LMFDB - Embedded newform 1323.2.o.e.881.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(440,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("1323.440");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 441)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			881.4
Character	$\chi$	$=$	1323.881
Dual form			1323.2.o.e.440.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.80506 + 1.04215i) q^{2} +(1.17216 - 2.03024i) q^{4} +(1.65233 - 2.86191i) q^{5} +0.717672i q^{8} +O(q^{10})$	\(q+(-1.80506 + 1.04215i) q^{2} +(1.17216 - 2.03024i) q^{4} +(1.65233 - 2.86191i) q^{5} +0.717672i q^{8} +6.88790i q^{10} +(-2.30482 + 1.33069i) q^{11} +(-2.11249 - 1.21964i) q^{13} +(1.59640 + 2.76504i) q^{16} -7.18034 q^{17} -4.90454i q^{19} +(-3.87358 - 6.70924i) q^{20} +(2.77356 - 4.80394i) q^{22} +(4.32174 + 2.49516i) q^{23} +(-2.96036 - 5.12749i) q^{25} +5.08422 q^{26} +(-5.50701 + 3.17947i) q^{29} +(-2.30833 - 1.33271i) q^{31} +(-7.00624 - 4.04505i) q^{32} +(12.9609 - 7.48301i) q^{34} -1.68957 q^{37} +(5.11128 + 8.85299i) q^{38} +(2.05391 + 1.18583i) q^{40} +(0.553137 - 0.958062i) q^{41} +(2.93481 + 5.08323i) q^{43} +6.23912i q^{44} -10.4013 q^{46} +(2.44098 + 4.22790i) q^{47} +(10.6873 + 6.17029i) q^{50} +(-4.95235 + 2.85924i) q^{52} +10.3232i q^{53} +8.79491i q^{55} +(6.62698 - 11.4783i) q^{58} +(-2.56820 + 4.44826i) q^{59} +(-4.44613 + 2.56698i) q^{61} +5.55556 q^{62} +10.4766 q^{64} +(-6.98103 + 4.03050i) q^{65} +(-4.16544 + 7.21476i) q^{67} +(-8.41652 + 14.5778i) q^{68} -2.07026i q^{71} +8.01491i q^{73} +(3.04978 - 1.76079i) q^{74} +(-9.95741 - 5.74891i) q^{76} +(-2.50501 - 4.33881i) q^{79} +10.5511 q^{80} +2.30581i q^{82} +(1.04482 + 1.80968i) q^{83} +(-11.8643 + 20.5495i) q^{85} +(-10.5950 - 6.11703i) q^{86} +(-0.954997 - 1.65410i) q^{88} +1.08253 q^{89} +(10.1315 - 5.84945i) q^{92} +(-8.81223 - 5.08774i) q^{94} +(-14.0364 - 8.10390i) q^{95} +(9.47203 - 5.46868i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4}+O(q^{10}) $ 48 * q + 24 * q^4	$ 48 q + 24 q^{4} + 24 q^{11} - 24 q^{16} + 48 q^{23} - 24 q^{25} - 120 q^{32} - 48 q^{50} - 48 q^{64} - 120 q^{65} + 168 q^{74} - 24 q^{79} - 24 q^{85} - 24 q^{86} + 144 q^{92} - 96 q^{95}+O(q^{100}) $ 48 * q + 24 * q^4 + 24 * q^11 - 24 * q^16 + 48 * q^23 - 24 * q^25 - 120 * q^32 - 48 * q^50 - 48 * q^64 - 120 * q^65 + 168 * q^74 - 24 * q^79 - 24 * q^85 - 24 * q^86 + 144 * q^92 - 96 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

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	$0.597050\pi$
$3$		0			0
$3$		0			0
$4$	1.17216	−	2.03024i	0.586081	−	1.01512i
$5$	1.65233	−	2.86191i	0.738942	−	1.27989i	−0.214029	−	0.976827i	$-0.568659\pi$
$5$	1.65233	−	2.86191i	0.738942	−	1.27989i	0.952972	−	0.303059i	$-0.0980078\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			0.717672i			0.253735i
$9$		0			0
$10$			6.88790i			2.17814i
$11$	−2.30482	+	1.33069i	−0.694929	+	0.401217i	−0.805456	−	0.592656i	$-0.798079\pi$
$11$	−2.30482	+	1.33069i	−0.694929	+	0.401217i	0.110527	+	0.993873i	$0.464746\pi$
$12$		0			0
$13$	−2.11249	−	1.21964i	−0.585899	−	0.338269i	0.177576	−	0.984107i	$-0.443175\pi$
$13$	−2.11249	−	1.21964i	−0.585899	−	0.338269i	−0.763474	+	0.645839i	$0.776508\pi$
$14$		0			0
$15$		0			0
$16$	1.59640	+	2.76504i	0.399100	+	0.691261i
$17$	−7.18034			−1.74149			−0.870744	−	0.491736i	$-0.836363\pi$
$17$	−7.18034			−1.74149			−0.870744	+	0.491736i	$0.836363\pi$
$18$		0			0
$19$		−	4.90454i		−	1.12518i	−0.826736	−	0.562589i	$-0.809805\pi$
$19$		−	4.90454i		−	1.12518i	0.826736	−	0.562589i	$-0.190195\pi$
$20$	−3.87358	−	6.70924i	−0.866160	−	1.50023i
$21$		0			0
$22$	2.77356	−	4.80394i	0.591324	−	1.02420i
$23$	4.32174	+	2.49516i	0.901145	+	0.520276i	0.877571	−	0.479446i	$-0.159162\pi$
$23$	4.32174	+	2.49516i	0.901145	+	0.520276i	0.0235732	+	0.999722i	$0.492496\pi$
$24$		0			0
$25$	−2.96036	−	5.12749i	−0.592072	−	1.02550i
$26$	5.08422			0.997098
$27$		0			0
$28$		0			0
$29$	−5.50701	+	3.17947i	−1.02263	+	0.590413i	−0.914863	−	0.403764i	$-0.867702\pi$
$29$	−5.50701	+	3.17947i	−1.02263	+	0.590413i	−0.107762	+	0.994177i	$0.534368\pi$
$30$		0			0
$31$	−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			0
$34$	12.9609	−	7.48301i	2.22278	−	1.28333i
$35$		0			0
$36$		0			0
$37$	−1.68957			−0.277764			−0.138882	−	0.990309i	$-0.544351\pi$
$37$	−1.68957			−0.277764			−0.138882	+	0.990309i	$0.544351\pi$
$38$	5.11128	+	8.85299i	0.829159	+	1.43614i
$39$		0			0
$40$	2.05391	+	1.18583i	0.324752	+	0.187496i
$41$	0.553137	−	0.958062i	0.0863855	−	0.149624i	−0.819595	−	0.572943i	$-0.805802\pi$
$41$	0.553137	−	0.958062i	0.0863855	−	0.149624i	0.905981	+	0.423319i	$0.139135\pi$
$42$		0			0
$43$	2.93481	+	5.08323i	0.447554	+	0.775186i	0.998226	−	0.0595356i	$-0.0189620\pi$
$43$	2.93481	+	5.08323i	0.447554	+	0.775186i	−0.550672	+	0.834721i	$0.685629\pi$
$44$			6.23912i			0.940582i
$45$		0			0
$46$	−10.4013			−1.53359
$47$	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	$0.717455\pi$
$48$		0			0
$49$		0			0
$50$	10.6873	+	6.17029i	1.51141	+	0.872610i
$51$		0			0
$52$	−4.95235	+	2.85924i	−0.686767	+	0.396505i
$53$			10.3232i			1.41800i	0.705210	+	0.708999i	$0.250853\pi$
$53$			10.3232i			1.41800i	−0.705210	+	0.708999i	$0.749147\pi$
$54$		0			0
$55$			8.79491i			1.18591i
$56$		0			0
$57$		0			0
$58$	6.62698	−	11.4783i	0.870166	−	1.50717i
$59$	−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	$0.275184\pi$
$60$		0			0
$61$	−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
$66$		0			0
$67$	−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	$0.996723\pi$
$68$	−8.41652	+	14.5778i	−1.02065	+	1.76782i
$69$		0			0
$70$		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			0
$73$			8.01491i			0.938075i	0.883178	+	0.469037i	$0.155399\pi$
$73$			8.01491i			0.938075i	−0.883178	+	0.469037i	$0.844601\pi$
$74$	3.04978	−	1.76079i	0.354530	−	0.204688i
$75$		0			0
$76$	−9.95741	−	5.74891i	−1.14219	−	0.659445i
$77$		0			0
$78$		0			0
$79$	−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	$0.924277\pi$
$80$	10.5511			1.17965
$81$		0			0
$82$			2.30581i			0.254634i
$83$	1.04482	+	1.80968i	0.114684	+	0.198638i	0.917653	−	0.397382i	$-0.130081\pi$
$83$	1.04482	+	1.80968i	0.114684	+	0.198638i	−0.802970	+	0.596020i	$0.796748\pi$
$84$		0			0
$85$	−11.8643	+	20.5495i	−1.28686	+	2.22891i
$86$	−10.5950	−	6.11703i	−1.14249	−	0.659616i
$87$		0			0
$88$	−0.954997	−	1.65410i	−0.101803	−	0.176328i
$89$	1.08253			0.114748			0.0573741	−	0.998353i	$-0.481727\pi$
$89$	1.08253			0.114748			0.0573741	+	0.998353i	$0.481727\pi$
$90$		0			0
$91$		0			0
$92$	10.1315	−	5.84945i	1.05629	−	0.609847i
$93$		0			0
$94$	−8.81223	−	5.08774i	−0.908912	−	0.524761i
$95$	−14.0364	−	8.10390i	−1.44010	−	0.831442i
$96$		0			0
$97$	9.47203	−	5.46868i	0.961739	−	0.555260i	0.0650310	−	0.997883i	$-0.479285\pi$
$97$	9.47203	−	5.46868i	0.961739	−	0.555260i	0.896708	+	0.442623i	$0.145952\pi$
$98$		0			0
$99$		0			0
$100$	−13.8801			−1.38801
$101$	−0.263957	−	0.457188i	−0.0262647	−	0.0454919i	0.852594	−	0.522573i	$-0.175028\pi$
$101$	−0.263957	−	0.457188i	−0.0262647	−	0.0454919i	−0.878859	+	0.477082i	$0.841695\pi$
$102$		0			0
$103$	−0.678733	−	0.391867i	−0.0668775	−	0.0386118i	0.466188	−	0.884685i	$-0.345627\pi$
$103$	−0.678733	−	0.391867i	−0.0668775	−	0.0386118i	−0.533066	+	0.846074i	$0.678960\pi$
$104$	0.875305	−	1.51607i	0.0858308	−	0.148663i
$105$		0			0
$106$	−10.7583	−	18.6340i	−1.04494	−	1.80989i
$107$		−	5.35086i		−	0.517288i	−0.965973	−	0.258644i	$-0.916724\pi$
$107$		−	5.35086i		−	0.517288i	0.965973	−	0.258644i	$-0.0832756\pi$
$108$		0			0
$109$	5.96522			0.571364			0.285682	−	0.958324i	$-0.407780\pi$
$109$	5.96522			0.571364			0.285682	+	0.958324i	$0.407780\pi$
$110$	−9.16563	−	15.8753i	−0.873909	−	1.51365i
$111$		0			0
$112$		0			0
$113$	−10.0024	−	5.77487i	−0.940944	−	0.543254i	−0.0506876	−	0.998715i	$-0.516141\pi$
$113$	−10.0024	−	5.77487i	−0.940944	−	0.543254i	−0.890256	+	0.455461i	$0.849475\pi$
$114$		0			0
$115$	14.2818	−	8.24562i	1.33179	−	0.768908i
$116$			14.9074i			1.38412i
$117$		0			0
$118$		−	10.7058i		−	0.985551i
$119$		0			0
$120$		0			0
$121$	−1.95854	+	3.39230i	−0.178049	+	0.308391i
$122$	5.35036	−	9.26709i	0.484399	−	0.839003i
$123$		0			0
$124$	−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
$129$		0			0
$130$	8.40079	−	14.5506i	0.736798	−	1.27617i
$131$	2.07563	−	3.59509i	0.181349	−	0.314105i	−0.760991	−	0.648762i	$-0.775287\pi$
$131$	2.07563	−	3.59509i	0.181349	−	0.314105i	0.942340	+	0.334657i	$0.108620\pi$
$132$		0			0
$133$		0			0
$134$		−	17.3641i		−	1.50003i
$135$		0			0
$136$		−	5.15313i		−	0.441877i
$137$	5.45092	−	3.14709i	0.465704	−	0.268874i	−0.248736	−	0.968571i	$-0.580015\pi$
$137$	5.45092	−	3.14709i	0.465704	−	0.268874i	0.714440	+	0.699697i	$0.246682\pi$
$138$		0			0
$139$	−1.32575	−	0.765423i	−0.112449	−	0.0649223i	0.442721	−	0.896660i	$-0.354013\pi$
$139$	−1.32575	−	0.765423i	−0.112449	−	0.0649223i	−0.555170	+	0.831737i	$0.687347\pi$
$140$		0			0
$141$		0			0
$142$	2.15753	+	3.73695i	0.181056	+	0.313598i
$143$	6.49186			0.542877
$144$		0			0
$145$			21.0141i			1.74513i
$146$	−8.35276	−	14.4674i	−0.691279	−	1.19733i
$147$		0			0
$148$	−1.98045	+	3.43025i	−0.162792	+	0.281965i
$149$	4.63163	+	2.67407i	0.379438	+	0.219069i	0.677574	−	0.735455i	$-0.263031\pi$
$149$	4.63163	+	2.67407i	0.379438	+	0.219069i	−0.298136	+	0.954523i	$0.596365\pi$
$150$		0			0
$151$	−5.74384	−	9.94862i	−0.467427	−	0.809607i	0.531880	−	0.846820i	$-0.321486\pi$
$151$	−5.74384	−	9.94862i	−0.467427	−	0.809607i	−0.999307	+	0.0372121i	$0.988152\pi$
$152$	3.51985			0.285498
$153$		0			0
$154$		0			0
$155$	−7.62821	+	4.40415i	−0.612713	+	0.353750i
$156$		0			0
$157$	−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
$159$		0			0
$160$	−23.1532	+	13.3675i	−1.83042	+	1.05679i
$161$		0			0
$162$		0			0
$163$	−23.0921			−1.80871			−0.904356	−	0.426778i	$-0.859649\pi$
$163$	−23.0921			−1.80871			−0.904356	+	0.426778i	$0.859649\pi$
$164$	−1.29673	−	2.24601i	−0.101258	−	0.175384i
$165$		0			0
$166$	−3.77192	−	2.17772i	−0.292757	−	0.169024i
$167$	−7.95418	+	13.7770i	−0.615513	+	1.06610i	0.374782	+	0.927113i	$0.377718\pi$
$167$	−7.95418	+	13.7770i	−0.615513	+	1.06610i	−0.990294	+	0.138986i	$0.955616\pi$
$168$		0			0
$169$	−3.52493	−	6.10536i	−0.271149	−	0.469643i
$170$		−	49.4575i		−	3.79321i
$171$		0			0
$172$	13.7603			1.04921
$173$	−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	$-0.417710\pi$
$174$		0			0
$175$		0			0
$176$	−7.35882	−	4.24861i	−0.554692	−	0.320251i
$177$		0			0
$178$	−1.95404	+	1.12816i	−0.146461	+	0.0845595i
$179$		−	22.0307i		−	1.64665i	−0.567568	−	0.823326i	$-0.692116\pi$
$179$		−	22.0307i		−	1.64665i	0.567568	−	0.823326i	$-0.307884\pi$
$180$		0			0
$181$			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
$183$		0			0
$184$	−1.79070	+	3.10159i	−0.132012	+	0.228652i
$185$	−2.79173	+	4.83541i	−0.205252	+	0.355507i
$186$		0			0
$187$	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	$0.520389\pi$
$192$		0			0
$193$	−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	$0.785638\pi$
$194$	−11.3984	+	19.7426i	−0.818356	+	1.41744i
$195$		0			0
$196$		0			0
$197$			4.18301i			0.298027i	0.988835	+	0.149014i	$0.0476098\pi$
$197$			4.18301i			0.298027i	−0.988835	+	0.149014i	$0.952390\pi$
$198$		0			0
$199$		−	22.0077i		−	1.56008i	−0.625729	−	0.780041i	$-0.715198\pi$
$199$		−	22.0077i		−	1.56008i	0.625729	−	0.780041i	$-0.284802\pi$
$200$	3.67986	−	2.12457i	0.260205	−	0.150230i
$201$		0			0
$202$	0.952918	+	0.550168i	0.0670471	+	0.0387097i
$203$		0			0
$204$		0			0
$205$	−1.82793	−	3.16606i	−0.127668	−	0.221127i
$206$	1.63354			0.113814
$207$		0			0
$208$		−	7.78816i		−	0.540012i
$209$	6.52641	+	11.3041i	0.451441	+	0.781919i
$210$		0			0
$211$	12.2926	−	21.2914i	0.846257	−	1.46576i	−0.0382677	−	0.999268i	$-0.512184\pi$
$211$	12.2926	−	21.2914i	0.846257	−	1.46576i	0.884525	−	0.466493i	$-0.154483\pi$
$212$	20.9586	+	12.1004i	1.43944	+	0.831061i
$213$		0			0
$214$	5.57641	+	9.65863i	0.381196	+	0.660250i
$215$	19.3970			1.32287
$216$		0			0
$217$		0			0
$218$	−10.7676	+	6.21666i	−0.729272	+	0.421045i
$219$		0			0
$220$	17.8558	+	10.3091i	1.20384	+	0.695036i
$221$	15.1684	+	8.75747i	1.02034	+	0.589091i
$222$		0			0
$223$	7.31908	−	4.22567i	0.490122	−	0.282972i	−0.234503	−	0.972115i	$-0.575346\pi$
$223$	7.31908	−	4.22567i	0.490122	−	0.282972i	0.724625	+	0.689143i	$0.242013\pi$
$224$		0			0
$225$		0			0
$226$	24.0732			1.60132
$227$	−2.91475	−	5.04849i	−0.193458	−	0.335080i	0.752936	−	0.658094i	$-0.228637\pi$
$227$	−2.91475	−	5.04849i	−0.193458	−	0.335080i	−0.946394	+	0.323014i	$0.895304\pi$
$228$		0			0
$229$	−4.15541	−	2.39913i	−0.274597	−	0.158539i	0.356378	−	0.934342i	$-0.384012\pi$
$229$	−4.15541	−	2.39913i	−0.274597	−	0.158539i	−0.630975	+	0.775803i	$0.717345\pi$
$230$	−17.1864	+	29.7677i	−1.13324	+	1.96282i
$231$		0			0
$232$	−2.28182	−	3.95223i	−0.149809	−	0.259476i
$233$			23.0463i			1.50981i	0.655831	+	0.754907i	$0.272318\pi$
$233$			23.0463i			1.50981i	−0.655831	+	0.754907i	$0.727682\pi$
$234$		0			0
$235$	16.1332			1.05241
$236$	6.02069	+	10.4281i	0.391914	+	0.678815i
$237$		0			0
$238$		0			0
$239$	−5.91972	−	3.41775i	−0.382915	−	0.221076i	0.296171	−	0.955135i	$-0.404290\pi$
$239$	−5.91972	−	3.41775i	−0.382915	−	0.221076i	−0.679086	+	0.734059i	$0.737624\pi$
$240$		0			0
$241$	3.89112	−	2.24654i	0.250649	−	0.144712i	−0.369412	−	0.929266i	$-0.620441\pi$
$241$	3.89112	−	2.24654i	0.250649	−	0.144712i	0.620061	+	0.784553i	$0.287108\pi$
$242$		−	8.16440i		−	0.524828i
$243$		0			0
$244$			12.0356i			0.770503i
$245$		0			0
$246$		0			0
$247$	−5.98180	+	10.3608i	−0.380613	+	0.659241i
$248$	0.956451	−	1.65662i	0.0607347	−	0.105196i
$249$		0			0
$250$	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
$255$		0			0
$256$	−4.58192	+	7.93613i	−0.286370	+	0.496008i
$257$	−10.7433	+	18.6079i	−0.670146	+	1.16073i	0.307716	+	0.951478i	$0.400435\pi$
$257$	−10.7433	+	18.6079i	−0.670146	+	1.16073i	−0.977862	+	0.209249i	$0.932898\pi$
$258$		0			0
$259$		0			0
$260$			18.8976i			1.17198i
$261$		0			0
$262$			8.65248i			0.534552i
$263$	−9.60394	+	5.54484i	−0.592205	+	0.341909i	−0.765969	−	0.642878i	$-0.777740\pi$
$263$	−9.60394	+	5.54484i	−0.592205	+	0.341909i	0.173764	+	0.984787i	$0.444407\pi$
$264$		0			0
$265$	29.5440	+	17.0572i	1.81487	+	1.04782i
$266$		0			0
$267$		0			0
$268$	9.76514	+	16.9137i	0.596501	+	1.03317i
$269$	−22.0575			−1.34487			−0.672435	−	0.740156i	$-0.734752\pi$
$269$	−22.0575			−1.34487			−0.672435	+	0.740156i	$0.734752\pi$
$270$		0			0
$271$		−	4.74436i		−	0.288199i	−0.989563	−	0.144100i	$-0.953971\pi$
$271$		−	4.74436i		−	0.288199i	0.989563	−	0.144100i	$-0.0460286\pi$
$272$	−11.4627	−	19.8540i	−0.695028	−	1.20382i
$273$		0			0
$274$	−6.55950	+	11.3614i	−0.396274	+	0.686366i
$275$	13.6462	+	7.87862i	0.822895	+	0.475099i
$276$		0			0
$277$	3.21329	+	5.56558i	0.193068	+	0.334404i	0.946265	−	0.323391i	$-0.104823\pi$
$277$	3.21329	+	5.56558i	0.193068	+	0.334404i	−0.753197	+	0.657794i	$0.771490\pi$
$278$	3.19075			0.191368
$279$		0			0
$280$		0			0
$281$	17.0883	−	9.86595i	1.01940	−	0.588553i	0.105473	−	0.994422i	$-0.466364\pi$
$281$	17.0883	−	9.86595i	1.01940	−	0.588553i	0.913931	+	0.405869i	$0.133031\pi$
$282$		0			0
$283$	−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
$285$		0			0
$286$	−11.7182	+	6.76551i	−0.692912	+	0.400053i
$287$		0			0
$288$		0			0
$289$	34.5573			2.03278
$290$	−21.8999	−	37.9317i	−1.28600	−	2.22743i
$291$		0			0
$292$	16.2722	+	9.39477i	0.952260	+	0.549787i
$293$	15.0393	−	26.0488i	0.878603	−	1.52178i	0.0257278	−	0.999669i	$-0.491810\pi$
$293$	15.0393	−	26.0488i	0.878603	−	1.52178i	0.852875	−	0.522115i	$-0.174857\pi$
$294$		0			0
$295$	8.48701	+	14.6999i	0.494133	+	0.855863i
$296$		−	1.21256i		−	0.0704787i
$297$		0			0
$298$	−11.1472			−0.645738
$299$	−6.08641	−	10.5420i	−0.351986	−	0.609658i
$300$		0			0
$301$		0			0
$302$	20.7360	+	11.9719i	1.19322	+	0.688906i
$303$		0			0
$304$	13.5613	−	7.82960i	0.777792	−	0.449059i
$305$			16.9659i			0.971466i
$306$		0			0
$307$		−	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			0
$310$	9.17959	−	15.8995i	0.521366	−	0.903032i
$311$	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	$0.00955846\pi$
$312$		0			0
$313$	−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	$0.353657\pi$
$318$		0			0
$319$	8.46176	−	14.6562i	0.473768	−	0.820590i
$320$	17.3108	−	29.9832i	0.967704	−	1.67611i
$321$		0			0
$322$		0			0
$323$			35.2163i			1.95949i
$324$		0			0
$325$			14.4423i			0.801117i
$326$	41.6826	−	24.0655i	2.30859	−	1.33286i
$327$		0			0
$328$	0.687575	+	0.396971i	0.0379650	+	0.0219191i
$329$		0			0
$330$		0			0
$331$	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	$0.726830\pi$
$332$	4.89878			0.268855
$333$		0			0
$334$		−	33.1578i		−	1.81432i
$335$	13.7653	+	23.8423i	0.752080	+	1.30264i
$336$		0			0
$337$	2.34636	−	4.06402i	0.127815	−	0.221381i	−0.795015	−	0.606590i	$-0.792537\pi$
$337$	2.34636	−	4.06402i	0.127815	−	0.221381i	0.922830	+	0.385208i	$0.125870\pi$
$338$	12.7254	+	7.34703i	0.692172	+	0.399626i
$339$		0			0
$340$	27.8137	+	48.1747i	1.50841	+	2.61264i
$341$	7.09369			0.384145
$342$		0			0
$343$		0			0
$344$	−3.64810	+	2.10623i	−0.196692	+	0.113560i
$345$		0			0
$346$	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	$0.730281\pi$
$348$		0			0
$349$	−18.0496	+	10.4209i	−0.966171	+	0.557819i	−0.898067	−	0.439859i	$-0.855028\pi$
$349$	−18.0496	+	10.4209i	−0.966171	+	0.557819i	−0.0681042	+	0.997678i	$0.521695\pi$
$350$		0			0
$351$		0			0
$352$	21.5308			1.14760
$353$	3.54953	+	6.14797i	0.188923	+	0.327224i	0.944891	−	0.327384i	$-0.106167\pi$
$353$	3.54953	+	6.14797i	0.188923	+	0.327224i	−0.755969	+	0.654608i	$0.772834\pi$
$354$		0			0
$355$	−5.92491	−	3.42075i	−0.314462	−	0.181554i
$356$	1.26890	−	2.19780i	0.0672517	−	0.116483i
$357$		0			0
$358$	22.9593	+	39.7668i	1.21344	+	2.10174i
$359$			9.89233i			0.522097i	0.965326	+	0.261049i	$0.0840683\pi$
$359$			9.89233i			0.522097i	−0.965326	+	0.261049i	$0.915932\pi$
$360$		0			0
$361$	−5.05452			−0.266027
$362$	−18.4446	−	31.9470i	−0.969426	−	1.67910i
$363$		0			0
$364$		0			0
$365$	22.9380	+	13.2432i	1.20063	+	0.693183i
$366$		0			0
$367$	−27.0321	+	15.6070i	−1.41107	+	0.814680i	−0.995489	−	0.0948779i	$-0.969754\pi$
$367$	−27.0321	+	15.6070i	−1.41107	+	0.814680i	−0.415578	+	0.909558i	$0.636421\pi$
$368$			15.9331i			0.830568i
$369$		0			0
$370$		−	11.6376i		−	0.605011i
$371$		0			0
$372$		0			0
$373$	−14.5232	+	25.1549i	−0.751981	+	1.30247i	0.194881	+	0.980827i	$0.437568\pi$
$373$	−14.5232	+	25.1549i	−0.751981	+	1.30247i	−0.946861	+	0.321642i	$0.895765\pi$
$374$	−19.9151	+	34.4939i	−1.02978	+	1.78364i
$375$		0			0
$376$	−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
$381$		0			0
$382$	15.9701	−	27.6611i	0.817102	−	1.41526i
$383$	6.60511	−	11.4404i	0.337505	−	0.584576i	−0.646458	−	0.762950i	$-0.723750\pi$
$383$	6.60511	−	11.4404i	0.337505	−	0.584576i	0.983963	+	0.178374i	$0.0570836\pi$
$384$		0			0
$385$		0			0
$386$		−	53.9140i		−	2.74415i
$387$		0			0
$388$		−	25.6407i		−	1.30171i
$389$	29.2921	−	16.9118i	1.48517	−	0.857461i	0.485309	−	0.874343i	$-0.338707\pi$
$389$	29.2921	−	16.9118i	1.48517	−	0.857461i	0.999857	+	0.0168815i	$0.00537382\pi$
$390$		0			0
$391$	−31.0316	−	17.9161i	−1.56933	−	0.906055i
$392$		0			0
$393$		0			0
$394$	−4.35933	−	7.55059i	−0.219620	−	0.380393i
$395$	−16.5564			−0.833043
$396$		0			0
$397$			8.57345i			0.430289i	0.976582	+	0.215145i	$0.0690223\pi$
$397$			8.57345i			0.430289i	−0.976582	+	0.215145i	$0.930978\pi$
$398$	22.9353	+	39.7251i	1.14964	+	1.99124i
$399$		0			0
$400$	9.45183	−	16.3710i	0.472591	−	0.818552i
$401$	−13.9743	−	8.06808i	−0.697844	−	0.402900i	0.108700	−	0.994075i	$-0.465331\pi$
$401$	−13.9743	−	8.06808i	−0.697844	−	0.402900i	−0.806544	+	0.591174i	$0.798665\pi$
$402$		0			0
$403$	3.25087	+	5.63068i	0.161938	+	0.280484i
$404$	−1.23760			−0.0615730
$405$		0			0
$406$		0			0
$407$	3.89416	−	2.24830i	0.193026	−	0.111444i
$408$		0			0
$409$	−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			0
$412$	−1.59117	+	0.918662i	−0.0783913	+	0.0452592i
$413$		0			0
$414$		0			0
$415$	6.90551			0.338978
$416$	9.86706	+	17.0902i	0.483772	+	0.837918i
$417$		0			0
$418$	−23.5611	−	13.6030i	−1.15241	−	0.665345i
$419$	−0.589031	+	1.02023i	−0.0287760	+	0.0498415i	−0.880055	−	0.474872i	$-0.842494\pi$
$419$	−0.589031	+	1.02023i	−0.0287760	+	0.0498415i	0.851279	+	0.524714i	$0.175828\pi$
$420$		0			0
$421$	3.43544	+	5.95035i	0.167433	+	0.290002i	0.937517	−	0.347941i	$-0.113119\pi$
$421$	3.43544	+	5.95035i	0.167433	+	0.290002i	−0.770084	+	0.637943i	$0.779786\pi$
$422$			51.2430i			2.49447i
$423$		0			0
$424$	−7.40866			−0.359796
$425$	21.2564	+	36.8172i	1.03109	+	1.78589i
$426$		0			0
$427$		0			0
$428$	−10.8636	−	6.27208i	−0.525110	−	0.303172i
$429$		0			0
$430$	−35.0128	+	20.2146i	−1.68847	+	0.974837i
$431$		−	0.811164i		−	0.0390724i	−0.999809	−	0.0195362i	$-0.993781\pi$
$431$		−	0.811164i		−	0.0390724i	0.999809	−	0.0195362i	$-0.00621896\pi$
$432$		0			0
$433$		−	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
$435$		0			0
$436$	6.99219	−	12.1108i	0.334865	−	0.580004i
$437$	12.2376	−	21.1961i	0.585404	−	1.01395i
$438$		0			0
$439$	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	$0.239377\pi$
$444$		0			0
$445$	1.78870	−	3.09811i	0.0847924	−	0.146865i
$446$	−8.80759	+	15.2552i	−0.417051	+	0.722354i
$447$		0			0
$448$		0			0
$449$			22.0163i			1.03901i	0.854466	+	0.519507i	$0.173884\pi$
$449$			22.0163i			1.03901i	−0.854466	+	0.519507i	$0.826116\pi$
$450$		0			0
$451$			2.94421i			0.138637i
$452$	−23.4488	+	13.5382i	−1.10294	+	0.636781i
$453$		0			0
$454$	10.5226	+	6.07522i	0.493849	+	0.285124i
$455$		0			0
$456$		0			0
$457$	−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	$-0.357784\pi$
$458$	10.0010			0.467317
$459$		0			0
$460$		−	38.6608i		−	1.80257i
$461$	−16.3899	−	28.3881i	−0.763352	−	1.32216i	−0.941114	−	0.338091i	$-0.890219\pi$
$461$	−16.3899	−	28.3881i	−0.763352	−	1.32216i	0.177762	−	0.984074i	$-0.443114\pi$
$462$		0			0
$463$	15.7659	−	27.3074i	0.732704	−	1.26908i	−0.223020	−	0.974814i	$-0.571591\pi$
$463$	15.7659	−	27.3074i	0.732704	−	1.26908i	0.955723	−	0.294266i	$-0.0950753\pi$
$464$	−17.5828	−	10.1514i	−0.816259	−	0.471267i
$465$		0			0
$466$	−24.0178	−	41.6000i	−1.11260	−	1.92708i
$467$	33.1531			1.53414			0.767070	−	0.641563i	$-0.221714\pi$
$467$	33.1531			1.53414			0.767070	+	0.641563i	$0.221714\pi$
$468$		0			0
$469$		0			0
$470$	−29.1213	+	16.8132i	−1.34327	+	0.775536i
$471$		0			0
$472$	−3.19239	−	1.84313i	−0.146942	−	0.0848368i
$473$	−13.5284	−	7.81062i	−0.622036	−	0.359133i
$474$		0			0
$475$	−25.1480	+	14.5192i	−1.15387	+	0.666187i
$476$		0			0
$477$		0			0
$478$	14.2473			0.651655
$479$	11.3972	+	19.7406i	0.520754	+	0.901972i	0.999709	+	0.0241323i	$0.00768229\pi$
$479$	11.3972	+	19.7406i	0.520754	+	0.901972i	−0.478955	+	0.877839i	$0.658984\pi$
$480$		0			0
$481$	3.56921	+	2.06068i	0.162742	+	0.0939590i
$482$	−4.68247	+	8.11027i	−0.213281	+	0.369413i
$483$		0			0
$484$	4.59146	+	7.95264i	0.208703	+	0.361484i
$485$		−	36.1441i		−	1.64122i
$486$		0			0
$487$	−2.73119			−0.123762			−0.0618811	−	0.998084i	$-0.519710\pi$
$487$	−2.73119			−0.123762			−0.0618811	+	0.998084i	$0.519710\pi$
$488$	−1.84225	−	3.19087i	−0.0833946	−	0.144444i
$489$		0			0
$490$		0			0
$491$	−21.6775	−	12.5155i	−0.978291	−	0.564817i	−0.0765375	−	0.997067i	$-0.524387\pi$
$491$	−21.6775	−	12.5155i	−0.978291	−	0.564817i	−0.901754	+	0.432250i	$0.857720\pi$
$492$		0			0
$493$	39.5422	−	22.8297i	1.78089	−	1.02820i
$494$		−	24.9358i		−	1.12191i
$495$		0			0
$496$		−	8.51016i		−	0.382118i
$497$		0			0
$498$		0			0
$499$	−4.29981	+	7.44749i	−0.192486	+	0.333395i	−0.946073	−	0.323952i	$-0.894988\pi$
$499$	−4.29981	+	7.44749i	−0.192486	+	0.333395i	0.753588	+	0.657348i	$0.228322\pi$
$500$	−3.56648	+	6.17732i	−0.159498	+	0.276258i
$501$		0			0
$502$	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
$507$		0			0
$508$	−22.3829	+	38.7683i	−0.993079	+	1.72006i
$509$	16.2909	−	28.2167i	0.722083	−	1.25068i	−0.238080	−	0.971245i	$-0.576518\pi$
$509$	16.2909	−	28.2167i	0.722083	−	1.25068i	0.960163	−	0.279439i	$-0.0901485\pi$
$510$		0			0
$511$		0			0
$512$		−	30.4128i		−	1.34407i
$513$		0			0
$514$		−	44.7844i		−	1.97536i
$515$	−2.24298	+	1.29498i	−0.0988373	+	0.0570638i
$516$		0			0
$517$	−11.2520	−	6.49636i	−0.494864	−	0.285710i
$518$		0			0
$519$		0			0
$520$	−2.89258	−	5.01009i	−0.126848	−	0.219707i
$521$	7.36912			0.322847			0.161424	−	0.986885i	$-0.448391\pi$
$521$	7.36912			0.322847			0.161424	+	0.986885i	$0.448391\pi$
$522$		0			0
$523$			43.4157i			1.89843i	0.314622	+	0.949217i	$0.398122\pi$
$523$			43.4157i			1.89843i	−0.314622	+	0.949217i	$0.601878\pi$
$524$	−4.86594	−	8.42806i	−0.212570	−	0.368181i
$525$		0			0
$526$	11.5571	−	20.0175i	0.503915	−	0.872806i
$527$	16.5746	+	9.56933i	0.722000	+	0.416847i
$528$		0			0
$529$	0.951610	+	1.64824i	0.0413744	+	0.0716625i
$530$	−71.1050			−3.08860
$531$		0			0
$532$		0			0
$533$	−2.33699	+	1.34926i	−0.101226	+	0.0584430i
$534$		0			0
$535$	−15.3137	−	8.84137i	−0.662069	−	0.382246i
$536$	−5.17783	−	2.98942i	−0.223648	−	0.129123i
$537$		0			0
$538$	39.8151	−	22.9873i	1.71655	−	0.991052i
$539$		0			0
$540$		0			0
$541$	−21.6442			−0.930555			−0.465278	−	0.885165i	$-0.654045\pi$
$541$	−21.6442			−0.930555			−0.465278	+	0.885165i	$0.654045\pi$
$542$	4.94434	+	8.56385i	0.212378	+	0.367849i
$543$		0			0
$544$	50.3072	+	29.0449i	2.15690	+	1.24529i
$545$	9.85648	−	17.0719i	0.422205	−	0.731281i
$546$		0			0
$547$	−11.9092	−	20.6273i	−0.509200	−	0.881960i	−0.999943	−	0.0106561i	$-0.996608\pi$
$547$	−11.9092	−	20.6273i	−0.509200	−	0.881960i	0.490743	−	0.871304i	$-0.336725\pi$
$548$		−	14.7556i		−	0.630328i
$549$		0			0
$550$	−32.8429			−1.40043
$551$	15.5938	+	27.0093i	0.664320	+	1.15064i
$552$		0			0
$553$		0			0
$554$	−11.6004	−	6.69748i	−0.492852	−	0.284548i
$555$		0			0
$556$	−3.10799	+	1.79440i	−0.131808	+	0.0760994i
$557$		−	10.8777i		−	0.460905i	−0.973084	−	0.230452i	$-0.925979\pi$
$557$		−	10.8777i		−	0.460905i	0.973084	−	0.230452i	$-0.0740206\pi$
$558$		0			0
$559$		−	14.3177i		−	0.605574i
$560$		0			0
$561$		0			0
$562$	−20.5636	+	35.6173i	−0.867425	+	1.50242i
$563$	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	$0.0758590\pi$
$564$		0			0
$565$	−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	$0.398089\pi$
$570$		0			0
$571$	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	$-0.0891578\pi$
$572$	7.60951	−	13.1801i	0.318170	−	0.551086i
$573$		0			0
$574$		0			0
$575$		−	29.5462i		−	1.23216i
$576$		0			0
$577$			24.1352i			1.00476i	0.864647	+	0.502381i	$0.167542\pi$
$577$			24.1352i			1.00476i	−0.864647	+	0.502381i	$0.832458\pi$
$578$	−62.3780	+	36.0140i	−2.59458	+	1.49798i
$579$		0			0
$580$	42.6637	+	24.6319i	1.77151	+	1.02278i
$581$		0			0
$582$		0			0
$583$	−13.7369	−	23.7930i	−0.568925	−	0.985407i
$584$	−5.75208			−0.238023
$585$		0			0
$586$			62.6928i			2.58981i
$587$	−3.96848	−	6.87362i	−0.163797	−	0.283704i	0.772431	−	0.635099i	$-0.219041\pi$
$587$	−3.96848	−	6.87362i	−0.163797	−	0.283704i	−0.936227	+	0.351395i	$0.885707\pi$
$588$		0			0
$589$	−6.53634	+	11.3213i	−0.269325	+	0.466485i
$590$	−30.6391	−	17.6895i	−1.26139	−	0.728266i
$591$		0			0
$592$	−2.69724	−	4.67175i	−0.110856	−	0.192008i
$593$	−41.8293			−1.71772			−0.858862	−	0.512207i	$-0.828828\pi$
$593$	−41.8293			−1.71772			−0.858862	+	0.512207i	$0.828828\pi$
$594$		0			0
$595$		0			0
$596$	10.8580	−	6.26889i	0.444763	−	0.256784i
$597$		0			0
$598$	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			0
$601$	−12.6427	+	7.29924i	−0.515705	+	0.297742i	−0.735176	−	0.677877i	$-0.762900\pi$
$601$	−12.6427	+	7.29924i	−0.515705	+	0.297742i	0.219471	+	0.975619i	$0.429567\pi$
$602$		0			0
$603$		0			0
$604$	−26.9308			−1.09580
$605$	6.47230	+	11.2104i	0.263137	+	0.455766i
$606$		0			0
$607$	9.51436	+	5.49312i	0.386176	+	0.222959i	0.680502	−	0.732746i	$-0.261762\pi$
$607$	9.51436	+	5.49312i	0.386176	+	0.222959i	−0.294326	+	0.955705i	$0.595095\pi$
$608$	−19.8391	+	34.3624i	−0.804583	+	1.39358i
$609$		0			0
$610$	−17.6811	−	30.6245i	−0.715885	−	1.23995i
$611$		−	11.9085i		−	0.481767i
$612$		0			0
$613$	23.8135			0.961818			0.480909	−	0.876770i	$-0.340307\pi$
$613$	23.8135			0.961818			0.480909	+	0.876770i	$0.340307\pi$
$614$	24.4382	+	42.3282i	0.986244	+	1.70823i
$615$		0			0
$616$		0			0
$617$	36.5255	+	21.0880i	1.47046	+	0.848971i	0.999450	−	0.0331557i	$-0.0105557\pi$
$617$	36.5255	+	21.0880i	1.47046	+	0.848971i	0.471011	+	0.882127i	$0.343889\pi$
$618$		0			0
$619$	−22.6532	+	13.0789i	−0.910511	+	0.525683i	−0.880595	−	0.473869i	$-0.842857\pi$
$619$	−22.6532	+	13.0789i	−0.910511	+	0.525683i	−0.0299151	+	0.999552i	$0.509524\pi$
$620$			20.6495i			0.829304i
$621$		0			0
$622$			34.8290i			1.39652i
$623$		0			0
$624$		0			0
$625$	9.77434	−	16.9297i	0.390974	−	0.677186i
$626$	15.4942	−	26.8368i	0.619274	−	1.07261i
$627$		0			0
$628$	−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
$633$		0			0
$634$	2.36776	−	4.10109i	0.0940359	−	0.162875i
$635$	−31.5518	+	54.6493i	−1.25209	+	2.16869i
$636$		0			0
$637$		0			0
$638$			35.2738i			1.39650i
$639$		0			0
$640$			18.6921i			0.738869i
$641$	−15.2483	+	8.80362i	−0.602272	+	0.347722i	−0.769935	−	0.638122i	$-0.779711\pi$
$641$	−15.2483	+	8.80362i	−0.602272	+	0.347722i	0.167663	+	0.985844i	$0.446378\pi$
$642$		0			0
$643$	43.1158	+	24.8929i	1.70032	+	0.981680i	0.945428	+	0.325832i	$0.105645\pi$
$643$	43.1158	+	24.8929i	1.70032	+	0.981680i	0.754893	+	0.655848i	$0.227689\pi$
$644$		0			0
$645$		0			0
$646$	−36.7007	−	63.5675i	−1.44397	−	2.50103i
$647$	−11.5407			−0.453712			−0.226856	−	0.973928i	$-0.572845\pi$
$647$	−11.5407			−0.453712			−0.226856	+	0.973928i	$0.572845\pi$
$648$		0			0
$649$		−	13.6699i		−	0.536590i
$650$	−15.0511	−	26.0693i	−0.590354	−	1.02252i
$651$		0			0
$652$	−27.0677	+	46.8826i	−1.06005	+	1.83606i
$653$	−18.2249	−	10.5222i	−0.713197	−	0.411765i	0.0990464	−	0.995083i	$-0.468421\pi$
$653$	−18.2249	−	10.5222i	−0.713197	−	0.411765i	−0.812244	+	0.583318i	$0.801754\pi$
$654$		0			0
$655$	−6.85923	−	11.8805i	−0.268012	−	0.464211i
$656$	3.53211			0.137906
$657$		0			0
$658$		0			0
$659$	31.8016	−	18.3607i	1.23881	−	0.715230i	0.269962	−	0.962871i	$-0.412989\pi$
$659$	31.8016	−	18.3607i	1.23881	−	0.715230i	0.968852	+	0.247641i	$0.0796555\pi$
$660$		0			0
$661$	−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
$663$		0			0
$664$	−1.29875	+	0.749836i	−0.0504015	+	0.0290993i
$665$		0			0
$666$		0			0
$667$	−31.7331			−1.22871
$668$	18.6472	+	32.2978i	0.721480	+	1.24964i
$669$		0			0
$670$	−49.6945	−	28.6911i	−1.91987	−	1.10844i
$671$	6.83168	−	11.8328i	0.263734	−	0.456801i
$672$		0			0
$673$	24.7594	+	42.8846i	0.954406	+	1.65308i	0.735722	+	0.677284i	$0.236843\pi$
$673$	24.7594	+	42.8846i	0.954406	+	1.65308i	0.218684	+	0.975796i	$0.429824\pi$
$674$			9.78107i			0.376753i
$675$		0			0
$676$	−16.5272			−0.635660
$677$	−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	$-0.360867\pi$
$678$		0			0
$679$		0			0
$680$	−14.7478	−	8.51465i	−0.565553	−	0.326522i
$681$		0			0
$682$	−12.8045	+	7.39271i	−0.490311	+	0.283081i
$683$			30.2348i			1.15690i	0.815717	+	0.578451i	$0.196342\pi$
$683$			30.2348i			1.15690i	−0.815717	+	0.578451i	$0.803658\pi$
$684$		0			0
$685$		−	20.8001i		−	0.794731i
$686$		0			0
$687$		0			0
$688$	−9.37024	+	16.2297i	−0.357237	+	0.618753i
$689$	12.5906	−	21.8076i	0.479664	−	0.830802i
$690$		0			0
$691$	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
$696$		0			0
$697$	−3.97172	+	6.87921i	−0.150439	+	0.260569i
$698$	21.7204	−	37.6208i	0.822128	−	1.42397i
$699$		0			0
$700$		0			0
$701$		−	0.757329i		−	0.0286039i	−0.999898	−	0.0143020i	$-0.995447\pi$
$701$		−	0.757329i		−	0.0286039i	0.999898	−	0.0143020i	$-0.00455261\pi$
$702$		0			0
$703$			8.28659i			0.312535i
$704$	−24.1467	+	13.9411i	−0.910065	+	0.525426i
$705$		0			0
$706$	−12.8142	−	7.39831i	−0.482270	−	0.278439i
$707$		0			0
$708$		0			0
$709$	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	$0.700992\pi$
$710$	14.2598			0.535159
$711$		0			0
$712$			0.776904i			0.0291157i
$713$	−6.65065	−	11.5193i	−0.249069	−	0.431400i
$714$		0			0
$715$	10.7267	−	18.5791i	0.401155	−	0.694820i
$716$	−44.7277	−	25.8235i	−1.67155	−	0.965071i
$717$		0			0
$718$	−10.3093	−	17.8562i	−0.384740	−	0.666389i
$719$	−44.2509			−1.65028			−0.825140	−	0.564929i	$-0.808904\pi$
$719$	−44.2509			−1.65028			−0.825140	+	0.564929i	$0.808904\pi$
$720$		0			0
$721$		0			0
$722$	9.12371	−	5.26758i	0.339549	−	0.196039i
$723$		0			0
$724$	35.9324	+	20.7456i	1.33542	+	0.771003i
$725$	32.6054	+	18.8248i	1.21094	+	0.699134i
$726$		0			0
$727$	−2.95166	+	1.70414i	−0.109471	+	0.0632031i	−0.553736	−	0.832692i	$-0.686798\pi$
$727$	−2.95166	+	1.70414i	−0.109471	+	0.0632031i	0.444265	+	0.895895i	$0.353465\pi$
$728$		0			0
$729$		0			0
$730$	−55.2059			−2.04326
$731$	−21.0729	−	36.4994i	−0.779410	−	1.34998i
$732$		0			0
$733$	−5.46407	−	3.15468i	−0.201820	−	0.116521i	0.395684	−	0.918387i	$-0.370508\pi$
$733$	−5.46407	−	3.15468i	−0.201820	−	0.116521i	−0.597504	+	0.801866i	$0.703841\pi$
$734$	32.5298	−	56.3432i	1.20070	−	2.07967i
$735$		0			0
$736$	−20.1861	−	34.9633i	−0.744069	−	1.28876i
$737$		−	22.1716i		−	0.816701i
$738$		0			0
$739$	−4.90776			−0.180535			−0.0902674	−	0.995918i	$-0.528772\pi$
$739$	−4.90776			−0.180535			−0.0902674	+	0.995918i	$0.528772\pi$
$740$	6.54471	+	11.3358i	0.240588	+	0.416711i
$741$		0			0
$742$		0			0
$743$	−26.1921	−	15.1220i	−0.960895	−	0.554773i	−0.0644465	−	0.997921i	$-0.520528\pi$
$743$	−26.1921	−	15.1220i	−0.960895	−	0.554773i	−0.896448	+	0.443148i	$0.853862\pi$
$744$		0			0
$745$	15.3059	−	8.83688i	0.560766	−	0.323758i
$746$		−	60.5414i		−	2.21658i
$747$		0			0
$748$		−	44.7990i		−	1.63801i
$749$		0			0
$750$		0			0
$751$	25.0321	−	43.3569i	0.913435	−	1.58212i	0.104257	−	0.994550i	$-0.466753\pi$
$751$	25.0321	−	43.3569i	0.913435	−	1.58212i	0.809177	−	0.587565i	$-0.199913\pi$
$752$	−7.79355	+	13.4988i	−0.284202	+	0.492252i
$753$		0			0
$754$	−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
$759$		0			0
$760$	5.81594	−	10.0735i	0.210966	−	0.365405i
$761$	−5.27174	+	9.13092i	−0.191100	+	0.330996i	−0.945615	−	0.325287i	$-0.894539\pi$
$761$	−5.27174	+	9.13092i	−0.191100	+	0.330996i	0.754515	+	0.656283i	$0.227872\pi$
$762$		0			0
$763$		0			0
$764$			35.9248i			1.29971i
$765$		0			0
$766$			27.5341i			0.994848i
$767$	10.8506	−	6.26459i	0.391792	−	0.226201i
$768$		0			0
$769$	12.4720	+	7.20070i	0.449751	+	0.259664i	0.707725	−	0.706488i	$-0.249722\pi$
$769$	12.4720	+	7.20070i	0.449751	+	0.259664i	−0.257974	+	0.966152i	$0.583055\pi$
$770$		0			0
$771$		0			0
$772$	30.3199	+	52.5156i	1.09124	+	1.89008i
$773$	21.8771			0.786866			0.393433	−	0.919353i	$-0.371287\pi$
$773$	21.8771			0.786866			0.393433	+	0.919353i	$0.371287\pi$
$774$		0			0
$775$			15.7812i			0.566879i
$776$	3.92472	+	6.79781i	0.140889	+	0.244027i
$777$		0			0
$778$	−35.2493	+	61.0536i	−1.26375	+	2.18888i
$779$	−4.69885	−	2.71288i	−0.168354	−	0.0971992i
$780$		0			0
$781$	2.75487	+	4.77158i	0.0985771	+	0.170740i
$782$	74.6851			2.67073
$783$		0			0
$784$		0			0
$785$	−19.0759	+	11.0135i	−0.680847	+	0.393087i
$786$		0			0
$787$	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			0
$790$	29.8853	−	17.2543i	1.06327	−	0.613880i
$791$		0			0
$792$		0			0
$793$	12.5232			0.444712
$794$	−8.93484	−	15.4756i	−0.317086	−	0.549208i
$795$		0			0
$796$	−44.6809	−	25.7965i	−1.58367	−	0.914334i
$797$	21.3285	−	36.9420i	0.755493	−	1.30855i	−0.189636	−	0.981854i	$-0.560731\pi$
$797$	21.3285	−	36.9420i	0.755493	−	1.30855i	0.945129	−	0.326697i	$-0.105936\pi$
$798$		0			0
$799$	−17.5271	−	30.3578i	−0.620063	−	1.07398i
$800$			47.8992i			1.69349i
$801$		0			0
$802$	33.6326			1.18761
$803$	−10.6653	−	18.4729i	−0.376372	−	0.651895i
$804$		0			0
$805$		0			0
$806$	−11.7360	−	6.77581i	−0.413384	−	0.238668i
$807$		0			0
$808$	0.328111	−	0.189435i	0.0115429	−	0.00666430i
$809$			35.7254i			1.25604i	0.778198	+	0.628019i	$0.216134\pi$
$809$			35.7254i			1.25604i	−0.778198	+	0.628019i	$0.783866\pi$
$810$		0			0
$811$		−	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
$813$		0			0
$814$	−4.68613	+	8.11662i	−0.164249	+	0.284487i
$815$	−38.1557	+	66.0875i	−1.33653	+	2.31495i
$816$		0			0
$817$	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	$0.432564\pi$
$822$		0			0
$823$	−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	$0.989059\pi$
$824$	0.281232	−	0.487108i	0.00979717	−	0.0169692i
$825$		0			0
$826$		0			0
$827$		−	15.4454i		−	0.537089i	−0.963267	−	0.268545i	$-0.913457\pi$
$827$		−	15.4454i		−	0.537089i	0.963267	−	0.268545i	$-0.0865426\pi$
$828$		0			0
$829$		−	40.8946i		−	1.42033i	−0.704036	−	0.710164i	$-0.748621\pi$
$829$		−	40.8946i		−	1.42033i	0.704036	−	0.710164i	$-0.251379\pi$
$830$	−12.4649	+	7.19659i	−0.432662	+	0.249797i
$831$		0			0
$832$	−22.1318	−	12.7778i	−0.767281	−	0.442990i
$833$		0			0
$834$		0			0
$835$	26.2858	+	45.5283i	0.909657	+	1.57557i
$836$	30.6000			1.05832
$837$		0			0
$838$		−	2.45544i		−	0.0848217i
$839$	16.8620	+	29.2058i	0.582140	+	1.00830i	0.995225	+	0.0976035i	$0.0311177\pi$
$839$	16.8620	+	29.2058i	0.582140	+	1.00830i	−0.413086	+	0.910692i	$0.635549\pi$
$840$		0			0
$841$	5.71808	−	9.90401i	0.197175	−	0.341517i
$842$	−12.4023	−	7.16049i	−0.427413	−	0.246767i
$843$		0			0
$844$	−28.8178	−	49.9139i	−0.991950	−	1.71811i
$845$	−23.2973			−0.801453
$846$		0			0
$847$		0			0
$848$	−28.5440	+	16.4799i	−0.980206	+	0.565922i
$849$		0			0
$850$	−76.7381	−	44.3048i	−2.63210	−	1.51964i
$851$	−7.30190	−	4.21575i	−0.250306	−	0.144514i
$852$		0			0
$853$	37.6715	−	21.7497i	1.28985	−	0.744694i	0.311221	−	0.950337i	$-0.399262\pi$
$853$	37.6715	−	21.7497i	1.28985	−	0.744694i	0.978627	+	0.205643i	$0.0659286\pi$
$854$		0			0
$855$		0			0
$856$	3.84017			0.131254
$857$	4.21534	+	7.30118i	0.143993	+	0.249404i	0.928997	−	0.370088i	$-0.120672\pi$
$857$	4.21534	+	7.30118i	0.143993	+	0.249404i	−0.785004	+	0.619491i	$0.787339\pi$
$858$		0			0
$859$	2.07929	+	1.20048i	0.0709445	+	0.0409598i	0.535053	−	0.844819i	$-0.320292\pi$
$859$	2.07929	+	1.20048i	0.0709445	+	0.0409598i	−0.464108	+	0.885779i	$0.653625\pi$
$860$	22.7364	−	39.3807i	0.775306	−	1.34287i
$861$		0			0
$862$	0.845356	+	1.46420i	0.0287929	+	0.0498708i
$863$			9.37637i			0.319175i	0.987184	+	0.159588i	$0.0510165\pi$
$863$			9.37637i			0.319175i	−0.987184	+	0.159588i	$0.948984\pi$
$864$		0			0
$865$	−61.6712			−2.09688
$866$	8.95898	+	15.5174i	0.304439	+	0.527303i
$867$		0			0
$868$		0			0
$869$	11.5472	+	6.66678i	0.391712	+	0.226155i
$870$		0			0
$871$	17.5989	−	10.1607i	0.596316	−	0.344283i
$872$			4.28107i			0.144975i
$873$		0			0
$874$			51.0137i			1.72557i
$875$		0			0
$876$		0			0
$877$	−1.71542	+	2.97119i	−0.0579256	+	0.100330i	−0.893534	−	0.448995i	$-0.851782\pi$
$877$	−1.71542	+	2.97119i	−0.0579256	+	0.100330i	0.835608	+	0.549326i	$0.185115\pi$
$878$	−28.7568	+	49.8082i	−0.970493	+	1.68094i
$879$		0			0
$880$	−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
$885$		0			0
$886$	−12.7619	+	22.1043i	−0.428745	+	0.742607i
$887$	17.5766	−	30.4436i	0.590164	−	1.02219i	−0.404045	−	0.914739i	$-0.632396\pi$
$887$	17.5766	−	30.4436i	0.590164	−	1.02219i	0.994210	−	0.107456i	$-0.0342704\pi$
$888$		0			0
$889$		0			0
$890$			7.45638i			0.249938i
$891$		0			0
$892$		−	19.8127i		−	0.663378i
$893$	20.7359	−	11.9719i	0.693901	−	0.400624i
$894$		0			0
$895$	−63.0500	−	36.4019i	−2.10753	−	1.21678i
$896$		0			0
$897$		0			0
$898$	−22.9443	−	39.7407i	−0.765662	−	1.32617i
$899$	16.9493			0.565290
$900$		0			0
$901$		−	74.1239i		−	2.46943i
$902$	−3.06832	−	5.31448i	−0.102164	−	0.176953i
$903$		0			0
$904$	4.14446	−	7.17842i	0.137843	−	0.238751i
$905$	50.6517	+	29.2438i	1.68372	+	0.972097i
$906$		0			0
$907$	−19.0816	−	33.0504i	−0.633596	−	1.09742i	−0.986811	−	0.161878i	$-0.948245\pi$
$907$	−19.0816	−	33.0504i	−0.633596	−	1.09742i	0.353215	−	0.935542i	$-0.385088\pi$
$908$	−13.6662			−0.453529
$909$		0			0
$910$		0			0
$911$	39.9027	−	23.0378i	1.32203	−	0.763277i	0.337981	−	0.941153i	$-0.390256\pi$
$911$	39.9027	−	23.0378i	1.32203	−	0.763277i	0.984053	+	0.177876i	$0.0569226\pi$
$912$		0			0
$913$	−4.81623	−	2.78065i	−0.159394	−	0.0920261i
$914$	43.6028	+	25.1741i	1.44225	+	0.832686i
$915$		0			0
$916$	−9.74163	+	5.62433i	−0.321872	+	0.185833i
$917$		0			0
$918$		0			0
$919$	10.5515			0.348061			0.174031	−	0.984740i	$-0.444321\pi$
$919$	10.5515			0.348061			0.174031	+	0.984740i	$0.444321\pi$
$920$	5.91765	+	10.2497i	0.195099	+	0.337922i
$921$		0			0
$922$	59.1694	+	34.1615i	1.94864	+	1.12505i
$923$	−2.52499	+	4.37340i	−0.0831109	+	0.143952i
$924$		0			0
$925$	5.00175	+	8.66328i	0.164456	+	0.284847i
$926$			65.7219i			2.15975i
$927$		0			0
$928$	51.4445			1.68875
$929$	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	$0.498839\pi$
$930$		0			0
$931$		0			0
$932$	46.7896	+	27.0140i	1.53265	+	0.884873i
$933$		0			0
$934$	−59.8433	+	34.5505i	−1.95813	+	1.13053i
$935$		−	63.1505i		−	2.06524i
$936$		0			0
$937$			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
$939$		0			0
$940$	18.9107	−	32.7543i	0.616798	−	1.06833i
$941$	−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	$0.171911\pi$
$942$		0			0
$943$	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	$0.389549\pi$
$948$		0			0
$949$	9.77535	−	16.9314i	0.317321	−	0.549616i
$950$	30.2624	−	52.4161i	0.981843	−	1.70060i
$951$		0			0
$952$		0			0
$953$			26.7466i			0.866408i	0.901296	+	0.433204i	$0.142617\pi$
$953$			26.7466i			0.866408i	−0.901296	+	0.433204i	$0.857383\pi$
$954$		0			0
$955$			50.6411i			1.63871i
$956$	−13.8777	+	8.01232i	−0.448838	+	0.259137i
$957$		0			0
$958$	−41.1454	−	23.7553i	−1.32935	−	0.767500i
$959$		0			0
$960$		0			0
$961$	−11.9478	−	20.6941i	−0.385411	−	0.667552i
$962$	−8.59017			−0.276958
$963$		0			0
$964$		−	10.5332i		−	0.339252i
$965$	42.7402	+	74.0281i	1.37585	+	2.38305i
$966$		0			0
$967$	1.62313	−	2.81134i	0.0521962	−	0.0904065i	−0.838747	−	0.544522i	$-0.816711\pi$
$967$	1.62313	−	2.81134i	0.0521962	−	0.0904065i	0.890943	+	0.454115i	$0.150045\pi$
$968$	−2.43456	−	1.40559i	−0.0782497	−	0.0451775i
$969$		0			0
$970$	37.6677	+	65.2424i	1.20944	+	2.09481i
$971$	8.82846			0.283319			0.141659	−	0.989915i	$-0.454756\pi$
$971$	8.82846			0.283319			0.141659	+	0.989915i	$0.454756\pi$
$972$		0			0
$973$		0			0
$974$	4.92997	−	2.84632i	0.157966	−	0.0912019i
$975$		0			0
$976$	−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	$0.900388\pi$
$978$		0			0
$979$	−2.49504	+	1.44051i	−0.0797419	+	0.0460390i
$980$		0			0
$981$		0			0
$982$	52.1722			1.66488
$983$	2.35194	+	4.07368i	0.0750153	+	0.129930i	0.901093	−	0.433626i	$-0.142766\pi$
$983$	2.35194	+	4.07368i	0.0750153	+	0.129930i	−0.826078	+	0.563556i	$0.809433\pi$
$984$		0			0
$985$	11.9714	+	6.91170i	0.381441	+	0.220225i
$986$	−47.5840	+	82.4179i	−1.51538	+	2.62472i
$987$		0			0
$988$	14.0233	+	24.2890i	0.446139	+	0.772736i
$989$			29.2912i			0.931406i
$990$		0			0
$991$	37.8654			1.20284			0.601418	−	0.798935i	$-0.294603\pi$
$991$	37.8654			1.20284			0.601418	+	0.798935i	$0.294603\pi$
$992$	10.7818	+	18.6746i	0.342322	+	0.592919i
$993$		0			0
$994$		0			0
$995$	−62.9840	−	36.3638i	−1.99673	−	1.15281i
$996$		0			0
$997$	3.18336	−	1.83791i	0.100818	−	0.0582073i	−0.448743	−	0.893661i	$-0.648128\pi$
$997$	3.18336	−	1.83791i	0.100818	−	0.0582073i	0.549561	+	0.835453i	$0.314795\pi$
$998$		−	17.9242i		−	0.567381i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.o.e.881.4		48
3.2	odd	2		441.2.o.e.293.22	yes	48
7.2	even	3		1323.2.s.d.962.21		48
7.3	odd	6		1323.2.i.d.1097.23		48
7.4	even	3		1323.2.i.d.1097.16		48
7.5	odd	6		1323.2.s.d.962.22		48
7.6	odd	2	inner	1323.2.o.e.881.3		48
9.2	odd	6	inner	1323.2.o.e.440.3		48
9.7	even	3		441.2.o.e.146.21	✓	48
21.2	odd	6		441.2.s.d.374.3		48
21.5	even	6		441.2.s.d.374.4		48
21.11	odd	6		441.2.i.d.68.22		48
21.17	even	6		441.2.i.d.68.21		48
21.20	even	2		441.2.o.e.293.21	yes	48
63.2	odd	6		1323.2.i.d.521.23		48
63.11	odd	6		1323.2.s.d.656.22		48
63.16	even	3		441.2.i.d.227.3		48
63.20	even	6	inner	1323.2.o.e.440.4		48
63.25	even	3		441.2.s.d.362.4		48
63.34	odd	6		441.2.o.e.146.22	yes	48
63.38	even	6		1323.2.s.d.656.21		48
63.47	even	6		1323.2.i.d.521.16		48
63.52	odd	6		441.2.s.d.362.3		48
63.61	odd	6		441.2.i.d.227.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.21		48	21.17	even	6
441.2.i.d.68.22		48	21.11	odd	6
441.2.i.d.227.3		48	63.16	even	3
441.2.i.d.227.4		48	63.61	odd	6
441.2.o.e.146.21	✓	48	9.7	even	3
441.2.o.e.146.22	yes	48	63.34	odd	6
441.2.o.e.293.21	yes	48	21.20	even	2
441.2.o.e.293.22	yes	48	3.2	odd	2
441.2.s.d.362.3		48	63.52	odd	6
441.2.s.d.362.4		48	63.25	even	3
441.2.s.d.374.3		48	21.2	odd	6
441.2.s.d.374.4		48	21.5	even	6
1323.2.i.d.521.16		48	63.47	even	6
1323.2.i.d.521.23		48	63.2	odd	6
1323.2.i.d.1097.16		48	7.4	even	3
1323.2.i.d.1097.23		48	7.3	odd	6
1323.2.o.e.440.3		48	9.2	odd	6	inner
1323.2.o.e.440.4		48	63.20	even	6	inner
1323.2.o.e.881.3		48	7.6	odd	2	inner
1323.2.o.e.881.4		48	1.1	even	1	trivial
1323.2.s.d.656.21		48	63.38	even	6
1323.2.s.d.656.22		48	63.11	odd	6
1323.2.s.d.962.21		48	7.2	even	3
1323.2.s.d.962.22		48	7.5	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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.80506 + 1.04215i) q^{2} +(1.17216 - 2.03024i) q^{4} +(1.65233 - 2.86191i) q^{5} +0.717672i q^{8} +O(q^{10})\)	\(q+(-1.80506 + 1.04215i) q^{2} +(1.17216 - 2.03024i) q^{4} +(1.65233 - 2.86191i) q^{5} +0.717672i q^{8} +6.88790i q^{10} +(-2.30482 + 1.33069i) q^{11} +(-2.11249 - 1.21964i) q^{13} +(1.59640 + 2.76504i) q^{16} -7.18034 q^{17} -4.90454i q^{19} +(-3.87358 - 6.70924i) q^{20} +(2.77356 - 4.80394i) q^{22} +(4.32174 + 2.49516i) q^{23} +(-2.96036 - 5.12749i) q^{25} +5.08422 q^{26} +(-5.50701 + 3.17947i) q^{29} +(-2.30833 - 1.33271i) q^{31} +(-7.00624 - 4.04505i) q^{32} +(12.9609 - 7.48301i) q^{34} -1.68957 q^{37} +(5.11128 + 8.85299i) q^{38} +(2.05391 + 1.18583i) q^{40} +(0.553137 - 0.958062i) q^{41} +(2.93481 + 5.08323i) q^{43} +6.23912i q^{44} -10.4013 q^{46} +(2.44098 + 4.22790i) q^{47} +(10.6873 + 6.17029i) q^{50} +(-4.95235 + 2.85924i) q^{52} +10.3232i q^{53} +8.79491i q^{55} +(6.62698 - 11.4783i) q^{58} +(-2.56820 + 4.44826i) q^{59} +(-4.44613 + 2.56698i) q^{61} +5.55556 q^{62} +10.4766 q^{64} +(-6.98103 + 4.03050i) q^{65} +(-4.16544 + 7.21476i) q^{67} +(-8.41652 + 14.5778i) q^{68} -2.07026i q^{71} +8.01491i q^{73} +(3.04978 - 1.76079i) q^{74} +(-9.95741 - 5.74891i) q^{76} +(-2.50501 - 4.33881i) q^{79} +10.5511 q^{80} +2.30581i q^{82} +(1.04482 + 1.80968i) q^{83} +(-11.8643 + 20.5495i) q^{85} +(-10.5950 - 6.11703i) q^{86} +(-0.954997 - 1.65410i) q^{88} +1.08253 q^{89} +(10.1315 - 5.84945i) q^{92} +(-8.81223 - 5.08774i) q^{94} +(-14.0364 - 8.10390i) q^{95} +(9.47203 - 5.46868i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4}+O(q^{10}) \) 48 * q + 24 * q^4	\( 48 q + 24 q^{4} + 24 q^{11} - 24 q^{16} + 48 q^{23} - 24 q^{25} - 120 q^{32} - 48 q^{50} - 48 q^{64} - 120 q^{65} + 168 q^{74} - 24 q^{79} - 24 q^{85} - 24 q^{86} + 144 q^{92} - 96 q^{95}+O(q^{100}) \) 48 * q + 24 * q^4 + 24 * q^11 - 24 * q^16 + 48 * q^23 - 24 * q^25 - 120 * q^32 - 48 * q^50 - 48 * q^64 - 120 * q^65 + 168 * q^74 - 24 * q^79 - 24 * q^85 - 24 * q^86 + 144 * q^92 - 96 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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