LMFDB - Embedded newform 1323.2.s.c.656.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(656,1323)]

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([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("1323.656");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.s (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:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			656.4
Root			$-0.474636 - 0.274031i$ of defining polynomial
Character	$\chi$	$=$	1323.656
Dual form			1323.2.s.c.962.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.555632 + 0.320794i) q^{2} +(-0.794182 + 1.37556i) q^{4} +2.21105 q^{5} -2.30225i q^{8} +O(q^{10})$	\(q+(-0.555632 + 0.320794i) q^{2} +(-0.794182 + 1.37556i) q^{4} +2.21105 q^{5} -2.30225i q^{8} +(-1.22853 + 0.709292i) q^{10} -3.39272i q^{11} +(-1.56060 + 0.901012i) q^{13} +(-0.849814 - 1.47192i) q^{16} +(-2.98450 - 5.16931i) q^{17} +(-1.42391 - 0.822093i) q^{19} +(-1.75597 + 3.04144i) q^{20} +(1.08836 + 1.88510i) q^{22} -2.37364i q^{23} -0.111264 q^{25} +(0.578079 - 1.00126i) q^{26} +(-2.44437 - 1.41126i) q^{29} +(-9.28558 - 5.36103i) q^{31} +(4.93199 + 2.84748i) q^{32} +(3.31657 + 1.91482i) q^{34} +(-0.849814 + 1.47192i) q^{37} +1.05489 q^{38} -5.09039i q^{40} +(0.455074 + 0.788211i) q^{41} +(-1.96108 + 3.39669i) q^{43} +(4.66690 + 2.69443i) q^{44} +(0.761450 + 1.31887i) q^{46} +(-0.123005 - 0.213051i) q^{47} +(0.0618219 - 0.0356929i) q^{50} -2.86227i q^{52} +(-6.82072 + 3.93795i) q^{53} -7.50146i q^{55} +1.81089 q^{58} +(5.39093 - 9.33736i) q^{59} +(-1.22853 + 0.709292i) q^{61} +6.87916 q^{62} -0.254572 q^{64} +(-3.45056 + 1.99218i) q^{65} +(3.99381 - 6.91748i) q^{67} +9.48096 q^{68} +12.1743i q^{71} +(-0.369016 + 0.213051i) q^{73} -1.09046i q^{74} +(2.26168 - 1.30578i) q^{76} +(2.49381 + 4.31941i) q^{79} +(-1.87898 - 3.25449i) q^{80} +(-0.505707 - 0.291970i) q^{82} +(4.28541 - 7.42254i) q^{83} +(-6.59888 - 11.4296i) q^{85} -2.51641i q^{86} -7.81089 q^{88} +(5.26792 - 9.12431i) q^{89} +(3.26509 + 1.88510i) q^{92} +(0.136691 + 0.0789188i) q^{94} +(-3.14833 - 1.81769i) q^{95} +(-6.30108 - 3.63793i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} + 2 q^{4}+O(q^{10}) $ 12 * q - 6 * q^2 + 2 * q^4	$ 12 q - 6 q^{2} + 2 q^{4} + 2 q^{16} - 10 q^{22} - 30 q^{29} - 12 q^{32} + 2 q^{37} - 10 q^{43} + 54 q^{44} + 20 q^{46} + 36 q^{50} - 12 q^{53} - 4 q^{58} + 16 q^{64} - 78 q^{65} + 12 q^{67} - 6 q^{79} - 6 q^{85} - 68 q^{88} - 30 q^{92} + 72 q^{95}+O(q^{100}) $ 12 * q - 6 * q^2 + 2 * q^4 + 2 * q^16 - 10 * q^22 - 30 * q^29 - 12 * q^32 + 2 * q^37 - 10 * q^43 + 54 * q^44 + 20 * q^46 + 36 * q^50 - 12 * q^53 - 4 * q^58 + 16 * q^64 - 78 * q^65 + 12 * q^67 - 6 * q^79 - 6 * q^85 - 68 * q^88 - 30 * q^92 + 72 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.555632	+	0.320794i	−0.392891	+	0.226836i	−0.683412	−	0.730033i	$-0.739505\pi$
$2$	−0.555632	+	0.320794i	−0.392891	+	0.226836i	0.290521	+	0.956869i	$0.406171\pi$
$3$		0			0
$3$		0			0
$4$	−0.794182	+	1.37556i	−0.397091	+	0.687782i
$5$	2.21105			0.988811			0.494405	−	0.869231i	$-0.335386\pi$
$5$	2.21105			0.988811			0.494405	+	0.869231i	$0.335386\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	2.30225i		−	0.813970i
$9$		0			0
$10$	−1.22853	+	0.709292i	−0.388495	+	0.224298i
$11$		−	3.39272i		−	1.02294i	−0.859300	−	0.511471i	$-0.829101\pi$
$11$		−	3.39272i		−	1.02294i	0.859300	−	0.511471i	$-0.170899\pi$
$12$		0			0
$13$	−1.56060	+	0.901012i	−0.432832	+	0.249896i	−0.700552	−	0.713601i	$-0.747063\pi$
$13$	−1.56060	+	0.901012i	−0.432832	+	0.249896i	0.267720	+	0.963497i	$0.413730\pi$
$14$		0			0
$15$		0			0
$16$	−0.849814	−	1.47192i	−0.212454	−	0.367980i
$17$	−2.98450	−	5.16931i	−0.723849	−	1.25374i	−0.959446	−	0.281892i	$-0.909038\pi$
$17$	−2.98450	−	5.16931i	−0.723849	−	1.25374i	0.235597	−	0.971851i	$-0.424295\pi$
$18$		0			0
$19$	−1.42391	−	0.822093i	−0.326667	−	0.188601i	0.327694	−	0.944784i	$-0.393729\pi$
$19$	−1.42391	−	0.822093i	−0.326667	−	0.188601i	−0.654360	+	0.756183i	$0.727062\pi$
$20$	−1.75597	+	3.04144i	−0.392648	+	0.680086i
$21$		0			0
$22$	1.08836	+	1.88510i	0.232040	+	0.401905i
$23$		−	2.37364i		−	0.494938i	−0.968896	−	0.247469i	$-0.920401\pi$
$23$		−	2.37364i		−	0.494938i	0.968896	−	0.247469i	$-0.0795988\pi$
$24$		0			0
$25$	−0.111264			−0.0222528
$26$	0.578079	−	1.00126i	0.113371	−	0.196364i
$27$		0			0
$28$		0			0
$29$	−2.44437	−	1.41126i	−0.453908	−	0.262064i	0.255571	−	0.966790i	$-0.417736\pi$
$29$	−2.44437	−	1.41126i	−0.453908	−	0.262064i	−0.709479	+	0.704726i	$0.751070\pi$
$30$		0			0
$31$	−9.28558	−	5.36103i	−1.66774	−	0.962870i	−0.968853	−	0.247638i	$-0.920346\pi$
$31$	−9.28558	−	5.36103i	−1.66774	−	0.962870i	−0.698887	−	0.715232i	$-0.746321\pi$
$32$	4.93199	+	2.84748i	0.871861	+	0.503369i
$33$		0			0
$34$	3.31657	+	1.91482i	0.568788	+	0.328390i
$35$		0			0
$36$		0			0
$37$	−0.849814	+	1.47192i	−0.139709	+	0.241982i	−0.927386	−	0.374105i	$-0.877950\pi$
$37$	−0.849814	+	1.47192i	−0.139709	+	0.241982i	0.787678	+	0.616088i	$0.211283\pi$
$38$	1.05489			0.171126
$39$		0			0
$40$		−	5.09039i		−	0.804862i
$41$	0.455074	+	0.788211i	0.0710706	+	0.123098i	0.899371	−	0.437187i	$-0.144025\pi$
$41$	0.455074	+	0.788211i	0.0710706	+	0.123098i	−0.828300	+	0.560285i	$0.810692\pi$
$42$		0			0
$43$	−1.96108	+	3.39669i	−0.299062	+	0.517990i	−0.975922	−	0.218122i	$-0.930007\pi$
$43$	−1.96108	+	3.39669i	−0.299062	+	0.517990i	0.676860	+	0.736112i	$0.263340\pi$
$44$	4.66690	+	2.69443i	0.703561	+	0.406201i
$45$		0			0
$46$	0.761450	+	1.31887i	0.112270	+	0.194457i
$47$	−0.123005	−	0.213051i	−0.0179422	−	0.0310767i	0.856915	−	0.515458i	$-0.172378\pi$
$47$	−0.123005	−	0.213051i	−0.0179422	−	0.0310767i	−0.874857	+	0.484381i	$0.839045\pi$
$48$		0			0
$49$		0			0
$50$	0.0618219	−	0.0356929i	0.00874294	−	0.00504774i
$51$		0			0
$52$		−	2.86227i		−	0.396925i
$53$	−6.82072	+	3.93795i	−0.936899	+	0.540919i	−0.888987	−	0.457933i	$-0.848590\pi$
$53$	−6.82072	+	3.93795i	−0.936899	+	0.540919i	−0.0479118	+	0.998852i	$0.515257\pi$
$54$		0			0
$55$		−	7.50146i		−	1.01150i
$56$		0			0
$57$		0			0
$58$	1.81089			0.237782
$59$	5.39093	−	9.33736i	0.701839	−	1.21562i	−0.265981	−	0.963978i	$-0.585696\pi$
$59$	5.39093	−	9.33736i	0.701839	−	1.21562i	0.967820	−	0.251643i	$-0.0809709\pi$
$60$		0			0
$61$	−1.22853	+	0.709292i	−0.157297	+	0.0908155i	−0.576582	−	0.817039i	$-0.695614\pi$
$61$	−1.22853	+	0.709292i	−0.157297	+	0.0908155i	0.419285	+	0.907855i	$0.362281\pi$
$62$	6.87916			0.873654
$63$		0			0
$64$	−0.254572			−0.0318214
$65$	−3.45056	+	1.99218i	−0.427989	+	0.247100i
$66$		0			0
$67$	3.99381	−	6.91748i	0.487922	−	0.845105i	−0.511982	−	0.858996i	$-0.671089\pi$
$67$	3.99381	−	6.91748i	0.487922	−	0.845105i	0.999904	+	0.0138913i	$0.00442187\pi$
$68$	9.48096			1.14974
$69$		0			0
$70$		0			0
$71$			12.1743i			1.44482i	0.691463	+	0.722412i	$0.256966\pi$
$71$			12.1743i			1.44482i	−0.691463	+	0.722412i	$0.743034\pi$
$72$		0			0
$73$	−0.369016	+	0.213051i	−0.0431900	+	0.0249358i	−0.521440	−	0.853288i	$-0.674605\pi$
$73$	−0.369016	+	0.213051i	−0.0431900	+	0.0249358i	0.478250	+	0.878224i	$0.341271\pi$
$74$		−	1.09046i		−	0.126764i
$75$		0			0
$76$	2.26168	−	1.30578i	0.259433	−	0.149784i
$77$		0			0
$78$		0			0
$79$	2.49381	+	4.31941i	0.280576	+	0.485971i	0.971527	−	0.236930i	$-0.0761413\pi$
$79$	2.49381	+	4.31941i	0.280576	+	0.485971i	−0.690951	+	0.722902i	$0.742808\pi$
$80$	−1.87898	−	3.25449i	−0.210076	−	0.363863i
$81$		0			0
$82$	−0.505707	−	0.291970i	−0.0558460	−	0.0322427i
$83$	4.28541	−	7.42254i	0.470384	−	0.814730i	−0.529042	−	0.848596i	$-0.677449\pi$
$83$	4.28541	−	7.42254i	0.470384	−	0.814730i	0.999426	+	0.0338660i	$0.0107819\pi$
$84$		0			0
$85$	−6.59888	−	11.4296i	−0.715750	−	1.23971i
$86$		−	2.51641i		−	0.271352i
$87$		0			0
$88$	−7.81089			−0.832644
$89$	5.26792	−	9.12431i	0.558399	−	0.967175i	−0.439231	−	0.898374i	$-0.644749\pi$
$89$	5.26792	−	9.12431i	0.558399	−	0.967175i	0.997630	−	0.0688014i	$-0.0219175\pi$
$90$		0			0
$91$		0			0
$92$	3.26509	+	1.88510i	0.340409	+	0.196535i
$93$		0			0
$94$	0.136691	+	0.0789188i	0.0140986	+	0.00813985i
$95$	−3.14833	−	1.81769i	−0.323012	−	0.186491i
$96$		0			0
$97$	−6.30108	−	3.63793i	−0.639777	−	0.369376i	0.144751	−	0.989468i	$-0.453762\pi$
$97$	−6.30108	−	3.63793i	−0.639777	−	0.369376i	−0.784529	+	0.620092i	$0.787095\pi$
$98$		0			0
$99$		0			0
$100$	0.0883640	−	0.153051i	0.00883640	−	0.0153051i
$101$	−4.66811			−0.464494			−0.232247	−	0.972657i	$-0.574608\pi$
$101$	−4.66811			−0.464494			−0.232247	+	0.972657i	$0.574608\pi$
$102$		0			0
$103$		−	6.24071i		−	0.614916i	−0.951562	−	0.307458i	$-0.900522\pi$
$103$		−	6.24071i		−	0.614916i	0.951562	−	0.307458i	$-0.0994783\pi$
$104$	2.07436	+	3.59289i	0.203407	+	0.352312i
$105$		0			0
$106$	2.52654	−	4.37610i	0.245399	−	0.425044i
$107$	1.28985	+	0.744696i	0.124695	+	0.0719925i	0.561050	−	0.827782i	$-0.310398\pi$
$107$	1.28985	+	0.744696i	0.124695	+	0.0719925i	−0.436355	+	0.899774i	$0.643731\pi$
$108$		0			0
$109$	2.19344	+	3.79915i	0.210093	+	0.363892i	0.951744	−	0.306895i	$-0.0992899\pi$
$109$	2.19344	+	3.79915i	0.210093	+	0.363892i	−0.741650	+	0.670787i	$0.765957\pi$
$110$	2.40643	+	4.16805i	0.229444	+	0.397408i
$111$		0			0
$112$		0			0
$113$	14.8764	−	8.58887i	1.39945	−	0.807973i	0.405115	−	0.914266i	$-0.367231\pi$
$113$	14.8764	−	8.58887i	1.39945	−	0.807973i	0.994335	+	0.106293i	$0.0338981\pi$
$114$		0			0
$115$		−	5.24823i		−	0.489400i
$116$	3.88255	−	2.24159i	0.360485	−	0.208126i
$117$		0			0
$118$			6.91752i			0.636809i
$119$		0			0
$120$		0			0
$121$	−0.510520			−0.0464110
$122$	0.455074	−	0.788211i	0.0412004	−	0.0713612i
$123$		0			0
$124$	14.7489	−	8.51527i	1.32449	−	0.764694i
$125$	−11.3013			−1.01081
$126$		0			0
$127$	6.32141			0.560935			0.280467	−	0.959864i	$-0.409511\pi$
$127$	6.32141			0.560935			0.280467	+	0.959864i	$0.409511\pi$
$128$	−9.72253	+	5.61330i	−0.859358	+	0.496151i
$129$		0			0
$130$	1.27816	−	2.21384i	0.112102	−	0.194167i
$131$	−17.0243			−1.48742			−0.743708	−	0.668505i	$-0.766935\pi$
$131$	−17.0243			−1.48742			−0.743708	+	0.668505i	$0.766935\pi$
$132$		0			0
$133$		0			0
$134$			5.12477i			0.442712i
$135$		0			0
$136$	−11.9011	+	6.87109i	−1.02051	+	0.589191i
$137$			6.26517i			0.535270i	0.963520	+	0.267635i	$0.0862421\pi$
$137$			6.26517i			0.535270i	−0.963520	+	0.267635i	$0.913758\pi$
$138$		0			0
$139$	6.65488	−	3.84220i	0.564460	−	0.325891i	−0.190474	−	0.981692i	$-0.561002\pi$
$139$	6.65488	−	3.84220i	0.564460	−	0.325891i	0.754934	+	0.655801i	$0.227669\pi$
$140$		0			0
$141$		0			0
$142$	−3.90545	−	6.76443i	−0.327738	−	0.567658i
$143$	3.05688	+	5.29467i	0.255629	+	0.442762i
$144$		0			0
$145$	−5.40462	−	3.12036i	−0.448829	−	0.259132i
$146$	0.136691	−	0.236756i	0.0113127	−	0.0195941i
$147$		0			0
$148$	−1.34981	−	2.33795i	−0.110954	−	0.192178i
$149$		−	15.4377i		−	1.26471i	−0.774679	−	0.632355i	$-0.782089\pi$
$149$		−	15.4377i		−	1.26471i	0.774679	−	0.632355i	$-0.217911\pi$
$150$		0			0
$151$	11.6872			0.951095			0.475547	−	0.879690i	$-0.342250\pi$
$151$	11.6872			0.951095			0.475547	+	0.879690i	$0.342250\pi$
$152$	−1.89267	+	3.27819i	−0.153516	+	0.265897i
$153$		0			0
$154$		0			0
$155$	−20.5309	−	11.8535i	−1.64908	−	0.952096i
$156$		0			0
$157$	4.93586	+	2.84972i	0.393924	+	0.227432i	0.683859	−	0.729614i	$-0.260300\pi$
$157$	4.93586	+	2.84972i	0.393924	+	0.227432i	−0.289935	+	0.957046i	$0.593634\pi$
$158$	−2.77128	−	1.60000i	−0.220471	−	0.127289i
$159$		0			0
$160$	10.9049	+	6.29593i	0.862105	+	0.497737i
$161$		0			0
$162$		0			0
$163$	5.10507	−	8.84225i	0.399860	−	0.692578i	−0.593848	−	0.804577i	$-0.702392\pi$
$163$	5.10507	−	8.84225i	0.399860	−	0.692578i	0.993708	+	0.111999i	$0.0357253\pi$
$164$	−1.44565			−0.112886
$165$		0			0
$166$			5.49894i			0.426800i
$167$	−1.80661	−	3.12914i	−0.139800	−	0.242140i	0.787621	−	0.616160i	$-0.211312\pi$
$167$	−1.80661	−	3.12914i	−0.139800	−	0.242140i	−0.927421	+	0.374020i	$0.877979\pi$
$168$		0			0
$169$	−4.87636	+	8.44610i	−0.375104	+	0.649700i
$170$	7.33310	+	4.23377i	0.562423	+	0.324715i
$171$		0			0
$172$	−3.11491	−	5.39518i	−0.237509	−	0.411378i
$173$	−9.03957	−	15.6570i	−0.687266	−	1.19038i	−0.972719	−	0.231987i	$-0.925477\pi$
$173$	−9.03957	−	15.6570i	−0.687266	−	1.19038i	0.285453	−	0.958393i	$-0.407856\pi$
$174$		0			0
$175$		0			0
$176$	−4.99381	+	2.88318i	−0.376423	+	0.217328i
$177$		0			0
$178$			6.75968i			0.506660i
$179$	4.35779	−	2.51597i	0.325716	−	0.188052i	−0.328221	−	0.944601i	$-0.606449\pi$
$179$	4.35779	−	2.51597i	0.325716	−	0.188052i	0.653938	+	0.756548i	$0.273116\pi$
$180$		0			0
$181$			13.5592i			1.00785i	0.863747	+	0.503925i	$0.168111\pi$
$181$			13.5592i			1.00785i	−0.863747	+	0.503925i	$0.831889\pi$
$182$		0			0
$183$		0			0
$184$	−5.46472			−0.402865
$185$	−1.87898	+	3.25449i	−0.138145	+	0.239275i
$186$		0			0
$187$	−17.5380	+	10.1256i	−1.28251	+	0.740455i
$188$	0.390754			0.0284987
$189$		0			0
$190$	2.33242			0.169211
$191$	−8.86948	+	5.12080i	−0.641773	+	0.370528i	−0.785297	−	0.619119i	$-0.787490\pi$
$191$	−8.86948	+	5.12080i	−0.641773	+	0.370528i	0.143524	+	0.989647i	$0.454156\pi$
$192$		0			0
$193$	−8.06615	+	13.9710i	−0.580614	+	1.00565i	0.414792	+	0.909916i	$0.363854\pi$
$193$	−8.06615	+	13.9710i	−0.580614	+	1.00565i	−0.995407	+	0.0957374i	$0.969479\pi$
$194$	4.66811			0.335151
$195$		0			0
$196$		0			0
$197$			3.86303i			0.275230i	0.990486	+	0.137615i	$0.0439436\pi$
$197$			3.86303i			0.275230i	−0.990486	+	0.137615i	$0.956056\pi$
$198$		0			0
$199$	13.1665	−	7.60171i	0.933352	−	0.538871i	0.0454817	−	0.998965i	$-0.485518\pi$
$199$	13.1665	−	7.60171i	0.933352	−	0.538871i	0.887870	+	0.460094i	$0.152184\pi$
$200$			0.256158i			0.0181131i
$201$		0			0
$202$	2.59375	−	1.49750i	0.182496	−	0.105364i
$203$		0			0
$204$		0			0
$205$	1.00619	+	1.74277i	0.0702753	+	0.121720i
$206$	2.00199	+	3.46754i	0.139485	+	0.241595i
$207$		0			0
$208$	2.65244	+	1.53138i	0.183913	+	0.106182i
$209$	−2.78913	+	4.83091i	−0.192928	+	0.334161i
$210$		0			0
$211$	11.9523	+	20.7021i	0.822833	+	1.42519i	0.903564	+	0.428453i	$0.140941\pi$
$211$	11.9523	+	20.7021i	0.822833	+	1.42519i	−0.0807311	+	0.996736i	$0.525726\pi$
$212$		−	12.5098i		−	0.859176i
$213$		0			0
$214$	−0.955577			−0.0653219
$215$	−4.33604	+	7.51024i	−0.295715	+	0.512194i
$216$		0			0
$217$		0			0
$218$	−2.43749	−	1.40729i	−0.165088	−	0.0953134i
$219$		0			0
$220$	10.3187	+	5.95752i	0.695689	+	0.401656i
$221$	9.31522	+	5.37815i	0.626610	+	0.361773i
$222$		0			0
$223$	−16.6198	−	9.59545i	−1.11294	−	0.642559i	−0.173354	−	0.984860i	$-0.555461\pi$
$223$	−16.6198	−	9.59545i	−1.11294	−	0.642559i	−0.939591	+	0.342300i	$0.888794\pi$
$224$		0			0
$225$		0			0
$226$	−5.51052	+	9.54450i	−0.366554	+	0.634891i
$227$	8.67208			0.575586			0.287793	−	0.957693i	$-0.407078\pi$
$227$	8.67208			0.575586			0.287793	+	0.957693i	$0.407078\pi$
$228$		0			0
$229$			14.3688i			0.949515i	0.880117	+	0.474758i	$0.157464\pi$
$229$			14.3688i			0.949515i	−0.880117	+	0.474758i	$0.842536\pi$
$230$	1.68360	+	2.91609i	0.111014	+	0.192281i
$231$		0			0
$232$	−3.24907	+	5.62755i	−0.213312	+	0.369467i
$233$	25.7348	+	14.8580i	1.68594	+	0.973381i	0.957570	+	0.288202i	$0.0930576\pi$
$233$	25.7348	+	14.8580i	1.68594	+	0.973381i	0.728375	+	0.685178i	$0.240276\pi$
$234$		0			0
$235$	−0.271971	−	0.471067i	−0.0177414	−	0.0307290i
$236$	8.56276	+	14.8311i	0.557388	+	0.965425i
$237$		0			0
$238$		0			0
$239$	13.7101	−	7.91556i	0.886836	−	0.512015i	0.0139296	−	0.999903i	$-0.495566\pi$
$239$	13.7101	−	7.91556i	0.886836	−	0.512015i	0.872906	+	0.487888i	$0.162233\pi$
$240$		0			0
$241$			5.02263i			0.323536i	0.986829	+	0.161768i	$0.0517196\pi$
$241$			5.02263i			0.323536i	−0.986829	+	0.161768i	$0.948280\pi$
$242$	0.283662	−	0.163772i	0.0182345	−	0.0105277i
$243$		0			0
$244$		−	2.25323i		−	0.144248i
$245$		0			0
$246$		0			0
$247$	2.96286			0.188522
$248$	−12.3425	+	21.3778i	−0.783747	+	1.35749i
$249$		0			0
$250$	6.27934	−	3.62538i	0.397140	−	0.229289i
$251$	7.29728			0.460600			0.230300	−	0.973120i	$-0.426029\pi$
$251$	7.29728			0.460600			0.230300	+	0.973120i	$0.426029\pi$
$252$		0			0
$253$	−8.05308			−0.506293
$254$	−3.51238	+	2.02787i	−0.220386	+	0.127240i
$255$		0			0
$256$	3.85600	−	6.67879i	0.241000	−	0.417425i
$257$	−8.00794			−0.499522			−0.249761	−	0.968308i	$-0.580352\pi$
$257$	−8.00794			−0.499522			−0.249761	+	0.968308i	$0.580352\pi$
$258$		0			0
$259$		0			0
$260$		−	6.32862i		−	0.392484i
$261$		0			0
$262$	9.45922	−	5.46128i	0.584393	−	0.337399i
$263$		−	15.7098i		−	0.968707i	−0.874872	−	0.484353i	$-0.839055\pi$
$263$		−	15.7098i		−	0.968707i	0.874872	−	0.484353i	$-0.160945\pi$
$264$		0			0
$265$	−15.0810	+	8.70699i	−0.926416	+	0.534866i
$266$		0			0
$267$		0			0
$268$	6.34362	+	10.9875i	0.387499	+	0.671167i
$269$	5.24619	+	9.08666i	0.319866	+	0.554024i	0.980460	−	0.196720i	$-0.0630289\pi$
$269$	5.24619	+	9.08666i	0.319866	+	0.554024i	−0.660594	+	0.750743i	$0.729696\pi$
$270$		0			0
$271$	19.2722	+	11.1268i	1.17071	+	0.675907i	0.953846	−	0.300296i	$-0.0970853\pi$
$271$	19.2722	+	11.1268i	1.17071	+	0.675907i	0.216859	+	0.976203i	$0.430419\pi$
$272$	−5.07255	+	8.78591i	−0.307568	+	0.532724i
$273$		0			0
$274$	−2.00983	−	3.48113i	−0.121418	−	0.210303i
$275$			0.377488i			0.0227634i
$276$		0			0
$277$	−22.8502			−1.37294			−0.686468	−	0.727160i	$-0.740840\pi$
$277$	−22.8502			−1.37294			−0.686468	+	0.727160i	$0.740840\pi$
$278$	−2.46511	+	4.26970i	−0.147848	+	0.256079i
$279$		0			0
$280$		0			0
$281$	−0.796041	−	0.459595i	−0.0474878	−	0.0274171i	0.476068	−	0.879408i	$-0.342062\pi$
$281$	−0.796041	−	0.459595i	−0.0474878	−	0.0274171i	−0.523556	+	0.851991i	$0.675395\pi$
$282$		0			0
$283$	19.1573	+	11.0605i	1.13878	+	0.657477i	0.946129	−	0.323790i	$-0.104957\pi$
$283$	19.1573	+	11.0605i	1.13878	+	0.657477i	0.192654	+	0.981267i	$0.438290\pi$
$284$	−16.7465	−	9.66861i	−0.993723	−	0.573726i
$285$		0			0
$286$	−3.39700	−	1.96126i	−0.200869	−	0.115972i
$287$		0			0
$288$		0			0
$289$	−9.31453	+	16.1332i	−0.547914	+	0.949014i
$290$	4.00397			0.235121
$291$		0			0
$292$		−	0.676806i		−	0.0396071i
$293$	−14.6259	−	25.3328i	−0.854453	−	1.47996i	−0.877152	−	0.480214i	$-0.840559\pi$
$293$	−14.6259	−	25.3328i	−0.854453	−	1.47996i	0.0226986	−	0.999742i	$-0.492774\pi$
$294$		0			0
$295$	11.9196	−	20.6454i	0.693986	−	1.20202i
$296$	3.38874	+	1.95649i	0.196966	+	0.113719i
$297$		0			0
$298$	4.95234	+	8.57771i	0.286881	+	0.496893i
$299$	2.13868	+	3.70430i	0.123683	+	0.214225i
$300$		0			0
$301$		0			0
$302$	−6.49381	+	3.74920i	−0.373677	+	0.215742i
$303$		0			0
$304$			2.79450i			0.160276i
$305$	−2.71634	+	1.56828i	−0.155537	+	0.0897994i
$306$		0			0
$307$		−	14.8451i		−	0.847254i	−0.905837	−	0.423627i	$-0.860757\pi$
$307$		−	14.8451i		−	0.847254i	0.905837	−	0.423627i	$-0.139243\pi$
$308$		0			0
$309$		0			0
$310$	15.2101			0.863878
$311$	−9.69002	+	16.7836i	−0.549471	+	0.951711i	0.448840	+	0.893612i	$0.351837\pi$
$311$	−9.69002	+	16.7836i	−0.549471	+	0.951711i	−0.998311	+	0.0580991i	$0.981496\pi$
$312$		0			0
$313$	−12.6608	+	7.30974i	−0.715633	+	0.413171i	−0.813143	−	0.582064i	$-0.802245\pi$
$313$	−12.6608	+	7.30974i	−0.715633	+	0.413171i	0.0975102	+	0.995235i	$0.468912\pi$
$314$	−3.65669			−0.206359
$315$		0			0
$316$	−7.92216			−0.445656
$317$	−14.7046	+	8.48973i	−0.825895	+	0.476831i	−0.852445	−	0.522817i	$-0.824881\pi$
$317$	−14.7046	+	8.48973i	−0.825895	+	0.476831i	0.0265499	+	0.999647i	$0.491548\pi$
$318$		0			0
$319$	−4.78799	+	8.29305i	−0.268076	+	0.464321i
$320$	−0.562870			−0.0314654
$321$		0			0
$322$		0			0
$323$			9.81416i			0.546074i
$324$		0			0
$325$	0.173639	−	0.100250i	0.00963174	−	0.00556089i
$326$			6.55072i			0.362811i
$327$		0			0
$328$	1.81466	−	1.04769i	0.100198	−	0.0578493i
$329$		0			0
$330$		0			0
$331$	−9.94801	−	17.2305i	−0.546792	−	0.947072i	−0.998492	−	0.0549016i	$-0.982515\pi$
$331$	−9.94801	−	17.2305i	−0.546792	−	0.947072i	0.451700	−	0.892170i	$-0.350818\pi$
$332$	6.80678	+	11.7897i	0.373571	+	0.647044i
$333$		0			0
$334$	2.00762	+	1.15910i	0.109852	+	0.0634231i
$335$	8.83051	−	15.2949i	0.482462	−	0.835649i
$336$		0			0
$337$	0.490168	+	0.848996i	0.0267012	+	0.0462478i	0.879067	−	0.476698i	$-0.158166\pi$
$337$	0.490168	+	0.848996i	0.0267012	+	0.0462478i	−0.852366	+	0.522946i	$0.824833\pi$
$338$		−	6.25723i		−	0.340348i
$339$		0			0
$340$	20.9629			1.13687
$341$	−18.1885	+	31.5033i	−0.984960	+	1.70600i
$342$		0			0
$343$		0			0
$344$	7.82004	+	4.51490i	0.421628	+	0.243427i
$345$		0			0
$346$	10.0454	+	5.79969i	0.540041	+	0.311793i
$347$	18.3702	+	10.6060i	0.986162	+	0.569361i	0.904125	−	0.427268i	$-0.140524\pi$
$347$	18.3702	+	10.6060i	0.986162	+	0.569361i	0.0820373	+	0.996629i	$0.473857\pi$
$348$		0			0
$349$	8.69945	+	5.02263i	0.465671	+	0.268855i	0.714426	−	0.699711i	$-0.246688\pi$
$349$	8.69945	+	5.02263i	0.465671	+	0.268855i	−0.248755	+	0.968566i	$0.580021\pi$
$350$		0			0
$351$		0			0
$352$	9.66071	−	16.7328i	0.514917	−	0.891863i
$353$	2.74655			0.146184			0.0730920	−	0.997325i	$-0.476713\pi$
$353$	2.74655			0.146184			0.0730920	+	0.997325i	$0.476713\pi$
$354$		0			0
$355$			26.9180i			1.42866i
$356$	8.36738	+	14.4927i	0.443470	+	0.768113i
$357$		0			0
$358$	−1.61422	+	2.79591i	−0.0853140	+	0.147768i
$359$	−8.66140	−	5.00066i	−0.457131	−	0.263925i	0.253706	−	0.967281i	$-0.418350\pi$
$359$	−8.66140	−	5.00066i	−0.457131	−	0.263925i	−0.710837	+	0.703357i	$0.751684\pi$
$360$		0			0
$361$	−8.14833	−	14.1133i	−0.428859	−	0.742806i
$362$	−4.34973	−	7.53395i	−0.228616	−	0.395975i
$363$		0			0
$364$		0			0
$365$	−0.815912	+	0.471067i	−0.0427068	+	0.0246568i
$366$		0			0
$367$			5.81461i			0.303520i	0.988417	+	0.151760i	$0.0484941\pi$
$367$			5.81461i			0.303520i	−0.988417	+	0.151760i	$0.951506\pi$
$368$	−3.49381	+	2.01715i	−0.182127	+	0.105151i
$369$		0			0
$370$		−	2.41106i		−	0.125345i
$371$		0			0
$372$		0			0
$373$	−15.5192			−0.803553			−0.401776	−	0.915738i	$-0.631607\pi$
$373$	−15.5192			−0.803553			−0.401776	+	0.915738i	$0.631607\pi$
$374$	6.49645	−	11.2522i	0.335924	−	0.581837i
$375$		0			0
$376$	−0.490498	+	0.283189i	−0.0252955	+	0.0146044i
$377$	5.08623			0.261954
$378$		0			0
$379$	2.79714			0.143679			0.0718396	−	0.997416i	$-0.477113\pi$
$379$	2.79714			0.143679			0.0718396	+	0.997416i	$0.477113\pi$
$380$	5.00069	−	2.88715i	0.256530	−	0.148108i
$381$		0			0
$382$	3.28544	−	5.69056i	0.168098	−	0.291154i
$383$	−3.48458			−0.178054			−0.0890268	−	0.996029i	$-0.528376\pi$
$383$	−3.48458			−0.178054			−0.0890268	+	0.996029i	$0.528376\pi$
$384$		0			0
$385$		0			0
$386$		−	10.3503i		−	0.526817i
$387$		0			0
$388$	10.0084	−	5.77835i	0.508100	−	0.293352i
$389$		−	7.35563i		−	0.372945i	−0.982460	−	0.186473i	$-0.940294\pi$
$389$		−	7.35563i		−	0.372945i	0.982460	−	0.186473i	$-0.0597056\pi$
$390$		0			0
$391$	−12.2701	+	7.08414i	−0.620525	+	0.358260i
$392$		0			0
$393$		0			0
$394$	−1.23924	−	2.14642i	−0.0624319	−	0.108135i
$395$	5.51394	+	9.55042i	0.277436	+	0.480534i
$396$		0			0
$397$	−16.7002	−	9.64189i	−0.838161	−	0.483912i	0.0184778	−	0.999829i	$-0.494118\pi$
$397$	−16.7002	−	9.64189i	−0.838161	−	0.483912i	−0.856639	+	0.515917i	$0.827451\pi$
$398$	−4.87717	+	8.44751i	−0.244470	+	0.423435i
$399$		0			0
$400$	0.0945538	+	0.163772i	0.00472769	+	0.00818860i
$401$		−	11.0918i		−	0.553897i	−0.960885	−	0.276949i	$-0.910677\pi$
$401$		−	11.0918i		−	0.553897i	0.960885	−	0.276949i	$-0.0893232\pi$
$402$		0			0
$403$	19.3214			0.962468
$404$	3.70733	−	6.42128i	0.184446	−	0.319471i
$405$		0			0
$406$		0			0
$407$	4.99381	+	2.88318i	0.247534	+	0.142914i
$408$		0			0
$409$	−17.5597	−	10.1381i	−0.868274	−	0.501298i	−0.00149954	−	0.999999i	$-0.500477\pi$
$409$	−17.5597	−	10.1381i	−0.868274	−	0.501298i	−0.866774	+	0.498701i	$0.833811\pi$
$410$	−1.11814	−	0.645560i	−0.0552211	−	0.0318819i
$411$		0			0
$412$	8.58450	+	4.95626i	0.422928	+	0.244178i
$413$		0			0
$414$		0			0
$415$	9.47524	−	16.4116i	0.465121	−	0.805614i
$416$	−10.2625			−0.503159
$417$		0			0
$418$		−	3.57895i		−	0.175052i
$419$	5.54936	+	9.61177i	0.271104	+	0.469566i	0.969145	−	0.246492i	$-0.0792779\pi$
$419$	5.54936	+	9.61177i	0.271104	+	0.469566i	−0.698041	+	0.716058i	$0.745945\pi$
$420$		0			0
$421$	4.59269	−	7.95478i	0.223834	−	0.387692i	−0.732135	−	0.681160i	$-0.761476\pi$
$421$	4.59269	−	7.95478i	0.223834	−	0.387692i	0.955969	+	0.293467i	$0.0948092\pi$
$422$	−13.2822	−	7.66849i	−0.646568	−	0.373296i
$423$		0			0
$424$	9.06615	+	15.7030i	0.440291	+	0.762607i
$425$	0.332068	+	0.575159i	0.0161077	+	0.0278993i
$426$		0			0
$427$		0			0
$428$	−2.04875	+	1.18285i	−0.0990302	+	0.0571751i
$429$		0			0
$430$		−	5.56391i		−	0.268315i
$431$	−13.0858	+	7.55510i	−0.630322	+	0.363916i	−0.780877	−	0.624685i	$-0.785227\pi$
$431$	−13.0858	+	7.55510i	−0.630322	+	0.363916i	0.150555	+	0.988602i	$0.451894\pi$
$432$		0			0
$433$		−	3.33578i		−	0.160307i	−0.996783	−	0.0801537i	$-0.974459\pi$
$433$		−	3.33578i		−	0.160307i	0.996783	−	0.0801537i	$-0.0255411\pi$
$434$		0			0
$435$		0			0
$436$	−6.96796			−0.333705
$437$	−1.95135	+	3.37984i	−0.0933458	+	0.161680i
$438$		0			0
$439$	−5.91032	+	3.41233i	−0.282084	+	0.162861i	−0.634367	−	0.773032i	$-0.718739\pi$
$439$	−5.91032	+	3.41233i	−0.282084	+	0.162861i	0.352282	+	0.935894i	$0.385406\pi$
$440$	−17.2703			−0.823327
$441$		0			0
$442$	−6.90112			−0.328253
$443$	9.77747	−	5.64503i	0.464542	−	0.268203i	−0.249410	−	0.968398i	$-0.580237\pi$
$443$	9.77747	−	5.64503i	0.464542	−	0.268203i	0.713952	+	0.700195i	$0.246903\pi$
$444$		0			0
$445$	11.6476	−	20.1743i	0.552151	−	0.956354i
$446$	12.3127			0.583022
$447$		0			0
$448$		0			0
$449$			24.8554i			1.17300i	0.809950	+	0.586498i	$0.199494\pi$
$449$			24.8554i			1.17300i	−0.809950	+	0.586498i	$0.800506\pi$
$450$		0			0
$451$	2.67417	−	1.54394i	0.125922	−	0.0727011i
$452$			27.2845i			1.28335i
$453$		0			0
$454$	−4.81849	+	2.78195i	−0.226143	+	0.130564i
$455$		0			0
$456$		0			0
$457$	6.30470	+	10.9201i	0.294922	+	0.510819i	0.974967	−	0.222351i	$-0.0713732\pi$
$457$	6.30470	+	10.9201i	0.294922	+	0.510819i	−0.680045	+	0.733170i	$0.738040\pi$
$458$	−4.60942	−	7.98375i	−0.215384	−	0.373056i
$459$		0			0
$460$	7.21928	+	4.16805i	0.336601	+	0.194336i
$461$	−14.4031	+	24.9470i	−0.670821	+	1.16190i	0.306851	+	0.951758i	$0.400725\pi$
$461$	−14.4031	+	24.9470i	−0.670821	+	1.16190i	−0.977672	+	0.210138i	$0.932609\pi$
$462$		0			0
$463$	−12.5858	−	21.7993i	−0.584912	−	1.01310i	−0.994886	−	0.101001i	$-0.967796\pi$
$463$	−12.5858	−	21.7993i	−0.584912	−	1.01310i	0.409974	−	0.912097i	$-0.365538\pi$
$464$			4.79722i			0.222705i
$465$		0			0
$466$	−19.0655			−0.883191
$467$	12.7975	−	22.1660i	0.592199	−	1.02572i	−0.401736	−	0.915755i	$-0.631593\pi$
$467$	12.7975	−	22.1660i	0.592199	−	1.02572i	0.993936	−	0.109964i	$-0.0350735\pi$
$468$		0			0
$469$		0			0
$470$	0.302231	+	0.174493i	0.0139409	+	0.00804877i
$471$		0			0
$472$	−21.4970	−	12.4113i	−0.989479	−	0.571276i
$473$	11.5240	+	6.65338i	0.529874	+	0.305923i
$474$		0			0
$475$	0.158430	+	0.0914695i	0.00726926	+	0.00419691i
$476$		0			0
$477$		0			0
$478$	−5.07853	+	8.79628i	−0.232287	+	0.402332i
$479$	−0.535498			−0.0244675			−0.0122338	−	0.999925i	$-0.503894\pi$
$479$	−0.535498			−0.0244675			−0.0122338	+	0.999925i	$0.503894\pi$
$480$		0			0
$481$		−	3.06277i		−	0.139650i
$482$	−1.61123	−	2.79073i	−0.0733896	−	0.127114i
$483$		0			0
$484$	0.405446	−	0.702253i	0.0184294	−	0.0319206i
$485$	−13.9320	−	8.04364i	−0.632619	−	0.365243i
$486$		0			0
$487$	−17.0662	−	29.5594i	−0.773341	−	1.33947i	−0.935722	−	0.352738i	$-0.885251\pi$
$487$	−17.0662	−	29.5594i	−0.773341	−	1.33947i	0.162381	−	0.986728i	$-0.448083\pi$
$488$	1.63297	+	2.82839i	0.0739211	+	0.128035i
$489$		0			0
$490$		0			0
$491$	−5.86948	+	3.38874i	−0.264886	+	0.152932i	−0.626561	−	0.779372i	$-0.715538\pi$
$491$	−5.86948	+	3.38874i	−0.264886	+	0.152932i	0.361675	+	0.932304i	$0.382205\pi$
$492$		0			0
$493$			16.8476i			0.758778i
$494$	−1.64626	+	0.950469i	−0.0740688	+	0.0427636i
$495$		0			0
$496$			18.2235i			0.818260i
$497$		0			0
$498$		0			0
$499$	8.60074			0.385022			0.192511	−	0.981295i	$-0.438337\pi$
$499$	8.60074			0.385022			0.192511	+	0.981295i	$0.438337\pi$
$500$	8.97525	−	15.5456i	0.401385	−	0.695220i
$501$		0			0
$502$	−4.05460	+	2.34093i	−0.180966	+	0.104481i
$503$	2.96518			0.132211			0.0661055	−	0.997813i	$-0.478943\pi$
$503$	2.96518			0.132211			0.0661055	+	0.997813i	$0.478943\pi$
$504$		0			0
$505$	−10.3214			−0.459297
$506$	4.47455	−	2.58338i	0.198918	−	0.114845i
$507$		0			0
$508$	−5.02035	+	8.69551i	−0.222742	+	0.385801i
$509$	−6.09765			−0.270273			−0.135137	−	0.990827i	$-0.543147\pi$
$509$	−6.09765			−0.270273			−0.135137	+	0.990827i	$0.543147\pi$
$510$		0			0
$511$		0			0
$512$		−	17.5053i		−	0.773631i
$513$		0			0
$514$	4.44947	−	2.56890i	0.196258	−	0.113309i
$515$		−	13.7985i		−	0.608035i
$516$		0			0
$517$	−0.722823	+	0.417322i	−0.0317897	+	0.0183538i
$518$		0			0
$519$		0			0
$520$	4.58650	+	7.94406i	0.201132	+	0.348370i
$521$	−16.3464	−	28.3128i	−0.716150	−	1.24041i	−0.962514	−	0.271231i	$-0.912569\pi$
$521$	−16.3464	−	28.3128i	−0.716150	−	1.24041i	0.246364	−	0.969177i	$-0.420764\pi$
$522$		0			0
$523$	−1.73424	−	1.00126i	−0.0758329	−	0.0437821i	0.461604	−	0.887086i	$-0.347274\pi$
$523$	−1.73424	−	1.00126i	−0.0758329	−	0.0437821i	−0.537437	+	0.843304i	$0.680607\pi$
$524$	13.5204	−	23.4179i	0.590639	−	1.02302i
$525$		0			0
$526$	5.03961	+	8.72886i	0.219737	+	0.380596i
$527$			64.0001i			2.78789i
$528$		0			0
$529$	17.3658			0.755036
$530$	5.58631	−	9.67577i	0.242654	−	0.420289i
$531$		0			0
$532$		0			0
$533$	−1.42037	−	0.820053i	−0.0615232	−	0.0355204i
$534$		0			0
$535$	2.85192	+	1.64656i	0.123299	+	0.0711870i
$536$	−15.9258	−	9.19476i	−0.687890	−	0.397153i
$537$		0			0
$538$	−5.82990	−	3.36589i	−0.251345	−	0.145114i
$539$		0			0
$540$		0			0
$541$	5.72253	−	9.91171i	0.246031	−	0.426138i	−0.716390	−	0.697700i	$-0.754207\pi$
$541$	5.72253	−	9.91171i	0.246031	−	0.426138i	0.962421	+	0.271562i	$0.0875403\pi$
$542$	−14.2777			−0.613280
$543$		0			0
$544$		−	33.9933i		−	1.45745i
$545$	4.84980	+	8.40010i	0.207743	+	0.359821i
$546$		0			0
$547$	−3.91961	+	6.78896i	−0.167590	+	0.290275i	−0.937572	−	0.347791i	$-0.886932\pi$
$547$	−3.91961	+	6.78896i	−0.167590	+	0.290275i	0.769982	+	0.638066i	$0.220265\pi$
$548$	−8.61814	−	4.97569i	−0.368149	−	0.212551i
$549$		0			0
$550$	−0.121096	−	0.209744i	−0.00516355	−	0.00894353i
$551$	2.32037	+	4.01899i	0.0988510	+	0.171215i
$552$		0			0
$553$		0			0
$554$	12.6963	−	7.33022i	0.539415	−	0.311431i
$555$		0			0
$556$			12.2056i			0.517634i
$557$	0.0116910	−	0.00674980i	0.000495364	−	0.000285998i	−0.499752	−	0.866168i	$-0.666576\pi$
$557$	0.0116910	−	0.00674980i	0.000495364	−	0.000285998i	0.500248	+	0.865882i	$0.333242\pi$
$558$		0			0
$559$		−	7.06782i		−	0.298937i
$560$		0			0
$561$		0			0
$562$	0.589741			0.0248767
$563$	9.54528	−	16.5329i	0.402286	−	0.696779i	−0.591716	−	0.806147i	$-0.701549\pi$
$563$	9.54528	−	16.5329i	0.402286	−	0.696779i	0.994001	+	0.109368i	$0.0348826\pi$
$564$		0			0
$565$	32.8923	−	18.9904i	1.38379	−	0.798932i
$566$	−14.1925			−0.596557
$567$		0			0
$568$	28.0283			1.17604
$569$	32.3406	−	18.6719i	1.35579	−	0.782765i	0.366735	−	0.930325i	$-0.380475\pi$
$569$	32.3406	−	18.6719i	1.35579	−	0.782765i	0.989053	+	0.147561i	$0.0471422\pi$
$570$		0			0
$571$	−22.6421	+	39.2173i	−0.947544	+	1.64119i	−0.196968	+	0.980410i	$0.563110\pi$
$571$	−22.6421	+	39.2173i	−0.947544	+	1.64119i	−0.750576	+	0.660784i	$0.770224\pi$
$572$	−9.71086			−0.406032
$573$		0			0
$574$		0			0
$575$			0.264101i			0.0110138i
$576$		0			0
$577$	−32.1285	+	18.5494i	−1.33753	+	0.772221i	−0.986440	−	0.164123i	$-0.947521\pi$
$577$	−32.1285	+	18.5494i	−1.33753	+	0.772221i	−0.351086	+	0.936343i	$0.614187\pi$
$578$		−	11.9522i		−	0.497146i
$579$		0			0
$580$	8.58450	−	4.95626i	0.356452	−	0.205798i
$581$		0			0
$582$		0			0
$583$	13.3603	+	23.1408i	0.553329	+	0.958393i
$584$	0.490498	+	0.849568i	0.0202970	+	0.0351554i
$585$		0			0
$586$	16.2532	+	9.38380i	0.671414	+	0.387641i
$587$	17.0612	−	29.5509i	0.704191	−	1.21969i	−0.262792	−	0.964853i	$-0.584643\pi$
$587$	17.0612	−	29.5509i	0.704191	−	1.21969i	0.966983	−	0.254842i	$-0.0820235\pi$
$588$		0			0
$589$	8.81453	+	15.2672i	0.363197	+	0.629075i
$590$			15.2950i			0.629684i
$591$		0			0
$592$	2.88874			0.118726
$593$	9.84997	−	17.0607i	0.404490	−	0.700597i	−0.589772	−	0.807570i	$-0.700782\pi$
$593$	9.84997	−	17.0607i	0.404490	−	0.700597i	0.994262	+	0.106973i	$0.0341157\pi$
$594$		0			0
$595$		0			0
$596$	21.2356	+	12.2604i	0.869844	+	0.502205i
$597$		0			0
$598$	−2.37663	−	1.37215i	−0.0971878	−	0.0561114i
$599$	−9.74033	−	5.62358i	−0.397979	−	0.229773i	0.287632	−	0.957741i	$-0.407132\pi$
$599$	−9.74033	−	5.62358i	−0.397979	−	0.229773i	−0.685612	+	0.727967i	$0.740465\pi$
$600$		0			0
$601$	29.7646	+	17.1846i	1.21412	+	0.700975i	0.963655	−	0.267150i	$-0.0860818\pi$
$601$	29.7646	+	17.1846i	1.21412	+	0.700975i	0.250469	+	0.968125i	$0.419415\pi$
$602$		0			0
$603$		0			0
$604$	−9.28180	+	16.0766i	−0.377671	+	0.654146i
$605$	−1.12879			−0.0458917
$606$		0			0
$607$		−	39.0160i		−	1.58361i	−0.610775	−	0.791804i	$-0.709142\pi$
$607$		−	39.0160i		−	1.58361i	0.610775	−	0.791804i	$-0.290858\pi$
$608$	−4.68179	−	8.10910i	−0.189872	−	0.328868i
$609$		0			0
$610$	1.00619	−	1.74277i	0.0407394	−	0.0705628i
$611$	0.383923	+	0.221658i	0.0155319	+	0.00896733i
$612$		0			0
$613$	8.05494	+	13.9516i	0.325336	+	0.563499i	0.981580	−	0.191050i	$-0.0611892\pi$
$613$	8.05494	+	13.9516i	0.325336	+	0.563499i	−0.656244	+	0.754549i	$0.727856\pi$
$614$	4.76222	+	8.24840i	0.192187	+	0.332878i
$615$		0			0
$616$		0			0
$617$	−7.03569	+	4.06205i	−0.283246	+	0.163532i	−0.634892	−	0.772601i	$-0.718955\pi$
$617$	−7.03569	+	4.06205i	−0.283246	+	0.163532i	0.351646	+	0.936133i	$0.385622\pi$
$618$		0			0
$619$		−	37.4144i		−	1.50381i	−0.659270	−	0.751906i	$-0.729134\pi$
$619$		−	37.4144i		−	1.50381i	0.659270	−	0.751906i	$-0.270866\pi$
$620$	32.6105	−	18.8277i	1.30967	−	0.756138i
$621$		0			0
$622$		−	12.4340i		−	0.498559i
$623$		0			0
$624$		0			0
$625$	−24.4313			−0.977252
$626$	4.68985	−	8.12305i	0.187444	−	0.324662i
$627$		0			0
$628$	−7.83994	+	4.52639i	−0.312848	+	0.180623i
$629$	10.1451			0.404511
$630$		0			0
$631$	−19.8268			−0.789294			−0.394647	−	0.918833i	$-0.629133\pi$
$631$	−19.8268			−0.789294			−0.394647	+	0.918833i	$0.629133\pi$
$632$	9.94437	−	5.74138i	0.395566	−	0.228380i
$633$		0			0
$634$	5.44692	−	9.43434i	0.216325	−	0.374685i
$635$	13.9770			0.554658
$636$		0			0
$637$		0			0
$638$		−	6.14384i		−	0.243237i
$639$		0			0
$640$	−21.4970	+	12.4113i	−0.849743	+	0.490599i
$641$		−	9.25896i		−	0.365707i	−0.983140	−	0.182853i	$-0.941467\pi$
$641$		−	9.25896i		−	0.365707i	0.983140	−	0.182853i	$-0.0585334\pi$
$642$		0			0
$643$	36.3456	−	20.9841i	1.43333	−	0.827534i	0.435958	−	0.899967i	$-0.356410\pi$
$643$	36.3456	−	20.9841i	1.43333	−	0.827534i	0.997373	+	0.0724332i	$0.0230764\pi$
$644$		0			0
$645$		0			0
$646$	−3.14833	−	5.45306i	−0.123869	−	0.214548i
$647$	3.14293	+	5.44372i	0.123561	+	0.214015i	0.921170	−	0.389161i	$-0.127235\pi$
$647$	3.14293	+	5.44372i	0.123561	+	0.214015i	−0.797608	+	0.603176i	$0.793902\pi$
$648$		0			0
$649$	−31.6790	−	18.2899i	−1.24351	−	0.717941i
$650$	−0.0643195	+	0.111405i	−0.00252282	+	0.00436965i
$651$		0			0
$652$	8.10872	+	14.0447i	0.317562	+	0.550033i
$653$		−	23.2866i		−	0.911277i	−0.890165	−	0.455638i	$-0.849411\pi$
$653$		−	23.2866i		−	0.911277i	0.890165	−	0.455638i	$-0.150589\pi$
$654$		0			0
$655$	−37.6414			−1.47077
$656$	0.773456	−	1.33966i	0.0301984	−	0.0523051i
$657$		0			0
$658$		0			0
$659$	−25.8880	−	14.9464i	−1.00845	−	0.582230i	−0.0977141	−	0.995215i	$-0.531153\pi$
$659$	−25.8880	−	14.9464i	−1.00845	−	0.582230i	−0.910738	+	0.412984i	$0.864486\pi$
$660$		0			0
$661$	−17.6184	−	10.1720i	−0.685278	−	0.395645i	0.116563	−	0.993183i	$-0.462812\pi$
$661$	−17.6184	−	10.1720i	−0.685278	−	0.395645i	−0.801841	+	0.597538i	$0.796146\pi$
$662$	11.0549	+	6.38253i	0.429660	+	0.248064i
$663$		0			0
$664$	−17.0886	−	9.86609i	−0.663165	−	0.382879i
$665$		0			0
$666$		0			0
$667$	−3.34981	+	5.80205i	−0.129705	+	0.224656i
$668$	5.73910			0.222053
$669$		0			0
$670$			11.3311i			0.437759i
$671$	2.40643	+	4.16805i	0.0928990	+	0.160906i
$672$		0			0
$673$	−8.55996	+	14.8263i	−0.329962	+	0.571511i	−0.982504	−	0.186241i	$-0.940369\pi$
$673$	−8.55996	+	14.8263i	−0.329962	+	0.571511i	0.652542	+	0.757753i	$0.273703\pi$
$674$	−0.544706	−	0.314486i	−0.0209813	−	0.0121136i
$675$		0			0
$676$	−7.74543	−	13.4155i	−0.297901	−	0.515980i
$677$	−14.2078	−	24.6085i	−0.546048	−	0.945783i	−0.998540	−	0.0540148i	$-0.982798\pi$
$677$	−14.2078	−	24.6085i	−0.546048	−	0.945783i	0.452492	−	0.891769i	$-0.350535\pi$
$678$		0			0
$679$		0			0
$680$	−26.3138	+	15.1923i	−1.00909	+	0.582598i
$681$		0			0
$682$		−	23.3390i		−	0.893697i
$683$	−18.1236	+	10.4637i	−0.693482	+	0.400382i	−0.804915	−	0.593390i	$-0.797789\pi$
$683$	−18.1236	+	10.4637i	−0.693482	+	0.400382i	0.111433	+	0.993772i	$0.464456\pi$
$684$		0			0
$685$			13.8526i			0.529281i
$686$		0			0
$687$		0			0
$688$	6.66621			0.254147
$689$	7.09627	−	12.2911i	0.270346	−	0.468254i
$690$		0			0
$691$	20.7918	−	12.0041i	0.790957	−	0.456659i	−0.0493424	−	0.998782i	$-0.515713\pi$
$691$	20.7918	−	12.0041i	0.790957	−	0.456659i	0.840299	+	0.542123i	$0.182379\pi$
$692$	28.7163			1.09163
$693$		0			0
$694$	−13.6094			−0.516606
$695$	14.7143	−	8.49529i	0.558144	−	0.322245i
$696$		0			0
$697$	2.71634	−	4.70484i	0.102889	−	0.178208i
$698$	−6.44493			−0.243944
$699$		0			0
$700$		0			0
$701$		−	42.0117i		−	1.58676i	−0.608728	−	0.793379i	$-0.708320\pi$
$701$		−	42.0117i		−	1.58676i	0.608728	−	0.793379i	$-0.291680\pi$
$702$		0			0
$703$	2.42011	−	1.39725i	0.0912762	−	0.0526984i
$704$			0.863689i			0.0325515i
$705$		0			0
$706$	−1.52607	+	0.881077i	−0.0574344	+	0.0331598i
$707$		0			0
$708$		0			0
$709$	−18.6094	−	32.2324i	−0.698891	−	1.21051i	−0.968851	−	0.247643i	$-0.920344\pi$
$709$	−18.6094	−	32.2324i	−0.698891	−	1.21051i	0.269960	−	0.962871i	$-0.412989\pi$
$710$	−8.63513	−	14.9565i	−0.324071	−	0.561307i
$711$		0			0
$712$	−21.0065	−	12.1281i	−0.787251	−	0.454520i
$713$	−12.7252	+	22.0406i	−0.476561	+	0.825428i
$714$		0			0
$715$	6.75890	+	11.7068i	0.252769	+	0.437808i
$716$			7.99255i			0.298696i
$717$		0			0
$718$	6.41673			0.239470
$719$	9.14889	−	15.8463i	0.341196	−	0.590969i	−0.643459	−	0.765481i	$-0.722501\pi$
$719$	9.14889	−	15.8463i	0.341196	−	0.590969i	0.984655	+	0.174512i	$0.0558347\pi$
$720$		0			0
$721$		0			0
$722$	9.05494	+	5.22787i	0.336990	+	0.194561i
$723$		0			0
$724$	−18.6516	−	10.7685i	−0.693181	−	0.400208i
$725$	0.271971	+	0.157022i	0.0101007	+	0.00583166i
$726$		0			0
$727$	−28.3214	−	16.3514i	−1.05038	−	0.606439i	−0.127626	−	0.991822i	$-0.540736\pi$
$727$	−28.3214	−	16.3514i	−1.05038	−	0.606439i	−0.922756	+	0.385384i	$0.874069\pi$
$728$		0			0
$729$		0			0
$730$	0.302231	−	0.523480i	0.0111861	−	0.0193749i
$731$	23.4114			0.865901
$732$		0			0
$733$			0.498614i			0.0184167i	0.999958	+	0.00920836i	$0.00293115\pi$
$733$			0.498614i			0.0184167i	−0.999958	+	0.00920836i	$0.997069\pi$
$734$	−1.86529	−	3.23078i	−0.0688493	−	0.119250i
$735$		0			0
$736$	6.75890	−	11.7068i	0.249136	−	0.431517i
$737$	−23.4691	−	13.5499i	−0.864494	−	0.499116i
$738$		0			0
$739$	23.8523	+	41.3134i	0.877421	+	1.51974i	0.854162	+	0.520007i	$0.174071\pi$
$739$	23.8523	+	41.3134i	0.877421	+	1.51974i	0.0232588	+	0.999729i	$0.492596\pi$
$740$	−2.98450	−	5.16931i	−0.109713	−	0.190028i
$741$		0			0
$742$		0			0
$743$	−9.20534	+	5.31470i	−0.337711	+	0.194978i	−0.659259	−	0.751916i	$-0.729130\pi$
$743$	−9.20534	+	5.31470i	−0.337711	+	0.194978i	0.321548	+	0.946893i	$0.395797\pi$
$744$		0			0
$745$		−	34.1336i		−	1.25056i
$746$	8.62296	−	4.97847i	0.315709	−	0.182275i
$747$		0			0
$748$		−	32.1662i		−	1.17611i
$749$		0			0
$750$		0			0
$751$	19.1185			0.697646			0.348823	−	0.937189i	$-0.386581\pi$
$751$	19.1185			0.697646			0.348823	+	0.937189i	$0.386581\pi$
$752$	−0.209063	+	0.362108i	−0.00762375	+	0.0132047i
$753$		0			0
$754$	−2.82607	+	1.63164i	−0.102920	+	0.0594206i
$755$	25.8411			0.940453
$756$		0			0
$757$	28.5388			1.03726			0.518631	−	0.854998i	$-0.326442\pi$
$757$	28.5388			1.03726			0.518631	+	0.854998i	$0.326442\pi$
$758$	−1.55418	+	0.897305i	−0.0564503	+	0.0325916i
$759$		0			0
$760$	−4.18478	+	7.24825i	−0.151798	+	0.262922i
$761$	43.3300			1.57071			0.785355	−	0.619045i	$-0.212480\pi$
$761$	43.3300			1.57071			0.785355	+	0.619045i	$0.212480\pi$
$762$		0			0
$763$		0			0
$764$		−	16.2674i		−	0.588533i
$765$		0			0
$766$	1.93614	−	1.11783i	0.0699557	−	0.0403889i
$767$			19.4292i			0.701546i
$768$		0			0
$769$	5.75189	−	3.32086i	0.207419	−	0.119753i	−0.392693	−	0.919670i	$-0.628456\pi$
$769$	5.75189	−	3.32086i	0.207419	−	0.119753i	0.600111	+	0.799917i	$0.295123\pi$
$770$		0			0
$771$		0			0
$772$	−12.8120	−	22.1910i	−0.461113	−	0.798672i
$773$	−22.2415	−	38.5235i	−0.799973	−	1.38559i	−0.919633	−	0.392779i	$-0.871514\pi$
$773$	−22.2415	−	38.5235i	−0.799973	−	1.38559i	0.119660	−	0.992815i	$-0.461819\pi$
$774$		0			0
$775$	1.03315	+	0.596491i	0.0371119	+	0.0214266i
$776$	−8.37543	+	14.5067i	−0.300661	+	0.520759i
$777$		0			0
$778$	2.35965	+	4.08703i	0.0845974	+	0.146527i
$779$		−	1.49645i		−	0.0536159i
$780$		0			0
$781$	41.3039			1.47797
$782$	4.54510	−	7.87235i	0.162533	−	0.281515i
$783$		0			0
$784$		0			0
$785$	10.9134	+	6.30087i	0.389517	+	0.224888i
$786$		0			0
$787$	19.0399	+	10.9927i	0.678700	+	0.391848i	0.799365	−	0.600846i	$-0.205169\pi$
$787$	19.0399	+	10.9927i	0.678700	+	0.391848i	−0.120665	+	0.992693i	$0.538503\pi$
$788$	−5.31385	−	3.06795i	−0.189298	−	0.109291i
$789$		0			0
$790$	−6.12744	−	3.53768i	−0.218004	−	0.125865i
$791$		0			0
$792$		0			0
$793$	1.27816	−	2.21384i	0.0453888	−	0.0786157i
$794$	12.3722			0.439075
$795$		0			0
$796$			24.1486i			0.855923i
$797$	9.71892	+	16.8337i	0.344262	+	0.596279i	0.985219	−	0.171297i	$-0.0547959\pi$
$797$	9.71892	+	16.8337i	0.344262	+	0.596279i	−0.640958	+	0.767576i	$0.721463\pi$
$798$		0			0
$799$	−0.734219	+	1.27171i	−0.0259748	+	0.0449897i
$800$	−0.548754	−	0.316823i	−0.0194014	−	0.0112014i
$801$		0			0
$802$	3.55818	+	6.16295i	0.125644	+	0.217621i
$803$	0.722823	+	1.25197i	0.0255079	+	0.0441809i
$804$		0			0
$805$		0			0
$806$	−10.7356	+	6.19820i	−0.378145	+	0.218322i
$807$		0			0
$808$			10.7472i			0.378084i
$809$	18.1916	−	10.5029i	0.639582	−	0.369263i	−0.144872	−	0.989450i	$-0.546277\pi$
$809$	18.1916	−	10.5029i	0.639582	−	0.369263i	0.784453	+	0.620188i	$0.212944\pi$
$810$		0			0
$811$			37.3291i			1.31080i	0.755281	+	0.655401i	$0.227500\pi$
$811$			37.3291i			1.31080i	−0.755281	+	0.655401i	$0.772500\pi$
$812$		0			0
$813$		0			0
$814$	−3.69963			−0.129672
$815$	11.2876	−	19.5506i	0.395386	−	0.684829i
$816$		0			0
$817$	5.58478	−	3.22438i	0.195387	−	0.112807i
$818$	13.0090			0.454849
$819$		0			0
$820$	−3.19639			−0.111623
$821$	−10.9017	+	6.29412i	−0.380473	+	0.219666i	−0.678024	−	0.735040i	$-0.737163\pi$
$821$	−10.9017	+	6.29412i	−0.380473	+	0.219666i	0.297551	+	0.954706i	$0.403830\pi$
$822$		0			0
$823$	22.4189	−	38.8307i	0.781474	−	1.35355i	−0.149608	−	0.988745i	$-0.547801\pi$
$823$	22.4189	−	38.8307i	0.781474	−	1.35355i	0.931083	−	0.364808i	$-0.118865\pi$
$824$	−14.3677			−0.500523
$825$		0			0
$826$		0			0
$827$		−	25.7293i		−	0.894695i	−0.894360	−	0.447347i	$-0.852369\pi$
$827$		−	25.7293i		−	0.894695i	0.894360	−	0.447347i	$-0.147631\pi$
$828$		0			0
$829$	−14.6902	+	8.48139i	−0.510212	+	0.294571i	−0.732921	−	0.680314i	$-0.761843\pi$
$829$	−14.6902	+	8.48139i	−0.510212	+	0.294571i	0.222709	+	0.974885i	$0.428510\pi$
$830$			12.1584i			0.422025i
$831$		0			0
$832$	0.397284	−	0.229372i	0.0137733	−	0.00795204i
$833$		0			0
$834$		0			0
$835$	−3.99450	−	6.91867i	−0.138235	−	0.239431i
$836$	−4.43015	−	7.67324i	−0.153220	−	0.265385i
$837$		0			0
$838$	−6.16680	−	3.56041i	−0.213029	−	0.122992i
$839$	13.3539	−	23.1296i	0.461027	−	0.798522i	−0.537986	−	0.842954i	$-0.680815\pi$
$839$	13.3539	−	23.1296i	0.461027	−	0.798522i	0.999012	+	0.0444321i	$0.0141478\pi$
$840$		0			0
$841$	−10.5167	−	18.2155i	−0.362645	−	0.628120i
$842$			5.89324i			0.203095i
$843$		0			0
$844$	−37.9693			−1.30696
$845$	−10.7819	+	18.6747i	−0.370907	+	0.642430i
$846$		0			0
$847$		0			0
$848$	11.5927	+	6.69305i	0.398095	+	0.229840i
$849$		0			0
$850$	−0.369016	−	0.213051i	−0.0126571	−	0.00730760i
$851$	3.49381	+	2.01715i	0.119766	+	0.0691471i
$852$		0			0
$853$	37.6287	+	21.7249i	1.28838	+	0.743848i	0.978366	−	0.206883i	$-0.0663319\pi$
$853$	37.6287	+	21.7249i	1.28838	+	0.743848i	0.310017	+	0.950731i	$0.399665\pi$
$854$		0			0
$855$		0			0
$856$	1.71448	−	2.96957i	0.0585997	−	0.101498i
$857$	−15.6686			−0.535229			−0.267615	−	0.963526i	$-0.586235\pi$
$857$	−15.6686			−0.535229			−0.267615	+	0.963526i	$0.586235\pi$
$858$		0			0
$859$		−	20.0431i		−	0.683862i	−0.939725	−	0.341931i	$-0.888919\pi$
$859$		−	20.0431i		−	0.683862i	0.939725	−	0.341931i	$-0.111081\pi$
$860$	−6.88721	−	11.9290i	−0.234852	−	0.406775i
$861$		0			0
$862$	4.84727	−	8.39571i	0.165099	−	0.285959i
$863$	−34.6600	−	20.0110i	−1.17984	−	0.681181i	−0.223863	−	0.974621i	$-0.571867\pi$
$863$	−34.6600	−	20.0110i	−1.17984	−	0.681181i	−0.955978	+	0.293439i	$0.905200\pi$
$864$		0			0
$865$	−19.9869	−	34.6184i	−0.679576	−	1.17706i
$866$	1.07010	+	1.85347i	0.0363635	+	0.0629834i
$867$		0			0
$868$		0			0
$869$	14.6545	−	8.46079i	0.497120	−	0.287013i
$870$		0			0
$871$			14.3939i			0.487718i
$872$	8.74660	−	5.04985i	0.296197	−	0.171010i
$873$		0			0
$874$		−	2.50393i		−	0.0846967i
$875$		0			0
$876$		0			0
$877$	45.2705			1.52868			0.764338	−	0.644815i	$-0.223066\pi$
$877$	45.2705			1.52868			0.764338	+	0.644815i	$0.223066\pi$
$878$	2.18931	−	3.79200i	0.0738856	−	0.127974i
$879$		0			0
$880$	−11.0416	+	6.37485i	−0.372211	+	0.214896i
$881$	−45.3385			−1.52749			−0.763746	−	0.645517i	$-0.776642\pi$
$881$	−45.3385			−1.52749			−0.763746	+	0.645517i	$0.776642\pi$
$882$		0			0
$883$	12.5650			0.422845			0.211423	−	0.977395i	$-0.432190\pi$
$883$	12.5650			0.422845			0.211423	+	0.977395i	$0.432190\pi$
$884$	−14.7960	+	8.54245i	−0.497642	+	0.287314i
$885$		0			0
$886$	−3.62178	+	6.27311i	−0.121676	+	0.210749i
$887$	35.7241			1.19950			0.599748	−	0.800189i	$-0.295267\pi$
$887$	35.7241			1.19950			0.599748	+	0.800189i	$0.295267\pi$
$888$		0			0
$889$		0			0
$890$			14.9460i			0.500991i
$891$		0			0
$892$	26.3983	−	15.2411i	0.883881	−	0.510309i
$893$			0.404487i			0.0135356i
$894$		0			0
$895$	9.63528	−	5.56293i	0.322072	−	0.185948i
$896$		0			0
$897$		0			0
$898$	−7.97346	−	13.8104i	−0.266078	−	0.460860i
$899$	15.1316	+	26.2087i	0.504667	+	0.874108i
$900$		0			0
$901$	40.7130	+	23.5056i	1.35635	+	0.783086i
$902$	−0.990571	+	1.71572i	−0.0329824	+	0.0571272i
$903$		0			0
$904$	−19.7738	−	34.2491i	−0.657665	−	1.13911i
$905$			29.9801i			0.996573i
$906$		0			0
$907$	−9.04208			−0.300237			−0.150119	−	0.988668i	$-0.547966\pi$
$907$	−9.04208			−0.300237			−0.150119	+	0.988668i	$0.547966\pi$
$908$	−6.88721	+	11.9290i	−0.228560	+	0.395878i
$909$		0			0
$910$		0			0
$911$	35.5171	+	20.5058i	1.17673	+	0.679388i	0.955257	−	0.295777i	$-0.0955787\pi$
$911$	35.5171	+	20.5058i	1.17673	+	0.679388i	0.221478	+	0.975165i	$0.428912\pi$
$912$		0			0
$913$	−25.1826	−	14.5392i	−0.833421	−	0.481176i
$914$	−7.00619	−	4.04503i	−0.231744	−	0.133798i
$915$		0			0
$916$	−19.7652	−	11.4114i	−0.653059	−	0.377044i
$917$		0			0
$918$		0			0
$919$	−5.11628	+	8.86166i	−0.168771	+	0.292319i	−0.937988	−	0.346668i	$-0.887313\pi$
$919$	−5.11628	+	8.86166i	−0.168771	+	0.292319i	0.769217	+	0.638987i	$0.220646\pi$
$920$	−12.0828			−0.398357
$921$		0			0
$922$		−	18.4818i		−	0.608665i
$923$	−10.9692	−	18.9992i	−0.361055	−	0.625366i
$924$		0			0
$925$	0.0945538	−	0.163772i	0.00310891	−	0.00538479i
$926$	13.9862	+	8.07492i	0.459614	+	0.265358i
$927$		0			0
$928$	−8.03706	−	13.9206i	−0.263830	−	0.456966i
$929$	12.8330	+	22.2273i	0.421036	+	0.729255i	0.996041	−	0.0888945i	$-0.0283334\pi$
$929$	12.8330	+	22.2273i	0.421036	+	0.729255i	−0.575005	+	0.818150i	$0.695000\pi$
$930$		0			0
$931$		0			0
$932$	−40.8763	+	23.5999i	−1.33895	+	0.773041i
$933$		0			0
$934$			16.4215i			0.537328i
$935$	−38.7774	+	22.3881i	−1.26816	+	0.732170i
$936$		0			0
$937$			15.9276i			0.520333i	0.965564	+	0.260167i	$0.0837775\pi$
$937$			15.9276i			0.520333i	−0.965564	+	0.260167i	$0.916223\pi$
$938$		0			0
$939$		0			0
$940$	0.863976			0.0281798
$941$	−19.6767	+	34.0810i	−0.641442	+	1.11101i	0.343669	+	0.939091i	$0.388330\pi$
$941$	−19.6767	+	34.0810i	−0.641442	+	1.11101i	−0.985111	+	0.171919i	$0.945003\pi$
$942$		0			0
$943$	1.87093	−	1.08018i	0.0609258	−	0.0351755i
$944$	−18.3252			−0.596433
$945$		0			0
$946$	−8.53747			−0.277577
$947$	28.9086	−	16.6904i	0.939403	−	0.542365i	0.0496302	−	0.998768i	$-0.484196\pi$
$947$	28.9086	−	16.6904i	0.939403	−	0.542365i	0.889773	+	0.456403i	$0.150862\pi$
$948$		0			0
$949$	0.383923	−	0.664975i	0.0124627	−	0.0215860i
$950$	−0.117372			−0.00380804
$951$		0			0
$952$		0			0
$953$			44.4622i			1.44027i	0.693832	+	0.720137i	$0.255921\pi$
$953$			44.4622i			1.44027i	−0.693832	+	0.720137i	$0.744079\pi$
$954$		0			0
$955$	−19.6108	+	11.3223i	−0.634592	+	0.366382i
$956$			25.1456i			0.813266i
$957$		0			0
$958$	0.297540	−	0.171785i	0.00961307	−	0.00555011i
$959$		0			0
$960$		0			0
$961$	41.9814	+	72.7138i	1.35424	+	2.34561i
$962$	0.982519	+	1.70177i	0.0316777	+	0.0548674i
$963$		0			0
$964$	−6.90895	−	3.98888i	−0.222522	−	0.128473i
$965$	−17.8347	+	30.8905i	−0.574118	+	0.994401i
$966$		0			0
$967$	−20.0556	−	34.7372i	−0.644943	−	1.11707i	−0.984315	−	0.176422i	$-0.943548\pi$
$967$	−20.0556	−	34.7372i	−0.644943	−	1.11707i	0.339371	−	0.940652i	$-0.389786\pi$
$968$			1.17535i			0.0377771i
$969$		0			0
$970$	10.3214			0.331401
$971$	−23.0013	+	39.8394i	−0.738147	+	1.27851i	0.215181	+	0.976574i	$0.430966\pi$
$971$	−23.0013	+	39.8394i	−0.738147	+	1.27851i	−0.953329	+	0.301934i	$0.902368\pi$
$972$		0			0
$973$		0			0
$974$	18.9650	+	10.9494i	0.607678	+	0.350843i
$975$		0			0
$976$	2.08804	+	1.20553i	0.0668366	+	0.0385882i
$977$	−46.8323	−	27.0386i	−1.49830	−	0.865042i	−0.498299	−	0.867005i	$-0.666042\pi$
$977$	−46.8323	−	27.0386i	−1.49830	−	0.865042i	−0.999998	+	0.00196335i	$0.999375\pi$
$978$		0			0
$979$	−30.9562	−	17.8726i	−0.989365	−	0.571210i
$980$		0			0
$981$		0			0
$982$	2.17418	−	3.76579i	0.0693809	−	0.120171i
$983$	−13.9578			−0.445185			−0.222592	−	0.974912i	$-0.571452\pi$
$983$	−13.9578			−0.445185			−0.222592	+	0.974912i	$0.571452\pi$
$984$		0			0
$985$			8.54135i			0.272150i
$986$	−5.40462	−	9.36107i	−0.172118	−	0.298117i
$987$		0			0
$988$	−2.35305	+	4.07560i	−0.0748605	+	0.129662i
$989$	8.06251	+	4.65489i	0.256373	+	0.148017i
$990$		0			0
$991$	18.5149	+	32.0687i	0.588144	+	1.01869i	0.994475	+	0.104969i	$0.0334744\pi$
$991$	18.5149	+	32.0687i	0.588144	+	1.01869i	−0.406332	+	0.913726i	$0.633192\pi$
$992$	−30.5309	−	52.8811i	−0.969358	−	1.67898i
$993$		0			0
$994$		0			0
$995$	29.1119	−	16.8077i	0.922909	−	0.532841i
$996$		0			0
$997$			50.1466i			1.58816i	0.607815	+	0.794079i	$0.292046\pi$
$997$			50.1466i			1.58816i	−0.607815	+	0.794079i	$0.707954\pi$
$998$	−4.77885	+	2.75907i	−0.151272	+	0.0873368i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.s.c.656.4		12
3.2	odd	2		441.2.s.c.362.3		12
7.2	even	3		189.2.o.a.62.3		12
7.3	odd	6		1323.2.i.c.521.4		12
7.4	even	3		1323.2.i.c.521.3		12
7.5	odd	6		189.2.o.a.62.4		12
7.6	odd	2	inner	1323.2.s.c.656.3		12
9.4	even	3		441.2.i.c.68.4		12
9.5	odd	6		1323.2.i.c.1097.4		12
21.2	odd	6		63.2.o.a.20.4	yes	12
21.5	even	6		63.2.o.a.20.3	✓	12
21.11	odd	6		441.2.i.c.227.3		12
21.17	even	6		441.2.i.c.227.4		12
21.20	even	2		441.2.s.c.362.4		12
28.19	even	6		3024.2.cc.a.2897.5		12
28.23	odd	6		3024.2.cc.a.2897.2		12
63.2	odd	6		567.2.c.c.566.7		12
63.4	even	3		441.2.s.c.374.4		12
63.5	even	6		189.2.o.a.125.3		12
63.13	odd	6		441.2.i.c.68.3		12
63.16	even	3		567.2.c.c.566.6		12
63.23	odd	6		189.2.o.a.125.4		12
63.31	odd	6		441.2.s.c.374.3		12
63.32	odd	6	inner	1323.2.s.c.962.3		12
63.40	odd	6		63.2.o.a.41.4	yes	12
63.41	even	6		1323.2.i.c.1097.3		12
63.47	even	6		567.2.c.c.566.8		12
63.58	even	3		63.2.o.a.41.3	yes	12
63.59	even	6	inner	1323.2.s.c.962.4		12
63.61	odd	6		567.2.c.c.566.5		12
84.23	even	6		1008.2.cc.a.209.1		12
84.47	odd	6		1008.2.cc.a.209.6		12
252.23	even	6		3024.2.cc.a.881.5		12
252.103	even	6		1008.2.cc.a.545.1		12
252.131	odd	6		3024.2.cc.a.881.2		12
252.247	odd	6		1008.2.cc.a.545.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.o.a.20.3	✓	12	21.5	even	6
63.2.o.a.20.4	yes	12	21.2	odd	6
63.2.o.a.41.3	yes	12	63.58	even	3
63.2.o.a.41.4	yes	12	63.40	odd	6
189.2.o.a.62.3		12	7.2	even	3
189.2.o.a.62.4		12	7.5	odd	6
189.2.o.a.125.3		12	63.5	even	6
189.2.o.a.125.4		12	63.23	odd	6
441.2.i.c.68.3		12	63.13	odd	6
441.2.i.c.68.4		12	9.4	even	3
441.2.i.c.227.3		12	21.11	odd	6
441.2.i.c.227.4		12	21.17	even	6
441.2.s.c.362.3		12	3.2	odd	2
441.2.s.c.362.4		12	21.20	even	2
441.2.s.c.374.3		12	63.31	odd	6
441.2.s.c.374.4		12	63.4	even	3
567.2.c.c.566.5		12	63.61	odd	6
567.2.c.c.566.6		12	63.16	even	3
567.2.c.c.566.7		12	63.2	odd	6
567.2.c.c.566.8		12	63.47	even	6
1008.2.cc.a.209.1		12	84.23	even	6
1008.2.cc.a.209.6		12	84.47	odd	6
1008.2.cc.a.545.1		12	252.103	even	6
1008.2.cc.a.545.6		12	252.247	odd	6
1323.2.i.c.521.3		12	7.4	even	3
1323.2.i.c.521.4		12	7.3	odd	6
1323.2.i.c.1097.3		12	63.41	even	6
1323.2.i.c.1097.4		12	9.5	odd	6
1323.2.s.c.656.3		12	7.6	odd	2	inner
1323.2.s.c.656.4		12	1.1	even	1	trivial
1323.2.s.c.962.3		12	63.32	odd	6	inner
1323.2.s.c.962.4		12	63.59	even	6	inner
3024.2.cc.a.881.2		12	252.131	odd	6
3024.2.cc.a.881.5		12	252.23	even	6
3024.2.cc.a.2897.2		12	28.23	odd	6
3024.2.cc.a.2897.5		12	28.19	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.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.555632 + 0.320794i) q^{2} +(-0.794182 + 1.37556i) q^{4} +2.21105 q^{5} -2.30225i q^{8} +O(q^{10})\)	\(q+(-0.555632 + 0.320794i) q^{2} +(-0.794182 + 1.37556i) q^{4} +2.21105 q^{5} -2.30225i q^{8} +(-1.22853 + 0.709292i) q^{10} -3.39272i q^{11} +(-1.56060 + 0.901012i) q^{13} +(-0.849814 - 1.47192i) q^{16} +(-2.98450 - 5.16931i) q^{17} +(-1.42391 - 0.822093i) q^{19} +(-1.75597 + 3.04144i) q^{20} +(1.08836 + 1.88510i) q^{22} -2.37364i q^{23} -0.111264 q^{25} +(0.578079 - 1.00126i) q^{26} +(-2.44437 - 1.41126i) q^{29} +(-9.28558 - 5.36103i) q^{31} +(4.93199 + 2.84748i) q^{32} +(3.31657 + 1.91482i) q^{34} +(-0.849814 + 1.47192i) q^{37} +1.05489 q^{38} -5.09039i q^{40} +(0.455074 + 0.788211i) q^{41} +(-1.96108 + 3.39669i) q^{43} +(4.66690 + 2.69443i) q^{44} +(0.761450 + 1.31887i) q^{46} +(-0.123005 - 0.213051i) q^{47} +(0.0618219 - 0.0356929i) q^{50} -2.86227i q^{52} +(-6.82072 + 3.93795i) q^{53} -7.50146i q^{55} +1.81089 q^{58} +(5.39093 - 9.33736i) q^{59} +(-1.22853 + 0.709292i) q^{61} +6.87916 q^{62} -0.254572 q^{64} +(-3.45056 + 1.99218i) q^{65} +(3.99381 - 6.91748i) q^{67} +9.48096 q^{68} +12.1743i q^{71} +(-0.369016 + 0.213051i) q^{73} -1.09046i q^{74} +(2.26168 - 1.30578i) q^{76} +(2.49381 + 4.31941i) q^{79} +(-1.87898 - 3.25449i) q^{80} +(-0.505707 - 0.291970i) q^{82} +(4.28541 - 7.42254i) q^{83} +(-6.59888 - 11.4296i) q^{85} -2.51641i q^{86} -7.81089 q^{88} +(5.26792 - 9.12431i) q^{89} +(3.26509 + 1.88510i) q^{92} +(0.136691 + 0.0789188i) q^{94} +(-3.14833 - 1.81769i) q^{95} +(-6.30108 - 3.63793i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} + 2 q^{4}+O(q^{10}) \) 12 * q - 6 * q^2 + 2 * q^4	\( 12 q - 6 q^{2} + 2 q^{4} + 2 q^{16} - 10 q^{22} - 30 q^{29} - 12 q^{32} + 2 q^{37} - 10 q^{43} + 54 q^{44} + 20 q^{46} + 36 q^{50} - 12 q^{53} - 4 q^{58} + 16 q^{64} - 78 q^{65} + 12 q^{67} - 6 q^{79} - 6 q^{85} - 68 q^{88} - 30 q^{92} + 72 q^{95}+O(q^{100}) \) 12 * q - 6 * q^2 + 2 * q^4 + 2 * q^16 - 10 * q^22 - 30 * q^29 - 12 * q^32 + 2 * q^37 - 10 * q^43 + 54 * q^44 + 20 * q^46 + 36 * q^50 - 12 * q^53 - 4 * q^58 + 16 * q^64 - 78 * q^65 + 12 * q^67 - 6 * q^79 - 6 * q^85 - 68 * q^88 - 30 * q^92 + 72 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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