LMFDB - Embedded newform 1323.2.o.e.440.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1323.440");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			440.12
Character	$\chi$	$=$	1323.440
Dual form			1323.2.o.e.881.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.105953 - 0.0611722i) q^{2} +(-0.992516 - 1.71909i) q^{4} +(0.264715 + 0.458500i) q^{5} +0.487547i q^{8} +O(q^{10})$	\(q+(-0.105953 - 0.0611722i) q^{2} +(-0.992516 - 1.71909i) q^{4} +(0.264715 + 0.458500i) q^{5} +0.487547i q^{8} -0.0647728i q^{10} +(3.64120 + 2.10225i) q^{11} +(-1.74714 + 1.00871i) q^{13} +(-1.95521 + 3.38652i) q^{16} -4.38762 q^{17} +5.24685i q^{19} +(0.525467 - 0.910136i) q^{20} +(-0.257198 - 0.445480i) q^{22} +(-5.43444 + 3.13757i) q^{23} +(2.35985 - 4.08738i) q^{25} +0.246821 q^{26} +(7.27689 + 4.20131i) q^{29} +(1.03204 - 0.595849i) q^{31} +(1.25878 - 0.726755i) q^{32} +(0.464883 + 0.268400i) q^{34} -3.23252 q^{37} +(0.320962 - 0.555922i) q^{38} +(-0.223540 + 0.129061i) q^{40} +(0.0994958 + 0.172332i) q^{41} +(3.96309 - 6.86427i) q^{43} -8.34605i q^{44} +0.767730 q^{46} +(-4.98595 + 8.63591i) q^{47} +(-0.500069 + 0.288715i) q^{50} +(3.46814 + 2.00233i) q^{52} +4.21753i q^{53} +2.22598i q^{55} +(-0.514008 - 0.890287i) q^{58} +(6.71960 + 11.6387i) q^{59} +(11.3564 + 6.55662i) q^{61} -0.145798 q^{62} +7.64300 q^{64} +(-0.924990 - 0.534043i) q^{65} +(3.29001 + 5.69847i) q^{67} +(4.35478 + 7.54270i) q^{68} -8.50587i q^{71} +5.61202i q^{73} +(0.342497 + 0.197741i) q^{74} +(9.01980 - 5.20758i) q^{76} +(-0.286342 + 0.495959i) q^{79} -2.07029 q^{80} -0.0243455i q^{82} +(-5.42692 + 9.39971i) q^{83} +(-1.16147 - 2.01172i) q^{85} +(-0.839806 + 0.484862i) q^{86} +(-1.02494 + 1.77525i) q^{88} -12.8738 q^{89} +(10.7875 + 6.22819i) q^{92} +(1.05656 - 0.610003i) q^{94} +(-2.40568 + 1.38892i) q^{95} +(0.493773 + 0.285080i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4}+O(q^{10}) $ 48 * q + 24 * q^4	$ 48 q + 24 q^{4} + 24 q^{11} - 24 q^{16} + 48 q^{23} - 24 q^{25} - 120 q^{32} - 48 q^{50} - 48 q^{64} - 120 q^{65} + 168 q^{74} - 24 q^{79} - 24 q^{85} - 24 q^{86} + 144 q^{92} - 96 q^{95}+O(q^{100}) $ 48 * q + 24 * q^4 + 24 * q^11 - 24 * q^16 + 48 * q^23 - 24 * q^25 - 120 * q^32 - 48 * q^50 - 48 * q^64 - 120 * q^65 + 168 * q^74 - 24 * q^79 - 24 * q^85 - 24 * q^86 + 144 * q^92 - 96 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.105953	−	0.0611722i	−0.0749204	−	0.0432553i	0.462072	−	0.886842i	$-0.347106\pi$
$2$	−0.105953	−	0.0611722i	−0.0749204	−	0.0432553i	−0.536992	+	0.843587i	$0.680440\pi$
$3$		0			0
$3$		0			0
$4$	−0.992516	−	1.71909i	−0.496258	−	0.859544i
$5$	0.264715	+	0.458500i	0.118384	+	0.205047i	0.919127	−	0.393960i	$-0.128895\pi$
$5$	0.264715	+	0.458500i	0.118384	+	0.205047i	−0.800743	+	0.599008i	$0.795562\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			0.487547i			0.172374i
$9$		0			0
$10$		−	0.0647728i		−	0.0204830i
$11$	3.64120	+	2.10225i	1.09786	+	0.633851i	0.935659	−	0.352906i	$-0.114807\pi$
$11$	3.64120	+	2.10225i	1.09786	+	0.633851i	0.162204	+	0.986757i	$0.448140\pi$
$12$		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
$17$	−4.38762			−1.06415			−0.532077	−	0.846696i	$-0.678588\pi$
$17$	−4.38762			−1.06415			−0.532077	+	0.846696i	$0.678588\pi$
$18$		0			0
$19$			5.24685i			1.20371i	0.798605	+	0.601855i	$0.205572\pi$
$19$			5.24685i			1.20371i	−0.798605	+	0.601855i	$0.794428\pi$
$20$	0.525467	−	0.910136i	0.117498	−	0.203513i
$21$		0			0
$22$	−0.257198	−	0.445480i	−0.0548348	−	0.0949767i
$23$	−5.43444	+	3.13757i	−1.13316	+	0.654230i	−0.944727	−	0.327857i	$-0.893674\pi$
$23$	−5.43444	+	3.13757i	−1.13316	+	0.654230i	−0.188431	+	0.982086i	$0.560340\pi$
$24$		0			0
$25$	2.35985	−	4.08738i	0.471970	−	0.817477i
$26$	0.246821			0.0484056
$27$		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	$-0.632537\pi$
$31$	1.03204	−	0.595849i	0.185360	−	0.107018i	0.589809	+	0.807543i	$0.299203\pi$
$32$	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
$37$	−3.23252			−0.531424			−0.265712	−	0.964053i	$-0.585607\pi$
$37$	−3.23252			−0.531424			−0.265712	+	0.964053i	$0.585607\pi$
$38$	0.320962	−	0.555922i	0.0520668	−	0.0901824i
$39$		0			0
$40$	−0.223540	+	0.129061i	−0.0353448	+	0.0204063i
$41$	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	$-0.0399067\pi$
$44$		−	8.34605i		−	1.25821i
$45$		0			0
$46$	0.767730			0.113196
$47$	−4.98595	+	8.63591i	−0.727275	+	1.25968i	0.230756	+	0.973012i	$0.425880\pi$
$47$	−4.98595	+	8.63591i	−0.727275	+	1.25968i	−0.958031	+	0.286665i	$0.907453\pi$
$48$		0			0
$49$		0			0
$50$	−0.500069	+	0.288715i	−0.0707204	+	0.0408304i
$51$		0			0
$52$	3.46814	+	2.00233i	0.480944	+	0.277673i
$53$			4.21753i			0.579323i	0.957129	+	0.289661i	$0.0935427\pi$
$53$			4.21753i			0.579323i	−0.957129	+	0.289661i	$0.906457\pi$
$54$		0			0
$55$			2.22598i			0.300152i
$56$		0			0
$57$		0			0
$58$	−0.514008	−	0.890287i	−0.0674925	−	0.116900i
$59$	6.71960	+	11.6387i	0.874817	+	1.51523i	0.856958	+	0.515387i	$0.172352\pi$
$59$	6.71960	+	11.6387i	0.874817	+	1.51523i	0.0178590	+	0.999841i	$0.494315\pi$
$60$		0			0
$61$	11.3564	+	6.55662i	1.45404	+	0.839489i	0.998707	−	0.0508335i	$-0.0161878\pi$
$61$	11.3564	+	6.55662i	1.45404	+	0.839489i	0.455330	+	0.890323i	$0.349521\pi$
$62$	−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	0.993960	−	0.109744i	$-0.0350030\pi$
$67$	3.29001	+	5.69847i	0.401939	+	0.696179i	−0.592021	+	0.805923i	$0.701670\pi$
$68$	4.35478	+	7.54270i	0.528095	+	0.914687i
$69$		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
$73$			5.61202i			0.656837i	0.944532	+	0.328419i	$0.106516\pi$
$73$			5.61202i			0.656837i	−0.944532	+	0.328419i	$0.893484\pi$
$74$	0.342497	+	0.197741i	0.0398145	+	0.0229869i
$75$		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	−0.881684	−	0.471841i	$-0.843590\pi$
$79$	−0.286342	+	0.495959i	−0.0322160	+	0.0557997i	0.849468	+	0.527640i	$0.176923\pi$
$80$	−2.07029			−0.231465
$81$		0			0
$82$		−	0.0243455i		−	0.00268851i
$83$	−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
$86$	−0.839806	+	0.484862i	−0.0905586	+	0.0522840i
$87$		0			0
$88$	−1.02494	+	1.77525i	−0.109259	+	0.189243i
$89$	−12.8738			−1.36461			−0.682307	−	0.731065i	$-0.739023\pi$
$89$	−12.8738			−1.36461			−0.682307	+	0.731065i	$0.739023\pi$
$90$		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
$100$	−9.36876			−0.936876
$101$	5.81552	−	10.0728i	0.578666	−	1.00228i	−0.416966	−	0.908922i	$-0.636907\pi$
$101$	5.81552	−	10.0728i	0.578666	−	1.00228i	0.995633	−	0.0933576i	$-0.0297600\pi$
$102$		0			0
$103$	5.54001	−	3.19853i	0.545874	−	0.315160i	−0.201582	−	0.979472i	$-0.564608\pi$
$103$	5.54001	−	3.19853i	0.545874	−	0.315160i	0.747456	+	0.664311i	$0.231275\pi$
$104$	−0.491795	−	0.851814i	−0.0482245	−	0.0835272i
$105$		0			0
$106$	0.257996	−	0.446862i	0.0250588	−	0.0434031i
$107$		−	0.253263i		−	0.0244839i	−0.999925	−	0.0122419i	$-0.996103\pi$
$107$		−	0.253263i		−	0.0244839i	0.999925	−	0.0122419i	$-0.00389683\pi$
$108$		0			0
$109$	11.9720			1.14671			0.573357	−	0.819306i	$-0.305641\pi$
$109$	11.9720			1.14671			0.573357	+	0.819306i	$0.305641\pi$
$110$	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
$115$	−2.87715	−	1.66113i	−0.268296	−	0.154901i
$116$		−	16.6795i		−	1.54865i
$117$		0			0
$118$		−	1.64421i		−	0.151362i
$119$		0			0
$120$		0			0
$121$	3.33888	+	5.78311i	0.303535	+	0.525737i
$122$	−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
$131$	2.72837	+	4.72567i	0.238379	+	0.412884i	0.960249	−	0.279144i	$-0.0900508\pi$
$131$	2.72837	+	4.72567i	0.238379	+	0.412884i	−0.721871	+	0.692028i	$0.756717\pi$
$132$		0			0
$133$		0			0
$134$		−	0.805030i		−	0.0695440i
$135$		0			0
$136$		−	2.13917i		−	0.183432i
$137$	1.39996	+	0.808270i	0.119607	+	0.0690551i	0.558610	−	0.829431i	$-0.311335\pi$
$137$	1.39996	+	0.808270i	0.119607	+	0.0690551i	−0.439003	+	0.898486i	$0.644668\pi$
$138$		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
$143$	−8.48226			−0.709322
$144$		0			0
$145$			4.44860i			0.369436i
$146$	0.343300	−	0.594613i	0.0284117	−	0.0492105i
$147$		0			0
$148$	3.20833	+	5.55699i	0.263723	+	0.456782i
$149$	−4.61426	+	2.66404i	−0.378015	+	0.218247i	−0.676954	−	0.736025i	$-0.736700\pi$
$149$	−4.61426	+	2.66404i	−0.378015	+	0.218247i	0.298939	+	0.954272i	$0.403367\pi$
$150$		0			0
$151$	1.32132	−	2.28859i	0.107527	−	0.186243i	−0.807241	−	0.590222i	$-0.799040\pi$
$151$	1.32132	−	2.28859i	0.107527	−	0.186243i	0.914768	+	0.403980i	$0.132373\pi$
$152$	−2.55808			−0.207488
$153$		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	$-0.841297\pi$
$157$	−11.3181	+	6.53448i	−0.903279	+	0.521508i	−0.0250163	+	0.999687i	$0.507964\pi$
$158$	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
$163$	17.0269			1.33365			0.666825	−	0.745214i	$-0.267653\pi$
$163$	17.0269			1.33365			0.666825	+	0.745214i	$0.267653\pi$
$164$	0.197502	−	0.342084i	0.0154223	−	0.0267123i
$165$		0			0
$166$	1.15000	−	0.663954i	0.0892575	−	0.0515328i
$167$	−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
$170$			0.284198i			0.0217970i
$171$		0			0
$172$	−15.7337			−1.19968
$173$	10.2433	−	17.7418i	0.778781	−	1.34889i	−0.153864	−	0.988092i	$-0.549172\pi$
$173$	10.2433	−	17.7418i	0.778781	−	1.34889i	0.932645	−	0.360796i	$-0.117495\pi$
$174$		0			0
$175$		0			0
$176$	−14.2386	+	8.22066i	−1.07327	+	0.619655i
$177$		0			0
$178$	1.36402	+	0.787516i	0.102237	+	0.0590268i
$179$			14.4071i			1.07684i	0.842676	+	0.538420i	$0.180979\pi$
$179$			14.4071i			1.07684i	−0.842676	+	0.538420i	$0.819021\pi$
$180$		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
$184$	−1.52971	−	2.64954i	−0.112772	−	0.195327i
$185$	−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	$-0.205122\pi$
$191$	9.38310	+	5.41734i	0.678937	+	0.391985i	−0.120517	+	0.992711i	$0.538455\pi$
$192$		0			0
$193$	−5.26223	−	9.11444i	−0.378783	−	0.656072i	0.612102	−	0.790779i	$-0.290324\pi$
$193$	−5.26223	−	9.11444i	−0.378783	−	0.656072i	−0.990886	+	0.134707i	$0.956991\pi$
$194$	−0.0348780	−	0.0604104i	−0.00250409	−	0.00433722i
$195$		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
$199$		−	12.5479i		−	0.889495i	−0.895656	−	0.444748i	$-0.853293\pi$
$199$		−	12.5479i		−	0.889495i	0.895656	−	0.444748i	$-0.146707\pi$
$200$	1.99279	+	1.15054i	0.140912	+	0.0813553i
$201$		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
$206$	−0.782644			−0.0545294
$207$		0			0
$208$		−	7.88898i		−	0.547002i
$209$	−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	$0.859608\pi$
$212$	7.25031	−	4.18597i	0.497953	−	0.287493i
$213$		0			0
$214$	−0.0154927	+	0.0268341i	−0.00105906	+	0.00183434i
$215$	4.19636			0.286189
$216$		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
$226$	0.605540			0.0402799
$227$	1.42300	−	2.46471i	0.0944480	−	0.163589i	−0.814930	−	0.579559i	$-0.803225\pi$
$227$	1.42300	−	2.46471i	0.0944480	−	0.163589i	0.909378	+	0.415970i	$0.136558\pi$
$228$		0			0
$229$	−20.5460	+	11.8623i	−1.35772	+	0.783880i	−0.989316	−	0.145786i	$-0.953429\pi$
$229$	−20.5460	+	11.8623i	−1.35772	+	0.783880i	−0.368404	+	0.929666i	$0.620096\pi$
$230$	0.203229	+	0.352004i	0.0134006	+	0.0232104i
$231$		0			0
$232$	−2.04834	+	3.54782i	−0.134480	+	0.232926i
$233$			18.7298i			1.22703i	0.789684	+	0.613514i	$0.210245\pi$
$233$			18.7298i			1.22703i	−0.789684	+	0.613514i	$0.789755\pi$
$234$		0			0
$235$	−5.27942			−0.344391
$236$	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
$241$	3.64082	+	2.10203i	0.234526	+	0.135403i	0.612658	−	0.790348i	$-0.290100\pi$
$241$	3.64082	+	2.10203i	0.234526	+	0.135403i	−0.378132	+	0.925752i	$0.623434\pi$
$242$		−	0.816987i		−	0.0525179i
$243$		0			0
$244$		−	26.0302i		−	1.66641i
$245$		0			0
$246$		0			0
$247$	−5.29257	−	9.16700i	−0.336758	−	0.583282i
$248$	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
$257$	−2.51960	−	4.36408i	−0.157169	−	0.272224i	0.776678	−	0.629898i	$-0.216903\pi$
$257$	−2.51960	−	4.36408i	−0.157169	−	0.272224i	−0.933847	+	0.357674i	$0.883570\pi$
$258$		0			0
$259$		0			0
$260$			2.12018i			0.131488i
$261$		0			0
$262$		−	0.667601i		−	0.0412445i
$263$	−12.2494	−	7.07220i	−0.755331	−	0.436091i	0.0722856	−	0.997384i	$-0.476971\pi$
$263$	−12.2494	−	7.07220i	−0.755331	−	0.436091i	−0.827617	+	0.561293i	$0.810304\pi$
$264$		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
$269$	−15.7771			−0.961948			−0.480974	−	0.876735i	$-0.659717\pi$
$269$	−15.7771			−0.961948			−0.480974	+	0.876735i	$0.659717\pi$
$270$		0			0
$271$		−	16.8078i		−	1.02100i	−0.859877	−	0.510501i	$-0.829460\pi$
$271$		−	16.8078i		−	1.02100i	0.859877	−	0.510501i	$-0.170540\pi$
$272$	8.57871	−	14.8588i	0.520160	−	0.900944i
$273$		0			0
$274$	−0.0988873	−	0.171278i	−0.00597400	−	0.0103473i
$275$	17.1854	−	9.92198i	1.03632	−	0.598318i
$276$		0			0
$277$	−8.91066	+	15.4337i	−0.535390	+	0.927322i	0.463755	+	0.885964i	$0.346502\pi$
$277$	−8.91066	+	15.4337i	−0.535390	+	0.927322i	−0.999144	+	0.0413586i	$0.986831\pi$
$278$	1.38317			0.0829568
$279$		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	$-0.444796\pi$
$283$	18.7047	−	10.7991i	1.11188	−	0.641942i	0.939315	+	0.343056i	$0.111462\pi$
$284$	−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
$289$	2.25120			0.132424
$290$	0.272131	−	0.471344i	0.0159801	−	0.0276783i
$291$		0			0
$292$	9.64756	−	5.57002i	0.564581	−	0.325961i
$293$	−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
$296$		−	1.57601i		−	0.0916035i
$297$		0			0
$298$	0.651862			0.0377613
$299$	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
$304$	−17.7686	−	10.2587i	−1.01910	−	0.588376i
$305$			6.94254i			0.397529i
$306$		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
$310$	−0.0385948	−	0.0668482i	−0.00219204	−	0.00379672i
$311$	10.0080	+	17.3344i	0.567501	+	0.982941i	0.996812	+	0.0797841i	$0.0254231\pi$
$311$	10.0080	+	17.3344i	0.567501	+	0.982941i	−0.429311	+	0.903157i	$0.641244\pi$
$312$		0			0
$313$	−15.9654	−	9.21765i	−0.902420	−	0.521012i	−0.0244352	−	0.999701i	$-0.507779\pi$
$313$	−15.9654	−	9.21765i	−0.902420	−	0.521012i	−0.877984	+	0.478689i	$0.841112\pi$
$314$	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	$-0.199365\pi$
$317$	12.5992	+	7.27416i	0.707642	+	0.408558i	−0.102545	+	0.994728i	$0.532699\pi$
$318$		0			0
$319$	17.6644	+	30.5956i	0.989016	+	1.71303i
$320$	2.02322	+	3.50431i	0.113101	+	0.195897i
$321$		0			0
$322$		0			0
$323$		−	23.0212i		−	1.28093i
$324$		0			0
$325$			9.52166i			0.528167i
$326$	−1.80406	−	1.04157i	−0.0999176	−	0.0576874i
$327$		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	−0.0927274	−	0.995692i	$-0.529559\pi$
$331$	14.8446	−	25.7115i	0.815930	−	1.41323i	0.908658	−	0.417541i	$-0.137108\pi$
$332$	21.5452			1.18245
$333$		0			0
$334$			2.60850i			0.142731i
$335$	−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	$0.914063\pi$
$338$	0.946163	−	0.546267i	0.0514645	−	0.0297130i
$339$		0			0
$340$	−2.30555	+	3.99333i	−0.125036	+	0.216569i
$341$	5.01049			0.271333
$342$		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	$-0.828784\pi$
$347$	−15.7313	+	9.08247i	−0.844501	+	0.487573i	0.0142910	+	0.999898i	$0.495451\pi$
$348$		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
$352$	6.11128			0.325732
$353$	10.4692	−	18.1332i	0.557221	−	0.965135i	−0.440506	−	0.897750i	$-0.645201\pi$
$353$	10.4692	−	18.1332i	0.557221	−	0.965135i	0.997727	−	0.0673857i	$-0.0214658\pi$
$354$		0			0
$355$	3.89994	−	2.25163i	0.206987	−	0.119504i
$356$	12.7774	+	22.1311i	0.677201	+	1.17295i
$357$		0			0
$358$	0.881317	−	1.52649i	0.0465791	−	0.0806773i
$359$		−	14.2265i		−	0.750845i	−0.926854	−	0.375422i	$-0.877498\pi$
$359$		−	14.2265i		−	0.750845i	0.926854	−	0.375422i	$-0.122502\pi$
$360$		0			0
$361$	−8.52944			−0.448918
$362$	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
$367$	10.7237	+	6.19136i	0.559775	+	0.323186i	0.753055	−	0.657957i	$-0.228579\pi$
$367$	10.7237	+	6.19136i	0.559775	+	0.323186i	−0.193280	+	0.981144i	$0.561913\pi$
$368$		−	24.5384i		−	1.27915i
$369$		0			0
$370$			0.209380i			0.0108851i
$371$		0			0
$372$		0			0
$373$	10.6559	+	18.4565i	0.551740	+	0.955642i	0.998149	+	0.0608130i	$0.0193693\pi$
$373$	10.6559	+	18.4565i	0.551740	+	0.955642i	−0.446409	+	0.894829i	$0.647297\pi$
$374$	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
$383$	−6.32174	−	10.9496i	−0.323026	−	0.559497i	0.658085	−	0.752944i	$-0.271367\pi$
$383$	−6.32174	−	10.9496i	−0.323026	−	0.559497i	−0.981111	+	0.193446i	$0.938033\pi$
$384$		0			0
$385$		0			0
$386$			1.28761i			0.0655375i
$387$		0			0
$388$		−	1.13179i		−	0.0574578i
$389$	−11.4538	−	6.61286i	−0.580732	−	0.335286i	0.180692	−	0.983540i	$-0.442166\pi$
$389$	−11.4538	−	6.61286i	−0.580732	−	0.335286i	−0.761424	+	0.648254i	$0.775499\pi$
$390$		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
$395$	−0.303196			−0.0152554
$396$		0			0
$397$		−	24.7882i		−	1.24409i	−0.782983	−	0.622043i	$-0.786303\pi$
$397$		−	24.7882i		−	1.24409i	0.782983	−	0.622043i	$-0.213697\pi$
$398$	−0.767582	+	1.32949i	−0.0384754	+	0.0666413i
$399$		0			0
$400$	9.22800	+	15.9834i	0.461400	+	0.799168i
$401$	−3.19615	+	1.84530i	−0.159608	+	0.0921499i	−0.577677	−	0.816266i	$-0.696041\pi$
$401$	−3.19615	+	1.84530i	−0.159608	+	0.0921499i	0.418068	+	0.908416i	$0.362707\pi$
$402$		0			0
$403$	−1.20208	+	2.08207i	−0.0598800	+	0.103715i
$404$	−23.0880			−1.14867
$405$		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	$-0.818208\pi$
$409$	−16.0535	+	9.26852i	−0.793797	+	0.458299i	0.0475008	+	0.998871i	$0.484874\pi$
$410$	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
$415$	−5.74635			−0.282077
$416$	−1.46618	+	2.53949i	−0.0718852	+	0.124509i
$417$		0			0
$418$	2.33737	−	1.34948i	0.114324	−	0.0660053i
$419$	−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	$0.925337\pi$
$422$			0.293051i			0.0142655i
$423$		0			0
$424$	−2.05624			−0.0998600
$425$	−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
$430$	−0.444618	−	0.256700i	−0.0214414	−	0.0123792i
$431$		−	6.76465i		−	0.325842i	−0.986639	−	0.162921i	$-0.947908\pi$
$431$		−	6.76465i		−	0.325842i	0.986639	−	0.162921i	$-0.0520915\pi$
$432$		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
$436$	−11.8824	−	20.5810i	−0.569066	−	0.985651i
$437$	−16.4624	−	28.5137i	−0.787503	−	1.36399i
$438$		0			0
$439$	22.8208	+	13.1756i	1.08918	+	0.628837i	0.933358	−	0.358948i	$-0.116864\pi$
$439$	22.8208	+	13.1756i	1.08918	+	0.628837i	0.155821	+	0.987785i	$0.450198\pi$
$440$	−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	$-0.291656\pi$
$443$	4.75958	+	2.74795i	0.226135	+	0.130559i	−0.382653	+	0.923892i	$0.624989\pi$
$444$		0			0
$445$	−3.40787	−	5.90261i	−0.161549	−	0.279810i
$446$	0.171074	+	0.296309i	0.00810060	+	0.0140306i
$447$		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
$451$			0.836659i			0.0393967i
$452$	8.50857	+	4.91242i	0.400209	+	0.231061i
$453$		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	−0.269826	+	0.962909i	$0.586966\pi$
$457$	−20.7109	+	35.8724i	−0.968817	+	1.67804i	−0.698991	+	0.715130i	$0.746367\pi$
$458$	2.90256			0.135628
$459$		0			0
$460$			6.59477i			0.307483i
$461$	−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	$0.876063\pi$
$464$	−28.4557	+	16.4289i	−1.32102	+	0.762692i
$465$		0			0
$466$	1.14574	−	1.98448i	0.0530755	−	0.0919294i
$467$	23.8882			1.10541			0.552707	−	0.833376i	$-0.313595\pi$
$467$	23.8882			1.10541			0.552707	+	0.833376i	$0.313595\pi$
$468$		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
$478$	1.57406			0.0719956
$479$	−0.947645	+	1.64137i	−0.0432990	+	0.0749961i	−0.886863	−	0.462033i	$-0.847120\pi$
$479$	−0.947645	+	1.64137i	−0.0432990	+	0.0749961i	0.843564	+	0.537029i	$0.180453\pi$
$480$		0			0
$481$	5.64768	−	3.26069i	0.257512	−	0.148675i
$482$	−0.257171	−	0.445434i	−0.0117138	−	0.0202890i
$483$		0			0
$484$	6.62778	−	11.4797i	0.301263	−	0.521803i
$485$			0.301860i			0.0137067i
$486$		0			0
$487$	28.2248			1.27899			0.639494	−	0.768796i	$-0.279144\pi$
$487$	28.2248			1.27899			0.639494	+	0.768796i	$0.279144\pi$
$488$	−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
$493$	−31.9282	−	18.4338i	−1.43797	−	0.830215i
$494$			1.29503i			0.0582663i
$495$		0			0
$496$			4.66003i			0.209242i
$497$		0			0
$498$		0			0
$499$	6.27844	+	10.8746i	0.281062	+	0.486813i	0.971646	−	0.236438i	$-0.0759801\pi$
$499$	6.27844	+	10.8746i	0.281062	+	0.486813i	−0.690585	+	0.723251i	$0.742647\pi$
$500$	−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
$509$	−9.33827	−	16.1744i	−0.413912	−	0.716916i	0.581402	−	0.813617i	$-0.302504\pi$
$509$	−9.33827	−	16.1744i	−0.413912	−	0.716916i	−0.995314	+	0.0967005i	$0.969171\pi$
$510$		0			0
$511$		0			0
$512$			9.49685i			0.419705i
$513$		0			0
$514$			0.616519i			0.0271935i
$515$	2.93305	+	1.69340i	0.129245	+	0.0746199i
$516$		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
$521$	−18.0665			−0.791508			−0.395754	−	0.918357i	$-0.629517\pi$
$521$	−18.0665			−0.791508			−0.395754	+	0.918357i	$0.629517\pi$
$522$		0			0
$523$			21.1338i			0.924116i	0.886850	+	0.462058i	$0.152889\pi$
$523$			21.1338i			0.924116i	−0.886850	+	0.462058i	$0.847111\pi$
$524$	5.41590	−	9.38061i	0.236595	−	0.409794i
$525$		0			0
$526$	0.865245	+	1.49865i	0.0377265	+	0.0653442i
$527$	−4.52820	+	2.61436i	−0.197252	+	0.113883i
$528$		0			0
$529$	8.18875	−	14.1833i	0.356033	−	0.616666i
$530$	0.273181			0.0118662
$531$		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
$541$	17.7732			0.764131			0.382065	−	0.924135i	$-0.375213\pi$
$541$	17.7732			0.764131			0.382065	+	0.924135i	$0.375213\pi$
$542$	−1.02817	+	1.78084i	−0.0441637	+	0.0764938i
$543$		0			0
$544$	−5.52304	+	3.18873i	−0.236798	+	0.136715i
$545$	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	$-0.0402673\pi$
$548$		−	3.20888i		−	0.137077i
$549$		0			0
$550$	−2.42780			−0.103522
$551$	−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
$556$	19.4352	+	11.2209i	0.824234	+	0.475872i
$557$			11.7214i			0.496651i	0.968677	+	0.248326i	$0.0798803\pi$
$557$			11.7214i			0.496651i	−0.968677	+	0.248326i	$0.920120\pi$
$558$		0			0
$559$			15.9905i			0.676326i
$560$		0			0
$561$		0			0
$562$	0.536671	+	0.929541i	0.0226381	+	0.0392103i
$563$	18.3014	+	31.6990i	0.771314	+	1.33595i	0.936843	+	0.349750i	$0.113733\pi$
$563$	18.3014	+	31.6990i	0.771314	+	1.33595i	−0.165529	+	0.986205i	$0.552933\pi$
$564$		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	$-0.623344\pi$
$569$	−32.6468	−	18.8486i	−1.36862	−	0.790176i	−0.990752	+	0.135682i	$0.956677\pi$
$570$		0			0
$571$	−14.1123	−	24.4432i	−0.590581	−	1.02292i	−0.994154	−	0.107968i	$-0.965565\pi$
$571$	−14.1123	−	24.4432i	−0.590581	−	1.02292i	0.403574	−	0.914947i	$-0.367768\pi$
$572$	8.41878	+	14.5817i	0.352007	+	0.609694i
$573$		0			0
$574$		0			0
$575$			29.6168i			1.23511i
$576$		0			0
$577$			9.38512i			0.390708i	0.980733	+	0.195354i	$0.0625855\pi$
$577$			9.38512i			0.390708i	−0.980733	+	0.195354i	$0.937414\pi$
$578$	−0.238523	−	0.137711i	−0.00992123	−	0.00572802i
$579$		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
$584$	−2.73612			−0.113222
$585$		0			0
$586$			2.39735i			0.0990338i
$587$	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
$590$	0.753870	−	0.435247i	0.0310363	−	0.0179188i
$591$		0			0
$592$	6.32025	−	10.9470i	0.259761	−	0.449919i
$593$	18.1416			0.744986			0.372493	−	0.928035i	$-0.378503\pi$
$593$	18.1416			0.744986			0.372493	+	0.928035i	$0.378503\pi$
$594$		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	$-0.712082\pi$
$599$	−6.02771	+	3.48010i	−0.246286	+	0.142193i	0.371777	+	0.928322i	$0.378749\pi$
$600$		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
$604$	−5.24571			−0.213445
$605$	−1.76770	+	3.06175i	−0.0718673	+	0.124478i
$606$		0			0
$607$	−11.0306	+	6.36850i	−0.447717	+	0.258489i	−0.706865	−	0.707348i	$-0.749891\pi$
$607$	−11.0306	+	6.36850i	−0.447717	+	0.258489i	0.259149	+	0.965837i	$0.416558\pi$
$608$	3.81318	+	6.60462i	0.154645	+	0.267853i
$609$		0			0
$610$	0.424690	−	0.735585i	0.0171952	−	0.0297830i
$611$		−	20.1176i		−	0.813870i
$612$		0			0
$613$	−10.3352			−0.417436			−0.208718	−	0.977976i	$-0.566929\pi$
$613$	−10.3352			−0.417436			−0.208718	+	0.977976i	$0.566929\pi$
$614$	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
$619$	35.2626	+	20.3588i	1.41732	+	0.818291i	0.996063	−	0.0886491i	$-0.0282550\pi$
$619$	35.2626	+	20.3588i	1.41732	+	0.818291i	0.421259	+	0.906940i	$0.361588\pi$
$620$		−	1.25240i		−	0.0502975i
$621$		0			0
$622$		−	2.44884i		−	0.0981897i
$623$		0			0
$624$		0			0
$625$	−10.4371	−	18.0775i	−0.417483	−	0.723101i
$626$	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
$635$	−0.975332	−	1.68932i	−0.0387049	−	0.0670388i
$636$		0			0
$637$		0			0
$638$		−	4.32228i		−	0.171121i
$639$		0			0
$640$		−	2.03412i		−	0.0804057i
$641$	30.5823	+	17.6567i	1.20793	+	0.697398i	0.962306	−	0.271968i	$-0.0876744\pi$
$641$	30.5823	+	17.6567i	1.20793	+	0.697398i	0.245622	+	0.969366i	$0.421008\pi$
$642$		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
$647$	14.9942			0.589482			0.294741	−	0.955577i	$-0.404767\pi$
$647$	14.9942			0.589482			0.294741	+	0.955577i	$0.404767\pi$
$648$		0			0
$649$			56.5050i			2.21801i
$650$	0.582461	−	1.00885i	0.0228460	−	0.0395704i
$651$		0			0
$652$	−16.8995	−	29.2708i	−0.661835	−	1.14633i
$653$	−4.15597	+	2.39945i	−0.162636	+	0.0938977i	−0.579109	−	0.815250i	$-0.696599\pi$
$653$	−4.15597	+	2.39945i	−0.162636	+	0.0938977i	0.416473	+	0.909148i	$0.363266\pi$
$654$		0			0
$655$	−1.44448	+	2.50191i	−0.0564405	+	0.0977577i
$656$	−0.778140			−0.0303812
$657$		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	$-0.532544\pi$
$661$	18.2131	−	10.5154i	0.708409	−	0.409000i	0.810472	+	0.585778i	$0.199211\pi$
$662$	−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
$667$	−52.7277			−2.04163
$668$	−21.1614	+	36.6526i	−0.818758	+	1.41813i
$669$		0			0
$670$	0.369106	−	0.213103i	0.0142598	−	0.00823290i
$671$	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	$0.0310772\pi$
$674$			1.12705i			0.0434124i
$675$		0			0
$676$	17.7263			0.681781
$677$	−9.03150	+	15.6430i	−0.347109	+	0.601210i	−0.985735	−	0.168308i	$-0.946170\pi$
$677$	−9.03150	+	15.6430i	−0.347109	+	0.601210i	0.638626	+	0.769517i	$0.279503\pi$
$678$		0			0
$679$		0			0
$680$	0.980808	−	0.566270i	0.0376123	−	0.0217155i
$681$		0			0
$682$	−0.530878	−	0.306503i	−0.0203284	−	0.0117366i
$683$			45.5647i			1.74349i	0.489963	+	0.871743i	$0.337010\pi$
$683$			45.5647i			1.74349i	−0.489963	+	0.871743i	$0.662990\pi$
$684$		0			0
$685$			0.855844i			0.0327001i
$686$		0			0
$687$		0			0
$688$	15.4973	+	26.8422i	0.590830	+	1.02335i
$689$	−4.25428	−	7.36863i	−0.162075	−	0.280723i
$690$		0			0
$691$	3.33627	+	1.92620i	0.126918	+	0.0732760i	0.562115	−	0.827059i	$-0.309988\pi$
$691$	3.33627	+	1.92620i	0.126918	+	0.0732760i	−0.435197	+	0.900335i	$0.643321\pi$
$692$	−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
$698$	0.402972	+	0.697967i	0.0152527	+	0.0264185i
$699$		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
$703$		−	16.9606i		−	0.639680i
$704$	27.8297	+	16.0675i	1.04887	+	0.605566i
$705$		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	−0.449326	−	0.893368i	$-0.648336\pi$
$709$	14.6187	−	25.3203i	0.549017	−	0.950925i	0.998342	−	0.0575566i	$-0.0183310\pi$
$710$	−0.550949			−0.0206767
$711$		0			0
$712$		−	6.27655i		−	0.235224i
$713$	−3.73904	+	6.47621i	−0.140028	+	0.242536i
$714$		0			0
$715$	−2.24538	−	3.88911i	−0.0839724	−	0.145445i
$716$	24.7672	−	14.2993i	0.925592	−	0.534391i
$717$		0			0
$718$	−0.870265	+	1.50734i	−0.0324780	+	0.0562536i
$719$	−3.37122			−0.125725			−0.0628627	−	0.998022i	$-0.520023\pi$
$719$	−3.37122			−0.125725			−0.0628627	+	0.998022i	$0.520023\pi$
$720$		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
$730$	0.363506			0.0134540
$731$	−17.3885	+	30.1178i	−0.643138	+	1.11395i
$732$		0			0
$733$	19.6875	−	11.3666i	0.727175	−	0.419835i	−0.0902126	−	0.995923i	$-0.528755\pi$
$733$	19.6875	−	11.3666i	0.727175	−	0.419835i	0.817388	+	0.576088i	$0.195421\pi$
$734$	−0.757478	−	1.31199i	−0.0279590	−	0.0484265i
$735$		0			0
$736$	−4.56050	+	7.89901i	−0.168102	+	0.291162i
$737$			27.6657i			1.01908i
$738$		0			0
$739$	−2.39022			−0.0879256			−0.0439628	−	0.999033i	$-0.513998\pi$
$739$	−2.39022			−0.0879256			−0.0439628	+	0.999033i	$0.513998\pi$
$740$	−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
$745$	−2.44292	−	1.41042i	−0.0895018	−	0.0516739i
$746$		−	2.60737i		−	0.0954627i
$747$		0			0
$748$			36.6193i			1.33893i
$749$		0			0
$750$		0			0
$751$	−13.2710	−	22.9861i	−0.484267	−	0.838775i	0.515570	−	0.856848i	$-0.327580\pi$
$751$	−13.2710	−	22.9861i	−0.484267	−	0.838775i	−0.999837	+	0.0180728i	$0.994247\pi$
$752$	−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
$761$	12.9578	+	22.4436i	0.469720	+	0.813578i	0.999401	−	0.0346186i	$-0.0110217\pi$
$761$	12.9578	+	22.4436i	0.469720	+	0.813578i	−0.529681	+	0.848197i	$0.677688\pi$
$762$		0			0
$763$		0			0
$764$		−	21.5072i		−	0.778102i
$765$		0			0
$766$			1.54686i			0.0558903i
$767$	−23.4802	−	13.5563i	−0.847821	−	0.489489i
$768$		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
$773$	20.3213			0.730905			0.365453	−	0.930830i	$-0.380914\pi$
$773$	20.3213			0.730905			0.365453	+	0.930830i	$0.380914\pi$
$774$		0			0
$775$		−	5.62446i		−	0.202037i
$776$	−0.138990	+	0.240738i	−0.00498945	+	0.00864197i
$777$		0			0
$778$	0.809047	+	1.40131i	0.0290058	+	0.0502394i
$779$	−0.904199	+	0.522039i	−0.0323963	+	0.0187040i
$780$		0			0
$781$	17.8814	−	30.9715i	0.639848	−	1.10825i
$782$	−3.36851			−0.120458
$783$		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	$-0.557034\pi$
$787$	16.4065	−	9.47232i	0.584830	−	0.337652i	0.763051	+	0.646339i	$0.223701\pi$
$788$	−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
$793$	−26.4550			−0.939445
$794$	−1.51635	+	2.62640i	−0.0538133	+	0.0932074i
$795$		0			0
$796$	−21.5709	+	12.4540i	−0.764560	+	0.441419i
$797$	−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
$800$		−	6.86014i		−	0.242543i
$801$		0			0
$802$	0.451525			0.0159439
$803$	−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
$808$	4.91095	+	2.83534i	0.172767	+	0.0997469i
$809$		−	11.9814i		−	0.421245i	−0.977568	−	0.210622i	$-0.932451\pi$
$809$		−	11.9814i		−	0.421245i	0.977568	−	0.210622i	$-0.0675490\pi$
$810$		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
$814$	0.831399	+	1.44003i	0.0291405	+	0.0504729i
$815$	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	$-0.562229\pi$
$821$	−32.6907	−	18.8740i	−1.14091	−	0.658707i	−0.946657	+	0.322244i	$0.895563\pi$
$822$		0			0
$823$	10.5082	+	18.2008i	0.366293	+	0.634438i	0.988983	−	0.148031i	$-0.0472934\pi$
$823$	10.5082	+	18.2008i	0.366293	+	0.634438i	−0.622690	+	0.782469i	$0.713960\pi$
$824$	1.55943	+	2.70101i	0.0543253	+	0.0940943i
$825$		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
$829$			25.0859i			0.871270i	0.900123	+	0.435635i	$0.143476\pi$
$829$			25.0859i			0.871270i	−0.900123	+	0.435635i	$0.856524\pi$
$830$	0.608845	+	0.351517i	0.0211333	+	0.0122013i
$831$		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
$836$	43.7905			1.51453
$837$		0			0
$838$			0.359677i			0.0124248i
$839$	−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
$842$	2.98960	−	1.72604i	0.103028	−	0.0594834i
$843$		0			0
$844$	−2.37737	+	4.11772i	−0.0818323	+	0.141738i
$845$	−4.72780			−0.162641
$846$		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
$856$	0.123478			0.00422038
$857$	−9.52098	+	16.4908i	−0.325231	+	0.563316i	−0.981559	−	0.191159i	$-0.938775\pi$
$857$	−9.52098	+	16.4908i	−0.325231	+	0.563316i	0.656328	+	0.754475i	$0.272109\pi$
$858$		0			0
$859$	8.88415	−	5.12927i	0.303123	−	0.175008i	−0.340722	−	0.940164i	$-0.610671\pi$
$859$	8.88415	−	5.12927i	0.303123	−	0.175008i	0.643845	+	0.765156i	$0.277338\pi$
$860$	−4.16495	−	7.21390i	−0.142024	−	0.245992i
$861$		0			0
$862$	−0.413809	+	0.716738i	−0.0140944	+	0.0244122i
$863$		−	4.40932i		−	0.150095i	−0.997180	−	0.0750475i	$-0.976089\pi$
$863$		−	4.40932i		−	0.150095i	0.997180	−	0.0750475i	$-0.0239108\pi$
$864$		0			0
$865$	10.8462			0.368781
$866$	−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
$871$	−11.4962	−	6.63736i	−0.389535	−	0.224898i
$872$			5.83693i			0.197663i
$873$		0			0
$874$			4.02816i			0.136255i
$875$		0			0
$876$		0			0
$877$	25.0586	+	43.4028i	0.846170	+	1.46561i	0.884601	+	0.466349i	$0.154431\pi$
$877$	25.0586	+	43.4028i	0.846170	+	1.46561i	−0.0384307	+	0.999261i	$0.512236\pi$
$878$	−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
$887$	−12.3919	−	21.4634i	−0.416080	−	0.720671i	0.579461	−	0.815000i	$-0.303263\pi$
$887$	−12.3919	−	21.4634i	−0.416080	−	0.720671i	−0.995541	+	0.0943286i	$0.969930\pi$
$888$		0			0
$889$		0			0
$890$			0.833869i			0.0279513i
$891$		0			0
$892$			5.55134i			0.185873i
$893$	−45.3113	−	26.1605i	−1.51629	−	0.875428i
$894$		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
$899$	10.0134			0.333965
$900$		0			0
$901$		−	18.5049i		−	0.616488i
$902$	0.0511803	−	0.0886468i	0.00170412	−	0.00295162i
$903$		0			0
$904$	−1.20655	−	2.08980i	−0.0401292	−	0.0695058i
$905$	−3.19716	+	1.84588i	−0.106277	+	0.0613592i
$906$		0			0
$907$	−22.0517	+	38.1946i	−0.732213	+	1.26823i	0.223722	+	0.974653i	$0.428179\pi$
$907$	−22.0517	+	38.1946i	−0.732213	+	1.26823i	−0.955935	+	0.293577i	$0.905154\pi$
$908$	−5.64941			−0.187482
$909$		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
$919$	52.7102			1.73875			0.869375	−	0.494154i	$-0.164522\pi$
$919$	52.7102			1.73875			0.869375	+	0.494154i	$0.164522\pi$
$920$	0.809876	−	1.40275i	0.0267008	−	0.0462472i
$921$		0			0
$922$	1.15412	−	0.666334i	0.0380091	−	0.0219446i
$923$	8.57999	+	14.8610i	0.282414	+	0.489155i
$924$		0			0
$925$	−7.62828	+	13.2126i	−0.250816	+	0.434426i
$926$			0.704655i			0.0231564i
$927$		0			0
$928$	12.2133			0.400922
$929$	−1.69009	+	2.92732i	−0.0554500	+	0.0960422i	−0.892418	−	0.451210i	$-0.850993\pi$
$929$	−1.69009	+	2.92732i	−0.0554500	+	0.0960422i	0.836968	+	0.547252i	$0.184326\pi$
$930$		0			0
$931$		0			0
$932$	32.1981	−	18.5896i	1.05468	−	0.608922i
$933$		0			0
$934$	−2.53103	−	1.46129i	−0.0828180	−	0.0478150i
$935$		−	9.76677i		−	0.319407i
$936$		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
$940$	5.23990	+	9.07578i	0.170907	+	0.296019i
$941$	−26.1882	−	45.3592i	−0.853710	−	1.47867i	−0.877837	−	0.478960i	$-0.841014\pi$
$941$	−26.1882	−	45.3592i	−0.853710	−	1.47867i	0.0241274	−	0.999709i	$-0.492319\pi$
$942$		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	$-0.294217\pi$
$947$	6.53348	+	3.77211i	0.212310	+	0.122577i	−0.390075	+	0.920783i	$0.627551\pi$
$948$		0			0
$949$	−5.66092	−	9.80500i	−0.183761	−	0.318284i
$950$	−1.51484	−	2.62379i	−0.0491480	−	0.0851269i
$951$		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
$955$			5.73620i			0.185619i
$956$	22.1174	+	12.7695i	0.715327	+	0.412994i
$957$		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
$962$	−0.797855			−0.0257239
$963$		0			0
$964$		−	8.34518i		−	0.268780i
$965$	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	$0.903758\pi$
$968$	−2.81954	+	1.62786i	−0.0906233	+	0.0523214i
$969$		0			0
$970$	0.0184654	−	0.0319831i	0.000592889	−	0.00102691i
$971$	3.47104			0.111391			0.0556955	−	0.998448i	$-0.482262\pi$
$971$	3.47104			0.111391			0.0556955	+	0.998448i	$0.482262\pi$
$972$		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	$-0.653616\pi$
$977$	2.21904	−	1.28116i	0.0709932	−	0.0409880i	0.535076	+	0.844804i	$0.320283\pi$
$978$		0			0
$979$	−46.8759	−	27.0638i	−1.49816	−	0.864963i
$980$		0			0
$981$		0			0
$982$	−0.325277			−0.0103800
$983$	19.5749	−	33.9047i	0.624343	−	1.08139i	−0.364325	−	0.931272i	$-0.618700\pi$
$983$	19.5749	−	33.9047i	0.624343	−	1.08139i	0.988668	−	0.150122i	$-0.0479665\pi$
$984$		0			0
$985$	7.11390	−	4.10721i	0.226668	−	0.130867i
$986$	2.25527	+	3.90624i	0.0718224	+	0.124400i
$987$		0			0
$988$	−10.5059	+	18.1968i	−0.334238	+	0.578917i
$989$			49.7380i			1.58158i
$990$		0			0
$991$	−16.2067			−0.514821			−0.257411	−	0.966302i	$-0.582869\pi$
$991$	−16.2067			−0.514821			−0.257411	+	0.966302i	$0.582869\pi$
$992$	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
$997$	−21.5007	−	12.4134i	−0.680933	−	0.393137i	0.119273	−	0.992861i	$-0.461943\pi$
$997$	−21.5007	−	12.4134i	−0.680933	−	0.393137i	−0.800207	+	0.599725i	$0.795277\pi$
$998$		−	1.53626i		−	0.0486296i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.13		48	63.4	even	3
441.2.i.d.68.14		48	63.31	odd	6
441.2.i.d.227.11		48	21.5	even	6
441.2.i.d.227.12		48	21.2	odd	6
441.2.o.e.146.13	✓	48	21.20	even	2
441.2.o.e.146.14	yes	48	3.2	odd	2
441.2.o.e.293.13	yes	48	9.4	even	3
441.2.o.e.293.14	yes	48	63.13	odd	6
441.2.s.d.362.11		48	21.11	odd	6
441.2.s.d.362.12		48	21.17	even	6
441.2.s.d.374.11		48	63.40	odd	6
441.2.s.d.374.12		48	63.58	even	3
1323.2.i.d.521.11		48	7.2	even	3
1323.2.i.d.521.12		48	7.5	odd	6
1323.2.i.d.1097.11		48	63.59	even	6
1323.2.i.d.1097.12		48	63.32	odd	6
1323.2.o.e.440.11		48	7.6	odd	2	inner
1323.2.o.e.440.12		48	1.1	even	1	trivial
1323.2.o.e.881.11		48	9.5	odd	6	inner
1323.2.o.e.881.12		48	63.41	even	6	inner
1323.2.s.d.656.13		48	7.3	odd	6
1323.2.s.d.656.14		48	7.4	even	3
1323.2.s.d.962.13		48	63.23	odd	6
1323.2.s.d.962.14		48	63.5	even	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.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.105953 - 0.0611722i) q^{2} +(-0.992516 - 1.71909i) q^{4} +(0.264715 + 0.458500i) q^{5} +0.487547i q^{8} +O(q^{10})\)	\(q+(-0.105953 - 0.0611722i) q^{2} +(-0.992516 - 1.71909i) q^{4} +(0.264715 + 0.458500i) q^{5} +0.487547i q^{8} -0.0647728i q^{10} +(3.64120 + 2.10225i) q^{11} +(-1.74714 + 1.00871i) q^{13} +(-1.95521 + 3.38652i) q^{16} -4.38762 q^{17} +5.24685i q^{19} +(0.525467 - 0.910136i) q^{20} +(-0.257198 - 0.445480i) q^{22} +(-5.43444 + 3.13757i) q^{23} +(2.35985 - 4.08738i) q^{25} +0.246821 q^{26} +(7.27689 + 4.20131i) q^{29} +(1.03204 - 0.595849i) q^{31} +(1.25878 - 0.726755i) q^{32} +(0.464883 + 0.268400i) q^{34} -3.23252 q^{37} +(0.320962 - 0.555922i) q^{38} +(-0.223540 + 0.129061i) q^{40} +(0.0994958 + 0.172332i) q^{41} +(3.96309 - 6.86427i) q^{43} -8.34605i q^{44} +0.767730 q^{46} +(-4.98595 + 8.63591i) q^{47} +(-0.500069 + 0.288715i) q^{50} +(3.46814 + 2.00233i) q^{52} +4.21753i q^{53} +2.22598i q^{55} +(-0.514008 - 0.890287i) q^{58} +(6.71960 + 11.6387i) q^{59} +(11.3564 + 6.55662i) q^{61} -0.145798 q^{62} +7.64300 q^{64} +(-0.924990 - 0.534043i) q^{65} +(3.29001 + 5.69847i) q^{67} +(4.35478 + 7.54270i) q^{68} -8.50587i q^{71} +5.61202i q^{73} +(0.342497 + 0.197741i) q^{74} +(9.01980 - 5.20758i) q^{76} +(-0.286342 + 0.495959i) q^{79} -2.07029 q^{80} -0.0243455i q^{82} +(-5.42692 + 9.39971i) q^{83} +(-1.16147 - 2.01172i) q^{85} +(-0.839806 + 0.484862i) q^{86} +(-1.02494 + 1.77525i) q^{88} -12.8738 q^{89} +(10.7875 + 6.22819i) q^{92} +(1.05656 - 0.610003i) q^{94} +(-2.40568 + 1.38892i) q^{95} +(0.493773 + 0.285080i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4}+O(q^{10}) \) 48 * q + 24 * q^4	\( 48 q + 24 q^{4} + 24 q^{11} - 24 q^{16} + 48 q^{23} - 24 q^{25} - 120 q^{32} - 48 q^{50} - 48 q^{64} - 120 q^{65} + 168 q^{74} - 24 q^{79} - 24 q^{85} - 24 q^{86} + 144 q^{92} - 96 q^{95}+O(q^{100}) \) 48 * q + 24 * q^4 + 24 * q^11 - 24 * q^16 + 48 * q^23 - 24 * q^25 - 120 * q^32 - 48 * q^50 - 48 * q^64 - 120 * q^65 + 168 * q^74 - 24 * q^79 - 24 * q^85 - 24 * q^86 + 144 * q^92 - 96 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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