LMFDB - Embedded newform 280.2.bo.a.17.8

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			17.8
Character	$\chi$	$=$	280.17
Dual form			280.2.bo.a.33.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.280752 - 0.0752271i) q^{3} +(2.21121 - 0.332503i) q^{5} +(1.13104 - 2.39181i) q^{7} +(-2.52491 + 1.45776i) q^{9} +O(q^{10})$	\(q+(0.280752 - 0.0752271i) q^{3} +(2.21121 - 0.332503i) q^{5} +(1.13104 - 2.39181i) q^{7} +(-2.52491 + 1.45776i) q^{9} +(1.58294 - 2.74174i) q^{11} +(1.12753 + 1.12753i) q^{13} +(0.595787 - 0.259694i) q^{15} +(0.781030 + 2.91484i) q^{17} +(-1.03536 - 1.79330i) q^{19} +(0.137613 - 0.756589i) q^{21} +(2.21537 + 0.593606i) q^{23} +(4.77888 - 1.47047i) q^{25} +(-1.21578 + 1.21578i) q^{27} -1.39922i q^{29} +(0.467508 + 0.269916i) q^{31} +(0.238160 - 0.888827i) q^{33} +(1.70568 - 5.66486i) q^{35} +(-1.72976 + 6.45554i) q^{37} +(0.401375 + 0.231734i) q^{39} -1.82954i q^{41} +(-6.50139 + 6.50139i) q^{43} +(-5.09840 + 4.06295i) q^{45} +(-12.4272 - 3.32985i) q^{47} +(-4.44149 - 5.41047i) q^{49} +(0.438550 + 0.759592i) q^{51} +(2.89567 + 10.8068i) q^{53} +(2.58858 - 6.58888i) q^{55} +(-0.425584 - 0.425584i) q^{57} +(2.55946 - 4.43312i) q^{59} +(-12.2942 + 7.09808i) q^{61} +(0.630899 + 7.68790i) q^{63} +(2.86810 + 2.11829i) q^{65} +(-3.08572 + 0.826816i) q^{67} +0.666623 q^{69} +7.61378 q^{71} +(3.08810 - 0.827453i) q^{73} +(1.23106 - 0.772338i) q^{75} +(-4.76733 - 6.88711i) q^{77} +(-14.7577 + 8.52036i) q^{79} +(4.12341 - 7.14195i) q^{81} +(4.62071 + 4.62071i) q^{83} +(2.69621 + 6.18563i) q^{85} +(-0.105259 - 0.392834i) q^{87} +(-8.86012 - 15.3462i) q^{89} +(3.97210 - 1.42155i) q^{91} +(0.151559 + 0.0406100i) q^{93} +(-2.88567 - 3.62109i) q^{95} +(3.71983 - 3.71983i) q^{97} +9.23019i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.280752	−	0.0752271i	0.162092	−	0.0434324i	−0.176860	−	0.984236i	$-0.556594\pi$
$3$	0.280752	−	0.0752271i	0.162092	−	0.0434324i	0.338952	+	0.940804i	$0.389927\pi$
$4$		0			0
$5$	2.21121	−	0.332503i	0.988882	−	0.148700i
$5$	2.21121	−	0.332503i	0.988882	−	0.148700i
$6$		0			0
$7$	1.13104	−	2.39181i	0.427494	−	0.904018i
$7$	1.13104	−	2.39181i	0.427494	−	0.904018i
$8$		0			0
$9$	−2.52491	+	1.45776i	−0.841638	+	0.485920i
$10$		0			0
$11$	1.58294	−	2.74174i	0.477275	−	0.826664i	−0.522386	−	0.852709i	$-0.674958\pi$
$11$	1.58294	−	2.74174i	0.477275	−	0.826664i	0.999661	+	0.0260448i	$0.00829127\pi$
$12$		0			0
$13$	1.12753	+	1.12753i	0.312719	+	0.312719i	0.845962	−	0.533243i	$-0.179027\pi$
$13$	1.12753	+	1.12753i	0.312719	+	0.312719i	−0.533243	+	0.845962i	$0.679027\pi$
$14$		0			0
$15$	0.595787	−	0.259694i	0.153831	−	0.0670526i
$16$		0			0
$17$	0.781030	+	2.91484i	0.189427	+	0.706953i	0.993639	+	0.112610i	$0.0359211\pi$
$17$	0.781030	+	2.91484i	0.189427	+	0.706953i	−0.804212	+	0.594343i	$0.797412\pi$
$18$		0			0
$19$	−1.03536	−	1.79330i	−0.237528	−	0.411411i	0.722476	−	0.691396i	$-0.243004\pi$
$19$	−1.03536	−	1.79330i	−0.237528	−	0.411411i	−0.960004	+	0.279985i	$0.909670\pi$
$20$		0			0
$21$	0.137613	−	0.756589i	0.0300296	−	0.165101i
$22$		0			0
$23$	2.21537	+	0.593606i	0.461936	+	0.123775i	0.482279	−	0.876018i	$-0.339809\pi$
$23$	2.21537	+	0.593606i	0.461936	+	0.123775i	−0.0203430	+	0.999793i	$0.506476\pi$
$24$		0			0
$25$	4.77888	−	1.47047i	0.955777	−	0.294093i
$26$		0			0
$27$	−1.21578	+	1.21578i	−0.233978	+	0.233978i
$28$		0			0
$29$		−	1.39922i		−	0.259829i	−0.991525	−	0.129914i	$-0.958530\pi$
$29$		−	1.39922i		−	0.259829i	0.991525	−	0.129914i	$-0.0414703\pi$
$30$		0			0
$31$	0.467508	+	0.269916i	0.0839669	+	0.0484783i	0.541396	−	0.840768i	$-0.317896\pi$
$31$	0.467508	+	0.269916i	0.0839669	+	0.0484783i	−0.457429	+	0.889246i	$0.651229\pi$
$32$		0			0
$33$	0.238160	−	0.888827i	0.0414584	−	0.154725i
$34$		0			0
$35$	1.70568	−	5.66486i	0.288313	−	0.957536i
$36$		0			0
$37$	−1.72976	+	6.45554i	−0.284370	+	1.06128i	0.664928	+	0.746907i	$0.268462\pi$
$37$	−1.72976	+	6.45554i	−0.284370	+	1.06128i	−0.949298	+	0.314376i	$0.898205\pi$
$38$		0			0
$39$	0.401375	+	0.231734i	0.0642714	+	0.0371071i
$40$		0			0
$41$		−	1.82954i		−	0.285726i	−0.989742	−	0.142863i	$-0.954369\pi$
$41$		−	1.82954i		−	0.285726i	0.989742	−	0.142863i	$-0.0456308\pi$
$42$		0			0
$43$	−6.50139	+	6.50139i	−0.991453	+	0.991453i	−0.999964	−	0.00851097i	$-0.997291\pi$
$43$	−6.50139	+	6.50139i	−0.991453	+	0.991453i	0.00851097	+	0.999964i	$0.497291\pi$
$44$		0			0
$45$	−5.09840	+	4.06295i	−0.760025	+	0.605669i
$46$		0			0
$47$	−12.4272	−	3.32985i	−1.81269	−	0.485709i	−0.816851	−	0.576849i	$-0.804282\pi$
$47$	−12.4272	−	3.32985i	−1.81269	−	0.485709i	−0.995838	+	0.0911405i	$0.970949\pi$
$48$		0			0
$49$	−4.44149	−	5.41047i	−0.634499	−	0.772924i
$50$		0			0
$51$	0.438550	+	0.759592i	0.0614093	+	0.106364i
$52$		0			0
$53$	2.89567	+	10.8068i	0.397751	+	1.48443i	0.817043	+	0.576577i	$0.195612\pi$
$53$	2.89567	+	10.8068i	0.397751	+	1.48443i	−0.419292	+	0.907852i	$0.637721\pi$
$54$		0			0
$55$	2.58858	−	6.58888i	0.349044	−	0.888445i
$56$		0			0
$57$	−0.425584	−	0.425584i	−0.0563699	−	0.0563699i
$58$		0			0
$59$	2.55946	−	4.43312i	0.333214	−	0.577143i	−0.649926	−	0.759997i	$-0.725200\pi$
$59$	2.55946	−	4.43312i	0.333214	−	0.577143i	0.983140	+	0.182854i	$0.0585336\pi$
$60$		0			0
$61$	−12.2942	+	7.09808i	−1.57412	+	0.908816i	−0.578459	+	0.815712i	$0.696346\pi$
$61$	−12.2942	+	7.09808i	−1.57412	+	0.908816i	−0.995656	+	0.0931040i	$0.970321\pi$
$62$		0			0
$63$	0.630899	+	7.68790i	0.0794858	+	0.968584i
$64$		0			0
$65$	2.86810	+	2.11829i	0.355744	+	0.262741i
$66$		0			0
$67$	−3.08572	+	0.826816i	−0.376981	+	0.101012i	−0.442334	−	0.896851i	$-0.645849\pi$
$67$	−3.08572	+	0.826816i	−0.376981	+	0.101012i	0.0653530	+	0.997862i	$0.479183\pi$
$68$		0			0
$69$	0.666623			0.0802520
$70$		0			0
$71$	7.61378			0.903590			0.451795	−	0.892122i	$-0.350784\pi$
$71$	7.61378			0.903590			0.451795	+	0.892122i	$0.350784\pi$
$72$		0			0
$73$	3.08810	−	0.827453i	0.361435	−	0.0968461i	−0.0735316	−	0.997293i	$-0.523427\pi$
$73$	3.08810	−	0.827453i	0.361435	−	0.0968461i	0.434966	+	0.900447i	$0.356760\pi$
$74$		0			0
$75$	1.23106	−	0.772338i	0.142151	−	0.0891819i
$76$		0			0
$77$	−4.76733	−	6.88711i	−0.543288	−	0.784859i
$78$		0			0
$79$	−14.7577	+	8.52036i	−1.66037	+	0.958616i	−0.687834	+	0.725868i	$0.741438\pi$
$79$	−14.7577	+	8.52036i	−1.66037	+	0.958616i	−0.972537	+	0.232748i	$0.925228\pi$
$80$		0			0
$81$	4.12341	−	7.14195i	0.458156	−	0.793550i
$82$		0			0
$83$	4.62071	+	4.62071i	0.507189	+	0.507189i	0.913662	−	0.406474i	$-0.133242\pi$
$83$	4.62071	+	4.62071i	0.507189	+	0.507189i	−0.406474	+	0.913662i	$0.633242\pi$
$84$		0			0
$85$	2.69621	+	6.18563i	0.292445	+	0.670925i
$86$		0			0
$87$	−0.105259	−	0.392834i	−0.0112850	−	0.0421162i
$88$		0			0
$89$	−8.86012	−	15.3462i	−0.939171	−	1.62669i	−0.767023	−	0.641620i	$-0.778263\pi$
$89$	−8.86012	−	15.3462i	−0.939171	−	1.62669i	−0.172148	−	0.985071i	$-0.555071\pi$
$90$		0			0
$91$	3.97210	−	1.42155i	0.416389	−	0.149019i
$92$		0			0
$93$	0.151559	+	0.0406100i	0.0157159	+	0.00421106i
$94$		0			0
$95$	−2.88567	−	3.62109i	−0.296064	−	0.371516i
$96$		0			0
$97$	3.71983	−	3.71983i	0.377692	−	0.377692i	−0.492577	−	0.870269i	$-0.663945\pi$
$97$	3.71983	−	3.71983i	0.377692	−	0.377692i	0.870269	+	0.492577i	$0.163945\pi$
$98$		0			0
$99$			9.23019i			0.927669i
$100$		0			0
$101$	−10.9262	−	6.30826i	−1.08720	−	0.627696i	−0.154371	−	0.988013i	$-0.549335\pi$
$101$	−10.9262	−	6.30826i	−1.08720	−	0.627696i	−0.932830	+	0.360317i	$0.882668\pi$
$102$		0			0
$103$	−1.51328	+	5.64765i	−0.149108	+	0.556479i	0.850430	+	0.526088i	$0.176342\pi$
$103$	−1.51328	+	5.64765i	−0.149108	+	0.556479i	−0.999538	+	0.0303910i	$0.990325\pi$
$104$		0			0
$105$	0.0527224	−	1.71873i	0.00514518	−	0.167731i
$106$		0			0
$107$	−1.64561	+	6.14150i	−0.159087	+	0.593721i	0.839633	+	0.543153i	$0.182770\pi$
$107$	−1.64561	+	6.14150i	−0.159087	+	0.593721i	−0.998721	+	0.0505679i	$0.983897\pi$
$108$		0			0
$109$	9.97396	+	5.75847i	0.955333	+	0.551562i	0.894733	−	0.446601i	$-0.147366\pi$
$109$	9.97396	+	5.75847i	0.955333	+	0.551562i	0.0605992	+	0.998162i	$0.480699\pi$
$110$		0			0
$111$			1.94253i			0.184376i
$112$		0			0
$113$	11.7681	−	11.7681i	1.10705	−	1.10705i	0.113517	−	0.993536i	$-0.463788\pi$
$113$	11.7681	−	11.7681i	1.10705	−	1.10705i	0.993536	−	0.113517i	$-0.0362117\pi$
$114$		0			0
$115$	5.09601	+	0.575970i	0.475206	+	0.0537095i
$116$		0			0
$117$	−4.49057	−	1.20324i	−0.415153	−	0.111240i
$118$		0			0
$119$	7.85512	+	1.42873i	0.720078	+	0.130972i
$120$		0			0
$121$	0.488591	+	0.846264i	0.0444173	+	0.0769331i
$122$		0			0
$123$	−0.137631	−	0.513646i	−0.0124098	−	0.0463139i
$124$		0			0
$125$	10.0782	−	4.84050i	0.901419	−	0.432948i
$126$		0			0
$127$	8.63098	+	8.63098i	0.765876	+	0.765876i	0.977378	−	0.211502i	$-0.0678354\pi$
$127$	8.63098	+	8.63098i	0.765876	+	0.765876i	−0.211502	+	0.977378i	$0.567835\pi$
$128$		0			0
$129$	−1.33619	+	2.31436i	−0.117645	+	0.203768i
$130$		0			0
$131$	9.14667	−	5.28083i	0.799148	−	0.461389i	−0.0440249	−	0.999030i	$-0.514018\pi$
$131$	9.14667	−	5.28083i	0.799148	−	0.461389i	0.843173	+	0.537642i	$0.180685\pi$
$132$		0			0
$133$	−5.46026	+	0.448090i	−0.473464	+	0.0388543i
$134$		0			0
$135$	−2.28410	+	3.09260i	−0.196584	+	0.266169i
$136$		0			0
$137$	8.82003	−	2.36332i	0.753546	−	0.201912i	0.138456	−	0.990369i	$-0.455786\pi$
$137$	8.82003	−	2.36332i	0.753546	−	0.201912i	0.615090	+	0.788457i	$0.289119\pi$
$138$		0			0
$139$	−12.2197			−1.03646			−0.518229	−	0.855242i	$-0.673408\pi$
$139$	−12.2197			−1.03646			−0.518229	+	0.855242i	$0.673408\pi$
$140$		0			0
$141$	−3.73944			−0.314918
$142$		0			0
$143$	4.87618	−	1.30657i	0.407767	−	0.109261i
$144$		0			0
$145$	−0.465245	−	3.09397i	−0.0386365	−	0.256940i
$146$		0			0
$147$	−1.65397	−	1.18488i	−0.136417	−	0.0977270i
$148$		0			0
$149$	8.41513	−	4.85848i	0.689394	−	0.398022i	−0.113991	−	0.993482i	$-0.536363\pi$
$149$	8.41513	−	4.85848i	0.689394	−	0.398022i	0.803385	+	0.595460i	$0.203030\pi$
$150$		0			0
$151$	9.68938	−	16.7825i	0.788510	−	1.36574i	−0.138369	−	0.990381i	$-0.544186\pi$
$151$	9.68938	−	16.7825i	0.788510	−	1.36574i	0.926880	−	0.375359i	$-0.122481\pi$
$152$		0			0
$153$	−6.22117	−	6.22117i	−0.502952	−	0.502952i
$154$		0			0
$155$	1.12350	+	0.441392i	0.0902421	+	0.0354535i
$156$		0			0
$157$	4.70161	+	17.5466i	0.375229	+	1.40037i	0.853010	+	0.521895i	$0.174775\pi$
$157$	4.70161	+	17.5466i	0.375229	+	1.40037i	−0.477781	+	0.878479i	$0.658559\pi$
$158$		0			0
$159$	1.62593	+	2.81619i	0.128945	+	0.223339i
$160$		0			0
$161$	3.92546	−	4.62734i	0.309370	−	0.364685i
$162$		0			0
$163$	−12.8407	−	3.44064i	−1.00576	−	0.269492i	−0.281902	−	0.959443i	$-0.590965\pi$
$163$	−12.8407	−	3.44064i	−1.00576	−	0.269492i	−0.723856	+	0.689951i	$0.757632\pi$
$164$		0			0
$165$	0.231085	−	2.04457i	0.0179899	−	0.159170i
$166$		0			0
$167$	7.01514	−	7.01514i	0.542848	−	0.542848i	−0.381515	−	0.924363i	$-0.624597\pi$
$167$	7.01514	−	7.01514i	0.542848	−	0.542848i	0.924363	+	0.381515i	$0.124597\pi$
$168$		0			0
$169$		−	10.4574i		−	0.804413i
$170$		0			0
$171$	5.22839	+	3.01861i	0.399825	+	0.230839i
$172$		0			0
$173$	3.38896	−	12.6478i	0.257658	−	0.961592i	−0.708935	−	0.705274i	$-0.750824\pi$
$173$	3.38896	−	12.6478i	0.257658	−	0.961592i	0.966593	−	0.256318i	$-0.0825093\pi$
$174$		0			0
$175$	1.88804	−	13.0933i	0.142722	−	0.989763i
$176$		0			0
$177$	0.385082	−	1.43715i	0.0289445	−	0.108023i
$178$		0			0
$179$	9.39353	+	5.42335i	0.702105	+	0.405361i	0.808131	−	0.589003i	$-0.200479\pi$
$179$	9.39353	+	5.42335i	0.702105	+	0.405361i	−0.106026	+	0.994363i	$0.533813\pi$
$180$		0			0
$181$			14.0160i			1.04180i	0.853617	+	0.520901i	$0.174404\pi$
$181$			14.0160i			1.04180i	−0.853617	+	0.520901i	$0.825596\pi$
$182$		0			0
$183$	−2.91766	+	2.91766i	−0.215679	+	0.215679i
$184$		0			0
$185$	−1.67836	+	14.8497i	−0.123396	+	1.09177i
$186$		0			0
$187$	9.22805	+	2.47265i	0.674822	+	0.180818i
$188$		0			0
$189$	1.53282	+	4.28302i	0.111496	+	0.311544i
$190$		0			0
$191$	10.5152	+	18.2128i	0.760852	+	1.31784i	0.942412	+	0.334455i	$0.108552\pi$
$191$	10.5152	+	18.2128i	0.760852	+	1.31784i	−0.181559	+	0.983380i	$0.558114\pi$
$192$		0			0
$193$	3.50376	+	13.0762i	0.252206	+	0.941246i	0.969623	+	0.244602i	$0.0786575\pi$
$193$	3.50376	+	13.0762i	0.252206	+	0.941246i	−0.717417	+	0.696644i	$0.754676\pi$
$194$		0			0
$195$	0.964576	+	0.378954i	0.0690747	+	0.0271374i
$196$		0			0
$197$	−8.95252	−	8.95252i	−0.637840	−	0.637840i	0.312182	−	0.950022i	$-0.398940\pi$
$197$	−8.95252	−	8.95252i	−0.637840	−	0.637840i	−0.950022	+	0.312182i	$0.898940\pi$
$198$		0			0
$199$	6.80780	−	11.7915i	0.482592	−	0.835875i	−0.517208	−	0.855860i	$-0.673029\pi$
$199$	6.80780	−	11.7915i	0.482592	−	0.835875i	0.999800	+	0.0199852i	$0.00636192\pi$
$200$		0			0
$201$	−0.804122	+	0.464260i	−0.0567184	+	0.0327464i
$202$		0			0
$203$	−3.34667	−	1.58258i	−0.234890	−	0.111075i
$204$		0			0
$205$	−0.608327	−	4.04549i	−0.0424874	−	0.282549i
$206$		0			0
$207$	−6.45895	+	1.73067i	−0.448928	+	0.120290i
$208$		0			0
$209$	−6.55566			−0.453465
$210$		0			0
$211$	−19.2166			−1.32293			−0.661464	−	0.749977i	$-0.730064\pi$
$211$	−19.2166			−1.32293			−0.661464	+	0.749977i	$0.730064\pi$
$212$		0			0
$213$	2.13758	−	0.572763i	0.146465	−	0.0392451i
$214$		0			0
$215$	−12.2142	+	16.5377i	−0.833001	+	1.12786i
$216$		0			0
$217$	1.17436	−	0.812903i	0.0797206	−	0.0551834i
$218$		0			0
$219$	0.804741	−	0.464618i	0.0543794	−	0.0313960i
$220$		0			0
$221$	−2.40593	+	4.16719i	−0.161840	+	0.280315i
$222$		0			0
$223$	−12.2014	−	12.2014i	−0.817068	−	0.817068i	0.168614	−	0.985682i	$-0.446071\pi$
$223$	−12.2014	−	12.2014i	−0.817068	−	0.817068i	−0.985682	+	0.168614i	$0.946071\pi$
$224$		0			0
$225$	−9.92268	+	10.6793i	−0.661512	+	0.711951i
$226$		0			0
$227$	−4.58309	−	17.1043i	−0.304191	−	1.13525i	−0.933640	−	0.358213i	$-0.883386\pi$
$227$	−4.58309	−	17.1043i	−0.304191	−	1.13525i	0.629449	−	0.777042i	$-0.283281\pi$
$228$		0			0
$229$	3.44116	+	5.96026i	0.227398	+	0.393865i	0.957036	−	0.289968i	$-0.0936448\pi$
$229$	3.44116	+	5.96026i	0.227398	+	0.393865i	−0.729638	+	0.683833i	$0.760311\pi$
$230$		0			0
$231$	−1.85653	−	1.57493i	−0.122151	−	0.103623i
$232$		0			0
$233$	−0.997989	−	0.267410i	−0.0653804	−	0.0175186i	0.225981	−	0.974132i	$-0.427441\pi$
$233$	−0.997989	−	0.267410i	−0.0653804	−	0.0175186i	−0.291361	+	0.956613i	$0.594108\pi$
$234$		0			0
$235$	−28.5862	−	3.23092i	−1.86476	−	0.210762i
$236$		0			0
$237$	−3.50229	+	3.50229i	−0.227498	+	0.227498i
$238$		0			0
$239$			2.59385i			0.167782i	0.996475	+	0.0838910i	$0.0267348\pi$
$239$			2.59385i			0.167782i	−0.996475	+	0.0838910i	$0.973265\pi$
$240$		0			0
$241$	−18.8567	−	10.8869i	−1.21467	−	0.701288i	−0.250894	−	0.968015i	$-0.580724\pi$
$241$	−18.8567	−	10.8869i	−1.21467	−	0.701288i	−0.963772	+	0.266727i	$0.914058\pi$
$242$		0			0
$243$	1.95541	−	7.29768i	0.125439	−	0.468146i
$244$		0			0
$245$	−11.6201	−	10.4869i	−0.742378	−	0.669981i
$246$		0			0
$247$	0.854592	−	3.18938i	0.0543764	−	0.202936i
$248$		0			0
$249$	1.64487	+	0.949668i	0.104240	+	0.0601828i
$250$		0			0
$251$			27.3745i			1.72787i	0.503607	+	0.863933i	$0.332006\pi$
$251$			27.3745i			1.72787i	−0.503607	+	0.863933i	$0.667994\pi$
$252$		0			0
$253$	5.13431	−	5.13431i	0.322791	−	0.322791i
$254$		0			0
$255$	1.22229	+	1.53380i	0.0765430	+	0.0960500i
$256$		0			0
$257$	16.6938	+	4.47308i	1.04133	+	0.279023i	0.738664	−	0.674074i	$-0.235457\pi$
$257$	16.6938	+	4.47308i	1.04133	+	0.279023i	0.302665	+	0.953097i	$0.402124\pi$
$258$		0			0
$259$	13.4840	+	11.4387i	0.837854	+	0.710768i
$260$		0			0
$261$	2.03973	+	3.53291i	0.126256	+	0.218682i
$262$		0			0
$263$	−0.213266	−	0.795918i	−0.0131505	−	0.0490784i	0.959039	−	0.283275i	$-0.0914208\pi$
$263$	−0.213266	−	0.795918i	−0.0131505	−	0.0490784i	−0.972189	+	0.234196i	$0.924754\pi$
$264$		0			0
$265$	9.99623	+	22.9333i	0.614064	+	1.40878i
$266$		0			0
$267$	−3.64194	−	3.64194i	−0.222883	−	0.222883i
$268$		0			0
$269$	−4.11282	+	7.12362i	−0.250763	+	0.434335i	−0.963736	−	0.266857i	$-0.914015\pi$
$269$	−4.11282	+	7.12362i	−0.250763	+	0.434335i	0.712973	+	0.701192i	$0.247348\pi$
$270$		0			0
$271$	−12.4591	+	7.19325i	−0.756834	+	0.436959i	−0.828158	−	0.560495i	$-0.810611\pi$
$271$	−12.4591	+	7.19325i	−0.756834	+	0.436959i	0.0713236	+	0.997453i	$0.477278\pi$
$272$		0			0
$273$	1.00823	−	0.697911i	0.0610211	−	0.0422395i
$274$		0			0
$275$	3.53306	−	15.4301i	0.213052	−	0.930470i
$276$		0			0
$277$	−0.770139	+	0.206358i	−0.0462732	+	0.0123989i	−0.281881	−	0.959449i	$-0.590958\pi$
$277$	−0.770139	+	0.206358i	−0.0462732	+	0.0123989i	0.235608	+	0.971848i	$0.424292\pi$
$278$		0			0
$279$	−1.57389			−0.0942263
$280$		0			0
$281$	0.874556			0.0521716			0.0260858	−	0.999660i	$-0.491696\pi$
$281$	0.874556			0.0521716			0.0260858	+	0.999660i	$0.491696\pi$
$282$		0			0
$283$	15.7926	−	4.23160i	0.938770	−	0.251543i	0.243180	−	0.969981i	$-0.421810\pi$
$283$	15.7926	−	4.23160i	0.938770	−	0.251543i	0.695590	+	0.718439i	$0.255143\pi$
$284$		0			0
$285$	−1.08256	−	0.799546i	−0.0641254	−	0.0473610i
$286$		0			0
$287$	−4.37591	−	2.06928i	−0.258302	−	0.122146i
$288$		0			0
$289$	6.83614	−	3.94685i	0.402126	−	0.232167i
$290$		0			0
$291$	0.764516	−	1.32418i	0.0448167	−	0.0776248i
$292$		0			0
$293$	−14.3739	−	14.3739i	−0.839732	−	0.839732i	0.149092	−	0.988823i	$-0.452365\pi$
$293$	−14.3739	−	14.3739i	−0.839732	−	0.839732i	−0.988823	+	0.149092i	$0.952365\pi$
$294$		0			0
$295$	4.18548	−	10.6536i	0.243688	−	0.620275i
$296$		0			0
$297$	1.40884	+	5.25787i	0.0817493	+	0.305093i
$298$		0			0
$299$	1.82858	+	3.16719i	0.105749	+	0.183163i
$300$		0			0
$301$	8.19674	+	22.9034i	0.472452	+	1.32013i
$302$		0			0
$303$	−3.54211	−	0.949105i	−0.203489	−	0.0545247i
$304$		0			0
$305$	−24.8250	+	19.7832i	−1.42147	+	1.13278i
$306$		0			0
$307$	19.5084	−	19.5084i	1.11340	−	1.11340i	0.120716	−	0.992687i	$-0.461481\pi$
$307$	19.5084	−	19.5084i	1.11340	−	1.11340i	0.992687	−	0.120716i	$-0.0385190\pi$
$308$		0			0
$309$			1.69943i			0.0966770i
$310$		0			0
$311$	−23.3033	−	13.4542i	−1.32141	−	0.762916i	−0.337456	−	0.941341i	$-0.609566\pi$
$311$	−23.3033	−	13.4542i	−1.32141	−	0.762916i	−0.983953	+	0.178425i	$0.942900\pi$
$312$		0			0
$313$	−2.28226	+	8.51752i	−0.129001	+	0.481439i	−0.999951	−	0.00993361i	$-0.996838\pi$
$313$	−2.28226	+	8.51752i	−0.129001	+	0.481439i	0.870949	+	0.491373i	$0.163505\pi$
$314$		0			0
$315$	3.95130	+	16.7898i	0.222630	+	0.945996i
$316$		0			0
$317$	1.51023	−	5.63627i	0.0848232	−	0.316564i	−0.910457	−	0.413603i	$-0.864270\pi$
$317$	1.51023	−	5.63627i	0.0848232	−	0.316564i	0.995281	+	0.0970383i	$0.0309369\pi$
$318$		0			0
$319$	−3.83629	−	2.21489i	−0.214791	−	0.124010i
$320$		0			0
$321$			1.84803i			0.103147i
$322$		0			0
$323$	4.41853	−	4.41853i	0.245854	−	0.245854i
$324$		0			0
$325$	7.04630	+	3.73032i	0.390858	+	0.206921i
$326$		0			0
$327$	3.23340	+	0.866387i	0.178807	+	0.0479113i
$328$		0			0
$329$	−22.0200	+	25.9572i	−1.21400	+	1.43107i
$330$		0			0
$331$	−12.2485	−	21.2150i	−0.673237	−	1.16608i	−0.976981	−	0.213327i	$-0.931570\pi$
$331$	−12.2485	−	21.2150i	−0.673237	−	1.16608i	0.303744	−	0.952754i	$-0.401763\pi$
$332$		0			0
$333$	−5.04314	−	18.8212i	−0.276362	−	1.03140i
$334$		0			0
$335$	−6.54825	+	2.85427i	−0.357769	+	0.155946i
$336$		0			0
$337$	5.54436	+	5.54436i	0.302021	+	0.302021i	0.841804	−	0.539783i	$-0.181494\pi$
$337$	5.54436	+	5.54436i	0.302021	+	0.302021i	−0.539783	+	0.841804i	$0.681494\pi$
$338$		0			0
$339$	2.41864	−	4.18921i	0.131362	−	0.227526i
$340$		0			0
$341$	1.48008	−	0.854522i	0.0801506	−	0.0462749i
$342$		0			0
$343$	−17.9643	+	4.50373i	−0.969982	+	0.243178i
$344$		0			0
$345$	1.47404	−	0.221654i	0.0793598	−	0.0119335i
$346$		0			0
$347$	−26.1167	+	6.99795i	−1.40202	+	0.375670i	−0.879069	−	0.476695i	$-0.841835\pi$
$347$	−26.1167	+	6.99795i	−1.40202	+	0.375670i	−0.522949	+	0.852364i	$0.675168\pi$
$348$		0			0
$349$	13.8090			0.739179			0.369590	−	0.929195i	$-0.379498\pi$
$349$	13.8090			0.739179			0.369590	+	0.929195i	$0.379498\pi$
$350$		0			0
$351$	−2.74165			−0.146339
$352$		0			0
$353$	−6.51881	+	1.74671i	−0.346961	+	0.0929680i	−0.428091	−	0.903736i	$-0.640814\pi$
$353$	−6.51881	+	1.74671i	−0.346961	+	0.0929680i	0.0811298	+	0.996704i	$0.474147\pi$
$354$		0			0
$355$	16.8357	−	2.53161i	0.893544	−	0.134364i
$356$		0			0
$357$	2.31282	−	0.189799i	0.122407	−	0.0100452i
$358$		0			0
$359$	20.6255	−	11.9082i	1.08857	−	0.628488i	0.155377	−	0.987855i	$-0.450341\pi$
$359$	20.6255	−	11.9082i	1.08857	−	0.628488i	0.933196	+	0.359367i	$0.117007\pi$
$360$		0			0
$361$	7.35606	−	12.7411i	0.387161	−	0.670582i
$362$		0			0
$363$	0.200835	+	0.200835i	0.0105411	+	0.0105411i
$364$		0			0
$365$	6.55330	−	2.85647i	0.343015	−	0.149515i
$366$		0			0
$367$	3.69329	+	13.7835i	0.192788	+	0.719494i	0.992828	+	0.119548i	$0.0381447\pi$
$367$	3.69329	+	13.7835i	0.192788	+	0.719494i	−0.800040	+	0.599946i	$0.795189\pi$
$368$		0			0
$369$	2.66703	+	4.61943i	0.138840	+	0.240478i
$370$		0			0
$371$	29.1229	+	5.29705i	1.51199	+	0.275009i
$372$		0			0
$373$	−6.79696	−	1.82124i	−0.351933	−	0.0943002i	0.0785216	−	0.996912i	$-0.474980\pi$
$373$	−6.79696	−	1.82124i	−0.351933	−	0.0943002i	−0.430455	+	0.902612i	$0.641647\pi$
$374$		0			0
$375$	2.46532	−	2.11713i	0.127309	−	0.109328i
$376$		0			0
$377$	1.57766	−	1.57766i	0.0812535	−	0.0812535i
$378$		0			0
$379$		−	12.7830i		−	0.656616i	−0.944571	−	0.328308i	$-0.893522\pi$
$379$		−	12.7830i		−	0.656616i	0.944571	−	0.328308i	$-0.106478\pi$
$380$		0			0
$381$	3.07245	+	1.77388i	0.157406	+	0.0908785i
$382$		0			0
$383$	5.14216	−	19.1908i	0.262752	−	0.980603i	−0.700860	−	0.713299i	$-0.747200\pi$
$383$	5.14216	−	19.1908i	0.262752	−	0.980603i	0.963612	−	0.267305i	$-0.0861330\pi$
$384$		0			0
$385$	−12.8315	−	13.6437i	−0.653956	−	0.695346i
$386$		0			0
$387$	6.93799	−	25.8929i	0.352678	−	1.31621i
$388$		0			0
$389$	20.2010	+	11.6631i	1.02423	+	0.591342i	0.915327	−	0.402710i	$-0.131932\pi$
$389$	20.2010	+	11.6631i	1.02423	+	0.591342i	0.108906	+	0.994052i	$0.465265\pi$
$390$		0			0
$391$			6.92107i			0.350013i
$392$		0			0
$393$	2.17068	−	2.17068i	0.109496	−	0.109496i
$394$		0			0
$395$	−29.7993	+	23.7473i	−1.49937	+	1.19486i
$396$		0			0
$397$	24.9302	+	6.68004i	1.25121	+	0.335261i	0.822805	−	0.568324i	$-0.192408\pi$
$397$	24.9302	+	6.68004i	1.25121	+	0.335261i	0.428408	+	0.903585i	$0.359075\pi$
$398$		0			0
$399$	−1.49927	+	0.536562i	−0.0750572	+	0.0268617i
$400$		0			0
$401$	3.12717	+	5.41642i	0.156163	+	0.270483i	0.933482	−	0.358624i	$-0.116754\pi$
$401$	3.12717	+	5.41642i	0.156163	+	0.270483i	−0.777319	+	0.629107i	$0.783421\pi$
$402$		0			0
$403$	0.222790	+	0.831464i	0.0110980	+	0.0414182i
$404$		0			0
$405$	6.74299	−	17.1634i	0.335062	−	0.852855i
$406$		0			0
$407$	14.9613	+	14.9613i	0.741603	+	0.741603i
$408$		0			0
$409$	15.7822	−	27.3355i	0.780379	−	1.35166i	−0.151342	−	0.988481i	$-0.548360\pi$
$409$	15.7822	−	27.3355i	0.780379	−	1.35166i	0.931721	−	0.363174i	$-0.118307\pi$
$410$		0			0
$411$	2.29845	−	1.32701i	0.113374	−	0.0654567i
$412$		0			0
$413$	−7.70831	−	11.1358i	−0.379301	−	0.547956i
$414$		0			0
$415$	11.7537	+	8.68095i	0.576969	+	0.426131i
$416$		0			0
$417$	−3.43069	+	0.919250i	−0.168001	+	0.0450159i
$418$		0			0
$419$	−10.8473			−0.529923			−0.264962	−	0.964259i	$-0.585359\pi$
$419$	−10.8473			−0.529923			−0.264962	+	0.964259i	$0.585359\pi$
$420$		0			0
$421$	15.3927			0.750194			0.375097	−	0.926986i	$-0.377609\pi$
$421$	15.3927			0.750194			0.375097	+	0.926986i	$0.377609\pi$
$422$		0			0
$423$	36.2317	−	9.70824i	1.76164	−	0.472031i
$424$		0			0
$425$	8.01863	+	12.7812i	0.388961	+	0.619980i
$426$		0			0
$427$	3.07195	+	37.4337i	0.148662	+	1.81154i
$428$		0			0
$429$	1.27071	−	0.733643i	0.0613503	−	0.0354206i
$430$		0			0
$431$	5.16396	−	8.94425i	0.248739	−	0.430829i	−0.714437	−	0.699700i	$-0.753317\pi$
$431$	5.16396	−	8.94425i	0.248739	−	0.430829i	0.963176	+	0.268871i	$0.0866504\pi$
$432$		0			0
$433$	−5.83240	−	5.83240i	−0.280287	−	0.280287i	0.552936	−	0.833224i	$-0.313507\pi$
$433$	−5.83240	−	5.83240i	−0.280287	−	0.280287i	−0.833224	+	0.552936i	$0.813507\pi$
$434$		0			0
$435$	−0.363369	−	0.833638i	−0.0174222	−	0.0399699i
$436$		0			0
$437$	−1.22919	−	4.58741i	−0.0588002	−	0.219445i
$438$		0			0
$439$	3.26217	+	5.65024i	0.155695	+	0.269671i	0.933312	−	0.359067i	$-0.116905\pi$
$439$	3.26217	+	5.65024i	0.155695	+	0.269671i	−0.777617	+	0.628738i	$0.783572\pi$
$440$		0			0
$441$	19.1015	+	7.18634i	0.909597	+	0.342207i
$442$		0			0
$443$	−5.19032	−	1.39074i	−0.246600	−	0.0660762i	0.133402	−	0.991062i	$-0.457410\pi$
$443$	−5.19032	−	1.39074i	−0.246600	−	0.0660762i	−0.380002	+	0.924986i	$0.624077\pi$
$444$		0			0
$445$	−24.6942	−	30.9876i	−1.17062	−	1.46895i
$446$		0			0
$447$	1.99707	−	1.99707i	0.0944582	−	0.0944582i
$448$		0			0
$449$			9.24051i			0.436087i	0.975939	+	0.218043i	$0.0699674\pi$
$449$			9.24051i			0.436087i	−0.975939	+	0.218043i	$0.930033\pi$
$450$		0			0
$451$	−5.01611	−	2.89605i	−0.236199	−	0.136370i
$452$		0			0
$453$	1.45781	−	5.44061i	0.0684938	−	0.255622i
$454$		0			0
$455$	8.31048	−	4.46407i	0.389601	−	0.209279i
$456$		0			0
$457$	6.35049	−	23.7003i	0.297063	−	1.10865i	−0.642502	−	0.766284i	$-0.722103\pi$
$457$	6.35049	−	23.7003i	0.297063	−	1.10865i	0.939565	−	0.342371i	$-0.111230\pi$
$458$		0			0
$459$	−4.49338	−	2.59425i	−0.209733	−	0.121089i
$460$		0			0
$461$		−	11.2955i		−	0.526084i	−0.964784	−	0.263042i	$-0.915274\pi$
$461$		−	11.2955i		−	0.526084i	0.964784	−	0.263042i	$-0.0847258\pi$
$462$		0			0
$463$	−8.69735	+	8.69735i	−0.404200	+	0.404200i	−0.879710	−	0.475510i	$-0.842263\pi$
$463$	−8.69735	+	8.69735i	−0.404200	+	0.404200i	0.475510	+	0.879710i	$0.342263\pi$
$464$		0			0
$465$	0.348630	+	0.0394035i	0.0161673	+	0.00182729i
$466$		0			0
$467$	29.5319	+	7.91305i	1.36657	+	0.366172i	0.866226	−	0.499653i	$-0.166539\pi$
$467$	29.5319	+	7.91305i	1.36657	+	0.366172i	0.500347	+	0.865825i	$0.333206\pi$
$468$		0			0
$469$	−1.51249	+	8.31561i	−0.0698404	+	0.383979i
$470$		0			0
$471$	2.63997	+	4.57256i	0.121643	+	0.210692i
$472$		0			0
$473$	7.53377	+	28.1164i	0.346403	+	1.29279i
$474$		0			0
$475$	−7.58485	−	7.04749i	−0.348017	−	0.323361i
$476$		0			0
$477$	−23.0650	−	23.0650i	−1.05608	−	1.05608i
$478$		0			0
$479$	−6.71144	+	11.6246i	−0.306653	+	0.531139i	−0.977628	−	0.210341i	$-0.932543\pi$
$479$	−6.71144	+	11.6246i	−0.306653	+	0.531139i	0.670975	+	0.741480i	$0.265876\pi$
$480$		0			0
$481$	−9.22912	+	5.32844i	−0.420812	+	0.242956i
$482$		0			0
$483$	0.753978	−	1.59443i	0.0343072	−	0.0725493i
$484$		0			0
$485$	6.98847	−	9.46218i	0.317330	−	0.429655i
$486$		0			0
$487$	−3.62535	+	0.971410i	−0.164280	+	0.0440188i	−0.340022	−	0.940418i	$-0.610434\pi$
$487$	−3.62535	+	0.971410i	−0.164280	+	0.0440188i	0.175741	+	0.984436i	$0.443768\pi$
$488$		0			0
$489$	−3.86387			−0.174730
$490$		0			0
$491$	−11.4041			−0.514658			−0.257329	−	0.966324i	$-0.582842\pi$
$491$	−11.4041			−0.514658			−0.257329	+	0.966324i	$0.582842\pi$
$492$		0			0
$493$	4.07851	−	1.09283i	0.183687	−	0.0492187i
$494$		0			0
$495$	3.06907	+	20.4099i	0.137944	+	0.917356i
$496$		0			0
$497$	8.61151	−	18.2107i	0.386279	−	0.816862i
$498$		0			0
$499$	4.12649	−	2.38243i	0.184727	−	0.106652i	−0.404785	−	0.914412i	$-0.632654\pi$
$499$	4.12649	−	2.38243i	0.184727	−	0.106652i	0.589512	+	0.807760i	$0.299320\pi$
$500$		0			0
$501$	1.44178	−	2.49724i	0.0644141	−	0.111568i
$502$		0			0
$503$	−3.82918	−	3.82918i	−0.170735	−	0.170735i	0.616567	−	0.787302i	$-0.288523\pi$
$503$	−3.82918	−	3.82918i	−0.170735	−	0.170735i	−0.787302	+	0.616567i	$0.788523\pi$
$504$		0			0
$505$	−26.2577	−	10.3159i	−1.16845	−	0.459051i
$506$		0			0
$507$	−0.786678	−	2.93592i	−0.0349376	−	0.130389i
$508$		0			0
$509$	6.57904	+	11.3952i	0.291611	+	0.505085i	0.974191	−	0.225726i	$-0.0724755\pi$
$509$	6.57904	+	11.3952i	0.291611	+	0.505085i	−0.682580	+	0.730811i	$0.739142\pi$
$510$		0			0
$511$	1.51366	−	8.32202i	0.0669603	−	0.368145i
$512$		0			0
$513$	3.43903	+	0.921487i	0.151837	+	0.0406846i
$514$		0			0
$515$	−1.46832	+	12.9913i	−0.0647020	+	0.572465i
$516$		0			0
$517$	−28.8011	+	28.8011i	−1.26667	+	1.26667i
$518$		0			0
$519$		−	3.80582i		−	0.167057i
$520$		0			0
$521$	−12.2934	−	7.09760i	−0.538584	−	0.310951i	0.205921	−	0.978569i	$-0.433981\pi$
$521$	−12.2934	−	7.09760i	−0.538584	−	0.310951i	−0.744505	+	0.667617i	$0.767314\pi$
$522$		0			0
$523$	3.68575	−	13.7554i	0.161167	−	0.601482i	−0.837332	−	0.546695i	$-0.815886\pi$
$523$	3.68575	−	13.7554i	0.161167	−	0.601482i	0.998498	−	0.0547863i	$-0.0174478\pi$
$524$		0			0
$525$	−0.454903	−	3.81800i	−0.0198536	−	0.166631i
$526$		0			0
$527$	−0.421624	+	1.57352i	−0.0183662	+	0.0685438i
$528$		0			0
$529$	−15.3631	−	8.86989i	−0.667961	−	0.385647i
$530$		0			0
$531$			14.9243i			0.647661i
$532$		0			0
$533$	2.06285	−	2.06285i	0.0893520	−	0.0893520i
$534$		0			0
$535$	−1.59672	+	14.1273i	−0.0690322	+	0.610777i
$536$		0			0
$537$	3.04523	+	0.815967i	0.131411	+	0.0352116i
$538$		0			0
$539$	−21.8647	+	3.61294i	−0.941779	+	0.155620i
$540$		0			0
$541$	−5.35421	−	9.27376i	−0.230195	−	0.398710i	0.727670	−	0.685927i	$-0.240603\pi$
$541$	−5.35421	−	9.27376i	−0.230195	−	0.398710i	−0.957865	+	0.287217i	$0.907270\pi$
$542$		0			0
$543$	1.05438	+	3.93502i	0.0452480	+	0.168868i
$544$		0			0
$545$	23.9692	+	9.41681i	1.02673	+	0.403372i
$546$		0			0
$547$	7.38586	+	7.38586i	0.315797	+	0.315797i	0.847150	−	0.531354i	$-0.178316\pi$
$547$	7.38586	+	7.38586i	0.315797	+	0.315797i	−0.531354	+	0.847150i	$0.678316\pi$
$548$		0			0
$549$	20.6946	−	35.8441i	0.883223	−	1.52979i
$550$		0			0
$551$	−2.50922	+	1.44870i	−0.106896	+	0.0617166i
$552$		0			0
$553$	3.68750	+	44.9345i	0.156808	+	1.91081i
$554$		0			0
$555$	0.645896	+	4.29533i	0.0274168	+	0.182327i
$556$		0			0
$557$	−32.5503	+	8.72182i	−1.37920	+	0.369556i	−0.870831	−	0.491583i	$-0.836418\pi$
$557$	−32.5503	+	8.72182i	−1.37920	+	0.369556i	−0.508370	+	0.861139i	$0.669752\pi$
$558$		0			0
$559$	−14.6610			−0.620093
$560$		0			0
$561$	2.77680			0.117237
$562$		0			0
$563$	−14.6864	+	3.93520i	−0.618957	+	0.165849i	−0.554653	−	0.832081i	$-0.687149\pi$
$563$	−14.6864	+	3.93520i	−0.618957	+	0.165849i	−0.0643032	+	0.997930i	$0.520482\pi$
$564$		0			0
$565$	22.1089	−	29.9347i	0.930127	−	1.25936i
$566$		0			0
$567$	−12.4184	−	17.9402i	−0.521525	−	0.753419i
$568$		0			0
$569$	−28.8138	+	16.6356i	−1.20794	+	0.697403i	−0.962308	−	0.271961i	$-0.912328\pi$
$569$	−28.8138	+	16.6356i	−1.20794	+	0.697403i	−0.245629	+	0.969364i	$0.578994\pi$
$570$		0			0
$571$	−9.67235	+	16.7530i	−0.404775	+	0.701091i	−0.994295	−	0.106663i	$-0.965984\pi$
$571$	−9.67235	+	16.7530i	−0.404775	+	0.701091i	0.589520	+	0.807754i	$0.299317\pi$
$572$		0			0
$573$	4.32226	+	4.32226i	0.180565	+	0.180565i
$574$		0			0
$575$	11.4599	−	0.420851i	0.477909	−	0.0175507i
$576$		0			0
$577$	1.19999	+	4.47841i	0.0499561	+	0.186439i	0.986395	−	0.164392i	$-0.0525661\pi$
$577$	1.19999	+	4.47841i	0.0499561	+	0.186439i	−0.936439	+	0.350830i	$0.885899\pi$
$578$		0			0
$579$	1.96737	+	3.40759i	0.0817612	+	0.141615i
$580$		0			0
$581$	16.2781	−	5.82563i	0.675328	−	0.241688i
$582$		0			0
$583$	34.2131	+	9.16737i	1.41696	+	0.379674i
$584$		0			0
$585$	−10.3297	−	1.16749i	−0.427079	−	0.0482700i
$586$		0			0
$587$	−11.9958	+	11.9958i	−0.495119	+	0.495119i	−0.909915	−	0.414796i	$-0.863853\pi$
$587$	−11.9958	+	11.9958i	−0.495119	+	0.495119i	0.414796	+	0.909915i	$0.363853\pi$
$588$		0			0
$589$		−	1.11784i		−	0.0460598i
$590$		0			0
$591$	−3.18690	−	1.83996i	−0.131092	−	0.0756859i
$592$		0			0
$593$	−7.09071	+	26.4629i	−0.291180	+	1.08670i	0.653023	+	0.757338i	$0.273500\pi$
$593$	−7.09071	+	26.4629i	−0.291180	+	1.08670i	−0.944204	+	0.329362i	$0.893166\pi$
$594$		0			0
$595$	17.8444	+	0.547379i	0.731547	+	0.0224403i
$596$		0			0
$597$	1.02426	−	3.82260i	0.0419203	−	0.156449i
$598$		0			0
$599$	13.8703	+	8.00801i	0.566725	+	0.327199i	0.755840	−	0.654756i	$-0.227229\pi$
$599$	13.8703	+	8.00801i	0.566725	+	0.327199i	−0.189116	+	0.981955i	$0.560562\pi$
$600$		0			0
$601$		−	0.757785i		−	0.0309107i	−0.999881	−	0.0154553i	$-0.995080\pi$
$601$		−	0.757785i		−	0.0309107i	0.999881	−	0.0154553i	$-0.00491978\pi$
$602$		0			0
$603$	6.58588	−	6.58588i	0.268198	−	0.268198i
$604$		0			0
$605$	1.36176	+	1.70881i	0.0553635	+	0.0694729i
$606$		0			0
$607$	−33.2529	−	8.91009i	−1.34969	−	0.361649i	−0.489672	−	0.871907i	$-0.662884\pi$
$607$	−33.2529	−	8.91009i	−1.34969	−	0.361649i	−0.860022	+	0.510257i	$0.829550\pi$
$608$		0			0
$609$	−1.05864	−	0.192551i	−0.0428981	−	0.00780255i
$610$		0			0
$611$	−10.2575	−	17.7664i	−0.414972	−	0.718753i
$612$		0			0
$613$	0.805086	+	3.00462i	0.0325171	+	0.121355i	0.980277	−	0.197630i	$-0.0633245\pi$
$613$	0.805086	+	3.00462i	0.0325171	+	0.121355i	−0.947760	+	0.318986i	$0.896658\pi$
$614$		0			0
$615$	−0.475120	−	1.09002i	−0.0191587	−	0.0439537i
$616$		0			0
$617$	−20.2993	−	20.2993i	−0.817221	−	0.817221i	0.168484	−	0.985704i	$-0.446113\pi$
$617$	−20.2993	−	20.2993i	−0.817221	−	0.817221i	−0.985704	+	0.168484i	$0.946113\pi$
$618$		0			0
$619$	5.85033	−	10.1331i	0.235145	−	0.407282i	−0.724170	−	0.689621i	$-0.757777\pi$
$619$	5.85033	−	10.1331i	0.235145	−	0.407282i	0.959315	+	0.282339i	$0.0911103\pi$
$620$		0			0
$621$	−3.41510	+	1.97171i	−0.137043	+	0.0791220i
$622$		0			0
$623$	−46.7263	+	3.83454i	−1.87205	+	0.153628i
$624$		0			0
$625$	20.6755	−	14.0544i	0.827018	−	0.562175i
$626$		0			0
$627$	−1.84051	+	0.493164i	−0.0735030	+	0.0196951i
$628$		0			0
$629$	−20.1679			−0.804145
$630$		0			0
$631$	−48.6183			−1.93546			−0.967731	−	0.251985i	$-0.918917\pi$
$631$	−48.6183			−1.93546			−0.967731	+	0.251985i	$0.918917\pi$
$632$		0			0
$633$	−5.39510	+	1.44561i	−0.214436	+	0.0574579i
$634$		0			0
$635$	21.9547	+	16.2151i	0.871247	+	0.643476i
$636$		0			0
$637$	1.09255	−	11.1083i	0.0432883	−	0.440128i
$638$		0			0
$639$	−19.2241	+	11.0991i	−0.760496	+	0.439072i
$640$		0			0
$641$	6.57455	−	11.3874i	0.259679	−	0.449777i	−0.706477	−	0.707736i	$-0.749717\pi$
$641$	6.57455	−	11.3874i	0.259679	−	0.449777i	0.966156	+	0.257959i	$0.0830499\pi$
$642$		0			0
$643$	13.2857	+	13.2857i	0.523935	+	0.523935i	0.918758	−	0.394822i	$-0.129194\pi$
$643$	13.2857	+	13.2857i	0.523935	+	0.523935i	−0.394822	+	0.918758i	$0.629194\pi$
$644$		0			0
$645$	−2.18507	+	5.56181i	−0.0860372	+	0.218996i
$646$		0			0
$647$	8.66879	+	32.3524i	0.340805	+	1.27190i	0.897437	+	0.441143i	$0.145427\pi$
$647$	8.66879	+	32.3524i	0.340805	+	1.27190i	−0.556631	+	0.830760i	$0.687906\pi$
$648$		0			0
$649$	−8.10296	−	14.0347i	−0.318069	−	0.550912i
$650$		0			0
$651$	0.268550	−	0.316567i	0.0105253	−	0.0124072i
$652$		0			0
$653$	−0.471665	−	0.126382i	−0.0184577	−	0.00494572i	0.249578	−	0.968355i	$-0.419708\pi$
$653$	−0.471665	−	0.126382i	−0.0184577	−	0.00494572i	−0.268036	+	0.963409i	$0.586375\pi$
$654$		0			0
$655$	18.4693	−	14.7183i	0.721655	−	0.575092i
$656$		0			0
$657$	−6.59095	+	6.59095i	−0.257138	+	0.257138i
$658$		0			0
$659$		−	42.0886i		−	1.63954i	−0.572693	−	0.819770i	$-0.694101\pi$
$659$		−	42.0886i		−	1.63954i	0.572693	−	0.819770i	$-0.305899\pi$
$660$		0			0
$661$	−13.0631	−	7.54198i	−0.508095	−	0.293349i	0.223955	−	0.974599i	$-0.428103\pi$
$661$	−13.0631	−	7.54198i	−0.508095	−	0.293349i	−0.732050	+	0.681251i	$0.761436\pi$
$662$		0			0
$663$	−0.361982	+	1.35094i	−0.0140582	+	0.0524660i
$664$		0			0
$665$	−11.9248	+	2.80637i	−0.462423	+	0.108826i
$666$		0			0
$667$	0.830586	−	3.09979i	0.0321604	−	0.120024i
$668$		0			0
$669$	−4.34345	−	2.50769i	−0.167927	−	0.0969530i
$670$		0			0
$671$			44.9434i			1.73502i
$672$		0			0
$673$	−24.5243	+	24.5243i	−0.945344	+	0.945344i	−0.998582	−	0.0532383i	$-0.983046\pi$
$673$	−24.5243	+	24.5243i	−0.945344	+	0.945344i	0.0532383	+	0.998582i	$0.483046\pi$
$674$		0			0
$675$	−4.02232	+	7.59786i	−0.154819	+	0.292442i
$676$		0			0
$677$	−19.2914	−	5.16911i	−0.741428	−	0.198665i	−0.131715	−	0.991288i	$-0.542048\pi$
$677$	−19.2914	−	5.16911i	−0.741428	−	0.198665i	−0.609712	+	0.792623i	$0.708715\pi$
$678$		0			0
$679$	−4.68984	−	13.1044i	−0.179979	−	0.502901i
$680$		0			0
$681$	−2.57342	−	4.45730i	−0.0986137	−	0.170804i
$682$		0			0
$683$	10.7678	+	40.1858i	0.412017	+	1.53767i	0.790736	+	0.612157i	$0.209698\pi$
$683$	10.7678	+	40.1858i	0.412017	+	1.53767i	−0.378720	+	0.925511i	$0.623636\pi$
$684$		0			0
$685$	18.7171	−	8.15848i	0.715144	−	0.311720i
$686$		0			0
$687$	1.41448	+	1.41448i	0.0539659	+	0.0539659i
$688$		0			0
$689$	−8.92000	+	15.4499i	−0.339825	+	0.588594i
$690$		0			0
$691$	2.73858	−	1.58112i	0.104181	−	0.0601487i	−0.447004	−	0.894532i	$-0.647509\pi$
$691$	2.73858	−	1.58112i	0.104181	−	0.0601487i	0.551185	+	0.834383i	$0.314176\pi$
$692$		0			0
$693$	22.0769	+	10.4397i	0.838630	+	0.396573i
$694$		0			0
$695$	−27.0202	+	4.06307i	−1.02493	+	0.154121i
$696$		0			0
$697$	5.33282	−	1.42892i	0.201995	−	0.0541243i
$698$		0			0
$699$	−0.300304			−0.0113585
$700$		0			0
$701$	29.5372			1.11560			0.557802	−	0.829974i	$-0.311645\pi$
$701$	29.5372			1.11560			0.557802	+	0.829974i	$0.311645\pi$
$702$		0			0
$703$	13.3676	−	3.58184i	0.504169	−	0.135092i
$704$		0			0
$705$	−8.26868	+	1.24338i	−0.311417	+	0.0468282i
$706$		0			0
$707$	−27.4462	+	18.9985i	−1.03222	+	0.714514i
$708$		0			0
$709$	3.64864	−	2.10654i	0.137028	−	0.0791129i	−0.429919	−	0.902867i	$-0.641458\pi$
$709$	3.64864	−	2.10654i	0.137028	−	0.0791129i	0.566947	+	0.823755i	$0.308125\pi$
$710$		0			0
$711$	24.8413	−	43.0264i	0.931621	−	1.61361i
$712$		0			0
$713$	0.875478	+	0.875478i	0.0327869	+	0.0327869i
$714$		0			0
$715$	10.3478	−	4.51044i	0.386986	−	0.168681i
$716$		0			0
$717$	0.195128	+	0.728227i	0.00728718	+	0.0271961i
$718$		0			0
$719$	−7.68285	−	13.3071i	−0.286522	−	0.496271i	0.686455	−	0.727172i	$-0.259166\pi$
$719$	−7.68285	−	13.3071i	−0.286522	−	0.496271i	−0.972977	+	0.230902i	$0.925832\pi$
$720$		0			0
$721$	11.7965	+	10.0072i	0.439325	+	0.372688i
$722$		0			0
$723$	−6.11303	−	1.63798i	−0.227346	−	0.0609172i
$724$		0			0
$725$	−2.05751	−	6.68672i	−0.0764140	−	0.248338i
$726$		0			0
$727$	33.3701	−	33.3701i	1.23763	−	1.23763i	0.276659	−	0.960968i	$-0.410773\pi$
$727$	33.3701	−	33.3701i	1.23763	−	1.23763i	0.960968	−	0.276659i	$-0.0892271\pi$
$728$		0			0
$729$			22.5445i			0.834982i
$730$		0			0
$731$	−24.0283	−	13.8727i	−0.888719	−	0.513102i
$732$		0			0
$733$	−2.60032	+	9.70454i	−0.0960451	+	0.358445i	−0.997176	−	0.0751022i	$-0.976072\pi$
$733$	−2.60032	+	9.70454i	−0.0960451	+	0.358445i	0.901131	+	0.433548i	$0.142738\pi$
$734$		0			0
$735$	−4.05125	−	2.07006i	−0.149432	−	0.0763553i
$736$		0			0
$737$	−2.61760	+	9.76903i	−0.0964207	+	0.359847i
$738$		0			0
$739$	13.2797	+	7.66706i	0.488503	+	0.282037i	0.723953	−	0.689849i	$-0.242323\pi$
$739$	13.2797	+	7.66706i	0.488503	+	0.282037i	−0.235450	+	0.971886i	$0.575656\pi$
$740$		0			0
$741$		−	0.959713i		−	0.0352559i
$742$		0			0
$743$	22.6408	−	22.6408i	0.830610	−	0.830610i	−0.156990	−	0.987600i	$-0.550179\pi$
$743$	22.6408	−	22.6408i	0.830610	−	0.830610i	0.987600	+	0.156990i	$0.0501792\pi$
$744$		0			0
$745$	16.9921	−	13.5412i	0.622544	−	0.496110i
$746$		0			0
$747$	−18.4028	−	4.93101i	−0.673322	−	0.180416i
$748$		0			0
$749$	12.8280	+	10.8823i	0.468726	+	0.397630i
$750$		0			0
$751$	23.9970	+	41.5640i	0.875663	+	1.51669i	0.856055	+	0.516885i	$0.172908\pi$
$751$	23.9970	+	41.5640i	0.875663	+	1.51669i	0.0196079	+	0.999808i	$0.493758\pi$
$752$		0			0
$753$	2.05931	+	7.68544i	0.0750454	+	0.280073i
$754$		0			0
$755$	15.8450	−	40.3313i	0.576658	−	1.46781i
$756$		0			0
$757$	23.0503	+	23.0503i	0.837777	+	0.837777i	0.988566	−	0.150789i	$-0.0481814\pi$
$757$	23.0503	+	23.0503i	0.837777	+	0.837777i	−0.150789	+	0.988566i	$0.548181\pi$
$758$		0			0
$759$	1.05523	−	1.82770i	0.0383023	−	0.0663415i
$760$		0			0
$761$	9.13419	−	5.27363i	0.331114	−	0.191169i	−0.325221	−	0.945638i	$-0.605439\pi$
$761$	9.13419	−	5.27363i	0.331114	−	0.191169i	0.656336	+	0.754469i	$0.272106\pi$
$762$		0			0
$763$	25.0541	−	17.3427i	0.907020	−	0.627849i
$764$		0			0
$765$	−15.8249	−	11.6877i	−0.572149	−	0.422571i
$766$		0			0
$767$	7.88431	−	2.11260i	0.284686	−	0.0762814i
$768$		0			0
$769$	−30.8875			−1.11383			−0.556917	−	0.830568i	$-0.688016\pi$
$769$	−30.8875			−1.11383			−0.556917	+	0.830568i	$0.688016\pi$
$770$		0			0
$771$	5.02330			0.180910
$772$		0			0
$773$	12.1882	−	3.26583i	0.438380	−	0.117464i	−0.0328772	−	0.999459i	$-0.510467\pi$
$773$	12.1882	−	3.26583i	0.438380	−	0.117464i	0.471257	+	0.881996i	$0.343800\pi$
$774$		0			0
$775$	2.63107	+	0.602441i	0.0945107	+	0.0216403i
$776$		0			0
$777$	4.64615	+	2.19708i	0.166680	+	0.0788197i
$778$		0			0
$779$	−3.28091	+	1.89423i	−0.117551	+	0.0678679i
$780$		0			0
$781$	12.0522	−	20.8750i	0.431261	−	0.746966i
$782$		0			0
$783$	1.70115	+	1.70115i	0.0607941	+	0.0607941i
$784$		0			0
$785$	16.2305	+	37.2360i	0.579293	+	1.32901i
$786$		0			0
$787$	−0.702207	−	2.62067i	−0.0250310	−	0.0934169i	0.952280	−	0.305225i	$-0.0987316\pi$
$787$	−0.702207	−	2.62067i	−0.0250310	−	0.0934169i	−0.977311	+	0.211808i	$0.932065\pi$
$788$		0			0
$789$	−0.119749	−	0.207412i	−0.00426319	−	0.00738406i
$790$		0			0
$791$	−14.8369	−	41.4574i	−0.527538	−	1.47405i
$792$		0			0
$793$	−21.8653	−	5.85879i	−0.776460	−	0.208052i
$794$		0			0
$795$	4.53166	+	5.68656i	0.160721	+	0.201682i
$796$		0			0
$797$	−1.49610	+	1.49610i	−0.0529945	+	0.0529945i	−0.733107	−	0.680113i	$-0.761931\pi$
$797$	−1.49610	+	1.49610i	−0.0529945	+	0.0529945i	0.680113	+	0.733107i	$0.261931\pi$
$798$		0			0
$799$		−	38.8239i		−	1.37349i
$800$		0			0
$801$	44.7421	+	25.8318i	1.58088	+	0.912723i
$802$		0			0
$803$	2.61962	−	9.77656i	0.0924444	−	0.345007i
$804$		0			0
$805$	7.14141	−	11.5372i	0.251702	−	0.406634i
$806$		0			0
$807$	−0.618792	+	2.30936i	−0.0217825	+	0.0812934i
$808$		0			0
$809$	−18.6010	−	10.7393i	−0.653976	−	0.377573i	0.136002	−	0.990709i	$-0.456575\pi$
$809$	−18.6010	−	10.7393i	−0.653976	−	0.377573i	−0.789978	+	0.613135i	$0.789908\pi$
$810$		0			0
$811$		−	34.0584i		−	1.19595i	−0.801515	−	0.597975i	$-0.795972\pi$
$811$		−	34.0584i		−	1.19595i	0.801515	−	0.597975i	$-0.204028\pi$
$812$		0			0
$813$	−2.95677	+	2.95677i	−0.103699	+	0.103699i
$814$		0			0
$815$	−29.5374	−	3.33842i	−1.03465	−	0.116940i
$816$		0			0
$817$	18.3902	+	4.92764i	0.643392	+	0.172396i
$818$		0			0
$819$	−7.95694	+	9.37965i	−0.278038	+	0.327752i
$820$		0			0
$821$	21.8070	+	37.7709i	0.761071	+	1.31821i	0.942299	+	0.334772i	$0.108659\pi$
$821$	21.8070	+	37.7709i	0.761071	+	1.31821i	−0.181228	+	0.983441i	$0.558007\pi$
$822$		0			0
$823$	5.28421	+	19.7209i	0.184196	+	0.687429i	0.994801	+	0.101836i	$0.0324716\pi$
$823$	5.28421	+	19.7209i	0.184196	+	0.687429i	−0.810605	+	0.585593i	$0.800862\pi$
$824$		0			0
$825$	−0.168849	−	4.59781i	−0.00587858	−	0.160075i
$826$		0			0
$827$	14.5724	+	14.5724i	0.506734	+	0.506734i	0.913522	−	0.406789i	$-0.133351\pi$
$827$	14.5724	+	14.5724i	0.506734	+	0.506734i	−0.406789	+	0.913522i	$0.633351\pi$
$828$		0			0
$829$	−6.36587	+	11.0260i	−0.221096	+	0.382949i	−0.955141	−	0.296151i	$-0.904297\pi$
$829$	−6.36587	+	11.0260i	−0.221096	+	0.382949i	0.734045	+	0.679101i	$0.237630\pi$
$830$		0			0
$831$	−0.200694	+	0.115871i	−0.00696199	+	0.00401951i
$832$		0			0
$833$	12.3017	−	17.1720i	0.426229	−	0.594974i
$834$		0			0
$835$	13.1794	−	17.8445i	0.456091	−	0.617534i
$836$		0			0
$837$	−0.896547	+	0.240229i	−0.0309892	+	0.00830353i
$838$		0			0
$839$	24.5626			0.847996			0.423998	−	0.905663i	$-0.360626\pi$
$839$	24.5626			0.847996			0.423998	+	0.905663i	$0.360626\pi$
$840$		0			0
$841$	27.0422			0.932489
$842$		0			0
$843$	0.245533	−	0.0657903i	0.00845660	−	0.00226594i
$844$		0			0
$845$	−3.47711	−	23.1234i	−0.119616	−	0.795470i
$846$		0			0
$847$	2.57672	−	0.211456i	0.0885371	−	0.00726570i
$848$		0			0
$849$	4.11545	−	2.37606i	0.141242	−	0.0815461i
$850$		0			0
$851$	−7.66409	+	13.2746i	−0.262722	+	0.455047i
$852$		0			0
$853$	−33.2374	−	33.2374i	−1.13803	−	1.13803i	−0.988803	−	0.149224i	$-0.952322\pi$
$853$	−33.2374	−	33.2374i	−1.13803	−	1.13803i	−0.149224	−	0.988803i	$-0.547678\pi$
$854$		0			0
$855$	12.5648	+	4.93633i	0.429706	+	0.168819i
$856$		0			0
$857$	−1.07074	−	3.99604i	−0.0365756	−	0.136502i	0.945224	−	0.326423i	$-0.105843\pi$
$857$	−1.07074	−	3.99604i	−0.0365756	−	0.136502i	−0.981799	+	0.189921i	$0.939177\pi$
$858$		0			0
$859$	−11.2898	−	19.5545i	−0.385202	−	0.667190i	0.606595	−	0.795011i	$-0.292535\pi$
$859$	−11.2898	−	19.5545i	−0.385202	−	0.667190i	−0.991797	+	0.127821i	$0.959202\pi$
$860$		0			0
$861$	−1.38421	−	0.251768i	−0.0471737	−	0.00858023i
$862$		0			0
$863$	13.5771	+	3.63796i	0.462169	+	0.123838i	0.482388	−	0.875958i	$-0.339770\pi$
$863$	13.5771	+	3.63796i	0.462169	+	0.123838i	−0.0202190	+	0.999796i	$0.506436\pi$
$864$		0			0
$865$	3.28827	−	29.0937i	0.111805	−	0.989215i
$866$		0			0
$867$	1.62235	−	1.62235i	0.0550978	−	0.0550978i
$868$		0			0
$869$			53.9490i			1.83009i
$870$		0			0
$871$	−4.41148	−	2.54697i	−0.149477	−	0.0863008i
$872$		0			0
$873$	−3.96963	+	14.8149i	−0.134352	+	0.501408i
$874$		0			0
$875$	−0.178720	−	29.5799i	−0.00604185	−	0.999982i
$876$		0			0
$877$	−13.7248	+	51.2217i	−0.463454	+	1.72963i	0.198510	+	0.980099i	$0.436390\pi$
$877$	−13.7248	+	51.2217i	−0.463454	+	1.72963i	−0.661964	+	0.749536i	$0.730277\pi$
$878$		0			0
$879$	−5.11680	−	2.95419i	−0.172585	−	0.0996422i
$880$		0			0
$881$		−	32.9976i		−	1.11172i	−0.831276	−	0.555859i	$-0.812389\pi$
$881$		−	32.9976i		−	1.11172i	0.831276	−	0.555859i	$-0.187611\pi$
$882$		0			0
$883$	−36.0519	+	36.0519i	−1.21324	+	1.21324i	−0.243289	+	0.969954i	$0.578226\pi$
$883$	−36.0519	+	36.0519i	−1.21324	+	1.21324i	−0.969954	+	0.243289i	$0.921774\pi$
$884$		0			0
$885$	0.373641	−	3.30587i	0.0125598	−	0.111126i
$886$		0			0
$887$	−35.9330	−	9.62823i	−1.20651	−	0.323284i	−0.401120	−	0.916025i	$-0.631379\pi$
$887$	−35.9330	−	9.62823i	−1.20651	−	0.323284i	−0.805393	+	0.592741i	$0.798046\pi$
$888$		0			0
$889$	30.4057	−	10.8817i	1.01977	−	0.364959i
$890$		0			0
$891$	−13.0542	−	22.6106i	−0.437333	−	0.757483i
$892$		0			0
$893$	6.89519	+	25.7332i	0.230739	+	0.861129i
$894$		0			0
$895$	22.5743	+	8.86879i	0.754576	+	0.296451i
$896$		0			0
$897$	0.751634	+	0.751634i	0.0250963	+	0.0250963i
$898$		0			0
$899$	0.377672	−	0.654147i	0.0125961	−	0.0218170i
$900$		0			0
$901$	−29.2385	+	16.8809i	−0.974076	+	0.562383i
$902$		0			0
$903$	4.02420	+	5.81355i	0.133917	+	0.193463i
$904$		0			0
$905$	4.66037	+	30.9923i	0.154916	+	1.03022i
$906$		0			0
$907$	13.1346	−	3.51941i	0.436128	−	0.116860i	−0.0340732	−	0.999419i	$-0.510848\pi$
$907$	13.1346	−	3.51941i	0.436128	−	0.116860i	0.470201	+	0.882559i	$0.344181\pi$
$908$		0			0
$909$	36.7837			1.22004
$910$		0			0
$911$	17.0743			0.565695			0.282848	−	0.959165i	$-0.408721\pi$
$911$	17.0743			0.565695			0.282848	+	0.959165i	$0.408721\pi$
$912$		0			0
$913$	19.9831	−	5.35445i	0.661343	−	0.177206i
$914$		0			0
$915$	−5.48142	+	7.42167i	−0.181210	+	0.245353i
$916$		0			0
$917$	−2.28547	−	27.8499i	−0.0754730	−	0.919685i
$918$		0			0
$919$	−13.4130	+	7.74398i	−0.442453	+	0.255450i	−0.704638	−	0.709567i	$-0.748890\pi$
$919$	−13.4130	+	7.74398i	−0.442453	+	0.255450i	0.262185	+	0.965018i	$0.415557\pi$
$920$		0			0
$921$	4.00945	−	6.94457i	0.132116	−	0.228831i
$922$		0			0
$923$	8.58473	+	8.58473i	0.282570	+	0.282570i
$924$		0			0
$925$	1.22635	+	33.3938i	0.0403222	+	1.09798i
$926$		0			0
$927$	−4.41201	−	16.4658i	−0.144909	−	0.540809i
$928$		0			0
$929$	−19.3788	−	33.5651i	−0.635799	−	1.10124i	−0.986345	−	0.164691i	$-0.947337\pi$
$929$	−19.3788	−	33.5651i	−0.635799	−	1.10124i	0.350546	−	0.936545i	$-0.385996\pi$
$930$		0			0
$931$	−5.10403	+	13.5667i	−0.167278	+	0.444630i
$932$		0			0
$933$	−7.55456	−	2.02424i	−0.247325	−	0.0662706i
$934$		0			0
$935$	21.2273	+	2.39919i	0.694207	+	0.0784618i
$936$		0			0
$937$	3.79216	−	3.79216i	0.123884	−	0.123884i	−0.642446	−	0.766331i	$-0.722080\pi$
$937$	3.79216	−	3.79216i	0.123884	−	0.123884i	0.766331	+	0.642446i	$0.222080\pi$
$938$		0			0
$939$			2.56300i			0.0836402i
$940$		0			0
$941$	−20.5591	−	11.8698i	−0.670207	−	0.386944i	0.125948	−	0.992037i	$-0.459803\pi$
$941$	−20.5591	−	11.8698i	−0.670207	−	0.386944i	−0.796155	+	0.605093i	$0.793136\pi$
$942$		0			0
$943$	1.08602	−	4.05310i	0.0353658	−	0.131987i
$944$		0			0
$945$	4.81350	+	8.96099i	0.156583	+	0.291501i
$946$		0			0
$947$	1.21208	−	4.52355i	0.0393873	−	0.146996i	−0.943432	−	0.331566i	$-0.892423\pi$
$947$	1.21208	−	4.52355i	0.0393873	−	0.146996i	0.982819	+	0.184571i	$0.0590895\pi$
$948$		0			0
$949$	4.41488	+	2.54893i	0.143313	+	0.0827419i
$950$		0			0
$951$		−	1.69600i		−	0.0549966i
$952$		0			0
$953$	36.2145	−	36.2145i	1.17310	−	1.17310i	0.191638	−	0.981466i	$-0.438620\pi$
$953$	36.2145	−	36.2145i	1.17310	−	1.17310i	0.981466	−	0.191638i	$-0.0613798\pi$
$954$		0			0
$955$	29.3071	+	36.7761i	0.948356	+	1.19005i
$956$		0			0
$957$	−1.24367	−	0.333239i	−0.0402020	−	0.0107721i
$958$		0			0
$959$	4.32321	−	23.7688i	0.139604	−	0.767536i
$960$		0			0
$961$	−15.3543	−	26.5944i	−0.495300	−	0.857884i
$962$		0			0
$963$	−4.79781	−	17.9057i	−0.154607	−	0.577002i
$964$		0			0
$965$	12.0954	+	27.7492i	0.389365	+	0.893279i
$966$		0			0
$967$	14.1312	+	14.1312i	0.454429	+	0.454429i	0.896821	−	0.442393i	$-0.145870\pi$
$967$	14.1312	+	14.1312i	0.454429	+	0.454429i	−0.442393	+	0.896821i	$0.645870\pi$
$968$		0			0
$969$	0.908116	−	1.57290i	0.0291729	−	0.0505289i
$970$		0			0
$971$	31.2377	−	18.0351i	1.00247	−	0.578774i	0.0934894	−	0.995620i	$-0.470198\pi$
$971$	31.2377	−	18.0351i	1.00247	−	0.578774i	0.908977	+	0.416846i	$0.136865\pi$
$972$		0			0
$973$	−13.8209	+	29.2271i	−0.443079	+	0.936977i
$974$		0			0
$975$	2.25888	+	0.517221i	0.0723421	+	0.0165643i
$976$		0			0
$977$	17.5667	−	4.70697i	0.562007	−	0.150589i	0.0333788	−	0.999443i	$-0.489373\pi$
$977$	17.5667	−	4.70697i	0.562007	−	0.150589i	0.528628	+	0.848853i	$0.322707\pi$
$978$		0			0
$979$	−56.1002			−1.79297
$980$		0			0
$981$	−33.5779			−1.07206
$982$		0			0
$983$	−29.4010	+	7.87798i	−0.937747	+	0.251269i	−0.695155	−	0.718860i	$-0.744664\pi$
$983$	−29.4010	+	7.87798i	−0.937747	+	0.251269i	−0.242592	+	0.970128i	$0.577998\pi$
$984$		0			0
$985$	−22.7726	−	16.8191i	−0.725596	−	0.535902i
$986$		0			0
$987$	−4.22946	+	8.94403i	−0.134625	+	0.284691i
$988$		0			0
$989$	−18.2622	+	10.5437i	−0.580705	+	0.335270i
$990$		0			0
$991$	6.37905	−	11.0488i	0.202637	−	0.350978i	−0.746740	−	0.665116i	$-0.768382\pi$
$991$	6.37905	−	11.0488i	0.202637	−	0.350978i	0.949377	+	0.314138i	$0.101715\pi$
$992$		0			0
$993$	−5.03472	−	5.03472i	−0.159772	−	0.159772i
$994$		0			0
$995$	11.1328	−	28.3370i	0.352933	−	0.898343i
$996$		0			0
$997$	2.47705	+	9.24446i	0.0784488	+	0.292775i	0.993993	−	0.109442i	$-0.0349064\pi$
$997$	2.47705	+	9.24446i	0.0784488	+	0.292775i	−0.915544	+	0.402217i	$0.868240\pi$
$998$		0			0
$999$	−5.74553	−	9.95154i	−0.181780	−	0.314853i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bo.a.17.8	✓	48
4.3	odd	2		560.2.ci.e.17.5		48
5.3	odd	4	inner	280.2.bo.a.73.8	yes	48
7.5	odd	6	inner	280.2.bo.a.257.8	yes	48
20.3	even	4		560.2.ci.e.353.5		48
28.19	even	6		560.2.ci.e.257.5		48
35.33	even	12	inner	280.2.bo.a.33.8	yes	48
140.103	odd	12		560.2.ci.e.33.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bo.a.17.8	✓	48	1.1	even	1	trivial
280.2.bo.a.33.8	yes	48	35.33	even	12	inner
280.2.bo.a.73.8	yes	48	5.3	odd	4	inner
280.2.bo.a.257.8	yes	48	7.5	odd	6	inner
560.2.ci.e.17.5		48	4.3	odd	2
560.2.ci.e.33.5		48	140.103	odd	12
560.2.ci.e.257.5		48	28.19	even	6
560.2.ci.e.353.5		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)

\(f(q)\)	\(=\)	\(q+(0.280752 - 0.0752271i) q^{3} +(2.21121 - 0.332503i) q^{5} +(1.13104 - 2.39181i) q^{7} +(-2.52491 + 1.45776i) q^{9} +O(q^{10})\)	\(q+(0.280752 - 0.0752271i) q^{3} +(2.21121 - 0.332503i) q^{5} +(1.13104 - 2.39181i) q^{7} +(-2.52491 + 1.45776i) q^{9} +(1.58294 - 2.74174i) q^{11} +(1.12753 + 1.12753i) q^{13} +(0.595787 - 0.259694i) q^{15} +(0.781030 + 2.91484i) q^{17} +(-1.03536 - 1.79330i) q^{19} +(0.137613 - 0.756589i) q^{21} +(2.21537 + 0.593606i) q^{23} +(4.77888 - 1.47047i) q^{25} +(-1.21578 + 1.21578i) q^{27} -1.39922i q^{29} +(0.467508 + 0.269916i) q^{31} +(0.238160 - 0.888827i) q^{33} +(1.70568 - 5.66486i) q^{35} +(-1.72976 + 6.45554i) q^{37} +(0.401375 + 0.231734i) q^{39} -1.82954i q^{41} +(-6.50139 + 6.50139i) q^{43} +(-5.09840 + 4.06295i) q^{45} +(-12.4272 - 3.32985i) q^{47} +(-4.44149 - 5.41047i) q^{49} +(0.438550 + 0.759592i) q^{51} +(2.89567 + 10.8068i) q^{53} +(2.58858 - 6.58888i) q^{55} +(-0.425584 - 0.425584i) q^{57} +(2.55946 - 4.43312i) q^{59} +(-12.2942 + 7.09808i) q^{61} +(0.630899 + 7.68790i) q^{63} +(2.86810 + 2.11829i) q^{65} +(-3.08572 + 0.826816i) q^{67} +0.666623 q^{69} +7.61378 q^{71} +(3.08810 - 0.827453i) q^{73} +(1.23106 - 0.772338i) q^{75} +(-4.76733 - 6.88711i) q^{77} +(-14.7577 + 8.52036i) q^{79} +(4.12341 - 7.14195i) q^{81} +(4.62071 + 4.62071i) q^{83} +(2.69621 + 6.18563i) q^{85} +(-0.105259 - 0.392834i) q^{87} +(-8.86012 - 15.3462i) q^{89} +(3.97210 - 1.42155i) q^{91} +(0.151559 + 0.0406100i) q^{93} +(-2.88567 - 3.62109i) q^{95} +(3.71983 - 3.71983i) q^{97} +9.23019i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{7}+O(q^{10}) \) 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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