LMFDB - Embedded newform 1386.2.r.d.89.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(89,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("1386.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.r (of order $6$, degree $2$, 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:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.2
Character	$\chi$	$=$	1386.89
Dual form			1386.2.r.d.1277.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.651304 - 1.12809i) q^{5} +(-0.212626 - 2.63719i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.651304 - 1.12809i) q^{5} +(-0.212626 - 2.63719i) q^{7} -1.00000i q^{8} +(-1.12809 + 0.651304i) q^{10} +(0.866025 - 0.500000i) q^{11} +1.37037i q^{13} +(-1.13446 + 2.39019i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.86353 - 4.95978i) q^{17} +(-0.481496 - 0.277992i) q^{19} +1.30261 q^{20} -1.00000 q^{22} +(-5.02204 - 2.89948i) q^{23} +(1.65161 + 2.86067i) q^{25} +(0.685187 - 1.18678i) q^{26} +(2.17756 - 1.50274i) q^{28} -6.53981i q^{29} +(0.660821 - 0.381525i) q^{31} +(0.866025 - 0.500000i) q^{32} +5.72706i q^{34} +(-3.11348 - 1.47775i) q^{35} +(-3.34141 + 5.78749i) q^{37} +(0.277992 + 0.481496i) q^{38} +(-1.12809 - 0.651304i) q^{40} +2.25518 q^{41} +3.91214 q^{43} +(0.866025 + 0.500000i) q^{44} +(2.89948 + 5.02204i) q^{46} +(0.483428 - 0.837321i) q^{47} +(-6.90958 + 1.12147i) q^{49} -3.30321i q^{50} +(-1.18678 + 0.685187i) q^{52} +(-7.40860 + 4.27736i) q^{53} -1.30261i q^{55} +(-2.63719 + 0.212626i) q^{56} +(-3.26990 + 5.66364i) q^{58} +(-0.499578 - 0.865295i) q^{59} +(0.127371 + 0.0735377i) q^{61} -0.763050 q^{62} -1.00000 q^{64} +(1.54591 + 0.892530i) q^{65} +(-3.60430 - 6.24283i) q^{67} +(2.86353 - 4.95978i) q^{68} +(1.95748 + 2.83651i) q^{70} -1.17582i q^{71} +(-1.44038 + 0.831605i) q^{73} +(5.78749 - 3.34141i) q^{74} -0.555984i q^{76} +(-1.50274 - 2.17756i) q^{77} +(0.361898 - 0.626826i) q^{79} +(0.651304 + 1.12809i) q^{80} +(-1.95305 - 1.12759i) q^{82} -5.54322 q^{83} -7.46011 q^{85} +(-3.38801 - 1.95607i) q^{86} +(-0.500000 - 0.866025i) q^{88} +(4.25940 - 7.37750i) q^{89} +(3.61394 - 0.291378i) q^{91} -5.79896i q^{92} +(-0.837321 + 0.483428i) q^{94} +(-0.627201 + 0.362114i) q^{95} -12.9667i q^{97} +(6.54461 + 2.48356i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{4} + 8 q^{7}+O(q^{10}) $ 24 * q + 12 * q^4 + 8 * q^7	$ 24 q + 12 q^{4} + 8 q^{7} - 12 q^{16} + 12 q^{19} - 24 q^{22} + 4 q^{25} + 4 q^{28} + 20 q^{37} + 24 q^{43} + 12 q^{46} + 40 q^{49} - 28 q^{58} - 120 q^{61} - 24 q^{64} - 32 q^{67} + 48 q^{70} - 48 q^{73} - 64 q^{79} - 48 q^{82} + 32 q^{85} - 12 q^{88} + 56 q^{91} + 60 q^{94}+O(q^{100}) $ 24 * q + 12 * q^4 + 8 * q^7 - 12 * q^16 + 12 * q^19 - 24 * q^22 + 4 * q^25 + 4 * q^28 + 20 * q^37 + 24 * q^43 + 12 * q^46 + 40 * q^49 - 28 * q^58 - 120 * q^61 - 24 * q^64 - 32 * q^67 + 48 * q^70 - 48 * q^73 - 64 * q^79 - 48 * q^82 + 32 * q^85 - 12 * q^88 + 56 * q^91 + 60 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.651304	−	1.12809i	0.291272	−	0.504498i	−0.682839	−	0.730569i	$-0.739255\pi$
$5$	0.651304	−	1.12809i	0.291272	−	0.504498i	0.974111	+	0.226071i	$0.0725882\pi$
$6$		0			0
$7$	−0.212626	−	2.63719i	−0.0803652	−	0.996765i
$7$	−0.212626	−	2.63719i	−0.0803652	−	0.996765i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−1.12809	+	0.651304i	−0.356734	+	0.205960i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$12$		0			0
$13$			1.37037i			0.380073i	0.981777	+	0.190037i	$0.0608607\pi$
$13$			1.37037i			0.380073i	−0.981777	+	0.190037i	$0.939139\pi$
$14$	−1.13446	+	2.39019i	−0.303196	+	0.638805i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.86353	−	4.95978i	−0.694508	−	1.20292i	−0.970346	−	0.241719i	$-0.922289\pi$
$17$	−2.86353	−	4.95978i	−0.694508	−	1.20292i	0.275838	−	0.961204i	$-0.411045\pi$
$18$		0			0
$19$	−0.481496	−	0.277992i	−0.110463	−	0.0637757i	0.443751	−	0.896150i	$-0.353648\pi$
$19$	−0.481496	−	0.277992i	−0.110463	−	0.0637757i	−0.554214	+	0.832375i	$0.686981\pi$
$20$	1.30261			0.291272
$21$		0			0
$22$	−1.00000			−0.213201
$23$	−5.02204	−	2.89948i	−1.04717	−	0.604583i	−0.125313	−	0.992117i	$-0.539994\pi$
$23$	−5.02204	−	2.89948i	−1.04717	−	0.604583i	−0.921855	+	0.387534i	$0.873327\pi$
$24$		0			0
$25$	1.65161	+	2.86067i	0.330321	+	0.572133i
$26$	0.685187	−	1.18678i	0.134376	−	0.232746i
$27$		0			0
$28$	2.17756	−	1.50274i	0.411521	−	0.283991i
$29$		−	6.53981i		−	1.21441i	−0.794545	−	0.607206i	$-0.792290\pi$
$29$		−	6.53981i		−	1.21441i	0.794545	−	0.607206i	$-0.207710\pi$
$30$		0			0
$31$	0.660821	−	0.381525i	0.118687	−	0.0685239i	−0.439481	−	0.898252i	$-0.644838\pi$
$31$	0.660821	−	0.381525i	0.118687	−	0.0685239i	0.558168	+	0.829728i	$0.311504\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$			5.72706i			0.982183i
$35$	−3.11348	−	1.47775i	−0.526274	−	0.249786i
$36$		0			0
$37$	−3.34141	+	5.78749i	−0.549324	+	0.951457i	0.448997	+	0.893533i	$0.351781\pi$
$37$	−3.34141	+	5.78749i	−0.549324	+	0.951457i	−0.998321	+	0.0579236i	$0.981552\pi$
$38$	0.277992	+	0.481496i	0.0450962	+	0.0781090i
$39$		0			0
$40$	−1.12809	−	0.651304i	−0.178367	−	0.102980i
$41$	2.25518			0.352200			0.176100	−	0.984372i	$-0.443652\pi$
$41$	2.25518			0.352200			0.176100	+	0.984372i	$0.443652\pi$
$42$		0			0
$43$	3.91214			0.596595			0.298298	−	0.954473i	$-0.403581\pi$
$43$	3.91214			0.596595			0.298298	+	0.954473i	$0.403581\pi$
$44$	0.866025	+	0.500000i	0.130558	+	0.0753778i
$45$		0			0
$46$	2.89948	+	5.02204i	0.427505	+	0.740460i
$47$	0.483428	−	0.837321i	0.0705152	−	0.122136i	−0.828612	−	0.559823i	$-0.810869\pi$
$47$	0.483428	−	0.837321i	0.0705152	−	0.122136i	0.899127	+	0.437687i	$0.144202\pi$
$48$		0			0
$49$	−6.90958	+	1.12147i	−0.987083	+	0.160211i
$50$		−	3.30321i		−	0.467145i
$51$		0			0
$52$	−1.18678	+	0.685187i	−0.164577	+	0.0950183i
$53$	−7.40860	+	4.27736i	−1.01765	+	0.587540i	−0.913422	−	0.407013i	$-0.866570\pi$
$53$	−7.40860	+	4.27736i	−1.01765	+	0.587540i	−0.104227	+	0.994554i	$0.533237\pi$
$54$		0			0
$55$		−	1.30261i		−	0.175644i
$56$	−2.63719	+	0.212626i	−0.352410	+	0.0284134i
$57$		0			0
$58$	−3.26990	+	5.66364i	−0.429359	+	0.743672i
$59$	−0.499578	−	0.865295i	−0.0650396	−	0.112652i	0.831672	−	0.555267i	$-0.187384\pi$
$59$	−0.499578	−	0.865295i	−0.0650396	−	0.112652i	−0.896712	+	0.442615i	$0.854051\pi$
$60$		0			0
$61$	0.127371	+	0.0735377i	0.0163082	+	0.00941554i	0.508132	−	0.861279i	$-0.330336\pi$
$61$	0.127371	+	0.0735377i	0.0163082	+	0.00941554i	−0.491824	+	0.870695i	$0.663670\pi$
$62$	−0.763050			−0.0969075
$63$		0			0
$64$	−1.00000			−0.125000
$65$	1.54591	+	0.892530i	0.191746	+	0.110705i
$66$		0			0
$67$	−3.60430	−	6.24283i	−0.440335	−	0.762683i	0.557379	−	0.830258i	$-0.311807\pi$
$67$	−3.60430	−	6.24283i	−0.440335	−	0.762683i	−0.997714	+	0.0675752i	$0.978474\pi$
$68$	2.86353	−	4.95978i	0.347254	−	0.601462i
$69$		0			0
$70$	1.95748	+	2.83651i	0.233963	+	0.339028i
$71$		−	1.17582i		−	0.139544i	−0.997563	−	0.0697720i	$-0.977773\pi$
$71$		−	1.17582i		−	0.139544i	0.997563	−	0.0697720i	$-0.0222272\pi$
$72$		0			0
$73$	−1.44038	+	0.831605i	−0.168584	+	0.0973320i	−0.581918	−	0.813247i	$-0.697698\pi$
$73$	−1.44038	+	0.831605i	−0.168584	+	0.0973320i	0.413334	+	0.910579i	$0.364364\pi$
$74$	5.78749	−	3.34141i	0.672782	−	0.388431i
$75$		0			0
$76$		−	0.555984i		−	0.0637757i
$77$	−1.50274	−	2.17756i	−0.171253	−	0.248156i
$78$		0			0
$79$	0.361898	−	0.626826i	0.0407167	−	0.0705235i	−0.844949	−	0.534847i	$-0.820369\pi$
$79$	0.361898	−	0.626826i	0.0407167	−	0.0705235i	0.885666	+	0.464324i	$0.153703\pi$
$80$	0.651304	+	1.12809i	0.0728180	+	0.126125i
$81$		0			0
$82$	−1.95305	−	1.12759i	−0.215678	−	0.124522i
$83$	−5.54322			−0.608448			−0.304224	−	0.952601i	$-0.598397\pi$
$83$	−5.54322			−0.608448			−0.304224	+	0.952601i	$0.598397\pi$
$84$		0			0
$85$	−7.46011			−0.809163
$86$	−3.38801	−	1.95607i	−0.365338	−	0.210928i
$87$		0			0
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	4.25940	−	7.37750i	0.451496	−	0.782014i	−0.546983	−	0.837144i	$-0.684224\pi$
$89$	4.25940	−	7.37750i	0.451496	−	0.782014i	0.998479	+	0.0551297i	$0.0175572\pi$
$90$		0			0
$91$	3.61394	−	0.291378i	0.378844	−	0.0305447i
$92$		−	5.79896i		−	0.604583i
$93$		0			0
$94$	−0.837321	+	0.483428i	−0.0863631	+	0.0498618i
$95$	−0.627201	+	0.362114i	−0.0643494	+	0.0371522i
$96$		0			0
$97$		−	12.9667i		−	1.31657i	−0.752769	−	0.658285i	$-0.771282\pi$
$97$		−	12.9667i		−	1.31657i	0.752769	−	0.658285i	$-0.228718\pi$
$98$	6.54461	+	2.48356i	0.661105	+	0.250878i
$99$		0			0
$100$	−1.65161	+	2.86067i	−0.165161	+	0.286067i
$101$	3.67391	+	6.36340i	0.365568	+	0.633182i	0.988867	−	0.148801i	$-0.0475415\pi$
$101$	3.67391	+	6.36340i	0.365568	+	0.633182i	−0.623299	+	0.781983i	$0.714208\pi$
$102$		0			0
$103$	−15.4637	−	8.92798i	−1.52369	−	0.879700i	−0.999607	−	0.0280307i	$-0.991076\pi$
$103$	−15.4637	−	8.92798i	−1.52369	−	0.879700i	−0.524079	−	0.851670i	$-0.675590\pi$
$104$	1.37037			0.134376
$105$		0			0
$106$	8.55471			0.830907
$107$	−8.72859	−	5.03946i	−0.843825	−	0.487183i	0.0147376	−	0.999891i	$-0.495309\pi$
$107$	−8.72859	−	5.03946i	−0.843825	−	0.487183i	−0.858563	+	0.512709i	$0.828642\pi$
$108$		0			0
$109$	0.368886	+	0.638929i	0.0353329	+	0.0611983i	0.883151	−	0.469089i	$-0.155418\pi$
$109$	0.368886	+	0.638929i	0.0353329	+	0.0611983i	−0.847818	+	0.530287i	$0.822084\pi$
$110$	−0.651304	+	1.12809i	−0.0620994	+	0.107559i
$111$		0			0
$112$	2.39019	+	1.13446i	0.225852	+	0.107196i
$113$		−	4.81235i		−	0.452708i	−0.974045	−	0.226354i	$-0.927319\pi$
$113$		−	4.81235i		−	0.452708i	0.974045	−	0.226354i	$-0.0726806\pi$
$114$		0			0
$115$	−6.54176	+	3.77689i	−0.610022	+	0.352196i
$116$	5.66364	−	3.26990i	0.525856	−	0.303603i
$117$		0			0
$118$			0.999157i			0.0919798i
$119$	−12.4710	+	8.60626i	−1.14322	+	0.788935i
$120$		0			0
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	−0.0735377	−	0.127371i	−0.00665779	−	0.0115316i
$123$		0			0
$124$	0.660821	+	0.381525i	0.0593435	+	0.0342620i
$125$	10.8158			0.967397
$126$		0			0
$127$	12.5158			1.11060			0.555299	−	0.831651i	$-0.312604\pi$
$127$	12.5158			1.11060			0.555299	+	0.831651i	$0.312604\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−0.892530	−	1.54591i	−0.0782801	−	0.135585i
$131$	7.42443	−	12.8595i	0.648675	−	1.12354i	−0.334764	−	0.942302i	$-0.608657\pi$
$131$	7.42443	−	12.8595i	0.648675	−	1.12354i	0.983440	−	0.181237i	$-0.0580100\pi$
$132$		0			0
$133$	−0.630739	+	1.32891i	−0.0546920	+	0.115231i
$134$			7.20860i			0.622728i
$135$		0			0
$136$	−4.95978	+	2.86353i	−0.425298	+	0.245546i
$137$	−18.1030	+	10.4518i	−1.54664	+	0.892953i	−0.548246	+	0.836317i	$0.684704\pi$
$137$	−18.1030	+	10.4518i	−1.54664	+	0.892953i	−0.998395	+	0.0566359i	$0.981963\pi$
$138$		0			0
$139$		−	3.21195i		−	0.272434i	−0.990679	−	0.136217i	$-0.956506\pi$
$139$		−	3.21195i		−	0.272434i	0.990679	−	0.136217i	$-0.0434944\pi$
$140$	−0.276969	−	3.43523i	−0.0234081	−	0.290330i
$141$		0			0
$142$	−0.587909	+	1.01829i	−0.0493363	+	0.0854529i
$143$	0.685187	+	1.18678i	0.0572982	+	0.0992434i
$144$		0			0
$145$	−7.37750	−	4.25940i	−0.612668	−	0.353724i
$146$	1.66321			0.137648
$147$		0			0
$148$	−6.68281			−0.549324
$149$	−17.7299	−	10.2363i	−1.45249	−	0.838594i	−0.453865	−	0.891071i	$-0.649955\pi$
$149$	−17.7299	−	10.2363i	−1.45249	−	0.838594i	−0.998622	+	0.0524768i	$0.983288\pi$
$150$		0			0
$151$	−7.80068	−	13.5112i	−0.634810	−	1.09952i	−0.986555	−	0.163428i	$-0.947745\pi$
$151$	−7.80068	−	13.5112i	−0.634810	−	1.09952i	0.351745	−	0.936096i	$-0.385588\pi$
$152$	−0.277992	+	0.481496i	−0.0225481	+	0.0390545i
$153$		0			0
$154$	0.212626	+	2.63719i	0.0171339	+	0.212511i
$155$		−	0.993956i		−	0.0798364i
$156$		0			0
$157$	−6.72012	+	3.87986i	−0.536324	+	0.309647i	−0.743588	−	0.668638i	$-0.766877\pi$
$157$	−6.72012	+	3.87986i	−0.536324	+	0.309647i	0.207264	+	0.978285i	$0.433544\pi$
$158$	−0.626826	+	0.361898i	−0.0498676	+	0.0287911i
$159$		0			0
$160$		−	1.30261i		−	0.102980i
$161$	−6.57867	+	13.8606i	−0.518472	+	1.09237i
$162$		0			0
$163$	−2.36269	+	4.09229i	−0.185060	+	0.320533i	−0.943597	−	0.331097i	$-0.892581\pi$
$163$	−2.36269	+	4.09229i	−0.185060	+	0.320533i	0.758537	+	0.651630i	$0.225915\pi$
$164$	1.12759	+	1.95305i	0.0880501	+	0.152507i
$165$		0			0
$166$	4.80057	+	2.77161i	0.372597	+	0.215119i
$167$	2.49753			0.193264			0.0966322	−	0.995320i	$-0.469193\pi$
$167$	2.49753			0.193264			0.0966322	+	0.995320i	$0.469193\pi$
$168$		0			0
$169$	11.1221			0.855544
$170$	6.46065	+	3.73006i	0.495509	+	0.286082i
$171$		0			0
$172$	1.95607	+	3.38801i	0.149149	+	0.258333i
$173$	−7.76337	+	13.4466i	−0.590238	+	1.02232i	0.403962	+	0.914776i	$0.367633\pi$
$173$	−7.76337	+	13.4466i	−0.590238	+	1.02232i	−0.994200	+	0.107547i	$0.965701\pi$
$174$		0			0
$175$	7.19295	−	4.96386i	0.543736	−	0.375232i
$176$			1.00000i			0.0753778i
$177$		0			0
$178$	−7.37750	+	4.25940i	−0.552967	+	0.319256i
$179$	−7.40921	+	4.27771i	−0.553790	+	0.319731i	−0.750649	−	0.660701i	$-0.770259\pi$
$179$	−7.40921	+	4.27771i	−0.553790	+	0.319731i	0.196859	+	0.980432i	$0.436926\pi$
$180$		0			0
$181$			22.8485i			1.69832i	0.528140	+	0.849158i	$0.322890\pi$
$181$			22.8485i			1.69832i	−0.528140	+	0.849158i	$0.677110\pi$
$182$	−3.27545	−	1.55463i	−0.242793	−	0.115237i
$183$		0			0
$184$	−2.89948	+	5.02204i	−0.213752	+	0.370230i
$185$	4.35254	+	7.53883i	0.320005	+	0.554266i
$186$		0			0
$187$	−4.95978	−	2.86353i	−0.362695	−	0.209402i
$188$	0.966856			0.0705152
$189$		0			0
$190$	0.724229			0.0525411
$191$	14.0830	+	8.13084i	1.01901	+	0.588327i	0.913818	−	0.406125i	$-0.133120\pi$
$191$	14.0830	+	8.13084i	1.01901	+	0.588327i	0.105195	+	0.994452i	$0.466453\pi$
$192$		0			0
$193$	−2.83770	−	4.91503i	−0.204262	−	0.353792i	0.745635	−	0.666354i	$-0.232146\pi$
$193$	−2.83770	−	4.91503i	−0.204262	−	0.353792i	−0.949897	+	0.312562i	$0.898813\pi$
$194$	−6.48336	+	11.2295i	−0.465478	+	0.806231i
$195$		0			0
$196$	−4.42602	−	5.42313i	−0.316144	−	0.387367i
$197$			2.08781i			0.148750i	0.997230	+	0.0743750i	$0.0236962\pi$
$197$			2.08781i			0.148750i	−0.997230	+	0.0743750i	$0.976304\pi$
$198$		0			0
$199$	15.0881	−	8.71113i	1.06957	−	0.617516i	0.141505	−	0.989937i	$-0.454806\pi$
$199$	15.0881	−	8.71113i	1.06957	−	0.617516i	0.928064	+	0.372422i	$0.121472\pi$
$200$	2.86067	−	1.65161i	0.202280	−	0.116786i
$201$		0			0
$202$		−	7.34782i		−	0.516991i
$203$	−17.2467	+	1.39054i	−1.21048	+	0.0975965i
$204$		0			0
$205$	1.46881	−	2.54405i	0.102586	−	0.177684i
$206$	8.92798	+	15.4637i	0.622042	+	1.07741i
$207$		0			0
$208$	−1.18678	−	0.685187i	−0.0822883	−	0.0475092i
$209$	−0.555984			−0.0384582
$210$		0			0
$211$	25.5583			1.75951			0.879753	−	0.475431i	$-0.157708\pi$
$211$	25.5583			1.75951			0.879753	+	0.475431i	$0.157708\pi$
$212$	−7.40860	−	4.27736i	−0.508825	−	0.293770i
$213$		0			0
$214$	5.03946	+	8.72859i	0.344490	+	0.596674i
$215$	2.54799	−	4.41325i	0.173772	−	0.300981i
$216$		0			0
$217$	−1.14666	−	1.66159i	−0.0778406	−	0.112796i
$218$		−	0.737772i		−	0.0499682i
$219$		0			0
$220$	1.12809	−	0.651304i	0.0760559	−	0.0439109i
$221$	6.79675	−	3.92411i	0.457199	−	0.263964i
$222$		0			0
$223$		−	9.64025i		−	0.645559i	−0.946474	−	0.322779i	$-0.895383\pi$
$223$		−	9.64025i		−	0.645559i	0.946474	−	0.322779i	$-0.104617\pi$
$224$	−1.50274	−	2.17756i	−0.100406	−	0.145495i
$225$		0			0
$226$	−2.40618	+	4.16762i	−0.160056	+	0.277226i
$227$	−3.53947	−	6.13055i	−0.234923	−	0.406899i	0.724327	−	0.689456i	$-0.242150\pi$
$227$	−3.53947	−	6.13055i	−0.234923	−	0.406899i	−0.959250	+	0.282558i	$0.908817\pi$
$228$		0			0
$229$	−16.3612	−	9.44614i	−1.08118	−	0.624219i	−0.149965	−	0.988691i	$-0.547916\pi$
$229$	−16.3612	−	9.44614i	−1.08118	−	0.624219i	−0.931214	+	0.364473i	$0.881249\pi$
$230$	7.55377			0.498081
$231$		0			0
$232$	−6.53981			−0.429359
$233$	8.01488	+	4.62739i	0.525072	+	0.303151i	0.739007	−	0.673697i	$-0.235295\pi$
$233$	8.01488	+	4.62739i	0.525072	+	0.303151i	−0.213935	+	0.976848i	$0.568628\pi$
$234$		0			0
$235$	−0.629717	−	1.09070i	−0.0410782	−	0.0711495i
$236$	0.499578	−	0.865295i	0.0325198	−	0.0563259i
$237$		0			0
$238$	15.1034	−	1.21772i	0.979006	−	0.0789333i
$239$			4.86932i			0.314970i	0.987521	+	0.157485i	$0.0503386\pi$
$239$			4.86932i			0.314970i	−0.987521	+	0.157485i	$0.949661\pi$
$240$		0			0
$241$	18.4869	−	10.6734i	1.19085	−	0.687535i	0.232347	−	0.972633i	$-0.425360\pi$
$241$	18.4869	−	10.6734i	1.19085	−	0.687535i	0.958498	+	0.285098i	$0.0920262\pi$
$242$	−0.866025	+	0.500000i	−0.0556702	+	0.0321412i
$243$		0			0
$244$			0.147075i			0.00941554i
$245$	−3.23511	+	8.52506i	−0.206684	+	0.544646i
$246$		0			0
$247$	0.380953	−	0.659829i	0.0242394	−	0.0419839i
$248$	−0.381525	−	0.660821i	−0.0242269	−	0.0419622i
$249$		0			0
$250$	−9.36679	−	5.40792i	−0.592408	−	0.342027i
$251$	21.2321			1.34016			0.670078	−	0.742291i	$-0.266261\pi$
$251$	21.2321			1.34016			0.670078	+	0.742291i	$0.266261\pi$
$252$		0			0
$253$	−5.79896			−0.364577
$254$	−10.8390	−	6.25791i	−0.680100	−	0.392656i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.21276	−	12.4929i	0.449920	−	0.779284i	−0.548461	−	0.836176i	$-0.684786\pi$
$257$	7.21276	−	12.4929i	0.449920	−	0.779284i	0.998380	+	0.0568927i	$0.0181193\pi$
$258$		0			0
$259$	15.9732	+	7.58136i	0.992526	+	0.471083i
$260$			1.78506i			0.110705i
$261$		0			0
$262$	−12.8595	+	7.42443i	−0.794462	+	0.458683i
$263$	14.7636	−	8.52378i	0.910364	−	0.525599i	0.0298158	−	0.999555i	$-0.490508\pi$
$263$	14.7636	−	8.52378i	0.910364	−	0.525599i	0.880548	+	0.473956i	$0.157175\pi$
$264$		0			0
$265$			11.1434i			0.684536i
$266$	1.21069	−	0.835497i	0.0742321	−	0.0512276i
$267$		0			0
$268$	3.60430	−	6.24283i	0.220168	−	0.381342i
$269$	11.1844	+	19.3720i	0.681927	+	1.18113i	0.974392	+	0.224857i	$0.0721914\pi$
$269$	11.1844	+	19.3720i	0.681927	+	1.18113i	−0.292464	+	0.956276i	$0.594475\pi$
$270$		0			0
$271$	−1.99443	−	1.15148i	−0.121153	−	0.0699476i	0.438199	−	0.898878i	$-0.355617\pi$
$271$	−1.99443	−	1.15148i	−0.121153	−	0.0699476i	−0.559352	+	0.828930i	$0.688950\pi$
$272$	5.72706			0.347254
$273$		0			0
$274$	20.9035			1.26283
$275$	2.86067	+	1.65161i	0.172505	+	0.0995956i
$276$		0			0
$277$	3.66323	+	6.34490i	0.220102	+	0.381228i	0.954839	−	0.297124i	$-0.0960276\pi$
$277$	3.66323	+	6.34490i	0.220102	+	0.381228i	−0.734737	+	0.678352i	$0.762694\pi$
$278$	−1.60597	+	2.78163i	−0.0963199	+	0.166831i
$279$		0			0
$280$	−1.47775	+	3.11348i	−0.0883126	+	0.186066i
$281$			11.0454i			0.658911i	0.944171	+	0.329456i	$0.106865\pi$
$281$			11.0454i			0.658911i	−0.944171	+	0.329456i	$0.893135\pi$
$282$		0			0
$283$	25.8803	−	14.9420i	1.53842	−	0.888209i	0.539491	−	0.841991i	$-0.318617\pi$
$283$	25.8803	−	14.9420i	1.53842	−	0.888209i	0.998931	−	0.0462173i	$-0.0147167\pi$
$284$	1.01829	−	0.587909i	0.0604243	−	0.0348860i
$285$		0			0
$286$		−	1.37037i		−	0.0810319i
$287$	−0.479512	−	5.94735i	−0.0283047	−	0.351061i
$288$		0			0
$289$	−7.89960	+	13.6825i	−0.464683	+	0.804854i
$290$	4.25940	+	7.37750i	0.250121	+	0.433222i
$291$		0			0
$292$	−1.44038	−	0.831605i	−0.0842920	−	0.0486660i
$293$	24.4813			1.43021			0.715106	−	0.699016i	$-0.246379\pi$
$293$	24.4813			1.43021			0.715106	+	0.699016i	$0.246379\pi$
$294$		0			0
$295$	−1.30151			−0.0757768
$296$	5.78749	+	3.34141i	0.336391	+	0.194215i
$297$		0			0
$298$	10.2363	+	17.7299i	0.592975	+	1.02706i
$299$	3.97337	−	6.88208i	0.229786	−	0.398001i
$300$		0			0
$301$	−0.831824	−	10.3171i	−0.0479455	−	0.594665i
$302$			15.6014i			0.897757i
$303$		0			0
$304$	0.481496	−	0.277992i	0.0276157	−	0.0159439i
$305$	0.165915	−	0.0957908i	0.00950024	−	0.00548497i
$306$		0			0
$307$			8.72480i			0.497951i	0.968510	+	0.248975i	$0.0800939\pi$
$307$			8.72480i			0.497951i	−0.968510	+	0.248975i	$0.919906\pi$
$308$	1.13446	−	2.39019i	0.0646417	−	0.136194i
$309$		0			0
$310$	−0.496978	+	0.860791i	−0.0282264	+	0.0488896i
$311$	1.31098	+	2.27069i	0.0743390	+	0.128759i	0.900799	−	0.434237i	$-0.142982\pi$
$311$	1.31098	+	2.27069i	0.0743390	+	0.128759i	−0.826460	+	0.562996i	$0.809649\pi$
$312$		0			0
$313$	−20.4146	−	11.7864i	−1.15390	−	0.666205i	−0.204066	−	0.978957i	$-0.565416\pi$
$313$	−20.4146	−	11.7864i	−1.15390	−	0.666205i	−0.949835	+	0.312752i	$0.898749\pi$
$314$	7.75972			0.437906
$315$		0			0
$316$	0.723797			0.0407167
$317$	16.3099	+	9.41654i	0.916057	+	0.528886i	0.882375	−	0.470547i	$-0.155943\pi$
$317$	16.3099	+	9.41654i	0.916057	+	0.528886i	0.0336819	+	0.999433i	$0.489277\pi$
$318$		0			0
$319$	−3.26990	−	5.66364i	−0.183079	−	0.317103i
$320$	−0.651304	+	1.12809i	−0.0364090	+	0.0630623i
$321$		0			0
$322$	12.6276	−	8.71431i	0.703709	−	0.485629i
$323$			3.18415i			0.177171i
$324$		0			0
$325$	−3.92018	+	2.26332i	−0.217452	+	0.125546i
$326$	4.09229	−	2.36269i	0.226651	−	0.130857i
$327$		0			0
$328$		−	2.25518i		−	0.124522i
$329$	−2.31097	−	1.09686i	−0.127408	−	0.0604716i
$330$		0			0
$331$	−1.00063	+	1.73314i	−0.0549997	+	0.0952622i	−0.892214	−	0.451612i	$-0.850849\pi$
$331$	−1.00063	+	1.73314i	−0.0549997	+	0.0952622i	0.837215	+	0.546874i	$0.184182\pi$
$332$	−2.77161	−	4.80057i	−0.152112	−	0.263466i
$333$		0			0
$334$	−2.16292	−	1.24876i	−0.118350	−	0.0683293i
$335$	−9.38998			−0.513029
$336$		0			0
$337$	−2.24786			−0.122449			−0.0612243	−	0.998124i	$-0.519500\pi$
$337$	−2.24786			−0.122449			−0.0612243	+	0.998124i	$0.519500\pi$
$338$	−9.63200	−	5.56104i	−0.523912	−	0.302481i
$339$		0			0
$340$	−3.73006	−	6.46065i	−0.202291	−	0.350378i
$341$	0.381525	−	0.660821i	0.0206607	−	0.0357855i
$342$		0			0
$343$	4.42670	+	17.9834i	0.239020	+	0.971015i
$344$		−	3.91214i		−	0.210928i
$345$		0			0
$346$	13.4466	−	7.76337i	0.722891	−	0.417361i
$347$	15.0915	−	8.71306i	0.810152	−	0.467741i	−0.0368567	−	0.999321i	$-0.511735\pi$
$347$	15.0915	−	8.71306i	0.810152	−	0.467741i	0.847009	+	0.531579i	$0.178401\pi$
$348$		0			0
$349$		−	24.6300i		−	1.31841i	−0.751962	−	0.659206i	$-0.770892\pi$
$349$		−	24.6300i		−	1.31841i	0.751962	−	0.659206i	$-0.229108\pi$
$350$	−8.71121	+	0.702350i	−0.465634	+	0.0375422i
$351$		0			0
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	7.91758	+	13.7137i	0.421410	+	0.729904i	0.996078	−	0.0884828i	$-0.0282018\pi$
$353$	7.91758	+	13.7137i	0.421410	+	0.729904i	−0.574667	+	0.818387i	$0.694869\pi$
$354$		0			0
$355$	−1.32643	−	0.765815i	−0.0703997	−	0.0406453i
$356$	8.51881			0.451496
$357$		0			0
$358$	8.55542			0.452168
$359$	−11.6373	−	6.71878i	−0.614192	−	0.354604i	0.160413	−	0.987050i	$-0.448718\pi$
$359$	−11.6373	−	6.71878i	−0.614192	−	0.354604i	−0.774604	+	0.632446i	$0.782051\pi$
$360$		0			0
$361$	−9.34544	−	16.1868i	−0.491865	−	0.851936i
$362$	11.4242	−	19.7874i	0.600445	−	1.04000i
$363$		0			0
$364$	2.05931	+	2.98408i	0.107937	+	0.156408i
$365$			2.16651i			0.113400i
$366$		0			0
$367$	29.7226	−	17.1603i	1.55151	−	0.895763i	0.553487	−	0.832858i	$-0.313297\pi$
$367$	29.7226	−	17.1603i	1.55151	−	0.895763i	0.998020	−	0.0629050i	$-0.0200365\pi$
$368$	5.02204	−	2.89948i	0.261792	−	0.151146i
$369$		0			0
$370$		−	8.70509i		−	0.452556i
$371$	12.8555	+	18.6284i	0.667423	+	0.967140i
$372$		0			0
$373$	−5.02865	+	8.70988i	−0.260374	+	0.450980i	−0.966341	−	0.257264i	$-0.917179\pi$
$373$	−5.02865	+	8.70988i	−0.260374	+	0.450980i	0.705968	+	0.708244i	$0.250512\pi$
$374$	2.86353	+	4.95978i	0.148070	+	0.256464i
$375$		0			0
$376$	−0.837321	−	0.483428i	−0.0431816	−	0.0249309i
$377$	8.96198			0.461566
$378$		0			0
$379$	4.33975			0.222918			0.111459	−	0.993769i	$-0.464448\pi$
$379$	4.33975			0.222918			0.111459	+	0.993769i	$0.464448\pi$
$380$	−0.627201	−	0.362114i	−0.0321747	−	0.0185761i
$381$		0			0
$382$	−8.13084	−	14.0830i	−0.416010	−	0.720551i
$383$	−8.82958	+	15.2933i	−0.451170	+	0.781450i	−0.998459	−	0.0554940i	$-0.982327\pi$
$383$	−8.82958	+	15.2933i	−0.451170	+	0.781450i	0.547289	+	0.836944i	$0.315660\pi$
$384$		0			0
$385$	−3.43523	+	0.276969i	−0.175076	+	0.0141156i
$386$			5.67539i			0.288870i
$387$		0			0
$388$	11.2295	−	6.48336i	0.570092	−	0.329143i
$389$	1.71694	−	0.991276i	0.0870523	−	0.0502597i	−0.455842	−	0.890061i	$-0.650662\pi$
$389$	1.71694	−	0.991276i	0.0870523	−	0.0502597i	0.542894	+	0.839801i	$0.317328\pi$
$390$		0			0
$391$			33.2110i			1.67955i
$392$	1.12147	+	6.90958i	0.0566430	+	0.348986i
$393$		0			0
$394$	1.04390	−	1.80809i	0.0525911	−	0.0910905i
$395$	−0.471412	−	0.816509i	−0.0237193	−	0.0410830i
$396$		0			0
$397$	32.6030	+	18.8234i	1.63630	+	0.944717i	0.982092	+	0.188401i	$0.0603305\pi$
$397$	32.6030	+	18.8234i	1.63630	+	0.944717i	0.654206	+	0.756316i	$0.273003\pi$
$398$	−17.4223			−0.873299
$399$		0			0
$400$	−3.30321			−0.165161
$401$	−28.2285	−	16.2978i	−1.40967	−	0.813871i	−0.414310	−	0.910136i	$-0.635977\pi$
$401$	−28.2285	−	16.2978i	−1.40967	−	0.813871i	−0.995356	+	0.0962648i	$0.969310\pi$
$402$		0			0
$403$	0.522832	+	0.905572i	0.0260441	+	0.0451097i
$404$	−3.67391	+	6.36340i	−0.182784	+	0.316591i
$405$		0			0
$406$	15.6314	+	7.41913i	0.775772	+	0.368205i
$407$			6.68281i			0.331255i
$408$		0			0
$409$	30.7939	−	17.7789i	1.52266	−	0.879110i	0.523022	−	0.852319i	$-0.324805\pi$
$409$	30.7939	−	17.7789i	1.52266	−	0.879110i	0.999641	−	0.0267904i	$-0.00852867\pi$
$410$	−2.54405	+	1.46881i	−0.125642	+	0.0725394i
$411$		0			0
$412$		−	17.8560i		−	0.879700i
$413$	−2.17573	+	1.50147i	−0.107061	+	0.0738825i
$414$		0			0
$415$	−3.61032	+	6.25326i	−0.177224	+	0.306961i
$416$	0.685187	+	1.18678i	0.0335940	+	0.0581866i
$417$		0			0
$418$	0.481496	+	0.277992i	0.0235507	+	0.0135970i
$419$	−4.47363			−0.218551			−0.109275	−	0.994012i	$-0.534853\pi$
$419$	−4.47363			−0.218551			−0.109275	+	0.994012i	$0.534853\pi$
$420$		0			0
$421$	0.772473			0.0376480			0.0188240	−	0.999823i	$-0.494008\pi$
$421$	0.772473			0.0376480			0.0188240	+	0.999823i	$0.494008\pi$
$422$	−22.1341	−	12.7791i	−1.07747	−	0.622079i
$423$		0			0
$424$	4.27736	+	7.40860i	0.207727	+	0.359793i
$425$	9.45884	−	16.3832i	0.458821	−	0.794702i
$426$		0			0
$427$	0.166851	−	0.351538i	0.00807447	−	0.0170121i
$428$		−	10.0789i		−	0.487183i
$429$		0			0
$430$	−4.41325	+	2.54799i	−0.212826	+	0.122875i
$431$	−7.03670	+	4.06264i	−0.338946	+	0.195690i	−0.659806	−	0.751436i	$-0.729361\pi$
$431$	−7.03670	+	4.06264i	−0.338946	+	0.195690i	0.320860	+	0.947127i	$0.396028\pi$
$432$		0			0
$433$			34.5052i			1.65822i	0.559088	+	0.829108i	$0.311151\pi$
$433$			34.5052i			1.65822i	−0.559088	+	0.829108i	$0.688849\pi$
$434$	0.162245	+	2.01231i	0.00778799	+	0.0965940i
$435$		0			0
$436$	−0.368886	+	0.638929i	−0.0176664	+	0.0305992i
$437$	1.61206	+	2.79217i	0.0771154	+	0.133568i
$438$		0			0
$439$	12.2137	+	7.05159i	0.582929	+	0.336554i	0.762296	−	0.647228i	$-0.224072\pi$
$439$	12.2137	+	7.05159i	0.582929	+	0.336554i	−0.179368	+	0.983782i	$0.557405\pi$
$440$	−1.30261			−0.0620994
$441$		0			0
$442$	−7.84821			−0.373301
$443$	−13.6938	−	7.90614i	−0.650614	−	0.375632i	0.138077	−	0.990421i	$-0.455908\pi$
$443$	−13.6938	−	7.90614i	−0.650614	−	0.375632i	−0.788691	+	0.614789i	$0.789241\pi$
$444$		0			0
$445$	−5.54833	−	9.61000i	−0.263016	−	0.455558i
$446$	−4.82012	+	8.34870i	−0.228240	+	0.395322i
$447$		0			0
$448$	0.212626	+	2.63719i	0.0100457	+	0.124596i
$449$			33.1895i			1.56631i	0.621828	+	0.783154i	$0.286390\pi$
$449$			33.1895i			1.56631i	−0.621828	+	0.783154i	$0.713610\pi$
$450$		0			0
$451$	1.95305	−	1.12759i	0.0919653	−	0.0530962i
$452$	4.16762	−	2.40618i	0.196028	−	0.113177i
$453$		0			0
$454$			7.07894i			0.332231i
$455$	2.02507	−	4.26663i	0.0949369	−	0.200023i
$456$		0			0
$457$	−8.53304	+	14.7797i	−0.399159	+	0.691363i	−0.993622	−	0.112759i	$-0.964031\pi$
$457$	−8.53304	+	14.7797i	−0.399159	+	0.691363i	0.594463	+	0.804123i	$0.297364\pi$
$458$	9.44614	+	16.3612i	0.441389	+	0.764509i
$459$		0			0
$460$	−6.54176	−	3.77689i	−0.305011	−	0.176098i
$461$	32.1100			1.49551			0.747755	−	0.663974i	$-0.231132\pi$
$461$	32.1100			1.49551			0.747755	+	0.663974i	$0.231132\pi$
$462$		0			0
$463$	21.5146			0.999867			0.499933	−	0.866064i	$-0.333358\pi$
$463$	21.5146			0.999867			0.499933	+	0.866064i	$0.333358\pi$
$464$	5.66364	+	3.26990i	0.262928	+	0.151801i
$465$		0			0
$466$	−4.62739	−	8.01488i	−0.214360	−	0.371282i
$467$	19.8774	−	34.4287i	0.919817	−	1.59317i	0.120126	−	0.992759i	$-0.461670\pi$
$467$	19.8774	−	34.4287i	0.919817	−	1.59317i	0.799691	−	0.600411i	$-0.204996\pi$
$468$		0			0
$469$	−15.6972	+	10.8326i	−0.724828	+	0.500204i
$470$			1.25943i			0.0580934i
$471$		0			0
$472$	−0.865295	+	0.499578i	−0.0398284	+	0.0229950i
$473$	3.38801	−	1.95607i	0.155781	−	0.0899401i
$474$		0			0
$475$		−	1.83653i		−	0.0842659i
$476$	−13.6888	−	6.49710i	−0.627423	−	0.297794i
$477$		0			0
$478$	2.43466	−	4.21695i	0.111359	−	0.192879i
$479$	5.58073	+	9.66610i	0.254990	+	0.441655i	0.964893	−	0.262644i	$-0.0845945\pi$
$479$	5.58073	+	9.66610i	0.254990	+	0.441655i	−0.709903	+	0.704300i	$0.751261\pi$
$480$		0			0
$481$	−7.93102	−	4.57898i	−0.361623	−	0.208783i
$482$	−21.3468			−0.972321
$483$		0			0
$484$	1.00000			0.0454545
$485$	−14.6276	−	8.44528i	−0.664207	−	0.383480i
$486$		0			0
$487$	−13.5154	−	23.4094i	−0.612442	−	1.06078i	−0.990828	−	0.135133i	$-0.956854\pi$
$487$	−13.5154	−	23.4094i	−0.612442	−	1.06078i	0.378385	−	0.925648i	$-0.376479\pi$
$488$	0.0735377	−	0.127371i	0.00332890	−	0.00576582i
$489$		0			0
$490$	7.06422	−	5.76536i	0.319129	−	0.260453i
$491$		−	21.7459i		−	0.981380i	−0.871334	−	0.490690i	$-0.836745\pi$
$491$		−	21.7459i		−	0.981380i	0.871334	−	0.490690i	$-0.163255\pi$
$492$		0			0
$493$	−32.4360	+	18.7269i	−1.46084	+	0.843419i
$494$	−0.659829	+	0.380953i	−0.0296871	+	0.0171399i
$495$		0			0
$496$			0.763050i			0.0342620i
$497$	−3.10086	+	0.250010i	−0.139093	+	0.0112145i
$498$		0			0
$499$	8.55069	−	14.8102i	0.382782	−	0.662997i	−0.608677	−	0.793418i	$-0.708300\pi$
$499$	8.55069	−	14.8102i	0.382782	−	0.662997i	0.991459	+	0.130421i	$0.0416328\pi$
$500$	5.40792	+	9.36679i	0.241849	+	0.418895i
$501$		0			0
$502$	−18.3875	−	10.6160i	−0.820675	−	0.473817i
$503$	−20.0922			−0.895867			−0.447933	−	0.894067i	$-0.647840\pi$
$503$	−20.0922			−0.895867			−0.447933	+	0.894067i	$0.647840\pi$
$504$		0			0
$505$	9.57133			0.425919
$506$	5.02204	+	2.89948i	0.223257	+	0.128898i
$507$		0			0
$508$	6.25791	+	10.8390i	0.277650	+	0.480903i
$509$	−5.05011	+	8.74704i	−0.223842	+	0.387706i	−0.955971	−	0.293460i	$-0.905193\pi$
$509$	−5.05011	+	8.74704i	−0.223842	+	0.387706i	0.732129	+	0.681166i	$0.238527\pi$
$510$		0			0
$511$	2.49937	+	3.62175i	0.110565	+	0.160217i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−12.4929	+	7.21276i	−0.551037	+	0.318141i
$515$	−20.1432	+	11.6297i	−0.887614	+	0.512464i
$516$		0			0
$517$		−	0.966856i		−	0.0425223i
$518$	−10.0425	−	14.5522i	−0.441242	−	0.639389i
$519$		0			0
$520$	0.892530	−	1.54591i	0.0391400	−	0.0677925i
$521$	16.2935	+	28.2211i	0.713829	+	1.23639i	0.963409	+	0.268035i	$0.0863741\pi$
$521$	16.2935	+	28.2211i	0.713829	+	1.23639i	−0.249580	+	0.968354i	$0.580293\pi$
$522$		0			0
$523$	25.5548	+	14.7541i	1.11743	+	0.645150i	0.940744	−	0.339116i	$-0.110128\pi$
$523$	25.5548	+	14.7541i	1.11743	+	0.645150i	0.176689	+	0.984267i	$0.443461\pi$
$524$	14.8489			0.648675
$525$		0			0
$526$	−17.0476			−0.743309
$527$	−3.78456	−	2.18502i	−0.164858	−	0.0951808i
$528$		0			0
$529$	5.31396	+	9.20404i	0.231042	+	0.400176i
$530$	5.57172	−	9.65050i	0.242020	−	0.419191i
$531$		0			0
$532$	−1.46624	+	0.118217i	−0.0635694	+	0.00512535i
$533$			3.09044i			0.133862i
$534$		0			0
$535$	−11.3699	+	6.56444i	−0.491565	+	0.283805i
$536$	−6.24283	+	3.60430i	−0.269649	+	0.155682i
$537$		0			0
$538$		−	22.3689i		−	0.964391i
$539$	−5.42313	+	4.42602i	−0.233591	+	0.190642i
$540$		0			0
$541$	−11.9017	+	20.6144i	−0.511694	+	0.886281i	0.488214	+	0.872724i	$0.337649\pi$
$541$	−11.9017	+	20.6144i	−0.511694	+	0.886281i	−0.999908	+	0.0135565i	$0.995685\pi$
$542$	1.15148	+	1.99443i	0.0494604	+	0.0856679i
$543$		0			0
$544$	−4.95978	−	2.86353i	−0.212649	−	0.122773i
$545$	0.961028			0.0411659
$546$		0			0
$547$	−43.4345			−1.85713			−0.928563	−	0.371174i	$-0.878955\pi$
$547$	−43.4345			−1.85713			−0.928563	+	0.371174i	$0.878955\pi$
$548$	−18.1030	−	10.4518i	−0.773320	−	0.446477i
$549$		0			0
$550$	−1.65161	−	2.86067i	−0.0704247	−	0.121979i
$551$	−1.81801	+	3.14889i	−0.0774500	+	0.134147i
$552$		0			0
$553$	−1.73001	−	0.821116i	−0.0735676	−	0.0349174i
$554$		−	7.32646i		−	0.311271i
$555$		0			0
$556$	2.78163	−	1.60597i	0.117967	−	0.0681085i
$557$	13.5945	−	7.84877i	0.576016	−	0.332563i	−0.183532	−	0.983014i	$-0.558753\pi$
$557$	13.5945	−	7.84877i	0.576016	−	0.332563i	0.759549	+	0.650451i	$0.225420\pi$
$558$		0			0
$559$			5.36109i			0.226750i
$560$	2.83651	−	1.95748i	0.119865	−	0.0827185i
$561$		0			0
$562$	5.52268	−	9.56557i	0.232960	−	0.403499i
$563$	−16.4468	−	28.4867i	−0.693151	−	1.20057i	−0.970800	−	0.239890i	$-0.922889\pi$
$563$	−16.4468	−	28.4867i	−0.693151	−	1.20057i	0.277649	−	0.960683i	$-0.410445\pi$
$564$		0			0
$565$	−5.42878	−	3.13431i	−0.228390	−	0.131861i
$566$	−29.8840			−1.25612
$567$		0			0
$568$	−1.17582			−0.0493363
$569$	−9.79385	−	5.65448i	−0.410580	−	0.237048i	0.280459	−	0.959866i	$-0.409513\pi$
$569$	−9.79385	−	5.65448i	−0.410580	−	0.237048i	−0.691039	+	0.722818i	$0.742847\pi$
$570$		0			0
$571$	10.1162	+	17.5218i	0.423350	+	0.733264i	0.996265	−	0.0863510i	$-0.0275207\pi$
$571$	10.1162	+	17.5218i	0.423350	+	0.733264i	−0.572915	+	0.819615i	$0.694187\pi$
$572$	−0.685187	+	1.18678i	−0.0286491	+	0.0496217i
$573$		0			0
$574$	−2.55841	+	5.39032i	−0.106786	+	0.224987i
$575$		−	19.1552i		−	0.798826i
$576$		0			0
$577$	−17.8277	+	10.2928i	−0.742178	+	0.428497i	−0.822861	−	0.568243i	$-0.807623\pi$
$577$	−17.8277	+	10.2928i	−0.742178	+	0.428497i	0.0806827	+	0.996740i	$0.474290\pi$
$578$	13.6825	−	7.89960i	0.569118	−	0.328580i
$579$		0			0
$580$		−	8.51881i		−	0.353724i
$581$	1.17864	+	14.6185i	0.0488980	+	0.606480i
$582$		0			0
$583$	−4.27736	+	7.40860i	−0.177150	+	0.306833i
$584$	0.831605	+	1.44038i	0.0344121	+	0.0596034i
$585$		0			0
$586$	−21.2014	−	12.2406i	−0.875822	−	0.505656i
$587$	26.7987			1.10610			0.553050	−	0.833148i	$-0.313464\pi$
$587$	26.7987			1.10610			0.553050	+	0.833148i	$0.313464\pi$
$588$		0			0
$589$	−0.424243			−0.0174806
$590$	1.12714	+	0.650755i	0.0464036	+	0.0267912i
$591$		0			0
$592$	−3.34141	−	5.78749i	−0.137331	−	0.237864i
$593$	19.4485	−	33.6858i	0.798653	−	1.38331i	−0.121840	−	0.992550i	$-0.538879\pi$
$593$	19.4485	−	33.6858i	0.798653	−	1.38331i	0.920493	−	0.390759i	$-0.127787\pi$
$594$		0			0
$595$	1.58622	+	19.6738i	0.0650286	+	0.806546i
$596$		−	20.4727i		−	0.838594i
$597$		0			0
$598$	−6.88208	+	3.97337i	−0.281429	+	0.162483i
$599$	−24.0811	+	13.9032i	−0.983926	+	0.568070i	−0.903453	−	0.428687i	$-0.858976\pi$
$599$	−24.0811	+	13.9032i	−0.983926	+	0.568070i	−0.0804730	+	0.996757i	$0.525643\pi$
$600$		0			0
$601$			7.32197i			0.298669i	0.988787	+	0.149335i	$0.0477132\pi$
$601$			7.32197i			0.298669i	−0.988787	+	0.149335i	$0.952287\pi$
$602$	−4.43815	+	9.35075i	−0.180885	+	0.381108i
$603$		0			0
$604$	7.80068	−	13.5112i	0.317405	−	0.549762i
$605$	−0.651304	−	1.12809i	−0.0264793	−	0.0458635i
$606$		0			0
$607$	−5.43361	−	3.13710i	−0.220543	−	0.127331i	0.385658	−	0.922642i	$-0.373974\pi$
$607$	−5.43361	−	3.13710i	−0.220543	−	0.127331i	−0.606202	+	0.795311i	$0.707308\pi$
$608$	−0.555984			−0.0225481
$609$		0			0
$610$	−0.191582			−0.00775691
$611$	1.14744	+	0.662477i	0.0464206	+	0.0268009i
$612$		0			0
$613$	−3.08473	−	5.34292i	−0.124591	−	0.215798i	0.796982	−	0.604003i	$-0.206429\pi$
$613$	−3.08473	−	5.34292i	−0.124591	−	0.215798i	−0.921573	+	0.388205i	$0.873095\pi$
$614$	4.36240	−	7.55590i	0.176052	−	0.304931i
$615$		0			0
$616$	−2.17756	+	1.50274i	−0.0877365	+	0.0605470i
$617$		−	3.03336i		−	0.122119i	−0.998134	−	0.0610593i	$-0.980552\pi$
$617$		−	3.03336i		−	0.122119i	0.998134	−	0.0610593i	$-0.0194479\pi$
$618$		0			0
$619$	30.9228	−	17.8533i	1.24289	−	0.717583i	0.273209	−	0.961955i	$-0.411915\pi$
$619$	30.9228	−	17.8533i	1.24289	−	0.717583i	0.969682	+	0.244371i	$0.0785816\pi$
$620$	0.860791	−	0.496978i	0.0345702	−	0.0199591i
$621$		0			0
$622$		−	2.62196i		−	0.105131i
$623$	−20.3616	−	9.66422i	−0.815769	−	0.387189i
$624$		0			0
$625$	−1.21363	+	2.10207i	−0.0485453	+	0.0840830i
$626$	11.7864	+	20.4146i	0.471078	+	0.815931i
$627$		0			0
$628$	−6.72012	−	3.87986i	−0.268162	−	0.154823i
$629$	38.2729			1.52604
$630$		0			0
$631$	5.45597			0.217199			0.108599	−	0.994086i	$-0.465363\pi$
$631$	5.45597			0.217199			0.108599	+	0.994086i	$0.465363\pi$
$632$	−0.626826	−	0.361898i	−0.0249338	−	0.0143955i
$633$		0			0
$634$	−9.41654	−	16.3099i	−0.373979	−	0.647750i
$635$	8.15160	−	14.1190i	0.323486	−	0.560295i
$636$		0			0
$637$	−1.53684	−	9.46871i	−0.0608918	−	0.375164i
$638$			6.53981i			0.258913i
$639$		0			0
$640$	1.12809	−	0.651304i	0.0445917	−	0.0257451i
$641$	−32.8636	+	18.9738i	−1.29804	+	0.749421i	−0.980064	−	0.198680i	$-0.936335\pi$
$641$	−32.8636	+	18.9738i	−1.29804	+	0.749421i	−0.317971	+	0.948101i	$0.603001\pi$
$642$		0			0
$643$			2.15376i			0.0849360i	0.999098	+	0.0424680i	$0.0135221\pi$
$643$			2.15376i			0.0849360i	−0.999098	+	0.0424680i	$0.986478\pi$
$644$	−15.2930	+	1.23301i	−0.602628	+	0.0485875i
$645$		0			0
$646$	1.59208	−	2.75756i	0.0626394	−	0.108495i
$647$	2.88258	+	4.99277i	0.113326	+	0.196286i	0.917109	−	0.398636i	$-0.130516\pi$
$647$	2.88258	+	4.99277i	0.113326	+	0.196286i	−0.803783	+	0.594922i	$0.797183\pi$
$648$		0			0
$649$	−0.865295	−	0.499578i	−0.0339658	−	0.0196102i
$650$	4.52663			0.177549
$651$		0			0
$652$	−4.72537			−0.185060
$653$	−18.1451	−	10.4761i	−0.710071	−	0.409960i	0.101016	−	0.994885i	$-0.467791\pi$
$653$	−18.1451	−	10.4761i	−0.710071	−	0.409960i	−0.811087	+	0.584925i	$0.801124\pi$
$654$		0			0
$655$	−9.67112	−	16.7509i	−0.377882	−	0.654511i
$656$	−1.12759	+	1.95305i	−0.0440251	+	0.0762536i
$657$		0			0
$658$	1.45293	+	2.10539i	0.0566411	+	0.0820766i
$659$		−	29.5567i		−	1.15137i	−0.817673	−	0.575683i	$-0.804736\pi$
$659$		−	29.5567i		−	1.15137i	0.817673	−	0.575683i	$-0.195264\pi$
$660$		0			0
$661$	−3.57741	+	2.06542i	−0.139145	+	0.0803356i	−0.567957	−	0.823059i	$-0.692266\pi$
$661$	−3.57741	+	2.06542i	−0.139145	+	0.0803356i	0.428811	+	0.903394i	$0.358933\pi$
$662$	1.73314	−	1.00063i	0.0673605	−	0.0388906i
$663$		0			0
$664$			5.54322i			0.215119i
$665$	1.08833	+	1.57705i	0.0422034	+	0.0611555i
$666$		0			0
$667$	−18.9620	+	32.8432i	−0.734213	+	1.27169i
$668$	1.24876	+	2.16292i	0.0483161	+	0.0836860i
$669$		0			0
$670$	8.13196	+	4.69499i	0.314165	+	0.181383i
$671$	0.147075			0.00567778
$672$		0			0
$673$	14.0120			0.540123			0.270061	−	0.962843i	$-0.412956\pi$
$673$	14.0120			0.540123			0.270061	+	0.962843i	$0.412956\pi$
$674$	1.94670	+	1.12393i	0.0749841	+	0.0432921i
$675$		0			0
$676$	5.56104	+	9.63200i	0.213886	+	0.370462i
$677$	3.80304	−	6.58706i	0.146163	−	0.253161i	−0.783643	−	0.621211i	$-0.786641\pi$
$677$	3.80304	−	6.58706i	0.146163	−	0.253161i	0.929806	+	0.368050i	$0.119974\pi$
$678$		0			0
$679$	−34.1957	+	2.75707i	−1.31231	+	0.105807i
$680$			7.46011i			0.286082i
$681$		0			0
$682$	−0.660821	+	0.381525i	−0.0253041	+	0.0146094i
$683$	15.2464	−	8.80252i	0.583388	−	0.336819i	−0.179091	−	0.983833i	$-0.557316\pi$
$683$	15.2464	−	8.80252i	0.583388	−	0.336819i	0.762479	+	0.647013i	$0.223982\pi$
$684$		0			0
$685$			27.2291i			1.04037i
$686$	5.15808	−	17.7875i	0.196937	−	0.679129i
$687$		0			0
$688$	−1.95607	+	3.38801i	−0.0745744	+	0.129167i
$689$	−5.86158	−	10.1526i	−0.223308	−	0.386781i
$690$		0			0
$691$	−41.2387	−	23.8092i	−1.56879	−	0.905744i	−0.996310	−	0.0858285i	$-0.972646\pi$
$691$	−41.2387	−	23.8092i	−1.56879	−	0.905744i	−0.572485	−	0.819915i	$-0.694020\pi$
$692$	−15.5267			−0.590238
$693$		0			0
$694$	−17.4261			−0.661486
$695$	−3.62337	−	2.09196i	−0.137442	−	0.0793524i
$696$		0			0
$697$	−6.45778	−	11.1852i	−0.244606	−	0.423670i
$698$	−12.3150	+	21.3302i	−0.466129	+	0.807360i
$699$		0			0
$700$	7.89530	+	3.74735i	0.298414	+	0.141637i
$701$			40.9069i			1.54503i	0.634994	+	0.772517i	$0.281002\pi$
$701$			40.9069i			1.54503i	−0.634994	+	0.772517i	$0.718998\pi$
$702$		0			0
$703$	3.21775	−	1.85777i	0.121360	−	0.0700670i
$704$	−0.866025	+	0.500000i	−0.0326396	+	0.0188445i
$705$		0			0
$706$		−	15.8352i		−	0.595964i
$707$	16.0003	−	11.0418i	0.601755	−	0.415271i
$708$		0			0
$709$	−3.08240	+	5.33888i	−0.115762	+	0.200506i	−0.918084	−	0.396386i	$-0.870264\pi$
$709$	−3.08240	+	5.33888i	−0.115762	+	0.200506i	0.802322	+	0.596891i	$0.203598\pi$
$710$	0.765815	+	1.32643i	0.0287405	+	0.0497801i
$711$		0			0
$712$	−7.37750	−	4.25940i	−0.276484	−	0.159628i
$713$	−4.42490			−0.165714
$714$		0			0
$715$	1.78506			0.0667575
$716$	−7.40921	−	4.27771i	−0.276895	−	0.159866i
$717$		0			0
$718$	6.71878	+	11.6373i	0.250743	+	0.434299i
$719$	−9.93587	+	17.2094i	−0.370545	+	0.641804i	−0.989650	−	0.143505i	$-0.954163\pi$
$719$	−9.93587	+	17.2094i	−0.370545	+	0.641804i	0.619104	+	0.785309i	$0.287496\pi$
$720$		0			0
$721$	−20.2568	+	42.6792i	−0.754404	+	1.58945i
$722$			18.6909i			0.695603i
$723$		0			0
$724$	−19.7874	+	11.4242i	−0.735392	+	0.424579i
$725$	18.7082	−	10.8012i	0.694805	−	0.401146i
$726$		0			0
$727$		−	42.4001i		−	1.57253i	−0.617888	−	0.786266i	$-0.712011\pi$
$727$		−	42.4001i		−	1.57253i	0.617888	−	0.786266i	$-0.287989\pi$
$728$	−0.291378	−	3.61394i	−0.0107992	−	0.133942i
$729$		0			0
$730$	1.08326	−	1.87625i	0.0400931	−	0.0694433i
$731$	−11.2025	−	19.4033i	−0.414340	−	0.717658i
$732$		0			0
$733$	−14.9313	−	8.62060i	−0.551501	−	0.318409i	0.198226	−	0.980156i	$-0.436482\pi$
$733$	−14.9313	−	8.62060i	−0.551501	−	0.318409i	−0.749727	+	0.661747i	$0.769815\pi$
$734$	−34.3207			−1.26680
$735$		0			0
$736$	−5.79896			−0.213752
$737$	−6.24283	−	3.60430i	−0.229958	−	0.132766i
$738$		0			0
$739$	9.99251	+	17.3075i	0.367581	+	0.636668i	0.989187	−	0.146662i	$-0.0468529\pi$
$739$	9.99251	+	17.3075i	0.367581	+	0.636668i	−0.621606	+	0.783330i	$0.713520\pi$
$740$	−4.35254	+	7.53883i	−0.160003	+	0.277133i
$741$		0			0
$742$	−1.81896	−	22.5604i	−0.0667761	−	0.828220i
$743$			5.37602i			0.197227i	0.995126	+	0.0986136i	$0.0314408\pi$
$743$			5.37602i			0.197227i	−0.995126	+	0.0986136i	$0.968559\pi$
$744$		0			0
$745$	−23.0951	+	13.3339i	−0.846138	+	0.488518i
$746$	8.70988	−	5.02865i	0.318891	−	0.184112i
$747$		0			0
$748$		−	5.72706i		−	0.209402i
$749$	−11.4341	+	24.0905i	−0.417793	+	0.880248i
$750$		0			0
$751$	−22.6527	+	39.2356i	−0.826607	+	1.43173i	0.0740775	+	0.997252i	$0.476399\pi$
$751$	−22.6527	+	39.2356i	−0.826607	+	1.43173i	−0.900685	+	0.434473i	$0.856935\pi$
$752$	0.483428	+	0.837321i	0.0176288	+	0.0305340i
$753$		0			0
$754$	−7.76130	−	4.48099i	−0.282650	−	0.163188i
$755$	−20.3225			−0.739610
$756$		0			0
$757$	−13.5594			−0.492823			−0.246412	−	0.969165i	$-0.579251\pi$
$757$	−13.5594			−0.492823			−0.246412	+	0.969165i	$0.579251\pi$
$758$	−3.75833	−	2.16987i	−0.136509	−	0.0788133i
$759$		0			0
$760$	0.362114	+	0.627201i	0.0131353	+	0.0227510i
$761$	15.4116	−	26.6938i	0.558672	−	0.967648i	−0.438936	−	0.898518i	$-0.644644\pi$
$761$	15.4116	−	26.6938i	0.558672	−	0.967648i	0.997608	−	0.0691296i	$-0.0220222\pi$
$762$		0			0
$763$	1.60655	−	1.10868i	0.0581608	−	0.0401368i
$764$			16.2617i			0.588327i
$765$		0			0
$766$	15.2933	−	8.82958i	0.552569	−	0.319026i
$767$	1.18578	−	0.684609i	0.0428160	−	0.0247198i
$768$		0			0
$769$			17.6776i			0.637470i	0.947844	+	0.318735i	$0.103258\pi$
$769$			17.6776i			0.637470i	−0.947844	+	0.318735i	$0.896742\pi$
$770$	3.11348	+	1.47775i	0.112202	+	0.0532545i
$771$		0			0
$772$	2.83770	−	4.91503i	0.102131	−	0.176896i
$773$	6.74571	+	11.6839i	0.242626	+	0.420241i	0.961462	−	0.274939i	$-0.0886578\pi$
$773$	6.74571	+	11.6839i	0.242626	+	0.420241i	−0.718835	+	0.695180i	$0.755324\pi$
$774$		0			0
$775$	2.18283	+	1.26026i	0.0784096	+	0.0452698i
$776$	−12.9667			−0.465478
$777$		0			0
$778$	−1.98255			−0.0710779
$779$	−1.08586	−	0.626922i	−0.0389050	−	0.0224618i
$780$		0			0
$781$	−0.587909	−	1.01829i	−0.0210370	−	0.0364372i
$782$	16.6055	−	28.7615i	0.593811	−	1.02851i
$783$		0			0
$784$	2.48356	−	6.54461i	0.0886987	−	0.233736i
$785$			10.1079i			0.360766i
$786$		0			0
$787$	30.1209	−	17.3903i	1.07370	−	0.619898i	0.144507	−	0.989504i	$-0.453841\pi$
$787$	30.1209	−	17.3903i	1.07370	−	0.619898i	0.929189	+	0.369606i	$0.120507\pi$
$788$	−1.80809	+	1.04390i	−0.0644107	+	0.0371875i
$789$		0			0
$790$			0.942824i			0.0335442i
$791$	−12.6911	+	1.02323i	−0.451244	+	0.0363820i
$792$		0			0
$793$	−0.100774	+	0.174546i	−0.00357859	+	0.00619831i
$794$	−18.8234	−	32.6030i	−0.668016	−	1.15704i
$795$		0			0
$796$	15.0881	+	8.71113i	0.534785	+	0.308758i
$797$	−11.4732			−0.406401			−0.203201	−	0.979137i	$-0.565134\pi$
$797$	−11.4732			−0.406401			−0.203201	+	0.979137i	$0.565134\pi$
$798$		0			0
$799$	−5.53724			−0.195893
$800$	2.86067	+	1.65161i	0.101140	+	0.0583931i
$801$		0			0
$802$	16.2978	+	28.2285i	0.575494	+	0.996784i
$803$	−0.831605	+	1.44038i	−0.0293467	+	0.0508300i
$804$		0			0
$805$	11.3513	+	16.4488i	0.400082	+	0.579745i
$806$		−	1.04566i		−	0.0368319i
$807$		0			0
$808$	6.36340	−	3.67391i	0.223864	−	0.129248i
$809$	22.0848	−	12.7507i	0.776460	−	0.448289i	−0.0587142	−	0.998275i	$-0.518700\pi$
$809$	22.0848	−	12.7507i	0.776460	−	0.448289i	0.835174	+	0.549985i	$0.185367\pi$
$810$		0			0
$811$		−	18.6249i		−	0.654008i	−0.945023	−	0.327004i	$-0.893961\pi$
$811$		−	18.6249i		−	0.654008i	0.945023	−	0.327004i	$-0.106039\pi$
$812$	−9.82761	−	14.2408i	−0.344881	−	0.499756i
$813$		0			0
$814$	3.34141	−	5.78749i	0.117116	−	0.202851i
$815$	3.07766	+	5.33066i	0.107806	+	0.186725i
$816$		0			0
$817$	−1.88368	−	1.08754i	−0.0659015	−	0.0380483i
$818$	−35.5578			−1.24325
$819$		0			0
$820$	2.93762			0.102586
$821$	−19.2122	−	11.0922i	−0.670512	−	0.387120i	0.125759	−	0.992061i	$-0.459863\pi$
$821$	−19.2122	−	11.0922i	−0.670512	−	0.387120i	−0.796270	+	0.604941i	$0.793197\pi$
$822$		0			0
$823$	−21.8996	−	37.9312i	−0.763371	−	1.32220i	−0.941103	−	0.338119i	$-0.890209\pi$
$823$	−21.8996	−	37.9312i	−0.763371	−	1.32220i	0.177732	−	0.984079i	$-0.443124\pi$
$824$	−8.92798	+	15.4637i	−0.311021	+	0.538704i
$825$		0			0
$826$	2.63497	−	0.212447i	0.0916823	−	0.00739198i
$827$		−	36.7143i		−	1.27668i	−0.769754	−	0.638341i	$-0.779621\pi$
$827$		−	36.7143i		−	1.27668i	0.769754	−	0.638341i	$-0.220379\pi$
$828$		0			0
$829$	32.1439	−	18.5583i	1.11640	−	0.644555i	0.175922	−	0.984404i	$-0.443709\pi$
$829$	32.1439	−	18.5583i	1.11640	−	0.644555i	0.940480	+	0.339849i	$0.110376\pi$
$830$	6.25326	−	3.61032i	0.217054	−	0.125316i
$831$		0			0
$832$		−	1.37037i		−	0.0475092i
$833$	25.3480	+	31.0586i	0.878258	+	1.07612i
$834$		0			0
$835$	1.62665	−	2.81744i	0.0562925	−	0.0975015i
$836$	−0.277992	−	0.481496i	−0.00961455	−	0.0166529i
$837$		0			0
$838$	3.87427	+	2.23681i	0.133835	+	0.0772694i
$839$	−11.7171			−0.404517			−0.202259	−	0.979332i	$-0.564828\pi$
$839$	−11.7171			−0.404517			−0.202259	+	0.979332i	$0.564828\pi$
$840$		0			0
$841$	−13.7691			−0.474796
$842$	−0.668981	−	0.386236i	−0.0230546	−	0.0133106i
$843$		0			0
$844$	12.7791	+	22.1341i	0.439876	+	0.761888i
$845$	7.24385	−	12.5467i	0.249196	−	0.431620i
$846$		0			0
$847$	−2.39019	−	1.13446i	−0.0821279	−	0.0389804i
$848$		−	8.55471i		−	0.293770i
$849$		0			0
$850$	−16.3832	+	9.45884i	−0.561939	+	0.324436i
$851$	33.5614	−	19.3767i	1.15047	−	0.664224i
$852$		0			0
$853$			5.99115i			0.205133i	0.994726	+	0.102567i	$0.0327055\pi$
$853$			5.99115i			0.205133i	−0.994726	+	0.102567i	$0.967295\pi$
$854$	−0.320266	+	0.221016i	−0.0109593	+	0.00756300i
$855$		0			0
$856$	−5.03946	+	8.72859i	−0.172245	+	0.298337i
$857$	−24.0477	−	41.6518i	−0.821453	−	1.42280i	−0.904600	−	0.426261i	$-0.859830\pi$
$857$	−24.0477	−	41.6518i	−0.821453	−	1.42280i	0.0831470	−	0.996537i	$-0.473503\pi$
$858$		0			0
$859$	41.0197	+	23.6827i	1.39957	+	0.808045i	0.994348	−	0.106172i	$-0.0338594\pi$
$859$	41.0197	+	23.6827i	1.39957	+	0.808045i	0.405226	+	0.914216i	$0.367193\pi$
$860$	5.09598			0.173772
$861$		0			0
$862$	8.12528			0.276748
$863$	−25.1635	−	14.5281i	−0.856574	−	0.494543i	0.00628929	−	0.999980i	$-0.497998\pi$
$863$	−25.1635	−	14.5281i	−0.856574	−	0.494543i	−0.862864	+	0.505437i	$0.831331\pi$
$864$		0			0
$865$	10.1126	+	17.5156i	0.343840	+	0.595548i
$866$	17.2526	−	29.8824i	0.586268	−	1.01545i
$867$		0			0
$868$	0.865648	−	1.82383i	0.0293820	−	0.0619050i
$869$		−	0.723797i		−	0.0245531i
$870$		0			0
$871$	8.55501	−	4.93924i	0.289875	−	0.167360i
$872$	0.638929	−	0.368886i	0.0216369	−	0.0124921i
$873$		0			0
$874$		−	3.22413i		−	0.109058i
$875$	−2.29973	−	28.5234i	−0.0777451	−	0.964268i
$876$		0			0
$877$	−1.48397	+	2.57031i	−0.0501100	+	0.0867931i	−0.889992	−	0.455975i	$-0.849291\pi$
$877$	−1.48397	+	2.57031i	−0.0501100	+	0.0867931i	0.839882	+	0.542768i	$0.182624\pi$
$878$	−7.05159	−	12.2137i	−0.237980	−	0.412193i
$879$		0			0
$880$	1.12809	+	0.651304i	0.0380280	+	0.0219555i
$881$	7.81186			0.263188			0.131594	−	0.991304i	$-0.457990\pi$
$881$	7.81186			0.263188			0.131594	+	0.991304i	$0.457990\pi$
$882$		0			0
$883$	3.07807			0.103585			0.0517927	−	0.998658i	$-0.483507\pi$
$883$	3.07807			0.103585			0.0517927	+	0.998658i	$0.483507\pi$
$884$	6.79675	+	3.92411i	0.228599	+	0.131982i
$885$		0			0
$886$	7.90614	+	13.6938i	0.265612	+	0.460054i
$887$	−10.5062	+	18.1974i	−0.352765	+	0.611007i	−0.986733	−	0.162352i	$-0.948092\pi$
$887$	−10.5062	+	18.1974i	−0.352765	+	0.611007i	0.633968	+	0.773360i	$0.281425\pi$
$888$		0			0
$889$	−2.66119	−	33.0066i	−0.0892535	−	1.10701i
$890$			11.0967i			0.371961i
$891$		0			0
$892$	8.34870	−	4.82012i	0.279535	−	0.161390i
$893$	−0.465537	+	0.268778i	−0.0155786	+	0.00899431i
$894$		0			0
$895$			11.1444i			0.372515i
$896$	1.13446	−	2.39019i	0.0378995	−	0.0798506i
$897$		0			0
$898$	16.5947	−	28.7429i	0.553773	−	0.959163i
$899$	−2.49510	−	4.32164i	−0.0832163	−	0.144135i
$900$		0			0
$901$	42.4295	+	24.4967i	1.41353	+	0.816103i
$902$	−2.25518			−0.0750894
$903$		0			0
$904$	−4.81235			−0.160056
$905$	25.7752	+	14.8813i	0.856797	+	0.494672i
$906$		0			0
$907$	−16.8569	−	29.1970i	−0.559724	−	0.969470i	−0.997519	−	0.0703952i	$-0.977574\pi$
$907$	−16.8569	−	29.1970i	−0.559724	−	0.969470i	0.437796	−	0.899075i	$-0.355759\pi$
$908$	3.53947	−	6.13055i	0.117462	−	0.203449i
$909$		0			0
$910$	−3.88708	+	2.68248i	−0.128856	+	0.0889232i
$911$			22.8272i			0.756298i	0.925745	+	0.378149i	$0.123439\pi$
$911$			22.8272i			0.756298i	−0.925745	+	0.378149i	$0.876561\pi$
$912$		0			0
$913$	−4.80057	+	2.77161i	−0.158876	+	0.0917269i
$914$	14.7797	−	8.53304i	0.488868	−	0.282248i
$915$		0			0
$916$		−	18.8923i		−	0.624219i
$917$	−35.4916	−	16.8454i	−1.17204	−	0.556284i
$918$		0			0
$919$	8.07735	−	13.9904i	0.266447	−	0.461500i	−0.701495	−	0.712675i	$-0.747484\pi$
$919$	8.07735	−	13.9904i	0.266447	−	0.461500i	0.967942	+	0.251175i	$0.0808169\pi$
$920$	3.77689	+	6.54176i	0.124520	+	0.215675i
$921$		0			0
$922$	−27.8081	−	16.0550i	−0.915810	−	0.528743i
$923$	1.61131			0.0530369
$924$		0			0
$925$	−22.0747			−0.725813
$926$	−18.6322	−	10.7573i	−0.612291	−	0.353506i
$927$		0			0
$928$	−3.26990	−	5.66364i	−0.107340	−	0.185918i
$929$	−12.8229	+	22.2099i	−0.420706	+	0.728685i	−0.996009	−	0.0892562i	$-0.971551\pi$
$929$	−12.8229	+	22.2099i	−0.420706	+	0.728685i	0.575302	+	0.817941i	$0.304884\pi$
$930$		0			0
$931$	3.63870	+	1.38082i	0.119253	+	0.0452546i
$932$			9.25479i			0.303151i
$933$		0			0
$934$	−34.4287	+	19.8774i	−1.12654	+	0.650409i
$935$	−6.46065	+	3.73006i	−0.211286	+	0.121986i
$936$		0			0
$937$		−	43.9317i		−	1.43518i	−0.696463	−	0.717592i	$-0.745244\pi$
$937$		−	43.9317i		−	1.43518i	0.696463	−	0.717592i	$-0.254756\pi$
$938$	19.0105	−	1.53274i	0.620714	−	0.0500457i
$939$		0			0
$940$	0.629717	−	1.09070i	0.0205391	−	0.0355748i
$941$	−21.9166	−	37.9607i	−0.714460	−	1.23748i	−0.963167	−	0.268903i	$-0.913339\pi$
$941$	−21.9166	−	37.9607i	−0.714460	−	1.23748i	0.248707	−	0.968579i	$-0.419994\pi$
$942$		0			0
$943$	−11.3256	−	6.53886i	−0.368813	−	0.212934i
$944$	0.999157			0.0325198
$945$		0			0
$946$	−3.91214			−0.127195
$947$	15.4512	+	8.92077i	0.502097	+	0.289886i	0.729579	−	0.683896i	$-0.239716\pi$
$947$	15.4512	+	8.92077i	0.502097	+	0.289886i	−0.227482	+	0.973782i	$0.573049\pi$
$948$		0			0
$949$	−1.13961	−	1.97386i	−0.0369933	−	0.0640743i
$950$	−0.918266	+	1.59048i	−0.0297925	+	0.0516021i
$951$		0			0
$952$	8.60626	+	12.4710i	0.278931	+	0.404189i
$953$			5.09951i			0.165189i	0.996583	+	0.0825946i	$0.0263207\pi$
$953$			5.09951i			0.165189i	−0.996583	+	0.0825946i	$0.973679\pi$
$954$		0			0
$955$	18.3447	−	10.5913i	0.593620	−	0.342726i
$956$	−4.21695	+	2.43466i	−0.136386	+	0.0787425i
$957$		0			0
$958$		−	11.1615i		−	0.360610i
$959$	31.4125	+	45.5187i	1.01436	+	1.46988i
$960$		0			0
$961$	−15.2089	+	26.3425i	−0.490609	+	0.849760i
$962$	4.57898	+	7.93102i	0.147632	+	0.255706i
$963$		0			0
$964$	18.4869	+	10.6734i	0.595423	+	0.343767i
$965$	−7.39281			−0.237983
$966$		0			0
$967$	−36.1081			−1.16116			−0.580578	−	0.814204i	$-0.697174\pi$
$967$	−36.1081			−1.16116			−0.580578	+	0.814204i	$0.697174\pi$
$968$	−0.866025	−	0.500000i	−0.0278351	−	0.0160706i
$969$		0			0
$970$	8.44528	+	14.6276i	0.271161	+	0.469665i
$971$	15.1490	−	26.2388i	0.486153	−	0.842042i	−0.513720	−	0.857958i	$-0.671733\pi$
$971$	15.1490	−	26.2388i	0.486153	−	0.842042i	0.999873	+	0.0159157i	$0.00506633\pi$
$972$		0			0
$973$	−8.47053	+	0.682945i	−0.271553	+	0.0218942i
$974$			27.0308i			0.866124i
$975$		0			0
$976$	−0.127371	+	0.0735377i	−0.00407705	+	0.00235388i
$977$	21.0168	−	12.1341i	0.672388	−	0.388203i	−0.124593	−	0.992208i	$-0.539763\pi$
$977$	21.0168	−	12.1341i	0.672388	−	0.388203i	0.796981	+	0.604005i	$0.206429\pi$
$978$		0			0
$979$		−	8.51881i		−	0.272262i
$980$	−9.00048	+	1.46084i	−0.287510	+	0.0466649i
$981$		0			0
$982$	−10.8730	+	18.8325i	−0.346970	+	0.600970i
$983$	29.2363	+	50.6388i	0.932493	+	1.61513i	0.779044	+	0.626969i	$0.215705\pi$
$983$	29.2363	+	50.6388i	0.932493	+	1.61513i	0.153449	+	0.988157i	$0.450962\pi$
$984$		0			0
$985$	2.35524	+	1.35980i	0.0750441	+	0.0433267i
$986$	37.4539			1.19277
$987$		0			0
$988$	0.761905			0.0242394
$989$	−19.6469	−	11.3432i	−0.624736	−	0.360691i
$990$		0			0
$991$	22.1078	+	38.2918i	0.702277	+	1.21638i	0.967665	+	0.252238i	$0.0811665\pi$
$991$	22.1078	+	38.2918i	0.702277	+	1.21638i	−0.265388	+	0.964142i	$0.585500\pi$
$992$	0.381525	−	0.660821i	0.0121134	−	0.0209811i
$993$		0			0
$994$	2.81043	+	1.33392i	0.0891414	+	0.0423092i
$995$		−	22.6944i		−	0.719461i
$996$		0			0
$997$	−33.7758	+	19.5005i	−1.06969	+	0.617586i	−0.928097	−	0.372339i	$-0.878556\pi$
$997$	−33.7758	+	19.5005i	−1.06969	+	0.617586i	−0.141593	+	0.989925i	$0.545223\pi$
$998$	−14.8102	+	8.55069i	−0.468810	+	0.270667i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.r.d.89.2	✓	24
3.2	odd	2	inner	1386.2.r.d.89.11	yes	24
7.3	odd	6	inner	1386.2.r.d.1277.11	yes	24
21.17	even	6	inner	1386.2.r.d.1277.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.r.d.89.2	✓	24	1.1	even	1	trivial
1386.2.r.d.89.11	yes	24	3.2	odd	2	inner
1386.2.r.d.1277.2	yes	24	21.17	even	6	inner
1386.2.r.d.1277.11	yes	24	7.3	odd	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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.651304 - 1.12809i) q^{5} +(-0.212626 - 2.63719i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.651304 - 1.12809i) q^{5} +(-0.212626 - 2.63719i) q^{7} -1.00000i q^{8} +(-1.12809 + 0.651304i) q^{10} +(0.866025 - 0.500000i) q^{11} +1.37037i q^{13} +(-1.13446 + 2.39019i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.86353 - 4.95978i) q^{17} +(-0.481496 - 0.277992i) q^{19} +1.30261 q^{20} -1.00000 q^{22} +(-5.02204 - 2.89948i) q^{23} +(1.65161 + 2.86067i) q^{25} +(0.685187 - 1.18678i) q^{26} +(2.17756 - 1.50274i) q^{28} -6.53981i q^{29} +(0.660821 - 0.381525i) q^{31} +(0.866025 - 0.500000i) q^{32} +5.72706i q^{34} +(-3.11348 - 1.47775i) q^{35} +(-3.34141 + 5.78749i) q^{37} +(0.277992 + 0.481496i) q^{38} +(-1.12809 - 0.651304i) q^{40} +2.25518 q^{41} +3.91214 q^{43} +(0.866025 + 0.500000i) q^{44} +(2.89948 + 5.02204i) q^{46} +(0.483428 - 0.837321i) q^{47} +(-6.90958 + 1.12147i) q^{49} -3.30321i q^{50} +(-1.18678 + 0.685187i) q^{52} +(-7.40860 + 4.27736i) q^{53} -1.30261i q^{55} +(-2.63719 + 0.212626i) q^{56} +(-3.26990 + 5.66364i) q^{58} +(-0.499578 - 0.865295i) q^{59} +(0.127371 + 0.0735377i) q^{61} -0.763050 q^{62} -1.00000 q^{64} +(1.54591 + 0.892530i) q^{65} +(-3.60430 - 6.24283i) q^{67} +(2.86353 - 4.95978i) q^{68} +(1.95748 + 2.83651i) q^{70} -1.17582i q^{71} +(-1.44038 + 0.831605i) q^{73} +(5.78749 - 3.34141i) q^{74} -0.555984i q^{76} +(-1.50274 - 2.17756i) q^{77} +(0.361898 - 0.626826i) q^{79} +(0.651304 + 1.12809i) q^{80} +(-1.95305 - 1.12759i) q^{82} -5.54322 q^{83} -7.46011 q^{85} +(-3.38801 - 1.95607i) q^{86} +(-0.500000 - 0.866025i) q^{88} +(4.25940 - 7.37750i) q^{89} +(3.61394 - 0.291378i) q^{91} -5.79896i q^{92} +(-0.837321 + 0.483428i) q^{94} +(-0.627201 + 0.362114i) q^{95} -12.9667i q^{97} +(6.54461 + 2.48356i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{4} + 8 q^{7}+O(q^{10}) \) 24 * q + 12 * q^4 + 8 * q^7	\( 24 q + 12 q^{4} + 8 q^{7} - 12 q^{16} + 12 q^{19} - 24 q^{22} + 4 q^{25} + 4 q^{28} + 20 q^{37} + 24 q^{43} + 12 q^{46} + 40 q^{49} - 28 q^{58} - 120 q^{61} - 24 q^{64} - 32 q^{67} + 48 q^{70} - 48 q^{73} - 64 q^{79} - 48 q^{82} + 32 q^{85} - 12 q^{88} + 56 q^{91} + 60 q^{94}+O(q^{100}) \) 24 * q + 12 * q^4 + 8 * q^7 - 12 * q^16 + 12 * q^19 - 24 * q^22 + 4 * q^25 + 4 * q^28 + 20 * q^37 + 24 * q^43 + 12 * q^46 + 40 * q^49 - 28 * q^58 - 120 * q^61 - 24 * q^64 - 32 * q^67 + 48 * q^70 - 48 * q^73 - 64 * q^79 - 48 * q^82 + 32 * q^85 - 12 * q^88 + 56 * q^91 + 60 * q^94

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