LMFDB - Embedded newform 441.2.s.c.374.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,2,Mod(362,441)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(441, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("441.362"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.52140272914$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			374.4
Root			$-0.474636 - 0.274031i$ of defining polynomial
Character	$\chi$	$=$	441.374
Dual form			441.2.s.c.362.4

$q$-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} +(0.175815 - 1.72310i) q^{3} +(-0.794182 - 1.37556i) q^{4} +2.21105 q^{5} +(0.650451 - 0.901012i) q^{6} -2.30225i q^{8} +(-2.93818 - 0.605896i) q^{9} +(1.22853 + 0.709292i) q^{10} -3.39272i q^{11} +(-2.50987 + 1.12661i) q^{12} +(1.56060 + 0.901012i) q^{13} +(0.388736 - 3.80987i) q^{15} +(-0.849814 + 1.47192i) q^{16} +(-2.98450 + 5.16931i) q^{17} +(-1.43818 - 1.27921i) q^{18} +(1.42391 - 0.822093i) q^{19} +(-1.75597 - 3.04144i) q^{20} +(1.08836 - 1.88510i) q^{22} -2.37364i q^{23} +(-3.96702 - 0.404771i) q^{24} -0.111264 q^{25} +(0.578079 + 1.00126i) q^{26} +(-1.56060 + 4.95626i) q^{27} +(2.44437 - 1.41126i) q^{29} +(1.43818 - 1.99218i) q^{30} +(9.28558 - 5.36103i) q^{31} +(-4.93199 + 2.84748i) q^{32} +(-5.84600 - 0.596491i) q^{33} +(-3.31657 + 1.91482i) q^{34} +(1.50000 + 4.52284i) q^{36} +(-0.849814 - 1.47192i) q^{37} +1.05489 q^{38} +(1.82691 - 2.53066i) q^{39} -5.09039i q^{40} +(0.455074 - 0.788211i) q^{41} +(-1.96108 - 3.39669i) q^{43} +(-4.66690 + 2.69443i) q^{44} +(-6.49645 - 1.33966i) q^{45} +(0.761450 - 1.31887i) q^{46} +(-0.123005 + 0.213051i) q^{47} +(2.38686 + 1.72310i) q^{48} +(-0.0618219 - 0.0356929i) q^{50} +(8.38255 + 6.05146i) q^{51} -2.86227i q^{52} +(6.82072 + 3.93795i) q^{53} +(-2.45706 + 2.25323i) q^{54} -7.50146i q^{55} +(-1.16621 - 2.59808i) q^{57} +1.81089 q^{58} +(5.39093 + 9.33736i) q^{59} +(-5.54944 + 2.49100i) q^{60} +(1.22853 + 0.709292i) q^{61} +6.87916 q^{62} -0.254572 q^{64} +(3.45056 + 1.99218i) q^{65} +(-3.05688 - 2.20679i) q^{66} +(3.99381 + 6.91748i) q^{67} +9.48096 q^{68} +(-4.09003 - 0.417322i) q^{69} +12.1743i q^{71} +(-1.39493 + 6.76443i) q^{72} +(0.369016 + 0.213051i) q^{73} -1.09046i q^{74} +(-0.0195619 + 0.191720i) q^{75} +(-2.26168 - 1.30578i) q^{76} +(1.82691 - 0.820053i) q^{78} +(2.49381 - 4.31941i) q^{79} +(-1.87898 + 3.25449i) q^{80} +(8.26578 + 3.56046i) q^{81} +(0.505707 - 0.291970i) q^{82} +(4.28541 + 7.42254i) q^{83} +(-6.59888 + 11.4296i) q^{85} -2.51641i q^{86} +(-2.00199 - 4.46002i) q^{87} -7.81089 q^{88} +(5.26792 + 9.12431i) q^{89} +(-3.17988 - 2.82839i) q^{90} +(-3.26509 + 1.88510i) q^{92} +(-7.60507 - 16.9426i) q^{93} +(-0.136691 + 0.0789188i) q^{94} +(3.14833 - 1.81769i) q^{95} +(4.03940 + 8.99896i) q^{96} +(6.30108 - 3.63793i) q^{97} +(-2.05563 + 9.96840i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} + 2 q^{4} + 6 q^{15} + 2 q^{16} + 18 q^{18} - 10 q^{22} + 30 q^{29} - 18 q^{30} + 12 q^{32} + 18 q^{36} + 2 q^{37} - 12 q^{39} - 10 q^{43} - 54 q^{44} + 20 q^{46} - 36 q^{50} + 66 q^{51}+ \cdots - 24 q^{99}+O(q^{100}) $ 12 * q + 6 * q^2 + 2 * q^4 + 6 * q^15 + 2 * q^16 + 18 * q^18 - 10 * q^22 + 30 * q^29 - 18 * q^30 + 12 * q^32 + 18 * q^36 + 2 * q^37 - 12 * q^39 - 10 * q^43 - 54 * q^44 + 20 * q^46 - 36 * q^50 + 66 * q^51 + 12 * q^53 - 18 * q^57 - 4 * q^58 - 30 * q^60 + 16 * q^64 + 78 * q^65 + 12 * q^67 - 54 * q^72 - 12 * q^78 - 6 * q^79 + 24 * q^81 - 6 * q^85 - 68 * q^88 + 30 * q^92 - 54 * q^93 - 72 * q^95 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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	$-0.260495\pi$
$2$	0.555632	+	0.320794i	0.392891	+	0.226836i	−0.290521	+	0.956869i	$0.593829\pi$
$3$	0.175815	−	1.72310i	0.101507	−	0.994835i
$3$	0.175815	−	1.72310i	0.101507	−	0.994835i
$4$	−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	$0.335386\pi$
$6$	0.650451	−	0.901012i	0.265545	−	0.367836i
$7$		0			0
$7$		0			0
$8$		−	2.30225i		−	0.813970i
$9$	−2.93818	−	0.605896i	−0.979393	−	0.201965i
$10$	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	$-0.170899\pi$
$12$	−2.50987	+	1.12661i	−0.724537	+	0.325225i
$13$	1.56060	+	0.901012i	0.432832	+	0.249896i	0.700552	−	0.713601i	$-0.252937\pi$
$13$	1.56060	+	0.901012i	0.432832	+	0.249896i	−0.267720	+	0.963497i	$0.586270\pi$
$14$		0			0
$15$	0.388736	−	3.80987i	0.100371	−	0.983704i
$16$	−0.849814	+	1.47192i	−0.212454	+	0.367980i
$17$	−2.98450	+	5.16931i	−0.723849	+	1.25374i	0.235597	+	0.971851i	$0.424295\pi$
$17$	−2.98450	+	5.16931i	−0.723849	+	1.25374i	−0.959446	+	0.281892i	$0.909038\pi$
$18$	−1.43818	−	1.27921i	−0.338982	−	0.301512i
$19$	1.42391	−	0.822093i	0.326667	−	0.188601i	−0.327694	−	0.944784i	$-0.606271\pi$
$19$	1.42391	−	0.822093i	0.326667	−	0.188601i	0.654360	+	0.756183i	$0.272938\pi$
$20$	−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	$-0.0795988\pi$
$24$	−3.96702	−	0.404771i	−0.809765	−	0.0826235i
$25$	−0.111264			−0.0222528
$26$	0.578079	+	1.00126i	0.113371	+	0.196364i
$27$	−1.56060	+	4.95626i	−0.300337	+	0.953833i
$28$		0			0
$29$	2.44437	−	1.41126i	0.453908	−	0.262064i	−0.255571	−	0.966790i	$-0.582264\pi$
$29$	2.44437	−	1.41126i	0.453908	−	0.262064i	0.709479	+	0.704726i	$0.248930\pi$
$30$	1.43818	−	1.99218i	0.262574	−	0.363721i
$31$	9.28558	−	5.36103i	1.66774	−	0.962870i	0.698887	−	0.715232i	$-0.253679\pi$
$31$	9.28558	−	5.36103i	1.66774	−	0.962870i	0.968853	−	0.247638i	$-0.0796544\pi$
$32$	−4.93199	+	2.84748i	−0.871861	+	0.503369i
$33$	−5.84600	−	0.596491i	−1.01766	−	0.103836i
$34$	−3.31657	+	1.91482i	−0.568788	+	0.328390i
$35$		0			0
$36$	1.50000	+	4.52284i	0.250000	+	0.753807i
$37$	−0.849814	−	1.47192i	−0.139709	−	0.241982i	0.787678	−	0.616088i	$-0.211283\pi$
$37$	−0.849814	−	1.47192i	−0.139709	−	0.241982i	−0.927386	+	0.374105i	$0.877950\pi$
$38$	1.05489			0.171126
$39$	1.82691	−	2.53066i	0.292540	−	0.405230i
$40$		−	5.09039i		−	0.804862i
$41$	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
$45$	−6.49645	−	1.33966i	−0.968434	−	0.199705i
$46$	0.761450	−	1.31887i	0.112270	−	0.194457i
$47$	−0.123005	+	0.213051i	−0.0179422	+	0.0310767i	−0.874857	−	0.484381i	$-0.839045\pi$
$47$	−0.123005	+	0.213051i	−0.0179422	+	0.0310767i	0.856915	+	0.515458i	$0.172378\pi$
$48$	2.38686	+	1.72310i	0.344514	+	0.248709i
$49$		0			0
$50$	−0.0618219	−	0.0356929i	−0.00874294	−	0.00504774i
$51$	8.38255	+	6.05146i	1.17379	+	0.847373i
$52$		−	2.86227i		−	0.396925i
$53$	6.82072	+	3.93795i	0.936899	+	0.540919i	0.888987	−	0.457933i	$-0.151410\pi$
$53$	6.82072	+	3.93795i	0.936899	+	0.540919i	0.0479118	+	0.998852i	$0.484743\pi$
$54$	−2.45706	+	2.25323i	−0.334363	+	0.306625i
$55$		−	7.50146i		−	1.01150i
$56$		0			0
$57$	−1.16621	−	2.59808i	−0.154468	−	0.344124i
$58$	1.81089			0.237782
$59$	5.39093	+	9.33736i	0.701839	+	1.21562i	0.967820	+	0.251643i	$0.0809709\pi$
$59$	5.39093	+	9.33736i	0.701839	+	1.21562i	−0.265981	+	0.963978i	$0.585696\pi$
$60$	−5.54944	+	2.49100i	−0.716430	+	0.321586i
$61$	1.22853	+	0.709292i	0.157297	+	0.0908155i	0.576582	−	0.817039i	$-0.304386\pi$
$61$	1.22853	+	0.709292i	0.157297	+	0.0908155i	−0.419285	+	0.907855i	$0.637719\pi$
$62$	6.87916			0.873654
$63$		0			0
$64$	−0.254572			−0.0318214
$65$	3.45056	+	1.99218i	0.427989	+	0.247100i
$66$	−3.05688	−	2.20679i	−0.376275	−	0.271638i
$67$	3.99381	+	6.91748i	0.487922	+	0.845105i	0.999904	−	0.0138913i	$-0.00442187\pi$
$67$	3.99381	+	6.91748i	0.487922	+	0.845105i	−0.511982	+	0.858996i	$0.671089\pi$
$68$	9.48096			1.14974
$69$	−4.09003	−	0.417322i	−0.492382	−	0.0502396i
$70$		0			0
$71$			12.1743i			1.44482i	0.691463	+	0.722412i	$0.256966\pi$
$71$			12.1743i			1.44482i	−0.691463	+	0.722412i	$0.743034\pi$
$72$	−1.39493	+	6.76443i	−0.164394	+	0.797196i
$73$	0.369016	+	0.213051i	0.0431900	+	0.0249358i	0.521440	−	0.853288i	$-0.325395\pi$
$73$	0.369016	+	0.213051i	0.0431900	+	0.0249358i	−0.478250	+	0.878224i	$0.658729\pi$
$74$		−	1.09046i		−	0.126764i
$75$	−0.0195619	+	0.191720i	−0.00225882	+	0.0221379i
$76$	−2.26168	−	1.30578i	−0.259433	−	0.149784i
$77$		0			0
$78$	1.82691	−	0.820053i	0.206857	−	0.0928527i
$79$	2.49381	−	4.31941i	0.280576	−	0.485971i	−0.690951	−	0.722902i	$-0.742808\pi$
$79$	2.49381	−	4.31941i	0.280576	−	0.485971i	0.971527	+	0.236930i	$0.0761413\pi$
$80$	−1.87898	+	3.25449i	−0.210076	+	0.363863i
$81$	8.26578	+	3.56046i	0.918420	+	0.395607i
$82$	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
$86$		−	2.51641i		−	0.271352i
$87$	−2.00199	−	4.46002i	−0.214635	−	0.478165i
$88$	−7.81089			−0.832644
$89$	5.26792	+	9.12431i	0.558399	+	0.967175i	0.997630	+	0.0688014i	$0.0219175\pi$
$89$	5.26792	+	9.12431i	0.558399	+	0.967175i	−0.439231	+	0.898374i	$0.644749\pi$
$90$	−3.17988	−	2.82839i	−0.335189	−	0.298138i
$91$		0			0
$92$	−3.26509	+	1.88510i	−0.340409	+	0.196535i
$93$	−7.60507	−	16.9426i	−0.788609	−	1.75686i
$94$	−0.136691	+	0.0789188i	−0.0140986	+	0.00813985i
$95$	3.14833	−	1.81769i	0.323012	−	0.186491i
$96$	4.03940	+	8.99896i	0.412269	+	0.918453i
$97$	6.30108	−	3.63793i	0.639777	−	0.369376i	−0.144751	−	0.989468i	$-0.546238\pi$
$97$	6.30108	−	3.63793i	0.639777	−	0.369376i	0.784529	+	0.620092i	$0.212905\pi$
$98$		0			0
$99$	−2.05563	+	9.96840i	−0.206599	+	1.00186i
$100$	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	$0.574608\pi$
$102$	2.71634	+	6.05146i	0.268958	+	0.599183i
$103$		−	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	$-0.689602\pi$
$107$	−1.28985	+	0.744696i	−0.124695	+	0.0719925i	0.436355	+	0.899774i	$0.356269\pi$
$108$	8.05705	−	1.78947i	0.775290	−	0.172192i
$109$	2.19344	−	3.79915i	0.210093	−	0.363892i	−0.741650	−	0.670787i	$-0.765957\pi$
$109$	2.19344	−	3.79915i	0.210093	−	0.363892i	0.951744	+	0.306895i	$0.0992899\pi$
$110$	2.40643	−	4.16805i	0.229444	−	0.397408i
$111$	−2.68568	+	1.20553i	−0.254914	+	0.114424i
$112$		0			0
$113$	−14.8764	−	8.58887i	−1.39945	−	0.807973i	−0.405115	−	0.914266i	$-0.632769\pi$
$113$	−14.8764	−	8.58887i	−1.39945	−	0.807973i	−0.994335	+	0.106293i	$0.966102\pi$
$114$	0.185466	−	1.81769i	0.0173705	−	0.170242i
$115$		−	5.24823i		−	0.489400i
$116$	−3.88255	−	2.24159i	−0.360485	−	0.208126i
$117$	−4.03940	−	3.59289i	−0.373442	−	0.332163i
$118$			6.91752i			0.636809i
$119$		0			0
$120$	−8.77128	−	0.894969i	−0.800705	−	0.0816991i
$121$	−0.510520			−0.0464110
$122$	0.455074	+	0.788211i	0.0412004	+	0.0713612i
$123$	−1.27816	−	0.922719i	−0.115248	−	0.0831987i
$124$	−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
$129$	−6.19763	+	2.78195i	−0.545671	+	0.244937i
$130$	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	$0.766935\pi$
$132$	3.82228	+	8.51527i	0.332687	+	0.741159i
$133$		0			0
$134$			5.12477i			0.442712i
$135$	−3.45056	+	10.9585i	−0.296977	+	0.943161i
$136$	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	$0.913758\pi$
$138$	−2.13868	−	1.54394i	−0.182056	−	0.131429i
$139$	−6.65488	−	3.84220i	−0.564460	−	0.325891i	0.190474	−	0.981692i	$-0.438998\pi$
$139$	−6.65488	−	3.84220i	−0.564460	−	0.325891i	−0.754934	+	0.655801i	$0.772331\pi$
$140$		0			0
$141$	0.345483	+	0.249409i	0.0290950	+	0.0210040i
$142$	−3.90545	+	6.76443i	−0.327738	+	0.567658i
$143$	3.05688	−	5.29467i	0.255629	−	0.442762i
$144$	3.38874	−	3.80987i	0.282395	−	0.317489i
$145$	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	$-0.217911\pi$
$150$	−0.0723718	+	0.100250i	−0.00590914	+	0.00818540i
$151$	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
$153$	11.9011	−	13.3801i	0.962145	−	1.08171i
$154$		0			0
$155$	20.5309	−	11.8535i	1.64908	−	0.952096i
$156$	−4.93199	−	0.503230i	−0.394875	−	0.0402907i
$157$	−4.93586	+	2.84972i	−0.393924	+	0.227432i	−0.683859	−	0.729614i	$-0.739700\pi$
$157$	−4.93586	+	2.84972i	−0.393924	+	0.227432i	0.289935	+	0.957046i	$0.406366\pi$
$158$	2.77128	−	1.60000i	0.220471	−	0.127289i
$159$	7.98468	−	11.0605i	0.633226	−	0.877152i
$160$	−10.9049	+	6.29593i	−0.862105	+	0.497737i
$161$		0			0
$162$	3.45056	+	4.62992i	0.271101	+	0.363761i
$163$	5.10507	+	8.84225i	0.399860	+	0.692578i	0.993708	−	0.111999i	$-0.0357253\pi$
$163$	5.10507	+	8.84225i	0.399860	+	0.692578i	−0.593848	+	0.804577i	$0.702392\pi$
$164$	−1.44565			−0.112886
$165$	−12.9258	−	1.31887i	−1.00627	−	0.102674i
$166$			5.49894i			0.426800i
$167$	−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
$171$	−4.68179	+	1.55272i	−0.358026	+	0.118739i
$172$	−3.11491	+	5.39518i	−0.237509	+	0.411378i
$173$	−9.03957	+	15.6570i	−0.687266	+	1.19038i	0.285453	+	0.958393i	$0.407856\pi$
$173$	−9.03957	+	15.6570i	−0.687266	+	1.19038i	−0.972719	+	0.231987i	$0.925477\pi$
$174$	0.318382	−	3.12036i	0.0241365	−	0.236554i
$175$		0			0
$176$	4.99381	+	2.88318i	0.376423	+	0.217328i
$177$	17.0371	−	7.64749i	1.28058	−	0.574820i
$178$			6.75968i			0.506660i
$179$	−4.35779	−	2.51597i	−0.325716	−	0.188052i	0.328221	−	0.944601i	$-0.393551\pi$
$179$	−4.35779	−	2.51597i	−0.325716	−	0.188052i	−0.653938	+	0.756548i	$0.726884\pi$
$180$	3.31657	+	10.0002i	0.247203	+	0.745373i
$181$			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
$183$	1.43818	−	1.99218i	0.106313	−	0.147266i
$184$	−5.46472			−0.402865
$185$	−1.87898	−	3.25449i	−0.138145	−	0.239275i
$186$	1.20946	−	11.8535i	0.0886819	−	0.869141i
$187$	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	$-0.212510\pi$
$191$	8.86948	+	5.12080i	0.641773	+	0.370528i	−0.143524	+	0.989647i	$0.545844\pi$
$192$	−0.0447575	+	0.438653i	−0.00323010	+	0.0316571i
$193$	−8.06615	−	13.9710i	−0.580614	−	1.00565i	−0.995407	−	0.0957374i	$-0.969479\pi$
$193$	−8.06615	−	13.9710i	−0.580614	−	1.00565i	0.414792	−	0.909916i	$-0.363854\pi$
$194$	4.66811			0.335151
$195$	4.03940	−	5.59542i	0.289267	−	0.400696i
$196$		0			0
$197$			3.86303i			0.275230i	0.990486	+	0.137615i	$0.0439436\pi$
$197$			3.86303i			0.275230i	−0.990486	+	0.137615i	$0.956056\pi$
$198$	−4.33998	+	4.87933i	−0.308429	+	0.346759i
$199$	−13.1665	−	7.60171i	−0.933352	−	0.538871i	−0.0454817	−	0.998965i	$-0.514482\pi$
$199$	−13.1665	−	7.60171i	−0.933352	−	0.538871i	−0.887870	+	0.460094i	$0.847816\pi$
$200$			0.256158i			0.0181131i
$201$	12.6217	−	5.66555i	0.890267	−	0.399617i
$202$	−2.59375	−	1.49750i	−0.182496	−	0.105364i
$203$		0			0
$204$	1.66690	−	16.3367i	0.116706	−	1.14380i
$205$	1.00619	−	1.74277i	0.0702753	−	0.121720i
$206$	2.00199	−	3.46754i	0.139485	−	0.241595i
$207$	−1.43818	+	6.97418i	−0.0999603	+	0.484739i
$208$	−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	$-0.140941\pi$
$212$		−	12.5098i		−	0.859176i
$213$	20.9776	+	2.14043i	1.43736	+	0.146660i
$214$	−0.955577			−0.0653219
$215$	−4.33604	−	7.51024i	−0.295715	−	0.512194i
$216$	11.4106	+	3.59289i	0.776391	+	0.244465i
$217$		0			0
$218$	2.43749	−	1.40729i	0.165088	−	0.0953134i
$219$	0.431988	−	0.598395i	0.0291911	−	0.0404358i
$220$	−10.3187	+	5.95752i	−0.695689	+	0.401656i
$221$	−9.31522	+	5.37815i	−0.626610	+	0.361773i
$222$	−1.87898	−	0.191720i	−0.126109	−	0.0128674i
$223$	16.6198	−	9.59545i	1.11294	−	0.642559i	0.173354	−	0.984860i	$-0.444539\pi$
$223$	16.6198	−	9.59545i	1.11294	−	0.642559i	0.939591	+	0.342300i	$0.111206\pi$
$224$		0			0
$225$	0.326914	+	0.0674145i	0.0217943	+	0.00449430i
$226$	−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	$0.407078\pi$
$228$	−2.64764	+	3.66754i	−0.175344	+	0.242889i
$229$			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	−0.728375	+	0.685178i	$0.759724\pi$
$233$	−25.7348	+	14.8580i	−1.68594	+	0.973381i	−0.957570	+	0.288202i	$0.906942\pi$
$234$	−1.09184	−	3.29214i	−0.0713757	−	0.215214i
$235$	−0.271971	+	0.471067i	−0.0177414	+	0.0307290i
$236$	8.56276	−	14.8311i	0.557388	−	0.965425i
$237$	−7.00434	−	5.05651i	−0.454981	−	0.328456i
$238$		0			0
$239$	−13.7101	−	7.91556i	−0.886836	−	0.512015i	−0.0139296	−	0.999903i	$-0.504434\pi$
$239$	−13.7101	−	7.91556i	−0.886836	−	0.512015i	−0.872906	+	0.487888i	$0.837767\pi$
$240$	5.27747	+	3.80987i	0.340659	+	0.245926i
$241$			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
$243$	7.58829	−	13.6168i	0.486789	−	0.873519i
$244$		−	2.25323i		−	0.144248i
$245$		0			0
$246$	−0.414184	−	0.922719i	−0.0264074	−	0.0588304i
$247$	2.96286			0.188522
$248$	−12.3425	−	21.3778i	−0.783747	−	1.35749i
$249$	13.5433	−	6.07921i	0.858269	−	0.385254i
$250$	−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
$255$	18.5342	+	13.3801i	1.16066	+	0.837892i
$256$	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	$0.580352\pi$
$258$	−4.33604	−	0.442423i	−0.269950	−	0.0275441i
$259$		0			0
$260$		−	6.32862i		−	0.392484i
$261$	−8.03706	+	2.66549i	−0.497482	+	0.164990i
$262$	−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	$-0.160945\pi$
$264$	−1.37327	+	13.4590i	−0.0845191	+	0.828343i
$265$	15.0810	+	8.70699i	0.926416	+	0.534866i
$266$		0			0
$267$	16.6483	−	7.47299i	1.01886	−	0.457340i
$268$	6.34362	−	10.9875i	0.387499	−	0.671167i
$269$	5.24619	−	9.08666i	0.319866	−	0.554024i	−0.660594	−	0.750743i	$-0.729696\pi$
$269$	5.24619	−	9.08666i	0.319866	−	0.554024i	0.980460	+	0.196720i	$0.0630289\pi$
$270$	−5.43268	+	4.98199i	−0.330622	+	0.303195i
$271$	−19.2722	+	11.1268i	−1.17071	+	0.675907i	−0.953846	−	0.300296i	$-0.902915\pi$
$271$	−19.2722	+	11.1268i	−1.17071	+	0.675907i	−0.216859	+	0.976203i	$0.569581\pi$
$272$	−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
$276$	2.67417	+	5.95752i	0.160966	+	0.358601i
$277$	−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
$279$	−30.5309	+	10.1256i	−1.82784	+	0.606202i
$280$		0			0
$281$	0.796041	−	0.459595i	0.0474878	−	0.0274171i	−0.476068	−	0.879408i	$-0.657938\pi$
$281$	0.796041	−	0.459595i	0.0474878	−	0.0274171i	0.523556	+	0.851991i	$0.324605\pi$
$282$	0.111953	+	0.249409i	0.00666670	+	0.0148521i
$283$	−19.1573	+	11.0605i	−1.13878	+	0.657477i	−0.946129	−	0.323790i	$-0.895043\pi$
$283$	−19.1573	+	11.0605i	−1.13878	+	0.657477i	−0.192654	+	0.981267i	$0.561710\pi$
$284$	16.7465	−	9.66861i	0.993723	−	0.573726i
$285$	−2.57854	−	5.74447i	−0.152740	−	0.340273i
$286$	3.39700	−	1.96126i	0.200869	−	0.115972i
$287$		0			0
$288$	16.2163	−	5.37815i	0.955557	−	0.316910i
$289$	−9.31453	−	16.1332i	−0.547914	−	0.949014i
$290$	4.00397			0.235121
$291$	−5.16071	−	11.4970i	−0.302526	−	0.673967i
$292$		−	0.676806i		−	0.0396071i
$293$	−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
$297$	16.8152	+	5.29467i	0.975716	+	0.307228i
$298$	4.95234	−	8.57771i	0.286881	−	0.496893i
$299$	2.13868	−	3.70430i	0.123683	−	0.214225i
$300$	0.279258	−	0.125352i	0.0161230	−	0.00723718i
$301$		0			0
$302$	6.49381	+	3.74920i	0.373677	+	0.215742i
$303$	−0.820724	+	8.04364i	−0.0471494	+	0.462095i
$304$			2.79450i			0.160276i
$305$	2.71634	+	1.56828i	0.155537	+	0.0897994i
$306$	10.9049	−	3.61660i	0.623390	−	0.206747i
$307$		−	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
$309$	−10.7534	−	1.09721i	−0.611740	−	0.0624182i
$310$	15.2101			0.863878
$311$	−9.69002	−	16.7836i	−0.549471	−	0.951711i	−0.998311	−	0.0580991i	$-0.981496\pi$
$311$	−9.69002	−	16.7836i	−0.549471	−	0.951711i	0.448840	−	0.893612i	$-0.351837\pi$
$312$	−5.82623	−	4.20602i	−0.329845	−	0.238119i
$313$	12.6608	+	7.30974i	0.715633	+	0.413171i	0.813143	−	0.582064i	$-0.197755\pi$
$313$	12.6608	+	7.30974i	0.715633	+	0.413171i	−0.0975102	+	0.995235i	$0.531088\pi$
$314$	−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	$-0.175119\pi$
$317$	14.7046	+	8.48973i	0.825895	+	0.476831i	−0.0265499	+	0.999647i	$0.508452\pi$
$318$	7.98468	−	3.58411i	0.447759	−	0.200987i
$319$	−4.78799	−	8.29305i	−0.268076	−	0.464321i
$320$	−0.562870			−0.0314654
$321$	1.05641	+	2.35348i	0.0589633	+	0.131358i
$322$		0			0
$323$			9.81416i			0.546074i
$324$	−1.66690	−	14.1978i	−0.0926053	−	0.788764i
$325$	−0.173639	−	0.100250i	−0.00963174	−	0.00556089i
$326$			6.55072i			0.362811i
$327$	−6.16069	−	4.44747i	−0.340687	−	0.245946i
$328$	−1.81466	−	1.04769i	−0.100198	−	0.0578493i
$329$		0			0
$330$	−6.75890	−	4.87933i	−0.372065	−	0.268598i
$331$	−9.94801	+	17.2305i	−0.546792	+	0.947072i	0.451700	+	0.892170i	$0.350818\pi$
$331$	−9.94801	+	17.2305i	−0.546792	+	0.947072i	−0.998492	+	0.0549016i	$0.982515\pi$
$332$	6.80678	−	11.7897i	0.373571	−	0.647044i
$333$	1.60507	+	4.83967i	0.0879575	+	0.265212i
$334$	−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	$0.158166\pi$
$338$		−	6.25723i		−	0.340348i
$339$	−17.4150	+	24.1235i	−0.945853	+	1.31021i
$340$	20.9629			1.13687
$341$	−18.1885	−	31.5033i	−0.984960	−	1.70600i
$342$	−3.09946	−	0.639154i	−0.167599	−	0.0345615i
$343$		0			0
$344$	−7.82004	+	4.51490i	−0.421628	+	0.243427i
$345$	−9.04325	−	0.922719i	−0.486872	−	0.0496775i
$346$	−10.0454	+	5.79969i	−0.540041	+	0.311793i
$347$	−18.3702	+	10.6060i	−0.986162	+	0.569361i	−0.904125	−	0.427268i	$-0.859476\pi$
$347$	−18.3702	+	10.6060i	−0.986162	+	0.569361i	−0.0820373	+	0.996629i	$0.526143\pi$
$348$	−4.54510	+	6.29593i	−0.243643	+	0.337497i
$349$	−8.69945	+	5.02263i	−0.465671	+	0.268855i	−0.714426	−	0.699711i	$-0.753312\pi$
$349$	−8.69945	+	5.02263i	−0.465671	+	0.268855i	0.248755	+	0.968566i	$0.419979\pi$
$350$		0			0
$351$	−6.90112	+	6.32862i	−0.368354	+	0.337797i
$352$	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	$0.476713\pi$
$354$	11.9196	+	1.21620i	0.633520	+	0.0646406i
$355$			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	$-0.581650\pi$
$359$	8.66140	−	5.00066i	0.457131	−	0.263925i	0.710837	+	0.703357i	$0.248316\pi$
$360$	−3.08425	+	14.9565i	−0.162554	+	0.788276i
$361$	−8.14833	+	14.1133i	−0.428859	+	0.742806i
$362$	−4.34973	+	7.53395i	−0.228616	+	0.395975i
$363$	−0.0897572	+	0.879680i	−0.00471103	+	0.0461712i
$364$		0			0
$365$	0.815912	+	0.471067i	0.0427068	+	0.0246568i
$366$	1.43818	−	0.645560i	0.0751748	−	0.0337440i
$367$			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
$369$	−1.81466	+	2.04018i	−0.0944675	+	0.106207i
$370$		−	2.41106i		−	0.125345i
$371$		0			0
$372$	−17.2658	+	23.9168i	−0.895189	+	1.24003i
$373$	−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
$375$	−1.98693	+	19.4732i	−0.102605	+	1.00559i
$376$	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
$381$	1.11140	−	10.8925i	0.0569388	−	0.558037i
$382$	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	$0.528376\pi$
$384$	11.3817	−	15.7660i	0.580819	−	0.804557i
$385$		0			0
$386$		−	10.3503i		−	0.526817i
$387$	3.70396	+	11.1683i	0.188283	+	0.567716i
$388$	−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	$-0.0597056\pi$
$390$	4.03940	−	1.81318i	0.204543	−	0.0918138i
$391$	12.2701	+	7.08414i	0.620525	+	0.358260i
$392$		0			0
$393$	−2.99312	+	29.3346i	−0.150983	+	1.47973i
$394$	−1.23924	+	2.14642i	−0.0624319	+	0.108135i
$395$	5.51394	−	9.55042i	0.277436	−	0.480534i
$396$	15.3447	−	5.08907i	0.771101	−	0.255736i
$397$	16.7002	−	9.64189i	0.838161	−	0.483912i	−0.0184778	−	0.999829i	$-0.505882\pi$
$397$	16.7002	−	9.64189i	0.838161	−	0.483912i	0.856639	+	0.515917i	$0.172549\pi$
$398$	−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	$-0.0893232\pi$
$402$	8.83051	+	0.901012i	0.440426	+	0.0449384i
$403$	19.3214			0.962468
$404$	3.70733	+	6.42128i	0.184446	+	0.319471i
$405$	18.2760	+	7.87235i	0.908144	+	0.391180i
$406$		0			0
$407$	−4.99381	+	2.88318i	−0.247534	+	0.142914i
$408$	13.9320	−	19.2987i	0.689736	−	0.955430i
$409$	17.5597	−	10.1381i	0.868274	−	0.501298i	0.00149954	−	0.999999i	$-0.499523\pi$
$409$	17.5597	−	10.1381i	0.868274	−	0.501298i	0.866774	+	0.498701i	$0.166189\pi$
$410$	1.11814	−	0.645560i	0.0552211	−	0.0318819i
$411$	10.7955	+	1.10151i	0.532505	+	0.0543336i
$412$	−8.58450	+	4.95626i	−0.422928	+	0.244178i
$413$		0			0
$414$	−3.03637	+	3.41372i	−0.149230	+	0.167775i
$415$	9.47524	+	16.4116i	0.465121	+	0.805614i
$416$	−10.2625			−0.503159
$417$	−7.79054	+	10.7915i	−0.381504	+	0.528464i
$418$		−	3.57895i		−	0.175052i
$419$	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
$423$	0.490498	−	0.551454i	0.0238488	−	0.0268126i
$424$	9.06615	−	15.7030i	0.440291	−	0.762607i
$425$	0.332068	−	0.575159i	0.0161077	−	0.0278993i
$426$	10.9692	+	7.91878i	0.531459	+	0.383666i
$427$		0			0
$428$	2.04875	+	1.18285i	0.0990302	+	0.0571751i
$429$	−8.58582	−	6.19820i	−0.414527	−	0.299252i
$430$		−	5.56391i		−	0.268315i
$431$	13.0858	+	7.55510i	0.630322	+	0.363916i	0.780877	−	0.624685i	$-0.214773\pi$
$431$	13.0858	+	7.55510i	0.630322	+	0.363916i	−0.150555	+	0.988602i	$0.548106\pi$
$432$	−5.96901	−	6.50898i	−0.287184	−	0.313163i
$433$		−	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
$435$	−4.42649	−	9.86132i	−0.212234	−	0.472814i
$436$	−6.96796			−0.333705
$437$	−1.95135	−	3.37984i	−0.0933458	−	0.161680i
$438$	0.431988	−	0.193908i	0.0206412	−	0.00926529i
$439$	5.91032	+	3.41233i	0.282084	+	0.162861i	0.634367	−	0.773032i	$-0.281261\pi$
$439$	5.91032	+	3.41233i	0.282084	+	0.162861i	−0.352282	+	0.935894i	$0.614594\pi$
$440$	−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	$-0.419763\pi$
$443$	−9.77747	−	5.64503i	−0.464542	−	0.268203i	−0.713952	+	0.700195i	$0.753097\pi$
$444$	3.79121	+	2.73692i	0.179923	+	0.129888i
$445$	11.6476	+	20.1743i	0.552151	+	0.956354i
$446$	12.3127			0.583022
$447$	−26.6008	−	2.71419i	−1.25818	−	0.128377i
$448$		0			0
$449$			24.8554i			1.17300i	0.809950	+	0.586498i	$0.199494\pi$
$449$			24.8554i			1.17300i	−0.809950	+	0.586498i	$0.800506\pi$
$450$	0.160018	+	0.142330i	0.00754331	+	0.00670949i
$451$	−2.67417	−	1.54394i	−0.125922	−	0.0727011i
$452$			27.2845i			1.28335i
$453$	2.05480	−	20.1384i	0.0965427	−	0.946182i
$454$	4.81849	+	2.78195i	0.226143	+	0.130564i
$455$		0			0
$456$	−5.98143	+	2.68491i	−0.280106	+	0.125732i
$457$	6.30470	−	10.9201i	0.294922	−	0.510819i	−0.680045	−	0.733170i	$-0.738040\pi$
$457$	6.30470	−	10.9201i	0.294922	−	0.510819i	0.974967	+	0.222351i	$0.0713732\pi$
$458$	−4.60942	+	7.98375i	−0.215384	+	0.373056i
$459$	−20.9629	−	22.8592i	−0.978463	−	1.06698i
$460$	−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	$0.967796\pi$
$464$			4.79722i			0.222705i
$465$	−16.8152	−	37.4609i	−0.779786	−	1.73721i
$466$	−19.0655			−0.883191
$467$	12.7975	+	22.1660i	0.592199	+	1.02572i	0.993936	+	0.109964i	$0.0350735\pi$
$467$	12.7975	+	22.1660i	0.592199	+	1.02572i	−0.401736	+	0.915755i	$0.631593\pi$
$468$	−1.73424	+	8.40986i	−0.0801651	+	0.388746i
$469$		0			0
$470$	−0.302231	+	0.174493i	−0.0139409	+	0.00804877i
$471$	4.04256	+	9.00602i	0.186272	+	0.414976i
$472$	21.4970	−	12.4113i	0.989479	−	0.571276i
$473$	−11.5240	+	6.65338i	−0.529874	+	0.305923i
$474$	−2.26973	−	5.05651i	−0.104252	−	0.232253i
$475$	−0.158430	+	0.0914695i	−0.00726926	+	0.00419691i
$476$		0			0
$477$	−17.6545	−	15.7030i	−0.808345	−	0.718993i
$478$	−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	$0.503894\pi$
$480$	8.93130	+	19.8971i	0.407656	+	0.908176i
$481$		−	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
$486$	8.58450	−	5.13166i	0.389401	−	0.232777i
$487$	−17.0662	+	29.5594i	−0.773341	+	1.33947i	0.162381	+	0.986728i	$0.448083\pi$
$487$	−17.0662	+	29.5594i	−0.773341	+	1.33947i	−0.935722	+	0.352738i	$0.885251\pi$
$488$	1.63297	−	2.82839i	0.0739211	−	0.128035i
$489$	16.1337	−	7.24198i	0.729590	−	0.327493i
$490$		0			0
$491$	5.86948	+	3.38874i	0.264886	+	0.152932i	0.626561	−	0.779372i	$-0.284462\pi$
$491$	5.86948	+	3.38874i	0.264886	+	0.152932i	−0.361675	+	0.932304i	$0.617795\pi$
$492$	−0.254166	+	2.49100i	−0.0114587	+	0.112303i
$493$			16.8476i			0.758778i
$494$	1.64626	+	0.950469i	0.0740688	+	0.0427636i
$495$	−4.54510	+	22.0406i	−0.204287	+	0.990652i
$496$			18.2235i			0.818260i
$497$		0			0
$498$	9.47524	+	0.966796i	0.424596	+	0.0433232i
$499$	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
$501$	5.07420	+	3.66312i	0.226699	+	0.163656i
$502$	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
$507$	−15.4108	+	6.91752i	−0.684420	+	0.307218i
$508$	−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	$0.543147\pi$
$510$	6.00596	+	13.3801i	0.265948	+	0.592479i
$511$		0			0
$512$		−	17.5053i		−	0.773631i
$513$	1.85236	+	8.34021i	0.0817838	+	0.368229i
$514$	−4.44947	−	2.56890i	−0.196258	−	0.113309i
$515$		−	13.7985i		−	0.608035i
$516$	8.74880	+	6.31586i	0.385145	+	0.278040i
$517$	0.722823	+	0.417322i	0.0317897	+	0.0183538i
$518$		0			0
$519$	25.3893	+	18.3289i	1.11447	+	0.804548i
$520$	4.58650	−	7.94406i	0.201132	−	0.348370i
$521$	−16.3464	+	28.3128i	−0.716150	+	1.24041i	0.246364	+	0.969177i	$0.420764\pi$
$521$	−16.3464	+	28.3128i	−0.716150	+	1.24041i	−0.962514	+	0.271231i	$0.912569\pi$
$522$	−5.32072	−	1.09721i	−0.232882	−	0.0480237i
$523$	1.73424	−	1.00126i	0.0758329	−	0.0437821i	−0.461604	−	0.887086i	$-0.652726\pi$
$523$	1.73424	−	1.00126i	0.0758329	−	0.0437821i	0.537437	+	0.843304i	$0.319393\pi$
$524$	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
$528$	5.84600	−	8.09795i	0.254415	−	0.352418i
$529$	17.3658			0.755036
$530$	5.58631	+	9.67577i	0.242654	+	0.420289i
$531$	−10.1820	−	30.7012i	−0.441863	−	1.33232i
$532$		0			0
$533$	1.42037	−	0.820053i	0.0615232	−	0.0355204i
$534$	11.6476	+	1.18845i	0.504043	+	0.0514295i
$535$	−2.85192	+	1.64656i	−0.123299	+	0.0711870i
$536$	15.9258	−	9.19476i	0.687890	−	0.397153i
$537$	−5.10144	+	7.06658i	−0.220144	+	0.304945i
$538$	5.82990	−	3.36589i	0.251345	−	0.145114i
$539$		0			0
$540$	17.8145	−	3.95661i	0.766615	−	0.170265i
$541$	5.72253	+	9.91171i	0.246031	+	0.426138i	0.962421	−	0.271562i	$-0.0875403\pi$
$541$	5.72253	+	9.91171i	0.246031	+	0.426138i	−0.716390	+	0.697700i	$0.754207\pi$
$542$	−14.2777			−0.613280
$543$	23.3640	+	2.38392i	1.00264	+	0.102304i
$544$		−	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	0.769982	−	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
$549$	−3.17988	−	2.82839i	−0.135714	−	0.120713i
$550$	−0.121096	+	0.209744i	−0.00516355	+	0.00894353i
$551$	2.32037	−	4.01899i	0.0988510	−	0.171215i
$552$	−0.960781	+	9.41628i	−0.0408935	+	0.400784i
$553$		0			0
$554$	−12.6963	−	7.33022i	−0.539415	−	0.311431i
$555$	−5.93818	+	2.66549i	−0.252062	+	0.113144i
$556$			12.2056i			0.517634i
$557$	−0.0116910	−	0.00674980i	−0.000495364	−	0.000285998i	0.499752	−	0.866168i	$-0.333424\pi$
$557$	−0.0116910	−	0.00674980i	−0.000495364	−	0.000285998i	−0.500248	+	0.865882i	$0.666758\pi$
$558$	−20.2122	−	4.16805i	−0.855650	−	0.176448i
$559$		−	7.06782i		−	0.298937i
$560$		0			0
$561$	20.5309	−	28.4396i	0.866814	−	1.20072i
$562$	0.589741			0.0248767
$563$	9.54528	+	16.5329i	0.402286	+	0.696779i	0.994001	−	0.109368i	$-0.0348826\pi$
$563$	9.54528	+	16.5329i	0.402286	+	0.696779i	−0.591716	+	0.806147i	$0.701549\pi$
$564$	0.0687005	−	0.673310i	0.00289281	−	0.0283515i
$565$	−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	$-0.619525\pi$
$569$	−32.3406	−	18.6719i	−1.35579	−	0.782765i	−0.989053	+	0.147561i	$0.952858\pi$
$570$	0.410074	−	4.01899i	0.0171761	−	0.168337i
$571$	−22.6421	−	39.2173i	−0.947544	−	1.64119i	−0.750576	−	0.660784i	$-0.770224\pi$
$571$	−22.6421	−	39.2173i	−0.947544	−	1.64119i	−0.196968	−	0.980410i	$-0.563110\pi$
$572$	−9.71086			−0.406032
$573$	10.3831	−	14.3827i	0.433758	−	0.600847i
$574$		0			0
$575$			0.264101i			0.0110138i
$576$	0.747976	+	0.154244i	0.0311657	+	0.00642683i
$577$	32.1285	+	18.5494i	1.33753	+	0.772221i	0.986440	−	0.164123i	$-0.0524793\pi$
$577$	32.1285	+	18.5494i	1.33753	+	0.772221i	0.351086	+	0.936343i	$0.385813\pi$
$578$		−	11.9522i		−	0.497146i
$579$	−25.4916	+	11.4425i	−1.05940	+	0.475535i
$580$	−8.58450	−	4.95626i	−0.356452	−	0.205798i
$581$		0			0
$582$	0.820724	−	8.04364i	0.0340201	−	0.333419i
$583$	13.3603	−	23.1408i	0.553329	−	0.958393i
$584$	0.490498	−	0.849568i	0.0202970	−	0.0351554i
$585$	−8.93130	−	7.94406i	−0.369264	−	0.328446i
$586$	−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
$590$			15.2950i			0.629684i
$591$	6.65641	+	0.679179i	0.273808	+	0.0279377i
$592$	2.88874			0.118726
$593$	9.84997	+	17.0607i	0.404490	+	0.700597i	0.994262	−	0.106973i	$-0.0341157\pi$
$593$	9.84997	+	17.0607i	0.404490	+	0.700597i	−0.589772	+	0.807570i	$0.700782\pi$
$594$	7.64456	+	8.33610i	0.313660	+	0.342034i
$595$		0			0
$596$	−21.2356	+	12.2604i	−0.869844	+	0.502205i
$597$	−15.4134	+	21.3508i	−0.630829	+	0.873832i
$598$	2.37663	−	1.37215i	0.0971878	−	0.0561114i
$599$	9.74033	−	5.62358i	0.397979	−	0.229773i	−0.287632	−	0.957741i	$-0.592868\pi$
$599$	9.74033	−	5.62358i	0.397979	−	0.229773i	0.685612	+	0.727967i	$0.259535\pi$
$600$	0.441388	+	0.0450365i	0.0180196	+	0.00183861i
$601$	−29.7646	+	17.1846i	−1.21412	+	0.700975i	−0.963655	−	0.267150i	$-0.913918\pi$
$601$	−29.7646	+	17.1846i	−1.21412	+	0.700975i	−0.250469	+	0.968125i	$0.580585\pi$
$602$		0			0
$603$	−7.54325	−	22.7446i	−0.307185	−	0.926233i
$604$	−9.28180	−	16.0766i	−0.377671	−	0.654146i
$605$	−1.12879			−0.0458917
$606$	−3.03637	+	4.20602i	−0.123344	+	0.170858i
$607$		−	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
$612$	−27.8567	−	5.74447i	−1.12604	−	0.232207i
$613$	8.05494	−	13.9516i	0.325336	−	0.563499i	−0.656244	−	0.754549i	$-0.727856\pi$
$613$	8.05494	−	13.9516i	0.325336	−	0.563499i	0.981580	+	0.191050i	$0.0611892\pi$
$614$	4.76222	−	8.24840i	0.192187	−	0.332878i
$615$	−2.82607	−	2.04018i	−0.113958	−	0.0822678i
$616$		0			0
$617$	7.03569	+	4.06205i	0.283246	+	0.163532i	0.634892	−	0.772601i	$-0.281045\pi$
$617$	7.03569	+	4.06205i	0.283246	+	0.163532i	−0.351646	+	0.936133i	$0.614378\pi$
$618$	−5.62296	−	4.05928i	−0.226188	−	0.163288i
$619$		−	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
$621$	11.7644	+	3.70430i	0.472088	+	0.148648i
$622$		−	12.4340i		−	0.498559i
$623$		0			0
$624$	2.17240	+	4.83967i	0.0869655	+	0.193742i
$625$	−24.4313			−0.977252
$626$	4.68985	+	8.12305i	0.187444	+	0.324662i
$627$	−8.81453	+	3.95661i	−0.352019	+	0.158012i
$628$	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
$633$	−33.5704	−	24.2349i	−1.33430	−	0.963249i
$634$	5.44692	+	9.43434i	0.216325	+	0.374685i
$635$	13.9770			0.554658
$636$	−21.5557	−	2.19941i	−0.854738	−	0.0872123i
$637$		0			0
$638$		−	6.14384i		−	0.243237i
$639$	7.37636	−	35.7703i	0.291804	−	1.41505i
$640$	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	$-0.0585334\pi$
$642$	−0.168005	+	1.64656i	−0.00663063	+	0.0649845i
$643$	−36.3456	−	20.9841i	−1.43333	−	0.827534i	−0.435958	−	0.899967i	$-0.643590\pi$
$643$	−36.3456	−	20.9841i	−1.43333	−	0.827534i	−0.997373	+	0.0724332i	$0.976924\pi$
$644$		0			0
$645$	−13.7033	+	6.15103i	−0.539566	+	0.242197i
$646$	−3.14833	+	5.45306i	−0.123869	+	0.214548i
$647$	3.14293	−	5.44372i	0.123561	−	0.214015i	−0.797608	−	0.603176i	$-0.793902\pi$
$647$	3.14293	−	5.44372i	0.123561	−	0.214015i	0.921170	+	0.389161i	$0.127235\pi$
$648$	8.19708	−	19.0299i	0.322012	−	0.747566i
$649$	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	$-0.150589\pi$
$654$	−1.99635	−	4.44747i	−0.0780635	−	0.173910i
$655$	−37.6414			−1.47077
$656$	0.773456	+	1.33966i	0.0301984	+	0.0523051i
$657$	−0.955147	−	0.849568i	−0.0372638	−	0.0331448i
$658$		0			0
$659$	25.8880	−	14.9464i	1.00845	−	0.582230i	0.0977141	−	0.995215i	$-0.468847\pi$
$659$	25.8880	−	14.9464i	1.00845	−	0.582230i	0.910738	+	0.412984i	$0.135514\pi$
$660$	8.45125	+	18.8277i	0.328964	+	0.732866i
$661$	17.6184	−	10.1720i	0.685278	−	0.395645i	−0.116563	−	0.993183i	$-0.537188\pi$
$661$	17.6184	−	10.1720i	0.685278	−	0.395645i	0.801841	+	0.597538i	$0.203854\pi$
$662$	−11.0549	+	6.38253i	−0.429660	+	0.248064i
$663$	7.62935	+	16.9967i	0.296299	+	0.660096i
$664$	17.0886	−	9.86609i	0.663165	−	0.382879i
$665$		0			0
$666$	−0.660706	+	3.20397i	−0.0256019	+	0.124151i
$667$	−3.34981	−	5.80205i	−0.129705	−	0.224656i
$668$	5.73910			0.222053
$669$	−13.6120	−	30.3247i	−0.526269	−	1.17242i
$670$			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	0.652542	−	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
$675$	0.173639	−	0.551454i	0.00668335	−	0.0212255i
$676$	−7.74543	+	13.4155i	−0.297901	+	0.515980i
$677$	−14.2078	+	24.6085i	−0.546048	+	0.945783i	0.452492	+	0.891769i	$0.350535\pi$
$677$	−14.2078	+	24.6085i	−0.546048	+	0.945783i	−0.998540	+	0.0540148i	$0.982798\pi$
$678$	−17.4150	+	7.81713i	−0.668819	+	0.300215i
$679$		0			0
$680$	26.3138	+	15.1923i	1.00909	+	0.582598i
$681$	1.52468	−	14.9429i	0.0584260	−	0.572613i
$682$		−	23.3390i		−	0.893697i
$683$	18.1236	+	10.4637i	0.693482	+	0.400382i	0.804915	−	0.593390i	$-0.202211\pi$
$683$	18.1236	+	10.4637i	0.693482	+	0.400382i	−0.111433	+	0.993772i	$0.535544\pi$
$684$	5.85406	+	5.20697i	0.223835	+	0.199093i
$685$			13.8526i			0.529281i
$686$		0			0
$687$	24.7589	+	2.52625i	0.944611	+	0.0963824i
$688$	6.66621			0.254147
$689$	7.09627	+	12.2911i	0.270346	+	0.468254i
$690$	−4.72872	−	3.41372i	−0.180019	−	0.129958i
$691$	−20.7918	−	12.0041i	−0.790957	−	0.456659i	0.0493424	−	0.998782i	$-0.484287\pi$
$691$	−20.7918	−	12.0041i	−0.790957	−	0.456659i	−0.840299	+	0.542123i	$0.817621\pi$
$692$	28.7163			1.09163
$693$		0			0
$694$	−13.6094			−0.516606
$695$	−14.7143	−	8.49529i	−0.558144	−	0.322245i
$696$	−10.2681	+	4.60908i	−0.389211	+	0.174707i
$697$	2.71634	+	4.70484i	0.102889	+	0.178208i
$698$	−6.44493			−0.243944
$699$	21.0773	+	46.9561i	0.797218	+	1.77604i
$700$		0			0
$701$		−	42.0117i		−	1.58676i	−0.608728	−	0.793379i	$-0.708320\pi$
$701$		−	42.0117i		−	1.58676i	0.608728	−	0.793379i	$-0.291680\pi$
$702$	−5.86467	+	1.30254i	−0.221348	+	0.0491613i
$703$	−2.42011	−	1.39725i	−0.0912762	−	0.0526984i
$704$			0.863689i			0.0325515i
$705$	0.763881	+	0.551454i	0.0287694	+	0.0207690i
$706$	1.52607	+	0.881077i	0.0574344	+	0.0331598i
$707$		0			0
$708$	−24.0501	−	17.3621i	−0.903859	−	0.652506i
$709$	−18.6094	+	32.2324i	−0.698891	+	1.21051i	0.269960	+	0.962871i	$0.412989\pi$
$709$	−18.6094	+	32.2324i	−0.698891	+	1.21051i	−0.968851	+	0.247643i	$0.920344\pi$
$710$	−8.63513	+	14.9565i	−0.324071	+	0.561307i
$711$	−9.94437	+	11.1802i	−0.372943	+	0.419290i
$712$	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
$717$	−16.0498	+	22.2323i	−0.599390	+	0.830282i
$718$	6.41673			0.239470
$719$	9.14889	+	15.8463i	0.341196	+	0.590969i	0.984655	−	0.174512i	$-0.0558347\pi$
$719$	9.14889	+	15.8463i	0.341196	+	0.590969i	−0.643459	+	0.765481i	$0.722501\pi$
$720$	7.49266	−	8.42380i	0.279235	−	0.313937i
$721$		0			0
$722$	−9.05494	+	5.22787i	−0.336990	+	0.194561i
$723$	8.65452	+	0.883054i	0.321865	+	0.0328411i
$724$	18.6516	−	10.7685i	0.693181	−	0.400208i
$725$	−0.271971	+	0.157022i	−0.0101007	+	0.00583166i
$726$	−0.332068	+	0.459985i	−0.0123242	+	0.0170716i
$727$	28.3214	−	16.3514i	1.05038	−	0.606439i	0.127626	−	0.991822i	$-0.459264\pi$
$727$	28.3214	−	16.3514i	1.05038	−	0.606439i	0.922756	+	0.385384i	$0.125931\pi$
$728$		0			0
$729$	−22.1291	−	15.4695i	−0.819595	−	0.572943i
$730$	0.302231	+	0.523480i	0.0111861	+	0.0193749i
$731$	23.4114			0.865901
$732$	−3.88255	−	0.396151i	−0.143503	−	0.0146422i
$733$			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
$738$	−1.66276	+	0.551454i	−0.0612071	+	0.0202993i
$739$	23.8523	−	41.3134i	0.877421	−	1.51974i	0.0232588	−	0.999729i	$-0.492596\pi$
$739$	23.8523	−	41.3134i	0.877421	−	1.51974i	0.854162	−	0.520007i	$-0.174071\pi$
$740$	−2.98450	+	5.16931i	−0.109713	+	0.190028i
$741$	0.520916	−	5.10532i	0.0191363	−	0.187549i
$742$		0			0
$743$	9.20534	+	5.31470i	0.337711	+	0.194978i	0.659259	−	0.751916i	$-0.270870\pi$
$743$	9.20534	+	5.31470i	0.337711	+	0.194978i	−0.321548	+	0.946893i	$0.604203\pi$
$744$	−39.0061	+	17.5088i	−1.43003	+	0.641904i
$745$		−	34.1336i		−	1.25056i
$746$	−8.62296	−	4.97847i	−0.315709	−	0.182275i
$747$	−8.09400	−	24.4053i	−0.296144	−	0.892942i
$748$		−	32.1662i		−	1.17611i
$749$		0			0
$750$	−7.35091	+	10.1826i	−0.268417	+	0.371815i
$751$	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
$753$	1.28297	−	12.5740i	0.0467541	−	0.458221i
$754$	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
$759$	−1.41585	+	13.8763i	−0.0513923	+	0.503678i
$760$	−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	$0.212480\pi$
$762$	4.11177	−	5.69567i	0.148954	−	0.206332i
$763$		0			0
$764$		−	16.2674i		−	0.588533i
$765$	26.3138	−	29.5840i	0.951379	−	1.06961i
$766$	−1.93614	−	1.11783i	−0.0699557	−	0.0403889i
$767$			19.4292i			0.701546i
$768$	12.1862	−	5.47006i	0.439732	−	0.197384i
$769$	−5.75189	−	3.32086i	−0.207419	−	0.119753i	0.392693	−	0.919670i	$-0.371544\pi$
$769$	−5.75189	−	3.32086i	−0.207419	−	0.119753i	−0.600111	+	0.799917i	$0.704877\pi$
$770$		0			0
$771$	−1.40792	+	13.7985i	−0.0507049	+	0.496942i
$772$	−12.8120	+	22.1910i	−0.461113	+	0.798672i
$773$	−22.2415	+	38.5235i	−0.799973	+	1.38559i	0.119660	+	0.992815i	$0.461819\pi$
$773$	−22.2415	+	38.5235i	−0.799973	+	1.38559i	−0.919633	+	0.392779i	$0.871514\pi$
$774$	−1.52468	+	7.39366i	−0.0548036	+	0.265760i
$775$	−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
$780$	−10.9049	−	1.11267i	−0.390457	−	0.0398399i
$781$	41.3039			1.47797
$782$	4.54510	+	7.87235i	0.162533	+	0.281515i
$783$	3.17988	+	14.3173i	0.113640	+	0.511660i
$784$		0			0
$785$	−10.9134	+	6.30087i	−0.389517	+	0.224888i
$786$	−11.0734	+	15.3390i	−0.394976	+	0.547126i
$787$	−19.0399	+	10.9927i	−0.678700	+	0.391848i	−0.799365	−	0.600846i	$-0.794831\pi$
$787$	−19.0399	+	10.9927i	−0.678700	+	0.391848i	0.120665	+	0.992693i	$0.461497\pi$
$788$	5.31385	−	3.06795i	0.189298	−	0.109291i
$789$	−27.0696	−	2.76202i	−0.963703	−	0.0983305i
$790$	6.12744	−	3.53768i	0.218004	−	0.125865i
$791$		0			0
$792$	22.9498	+	4.73259i	0.815485	+	0.168165i
$793$	1.27816	+	2.21384i	0.0453888	+	0.0786157i
$794$	12.3722			0.439075
$795$	17.6545	−	24.4552i	0.626141	−	0.867338i
$796$			24.1486i			0.855923i
$797$	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
$801$	−9.94972	−	30.0007i	−0.351556	−	1.06002i
$802$	3.55818	−	6.16295i	0.125644	−	0.217621i
$803$	0.722823	−	1.25197i	0.0255079	−	0.0441809i
$804$	−17.8173	−	12.8625i	−0.628367	−	0.453625i
$805$		0			0
$806$	10.7356	+	6.19820i	0.378145	+	0.218322i
$807$	−14.7349	−	10.6373i	−0.518693	−	0.374451i
$808$			10.7472i			0.378084i
$809$	−18.1916	−	10.5029i	−0.639582	−	0.369263i	0.144872	−	0.989450i	$-0.453723\pi$
$809$	−18.1916	−	10.5029i	−0.639582	−	0.369263i	−0.784453	+	0.620188i	$0.787056\pi$
$810$	7.62935	+	10.2370i	0.268068	+	0.359691i
$811$			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
$813$	15.7844	+	35.1644i	0.553581	+	1.23327i
$814$	−3.69963			−0.129672
$815$	11.2876	+	19.5506i	0.395386	+	0.684829i
$816$	−16.0309	+	7.19583i	−0.561193	+	0.251905i
$817$	−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	$-0.262837\pi$
$821$	10.9017	+	6.29412i	0.380473	+	0.219666i	−0.297551	+	0.954706i	$0.596170\pi$
$822$	5.64499	+	4.07519i	0.196892	+	0.142138i
$823$	22.4189	+	38.8307i	0.781474	+	1.35355i	0.931083	+	0.364808i	$0.118865\pi$
$823$	22.4189	+	38.8307i	0.781474	+	1.35355i	−0.149608	+	0.988745i	$0.547801\pi$
$824$	−14.3677			−0.500523
$825$	0.650451	+	0.0663681i	0.0226458	+	0.00231064i
$826$		0			0
$827$		−	25.7293i		−	0.894695i	−0.894360	−	0.447347i	$-0.852369\pi$
$827$		−	25.7293i		−	0.894695i	0.894360	−	0.447347i	$-0.147631\pi$
$828$	10.7356	−	3.56046i	0.373088	−	0.123735i
$829$	14.6902	+	8.48139i	0.510212	+	0.294571i	0.732921	−	0.680314i	$-0.238157\pi$
$829$	14.6902	+	8.48139i	0.510212	+	0.294571i	−0.222709	+	0.974885i	$0.571490\pi$
$830$			12.1584i			0.422025i
$831$	−4.01741	+	39.3733i	−0.139363	+	1.36585i
$832$	−0.397284	−	0.229372i	−0.0137733	−	0.00795204i
$833$		0			0
$834$	−7.79054	+	3.49697i	−0.269764	+	0.121090i
$835$	−3.99450	+	6.91867i	−0.138235	+	0.239431i
$836$	−4.43015	+	7.67324i	−0.153220	+	0.265385i
$837$	12.0796	+	54.3882i	0.417533	+	1.87993i
$838$	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
$842$			5.89324i			0.203095i
$843$	−0.651973	−	1.45247i	−0.0224552	−	0.0500256i
$844$	−37.9693			−1.30696
$845$	−10.7819	−	18.6747i	−0.370907	−	0.642430i
$846$	0.449440	−	0.149057i	0.0154521	−	0.00512467i
$847$		0			0
$848$	−11.5927	+	6.69305i	−0.398095	+	0.229840i
$849$	15.6902	+	34.9546i	0.538486	+	1.19964i
$850$	0.369016	−	0.213051i	0.0126571	−	0.00730760i
$851$	−3.49381	+	2.01715i	−0.119766	+	0.0691471i
$852$	−13.7157	−	30.5559i	−0.469893	−	1.04683i
$853$	−37.6287	+	21.7249i	−1.28838	+	0.743848i	−0.978366	−	0.206883i	$-0.933668\pi$
$853$	−37.6287	+	21.7249i	−1.28838	+	0.743848i	−0.310017	+	0.950731i	$0.600335\pi$
$854$		0			0
$855$	−10.3517	+	3.43313i	−0.354020	+	0.117411i
$856$	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	$0.586235\pi$
$858$	−2.78221	−	6.19820i	−0.0949830	−	0.211603i
$859$		−	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	$-0.428133\pi$
$863$	34.6600	−	20.0110i	1.17984	−	0.681181i	0.955978	+	0.293439i	$0.0947998\pi$
$864$	−6.41603	−	28.8880i	−0.218278	−	0.982790i
$865$	−19.9869	+	34.6184i	−0.679576	+	1.17706i
$866$	1.07010	−	1.85347i	0.0363635	−	0.0629834i
$867$	−29.4369	+	13.2134i	−0.999730	+	0.448752i
$868$		0			0
$869$	−14.6545	−	8.46079i	−0.497120	−	0.287013i
$870$	0.703959	−	6.89926i	0.0238664	−	0.233907i
$871$			14.3939i			0.487718i
$872$	−8.74660	−	5.04985i	−0.296197	−	0.171010i
$873$	−20.7179	+	6.87109i	−0.701194	+	0.232551i
$874$		−	2.50393i		−	0.0846967i
$875$		0			0
$876$	−1.16621	−	0.118993i	−0.0394025	−	0.00402039i
$877$	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
$879$	41.0795	+	29.6558i	1.38558	+	1.00027i
$880$	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
$885$	37.6698	−	16.9090i	1.26626	−	0.568389i
$886$	−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	$0.295267\pi$
$888$	2.77544	+	6.18313i	0.0931377	+	0.207492i
$889$		0			0
$890$			14.9460i			0.500991i
$891$	12.0796	−	28.0434i	0.404683	−	0.939491i
$892$	−26.3983	−	15.2411i	−0.883881	−	0.510309i
$893$			0.404487i			0.0135356i
$894$	−13.9096	−	10.0415i	−0.465206	−	0.335838i
$895$	−9.63528	−	5.56293i	−0.322072	−	0.185948i
$896$		0			0
$897$	−6.00688	−	4.33643i	−0.200564	−	0.144789i
$898$	−7.97346	+	13.8104i	−0.266078	+	0.460860i
$899$	15.1316	−	26.2087i	0.504667	−	0.874108i
$900$	−0.166896	−	0.503230i	−0.00556321	−	0.0167743i
$901$	−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
$906$	7.60198	−	10.5303i	0.252559	−	0.349847i
$907$	−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
$909$	13.7157	+	2.82839i	0.454922	+	0.0938117i
$910$		0			0
$911$	−35.5171	+	20.5058i	−1.17673	+	0.679388i	−0.955257	−	0.295777i	$-0.904421\pi$
$911$	−35.5171	+	20.5058i	−1.17673	+	0.679388i	−0.221478	+	0.975165i	$0.571088\pi$
$912$	4.81522	+	0.491316i	0.159448	+	0.0162691i
$913$	25.1826	−	14.5392i	0.833421	−	0.481176i
$914$	7.00619	−	4.04503i	0.231744	−	0.133798i
$915$	3.17988	−	4.40481i	0.105124	−	0.145618i
$916$	19.7652	−	11.4114i	0.653059	−	0.377044i
$917$		0			0
$918$	−4.31453	−	19.4261i	−0.142401	−	0.641156i
$919$	−5.11628	−	8.86166i	−0.168771	−	0.292319i	0.769217	−	0.638987i	$-0.220646\pi$
$919$	−5.11628	−	8.86166i	−0.168771	−	0.292319i	−0.937988	+	0.346668i	$0.887313\pi$
$920$	−12.0828			−0.398357
$921$	−25.5796	−	2.60999i	−0.842877	−	0.0860021i
$922$		−	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
$927$	−3.78122	+	18.3363i	−0.124192	+	0.602244i
$928$	−8.03706	+	13.9206i	−0.263830	+	0.456966i
$929$	12.8330	−	22.2273i	0.421036	−	0.729255i	−0.575005	−	0.818150i	$-0.695000\pi$
$929$	12.8330	−	22.2273i	0.421036	−	0.729255i	0.996041	+	0.0888945i	$0.0283334\pi$
$930$	2.67417	−	26.2087i	0.0876896	−	0.859416i
$931$		0			0
$932$	40.8763	+	23.5999i	1.33895	+	0.773041i
$933$	−30.6236	+	13.7461i	−1.00257	+	0.450027i
$934$			16.4215i			0.537328i
$935$	38.7774	+	22.3881i	1.26816	+	0.732170i
$936$	−8.27175	+	9.29971i	−0.270371	+	0.303971i
$937$			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
$939$	14.8214	−	20.5308i	0.483679	−	0.669997i
$940$	0.863976			0.0281798
$941$	−19.6767	−	34.0810i	−0.641442	−	1.11101i	−0.985111	−	0.171919i	$-0.945003\pi$
$941$	−19.6767	−	34.0810i	−0.641442	−	1.11101i	0.343669	−	0.939091i	$-0.388330\pi$
$942$	−0.642902	+	6.30087i	−0.0209469	+	0.205293i
$943$	−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	$-0.515804\pi$
$947$	−28.9086	−	16.6904i	−0.939403	−	0.542365i	−0.889773	+	0.456403i	$0.849138\pi$
$948$	−1.39284	+	13.6507i	−0.0452372	+	0.443354i
$949$	0.383923	+	0.664975i	0.0124627	+	0.0215860i
$950$	−0.117372			−0.00380804
$951$	17.2140	−	23.8450i	0.558202	−	0.773228i
$952$		0			0
$953$			44.4622i			1.44027i	0.693832	+	0.720137i	$0.255921\pi$
$953$			44.4622i			1.44027i	−0.693832	+	0.720137i	$0.744079\pi$
$954$	−4.77197	−	14.3886i	−0.154498	−	0.465847i
$955$	19.6108	+	11.3223i	0.634592	+	0.366382i
$956$			25.1456i			0.813266i
$957$	−15.1316	+	6.79217i	−0.489135	+	0.219560i
$958$	−0.297540	−	0.171785i	−0.00961307	−	0.00555011i
$959$		0			0
$960$	−0.0989611	+	0.969884i	−0.00319395	+	0.0313029i
$961$	41.9814	−	72.7138i	1.35424	−	2.34561i
$962$	0.982519	−	1.70177i	0.0316777	−	0.0548674i
$963$	4.24102	−	1.40653i	0.136665	−	0.0453249i
$964$	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	$0.943548\pi$
$968$			1.17535i			0.0377771i
$969$	16.9108	+	1.72548i	0.543254	+	0.0554303i
$970$	10.3214			0.331401
$971$	−23.0013	−	39.8394i	−0.738147	−	1.27851i	−0.953329	−	0.301934i	$-0.902368\pi$
$971$	−23.0013	−	39.8394i	−0.738147	−	1.27851i	0.215181	−	0.976574i	$-0.430966\pi$
$972$	−24.7573	+	0.376055i	−0.794090	+	0.0120620i
$973$		0			0
$974$	−18.9650	+	10.9494i	−0.607678	+	0.350843i
$975$	−0.203270	+	0.281572i	−0.00650985	+	0.00901752i
$976$	−2.08804	+	1.20553i	−0.0668366	+	0.0385882i
$977$	46.8323	−	27.0386i	1.49830	−	0.865042i	0.498299	−	0.867005i	$-0.333958\pi$
$977$	46.8323	−	27.0386i	1.49830	−	0.865042i	0.999998	+	0.00196335i	$0.000624955\pi$
$978$	11.2876	+	1.15172i	0.360937	+	0.0368278i
$979$	30.9562	−	17.8726i	0.989365	−	0.571210i
$980$		0			0
$981$	−8.74660	+	9.83357i	−0.279257	+	0.313962i
$982$	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	$0.571452\pi$
$984$	−2.12433	+	2.94265i	−0.0677212	+	0.0938082i
$985$			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
$990$	−9.59591	+	10.7884i	−0.304978	+	0.342879i
$991$	18.5149	−	32.0687i	0.588144	−	1.01869i	−0.406332	−	0.913726i	$-0.633192\pi$
$991$	18.5149	−	32.0687i	0.588144	−	1.01869i	0.994475	−	0.104969i	$-0.0334744\pi$
$992$	−30.5309	+	52.8811i	−0.969358	+	1.67898i
$993$	27.9409	+	20.1708i	0.886677	+	0.640102i
$994$		0			0
$995$	−29.1119	−	16.8077i	−0.922909	−	0.532841i
$996$	−19.1181	−	13.8016i	−0.605782	−	0.437321i
$997$			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
$999$	8.62145	−	1.91482i	0.272770	−	0.0605824i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.s.c.374.4		12
3.2	odd	2		1323.2.s.c.962.3		12
7.2	even	3		441.2.i.c.68.4		12
7.3	odd	6		63.2.o.a.41.4	yes	12
7.4	even	3		63.2.o.a.41.3	yes	12
7.5	odd	6		441.2.i.c.68.3		12
7.6	odd	2	inner	441.2.s.c.374.3		12
9.2	odd	6		441.2.i.c.227.3		12
9.7	even	3		1323.2.i.c.521.3		12
21.2	odd	6		1323.2.i.c.1097.4		12
21.5	even	6		1323.2.i.c.1097.3		12
21.11	odd	6		189.2.o.a.125.4		12
21.17	even	6		189.2.o.a.125.3		12
21.20	even	2		1323.2.s.c.962.4		12
28.3	even	6		1008.2.cc.a.545.1		12
28.11	odd	6		1008.2.cc.a.545.6		12
63.2	odd	6	inner	441.2.s.c.362.3		12
63.4	even	3		567.2.c.c.566.6		12
63.11	odd	6		63.2.o.a.20.4	yes	12
63.16	even	3		1323.2.s.c.656.4		12
63.20	even	6		441.2.i.c.227.4		12
63.25	even	3		189.2.o.a.62.3		12
63.31	odd	6		567.2.c.c.566.5		12
63.32	odd	6		567.2.c.c.566.7		12
63.34	odd	6		1323.2.i.c.521.4		12
63.38	even	6		63.2.o.a.20.3	✓	12
63.47	even	6	inner	441.2.s.c.362.4		12
63.52	odd	6		189.2.o.a.62.4		12
63.59	even	6		567.2.c.c.566.8		12
63.61	odd	6		1323.2.s.c.656.3		12
84.11	even	6		3024.2.cc.a.881.5		12
84.59	odd	6		3024.2.cc.a.881.2		12
252.11	even	6		1008.2.cc.a.209.1		12
252.115	even	6		3024.2.cc.a.2897.5		12
252.151	odd	6		3024.2.cc.a.2897.2		12
252.227	odd	6		1008.2.cc.a.209.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.o.a.20.3	✓	12	63.38	even	6
63.2.o.a.20.4	yes	12	63.11	odd	6
63.2.o.a.41.3	yes	12	7.4	even	3
63.2.o.a.41.4	yes	12	7.3	odd	6
189.2.o.a.62.3		12	63.25	even	3
189.2.o.a.62.4		12	63.52	odd	6
189.2.o.a.125.3		12	21.17	even	6
189.2.o.a.125.4		12	21.11	odd	6
441.2.i.c.68.3		12	7.5	odd	6
441.2.i.c.68.4		12	7.2	even	3
441.2.i.c.227.3		12	9.2	odd	6
441.2.i.c.227.4		12	63.20	even	6
441.2.s.c.362.3		12	63.2	odd	6	inner
441.2.s.c.362.4		12	63.47	even	6	inner
441.2.s.c.374.3		12	7.6	odd	2	inner
441.2.s.c.374.4		12	1.1	even	1	trivial
567.2.c.c.566.5		12	63.31	odd	6
567.2.c.c.566.6		12	63.4	even	3
567.2.c.c.566.7		12	63.32	odd	6
567.2.c.c.566.8		12	63.59	even	6
1008.2.cc.a.209.1		12	252.11	even	6
1008.2.cc.a.209.6		12	252.227	odd	6
1008.2.cc.a.545.1		12	28.3	even	6
1008.2.cc.a.545.6		12	28.11	odd	6
1323.2.i.c.521.3		12	9.7	even	3
1323.2.i.c.521.4		12	63.34	odd	6
1323.2.i.c.1097.3		12	21.5	even	6
1323.2.i.c.1097.4		12	21.2	odd	6
1323.2.s.c.656.3		12	63.61	odd	6
1323.2.s.c.656.4		12	63.16	even	3
1323.2.s.c.962.3		12	3.2	odd	2
1323.2.s.c.962.4		12	21.20	even	2
3024.2.cc.a.881.2		12	84.59	odd	6
3024.2.cc.a.881.5		12	84.11	even	6
3024.2.cc.a.2897.2		12	252.151	odd	6
3024.2.cc.a.2897.5		12	252.115	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.555632 + 0.320794i) q^{2} +(0.175815 - 1.72310i) q^{3} +(-0.794182 - 1.37556i) q^{4} +2.21105 q^{5} +(0.650451 - 0.901012i) q^{6} -2.30225i q^{8} +(-2.93818 - 0.605896i) q^{9} +(1.22853 + 0.709292i) q^{10} -3.39272i q^{11} +(-2.50987 + 1.12661i) q^{12} +(1.56060 + 0.901012i) q^{13} +(0.388736 - 3.80987i) q^{15} +(-0.849814 + 1.47192i) q^{16} +(-2.98450 + 5.16931i) q^{17} +(-1.43818 - 1.27921i) q^{18} +(1.42391 - 0.822093i) q^{19} +(-1.75597 - 3.04144i) q^{20} +(1.08836 - 1.88510i) q^{22} -2.37364i q^{23} +(-3.96702 - 0.404771i) q^{24} -0.111264 q^{25} +(0.578079 + 1.00126i) q^{26} +(-1.56060 + 4.95626i) q^{27} +(2.44437 - 1.41126i) q^{29} +(1.43818 - 1.99218i) q^{30} +(9.28558 - 5.36103i) q^{31} +(-4.93199 + 2.84748i) q^{32} +(-5.84600 - 0.596491i) q^{33} +(-3.31657 + 1.91482i) q^{34} +(1.50000 + 4.52284i) q^{36} +(-0.849814 - 1.47192i) q^{37} +1.05489 q^{38} +(1.82691 - 2.53066i) q^{39} -5.09039i q^{40} +(0.455074 - 0.788211i) q^{41} +(-1.96108 - 3.39669i) q^{43} +(-4.66690 + 2.69443i) q^{44} +(-6.49645 - 1.33966i) q^{45} +(0.761450 - 1.31887i) q^{46} +(-0.123005 + 0.213051i) q^{47} +(2.38686 + 1.72310i) q^{48} +(-0.0618219 - 0.0356929i) q^{50} +(8.38255 + 6.05146i) q^{51} -2.86227i q^{52} +(6.82072 + 3.93795i) q^{53} +(-2.45706 + 2.25323i) q^{54} -7.50146i q^{55} +(-1.16621 - 2.59808i) q^{57} +1.81089 q^{58} +(5.39093 + 9.33736i) q^{59} +(-5.54944 + 2.49100i) q^{60} +(1.22853 + 0.709292i) q^{61} +6.87916 q^{62} -0.254572 q^{64} +(3.45056 + 1.99218i) q^{65} +(-3.05688 - 2.20679i) q^{66} +(3.99381 + 6.91748i) q^{67} +9.48096 q^{68} +(-4.09003 - 0.417322i) q^{69} +12.1743i q^{71} +(-1.39493 + 6.76443i) q^{72} +(0.369016 + 0.213051i) q^{73} -1.09046i q^{74} +(-0.0195619 + 0.191720i) q^{75} +(-2.26168 - 1.30578i) q^{76} +(1.82691 - 0.820053i) q^{78} +(2.49381 - 4.31941i) q^{79} +(-1.87898 + 3.25449i) q^{80} +(8.26578 + 3.56046i) q^{81} +(0.505707 - 0.291970i) q^{82} +(4.28541 + 7.42254i) q^{83} +(-6.59888 + 11.4296i) q^{85} -2.51641i q^{86} +(-2.00199 - 4.46002i) q^{87} -7.81089 q^{88} +(5.26792 + 9.12431i) q^{89} +(-3.17988 - 2.82839i) q^{90} +(-3.26509 + 1.88510i) q^{92} +(-7.60507 - 16.9426i) q^{93} +(-0.136691 + 0.0789188i) q^{94} +(3.14833 - 1.81769i) q^{95} +(4.03940 + 8.99896i) q^{96} +(6.30108 - 3.63793i) q^{97} +(-2.05563 + 9.96840i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 2 q^{4} + 6 q^{15} + 2 q^{16} + 18 q^{18} - 10 q^{22} + 30 q^{29} - 18 q^{30} + 12 q^{32} + 18 q^{36} + 2 q^{37} - 12 q^{39} - 10 q^{43} - 54 q^{44} + 20 q^{46} - 36 q^{50} + 66 q^{51}+ \cdots - 24 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 + 2 * q^4 + 6 * q^15 + 2 * q^16 + 18 * q^18 - 10 * q^22 + 30 * q^29 - 18 * q^30 + 12 * q^32 + 18 * q^36 + 2 * q^37 - 12 * q^39 - 10 * q^43 - 54 * q^44 + 20 * q^46 - 36 * q^50 + 66 * q^51 + 12 * q^53 - 18 * q^57 - 4 * q^58 - 30 * q^60 + 16 * q^64 + 78 * q^65 + 12 * q^67 - 54 * q^72 - 12 * q^78 - 6 * q^79 + 24 * q^81 - 6 * q^85 - 68 * q^88 + 30 * q^92 - 54 * q^93 - 72 * q^95 - 24 * q^99

Introduction

L-functions

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