LMFDB - Embedded newform 1323.2.i.d.1097.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1323,2,Mod(521,1323)] 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, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1323.521"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.i (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			1097.17
Character	$\chi$	$=$	1323.1097
Dual form			1323.2.i.d.521.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.83202i q^{2} -1.35631 q^{4} +(-0.322784 - 0.559079i) q^{5} -1.17925i q^{8} +(-1.02425 + 0.591348i) q^{10} +(4.60375 + 2.65797i) q^{11} +(4.44045 + 2.56370i) q^{13} -4.87304 q^{16} +(0.814931 + 1.41150i) q^{17} +(2.09039 + 1.20689i) q^{19} +(0.437796 + 0.758285i) q^{20} +(4.86947 - 8.43418i) q^{22} +(-1.27442 + 0.735784i) q^{23} +(2.29162 - 3.96920i) q^{25} +(4.69675 - 8.13502i) q^{26} +(6.43846 - 3.71724i) q^{29} +5.66726i q^{31} +6.56903i q^{32} +(2.58590 - 1.49297i) q^{34} +(3.99736 - 6.92362i) q^{37} +(2.21105 - 3.82965i) q^{38} +(-0.659294 + 0.380644i) q^{40} +(-5.99052 + 10.3759i) q^{41} +(-1.51281 - 2.62026i) q^{43} +(-6.24412 - 3.60504i) q^{44} +(1.34797 + 2.33476i) q^{46} -3.08353 q^{47} +(-7.27168 - 4.19830i) q^{50} +(-6.02264 - 3.47717i) q^{52} +(-2.04554 + 1.18100i) q^{53} -3.43181i q^{55} +(-6.81008 - 11.7954i) q^{58} +2.95836 q^{59} -10.6004i q^{61} +10.3825 q^{62} +2.28853 q^{64} -3.31008i q^{65} -10.1549 q^{67} +(-1.10530 - 1.91444i) q^{68} -4.76597i q^{71} +(10.2239 - 5.90277i) q^{73} +(-12.6842 - 7.32325i) q^{74} +(-2.83523 - 1.63692i) q^{76} +6.96209 q^{79} +(1.57294 + 2.72441i) q^{80} +(19.0089 + 10.9748i) q^{82} +(-3.51618 - 6.09021i) q^{83} +(0.526093 - 0.911221i) q^{85} +(-4.80038 + 2.77150i) q^{86} +(3.13442 - 5.42898i) q^{88} +(2.16337 - 3.74706i) q^{89} +(1.72850 - 0.997953i) q^{92} +5.64910i q^{94} -1.55826i q^{95} +(-14.3946 + 8.31075i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4} - 24 q^{11} + 48 q^{16} - 48 q^{23} - 24 q^{25} + 96 q^{44} - 48 q^{50} + 48 q^{53} - 48 q^{64} - 168 q^{74} + 48 q^{79} - 24 q^{85} + 24 q^{86} + 144 q^{92}+O(q^{100}) $ 48 * q - 48 * q^4 - 24 * q^11 + 48 * q^16 - 48 * q^23 - 24 * q^25 + 96 * q^44 - 48 * q^50 + 48 * q^53 - 48 * q^64 - 168 * q^74 + 48 * q^79 - 24 * q^85 + 24 * q^86 + 144 * q^92

Character values

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

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

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 $

$2$		−	1.83202i		−	1.29544i	−0.761880	−	0.647718i	$-0.775723\pi$
$2$		−	1.83202i		−	1.29544i	0.761880	−	0.647718i	$-0.224277\pi$
$3$		0			0
$3$		0			0
$4$	−1.35631			−0.678156
$5$	−0.322784	−	0.559079i	−0.144353	−	0.250028i	0.784778	−	0.619777i	$-0.212777\pi$
$5$	−0.322784	−	0.559079i	−0.144353	−	0.250028i	−0.929132	+	0.369749i	$0.879444\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	1.17925i		−	0.416928i
$9$		0			0
$10$	−1.02425	+	0.591348i	−0.323895	+	0.187001i
$11$	4.60375	+	2.65797i	1.38808	+	0.801410i	0.993099	−	0.117279i	$-0.0374171\pi$
$11$	4.60375	+	2.65797i	1.38808	+	0.801410i	0.394983	+	0.918688i	$0.370750\pi$
$12$		0			0
$13$	4.44045	+	2.56370i	1.23156	+	0.711041i	0.967355	−	0.253425i	$-0.0815572\pi$
$13$	4.44045	+	2.56370i	1.23156	+	0.711041i	0.264205	+	0.964467i	$0.414890\pi$
$14$		0			0
$15$		0			0
$16$	−4.87304			−1.21826
$17$	0.814931	+	1.41150i	0.197650	+	0.342339i	0.947766	−	0.318967i	$-0.103336\pi$
$17$	0.814931	+	1.41150i	0.197650	+	0.342339i	−0.750116	+	0.661306i	$0.770002\pi$
$18$		0			0
$19$	2.09039	+	1.20689i	0.479569	+	0.276879i	0.720237	−	0.693728i	$-0.244033\pi$
$19$	2.09039	+	1.20689i	0.479569	+	0.276879i	−0.240668	+	0.970608i	$0.577366\pi$
$20$	0.437796	+	0.758285i	0.0978942	+	0.169558i
$21$		0			0
$22$	4.86947	−	8.43418i	1.03818	−	1.79817i
$23$	−1.27442	+	0.735784i	−0.265734	+	0.153422i	−0.626947	−	0.779062i	$-0.715696\pi$
$23$	−1.27442	+	0.735784i	−0.265734	+	0.153422i	0.361213	+	0.932483i	$0.382363\pi$
$24$		0			0
$25$	2.29162	−	3.96920i	0.458324	−	0.793841i
$26$	4.69675	−	8.13502i	0.921109	−	1.59541i
$27$		0			0
$28$		0			0
$29$	6.43846	−	3.71724i	1.19559	−	0.690275i	0.236022	−	0.971748i	$-0.424156\pi$
$29$	6.43846	−	3.71724i	1.19559	−	0.690275i	0.959569	+	0.281473i	$0.0908229\pi$
$30$		0			0
$31$			5.66726i			1.01787i	0.860805	+	0.508935i	$0.169961\pi$
$31$			5.66726i			1.01787i	−0.860805	+	0.508935i	$0.830039\pi$
$32$			6.56903i			1.16125i
$33$		0			0
$34$	2.58590	−	1.49297i	0.443479	−	0.256043i
$35$		0			0
$36$		0			0
$37$	3.99736	−	6.92362i	0.657161	−	1.13824i	−0.324186	−	0.945993i	$-0.605090\pi$
$37$	3.99736	−	6.92362i	0.657161	−	1.13824i	0.981347	−	0.192244i	$-0.0615763\pi$
$38$	2.21105	−	3.82965i	0.358680	−	0.621251i
$39$		0			0
$40$	−0.659294	+	0.380644i	−0.104244	+	0.0601851i
$41$	−5.99052	+	10.3759i	−0.935562	+	1.62044i	−0.161934	+	0.986802i	$0.551773\pi$
$41$	−5.99052	+	10.3759i	−0.935562	+	1.62044i	−0.773628	+	0.633640i	$0.781560\pi$
$42$		0			0
$43$	−1.51281	−	2.62026i	−0.230701	−	0.399586i	0.727314	−	0.686305i	$-0.240769\pi$
$43$	−1.51281	−	2.62026i	−0.230701	−	0.399586i	−0.958015	+	0.286719i	$0.907435\pi$
$44$	−6.24412	−	3.60504i	−0.941336	−	0.543481i
$45$		0			0
$46$	1.34797	+	2.33476i	0.198748	+	0.344241i
$47$	−3.08353			−0.449779			−0.224889	−	0.974384i	$-0.572202\pi$
$47$	−3.08353			−0.449779			−0.224889	+	0.974384i	$0.572202\pi$
$48$		0			0
$49$		0			0
$50$	−7.27168	−	4.19830i	−1.02837	−	0.593730i
$51$		0			0
$52$	−6.02264	−	3.47717i	−0.835190	−	0.482197i
$53$	−2.04554	+	1.18100i	−0.280977	+	0.162222i	−0.633866	−	0.773443i	$-0.718533\pi$
$53$	−2.04554	+	1.18100i	−0.280977	+	0.162222i	0.352889	+	0.935665i	$0.385199\pi$
$54$		0			0
$55$		−	3.43181i		−	0.462745i
$56$		0			0
$57$		0			0
$58$	−6.81008	−	11.7954i	−0.894207	−	1.54881i
$59$	2.95836			0.385146			0.192573	−	0.981283i	$-0.438317\pi$
$59$	2.95836			0.385146			0.192573	+	0.981283i	$0.438317\pi$
$60$		0			0
$61$		−	10.6004i		−	1.35724i	−0.734491	−	0.678618i	$-0.762579\pi$
$61$		−	10.6004i		−	1.35724i	0.734491	−	0.678618i	$-0.237421\pi$
$62$	10.3825			1.31859
$63$		0			0
$64$	2.28853			0.286066
$65$		−	3.31008i		−	0.410565i
$66$		0			0
$67$	−10.1549			−1.24062			−0.620312	−	0.784355i	$-0.712994\pi$
$67$	−10.1549			−1.24062			−0.620312	+	0.784355i	$0.712994\pi$
$68$	−1.10530	−	1.91444i	−0.134037	−	0.232159i
$69$		0			0
$70$		0			0
$71$		−	4.76597i		−	0.565617i	−0.959176	−	0.282808i	$-0.908734\pi$
$71$		−	4.76597i		−	0.565617i	0.959176	−	0.282808i	$-0.0912661\pi$
$72$		0			0
$73$	10.2239	−	5.90277i	1.19662	−	0.690867i	0.236817	−	0.971554i	$-0.423896\pi$
$73$	10.2239	−	5.90277i	1.19662	−	0.690867i	0.959799	+	0.280687i	$0.0905624\pi$
$74$	−12.6842	−	7.32325i	−1.47451	−	0.851311i
$75$		0			0
$76$	−2.83523	−	1.63692i	−0.325223	−	0.187767i
$77$		0			0
$78$		0			0
$79$	6.96209			0.783296			0.391648	−	0.920115i	$-0.371905\pi$
$79$	6.96209			0.783296			0.391648	+	0.920115i	$0.371905\pi$
$80$	1.57294	+	2.72441i	0.175860	+	0.304599i
$81$		0			0
$82$	19.0089	+	10.9748i	2.09918	+	1.21196i
$83$	−3.51618	−	6.09021i	−0.385951	−	0.668487i	0.605949	−	0.795503i	$-0.292793\pi$
$83$	−3.51618	−	6.09021i	−0.385951	−	0.668487i	−0.991901	+	0.127016i	$0.959460\pi$
$84$		0			0
$85$	0.526093	−	0.911221i	0.0570628	−	0.0988357i
$86$	−4.80038	+	2.77150i	−0.517638	+	0.298859i
$87$		0			0
$88$	3.13442	−	5.42898i	0.334130	−	0.578731i
$89$	2.16337	−	3.74706i	0.229317	−	0.397188i	−0.728289	−	0.685270i	$-0.759684\pi$
$89$	2.16337	−	3.74706i	0.229317	−	0.397188i	0.957606	+	0.288082i	$0.0930176\pi$
$90$		0			0
$91$		0			0
$92$	1.72850	−	0.997953i	0.180209	−	0.104044i
$93$		0			0
$94$			5.64910i			0.582660i
$95$		−	1.55826i		−	0.159874i
$96$		0			0
$97$	−14.3946	+	8.31075i	−1.46156	+	0.843829i	−0.999083	−	0.0428048i	$-0.986371\pi$
$97$	−14.3946	+	8.31075i	−1.46156	+	0.843829i	−0.462472	+	0.886634i	$0.653037\pi$
$98$		0			0
$99$		0			0
$100$	−3.10815	+	5.38348i	−0.310815	+	0.538348i
$101$	−2.32577	+	4.02835i	−0.231423	+	0.400836i	−0.958227	−	0.286009i	$-0.907671\pi$
$101$	−2.32577	+	4.02835i	−0.231423	+	0.400836i	0.726804	+	0.686845i	$0.241005\pi$
$102$		0			0
$103$	8.92382	−	5.15217i	0.879290	−	0.507658i	0.00886554	−	0.999961i	$-0.497178\pi$
$103$	8.92382	−	5.15217i	0.879290	−	0.507658i	0.870424	+	0.492303i	$0.163845\pi$
$104$	3.02324	−	5.23641i	0.296453	−	0.513472i
$105$		0			0
$106$	2.16361	+	3.74749i	0.210149	+	0.363988i
$107$	−0.267212	−	0.154275i	−0.0258324	−	0.0149143i	0.487028	−	0.873386i	$-0.338081\pi$
$107$	−0.267212	−	0.154275i	−0.0258324	−	0.0149143i	−0.512861	+	0.858472i	$0.671414\pi$
$108$		0			0
$109$	3.14423	+	5.44596i	0.301162	+	0.521628i	0.976399	−	0.215972i	$-0.0692921\pi$
$109$	3.14423	+	5.44596i	0.301162	+	0.521628i	−0.675237	+	0.737601i	$0.735959\pi$
$110$	−6.28716			−0.599457
$111$		0			0
$112$		0			0
$113$	−7.72869	−	4.46216i	−0.727054	−	0.419765i	0.0902895	−	0.995916i	$-0.471221\pi$
$113$	−7.72869	−	4.46216i	−0.727054	−	0.419765i	−0.817343	+	0.576151i	$0.804554\pi$
$114$		0			0
$115$	0.822722	+	0.474999i	0.0767192	+	0.0442939i
$116$	−8.73256	+	5.04174i	−0.810797	+	0.468114i
$117$		0			0
$118$		−	5.41979i		−	0.498932i
$119$		0			0
$120$		0			0
$121$	8.62966	+	14.9470i	0.784515	+	1.35882i
$122$	−19.4201			−1.75821
$123$		0			0
$124$		−	7.68657i		−	0.690274i
$125$	−6.18664			−0.553350
$126$		0			0
$127$	−2.49989			−0.221829			−0.110915	−	0.993830i	$-0.535378\pi$
$127$	−2.49989			−0.221829			−0.110915	+	0.993830i	$0.535378\pi$
$128$			8.94541i			0.790670i
$129$		0			0
$130$	−6.06415			−0.531861
$131$	−1.26725	−	2.19494i	−0.110720	−	0.191773i	0.805341	−	0.592812i	$-0.201982\pi$
$131$	−1.26725	−	2.19494i	−0.110720	−	0.191773i	−0.916061	+	0.401039i	$0.868649\pi$
$132$		0			0
$133$		0			0
$134$			18.6041i			1.60715i
$135$		0			0
$136$	1.66452	−	0.961008i	0.142731	−	0.0824058i
$137$	1.05041	+	0.606456i	0.0897429	+	0.0518131i	0.544200	−	0.838956i	$-0.316833\pi$
$137$	1.05041	+	0.606456i	0.0897429	+	0.0518131i	−0.454457	+	0.890769i	$0.650167\pi$
$138$		0			0
$139$	−6.11754	−	3.53196i	−0.518883	−	0.299577i	0.217594	−	0.976039i	$-0.430179\pi$
$139$	−6.11754	−	3.53196i	−0.518883	−	0.299577i	−0.736478	+	0.676462i	$0.763512\pi$
$140$		0			0
$141$		0			0
$142$	−8.73137			−0.732721
$143$	13.6285	+	23.6052i	1.13967	+	1.97397i
$144$		0			0
$145$	−4.15646	−	2.39974i	−0.345175	−	0.199287i
$146$	−10.8140	−	18.7304i	−0.894974	−	1.55014i
$147$		0			0
$148$	−5.42166	+	9.39060i	−0.445658	+	0.771902i
$149$	6.00270	−	3.46566i	0.491760	−	0.283918i	−0.233544	−	0.972346i	$-0.575032\pi$
$149$	6.00270	−	3.46566i	0.491760	−	0.283918i	0.725304	+	0.688428i	$0.241699\pi$
$150$		0			0
$151$	−3.15939	+	5.47223i	−0.257108	+	0.445323i	−0.965466	−	0.260530i	$-0.916103\pi$
$151$	−3.15939	+	5.47223i	−0.257108	+	0.445323i	0.708358	+	0.705853i	$0.249436\pi$
$152$	1.42323	−	2.46510i	0.115439	−	0.199946i
$153$		0			0
$154$		0			0
$155$	3.16844	−	1.82930i	0.254495	−	0.146933i
$156$		0			0
$157$		−	1.99028i		−	0.158842i	−0.996841	−	0.0794208i	$-0.974693\pi$
$157$		−	1.99028i		−	0.158842i	0.996841	−	0.0794208i	$-0.0253071\pi$
$158$		−	12.7547i		−	1.01471i
$159$		0			0
$160$	3.67260	−	2.12038i	0.290345	−	0.167631i
$161$		0			0
$162$		0			0
$163$	2.99365	−	5.18515i	0.234480	−	0.406132i	−0.724641	−	0.689126i	$-0.757994\pi$
$163$	2.99365	−	5.18515i	0.234480	−	0.406132i	0.959122	+	0.282994i	$0.0913278\pi$
$164$	8.12502	−	14.0729i	0.634457	−	1.09891i
$165$		0			0
$166$	−11.1574	+	6.44173i	−0.865983	+	0.499976i
$167$	0.697990	−	1.20895i	0.0540121	−	0.0935516i	−0.837755	−	0.546046i	$-0.816132\pi$
$167$	0.697990	−	1.20895i	0.0540121	−	0.0935516i	0.891767	+	0.452494i	$0.149466\pi$
$168$		0			0
$169$	6.64508	+	11.5096i	0.511160	+	0.885355i
$170$	−1.66938	−	0.963816i	−0.128035	−	0.0739213i
$171$		0			0
$172$	2.05184	+	3.55389i	0.156451	+	0.270982i
$173$	7.61012			0.578586			0.289293	−	0.957241i	$-0.406580\pi$
$173$	7.61012			0.578586			0.289293	+	0.957241i	$0.406580\pi$
$174$		0			0
$175$		0			0
$176$	−22.4343	−	12.9524i	−1.69105	−	0.976326i
$177$		0			0
$178$	−6.86471	−	3.96334i	−0.514532	−	0.297065i
$179$	8.00888	−	4.62393i	0.598612	−	0.345609i	−0.169883	−	0.985464i	$-0.554339\pi$
$179$	8.00888	−	4.62393i	0.598612	−	0.345609i	0.768495	+	0.639855i	$0.221006\pi$
$180$		0			0
$181$		−	11.9634i		−	0.889234i	−0.895721	−	0.444617i	$-0.853340\pi$
$181$		−	11.9634i		−	0.889234i	0.895721	−	0.444617i	$-0.146660\pi$
$182$		0			0
$183$		0			0
$184$	0.867674	+	1.50286i	0.0639658	+	0.110792i
$185$	−5.16113			−0.379454
$186$		0			0
$187$			8.66426i			0.633593i
$188$	4.18223			0.305020
$189$		0			0
$190$	−2.85477			−0.207107
$191$			20.2749i			1.46704i	0.679666	+	0.733521i	$0.262125\pi$
$191$			20.2749i			1.46704i	−0.679666	+	0.733521i	$0.737875\pi$
$192$		0			0
$193$	−16.8917			−1.21589			−0.607944	−	0.793980i	$-0.708006\pi$
$193$	−16.8917			−1.21589			−0.607944	+	0.793980i	$0.708006\pi$
$194$	15.2255	+	26.3713i	1.09313	+	1.89335i
$195$		0			0
$196$		0			0
$197$			18.7102i			1.33305i	0.745484	+	0.666524i	$0.232219\pi$
$197$			18.7102i			1.33305i	−0.745484	+	0.666524i	$0.767781\pi$
$198$		0			0
$199$	−15.6271	+	9.02231i	−1.10778	+	0.639574i	−0.938252	−	0.345952i	$-0.887556\pi$
$199$	−15.6271	+	9.02231i	−1.10778	+	0.639574i	−0.169523	+	0.985526i	$0.554223\pi$
$200$	−4.68069	−	2.70240i	−0.330975	−	0.191088i
$201$		0			0
$202$	7.38004	+	4.26087i	0.519258	+	0.299794i
$203$		0			0
$204$		0			0
$205$	7.73458			0.540207
$206$	−9.43889	−	16.3486i	−0.657639	−	1.13906i
$207$		0			0
$208$	−21.6385	−	12.4930i	−1.50036	−	0.866234i
$209$	6.41576	+	11.1124i	0.443788	+	0.768663i
$210$		0			0
$211$	−4.03491	+	6.98868i	−0.277775	+	0.481120i	−0.970831	−	0.239763i	$-0.922930\pi$
$211$	−4.03491	+	6.98868i	−0.277775	+	0.481120i	0.693057	+	0.720883i	$0.256264\pi$
$212$	2.77440	−	1.60180i	0.190546	−	0.110012i
$213$		0			0
$214$	−0.282636	+	0.489540i	−0.0193206	+	0.0334642i
$215$	−0.976621	+	1.69156i	−0.0666050	+	0.115363i
$216$		0			0
$217$		0			0
$218$	9.97713	−	5.76030i	0.675736	−	0.390137i
$219$		0			0
$220$			4.65460i			0.313813i
$221$			8.35694i			0.562148i
$222$		0			0
$223$	−20.2450	+	11.6884i	−1.35570	+	0.782716i	−0.989041	−	0.147638i	$-0.952833\pi$
$223$	−20.2450	+	11.6884i	−1.35570	+	0.782716i	−0.366662	+	0.930354i	$0.619500\pi$
$224$		0			0
$225$		0			0
$226$	−8.17479	+	14.1591i	−0.543779	+	0.941852i
$227$	7.22154	−	12.5081i	0.479310	−	0.830190i	−0.520408	−	0.853918i	$-0.674220\pi$
$227$	7.22154	−	12.5081i	0.479310	−	0.830190i	0.999718	+	0.0237280i	$0.00755356\pi$
$228$		0			0
$229$	−11.3568	+	6.55685i	−0.750479	+	0.433289i	−0.825867	−	0.563865i	$-0.809314\pi$
$229$	−11.3568	+	6.55685i	−0.750479	+	0.433289i	0.0753881	+	0.997154i	$0.475980\pi$
$230$	0.870209	−	1.50725i	0.0573799	−	0.0993849i
$231$		0			0
$232$	−4.38357	−	7.59256i	−0.287795	−	0.498476i
$233$	7.31966	+	4.22601i	0.479527	+	0.276855i	0.720219	−	0.693746i	$-0.244041\pi$
$233$	7.31966	+	4.22601i	0.479527	+	0.276855i	−0.240692	+	0.970601i	$0.577374\pi$
$234$		0			0
$235$	0.995314	+	1.72393i	0.0649271	+	0.112457i
$236$	−4.01246			−0.261189
$237$		0			0
$238$		0			0
$239$	24.2111	+	13.9783i	1.56608	+	0.904179i	0.996619	+	0.0821642i	$0.0261832\pi$
$239$	24.2111	+	13.9783i	1.56608	+	0.904179i	0.569466	+	0.822015i	$0.307150\pi$
$240$		0			0
$241$	19.4058	+	11.2039i	1.25004	+	0.721710i	0.971117	−	0.238605i	$-0.0766900\pi$
$241$	19.4058	+	11.2039i	1.25004	+	0.721710i	0.278921	+	0.960314i	$0.410023\pi$
$242$	27.3833	−	15.8097i	1.76026	−	1.01629i
$243$		0			0
$244$			14.3774i			0.920418i
$245$		0			0
$246$		0			0
$247$	6.18819	+	10.7183i	0.393745	+	0.681987i
$248$	6.68312			0.424379
$249$		0			0
$250$			11.3341i			0.716829i
$251$	6.39587			0.403704			0.201852	−	0.979416i	$-0.435304\pi$
$251$	6.39587			0.403704			0.201852	+	0.979416i	$0.435304\pi$
$252$		0			0
$253$	−7.82278			−0.491814
$254$			4.57985i			0.287366i
$255$		0			0
$256$	20.9653			1.31033
$257$	1.65705	+	2.87009i	0.103364	+	0.179031i	0.913069	−	0.407806i	$-0.133706\pi$
$257$	1.65705	+	2.87009i	0.103364	+	0.179031i	−0.809705	+	0.586837i	$0.800373\pi$
$258$		0			0
$259$		0			0
$260$			4.48950i			0.278427i
$261$		0			0
$262$	−4.02118	+	2.32163i	−0.248429	+	0.143431i
$263$	19.6502	+	11.3451i	1.21169	+	0.699567i	0.963126	−	0.269050i	$-0.0867096\pi$
$263$	19.6502	+	11.3451i	1.21169	+	0.699567i	0.248559	+	0.968617i	$0.420043\pi$
$264$		0			0
$265$	1.32054	+	0.762413i	0.0811200	+	0.0468347i
$266$		0			0
$267$		0			0
$268$	13.7733			0.841336
$269$	−1.38050	−	2.39110i	−0.0841707	−	0.145788i	0.820867	−	0.571120i	$-0.193491\pi$
$269$	−1.38050	−	2.39110i	−0.0841707	−	0.145788i	−0.905038	+	0.425332i	$0.860157\pi$
$270$		0			0
$271$	−5.27342	−	3.04461i	−0.320337	−	0.184947i	0.331206	−	0.943559i	$-0.392545\pi$
$271$	−5.27342	−	3.04461i	−0.320337	−	0.184947i	−0.651543	+	0.758612i	$0.725878\pi$
$272$	−3.97119	−	6.87830i	−0.240789	−	0.417058i
$273$		0			0
$274$	1.11104	−	1.92438i	0.0671205	−	0.116256i
$275$	21.1001	−	12.1821i	1.27238	−	0.734611i
$276$		0			0
$277$	4.71684	−	8.16980i	0.283407	−	0.490876i	−0.688814	−	0.724938i	$-0.741869\pi$
$277$	4.71684	−	8.16980i	0.283407	−	0.490876i	0.972222	+	0.234062i	$0.0752019\pi$
$278$	−6.47064	+	11.2075i	−0.388083	+	0.672180i
$279$		0			0
$280$		0			0
$281$	−4.57153	+	2.63938i	−0.272715	+	0.157452i	−0.630121	−	0.776497i	$-0.716995\pi$
$281$	−4.57153	+	2.63938i	−0.272715	+	0.157452i	0.357406	+	0.933949i	$0.383661\pi$
$282$		0			0
$283$		−	19.6699i		−	1.16926i	−0.811302	−	0.584628i	$-0.801241\pi$
$283$		−	19.6699i		−	1.16926i	0.811302	−	0.584628i	$-0.198759\pi$
$284$			6.46414i			0.383576i
$285$		0			0
$286$	43.2453	−	24.9677i	2.55715	−	1.47637i
$287$		0			0
$288$		0			0
$289$	7.17178	−	12.4219i	0.421869	−	0.730699i
$290$	−4.39637	+	7.61474i	−0.258164	+	0.447153i
$291$		0			0
$292$	−13.8668	+	8.00600i	−0.811493	+	0.468516i
$293$	−9.11647	+	15.7902i	−0.532590	+	0.922473i	0.466686	+	0.884423i	$0.345448\pi$
$293$	−9.11647	+	15.7902i	−0.532590	+	0.922473i	−0.999276	+	0.0380495i	$0.987886\pi$
$294$		0			0
$295$	−0.954912	−	1.65396i	−0.0555971	−	0.0962970i
$296$	−8.16470	−	4.71389i	−0.474563	−	0.273989i
$297$		0			0
$298$	−6.34917	−	10.9971i	−0.367797	−	0.637044i
$299$	−7.54531			−0.436356
$300$		0			0
$301$		0			0
$302$	10.0253	+	5.78808i	0.576888	+	0.333067i
$303$		0			0
$304$	−10.1866	−	5.88122i	−0.584240	−	0.337311i
$305$	−5.92643	+	3.42163i	−0.339347	+	0.195922i
$306$		0			0
$307$			26.0447i			1.48645i	0.669042	+	0.743224i	$0.266704\pi$
$307$			26.0447i			1.48645i	−0.669042	+	0.743224i	$0.733296\pi$
$308$		0			0
$309$		0			0
$310$	−3.35132	−	5.80466i	−0.190342	−	0.329683i
$311$	−28.2866			−1.60398			−0.801992	−	0.597334i	$-0.796227\pi$
$311$	−28.2866			−1.60398			−0.801992	+	0.597334i	$0.796227\pi$
$312$		0			0
$313$			5.57595i			0.315171i	0.987505	+	0.157586i	$0.0503710\pi$
$313$			5.57595i			0.315171i	−0.987505	+	0.157586i	$0.949629\pi$
$314$	−3.64624			−0.205769
$315$		0			0
$316$	−9.44276			−0.531197
$317$		−	33.5681i		−	1.88537i	−0.333680	−	0.942686i	$-0.608291\pi$
$317$		−	33.5681i		−	1.88537i	0.333680	−	0.942686i	$-0.391709\pi$
$318$		0			0
$319$	39.5214			2.21277
$320$	−0.738701	−	1.27947i	−0.0412947	−	0.0715244i
$321$		0			0
$322$		0			0
$323$			3.93412i			0.218901i
$324$		0			0
$325$	20.3517	−	11.7500i	1.12891	−	0.651775i
$326$	−9.49931	−	5.48443i	−0.526118	−	0.303755i
$327$		0			0
$328$	12.2358	+	7.06433i	0.675608	+	0.390063i
$329$		0			0
$330$		0			0
$331$	−30.3735			−1.66948			−0.834739	−	0.550646i	$-0.814381\pi$
$331$	−30.3735			−1.66948			−0.834739	+	0.550646i	$0.814381\pi$
$332$	4.76904	+	8.26023i	0.261735	+	0.453339i
$333$		0			0
$334$	−2.21483	−	1.27873i	−0.121190	−	0.0699692i
$335$	3.27785	+	5.67741i	0.179088	+	0.310190i
$336$		0			0
$337$	1.86121	−	3.22371i	0.101387	−	0.175607i	−0.810870	−	0.585227i	$-0.801005\pi$
$337$	1.86121	−	3.22371i	0.101387	−	0.175607i	0.912256	+	0.409620i	$0.134339\pi$
$338$	21.0859	−	12.1739i	1.14692	−	0.662175i
$339$		0			0
$340$	−0.713547	+	1.23590i	−0.0386975	+	0.0670261i
$341$	−15.0634	+	26.0906i	−0.815730	+	1.41289i
$342$		0			0
$343$		0			0
$344$	−3.08995	+	1.78398i	−0.166599	+	0.0961858i
$345$		0			0
$346$		−	13.9419i		−	0.749522i
$347$			7.13637i			0.383100i	0.981483	+	0.191550i	$0.0613515\pi$
$347$			7.13637i			0.383100i	−0.981483	+	0.191550i	$0.938649\pi$
$348$		0			0
$349$	13.2087	−	7.62607i	0.707047	−	0.408214i	−0.102920	−	0.994690i	$-0.532818\pi$
$349$	13.2087	−	7.62607i	0.707047	−	0.408214i	0.809967	+	0.586476i	$0.199485\pi$
$350$		0			0
$351$		0			0
$352$	−17.4603	+	30.2421i	−0.930637	+	1.61191i
$353$	17.2359	−	29.8534i	0.917373	−	1.58894i	0.113985	−	0.993482i	$-0.463638\pi$
$353$	17.2359	−	29.8534i	0.917373	−	1.58894i	0.803389	−	0.595455i	$-0.203028\pi$
$354$		0			0
$355$	−2.66455	+	1.53838i	−0.141420	+	0.0816487i
$356$	−2.93420	+	5.08219i	−0.155512	+	0.269355i
$357$		0			0
$358$	−8.47115	−	14.6725i	−0.447714	−	0.775464i
$359$	5.73791	+	3.31278i	0.302835	+	0.174842i	0.643716	−	0.765265i	$-0.277392\pi$
$359$	5.73791	+	3.31278i	0.302835	+	0.174842i	−0.340881	+	0.940107i	$0.610725\pi$
$360$		0			0
$361$	−6.58684	−	11.4087i	−0.346676	−	0.600460i
$362$	−21.9173			−1.15195
$363$		0			0
$364$		0			0
$365$	−6.60022	−	3.81064i	−0.345472	−	0.199458i
$366$		0			0
$367$	2.68222	+	1.54858i	0.140011	+	0.0808352i	0.568369	−	0.822774i	$-0.307575\pi$
$367$	2.68222	+	1.54858i	0.140011	+	0.0808352i	−0.428358	+	0.903609i	$0.640908\pi$
$368$	6.21028	−	3.58551i	0.323733	−	0.186907i
$369$		0			0
$370$			9.45532i			0.491559i
$371$		0			0
$372$		0			0
$373$	−4.84999	−	8.40043i	−0.251123	−	0.434958i	0.712712	−	0.701457i	$-0.247467\pi$
$373$	−4.84999	−	8.40043i	−0.251123	−	0.434958i	−0.963835	+	0.266499i	$0.914133\pi$
$374$	15.8731			0.820780
$375$		0			0
$376$			3.63625i			0.187526i
$377$	38.1195			1.96326
$378$		0			0
$379$	7.76103			0.398657			0.199329	−	0.979933i	$-0.436124\pi$
$379$	7.76103			0.398657			0.199329	+	0.979933i	$0.436124\pi$
$380$			2.11349i			0.108420i
$381$		0			0
$382$	37.1442			1.90046
$383$	−12.3063	−	21.3152i	−0.628825	−	1.08916i	−0.987788	−	0.155804i	$-0.950203\pi$
$383$	−12.3063	−	21.3152i	−0.628825	−	1.08916i	0.358963	−	0.933352i	$-0.383130\pi$
$384$		0			0
$385$		0			0
$386$			30.9459i			1.57511i
$387$		0			0
$388$	19.5236	−	11.2720i	0.991162	−	0.572248i
$389$	5.56578	+	3.21340i	0.282196	+	0.162926i	0.634417	−	0.772991i	$-0.281240\pi$
$389$	5.56578	+	3.21340i	0.282196	+	0.162926i	−0.352221	+	0.935917i	$0.614573\pi$
$390$		0			0
$391$	−2.07712	−	1.19923i	−0.105044	−	0.0606474i
$392$		0			0
$393$		0			0
$394$	34.2776			1.72688
$395$	−2.24725	−	3.89235i	−0.113071	−	0.195846i
$396$		0			0
$397$	−11.4835	−	6.62998i	−0.576338	−	0.332749i	0.183339	−	0.983050i	$-0.441310\pi$
$397$	−11.4835	−	6.62998i	−0.576338	−	0.332749i	−0.759677	+	0.650301i	$0.774643\pi$
$398$	16.5291	+	28.6292i	0.828528	+	1.43505i
$399$		0			0
$400$	−11.1672	+	19.3421i	−0.558358	+	0.967105i
$401$	−13.6877	+	7.90259i	−0.683530	+	0.394636i	−0.801184	−	0.598418i	$-0.795796\pi$
$401$	−13.6877	+	7.90259i	−0.683530	+	0.394636i	0.117653	+	0.993055i	$0.462463\pi$
$402$		0			0
$403$	−14.5291	+	25.1652i	−0.723747	+	1.25357i
$404$	3.15447	−	5.46370i	0.156941	−	0.271829i
$405$		0			0
$406$		0			0
$407$	36.8056	−	21.2497i	1.82439	−	1.05331i
$408$		0			0
$409$		−	5.41851i		−	0.267928i	−0.990986	−	0.133964i	$-0.957229\pi$
$409$		−	5.41851i		−	0.267928i	0.990986	−	0.133964i	$-0.0427707\pi$
$410$		−	14.1699i		−	0.699803i
$411$		0			0
$412$	−12.1035	+	6.98795i	−0.596296	+	0.344271i
$413$		0			0
$414$		0			0
$415$	−2.26994	+	3.93165i	−0.111427	+	0.192997i
$416$	−16.8410	+	29.1694i	−0.825697	+	1.43015i
$417$		0			0
$418$	20.3582	−	11.7538i	0.995754	−	0.574899i
$419$	−12.2469	+	21.2123i	−0.598302	+	1.03629i	0.394770	+	0.918780i	$0.370824\pi$
$419$	−12.2469	+	21.2123i	−0.598302	+	1.03629i	−0.993072	+	0.117509i	$0.962509\pi$
$420$		0			0
$421$	5.99347	+	10.3810i	0.292104	+	0.505939i	0.974307	−	0.225224i	$-0.0723113\pi$
$421$	5.99347	+	10.3810i	0.292104	+	0.505939i	−0.682203	+	0.731163i	$0.738978\pi$
$422$	12.8034	+	7.39206i	0.623261	+	0.359840i
$423$		0			0
$424$	1.39269	+	2.41221i	0.0676350	+	0.117147i
$425$	7.47005			0.362351
$426$		0			0
$427$		0			0
$428$	0.362424	+	0.209245i	0.0175184	+	0.0101143i
$429$		0			0
$430$	3.09897	+	1.78919i	0.149446	+	0.0862825i
$431$	−26.6926	+	15.4110i	−1.28574	+	0.742320i	−0.977891	−	0.209117i	$-0.932941\pi$
$431$	−26.6926	+	15.4110i	−1.28574	+	0.742320i	−0.307845	+	0.951437i	$0.599608\pi$
$432$		0			0
$433$		−	6.06173i		−	0.291308i	−0.989336	−	0.145654i	$-0.953471\pi$
$433$		−	6.06173i		−	0.291308i	0.989336	−	0.145654i	$-0.0465287\pi$
$434$		0			0
$435$		0			0
$436$	−4.26455	−	7.38642i	−0.204235	−	0.353745i
$437$	−3.55204			−0.169917
$438$		0			0
$439$			27.1448i			1.29555i	0.761831	+	0.647776i	$0.224301\pi$
$439$			27.1448i			1.29555i	−0.761831	+	0.647776i	$0.775699\pi$
$440$	−4.04697			−0.192932
$441$		0			0
$442$	15.3101			0.728228
$443$			5.35163i			0.254264i	0.991886	+	0.127132i	$0.0405771\pi$
$443$			5.35163i			0.254264i	−0.991886	+	0.127132i	$0.959423\pi$
$444$		0			0
$445$	−2.79320			−0.132411
$446$	21.4135	+	37.0893i	1.01396	+	1.75623i
$447$		0			0
$448$		0			0
$449$		−	34.2418i		−	1.61597i	−0.589204	−	0.807985i	$-0.700558\pi$
$449$		−	34.2418i		−	1.61597i	0.589204	−	0.807985i	$-0.299442\pi$
$450$		0			0
$451$	−55.1577	+	31.8453i	−2.59727	+	1.49954i
$452$	10.4825	+	6.05208i	0.493056	+	0.284666i
$453$		0			0
$454$	−22.9151	−	13.2300i	−1.07546	−	0.620916i
$455$		0			0
$456$		0			0
$457$	−15.8604			−0.741917			−0.370958	−	0.928649i	$-0.620971\pi$
$457$	−15.8604			−0.741917			−0.370958	+	0.928649i	$0.620971\pi$
$458$	12.0123	+	20.8059i	0.561299	+	0.972198i
$459$		0			0
$460$	−1.11587	−	0.644247i	−0.0520276	−	0.0300382i
$461$	−6.50676	−	11.2700i	−0.303050	−	0.524898i	0.673775	−	0.738936i	$-0.264672\pi$
$461$	−6.50676	−	11.2700i	−0.303050	−	0.524898i	−0.976825	+	0.214038i	$0.931338\pi$
$462$		0			0
$463$	−6.01941	+	10.4259i	−0.279746	+	0.484534i	−0.971321	−	0.237770i	$-0.923583\pi$
$463$	−6.01941	+	10.4259i	−0.279746	+	0.484534i	0.691576	+	0.722304i	$0.256917\pi$
$464$	−31.3749	+	18.1143i	−1.45654	+	0.840935i
$465$		0			0
$466$	7.74215	−	13.4098i	0.358648	−	0.621197i
$467$	10.1728	−	17.6199i	0.470743	−	0.815351i	−0.528697	−	0.848811i	$-0.677319\pi$
$467$	10.1728	−	17.6199i	0.470743	−	0.815351i	0.999440	+	0.0334596i	$0.0106525\pi$
$468$		0			0
$469$		0			0
$470$	3.15829	−	1.82344i	0.145681	−	0.0841090i
$471$		0			0
$472$		−	3.48865i		−	0.160578i
$473$		−	16.0840i		−	0.739544i
$474$		0			0
$475$	9.58078	−	5.53146i	0.439596	−	0.253801i
$476$		0			0
$477$		0			0
$478$	25.6085	−	44.3553i	1.17131	−	2.02876i
$479$	−12.1492	+	21.0430i	−0.555109	+	0.961477i	0.442786	+	0.896627i	$0.353990\pi$
$479$	−12.1492	+	21.0430i	−0.555109	+	0.961477i	−0.997895	+	0.0648499i	$0.979343\pi$
$480$		0			0
$481$	35.5001	−	20.4960i	1.61867	−	0.934538i
$482$	20.5259	−	35.5519i	0.934929	−	1.61934i
$483$		0			0
$484$	−11.7045	−	20.2728i	−0.532023	−	0.921491i
$485$	9.29273	+	5.36516i	0.421961	+	0.243619i
$486$		0			0
$487$	13.6546	+	23.6504i	0.618747	+	1.07170i	0.989715	+	0.143055i	$0.0456927\pi$
$487$	13.6546	+	23.6504i	0.618747	+	1.07170i	−0.370968	+	0.928646i	$0.620974\pi$
$488$	−12.5005			−0.565871
$489$		0			0
$490$		0			0
$491$	13.2899	+	7.67290i	0.599763	+	0.346273i	0.768948	−	0.639311i	$-0.220780\pi$
$491$	13.2899	+	7.67290i	0.599763	+	0.346273i	−0.169185	+	0.985584i	$0.554114\pi$
$492$		0			0
$493$	10.4938	+	6.05859i	0.472616	+	0.272865i
$494$	19.6361	−	11.3369i	0.883471	−	0.510072i
$495$		0			0
$496$		−	27.6168i		−	1.24003i
$497$		0			0
$498$		0			0
$499$	5.15504	+	8.92879i	0.230771	+	0.399707i	0.958035	−	0.286650i	$-0.0925418\pi$
$499$	5.15504	+	8.92879i	0.230771	+	0.399707i	−0.727264	+	0.686358i	$0.759208\pi$
$500$	8.39101			0.375257
$501$		0			0
$502$		−	11.7174i		−	0.522972i
$503$	−24.6770			−1.10029			−0.550146	−	0.835068i	$-0.685428\pi$
$503$	−24.6770			−1.10029			−0.550146	+	0.835068i	$0.685428\pi$
$504$		0			0
$505$	3.00289			0.133627
$506$			14.3315i			0.637114i
$507$		0			0
$508$	3.39063			0.150435
$509$	−2.58601	−	4.47911i	−0.114623	−	0.198533i	0.803006	−	0.595971i	$-0.203233\pi$
$509$	−2.58601	−	4.47911i	−0.114623	−	0.198533i	−0.917629	+	0.397438i	$0.869899\pi$
$510$		0			0
$511$		0			0
$512$		−	20.5181i		−	0.906778i
$513$		0			0
$514$	5.25807	−	3.03575i	0.231924	−	0.133901i
$515$	−5.76093	−	3.32608i	−0.253857	−	0.146564i
$516$		0			0
$517$	−14.1958	−	8.19594i	−0.624330	−	0.360457i
$518$		0			0
$519$		0			0
$520$	−3.90342			−0.171176
$521$	−19.1664	−	33.1972i	−0.839696	−	1.45440i	−0.890149	−	0.455669i	$-0.849400\pi$
$521$	−19.1664	−	33.1972i	−0.839696	−	1.45440i	0.0504538	−	0.998726i	$-0.483933\pi$
$522$		0			0
$523$	−23.6468	−	13.6525i	−1.03400	−	0.596982i	−0.115874	−	0.993264i	$-0.536967\pi$
$523$	−23.6468	−	13.6525i	−1.03400	−	0.596982i	−0.918129	+	0.396282i	$0.870300\pi$
$524$	1.71878	+	2.97702i	0.0750855	+	0.130052i
$525$		0			0
$526$	20.7844	−	35.9997i	0.906245	−	1.56966i
$527$	−7.99934	+	4.61842i	−0.348457	+	0.201182i
$528$		0			0
$529$	−10.4172	+	18.0432i	−0.452924	+	0.784487i
$530$	1.39676	−	2.41926i	0.0606714	−	0.105086i
$531$		0			0
$532$		0			0
$533$	−53.2012	+	30.7158i	−2.30440	+	1.33045i
$534$		0			0
$535$			0.199190i			0.00861175i
$536$			11.9752i			0.517251i
$537$		0			0
$538$	−4.38055	+	2.52911i	−0.188859	+	0.109038i
$539$		0			0
$540$		0			0
$541$	−9.78052	+	16.9404i	−0.420498	+	0.728323i	−0.995988	−	0.0894853i	$-0.971478\pi$
$541$	−9.78052	+	16.9404i	−0.420498	+	0.728323i	0.575491	+	0.817808i	$0.304811\pi$
$542$	−5.57779	+	9.66102i	−0.239587	+	0.414977i
$543$		0			0
$544$	−9.27219	+	5.35330i	−0.397542	+	0.229521i
$545$	2.02981	−	3.51574i	0.0869476	−	0.150598i
$546$		0			0
$547$	12.6246	+	21.8665i	0.539790	+	0.934944i	0.998915	+	0.0465723i	$0.0148298\pi$
$547$	12.6246	+	21.8665i	0.539790	+	0.934944i	−0.459125	+	0.888372i	$0.651837\pi$
$548$	−1.42469	−	0.822544i	−0.0608597	−	0.0351373i
$549$		0			0
$550$	−22.3180	−	38.6559i	−0.951642	−	1.64829i
$551$	17.9452			0.764492
$552$		0			0
$553$		0			0
$554$	−14.9673	−	8.64136i	−0.635898	−	0.367136i
$555$		0			0
$556$	8.29730	+	4.79045i	0.351884	+	0.203160i
$557$	−28.8204	+	16.6395i	−1.22116	+	0.705036i	−0.965165	−	0.261642i	$-0.915736\pi$
$557$	−28.8204	+	16.6395i	−1.22116	+	0.705036i	−0.255994	+	0.966678i	$0.582403\pi$
$558$		0			0
$559$		−	15.5135i		−	0.656152i
$560$		0			0
$561$		0			0
$562$	4.83540	+	8.37516i	0.203969	+	0.353285i
$563$	30.5175			1.28616			0.643079	−	0.765800i	$-0.277657\pi$
$563$	30.5175			1.28616			0.643079	+	0.765800i	$0.277657\pi$
$564$		0			0
$565$			5.76126i			0.242378i
$566$	−36.0358			−1.51470
$567$		0			0
$568$	−5.62028			−0.235822
$569$		−	15.4781i		−	0.648876i	−0.945907	−	0.324438i	$-0.894825\pi$
$569$		−	15.4781i		−	0.648876i	0.945907	−	0.324438i	$-0.105175\pi$
$570$		0			0
$571$	−24.4085			−1.02146			−0.510731	−	0.859740i	$-0.670625\pi$
$571$	−24.4085			−1.02146			−0.510731	+	0.859740i	$0.670625\pi$
$572$	−18.4845	−	32.0160i	−0.772875	−	1.33866i
$573$		0			0
$574$		0			0
$575$			6.74455i			0.281267i
$576$		0			0
$577$	−12.6901	+	7.32664i	−0.528296	+	0.305012i	−0.740322	−	0.672252i	$-0.765327\pi$
$577$	−12.6901	+	7.32664i	−0.528296	+	0.305012i	0.212026	+	0.977264i	$0.431994\pi$
$578$	−22.7572	−	13.1389i	−0.946574	−	0.546505i
$579$		0			0
$580$	5.63746	+	3.25479i	0.234083	+	0.135148i
$581$		0			0
$582$		0			0
$583$	−12.5562			−0.520026
$584$	−6.96085	−	12.0565i	−0.288042	−	0.498904i
$585$		0			0
$586$	28.9280	+	16.7016i	1.19500	+	0.689936i
$587$	−11.6129	−	20.1141i	−0.479314	−	0.830197i	0.520404	−	0.853920i	$-0.325781\pi$
$587$	−11.6129	−	20.1141i	−0.479314	−	0.830197i	−0.999719	+	0.0237232i	$0.992448\pi$
$588$		0			0
$589$	−6.83975	+	11.8468i	−0.281827	+	0.488139i
$590$	−3.03009	+	1.74942i	−0.124747	+	0.0720225i
$591$		0			0
$592$	−19.4793	+	33.7391i	−0.800594	+	1.38667i
$593$	5.55605	−	9.62337i	0.228160	−	0.395184i	−0.729103	−	0.684404i	$-0.760062\pi$
$593$	5.55605	−	9.62337i	0.228160	−	0.395184i	0.957263	+	0.289220i	$0.0933958\pi$
$594$		0			0
$595$		0			0
$596$	−8.14153	+	4.70051i	−0.333490	+	0.192541i
$597$		0			0
$598$			13.8232i			0.565272i
$599$		−	15.6555i		−	0.639667i	−0.947474	−	0.319833i	$-0.896373\pi$
$599$		−	15.6555i		−	0.639667i	0.947474	−	0.319833i	$-0.103627\pi$
$600$		0			0
$601$	−30.5665	+	17.6476i	−1.24684	+	0.719861i	−0.970477	−	0.241194i	$-0.922461\pi$
$601$	−30.5665	+	17.6476i	−1.24684	+	0.719861i	−0.276358	+	0.961055i	$0.589128\pi$
$602$		0			0
$603$		0			0
$604$	4.28512	−	7.42205i	0.174359	−	0.301999i
$605$	5.57104	−	9.64932i	0.226495	−	0.392301i
$606$		0			0
$607$	33.6062	−	19.4025i	1.36403	−	0.787524i	0.373874	−	0.927479i	$-0.378029\pi$
$607$	33.6062	−	19.4025i	1.36403	−	0.787524i	0.990158	+	0.139955i	$0.0446959\pi$
$608$	−7.92809	+	13.7318i	−0.321526	+	0.556900i
$609$		0			0
$610$	6.26850	+	10.8574i	0.253804	+	0.439602i
$611$	−13.6923	−	7.90523i	−0.553929	−	0.319811i
$612$		0			0
$613$	−15.8786	−	27.5025i	−0.641330	−	1.11082i	−0.985136	−	0.171776i	$-0.945049\pi$
$613$	−15.8786	−	27.5025i	−0.641330	−	1.11082i	0.343806	−	0.939041i	$-0.388284\pi$
$614$	47.7145			1.92560
$615$		0			0
$616$		0			0
$617$	−1.25518	−	0.724680i	−0.0505317	−	0.0291745i	0.474521	−	0.880244i	$-0.342621\pi$
$617$	−1.25518	−	0.724680i	−0.0505317	−	0.0291745i	−0.525053	+	0.851070i	$0.675955\pi$
$618$		0			0
$619$	−25.2590	−	14.5833i	−1.01524	−	0.586152i	−0.102522	−	0.994731i	$-0.532691\pi$
$619$	−25.2590	−	14.5833i	−1.01524	−	0.586152i	−0.912723	+	0.408579i	$0.866024\pi$
$620$	−4.29740	+	2.48110i	−0.172588	+	0.0996435i
$621$		0			0
$622$			51.8217i			2.07786i
$623$		0			0
$624$		0			0
$625$	−9.46116	−	16.3872i	−0.378446	−	0.655488i
$626$	10.2153			0.408284
$627$		0			0
$628$			2.69944i			0.107719i
$629$	13.0303			0.519551
$630$		0			0
$631$	11.7428			0.467473			0.233736	−	0.972300i	$-0.424905\pi$
$631$	11.7428			0.467473			0.233736	+	0.972300i	$0.424905\pi$
$632$		−	8.21005i		−	0.326578i
$633$		0			0
$634$	−61.4976			−2.44238
$635$	0.806924	+	1.39763i	0.0320218	+	0.0554634i
$636$		0			0
$637$		0			0
$638$		−	72.4041i		−	2.86651i
$639$		0			0
$640$	5.00119	−	2.88744i	0.197689	−	0.114136i
$641$	−10.0267	−	5.78891i	−0.396030	−	0.228648i	0.288740	−	0.957408i	$-0.406764\pi$
$641$	−10.0267	−	5.78891i	−0.396030	−	0.228648i	−0.684770	+	0.728760i	$0.740097\pi$
$642$		0			0
$643$	13.1240	+	7.57712i	0.517558	+	0.298812i	0.735935	−	0.677052i	$-0.236743\pi$
$643$	13.1240	+	7.57712i	0.517558	+	0.298812i	−0.218377	+	0.975865i	$0.570076\pi$
$644$		0			0
$645$		0			0
$646$	7.20741			0.283572
$647$	6.22057	+	10.7743i	0.244556	+	0.423583i	0.962007	−	0.273026i	$-0.0880246\pi$
$647$	6.22057	+	10.7743i	0.244556	+	0.423583i	−0.717451	+	0.696609i	$0.754691\pi$
$648$		0			0
$649$	13.6195	+	7.86325i	0.534614	+	0.308659i
$650$	−21.5264	−	37.2847i	−0.844333	−	1.46243i
$651$		0			0
$652$	−4.06032	+	7.03268i	−0.159014	+	0.275421i
$653$	−3.97013	+	2.29216i	−0.155363	+	0.0896990i	−0.575666	−	0.817685i	$-0.695257\pi$
$653$	−3.97013	+	2.29216i	−0.155363	+	0.0896990i	0.420303	+	0.907384i	$0.361924\pi$
$654$		0			0
$655$	−0.818096	+	1.41698i	−0.0319656	+	0.0553661i
$656$	29.1921	−	50.5621i	1.13976	−	1.97412i
$657$		0			0
$658$		0			0
$659$	−15.6110	+	9.01301i	−0.608118	+	0.351097i	−0.772228	−	0.635345i	$-0.780858\pi$
$659$	−15.6110	+	9.01301i	−0.608118	+	0.351097i	0.164111	+	0.986442i	$0.447525\pi$
$660$		0			0
$661$			0.640781i			0.0249235i	0.999922	+	0.0124617i	$0.00396680\pi$
$661$			0.640781i			0.0249235i	−0.999922	+	0.0124617i	$0.996033\pi$
$662$			55.6449i			2.16270i
$663$		0			0
$664$	−7.18189	+	4.14647i	−0.278711	+	0.160914i
$665$		0			0
$666$		0			0
$667$	−5.47018	+	9.47462i	−0.211806	+	0.366859i
$668$	−0.946692	+	1.63972i	−0.0366286	+	0.0634426i
$669$		0			0
$670$	10.4012	−	6.00511i	0.401832	−	0.231998i
$671$	28.1755	−	48.8014i	1.08770	−	1.88396i
$672$		0			0
$673$	−11.0695	−	19.1729i	−0.426697	−	0.739061i	0.569880	−	0.821728i	$-0.306990\pi$
$673$	−11.0695	−	19.1729i	−0.426697	−	0.739061i	−0.996577	+	0.0826667i	$0.973656\pi$
$674$	−5.90591	−	3.40978i	−0.227487	−	0.131340i
$675$		0			0
$676$	−9.01280	−	15.6106i	−0.346646	−	0.600409i
$677$	−20.0320			−0.769893			−0.384947	−	0.922939i	$-0.625780\pi$
$677$	−20.0320			−0.769893			−0.384947	+	0.922939i	$0.625780\pi$
$678$		0			0
$679$		0			0
$680$	−1.07456	−	0.620397i	−0.0412074	−	0.0237911i
$681$		0			0
$682$	47.7986	+	27.5966i	1.83030	+	1.05673i
$683$	18.1316	−	10.4683i	0.693786	−	0.400558i	−0.111243	−	0.993793i	$-0.535483\pi$
$683$	18.1316	−	10.4683i	0.693786	−	0.400558i	0.805029	+	0.593235i	$0.202150\pi$
$684$		0			0
$685$		−	0.783018i		−	0.0299176i
$686$		0			0
$687$		0			0
$688$	7.37198	+	12.7686i	0.281054	+	0.486800i
$689$	−12.1109			−0.461387
$690$		0			0
$691$			1.54072i			0.0586116i	0.999570	+	0.0293058i	$0.00932966\pi$
$691$			1.54072i			0.0586116i	−0.999570	+	0.0293058i	$0.990670\pi$
$692$	−10.3217			−0.392372
$693$		0			0
$694$	13.0740			0.496282
$695$			4.56025i			0.172980i
$696$		0			0
$697$	−19.5274			−0.739654
$698$	−13.9711	−	24.1987i	−0.528815	−	0.915935i
$699$		0			0
$700$		0			0
$701$			31.6641i			1.19593i	0.801520	+	0.597967i	$0.204025\pi$
$701$			31.6641i			1.19593i	−0.801520	+	0.597967i	$0.795975\pi$
$702$		0			0
$703$	16.7121	−	9.64873i	0.630309	−	0.363909i
$704$	10.5358	+	6.08286i	0.397083	+	0.229256i
$705$		0			0
$706$	−54.6922	−	31.5766i	−2.05837	−	1.18840i
$707$		0			0
$708$		0			0
$709$	22.3524			0.839463			0.419732	−	0.907648i	$-0.362124\pi$
$709$	22.3524			0.839463			0.419732	+	0.907648i	$0.362124\pi$
$710$	2.81835	+	4.88152i	0.105771	+	0.183200i
$711$		0			0
$712$	−4.41873	−	2.55116i	−0.165599	−	0.0956086i
$713$	−4.16988	−	7.22244i	−0.156163	−	0.270482i
$714$		0			0
$715$	8.79812	−	15.2388i	0.329031	−	0.569898i
$716$	−10.8625	+	6.27149i	−0.405952	+	0.234377i
$717$		0			0
$718$	6.06910	−	10.5120i	0.226497	−	0.392304i
$719$	−19.4544	+	33.6959i	−0.725525	+	1.25665i	0.233232	+	0.972421i	$0.425070\pi$
$719$	−19.4544	+	33.6959i	−0.725525	+	1.25665i	−0.958757	+	0.284226i	$0.908264\pi$
$720$		0			0
$721$		0			0
$722$	−20.9011	+	12.0672i	−0.777858	+	0.449096i
$723$		0			0
$724$			16.2261i			0.603039i
$725$		−	34.0741i		−	1.26548i
$726$		0			0
$727$	11.4647	−	6.61915i	0.425202	−	0.245491i	−0.272098	−	0.962269i	$-0.587718\pi$
$727$	11.4647	−	6.61915i	0.425202	−	0.245491i	0.697301	+	0.716779i	$0.254384\pi$
$728$		0			0
$729$		0			0
$730$	−6.98119	+	12.0918i	−0.258385	+	0.447536i
$731$	2.46567	−	4.27066i	0.0911960	−	0.157956i
$732$		0			0
$733$	−28.1222	+	16.2364i	−1.03872	+	0.599704i	−0.919470	−	0.393161i	$-0.871382\pi$
$733$	−28.1222	+	16.2364i	−1.03872	+	0.599704i	−0.119248	+	0.992865i	$0.538048\pi$
$734$	2.83703	−	4.91389i	0.104717	−	0.181375i
$735$		0			0
$736$	−4.83338	−	8.37167i	−0.178161	−	0.308584i
$737$	−46.7508	−	26.9916i	−1.72209	−	0.994248i
$738$		0			0
$739$	6.91965	+	11.9852i	0.254543	+	0.440882i	0.964771	−	0.263090i	$-0.0847415\pi$
$739$	6.91965	+	11.9852i	0.254543	+	0.440882i	−0.710228	+	0.703972i	$0.751408\pi$
$740$	7.00011			0.257329
$741$		0			0
$742$		0			0
$743$	−31.8593	−	18.3940i	−1.16880	−	0.674810i	−0.215406	−	0.976525i	$-0.569108\pi$
$743$	−31.8593	−	18.3940i	−1.16880	−	0.674810i	−0.953398	+	0.301715i	$0.902441\pi$
$744$		0			0
$745$	−3.87515	−	2.23732i	−0.141975	−	0.0819690i
$746$	−15.3898	+	8.88530i	−0.563461	+	0.325314i
$747$		0			0
$748$		−	11.7514i		−	0.429675i
$749$		0			0
$750$		0			0
$751$	1.82952	+	3.16883i	0.0667602	+	0.115632i	0.897473	−	0.441068i	$-0.145400\pi$
$751$	1.82952	+	3.16883i	0.0667602	+	0.115632i	−0.830713	+	0.556701i	$0.812067\pi$
$752$	15.0262			0.547948
$753$		0			0
$754$		−	69.8359i		−	2.54327i
$755$	4.07921			0.148458
$756$		0			0
$757$	13.8901			0.504842			0.252421	−	0.967617i	$-0.418773\pi$
$757$	13.8901			0.504842			0.252421	+	0.967617i	$0.418773\pi$
$758$		−	14.2184i		−	0.516435i
$759$		0			0
$760$	−1.83758			−0.0666560
$761$	−6.82083	−	11.8140i	−0.247255	−	0.428258i	0.715508	−	0.698604i	$-0.246195\pi$
$761$	−6.82083	−	11.8140i	−0.247255	−	0.428258i	−0.962763	+	0.270346i	$0.912862\pi$
$762$		0			0
$763$		0			0
$764$		−	27.4991i		−	0.994884i
$765$		0			0
$766$	−39.0500	+	22.5455i	−1.41093	+	0.814602i
$767$	13.1365	+	7.58434i	0.474330	+	0.273855i
$768$		0			0
$769$	22.9328	+	13.2402i	0.826976	+	0.477455i	0.852816	−	0.522211i	$-0.174893\pi$
$769$	22.9328	+	13.2402i	0.826976	+	0.477455i	−0.0258399	+	0.999666i	$0.508226\pi$
$770$		0			0
$771$		0			0
$772$	22.9104			0.824562
$773$	−13.1109	−	22.7087i	−0.471566	−	0.816776i	0.527905	−	0.849303i	$-0.322978\pi$
$773$	−13.1109	−	22.7087i	−0.471566	−	0.816776i	−0.999471	+	0.0325274i	$0.989644\pi$
$774$		0			0
$775$	22.4945	+	12.9872i	0.808026	+	0.466514i
$776$	9.80047	+	16.9749i	0.351816	+	0.609364i
$777$		0			0
$778$	5.88703	−	10.1966i	0.211060	−	0.365567i
$779$	−25.0451	+	14.4598i	−0.897334	+	0.518076i
$780$		0			0
$781$	12.6678	−	21.9413i	0.453291	−	0.785123i
$782$	−2.19701	+	3.80533i	−0.0785649	+	0.136078i
$783$		0			0
$784$		0			0
$785$	−1.11272	+	0.642430i	−0.0397148	+	0.0229293i
$786$		0			0
$787$			29.0470i			1.03541i	0.855558	+	0.517706i	$0.173214\pi$
$787$			29.0470i			1.03541i	−0.855558	+	0.517706i	$0.826786\pi$
$788$		−	25.3769i		−	0.904014i
$789$		0			0
$790$	−7.13088	+	4.11702i	−0.253705	+	0.146477i
$791$		0			0
$792$		0			0
$793$	27.1761	−	47.0704i	0.965052	−	1.67152i
$794$	−12.1463	+	21.0380i	−0.431055	+	0.746610i
$795$		0			0
$796$	21.1952	−	12.2371i	0.751245	−	0.433731i
$797$	−15.8184	+	27.3983i	−0.560317	+	0.970498i	0.437151	+	0.899388i	$0.355987\pi$
$797$	−15.8184	+	27.3983i	−0.560317	+	0.970498i	−0.997469	+	0.0711097i	$0.977346\pi$
$798$		0			0
$799$	−2.51286	−	4.35240i	−0.0888986	−	0.153977i
$800$	26.0738	+	15.0537i	0.921848	+	0.532229i
$801$		0			0
$802$	14.4777	+	25.0762i	0.511227	+	0.885470i
$803$	62.7577			2.21467
$804$		0			0
$805$		0			0
$806$	46.1032	+	26.6177i	1.62392	+	0.937569i
$807$		0			0
$808$	4.75044	+	2.74267i	0.167120	+	0.0964868i
$809$	−34.5466	+	19.9455i	−1.21459	+	0.701245i	−0.963756	−	0.266784i	$-0.914039\pi$
$809$	−34.5466	+	19.9455i	−1.21459	+	0.701245i	−0.250836	+	0.968029i	$0.580706\pi$
$810$		0			0
$811$		−	28.9516i		−	1.01663i	−0.861172	−	0.508314i	$-0.830269\pi$
$811$		−	28.9516i		−	1.01663i	0.861172	−	0.508314i	$-0.169731\pi$
$812$		0			0
$813$		0			0
$814$	−38.9300	−	67.4288i	−1.36450	−	2.36338i
$815$	−3.86521			−0.135392
$816$		0			0
$817$		−	7.30317i		−	0.255505i
$818$	−9.92684			−0.347084
$819$		0			0
$820$	−10.4905			−0.366344
$821$		−	0.414973i		−	0.0144826i	−0.999974	−	0.00724132i	$-0.997695\pi$
$821$		−	0.414973i		−	0.0144826i	0.999974	−	0.00724132i	$-0.00230500\pi$
$822$		0			0
$823$	−13.0963			−0.456508			−0.228254	−	0.973602i	$-0.573302\pi$
$823$	−13.0963			−0.456508			−0.228254	+	0.973602i	$0.573302\pi$
$824$	−6.07570	−	10.5234i	−0.211657	−	0.366601i
$825$		0			0
$826$		0			0
$827$		−	35.2637i		−	1.22624i	−0.789990	−	0.613120i	$-0.789914\pi$
$827$		−	35.2637i		−	1.22624i	0.789990	−	0.613120i	$-0.210086\pi$
$828$		0			0
$829$	29.0164	−	16.7526i	1.00778	−	0.581842i	0.0972388	−	0.995261i	$-0.468999\pi$
$829$	29.0164	−	16.7526i	1.00778	−	0.581842i	0.910541	+	0.413419i	$0.135666\pi$
$830$	7.20287	+	4.15858i	0.250015	+	0.144346i
$831$		0			0
$832$	10.1621	+	5.86710i	0.352308	+	0.203405i
$833$		0			0
$834$		0			0
$835$	−0.901200			−0.0311873
$836$	−8.70178	−	15.0719i	−0.300957	−	0.521273i
$837$		0			0
$838$	38.8615	+	22.4367i	1.34245	+	0.775062i
$839$	22.4984	+	38.9684i	0.776731	+	1.34534i	0.933816	+	0.357753i	$0.116457\pi$
$839$	22.4984	+	38.9684i	0.776731	+	1.34534i	−0.157085	+	0.987585i	$0.550210\pi$
$840$		0			0
$841$	13.1358	−	22.7519i	0.452959	−	0.784548i
$842$	19.0182	−	10.9802i	0.655412	−	0.378402i
$843$		0			0
$844$	5.47260	−	9.47882i	0.188375	−	0.326275i
$845$	4.28985	−	7.43024i	0.147575	−	0.255608i
$846$		0			0
$847$		0			0
$848$	9.96802	−	5.75504i	0.342303	−	0.197629i
$849$		0			0
$850$		−	13.6853i		−	0.469402i
$851$			11.7648i			0.403291i
$852$		0			0
$853$	15.8457	−	9.14854i	0.542548	−	0.313240i	−0.203563	−	0.979062i	$-0.565252\pi$
$853$	15.8457	−	9.14854i	0.542548	−	0.313240i	0.746111	+	0.665822i	$0.231919\pi$
$854$		0			0
$855$		0			0
$856$	−0.181929	+	0.315111i	−0.00621822	+	0.0107703i
$857$	−5.28926	+	9.16126i	−0.180678	+	0.312943i	−0.942111	−	0.335300i	$-0.891162\pi$
$857$	−5.28926	+	9.16126i	−0.180678	+	0.312943i	0.761434	+	0.648243i	$0.224496\pi$
$858$		0			0
$859$	−28.2972	+	16.3374i	−0.965488	+	0.557425i	−0.897858	−	0.440286i	$-0.854877\pi$
$859$	−28.2972	+	16.3374i	−0.965488	+	0.557425i	−0.0676303	+	0.997710i	$0.521544\pi$
$860$	1.32460	−	2.29428i	0.0451686	−	0.0782343i
$861$		0			0
$862$	28.2332	+	48.9014i	0.961628	+	1.66559i
$863$	8.09878	+	4.67583i	0.275686	+	0.159167i	0.631469	−	0.775401i	$-0.282452\pi$
$863$	8.09878	+	4.67583i	0.275686	+	0.159167i	−0.355783	+	0.934569i	$0.615786\pi$
$864$		0			0
$865$	−2.45643	−	4.25465i	−0.0835210	−	0.144663i
$866$	−11.1052			−0.377372
$867$		0			0
$868$		0			0
$869$	32.0517	+	18.5050i	1.08728	+	0.627741i
$870$		0			0
$871$	−45.0925	−	26.0342i	−1.52790	−	0.882135i
$872$	6.42216	−	3.70783i	0.217482	−	0.125563i
$873$		0			0
$874$			6.50742i			0.220117i
$875$		0			0
$876$		0			0
$877$	−0.619077	−	1.07227i	−0.0209048	−	0.0362081i	0.855384	−	0.517995i	$-0.173321\pi$
$877$	−0.619077	−	1.07227i	−0.0209048	−	0.0362081i	−0.876289	+	0.481787i	$0.839988\pi$
$878$	49.7300			1.67831
$879$		0			0
$880$			16.7233i			0.563744i
$881$	−37.3480			−1.25828			−0.629142	−	0.777290i	$-0.716594\pi$
$881$	−37.3480			−1.25828			−0.629142	+	0.777290i	$0.716594\pi$
$882$		0			0
$883$	3.90708			0.131484			0.0657419	−	0.997837i	$-0.479059\pi$
$883$	3.90708			0.131484			0.0657419	+	0.997837i	$0.479059\pi$
$884$		−	11.3346i		−	0.381224i
$885$		0			0
$886$	9.80432			0.329383
$887$	−7.25578	−	12.5674i	−0.243625	−	0.421972i	0.718119	−	0.695920i	$-0.245003\pi$
$887$	−7.25578	−	12.5674i	−0.243625	−	0.421972i	−0.961744	+	0.273949i	$0.911670\pi$
$888$		0			0
$889$		0			0
$890$			5.11722i			0.171530i
$891$		0			0
$892$	27.4585	−	15.8532i	0.919379	−	0.530804i
$893$	−6.44579	−	3.72148i	−0.215700	−	0.124534i
$894$		0			0
$895$	−5.17028	−	2.98506i	−0.172823	−	0.0997797i
$896$		0			0
$897$		0			0
$898$	−62.7317			−2.09339
$899$	21.0666	+	36.4884i	0.702610	+	1.21696i
$900$		0			0
$901$	−3.33395	−	1.92486i	−0.111070	−	0.0641263i
$902$	58.3414	+	101.050i	1.94256	+	3.36460i
$903$		0			0
$904$	−5.26201	+	9.11407i	−0.175012	+	0.303129i
$905$	−6.68849	+	3.86160i	−0.222333	+	0.128364i
$906$		0			0
$907$	9.60695	−	16.6397i	0.318993	−	0.552513i	−0.661285	−	0.750135i	$-0.729989\pi$
$907$	9.60695	−	16.6397i	0.318993	−	0.552513i	0.980278	+	0.197622i	$0.0633219\pi$
$908$	−9.79466	+	16.9648i	−0.325047	+	0.562998i
$909$		0			0
$910$		0			0
$911$	−10.1252	+	5.84579i	−0.335463	+	0.193680i	−0.658264	−	0.752787i	$-0.728709\pi$
$911$	−10.1252	+	5.84579i	−0.335463	+	0.193680i	0.322801	+	0.946467i	$0.395376\pi$
$912$		0			0
$913$		−	37.3837i		−	1.23722i
$914$			29.0566i			0.961106i
$915$		0			0
$916$	15.4034	−	8.89314i	0.508942	−	0.293838i
$917$		0			0
$918$		0			0
$919$	−19.9930	+	34.6289i	−0.659508	+	1.14230i	0.321236	+	0.946999i	$0.395902\pi$
$919$	−19.9930	+	34.6289i	−0.659508	+	1.14230i	−0.980743	+	0.195301i	$0.937432\pi$
$920$	0.560143	−	0.970196i	0.0184674	−	0.0319864i
$921$		0			0
$922$	−20.6470	+	11.9205i	−0.679972	+	0.392582i
$923$	12.2185	−	21.1631i	0.402177	−	0.696591i
$924$		0			0
$925$	−18.3209	−	31.7326i	−0.602386	−	1.04336i
$926$	19.1005	+	11.0277i	0.627683	+	0.362393i
$927$		0			0
$928$	24.4187	+	42.2944i	0.801582	+	1.38838i
$929$	−12.7672			−0.418877			−0.209439	−	0.977822i	$-0.567164\pi$
$929$	−12.7672			−0.418877			−0.209439	+	0.977822i	$0.567164\pi$
$930$		0			0
$931$		0			0
$932$	−9.92775	−	5.73179i	−0.325194	−	0.187751i
$933$		0			0
$934$	−32.2801	−	18.6369i	−1.05624	−	0.609818i
$935$	4.84400	−	2.79669i	0.158416	−	0.0914614i
$936$		0			0
$937$		−	11.9436i		−	0.390179i	−0.980785	−	0.195090i	$-0.937500\pi$
$937$		−	11.9436i		−	0.390179i	0.980785	−	0.195090i	$-0.0624997\pi$
$938$		0			0
$939$		0			0
$940$	−1.34996	−	2.33819i	−0.0440307	−	0.0762634i
$941$	25.0317			0.816011			0.408006	−	0.912979i	$-0.366224\pi$
$941$	25.0317			0.816011			0.408006	+	0.912979i	$0.366224\pi$
$942$		0			0
$943$		−	17.6309i		−	0.574142i
$944$	−14.4162			−0.469208
$945$		0			0
$946$	−29.4663			−0.958032
$947$			32.7555i			1.06441i	0.846615	+	0.532205i	$0.178637\pi$
$947$			32.7555i			1.06441i	−0.846615	+	0.532205i	$0.821363\pi$
$948$		0			0
$949$	60.5316			1.96494
$950$	−10.1338	−	17.5522i	−0.328783	−	0.569469i
$951$		0			0
$952$		0			0
$953$		−	6.77705i		−	0.219530i	−0.993958	−	0.109765i	$-0.964990\pi$
$953$		−	6.77705i		−	0.219530i	0.993958	−	0.109765i	$-0.0350099\pi$
$954$		0			0
$955$	11.3353	−	6.54443i	0.366801	−	0.211773i
$956$	−32.8378	−	18.9589i	−1.06205	−	0.613175i
$957$		0			0
$958$	38.5512	+	22.2575i	1.24553	+	0.719109i
$959$		0			0
$960$		0			0
$961$	−1.11779			−0.0360578
$962$	−37.5492	−	65.0371i	−1.21063	−	2.09688i
$963$		0			0
$964$	−26.3203	−	15.1960i	−0.847721	−	0.489432i
$965$	5.45236	+	9.44377i	0.175518	+	0.304006i
$966$		0			0
$967$	20.7901	−	36.0096i	0.668566	−	1.15799i	−0.309739	−	0.950822i	$-0.600242\pi$
$967$	20.7901	−	36.0096i	0.668566	−	1.15799i	0.978305	−	0.207169i	$-0.0664249\pi$
$968$	17.6263	−	10.1765i	0.566530	−	0.327086i
$969$		0			0
$970$	9.82910	−	17.0245i	0.315593	−	0.546624i
$971$	−20.6257	+	35.7248i	−0.661910	+	1.14646i	0.318203	+	0.948023i	$0.396921\pi$
$971$	−20.6257	+	35.7248i	−0.661910	+	1.14646i	−0.980113	+	0.198439i	$0.936413\pi$
$972$		0			0
$973$		0			0
$974$	43.3281	−	25.0155i	1.38832	−	0.801547i
$975$		0			0
$976$			51.6560i			1.65347i
$977$			4.57847i			0.146478i	0.997314	+	0.0732391i	$0.0233336\pi$
$977$			4.57847i			0.146478i	−0.997314	+	0.0732391i	$0.976666\pi$
$978$		0			0
$979$	19.9192	−	11.5004i	0.636621	−	0.367553i
$980$		0			0
$981$		0			0
$982$	14.0569	−	24.3473i	0.448575	−	0.776955i
$983$	−12.2401	+	21.2004i	−0.390397	+	0.676188i	−0.992502	−	0.122229i	$-0.960996\pi$
$983$	−12.2401	+	21.2004i	−0.390397	+	0.676188i	0.602105	+	0.798417i	$0.294329\pi$
$984$		0			0
$985$	10.4605	−	6.03936i	0.333299	−	0.192430i
$986$	11.0995	−	19.2249i	0.353480	−	0.612245i
$987$		0			0
$988$	−8.39312	−	14.5373i	−0.267021	−	0.462494i
$989$	3.85589	+	2.22620i	0.122610	+	0.0707890i
$990$		0			0
$991$	21.0927	+	36.5337i	0.670032	+	1.16053i	0.977894	+	0.209099i	$0.0670531\pi$
$991$	21.0927	+	36.5337i	0.670032	+	1.16053i	−0.307862	+	0.951431i	$0.599614\pi$
$992$	−37.2284			−1.18200
$993$		0			0
$994$		0			0
$995$	10.0884	+	5.82452i	0.319822	+	0.184650i
$996$		0			0
$997$	−8.38168	−	4.83917i	−0.265451	−	0.153258i	0.361368	−	0.932423i	$-0.382310\pi$
$997$	−8.38168	−	4.83917i	−0.265451	−	0.153258i	−0.626818	+	0.779165i	$0.715643\pi$
$998$	16.3578	−	9.44415i	0.517796	−	0.298949i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.i.d.1097.17		48
3.2	odd	2		441.2.i.d.68.18		48
7.2	even	3		1323.2.o.e.881.8		48
7.3	odd	6		1323.2.s.d.962.17		48
7.4	even	3		1323.2.s.d.962.18		48
7.5	odd	6		1323.2.o.e.881.7		48
7.6	odd	2	inner	1323.2.i.d.1097.15		48
9.2	odd	6		1323.2.s.d.656.17		48
9.7	even	3		441.2.s.d.362.8		48
21.2	odd	6		441.2.o.e.293.17	yes	48
21.5	even	6		441.2.o.e.293.18	yes	48
21.11	odd	6		441.2.s.d.374.7		48
21.17	even	6		441.2.s.d.374.8		48
21.20	even	2		441.2.i.d.68.17		48
63.2	odd	6		1323.2.o.e.440.7		48
63.11	odd	6	inner	1323.2.i.d.521.15		48
63.16	even	3		441.2.o.e.146.18	yes	48
63.20	even	6		1323.2.s.d.656.18		48
63.25	even	3		441.2.i.d.227.7		48
63.34	odd	6		441.2.s.d.362.7		48
63.38	even	6	inner	1323.2.i.d.521.17		48
63.47	even	6		1323.2.o.e.440.8		48
63.52	odd	6		441.2.i.d.227.8		48
63.61	odd	6		441.2.o.e.146.17	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.17		48	21.20	even	2
441.2.i.d.68.18		48	3.2	odd	2
441.2.i.d.227.7		48	63.25	even	3
441.2.i.d.227.8		48	63.52	odd	6
441.2.o.e.146.17	✓	48	63.61	odd	6
441.2.o.e.146.18	yes	48	63.16	even	3
441.2.o.e.293.17	yes	48	21.2	odd	6
441.2.o.e.293.18	yes	48	21.5	even	6
441.2.s.d.362.7		48	63.34	odd	6
441.2.s.d.362.8		48	9.7	even	3
441.2.s.d.374.7		48	21.11	odd	6
441.2.s.d.374.8		48	21.17	even	6
1323.2.i.d.521.15		48	63.11	odd	6	inner
1323.2.i.d.521.17		48	63.38	even	6	inner
1323.2.i.d.1097.15		48	7.6	odd	2	inner
1323.2.i.d.1097.17		48	1.1	even	1	trivial
1323.2.o.e.440.7		48	63.2	odd	6
1323.2.o.e.440.8		48	63.47	even	6
1323.2.o.e.881.7		48	7.5	odd	6
1323.2.o.e.881.8		48	7.2	even	3
1323.2.s.d.656.17		48	9.2	odd	6
1323.2.s.d.656.18		48	63.20	even	6
1323.2.s.d.962.17		48	7.3	odd	6
1323.2.s.d.962.18		48	7.4	even	3

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.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.83202i q^{2} -1.35631 q^{4} +(-0.322784 - 0.559079i) q^{5} -1.17925i q^{8} +(-1.02425 + 0.591348i) q^{10} +(4.60375 + 2.65797i) q^{11} +(4.44045 + 2.56370i) q^{13} -4.87304 q^{16} +(0.814931 + 1.41150i) q^{17} +(2.09039 + 1.20689i) q^{19} +(0.437796 + 0.758285i) q^{20} +(4.86947 - 8.43418i) q^{22} +(-1.27442 + 0.735784i) q^{23} +(2.29162 - 3.96920i) q^{25} +(4.69675 - 8.13502i) q^{26} +(6.43846 - 3.71724i) q^{29} +5.66726i q^{31} +6.56903i q^{32} +(2.58590 - 1.49297i) q^{34} +(3.99736 - 6.92362i) q^{37} +(2.21105 - 3.82965i) q^{38} +(-0.659294 + 0.380644i) q^{40} +(-5.99052 + 10.3759i) q^{41} +(-1.51281 - 2.62026i) q^{43} +(-6.24412 - 3.60504i) q^{44} +(1.34797 + 2.33476i) q^{46} -3.08353 q^{47} +(-7.27168 - 4.19830i) q^{50} +(-6.02264 - 3.47717i) q^{52} +(-2.04554 + 1.18100i) q^{53} -3.43181i q^{55} +(-6.81008 - 11.7954i) q^{58} +2.95836 q^{59} -10.6004i q^{61} +10.3825 q^{62} +2.28853 q^{64} -3.31008i q^{65} -10.1549 q^{67} +(-1.10530 - 1.91444i) q^{68} -4.76597i q^{71} +(10.2239 - 5.90277i) q^{73} +(-12.6842 - 7.32325i) q^{74} +(-2.83523 - 1.63692i) q^{76} +6.96209 q^{79} +(1.57294 + 2.72441i) q^{80} +(19.0089 + 10.9748i) q^{82} +(-3.51618 - 6.09021i) q^{83} +(0.526093 - 0.911221i) q^{85} +(-4.80038 + 2.77150i) q^{86} +(3.13442 - 5.42898i) q^{88} +(2.16337 - 3.74706i) q^{89} +(1.72850 - 0.997953i) q^{92} +5.64910i q^{94} -1.55826i q^{95} +(-14.3946 + 8.31075i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4} - 24 q^{11} + 48 q^{16} - 48 q^{23} - 24 q^{25} + 96 q^{44} - 48 q^{50} + 48 q^{53} - 48 q^{64} - 168 q^{74} + 48 q^{79} - 24 q^{85} + 24 q^{86} + 144 q^{92}+O(q^{100}) \) 48 * q - 48 * q^4 - 24 * q^11 + 48 * q^16 - 48 * q^23 - 24 * q^25 + 96 * q^44 - 48 * q^50 + 48 * q^53 - 48 * q^64 - 168 * q^74 + 48 * q^79 - 24 * q^85 + 24 * q^86 + 144 * q^92

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more