LMFDB - Embedded newform 1323.2.i.d.521.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(521,1323)]

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, 1]))

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

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

chi := DirichletCharacter("1323.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.i (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			521.2
Character	$\chi$	$=$	1323.521
Dual form			1323.2.i.d.1097.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.57819i q^{2} -4.64709 q^{4} +(-1.16595 + 2.01948i) q^{5} -6.82470i q^{8} +O(q^{10})$	\(q+2.57819i q^{2} -4.64709 q^{4} +(-1.16595 + 2.01948i) q^{5} -6.82470i q^{8} +(-5.20660 - 3.00603i) q^{10} +(-3.78114 + 2.18304i) q^{11} +(-1.14392 + 0.660445i) q^{13} +8.30123 q^{16} +(2.89327 - 5.01130i) q^{17} +(0.584876 - 0.337678i) q^{19} +(5.41825 - 9.38468i) q^{20} +(-5.62830 - 9.74851i) q^{22} +(-4.81799 - 2.78167i) q^{23} +(-0.218858 - 0.379074i) q^{25} +(-1.70276 - 2.94926i) q^{26} +(-3.86926 - 2.23392i) q^{29} +4.01796i q^{31} +7.75278i q^{32} +(12.9201 + 7.45942i) q^{34} +(-1.50829 - 2.61243i) q^{37} +(0.870601 + 1.50792i) q^{38} +(13.7823 + 7.95723i) q^{40} +(3.29501 + 5.70713i) q^{41} +(3.89217 - 6.74143i) q^{43} +(17.5713 - 10.1448i) q^{44} +(7.17168 - 12.4217i) q^{46} +0.493410 q^{47} +(0.977326 - 0.564259i) q^{50} +(5.31591 - 3.06914i) q^{52} +(-3.59025 - 2.07283i) q^{53} -10.1812i q^{55} +(5.75947 - 9.97570i) q^{58} +4.31398 q^{59} -2.05145i q^{61} -10.3591 q^{62} -3.38572 q^{64} -3.08017i q^{65} -4.82437 q^{67} +(-13.4453 + 23.2879i) q^{68} +1.17135i q^{71} +(13.0902 + 7.55766i) q^{73} +(6.73536 - 3.88866i) q^{74} +(-2.71797 + 1.56922i) q^{76} -10.6086 q^{79} +(-9.67878 + 16.7641i) q^{80} +(-14.7141 + 8.49518i) q^{82} +(5.32432 - 9.22199i) q^{83} +(6.74680 + 11.6858i) q^{85} +(17.3807 + 10.0348i) q^{86} +(14.8986 + 25.8051i) q^{88} +(1.66268 + 2.87984i) q^{89} +(22.3896 + 12.9266i) q^{92} +1.27211i q^{94} +1.57486i q^{95} +(-12.7531 - 7.36299i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4}+O(q^{10}) $ 48 * q - 48 * q^4	$ 48 q - 48 q^{4} - 24 q^{11} + 48 q^{16} - 48 q^{23} - 24 q^{25} + 96 q^{44} - 48 q^{50} + 48 q^{53} - 48 q^{64} - 168 q^{74} + 48 q^{79} - 24 q^{85} + 24 q^{86} + 144 q^{92}+O(q^{100}) $ 48 * q - 48 * q^4 - 24 * q^11 + 48 * q^16 - 48 * q^23 - 24 * q^25 + 96 * q^44 - 48 * q^50 + 48 * q^53 - 48 * q^64 - 168 * q^74 + 48 * q^79 - 24 * q^85 + 24 * q^86 + 144 * q^92

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$			2.57819i			1.82306i	0.411235	+	0.911529i	$0.365098\pi$
$2$			2.57819i			1.82306i	−0.411235	+	0.911529i	$0.634902\pi$
$3$		0			0
$3$		0			0
$4$	−4.64709			−2.32354
$5$	−1.16595	+	2.01948i	−0.521427	+	0.903138i	0.478263	+	0.878217i	$0.341267\pi$
$5$	−1.16595	+	2.01948i	−0.521427	+	0.903138i	−0.999689	+	0.0249208i	$0.992067\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	6.82470i		−	2.41290i
$9$		0			0
$10$	−5.20660	−	3.00603i	−1.64647	−	0.950591i
$11$	−3.78114	+	2.18304i	−1.14006	+	0.658212i	−0.946444	−	0.322867i	$-0.895353\pi$
$11$	−3.78114	+	2.18304i	−1.14006	+	0.658212i	−0.193612	+	0.981078i	$0.562020\pi$
$12$		0			0
$13$	−1.14392	+	0.660445i	−0.317267	+	0.183174i	−0.650174	−	0.759785i	$-0.725304\pi$
$13$	−1.14392	+	0.660445i	−0.317267	+	0.183174i	0.332906	+	0.942960i	$0.391971\pi$
$14$		0			0
$15$		0			0
$16$	8.30123			2.07531
$17$	2.89327	−	5.01130i	0.701722	−	1.21542i	−0.266140	−	0.963935i	$-0.585748\pi$
$17$	2.89327	−	5.01130i	0.701722	−	1.21542i	0.967862	−	0.251484i	$-0.0809185\pi$
$18$		0			0
$19$	0.584876	−	0.337678i	0.134180	−	0.0774687i	−0.431407	−	0.902157i	$-0.641983\pi$
$19$	0.584876	−	0.337678i	0.134180	−	0.0774687i	0.565587	+	0.824688i	$0.308650\pi$
$20$	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	$-0.530288\pi$
$23$	−4.81799	−	2.78167i	−1.00462	−	0.580018i	−0.909612	+	0.415459i	$0.863621\pi$
$24$		0			0
$25$	−0.218858	−	0.379074i	−0.0437717	−	0.0758147i
$26$	−1.70276	−	2.94926i	−0.333938	−	0.578397i
$27$		0			0
$28$		0			0
$29$	−3.86926	−	2.23392i	−0.718503	−	0.414828i	0.0956983	−	0.995410i	$-0.469492\pi$
$29$	−3.86926	−	2.23392i	−0.718503	−	0.414828i	−0.814202	+	0.580582i	$0.802825\pi$
$30$		0			0
$31$			4.01796i			0.721646i	0.932634	+	0.360823i	$0.117504\pi$
$31$			4.01796i			0.721646i	−0.932634	+	0.360823i	$0.882496\pi$
$32$			7.75278i			1.37051i
$33$		0			0
$34$	12.9201	+	7.45942i	2.21578	+	1.27928i
$35$		0			0
$36$		0			0
$37$	−1.50829	−	2.61243i	−0.247961	−	0.429482i	0.714999	−	0.699126i	$-0.246427\pi$
$37$	−1.50829	−	2.61243i	−0.247961	−	0.429482i	−0.962960	+	0.269644i	$0.913094\pi$
$38$	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	$0.00539076\pi$
$41$	3.29501	+	5.70713i	0.514594	+	0.891303i	−0.485262	+	0.874369i	$0.661276\pi$
$42$		0			0
$43$	3.89217	−	6.74143i	0.593550	−	1.02806i	−0.400200	−	0.916428i	$-0.631059\pi$
$43$	3.89217	−	6.74143i	0.593550	−	1.02806i	0.993750	−	0.111631i	$-0.0356074\pi$
$44$	17.5713	−	10.1448i	2.64897	−	1.52938i
$45$		0			0
$46$	7.17168	−	12.4217i	1.05741	−	1.83148i
$47$	0.493410			0.0719712			0.0359856	−	0.999352i	$-0.488543\pi$
$47$	0.493410			0.0719712			0.0359856	+	0.999352i	$0.488543\pi$
$48$		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
$53$	−3.59025	−	2.07283i	−0.493159	−	0.284725i	0.232725	−	0.972543i	$-0.425236\pi$
$53$	−3.59025	−	2.07283i	−0.493159	−	0.284725i	−0.725884	+	0.687817i	$0.758569\pi$
$54$		0			0
$55$		−	10.1812i		−	1.37284i
$56$		0			0
$57$		0			0
$58$	5.75947	−	9.97570i	0.756256	−	1.30987i
$59$	4.31398			0.561633			0.280816	−	0.959762i	$-0.409395\pi$
$59$	4.31398			0.561633			0.280816	+	0.959762i	$0.409395\pi$
$60$		0			0
$61$		−	2.05145i		−	0.262661i	−0.991339	−	0.131330i	$-0.958075\pi$
$61$		−	2.05145i		−	0.262661i	0.991339	−	0.131330i	$-0.0419249\pi$
$62$	−10.3591			−1.31560
$63$		0			0
$64$	−3.38572			−0.423215
$65$		−	3.08017i		−	0.382048i
$66$		0			0
$67$	−4.82437			−0.589390			−0.294695	−	0.955591i	$-0.595218\pi$
$67$	−4.82437			−0.589390			−0.294695	+	0.955591i	$0.595218\pi$
$68$	−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
$73$	13.0902	+	7.55766i	1.53210	+	0.884557i	0.999265	+	0.0383363i	$0.0122058\pi$
$73$	13.0902	+	7.55766i	1.53210	+	0.884557i	0.532833	+	0.846221i	$0.321128\pi$
$74$	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
$79$	−10.6086			−1.19356			−0.596778	−	0.802406i	$-0.703553\pi$
$79$	−10.6086			−1.19356			−0.596778	+	0.802406i	$0.703553\pi$
$80$	−9.67878	+	16.7641i	−1.08212	+	1.87429i
$81$		0			0
$82$	−14.7141	+	8.49518i	−1.62490	+	0.938135i
$83$	5.32432	−	9.22199i	0.584420	−	1.01225i	−0.410527	−	0.911848i	$-0.634655\pi$
$83$	5.32432	−	9.22199i	0.584420	−	1.01225i	0.994947	−	0.100397i	$-0.0320113\pi$
$84$		0			0
$85$	6.74680	+	11.6858i	0.731793	+	1.26750i
$86$	17.3807	+	10.0348i	1.87421	+	1.08208i
$87$		0			0
$88$	14.8986	+	25.8051i	1.58820	+	2.75084i
$89$	1.66268	+	2.87984i	0.176243	+	0.305262i	0.940591	−	0.339542i	$-0.110272\pi$
$89$	1.66268	+	2.87984i	0.176243	+	0.305262i	−0.764348	+	0.644804i	$0.776939\pi$
$90$		0			0
$91$		0			0
$92$	22.3896	+	12.9266i	2.33428	+	1.34770i
$93$		0			0
$94$			1.27211i			0.131208i
$95$			1.57486i			0.161577i
$96$		0			0
$97$	−12.7531	−	7.36299i	−1.29488	−	0.747598i	−0.315363	−	0.948971i	$-0.602126\pi$
$97$	−12.7531	−	7.36299i	−1.29488	−	0.747598i	−0.979515	+	0.201373i	$0.935460\pi$
$98$		0			0
$99$		0			0
$100$	1.01705	+	1.76159i	0.101705	+	0.176159i
$101$	0.832092	+	1.44123i	0.0827963	+	0.143407i	0.904450	−	0.426580i	$-0.140282\pi$
$101$	0.832092	+	1.44123i	0.0827963	+	0.143407i	−0.821654	+	0.569987i	$0.806948\pi$
$102$		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
$107$	−15.8596	+	9.15652i	−1.53320	+	0.885194i	−0.533990	+	0.845491i	$0.679308\pi$
$107$	−15.8596	+	9.15652i	−1.53320	+	0.885194i	−0.999212	+	0.0397036i	$0.987359\pi$
$108$		0			0
$109$	7.98678	−	13.8335i	0.764995	−	1.32501i	−0.175254	−	0.984523i	$-0.556075\pi$
$109$	7.98678	−	13.8335i	0.764995	−	1.32501i	0.940249	−	0.340487i	$-0.110592\pi$
$110$	26.2492			2.50276
$111$		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
$116$	17.9808	+	10.3812i	1.66947	+	0.963871i
$117$		0			0
$118$			11.1223i			1.02389i
$119$		0			0
$120$		0			0
$121$	4.03134	−	6.98248i	0.366485	−	0.634771i
$122$	5.28903			0.478846
$123$		0			0
$124$		−	18.6718i		−	1.67678i
$125$	−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	$0.762920\pi$
$128$			6.77652i			0.598965i
$129$		0			0
$130$	7.94128			0.696496
$131$	3.55989	−	6.16591i	0.311029	−	0.538718i	−0.667556	−	0.744559i	$-0.732660\pi$
$131$	3.55989	−	6.16591i	0.311029	−	0.538718i	0.978585	+	0.205841i	$0.0659930\pi$
$132$		0			0
$133$		0			0
$134$		−	12.4382i		−	1.07449i
$135$		0			0
$136$	−34.2006	−	19.7457i	−2.93268	−	1.69318i
$137$	−0.716584	+	0.413720i	−0.0612219	+	0.0353465i	−0.530298	−	0.847811i	$-0.677920\pi$
$137$	−0.716584	+	0.413720i	−0.0612219	+	0.0353465i	0.469077	+	0.883157i	$0.344587\pi$
$138$		0			0
$139$	−12.0735	+	6.97062i	−1.02406	+	0.591241i	−0.915277	−	0.402825i	$-0.868028\pi$
$139$	−12.0735	+	6.97062i	−1.02406	+	0.591241i	−0.108782	+	0.994066i	$0.534695\pi$
$140$		0			0
$141$		0			0
$142$	−3.01997			−0.253430
$143$	2.88356	−	4.99447i	0.241135	−	0.417658i
$144$		0			0
$145$	9.02269	−	5.20925i	0.749294	−	0.432605i
$146$	−19.4851	+	33.7492i	−1.61260	+	2.79310i
$147$		0			0
$148$	7.00915	+	12.1402i	0.576149	+	0.997919i
$149$	−9.46916	−	5.46702i	−0.775744	−	0.447876i	0.0591761	−	0.998248i	$-0.481153\pi$
$149$	−9.46916	−	5.46702i	−0.775744	−	0.447876i	−0.834920	+	0.550372i	$0.814486\pi$
$150$		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	$0.641269\pi$
$152$	−2.30455	−	3.99160i	−0.186924	−	0.323762i
$153$		0			0
$154$		0			0
$155$	−8.11417	−	4.68472i	−0.651746	−	0.376286i
$156$		0			0
$157$		−	15.7779i		−	1.25921i	−0.776914	−	0.629606i	$-0.783216\pi$
$157$		−	15.7779i		−	1.25921i	0.776914	−	0.629606i	$-0.216784\pi$
$158$		−	27.3509i		−	2.17592i
$159$		0			0
$160$	−15.6566	−	9.03932i	−1.23776	−	0.714621i
$161$		0			0
$162$		0			0
$163$	3.38276	+	5.85911i	0.264958	+	0.458921i	0.967553	−	0.252669i	$-0.0813085\pi$
$163$	3.38276	+	5.85911i	0.264958	+	0.458921i	−0.702594	+	0.711590i	$0.747975\pi$
$164$	−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	$-0.902099\pi$
$167$	−9.54631	−	16.5347i	−0.738716	−	1.27949i	0.214358	−	0.976755i	$-0.431234\pi$
$168$		0			0
$169$	−5.62763	+	9.74733i	−0.432894	+	0.749795i
$170$	−30.1283	+	17.3946i	−2.31073	+	1.33410i
$171$		0			0
$172$	−18.0872	+	31.3280i	−1.37914	+	2.38874i
$173$	−21.8491			−1.66116			−0.830579	−	0.556902i	$-0.811990\pi$
$173$	−21.8491			−1.66116			−0.830579	+	0.556902i	$0.811990\pi$
$174$		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
$179$	−14.8866	−	8.59481i	−1.11268	−	0.642406i	−0.173158	−	0.984894i	$-0.555397\pi$
$179$	−14.8866	−	8.59481i	−1.11268	−	0.642406i	−0.939522	+	0.342488i	$0.888730\pi$
$180$		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
$185$	7.03433			0.517175
$186$		0			0
$187$			25.2645i			1.84753i
$188$	−2.29292			−0.167228
$189$		0			0
$190$	−4.06029			−0.294565
$191$			0.954076i			0.0690345i	0.999404	+	0.0345173i	$0.0109894\pi$
$191$			0.954076i			0.0690345i	−0.999404	+	0.0345173i	$0.989011\pi$
$192$		0			0
$193$	−1.69441			−0.121966			−0.0609830	−	0.998139i	$-0.519424\pi$
$193$	−1.69441			−0.121966			−0.0609830	+	0.998139i	$0.519424\pi$
$194$	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
$199$	3.77420	+	2.17903i	0.267546	+	0.154468i	0.627772	−	0.778397i	$-0.283967\pi$
$199$	3.77420	+	2.17903i	0.267546	+	0.154468i	−0.360226	+	0.932865i	$0.617300\pi$
$200$	−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
$205$	−15.3672			−1.07329
$206$	2.09559	−	3.62966i	0.146006	−	0.252891i
$207$		0			0
$208$	−9.49598	+	5.48250i	−0.658427	+	0.380143i
$209$	−1.47433	+	2.55362i	−0.101982	+	0.176637i
$210$		0			0
$211$	−2.24368	−	3.88617i	−0.154461	−	0.267535i	0.778401	−	0.627767i	$-0.216031\pi$
$211$	−2.24368	−	3.88617i	−0.154461	−	0.267535i	−0.932863	+	0.360232i	$0.882698\pi$
$212$	16.6842	+	9.63263i	1.14588	+	0.661571i
$213$		0			0
$214$	−23.6073	−	40.8890i	−1.61376	−	2.79512i
$215$	9.07611	+	15.7203i	0.618986	+	1.07211i
$216$		0			0
$217$		0			0
$218$	35.6655	+	20.5915i	2.41557	+	1.39463i
$219$		0			0
$220$			47.3130i			3.18984i
$221$			7.64339i			0.514150i
$222$		0			0
$223$	18.0005	+	10.3926i	1.20540	+	0.695939i	0.961751	−	0.273924i	$-0.0883218\pi$
$223$	18.0005	+	10.3926i	1.20540	+	0.695939i	0.243650	+	0.969863i	$0.421655\pi$
$224$		0			0
$225$		0			0
$226$	7.55591	+	13.0872i	0.502612	+	0.870549i
$227$	−14.1579	−	24.5223i	−0.939696	−	1.62760i	−0.766039	−	0.642795i	$-0.777775\pi$
$227$	−14.1579	−	24.5223i	−0.939696	−	1.62760i	−0.173657	−	0.984806i	$-0.555558\pi$
$228$		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
$233$	13.1926	−	7.61674i	0.864275	−	0.498989i	−0.00116682	−	0.999999i	$-0.500371\pi$
$233$	13.1926	−	7.61674i	0.864275	−	0.498989i	0.865441	+	0.501010i	$0.167038\pi$
$234$		0			0
$235$	−0.575289	+	0.996430i	−0.0375277	+	0.0649999i
$236$	−20.0474			−1.30498
$237$		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	−0.370076	−	0.929002i	$-0.620668\pi$
$241$	3.87212	−	2.23557i	0.249425	−	0.144006i	0.619501	+	0.784996i	$0.287335\pi$
$242$	18.0022	+	10.3936i	1.15722	+	0.668124i
$243$		0			0
$244$			9.53325i			0.610304i
$245$		0			0
$246$		0			0
$247$	−0.446036	+	0.772557i	−0.0283806	+	0.0491566i
$248$	27.4214			1.74126
$249$		0			0
$250$		−	27.4288i		−	1.73475i
$251$	11.6265			0.733861			0.366931	−	0.930248i	$-0.380409\pi$
$251$	11.6265			0.733861			0.366931	+	0.930248i	$0.380409\pi$
$252$		0			0
$253$	24.2900			1.52710
$254$		−	42.7232i		−	2.68069i
$255$		0			0
$256$	−24.2426			−1.51516
$257$	−1.05140	+	1.82108i	−0.0655846	+	0.113596i	−0.896953	−	0.442126i	$-0.854225\pi$
$257$	−1.05140	+	1.82108i	−0.0655846	+	0.113596i	0.831369	+	0.555721i	$0.187558\pi$
$258$		0			0
$259$		0			0
$260$			14.3138i			0.887705i
$261$		0			0
$262$	15.8969	+	9.17809i	0.982114	+	0.567024i
$263$	−1.90773	+	1.10143i	−0.117636	+	0.0679170i	−0.557663	−	0.830067i	$-0.688302\pi$
$263$	−1.90773	+	1.10143i	−0.117636	+	0.0679170i	0.440028	+	0.897984i	$0.354969\pi$
$264$		0			0
$265$	8.37207	−	4.83362i	0.514292	−	0.296927i
$266$		0			0
$267$		0			0
$268$	22.4192			1.36947
$269$	−13.9312	+	24.1295i	−0.849398	+	1.47120i	0.0323483	+	0.999477i	$0.489701\pi$
$269$	−13.9312	+	24.1295i	−0.849398	+	1.47120i	−0.881746	+	0.471724i	$0.843632\pi$
$270$		0			0
$271$	−9.94228	+	5.74018i	−0.603950	+	0.348691i	−0.770594	−	0.637326i	$-0.780040\pi$
$271$	−9.94228	+	5.74018i	−0.603950	+	0.348691i	0.166644	+	0.986017i	$0.446707\pi$
$272$	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	$0.734199\pi$
$278$	−17.9716	−	31.1278i	−1.07787	−	1.86692i
$279$		0			0
$280$		0			0
$281$	−9.45116	−	5.45663i	−0.563809	−	0.325515i	0.190864	−	0.981617i	$-0.438871\pi$
$281$	−9.45116	−	5.45663i	−0.563809	−	0.325515i	−0.754673	+	0.656101i	$0.772204\pi$
$282$		0			0
$283$			11.8664i			0.705386i	0.935739	+	0.352693i	$0.114734\pi$
$283$			11.8664i			0.705386i	−0.935739	+	0.352693i	$0.885266\pi$
$284$		−	5.44336i		−	0.323004i
$285$		0			0
$286$	12.8767	+	7.43437i	0.761415	+	0.439603i
$287$		0			0
$288$		0			0
$289$	−8.24207	−	14.2757i	−0.484828	−	0.839746i
$290$	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	$-0.978265\pi$
$293$	−9.55012	−	16.5413i	−0.557924	−	0.966353i	0.439746	−	0.898122i	$-0.355069\pi$
$294$		0			0
$295$	−5.02987	+	8.71199i	−0.292850	+	0.507232i
$296$	−17.8291	+	10.2936i	−1.03629	+	0.598305i
$297$		0			0
$298$	14.0950	−	24.4133i	0.816504	−	1.41423i
$299$	7.34855			0.424978
$300$		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
$305$	4.14285	+	2.39188i	0.237219	+	0.136958i
$306$		0			0
$307$		−	2.35488i		−	0.134400i	−0.997740	−	0.0672001i	$-0.978593\pi$
$307$		−	2.35488i		−	0.134400i	0.997740	−	0.0672001i	$-0.0214066\pi$
$308$		0			0
$309$		0			0
$310$	12.0781	−	20.9199i	0.685991	−	1.18817i
$311$	7.84967			0.445114			0.222557	−	0.974920i	$-0.428560\pi$
$311$	7.84967			0.445114			0.222557	+	0.974920i	$0.428560\pi$
$312$		0			0
$313$			30.0532i			1.69870i	0.527826	+	0.849352i	$0.323007\pi$
$313$			30.0532i			1.69870i	−0.527826	+	0.849352i	$0.676993\pi$
$314$	40.6785			2.29562
$315$		0			0
$316$	49.2989			2.77328
$317$		−	11.1071i		−	0.623838i	−0.950109	−	0.311919i	$-0.899028\pi$
$317$		−	11.1071i		−	0.623838i	0.950109	−	0.311919i	$-0.100972\pi$
$318$		0			0
$319$	19.5069			1.09218
$320$	3.94757	−	6.83739i	0.220676	−	0.382222i
$321$		0			0
$322$		0			0
$323$		−	3.90798i		−	0.217446i
$324$		0			0
$325$	0.500715	+	0.289088i	0.0277746	+	0.0160357i
$326$	−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
$331$	−17.2672			−0.949093			−0.474547	−	0.880230i	$-0.657388\pi$
$331$	−17.2672			−0.949093			−0.474547	+	0.880230i	$0.657388\pi$
$332$	−24.7426	+	42.8554i	−1.35792	+	2.35199i
$333$		0			0
$334$	42.6297	−	24.6123i	2.33259	−	1.34672i
$335$	5.62495	−	9.74270i	0.307324	−	0.532300i
$336$		0			0
$337$	−3.82962	−	6.63309i	−0.208612	−	0.361327i	0.742665	−	0.669663i	$-0.233561\pi$
$337$	−3.82962	−	6.63309i	−0.208612	−	0.361327i	−0.951278	+	0.308336i	$0.900228\pi$
$338$	−25.1305	−	14.5091i	−1.36692	−	0.789192i
$339$		0			0
$340$	−31.3530	−	54.3049i	−1.70035	−	2.94510i
$341$	−8.77137	−	15.1925i	−0.474996	−	0.822717i
$342$		0			0
$343$		0			0
$344$	−46.0082	−	26.5629i	−2.48060	−	1.43217i
$345$		0			0
$346$		−	56.3312i		−	3.02839i
$347$			13.1652i			0.706747i	0.935482	+	0.353374i	$0.114966\pi$
$347$			13.1652i			0.706747i	−0.935482	+	0.353374i	$0.885034\pi$
$348$		0			0
$349$	−1.05185	−	0.607283i	−0.0563040	−	0.0325071i	0.471584	−	0.881821i	$-0.343682\pi$
$349$	−1.05185	−	0.607283i	−0.0563040	−	0.0325071i	−0.527888	+	0.849314i	$0.677016\pi$
$350$		0			0
$351$		0			0
$352$	−16.9246	−	29.3143i	−0.902087	−	1.56246i
$353$	13.4114	+	23.2292i	0.713816	+	1.23637i	0.963414	+	0.268016i	$0.0863681\pi$
$353$	13.4114	+	23.2292i	0.713816	+	1.23637i	−0.249598	+	0.968349i	$0.580299\pi$
$354$		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
$359$	6.45209	−	3.72512i	0.340529	−	0.196604i	−0.319977	−	0.947425i	$-0.603675\pi$
$359$	6.45209	−	3.72512i	0.340529	−	0.196604i	0.660506	+	0.750821i	$0.270342\pi$
$360$		0			0
$361$	−9.27195	+	16.0595i	−0.487997	+	0.845236i
$362$	42.9171			2.25567
$363$		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	$0.966963\pi$
$368$	−39.9952	−	23.0913i	−2.08490	−	1.20371i
$369$		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	$-0.117725\pi$
$374$	−65.1369			−3.36815
$375$		0			0
$376$		−	3.36737i		−	0.173659i
$377$	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	$0.745041\pi$
$380$		−	7.31850i		−	0.375431i
$381$		0			0
$382$	−2.45979			−0.125854
$383$	−1.83015	+	3.16992i	−0.0935164	+	0.161975i	−0.908988	−	0.416821i	$-0.863144\pi$
$383$	−1.83015	+	3.16992i	−0.0935164	+	0.161975i	0.815472	+	0.578796i	$0.196477\pi$
$384$		0			0
$385$		0			0
$386$		−	4.36851i		−	0.222351i
$387$		0			0
$388$	59.2646	+	34.2164i	3.00870	+	1.73708i
$389$	10.5387	−	6.08449i	0.534331	−	0.308496i	−0.208447	−	0.978034i	$-0.566841\pi$
$389$	10.5387	−	6.08449i	0.534331	−	0.308496i	0.742778	+	0.669537i	$0.233508\pi$
$390$		0			0
$391$	−27.8795	+	16.0962i	−1.40993	+	0.814022i
$392$		0			0
$393$		0			0
$394$	32.8684			1.65589
$395$	12.3690	−	21.4237i	0.622352	−	1.07795i
$396$		0			0
$397$	23.1870	−	13.3870i	1.16372	−	0.671876i	0.211530	−	0.977371i	$-0.432155\pi$
$397$	23.1870	−	13.3870i	1.16372	−	0.671876i	0.952194	+	0.305495i	$0.0988220\pi$
$398$	−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	$-0.271510\pi$
$401$	6.69428	+	3.86494i	0.334296	+	0.193006i	−0.323451	+	0.946245i	$0.604843\pi$
$402$		0			0
$403$	−2.65364	−	4.59624i	−0.132187	−	0.228955i
$404$	−3.86680	−	6.69750i	−0.192381	−	0.333213i
$405$		0			0
$406$		0			0
$407$	11.4061	+	6.58532i	0.565380	+	0.326422i
$408$		0			0
$409$		−	9.06047i		−	0.448012i	−0.974588	−	0.224006i	$-0.928087\pi$
$409$		−	9.06047i		−	0.448012i	0.974588	−	0.224006i	$-0.0719135\pi$
$410$		−	39.6197i		−	1.95668i
$411$		0			0
$412$	6.54231	+	3.77720i	0.322316	+	0.186090i
$413$		0			0
$414$		0			0
$415$	12.4157	+	21.5047i	0.609464	+	1.05562i
$416$	−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	$-0.115052\pi$
$419$	3.30466	+	5.72384i	0.161443	+	0.279628i	−0.773943	+	0.633255i	$0.781718\pi$
$420$		0			0
$421$	6.39209	−	11.0714i	0.311531	−	0.539588i	−0.667163	−	0.744912i	$-0.732491\pi$
$421$	6.39209	−	11.0714i	0.311531	−	0.539588i	0.978694	+	0.205324i	$0.0658248\pi$
$422$	10.0193	−	5.78464i	0.487732	−	0.281592i
$423$		0			0
$424$	−14.1465	+	24.5024i	−0.687013	+	1.18994i
$425$	−2.53287			−0.122862
$426$		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
$431$	−18.9756	−	10.9556i	−0.914023	−	0.527712i	−0.0322998	−	0.999478i	$-0.510283\pi$
$431$	−18.9756	−	10.9556i	−0.914023	−	0.527712i	−0.881723	+	0.471767i	$0.843616\pi$
$432$		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
$437$	−3.75724			−0.179733
$438$		0			0
$439$		−	37.8737i		−	1.80761i	−0.427942	−	0.903806i	$-0.640761\pi$
$439$		−	37.8737i		−	1.80761i	0.427942	−	0.903806i	$-0.359239\pi$
$440$	−69.4838			−3.31251
$441$		0			0
$442$	−19.7061			−0.937326
$443$			20.4624i			0.972200i	0.873903	+	0.486100i	$0.161581\pi$
$443$			20.4624i			0.972200i	−0.873903	+	0.486100i	$0.838419\pi$
$444$		0			0
$445$	−7.75436			−0.367592
$446$	−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
$451$	−24.9178	−	14.3863i	−1.17333	−	0.677424i
$452$	−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
$457$	−0.254179			−0.0118900			−0.00594501	−	0.999982i	$-0.501892\pi$
$457$	−0.254179			−0.0118900			−0.00594501	+	0.999982i	$0.501892\pi$
$458$	28.0839	−	48.6428i	1.31228	−	2.27293i
$459$		0			0
$460$	−52.2101	+	30.1435i	−2.43431	+	1.40545i
$461$	12.2175	−	21.1613i	0.569025	−	0.985581i	−0.427637	−	0.903950i	$-0.640654\pi$
$461$	12.2175	−	21.1613i	0.569025	−	0.985581i	0.996663	−	0.0816304i	$-0.0260127\pi$
$462$		0			0
$463$	0.409986	+	0.710116i	0.0190536	+	0.0330019i	0.875395	−	0.483408i	$-0.160601\pi$
$463$	0.409986	+	0.710116i	0.0190536	+	0.0330019i	−0.856341	+	0.516410i	$0.827268\pi$
$464$	−32.1196	−	18.5443i	−1.49112	−	0.860896i
$465$		0			0
$466$	19.6374	+	34.0130i	0.909686	+	1.57562i
$467$	−0.909625	−	1.57552i	−0.0420924	−	0.0729062i	0.844212	−	0.536010i	$-0.180069\pi$
$467$	−0.909625	−	1.57552i	−0.0420924	−	0.0729062i	−0.886304	+	0.463104i	$0.846736\pi$
$468$		0			0
$469$		0			0
$470$	−2.56899	−	1.48321i	−0.118499	−	0.0684152i
$471$		0			0
$472$		−	29.4416i		−	1.35516i
$473$			33.9870i			1.56273i
$474$		0			0
$475$	−0.256010	−	0.147807i	−0.0117465	−	0.00678187i
$476$		0			0
$477$		0			0
$478$	7.37004	+	12.7653i	0.337098	+	0.583871i
$479$	0.681074	+	1.17965i	0.0311191	+	0.0538998i	0.881166	−	0.472808i	$-0.156760\pi$
$479$	0.681074	+	1.17965i	0.0311191	+	0.0538998i	−0.850046	+	0.526708i	$0.823426\pi$
$480$		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
$485$	29.7388	−	17.1697i	1.35037	−	0.779635i
$486$		0			0
$487$	−15.8061	+	27.3769i	−0.716241	+	1.24057i	0.246238	+	0.969209i	$0.420806\pi$
$487$	−15.8061	+	27.3769i	−0.716241	+	1.24057i	−0.962479	+	0.271357i	$0.912528\pi$
$488$	−14.0005			−0.633773
$489$		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
$494$	−1.99180	−	1.14997i	−0.0896154	−	0.0517395i
$495$		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	$0.959754\pi$
$500$	49.4392			2.21099
$501$		0			0
$502$			29.9755i			1.33787i
$503$	0.276948			0.0123485			0.00617426	−	0.999981i	$-0.498035\pi$
$503$	0.276948			0.0123485			0.00617426	+	0.999981i	$0.498035\pi$
$504$		0			0
$505$	−3.88070			−0.172689
$506$			62.6243i			2.78399i
$507$		0			0
$508$	77.0067			3.41662
$509$	9.21476	−	15.9604i	0.408437	−	0.707434i	−0.586278	−	0.810110i	$-0.699407\pi$
$509$	9.21476	−	15.9604i	0.408437	−	0.707434i	0.994715	+	0.102676i	$0.0327406\pi$
$510$		0			0
$511$		0			0
$512$		−	48.9492i		−	2.16327i
$513$		0			0
$514$	−4.69510	−	2.71072i	−0.207092	−	0.119565i
$515$	3.28291	−	1.89539i	0.144662	−	0.0835208i
$516$		0			0
$517$	−1.86565	+	1.07713i	−0.0820512	+	0.0473723i
$518$		0			0
$519$		0			0
$520$	−21.0212			−0.921842
$521$	−11.6264	+	20.1374i	−0.509360	+	0.882237i	0.490581	+	0.871395i	$0.336785\pi$
$521$	−11.6264	+	20.1374i	−0.509360	+	0.882237i	−0.999941	+	0.0108420i	$0.996549\pi$
$522$		0			0
$523$	11.5227	−	6.65262i	0.503852	−	0.290899i	−0.226451	−	0.974023i	$-0.572712\pi$
$523$	11.5227	−	6.65262i	0.503852	−	0.290899i	0.730303	+	0.683124i	$0.239379\pi$
$524$	−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
$530$	12.4620	+	21.5848i	0.541315	+	0.937585i
$531$		0			0
$532$		0			0
$533$	−7.53848	−	4.35235i	−0.326528	−	0.188521i
$534$		0			0
$535$		−	42.7040i		−	1.84626i
$536$			32.9249i			1.42214i
$537$		0			0
$538$	−62.2105	−	35.9172i	−2.68208	−	1.54850i
$539$		0			0
$540$		0			0
$541$	15.0846	+	26.1273i	0.648537	+	1.12330i	0.983472	+	0.181059i	$0.0579524\pi$
$541$	15.0846	+	26.1273i	0.648537	+	1.12330i	−0.334935	+	0.942241i	$0.608714\pi$
$542$	−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	$0.174453\pi$
$548$	3.33002	−	1.92259i	0.142252	−	0.0821290i
$549$		0			0
$550$	−2.46360	+	4.26708i	−0.105048	+	0.181949i
$551$	−3.01738			−0.128545
$552$		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
$557$	8.35388	+	4.82312i	0.353965	+	0.204362i	0.666430	−	0.745567i	$-0.267821\pi$
$557$	8.35388	+	4.82312i	0.353965	+	0.204362i	−0.312465	+	0.949929i	$0.601155\pi$
$558$		0			0
$559$			10.2822i			0.434893i
$560$		0			0
$561$		0			0
$562$	14.0683	−	24.3669i	0.593434	−	1.02786i
$563$	3.08791			0.130140			0.0650698	−	0.997881i	$-0.479273\pi$
$563$	3.08791			0.130140			0.0650698	+	0.997881i	$0.479273\pi$
$564$		0			0
$565$			13.6681i			0.575023i
$566$	−30.5940			−1.28596
$567$		0			0
$568$	7.99411			0.335425
$569$			8.43610i			0.353660i	0.984241	+	0.176830i	$0.0565842\pi$
$569$			8.43610i			0.353660i	−0.984241	+	0.176830i	$0.943416\pi$
$570$		0			0
$571$	−34.0415			−1.42459			−0.712297	−	0.701879i	$-0.752345\pi$
$571$	−34.0415			−1.42459			−0.712297	+	0.701879i	$0.752345\pi$
$572$	−13.4001	+	23.2097i	−0.560288	+	0.970447i
$573$		0			0
$574$		0			0
$575$			2.43516i			0.101553i
$576$		0			0
$577$	15.6796	+	9.05260i	0.652749	+	0.376865i	0.789509	−	0.613739i	$-0.210335\pi$
$577$	15.6796	+	9.05260i	0.652749	+	0.376865i	−0.136760	+	0.990604i	$0.543669\pi$
$578$	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
$583$	18.1003			0.749638
$584$	51.5787	−	89.3370i	2.13434	−	3.69679i
$585$		0			0
$586$	42.6467	−	24.6221i	1.76172	−	1.01713i
$587$	−4.04900	+	7.01308i	−0.167120	+	0.289461i	−0.937406	−	0.348238i	$-0.886780\pi$
$587$	−4.04900	+	7.01308i	−0.167120	+	0.289461i	0.770286	+	0.637699i	$0.220113\pi$
$588$		0			0
$589$	1.35678	+	2.35001i	0.0559050	+	0.0968304i
$590$	−22.4612	−	12.9680i	−0.924713	−	0.533883i
$591$		0			0
$592$	−12.5207	−	21.6864i	−0.514596	−	0.891306i
$593$	3.33216	+	5.77148i	0.136836	+	0.237006i	0.926297	−	0.376794i	$-0.122973\pi$
$593$	3.33216	+	5.77148i	0.136836	+	0.237006i	−0.789462	+	0.613800i	$0.789640\pi$
$594$		0			0
$595$		0			0
$596$	44.0040	+	25.4057i	1.80247	+	1.04066i
$597$		0			0
$598$			18.9460i			0.774759i
$599$			3.58607i			0.146523i	0.997313	+	0.0732614i	$0.0233407\pi$
$599$			3.58607i			0.146523i	−0.997313	+	0.0732614i	$0.976659\pi$
$600$		0			0
$601$	4.86949	+	2.81140i	0.198631	+	0.114679i	0.596017	−	0.802972i	$-0.296749\pi$
$601$	4.86949	+	2.81140i	0.198631	+	0.114679i	−0.397386	+	0.917652i	$0.630083\pi$
$602$		0			0
$603$		0			0
$604$	−32.4030	−	56.1237i	−1.31846	−	2.28364i
$605$	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
$611$	−0.564423	+	0.325870i	−0.0228341	+	0.0131833i
$612$		0			0
$613$	3.41019	−	5.90662i	0.137736	−	0.238566i	−0.788903	−	0.614518i	$-0.789351\pi$
$613$	3.41019	−	5.90662i	0.137736	−	0.238566i	0.926639	+	0.375951i	$0.122684\pi$
$614$	6.07134			0.245019
$615$		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	−0.887453	−	0.460899i	$-0.847527\pi$
$619$	−23.1886	+	13.3880i	−0.932029	+	0.538107i	−0.0445762	+	0.999006i	$0.514194\pi$
$620$	37.7072	+	21.7703i	1.51436	+	0.874316i
$621$		0			0
$622$			20.2380i			0.811469i
$623$		0			0
$624$		0			0
$625$	13.4985	−	23.3801i	0.539940	−	0.935203i
$626$	−77.4829			−3.09684
$627$		0			0
$628$			73.3212i			2.92583i
$629$	−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	$0.571316\pi$
$632$			72.4002i			2.87993i
$633$		0			0
$634$	28.6363			1.13729
$635$	19.3208	−	33.4647i	0.766724	−	1.32801i
$636$		0			0
$637$		0			0
$638$			50.2927i			1.99111i
$639$		0			0
$640$	−13.6850	−	7.90105i	−0.540948	−	0.312317i
$641$	38.6251	−	22.3002i	1.52560	−	0.880805i	0.526059	−	0.850448i	$-0.323669\pi$
$641$	38.6251	−	22.3002i	1.52560	−	0.880805i	0.999539	−	0.0303565i	$-0.00966427\pi$
$642$		0			0
$643$	−23.6268	+	13.6410i	−0.931751	+	0.537947i	−0.887365	−	0.461068i	$-0.847466\pi$
$643$	−23.6268	+	13.6410i	−0.931751	+	0.537947i	−0.0443860	+	0.999014i	$0.514133\pi$
$644$		0			0
$645$		0			0
$646$	10.0755			0.396417
$647$	−22.4675	+	38.9148i	−0.883288	+	1.52990i	−0.0356246	+	0.999365i	$0.511342\pi$
$647$	−22.4675	+	38.9148i	−0.883288	+	1.52990i	−0.847663	+	0.530534i	$0.821991\pi$
$648$		0			0
$649$	−16.3118	+	9.41760i	−0.640293	+	0.369673i
$650$	−0.745324	+	1.29094i	−0.0292340	+	0.0506348i
$651$		0			0
$652$	−15.7200	−	27.2278i	−0.615642	−	1.06632i
$653$	−24.0549	−	13.8881i	−0.941343	−	0.543484i	−0.0509617	−	0.998701i	$-0.516229\pi$
$653$	−24.0549	−	13.8881i	−0.941343	−	0.543484i	−0.890381	+	0.455216i	$0.849562\pi$
$654$		0			0
$655$	8.30128	+	14.3782i	0.324358	+	0.561804i
$656$	27.3526	+	47.3762i	1.06794	+	1.84973i
$657$		0			0
$658$		0			0
$659$	−0.801975	−	0.463021i	−0.0312405	−	0.0180367i	0.484298	−	0.874903i	$-0.339075\pi$
$659$	−0.801975	−	0.463021i	−0.0312405	−	0.0180367i	−0.515539	+	0.856866i	$0.672408\pi$
$660$		0			0
$661$			32.6813i			1.27115i	0.772037	+	0.635577i	$0.219238\pi$
$661$			32.6813i			1.27115i	−0.772037	+	0.635577i	$0.780762\pi$
$662$		−	44.5183i		−	1.73025i
$663$		0			0
$664$	−62.9373	−	36.3369i	−2.44244	−	1.41014i
$665$		0			0
$666$		0			0
$667$	12.4280	+	21.5260i	0.481215	+	0.833489i
$668$	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	$0.959845\pi$
$674$	17.1014	−	9.87349i	0.658721	−	0.380313i
$675$		0			0
$676$	26.1521	−	45.2967i	1.00585	−	1.74218i
$677$	21.5765			0.829252			0.414626	−	0.909992i	$-0.363912\pi$
$677$	21.5765			0.829252			0.414626	+	0.909992i	$0.363912\pi$
$678$		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
$683$	31.4015	+	18.1296i	1.20154	+	0.693711i	0.960898	−	0.276902i	$-0.0893077\pi$
$683$	31.4015	+	18.1296i	1.20154	+	0.693711i	0.240645	+	0.970613i	$0.422641\pi$
$684$		0			0
$685$		−	1.92950i		−	0.0737224i
$686$		0			0
$687$		0			0
$688$	32.3098	−	55.9622i	1.23180	−	2.13354i
$689$	5.47596			0.208618
$690$		0			0
$691$			7.11745i			0.270761i	0.990794	+	0.135380i	$0.0432256\pi$
$691$			7.11745i			0.270761i	−0.990794	+	0.135380i	$0.956774\pi$
$692$	101.535			3.85977
$693$		0			0
$694$	−33.9426			−1.28844
$695$		−	32.5095i		−	1.23315i
$696$		0			0
$697$	38.1335			1.44441
$698$	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
$703$	−1.76433	−	1.01863i	−0.0665428	−	0.0384185i
$704$	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
$709$	−38.0722			−1.42983			−0.714916	−	0.699211i	$-0.753535\pi$
$709$	−38.0722			−1.42983			−0.714916	+	0.699211i	$0.753535\pi$
$710$	3.52112	−	6.09875i	0.132145	−	0.228882i
$711$		0			0
$712$	19.6540	−	11.3473i	0.736566	−	0.425257i
$713$	11.1766	−	19.3585i	0.418568	−	0.724980i
$714$		0			0
$715$	6.72414	+	11.6466i	0.251469	+	0.435556i
$716$	69.1795	+	39.9408i	2.58536	+	1.49266i
$717$		0			0
$718$	9.60408	+	16.6348i	0.358421	+	0.620803i
$719$	19.1057	+	33.0921i	0.712523	+	1.23413i	0.963907	+	0.266238i	$0.0857807\pi$
$719$	19.1057	+	33.0921i	0.712523	+	1.23413i	−0.251385	+	0.967887i	$0.580886\pi$
$720$		0			0
$721$		0			0
$722$	−41.4045	−	23.9049i	−1.54091	−	0.889647i
$723$		0			0
$724$			77.3562i			2.87492i
$725$			1.95565i			0.0726309i
$726$		0			0
$727$	17.7563	+	10.2516i	0.658546	+	0.380212i	0.791723	−	0.610881i	$-0.209184\pi$
$727$	17.7563	+	10.2516i	0.658546	+	0.380212i	−0.133177	+	0.991092i	$0.542518\pi$
$728$		0			0
$729$		0			0
$730$	−45.4372	−	78.6995i	−1.68170	−	2.91280i
$731$	−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
$737$	18.2416	−	10.5318i	0.671938	−	0.387944i
$738$		0			0
$739$	−12.0805	+	20.9240i	−0.444387	+	0.769701i	−0.998009	−	0.0630670i	$-0.979912\pi$
$739$	−12.0805	+	20.9240i	−0.444387	+	0.769701i	0.553622	+	0.832768i	$0.313245\pi$
$740$	−32.6892			−1.20168
$741$		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
$746$	67.2045	+	38.8005i	2.46053	+	1.42059i
$747$		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	$0.184335\pi$
$752$	4.09591			0.149362
$753$		0			0
$754$			15.2153i			0.554107i
$755$	−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	$0.211036\pi$
$758$		−	69.8680i		−	2.53772i
$759$		0			0
$760$	10.7479			0.389869
$761$	−14.6319	+	25.3432i	−0.530406	+	0.918690i	0.468965	+	0.883217i	$0.344627\pi$
$761$	−14.6319	+	25.3432i	−0.530406	+	0.918690i	−0.999371	+	0.0354731i	$0.988706\pi$
$762$		0			0
$763$		0			0
$764$		−	4.43367i		−	0.160405i
$765$		0			0
$766$	−8.17266	−	4.71849i	−0.295290	−	0.170486i
$767$	−4.93487	+	2.84915i	−0.178188	+	0.102877i
$768$		0			0
$769$	29.6496	−	17.1182i	1.06919	−	0.617299i	0.141232	−	0.989977i	$-0.454894\pi$
$769$	29.6496	−	17.1182i	1.06919	−	0.617299i	0.927961	+	0.372678i	$0.121560\pi$
$770$		0			0
$771$		0			0
$772$	7.87405			0.283393
$773$	−16.9927	+	29.4322i	−0.611185	+	1.05860i	0.379856	+	0.925046i	$0.375974\pi$
$773$	−16.9927	+	29.4322i	−0.611185	+	1.05860i	−0.991041	+	0.133558i	$0.957360\pi$
$774$		0			0
$775$	1.52310	−	0.879363i	0.0547114	−	0.0315877i
$776$	−50.2502	+	87.0359i	−1.80388	+	3.12441i
$777$		0			0
$778$	15.6870	+	27.1707i	0.562406	+	0.974117i
$779$	3.85435	+	2.22531i	0.138096	+	0.0797299i
$780$		0			0
$781$	−2.55710	−	4.42904i	−0.0915004	−	0.158483i
$782$	−41.4993	−	71.8788i	−1.48401	−	2.57038i
$783$		0			0
$784$		0			0
$785$	31.8631	+	18.3962i	1.13724	+	0.656587i
$786$		0			0
$787$		−	27.5078i		−	0.980549i	−0.871568	−	0.490274i	$-0.836897\pi$
$787$		−	27.5078i		−	0.980549i	0.871568	−	0.490274i	$-0.163103\pi$
$788$			59.2439i			2.11048i
$789$		0			0
$790$	55.2346	+	31.8897i	1.96516	+	1.13458i
$791$		0			0
$792$		0			0
$793$	1.35487	+	2.34670i	0.0481128	+	0.0833338i
$794$	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	0.949277	+	0.314440i	$0.101817\pi$
$797$	21.0873	+	36.5243i	0.746952	+	1.29376i	−0.202326	+	0.979318i	$0.564850\pi$
$798$		0			0
$799$	1.42757	−	2.47262i	0.0505038	−	0.0874751i
$800$	2.93888	−	1.69676i	0.103905	−	0.0599896i
$801$		0			0
$802$	−9.96458	+	17.2592i	−0.351861	+	0.609442i
$803$	−65.9947			−2.32890
$804$		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
$809$	−4.18377	−	2.41550i	−0.147094	−	0.0849245i	0.424647	−	0.905359i	$-0.360398\pi$
$809$	−4.18377	−	2.41550i	−0.147094	−	0.0849245i	−0.571740	+	0.820435i	$0.693732\pi$
$810$		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
$815$	−15.7765			−0.552625
$816$		0			0
$817$		−	5.25720i		−	0.183926i
$818$	23.3597			0.816751
$819$		0			0
$820$	71.4128			2.49384
$821$			16.7957i			0.586172i	0.956086	+	0.293086i	$0.0946823\pi$
$821$			16.7957i			0.586172i	−0.956086	+	0.293086i	$0.905318\pi$
$822$		0			0
$823$	−15.0350			−0.524087			−0.262043	−	0.965056i	$-0.584396\pi$
$823$	−15.0350			−0.524087			−0.262043	+	0.965056i	$0.584396\pi$
$824$	−5.54719	+	9.60802i	−0.193246	+	0.334711i
$825$		0			0
$826$		0			0
$827$		−	29.2462i		−	1.01699i	−0.861065	−	0.508495i	$-0.830202\pi$
$827$		−	29.2462i		−	1.01699i	0.861065	−	0.508495i	$-0.169798\pi$
$828$		0			0
$829$	−1.30270	−	0.752115i	−0.0452447	−	0.0261220i	0.477207	−	0.878791i	$-0.341649\pi$
$829$	−1.30270	−	0.752115i	−0.0452447	−	0.0261220i	−0.522452	+	0.852669i	$0.674983\pi$
$830$	−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
$835$	44.5219			1.54075
$836$	6.85135	−	11.8669i	0.236959	−	0.410425i
$837$		0			0
$838$	−14.7572	+	8.52005i	−0.509778	+	0.294320i
$839$	−22.9477	+	39.7466i	−0.792243	+	1.37221i	0.132331	+	0.991206i	$0.457754\pi$
$839$	−22.9477	+	39.7466i	−0.792243	+	1.37221i	−0.924575	+	0.381000i	$0.875580\pi$
$840$		0			0
$841$	−4.51923	−	7.82753i	−0.155835	−	0.269915i
$842$	28.5443	+	16.4800i	0.983701	+	0.567940i
$843$		0			0
$844$	10.4266	+	18.0593i	0.358897	+	0.621628i
$845$	−13.1230	−	22.7297i	−0.451445	−	0.781926i
$846$		0			0
$847$		0			0
$848$	−29.8035	−	17.2071i	−1.02346	−	0.590893i
$849$		0			0
$850$		−	6.53023i		−	0.223985i
$851$			16.7822i			0.575288i
$852$		0			0
$853$	24.3086	+	14.0346i	0.832310	+	0.480534i	0.854643	−	0.519216i	$-0.173776\pi$
$853$	24.3086	+	14.0346i	0.832310	+	0.480534i	−0.0223330	+	0.999751i	$0.507109\pi$
$854$		0			0
$855$		0			0
$856$	62.4905	+	108.237i	2.13588	+	3.69946i
$857$	−8.55426	−	14.8164i	−0.292208	−	0.506119i	0.682123	−	0.731237i	$-0.261057\pi$
$857$	−8.55426	−	14.8164i	−0.292208	−	0.506119i	−0.974332	+	0.225118i	$0.927723\pi$
$858$		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
$863$	−38.7134	+	22.3512i	−1.31782	+	0.760844i	−0.983378	−	0.181573i	$-0.941881\pi$
$863$	−38.7134	+	22.3512i	−1.31782	+	0.760844i	−0.334442	+	0.942416i	$0.608548\pi$
$864$		0			0
$865$	25.4749	−	44.1238i	0.866172	−	1.50025i
$866$	21.1716			0.719442
$867$		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
$872$	−94.4096	−	54.5074i	−3.19711	−	1.84585i
$873$		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	$0.135723\pi$
$878$	97.6457			3.29538
$879$		0			0
$880$		−	84.5167i		−	2.84906i
$881$	9.98120			0.336275			0.168138	−	0.985764i	$-0.446225\pi$
$881$	9.98120			0.336275			0.168138	+	0.985764i	$0.446225\pi$
$882$		0			0
$883$	−32.0942			−1.08006			−0.540028	−	0.841647i	$-0.681586\pi$
$883$	−32.0942			−1.08006			−0.540028	+	0.841647i	$0.681586\pi$
$884$		−	35.5195i		−	1.19465i
$885$		0			0
$886$	−52.7561			−1.77238
$887$	4.26812	−	7.39260i	0.143309	−	0.248219i	−0.785432	−	0.618949i	$-0.787559\pi$
$887$	4.26812	−	7.39260i	0.143309	−	0.248219i	0.928741	+	0.370729i	$0.120892\pi$
$888$		0			0
$889$		0			0
$890$		−	19.9922i		−	0.670141i
$891$		0			0
$892$	−83.6498	−	48.2952i	−2.80080	−	1.61704i
$893$	0.288584	−	0.166614i	0.00965709	−	0.00557552i
$894$		0			0
$895$	34.7140	−	20.0422i	1.16036	−	0.669935i
$896$		0			0
$897$		0			0
$898$	−92.0554			−3.07193
$899$	8.97579	−	15.5465i	0.299359	−	0.518505i
$900$		0			0
$901$	−20.7752	+	11.9945i	−0.692121	+	0.399596i
$902$	37.0906	−	64.2429i	1.23498	−	2.13905i
$903$		0			0
$904$	−20.0011	−	34.6430i	−0.665228	−	1.15221i
$905$	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	$-0.345292\pi$
$908$	65.7932	+	113.957i	2.18342	+	3.78180i
$909$		0			0
$910$		0			0
$911$	−26.3261	−	15.1994i	−0.872221	−	0.503577i	−0.00413539	−	0.999991i	$-0.501316\pi$
$911$	−26.3261	−	15.1994i	−0.872221	−	0.503577i	−0.868086	+	0.496414i	$0.834650\pi$
$912$		0			0
$913$			46.4928i			1.53869i
$914$		−	0.655324i		−	0.0216762i
$915$		0			0
$916$	87.6765	+	50.6201i	2.89691	+	1.67253i
$917$		0			0
$918$		0			0
$919$	8.72153	+	15.1061i	0.287697	+	0.498305i	0.973260	−	0.229708i	$-0.0737772\pi$
$919$	8.72153	+	15.1061i	0.287697	+	0.498305i	−0.685563	+	0.728013i	$0.740444\pi$
$920$	−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
$926$	−1.83082	+	1.05702i	−0.0601644	+	0.0347359i
$927$		0			0
$928$	17.3191	−	29.9975i	0.568527	−	0.984717i
$929$	−10.4278			−0.342126			−0.171063	−	0.985260i	$-0.554720\pi$
$929$	−10.4278			−0.342126			−0.171063	+	0.985260i	$0.554720\pi$
$930$		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
$935$	−51.0212	−	29.4571i	−1.66857	−	0.963350i
$936$		0			0
$937$			51.3201i			1.67655i	0.545245	+	0.838277i	$0.316437\pi$
$937$			51.3201i			1.67655i	−0.545245	+	0.838277i	$0.683563\pi$
$938$		0			0
$939$		0			0
$940$	2.67342	−	4.63049i	0.0871973	−	0.151030i
$941$	−49.3347			−1.60827			−0.804133	−	0.594450i	$-0.797370\pi$
$941$	−49.3347			−1.60827			−0.804133	+	0.594450i	$0.797370\pi$
$942$		0			0
$943$		−	36.6625i		−	1.19389i
$944$	35.8114			1.16556
$945$		0			0
$946$	−87.6252			−2.84894
$947$		−	43.9327i		−	1.42762i	−0.700339	−	0.713810i	$-0.746968\pi$
$947$		−	43.9327i		−	1.42762i	0.700339	−	0.713810i	$-0.253032\pi$
$948$		0			0
$949$	−19.9657			−0.648113
$950$	0.381076	−	0.660044i	0.0123637	−	0.0214146i
$951$		0			0
$952$		0			0
$953$		−	21.0833i		−	0.682956i	−0.939890	−	0.341478i	$-0.889072\pi$
$953$		−	21.0833i		−	0.682956i	0.939890	−	0.341478i	$-0.110928\pi$
$954$		0			0
$955$	−1.92673	−	1.11240i	−0.0623477	−	0.0359964i
$956$	−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
$961$	14.8560			0.479226
$962$	−5.13650	+	8.89667i	−0.165607	+	0.286840i
$963$		0			0
$964$	−17.9941	+	10.3889i	−0.579550	+	0.334603i
$965$	1.97558	−	3.42181i	0.0635963	−	0.110152i
$966$		0			0
$967$	−27.6671	−	47.9209i	−0.889716	−	1.54103i	−0.840212	−	0.542259i	$-0.817569\pi$
$967$	−27.6671	−	47.9209i	−0.889716	−	1.54103i	−0.0495039	−	0.998774i	$-0.515764\pi$
$968$	−47.6533	−	27.5127i	−1.53164	−	0.884290i
$969$		0			0
$970$	44.2668	+	76.6723i	1.42132	+	2.46180i
$971$	3.41733	+	5.91898i	0.109667	+	0.189949i	0.915635	−	0.402010i	$-0.131688\pi$
$971$	3.41733	+	5.91898i	0.109667	+	0.189949i	−0.805968	+	0.591959i	$0.798355\pi$
$972$		0			0
$973$		0			0
$974$	−70.5830	−	40.7511i	−2.26162	−	1.30575i
$975$		0			0
$976$		−	17.0295i		−	0.545102i
$977$		−	36.0246i		−	1.15253i	−0.817264	−	0.576264i	$-0.804510\pi$
$977$		−	36.0246i		−	1.15253i	0.817264	−	0.576264i	$-0.195490\pi$
$978$		0			0
$979$	−12.5736	−	7.25938i	−0.401854	−	0.232011i
$980$		0			0
$981$		0			0
$982$	2.93856	+	5.08973i	0.0937731	+	0.162420i
$983$	−20.6863	−	35.8298i	−0.659791	−	1.14279i	−0.980670	−	0.195671i	$-0.937311\pi$
$983$	−20.6863	−	35.8298i	−0.659791	−	1.14279i	0.320878	−	0.947120i	$-0.396022\pi$
$984$		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
$989$	−37.5048	+	21.6534i	−1.19258	+	0.688539i
$990$		0			0
$991$	10.8367	−	18.7697i	0.344239	−	0.596240i	−0.640976	−	0.767561i	$-0.721470\pi$
$991$	10.8367	−	18.7697i	0.344239	−	0.596240i	0.985215	+	0.171321i	$0.0548036\pi$
$992$	−31.1504			−0.989025
$993$		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	$0.263693\pi$
$998$	−60.3721	−	34.8559i	−1.91105	−	1.10334i
$999$		0			0

Twists

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

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

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.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.57819i q^{2} -4.64709 q^{4} +(-1.16595 + 2.01948i) q^{5} -6.82470i q^{8} +O(q^{10})\)	\(q+2.57819i q^{2} -4.64709 q^{4} +(-1.16595 + 2.01948i) q^{5} -6.82470i q^{8} +(-5.20660 - 3.00603i) q^{10} +(-3.78114 + 2.18304i) q^{11} +(-1.14392 + 0.660445i) q^{13} +8.30123 q^{16} +(2.89327 - 5.01130i) q^{17} +(0.584876 - 0.337678i) q^{19} +(5.41825 - 9.38468i) q^{20} +(-5.62830 - 9.74851i) q^{22} +(-4.81799 - 2.78167i) q^{23} +(-0.218858 - 0.379074i) q^{25} +(-1.70276 - 2.94926i) q^{26} +(-3.86926 - 2.23392i) q^{29} +4.01796i q^{31} +7.75278i q^{32} +(12.9201 + 7.45942i) q^{34} +(-1.50829 - 2.61243i) q^{37} +(0.870601 + 1.50792i) q^{38} +(13.7823 + 7.95723i) q^{40} +(3.29501 + 5.70713i) q^{41} +(3.89217 - 6.74143i) q^{43} +(17.5713 - 10.1448i) q^{44} +(7.17168 - 12.4217i) q^{46} +0.493410 q^{47} +(0.977326 - 0.564259i) q^{50} +(5.31591 - 3.06914i) q^{52} +(-3.59025 - 2.07283i) q^{53} -10.1812i q^{55} +(5.75947 - 9.97570i) q^{58} +4.31398 q^{59} -2.05145i q^{61} -10.3591 q^{62} -3.38572 q^{64} -3.08017i q^{65} -4.82437 q^{67} +(-13.4453 + 23.2879i) q^{68} +1.17135i q^{71} +(13.0902 + 7.55766i) q^{73} +(6.73536 - 3.88866i) q^{74} +(-2.71797 + 1.56922i) q^{76} -10.6086 q^{79} +(-9.67878 + 16.7641i) q^{80} +(-14.7141 + 8.49518i) q^{82} +(5.32432 - 9.22199i) q^{83} +(6.74680 + 11.6858i) q^{85} +(17.3807 + 10.0348i) q^{86} +(14.8986 + 25.8051i) q^{88} +(1.66268 + 2.87984i) q^{89} +(22.3896 + 12.9266i) q^{92} +1.27211i q^{94} +1.57486i q^{95} +(-12.7531 - 7.36299i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4}+O(q^{10}) \) 48 * q - 48 * q^4	\( 48 q - 48 q^{4} - 24 q^{11} + 48 q^{16} - 48 q^{23} - 24 q^{25} + 96 q^{44} - 48 q^{50} + 48 q^{53} - 48 q^{64} - 168 q^{74} + 48 q^{79} - 24 q^{85} + 24 q^{86} + 144 q^{92}+O(q^{100}) \) 48 * q - 48 * q^4 - 24 * q^11 + 48 * q^16 - 48 * q^23 - 24 * q^25 + 96 * q^44 - 48 * q^50 + 48 * q^53 - 48 * q^64 - 168 * q^74 + 48 * q^79 - 24 * q^85 + 24 * q^86 + 144 * q^92

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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