LMFDB - Embedded newform 1323.2.s.d.656.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			656.23
Character	$\chi$	$=$	1323.656
Dual form			1323.2.s.d.962.23

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.23278 - 1.28910i) q^{2} +(2.32354 - 4.02449i) q^{4} +2.33189 q^{5} -6.82470i q^{8} +(5.20660 - 3.00603i) q^{10} -4.36608i q^{11} +(-1.14392 + 0.660445i) q^{13} +(-4.15061 - 7.18908i) q^{16} +(2.89327 + 5.01130i) q^{17} +(-0.584876 - 0.337678i) q^{19} +(5.41825 - 9.38468i) q^{20} +(-5.62830 - 9.74851i) q^{22} +5.56333i q^{23} +0.437717 q^{25} +(-1.70276 + 2.94926i) q^{26} +(-3.86926 - 2.23392i) q^{29} +(-3.47965 - 2.00898i) q^{31} +(-6.71411 - 3.87639i) q^{32} +(12.9201 + 7.45942i) q^{34} +(-1.50829 + 2.61243i) q^{37} -1.74120 q^{38} -15.9145i q^{40} +(3.29501 + 5.70713i) q^{41} +(3.89217 - 6.74143i) q^{43} +(-17.5713 - 10.1448i) q^{44} +(7.17168 + 12.4217i) q^{46} +(-0.246705 - 0.427306i) q^{47} +(0.977326 - 0.564259i) q^{50} +6.13829i q^{52} +(3.59025 - 2.07283i) q^{53} -10.1812i q^{55} -11.5189 q^{58} +(-2.15699 + 3.73602i) q^{59} +(-1.77661 + 1.02572i) q^{61} -10.3591 q^{62} -3.38572 q^{64} +(-2.66751 + 1.54009i) q^{65} +(2.41218 - 4.17802i) q^{67} +26.8906 q^{68} +1.17135i q^{71} +(-13.0902 + 7.55766i) q^{73} +7.77733i q^{74} +(-2.71797 + 1.56922i) q^{76} +(5.30428 + 9.18728i) q^{79} +(-9.67878 - 16.7641i) q^{80} +(14.7141 + 8.49518i) q^{82} +(5.32432 - 9.22199i) q^{83} +(6.74680 + 11.6858i) q^{85} -20.0695i q^{86} -29.7972 q^{88} +(1.66268 - 2.87984i) q^{89} +(22.3896 + 12.9266i) q^{92} +(-1.10168 - 0.636053i) q^{94} +(-1.36387 - 0.787429i) q^{95} +(-12.7531 - 7.36299i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4} - 24 q^{16} + 48 q^{25} + 120 q^{32} - 96 q^{44} - 48 q^{50} - 48 q^{53} - 48 q^{64} + 120 q^{65} - 24 q^{79} - 24 q^{85} + 144 q^{92} + 96 q^{95}+O(q^{100}) $ 48 * q + 24 * q^4 - 24 * q^16 + 48 * q^25 + 120 * q^32 - 96 * q^44 - 48 * q^50 - 48 * q^53 - 48 * q^64 + 120 * q^65 - 24 * q^79 - 24 * q^85 + 144 * q^92 + 96 * q^95

Character values

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

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

Coefficient data

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

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

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

$2$	2.23278	−	1.28910i	1.57882	−	0.911529i	0.583790	−	0.811905i	$-0.301569\pi$
$2$	2.23278	−	1.28910i	1.57882	−	0.911529i	0.995025	−	0.0996245i	$-0.0317642\pi$
$3$		0			0
$3$		0			0
$4$	2.32354	−	4.02449i	1.16177	−	2.01225i
$5$	2.33189			1.04285			0.521427	−	0.853296i	$-0.325400\pi$
$5$	2.33189			1.04285			0.521427	+	0.853296i	$0.325400\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	6.82470i		−	2.41290i
$9$		0			0
$10$	5.20660	−	3.00603i	1.64647	−	0.950591i
$11$		−	4.36608i		−	1.31642i	−0.752833	−	0.658212i	$-0.771313\pi$
$11$		−	4.36608i		−	1.31642i	0.752833	−	0.658212i	$-0.228687\pi$
$12$		0			0
$13$	−1.14392	+	0.660445i	−0.317267	+	0.183174i	−0.650174	−	0.759785i	$-0.725304\pi$
$13$	−1.14392	+	0.660445i	−0.317267	+	0.183174i	0.332906	+	0.942960i	$0.391971\pi$
$14$		0			0
$15$		0			0
$16$	−4.15061	−	7.18908i	−1.03765	−	1.79727i
$17$	2.89327	+	5.01130i	0.701722	+	1.21542i	0.967862	+	0.251484i	$0.0809185\pi$
$17$	2.89327	+	5.01130i	0.701722	+	1.21542i	−0.266140	+	0.963935i	$0.585748\pi$
$18$		0			0
$19$	−0.584876	−	0.337678i	−0.134180	−	0.0774687i	0.431407	−	0.902157i	$-0.358017\pi$
$19$	−0.584876	−	0.337678i	−0.134180	−	0.0774687i	−0.565587	+	0.824688i	$0.691350\pi$
$20$	5.41825	−	9.38468i	1.21156	−	2.09848i
$21$		0			0
$22$	−5.62830	−	9.74851i	−1.19996	−	2.07839i
$23$			5.56333i			1.16004i	0.814604	+	0.580018i	$0.196954\pi$
$23$			5.56333i			1.16004i	−0.814604	+	0.580018i	$0.803046\pi$
$24$		0			0
$25$	0.437717			0.0875433
$26$	−1.70276	+	2.94926i	−0.333938	+	0.578397i
$27$		0			0
$28$		0			0
$29$	−3.86926	−	2.23392i	−0.718503	−	0.414828i	0.0956983	−	0.995410i	$-0.469492\pi$
$29$	−3.86926	−	2.23392i	−0.718503	−	0.414828i	−0.814202	+	0.580582i	$0.802825\pi$
$30$		0			0
$31$	−3.47965	−	2.00898i	−0.624964	−	0.360823i	0.153835	−	0.988097i	$-0.450838\pi$
$31$	−3.47965	−	2.00898i	−0.624964	−	0.360823i	−0.778799	+	0.627273i	$0.784171\pi$
$32$	−6.71411	−	3.87639i	−1.18690	−	0.685256i
$33$		0			0
$34$	12.9201	+	7.45942i	2.21578	+	1.27928i
$35$		0			0
$36$		0			0
$37$	−1.50829	+	2.61243i	−0.247961	+	0.429482i	−0.962960	−	0.269644i	$-0.913094\pi$
$37$	−1.50829	+	2.61243i	−0.247961	+	0.429482i	0.714999	+	0.699126i	$0.246427\pi$
$38$	−1.74120			−0.282460
$39$		0			0
$40$		−	15.9145i		−	2.51630i
$41$	3.29501	+	5.70713i	0.514594	+	0.891303i	0.999857	+	0.0169348i	$0.00539076\pi$
$41$	3.29501	+	5.70713i	0.514594	+	0.891303i	−0.485262	+	0.874369i	$0.661276\pi$
$42$		0			0
$43$	3.89217	−	6.74143i	0.593550	−	1.02806i	−0.400200	−	0.916428i	$-0.631059\pi$
$43$	3.89217	−	6.74143i	0.593550	−	1.02806i	0.993750	−	0.111631i	$-0.0356074\pi$
$44$	−17.5713	−	10.1448i	−2.64897	−	1.52938i
$45$		0			0
$46$	7.17168	+	12.4217i	1.05741	+	1.83148i
$47$	−0.246705	−	0.427306i	−0.0359856	−	0.0623289i	0.847472	−	0.530841i	$-0.178124\pi$
$47$	−0.246705	−	0.427306i	−0.0359856	−	0.0623289i	−0.883457	+	0.468512i	$0.844790\pi$
$48$		0			0
$49$		0			0
$50$	0.977326	−	0.564259i	0.138215	−	0.0797983i
$51$		0			0
$52$			6.13829i			0.851227i
$53$	3.59025	−	2.07283i	0.493159	−	0.284725i	−0.232725	−	0.972543i	$-0.574764\pi$
$53$	3.59025	−	2.07283i	0.493159	−	0.284725i	0.725884	+	0.687817i	$0.241431\pi$
$54$		0			0
$55$		−	10.1812i		−	1.37284i
$56$		0			0
$57$		0			0
$58$	−11.5189			−1.51251
$59$	−2.15699	+	3.73602i	−0.280816	+	0.486388i	−0.971586	−	0.236687i	$-0.923939\pi$
$59$	−2.15699	+	3.73602i	−0.280816	+	0.486388i	0.690770	+	0.723075i	$0.257272\pi$
$60$		0			0
$61$	−1.77661	+	1.02572i	−0.227471	+	0.131330i	−0.609405	−	0.792859i	$-0.708592\pi$
$61$	−1.77661	+	1.02572i	−0.227471	+	0.131330i	0.381934	+	0.924190i	$0.375258\pi$
$62$	−10.3591			−1.31560
$63$		0			0
$64$	−3.38572			−0.423215
$65$	−2.66751	+	1.54009i	−0.330863	+	0.191024i
$66$		0			0
$67$	2.41218	−	4.17802i	0.294695	−	0.510427i	−0.680219	−	0.733009i	$-0.738115\pi$
$67$	2.41218	−	4.17802i	0.294695	−	0.510427i	0.974914	+	0.222582i	$0.0714486\pi$
$68$	26.8906			3.26096
$69$		0			0
$70$		0			0
$71$			1.17135i			0.139014i	0.997581	+	0.0695068i	$0.0221426\pi$
$71$			1.17135i			0.139014i	−0.997581	+	0.0695068i	$0.977857\pi$
$72$		0			0
$73$	−13.0902	+	7.55766i	−1.53210	+	0.884557i	−0.532833	+	0.846221i	$0.678872\pi$
$73$	−13.0902	+	7.55766i	−1.53210	+	0.884557i	−0.999265	+	0.0383363i	$0.987794\pi$
$74$			7.77733i			0.904096i
$75$		0			0
$76$	−2.71797	+	1.56922i	−0.311772	+	0.180002i
$77$		0			0
$78$		0			0
$79$	5.30428	+	9.18728i	0.596778	+	1.03365i	0.993293	+	0.115622i	$0.0368861\pi$
$79$	5.30428	+	9.18728i	0.596778	+	1.03365i	−0.396515	+	0.918028i	$0.629781\pi$
$80$	−9.67878	−	16.7641i	−1.08212	−	1.87429i
$81$		0			0
$82$	14.7141	+	8.49518i	1.62490	+	0.938135i
$83$	5.32432	−	9.22199i	0.584420	−	1.01225i	−0.410527	−	0.911848i	$-0.634655\pi$
$83$	5.32432	−	9.22199i	0.584420	−	1.01225i	0.994947	−	0.100397i	$-0.0320113\pi$
$84$		0			0
$85$	6.74680	+	11.6858i	0.731793	+	1.26750i
$86$		−	20.0695i		−	2.16415i
$87$		0			0
$88$	−29.7972			−3.17639
$89$	1.66268	−	2.87984i	0.176243	−	0.305262i	−0.764348	−	0.644804i	$-0.776939\pi$
$89$	1.66268	−	2.87984i	0.176243	−	0.305262i	0.940591	+	0.339542i	$0.110272\pi$
$90$		0			0
$91$		0			0
$92$	22.3896	+	12.9266i	2.33428	+	1.34770i
$93$		0			0
$94$	−1.10168	−	0.636053i	−0.113629	−	0.0656039i
$95$	−1.36387	−	0.787429i	−0.139930	−	0.0807886i
$96$		0			0
$97$	−12.7531	−	7.36299i	−1.29488	−	0.747598i	−0.315363	−	0.948971i	$-0.602126\pi$
$97$	−12.7531	−	7.36299i	−1.29488	−	0.747598i	−0.979515	+	0.201373i	$0.935460\pi$
$98$		0			0
$99$		0			0
$100$	1.01705	−	1.76159i	0.101705	−	0.176159i
$101$	−1.66418			−0.165593			−0.0827963	−	0.996566i	$-0.526385\pi$
$101$	−1.66418			−0.165593			−0.0827963	+	0.996566i	$0.526385\pi$
$102$		0			0
$103$			1.62562i			0.160177i	0.996788	+	0.0800887i	$0.0255204\pi$
$103$			1.62562i			0.160177i	−0.996788	+	0.0800887i	$0.974480\pi$
$104$	4.50734	+	7.80694i	0.441981	+	0.765533i
$105$		0			0
$106$	5.34416	−	9.25636i	0.519071	−	0.899057i
$107$	15.8596	+	9.15652i	1.53320	+	0.885194i	0.999212	+	0.0397036i	$0.0126414\pi$
$107$	15.8596	+	9.15652i	1.53320	+	0.885194i	0.533990	+	0.845491i	$0.320692\pi$
$108$		0			0
$109$	7.98678	+	13.8335i	0.764995	+	1.32501i	0.940249	+	0.340487i	$0.110592\pi$
$109$	7.98678	+	13.8335i	0.764995	+	1.32501i	−0.175254	+	0.984523i	$0.556075\pi$
$110$	−13.1246	−	22.7325i	−1.25138	−	2.16746i
$111$		0			0
$112$		0			0
$113$	5.07612	−	2.93070i	0.477521	−	0.275697i	−0.241862	−	0.970311i	$-0.577758\pi$
$113$	5.07612	−	2.93070i	0.477521	−	0.275697i	0.719383	+	0.694614i	$0.244425\pi$
$114$		0			0
$115$			12.9731i			1.20975i
$116$	−17.9808	+	10.3812i	−1.66947	+	0.963871i
$117$		0			0
$118$			11.1223i			1.02389i
$119$		0			0
$120$		0			0
$121$	−8.06267			−0.732970
$122$	−2.64451	+	4.58043i	−0.239423	+	0.414693i
$123$		0			0
$124$	−16.1702	+	9.33589i	−1.45213	+	0.838388i
$125$	−10.6387			−0.951559
$126$		0			0
$127$	−16.5710			−1.47044			−0.735218	−	0.677831i	$-0.762920\pi$
$127$	−16.5710			−1.47044			−0.735218	+	0.677831i	$0.762920\pi$
$128$	5.86864	−	3.38826i	0.518719	−	0.299483i
$129$		0			0
$130$	−3.97064	+	6.87735i	−0.348248	+	0.603183i
$131$	−7.11978			−0.622058			−0.311029	−	0.950400i	$-0.600674\pi$
$131$	−7.11978			−0.622058			−0.311029	+	0.950400i	$0.600674\pi$
$132$		0			0
$133$		0			0
$134$		−	12.4382i		−	1.07449i
$135$		0			0
$136$	34.2006	−	19.7457i	2.93268	−	1.69318i
$137$		−	0.827439i		−	0.0706929i	−0.999375	−	0.0353465i	$-0.988747\pi$
$137$		−	0.827439i		−	0.0706929i	0.999375	−	0.0353465i	$-0.0112535\pi$
$138$		0			0
$139$	−12.0735	+	6.97062i	−1.02406	+	0.591241i	−0.915277	−	0.402825i	$-0.868028\pi$
$139$	−12.0735	+	6.97062i	−1.02406	+	0.591241i	−0.108782	+	0.994066i	$0.534695\pi$
$140$		0			0
$141$		0			0
$142$	1.50998	+	2.61537i	0.126715	+	0.219477i
$143$	2.88356	+	4.99447i	0.241135	+	0.417658i
$144$		0			0
$145$	−9.02269	−	5.20925i	−0.749294	−	0.432605i
$146$	−19.4851	+	33.7492i	−1.61260	+	2.79310i
$147$		0			0
$148$	7.00915	+	12.1402i	0.576149	+	0.997919i
$149$			10.9340i			0.895752i	0.894096	+	0.447876i	$0.147819\pi$
$149$			10.9340i			0.895752i	−0.894096	+	0.447876i	$0.852181\pi$
$150$		0			0
$151$	−13.9455			−1.13487			−0.567436	−	0.823418i	$-0.692065\pi$
$151$	−13.9455			−1.13487			−0.567436	+	0.823418i	$0.692065\pi$
$152$	−2.30455	+	3.99160i	−0.186924	+	0.323762i
$153$		0			0
$154$		0			0
$155$	−8.11417	−	4.68472i	−0.651746	−	0.376286i
$156$		0			0
$157$	13.6641	+	7.88894i	1.09051	+	0.629606i	0.933712	−	0.358024i	$-0.116550\pi$
$157$	13.6641	+	7.88894i	1.09051	+	0.629606i	0.156798	+	0.987631i	$0.449883\pi$
$158$	23.6866	+	13.6755i	1.88440	+	1.08796i
$159$		0			0
$160$	−15.6566	−	9.03932i	−1.23776	−	0.714621i
$161$		0			0
$162$		0			0
$163$	3.38276	−	5.85911i	0.264958	−	0.458921i	−0.702594	−	0.711590i	$-0.747975\pi$
$163$	3.38276	−	5.85911i	0.264958	−	0.458921i	0.967553	+	0.252669i	$0.0813085\pi$
$164$	30.6244			2.39136
$165$		0			0
$166$		−	27.4543i		−	2.13086i
$167$	−9.54631	−	16.5347i	−0.738716	−	1.27949i	−0.953074	−	0.302738i	$-0.902099\pi$
$167$	−9.54631	−	16.5347i	−0.738716	−	1.27949i	0.214358	−	0.976755i	$-0.431234\pi$
$168$		0			0
$169$	−5.62763	+	9.74733i	−0.432894	+	0.749795i
$170$	30.1283	+	17.3946i	2.31073	+	1.33410i
$171$		0			0
$172$	−18.0872	−	31.3280i	−1.37914	−	2.38874i
$173$	10.9246	+	18.9219i	0.830579	+	1.43860i	0.897580	+	0.440851i	$0.145323\pi$
$173$	10.9246	+	18.9219i	0.830579	+	1.43860i	−0.0670016	+	0.997753i	$0.521343\pi$
$174$		0			0
$175$		0			0
$176$	−31.3881	+	18.1219i	−2.36597	+	1.36599i
$177$		0			0
$178$		−	8.57340i		−	0.642603i
$179$	14.8866	−	8.59481i	1.11268	−	0.642406i	0.173158	−	0.984894i	$-0.444603\pi$
$179$	14.8866	−	8.59481i	1.11268	−	0.642406i	0.939522	+	0.342488i	$0.111270\pi$
$180$		0			0
$181$		−	16.6462i		−	1.23730i	−0.785666	−	0.618650i	$-0.787680\pi$
$181$		−	16.6462i		−	1.23730i	0.785666	−	0.618650i	$-0.212320\pi$
$182$		0			0
$183$		0			0
$184$	37.9681			2.79904
$185$	−3.51717	+	6.09191i	−0.258587	+	0.447886i
$186$		0			0
$187$	21.8797	−	12.6323i	1.60000	−	0.923763i
$188$	−2.29292			−0.167228
$189$		0			0
$190$	−4.06029			−0.294565
$191$	0.826254	−	0.477038i	0.0597857	−	0.0345173i	−0.469809	−	0.882768i	$-0.655677\pi$
$191$	0.826254	−	0.477038i	0.0597857	−	0.0345173i	0.529595	+	0.848251i	$0.322344\pi$
$192$		0			0
$193$	0.847203	−	1.46740i	0.0609830	−	0.105626i	−0.833922	−	0.551882i	$-0.813910\pi$
$193$	0.847203	−	1.46740i	0.0609830	−	0.105626i	0.894905	+	0.446257i	$0.147243\pi$
$194$	−37.9664			−2.72583
$195$		0			0
$196$		0			0
$197$		−	12.7486i		−	0.908301i	−0.890925	−	0.454150i	$-0.849943\pi$
$197$		−	12.7486i		−	0.908301i	0.890925	−	0.454150i	$-0.150057\pi$
$198$		0			0
$199$	−3.77420	+	2.17903i	−0.267546	+	0.154468i	−0.627772	−	0.778397i	$-0.716033\pi$
$199$	−3.77420	+	2.17903i	−0.267546	+	0.154468i	0.360226	+	0.932865i	$0.382700\pi$
$200$		−	2.98728i		−	0.211233i
$201$		0			0
$202$	−3.71576	+	2.14530i	−0.261440	+	0.150942i
$203$		0			0
$204$		0			0
$205$	7.68361	+	13.3084i	0.536646	+	0.929499i
$206$	2.09559	+	3.62966i	0.146006	+	0.252891i
$207$		0			0
$208$	9.49598	+	5.48250i	0.658427	+	0.380143i
$209$	−1.47433	+	2.55362i	−0.101982	+	0.176637i
$210$		0			0
$211$	−2.24368	−	3.88617i	−0.154461	−	0.267535i	0.778401	−	0.627767i	$-0.216031\pi$
$211$	−2.24368	−	3.88617i	−0.154461	−	0.267535i	−0.932863	+	0.360232i	$0.882698\pi$
$212$		−	19.2653i		−	1.32314i
$213$		0			0
$214$	47.2146			3.22752
$215$	9.07611	−	15.7203i	0.618986	−	1.07211i
$216$		0			0
$217$		0			0
$218$	35.6655	+	20.5915i	2.41557	+	1.39463i
$219$		0			0
$220$	−40.9743	−	23.6565i	−2.76249	−	1.59492i
$221$	−6.61937	−	3.82170i	−0.445267	−	0.257075i
$222$		0			0
$223$	18.0005	+	10.3926i	1.20540	+	0.695939i	0.961751	−	0.273924i	$-0.0883218\pi$
$223$	18.0005	+	10.3926i	1.20540	+	0.695939i	0.243650	+	0.969863i	$0.421655\pi$
$224$		0			0
$225$		0			0
$226$	7.55591	−	13.0872i	0.502612	−	0.870549i
$227$	28.3159			1.87939			0.939696	−	0.342012i	$-0.111108\pi$
$227$	28.3159			1.87939			0.939696	+	0.342012i	$0.111108\pi$
$228$		0			0
$229$			21.7857i			1.43964i	0.694160	+	0.719821i	$0.255776\pi$
$229$			21.7857i			1.43964i	−0.694160	+	0.719821i	$0.744224\pi$
$230$	16.7236	+	28.9661i	1.10272	+	1.90997i
$231$		0			0
$232$	−15.2458	+	26.4065i	−1.00094	+	1.73367i
$233$	−13.1926	−	7.61674i	−0.864275	−	0.498989i	0.00116682	−	0.999999i	$-0.499629\pi$
$233$	−13.1926	−	7.61674i	−0.864275	−	0.498989i	−0.865441	+	0.501010i	$0.832962\pi$
$234$		0			0
$235$	−0.575289	−	0.996430i	−0.0375277	−	0.0649999i
$236$	10.0237	+	17.3616i	0.652489	+	1.13014i
$237$		0			0
$238$		0			0
$239$	4.95125	−	2.85861i	0.320270	−	0.184908i	−0.331243	−	0.943545i	$-0.607468\pi$
$239$	4.95125	−	2.85861i	0.320270	−	0.184908i	0.651513	+	0.758638i	$0.274135\pi$
$240$		0			0
$241$			4.47114i			0.288011i	0.989577	+	0.144006i	$0.0459984\pi$
$241$			4.47114i			0.288011i	−0.989577	+	0.144006i	$0.954002\pi$
$242$	−18.0022	+	10.3936i	−1.15722	+	0.668124i
$243$		0			0
$244$			9.53325i			0.610304i
$245$		0			0
$246$		0			0
$247$	0.892072			0.0567612
$248$	−13.7107	+	23.7476i	−0.870629	+	1.50797i
$249$		0			0
$250$	−23.7540	+	13.7144i	−1.50234	+	0.867374i
$251$	11.6265			0.733861			0.366931	−	0.930248i	$-0.380409\pi$
$251$	11.6265			0.733861			0.366931	+	0.930248i	$0.380409\pi$
$252$		0			0
$253$	24.2900			1.52710
$254$	−36.9993	+	21.3616i	−2.32155	+	1.34034i
$255$		0			0
$256$	12.1213	−	20.9947i	0.757582	−	1.31217i
$257$	2.10280			0.131169			0.0655846	−	0.997847i	$-0.479109\pi$
$257$	2.10280			0.131169			0.0655846	+	0.997847i	$0.479109\pi$
$258$		0			0
$259$		0			0
$260$			14.3138i			0.887705i
$261$		0			0
$262$	−15.8969	+	9.17809i	−0.982114	+	0.567024i
$263$		−	2.20286i		−	0.135834i	−0.997691	−	0.0679170i	$-0.978365\pi$
$263$		−	2.20286i		−	0.135834i	0.997691	−	0.0679170i	$-0.0216353\pi$
$264$		0			0
$265$	8.37207	−	4.83362i	0.514292	−	0.296927i
$266$		0			0
$267$		0			0
$268$	−11.2096	−	19.4156i	−0.684737	−	1.18600i
$269$	−13.9312	−	24.1295i	−0.849398	−	1.47120i	−0.881746	−	0.471724i	$-0.843632\pi$
$269$	−13.9312	−	24.1295i	−0.849398	−	1.47120i	0.0323483	−	0.999477i	$-0.489701\pi$
$270$		0			0
$271$	9.94228	+	5.74018i	0.603950	+	0.348691i	0.770594	−	0.637326i	$-0.219960\pi$
$271$	9.94228	+	5.74018i	0.603950	+	0.348691i	−0.166644	+	0.986017i	$0.553293\pi$
$272$	24.0177	−	41.5999i	1.45629	−	2.52237i
$273$		0			0
$274$	−1.06665	−	1.84749i	−0.0644387	−	0.111611i
$275$		−	1.91111i		−	0.115244i
$276$		0			0
$277$	−10.2000			−0.612859			−0.306429	−	0.951893i	$-0.599134\pi$
$277$	−10.2000			−0.612859			−0.306429	+	0.951893i	$0.599134\pi$
$278$	−17.9716	+	31.1278i	−1.07787	+	1.86692i
$279$		0			0
$280$		0			0
$281$	−9.45116	−	5.45663i	−0.563809	−	0.325515i	0.190864	−	0.981617i	$-0.438871\pi$
$281$	−9.45116	−	5.45663i	−0.563809	−	0.325515i	−0.754673	+	0.656101i	$0.772204\pi$
$282$		0			0
$283$	−10.2766	−	5.93322i	−0.610882	−	0.352693i	0.162428	−	0.986720i	$-0.448067\pi$
$283$	−10.2766	−	5.93322i	−0.610882	−	0.352693i	−0.773311	+	0.634027i	$0.781401\pi$
$284$	4.71409	+	2.72168i	0.279730	+	0.161502i
$285$		0			0
$286$	12.8767	+	7.43437i	0.761415	+	0.439603i
$287$		0			0
$288$		0			0
$289$	−8.24207	+	14.2757i	−0.484828	+	0.839746i
$290$	−26.8609			−1.57733
$291$		0			0
$292$			70.2422i			4.11061i
$293$	−9.55012	−	16.5413i	−0.557924	−	0.966353i	−0.997670	−	0.0682302i	$-0.978265\pi$
$293$	−9.55012	−	16.5413i	−0.557924	−	0.966353i	0.439746	−	0.898122i	$-0.355069\pi$
$294$		0			0
$295$	−5.02987	+	8.71199i	−0.292850	+	0.507232i
$296$	17.8291	+	10.2936i	1.03629	+	0.598305i
$297$		0			0
$298$	14.0950	+	24.4133i	0.816504	+	1.41423i
$299$	−3.67427	−	6.36403i	−0.212489	−	0.368041i
$300$		0			0
$301$		0			0
$302$	−31.1373	+	17.9772i	−1.79175	+	1.03447i
$303$		0			0
$304$			5.60629i			0.321543i
$305$	−4.14285	+	2.39188i	−0.237219	+	0.136958i
$306$		0			0
$307$		−	2.35488i		−	0.134400i	−0.997740	−	0.0672001i	$-0.978593\pi$
$307$		−	2.35488i		−	0.134400i	0.997740	−	0.0672001i	$-0.0214066\pi$
$308$		0			0
$309$		0			0
$310$	−24.1562			−1.37198
$311$	−3.92483	+	6.79801i	−0.222557	+	0.385480i	−0.955584	−	0.294720i	$-0.904774\pi$
$311$	−3.92483	+	6.79801i	−0.222557	+	0.385480i	0.733027	+	0.680200i	$0.238107\pi$
$312$		0			0
$313$	26.0268	−	15.0266i	1.47112	−	0.849352i	0.471647	−	0.881787i	$-0.343660\pi$
$313$	26.0268	−	15.0266i	1.47112	−	0.849352i	0.999474	+	0.0324349i	$0.0103262\pi$
$314$	40.6785			2.29562
$315$		0			0
$316$	49.2989			2.77328
$317$	−9.61906	+	5.55356i	−0.540260	+	0.311919i	−0.745184	−	0.666859i	$-0.767639\pi$
$317$	−9.61906	+	5.55356i	−0.540260	+	0.311919i	0.204924	+	0.978778i	$0.434305\pi$
$318$		0			0
$319$	−9.75347	+	16.8935i	−0.546089	+	0.945854i
$320$	−7.89513			−0.441351
$321$		0			0
$322$		0			0
$323$		−	3.90798i		−	0.217446i
$324$		0			0
$325$	−0.500715	+	0.289088i	−0.0277746	+	0.0160357i
$326$		−	17.4428i		−	0.966069i
$327$		0			0
$328$	38.9494	−	22.4875i	2.15062	−	1.24166i
$329$		0			0
$330$		0			0
$331$	8.63362	+	14.9539i	0.474547	+	0.821939i	0.999575	−	0.0291457i	$-0.00927866\pi$
$331$	8.63362	+	14.9539i	0.474547	+	0.821939i	−0.525028	+	0.851085i	$0.675945\pi$
$332$	−24.7426	−	42.8554i	−1.35792	−	2.35199i
$333$		0			0
$334$	−42.6297	−	24.6123i	−2.33259	−	1.34672i
$335$	5.62495	−	9.74270i	0.307324	−	0.532300i
$336$		0			0
$337$	−3.82962	−	6.63309i	−0.208612	−	0.361327i	0.742665	−	0.669663i	$-0.233561\pi$
$337$	−3.82962	−	6.63309i	−0.208612	−	0.361327i	−0.951278	+	0.308336i	$0.900228\pi$
$338$			29.0182i			1.57838i
$339$		0			0
$340$	62.7059			3.40071
$341$	−8.77137	+	15.1925i	−0.474996	+	0.822717i
$342$		0			0
$343$		0			0
$344$	−46.0082	−	26.5629i	−2.48060	−	1.43217i
$345$		0			0
$346$	48.7843	+	28.1656i	2.62266	+	1.51419i
$347$	−11.4014	−	6.58262i	−0.612061	−	0.353374i	0.161711	−	0.986838i	$-0.448299\pi$
$347$	−11.4014	−	6.58262i	−0.612061	−	0.353374i	−0.773772	+	0.633465i	$0.781632\pi$
$348$		0			0
$349$	−1.05185	−	0.607283i	−0.0563040	−	0.0325071i	0.471584	−	0.881821i	$-0.343682\pi$
$349$	−1.05185	−	0.607283i	−0.0563040	−	0.0325071i	−0.527888	+	0.849314i	$0.677016\pi$
$350$		0			0
$351$		0			0
$352$	−16.9246	+	29.3143i	−0.902087	+	1.56246i
$353$	−26.8228			−1.42763			−0.713816	−	0.700333i	$-0.753035\pi$
$353$	−26.8228			−1.42763			−0.713816	+	0.700333i	$0.753035\pi$
$354$		0			0
$355$			2.73146i			0.144971i
$356$	−7.72659	−	13.3829i	−0.409509	−	0.709290i
$357$		0			0
$358$	22.1591	−	38.3807i	1.17114	−	2.02848i
$359$	−6.45209	−	3.72512i	−0.340529	−	0.196604i	0.319977	−	0.947425i	$-0.396325\pi$
$359$	−6.45209	−	3.72512i	−0.340529	−	0.196604i	−0.660506	+	0.750821i	$0.729658\pi$
$360$		0			0
$361$	−9.27195	−	16.0595i	−0.487997	−	0.845236i
$362$	−21.4585	−	37.1673i	−1.12784	−	1.95347i
$363$		0			0
$364$		0			0
$365$	−30.5250	+	17.6236i	−1.59775	+	0.922463i
$366$		0			0
$367$		−	34.9875i		−	1.82633i	−0.407588	−	0.913166i	$-0.633630\pi$
$367$		−	34.9875i		−	1.82633i	0.407588	−	0.913166i	$-0.366370\pi$
$368$	39.9952	−	23.0913i	2.08490	−	1.20371i
$369$		0			0
$370$			18.1359i			0.942840i
$371$		0			0
$372$		0			0
$373$	−30.0990			−1.55847			−0.779233	−	0.626734i	$-0.784391\pi$
$373$	−30.0990			−1.55847			−0.779233	+	0.626734i	$0.784391\pi$
$374$	32.5684	−	56.4102i	1.68407	−	2.91690i
$375$		0			0
$376$	−2.91623	+	1.68369i	−0.150393	+	0.0868295i
$377$	5.90152			0.303944
$378$		0			0
$379$	−27.0996			−1.39201			−0.696006	−	0.718036i	$-0.745041\pi$
$379$	−27.0996			−1.39201			−0.696006	+	0.718036i	$0.745041\pi$
$380$	−6.33801	+	3.65925i	−0.325133	+	0.187716i
$381$		0			0
$382$	1.22990	−	2.13024i	0.0629270	−	0.108993i
$383$	3.66030			0.187033			0.0935164	−	0.995618i	$-0.470189\pi$
$383$	3.66030			0.187033			0.0935164	+	0.995618i	$0.470189\pi$
$384$		0			0
$385$		0			0
$386$		−	4.36851i		−	0.222351i
$387$		0			0
$388$	−59.2646	+	34.2164i	−3.00870	+	1.73708i
$389$			12.1690i			0.616992i	0.951226	+	0.308496i	$0.0998257\pi$
$389$			12.1690i			0.616992i	−0.951226	+	0.308496i	$0.900174\pi$
$390$		0			0
$391$	−27.8795	+	16.0962i	−1.40993	+	0.814022i
$392$		0			0
$393$		0			0
$394$	−16.4342	−	28.4649i	−0.827943	−	1.43404i
$395$	12.3690	+	21.4237i	0.622352	+	1.07795i
$396$		0			0
$397$	−23.1870	−	13.3870i	−1.16372	−	0.671876i	−0.211530	−	0.977371i	$-0.567845\pi$
$397$	−23.1870	−	13.3870i	−1.16372	−	0.671876i	−0.952194	+	0.305495i	$0.901178\pi$
$398$	−5.61797	+	9.73061i	−0.281603	+	0.487752i
$399$		0			0
$400$	−1.81679	−	3.14678i	−0.0908397	−	0.157339i
$401$		−	7.72989i		−	0.386012i	−0.981198	−	0.193006i	$-0.938176\pi$
$401$		−	7.72989i		−	0.386012i	0.981198	−	0.193006i	$-0.0618237\pi$
$402$		0			0
$403$	5.30728			0.264374
$404$	−3.86680	+	6.69750i	−0.192381	+	0.333213i
$405$		0			0
$406$		0			0
$407$	11.4061	+	6.58532i	0.565380	+	0.326422i
$408$		0			0
$409$	7.84660	+	4.53024i	0.387989	+	0.224006i	0.681289	−	0.732015i	$-0.261420\pi$
$409$	7.84660	+	4.53024i	0.387989	+	0.224006i	−0.293299	+	0.956021i	$0.594753\pi$
$410$	34.3116	+	19.8098i	1.69453	+	0.978338i
$411$		0			0
$412$	6.54231	+	3.77720i	0.322316	+	0.186090i
$413$		0			0
$414$		0			0
$415$	12.4157	−	21.5047i	0.609464	−	1.05562i
$416$	10.2406			0.502085
$417$		0			0
$418$			7.60223i			0.371837i
$419$	3.30466	+	5.72384i	0.161443	+	0.279628i	0.935386	−	0.353627i	$-0.115052\pi$
$419$	3.30466	+	5.72384i	0.161443	+	0.279628i	−0.773943	+	0.633255i	$0.781718\pi$
$420$		0			0
$421$	6.39209	−	11.0714i	0.311531	−	0.539588i	−0.667163	−	0.744912i	$-0.732491\pi$
$421$	6.39209	−	11.0714i	0.311531	−	0.539588i	0.978694	+	0.205324i	$0.0658248\pi$
$422$	−10.0193	−	5.78464i	−0.487732	−	0.281592i
$423$		0			0
$424$	−14.1465	−	24.5024i	−0.687013	−	1.18994i
$425$	1.26643	+	2.19353i	0.0614311	+	0.106402i
$426$		0			0
$427$		0			0
$428$	73.7007	−	42.5511i	3.56246	−	2.05679i
$429$		0			0
$430$		−	46.7999i		−	2.25689i
$431$	18.9756	−	10.9556i	0.914023	−	0.527712i	0.0322998	−	0.999478i	$-0.489717\pi$
$431$	18.9756	−	10.9556i	0.914023	−	0.527712i	0.881723	+	0.471767i	$0.156384\pi$
$432$		0			0
$433$		−	8.21181i		−	0.394635i	−0.980340	−	0.197317i	$-0.936777\pi$
$433$		−	8.21181i		−	0.394635i	0.980340	−	0.197317i	$-0.0632229\pi$
$434$		0			0
$435$		0			0
$436$	74.2305			3.55500
$437$	1.87862	−	3.25386i	0.0898665	−	0.155653i
$438$		0			0
$439$	−32.7996	+	18.9368i	−1.56544	+	0.903806i	−0.568749	+	0.822511i	$0.692572\pi$
$439$	−32.7996	+	18.9368i	−1.56544	+	0.903806i	−0.996690	+	0.0812949i	$0.974094\pi$
$440$	−69.4838			−3.31251
$441$		0			0
$442$	−19.7061			−0.937326
$443$	17.7210	−	10.2312i	0.841950	−	0.486100i	−0.0159769	−	0.999872i	$-0.505086\pi$
$443$	17.7210	−	10.2312i	0.841950	−	0.486100i	0.857926	+	0.513773i	$0.171752\pi$
$444$		0			0
$445$	3.87718	−	6.71547i	0.183796	−	0.318344i
$446$	53.5882			2.53747
$447$		0			0
$448$		0			0
$449$			35.7054i			1.68504i	0.538665	+	0.842520i	$0.318929\pi$
$449$			35.7054i			1.68504i	−0.538665	+	0.842520i	$0.681071\pi$
$450$		0			0
$451$	24.9178	−	14.3863i	1.17333	−	0.677424i
$452$		−	27.2384i		−	1.28119i
$453$		0			0
$454$	63.2232	−	36.5019i	2.96721	−	1.71312i
$455$		0			0
$456$		0			0
$457$	0.127090	+	0.220126i	0.00594501	+	0.0102971i	0.868983	−	0.494843i	$-0.164774\pi$
$457$	0.127090	+	0.220126i	0.00594501	+	0.0102971i	−0.863038	+	0.505140i	$0.831441\pi$
$458$	28.0839	+	48.6428i	1.31228	+	2.27293i
$459$		0			0
$460$	52.2101	+	30.1435i	2.43431	+	1.40545i
$461$	12.2175	−	21.1613i	0.569025	−	0.985581i	−0.427637	−	0.903950i	$-0.640654\pi$
$461$	12.2175	−	21.1613i	0.569025	−	0.985581i	0.996663	−	0.0816304i	$-0.0260127\pi$
$462$		0			0
$463$	0.409986	+	0.710116i	0.0190536	+	0.0330019i	0.875395	−	0.483408i	$-0.160601\pi$
$463$	0.409986	+	0.710116i	0.0190536	+	0.0330019i	−0.856341	+	0.516410i	$0.827268\pi$
$464$			37.0885i			1.72179i
$465$		0			0
$466$	−39.2749			−1.81937
$467$	−0.909625	+	1.57552i	−0.0420924	+	0.0729062i	−0.886304	−	0.463104i	$-0.846736\pi$
$467$	−0.909625	+	1.57552i	−0.0420924	+	0.0729062i	0.844212	+	0.536010i	$0.180069\pi$
$468$		0			0
$469$		0			0
$470$	−2.56899	−	1.48321i	−0.118499	−	0.0684152i
$471$		0			0
$472$	25.4972	+	14.7208i	1.17360	+	0.677581i
$473$	−29.4336	−	16.9935i	−1.35336	−	0.781363i
$474$		0			0
$475$	−0.256010	−	0.147807i	−0.0117465	−	0.00678187i
$476$		0			0
$477$		0			0
$478$	7.37004	−	12.7653i	0.337098	−	0.583871i
$479$	−1.36215			−0.0622381			−0.0311191	−	0.999516i	$-0.509907\pi$
$479$	−1.36215			−0.0622381			−0.0311191	+	0.999516i	$0.509907\pi$
$480$		0			0
$481$		−	3.98457i		−	0.181681i
$482$	5.76373	+	9.98308i	0.262531	+	0.454717i
$483$		0			0
$484$	−18.7340	+	32.4482i	−0.851544	+	1.47492i
$485$	−29.7388	−	17.1697i	−1.35037	−	0.779635i
$486$		0			0
$487$	−15.8061	−	27.3769i	−0.716241	−	1.24057i	−0.962479	−	0.271357i	$-0.912528\pi$
$487$	−15.8061	−	27.3769i	−0.716241	−	1.24057i	0.246238	−	0.969209i	$-0.420806\pi$
$488$	7.00026	+	12.1248i	0.316887	+	0.548864i
$489$		0			0
$490$		0			0
$491$	1.97415	−	1.13977i	0.0890919	−	0.0514373i	−0.454792	−	0.890598i	$-0.650286\pi$
$491$	1.97415	−	1.13977i	0.0890919	−	0.0514373i	0.543884	+	0.839160i	$0.316953\pi$
$492$		0			0
$493$		−	25.8533i		−	1.16438i
$494$	1.99180	−	1.14997i	0.0896154	−	0.0517395i
$495$		0			0
$496$			33.3540i			1.49764i
$497$		0			0
$498$		0			0
$499$	27.0390			1.21043			0.605215	−	0.796062i	$-0.293087\pi$
$499$	27.0390			1.21043			0.605215	+	0.796062i	$0.293087\pi$
$500$	−24.7196	+	42.8156i	−1.10549	+	1.91477i
$501$		0			0
$502$	25.9595	−	14.9877i	1.15863	−	0.668936i
$503$	0.276948			0.0123485			0.00617426	−	0.999981i	$-0.498035\pi$
$503$	0.276948			0.0123485			0.00617426	+	0.999981i	$0.498035\pi$
$504$		0			0
$505$	−3.88070			−0.172689
$506$	54.2342	−	31.3121i	2.41100	−	1.39199i
$507$		0			0
$508$	−38.5033	+	66.6897i	−1.70831	+	2.95888i
$509$	−18.4295			−0.816874			−0.408437	−	0.912786i	$-0.633926\pi$
$509$	−18.4295			−0.816874			−0.408437	+	0.912786i	$0.633926\pi$
$510$		0			0
$511$		0			0
$512$		−	48.9492i		−	2.16327i
$513$		0			0
$514$	4.69510	−	2.71072i	0.207092	−	0.119565i
$515$			3.79078i			0.167042i
$516$		0			0
$517$	−1.86565	+	1.07713i	−0.0820512	+	0.0473723i
$518$		0			0
$519$		0			0
$520$	10.5106	+	18.2049i	0.460921	+	0.798339i
$521$	−11.6264	−	20.1374i	−0.509360	−	0.882237i	−0.999941	−	0.0108420i	$-0.996549\pi$
$521$	−11.6264	−	20.1374i	−0.509360	−	0.882237i	0.490581	−	0.871395i	$-0.336785\pi$
$522$		0			0
$523$	−11.5227	−	6.65262i	−0.503852	−	0.290899i	0.226451	−	0.974023i	$-0.427288\pi$
$523$	−11.5227	−	6.65262i	−0.503852	−	0.290899i	−0.730303	+	0.683124i	$0.760621\pi$
$524$	−16.5431	+	28.6535i	−0.722689	+	1.25173i
$525$		0			0
$526$	−2.83970	−	4.91850i	−0.123817	−	0.214457i
$527$		−	23.2501i		−	1.01279i
$528$		0			0
$529$	−7.95068			−0.345682
$530$	12.4620	−	21.5848i	0.541315	−	0.937585i
$531$		0			0
$532$		0			0
$533$	−7.53848	−	4.35235i	−0.326528	−	0.188521i
$534$		0			0
$535$	36.9828	+	21.3520i	1.59890	+	0.923128i
$536$	−28.5138	−	16.4624i	−1.23161	−	0.711069i
$537$		0			0
$538$	−62.2105	−	35.9172i	−2.68208	−	1.54850i
$539$		0			0
$540$		0			0
$541$	15.0846	−	26.1273i	0.648537	−	1.12330i	−0.334935	−	0.942241i	$-0.608714\pi$
$541$	15.0846	−	26.1273i	0.648537	−	1.12330i	0.983472	−	0.181059i	$-0.0579524\pi$
$542$	29.5986			1.27137
$543$		0			0
$544$		−	44.8619i		−	1.92344i
$545$	18.6243	+	32.2582i	0.797778	+	1.38179i
$546$		0			0
$547$	−0.572061	+	0.990840i	−0.0244596	+	0.0423652i	−0.877996	−	0.478668i	$-0.841120\pi$
$547$	−0.572061	+	0.990840i	−0.0244596	+	0.0423652i	0.853537	+	0.521033i	$0.174453\pi$
$548$	−3.33002	−	1.92259i	−0.142252	−	0.0821290i
$549$		0			0
$550$	−2.46360	−	4.26708i	−0.105048	−	0.181949i
$551$	1.50869	+	2.61313i	0.0642724	+	0.111323i
$552$		0			0
$553$		0			0
$554$	−22.7744	+	13.1488i	−0.967591	+	0.558639i
$555$		0			0
$556$			64.7862i			2.74755i
$557$	−8.35388	+	4.82312i	−0.353965	+	0.204362i	−0.666430	−	0.745567i	$-0.732179\pi$
$557$	−8.35388	+	4.82312i	−0.353965	+	0.204362i	0.312465	+	0.949929i	$0.398845\pi$
$558$		0			0
$559$			10.2822i			0.434893i
$560$		0			0
$561$		0			0
$562$	−28.1365			−1.18687
$563$	−1.54395	+	2.67420i	−0.0650698	+	0.112704i	−0.896725	−	0.442588i	$-0.854060\pi$
$563$	−1.54395	+	2.67420i	−0.0650698	+	0.112704i	0.831655	+	0.555292i	$0.187394\pi$
$564$		0			0
$565$	11.8370	−	6.83407i	0.497985	−	0.287512i
$566$	−30.5940			−1.28596
$567$		0			0
$568$	7.99411			0.335425
$569$	7.30588	−	4.21805i	0.306278	−	0.176830i	−0.338982	−	0.940793i	$-0.610082\pi$
$569$	7.30588	−	4.21805i	0.306278	−	0.176830i	0.645260	+	0.763963i	$0.276749\pi$
$570$		0			0
$571$	17.0208	−	29.4808i	0.712297	−	1.23373i	−0.251696	−	0.967806i	$-0.580988\pi$
$571$	17.0208	−	29.4808i	0.712297	−	1.23373i	0.963993	−	0.265928i	$-0.0856782\pi$
$572$	26.8003			1.12058
$573$		0			0
$574$		0			0
$575$			2.43516i			0.101553i
$576$		0			0
$577$	−15.6796	+	9.05260i	−0.652749	+	0.376865i	−0.789509	−	0.613739i	$-0.789665\pi$
$577$	−15.6796	+	9.05260i	−0.652749	+	0.376865i	0.136760	+	0.990604i	$0.456331\pi$
$578$			42.4993i			1.76774i
$579$		0			0
$580$	−41.9292	+	24.2078i	−1.74102	+	1.00518i
$581$		0			0
$582$		0			0
$583$	−9.05015	−	15.6753i	−0.374819	−	0.649206i
$584$	51.5787	+	89.3370i	2.13434	+	3.69679i
$585$		0			0
$586$	−42.6467	−	24.6221i	−1.76172	−	1.01713i
$587$	−4.04900	+	7.01308i	−0.167120	+	0.289461i	−0.937406	−	0.348238i	$-0.886780\pi$
$587$	−4.04900	+	7.01308i	−0.167120	+	0.289461i	0.770286	+	0.637699i	$0.220113\pi$
$588$		0			0
$589$	1.35678	+	2.35001i	0.0559050	+	0.0968304i
$590$			25.9360i			1.06777i
$591$		0			0
$592$	25.0413			1.02919
$593$	3.33216	−	5.77148i	0.136836	−	0.237006i	−0.789462	−	0.613800i	$-0.789640\pi$
$593$	3.33216	−	5.77148i	0.136836	−	0.237006i	0.926297	+	0.376794i	$0.122973\pi$
$594$		0			0
$595$		0			0
$596$	44.0040	+	25.4057i	1.80247	+	1.04066i
$597$		0			0
$598$	−16.4077	−	9.47299i	−0.670961	−	0.387380i
$599$	−3.10562	−	1.79303i	−0.126892	−	0.0732614i	0.435210	−	0.900329i	$-0.356674\pi$
$599$	−3.10562	−	1.79303i	−0.126892	−	0.0732614i	−0.562103	+	0.827068i	$0.690007\pi$
$600$		0			0
$601$	4.86949	+	2.81140i	0.198631	+	0.114679i	0.596017	−	0.802972i	$-0.296749\pi$
$601$	4.86949	+	2.81140i	0.198631	+	0.114679i	−0.397386	+	0.917652i	$0.630083\pi$
$602$		0			0
$603$		0			0
$604$	−32.4030	+	56.1237i	−1.31846	+	2.28364i
$605$	−18.8013			−0.764381
$606$		0			0
$607$		−	2.23133i		−	0.0905669i	−0.998974	−	0.0452834i	$-0.985581\pi$
$607$		−	2.23133i		−	0.0905669i	0.998974	−	0.0452834i	$-0.0144191\pi$
$608$	2.61795	+	4.53442i	0.106172	+	0.183895i
$609$		0			0
$610$	−6.16672	+	10.6811i	−0.249683	+	0.432464i
$611$	0.564423	+	0.325870i	0.0228341	+	0.0131833i
$612$		0			0
$613$	3.41019	+	5.90662i	0.137736	+	0.238566i	0.926639	−	0.375951i	$-0.122684\pi$
$613$	3.41019	+	5.90662i	0.137736	+	0.238566i	−0.788903	+	0.614518i	$0.789351\pi$
$614$	−3.03567	−	5.25793i	−0.122510	−	0.212193i
$615$		0			0
$616$		0			0
$617$	2.35139	−	1.35757i	0.0946632	−	0.0546538i	−0.451921	−	0.892058i	$-0.649261\pi$
$617$	2.35139	−	1.35757i	0.0946632	−	0.0546538i	0.546584	+	0.837404i	$0.315928\pi$
$618$		0			0
$619$		−	26.7759i		−	1.07621i	−0.842876	−	0.538107i	$-0.819140\pi$
$619$		−	26.7759i		−	1.07621i	0.842876	−	0.538107i	$-0.180860\pi$
$620$	−37.7072	+	21.7703i	−1.51436	+	0.874316i
$621$		0			0
$622$			20.2380i			0.811469i
$623$		0			0
$624$		0			0
$625$	−26.9970			−1.07988
$626$	38.7414	−	67.1021i	1.54842	−	2.68194i
$627$		0			0
$628$	63.4980	−	36.6606i	2.53385	−	1.46292i
$629$	−17.4556			−0.696000
$630$		0			0
$631$	−11.1620			−0.444354			−0.222177	−	0.975006i	$-0.571316\pi$
$631$	−11.1620			−0.444354			−0.222177	+	0.975006i	$0.571316\pi$
$632$	62.7004	−	36.2001i	2.49409	−	1.43996i
$633$		0			0
$634$	−14.3182	+	24.7998i	−0.568647	+	0.984926i
$635$	−38.6417			−1.53345
$636$		0			0
$637$		0			0
$638$			50.2927i			1.99111i
$639$		0			0
$640$	13.6850	−	7.90105i	0.540948	−	0.312317i
$641$			44.6004i			1.76161i	0.473480	+	0.880805i	$0.342998\pi$
$641$			44.6004i			1.76161i	−0.473480	+	0.880805i	$0.657002\pi$
$642$		0			0
$643$	−23.6268	+	13.6410i	−0.931751	+	0.537947i	−0.887365	−	0.461068i	$-0.847466\pi$
$643$	−23.6268	+	13.6410i	−0.931751	+	0.537947i	−0.0443860	+	0.999014i	$0.514133\pi$
$644$		0			0
$645$		0			0
$646$	−5.03777	−	8.72568i	−0.198208	−	0.343307i
$647$	−22.4675	−	38.9148i	−0.883288	−	1.52990i	−0.847663	−	0.530534i	$-0.821991\pi$
$647$	−22.4675	−	38.9148i	−0.883288	−	1.52990i	−0.0356246	−	0.999365i	$-0.511342\pi$
$648$		0			0
$649$	16.3118	+	9.41760i	0.640293	+	0.369673i
$650$	−0.745324	+	1.29094i	−0.0292340	+	0.0506348i
$651$		0			0
$652$	−15.7200	−	27.2278i	−0.615642	−	1.06632i
$653$			27.7763i			1.08697i	0.839419	+	0.543484i	$0.182895\pi$
$653$			27.7763i			1.08697i	−0.839419	+	0.543484i	$0.817105\pi$
$654$		0			0
$655$	−16.6026			−0.648715
$656$	27.3526	−	47.3762i	1.06794	−	1.84973i
$657$		0			0
$658$		0			0
$659$	−0.801975	−	0.463021i	−0.0312405	−	0.0180367i	0.484298	−	0.874903i	$-0.339075\pi$
$659$	−0.801975	−	0.463021i	−0.0312405	−	0.0180367i	−0.515539	+	0.856866i	$0.672408\pi$
$660$		0			0
$661$	−28.3028	−	16.3406i	−1.10085	−	0.635577i	−0.164408	−	0.986392i	$-0.552571\pi$
$661$	−28.3028	−	16.3406i	−1.10085	−	0.635577i	−0.936445	+	0.350815i	$0.885905\pi$
$662$	38.5540	+	22.2592i	1.49844	+	0.865126i
$663$		0			0
$664$	−62.9373	−	36.3369i	−2.44244	−	1.41014i
$665$		0			0
$666$		0			0
$667$	12.4280	−	21.5260i	0.481215	−	0.833489i
$668$	−88.7251			−3.43288
$669$		0			0
$670$		−	29.0044i		−	1.12054i
$671$	4.47839	+	7.75681i	0.172886	+	0.299448i
$672$		0			0
$673$	−15.6947	+	27.1840i	−0.604987	+	1.04787i	0.387067	+	0.922052i	$0.373488\pi$
$673$	−15.6947	+	27.1840i	−0.604987	+	1.04787i	−0.992054	+	0.125816i	$0.959845\pi$
$674$	−17.1014	−	9.87349i	−0.658721	−	0.380313i
$675$		0			0
$676$	26.1521	+	45.2967i	1.00585	+	1.74218i
$677$	−10.7882	−	18.6858i	−0.414626	−	0.718153i	0.580763	−	0.814072i	$-0.302754\pi$
$677$	−10.7882	−	18.6858i	−0.414626	−	0.718153i	−0.995389	+	0.0959196i	$0.969421\pi$
$678$		0			0
$679$		0			0
$680$	79.7521	−	46.0449i	3.05835	−	1.76574i
$681$		0			0
$682$			45.2286i			1.73189i
$683$	−31.4015	+	18.1296i	−1.20154	+	0.693711i	−0.960898	−	0.276902i	$-0.910692\pi$
$683$	−31.4015	+	18.1296i	−1.20154	+	0.693711i	−0.240645	+	0.970613i	$0.577359\pi$
$684$		0			0
$685$		−	1.92950i		−	0.0737224i
$686$		0			0
$687$		0			0
$688$	−64.6195			−2.46360
$689$	−2.73798	+	4.74232i	−0.104309	+	0.180668i
$690$		0			0
$691$	6.16389	−	3.55872i	0.234485	−	0.135380i	−0.378154	−	0.925743i	$-0.623441\pi$
$691$	6.16389	−	3.55872i	0.234485	−	0.135380i	0.612640	+	0.790362i	$0.290108\pi$
$692$	101.535			3.85977
$693$		0			0
$694$	−33.9426			−1.28844
$695$	−28.1540	+	16.2547i	−1.06794	+	0.616577i
$696$		0			0
$697$	−19.0667	+	33.0246i	−0.722204	+	1.25089i
$698$	−3.13139			−0.118525
$699$		0			0
$700$		0			0
$701$			29.4609i			1.11272i	0.830940	+	0.556362i	$0.187803\pi$
$701$			29.4609i			1.11272i	−0.830940	+	0.556362i	$0.812197\pi$
$702$		0			0
$703$	1.76433	−	1.01863i	0.0665428	−	0.0384185i
$704$			14.7823i			0.557130i
$705$		0			0
$706$	−59.8894	+	34.5772i	−2.25397	+	1.30133i
$707$		0			0
$708$		0			0
$709$	19.0361	+	32.9715i	0.714916	+	1.23827i	0.962992	+	0.269530i	$0.0868683\pi$
$709$	19.0361	+	32.9715i	0.714916	+	1.23827i	−0.248076	+	0.968740i	$0.579798\pi$
$710$	3.52112	+	6.09875i	0.132145	+	0.228882i
$711$		0			0
$712$	−19.6540	−	11.3473i	−0.736566	−	0.425257i
$713$	11.1766	−	19.3585i	0.418568	−	0.724980i
$714$		0			0
$715$	6.72414	+	11.6466i	0.251469	+	0.435556i
$716$		−	79.8816i		−	2.98532i
$717$		0			0
$718$	−19.2082			−0.716842
$719$	19.1057	−	33.0921i	0.712523	−	1.23413i	−0.251385	−	0.967887i	$-0.580886\pi$
$719$	19.1057	−	33.0921i	0.712523	−	1.23413i	0.963907	−	0.266238i	$-0.0857807\pi$
$720$		0			0
$721$		0			0
$722$	−41.4045	−	23.9049i	−1.54091	−	0.889647i
$723$		0			0
$724$	−66.9924	−	38.6781i	−2.48975	−	1.43746i
$725$	−1.69364	−	0.977823i	−0.0629002	−	0.0363154i
$726$		0			0
$727$	17.7563	+	10.2516i	0.658546	+	0.380212i	0.791723	−	0.610881i	$-0.209184\pi$
$727$	17.7563	+	10.2516i	0.658546	+	0.380212i	−0.133177	+	0.991092i	$0.542518\pi$
$728$		0			0
$729$		0			0
$730$	−45.4372	+	78.6995i	−1.68170	+	2.91280i
$731$	45.0444			1.66603
$732$		0			0
$733$			1.03995i			0.0384116i	0.999816	+	0.0192058i	$0.00611377\pi$
$733$			1.03995i			0.0384116i	−0.999816	+	0.0192058i	$0.993886\pi$
$734$	−45.1023	−	78.1194i	−1.66475	−	2.88344i
$735$		0			0
$736$	21.5657	−	37.3528i	0.794921	−	1.37684i
$737$	−18.2416	−	10.5318i	−0.671938	−	0.387944i
$738$		0			0
$739$	−12.0805	−	20.9240i	−0.444387	−	0.769701i	0.553622	−	0.832768i	$-0.313245\pi$
$739$	−12.0805	−	20.9240i	−0.444387	−	0.769701i	−0.998009	+	0.0630670i	$0.979912\pi$
$740$	16.3446	+	28.3096i	0.600839	+	1.04068i
$741$		0			0
$742$		0			0
$743$	13.1637	−	7.60008i	0.482930	−	0.278820i	−0.238707	−	0.971092i	$-0.576723\pi$
$743$	13.1637	−	7.60008i	0.482930	−	0.278820i	0.721637	+	0.692272i	$0.243390\pi$
$744$		0			0
$745$			25.4970i			0.934138i
$746$	−67.2045	+	38.8005i	−2.46053	+	1.42059i
$747$		0			0
$748$		−	117.406i		−	4.29281i
$749$		0			0
$750$		0			0
$751$	3.04074			0.110958			0.0554791	−	0.998460i	$-0.482331\pi$
$751$	3.04074			0.110958			0.0554791	+	0.998460i	$0.482331\pi$
$752$	−2.04795	+	3.54716i	−0.0746812	+	0.129352i
$753$		0			0
$754$	13.1768	−	7.60763i	0.479871	−	0.277053i
$755$	−32.5195			−1.18350
$756$		0			0
$757$	43.3700			1.57631			0.788155	−	0.615477i	$-0.211036\pi$
$757$	43.3700			1.57631			0.788155	+	0.615477i	$0.211036\pi$
$758$	−60.5075	+	34.9340i	−2.19773	+	1.26886i
$759$		0			0
$760$	−5.37397	+	9.30799i	−0.194934	+	0.337636i
$761$	29.2638			1.06081			0.530406	−	0.847744i	$-0.322040\pi$
$761$	29.2638			1.06081			0.530406	+	0.847744i	$0.322040\pi$
$762$		0			0
$763$		0			0
$764$		−	4.43367i		−	0.160405i
$765$		0			0
$766$	8.17266	−	4.71849i	0.295290	−	0.170486i
$767$		−	5.69830i		−	0.205754i
$768$		0			0
$769$	29.6496	−	17.1182i	1.06919	−	0.617299i	0.141232	−	0.989977i	$-0.454894\pi$
$769$	29.6496	−	17.1182i	1.06919	−	0.617299i	0.927961	+	0.372678i	$0.121560\pi$
$770$		0			0
$771$		0			0
$772$	−3.93702	−	6.81912i	−0.141697	−	0.245426i
$773$	−16.9927	−	29.4322i	−0.611185	−	1.05860i	−0.991041	−	0.133558i	$-0.957360\pi$
$773$	−16.9927	−	29.4322i	−0.611185	−	1.05860i	0.379856	−	0.925046i	$-0.375974\pi$
$774$		0			0
$775$	−1.52310	−	0.879363i	−0.0547114	−	0.0315877i
$776$	−50.2502	+	87.0359i	−1.80388	+	3.12441i
$777$		0			0
$778$	15.6870	+	27.1707i	0.562406	+	0.974117i
$779$		−	4.45062i		−	0.159460i
$780$		0			0
$781$	5.11421			0.183001
$782$	−41.4993	+	71.8788i	−1.48401	+	2.57038i
$783$		0			0
$784$		0			0
$785$	31.8631	+	18.3962i	1.13724	+	0.656587i
$786$		0			0
$787$	23.8225	+	13.7539i	0.849180	+	0.490274i	0.860374	−	0.509663i	$-0.170230\pi$
$787$	23.8225	+	13.7539i	0.849180	+	0.490274i	−0.0111939	+	0.999937i	$0.503563\pi$
$788$	−51.3067	−	29.6219i	−1.82773	−	1.05524i
$789$		0			0
$790$	55.2346	+	31.8897i	1.96516	+	1.13458i
$791$		0			0
$792$		0			0
$793$	1.35487	−	2.34670i	0.0481128	−	0.0833338i
$794$	−69.0288			−2.44974
$795$		0			0
$796$			20.2523i			0.717824i
$797$	21.0873	+	36.5243i	0.746952	+	1.29376i	0.949277	+	0.314440i	$0.101817\pi$
$797$	21.0873	+	36.5243i	0.746952	+	1.29376i	−0.202326	+	0.979318i	$0.564850\pi$
$798$		0			0
$799$	1.42757	−	2.47262i	0.0505038	−	0.0874751i
$800$	−2.93888	−	1.69676i	−0.103905	−	0.0599896i
$801$		0			0
$802$	−9.96458	−	17.2592i	−0.351861	−	0.609442i
$803$	32.9974	+	57.1531i	1.16445	+	2.01689i
$804$		0			0
$805$		0			0
$806$	11.8500	−	6.84160i	0.417398	−	0.240985i
$807$		0			0
$808$			11.3576i			0.399558i
$809$	4.18377	−	2.41550i	0.147094	−	0.0849245i	−0.424647	−	0.905359i	$-0.639602\pi$
$809$	4.18377	−	2.41550i	0.147094	−	0.0849245i	0.571740	+	0.820435i	$0.306268\pi$
$810$		0			0
$811$		−	6.46035i		−	0.226853i	−0.993546	−	0.113427i	$-0.963817\pi$
$811$		−	6.46035i		−	0.226853i	0.993546	−	0.113427i	$-0.0361827\pi$
$812$		0			0
$813$		0			0
$814$	33.9565			1.19017
$815$	7.88823	−	13.6628i	0.276313	−	0.478587i
$816$		0			0
$817$	−4.55287	+	2.62860i	−0.159285	+	0.0919631i
$818$	23.3597			0.816751
$819$		0			0
$820$	71.4128			2.49384
$821$	14.5455	−	8.39783i	0.507640	−	0.293086i	−0.224223	−	0.974538i	$-0.571984\pi$
$821$	14.5455	−	8.39783i	0.507640	−	0.293086i	0.731863	+	0.681452i	$0.238651\pi$
$822$		0			0
$823$	7.51749	−	13.0207i	0.262043	−	0.453872i	−0.704741	−	0.709464i	$-0.748937\pi$
$823$	7.51749	−	13.0207i	0.262043	−	0.453872i	0.966785	+	0.255592i	$0.0822703\pi$
$824$	11.0944			0.386491
$825$		0			0
$826$		0			0
$827$		−	29.2462i		−	1.01699i	−0.861065	−	0.508495i	$-0.830202\pi$
$827$		−	29.2462i		−	1.01699i	0.861065	−	0.508495i	$-0.169798\pi$
$828$		0			0
$829$	1.30270	−	0.752115i	0.0452447	−	0.0261220i	−0.477207	−	0.878791i	$-0.658351\pi$
$829$	1.30270	−	0.752115i	0.0452447	−	0.0261220i	0.522452	+	0.852669i	$0.325017\pi$
$830$		−	64.0204i		−	2.22218i
$831$		0			0
$832$	3.87301	−	2.23608i	0.134272	−	0.0775222i
$833$		0			0
$834$		0			0
$835$	−22.2610	−	38.5571i	−0.770373	−	1.33432i
$836$	6.85135	+	11.8669i	0.236959	+	0.410425i
$837$		0			0
$838$	14.7572	+	8.52005i	0.509778	+	0.294320i
$839$	−22.9477	+	39.7466i	−0.792243	+	1.37221i	0.132331	+	0.991206i	$0.457754\pi$
$839$	−22.9477	+	39.7466i	−0.792243	+	1.37221i	−0.924575	+	0.381000i	$0.875580\pi$
$840$		0			0
$841$	−4.51923	−	7.82753i	−0.155835	−	0.269915i
$842$		−	32.9601i		−	1.13588i
$843$		0			0
$844$	−20.8531			−0.717795
$845$	−13.1230	+	22.7297i	−0.451445	+	0.781926i
$846$		0			0
$847$		0			0
$848$	−29.8035	−	17.2071i	−1.02346	−	0.590893i
$849$		0			0
$850$	5.65534	+	3.26511i	0.193977	+	0.111992i
$851$	−14.5338	−	8.39112i	−0.498214	−	0.287644i
$852$		0			0
$853$	24.3086	+	14.0346i	0.832310	+	0.480534i	0.854643	−	0.519216i	$-0.173776\pi$
$853$	24.3086	+	14.0346i	0.832310	+	0.480534i	−0.0223330	+	0.999751i	$0.507109\pi$
$854$		0			0
$855$		0			0
$856$	62.4905	−	108.237i	2.13588	−	3.69946i
$857$	17.1085			0.584416			0.292208	−	0.956355i	$-0.405610\pi$
$857$	17.1085			0.584416			0.292208	+	0.956355i	$0.405610\pi$
$858$		0			0
$859$		−	5.20765i		−	0.177683i	−0.996046	−	0.0888414i	$-0.971684\pi$
$859$		−	5.20765i		−	0.177683i	0.996046	−	0.0888414i	$-0.0283164\pi$
$860$	−42.1775	−	73.0535i	−1.43824	−	2.49110i
$861$		0			0
$862$	28.2456	−	48.9228i	0.962049	−	1.66632i
$863$	38.7134	+	22.3512i	1.31782	+	0.760844i	0.983378	−	0.181573i	$-0.0581187\pi$
$863$	38.7134	+	22.3512i	1.31782	+	0.760844i	0.334442	+	0.942416i	$0.391452\pi$
$864$		0			0
$865$	25.4749	+	44.1238i	0.866172	+	1.50025i
$866$	−10.5858	−	18.3352i	−0.359721	−	0.623055i
$867$		0			0
$868$		0			0
$869$	40.1124	−	23.1589i	1.36072	−	0.785613i
$870$		0			0
$871$			6.37246i			0.215922i
$872$	94.4096	−	54.5074i	3.19711	−	1.84585i
$873$		0			0
$874$		−	9.68688i		−	0.327664i
$875$		0			0
$876$		0			0
$877$	−5.74863			−0.194117			−0.0970587	−	0.995279i	$-0.530943\pi$
$877$	−5.74863			−0.194117			−0.0970587	+	0.995279i	$0.530943\pi$
$878$	−48.8229	+	84.5637i	−1.64769	+	2.85389i
$879$		0			0
$880$	−73.1936	+	42.2584i	−2.46736	+	1.42453i
$881$	9.98120			0.336275			0.168138	−	0.985764i	$-0.446225\pi$
$881$	9.98120			0.336275			0.168138	+	0.985764i	$0.446225\pi$
$882$		0			0
$883$	−32.0942			−1.08006			−0.540028	−	0.841647i	$-0.681586\pi$
$883$	−32.0942			−1.08006			−0.540028	+	0.841647i	$0.681586\pi$
$884$	−30.7608	+	17.7597i	−1.03460	+	0.597325i
$885$		0			0
$886$	26.3781	−	45.6881i	0.886188	−	1.53492i
$887$	−8.53623			−0.286619			−0.143309	−	0.989678i	$-0.545774\pi$
$887$	−8.53623			−0.286619			−0.143309	+	0.989678i	$0.545774\pi$
$888$		0			0
$889$		0			0
$890$		−	19.9922i		−	0.670141i
$891$		0			0
$892$	83.6498	−	48.2952i	2.80080	−	1.61704i
$893$			0.333228i			0.0111510i
$894$		0			0
$895$	34.7140	−	20.0422i	1.16036	−	0.669935i
$896$		0			0
$897$		0			0
$898$	46.0277	+	79.7223i	1.53596	+	2.66037i
$899$	8.97579	+	15.5465i	0.299359	+	0.518505i
$900$		0			0
$901$	20.7752	+	11.9945i	0.692121	+	0.399596i
$902$	37.0906	−	64.2429i	1.23498	−	2.13905i
$903$		0			0
$904$	−20.0011	−	34.6430i	−0.665228	−	1.15221i
$905$		−	38.8171i		−	1.29032i
$906$		0			0
$907$	32.0544			1.06435			0.532175	−	0.846634i	$-0.321375\pi$
$907$	32.0544			1.06435			0.532175	+	0.846634i	$0.321375\pi$
$908$	65.7932	−	113.957i	2.18342	−	3.78180i
$909$		0			0
$910$		0			0
$911$	−26.3261	−	15.1994i	−0.872221	−	0.503577i	−0.00413539	−	0.999991i	$-0.501316\pi$
$911$	−26.3261	−	15.1994i	−0.872221	−	0.503577i	−0.868086	+	0.496414i	$0.834650\pi$
$912$		0			0
$913$	−40.2640	−	23.2464i	−1.33254	−	0.769344i
$914$	0.567527	+	0.327662i	0.0187721	+	0.0108381i
$915$		0			0
$916$	87.6765	+	50.6201i	2.89691	+	1.67253i
$917$		0			0
$918$		0			0
$919$	8.72153	−	15.1061i	0.287697	−	0.498305i	−0.685563	−	0.728013i	$-0.740444\pi$
$919$	8.72153	−	15.1061i	0.287697	−	0.498305i	0.973260	+	0.229708i	$0.0737772\pi$
$920$	88.5374			2.91899
$921$		0			0
$922$		−	62.9981i		−	2.07473i
$923$	−0.773612	−	1.33994i	−0.0254637	−	0.0441045i
$924$		0			0
$925$	−0.660203	+	1.14351i	−0.0217074	+	0.0375982i
$926$	1.83082	+	1.05702i	0.0601644	+	0.0347359i
$927$		0			0
$928$	17.3191	+	29.9975i	0.568527	+	0.984717i
$929$	5.21392	+	9.03077i	0.171063	+	0.296290i	0.938792	−	0.344485i	$-0.111946\pi$
$929$	5.21392	+	9.03077i	0.171063	+	0.296290i	−0.767729	+	0.640775i	$0.778613\pi$
$930$		0			0
$931$		0			0
$932$	−61.3070	+	35.3956i	−2.00818	+	1.15942i
$933$		0			0
$934$			4.69038i			0.153474i
$935$	51.0212	−	29.4571i	1.66857	−	0.963350i
$936$		0			0
$937$			51.3201i			1.67655i	0.545245	+	0.838277i	$0.316437\pi$
$937$			51.3201i			1.67655i	−0.545245	+	0.838277i	$0.683563\pi$
$938$		0			0
$939$		0			0
$940$	−5.34683			−0.174395
$941$	24.6673	−	42.7251i	0.804133	−	1.39280i	−0.112742	−	0.993624i	$-0.535963\pi$
$941$	24.6673	−	42.7251i	0.804133	−	1.39280i	0.916875	−	0.399174i	$-0.130703\pi$
$942$		0			0
$943$	−31.7506	+	18.3312i	−1.03394	+	0.596947i
$944$	35.8114			1.16556
$945$		0			0
$946$	−87.6252			−2.84894
$947$	−38.0468	+	21.9663i	−1.23636	+	0.713810i	−0.968347	−	0.249607i	$-0.919699\pi$
$947$	−38.0468	+	21.9663i	−1.23636	+	0.713810i	−0.268008	+	0.963417i	$0.586365\pi$
$948$		0			0
$949$	9.98283	−	17.2908i	0.324056	−	0.561282i
$950$	−0.762153			−0.0247275
$951$		0			0
$952$		0			0
$953$		−	21.0833i		−	0.682956i	−0.939890	−	0.341478i	$-0.889072\pi$
$953$		−	21.0833i		−	0.682956i	0.939890	−	0.341478i	$-0.110928\pi$
$954$		0			0
$955$	1.92673	−	1.11240i	0.0623477	−	0.0359964i
$956$		−	26.5684i		−	0.859283i
$957$		0			0
$958$	−3.04138	+	1.75594i	−0.0982625	+	0.0567319i
$959$		0			0
$960$		0			0
$961$	−7.42801	−	12.8657i	−0.239613	−	0.415022i
$962$	−5.13650	−	8.89667i	−0.165607	−	0.286840i
$963$		0			0
$964$	17.9941	+	10.3889i	0.579550	+	0.334603i
$965$	1.97558	−	3.42181i	0.0635963	−	0.110152i
$966$		0			0
$967$	−27.6671	−	47.9209i	−0.889716	−	1.54103i	−0.840212	−	0.542259i	$-0.817569\pi$
$967$	−27.6671	−	47.9209i	−0.889716	−	1.54103i	−0.0495039	−	0.998774i	$-0.515764\pi$
$968$			55.0253i			1.76858i
$969$		0			0
$970$	−88.5336			−2.84264
$971$	3.41733	−	5.91898i	0.109667	−	0.189949i	−0.805968	−	0.591959i	$-0.798355\pi$
$971$	3.41733	−	5.91898i	0.109667	−	0.189949i	0.915635	+	0.402010i	$0.131688\pi$
$972$		0			0
$973$		0			0
$974$	−70.5830	−	40.7511i	−2.26162	−	1.30575i
$975$		0			0
$976$	14.7480	+	8.51477i	0.472072	+	0.272551i
$977$	31.1982	+	18.0123i	0.998118	+	0.576264i	0.907691	−	0.419639i	$-0.137843\pi$
$977$	31.1982	+	18.0123i	0.998118	+	0.576264i	0.0904272	+	0.995903i	$0.471177\pi$
$978$		0			0
$979$	−12.5736	−	7.25938i	−0.401854	−	0.232011i
$980$		0			0
$981$		0			0
$982$	2.93856	−	5.08973i	0.0937731	−	0.162420i
$983$	41.3726			1.31958			0.659791	−	0.751449i	$-0.270645\pi$
$983$	41.3726			1.31958			0.659791	+	0.751449i	$0.270645\pi$
$984$		0			0
$985$		−	29.7284i		−	0.947225i
$986$	−33.3275	−	57.7249i	−1.06136	−	1.83833i
$987$		0			0
$988$	2.07277	−	3.59014i	0.0659435	−	0.114218i
$989$	37.5048	+	21.6534i	1.19258	+	0.688539i
$990$		0			0
$991$	10.8367	+	18.7697i	0.344239	+	0.596240i	0.985215	−	0.171321i	$-0.0548036\pi$
$991$	10.8367	+	18.7697i	0.344239	+	0.596240i	−0.640976	+	0.767561i	$0.721470\pi$
$992$	15.5752	+	26.9770i	0.494512	+	0.856520i
$993$		0			0
$994$		0			0
$995$	−8.80102	+	5.08127i	−0.279011	+	0.161087i
$996$		0			0
$997$			13.7062i			0.434078i	0.976163	+	0.217039i	$0.0696399\pi$
$997$			13.7062i			0.434078i	−0.976163	+	0.217039i	$0.930360\pi$
$998$	60.3721	−	34.8559i	1.91105	−	1.10334i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.s.d.656.23		48
3.2	odd	2		441.2.s.d.362.2		48
7.2	even	3		1323.2.o.e.440.2		48
7.3	odd	6		1323.2.i.d.521.14		48
7.4	even	3		1323.2.i.d.521.2		48
7.5	odd	6		1323.2.o.e.440.1		48
7.6	odd	2	inner	1323.2.s.d.656.24		48
9.4	even	3		441.2.i.d.68.23		48
9.5	odd	6		1323.2.i.d.1097.14		48
21.2	odd	6		441.2.o.e.146.23	✓	48
21.5	even	6		441.2.o.e.146.24	yes	48
21.11	odd	6		441.2.i.d.227.2		48
21.17	even	6		441.2.i.d.227.1		48
21.20	even	2		441.2.s.d.362.1		48
63.4	even	3		441.2.s.d.374.1		48
63.5	even	6		1323.2.o.e.881.2		48
63.13	odd	6		441.2.i.d.68.24		48
63.23	odd	6		1323.2.o.e.881.1		48
63.31	odd	6		441.2.s.d.374.2		48
63.32	odd	6	inner	1323.2.s.d.962.24		48
63.40	odd	6		441.2.o.e.293.23	yes	48
63.41	even	6		1323.2.i.d.1097.2		48
63.58	even	3		441.2.o.e.293.24	yes	48
63.59	even	6	inner	1323.2.s.d.962.23		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.23		48	9.4	even	3
441.2.i.d.68.24		48	63.13	odd	6
441.2.i.d.227.1		48	21.17	even	6
441.2.i.d.227.2		48	21.11	odd	6
441.2.o.e.146.23	✓	48	21.2	odd	6
441.2.o.e.146.24	yes	48	21.5	even	6
441.2.o.e.293.23	yes	48	63.40	odd	6
441.2.o.e.293.24	yes	48	63.58	even	3
441.2.s.d.362.1		48	21.20	even	2
441.2.s.d.362.2		48	3.2	odd	2
441.2.s.d.374.1		48	63.4	even	3
441.2.s.d.374.2		48	63.31	odd	6
1323.2.i.d.521.2		48	7.4	even	3
1323.2.i.d.521.14		48	7.3	odd	6
1323.2.i.d.1097.2		48	63.41	even	6
1323.2.i.d.1097.14		48	9.5	odd	6
1323.2.o.e.440.1		48	7.5	odd	6
1323.2.o.e.440.2		48	7.2	even	3
1323.2.o.e.881.1		48	63.23	odd	6
1323.2.o.e.881.2		48	63.5	even	6
1323.2.s.d.656.23		48	1.1	even	1	trivial
1323.2.s.d.656.24		48	7.6	odd	2	inner
1323.2.s.d.962.23		48	63.59	even	6	inner
1323.2.s.d.962.24		48	63.32	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.23278 - 1.28910i) q^{2} +(2.32354 - 4.02449i) q^{4} +2.33189 q^{5} -6.82470i q^{8} +(5.20660 - 3.00603i) q^{10} -4.36608i q^{11} +(-1.14392 + 0.660445i) q^{13} +(-4.15061 - 7.18908i) q^{16} +(2.89327 + 5.01130i) q^{17} +(-0.584876 - 0.337678i) q^{19} +(5.41825 - 9.38468i) q^{20} +(-5.62830 - 9.74851i) q^{22} +5.56333i q^{23} +0.437717 q^{25} +(-1.70276 + 2.94926i) q^{26} +(-3.86926 - 2.23392i) q^{29} +(-3.47965 - 2.00898i) q^{31} +(-6.71411 - 3.87639i) q^{32} +(12.9201 + 7.45942i) q^{34} +(-1.50829 + 2.61243i) q^{37} -1.74120 q^{38} -15.9145i q^{40} +(3.29501 + 5.70713i) q^{41} +(3.89217 - 6.74143i) q^{43} +(-17.5713 - 10.1448i) q^{44} +(7.17168 + 12.4217i) q^{46} +(-0.246705 - 0.427306i) q^{47} +(0.977326 - 0.564259i) q^{50} +6.13829i q^{52} +(3.59025 - 2.07283i) q^{53} -10.1812i q^{55} -11.5189 q^{58} +(-2.15699 + 3.73602i) q^{59} +(-1.77661 + 1.02572i) q^{61} -10.3591 q^{62} -3.38572 q^{64} +(-2.66751 + 1.54009i) q^{65} +(2.41218 - 4.17802i) q^{67} +26.8906 q^{68} +1.17135i q^{71} +(-13.0902 + 7.55766i) q^{73} +7.77733i q^{74} +(-2.71797 + 1.56922i) q^{76} +(5.30428 + 9.18728i) q^{79} +(-9.67878 - 16.7641i) q^{80} +(14.7141 + 8.49518i) q^{82} +(5.32432 - 9.22199i) q^{83} +(6.74680 + 11.6858i) q^{85} -20.0695i q^{86} -29.7972 q^{88} +(1.66268 - 2.87984i) q^{89} +(22.3896 + 12.9266i) q^{92} +(-1.10168 - 0.636053i) q^{94} +(-1.36387 - 0.787429i) q^{95} +(-12.7531 - 7.36299i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4} - 24 q^{16} + 48 q^{25} + 120 q^{32} - 96 q^{44} - 48 q^{50} - 48 q^{53} - 48 q^{64} + 120 q^{65} - 24 q^{79} - 24 q^{85} + 144 q^{92} + 96 q^{95}+O(q^{100}) \) 48 * q + 24 * q^4 - 24 * q^16 + 48 * q^25 + 120 * q^32 - 96 * q^44 - 48 * q^50 - 48 * q^53 - 48 * q^64 + 120 * q^65 - 24 * q^79 - 24 * q^85 + 144 * q^92 + 96 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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