LMFDB - Embedded newform 1323.2.f.g.442.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(442,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1323.442");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.f (of order $3$, 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:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 $ x^12 - 7x^10 + 37x^8 - 78x^6 + 123x^4 - 36*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{5} $
Twist minimal:	no (minimal twist has level 441)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			442.1
Root			$-0.474636 - 0.274031i$ of defining polynomial
Character	$\chi$	$=$	1323.442
Dual form			1323.2.f.g.883.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.849814 - 1.47192i) q^{2} +(-0.444368 + 0.769668i) q^{4} +(-0.474636 + 0.822093i) q^{5} -1.88874 q^{8} +O(q^{10})$	\(q+(-0.849814 - 1.47192i) q^{2} +(-0.444368 + 0.769668i) q^{4} +(-0.474636 + 0.822093i) q^{5} -1.88874 q^{8} +1.61341 q^{10} +(-0.294182 - 0.509538i) q^{11} +(2.50987 - 4.34722i) q^{13} +(2.49381 + 4.31941i) q^{16} +7.58242 q^{17} -4.46122 q^{19} +(-0.421826 - 0.730623i) q^{20} +(-0.500000 + 0.866025i) q^{22} +(1.23855 - 2.14523i) q^{23} +(2.04944 + 3.54974i) q^{25} -8.53169 q^{26} +(2.73855 + 4.74331i) q^{29} +(3.03731 - 5.26078i) q^{31} +(2.34981 - 4.07000i) q^{32} +(-6.44364 - 11.1607i) q^{34} -6.98762 q^{37} +(3.79121 + 6.56657i) q^{38} +(0.896461 - 1.55272i) q^{40} +(-0.527445 + 0.913562i) q^{41} +(-3.49381 - 6.05146i) q^{43} +0.522900 q^{44} -4.21015 q^{46} +(-3.73840 - 6.47510i) q^{47} +(3.48329 - 6.03323i) q^{50} +(2.23061 + 3.86353i) q^{52} -6.92216 q^{53} +0.558517 q^{55} +(4.65452 - 8.06186i) q^{58} +(5.21512 - 9.03284i) q^{59} +(-5.82644 - 10.0917i) q^{61} -10.3246 q^{62} +1.98762 q^{64} +(2.38255 + 4.12669i) q^{65} +(5.93199 - 10.2745i) q^{67} +(-3.36938 + 5.83594i) q^{68} -4.30037 q^{71} +4.46122 q^{73} +(5.93818 + 10.2852i) q^{74} +(1.98242 - 3.43366i) q^{76} +(0.666896 + 1.15510i) q^{79} -4.73460 q^{80} +1.79292 q^{82} +(-2.84194 - 4.92238i) q^{83} +(-3.59888 + 6.23345i) q^{85} +(-5.93818 + 10.2852i) q^{86} +(0.555632 + 0.962383i) q^{88} -0.843651 q^{89} +(1.10074 + 1.90654i) q^{92} +(-6.35389 + 11.0053i) q^{94} +(2.11745 - 3.66754i) q^{95} +(1.70317 + 2.94997i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 6 q^{4} - 24 q^{8}+O(q^{10}) $ 12 * q + 2 * q^2 - 6 * q^4 - 24 * q^8	$ 12 q + 2 q^{2} - 6 q^{4} - 24 q^{8} + 8 q^{11} - 6 q^{16} - 6 q^{22} + 4 q^{23} - 12 q^{25} + 22 q^{29} + 16 q^{32} - 12 q^{37} - 6 q^{43} + 28 q^{44} + 24 q^{46} + 56 q^{50} - 56 q^{53} - 18 q^{58} - 48 q^{64} - 6 q^{65} - 76 q^{71} + 36 q^{74} + 6 q^{79} + 30 q^{85} - 36 q^{86} + 6 q^{88} + 62 q^{92} + 60 q^{95}+O(q^{100}) $ 12 * q + 2 * q^2 - 6 * q^4 - 24 * q^8 + 8 * q^11 - 6 * q^16 - 6 * q^22 + 4 * q^23 - 12 * q^25 + 22 * q^29 + 16 * q^32 - 12 * q^37 - 6 * q^43 + 28 * q^44 + 24 * q^46 + 56 * q^50 - 56 * q^53 - 18 * q^58 - 48 * q^64 - 6 * q^65 - 76 * q^71 + 36 * q^74 + 6 * q^79 + 30 * q^85 - 36 * q^86 + 6 * q^88 + 62 * q^92 + 60 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.849814	−	1.47192i	−0.600909	−	1.04081i	−0.992684	−	0.120744i	$-0.961472\pi$
$2$	−0.849814	−	1.47192i	−0.600909	−	1.04081i	0.391774	−	0.920061i	$-0.371861\pi$
$3$		0			0
$3$		0			0
$4$	−0.444368	+	0.769668i	−0.222184	+	0.384834i
$5$	−0.474636	+	0.822093i	−0.212263	+	0.367651i	−0.952423	−	0.304781i	$-0.901417\pi$
$5$	−0.474636	+	0.822093i	−0.212263	+	0.367651i	0.740159	+	0.672432i	$0.234750\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.88874			−0.667769
$9$		0			0
$10$	1.61341			0.510204
$11$	−0.294182	−	0.509538i	−0.0886992	−	0.153632i	0.818262	−	0.574845i	$-0.194938\pi$
$11$	−0.294182	−	0.509538i	−0.0886992	−	0.153632i	−0.906962	+	0.421213i	$0.861604\pi$
$12$		0			0
$13$	2.50987	−	4.34722i	0.696112	−	1.20570i	−0.273692	−	0.961817i	$-0.588245\pi$
$13$	2.50987	−	4.34722i	0.696112	−	1.20570i	0.969804	−	0.243885i	$-0.0784218\pi$
$14$		0			0
$15$		0			0
$16$	2.49381	+	4.31941i	0.623453	+	1.07985i
$17$	7.58242			1.83901			0.919503	−	0.393083i	$-0.128591\pi$
$17$	7.58242			1.83901			0.919503	+	0.393083i	$0.128591\pi$
$18$		0			0
$19$	−4.46122			−1.02347			−0.511737	−	0.859142i	$-0.670998\pi$
$19$	−4.46122			−1.02347			−0.511737	+	0.859142i	$0.670998\pi$
$20$	−0.421826	−	0.730623i	−0.0943231	−	0.163372i
$21$		0			0
$22$	−0.500000	+	0.866025i	−0.106600	+	0.184637i
$23$	1.23855	−	2.14523i	0.258256	−	0.447312i	−0.707519	−	0.706694i	$-0.750186\pi$
$23$	1.23855	−	2.14523i	0.258256	−	0.447312i	0.965775	+	0.259382i	$0.0835190\pi$
$24$		0			0
$25$	2.04944	+	3.54974i	0.409888	+	0.709948i
$26$	−8.53169			−1.67320
$27$		0			0
$28$		0			0
$29$	2.73855	+	4.74331i	0.508536	+	0.880810i	0.999951	+	0.00988468i	$0.00314644\pi$
$29$	2.73855	+	4.74331i	0.508536	+	0.880810i	−0.491415	+	0.870925i	$0.663520\pi$
$30$		0			0
$31$	3.03731	−	5.26078i	0.545518	−	0.944865i	−0.453056	−	0.891482i	$-0.649666\pi$
$31$	3.03731	−	5.26078i	0.545518	−	0.944865i	0.998574	−	0.0533826i	$-0.0170003\pi$
$32$	2.34981	−	4.07000i	0.415392	−	0.719481i
$33$		0			0
$34$	−6.44364	−	11.1607i	−1.10508	−	1.91405i
$35$		0			0
$36$		0			0
$37$	−6.98762			−1.14876			−0.574379	−	0.818590i	$-0.694756\pi$
$37$	−6.98762			−1.14876			−0.574379	+	0.818590i	$0.694756\pi$
$38$	3.79121	+	6.56657i	0.615015	+	1.06524i
$39$		0			0
$40$	0.896461	−	1.55272i	0.141743	−	0.245506i
$41$	−0.527445	+	0.913562i	−0.0823731	+	0.142674i	−0.904269	−	0.426964i	$-0.859583\pi$
$41$	−0.527445	+	0.913562i	−0.0823731	+	0.142674i	0.821896	+	0.569638i	$0.192917\pi$
$42$		0			0
$43$	−3.49381	−	6.05146i	−0.532801	−	0.922838i	−0.999266	−	0.0382990i	$-0.987806\pi$
$43$	−3.49381	−	6.05146i	−0.532801	−	0.922838i	0.466465	−	0.884540i	$-0.345527\pi$
$44$	0.522900			0.0788302
$45$		0			0
$46$	−4.21015			−0.620753
$47$	−3.73840	−	6.47510i	−0.545301	−	0.944490i	−0.998588	−	0.0531249i	$-0.983082\pi$
$47$	−3.73840	−	6.47510i	−0.545301	−	0.944490i	0.453286	−	0.891365i	$-0.350251\pi$
$48$		0			0
$49$		0			0
$50$	3.48329	−	6.03323i	0.492612	−	0.853228i
$51$		0			0
$52$	2.23061	+	3.86353i	0.309330	+	0.535775i
$53$	−6.92216			−0.950831			−0.475416	−	0.879761i	$-0.657702\pi$
$53$	−6.92216			−0.950831			−0.475416	+	0.879761i	$0.657702\pi$
$54$		0			0
$55$	0.558517			0.0753104
$56$		0			0
$57$		0			0
$58$	4.65452	−	8.06186i	0.611168	−	1.05857i
$59$	5.21512	−	9.03284i	0.678950	−	1.17598i	−0.296347	−	0.955080i	$-0.595769\pi$
$59$	5.21512	−	9.03284i	0.678950	−	1.17598i	0.975297	−	0.220896i	$-0.0708981\pi$
$60$		0			0
$61$	−5.82644	−	10.0917i	−0.745999	−	1.29211i	−0.949726	−	0.313081i	$-0.898639\pi$
$61$	−5.82644	−	10.0917i	−0.745999	−	1.29211i	0.203727	−	0.979028i	$-0.434695\pi$
$62$	−10.3246			−1.31123
$63$		0			0
$64$	1.98762			0.248453
$65$	2.38255	+	4.12669i	0.295518	+	0.511853i
$66$		0			0
$67$	5.93199	−	10.2745i	0.724708	−	1.25523i	−0.234387	−	0.972143i	$-0.575308\pi$
$67$	5.93199	−	10.2745i	0.724708	−	1.25523i	0.959094	−	0.283087i	$-0.0913585\pi$
$68$	−3.36938	+	5.83594i	−0.408598	+	0.707712i
$69$		0			0
$70$		0			0
$71$	−4.30037			−0.510360			−0.255180	−	0.966894i	$-0.582135\pi$
$71$	−4.30037			−0.510360			−0.255180	+	0.966894i	$0.582135\pi$
$72$		0			0
$73$	4.46122			0.522146			0.261073	−	0.965319i	$-0.415924\pi$
$73$	4.46122			0.522146			0.261073	+	0.965319i	$0.415924\pi$
$74$	5.93818	+	10.2852i	0.690299	+	1.19563i
$75$		0			0
$76$	1.98242	−	3.43366i	0.227400	−	0.393868i
$77$		0			0
$78$		0			0
$79$	0.666896	+	1.15510i	0.0750317	+	0.129959i	0.901100	−	0.433611i	$-0.142761\pi$
$79$	0.666896	+	1.15510i	0.0750317	+	0.129959i	−0.826068	+	0.563570i	$0.809428\pi$
$80$	−4.73460			−0.529345
$81$		0			0
$82$	1.79292			0.197995
$83$	−2.84194	−	4.92238i	−0.311943	−	0.540301i	0.666840	−	0.745201i	$-0.267647\pi$
$83$	−2.84194	−	4.92238i	−0.311943	−	0.540301i	−0.978783	+	0.204900i	$0.934313\pi$
$84$		0			0
$85$	−3.59888	+	6.23345i	−0.390354	+	0.676113i
$86$	−5.93818	+	10.2852i	−0.640330	+	1.10908i
$87$		0			0
$88$	0.555632	+	0.962383i	0.0592306	+	0.102590i
$89$	−0.843651			−0.0894269			−0.0447134	−	0.999000i	$-0.514237\pi$
$89$	−0.843651			−0.0894269			−0.0447134	+	0.999000i	$0.514237\pi$
$90$		0			0
$91$		0			0
$92$	1.10074	+	1.90654i	0.114760	+	0.198771i
$93$		0			0
$94$	−6.35389	+	11.0053i	−0.655353	+	1.13511i
$95$	2.11745	−	3.66754i	0.217246	−	0.376281i
$96$		0			0
$97$	1.70317	+	2.94997i	0.172930	+	0.299524i	0.939443	−	0.342705i	$-0.111343\pi$
$97$	1.70317	+	2.94997i	0.172930	+	0.299524i	−0.766513	+	0.642229i	$0.778010\pi$
$98$		0			0
$99$		0			0
$100$	−3.64283			−0.364283
$101$	−4.79329	−	8.30222i	−0.476950	−	0.826102i	0.522701	−	0.852516i	$-0.324924\pi$
$101$	−4.79329	−	8.30222i	−0.476950	−	0.826102i	−0.999651	+	0.0264143i	$0.991591\pi$
$102$		0			0
$103$	5.82644	−	10.0917i	0.574096	−	0.994364i	−0.422043	−	0.906576i	$-0.638687\pi$
$103$	5.82644	−	10.0917i	0.574096	−	0.994364i	0.996139	−	0.0877882i	$-0.0279799\pi$
$104$	−4.74048	+	8.21075i	−0.464842	+	0.805130i
$105$		0			0
$106$	5.88255	+	10.1889i	0.571363	+	0.989630i
$107$	3.79851			0.367216			0.183608	−	0.983000i	$-0.441222\pi$
$107$	3.79851			0.367216			0.183608	+	0.983000i	$0.441222\pi$
$108$		0			0
$109$	−12.8640			−1.23215			−0.616073	−	0.787689i	$-0.711277\pi$
$109$	−12.8640			−1.23215			−0.616073	+	0.787689i	$0.711277\pi$
$110$	−0.474636	−	0.822093i	−0.0452547	−	0.0783835i
$111$		0			0
$112$		0			0
$113$	4.51052	−	7.81245i	0.424314	−	0.734934i	−0.572042	−	0.820224i	$-0.693849\pi$
$113$	4.51052	−	7.81245i	0.424314	−	0.734934i	0.996356	+	0.0852908i	$0.0271819\pi$
$114$		0			0
$115$	1.17572	+	2.03641i	0.109636	+	0.189896i
$116$	−4.86769			−0.451954
$117$		0			0
$118$	−17.7275			−1.63195
$119$		0			0
$120$		0			0
$121$	5.32691	−	9.22649i	0.484265	−	0.838771i
$122$	−9.90278	+	17.1521i	−0.896556	+	1.55288i
$123$		0			0
$124$	2.69937	+	4.67545i	0.242411	+	0.419867i
$125$	−8.63731			−0.772544
$126$		0			0
$127$	6.43268			0.570808			0.285404	−	0.958407i	$-0.407872\pi$
$127$	6.43268			0.570808			0.285404	+	0.958407i	$0.407872\pi$
$128$	−6.38874	−	11.0656i	−0.564690	−	0.978071i
$129$		0			0
$130$	4.04944	−	7.01384i	0.355160	−	0.615154i
$131$	3.31657	−	5.74447i	0.289770	−	0.501897i	−0.683984	−	0.729497i	$-0.739754\pi$
$131$	3.31657	−	5.74447i	0.289770	−	0.501897i	0.973755	+	0.227600i	$0.0730877\pi$
$132$		0			0
$133$		0			0
$134$	−20.1643			−1.74193
$135$		0			0
$136$	−14.3212			−1.22803
$137$	7.01671	+	12.1533i	0.599478	+	1.03833i	0.992898	+	0.118968i	$0.0379585\pi$
$137$	7.01671	+	12.1533i	0.599478	+	1.03833i	−0.393420	+	0.919359i	$0.628708\pi$
$138$		0			0
$139$	−4.40254	+	7.62541i	−0.373418	+	0.646779i	−0.990089	−	0.140442i	$-0.955148\pi$
$139$	−4.40254	+	7.62541i	−0.373418	+	0.646779i	0.616671	+	0.787221i	$0.288481\pi$
$140$		0			0
$141$		0			0
$142$	3.65452	+	6.32981i	0.306680	+	0.531186i
$143$	−2.95343			−0.246978
$144$		0			0
$145$	−5.19925			−0.431774
$146$	−3.79121	−	6.56657i	−0.313763	−	0.543453i
$147$		0			0
$148$	3.10507	−	5.37815i	0.255236	−	0.442081i
$149$	−2.18292	+	3.78092i	−0.178832	+	0.309745i	−0.941481	−	0.337067i	$-0.890565\pi$
$149$	−2.18292	+	3.78092i	−0.178832	+	0.309745i	0.762649	+	0.646813i	$0.223898\pi$
$150$		0			0
$151$	6.32691	+	10.9585i	0.514877	+	0.891793i	0.999851	+	0.0172645i	$0.00549573\pi$
$151$	6.32691	+	10.9585i	0.514877	+	0.891793i	−0.484974	+	0.874529i	$0.661171\pi$
$152$	8.42607			0.683444
$153$		0			0
$154$		0			0
$155$	2.88323	+	4.99391i	0.231587	+	0.401120i
$156$		0			0
$157$	−5.63694	+	9.76347i	−0.449877	+	0.779210i	−0.998378	−	0.0569405i	$-0.981865\pi$
$157$	−5.63694	+	9.76347i	−0.449877	+	0.779210i	0.548501	+	0.836150i	$0.315199\pi$
$158$	1.13348	−	1.96324i	0.0901745	−	0.156187i
$159$		0			0
$160$	2.23061	+	3.86353i	0.176345	+	0.305439i
$161$		0			0
$162$		0			0
$163$	−1.66621			−0.130507			−0.0652537	−	0.997869i	$-0.520786\pi$
$163$	−1.66621			−0.130507			−0.0652537	+	0.997869i	$0.520786\pi$
$164$	−0.468760	−	0.811916i	−0.0366040	−	0.0634000i
$165$		0			0
$166$	−4.83024	+	8.36622i	−0.374899	+	0.649344i
$167$	1.95135	−	3.37984i	0.151000	−	0.261540i	−0.780595	−	0.625037i	$-0.785084\pi$
$167$	1.95135	−	3.37984i	0.151000	−	0.261540i	0.931595	+	0.363497i	$0.118417\pi$
$168$		0			0
$169$	−6.09888	−	10.5636i	−0.469145	−	0.812583i
$170$	12.2335			0.938269
$171$		0			0
$172$	6.21015			0.473519
$173$	8.05705	+	13.9552i	0.612566	+	1.06100i	0.990806	+	0.135288i	$0.0431961\pi$
$173$	8.05705	+	13.9552i	0.612566	+	1.06100i	−0.378240	+	0.925708i	$0.623471\pi$
$174$		0			0
$175$		0			0
$176$	1.46727	−	2.54138i	0.110599	−	0.191564i
$177$		0			0
$178$	0.716947	+	1.24179i	0.0537374	+	0.0930760i
$179$	−14.2880			−1.06793			−0.533967	−	0.845505i	$-0.679299\pi$
$179$	−14.2880			−1.06793			−0.533967	+	0.845505i	$0.679299\pi$
$180$		0			0
$181$	12.8873			0.957905			0.478952	−	0.877841i	$-0.341017\pi$
$181$	12.8873			0.957905			0.478952	+	0.877841i	$0.341017\pi$
$182$		0			0
$183$		0			0
$184$	−2.33929	+	4.05178i	−0.172455	+	0.298701i
$185$	3.31657	−	5.74447i	0.243839	−	0.422342i
$186$		0			0
$187$	−2.23061	−	3.86353i	−0.163118	−	0.282529i
$188$	6.64490			0.484629
$189$		0			0
$190$	−7.19777			−0.522181
$191$	−1.08217	−	1.87438i	−0.0783034	−	0.135625i	0.824215	−	0.566277i	$-0.191617\pi$
$191$	−1.08217	−	1.87438i	−0.0783034	−	0.135625i	−0.902518	+	0.430652i	$0.858284\pi$
$192$		0			0
$193$	−5.21565	+	9.03377i	−0.375431	+	0.650265i	−0.990391	−	0.138293i	$-0.955839\pi$
$193$	−5.21565	+	9.03377i	−0.375431	+	0.650265i	0.614961	+	0.788558i	$0.289172\pi$
$194$	2.89475	−	5.01385i	0.207831	−	0.359973i
$195$		0			0
$196$		0			0
$197$	18.7848			1.33836			0.669179	−	0.743101i	$-0.266646\pi$
$197$	18.7848			1.33836			0.669179	+	0.743101i	$0.266646\pi$
$198$		0			0
$199$	8.42607			0.597308			0.298654	−	0.954361i	$-0.403462\pi$
$199$	8.42607			0.597308			0.298654	+	0.954361i	$0.403462\pi$
$200$	−3.87085	−	6.70452i	−0.273711	−	0.474081i
$201$		0			0
$202$	−8.14681	+	14.1107i	−0.573208	+	0.992825i
$203$		0			0
$204$		0			0
$205$	−0.500689	−	0.867218i	−0.0349696	−	0.0605692i
$206$	−19.8056			−1.37992
$207$		0			0
$208$	25.0365			1.73597
$209$	1.31241	+	2.27316i	0.0907814	+	0.157238i
$210$		0			0
$211$	−5.61126	+	9.71899i	−0.386295	+	0.669083i	−0.991948	−	0.126646i	$-0.959579\pi$
$211$	−5.61126	+	9.71899i	−0.386295	+	0.669083i	0.605653	+	0.795729i	$0.292912\pi$
$212$	3.07598	−	5.32776i	0.211259	−	0.365912i
$213$		0			0
$214$	−3.22803	−	5.59111i	−0.220664	−	0.382200i
$215$	6.63315			0.452377
$216$		0			0
$217$		0			0
$218$	10.9320	+	18.9348i	0.740408	+	1.28242i
$219$		0			0
$220$	−0.248187	+	0.429872i	−0.0167328	+	0.0289820i
$221$	19.0309	−	32.9624i	1.28016	−	2.21729i
$222$		0			0
$223$	10.3774	+	17.9742i	0.694923	+	1.20364i	0.970206	+	0.242279i	$0.0778951\pi$
$223$	10.3774	+	17.9742i	0.694923	+	1.20364i	−0.275283	+	0.961363i	$0.588772\pi$
$224$		0			0
$225$		0			0
$226$	−15.3324			−1.01990
$227$	−5.21512	−	9.03284i	−0.346139	−	0.599531i	0.639421	−	0.768857i	$-0.279174\pi$
$227$	−5.21512	−	9.03284i	−0.346139	−	0.599531i	−0.985560	+	0.169326i	$0.945841\pi$
$228$		0			0
$229$	−7.52961	+	13.0417i	−0.497570	+	0.861817i	−0.999996	−	0.00280316i	$-0.999108\pi$
$229$	−7.52961	+	13.0417i	−0.497570	+	0.861817i	0.502426	+	0.864620i	$0.332441\pi$
$230$	1.99829	−	3.46113i	0.131763	−	0.228220i
$231$		0			0
$232$	−5.17240	−	8.95886i	−0.339585	−	0.588178i
$233$	−4.38688			−0.287394			−0.143697	−	0.989622i	$-0.545899\pi$
$233$	−4.38688			−0.287394			−0.143697	+	0.989622i	$0.545899\pi$
$234$		0			0
$235$	7.09751			0.462990
$236$	4.63486	+	8.02781i	0.301704	+	0.522566i
$237$		0			0
$238$		0			0
$239$	−4.77561	+	8.27160i	−0.308909	+	0.535046i	−0.978124	−	0.208023i	$-0.933297\pi$
$239$	−4.77561	+	8.27160i	−0.308909	+	0.535046i	0.669215	+	0.743069i	$0.266630\pi$
$240$		0			0
$241$	−5.26792	−	9.12431i	−0.339337	−	0.587749i	0.644971	−	0.764207i	$-0.276869\pi$
$241$	−5.26792	−	9.12431i	−0.339337	−	0.587749i	−0.984308	+	0.176458i	$0.943536\pi$
$242$	−18.1075			−1.16400
$243$		0			0
$244$	10.3563			0.662996
$245$		0			0
$246$		0			0
$247$	−11.1971	+	19.3939i	−0.712453	+	1.23401i
$248$	−5.73668	+	9.93623i	−0.364280	+	0.630951i
$249$		0			0
$250$	7.34011	+	12.7134i	0.464229	+	0.804068i
$251$	24.4346			1.54230			0.771148	−	0.636656i	$-0.219683\pi$
$251$	24.4346			1.54230			0.771148	+	0.636656i	$0.219683\pi$
$252$		0			0
$253$	−1.45744			−0.0916282
$254$	−5.46658	−	9.46839i	−0.343004	−	0.594100i
$255$		0			0
$256$	−8.87085	+	15.3648i	−0.554428	+	0.960298i
$257$	2.00416	−	3.47131i	0.125016	−	0.216534i	−0.796723	−	0.604345i	$-0.793435\pi$
$257$	2.00416	−	3.47131i	0.125016	−	0.216534i	0.921739	+	0.387810i	$0.126768\pi$
$258$		0			0
$259$		0			0
$260$	−4.23491			−0.262638
$261$		0			0
$262$	−11.2739			−0.696503
$263$	8.84362	+	15.3176i	0.545321	+	0.944524i	0.998587	+	0.0531485i	$0.0169257\pi$
$263$	8.84362	+	15.3176i	0.545321	+	0.944524i	−0.453265	+	0.891376i	$0.649741\pi$
$264$		0			0
$265$	3.28550	−	5.69066i	0.201827	−	0.349574i
$266$		0			0
$267$		0			0
$268$	5.27197	+	9.13132i	0.322037	+	0.557784i
$269$	14.2273			0.867455			0.433727	−	0.901044i	$-0.357198\pi$
$269$	14.2273			0.867455			0.433727	+	0.901044i	$0.357198\pi$
$270$		0			0
$271$	−5.39874			−0.327950			−0.163975	−	0.986464i	$-0.552432\pi$
$271$	−5.39874			−0.327950			−0.163975	+	0.986464i	$0.552432\pi$
$272$	18.9091	+	32.7515i	1.14653	+	1.98585i
$273$		0			0
$274$	11.9258	−	20.6561i	0.720464	−	1.24788i
$275$	1.20582	−	2.08854i	0.0727136	−	0.125944i
$276$		0			0
$277$	−3.83310	−	6.63913i	−0.230309	−	0.398907i	0.727590	−	0.686012i	$-0.240640\pi$
$277$	−3.83310	−	6.63913i	−0.230309	−	0.398907i	−0.957899	+	0.287105i	$0.907307\pi$
$278$	14.9653			0.897562
$279$		0			0
$280$		0			0
$281$	−11.3312	−	19.6263i	−0.675965	−	1.17081i	−0.976186	−	0.216936i	$-0.930394\pi$
$281$	−11.3312	−	19.6263i	−0.675965	−	1.17081i	0.300220	−	0.953870i	$-0.402940\pi$
$282$		0			0
$283$	15.9246	−	27.5822i	0.946619	−	1.63959i	0.194144	−	0.980973i	$-0.437807\pi$
$283$	15.9246	−	27.5822i	0.946619	−	1.63959i	0.752476	−	0.658620i	$-0.228859\pi$
$284$	1.91095	−	3.30986i	0.113394	−	0.196404i
$285$		0			0
$286$	2.50987	+	4.34722i	0.148412	+	0.257057i
$287$		0			0
$288$		0			0
$289$	40.4930			2.38194
$290$	4.41840	+	7.65289i	0.259457	+	0.449393i
$291$		0			0
$292$	−1.98242	+	3.43366i	−0.116013	+	0.200940i
$293$	13.7468	−	23.8102i	0.803097	−	1.39100i	−0.114472	−	0.993427i	$-0.536517\pi$
$293$	13.7468	−	23.8102i	0.803097	−	1.39100i	0.917568	−	0.397578i	$-0.130149\pi$
$294$		0			0
$295$	4.95056	+	8.57462i	0.288233	+	0.499234i
$296$	13.1978			0.767105
$297$		0			0
$298$	7.42030			0.429846
$299$	−6.21720	−	10.7685i	−0.359550	−	0.622758i
$300$		0			0
$301$		0			0
$302$	10.7534	−	18.6254i	0.618789	−	1.07177i
$303$		0			0
$304$	−11.1254	−	19.2698i	−0.638088	−	1.10520i
$305$	11.0617			0.633394
$306$		0			0
$307$	14.8176			0.845683			0.422841	−	0.906204i	$-0.361033\pi$
$307$	14.8176			0.845683			0.422841	+	0.906204i	$0.361033\pi$
$308$		0			0
$309$		0			0
$310$	4.90043	−	8.48779i	0.278326	−	0.482074i
$311$	14.5318	−	25.1698i	0.824021	−	1.42725i	−0.0786442	−	0.996903i	$-0.525059\pi$
$311$	14.5318	−	25.1698i	0.824021	−	1.42725i	0.902665	−	0.430343i	$-0.141608\pi$
$312$		0			0
$313$	12.2390	+	21.1986i	0.691790	+	1.19822i	0.971251	+	0.238058i	$0.0765110\pi$
$313$	12.2390	+	21.1986i	0.691790	+	1.19822i	−0.279461	+	0.960157i	$0.590156\pi$
$314$	19.1614			1.08134
$315$		0			0
$316$	−1.18539			−0.0666834
$317$	−3.69344	−	6.39722i	−0.207444	−	0.359304i	0.743465	−	0.668775i	$-0.233181\pi$
$317$	−3.69344	−	6.39722i	−0.207444	−	0.359304i	−0.950909	+	0.309472i	$0.899848\pi$
$318$		0			0
$319$	1.61126	−	2.79079i	0.0902135	−	0.156254i
$320$	−0.943395	+	1.63401i	−0.0527374	+	0.0913438i
$321$		0			0
$322$		0			0
$323$	−33.8268			−1.88218
$324$		0			0
$325$	20.5753			1.14131
$326$	1.41597	+	2.45253i	0.0784231	+	0.135833i
$327$		0			0
$328$	0.996205	−	1.72548i	0.0550062	−	0.0952736i
$329$		0			0
$330$		0			0
$331$	−10.0309	−	17.3740i	−0.551347	−	0.954960i	−0.998178	−	0.0603420i	$-0.980781\pi$
$331$	−10.0309	−	17.3740i	−0.551347	−	0.954960i	0.446831	−	0.894618i	$-0.352552\pi$
$332$	5.05146			0.277235
$333$		0			0
$334$	−6.63315			−0.362950
$335$	5.63106	+	9.75329i	0.307658	+	0.532879i
$336$		0			0
$337$	−3.20327	+	5.54823i	−0.174493	+	0.302231i	−0.939986	−	0.341214i	$-0.889162\pi$
$337$	−3.20327	+	5.54823i	−0.174493	+	0.302231i	0.765493	+	0.643445i	$0.222495\pi$
$338$	−10.3658	+	17.9542i	−0.563827	+	0.976577i
$339$		0			0
$340$	−3.19846	−	5.53989i	−0.173461	−	0.300443i
$341$	−3.57409			−0.193548
$342$		0			0
$343$		0			0
$344$	6.59888	+	11.4296i	0.355788	+	0.616243i
$345$		0			0
$346$	13.6940	−	23.7187i	0.736194	−	1.27512i
$347$	−14.5963	+	25.2816i	−0.783572	+	1.35719i	0.146276	+	0.989244i	$0.453271\pi$
$347$	−14.5963	+	25.2816i	−0.783572	+	1.35719i	−0.929848	+	0.367943i	$0.880062\pi$
$348$		0			0
$349$	2.17192	+	3.76188i	0.116260	+	0.201369i	0.918283	−	0.395925i	$-0.129576\pi$
$349$	2.17192	+	3.76188i	0.116260	+	0.201369i	−0.802022	+	0.597294i	$0.796243\pi$
$350$		0			0
$351$		0			0
$352$	−2.76509			−0.147380
$353$	12.8503	+	22.2574i	0.683955	+	1.18464i	0.973764	+	0.227560i	$0.0730747\pi$
$353$	12.8503	+	22.2574i	0.683955	+	1.18464i	−0.289809	+	0.957084i	$0.593592\pi$
$354$		0			0
$355$	2.04111	−	3.53530i	0.108331	−	0.187635i
$356$	0.374892	−	0.649331i	0.0198692	−	0.0344145i
$357$		0			0
$358$	12.1421	+	21.0308i	0.641732	+	1.11151i
$359$	−20.6872			−1.09183			−0.545916	−	0.837840i	$-0.683818\pi$
$359$	−20.6872			−1.09183			−0.545916	+	0.837840i	$0.683818\pi$
$360$		0			0
$361$	0.902493			0.0474996
$362$	−10.9518	−	18.9691i	−0.575614	−	0.996992i
$363$		0			0
$364$		0			0
$365$	−2.11745	+	3.66754i	−0.110833	+	0.191968i
$366$		0			0
$367$	1.42391	+	2.46628i	0.0743273	+	0.128739i	0.900794	−	0.434248i	$-0.142986\pi$
$367$	1.42391	+	2.46628i	0.0743273	+	0.128739i	−0.826466	+	0.562986i	$0.809652\pi$
$368$	12.3548			0.644040
$369$		0			0
$370$	−11.2739			−0.586101
$371$		0			0
$372$		0			0
$373$	−10.7163	+	18.5612i	−0.554871	+	0.961065i	0.443043	+	0.896501i	$0.353899\pi$
$373$	−10.7163	+	18.5612i	−0.554871	+	0.961065i	−0.997914	+	0.0645641i	$0.979434\pi$
$374$	−3.79121	+	6.56657i	−0.196039	+	0.339549i
$375$		0			0
$376$	7.06085	+	12.2297i	0.364135	+	0.630701i
$377$	27.4936			1.41599
$378$		0			0
$379$	27.0494			1.38943			0.694716	−	0.719284i	$-0.255530\pi$
$379$	27.0494			1.38943			0.694716	+	0.719284i	$0.255530\pi$
$380$	1.88186	+	3.25947i	0.0965372	+	0.167207i
$381$		0			0
$382$	−1.83929	+	3.18575i	−0.0941064	+	0.162997i
$383$	−7.21340	+	12.4940i	−0.368588	+	0.638412i	−0.989345	−	0.145590i	$-0.953492\pi$
$383$	−7.21340	+	12.4940i	−0.368588	+	0.638412i	0.620757	+	0.784003i	$0.286825\pi$
$384$		0			0
$385$		0			0
$386$	17.7293			0.902399
$387$		0			0
$388$	−3.02733			−0.153689
$389$	−3.05377	−	5.28929i	−0.154832	−	0.268178i	0.778166	−	0.628059i	$-0.216150\pi$
$389$	−3.05377	−	5.28929i	−0.154832	−	0.268178i	−0.932998	+	0.359882i	$0.882817\pi$
$390$		0			0
$391$	9.39120	−	16.2660i	0.474933	−	0.822609i
$392$		0			0
$393$		0			0
$394$	−15.9635	−	27.6497i	−0.804232	−	1.39297i
$395$	−1.26613			−0.0637059
$396$		0			0
$397$	−12.8873			−0.646794			−0.323397	−	0.946263i	$-0.604825\pi$
$397$	−12.8873			−0.646794			−0.323397	+	0.946263i	$0.604825\pi$
$398$	−7.16059	−	12.4025i	−0.358928	−	0.621682i
$399$		0			0
$400$	−10.2218	+	17.7047i	−0.511092	+	0.885237i
$401$	4.19530	−	7.26647i	0.209503	−	0.362870i	−0.742055	−	0.670339i	$-0.766149\pi$
$401$	4.19530	−	7.26647i	0.209503	−	0.362870i	0.951558	+	0.307469i	$0.0994820\pi$
$402$		0			0
$403$	−15.2465	−	26.4078i	−0.759483	−	1.31546i
$404$	8.51994			0.423883
$405$		0			0
$406$		0			0
$407$	2.05563	+	3.56046i	0.101894	+	0.176485i
$408$		0			0
$409$	−3.40633	+	5.89994i	−0.168432	+	0.291733i	−0.937869	−	0.346990i	$-0.887204\pi$
$409$	−3.40633	+	5.89994i	−0.168432	+	0.291733i	0.769437	+	0.638723i	$0.220537\pi$
$410$	−0.850985	+	1.47395i	−0.0420271	+	0.0727931i
$411$		0			0
$412$	5.17817	+	8.96885i	0.255110	+	0.441864i
$413$		0			0
$414$		0			0
$415$	5.39554			0.264857
$416$	−11.7955	−	20.4303i	−0.578320	−	1.00168i
$417$		0			0
$418$	2.23061	−	3.86353i	0.109103	−	0.188971i
$419$	−5.16231	+	8.94137i	−0.252195	+	0.436815i	−0.964130	−	0.265431i	$-0.914486\pi$
$419$	−5.16231	+	8.94137i	−0.252195	+	0.436815i	0.711935	+	0.702246i	$0.247819\pi$
$420$		0			0
$421$	−1.56801	−	2.71588i	−0.0764202	−	0.132364i	0.825283	−	0.564720i	$-0.191016\pi$
$421$	−1.56801	−	2.71588i	−0.0764202	−	0.132364i	−0.901703	+	0.432356i	$0.857682\pi$
$422$	19.0741			0.928514
$423$		0			0
$424$	13.0741			0.634936
$425$	15.5397	+	26.9156i	0.753787	+	1.30560i
$426$		0			0
$427$		0			0
$428$	−1.68794	+	2.92359i	−0.0815895	+	0.141317i
$429$		0			0
$430$	−5.63694	−	9.76347i	−0.271837	−	0.470836i
$431$	−31.8726			−1.53525			−0.767625	−	0.640899i	$-0.778562\pi$
$431$	−31.8726			−1.53525			−0.767625	+	0.640899i	$0.778562\pi$
$432$		0			0
$433$	7.48855			0.359877			0.179938	−	0.983678i	$-0.442410\pi$
$433$	7.48855			0.359877			0.179938	+	0.983678i	$0.442410\pi$
$434$		0			0
$435$		0			0
$436$	5.71634	−	9.90099i	0.273763	−	0.474171i
$437$	−5.52544	+	9.57035i	−0.264318	+	0.457812i
$438$		0			0
$439$	−1.14465	−	1.98259i	−0.0546311	−	0.0946238i	0.837417	−	0.546565i	$-0.184065\pi$
$439$	−1.14465	−	1.98259i	−0.0546311	−	0.0946238i	−0.892048	+	0.451941i	$0.850732\pi$
$440$	−1.05489			−0.0502900
$441$		0			0
$442$	−64.6908			−3.07703
$443$	18.6749	+	32.3458i	0.887270	+	1.53680i	0.843090	+	0.537773i	$0.180734\pi$
$443$	18.6749	+	32.3458i	0.887270	+	1.53680i	0.0441800	+	0.999024i	$0.485933\pi$
$444$		0			0
$445$	0.400427	−	0.693560i	0.0189821	−	0.0328779i
$446$	17.6378	−	30.5495i	0.835172	−	1.44656i
$447$		0			0
$448$		0			0
$449$	6.20286			0.292731			0.146366	−	0.989231i	$-0.453242\pi$
$449$	6.20286			0.292731			0.146366	+	0.989231i	$0.453242\pi$
$450$		0			0
$451$	0.620660			0.0292257
$452$	4.00866	+	6.94320i	0.188552	+	0.326581i
$453$		0			0
$454$	−8.86376	+	15.3525i	−0.415997	+	0.720527i
$455$		0			0
$456$		0			0
$457$	−10.0858	−	17.4691i	−0.471795	−	0.817172i	0.527685	−	0.849440i	$-0.323060\pi$
$457$	−10.0858	−	17.4691i	−0.471795	−	0.817172i	−0.999479	+	0.0322682i	$0.989727\pi$
$458$	25.5951			1.19598
$459$		0			0
$460$	−2.08981			−0.0974378
$461$	−11.2680	−	19.5168i	−0.524803	−	0.908986i	−0.999583	−	0.0288813i	$-0.990806\pi$
$461$	−11.2680	−	19.5168i	−0.524803	−	0.908986i	0.474780	−	0.880105i	$-0.342528\pi$
$462$		0			0
$463$	13.8145	−	23.9275i	0.642016	−	1.11200i	−0.342966	−	0.939348i	$-0.611432\pi$
$463$	13.8145	−	23.9275i	0.642016	−	1.11200i	0.984982	−	0.172656i	$-0.0552350\pi$
$464$	−13.6588	+	23.6578i	−0.634096	+	1.09829i
$465$		0			0
$466$	3.72803	+	6.45714i	0.172698	+	0.299121i
$467$	−20.1224			−0.931155			−0.465577	−	0.885007i	$-0.654153\pi$
$467$	−20.1224			−0.931155			−0.465577	+	0.885007i	$0.654153\pi$
$468$		0			0
$469$		0			0
$470$	−6.03156	−	10.4470i	−0.278215	−	0.481883i
$471$		0			0
$472$	−9.84997	+	17.0607i	−0.453382	+	0.785280i
$473$	−2.05563	+	3.56046i	−0.0945181	+	0.163710i
$474$		0			0
$475$	−9.14301	−	15.8362i	−0.419510	−	0.726613i
$476$		0			0
$477$		0			0
$478$	16.2335			0.742504
$479$	−4.79329	−	8.30222i	−0.219011	−	0.379338i	0.735495	−	0.677530i	$-0.236950\pi$
$479$	−4.79329	−	8.30222i	−0.219011	−	0.379338i	−0.954506	+	0.298192i	$0.903616\pi$
$480$		0			0
$481$	−17.5380	+	30.3767i	−0.799664	+	1.38506i
$482$	−8.95351	+	15.5079i	−0.407821	+	0.706367i
$483$		0			0
$484$	4.73422	+	8.19991i	0.215192	+	0.372723i
$485$	−3.23353			−0.146827
$486$		0			0
$487$	13.0741			0.592445			0.296223	−	0.955119i	$-0.404273\pi$
$487$	13.0741			0.592445			0.296223	+	0.955119i	$0.404273\pi$
$488$	11.0046	+	19.0605i	0.498155	+	0.862830i
$489$		0			0
$490$		0			0
$491$	7.67054	−	13.2858i	0.346167	−	0.599578i	−0.639398	−	0.768876i	$-0.720817\pi$
$491$	7.67054	−	13.2858i	0.346167	−	0.599578i	0.985565	+	0.169298i	$0.0541499\pi$
$492$		0			0
$493$	20.7648	+	35.9657i	0.935201	+	1.61982i
$494$	38.0617			1.71248
$495$		0			0
$496$	30.2979			1.36042
$497$		0			0
$498$		0			0
$499$	−2.43268	+	4.21352i	−0.108902	+	0.188623i	−0.915326	−	0.402715i	$-0.868067\pi$
$499$	−2.43268	+	4.21352i	−0.108902	+	0.188623i	0.806424	+	0.591338i	$0.201400\pi$
$500$	3.83814	−	6.64786i	0.171647	−	0.297301i
$501$		0			0
$502$	−20.7648	−	35.9657i	−0.926780	−	1.60523i
$503$	−16.0085			−0.713783			−0.356892	−	0.934146i	$-0.616163\pi$
$503$	−16.0085			−0.713783			−0.356892	+	0.934146i	$0.616163\pi$
$504$		0			0
$505$	9.10026			0.404956
$506$	1.23855	+	2.14523i	0.0550603	+	0.0953672i
$507$		0			0
$508$	−2.85848	+	4.95102i	−0.126824	+	0.219666i
$509$	−15.5925	+	27.0071i	−0.691127	+	1.19707i	0.280342	+	0.959900i	$0.409552\pi$
$509$	−15.5925	+	27.0071i	−0.691127	+	1.19707i	−0.971469	+	0.237167i	$0.923781\pi$
$510$		0			0
$511$		0			0
$512$	4.59937			0.203265
$513$		0			0
$514$	−6.81266			−0.300494
$515$	5.53087	+	9.57975i	0.243719	+	0.422134i
$516$		0			0
$517$	−2.19954	+	3.80971i	−0.0967356	+	0.167551i
$518$		0			0
$519$		0			0
$520$	−4.50000	−	7.79423i	−0.197338	−	0.341800i
$521$	−20.9661			−0.918541			−0.459270	−	0.888297i	$-0.651889\pi$
$521$	−20.9661			−0.918541			−0.459270	+	0.888297i	$0.651889\pi$
$522$		0			0
$523$	43.5642			1.90493			0.952465	−	0.304647i	$-0.0985383\pi$
$523$	43.5642			1.90493			0.952465	+	0.304647i	$0.0985383\pi$
$524$	2.94756	+	5.10532i	0.128765	+	0.223027i
$525$		0			0
$526$	15.0309	−	26.0342i	0.655377	−	1.13515i
$527$	23.0302	−	39.8894i	1.00321	−	1.73761i
$528$		0			0
$529$	8.43199	+	14.6046i	0.366608	+	0.634984i
$530$	−11.1683			−0.485118
$531$		0			0
$532$		0			0
$533$	2.64764	+	4.58584i	0.114682	+	0.198635i
$534$		0			0
$535$	−1.80291	+	3.12273i	−0.0779466	+	0.135007i
$536$	−11.2040	+	19.4058i	−0.483937	+	0.838204i
$537$		0			0
$538$	−12.0906	−	20.9415i	−0.521262	−	0.902852i
$539$		0			0
$540$		0			0
$541$	9.86535			0.424145			0.212072	−	0.977254i	$-0.431979\pi$
$541$	9.86535			0.424145			0.212072	+	0.977254i	$0.431979\pi$
$542$	4.58793	+	7.94652i	0.197068	+	0.341332i
$543$		0			0
$544$	17.8173	−	30.8604i	0.763909	−	1.32313i
$545$	6.10570	−	10.5754i	0.261539	−	0.453000i
$546$		0			0
$547$	−0.284350	−	0.492509i	−0.0121579	−	0.0210582i	0.859882	−	0.510492i	$-0.170537\pi$
$547$	−0.284350	−	0.492509i	−0.0121579	−	0.0210582i	−0.872040	+	0.489434i	$0.837203\pi$
$548$	−12.4720			−0.532778
$549$		0			0
$550$	−4.09888			−0.174777
$551$	−12.2173	−	21.1609i	−0.520473	−	0.901487i
$552$		0			0
$553$		0			0
$554$	−6.51485	+	11.2841i	−0.276789	+	0.479413i
$555$		0			0
$556$	−3.91269	−	6.77698i	−0.165935	−	0.287408i
$557$	2.58699			0.109614			0.0548071	−	0.998497i	$-0.482546\pi$
$557$	2.58699			0.109614			0.0548071	+	0.998497i	$0.482546\pi$
$558$		0			0
$559$	−35.0760			−1.48356
$560$		0			0
$561$		0			0
$562$	−19.2589	+	33.3574i	−0.812388	+	1.40710i
$563$	−16.6416	+	28.8240i	−0.701358	+	1.21479i	0.266632	+	0.963798i	$0.414089\pi$
$563$	−16.6416	+	28.8240i	−0.701358	+	1.21479i	−0.967990	+	0.250989i	$0.919244\pi$
$564$		0			0
$565$	4.28171	+	7.41613i	0.180133	+	0.311999i
$566$	−54.1318			−2.27533
$567$		0			0
$568$	8.12227			0.340803
$569$	−2.67673	−	4.63623i	−0.112214	−	0.194361i	0.804448	−	0.594022i	$-0.202461\pi$
$569$	−2.67673	−	4.63623i	−0.112214	−	0.194361i	−0.916663	+	0.399662i	$0.869128\pi$
$570$		0			0
$571$	−2.45056	+	4.24449i	−0.102553	+	0.177626i	−0.912736	−	0.408551i	$-0.866034\pi$
$571$	−2.45056	+	4.24449i	−0.102553	+	0.177626i	0.810183	+	0.586177i	$0.199368\pi$
$572$	1.31241	−	2.27316i	0.0548747	−	0.0950457i
$573$		0			0
$574$		0			0
$575$	10.1533			0.423424
$576$		0			0
$577$	−36.0757			−1.50185			−0.750925	−	0.660387i	$-0.770392\pi$
$577$	−36.0757			−1.50185			−0.750925	+	0.660387i	$0.770392\pi$
$578$	−34.4116	−	59.6026i	−1.43133	−	2.47914i
$579$		0			0
$580$	2.31038	−	4.00170i	0.0959333	−	0.166161i
$581$		0			0
$582$		0			0
$583$	2.03637	+	3.52710i	0.0843380	+	0.146078i
$584$	−8.42607			−0.348673
$585$		0			0
$586$	−46.7289			−1.93035
$587$	0.527445	+	0.913562i	0.0217700	+	0.0377068i	0.876705	−	0.481028i	$-0.159737\pi$
$587$	0.527445	+	0.913562i	0.0217700	+	0.0377068i	−0.854935	+	0.518735i	$0.826403\pi$
$588$		0			0
$589$	−13.5501	+	23.4695i	−0.558323	+	0.967045i
$590$	8.41411	−	14.5737i	0.346403	−	0.599988i
$591$		0			0
$592$	−17.4258	−	30.1824i	−0.716196	−	1.24049i
$593$	15.0710			0.618890			0.309445	−	0.950917i	$-0.399857\pi$
$593$	15.0710			0.618890			0.309445	+	0.950917i	$0.399857\pi$
$594$		0			0
$595$		0			0
$596$	−1.94004	−	3.36024i	−0.0794670	−	0.137641i
$597$		0			0
$598$	−10.5669	+	18.3024i	−0.432114	+	0.748443i
$599$	21.0283	−	36.4221i	0.859194	−	1.48817i	−0.0135047	−	0.999909i	$-0.504299\pi$
$599$	21.0283	−	36.4221i	0.859194	−	1.48817i	0.872699	−	0.488259i	$-0.162368\pi$
$600$		0			0
$601$	−9.44989	−	16.3677i	−0.385469	−	0.667652i	0.606365	−	0.795186i	$-0.292627\pi$
$601$	−9.44989	−	16.3677i	−0.385469	−	0.667652i	−0.991834	+	0.127534i	$0.959294\pi$
$602$		0			0
$603$		0			0
$604$	−11.2459			−0.457590
$605$	5.05669	+	8.75844i	0.205583	+	0.356081i
$606$		0			0
$607$	14.7213	−	25.4980i	0.597518	−	1.03493i	−0.395668	−	0.918393i	$-0.629487\pi$
$607$	14.7213	−	25.4980i	0.597518	−	1.03493i	0.993186	−	0.116538i	$-0.0371796\pi$
$608$	−10.4830	+	18.1572i	−0.425143	+	0.736370i
$609$		0			0
$610$	−9.40043	−	16.2820i	−0.380612	−	0.659240i
$611$	−37.5316			−1.51836
$612$		0			0
$613$	−11.6676			−0.471249			−0.235625	−	0.971844i	$-0.575714\pi$
$613$	−11.6676			−0.471249			−0.235625	+	0.971844i	$0.575714\pi$
$614$	−12.5922	−	21.8103i	−0.508179	−	0.880191i
$615$		0			0
$616$		0			0
$617$	−16.4054	+	28.4151i	−0.660458	+	1.14395i	0.320037	+	0.947405i	$0.396305\pi$
$617$	−16.4054	+	28.4151i	−0.660458	+	1.14395i	−0.980495	+	0.196542i	$0.937029\pi$
$618$		0			0
$619$	12.0806	+	20.9242i	0.485560	+	0.841014i	0.999862	−	0.0165947i	$-0.00528250\pi$
$619$	12.0806	+	20.9242i	0.485560	+	0.841014i	−0.514303	+	0.857609i	$0.671949\pi$
$620$	−5.12487			−0.205820
$621$		0			0
$622$	−49.3972			−1.98065
$623$		0			0
$624$		0			0
$625$	−6.14764	+	10.6480i	−0.245906	+	0.425921i
$626$	20.8018	−	36.0297i	0.831406	−	1.44004i
$627$		0			0
$628$	−5.00975	−	8.67714i	−0.199911	−	0.346256i
$629$	−52.9830			−2.11257
$630$		0			0
$631$	−11.1003			−0.441894			−0.220947	−	0.975286i	$-0.570915\pi$
$631$	−11.1003			−0.441894			−0.220947	+	0.975286i	$0.570915\pi$
$632$	−1.25959	−	2.18168i	−0.0501038	−	0.0867824i
$633$		0			0
$634$	−6.27747	+	10.8729i	−0.249310	+	0.431818i
$635$	−3.05318	+	5.28826i	−0.121162	+	0.209858i
$636$		0			0
$637$		0			0
$638$	−5.47710			−0.216840
$639$		0			0
$640$	12.1293			0.479452
$641$	3.65019	+	6.32231i	0.144174	+	0.249716i	0.929064	−	0.369918i	$-0.120614\pi$
$641$	3.65019	+	6.32231i	0.144174	+	0.249716i	−0.784891	+	0.619634i	$0.787281\pi$
$642$		0			0
$643$	−10.6256	+	18.4041i	−0.419033	+	0.725787i	−0.995842	−	0.0910922i	$-0.970964\pi$
$643$	−10.6256	+	18.4041i	−0.419033	+	0.725787i	0.576809	+	0.816879i	$0.304298\pi$
$644$		0			0
$645$		0			0
$646$	28.7465	+	49.7904i	1.13102	+	1.95898i
$647$	−16.9460			−0.666216			−0.333108	−	0.942889i	$-0.608097\pi$
$647$	−16.9460			−0.666216			−0.333108	+	0.942889i	$0.608097\pi$
$648$		0			0
$649$	−6.13677			−0.240889
$650$	−17.4852	−	30.2853i	−0.685826	−	1.18789i
$651$		0			0
$652$	0.740409	−	1.28243i	0.0289967	−	0.0502237i
$653$	−1.86652	+	3.23292i	−0.0730427	+	0.126514i	−0.900233	−	0.435408i	$-0.856604\pi$
$653$	−1.86652	+	3.23292i	−0.0730427	+	0.126514i	0.827191	+	0.561921i	$0.189938\pi$
$654$		0			0
$655$	3.14833	+	5.45306i	0.123015	+	0.213069i
$656$	−5.26140			−0.205423
$657$		0			0
$658$		0			0
$659$	−11.7992	−	20.4368i	−0.459632	−	0.796105i	0.539310	−	0.842107i	$-0.318685\pi$
$659$	−11.7992	−	20.4368i	−0.459632	−	0.796105i	−0.998941	+	0.0460022i	$0.985352\pi$
$660$		0			0
$661$	−17.2588	+	29.8930i	−0.671288	+	1.16270i	0.306252	+	0.951951i	$0.400925\pi$
$661$	−17.2588	+	29.8930i	−0.671288	+	1.16270i	−0.977539	+	0.210754i	$0.932408\pi$
$662$	−17.0488	+	29.5293i	−0.662619	+	1.14769i
$663$		0			0
$664$	5.36767	+	9.29708i	0.208306	+	0.360796i
$665$		0			0
$666$		0			0
$667$	13.5673			0.525329
$668$	1.73424	+	3.00379i	0.0670996	+	0.116220i
$669$		0			0
$670$	9.57072	−	16.5770i	0.369749	−	0.640424i
$671$	−3.42807	+	5.93759i	−0.132339	+	0.229218i
$672$		0			0
$673$	12.2287	+	21.1808i	0.471382	+	0.816458i	0.999464	−	0.0327353i	$-0.0104218\pi$
$673$	12.2287	+	21.1808i	0.471382	+	0.816458i	−0.528082	+	0.849194i	$0.677088\pi$
$674$	10.8887			0.419418
$675$		0			0
$676$	10.8406			0.416946
$677$	−4.16022	−	7.20572i	−0.159890	−	0.276938i	0.774939	−	0.632037i	$-0.217781\pi$
$677$	−4.16022	−	7.20572i	−0.159890	−	0.276938i	−0.934829	+	0.355098i	$0.884447\pi$
$678$		0			0
$679$		0			0
$680$	6.79734	−	11.7733i	0.260666	−	0.451487i
$681$		0			0
$682$	3.03731	+	5.26078i	0.116305	+	0.201446i
$683$	42.4624			1.62478			0.812389	−	0.583116i	$-0.198167\pi$
$683$	42.4624			1.62478			0.812389	+	0.583116i	$0.198167\pi$
$684$		0			0
$685$	−13.3215			−0.508989
$686$		0			0
$687$		0			0
$688$	17.4258	−	30.1824i	0.664352	−	1.15069i
$689$	−17.3737	+	30.0921i	−0.661885	+	1.14642i
$690$		0			0
$691$	−17.6964	−	30.6511i	−0.673204	−	1.16602i	−0.976990	−	0.213284i	$-0.931584\pi$
$691$	−17.6964	−	30.6511i	−0.673204	−	1.16602i	0.303786	−	0.952740i	$-0.401749\pi$
$692$	−14.3212			−0.544410
$693$		0			0
$694$	49.6167			1.88342
$695$	−4.17920	−	7.23859i	−0.158526	−	0.274575i
$696$		0			0
$697$	−3.99931	+	6.92701i	−0.151485	+	0.262379i
$698$	3.69146	−	6.39380i	0.139724	−	0.242009i
$699$		0			0
$700$		0			0
$701$	7.00372			0.264527			0.132263	−	0.991215i	$-0.457776\pi$
$701$	7.00372			0.264527			0.132263	+	0.991215i	$0.457776\pi$
$702$		0			0
$703$	31.1733			1.17572
$704$	−0.584722	−	1.01277i	−0.0220375	−	0.0381701i
$705$		0			0
$706$	21.8408	−	37.8294i	0.821989	−	1.42373i
$707$		0			0
$708$		0			0
$709$	1.11126	+	1.92477i	0.0417344	+	0.0722861i	0.886138	−	0.463421i	$-0.153378\pi$
$709$	1.11126	+	1.92477i	0.0417344	+	0.0722861i	−0.844404	+	0.535707i	$0.820045\pi$
$710$	−6.93825			−0.260388
$711$		0			0
$712$	1.59343			0.0597165
$713$	−7.52373	−	13.0315i	−0.281766	−	0.488033i
$714$		0			0
$715$	1.40180	−	2.42800i	0.0524245	−	0.0908019i
$716$	6.34913	−	10.9970i	0.237278	−	0.410977i
$717$		0			0
$718$	17.5803	+	30.4500i	0.656092	+	1.13638i
$719$	−26.0175			−0.970291			−0.485145	−	0.874434i	$-0.661233\pi$
$719$	−26.0175			−0.970291			−0.485145	+	0.874434i	$0.661233\pi$
$720$		0			0
$721$		0			0
$722$	−0.766951	−	1.32840i	−0.0285430	−	0.0494379i
$723$		0			0
$724$	−5.72670	+	9.91893i	−0.212831	+	0.368634i
$725$	−11.2250	+	19.4423i	−0.416886	+	0.722068i
$726$		0			0
$727$	0.685875	+	1.18797i	0.0254377	+	0.0440594i	0.878464	−	0.477809i	$-0.158569\pi$
$727$	0.685875	+	1.18797i	0.0254377	+	0.0440594i	−0.853026	+	0.521868i	$0.825235\pi$
$728$		0			0
$729$		0			0
$730$	7.19777			0.266401
$731$	−26.4915	−	45.8847i	−0.979824	−	1.69711i
$732$		0			0
$733$	0.400087	−	0.692971i	0.0147776	−	0.0255955i	−0.858542	−	0.512743i	$-0.828629\pi$
$733$	0.400087	−	0.692971i	0.0147776	−	0.0255955i	0.873320	+	0.487148i	$0.161963\pi$
$734$	2.42011	−	4.19176i	0.0893280	−	0.154721i
$735$		0			0
$736$	−5.82072	−	10.0818i	−0.214555	−	0.371620i
$737$	−6.98034			−0.257124
$738$		0			0
$739$	5.37093			0.197573			0.0987865	−	0.995109i	$-0.468504\pi$
$739$	5.37093			0.197573			0.0987865	+	0.995109i	$0.468504\pi$
$740$	2.94756	+	5.10532i	0.108354	+	0.187675i
$741$		0			0
$742$		0			0
$743$	−6.63162	+	11.4863i	−0.243290	+	0.421391i	−0.961650	−	0.274281i	$-0.911560\pi$
$743$	−6.63162	+	11.4863i	−0.243290	+	0.421391i	0.718359	+	0.695672i	$0.244893\pi$
$744$		0			0
$745$	−2.07218	−	3.58912i	−0.0759188	−	0.131495i
$746$	36.4276			1.33371
$747$		0			0
$748$	3.96485			0.144969
$749$		0			0
$750$		0			0
$751$	−2.77816	+	4.81191i	−0.101377	+	0.175589i	−0.912252	−	0.409629i	$-0.865658\pi$
$751$	−2.77816	+	4.81191i	−0.101377	+	0.175589i	0.810875	+	0.585219i	$0.198991\pi$
$752$	18.6457	−	32.2953i	0.679939	−	1.17769i
$753$		0			0
$754$	−23.3645	−	40.4684i	−0.850883	−	1.47377i
$755$	−12.0119			−0.437158
$756$		0			0
$757$	−13.3942			−0.486819			−0.243410	−	0.969924i	$-0.578266\pi$
$757$	−13.3942			−0.486819			−0.243410	+	0.969924i	$0.578266\pi$
$758$	−22.9869	−	39.8145i	−0.834923	−	1.44613i
$759$		0			0
$760$	−3.99931	+	6.92701i	−0.145070	+	0.251269i
$761$	−6.42191	+	11.1231i	−0.232794	+	0.403211i	−0.958629	−	0.284658i	$-0.908120\pi$
$761$	−6.42191	+	11.1231i	−0.232794	+	0.403211i	0.725835	+	0.687868i	$0.241453\pi$
$762$		0			0
$763$		0			0
$764$	1.92353			0.0695910
$765$		0			0
$766$	24.5202			0.885951
$767$	−26.1785	−	45.3425i	−0.945251	−	1.63722i
$768$		0			0
$769$	−1.48259	+	2.56793i	−0.0534636	+	0.0926018i	−0.891519	−	0.452984i	$-0.850359\pi$
$769$	−1.48259	+	2.56793i	−0.0534636	+	0.0926018i	0.838055	+	0.545586i	$0.183693\pi$
$770$		0			0
$771$		0			0
$772$	−4.63533	−	8.02864i	−0.166829	−	0.288957i
$773$	19.2788			0.693409			0.346705	−	0.937974i	$-0.387301\pi$
$773$	19.2788			0.693409			0.346705	+	0.937974i	$0.387301\pi$
$774$		0			0
$775$	24.8992			0.894406
$776$	−3.21683	−	5.57171i	−0.115477	−	0.200013i
$777$		0			0
$778$	−5.19028	+	8.98983i	−0.186080	+	0.322301i
$779$	2.35305	−	4.07560i	0.0843068	−	0.146024i
$780$		0			0
$781$	1.26509	+	2.19120i	0.0452685	+	0.0784074i
$782$	−31.9231			−1.14157
$783$		0			0
$784$		0			0
$785$	−5.35098	−	9.26818i	−0.190985	−	0.330795i
$786$		0			0
$787$	−6.82265	+	11.8172i	−0.243201	+	0.421237i	−0.961624	−	0.274370i	$-0.911531\pi$
$787$	−6.82265	+	11.8172i	−0.243201	+	0.421237i	0.718423	+	0.695606i	$0.244864\pi$
$788$	−8.34734	+	14.4580i	−0.297362	+	0.515046i
$789$		0			0
$790$	1.07598	+	1.86364i	0.0382815	+	0.0663055i
$791$		0			0
$792$		0			0
$793$	−58.4944			−2.07720
$794$	10.9518	+	18.9691i	0.388665	+	0.673187i
$795$		0			0
$796$	−3.74427	+	6.48527i	−0.132712	+	0.229864i
$797$	−11.4792	+	19.8826i	−0.406616	+	0.704279i	−0.994508	−	0.104660i	$-0.966625\pi$
$797$	−11.4792	+	19.8826i	−0.406616	+	0.704279i	0.587892	+	0.808939i	$0.299958\pi$
$798$		0			0
$799$	−28.3461	−	49.0969i	−1.00281	−	1.73692i
$800$	19.2632			0.681058
$801$		0			0
$802$	−14.2609			−0.503570
$803$	−1.31241	−	2.27316i	−0.0463140	−	0.0802182i
$804$		0			0
$805$		0			0
$806$	−25.9134	+	44.8834i	−0.912761	+	1.58095i
$807$		0			0
$808$	9.05326	+	15.6807i	0.318492	+	0.551645i
$809$	−39.4582			−1.38728			−0.693639	−	0.720323i	$-0.743994\pi$
$809$	−39.4582			−1.38728			−0.693639	+	0.720323i	$0.743994\pi$
$810$		0			0
$811$	−0.496374			−0.0174300			−0.00871502	−	0.999962i	$-0.502774\pi$
$811$	−0.496374			−0.0174300			−0.00871502	+	0.999962i	$0.502774\pi$
$812$		0			0
$813$		0			0
$814$	3.49381	−	6.05146i	0.122458	−	0.212103i
$815$	0.790841	−	1.36978i	0.0277020	−	0.0479812i
$816$		0			0
$817$	15.5867	+	26.9969i	0.545308	+	0.944501i
$818$	11.5790			0.404850
$819$		0			0
$820$	0.889960			0.0310788
$821$	23.5519	+	40.7931i	0.821967	+	1.42369i	0.904215	+	0.427077i	$0.140457\pi$
$821$	23.5519	+	40.7931i	0.821967	+	1.42369i	−0.0822476	+	0.996612i	$0.526210\pi$
$822$		0			0
$823$	1.09888	−	1.90332i	0.0383047	−	0.0663457i	−0.846237	−	0.532806i	$-0.821138\pi$
$823$	1.09888	−	1.90332i	0.0383047	−	0.0663457i	0.884542	+	0.466460i	$0.154471\pi$
$824$	−11.0046	+	19.0605i	−0.383364	+	0.664005i
$825$		0			0
$826$		0			0
$827$	55.3360			1.92422			0.962110	−	0.272661i	$-0.0879036\pi$
$827$	55.3360			1.92422			0.962110	+	0.272661i	$0.0879036\pi$
$828$		0			0
$829$	−20.3206			−0.705764			−0.352882	−	0.935668i	$-0.614798\pi$
$829$	−20.3206			−0.705764			−0.352882	+	0.935668i	$0.614798\pi$
$830$	−4.58520	−	7.94181i	−0.159155	−	0.275664i
$831$		0			0
$832$	4.98867	−	8.64062i	0.172951	−	0.299560i
$833$		0			0
$834$		0			0
$835$	1.85236	+	3.20839i	0.0641036	+	0.111031i
$836$	−2.33277			−0.0806806
$837$		0			0
$838$	17.5480			0.606186
$839$	12.2760	+	21.2626i	0.423813	+	0.734066i	0.996309	−	0.0858417i	$-0.0273579\pi$
$839$	12.2760	+	21.2626i	0.423813	+	0.734066i	−0.572496	+	0.819908i	$0.694025\pi$
$840$		0			0
$841$	−0.499311	+	0.864833i	−0.0172176	+	0.0298218i
$842$	−2.66504	+	4.61598i	−0.0918432	+	0.159077i
$843$		0			0
$844$	−4.98693	−	8.63762i	−0.171657	−	0.297319i
$845$	11.5790			0.398329
$846$		0			0
$847$		0			0
$848$	−17.2625	−	29.8996i	−0.592798	−	1.02676i
$849$		0			0
$850$	26.4118	−	45.7465i	0.905916	−	1.56909i
$851$	−8.65452	+	14.9901i	−0.296673	+	0.513853i
$852$		0			0
$853$	−26.7708	−	46.3684i	−0.916614	−	1.58762i	−0.804521	−	0.593925i	$-0.797578\pi$
$853$	−26.7708	−	46.3684i	−0.916614	−	1.58762i	−0.112093	−	0.993698i	$-0.535756\pi$
$854$		0			0
$855$		0			0
$856$	−7.17439			−0.245215
$857$	27.0777	+	46.8999i	0.924955	+	1.60207i	0.791633	+	0.610996i	$0.209231\pi$
$857$	27.0777	+	46.8999i	0.924955	+	1.60207i	0.133322	+	0.991073i	$0.457436\pi$
$858$		0			0
$859$	0.896461	−	1.55272i	0.0305869	−	0.0529780i	−0.850327	−	0.526255i	$-0.823596\pi$
$859$	0.896461	−	1.55272i	0.0305869	−	0.0529780i	0.880914	+	0.473277i	$0.156929\pi$
$860$	−2.94756	+	5.10532i	−0.100511	+	0.174090i
$861$		0			0
$862$	27.0858	+	46.9140i	0.922547	+	1.59790i
$863$	32.5709			1.10873			0.554363	−	0.832275i	$-0.312962\pi$
$863$	32.5709			1.10873			0.554363	+	0.832275i	$0.312962\pi$
$864$		0			0
$865$	−15.2967			−0.520102
$866$	−6.36387	−	11.0226i	−0.216253	−	0.374562i
$867$		0			0
$868$		0			0
$869$	0.392378	−	0.679618i	0.0133105	−	0.0230545i
$870$		0			0
$871$	−29.7770	−	51.5753i	−1.00896	−	1.74756i
$872$	24.2967			0.822789
$873$		0			0
$874$	18.7824			0.635324
$875$		0			0
$876$		0			0
$877$	18.3647	−	31.8085i	0.620131	−	1.07410i	−0.369330	−	0.929298i	$-0.620413\pi$
$877$	18.3647	−	31.8085i	0.620131	−	1.07410i	0.989461	−	0.144800i	$-0.0462538\pi$
$878$	−1.94548	+	3.36966i	−0.0656566	+	0.113721i
$879$		0			0
$880$	1.39284	+	2.41246i	0.0469525	+	0.0813241i
$881$	25.3721			0.854807			0.427403	−	0.904061i	$-0.359428\pi$
$881$	25.3721			0.854807			0.427403	+	0.904061i	$0.359428\pi$
$882$		0			0
$883$	−16.9381			−0.570012			−0.285006	−	0.958526i	$-0.591996\pi$
$883$	−16.9381			−0.570012			−0.285006	+	0.958526i	$0.591996\pi$
$884$	16.9134	+	29.2949i	0.568860	+	0.985294i
$885$		0			0
$886$	31.7403	−	54.9759i	1.06634	−	1.84695i
$887$	24.0069	−	41.5811i	0.806071	−	1.39616i	−0.109494	−	0.993987i	$-0.534923\pi$
$887$	24.0069	−	41.5811i	0.806071	−	1.39616i	0.915566	−	0.402169i	$-0.131744\pi$
$888$		0			0
$889$		0			0
$890$	−1.36115			−0.0456260
$891$		0			0
$892$	−18.4456			−0.617603
$893$	16.6778	+	28.8868i	0.558102	+	0.966661i
$894$		0			0
$895$	6.78159	−	11.7461i	0.226684	−	0.392627i
$896$		0			0
$897$		0			0
$898$	−5.27128	−	9.13013i	−0.175905	−	0.304676i
$899$	33.2713			1.10966
$900$		0			0
$901$	−52.4867			−1.74858
$902$	−0.527445	−	0.913562i	−0.0175620	−	0.0304183i
$903$		0			0
$904$	−8.51918	+	14.7557i	−0.283344	+	0.490766i
$905$	−6.11677	+	10.5945i	−0.203328	+	0.352175i
$906$		0			0
$907$	12.3887	+	21.4579i	0.411361	+	0.712499i	0.995039	−	0.0994869i	$-0.0317201\pi$
$907$	12.3887	+	21.4579i	0.411361	+	0.712499i	−0.583678	+	0.811985i	$0.698387\pi$
$908$	9.26972			0.307626
$909$		0			0
$910$		0			0
$911$	15.7916	+	27.3519i	0.523200	+	0.906209i	0.999635	+	0.0269997i	$0.00859533\pi$
$911$	15.7916	+	27.3519i	0.523200	+	0.906209i	−0.476435	+	0.879210i	$0.658071\pi$
$912$		0			0
$913$	−1.67209	+	2.89615i	−0.0553382	+	0.0958486i
$914$	−17.1421	+	29.6911i	−0.567011	+	0.982093i
$915$		0			0
$916$	−6.69183	−	11.5906i	−0.221104	−	0.382964i
$917$		0			0
$918$		0			0
$919$	1.59208			0.0525180			0.0262590	−	0.999655i	$-0.491641\pi$
$919$	1.59208			0.0525180			0.0262590	+	0.999655i	$0.491641\pi$
$920$	−2.22062	−	3.84623i	−0.0732118	−	0.126807i
$921$		0			0
$922$	−19.1514	+	33.1712i	−0.630718	+	1.09244i
$923$	−10.7934	+	18.6947i	−0.355268	+	0.615342i
$924$		0			0
$925$	−14.3207	−	24.8042i	−0.470863	−	0.815558i
$926$	−46.9591			−1.54317
$927$		0			0
$928$	25.7403			0.844968
$929$	13.5356	+	23.4443i	0.444087	+	0.769182i	0.997988	−	0.0634007i	$-0.0201946\pi$
$929$	13.5356	+	23.4443i	0.444087	+	0.769182i	−0.553901	+	0.832583i	$0.686861\pi$
$930$		0			0
$931$		0			0
$932$	1.94939	−	3.37644i	0.0638543	−	0.110599i
$933$		0			0
$934$	17.1003	+	29.6186i	0.559540	+	0.969151i
$935$	4.23491			0.138496
$936$		0			0
$937$	32.6624			1.06704			0.533518	−	0.845789i	$-0.320870\pi$
$937$	32.6624			1.06704			0.533518	+	0.845789i	$0.320870\pi$
$938$		0			0
$939$		0			0
$940$	−3.15390	+	5.46272i	−0.102869	+	0.178174i
$941$	2.36143	−	4.09011i	0.0769803	−	0.133334i	−0.824965	−	0.565183i	$-0.808805\pi$
$941$	2.36143	−	4.09011i	0.0769803	−	0.133334i	0.901946	+	0.431849i	$0.142139\pi$
$942$		0			0
$943$	1.30654	+	2.26299i	0.0425466	+	0.0736929i
$944$	52.0220			1.69317
$945$		0			0
$946$	6.98762			0.227187
$947$	28.3905	+	49.1738i	0.922568	+	1.59793i	0.795427	+	0.606050i	$0.207247\pi$
$947$	28.3905	+	49.1738i	0.922568	+	1.59793i	0.127141	+	0.991885i	$0.459420\pi$
$948$		0			0
$949$	11.1971	−	19.3939i	0.363473	−	0.629553i
$950$	−15.5397	+	26.9156i	−0.504175	+	0.873257i
$951$		0			0
$952$		0			0
$953$	47.1693			1.52796			0.763982	−	0.645238i	$-0.223242\pi$
$953$	47.1693			1.52796			0.763982	+	0.645238i	$0.223242\pi$
$954$		0			0
$955$	2.05455			0.0664838
$956$	−4.24426	−	7.35127i	−0.137269	−	0.237757i
$957$		0			0
$958$	−8.14681	+	14.1107i	−0.263211	+	0.455896i
$959$		0			0
$960$		0			0
$961$	−2.95056	−	5.11052i	−0.0951793	−	0.164855i
$962$	59.6162			1.92210
$963$		0			0
$964$	9.36359			0.301581
$965$	−4.95107	−	8.57550i	−0.159380	−	0.276055i
$966$		0			0
$967$	−23.6985	+	41.0469i	−0.762091	+	1.31998i	0.179680	+	0.983725i	$0.442494\pi$
$967$	−23.6985	+	41.0469i	−0.762091	+	1.31998i	−0.941771	+	0.336255i	$0.890840\pi$
$968$	−10.0611	+	17.4264i	−0.323377	+	0.560106i
$969$		0			0
$970$	2.74790	+	4.75950i	0.0882297	+	0.152818i
$971$	−22.7473			−0.729994			−0.364997	−	0.931009i	$-0.618930\pi$
$971$	−22.7473			−0.729994			−0.364997	+	0.931009i	$0.618930\pi$
$972$		0			0
$973$		0			0
$974$	−11.1106	−	19.2441i	−0.356006	−	0.616620i
$975$		0			0
$976$	29.0601	−	50.3335i	0.930190	−	1.61114i
$977$	17.8425	−	30.9040i	0.570831	−	0.988708i	−0.425650	−	0.904888i	$-0.639955\pi$
$977$	17.8425	−	30.9040i	0.570831	−	0.988708i	0.996481	−	0.0838200i	$-0.0267121\pi$
$978$		0			0
$979$	0.248187	+	0.429872i	0.00793209	+	0.0137388i
$980$		0			0
$981$		0			0
$982$	−26.0741			−0.832059
$983$	12.0067	+	20.7962i	0.382954	+	0.663296i	0.991483	−	0.130236i	$-0.0415735\pi$
$983$	12.0067	+	20.7962i	0.382954	+	0.663296i	−0.608529	+	0.793532i	$0.708240\pi$
$984$		0			0
$985$	−8.91591	+	15.4428i	−0.284085	+	0.492049i
$986$	35.2925	−	61.1284i	1.12394	−	1.94672i
$987$		0			0
$988$	−9.95125	−	17.2361i	−0.316591	−	0.548352i
$989$	−17.3090			−0.550395
$990$		0			0
$991$	−44.4189			−1.41101			−0.705507	−	0.708703i	$-0.749281\pi$
$991$	−44.4189			−1.41101			−0.705507	+	0.708703i	$0.749281\pi$
$992$	−14.2742	−	24.7237i	−0.453208	−	0.784979i
$993$		0			0
$994$		0			0
$995$	−3.99931	+	6.92701i	−0.126787	+	0.219601i
$996$		0			0
$997$	−4.52336	−	7.83470i	−0.143256	−	0.248127i	0.785465	−	0.618906i	$-0.212424\pi$
$997$	−4.52336	−	7.83470i	−0.143256	−	0.248127i	−0.928721	+	0.370779i	$0.879091\pi$
$998$	8.26929			0.261760
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.f.g.442.1		12
3.2	odd	2		441.2.f.g.148.6	yes	12
7.2	even	3		1323.2.g.g.361.2		12
7.3	odd	6		1323.2.h.g.226.6		12
7.4	even	3		1323.2.h.g.226.5		12
7.5	odd	6		1323.2.g.g.361.1		12
7.6	odd	2	inner	1323.2.f.g.442.2		12
9.2	odd	6		441.2.f.g.295.6	yes	12
9.4	even	3		3969.2.a.bd.1.6		6
9.5	odd	6		3969.2.a.be.1.1		6
9.7	even	3	inner	1323.2.f.g.883.1		12
21.2	odd	6		441.2.g.g.67.5		12
21.5	even	6		441.2.g.g.67.6		12
21.11	odd	6		441.2.h.g.373.2		12
21.17	even	6		441.2.h.g.373.1		12
21.20	even	2		441.2.f.g.148.5	✓	12
63.2	odd	6		441.2.h.g.214.2		12
63.11	odd	6		441.2.g.g.79.5		12
63.13	odd	6		3969.2.a.bd.1.5		6
63.16	even	3		1323.2.h.g.802.5		12
63.20	even	6		441.2.f.g.295.5	yes	12
63.25	even	3		1323.2.g.g.667.2		12
63.34	odd	6	inner	1323.2.f.g.883.2		12
63.38	even	6		441.2.g.g.79.6		12
63.41	even	6		3969.2.a.be.1.2		6
63.47	even	6		441.2.h.g.214.1		12
63.52	odd	6		1323.2.g.g.667.1		12
63.61	odd	6		1323.2.h.g.802.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.g.148.5	✓	12	21.20	even	2
441.2.f.g.148.6	yes	12	3.2	odd	2
441.2.f.g.295.5	yes	12	63.20	even	6
441.2.f.g.295.6	yes	12	9.2	odd	6
441.2.g.g.67.5		12	21.2	odd	6
441.2.g.g.67.6		12	21.5	even	6
441.2.g.g.79.5		12	63.11	odd	6
441.2.g.g.79.6		12	63.38	even	6
441.2.h.g.214.1		12	63.47	even	6
441.2.h.g.214.2		12	63.2	odd	6
441.2.h.g.373.1		12	21.17	even	6
441.2.h.g.373.2		12	21.11	odd	6
1323.2.f.g.442.1		12	1.1	even	1	trivial
1323.2.f.g.442.2		12	7.6	odd	2	inner
1323.2.f.g.883.1		12	9.7	even	3	inner
1323.2.f.g.883.2		12	63.34	odd	6	inner
1323.2.g.g.361.1		12	7.5	odd	6
1323.2.g.g.361.2		12	7.2	even	3
1323.2.g.g.667.1		12	63.52	odd	6
1323.2.g.g.667.2		12	63.25	even	3
1323.2.h.g.226.5		12	7.4	even	3
1323.2.h.g.226.6		12	7.3	odd	6
1323.2.h.g.802.5		12	63.16	even	3
1323.2.h.g.802.6		12	63.61	odd	6
3969.2.a.bd.1.5		6	63.13	odd	6
3969.2.a.bd.1.6		6	9.4	even	3
3969.2.a.be.1.1		6	9.5	odd	6
3969.2.a.be.1.2		6	63.41	even	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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.849814 - 1.47192i) q^{2} +(-0.444368 + 0.769668i) q^{4} +(-0.474636 + 0.822093i) q^{5} -1.88874 q^{8} +O(q^{10})\)	\(q+(-0.849814 - 1.47192i) q^{2} +(-0.444368 + 0.769668i) q^{4} +(-0.474636 + 0.822093i) q^{5} -1.88874 q^{8} +1.61341 q^{10} +(-0.294182 - 0.509538i) q^{11} +(2.50987 - 4.34722i) q^{13} +(2.49381 + 4.31941i) q^{16} +7.58242 q^{17} -4.46122 q^{19} +(-0.421826 - 0.730623i) q^{20} +(-0.500000 + 0.866025i) q^{22} +(1.23855 - 2.14523i) q^{23} +(2.04944 + 3.54974i) q^{25} -8.53169 q^{26} +(2.73855 + 4.74331i) q^{29} +(3.03731 - 5.26078i) q^{31} +(2.34981 - 4.07000i) q^{32} +(-6.44364 - 11.1607i) q^{34} -6.98762 q^{37} +(3.79121 + 6.56657i) q^{38} +(0.896461 - 1.55272i) q^{40} +(-0.527445 + 0.913562i) q^{41} +(-3.49381 - 6.05146i) q^{43} +0.522900 q^{44} -4.21015 q^{46} +(-3.73840 - 6.47510i) q^{47} +(3.48329 - 6.03323i) q^{50} +(2.23061 + 3.86353i) q^{52} -6.92216 q^{53} +0.558517 q^{55} +(4.65452 - 8.06186i) q^{58} +(5.21512 - 9.03284i) q^{59} +(-5.82644 - 10.0917i) q^{61} -10.3246 q^{62} +1.98762 q^{64} +(2.38255 + 4.12669i) q^{65} +(5.93199 - 10.2745i) q^{67} +(-3.36938 + 5.83594i) q^{68} -4.30037 q^{71} +4.46122 q^{73} +(5.93818 + 10.2852i) q^{74} +(1.98242 - 3.43366i) q^{76} +(0.666896 + 1.15510i) q^{79} -4.73460 q^{80} +1.79292 q^{82} +(-2.84194 - 4.92238i) q^{83} +(-3.59888 + 6.23345i) q^{85} +(-5.93818 + 10.2852i) q^{86} +(0.555632 + 0.962383i) q^{88} -0.843651 q^{89} +(1.10074 + 1.90654i) q^{92} +(-6.35389 + 11.0053i) q^{94} +(2.11745 - 3.66754i) q^{95} +(1.70317 + 2.94997i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 6 q^{4} - 24 q^{8}+O(q^{10}) \) 12 * q + 2 * q^2 - 6 * q^4 - 24 * q^8	\( 12 q + 2 q^{2} - 6 q^{4} - 24 q^{8} + 8 q^{11} - 6 q^{16} - 6 q^{22} + 4 q^{23} - 12 q^{25} + 22 q^{29} + 16 q^{32} - 12 q^{37} - 6 q^{43} + 28 q^{44} + 24 q^{46} + 56 q^{50} - 56 q^{53} - 18 q^{58} - 48 q^{64} - 6 q^{65} - 76 q^{71} + 36 q^{74} + 6 q^{79} + 30 q^{85} - 36 q^{86} + 6 q^{88} + 62 q^{92} + 60 q^{95}+O(q^{100}) \) 12 * q + 2 * q^2 - 6 * q^4 - 24 * q^8 + 8 * q^11 - 6 * q^16 - 6 * q^22 + 4 * q^23 - 12 * q^25 + 22 * q^29 + 16 * q^32 - 12 * q^37 - 6 * q^43 + 28 * q^44 + 24 * q^46 + 56 * q^50 - 56 * q^53 - 18 * q^58 - 48 * q^64 - 6 * q^65 - 76 * q^71 + 36 * q^74 + 6 * q^79 + 30 * q^85 - 36 * q^86 + 6 * q^88 + 62 * q^92 + 60 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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