LMFDB - Embedded newform 1764.2.bm.a.1697.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(1685,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 5]))

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

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

chi := DirichletCharacter("1764.1685");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.bm (of order $6$, degree $2$, 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:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 5x^14 - 17x^13 + 22x^12 - 31x^11 + 62x^10 - 52x^9 + 52x^8 - 156x^7 + 558x^6 - 837x^5 + 1782x^4 - 4131x^3 + 3645x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1697.2
Root			$-0.268067 + 1.71118i$ of defining polynomial
Character	$\chi$	$=$	1764.1697
Dual form			1764.2.bm.a.1685.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.42826 + 0.979841i) q^{3} +1.68574 q^{5} +(1.07983 - 2.79892i) q^{9} +O(q^{10})$	\(q+(-1.42826 + 0.979841i) q^{3} +1.68574 q^{5} +(1.07983 - 2.79892i) q^{9} -3.90538i q^{11} +(-5.24391 - 3.02757i) q^{13} +(-2.40766 + 1.65175i) q^{15} +(-0.201244 + 0.348565i) q^{17} +(0.145617 - 0.0840718i) q^{19} +8.88395i q^{23} -2.15829 q^{25} +(1.20023 + 5.05563i) q^{27} +(-6.15380 + 3.55290i) q^{29} +(-5.44527 + 3.14383i) q^{31} +(3.82665 + 5.57788i) q^{33} +(3.13257 + 5.42578i) q^{37} +(10.4562 - 0.814049i) q^{39} +(1.64707 - 2.85281i) q^{41} +(1.80474 + 3.12590i) q^{43} +(1.82030 - 4.71825i) q^{45} +(-4.38482 + 7.59474i) q^{47} +(-0.0541101 - 0.695026i) q^{51} +(-4.94628 - 2.85574i) q^{53} -6.58345i q^{55} +(-0.125601 + 0.262757i) q^{57} +(-2.25163 - 3.89994i) q^{59} +(-4.43678 - 2.56157i) q^{61} +(-8.83986 - 5.10369i) q^{65} +(2.95521 + 5.11857i) q^{67} +(-8.70486 - 12.6886i) q^{69} +11.4308i q^{71} +(6.05559 + 3.49620i) q^{73} +(3.08259 - 2.11478i) q^{75} +(-0.603968 + 1.04610i) q^{79} +(-6.66796 - 6.04470i) q^{81} +(0.181350 + 0.314108i) q^{83} +(-0.339244 + 0.587588i) q^{85} +(5.30793 - 11.1042i) q^{87} +(-1.38526 - 2.39934i) q^{89} +(4.69679 - 9.82569i) q^{93} +(0.245471 - 0.141723i) q^{95} +(-0.508914 + 0.293821i) q^{97} +(-10.9309 - 4.21713i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 3 q^{13} - 3 q^{15} + 9 q^{17} + 16 q^{25} + 9 q^{27} + 6 q^{29} - 6 q^{31} + 27 q^{33} + q^{37} - 3 q^{39} - 6 q^{41} - 2 q^{43} + 15 q^{45} + 18 q^{47} + 15 q^{51} + 15 q^{57} + 15 q^{59} - 3 q^{61} - 39 q^{65} - 7 q^{67} + 21 q^{69} + 15 q^{75} - q^{79} + 6 q^{85} + 3 q^{87} + 21 q^{89} - 69 q^{93} + 6 q^{95} - 3 q^{97} - 9 q^{99}+O(q^{100}) $ 16 * q - 3 * q^13 - 3 * q^15 + 9 * q^17 + 16 * q^25 + 9 * q^27 + 6 * q^29 - 6 * q^31 + 27 * q^33 + q^37 - 3 * q^39 - 6 * q^41 - 2 * q^43 + 15 * q^45 + 18 * q^47 + 15 * q^51 + 15 * q^57 + 15 * q^59 - 3 * q^61 - 39 * q^65 - 7 * q^67 + 21 * q^69 + 15 * q^75 - q^79 + 6 * q^85 + 3 * q^87 + 21 * q^89 - 69 * q^93 + 6 * q^95 - 3 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	−1.42826	+	0.979841i	−0.824603	+	0.565711i
$3$	−1.42826	+	0.979841i	−0.824603	+	0.565711i
$4$		0			0
$5$	1.68574			0.753885			0.376942	−	0.926237i	$-0.376975\pi$
$5$	1.68574			0.753885			0.376942	+	0.926237i	$0.376975\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	1.07983	−	2.79892i	0.359942	−	0.932975i
$10$		0			0
$11$		−	3.90538i		−	1.17752i	−0.808309	−	0.588758i	$-0.799617\pi$
$11$		−	3.90538i		−	1.17752i	0.808309	−	0.588758i	$-0.200383\pi$
$12$		0			0
$13$	−5.24391	−	3.02757i	−1.45440	−	0.839698i	−0.455673	−	0.890147i	$-0.650601\pi$
$13$	−5.24391	−	3.02757i	−1.45440	−	0.839698i	−0.998727	+	0.0504496i	$0.983935\pi$
$14$		0			0
$15$	−2.40766	+	1.65175i	−0.621656	+	0.426481i
$16$		0			0
$17$	−0.201244	+	0.348565i	−0.0488088	+	0.0845393i	−0.889398	−	0.457134i	$-0.848876\pi$
$17$	−0.201244	+	0.348565i	−0.0488088	+	0.0845393i	0.840589	+	0.541674i	$0.182209\pi$
$18$		0			0
$19$	0.145617	−	0.0840718i	0.0334067	−	0.0192874i	−0.483204	−	0.875508i	$-0.660527\pi$
$19$	0.145617	−	0.0840718i	0.0334067	−	0.0192874i	0.516610	+	0.856221i	$0.327194\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$			8.88395i			1.85243i	0.376993	+	0.926216i	$0.376958\pi$
$23$			8.88395i			1.85243i	−0.376993	+	0.926216i	$0.623042\pi$
$24$		0			0
$25$	−2.15829			−0.431658
$26$		0			0
$27$	1.20023	+	5.05563i	0.230985	+	0.972957i
$28$		0			0
$29$	−6.15380	+	3.55290i	−1.14273	+	0.659757i	−0.947106	−	0.320921i	$-0.896007\pi$
$29$	−6.15380	+	3.55290i	−1.14273	+	0.659757i	−0.195627	+	0.980678i	$0.562674\pi$
$30$		0			0
$31$	−5.44527	+	3.14383i	−0.978000	+	0.564649i	−0.901666	−	0.432434i	$-0.857655\pi$
$31$	−5.44527	+	3.14383i	−0.978000	+	0.564649i	−0.0763342	+	0.997082i	$0.524322\pi$
$32$		0			0
$33$	3.82665	+	5.57788i	0.666134	+	0.970984i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.13257	+	5.42578i	0.514992	+	0.891992i	0.999849	+	0.0173987i	$0.00553846\pi$
$37$	3.13257	+	5.42578i	0.514992	+	0.891992i	−0.484857	+	0.874594i	$0.661128\pi$
$38$		0			0
$39$	10.4562	−	0.814049i	1.67433	−	0.130352i
$40$		0			0
$41$	1.64707	−	2.85281i	0.257229	−	0.445534i	−0.708269	−	0.705942i	$-0.750524\pi$
$41$	1.64707	−	2.85281i	0.257229	−	0.445534i	0.965499	+	0.260408i	$0.0838571\pi$
$42$		0			0
$43$	1.80474	+	3.12590i	0.275220	+	0.476695i	0.970191	−	0.242343i	$-0.0779161\pi$
$43$	1.80474	+	3.12590i	0.275220	+	0.476695i	−0.694971	+	0.719038i	$0.744583\pi$
$44$		0			0
$45$	1.82030	−	4.71825i	0.271355	−	0.703355i
$46$		0			0
$47$	−4.38482	+	7.59474i	−0.639592	+	1.10781i	0.345930	+	0.938260i	$0.387563\pi$
$47$	−4.38482	+	7.59474i	−0.639592	+	1.10781i	−0.985522	+	0.169546i	$0.945770\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−0.0541101	−	0.695026i	−0.00757693	−	0.0973231i
$52$		0			0
$53$	−4.94628	−	2.85574i	−0.679424	−	0.392266i	0.120214	−	0.992748i	$-0.461642\pi$
$53$	−4.94628	−	2.85574i	−0.679424	−	0.392266i	−0.799638	+	0.600482i	$0.794975\pi$
$54$		0			0
$55$		−	6.58345i		−	0.887712i
$56$		0			0
$57$	−0.125601	+	0.262757i	−0.0166362	+	0.0348030i
$58$		0			0
$59$	−2.25163	−	3.89994i	−0.293138	−	0.507729i	0.681412	−	0.731900i	$-0.261366\pi$
$59$	−2.25163	−	3.89994i	−0.293138	−	0.507729i	−0.974550	+	0.224171i	$0.928033\pi$
$60$		0			0
$61$	−4.43678	−	2.56157i	−0.568071	−	0.327976i	0.188308	−	0.982110i	$-0.439700\pi$
$61$	−4.43678	−	2.56157i	−0.568071	−	0.327976i	−0.756379	+	0.654134i	$0.773033\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−8.83986	−	5.10369i	−1.09645	−	0.633035i
$66$		0			0
$67$	2.95521	+	5.11857i	0.361036	+	0.625332i	0.988132	−	0.153610i	$-0.0490899\pi$
$67$	2.95521	+	5.11857i	0.361036	+	0.625332i	−0.627096	+	0.778942i	$0.715757\pi$
$68$		0			0
$69$	−8.70486	−	12.6886i	−1.04794	−	1.52752i
$70$		0			0
$71$			11.4308i			1.35658i	0.734792	+	0.678292i	$0.237280\pi$
$71$			11.4308i			1.35658i	−0.734792	+	0.678292i	$0.762720\pi$
$72$		0			0
$73$	6.05559	+	3.49620i	0.708753	+	0.409199i	0.810599	−	0.585601i	$-0.199142\pi$
$73$	6.05559	+	3.49620i	0.708753	+	0.409199i	−0.101846	+	0.994800i	$0.532475\pi$
$74$		0			0
$75$	3.08259	−	2.11478i	0.355947	−	0.244194i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−0.603968	+	1.04610i	−0.0679517	+	0.117696i	−0.898000	−	0.439996i	$-0.854980\pi$
$79$	−0.603968	+	1.04610i	−0.0679517	+	0.117696i	0.830048	+	0.557692i	$0.188313\pi$
$80$		0			0
$81$	−6.66796	−	6.04470i	−0.740884	−	0.671633i
$82$		0			0
$83$	0.181350	+	0.314108i	0.0199058	+	0.0344779i	0.875807	−	0.482662i	$-0.160330\pi$
$83$	0.181350	+	0.314108i	0.0199058	+	0.0344779i	−0.855901	+	0.517140i	$0.826997\pi$
$84$		0			0
$85$	−0.339244	+	0.587588i	−0.0367962	+	0.0637329i
$86$		0			0
$87$	5.30793	−	11.1042i	0.569069	−	1.19049i
$88$		0			0
$89$	−1.38526	−	2.39934i	−0.146837	−	0.254329i	0.783220	−	0.621745i	$-0.213576\pi$
$89$	−1.38526	−	2.39934i	−0.146837	−	0.254329i	−0.930057	+	0.367416i	$0.880243\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	4.69679	−	9.82569i	0.487034	−	1.01888i
$94$		0			0
$95$	0.245471	−	0.141723i	0.0251848	−	0.0145405i
$96$		0			0
$97$	−0.508914	+	0.293821i	−0.0516723	+	0.0298330i	−0.525614	−	0.850723i	$-0.676164\pi$
$97$	−0.508914	+	0.293821i	−0.0516723	+	0.0298330i	0.473941	+	0.880556i	$0.342831\pi$
$98$		0			0
$99$	−10.9309	−	4.21713i	−1.09859	−	0.423837i
$100$		0			0
$101$	−13.8466			−1.37779			−0.688893	−	0.724863i	$-0.741903\pi$
$101$	−13.8466			−1.37779			−0.688893	+	0.724863i	$0.741903\pi$
$102$		0			0
$103$			12.0793i			1.19021i	0.803647	+	0.595106i	$0.202890\pi$
$103$			12.0793i			1.19021i	−0.803647	+	0.595106i	$0.797110\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	15.9299	−	9.19711i	1.54000	−	0.889118i	0.541159	−	0.840920i	$-0.317986\pi$
$107$	15.9299	−	9.19711i	1.54000	−	0.889118i	0.998838	−	0.0481978i	$-0.0153478\pi$
$108$		0			0
$109$	−5.51036	+	9.54422i	−0.527796	+	0.914170i	0.471679	+	0.881771i	$0.343648\pi$
$109$	−5.51036	+	9.54422i	−0.527796	+	0.914170i	−0.999475	+	0.0323997i	$0.989685\pi$
$110$		0			0
$111$	−9.79051	−	4.67997i	−0.929274	−	0.444203i
$112$		0			0
$113$	−7.36811	−	4.25398i	−0.693133	−	0.400181i	0.111652	−	0.993747i	$-0.464386\pi$
$113$	−7.36811	−	4.25398i	−0.693133	−	0.400181i	−0.804785	+	0.593567i	$0.797719\pi$
$114$		0			0
$115$			14.9760i			1.39652i
$116$		0			0
$117$	−14.1365	+	11.4081i	−1.30692	+	1.05468i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−4.25200			−0.386545
$122$		0			0
$123$	0.442862	+	5.68841i	0.0399315	+	0.512906i
$124$		0			0
$125$	−12.0670			−1.07930
$126$		0			0
$127$	−10.6312			−0.943365			−0.471682	−	0.881769i	$-0.656353\pi$
$127$	−10.6312			−0.943365			−0.471682	+	0.881769i	$0.656353\pi$
$128$		0			0
$129$	−5.64050	−	2.69622i	−0.496619	−	0.237389i
$130$		0			0
$131$	−6.33480			−0.553474			−0.276737	−	0.960946i	$-0.589253\pi$
$131$	−6.33480			−0.553474			−0.276737	+	0.960946i	$0.589253\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	2.02328	+	8.52247i	0.174136	+	0.733498i
$136$		0			0
$137$		−	16.6459i		−	1.42216i	−0.703113	−	0.711078i	$-0.748207\pi$
$137$		−	16.6459i		−	1.42216i	0.703113	−	0.711078i	$-0.251793\pi$
$138$		0			0
$139$	4.24007	+	2.44800i	0.359638	+	0.207637i	0.668922	−	0.743333i	$-0.266756\pi$
$139$	4.24007	+	2.44800i	0.359638	+	0.207637i	−0.309284	+	0.950970i	$0.600089\pi$
$140$		0			0
$141$	−1.17898	−	15.1437i	−0.0992884	−	1.27533i
$142$		0			0
$143$	−11.8238	+	20.4795i	−0.988758	+	1.71258i
$144$		0			0
$145$	−10.3737	+	5.98926i	−0.861489	+	0.497381i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	5.28696i		−	0.433125i	−0.976269	−	0.216562i	$-0.930516\pi$
$149$		−	5.28696i		−	0.433125i	0.976269	−	0.216562i	$-0.0694845\pi$
$150$		0			0
$151$	−14.5833			−1.18677			−0.593385	−	0.804919i	$-0.702209\pi$
$151$	−14.5833			−1.18677			−0.593385	+	0.804919i	$0.702209\pi$
$152$		0			0
$153$	0.758298	+	0.939655i	0.0613047	+	0.0759666i
$154$		0			0
$155$	−9.17930	+	5.29967i	−0.737299	+	0.425680i
$156$		0			0
$157$	15.4160	−	8.90044i	1.23033	−	0.710332i	0.263232	−	0.964732i	$-0.415211\pi$
$157$	15.4160	−	8.90044i	1.23033	−	0.710332i	0.967099	+	0.254400i	$0.0818781\pi$
$158$		0			0
$159$	9.86272	−	0.767846i	0.782165	−	0.0608942i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	0.0482228	+	0.0835243i	0.00377710	+	0.00654213i	0.867908	−	0.496725i	$-0.165464\pi$
$163$	0.0482228	+	0.0835243i	0.00377710	+	0.00654213i	−0.864131	+	0.503267i	$0.832131\pi$
$164$		0			0
$165$	6.45073	+	9.40284i	0.502188	+	0.732010i
$166$		0			0
$167$	2.47872	−	4.29327i	0.191809	−	0.332224i	−0.754041	−	0.656828i	$-0.771898\pi$
$167$	2.47872	−	4.29327i	0.191809	−	0.332224i	0.945850	+	0.324604i	$0.105231\pi$
$168$		0			0
$169$	11.8324	+	20.4943i	0.910185	+	1.57649i
$170$		0			0
$171$	−0.0780701	−	0.498353i	−0.00597017	−	0.0381100i
$172$		0			0
$173$	7.40033	−	12.8177i	0.562637	−	0.974515i	−0.434629	−	0.900610i	$-0.643120\pi$
$173$	7.40033	−	12.8177i	0.562637	−	0.974515i	0.997265	−	0.0739055i	$-0.0235463\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	7.03723	+	3.36387i	0.528950	+	0.252844i
$178$		0			0
$179$	0.592751	+	0.342225i	0.0443043	+	0.0255791i	0.521989	−	0.852952i	$-0.325190\pi$
$179$	0.592751	+	0.342225i	0.0443043	+	0.0255791i	−0.477684	+	0.878532i	$0.658524\pi$
$180$		0			0
$181$			7.84745i			0.583297i	0.956526	+	0.291648i	$0.0942037\pi$
$181$			7.84745i			0.583297i	−0.956526	+	0.291648i	$0.905796\pi$
$182$		0			0
$183$	8.84678	−	0.688752i	0.653973	−	0.0509140i
$184$		0			0
$185$	5.28070	+	9.14644i	0.388245	+	0.672459i
$186$		0			0
$187$	1.36128	+	0.785934i	0.0995464	+	0.0574732i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−16.9694	−	9.79729i	−1.22786	−	0.708907i	−0.261281	−	0.965263i	$-0.584145\pi$
$191$	−16.9694	−	9.79729i	−1.22786	−	0.708907i	−0.966582	+	0.256356i	$0.917478\pi$
$192$		0			0
$193$	−9.18116	−	15.9022i	−0.660875	−	1.14467i	−0.980386	−	0.197086i	$-0.936852\pi$
$193$	−9.18116	−	15.9022i	−0.660875	−	1.14467i	0.319512	−	0.947582i	$-0.396481\pi$
$194$		0			0
$195$	17.6264	−	1.37227i	1.26225	−	0.0982705i
$196$		0			0
$197$			5.92313i			0.422006i	0.977485	+	0.211003i	$0.0676730\pi$
$197$			5.92313i			0.422006i	−0.977485	+	0.211003i	$0.932327\pi$
$198$		0			0
$199$	13.6268	+	7.86741i	0.965975	+	0.557706i	0.898007	−	0.439982i	$-0.145015\pi$
$199$	13.6268	+	7.86741i	0.965975	+	0.557706i	0.0679681	+	0.997687i	$0.478348\pi$
$200$		0			0
$201$	−9.23617	−	4.41499i	−0.651469	−	0.311409i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	2.77653	−	4.80909i	0.193921	−	0.335881i
$206$		0			0
$207$	24.8655	+	9.59312i	1.72827	+	0.666768i
$208$		0			0
$209$	−0.328332	−	0.568688i	−0.0227112	−	0.0393370i
$210$		0			0
$211$	5.06619	−	8.77489i	0.348771	−	0.604088i	−0.637261	−	0.770648i	$-0.719933\pi$
$211$	5.06619	−	8.77489i	0.348771	−	0.604088i	0.986031	+	0.166560i	$0.0532659\pi$
$212$		0			0
$213$	−11.2003	−	16.3261i	−0.767435	−	1.11864i
$214$		0			0
$215$	3.04231	+	5.26944i	0.207484	+	0.359373i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−12.0746	+	0.940052i	−0.815928	+	0.0635228i
$220$		0			0
$221$	2.11061	−	1.21856i	0.141975	−	0.0819693i
$222$		0			0
$223$	13.3944	−	7.73325i	0.896955	−	0.517857i	0.0207437	−	0.999785i	$-0.493397\pi$
$223$	13.3944	−	7.73325i	0.896955	−	0.517857i	0.876211	+	0.481928i	$0.160063\pi$
$224$		0			0
$225$	−2.33058	+	6.04089i	−0.155372	+	0.402726i
$226$		0			0
$227$	−28.0719			−1.86320			−0.931600	−	0.363486i	$-0.881586\pi$
$227$	−28.0719			−1.86320			−0.931600	+	0.363486i	$0.881586\pi$
$228$		0			0
$229$		−	17.0264i		−	1.12514i	−0.826751	−	0.562568i	$-0.809814\pi$
$229$		−	17.0264i		−	1.12514i	0.826751	−	0.562568i	$-0.190186\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−16.0015	+	9.23847i	−1.04829	+	0.605233i	−0.922171	−	0.386782i	$-0.873587\pi$
$233$	−16.0015	+	9.23847i	−1.04829	+	0.605233i	−0.126122	+	0.992015i	$0.540253\pi$
$234$		0			0
$235$	−7.39166	+	12.8027i	−0.482179	+	0.835158i
$236$		0			0
$237$	−0.162394	−	2.08590i	−0.0105486	−	0.135493i
$238$		0			0
$239$	−6.06656	−	3.50253i	−0.392413	−	0.226560i	0.290792	−	0.956786i	$-0.406081\pi$
$239$	−6.06656	−	3.50253i	−0.392413	−	0.226560i	−0.683205	+	0.730226i	$0.739415\pi$
$240$		0			0
$241$		−	6.21759i		−	0.400510i	−0.979744	−	0.200255i	$-0.935823\pi$
$241$		−	6.21759i		−	0.400510i	0.979744	−	0.200255i	$-0.0641771\pi$
$242$		0			0
$243$	15.4464	+	2.09984i	0.990886	+	0.134705i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−1.01813			−0.0647823
$248$		0			0
$249$	−0.566791	−	0.270932i	−0.0359189	−	0.0171696i
$250$		0			0
$251$	9.81844			0.619734			0.309867	−	0.950780i	$-0.399715\pi$
$251$	9.81844			0.619734			0.309867	+	0.950780i	$0.399715\pi$
$252$		0			0
$253$	34.6952			2.18127
$254$		0			0
$255$	−0.0912155	−	1.17163i	−0.00571213	−	0.0733704i
$256$		0			0
$257$	1.33581			0.0833254			0.0416627	−	0.999132i	$-0.486735\pi$
$257$	1.33581			0.0833254			0.0416627	+	0.999132i	$0.486735\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	3.29927	+	21.0605i	0.204219	+	1.30361i
$262$		0			0
$263$		−	20.3502i		−	1.25485i	−0.778678	−	0.627424i	$-0.784109\pi$
$263$		−	20.3502i		−	1.25485i	0.778678	−	0.627424i	$-0.215891\pi$
$264$		0			0
$265$	−8.33814	−	4.81402i	−0.512208	−	0.295723i
$266$		0			0
$267$	4.32947	+	2.06954i	0.264959	+	0.126654i
$268$		0			0
$269$	13.3614	−	23.1426i	0.814659	−	1.41103i	−0.0949131	−	0.995486i	$-0.530257\pi$
$269$	13.3614	−	23.1426i	0.814659	−	1.41103i	0.909572	−	0.415546i	$-0.136409\pi$
$270$		0			0
$271$	−3.76517	+	2.17382i	−0.228718	+	0.132050i	−0.609980	−	0.792417i	$-0.708823\pi$
$271$	−3.76517	+	2.17382i	−0.228718	+	0.132050i	0.381263	+	0.924467i	$0.375489\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$			8.42894i			0.508284i
$276$		0			0
$277$	−4.39803			−0.264252			−0.132126	−	0.991233i	$-0.542180\pi$
$277$	−4.39803			−0.264252			−0.132126	+	0.991233i	$0.542180\pi$
$278$		0			0
$279$	2.91940	+	18.6357i	0.174780	+	1.11569i
$280$		0			0
$281$	4.62273	−	2.66893i	0.275769	−	0.159215i	−0.355738	−	0.934586i	$-0.615770\pi$
$281$	4.62273	−	2.66893i	0.275769	−	0.159215i	0.631506	+	0.775371i	$0.282437\pi$
$282$		0			0
$283$	15.5431	−	8.97381i	0.923941	−	0.533437i	0.0390505	−	0.999237i	$-0.487567\pi$
$283$	15.5431	−	8.97381i	0.923941	−	0.533437i	0.884890	+	0.465800i	$0.154233\pi$
$284$		0			0
$285$	−0.211730	+	0.442939i	−0.0125418	+	0.0262375i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	8.41900	+	14.5821i	0.495235	+	0.857773i
$290$		0			0
$291$	0.438960	−	0.918306i	0.0257323	−	0.0538320i
$292$		0			0
$293$	−13.1126	+	22.7117i	−0.766048	+	1.32683i	0.173642	+	0.984809i	$0.444446\pi$
$293$	−13.1126	+	22.7117i	−0.766048	+	1.32683i	−0.939691	+	0.342026i	$0.888887\pi$
$294$		0			0
$295$	−3.79566	−	6.57428i	−0.220992	−	0.382769i
$296$		0			0
$297$	19.7442	−	4.68737i	1.14567	−	0.271989i
$298$		0			0
$299$	26.8968	−	46.5867i	1.55548	−	2.69418i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	19.7764	−	13.5674i	1.13613	−	0.779429i
$304$		0			0
$305$	−7.47924	−	4.31814i	−0.428260	−	0.247256i
$306$		0			0
$307$			7.19520i			0.410652i	0.978694	+	0.205326i	$0.0658254\pi$
$307$			7.19520i			0.410652i	−0.978694	+	0.205326i	$0.934175\pi$
$308$		0			0
$309$	−11.8358	−	17.2524i	−0.673317	−	0.981454i
$310$		0			0
$311$	−1.08721	−	1.88311i	−0.0616503	−	0.106781i	0.833553	−	0.552440i	$-0.186303\pi$
$311$	−1.08721	−	1.88311i	−0.0616503	−	0.106781i	−0.895203	+	0.445658i	$0.852970\pi$
$312$		0			0
$313$	10.2870	+	5.93922i	0.581457	+	0.335704i	0.761712	−	0.647916i	$-0.224359\pi$
$313$	10.2870	+	5.93922i	0.581457	+	0.335704i	−0.180255	+	0.983620i	$0.557692\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.09969	+	4.09901i	0.398758	+	0.230223i	0.685948	−	0.727651i	$-0.259388\pi$
$317$	7.09969	+	4.09901i	0.398758	+	0.230223i	−0.287190	+	0.957874i	$0.592721\pi$
$318$		0			0
$319$	13.8754	+	24.0329i	0.776875	+	1.34559i
$320$		0			0
$321$	−13.7402	+	28.7445i	−0.766903	+	1.60436i
$322$		0			0
$323$			0.0676757i			0.00376558i
$324$		0			0
$325$	11.3179	+	6.53438i	0.627803	+	0.362462i
$326$		0			0
$327$	−1.48162	−	19.0308i	−0.0819336	−	1.05241i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−8.58540	+	14.8704i	−0.471897	+	0.817349i	−0.999483	−	0.0321526i	$-0.989764\pi$
$331$	−8.58540	+	14.8704i	−0.471897	+	0.817349i	0.527586	+	0.849501i	$0.323097\pi$
$332$		0			0
$333$	18.5690	−	2.90895i	1.01757	−	0.159409i
$334$		0			0
$335$	4.98170	+	8.62856i	0.272179	+	0.471428i
$336$		0			0
$337$	3.95399	−	6.84850i	0.215387	−	0.373062i	−0.738005	−	0.674795i	$-0.764232\pi$
$337$	3.95399	−	6.84850i	0.215387	−	0.373062i	0.953392	+	0.301733i	$0.0975653\pi$
$338$		0			0
$339$	14.6918	−	1.14380i	0.797947	−	0.0621229i
$340$		0			0
$341$	12.2779	+	21.2659i	0.664883	+	1.15161i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−14.6741	−	21.3896i	−0.790027	−	1.15158i
$346$		0			0
$347$	−0.443850	+	0.256257i	−0.0238271	+	0.0137566i	−0.511866	−	0.859065i	$-0.671046\pi$
$347$	−0.443850	+	0.256257i	−0.0238271	+	0.0137566i	0.488039	+	0.872822i	$0.337712\pi$
$348$		0			0
$349$	5.74612	−	3.31752i	0.307583	−	0.177583i	−0.338262	−	0.941052i	$-0.609839\pi$
$349$	5.74612	−	3.31752i	0.307583	−	0.177583i	0.645844	+	0.763469i	$0.276506\pi$
$350$		0			0
$351$	9.01239	−	30.1451i	0.481046	−	1.60903i
$352$		0			0
$353$	−18.0687			−0.961702			−0.480851	−	0.876802i	$-0.659672\pi$
$353$	−18.0687			−0.961702			−0.480851	+	0.876802i	$0.659672\pi$
$354$		0			0
$355$			19.2693i			1.02271i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1.52677	+	0.881479i	−0.0805796	+	0.0465227i	−0.539748	−	0.841826i	$-0.681481\pi$
$359$	−1.52677	+	0.881479i	−0.0805796	+	0.0465227i	0.459169	+	0.888349i	$0.348147\pi$
$360$		0			0
$361$	−9.48586	+	16.4300i	−0.499256	+	0.864737i
$362$		0			0
$363$	6.07294	−	4.16628i	0.318747	−	0.218673i
$364$		0			0
$365$	10.2081	+	5.89367i	0.534318	+	0.308489i
$366$		0			0
$367$			33.4417i			1.74564i	0.488038	+	0.872822i	$0.337713\pi$
$367$			33.4417i			1.74564i	−0.488038	+	0.872822i	$0.662287\pi$
$368$		0			0
$369$	−6.20625	−	7.69056i	−0.323085	−	0.400355i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	25.5688			1.32390			0.661952	−	0.749546i	$-0.269728\pi$
$373$	25.5688			1.32390			0.661952	+	0.749546i	$0.269728\pi$
$374$		0			0
$375$	17.2347	−	11.8237i	0.889999	−	0.610575i
$376$		0			0
$377$	43.0267			2.21599
$378$		0			0
$379$	25.7920			1.32485			0.662423	−	0.749130i	$-0.269528\pi$
$379$	25.7920			1.32485			0.662423	+	0.749130i	$0.269528\pi$
$380$		0			0
$381$	15.1840	−	10.4169i	0.777902	−	0.533672i
$382$		0			0
$383$	−32.8316			−1.67762			−0.838808	−	0.544427i	$-0.816747\pi$
$383$	−32.8316			−1.67762			−0.838808	+	0.544427i	$0.816747\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	10.6979	−	1.67590i	0.543807	−	0.0851908i
$388$		0			0
$389$			20.1544i			1.02187i	0.859619	+	0.510935i	$0.170701\pi$
$389$			20.1544i			1.02187i	−0.859619	+	0.510935i	$0.829299\pi$
$390$		0			0
$391$	−3.09663	−	1.78784i	−0.156603	−	0.0904150i
$392$		0			0
$393$	9.04771	−	6.20709i	0.456396	−	0.313106i
$394$		0			0
$395$	−1.01813	+	1.76346i	−0.0512278	+	0.0887291i
$396$		0			0
$397$	30.2125	−	17.4432i	1.51632	−	0.875449i	0.516506	−	0.856284i	$-0.327232\pi$
$397$	30.2125	−	17.4432i	1.51632	−	0.875449i	0.999816	−	0.0191652i	$-0.00610086\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			9.66245i			0.482520i	0.970461	+	0.241260i	$0.0775606\pi$
$401$			9.66245i			0.482520i	−0.970461	+	0.241260i	$0.922439\pi$
$402$		0			0
$403$	38.0727			1.89654
$404$		0			0
$405$	−11.2404	−	10.1898i	−0.558541	−	0.506334i
$406$		0			0
$407$	21.1897	−	12.2339i	1.05034	−	0.606412i
$408$		0			0
$409$	−32.1202	+	18.5446i	−1.58824	+	0.916973i	−0.594647	+	0.803987i	$0.702708\pi$
$409$	−32.1202	+	18.5446i	−1.58824	+	0.916973i	−0.993597	+	0.112986i	$0.963958\pi$
$410$		0			0
$411$	16.3103	+	23.7746i	0.804530	+	1.17271i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	0.305709	+	0.529504i	0.0150067	+	0.0259923i
$416$		0			0
$417$	−8.45455	+	0.658216i	−0.414021	+	0.0322330i
$418$		0			0
$419$	1.84193	−	3.19031i	0.0899841	−	0.155857i	−0.817520	−	0.575900i	$-0.804652\pi$
$419$	1.84193	−	3.19031i	0.0899841	−	0.155857i	0.907504	+	0.420043i	$0.137985\pi$
$420$		0			0
$421$	−8.55139	−	14.8114i	−0.416769	−	0.721866i	0.578843	−	0.815439i	$-0.303504\pi$
$421$	−8.55139	−	14.8114i	−0.416769	−	0.721866i	−0.995612	+	0.0935732i	$0.970171\pi$
$422$		0			0
$423$	16.5223	+	20.4738i	0.803339	+	0.995469i
$424$		0			0
$425$	0.434342	−	0.752303i	0.0210687	−	0.0364921i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−3.17917	−	40.8354i	−0.153492	−	1.97155i
$430$		0			0
$431$	−27.3242	−	15.7756i	−1.31616	−	0.759885i	−0.333051	−	0.942909i	$-0.608078\pi$
$431$	−27.3242	−	15.7756i	−1.31616	−	0.759885i	−0.983108	+	0.183024i	$0.941411\pi$
$432$		0			0
$433$			10.0692i			0.483893i	0.970290	+	0.241947i	$0.0777859\pi$
$433$			10.0692i			0.483893i	−0.970290	+	0.241947i	$0.922214\pi$
$434$		0			0
$435$	8.94777	−	18.7188i	0.429013	−	0.897496i
$436$		0			0
$437$	0.746890	+	1.29365i	0.0357286	+	0.0618837i
$438$		0			0
$439$	−24.1966	−	13.9699i	−1.15484	−	0.666748i	−0.204779	−	0.978808i	$-0.565648\pi$
$439$	−24.1966	−	13.9699i	−1.15484	−	0.666748i	−0.950062	+	0.312060i	$0.898981\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−30.1930	−	17.4319i	−1.43451	−	0.828215i	−0.437050	−	0.899437i	$-0.643977\pi$
$443$	−30.1930	−	17.4319i	−1.43451	−	0.828215i	−0.997460	+	0.0712223i	$0.977310\pi$
$444$		0			0
$445$	−2.33518	−	4.04466i	−0.110698	−	0.191735i
$446$		0			0
$447$	5.18038	+	7.55113i	0.245023	+	0.357156i
$448$		0			0
$449$			23.2411i			1.09682i	0.836211	+	0.548408i	$0.184766\pi$
$449$			23.2411i			1.09682i	−0.836211	+	0.548408i	$0.815234\pi$
$450$		0			0
$451$	−11.1413	−	6.43244i	−0.524624	−	0.302892i
$452$		0			0
$453$	20.8286	−	14.2893i	0.978614	−	0.671369i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	3.10938	−	5.38560i	0.145451	−	0.251928i	−0.784090	−	0.620647i	$-0.786870\pi$
$457$	3.10938	−	5.38560i	0.145451	−	0.251928i	0.929541	+	0.368719i	$0.120203\pi$
$458$		0			0
$459$	−2.00375	−	0.599056i	−0.0935272	−	0.0279616i
$460$		0			0
$461$	−2.17165	−	3.76140i	−0.101144	−	0.175186i	0.811012	−	0.585029i	$-0.198917\pi$
$461$	−2.17165	−	3.76140i	−0.101144	−	0.175186i	−0.912156	+	0.409843i	$0.865584\pi$
$462$		0			0
$463$	3.57451	−	6.19124i	0.166122	−	0.287731i	−0.770931	−	0.636918i	$-0.780209\pi$
$463$	3.57451	−	6.19124i	0.166122	−	0.287731i	0.937053	+	0.349187i	$0.113542\pi$
$464$		0			0
$465$	7.91755	−	16.5635i	0.367168	−	0.768115i
$466$		0			0
$467$	0.944451	+	1.63584i	0.0437040	+	0.0756975i	0.887050	−	0.461673i	$-0.152751\pi$
$467$	0.944451	+	1.63584i	0.0437040	+	0.0756975i	−0.843346	+	0.537371i	$0.819417\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−13.2970	+	27.8173i	−0.612693	+	1.28175i
$472$		0			0
$473$	12.2078	−	7.04818i	0.561316	−	0.324076i
$474$		0			0
$475$	−0.314283	+	0.181451i	−0.0144203	+	0.00832555i
$476$		0			0
$477$	−13.3341	+	10.7606i	−0.610527	+	0.492693i
$478$		0			0
$479$	10.4498			0.477465			0.238732	−	0.971085i	$-0.423268\pi$
$479$	10.4498			0.477465			0.238732	+	0.971085i	$0.423268\pi$
$480$		0			0
$481$		−	37.9364i		−	1.72975i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.857895	+	0.495306i	−0.0389550	+	0.0224907i
$486$		0			0
$487$	−11.8298	+	20.4898i	−0.536060	+	0.928483i	0.463052	+	0.886331i	$0.346754\pi$
$487$	−11.8298	+	20.4898i	−0.536060	+	0.928483i	−0.999111	+	0.0421513i	$0.986579\pi$
$488$		0			0
$489$	−0.150715	−	0.0720434i	−0.00681557	−	0.00325792i
$490$		0			0
$491$	−11.6767	−	6.74152i	−0.526960	−	0.304241i	0.212817	−	0.977092i	$-0.431736\pi$
$491$	−11.6767	−	6.74152i	−0.526960	−	0.304241i	−0.739778	+	0.672851i	$0.765069\pi$
$492$		0			0
$493$		−	2.86000i		−	0.128808i
$494$		0			0
$495$	−18.4266	−	7.10897i	−0.828213	−	0.319524i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−12.0807			−0.540807			−0.270403	−	0.962747i	$-0.587157\pi$
$499$	−12.0807			−0.540807			−0.270403	+	0.962747i	$0.587157\pi$
$500$		0			0
$501$	0.666475	+	8.56064i	0.0297759	+	0.382461i
$502$		0			0
$503$	20.5283			0.915310			0.457655	−	0.889130i	$-0.348690\pi$
$503$	20.5283			0.915310			0.457655	+	0.889130i	$0.348690\pi$
$504$		0			0
$505$	−23.3417			−1.03869
$506$		0			0
$507$	−36.9809	−	17.6773i	−1.64238	−	0.785074i
$508$		0			0
$509$	−8.18085			−0.362610			−0.181305	−	0.983427i	$-0.558032\pi$
$509$	−8.18085			−0.362610			−0.181305	+	0.983427i	$0.558032\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	0.599810	+	0.635279i	0.0264823	+	0.0280482i
$514$		0			0
$515$			20.3626i			0.897283i
$516$		0			0
$517$	29.6603	+	17.1244i	1.30446	+	0.753131i
$518$		0			0
$519$	1.98979	+	25.5582i	0.0873421	+	1.12188i
$520$		0			0
$521$	13.8746	−	24.0314i	0.607856	−	1.05284i	−0.383738	−	0.923442i	$-0.625363\pi$
$521$	13.8746	−	24.0314i	0.607856	−	1.05284i	0.991593	−	0.129395i	$-0.0413034\pi$
$522$		0			0
$523$	−19.8843	+	11.4802i	−0.869478	+	0.501993i	−0.867175	−	0.498004i	$-0.834066\pi$
$523$	−19.8843	+	11.4802i	−0.869478	+	0.501993i	−0.00230311	+	0.999997i	$0.500733\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	2.53071i		−	0.110239i
$528$		0			0
$529$	−55.9246			−2.43151
$530$		0			0
$531$	−13.3470	+	2.09089i	−0.579211	+	0.0907370i
$532$		0			0
$533$	−17.2742	+	9.97325i	−0.748228	+	0.431990i
$534$		0			0
$535$	26.8536	−	15.5039i	1.16098	−	0.670292i
$536$		0			0
$537$	−1.18193	+	0.0920169i	−0.0510039	+	0.00397082i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−2.60405	−	4.51035i	−0.111957	−	0.193915i	0.804602	−	0.593814i	$-0.202379\pi$
$541$	−2.60405	−	4.51035i	−0.111957	−	0.193915i	−0.916559	+	0.399899i	$0.869045\pi$
$542$		0			0
$543$	−7.68925	−	11.2082i	−0.329977	−	0.480988i
$544$		0			0
$545$	−9.28902	+	16.0890i	−0.397898	+	0.689179i
$546$		0			0
$547$	10.6224	+	18.3985i	0.454181	+	0.786664i	0.998641	−	0.0521229i	$-0.0165988\pi$
$547$	10.6224	+	18.3985i	0.454181	+	0.786664i	−0.544460	+	0.838787i	$0.683265\pi$
$548$		0			0
$549$	−11.9606	+	9.65215i	−0.510466	+	0.411944i
$550$		0			0
$551$	−0.597397	+	1.03472i	−0.0254500	+	0.0440807i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−16.5042	−	7.88920i	−0.700566	−	0.334878i
$556$		0			0
$557$	−11.0945	−	6.40543i	−0.470090	−	0.271407i	0.246187	−	0.969222i	$-0.420822\pi$
$557$	−11.0945	−	6.40543i	−0.470090	−	0.271407i	−0.716277	+	0.697816i	$0.754156\pi$
$558$		0			0
$559$		−	21.8559i		−	0.924406i
$560$		0			0
$561$	−2.71434	+	0.211321i	−0.114600	+	0.00892197i
$562$		0			0
$563$	18.7396	+	32.4580i	0.789781	+	1.36794i	0.926101	+	0.377277i	$0.123139\pi$
$563$	18.7396	+	32.4580i	0.789781	+	1.36794i	−0.136319	+	0.990665i	$0.543527\pi$
$564$		0			0
$565$	−12.4207	−	7.17109i	−0.522542	−	0.301690i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.94906	+	3.43469i	0.249397	+	0.143990i	0.619488	−	0.785006i	$-0.287340\pi$
$569$	5.94906	+	3.43469i	0.249397	+	0.143990i	−0.370091	+	0.928996i	$0.620673\pi$
$570$		0			0
$571$	−0.0847909	−	0.146862i	−0.00354839	−	0.00614599i	0.864246	−	0.503070i	$-0.167796\pi$
$571$	−0.0847909	−	0.146862i	−0.00354839	−	0.00614599i	−0.867794	+	0.496924i	$0.834463\pi$
$572$		0			0
$573$	33.8364	−	2.63428i	1.41354	−	0.110049i
$574$		0			0
$575$		−	19.1741i		−	0.799617i
$576$		0			0
$577$	5.41193	+	3.12458i	0.225302	+	0.130078i	0.608403	−	0.793628i	$-0.291811\pi$
$577$	5.41193	+	3.12458i	0.225302	+	0.130078i	−0.383101	+	0.923706i	$0.625144\pi$
$578$		0			0
$579$	28.6947	+	13.7164i	1.19251	+	0.570033i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−11.1527	+	19.3171i	−0.461900	+	0.800033i
$584$		0			0
$585$	−23.8304	+	19.2310i	−0.985264	+	0.795104i
$586$		0			0
$587$	−10.7881	−	18.6855i	−0.445273	−	0.771235i	0.552799	−	0.833315i	$-0.313560\pi$
$587$	−10.7881	−	18.6855i	−0.445273	−	0.771235i	−0.998071	+	0.0620801i	$0.980227\pi$
$588$		0			0
$589$	−0.528615	+	0.915588i	−0.0217812	+	0.0377261i
$590$		0			0
$591$	−5.80373	−	8.45975i	−0.238733	−	0.347987i
$592$		0			0
$593$	−4.13036	−	7.15399i	−0.169613	−	0.293779i	0.768671	−	0.639645i	$-0.220919\pi$
$593$	−4.13036	−	7.15399i	−0.169613	−	0.293779i	−0.938284	+	0.345866i	$0.887585\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−27.1713	+	2.11538i	−1.11205	+	0.0865766i
$598$		0			0
$599$	30.7618	−	17.7603i	1.25689	−	0.725667i	0.284422	−	0.958699i	$-0.408198\pi$
$599$	30.7618	−	17.7603i	1.25689	−	0.725667i	0.972469	+	0.233033i	$0.0748649\pi$
$600$		0			0
$601$	−35.8981	+	20.7258i	−1.46432	+	0.845423i	−0.999206	−	0.0398308i	$-0.987318\pi$
$601$	−35.8981	+	20.7258i	−1.46432	+	0.845423i	−0.465109	+	0.885254i	$0.653985\pi$
$602$		0			0
$603$	17.5176	−	2.74424i	0.713371	−	0.111754i
$604$		0			0
$605$	−7.16776			−0.291411
$606$		0			0
$607$		−	2.41990i		−	0.0982206i	−0.998793	−	0.0491103i	$-0.984361\pi$
$607$		−	2.41990i		−	0.0982206i	0.998793	−	0.0491103i	$-0.0156386\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	45.9873	−	26.5508i	1.86045	−	1.07413i
$612$		0			0
$613$	21.3228	−	36.9321i	0.861219	−	1.49168i	−0.00953416	−	0.999955i	$-0.503035\pi$
$613$	21.3228	−	36.9321i	0.861219	−	1.49168i	0.870753	−	0.491720i	$-0.163632\pi$
$614$		0			0
$615$	0.746549	+	9.58916i	0.0301038	+	0.386672i
$616$		0			0
$617$	13.2535	+	7.65193i	0.533567	+	0.308055i	0.742468	−	0.669882i	$-0.233655\pi$
$617$	13.2535	+	7.65193i	0.533567	+	0.308055i	−0.208901	+	0.977937i	$0.566989\pi$
$618$		0			0
$619$		−	27.6178i		−	1.11005i	−0.831833	−	0.555026i	$-0.812708\pi$
$619$		−	27.6178i		−	1.11005i	0.831833	−	0.555026i	$-0.187292\pi$
$620$		0			0
$621$	−44.9140	+	10.6628i	−1.80234	+	0.427884i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−9.55034			−0.382014
$626$		0			0
$627$	1.02617	+	0.490519i	0.0409811	+	0.0195894i
$628$		0			0
$629$	−2.52164			−0.100545
$630$		0			0
$631$	8.28775			0.329930			0.164965	−	0.986299i	$-0.447249\pi$
$631$	8.28775			0.329930			0.164965	+	0.986299i	$0.447249\pi$
$632$		0			0
$633$	1.36219	+	17.4968i	0.0541421	+	0.695437i
$634$		0			0
$635$	−17.9214			−0.711188
$636$		0			0
$637$		0			0
$638$		0			0
$639$	31.9939	+	12.3432i	1.26566	+	0.488291i
$640$		0			0
$641$			9.91088i			0.391456i	0.980658	+	0.195728i	$0.0627070\pi$
$641$			9.91088i			0.391456i	−0.980658	+	0.195728i	$0.937293\pi$
$642$		0			0
$643$	−6.83668	−	3.94716i	−0.269612	−	0.155661i	0.359099	−	0.933299i	$-0.383084\pi$
$643$	−6.83668	−	3.94716i	−0.269612	−	0.155661i	−0.628711	+	0.777639i	$0.716417\pi$
$644$		0			0
$645$	−9.50841	−	4.54512i	−0.374393	−	0.178964i
$646$		0			0
$647$	−2.15966	+	3.74063i	−0.0849049	+	0.147060i	−0.905351	−	0.424665i	$-0.860392\pi$
$647$	−2.15966	+	3.74063i	−0.0849049	+	0.147060i	0.820446	+	0.571724i	$0.193725\pi$
$648$		0			0
$649$	−15.2308	+	8.79348i	−0.597859	+	0.345174i
$650$		0			0
$651$		0			0
$652$		0			0
$653$			43.3997i			1.69836i	0.528102	+	0.849181i	$0.322904\pi$
$653$			43.3997i			1.69836i	−0.528102	+	0.849181i	$0.677096\pi$
$654$		0			0
$655$	−10.6788			−0.417256
$656$		0			0
$657$	16.3246	−	13.1739i	0.636882	−	0.513961i
$658$		0			0
$659$	−9.34894	+	5.39761i	−0.364183	+	0.210261i	−0.670914	−	0.741535i	$-0.734098\pi$
$659$	−9.34894	+	5.39761i	−0.364183	+	0.210261i	0.306731	+	0.951796i	$0.400765\pi$
$660$		0			0
$661$	−3.39495	+	1.96008i	−0.132048	+	0.0762381i	−0.564569	−	0.825386i	$-0.690958\pi$
$661$	−3.39495	+	1.96008i	−0.132048	+	0.0762381i	0.432521	+	0.901624i	$0.357624\pi$
$662$		0			0
$663$	−1.82049	+	3.80848i	−0.0707021	+	0.147909i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−31.5638	−	54.6701i	−1.22216	−	2.11683i
$668$		0			0
$669$	−11.5532	+	24.1694i	−0.446674	+	0.934444i
$670$		0			0
$671$	−10.0039	+	17.3273i	−0.386197	+	0.668913i
$672$		0			0
$673$	−12.3404	−	21.3742i	−0.475687	−	0.823915i	0.523925	−	0.851765i	$-0.324467\pi$
$673$	−12.3404	−	21.3742i	−0.475687	−	0.823915i	−0.999612	+	0.0278497i	$0.991134\pi$
$674$		0			0
$675$	−2.59045	−	10.9115i	−0.0997065	−	0.419985i
$676$		0			0
$677$	−7.36327	+	12.7536i	−0.282994	+	0.490159i	−0.972121	−	0.234481i	$-0.924661\pi$
$677$	−7.36327	+	12.7536i	−0.282994	+	0.490159i	0.689127	+	0.724641i	$0.257994\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	40.0939	−	27.5060i	1.53640	−	1.05403i
$682$		0			0
$683$	−1.60128	−	0.924499i	−0.0612712	−	0.0353750i	0.469051	−	0.883171i	$-0.344596\pi$
$683$	−1.60128	−	0.924499i	−0.0612712	−	0.0353750i	−0.530323	+	0.847796i	$0.677929\pi$
$684$		0			0
$685$		−	28.0606i		−	1.07214i
$686$		0			0
$687$	16.6831	+	24.3180i	0.636502	+	0.927790i
$688$		0			0
$689$	17.2919	+	29.9505i	0.658769	+	1.14102i
$690$		0			0
$691$	33.7613	+	19.4921i	1.28434	+	0.741514i	0.977639	−	0.210292i	$-0.0674415\pi$
$691$	33.7613	+	19.4921i	1.28434	+	0.741514i	0.306701	+	0.951806i	$0.400775\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	7.14764	+	4.12669i	0.271126	+	0.156534i
$696$		0			0
$697$	0.662926	+	1.14822i	0.0251101	+	0.0434920i
$698$		0			0
$699$	13.8020	−	28.8738i	0.522040	−	1.09211i
$700$		0			0
$701$		−	25.4389i		−	0.960813i	−0.877046	−	0.480406i	$-0.840489\pi$
$701$		−	25.4389i		−	0.960813i	0.877046	−	0.480406i	$-0.159511\pi$
$702$		0			0
$703$	0.912310	+	0.526722i	0.0344084	+	0.0198657i
$704$		0			0
$705$	−1.98746	−	25.5282i	−0.0748520	−	0.961448i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	7.14517	−	12.3758i	0.268342	−	0.464783i	−0.700092	−	0.714053i	$-0.746857\pi$
$709$	7.14517	−	12.3758i	0.268342	−	0.464783i	0.968434	+	0.249270i	$0.0801908\pi$
$710$		0			0
$711$	2.27578	+	2.82007i	0.0853486	+	0.105761i
$712$		0			0
$713$	−27.9296	−	48.3756i	−1.04597	−	1.81168i
$714$		0			0
$715$	−19.9319	+	34.5230i	−0.745410	+	1.29109i
$716$		0			0
$717$	12.0965	−	0.941755i	0.451753	−	0.0351705i
$718$		0			0
$719$	16.7344	+	28.9848i	0.624088	+	1.08095i	0.988716	+	0.149799i	$0.0478626\pi$
$719$	16.7344	+	28.9848i	0.624088	+	1.08095i	−0.364629	+	0.931153i	$0.618804\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	6.09225	+	8.88030i	0.226573	+	0.330262i
$724$		0			0
$725$	13.2817	−	7.66819i	0.493269	−	0.284789i
$726$		0			0
$727$	−12.1354	+	7.00636i	−0.450076	+	0.259851i	−0.707862	−	0.706350i	$-0.750340\pi$
$727$	−12.1354	+	7.00636i	−0.450076	+	0.259851i	0.257786	+	0.966202i	$0.417007\pi$
$728$		0			0
$729$	−24.1189	+	12.1359i	−0.893292	+	0.449477i
$730$		0			0
$731$	−1.45277			−0.0537326
$732$		0			0
$733$			27.3077i			1.00863i	0.863519	+	0.504316i	$0.168255\pi$
$733$			27.3077i			1.00863i	−0.863519	+	0.504316i	$0.831745\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	19.9899	−	11.5412i	0.736339	−	0.425126i
$738$		0			0
$739$	26.3157	−	45.5801i	0.968039	−	1.67669i	0.266819	−	0.963747i	$-0.414027\pi$
$739$	26.3157	−	45.5801i	0.968039	−	1.67669i	0.701220	−	0.712945i	$-0.252639\pi$
$740$		0			0
$741$	1.45416	−	0.997609i	0.0534197	−	0.0366481i
$742$		0			0
$743$	−30.9523	−	17.8703i	−1.13553	−	0.655599i	−0.190211	−	0.981743i	$-0.560917\pi$
$743$	−30.9523	−	17.8703i	−1.13553	−	0.655599i	−0.945320	+	0.326144i	$0.894250\pi$
$744$		0			0
$745$		−	8.91243i		−	0.326526i
$746$		0			0
$747$	1.07499	−	0.168404i	0.0393319	−	0.00616159i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−33.1282			−1.20887			−0.604433	−	0.796656i	$-0.706600\pi$
$751$	−33.1282			−1.20887			−0.604433	+	0.796656i	$0.706600\pi$
$752$		0			0
$753$	−14.0232	+	9.62051i	−0.511035	+	0.350591i
$754$		0			0
$755$	−24.5836			−0.894687
$756$		0			0
$757$	−13.6903			−0.497584			−0.248792	−	0.968557i	$-0.580034\pi$
$757$	−13.6903			−0.497584			−0.248792	+	0.968557i	$0.580034\pi$
$758$		0			0
$759$	−49.5536	+	33.9958i	−1.79868	+	1.23397i
$760$		0			0
$761$	13.0347			0.472509			0.236255	−	0.971691i	$-0.424080\pi$
$761$	13.0347			0.472509			0.236255	+	0.971691i	$0.424080\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	1.27829	+	1.58401i	0.0462167	+	0.0572701i
$766$		0			0
$767$			27.2679i			0.984588i
$768$		0			0
$769$	18.4866	+	10.6732i	0.666642	+	0.384886i	0.794803	−	0.606867i	$-0.207574\pi$
$769$	18.4866	+	10.6732i	0.666642	+	0.384886i	−0.128161	+	0.991753i	$0.540907\pi$
$770$		0			0
$771$	−1.90788	+	1.30888i	−0.0687104	+	0.0471381i
$772$		0			0
$773$	5.73940	−	9.94093i	0.206432	−	0.357550i	−0.744156	−	0.668006i	$-0.767148\pi$
$773$	5.73940	−	9.94093i	0.206432	−	0.357550i	0.950588	+	0.310455i	$0.100482\pi$
$774$		0			0
$775$	11.7525	−	6.78529i	0.422161	−	0.243735i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	0.553889i		−	0.0198451i
$780$		0			0
$781$	44.6416			1.59740
$782$		0			0
$783$	−25.3482	−	26.8471i	−0.905870	−	0.959436i
$784$		0			0
$785$	25.9873	−	15.0038i	0.927528	−	0.535509i
$786$		0			0
$787$	−35.6808	+	20.6003i	−1.27188	+	0.734322i	−0.975342	−	0.220698i	$-0.929166\pi$
$787$	−35.6808	+	20.6003i	−1.27188	+	0.734322i	−0.296541	+	0.955020i	$0.595833\pi$
$788$		0			0
$789$	19.9400	+	29.0653i	0.709881	+	1.03475i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	15.5107	+	26.8653i	0.550801	+	0.954016i
$794$		0			0
$795$	16.6260	−	1.29439i	0.589662	−	0.0459072i
$796$		0			0
$797$	−25.0066	+	43.3127i	−0.885779	+	1.53421i	−0.0409600	+	0.999161i	$0.513042\pi$
$797$	−25.0066	+	43.3127i	−0.885779	+	1.53421i	−0.844819	+	0.535053i	$0.820292\pi$
$798$		0			0
$799$	−1.76484	−	3.05679i	−0.0624355	−	0.108141i
$800$		0			0
$801$	−8.21141	+	1.28637i	−0.290136	+	0.0454516i
$802$		0			0
$803$	13.6540	−	23.6494i	0.481838	−	0.834568i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	3.59259	+	46.1456i	0.126465	+	1.62440i
$808$		0			0
$809$	43.8995	+	25.3454i	1.54343	+	0.891097i	0.998619	+	0.0525356i	$0.0167303\pi$
$809$	43.8995	+	25.3454i	1.54343	+	0.891097i	0.544807	+	0.838562i	$0.316603\pi$
$810$		0			0
$811$			8.96566i			0.314827i	0.987533	+	0.157413i	$0.0503155\pi$
$811$			8.96566i			0.314827i	−0.987533	+	0.157413i	$0.949684\pi$
$812$		0			0
$813$	3.24762	−	6.79403i	0.113899	−	0.238277i
$814$		0			0
$815$	0.0812910	+	0.140800i	0.00284750	+	0.00493201i
$816$		0			0
$817$	0.525599	+	0.303455i	0.0183884	+	0.0106165i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−28.2190	−	16.2922i	−0.984849	−	0.568603i	−0.0811184	−	0.996704i	$-0.525849\pi$
$821$	−28.2190	−	16.2922i	−0.984849	−	0.568603i	−0.903731	+	0.428102i	$0.859183\pi$
$822$		0			0
$823$	10.0877	+	17.4724i	0.351636	+	0.609051i	0.986536	−	0.163543i	$-0.0522923\pi$
$823$	10.0877	+	17.4724i	0.351636	+	0.609051i	−0.634901	+	0.772594i	$0.718959\pi$
$824$		0			0
$825$	−8.25902	−	12.0387i	−0.287542	−	0.419133i
$826$		0			0
$827$		−	0.253288i		−	0.00880770i	−0.999990	−	0.00440385i	$-0.998598\pi$
$827$		−	0.253288i		−	0.00880770i	0.999990	−	0.00440385i	$-0.00140179\pi$
$828$		0			0
$829$	6.10909	+	3.52708i	0.212177	+	0.122501i	0.602323	−	0.798253i	$-0.294242\pi$
$829$	6.10909	+	3.52708i	0.212177	+	0.122501i	−0.390146	+	0.920753i	$0.627575\pi$
$830$		0			0
$831$	6.28151	−	4.30937i	0.217903	−	0.149490i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	4.17848	−	7.23733i	0.144602	−	0.250458i
$836$		0			0
$837$	−22.4297	−	23.7560i	−0.775282	−	0.821127i
$838$		0			0
$839$	17.0936	+	29.6069i	0.590136	+	1.02215i	0.994214	+	0.107420i	$0.0342591\pi$
$839$	17.0936	+	29.6069i	0.590136	+	1.02215i	−0.404078	+	0.914725i	$0.632408\pi$
$840$		0			0
$841$	10.7462	−	18.6130i	0.370558	−	0.641826i
$842$		0			0
$843$	−3.98731	+	8.34145i	−0.137330	+	0.287295i
$844$		0			0
$845$	19.9463	+	34.5480i	0.686174	+	1.18849i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−13.4066	+	28.0466i	−0.460113	+	0.962558i
$850$		0			0
$851$	−48.2024	+	27.8296i	−1.65236	+	0.953988i
$852$		0			0
$853$	21.7586	−	12.5623i	0.745000	−	0.430126i	−0.0788844	−	0.996884i	$-0.525136\pi$
$853$	21.7586	−	12.5623i	0.745000	−	0.430126i	0.823884	+	0.566758i	$0.191802\pi$
$854$		0			0
$855$	−0.131606	−	0.840092i	−0.00450082	−	0.0287305i
$856$		0			0
$857$	−42.1907			−1.44121			−0.720604	−	0.693347i	$-0.756135\pi$
$857$	−42.1907			−1.44121			−0.720604	+	0.693347i	$0.756135\pi$
$858$		0			0
$859$			4.71278i			0.160798i	0.996763	+	0.0803990i	$0.0256195\pi$
$859$			4.71278i			0.160798i	−0.996763	+	0.0803990i	$0.974381\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	30.8409	−	17.8060i	1.04984	−	0.606123i	0.127232	−	0.991873i	$-0.459391\pi$
$863$	30.8409	−	17.8060i	1.04984	−	0.606123i	0.922603	+	0.385750i	$0.126057\pi$
$864$		0			0
$865$	12.4750	−	21.6074i	0.424163	−	0.734672i
$866$		0			0
$867$	−26.3127	−	12.5777i	−0.893625	−	0.427162i
$868$		0			0
$869$	4.08543	+	2.35873i	0.138589	+	0.0800143i
$870$		0			0
$871$		−	35.7884i		−	1.21264i
$872$		0			0
$873$	0.272846	+	1.74169i	0.00923444	+	0.0589471i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	40.9064			1.38131			0.690655	−	0.723184i	$-0.257322\pi$
$877$	40.9064			1.38131			0.690655	+	0.723184i	$0.257322\pi$
$878$		0			0
$879$	−3.52570	−	45.2865i	−0.118919	−	1.52747i
$880$		0			0
$881$	−37.4443			−1.26153			−0.630765	−	0.775974i	$-0.717259\pi$
$881$	−37.4443			−1.26153			−0.630765	+	0.775974i	$0.717259\pi$
$882$		0			0
$883$	−49.8357			−1.67711			−0.838553	−	0.544821i	$-0.816598\pi$
$883$	−49.8357			−1.67711			−0.838553	+	0.544821i	$0.816598\pi$
$884$		0			0
$885$	11.8629	+	5.67060i	0.398768	+	0.190615i
$886$		0			0
$887$	−28.8965			−0.970248			−0.485124	−	0.874445i	$-0.661226\pi$
$887$	−28.8965			−0.970248			−0.485124	+	0.874445i	$0.661226\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−23.6068	+	26.0409i	−0.790859	+	0.872403i
$892$		0			0
$893$			1.47456i			0.0493443i
$894$		0			0
$895$	0.999223	+	0.576902i	0.0334003	+	0.0192837i
$896$		0			0
$897$	7.23198	+	92.8922i	0.241469	+	3.10158i
$898$		0			0
$899$	22.3394	−	38.6930i	0.745062	−	1.29048i
$900$		0			0
$901$	1.99082	−	1.14940i	0.0663238	−	0.0382920i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			13.2287i			0.439738i
$906$		0			0
$907$	−14.8700			−0.493749			−0.246874	−	0.969048i	$-0.579403\pi$
$907$	−14.8700			−0.493749			−0.246874	+	0.969048i	$0.579403\pi$
$908$		0			0
$909$	−14.9519	+	38.7555i	−0.495923	+	1.28544i
$910$		0			0
$911$	7.81616	−	4.51266i	0.258961	−	0.149511i	−0.364899	−	0.931047i	$-0.618897\pi$
$911$	7.81616	−	4.51266i	0.258961	−	0.149511i	0.623861	+	0.781536i	$0.285563\pi$
$912$		0			0
$913$	1.22671	−	0.708243i	0.0405982	−	0.0234394i
$914$		0			0
$915$	14.9134	−	1.16106i	0.493020	−	0.0383833i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	13.2083	+	22.8774i	0.435702	+	0.754657i	0.997353	−	0.0727170i	$-0.0231670\pi$
$919$	13.2083	+	22.8774i	0.435702	+	0.754657i	−0.561651	+	0.827374i	$0.689834\pi$
$920$		0			0
$921$	−7.05015	−	10.2766i	−0.232310	−	0.338625i
$922$		0			0
$923$	34.6075	−	59.9420i	1.13912	−	1.97302i
$924$		0			0
$925$	−6.76100	−	11.7104i	−0.222300	−	0.385036i
$926$		0			0
$927$	33.8092	+	13.0436i	1.11044	+	0.428407i
$928$		0			0
$929$	−11.1259	+	19.2706i	−0.365029	+	0.632249i	−0.988781	−	0.149373i	$-0.952274\pi$
$929$	−11.1259	+	19.2706i	−0.365029	+	0.632249i	0.623752	+	0.781623i	$0.285608\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	3.39797	+	1.62427i	0.111244	+	0.0531761i
$934$		0			0
$935$	2.29476	+	1.32488i	0.0750465	+	0.0433281i
$936$		0			0
$937$		−	14.6822i		−	0.479647i	−0.970817	−	0.239823i	$-0.922910\pi$
$937$		−	14.6822i		−	0.479647i	0.970817	−	0.239823i	$-0.0770896\pi$
$938$		0			0
$939$	−20.5120	+	1.59693i	−0.669383	+	0.0521137i
$940$		0			0
$941$	−23.0396	−	39.9058i	−0.751070	−	1.30089i	−0.947305	−	0.320334i	$-0.896205\pi$
$941$	−23.0396	−	39.9058i	−0.751070	−	1.30089i	0.196235	−	0.980557i	$-0.437129\pi$
$942$		0			0
$943$	25.3442	+	14.6325i	0.825322	+	0.476500i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	6.96116	+	4.01903i	0.226207	+	0.130601i	0.608821	−	0.793308i	$-0.291643\pi$
$947$	6.96116	+	4.01903i	0.226207	+	0.130601i	−0.382614	+	0.923908i	$0.624976\pi$
$948$		0			0
$949$	−21.1700	−	36.6675i	−0.687206	−	1.19028i
$950$		0			0
$951$	−14.1565	+	1.10213i	−0.459057	+	0.0357392i
$952$		0			0
$953$			54.9348i			1.77951i	0.456437	+	0.889756i	$0.349125\pi$
$953$			54.9348i			1.77951i	−0.456437	+	0.889756i	$0.650875\pi$
$954$		0			0
$955$	−28.6060	−	16.5157i	−0.925667	−	0.534434i
$956$		0			0
$957$	−43.3661	−	20.7295i	−1.40183	−	0.670089i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	4.26733	−	7.39124i	0.137656	−	0.238427i
$962$		0			0
$963$	−8.54055	−	54.5177i	−0.275215	−	1.75681i
$964$		0			0
$965$	−15.4770	−	26.8070i	−0.498223	−	0.862948i
$966$		0			0
$967$	−26.5917	+	46.0582i	−0.855132	+	1.48113i	0.0213900	+	0.999771i	$0.493191\pi$
$967$	−26.5917	+	46.0582i	−0.855132	+	1.48113i	−0.876522	+	0.481361i	$0.840143\pi$
$968$		0			0
$969$	−0.0663114	−	0.0966582i	−0.00213023	−	0.00310511i
$970$		0			0
$971$	−7.61403	−	13.1879i	−0.244346	−	0.423219i	0.717602	−	0.696454i	$-0.245240\pi$
$971$	−7.61403	−	13.1879i	−0.244346	−	0.423219i	−0.961947	+	0.273234i	$0.911907\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−22.5675	+	1.75695i	−0.722737	+	0.0562676i
$976$		0			0
$977$	1.49418	−	0.862667i	0.0478031	−	0.0275992i	−0.475908	−	0.879495i	$-0.657880\pi$
$977$	1.49418	−	0.862667i	0.0478031	−	0.0275992i	0.523711	+	0.851896i	$0.324547\pi$
$978$		0			0
$979$	−9.37033	+	5.40997i	−0.299477	+	0.172903i
$980$		0			0
$981$	20.7633	+	25.7292i	0.662922	+	0.821469i
$982$		0			0
$983$	60.2383			1.92130			0.960651	−	0.277758i	$-0.0895912\pi$
$983$	60.2383			1.92130			0.960651	+	0.277758i	$0.0895912\pi$
$984$		0			0
$985$			9.98485i			0.318144i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−27.7703	+	16.0332i	−0.883044	+	0.509826i
$990$		0			0
$991$	−2.87312	+	4.97639i	−0.0912676	+	0.158080i	−0.908045	−	0.418873i	$-0.862425\pi$
$991$	−2.87312	+	4.97639i	−0.0912676	+	0.158080i	0.816777	+	0.576953i	$0.195759\pi$
$992$		0			0
$993$	−2.30843	−	29.6510i	−0.0732558	−	0.940946i
$994$		0			0
$995$	22.9711	+	13.2624i	0.728234	+	0.420446i
$996$		0			0
$997$		−	0.0259240i		−	0.000821020i	−1.00000		0.000410510i	$-0.999869\pi$
$997$		−	0.0259240i		−	0.000821020i	1.00000		0.000410510i	$-0.000130669\pi$
$998$		0			0
$999$	−23.6709	+	22.3494i	−0.748915	+	0.707102i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.bm.a.1697.2		16
3.2	odd	2		5292.2.bm.a.2285.3		16
7.2	even	3		252.2.w.a.5.4	✓	16
7.3	odd	6		1764.2.x.b.293.1		16
7.4	even	3		1764.2.x.a.293.8		16
7.5	odd	6		1764.2.w.b.509.5		16
7.6	odd	2		252.2.bm.a.185.7	yes	16
9.2	odd	6		1764.2.w.b.1109.5		16
9.7	even	3		5292.2.w.b.521.3		16
21.2	odd	6		756.2.w.a.341.6		16
21.5	even	6		5292.2.w.b.1097.3		16
21.11	odd	6		5292.2.x.a.881.6		16
21.17	even	6		5292.2.x.b.881.3		16
21.20	even	2		756.2.bm.a.17.6		16
28.23	odd	6		1008.2.ca.d.257.5		16
28.27	even	2		1008.2.df.d.689.2		16
63.2	odd	6		252.2.bm.a.173.7	yes	16
63.11	odd	6		1764.2.x.b.1469.1		16
63.13	odd	6		2268.2.t.a.1781.6		16
63.16	even	3		756.2.bm.a.89.6		16
63.20	even	6		252.2.w.a.101.4	yes	16
63.23	odd	6		2268.2.t.a.2105.6		16
63.25	even	3		5292.2.x.b.4409.3		16
63.34	odd	6		756.2.w.a.521.6		16
63.38	even	6		1764.2.x.a.1469.8		16
63.41	even	6		2268.2.t.b.1781.3		16
63.47	even	6	inner	1764.2.bm.a.1685.2		16
63.52	odd	6		5292.2.x.a.4409.6		16
63.58	even	3		2268.2.t.b.2105.3		16
63.61	odd	6		5292.2.bm.a.4625.3		16
84.23	even	6		3024.2.ca.d.2609.6		16
84.83	odd	2		3024.2.df.d.17.6		16
252.79	odd	6		3024.2.df.d.1601.6		16
252.83	odd	6		1008.2.ca.d.353.5		16
252.191	even	6		1008.2.df.d.929.2		16
252.223	even	6		3024.2.ca.d.2033.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.4	✓	16	7.2	even	3
252.2.w.a.101.4	yes	16	63.20	even	6
252.2.bm.a.173.7	yes	16	63.2	odd	6
252.2.bm.a.185.7	yes	16	7.6	odd	2
756.2.w.a.341.6		16	21.2	odd	6
756.2.w.a.521.6		16	63.34	odd	6
756.2.bm.a.17.6		16	21.20	even	2
756.2.bm.a.89.6		16	63.16	even	3
1008.2.ca.d.257.5		16	28.23	odd	6
1008.2.ca.d.353.5		16	252.83	odd	6
1008.2.df.d.689.2		16	28.27	even	2
1008.2.df.d.929.2		16	252.191	even	6
1764.2.w.b.509.5		16	7.5	odd	6
1764.2.w.b.1109.5		16	9.2	odd	6
1764.2.x.a.293.8		16	7.4	even	3
1764.2.x.a.1469.8		16	63.38	even	6
1764.2.x.b.293.1		16	7.3	odd	6
1764.2.x.b.1469.1		16	63.11	odd	6
1764.2.bm.a.1685.2		16	63.47	even	6	inner
1764.2.bm.a.1697.2		16	1.1	even	1	trivial
2268.2.t.a.1781.6		16	63.13	odd	6
2268.2.t.a.2105.6		16	63.23	odd	6
2268.2.t.b.1781.3		16	63.41	even	6
2268.2.t.b.2105.3		16	63.58	even	3
3024.2.ca.d.2033.6		16	252.223	even	6
3024.2.ca.d.2609.6		16	84.23	even	6
3024.2.df.d.17.6		16	84.83	odd	2
3024.2.df.d.1601.6		16	252.79	odd	6
5292.2.w.b.521.3		16	9.7	even	3
5292.2.w.b.1097.3		16	21.5	even	6
5292.2.x.a.881.6		16	21.11	odd	6
5292.2.x.a.4409.6		16	63.52	odd	6
5292.2.x.b.881.3		16	21.17	even	6
5292.2.x.b.4409.3		16	63.25	even	3
5292.2.bm.a.2285.3		16	3.2	odd	2
5292.2.bm.a.4625.3		16	63.61	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.bm (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.42826 + 0.979841i) q^{3} +1.68574 q^{5} +(1.07983 - 2.79892i) q^{9} +O(q^{10})\)	\(q+(-1.42826 + 0.979841i) q^{3} +1.68574 q^{5} +(1.07983 - 2.79892i) q^{9} -3.90538i q^{11} +(-5.24391 - 3.02757i) q^{13} +(-2.40766 + 1.65175i) q^{15} +(-0.201244 + 0.348565i) q^{17} +(0.145617 - 0.0840718i) q^{19} +8.88395i q^{23} -2.15829 q^{25} +(1.20023 + 5.05563i) q^{27} +(-6.15380 + 3.55290i) q^{29} +(-5.44527 + 3.14383i) q^{31} +(3.82665 + 5.57788i) q^{33} +(3.13257 + 5.42578i) q^{37} +(10.4562 - 0.814049i) q^{39} +(1.64707 - 2.85281i) q^{41} +(1.80474 + 3.12590i) q^{43} +(1.82030 - 4.71825i) q^{45} +(-4.38482 + 7.59474i) q^{47} +(-0.0541101 - 0.695026i) q^{51} +(-4.94628 - 2.85574i) q^{53} -6.58345i q^{55} +(-0.125601 + 0.262757i) q^{57} +(-2.25163 - 3.89994i) q^{59} +(-4.43678 - 2.56157i) q^{61} +(-8.83986 - 5.10369i) q^{65} +(2.95521 + 5.11857i) q^{67} +(-8.70486 - 12.6886i) q^{69} +11.4308i q^{71} +(6.05559 + 3.49620i) q^{73} +(3.08259 - 2.11478i) q^{75} +(-0.603968 + 1.04610i) q^{79} +(-6.66796 - 6.04470i) q^{81} +(0.181350 + 0.314108i) q^{83} +(-0.339244 + 0.587588i) q^{85} +(5.30793 - 11.1042i) q^{87} +(-1.38526 - 2.39934i) q^{89} +(4.69679 - 9.82569i) q^{93} +(0.245471 - 0.141723i) q^{95} +(-0.508914 + 0.293821i) q^{97} +(-10.9309 - 4.21713i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 3 q^{13} - 3 q^{15} + 9 q^{17} + 16 q^{25} + 9 q^{27} + 6 q^{29} - 6 q^{31} + 27 q^{33} + q^{37} - 3 q^{39} - 6 q^{41} - 2 q^{43} + 15 q^{45} + 18 q^{47} + 15 q^{51} + 15 q^{57} + 15 q^{59} - 3 q^{61} - 39 q^{65} - 7 q^{67} + 21 q^{69} + 15 q^{75} - q^{79} + 6 q^{85} + 3 q^{87} + 21 q^{89} - 69 q^{93} + 6 q^{95} - 3 q^{97} - 9 q^{99}+O(q^{100}) \) 16 * q - 3 * q^13 - 3 * q^15 + 9 * q^17 + 16 * q^25 + 9 * q^27 + 6 * q^29 - 6 * q^31 + 27 * q^33 + q^37 - 3 * q^39 - 6 * q^41 - 2 * q^43 + 15 * q^45 + 18 * q^47 + 15 * q^51 + 15 * q^57 + 15 * q^59 - 3 * q^61 - 39 * q^65 - 7 * q^67 + 21 * q^69 + 15 * q^75 - q^79 + 6 * q^85 + 3 * q^87 + 21 * q^89 - 69 * q^93 + 6 * q^95 - 3 * q^97 - 9 * q^99

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