LMFDB - Embedded newform 1323.2.o.e.440.1

Newspace parameters

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

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			440.1
Character	$\chi$	$=$	1323.440
Dual form			1323.2.o.e.881.1

$q$-expansion

$f(q)$	$=$	$q+(-2.23278 - 1.28910i) q^{2} +(2.32354 + 4.02449i) q^{4} +(1.16595 + 2.01948i) q^{5} -6.82470i q^{8} +O(q^{10})$	\(q+(-2.23278 - 1.28910i) q^{2} +(2.32354 + 4.02449i) q^{4} +(1.16595 + 2.01948i) q^{5} -6.82470i q^{8} -6.01207i q^{10} +(3.78114 + 2.18304i) q^{11} +(1.14392 - 0.660445i) q^{13} +(-4.15061 + 7.18908i) q^{16} +5.78655 q^{17} -0.675357i q^{19} +(-5.41825 + 9.38468i) q^{20} +(-5.62830 - 9.74851i) q^{22} +(4.81799 - 2.78167i) q^{23} +(-0.218858 + 0.379074i) q^{25} -3.40551 q^{26} +(-3.86926 - 2.23392i) q^{29} +(-3.47965 + 2.00898i) q^{31} +(6.71411 - 3.87639i) q^{32} +(-12.9201 - 7.45942i) q^{34} +3.01658 q^{37} +(-0.870601 + 1.50792i) q^{38} +(13.7823 - 7.95723i) q^{40} +(-3.29501 - 5.70713i) q^{41} +(3.89217 - 6.74143i) q^{43} +20.2896i q^{44} -14.3434 q^{46} +(0.246705 - 0.427306i) q^{47} +(0.977326 - 0.564259i) q^{50} +(5.31591 + 3.06914i) q^{52} +4.14566i q^{53} +10.1812i q^{55} +(5.75947 + 9.97570i) q^{58} +(2.15699 + 3.73602i) q^{59} +(-1.77661 - 1.02572i) q^{61} +10.3591 q^{62} -3.38572 q^{64} +(2.66751 + 1.54009i) q^{65} +(2.41218 + 4.17802i) q^{67} +(13.4453 + 23.2879i) q^{68} +1.17135i q^{71} +15.1153i q^{73} +(-6.73536 - 3.88866i) q^{74} +(2.71797 - 1.56922i) q^{76} +(5.30428 - 9.18728i) q^{79} -19.3576 q^{80} +16.9904i q^{82} +(-5.32432 + 9.22199i) q^{83} +(6.74680 + 11.6858i) q^{85} +(-17.3807 + 10.0348i) q^{86} +(14.8986 - 25.8051i) q^{88} +3.32535 q^{89} +(22.3896 + 12.9266i) q^{92} +(-1.10168 + 0.636053i) q^{94} +(1.36387 - 0.787429i) q^{95} +(12.7531 + 7.36299i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48q + 24q^{4} + O(q^{10}) $	$ 48q + 24q^{4} + 24q^{11} - 24q^{16} + 48q^{23} - 24q^{25} - 120q^{32} - 48q^{50} - 48q^{64} - 120q^{65} + 168q^{74} - 24q^{79} - 24q^{85} - 24q^{86} + 144q^{92} - 96q^{95} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−2.23278	−	1.28910i	−1.57882	−	0.911529i	−0.995025	−	0.0996245i	$-0.968236\pi$
$2$	−2.23278	−	1.28910i	−1.57882	−	0.911529i	−0.583790	−	0.811905i	$-0.698431\pi$
$3$		0			0
$3$		0			0
$4$	2.32354	+	4.02449i	1.16177	+	2.01225i
$5$	1.16595	+	2.01948i	0.521427	+	0.903138i	0.999689	+	0.0249208i	$0.00793335\pi$
$5$	1.16595	+	2.01948i	0.521427	+	0.903138i	−0.478263	+	0.878217i	$0.658733\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	6.82470i		−	2.41290i
$9$		0			0
$10$		−	6.01207i		−	1.90118i
$11$	3.78114	+	2.18304i	1.14006	+	0.658212i	0.946444	−	0.322867i	$-0.104647\pi$
$11$	3.78114	+	2.18304i	1.14006	+	0.658212i	0.193612	+	0.981078i	$0.437980\pi$
$12$		0			0
$13$	1.14392	−	0.660445i	0.317267	−	0.183174i	−0.332906	−	0.942960i	$-0.608029\pi$
$13$	1.14392	−	0.660445i	0.317267	−	0.183174i	0.650174	+	0.759785i	$0.274696\pi$
$14$		0			0
$15$		0			0
$16$	−4.15061	+	7.18908i	−1.03765	+	1.79727i
$17$	5.78655			1.40344			0.701722	−	0.712451i	$-0.252415\pi$
$17$	5.78655			1.40344			0.701722	+	0.712451i	$0.252415\pi$
$18$		0			0
$19$		−	0.675357i		−	0.154937i	−0.996995	−	0.0774687i	$-0.975316\pi$
$19$		−	0.675357i		−	0.154937i	0.996995	−	0.0774687i	$-0.0246838\pi$
$20$	−5.41825	+	9.38468i	−1.21156	+	2.09848i
$21$		0			0
$22$	−5.62830	−	9.74851i	−1.19996	−	2.07839i
$23$	4.81799	−	2.78167i	1.00462	−	0.580018i	0.0950080	−	0.995477i	$-0.469712\pi$
$23$	4.81799	−	2.78167i	1.00462	−	0.580018i	0.909612	+	0.415459i	$0.136379\pi$
$24$		0			0
$25$	−0.218858	+	0.379074i	−0.0437717	+	0.0758147i
$26$	−3.40551			−0.667875
$27$		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	−0.778799	−	0.627273i	$-0.784171\pi$
$31$	−3.47965	+	2.00898i	−0.624964	+	0.360823i	0.153835	+	0.988097i	$0.450838\pi$
$32$	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
$37$	3.01658			0.495923			0.247961	−	0.968770i	$-0.420239\pi$
$37$	3.01658			0.495923			0.247961	+	0.968770i	$0.420239\pi$
$38$	−0.870601	+	1.50792i	−0.141230	+	0.244618i
$39$		0			0
$40$	13.7823	−	7.95723i	2.17918	−	1.25815i
$41$	−3.29501	−	5.70713i	−0.514594	−	0.891303i	−0.999857	−	0.0169348i	$-0.994609\pi$
$41$	−3.29501	−	5.70713i	−0.514594	−	0.891303i	0.485262	−	0.874369i	$-0.338724\pi$
$42$		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	$-0.0356074\pi$
$44$			20.2896i			3.05877i
$45$		0			0
$46$	−14.3434			−2.11481
$47$	0.246705	−	0.427306i	0.0359856	−	0.0623289i	−0.847472	−	0.530841i	$-0.821876\pi$
$47$	0.246705	−	0.427306i	0.0359856	−	0.0623289i	0.883457	+	0.468512i	$0.155210\pi$
$48$		0			0
$49$		0			0
$50$	0.977326	−	0.564259i	0.138215	−	0.0797983i
$51$		0			0
$52$	5.31591	+	3.06914i	0.737184	+	0.425614i
$53$			4.14566i			0.569451i	0.958609	+	0.284725i	$0.0919024\pi$
$53$			4.14566i			0.569451i	−0.958609	+	0.284725i	$0.908098\pi$
$54$		0			0
$55$			10.1812i			1.37284i
$56$		0			0
$57$		0			0
$58$	5.75947	+	9.97570i	0.756256	+	1.30987i
$59$	2.15699	+	3.73602i	0.280816	+	0.486388i	0.971586	−	0.236687i	$-0.0760615\pi$
$59$	2.15699	+	3.73602i	0.280816	+	0.486388i	−0.690770	+	0.723075i	$0.742728\pi$
$60$		0			0
$61$	−1.77661	−	1.02572i	−0.227471	−	0.131330i	0.381934	−	0.924190i	$-0.375258\pi$
$61$	−1.77661	−	1.02572i	−0.227471	−	0.131330i	−0.609405	+	0.792859i	$0.708592\pi$
$62$	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	0.974914	−	0.222582i	$-0.0714486\pi$
$67$	2.41218	+	4.17802i	0.294695	+	0.510427i	−0.680219	+	0.733009i	$0.738115\pi$
$68$	13.4453	+	23.2879i	1.63048	+	2.82408i
$69$		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
$73$			15.1153i			1.76911i	0.466432	+	0.884557i	$0.345539\pi$
$73$			15.1153i			1.76911i	−0.466432	+	0.884557i	$0.654461\pi$
$74$	−6.73536	−	3.88866i	−0.782970	−	0.452048i
$75$		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	−0.396515	−	0.918028i	$-0.629781\pi$
$79$	5.30428	−	9.18728i	0.596778	−	1.03365i	0.993293	−	0.115622i	$-0.0368861\pi$
$80$	−19.3576			−2.16424
$81$		0			0
$82$			16.9904i			1.87627i
$83$	−5.32432	+	9.22199i	−0.584420	+	1.01225i	0.410527	+	0.911848i	$0.365345\pi$
$83$	−5.32432	+	9.22199i	−0.584420	+	1.01225i	−0.994947	+	0.100397i	$0.967989\pi$
$84$		0			0
$85$	6.74680	+	11.6858i	0.731793	+	1.26750i
$86$	−17.3807	+	10.0348i	−1.87421	+	1.08208i
$87$		0			0
$88$	14.8986	−	25.8051i	1.58820	−	2.75084i
$89$	3.32535			0.352486			0.176243	−	0.984347i	$-0.443605\pi$
$89$	3.32535			0.352486			0.176243	+	0.984347i	$0.443605\pi$
$90$		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	0.979515	−	0.201373i	$-0.0645403\pi$
$97$	12.7531	+	7.36299i	1.29488	+	0.747598i	0.315363	+	0.948971i	$0.397874\pi$
$98$		0			0
$99$		0			0
$100$	−2.03411			−0.203411
$101$	−0.832092	+	1.44123i	−0.0827963	+	0.143407i	−0.904450	−	0.426580i	$-0.859718\pi$
$101$	−0.832092	+	1.44123i	−0.0827963	+	0.143407i	0.821654	+	0.569987i	$0.193052\pi$
$102$		0			0
$103$	−1.40783	+	0.812812i	−0.138718	+	0.0800887i	−0.567753	−	0.823199i	$-0.692187\pi$
$103$	−1.40783	+	0.812812i	−0.138718	+	0.0800887i	0.429035	+	0.903288i	$0.358854\pi$
$104$	−4.50734	−	7.80694i	−0.441981	−	0.765533i
$105$		0			0
$106$	5.34416	−	9.25636i	0.519071	−	0.899057i
$107$		−	18.3130i		−	1.77039i	−0.465221	−	0.885194i	$-0.654025\pi$
$107$		−	18.3130i		−	1.77039i	0.465221	−	0.885194i	$-0.345975\pi$
$108$		0			0
$109$	−15.9736			−1.52999			−0.764995	−	0.644036i	$-0.777259\pi$
$109$	−15.9736			−1.52999			−0.764995	+	0.644036i	$0.777259\pi$
$110$	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
$115$	11.2350	+	6.48654i	1.04767	+	0.604873i
$116$		−	20.7624i		−	1.92774i
$117$		0			0
$118$		−	11.1223i		−	1.02389i
$119$		0			0
$120$		0			0
$121$	4.03134	+	6.98248i	0.366485	+	0.634771i
$122$	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
$131$	−3.55989	−	6.16591i	−0.311029	−	0.538718i	0.667556	−	0.744559i	$-0.267340\pi$
$131$	−3.55989	−	6.16591i	−0.311029	−	0.538718i	−0.978585	+	0.205841i	$0.934007\pi$
$132$		0			0
$133$		0			0
$134$		−	12.4382i		−	1.07449i
$135$		0			0
$136$		−	39.4914i		−	3.38636i
$137$	0.716584	+	0.413720i	0.0612219	+	0.0353465i	0.530298	−	0.847811i	$-0.322080\pi$
$137$	0.716584	+	0.413720i	0.0612219	+	0.0353465i	−0.469077	+	0.883157i	$0.655413\pi$
$138$		0			0
$139$	12.0735	−	6.97062i	1.02406	−	0.591241i	0.108782	−	0.994066i	$-0.465305\pi$
$139$	12.0735	−	6.97062i	1.02406	−	0.591241i	0.915277	+	0.402825i	$0.131972\pi$
$140$		0			0
$141$		0			0
$142$	1.50998	−	2.61537i	0.126715	−	0.219477i
$143$	5.76711			0.482270
$144$		0			0
$145$		−	10.4185i		−	0.865210i
$146$	19.4851	−	33.7492i	1.61260	−	2.79310i
$147$		0			0
$148$	7.00915	+	12.1402i	0.576149	+	0.997919i
$149$	9.46916	−	5.46702i	0.775744	−	0.447876i	−0.0591761	−	0.998248i	$-0.518847\pi$
$149$	9.46916	−	5.46702i	0.775744	−	0.447876i	0.834920	+	0.550372i	$0.185514\pi$
$150$		0			0
$151$	6.97277	−	12.0772i	0.567436	−	0.982828i	−0.429383	−	0.903123i	$-0.641269\pi$
$151$	6.97277	−	12.0772i	0.567436	−	0.982828i	0.996818	−	0.0797050i	$-0.0253978\pi$
$152$	−4.60911			−0.373848
$153$		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	0.156798	−	0.987631i	$-0.449883\pi$
$157$	13.6641	−	7.88894i	1.09051	−	0.629606i	0.933712	+	0.358024i	$0.116550\pi$
$158$	−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
$163$	−6.76552			−0.529916			−0.264958	−	0.964260i	$-0.585358\pi$
$163$	−6.76552			−0.529916			−0.264958	+	0.964260i	$0.585358\pi$
$164$	15.3122	−	26.5215i	1.19568	−	2.07098i
$165$		0			0
$166$	23.7761	−	13.7271i	1.84538	−	1.06543i
$167$	9.54631	+	16.5347i	0.738716	+	1.27949i	0.953074	+	0.302738i	$0.0979008\pi$
$167$	9.54631	+	16.5347i	0.738716	+	1.27949i	−0.214358	+	0.976755i	$0.568766\pi$
$168$		0			0
$169$	−5.62763	+	9.74733i	−0.432894	+	0.749795i
$170$		−	34.7891i		−	2.66820i
$171$		0			0
$172$	36.1745			2.75828
$173$	−10.9246	+	18.9219i	−0.830579	+	1.43860i	0.0670016	+	0.997753i	$0.478657\pi$
$173$	−10.9246	+	18.9219i	−0.830579	+	1.43860i	−0.897580	+	0.440851i	$0.854677\pi$
$174$		0			0
$175$		0			0
$176$	−31.3881	+	18.1219i	−2.36597	+	1.36599i
$177$		0			0
$178$	−7.42478	−	4.28670i	−0.556511	−	0.321302i
$179$			17.1896i			1.28481i	0.766364	+	0.642406i	$0.222064\pi$
$179$			17.1896i			1.28481i	−0.766364	+	0.642406i	$0.777936\pi$
$180$		0			0
$181$			16.6462i			1.23730i	0.785666	+	0.618650i	$0.212320\pi$
$181$			16.6462i			1.23730i	−0.785666	+	0.618650i	$0.787680\pi$
$182$		0			0
$183$		0			0
$184$	−18.9840	−	32.8813i	−1.39952	−	2.42404i
$185$	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	$-0.344323\pi$
$191$	−0.826254	−	0.477038i	−0.0597857	−	0.0345173i	−0.529595	+	0.848251i	$0.677656\pi$
$192$		0			0
$193$	0.847203	+	1.46740i	0.0609830	+	0.105626i	0.894905	−	0.446257i	$-0.147243\pi$
$193$	0.847203	+	1.46740i	0.0609830	+	0.105626i	−0.833922	+	0.551882i	$0.813910\pi$
$194$	−18.9832	−	32.8799i	−1.36292	−	2.36064i
$195$		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
$199$			4.35807i			0.308935i	0.987998	+	0.154468i	$0.0493662\pi$
$199$			4.35807i			0.308935i	−0.987998	+	0.154468i	$0.950634\pi$
$200$	2.58706	+	1.49364i	0.182933	+	0.105616i
$201$		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
$206$	4.19117			0.292013
$207$		0			0
$208$			10.9650i			0.760287i
$209$	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	$0.882698\pi$
$212$	−16.6842	+	9.63263i	−1.14588	+	0.661571i
$213$		0			0
$214$	−23.6073	+	40.8890i	−1.61376	+	2.79512i
$215$	18.1522			1.23797
$216$		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	−0.243650	−	0.969863i	$-0.578345\pi$
$223$	−18.0005	−	10.3926i	−1.20540	−	0.695939i	−0.961751	+	0.273924i	$0.911678\pi$
$224$		0			0
$225$		0			0
$226$	−15.1118			−1.00522
$227$	14.1579	−	24.5223i	0.939696	−	1.62760i	0.173657	−	0.984806i	$-0.444442\pi$
$227$	14.1579	−	24.5223i	0.939696	−	1.62760i	0.766039	−	0.642795i	$-0.222225\pi$
$228$		0			0
$229$	−18.8670	+	10.8929i	−1.24677	+	0.719821i	−0.970463	−	0.241250i	$-0.922443\pi$
$229$	−18.8670	+	10.8929i	−1.24677	+	0.719821i	−0.276303	+	0.961071i	$0.589109\pi$
$230$	−16.7236	−	28.9661i	−1.10272	−	1.90997i
$231$		0			0
$232$	−15.2458	+	26.4065i	−1.00094	+	1.73367i
$233$			15.2335i			0.997978i	0.866608	+	0.498989i	$0.166295\pi$
$233$			15.2335i			0.997978i	−0.866608	+	0.498989i	$0.833705\pi$
$234$		0			0
$235$	1.15058			0.0750554
$236$	−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
$241$	3.87212	+	2.23557i	0.249425	+	0.144006i	0.619501	−	0.784996i	$-0.287335\pi$
$241$	3.87212	+	2.23557i	0.249425	+	0.144006i	−0.370076	+	0.929002i	$0.620668\pi$
$242$		−	20.7871i		−	1.33625i
$243$		0			0
$244$		−	9.53325i		−	0.610304i
$245$		0			0
$246$		0			0
$247$	−0.446036	−	0.772557i	−0.0283806	−	0.0491566i
$248$	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	$-0.619591\pi$
$251$	−11.6265			−0.733861			−0.366931	+	0.930248i	$0.619591\pi$
$252$		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
$257$	1.05140	+	1.82108i	0.0655846	+	0.113596i	0.896953	−	0.442126i	$-0.145775\pi$
$257$	1.05140	+	1.82108i	0.0655846	+	0.113596i	−0.831369	+	0.555721i	$0.812442\pi$
$258$		0			0
$259$		0			0
$260$			14.3138i			0.887705i
$261$		0			0
$262$			18.3562i			1.13405i
$263$	1.90773	+	1.10143i	0.117636	+	0.0679170i	0.557663	−	0.830067i	$-0.311698\pi$
$263$	1.90773	+	1.10143i	0.117636	+	0.0679170i	−0.440028	+	0.897984i	$0.645031\pi$
$264$		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
$269$	−27.8623			−1.69880			−0.849398	−	0.527753i	$-0.823035\pi$
$269$	−27.8623			−1.69880			−0.849398	+	0.527753i	$0.823035\pi$
$270$		0			0
$271$			11.4804i			0.697382i	0.937238	+	0.348691i	$0.113374\pi$
$271$			11.4804i			0.697382i	−0.937238	+	0.348691i	$0.886626\pi$
$272$	−24.0177	+	41.5999i	−1.45629	+	2.52237i
$273$		0			0
$274$	−1.06665	−	1.84749i	−0.0644387	−	0.111611i
$275$	−1.65507	+	0.955553i	−0.0998043	+	0.0576220i
$276$		0			0
$277$	5.10000	−	8.83346i	0.306429	−	0.530751i	−0.671149	−	0.741322i	$-0.734199\pi$
$277$	5.10000	−	8.83346i	0.306429	−	0.530751i	0.977579	+	0.210571i	$0.0675323\pi$
$278$	−35.9432			−2.15573
$279$		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	−0.773311	−	0.634027i	$-0.781401\pi$
$283$	−10.2766	+	5.93322i	−0.610882	+	0.352693i	0.162428	+	0.986720i	$0.448067\pi$
$284$	−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
$289$	16.4841			0.969655
$290$	−13.4305	+	23.2622i	−0.788664	+	1.36601i
$291$		0			0
$292$	−60.8315	+	35.1211i	−3.55989	+	2.05531i
$293$	9.55012	+	16.5413i	0.557924	+	0.966353i	0.997670	+	0.0682302i	$0.0217352\pi$
$293$	9.55012	+	16.5413i	0.557924	+	0.966353i	−0.439746	+	0.898122i	$0.644931\pi$
$294$		0			0
$295$	−5.02987	+	8.71199i	−0.292850	+	0.507232i
$296$		−	20.5872i		−	1.19661i
$297$		0			0
$298$	−28.1901			−1.63301
$299$	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
$304$	4.85519	+	2.80315i	0.278464	+	0.160771i
$305$		−	4.78375i		−	0.273917i
$306$		0			0
$307$			2.35488i			0.134400i	0.997740	+	0.0672001i	$0.0214066\pi$
$307$			2.35488i			0.134400i	−0.997740	+	0.0672001i	$0.978593\pi$
$308$		0			0
$309$		0			0
$310$	12.0781	+	20.9199i	0.685991	+	1.18817i
$311$	3.92483	+	6.79801i	0.222557	+	0.385480i	0.955584	−	0.294720i	$-0.0952263\pi$
$311$	3.92483	+	6.79801i	0.222557	+	0.385480i	−0.733027	+	0.680200i	$0.761893\pi$
$312$		0			0
$313$	26.0268	+	15.0266i	1.47112	+	0.849352i	0.999474	−	0.0324349i	$-0.0103262\pi$
$313$	26.0268	+	15.0266i	1.47112	+	0.849352i	0.471647	+	0.881787i	$0.343660\pi$
$314$	−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	$-0.232361\pi$
$317$	9.61906	+	5.55356i	0.540260	+	0.311919i	−0.204924	+	0.978778i	$0.565695\pi$
$318$		0			0
$319$	−9.75347	−	16.8935i	−0.546089	−	0.945854i
$320$	−3.94757	−	6.83739i	−0.220676	−	0.382222i
$321$		0			0
$322$		0			0
$323$		−	3.90798i		−	0.217446i
$324$		0			0
$325$			0.578175i			0.0320714i
$326$	15.1059	+	8.72141i	0.836640	+	0.483034i
$327$		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	−0.525028	−	0.851085i	$-0.675945\pi$
$331$	8.63362	−	14.9539i	0.474547	−	0.821939i	0.999575	+	0.0291457i	$0.00927866\pi$
$332$	−49.4851			−2.71585
$333$		0			0
$334$		−	49.2245i		−	2.69345i
$335$	−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	$0.900228\pi$
$338$	25.1305	−	14.5091i	1.36692	−	0.789192i
$339$		0			0
$340$	−31.3530	+	54.3049i	−1.70035	+	2.94510i
$341$	−17.5427			−0.949992
$342$		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	$-0.551701\pi$
$347$	11.4014	−	6.58262i	0.612061	−	0.353374i	0.773772	+	0.633465i	$0.218368\pi$
$348$		0			0
$349$	1.05185	+	0.607283i	0.0563040	+	0.0325071i	0.527888	−	0.849314i	$-0.322984\pi$
$349$	1.05185	+	0.607283i	0.0563040	+	0.0325071i	−0.471584	+	0.881821i	$0.656318\pi$
$350$		0			0
$351$		0			0
$352$	33.8493			1.80417
$353$	−13.4114	+	23.2292i	−0.713816	+	1.23637i	0.249598	+	0.968349i	$0.419701\pi$
$353$	−13.4114	+	23.2292i	−0.713816	+	1.23637i	−0.963414	+	0.268016i	$0.913632\pi$
$354$		0			0
$355$	−2.36551	+	1.36573i	−0.125548	+	0.0724854i
$356$	7.72659	+	13.3829i	0.409509	+	0.709290i
$357$		0			0
$358$	22.1591	−	38.3807i	1.17114	−	2.02848i
$359$			7.45024i			0.393208i	0.980483	+	0.196604i	$0.0629914\pi$
$359$			7.45024i			0.393208i	−0.980483	+	0.196604i	$0.937009\pi$
$360$		0			0
$361$	18.5439			0.975994
$362$	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
$367$	−30.3000	−	17.4937i	−1.58165	−	0.913166i	−0.994619	−	0.103601i	$-0.966963\pi$
$367$	−30.3000	−	17.4937i	−1.58165	−	0.913166i	−0.587031	−	0.809565i	$-0.699703\pi$
$368$			46.1825i			2.40743i
$369$		0			0
$370$		−	18.1359i		−	0.942840i
$371$		0			0
$372$		0			0
$373$	15.0495	+	26.0665i	0.779233	+	1.34967i	0.932384	+	0.361469i	$0.117725\pi$
$373$	15.0495	+	26.0665i	0.779233	+	1.34967i	−0.153151	+	0.988203i	$0.548942\pi$
$374$	−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
$383$	1.83015	+	3.16992i	0.0935164	+	0.161975i	0.908988	−	0.416821i	$-0.136856\pi$
$383$	1.83015	+	3.16992i	0.0935164	+	0.161975i	−0.815472	+	0.578796i	$0.803523\pi$
$384$		0			0
$385$		0			0
$386$		−	4.36851i		−	0.222351i
$387$		0			0
$388$			68.4329i			3.47415i
$389$	−10.5387	−	6.08449i	−0.534331	−	0.308496i	0.208447	−	0.978034i	$-0.433159\pi$
$389$	−10.5387	−	6.08449i	−0.534331	−	0.308496i	−0.742778	+	0.669537i	$0.766492\pi$
$390$		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
$395$	24.7380			1.24470
$396$		0			0
$397$		−	26.7741i		−	1.34375i	−0.740663	−	0.671876i	$-0.765489\pi$
$397$		−	26.7741i		−	1.34375i	0.740663	−	0.671876i	$-0.234511\pi$
$398$	5.61797	−	9.73061i	0.281603	−	0.487752i
$399$		0			0
$400$	−1.81679	−	3.14678i	−0.0908397	−	0.157339i
$401$	−6.69428	+	3.86494i	−0.334296	+	0.193006i	−0.657747	−	0.753239i	$-0.728490\pi$
$401$	−6.69428	+	3.86494i	−0.334296	+	0.193006i	0.323451	+	0.946245i	$0.395157\pi$
$402$		0			0
$403$	−2.65364	+	4.59624i	−0.132187	+	0.228955i
$404$	−7.73361			−0.384761
$405$		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	−0.293299	−	0.956021i	$-0.594753\pi$
$409$	7.84660	−	4.53024i	0.387989	−	0.224006i	0.681289	+	0.732015i	$0.261420\pi$
$410$	−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
$415$	−24.8315			−1.21893
$416$	5.12029	−	8.86860i	0.251043	−	0.434819i
$417$		0			0
$418$	−6.58372	+	3.80111i	−0.322020	+	0.185919i
$419$	−3.30466	−	5.72384i	−0.161443	−	0.279628i	0.773943	−	0.633255i	$-0.218282\pi$
$419$	−3.30466	−	5.72384i	−0.161443	−	0.279628i	−0.935386	+	0.353627i	$0.884948\pi$
$420$		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	$0.0658248\pi$
$422$			11.5693i			0.563184i
$423$		0			0
$424$	28.2929			1.37403
$425$	−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
$430$	−40.5299	−	23.4000i	−1.95453	−	1.12845i
$431$			21.9112i			1.05542i	0.849424	+	0.527712i	$0.176950\pi$
$431$			21.9112i			1.05542i	−0.849424	+	0.527712i	$0.823050\pi$
$432$		0			0
$433$			8.21181i			0.394635i	0.980340	+	0.197317i	$0.0632229\pi$
$433$			8.21181i			0.394635i	−0.980340	+	0.197317i	$0.936777\pi$
$434$		0			0
$435$		0			0
$436$	−37.1153	−	64.2855i	−1.77750	−	3.07872i
$437$	−1.87862	−	3.25386i	−0.0898665	−	0.155653i
$438$		0			0
$439$	−32.7996	−	18.9368i	−1.56544	−	0.903806i	−0.996690	−	0.0812949i	$-0.974094\pi$
$439$	−32.7996	−	18.9368i	−1.56544	−	0.903806i	−0.568749	−	0.822511i	$-0.692572\pi$
$440$	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	$-0.494914\pi$
$443$	−17.7210	−	10.2312i	−0.841950	−	0.486100i	−0.857926	+	0.513773i	$0.828248\pi$
$444$		0			0
$445$	3.87718	+	6.71547i	0.183796	+	0.318344i
$446$	26.7941	+	46.4087i	1.26874	+	2.19752i
$447$		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
$451$		−	28.7726i		−	1.35485i
$452$	23.5892	+	13.6192i	1.10954	+	0.640594i
$453$		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	−0.863038	−	0.505140i	$-0.831441\pi$
$457$	0.127090	−	0.220126i	0.00594501	−	0.0102971i	0.868983	+	0.494843i	$0.164774\pi$
$458$	56.1678			2.62455
$459$		0			0
$460$			60.2870i			2.81090i
$461$	−12.2175	+	21.1613i	−0.569025	+	0.985581i	0.427637	+	0.903950i	$0.359346\pi$
$461$	−12.2175	+	21.1613i	−0.569025	+	0.985581i	−0.996663	+	0.0816304i	$0.973987\pi$
$462$		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	$0.827268\pi$
$464$	32.1196	−	18.5443i	1.49112	−	0.860896i
$465$		0			0
$466$	19.6374	−	34.0130i	0.909686	−	1.57562i
$467$	−1.81925			−0.0841848			−0.0420924	−	0.999114i	$-0.513402\pi$
$467$	−1.81925			−0.0841848			−0.0420924	+	0.999114i	$0.513402\pi$
$468$		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
$478$	−14.7401			−0.674196
$479$	−0.681074	+	1.17965i	−0.0311191	+	0.0538998i	−0.881166	−	0.472808i	$-0.843240\pi$
$479$	−0.681074	+	1.17965i	−0.0311191	+	0.0538998i	0.850046	+	0.526708i	$0.176574\pi$
$480$		0			0
$481$	3.45074	−	1.99228i	0.157340	−	0.0908403i
$482$	−5.76373	−	9.98308i	−0.262531	−	0.454717i
$483$		0			0
$484$	−18.7340	+	32.4482i	−0.851544	+	1.47492i
$485$			34.3394i			1.55927i
$486$		0			0
$487$	31.6121			1.43248			0.716241	−	0.697853i	$-0.245861\pi$
$487$	31.6121			1.43248			0.716241	+	0.697853i	$0.245861\pi$
$488$	−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
$493$	−22.3897	−	12.9267i	−1.00838	−	0.582188i
$494$			2.29993i			0.103479i
$495$		0			0
$496$		−	33.3540i		−	1.49764i
$497$		0			0
$498$		0			0
$499$	−13.5195	−	23.4164i	−0.605215	−	1.04826i	−0.992017	−	0.126101i	$-0.959754\pi$
$499$	−13.5195	−	23.4164i	−0.605215	−	1.04826i	0.386802	−	0.922163i	$-0.373580\pi$
$500$	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	$-0.501965\pi$
$503$	−0.276948			−0.0123485			−0.00617426	+	0.999981i	$0.501965\pi$
$504$		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
$509$	−9.21476	−	15.9604i	−0.408437	−	0.707434i	0.586278	−	0.810110i	$-0.300593\pi$
$509$	−9.21476	−	15.9604i	−0.408437	−	0.707434i	−0.994715	+	0.102676i	$0.967259\pi$
$510$		0			0
$511$		0			0
$512$		−	48.9492i		−	2.16327i
$513$		0			0
$514$		−	5.42143i		−	0.239129i
$515$	−3.28291	−	1.89539i	−0.144662	−	0.0835208i
$516$		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
$521$	−23.2527			−1.01872			−0.509360	−	0.860554i	$-0.670118\pi$
$521$	−23.2527			−1.01872			−0.509360	+	0.860554i	$0.670118\pi$
$522$		0			0
$523$		−	13.3052i		−	0.581798i	−0.956754	−	0.290899i	$-0.906046\pi$
$523$		−	13.3052i		−	0.581798i	0.956754	−	0.290899i	$-0.0939543\pi$
$524$	16.5431	−	28.6535i	0.722689	−	1.25173i
$525$		0			0
$526$	−2.83970	−	4.91850i	−0.123817	−	0.214457i
$527$	−20.1352	+	11.6251i	−0.877102	+	0.506395i
$528$		0			0
$529$	3.97534	−	6.88549i	0.172841	−	0.299369i
$530$	24.9240			1.08263
$531$		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
$541$	−30.1692			−1.29707			−0.648537	−	0.761183i	$-0.724619\pi$
$541$	−30.1692			−1.29707			−0.648537	+	0.761183i	$0.724619\pi$
$542$	14.7993	−	25.6331i	0.635684	−	1.10104i
$543$		0			0
$544$	38.8515	−	22.4309i	1.66574	−	0.961718i
$545$	−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	$0.174453\pi$
$548$			3.84518i			0.164258i
$549$		0			0
$550$	4.92720			0.210097
$551$	−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
$556$	56.1065	+	32.3931i	2.37944	+	1.37377i
$557$		−	9.64623i		−	0.408724i	−0.978895	−	0.204362i	$-0.934488\pi$
$557$		−	9.64623i		−	0.408724i	0.978895	−	0.204362i	$-0.0655120\pi$
$558$		0			0
$559$		−	10.2822i		−	0.434893i
$560$		0			0
$561$		0			0
$562$	14.0683	+	24.3669i	0.593434	+	1.02786i
$563$	1.54395	+	2.67420i	0.0650698	+	0.112704i	0.896725	−	0.442588i	$-0.145940\pi$
$563$	1.54395	+	2.67420i	0.0650698	+	0.112704i	−0.831655	+	0.555292i	$0.812606\pi$
$564$		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	$-0.389918\pi$
$569$	−7.30588	−	4.21805i	−0.306278	−	0.176830i	−0.645260	+	0.763963i	$0.723251\pi$
$570$		0			0
$571$	17.0208	+	29.4808i	0.712297	+	1.23373i	0.963993	+	0.265928i	$0.0856782\pi$
$571$	17.0208	+	29.4808i	0.712297	+	1.23373i	−0.251696	+	0.967806i	$0.580988\pi$
$572$	13.4001	+	23.2097i	0.560288	+	0.970447i
$573$		0			0
$574$		0			0
$575$			2.43516i			0.101553i
$576$		0			0
$577$			18.1052i			0.753730i	0.926268	+	0.376865i	$0.122998\pi$
$577$			18.1052i			0.753730i	−0.926268	+	0.376865i	$0.877002\pi$
$578$	−36.8055	−	21.2497i	−1.53091	−	0.883869i
$579$		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
$584$	103.157			4.26869
$585$		0			0
$586$		−	49.2441i		−	2.03426i
$587$	4.04900	−	7.01308i	0.167120	−	0.289461i	−0.770286	−	0.637699i	$-0.779887\pi$
$587$	4.04900	−	7.01308i	0.167120	−	0.289461i	0.937406	+	0.348238i	$0.113220\pi$
$588$		0			0
$589$	1.35678	+	2.35001i	0.0559050	+	0.0968304i
$590$	22.4612	−	12.9680i	0.924713	−	0.533883i
$591$		0			0
$592$	−12.5207	+	21.6864i	−0.514596	+	0.891306i
$593$	6.66433			0.273671			0.136836	−	0.990594i	$-0.456307\pi$
$593$	6.66433			0.273671			0.136836	+	0.990594i	$0.456307\pi$
$594$		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	$-0.643326\pi$
$599$	3.10562	−	1.79303i	0.126892	−	0.0732614i	0.562103	+	0.827068i	$0.309993\pi$
$600$		0			0
$601$	−4.86949	−	2.81140i	−0.198631	−	0.114679i	0.397386	−	0.917652i	$-0.369917\pi$
$601$	−4.86949	−	2.81140i	−0.198631	−	0.114679i	−0.596017	+	0.802972i	$0.703251\pi$
$602$		0			0
$603$		0			0
$604$	64.8061			2.63692
$605$	−9.40064	+	16.2824i	−0.382190	+	0.661973i
$606$		0			0
$607$	1.93239	−	1.11566i	0.0784332	−	0.0452834i	−0.460270	−	0.887779i	$-0.652248\pi$
$607$	1.93239	−	1.11566i	0.0784332	−	0.0452834i	0.538704	+	0.842495i	$0.318914\pi$
$608$	−2.61795	−	4.53442i	−0.106172	−	0.183895i
$609$		0			0
$610$	−6.16672	+	10.6811i	−0.249683	+	0.432464i
$611$		−	0.651740i		−	0.0263666i
$612$		0			0
$613$	−6.82038			−0.275473			−0.137736	−	0.990469i	$-0.543983\pi$
$613$	−6.82038			−0.275473			−0.137736	+	0.990469i	$0.543983\pi$
$614$	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
$619$	−23.1886	−	13.3880i	−0.932029	−	0.538107i	−0.0445762	−	0.999006i	$-0.514194\pi$
$619$	−23.1886	−	13.3880i	−0.932029	−	0.538107i	−0.887453	+	0.460899i	$0.847527\pi$
$620$		−	43.5406i		−	1.74863i
$621$		0			0
$622$		−	20.2380i		−	0.811469i
$623$		0			0
$624$		0			0
$625$	13.4985	+	23.3801i	0.539940	+	0.935203i
$626$	−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
$635$	−19.3208	−	33.4647i	−0.766724	−	1.32801i
$636$		0			0
$637$		0			0
$638$			50.2927i			1.99111i
$639$		0			0
$640$		−	15.8021i		−	0.624633i
$641$	−38.6251	−	22.3002i	−1.52560	−	0.880805i	−0.999539	−	0.0303565i	$-0.990336\pi$
$641$	−38.6251	−	22.3002i	−1.52560	−	0.880805i	−0.526059	−	0.850448i	$-0.676331\pi$
$642$		0			0
$643$	23.6268	−	13.6410i	0.931751	−	0.537947i	0.0443860	−	0.999014i	$-0.485867\pi$
$643$	23.6268	−	13.6410i	0.931751	−	0.537947i	0.887365	+	0.461068i	$0.152534\pi$
$644$		0			0
$645$		0			0
$646$	−5.03777	+	8.72568i	−0.198208	+	0.343307i
$647$	−44.9350			−1.76658			−0.883288	−	0.468831i	$-0.844675\pi$
$647$	−44.9350			−1.76658			−0.883288	+	0.468831i	$0.844675\pi$
$648$		0			0
$649$			18.8352i			0.739347i
$650$	0.745324	−	1.29094i	0.0292340	−	0.0506348i
$651$		0			0
$652$	−15.7200	−	27.2278i	−0.615642	−	1.06632i
$653$	24.0549	−	13.8881i	0.941343	−	0.543484i	0.0509617	−	0.998701i	$-0.483771\pi$
$653$	24.0549	−	13.8881i	0.941343	−	0.543484i	0.890381	+	0.455216i	$0.150438\pi$
$654$		0			0
$655$	8.30128	−	14.3782i	0.324358	−	0.561804i
$656$	54.7053			2.13588
$657$		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	−0.936445	−	0.350815i	$-0.885905\pi$
$661$	−28.3028	+	16.3406i	−1.10085	+	0.635577i	−0.164408	+	0.986392i	$0.552571\pi$
$662$	−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
$667$	−24.8561			−0.962430
$668$	−44.3625	+	76.8382i	−1.71644	+	2.97296i
$669$		0			0
$670$	25.1186	−	14.5022i	0.970415	−	0.560269i
$671$	−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	$0.959845\pi$
$674$			19.7470i			0.760625i
$675$		0			0
$676$	−52.3041			−2.01170
$677$	10.7882	−	18.6858i	0.414626	−	0.718153i	−0.580763	−	0.814072i	$-0.697246\pi$
$677$	10.7882	−	18.6858i	0.414626	−	0.718153i	0.995389	+	0.0959196i	$0.0305792\pi$
$678$		0			0
$679$		0			0
$680$	79.7521	−	46.0449i	3.05835	−	1.76574i
$681$		0			0
$682$	39.1691	+	22.6143i	1.49986	+	0.865946i
$683$		−	36.2593i		−	1.38742i	−0.720253	−	0.693711i	$-0.755974\pi$
$683$		−	36.2593i		−	1.38742i	0.720253	−	0.693711i	$-0.244026\pi$
$684$		0			0
$685$			1.92950i			0.0737224i
$686$		0			0
$687$		0			0
$688$	32.3098	+	55.9622i	1.23180	+	2.13354i
$689$	2.73798	+	4.74232i	0.104309	+	0.180668i
$690$		0			0
$691$	6.16389	+	3.55872i	0.234485	+	0.135380i	0.612640	−	0.790362i	$-0.290108\pi$
$691$	6.16389	+	3.55872i	0.234485	+	0.135380i	−0.378154	+	0.925743i	$0.623441\pi$
$692$	−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
$698$	−1.56569	−	2.71186i	−0.0592624	−	0.102645i
$699$		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
$703$		−	2.03727i		−	0.0768370i
$704$	−12.8019	−	7.39117i	−0.482489	−	0.278565i
$705$		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	−0.248076	−	0.968740i	$-0.579798\pi$
$709$	19.0361	−	32.9715i	0.714916	−	1.23827i	0.962992	−	0.269530i	$-0.0868683\pi$
$710$	7.04224			0.264290
$711$		0			0
$712$		−	22.6945i		−	0.850513i
$713$	−11.1766	+	19.3585i	−0.418568	+	0.724980i
$714$		0			0
$715$	6.72414	+	11.6466i	0.251469	+	0.435556i
$716$	−69.1795	+	39.9408i	−2.58536	+	1.49266i
$717$		0			0
$718$	9.60408	−	16.6348i	0.358421	−	0.620803i
$719$	38.2114			1.42505			0.712523	−	0.701649i	$-0.247553\pi$
$719$	38.2114			1.42505			0.712523	+	0.701649i	$0.247553\pi$
$720$		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	0.133177	−	0.991092i	$-0.457482\pi$
$727$	−17.7563	−	10.2516i	−0.658546	−	0.380212i	−0.791723	+	0.610881i	$0.790816\pi$
$728$		0			0
$729$		0			0
$730$	90.8743			3.36341
$731$	22.5222	−	39.0096i	0.833014	−	1.44282i
$732$		0			0
$733$	−0.900627	+	0.519977i	−0.0332654	+	0.0192058i	−0.516540	−	0.856263i	$-0.672780\pi$
$733$	−0.900627	+	0.519977i	−0.0332654	+	0.0192058i	0.483275	+	0.875469i	$0.339447\pi$
$734$	45.1023	+	78.1194i	1.66475	+	2.88344i
$735$		0			0
$736$	21.5657	−	37.3528i	0.794921	−	1.37684i
$737$			21.0636i			0.775887i
$738$		0			0
$739$	24.1609			0.888774			0.444387	−	0.895835i	$-0.353422\pi$
$739$	24.1609			0.888774			0.444387	+	0.895835i	$0.353422\pi$
$740$	−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
$745$	22.0810	+	12.7485i	0.808987	+	0.467069i
$746$		−	77.6010i		−	2.84118i
$747$		0			0
$748$			117.406i			4.29281i
$749$		0			0
$750$		0			0
$751$	−1.52037	−	2.63336i	−0.0554791	−	0.0960926i	0.836952	−	0.547276i	$-0.184335\pi$
$751$	−1.52037	−	2.63336i	−0.0554791	−	0.0960926i	−0.892431	+	0.451184i	$0.851002\pi$
$752$	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
$761$	14.6319	+	25.3432i	0.530406	+	0.918690i	0.999371	+	0.0354731i	$0.0112938\pi$
$761$	14.6319	+	25.3432i	0.530406	+	0.918690i	−0.468965	+	0.883217i	$0.655373\pi$
$762$		0			0
$763$		0			0
$764$		−	4.43367i		−	0.160405i
$765$		0			0
$766$		−	9.43698i		−	0.340972i
$767$	4.93487	+	2.84915i	0.178188	+	0.102877i
$768$		0			0
$769$	−29.6496	+	17.1182i	−1.06919	+	0.617299i	−0.927961	−	0.372678i	$-0.878440\pi$
$769$	−29.6496	+	17.1182i	−1.06919	+	0.617299i	−0.141232	+	0.989977i	$0.545106\pi$
$770$		0			0
$771$		0			0
$772$	−3.93702	+	6.81912i	−0.141697	+	0.245426i
$773$	−33.9854			−1.22237			−0.611185	−	0.791488i	$-0.709307\pi$
$773$	−33.9854			−1.22237			−0.611185	+	0.791488i	$0.709307\pi$
$774$		0			0
$775$		−	1.75873i		−	0.0631753i
$776$	50.2502	−	87.0359i	1.80388	−	3.12441i
$777$		0			0
$778$	15.6870	+	27.1707i	0.562406	+	0.974117i
$779$	−3.85435	+	2.22531i	−0.138096	+	0.0797299i
$780$		0			0
$781$	−2.55710	+	4.42904i	−0.0915004	+	0.158483i
$782$	−82.9985			−2.96802
$783$		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	−0.0111939	−	0.999937i	$-0.503563\pi$
$787$	23.8225	−	13.7539i	0.849180	−	0.490274i	0.860374	+	0.509663i	$0.170230\pi$
$788$	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
$793$	−2.70974			−0.0962255
$794$	−34.5144	+	59.7807i	−1.22487	+	2.12154i
$795$		0			0
$796$	−17.5390	+	10.1262i	−0.621654	+	0.358912i

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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-2.23278 - 1.28910i) q^{2} +(2.32354 + 4.02449i) q^{4} +(1.16595 + 2.01948i) q^{5} -6.82470i q^{8} +O(q^{10})\)	\(q+(-2.23278 - 1.28910i) q^{2} +(2.32354 + 4.02449i) q^{4} +(1.16595 + 2.01948i) q^{5} -6.82470i q^{8} -6.01207i q^{10} +(3.78114 + 2.18304i) q^{11} +(1.14392 - 0.660445i) q^{13} +(-4.15061 + 7.18908i) q^{16} +5.78655 q^{17} -0.675357i q^{19} +(-5.41825 + 9.38468i) q^{20} +(-5.62830 - 9.74851i) q^{22} +(4.81799 - 2.78167i) q^{23} +(-0.218858 + 0.379074i) q^{25} -3.40551 q^{26} +(-3.86926 - 2.23392i) q^{29} +(-3.47965 + 2.00898i) q^{31} +(6.71411 - 3.87639i) q^{32} +(-12.9201 - 7.45942i) q^{34} +3.01658 q^{37} +(-0.870601 + 1.50792i) q^{38} +(13.7823 - 7.95723i) q^{40} +(-3.29501 - 5.70713i) q^{41} +(3.89217 - 6.74143i) q^{43} +20.2896i q^{44} -14.3434 q^{46} +(0.246705 - 0.427306i) q^{47} +(0.977326 - 0.564259i) q^{50} +(5.31591 + 3.06914i) q^{52} +4.14566i q^{53} +10.1812i q^{55} +(5.75947 + 9.97570i) q^{58} +(2.15699 + 3.73602i) q^{59} +(-1.77661 - 1.02572i) q^{61} +10.3591 q^{62} -3.38572 q^{64} +(2.66751 + 1.54009i) q^{65} +(2.41218 + 4.17802i) q^{67} +(13.4453 + 23.2879i) q^{68} +1.17135i q^{71} +15.1153i q^{73} +(-6.73536 - 3.88866i) q^{74} +(2.71797 - 1.56922i) q^{76} +(5.30428 - 9.18728i) q^{79} -19.3576 q^{80} +16.9904i q^{82} +(-5.32432 + 9.22199i) q^{83} +(6.74680 + 11.6858i) q^{85} +(-17.3807 + 10.0348i) q^{86} +(14.8986 - 25.8051i) q^{88} +3.32535 q^{89} +(22.3896 + 12.9266i) q^{92} +(-1.10168 + 0.636053i) q^{94} +(1.36387 - 0.787429i) q^{95} +(12.7531 + 7.36299i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48q + 24q^{4} + O(q^{10}) \)	\( 48q + 24q^{4} + 24q^{11} - 24q^{16} + 48q^{23} - 24q^{25} - 120q^{32} - 48q^{50} - 48q^{64} - 120q^{65} + 168q^{74} - 24q^{79} - 24q^{85} - 24q^{86} + 144q^{92} - 96q^{95} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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