LMFDB - Embedded newform 1323.2.s.d.656.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(656,1323)]

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, 5]))

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

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

chi := DirichletCharacter("1323.656");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: 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			656.14
Character	$\chi$	$=$	1323.656
Dual form			1323.2.s.d.962.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.105953 - 0.0611722i) q^{2} +(-0.992516 + 1.71909i) q^{4} -0.529430 q^{5} +0.487547i q^{8} +O(q^{10})$	\(q+(0.105953 - 0.0611722i) q^{2} +(-0.992516 + 1.71909i) q^{4} -0.529430 q^{5} +0.487547i q^{8} +(-0.0560949 + 0.0323864i) q^{10} -4.20449i q^{11} +(-1.74714 + 1.00871i) q^{13} +(-1.95521 - 3.38652i) q^{16} +(2.19381 + 3.79979i) q^{17} +(-4.54391 - 2.62343i) q^{19} +(0.525467 - 0.910136i) q^{20} +(-0.257198 - 0.445480i) q^{22} -6.27515i q^{23} -4.71970 q^{25} +(-0.123411 + 0.213753i) q^{26} +(7.27689 + 4.20131i) q^{29} +(-1.03204 - 0.595849i) q^{31} +(-1.25878 - 0.726755i) q^{32} +(0.464883 + 0.268400i) q^{34} +(1.61626 - 2.79945i) q^{37} -0.641923 q^{38} -0.258122i q^{40} +(0.0994958 + 0.172332i) q^{41} +(3.96309 - 6.86427i) q^{43} +(7.22789 + 4.17303i) q^{44} +(-0.383865 - 0.664873i) q^{46} +(-4.98595 - 8.63591i) q^{47} +(-0.500069 + 0.288715i) q^{50} -4.00466i q^{52} +(3.65249 - 2.10877i) q^{53} +2.22598i q^{55} +1.02802 q^{58} +(6.71960 - 11.6387i) q^{59} +(-11.3564 + 6.55662i) q^{61} -0.145798 q^{62} +7.64300 q^{64} +(0.924990 - 0.534043i) q^{65} +(3.29001 - 5.69847i) q^{67} -8.70956 q^{68} -8.50587i q^{71} +(4.86015 - 2.80601i) q^{73} -0.395481i q^{74} +(9.01980 - 5.20758i) q^{76} +(-0.286342 - 0.495959i) q^{79} +(1.03514 + 1.79292i) q^{80} +(0.0210838 + 0.0121728i) q^{82} +(-5.42692 + 9.39971i) q^{83} +(-1.16147 - 2.01172i) q^{85} -0.969724i q^{86} +2.04989 q^{88} +(6.43688 - 11.1490i) q^{89} +(10.7875 + 6.22819i) q^{92} +(-1.05656 - 0.610003i) q^{94} +(2.40568 + 1.38892i) q^{95} +(0.493773 + 0.285080i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4}+O(q^{10}) $ 48 * q + 24 * q^4	$ 48 q + 24 q^{4} - 24 q^{16} + 48 q^{25} + 120 q^{32} - 96 q^{44} - 48 q^{50} - 48 q^{53} - 48 q^{64} + 120 q^{65} - 24 q^{79} - 24 q^{85} + 144 q^{92} + 96 q^{95}+O(q^{100}) $ 48 * q + 24 * q^4 - 24 * q^16 + 48 * q^25 + 120 * q^32 - 96 * q^44 - 48 * q^50 - 48 * q^53 - 48 * q^64 + 120 * q^65 - 24 * q^79 - 24 * q^85 + 144 * q^92 + 96 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.105953	−	0.0611722i	0.0749204	−	0.0432553i	−0.462072	−	0.886842i	$-0.652894\pi$
$2$	0.105953	−	0.0611722i	0.0749204	−	0.0432553i	0.536992	+	0.843587i	$0.319560\pi$
$3$		0			0
$3$		0			0
$4$	−0.992516	+	1.71909i	−0.496258	+	0.859544i
$5$	−0.529430			−0.236768			−0.118384	−	0.992968i	$-0.537771\pi$
$5$	−0.529430			−0.236768			−0.118384	+	0.992968i	$0.537771\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			0.487547i			0.172374i
$9$		0			0
$10$	−0.0560949	+	0.0323864i	−0.0177388	+	0.0102415i
$11$		−	4.20449i		−	1.26770i	−0.773455	−	0.633851i	$-0.781473\pi$
$11$		−	4.20449i		−	1.26770i	0.773455	−	0.633851i	$-0.218527\pi$
$12$		0			0
$13$	−1.74714	+	1.00871i	−0.484570	+	0.279767i	−0.722319	−	0.691560i	$-0.756924\pi$
$13$	−1.74714	+	1.00871i	−0.484570	+	0.279767i	0.237749	+	0.971327i	$0.423590\pi$
$14$		0			0
$15$		0			0
$16$	−1.95521	−	3.38652i	−0.488802	−	0.846630i
$17$	2.19381	+	3.79979i	0.532077	+	0.921584i	0.999299	+	0.0374442i	$0.0119216\pi$
$17$	2.19381	+	3.79979i	0.532077	+	0.921584i	−0.467222	+	0.884140i	$0.654745\pi$
$18$		0			0
$19$	−4.54391	−	2.62343i	−1.04244	−	0.601855i	−0.121919	−	0.992540i	$-0.538905\pi$
$19$	−4.54391	−	2.62343i	−1.04244	−	0.601855i	−0.920524	+	0.390685i	$0.872238\pi$
$20$	0.525467	−	0.910136i	0.117498	−	0.203513i
$21$		0			0
$22$	−0.257198	−	0.445480i	−0.0548348	−	0.0949767i
$23$		−	6.27515i		−	1.30846i	−0.756296	−	0.654230i	$-0.772993\pi$
$23$		−	6.27515i		−	1.30846i	0.756296	−	0.654230i	$-0.227007\pi$
$24$		0			0
$25$	−4.71970			−0.943941
$26$	−0.123411	+	0.213753i	−0.0242028	+	0.0419205i
$27$		0			0
$28$		0			0
$29$	7.27689	+	4.20131i	1.35128	+	0.780164i	0.988429	−	0.151681i	$-0.0484687\pi$
$29$	7.27689	+	4.20131i	1.35128	+	0.780164i	0.362855	+	0.931846i	$0.381802\pi$
$30$		0			0
$31$	−1.03204	−	0.595849i	−0.185360	−	0.107018i	0.404449	−	0.914561i	$-0.367463\pi$
$31$	−1.03204	−	0.595849i	−0.185360	−	0.107018i	−0.589809	+	0.807543i	$0.700797\pi$
$32$	−1.25878	−	0.726755i	−0.222522	−	0.128473i
$33$		0			0
$34$	0.464883	+	0.268400i	0.0797268	+	0.0460303i
$35$		0			0
$36$		0			0
$37$	1.61626	−	2.79945i	0.265712	−	0.460226i	−0.702038	−	0.712139i	$-0.747726\pi$
$37$	1.61626	−	2.79945i	0.265712	−	0.460226i	0.967750	+	0.251913i	$0.0810597\pi$
$38$	−0.641923			−0.104134
$39$		0			0
$40$		−	0.258122i		−	0.0408126i
$41$	0.0994958	+	0.172332i	0.0155386	+	0.0269137i	0.873690	−	0.486483i	$-0.161720\pi$
$41$	0.0994958	+	0.172332i	0.0155386	+	0.0269137i	−0.858152	+	0.513396i	$0.828387\pi$
$42$		0			0
$43$	3.96309	−	6.86427i	0.604366	−	1.04679i	−0.387786	−	0.921750i	$-0.626760\pi$
$43$	3.96309	−	6.86427i	0.604366	−	1.04679i	0.992151	−	0.125042i	$-0.0399067\pi$
$44$	7.22789	+	4.17303i	1.08965	+	0.629107i
$45$		0			0
$46$	−0.383865	−	0.664873i	−0.0565978	−	0.0980302i
$47$	−4.98595	−	8.63591i	−0.727275	−	1.25968i	−0.958031	−	0.286665i	$-0.907453\pi$
$47$	−4.98595	−	8.63591i	−0.727275	−	1.25968i	0.230756	−	0.973012i	$-0.425880\pi$
$48$		0			0
$49$		0			0
$50$	−0.500069	+	0.288715i	−0.0707204	+	0.0408304i
$51$		0			0
$52$		−	4.00466i		−	0.555346i
$53$	3.65249	−	2.10877i	0.501708	−	0.289661i	−0.227711	−	0.973729i	$-0.573124\pi$
$53$	3.65249	−	2.10877i	0.501708	−	0.289661i	0.729419	+	0.684068i	$0.239791\pi$
$54$		0			0
$55$			2.22598i			0.300152i
$56$		0			0
$57$		0			0
$58$	1.02802			0.134985
$59$	6.71960	−	11.6387i	0.874817	−	1.51523i	0.0178590	−	0.999841i	$-0.494315\pi$
$59$	6.71960	−	11.6387i	0.874817	−	1.51523i	0.856958	−	0.515387i	$-0.172352\pi$
$60$		0			0
$61$	−11.3564	+	6.55662i	−1.45404	+	0.839489i	−0.998707	−	0.0508335i	$-0.983812\pi$
$61$	−11.3564	+	6.55662i	−1.45404	+	0.839489i	−0.455330	+	0.890323i	$0.650479\pi$
$62$	−0.145798			−0.0185163
$63$		0			0
$64$	7.64300			0.955375
$65$	0.924990	−	0.534043i	0.114731	−	0.0662399i
$66$		0			0
$67$	3.29001	−	5.69847i	0.401939	−	0.696179i	−0.592021	−	0.805923i	$-0.701670\pi$
$67$	3.29001	−	5.69847i	0.401939	−	0.696179i	0.993960	+	0.109744i	$0.0350030\pi$
$68$	−8.70956			−1.05619
$69$		0			0
$70$		0			0
$71$		−	8.50587i		−	1.00946i	−0.863277	−	0.504730i	$-0.831592\pi$
$71$		−	8.50587i		−	1.00946i	0.863277	−	0.504730i	$-0.168408\pi$
$72$		0			0
$73$	4.86015	−	2.80601i	0.568838	−	0.328419i	−0.187847	−	0.982198i	$-0.560151\pi$
$73$	4.86015	−	2.80601i	0.568838	−	0.328419i	0.756685	+	0.653780i	$0.226818\pi$
$74$		−	0.395481i		−	0.0459738i
$75$		0			0
$76$	9.01980	−	5.20758i	1.03464	−	0.597351i
$77$		0			0
$78$		0			0
$79$	−0.286342	−	0.495959i	−0.0322160	−	0.0557997i	0.849468	−	0.527640i	$-0.176923\pi$
$79$	−0.286342	−	0.495959i	−0.0322160	−	0.0557997i	−0.881684	+	0.471841i	$0.843590\pi$
$80$	1.03514	+	1.79292i	0.115733	+	0.200455i
$81$		0			0
$82$	0.0210838	+	0.0121728i	0.00232832	+	0.00134426i
$83$	−5.42692	+	9.39971i	−0.595682	+	1.03175i	0.397768	+	0.917486i	$0.369785\pi$
$83$	−5.42692	+	9.39971i	−0.595682	+	1.03175i	−0.993450	+	0.114266i	$0.963548\pi$
$84$		0			0
$85$	−1.16147	−	2.01172i	−0.125979	−	0.218202i
$86$		−	0.969724i		−	0.104568i
$87$		0			0
$88$	2.04989			0.218519
$89$	6.43688	−	11.1490i	0.682307	−	1.18179i	−0.291968	−	0.956428i	$-0.594310\pi$
$89$	6.43688	−	11.1490i	0.682307	−	1.18179i	0.974275	−	0.225363i	$-0.0723568\pi$
$90$		0			0
$91$		0			0
$92$	10.7875	+	6.22819i	1.12468	+	0.649333i
$93$		0			0
$94$	−1.05656	−	0.610003i	−0.108975	−	0.0629170i
$95$	2.40568	+	1.38892i	0.246817	+	0.142500i
$96$		0			0
$97$	0.493773	+	0.285080i	0.0501351	+	0.0289455i	0.524858	−	0.851190i	$-0.324118\pi$
$97$	0.493773	+	0.285080i	0.0501351	+	0.0289455i	−0.474723	+	0.880135i	$0.657452\pi$
$98$		0			0
$99$		0			0
$100$	4.68438	−	8.11359i	0.468438	−	0.811359i
$101$	−11.6310			−1.15733			−0.578666	−	0.815564i	$-0.696427\pi$
$101$	−11.6310			−1.15733			−0.578666	+	0.815564i	$0.696427\pi$
$102$		0			0
$103$			6.39705i			0.630320i	0.949038	+	0.315160i	$0.102058\pi$
$103$			6.39705i			0.630320i	−0.949038	+	0.315160i	$0.897942\pi$
$104$	−0.491795	−	0.851814i	−0.0482245	−	0.0835272i
$105$		0			0
$106$	0.257996	−	0.446862i	0.0250588	−	0.0434031i
$107$	0.219332	+	0.126632i	0.0212037	+	0.0122419i	0.510564	−	0.859840i	$-0.329437\pi$
$107$	0.219332	+	0.126632i	0.0212037	+	0.0122419i	−0.489361	+	0.872081i	$0.662770\pi$
$108$		0			0
$109$	−5.98602	−	10.3681i	−0.573357	−	0.993084i	−0.996218	−	0.0868891i	$-0.972307\pi$
$109$	−5.98602	−	10.3681i	−0.573357	−	0.993084i	0.422861	−	0.906195i	$-0.361026\pi$
$110$	0.136168	+	0.235851i	0.0129831	+	0.0224875i
$111$		0			0
$112$		0			0
$113$	−4.28636	+	2.47473i	−0.403227	+	0.232803i	−0.687875	−	0.725829i	$-0.741456\pi$
$113$	−4.28636	+	2.47473i	−0.403227	+	0.232803i	0.284648	+	0.958632i	$0.408123\pi$
$114$		0			0
$115$			3.32225i			0.309801i
$116$	−14.4449	+	8.33974i	−1.34117	+	0.774326i
$117$		0			0
$118$		−	1.64421i		−	0.151362i
$119$		0			0
$120$		0			0
$121$	−6.67776			−0.607069
$122$	−0.802166	+	1.38939i	−0.0726247	+	0.125790i
$123$		0			0
$124$	2.04863	−	1.18278i	0.183973	−	0.106217i
$125$	5.14590			0.460263
$126$		0			0
$127$	−3.68446			−0.326943			−0.163472	−	0.986548i	$-0.552269\pi$
$127$	−3.68446			−0.326943			−0.163472	+	0.986548i	$0.552269\pi$
$128$	3.32736	−	1.92105i	0.294100	−	0.169798i
$129$		0			0
$130$	0.0653372	−	0.113167i	0.00573045	−	0.00992543i
$131$	−5.45673			−0.476757			−0.238379	−	0.971172i	$-0.576616\pi$
$131$	−5.45673			−0.476757			−0.238379	+	0.971172i	$0.576616\pi$
$132$		0			0
$133$		0			0
$134$		−	0.805030i		−	0.0695440i
$135$		0			0
$136$	−1.85257	+	1.06958i	−0.158857	+	0.0917161i
$137$		−	1.61654i		−	0.138110i	−0.997613	−	0.0690551i	$-0.978002\pi$
$137$		−	1.61654i		−	0.138110i	0.997613	−	0.0690551i	$-0.0219984\pi$
$138$		0			0
$139$	−9.79085	+	5.65275i	−0.830449	+	0.479460i	−0.854006	−	0.520262i	$-0.825834\pi$
$139$	−9.79085	+	5.65275i	−0.830449	+	0.479460i	0.0235572	+	0.999722i	$0.492501\pi$
$140$		0			0
$141$		0			0
$142$	−0.520323	−	0.901226i	−0.0436645	−	0.0756292i
$143$	4.24113	+	7.34585i	0.354661	+	0.614291i
$144$		0			0
$145$	−3.85260	−	2.22430i	−0.319941	−	0.184718i
$146$	0.343300	−	0.594613i	0.0284117	−	0.0492105i
$147$		0			0
$148$	3.20833	+	5.55699i	0.263723	+	0.456782i
$149$		−	5.32808i		−	0.436494i	−0.975894	−	0.218247i	$-0.929966\pi$
$149$		−	5.32808i		−	0.436494i	0.975894	−	0.218247i	$-0.0700338\pi$
$150$		0			0
$151$	−2.64263			−0.215054			−0.107527	−	0.994202i	$-0.534293\pi$
$151$	−2.64263			−0.215054			−0.107527	+	0.994202i	$0.534293\pi$
$152$	1.27904	−	2.21537i	0.103744	−	0.179690i
$153$		0			0
$154$		0			0
$155$	0.546393	+	0.315460i	0.0438873	+	0.0253384i
$156$		0			0
$157$	11.3181	+	6.53448i	0.903279	+	0.521508i	0.878263	−	0.478179i	$-0.158703\pi$
$157$	11.3181	+	6.53448i	0.903279	+	0.521508i	0.0250163	+	0.999687i	$0.492036\pi$
$158$	−0.0606778	−	0.0350324i	−0.00482727	−	0.00278703i
$159$		0			0
$160$	0.666434	+	0.384766i	0.0526862	+	0.0304184i
$161$		0			0
$162$		0			0
$163$	−8.51345	+	14.7457i	−0.666825	+	1.15498i	0.311962	+	0.950095i	$0.399014\pi$
$163$	−8.51345	+	14.7457i	−0.666825	+	1.15498i	−0.978787	+	0.204880i	$0.934319\pi$
$164$	−0.395005			−0.0308447
$165$		0			0
$166$			1.32791i			0.103066i
$167$	−10.6605	−	18.4645i	−0.824932	−	1.42882i	−0.901971	−	0.431796i	$-0.857880\pi$
$167$	−10.6605	−	18.4645i	−0.824932	−	1.42882i	0.0770396	−	0.997028i	$-0.475453\pi$
$168$		0			0
$169$	−4.46499	+	7.73360i	−0.343461	+	0.594892i
$170$	−0.246123	−	0.142099i	−0.0188768	−	0.0108985i
$171$		0			0
$172$	7.86686	+	13.6258i	0.599842	+	1.03896i
$173$	10.2433	+	17.7418i	0.778781	+	1.34889i	0.932645	+	0.360796i	$0.117495\pi$
$173$	10.2433	+	17.7418i	0.778781	+	1.34889i	−0.153864	+	0.988092i	$0.549172\pi$
$174$		0			0
$175$		0			0
$176$	−14.2386	+	8.22066i	−1.07327	+	0.619655i
$177$		0			0
$178$		−	1.57503i		−	0.118054i
$179$	12.4770	−	7.20357i	0.932571	−	0.538420i	0.0449475	−	0.998989i	$-0.485688\pi$
$179$	12.4770	−	7.20357i	0.932571	−	0.538420i	0.887624	+	0.460569i	$0.152355\pi$
$180$		0			0
$181$			6.97309i			0.518306i	0.965836	+	0.259153i	$0.0834434\pi$
$181$			6.97309i			0.518306i	−0.965836	+	0.259153i	$0.916557\pi$
$182$		0			0
$183$		0			0
$184$	3.05943			0.225544
$185$	−0.855697	+	1.48211i	−0.0629121	+	0.108967i
$186$		0			0
$187$	15.9762	−	9.22386i	1.16829	−	0.674515i
$188$	19.7945			1.44366
$189$		0			0
$190$	0.339853			0.0246555
$191$	−9.38310	+	5.41734i	−0.678937	+	0.391985i	−0.799455	−	0.600727i	$-0.794878\pi$
$191$	−9.38310	+	5.41734i	−0.678937	+	0.391985i	0.120517	+	0.992711i	$0.461545\pi$
$192$		0			0
$193$	−5.26223	+	9.11444i	−0.378783	+	0.656072i	−0.990886	−	0.134707i	$-0.956991\pi$
$193$	−5.26223	+	9.11444i	−0.378783	+	0.656072i	0.612102	+	0.790779i	$0.290324\pi$
$194$	0.0697560			0.00500819
$195$		0			0
$196$		0			0
$197$		−	15.5156i		−	1.10544i	−0.833366	−	0.552721i	$-0.813590\pi$
$197$		−	15.5156i		−	1.10544i	0.833366	−	0.552721i	$-0.186410\pi$
$198$		0			0
$199$	−10.8668	+	6.27394i	−0.770326	+	0.444748i	−0.832991	−	0.553287i	$-0.813373\pi$
$199$	−10.8668	+	6.27394i	−0.770326	+	0.444748i	0.0626651	+	0.998035i	$0.480040\pi$
$200$		−	2.30108i		−	0.162711i
$201$		0			0
$202$	−1.23235	+	0.711497i	−0.0867078	+	0.0500608i
$203$		0			0
$204$		0			0
$205$	−0.0526760	−	0.0912375i	−0.00367905	−	0.00637231i
$206$	0.391322	+	0.677790i	0.0272647	+	0.0472238i
$207$		0			0
$208$	6.83206	+	3.94449i	0.473718	+	0.273501i
$209$	−11.0302	+	19.1048i	−0.762973	+	1.32151i
$210$		0			0
$211$	−1.19765	−	2.07438i	−0.0824494	−	0.142807i	0.821852	−	0.569701i	$-0.192941\pi$
$211$	−1.19765	−	2.07438i	−0.0824494	−	0.142807i	−0.904302	+	0.426894i	$0.859608\pi$
$212$			8.37194i			0.574987i
$213$		0			0
$214$	0.0309854			0.00211812
$215$	−2.09818	+	3.63415i	−0.143095	+	0.247847i
$216$		0			0
$217$		0			0
$218$	−1.26848	−	0.732357i	−0.0859123	−	0.0496015i
$219$		0			0
$220$	−3.82666	−	2.20932i	−0.257993	−	0.148953i
$221$	−7.66580	−	4.42585i	−0.515657	−	0.297715i
$222$		0			0
$223$	−2.42193	−	1.39830i	−0.162184	−	0.0936370i	0.416711	−	0.909039i	$-0.363183\pi$
$223$	−2.42193	−	1.39830i	−0.162184	−	0.0936370i	−0.578895	+	0.815402i	$0.696516\pi$
$224$		0			0
$225$		0			0
$226$	−0.302770	+	0.524413i	−0.0201400	+	0.0348834i
$227$	−2.84601			−0.188896			−0.0944480	−	0.995530i	$-0.530109\pi$
$227$	−2.84601			−0.188896			−0.0944480	+	0.995530i	$0.530109\pi$
$228$		0			0
$229$		−	23.7245i		−	1.56776i	−0.620912	−	0.783880i	$-0.713238\pi$
$229$		−	23.7245i		−	1.56776i	0.620912	−	0.783880i	$-0.286762\pi$
$230$	0.203229	+	0.352004i	0.0134006	+	0.0232104i
$231$		0			0
$232$	−2.04834	+	3.54782i	−0.134480	+	0.232926i
$233$	−16.2205	−	9.36488i	−1.06264	−	0.613514i	−0.136477	−	0.990643i	$-0.543578\pi$
$233$	−16.2205	−	9.36488i	−1.06264	−	0.613514i	−0.926161	+	0.377129i	$0.876911\pi$
$234$		0			0
$235$	2.63971	+	4.57211i	0.172196	+	0.298251i
$236$	13.3386	+	23.1032i	0.868270	+	1.50389i
$237$		0			0
$238$		0			0
$239$	−11.1421	+	6.43288i	−0.720721	+	0.416109i	−0.815018	−	0.579436i	$-0.803273\pi$
$239$	−11.1421	+	6.43288i	−0.720721	+	0.416109i	0.0942969	+	0.995544i	$0.469940\pi$
$240$		0			0
$241$		−	4.20405i		−	0.270807i	−0.990791	−	0.135403i	$-0.956767\pi$
$241$		−	4.20405i		−	0.270807i	0.990791	−	0.135403i	$-0.0432331\pi$
$242$	−0.707531	+	0.408493i	−0.0454818	+	0.0262590i
$243$		0			0
$244$		−	26.0302i		−	1.66641i
$245$		0			0
$246$		0			0
$247$	10.5851			0.673516
$248$	0.290504	−	0.503168i	0.0184470	−	0.0319512i
$249$		0			0
$250$	0.545226	−	0.314786i	0.0344831	−	0.0199088i
$251$	7.50592			0.473770			0.236885	−	0.971538i	$-0.423874\pi$
$251$	7.50592			0.473770			0.236885	+	0.971538i	$0.423874\pi$
$252$		0			0
$253$	−26.3838			−1.65874
$254$	−0.390381	+	0.225387i	−0.0244947	+	0.0141420i
$255$		0			0
$256$	−7.40797	+	12.8310i	−0.462998	+	0.801936i
$257$	5.03921			0.314337			0.157169	−	0.987572i	$-0.449763\pi$
$257$	5.03921			0.314337			0.157169	+	0.987572i	$0.449763\pi$
$258$		0			0
$259$		0			0
$260$			2.12018i			0.131488i
$261$		0			0
$262$	−0.578160	+	0.333801i	−0.0357188	+	0.0206223i
$263$			14.1444i			0.872182i	0.899903	+	0.436091i	$0.143637\pi$
$263$			14.1444i			0.872182i	−0.899903	+	0.436091i	$0.856363\pi$
$264$		0			0
$265$	−1.93374	+	1.11644i	−0.118789	+	0.0685826i
$266$		0			0
$267$		0			0
$268$	6.53078	+	11.3116i	0.398931	+	0.690969i
$269$	7.88856	+	13.6634i	0.480974	+	0.833071i	0.999762	−	0.0218318i	$-0.00694983\pi$
$269$	7.88856	+	13.6634i	0.480974	+	0.833071i	−0.518788	+	0.854903i	$0.673616\pi$
$270$		0			0
$271$	14.5560	+	8.40390i	0.884213	+	0.510501i	0.872045	−	0.489425i	$-0.162793\pi$
$271$	14.5560	+	8.40390i	0.884213	+	0.510501i	0.0121677	+	0.999926i	$0.496127\pi$
$272$	8.57871	−	14.8588i	0.520160	−	0.900944i
$273$		0			0
$274$	−0.0988873	−	0.171278i	−0.00597400	−	0.0103473i
$275$			19.8440i			1.19664i
$276$		0			0
$277$	17.8213			1.07078			0.535390	−	0.844605i	$-0.320165\pi$
$277$	17.8213			1.07078			0.535390	+	0.844605i	$0.320165\pi$
$278$	−0.691583	+	1.19786i	−0.0414784	+	0.0718427i
$279$		0			0
$280$		0			0
$281$	−7.59774	−	4.38656i	−0.453243	−	0.261680i	0.255956	−	0.966688i	$-0.417610\pi$
$281$	−7.59774	−	4.38656i	−0.453243	−	0.261680i	−0.709199	+	0.705008i	$0.750943\pi$
$282$		0			0
$283$	−18.7047	−	10.7991i	−1.11188	−	0.641942i	−0.172562	−	0.984999i	$-0.555204\pi$
$283$	−18.7047	−	10.7991i	−1.11188	−	0.641942i	−0.939315	+	0.343056i	$0.888538\pi$
$284$	14.6223	+	8.44221i	0.867676	+	0.500953i
$285$		0			0
$286$	0.898724	+	0.518879i	0.0531427	+	0.0306819i
$287$		0			0
$288$		0			0
$289$	−1.12560	+	1.94960i	−0.0662118	+	0.114682i
$290$	−0.544262			−0.0319601
$291$		0			0
$292$			11.1400i			0.651921i
$293$	−9.79756	−	16.9699i	−0.572379	−	0.991390i	−0.996321	−	0.0857006i	$-0.972687\pi$
$293$	−9.79756	−	16.9699i	−0.572379	−	0.991390i	0.423942	−	0.905690i	$-0.360646\pi$
$294$		0			0
$295$	−3.55755	+	6.16186i	−0.207129	+	0.358758i
$296$	1.36486	+	0.788003i	0.0793309	+	0.0458017i
$297$		0			0
$298$	−0.325931	−	0.564529i	−0.0188807	−	0.0327023i
$299$	6.32983	+	10.9636i	0.366063	+	0.634040i
$300$		0			0
$301$		0			0
$302$	−0.279996	+	0.161656i	−0.0161120	+	0.00930224i
$303$		0			0
$304$			20.5174i			1.17675i
$305$	6.01241	−	3.47127i	0.344270	−	0.198764i
$306$		0			0
$307$			27.7677i			1.58478i	0.610012	+	0.792392i	$0.291165\pi$
$307$			27.7677i			1.58478i	−0.610012	+	0.792392i	$0.708835\pi$
$308$		0			0
$309$		0			0
$310$	0.0771896			0.00438407
$311$	10.0080	−	17.3344i	0.567501	−	0.982941i	−0.429311	−	0.903157i	$-0.641244\pi$
$311$	10.0080	−	17.3344i	0.567501	−	0.982941i	0.996812	−	0.0797841i	$-0.0254231\pi$
$312$		0			0
$313$	15.9654	−	9.21765i	0.902420	−	0.521012i	0.0244352	−	0.999701i	$-0.492221\pi$
$313$	15.9654	−	9.21765i	0.902420	−	0.521012i	0.877984	+	0.478689i	$0.158888\pi$
$314$	1.59891			0.0902320
$315$		0			0
$316$	1.13680			0.0639498
$317$	−12.5992	+	7.27416i	−0.707642	+	0.408558i	−0.810187	−	0.586171i	$-0.800635\pi$
$317$	−12.5992	+	7.27416i	−0.707642	+	0.408558i	0.102545	+	0.994728i	$0.467301\pi$
$318$		0			0
$319$	17.6644	−	30.5956i	0.989016	−	1.71303i
$320$	−4.04643			−0.226202
$321$		0			0
$322$		0			0
$323$		−	23.0212i		−	1.28093i
$324$		0			0
$325$	8.24600	−	4.76083i	0.457406	−	0.264083i
$326$			2.08315i			0.115375i
$327$		0			0
$328$	−0.0840197	+	0.0485088i	−0.00463921	+	0.00267845i
$329$		0			0
$330$		0			0
$331$	14.8446	+	25.7115i	0.815930	+	1.41323i	0.908658	+	0.417541i	$0.137108\pi$
$331$	14.8446	+	25.7115i	0.815930	+	1.41323i	−0.0927274	+	0.995692i	$0.529559\pi$
$332$	−10.7726	−	18.6587i	−0.591224	−	1.02403i
$333$		0			0
$334$	−2.25903	−	1.30425i	−0.123608	−	0.0713653i
$335$	−1.74183	+	3.01694i	−0.0951664	+	0.164833i
$336$		0			0
$337$	−4.60606	−	7.97793i	−0.250908	−	0.434586i	0.712868	−	0.701298i	$-0.247396\pi$
$337$	−4.60606	−	7.97793i	−0.250908	−	0.434586i	−0.963776	+	0.266713i	$0.914063\pi$
$338$			1.09253i			0.0594260i
$339$		0			0
$340$	4.61110			0.250072
$341$	−2.50524	+	4.33921i	−0.135667	+	0.234981i
$342$		0			0
$343$		0			0
$344$	3.34665	+	1.93219i	0.180439	+	0.104177i
$345$		0			0
$346$	2.17062	+	1.25321i	0.116693	+	0.0673728i
$347$	15.7313	+	9.08247i	0.844501	+	0.487573i	0.858791	−	0.512325i	$-0.171216\pi$
$347$	15.7313	+	9.08247i	0.844501	+	0.487573i	−0.0142910	+	0.999898i	$0.504549\pi$
$348$		0			0
$349$	−5.70494	−	3.29375i	−0.305378	−	0.176310i	0.339478	−	0.940614i	$-0.389750\pi$
$349$	−5.70494	−	3.29375i	−0.305378	−	0.176310i	−0.644856	+	0.764304i	$0.723083\pi$
$350$		0			0
$351$		0			0
$352$	−3.05564	+	5.29252i	−0.162866	+	0.282092i
$353$	−20.9385			−1.11444			−0.557221	−	0.830364i	$-0.688132\pi$
$353$	−20.9385			−1.11444			−0.557221	+	0.830364i	$0.688132\pi$
$354$		0			0
$355$			4.50326i			0.239008i
$356$	12.7774	+	22.1311i	0.677201	+	1.17295i
$357$		0			0
$358$	0.881317	−	1.52649i	0.0465791	−	0.0806773i
$359$	12.3205	+	7.11324i	0.650251	+	0.375422i	0.788552	−	0.614968i	$-0.210831\pi$
$359$	12.3205	+	7.11324i	0.650251	+	0.375422i	−0.138302	+	0.990390i	$0.544164\pi$
$360$		0			0
$361$	4.26472	+	7.38671i	0.224459	+	0.388774i
$362$	0.426560	+	0.738823i	0.0224195	+	0.0388317i
$363$		0			0
$364$		0			0
$365$	−2.57311	+	1.48559i	−0.134683	+	0.0777591i
$366$		0			0
$367$		−	12.3827i		−	0.646373i	−0.946335	−	0.323186i	$-0.895246\pi$
$367$		−	12.3827i		−	0.646373i	0.946335	−	0.323186i	$-0.104754\pi$
$368$	−21.2509	+	12.2692i	−1.10778	+	0.639577i
$369$		0			0
$370$			0.209380i			0.0108851i
$371$		0			0
$372$		0			0
$373$	−21.3117			−1.10348			−0.551740	−	0.834016i	$-0.686036\pi$
$373$	−21.3117			−1.10348			−0.551740	+	0.834016i	$0.686036\pi$
$374$	1.12849	−	1.95460i	0.0583527	−	0.101070i
$375$		0			0
$376$	4.21041	−	2.43088i	0.217135	−	0.125363i
$377$	−16.9517			−0.873057
$378$		0			0
$379$	10.6001			0.544489			0.272244	−	0.962228i	$-0.412234\pi$
$379$	10.6001			0.544489			0.272244	+	0.962228i	$0.412234\pi$
$380$	−4.77535	+	2.75705i	−0.244970	+	0.141434i
$381$		0			0
$382$	−0.662781	+	1.14797i	−0.0339108	+	0.0587353i
$383$	12.6435			0.646052			0.323026	−	0.946390i	$-0.395300\pi$
$383$	12.6435			0.646052			0.323026	+	0.946390i	$0.395300\pi$
$384$		0			0
$385$		0			0
$386$			1.28761i			0.0655375i
$387$		0			0
$388$	−0.980156	+	0.565893i	−0.0497599	+	0.0287289i
$389$			13.2257i			0.670571i	0.942117	+	0.335286i	$0.108833\pi$
$389$			13.2257i			0.670571i	−0.942117	+	0.335286i	$0.891167\pi$
$390$		0			0
$391$	23.8442	−	13.7665i	1.20586	−	0.696201i
$392$		0			0
$393$		0			0
$394$	−0.949125	−	1.64393i	−0.0478162	−	0.0828201i
$395$	0.151598	+	0.262575i	0.00762772	+	0.0132116i
$396$		0			0
$397$	21.4672	+	12.3941i	1.07741	+	0.622043i	0.930197	−	0.367062i	$-0.119636\pi$
$397$	21.4672	+	12.3941i	1.07741	+	0.622043i	0.147214	+	0.989105i	$0.452970\pi$
$398$	−0.767582	+	1.32949i	−0.0384754	+	0.0666413i
$399$		0			0
$400$	9.22800	+	15.9834i	0.461400	+	0.799168i
$401$		−	3.69060i		−	0.184300i	−0.995745	−	0.0921499i	$-0.970626\pi$
$401$		−	3.69060i		−	0.184300i	0.995745	−	0.0921499i	$-0.0293739\pi$
$402$		0			0
$403$	2.40416			0.119760
$404$	11.5440	−	19.9948i	0.574336	−	0.994778i
$405$		0			0
$406$		0			0
$407$	−11.7703	−	6.79556i	−0.583430	−	0.336843i
$408$		0			0
$409$	16.0535	+	9.26852i	0.793797	+	0.458299i	0.841297	−	0.540573i	$-0.181792\pi$
$409$	16.0535	+	9.26852i	0.793797	+	0.458299i	−0.0475008	+	0.998871i	$0.515126\pi$
$410$	−0.0111624	−	0.00644462i	−0.000551272	−	0.000318277i
$411$		0			0
$412$	−10.9971	−	6.34918i	−0.541788	−	0.312802i
$413$		0			0
$414$		0			0
$415$	2.87317	−	4.97648i	0.141039	−	0.244286i
$416$	2.93235			0.143770
$417$		0			0
$418$			2.69896i			0.132011i
$419$	−1.46994	−	2.54600i	−0.0718111	−	0.124380i	0.827884	−	0.560899i	$-0.189545\pi$
$419$	−1.46994	−	2.54600i	−0.0718111	−	0.124380i	−0.899695	+	0.436519i	$0.856211\pi$
$420$		0			0
$421$	−14.1081	+	24.4359i	−0.687585	+	1.19093i	0.285031	+	0.958518i	$0.407996\pi$
$421$	−14.1081	+	24.4359i	−0.687585	+	1.19093i	−0.972617	+	0.232415i	$0.925337\pi$
$422$	−0.253790	−	0.146525i	−0.0123543	−	0.00713275i
$423$		0			0
$424$	1.02812	+	1.78076i	0.0499300	+	0.0864813i
$425$	−10.3541	−	17.9339i	−0.502249	−	0.869921i
$426$		0			0
$427$		0			0
$428$	−0.435382	+	0.251368i	−0.0210450	+	0.0121503i
$429$		0			0
$430$			0.513401i			0.0247584i
$431$	−5.85836	+	3.38232i	−0.282187	+	0.162921i	−0.634413	−	0.772994i	$-0.718758\pi$
$431$	−5.85836	+	3.38232i	−0.282187	+	0.162921i	0.352226	+	0.935915i	$0.385425\pi$
$432$		0			0
$433$		−	28.3475i		−	1.36229i	−0.732146	−	0.681147i	$-0.761481\pi$
$433$		−	28.3475i		−	1.36229i	0.732146	−	0.681147i	$-0.238519\pi$
$434$		0			0
$435$		0			0
$436$	23.7649			1.13813
$437$	−16.4624	+	28.5137i	−0.787503	+	1.36399i
$438$		0			0
$439$	−22.8208	+	13.1756i	−1.08918	+	0.628837i	−0.933358	−	0.358948i	$-0.883136\pi$
$439$	−22.8208	+	13.1756i	−1.08918	+	0.628837i	−0.155821	+	0.987785i	$0.549802\pi$
$440$	−1.08527			−0.0517382
$441$		0			0
$442$	−1.08296			−0.0515110
$443$	−4.75958	+	2.74795i	−0.226135	+	0.130559i	−0.608788	−	0.793333i	$-0.708344\pi$
$443$	−4.75958	+	2.74795i	−0.226135	+	0.130559i	0.382653	+	0.923892i	$0.375011\pi$
$444$		0			0
$445$	−3.40787	+	5.90261i	−0.161549	+	0.279810i
$446$	−0.342148			−0.0162012
$447$		0			0
$448$		0			0
$449$			7.38342i			0.348445i	0.984706	+	0.174223i	$0.0557412\pi$
$449$			7.38342i			0.348445i	−0.984706	+	0.174223i	$0.944259\pi$
$450$		0			0
$451$	0.724568	−	0.418329i	0.0341186	−	0.0196984i
$452$		−	9.82485i		−	0.462122i
$453$		0			0
$454$	−0.301544	+	0.174097i	−0.0141522	+	0.00817076i
$455$		0			0
$456$		0			0
$457$	−20.7109	−	35.8724i	−0.968817	−	1.67804i	−0.698991	−	0.715130i	$-0.746367\pi$
$457$	−20.7109	−	35.8724i	−0.968817	−	1.67804i	−0.269826	−	0.962909i	$-0.586966\pi$
$458$	−1.45128	−	2.51369i	−0.0678139	−	0.117457i
$459$		0			0
$460$	−5.71124	−	3.29739i	−0.266288	−	0.153741i
$461$	−5.44638	+	9.43341i	−0.253663	+	0.439357i	−0.964532	−	0.263968i	$-0.914969\pi$
$461$	−5.44638	+	9.43341i	−0.253663	+	0.439357i	0.710868	+	0.703325i	$0.248302\pi$
$462$		0			0
$463$	−2.87980	−	4.98796i	−0.133836	−	0.231810i	0.791316	−	0.611407i	$-0.209396\pi$
$463$	−2.87980	−	4.98796i	−0.133836	−	0.231810i	−0.925152	+	0.379597i	$0.876063\pi$
$464$		−	32.8578i		−	1.52538i
$465$		0			0
$466$	−2.29148			−0.106151
$467$	−11.9441	+	20.6878i	−0.552707	+	0.957316i	0.445371	+	0.895346i	$0.353072\pi$
$467$	−11.9441	+	20.6878i	−0.552707	+	0.957316i	−0.998078	+	0.0619701i	$0.980262\pi$
$468$		0			0
$469$		0			0
$470$	0.559372	+	0.322954i	0.0258019	+	0.0148967i
$471$		0			0
$472$	5.67440	+	3.27612i	0.261185	+	0.150795i
$473$	−28.8608	−	16.6628i	−1.32702	−	0.766156i
$474$		0			0
$475$	21.4459	+	12.3818i	0.984005	+	0.568116i
$476$		0			0
$477$		0			0
$478$	−0.787028	+	1.36317i	−0.0359978	+	0.0623500i
$479$	1.89529			0.0865980			0.0432990	−	0.999062i	$-0.486213\pi$
$479$	1.89529			0.0865980			0.0432990	+	0.999062i	$0.486213\pi$
$480$		0			0
$481$			6.52138i			0.297349i
$482$	−0.257171	−	0.445434i	−0.0117138	−	0.0202890i
$483$		0			0
$484$	6.62778	−	11.4797i	0.301263	−	0.521803i
$485$	−0.261418	−	0.150930i	−0.0118704	−	0.00685337i
$486$		0			0
$487$	−14.1124	−	24.4434i	−0.639494	−	1.10764i	−0.985544	−	0.169420i	$-0.945811\pi$
$487$	−14.1124	−	24.4434i	−0.639494	−	1.10764i	0.346050	−	0.938216i	$-0.387523\pi$
$488$	−3.19666	−	5.53677i	−0.144706	−	0.250638i
$489$		0			0
$490$		0			0
$491$	2.30250	−	1.32935i	0.103910	−	0.0599927i	−0.447144	−	0.894462i	$-0.647559\pi$
$491$	2.30250	−	1.32935i	0.103910	−	0.0599927i	0.551055	+	0.834469i	$0.314226\pi$
$492$		0			0
$493$			36.8675i			1.66043i
$494$	1.12153	−	0.647517i	0.0504601	−	0.0291332i
$495$		0			0
$496$			4.66003i			0.209242i
$497$		0			0
$498$		0			0
$499$	−12.5569			−0.562123			−0.281062	−	0.959690i	$-0.590687\pi$
$499$	−12.5569			−0.562123			−0.281062	+	0.959690i	$0.590687\pi$
$500$	−5.10739	+	8.84625i	−0.228409	+	0.395617i
$501$		0			0
$502$	0.795278	−	0.459154i	0.0354950	−	0.0204930i
$503$	−18.1502			−0.809278			−0.404639	−	0.914476i	$-0.632603\pi$
$503$	−18.1502			−0.809278			−0.404639	+	0.914476i	$0.632603\pi$
$504$		0			0
$505$	6.15782			0.274020
$506$	−2.79546	+	1.61396i	−0.124273	+	0.0717491i
$507$		0			0
$508$	3.65689	−	6.33391i	0.162248	−	0.281022i
$509$	18.6765			0.827823			0.413912	−	0.910317i	$-0.364162\pi$
$509$	18.6765			0.827823			0.413912	+	0.910317i	$0.364162\pi$
$510$		0			0
$511$		0			0
$512$			9.49685i			0.419705i
$513$		0			0
$514$	0.533921	−	0.308260i	0.0235503	−	0.0135967i
$515$		−	3.38679i		−	0.149240i
$516$		0			0
$517$	−36.3096	+	20.9634i	−1.59690	+	0.921968i
$518$		0			0
$519$		0			0
$520$	0.260371	+	0.450975i	0.0114180	+	0.0197766i
$521$	9.03326	+	15.6461i	0.395754	+	0.685466i	0.993197	−	0.116445i	$-0.0371499\pi$
$521$	9.03326	+	15.6461i	0.395754	+	0.685466i	−0.597443	+	0.801911i	$0.703817\pi$
$522$		0			0
$523$	−18.3024	−	10.5669i	−0.800308	−	0.462058i	0.0432710	−	0.999063i	$-0.486222\pi$
$523$	−18.3024	−	10.5669i	−0.800308	−	0.462058i	−0.843579	+	0.537005i	$0.819555\pi$
$524$	5.41590	−	9.38061i	0.236595	−	0.409794i
$525$		0			0
$526$	0.865245	+	1.49865i	0.0377265	+	0.0653442i
$527$		−	5.22872i		−	0.227766i
$528$		0			0
$529$	−16.3775			−0.712065
$530$	−0.136591	+	0.236582i	−0.00593312	+	0.0102765i
$531$		0			0
$532$		0			0
$533$	−0.347667	−	0.200725i	−0.0150591	−	0.00869439i
$534$		0			0
$535$	−0.116121	−	0.0670425i	−0.00502035	−	0.00289850i
$536$	2.77827	+	1.60403i	0.120003	+	0.0692837i
$537$		0			0
$538$	1.67164	+	0.965122i	0.0720695	+	0.0416093i
$539$		0			0
$540$		0			0
$541$	−8.88661	+	15.3921i	−0.382065	+	0.661757i	−0.991357	−	0.131189i	$-0.958120\pi$
$541$	−8.88661	+	15.3921i	−0.382065	+	0.661757i	0.609292	+	0.792946i	$0.291454\pi$
$542$	2.05634			0.0883274
$543$		0			0
$544$		−	6.37745i		−	0.273431i
$545$	3.16918	+	5.48918i	0.135753	+	0.235131i
$546$		0			0
$547$	14.1560	−	24.5190i	0.605268	−	1.04835i	−0.386741	−	0.922188i	$-0.626399\pi$
$547$	14.1560	−	24.5190i	0.605268	−	1.04835i	0.992009	−	0.126166i	$-0.0402673\pi$
$548$	2.77897	+	1.60444i	0.118712	+	0.0685383i
$549$		0			0
$550$	1.21390	+	2.10254i	0.0517608	+	0.0896524i
$551$	−22.0437	−	38.1808i	−0.939092	−	1.62655i
$552$		0			0
$553$		0			0
$554$	1.88823	−	1.09017i	0.0802232	−	0.0463169i
$555$		0			0
$556$		−	22.4418i		−	0.951744i
$557$	10.1510	−	5.86069i	0.430113	−	0.248326i	−0.269282	−	0.963061i	$-0.586786\pi$
$557$	10.1510	−	5.86069i	0.430113	−	0.248326i	0.699395	+	0.714736i	$0.253453\pi$
$558$		0			0
$559$			15.9905i			0.676326i
$560$		0			0
$561$		0			0
$562$	−1.07334			−0.0452762
$563$	18.3014	−	31.6990i	0.771314	−	1.33595i	−0.165529	−	0.986205i	$-0.552933\pi$
$563$	18.3014	−	31.6990i	0.771314	−	1.33595i	0.936843	−	0.349750i	$-0.113733\pi$
$564$		0			0
$565$	2.26933	−	1.31020i	0.0954713	−	0.0551204i
$566$	−2.64243			−0.111070
$567$		0			0
$568$	4.14701			0.174005
$569$	32.6468	−	18.8486i	1.36862	−	0.790176i	0.377872	−	0.925858i	$-0.376656\pi$
$569$	32.6468	−	18.8486i	1.36862	−	0.790176i	0.990752	+	0.135682i	$0.0433225\pi$
$570$		0			0
$571$	−14.1123	+	24.4432i	−0.590581	+	1.02292i	0.403574	+	0.914947i	$0.367768\pi$
$571$	−14.1123	+	24.4432i	−0.590581	+	1.02292i	−0.994154	+	0.107968i	$0.965565\pi$
$572$	−16.8376			−0.704013
$573$		0			0
$574$		0			0
$575$			29.6168i			1.23511i
$576$		0			0
$577$	8.12775	−	4.69256i	0.338363	−	0.195354i	−0.321185	−	0.947016i	$-0.604081\pi$
$577$	8.12775	−	4.69256i	0.338363	−	0.195354i	0.659548	+	0.751663i	$0.270748\pi$
$578$			0.275422i			0.0114560i
$579$		0			0
$580$	7.64754	−	4.41531i	0.317547	−	0.183336i
$581$		0			0
$582$		0			0
$583$	−8.86629	−	15.3569i	−0.367204	−	0.636017i
$584$	1.36806	+	2.36955i	0.0566108	+	0.0980527i
$585$		0			0
$586$	−2.07617	−	1.19868i	−0.0857657	−	0.0495169i
$587$	23.1819	−	40.1523i	0.956821	−	1.65726i	0.226675	−	0.973971i	$-0.427215\pi$
$587$	23.1819	−	40.1523i	0.956821	−	1.65726i	0.730146	−	0.683291i	$-0.239452\pi$
$588$		0			0
$589$	3.12633	+	5.41496i	0.128818	+	0.223120i
$590$			0.870494i			0.0358377i
$591$		0			0
$592$	−12.6405			−0.519522
$593$	−9.07080	+	15.7111i	−0.372493	+	0.645177i	−0.989948	−	0.141429i	$-0.954830\pi$
$593$	−9.07080	+	15.7111i	−0.372493	+	0.645177i	0.617455	+	0.786606i	$0.288164\pi$
$594$		0			0
$595$		0			0
$596$	9.15945	+	5.28821i	0.375186	+	0.216613i
$597$		0			0
$598$	1.34133	+	0.774419i	0.0548512	+	0.0316684i
$599$	6.02771	+	3.48010i	0.246286	+	0.142193i	0.618062	−	0.786129i	$-0.287918\pi$
$599$	6.02771	+	3.48010i	0.246286	+	0.142193i	−0.371777	+	0.928322i	$0.621251\pi$
$600$		0			0
$601$	2.08865	+	1.20588i	0.0851976	+	0.0491889i	0.541994	−	0.840383i	$-0.317670\pi$
$601$	2.08865	+	1.20588i	0.0851976	+	0.0491889i	−0.456796	+	0.889572i	$0.651003\pi$
$602$		0			0
$603$		0			0
$604$	2.62285	−	4.54292i	0.106722	−	0.184849i
$605$	3.53540			0.143735
$606$		0			0
$607$		−	12.7370i		−	0.516979i	−0.966014	−	0.258489i	$-0.916775\pi$
$607$		−	12.7370i		−	0.516979i	0.966014	−	0.258489i	$-0.0832247\pi$
$608$	3.81318	+	6.60462i	0.154645	+	0.267853i
$609$		0			0
$610$	0.424690	−	0.735585i	0.0171952	−	0.0297830i
$611$	17.4223	+	10.0588i	0.704832	+	0.406935i
$612$		0			0
$613$	5.16761	+	8.95057i	0.208718	+	0.361510i	0.951311	−	0.308233i	$-0.0997376\pi$
$613$	5.16761	+	8.95057i	0.208718	+	0.361510i	−0.742593	+	0.669743i	$0.766404\pi$
$614$	1.69861	+	2.94208i	0.0685503	+	0.118733i
$615$		0			0
$616$		0			0
$617$	41.3741	−	23.8873i	1.66566	−	0.961668i	0.695721	−	0.718313i	$-0.255085\pi$
$617$	41.3741	−	23.8873i	1.66566	−	0.961668i	0.969937	−	0.243355i	$-0.0782481\pi$
$618$		0			0
$619$		−	40.7177i		−	1.63658i	−0.574804	−	0.818291i	$-0.694922\pi$
$619$		−	40.7177i		−	1.63658i	0.574804	−	0.818291i	$-0.305078\pi$
$620$	−1.08461	+	0.626198i	−0.0435589	+	0.0251487i
$621$		0			0
$622$		−	2.44884i		−	0.0981897i
$623$		0			0
$624$		0			0
$625$	20.8741			0.834965
$626$	1.12773	−	1.95328i	0.0450731	−	0.0780689i
$627$		0			0
$628$	−22.4667	+	12.9711i	−0.896519	+	0.517605i
$629$	14.1831			0.565517
$630$		0			0
$631$	11.4782			0.456942			0.228471	−	0.973551i	$-0.426627\pi$
$631$	11.4782			0.456942			0.228471	+	0.973551i	$0.426627\pi$
$632$	0.241803	−	0.139605i	0.00961841	−	0.00555319i
$633$		0			0
$634$	−0.889953	+	1.54144i	−0.0353446	+	0.0612186i
$635$	1.95066			0.0774097
$636$		0			0
$637$		0			0
$638$		−	4.32228i		−	0.171121i
$639$		0			0
$640$	−1.76160	+	1.01706i	−0.0696334	+	0.0402029i
$641$		−	35.3134i		−	1.39480i	−0.716684	−	0.697398i	$-0.754341\pi$
$641$		−	35.3134i		−	1.39480i	0.716684	−	0.697398i	$-0.245659\pi$
$642$		0			0
$643$	6.09416	−	3.51846i	0.240330	−	0.138755i	−0.374998	−	0.927025i	$-0.622357\pi$
$643$	6.09416	−	3.51846i	0.240330	−	0.138755i	0.615328	+	0.788271i	$0.289023\pi$
$644$		0			0
$645$		0			0
$646$	−1.40826	−	2.43917i	−0.0554071	−	0.0959680i
$647$	−7.49709	−	12.9853i	−0.294741	−	0.510507i	0.680184	−	0.733042i	$-0.261900\pi$
$647$	−7.49709	−	12.9853i	−0.294741	−	0.510507i	−0.974925	+	0.222535i	$0.928567\pi$
$648$		0			0
$649$	−48.9347	−	28.2525i	−1.92086	−	1.10901i
$650$	0.582461	−	1.00885i	0.0228460	−	0.0395704i
$651$		0			0
$652$	−16.8995	−	29.2708i	−0.661835	−	1.14633i
$653$		−	4.79890i		−	0.187795i	−0.995582	−	0.0938977i	$-0.970067\pi$
$653$		−	4.79890i		−	0.187795i	0.995582	−	0.0938977i	$-0.0299327\pi$
$654$		0			0
$655$	2.88896			0.112881
$656$	0.389070	−	0.673889i	0.0151906	−	0.0263109i
$657$		0			0
$658$		0			0
$659$	13.4562	+	7.76893i	0.524179	+	0.302635i	0.738643	−	0.674097i	$-0.235467\pi$
$659$	13.4562	+	7.76893i	0.524179	+	0.302635i	−0.214464	+	0.976732i	$0.568800\pi$
$660$		0			0
$661$	−18.2131	−	10.5154i	−0.708409	−	0.409000i	0.102062	−	0.994778i	$-0.467456\pi$
$661$	−18.2131	−	10.5154i	−0.708409	−	0.409000i	−0.810472	+	0.585778i	$0.800789\pi$
$662$	3.14566	+	1.81615i	0.122260	+	0.0705866i
$663$		0			0
$664$	−4.58280	−	2.64588i	−0.177847	−	0.102680i
$665$		0			0
$666$		0			0
$667$	26.3639	−	45.6636i	1.02081	−	1.76810i
$668$	42.3227			1.63752
$669$		0			0
$670$			0.426207i			0.0164658i
$671$	27.5673	+	47.7479i	1.06422	+	1.84329i
$672$		0			0
$673$	10.7194	−	18.5665i	0.413201	−	0.715686i	−0.582036	−	0.813163i	$-0.697744\pi$
$673$	10.7194	−	18.5665i	0.413201	−	0.715686i	0.995238	+	0.0974770i	$0.0310772\pi$
$674$	−0.976056	−	0.563526i	−0.0375963	−	0.0217062i
$675$		0			0
$676$	−8.86315	−	15.3514i	−0.340891	−	0.590440i
$677$	−9.03150	−	15.6430i	−0.347109	−	0.601210i	0.638626	−	0.769517i	$-0.279503\pi$
$677$	−9.03150	−	15.6430i	−0.347109	−	0.601210i	−0.985735	+	0.168308i	$0.946170\pi$
$678$		0			0
$679$		0			0
$680$	0.980808	−	0.566270i	0.0376123	−	0.0217155i
$681$		0			0
$682$			0.613005i			0.0234732i
$683$	39.4602	−	22.7824i	1.50990	−	0.871743i	0.509970	−	0.860192i	$-0.329657\pi$
$683$	39.4602	−	22.7824i	1.50990	−	0.871743i	0.999933	−	0.0115508i	$-0.00367681\pi$
$684$		0			0
$685$			0.855844i			0.0327001i
$686$		0			0
$687$		0			0
$688$	−30.9947			−1.18166
$689$	−4.25428	+	7.36863i	−0.162075	+	0.280723i
$690$		0			0
$691$	−3.33627	+	1.92620i	−0.126918	+	0.0732760i	−0.562115	−	0.827059i	$-0.690012\pi$
$691$	−3.33627	+	1.92620i	−0.126918	+	0.0732760i	0.435197	+	0.900335i	$0.356679\pi$
$692$	−40.6664			−1.54590
$693$		0			0
$694$	2.22238			0.0843604
$695$	5.18357	−	2.99273i	0.196624	−	0.113521i
$696$		0			0
$697$	−0.436550	+	0.756126i	−0.0165355	+	0.0286403i
$698$	−0.805943			−0.0305054
$699$		0			0
$700$		0			0
$701$			46.5216i			1.75710i	0.477653	+	0.878549i	$0.341488\pi$
$701$			46.5216i			1.75710i	−0.477653	+	0.878549i	$0.658512\pi$
$702$		0			0
$703$	−14.6883	+	8.48028i	−0.553979	+	0.319840i
$704$		−	32.1349i		−	1.21113i
$705$		0			0
$706$	−2.21850	+	1.28085i	−0.0834944	+	0.0482055i
$707$		0			0
$708$		0			0
$709$	14.6187	+	25.3203i	0.549017	+	0.950925i	0.998342	+	0.0575566i	$0.0183310\pi$
$709$	14.6187	+	25.3203i	0.549017	+	0.950925i	−0.449326	+	0.893368i	$0.648336\pi$
$710$	0.275474	+	0.477136i	0.0103384	+	0.0179066i
$711$		0			0
$712$	5.43565	+	3.13828i	0.203710	+	0.117612i
$713$	−3.73904	+	6.47621i	−0.140028	+	0.242536i
$714$		0			0
$715$	−2.24538	−	3.88911i	−0.0839724	−	0.145445i
$716$			28.5986i			1.06878i
$717$		0			0
$718$	1.74053			0.0649560
$719$	1.68561	−	2.91956i	0.0628627	−	0.108881i	−0.832881	−	0.553452i	$-0.813310\pi$
$719$	1.68561	−	2.91956i	0.0628627	−	0.108881i	0.895744	+	0.444570i	$0.146644\pi$
$720$		0			0
$721$		0			0
$722$	0.903723	+	0.521765i	0.0336331	+	0.0194181i
$723$		0			0
$724$	−11.9874	−	6.92091i	−0.445507	−	0.257214i
$725$	−34.3448	−	19.8290i	−1.27553	−	0.736429i
$726$		0			0
$727$	−4.34397	−	2.50799i	−0.161109	−	0.0930164i	0.417278	−	0.908779i	$-0.362984\pi$
$727$	−4.34397	−	2.50799i	−0.161109	−	0.0930164i	−0.578387	+	0.815763i	$0.696318\pi$
$728$		0			0
$729$		0			0
$730$	−0.181753	+	0.314806i	−0.00672698	+	0.0116515i
$731$	34.7771			1.28628
$732$		0			0
$733$			22.7332i			0.839670i	0.907601	+	0.419835i	$0.137912\pi$
$733$			22.7332i			0.839670i	−0.907601	+	0.419835i	$0.862088\pi$
$734$	−0.757478	−	1.31199i	−0.0279590	−	0.0484265i
$735$		0			0
$736$	−4.56050	+	7.89901i	−0.168102	+	0.291162i
$737$	−23.9592	−	13.8328i	−0.882547	−	0.509539i
$738$		0			0
$739$	1.19511	+	2.06999i	0.0439628	+	0.0761458i	0.887170	−	0.461444i	$-0.152668\pi$
$739$	1.19511	+	2.06999i	0.0439628	+	0.0761458i	−0.843207	+	0.537589i	$0.819335\pi$
$740$	−1.69859	−	2.94204i	−0.0624413	−	0.108151i
$741$		0			0
$742$		0			0
$743$	36.1039	−	20.8446i	1.32453	−	0.764715i	0.340078	−	0.940397i	$-0.389546\pi$
$743$	36.1039	−	20.8446i	1.32453	−	0.764715i	0.984447	+	0.175682i	$0.0562131\pi$
$744$		0			0
$745$			2.82085i			0.103348i
$746$	−2.25805	+	1.30369i	−0.0826732	+	0.0477314i
$747$		0			0
$748$			36.6193i			1.33893i
$749$		0			0
$750$		0			0
$751$	26.5421			0.968534			0.484267	−	0.874920i	$-0.339086\pi$
$751$	26.5421			0.968534			0.484267	+	0.874920i	$0.339086\pi$
$752$	−19.4971	+	33.7700i	−0.710987	+	1.23147i
$753$		0			0
$754$	−1.79609	+	1.03697i	−0.0654097	+	0.0377643i
$755$	1.39909			0.0509180
$756$		0			0
$757$	20.3580			0.739923			0.369961	−	0.929047i	$-0.379371\pi$
$757$	20.3580			0.739923			0.369961	+	0.929047i	$0.379371\pi$
$758$	1.12311	−	0.648430i	0.0407933	−	0.0235520i
$759$		0			0
$760$	−0.677163	+	1.17288i	−0.0245633	+	0.0425448i
$761$	−25.9156			−0.939439			−0.469720	−	0.882816i	$-0.655645\pi$
$761$	−25.9156			−0.939439			−0.469720	+	0.882816i	$0.655645\pi$
$762$		0			0
$763$		0			0
$764$		−	21.5072i		−	0.778102i
$765$		0			0
$766$	1.33962	−	0.773430i	0.0484024	−	0.0279452i
$767$			27.1126i			0.978979i
$768$		0			0
$769$	18.8269	−	10.8697i	0.678914	−	0.391971i	−0.120532	−	0.992709i	$-0.538460\pi$
$769$	18.8269	−	10.8697i	0.678914	−	0.391971i	0.799446	+	0.600738i	$0.205127\pi$
$770$		0			0
$771$		0			0
$772$	−10.4457	−	18.0925i	−0.375948	−	0.651162i
$773$	−10.1606	−	17.5987i	−0.365453	−	0.632982i	0.623396	−	0.781906i	$-0.285752\pi$
$773$	−10.1606	−	17.5987i	−0.365453	−	0.632982i	−0.988849	+	0.148924i	$0.952419\pi$
$774$		0			0
$775$	4.87093	+	2.81223i	0.174969	+	0.101018i
$776$	−0.138990	+	0.240738i	−0.00498945	+	0.00864197i
$777$		0			0
$778$	0.809047	+	1.40131i	0.0290058	+	0.0502394i
$779$		−	1.04408i		−	0.0374080i
$780$		0			0
$781$	−35.7629			−1.27970
$782$	1.68425	−	2.91721i	0.0602288	−	0.104319i
$783$		0			0
$784$		0			0
$785$	−5.99211	−	3.45955i	−0.213868	−	0.123477i
$786$		0			0
$787$	−16.4065	−	9.47232i	−0.584830	−	0.337652i	0.178221	−	0.983991i	$-0.442966\pi$
$787$	−16.4065	−	9.47232i	−0.584830	−	0.337652i	−0.763051	+	0.646339i	$0.776299\pi$
$788$	26.6727	+	15.3995i	0.950176	+	0.548584i
$789$		0			0
$790$	0.0321246	+	0.0185472i	0.00114294	+	0.000659879i
$791$		0			0
$792$		0			0
$793$	13.2275	−	22.9107i	0.469722	−	0.813583i
$794$	3.03270			0.107627
$795$		0			0
$796$		−	24.9079i		−	0.882838i
$797$	−11.4342	−	19.8047i	−0.405022	−	0.701518i	0.589302	−	0.807913i	$-0.299403\pi$
$797$	−11.4342	−	19.8047i	−0.405022	−	0.701518i	−0.994324	+	0.106394i	$0.966069\pi$
$798$		0			0
$799$	21.8764	−	37.8911i	0.773932	−	1.34049i
$800$	5.94106	+	3.43007i	0.210048	+	0.121271i
$801$		0			0
$802$	−0.225762	−	0.391032i	−0.00797194	−	0.0138078i
$803$	−11.7978	−	20.4345i	−0.416337	−	0.721117i
$804$		0			0
$805$		0			0
$806$	0.254729	−	0.147068i	0.00897246	−	0.00518025i
$807$		0			0
$808$		−	5.67068i		−	0.199494i
$809$	−10.3762	+	5.99072i	−0.364809	+	0.210622i	−0.671188	−	0.741287i	$-0.734216\pi$
$809$	−10.3762	+	5.99072i	−0.364809	+	0.210622i	0.306379	+	0.951909i	$0.400882\pi$
$810$		0			0
$811$		−	36.9371i		−	1.29704i	−0.761199	−	0.648519i	$-0.775389\pi$
$811$		−	36.9371i		−	1.29704i	0.761199	−	0.648519i	$-0.224611\pi$
$812$		0			0
$813$		0			0
$814$	−1.66280			−0.0582811
$815$	4.50728	−	7.80683i	0.157883	−	0.273461i
$816$		0			0
$817$	−36.0158	+	20.7937i	−1.26003	+	0.727481i
$818$	2.26790			0.0792954
$819$		0			0
$820$	0.209127			0.00730304
$821$	32.6907	−	18.8740i	1.14091	−	0.658707i	0.194257	−	0.980951i	$-0.437771\pi$
$821$	32.6907	−	18.8740i	1.14091	−	0.658707i	0.946657	+	0.322244i	$0.104437\pi$
$822$		0			0
$823$	10.5082	−	18.2008i	0.366293	−	0.634438i	−0.622690	−	0.782469i	$-0.713960\pi$
$823$	10.5082	−	18.2008i	0.366293	−	0.634438i	0.988983	+	0.148031i	$0.0472934\pi$
$824$	−3.11886			−0.108651
$825$		0			0
$826$		0			0
$827$			23.9104i			0.831447i	0.909491	+	0.415724i	$0.136472\pi$
$827$			23.9104i			0.831447i	−0.909491	+	0.415724i	$0.863528\pi$
$828$		0			0
$829$	21.7251	−	12.5430i	0.754542	−	0.435635i	−0.0727906	−	0.997347i	$-0.523190\pi$
$829$	21.7251	−	12.5430i	0.754542	−	0.435635i	0.827333	+	0.561712i	$0.189857\pi$
$830$		−	0.703034i		−	0.0244027i
$831$		0			0
$832$	−13.3534	+	7.70960i	−0.462946	+	0.267282i
$833$		0			0
$834$		0			0
$835$	5.64397	+	9.77564i	0.195318	+	0.338300i
$836$	−21.8952	−	37.9237i	−0.757263	−	1.31162i
$837$		0			0
$838$	−0.311489	−	0.179838i	−0.0107602	−	0.00621242i
$839$	−3.72840	+	6.45777i	−0.128719	+	0.222947i	−0.923180	−	0.384367i	$-0.874420\pi$
$839$	−3.72840	+	6.45777i	−0.128719	+	0.222947i	0.794462	+	0.607314i	$0.207753\pi$
$840$		0			0
$841$	20.8021	+	36.0303i	0.717313	+	1.24242i
$842$			3.45209i			0.118967i
$843$		0			0
$844$	4.75473			0.163665
$845$	2.36390	−	4.09439i	0.0813206	−	0.140851i
$846$		0			0
$847$		0			0
$848$	−14.2828	−	8.24615i	−0.490472	−	0.283174i
$849$		0			0
$850$	−2.19411	−	1.26677i	−0.0752574	−	0.0434499i
$851$	−17.5670	−	10.1423i	−0.602187	−	0.347673i
$852$		0			0
$853$	−2.19184	−	1.26546i	−0.0750472	−	0.0433285i	0.462007	−	0.886876i	$-0.347130\pi$
$853$	−2.19184	−	1.26546i	−0.0750472	−	0.0433285i	−0.537054	+	0.843548i	$0.680463\pi$
$854$		0			0
$855$		0			0
$856$	−0.0617388	+	0.106935i	−0.00211019	+	0.00365495i
$857$	19.0420			0.650461			0.325231	−	0.945635i	$-0.394558\pi$
$857$	19.0420			0.650461			0.325231	+	0.945635i	$0.394558\pi$
$858$		0			0
$859$			10.2585i			0.350017i	0.984567	+	0.175008i	$0.0559952\pi$
$859$			10.2585i			0.350017i	−0.984567	+	0.175008i	$0.944005\pi$
$860$	−4.16495	−	7.21390i	−0.142024	−	0.245992i
$861$		0			0
$862$	−0.413809	+	0.716738i	−0.0140944	+	0.0244122i
$863$	3.81858	+	2.20466i	0.129986	+	0.0750475i	0.563583	−	0.826059i	$-0.309422\pi$
$863$	3.81858	+	2.20466i	0.129986	+	0.0750475i	−0.433597	+	0.901107i	$0.642756\pi$
$864$		0			0
$865$	−5.42309	−	9.39306i	−0.184390	−	0.319374i
$866$	−1.73408	−	3.00352i	−0.0589265	−	0.102064i
$867$		0			0
$868$		0			0
$869$	−2.08526	+	1.20392i	−0.0707375	+	0.0408403i
$870$		0			0
$871$			13.2747i			0.449797i
$872$	5.05493	−	2.91847i	0.171182	−	0.0988317i
$873$		0			0
$874$			4.02816i			0.136255i
$875$		0			0
$876$		0			0
$877$	−50.1173			−1.69234			−0.846170	−	0.532913i	$-0.821097\pi$
$877$	−50.1173			−1.69234			−0.846170	+	0.532913i	$0.821097\pi$
$878$	−1.61196	+	2.79200i	−0.0544011	+	0.0942255i
$879$		0			0
$880$	7.53833	−	4.35226i	0.254117	−	0.146715i
$881$	42.5809			1.43459			0.717294	−	0.696771i	$-0.245381\pi$
$881$	42.5809			1.43459			0.717294	+	0.696771i	$0.245381\pi$
$882$		0			0
$883$	−15.6590			−0.526967			−0.263483	−	0.964664i	$-0.584871\pi$
$883$	−15.6590			−0.526967			−0.263483	+	0.964664i	$0.584871\pi$
$884$	15.2169	−	8.78546i	0.511798	−	0.295487i
$885$		0			0
$886$	−0.336196	+	0.582309i	−0.0112947	+	0.0195630i
$887$	24.7838			0.832159			0.416080	−	0.909328i	$-0.363404\pi$
$887$	24.7838			0.832159			0.416080	+	0.909328i	$0.363404\pi$
$888$		0			0
$889$		0			0
$890$			0.833869i			0.0279513i
$891$		0			0
$892$	4.80760	−	2.77567i	0.160970	−	0.0929363i
$893$			52.3210i			1.75086i
$894$		0			0
$895$	−6.60567	+	3.81379i	−0.220803	+	0.127481i
$896$		0			0
$897$		0			0
$898$	0.451660	+	0.782299i	0.0150721	+	0.0261056i
$899$	−5.00670	−	8.67186i	−0.166983	−	0.289223i
$900$		0			0
$901$	16.0257	+	9.25246i	0.533895	+	0.308244i
$902$	0.0511803	−	0.0886468i	0.00170412	−	0.00295162i
$903$		0			0
$904$	−1.20655	−	2.08980i	−0.0401292	−	0.0695058i
$905$		−	3.69176i		−	0.122718i
$906$		0			0
$907$	44.1033			1.46443			0.732213	−	0.681076i	$-0.238487\pi$
$907$	44.1033			1.46443			0.732213	+	0.681076i	$0.238487\pi$
$908$	2.82471	−	4.89254i	0.0937412	−	0.162365i
$909$		0			0
$910$		0			0
$911$	−22.3259	−	12.8899i	−0.739691	−	0.427061i	0.0822657	−	0.996610i	$-0.473784\pi$
$911$	−22.3259	−	12.8899i	−0.739691	−	0.427061i	−0.821957	+	0.569549i	$0.807118\pi$
$912$		0			0
$913$	39.5210	+	22.8175i	1.30795	+	0.755148i
$914$	−4.38879	−	2.53387i	−0.145168	−	0.0838129i
$915$		0			0
$916$	40.7845	+	23.5470i	1.34756	+	0.778013i
$917$		0			0
$918$		0			0
$919$	−26.3551	+	45.6484i	−0.869375	+	1.50580i	−0.00673776	+	0.999977i	$0.502145\pi$
$919$	−26.3551	+	45.6484i	−0.869375	+	1.50580i	−0.862637	+	0.505824i	$0.831189\pi$
$920$	−1.61975			−0.0534016
$921$		0			0
$922$			1.33267i			0.0438891i
$923$	8.57999	+	14.8610i	0.282414	+	0.489155i
$924$		0			0
$925$	−7.62828	+	13.2126i	−0.250816	+	0.434426i
$926$	−0.610249	−	0.352327i	−0.0200540	−	0.0115782i
$927$		0			0
$928$	−6.10666	−	10.5770i	−0.200461	−	0.347208i
$929$	−1.69009	−	2.92732i	−0.0554500	−	0.0960422i	0.836968	−	0.547252i	$-0.184326\pi$
$929$	−1.69009	−	2.92732i	−0.0554500	−	0.0960422i	−0.892418	+	0.451210i	$0.850993\pi$
$930$		0			0
$931$		0			0
$932$	32.1981	−	18.5896i	1.05468	−	0.608922i
$933$		0			0
$934$			2.92259i			0.0956300i
$935$	−8.45827	+	4.88338i	−0.276615	+	0.159704i
$936$		0			0
$937$			8.26186i			0.269903i	0.990852	+	0.134952i	$0.0430879\pi$
$937$			8.26186i			0.269903i	−0.990852	+	0.134952i	$0.956912\pi$
$938$		0			0
$939$		0			0
$940$	−10.4798			−0.341814
$941$	−26.1882	+	45.3592i	−0.853710	+	1.47867i	0.0241274	+	0.999709i	$0.492319\pi$
$941$	−26.1882	+	45.3592i	−0.853710	+	1.47867i	−0.877837	+	0.478960i	$0.841014\pi$
$942$		0			0
$943$	1.08141	−	0.624351i	0.0352155	−	0.0203317i
$944$	−52.5528			−1.71045
$945$		0			0
$946$	−4.07720			−0.132561
$947$	−6.53348	+	3.77211i	−0.212310	+	0.122577i	−0.602384	−	0.798206i	$-0.705783\pi$
$947$	−6.53348	+	3.77211i	−0.212310	+	0.122577i	0.390075	+	0.920783i	$0.372449\pi$
$948$		0			0
$949$	−5.66092	+	9.80500i	−0.183761	+	0.318284i
$950$	3.02969			0.0982960
$951$		0			0
$952$		0			0
$953$			45.2795i			1.46675i	0.679825	+	0.733374i	$0.262056\pi$
$953$			45.2795i			1.46675i	−0.679825	+	0.733374i	$0.737944\pi$
$954$		0			0
$955$	4.96769	−	2.86810i	0.160751	−	0.0928095i
$956$		−	25.5390i		−	0.825989i
$957$		0			0
$958$	0.200812	−	0.115939i	0.00648795	−	0.00374582i
$959$		0			0
$960$		0			0
$961$	−14.7899	−	25.6169i	−0.477094	−	0.826352i
$962$	0.398927	+	0.690963i	0.0128619	+	0.0222775i
$963$		0			0
$964$	7.22714	+	4.17259i	0.232770	+	0.134390i
$965$	2.78598	−	4.82546i	0.0896838	−	0.155337i
$966$		0			0
$967$	−6.82403	−	11.8196i	−0.219446	−	0.380092i	0.735193	−	0.677858i	$-0.237092\pi$
$967$	−6.82403	−	11.8196i	−0.219446	−	0.380092i	−0.954639	+	0.297766i	$0.903758\pi$
$968$		−	3.25572i		−	0.104643i
$969$		0			0
$970$	−0.0369309			−0.00118578
$971$	−1.73552	+	3.00601i	−0.0556955	+	0.0964675i	−0.892529	−	0.450990i	$-0.851071\pi$
$971$	−1.73552	+	3.00601i	−0.0556955	+	0.0964675i	0.836833	+	0.547458i	$0.184404\pi$
$972$		0			0
$973$		0			0
$974$	−2.99051	−	1.72657i	−0.0958222	−	0.0553230i
$975$		0			0
$976$	44.4082	+	25.6391i	1.42147	+	0.820688i
$977$	−2.21904	−	1.28116i	−0.0709932	−	0.0409880i	0.464083	−	0.885792i	$-0.346384\pi$
$977$	−2.21904	−	1.28116i	−0.0709932	−	0.0409880i	−0.535076	+	0.844804i	$0.679717\pi$
$978$		0			0
$979$	−46.8759	−	27.0638i	−1.49816	−	0.864963i
$980$		0			0
$981$		0			0
$982$	0.162638	−	0.281698i	0.00519000	−	0.00898935i
$983$	−39.1498			−1.24869			−0.624343	−	0.781150i	$-0.714633\pi$
$983$	−39.1498			−1.24869			−0.624343	+	0.781150i	$0.714633\pi$
$984$		0			0
$985$			8.21443i			0.261733i
$986$	2.25527	+	3.90624i	0.0718224	+	0.124400i
$987$		0			0
$988$	−10.5059	+	18.1968i	−0.334238	+	0.578917i
$989$	−43.0743	−	24.8690i	−1.36968	−	0.790788i
$990$		0			0
$991$	8.10333	+	14.0354i	0.257411	+	0.445848i	0.965547	−	0.260227i	$-0.0837974\pi$
$991$	8.10333	+	14.0354i	0.257411	+	0.445848i	−0.708137	+	0.706075i	$0.750464\pi$
$992$	0.866073	+	1.50008i	0.0274978	+	0.0476277i
$993$		0			0
$994$		0			0
$995$	5.75320	−	3.32161i	0.182389	−	0.105302i
$996$		0			0
$997$			24.8268i			0.786274i	0.919480	+	0.393137i	$0.128610\pi$
$997$			24.8268i			0.786274i	−0.919480	+	0.393137i	$0.871390\pi$
$998$	−1.33044	+	0.768132i	−0.0421145	+	0.0243148i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.s.d.656.14		48
3.2	odd	2		441.2.s.d.362.11		48
7.2	even	3		1323.2.o.e.440.12		48
7.3	odd	6		1323.2.i.d.521.12		48
7.4	even	3		1323.2.i.d.521.11		48
7.5	odd	6		1323.2.o.e.440.11		48
7.6	odd	2	inner	1323.2.s.d.656.13		48
9.4	even	3		441.2.i.d.68.13		48
9.5	odd	6		1323.2.i.d.1097.12		48
21.2	odd	6		441.2.o.e.146.14	yes	48
21.5	even	6		441.2.o.e.146.13	✓	48
21.11	odd	6		441.2.i.d.227.12		48
21.17	even	6		441.2.i.d.227.11		48
21.20	even	2		441.2.s.d.362.12		48
63.4	even	3		441.2.s.d.374.12		48
63.5	even	6		1323.2.o.e.881.12		48
63.13	odd	6		441.2.i.d.68.14		48
63.23	odd	6		1323.2.o.e.881.11		48
63.31	odd	6		441.2.s.d.374.11		48
63.32	odd	6	inner	1323.2.s.d.962.13		48
63.40	odd	6		441.2.o.e.293.14	yes	48
63.41	even	6		1323.2.i.d.1097.11		48
63.58	even	3		441.2.o.e.293.13	yes	48
63.59	even	6	inner	1323.2.s.d.962.14		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.13		48	9.4	even	3
441.2.i.d.68.14		48	63.13	odd	6
441.2.i.d.227.11		48	21.17	even	6
441.2.i.d.227.12		48	21.11	odd	6
441.2.o.e.146.13	✓	48	21.5	even	6
441.2.o.e.146.14	yes	48	21.2	odd	6
441.2.o.e.293.13	yes	48	63.58	even	3
441.2.o.e.293.14	yes	48	63.40	odd	6
441.2.s.d.362.11		48	3.2	odd	2
441.2.s.d.362.12		48	21.20	even	2
441.2.s.d.374.11		48	63.31	odd	6
441.2.s.d.374.12		48	63.4	even	3
1323.2.i.d.521.11		48	7.4	even	3
1323.2.i.d.521.12		48	7.3	odd	6
1323.2.i.d.1097.11		48	63.41	even	6
1323.2.i.d.1097.12		48	9.5	odd	6
1323.2.o.e.440.11		48	7.5	odd	6
1323.2.o.e.440.12		48	7.2	even	3
1323.2.o.e.881.11		48	63.23	odd	6
1323.2.o.e.881.12		48	63.5	even	6
1323.2.s.d.656.13		48	7.6	odd	2	inner
1323.2.s.d.656.14		48	1.1	even	1	trivial
1323.2.s.d.962.13		48	63.32	odd	6	inner
1323.2.s.d.962.14		48	63.59	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.105953 - 0.0611722i) q^{2} +(-0.992516 + 1.71909i) q^{4} -0.529430 q^{5} +0.487547i q^{8} +O(q^{10})\)	\(q+(0.105953 - 0.0611722i) q^{2} +(-0.992516 + 1.71909i) q^{4} -0.529430 q^{5} +0.487547i q^{8} +(-0.0560949 + 0.0323864i) q^{10} -4.20449i q^{11} +(-1.74714 + 1.00871i) q^{13} +(-1.95521 - 3.38652i) q^{16} +(2.19381 + 3.79979i) q^{17} +(-4.54391 - 2.62343i) q^{19} +(0.525467 - 0.910136i) q^{20} +(-0.257198 - 0.445480i) q^{22} -6.27515i q^{23} -4.71970 q^{25} +(-0.123411 + 0.213753i) q^{26} +(7.27689 + 4.20131i) q^{29} +(-1.03204 - 0.595849i) q^{31} +(-1.25878 - 0.726755i) q^{32} +(0.464883 + 0.268400i) q^{34} +(1.61626 - 2.79945i) q^{37} -0.641923 q^{38} -0.258122i q^{40} +(0.0994958 + 0.172332i) q^{41} +(3.96309 - 6.86427i) q^{43} +(7.22789 + 4.17303i) q^{44} +(-0.383865 - 0.664873i) q^{46} +(-4.98595 - 8.63591i) q^{47} +(-0.500069 + 0.288715i) q^{50} -4.00466i q^{52} +(3.65249 - 2.10877i) q^{53} +2.22598i q^{55} +1.02802 q^{58} +(6.71960 - 11.6387i) q^{59} +(-11.3564 + 6.55662i) q^{61} -0.145798 q^{62} +7.64300 q^{64} +(0.924990 - 0.534043i) q^{65} +(3.29001 - 5.69847i) q^{67} -8.70956 q^{68} -8.50587i q^{71} +(4.86015 - 2.80601i) q^{73} -0.395481i q^{74} +(9.01980 - 5.20758i) q^{76} +(-0.286342 - 0.495959i) q^{79} +(1.03514 + 1.79292i) q^{80} +(0.0210838 + 0.0121728i) q^{82} +(-5.42692 + 9.39971i) q^{83} +(-1.16147 - 2.01172i) q^{85} -0.969724i q^{86} +2.04989 q^{88} +(6.43688 - 11.1490i) q^{89} +(10.7875 + 6.22819i) q^{92} +(-1.05656 - 0.610003i) q^{94} +(2.40568 + 1.38892i) q^{95} +(0.493773 + 0.285080i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4}+O(q^{10}) \) 48 * q + 24 * q^4	\( 48 q + 24 q^{4} - 24 q^{16} + 48 q^{25} + 120 q^{32} - 96 q^{44} - 48 q^{50} - 48 q^{53} - 48 q^{64} + 120 q^{65} - 24 q^{79} - 24 q^{85} + 144 q^{92} + 96 q^{95}+O(q^{100}) \) 48 * q + 24 * q^4 - 24 * q^16 + 48 * q^25 + 120 * q^32 - 96 * q^44 - 48 * q^50 - 48 * q^53 - 48 * q^64 + 120 * q^65 - 24 * q^79 - 24 * q^85 + 144 * q^92 + 96 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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