LMFDB - Embedded newform 1323.2.i.c.1097.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(521,1323)]

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, 1]))

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

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

chi := DirichletCharacter("1323.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.i (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			1097.3
Root			$-0.474636 + 0.274031i$ of defining polynomial
Character	$\chi$	$=$	1323.1097
Dual form			1323.2.i.c.521.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.641589i q^{2} +1.58836 q^{4} +(-1.10552 - 1.91482i) q^{5} +2.30225i q^{8} +O(q^{10})$	\(q+0.641589i q^{2} +1.58836 q^{4} +(-1.10552 - 1.91482i) q^{5} +2.30225i q^{8} +(1.22853 - 0.709292i) q^{10} +(-2.93818 - 1.69636i) q^{11} +(-1.56060 - 0.901012i) q^{13} +1.69963 q^{16} +(-2.98450 - 5.16931i) q^{17} +(1.42391 + 0.822093i) q^{19} +(-1.75597 - 3.04144i) q^{20} +(1.08836 - 1.88510i) q^{22} +(2.05563 - 1.18682i) q^{23} +(0.0556321 - 0.0963576i) q^{25} +(0.578079 - 1.00126i) q^{26} +(-2.44437 + 1.41126i) q^{29} -10.7221i q^{31} +5.69497i q^{32} +(3.31657 - 1.91482i) q^{34} +(-0.849814 + 1.47192i) q^{37} +(-0.527445 + 0.913562i) q^{38} +(4.40841 - 2.54520i) q^{40} +(0.455074 - 0.788211i) q^{41} +(-1.96108 - 3.39669i) q^{43} +(-4.66690 - 2.69443i) q^{44} +(0.761450 + 1.31887i) q^{46} +0.246010 q^{47} +(0.0618219 + 0.0356929i) q^{50} +(-2.47880 - 1.43113i) q^{52} +(6.82072 - 3.93795i) q^{53} +7.50146i q^{55} +(-0.905446 - 1.56828i) q^{58} -10.7819 q^{59} +1.41858i q^{61} +6.87916 q^{62} -0.254572 q^{64} +3.98436i q^{65} -7.98762 q^{67} +(-4.74048 - 8.21075i) q^{68} -12.1743i q^{71} +(0.369016 - 0.213051i) q^{73} +(-0.944368 - 0.545231i) q^{74} +(2.26168 + 1.30578i) q^{76} -4.98762 q^{79} +(-1.87898 - 3.25449i) q^{80} +(0.505707 + 0.291970i) q^{82} +(4.28541 + 7.42254i) q^{83} +(-6.59888 + 11.4296i) q^{85} +(2.17928 - 1.25821i) q^{86} +(3.90545 - 6.76443i) q^{88} +(5.26792 - 9.12431i) q^{89} +(3.26509 - 1.88510i) q^{92} +0.157838i q^{94} -3.63537i q^{95} +(-6.30108 + 3.63793i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{4}+O(q^{10}) $ 12 * q - 4 * q^4	$ 12 q - 4 q^{4} - 4 q^{16} - 10 q^{22} + 24 q^{23} - 30 q^{29} + 2 q^{37} - 10 q^{43} - 54 q^{44} + 20 q^{46} + 36 q^{50} + 12 q^{53} + 2 q^{58} + 16 q^{64} - 24 q^{67} - 12 q^{74} + 12 q^{79} - 6 q^{85} + 96 q^{86} + 34 q^{88} - 30 q^{92}+O(q^{100}) $ 12 * q - 4 * q^4 - 4 * q^16 - 10 * q^22 + 24 * q^23 - 30 * q^29 + 2 * q^37 - 10 * q^43 - 54 * q^44 + 20 * q^46 + 36 * q^50 + 12 * q^53 + 2 * q^58 + 16 * q^64 - 24 * q^67 - 12 * q^74 + 12 * q^79 - 6 * q^85 + 96 * q^86 + 34 * q^88 - 30 * q^92

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$			0.641589i			0.453672i	0.973933	+	0.226836i	$0.0728381\pi$
$2$			0.641589i			0.453672i	−0.973933	+	0.226836i	$0.927162\pi$
$3$		0			0
$3$		0			0
$4$	1.58836			0.794182
$5$	−1.10552	−	1.91482i	−0.494405	−	0.856335i	0.505574	−	0.862783i	$-0.331281\pi$
$5$	−1.10552	−	1.91482i	−0.494405	−	0.856335i	−0.999979	+	0.00644798i	$0.997948\pi$
$6$		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
$11$	−2.93818	−	1.69636i	−0.885894	−	0.511471i	−0.0132968	−	0.999912i	$-0.504233\pi$
$11$	−2.93818	−	1.69636i	−0.885894	−	0.511471i	−0.872597	+	0.488440i	$0.837566\pi$
$12$		0			0
$13$	−1.56060	−	0.901012i	−0.432832	−	0.249896i	0.267720	−	0.963497i	$-0.413730\pi$
$13$	−1.56060	−	0.901012i	−0.432832	−	0.249896i	−0.700552	+	0.713601i	$0.747063\pi$
$14$		0			0
$15$		0			0
$16$	1.69963			0.424907
$17$	−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	0.654360	−	0.756183i	$-0.272938\pi$
$19$	1.42391	+	0.822093i	0.326667	+	0.188601i	−0.327694	+	0.944784i	$0.606271\pi$
$20$	−1.75597	−	3.04144i	−0.392648	−	0.680086i
$21$		0			0
$22$	1.08836	−	1.88510i	0.232040	−	0.401905i
$23$	2.05563	−	1.18682i	0.428629	−	0.247469i	−0.270133	−	0.962823i	$-0.587068\pi$
$23$	2.05563	−	1.18682i	0.428629	−	0.247469i	0.698762	+	0.715354i	$0.253734\pi$
$24$		0			0
$25$	0.0556321	−	0.0963576i	0.0111264	−	0.0192715i
$26$	0.578079	−	1.00126i	0.113371	−	0.196364i
$27$		0			0
$28$		0			0
$29$	−2.44437	+	1.41126i	−0.453908	+	0.262064i	−0.709479	−	0.704726i	$-0.751070\pi$
$29$	−2.44437	+	1.41126i	−0.453908	+	0.262064i	0.255571	+	0.966790i	$0.417736\pi$
$30$		0			0
$31$		−	10.7221i		−	1.92574i	−0.269966	−	0.962870i	$-0.587012\pi$
$31$		−	10.7221i		−	1.92574i	0.269966	−	0.962870i	$-0.412988\pi$
$32$			5.69497i			1.00674i
$33$		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	$0.211283\pi$
$38$	−0.527445	+	0.913562i	−0.0855630	+	0.148199i
$39$		0			0
$40$	4.40841	−	2.54520i	0.697031	−	0.402431i
$41$	0.455074	−	0.788211i	0.0710706	−	0.123098i	−0.828300	−	0.560285i	$-0.810692\pi$
$41$	0.455074	−	0.788211i	0.0710706	−	0.123098i	0.899371	+	0.437187i	$0.144025\pi$
$42$		0			0
$43$	−1.96108	−	3.39669i	−0.299062	−	0.517990i	0.676860	−	0.736112i	$-0.263340\pi$
$43$	−1.96108	−	3.39669i	−0.299062	−	0.517990i	−0.975922	+	0.218122i	$0.930007\pi$
$44$	−4.66690	−	2.69443i	−0.703561	−	0.406201i
$45$		0			0
$46$	0.761450	+	1.31887i	0.112270	+	0.194457i
$47$	0.246010			0.0358843			0.0179422	−	0.999839i	$-0.494289\pi$
$47$	0.246010			0.0358843			0.0179422	+	0.999839i	$0.494289\pi$
$48$		0			0
$49$		0			0
$50$	0.0618219	+	0.0356929i	0.00874294	+	0.00504774i
$51$		0			0
$52$	−2.47880	−	1.43113i	−0.343747	−	0.198463i
$53$	6.82072	−	3.93795i	0.936899	−	0.540919i	0.0479118	−	0.998852i	$-0.484743\pi$
$53$	6.82072	−	3.93795i	0.936899	−	0.540919i	0.888987	+	0.457933i	$0.151410\pi$
$54$		0			0
$55$			7.50146i			1.01150i
$56$		0			0
$57$		0			0
$58$	−0.905446	−	1.56828i	−0.118891	−	0.205925i
$59$	−10.7819			−1.40368			−0.701839	−	0.712335i	$-0.747638\pi$
$59$	−10.7819			−1.40368			−0.701839	+	0.712335i	$0.747638\pi$
$60$		0			0
$61$			1.41858i			0.181631i	0.995868	+	0.0908155i	$0.0289474\pi$
$61$			1.41858i			0.181631i	−0.995868	+	0.0908155i	$0.971053\pi$
$62$	6.87916			0.873654
$63$		0			0
$64$	−0.254572			−0.0318214
$65$			3.98436i			0.494199i
$66$		0			0
$67$	−7.98762			−0.975843			−0.487922	−	0.872887i	$-0.662245\pi$
$67$	−7.98762			−0.975843			−0.487922	+	0.872887i	$0.662245\pi$
$68$	−4.74048	−	8.21075i	−0.574868	−	0.995700i
$69$		0			0
$70$		0			0
$71$		−	12.1743i		−	1.44482i	−0.691463	−	0.722412i	$-0.743034\pi$
$71$		−	12.1743i		−	1.44482i	0.691463	−	0.722412i	$-0.256966\pi$
$72$		0			0
$73$	0.369016	−	0.213051i	0.0431900	−	0.0249358i	−0.478250	−	0.878224i	$-0.658729\pi$
$73$	0.369016	−	0.213051i	0.0431900	−	0.0249358i	0.521440	+	0.853288i	$0.325395\pi$
$74$	−0.944368	−	0.545231i	−0.109781	−	0.0633818i
$75$		0			0
$76$	2.26168	+	1.30578i	0.259433	+	0.149784i
$77$		0			0
$78$		0			0
$79$	−4.98762			−0.561151			−0.280576	−	0.959832i	$-0.590525\pi$
$79$	−4.98762			−0.561151			−0.280576	+	0.959832i	$0.590525\pi$
$80$	−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	0.999426	−	0.0338660i	$-0.0107819\pi$
$83$	4.28541	+	7.42254i	0.470384	+	0.814730i	−0.529042	+	0.848596i	$0.677449\pi$
$84$		0			0
$85$	−6.59888	+	11.4296i	−0.715750	+	1.23971i
$86$	2.17928	−	1.25821i	0.234997	−	0.135676i
$87$		0			0
$88$	3.90545	−	6.76443i	0.416322	−	0.721091i
$89$	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
$94$			0.157838i			0.0162797i
$95$		−	3.63537i		−	0.372982i
$96$		0			0
$97$	−6.30108	+	3.63793i	−0.639777	+	0.369376i	−0.784529	−	0.620092i	$-0.787095\pi$
$97$	−6.30108	+	3.63793i	−0.639777	+	0.369376i	0.144751	+	0.989468i	$0.453762\pi$
$98$		0			0
$99$		0			0
$100$	0.0883640	−	0.153051i	0.00883640	−	0.0153051i
$101$	2.33405	−	4.04270i	0.232247	−	0.402264i	−0.726222	−	0.687460i	$-0.758726\pi$
$101$	2.33405	−	4.04270i	0.232247	−	0.402264i	0.958469	+	0.285197i	$0.0920589\pi$
$102$		0			0
$103$	5.40462	−	3.12036i	0.532533	−	0.307458i	−0.209515	−	0.977806i	$-0.567188\pi$
$103$	5.40462	−	3.12036i	0.532533	−	0.307458i	0.742047	+	0.670348i	$0.233855\pi$
$104$	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	0.436355	−	0.899774i	$-0.356269\pi$
$107$	−1.28985	−	0.744696i	−0.124695	−	0.0719925i	−0.561050	+	0.827782i	$0.689602\pi$
$108$		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	$0.765957\pi$
$110$	−4.81285			−0.458887
$111$		0			0
$112$		0			0
$113$	14.8764	+	8.58887i	1.39945	+	0.807973i	0.994335	−	0.106293i	$-0.0338981\pi$
$113$	14.8764	+	8.58887i	1.39945	+	0.807973i	0.405115	+	0.914266i	$0.367231\pi$
$114$		0			0
$115$	−4.54510	−	2.62412i	−0.423833	−	0.244700i
$116$	−3.88255	+	2.24159i	−0.360485	+	0.208126i
$117$		0			0
$118$		−	6.91752i		−	0.636809i
$119$		0			0
$120$		0			0
$121$	0.255260	+	0.442124i	0.0232055	+	0.0401931i
$122$	−0.910147			−0.0824009
$123$		0			0
$124$		−	17.0305i		−	1.52939i
$125$	−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	$0.409511\pi$
$128$			11.2266i			0.992301i
$129$		0			0
$130$	−2.55632			−0.224204
$131$	8.51213	+	14.7434i	0.743708	+	1.28814i	0.950796	+	0.309818i	$0.100268\pi$
$131$	8.51213	+	14.7434i	0.743708	+	1.28814i	−0.207088	+	0.978322i	$0.566399\pi$
$132$		0			0
$133$		0			0
$134$		−	5.12477i		−	0.442712i
$135$		0			0
$136$	11.9011	−	6.87109i	1.02051	−	0.589191i
$137$	5.42580	+	3.13259i	0.463557	+	0.267635i	0.713539	−	0.700616i	$-0.247091\pi$
$137$	5.42580	+	3.13259i	0.463557	+	0.267635i	−0.249982	+	0.968251i	$0.580425\pi$
$138$		0			0
$139$	6.65488	+	3.84220i	0.564460	+	0.325891i	0.754934	−	0.655801i	$-0.227669\pi$
$139$	6.65488	+	3.84220i	0.564460	+	0.325891i	−0.190474	+	0.981692i	$0.561002\pi$
$140$		0			0
$141$		0			0
$142$	7.81089			0.655476
$143$	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
$149$	13.3695	−	7.71887i	1.09527	−	0.632355i	0.160296	−	0.987069i	$-0.448755\pi$
$149$	13.3695	−	7.71887i	1.09527	−	0.632355i	0.934975	+	0.354714i	$0.115422\pi$
$150$		0			0
$151$	−5.84362	+	10.1215i	−0.475547	+	0.823672i	−0.999608	−	0.0280089i	$-0.991083\pi$
$151$	−5.84362	+	10.1215i	−0.475547	+	0.823672i	0.524060	+	0.851681i	$0.324417\pi$
$152$	−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
$157$			5.69944i			0.454865i	0.973794	+	0.227432i	$0.0730330\pi$
$157$			5.69944i			0.454865i	−0.973794	+	0.227432i	$0.926967\pi$
$158$		−	3.20000i		−	0.254578i
$159$		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	$0.0357253\pi$
$164$	0.722823	−	1.25197i	0.0564430	−	0.0977621i
$165$		0			0
$166$	−4.76222	+	2.74947i	−0.369620	+	0.213400i
$167$	−1.80661	+	3.12914i	−0.139800	+	0.242140i	−0.927421	−	0.374020i	$-0.877979\pi$
$167$	−1.80661	+	3.12914i	−0.139800	+	0.242140i	0.787621	+	0.616160i	$0.211312\pi$
$168$		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
$173$	18.0791			1.37453			0.687266	−	0.726406i	$-0.258811\pi$
$173$	18.0791			1.37453			0.687266	+	0.726406i	$0.258811\pi$
$174$		0			0
$175$		0			0
$176$	−4.99381	−	2.88318i	−0.376423	−	0.217328i
$177$		0			0
$178$	5.85406	+	3.37984i	0.438780	+	0.253330i
$179$	−4.35779	+	2.51597i	−0.325716	+	0.188052i	−0.653938	−	0.756548i	$-0.726884\pi$
$179$	−4.35779	+	2.51597i	−0.325716	+	0.188052i	0.328221	+	0.944601i	$0.393551\pi$
$180$		0			0
$181$		−	13.5592i		−	1.00785i	−0.863747	−	0.503925i	$-0.831889\pi$
$181$		−	13.5592i		−	1.00785i	0.863747	−	0.503925i	$-0.168111\pi$
$182$		0			0
$183$		0			0
$184$	2.73236	+	4.73259i	0.201432	+	0.348891i
$185$	3.75796			0.276291
$186$		0			0
$187$			20.2512i			1.48091i
$188$	0.390754			0.0284987
$189$		0			0
$190$	2.33242			0.169211
$191$			10.2416i			0.741055i	0.928821	+	0.370528i	$0.120823\pi$
$191$			10.2416i			0.741055i	−0.928821	+	0.370528i	$0.879177\pi$
$192$		0			0
$193$	16.1323			1.16123			0.580614	−	0.814179i	$-0.302812\pi$
$193$	16.1323			1.16123			0.580614	+	0.814179i	$0.302812\pi$
$194$	−2.33405	−	4.04270i	−0.167575	−	0.290249i
$195$		0			0
$196$		0			0
$197$		−	3.86303i		−	0.275230i	−0.990486	−	0.137615i	$-0.956056\pi$
$197$		−	3.86303i		−	0.275230i	0.990486	−	0.137615i	$-0.0439436\pi$
$198$		0			0
$199$	−13.1665	+	7.60171i	−0.933352	+	0.538871i	−0.887870	−	0.460094i	$-0.847816\pi$
$199$	−13.1665	+	7.60171i	−0.933352	+	0.538871i	−0.0454817	+	0.998965i	$0.514482\pi$
$200$	0.221840	+	0.128079i	0.0156864	+	0.00905656i
$201$		0			0
$202$	2.59375	+	1.49750i	0.182496	+	0.105364i
$203$		0			0
$204$		0			0
$205$	−2.01238			−0.140551
$206$	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	−0.0807311	−	0.996736i	$-0.525726\pi$
$211$	11.9523	−	20.7021i	0.822833	−	1.42519i	0.903564	−	0.428453i	$-0.140941\pi$
$212$	10.8338	−	6.25489i	0.744068	−	0.429588i
$213$		0			0
$214$	0.477789	−	0.827554i	0.0326610	−	0.0565704i
$215$	−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
$220$			11.9150i			0.803312i
$221$			10.7563i			0.723547i
$222$		0			0
$223$	−16.6198	+	9.59545i	−1.11294	+	0.642559i	−0.939591	−	0.342300i	$-0.888794\pi$
$223$	−16.6198	+	9.59545i	−1.11294	+	0.642559i	−0.173354	+	0.984860i	$0.555461\pi$
$224$		0			0
$225$		0			0
$226$	−5.51052	+	9.54450i	−0.366554	+	0.634891i
$227$	−4.33604	+	7.51024i	−0.287793	+	0.498472i	−0.973283	−	0.229610i	$-0.926255\pi$
$227$	−4.33604	+	7.51024i	−0.287793	+	0.498472i	0.685490	+	0.728082i	$0.259588\pi$
$228$		0			0
$229$	−12.4437	+	7.18439i	−0.822304	+	0.474758i	−0.851211	−	0.524824i	$-0.824131\pi$
$229$	−12.4437	+	7.18439i	−0.822304	+	0.474758i	0.0289060	+	0.999582i	$0.490798\pi$
$230$	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	$-0.906942\pi$
$233$	−25.7348	−	14.8580i	−1.68594	−	0.973381i	−0.728375	−	0.685178i	$-0.759724\pi$
$234$		0			0
$235$	−0.271971	−	0.471067i	−0.0177414	−	0.0307290i
$236$	−17.1255			−1.11478
$237$		0			0
$238$		0			0
$239$	13.7101	+	7.91556i	0.886836	+	0.512015i	0.872906	−	0.487888i	$-0.162233\pi$
$239$	13.7101	+	7.91556i	0.886836	+	0.512015i	0.0139296	+	0.999903i	$0.495566\pi$
$240$		0			0
$241$	4.34973	+	2.51132i	0.280190	+	0.161768i	0.633510	−	0.773735i	$-0.281614\pi$
$241$	4.34973	+	2.51132i	0.280190	+	0.161768i	−0.353319	+	0.935503i	$0.614947\pi$
$242$	−0.283662	+	0.163772i	−0.0182345	+	0.0105277i
$243$		0			0
$244$			2.25323i			0.144248i
$245$		0			0
$246$		0			0
$247$	−1.48143	−	2.56591i	−0.0942612	−	0.163265i
$248$	24.6849			1.56749
$249$		0			0
$250$		−	7.25076i		−	0.458578i
$251$	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
$254$			4.05575i			0.254480i
$255$		0			0
$256$	−7.71201			−0.482000
$257$	4.00397	+	6.93508i	0.249761	+	0.432598i	0.963459	−	0.267855i	$-0.0863147\pi$
$257$	4.00397	+	6.93508i	0.249761	+	0.432598i	−0.713699	+	0.700453i	$0.752981\pi$
$258$		0			0
$259$		0			0
$260$			6.32862i			0.392484i
$261$		0			0
$262$	−9.45922	+	5.46128i	−0.584393	+	0.337399i
$263$	−13.6051	−	7.85489i	−0.838925	−	0.484353i	0.0179738	−	0.999838i	$-0.494278\pi$
$263$	−13.6051	−	7.85489i	−0.838925	−	0.484353i	−0.856899	+	0.515485i	$0.827612\pi$
$264$		0			0
$265$	−15.0810	−	8.70699i	−0.926416	−	0.534866i
$266$		0			0
$267$		0			0
$268$	−12.6872			−0.774997
$269$	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	−0.216859	−	0.976203i	$-0.569581\pi$
$271$	−19.2722	−	11.1268i	−1.17071	−	0.675907i	−0.953846	+	0.300296i	$0.902915\pi$
$272$	−5.07255	−	8.78591i	−0.307568	−	0.532724i
$273$		0			0
$274$	−2.00983	+	3.48113i	−0.121418	+	0.210303i
$275$	−0.326914	+	0.188744i	−0.0197137	+	0.0113817i
$276$		0			0
$277$	11.4251	−	19.7889i	0.686468	−	1.18900i	−0.286505	−	0.958079i	$-0.592493\pi$
$277$	11.4251	−	19.7889i	0.686468	−	1.18900i	0.972973	−	0.230919i	$-0.0741733\pi$
$278$	−2.46511	+	4.26970i	−0.147848	+	0.256079i
$279$		0			0
$280$		0			0
$281$	−0.796041	+	0.459595i	−0.0474878	+	0.0274171i	−0.523556	−	0.851991i	$-0.675395\pi$
$281$	−0.796041	+	0.459595i	−0.0474878	+	0.0274171i	0.476068	+	0.879408i	$0.342062\pi$
$282$		0			0
$283$			22.1209i			1.31495i	0.753475	+	0.657477i	$0.228376\pi$
$283$			22.1209i			1.31495i	−0.753475	+	0.657477i	$0.771624\pi$
$284$		−	19.3372i		−	1.14745i
$285$		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
$290$	−2.00199	+	3.46754i	−0.117561	+	0.203621i
$291$		0			0
$292$	0.586131	−	0.338403i	0.0343007	−	0.0198035i
$293$	−14.6259	+	25.3328i	−0.854453	+	1.47996i	0.0226986	+	0.999742i	$0.492774\pi$
$293$	−14.6259	+	25.3328i	−0.854453	+	1.47996i	−0.877152	+	0.480214i	$0.840559\pi$
$294$		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
$299$	−4.27735			−0.247366
$300$		0			0
$301$		0			0
$302$	−6.49381	−	3.74920i	−0.373677	−	0.215742i
$303$		0			0
$304$	2.42011	+	1.39725i	0.138803	+	0.0801379i
$305$	2.71634	−	1.56828i	0.155537	−	0.0897994i
$306$		0			0
$307$			14.8451i			0.847254i	0.905837	+	0.423627i	$0.139243\pi$
$307$			14.8451i			0.847254i	−0.905837	+	0.423627i	$0.860757\pi$
$308$		0			0
$309$		0			0
$310$	−7.60507	−	13.1724i	−0.431939	−	0.748141i
$311$	19.3800			1.09894			0.549471	−	0.835513i	$-0.314829\pi$
$311$	19.3800			1.09894			0.549471	+	0.835513i	$0.314829\pi$
$312$		0			0
$313$			14.6195i			0.826342i	0.910653	+	0.413171i	$0.135579\pi$
$313$			14.6195i			0.826342i	−0.910653	+	0.413171i	$0.864421\pi$
$314$	−3.65669			−0.206359
$315$		0			0
$316$	−7.92216			−0.445656
$317$			16.9795i			0.953662i	0.878995	+	0.476831i	$0.158215\pi$
$317$			16.9795i			0.953662i	−0.878995	+	0.476831i	$0.841785\pi$
$318$		0			0
$319$	9.57598			0.536152
$320$	0.281435	+	0.487460i	0.0157327	+	0.0272498i
$321$		0			0
$322$		0			0
$323$		−	9.81416i		−	0.546074i
$324$		0			0
$325$	−0.173639	+	0.100250i	−0.00963174	+	0.00556089i
$326$	5.67309	+	3.27536i	0.314203	+	0.181405i
$327$		0			0
$328$	1.81466	+	1.04769i	0.100198	+	0.0578493i
$329$		0			0
$330$		0			0
$331$	19.8960			1.09358			0.546792	−	0.837268i	$-0.315849\pi$
$331$	19.8960			1.09358			0.546792	+	0.837268i	$0.315849\pi$
$332$	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	−0.852366	−	0.522946i	$-0.824833\pi$
$337$	0.490168	−	0.848996i	0.0267012	−	0.0462478i	0.879067	+	0.476698i	$0.158166\pi$
$338$	5.41892	−	3.12861i	0.294750	−	0.170174i
$339$		0			0
$340$	−10.4814	+	18.1544i	−0.568435	+	0.984559i
$341$	−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
$346$			11.5994i			0.623586i
$347$			21.2120i			1.13872i	0.822088	+	0.569361i	$0.192809\pi$
$347$			21.2120i			1.13872i	−0.822088	+	0.569361i	$0.807191\pi$
$348$		0			0
$349$	8.69945	−	5.02263i	0.465671	−	0.268855i	−0.248755	−	0.968566i	$-0.580021\pi$
$349$	8.69945	−	5.02263i	0.465671	−	0.268855i	0.714426	+	0.699711i	$0.246688\pi$
$350$		0			0
$351$		0			0
$352$	9.66071	−	16.7328i	0.514917	−	0.891863i
$353$	−1.37327	+	2.37858i	−0.0730920	+	0.126599i	−0.900255	−	0.435363i	$-0.856620\pi$
$353$	−1.37327	+	2.37858i	−0.0730920	+	0.126599i	0.827163	+	0.561962i	$0.189953\pi$
$354$		0			0
$355$	−23.3116	+	13.4590i	−1.23725	+	0.714329i
$356$	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	0.710837	−	0.703357i	$-0.248316\pi$
$359$	8.66140	+	5.00066i	0.457131	+	0.263925i	−0.253706	+	0.967281i	$0.581650\pi$
$360$		0			0
$361$	−8.14833	−	14.1133i	−0.428859	−	0.742806i
$362$	8.69945			0.457233
$363$		0			0
$364$		0			0
$365$	−0.815912	−	0.471067i	−0.0427068	−	0.0246568i
$366$		0			0
$367$	5.03560	+	2.90731i	0.262856	+	0.151760i	0.625637	−	0.780114i	$-0.284839\pi$
$367$	5.03560	+	2.90731i	0.262856	+	0.151760i	−0.362781	+	0.931875i	$0.618173\pi$
$368$	3.49381	−	2.01715i	0.182127	−	0.105151i
$369$		0			0
$370$			2.41106i			0.125345i
$371$		0			0
$372$		0			0
$373$	7.75959	+	13.4400i	0.401776	+	0.695897i	0.993940	−	0.109920i	$-0.0350596\pi$
$373$	7.75959	+	13.4400i	0.401776	+	0.695897i	−0.592164	+	0.805817i	$0.701726\pi$
$374$	−12.9929			−0.671847
$375$		0			0
$376$			0.566378i			0.0292087i
$377$	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	$0.477113\pi$
$380$		−	5.77430i		−	0.296215i
$381$		0			0
$382$	−6.57089			−0.336196
$383$	1.74229	+	3.01773i	0.0890268	+	0.154199i	0.907100	−	0.420915i	$-0.138291\pi$
$383$	1.74229	+	3.01773i	0.0890268	+	0.154199i	−0.818073	+	0.575114i	$0.804958\pi$
$384$		0			0
$385$		0			0
$386$			10.3503i			0.526817i
$387$		0			0
$388$	−10.0084	+	5.77835i	−0.508100	+	0.293352i
$389$	−6.37017	−	3.67782i	−0.322980	−	0.186473i	0.329740	−	0.944072i	$-0.393039\pi$
$389$	−6.37017	−	3.67782i	−0.322980	−	0.186473i	−0.652720	+	0.757599i	$0.726372\pi$
$390$		0			0
$391$	−12.2701	−	7.08414i	−0.620525	−	0.358260i
$392$		0			0
$393$		0			0
$394$	2.47848			0.124864
$395$	5.51394	+	9.55042i	0.277436	+	0.480534i
$396$		0			0
$397$	16.7002	+	9.64189i	0.838161	+	0.483912i	0.856639	−	0.515917i	$-0.172549\pi$
$397$	16.7002	+	9.64189i	0.838161	+	0.483912i	−0.0184778	+	0.999829i	$0.505882\pi$
$398$	−4.87717	−	8.44751i	−0.244470	−	0.423435i
$399$		0			0
$400$	0.0945538	−	0.163772i	0.00472769	−	0.00818860i
$401$	9.60576	−	5.54589i	0.479689	−	0.276949i	−0.240598	−	0.970625i	$-0.577344\pi$
$401$	9.60576	−	5.54589i	0.479689	−	0.276949i	0.720287	+	0.693676i	$0.244010\pi$
$402$		0			0
$403$	−9.66071	+	16.7328i	−0.481234	+	0.833522i
$404$	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
$409$		−	20.2763i		−	1.00260i	−0.865275	−	0.501298i	$-0.832856\pi$
$409$		−	20.2763i		−	1.00260i	0.865275	−	0.501298i	$-0.167144\pi$
$410$		−	1.29112i		−	0.0637639i
$411$		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
$416$	5.13123	−	8.88756i	0.251579	−	0.435748i
$417$		0			0
$418$	3.09946	−	1.78947i	0.151599	−	0.0875260i
$419$	5.54936	−	9.61177i	0.271104	−	0.469566i	−0.698041	−	0.716058i	$-0.745945\pi$
$419$	5.54936	−	9.61177i	0.271104	−	0.469566i	0.969145	+	0.246492i	$0.0792779\pi$
$420$		0			0
$421$	4.59269	+	7.95478i	0.223834	+	0.387692i	0.955969	−	0.293467i	$-0.0948092\pi$
$421$	4.59269	+	7.95478i	0.223834	+	0.387692i	−0.732135	+	0.681160i	$0.761476\pi$
$422$	13.2822	+	7.66849i	0.646568	+	0.373296i
$423$		0			0
$424$	9.06615	+	15.7030i	0.440291	+	0.762607i
$425$	−0.664137			−0.0322154
$426$		0			0
$427$		0			0
$428$	−2.04875	−	1.18285i	−0.0990302	−	0.0571751i
$429$		0			0
$430$	−4.81849	−	2.78195i	−0.232368	−	0.134158i
$431$	13.0858	−	7.55510i	0.630322	−	0.363916i	−0.150555	−	0.988602i	$-0.548106\pi$
$431$	13.0858	−	7.55510i	0.630322	−	0.363916i	0.780877	+	0.624685i	$0.214773\pi$
$432$		0			0
$433$			3.33578i			0.160307i	0.996783	+	0.0801537i	$0.0255411\pi$
$433$			3.33578i			0.160307i	−0.996783	+	0.0801537i	$0.974459\pi$
$434$		0			0
$435$		0			0
$436$	3.48398	+	6.03443i	0.166852	+	0.288997i
$437$	3.90270			0.186692
$438$		0			0
$439$			6.82465i			0.325723i	0.986649	+	0.162861i	$0.0520724\pi$
$439$			6.82465i			0.325723i	−0.986649	+	0.162861i	$0.947928\pi$
$440$	−17.2703			−0.823327
$441$		0			0
$442$	−6.90112			−0.328253
$443$		−	11.2901i		−	0.536407i	−0.963362	−	0.268203i	$-0.913570\pi$
$443$		−	11.2901i		−	0.536407i	0.963362	−	0.268203i	$-0.0864299\pi$
$444$		0			0
$445$	−23.2953			−1.10430
$446$	−6.15633	−	10.6631i	−0.291511	−	0.504912i
$447$		0			0
$448$		0			0
$449$		−	24.8554i		−	1.17300i	−0.809950	−	0.586498i	$-0.800506\pi$
$449$		−	24.8554i		−	1.17300i	0.809950	−	0.586498i	$-0.199494\pi$
$450$		0			0
$451$	−2.67417	+	1.54394i	−0.125922	+	0.0727011i
$452$	23.6291	+	13.6422i	1.11142	+	0.641677i
$453$		0			0
$454$	−4.81849	−	2.78195i	−0.226143	−	0.130564i
$455$		0			0
$456$		0			0
$457$	−12.6094			−0.589843			−0.294922	−	0.955521i	$-0.595294\pi$
$457$	−12.6094			−0.589843			−0.294922	+	0.955521i	$0.595294\pi$
$458$	−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	−0.977672	−	0.210138i	$-0.932609\pi$
$461$	−14.4031	−	24.9470i	−0.670821	−	1.16190i	0.306851	−	0.951758i	$-0.400725\pi$
$462$		0			0
$463$	−12.5858	+	21.7993i	−0.584912	+	1.01310i	0.409974	+	0.912097i	$0.365538\pi$
$463$	−12.5858	+	21.7993i	−0.584912	+	1.01310i	−0.994886	+	0.101001i	$0.967796\pi$
$464$	−4.15452	+	2.39861i	−0.192869	+	0.111353i
$465$		0			0
$466$	9.53273	−	16.5112i	0.441595	−	0.764865i
$467$	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
$472$		−	24.8226i		−	1.14255i
$473$			13.3068i			0.611846i
$474$		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
$479$	0.267749	−	0.463755i	0.0122338	−	0.0211895i	−0.859844	−	0.510557i	$-0.829439\pi$
$479$	0.267749	−	0.463755i	0.0122338	−	0.0211895i	0.872077	+	0.489368i	$0.162772\pi$
$480$		0			0
$481$	2.65244	−	1.53138i	0.120941	−	0.0698251i
$482$	−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	$-0.448083\pi$
$488$	−3.26594			−0.147842
$489$		0			0
$490$		0			0
$491$	−5.86948	−	3.38874i	−0.264886	−	0.152932i	0.361675	−	0.932304i	$-0.382205\pi$
$491$	−5.86948	−	3.38874i	−0.264886	−	0.152932i	−0.626561	+	0.779372i	$0.715538\pi$
$492$		0			0
$493$	14.5905	+	8.42380i	0.657121	+	0.379389i
$494$	1.64626	−	0.950469i	0.0740688	−	0.0427636i
$495$		0			0
$496$		−	18.2235i		−	0.818260i
$497$		0			0
$498$		0			0
$499$	−4.30037	−	7.44846i	−0.192511	−	0.333439i	0.753571	−	0.657367i	$-0.228330\pi$
$499$	−4.30037	−	7.44846i	−0.192511	−	0.333439i	−0.946082	+	0.323928i	$0.894996\pi$
$500$	−17.9505			−0.802771
$501$		0			0
$502$			4.68185i			0.208961i
$503$	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
$506$		−	5.16677i		−	0.229691i
$507$		0			0
$508$	10.0407			0.445484
$509$	3.04882	+	5.28072i	0.135137	+	0.234064i	0.925650	−	0.378382i	$-0.123519\pi$
$509$	3.04882	+	5.28072i	0.135137	+	0.234064i	−0.790513	+	0.612445i	$0.790186\pi$
$510$		0			0
$511$		0			0
$512$			17.5053i			0.773631i
$513$		0			0
$514$	−4.44947	+	2.56890i	−0.196258	+	0.113309i
$515$	−11.9499	−	6.89926i	−0.526574	−	0.304018i
$516$		0			0
$517$	−0.722823	−	0.417322i	−0.0317897	−	0.0183538i
$518$		0			0
$519$		0			0
$520$	−9.17301			−0.402263
$521$	−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	0.537437	−	0.843304i	$-0.319393\pi$
$523$	1.73424	+	1.00126i	0.0758329	+	0.0437821i	−0.461604	+	0.887086i	$0.652726\pi$
$524$	13.5204	+	23.4179i	0.590639	+	1.02302i
$525$		0			0
$526$	5.03961	−	8.72886i	0.219737	−	0.380596i
$527$	−55.4257	+	32.0001i	−2.41438	+	1.39394i
$528$		0			0
$529$	−8.68292	+	15.0393i	−0.377518	+	0.653881i
$530$	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
$535$			3.29312i			0.142374i
$536$		−	18.3895i		−	0.794307i
$537$		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	$0.0875403\pi$
$542$	7.13885	−	12.3649i	0.306640	−	0.531116i
$543$		0			0
$544$	29.4391	−	16.9967i	1.26219	−	0.728726i
$545$	4.84980	−	8.40010i	0.207743	−	0.359821i
$546$		0			0
$547$	−3.91961	−	6.78896i	−0.167590	−	0.290275i	0.769982	−	0.638066i	$-0.220265\pi$
$547$	−3.91961	−	6.78896i	−0.167590	−	0.290275i	−0.937572	+	0.347791i	$0.886932\pi$
$548$	8.61814	+	4.97569i	0.368149	+	0.212551i
$549$		0			0
$550$	−0.121096	−	0.209744i	−0.00516355	−	0.00894353i
$551$	−4.64074			−0.197702
$552$		0			0
$553$		0			0
$554$	12.6963	+	7.33022i	0.539415	+	0.311431i
$555$		0			0
$556$	10.5704	+	6.10281i	0.448284	+	0.258817i
$557$	−0.0116910	+	0.00674980i	−0.000495364	+	0.000285998i	−0.500248	−	0.865882i	$-0.666758\pi$
$557$	−0.0116910	+	0.00674980i	−0.000495364	+	0.000285998i	0.499752	+	0.866168i	$0.333424\pi$
$558$		0			0
$559$			7.06782i			0.298937i
$560$		0			0
$561$		0			0
$562$	−0.294871	−	0.510731i	−0.0124384	−	0.0215439i
$563$	−19.0906			−0.804571			−0.402286	−	0.915514i	$-0.631784\pi$
$563$	−19.0906			−0.804571			−0.402286	+	0.915514i	$0.631784\pi$
$564$		0			0
$565$		−	37.9808i		−	1.59786i
$566$	−14.1925			−0.596557
$567$		0			0
$568$	28.0283			1.17604
$569$		−	37.3437i		−	1.56553i	−0.622318	−	0.782765i	$-0.713809\pi$
$569$		−	37.3437i		−	1.56553i	0.622318	−	0.782765i	$-0.286191\pi$
$570$		0			0
$571$	45.2843			1.89509			0.947544	−	0.319626i	$-0.103557\pi$
$571$	45.2843			1.89509			0.947544	+	0.319626i	$0.103557\pi$
$572$	4.85543	+	8.40986i	0.203016	+	0.351634i
$573$		0			0
$574$		0			0
$575$		−	0.264101i		−	0.0110138i
$576$		0			0
$577$	32.1285	−	18.5494i	1.33753	−	0.772221i	0.351086	−	0.936343i	$-0.385813\pi$
$577$	32.1285	−	18.5494i	1.33753	−	0.772221i	0.986440	+	0.164123i	$0.0524793\pi$
$578$	−10.3509	−	5.97610i	−0.430541	−	0.248573i
$579$		0			0
$580$	8.58450	+	4.95626i	0.356452	+	0.205798i
$581$		0			0
$582$		0			0
$583$	−26.7207			−1.10666
$584$	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	0.966983	+	0.254842i	$0.0820235\pi$
$587$	17.0612	+	29.5509i	0.704191	+	1.21969i	−0.262792	+	0.964853i	$0.584643\pi$
$588$		0			0
$589$	8.81453	−	15.2672i	0.363197	−	0.629075i
$590$	−13.2458	+	7.64749i	−0.545322	+	0.314842i
$591$		0			0
$592$	−1.44437	+	2.50172i	−0.0593632	+	0.102820i
$593$	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
$598$		−	2.74430i		−	0.112223i
$599$		−	11.2472i		−	0.459547i	−0.973244	−	0.229773i	$-0.926201\pi$
$599$		−	11.2472i		−	0.459547i	0.973244	−	0.229773i	$-0.0737985\pi$
$600$		0			0
$601$	29.7646	−	17.1846i	1.21412	−	0.700975i	0.250469	−	0.968125i	$-0.419415\pi$
$601$	29.7646	−	17.1846i	1.21412	−	0.700975i	0.963655	+	0.267150i	$0.0860818\pi$
$602$		0			0
$603$		0			0
$604$	−9.28180	+	16.0766i	−0.377671	+	0.654146i
$605$	0.564393	−	0.977557i	0.0229458	−	0.0397433i
$606$		0			0
$607$	33.7888	−	19.5080i	1.37145	−	0.791804i	0.380335	−	0.924849i	$-0.375809\pi$
$607$	33.7888	−	19.5080i	1.37145	−	0.791804i	0.991110	+	0.133044i	$0.0424753\pi$
$608$	−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	$0.727856\pi$
$614$	−9.52444			−0.384375
$615$		0			0
$616$		0			0
$617$	−7.03569	−	4.06205i	−0.283246	−	0.163532i	0.351646	−	0.936133i	$-0.385622\pi$
$617$	−7.03569	−	4.06205i	−0.283246	−	0.163532i	−0.634892	+	0.772601i	$0.718955\pi$
$618$		0			0
$619$	−32.4018	−	18.7072i	−1.30234	−	0.751906i	−0.321535	−	0.946898i	$-0.604199\pi$
$619$	−32.4018	−	18.7072i	−1.30234	−	0.751906i	−0.980805	+	0.194991i	$0.937532\pi$
$620$	−32.6105	+	18.8277i	−1.30967	+	0.756138i
$621$		0			0
$622$			12.4340i			0.498559i
$623$		0			0
$624$		0			0
$625$	12.2156	+	21.1581i	0.488626	+	0.846325i
$626$	−9.37969			−0.374888
$627$		0			0
$628$			9.05278i			0.361245i
$629$	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	$0.629133\pi$
$632$		−	11.4828i		−	0.456760i
$633$		0			0
$634$	−10.8938			−0.432649
$635$	−6.98848	−	12.1044i	−0.277329	−	0.480348i
$636$		0			0
$637$		0			0
$638$			6.14384i			0.243237i
$639$		0			0
$640$	21.4970	−	12.4113i	0.849743	−	0.490599i
$641$	−8.01849	−	4.62948i	−0.316711	−	0.182853i	0.333214	−	0.942851i	$-0.391867\pi$
$641$	−8.01849	−	4.62948i	−0.316711	−	0.182853i	−0.649926	+	0.759998i	$0.725200\pi$
$642$		0			0
$643$	36.3456	+	20.9841i	1.43333	+	0.827534i	0.997373	−	0.0724332i	$-0.0230764\pi$
$643$	36.3456	+	20.9841i	1.43333	+	0.827534i	0.435958	+	0.899967i	$0.356410\pi$
$644$		0			0
$645$		0			0
$646$	6.29665			0.247739
$647$	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
$653$	20.1668	−	11.6433i	0.789189	−	0.455638i	−0.0504882	−	0.998725i	$-0.516078\pi$
$653$	20.1668	−	11.6433i	0.789189	−	0.455638i	0.839677	+	0.543086i	$0.182744\pi$
$654$		0			0
$655$	18.8207	−	32.5985i	0.735387	−	1.27373i
$656$	0.773456	−	1.33966i	0.0301984	−	0.0523051i
$657$		0			0
$658$		0			0
$659$	−25.8880	+	14.9464i	−1.00845	+	0.582230i	−0.910738	−	0.412984i	$-0.864486\pi$
$659$	−25.8880	+	14.9464i	−1.00845	+	0.582230i	−0.0977141	+	0.995215i	$0.531153\pi$
$660$		0			0
$661$		−	20.3440i		−	0.791291i	−0.918403	−	0.395645i	$-0.870521\pi$
$661$		−	20.3440i		−	0.791291i	0.918403	−	0.395645i	$-0.129479\pi$
$662$			12.7651i			0.496128i
$663$		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
$668$	−2.86955	+	4.97021i	−0.111026	+	0.192303i
$669$		0			0
$670$	−9.81303	+	5.66555i	−0.379110	+	0.218879i
$671$	2.40643	−	4.16805i	0.0928990	−	0.160906i
$672$		0			0
$673$	−8.55996	−	14.8263i	−0.329962	−	0.571511i	0.652542	−	0.757753i	$-0.273703\pi$
$673$	−8.55996	−	14.8263i	−0.329962	−	0.571511i	−0.982504	+	0.186241i	$0.940369\pi$
$674$	0.544706	+	0.314486i	0.0209813	+	0.0121136i
$675$		0			0
$676$	−7.74543	−	13.4155i	−0.297901	−	0.515980i
$677$	28.4155			1.09210			0.546048	−	0.837754i	$-0.316132\pi$
$677$	28.4155			1.09210			0.546048	+	0.837754i	$0.316132\pi$
$678$		0			0
$679$		0			0
$680$	−26.3138	−	15.1923i	−1.00909	−	0.582598i
$681$		0			0
$682$	−20.2122	−	11.6695i	−0.773965	−	0.446849i
$683$	18.1236	−	10.4637i	0.693482	−	0.400382i	−0.111433	−	0.993772i	$-0.535544\pi$
$683$	18.1236	−	10.4637i	0.693482	−	0.400382i	0.804915	+	0.593390i	$0.202211\pi$
$684$		0			0
$685$		−	13.8526i		−	0.529281i
$686$		0			0
$687$		0			0
$688$	−3.33310	−	5.77311i	−0.127073	−	0.220098i
$689$	−14.1925			−0.540693
$690$		0			0
$691$		−	24.0083i		−	0.913318i	−0.889642	−	0.456659i	$-0.849046\pi$
$691$		−	24.0083i		−	0.913318i	0.889642	−	0.456659i	$-0.150954\pi$
$692$	28.7163			1.09163
$693$		0			0
$694$	−13.6094			−0.516606
$695$		−	16.9906i		−	0.644489i
$696$		0			0
$697$	−5.43268			−0.205777
$698$	3.22246	+	5.58147i	0.121972	+	0.211262i
$699$		0			0
$700$		0			0
$701$			42.0117i			1.58676i	0.608728	+	0.793379i	$0.291680\pi$
$701$			42.0117i			1.58676i	−0.608728	+	0.793379i	$0.708320\pi$
$702$		0			0
$703$	−2.42011	+	1.39725i	−0.0912762	+	0.0526984i
$704$	0.747976	+	0.431844i	0.0281904	+	0.0162757i
$705$		0			0
$706$	−1.52607	−	0.881077i	−0.0574344	−	0.0331598i
$707$		0			0
$708$		0			0
$709$	37.2188			1.39778			0.698891	−	0.715228i	$-0.253677\pi$
$709$	37.2188			1.39778			0.698891	+	0.715228i	$0.253677\pi$
$710$	−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
$716$	−6.92175	+	3.99627i	−0.258678	+	0.149348i
$717$		0			0
$718$	−3.20837	+	5.55705i	−0.119735	+	0.207387i
$719$	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
$724$		−	21.5370i		−	0.800416i
$725$			0.314045i			0.0116633i
$726$		0			0
$727$	−28.3214	+	16.3514i	−1.05038	+	0.606439i	−0.922756	−	0.385384i	$-0.874069\pi$
$727$	−28.3214	+	16.3514i	−1.05038	+	0.606439i	−0.127626	+	0.991822i	$0.540736\pi$
$728$		0			0
$729$		0			0
$730$	0.302231	−	0.523480i	0.0111861	−	0.0193749i
$731$	−11.7057	+	20.2749i	−0.432951	+	0.749893i
$732$		0			0
$733$	−0.431812	+	0.249307i	−0.0159494	+	0.00920836i	−0.507953	−	0.861385i	$-0.669598\pi$
$733$	−0.431812	+	0.249307i	−0.0159494	+	0.00920836i	0.492004	+	0.870593i	$0.336264\pi$
$734$	−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	$0.492596\pi$
$740$	5.96901			0.219425
$741$		0			0
$742$		0			0
$743$	−9.20534	−	5.31470i	−0.337711	−	0.194978i	0.321548	−	0.946893i	$-0.395797\pi$
$743$	−9.20534	−	5.31470i	−0.337711	−	0.194978i	−0.659259	+	0.751916i	$0.729130\pi$
$744$		0			0
$745$	−29.5606	−	17.0668i	−1.08302	−	0.625279i
$746$	−8.62296	+	4.97847i	−0.315709	+	0.182275i
$747$		0			0
$748$			32.1662i			1.17611i
$749$		0			0
$750$		0			0
$751$	−9.55927	−	16.5571i	−0.348823	−	0.604179i	0.637218	−	0.770684i	$-0.280085\pi$
$751$	−9.55927	−	16.5571i	−0.348823	−	0.604179i	−0.986041	+	0.166505i	$0.946752\pi$
$752$	0.418126			0.0152475
$753$		0			0
$754$			3.26327i			0.118841i
$755$	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	$0.326442\pi$
$758$			1.79461i			0.0651832i
$759$		0			0
$760$	8.36955			0.303596
$761$	−21.6650	−	37.5249i	−0.785355	−	1.36028i	−0.928787	−	0.370615i	$-0.879147\pi$
$761$	−21.6650	−	37.5249i	−0.785355	−	1.36028i	0.143431	−	0.989660i	$-0.454186\pi$
$762$		0			0
$763$		0			0
$764$			16.2674i			0.588533i
$765$		0			0
$766$	−1.93614	+	1.11783i	−0.0699557	+	0.0403889i
$767$	16.8261	+	9.71458i	0.607557	+	0.350773i
$768$		0			0
$769$	5.75189	+	3.32086i	0.207419	+	0.119753i	0.600111	−	0.799917i	$-0.295123\pi$
$769$	5.75189	+	3.32086i	0.207419	+	0.119753i	−0.392693	+	0.919670i	$0.628456\pi$
$770$		0			0
$771$		0			0
$772$	25.6240			0.922227
$773$	−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
$779$	1.29596	−	0.748226i	0.0464328	−	0.0268080i
$780$		0			0
$781$	−20.6520	+	35.7703i	−0.738986	+	1.27996i
$782$	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
$787$			21.9854i			0.783695i	0.920030	+	0.391848i	$0.128164\pi$
$787$			21.9854i			0.783695i	−0.920030	+	0.391848i	$0.871836\pi$
$788$		−	6.13590i		−	0.218582i
$789$		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
$794$	−6.18612	+	10.7147i	−0.219537	+	0.380250i
$795$		0			0
$796$	−20.9133	+	12.0743i	−0.741251	+	0.427962i
$797$	9.71892	−	16.8337i	0.344262	−	0.596279i	−0.640958	−	0.767576i	$-0.721463\pi$
$797$	9.71892	−	16.8337i	0.344262	−	0.596279i	0.985219	+	0.171297i	$0.0547959\pi$
$798$		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
$803$	−1.44565			−0.0510157
$804$		0			0
$805$		0			0
$806$	−10.7356	−	6.19820i	−0.378145	−	0.218322i
$807$		0			0
$808$	9.30732	+	5.37358i	0.327430	+	0.189042i
$809$	−18.1916	+	10.5029i	−0.639582	+	0.369263i	−0.784453	−	0.620188i	$-0.787056\pi$
$809$	−18.1916	+	10.5029i	−0.639582	+	0.369263i	0.144872	+	0.989450i	$0.453723\pi$
$810$		0			0
$811$		−	37.3291i		−	1.31080i	−0.755281	−	0.655401i	$-0.772500\pi$
$811$		−	37.3291i		−	1.31080i	0.755281	−	0.655401i	$-0.227500\pi$
$812$		0			0
$813$		0			0
$814$	1.84981	+	3.20397i	0.0648359	+	0.112299i
$815$	−22.5751			−0.790772
$816$		0			0
$817$		−	6.44875i		−	0.225613i
$818$	13.0090			0.454849
$819$		0			0
$820$	−3.19639			−0.111623
$821$			12.5882i			0.439332i	0.975575	+	0.219666i	$0.0704968\pi$
$821$			12.5882i			0.439332i	−0.975575	+	0.219666i	$0.929503\pi$
$822$		0			0
$823$	−44.8378			−1.56295			−0.781474	−	0.623937i	$-0.785532\pi$
$823$	−44.8378			−1.56295			−0.781474	+	0.623937i	$0.785532\pi$
$824$	7.18385	+	12.4428i	0.250261	+	0.433465i
$825$		0			0
$826$		0			0
$827$			25.7293i			0.894695i	0.894360	+	0.447347i	$0.147631\pi$
$827$			25.7293i			0.894695i	−0.894360	+	0.447347i	$0.852369\pi$
$828$		0			0
$829$	14.6902	−	8.48139i	0.510212	−	0.294571i	−0.222709	−	0.974885i	$-0.571490\pi$
$829$	14.6902	−	8.48139i	0.510212	−	0.294571i	0.732921	+	0.680314i	$0.238157\pi$
$830$	10.5295	+	6.07921i	0.365484	+	0.211012i
$831$		0			0
$832$	0.397284	+	0.229372i	0.0137733	+	0.00795204i
$833$		0			0
$834$		0			0
$835$	7.98900			0.276471
$836$	−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	0.999012	−	0.0444321i	$-0.0141478\pi$
$839$	13.3539	+	23.1296i	0.461027	+	0.798522i	−0.537986	+	0.842954i	$0.680815\pi$
$840$		0			0
$841$	−10.5167	+	18.2155i	−0.362645	+	0.628120i
$842$	−5.10370	+	2.94662i	−0.175885	+	0.101547i
$843$		0			0
$844$	18.9847	−	32.8824i	0.653479	−	1.13186i
$845$	−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
$850$		−	0.426103i		−	0.0146152i
$851$			4.03430i			0.138294i
$852$		0			0
$853$	37.6287	−	21.7249i	1.28838	−	0.743848i	0.310017	−	0.950731i	$-0.399665\pi$
$853$	37.6287	−	21.7249i	1.28838	−	0.743848i	0.978366	+	0.206883i	$0.0663319\pi$
$854$		0			0
$855$		0			0
$856$	1.71448	−	2.96957i	0.0585997	−	0.101498i
$857$	7.83430	−	13.5694i	0.267615	−	0.463522i	−0.700631	−	0.713524i	$-0.747098\pi$
$857$	7.83430	−	13.5694i	0.267615	−	0.463522i	0.968245	+	0.250002i	$0.0804312\pi$
$858$		0			0
$859$	17.3578	−	10.0216i	0.592242	−	0.341931i	−0.173742	−	0.984791i	$-0.555586\pi$
$859$	17.3578	−	10.0216i	0.592242	−	0.341931i	0.765984	+	0.642860i	$0.222252\pi$
$860$	−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	0.955978	−	0.293439i	$-0.0947998\pi$
$863$	34.6600	+	20.0110i	1.17984	+	0.681181i	0.223863	+	0.974621i	$0.428133\pi$
$864$		0			0
$865$	−19.9869	−	34.6184i	−0.679576	−	1.17706i
$866$	−2.14020			−0.0727269
$867$		0			0
$868$		0			0
$869$	14.6545	+	8.46079i	0.497120	+	0.287013i
$870$		0			0
$871$	12.4655	+	7.19694i	0.422376	+	0.243859i
$872$	−8.74660	+	5.04985i	−0.296197	+	0.171010i
$873$		0			0
$874$			2.50393i			0.0846967i
$875$		0			0
$876$		0			0
$877$	−22.6353	−	39.2054i	−0.764338	−	1.32387i	−0.940596	−	0.339529i	$-0.889732\pi$
$877$	−22.6353	−	39.2054i	−0.764338	−	1.32387i	0.176257	−	0.984344i	$-0.443601\pi$
$878$	−4.37862			−0.147771
$879$		0			0
$880$			12.7497i			0.429792i
$881$	−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	$0.432190\pi$
$884$			17.0849i			0.574628i
$885$		0			0
$886$	7.24357			0.243352
$887$	−17.8620	−	30.9379i	−0.599748	−	1.03879i	−0.992858	−	0.119303i	$-0.961934\pi$
$887$	−17.8620	−	30.9379i	−0.599748	−	1.03879i	0.393110	−	0.919492i	$-0.371399\pi$
$888$		0			0
$889$		0			0
$890$		−	14.9460i		−	0.500991i
$891$		0			0
$892$	−26.3983	+	15.2411i	−0.883881	+	0.510309i
$893$	0.350296	+	0.202243i	0.0117222	+	0.00676782i
$894$		0			0
$895$	9.63528	+	5.56293i	0.322072	+	0.185948i
$896$		0			0
$897$		0			0
$898$	15.9469			0.532155
$899$	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
$905$	−25.9635	+	14.9901i	−0.863058	+	0.498287i
$906$		0			0
$907$	4.52104	−	7.83067i	0.150119	−	0.260013i	−0.781152	−	0.624341i	$-0.785368\pi$
$907$	4.52104	−	7.83067i	0.150119	−	0.260013i	0.931271	+	0.364327i	$0.118701\pi$
$908$	−6.88721	+	11.9290i	−0.228560	+	0.395878i
$909$		0			0
$910$		0			0
$911$	35.5171	−	20.5058i	1.17673	−	0.679388i	0.221478	−	0.975165i	$-0.428912\pi$
$911$	35.5171	−	20.5058i	1.17673	−	0.679388i	0.955257	+	0.295777i	$0.0955787\pi$
$912$		0			0
$913$		−	29.0783i		−	0.962352i
$914$		−	8.09005i		−	0.267595i
$915$		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	$0.220646\pi$
$920$	6.04138	−	10.4640i	0.199178	−	0.344987i
$921$		0			0
$922$	16.0057	−	9.24088i	0.527119	−	0.304332i
$923$	−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
$929$	−25.6659			−0.842071			−0.421036	−	0.907044i	$-0.638333\pi$
$929$	−25.6659			−0.842071			−0.421036	+	0.907044i	$0.638333\pi$
$930$		0			0
$931$		0			0
$932$	−40.8763	−	23.5999i	−1.33895	−	0.773041i
$933$		0			0
$934$	14.2214	+	8.21075i	0.465340	+	0.268664i
$935$	38.7774	−	22.3881i	1.26816	−	0.732170i
$936$		0			0
$937$		−	15.9276i		−	0.520333i	−0.965564	−	0.260167i	$-0.916223\pi$
$937$		−	15.9276i		−	0.520333i	0.965564	−	0.260167i	$-0.0837775\pi$
$938$		0			0
$939$		0			0
$940$	−0.431988	−	0.748226i	−0.0140899	−	0.0244044i
$941$	39.3534			1.28288			0.641442	−	0.767172i	$-0.278337\pi$
$941$	39.3534			1.28288			0.641442	+	0.767172i	$0.278337\pi$
$942$		0			0
$943$		−	2.16036i		−	0.0703510i
$944$	−18.3252			−0.596433
$945$		0			0
$946$	−8.53747			−0.277577
$947$		−	33.3808i		−	1.08473i	−0.840143	−	0.542365i	$-0.817529\pi$
$947$		−	33.3808i		−	1.08473i	0.840143	−	0.542365i	$-0.182471\pi$
$948$		0			0
$949$	−0.767847			−0.0249254
$950$	0.0586858	+	0.101647i	0.00190402	+	0.00329786i
$951$		0			0
$952$		0			0
$953$		−	44.4622i		−	1.44027i	−0.693832	−	0.720137i	$-0.744079\pi$
$953$		−	44.4622i		−	1.44027i	0.693832	−	0.720137i	$-0.255921\pi$
$954$		0			0
$955$	19.6108	−	11.3223i	0.634592	−	0.366382i
$956$	21.7767	+	12.5728i	0.704309	+	0.406633i
$957$		0			0
$958$	0.297540	+	0.171785i	0.00961307	+	0.00555011i
$959$		0			0
$960$		0			0
$961$	−83.9627			−2.70847
$962$	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	0.339371	+	0.940652i	$0.389786\pi$
$967$	−20.0556	+	34.7372i	−0.644943	+	1.11707i	−0.984315	+	0.176422i	$0.943548\pi$
$968$	−1.01788	+	0.587674i	−0.0327159	+	0.0188886i
$969$		0			0
$970$	−5.16071	+	8.93861i	−0.165700	+	0.287001i
$971$	−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
$976$			2.41106i			0.0771763i
$977$		−	54.0772i		−	1.73008i	−0.501699	−	0.865042i	$-0.667292\pi$
$977$		−	54.0772i		−	1.73008i	0.501699	−	0.865042i	$-0.332708\pi$
$978$		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
$983$	6.97890	−	12.0878i	0.222592	−	0.385541i	−0.733002	−	0.680226i	$-0.761881\pi$
$983$	6.97890	−	12.0878i	0.222592	−	0.385541i	0.955594	+	0.294685i	$0.0952148\pi$
$984$		0			0
$985$	−7.39703	+	4.27068i	−0.235689	+	0.136075i
$986$	−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	$0.633192\pi$
$992$	61.0618			1.93872
$993$		0			0
$994$		0			0
$995$	29.1119	+	16.8077i	0.922909	+	0.532841i
$996$		0			0
$997$	43.4282	+	25.0733i	1.37538	+	0.794079i	0.991600	−	0.129344i	$-0.0412871\pi$
$997$	43.4282	+	25.0733i	1.37538	+	0.794079i	0.383785	+	0.923422i	$0.374620\pi$
$998$	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.i.c.1097.3		12
3.2	odd	2		441.2.i.c.68.3		12
7.2	even	3		189.2.o.a.125.3		12
7.3	odd	6		1323.2.s.c.962.3		12
7.4	even	3		1323.2.s.c.962.4		12
7.5	odd	6		189.2.o.a.125.4		12
7.6	odd	2	inner	1323.2.i.c.1097.4		12
9.2	odd	6		1323.2.s.c.656.3		12
9.7	even	3		441.2.s.c.362.4		12
21.2	odd	6		63.2.o.a.41.4	yes	12
21.5	even	6		63.2.o.a.41.3	yes	12
21.11	odd	6		441.2.s.c.374.3		12
21.17	even	6		441.2.s.c.374.4		12
21.20	even	2		441.2.i.c.68.4		12
28.19	even	6		3024.2.cc.a.881.5		12
28.23	odd	6		3024.2.cc.a.881.2		12
63.2	odd	6		189.2.o.a.62.4		12
63.5	even	6		567.2.c.c.566.6		12
63.11	odd	6	inner	1323.2.i.c.521.4		12
63.16	even	3		63.2.o.a.20.3	✓	12
63.20	even	6		1323.2.s.c.656.4		12
63.23	odd	6		567.2.c.c.566.5		12
63.25	even	3		441.2.i.c.227.4		12
63.34	odd	6		441.2.s.c.362.3		12
63.38	even	6	inner	1323.2.i.c.521.3		12
63.40	odd	6		567.2.c.c.566.7		12
63.47	even	6		189.2.o.a.62.3		12
63.52	odd	6		441.2.i.c.227.3		12
63.58	even	3		567.2.c.c.566.8		12
63.61	odd	6		63.2.o.a.20.4	yes	12
84.23	even	6		1008.2.cc.a.545.1		12
84.47	odd	6		1008.2.cc.a.545.6		12
252.47	odd	6		3024.2.cc.a.2897.2		12
252.79	odd	6		1008.2.cc.a.209.6		12
252.187	even	6		1008.2.cc.a.209.1		12
252.191	even	6		3024.2.cc.a.2897.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.o.a.20.3	✓	12	63.16	even	3
63.2.o.a.20.4	yes	12	63.61	odd	6
63.2.o.a.41.3	yes	12	21.5	even	6
63.2.o.a.41.4	yes	12	21.2	odd	6
189.2.o.a.62.3		12	63.47	even	6
189.2.o.a.62.4		12	63.2	odd	6
189.2.o.a.125.3		12	7.2	even	3
189.2.o.a.125.4		12	7.5	odd	6
441.2.i.c.68.3		12	3.2	odd	2
441.2.i.c.68.4		12	21.20	even	2
441.2.i.c.227.3		12	63.52	odd	6
441.2.i.c.227.4		12	63.25	even	3
441.2.s.c.362.3		12	63.34	odd	6
441.2.s.c.362.4		12	9.7	even	3
441.2.s.c.374.3		12	21.11	odd	6
441.2.s.c.374.4		12	21.17	even	6
567.2.c.c.566.5		12	63.23	odd	6
567.2.c.c.566.6		12	63.5	even	6
567.2.c.c.566.7		12	63.40	odd	6
567.2.c.c.566.8		12	63.58	even	3
1008.2.cc.a.209.1		12	252.187	even	6
1008.2.cc.a.209.6		12	252.79	odd	6
1008.2.cc.a.545.1		12	84.23	even	6
1008.2.cc.a.545.6		12	84.47	odd	6
1323.2.i.c.521.3		12	63.38	even	6	inner
1323.2.i.c.521.4		12	63.11	odd	6	inner
1323.2.i.c.1097.3		12	1.1	even	1	trivial
1323.2.i.c.1097.4		12	7.6	odd	2	inner
1323.2.s.c.656.3		12	9.2	odd	6
1323.2.s.c.656.4		12	63.20	even	6
1323.2.s.c.962.3		12	7.3	odd	6
1323.2.s.c.962.4		12	7.4	even	3
3024.2.cc.a.881.2		12	28.23	odd	6
3024.2.cc.a.881.5		12	28.19	even	6
3024.2.cc.a.2897.2		12	252.47	odd	6
3024.2.cc.a.2897.5		12	252.191	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.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.641589i q^{2} +1.58836 q^{4} +(-1.10552 - 1.91482i) q^{5} +2.30225i q^{8} +O(q^{10})\)	\(q+0.641589i q^{2} +1.58836 q^{4} +(-1.10552 - 1.91482i) q^{5} +2.30225i q^{8} +(1.22853 - 0.709292i) q^{10} +(-2.93818 - 1.69636i) q^{11} +(-1.56060 - 0.901012i) q^{13} +1.69963 q^{16} +(-2.98450 - 5.16931i) q^{17} +(1.42391 + 0.822093i) q^{19} +(-1.75597 - 3.04144i) q^{20} +(1.08836 - 1.88510i) q^{22} +(2.05563 - 1.18682i) q^{23} +(0.0556321 - 0.0963576i) q^{25} +(0.578079 - 1.00126i) q^{26} +(-2.44437 + 1.41126i) q^{29} -10.7221i q^{31} +5.69497i q^{32} +(3.31657 - 1.91482i) q^{34} +(-0.849814 + 1.47192i) q^{37} +(-0.527445 + 0.913562i) q^{38} +(4.40841 - 2.54520i) q^{40} +(0.455074 - 0.788211i) q^{41} +(-1.96108 - 3.39669i) q^{43} +(-4.66690 - 2.69443i) q^{44} +(0.761450 + 1.31887i) q^{46} +0.246010 q^{47} +(0.0618219 + 0.0356929i) q^{50} +(-2.47880 - 1.43113i) q^{52} +(6.82072 - 3.93795i) q^{53} +7.50146i q^{55} +(-0.905446 - 1.56828i) q^{58} -10.7819 q^{59} +1.41858i q^{61} +6.87916 q^{62} -0.254572 q^{64} +3.98436i q^{65} -7.98762 q^{67} +(-4.74048 - 8.21075i) q^{68} -12.1743i q^{71} +(0.369016 - 0.213051i) q^{73} +(-0.944368 - 0.545231i) q^{74} +(2.26168 + 1.30578i) q^{76} -4.98762 q^{79} +(-1.87898 - 3.25449i) q^{80} +(0.505707 + 0.291970i) q^{82} +(4.28541 + 7.42254i) q^{83} +(-6.59888 + 11.4296i) q^{85} +(2.17928 - 1.25821i) q^{86} +(3.90545 - 6.76443i) q^{88} +(5.26792 - 9.12431i) q^{89} +(3.26509 - 1.88510i) q^{92} +0.157838i q^{94} -3.63537i q^{95} +(-6.30108 + 3.63793i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{4}+O(q^{10}) \) 12 * q - 4 * q^4	\( 12 q - 4 q^{4} - 4 q^{16} - 10 q^{22} + 24 q^{23} - 30 q^{29} + 2 q^{37} - 10 q^{43} - 54 q^{44} + 20 q^{46} + 36 q^{50} + 12 q^{53} + 2 q^{58} + 16 q^{64} - 24 q^{67} - 12 q^{74} + 12 q^{79} - 6 q^{85} + 96 q^{86} + 34 q^{88} - 30 q^{92}+O(q^{100}) \) 12 * q - 4 * q^4 - 4 * q^16 - 10 * q^22 + 24 * q^23 - 30 * q^29 + 2 * q^37 - 10 * q^43 - 54 * q^44 + 20 * q^46 + 36 * q^50 + 12 * q^53 + 2 * q^58 + 16 * q^64 - 24 * q^67 - 12 * q^74 + 12 * q^79 - 6 * q^85 + 96 * q^86 + 34 * q^88 - 30 * q^92

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more