LMFDB - Embedded newform 1323.2.s.d.656.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1323,2,Mod(656,1323)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1323, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1323.656"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$10.5642081874$
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			656.22
Character	$\chi$	$=$	1323.656
Dual form			1323.2.s.d.962.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.80506 - 1.04215i) q^{2} +(1.17216 - 2.03024i) q^{4} +3.30465 q^{5} -0.717672i q^{8} +(5.96509 - 3.44395i) q^{10} +2.66137i q^{11} +(2.11249 - 1.21964i) q^{13} +(1.59640 + 2.76504i) q^{16} +(-3.59017 - 6.21836i) q^{17} +(4.24746 + 2.45227i) q^{19} +(3.87358 - 6.70924i) q^{20} +(2.77356 + 4.80394i) q^{22} +4.99031i q^{23} +5.92072 q^{25} +(2.54211 - 4.40306i) q^{26} +(-5.50701 - 3.17947i) q^{29} +(-2.30833 - 1.33271i) q^{31} +(7.00624 + 4.04505i) q^{32} +(-12.9609 - 7.48301i) q^{34} +(0.844787 - 1.46321i) q^{37} +10.2226 q^{38} -2.37166i q^{40} +(-0.553137 - 0.958062i) q^{41} +(2.93481 - 5.08323i) q^{43} +(5.40324 + 3.11956i) q^{44} +(5.20066 + 9.00781i) q^{46} +(-2.44098 - 4.22790i) q^{47} +(10.6873 - 6.17029i) q^{50} -5.71848i q^{52} +(-8.94013 + 5.16159i) q^{53} +8.79491i q^{55} -13.2540 q^{58} +(2.56820 - 4.44826i) q^{59} +(-4.44613 + 2.56698i) q^{61} -5.55556 q^{62} +10.4766 q^{64} +(6.98103 - 4.03050i) q^{65} +(-4.16544 + 7.21476i) q^{67} -16.8330 q^{68} +2.07026i q^{71} +(6.94112 - 4.00746i) q^{73} -3.52159i q^{74} +(9.95741 - 5.74891i) q^{76} +(-2.50501 - 4.33881i) q^{79} +(5.27554 + 9.13750i) q^{80} +(-1.99689 - 1.15291i) q^{82} +(-1.04482 + 1.80968i) q^{83} +(-11.8643 - 20.5495i) q^{85} -12.2341i q^{86} +1.90999 q^{88} +(0.541267 - 0.937501i) q^{89} +(10.1315 + 5.84945i) q^{92} +(-8.81223 - 5.08774i) q^{94} +(14.0364 + 8.10390i) q^{95} +(-9.47203 - 5.46868i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4} - 24 q^{16} + 48 q^{25} + 120 q^{32} - 96 q^{44} - 48 q^{50} - 48 q^{53} - 48 q^{64} + 120 q^{65} - 24 q^{79} - 24 q^{85} + 144 q^{92} + 96 q^{95}+O(q^{100}) $ 48 * q + 24 * q^4 - 24 * q^16 + 48 * q^25 + 120 * q^32 - 96 * q^44 - 48 * q^50 - 48 * q^53 - 48 * q^64 + 120 * q^65 - 24 * q^79 - 24 * q^85 + 144 * q^92 + 96 * q^95

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.80506	−	1.04215i	1.27637	−	0.736913i	0.300191	−	0.953879i	$-0.402950\pi$
$2$	1.80506	−	1.04215i	1.27637	−	0.736913i	0.976179	+	0.216966i	$0.0696162\pi$
$3$		0			0
$3$		0			0
$4$	1.17216	−	2.03024i	0.586081	−	1.01512i
$5$	3.30465			1.47788			0.738942	−	0.673769i	$-0.235326\pi$
$5$	3.30465			1.47788			0.738942	+	0.673769i	$0.235326\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	0.717672i		−	0.253735i
$9$		0			0
$10$	5.96509	−	3.44395i	1.88633	−	1.08907i
$11$			2.66137i			0.802434i	0.915983	+	0.401217i	$0.131413\pi$
$11$			2.66137i			0.802434i	−0.915983	+	0.401217i	$0.868587\pi$
$12$		0			0
$13$	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
$15$		0			0
$16$	1.59640	+	2.76504i	0.399100	+	0.691261i
$17$	−3.59017	−	6.21836i	−0.870744	−	1.50817i	−0.861228	−	0.508219i	$-0.830304\pi$
$17$	−3.59017	−	6.21836i	−0.870744	−	1.50817i	−0.00951656	−	0.999955i	$-0.503029\pi$
$18$		0			0
$19$	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	$0.174171\pi$
$23$			4.99031i			1.04055i	−0.853998	+	0.520276i	$0.825829\pi$
$24$		0			0
$25$	5.92072			1.18414
$26$	2.54211	−	4.40306i	0.498549	−	0.863512i
$27$		0			0
$28$		0			0
$29$	−5.50701	−	3.17947i	−1.02263	−	0.590413i	−0.107762	−	0.994177i	$-0.534368\pi$
$29$	−5.50701	−	3.17947i	−1.02263	−	0.590413i	−0.914863	+	0.403764i	$0.867702\pi$
$30$		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
$37$	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
$39$		0			0
$40$		−	2.37166i		−	0.374992i
$41$	−0.553137	−	0.958062i	−0.0863855	−	0.149624i	0.819595	−	0.572943i	$-0.194198\pi$
$41$	−0.553137	−	0.958062i	−0.0863855	−	0.149624i	−0.905981	+	0.423319i	$0.860865\pi$
$42$		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
$45$		0			0
$46$	5.20066	+	9.00781i	0.766796	+	1.32813i
$47$	−2.44098	−	4.22790i	−0.356053	−	0.616703i	0.631244	−	0.775584i	$-0.282545\pi$
$47$	−2.44098	−	4.22790i	−0.356053	−	0.616703i	−0.987298	+	0.158881i	$0.949211\pi$
$48$		0			0
$49$		0			0
$50$	10.6873	−	6.17029i	1.51141	−	0.872610i
$51$		0			0
$52$		−	5.71848i		−	0.793011i
$53$	−8.94013	+	5.16159i	−1.22802	+	0.708999i	−0.966616	−	0.256230i	$-0.917519\pi$
$53$	−8.94013	+	5.16159i	−1.22802	+	0.708999i	−0.261406	+	0.965229i	$0.584186\pi$
$54$		0			0
$55$			8.79491i			1.18591i
$56$		0			0
$57$		0			0
$58$	−13.2540			−1.74033
$59$	2.56820	−	4.44826i	0.334351	−	0.579114i	−0.649009	−	0.760781i	$-0.724816\pi$
$59$	2.56820	−	4.44826i	0.334351	−	0.579114i	0.983360	+	0.181667i	$0.0581494\pi$
$60$		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	$0.996723\pi$
$68$	−16.8330			−2.04131
$69$		0			0
$70$		0			0
$71$			2.07026i			0.245695i	0.992426	+	0.122848i	$0.0392026\pi$
$71$			2.07026i			0.245695i	−0.992426	+	0.122848i	$0.960797\pi$
$72$		0			0
$73$	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
$75$		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	$0.924277\pi$
$80$	5.27554	+	9.13750i	0.589823	+	1.02160i
$81$		0			0
$82$	−1.99689	−	1.15291i	−0.220520	−	0.127317i
$83$	−1.04482	+	1.80968i	−0.114684	+	0.198638i	−0.917653	−	0.397382i	$-0.869919\pi$
$83$	−1.04482	+	1.80968i	−0.114684	+	0.198638i	0.802970	+	0.596020i	$0.203252\pi$
$84$		0			0
$85$	−11.8643	−	20.5495i	−1.28686	−	2.22891i
$86$		−	12.2341i		−	1.31923i
$87$		0			0
$88$	1.90999			0.203606
$89$	0.541267	−	0.937501i	0.0573741	−	0.0993749i	−0.835912	−	0.548864i	$-0.815061\pi$
$89$	0.541267	−	0.937501i	0.0573741	−	0.0993749i	0.893286	+	0.449489i	$0.148394\pi$
$90$		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	$-0.520715\pi$
$97$	−9.47203	−	5.46868i	−0.961739	−	0.555260i	−0.896708	+	0.442623i	$0.854048\pi$
$98$		0			0
$99$		0			0
$100$	6.94004	−	12.0205i	0.694004	−	1.20205i
$101$	−0.527915			−0.0525295			−0.0262647	−	0.999655i	$-0.508361\pi$
$101$	−0.527915			−0.0525295			−0.0262647	+	0.999655i	$0.508361\pi$
$102$		0			0
$103$			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	0.258994	−	0.965879i	$-0.416609\pi$
$107$	−4.63398	−	2.67543i	−0.447984	−	0.258644i	−0.706978	+	0.707235i	$0.749942\pi$
$108$		0			0
$109$	−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
$111$		0			0
$112$		0			0
$113$	−10.0024	+	5.77487i	−0.940944	+	0.543254i	−0.890256	−	0.455461i	$-0.849475\pi$
$113$	−10.0024	+	5.77487i	−0.940944	+	0.543254i	−0.0506876	+	0.998715i	$0.516141\pi$
$114$		0			0
$115$			16.4912i			1.53782i
$116$	−12.9102	+	7.45371i	−1.19868	+	0.692059i
$117$		0			0
$118$		−	10.7058i		−	0.985551i
$119$		0			0
$120$		0			0
$121$	3.91709			0.356099
$122$	−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
$131$	4.15126			0.362697			0.181349	−	0.983419i	$-0.441954\pi$
$131$	4.15126			0.362697			0.181349	+	0.983419i	$0.441954\pi$
$132$		0			0
$133$		0			0
$134$			17.3641i			1.50003i
$135$		0			0
$136$	−4.46274	+	2.57657i	−0.382677	+	0.220939i
$137$		−	6.29419i		−	0.537749i	−0.963175	−	0.268874i	$-0.913348\pi$
$137$		−	6.29419i		−	0.537749i	0.963175	−	0.268874i	$-0.0866516\pi$
$138$		0			0
$139$	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
$141$		0			0
$142$	2.15753	+	3.73695i	0.181056	+	0.313598i
$143$	3.24593	+	5.62212i	0.271438	+	0.470145i
$144$		0			0
$145$	−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	$0.0703019\pi$
$149$			5.34815i			0.438137i	−0.975709	+	0.219069i	$0.929698\pi$
$150$		0			0
$151$	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
$153$		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
$163$	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			0
$166$			4.35543i			0.338047i
$167$	7.95418	+	13.7770i	0.615513	+	1.06610i	0.990294	+	0.138986i	$0.0443844\pi$
$167$	7.95418	+	13.7770i	0.615513	+	1.06610i	−0.374782	+	0.927113i	$0.622282\pi$
$168$		0			0
$169$	−3.52493	+	6.10536i	−0.271149	+	0.469643i
$170$	−42.8314	−	24.7287i	−3.28502	−	1.89661i
$171$		0			0
$172$	−6.88013	−	11.9167i	−0.524605	−	0.908643i
$173$	9.33097	+	16.1617i	0.709421	+	1.22875i	0.965072	+	0.261984i	$0.0843767\pi$
$173$	9.33097	+	16.1617i	0.709421	+	1.22875i	−0.255651	+	0.966769i	$0.582290\pi$
$174$		0			0
$175$		0			0
$176$	−7.35882	+	4.24861i	−0.554692	+	0.320251i
$177$		0			0
$178$		−	2.25633i		−	0.169119i
$179$	19.0792	−	11.0154i	1.42604	−	0.823326i	0.429237	−	0.903192i	$-0.358782\pi$
$179$	19.0792	−	11.0154i	1.42604	−	0.823326i	0.996806	+	0.0798653i	$0.0254490\pi$
$180$		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
$184$	3.58141			0.264025
$185$	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	0.0640104	−	0.997949i	$-0.479611\pi$
$191$	13.2711	−	7.66209i	0.960265	−	0.554409i	0.896255	+	0.443540i	$0.146278\pi$
$192$		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	$0.785638\pi$
$194$	−22.7968			−1.63671
$195$		0			0
$196$		0			0
$197$		−	4.18301i		−	0.298027i	−0.988835	−	0.149014i	$-0.952390\pi$
$197$		−	4.18301i		−	0.298027i	0.988835	−	0.149014i	$-0.0476098\pi$
$198$		0			0
$199$	−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
$201$		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
$206$	0.816769	+	1.41469i	0.0569070	+	0.0985658i
$207$		0			0
$208$	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			0
$214$	−11.1528			−0.762392
$215$	9.69851	−	16.7983i	0.661433	−	1.14564i
$216$		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	$-0.424654\pi$
$223$	−7.31908	−	4.22567i	−0.490122	−	0.282972i	−0.724625	+	0.689143i	$0.757987\pi$
$224$		0			0
$225$		0			0
$226$	−12.0366	+	20.8480i	−0.800662	+	1.38679i
$227$	−5.82949			−0.386917			−0.193458	−	0.981108i	$-0.561970\pi$
$227$	−5.82949			−0.386917			−0.193458	+	0.981108i	$0.561970\pi$
$228$		0			0
$229$			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	0.981685	−	0.190513i	$-0.0610151\pi$
$233$	19.9587	+	11.5232i	1.30754	+	0.754907i	0.325853	+	0.945420i	$0.394348\pi$
$234$		0			0
$235$	−8.06659	−	13.9717i	−0.526206	−	0.911416i
$236$	−6.02069	−	10.4281i	−0.391914	−	0.678815i
$237$		0			0
$238$		0			0
$239$	−5.91972	+	3.41775i	−0.382915	+	0.221076i	−0.679086	−	0.734059i	$-0.737624\pi$
$239$	−5.91972	+	3.41775i	−0.382915	+	0.221076i	0.296171	+	0.955135i	$0.404290\pi$
$240$		0			0
$241$			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
$243$		0			0
$244$			12.0356i			0.770503i
$245$		0			0
$246$		0			0
$247$	11.9636			0.761225
$248$	−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	$-0.495304\pi$
$251$	0.467438			0.0295044			0.0147522	+	0.999891i	$0.495304\pi$
$252$		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
$257$	−21.4865			−1.34029			−0.670146	−	0.742229i	$-0.733769\pi$
$257$	−21.4865			−1.34029			−0.670146	+	0.742229i	$0.733769\pi$
$258$		0			0
$259$		0			0
$260$		−	18.8976i		−	1.17198i
$261$		0			0
$262$	7.49327	−	4.32624i	0.462936	−	0.267276i
$263$			11.0897i			0.683819i	0.939733	+	0.341909i	$0.111074\pi$
$263$			11.0897i			0.683819i	−0.939733	+	0.341909i	$0.888926\pi$
$264$		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
$269$	−11.0288	−	19.1024i	−0.672435	−	1.16469i	−0.977212	−	0.212268i	$-0.931915\pi$
$269$	−11.0288	−	19.1024i	−0.672435	−	1.16469i	0.304776	−	0.952424i	$-0.401418\pi$
$270$		0			0
$271$	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
$276$		0			0
$277$	−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
$279$		0			0
$280$		0			0
$281$	17.0883	+	9.86595i	1.01940	+	0.588553i	0.913931	−	0.405869i	$-0.133031\pi$
$281$	17.0883	+	9.86595i	1.01940	+	0.588553i	0.105473	+	0.994422i	$0.466364\pi$
$282$		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
$289$	−17.2787	+	29.9275i	−1.01639	+	1.76044i
$290$	−43.7997			−2.57201
$291$		0			0
$292$		−	18.7895i		−	1.09957i
$293$	−15.0393	−	26.0488i	−0.878603	−	1.52178i	−0.852875	−	0.522115i	$-0.825143\pi$
$293$	−15.0393	−	26.0488i	−0.878603	−	1.52178i	−0.0257278	−	0.999669i	$-0.508190\pi$
$294$		0			0
$295$	8.48701	−	14.6999i	0.494133	−	0.855863i
$296$	−1.05011	−	0.606281i	−0.0610363	−	0.0352393i
$297$		0			0
$298$	5.57358	+	9.65373i	0.322869	+	0.559225i
$299$	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
$304$			15.6592i			0.898117i
$305$	−14.6929	+	8.48296i	−0.841314	+	0.485733i
$306$		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
$310$	−18.3592			−1.04273
$311$	−8.35507	+	14.4714i	−0.473773	+	0.820599i	−0.999549	−	0.0300243i	$-0.990442\pi$
$311$	−8.35507	+	14.4714i	−0.473773	+	0.820599i	0.525776	+	0.850623i	$0.323775\pi$
$312$		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	−0.443725	−	0.896163i	$-0.646343\pi$
$317$	1.96761	−	1.13600i	0.110512	−	0.0638040i	0.554237	+	0.832359i	$0.313010\pi$
$318$		0			0
$319$	8.46176	−	14.6562i	0.473768	−	0.820590i
$320$	34.6216			1.93541
$321$		0			0
$322$		0			0
$323$		−	35.2163i		−	1.95949i
$324$		0			0
$325$	12.5074	−	7.22117i	0.693788	−	0.400559i
$326$		−	48.1309i		−	2.66573i
$327$		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	$0.726830\pi$
$332$	2.44939	+	4.24247i	0.134428	+	0.232836i
$333$		0			0
$334$	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
$339$		0			0
$340$	−55.6273			−3.01681
$341$	3.54685	−	6.14332i	0.192073	−	0.332679i
$342$		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	0.661975	−	0.749526i	$-0.269719\pi$
$347$	6.40529	+	3.69809i	0.343854	+	0.198524i	−0.318121	+	0.948050i	$0.603052\pi$
$348$		0			0
$349$	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
$351$		0			0
$352$	−10.7654	+	18.6462i	−0.573798	+	0.993847i
$353$	7.09907			0.377845			0.188923	−	0.981992i	$-0.439500\pi$
$353$	7.09907			0.377845			0.188923	+	0.981992i	$0.439500\pi$
$354$		0			0
$355$			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	0.708737	−	0.705472i	$-0.249265\pi$
$359$	8.56701	+	4.94616i	0.452149	+	0.261049i	−0.256588	+	0.966521i	$0.582598\pi$
$360$		0			0
$361$	2.52726	+	4.37734i	0.133014	+	0.230386i
$362$	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
$367$		−	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
$369$		0			0
$370$		−	11.6376i		−	0.605011i
$371$		0			0
$372$		0			0
$373$	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
$375$		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
$383$	13.2102			0.675011			0.337505	−	0.941324i	$-0.390417\pi$
$383$	13.2102			0.675011			0.337505	+	0.941324i	$0.390417\pi$
$384$		0			0
$385$		0			0
$386$			53.9140i			2.74415i
$387$		0			0
$388$	−22.2055	+	12.8203i	−1.12731	+	0.650854i
$389$		−	33.8236i		−	1.71492i	−0.514549	−	0.857461i	$-0.672040\pi$
$389$		−	33.8236i		−	1.71492i	0.514549	−	0.857461i	$-0.327960\pi$
$390$		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
$395$	−8.27820	−	14.3383i	−0.416521	−	0.721436i
$396$		0			0
$397$	−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	$-0.868002\pi$
$401$		−	16.1362i		−	0.805801i	0.915244	−	0.402900i	$-0.131998\pi$
$402$		0			0
$403$	−6.50175			−0.323875
$404$	−0.618801	+	1.07180i	−0.0307865	+	0.0533238i
$405$		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
$415$	−3.45276	+	5.98035i	−0.169489	+	0.293564i
$416$	19.7341			0.967544
$417$		0			0
$418$			27.2060i			1.33069i
$419$	0.589031	+	1.02023i	0.0287760	+	0.0498415i	0.880055	−	0.474872i	$-0.157506\pi$
$419$	0.589031	+	1.02023i	0.0287760	+	0.0498415i	−0.851279	+	0.524714i	$0.824172\pi$
$420$		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
$423$		0			0
$424$	3.70433	+	6.41609i	0.179898	+	0.311593i
$425$	−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
$430$		−	40.4293i		−	1.94967i
$431$	0.702488	−	0.405582i	0.0338377	−	0.0195362i	−0.482986	−	0.875628i	$-0.660448\pi$
$431$	0.702488	−	0.405582i	0.0338377	−	0.0195362i	0.516823	+	0.856092i	$0.327114\pi$
$432$		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
$436$	−13.9844			−0.669731
$437$	−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	−0.730308	−	0.683118i	$-0.760623\pi$
$443$	−10.6051	+	6.12286i	−0.503864	+	0.290906i	0.226444	+	0.974024i	$0.427290\pi$
$444$		0			0
$445$	1.78870	−	3.09811i	0.0847924	−	0.146865i
$446$	−17.6152			−0.834103
$447$		0			0
$448$		0			0
$449$		−	22.0163i		−	1.03901i	−0.854466	−	0.519507i	$-0.826116\pi$
$449$		−	22.0163i		−	1.03901i	0.854466	−	0.519507i	$-0.173884\pi$
$450$		0			0
$451$	2.54976	−	1.47211i	0.120064	−	0.0693187i
$452$			27.0763i			1.27356i
$453$		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	$-0.357784\pi$
$458$	5.00051	+	8.66114i	0.233659	+	0.404709i
$459$		0			0
$460$	33.4812	+	19.3304i	1.56107	+	0.901284i
$461$	16.3899	−	28.3881i	0.763352	−	1.32216i	−0.177762	−	0.984074i	$-0.556886\pi$
$461$	16.3899	−	28.3881i	0.763352	−	1.32216i	0.941114	−	0.338091i	$-0.109781\pi$
$462$		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
$465$		0			0
$466$	48.0355			2.22520
$467$	16.5765	−	28.7114i	0.767070	−	1.32860i	−0.172075	−	0.985084i	$-0.555047\pi$
$467$	16.5765	−	28.7114i	0.767070	−	1.32860i	0.939145	−	0.343521i	$-0.111620\pi$
$468$		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
$478$	−7.12364	+	12.3385i	−0.325828	+	0.564350i
$479$	22.7945			1.04151			0.520754	−	0.853707i	$-0.325651\pi$
$479$	22.7945			1.04151			0.520754	+	0.853707i	$0.325651\pi$
$480$		0			0
$481$		−	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
$486$		0			0
$487$	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
$489$		0			0
$490$		0			0
$491$	−21.6775	+	12.5155i	−0.978291	+	0.564817i	−0.901754	−	0.432250i	$-0.857720\pi$
$491$	−21.6775	+	12.5155i	−0.978291	+	0.564817i	−0.0765375	+	0.997067i	$0.524387\pi$
$492$		0			0
$493$			45.6594i			2.05640i
$494$	21.5950	−	12.4679i	0.971605	−	0.560957i
$495$		0			0
$496$		−	8.51016i		−	0.382118i
$497$		0			0
$498$		0			0
$499$	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
$501$		0			0
$502$	0.843754	−	0.487141i	0.0376586	−	0.0217422i
$503$	39.0362			1.74054			0.870269	−	0.492577i	$-0.163945\pi$
$503$	39.0362			1.74054			0.870269	+	0.492577i	$0.163945\pi$
$504$		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
$509$	32.5819			1.44417			0.722083	−	0.691806i	$-0.243185\pi$
$509$	32.5819			1.44417			0.722083	+	0.691806i	$0.243185\pi$
$510$		0			0
$511$		0			0
$512$			30.4128i			1.34407i
$513$		0			0
$514$	−38.7845	+	22.3922i	−1.71071	+	0.987679i
$515$			2.58997i			0.114128i
$516$		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
$521$	3.68456	+	6.38185i	0.161424	+	0.279594i	0.935379	−	0.353646i	$-0.115058\pi$
$521$	3.68456	+	6.38185i	0.161424	+	0.279594i	−0.773956	+	0.633240i	$0.781725\pi$
$522$		0			0
$523$	−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
$528$		0			0
$529$	−1.90322			−0.0827487
$530$	−35.5525	+	61.5787i	−1.54430	+	2.67481i
$531$		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
$541$	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			0
$544$		−	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
$549$		0			0
$550$	16.4214	+	28.4428i	0.700213	+	1.21280i
$551$	−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
$556$		−	3.58880i		−	0.152199i
$557$	9.42040	−	5.43887i	0.399155	−	0.230452i	−0.286964	−	0.957941i	$-0.592646\pi$
$557$	9.42040	−	5.43887i	0.399155	−	0.230452i	0.686119	+	0.727489i	$0.259313\pi$
$558$		0			0
$559$		−	14.3177i		−	0.605574i
$560$		0			0
$561$		0			0
$562$	41.1273			1.73485
$563$	−6.67759	+	11.5659i	−0.281427	+	0.487445i	−0.971736	−	0.236069i	$-0.924141\pi$
$563$	−6.67759	+	11.5659i	−0.281427	+	0.487445i	0.690310	+	0.723514i	$0.257474\pi$
$564$		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	−0.314721	−	0.949184i	$-0.601911\pi$
$569$	8.34729	−	4.81931i	0.349937	−	0.202036i	0.664657	+	0.747148i	$0.268578\pi$
$570$		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	$-0.0891578\pi$
$572$	15.2190			0.636339
$573$		0			0
$574$		0			0
$575$			29.5462i			1.23216i
$576$		0			0
$577$	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
$579$		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
$584$	−2.87604	−	4.98145i	−0.119011	−	0.206134i
$585$		0			0
$586$	−54.2935	−	31.3464i	−2.24284	−	1.29491i
$587$	3.96848	−	6.87362i	0.163797	−	0.283704i	−0.772431	−	0.635099i	$-0.780959\pi$
$587$	3.96848	−	6.87362i	0.163797	−	0.283704i	0.936227	+	0.351395i	$0.114293\pi$
$588$		0			0
$589$	−6.53634	−	11.3213i	−0.269325	−	0.466485i
$590$		−	35.3790i		−	1.45653i
$591$		0			0
$592$	5.39447			0.221711
$593$	−20.9147	+	36.2252i	−0.858862	+	1.48759i	0.0141532	+	0.999900i	$0.495495\pi$
$593$	−20.9147	+	36.2252i	−0.858862	+	1.48759i	−0.873015	+	0.487693i	$0.837839\pi$
$594$		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	0.337235	−	0.941421i	$-0.390508\pi$
$599$	−7.57344	−	4.37253i	−0.309442	−	0.178657i	−0.646677	+	0.762764i	$0.723842\pi$
$600$		0			0
$601$	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
$603$		0			0
$604$	13.4654	−	23.3228i	0.547900	−	0.948990i
$605$	12.9446			0.526273
$606$		0			0
$607$		−	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
$612$		0			0
$613$	−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
$615$		0			0
$616$		0			0
$617$	36.5255	−	21.0880i	1.47046	−	0.848971i	0.471011	−	0.882127i	$-0.343889\pi$
$617$	36.5255	−	21.0880i	1.47046	−	0.848971i	0.999450	+	0.0331557i	$0.0105557\pi$
$618$		0			0
$619$		−	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
$621$		0			0
$622$			34.8290i			1.39652i
$623$		0			0
$624$		0			0
$625$	−19.5487			−0.781947
$626$	−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
$635$	−63.1036			−2.50419
$636$		0			0
$637$		0			0
$638$		−	35.2738i		−	1.39650i
$639$		0			0
$640$	16.1878	−	9.34604i	0.639879	−	0.369435i
$641$			17.6072i			0.695444i	0.937598	+	0.347722i	$0.113045\pi$
$641$			17.6072i			0.695444i	−0.937598	+	0.347722i	$0.886955\pi$
$642$		0			0
$643$	−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
$645$		0			0
$646$	−36.7007	−	63.5675i	−1.44397	−	2.50103i
$647$	−5.77035	−	9.99454i	−0.226856	−	0.392926i	0.730019	−	0.683427i	$-0.239511\pi$
$647$	−5.77035	−	9.99454i	−0.226856	−	0.392926i	−0.956875	+	0.290501i	$0.906178\pi$
$648$		0			0
$649$	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	$-0.864913\pi$
$653$		−	21.0444i		−	0.823529i	0.911290	−	0.411765i	$-0.135087\pi$
$654$		0			0
$655$	13.7185			0.536024
$656$	1.76606	−	3.05890i	0.0689529	−	0.119430i
$657$		0			0
$658$		0			0
$659$	31.8016	+	18.3607i	1.23881	+	0.715230i	0.968852	−	0.247641i	$-0.0796555\pi$
$659$	31.8016	+	18.3607i	1.23881	+	0.715230i	0.269962	+	0.962871i	$0.412989\pi$
$660$		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
$667$	15.8666	−	27.4817i	0.614356	−	1.06410i
$668$	37.2943			1.44296
$669$		0			0
$670$			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
$675$		0			0
$676$	8.26358	+	14.3129i	0.317830	+	0.550498i
$677$	14.9077	+	25.8208i	0.572948	+	0.992374i	0.996261	+	0.0863911i	$0.0275335\pi$
$677$	14.9077	+	25.8208i	0.572948	+	0.992374i	−0.423314	+	0.905983i	$0.639133\pi$
$678$		0			0
$679$		0			0
$680$	−14.7478	+	8.51465i	−0.565553	+	0.326522i
$681$		0			0
$682$		−	14.7854i		−	0.566163i
$683$	−26.1841	+	15.1174i	−1.00191	+	0.578451i	−0.908812	−	0.417207i	$-0.863009\pi$
$683$	−26.1841	+	15.1174i	−1.00191	+	0.578451i	−0.0930943	+	0.995657i	$0.529676\pi$
$684$		0			0
$685$		−	20.8001i		−	0.794731i
$686$		0			0
$687$		0			0
$688$	18.7405			0.714474
$689$	−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
$698$	43.4407			1.64426
$699$		0			0
$700$		0			0
$701$			0.757329i			0.0286039i	0.999898	+	0.0143020i	$0.00455261\pi$
$701$			0.757329i			0.0286039i	−0.999898	+	0.0143020i	$0.995447\pi$
$702$		0			0
$703$	7.17640	−	4.14329i	0.270663	−	0.156267i
$704$			27.8823i			1.05085i
$705$		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	$0.700992\pi$
$710$	7.12988	+	12.3493i	0.267580	+	0.463461i
$711$		0			0
$712$	−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
$717$		0			0
$718$	20.6186			0.769480
$719$	−22.1254	+	38.3224i	−0.825140	+	1.42918i	0.0766729	+	0.997056i	$0.475570\pi$
$719$	−22.1254	+	38.3224i	−0.825140	+	1.42918i	−0.901813	+	0.432127i	$0.857763\pi$
$720$		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	$-0.313202\pi$
$727$	2.95166	+	1.70414i	0.109471	+	0.0632031i	−0.444265	+	0.895895i	$0.646535\pi$
$728$		0			0
$729$		0			0
$730$	27.6029	−	47.8097i	1.02163	−	1.76952i
$731$	−42.1458			−1.55882
$732$		0			0
$733$			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
$738$		0			0
$739$	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
$741$		0			0
$742$		0			0
$743$	−26.1921	+	15.1220i	−0.960895	+	0.554773i	−0.896448	−	0.443148i	$-0.853862\pi$
$743$	−26.1921	+	15.1220i	−0.960895	+	0.554773i	−0.0644465	+	0.997921i	$0.520528\pi$
$744$		0			0
$745$			17.6738i			0.647516i
$746$	52.4304	−	30.2707i	1.91961	−	1.10829i
$747$		0			0
$748$		−	44.7990i		−	1.63801i
$749$		0			0
$750$		0			0
$751$	−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			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
$761$	−10.5435			−0.382201			−0.191100	−	0.981570i	$-0.561206\pi$
$761$	−10.5435			−0.382201			−0.191100	+	0.981570i	$0.561206\pi$
$762$		0			0
$763$		0			0
$764$		−	35.9248i		−	1.29971i
$765$		0			0
$766$	23.8452	−	13.7671i	0.861563	−	0.497424i
$767$		−	12.5292i		−	0.452403i
$768$		0			0
$769$	−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
$771$		0			0
$772$	30.3199	+	52.5156i	1.09124	+	1.89008i
$773$	10.9386	+	18.9462i	0.393433	+	0.681446i	0.992900	−	0.118954i	$-0.0379541\pi$
$773$	10.9386	+	18.9462i	0.393433	+	0.681446i	−0.599467	+	0.800400i	$0.704621\pi$
$774$		0			0
$775$	−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			0
$781$	−5.50974			−0.197154
$782$	37.3425	−	64.6792i	1.33537	−	2.31292i
$783$		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
$793$	−6.26160	+	10.8454i	−0.222356	+	0.385132i
$794$	−17.8697			−0.634171
$795$		0			0
$796$			51.5930i			1.82867i
$797$	−21.3285	−	36.9420i	−0.755493	−	1.30855i	−0.945129	−	0.326697i	$-0.894064\pi$
$797$	−21.3285	−	36.9420i	−0.755493	−	1.30855i	0.189636	−	0.981854i	$-0.439269\pi$
$798$		0			0
$799$	−17.5271	+	30.3578i	−0.620063	+	1.07398i
$800$	41.4820	+	23.9496i	1.46661	+	0.846747i
$801$		0			0
$802$	−16.8163	−	29.1267i	−0.593805	−	1.02850i
$803$	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
$808$			0.378870i			0.0133286i
$809$	−30.9391	+	17.8627i	−1.08776	+	0.628019i	−0.932979	−	0.359930i	$-0.882801\pi$
$809$	−30.9391	+	17.8627i	−1.08776	+	0.628019i	−0.154781	+	0.987949i	$0.549467\pi$
$810$		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
$814$	9.37226			0.328498
$815$	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	−0.210275	−	0.977642i	$-0.567436\pi$
$821$	15.2220	−	8.78841i	0.531251	−	0.306718i	0.741526	+	0.670925i	$0.234103\pi$
$822$		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	$0.989059\pi$
$824$	0.562464			0.0195943
$825$		0			0
$826$		0			0
$827$			15.4454i			0.537089i	0.963267	+	0.268545i	$0.0865426\pi$
$827$			15.4454i			0.537089i	−0.963267	+	0.268545i	$0.913457\pi$
$828$		0			0
$829$	−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
$831$		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
$836$	15.3000	+	26.5004i	0.529162	+	0.916535i
$837$		0			0
$838$	2.12647	+	1.22772i	0.0734577	+	0.0424108i
$839$	−16.8620	+	29.2058i	−0.582140	+	1.00830i	0.413086	+	0.910692i	$0.364451\pi$
$839$	−16.8620	+	29.2058i	−0.582140	+	1.00830i	−0.995225	+	0.0976035i	$0.968882\pi$
$840$		0			0
$841$	5.71808	+	9.90401i	0.197175	+	0.341517i
$842$		−	14.3210i		−	0.493534i
$843$		0			0
$844$	57.6356			1.98390
$845$	−11.6487	+	20.1761i	−0.400726	+	0.694079i
$846$		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	$-0.600738\pi$
$853$	−37.6715	−	21.7497i	−1.28985	−	0.744694i	−0.978627	+	0.205643i	$0.934071\pi$
$854$		0			0
$855$		0			0
$856$	−1.92008	+	3.32568i	−0.0656271	+	0.113669i
$857$	8.43068			0.287986			0.143993	−	0.989579i	$-0.454006\pi$
$857$	8.43068			0.287986			0.143993	+	0.989579i	$0.454006\pi$
$858$		0			0
$859$		−	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	0.631799	−	0.775132i	$-0.282317\pi$
$863$	8.12017	+	4.68818i	0.276414	+	0.159588i	−0.355385	+	0.934720i	$0.615650\pi$
$864$		0			0
$865$	30.8356	+	53.4089i	1.04844	+	1.81596i
$866$	−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
$871$			20.3214i			0.688566i
$872$	−3.70751	+	2.14053i	−0.125552	+	0.0724877i
$873$		0			0
$874$			51.0137i			1.72557i
$875$		0			0
$876$		0			0
$877$	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
$879$		0			0
$880$	−24.3183	+	14.0402i	−0.819770	+	0.473295i
$881$	43.4962			1.46542			0.732712	−	0.680539i	$-0.238254\pi$
$881$	43.4962			1.46542			0.732712	+	0.680539i	$0.238254\pi$
$882$		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
$887$	35.1532			1.18033			0.590164	−	0.807283i	$-0.299063\pi$
$887$	35.1532			1.18033			0.590164	+	0.807283i	$0.299063\pi$
$888$		0			0
$889$		0			0
$890$		−	7.45638i		−	0.249938i
$891$		0			0
$892$	−17.1583	+	9.90634i	−0.574502	+	0.331689i
$893$		−	23.9438i		−	0.801248i
$894$		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
$899$	8.47464	+	14.6785i	0.282645	+	0.489556i
$900$		0			0
$901$	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
$906$		0			0
$907$	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
$909$		0			0
$910$		0			0
$911$	39.9027	+	23.0378i	1.32203	+	0.763277i	0.984053	−	0.177876i	$-0.0569226\pi$
$911$	39.9027	+	23.0378i	1.32203	+	0.763277i	0.337981	+	0.941153i	$0.390256\pi$
$912$		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
$919$	−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			0
$922$		−	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			0
$928$	−25.7223	−	44.5523i	−0.844375	−	1.46250i
$929$	−26.4514	−	45.8152i	−0.867843	−	1.50315i	−0.864196	−	0.503155i	$-0.832172\pi$
$929$	−26.4514	−	45.8152i	−0.867843	−	1.50315i	−0.00364718	−	0.999993i	$-0.501161\pi$
$930$		0			0
$931$		0			0
$932$	46.7896	−	27.0140i	1.53265	−	0.884873i
$933$		0			0
$934$		−	69.1010i		−	2.26106i
$935$	54.6899	−	31.5752i	1.78855	−	1.03262i
$936$		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
$940$	−37.8214			−1.23360
$941$	0.505336	−	0.875268i	0.0164735	−	0.0285329i	−0.857671	−	0.514199i	$-0.828089\pi$
$941$	0.505336	−	0.875268i	0.0164735	−	0.0285329i	0.874145	+	0.485666i	$0.161423\pi$
$942$		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	−0.340069	−	0.940400i	$-0.610451\pi$
$947$	9.36454	−	5.40662i	0.304307	−	0.175692i	0.644376	+	0.764709i	$0.277117\pi$
$948$		0			0
$949$	9.77535	−	16.9314i	0.317321	−	0.549616i
$950$	60.5249			1.96369
$951$		0			0
$952$		0			0
$953$		−	26.7466i		−	0.866408i	−0.901296	−	0.433204i	$-0.857383\pi$
$953$		−	26.7466i		−	0.866408i	0.901296	−	0.433204i	$-0.142617\pi$
$954$		0			0
$955$	43.8564	−	25.3205i	1.41916	−	0.819353i
$956$			16.0246i			0.518274i
$957$		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
$962$	−4.29509	−	7.43931i	−0.138479	−	0.239853i
$963$		0			0
$964$	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			0
$970$	−75.3354			−2.41887
$971$	4.41423	−	7.64567i	0.141659	−	0.245361i	−0.786462	−	0.617638i	$-0.788090\pi$
$971$	4.41423	−	7.64567i	0.141659	−	0.245361i	0.928122	+	0.372277i	$0.121423\pi$
$972$		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	0.951432	−	0.307859i	$-0.0996124\pi$
$977$	36.2748	+	20.9433i	1.16053	+	0.670035i	0.209102	+	0.977894i	$0.432946\pi$
$978$		0			0
$979$	2.49504	+	1.44051i	0.0797419	+	0.0460390i
$980$		0			0
$981$		0			0
$982$	−26.0861	+	45.1825i	−0.832441	+	1.44183i
$983$	4.70388			0.150031			0.0750153	−	0.997182i	$-0.476099\pi$
$983$	4.70388			0.150031			0.0750153	+	0.997182i	$0.476099\pi$
$984$		0			0
$985$		−	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
$990$		0			0
$991$	−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
$993$		0			0
$994$		0			0
$995$	−62.9840	+	36.3638i	−1.99673	+	1.15281i
$996$		0			0
$997$			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
$999$		0			0

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(1.80506 - 1.04215i) q^{2} +(1.17216 - 2.03024i) q^{4} +3.30465 q^{5} -0.717672i q^{8} +(5.96509 - 3.44395i) q^{10} +2.66137i q^{11} +(2.11249 - 1.21964i) q^{13} +(1.59640 + 2.76504i) q^{16} +(-3.59017 - 6.21836i) q^{17} +(4.24746 + 2.45227i) q^{19} +(3.87358 - 6.70924i) q^{20} +(2.77356 + 4.80394i) q^{22} +4.99031i q^{23} +5.92072 q^{25} +(2.54211 - 4.40306i) q^{26} +(-5.50701 - 3.17947i) q^{29} +(-2.30833 - 1.33271i) q^{31} +(7.00624 + 4.04505i) q^{32} +(-12.9609 - 7.48301i) q^{34} +(0.844787 - 1.46321i) q^{37} +10.2226 q^{38} -2.37166i q^{40} +(-0.553137 - 0.958062i) q^{41} +(2.93481 - 5.08323i) q^{43} +(5.40324 + 3.11956i) q^{44} +(5.20066 + 9.00781i) q^{46} +(-2.44098 - 4.22790i) q^{47} +(10.6873 - 6.17029i) q^{50} -5.71848i q^{52} +(-8.94013 + 5.16159i) q^{53} +8.79491i q^{55} -13.2540 q^{58} +(2.56820 - 4.44826i) q^{59} +(-4.44613 + 2.56698i) q^{61} -5.55556 q^{62} +10.4766 q^{64} +(6.98103 - 4.03050i) q^{65} +(-4.16544 + 7.21476i) q^{67} -16.8330 q^{68} +2.07026i q^{71} +(6.94112 - 4.00746i) q^{73} -3.52159i q^{74} +(9.95741 - 5.74891i) q^{76} +(-2.50501 - 4.33881i) q^{79} +(5.27554 + 9.13750i) q^{80} +(-1.99689 - 1.15291i) q^{82} +(-1.04482 + 1.80968i) q^{83} +(-11.8643 - 20.5495i) q^{85} -12.2341i q^{86} +1.90999 q^{88} +(0.541267 - 0.937501i) q^{89} +(10.1315 + 5.84945i) q^{92} +(-8.81223 - 5.08774i) q^{94} +(14.0364 + 8.10390i) q^{95} +(-9.47203 - 5.46868i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4} - 24 q^{16} + 48 q^{25} + 120 q^{32} - 96 q^{44} - 48 q^{50} - 48 q^{53} - 48 q^{64} + 120 q^{65} - 24 q^{79} - 24 q^{85} + 144 q^{92} + 96 q^{95}+O(q^{100}) \) 48 * q + 24 * q^4 - 24 * q^16 + 48 * q^25 + 120 * q^32 - 96 * q^44 - 48 * q^50 - 48 * q^53 - 48 * q^64 + 120 * q^65 - 24 * q^79 - 24 * q^85 + 144 * q^92 + 96 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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