LMFDB - Embedded newform 1323.2.o.e.881.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1323,2,Mod(440,1323)] 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, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1323.440"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [48,0,0,24,0,0,0,0,0,0,24,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == 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			881.24
Character	$\chi$	$=$	1323.881
Dual form			1323.2.o.e.440.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.34591 - 1.35441i) q^{2} +(2.66888 - 4.62263i) q^{4} +(0.601464 - 1.04177i) q^{5} -9.04141i q^{8} -3.25853i q^{10} +(2.15351 - 1.24333i) q^{11} +(-1.63211 - 0.942300i) q^{13} +(-6.90806 - 11.9651i) q^{16} -1.20373 q^{17} +7.47013i q^{19} +(-3.21047 - 5.56070i) q^{20} +(3.36797 - 5.83350i) q^{22} +(-2.63359 - 1.52050i) q^{23} +(1.77648 + 3.07696i) q^{25} -5.10506 q^{26} +(0.173847 - 0.100371i) q^{29} +(3.03381 + 1.75157i) q^{31} +(-16.7513 - 9.67135i) q^{32} +(-2.82384 + 1.63034i) q^{34} +1.73092 q^{37} +(10.1177 + 17.5243i) q^{38} +(-9.41904 - 5.43809i) q^{40} +(3.36029 - 5.82020i) q^{41} +(0.00656005 + 0.0113623i) q^{43} -13.2732i q^{44} -8.23756 q^{46} +(-0.717403 - 1.24258i) q^{47} +(8.33495 + 4.81219i) q^{50} +(-8.71182 + 5.02977i) q^{52} +9.90831i q^{53} -2.99128i q^{55} +(0.271887 - 0.470923i) q^{58} +(6.10954 - 10.5820i) q^{59} +(-9.73903 + 5.62283i) q^{61} +9.48942 q^{62} -24.7638 q^{64} +(-1.96331 + 1.13352i) q^{65} +(2.57932 - 4.46752i) q^{67} +(-3.21260 + 5.56438i) q^{68} +12.0452i q^{71} -8.67204i q^{73} +(4.06058 - 2.34438i) q^{74} +(34.5317 + 19.9369i) q^{76} +(-2.74801 - 4.75969i) q^{79} -16.6198 q^{80} -18.2049i q^{82} +(1.60854 + 2.78607i) q^{83} +(-0.723998 + 1.25400i) q^{85} +(0.0307786 + 0.0177700i) q^{86} +(-11.2415 - 19.4708i) q^{88} -7.96728 q^{89} +(-14.0574 + 8.11607i) q^{92} +(-3.36593 - 1.94332i) q^{94} +(7.78214 + 4.49302i) q^{95} +(-2.06260 + 1.19084i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4} + 24 q^{11} - 24 q^{16} + 48 q^{23} - 24 q^{25} - 120 q^{32} - 48 q^{50} - 48 q^{64} - 120 q^{65} + 168 q^{74} - 24 q^{79} - 24 q^{85} - 24 q^{86} + 144 q^{92} - 96 q^{95}+O(q^{100}) $ 48 * q + 24 * q^4 + 24 * q^11 - 24 * q^16 + 48 * q^23 - 24 * q^25 - 120 * q^32 - 48 * q^50 - 48 * q^64 - 120 * q^65 + 168 * q^74 - 24 * q^79 - 24 * q^85 - 24 * q^86 + 144 * q^92 - 96 * q^95

Character values

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

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

Coefficient data

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

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

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

$2$	2.34591	−	1.35441i	1.65881	−	0.957716i	0.685548	−	0.728027i	$-0.259563\pi$
$2$	2.34591	−	1.35441i	1.65881	−	0.957716i	0.973264	−	0.229689i	$-0.0737707\pi$
$3$		0			0
$3$		0			0
$4$	2.66888	−	4.62263i	1.33444	−	2.31132i
$5$	0.601464	−	1.04177i	0.268983	−	0.465892i	−0.699616	−	0.714519i	$-0.746646\pi$
$5$	0.601464	−	1.04177i	0.268983	−	0.465892i	0.968599	+	0.248626i	$0.0799791\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	9.04141i		−	3.19662i
$9$		0			0
$10$		−	3.25853i		−	1.03044i
$11$	2.15351	−	1.24333i	0.649309	−	0.374879i	−0.138882	−	0.990309i	$-0.544351\pi$
$11$	2.15351	−	1.24333i	0.649309	−	0.374879i	0.788191	+	0.615430i	$0.211018\pi$
$12$		0			0
$13$	−1.63211	−	0.942300i	−0.452666	−	0.261347i	0.256289	−	0.966600i	$-0.417500\pi$
$13$	−1.63211	−	0.942300i	−0.452666	−	0.261347i	−0.708956	+	0.705253i	$0.750833\pi$
$14$		0			0
$15$		0			0
$16$	−6.90806	−	11.9651i	−1.72702	−	2.99128i
$17$	−1.20373			−0.291947			−0.145973	−	0.989289i	$-0.546631\pi$
$17$	−1.20373			−0.291947			−0.145973	+	0.989289i	$0.546631\pi$
$18$		0			0
$19$			7.47013i			1.71377i	0.515511	+	0.856883i	$0.327602\pi$
$19$			7.47013i			1.71377i	−0.515511	+	0.856883i	$0.672398\pi$
$20$	−3.21047	−	5.56070i	−0.717883	−	1.24341i
$21$		0			0
$22$	3.36797	−	5.83350i	0.718054	−	1.24371i
$23$	−2.63359	−	1.52050i	−0.549141	−	0.317047i	0.199634	−	0.979870i	$-0.436025\pi$
$23$	−2.63359	−	1.52050i	−0.549141	−	0.317047i	−0.748775	+	0.662824i	$0.769358\pi$
$24$		0			0
$25$	1.77648	+	3.07696i	0.355296	+	0.615391i
$26$	−5.10506			−1.00118
$27$		0			0
$28$		0			0
$29$	0.173847	−	0.100371i	0.0322826	−	0.0186384i	−0.483772	−	0.875194i	$-0.660734\pi$
$29$	0.173847	−	0.100371i	0.0322826	−	0.0186384i	0.516054	+	0.856556i	$0.327400\pi$
$30$		0			0
$31$	3.03381	+	1.75157i	0.544889	+	0.314592i	0.747058	−	0.664759i	$-0.231466\pi$
$31$	3.03381	+	1.75157i	0.544889	+	0.314592i	−0.202169	+	0.979351i	$0.564799\pi$
$32$	−16.7513	−	9.67135i	−2.96124	−	1.70967i
$33$		0			0
$34$	−2.82384	+	1.63034i	−0.484285	+	0.279602i
$35$		0			0
$36$		0			0
$37$	1.73092			0.284561			0.142280	−	0.989826i	$-0.454557\pi$
$37$	1.73092			0.284561			0.142280	+	0.989826i	$0.454557\pi$
$38$	10.1177	+	17.5243i	1.64130	+	2.84282i
$39$		0			0
$40$	−9.41904	−	5.43809i	−1.48928	−	0.859837i
$41$	3.36029	−	5.82020i	0.524790	−	0.908963i	−0.474793	−	0.880097i	$-0.657477\pi$
$41$	3.36029	−	5.82020i	0.524790	−	0.908963i	0.999583	−	0.0288655i	$-0.00918944\pi$
$42$		0			0
$43$	0.00656005	+	0.0113623i	0.00100040	+	0.00173274i	0.866525	−	0.499133i	$-0.166348\pi$
$43$	0.00656005	+	0.0113623i	0.00100040	+	0.00173274i	−0.865525	+	0.500866i	$0.833015\pi$
$44$		−	13.2732i		−	2.00101i
$45$		0			0
$46$	−8.23756			−1.21456
$47$	−0.717403	−	1.24258i	−0.104644	−	0.181249i	0.808949	−	0.587879i	$-0.200037\pi$
$47$	−0.717403	−	1.24258i	−0.104644	−	0.181249i	−0.913593	+	0.406631i	$0.866704\pi$
$48$		0			0
$49$		0			0
$50$	8.33495	+	4.81219i	1.17874	+	0.680546i
$51$		0			0
$52$	−8.71182	+	5.02977i	−1.20811	+	0.697504i
$53$			9.90831i			1.36101i	0.732743	+	0.680506i	$0.238240\pi$
$53$			9.90831i			1.36101i	−0.732743	+	0.680506i	$0.761760\pi$
$54$		0			0
$55$		−	2.99128i		−	0.403344i
$56$		0			0
$57$		0			0
$58$	0.271887	−	0.470923i	0.0357005	−	0.0618352i
$59$	6.10954	−	10.5820i	0.795394	−	1.37766i	−0.127194	−	0.991878i	$-0.540597\pi$
$59$	6.10954	−	10.5820i	0.795394	−	1.37766i	0.922588	−	0.385786i	$-0.126070\pi$
$60$		0			0
$61$	−9.73903	+	5.62283i	−1.24696	+	0.719930i	−0.970501	−	0.241097i	$-0.922493\pi$
$61$	−9.73903	+	5.62283i	−1.24696	+	0.719930i	−0.276454	+	0.961027i	$0.589159\pi$
$62$	9.48942			1.20516
$63$		0			0
$64$	−24.7638			−3.09548
$65$	−1.96331	+	1.13352i	−0.243519	+	0.140596i
$66$		0			0
$67$	2.57932	−	4.46752i	0.315115	−	0.545794i	−0.664347	−	0.747424i	$-0.731290\pi$
$67$	2.57932	−	4.46752i	0.315115	−	0.545794i	0.979462	+	0.201630i	$0.0646237\pi$
$68$	−3.21260	+	5.56438i	−0.389585	+	0.674781i
$69$		0			0
$70$		0			0
$71$			12.0452i			1.42950i	0.699379	+	0.714751i	$0.253460\pi$
$71$			12.0452i			1.42950i	−0.699379	+	0.714751i	$0.746540\pi$
$72$		0			0
$73$		−	8.67204i		−	1.01499i	−0.861656	−	0.507493i	$-0.830572\pi$
$73$		−	8.67204i		−	1.01499i	0.861656	−	0.507493i	$-0.169428\pi$
$74$	4.06058	−	2.34438i	0.472033	−	0.272528i
$75$		0			0
$76$	34.5317	+	19.9369i	3.96106	+	2.28692i
$77$		0			0
$78$		0			0
$79$	−2.74801	−	4.75969i	−0.309175	−	0.535507i	0.669007	−	0.743256i	$-0.266719\pi$
$79$	−2.74801	−	4.75969i	−0.309175	−	0.535507i	−0.978182	+	0.207749i	$0.933386\pi$
$80$	−16.6198			−1.85815
$81$		0			0
$82$		−	18.2049i		−	2.01040i
$83$	1.60854	+	2.78607i	0.176560	+	0.305811i	0.940700	−	0.339239i	$-0.110170\pi$
$83$	1.60854	+	2.78607i	0.176560	+	0.305811i	−0.764140	+	0.645051i	$0.776836\pi$
$84$		0			0
$85$	−0.723998	+	1.25400i	−0.0785286	+	0.136016i
$86$	0.0307786	+	0.0177700i	0.00331894	+	0.00191619i
$87$		0			0
$88$	−11.2415	−	19.4708i	−1.19835	−	2.07559i
$89$	−7.96728			−0.844530			−0.422265	−	0.906473i	$-0.638765\pi$
$89$	−7.96728			−0.844530			−0.422265	+	0.906473i	$0.638765\pi$
$90$		0			0
$91$		0			0
$92$	−14.0574	+	8.11607i	−1.46559	+	0.846159i
$93$		0			0
$94$	−3.36593	−	1.94332i	−0.347170	−	0.200438i
$95$	7.78214	+	4.49302i	0.798430	+	0.460974i
$96$		0			0
$97$	−2.06260	+	1.19084i	−0.209425	+	0.120912i	−0.601044	−	0.799216i	$-0.705249\pi$
$97$	−2.06260	+	1.19084i	−0.209425	+	0.120912i	0.391619	+	0.920128i	$0.371915\pi$
$98$		0			0
$99$		0			0
$100$	18.9648			1.89648
$101$	−4.73272	−	8.19730i	−0.470923	−	0.815662i	0.528524	−	0.848918i	$-0.322746\pi$
$101$	−4.73272	−	8.19730i	−0.470923	−	0.815662i	−0.999447	+	0.0332561i	$0.989412\pi$
$102$		0			0
$103$	14.9460	+	8.62908i	1.47267	+	0.850249i	0.999528	−	0.0307347i	$-0.00978469\pi$
$103$	14.9460	+	8.62908i	1.47267	+	0.850249i	0.473147	+	0.880984i	$0.343118\pi$
$104$	−8.51973	+	14.7566i	−0.835428	+	1.44700i
$105$		0			0
$106$	13.4200	+	23.2441i	1.30346	+	2.25766i
$107$			9.88349i			0.955473i	0.878503	+	0.477737i	$0.158543\pi$
$107$			9.88349i			0.955473i	−0.878503	+	0.477737i	$0.841457\pi$
$108$		0			0
$109$	10.4136			0.997438			0.498719	−	0.866764i	$-0.333804\pi$
$109$	10.4136			0.997438			0.498719	+	0.866764i	$0.333804\pi$
$110$	−4.05143	−	7.01729i	−0.386289	−	0.669072i
$111$		0			0
$112$		0			0
$113$	9.56137	+	5.52026i	0.899458	+	0.519303i	0.877024	−	0.480446i	$-0.159525\pi$
$113$	9.56137	+	5.52026i	0.899458	+	0.519303i	0.0224339	+	0.999748i	$0.492858\pi$
$114$		0			0
$115$	−3.16802	+	1.82906i	−0.295419	+	0.170560i
$116$		−	1.07151i		−	0.0994871i
$117$		0			0
$118$		−	33.0994i		−	3.04705i
$119$		0			0
$120$		0			0
$121$	−2.40825	+	4.17121i	−0.218932	+	0.379201i
$122$	−15.2313	+	26.3814i	−1.37898	+	2.38846i
$123$		0			0
$124$	16.1937	−	9.34946i	1.45424	−	0.839607i
$125$	10.2886			0.920241
$126$		0			0
$127$	13.8634			1.23018			0.615090	−	0.788457i	$-0.289119\pi$
$127$	13.8634			1.23018			0.615090	+	0.788457i	$0.289119\pi$
$128$	−24.5913	+	14.1978i	−2.17359	+	1.25492i
$129$		0			0
$130$	−3.07051	+	5.31828i	−0.269302	+	0.466444i
$131$	−6.17975	+	10.7036i	−0.539927	+	0.935181i	0.458981	+	0.888446i	$0.348215\pi$
$131$	−6.17975	+	10.7036i	−0.539927	+	0.935181i	−0.998907	+	0.0467344i	$0.985119\pi$
$132$		0			0
$133$		0			0
$134$		−	13.9739i		−	1.20716i
$135$		0			0
$136$			10.8834i			0.933243i
$137$	−10.0991	+	5.83070i	−0.862822	+	0.498150i	−0.864956	−	0.501847i	$-0.832654\pi$
$137$	−10.0991	+	5.83070i	−0.862822	+	0.498150i	0.00213432	+	0.999998i	$0.499321\pi$
$138$		0			0
$139$	−8.73893	−	5.04543i	−0.741227	−	0.427947i	0.0812884	−	0.996691i	$-0.474097\pi$
$139$	−8.73893	−	5.04543i	−0.741227	−	0.427947i	−0.822515	+	0.568743i	$0.807430\pi$
$140$		0			0
$141$		0			0
$142$	16.3142	+	28.2570i	1.36906	+	2.37128i
$143$	−4.68637			−0.391894
$144$		0			0
$145$		−	0.241478i		−	0.0200536i
$146$	−11.7455	−	20.3439i	−0.972067	−	1.68367i
$147$		0			0
$148$	4.61960	−	8.00138i	0.379729	−	0.657710i
$149$	−4.15010	−	2.39606i	−0.339990	−	0.196293i	0.320278	−	0.947324i	$-0.396224\pi$
$149$	−4.15010	−	2.39606i	−0.339990	−	0.196293i	−0.660267	+	0.751031i	$0.729557\pi$
$150$		0			0
$151$	5.65924	+	9.80209i	0.460542	+	0.797683i	0.998988	−	0.0449774i	$-0.0143216\pi$
$151$	5.65924	+	9.80209i	0.460542	+	0.797683i	−0.538446	+	0.842660i	$0.680988\pi$
$152$	67.5406			5.47826
$153$		0			0
$154$		0			0
$155$	3.64946	−	2.10702i	0.293132	−	0.169240i
$156$		0			0
$157$	12.7580	+	7.36581i	1.01820	+	0.587856i	0.913581	−	0.406657i	$-0.133306\pi$
$157$	12.7580	+	7.36581i	1.01820	+	0.587856i	0.104615	+	0.994513i	$0.466639\pi$
$158$	−12.8932	−	7.44388i	−1.02573	−	0.592203i
$159$		0			0
$160$	−20.1506	+	11.6339i	−1.59304	+	0.919744i
$161$		0			0
$162$		0			0
$163$	−18.1580			−1.42224			−0.711122	−	0.703069i	$-0.751813\pi$
$163$	−18.1580			−1.42224			−0.711122	+	0.703069i	$0.751813\pi$
$164$	−17.9364	−	31.0668i	−1.40060	−	2.42591i
$165$		0			0
$166$	7.54700	+	4.35726i	0.585761	+	0.338189i
$167$	0.599436	−	1.03825i	0.0463857	−	0.0803425i	−0.841900	−	0.539633i	$-0.818563\pi$
$167$	0.599436	−	1.03825i	0.0463857	−	0.0803425i	0.888286	+	0.459291i	$0.151896\pi$
$168$		0			0
$169$	−4.72414	−	8.18245i	−0.363395	−	0.629419i
$170$			3.92238i			0.300833i
$171$		0			0
$172$	0.0700319			0.00533988
$173$	9.00403	+	15.5954i	0.684564	+	1.18570i	0.973574	+	0.228373i	$0.0733405\pi$
$173$	9.00403	+	15.5954i	0.684564	+	1.18570i	−0.289010	+	0.957326i	$0.593326\pi$
$174$		0			0
$175$		0			0
$176$	−29.7532	−	17.1780i	−2.24273	−	1.29484i
$177$		0			0
$178$	−18.6906	+	10.7910i	−1.40092	+	0.808819i
$179$		−	15.1424i		−	1.13179i	−0.824476	−	0.565897i	$-0.808530\pi$
$179$		−	15.1424i		−	1.13179i	0.824476	−	0.565897i	$-0.191470\pi$
$180$		0			0
$181$		−	7.98716i		−	0.593681i	−0.954927	−	0.296840i	$-0.904067\pi$
$181$		−	7.98716i		−	0.593681i	0.954927	−	0.296840i	$-0.0959329\pi$
$182$		0			0
$183$		0			0
$184$	−13.7475	+	23.8114i	−1.01348	+	1.75540i
$185$	1.04108	−	1.80321i	0.0765420	−	0.132575i
$186$		0			0
$187$	−2.59224	+	1.49663i	−0.189563	+	0.109445i
$188$	−7.65865			−0.558564
$189$		0			0
$190$	24.3416			1.76593
$191$	−13.8711	+	8.00848i	−1.00368	+	0.579473i	−0.909334	−	0.416067i	$-0.863408\pi$
$191$	−13.8711	+	8.00848i	−1.00368	+	0.579473i	−0.0943426	+	0.995540i	$0.530075\pi$
$192$		0			0
$193$	6.85468	−	11.8726i	0.493410	−	0.854612i	−0.506561	−	0.862204i	$-0.669083\pi$
$193$	6.85468	−	11.8726i	0.493410	−	0.854612i	0.999971	+	0.00759239i	$0.00241676\pi$
$194$	−3.22579	+	5.58724i	−0.231598	+	0.401140i
$195$		0			0
$196$		0			0
$197$			18.9248i			1.34834i	0.738577	+	0.674170i	$0.235498\pi$
$197$			18.9248i			1.34834i	−0.738577	+	0.674170i	$0.764502\pi$
$198$		0			0
$199$		−	24.8325i		−	1.76033i	−0.474672	−	0.880163i	$-0.657433\pi$
$199$		−	24.8325i		−	1.76033i	0.474672	−	0.880163i	$-0.342567\pi$
$200$	27.8200	−	16.0619i	1.96717	−	1.13575i
$201$		0			0
$202$	−22.2051	−	12.8201i	−1.56235	−	0.902020i
$203$		0			0
$204$		0			0
$205$	−4.04219	−	7.00129i	−0.282319	−	0.488991i
$206$	46.7494			3.25719
$207$		0			0
$208$			26.0379i			1.80540i
$209$	9.28786	+	16.0870i	0.642454	+	1.11276i
$210$		0			0
$211$	3.60761	−	6.24857i	0.248358	−	0.430169i	−0.714712	−	0.699419i	$-0.753442\pi$
$211$	3.60761	−	6.24857i	0.248358	−	0.430169i	0.963070	+	0.269250i	$0.0867757\pi$
$212$	45.8025	+	26.4441i	3.14573	+	1.81619i
$213$		0			0
$214$	13.3863	+	23.1858i	0.915072	+	1.58495i
$215$	0.0157825			0.00107636
$216$		0			0
$217$		0			0
$218$	24.4293	−	14.1043i	1.65456	−	0.955262i
$219$		0			0
$220$	−13.8276	−	7.98336i	−0.932255	−	0.538238i
$221$	1.96462	+	1.13427i	0.132154	+	0.0762994i
$222$		0			0
$223$	21.0706	−	12.1651i	1.41099	−	0.814635i	0.415508	−	0.909590i	$-0.363604\pi$
$223$	21.0706	−	12.1651i	1.41099	−	0.814635i	0.995482	+	0.0949545i	$0.0302705\pi$
$224$		0			0
$225$		0			0
$226$	29.9069			1.98938
$227$	−0.240288	−	0.416192i	−0.0159485	−	0.0276236i	0.857941	−	0.513748i	$-0.171743\pi$
$227$	−0.240288	−	0.416192i	−0.0159485	−	0.0276236i	−0.873890	+	0.486125i	$0.838410\pi$
$228$		0			0
$229$	−7.80442	−	4.50588i	−0.515730	−	0.297757i	0.219456	−	0.975622i	$-0.429572\pi$
$229$	−7.80442	−	4.50588i	−0.515730	−	0.297757i	−0.735186	+	0.677865i	$0.762905\pi$
$230$	−4.95460	+	8.58162i	−0.326697	+	0.565855i
$231$		0			0
$232$	−0.907493	−	1.57182i	−0.0595799	−	0.103195i
$233$		−	11.1168i		−	0.728285i	−0.931343	−	0.364143i	$-0.881362\pi$
$233$		−	11.1168i		−	0.728285i	0.931343	−	0.364143i	$-0.118638\pi$
$234$		0			0
$235$	−1.72597			−0.112590
$236$	−32.6112	−	56.4843i	−2.12281	−	3.67682i
$237$		0			0
$238$		0			0
$239$	−12.0446	−	6.95395i	−0.779100	−	0.449813i	0.0570114	−	0.998374i	$-0.481843\pi$
$239$	−12.0446	−	6.95395i	−0.779100	−	0.449813i	−0.836111	+	0.548560i	$0.815176\pi$
$240$		0			0
$241$	−10.7181	+	6.18807i	−0.690411	+	0.398609i	−0.803766	−	0.594946i	$-0.797173\pi$
$241$	−10.7181	+	6.18807i	−0.690411	+	0.398609i	0.113355	+	0.993555i	$0.463840\pi$
$242$			13.0471i			0.838698i
$243$		0			0
$244$			60.0266i			3.84281i
$245$		0			0
$246$		0			0
$247$	7.03911	−	12.1921i	0.447888	−	0.775764i
$248$	15.8367	−	27.4299i	1.00563	−	1.74180i
$249$		0			0
$250$	24.1362	−	13.9350i	1.52651	−	0.881329i
$251$	−19.7147			−1.24438			−0.622191	−	0.782866i	$-0.713757\pi$
$251$	−19.7147			−1.24438			−0.622191	+	0.782866i	$0.713757\pi$
$252$		0			0
$253$	−7.56196			−0.475416
$254$	32.5224	−	18.7768i	2.04064	−	1.17816i
$255$		0			0
$256$	−13.6956	+	23.7214i	−0.855973	+	1.48259i
$257$	−5.62025	+	9.73456i	−0.350581	+	0.607225i	−0.986351	−	0.164654i	$-0.947349\pi$
$257$	−5.62025	+	9.73456i	−0.350581	+	0.607225i	0.635770	+	0.771879i	$0.280683\pi$
$258$		0			0
$259$		0			0
$260$			12.1009i			0.750466i
$261$		0			0
$262$			33.4797i			2.06839i
$263$	2.82146	−	1.62897i	0.173979	−	0.100447i	−0.410482	−	0.911869i	$-0.634640\pi$
$263$	2.82146	−	1.62897i	0.173979	−	0.100447i	0.584461	+	0.811422i	$0.301306\pi$
$264$		0			0
$265$	10.3221	+	5.95949i	0.634084	+	0.366089i
$266$		0			0
$267$		0			0
$268$	−13.7678	−	23.8465i	−0.841002	−	1.45666i
$269$	0.242293			0.0147729			0.00738644	−	0.999973i	$-0.497649\pi$
$269$	0.242293			0.0147729			0.00738644	+	0.999973i	$0.497649\pi$
$270$		0			0
$271$			1.07305i			0.0651830i	0.999469	+	0.0325915i	$0.0103760\pi$
$271$			1.07305i			0.0651830i	−0.999469	+	0.0325915i	$0.989624\pi$
$272$	8.31542	+	14.4027i	0.504196	+	0.873294i
$273$		0			0
$274$	−15.7944	+	27.3567i	−0.954173	+	1.65268i
$275$	7.65136	+	4.41751i	0.461394	+	0.266386i
$276$		0			0
$277$	2.45076	+	4.24485i	0.147252	+	0.255048i	0.930211	−	0.367025i	$-0.119624\pi$
$277$	2.45076	+	4.24485i	0.147252	+	0.255048i	−0.782959	+	0.622074i	$0.786290\pi$
$278$	−27.3344			−1.63941
$279$		0			0
$280$		0			0
$281$	−11.5613	+	6.67494i	−0.689691	+	0.398194i	−0.803496	−	0.595310i	$-0.797029\pi$
$281$	−11.5613	+	6.67494i	−0.689691	+	0.398194i	0.113805	+	0.993503i	$0.463696\pi$
$282$		0			0
$283$	3.25329	+	1.87829i	0.193388	+	0.111653i	0.593568	−	0.804784i	$-0.297719\pi$
$283$	3.25329	+	1.87829i	0.193388	+	0.111653i	−0.400180	+	0.916437i	$0.631052\pi$
$284$	55.6805	+	32.1472i	3.30403	+	1.90758i
$285$		0			0
$286$	−10.9938	+	6.34729i	−0.650078	+	0.375323i
$287$		0			0
$288$		0			0
$289$	−15.5510			−0.914767
$290$	−0.327061	−	0.566486i	−0.0192057	−	0.0332652i
$291$		0			0
$292$	−40.0876	−	23.1446i	−2.34595	−	1.35444i
$293$	6.38430	−	11.0579i	0.372975	−	0.646011i	−0.617047	−	0.786926i	$-0.711671\pi$
$293$	6.38430	−	11.0579i	0.372975	−	0.646011i	0.990022	+	0.140915i	$0.0450045\pi$
$294$		0			0
$295$	−7.34934	−	12.7294i	−0.427895	−	0.741136i
$296$		−	15.6499i		−	0.909633i
$297$		0			0
$298$	−12.9810			−0.751972
$299$	2.86554	+	4.96326i	0.165718	+	0.287033i
$300$		0			0
$301$		0			0
$302$	26.5522	+	15.3299i	1.52791	+	0.882137i
$303$		0			0
$304$	89.3810	−	51.6042i	5.12635	−	2.95970i
$305$			13.5277i			0.774596i
$306$		0			0
$307$			10.7257i			0.612148i	0.952008	+	0.306074i	$0.0990155\pi$
$307$			10.7257i			0.612148i	−0.952008	+	0.306074i	$0.900984\pi$
$308$		0			0
$309$		0			0
$310$	5.70755	−	9.88576i	0.324167	−	0.561473i
$311$	−9.41743	+	16.3115i	−0.534013	+	0.924938i	0.465197	+	0.885207i	$0.345983\pi$
$311$	−9.41743	+	16.3115i	−0.534013	+	0.924938i	−0.999210	+	0.0397310i	$0.987350\pi$
$312$		0			0
$313$	−22.5774	+	13.0351i	−1.27615	+	0.736787i	−0.976139	−	0.217148i	$-0.930324\pi$
$313$	−22.5774	+	13.0351i	−1.27615	+	0.736787i	−0.300013	+	0.953935i	$0.596991\pi$
$314$	39.9054			2.25199
$315$		0			0
$316$	−29.3364			−1.65030
$317$	−12.0290	+	6.94495i	−0.675616	+	0.390067i	−0.798201	−	0.602391i	$-0.794215\pi$
$317$	−12.0290	+	6.94495i	−0.675616	+	0.390067i	0.122585	+	0.992458i	$0.460882\pi$
$318$		0			0
$319$	0.249588	−	0.432300i	0.0139743	−	0.0242041i
$320$	−14.8946	+	25.7981i	−0.832631	+	1.44216i
$321$		0			0
$322$		0			0
$323$		−	8.99200i		−	0.500328i
$324$		0			0
$325$		−	6.69592i		−	0.371423i
$326$	−42.5971	+	24.5935i	−2.35924	+	1.36211i
$327$		0			0
$328$	−52.6228	−	30.3818i	−2.90561	−	1.67755i
$329$		0			0
$330$		0			0
$331$	−2.24230	−	3.88378i	−0.123248	−	0.213472i	0.797799	−	0.602924i	$-0.205998\pi$
$331$	−2.24230	−	3.88378i	−0.123248	−	0.213472i	−0.921047	+	0.389452i	$0.872664\pi$
$332$	17.1720			0.942435
$333$		0			0
$334$		−	3.24754i		−	0.177697i
$335$	−3.10274	−	5.37411i	−0.169521	−	0.293619i
$336$		0			0
$337$	−16.4010	+	28.4074i	−0.893420	+	1.54745i	−0.0576723	+	0.998336i	$0.518368\pi$
$337$	−16.4010	+	28.4074i	−0.893420	+	1.54745i	−0.835748	+	0.549113i	$0.814965\pi$
$338$	−22.1649	−	12.7969i	−1.20561	−	0.696059i
$339$		0			0
$340$	3.86453	+	6.69356i	0.209583	+	0.363009i
$341$	8.71114			0.471735
$342$		0			0
$343$		0			0
$344$	0.102732	−	0.0593121i	0.00553891	−	0.00319789i
$345$		0			0
$346$	42.2454	+	24.3904i	2.27112	+	1.31123i
$347$	−11.6112	−	6.70374i	−0.623323	−	0.359876i	0.154839	−	0.987940i	$-0.450514\pi$
$347$	−11.6112	−	6.70374i	−0.623323	−	0.359876i	−0.778162	+	0.628064i	$0.783848\pi$
$348$		0			0
$349$	−19.3276	+	11.1588i	−1.03458	+	0.597316i	−0.918294	−	0.395899i	$-0.870433\pi$
$349$	−19.3276	+	11.1588i	−1.03458	+	0.597316i	−0.116288	+	0.993215i	$0.537100\pi$
$350$		0			0
$351$		0			0
$352$	−48.0988			−2.56368
$353$	8.60842	+	14.9102i	0.458180	+	0.793591i	0.998865	−	0.0476341i	$-0.0151682\pi$
$353$	8.60842	+	14.9102i	0.458180	+	0.793591i	−0.540685	+	0.841225i	$0.681835\pi$
$354$		0			0
$355$	12.5483	+	7.24476i	0.665994	+	0.384512i
$356$	−21.2637	+	36.8298i	−1.12697	+	1.95198i
$357$		0			0
$358$	−20.5090	−	35.5227i	−1.08394	−	1.87743i
$359$		−	6.49943i		−	0.343027i	−0.985182	−	0.171513i	$-0.945134\pi$
$359$		−	6.49943i		−	0.343027i	0.985182	−	0.171513i	$-0.0548656\pi$
$360$		0			0
$361$	−36.8029			−1.93699
$362$	−10.8179	−	18.7372i	−0.568577	−	0.984805i
$363$		0			0
$364$		0			0
$365$	−9.03424	−	5.21592i	−0.472874	−	0.273014i
$366$		0			0
$367$	7.79734	−	4.50180i	0.407018	−	0.234992i	−0.282490	−	0.959270i	$-0.591160\pi$
$367$	7.79734	−	4.50180i	0.407018	−	0.234992i	0.689508	+	0.724278i	$0.257827\pi$
$368$			42.0149i			2.19018i
$369$		0			0
$370$		−	5.64024i		−	0.293222i
$371$		0			0
$372$		0			0
$373$	−5.75312	+	9.96470i	−0.297885	+	0.515953i	−0.975652	−	0.219324i	$-0.929615\pi$
$373$	−5.75312	+	9.96470i	−0.297885	+	0.515953i	0.677767	+	0.735277i	$0.262948\pi$
$374$	−4.05412	+	7.02194i	−0.209633	+	0.363096i
$375$		0			0
$376$	−11.2347	+	6.48634i	−0.579384	+	0.334507i
$377$	−0.378318			−0.0194844
$378$		0			0
$379$	17.0982			0.878275			0.439138	−	0.898420i	$-0.355284\pi$
$379$	17.0982			0.878275			0.439138	+	0.898420i	$0.355284\pi$
$380$	41.5391	−	23.9826i	2.13091	−	1.23028i
$381$		0			0
$382$	−21.6936	+	37.5744i	−1.10994	+	1.92247i
$383$	8.10778	−	14.0431i	0.414288	−	0.717569i	−0.581065	−	0.813857i	$-0.697364\pi$
$383$	8.10778	−	14.0431i	0.414288	−	0.717569i	0.995353	+	0.0962885i	$0.0306971\pi$
$384$		0			0
$385$		0			0
$386$		−	37.1363i		−	1.89019i
$387$		0			0
$388$			12.7129i			0.645398i
$389$	16.2358	−	9.37376i	0.823189	−	0.475269i	−0.0283257	−	0.999599i	$-0.509018\pi$
$389$	16.2358	−	9.37376i	0.823189	−	0.475269i	0.851515	+	0.524330i	$0.175684\pi$
$390$		0			0
$391$	3.17012	+	1.83027i	0.160320	+	0.0925607i
$392$		0			0
$393$		0			0
$394$	25.6321	+	44.3961i	1.29133	+	2.23664i
$395$	−6.61131			−0.332651
$396$		0			0
$397$		−	30.9709i		−	1.55438i	−0.629264	−	0.777192i	$-0.716643\pi$
$397$		−	30.9709i		−	1.55438i	0.629264	−	0.777192i	$-0.283357\pi$
$398$	−33.6334	−	58.2548i	−1.68589	−	2.92005i
$399$		0			0
$400$	24.5441	−	42.5116i	1.22720	−	2.12558i
$401$	0.801065	+	0.462495i	0.0400033	+	0.0230959i	0.519868	−	0.854246i	$-0.325981\pi$
$401$	0.801065	+	0.462495i	0.0400033	+	0.0230959i	−0.479865	+	0.877342i	$0.659314\pi$
$402$		0			0
$403$	−3.30101	−	5.71752i	−0.164435	−	0.284810i
$404$	−50.5242			−2.51367
$405$		0			0
$406$		0			0
$407$	3.72755	−	2.15210i	0.184768	−	0.106676i
$408$		0			0
$409$	−6.56585	−	3.79079i	−0.324660	−	0.187443i	0.328808	−	0.944397i	$-0.393353\pi$
$409$	−6.56585	−	3.79079i	−0.324660	−	0.187443i	−0.653468	+	0.756954i	$0.726687\pi$
$410$	−18.9653	−	10.9496i	−0.936629	−	0.540763i
$411$		0			0
$412$	79.7782	−	46.0599i	3.93039	−	2.26921i
$413$		0			0
$414$		0			0
$415$	3.86992			0.189967
$416$	18.2266	+	31.5695i	0.893635	+	1.54782i
$417$		0			0
$418$	43.5770	+	25.1592i	2.13142	+	1.23058i
$419$	2.85061	−	4.93740i	0.139262	−	0.241208i	−0.787956	−	0.615732i	$-0.788860\pi$
$419$	2.85061	−	4.93740i	0.139262	−	0.241208i	0.927217	+	0.374524i	$0.122194\pi$
$420$		0			0
$421$	−5.86189	−	10.1531i	−0.285691	−	0.494832i	0.687085	−	0.726577i	$-0.258890\pi$
$421$	−5.86189	−	10.1531i	−0.285691	−	0.494832i	−0.972777	+	0.231745i	$0.925557\pi$
$422$		−	19.5448i		−	0.951426i
$423$		0			0
$424$	89.5851			4.35064
$425$	−2.13840	−	3.70381i	−0.103728	−	0.179661i
$426$		0			0
$427$		0			0
$428$	45.6877	+	26.3778i	2.20840	+	1.27502i
$429$		0			0
$430$	0.0370245	−	0.0213761i	0.00178548	−	0.00103085i
$431$		−	26.9014i		−	1.29579i	−0.761728	−	0.647897i	$-0.775649\pi$
$431$		−	26.9014i		−	1.29579i	0.761728	−	0.647897i	$-0.224351\pi$
$432$		0			0
$433$			28.1028i			1.35053i	0.737574	+	0.675266i	$0.235971\pi$
$433$			28.1028i			1.35053i	−0.737574	+	0.675266i	$0.764029\pi$
$434$		0			0
$435$		0			0
$436$	27.7925	−	48.1381i	1.33102	−	2.30539i
$437$	11.3584	−	19.6733i	0.543344	−	0.941099i
$438$		0			0
$439$	−8.07680	+	4.66314i	−0.385485	+	0.222560i	−0.680202	−	0.733025i	$-0.738108\pi$
$439$	−8.07680	+	4.66314i	−0.385485	+	0.222560i	0.294717	+	0.955585i	$0.404775\pi$
$440$	−27.0454			−1.28934
$441$		0			0
$442$	6.14510			0.292292
$443$	−9.82131	+	5.67034i	−0.466624	+	0.269406i	−0.714826	−	0.699303i	$-0.753494\pi$
$443$	−9.82131	+	5.67034i	−0.466624	+	0.269406i	0.248201	+	0.968709i	$0.420161\pi$
$444$		0			0
$445$	−4.79203	+	8.30004i	−0.227164	+	0.393460i
$446$	32.9532	−	57.0766i	1.56038	−	2.70265i
$447$		0			0
$448$		0			0
$449$		−	15.3295i		−	0.723444i	−0.932286	−	0.361722i	$-0.882189\pi$
$449$		−	15.3295i		−	0.723444i	0.932286	−	0.361722i	$-0.117811\pi$
$450$		0			0
$451$		−	16.7118i		−	0.786930i
$452$	51.0363	−	29.4658i	2.40054	−	1.38596i
$453$		0			0
$454$	−1.12739	−	0.650900i	−0.0529111	−	0.0305483i
$455$		0			0
$456$		0			0
$457$	4.58649	+	7.94404i	0.214547	+	0.371606i	0.953132	−	0.302554i	$-0.0978391\pi$
$457$	4.58649	+	7.94404i	0.214547	+	0.371606i	−0.738585	+	0.674160i	$0.764506\pi$
$458$	−24.4113			−1.14067
$459$		0			0
$460$			19.5261i			0.910410i
$461$	16.5365	+	28.6420i	0.770181	+	1.33399i	0.937464	+	0.348083i	$0.113167\pi$
$461$	16.5365	+	28.6420i	0.770181	+	1.33399i	−0.167283	+	0.985909i	$0.553499\pi$
$462$		0			0
$463$	3.91594	−	6.78260i	0.181989	−	0.315214i	−0.760569	−	0.649257i	$-0.775080\pi$
$463$	3.91594	−	6.78260i	0.181989	−	0.315214i	0.942558	+	0.334043i	$0.108413\pi$
$464$	−2.40190	−	1.38674i	−0.111505	−	0.0643776i
$465$		0			0
$466$	−15.0567	−	26.0790i	−0.697490	−	1.20809i
$467$	20.6770			0.956816			0.478408	−	0.878138i	$-0.341214\pi$
$467$	20.6770			0.956816			0.478408	+	0.878138i	$0.341214\pi$
$468$		0			0
$469$		0			0
$470$	−4.04898	+	2.33768i	−0.186765	+	0.107829i
$471$		0			0
$472$	−95.6765	−	55.2389i	−4.40387	−	2.54257i
$473$	0.0282543	+	0.0163126i	0.00129913	+	0.000750056i
$474$		0			0
$475$	−22.9853	+	13.2706i	−1.05464	+	0.608895i
$476$		0			0
$477$		0			0
$478$	−37.6741			−1.72317
$479$	−1.32999	−	2.30361i	−0.0607688	−	0.105255i	0.834040	−	0.551703i	$-0.186022\pi$
$479$	−1.32999	−	2.30361i	−0.0607688	−	0.105255i	−0.894809	+	0.446449i	$0.852689\pi$
$480$		0			0
$481$	−2.82505	−	1.63104i	−0.128811	−	0.0743691i
$482$	−16.7624	+	29.0334i	−0.763508	+	1.32243i
$483$		0			0
$484$	12.8547	+	22.2649i	0.584303	+	1.01204i
$485$			2.86500i			0.130093i
$486$		0			0
$487$	−1.04380			−0.0472991			−0.0236495	−	0.999720i	$-0.507529\pi$
$487$	−1.04380			−0.0472991			−0.0236495	+	0.999720i	$0.507529\pi$
$488$	50.8383	+	88.0546i	2.30134	+	3.98604i
$489$		0			0
$490$		0			0
$491$	−36.0415	−	20.8085i	−1.62653	−	0.939076i	−0.985118	−	0.171878i	$-0.945016\pi$
$491$	−36.0415	−	20.8085i	−1.62653	−	0.939076i	−0.641410	−	0.767198i	$-0.721650\pi$
$492$		0			0
$493$	−0.209265	+	0.120819i	−0.00942480	+	0.00544141i
$494$		−	38.1355i		−	1.71580i
$495$		0			0
$496$		−	48.3999i		−	2.17322i
$497$		0			0
$498$		0			0
$499$	16.1447	−	27.9635i	0.722738	−	1.25182i	−0.237161	−	0.971470i	$-0.576217\pi$
$499$	16.1447	−	27.9635i	0.722738	−	1.25182i	0.959898	−	0.280348i	$-0.0904499\pi$
$500$	27.4590	−	47.5604i	1.22800	−	2.12697i
$501$		0			0
$502$	−46.2490	+	26.7019i	−2.06420	+	1.19176i
$503$	−39.9702			−1.78218			−0.891091	−	0.453825i	$-0.850059\pi$
$503$	−39.9702			−1.78218			−0.891091	+	0.453825i	$0.850059\pi$
$504$		0			0
$505$	−11.3862			−0.506681
$506$	−17.7397	+	10.2420i	−0.788626	+	0.455314i
$507$		0			0
$508$	36.9998	−	64.0856i	1.64160	−	2.84334i
$509$	11.3631	−	19.6815i	0.503661	−	0.872367i	−0.496330	−	0.868134i	$-0.665319\pi$
$509$	11.3631	−	19.6815i	0.503661	−	0.872367i	0.999991	−	0.00423260i	$-0.00134728\pi$
$510$		0			0
$511$		0			0
$512$			17.4067i			0.769277i
$513$		0			0
$514$			30.4486i			1.34303i
$515$	17.9790	−	10.3802i	0.792249	−	0.457405i
$516$		0			0
$517$	−3.08988	−	1.78394i	−0.135893	−	0.0784576i
$518$		0			0
$519$		0			0
$520$	10.2486	+	17.7511i	0.449432	+	0.778439i
$521$	−30.0359			−1.31590			−0.657948	−	0.753063i	$-0.728575\pi$
$521$	−30.0359			−1.31590			−0.657948	+	0.753063i	$0.728575\pi$
$522$		0			0
$523$			0.779769i			0.0340969i	0.999855	+	0.0170485i	$0.00542696\pi$
$523$			0.779769i			0.0340969i	−0.999855	+	0.0170485i	$0.994573\pi$
$524$	32.9860	+	57.1334i	1.44100	+	2.49588i
$525$		0			0
$526$	4.41260	−	7.64285i	0.192399	−	0.333244i
$527$	−3.65188	−	2.10841i	−0.159078	−	0.0918439i
$528$		0			0
$529$	−6.87614	−	11.9098i	−0.298963	−	0.517819i
$530$	32.2865			1.40244
$531$		0			0
$532$		0			0
$533$	−10.9688	+	6.33281i	−0.475110	+	0.274305i
$534$		0			0
$535$	10.2963	+	5.94457i	0.445147	+	0.257006i
$536$	−40.3927	−	23.3207i	−1.74470	−	1.00730i
$537$		0			0
$538$	0.568399	−	0.328165i	0.0245054	−	0.0141482i
$539$		0			0
$540$		0			0
$541$	2.04030			0.0877196			0.0438598	−	0.999038i	$-0.486035\pi$
$541$	2.04030			0.0877196			0.0438598	+	0.999038i	$0.486035\pi$
$542$	1.45335	+	2.51728i	0.0624268	+	0.108126i
$543$		0			0
$544$	20.1640	+	11.6417i	0.864522	+	0.499132i
$545$	6.26338	−	10.8485i	0.268294	−	0.464699i
$546$		0			0
$547$	−8.93590	−	15.4774i	−0.382071	−	0.661767i	0.609287	−	0.792950i	$-0.291456\pi$
$547$	−8.93590	−	15.4774i	−0.382071	−	0.661767i	−0.991358	+	0.131183i	$0.958123\pi$
$548$			62.2457i			2.65901i
$549$		0			0
$550$	23.9326			1.02049
$551$	0.749783	+	1.29866i	0.0319418	+	0.0553249i
$552$		0			0
$553$		0			0
$554$	11.4986	+	6.63870i	0.488527	+	0.282051i
$555$		0			0
$556$	−46.6463	+	26.9313i	−1.97824	+	1.14214i
$557$			42.9605i			1.82029i	0.414285	+	0.910147i	$0.364032\pi$
$557$			42.9605i			1.82029i	−0.414285	+	0.910147i	$0.635968\pi$
$558$		0			0
$559$		−	0.0247261i		−	0.00104580i
$560$		0			0
$561$		0			0
$562$	−18.0813	+	31.3177i	−0.762713	+	1.32106i
$563$	−0.773739	+	1.34016i	−0.0326092	+	0.0564808i	−0.881869	−	0.471494i	$-0.843715\pi$
$563$	−0.773739	+	1.34016i	−0.0326092	+	0.0564808i	0.849260	+	0.527975i	$0.177048\pi$
$564$		0			0
$565$	11.5016	−	6.64048i	0.483878	−	0.279367i
$566$	10.1759			0.427726
$567$		0			0
$568$	108.906			4.56958
$569$	8.65905	−	4.99931i	0.363006	−	0.209582i	−0.307392	−	0.951583i	$-0.599456\pi$
$569$	8.65905	−	4.99931i	0.363006	−	0.209582i	0.670399	+	0.742001i	$0.266123\pi$
$570$		0			0
$571$	1.39715	−	2.41994i	0.0584689	−	0.101271i	−0.835309	−	0.549780i	$-0.814711\pi$
$571$	1.39715	−	2.41994i	0.0584689	−	0.101271i	0.893778	+	0.448509i	$0.148045\pi$
$572$	−12.5073	+	21.6634i	−0.522958	+	0.905790i
$573$		0			0
$574$		0			0
$575$		−	10.8046i		−	0.450582i
$576$		0			0
$577$		−	3.73764i		−	0.155600i	−0.996969	−	0.0778000i	$-0.975210\pi$
$577$		−	3.73764i		−	0.155600i	0.996969	−	0.0778000i	$-0.0247896\pi$
$578$	−36.4814	+	21.0626i	−1.51743	+	0.876087i
$579$		0			0
$580$	−1.11626	−	0.644475i	−0.0463503	−	0.0267604i
$581$		0			0
$582$		0			0
$583$	12.3193	+	21.3377i	0.510214	+	0.883717i
$584$	−78.4074			−3.24452
$585$		0			0
$586$		−	34.5879i		−	1.42881i
$587$	−13.1249	−	22.7331i	−0.541725	−	0.938295i	−0.998805	−	0.0488692i	$-0.984438\pi$
$587$	−13.1249	−	22.7331i	−0.541725	−	0.938295i	0.457081	−	0.889425i	$-0.348895\pi$
$588$		0			0
$589$	−13.0845	+	22.6630i	−0.539136	+	0.933812i
$590$	−34.4819	−	19.9081i	−1.41960	−	0.819604i
$591$		0			0
$592$	−11.9573	−	20.7106i	−0.491441	−	0.851201i
$593$	−3.59667			−0.147698			−0.0738488	−	0.997269i	$-0.523528\pi$
$593$	−3.59667			−0.147698			−0.0738488	+	0.997269i	$0.523528\pi$
$594$		0			0
$595$		0			0
$596$	−22.1522	+	12.7896i	−0.907391	+	0.523882i
$597$		0			0
$598$	13.4446	+	7.76226i	0.549792	+	0.317422i
$599$	−20.6400	−	11.9165i	−0.843326	−	0.486895i	0.0150672	−	0.999886i	$-0.495204\pi$
$599$	−20.6400	−	11.9165i	−0.843326	−	0.486895i	−0.858394	+	0.512992i	$0.828537\pi$
$600$		0			0
$601$	14.6034	−	8.43126i	0.595684	−	0.343918i	−0.171658	−	0.985157i	$-0.554912\pi$
$601$	14.6034	−	8.43126i	0.595684	−	0.343918i	0.767342	+	0.641238i	$0.221579\pi$
$602$		0			0
$603$		0			0
$604$	60.4153			2.45826
$605$	2.89695	+	5.01767i	0.117778	+	0.203997i
$606$		0			0
$607$	9.07737	+	5.24082i	0.368439	+	0.212718i	0.672776	−	0.739846i	$-0.265102\pi$
$607$	9.07737	+	5.24082i	0.368439	+	0.212718i	−0.304337	+	0.952564i	$0.598435\pi$
$608$	72.2463	−	125.134i	2.92997	−	5.07487i
$609$		0			0
$610$	18.3222	+	31.7349i	0.741842	+	1.28491i
$611$			2.70404i			0.109394i
$612$		0			0
$613$	−47.9001			−1.93467			−0.967333	−	0.253510i	$-0.918415\pi$
$613$	−47.9001			−1.93467			−0.967333	+	0.253510i	$0.918415\pi$
$614$	14.5270	+	25.1616i	0.586264	+	1.01544i
$615$		0			0
$616$		0			0
$617$	−4.69477	−	2.71053i	−0.189004	−	0.109122i	0.402512	−	0.915415i	$-0.368137\pi$
$617$	−4.69477	−	2.71053i	−0.189004	−	0.109122i	−0.591516	+	0.806293i	$0.701470\pi$
$618$		0			0
$619$	−27.9729	+	16.1501i	−1.12432	+	0.649129i	−0.942501	−	0.334202i	$-0.891533\pi$
$619$	−27.9729	+	16.1501i	−1.12432	+	0.649129i	−0.181823	+	0.983331i	$0.558200\pi$
$620$		−	22.4935i		−	0.903359i
$621$		0			0
$622$			51.0204i			2.04573i
$623$		0			0
$624$		0			0
$625$	−2.69418	+	4.66646i	−0.107767	+	0.186658i
$626$	−35.3098	+	61.1584i	−1.41126	+	2.44438i
$627$		0			0
$628$	68.0989	−	39.3169i	2.71744	−	1.56892i
$629$	−2.08355			−0.0830765
$630$		0			0
$631$	−18.3539			−0.730656			−0.365328	−	0.930879i	$-0.619043\pi$
$631$	−18.3539			−0.730656			−0.365328	+	0.930879i	$0.619043\pi$
$632$	−43.0343	+	24.8459i	−1.71181	+	0.988315i
$633$		0			0
$634$	−18.8127	+	32.5845i	−0.747147	+	1.29410i
$635$	8.33836	−	14.4425i	0.330898	−	0.573132i
$636$		0			0
$637$		0			0
$638$		−	1.35218i		−	0.0535335i
$639$		0			0
$640$			34.1579i			1.35021i
$641$	−9.07003	+	5.23658i	−0.358245	+	0.206833i	−0.668310	−	0.743882i	$-0.732982\pi$
$641$	−9.07003	+	5.23658i	−0.358245	+	0.206833i	0.310066	+	0.950715i	$0.399649\pi$
$642$		0			0
$643$	−3.37572	−	1.94897i	−0.133125	−	0.0768600i	0.431958	−	0.901894i	$-0.357823\pi$
$643$	−3.37572	−	1.94897i	−0.133125	−	0.0768600i	−0.565084	+	0.825034i	$0.691156\pi$
$644$		0			0
$645$		0			0
$646$	−12.1789	−	21.0945i	−0.479172	−	0.829950i
$647$	12.4054			0.487706			0.243853	−	0.969812i	$-0.421589\pi$
$647$	12.4054			0.487706			0.243853	+	0.969812i	$0.421589\pi$
$648$		0			0
$649$		−	30.3847i		−	1.19271i
$650$	−9.06905	−	15.7081i	−0.355717	−	0.616120i
$651$		0			0
$652$	−48.4615	+	83.9377i	−1.89790	+	3.28726i
$653$	12.2749	+	7.08690i	0.480353	+	0.277332i	0.720564	−	0.693389i	$-0.243883\pi$
$653$	12.2749	+	7.08690i	0.480353	+	0.277332i	−0.240211	+	0.970721i	$0.577216\pi$
$654$		0			0
$655$	7.43379	+	12.8757i	0.290462	+	0.503095i
$656$	−92.8525			−3.62528
$657$		0			0
$658$		0			0
$659$	17.2962	−	9.98594i	0.673763	−	0.388997i	−0.123738	−	0.992315i	$-0.539488\pi$
$659$	17.2962	−	9.98594i	0.673763	−	0.388997i	0.797501	+	0.603318i	$0.206155\pi$
$660$		0			0
$661$	21.0493	+	12.1528i	0.818721	+	0.472689i	0.849975	−	0.526823i	$-0.176617\pi$
$661$	21.0493	+	12.1528i	0.818721	+	0.472689i	−0.0312540	+	0.999511i	$0.509950\pi$
$662$	−10.5205	−	6.07401i	−0.408891	−	0.236073i
$663$		0			0
$664$	25.1900	−	14.5435i	0.977563	−	0.564396i
$665$		0			0
$666$		0			0
$667$	−0.610456			−0.0236370
$668$	−3.19964	−	5.54194i	−0.123798	−	0.214424i
$669$		0			0
$670$	−14.5575	−	8.40480i	−0.562407	−	0.324706i
$671$	−13.9821	+	24.2177i	−0.539773	+	0.934914i
$672$		0			0
$673$	−1.82521	−	3.16135i	−0.0703566	−	0.121861i	0.828701	−	0.559692i	$-0.189080\pi$
$673$	−1.82521	−	3.16135i	−0.0703566	−	0.121861i	−0.899058	+	0.437830i	$0.855747\pi$
$674$			88.8551i			3.42257i
$675$		0			0
$676$	−50.4326			−1.93972
$677$	−0.968676	−	1.67780i	−0.0372292	−	0.0644829i	0.846810	−	0.531895i	$-0.178520\pi$
$677$	−0.968676	−	1.67780i	−0.0372292	−	0.0644829i	−0.884040	+	0.467412i	$0.845187\pi$
$678$		0			0
$679$		0			0
$680$	11.3379	+	6.54597i	0.434790	+	0.251026i
$681$		0			0
$682$	20.4356	−	11.7985i	0.782519	−	0.451788i
$683$		−	19.4931i		−	0.745884i	−0.927855	−	0.372942i	$-0.878349\pi$
$683$		−	19.4931i		−	0.745884i	0.927855	−	0.372942i	$-0.121651\pi$
$684$		0			0
$685$			14.0278i			0.535976i
$686$		0			0
$687$		0			0
$688$	0.0906345	−	0.156983i	0.00345541	−	0.00598494i
$689$	9.33660	−	16.1715i	0.355696	−	0.616084i
$690$		0			0
$691$	35.7855	−	20.6608i	1.36134	−	0.785972i	0.371541	−	0.928416i	$-0.378829\pi$
$691$	35.7855	−	20.6608i	1.36134	−	0.785972i	0.989803	+	0.142444i	$0.0454960\pi$
$692$	96.1226			3.65403
$693$		0			0
$694$	−36.3186			−1.37863
$695$	−10.5123	+	6.06929i	−0.398755	+	0.230221i
$696$		0			0
$697$	−4.04488	+	7.00593i	−0.153211	+	0.265369i
$698$	−30.2273	+	52.3552i	−1.14412	+	1.98167i
$699$		0			0
$700$		0			0
$701$			27.3333i			1.03236i	0.856479	+	0.516182i	$0.172647\pi$
$701$			27.3333i			1.03236i	−0.856479	+	0.516182i	$0.827353\pi$
$702$		0			0
$703$			12.9302i			0.487671i
$704$	−53.3293	+	30.7897i	−2.00992	+	1.16043i
$705$		0			0
$706$	40.3893	+	23.3187i	1.52007	+	0.877613i
$707$		0			0
$708$		0			0
$709$	−1.35635	−	2.34926i	−0.0509387	−	0.0882283i	0.839432	−	0.543465i	$-0.182888\pi$
$709$	−1.35635	−	2.34926i	−0.0509387	−	0.0882283i	−0.890370	+	0.455237i	$0.849555\pi$
$710$	39.2496			1.47301
$711$		0			0
$712$			72.0354i			2.69964i
$713$	−5.32654	−	9.22584i	−0.199480	−	0.345510i
$714$		0			0
$715$	−2.81868	+	4.88210i	−0.105413	+	0.182580i
$716$	−69.9976	−	40.4131i	−2.61593	−	1.51031i
$717$		0			0
$718$	−8.80292	−	15.2471i	−0.328522	−	0.569017i
$719$	16.2786			0.607090			0.303545	−	0.952817i	$-0.401830\pi$
$719$	16.2786			0.607090			0.303545	+	0.952817i	$0.401830\pi$
$720$		0			0
$721$		0			0
$722$	−86.3365	+	49.8464i	−3.21311	+	1.85509i
$723$		0			0
$724$	−36.9217	−	21.3167i	−1.37218	−	0.792231i
$725$	0.617673	+	0.356614i	0.0229398	+	0.0132443i
$726$		0			0
$727$	0.980123	−	0.565874i	0.0363508	−	0.0209871i	−0.481714	−	0.876328i	$-0.659986\pi$
$727$	0.980123	−	0.565874i	0.0363508	−	0.0209871i	0.518065	+	0.855341i	$0.326652\pi$
$728$		0			0
$729$		0			0
$730$	−28.2581			−1.04588
$731$	−0.00789650	−	0.0136771i	−0.000292063	−	0.000505867i
$732$		0			0
$733$	−33.2085	−	19.1729i	−1.22658	−	0.708169i	−0.260270	−	0.965536i	$-0.583812\pi$
$733$	−33.2085	−	19.1729i	−1.22658	−	0.708169i	−0.966314	+	0.257367i	$0.917145\pi$
$734$	12.1946	−	21.1217i	0.450111	−	0.779615i
$735$		0			0
$736$	29.4106	+	50.9407i	1.08409	+	1.87770i
$737$		−	12.8278i		−	0.472519i
$738$		0			0
$739$	10.7298			0.394701			0.197351	−	0.980333i	$-0.436766\pi$
$739$	10.7298			0.394701			0.197351	+	0.980333i	$0.436766\pi$
$740$	−5.55705	−	9.62509i	−0.204281	−	0.353825i
$741$		0			0
$742$		0			0
$743$	11.3308	+	6.54185i	0.415687	+	0.239997i	0.693230	−	0.720716i	$-0.256187\pi$
$743$	11.3308	+	6.54185i	0.415687	+	0.239997i	−0.277543	+	0.960713i	$0.589520\pi$
$744$		0			0
$745$	−4.99228	+	2.88229i	−0.182903	+	0.105599i
$746$			31.1685i			1.14116i
$747$		0			0
$748$			15.9773i			0.584188i
$749$		0			0
$750$		0			0
$751$	−13.1677	+	22.8071i	−0.480495	+	0.832242i	−0.999750	−	0.0223774i	$-0.992876\pi$
$751$	−13.1677	+	22.8071i	−0.480495	+	0.832242i	0.519254	+	0.854620i	$0.326210\pi$
$752$	−9.91173	+	17.1676i	−0.361444	+	0.626039i
$753$		0			0
$754$	−0.887501	+	0.512399i	−0.0323209	+	0.0186605i
$755$	13.6153			0.495512
$756$		0			0
$757$	−32.6280			−1.18588			−0.592942	−	0.805245i	$-0.702034\pi$
$757$	−32.6280			−1.18588			−0.592942	+	0.805245i	$0.702034\pi$
$758$	40.1109	−	23.1580i	1.45689	−	0.841138i
$759$		0			0
$760$	40.6232	−	70.3615i	1.47356	−	2.55228i
$761$	−12.6727	+	21.9498i	−0.459385	+	0.795679i	−0.998929	−	0.0462793i	$-0.985264\pi$
$761$	−12.6727	+	21.9498i	−0.459385	+	0.795679i	0.539543	+	0.841958i	$0.318597\pi$
$762$		0			0
$763$		0			0
$764$			85.4946i			3.09309i
$765$		0			0
$766$		−	43.9252i		−	1.58708i
$767$	−19.9429	+	11.5140i	−0.720097	+	0.415748i
$768$		0			0
$769$	11.4964	+	6.63744i	0.414570	+	0.239352i	0.692752	−	0.721176i	$-0.256398\pi$
$769$	11.4964	+	6.63744i	0.414570	+	0.239352i	−0.278181	+	0.960529i	$0.589732\pi$
$770$		0			0
$771$		0			0
$772$	−36.5886	−	63.3733i	−1.31685	−	2.28085i
$773$	−16.0136			−0.575969			−0.287985	−	0.957635i	$-0.592985\pi$
$773$	−16.0136			−0.575969			−0.287985	+	0.957635i	$0.592985\pi$
$774$		0			0
$775$			12.4465i			0.447093i
$776$	10.7669	+	18.6488i	0.386509	+	0.669454i
$777$		0			0
$778$	25.3919	−	43.9801i	0.910344	−	1.57676i
$779$	43.4777	+	25.1019i	1.55775	+	0.899367i
$780$		0			0
$781$	14.9762	+	25.9395i	0.535890	+	0.928189i
$782$	9.91577			0.354587
$783$		0			0
$784$		0			0
$785$	15.3469	−	8.86054i	0.547755	−	0.316246i
$786$		0			0
$787$	−4.24659	−	2.45177i	−0.151375	−	0.0873961i	0.422400	−	0.906410i	$-0.361188\pi$
$787$	−4.24659	−	2.45177i	−0.151375	−	0.0873961i	−0.573774	+	0.819014i	$0.694521\pi$
$788$	87.4826	+	50.5081i	3.11644	+	1.79928i
$789$		0			0
$790$	−15.5096	+	8.95445i	−0.551806	+	0.318585i
$791$		0			0
$792$		0			0
$793$	21.1936			0.752606
$794$	−41.9474	−	72.6551i	−1.48866	−	2.57843i
$795$		0			0
$796$	−114.791	−	66.2748i	−4.06867	−	2.34905i
$797$	−21.3994	+	37.0649i	−0.758006	+	1.31290i	0.185860	+	0.982576i	$0.440493\pi$
$797$	−21.3994	+	37.0649i	−0.758006	+	1.31290i	−0.943866	+	0.330328i	$0.892841\pi$
$798$		0			0
$799$	0.863557	+	1.49572i	0.0305505	+	0.0529149i
$800$		−	68.7239i		−	2.42976i
$801$		0			0
$802$	2.50564			0.0884772
$803$	−10.7822	−	18.6754i	−0.380496	−	0.659039i
$804$		0			0
$805$		0			0
$806$	−15.4878	−	8.94188i	−0.545534	−	0.314964i
$807$		0			0
$808$	−74.1152	+	42.7904i	−2.60736	+	1.50536i
$809$		−	35.2933i		−	1.24085i	−0.784267	−	0.620424i	$-0.786961\pi$
$809$		−	35.2933i		−	1.24085i	0.784267	−	0.620424i	$-0.213039\pi$
$810$		0			0
$811$		−	21.0223i		−	0.738193i	−0.929391	−	0.369096i	$-0.879667\pi$
$811$		−	21.0223i		−	0.738193i	0.929391	−	0.369096i	$-0.120333\pi$
$812$		0			0
$813$		0			0
$814$	5.82968	−	10.0973i	0.204330	−	0.353910i
$815$	−10.9214	+	18.9164i	−0.382559	+	0.662612i
$816$		0			0
$817$	−0.0848782	+	0.0490044i	−0.00296951	+	0.00171445i
$818$	−20.5372			−0.718067
$819$		0			0
$820$	−43.1525			−1.50695
$821$	29.8623	−	17.2410i	1.04220	−	0.601716i	0.121746	−	0.992561i	$-0.461151\pi$
$821$	29.8623	−	17.2410i	1.04220	−	0.601716i	0.920456	+	0.390845i	$0.127817\pi$
$822$		0			0
$823$	19.4950	−	33.7663i	0.679552	−	1.17702i	−0.295564	−	0.955323i	$-0.595508\pi$
$823$	19.4950	−	33.7663i	0.679552	−	1.17702i	0.975116	−	0.221695i	$-0.0711590\pi$
$824$	78.0191	−	135.133i	2.71792	−	4.70758i
$825$		0			0
$826$		0			0
$827$		−	47.2537i		−	1.64317i	−0.570086	−	0.821585i	$-0.693090\pi$
$827$		−	47.2537i		−	1.64317i	0.570086	−	0.821585i	$-0.306910\pi$
$828$		0			0
$829$			49.1426i			1.70679i	0.521262	+	0.853397i	$0.325462\pi$
$829$			49.1426i			1.70679i	−0.521262	+	0.853397i	$0.674538\pi$
$830$	9.07850	−	5.24147i	0.315119	−	0.181934i
$831$		0			0
$832$	40.4174	+	23.3350i	1.40122	+	0.808995i
$833$		0			0
$834$		0			0
$835$	−0.721079	−	1.24894i	−0.0249540	−	0.0432215i
$836$	99.1526			3.42926
$837$		0			0
$838$		−	15.4436i		−	0.533492i
$839$	26.0780	+	45.1684i	0.900312	+	1.55939i	0.827090	+	0.562070i	$0.189995\pi$
$839$	26.0780	+	45.1684i	0.900312	+	1.55939i	0.0732219	+	0.997316i	$0.476672\pi$
$840$		0			0
$841$	−14.4799	+	25.0798i	−0.499305	+	0.864822i
$842$	−27.5030	−	15.8789i	−0.947816	−	0.547222i
$843$		0			0
$844$	−19.2565	−	33.3533i	−0.662838	−	1.14807i
$845$	−11.3656			−0.390989
$846$		0			0
$847$		0			0
$848$	118.554	−	68.4472i	4.07116	−	2.35049i
$849$		0			0
$850$	−10.0330	−	5.79255i	−0.344129	−	0.198683i
$851$	−4.55852	−	2.63186i	−0.156264	−	0.0902190i
$852$		0			0
$853$	13.4028	−	7.73808i	0.458902	−	0.264947i	−0.252681	−	0.967550i	$-0.581312\pi$
$853$	13.4028	−	7.73808i	0.458902	−	0.264947i	0.711582	+	0.702603i	$0.247979\pi$
$854$		0			0
$855$		0			0
$856$	89.3607			3.05429
$857$	24.4356	+	42.3238i	0.834706	+	1.44575i	0.894270	+	0.447528i	$0.147696\pi$
$857$	24.4356	+	42.3238i	0.834706	+	1.44575i	−0.0595642	+	0.998224i	$0.518971\pi$
$858$		0			0
$859$	8.45000	+	4.87861i	0.288310	+	0.166456i	0.637180	−	0.770715i	$-0.280101\pi$
$859$	8.45000	+	4.87861i	0.288310	+	0.166456i	−0.348869	+	0.937171i	$0.613434\pi$
$860$	0.0421217	−	0.0729569i	0.00143634	−	0.00248781i
$861$		0			0
$862$	−36.4356	−	63.1083i	−1.24100	−	2.14948i
$863$		−	27.6507i		−	0.941241i	−0.882336	−	0.470620i	$-0.844030\pi$
$863$		−	27.6507i		−	0.941241i	0.882336	−	0.470620i	$-0.155970\pi$
$864$		0			0
$865$	21.6624			0.736544
$866$	38.0628	+	65.9267i	1.29343	+	2.24028i
$867$		0			0
$868$		0			0
$869$	−11.8357	−	6.83337i	−0.401500	−	0.231806i
$870$		0			0
$871$	−8.41949	+	4.86100i	−0.285284	+	0.164709i
$872$		−	94.1533i		−	3.18843i
$873$		0			0
$874$		−	61.5357i		−	2.08148i
$875$		0			0
$876$		0			0
$877$	0.932622	−	1.61535i	0.0314924	−	0.0545465i	−0.849850	−	0.527025i	$-0.823307\pi$
$877$	0.932622	−	1.61535i	0.0314924	−	0.0545465i	0.881342	+	0.472479i	$0.156641\pi$
$878$	−12.6317	+	21.8787i	−0.426298	+	0.738370i
$879$		0			0
$880$	−35.7910	+	20.6639i	−1.20651	+	0.696581i
$881$	0.0273875			0.000922707			0.000461353	−	1.00000i	$-0.499853\pi$
$881$	0.0273875			0.000922707			0.000461353		1.00000i	$0.499853\pi$
$882$		0			0
$883$	36.2074			1.21848			0.609239	−	0.792987i	$-0.291475\pi$
$883$	36.2074			1.21848			0.609239	+	0.792987i	$0.291475\pi$
$884$	10.4866	−	6.05447i	0.352704	−	0.203634i
$885$		0			0
$886$	−15.3600	+	26.6043i	−0.516028	+	0.893787i
$887$	−12.6626	+	21.9323i	−0.425170	+	0.736415i	−0.996436	−	0.0843491i	$-0.973119\pi$
$887$	−12.6626	+	21.9323i	−0.425170	+	0.736415i	0.571267	+	0.820765i	$0.306452\pi$
$888$		0			0
$889$		0			0
$890$			25.9616i			0.870235i
$891$		0			0
$892$		−	129.869i		−	4.34832i
$893$	9.28223	−	5.35910i	0.310618	−	0.179335i
$894$		0			0
$895$	−15.7748	−	9.10759i	−0.527294	−	0.304433i
$896$		0			0
$897$		0			0
$898$	−20.7625	−	35.9617i	−0.692854	−	1.20006i
$899$	0.703226			0.0234539
$900$		0			0
$901$		−	11.9269i		−	0.397342i
$902$	−22.6348	−	39.2046i	−0.753655	−	1.30537i
$903$		0			0
$904$	49.9110	−	86.4483i	1.66001	−	2.87523i
$905$	−8.32075	−	4.80399i	−0.276591	−	0.159690i
$906$		0			0
$907$	19.4060	+	33.6122i	0.644366	+	1.11608i	0.984447	+	0.175679i	$0.0562121\pi$
$907$	19.4060	+	33.6122i	0.644366	+	1.11608i	−0.340081	+	0.940396i	$0.610455\pi$
$908$	−2.56520			−0.0851292
$909$		0			0
$910$		0			0
$911$	43.6110	−	25.1788i	1.44490	−	0.834211i	0.446725	−	0.894671i	$-0.352590\pi$
$911$	43.6110	−	25.1788i	1.44490	−	0.834211i	0.998171	+	0.0604602i	$0.0192568\pi$
$912$		0			0
$913$	6.92803	+	3.99990i	0.229284	+	0.132377i
$914$	21.5190	+	12.4240i	0.711787	+	0.410950i
$915$		0			0
$916$	−41.6581	+	24.0513i	−1.37642	+	0.794677i
$917$		0			0
$918$		0			0
$919$	−2.99690			−0.0988585			−0.0494293	−	0.998778i	$-0.515740\pi$
$919$	−2.99690			−0.0988585			−0.0494293	+	0.998778i	$0.515740\pi$
$920$	16.5372	+	28.6434i	0.545217	+	0.944343i
$921$		0			0
$922$	77.5863	+	44.7945i	2.55517	+	1.47523i
$923$	11.3502	−	19.6591i	0.373596	−	0.647088i
$924$		0			0
$925$	3.07494	+	5.32595i	0.101103	+	0.175116i
$926$		−	21.2152i		−	0.697175i
$927$		0			0
$928$	−3.88289			−0.127462
$929$	−16.1108	−	27.9047i	−0.528577	−	0.915522i	−0.999445	−	0.0333184i	$-0.989392\pi$
$929$	−16.1108	−	27.9047i	−0.528577	−	0.915522i	0.470868	−	0.882204i	$-0.343941\pi$
$930$		0			0
$931$		0			0
$932$	−51.3888	−	29.6694i	−1.68330	−	0.971852i
$933$		0			0
$934$	48.5064	−	28.0052i	1.58718	−	0.916358i
$935$			3.60068i			0.117755i
$936$		0			0
$937$		−	3.07038i		−	0.100305i	−0.998742	−	0.0501525i	$-0.984029\pi$
$937$		−	3.07038i		−	0.100305i	0.998742	−	0.0501525i	$-0.0159708\pi$
$938$		0			0
$939$		0			0
$940$	−4.60640	+	7.97852i	−0.150244	+	0.260231i
$941$	19.4136	−	33.6253i	0.632865	−	1.09615i	−0.354099	−	0.935208i	$-0.615212\pi$
$941$	19.4136	−	33.6253i	0.632865	−	1.09615i	0.986963	−	0.160946i	$-0.0514543\pi$
$942$		0			0
$943$	−17.6993	+	10.2187i	−0.576367	+	0.332766i
$944$	−168.820			−5.49464
$945$		0			0
$946$	0.0883763			0.00287336
$947$	−16.2391	+	9.37567i	−0.527701	+	0.304668i	−0.740080	−	0.672519i	$-0.765212\pi$
$947$	−16.2391	+	9.37567i	−0.527701	+	0.304668i	0.212379	+	0.977187i	$0.431879\pi$
$948$		0			0
$949$	−8.17166	+	14.1537i	−0.265263	+	0.459450i
$950$	−35.9477	+	62.2632i	−1.16630	+	2.02008i
$951$		0			0
$952$		0			0
$953$			47.6453i			1.54338i	0.635997	+	0.771692i	$0.280589\pi$
$953$			47.6453i			1.54338i	−0.635997	+	0.771692i	$0.719411\pi$
$954$		0			0
$955$			19.2672i			0.623474i
$956$	−64.2911	+	37.1185i	−2.07932	+	1.20050i
$957$		0			0
$958$	−6.24009	−	3.60272i	−0.201608	−	0.116398i
$959$		0			0
$960$		0			0
$961$	−9.36399	−	16.2189i	−0.302064	−	0.523191i
$962$	−8.83643			−0.284898
$963$		0			0
$964$			66.0608i			2.12768i
$965$	−8.24569	−	14.2819i	−0.265438	−	0.459752i
$966$		0			0
$967$	25.8005	−	44.6878i	0.829689	−	1.43706i	−0.0685936	−	0.997645i	$-0.521851\pi$
$967$	25.8005	−	44.6878i	0.829689	−	1.43706i	0.898282	−	0.439419i	$-0.144815\pi$
$968$	37.7137	+	21.7740i	1.21216	+	0.699843i
$969$		0			0
$970$	3.88040	+	6.72104i	0.124592	+	0.215800i
$971$	28.3866			0.910971			0.455485	−	0.890243i	$-0.349466\pi$
$971$	28.3866			0.910971			0.455485	+	0.890243i	$0.349466\pi$
$972$		0			0
$973$		0			0
$974$	−2.44867	+	1.41374i	−0.0784603	+	0.0452991i
$975$		0			0
$976$	134.556	+	77.6858i	4.30702	+	2.48666i
$977$	−35.6722	−	20.5954i	−1.14126	−	0.658904i	−0.194515	−	0.980900i	$-0.562313\pi$
$977$	−35.6722	−	20.5954i	−1.14126	−	0.658904i	−0.946741	+	0.321995i	$0.895647\pi$
$978$		0			0
$979$	−17.1576	+	9.90597i	−0.548361	+	0.316596i
$980$		0			0
$981$		0			0
$982$	−112.734			−3.59747
$983$	−26.4017	−	45.7291i	−0.842085	−	1.45853i	−0.888129	−	0.459594i	$-0.847995\pi$
$983$	−26.4017	−	45.7291i	−0.842085	−	1.45853i	0.0460447	−	0.998939i	$-0.485338\pi$
$984$		0			0
$985$	19.7153	+	11.3826i	0.628181	+	0.362680i
$986$	−0.327278	+	0.566862i	−0.0104227	+	0.0180526i
$987$		0			0
$988$	−37.5731	−	65.0784i	−1.19536	−	2.07042i
$989$		−	0.0398983i		−	0.00126869i
$990$		0			0
$991$	16.4897			0.523813			0.261907	−	0.965093i	$-0.415649\pi$
$991$	16.4897			0.523813			0.261907	+	0.965093i	$0.415649\pi$
$992$	−33.8801	−	58.6821i	−1.07570	−	1.86316i
$993$		0			0
$994$		0			0
$995$	−25.8696	−	14.9358i	−0.820122	−	0.473498i
$996$		0			0
$997$	42.4857	−	24.5291i	1.34553	−	0.776845i	0.357921	−	0.933752i	$-0.383486\pi$
$997$	42.4857	−	24.5291i	1.34553	−	0.776845i	0.987613	+	0.156907i	$0.0501523\pi$
$998$		−	87.4667i		−	2.76871i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.o.e.881.24		48
3.2	odd	2		441.2.o.e.293.2	yes	48
7.2	even	3		1323.2.s.d.962.2		48
7.3	odd	6		1323.2.i.d.1097.6		48
7.4	even	3		1323.2.i.d.1097.21		48
7.5	odd	6		1323.2.s.d.962.1		48
7.6	odd	2	inner	1323.2.o.e.881.23		48
9.2	odd	6	inner	1323.2.o.e.440.23		48
9.7	even	3		441.2.o.e.146.1	✓	48
21.2	odd	6		441.2.s.d.374.23		48
21.5	even	6		441.2.s.d.374.24		48
21.11	odd	6		441.2.i.d.68.1		48
21.17	even	6		441.2.i.d.68.2		48
21.20	even	2		441.2.o.e.293.1	yes	48
63.2	odd	6		1323.2.i.d.521.6		48
63.11	odd	6		1323.2.s.d.656.1		48
63.16	even	3		441.2.i.d.227.24		48
63.20	even	6	inner	1323.2.o.e.440.24		48
63.25	even	3		441.2.s.d.362.24		48
63.34	odd	6		441.2.o.e.146.2	yes	48
63.38	even	6		1323.2.s.d.656.2		48
63.47	even	6		1323.2.i.d.521.21		48
63.52	odd	6		441.2.s.d.362.23		48
63.61	odd	6		441.2.i.d.227.23		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.1		48	21.11	odd	6
441.2.i.d.68.2		48	21.17	even	6
441.2.i.d.227.23		48	63.61	odd	6
441.2.i.d.227.24		48	63.16	even	3
441.2.o.e.146.1	✓	48	9.7	even	3
441.2.o.e.146.2	yes	48	63.34	odd	6
441.2.o.e.293.1	yes	48	21.20	even	2
441.2.o.e.293.2	yes	48	3.2	odd	2
441.2.s.d.362.23		48	63.52	odd	6
441.2.s.d.362.24		48	63.25	even	3
441.2.s.d.374.23		48	21.2	odd	6
441.2.s.d.374.24		48	21.5	even	6
1323.2.i.d.521.6		48	63.2	odd	6
1323.2.i.d.521.21		48	63.47	even	6
1323.2.i.d.1097.6		48	7.3	odd	6
1323.2.i.d.1097.21		48	7.4	even	3
1323.2.o.e.440.23		48	9.2	odd	6	inner
1323.2.o.e.440.24		48	63.20	even	6	inner
1323.2.o.e.881.23		48	7.6	odd	2	inner
1323.2.o.e.881.24		48	1.1	even	1	trivial
1323.2.s.d.656.1		48	63.11	odd	6
1323.2.s.d.656.2		48	63.38	even	6
1323.2.s.d.962.1		48	7.5	odd	6
1323.2.s.d.962.2		48	7.2	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.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.34591 - 1.35441i) q^{2} +(2.66888 - 4.62263i) q^{4} +(0.601464 - 1.04177i) q^{5} -9.04141i q^{8} -3.25853i q^{10} +(2.15351 - 1.24333i) q^{11} +(-1.63211 - 0.942300i) q^{13} +(-6.90806 - 11.9651i) q^{16} -1.20373 q^{17} +7.47013i q^{19} +(-3.21047 - 5.56070i) q^{20} +(3.36797 - 5.83350i) q^{22} +(-2.63359 - 1.52050i) q^{23} +(1.77648 + 3.07696i) q^{25} -5.10506 q^{26} +(0.173847 - 0.100371i) q^{29} +(3.03381 + 1.75157i) q^{31} +(-16.7513 - 9.67135i) q^{32} +(-2.82384 + 1.63034i) q^{34} +1.73092 q^{37} +(10.1177 + 17.5243i) q^{38} +(-9.41904 - 5.43809i) q^{40} +(3.36029 - 5.82020i) q^{41} +(0.00656005 + 0.0113623i) q^{43} -13.2732i q^{44} -8.23756 q^{46} +(-0.717403 - 1.24258i) q^{47} +(8.33495 + 4.81219i) q^{50} +(-8.71182 + 5.02977i) q^{52} +9.90831i q^{53} -2.99128i q^{55} +(0.271887 - 0.470923i) q^{58} +(6.10954 - 10.5820i) q^{59} +(-9.73903 + 5.62283i) q^{61} +9.48942 q^{62} -24.7638 q^{64} +(-1.96331 + 1.13352i) q^{65} +(2.57932 - 4.46752i) q^{67} +(-3.21260 + 5.56438i) q^{68} +12.0452i q^{71} -8.67204i q^{73} +(4.06058 - 2.34438i) q^{74} +(34.5317 + 19.9369i) q^{76} +(-2.74801 - 4.75969i) q^{79} -16.6198 q^{80} -18.2049i q^{82} +(1.60854 + 2.78607i) q^{83} +(-0.723998 + 1.25400i) q^{85} +(0.0307786 + 0.0177700i) q^{86} +(-11.2415 - 19.4708i) q^{88} -7.96728 q^{89} +(-14.0574 + 8.11607i) q^{92} +(-3.36593 - 1.94332i) q^{94} +(7.78214 + 4.49302i) q^{95} +(-2.06260 + 1.19084i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4} + 24 q^{11} - 24 q^{16} + 48 q^{23} - 24 q^{25} - 120 q^{32} - 48 q^{50} - 48 q^{64} - 120 q^{65} + 168 q^{74} - 24 q^{79} - 24 q^{85} - 24 q^{86} + 144 q^{92} - 96 q^{95}+O(q^{100}) \) 48 * q + 24 * q^4 + 24 * q^11 - 24 * q^16 + 48 * q^23 - 24 * q^25 - 120 * q^32 - 48 * q^50 - 48 * q^64 - 120 * q^65 + 168 * q^74 - 24 * q^79 - 24 * q^85 - 24 * q^86 + 144 * q^92 - 96 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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