LMFDB - Embedded newform 560.2.ci.e.33.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(17,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, 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("560.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.ci (of order $12$, degree $4$, not 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			33.5
Character	$\chi$	$=$	560.33
Dual form			560.2.ci.e.17.5

$q$-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 $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.280752	−	0.0752271i	−0.162092	−	0.0434324i	0.176860	−	0.984236i	$-0.443406\pi$
$3$	−0.280752	−	0.0752271i	−0.162092	−	0.0434324i	−0.338952	+	0.940804i	$0.610073\pi$
$4$		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	$-0.325042\pi$
$11$	−1.58294	−	2.74174i	−0.477275	−	0.826664i	−0.999661	+	0.0260448i	$0.991709\pi$
$12$		0			0
$13$	1.12753	−	1.12753i	0.312719	−	0.312719i	−0.533243	−	0.845962i	$-0.679027\pi$
$13$	1.12753	−	1.12753i	0.312719	−	0.312719i	0.845962	+	0.533243i	$0.179027\pi$
$14$		0			0
$15$	−0.595787	−	0.259694i	−0.153831	−	0.0670526i
$16$		0			0
$17$	0.781030	−	2.91484i	0.189427	−	0.706953i	−0.804212	−	0.594343i	$-0.797412\pi$
$17$	0.781030	−	2.91484i	0.189427	−	0.706953i	0.993639	−	0.112610i	$-0.0359211\pi$
$18$		0			0
$19$	1.03536	−	1.79330i	0.237528	−	0.411411i	−0.722476	−	0.691396i	$-0.756996\pi$
$19$	1.03536	−	1.79330i	0.237528	−	0.411411i	0.960004	+	0.279985i	$0.0903295\pi$
$20$		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	$-0.660191\pi$
$23$	−2.21537	+	0.593606i	−0.461936	+	0.123775i	0.0203430	+	0.999793i	$0.493524\pi$
$24$		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	$0.0414703\pi$
$29$			1.39922i			0.259829i	−0.991525	+	0.129914i	$0.958530\pi$
$30$		0			0
$31$	−0.467508	+	0.269916i	−0.0839669	+	0.0484783i	−0.541396	−	0.840768i	$-0.682104\pi$
$31$	−0.467508	+	0.269916i	−0.0839669	+	0.0484783i	0.457429	+	0.889246i	$0.348771\pi$
$32$		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	−0.949298	−	0.314376i	$-0.898205\pi$
$37$	−1.72976	−	6.45554i	−0.284370	−	1.06128i	0.664928	−	0.746907i	$-0.268462\pi$
$38$		0			0
$39$	−0.401375	+	0.231734i	−0.0642714	+	0.0371071i
$40$		0			0
$41$			1.82954i			0.285726i	0.989742	+	0.142863i	$0.0456308\pi$
$41$			1.82954i			0.285726i	−0.989742	+	0.142863i	$0.954369\pi$
$42$		0			0
$43$	6.50139	+	6.50139i	0.991453	+	0.991453i	0.999964	−	0.00851097i	$-0.00270916\pi$
$43$	6.50139	+	6.50139i	0.991453	+	0.991453i	−0.00851097	+	0.999964i	$0.502709\pi$
$44$		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	$-0.195718\pi$
$47$	12.4272	−	3.32985i	1.81269	−	0.485709i	0.995838	+	0.0911405i	$0.0290512\pi$
$48$		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	−0.419292	−	0.907852i	$-0.637721\pi$
$53$	2.89567	−	10.8068i	0.397751	−	1.48443i	0.817043	−	0.576577i	$-0.195612\pi$
$54$		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	$-0.274800\pi$
$59$	−2.55946	−	4.43312i	−0.333214	−	0.577143i	−0.983140	+	0.182854i	$0.941466\pi$
$60$		0			0
$61$	−12.2942	−	7.09808i	−1.57412	−	0.908816i	−0.995656	−	0.0931040i	$-0.970321\pi$
$61$	−12.2942	−	7.09808i	−1.57412	−	0.908816i	−0.578459	−	0.815712i	$-0.696346\pi$
$62$		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	$-0.354151\pi$
$67$	3.08572	+	0.826816i	0.376981	+	0.101012i	−0.0653530	+	0.997862i	$0.520817\pi$
$68$		0			0
$69$	0.666623			0.0802520
$70$		0			0
$71$	−7.61378			−0.903590			−0.451795	−	0.892122i	$-0.649216\pi$
$71$	−7.61378			−0.903590			−0.451795	+	0.892122i	$0.649216\pi$
$72$		0			0
$73$	3.08810	+	0.827453i	0.361435	+	0.0968461i	0.434966	−	0.900447i	$-0.356760\pi$
$73$	3.08810	+	0.827453i	0.361435	+	0.0968461i	−0.0735316	+	0.997293i	$0.523427\pi$
$74$		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	0.972537	+	0.232748i	$0.0747718\pi$
$79$	14.7577	+	8.52036i	1.66037	+	0.958616i	0.687834	+	0.725868i	$0.258562\pi$
$80$		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	$-0.866758\pi$
$83$	−4.62071	+	4.62071i	−0.507189	+	0.507189i	0.406474	+	0.913662i	$0.366758\pi$
$84$		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	−0.172148	+	0.985071i	$0.555071\pi$
$89$	−8.86012	+	15.3462i	−0.939171	+	1.62669i	−0.767023	+	0.641620i	$0.778263\pi$
$90$		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	0.870269	−	0.492577i	$-0.163945\pi$
$97$	3.71983	+	3.71983i	0.377692	+	0.377692i	−0.492577	+	0.870269i	$0.663945\pi$
$98$		0			0
$99$			9.23019i			0.927669i
$100$		0			0
$101$	−10.9262	+	6.30826i	−1.08720	+	0.627696i	−0.932830	−	0.360317i	$-0.882668\pi$
$101$	−10.9262	+	6.30826i	−1.08720	+	0.627696i	−0.154371	+	0.988013i	$0.549335\pi$
$102$		0			0
$103$	1.51328	+	5.64765i	0.149108	+	0.556479i	0.999538	+	0.0303910i	$0.00967523\pi$
$103$	1.51328	+	5.64765i	0.149108	+	0.556479i	−0.850430	+	0.526088i	$0.823658\pi$
$104$		0			0
$105$	0.0527224	+	1.71873i	0.00514518	+	0.167731i
$106$		0			0
$107$	1.64561	+	6.14150i	0.159087	+	0.593721i	0.998721	+	0.0505679i	$0.0161031\pi$
$107$	1.64561	+	6.14150i	0.159087	+	0.593721i	−0.839633	+	0.543153i	$0.817230\pi$
$108$		0			0
$109$	9.97396	−	5.75847i	0.955333	−	0.551562i	0.0605992	−	0.998162i	$-0.480699\pi$
$109$	9.97396	−	5.75847i	0.955333	−	0.551562i	0.894733	+	0.446601i	$0.147366\pi$
$110$		0			0
$111$			1.94253i			0.184376i
$112$		0			0
$113$	11.7681	+	11.7681i	1.10705	+	1.10705i	0.993536	+	0.113517i	$0.0362117\pi$
$113$	11.7681	+	11.7681i	1.10705	+	1.10705i	0.113517	+	0.993536i	$0.463788\pi$
$114$		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	$-0.932165\pi$
$127$	−8.63098	+	8.63098i	−0.765876	+	0.765876i	0.211502	+	0.977378i	$0.432165\pi$
$128$		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	$-0.485982\pi$
$131$	−9.14667	−	5.28083i	−0.799148	−	0.461389i	−0.843173	+	0.537642i	$0.819315\pi$
$132$		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	0.615090	−	0.788457i	$-0.289119\pi$
$137$	8.82003	+	2.36332i	0.753546	+	0.201912i	0.138456	+	0.990369i	$0.455786\pi$
$138$		0			0
$139$	12.2197			1.03646			0.518229	−	0.855242i	$-0.326592\pi$
$139$	12.2197			1.03646			0.518229	+	0.855242i	$0.326592\pi$
$140$		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	0.803385	−	0.595460i	$-0.203030\pi$
$149$	8.41513	+	4.85848i	0.689394	+	0.398022i	−0.113991	+	0.993482i	$0.536363\pi$
$150$		0			0
$151$	−9.68938	−	16.7825i	−0.788510	−	1.36574i	−0.926880	−	0.375359i	$-0.877519\pi$
$151$	−9.68938	−	16.7825i	−0.788510	−	1.36574i	0.138369	−	0.990381i	$-0.455814\pi$
$152$		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	−0.477781	−	0.878479i	$-0.658559\pi$
$157$	4.70161	−	17.5466i	0.375229	−	1.40037i	0.853010	−	0.521895i	$-0.174775\pi$
$158$		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	$-0.409035\pi$
$163$	12.8407	−	3.44064i	1.00576	−	0.269492i	0.723856	+	0.689951i	$0.242368\pi$
$164$		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	$-0.375403\pi$
$167$	−7.01514	−	7.01514i	−0.542848	−	0.542848i	−0.924363	+	0.381515i	$0.875403\pi$
$168$		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	0.966593	+	0.256318i	$0.0825093\pi$
$173$	3.38896	+	12.6478i	0.257658	+	0.961592i	−0.708935	+	0.705274i	$0.750824\pi$
$174$		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	$-0.799521\pi$
$179$	−9.39353	+	5.42335i	−0.702105	+	0.405361i	0.106026	+	0.994363i	$0.466187\pi$
$180$		0			0
$181$		−	14.0160i		−	1.04180i	−0.853617	−	0.520901i	$-0.825596\pi$
$181$		−	14.0160i		−	1.04180i	0.853617	−	0.520901i	$-0.174404\pi$
$182$		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	0.181559	+	0.983380i	$0.441886\pi$
$191$	−10.5152	+	18.2128i	−0.760852	+	1.31784i	−0.942412	+	0.334455i	$0.891448\pi$
$192$		0			0
$193$	3.50376	−	13.0762i	0.252206	−	0.941246i	−0.717417	−	0.696644i	$-0.754676\pi$
$193$	3.50376	−	13.0762i	0.252206	−	0.941246i	0.969623	−	0.244602i	$-0.0786575\pi$
$194$		0			0
$195$	−0.964576	+	0.378954i	−0.0690747	+	0.0271374i
$196$		0			0
$197$	−8.95252	+	8.95252i	−0.637840	+	0.637840i	−0.950022	−	0.312182i	$-0.898940\pi$
$197$	−8.95252	+	8.95252i	−0.637840	+	0.637840i	0.312182	+	0.950022i	$0.398940\pi$
$198$		0			0
$199$	−6.80780	−	11.7915i	−0.482592	−	0.835875i	0.517208	−	0.855860i	$-0.326971\pi$
$199$	−6.80780	−	11.7915i	−0.482592	−	0.835875i	−0.999800	+	0.0199852i	$0.993638\pi$
$200$		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	$-0.269936\pi$
$211$	19.2166			1.32293			0.661464	+	0.749977i	$0.269936\pi$
$212$		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	$-0.553929\pi$
$223$	12.2014	−	12.2014i	0.817068	−	0.817068i	0.985682	+	0.168614i	$0.0539291\pi$
$224$		0			0
$225$	−9.92268	−	10.6793i	−0.661512	−	0.711951i
$226$		0			0
$227$	4.58309	−	17.1043i	0.304191	−	1.13525i	−0.629449	−	0.777042i	$-0.716719\pi$
$227$	4.58309	−	17.1043i	0.304191	−	1.13525i	0.933640	−	0.358213i	$-0.116614\pi$
$228$		0			0
$229$	3.44116	−	5.96026i	0.227398	−	0.393865i	−0.729638	−	0.683833i	$-0.760311\pi$
$229$	3.44116	−	5.96026i	0.227398	−	0.393865i	0.957036	+	0.289968i	$0.0936448\pi$
$230$		0			0
$231$	1.85653	−	1.57493i	0.122151	−	0.103623i
$232$		0			0
$233$	−0.997989	+	0.267410i	−0.0653804	+	0.0175186i	−0.291361	−	0.956613i	$-0.594108\pi$
$233$	−0.997989	+	0.267410i	−0.0653804	+	0.0175186i	0.225981	+	0.974132i	$0.427441\pi$
$234$		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	−0.963772	−	0.266727i	$-0.914058\pi$
$241$	−18.8567	+	10.8869i	−1.21467	+	0.701288i	−0.250894	+	0.968015i	$0.580724\pi$
$242$		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	0.302665	−	0.953097i	$-0.402124\pi$
$257$	16.6938	−	4.47308i	1.04133	−	0.279023i	0.738664	+	0.674074i	$0.235457\pi$
$258$		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	$-0.908579\pi$
$263$	0.213266	−	0.795918i	0.0131505	−	0.0490784i	0.972189	+	0.234196i	$0.0752458\pi$
$264$		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	0.712973	−	0.701192i	$-0.247348\pi$
$269$	−4.11282	−	7.12362i	−0.250763	−	0.434335i	−0.963736	+	0.266857i	$0.914015\pi$
$270$		0			0
$271$	12.4591	+	7.19325i	0.756834	+	0.436959i	0.828158	−	0.560495i	$-0.189389\pi$
$271$	12.4591	+	7.19325i	0.756834	+	0.436959i	−0.0713236	+	0.997453i	$0.522722\pi$
$272$		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	0.235608	−	0.971848i	$-0.424292\pi$
$277$	−0.770139	−	0.206358i	−0.0462732	−	0.0123989i	−0.281881	+	0.959449i	$0.590958\pi$
$278$		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	$-0.578190\pi$
$283$	−15.7926	−	4.23160i	−0.938770	−	0.251543i	−0.695590	+	0.718439i	$0.744857\pi$
$284$		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	−0.988823	−	0.149092i	$-0.952365\pi$
$293$	−14.3739	+	14.3739i	−0.839732	+	0.839732i	0.149092	+	0.988823i	$0.452365\pi$
$294$		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	−0.992687	−	0.120716i	$-0.961481\pi$
$307$	−19.5084	−	19.5084i	−1.11340	−	1.11340i	−0.120716	−	0.992687i	$-0.538519\pi$
$308$		0			0
$309$		−	1.69943i		−	0.0966770i
$310$		0			0
$311$	23.3033	−	13.4542i	1.32141	−	0.762916i	0.337456	−	0.941341i	$-0.390434\pi$
$311$	23.3033	−	13.4542i	1.32141	−	0.762916i	0.983953	+	0.178425i	$0.0571002\pi$
$312$		0			0
$313$	−2.28226	−	8.51752i	−0.129001	−	0.481439i	0.870949	−	0.491373i	$-0.163505\pi$
$313$	−2.28226	−	8.51752i	−0.129001	−	0.481439i	−0.999951	+	0.00993361i	$0.996838\pi$
$314$		0			0
$315$	−3.95130	+	16.7898i	−0.222630	+	0.945996i
$316$		0			0
$317$	1.51023	+	5.63627i	0.0848232	+	0.316564i	0.995281	−	0.0970383i	$-0.0309369\pi$
$317$	1.51023	+	5.63627i	0.0848232	+	0.316564i	−0.910457	+	0.413603i	$0.864270\pi$
$318$		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	−0.303744	−	0.952754i	$-0.598237\pi$
$331$	12.2485	−	21.2150i	0.673237	−	1.16608i	0.976981	−	0.213327i	$-0.0684300\pi$
$332$		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	−0.539783	−	0.841804i	$-0.681494\pi$
$337$	5.54436	−	5.54436i	0.302021	−	0.302021i	0.841804	+	0.539783i	$0.181494\pi$
$338$		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	$-0.158165\pi$
$347$	26.1167	+	6.99795i	1.40202	+	0.375670i	0.522949	+	0.852364i	$0.324832\pi$
$348$		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	0.0811298	−	0.996704i	$-0.474147\pi$
$353$	−6.51881	−	1.74671i	−0.346961	−	0.0929680i	−0.428091	+	0.903736i	$0.640814\pi$
$354$		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	$-0.549659\pi$
$359$	−20.6255	−	11.9082i	−1.08857	−	0.628488i	−0.933196	+	0.359367i	$0.882993\pi$
$360$		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	0.800040	+	0.599946i	$0.204811\pi$
$367$	−3.69329	+	13.7835i	−0.192788	+	0.719494i	−0.992828	+	0.119548i	$0.961855\pi$
$368$		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	−0.430455	−	0.902612i	$-0.641647\pi$
$373$	−6.79696	+	1.82124i	−0.351933	+	0.0943002i	0.0785216	+	0.996912i	$0.474980\pi$
$374$		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	−0.963612	−	0.267305i	$-0.913867\pi$
$383$	−5.14216	−	19.1908i	−0.262752	−	0.980603i	0.700860	−	0.713299i	$-0.252800\pi$
$384$		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	0.108906	−	0.994052i	$-0.465265\pi$
$389$	20.2010	−	11.6631i	1.02423	−	0.591342i	0.915327	+	0.402710i	$0.131932\pi$
$390$		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	0.428408	−	0.903585i	$-0.359075\pi$
$397$	24.9302	−	6.68004i	1.25121	−	0.335261i	0.822805	+	0.568324i	$0.192408\pi$
$398$		0			0
$399$	1.49927	+	0.536562i	0.0750572	+	0.0268617i
$400$		0			0
$401$	3.12717	−	5.41642i	0.156163	−	0.270483i	−0.777319	−	0.629107i	$-0.783421\pi$
$401$	3.12717	−	5.41642i	0.156163	−	0.270483i	0.933482	+	0.358624i	$0.116754\pi$
$402$		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	0.931721	+	0.363174i	$0.118307\pi$
$409$	15.7822	+	27.3355i	0.780379	+	1.35166i	−0.151342	+	0.988481i	$0.548360\pi$
$410$		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	$-0.414641\pi$
$419$	10.8473			0.529923			0.264962	+	0.964259i	$0.414641\pi$
$420$		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	$-0.246683\pi$
$431$	−5.16396	−	8.94425i	−0.248739	−	0.430829i	−0.963176	+	0.268871i	$0.913350\pi$
$432$		0			0
$433$	−5.83240	+	5.83240i	−0.280287	+	0.280287i	−0.833224	−	0.552936i	$-0.813507\pi$
$433$	−5.83240	+	5.83240i	−0.280287	+	0.280287i	0.552936	+	0.833224i	$0.313507\pi$
$434$		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	$-0.883095\pi$
$439$	−3.26217	+	5.65024i	−0.155695	+	0.269671i	0.777617	+	0.628738i	$0.216428\pi$
$440$		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	$-0.542590\pi$
$443$	5.19032	−	1.39074i	0.246600	−	0.0660762i	0.380002	+	0.924986i	$0.375923\pi$
$444$		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	$-0.930033\pi$
$449$		−	9.24051i		−	0.436087i	0.975939	−	0.218043i	$-0.0699674\pi$
$450$		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	0.939565	+	0.342371i	$0.111230\pi$
$457$	6.35049	+	23.7003i	0.297063	+	1.10865i	−0.642502	+	0.766284i	$0.722103\pi$
$458$		0			0
$459$	4.49338	−	2.59425i	0.209733	−	0.121089i
$460$		0			0
$461$			11.2955i			0.526084i	0.964784	+	0.263042i	$0.0847258\pi$
$461$			11.2955i			0.526084i	−0.964784	+	0.263042i	$0.915274\pi$
$462$		0			0
$463$	8.69735	+	8.69735i	0.404200	+	0.404200i	0.879710	−	0.475510i	$-0.157737\pi$
$463$	8.69735	+	8.69735i	0.404200	+	0.404200i	−0.475510	+	0.879710i	$0.657737\pi$
$464$		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	$-0.833461\pi$
$467$	−29.5319	+	7.91305i	−1.36657	+	0.366172i	−0.500347	+	0.865825i	$0.666794\pi$
$468$		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	$-0.0674574\pi$
$479$	6.71144	+	11.6246i	0.306653	+	0.531139i	−0.670975	+	0.741480i	$0.734124\pi$
$480$		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	$-0.389566\pi$
$487$	3.62535	+	0.971410i	0.164280	+	0.0440188i	−0.175741	+	0.984436i	$0.556232\pi$
$488$		0			0
$489$	−3.86387			−0.174730
$490$		0			0
$491$	11.4041			0.514658			0.257329	−	0.966324i	$-0.417158\pi$
$491$	11.4041			0.514658			0.257329	+	0.966324i	$0.417158\pi$
$492$		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	$-0.367346\pi$
$499$	−4.12649	−	2.38243i	−0.184727	−	0.106652i	−0.589512	+	0.807760i	$0.700680\pi$
$500$		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	$-0.711477\pi$
$503$	3.82918	−	3.82918i	0.170735	−	0.170735i	0.787302	+	0.616567i	$0.211477\pi$
$504$		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	−0.682580	−	0.730811i	$-0.739142\pi$
$509$	6.57904	−	11.3952i	0.291611	−	0.505085i	0.974191	+	0.225726i	$0.0724755\pi$
$510$		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	−0.744505	−	0.667617i	$-0.767314\pi$
$521$	−12.2934	+	7.09760i	−0.538584	+	0.310951i	0.205921	+	0.978569i	$0.433981\pi$
$522$		0			0
$523$	−3.68575	−	13.7554i	−0.161167	−	0.601482i	−0.998498	−	0.0547863i	$-0.982552\pi$
$523$	−3.68575	−	13.7554i	−0.161167	−	0.601482i	0.837332	−	0.546695i	$-0.184114\pi$
$524$		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	−0.957865	−	0.287217i	$-0.907270\pi$
$541$	−5.35421	+	9.27376i	−0.230195	+	0.398710i	0.727670	+	0.685927i	$0.240603\pi$
$542$		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	$-0.821684\pi$
$547$	−7.38586	+	7.38586i	−0.315797	+	0.315797i	0.531354	+	0.847150i	$0.321684\pi$
$548$		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	−0.508370	−	0.861139i	$-0.669752\pi$
$557$	−32.5503	−	8.72182i	−1.37920	−	0.369556i	−0.870831	+	0.491583i	$0.836418\pi$
$558$		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	$-0.312851\pi$
$563$	14.6864	+	3.93520i	0.618957	+	0.165849i	0.0643032	+	0.997930i	$0.479518\pi$
$564$		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	−0.245629	−	0.969364i	$-0.578994\pi$
$569$	−28.8138	−	16.6356i	−1.20794	−	0.697403i	−0.962308	+	0.271961i	$0.912328\pi$
$570$		0			0
$571$	9.67235	+	16.7530i	0.404775	+	0.701091i	0.994295	−	0.106663i	$-0.0340165\pi$
$571$	9.67235	+	16.7530i	0.404775	+	0.701091i	−0.589520	+	0.807754i	$0.700683\pi$
$572$		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	−0.936439	−	0.350830i	$-0.885899\pi$
$577$	1.19999	−	4.47841i	0.0499561	−	0.186439i	0.986395	+	0.164392i	$0.0525661\pi$
$578$		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	$-0.136147\pi$
$587$	11.9958	+	11.9958i	0.495119	+	0.495119i	−0.414796	+	0.909915i	$0.636147\pi$
$588$		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	−0.944204	−	0.329362i	$-0.893166\pi$
$593$	−7.09071	−	26.4629i	−0.291180	−	1.08670i	0.653023	−	0.757338i	$-0.273500\pi$
$594$		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	$-0.772771\pi$
$599$	−13.8703	+	8.00801i	−0.566725	+	0.327199i	0.189116	+	0.981955i	$0.439438\pi$
$600$		0			0
$601$			0.757785i			0.0309107i	0.999881	+	0.0154553i	$0.00491978\pi$
$601$			0.757785i			0.0309107i	−0.999881	+	0.0154553i	$0.995080\pi$
$602$		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	$-0.337116\pi$
$607$	33.2529	−	8.91009i	1.34969	−	0.361649i	0.860022	+	0.510257i	$0.170450\pi$
$608$		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	−0.947760	−	0.318986i	$-0.896658\pi$
$613$	0.805086	−	3.00462i	0.0325171	−	0.121355i	0.980277	+	0.197630i	$0.0633245\pi$
$614$		0			0
$615$	0.475120	−	1.09002i	0.0191587	−	0.0439537i
$616$		0			0
$617$	−20.2993	+	20.2993i	−0.817221	+	0.817221i	−0.985704	−	0.168484i	$-0.946113\pi$
$617$	−20.2993	+	20.2993i	−0.817221	+	0.817221i	0.168484	+	0.985704i	$0.446113\pi$
$618$		0			0
$619$	−5.85033	−	10.1331i	−0.235145	−	0.407282i	0.724170	−	0.689621i	$-0.242223\pi$
$619$	−5.85033	−	10.1331i	−0.235145	−	0.407282i	−0.959315	+	0.282339i	$0.908890\pi$
$620$		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	$-0.0810835\pi$
$631$	48.6183			1.93546			0.967731	+	0.251985i	$0.0810835\pi$
$632$		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	0.966156	−	0.257959i	$-0.0830499\pi$
$641$	6.57455	+	11.3874i	0.259679	+	0.449777i	−0.706477	+	0.707736i	$0.749717\pi$
$642$		0			0
$643$	−13.2857	+	13.2857i	−0.523935	+	0.523935i	−0.918758	−	0.394822i	$-0.870806\pi$
$643$	−13.2857	+	13.2857i	−0.523935	+	0.523935i	0.394822	+	0.918758i	$0.370806\pi$
$644$		0			0
$645$	−2.18507	−	5.56181i	−0.0860372	−	0.218996i
$646$		0			0
$647$	−8.66879	+	32.3524i	−0.340805	+	1.27190i	0.556631	+	0.830760i	$0.312094\pi$
$647$	−8.66879	+	32.3524i	−0.340805	+	1.27190i	−0.897437	+	0.441143i	$0.854573\pi$
$648$		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	−0.268036	−	0.963409i	$-0.586375\pi$
$653$	−0.471665	+	0.126382i	−0.0184577	+	0.00494572i	0.249578	+	0.968355i	$0.419708\pi$
$654$		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	−0.732050	−	0.681251i	$-0.761436\pi$
$661$	−13.0631	+	7.54198i	−0.508095	+	0.293349i	0.223955	+	0.974599i	$0.428103\pi$
$662$		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	0.0532383	−	0.998582i	$-0.483046\pi$
$673$	−24.5243	−	24.5243i	−0.945344	−	0.945344i	−0.998582	+	0.0532383i	$0.983046\pi$
$674$		0			0
$675$	4.02232	+	7.59786i	0.154819	+	0.292442i
$676$		0			0
$677$	−19.2914	+	5.16911i	−0.741428	+	0.198665i	−0.609712	−	0.792623i	$-0.708715\pi$
$677$	−19.2914	+	5.16911i	−0.741428	+	0.198665i	−0.131715	+	0.991288i	$0.542048\pi$
$678$		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	0.378720	+	0.925511i	$0.376364\pi$
$683$	−10.7678	+	40.1858i	−0.412017	+	1.53767i	−0.790736	+	0.612157i	$0.790302\pi$
$684$		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	$-0.352491\pi$
$691$	−2.73858	−	1.58112i	−0.104181	−	0.0601487i	−0.551185	+	0.834383i	$0.685824\pi$
$692$		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	0.566947	−	0.823755i	$-0.308125\pi$
$709$	3.64864	+	2.10654i	0.137028	+	0.0791129i	−0.429919	+	0.902867i	$0.641458\pi$
$710$		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	$-0.740834\pi$
$719$	7.68285	−	13.3071i	0.286522	−	0.496271i	0.972977	+	0.230902i	$0.0741675\pi$
$720$		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	−0.960968	−	0.276659i	$-0.910773\pi$
$727$	−33.3701	−	33.3701i	−1.23763	−	1.23763i	−0.276659	−	0.960968i	$-0.589227\pi$
$728$		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	0.901131	−	0.433548i	$-0.142738\pi$
$733$	−2.60032	−	9.70454i	−0.0960451	−	0.358445i	−0.997176	+	0.0751022i	$0.976072\pi$
$734$		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	$-0.757677\pi$
$739$	−13.2797	+	7.66706i	−0.488503	+	0.282037i	0.235450	+	0.971886i	$0.424344\pi$
$740$		0			0
$741$			0.959713i			0.0352559i
$742$		0			0
$743$	−22.6408	−	22.6408i	−0.830610	−	0.830610i	0.156990	−	0.987600i	$-0.449821\pi$
$743$	−22.6408	−	22.6408i	−0.830610	−	0.830610i	−0.987600	+	0.156990i	$0.949821\pi$
$744$		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	−0.0196079	+	0.999808i	$0.506242\pi$
$751$	−23.9970	+	41.5640i	−0.875663	+	1.51669i	−0.856055	+	0.516885i	$0.827092\pi$
$752$		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	−0.150789	−	0.988566i	$-0.548181\pi$
$757$	23.0503	−	23.0503i	0.837777	−	0.837777i	0.988566	+	0.150789i	$0.0481814\pi$
$758$		0			0
$759$	−1.05523	−	1.82770i	−0.0383023	−	0.0663415i
$760$		0			0
$761$	9.13419	+	5.27363i	0.331114	+	0.191169i	0.656336	−	0.754469i	$-0.272106\pi$
$761$	9.13419	+	5.27363i	0.331114	+	0.191169i	−0.325221	+	0.945638i	$0.605439\pi$
$762$		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	0.471257	−	0.881996i	$-0.343800\pi$
$773$	12.1882	+	3.26583i	0.438380	+	0.117464i	−0.0328772	+	0.999459i	$0.510467\pi$
$774$		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	$-0.901268\pi$
$787$	0.702207	−	2.62067i	0.0250310	−	0.0934169i	0.977311	+	0.211808i	$0.0679351\pi$
$788$		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	0.680113	−	0.733107i	$-0.261931\pi$
$797$	−1.49610	−	1.49610i	−0.0529945	−	0.0529945i	−0.733107	+	0.680113i	$0.761931\pi$
$798$		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	−0.789978	−	0.613135i	$-0.789908\pi$
$809$	−18.6010	+	10.7393i	−0.653976	+	0.377573i	0.136002	+	0.990709i	$0.456575\pi$
$810$		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	−0.181228	−	0.983441i	$-0.558007\pi$
$821$	21.8070	−	37.7709i	0.761071	−	1.31821i	0.942299	−	0.334772i	$-0.108659\pi$
$822$		0			0
$823$	−5.28421	+	19.7209i	−0.184196	+	0.687429i	0.810605	+	0.585593i	$0.199138\pi$
$823$	−5.28421	+	19.7209i	−0.184196	+	0.687429i	−0.994801	+	0.101836i	$0.967528\pi$
$824$		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	$-0.866649\pi$
$827$	−14.5724	+	14.5724i	−0.506734	+	0.506734i	0.406789	+	0.913522i	$0.366649\pi$
$828$		0			0
$829$	−6.36587	−	11.0260i	−0.221096	−	0.382949i	0.734045	−	0.679101i	$-0.237630\pi$
$829$	−6.36587	−	11.0260i	−0.221096	−	0.382949i	−0.955141	+	0.296151i	$0.904297\pi$
$830$		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	$-0.639374\pi$
$839$	−24.5626			−0.847996			−0.423998	+	0.905663i	$0.639374\pi$
$840$		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	−0.149224	+	0.988803i	$0.547678\pi$
$853$	−33.2374	+	33.2374i	−1.13803	+	1.13803i	−0.988803	+	0.149224i	$0.952322\pi$
$854$		0			0
$855$	−12.5648	+	4.93633i	−0.429706	+	0.168819i
$856$		0			0
$857$	−1.07074	+	3.99604i	−0.0365756	+	0.136502i	−0.981799	−	0.189921i	$-0.939177\pi$
$857$	−1.07074	+	3.99604i	−0.0365756	+	0.136502i	0.945224	+	0.326423i	$0.105843\pi$
$858$		0			0
$859$	11.2898	−	19.5545i	0.385202	−	0.667190i	−0.606595	−	0.795011i	$-0.707465\pi$
$859$	11.2898	−	19.5545i	0.385202	−	0.667190i	0.991797	+	0.127821i	$0.0407984\pi$
$860$		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	$-0.660230\pi$
$863$	−13.5771	+	3.63796i	−0.462169	+	0.123838i	0.0202190	+	0.999796i	$0.493564\pi$
$864$		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	−0.661964	−	0.749536i	$-0.730277\pi$
$877$	−13.7248	−	51.2217i	−0.463454	−	1.72963i	0.198510	−	0.980099i	$-0.436390\pi$
$878$		0			0
$879$	5.11680	−	2.95419i	0.172585	−	0.0996422i
$880$		0			0
$881$			32.9976i			1.11172i	0.831276	+	0.555859i	$0.187611\pi$
$881$			32.9976i			1.11172i	−0.831276	+	0.555859i	$0.812389\pi$
$882$		0			0
$883$	36.0519	+	36.0519i	1.21324	+	1.21324i	0.969954	+	0.243289i	$0.0782262\pi$
$883$	36.0519	+	36.0519i	1.21324	+	1.21324i	0.243289	+	0.969954i	$0.421774\pi$
$884$		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	$-0.368621\pi$
$887$	35.9330	−	9.62823i	1.20651	−	0.323284i	0.805393	+	0.592741i	$0.201954\pi$
$888$		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	$-0.489152\pi$
$907$	−13.1346	−	3.51941i	−0.436128	−	0.116860i	−0.470201	+	0.882559i	$0.655819\pi$
$908$		0			0
$909$	36.7837			1.22004
$910$		0			0
$911$	−17.0743			−0.565695			−0.282848	−	0.959165i	$-0.591279\pi$
$911$	−17.0743			−0.565695			−0.282848	+	0.959165i	$0.591279\pi$
$912$		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	$-0.251110\pi$
$919$	13.4130	+	7.74398i	0.442453	+	0.255450i	−0.262185	+	0.965018i	$0.584443\pi$
$920$		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	0.350546	+	0.936545i	$0.385996\pi$
$929$	−19.3788	+	33.5651i	−0.635799	+	1.10124i	−0.986345	+	0.164691i	$0.947337\pi$
$930$		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	0.766331	−	0.642446i	$-0.222080\pi$
$937$	3.79216	+	3.79216i	0.123884	+	0.123884i	−0.642446	+	0.766331i	$0.722080\pi$
$938$		0			0
$939$			2.56300i			0.0836402i
$940$		0			0
$941$	−20.5591	+	11.8698i	−0.670207	+	0.386944i	−0.796155	−	0.605093i	$-0.793136\pi$
$941$	−20.5591	+	11.8698i	−0.670207	+	0.386944i	0.125948	+	0.992037i	$0.459803\pi$
$942$		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	$-0.107577\pi$
$947$	−1.21208	−	4.52355i	−0.0393873	−	0.146996i	−0.982819	+	0.184571i	$0.940910\pi$
$948$		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	0.981466	+	0.191638i	$0.0613798\pi$
$953$	36.2145	+	36.2145i	1.17310	+	1.17310i	0.191638	+	0.981466i	$0.438620\pi$
$954$		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	$-0.854130\pi$
$967$	−14.1312	+	14.1312i	−0.454429	+	0.454429i	0.442393	+	0.896821i	$0.354130\pi$
$968$		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	$-0.529802\pi$
$971$	−31.2377	−	18.0351i	−1.00247	−	0.578774i	−0.908977	+	0.416846i	$0.863135\pi$
$972$		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	0.528628	−	0.848853i	$-0.322707\pi$
$977$	17.5667	+	4.70697i	0.562007	+	0.150589i	0.0333788	+	0.999443i	$0.489373\pi$
$978$		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	$-0.255336\pi$
$983$	29.4010	+	7.87798i	0.937747	+	0.251269i	0.242592	+	0.970128i	$0.422002\pi$
$984$		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	$-0.231618\pi$
$991$	−6.37905	−	11.0488i	−0.202637	−	0.350978i	−0.949377	+	0.314138i	$0.898285\pi$
$992$		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	−0.915544	−	0.402217i	$-0.868240\pi$
$997$	2.47705	−	9.24446i	0.0784488	−	0.292775i	0.993993	+	0.109442i	$0.0349064\pi$
$998$		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	560.2.ci.e.33.5		48
4.3	odd	2		280.2.bo.a.33.8	yes	48
5.2	odd	4	inner	560.2.ci.e.257.5		48
7.3	odd	6	inner	560.2.ci.e.353.5		48
20.7	even	4		280.2.bo.a.257.8	yes	48
28.3	even	6		280.2.bo.a.73.8	yes	48
35.17	even	12	inner	560.2.ci.e.17.5		48
140.87	odd	12		280.2.bo.a.17.8	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bo.a.17.8	✓	48	140.87	odd	12
280.2.bo.a.33.8	yes	48	4.3	odd	2
280.2.bo.a.73.8	yes	48	28.3	even	6
280.2.bo.a.257.8	yes	48	20.7	even	4
560.2.ci.e.17.5		48	35.17	even	12	inner
560.2.ci.e.33.5		48	1.1	even	1	trivial
560.2.ci.e.257.5		48	5.2	odd	4	inner
560.2.ci.e.353.5		48	7.3	odd	6	inner

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.ci (of order \(12\), degree \(4\), not 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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