LMFDB - Embedded newform 441.2.s.d.362.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(362,441)]

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([1, 5]))

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

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

chi := DirichletCharacter("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: 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:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			362.4
Character	$\chi$	$=$	441.362
Dual form			441.2.s.d.374.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.80506 + 1.04215i) q^{2} +(1.73189 + 0.0239080i) q^{3} +(1.17216 - 2.03024i) q^{4} -3.30465 q^{5} +(-3.15107 + 1.76173i) q^{6} +0.717672i q^{8} +(2.99886 + 0.0828118i) q^{9} +O(q^{10})$	\(q+(-1.80506 + 1.04215i) q^{2} +(1.73189 + 0.0239080i) q^{3} +(1.17216 - 2.03024i) q^{4} -3.30465 q^{5} +(-3.15107 + 1.76173i) q^{6} +0.717672i q^{8} +(2.99886 + 0.0828118i) q^{9} +(5.96509 - 3.44395i) q^{10} -2.66137i q^{11} +(2.07859 - 3.48812i) q^{12} +(2.11249 - 1.21964i) q^{13} +(-5.72328 - 0.0790075i) q^{15} +(1.59640 + 2.76504i) q^{16} +(3.59017 + 6.21836i) q^{17} +(-5.49942 + 2.97578i) q^{18} +(4.24746 + 2.45227i) q^{19} +(-3.87358 + 6.70924i) q^{20} +(2.77356 + 4.80394i) q^{22} -4.99031i q^{23} +(-0.0171581 + 1.24293i) q^{24} +5.92072 q^{25} +(-2.54211 + 4.40306i) q^{26} +(5.19170 + 0.215117i) q^{27} +(5.50701 + 3.17947i) q^{29} +(10.4132 - 5.82191i) q^{30} +(-2.30833 - 1.33271i) q^{31} +(-7.00624 - 4.04505i) q^{32} +(0.0636281 - 4.60920i) q^{33} +(-12.9609 - 7.48301i) q^{34} +(3.68327 - 5.99134i) q^{36} +(0.844787 - 1.46321i) q^{37} -10.2226 q^{38} +(3.68775 - 2.06178i) q^{39} -2.37166i q^{40} +(0.553137 + 0.958062i) q^{41} +(2.93481 - 5.08323i) q^{43} +(-5.40324 - 3.11956i) q^{44} +(-9.91018 - 0.273664i) q^{45} +(5.20066 + 9.00781i) q^{46} +(2.44098 + 4.22790i) q^{47} +(2.69867 + 4.82691i) q^{48} +(-10.6873 + 6.17029i) q^{50} +(6.06910 + 10.8553i) q^{51} -5.71848i q^{52} +(8.94013 - 5.16159i) q^{53} +(-9.59551 + 5.02224i) q^{54} +8.79491i q^{55} +(7.29748 + 4.34860i) q^{57} -13.2540 q^{58} +(-2.56820 + 4.44826i) q^{59} +(-6.86901 + 11.5270i) q^{60} +(-4.44613 + 2.56698i) q^{61} +5.55556 q^{62} +10.4766 q^{64} +(-6.98103 + 4.03050i) q^{65} +(4.68863 + 8.38619i) q^{66} +(-4.16544 + 7.21476i) q^{67} +16.8330 q^{68} +(0.119308 - 8.64265i) q^{69} -2.07026i q^{71} +(-0.0594317 + 2.15220i) q^{72} +(6.94112 - 4.00746i) q^{73} +3.52159i q^{74} +(10.2540 + 0.141552i) q^{75} +(9.95741 - 5.74891i) q^{76} +(-4.50791 + 7.56483i) q^{78} +(-2.50501 - 4.33881i) q^{79} +(-5.27554 - 9.13750i) q^{80} +(8.98628 + 0.496681i) q^{81} +(-1.99689 - 1.15291i) q^{82} +(1.04482 - 1.80968i) q^{83} +(-11.8643 - 20.5495i) q^{85} +12.2341i q^{86} +(9.46149 + 5.63814i) q^{87} +1.90999 q^{88} +(-0.541267 + 0.937501i) q^{89} +(18.1737 - 9.83393i) q^{90} +(-10.1315 - 5.84945i) q^{92} +(-3.96589 - 2.36329i) q^{93} +(-8.81223 - 5.08774i) q^{94} +(-14.0364 - 8.10390i) q^{95} +(-12.0373 - 7.17307i) q^{96} +(-9.47203 - 5.46868i) q^{97} +(0.220393 - 7.98108i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4} - 8 q^{9}+O(q^{10}) $ 48 * q + 24 * q^4 - 8 * q^9	$ 48 q + 24 q^{4} - 8 q^{9} - 40 q^{15} - 24 q^{16} + 32 q^{18} + 48 q^{25} + 48 q^{30} - 120 q^{32} - 8 q^{36} - 32 q^{39} + 96 q^{44} + 48 q^{50} + 48 q^{53} + 80 q^{57} - 72 q^{60} - 48 q^{64} - 120 q^{65} + 32 q^{72} - 88 q^{78} - 24 q^{79} + 120 q^{81} - 24 q^{85} - 144 q^{92} + 16 q^{93} - 96 q^{95} - 72 q^{99}+O(q^{100}) $ 48 * q + 24 * q^4 - 8 * q^9 - 40 * q^15 - 24 * q^16 + 32 * q^18 + 48 * q^25 + 48 * q^30 - 120 * q^32 - 8 * q^36 - 32 * q^39 + 96 * q^44 + 48 * q^50 + 48 * q^53 + 80 * q^57 - 72 * q^60 - 48 * q^64 - 120 * q^65 + 32 * q^72 - 88 * q^78 - 24 * q^79 + 120 * q^81 - 24 * q^85 - 144 * q^92 + 16 * q^93 - 96 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.80506	+	1.04215i	−1.27637	+	0.736913i	−0.976179	−	0.216966i	$-0.930384\pi$
$2$	−1.80506	+	1.04215i	−1.27637	+	0.736913i	−0.300191	+	0.953879i	$0.597050\pi$
$3$	1.73189	+	0.0239080i	0.999905	+	0.0138033i
$3$	1.73189	+	0.0239080i	0.999905	+	0.0138033i
$4$	1.17216	−	2.03024i	0.586081	−	1.01512i
$5$	−3.30465			−1.47788			−0.738942	−	0.673769i	$-0.764674\pi$
$5$	−3.30465			−1.47788			−0.738942	+	0.673769i	$0.764674\pi$
$6$	−3.15107	+	1.76173i	−1.28642	+	0.719224i
$7$		0			0
$7$		0			0
$8$			0.717672i			0.253735i
$9$	2.99886	+	0.0828118i	0.999619	+	0.0276039i
$10$	5.96509	−	3.44395i	1.88633	−	1.08907i
$11$		−	2.66137i		−	0.802434i	−0.915983	−	0.401217i	$-0.868587\pi$
$11$		−	2.66137i		−	0.802434i	0.915983	−	0.401217i	$-0.131413\pi$
$12$	2.07859	−	3.48812i	0.600037	−	1.00693i
$13$	2.11249	−	1.21964i	0.585899	−	0.338269i	−0.177576	−	0.984107i	$-0.556825\pi$
$13$	2.11249	−	1.21964i	0.585899	−	0.338269i	0.763474	+	0.645839i	$0.223492\pi$
$14$		0			0
$15$	−5.72328	−	0.0790075i	−1.47774	−	0.0203997i
$16$	1.59640	+	2.76504i	0.399100	+	0.691261i
$17$	3.59017	+	6.21836i	0.870744	+	1.50817i	0.861228	+	0.508219i	$0.169696\pi$
$17$	3.59017	+	6.21836i	0.870744	+	1.50817i	0.00951656	+	0.999955i	$0.496971\pi$
$18$	−5.49942	+	2.97578i	−1.29623	+	0.701399i
$19$	4.24746	+	2.45227i	0.974433	+	0.562589i	0.900585	−	0.434680i	$-0.143139\pi$
$19$	4.24746	+	2.45227i	0.974433	+	0.562589i	0.0738485	+	0.997269i	$0.476472\pi$
$20$	−3.87358	+	6.70924i	−0.866160	+	1.50023i
$21$		0			0
$22$	2.77356	+	4.80394i	0.591324	+	1.02420i
$23$		−	4.99031i		−	1.04055i	−0.853998	−	0.520276i	$-0.825829\pi$
$23$		−	4.99031i		−	1.04055i	0.853998	−	0.520276i	$-0.174171\pi$
$24$	−0.0171581	+	1.24293i	−0.00350238	+	0.253711i
$25$	5.92072			1.18414
$26$	−2.54211	+	4.40306i	−0.498549	+	0.863512i
$27$	5.19170	+	0.215117i	0.999143	+	0.0413993i
$28$		0			0
$29$	5.50701	+	3.17947i	1.02263	+	0.590413i	0.914863	−	0.403764i	$-0.132298\pi$
$29$	5.50701	+	3.17947i	1.02263	+	0.590413i	0.107762	+	0.994177i	$0.465632\pi$
$30$	10.4132	−	5.82191i	1.90118	−	1.06293i
$31$	−2.30833	−	1.33271i	−0.414588	−	0.239362i	0.278171	−	0.960531i	$-0.410272\pi$
$31$	−2.30833	−	1.33271i	−0.414588	−	0.239362i	−0.692759	+	0.721169i	$0.743605\pi$
$32$	−7.00624	−	4.04505i	−1.23854	−	0.715071i
$33$	0.0636281	−	4.60920i	0.0110762	−	0.802358i
$34$	−12.9609	−	7.48301i	−2.22278	−	1.28333i
$35$		0			0
$36$	3.68327	−	5.99134i	0.613879	−	0.998556i
$37$	0.844787	−	1.46321i	0.138882	−	0.240551i	−0.788192	−	0.615430i	$-0.788982\pi$
$37$	0.844787	−	1.46321i	0.138882	−	0.240551i	0.927074	+	0.374879i	$0.122316\pi$
$38$	−10.2226			−1.65832
$39$	3.68775	−	2.06178i	0.590512	−	0.330149i
$40$		−	2.37166i		−	0.374992i
$41$	0.553137	+	0.958062i	0.0863855	+	0.149624i	0.905981	−	0.423319i	$-0.139135\pi$
$41$	0.553137	+	0.958062i	0.0863855	+	0.149624i	−0.819595	+	0.572943i	$0.805802\pi$
$42$		0			0
$43$	2.93481	−	5.08323i	0.447554	−	0.775186i	−0.550672	−	0.834721i	$-0.685629\pi$
$43$	2.93481	−	5.08323i	0.447554	−	0.775186i	0.998226	+	0.0595356i	$0.0189620\pi$
$44$	−5.40324	−	3.11956i	−0.814568	−	0.470291i
$45$	−9.91018	−	0.273664i	−1.47732	−	0.0407954i
$46$	5.20066	+	9.00781i	0.766796	+	1.32813i
$47$	2.44098	+	4.22790i	0.356053	+	0.616703i	0.987298	−	0.158881i	$-0.0507888\pi$
$47$	2.44098	+	4.22790i	0.356053	+	0.616703i	−0.631244	+	0.775584i	$0.717455\pi$
$48$	2.69867	+	4.82691i	0.389520	+	0.696704i
$49$		0			0
$50$	−10.6873	+	6.17029i	−1.51141	+	0.872610i
$51$	6.06910	+	10.8553i	0.849844	+	1.52005i
$52$		−	5.71848i		−	0.793011i
$53$	8.94013	−	5.16159i	1.22802	−	0.708999i	0.261406	−	0.965229i	$-0.415814\pi$
$53$	8.94013	−	5.16159i	1.22802	−	0.708999i	0.966616	+	0.256230i	$0.0824806\pi$
$54$	−9.59551	+	5.02224i	−1.30578	+	0.683440i
$55$			8.79491i			1.18591i
$56$		0			0
$57$	7.29748	+	4.34860i	0.966575	+	0.575986i
$58$	−13.2540			−1.74033
$59$	−2.56820	+	4.44826i	−0.334351	+	0.579114i	−0.983360	−	0.181667i	$-0.941851\pi$
$59$	−2.56820	+	4.44826i	−0.334351	+	0.579114i	0.649009	+	0.760781i	$0.275184\pi$
$60$	−6.86901	+	11.5270i	−0.886785	+	1.48813i
$61$	−4.44613	+	2.56698i	−0.569269	+	0.328668i	−0.756857	−	0.653580i	$-0.773266\pi$
$61$	−4.44613	+	2.56698i	−0.569269	+	0.328668i	0.187588	+	0.982248i	$0.439933\pi$
$62$	5.55556			0.705556
$63$		0			0
$64$	10.4766			1.30958
$65$	−6.98103	+	4.03050i	−0.865891	+	0.499922i
$66$	4.68863	+	8.38619i	0.577130	+	1.03227i
$67$	−4.16544	+	7.21476i	−0.508890	+	0.881423i	0.491057	+	0.871127i	$0.336611\pi$
$67$	−4.16544	+	7.21476i	−0.508890	+	0.881423i	−0.999947	+	0.0102956i	$0.996723\pi$
$68$	16.8330			2.04131
$69$	0.119308	−	8.64265i	0.0143630	−	1.04045i
$70$		0			0
$71$		−	2.07026i		−	0.245695i	−0.992426	−	0.122848i	$-0.960797\pi$
$71$		−	2.07026i		−	0.245695i	0.992426	−	0.122848i	$-0.0392026\pi$
$72$	−0.0594317	+	2.15220i	−0.00700410	+	0.253639i
$73$	6.94112	−	4.00746i	0.812396	−	0.469037i	−0.0353910	−	0.999374i	$-0.511268\pi$
$73$	6.94112	−	4.00746i	0.812396	−	0.469037i	0.847787	+	0.530336i	$0.177934\pi$
$74$			3.52159i			0.409376i
$75$	10.2540	+	0.141552i	1.18403	+	0.0163451i
$76$	9.95741	−	5.74891i	1.14219	−	0.659445i
$77$		0			0
$78$	−4.50791	+	7.56483i	−0.510421	+	0.856548i
$79$	−2.50501	−	4.33881i	−0.281836	−	0.488155i	0.690001	−	0.723809i	$-0.257610\pi$
$79$	−2.50501	−	4.33881i	−0.281836	−	0.488155i	−0.971837	+	0.235654i	$0.924277\pi$
$80$	−5.27554	−	9.13750i	−0.589823	−	1.02160i
$81$	8.98628	+	0.496681i	0.998476	+	0.0551868i
$82$	−1.99689	−	1.15291i	−0.220520	−	0.127317i
$83$	1.04482	−	1.80968i	0.114684	−	0.198638i	−0.802970	−	0.596020i	$-0.796748\pi$
$83$	1.04482	−	1.80968i	0.114684	−	0.198638i	0.917653	+	0.397382i	$0.130081\pi$
$84$		0			0
$85$	−11.8643	−	20.5495i	−1.28686	−	2.22891i
$86$			12.2341i			1.31923i
$87$	9.46149	+	5.63814i	1.01438	+	0.604472i
$88$	1.90999			0.203606
$89$	−0.541267	+	0.937501i	−0.0573741	+	0.0993749i	−0.893286	−	0.449489i	$-0.851606\pi$
$89$	−0.541267	+	0.937501i	−0.0573741	+	0.0993749i	0.835912	+	0.548864i	$0.184939\pi$
$90$	18.1737	−	9.83393i	1.91567	−	1.03659i
$91$		0			0
$92$	−10.1315	−	5.84945i	−1.05629	−	0.609847i
$93$	−3.96589	−	2.36329i	−0.411244	−	0.245062i
$94$	−8.81223	−	5.08774i	−0.908912	−	0.524761i
$95$	−14.0364	−	8.10390i	−1.44010	−	0.831442i
$96$	−12.0373	−	7.17307i	−1.22855	−	0.732099i
$97$	−9.47203	−	5.46868i	−0.961739	−	0.555260i	−0.0650310	−	0.997883i	$-0.520715\pi$
$97$	−9.47203	−	5.46868i	−0.961739	−	0.555260i	−0.896708	+	0.442623i	$0.854048\pi$
$98$		0			0
$99$	0.220393	−	7.98108i	0.0221503	−	0.802129i
$100$	6.94004	−	12.0205i	0.694004	−	1.20205i
$101$	0.527915			0.0525295			0.0262647	−	0.999655i	$-0.491639\pi$
$101$	0.527915			0.0525295			0.0262647	+	0.999655i	$0.491639\pi$
$102$	−22.2680	−	13.2696i	−2.20486	−	1.31388i
$103$			0.783733i			0.0772235i	0.999254	+	0.0386118i	$0.0122936\pi$
$103$			0.783733i			0.0772235i	−0.999254	+	0.0386118i	$0.987706\pi$
$104$	0.875305	+	1.51607i	0.0858308	+	0.148663i
$105$		0			0
$106$	−10.7583	+	18.6340i	−1.04494	+	1.80989i
$107$	4.63398	+	2.67543i	0.447984	+	0.258644i	0.706978	−	0.707235i	$-0.250058\pi$
$107$	4.63398	+	2.67543i	0.447984	+	0.258644i	−0.258994	+	0.965879i	$0.583391\pi$
$108$	6.52225	−	10.2883i	0.627603	−	0.989988i
$109$	−2.98261	−	5.16603i	−0.285682	−	0.494816i	0.687092	−	0.726570i	$-0.258887\pi$
$109$	−2.98261	−	5.16603i	−0.285682	−	0.494816i	−0.972774	+	0.231754i	$0.925553\pi$
$110$	−9.16563	−	15.8753i	−0.873909	−	1.51365i
$111$	1.49806	−	2.51392i	0.142189	−	0.238611i
$112$		0			0
$113$	10.0024	−	5.77487i	0.940944	−	0.543254i	0.0506876	−	0.998715i	$-0.483859\pi$
$113$	10.0024	−	5.77487i	0.940944	−	0.543254i	0.890256	+	0.455461i	$0.150525\pi$
$114$	−17.7043	−	0.244401i	−1.65816	−	0.0228902i
$115$			16.4912i			1.53782i
$116$	12.9102	−	7.45371i	1.19868	−	0.692059i
$117$	6.43605	−	3.48260i	0.595013	−	0.321967i
$118$		−	10.7058i		−	0.985551i
$119$		0			0
$120$	0.0567015	−	4.10744i	0.00517612	−	0.374956i
$121$	3.91709			0.356099
$122$	5.35036	−	9.26709i	0.484399	−	0.839003i
$123$	0.935065	+	1.67248i	0.0843120	+	0.150802i
$124$	−5.41146	+	3.12431i	−0.485963	+	0.280571i
$125$	−3.04265			−0.272143
$126$		0			0
$127$	−19.0954			−1.69444			−0.847221	−	0.531241i	$-0.821726\pi$
$127$	−19.0954			−1.69444			−0.847221	+	0.531241i	$0.821726\pi$
$128$	−4.89849	+	2.82815i	−0.432970	+	0.249975i
$129$	5.20428	−	8.73341i	0.458211	−	0.768934i
$130$	8.40079	−	14.5506i	0.736798	−	1.27617i
$131$	−4.15126			−0.362697			−0.181349	−	0.983419i	$-0.558046\pi$
$131$	−4.15126			−0.362697			−0.181349	+	0.983419i	$0.558046\pi$
$132$	−9.28320	−	5.53190i	−0.807999	−	0.481490i
$133$		0			0
$134$		−	17.3641i		−	1.50003i
$135$	−17.1567	−	0.710887i	−1.47662	−	0.0611834i
$136$	−4.46274	+	2.57657i	−0.382677	+	0.220939i
$137$			6.29419i			0.537749i	0.963175	+	0.268874i	$0.0866516\pi$
$137$			6.29419i			0.537749i	−0.963175	+	0.268874i	$0.913348\pi$
$138$	8.79160	+	15.7248i	0.748390	+	1.33859i
$139$	1.32575	−	0.765423i	0.112449	−	0.0649223i	−0.442721	−	0.896660i	$-0.645987\pi$
$139$	1.32575	−	0.765423i	0.112449	−	0.0649223i	0.555170	+	0.831737i	$0.312653\pi$
$140$		0			0
$141$	4.12642	+	7.38060i	0.347507	+	0.621559i
$142$	2.15753	+	3.73695i	0.181056	+	0.313598i
$143$	−3.24593	−	5.62212i	−0.271438	−	0.470145i
$144$	4.55839	+	8.42417i	0.379866	+	0.702014i
$145$	−18.1987	−	10.5070i	−1.51132	−	0.872563i
$146$	−8.35276	+	14.4674i	−0.691279	+	1.19733i
$147$		0			0
$148$	−1.98045	−	3.43025i	−0.162792	−	0.281965i
$149$		−	5.34815i		−	0.438137i	−0.975709	−	0.219069i	$-0.929698\pi$
$149$		−	5.34815i		−	0.438137i	0.975709	−	0.219069i	$-0.0703019\pi$
$150$	−18.6566	+	10.4307i	−1.52331	+	0.851665i
$151$	11.4877			0.934854			0.467427	−	0.884032i	$-0.345181\pi$
$151$	11.4877			0.934854			0.467427	+	0.884032i	$0.345181\pi$
$152$	−1.75993	+	3.04828i	−0.142749	+	0.247248i
$153$	10.2515	+	18.9453i	0.828781	+	1.53163i
$154$		0			0
$155$	7.62821	+	4.40415i	0.612713	+	0.353750i
$156$	0.136717	−	9.90376i	0.0109461	−	0.792935i
$157$	−5.77243	−	3.33271i	−0.460690	−	0.265979i	0.251644	−	0.967820i	$-0.419029\pi$
$157$	−5.77243	−	3.33271i	−0.460690	−	0.265979i	−0.712334	+	0.701840i	$0.752362\pi$
$158$	9.04340	+	5.22121i	0.719454	+	0.415377i
$159$	15.6067	−	8.72554i	1.23769	−	0.691980i
$160$	23.1532	+	13.3675i	1.83042	+	1.05679i
$161$		0			0
$162$	−16.7384	+	8.46853i	−1.31509	+	0.665351i
$163$	11.5460	−	19.9983i	0.904356	−	1.56639i	0.0825775	−	0.996585i	$-0.473685\pi$
$163$	11.5460	−	19.9983i	0.904356	−	1.56639i	0.821779	−	0.569807i	$-0.192982\pi$
$164$	2.59346			0.202516
$165$	−0.210269	+	15.2318i	−0.0163694	+	1.18579i
$166$			4.35543i			0.338047i
$167$	−7.95418	−	13.7770i	−0.615513	−	1.06610i	−0.990294	−	0.138986i	$-0.955616\pi$
$167$	−7.95418	−	13.7770i	−0.615513	−	1.06610i	0.374782	−	0.927113i	$-0.377718\pi$
$168$		0			0
$169$	−3.52493	+	6.10536i	−0.271149	+	0.469643i
$170$	42.8314	+	24.7287i	3.28502	+	1.89661i
$171$	12.5344	+	7.70575i	0.958532	+	0.589273i
$172$	−6.88013	−	11.9167i	−0.524605	−	0.908643i
$173$	−9.33097	−	16.1617i	−0.709421	−	1.22875i	−0.965072	−	0.261984i	$-0.915623\pi$
$173$	−9.33097	−	16.1617i	−0.709421	−	1.22875i	0.255651	−	0.966769i	$-0.417710\pi$
$174$	−22.9544	−	0.316876i	−1.74017	−	0.0240223i
$175$		0			0
$176$	7.35882	−	4.24861i	0.554692	−	0.320251i
$177$	−4.55418	+	7.64247i	−0.342313	+	0.574443i
$178$		−	2.25633i		−	0.169119i
$179$	−19.0792	+	11.0154i	−1.42604	+	0.823326i	−0.996806	−	0.0798653i	$-0.974551\pi$
$179$	−19.0792	+	11.0154i	−1.42604	+	0.823326i	−0.429237	+	0.903192i	$0.641218\pi$
$180$	−12.1719	+	19.7993i	−0.907242	+	1.47575i
$181$			17.6986i			1.31552i	0.753226	+	0.657762i	$0.228497\pi$
$181$			17.6986i			1.31552i	−0.753226	+	0.657762i	$0.771503\pi$
$182$		0			0
$183$	−7.76157	+	4.33941i	−0.573751	+	0.320779i
$184$	3.58141			0.264025
$185$	−2.79173	+	4.83541i	−0.205252	+	0.355507i
$186$	9.62159	+	0.132822i	0.705489	+	0.00973899i
$187$	16.5494	−	9.55479i	1.21021	−	0.698715i
$188$	11.4449			0.834704
$189$		0			0
$190$	33.7820			2.45080
$191$	−13.2711	+	7.66209i	−0.960265	+	0.554409i	−0.896255	−	0.443540i	$-0.853722\pi$
$191$	−13.2711	+	7.66209i	−0.960265	+	0.554409i	−0.0640104	+	0.997949i	$0.520389\pi$
$192$	18.1443	+	0.250475i	1.30946	+	0.0180765i
$193$	−12.9333	+	22.4012i	−0.930962	+	1.61247i	−0.149280	+	0.988795i	$0.547696\pi$
$193$	−12.9333	+	22.4012i	−0.930962	+	1.61247i	−0.781681	+	0.623678i	$0.785638\pi$
$194$	22.7968			1.63671
$195$	−12.1867	+	6.81347i	−0.872709	+	0.487922i
$196$		0			0
$197$			4.18301i			0.298027i	0.988835	+	0.149014i	$0.0476098\pi$
$197$			4.18301i			0.298027i	−0.988835	+	0.149014i	$0.952390\pi$
$198$	7.91967	+	14.6360i	0.562827	+	1.04014i
$199$	−19.0592	+	11.0038i	−1.35107	+	0.780041i	−0.988399	−	0.151876i	$-0.951468\pi$
$199$	−19.0592	+	11.0038i	−1.35107	+	0.780041i	−0.362671	+	0.931917i	$0.618135\pi$
$200$			4.24914i			0.300459i
$201$	−7.38656	+	12.3955i	−0.521008	+	0.874315i
$202$	−0.952918	+	0.550168i	−0.0670471	+	0.0387097i
$203$		0			0
$204$	29.1529	+	0.402444i	2.04111	+	0.0281767i
$205$	−1.82793	−	3.16606i	−0.127668	−	0.221127i
$206$	−0.816769	−	1.41469i	−0.0569070	−	0.0985658i
$207$	0.413257	−	14.9652i	0.0287233	−	1.04016i
$208$	6.74474	+	3.89408i	0.467664	+	0.270006i
$209$	6.52641	−	11.3041i	0.451441	−	0.781919i
$210$		0			0
$211$	12.2926	+	21.2914i	0.846257	+	1.46576i	0.884525	+	0.466493i	$0.154483\pi$
$211$	12.2926	+	21.2914i	0.846257	+	1.46576i	−0.0382677	+	0.999268i	$0.512184\pi$
$212$		−	24.2009i		−	1.66212i
$213$	0.0494958	−	3.58546i	0.00339140	−	0.245672i
$214$	−11.1528			−0.762392
$215$	−9.69851	+	16.7983i	−0.661433	+	1.14564i
$216$	−0.154384	+	3.72594i	−0.0105045	+	0.253518i
$217$		0			0
$218$	10.7676	+	6.21666i	0.729272	+	0.421045i
$219$	12.1170	−	6.77451i	0.818793	−	0.457779i
$220$	17.8558	+	10.3091i	1.20384	+	0.695036i
$221$	15.1684	+	8.75747i	1.02034	+	0.589091i
$222$	−0.0841940	+	6.09899i	−0.00565073	+	0.409337i
$223$	−7.31908	−	4.22567i	−0.490122	−	0.282972i	0.234503	−	0.972115i	$-0.424654\pi$
$223$	−7.31908	−	4.22567i	−0.490122	−	0.282972i	−0.724625	+	0.689143i	$0.757987\pi$
$224$		0			0
$225$	17.7554	+	0.490305i	1.18369	+	0.0326870i
$226$	−12.0366	+	20.8480i	−0.800662	+	1.38679i
$227$	5.82949			0.386917			0.193458	−	0.981108i	$-0.438030\pi$
$227$	5.82949			0.386917			0.193458	+	0.981108i	$0.438030\pi$
$228$	17.3825	−	9.71840i	1.15119	−	0.643617i
$229$			4.79826i			0.317078i	0.987353	+	0.158539i	$0.0506783\pi$
$229$			4.79826i			0.317078i	−0.987353	+	0.158539i	$0.949322\pi$
$230$	−17.1864	−	29.7677i	−1.13324	−	1.96282i
$231$		0			0
$232$	−2.28182	+	3.95223i	−0.149809	+	0.259476i
$233$	−19.9587	−	11.5232i	−1.30754	−	0.754907i	−0.325853	−	0.945420i	$-0.605652\pi$
$233$	−19.9587	−	11.5232i	−1.30754	−	0.754907i	−0.981685	+	0.190513i	$0.938985\pi$
$234$	−7.98805	+	12.9936i	−0.522195	+	0.849421i
$235$	−8.06659	−	13.9717i	−0.526206	−	0.911416i
$236$	6.02069	+	10.4281i	0.391914	+	0.678815i
$237$	−4.23467	−	7.57422i	−0.275071	−	0.491998i
$238$		0			0
$239$	5.91972	−	3.41775i	0.382915	−	0.221076i	−0.296171	−	0.955135i	$-0.595710\pi$
$239$	5.91972	−	3.41775i	0.382915	−	0.221076i	0.679086	+	0.734059i	$0.262376\pi$
$240$	−8.91818	−	15.9512i	−0.575666	−	1.02965i
$241$			4.49308i			0.289424i	0.989474	+	0.144712i	$0.0462256\pi$
$241$			4.49308i			0.289424i	−0.989474	+	0.144712i	$0.953774\pi$
$242$	−7.07058	+	4.08220i	−0.454514	+	0.262414i
$243$	15.5513	+	1.07504i	0.997619	+	0.0689638i
$244$			12.0356i			0.770503i
$245$		0			0
$246$	−3.43083	−	2.04444i	−0.218741	−	0.130349i
$247$	11.9636			0.761225
$248$	0.956451	−	1.65662i	0.0607347	−	0.105196i
$249$	1.85277	−	3.10917i	0.117415	−	0.197036i
$250$	5.49217	−	3.17091i	0.347355	−	0.200546i
$251$	−0.467438			−0.0295044			−0.0147522	−	0.999891i	$-0.504696\pi$
$251$	−0.467438			−0.0295044			−0.0147522	+	0.999891i	$0.504696\pi$
$252$		0			0
$253$	−13.2811			−0.834975
$254$	34.4683	−	19.9003i	2.16273	−	1.24866i
$255$	−20.0563	−	35.8731i	−1.25597	−	2.24646i
$256$	−4.58192	+	7.93613i	−0.286370	+	0.496008i
$257$	21.4865			1.34029			0.670146	−	0.742229i	$-0.266231\pi$
$257$	21.4865			1.34029			0.670146	+	0.742229i	$0.266231\pi$
$258$	−0.292492	+	21.1880i	−0.0182097	+	1.31911i
$259$		0			0
$260$			18.8976i			1.17198i
$261$	16.2514	+	9.99083i	1.00594	+	0.618417i
$262$	7.49327	−	4.32624i	0.462936	−	0.267276i
$263$		−	11.0897i		−	0.683819i	−0.939733	−	0.341909i	$-0.888926\pi$
$263$		−	11.0897i		−	0.683819i	0.939733	−	0.341909i	$-0.111074\pi$
$264$	3.30789	+	0.0456641i	0.203587	+	0.00281043i
$265$	−29.5440	+	17.0572i	−1.81487	+	1.04782i
$266$		0			0
$267$	−0.959826	+	1.61070i	−0.0587404	+	0.0985735i
$268$	9.76514	+	16.9137i	0.596501	+	1.03317i
$269$	11.0288	+	19.1024i	0.672435	+	1.16469i	0.977212	+	0.212268i	$0.0680850\pi$
$269$	11.0288	+	19.1024i	0.672435	+	1.16469i	−0.304776	+	0.952424i	$0.598582\pi$
$270$	31.7098	−	16.5967i	1.92980	−	1.01005i
$271$	4.10874	+	2.37218i	0.249588	+	0.144100i	0.619576	−	0.784937i	$-0.287305\pi$
$271$	4.10874	+	2.37218i	0.249588	+	0.144100i	−0.369988	+	0.929037i	$0.620638\pi$
$272$	−11.4627	+	19.8540i	−0.695028	+	1.20382i
$273$		0			0
$274$	−6.55950	−	11.3614i	−0.396274	−	0.686366i
$275$		−	15.7572i		−	0.950198i
$276$	−17.4068	−	10.3728i	−1.04777	−	0.624370i
$277$	−6.42658			−0.386136			−0.193068	−	0.981185i	$-0.561844\pi$
$277$	−6.42658			−0.386136			−0.193068	+	0.981185i	$0.561844\pi$
$278$	−1.59537	+	2.76327i	−0.0956842	+	0.165730i
$279$	−6.81198	−	4.18777i	−0.407822	−	0.250715i
$280$		0			0
$281$	−17.0883	−	9.86595i	−1.01940	−	0.588553i	−0.105473	−	0.994422i	$-0.533636\pi$
$281$	−17.0883	−	9.86595i	−1.01940	−	0.588553i	−0.913931	+	0.405869i	$0.866969\pi$
$282$	−15.1401	−	9.02207i	−0.901582	−	0.537257i
$283$	−4.85087	−	2.80065i	−0.288354	−	0.166481i	0.348845	−	0.937180i	$-0.386574\pi$
$283$	−4.85087	−	2.80065i	−0.288354	−	0.166481i	−0.637199	+	0.770699i	$0.719907\pi$
$284$	−4.20314	−	2.42668i	−0.249410	−	0.143997i
$285$	−24.1156	−	14.3706i	−1.42849	−	0.851241i
$286$	11.7182	+	6.76551i	0.692912	+	0.400053i
$287$		0			0
$288$	−20.6757	−	12.7107i	−1.21833	−	0.748987i
$289$	−17.2787	+	29.9275i	−1.01639	+	1.76044i
$290$	43.7997			2.57201
$291$	−16.2737	−	9.69758i	−0.953983	−	0.568482i
$292$		−	18.7895i		−	1.09957i
$293$	15.0393	+	26.0488i	0.878603	+	1.52178i	0.852875	+	0.522115i	$0.174857\pi$
$293$	15.0393	+	26.0488i	0.878603	+	1.52178i	0.0257278	+	0.999669i	$0.491810\pi$
$294$		0			0
$295$	8.48701	−	14.6999i	0.494133	−	0.855863i
$296$	1.05011	+	0.606281i	0.0610363	+	0.0352393i
$297$	0.572507	−	13.8170i	0.0332202	−	0.801747i
$298$	5.57358	+	9.65373i	0.322869	+	0.559225i
$299$	−6.08641	−	10.5420i	−0.351986	−	0.609658i
$300$	12.3067	−	20.6522i	0.710530	−	1.19236i
$301$		0			0
$302$	−20.7360	+	11.9719i	−1.19322	+	0.688906i
$303$	0.914288	+	0.0126214i	0.0525245	+	0.000725079i
$304$			15.6592i			0.898117i
$305$	14.6929	−	8.48296i	0.841314	−	0.485733i
$306$	−38.2484	−	23.5138i	−2.18651	−	1.34419i
$307$		−	23.4497i		−	1.33835i	−0.743106	−	0.669173i	$-0.766648\pi$
$307$		−	23.4497i		−	1.33835i	0.743106	−	0.669173i	$-0.233352\pi$
$308$		0			0
$309$	−0.0187375	+	1.35734i	−0.00106594	+	0.0772162i
$310$	−18.3592			−1.04273
$311$	8.35507	−	14.4714i	0.473773	−	0.820599i	−0.525776	−	0.850623i	$-0.676225\pi$
$311$	8.35507	−	14.4714i	0.473773	−	0.820599i	0.999549	+	0.0300243i	$0.00955846\pi$
$312$	1.47968	+	2.64659i	0.0837705	+	0.149834i
$313$	−12.8757	+	7.43377i	−0.727776	+	0.420182i	−0.817608	−	0.575775i	$-0.804700\pi$
$313$	−12.8757	+	7.43377i	−0.727776	+	0.420182i	0.0898319	+	0.995957i	$0.471367\pi$
$314$	13.8928			0.784014
$315$		0			0
$316$	−11.7451			−0.660715
$317$	−1.96761	+	1.13600i	−0.110512	+	0.0638040i	−0.554237	−	0.832359i	$-0.686990\pi$
$317$	−1.96761	+	1.13600i	−0.110512	+	0.0638040i	0.443725	+	0.896163i	$0.353657\pi$
$318$	−19.0777	+	32.0147i	−1.06982	+	1.79529i
$319$	8.46176	−	14.6562i	0.473768	−	0.820590i
$320$	−34.6216			−1.93541
$321$	7.96157	+	4.74433i	0.444371	+	0.264803i
$322$		0			0
$323$			35.2163i			1.95949i
$324$	11.5418	−	17.6621i	0.641209	−	0.981230i
$325$	12.5074	−	7.22117i	0.693788	−	0.400559i
$326$			48.1309i			2.66573i
$327$	−5.04203	−	9.01828i	−0.278825	−	0.498712i
$328$	−0.687575	+	0.396971i	−0.0379650	+	0.0219191i
$329$		0			0
$330$	−15.4943	−	27.7134i	−0.852932	−	1.52557i
$331$	5.97440	+	10.3480i	0.328383	+	0.568775i	0.982191	−	0.187885i	$-0.0601631\pi$
$331$	5.97440	+	10.3480i	0.328383	+	0.568775i	−0.653808	+	0.756660i	$0.726830\pi$
$332$	−2.44939	−	4.24247i	−0.134428	−	0.232836i
$333$	2.65457	−	4.31801i	0.145469	−	0.236626i
$334$	28.7155	+	16.5789i	1.57124	+	0.907158i
$335$	13.7653	−	23.8423i	0.752080	−	1.30264i
$336$		0			0
$337$	2.34636	+	4.06402i	0.127815	+	0.221381i	0.922830	−	0.385208i	$-0.125870\pi$
$337$	2.34636	+	4.06402i	0.127815	+	0.221381i	−0.795015	+	0.606590i	$0.792537\pi$
$338$		−	14.6941i		−	0.799251i
$339$	17.4610	−	9.76228i	0.948353	−	0.530214i
$340$	−55.6273			−3.01681
$341$	−3.54685	+	6.14332i	−0.192073	+	0.332679i
$342$	−30.6560	−	0.846548i	−1.65769	−	0.0457761i
$343$		0			0
$344$	3.64810	+	2.10623i	0.196692	+	0.113560i
$345$	−0.394272	+	28.5609i	−0.0212269	+	1.53767i
$346$	33.6859	+	19.4486i	1.81097	+	1.04556i
$347$	−6.40529	−	3.69809i	−0.343854	−	0.198524i	0.318121	−	0.948050i	$-0.396948\pi$
$347$	−6.40529	−	3.69809i	−0.343854	−	0.198524i	−0.661975	+	0.749526i	$0.730281\pi$
$348$	22.5372	−	12.6003i	1.20812	−	0.675448i
$349$	18.0496	+	10.4209i	0.966171	+	0.557819i	0.898067	−	0.439859i	$-0.144972\pi$
$349$	18.0496	+	10.4209i	0.966171	+	0.557819i	0.0681042	+	0.997678i	$0.478305\pi$
$350$		0			0
$351$	11.2298	−	5.87760i	0.599400	−	0.313723i
$352$	−10.7654	+	18.6462i	−0.573798	+	0.993847i
$353$	−7.09907			−0.377845			−0.188923	−	0.981992i	$-0.560500\pi$
$353$	−7.09907			−0.377845			−0.188923	+	0.981992i	$0.560500\pi$
$354$	0.255955	−	18.5413i	0.0136038	−	0.985457i
$355$			6.84150i			0.363109i
$356$	1.26890	+	2.19780i	0.0672517	+	0.116483i
$357$		0			0
$358$	22.9593	−	39.7668i	1.21344	−	2.10174i
$359$	−8.56701	−	4.94616i	−0.452149	−	0.261049i	0.256588	−	0.966521i	$-0.417402\pi$
$359$	−8.56701	−	4.94616i	−0.452149	−	0.261049i	−0.708737	+	0.705472i	$0.750735\pi$
$360$	0.196401	−	7.11226i	0.0103512	−	0.374849i
$361$	2.52726	+	4.37734i	0.133014	+	0.230386i
$362$	−18.4446	−	31.9470i	−0.969426	−	1.67910i
$363$	6.78395	+	0.0936497i	0.356065	+	0.00491533i
$364$		0			0
$365$	−22.9380	+	13.2432i	−1.20063	+	0.693183i
$366$	9.48777	−	15.9216i	0.495934	−	0.832237i
$367$		−	31.2140i		−	1.62936i	−0.579911	−	0.814680i	$-0.696913\pi$
$367$		−	31.2140i		−	1.62936i	0.579911	−	0.814680i	$-0.303087\pi$
$368$	13.7984	−	7.96653i	0.719293	−	0.415284i
$369$	1.57944	+	2.91890i	0.0822224	+	0.151952i
$370$		−	11.6376i		−	0.605011i
$371$		0			0
$372$	−9.44673	+	5.28157i	−0.489790	+	0.273837i
$373$	29.0463			1.50396			0.751981	−	0.659185i	$-0.229099\pi$
$373$	29.0463			1.50396			0.751981	+	0.659185i	$0.229099\pi$
$374$	−19.9151	+	34.4939i	−1.02978	+	1.78364i
$375$	−5.26953	−	0.0727437i	−0.272117	−	0.00375647i
$376$	−3.03425	+	1.75182i	−0.156479	+	0.0903434i
$377$	15.5113			0.798873
$378$		0			0
$379$	−0.518354			−0.0266261			−0.0133130	−	0.999911i	$-0.504238\pi$
$379$	−0.518354			−0.0266261			−0.0133130	+	0.999911i	$0.504238\pi$
$380$	−32.9058	+	18.9981i	−1.68803	+	0.974584i
$381$	−33.0710	−	0.456532i	−1.69428	−	0.0233888i
$382$	15.9701	−	27.6611i	0.817102	−	1.41526i
$383$	−13.2102			−0.675011			−0.337505	−	0.941324i	$-0.609583\pi$
$383$	−13.2102			−0.675011			−0.337505	+	0.941324i	$0.609583\pi$
$384$	−8.55125	+	4.78091i	−0.436379	+	0.243975i
$385$		0			0
$386$		−	53.9140i		−	2.74415i
$387$	9.22201	−	15.0009i	0.468781	−	0.762536i
$388$	−22.2055	+	12.8203i	−1.12731	+	0.650854i
$389$			33.8236i			1.71492i	0.514549	+	0.857461i	$0.327960\pi$
$389$			33.8236i			1.71492i	−0.514549	+	0.857461i	$0.672040\pi$
$390$	14.8971	−	24.9991i	0.754343	−	1.26588i
$391$	31.0316	−	17.9161i	1.56933	−	0.906055i
$392$		0			0
$393$	−7.18950	−	0.0992482i	−0.362662	−	0.00500641i
$394$	−4.35933	−	7.55059i	−0.219620	−	0.380393i
$395$	8.27820	+	14.3383i	0.416521	+	0.721436i
$396$	−15.9452	−	9.80256i	−0.801276	−	0.492597i
$397$	−7.42483	−	4.28673i	−0.372641	−	0.215145i	0.301970	−	0.953317i	$-0.402356\pi$
$397$	−7.42483	−	4.28673i	−0.372641	−	0.215145i	−0.674612	+	0.738173i	$0.735689\pi$
$398$	22.9353	−	39.7251i	1.14964	−	1.99124i
$399$		0			0
$400$	9.45183	+	16.3710i	0.472591	+	0.818552i
$401$			16.1362i			0.805801i	0.915244	+	0.402900i	$0.131998\pi$
$401$			16.1362i			0.805801i	−0.915244	+	0.402900i	$0.868002\pi$
$402$	0.415140	−	30.0726i	0.0207053	−	1.49989i
$403$	−6.50175			−0.323875
$404$	0.618801	−	1.07180i	0.0307865	−	0.0533238i
$405$	−29.6965	−	1.64136i	−1.47563	−	0.0815598i
$406$		0			0
$407$	−3.89416	−	2.24830i	−0.193026	−	0.111444i
$408$	−7.79056	+	4.35562i	−0.385690	+	0.215635i
$409$	−14.1364	−	8.16165i	−0.699000	−	0.403568i	0.107975	−	0.994154i	$-0.465563\pi$
$409$	−14.1364	−	8.16165i	−0.699000	−	0.403568i	−0.806975	+	0.590586i	$0.798897\pi$
$410$	6.59903	+	3.80995i	0.325903	+	0.188160i
$411$	−0.150481	+	10.9008i	−0.00742269	+	0.537697i
$412$	1.59117	+	0.918662i	0.0783913	+	0.0452592i
$413$		0			0
$414$	14.8501	+	27.4438i	0.729842	+	1.34879i
$415$	−3.45276	+	5.98035i	−0.169489	+	0.293564i
$416$	−19.7341			−0.967544
$417$	2.31435	−	1.29393i	0.113334	−	0.0633640i
$418$			27.2060i			1.33069i
$419$	−0.589031	−	1.02023i	−0.0287760	−	0.0498415i	0.851279	−	0.524714i	$-0.175828\pi$
$419$	−0.589031	−	1.02023i	−0.0287760	−	0.0498415i	−0.880055	+	0.474872i	$0.842494\pi$
$420$		0			0
$421$	3.43544	−	5.95035i	0.167433	−	0.290002i	−0.770084	−	0.637943i	$-0.779786\pi$
$421$	3.43544	−	5.95035i	0.167433	−	0.290002i	0.937517	+	0.347941i	$0.113119\pi$
$422$	−44.3777	−	25.6215i	−2.16027	−	1.24724i
$423$	6.97003	+	12.8810i	0.338894	+	0.626296i
$424$	3.70433	+	6.41609i	0.179898	+	0.311593i
$425$	21.2564	+	36.8172i	1.03109	+	1.78589i
$426$	3.64725	+	6.52355i	0.176710	+	0.316067i
$427$		0			0
$428$	10.8636	−	6.27208i	0.525110	−	0.303172i
$429$	−5.48717	−	9.81447i	−0.264923	−	0.473847i
$430$		−	40.4293i		−	1.94967i
$431$	−0.702488	+	0.405582i	−0.0338377	+	0.0195362i	−0.516823	−	0.856092i	$-0.672886\pi$
$431$	−0.702488	+	0.405582i	−0.0338377	+	0.0195362i	0.482986	+	0.875628i	$0.339552\pi$
$432$	7.69321	+	14.6987i	0.370140	+	0.707191i
$433$		−	8.59662i		−	0.413127i	−0.978433	−	0.206564i	$-0.933772\pi$
$433$		−	8.59662i		−	0.413127i	0.978433	−	0.206564i	$-0.0662280\pi$
$434$		0			0
$435$	−31.2669	−	18.6321i	−1.49913	−	0.893341i
$436$	−13.9844			−0.669731
$437$	12.2376	−	21.1961i	0.585404	−	1.01395i
$438$	−14.8119	+	24.8562i	−0.707740	+	1.18767i
$439$	23.8968	−	13.7968i	1.14053	−	0.658486i	0.193969	−	0.981008i	$-0.437864\pi$
$439$	23.8968	−	13.7968i	1.14053	−	0.658486i	0.946562	+	0.322522i	$0.104530\pi$
$440$	−6.31186			−0.300906
$441$		0			0
$442$	−36.5065			−1.73643
$443$	10.6051	−	6.12286i	0.503864	−	0.290906i	−0.226444	−	0.974024i	$-0.572710\pi$
$443$	10.6051	−	6.12286i	0.503864	−	0.290906i	0.730308	+	0.683118i	$0.239377\pi$
$444$	−3.34791	−	5.98814i	−0.158885	−	0.284185i
$445$	1.78870	−	3.09811i	0.0847924	−	0.146865i
$446$	17.6152			0.834103
$447$	0.127863	−	9.26238i	0.00604773	−	0.438096i
$448$		0			0
$449$			22.0163i			1.03901i	0.854466	+	0.519507i	$0.173884\pi$
$449$			22.0163i			1.03901i	−0.854466	+	0.519507i	$0.826116\pi$
$450$	−32.5605	+	17.6188i	−1.53492	+	0.830557i
$451$	2.54976	−	1.47211i	0.120064	−	0.0693187i
$452$		−	27.0763i		−	1.27356i
$453$	19.8954	+	0.274647i	0.934765	+	0.0129041i
$454$	−10.5226	+	6.07522i	−0.493849	+	0.285124i
$455$		0			0
$456$	−3.12087	+	5.23720i	−0.146148	+	0.245254i
$457$	−12.0780	−	20.9196i	−0.564983	−	0.978579i	−0.997051	−	0.0767380i	$-0.975550\pi$
$457$	−12.0780	−	20.9196i	−0.564983	−	0.978579i	0.432069	−	0.901841i	$-0.357784\pi$
$458$	−5.00051	−	8.66114i	−0.233659	−	0.404709i
$459$	17.3014	+	33.0561i	0.807561	+	1.54293i
$460$	33.4812	+	19.3304i	1.56107	+	0.901284i
$461$	−16.3899	+	28.3881i	−0.763352	+	1.32216i	0.177762	+	0.984074i	$0.443114\pi$
$461$	−16.3899	+	28.3881i	−0.763352	+	1.32216i	−0.941114	+	0.338091i	$0.890219\pi$
$462$		0			0
$463$	15.7659	+	27.3074i	0.732704	+	1.26908i	0.955723	+	0.294266i	$0.0950753\pi$
$463$	15.7659	+	27.3074i	0.732704	+	1.26908i	−0.223020	+	0.974814i	$0.571591\pi$
$464$			20.3028i			0.942535i
$465$	13.1059	+	7.80986i	0.607771	+	0.362174i
$466$	48.0355			2.22520
$467$	−16.5765	+	28.7114i	−0.767070	+	1.32860i	0.172075	+	0.985084i	$0.444953\pi$
$467$	−16.5765	+	28.7114i	−0.767070	+	1.32860i	−0.939145	+	0.343521i	$0.888380\pi$
$468$	0.473558	−	17.1489i	0.0218902	−	0.792709i
$469$		0			0
$470$	29.1213	+	16.8132i	1.34327	+	0.775536i
$471$	−9.91751	−	5.90988i	−0.456975	−	0.272313i
$472$	−3.19239	−	1.84313i	−0.146942	−	0.0848368i
$473$	−13.5284	−	7.81062i	−0.622036	−	0.359133i
$474$	15.5373	+	9.25875i	0.713652	+	0.425268i
$475$	25.1480	+	14.5192i	1.15387	+	0.666187i
$476$		0			0
$477$	27.2376	−	14.7385i	1.24712	−	0.674830i
$478$	−7.12364	+	12.3385i	−0.325828	+	0.564350i
$479$	−22.7945			−1.04151			−0.520754	−	0.853707i	$-0.674349\pi$
$479$	−22.7945			−1.04151			−0.520754	+	0.853707i	$0.674349\pi$
$480$	39.7790	+	23.7045i	1.81566	+	1.08196i
$481$		−	4.12136i		−	0.187918i
$482$	−4.68247	−	8.11027i	−0.213281	−	0.369413i
$483$		0			0
$484$	4.59146	−	7.95264i	0.208703	−	0.361484i
$485$	31.3017	+	18.0721i	1.42134	+	0.820611i
$486$	−29.1915	+	14.2664i	−1.32415	+	0.647135i
$487$	1.36560	+	2.36528i	0.0618811	+	0.107181i	0.895306	−	0.445451i	$-0.146957\pi$
$487$	1.36560	+	2.36528i	0.0618811	+	0.107181i	−0.833425	+	0.552632i	$0.813623\pi$
$488$	−1.84225	−	3.19087i	−0.0833946	−	0.144444i
$489$	20.4746	−	34.3588i	0.925892	−	1.55376i
$490$		0			0
$491$	21.6775	−	12.5155i	0.978291	−	0.564817i	0.0765375	−	0.997067i	$-0.475613\pi$
$491$	21.6775	−	12.5155i	0.978291	−	0.564817i	0.901754	+	0.432250i	$0.142280\pi$
$492$	4.49158	+	0.0620045i	0.202496	+	0.00279538i
$493$			45.6594i			2.05640i
$494$	−21.5950	+	12.4679i	−0.971605	+	0.560957i
$495$	−0.728322	+	26.3747i	−0.0327357	+	1.18545i
$496$		−	8.51016i		−	0.382118i
$497$		0			0
$498$	−0.104130	+	7.54311i	−0.00466616	+	0.338015i
$499$	8.59962			0.384972			0.192486	−	0.981300i	$-0.438345\pi$
$499$	8.59962			0.384972			0.192486	+	0.981300i	$0.438345\pi$
$500$	−3.56648	+	6.17732i	−0.159498	+	0.276258i
$501$	−13.4463	−	24.0504i	−0.600738	−	1.07449i
$502$	0.843754	−	0.487141i	0.0376586	−	0.0217422i
$503$	−39.0362			−1.74054			−0.870269	−	0.492577i	$-0.836055\pi$
$503$	−39.0362			−1.74054			−0.870269	+	0.492577i	$0.836055\pi$
$504$		0			0
$505$	−1.74457			−0.0776325
$506$	23.9732	−	13.8409i	1.06574	−	0.615304i
$507$	−6.25075	+	10.4895i	−0.277605	+	0.465856i
$508$	−22.3829	+	38.7683i	−0.993079	+	1.72006i
$509$	−32.5819			−1.44417			−0.722083	−	0.691806i	$-0.756815\pi$
$509$	−32.5819			−1.44417			−0.722083	+	0.691806i	$0.756815\pi$
$510$	73.5879	+	43.8513i	3.25853	+	1.94177i
$511$		0			0
$512$		−	30.4128i		−	1.34407i
$513$	21.5240	+	13.6451i	0.950307	+	0.602448i
$514$	−38.7845	+	22.3922i	−1.71071	+	0.987679i
$515$		−	2.58997i		−	0.114128i
$516$	−11.6307	−	20.8029i	−0.512013	−	0.915797i
$517$	11.2520	−	6.49636i	0.494864	−	0.285710i
$518$		0			0
$519$	−15.7738	−	28.2133i	−0.692392	−	1.23843i
$520$	−2.89258	−	5.01009i	−0.126848	−	0.219707i
$521$	−3.68456	−	6.38185i	−0.161424	−	0.279594i	0.773956	−	0.633240i	$-0.218275\pi$
$521$	−3.68456	−	6.38185i	−0.161424	−	0.279594i	−0.935379	+	0.353646i	$0.884942\pi$
$522$	−39.7468	−	1.09758i	−1.73967	−	0.0480400i
$523$	−37.5991	−	21.7078i	−1.64409	−	0.949217i	−0.979357	−	0.202138i	$-0.935211\pi$
$523$	−37.5991	−	21.7078i	−1.64409	−	0.949217i	−0.664735	−	0.747079i	$-0.731455\pi$
$524$	−4.86594	+	8.42806i	−0.212570	+	0.368181i
$525$		0			0
$526$	11.5571	+	20.0175i	0.503915	+	0.872806i
$527$		−	19.1387i		−	0.833693i
$528$	12.8462	−	7.18218i	0.559059	−	0.312564i
$529$	−1.90322			−0.0827487
$530$	35.5525	−	61.5787i	1.54430	−	2.67481i
$531$	−8.07004	+	13.1270i	−0.350210	+	0.569664i
$532$		0			0
$533$	2.33699	+	1.34926i	0.101226	+	0.0584430i
$534$	0.0539442	−	3.90770i	0.00233440	−	0.169103i
$535$	−15.3137	−	8.84137i	−0.662069	−	0.382246i
$536$	−5.17783	−	2.98942i	−0.223648	−	0.129123i
$537$	−33.3063	+	18.6212i	−1.43727	+	0.803564i
$538$	−39.8151	−	22.9873i	−1.71655	−	0.991052i
$539$		0			0
$540$	−21.5537	+	33.9991i	−0.927526	+	1.46309i
$541$	10.8221	−	18.7444i	0.465278	−	0.805884i	−0.533936	−	0.845525i	$-0.679288\pi$
$541$	10.8221	−	18.7444i	0.465278	−	0.805884i	0.999214	+	0.0396402i	$0.0126212\pi$
$542$	−9.88869			−0.424755
$543$	−0.423137	+	30.6519i	−0.0181585	+	1.31540i
$544$		−	58.0897i		−	2.49058i
$545$	9.85648	+	17.0719i	0.422205	+	0.731281i
$546$		0			0
$547$	−11.9092	+	20.6273i	−0.509200	+	0.881960i	0.490743	+	0.871304i	$0.336725\pi$
$547$	−11.9092	+	20.6273i	−0.509200	+	0.881960i	−0.999943	+	0.0106561i	$0.996608\pi$
$548$	12.7787	+	7.37780i	0.545880	+	0.315164i
$549$	−13.5459	+	7.32980i	−0.578125	+	0.312828i
$550$	16.4214	+	28.4428i	0.700213	+	1.21280i
$551$	15.5938	+	27.0093i	0.664320	+	1.15064i
$552$	6.20259	+	0.0856243i	0.264000	+	0.00364441i
$553$		0			0
$554$	11.6004	−	6.69748i	0.492852	−	0.284548i
$555$	−4.95056	+	8.30764i	−0.210140	+	0.352640i
$556$		−	3.58880i		−	0.152199i
$557$	−9.42040	+	5.43887i	−0.399155	+	0.230452i	−0.686119	−	0.727489i	$-0.740687\pi$
$557$	−9.42040	+	5.43887i	−0.399155	+	0.230452i	0.286964	+	0.957941i	$0.407354\pi$
$558$	16.6603	+	0.460066i	0.705287	+	0.0194761i
$559$		−	14.3177i		−	0.605574i
$560$		0			0
$561$	28.8901	−	16.1521i	1.21974	−	0.681944i
$562$	41.1273			1.73485
$563$	6.67759	−	11.5659i	0.281427	−	0.487445i	−0.690310	−	0.723514i	$-0.742526\pi$
$563$	6.67759	−	11.5659i	0.281427	−	0.487445i	0.971736	+	0.236069i	$0.0758590\pi$
$564$	19.8212	+	0.273624i	0.834625	+	0.0115217i
$565$	−33.0543	+	19.0839i	−1.39061	+	0.802867i
$566$	11.6748			0.490729
$567$		0			0
$568$	1.48577			0.0623415
$569$	−8.34729	+	4.81931i	−0.349937	+	0.202036i	−0.664657	−	0.747148i	$-0.731422\pi$
$569$	−8.34729	+	4.81931i	−0.349937	+	0.202036i	0.314721	+	0.949184i	$0.398089\pi$
$570$	58.5065	+	0.807659i	2.45057	+	0.0338291i
$571$	17.2031	−	29.7966i	0.719926	−	1.24695i	−0.241102	−	0.970500i	$-0.577509\pi$
$571$	17.2031	−	29.7966i	0.719926	−	1.24695i	0.961028	−	0.276449i	$-0.0891578\pi$
$572$	−15.2190			−0.636339
$573$	−23.1673	+	12.9526i	−0.967826	+	0.541102i
$574$		0			0
$575$		−	29.5462i		−	1.23216i
$576$	31.4179	+	0.867589i	1.30908	+	0.0361496i
$577$	20.9017	−	12.0676i	0.870149	−	0.502381i	0.00275107	−	0.999996i	$-0.499124\pi$
$577$	20.9017	−	12.0676i	0.870149	−	0.502381i	0.867398	+	0.497616i	$0.165791\pi$
$578$		−	72.0280i		−	2.99597i
$579$	−22.9346	+	38.4871i	−0.953130	+	1.59947i
$580$	−42.6637	+	24.6319i	−1.77151	+	1.02278i
$581$		0			0
$582$	39.4814	+	0.545025i	1.63656	+	0.0225920i
$583$	−13.7369	−	23.7930i	−0.568925	−	0.985407i
$584$	2.87604	+	4.98145i	0.119011	+	0.206134i
$585$	−21.2689	+	11.5088i	−0.879360	+	0.475830i
$586$	−54.2935	−	31.3464i	−2.24284	−	1.29491i
$587$	−3.96848	+	6.87362i	−0.163797	+	0.283704i	−0.936227	−	0.351395i	$-0.885707\pi$
$587$	−3.96848	+	6.87362i	−0.163797	+	0.283704i	0.772431	+	0.635099i	$0.219041\pi$
$588$		0			0
$589$	−6.53634	−	11.3213i	−0.269325	−	0.466485i
$590$			35.3790i			1.45653i
$591$	−0.100007	+	7.24450i	−0.00411375	+	0.297999i
$592$	5.39447			0.221711
$593$	20.9147	−	36.2252i	0.858862	−	1.48759i	−0.0141532	−	0.999900i	$-0.504505\pi$
$593$	20.9147	−	36.2252i	0.858862	−	1.48759i	0.873015	−	0.487693i	$-0.162161\pi$
$594$	13.3661	+	25.5372i	0.548416	+	1.04781i
$595$		0			0
$596$	−10.8580	−	6.26889i	−0.444763	−	0.256784i
$597$	−33.2714	+	18.6017i	−1.36171	+	0.761317i
$598$	21.9727	+	12.6859i	0.898529	+	0.518766i
$599$	7.57344	+	4.37253i	0.309442	+	0.178657i	0.646677	−	0.762764i	$-0.276158\pi$
$599$	7.57344	+	4.37253i	0.309442	+	0.178657i	−0.337235	+	0.941421i	$0.609492\pi$
$600$	−0.101588	+	7.35902i	−0.00414732	+	0.300431i
$601$	12.6427	+	7.29924i	0.515705	+	0.297742i	0.735176	−	0.677877i	$-0.237100\pi$
$601$	12.6427	+	7.29924i	0.515705	+	0.297742i	−0.219471	+	0.975619i	$0.570433\pi$
$602$		0			0
$603$	−13.0890	+	21.2911i	−0.533027	+	0.867040i
$604$	13.4654	−	23.3228i	0.547900	−	0.948990i
$605$	−12.9446			−0.526273
$606$	−1.66350	+	0.930045i	−0.0675750	+	0.0377805i
$607$		−	10.9862i		−	0.445918i	−0.974828	−	0.222959i	$-0.928428\pi$
$607$		−	10.9862i		−	0.445918i	0.974828	−	0.222959i	$-0.0715716\pi$
$608$	−19.8391	−	34.3624i	−0.804583	−	1.39358i
$609$		0			0
$610$	−17.6811	+	30.6245i	−0.715885	+	1.23995i
$611$	10.3131	+	5.95426i	0.417222	+	0.240883i
$612$	50.4799	+	1.39397i	2.04053	+	0.0563481i
$613$	−11.9068	−	20.6231i	−0.480909	−	0.832959i	0.518851	−	0.854865i	$-0.326360\pi$
$613$	−11.9068	−	20.6231i	−0.480909	−	0.832959i	−0.999760	+	0.0219056i	$0.993027\pi$
$614$	24.4382	+	42.3282i	0.986244	+	1.70823i
$615$	−3.09007	−	5.52696i	−0.124603	−	0.222868i
$616$		0			0
$617$	−36.5255	+	21.0880i	−1.47046	+	0.848971i	−0.999450	−	0.0331557i	$-0.989444\pi$
$617$	−36.5255	+	21.0880i	−1.47046	+	0.848971i	−0.471011	+	0.882127i	$0.656111\pi$
$618$	−1.38073	−	2.46960i	−0.0555411	−	0.0993419i
$619$		−	26.1577i		−	1.05137i	−0.850680	−	0.525683i	$-0.823810\pi$
$619$		−	26.1577i		−	1.05137i	0.850680	−	0.525683i	$-0.176190\pi$
$620$	17.8830	−	10.3247i	0.718198	−	0.414652i
$621$	1.07350	−	25.9082i	0.0430781	−	1.03966i
$622$			34.8290i			1.39652i
$623$		0			0
$624$	11.5880	+	6.90535i	0.463892	+	0.276435i
$625$	−19.5487			−0.781947
$626$	15.4942	−	26.8368i	0.619274	−	1.07261i
$627$	11.5733	−	19.4213i	0.462191	−	0.775613i
$628$	−13.5324	+	7.81295i	−0.540003	+	0.311771i
$629$	12.1317			0.483724
$630$		0			0
$631$	−19.2419			−0.766009			−0.383004	−	0.923746i	$-0.625111\pi$
$631$	−19.2419			−0.766009			−0.383004	+	0.923746i	$0.625111\pi$
$632$	3.11385	−	1.79778i	0.123862	−	0.0715118i
$633$	20.7803	+	37.1682i	0.825944	+	1.47730i
$634$	2.36776	−	4.10109i	0.0940359	−	0.162875i
$635$	63.1036			2.50419
$636$	0.578593	−	41.9131i	0.0229427	−	1.66196i
$637$		0			0
$638$			35.2738i			1.39650i
$639$	0.171442	−	6.20842i	0.00678215	−	0.245601i
$640$	16.1878	−	9.34604i	0.639879	−	0.369435i
$641$		−	17.6072i		−	0.695444i	−0.937598	−	0.347722i	$-0.886955\pi$
$641$		−	17.6072i		−	0.695444i	0.937598	−	0.347722i	$-0.113045\pi$
$642$	−19.3154	−	0.266642i	−0.762319	−	0.0105235i
$643$	−43.1158	+	24.8929i	−1.70032	+	0.981680i	−0.754893	+	0.655848i	$0.772311\pi$
$643$	−43.1158	+	24.8929i	−1.70032	+	0.981680i	−0.945428	+	0.325832i	$0.894355\pi$
$644$		0			0
$645$	−17.1983	+	28.8609i	−0.677183	+	1.13640i
$646$	−36.7007	−	63.5675i	−1.44397	−	2.50103i
$647$	5.77035	+	9.99454i	0.226856	+	0.392926i	0.956875	−	0.290501i	$-0.0938221\pi$
$647$	5.77035	+	9.99454i	0.226856	+	0.392926i	−0.730019	+	0.683427i	$0.760489\pi$
$648$	−0.356454	+	6.44921i	−0.0140029	+	0.253349i
$649$	11.8385	+	6.83495i	0.464701	+	0.268295i
$650$	−15.0511	+	26.0693i	−0.590354	+	1.02252i
$651$		0			0
$652$	−27.0677	−	46.8826i	−1.06005	−	1.83606i
$653$			21.0444i			0.823529i	0.911290	+	0.411765i	$0.135087\pi$
$653$			21.0444i			0.823529i	−0.911290	+	0.411765i	$0.864913\pi$
$654$	18.4996	+	11.0240i	0.723391	+	0.431072i
$655$	13.7185			0.536024
$656$	−1.76606	+	3.05890i	−0.0689529	+	0.119430i
$657$	21.1473	−	11.4430i	0.825034	−	0.446433i
$658$		0			0
$659$	−31.8016	−	18.3607i	−1.23881	−	0.715230i	−0.269962	−	0.962871i	$-0.587011\pi$
$659$	−31.8016	−	18.3607i	−1.23881	−	0.715230i	−0.968852	+	0.247641i	$0.920345\pi$
$660$	30.6777	+	18.2810i	1.19413	+	0.711587i
$661$	−19.9819	−	11.5365i	−0.777205	−	0.448719i	0.0582339	−	0.998303i	$-0.481453\pi$
$661$	−19.9819	−	11.5365i	−0.777205	−	0.448719i	−0.835439	+	0.549583i	$0.814786\pi$
$662$	−21.5683	−	12.4525i	−0.838276	−	0.483979i
$663$	26.0605	+	15.5296i	1.01211	+	0.603119i
$664$	1.29875	+	0.749836i	0.0504015	+	0.0290993i
$665$		0			0
$666$	−0.291629	+	10.5607i	−0.0113004	+	0.409220i
$667$	15.8666	−	27.4817i	0.614356	−	1.06410i
$668$	−37.2943			−1.44296
$669$	−12.5748	−	7.49337i	−0.486169	−	0.289710i
$670$			57.3823i			2.21687i
$671$	6.83168	+	11.8328i	0.263734	+	0.456801i
$672$		0			0
$673$	24.7594	−	42.8846i	0.954406	−	1.65308i	0.218684	−	0.975796i	$-0.429824\pi$
$673$	24.7594	−	42.8846i	0.954406	−	1.65308i	0.735722	−	0.677284i	$-0.236843\pi$
$674$	−8.47065	−	4.89053i	−0.326277	−	0.188376i
$675$	30.7386	+	1.27365i	1.18313	+	0.0490227i
$676$	8.26358	+	14.3129i	0.317830	+	0.550498i
$677$	−14.9077	−	25.8208i	−0.572948	−	0.992374i	−0.996261	−	0.0863911i	$-0.972467\pi$
$677$	−14.9077	−	25.8208i	−0.572948	−	0.992374i	0.423314	−	0.905983i	$-0.360867\pi$
$678$	−21.3444	+	35.8185i	−0.819727	+	1.37560i
$679$		0			0
$680$	14.7478	−	8.51465i	0.565553	−	0.326522i
$681$	10.0960	+	0.139371i	0.386880	+	0.00534072i
$682$		−	14.7854i		−	0.566163i
$683$	26.1841	−	15.1174i	1.00191	−	0.578451i	0.0930943	−	0.995657i	$-0.470324\pi$
$683$	26.1841	−	15.1174i	1.00191	−	0.578451i	0.908812	+	0.417207i	$0.136991\pi$
$684$	30.3369	−	16.4156i	1.15996	−	0.627665i
$685$		−	20.8001i		−	0.794731i
$686$		0			0
$687$	−0.114717	+	8.31003i	−0.00437671	+	0.317048i
$688$	18.7405			0.714474
$689$	12.5906	−	21.8076i	0.479664	−	0.830802i
$690$	−29.0532	−	51.9651i	−1.10603	−	1.97828i
$691$	26.7555	−	15.4473i	1.01783	−	0.587642i	0.104352	−	0.994540i	$-0.466723\pi$
$691$	26.7555	−	15.4473i	1.01783	−	0.587642i	0.913473	+	0.406899i	$0.133390\pi$
$692$	−43.7496			−1.66311
$693$		0			0
$694$	15.4159			0.585180
$695$	−4.38115	+	2.52946i	−0.166186	+	0.0959478i
$696$	−4.04634	+	6.79025i	−0.153376	+	0.257384i
$697$	−3.97172	+	6.87921i	−0.150439	+	0.260569i
$698$	−43.4407			−1.64426
$699$	−34.2907	−	20.4340i	−1.29699	−	0.772884i
$700$		0			0
$701$		−	0.757329i		−	0.0286039i	−0.999898	−	0.0143020i	$-0.995447\pi$
$701$		−	0.757329i		−	0.0286039i	0.999898	−	0.0143020i	$-0.00455261\pi$
$702$	−14.1450	+	22.3125i	−0.533870	+	0.842132i
$703$	7.17640	−	4.14329i	0.270663	−	0.156267i
$704$		−	27.8823i		−	1.05085i
$705$	−13.6364	−	24.3903i	−0.513575	−	0.918592i
$706$	12.8142	−	7.39831i	0.482270	−	0.278439i
$707$		0			0
$708$	10.1778	+	18.2043i	0.382507	+	0.684160i
$709$	10.7544	+	18.6271i	0.403889	+	0.699556i	0.994191	−	0.107626i	$-0.0343249\pi$
$709$	10.7544	+	18.6271i	0.403889	+	0.699556i	−0.590303	+	0.807182i	$0.700992\pi$
$710$	−7.12988	−	12.3493i	−0.267580	−	0.463461i
$711$	−7.15287	−	13.2189i	−0.268254	−	0.495748i
$712$	−0.672819	−	0.388452i	−0.0252149	−	0.0145579i
$713$	−6.65065	+	11.5193i	−0.249069	+	0.431400i
$714$		0			0
$715$	10.7267	+	18.5791i	0.401155	+	0.694820i
$716$			51.6471i			1.93014i
$717$	10.3340	−	5.77763i	0.385930	−	0.215770i
$718$	20.6186			0.769480
$719$	22.1254	−	38.3224i	0.825140	−	1.42918i	−0.0766729	−	0.997056i	$-0.524430\pi$
$719$	22.1254	−	38.3224i	0.825140	−	1.42918i	0.901813	−	0.432127i	$-0.142237\pi$
$720$	−15.0639	−	27.8389i	−0.561398	−	1.03750i
$721$		0			0
$722$	−9.12371	−	5.26758i	−0.339549	−	0.196039i
$723$	−0.107420	+	7.78150i	−0.00399501	+	0.289397i
$724$	35.9324	+	20.7456i	1.33542	+	0.771003i
$725$	32.6054	+	18.8248i	1.21094	+	0.699134i
$726$	−12.3430	+	6.90086i	−0.458093	+	0.256115i
$727$	2.95166	+	1.70414i	0.109471	+	0.0632031i	0.553736	−	0.832692i	$-0.313202\pi$
$727$	2.95166	+	1.70414i	0.109471	+	0.0632031i	−0.444265	+	0.895895i	$0.646535\pi$
$728$		0			0
$729$	26.9074	+	2.23365i	0.996572	+	0.0827276i
$730$	27.6029	−	47.8097i	1.02163	−	1.76952i
$731$	42.1458			1.55882
$732$	−0.287748	+	20.8444i	−0.0106355	+	0.770429i
$733$			6.30937i			0.233042i	0.993188	+	0.116521i	$0.0371742\pi$
$733$			6.30937i			0.233042i	−0.993188	+	0.116521i	$0.962826\pi$
$734$	32.5298	+	56.3432i	1.20070	+	2.07967i
$735$		0			0
$736$	−20.1861	+	34.9633i	−0.744069	+	1.28876i
$737$	19.2012	+	11.0858i	0.707284	+	0.408351i
$738$	−5.89292	−	3.62277i	−0.216921	−	0.133356i
$739$	2.45388	+	4.25024i	0.0902674	+	0.156348i	0.907624	−	0.419785i	$-0.137895\pi$
$739$	2.45388	+	4.25024i	0.0902674	+	0.156348i	−0.817356	+	0.576133i	$0.804561\pi$
$740$	6.54471	+	11.3358i	0.240588	+	0.416711i
$741$	20.7196	+	0.286025i	0.761153	+	0.0105074i
$742$		0			0
$743$	26.1921	−	15.1220i	0.960895	−	0.554773i	0.0644465	−	0.997921i	$-0.479472\pi$
$743$	26.1921	−	15.1220i	0.960895	−	0.554773i	0.896448	+	0.443148i	$0.146138\pi$
$744$	1.69607	−	2.84621i	0.0621810	−	0.104347i
$745$			17.6738i			0.647516i
$746$	−52.4304	+	30.2707i	−1.91961	+	1.10829i
$747$	3.28312	−	5.34044i	0.120123	−	0.195396i
$748$		−	44.7990i		−	1.63801i
$749$		0			0
$750$	9.58762	−	5.36034i	0.350091	−	0.195732i
$751$	−50.0642			−1.82687			−0.913435	−	0.406986i	$-0.866580\pi$
$751$	−50.0642			−1.82687			−0.913435	+	0.406986i	$0.866580\pi$
$752$	−7.79355	+	13.4988i	−0.284202	+	0.492252i
$753$	−0.809549	−	0.0111755i	−0.0295016	−	0.000407258i
$754$	−27.9988	+	16.1651i	−1.01966	+	0.588700i
$755$	−37.9628			−1.38161
$756$		0			0
$757$	37.2695			1.35458			0.677291	−	0.735716i	$-0.263154\pi$
$757$	37.2695			1.35458			0.677291	+	0.735716i	$0.263154\pi$
$758$	0.935660	−	0.540204i	0.0339847	−	0.0196211i
$759$	−23.0013	−	0.317524i	−0.834895	−	0.0115254i
$760$	5.81594	−	10.0735i	0.210966	−	0.365405i
$761$	10.5435			0.382201			0.191100	−	0.981570i	$-0.438794\pi$
$761$	10.5435			0.382201			0.191100	+	0.981570i	$0.438794\pi$
$762$	60.1710	−	33.6410i	2.17976	−	1.21868i
$763$		0			0
$764$			35.9248i			1.29971i
$765$	−33.8775	−	62.6075i	−1.22484	−	2.26358i
$766$	23.8452	−	13.7671i	0.861563	−	0.497424i
$767$			12.5292i			0.452403i
$768$	−8.12511	+	13.6349i	−0.293190	+	0.492008i
$769$	−12.4720	+	7.20070i	−0.449751	+	0.259664i	−0.707725	−	0.706488i	$-0.750278\pi$
$769$	−12.4720	+	7.20070i	−0.449751	+	0.259664i	0.257974	+	0.966152i	$0.416945\pi$
$770$		0			0
$771$	37.2122	+	0.513699i	1.34016	+	0.0185004i
$772$	30.3199	+	52.5156i	1.09124	+	1.89008i
$773$	−10.9386	−	18.9462i	−0.393433	−	0.681446i	0.599467	−	0.800400i	$-0.295379\pi$
$773$	−10.9386	−	18.9462i	−0.393433	−	0.681446i	−0.992900	+	0.118954i	$0.962046\pi$
$774$	−1.01312	+	36.6882i	−0.0364160	+	1.31873i
$775$	−13.6669	−	7.89062i	−0.490931	−	0.283439i
$776$	3.92472	−	6.79781i	0.140889	−	0.244027i
$777$		0			0
$778$	−35.2493	−	61.0536i	−1.26375	−	2.18888i
$779$			5.42577i			0.194398i
$780$	−0.451803	+	32.7285i	−0.0161771	+	1.17187i
$781$	−5.50974			−0.197154
$782$	−37.3425	+	64.6792i	−1.33537	+	2.31292i
$783$	27.9068	+	17.6915i	0.997306	+	0.632243i
$784$		0			0
$785$	19.0759	+	11.0135i	0.680847	+	0.393087i
$786$	13.0809	−	7.31341i	0.466581	−	0.260861i
$787$	23.9804	+	13.8451i	0.854807	+	0.493523i	0.862270	−	0.506449i	$-0.169042\pi$
$787$	23.9804	+	13.8451i	0.854807	+	0.493523i	−0.00746275	+	0.999972i	$0.502375\pi$
$788$	8.49253	+	4.90316i	0.302534	+	0.174668i
$789$	0.265132	−	19.2061i	0.00943894	−	0.683754i
$790$	−29.8853	−	17.2543i	−1.06327	−	0.613880i
$791$		0			0
$792$	5.72780	+	0.158170i	0.203528	+	0.00562033i
$793$	−6.26160	+	10.8454i	−0.222356	+	0.385132i
$794$	17.8697			0.634171
$795$	−51.5747	+	28.8349i	−1.82917	+	1.02267i
$796$			51.5930i			1.82867i
$797$	21.3285	+	36.9420i	0.755493	+	1.30855i	0.945129	+	0.326697i	$0.105936\pi$
$797$	21.3285	+	36.9420i	0.755493	+	1.30855i	−0.189636	+	0.981854i	$0.560731\pi$
$798$		0			0
$799$	−17.5271	+	30.3578i	−0.620063	+	1.07398i
$800$	−41.4820	−	23.9496i	−1.46661	−	0.846747i
$801$	−1.70082	+	2.76661i	−0.0600954	+	0.0977533i
$802$	−16.8163	−	29.1267i	−0.593805	−	1.02850i
$803$	−10.6653	−	18.4729i	−0.376372	−	0.651895i
$804$	16.5077	+	29.5261i	0.582183	+	1.04130i
$805$		0			0
$806$	11.7360	−	6.77581i	0.413384	−	0.238668i
$807$	18.6438	+	33.3468i	0.656295	+	1.17386i
$808$			0.378870i			0.0133286i
$809$	30.9391	−	17.8627i	1.08776	−	0.628019i	0.154781	−	0.987949i	$-0.450533\pi$
$809$	30.9391	−	17.8627i	1.08776	−	0.628019i	0.932979	+	0.359930i	$0.117199\pi$
$810$	55.3146	−	27.9855i	1.94356	−	0.983312i
$811$		−	5.85377i		−	0.205554i	−0.994704	−	0.102777i	$-0.967227\pi$
$811$		−	5.85377i		−	0.205554i	0.994704	−	0.102777i	$-0.0327728\pi$
$812$		0			0
$813$	7.05915	+	4.20658i	0.247575	+	0.147531i
$814$	9.37226			0.328498
$815$	−38.1557	+	66.0875i	−1.33653	+	2.31495i
$816$	−20.3267	+	34.1107i	−0.711578	+	1.19411i
$817$	24.9309	−	14.3939i	0.872223	−	0.503578i
$818$	34.0227			1.18958
$819$		0			0
$820$	−8.57050			−0.299295
$821$	−15.2220	+	8.78841i	−0.531251	+	0.306718i	−0.741526	−	0.670925i	$-0.765897\pi$
$821$	−15.2220	+	8.78841i	−0.531251	+	0.306718i	0.210275	+	0.977642i	$0.432564\pi$
$822$	−11.0887	−	19.8334i	−0.386762	−	0.691771i
$823$	−15.1893	+	26.3086i	−0.529465	+	0.917060i	0.469945	+	0.882696i	$0.344274\pi$
$823$	−15.1893	+	26.3086i	−0.529465	+	0.917060i	−0.999409	+	0.0343640i	$0.989059\pi$
$824$	−0.562464			−0.0195943
$825$	0.376724	−	27.2898i	0.0131158	−	0.950107i
$826$		0			0
$827$		−	15.4454i		−	0.537089i	−0.963267	−	0.268545i	$-0.913457\pi$
$827$		−	15.4454i		−	0.537089i	0.963267	−	0.268545i	$-0.0865426\pi$
$828$	−29.8987	−	18.3807i	−1.03905	−	0.638773i
$829$	−35.4158	+	20.4473i	−1.23004	+	0.710164i	−0.967038	−	0.254631i	$-0.918046\pi$
$829$	−35.4158	+	20.4473i	−1.23004	+	0.710164i	−0.263002	+	0.964795i	$0.584713\pi$
$830$		−	14.3932i		−	0.499595i
$831$	−11.1301	−	0.153647i	−0.386099	−	0.00532994i
$832$	22.1318	−	12.7778i	0.767281	−	0.442990i
$833$		0			0
$834$	−2.82907	+	4.74752i	−0.0979627	+	0.164393i
$835$	26.2858	+	45.5283i	0.909657	+	1.57557i
$836$	−15.3000	−	26.5004i	−0.529162	−	0.916535i
$837$	−11.6974	−	7.41560i	−0.404323	−	0.256321i
$838$	2.12647	+	1.22772i	0.0734577	+	0.0424108i
$839$	16.8620	−	29.2058i	0.582140	−	1.00830i	−0.413086	−	0.910692i	$-0.635549\pi$
$839$	16.8620	−	29.2058i	0.582140	−	1.00830i	0.995225	−	0.0976035i	$-0.0311177\pi$
$840$		0			0
$841$	5.71808	+	9.90401i	0.197175	+	0.341517i
$842$			14.3210i			0.493534i
$843$	−29.3592	−	17.4953i	−1.01118	−	0.602568i
$844$	57.6356			1.98390
$845$	11.6487	−	20.1761i	0.400726	−	0.694079i
$846$	−26.0053	−	15.9872i	−0.894080	−	0.549650i
$847$		0			0
$848$	28.5440	+	16.4799i	0.980206	+	0.565922i
$849$	−8.33419	−	4.96638i	−0.286029	−	0.170446i
$850$	−76.7381	−	44.3048i	−2.63210	−	1.51964i
$851$	−7.30190	−	4.21575i	−0.250306	−	0.144514i
$852$	−7.22133	−	4.30322i	−0.247399	−	0.147426i
$853$	−37.6715	−	21.7497i	−1.28985	−	0.744694i	−0.311221	−	0.950337i	$-0.600738\pi$
$853$	−37.6715	−	21.7497i	−1.28985	−	0.744694i	−0.978627	+	0.205643i	$0.934071\pi$
$854$		0			0
$855$	−41.4219	−	25.4648i	−1.41660	−	0.870878i
$856$	−1.92008	+	3.32568i	−0.0656271	+	0.113669i
$857$	−8.43068			−0.287986			−0.143993	−	0.989579i	$-0.545994\pi$
$857$	−8.43068			−0.287986			−0.143993	+	0.989579i	$0.545994\pi$
$858$	20.1328	+	11.9972i	0.687324	+	0.409579i
$859$		−	2.40096i		−	0.0819197i	−0.999161	−	0.0409598i	$-0.986958\pi$
$859$		−	2.40096i		−	0.0819197i	0.999161	−	0.0409598i	$-0.0130416\pi$
$860$	22.7364	+	39.3807i	0.775306	+	1.34287i
$861$		0			0
$862$	0.845356	−	1.46420i	0.0287929	−	0.0498708i
$863$	−8.12017	−	4.68818i	−0.276414	−	0.159588i	0.355385	−	0.934720i	$-0.384350\pi$
$863$	−8.12017	−	4.68818i	−0.276414	−	0.159588i	−0.631799	+	0.775132i	$0.717683\pi$
$864$	−35.5041	−	22.5079i	−1.20787	−	0.765733i
$865$	30.8356	+	53.4089i	1.04844	+	1.81596i
$866$	8.95898	+	15.5174i	0.304439	+	0.527303i
$867$	−30.6402	+	51.4179i	−1.04059	+	1.74625i
$868$		0			0
$869$	−11.5472	+	6.66678i	−0.391712	+	0.226155i
$870$	75.8562	+	1.04716i	2.57176	+	0.0355022i
$871$			20.3214i			0.688566i
$872$	3.70751	−	2.14053i	0.125552	−	0.0724877i
$873$	−27.9524	−	17.1842i	−0.946045	−	0.581596i
$874$			51.0137i			1.72557i
$875$		0			0
$876$	0.449220	−	32.5413i	0.0151777	−	1.09947i
$877$	3.43084			0.115851			0.0579256	−	0.998321i	$-0.481551\pi$
$877$	3.43084			0.115851			0.0579256	+	0.998321i	$0.481551\pi$
$878$	−28.7568	+	49.8082i	−0.970493	+	1.68094i
$879$	25.4235	+	45.4730i	0.857513	+	1.53377i
$880$	−24.3183	+	14.0402i	−0.819770	+	0.473295i
$881$	−43.4962			−1.46542			−0.732712	−	0.680539i	$-0.761746\pi$
$881$	−43.4962			−1.46542			−0.732712	+	0.680539i	$0.761746\pi$
$882$		0			0
$883$	49.6074			1.66942			0.834711	−	0.550688i	$-0.185635\pi$
$883$	49.6074			1.66942			0.834711	+	0.550688i	$0.185635\pi$
$884$	35.5596	−	20.5303i	1.19600	−	0.690510i
$885$	15.0500	−	25.2557i	0.505900	−	0.848961i
$886$	−12.7619	+	22.1043i	−0.428745	+	0.742607i
$887$	−35.1532			−1.18033			−0.590164	−	0.807283i	$-0.700937\pi$
$887$	−35.1532			−1.18033			−0.590164	+	0.807283i	$0.700937\pi$
$888$	1.80417	+	1.07511i	0.0605441	+	0.0360785i
$889$		0			0
$890$			7.45638i			0.249938i
$891$	1.32185	−	23.9159i	0.0442838	−	0.801212i
$892$	−17.1583	+	9.90634i	−0.574502	+	0.331689i
$893$			23.9438i			0.801248i
$894$	9.42201	+	16.8524i	0.315119	+	0.563629i
$895$	63.0500	−	36.4019i	2.10753	−	1.21678i
$896$		0			0
$897$	−10.2889	−	18.4030i	−0.343537	−	0.614458i
$898$	−22.9443	−	39.7407i	−0.765662	−	1.32617i
$899$	−8.47464	−	14.6785i	−0.282645	−	0.489556i
$900$	21.8076	−	35.4730i	0.726920	−	1.18243i
$901$	64.1932	+	37.0620i	2.13859	+	1.23471i
$902$	−3.06832	+	5.31448i	−0.102164	+	0.176953i
$903$		0			0
$904$	4.14446	+	7.17842i	0.137843	+	0.238751i
$905$		−	58.4876i		−	1.94419i
$906$	−36.1985	+	20.2382i	−1.20262	+	0.672370i
$907$	38.1633			1.26719			0.633596	−	0.773664i	$-0.281578\pi$
$907$	38.1633			1.26719			0.633596	+	0.773664i	$0.281578\pi$
$908$	6.83310	−	11.8353i	0.226765	−	0.392768i
$909$	1.58314	+	0.0437176i	0.0525095	+	0.00145002i
$910$		0			0
$911$	−39.9027	−	23.0378i	−1.32203	−	0.763277i	−0.337981	−	0.941153i	$-0.609744\pi$
$911$	−39.9027	−	23.0378i	−1.32203	−	0.763277i	−0.984053	+	0.177876i	$0.943077\pi$
$912$	−0.374380	+	27.1200i	−0.0123970	+	0.898031i
$913$	−4.81623	−	2.78065i	−0.159394	−	0.0920261i
$914$	43.6028	+	25.1741i	1.44225	+	0.832686i
$915$	25.6493	−	14.3402i	0.847939	−	0.474074i
$916$	9.74163	+	5.62433i	0.321872	+	0.185833i
$917$		0			0
$918$	−65.6796	−	41.6376i	−2.16775	−	1.37425i
$919$	−5.27574	+	9.13785i	−0.174031	+	0.301430i	−0.939825	−	0.341655i	$-0.889013\pi$
$919$	−5.27574	+	9.13785i	−0.174031	+	0.301430i	0.765795	+	0.643085i	$0.222346\pi$
$920$	−11.8353			−0.390198
$921$	0.560636	−	40.6122i	0.0184736	−	1.33822i
$922$		−	68.3229i		−	2.25009i
$923$	−2.52499	−	4.37340i	−0.0831109	−	0.143952i
$924$		0			0
$925$	5.00175	−	8.66328i	0.164456	−	0.284847i
$926$	−56.9168	−	32.8609i	−1.87040	−	1.07988i
$927$	−0.0649024	+	2.35030i	−0.00213167	+	0.0771941i
$928$	−25.7223	−	44.5523i	−0.844375	−	1.46250i
$929$	26.4514	+	45.8152i	0.867843	+	1.50315i	0.864196	+	0.503155i	$0.167828\pi$
$929$	26.4514	+	45.8152i	0.867843	+	1.50315i	0.00364718	+	0.999993i	$0.498839\pi$
$930$	−31.7960	−	0.438931i	−1.04263	−	0.0143931i
$931$		0			0
$932$	−46.7896	+	27.0140i	−1.53265	+	0.884873i
$933$	14.8160	−	24.8631i	0.485055	−	0.813981i
$934$		−	69.1010i		−	2.26106i
$935$	−54.6899	+	31.5752i	−1.78855	+	1.03262i
$936$	2.49937	+	4.61897i	0.0816944	+	0.150976i
$937$			10.3265i			0.337353i	0.985671	+	0.168676i	$0.0539493\pi$
$937$			10.3265i			0.337353i	−0.985671	+	0.168676i	$0.946051\pi$
$938$		0			0
$939$	−22.4769	+	12.5666i	−0.733507	+	0.410096i
$940$	−37.8214			−1.23360
$941$	−0.505336	+	0.875268i	−0.0164735	+	0.0285329i	−0.874145	−	0.485666i	$-0.838577\pi$
$941$	−0.505336	+	0.875268i	−0.0164735	+	0.0285329i	0.857671	+	0.514199i	$0.171911\pi$
$942$	24.0607	+	0.332148i	0.783940	+	0.0108220i
$943$	4.78103	−	2.76033i	0.155692	−	0.0898887i
$944$	−16.3995			−0.533758
$945$		0			0
$946$	32.5594			1.05860
$947$	−9.36454	+	5.40662i	−0.304307	+	0.175692i	−0.644376	−	0.764709i	$-0.722883\pi$
$947$	−9.36454	+	5.40662i	−0.304307	+	0.175692i	0.340069	+	0.940400i	$0.389549\pi$
$948$	−20.3412	−	0.280802i	−0.660652	−	0.00912003i
$949$	9.77535	−	16.9314i	0.317321	−	0.549616i
$950$	−60.5249			−1.96369
$951$	−3.43483	+	1.92038i	−0.111382	+	0.0622725i
$952$		0			0
$953$			26.7466i			0.866408i	0.901296	+	0.433204i	$0.142617\pi$
$953$			26.7466i			0.866408i	−0.901296	+	0.433204i	$0.857383\pi$
$954$	−33.8058	+	54.9896i	−1.09450	+	1.78036i
$955$	43.8564	−	25.3205i	1.41916	−	0.819353i
$956$		−	16.0246i		−	0.518274i
$957$	15.0052	−	25.1806i	0.485049	−	0.813972i
$958$	41.1454	−	23.7553i	1.32935	−	0.767500i
$959$		0			0
$960$	−59.9607	−	0.827734i	−1.93522	−	0.0267150i
$961$	−11.9478	−	20.6941i	−0.385411	−	0.667552i
$962$	4.29509	+	7.43931i	0.138479	+	0.239853i
$963$	13.6751	+	8.40699i	0.440674	+	0.270911i
$964$	9.12204	+	5.26661i	0.293801	+	0.169626i
$965$	42.7402	−	74.0281i	1.37585	−	2.38305i
$966$		0			0
$967$	1.62313	+	2.81134i	0.0521962	+	0.0904065i	0.890943	−	0.454115i	$-0.150045\pi$
$967$	1.62313	+	2.81134i	0.0521962	+	0.0904065i	−0.838747	+	0.544522i	$0.816711\pi$
$968$			2.81119i			0.0903549i
$969$	−0.841950	+	60.9906i	−0.0270473	+	1.95930i
$970$	−75.3354			−2.41887
$971$	−4.41423	+	7.64567i	−0.141659	+	0.245361i	−0.928122	−	0.372277i	$-0.878577\pi$
$971$	−4.41423	+	7.64567i	−0.141659	+	0.245361i	0.786462	+	0.617638i	$0.211910\pi$
$972$	20.4113	−	30.3129i	0.654692	−	0.972286i
$973$		0			0
$974$	−4.92997	−	2.84632i	−0.157966	−	0.0912019i
$975$	21.8341	−	12.2072i	0.699251	−	0.390944i
$976$	−14.1956	−	8.19584i	−0.454390	−	0.262342i
$977$	−36.2748	−	20.9433i	−1.16053	−	0.670035i	−0.209102	−	0.977894i	$-0.567054\pi$
$977$	−36.2748	−	20.9433i	−1.16053	−	0.670035i	−0.951432	+	0.307859i	$0.900388\pi$
$978$	−1.15071	+	83.3573i	−0.0367958	+	2.66547i
$979$	2.49504	+	1.44051i	0.0797419	+	0.0460390i
$980$		0			0
$981$	−8.51661	−	15.7392i	−0.271914	−	0.502513i
$982$	−26.0861	+	45.1825i	−0.832441	+	1.44183i
$983$	−4.70388			−0.150031			−0.0750153	−	0.997182i	$-0.523901\pi$
$983$	−4.70388			−0.150031			−0.0750153	+	0.997182i	$0.523901\pi$
$984$	−1.20029	+	0.671071i	−0.0382639	+	0.0213929i
$985$		−	13.8234i		−	0.440450i
$986$	−47.5840	−	82.4179i	−1.51538	−	2.62472i
$987$		0			0
$988$	14.0233	−	24.2890i	0.446139	−	0.772736i
$989$	−25.3669	−	14.6456i	−0.806621	−	0.465703i
$990$	−26.1718	−	48.3669i	−0.831793	−	1.53720i
$991$	−18.9327	−	32.7924i	−0.601418	−	1.04169i	−0.992607	−	0.121375i	$-0.961269\pi$
$991$	−18.9327	−	32.7924i	−0.601418	−	1.04169i	0.391189	−	0.920310i	$-0.372064\pi$
$992$	10.7818	+	18.6746i	0.342322	+	0.592919i
$993$	10.0996	+	18.0643i	0.320500	+	0.573254i
$994$		0			0
$995$	62.9840	−	36.3638i	1.99673	−	1.15281i
$996$	−4.14063	−	7.40603i	−0.131201	−	0.234669i
$997$			3.67583i			0.116415i	0.998305	+	0.0582073i	$0.0185384\pi$
$997$			3.67583i			0.116415i	−0.998305	+	0.0582073i	$0.981462\pi$
$998$	−15.5228	+	8.96211i	−0.491367	+	0.283691i
$999$	4.70064	−	7.41484i	0.148722	−	0.234595i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.s.d.362.4		48
3.2	odd	2		1323.2.s.d.656.22		48
7.2	even	3		441.2.o.e.146.21	✓	48
7.3	odd	6		441.2.i.d.227.4		48
7.4	even	3		441.2.i.d.227.3		48
7.5	odd	6		441.2.o.e.146.22	yes	48
7.6	odd	2	inner	441.2.s.d.362.3		48
9.4	even	3		1323.2.i.d.1097.16		48
9.5	odd	6		441.2.i.d.68.22		48
21.2	odd	6		1323.2.o.e.440.3		48
21.5	even	6		1323.2.o.e.440.4		48
21.11	odd	6		1323.2.i.d.521.23		48
21.17	even	6		1323.2.i.d.521.16		48
21.20	even	2		1323.2.s.d.656.21		48
63.4	even	3		1323.2.s.d.962.21		48
63.5	even	6		441.2.o.e.293.21	yes	48
63.13	odd	6		1323.2.i.d.1097.23		48
63.23	odd	6		441.2.o.e.293.22	yes	48
63.31	odd	6		1323.2.s.d.962.22		48
63.32	odd	6	inner	441.2.s.d.374.3		48
63.40	odd	6		1323.2.o.e.881.3		48
63.41	even	6		441.2.i.d.68.21		48
63.58	even	3		1323.2.o.e.881.4		48
63.59	even	6	inner	441.2.s.d.374.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.21		48	63.41	even	6
441.2.i.d.68.22		48	9.5	odd	6
441.2.i.d.227.3		48	7.4	even	3
441.2.i.d.227.4		48	7.3	odd	6
441.2.o.e.146.21	✓	48	7.2	even	3
441.2.o.e.146.22	yes	48	7.5	odd	6
441.2.o.e.293.21	yes	48	63.5	even	6
441.2.o.e.293.22	yes	48	63.23	odd	6
441.2.s.d.362.3		48	7.6	odd	2	inner
441.2.s.d.362.4		48	1.1	even	1	trivial
441.2.s.d.374.3		48	63.32	odd	6	inner
441.2.s.d.374.4		48	63.59	even	6	inner
1323.2.i.d.521.16		48	21.17	even	6
1323.2.i.d.521.23		48	21.11	odd	6
1323.2.i.d.1097.16		48	9.4	even	3
1323.2.i.d.1097.23		48	63.13	odd	6
1323.2.o.e.440.3		48	21.2	odd	6
1323.2.o.e.440.4		48	21.5	even	6
1323.2.o.e.881.3		48	63.40	odd	6
1323.2.o.e.881.4		48	63.58	even	3
1323.2.s.d.656.21		48	21.20	even	2
1323.2.s.d.656.22		48	3.2	odd	2
1323.2.s.d.962.21		48	63.4	even	3
1323.2.s.d.962.22		48	63.31	odd	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.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.80506 + 1.04215i) q^{2} +(1.73189 + 0.0239080i) q^{3} +(1.17216 - 2.03024i) q^{4} -3.30465 q^{5} +(-3.15107 + 1.76173i) q^{6} +0.717672i q^{8} +(2.99886 + 0.0828118i) q^{9} +O(q^{10})\)	\(q+(-1.80506 + 1.04215i) q^{2} +(1.73189 + 0.0239080i) q^{3} +(1.17216 - 2.03024i) q^{4} -3.30465 q^{5} +(-3.15107 + 1.76173i) q^{6} +0.717672i q^{8} +(2.99886 + 0.0828118i) q^{9} +(5.96509 - 3.44395i) q^{10} -2.66137i q^{11} +(2.07859 - 3.48812i) q^{12} +(2.11249 - 1.21964i) q^{13} +(-5.72328 - 0.0790075i) q^{15} +(1.59640 + 2.76504i) q^{16} +(3.59017 + 6.21836i) q^{17} +(-5.49942 + 2.97578i) q^{18} +(4.24746 + 2.45227i) q^{19} +(-3.87358 + 6.70924i) q^{20} +(2.77356 + 4.80394i) q^{22} -4.99031i q^{23} +(-0.0171581 + 1.24293i) q^{24} +5.92072 q^{25} +(-2.54211 + 4.40306i) q^{26} +(5.19170 + 0.215117i) q^{27} +(5.50701 + 3.17947i) q^{29} +(10.4132 - 5.82191i) q^{30} +(-2.30833 - 1.33271i) q^{31} +(-7.00624 - 4.04505i) q^{32} +(0.0636281 - 4.60920i) q^{33} +(-12.9609 - 7.48301i) q^{34} +(3.68327 - 5.99134i) q^{36} +(0.844787 - 1.46321i) q^{37} -10.2226 q^{38} +(3.68775 - 2.06178i) q^{39} -2.37166i q^{40} +(0.553137 + 0.958062i) q^{41} +(2.93481 - 5.08323i) q^{43} +(-5.40324 - 3.11956i) q^{44} +(-9.91018 - 0.273664i) q^{45} +(5.20066 + 9.00781i) q^{46} +(2.44098 + 4.22790i) q^{47} +(2.69867 + 4.82691i) q^{48} +(-10.6873 + 6.17029i) q^{50} +(6.06910 + 10.8553i) q^{51} -5.71848i q^{52} +(8.94013 - 5.16159i) q^{53} +(-9.59551 + 5.02224i) q^{54} +8.79491i q^{55} +(7.29748 + 4.34860i) q^{57} -13.2540 q^{58} +(-2.56820 + 4.44826i) q^{59} +(-6.86901 + 11.5270i) q^{60} +(-4.44613 + 2.56698i) q^{61} +5.55556 q^{62} +10.4766 q^{64} +(-6.98103 + 4.03050i) q^{65} +(4.68863 + 8.38619i) q^{66} +(-4.16544 + 7.21476i) q^{67} +16.8330 q^{68} +(0.119308 - 8.64265i) q^{69} -2.07026i q^{71} +(-0.0594317 + 2.15220i) q^{72} +(6.94112 - 4.00746i) q^{73} +3.52159i q^{74} +(10.2540 + 0.141552i) q^{75} +(9.95741 - 5.74891i) q^{76} +(-4.50791 + 7.56483i) q^{78} +(-2.50501 - 4.33881i) q^{79} +(-5.27554 - 9.13750i) q^{80} +(8.98628 + 0.496681i) q^{81} +(-1.99689 - 1.15291i) q^{82} +(1.04482 - 1.80968i) q^{83} +(-11.8643 - 20.5495i) q^{85} +12.2341i q^{86} +(9.46149 + 5.63814i) q^{87} +1.90999 q^{88} +(-0.541267 + 0.937501i) q^{89} +(18.1737 - 9.83393i) q^{90} +(-10.1315 - 5.84945i) q^{92} +(-3.96589 - 2.36329i) q^{93} +(-8.81223 - 5.08774i) q^{94} +(-14.0364 - 8.10390i) q^{95} +(-12.0373 - 7.17307i) q^{96} +(-9.47203 - 5.46868i) q^{97} +(0.220393 - 7.98108i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4} - 8 q^{9}+O(q^{10}) \) 48 * q + 24 * q^4 - 8 * q^9	\( 48 q + 24 q^{4} - 8 q^{9} - 40 q^{15} - 24 q^{16} + 32 q^{18} + 48 q^{25} + 48 q^{30} - 120 q^{32} - 8 q^{36} - 32 q^{39} + 96 q^{44} + 48 q^{50} + 48 q^{53} + 80 q^{57} - 72 q^{60} - 48 q^{64} - 120 q^{65} + 32 q^{72} - 88 q^{78} - 24 q^{79} + 120 q^{81} - 24 q^{85} - 144 q^{92} + 16 q^{93} - 96 q^{95} - 72 q^{99}+O(q^{100}) \) 48 * q + 24 * q^4 - 8 * q^9 - 40 * q^15 - 24 * q^16 + 32 * q^18 + 48 * q^25 + 48 * q^30 - 120 * q^32 - 8 * q^36 - 32 * q^39 + 96 * q^44 + 48 * q^50 + 48 * q^53 + 80 * q^57 - 72 * q^60 - 48 * q^64 - 120 * q^65 + 32 * q^72 - 88 * q^78 - 24 * q^79 + 120 * q^81 - 24 * q^85 - 144 * q^92 + 16 * q^93 - 96 * q^95 - 72 * q^99

Introduction

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