LMFDB - Embedded newform 441.2.i.d.227.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,2,Mod(68,441)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(441, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("441.68"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage: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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			227.7
Character	$\chi$	$=$	441.227
Dual form			441.2.i.d.68.17

$q$-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} +(-1.55144 + 0.770089i) q^{3} -1.35631 q^{4} +(-0.322784 + 0.559079i) q^{5} +(1.41082 + 2.84227i) q^{6} -1.17925i q^{8} +(1.81393 - 2.38949i) q^{9} +(1.02425 + 0.591348i) q^{10} +(-4.60375 + 2.65797i) q^{11} +(2.10424 - 1.04448i) q^{12} +(-4.44045 + 2.56370i) q^{13} +(0.0702397 - 1.11595i) q^{15} -4.87304 q^{16} +(0.814931 - 1.41150i) q^{17} +(-4.37761 - 3.32316i) q^{18} +(-2.09039 + 1.20689i) q^{19} +(0.437796 - 0.758285i) q^{20} +(4.86947 + 8.43418i) q^{22} +(1.27442 + 0.735784i) q^{23} +(0.908129 + 1.82954i) q^{24} +(2.29162 + 3.96920i) q^{25} +(4.69675 + 8.13502i) q^{26} +(-0.974073 + 5.10404i) q^{27} +(-6.43846 - 3.71724i) q^{29} +(-2.04445 - 0.128681i) q^{30} +5.66726i q^{31} +6.56903i q^{32} +(5.09556 - 7.66898i) q^{33} +(-2.58590 - 1.49297i) q^{34} +(-2.46025 + 3.24090i) q^{36} +(3.99736 + 6.92362i) q^{37} +(2.21105 + 3.82965i) q^{38} +(4.91482 - 7.39696i) q^{39} +(0.659294 + 0.380644i) q^{40} +(-5.99052 - 10.3759i) q^{41} +(-1.51281 + 2.62026i) q^{43} +(6.24412 - 3.60504i) q^{44} +(0.750407 + 1.78542i) q^{45} +(1.34797 - 2.33476i) q^{46} -3.08353 q^{47} +(7.56023 - 3.75268i) q^{48} +(7.27168 - 4.19830i) q^{50} +(-0.177334 + 2.81743i) q^{51} +(6.02264 - 3.47717i) q^{52} +(2.04554 + 1.18100i) q^{53} +(9.35072 + 1.78453i) q^{54} -3.43181i q^{55} +(2.31371 - 3.48220i) q^{57} +(-6.81008 + 11.7954i) q^{58} +2.95836 q^{59} +(-0.0952669 + 1.51357i) q^{60} -10.6004i q^{61} +10.3825 q^{62} +2.28853 q^{64} -3.31008i q^{65} +(-14.0498 - 9.33518i) q^{66} -10.1549 q^{67} +(-1.10530 + 1.91444i) q^{68} +(-2.54380 - 0.160111i) q^{69} -4.76597i q^{71} +(-2.81781 - 2.13908i) q^{72} +(-10.2239 - 5.90277i) q^{73} +(12.6842 - 7.32325i) q^{74} +(-6.61195 - 4.39323i) q^{75} +(2.83523 - 1.63692i) q^{76} +(-13.5514 - 9.00406i) q^{78} +6.96209 q^{79} +(1.57294 - 2.72441i) q^{80} +(-2.41935 - 8.66872i) q^{81} +(-19.0089 + 10.9748i) q^{82} +(-3.51618 + 6.09021i) q^{83} +(0.526093 + 0.911221i) q^{85} +(4.80038 + 2.77150i) q^{86} +(12.8515 + 0.808893i) q^{87} +(3.13442 + 5.42898i) q^{88} +(2.16337 + 3.74706i) q^{89} +(3.27093 - 1.37476i) q^{90} +(-1.72850 - 0.997953i) q^{92} +(-4.36429 - 8.79240i) q^{93} +5.64910i q^{94} -1.55826i q^{95} +(-5.05873 - 10.1914i) q^{96} +(14.3946 + 8.31075i) q^{97} +(-1.99965 + 15.8220i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4} - 8 q^{9} + 24 q^{11} - 40 q^{15} + 48 q^{16} - 16 q^{18} + 48 q^{23} - 24 q^{25} - 24 q^{30} - 8 q^{36} - 56 q^{39} - 96 q^{44} + 48 q^{50} - 24 q^{51} - 48 q^{53} + 80 q^{57} + 168 q^{60}+ \cdots - 72 q^{99}+O(q^{100}) $ 48 * q - 48 * q^4 - 8 * q^9 + 24 * q^11 - 40 * q^15 + 48 * q^16 - 16 * q^18 + 48 * q^23 - 24 * q^25 - 24 * q^30 - 8 * q^36 - 56 * q^39 - 96 * q^44 + 48 * q^50 - 24 * q^51 - 48 * q^53 + 80 * q^57 + 168 * q^60 - 48 * q^64 - 88 * q^72 + 168 * q^74 - 88 * q^78 + 48 * q^79 - 24 * q^81 - 24 * q^85 - 24 * q^86 - 144 * q^92 + 16 * q^93 - 72 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$		−	1.83202i		−	1.29544i	−0.761880	−	0.647718i	$-0.775723\pi$
$2$		−	1.83202i		−	1.29544i	0.761880	−	0.647718i	$-0.224277\pi$
$3$	−1.55144	+	0.770089i	−0.895724	+	0.444611i
$3$	−1.55144	+	0.770089i	−0.895724	+	0.444611i
$4$	−1.35631			−0.678156
$5$	−0.322784	+	0.559079i	−0.144353	+	0.250028i	−0.929132	−	0.369749i	$-0.879444\pi$
$5$	−0.322784	+	0.559079i	−0.144353	+	0.250028i	0.784778	+	0.619777i	$0.212777\pi$
$6$	1.41082	+	2.84227i	0.575966	+	1.16035i
$7$		0			0
$7$		0			0
$8$		−	1.17925i		−	0.416928i
$9$	1.81393	−	2.38949i	0.604642	−	0.796497i
$10$	1.02425	+	0.591348i	0.323895	+	0.187001i
$11$	−4.60375	+	2.65797i	−1.38808	+	0.801410i	−0.993099	−	0.117279i	$-0.962583\pi$
$11$	−4.60375	+	2.65797i	−1.38808	+	0.801410i	−0.394983	+	0.918688i	$0.629250\pi$
$12$	2.10424	−	1.04448i	0.607440	−	0.301516i
$13$	−4.44045	+	2.56370i	−1.23156	+	0.711041i	−0.967355	−	0.253425i	$-0.918443\pi$
$13$	−4.44045	+	2.56370i	−1.23156	+	0.711041i	−0.264205	+	0.964467i	$0.585110\pi$
$14$		0			0
$15$	0.0702397	−	1.11595i	0.0181358	−	0.288137i
$16$	−4.87304			−1.21826
$17$	0.814931	−	1.41150i	0.197650	−	0.342339i	−0.750116	−	0.661306i	$-0.770002\pi$
$17$	0.814931	−	1.41150i	0.197650	−	0.342339i	0.947766	+	0.318967i	$0.103336\pi$
$18$	−4.37761	−	3.32316i	−1.03181	−	0.783275i
$19$	−2.09039	+	1.20689i	−0.479569	+	0.276879i	−0.720237	−	0.693728i	$-0.755967\pi$
$19$	−2.09039	+	1.20689i	−0.479569	+	0.276879i	0.240668	+	0.970608i	$0.422634\pi$
$20$	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	$-0.284304\pi$
$23$	1.27442	+	0.735784i	0.265734	+	0.153422i	−0.361213	+	0.932483i	$0.617637\pi$
$24$	0.908129	+	1.82954i	0.185371	+	0.373453i
$25$	2.29162	+	3.96920i	0.458324	+	0.793841i
$26$	4.69675	+	8.13502i	0.921109	+	1.59541i
$27$	−0.974073	+	5.10404i	−0.187461	+	0.982272i
$28$		0			0
$29$	−6.43846	−	3.71724i	−1.19559	−	0.690275i	−0.236022	−	0.971748i	$-0.575844\pi$
$29$	−6.43846	−	3.71724i	−1.19559	−	0.690275i	−0.959569	+	0.281473i	$0.909177\pi$
$30$	−2.04445	−	0.128681i	−0.373263	−	0.0234938i
$31$			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
$33$	5.09556	−	7.66898i	0.887022	−	1.33500i
$34$	−2.58590	−	1.49297i	−0.443479	−	0.256043i
$35$		0			0
$36$	−2.46025	+	3.24090i	−0.410042	+	0.540150i
$37$	3.99736	+	6.92362i	0.657161	+	1.13824i	0.981347	+	0.192244i	$0.0615763\pi$
$37$	3.99736	+	6.92362i	0.657161	+	1.13824i	−0.324186	+	0.945993i	$0.605090\pi$
$38$	2.21105	+	3.82965i	0.358680	+	0.621251i
$39$	4.91482	−	7.39696i	0.787000	−	1.18446i
$40$	0.659294	+	0.380644i	0.104244	+	0.0601851i
$41$	−5.99052	−	10.3759i	−0.935562	−	1.62044i	−0.773628	−	0.633640i	$-0.781560\pi$
$41$	−5.99052	−	10.3759i	−0.935562	−	1.62044i	−0.161934	−	0.986802i	$-0.551773\pi$
$42$		0			0
$43$	−1.51281	+	2.62026i	−0.230701	+	0.399586i	−0.958015	−	0.286719i	$-0.907435\pi$
$43$	−1.51281	+	2.62026i	−0.230701	+	0.399586i	0.727314	+	0.686305i	$0.240769\pi$
$44$	6.24412	−	3.60504i	0.941336	−	0.543481i
$45$	0.750407	+	1.78542i	0.111864	+	0.266154i
$46$	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	$0.572202\pi$
$48$	7.56023	−	3.75268i	1.09122	−	0.541652i
$49$		0			0
$50$	7.27168	−	4.19830i	1.02837	−	0.593730i
$51$	−0.177334	+	2.81743i	−0.0248317	+	0.394519i
$52$	6.02264	−	3.47717i	0.835190	−	0.482197i
$53$	2.04554	+	1.18100i	0.280977	+	0.162222i	0.633866	−	0.773443i	$-0.281467\pi$
$53$	2.04554	+	1.18100i	0.280977	+	0.162222i	−0.352889	+	0.935665i	$0.614801\pi$
$54$	9.35072	+	1.78453i	1.27247	+	0.242843i
$55$		−	3.43181i		−	0.462745i
$56$		0			0
$57$	2.31371	−	3.48220i	0.306458	−	0.461229i
$58$	−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	$0.438317\pi$
$60$	−0.0952669	+	1.51357i	−0.0122989	+	0.195402i
$61$		−	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
$66$	−14.0498	−	9.33518i	−1.72941	−	1.14908i
$67$	−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
$69$	−2.54380	−	0.160111i	−0.306237	−	0.0192751i
$70$		0			0
$71$		−	4.76597i		−	0.565617i	−0.959176	−	0.282808i	$-0.908734\pi$
$71$		−	4.76597i		−	0.565617i	0.959176	−	0.282808i	$-0.0912661\pi$
$72$	−2.81781	−	2.13908i	−0.332082	−	0.252092i
$73$	−10.2239	−	5.90277i	−1.19662	−	0.690867i	−0.236817	−	0.971554i	$-0.576104\pi$
$73$	−10.2239	−	5.90277i	−1.19662	−	0.690867i	−0.959799	+	0.280687i	$0.909438\pi$
$74$	12.6842	−	7.32325i	1.47451	−	0.851311i
$75$	−6.61195	−	4.39323i	−0.763482	−	0.507286i
$76$	2.83523	−	1.63692i	0.325223	−	0.187767i
$77$		0			0
$78$	−13.5514	−	9.00406i	−1.53440	−	1.01951i
$79$	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
$81$	−2.41935	−	8.66872i	−0.268816	−	0.963191i
$82$	−19.0089	+	10.9748i	−2.09918	+	1.21196i
$83$	−3.51618	+	6.09021i	−0.385951	+	0.668487i	−0.991901	−	0.127016i	$-0.959460\pi$
$83$	−3.51618	+	6.09021i	−0.385951	+	0.668487i	0.605949	+	0.795503i	$0.292793\pi$
$84$		0			0
$85$	0.526093	+	0.911221i	0.0570628	+	0.0988357i
$86$	4.80038	+	2.77150i	0.517638	+	0.298859i
$87$	12.8515	+	0.808893i	1.37782	+	0.0867225i
$88$	3.13442	+	5.42898i	0.334130	+	0.578731i
$89$	2.16337	+	3.74706i	0.229317	+	0.397188i	0.957606	−	0.288082i	$-0.0930176\pi$
$89$	2.16337	+	3.74706i	0.229317	+	0.397188i	−0.728289	+	0.685270i	$0.759684\pi$
$90$	3.27093	−	1.37476i	0.344786	−	0.144913i
$91$		0			0
$92$	−1.72850	−	0.997953i	−0.180209	−	0.104044i
$93$	−4.36429	−	8.79240i	−0.452556	−	0.911730i
$94$			5.64910i			0.582660i
$95$		−	1.55826i		−	0.159874i
$96$	−5.05873	−	10.1914i	−0.516305	−	1.04016i
$97$	14.3946	+	8.31075i	1.46156	+	0.843829i	0.999083	−	0.0428048i	$-0.0136294\pi$
$97$	14.3946	+	8.31075i	1.46156	+	0.843829i	0.462472	+	0.886634i	$0.346963\pi$
$98$		0			0
$99$	−1.99965	+	15.8220i	−0.200972	+	1.59017i
$100$	−3.10815	−	5.38348i	−0.310815	−	0.538348i
$101$	−2.32577	−	4.02835i	−0.231423	−	0.400836i	0.726804	−	0.686845i	$-0.241005\pi$
$101$	−2.32577	−	4.02835i	−0.231423	−	0.400836i	−0.958227	+	0.286009i	$0.907671\pi$
$102$	5.16159	+	0.324879i	0.511074	+	0.0321678i
$103$	−8.92382	−	5.15217i	−0.879290	−	0.507658i	−0.00886554	−	0.999961i	$-0.502822\pi$
$103$	−8.92382	−	5.15217i	−0.879290	−	0.507658i	−0.870424	+	0.492303i	$0.836155\pi$
$104$	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	$-0.661919\pi$
$107$	0.267212	−	0.154275i	0.0258324	−	0.0149143i	0.512861	+	0.858472i	$0.328586\pi$
$108$	1.32115	−	6.92267i	0.127127	−	0.666134i
$109$	3.14423	−	5.44596i	0.301162	−	0.521628i	−0.675237	−	0.737601i	$-0.735959\pi$
$109$	3.14423	−	5.44596i	0.301162	−	0.521628i	0.976399	+	0.215972i	$0.0692921\pi$
$110$	−6.28716			−0.599457
$111$	−11.5335	−	7.66326i	−1.09471	−	0.727365i
$112$		0			0
$113$	7.72869	−	4.46216i	0.727054	−	0.419765i	−0.0902895	−	0.995916i	$-0.528779\pi$
$113$	7.72869	−	4.46216i	0.727054	−	0.419765i	0.817343	+	0.576151i	$0.195446\pi$
$114$	−6.37948	−	4.23876i	−0.597493	−	0.396997i
$115$	−0.822722	+	0.474999i	−0.0767192	+	0.0442939i
$116$	8.73256	+	5.04174i	0.810797	+	0.468114i
$117$	−1.92872	+	15.2608i	−0.178310	+	1.41086i
$118$		−	5.41979i		−	0.498932i
$119$		0			0
$120$	−1.31598	−	0.0828302i	−0.120132	−	0.00756133i
$121$	8.62966	−	14.9470i	0.784515	−	1.35882i
$122$	−19.4201			−1.75821
$123$	17.2843	+	11.4843i	1.55847	+	1.03551i
$124$		−	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
$129$	0.329196	−	5.23017i	0.0289840	−	0.460491i
$130$	−6.06415			−0.531861
$131$	−1.26725	+	2.19494i	−0.110720	+	0.191773i	−0.916061	−	0.401039i	$-0.868649\pi$
$131$	−1.26725	+	2.19494i	−0.110720	+	0.191773i	0.805341	+	0.592812i	$0.201982\pi$
$132$	−6.91116	+	10.4015i	−0.601540	+	0.905337i
$133$		0			0
$134$			18.6041i			1.60715i
$135$	−2.53914	−	2.19209i	−0.218535	−	0.188665i
$136$	−1.66452	−	0.961008i	−0.142731	−	0.0824058i
$137$	−1.05041	+	0.606456i	−0.0897429	+	0.0518131i	−0.544200	−	0.838956i	$-0.683167\pi$
$137$	−1.05041	+	0.606456i	−0.0897429	+	0.0518131i	0.454457	+	0.890769i	$0.349833\pi$
$138$	−0.293327	+	4.66030i	−0.0249696	+	0.396711i
$139$	6.11754	−	3.53196i	0.518883	−	0.299577i	−0.217594	−	0.976039i	$-0.569821\pi$
$139$	6.11754	−	3.53196i	0.518883	−	0.299577i	0.736478	+	0.676462i	$0.236488\pi$
$140$		0			0
$141$	4.78390	−	2.37459i	0.402877	−	0.199977i
$142$	−8.73137			−0.732721
$143$	13.6285	−	23.6052i	1.13967	−	1.97397i
$144$	−8.83934	+	11.6441i	−0.736611	+	0.970341i
$145$	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	$-0.424968\pi$
$149$	−6.00270	−	3.46566i	−0.491760	−	0.283918i	−0.725304	+	0.688428i	$0.758301\pi$
$150$	−8.04849	+	12.1133i	−0.657157	+	0.989043i
$151$	−3.15939	−	5.47223i	−0.257108	−	0.445323i	0.708358	−	0.705853i	$-0.249436\pi$
$151$	−3.15939	−	5.47223i	−0.257108	−	0.445323i	−0.965466	+	0.260530i	$0.916103\pi$
$152$	1.42323	+	2.46510i	0.115439	+	0.199946i
$153$	−1.89455	−	4.50763i	−0.153165	−	0.364420i
$154$		0			0
$155$	−3.16844	−	1.82930i	−0.254495	−	0.146933i
$156$	−6.66602	+	10.0326i	−0.533709	+	0.803250i
$157$		−	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
$159$	−4.08301	−	0.256991i	−0.323804	−	0.0203807i
$160$	−3.67260	−	2.12038i	−0.290345	−	0.167631i
$161$		0			0
$162$	−15.8813	+	4.43230i	−1.24775	+	0.348234i
$163$	2.99365	+	5.18515i	0.234480	+	0.406132i	0.959122	−	0.282994i	$-0.0913278\pi$
$163$	2.99365	+	5.18515i	0.234480	+	0.406132i	−0.724641	+	0.689126i	$0.757994\pi$
$164$	8.12502	+	14.0729i	0.634457	+	1.09891i
$165$	2.64280	+	5.32424i	0.205742	+	0.414492i
$166$	11.1574	+	6.44173i	0.865983	+	0.499976i
$167$	0.697990	+	1.20895i	0.0540121	+	0.0935516i	0.891767	−	0.452494i	$-0.149466\pi$
$167$	0.697990	+	1.20895i	0.0540121	+	0.0935516i	−0.837755	+	0.546046i	$0.816132\pi$
$168$		0			0
$169$	6.64508	−	11.5096i	0.511160	−	0.885355i
$170$	1.66938	−	0.963816i	0.128035	−	0.0739213i
$171$	−0.907966	+	7.18419i	−0.0694339	+	0.549388i
$172$	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	$0.406580\pi$
$174$	1.48191	−	23.5442i	0.112343	−	1.78488i
$175$		0			0
$176$	22.4343	−	12.9524i	1.69105	−	0.976326i
$177$	−4.58972	+	2.27820i	−0.344984	+	0.171240i
$178$	6.86471	−	3.96334i	0.514532	−	0.297065i
$179$	−8.00888	−	4.62393i	−0.598612	−	0.345609i	0.169883	−	0.985464i	$-0.445661\pi$
$179$	−8.00888	−	4.62393i	−0.598612	−	0.345609i	−0.768495	+	0.639855i	$0.778994\pi$
$180$	−1.01779	−	2.42158i	−0.0758613	−	0.180494i
$181$		−	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
$183$	8.16322	+	16.4458i	0.603443	+	1.21571i
$184$	0.867674	−	1.50286i	0.0639658	−	0.110792i
$185$	−5.16113			−0.379454
$186$	−16.1079	+	7.99549i	−1.18109	+	0.586258i
$187$			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	$0.737875\pi$
$192$	−3.55052	+	1.76237i	−0.256236	+	0.127188i
$193$	−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
$195$	2.54906	+	5.13539i	0.182542	+	0.367753i
$196$		0			0
$197$			18.7102i			1.33305i	0.745484	+	0.666524i	$0.232219\pi$
$197$			18.7102i			1.33305i	−0.745484	+	0.666524i	$0.767781\pi$
$198$	28.9863	+	3.66340i	2.05996	+	0.260346i
$199$	15.6271	+	9.02231i	1.10778	+	0.639574i	0.938252	−	0.345952i	$-0.112444\pi$
$199$	15.6271	+	9.02231i	1.10778	+	0.639574i	0.169523	+	0.985526i	$0.445777\pi$
$200$	4.68069	−	2.70240i	0.330975	−	0.191088i
$201$	15.7548	−	7.82021i	1.11126	−	0.551595i
$202$	−7.38004	+	4.26087i	−0.519258	+	0.299794i
$203$		0			0
$204$	0.240520	−	3.82131i	0.0168397	−	0.267545i
$205$	7.73458			0.540207
$206$	−9.43889	+	16.3486i	−0.657639	+	1.13906i
$207$	4.06984	−	1.71055i	0.282874	−	0.118891i
$208$	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	0.693057	−	0.720883i	$-0.256264\pi$
$211$	−4.03491	−	6.98868i	−0.277775	−	0.481120i	−0.970831	+	0.239763i	$0.922930\pi$
$212$	−2.77440	−	1.60180i	−0.190546	−	0.110012i
$213$	3.67022	+	7.39411i	0.251479	+	0.506636i
$214$	−0.282636	−	0.489540i	−0.0193206	−	0.0334642i
$215$	−0.976621	−	1.69156i	−0.0666050	−	0.115363i
$216$	6.01894	+	1.14868i	0.409537	+	0.0781576i
$217$		0			0
$218$	−9.97713	−	5.76030i	−0.675736	−	0.390137i
$219$	20.4074	+	1.28448i	1.37900	+	0.0867968i
$220$			4.65460i			0.313813i
$221$			8.35694i			0.562148i
$222$	−14.0393	+	21.1296i	−0.942255	+	1.41812i
$223$	20.2450	+	11.6884i	1.35570	+	0.782716i	0.989041	−	0.147638i	$-0.0471671\pi$
$223$	20.2450	+	11.6884i	1.35570	+	0.782716i	0.366662	+	0.930354i	$0.380500\pi$
$224$		0			0
$225$	13.6412	+	1.72403i	0.909414	+	0.114935i
$226$	−8.17479	−	14.1591i	−0.543779	−	0.941852i
$227$	7.22154	+	12.5081i	0.479310	+	0.830190i	0.999718	−	0.0237280i	$-0.00755356\pi$
$227$	7.22154	+	12.5081i	0.479310	+	0.830190i	−0.520408	+	0.853918i	$0.674220\pi$
$228$	−3.13811	+	4.72296i	−0.207826	+	0.312785i
$229$	11.3568	+	6.55685i	0.750479	+	0.433289i	0.825867	−	0.563865i	$-0.190686\pi$
$229$	11.3568	+	6.55685i	0.750479	+	0.433289i	−0.0753881	+	0.997154i	$0.524020\pi$
$230$	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	$-0.755959\pi$
$233$	−7.31966	+	4.22601i	−0.479527	+	0.276855i	0.240692	+	0.970601i	$0.422626\pi$
$234$	27.9581	+	3.53346i	1.82768	+	0.230989i
$235$	0.995314	−	1.72393i	0.0649271	−	0.112457i
$236$	−4.01246			−0.261189
$237$	−10.8013	+	5.36143i	−0.701617	+	0.348262i
$238$		0			0
$239$	−24.2111	+	13.9783i	−1.56608	+	0.904179i	−0.569466	+	0.822015i	$0.692850\pi$
$239$	−24.2111	+	13.9783i	−1.56608	+	0.904179i	−0.996619	+	0.0821642i	$0.973817\pi$
$240$	−0.342281	+	5.43807i	−0.0220941	+	0.351026i
$241$	−19.4058	+	11.2039i	−1.25004	+	0.721710i	−0.971117	−	0.238605i	$-0.923310\pi$
$241$	−19.4058	+	11.2039i	−1.25004	+	0.721710i	−0.278921	+	0.960314i	$0.589977\pi$
$242$	−27.3833	−	15.8097i	−1.76026	−	1.01629i
$243$	10.4292	+	11.5859i	0.669031	+	0.743235i
$244$			14.3774i			0.920418i
$245$		0			0
$246$	21.0396	−	31.6652i	1.34143	−	2.01890i
$247$	6.18819	−	10.7183i	0.393745	−	0.681987i
$248$	6.68312			0.424379
$249$	0.765142	−	12.1564i	0.0484889	−	0.770378i
$250$			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
$255$	−1.51792	−	1.00856i	−0.0950560	−	0.0631587i
$256$	20.9653			1.31033
$257$	1.65705	−	2.87009i	0.103364	−	0.179031i	−0.809705	−	0.586837i	$-0.800373\pi$
$257$	1.65705	−	2.87009i	0.103364	−	0.179031i	0.913069	+	0.407806i	$0.133706\pi$
$258$	−9.58180	−	0.603094i	−0.596537	−	0.0375470i
$259$		0			0
$260$			4.48950i			0.278427i
$261$	−20.5612	+	8.64184i	−1.27271	+	0.534916i
$262$	4.02118	+	2.32163i	0.248429	+	0.143431i
$263$	−19.6502	+	11.3451i	−1.21169	+	0.699567i	−0.963126	−	0.269050i	$-0.913290\pi$
$263$	−19.6502	+	11.3451i	−1.21169	+	0.699567i	−0.248559	+	0.968617i	$0.579957\pi$
$264$	−9.04366	−	6.00894i	−0.556599	−	0.369825i
$265$	−1.32054	+	0.762413i	−0.0811200	+	0.0468347i
$266$		0			0
$267$	−6.24191	−	4.14736i	−0.381999	−	0.253814i
$268$	13.7733			0.841336
$269$	−1.38050	+	2.39110i	−0.0841707	+	0.145788i	−0.905038	−	0.425332i	$-0.860157\pi$
$269$	−1.38050	+	2.39110i	−0.0841707	+	0.145788i	0.820867	+	0.571120i	$0.193491\pi$
$270$	−4.01595	+	4.65177i	−0.244403	+	0.283098i
$271$	5.27342	−	3.04461i	0.320337	−	0.184947i	−0.331206	−	0.943559i	$-0.607455\pi$
$271$	5.27342	−	3.04461i	0.320337	−	0.184947i	0.651543	+	0.758612i	$0.274122\pi$
$272$	−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
$276$	3.45018	+	0.217160i	0.207677	+	0.0130715i
$277$	4.71684	+	8.16980i	0.283407	+	0.490876i	0.972222	−	0.234062i	$-0.0752019\pi$
$277$	4.71684	+	8.16980i	0.283407	+	0.490876i	−0.688814	+	0.724938i	$0.741869\pi$
$278$	−6.47064	−	11.2075i	−0.388083	−	0.672180i
$279$	13.5419	+	10.2800i	0.810730	+	0.615446i
$280$		0			0
$281$	4.57153	+	2.63938i	0.272715	+	0.157452i	0.630121	−	0.776497i	$-0.283005\pi$
$281$	4.57153	+	2.63938i	0.272715	+	0.157452i	−0.357406	+	0.933949i	$0.616339\pi$
$282$	−4.35031	−	8.76423i	−0.259057	−	0.521902i
$283$		−	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
$285$	1.20000	+	2.41754i	0.0710818	+	0.143203i
$286$	−43.2453	−	24.9677i	−2.55715	−	1.47637i
$287$		0			0
$288$	15.6966	+	11.9157i	0.924933	+	0.702141i
$289$	7.17178	+	12.4219i	0.421869	+	0.730699i
$290$	−4.39637	−	7.61474i	−0.258164	−	0.447153i
$291$	−28.7324	−	1.80847i	−1.68433	−	0.106014i
$292$	13.8668	+	8.00600i	0.811493	+	0.468516i
$293$	−9.11647	−	15.7902i	−0.532590	−	0.922473i	−0.999276	−	0.0380495i	$-0.987886\pi$
$293$	−9.11647	−	15.7902i	−0.532590	−	0.922473i	0.466686	−	0.884423i	$-0.345448\pi$
$294$		0			0
$295$	−0.954912	+	1.65396i	−0.0555971	+	0.0962970i
$296$	8.16470	−	4.71389i	0.474563	−	0.273989i
$297$	−9.08201	−	26.0868i	−0.526992	−	1.51371i
$298$	−6.34917	+	10.9971i	−0.367797	+	0.637044i
$299$	−7.54531			−0.436356
$300$	8.96787	+	5.95858i	0.517760	+	0.344019i
$301$		0			0
$302$	−10.0253	+	5.78808i	−0.576888	+	0.333067i
$303$	6.71048	+	4.45869i	0.385507	+	0.256145i
$304$	10.1866	−	5.88122i	0.584240	−	0.337311i
$305$	5.92643	+	3.42163i	0.339347	+	0.195922i
$306$	−8.25808	+	3.47086i	−0.472083	+	0.198416i
$307$			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
$309$	17.8124	+	1.12114i	1.01331	+	0.0637795i
$310$	−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	$0.796227\pi$
$312$	−8.72288	−	5.79581i	−0.493836	−	0.328123i
$313$			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	$-0.391709\pi$
$318$	−0.470814	+	7.48017i	−0.0264019	+	0.419467i
$319$	39.5214			2.21277
$320$	−0.738701	+	1.27947i	−0.0412947	+	0.0715244i
$321$	−0.295758	+	0.445126i	−0.0165076	+	0.0248445i
$322$		0			0
$323$			3.93412i			0.218901i
$324$	3.28139	+	11.7575i	0.182299	+	0.653194i
$325$	−20.3517	−	11.7500i	−1.12891	−	0.651775i
$326$	9.49931	−	5.48443i	0.526118	−	0.303755i
$327$	−0.684201	+	10.8704i	−0.0378364	+	0.601135i
$328$	−12.2358	+	7.06433i	−0.675608	+	0.390063i
$329$		0			0
$330$	9.75414	−	4.84167i	0.536948	−	0.266525i
$331$	−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
$333$	23.7949	+	3.00729i	1.30395	+	0.164798i
$334$	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	0.912256	−	0.409620i	$-0.134339\pi$
$337$	1.86121	+	3.22371i	0.101387	+	0.175607i	−0.810870	+	0.585227i	$0.801005\pi$
$338$	−21.0859	−	12.1739i	−1.14692	−	0.662175i
$339$	−8.55433	+	12.8745i	−0.464607	+	0.699249i
$340$	−0.713547	−	1.23590i	−0.0386975	−	0.0670261i
$341$	−15.0634	−	26.0906i	−0.815730	−	1.41289i
$342$	13.1616	+	1.66342i	0.711698	+	0.0899472i
$343$		0			0
$344$	3.08995	+	1.78398i	0.166599	+	0.0961858i
$345$	0.910612	−	1.37050i	0.0490257	−	0.0737853i
$346$		−	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	$0.938649\pi$
$348$	−17.4306	−	1.09711i	−0.934379	−	0.0588114i
$349$	−13.2087	−	7.62607i	−0.707047	−	0.408214i	0.102920	−	0.994690i	$-0.467182\pi$
$349$	−13.2087	−	7.62607i	−0.707047	−	0.408214i	−0.809967	+	0.586476i	$0.800515\pi$
$350$		0			0
$351$	−8.75987	−	25.1615i	−0.467567	−	1.34302i
$352$	−17.4603	−	30.2421i	−0.930637	−	1.61191i
$353$	17.2359	+	29.8534i	0.917373	+	1.58894i	0.803389	+	0.595455i	$0.203028\pi$
$353$	17.2359	+	29.8534i	0.917373	+	1.58894i	0.113985	+	0.993482i	$0.463638\pi$
$354$	4.17372	+	8.40847i	0.221831	+	0.446905i
$355$	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	$-0.722608\pi$
$359$	−5.73791	+	3.31278i	−0.302835	+	0.174842i	0.340881	+	0.940107i	$0.389275\pi$
$360$	2.10546	−	0.884919i	0.110967	−	0.0466393i
$361$	−6.58684	+	11.4087i	−0.346676	+	0.600460i
$362$	−21.9173			−1.15195
$363$	−1.87786	+	29.8350i	−0.0985622	+	1.56593i
$364$		0			0
$365$	6.60022	−	3.81064i	0.345472	−	0.199458i
$366$	30.1291	−	14.9552i	1.57487	−	0.781722i
$367$	−2.68222	+	1.54858i	−0.140011	+	0.0808352i	−0.568369	−	0.822774i	$-0.692425\pi$
$367$	−2.68222	+	1.54858i	−0.140011	+	0.0808352i	0.428358	+	0.903609i	$0.359092\pi$
$368$	−6.21028	−	3.58551i	−0.323733	−	0.186907i
$369$	−35.6595	−	4.50679i	−1.85636	−	0.234614i
$370$			9.45532i			0.491559i
$371$		0			0
$372$	5.91934	+	11.9252i	0.306904	+	0.618295i
$373$	−4.84999	+	8.40043i	−0.251123	+	0.434958i	−0.963835	−	0.266499i	$-0.914133\pi$
$373$	−4.84999	+	8.40043i	−0.251123	+	0.434958i	0.712712	+	0.701457i	$0.247467\pi$
$374$	15.8731			0.820780
$375$	9.59819	−	4.76426i	0.495648	−	0.246025i
$376$			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
$381$	3.87842	−	1.92514i	0.198698	−	0.0986277i
$382$	37.1442			1.90046
$383$	−12.3063	+	21.3152i	−0.628825	+	1.08916i	0.358963	+	0.933352i	$0.383130\pi$
$383$	−12.3063	+	21.3152i	−0.628825	+	1.08916i	−0.987788	+	0.155804i	$0.950203\pi$
$384$	−6.88876	−	13.8783i	−0.351541	−	0.708222i
$385$		0			0
$386$			30.9459i			1.57511i
$387$	3.51697	+	8.36780i	0.178778	+	0.425359i
$388$	−19.5236	−	11.2720i	−0.991162	−	0.572248i
$389$	−5.56578	+	3.21340i	−0.282196	+	0.162926i	−0.634417	−	0.772991i	$-0.718760\pi$
$389$	−5.56578	+	3.21340i	−0.282196	+	0.162926i	0.352221	+	0.935917i	$0.385427\pi$
$390$	9.40816	−	4.66994i	0.476401	−	0.236471i
$391$	2.07712	−	1.19923i	0.105044	−	0.0606474i
$392$		0			0
$393$	0.275761	−	4.38121i	0.0139103	−	0.221003i
$394$	34.2776			1.72688
$395$	−2.24725	+	3.89235i	−0.113071	+	0.195846i
$396$	2.71214	−	21.4596i	0.136290	−	1.07838i
$397$	11.4835	−	6.62998i	0.576338	−	0.332749i	−0.183339	−	0.983050i	$-0.558690\pi$
$397$	11.4835	−	6.62998i	0.576338	−	0.332749i	0.759677	+	0.650301i	$0.225357\pi$
$398$	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	$-0.204204\pi$
$401$	13.6877	+	7.90259i	0.683530	+	0.394636i	−0.117653	+	0.993055i	$0.537537\pi$
$402$	−14.3268	−	28.8631i	−0.714556	−	1.43956i
$403$	−14.5291	−	25.1652i	−0.723747	−	1.25357i
$404$	3.15447	+	5.46370i	0.156941	+	0.271829i
$405$	5.62742	+	1.44552i	0.279629	+	0.0718286i
$406$		0			0
$407$	−36.8056	−	21.2497i	−1.82439	−	1.05331i
$408$	3.32246	+	0.209121i	0.164486	+	0.0103530i
$409$		−	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
$411$	1.16263	−	1.74979i	0.0573481	−	0.0863109i
$412$	12.1035	+	6.98795i	0.596296	+	0.344271i
$413$		0			0
$414$	−3.13376	−	7.45605i	−0.154016	−	0.366445i
$415$	−2.26994	−	3.93165i	−0.111427	−	0.192997i
$416$	−16.8410	−	29.1694i	−0.825697	−	1.43015i
$417$	−6.77107	+	10.1907i	−0.331581	+	0.499040i
$418$	−20.3582	−	11.7538i	−0.995754	−	0.574899i
$419$	−12.2469	−	21.2123i	−0.598302	−	1.03629i	−0.993072	−	0.117509i	$-0.962509\pi$
$419$	−12.2469	−	21.2123i	−0.598302	−	1.03629i	0.394770	−	0.918780i	$-0.370824\pi$
$420$		0			0
$421$	5.99347	−	10.3810i	0.292104	−	0.505939i	−0.682203	−	0.731163i	$-0.738978\pi$
$421$	5.99347	−	10.3810i	0.292104	−	0.505939i	0.974307	+	0.225224i	$0.0723113\pi$
$422$	−12.8034	+	7.39206i	−0.623261	+	0.359840i
$423$	−5.59329	+	7.36806i	−0.271955	+	0.358248i
$424$	1.39269	−	2.41221i	0.0676350	−	0.117147i
$425$	7.47005			0.362351
$426$	13.5462	−	6.72394i	0.656315	−	0.325776i
$427$		0			0
$428$	−0.362424	+	0.209245i	−0.0175184	+	0.0101143i
$429$	−2.96563	+	47.1172i	−0.143182	+	2.27484i
$430$	−3.09897	+	1.78919i	−0.149446	+	0.0862825i
$431$	26.6926	+	15.4110i	1.28574	+	0.742320i	0.977891	−	0.209117i	$-0.0670590\pi$
$431$	26.6926	+	15.4110i	1.28574	+	0.742320i	0.307845	+	0.951437i	$0.400392\pi$
$432$	4.74670	−	24.8722i	0.228376	−	1.19666i
$433$		−	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
$435$	−4.60049	+	6.92389i	−0.220577	+	0.331975i
$436$	−4.26455	+	7.38642i	−0.204235	+	0.353745i
$437$	−3.55204			−0.169917
$438$	2.35319	−	37.3869i	0.112440	−	1.78641i
$439$			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	$0.959423\pi$
$444$	15.6430	+	10.3938i	0.742383	+	0.493267i
$445$	−2.79320			−0.132411
$446$	21.4135	−	37.0893i	1.01396	−	1.75623i
$447$	11.9817	+	0.754147i	0.566714	+	0.0356699i
$448$		0			0
$449$		−	34.2418i		−	1.61597i	−0.589204	−	0.807985i	$-0.700558\pi$
$449$		−	34.2418i		−	1.61597i	0.589204	−	0.807985i	$-0.299442\pi$
$450$	3.15847	−	24.9910i	0.148891	−	1.17809i
$451$	55.1577	+	31.8453i	2.59727	+	1.49954i
$452$	−10.4825	+	6.05208i	−0.493056	+	0.284666i
$453$	9.11571	+	6.05681i	0.428293	+	0.284574i
$454$	22.9151	−	13.2300i	1.07546	−	0.620916i
$455$		0			0
$456$	−4.10640	−	2.72844i	−0.192300	−	0.127771i
$457$	−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
$459$	6.41055	+	5.53434i	0.299219	+	0.258321i
$460$	1.11587	−	0.644247i	0.0520276	−	0.0300382i
$461$	−6.50676	+	11.2700i	−0.303050	+	0.524898i	−0.976825	−	0.214038i	$-0.931338\pi$
$461$	−6.50676	+	11.2700i	−0.303050	+	0.524898i	0.673775	+	0.738936i	$0.264672\pi$
$462$		0			0
$463$	−6.01941	−	10.4259i	−0.279746	−	0.484534i	0.691576	−	0.722304i	$-0.256917\pi$
$463$	−6.01941	−	10.4259i	−0.279746	−	0.484534i	−0.971321	+	0.237770i	$0.923583\pi$
$464$	31.3749	+	18.1143i	1.45654	+	0.840935i
$465$	6.32437	+	0.398066i	0.293286	+	0.0184599i
$466$	7.74215	+	13.4098i	0.358648	+	0.621197i
$467$	10.1728	+	17.6199i	0.470743	+	0.815351i	0.999440	−	0.0334596i	$-0.0106525\pi$
$467$	10.1728	+	17.6199i	0.470743	+	0.815351i	−0.528697	+	0.848811i	$0.677319\pi$
$468$	2.61594	−	20.6984i	0.120922	−	0.956783i
$469$		0			0
$470$	−3.15829	−	1.82344i	−0.145681	−	0.0841090i
$471$	1.53269	+	3.08780i	0.0706227	+	0.142278i
$472$		−	3.48865i		−	0.160578i
$473$		−	16.0840i		−	0.739544i
$474$	9.82226	+	19.7882i	0.451151	+	0.908900i
$475$	−9.58078	−	5.53146i	−0.439596	−	0.253801i
$476$		0			0
$477$	6.53244	−	2.74557i	0.299100	−	0.125711i
$478$	25.6085	+	44.3553i	1.17131	+	2.02876i
$479$	−12.1492	−	21.0430i	−0.555109	−	0.961477i	−0.997895	−	0.0648499i	$-0.979343\pi$
$479$	−12.1492	−	21.0430i	−0.555109	−	0.961477i	0.442786	−	0.896627i	$-0.353990\pi$
$480$	7.33070	+	0.461406i	0.334599	+	0.0210602i
$481$	−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
$486$	21.2256	−	19.1065i	0.962813	−	0.866687i
$487$	13.6546	−	23.6504i	0.618747	−	1.07170i	−0.370968	−	0.928646i	$-0.620974\pi$
$487$	13.6546	−	23.6504i	0.618747	−	1.07170i	0.989715	−	0.143055i	$-0.0456927\pi$
$488$	−12.5005			−0.565871
$489$	−8.63748	−	5.73907i	−0.390601	−	0.259530i
$490$		0			0
$491$	−13.2899	+	7.67290i	−0.599763	+	0.346273i	−0.768948	−	0.639311i	$-0.779220\pi$
$491$	−13.2899	+	7.67290i	−0.599763	+	0.346273i	0.169185	+	0.985584i	$0.445886\pi$
$492$	−23.4429	−	15.5763i	−1.05689	−	0.702235i
$493$	−10.4938	+	6.05859i	−0.472616	+	0.272865i
$494$	−19.6361	−	11.3369i	−0.883471	−	0.510072i
$495$	−8.20028	−	6.22505i	−0.368575	−	0.279795i
$496$		−	27.6168i		−	1.24003i
$497$		0			0
$498$	−22.2708	−	1.40176i	−0.997976	−	0.0628143i
$499$	5.15504	−	8.92879i	0.230771	−	0.399707i	−0.727264	−	0.686358i	$-0.759208\pi$
$499$	5.15504	−	8.92879i	0.230771	−	0.399707i	0.958035	+	0.286650i	$0.0925418\pi$
$500$	8.39101			0.375257
$501$	−2.01389	−	1.33810i	−0.0899740	−	0.0597820i
$502$		−	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
$507$	−1.44601	+	22.9738i	−0.0642194	+	1.02030i
$508$	3.39063			0.150435
$509$	−2.58601	+	4.47911i	−0.114623	+	0.198533i	−0.917629	−	0.397438i	$-0.869899\pi$
$509$	−2.58601	+	4.47911i	−0.114623	+	0.198533i	0.803006	+	0.595971i	$0.203233\pi$
$510$	−1.84771	+	2.78087i	−0.0818181	+	0.123139i
$511$		0			0
$512$		−	20.5181i		−	0.906778i
$513$	−4.12381	−	11.8450i	−0.182071	−	0.522971i
$514$	−5.25807	−	3.03575i	−0.231924	−	0.133901i
$515$	5.76093	−	3.32608i	0.253857	−	0.146564i
$516$	−0.446492	+	7.09374i	−0.0196557	+	0.312285i
$517$	14.1958	−	8.19594i	0.624330	−	0.360457i
$518$		0			0
$519$	−11.8066	+	5.86047i	−0.518254	+	0.257246i
$520$	−3.90342			−0.171176
$521$	−19.1664	+	33.1972i	−0.839696	+	1.45440i	0.0504538	+	0.998726i	$0.483933\pi$
$521$	−19.1664	+	33.1972i	−0.839696	+	1.45440i	−0.890149	+	0.455669i	$0.849400\pi$
$522$	15.8320	+	37.6686i	0.692950	+	1.64871i
$523$	23.6468	−	13.6525i	1.03400	−	0.596982i	0.115874	−	0.993264i	$-0.463033\pi$
$523$	23.6468	−	13.6525i	1.03400	−	0.596982i	0.918129	+	0.396282i	$0.129700\pi$
$524$	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
$528$	−24.8309	+	37.3713i	−1.08062	+	1.62638i
$529$	−10.4172	−	18.0432i	−0.452924	−	0.784487i
$530$	1.39676	+	2.41926i	0.0606714	+	0.105086i
$531$	5.36625	−	7.06898i	0.232875	−	0.306768i
$532$		0			0
$533$	53.2012	+	30.7158i	2.30440	+	1.33045i
$534$	−7.59805	+	11.4353i	−0.328800	+	0.494855i
$535$			0.199190i			0.00861175i
$536$			11.9752i			0.517251i
$537$	15.9861	+	1.00619i	0.689853	+	0.0434205i
$538$	4.38055	+	2.52911i	0.188859	+	0.109038i
$539$		0			0
$540$	3.44387	+	2.97315i	0.148201	+	0.127944i
$541$	−9.78052	−	16.9404i	−0.420498	−	0.728323i	0.575491	−	0.817808i	$-0.304811\pi$
$541$	−9.78052	−	16.9404i	−0.420498	−	0.728323i	−0.995988	+	0.0894853i	$0.971478\pi$
$542$	−5.57779	−	9.66102i	−0.239587	−	0.414977i
$543$	9.21290	+	18.5605i	0.395363	+	0.796508i
$544$	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	−0.459125	−	0.888372i	$-0.651837\pi$
$547$	12.6246	−	21.8665i	0.539790	−	0.934944i	0.998915	−	0.0465723i	$-0.0148298\pi$
$548$	1.42469	−	0.822544i	0.0608597	−	0.0351373i
$549$	−25.3295	−	19.2283i	−1.08104	−	0.820642i
$550$	−22.3180	+	38.6559i	−0.951642	+	1.64829i
$551$	17.9452			0.764492
$552$	−0.188811	+	2.99978i	−0.00803632	+	0.127679i
$553$		0			0
$554$	14.9673	−	8.64136i	0.635898	−	0.367136i
$555$	8.00718	−	3.97453i	0.339886	−	0.168710i
$556$	−8.29730	+	4.79045i	−0.351884	+	0.203160i
$557$	28.8204	+	16.6395i	1.22116	+	0.705036i	0.965165	−	0.261642i	$-0.0842640\pi$
$557$	28.8204	+	16.6395i	1.22116	+	0.705036i	0.255994	+	0.966678i	$0.417597\pi$
$558$	18.8332	−	24.8090i	0.797272	−	1.05025i
$559$		−	15.5135i		−	0.656152i
$560$		0			0
$561$	−6.67225	−	13.4421i	−0.281703	−	0.567525i
$562$	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	$0.277657\pi$
$564$	−6.48847	+	3.22069i	−0.273214	+	0.135615i
$565$			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	$-0.105175\pi$
$570$	4.42900	−	2.19843i	0.185510	−	0.0920819i
$571$	−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
$573$	−15.6135	−	31.4553i	−0.652264	−	1.31407i
$574$		0			0
$575$			6.74455i			0.281267i
$576$	4.15122	−	5.46843i	0.172968	−	0.227851i
$577$	12.6901	+	7.32664i	0.528296	+	0.305012i	0.740322	−	0.672252i	$-0.234673\pi$
$577$	12.6901	+	7.32664i	0.528296	+	0.305012i	−0.212026	+	0.977264i	$0.568006\pi$
$578$	22.7572	−	13.1389i	0.946574	−	0.546505i
$579$	26.2064	−	13.0081i	1.08910	−	0.540598i
$580$	−5.63746	+	3.25479i	−0.234083	+	0.135148i
$581$		0			0
$582$	−3.31316	+	52.6385i	−0.137335	+	2.18194i
$583$	−12.5562			−0.520026
$584$	−6.96085	+	12.0565i	−0.288042	+	0.498904i
$585$	−7.90942	−	6.00424i	−0.327014	−	0.248245i
$586$	−28.9280	+	16.7016i	−1.19500	+	0.689936i
$587$	−11.6129	+	20.1141i	−0.479314	+	0.830197i	−0.999719	−	0.0237232i	$-0.992448\pi$
$587$	−11.6129	+	20.1141i	−0.479314	+	0.830197i	0.520404	+	0.853920i	$0.325781\pi$
$588$		0			0
$589$	−6.83975	−	11.8468i	−0.281827	−	0.488139i
$590$	3.03009	+	1.74942i	0.124747	+	0.0720225i
$591$	−14.4085	−	29.0278i	−0.592688	−	1.19404i
$592$	−19.4793	−	33.7391i	−0.800594	−	1.38667i
$593$	5.55605	+	9.62337i	0.228160	+	0.395184i	0.957263	−	0.289220i	$-0.0933958\pi$
$593$	5.55605	+	9.62337i	0.228160	+	0.395184i	−0.729103	+	0.684404i	$0.760062\pi$
$594$	−47.7916	+	16.6385i	−1.96091	+	0.682684i
$595$		0			0
$596$	8.14153	+	4.70051i	0.333490	+	0.192541i
$597$	−31.1925	−	1.96330i	−1.27662	−	0.0803527i
$598$			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	$-0.103627\pi$
$600$	−5.18072	+	7.79715i	−0.211502	+	0.318317i
$601$	30.5665	+	17.6476i	1.24684	+	0.719861i	0.970477	−	0.241194i	$-0.0775390\pi$
$601$	30.5665	+	17.6476i	1.24684	+	0.719861i	0.276358	+	0.961055i	$0.410872\pi$
$602$		0			0
$603$	−18.4203	+	24.2652i	−0.750133	+	0.988154i
$604$	4.28512	+	7.42205i	0.174359	+	0.301999i
$605$	5.57104	+	9.64932i	0.226495	+	0.392301i
$606$	8.16843	−	12.2938i	0.331820	−	0.499400i
$607$	−33.6062	−	19.4025i	−1.36403	−	0.787524i	−0.373874	−	0.927479i	$-0.621971\pi$
$607$	−33.6062	−	19.4025i	−1.36403	−	0.787524i	−0.990158	+	0.139955i	$0.955304\pi$
$608$	−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
$612$	2.56960	+	6.11375i	0.103870	+	0.247134i
$613$	−15.8786	+	27.5025i	−0.641330	+	1.11082i	0.343806	+	0.939041i	$0.388284\pi$
$613$	−15.8786	+	27.5025i	−0.641330	+	1.11082i	−0.985136	+	0.171776i	$0.945049\pi$
$614$	47.7145			1.92560
$615$	−11.9997	+	5.95632i	−0.483876	+	0.240182i
$616$		0			0
$617$	1.25518	−	0.724680i	0.0505317	−	0.0291745i	−0.474521	−	0.880244i	$-0.657379\pi$
$617$	1.25518	−	0.724680i	0.0505317	−	0.0291745i	0.525053	+	0.851070i	$0.324045\pi$
$618$	2.05396	−	32.6327i	0.0826223	−	1.31268i
$619$	25.2590	−	14.5833i	1.01524	−	0.586152i	0.102522	−	0.994731i	$-0.467309\pi$
$619$	25.2590	−	14.5833i	1.01524	−	0.586152i	0.912723	+	0.408579i	$0.133976\pi$
$620$	4.29740	+	2.48110i	0.172588	+	0.0996435i
$621$	−4.99684	+	5.78795i	−0.200516	+	0.232263i
$622$			51.8217i			2.07786i
$623$		0			0
$624$	−23.9501	+	36.0457i	−0.958771	+	1.44298i
$625$	−9.46116	+	16.3872i	−0.378446	+	0.655488i
$626$	10.2153			0.408284
$627$	−1.39611	+	22.1810i	−0.0557551	+	0.885822i
$628$			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
$633$	11.6418	+	7.73526i	0.462721	+	0.307449i
$634$	−61.4976			−2.44238
$635$	0.806924	−	1.39763i	0.0320218	−	0.0554634i
$636$	5.53783	+	0.348560i	0.219589	+	0.0138213i
$637$		0			0
$638$		−	72.4041i		−	2.86651i
$639$	−11.3883	−	8.64512i	−0.450512	−	0.341996i
$640$	−5.00119	−	2.88744i	−0.197689	−	0.114136i
$641$	10.0267	−	5.78891i	0.396030	−	0.228648i	−0.288740	−	0.957408i	$-0.593236\pi$
$641$	10.0267	−	5.78891i	0.396030	−	0.228648i	0.684770	+	0.728760i	$0.259903\pi$
$642$	0.815481	+	0.541836i	0.0321845	+	0.0213846i
$643$	−13.1240	+	7.57712i	−0.517558	+	0.298812i	−0.735935	−	0.677052i	$-0.763257\pi$
$643$	−13.1240	+	7.57712i	−0.517558	+	0.298812i	0.218377	+	0.975865i	$0.429924\pi$
$644$		0			0
$645$	2.81782	+	1.87226i	0.110951	+	0.0737203i
$646$	7.20741			0.283572
$647$	6.22057	−	10.7743i	0.244556	−	0.423583i	−0.717451	−	0.696609i	$-0.754691\pi$
$647$	6.22057	−	10.7743i	0.244556	−	0.423583i	0.962007	+	0.273026i	$0.0880246\pi$
$648$	−10.2226	+	2.85302i	−0.401582	+	0.112077i
$649$	−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	$-0.304743\pi$
$653$	3.97013	+	2.29216i	0.155363	+	0.0896990i	−0.420303	+	0.907384i	$0.638076\pi$
$654$	19.9148	+	1.25347i	0.778732	+	0.0490147i
$655$	−0.818096	−	1.41698i	−0.0319656	−	0.0553661i
$656$	29.1921	+	50.5621i	1.13976	+	1.97412i
$657$	−32.6500	+	13.7227i	−1.27380	+	0.535375i
$658$		0			0
$659$	15.6110	+	9.01301i	0.608118	+	0.351097i	0.772228	−	0.635345i	$-0.219142\pi$
$659$	15.6110	+	9.01301i	0.608118	+	0.351097i	−0.164111	+	0.986442i	$0.552475\pi$
$660$	−3.58446	−	7.22133i	−0.139525	−	0.281090i
$661$			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
$663$	−6.43559	−	12.9653i	−0.249937	−	0.503530i
$664$	7.18189	+	4.14647i	0.278711	+	0.160914i
$665$		0			0
$666$	5.50943	−	43.5927i	0.213486	−	1.68918i
$667$	−5.47018	−	9.47462i	−0.211806	−	0.366859i
$668$	−0.946692	−	1.63972i	−0.0366286	−	0.0634426i
$669$	−40.4100	−	2.54347i	−1.56234	−	0.0983363i
$670$	−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	−0.996577	−	0.0826667i	$-0.973656\pi$
$673$	−11.0695	+	19.1729i	−0.426697	+	0.739061i	0.569880	+	0.821728i	$0.306990\pi$
$674$	5.90591	−	3.40978i	0.227487	−	0.131340i
$675$	−22.4912	+	7.83022i	−0.865685	+	0.301385i
$676$	−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	$0.625780\pi$
$678$	23.5865	+	15.6717i	0.905833	+	0.601869i
$679$		0			0
$680$	1.07456	−	0.620397i	0.0412074	−	0.0237911i
$681$	−20.8361	−	13.8443i	−0.798441	−	0.530514i
$682$	−47.7986	+	27.5966i	−1.83030	+	1.05673i
$683$	−18.1316	−	10.4683i	−0.693786	−	0.400558i	0.111243	−	0.993793i	$-0.464517\pi$
$683$	−18.1316	−	10.4683i	−0.693786	−	0.400558i	−0.805029	+	0.593235i	$0.797850\pi$
$684$	1.23149	−	9.74400i	0.0470870	−	0.372571i
$685$		−	0.783018i		−	0.0299176i
$686$		0			0
$687$	−22.6688	−	1.42681i	−0.864867	−	0.0544361i
$688$	7.37198	−	12.7686i	0.281054	−	0.486800i
$689$	−12.1109			−0.461387
$690$	−2.51079	−	1.66826i	−0.0955842	−	0.0635097i
$691$			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
$696$	0.953889	−	15.1551i	0.0361571	−	0.574454i
$697$	−19.5274			−0.739654
$698$	−13.9711	+	24.1987i	−0.528815	+	0.915935i
$699$	8.10161	−	12.1932i	0.306431	−	0.461189i
$700$		0			0
$701$			31.6641i			1.19593i	0.801520	+	0.597967i	$0.204025\pi$
$701$			31.6641i			1.19593i	−0.801520	+	0.597967i	$0.795975\pi$
$702$	−46.0964	+	16.0483i	−1.73980	+	0.605704i
$703$	−16.7121	−	9.64873i	−0.630309	−	0.363909i
$704$	−10.5358	+	6.08286i	−0.397083	+	0.229256i
$705$	−0.216586	+	3.44106i	−0.00815710	+	0.129598i
$706$	54.6922	−	31.5766i	2.05837	−	1.18840i
$707$		0			0
$708$	6.22509	−	3.08995i	0.233953	−	0.116127i
$709$	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
$711$	12.6287	−	16.6358i	0.473613	−	0.623893i
$712$	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
$717$	26.7975	−	40.3311i	1.00077	−	1.50619i
$718$	6.06910	+	10.5120i	0.226497	+	0.392304i
$719$	−19.4544	−	33.6959i	−0.725525	−	1.25665i	−0.958757	−	0.284226i	$-0.908264\pi$
$719$	−19.4544	−	33.6959i	−0.725525	−	1.25665i	0.233232	−	0.972421i	$-0.425070\pi$
$720$	−3.65677	−	8.70041i	−0.136280	−	0.324245i
$721$		0			0
$722$	20.9011	+	12.0672i	0.777858	+	0.449096i
$723$	21.4789	−	32.3264i	0.798808	−	1.20223i
$724$			16.2261i			0.603039i
$725$		−	34.0741i		−	1.26548i
$726$	54.6584	+	3.44029i	2.02856	+	0.127681i
$727$	−11.4647	−	6.61915i	−0.425202	−	0.245491i	0.272098	−	0.962269i	$-0.412282\pi$
$727$	−11.4647	−	6.61915i	−0.425202	−	0.245491i	−0.697301	+	0.716779i	$0.745616\pi$
$728$		0			0
$729$	−25.1024	−	9.94341i	−0.929717	−	0.368274i
$730$	−6.98119	−	12.0918i	−0.258385	−	0.447536i
$731$	2.46567	+	4.27066i	0.0911960	+	0.157956i
$732$	−11.0719	−	22.3056i	−0.409228	−	0.824440i
$733$	28.1222	+	16.2364i	1.03872	+	0.599704i	0.919470	−	0.393161i	$-0.128618\pi$
$733$	28.1222	+	16.2364i	1.03872	+	0.599704i	0.119248	+	0.992865i	$0.461952\pi$
$734$	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
$738$	−8.25654	+	65.3290i	−0.303927	+	2.40479i
$739$	6.91965	−	11.9852i	0.254543	−	0.440882i	−0.710228	−	0.703972i	$-0.751408\pi$
$739$	6.91965	−	11.9852i	0.254543	−	0.440882i	0.964771	+	0.263090i	$0.0847415\pi$
$740$	7.00011			0.257329
$741$	−1.34659	+	21.3942i	−0.0494681	+	0.785936i
$742$		0			0
$743$	31.8593	−	18.3940i	1.16880	−	0.674810i	0.215406	−	0.976525i	$-0.430892\pi$
$743$	31.8593	−	18.3940i	1.16880	−	0.674810i	0.953398	+	0.301715i	$0.0975591\pi$
$744$	−10.3685	+	5.14660i	−0.380126	+	0.188683i
$745$	3.87515	−	2.23732i	0.141975	−	0.0819690i
$746$	15.3898	+	8.88530i	0.563461	+	0.325314i
$747$	8.17441	+	19.4491i	0.299086	+	0.711605i
$748$		−	11.7514i		−	0.429675i
$749$		0			0
$750$	−8.72824	−	17.5841i	−0.318710	−	0.642081i
$751$	1.82952	−	3.16883i	0.0667602	−	0.115632i	−0.830713	−	0.556701i	$-0.812067\pi$
$751$	1.82952	−	3.16883i	0.0667602	−	0.115632i	0.897473	+	0.441068i	$0.145400\pi$
$752$	15.0262			0.547948
$753$	−9.92280	+	4.92539i	−0.361607	+	0.179491i
$754$		−	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
$759$	12.1366	−	6.02424i	0.440529	−	0.218666i
$760$	−1.83758			−0.0666560
$761$	−6.82083	+	11.8140i	−0.247255	+	0.428258i	−0.962763	−	0.270346i	$-0.912862\pi$
$761$	−6.82083	+	11.8140i	−0.247255	+	0.428258i	0.715508	+	0.698604i	$0.246195\pi$
$762$	−3.52689	−	7.10536i	−0.127766	−	0.257400i
$763$		0			0
$764$		−	27.4991i		−	0.994884i
$765$	3.13165	+	0.395790i	0.113225	+	0.0143098i
$766$	39.0500	+	22.5455i	1.41093	+	0.814602i
$767$	−13.1365	+	7.58434i	−0.474330	+	0.273855i
$768$	−32.5263	+	16.1451i	−1.17369	+	0.582587i
$769$	−22.9328	+	13.2402i	−0.826976	+	0.477455i	−0.852816	−	0.522211i	$-0.825107\pi$
$769$	−22.9328	+	13.2402i	−0.826976	+	0.477455i	0.0258399	+	0.999666i	$0.491774\pi$
$770$		0			0
$771$	−0.360583	+	5.72884i	−0.0129861	+	0.206319i
$772$	22.9104			0.824562
$773$	−13.1109	+	22.7087i	−0.471566	+	0.816776i	−0.999471	−	0.0325274i	$-0.989644\pi$
$773$	−13.1109	+	22.7087i	−0.471566	+	0.816776i	0.527905	+	0.849303i	$0.322978\pi$
$774$	15.3300	−	6.44317i	0.551026	−	0.231595i
$775$	−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
$780$	−3.45732	−	6.96519i	−0.123792	−	0.249394i
$781$	12.6678	+	21.9413i	0.453291	+	0.785123i
$782$	−2.19701	−	3.80533i	−0.0785649	−	0.136078i
$783$	25.2445	−	29.2412i	0.902164	−	1.04500i
$784$		0			0
$785$	1.11272	+	0.642430i	0.0397148	+	0.0229293i
$786$	−8.02648	−	0.505200i	−0.286295	−	0.0180199i
$787$			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
$789$	21.7494	−	32.7336i	0.774300	−	1.16535i
$790$	7.13088	+	4.11702i	0.253705	+	0.146477i
$791$		0			0
$792$	18.6581	+	2.35809i	0.662987	+	0.0837909i
$793$	27.1761	+	47.0704i	0.965052	+	1.67152i
$794$	−12.1463	−	21.0380i	−0.431055	−	0.746610i
$795$	1.46161	−	2.19977i	0.0518379	−	0.0780178i
$796$	−21.1952	−	12.2371i	−0.751245	−	0.433731i
$797$	−15.8184	−	27.3983i	−0.560317	−	0.970498i	−0.997469	−	0.0711097i	$-0.977346\pi$
$797$	−15.8184	−	27.3983i	−0.560317	−	0.970498i	0.437151	−	0.899388i	$-0.355987\pi$
$798$		0			0
$799$	−2.51286	+	4.35240i	−0.0888986	+	0.153977i
$800$	−26.0738	+	15.0537i	−0.921848	+	0.532229i
$801$	12.8778	+	1.62754i	0.455014	+	0.0575064i
$802$	14.4777	−	25.0762i	0.511227	−	0.885470i
$803$	62.7577			2.21467
$804$	−21.3684	+	10.6066i	−0.753605	+	0.374068i
$805$		0			0
$806$	−46.1032	+	26.6177i	−1.62392	+	0.937569i
$807$	0.300405	−	4.77276i	0.0105748	−	0.168009i
$808$	−4.75044	+	2.74267i	−0.167120	+	0.0964868i
$809$	34.5466	+	19.9455i	1.21459	+	0.701245i	0.963756	−	0.266784i	$-0.0859610\pi$
$809$	34.5466	+	19.9455i	1.21459	+	0.701245i	0.250836	+	0.968029i	$0.419294\pi$
$810$	2.64823	−	10.3096i	0.0930493	−	0.362242i
$811$		−	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
$813$	−5.83676	+	8.78452i	−0.204704	+	0.308087i
$814$	−38.9300	+	67.4288i	−1.36450	+	2.36338i
$815$	−3.86521			−0.135392
$816$	0.864154	−	13.7294i	0.0302514	−	0.480627i
$817$		−	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	$-0.00230500\pi$
$822$	−3.20566	−	2.12996i	−0.111810	−	0.0742909i
$823$	−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
$825$	42.1168	+	2.65090i	1.46632	+	0.0922926i
$826$		0			0
$827$		−	35.2637i		−	1.22624i	−0.789990	−	0.613120i	$-0.789914\pi$
$827$		−	35.2637i		−	1.22624i	0.789990	−	0.613120i	$-0.210086\pi$
$828$	−5.51998	+	2.32004i	−0.191833	+	0.0806268i
$829$	−29.0164	−	16.7526i	−1.00778	−	0.581842i	−0.0972388	−	0.995261i	$-0.531001\pi$
$829$	−29.0164	−	16.7526i	−1.00778	−	0.581842i	−0.910541	+	0.413419i	$0.864334\pi$
$830$	−7.20287	+	4.15858i	−0.250015	+	0.144346i
$831$	−13.6094	−	9.04256i	−0.472103	−	0.313683i
$832$	−10.1621	+	5.86710i	−0.352308	+	0.203405i
$833$		0			0
$834$	18.6696	+	12.4048i	0.646474	+	0.429542i
$835$	−0.901200			−0.0311873
$836$	−8.70178	+	15.0719i	−0.300957	+	0.521273i
$837$	−28.9259	−	5.52032i	−0.999825	−	0.190810i
$838$	−38.8615	+	22.4367i	−1.34245	+	0.775062i
$839$	22.4984	−	38.9684i	0.776731	−	1.34534i	−0.157085	−	0.987585i	$-0.550210\pi$
$839$	22.4984	−	38.9684i	0.776731	−	1.34534i	0.933816	−	0.357753i	$-0.116457\pi$
$840$		0			0
$841$	13.1358	+	22.7519i	0.452959	+	0.784548i
$842$	−19.0182	−	10.9802i	−0.655412	−	0.378402i
$843$	−9.12501	−	0.574343i	−0.314282	−	0.0197814i
$844$	5.47260	+	9.47882i	0.188375	+	0.326275i
$845$	4.28985	+	7.43024i	0.147575	+	0.255608i
$846$	13.4985	+	10.2470i	0.464087	+	0.352301i
$847$		0			0
$848$	−9.96802	−	5.75504i	−0.342303	−	0.197629i
$849$	15.1476	+	30.5167i	0.519864	+	1.04733i
$850$		−	13.6853i		−	0.469402i
$851$			11.7648i			0.403291i
$852$	−4.97797	−	10.0287i	−0.170542	−	0.343578i
$853$	−15.8457	−	9.14854i	−0.542548	−	0.313240i	0.203563	−	0.979062i	$-0.434748\pi$
$853$	−15.8457	−	9.14854i	−0.542548	−	0.313240i	−0.746111	+	0.665822i	$0.768081\pi$
$854$		0			0
$855$	−3.72345	−	2.82657i	−0.127339	−	0.0966665i
$856$	−0.181929	−	0.315111i	−0.00621822	−	0.0107703i
$857$	−5.28926	−	9.16126i	−0.180678	−	0.312943i	0.761434	−	0.648243i	$-0.224496\pi$
$857$	−5.28926	−	9.16126i	−0.180678	−	0.312943i	−0.942111	+	0.335300i	$0.891162\pi$
$858$	86.3198	+	5.43311i	2.94691	+	0.185483i
$859$	28.2972	+	16.3374i	0.965488	+	0.557425i	0.897858	−	0.440286i	$-0.145123\pi$
$859$	28.2972	+	16.3374i	0.965488	+	0.557425i	0.0676303	+	0.997710i	$0.478456\pi$
$860$	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	$-0.717548\pi$
$863$	−8.09878	+	4.67583i	−0.275686	+	0.159167i	0.355783	+	0.934569i	$0.384214\pi$
$864$	−33.5285	−	6.39871i	−1.14066	−	0.217689i
$865$	−2.45643	+	4.25465i	−0.0835210	+	0.144663i
$866$	−11.1052			−0.377372
$867$	−20.6925	−	13.7489i	−0.702755	−	0.466937i
$868$		0			0
$869$	−32.0517	+	18.5050i	−1.08728	+	0.627741i
$870$	12.6847	+	8.42821i	0.430053	+	0.285743i
$871$	45.0925	−	26.0342i	1.52790	−	0.882135i
$872$	−6.42216	−	3.70783i	−0.217482	−	0.125563i
$873$	45.9693	−	19.3208i	1.55583	−	0.653910i
$874$			6.50742i			0.220117i
$875$		0			0
$876$	−27.6788	−	1.74215i	−0.935181	−	0.0588618i
$877$	−0.619077	+	1.07227i	−0.0209048	+	0.0362081i	−0.876289	−	0.481787i	$-0.839988\pi$
$877$	−0.619077	+	1.07227i	−0.0209048	+	0.0362081i	0.855384	+	0.517995i	$0.173321\pi$
$878$	49.7300			1.67831
$879$	26.3035	+	17.4770i	0.887195	+	0.589485i
$880$			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
$885$	0.207794	−	3.30138i	0.00698493	−	0.110975i
$886$	9.80432			0.329383
$887$	−7.25578	+	12.5674i	−0.243625	+	0.421972i	−0.961744	−	0.273949i	$-0.911670\pi$
$887$	−7.25578	+	12.5674i	−0.243625	+	0.421972i	0.718119	+	0.695920i	$0.245003\pi$
$888$	−9.03691	+	13.6009i	−0.303259	+	0.456415i
$889$		0			0
$890$			5.11722i			0.171530i
$891$	34.1793	+	33.4781i	1.14505	+	1.12156i
$892$	−27.4585	−	15.8532i	−0.919379	−	0.530804i
$893$	6.44579	−	3.72148i	0.215700	−	0.124534i
$894$	1.38162	−	21.9507i	0.0462081	−	0.734142i
$895$	5.17028	−	2.98506i	0.172823	−	0.0997797i
$896$		0			0
$897$	11.7061	−	5.81056i	0.390855	−	0.194009i
$898$	−62.7317			−2.09339
$899$	21.0666	−	36.4884i	0.702610	−	1.21696i
$900$	−18.5017	−	2.33832i	−0.616725	−	0.0779441i
$901$	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
$906$	11.0962	−	16.7002i	0.368647	−	0.554827i
$907$	9.60695	+	16.6397i	0.318993	+	0.552513i	0.980278	−	0.197622i	$-0.0633219\pi$
$907$	9.60695	+	16.6397i	0.318993	+	0.552513i	−0.661285	+	0.750135i	$0.729989\pi$
$908$	−9.79466	−	16.9648i	−0.325047	−	0.562998i
$909$	−13.8445	−	1.74972i	−0.459193	−	0.0580346i
$910$		0			0
$911$	10.1252	+	5.84579i	0.335463	+	0.193680i	0.658264	−	0.752787i	$-0.271291\pi$
$911$	10.1252	+	5.84579i	0.335463	+	0.193680i	−0.322801	+	0.946467i	$0.604624\pi$
$912$	−11.2748	+	16.9689i	−0.373345	+	0.561897i
$913$		−	37.3837i		−	1.23722i
$914$			29.0566i			0.961106i
$915$	−11.8295	−	0.744565i	−0.391070	−	0.0246146i
$916$	−15.4034	−	8.89314i	−0.508942	−	0.293838i
$917$		0			0
$918$	10.1390	−	11.7443i	0.334638	−	0.387619i
$919$	−19.9930	−	34.6289i	−0.659508	−	1.14230i	−0.980743	−	0.195301i	$-0.937432\pi$
$919$	−19.9930	−	34.6289i	−0.659508	−	1.14230i	0.321236	−	0.946999i	$-0.395902\pi$
$920$	0.560143	+	0.970196i	0.0184674	+	0.0319864i
$921$	−20.0567	−	40.4067i	−0.660892	−	1.33145i
$922$	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
$927$	−28.4982	+	11.9777i	−0.936004	+	0.393401i
$928$	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	$0.567164\pi$
$930$	0.729267	−	11.5864i	0.0239136	−	0.379933i
$931$		0			0
$932$	9.92775	−	5.73179i	0.325194	−	0.187751i
$933$	43.8849	−	21.7832i	1.43673	−	0.713149i
$934$	32.2801	−	18.6369i	1.05624	−	0.609818i
$935$	−4.84400	−	2.79669i	−0.158416	−	0.0914614i
$936$	17.9963	+	2.27444i	0.588228	+	0.0743425i
$937$		−	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
$939$	−4.29398	−	8.65074i	−0.140129	−	0.282306i
$940$	−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	$0.366224\pi$
$942$	5.65692	−	2.80793i	0.184312	−	0.0914872i
$943$		−	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	$0.821363\pi$
$948$	14.6499	−	7.27177i	0.475806	−	0.236176i
$949$	60.5316			1.96494
$950$	−10.1338	+	17.5522i	−0.328783	+	0.569469i
$951$	25.8504	+	52.0789i	0.838258	+	1.68877i
$952$		0			0
$953$		−	6.77705i		−	0.219530i	−0.993958	−	0.109765i	$-0.964990\pi$
$953$		−	6.77705i		−	0.219530i	0.993958	−	0.109765i	$-0.0350099\pi$
$954$	−5.02996	−	11.9676i	−0.162851	−	0.387465i
$955$	−11.3353	−	6.54443i	−0.366801	−	0.211773i
$956$	32.8378	−	18.9589i	1.06205	−	0.613175i
$957$	−61.3150	+	30.4350i	−1.98203	+	0.983823i
$958$	−38.5512	+	22.2575i	−1.24553	+	0.719109i
$959$		0			0
$960$	0.160746	−	2.55388i	0.00518804	−	0.0824262i
$961$	−1.11779			−0.0360578
$962$	−37.5492	+	65.0371i	−1.21063	+	2.09688i
$963$	0.116064	−	0.918346i	0.00374012	−	0.0295933i
$964$	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	0.978305	+	0.207169i	$0.0664249\pi$
$967$	20.7901	+	36.0096i	0.668566	+	1.15799i	−0.309739	+	0.950822i	$0.600242\pi$
$968$	−17.6263	−	10.1765i	−0.566530	−	0.327086i
$969$	−3.02963	−	6.10355i	−0.0973256	−	0.196074i
$970$	9.82910	+	17.0245i	0.315593	+	0.546624i
$971$	−20.6257	−	35.7248i	−0.661910	−	1.14646i	−0.980113	−	0.198439i	$-0.936413\pi$
$971$	−20.6257	−	35.7248i	−0.661910	−	1.14646i	0.318203	−	0.948023i	$-0.396921\pi$
$972$	−14.1452	−	15.7141i	−0.453707	−	0.504029i
$973$		0			0
$974$	−43.3281	−	25.0155i	−1.38832	−	0.801547i
$975$	40.6229	+	2.55687i	1.30098	+	0.0818855i
$976$			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	$0.976666\pi$
$978$	−10.5141	+	15.8241i	−0.336204	+	0.505998i
$979$	−19.9192	−	11.5004i	−0.636621	−	0.367553i
$980$		0			0
$981$	−7.30968	−	17.3917i	−0.233380	−	0.555273i
$982$	14.0569	+	24.3473i	0.448575	+	0.776955i
$983$	−12.2401	−	21.2004i	−0.390397	−	0.676188i	0.602105	−	0.798417i	$-0.294329\pi$
$983$	−12.2401	−	21.2004i	−0.390397	−	0.676188i	−0.992502	+	0.122229i	$0.960996\pi$
$984$	13.5429	−	20.3825i	0.431732	−	0.649771i
$985$	−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
$990$	−11.4044	+	15.0231i	−0.362457	+	0.477466i
$991$	21.0927	−	36.5337i	0.670032	−	1.16053i	−0.307862	−	0.951431i	$-0.599614\pi$
$991$	21.0927	−	36.5337i	0.670032	−	1.16053i	0.977894	−	0.209099i	$-0.0670531\pi$
$992$	−37.2284			−1.18200
$993$	47.1226	−	23.3903i	1.49539	−	0.742268i
$994$		0			0
$995$	−10.0884	+	5.82452i	−0.319822	+	0.184650i
$996$	−1.03777	+	16.4878i	−0.0328830	+	0.522437i
$997$	8.38168	−	4.83917i	0.265451	−	0.153258i	−0.361368	−	0.932423i	$-0.617690\pi$
$997$	8.38168	−	4.83917i	0.265451	−	0.153258i	0.626818	+	0.779165i	$0.284357\pi$
$998$	−16.3578	−	9.44415i	−0.517796	−	0.298949i
$999$	−39.2321	+	13.6585i	−1.24125	+	0.432137i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.i.d.227.7		48
3.2	odd	2		1323.2.i.d.521.15		48
7.2	even	3		441.2.s.d.362.8		48
7.3	odd	6		441.2.o.e.146.17	✓	48
7.4	even	3		441.2.o.e.146.18	yes	48
7.5	odd	6		441.2.s.d.362.7		48
7.6	odd	2	inner	441.2.i.d.227.8		48
9.4	even	3		1323.2.s.d.962.18		48
9.5	odd	6		441.2.s.d.374.7		48
21.2	odd	6		1323.2.s.d.656.17		48
21.5	even	6		1323.2.s.d.656.18		48
21.11	odd	6		1323.2.o.e.440.7		48
21.17	even	6		1323.2.o.e.440.8		48
21.20	even	2		1323.2.i.d.521.17		48
63.4	even	3		1323.2.o.e.881.8		48
63.5	even	6	inner	441.2.i.d.68.17		48
63.13	odd	6		1323.2.s.d.962.17		48
63.23	odd	6	inner	441.2.i.d.68.18		48
63.31	odd	6		1323.2.o.e.881.7		48
63.32	odd	6		441.2.o.e.293.17	yes	48
63.40	odd	6		1323.2.i.d.1097.15		48
63.41	even	6		441.2.s.d.374.8		48
63.58	even	3		1323.2.i.d.1097.17		48
63.59	even	6		441.2.o.e.293.18	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.17		48	63.5	even	6	inner
441.2.i.d.68.18		48	63.23	odd	6	inner
441.2.i.d.227.7		48	1.1	even	1	trivial
441.2.i.d.227.8		48	7.6	odd	2	inner
441.2.o.e.146.17	✓	48	7.3	odd	6
441.2.o.e.146.18	yes	48	7.4	even	3
441.2.o.e.293.17	yes	48	63.32	odd	6
441.2.o.e.293.18	yes	48	63.59	even	6
441.2.s.d.362.7		48	7.5	odd	6
441.2.s.d.362.8		48	7.2	even	3
441.2.s.d.374.7		48	9.5	odd	6
441.2.s.d.374.8		48	63.41	even	6
1323.2.i.d.521.15		48	3.2	odd	2
1323.2.i.d.521.17		48	21.20	even	2
1323.2.i.d.1097.15		48	63.40	odd	6
1323.2.i.d.1097.17		48	63.58	even	3
1323.2.o.e.440.7		48	21.11	odd	6
1323.2.o.e.440.8		48	21.17	even	6
1323.2.o.e.881.7		48	63.31	odd	6
1323.2.o.e.881.8		48	63.4	even	3
1323.2.s.d.656.17		48	21.2	odd	6
1323.2.s.d.656.18		48	21.5	even	6
1323.2.s.d.962.17		48	63.13	odd	6
1323.2.s.d.962.18		48	9.4	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.83202i q^{2} +(-1.55144 + 0.770089i) q^{3} -1.35631 q^{4} +(-0.322784 + 0.559079i) q^{5} +(1.41082 + 2.84227i) q^{6} -1.17925i q^{8} +(1.81393 - 2.38949i) q^{9} +(1.02425 + 0.591348i) q^{10} +(-4.60375 + 2.65797i) q^{11} +(2.10424 - 1.04448i) q^{12} +(-4.44045 + 2.56370i) q^{13} +(0.0702397 - 1.11595i) q^{15} -4.87304 q^{16} +(0.814931 - 1.41150i) q^{17} +(-4.37761 - 3.32316i) q^{18} +(-2.09039 + 1.20689i) q^{19} +(0.437796 - 0.758285i) q^{20} +(4.86947 + 8.43418i) q^{22} +(1.27442 + 0.735784i) q^{23} +(0.908129 + 1.82954i) q^{24} +(2.29162 + 3.96920i) q^{25} +(4.69675 + 8.13502i) q^{26} +(-0.974073 + 5.10404i) q^{27} +(-6.43846 - 3.71724i) q^{29} +(-2.04445 - 0.128681i) q^{30} +5.66726i q^{31} +6.56903i q^{32} +(5.09556 - 7.66898i) q^{33} +(-2.58590 - 1.49297i) q^{34} +(-2.46025 + 3.24090i) q^{36} +(3.99736 + 6.92362i) q^{37} +(2.21105 + 3.82965i) q^{38} +(4.91482 - 7.39696i) q^{39} +(0.659294 + 0.380644i) q^{40} +(-5.99052 - 10.3759i) q^{41} +(-1.51281 + 2.62026i) q^{43} +(6.24412 - 3.60504i) q^{44} +(0.750407 + 1.78542i) q^{45} +(1.34797 - 2.33476i) q^{46} -3.08353 q^{47} +(7.56023 - 3.75268i) q^{48} +(7.27168 - 4.19830i) q^{50} +(-0.177334 + 2.81743i) q^{51} +(6.02264 - 3.47717i) q^{52} +(2.04554 + 1.18100i) q^{53} +(9.35072 + 1.78453i) q^{54} -3.43181i q^{55} +(2.31371 - 3.48220i) q^{57} +(-6.81008 + 11.7954i) q^{58} +2.95836 q^{59} +(-0.0952669 + 1.51357i) q^{60} -10.6004i q^{61} +10.3825 q^{62} +2.28853 q^{64} -3.31008i q^{65} +(-14.0498 - 9.33518i) q^{66} -10.1549 q^{67} +(-1.10530 + 1.91444i) q^{68} +(-2.54380 - 0.160111i) q^{69} -4.76597i q^{71} +(-2.81781 - 2.13908i) q^{72} +(-10.2239 - 5.90277i) q^{73} +(12.6842 - 7.32325i) q^{74} +(-6.61195 - 4.39323i) q^{75} +(2.83523 - 1.63692i) q^{76} +(-13.5514 - 9.00406i) q^{78} +6.96209 q^{79} +(1.57294 - 2.72441i) q^{80} +(-2.41935 - 8.66872i) q^{81} +(-19.0089 + 10.9748i) q^{82} +(-3.51618 + 6.09021i) q^{83} +(0.526093 + 0.911221i) q^{85} +(4.80038 + 2.77150i) q^{86} +(12.8515 + 0.808893i) q^{87} +(3.13442 + 5.42898i) q^{88} +(2.16337 + 3.74706i) q^{89} +(3.27093 - 1.37476i) q^{90} +(-1.72850 - 0.997953i) q^{92} +(-4.36429 - 8.79240i) q^{93} +5.64910i q^{94} -1.55826i q^{95} +(-5.05873 - 10.1914i) q^{96} +(14.3946 + 8.31075i) q^{97} +(-1.99965 + 15.8220i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4} - 8 q^{9} + 24 q^{11} - 40 q^{15} + 48 q^{16} - 16 q^{18} + 48 q^{23} - 24 q^{25} - 24 q^{30} - 8 q^{36} - 56 q^{39} - 96 q^{44} + 48 q^{50} - 24 q^{51} - 48 q^{53} + 80 q^{57} + 168 q^{60}+ \cdots - 72 q^{99}+O(q^{100}) \) 48 * q - 48 * q^4 - 8 * q^9 + 24 * q^11 - 40 * q^15 + 48 * q^16 - 16 * q^18 + 48 * q^23 - 24 * q^25 - 24 * q^30 - 8 * q^36 - 56 * q^39 - 96 * q^44 + 48 * q^50 - 24 * q^51 - 48 * q^53 + 80 * q^57 + 168 * q^60 - 48 * q^64 - 88 * q^72 + 168 * q^74 - 88 * q^78 + 48 * q^79 - 24 * q^81 - 24 * q^85 - 24 * q^86 - 144 * q^92 + 16 * q^93 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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