LMFDB - Embedded newform 441.2.i.c.68.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(68,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("441.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.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:	$3.52140272914$
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			68.4
Root			$-0.474636 + 0.274031i$ of defining polynomial
Character	$\chi$	$=$	441.68
Dual form			441.2.i.c.227.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.641589i q^{2} +(1.40434 + 1.01381i) q^{3} +1.58836 q^{4} +(-1.10552 - 1.91482i) q^{5} +(0.650451 - 0.901012i) q^{6} -2.30225i q^{8} +(0.944368 + 2.84748i) q^{9} +O(q^{10})$	\(q-0.641589i q^{2} +(1.40434 + 1.01381i) q^{3} +1.58836 q^{4} +(-1.10552 - 1.91482i) q^{5} +(0.650451 - 0.901012i) q^{6} -2.30225i q^{8} +(0.944368 + 2.84748i) q^{9} +(-1.22853 + 0.709292i) q^{10} +(2.93818 + 1.69636i) q^{11} +(2.23061 + 1.61030i) q^{12} +(1.56060 + 0.901012i) q^{13} +(0.388736 - 3.80987i) q^{15} +1.69963 q^{16} +(-2.98450 - 5.16931i) q^{17} +(1.82691 - 0.605896i) q^{18} +(-1.42391 - 0.822093i) q^{19} +(-1.75597 - 3.04144i) q^{20} +(1.08836 - 1.88510i) q^{22} +(-2.05563 + 1.18682i) q^{23} +(2.33405 - 3.23316i) q^{24} +(0.0556321 - 0.0963576i) q^{25} +(0.578079 - 1.00126i) q^{26} +(-1.56060 + 4.95626i) q^{27} +(2.44437 - 1.41126i) q^{29} +(-2.44437 - 0.249409i) q^{30} +10.7221i q^{31} -5.69497i q^{32} +(2.40643 + 5.36103i) q^{33} +(-3.31657 + 1.91482i) q^{34} +(1.50000 + 4.52284i) q^{36} +(-0.849814 + 1.47192i) q^{37} +(-0.527445 + 0.913562i) q^{38} +(1.27816 + 2.84748i) q^{39} +(-4.40841 + 2.54520i) q^{40} +(0.455074 - 0.788211i) q^{41} +(-1.96108 - 3.39669i) q^{43} +(4.66690 + 2.69443i) q^{44} +(4.40841 - 4.95626i) q^{45} +(0.761450 + 1.31887i) q^{46} +0.246010 q^{47} +(2.38686 + 1.72310i) q^{48} +(-0.0618219 - 0.0356929i) q^{50} +(1.04944 - 10.2852i) q^{51} +(2.47880 + 1.43113i) q^{52} +(-6.82072 + 3.93795i) q^{53} +(3.17988 + 1.00126i) q^{54} -7.50146i q^{55} +(-1.16621 - 2.59808i) q^{57} +(-0.905446 - 1.56828i) q^{58} -10.7819 q^{59} +(0.617454 - 6.05146i) q^{60} -1.41858i q^{61} +6.87916 q^{62} -0.254572 q^{64} -3.98436i q^{65} +(3.43958 - 1.54394i) q^{66} -7.98762 q^{67} +(-4.74048 - 8.21075i) q^{68} +(-4.09003 - 0.417322i) q^{69} +12.1743i q^{71} +(6.55563 - 2.17417i) q^{72} +(-0.369016 + 0.213051i) q^{73} +(0.944368 + 0.545231i) q^{74} +(0.175815 - 0.0789188i) q^{75} +(-2.26168 - 1.30578i) q^{76} +(1.82691 - 0.820053i) q^{78} -4.98762 q^{79} +(-1.87898 - 3.25449i) q^{80} +(-7.21634 + 5.37815i) q^{81} +(-0.505707 - 0.291970i) q^{82} +(4.28541 + 7.42254i) q^{83} +(-6.59888 + 11.4296i) q^{85} +(-2.17928 + 1.25821i) q^{86} +(4.86348 + 0.496241i) q^{87} +(3.90545 - 6.76443i) q^{88} +(5.26792 - 9.12431i) q^{89} +(-3.17988 - 2.82839i) q^{90} +(-3.26509 + 1.88510i) q^{92} +(-10.8702 + 15.0575i) q^{93} -0.157838i q^{94} +3.63537i q^{95} +(5.77363 - 7.99770i) q^{96} +(6.30108 - 3.63793i) q^{97} +(-2.05563 + 9.96840i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{4} + 12 q^{9}+O(q^{10}) $ 12 * q - 4 * q^4 + 12 * q^9	$ 12 q - 4 q^{4} + 12 q^{9} + 6 q^{15} - 4 q^{16} - 12 q^{18} - 10 q^{22} - 24 q^{23} + 30 q^{29} - 30 q^{30} + 18 q^{36} + 2 q^{37} + 12 q^{39} - 10 q^{43} + 54 q^{44} + 20 q^{46} - 36 q^{50} - 24 q^{51} - 12 q^{53} - 18 q^{57} + 2 q^{58} + 42 q^{60} + 16 q^{64} - 24 q^{67} + 78 q^{72} + 12 q^{74} - 12 q^{78} + 12 q^{79} - 48 q^{81} - 6 q^{85} - 96 q^{86} + 34 q^{88} + 30 q^{92} - 24 q^{93} - 24 q^{99}+O(q^{100}) $ 12 * q - 4 * q^4 + 12 * q^9 + 6 * q^15 - 4 * q^16 - 12 * q^18 - 10 * q^22 - 24 * q^23 + 30 * q^29 - 30 * q^30 + 18 * q^36 + 2 * q^37 + 12 * q^39 - 10 * q^43 + 54 * q^44 + 20 * q^46 - 36 * q^50 - 24 * q^51 - 12 * q^53 - 18 * q^57 + 2 * q^58 + 42 * q^60 + 16 * q^64 - 24 * q^67 + 78 * q^72 + 12 * q^74 - 12 * q^78 + 12 * q^79 - 48 * q^81 - 6 * q^85 - 96 * q^86 + 34 * q^88 + 30 * q^92 - 24 * q^93 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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	$-0.927162\pi$
$2$		−	0.641589i		−	0.453672i	0.973933	−	0.226836i	$-0.0728381\pi$
$3$	1.40434	+	1.01381i	0.810799	+	0.585325i
$3$	1.40434	+	1.01381i	0.810799	+	0.585325i
$4$	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	$0.997948\pi$
$6$	0.650451	−	0.901012i	0.265545	−	0.367836i
$7$		0			0
$7$		0			0
$8$		−	2.30225i		−	0.813970i
$9$	0.944368	+	2.84748i	0.314789	+	0.949162i
$10$	−1.22853	+	0.709292i	−0.388495	+	0.224298i
$11$	2.93818	+	1.69636i	0.885894	+	0.511471i	0.872597	−	0.488440i	$-0.162434\pi$
$11$	2.93818	+	1.69636i	0.885894	+	0.511471i	0.0132968	+	0.999912i	$0.495767\pi$
$12$	2.23061	+	1.61030i	0.643922	+	0.464855i
$13$	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
$16$	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	$-0.424295\pi$
$18$	1.82691	−	0.605896i	0.430608	−	0.142811i
$19$	−1.42391	−	0.822093i	−0.326667	−	0.188601i	0.327694	−	0.944784i	$-0.393729\pi$
$19$	−1.42391	−	0.822093i	−0.326667	−	0.188601i	−0.654360	+	0.756183i	$0.727062\pi$
$20$	−1.75597	−	3.04144i	−0.392648	−	0.680086i
$21$		0			0
$22$	1.08836	−	1.88510i	0.232040	−	0.401905i
$23$	−2.05563	+	1.18682i	−0.428629	+	0.247469i	−0.698762	−	0.715354i	$-0.746266\pi$
$23$	−2.05563	+	1.18682i	−0.428629	+	0.247469i	0.270133	+	0.962823i	$0.412932\pi$
$24$	2.33405	−	3.23316i	0.476437	−	0.659966i
$25$	0.0556321	−	0.0963576i	0.0111264	−	0.0192715i
$26$	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	$0.248930\pi$
$30$	−2.44437	−	0.249409i	−0.446278	−	0.0455356i
$31$			10.7221i			1.92574i	0.269966	+	0.962870i	$0.412988\pi$
$31$			10.7221i			1.92574i	−0.269966	+	0.962870i	$0.587012\pi$
$32$		−	5.69497i		−	1.00674i
$33$	2.40643	+	5.36103i	0.418905	+	0.933236i
$34$	−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	−0.927386	−	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
$39$	1.27816	+	2.84748i	0.204669	+	0.455962i
$40$	−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
$45$	4.40841	−	4.95626i	0.657167	−	0.738836i
$46$	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	$0.494289\pi$
$48$	2.38686	+	1.72310i	0.344514	+	0.248709i
$49$		0			0
$50$	−0.0618219	−	0.0356929i	−0.00874294	−	0.00504774i
$51$	1.04944	−	10.2852i	0.146951	−	1.44022i
$52$	2.47880	+	1.43113i	0.343747	+	0.198463i
$53$	−6.82072	+	3.93795i	−0.936899	+	0.540919i	−0.888987	−	0.457933i	$-0.848590\pi$
$53$	−6.82072	+	3.93795i	−0.936899	+	0.540919i	−0.0479118	+	0.998852i	$0.515257\pi$
$54$	3.17988	+	1.00126i	0.432727	+	0.136254i
$55$		−	7.50146i		−	1.01150i
$56$		0			0
$57$	−1.16621	−	2.59808i	−0.154468	−	0.344124i
$58$	−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	$0.747638\pi$
$60$	0.617454	−	6.05146i	0.0797130	−	0.781240i
$61$		−	1.41858i		−	0.181631i	−0.995868	−	0.0908155i	$-0.971053\pi$
$61$		−	1.41858i		−	0.181631i	0.995868	−	0.0908155i	$-0.0289474\pi$
$62$	6.87916			0.873654
$63$		0			0
$64$	−0.254572			−0.0318214
$65$		−	3.98436i		−	0.494199i
$66$	3.43958	−	1.54394i	0.423383	−	0.190045i
$67$	−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
$69$	−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	$0.743034\pi$
$72$	6.55563	−	2.17417i	0.772589	−	0.256229i
$73$	−0.369016	+	0.213051i	−0.0431900	+	0.0249358i	−0.521440	−	0.853288i	$-0.674605\pi$
$73$	−0.369016	+	0.213051i	−0.0431900	+	0.0249358i	0.478250	+	0.878224i	$0.341271\pi$
$74$	0.944368	+	0.545231i	0.109781	+	0.0633818i
$75$	0.175815	−	0.0789188i	0.0203014	−	0.00911275i
$76$	−2.26168	−	1.30578i	−0.259433	−	0.149784i
$77$		0			0
$78$	1.82691	−	0.820053i	0.206857	−	0.0928527i
$79$	−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
$81$	−7.21634	+	5.37815i	−0.801815	+	0.597572i
$82$	−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
$87$	4.86348	+	0.496241i	0.521420	+	0.0532026i
$88$	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	$-0.0219175\pi$
$90$	−3.17988	−	2.82839i	−0.335189	−	0.298138i
$91$		0			0
$92$	−3.26509	+	1.88510i	−0.340409	+	0.196535i
$93$	−10.8702	+	15.0575i	−1.12718	+	1.56139i
$94$		−	0.157838i		−	0.0162797i
$95$			3.63537i			0.372982i
$96$	5.77363	−	7.99770i	0.589269	−	0.816262i
$97$	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
$101$	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	$0.0920589\pi$
$102$	−6.59888	−	0.673310i	−0.653387	−	0.0666676i
$103$	−5.40462	+	3.12036i	−0.532533	+	0.307458i	−0.742047	−	0.670348i	$-0.766145\pi$
$103$	−5.40462	+	3.12036i	−0.532533	+	0.307458i	0.209515	+	0.977806i	$0.432812\pi$
$104$	2.07436	−	3.59289i	0.203407	−	0.352312i
$105$		0			0
$106$	2.52654	+	4.37610i	0.245399	+	0.425044i
$107$	1.28985	+	0.744696i	0.124695	+	0.0719925i	0.561050	−	0.827782i	$-0.310398\pi$
$107$	1.28985	+	0.744696i	0.124695	+	0.0719925i	−0.436355	+	0.899774i	$0.643731\pi$
$108$	−2.47880	+	7.87235i	−0.238522	+	0.757517i
$109$	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
$111$	−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	$0.966102\pi$
$114$	−1.66690	+	0.748226i	−0.156119	+	0.0700777i
$115$	4.54510	+	2.62412i	0.423833	+	0.244700i
$116$	3.88255	−	2.24159i	0.360485	−	0.208126i
$117$	−1.09184	+	5.29467i	−0.100940	+	0.489492i
$118$			6.91752i			0.636809i
$119$		0			0
$120$	−8.77128	−	0.894969i	−0.800705	−	0.0816991i
$121$	0.255260	+	0.442124i	0.0232055	+	0.0401931i
$122$	−0.910147			−0.0824009
$123$	1.43818	−	0.645560i	0.129676	−	0.0582082i
$124$			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
$129$	0.689575	−	6.75829i	0.0607137	−	0.595034i
$130$	−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	$0.566399\pi$
$132$	3.82228	+	8.51527i	0.332687	+	0.741159i
$133$		0			0
$134$			5.12477i			0.442712i
$135$	11.2156	−	2.49100i	0.965289	−	0.214391i
$136$	−11.9011	+	6.87109i	−1.02051	+	0.589191i
$137$	−5.42580	−	3.13259i	−0.463557	−	0.267635i	0.249982	−	0.968251i	$-0.419575\pi$
$137$	−5.42580	−	3.13259i	−0.463557	−	0.267635i	−0.713539	+	0.700616i	$0.752909\pi$
$138$	−0.267749	+	2.62412i	−0.0227923	+	0.223380i
$139$	−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
$142$	7.81089			0.655476
$143$	3.05688	+	5.29467i	0.255629	+	0.442762i
$144$	1.60507	+	4.83967i	0.133756	+	0.403305i
$145$	−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	−0.934975	−	0.354714i	$-0.884578\pi$
$149$	−13.3695	+	7.71887i	−1.09527	+	0.632355i	−0.160296	+	0.987069i	$0.551245\pi$
$150$	−0.0506334	−	0.112801i	−0.00413420	−	0.00921016i
$151$	−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
$153$	11.9011	−	13.3801i	0.962145	−	1.08171i
$154$		0			0
$155$	20.5309	−	11.8535i	1.64908	−	0.952096i
$156$	2.03018	+	4.52284i	0.162545	+	0.362117i
$157$		−	5.69944i		−	0.454865i	−0.973794	−	0.227432i	$-0.926967\pi$
$157$		−	5.69944i		−	0.454865i	0.973794	−	0.227432i	$-0.0730330\pi$
$158$			3.20000i			0.254578i
$159$	−13.5710	−	1.38470i	−1.07625	−	0.109814i
$160$	−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	−0.593848	−	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
$165$	7.60507	−	10.5346i	0.592054	−	0.820120i
$166$	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
$171$	0.996205	−	4.83091i	0.0761817	−	0.369429i
$172$	−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	$0.258811\pi$
$174$	0.318382	−	3.12036i	0.0241365	−	0.236554i
$175$		0			0
$176$	4.99381	+	2.88318i	0.376423	+	0.217328i
$177$	−15.1414	−	10.9308i	−1.13810	−	0.821608i
$178$	−5.85406	−	3.37984i	−0.438780	−	0.253330i
$179$	4.35779	−	2.51597i	0.325716	−	0.188052i	−0.328221	−	0.944601i	$-0.606449\pi$
$179$	4.35779	−	2.51597i	0.325716	−	0.188052i	0.653938	+	0.756548i	$0.273116\pi$
$180$	7.00216	−	7.87235i	0.521910	−	0.586770i
$181$			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
$184$	2.73236	+	4.73259i	0.201432	+	0.348891i
$185$	3.75796			0.276291
$186$	9.66071	+	6.97418i	0.708357	+	0.511371i
$187$		−	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	$-0.879177\pi$
$191$		−	10.2416i		−	0.741055i	0.928821	−	0.370528i	$-0.120823\pi$
$192$	−0.357506	−	0.258088i	−0.0258008	−	0.0186259i
$193$	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
$195$	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	$0.956056\pi$
$198$	6.39561	+	1.31887i	0.454517	+	0.0937280i
$199$	13.1665	−	7.60171i	0.933352	−	0.538871i	0.0454817	−	0.998965i	$-0.485518\pi$
$199$	13.1665	−	7.60171i	0.933352	−	0.538871i	0.887870	+	0.460094i	$0.152184\pi$
$200$	−0.221840	−	0.128079i	−0.0156864	−	0.00905656i
$201$	−11.2174	−	8.09795i	−0.791212	−	0.571185i
$202$	−2.59375	−	1.49750i	−0.182496	−	0.105364i
$203$		0			0
$204$	1.66690	−	16.3367i	0.116706	−	1.14380i
$205$	−2.01238			−0.140551
$206$	2.00199	+	3.46754i	0.139485	+	0.241595i
$207$	−5.32072	−	4.73259i	−0.369816	−	0.328937i
$208$	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
$213$	−12.3425	+	17.0969i	−0.845691	+	1.17146i
$214$	0.477789	−	0.827554i	0.0326610	−	0.0565704i
$215$	−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
$219$	−0.734219	−	0.0749153i	−0.0496139	−	0.00506231i
$220$		−	11.9150i		−	0.803312i
$221$		−	10.7563i		−	0.723547i
$222$	0.773456	+	1.72310i	0.0519110	+	0.115647i
$223$	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
$227$	−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	$0.259588\pi$
$228$	−1.85236	−	4.12669i	−0.122676	−	0.273297i
$229$	12.4437	−	7.18439i	0.822304	−	0.474758i	−0.0289060	−	0.999582i	$-0.509202\pi$
$229$	12.4437	−	7.18439i	0.822304	−	0.474758i	0.851211	+	0.524824i	$0.175869\pi$
$230$	1.68360	−	2.91609i	0.111014	−	0.192281i
$231$		0			0
$232$	−3.24907	−	5.62755i	−0.213312	−	0.369467i
$233$	25.7348	+	14.8580i	1.68594	+	0.973381i	0.957570	+	0.288202i	$0.0930576\pi$
$233$	25.7348	+	14.8580i	1.68594	+	0.973381i	0.728375	+	0.685178i	$0.240276\pi$
$234$	3.39700	+	0.700511i	0.222069	+	0.0457938i
$235$	−0.271971	−	0.471067i	−0.0177414	−	0.0307290i
$236$	−17.1255			−1.11478
$237$	−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	$0.837767\pi$
$240$	0.660706	−	6.47536i	0.0426484	−	0.417983i
$241$	−4.34973	−	2.51132i	−0.280190	−	0.161768i	0.353319	−	0.935503i	$-0.385053\pi$
$241$	−4.34973	−	2.51132i	−0.280190	−	0.161768i	−0.633510	+	0.773735i	$0.718386\pi$
$242$	0.283662	−	0.163772i	0.0182345	−	0.0105277i
$243$	−15.5867	+	0.236756i	−0.999885	+	0.0151879i
$244$		−	2.25323i		−	0.144248i
$245$		0			0
$246$	−0.414184	−	0.922719i	−0.0264074	−	0.0588304i
$247$	−1.48143	−	2.56591i	−0.0942612	−	0.163265i
$248$	24.6849			1.56749
$249$	−1.50688	+	14.7684i	−0.0954945	+	0.935910i
$250$			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
$255$	−20.8546	+	9.36107i	−1.30596	+	0.586213i
$256$	−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	$0.752981\pi$
$258$	−4.33604	−	0.442423i	−0.269950	−	0.0275441i
$259$		0			0
$260$		−	6.32862i		−	0.392484i
$261$	6.32691	+	5.62755i	0.391626	+	0.348337i
$262$	9.45922	−	5.46128i	0.584393	−	0.337399i
$263$	13.6051	+	7.85489i	0.838925	+	0.484353i	0.856899	−	0.515485i	$-0.172388\pi$
$263$	13.6051	+	7.85489i	0.838925	+	0.484353i	−0.0179738	+	0.999838i	$0.505722\pi$
$264$	12.3425	−	5.54020i	0.759626	−	0.340976i
$265$	15.0810	+	8.70699i	0.926416	+	0.534866i
$266$		0			0
$267$	16.6483	−	7.47299i	1.01886	−	0.457340i
$268$	−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	$0.729696\pi$
$270$	−1.59820	−	7.19583i	−0.0972631	−	0.437924i
$271$	19.2722	+	11.1268i	1.17071	+	0.675907i	0.953846	−	0.300296i	$-0.0970853\pi$
$271$	19.2722	+	11.1268i	1.17071	+	0.675907i	0.216859	+	0.976203i	$0.430419\pi$
$272$	−5.07255	−	8.78591i	−0.307568	−	0.532724i
$273$		0			0
$274$	−2.00983	+	3.48113i	−0.121418	+	0.210303i
$275$	0.326914	−	0.188744i	0.0197137	−	0.0113817i
$276$	−6.49645	−	0.662859i	−0.391041	−	0.0398994i
$277$	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
$279$	−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	$0.324605\pi$
$282$	0.160018	−	0.221658i	0.00952891	−	0.0131996i
$283$		−	22.1209i		−	1.31495i	−0.753475	−	0.657477i	$-0.771624\pi$
$283$		−	22.1209i		−	1.31495i	0.753475	−	0.657477i	$-0.228376\pi$
$284$			19.3372i			1.14745i
$285$	−3.68559	+	5.10532i	−0.218315	+	0.302413i
$286$	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
$290$	−2.00199	+	3.46754i	−0.117561	+	0.203621i
$291$	12.5371	+	1.27921i	0.734936	+	0.0749884i
$292$	−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
$297$	−12.9929	+	11.9150i	−0.753925	+	0.691381i
$298$	4.95234	+	8.57771i	0.286881	+	0.496893i
$299$	−4.27735			−0.247366
$300$	0.279258	−	0.125352i	0.0161230	−	0.00723718i
$301$		0			0
$302$	6.49381	+	3.74920i	0.373677	+	0.215742i
$303$	7.37636	−	3.31105i	0.423761	−	0.190215i
$304$	−2.42011	−	1.39725i	−0.138803	−	0.0801379i
$305$	−2.71634	+	1.56828i	−0.155537	+	0.0897994i
$306$	−8.58450	−	7.63559i	−0.490743	−	0.436498i
$307$		−	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
$310$	−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	$0.314829\pi$
$312$	6.55563	−	2.94265i	0.371140	−	0.166595i
$313$		−	14.6195i		−	0.826342i	−0.910653	−	0.413171i	$-0.864421\pi$
$313$		−	14.6195i		−	0.826342i	0.910653	−	0.413171i	$-0.135579\pi$
$314$	−3.65669			−0.206359
$315$		0			0
$316$	−7.92216			−0.445656
$317$		−	16.9795i		−	0.953662i	−0.878995	−	0.476831i	$-0.841785\pi$
$317$		−	16.9795i		−	0.953662i	0.878995	−	0.476831i	$-0.158215\pi$
$318$	−0.888409	+	8.70699i	−0.0498195	+	0.488264i
$319$	9.57598			0.536152
$320$	0.281435	+	0.487460i	0.0157327	+	0.0272498i
$321$	1.05641	+	2.35348i	0.0589633	+	0.131358i
$322$		0			0
$323$			9.81416i			0.546074i
$324$	−11.4622	+	8.54245i	−0.636787	+	0.474581i
$325$	0.173639	−	0.100250i	0.00963174	−	0.00556089i
$326$	−5.67309	−	3.27536i	−0.314203	−	0.181405i
$327$	−0.771279	+	7.55905i	−0.0426518	+	0.418016i
$328$	−1.81466	−	1.04769i	−0.100198	−	0.0578493i
$329$		0			0
$330$	−6.75890	−	4.87933i	−0.372065	−	0.268598i
$331$	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
$333$	−4.99381	−	1.02980i	−0.273659	−	0.0564326i
$334$	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
$339$	−12.1840	−	27.1436i	−0.661746	−	1.47424i
$340$	−10.4814	+	18.1544i	−0.568435	+	0.984559i
$341$	−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
$345$	3.72253	+	8.29305i	0.200414	+	0.446483i
$346$		−	11.5994i		−	0.623586i
$347$		−	21.2120i		−	1.13872i	−0.822088	−	0.569361i	$-0.807191\pi$
$347$		−	21.2120i		−	1.13872i	0.822088	−	0.569361i	$-0.192809\pi$
$348$	7.72498	+	0.788211i	0.414103	+	0.0422525i
$349$	−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
$353$	−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	$0.189953\pi$
$354$	−7.01307	+	9.71458i	−0.372740	+	0.516324i
$355$	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	0.253706	−	0.967281i	$-0.418350\pi$
$359$	−8.66140	−	5.00066i	−0.457131	−	0.263925i	−0.710837	+	0.703357i	$0.751684\pi$
$360$	−11.4106	−	10.1493i	−0.601390	−	0.534914i
$361$	−8.14833	−	14.1133i	−0.428859	−	0.742806i
$362$	8.69945			0.457233
$363$	−0.0897572	+	0.879680i	−0.00471103	+	0.0461712i
$364$		0			0
$365$	0.815912	+	0.471067i	0.0427068	+	0.0246568i
$366$	−1.27816	−	0.922719i	−0.0668105	−	0.0482313i
$367$	−5.03560	−	2.90731i	−0.262856	−	0.151760i	0.362781	−	0.931875i	$-0.381827\pi$
$367$	−5.03560	−	2.90731i	−0.262856	−	0.151760i	−0.625637	+	0.780114i	$0.715161\pi$
$368$	−3.49381	+	2.01715i	−0.182127	+	0.105151i
$369$	2.67417	+	0.551454i	0.139212	+	0.0287076i
$370$		−	2.41106i		−	0.125345i
$371$		0			0
$372$	−17.2658	+	23.9168i	−0.895189	+	1.24003i
$373$	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
$375$	−15.8709	−	11.4574i	−0.819567	−	0.591655i
$376$		−	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
$381$	8.87744	+	6.40873i	0.454805	+	0.328329i
$382$	−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	$0.804958\pi$
$384$	11.3817	−	15.7660i	0.580819	−	0.804557i
$385$		0			0
$386$		−	10.3503i		−	0.526817i
$387$	7.82004	−	8.79186i	0.397515	−	0.446915i
$388$	10.0084	−	5.77835i	0.508100	−	0.293352i
$389$	6.37017	+	3.67782i	0.322980	+	0.186473i	0.652720	−	0.757599i	$-0.273628\pi$
$389$	6.37017	+	3.67782i	0.322980	+	0.186473i	−0.329740	+	0.944072i	$0.606961\pi$
$390$	−3.58996	−	2.59163i	−0.181784	−	0.131232i
$391$	12.2701	+	7.08414i	0.620525	+	0.358260i
$392$		0			0
$393$	−2.99312	+	29.3346i	−0.150983	+	1.47973i
$394$	2.47848			0.124864
$395$	5.51394	+	9.55042i	0.277436	+	0.480534i
$396$	−3.26509	+	15.8335i	−0.164077	+	0.795661i
$397$	−16.7002	−	9.64189i	−0.838161	−	0.483912i	0.0184778	−	0.999829i	$-0.494118\pi$
$397$	−16.7002	−	9.64189i	−0.838161	−	0.483912i	−0.856639	+	0.515917i	$0.827451\pi$
$398$	−4.87717	−	8.44751i	−0.244470	−	0.423435i
$399$		0			0
$400$	0.0945538	−	0.163772i	0.00472769	−	0.00818860i
$401$	−9.60576	+	5.54589i	−0.479689	+	0.276949i	−0.720287	−	0.693676i	$-0.755990\pi$
$401$	−9.60576	+	5.54589i	−0.479689	+	0.276949i	0.240598	+	0.970625i	$0.422656\pi$
$402$	−5.19555	+	7.19694i	−0.259131	+	0.358951i
$403$	−9.66071	+	16.7328i	−0.481234	+	0.833522i
$404$	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
$408$	−23.6792	−	2.41608i	−1.17230	−	0.119614i
$409$			20.2763i			1.00260i	0.865275	+	0.501298i	$0.167144\pi$
$409$			20.2763i			1.00260i	−0.865275	+	0.501298i	$0.832856\pi$
$410$			1.29112i			0.0637639i
$411$	−4.44384	−	9.89997i	−0.219198	−	0.488330i
$412$	−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
$416$	5.13123	−	8.88756i	0.251579	−	0.435748i
$417$	−5.45048	−	12.1426i	−0.266911	−	0.594625i
$418$	−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
$423$	0.232324	+	0.700511i	0.0112960	+	0.0340600i
$424$	9.06615	+	15.7030i	0.440291	+	0.762607i
$425$	−0.664137			−0.0322154
$426$	10.9692	+	7.91878i	0.531459	+	0.383666i
$427$		0			0
$428$	2.04875	+	1.18285i	0.0990302	+	0.0571751i
$429$	−1.07489	+	10.5346i	−0.0518962	+	0.508617i
$430$	4.81849	+	2.78195i	0.232368	+	0.134158i
$431$	−13.0858	+	7.55510i	−0.630322	+	0.363916i	−0.780877	−	0.624685i	$-0.785227\pi$
$431$	−13.0858	+	7.55510i	−0.630322	+	0.363916i	0.150555	+	0.988602i	$0.451894\pi$
$432$	−2.65244	+	8.42380i	−0.127615	+	0.405290i
$433$		−	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
$436$	3.48398	+	6.03443i	0.166852	+	0.288997i
$437$	3.90270			0.186692
$438$	−0.0480648	+	0.471067i	−0.00229663	+	0.0225084i
$439$		−	6.82465i		−	0.325723i	−0.986649	−	0.162861i	$-0.947928\pi$
$439$		−	6.82465i		−	0.325723i	0.986649	−	0.162861i	$-0.0520724\pi$
$440$	−17.2703			−0.823327
$441$		0			0
$442$	−6.90112			−0.328253
$443$			11.2901i			0.536407i	0.963362	+	0.268203i	$0.0864299\pi$
$443$			11.2901i			0.536407i	−0.963362	+	0.268203i	$0.913570\pi$
$444$	−4.26584	+	1.91482i	−0.202448	+	0.0908735i
$445$	−23.2953			−1.10430
$446$	−6.15633	−	10.6631i	−0.291511	−	0.504912i
$447$	−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	$0.800506\pi$
$450$	0.0432524	−	0.209744i	0.00203894	−	0.00988744i
$451$	2.67417	−	1.54394i	0.125922	−	0.0727011i
$452$	−23.6291	−	13.6422i	−1.11142	−	0.641677i
$453$	−18.4677	+	8.28967i	−0.867689	+	0.389483i
$454$	4.81849	+	2.78195i	0.226143	+	0.130564i
$455$		0			0
$456$	−5.98143	+	2.68491i	−0.280106	+	0.125732i
$457$	−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
$459$	30.2781	−	6.72477i	1.41326	−	0.313885i
$460$	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
$465$	40.8497	+	4.16805i	1.89436	+	0.193289i
$466$	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	$-0.0350735\pi$
$468$	−1.73424	+	8.40986i	−0.0801651	+	0.388746i
$469$		0			0
$470$	−0.302231	+	0.174493i	−0.0139409	+	0.00804877i
$471$	5.77816	−	8.00397i	0.266244	−	0.368804i
$472$			24.8226i			1.14255i
$473$		−	13.3068i		−	0.611846i
$474$	−3.24420	+	4.49390i	−0.149011	+	0.206412i
$475$	−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
$479$	0.267749	−	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	$0.162772\pi$
$480$	−21.6971	−	2.21384i	−0.990332	−	0.101047i
$481$	−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
$486$	0.151900	+	10.0002i	0.00689033	+	0.453619i
$487$	−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
$489$	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	$0.617795\pi$
$492$	2.28435	−	1.02538i	0.102986	−	0.0462279i
$493$	−14.5905	−	8.42380i	−0.657121	−	0.379389i
$494$	−1.64626	+	0.950469i	−0.0740688	+	0.0427636i
$495$	21.3603	−	7.08414i	0.960074	−	0.318408i
$496$			18.2235i			0.818260i
$497$		0			0
$498$	9.47524	+	0.966796i	0.424596	+	0.0433232i
$499$	−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
$501$	−5.70946	+	2.56283i	−0.255080	+	0.114499i
$502$		−	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
$507$	1.71467	−	16.8049i	0.0761514	−	0.746334i
$508$	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	$0.790186\pi$
$510$	6.00596	+	13.3801i	0.265948	+	0.592479i
$511$		0			0
$512$		−	17.5053i		−	0.773631i
$513$	6.29665	−	5.77430i	0.278004	−	0.254941i
$514$	4.44947	−	2.56890i	0.196258	−	0.113309i
$515$	11.9499	+	6.89926i	0.526574	+	0.304018i
$516$	1.09530	−	10.7346i	0.0482177	−	0.472565i
$517$	0.722823	+	0.417322i	0.0317897	+	0.0183538i
$518$		0			0
$519$	25.3893	+	18.3289i	1.11447	+	0.804548i
$520$	−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	$-0.420764\pi$
$522$	3.61058	−	4.05928i	0.158031	−	0.177670i
$523$	−1.73424	−	1.00126i	−0.0758329	−	0.0437821i	0.461604	−	0.887086i	$-0.347274\pi$
$523$	−1.73424	−	1.00126i	−0.0758329	−	0.0437821i	−0.537437	+	0.843304i	$0.680607\pi$
$524$	13.5204	+	23.4179i	0.590639	+	1.02302i
$525$		0			0
$526$	5.03961	−	8.72886i	0.219737	−	0.380596i
$527$	55.4257	−	32.0001i	2.41438	−	1.39394i
$528$	4.09003	+	9.11176i	0.177996	+	0.396539i
$529$	−8.68292	+	15.0393i	−0.377518	+	0.653881i
$530$	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
$534$	−4.79459	−	10.6814i	−0.207482	−	0.462228i
$535$		−	3.29312i		−	0.142374i
$536$			18.3895i			0.794307i
$537$	8.67056	+	0.884691i	0.374162	+	0.0381772i
$538$	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	−0.716390	−	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
$543$	−13.7465	+	19.0418i	−0.589920	+	0.817163i
$544$	−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
$549$	4.03940	−	1.33966i	0.172397	−	0.0571755i
$550$	−0.121096	−	0.209744i	−0.00516355	−	0.00894353i
$551$	−4.64074			−0.197702
$552$	−0.960781	+	9.41628i	−0.0408935	+	0.400784i
$553$		0			0
$554$	−12.6963	−	7.33022i	−0.539415	−	0.311431i
$555$	5.27747	+	3.80987i	0.224016	+	0.161720i
$556$	−10.5704	−	6.10281i	−0.448284	−	0.258817i
$557$	0.0116910	−	0.00674980i	0.000495364	−	0.000285998i	−0.499752	−	0.866168i	$-0.666576\pi$
$557$	0.0116910	−	0.00674980i	0.000495364	−	0.000285998i	0.500248	+	0.865882i	$0.333242\pi$
$558$	6.49645	+	19.5883i	0.275017	+	0.829239i
$559$		−	7.06782i		−	0.298937i
$560$		0			0
$561$	20.5309	−	28.4396i	0.866814	−	1.20072i
$562$	−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	$0.631784\pi$
$564$	0.548754	+	0.396151i	0.0231067	+	0.0166810i
$565$			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	$0.286191\pi$
$569$			37.3437i			1.56553i	−0.622318	+	0.782765i	$0.713809\pi$
$570$	3.27551	+	2.36463i	0.137196	+	0.0990435i
$571$	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
$573$	10.3831	−	14.3827i	0.433758	−	0.600847i
$574$		0			0
$575$			0.264101i			0.0110138i
$576$	−0.240409	−	0.724889i	−0.0100170	−	0.0302037i
$577$	−32.1285	+	18.5494i	−1.33753	+	0.772221i	−0.986440	−	0.164123i	$-0.947521\pi$
$577$	−32.1285	+	18.5494i	−1.33753	+	0.772221i	−0.351086	+	0.936343i	$0.614187\pi$
$578$	10.3509	+	5.97610i	0.430541	+	0.248573i
$579$	22.6553	+	16.3551i	0.941523	+	0.679696i
$580$	−8.58450	−	4.95626i	−0.356452	−	0.205798i
$581$		0			0
$582$	0.820724	−	8.04364i	0.0340201	−	0.333419i
$583$	−26.7207			−1.10666
$584$	0.490498	+	0.849568i	0.0202970	+	0.0351554i
$585$	11.3454	−	3.76270i	0.469075	−	0.155569i
$586$	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
$591$	−3.91639	+	5.42503i	−0.161099	+	0.223156i
$592$	−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	$0.0341157\pi$
$594$	7.64456	+	8.33610i	0.313660	+	0.342034i
$595$		0			0
$596$	−21.2356	+	12.2604i	−0.869844	+	0.502205i
$597$	26.1971	+	2.67299i	1.07218	+	0.109398i
$598$			2.74430i			0.112223i
$599$			11.2472i			0.459547i	0.973244	+	0.229773i	$0.0737985\pi$
$599$			11.2472i			0.459547i	−0.973244	+	0.229773i	$0.926201\pi$
$600$	−0.181691	−	0.404771i	−0.00741750	−	0.0165247i
$601$	−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
$605$	0.564393	−	0.977557i	0.0229458	−	0.0397433i
$606$	−2.12433	−	4.73259i	−0.0862951	−	0.192248i
$607$	−33.7888	+	19.5080i	−1.37145	+	0.791804i	−0.991110	−	0.133044i	$-0.957525\pi$
$607$	−33.7888	+	19.5080i	−1.37145	+	0.791804i	−0.380335	+	0.924849i	$0.624191\pi$
$608$	−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
$612$	18.9032	−	21.2524i	0.764118	−	0.859078i
$613$	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
$615$	−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	$0.614378\pi$
$618$	−0.703959	+	6.89926i	−0.0283174	+	0.277529i
$619$	32.4018	+	18.7072i	1.30234	+	0.751906i	0.980805	−	0.194991i	$-0.0624678\pi$
$619$	32.4018	+	18.7072i	1.30234	+	0.751906i	0.321535	+	0.946898i	$0.395801\pi$
$620$	32.6105	−	18.8277i	1.30967	−	0.756138i
$621$	−2.67417	−	12.0404i	−0.107311	−	0.483165i
$622$		−	12.4340i		−	0.498559i
$623$		0			0
$624$	2.17240	+	4.83967i	0.0869655	+	0.193742i
$625$	12.2156	+	21.1581i	0.488626	+	0.846325i
$626$	−9.37969			−0.374888
$627$	0.980742	−	9.61192i	0.0391671	−	0.383863i
$628$		−	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
$633$	37.7732	−	16.9554i	1.50135	−	0.673916i
$634$	−10.8938			−0.432649
$635$	−6.98848	−	12.1044i	−0.277329	−	0.480348i
$636$	−21.5557	−	2.19941i	−0.854738	−	0.0872123i
$637$		0			0
$638$		−	6.14384i		−	0.243237i
$639$	−34.6661	+	11.4970i	−1.37137	+	0.454815i
$640$	−21.4970	+	12.4113i	−0.849743	+	0.490599i
$641$	8.01849	+	4.62948i	0.316711	+	0.182853i	0.649926	−	0.759998i	$-0.274800\pi$
$641$	8.01849	+	4.62948i	0.316711	+	0.182853i	−0.333214	+	0.942851i	$0.608133\pi$
$642$	1.50996	−	0.677783i	0.0595935	−	0.0267500i
$643$	−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
$646$	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	$0.793902\pi$
$648$	12.3819	+	16.6138i	0.486405	+	0.652653i
$649$	−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	−0.839677	−	0.543086i	$-0.817256\pi$
$653$	−20.1668	+	11.6433i	−0.789189	+	0.455638i	0.0504882	+	0.998725i	$0.483922\pi$
$654$	4.84980	+	0.494844i	0.189642	+	0.0193499i
$655$	18.8207	−	32.5985i	0.735387	−	1.27373i
$656$	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	$0.135514\pi$
$660$	12.0796	−	16.7328i	0.470199	−	0.651325i
$661$			20.3440i			0.791291i	0.918403	+	0.395645i	$0.129479\pi$
$661$			20.3440i			0.791291i	−0.918403	+	0.395645i	$0.870521\pi$
$662$		−	12.7651i		−	0.496128i
$663$	10.9049	−	15.1055i	0.423510	−	0.586651i
$664$	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
$668$	−2.86955	+	4.97021i	−0.111026	+	0.192303i
$669$	33.0679	+	3.37405i	1.27848	+	0.130448i
$670$	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
$675$	0.390754	+	0.426103i	0.0150401	+	0.0164007i
$676$	−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	$0.316132\pi$
$678$	−17.4150	+	7.81713i	−0.668819	+	0.300215i
$679$		0			0
$680$	26.3138	+	15.1923i	1.00909	+	0.582598i
$681$	−13.7033	+	6.15103i	−0.525110	+	0.235708i
$682$	20.2122	+	11.6695i	0.773965	+	0.446849i
$683$	−18.1236	+	10.4637i	−0.693482	+	0.400382i	−0.804915	−	0.593390i	$-0.797789\pi$
$683$	−18.1236	+	10.4637i	−0.693482	+	0.400382i	0.111433	+	0.993772i	$0.464456\pi$
$684$	1.58234	−	7.67324i	0.0605021	−	0.293394i
$685$			13.8526i			0.529281i
$686$		0			0
$687$	24.7589	+	2.52625i	0.944611	+	0.0963824i
$688$	−3.33310	−	5.77311i	−0.127073	−	0.220098i
$689$	−14.1925			−0.540693
$690$	5.32072	−	2.38833i	0.202557	−	0.0909222i
$691$			24.0083i			0.913318i	0.889642	+	0.456659i	$0.150954\pi$
$691$			24.0083i			0.913318i	−0.889642	+	0.456659i	$0.849046\pi$
$692$	28.7163			1.09163
$693$		0			0
$694$	−13.6094			−0.516606
$695$			16.9906i			0.644489i
$696$	1.14247	−	11.1970i	0.0433053	−	0.424420i
$697$	−5.43268			−0.205777
$698$	3.22246	+	5.58147i	0.121972	+	0.211262i
$699$	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	$-0.291680\pi$
$702$	4.06037	+	4.42768i	0.153249	+	0.167112i
$703$	2.42011	−	1.39725i	0.0912762	−	0.0526984i
$704$	−0.747976	−	0.431844i	−0.0281904	−	0.0162757i
$705$	0.0956331	−	0.937267i	0.00360175	−	0.0352995i
$706$	1.52607	+	0.881077i	0.0574344	+	0.0331598i
$707$		0			0
$708$	−24.0501	−	17.3621i	−0.903859	−	0.652506i
$709$	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
$711$	−4.71015	−	14.2022i	−0.176644	−	0.532623i
$712$	−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
$717$	−11.2289	−	25.0157i	−0.419350	−	0.934228i
$718$	−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	$0.0558347\pi$
$720$	7.49266	−	8.42380i	0.279235	−	0.313937i
$721$		0			0
$722$	−9.05494	+	5.22787i	−0.336990	+	0.194561i
$723$	−3.56251	−	7.93656i	−0.132491	−	0.295164i
$724$			21.5370i			0.800416i
$725$		−	0.314045i		−	0.0116633i
$726$	0.564393	+	0.0575872i	0.0209466	+	0.00213726i
$727$	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
$731$	−11.7057	+	20.2749i	−0.432951	+	0.749893i
$732$	2.28435	−	3.16431i	0.0844320	−	0.116956i
$733$	0.431812	−	0.249307i	0.0159494	−	0.00920836i	−0.492004	−	0.870593i	$-0.663736\pi$
$733$	0.431812	−	0.249307i	0.0159494	−	0.00920836i	0.507953	+	0.861385i	$0.330402\pi$
$734$	−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
$738$	0.353807	−	1.71572i	0.0130238	−	0.0631565i
$739$	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
$741$	0.520916	−	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	$0.604203\pi$
$744$	34.6661	+	25.0259i	1.27092	+	0.917493i
$745$	29.5606	+	17.0668i	1.08302	+	0.625279i
$746$	8.62296	−	4.97847i	0.315709	−	0.182275i
$747$	−17.0886	+	19.2122i	−0.625238	+	0.702939i
$748$		−	32.1662i		−	1.17611i
$749$		0			0
$750$	−7.35091	+	10.1826i	−0.268417	+	0.371815i
$751$	−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
$753$	10.2479	+	7.39808i	0.373454	+	0.269601i
$754$		−	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
$759$	−11.3093	−	8.16432i	−0.410502	−	0.296346i
$760$	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	$-0.454186\pi$
$762$	4.11177	−	5.69567i	0.148954	−	0.206332i
$763$		0			0
$764$		−	16.2674i		−	0.588533i
$765$	−38.7774	−	7.99647i	−1.40200	−	0.289113i
$766$	1.93614	−	1.11783i	0.0699557	−	0.0403889i
$767$	−16.8261	−	9.71458i	−0.607557	−	0.350773i
$768$	−10.8303	−	7.81853i	−0.390805	−	0.282127i
$769$	−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
$772$	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	$-0.461819\pi$
$774$	−5.64076	−	5.01725i	−0.202753	−	0.180341i
$775$	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
$780$	6.41603	−	8.88756i	0.229731	−	0.318226i
$781$	−20.6520	+	35.7703i	−0.738986	+	1.27996i
$782$	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
$786$	18.8207	+	1.92035i	0.671313	+	0.0684967i
$787$		−	21.9854i		−	0.783695i	−0.920030	−	0.391848i	$-0.871836\pi$
$787$		−	21.9854i		−	0.783695i	0.920030	−	0.391848i	$-0.128164\pi$
$788$			6.13590i			0.218582i
$789$	11.1428	+	24.8240i	0.396695	+	0.883757i
$790$	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
$794$	−6.18612	+	10.7147i	−0.219537	+	0.380250i
$795$	12.3516	+	27.5169i	0.438066	+	0.975923i
$796$	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
$801$	30.9562	+	6.38363i	1.09378	+	0.225554i
$802$	3.55818	+	6.16295i	0.125644	+	0.217621i
$803$	−1.44565			−0.0510157
$804$	−17.8173	−	12.8625i	−0.628367	−	0.453625i
$805$		0			0
$806$	10.7356	+	6.19820i	0.378145	+	0.218322i
$807$	−1.84472	+	18.0795i	−0.0649372	+	0.636427i
$808$	−9.30732	−	5.37358i	−0.327430	−	0.189042i
$809$	18.1916	−	10.5029i	0.639582	−	0.369263i	−0.144872	−	0.989450i	$-0.546277\pi$
$809$	18.1916	−	10.5029i	0.639582	−	0.369263i	0.784453	+	0.620188i	$0.212944\pi$
$810$	5.05081	−	11.7257i	0.177467	−	0.411999i
$811$			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
$814$	1.84981	+	3.20397i	0.0648359	+	0.112299i
$815$	−22.5751			−0.790772
$816$	1.78366	−	17.4811i	0.0624406	−	0.611959i
$817$			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	$-0.929503\pi$
$821$		−	12.5882i		−	0.439332i	0.975575	−	0.219666i	$-0.0704968\pi$
$822$	−6.35171	+	2.85111i	−0.221541	+	0.0994440i
$823$	−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
$825$	0.650451	+	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	$-0.147631\pi$
$828$	−8.45125	−	7.51707i	−0.293701	−	0.261236i
$829$	−14.6902	+	8.48139i	−0.510212	+	0.294571i	−0.732921	−	0.680314i	$-0.761843\pi$
$829$	−14.6902	+	8.48139i	−0.510212	+	0.294571i	0.222709	+	0.974885i	$0.428510\pi$
$830$	−10.5295	−	6.07921i	−0.365484	−	0.211012i
$831$	36.1070	−	16.2075i	1.25254	−	0.562231i
$832$	−0.397284	−	0.229372i	−0.0137733	−	0.00795204i
$833$		0			0
$834$	−7.79054	+	3.49697i	−0.269764	+	0.121090i
$835$	7.98900			0.276471
$836$	−4.43015	−	7.67324i	−0.153220	−	0.265385i
$837$	−53.1414	−	16.7328i	−1.83683	−	0.578371i
$838$	−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
$843$	1.58386	+	0.161607i	0.0545510	+	0.00556605i
$844$	18.9847	−	32.8824i	0.653479	−	1.13186i
$845$	−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
$849$	22.4265	−	31.0654i	0.769675	−	1.06616i
$850$			0.426103i			0.0146152i
$851$		−	4.03430i		−	0.138294i
$852$	−19.6043	+	27.1561i	−0.671633	+	0.930353i
$853$	−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
$857$	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	$0.0804312\pi$
$858$	6.75890	+	0.689637i	0.230745	+	0.0235438i
$859$	−17.3578	+	10.0216i	−0.592242	+	0.341931i	−0.765984	−	0.642860i	$-0.777748\pi$
$859$	−17.3578	+	10.0216i	−0.592242	+	0.341931i	0.173742	+	0.984791i	$0.444414\pi$
$860$	−6.88721	+	11.9290i	−0.234852	+	0.406775i
$861$		0			0
$862$	4.84727	+	8.39571i	0.165099	+	0.285959i
$863$	−34.6600	−	20.0110i	−1.17984	−	0.681181i	−0.223863	−	0.974621i	$-0.571867\pi$
$863$	−34.6600	−	20.0110i	−1.17984	−	0.681181i	−0.955978	+	0.293439i	$0.905200\pi$
$864$	28.2258	+	8.88756i	0.960260	+	0.302361i
$865$	−19.9869	−	34.6184i	−0.679576	−	1.17706i
$866$	−2.14020			−0.0727269
$867$	−29.4369	+	13.2134i	−0.999730	+	0.448752i
$868$		0			0
$869$	−14.6545	−	8.46079i	−0.497120	−	0.287013i
$870$	−6.32691	+	2.83998i	−0.214502	+	0.0962845i
$871$	−12.4655	−	7.19694i	−0.422376	−	0.243859i
$872$	8.74660	−	5.04985i	0.296197	−	0.171010i
$873$	16.3095	+	14.5067i	0.551992	+	0.490977i
$874$		−	2.50393i		−	0.0846967i
$875$		0			0
$876$	−1.16621	−	0.118993i	−0.0394025	−	0.00402039i
$877$	−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
$879$	−46.2225	+	20.7480i	−1.55904	+	0.699814i
$880$		−	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
$885$	−4.19130	+	41.0775i	−0.140889	+	1.38080i
$886$	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	$-0.371399\pi$
$888$	2.77544	+	6.18313i	0.0931377	+	0.207492i
$889$		0			0
$890$			14.9460i			0.500991i
$891$	−30.3261	+	3.56046i	−1.01596	+	0.119280i
$892$	26.3983	−	15.2411i	0.883881	−	0.510309i
$893$	−0.350296	−	0.202243i	−0.0117222	−	0.00676782i
$894$	−1.74139	+	17.0668i	−0.0582409	+	0.570799i
$895$	−9.63528	−	5.56293i	−0.322072	−	0.185948i
$896$		0			0
$897$	−6.00688	−	4.33643i	−0.200564	−	0.144789i
$898$	15.9469			0.532155
$899$	15.1316	+	26.2087i	0.504667	+	0.874108i
$900$	0.519258	+	0.107079i	0.0173086	+	0.00356929i
$901$	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
$906$	5.31856	+	11.8487i	0.176697	+	0.393646i
$907$	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
$909$	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	$0.571088\pi$
$912$	−1.98212	−	4.41576i	−0.0656345	−	0.146221i
$913$			29.0783i			0.962352i
$914$			8.09005i			0.267595i
$915$	−5.40462	−	0.551454i	−0.178671	−	0.0182305i
$916$	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	−0.937988	−	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
$921$	15.0501	−	20.8476i	0.495919	−	0.686952i
$922$	−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
$927$	−13.9891	−	12.4428i	−0.459463	−	0.408675i
$928$	−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	$0.638333\pi$
$930$	2.67417	−	26.2087i	0.0876896	−	0.859416i
$931$		0			0
$932$	40.8763	+	23.5999i	1.33895	+	0.773041i
$933$	27.2163	+	19.6477i	0.891020	+	0.643238i
$934$	−14.2214	−	8.21075i	−0.465340	−	0.268664i
$935$	−38.7774	+	22.3881i	−1.26816	+	0.732170i
$936$	12.1897	+	2.51369i	0.398432	+	0.0821625i
$937$			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
$940$	−0.431988	−	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	$0.278337\pi$
$942$	−5.13526	−	3.70720i	−0.167316	−	0.120787i
$943$			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	$0.182471\pi$
$947$			33.3808i			1.08473i	−0.840143	+	0.542365i	$0.817529\pi$
$948$	−11.1254	−	8.03158i	−0.361337	−	0.260854i
$949$	−0.767847			−0.0249254
$950$	0.0586858	+	0.101647i	0.00190402	+	0.00329786i
$951$	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	$0.744079\pi$
$954$	−10.0749	+	11.3269i	−0.326187	+	0.366723i
$955$	−19.6108	+	11.3223i	−0.634592	+	0.366382i
$956$	−21.7767	−	12.5728i	−0.704309	−	0.406633i
$957$	13.4480	+	9.70825i	0.434712	+	0.313823i
$958$	−0.297540	−	0.171785i	−0.00961307	−	0.00555011i
$959$		0			0
$960$	−0.0989611	+	0.969884i	−0.00319395	+	0.0313029i
$961$	−83.9627			−2.70847
$962$	0.982519	+	1.70177i	0.0316777	+	0.0548674i
$963$	−0.902416	+	4.37610i	−0.0290800	+	0.141018i
$964$	−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
$969$	−9.94972	+	13.7825i	−0.319631	+	0.442756i
$970$	−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	$0.902368\pi$
$972$	−24.7573	+	0.376055i	−0.794090	+	0.0120620i
$973$		0			0
$974$	−18.9650	+	10.9494i	−0.607678	+	0.350843i
$975$	0.345483	+	0.0352510i	0.0110643	+	0.00112894i
$976$		−	2.41106i		−	0.0771763i
$977$			54.0772i			1.73008i	0.501699	+	0.865042i	$0.332708\pi$
$977$			54.0772i			1.73008i	−0.501699	+	0.865042i	$0.667292\pi$
$978$	−4.64637	−	10.3512i	−0.148575	−	0.330994i
$979$	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
$983$	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	$0.0952148\pi$
$984$	−1.48624	−	3.31105i	−0.0473797	−	0.105552i
$985$	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
$990$	−4.54510	−	13.7045i	−0.144453	−	0.435558i
$991$	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
$993$	27.9409	+	20.1708i	0.886677	+	0.640102i
$994$		0			0
$995$	−29.1119	−	16.8077i	−0.922909	−	0.532841i
$996$	−2.39347	+	23.4576i	−0.0758401	+	0.743283i
$997$	−43.4282	−	25.0733i	−1.37538	−	0.794079i	−0.383785	−	0.923422i	$-0.625380\pi$
$997$	−43.4282	−	25.0733i	−1.37538	−	0.794079i	−0.991600	+	0.129344i	$0.958713\pi$
$998$	−4.77885	+	2.75907i	−0.151272	+	0.0873368i
$999$	−5.96901	−	6.50898i	−0.188851	−	0.205935i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.i.c.68.4		12
3.2	odd	2		1323.2.i.c.1097.4		12
7.2	even	3		63.2.o.a.41.3	yes	12
7.3	odd	6		441.2.s.c.374.3		12
7.4	even	3		441.2.s.c.374.4		12
7.5	odd	6		63.2.o.a.41.4	yes	12
7.6	odd	2	inner	441.2.i.c.68.3		12
9.2	odd	6		441.2.s.c.362.3		12
9.7	even	3		1323.2.s.c.656.4		12
21.2	odd	6		189.2.o.a.125.4		12
21.5	even	6		189.2.o.a.125.3		12
21.11	odd	6		1323.2.s.c.962.3		12
21.17	even	6		1323.2.s.c.962.4		12
21.20	even	2		1323.2.i.c.1097.3		12
28.19	even	6		1008.2.cc.a.545.1		12
28.23	odd	6		1008.2.cc.a.545.6		12
63.2	odd	6		63.2.o.a.20.4	yes	12
63.5	even	6		567.2.c.c.566.8		12
63.11	odd	6	inner	441.2.i.c.227.3		12
63.16	even	3		189.2.o.a.62.3		12
63.20	even	6		441.2.s.c.362.4		12
63.23	odd	6		567.2.c.c.566.7		12
63.25	even	3		1323.2.i.c.521.3		12
63.34	odd	6		1323.2.s.c.656.3		12
63.38	even	6	inner	441.2.i.c.227.4		12
63.40	odd	6		567.2.c.c.566.5		12
63.47	even	6		63.2.o.a.20.3	✓	12
63.52	odd	6		1323.2.i.c.521.4		12
63.58	even	3		567.2.c.c.566.6		12
63.61	odd	6		189.2.o.a.62.4		12
84.23	even	6		3024.2.cc.a.881.5		12
84.47	odd	6		3024.2.cc.a.881.2		12
252.47	odd	6		1008.2.cc.a.209.6		12
252.79	odd	6		3024.2.cc.a.2897.2		12
252.187	even	6		3024.2.cc.a.2897.5		12
252.191	even	6		1008.2.cc.a.209.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.o.a.20.3	✓	12	63.47	even	6
63.2.o.a.20.4	yes	12	63.2	odd	6
63.2.o.a.41.3	yes	12	7.2	even	3
63.2.o.a.41.4	yes	12	7.5	odd	6
189.2.o.a.62.3		12	63.16	even	3
189.2.o.a.62.4		12	63.61	odd	6
189.2.o.a.125.3		12	21.5	even	6
189.2.o.a.125.4		12	21.2	odd	6
441.2.i.c.68.3		12	7.6	odd	2	inner
441.2.i.c.68.4		12	1.1	even	1	trivial
441.2.i.c.227.3		12	63.11	odd	6	inner
441.2.i.c.227.4		12	63.38	even	6	inner
441.2.s.c.362.3		12	9.2	odd	6
441.2.s.c.362.4		12	63.20	even	6
441.2.s.c.374.3		12	7.3	odd	6
441.2.s.c.374.4		12	7.4	even	3
567.2.c.c.566.5		12	63.40	odd	6
567.2.c.c.566.6		12	63.58	even	3
567.2.c.c.566.7		12	63.23	odd	6
567.2.c.c.566.8		12	63.5	even	6
1008.2.cc.a.209.1		12	252.191	even	6
1008.2.cc.a.209.6		12	252.47	odd	6
1008.2.cc.a.545.1		12	28.19	even	6
1008.2.cc.a.545.6		12	28.23	odd	6
1323.2.i.c.521.3		12	63.25	even	3
1323.2.i.c.521.4		12	63.52	odd	6
1323.2.i.c.1097.3		12	21.20	even	2
1323.2.i.c.1097.4		12	3.2	odd	2
1323.2.s.c.656.3		12	63.34	odd	6
1323.2.s.c.656.4		12	9.7	even	3
1323.2.s.c.962.3		12	21.11	odd	6
1323.2.s.c.962.4		12	21.17	even	6
3024.2.cc.a.881.2		12	84.47	odd	6
3024.2.cc.a.881.5		12	84.23	even	6
3024.2.cc.a.2897.2		12	252.79	odd	6
3024.2.cc.a.2897.5		12	252.187	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.641589i q^{2} +(1.40434 + 1.01381i) q^{3} +1.58836 q^{4} +(-1.10552 - 1.91482i) q^{5} +(0.650451 - 0.901012i) q^{6} -2.30225i q^{8} +(0.944368 + 2.84748i) q^{9} +O(q^{10})\)	\(q-0.641589i q^{2} +(1.40434 + 1.01381i) q^{3} +1.58836 q^{4} +(-1.10552 - 1.91482i) q^{5} +(0.650451 - 0.901012i) q^{6} -2.30225i q^{8} +(0.944368 + 2.84748i) q^{9} +(-1.22853 + 0.709292i) q^{10} +(2.93818 + 1.69636i) q^{11} +(2.23061 + 1.61030i) q^{12} +(1.56060 + 0.901012i) q^{13} +(0.388736 - 3.80987i) q^{15} +1.69963 q^{16} +(-2.98450 - 5.16931i) q^{17} +(1.82691 - 0.605896i) q^{18} +(-1.42391 - 0.822093i) q^{19} +(-1.75597 - 3.04144i) q^{20} +(1.08836 - 1.88510i) q^{22} +(-2.05563 + 1.18682i) q^{23} +(2.33405 - 3.23316i) q^{24} +(0.0556321 - 0.0963576i) q^{25} +(0.578079 - 1.00126i) q^{26} +(-1.56060 + 4.95626i) q^{27} +(2.44437 - 1.41126i) q^{29} +(-2.44437 - 0.249409i) q^{30} +10.7221i q^{31} -5.69497i q^{32} +(2.40643 + 5.36103i) q^{33} +(-3.31657 + 1.91482i) q^{34} +(1.50000 + 4.52284i) q^{36} +(-0.849814 + 1.47192i) q^{37} +(-0.527445 + 0.913562i) q^{38} +(1.27816 + 2.84748i) q^{39} +(-4.40841 + 2.54520i) q^{40} +(0.455074 - 0.788211i) q^{41} +(-1.96108 - 3.39669i) q^{43} +(4.66690 + 2.69443i) q^{44} +(4.40841 - 4.95626i) q^{45} +(0.761450 + 1.31887i) q^{46} +0.246010 q^{47} +(2.38686 + 1.72310i) q^{48} +(-0.0618219 - 0.0356929i) q^{50} +(1.04944 - 10.2852i) q^{51} +(2.47880 + 1.43113i) q^{52} +(-6.82072 + 3.93795i) q^{53} +(3.17988 + 1.00126i) q^{54} -7.50146i q^{55} +(-1.16621 - 2.59808i) q^{57} +(-0.905446 - 1.56828i) q^{58} -10.7819 q^{59} +(0.617454 - 6.05146i) q^{60} -1.41858i q^{61} +6.87916 q^{62} -0.254572 q^{64} -3.98436i q^{65} +(3.43958 - 1.54394i) q^{66} -7.98762 q^{67} +(-4.74048 - 8.21075i) q^{68} +(-4.09003 - 0.417322i) q^{69} +12.1743i q^{71} +(6.55563 - 2.17417i) q^{72} +(-0.369016 + 0.213051i) q^{73} +(0.944368 + 0.545231i) q^{74} +(0.175815 - 0.0789188i) q^{75} +(-2.26168 - 1.30578i) q^{76} +(1.82691 - 0.820053i) q^{78} -4.98762 q^{79} +(-1.87898 - 3.25449i) q^{80} +(-7.21634 + 5.37815i) q^{81} +(-0.505707 - 0.291970i) q^{82} +(4.28541 + 7.42254i) q^{83} +(-6.59888 + 11.4296i) q^{85} +(-2.17928 + 1.25821i) q^{86} +(4.86348 + 0.496241i) q^{87} +(3.90545 - 6.76443i) q^{88} +(5.26792 - 9.12431i) q^{89} +(-3.17988 - 2.82839i) q^{90} +(-3.26509 + 1.88510i) q^{92} +(-10.8702 + 15.0575i) q^{93} -0.157838i q^{94} +3.63537i q^{95} +(5.77363 - 7.99770i) q^{96} +(6.30108 - 3.63793i) q^{97} +(-2.05563 + 9.96840i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{4} + 12 q^{9}+O(q^{10}) \) 12 * q - 4 * q^4 + 12 * q^9	\( 12 q - 4 q^{4} + 12 q^{9} + 6 q^{15} - 4 q^{16} - 12 q^{18} - 10 q^{22} - 24 q^{23} + 30 q^{29} - 30 q^{30} + 18 q^{36} + 2 q^{37} + 12 q^{39} - 10 q^{43} + 54 q^{44} + 20 q^{46} - 36 q^{50} - 24 q^{51} - 12 q^{53} - 18 q^{57} + 2 q^{58} + 42 q^{60} + 16 q^{64} - 24 q^{67} + 78 q^{72} + 12 q^{74} - 12 q^{78} + 12 q^{79} - 48 q^{81} - 6 q^{85} - 96 q^{86} + 34 q^{88} + 30 q^{92} - 24 q^{93} - 24 q^{99}+O(q^{100}) \) 12 * q - 4 * q^4 + 12 * q^9 + 6 * q^15 - 4 * q^16 - 12 * q^18 - 10 * q^22 - 24 * q^23 + 30 * q^29 - 30 * q^30 + 18 * q^36 + 2 * q^37 + 12 * q^39 - 10 * q^43 + 54 * q^44 + 20 * q^46 - 36 * q^50 - 24 * q^51 - 12 * q^53 - 18 * q^57 + 2 * q^58 + 42 * q^60 + 16 * q^64 - 24 * q^67 + 78 * q^72 + 12 * q^74 - 12 * q^78 + 12 * q^79 - 48 * q^81 - 6 * q^85 - 96 * q^86 + 34 * q^88 + 30 * q^92 - 24 * q^93 - 24 * q^99

Introduction

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