+	11.7221i	−0.851161	+	0.491418i	−0.861042	−	0.508533i	$-0.830188\pi$
$569$	−20.3034	+	11.7221i	−0.851161	+	0.491418i	0.00988157	+	0.999951i	$0.496855\pi$
$570$		0			0
$571$	−1.81550	+	3.14454i	−0.0759764	+	0.131595i	−0.901510	−	0.432757i	$-0.857541\pi$
$571$	−1.81550	+	3.14454i	−0.0759764	+	0.131595i	0.825534	+	0.564352i	$0.190874\pi$
$572$		0			0
$573$	−23.6501	−	23.6501i	−0.987996	−	0.987996i
$574$		0			0
$575$	16.1235	−	29.6548i	0.672398	−	1.23669i
$576$		0			0
$577$	−8.92952	−	33.3254i	−0.371741	−	1.38736i	−0.858049	−	0.513568i	$-0.828323\pi$
$577$	−8.92952	−	33.3254i	−0.371741	−	1.38736i	0.486308	−	0.873788i	$-0.338343\pi$
$578$		0			0
$579$	0.408631	+	0.707769i	0.0169821	+	0.0294139i
$580$		0			0
$581$	20.8734	−	6.30594i	0.865977	−	0.261614i
$582$		0			0
$583$	61.4725	+	16.4715i	2.54593	+	0.682180i
$584$		0			0
$585$	1.25912	+	2.93304i	0.0520584	+	0.121266i
$586$		0			0
$587$	−13.1856	+	13.1856i	−0.544227	+	0.544227i	−0.924765	−	0.380538i	$-0.875739\pi$
$587$	−13.1856	+	13.1856i	−0.544227	+	0.544227i	0.380538	+	0.924765i	$0.375739\pi$
$588$		0			0
$589$			11.8844i			0.489688i
$590$		0			0
$591$	21.9592	+	12.6781i	0.903280	+	0.521509i
$592$		0			0
$593$	−5.19125	+	19.3740i	−0.213179	+	0.795595i	0.773621	+	0.633649i	$0.218444\pi$
$593$	−5.19125	+	19.3740i	−0.213179	+	0.795595i	−0.986800	+	0.161946i	$0.948223\pi$
$594$		0			0
$595$	11.4200	+	24.4423i	0.468176	+	1.00204i
$596$		0			0
$597$	5.32045	−	19.8562i	0.217752	−	0.812660i
$598$		0			0
$599$	−29.2830	−	16.9065i	−1.19647	−	0.690783i	−0.236704	−	0.971582i	$-0.576067\pi$
$599$	−29.2830	−	16.9065i	−1.19647	−	0.690783i	−0.959767	+	0.280799i	$0.909401\pi$
$600$		0			0
$601$		−	6.43168i		−	0.262354i	−0.991359	−	0.131177i	$-0.958124\pi$
$601$		−	6.43168i		−	0.262354i	0.991359	−	0.131177i	$-0.0418756\pi$
$602$		0			0
$603$	−4.10050	+	4.10050i	−0.166985	+	0.166985i
$604$		0			0
$605$	22.6721	−	56.7801i	0.921750	−	2.30844i
$606$		0			0
$607$	−3.68755	−	0.988075i	−0.149673	−	0.0401047i	0.183205	−	0.983075i	$-0.441353\pi$
$607$	−3.68755	−	0.988075i	−0.149673	−	0.0401047i	−0.332878	+	0.942970i	$0.608020\pi$
$608$		0			0
$609$	−28.3131	−	6.63571i	−1.14731	−	0.268892i
$610$		0			0
$611$	4.95104	+	8.57546i	0.200298	+	0.346926i
$612$		0			0
$613$	−11.8572	−	44.2518i	−0.478909	−	1.78731i	−0.606047	−	0.795429i	$-0.707246\pi$
$613$	−11.8572	−	44.2518i	−0.478909	−	1.78731i	0.127138	−	0.991885i	$-0.459421\pi$
$614$		0			0
$615$	−6.96938	+	9.32747i	−0.281032	+	0.376120i
$616$		0			0
$617$	15.0385	+	15.0385i	0.605429	+	0.605429i	0.941748	−	0.336319i	$-0.109182\pi$
$617$	15.0385	+	15.0385i	0.605429	+	0.605429i	−0.336319	+	0.941748i	$0.609182\pi$
$618$		0			0
$619$	−0.630180	+	1.09150i	−0.0253291	+	0.0438712i	−0.878412	−	0.477904i	$-0.841397\pi$
$619$	−0.630180	+	1.09150i	−0.0253291	+	0.0438712i	0.853083	+	0.521775i	$0.174730\pi$
$620$		0			0
$621$	−20.7147	+	11.9596i	−0.831253	+	0.479924i
$622$		0			0
$623$	−24.2536	+	0.766326i	−0.971699	+	0.0307022i
$624$		0			0
$625$	−22.2620	−	11.3756i	−0.890479	−	0.455025i
$626$		0			0
$627$	58.8446	−	15.7674i	2.35003	−	0.629688i
$628$		0			0
$629$	31.2525			1.24612
$630$		0			0
$631$	−28.6052			−1.13876			−0.569378	−	0.822076i	$-0.692816\pi$
$631$	−28.6052			−1.13876			−0.569378	+	0.822076i	$0.692816\pi$
$632$		0			0
$633$	−18.5222	+	4.96301i	−0.736191	+	0.197262i
$634$		0			0
$635$	1.71860	−	14.4844i	0.0682007	−	0.574794i
$636$		0			0
$637$	1.52938	−	7.59822i	0.0605963	−	0.301052i
$638$		0			0
$639$	11.5575	−	6.67274i	0.457208	−	0.263969i
$640$		0			0
$641$	5.62256	−	9.73856i	0.222078	−	0.384650i	−0.733361	−	0.679839i	$-0.762049\pi$
$641$	5.62256	−	9.73856i	0.222078	−	0.384650i	0.955439	+	0.295190i	$0.0953828\pi$
$642$		0			0
$643$	−34.9847	−	34.9847i	−1.37966	−	1.37966i	−0.845178	−	0.534485i	$-0.820506\pi$
$643$	−34.9847	−	34.9847i	−1.37966	−	1.37966i	−0.534485	−	0.845178i	$-0.679494\pi$
$644$		0			0
$645$	−2.62218	+	0.379420i	−0.103248	+	0.0149397i
$646$		0			0
$647$	−4.92794	−	18.3913i	−0.193737	−	0.723038i	−0.992590	−	0.121511i	$-0.961226\pi$
$647$	−4.92794	−	18.3913i	−0.193737	−	0.723038i	0.798853	−	0.601527i	$-0.205441\pi$
$648$		0			0
$649$	0.440133	+	0.762332i	0.0172767	+	0.0299242i
$650$		0			0
$651$	−9.38220	+	9.99444i	−0.367718	+	0.391713i
$652$		0			0
$653$	−35.7631	−	9.58269i	−1.39952	−	0.375000i	−0.521346	−	0.853345i	$-0.674570\pi$
$653$	−35.7631	−	9.58269i	−1.39952	−	0.375000i	−0.878171	+	0.478346i	$0.841237\pi$
$654$		0			0
$655$	42.1862	+	16.8448i	1.64835	+	0.658180i
$656$		0			0
$657$	−1.70457	+	1.70457i	−0.0665017	+	0.0665017i
$658$		0			0
$659$		−	43.8946i		−	1.70989i	−0.518719	−	0.854945i	$-0.673591\pi$
$659$		−	43.8946i		−	1.70989i	0.518719	−	0.854945i	$-0.326409\pi$
$660$		0			0
$661$	31.7743	+	18.3449i	1.23588	+	0.713534i	0.968249	−	0.249988i	$-0.0804266\pi$
$661$	31.7743	+	18.3449i	1.23588	+	0.713534i	0.267629	+	0.963522i	$0.413760\pi$
$662$		0			0
$663$	2.70650	−	10.1008i	0.105112	−	0.392283i
$664$		0			0
$665$	18.0811	+	21.5154i	0.701156	+	0.834330i
$666$		0			0
$667$	9.27301	−	34.6074i	0.359053	−	1.34000i
$668$		0			0
$669$	−5.74622	−	3.31758i	−0.222162	−	0.128265i
$670$		0			0
$671$			19.1444i			0.739061i
$672$		0			0
$673$	4.16595	−	4.16595i	0.160586	−	0.160586i	−0.622240	−	0.782826i	$-0.713777\pi$
$673$	4.16595	−	4.16595i	0.160586	−	0.160586i	0.782826	+	0.622240i	$0.213777\pi$
$674$		0			0
$675$	9.24759	+	15.1104i	0.355940	+	0.581599i
$676$		0			0
$677$	−17.5741	−	4.70896i	−0.675427	−	0.180980i	−0.0952289	−	0.995455i	$-0.530358\pi$
$677$	−17.5741	−	4.70896i	−0.675427	−	0.180980i	−0.580198	+	0.814475i	$0.697025\pi$
$678$		0			0
$679$	−2.86294	−	9.47668i	−0.109869	−	0.363682i
$680$		0			0
$681$	22.9028	+	39.6687i	0.877635	+	1.52011i
$682$		0			0
$683$	−12.5644	−	46.8911i	−0.480765	−	1.79424i	−0.598417	−	0.801185i	$-0.704203\pi$
$683$	−12.5644	−	46.8911i	−0.480765	−	1.79424i	0.117652	−	0.993055i	$-0.462463\pi$
$684$		0			0
$685$	12.6981	+	9.48787i	0.485170	+	0.362513i
$686$		0			0
$687$	9.26604	+	9.26604i	0.353521	+	0.353521i
$688$		0			0
$689$	5.68992	−	9.85523i	0.216769	−	0.375454i
$690$		0			0
$691$	28.7175	−	16.5800i	1.09246	−	0.630734i	0.158233	−	0.987402i	$-0.449420\pi$
$691$	28.7175	−	16.5800i	1.09246	−	0.630734i	0.934231	+	0.356668i	$0.116087\pi$
$692$		0			0
$693$	18.6156	+	9.97752i	0.707148	+	0.379015i
$694$		0			0
$695$	−10.9919	−	13.9515i	−0.416947	−	0.529211i
$696$		0			0
$697$	11.0750	−	2.96754i	0.419496	−	0.112404i
$698$		0			0
$699$	−21.7385			−0.822224
$700$		0			0
$701$	−49.8387			−1.88238			−0.941191	−	0.337874i	$-0.890292\pi$
$701$	−49.8387			−1.88238			−0.941191	+	0.337874i	$0.890292\pi$
$702$		0			0
$703$	31.4469	−	8.42616i	1.18604	−	0.317799i
$704$		0			0
$705$	−25.6306	−	32.5317i	−0.965305	−	1.22521i
$706$		0			0
$707$	−11.3278	+	7.02618i	−0.426025	+	0.264247i
$708$		0			0
$709$	−14.8597	+	8.57923i	−0.558066	+	0.322200i	−0.752369	−	0.658742i	$-0.771089\pi$
$709$	−14.8597	+	8.57923i	−0.558066	+	0.322200i	0.194303	+	0.980942i	$0.437756\pi$
$710$		0			0
$711$	4.03715	−	6.99255i	0.151405	−	0.262241i
$712$		0			0
$713$	−11.9424	−	11.9424i	−0.447245	−	0.447245i
$714$		0			0
$715$	−12.2811	−	9.17630i	−0.459288	−	0.343174i
$716$		0			0
$717$	1.53983	+	5.74671i	0.0575059	+	0.214615i
$718$		0			0
$719$	16.7860	+	29.0742i	0.626012	+	1.08429i	0.988344	+	0.152236i	$0.0486474\pi$
$719$	16.7860	+	29.0742i	0.626012	+	1.08429i	−0.362332	+	0.932049i	$0.618019\pi$
$720$		0			0
$721$	−5.29202	−	4.96785i	−0.197085	−	0.185012i
$722$		0			0
$723$	−59.3507	−	15.9030i	−2.20728	−	0.591438i
$724$		0			0
$725$	−25.7990	−	6.20964i	−0.958150	−	0.230620i
$726$		0			0
$727$	−1.55262	+	1.55262i	−0.0575835	+	0.0575835i	−0.735312	−	0.677729i	$-0.762964\pi$
$727$	−1.55262	+	1.55262i	−0.0575835	+	0.0575835i	0.677729	+	0.735312i	$0.262964\pi$
$728$		0			0
$729$		−	7.56747i		−	0.280277i
$730$		0			0
$731$	2.25946	+	1.30450i	0.0835691	+	0.0482486i
$732$		0			0
$733$	4.45750	−	16.6356i	0.164641	−	0.614450i	−0.833444	−	0.552604i	$-0.813634\pi$
$733$	4.45750	−	16.6356i	0.164641	−	0.614450i	0.998086	−	0.0618467i	$-0.0196990\pi$
$734$		0			0
$735$	−1.77971	+	32.3680i	−0.0656456	+	1.19391i
$736$		0			0
$737$	7.20880	−	26.9036i	0.265539	−	0.991007i
$738$		0			0
$739$	40.9386	+	23.6359i	1.50595	+	0.869461i	0.999976	+	0.00691159i	$0.00220004\pi$
$739$	40.9386	+	23.6359i	1.50595	+	0.869461i	0.505974	+	0.862549i	$0.331133\pi$
$740$		0			0
$741$		−	10.8934i		−	0.400177i
$742$		0			0
$743$	−2.52069	+	2.52069i	−0.0924753	+	0.0924753i	−0.751831	−	0.659356i	$-0.770829\pi$
$743$	−2.52069	+	2.52069i	−0.0924753	+	0.0924753i	0.659356	+	0.751831i	$0.270829\pi$
$744$		0			0
$745$	−6.27213	−	2.50444i	−0.229793	−	0.0917555i
$746$		0			0
$747$	10.2631	+	2.74999i	0.375507	+	0.100617i
$748$		0			0
$749$	28.2908	+	26.5578i	1.03372	+	0.970401i
$750$		0			0
$751$	6.40069	+	11.0863i	0.233564	+	0.404546i	0.958855	−	0.283898i	$-0.0916277\pi$
$751$	6.40069	+	11.0863i	0.233564	+	0.404546i	−0.725290	+	0.688443i	$0.758294\pi$
$752$		0			0
$753$	8.07766	+	30.1462i	0.294366	+	1.09859i
$754$		0			0
$755$	8.88960	−	1.28629i	0.323526	−	0.0468131i
$756$		0			0
$757$	22.6605	+	22.6605i	0.823609	+	0.823609i	0.986624	−	0.163014i	$-0.0521217\pi$
$757$	22.6605	+	22.6605i	0.823609	+	0.823609i	−0.163014	+	0.986624i	$0.552122\pi$
$758$		0			0
$759$	−43.2873	+	74.9758i	−1.57123	+	2.72145i
$760$		0			0
$761$	9.29607	−	5.36709i	0.336982	−	0.194557i	−0.321955	−	0.946755i	$-0.604340\pi$
$761$	9.29607	−	5.36709i	0.336982	−	0.194557i	0.658937	+	0.752198i	$0.271007\pi$
$762$		0			0
$763$	33.8513	−	20.9967i	1.22550	−	0.760130i
$764$		0			0
$765$	−1.54894	+	13.0545i	−0.0560021	+	0.471985i
$766$		0			0
$767$	0.152040	−	0.0407389i	0.00548983	−	0.00147100i
$768$		0			0
$769$	10.4824			0.378005			0.189002	−	0.981977i	$-0.439475\pi$
$769$	10.4824			0.378005			0.189002	+	0.981977i	$0.439475\pi$
$770$		0			0
$771$	−48.8698			−1.76000
$772$		0			0
$773$	16.3424	−	4.37894i	0.587796	−	0.157499i	0.0473503	−	0.998878i	$-0.484922\pi$
$773$	16.3424	−	4.37894i	0.587796	−	0.157499i	0.540446	+	0.841379i	$0.318256\pi$
$774$		0			0
$775$	−8.61570	+	9.06849i	−0.309485	+	0.325750i
$776$		0			0
$777$	33.0980	+	17.7397i	1.18738	+	0.636409i
$778$		0			0
$779$	10.3438	−	5.97200i	0.370605	−	0.213969i
$780$		0			0
$781$	−32.0493	+	55.5111i	−1.14682	+	1.98634i
$782$		0			0
$783$	13.2963	+	13.2963i	0.475172	+	0.475172i
$784$		0			0
$785$	−5.11511	+	6.84581i	−0.182566	+	0.244337i
$786$		0			0
$787$	−9.55515	−	35.6603i	−0.340604	−	1.27115i	−0.897664	−	0.440680i	$-0.854737\pi$
$787$	−9.55515	−	35.6603i	−0.340604	−	1.27115i	0.557060	−	0.830472i	$-0.311929\pi$
$788$		0			0
$789$	20.8759	+	36.1581i	0.743201	+	1.28726i
$790$		0			0
$791$	−1.52906	−	5.06138i	−0.0543671	−	0.179962i
$792$		0			0
$793$	3.30662	+	0.886006i	0.117421	+	0.0314630i
$794$		0			0
$795$	−17.6499	+	44.2026i	−0.625979	+	1.56771i
$796$		0			0
$797$	10.9328	−	10.9328i	0.387258	−	0.387258i	−0.486450	−	0.873708i	$-0.661708\pi$
$797$	10.9328	−	10.9328i	0.387258	−	0.387258i	0.873708	+	0.486450i	$0.161708\pi$
$798$		0			0
$799$			40.7825i			1.44278i
$800$		0			0
$801$	−10.2400	−	5.91204i	−0.361811	−	0.208892i
$802$		0			0
$803$	2.99669	−	11.1838i	0.105751	−	0.394667i
$804$		0			0
$805$	−39.7896	−	3.45098i	−1.40240	−	0.121631i
$806$		0			0
$807$	6.87863	−	25.6714i	0.242139	−	0.903676i
$808$		0			0
$809$	−28.0999	−	16.2235i	−0.987941	−	0.570388i	−0.0832827	−	0.996526i	$-0.526540\pi$
$809$	−28.0999	−	16.2235i	−0.987941	−	0.570388i	−0.904658	+	0.426138i	$0.859874\pi$
$810$		0			0
$811$			31.4334i			1.10378i	0.833918	+	0.551889i	$0.186093\pi$
$811$			31.4334i			1.10378i	−0.833918	+	0.551889i	$0.813907\pi$
$812$		0			0
$813$	−2.56267	+	2.56267i	−0.0898767	+	0.0898767i
$814$		0			0
$815$	−7.78496	−	18.1345i	−0.272695	−	0.635224i
$816$		0			0
$817$	2.62523	+	0.703427i	0.0918451	+	0.0246098i
$818$		0			0
$819$	2.58485	−	2.75352i	0.0903220	−	0.0962159i
$820$		0			0
$821$	0.0234891	+	0.0406843i	0.000819775	+	0.00141989i	0.866435	−	0.499290i	$-0.166406\pi$
$821$	0.0234891	+	0.0406843i	0.000819775	+	0.00141989i	−0.865615	+	0.500710i	$0.833072\pi$
$822$		0			0
$823$	5.64342	+	21.0615i	0.196717	+	0.734158i	0.991816	+	0.127678i	$0.0407524\pi$
$823$	5.64342	+	21.0615i	0.196717	+	0.734158i	−0.795099	+	0.606480i	$0.792581\pi$
$824$		0			0
$825$	56.3325	+	30.6284i	1.96125	+	1.06634i
$826$		0			0
$827$	24.9954	+	24.9954i	0.869175	+	0.869175i	0.992381	−	0.123206i	$-0.0393175\pi$
$827$	24.9954	+	24.9954i	0.869175	+	0.869175i	−0.123206	+	0.992381i	$0.539318\pi$
$828$		0			0
$829$	14.5795	−	25.2525i	0.506368	−	0.877055i	−0.493605	−	0.869686i	$-0.664321\pi$
$829$	14.5795	−	25.2525i	0.506368	−	0.877055i	0.999973	−	0.00736882i	$-0.00234559\pi$
$830$		0			0
$831$	−10.1177	+	5.84145i	−0.350979	+	0.202638i
$832$		0			0
$833$	21.1019	−	23.9519i	0.731139	−	0.829883i
$834$		0			0
$835$	18.5638	+	2.20263i	0.642426	+	0.0762253i
$836$		0			0
$837$	8.56193	−	2.29416i	0.295943	−	0.0792978i
$838$		0			0
$839$	6.64683			0.229474			0.114737	−	0.993396i	$-0.463397\pi$
$839$	6.64683			0.229474			0.114737	+	0.993396i	$0.463397\pi$
$840$		0			0
$841$	0.834107			0.0287623
$842$		0			0
$843$	−37.5514	+	10.0619i	−1.29334	+	0.346549i
$844$		0			0
$845$	20.6802	−	16.2932i	0.711421	−	0.560504i
$846$		0			0
$847$	−72.3047	+	2.28457i	−2.48442	+	0.0784988i
$848$		0			0
$849$	22.3710	−	12.9159i	0.767772	−	0.443274i
$850$		0			0
$851$	−23.1330	+	40.0675i	−0.792988	+	1.37350i
$852$		0			0
$853$	17.5756	+	17.5756i	0.601778	+	0.601778i	0.940784	−	0.339006i	$-0.110091\pi$
$853$	17.5756	+	17.5756i	0.601778	+	0.601778i	−0.339006	+	0.940784i	$0.610091\pi$
$854$		0			0
$855$	1.96111	+	13.5533i	0.0670687	+	0.463512i
$856$		0			0
$857$	1.32710	+	4.95282i	0.0453330	+	0.169185i	0.984881	−	0.173232i	$-0.0554211\pi$
$857$	1.32710	+	4.95282i	0.0453330	+	0.169185i	−0.939548	+	0.342417i	$0.888754\pi$
$858$		0			0
$859$	−12.3210	−	21.3406i	−0.420388	−	0.728133i	0.575589	−	0.817739i	$-0.304773\pi$
$859$	−12.3210	−	21.3406i	−0.420388	−	0.728133i	−0.995977	+	0.0896055i	$0.971439\pi$
$860$		0			0
$861$	13.4135	+	3.14369i	0.457129	+	0.107137i
$862$		0			0
$863$	−21.0853	−	5.64980i	−0.717753	−	0.192321i	−0.118584	−	0.992944i	$-0.537836\pi$
$863$	−21.0853	−	5.64980i	−0.717753	−	0.192321i	−0.599169	+	0.800623i	$0.704502\pi$
$864$		0			0
$865$	−46.0794	+	19.7814i	−1.56675	+	0.672589i
$866$		0			0
$867$	5.55843	−	5.55843i	0.188774	−	0.188774i
$868$		0			0
$869$			38.7811i			1.31556i
$870$		0			0
$871$	−4.31317	−	2.49021i	−0.146146	−	0.0843775i
$872$		0			0
$873$	1.24851	−	4.65951i	0.0422557	−	0.157700i
$874$		0			0
$875$	−1.80078	+	29.5255i	−0.0608773	+	0.998145i
$876$		0			0
$877$	−2.72257	+	10.1608i	−0.0919346	+	0.343105i	−0.996537	−	0.0831520i	$-0.973501\pi$
$877$	−2.72257	+	10.1608i	−0.0919346	+	0.343105i	0.904602	+	0.426257i	$0.140168\pi$
$878$		0			0
$879$	−2.05623	−	1.18716i	−0.0693549	−	0.0400421i
$880$		0			0
$881$			20.7283i			0.698355i	0.937057	+	0.349177i	$0.113539\pi$
$881$			20.7283i			0.698355i	−0.937057	+	0.349177i	$0.886461\pi$
$882$		0			0
$883$	−17.1930	+	17.1930i	−0.578591	+	0.578591i	−0.934515	−	0.355924i	$-0.884166\pi$
$883$	−17.1930	+	17.1930i	−0.578591	+	0.578591i	0.355924	+	0.934515i	$0.384166\pi$
$884$		0			0
$885$	−0.604950	+	0.259699i	−0.0203352	+	0.00872968i
$886$		0			0
$887$	−0.403588	−	0.108141i	−0.0135512	−	0.00363102i	0.252037	−	0.967718i	$-0.418900\pi$
$887$	−0.403588	−	0.108141i	−0.0135512	−	0.00363102i	−0.265588	+	0.964087i	$0.585566\pi$
$888$		0			0
$889$	−16.5209	+	4.99102i	−0.554093	+	0.167393i
$890$		0			0
$891$	−34.6931	−	60.0902i	−1.16226	−	2.01310i
$892$		0			0
$893$	10.9956	+	41.0362i	0.367955	+	1.37323i
$894$		0			0
$895$	−3.63034	−	25.0893i	−0.121349	−	0.838643i
$896$		0			0
$897$	10.9465	+	10.9465i	0.365492	+	0.365492i
$898$		0			0
$899$	−6.63857	+	11.4983i	−0.221409	+	0.383491i
$900$		0			0
$901$	40.5896	−	23.4344i	1.35223	−	0.780713i
$902$		0			0
$903$	1.65241	+	2.66406i	0.0549889	+	0.0886544i
$904$		0			0
$905$	−15.6480	+	12.3285i	−0.520157	+	0.409814i
$906$		0			0
$907$	−11.4126	+	3.05799i	−0.378949	+	0.101539i	−0.443265	−	0.896391i	$-0.646180\pi$
$907$	−11.4126	+	3.05799i	−0.378949	+	0.101539i	0.0643163	+	0.997930i	$0.479513\pi$
$908$		0			0
$909$	−6.49533			−0.215436
$910$		0			0
$911$	−19.7567			−0.654569			−0.327284	−	0.944926i	$-0.606133\pi$
$911$	−19.7567			−0.654569			−0.327284	+	0.944926i	$0.606133\pi$
$912$		0			0
$913$	−49.2939	+	13.2083i	−1.63139	+	0.437130i
$914$		0			0
$915$	−14.2181	−	1.68700i	−0.470035	−	0.0557707i
$916$		0			0
$917$	−1.69738	−	53.7206i	−0.0560524	−	1.77401i
$918$		0			0
$919$	43.7658	−	25.2682i	1.44370	−	0.833521i	0.445607	−	0.895229i	$-0.352988\pi$
$919$	43.7658	−	25.2682i	1.44370	−	0.833521i	0.998094	+	0.0617072i	$0.0196545\pi$
$920$		0			0
$921$	−6.85918	+	11.8804i	−0.226018	+	0.391474i
$922$		0			0
$923$	8.10463	+	8.10463i	0.266767	+	0.266767i
$924$		0			0
$925$	30.1044	+	16.3680i	0.989827	+	0.538177i
$926$		0			0
$927$	−0.915408	−	3.41635i	−0.0300659	−	0.112208i
$928$		0			0
$929$	5.54432	+	9.60305i	0.181903	+	0.315066i	0.942529	−	0.334125i	$-0.108441\pi$
$929$	5.54432	+	9.60305i	0.181903	+	0.315066i	−0.760625	+	0.649191i	$0.775108\pi$
$930$		0			0
$931$	14.7754	−	29.7903i	0.484244	−	0.976337i
$932$		0			0
$933$	−13.6331	−	3.65297i	−0.446327	−	0.119593i
$934$		0			0
$935$	−24.9076	−	58.0204i	−0.814564	−	1.89747i
$936$		0			0
$937$	−18.1969	+	18.1969i	−0.594467	+	0.594467i	−0.938835	−	0.344368i	$-0.888093\pi$
$937$	−18.1969	+	18.1969i	−0.594467	+	0.594467i	0.344368	+	0.938835i	$0.388093\pi$
$938$		0			0
$939$		−	55.8401i		−	1.82227i
$940$		0			0
$941$	21.1444	+	12.2077i	0.689288	+	0.397960i	0.803345	−	0.595514i	$-0.203051\pi$
$941$	21.1444	+	12.2077i	0.689288	+	0.397960i	−0.114057	+	0.993474i	$0.536385\pi$
$942$		0			0
$943$	−4.39313	+	16.3954i	−0.143060	+	0.533907i
$944$		0			0
$945$	12.0100	−	17.1796i	0.390686	−	0.558852i
$946$		0			0
$947$	−7.65277	+	28.5605i	−0.248682	+	0.928093i	0.722815	+	0.691041i	$0.242848\pi$
$947$	−7.65277	+	28.5605i	−0.248682	+	0.928093i	−0.971497	+	0.237051i	$0.923819\pi$
$948$		0			0
$949$	−1.79298	−	1.03518i	−0.0582025	−	0.0336032i
$950$		0			0
$951$		−	38.5439i		−	1.24987i
$952$		0			0
$953$	3.22919	−	3.22919i	0.104604	−	0.104604i	−0.652868	−	0.757472i	$-0.726434\pi$
$953$	3.22919	−	3.22919i	0.104604	−	0.104604i	0.757472	+	0.652868i	$0.226434\pi$
$954$		0			0
$955$	−13.3911	+	33.5367i	−0.433325	+	1.08522i
$956$		0			0
$957$	65.7405	+	17.6151i	2.12509	+	0.569416i
$958$		0			0
$959$	4.27971	−	18.2606i	0.138199	−	0.589666i
$960$		0			0
$961$	−12.3706	−	21.4266i	−0.399053	−	0.691180i
$962$		0			0
$963$	4.89371	+	18.2636i	0.157698	+	0.588536i
$964$		0			0
$965$	0.528157	−	0.706860i	0.0170020	−	0.0227546i
$966$		0			0
$967$	−25.9312	−	25.9312i	−0.833892	−	0.833892i	0.154154	−	0.988047i	$-0.450735\pi$
$967$	−25.9312	−	25.9312i	−0.833892	−	0.833892i	−0.988047	+	0.154154i	$0.950735\pi$
$968$		0			0
$969$	22.4326	−	38.8544i	0.720638	−	1.24818i
$970$		0			0
$971$	46.0713	−	26.5993i	1.47850	−	0.853612i	0.478795	−	0.877927i	$-0.341074\pi$
$971$	46.0713	−	26.5993i	1.47850	−	0.853612i	0.999704	+	0.0243150i	$0.00774047\pi$
$972$		0			0
$973$	−9.92777	+	18.5228i	−0.318270	+	0.593813i
$974$		0			0
$975$	7.89722	−	8.31226i	0.252914	−	0.266205i
$976$		0			0
$977$	−25.3326	+	6.78784i	−0.810461	+	0.217162i	−0.640172	−	0.768232i	$-0.721137\pi$
$977$	−25.3326	+	6.78784i	−0.810461	+	0.217162i	−0.170289	+	0.985394i	$0.554470\pi$
$978$		0			0
$979$	56.7914			1.81506
$980$		0			0
$981$	19.4103			0.619723
$982$		0			0
$983$	51.9494	−	13.9198i	1.65693	−	0.443973i	0.695389	−	0.718634i	$-0.255232\pi$
$983$	51.9494	−	13.9198i	1.65693	−	0.443973i	0.961541	+	0.274661i	$0.0885656\pi$
$984$		0			0
$985$	3.22569	−	27.1861i	0.102779	−	0.866220i
$986$		0			0
$987$	−23.1493	+	43.1908i	−0.736849	+	1.37478i
$988$		0			0
$989$	−3.34489	+	1.93117i	−0.106361	+	0.0614077i
$990$		0			0
$991$	15.9710	−	27.6625i	0.507334	−	0.878729i	−0.492630	−	0.870239i	$-0.663964\pi$
$991$	15.9710	−	27.6625i	0.507334	−	0.878729i	0.999964	−	0.00848990i	$-0.00270245\pi$
$992$		0			0
$993$	−20.6061	−	20.6061i	−0.653916	−	0.653916i
$994$		0			0
$995$	−21.9659	+	3.17839i	−0.696366	+	0.100762i
$996$		0			0
$997$	7.72489	+	28.8297i	0.244650	+	0.913045i	0.973559	+	0.228435i	$0.0733608\pi$
$997$	7.72489	+	28.8297i	0.244650	+	0.913045i	−0.728910	+	0.684610i	$0.759973\pi$
$998$		0			0
$999$	−12.1410	−	21.0288i	−0.384124	−	0.665322i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bo.a.17.3	✓	48
4.3	odd	2		560.2.ci.e.17.10		48
5.3	odd	4	inner	280.2.bo.a.73.3	yes	48
7.5	odd	6	inner	280.2.bo.a.257.3	yes	48
20.3	even	4		560.2.ci.e.353.10		48
28.19	even	6		560.2.ci.e.257.10		48
35.33	even	12	inner	280.2.bo.a.33.3	yes	48
140.103	odd	12		560.2.ci.e.33.10		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bo.a.17.3	✓	48	1.1	even	1	trivial
280.2.bo.a.33.3	yes	48	35.33	even	12	inner
280.2.bo.a.73.3	yes	48	5.3	odd	4	inner
280.2.bo.a.257.3	yes	48	7.5	odd	6	inner
560.2.ci.e.17.10		48	4.3	odd	2
560.2.ci.e.33.10		48	140.103	odd	12
560.2.ci.e.257.10		48	28.19	even	6
560.2.ci.e.353.10		48	20.3	even	4

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00047 + 0.536025i) q^{3} +(1.38383 + 1.75642i) q^{5} +(1.24986 - 2.33192i) q^{7} +(1.11649 - 0.644605i) q^{9} +O(q^{10})\)	\(q+(-2.00047 + 0.536025i) q^{3} +(1.38383 + 1.75642i) q^{5} +(1.24986 - 2.33192i) q^{7} +(1.11649 - 0.644605i) q^{9} +(-3.09606 + 5.36253i) q^{11} +(0.782930 + 0.782930i) q^{13} +(-3.70979 - 2.77191i) q^{15} +(1.18027 + 4.40483i) q^{17} +(2.37523 + 4.11401i) q^{19} +(-1.25033 + 5.33490i) q^{21} +(-6.52089 - 1.74727i) q^{23} +(-1.17005 + 4.86117i) q^{25} +(2.50536 - 2.50536i) q^{27} +5.30715i q^{29} +(2.16657 + 1.25087i) q^{31} +(3.31913 - 12.3871i) q^{33} +(5.82543 - 1.03170i) q^{35} +(1.77376 - 6.61976i) q^{37} +(-1.98590 - 1.14656i) q^{39} -2.51428i q^{41} +(0.404551 - 0.404551i) q^{43} +(2.67723 + 1.06901i) q^{45} +(8.63838 + 2.31465i) q^{47} +(-3.87572 - 5.82913i) q^{49} +(-4.72220 - 8.17909i) q^{51} +(-2.66008 - 9.92755i) q^{53} +(-13.7033 + 1.98282i) q^{55} +(-6.95679 - 6.95679i) q^{57} +(0.0710796 - 0.123113i) q^{59} +(2.67752 - 1.54587i) q^{61} +(-0.107719 - 3.40923i) q^{63} +(-0.291718 + 2.45860i) q^{65} +(-4.34482 + 1.16419i) q^{67} +13.9814 q^{69} +10.3517 q^{71} +(-1.80614 + 0.483952i) q^{73} +(-0.265056 - 10.3518i) q^{75} +(8.63537 + 13.9221i) q^{77} +(5.42390 - 3.13149i) q^{79} +(-5.60278 + 9.70431i) q^{81} +(5.82768 + 5.82768i) q^{83} +(-6.10346 + 8.16858i) q^{85} +(-2.84477 - 10.6168i) q^{87} +(-4.58578 - 7.94281i) q^{89} +(2.80428 - 0.847183i) q^{91} +(-5.00466 - 1.34100i) q^{93} +(-3.93905 + 9.86498i) q^{95} +(2.64580 - 2.64580i) q^{97} +7.98294i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{7}+O(q^{10}) \) 48 * q - 4 * q^7	\( 48 q - 4 q^{7} + 4 q^{11} + 8 q^{15} - 4 q^{21} - 4 q^{23} - 8 q^{25} - 36 q^{33} + 24 q^{35} + 8 q^{37} - 16 q^{43} + 48 q^{45} + 24 q^{51} + 16 q^{53} - 96 q^{57} - 36 q^{61} - 68 q^{63} + 12 q^{65} - 16 q^{67} - 64 q^{71} - 48 q^{73} - 48 q^{75} + 4 q^{77} - 40 q^{85} - 12 q^{87} - 80 q^{91} + 24 q^{95}+O(q^{100}) \) 48 * q - 4 * q^7 + 4 * q^11 + 8 * q^15 - 4 * q^21 - 4 * q^23 - 8 * q^25 - 36 * q^33 + 24 * q^35 + 8 * q^37 - 16 * q^43 + 48 * q^45 + 24 * q^51 + 16 * q^53 - 96 * q^57 - 36 * q^61 - 68 * q^63 + 12 * q^65 - 16 * q^67 - 64 * q^71 - 48 * q^73 - 48 * q^75 + 4 * q^77 - 40 * q^85 - 12 * q^87 - 80 * q^91 + 24 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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