LMFDB - Embedded newform 1323.2.o.e.881.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(440,1323)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1323.440");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

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

Embedding invariants

Embedding label			881.1
Character	$\chi$	$=$	1323.881
Dual form			1323.2.o.e.440.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−2.23278	+	1.28910i	−1.57882	+	0.911529i	−0.583790	+	0.811905i	$0.698431\pi$
$2$	−2.23278	+	1.28910i	−1.57882	+	0.911529i	−0.995025	+	0.0996245i	$0.968236\pi$
$3$		0			0
$3$		0			0
$4$	2.32354	−	4.02449i	1.16177	−	2.01225i
$5$	1.16595	−	2.01948i	0.521427	−	0.903138i	−0.478263	−	0.878217i	$-0.658733\pi$
$5$	1.16595	−	2.01948i	0.521427	−	0.903138i	0.999689	−	0.0249208i	$-0.00793335\pi$
$6$		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	0.193612	−	0.981078i	$-0.437980\pi$
$11$	3.78114	−	2.18304i	1.14006	−	0.658212i	0.946444	+	0.322867i	$0.104647\pi$
$12$		0			0
$13$	1.14392	+	0.660445i	0.317267	+	0.183174i	0.650174	−	0.759785i	$-0.274696\pi$
$13$	1.14392	+	0.660445i	0.317267	+	0.183174i	−0.332906	+	0.942960i	$0.608029\pi$
$14$		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	$0.0246838\pi$
$19$			0.675357i			0.154937i	−0.996995	+	0.0774687i	$0.975316\pi$
$20$	−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	0.909612	−	0.415459i	$-0.136379\pi$
$23$	4.81799	+	2.78167i	1.00462	+	0.580018i	0.0950080	+	0.995477i	$0.469712\pi$
$24$		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	−0.814202	−	0.580582i	$-0.802825\pi$
$29$	−3.86926	+	2.23392i	−0.718503	+	0.414828i	0.0956983	+	0.995410i	$0.469492\pi$
$30$		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
$37$	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	0.485262	+	0.874369i	$0.338724\pi$
$41$	−3.29501	+	5.70713i	−0.514594	+	0.891303i	−0.999857	+	0.0169348i	$0.994609\pi$
$42$		0			0
$43$	3.89217	+	6.74143i	0.593550	+	1.02806i	0.993750	+	0.111631i	$0.0356074\pi$
$43$	3.89217	+	6.74143i	0.593550	+	1.02806i	−0.400200	+	0.916428i	$0.631059\pi$
$44$		−	20.2896i		−	3.05877i
$45$		0			0
$46$	−14.3434			−2.11481
$47$	0.246705	+	0.427306i	0.0359856	+	0.0623289i	0.883457	−	0.468512i	$-0.155210\pi$
$47$	0.246705	+	0.427306i	0.0359856	+	0.0623289i	−0.847472	+	0.530841i	$0.821876\pi$
$48$		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	$-0.908098\pi$
$53$		−	4.14566i		−	0.569451i	0.958609	−	0.284725i	$-0.0919024\pi$
$54$		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	−0.690770	−	0.723075i	$-0.742728\pi$
$59$	2.15699	−	3.73602i	0.280816	−	0.486388i	0.971586	+	0.236687i	$0.0760615\pi$
$60$		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	$0.0714486\pi$
$68$	13.4453	−	23.2879i	1.63048	−	2.82408i
$69$		0			0
$70$		0			0
$71$		−	1.17135i		−	0.139014i	−0.997581	−	0.0695068i	$-0.977857\pi$
$71$		−	1.17135i		−	0.139014i	0.997581	−	0.0695068i	$-0.0221426\pi$
$72$		0			0
$73$		−	15.1153i		−	1.76911i	−0.466432	−	0.884557i	$-0.654461\pi$
$73$		−	15.1153i		−	1.76911i	0.466432	−	0.884557i	$-0.345539\pi$
$74$	−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	0.993293	+	0.115622i	$0.0368861\pi$
$79$	5.30428	+	9.18728i	0.596778	+	1.03365i	−0.396515	+	0.918028i	$0.629781\pi$
$80$	−19.3576			−2.16424
$81$		0			0
$82$		−	16.9904i		−	1.87627i
$83$	−5.32432	−	9.22199i	−0.584420	−	1.01225i	−0.994947	−	0.100397i	$-0.967989\pi$
$83$	−5.32432	−	9.22199i	−0.584420	−	1.01225i	0.410527	−	0.911848i	$-0.365345\pi$
$84$		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	0.315363	−	0.948971i	$-0.397874\pi$
$97$	12.7531	−	7.36299i	1.29488	−	0.747598i	0.979515	+	0.201373i	$0.0645403\pi$
$98$		0			0
$99$		0			0
$100$	−2.03411			−0.203411
$101$	−0.832092	−	1.44123i	−0.0827963	−	0.143407i	0.821654	−	0.569987i	$-0.193052\pi$
$101$	−0.832092	−	1.44123i	−0.0827963	−	0.143407i	−0.904450	+	0.426580i	$0.859718\pi$
$102$		0			0
$103$	−1.40783	−	0.812812i	−0.138718	−	0.0800887i	0.429035	−	0.903288i	$-0.358854\pi$
$103$	−1.40783	−	0.812812i	−0.138718	−	0.0800887i	−0.567753	+	0.823199i	$0.692187\pi$
$104$	−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	$0.345975\pi$
$107$			18.3130i			1.77039i	−0.465221	+	0.885194i	$0.654025\pi$
$108$		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	0.719383	−	0.694614i	$-0.244425\pi$
$113$	5.07612	+	2.93070i	0.477521	+	0.275697i	−0.241862	+	0.970311i	$0.577758\pi$
$114$		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	−0.978585	−	0.205841i	$-0.934007\pi$
$131$	−3.55989	+	6.16591i	−0.311029	+	0.538718i	0.667556	+	0.744559i	$0.267340\pi$
$132$		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	−0.469077	−	0.883157i	$-0.655413\pi$
$137$	0.716584	−	0.413720i	0.0612219	−	0.0353465i	0.530298	+	0.847811i	$0.322080\pi$
$138$		0			0
$139$	12.0735	+	6.97062i	1.02406	+	0.591241i	0.915277	−	0.402825i	$-0.131972\pi$
$139$	12.0735	+	6.97062i	1.02406	+	0.591241i	0.108782	+	0.994066i	$0.465305\pi$
$140$		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	0.834920	−	0.550372i	$-0.185514\pi$
$149$	9.46916	+	5.46702i	0.775744	+	0.447876i	−0.0591761	+	0.998248i	$0.518847\pi$
$150$		0			0
$151$	6.97277	+	12.0772i	0.567436	+	0.982828i	0.996818	+	0.0797050i	$0.0253978\pi$
$151$	6.97277	+	12.0772i	0.567436	+	0.982828i	−0.429383	+	0.903123i	$0.641269\pi$
$152$	−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	0.933712	−	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
$163$	−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	−0.214358	−	0.976755i	$-0.568766\pi$
$167$	9.54631	−	16.5347i	0.738716	−	1.27949i	0.953074	−	0.302738i	$-0.0979008\pi$
$168$		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	−0.897580	−	0.440851i	$-0.854677\pi$
$173$	−10.9246	−	18.9219i	−0.830579	−	1.43860i	0.0670016	−	0.997753i	$-0.478657\pi$
$174$		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	$-0.777936\pi$
$179$		−	17.1896i		−	1.28481i	0.766364	−	0.642406i	$-0.222064\pi$
$180$		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
$184$	−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	−0.529595	−	0.848251i	$-0.677656\pi$
$191$	−0.826254	+	0.477038i	−0.0597857	+	0.0345173i	0.469809	+	0.882768i	$0.344323\pi$
$192$		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	$0.147243\pi$
$194$	−18.9832	+	32.8799i	−1.36292	+	2.36064i
$195$		0			0
$196$		0			0
$197$			12.7486i			0.908301i	0.890925	+	0.454150i	$0.150057\pi$
$197$			12.7486i			0.908301i	−0.890925	+	0.454150i	$0.849943\pi$
$198$		0			0
$199$		−	4.35807i		−	0.308935i	−0.987998	−	0.154468i	$-0.950634\pi$
$199$		−	4.35807i		−	0.308935i	0.987998	−	0.154468i	$-0.0493662\pi$
$200$	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	−0.932863	−	0.360232i	$-0.882698\pi$
$211$	−2.24368	+	3.88617i	−0.154461	+	0.267535i	0.778401	+	0.627767i	$0.216031\pi$
$212$	−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	−0.961751	−	0.273924i	$-0.911678\pi$
$223$	−18.0005	+	10.3926i	−1.20540	+	0.695939i	−0.243650	+	0.969863i	$0.578345\pi$
$224$		0			0
$225$		0			0
$226$	−15.1118			−1.00522
$227$	14.1579	+	24.5223i	0.939696	+	1.62760i	0.766039	+	0.642795i	$0.222225\pi$
$227$	14.1579	+	24.5223i	0.939696	+	1.62760i	0.173657	+	0.984806i	$0.444442\pi$
$228$		0			0
$229$	−18.8670	−	10.8929i	−1.24677	−	0.719821i	−0.276303	−	0.961071i	$-0.589109\pi$
$229$	−18.8670	−	10.8929i	−1.24677	−	0.719821i	−0.970463	+	0.241250i	$0.922443\pi$
$230$	−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	$-0.833705\pi$
$233$		−	15.2335i		−	0.997978i	0.866608	−	0.498989i	$-0.166295\pi$
$234$		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	0.651513	−	0.758638i	$-0.274135\pi$
$239$	4.95125	+	2.85861i	0.320270	+	0.184908i	−0.331243	+	0.943545i	$0.607468\pi$
$240$		0			0
$241$	3.87212	−	2.23557i	0.249425	−	0.144006i	−0.370076	−	0.929002i	$-0.620668\pi$
$241$	3.87212	−	2.23557i	0.249425	−	0.144006i	0.619501	+	0.784996i	$0.287335\pi$
$242$			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	−0.831369	−	0.555721i	$-0.812442\pi$
$257$	1.05140	−	1.82108i	0.0655846	−	0.113596i	0.896953	+	0.442126i	$0.145775\pi$
$258$		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	−0.440028	−	0.897984i	$-0.645031\pi$
$263$	1.90773	−	1.10143i	0.117636	−	0.0679170i	0.557663	+	0.830067i	$0.311698\pi$
$264$		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	$-0.886626\pi$
$271$		−	11.4804i		−	0.697382i	0.937238	−	0.348691i	$-0.113374\pi$
$272$	−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	0.977579	−	0.210571i	$-0.0675323\pi$
$277$	5.10000	+	8.83346i	0.306429	+	0.530751i	−0.671149	+	0.741322i	$0.734199\pi$
$278$	−35.9432			−2.15573
$279$		0			0
$280$		0			0
$281$	−9.45116	+	5.45663i	−0.563809	+	0.325515i	−0.754673	−	0.656101i	$-0.772204\pi$
$281$	−9.45116	+	5.45663i	−0.563809	+	0.325515i	0.190864	+	0.981617i	$0.438871\pi$
$282$		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
$289$	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	−0.439746	−	0.898122i	$-0.644931\pi$
$293$	9.55012	−	16.5413i	0.557924	−	0.966353i	0.997670	−	0.0682302i	$-0.0217352\pi$
$294$		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	$-0.978593\pi$
$307$		−	2.35488i		−	0.134400i	0.997740	−	0.0672001i	$-0.0214066\pi$
$308$		0			0
$309$		0			0
$310$	12.0781	−	20.9199i	0.685991	−	1.18817i
$311$	3.92483	−	6.79801i	0.222557	−	0.385480i	−0.733027	−	0.680200i	$-0.761893\pi$
$311$	3.92483	−	6.79801i	0.222557	−	0.385480i	0.955584	+	0.294720i	$0.0952263\pi$
$312$		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	−0.204924	−	0.978778i	$-0.565695\pi$
$317$	9.61906	−	5.55356i	0.540260	−	0.311919i	0.745184	+	0.666859i	$0.232361\pi$
$318$		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	0.999575	−	0.0291457i	$-0.00927866\pi$
$331$	8.63362	+	14.9539i	0.474547	+	0.821939i	−0.525028	+	0.851085i	$0.675945\pi$
$332$	−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	−0.951278	−	0.308336i	$-0.900228\pi$
$337$	−3.82962	+	6.63309i	−0.208612	+	0.361327i	0.742665	+	0.669663i	$0.233561\pi$
$338$	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	0.773772	−	0.633465i	$-0.218368\pi$
$347$	11.4014	+	6.58262i	0.612061	+	0.353374i	−0.161711	+	0.986838i	$0.551701\pi$
$348$		0			0
$349$	1.05185	−	0.607283i	0.0563040	−	0.0325071i	−0.471584	−	0.881821i	$-0.656318\pi$
$349$	1.05185	−	0.607283i	0.0563040	−	0.0325071i	0.527888	+	0.849314i	$0.322984\pi$
$350$		0			0
$351$		0			0
$352$	33.8493			1.80417
$353$	−13.4114	−	23.2292i	−0.713816	−	1.23637i	−0.963414	−	0.268016i	$-0.913632\pi$
$353$	−13.4114	−	23.2292i	−0.713816	−	1.23637i	0.249598	−	0.968349i	$-0.419701\pi$
$354$		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	$-0.937009\pi$
$359$		−	7.45024i		−	0.393208i	0.980483	−	0.196604i	$-0.0629914\pi$
$360$		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	−0.587031	+	0.809565i	$0.699703\pi$
$367$	−30.3000	+	17.4937i	−1.58165	+	0.913166i	−0.994619	+	0.103601i	$0.966963\pi$
$368$		−	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	−0.153151	−	0.988203i	$-0.548942\pi$
$373$	15.0495	−	26.0665i	0.779233	−	1.34967i	0.932384	−	0.361469i	$-0.117725\pi$
$374$	−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	−0.815472	−	0.578796i	$-0.803523\pi$
$383$	1.83015	−	3.16992i	0.0935164	−	0.161975i	0.908988	+	0.416821i	$0.136856\pi$
$384$		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	−0.742778	−	0.669537i	$-0.766492\pi$
$389$	−10.5387	+	6.08449i	−0.534331	+	0.308496i	0.208447	+	0.978034i	$0.433159\pi$
$390$		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	$0.234511\pi$
$397$			26.7741i			1.34375i	−0.740663	+	0.671876i	$0.765489\pi$
$398$	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	0.323451	−	0.946245i	$-0.395157\pi$
$401$	−6.69428	−	3.86494i	−0.334296	−	0.193006i	−0.657747	+	0.753239i	$0.728490\pi$
$402$		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	0.681289	−	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
$415$	−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	−0.935386	−	0.353627i	$-0.884948\pi$
$419$	−3.30466	+	5.72384i	−0.161443	+	0.279628i	0.773943	+	0.633255i	$0.218282\pi$
$420$		0			0
$421$	6.39209	+	11.0714i	0.311531	+	0.539588i	0.978694	−	0.205324i	$-0.0658248\pi$
$421$	6.39209	+	11.0714i	0.311531	+	0.539588i	−0.667163	+	0.744912i	$0.732491\pi$
$422$		−	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	$-0.823050\pi$
$431$		−	21.9112i		−	1.05542i	0.849424	−	0.527712i	$-0.176950\pi$
$432$		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
$436$	−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	−0.568749	+	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	−0.857926	−	0.513773i	$-0.828248\pi$
$443$	−17.7210	+	10.2312i	−0.841950	+	0.486100i	0.0159769	+	0.999872i	$0.494914\pi$
$444$		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	$-0.681071\pi$
$449$		−	35.7054i		−	1.68504i	0.538665	−	0.842520i	$-0.318929\pi$
$450$		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	0.868983	−	0.494843i	$-0.164774\pi$
$457$	0.127090	+	0.220126i	0.00594501	+	0.0102971i	−0.863038	+	0.505140i	$0.831441\pi$
$458$	56.1678			2.62455
$459$		0			0
$460$		−	60.2870i		−	2.81090i
$461$	−12.2175	−	21.1613i	−0.569025	−	0.985581i	−0.996663	−	0.0816304i	$-0.973987\pi$
$461$	−12.2175	−	21.1613i	−0.569025	−	0.985581i	0.427637	−	0.903950i	$-0.359346\pi$
$462$		0			0
$463$	0.409986	−	0.710116i	0.0190536	−	0.0330019i	−0.856341	−	0.516410i	$-0.827268\pi$
$463$	0.409986	−	0.710116i	0.0190536	−	0.0330019i	0.875395	+	0.483408i	$0.160601\pi$
$464$	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	0.850046	−	0.526708i	$-0.176574\pi$
$479$	−0.681074	−	1.17965i	−0.0311191	−	0.0538998i	−0.881166	+	0.472808i	$0.843240\pi$
$480$		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	0.543884	−	0.839160i	$-0.316953\pi$
$491$	1.97415	+	1.13977i	0.0890919	+	0.0514373i	−0.454792	+	0.890598i	$0.650286\pi$
$492$		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	0.386802	+	0.922163i	$0.373580\pi$
$499$	−13.5195	+	23.4164i	−0.605215	+	1.04826i	−0.992017	+	0.126101i	$0.959754\pi$
$500$	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	−0.994715	−	0.102676i	$-0.967259\pi$
$509$	−9.21476	+	15.9604i	−0.408437	+	0.707434i	0.586278	+	0.810110i	$0.300593\pi$
$510$		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	$0.0939543\pi$
$523$			13.3052i			0.581798i	−0.956754	+	0.290899i	$0.906046\pi$
$524$	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	0.853537	−	0.521033i	$-0.174453\pi$
$547$	−0.572061	−	0.990840i	−0.0244596	−	0.0423652i	−0.877996	+	0.478668i	$0.841120\pi$
$548$		−	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	$0.0655120\pi$
$557$			9.64623i			0.408724i	−0.978895	+	0.204362i	$0.934488\pi$
$558$		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	−0.831655	−	0.555292i	$-0.812606\pi$
$563$	1.54395	−	2.67420i	0.0650698	−	0.112704i	0.896725	+	0.442588i	$0.145940\pi$
$564$		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	−0.645260	−	0.763963i	$-0.723251\pi$
$569$	−7.30588	+	4.21805i	−0.306278	+	0.176830i	0.338982	+	0.940793i	$0.389918\pi$
$570$		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	$-0.0856782\pi$
$572$	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	$-0.877002\pi$
$577$		−	18.1052i		−	0.753730i	0.926268	−	0.376865i	$-0.122998\pi$
$578$	−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	0.937406	−	0.348238i	$-0.113220\pi$
$587$	4.04900	+	7.01308i	0.167120	+	0.289461i	−0.770286	+	0.637699i	$0.779887\pi$
$588$		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	0.562103	−	0.827068i	$-0.309993\pi$
$599$	3.10562	+	1.79303i	0.126892	+	0.0732614i	−0.435210	+	0.900329i	$0.643326\pi$
$600$		0			0
$601$	−4.86949	+	2.81140i	−0.198631	+	0.114679i	−0.596017	−	0.802972i	$-0.703251\pi$
$601$	−4.86949	+	2.81140i	−0.198631	+	0.114679i	0.397386	+	0.917652i	$0.369917\pi$
$602$		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	0.538704	−	0.842495i	$-0.318914\pi$
$607$	1.93239	+	1.11566i	0.0784332	+	0.0452834i	−0.460270	+	0.887779i	$0.652248\pi$
$608$	−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	0.546584	−	0.837404i	$-0.315928\pi$
$617$	2.35139	+	1.35757i	0.0946632	+	0.0546538i	−0.451921	+	0.892058i	$0.649261\pi$
$618$		0			0
$619$	−23.1886	+	13.3880i	−0.932029	+	0.538107i	−0.887453	−	0.460899i	$-0.847527\pi$
$619$	−23.1886	+	13.3880i	−0.932029	+	0.538107i	−0.0445762	+	0.999006i	$0.514194\pi$
$620$			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	−0.526059	+	0.850448i	$0.676331\pi$
$641$	−38.6251	+	22.3002i	−1.52560	+	0.880805i	−0.999539	+	0.0303565i	$0.990336\pi$
$642$		0			0
$643$	23.6268	+	13.6410i	0.931751	+	0.537947i	0.887365	−	0.461068i	$-0.152534\pi$
$643$	23.6268	+	13.6410i	0.931751	+	0.537947i	0.0443860	+	0.999014i	$0.485867\pi$
$644$		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	0.890381	−	0.455216i	$-0.150438\pi$
$653$	24.0549	+	13.8881i	0.941343	+	0.543484i	0.0509617	+	0.998701i	$0.483771\pi$
$654$		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	−0.515539	−	0.856866i	$-0.672408\pi$
$659$	−0.801975	+	0.463021i	−0.0312405	+	0.0180367i	0.484298	+	0.874903i	$0.339075\pi$
$660$		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
$667$	−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	−0.992054	−	0.125816i	$-0.959845\pi$
$673$	−15.6947	−	27.1840i	−0.604987	−	1.04787i	0.387067	−	0.922052i	$-0.373488\pi$
$674$		−	19.7470i		−	0.760625i
$675$		0			0
$676$	−52.3041			−2.01170
$677$	10.7882	+	18.6858i	0.414626	+	0.718153i	0.995389	−	0.0959196i	$-0.0305792\pi$
$677$	10.7882	+	18.6858i	0.414626	+	0.718153i	−0.580763	+	0.814072i	$0.697246\pi$
$678$		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	$0.244026\pi$
$683$			36.2593i			1.38742i	−0.720253	+	0.693711i	$0.755974\pi$
$684$		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	−0.378154	−	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
$698$	−1.56569	+	2.71186i	−0.0592624	+	0.102645i
$699$		0			0
$700$		0			0
$701$		−	29.4609i		−	1.11272i	−0.830940	−	0.556362i	$-0.812197\pi$
$701$		−	29.4609i		−	1.11272i	0.830940	−	0.556362i	$-0.187803\pi$
$702$		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	0.962992	+	0.269530i	$0.0868683\pi$
$709$	19.0361	+	32.9715i	0.714916	+	1.23827i	−0.248076	+	0.968740i	$0.579798\pi$
$710$	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	−0.791723	−	0.610881i	$-0.790816\pi$
$727$	−17.7563	+	10.2516i	−0.658546	+	0.380212i	0.133177	+	0.991092i	$0.457482\pi$
$728$		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	0.483275	−	0.875469i	$-0.339447\pi$
$733$	−0.900627	−	0.519977i	−0.0332654	−	0.0192058i	−0.516540	+	0.856263i	$0.672780\pi$
$734$	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	0.721637	−	0.692272i	$-0.243390\pi$
$743$	13.1637	+	7.60008i	0.482930	+	0.278820i	−0.238707	+	0.971092i	$0.576723\pi$
$744$		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	−0.892431	−	0.451184i	$-0.851002\pi$
$751$	−1.52037	+	2.63336i	−0.0554791	+	0.0960926i	0.836952	+	0.547276i	$0.184335\pi$
$752$	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	−0.468965	−	0.883217i	$-0.655373\pi$
$761$	14.6319	−	25.3432i	0.530406	−	0.918690i	0.999371	−	0.0354731i	$-0.0112938\pi$
$762$		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	−0.141232	−	0.989977i	$-0.545106\pi$
$769$	−29.6496	−	17.1182i	−1.06919	−	0.617299i	−0.927961	+	0.372678i	$0.878440\pi$
$770$		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	0.860374	−	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
$793$	−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
$797$	−21.0873	+	36.5243i	−0.746952	+	1.29376i	0.202326	+	0.979318i	$0.435150\pi$
$797$	−21.0873	+	36.5243i	−0.746952	+	1.29376i	−0.949277	+	0.314440i	$0.898183\pi$
$798$		0			0
$799$	1.42757	+	2.47262i	0.0505038	+	0.0874751i
$800$		−	3.39352i		−	0.119979i
$801$		0			0
$802$	19.9292			0.703723
$803$	−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
$808$	9.83594	−	5.67878i	0.346027	−	0.199779i
$809$		−	4.83100i		−	0.169849i	−0.996387	−	0.0849245i	$-0.972935\pi$
$809$		−	4.83100i		−	0.169849i	0.996387	−	0.0849245i	$-0.0270649\pi$
$810$		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
$814$	−16.9782	+	29.4071i	−0.595086	+	1.03072i
$815$	−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	−0.731863	−	0.681452i	$-0.761349\pi$
$821$	−14.5455	+	8.39783i	−0.507640	+	0.293086i	0.224223	+	0.974538i	$0.428016\pi$
$822$		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	$0.0822703\pi$
$824$	5.54719	−	9.60802i	0.193246	−	0.334711i
$825$		0			0
$826$		0			0
$827$			29.2462i			1.01699i	0.861065	+	0.508495i	$0.169798\pi$
$827$			29.2462i			1.01699i	−0.861065	+	0.508495i	$0.830202\pi$
$828$		0			0
$829$			1.50423i			0.0522440i	0.999659	+	0.0261220i	$0.00831584\pi$
$829$			1.50423i			0.0522440i	−0.999659	+	0.0261220i	$0.991684\pi$
$830$	55.4433	−	32.0102i	1.92446	−	1.11109i
$831$		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
$836$	13.7027			0.473917
$837$		0			0
$838$		−	17.0401i		−	0.588641i
$839$	22.9477	+	39.7466i	0.792243	+	1.37221i	0.924575	+	0.381000i	$0.124420\pi$
$839$	22.9477	+	39.7466i	0.792243	+	1.37221i	−0.132331	+	0.991206i	$0.542246\pi$
$840$		0			0
$841$	−4.51923	+	7.82753i	−0.155835	+	0.269915i
$842$	−28.5443	−	16.4800i	−0.983701	−	0.567940i
$843$		0			0
$844$	10.4266	+	18.0593i	0.358897	+	0.621628i
$845$	−26.2460			−0.902891
$846$		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	$-0.826224\pi$
$853$	−24.3086	+	14.0346i	−0.832310	+	0.480534i	0.0223330	+	0.999751i	$0.492891\pi$
$854$		0			0
$855$		0			0
$856$	−124.981			−4.27176
$857$	8.55426	+	14.8164i	0.292208	+	0.506119i	0.974332	−	0.225118i	$-0.0722767\pi$
$857$	8.55426	+	14.8164i	0.292208	+	0.506119i	−0.682123	+	0.731237i	$0.738943\pi$
$858$		0			0
$859$	4.50996	+	2.60383i	0.153878	+	0.0888414i	0.574962	−	0.818180i	$-0.305017\pi$
$859$	4.50996	+	2.60383i	0.153878	+	0.0888414i	−0.421084	+	0.907022i	$0.638350\pi$
$860$	42.1775	−	73.0535i	1.43824	−	2.49110i
$861$		0			0
$862$	28.2456	+	48.9228i	0.962049	+	1.66632i
$863$			44.7024i			1.52169i	0.648935	+	0.760844i	$0.275215\pi$
$863$			44.7024i			1.52169i	−0.648935	+	0.760844i	$0.724785\pi$
$864$		0			0
$865$	−50.9497			−1.73234
$866$	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
$871$	5.51871	−	3.18623i	0.186994	−	0.107961i
$872$		−	109.015i		−	3.69171i
$873$		0			0
$874$		−	9.68688i		−	0.327664i
$875$		0			0
$876$		0			0
$877$	2.87432	−	4.97846i	0.0970587	−	0.168111i	−0.813407	−	0.581695i	$-0.802390\pi$
$877$	2.87432	−	4.97846i	0.0970587	−	0.168111i	0.910466	+	0.413584i	$0.135723\pi$
$878$	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	$-0.553775\pi$
$881$	−9.98120			−0.336275			−0.168138	+	0.985764i	$0.553775\pi$
$882$		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
$887$	−4.26812	+	7.39260i	−0.143309	+	0.248219i	−0.928741	−	0.370729i	$-0.879108\pi$
$887$	−4.26812	+	7.39260i	−0.143309	+	0.248219i	0.785432	+	0.618949i	$0.212441\pi$
$888$		0			0
$889$		0			0
$890$			19.9922i			0.670141i
$891$		0			0
$892$			96.5904i			3.23409i
$893$	−0.288584	+	0.166614i	−0.00965709	+	0.00557552i
$894$		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
$899$	17.9516			0.598718
$900$		0			0
$901$		−	23.9891i		−	0.799192i
$902$	−37.0906	−	64.2429i	−1.23498	−	2.13905i
$903$		0			0
$904$	−20.0011	+	34.6430i	−0.665228	+	1.15221i
$905$	−33.6166	−	19.4085i	−1.11745	−	0.645162i
$906$		0			0
$907$	−16.0272	−	27.7599i	−0.532175	−	0.921754i	−0.999294	−	0.0375597i	$-0.988042\pi$
$907$	−16.0272	−	27.7599i	−0.532175	−	0.921754i	0.467120	−	0.884194i	$-0.345292\pi$
$908$	131.586			4.36685
$909$		0			0
$910$		0			0
$911$	−26.3261	+	15.1994i	−0.872221	+	0.503577i	−0.868086	−	0.496414i	$-0.834650\pi$
$911$	−26.3261	+	15.1994i	−0.872221	+	0.503577i	−0.00413539	+	0.999991i	$0.501316\pi$
$912$		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
$919$	−17.4431			−0.575393			−0.287697	−	0.957722i	$-0.592889\pi$
$919$	−17.4431			−0.575393			−0.287697	+	0.957722i	$0.592889\pi$
$920$	44.2687	+	76.6757i	1.45950	+	2.52792i
$921$		0			0
$922$	54.5580	+	31.4991i	1.79677	+	1.03737i
$923$	0.773612	−	1.33994i	0.0254637	−	0.0441045i
$924$		0			0
$925$	−0.660203	−	1.14351i	−0.0217074	−	0.0375982i
$926$			2.11405i			0.0694718i
$927$		0			0
$928$	−34.6382			−1.13705
$929$	−5.21392	−	9.03077i	−0.171063	−	0.296290i	0.767729	−	0.640775i	$-0.221387\pi$
$929$	−5.21392	−	9.03077i	−0.171063	−	0.296290i	−0.938792	+	0.344485i	$0.888054\pi$
$930$		0			0
$931$		0			0
$932$	−61.3070	−	35.3956i	−2.00818	−	1.15942i
$933$		0			0
$934$	4.06199	−	2.34519i	0.132912	−	0.0767369i
$935$		−	58.9142i		−	1.92670i
$936$		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
$940$	2.67342	−	4.63049i	0.0871973	−	0.151030i
$941$	−24.6673	+	42.7251i	−0.804133	+	1.39280i	0.112742	+	0.993624i	$0.464037\pi$
$941$	−24.6673	+	42.7251i	−0.804133	+	1.39280i	−0.916875	+	0.399174i	$0.869297\pi$
$942$		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	0.268008	−	0.963417i	$-0.413635\pi$
$947$	38.0468	−	21.9663i	1.23636	−	0.713810i	0.968347	+	0.249607i	$0.0803013\pi$
$948$		0			0
$949$	9.98283	−	17.2908i	0.324056	−	0.561282i
$950$	−0.381076	+	0.660044i	−0.0123637	+	0.0214146i
$951$		0			0
$952$		0			0
$953$			21.0833i			0.682956i	0.939890	+	0.341478i	$0.110928\pi$
$953$			21.0833i			0.682956i	−0.939890	+	0.341478i	$0.889072\pi$
$954$		0			0
$955$			2.22480i			0.0719929i
$956$	23.0089	−	13.2842i	0.744161	−	0.429641i
$957$		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
$962$	−10.2730			−0.331215
$963$		0			0
$964$		−	20.7778i		−	0.669207i
$965$	−1.97558	−	3.42181i	−0.0635963	−	0.110152i
$966$		0			0
$967$	−27.6671	+	47.9209i	−0.889716	+	1.54103i	−0.0495039	+	0.998774i	$0.515764\pi$
$967$	−27.6671	+	47.9209i	−0.889716	+	1.54103i	−0.840212	+	0.542259i	$0.817569\pi$
$968$	47.6533	+	27.5127i	1.53164	+	0.884290i
$969$		0			0
$970$	44.2668	+	76.6723i	1.42132	+	2.46180i
$971$	6.83465			0.219334			0.109667	−	0.993968i	$-0.465021\pi$
$971$	6.83465			0.219334			0.109667	+	0.993968i	$0.465021\pi$
$972$		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	−0.0904272	−	0.995903i	$-0.528823\pi$
$977$	−31.1982	−	18.0123i	−0.998118	−	0.576264i	−0.907691	+	0.419639i	$0.862157\pi$
$978$		0			0
$979$	12.5736	−	7.25938i	0.401854	−	0.232011i
$980$		0			0
$981$		0			0
$982$	−5.87711			−0.187546
$983$	20.6863	+	35.8298i	0.659791	+	1.14279i	0.980670	+	0.195671i	$0.0626886\pi$
$983$	20.6863	+	35.8298i	0.659791	+	1.14279i	−0.320878	+	0.947120i	$0.603978\pi$
$984$		0			0
$985$	25.7455	+	14.8642i	0.820321	+	0.473612i
$986$	33.3275	−	57.7249i	1.06136	−	1.83833i
$987$		0			0
$988$	2.07277	+	3.59014i	0.0659435	+	0.114218i
$989$			43.3068i			1.37708i
$990$		0			0
$991$	−21.6734			−0.688478			−0.344239	−	0.938882i	$-0.611863\pi$
$991$	−21.6734			−0.688478			−0.344239	+	0.938882i	$0.611863\pi$
$992$	−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
$997$	11.8699	−	6.85308i	0.375923	−	0.217039i	−0.300120	−	0.953901i	$-0.597027\pi$
$997$	11.8699	−	6.85308i	0.375923	−	0.217039i	0.676043	+	0.736862i	$0.263693\pi$
$998$		−	69.7117i		−	2.20669i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.o.e.881.1		48
3.2	odd	2		441.2.o.e.293.24	yes	48
7.2	even	3		1323.2.s.d.962.24		48
7.3	odd	6		1323.2.i.d.1097.2		48
7.4	even	3		1323.2.i.d.1097.14		48
7.5	odd	6		1323.2.s.d.962.23		48
7.6	odd	2	inner	1323.2.o.e.881.2		48
9.2	odd	6	inner	1323.2.o.e.440.2		48
9.7	even	3		441.2.o.e.146.23	✓	48
21.2	odd	6		441.2.s.d.374.1		48
21.5	even	6		441.2.s.d.374.2		48
21.11	odd	6		441.2.i.d.68.23		48
21.17	even	6		441.2.i.d.68.24		48
21.20	even	2		441.2.o.e.293.23	yes	48
63.2	odd	6		1323.2.i.d.521.2		48
63.11	odd	6		1323.2.s.d.656.23		48
63.16	even	3		441.2.i.d.227.2		48
63.20	even	6	inner	1323.2.o.e.440.1		48
63.25	even	3		441.2.s.d.362.2		48
63.34	odd	6		441.2.o.e.146.24	yes	48
63.38	even	6		1323.2.s.d.656.24		48
63.47	even	6		1323.2.i.d.521.14		48
63.52	odd	6		441.2.s.d.362.1		48
63.61	odd	6		441.2.i.d.227.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.23		48	21.11	odd	6
441.2.i.d.68.24		48	21.17	even	6
441.2.i.d.227.1		48	63.61	odd	6
441.2.i.d.227.2		48	63.16	even	3
441.2.o.e.146.23	✓	48	9.7	even	3
441.2.o.e.146.24	yes	48	63.34	odd	6
441.2.o.e.293.23	yes	48	21.20	even	2
441.2.o.e.293.24	yes	48	3.2	odd	2
441.2.s.d.362.1		48	63.52	odd	6
441.2.s.d.362.2		48	63.25	even	3
441.2.s.d.374.1		48	21.2	odd	6
441.2.s.d.374.2		48	21.5	even	6
1323.2.i.d.521.2		48	63.2	odd	6
1323.2.i.d.521.14		48	63.47	even	6
1323.2.i.d.1097.2		48	7.3	odd	6
1323.2.i.d.1097.14		48	7.4	even	3
1323.2.o.e.440.1		48	63.20	even	6	inner
1323.2.o.e.440.2		48	9.2	odd	6	inner
1323.2.o.e.881.1		48	1.1	even	1	trivial
1323.2.o.e.881.2		48	7.6	odd	2	inner
1323.2.s.d.656.23		48	63.11	odd	6
1323.2.s.d.656.24		48	63.38	even	6
1323.2.s.d.962.23		48	7.5	odd	6
1323.2.s.d.962.24		48	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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