LMFDB - Embedded newform 1386.2.bk.d.703.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(703,1386)]

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([0, 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("1386.703");

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.bk (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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			703.8
Character	$\chi$	$=$	1386.703
Dual form			1386.2.bk.d.901.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.53014 - 1.46078i) q^{5} +(-2.00583 + 1.72530i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.53014 - 1.46078i) q^{5} +(-2.00583 + 1.72530i) q^{7} +1.00000i q^{8} +(-1.46078 + 2.53014i) q^{10} +(-3.12781 + 1.10308i) q^{11} -1.09010 q^{13} +(0.874452 - 2.49706i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.00379 + 3.47067i) q^{17} +(-3.32709 - 5.76270i) q^{19} -2.92156i q^{20} +(2.15723 - 2.51920i) q^{22} +(0.874452 + 1.51460i) q^{23} +(1.76775 - 3.06183i) q^{25} +(0.944057 - 0.545052i) q^{26} +(0.491235 + 2.59975i) q^{28} -6.40584i q^{29} +(-7.56307 - 4.36654i) q^{31} +(0.866025 + 0.500000i) q^{32} -4.00758i q^{34} +(-2.55476 + 7.29532i) q^{35} +(-5.36015 - 9.28405i) q^{37} +(5.76270 + 3.32709i) q^{38} +(1.46078 + 2.53014i) q^{40} +4.63887 q^{41} -1.44860i q^{43} +(-0.608616 + 3.26030i) q^{44} +(-1.51460 - 0.874452i) q^{46} +(-1.67930 + 0.969544i) q^{47} +(1.04671 - 6.92130i) q^{49} +3.53550i q^{50} +(-0.545052 + 0.944057i) q^{52} +(-3.32405 + 5.75742i) q^{53} +(-6.30247 + 7.35998i) q^{55} +(-1.72530 - 2.00583i) q^{56} +(3.20292 + 5.54762i) q^{58} +(6.85519 + 3.95784i) q^{59} +(-1.37508 - 2.38171i) q^{61} +8.73308 q^{62} -1.00000 q^{64} +(-2.75812 + 1.59240i) q^{65} +(-1.70292 + 2.94954i) q^{67} +(2.00379 + 3.47067i) q^{68} +(-1.43517 - 7.59531i) q^{70} -13.1351 q^{71} +(-4.01166 + 6.94840i) q^{73} +(9.28405 + 5.36015i) q^{74} -6.65419 q^{76} +(4.37073 - 7.60899i) q^{77} +(-7.41153 + 4.27905i) q^{79} +(-2.53014 - 1.46078i) q^{80} +(-4.01738 + 2.31943i) q^{82} +8.82088 q^{83} +11.7084i q^{85} +(0.724298 + 1.25452i) q^{86} +(-1.10308 - 3.12781i) q^{88} +(-6.94840 + 4.01166i) q^{89} +(2.18656 - 1.88075i) q^{91} +1.74890 q^{92} +(0.969544 - 1.67930i) q^{94} +(-16.8360 - 9.72030i) q^{95} -12.9139i q^{97} +(2.55417 + 6.51738i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4}+O(q^{10}) $ 32 * q + 16 * q^4	$ 32 q + 16 q^{4} - 16 q^{16} + 20 q^{22} + 36 q^{25} + 12 q^{31} - 20 q^{37} - 44 q^{49} - 32 q^{64} + 48 q^{67} + 36 q^{70} + 72 q^{82} + 10 q^{88} + 144 q^{91}+O(q^{100}) $ 32 * q + 16 * q^4 - 16 * q^16 + 20 * q^22 + 36 * q^25 + 12 * q^31 - 20 * q^37 - 44 * q^49 - 32 * q^64 + 48 * q^67 + 36 * q^70 + 72 * q^82 + 10 * q^88 + 144 * q^91

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.866025	+	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
$5$	2.53014	−	1.46078i	1.13151	−	0.653280i	0.187199	−	0.982322i	$-0.440059\pi$
$5$	2.53014	−	1.46078i	1.13151	−	0.653280i	0.944315	+	0.329042i	$0.106726\pi$
$6$		0			0
$7$	−2.00583	+	1.72530i	−0.758133	+	0.652100i
$7$	−2.00583	+	1.72530i	−0.758133	+	0.652100i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−1.46078	+	2.53014i	−0.461939	+	0.800101i
$11$	−3.12781	+	1.10308i	−0.943072	+	0.332590i
$11$	−3.12781	+	1.10308i	−0.943072	+	0.332590i
$12$		0			0
$13$	−1.09010			−0.302340			−0.151170	−	0.988508i	$-0.548304\pi$
$13$	−1.09010			−0.302340			−0.151170	+	0.988508i	$0.548304\pi$
$14$	0.874452	−	2.49706i	0.233707	−	0.667369i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.00379	+	3.47067i	−0.485991	+	0.841760i	−0.999870	−	0.0161018i	$-0.994874\pi$
$17$	−2.00379	+	3.47067i	−0.485991	+	0.841760i	0.513880	+	0.857862i	$0.328208\pi$
$18$		0			0
$19$	−3.32709	−	5.76270i	−0.763288	−	1.32205i	−0.941147	−	0.337997i	$-0.890251\pi$
$19$	−3.32709	−	5.76270i	−0.763288	−	1.32205i	0.177859	−	0.984056i	$-0.443083\pi$
$20$		−	2.92156i		−	0.653280i
$21$		0			0
$22$	2.15723	−	2.51920i	0.459923	−	0.537095i
$23$	0.874452	+	1.51460i	0.182336	+	0.315815i	0.942676	−	0.333711i	$-0.108301\pi$
$23$	0.874452	+	1.51460i	0.182336	+	0.315815i	−0.760340	+	0.649526i	$0.774968\pi$
$24$		0			0
$25$	1.76775	−	3.06183i	0.353550	−	0.612366i
$26$	0.944057	−	0.545052i	0.185145	−	0.106893i
$27$		0			0
$28$	0.491235	+	2.59975i	0.0928346	+	0.491306i
$29$		−	6.40584i		−	1.18953i	−0.803898	−	0.594767i	$-0.797244\pi$
$29$		−	6.40584i		−	1.18953i	0.803898	−	0.594767i	$-0.202756\pi$
$30$		0			0
$31$	−7.56307	−	4.36654i	−1.35837	−	0.784253i	−0.368963	−	0.929444i	$-0.620287\pi$
$31$	−7.56307	−	4.36654i	−1.35837	−	0.784253i	−0.989404	+	0.145191i	$0.953620\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$		−	4.00758i		−	0.687294i
$35$	−2.55476	+	7.29532i	−0.431834	+	1.23313i
$36$		0			0
$37$	−5.36015	−	9.28405i	−0.881203	−	1.52629i	−0.850005	−	0.526775i	$-0.823401\pi$
$37$	−5.36015	−	9.28405i	−0.881203	−	1.52629i	−0.0311981	−	0.999513i	$-0.509932\pi$
$38$	5.76270	+	3.32709i	0.934833	+	0.539726i
$39$		0			0
$40$	1.46078	+	2.53014i	0.230969	+	0.400051i
$41$	4.63887			0.724469			0.362235	−	0.932087i	$-0.382014\pi$
$41$	4.63887			0.724469			0.362235	+	0.932087i	$0.382014\pi$
$42$		0			0
$43$		−	1.44860i		−	0.220909i	−0.993881	−	0.110454i	$-0.964769\pi$
$43$		−	1.44860i		−	0.220909i	0.993881	−	0.110454i	$-0.0352306\pi$
$44$	−0.608616	+	3.26030i	−0.0917523	+	0.491509i
$45$		0			0
$46$	−1.51460	−	0.874452i	−0.223315	−	0.128931i
$47$	−1.67930	+	0.969544i	−0.244951	+	0.141423i	−0.617450	−	0.786610i	$-0.711834\pi$
$47$	−1.67930	+	0.969544i	−0.244951	+	0.141423i	0.372499	+	0.928033i	$0.378501\pi$
$48$		0			0
$49$	1.04671	−	6.92130i	0.149530	−	0.988757i
$50$			3.53550i			0.499995i
$51$		0			0
$52$	−0.545052	+	0.944057i	−0.0755851	+	0.130917i
$53$	−3.32405	+	5.75742i	−0.456593	+	0.790842i	−0.998778	−	0.0494169i	$-0.984264\pi$
$53$	−3.32405	+	5.75742i	−0.456593	+	0.790842i	0.542185	+	0.840259i	$0.317597\pi$
$54$		0			0
$55$	−6.30247	+	7.35998i	−0.849825	+	0.992420i
$56$	−1.72530	−	2.00583i	−0.230552	−	0.268040i
$57$		0			0
$58$	3.20292	+	5.54762i	0.420564	+	0.728438i
$59$	6.85519	+	3.95784i	0.892469	+	0.515267i	0.874749	−	0.484576i	$-0.161026\pi$
$59$	6.85519	+	3.95784i	0.892469	+	0.515267i	0.0177199	+	0.999843i	$0.494359\pi$
$60$		0			0
$61$	−1.37508	−	2.38171i	−0.176061	−	0.304947i	0.764467	−	0.644663i	$-0.223002\pi$
$61$	−1.37508	−	2.38171i	−0.176061	−	0.304947i	−0.940528	+	0.339716i	$0.889669\pi$
$62$	8.73308			1.10910
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−2.75812	+	1.59240i	−0.342102	+	0.197513i
$66$		0			0
$67$	−1.70292	+	2.94954i	−0.208045	+	0.360344i	−0.951099	−	0.308888i	$-0.900043\pi$
$67$	−1.70292	+	2.94954i	−0.208045	+	0.360344i	0.743054	+	0.669232i	$0.233377\pi$
$68$	2.00379	+	3.47067i	0.242995	+	0.420880i
$69$		0			0
$70$	−1.43517	−	7.59531i	−0.171536	−	0.907813i
$71$	−13.1351			−1.55885			−0.779424	−	0.626497i	$-0.784488\pi$
$71$	−13.1351			−1.55885			−0.779424	+	0.626497i	$0.784488\pi$
$72$		0			0
$73$	−4.01166	+	6.94840i	−0.469529	+	0.813249i	−0.999393	−	0.0348341i	$-0.988910\pi$
$73$	−4.01166	+	6.94840i	−0.469529	+	0.813249i	0.529864	+	0.848083i	$0.322243\pi$
$74$	9.28405	+	5.36015i	1.07925	+	0.623105i
$75$		0			0
$76$	−6.65419			−0.763288
$77$	4.37073	−	7.60899i	0.498091	−	0.867125i
$78$		0			0
$79$	−7.41153	+	4.27905i	−0.833862	+	0.481430i	−0.855173	−	0.518342i	$-0.826549\pi$
$79$	−7.41153	+	4.27905i	−0.833862	+	0.481430i	0.0213112	+	0.999773i	$0.493216\pi$
$80$	−2.53014	−	1.46078i	−0.282879	−	0.163320i
$81$		0			0
$82$	−4.01738	+	2.31943i	−0.443645	+	0.256139i
$83$	8.82088			0.968218			0.484109	−	0.875008i	$-0.339144\pi$
$83$	8.82088			0.968218			0.484109	+	0.875008i	$0.339144\pi$
$84$		0			0
$85$			11.7084i			1.26995i
$86$	0.724298	+	1.25452i	0.0781031	+	0.135279i
$87$		0			0
$88$	−1.10308	−	3.12781i	−0.117588	−	0.333426i
$89$	−6.94840	+	4.01166i	−0.736529	+	0.425235i	−0.820806	−	0.571207i	$-0.806475\pi$
$89$	−6.94840	+	4.01166i	−0.736529	+	0.425235i	0.0842770	+	0.996442i	$0.473142\pi$
$90$		0			0
$91$	2.18656	−	1.88075i	0.229214	−	0.197156i
$92$	1.74890			0.182336
$93$		0			0
$94$	0.969544	−	1.67930i	0.100001	−	0.173206i
$95$	−16.8360	−	9.72030i	−1.72734	−	0.997281i
$96$		0			0
$97$		−	12.9139i		−	1.31121i	−0.755104	−	0.655605i	$-0.772414\pi$
$97$		−	12.9139i		−	1.31121i	0.755104	−	0.655605i	$-0.227586\pi$
$98$	2.55417	+	6.51738i	0.258010	+	0.658354i
$99$		0			0
$100$	−1.76775	−	3.06183i	−0.176775	−	0.306183i
$101$	4.55855	−	7.89564i	0.453593	−	0.785646i	−0.545013	−	0.838427i	$-0.683475\pi$
$101$	4.55855	−	7.89564i	0.453593	−	0.785646i	0.998606	+	0.0527815i	$0.0168087\pi$
$102$		0			0
$103$	1.09138	−	0.630108i	0.107537	−	0.0620864i	−0.445267	−	0.895398i	$-0.646891\pi$
$103$	1.09138	−	0.630108i	0.107537	−	0.0620864i	0.552804	+	0.833311i	$0.313558\pi$
$104$		−	1.09010i		−	0.106893i
$105$		0			0
$106$		−	6.64809i		−	0.645720i
$107$	−13.2910	+	7.67359i	−1.28489	+	0.741834i	−0.977739	−	0.209826i	$-0.932710\pi$
$107$	−13.2910	+	7.67359i	−1.28489	+	0.741834i	−0.307155	+	0.951660i	$0.599377\pi$
$108$		0			0
$109$	7.38959	+	4.26638i	0.707794	+	0.408645i	0.810244	−	0.586093i	$-0.199335\pi$
$109$	7.38959	+	4.26638i	0.707794	+	0.408645i	−0.102449	+	0.994738i	$0.532668\pi$
$110$	1.77811	−	9.52517i	0.169536	−	0.908189i
$111$		0			0
$112$	2.49706	+	0.874452i	0.235950	+	0.0826280i
$113$	−3.77623			−0.355238			−0.177619	−	0.984099i	$-0.556839\pi$
$113$	−3.77623			−0.355238			−0.177619	+	0.984099i	$0.556839\pi$
$114$		0			0
$115$	4.42498	+	2.55476i	0.412631	+	0.238233i
$116$	−5.54762	−	3.20292i	−0.515083	−	0.297384i
$117$		0			0
$118$	−7.91569			−0.728698
$119$	−1.96866	−	10.4187i	−0.180467	−	0.955081i
$120$		0			0
$121$	8.56645	−	6.90043i	0.778768	−	0.627312i
$122$	2.38171	+	1.37508i	0.215630	+	0.124494i
$123$		0			0
$124$	−7.56307	+	4.36654i	−0.679183	+	0.392127i
$125$			4.27863i			0.382692i
$126$		0			0
$127$			11.8004i			1.04711i	0.851991	+	0.523557i	$0.175395\pi$
$127$			11.8004i			1.04711i	−0.851991	+	0.523557i	$0.824605\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	1.59240	−	2.75812i	0.139663	−	0.241903i
$131$	−9.47606	−	16.4130i	−0.827927	−	1.43401i	−0.899661	−	0.436589i	$-0.856187\pi$
$131$	−9.47606	−	16.4130i	−0.827927	−	1.43401i	0.0717339	−	0.997424i	$-0.477147\pi$
$132$		0			0
$133$	16.6159	+	5.81877i	1.44078	+	0.504551i
$134$		−	3.40584i		−	0.294220i
$135$		0			0
$136$	−3.47067	−	2.00379i	−0.297607	−	0.171824i
$137$	6.62620	−	11.4769i	0.566115	−	0.980540i	−0.430830	−	0.902433i	$-0.641779\pi$
$137$	6.62620	−	11.4769i	0.566115	−	0.980540i	0.996945	−	0.0781066i	$-0.0248875\pi$
$138$		0			0
$139$	−2.77601			−0.235458			−0.117729	−	0.993046i	$-0.537561\pi$
$139$	−2.77601			−0.235458			−0.117729	+	0.993046i	$0.537561\pi$
$140$	5.04055	+	5.86015i	0.426004	+	0.495273i
$141$		0			0
$142$	11.3753	−	6.56754i	0.954595	−	0.551136i
$143$	3.40964	−	1.20247i	0.285128	−	0.100555i
$144$		0			0
$145$	−9.35751	−	16.2077i	−0.777099	−	1.34597i
$146$		−	8.02332i		−	0.664015i
$147$		0			0
$148$	−10.7203			−0.881203
$149$	11.9436	−	6.89564i	0.978458	−	0.564913i	0.0766540	−	0.997058i	$-0.475576\pi$
$149$	11.9436	−	6.89564i	0.978458	−	0.564913i	0.901804	+	0.432145i	$0.142243\pi$
$150$		0			0
$151$	−7.55104	−	4.35960i	−0.614495	−	0.354779i	0.160228	−	0.987080i	$-0.448777\pi$
$151$	−7.55104	−	4.35960i	−0.614495	−	0.354779i	−0.774723	+	0.632301i	$0.782111\pi$
$152$	5.76270	−	3.32709i	0.467416	−	0.269863i
$153$		0			0
$154$	0.0193276	+	8.77494i	0.00155746	+	0.707105i
$155$	−25.5142			−2.04935
$156$		0			0
$157$	13.0804	+	7.55200i	1.04393	+	0.602715i	0.920945	−	0.389693i	$-0.127419\pi$
$157$	13.0804	+	7.55200i	1.04393	+	0.602715i	0.122988	+	0.992408i	$0.460752\pi$
$158$	4.27905	−	7.41153i	0.340423	−	0.589629i
$159$		0			0
$160$	2.92156			0.230969
$161$	−4.36713	−	1.52933i	−0.344178	−	0.120528i
$162$		0			0
$163$	−11.6098	−	20.1087i	−0.909348	−	1.57504i	−0.814972	−	0.579500i	$-0.803248\pi$
$163$	−11.6098	−	20.1087i	−0.909348	−	1.57504i	−0.0943757	−	0.995537i	$-0.530085\pi$
$164$	2.31943	−	4.01738i	0.181117	−	0.313704i
$165$		0			0
$166$	−7.63911	+	4.41044i	−0.592910	+	0.342317i
$167$	−1.26022			−0.0975185			−0.0487592	−	0.998811i	$-0.515527\pi$
$167$	−1.26022			−0.0975185			−0.0487592	+	0.998811i	$0.515527\pi$
$168$		0			0
$169$	−11.8117			−0.908590
$170$	−5.85419	−	10.1398i	−0.448996	−	0.777684i
$171$		0			0
$172$	−1.25452	−	0.724298i	−0.0956564	−	0.0552272i
$173$	−2.99345	−	5.18480i	−0.227587	−	0.394193i	0.729505	−	0.683975i	$-0.239750\pi$
$173$	−2.99345	−	5.18480i	−0.227587	−	0.394193i	−0.957093	+	0.289782i	$0.906417\pi$
$174$		0			0
$175$	1.73676	+	9.19140i	0.131287	+	0.694804i
$176$	2.51920	+	2.15723i	0.189892	+	0.162607i
$177$		0			0
$178$	4.01166	−	6.94840i	0.300687	−	0.520805i
$179$	2.58708	−	4.48096i	0.193368	−	0.334923i	−0.752997	−	0.658024i	$-0.771392\pi$
$179$	2.58708	−	4.48096i	0.193368	−	0.334923i	0.946364	+	0.323102i	$0.104726\pi$
$180$		0			0
$181$			6.92820i			0.514969i	0.966282	+	0.257485i	$0.0828937\pi$
$181$			6.92820i			0.514969i	−0.966282	+	0.257485i	$0.917106\pi$
$182$	−0.953243	+	2.72206i	−0.0706591	+	0.201772i
$183$		0			0
$184$	−1.51460	+	0.874452i	−0.111657	+	0.0644655i
$185$	−27.1239	−	15.6600i	−1.99419	−	1.15134i
$186$		0			0
$187$	2.43908	−	13.0659i	0.178363	−	0.955476i
$188$			1.93909i			0.141423i
$189$		0			0
$190$	19.4406			1.41037
$191$	12.7663	+	22.1119i	0.923738	+	1.59996i	0.793578	+	0.608468i	$0.208216\pi$
$191$	12.7663	+	22.1119i	0.923738	+	1.59996i	0.130160	+	0.991493i	$0.458451\pi$
$192$		0			0
$193$	10.6629	+	6.15622i	0.767531	+	0.443134i	0.831993	−	0.554786i	$-0.187200\pi$
$193$	10.6629	+	6.15622i	0.767531	+	0.443134i	−0.0644622	+	0.997920i	$0.520533\pi$
$194$	6.45696	+	11.1838i	0.463583	+	0.802949i
$195$		0			0
$196$	−5.47067	−	4.36713i	−0.390762	−	0.311938i
$197$		−	0.0913794i		−	0.00651051i	−0.999995	−	0.00325526i	$-0.998964\pi$
$197$		−	0.0913794i		−	0.00651051i	0.999995	−	0.00325526i	$-0.00103618\pi$
$198$		0			0
$199$	4.09342	+	2.36334i	0.290175	+	0.167533i	0.638021	−	0.770019i	$-0.279753\pi$
$199$	4.09342	+	2.36334i	0.290175	+	0.167533i	−0.347846	+	0.937552i	$0.613087\pi$
$200$	3.06183	+	1.76775i	0.216504	+	0.124999i
$201$		0			0
$202$			9.11710i			0.641477i
$203$	11.0520	+	12.8490i	0.775696	+	0.901825i
$204$		0			0
$205$	11.7370	−	6.77636i	0.819747	−	0.473281i
$206$	−0.630108	+	1.09138i	−0.0439017	+	0.0760400i
$207$		0			0
$208$	0.545052	+	0.944057i	0.0377925	+	0.0654586i
$209$	16.7632	+	14.3546i	1.15954	+	0.992929i
$210$		0			0
$211$		−	13.5239i		−	0.931027i	−0.885041	−	0.465513i	$-0.845870\pi$
$211$		−	13.5239i		−	0.931027i	0.885041	−	0.465513i	$-0.154130\pi$
$212$	3.32405	+	5.75742i	0.228296	+	0.395421i
$213$		0			0
$214$	7.67359	−	13.2910i	0.524556	−	0.908557i
$215$	−2.11608	−	3.66516i	−0.144315	−	0.249962i
$216$		0			0
$217$	22.7038	−	4.28999i	1.54123	−	0.291224i
$218$	−8.53276			−0.577912
$219$		0			0
$220$	3.22270	+	9.13809i	0.217274	+	0.616090i
$221$	2.18434	−	3.78339i	0.146935	−	0.254498i
$222$		0			0
$223$			20.3880i			1.36528i	0.730756	+	0.682639i	$0.239168\pi$
$223$			20.3880i			1.36528i	−0.730756	+	0.682639i	$0.760832\pi$
$224$	−2.59975	+	0.491235i	−0.173703	+	0.0328220i
$225$		0			0
$226$	3.27031	−	1.88811i	0.217538	−	0.125595i
$227$	−6.92130	+	11.9880i	−0.459383	+	0.795674i	−0.998928	−	0.0462820i	$-0.985263\pi$
$227$	−6.92130	+	11.9880i	−0.459383	+	0.795674i	0.539546	+	0.841956i	$0.318596\pi$
$228$		0			0
$229$	−22.8847	+	13.2125i	−1.51226	+	0.873106i	−0.512367	+	0.858767i	$0.671231\pi$
$229$	−22.8847	+	13.2125i	−1.51226	+	0.873106i	−0.999897	+	0.0143394i	$0.995435\pi$
$230$	−5.10952			−0.336912
$231$		0			0
$232$	6.40584			0.420564
$233$	14.7702	−	8.52757i	0.967627	−	0.558660i	0.0691150	−	0.997609i	$-0.477982\pi$
$233$	14.7702	−	8.52757i	0.967627	−	0.558660i	0.898512	+	0.438949i	$0.144649\pi$
$234$		0			0
$235$	−2.83258	+	4.90617i	−0.184777	+	0.320043i
$236$	6.85519	−	3.95784i	0.446235	−	0.257634i
$237$		0			0
$238$	6.91426	+	8.03853i	0.448185	+	0.521060i
$239$			0.628916i			0.0406812i	0.999793	+	0.0203406i	$0.00647506\pi$
$239$			0.628916i			0.0406812i	−0.999793	+	0.0203406i	$0.993525\pi$
$240$		0			0
$241$	−10.0989	+	17.4917i	−0.650525	+	1.12674i	0.332471	+	0.943114i	$0.392118\pi$
$241$	−10.0989	+	17.4917i	−0.650525	+	1.12674i	−0.982996	+	0.183629i	$0.941216\pi$
$242$	−3.96855	+	10.2592i	−0.255108	+	0.659485i
$243$		0			0
$244$	−2.75016			−0.176061
$245$	−7.46216	−	19.0409i	−0.476740	−	1.21648i
$246$		0			0
$247$	3.62688	+	6.28193i	0.230773	+	0.399710i
$248$	4.36654	−	7.56307i	0.277275	−	0.480255i
$249$		0			0
$250$	−2.13932	−	3.70540i	−0.135302	−	0.234350i
$251$			27.4977i			1.73564i	0.496879	+	0.867820i	$0.334479\pi$
$251$			27.4977i			1.73564i	−0.496879	+	0.867820i	$0.665521\pi$
$252$		0			0
$253$	−4.40584	−	3.77279i	−0.276993	−	0.237193i
$254$	−5.90019	−	10.2194i	−0.370211	−	0.641223i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.28406	+	0.741351i	−0.0800973	+	0.0462442i	−0.539514	−	0.841977i	$-0.681392\pi$
$257$	−1.28406	+	0.741351i	−0.0800973	+	0.0462442i	0.459416	+	0.888221i	$0.348059\pi$
$258$		0			0
$259$	26.7693	+	9.37439i	1.66336	+	0.582496i
$260$			3.18480i			0.197513i
$261$		0			0
$262$	16.4130	+	9.47606i	1.01400	+	0.585433i
$263$	2.43498	+	1.40584i	0.150147	+	0.0866877i	0.573191	−	0.819421i	$-0.305705\pi$
$263$	2.43498	+	1.40584i	0.150147	+	0.0866877i	−0.423044	+	0.906109i	$0.639038\pi$
$264$		0			0
$265$			19.4228i			1.19313i
$266$	−17.2992	+	3.26877i	−1.06068	+	0.200421i
$267$		0			0
$268$	1.70292	+	2.94954i	0.104022	+	0.180172i
$269$	16.7013	+	9.64249i	1.01829	+	0.587913i	0.913610	−	0.406593i	$-0.133283\pi$
$269$	16.7013	+	9.64249i	1.01829	+	0.587913i	0.104685	+	0.994505i	$0.466616\pi$
$270$		0			0
$271$	−7.72236	−	13.3755i	−0.469100	−	0.812504i	0.530276	−	0.847825i	$-0.322088\pi$
$271$	−7.72236	−	13.3755i	−0.469100	−	0.812504i	−0.999376	+	0.0353204i	$0.988755\pi$
$272$	4.00758			0.242995
$273$		0			0
$274$			13.2524i			0.800607i
$275$	−2.15176	+	11.5268i	−0.129756	+	0.695092i
$276$		0			0
$277$	−22.3530	−	12.9055i	−1.34306	−	0.775418i	−0.355807	−	0.934559i	$-0.615794\pi$
$277$	−22.3530	−	12.9055i	−1.34306	−	0.775418i	−0.987256	+	0.159141i	$0.949127\pi$
$278$	2.40410	−	1.38801i	0.144188	−	0.0832471i
$279$		0			0
$280$	−7.29532	−	2.55476i	−0.435979	−	0.152676i
$281$			18.4993i			1.10357i	0.833985	+	0.551787i	$0.186054\pi$
$281$			18.4993i			1.10357i	−0.833985	+	0.551787i	$0.813946\pi$
$282$		0			0
$283$	10.0262	−	17.3658i	0.595994	−	1.03229i	−0.397412	−	0.917640i	$-0.630092\pi$
$283$	10.0262	−	17.3658i	0.595994	−	1.03229i	0.993406	−	0.114651i	$-0.0365751\pi$
$284$	−6.56754	+	11.3753i	−0.389712	+	0.675001i
$285$		0			0
$286$	−2.35160	+	2.74619i	−0.139053	+	0.162385i
$287$	−9.30478	+	8.00342i	−0.549244	+	0.472427i
$288$		0			0
$289$	0.469647	+	0.813452i	0.0276263	+	0.0478501i
$290$	16.2077	+	9.35751i	0.951748	+	0.549492i
$291$		0			0
$292$	4.01166	+	6.94840i	0.234765	+	0.406624i
$293$	−7.80439			−0.455937			−0.227969	−	0.973668i	$-0.573208\pi$
$293$	−7.80439			−0.455937			−0.227969	+	0.973668i	$0.573208\pi$
$294$		0			0
$295$	23.1261			1.34646
$296$	9.28405	−	5.36015i	0.539624	−	0.311552i
$297$		0			0
$298$	−6.89564	+	11.9436i	−0.399454	+	0.691875i
$299$	−0.953243	−	1.65107i	−0.0551275	−	0.0954836i
$300$		0			0
$301$	2.49926	+	2.90564i	0.144055	+	0.167478i
$302$	8.71919			0.501733
$303$		0			0
$304$	−3.32709	+	5.76270i	−0.190822	+	0.330513i
$305$	−6.95830	−	4.01738i	−0.398431	−	0.230034i
$306$		0			0
$307$	25.2099			1.43880			0.719402	−	0.694594i	$-0.244416\pi$
$307$	25.2099			1.43880			0.719402	+	0.694594i	$0.244416\pi$
$308$	−4.40421	−	7.58966i	−0.250953	−	0.432461i
$309$		0			0
$310$	22.0959	−	12.7571i	1.25496	−	0.724554i
$311$	−9.84609	−	5.68464i	−0.558321	−	0.322347i	0.194151	−	0.980972i	$-0.437805\pi$
$311$	−9.84609	−	5.68464i	−0.558321	−	0.322347i	−0.752471	+	0.658625i	$0.771138\pi$
$312$		0			0
$313$	−3.18253	+	1.83744i	−0.179887	+	0.103858i	−0.587240	−	0.809413i	$-0.699785\pi$
$313$	−3.18253	+	1.83744i	−0.179887	+	0.103858i	0.407352	+	0.913271i	$0.366452\pi$
$314$	−15.1040			−0.852368
$315$		0			0
$316$			8.55809i			0.481430i
$317$	−12.2854	−	21.2789i	−0.690016	−	1.19514i	−0.971832	−	0.235674i	$-0.924270\pi$
$317$	−12.2854	−	21.2789i	−0.690016	−	1.19514i	0.281816	−	0.959468i	$-0.409063\pi$
$318$		0			0
$319$	7.06612	+	20.0363i	0.395627	+	1.12182i
$320$	−2.53014	+	1.46078i	−0.141439	+	0.0816600i
$321$		0			0
$322$	4.54671	−	0.859123i	0.253378	−	0.0478770i
$323$	26.6672			1.48380
$324$		0			0
$325$	−1.92703	+	3.33771i	−0.106892	+	0.185143i
$326$	20.1087	+	11.6098i	1.11372	+	0.643006i
$327$		0			0
$328$			4.63887i			0.256139i
$329$	1.69564	−	4.84203i	0.0934836	−	0.266950i
$330$		0			0
$331$	−8.14527	−	14.1080i	−0.447705	−	0.775447i	0.550532	−	0.834814i	$-0.314425\pi$
$331$	−8.14527	−	14.1080i	−0.447705	−	0.775447i	−0.998236	+	0.0593671i	$0.981092\pi$
$332$	4.41044	−	7.63911i	0.242054	−	0.419251i
$333$		0			0
$334$	1.09138	−	0.630108i	0.0597176	−	0.0344780i
$335$			9.95035i			0.543646i
$336$		0			0
$337$			7.89181i			0.429895i	0.976626	+	0.214947i	$0.0689580\pi$
$337$			7.89181i			0.429895i	−0.976626	+	0.214947i	$0.931042\pi$
$338$	10.2292	−	5.90584i	0.556396	−	0.321235i
$339$		0			0
$340$	10.1398	+	5.85419i	0.549905	+	0.317488i
$341$	28.4725	+	5.31509i	1.54187	+	0.287828i
$342$		0			0
$343$	9.84177	+	15.6888i	0.531405	+	0.847118i
$344$	1.44860			0.0781031
$345$		0			0
$346$	5.18480	+	2.99345i	0.278737	+	0.160929i
$347$	8.30397	+	4.79430i	0.445780	+	0.257371i	0.706046	−	0.708166i	$-0.250477\pi$
$347$	8.30397	+	4.79430i	0.445780	+	0.257371i	−0.260266	+	0.965537i	$0.583810\pi$
$348$		0			0
$349$	−13.3463			−0.714410			−0.357205	−	0.934026i	$-0.616270\pi$
$349$	−13.3463			−0.714410			−0.357205	+	0.934026i	$0.616270\pi$
$350$	−6.09978	−	7.09161i	−0.326047	−	0.379062i
$351$		0			0
$352$	−3.26030	−	0.608616i	−0.173775	−	0.0324393i
$353$	−14.4249	−	8.32820i	−0.767758	−	0.443265i	0.0643160	−	0.997930i	$-0.479513\pi$
$353$	−14.4249	−	8.32820i	−0.767758	−	0.443265i	−0.832074	+	0.554664i	$0.812847\pi$
$354$		0			0
$355$	−33.2336	+	19.1875i	−1.76386	+	1.01836i
$356$			8.02332i			0.425235i
$357$		0			0
$358$			5.17417i			0.273463i
$359$	2.97964	−	1.72030i	0.157259	−	0.0907937i	−0.419305	−	0.907845i	$-0.637726\pi$
$359$	2.97964	−	1.72030i	0.157259	−	0.0907937i	0.576565	+	0.817052i	$0.304393\pi$
$360$		0			0
$361$	−12.6391	+	21.8916i	−0.665216	+	1.15219i
$362$	−3.46410	−	6.00000i	−0.182069	−	0.315353i
$363$		0			0
$364$	−0.535497	−	2.83399i	−0.0280676	−	0.148542i
$365$			23.4406i			1.22694i
$366$		0			0
$367$	31.2630	+	18.0497i	1.63191	+	0.942186i	0.983502	+	0.180896i	$0.0578998\pi$
$367$	31.2630	+	18.0497i	1.63191	+	0.942186i	0.648412	+	0.761290i	$0.275433\pi$
$368$	0.874452	−	1.51460i	0.0455840	−	0.0789537i
$369$		0			0
$370$	31.3200			1.62825
$371$	−3.26577	−	17.2834i	−0.169551	−	0.897307i
$372$		0			0
$373$	27.0363	−	15.6094i	1.39989	−	0.808226i	0.405508	−	0.914092i	$-0.367095\pi$
$373$	27.0363	−	15.6094i	1.39989	−	0.808226i	0.994380	+	0.105866i	$0.0337615\pi$
$374$	4.42067	+	12.5350i	0.228587	+	0.648168i
$375$		0			0
$376$	−0.969544	−	1.67930i	−0.0500004	−	0.0866032i
$377$			6.98302i			0.359644i
$378$		0			0
$379$	16.2905			0.836789			0.418395	−	0.908265i	$-0.362593\pi$
$379$	16.2905			0.836789			0.418395	+	0.908265i	$0.362593\pi$
$380$	−16.8360	+	9.72030i	−0.863671	+	0.498641i
$381$		0			0
$382$	−22.1119	−	12.7663i	−1.13134	−	0.653182i
$383$	4.63221	−	2.67441i	0.236695	−	0.136656i	−0.376962	−	0.926229i	$-0.623031\pi$
$383$	4.63221	−	2.67441i	0.236695	−	0.136656i	0.613657	+	0.789573i	$0.289698\pi$
$384$		0			0
$385$	−0.0564666	−	25.6365i	−0.00287781	−	1.30656i
$386$	−12.3124			−0.626686
$387$		0			0
$388$	−11.1838	−	6.45696i	−0.567770	−	0.327802i
$389$	17.8882	−	30.9833i	0.906968	−	1.57091i	0.0887143	−	0.996057i	$-0.471724\pi$
$389$	17.8882	−	30.9833i	0.906968	−	1.57091i	0.818254	−	0.574857i	$-0.194942\pi$
$390$		0			0
$391$	−7.00888			−0.354454
$392$	6.92130	+	1.04671i	0.349578	+	0.0528668i
$393$		0			0
$394$	0.0456897	+	0.0791369i	0.00230181	+	0.00398686i
$395$	−12.5015	+	21.6532i	−0.629018	+	1.08949i
$396$		0			0
$397$	10.0784	−	5.81877i	0.505821	−	0.292036i	−0.225293	−	0.974291i	$-0.572334\pi$
$397$	10.0784	−	5.81877i	0.505821	−	0.292036i	0.731114	+	0.682255i	$0.239001\pi$
$398$	−4.72667			−0.236927
$399$		0			0
$400$	−3.53550			−0.176775
$401$	−3.19750	−	5.53823i	−0.159676	−	0.276566i	0.775076	−	0.631868i	$-0.217711\pi$
$401$	−3.19750	−	5.53823i	−0.159676	−	0.276566i	−0.934752	+	0.355302i	$0.884378\pi$
$402$		0			0
$403$	8.24452	+	4.75998i	0.410689	+	0.237111i
$404$	−4.55855	−	7.89564i	−0.226796	−	0.392823i
$405$		0			0
$406$	−15.9958	−	5.60160i	−0.793858	−	0.278003i
$407$	27.0066	+	23.1261i	1.33867	+	1.14632i
$408$		0			0
$409$	−13.0643	+	22.6280i	−0.645988	+	1.11888i	0.338085	+	0.941116i	$0.390221\pi$
$409$	−13.0643	+	22.6280i	−0.645988	+	1.11888i	−0.984072	+	0.177768i	$0.943112\pi$
$410$	−6.77636	+	11.7370i	−0.334660	+	0.579649i
$411$		0			0
$412$		−	1.26022i		−	0.0620864i
$413$	−20.5788	+	3.88846i	−1.01262	+	0.191339i
$414$		0			0
$415$	22.3181	−	12.8854i	1.09555	−	0.632517i
$416$	−0.944057	−	0.545052i	−0.0462862	−	0.0267234i
$417$		0			0
$418$	−21.6947	−	4.04984i	−1.06112	−	0.198084i
$419$		−	13.1071i		−	0.640322i	−0.947363	−	0.320161i	$-0.896263\pi$
$419$		−	13.1071i		−	0.640322i	0.947363	−	0.320161i	$-0.103737\pi$
$420$		0			0
$421$	−1.64930			−0.0803821			−0.0401910	−	0.999192i	$-0.512797\pi$
$421$	−1.64930			−0.0803821			−0.0401910	+	0.999192i	$0.512797\pi$
$422$	6.76197	+	11.7121i	0.329168	+	0.570135i
$423$		0			0
$424$	−5.75742	−	3.32405i	−0.279605	−	0.161430i
$425$	7.08439	+	12.2705i	0.343644	+	0.595208i
$426$		0			0
$427$	6.86733	+	2.40488i	0.332333	+	0.116381i
$428$			15.3472i			0.741834i
$429$		0			0
$430$	3.66516	+	2.11608i	0.176750	+	0.102046i
$431$	−24.6918	−	14.2558i	−1.18936	−	0.686677i	−0.231199	−	0.972907i	$-0.574265\pi$
$431$	−24.6918	−	14.2558i	−1.18936	−	0.686677i	−0.958161	+	0.286229i	$0.907598\pi$
$432$		0			0
$433$		−	11.4064i		−	0.548159i	−0.961707	−	0.274079i	$-0.911627\pi$
$433$		−	11.4064i		−	0.548159i	0.961707	−	0.274079i	$-0.0883731\pi$
$434$	−17.5171	+	15.0671i	−0.840846	+	0.723246i
$435$		0			0
$436$	7.38959	−	4.26638i	0.353897	−	0.204323i
$437$	5.81877	−	10.0784i	0.278349	−	0.482115i
$438$		0			0
$439$	−6.44793	−	11.1681i	−0.307743	−	0.533026i	0.670125	−	0.742248i	$-0.266240\pi$
$439$	−6.44793	−	11.1681i	−0.307743	−	0.533026i	−0.977868	+	0.209222i	$0.932907\pi$
$440$	−7.35998	−	6.30247i	−0.350873	−	0.300458i
$441$		0			0
$442$			4.36868i			0.207797i
$443$	6.88052	+	11.9174i	0.326903	+	0.566213i	0.981896	−	0.189422i	$-0.0606616\pi$
$443$	6.88052	+	11.9174i	0.326903	+	0.566213i	−0.654993	+	0.755635i	$0.727328\pi$
$444$		0			0
$445$	−11.7203	+	20.3001i	−0.555595	+	0.962319i
$446$	−10.1940	−	17.6565i	−0.482699	−	0.836059i
$447$		0			0
$448$	2.00583	−	1.72530i	0.0947666	−	0.0815126i
$449$	−0.549957			−0.0259541			−0.0129770	−	0.999916i	$-0.504131\pi$
$449$	−0.549957			−0.0259541			−0.0129770	+	0.999916i	$0.504131\pi$
$450$		0			0
$451$	−14.5095	+	5.11702i	−0.683226	+	0.240951i
$452$	−1.88811	+	3.27031i	−0.0888094	+	0.153822i
$453$		0			0
$454$		−	13.8426i		−	0.649665i
$455$	2.78495	−	7.95265i	0.130561	−	0.372826i
$456$		0			0
$457$	9.58467	−	5.53371i	0.448352	−	0.258856i	−0.258782	−	0.965936i	$-0.583321\pi$
$457$	9.58467	−	5.53371i	0.448352	−	0.258856i	0.707134	+	0.707080i	$0.249988\pi$
$458$	13.2125	−	22.8847i	0.617379	−	1.06933i
$459$		0			0
$460$	4.42498	−	2.55476i	0.206316	−	0.119116i
$461$	5.65536			0.263396			0.131698	−	0.991290i	$-0.457957\pi$
$461$	5.65536			0.263396			0.131698	+	0.991290i	$0.457957\pi$
$462$		0			0
$463$	−12.4421			−0.578232			−0.289116	−	0.957294i	$-0.593361\pi$
$463$	−12.4421			−0.578232			−0.289116	+	0.957294i	$0.593361\pi$
$464$	−5.54762	+	3.20292i	−0.257542	+	0.148692i
$465$		0			0
$466$	−8.52757	+	14.7702i	−0.395032	+	0.684216i
$467$	25.2031	−	14.5510i	1.16626	−	0.673340i	0.213463	−	0.976951i	$-0.431526\pi$
$467$	25.2031	−	14.5510i	1.16626	−	0.673340i	0.952796	+	0.303611i	$0.0981923\pi$
$468$		0			0
$469$	−1.67307	−	8.85432i	−0.0772550	−	0.408854i
$470$		−	5.66516i		−	0.261314i
$471$		0			0
$472$	−3.95784	+	6.85519i	−0.182175	+	0.315536i
$473$	1.59791	+	4.53094i	0.0734720	+	0.208333i
$474$		0			0
$475$	−23.5259			−1.07944
$476$	−10.0072	−	3.50444i	−0.458679	−	0.160626i
$477$		0			0
$478$	−0.314458	−	0.544657i	−0.0143830	−	0.0249121i
$479$	5.28278	−	9.15005i	0.241376	−	0.418076i	−0.719730	−	0.694254i	$-0.755734\pi$
$479$	5.28278	−	9.15005i	0.241376	−	0.418076i	0.961107	+	0.276178i	$0.0890678\pi$
$480$		0			0
$481$	5.84311	+	10.1206i	0.266423	+	0.461458i
$482$		−	20.1977i		−	0.919981i
$483$		0			0
$484$	−1.69273	−	10.8690i	−0.0769421	−	0.494044i
$485$	−18.8644	−	32.6740i	−0.856587	−	1.48365i
$486$		0			0
$487$	14.6544	−	25.3822i	0.664056	−	1.15018i	−0.315484	−	0.948931i	$-0.602167\pi$
$487$	14.6544	−	25.3822i	0.664056	−	1.15018i	0.979540	−	0.201248i	$-0.0644998\pi$
$488$	2.38171	−	1.37508i	0.107815	−	0.0622470i
$489$		0			0
$490$	15.9829	+	12.7588i	0.722032	+	0.576384i
$491$		−	0.0239123i		−	0.00107915i	−1.00000		0.000539573i	$-0.999828\pi$
$491$		−	0.0239123i		−	0.00107915i	1.00000		0.000539573i	$-0.000171751\pi$
$492$		0			0
$493$	22.2325	+	12.8360i	1.00130	+	0.578102i
$494$	−6.28193	−	3.62688i	−0.282638	−	0.163181i
$495$		0			0
$496$			8.73308i			0.392127i
$497$	26.3468	−	22.6619i	1.18181	−	1.01653i
$498$		0			0
$499$	−9.16441	−	15.8732i	−0.410255	−	0.710583i	0.584662	−	0.811277i	$-0.301227\pi$
$499$	−9.16441	−	15.8732i	−0.410255	−	0.710583i	−0.994917	+	0.100694i	$0.967894\pi$
$500$	3.70540	+	2.13932i	0.165711	+	0.0956731i
$501$		0			0
$502$	−13.7489	−	23.8137i	−0.613641	−	1.06286i
$503$	−37.3095			−1.66355			−0.831773	−	0.555116i	$-0.812674\pi$
$503$	−37.3095			−1.66355			−0.831773	+	0.555116i	$0.812674\pi$
$504$		0			0
$505$		−	26.6361i		−	1.18529i
$506$	5.70196	+	1.06441i	0.253483	+	0.0473188i
$507$		0			0
$508$	10.2194	+	5.90019i	0.453413	+	0.261778i
$509$	−10.5002	+	6.06230i	−0.465413	+	0.268707i	−0.714318	−	0.699821i	$-0.753263\pi$
$509$	−10.5002	+	6.06230i	−0.465413	+	0.268707i	0.248904	+	0.968528i	$0.419930\pi$
$510$		0			0
$511$	−3.94133	−	20.8586i	−0.174354	−	0.922731i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	0.741351	−	1.28406i	0.0326996	−	0.0566373i
$515$	1.84090	−	3.18853i	0.0811196	−	0.140503i
$516$		0			0
$517$	4.18306	−	4.88495i	0.183971	−	0.214840i
$518$	−27.8701	+	5.26618i	−1.22454	+	0.231383i
$519$		0			0
$520$	−1.59240	−	2.75812i	−0.0698313	−	0.120951i
$521$	27.4207	+	15.8314i	1.20132	+	0.693585i	0.960850	−	0.277070i	$-0.0893635\pi$
$521$	27.4207	+	15.8314i	1.20132	+	0.693585i	0.240475	+	0.970655i	$0.422697\pi$
$522$		0			0
$523$	7.67457	+	13.2927i	0.335585	+	0.581251i	0.983597	−	0.180379i	$-0.0577325\pi$
$523$	7.67457	+	13.2927i	0.335585	+	0.581251i	−0.648012	+	0.761630i	$0.724399\pi$
$524$	−18.9521			−0.827927
$525$		0			0
$526$	−2.81167			−0.122595
$527$	30.3096	−	17.4993i	1.32031	−	0.762280i
$528$		0			0
$529$	9.97067	−	17.2697i	0.433507	−	0.750857i
$530$	−9.71139	−	16.8206i	−0.421836	−	0.730641i
$531$		0			0
$532$	13.3472	−	11.4804i	0.578673	−	0.497740i
$533$	−5.05684			−0.219036
$534$		0			0
$535$	−22.4188	+	38.8305i	−0.969250	+	1.67879i
$536$	−2.94954	−	1.70292i	−0.127401	−	0.0735549i
$537$		0			0
$538$	−19.2850			−0.831434
$539$	4.36080	+	22.8031i	0.187833	+	0.982201i
$540$		0			0
$541$	−5.20345	+	3.00421i	−0.223714	+	0.129161i	−0.607669	−	0.794191i	$-0.707895\pi$
$541$	−5.20345	+	3.00421i	−0.223714	+	0.129161i	0.383955	+	0.923352i	$0.374562\pi$
$542$	13.3755	+	7.72236i	0.574527	+	0.331704i
$543$		0			0
$544$	−3.47067	+	2.00379i	−0.148804	+	0.0859118i
$545$	24.9290			1.06784
$546$		0			0
$547$		−	2.05609i		−	0.0879123i	−0.999033	−	0.0439561i	$-0.986004\pi$
$547$		−	2.05609i		−	0.0879123i	0.999033	−	0.0439561i	$-0.0139962\pi$
$548$	−6.62620	−	11.4769i	−0.283057	−	0.490270i
$549$		0			0
$550$	−3.89992	−	11.0584i	−0.166293	−	0.471531i
$551$	−36.9149	+	21.3128i	−1.57263	+	0.907957i
$552$		0			0
$553$	7.48364	−	21.3701i	0.318237	−	0.908750i
$554$	25.8111			1.09661
$555$		0			0
$556$	−1.38801	+	2.40410i	−0.0588646	+	0.101956i
$557$	26.2306	+	15.1443i	1.11143	+	0.641683i	0.939199	−	0.343374i	$-0.111570\pi$
$557$	26.2306	+	15.1443i	1.11143	+	0.641683i	0.172228	+	0.985057i	$0.444903\pi$
$558$		0			0
$559$			1.57912i			0.0667896i
$560$	7.59531	−	1.43517i	0.320961	−	0.0606470i
$561$		0			0
$562$	−9.24963	−	16.0208i	−0.390172	−	0.675798i
$563$	−21.7610	+	37.6912i	−0.917119	+	1.58850i	−0.113350	+	0.993555i	$0.536158\pi$
$563$	−21.7610	+	37.6912i	−0.917119	+	1.58850i	−0.803769	+	0.594941i	$0.797175\pi$
$564$		0			0
$565$	−9.55440	+	5.51623i	−0.401956	+	0.232070i
$566$			20.0523i			0.842863i
$567$		0			0
$568$		−	13.1351i		−	0.551136i
$569$	15.5660	−	8.98702i	0.652560	−	0.376756i	−0.136876	−	0.990588i	$-0.543706\pi$
$569$	15.5660	−	8.98702i	0.652560	−	0.376756i	0.789436	+	0.613833i	$0.210373\pi$
$570$		0			0
$571$	34.0453	+	19.6561i	1.42475	+	0.822580i	0.996700	−	0.0811744i	$-0.0258671\pi$
$571$	34.0453	+	19.6561i	1.42475	+	0.822580i	0.428051	+	0.903755i	$0.359200\pi$
$572$	0.663454	−	3.55407i	0.0277404	−	0.148603i
$573$		0			0
$574$	4.05647	−	11.5836i	0.169314	−	0.483488i
$575$	6.18324			0.257859
$576$		0			0
$577$	21.8053	+	12.5893i	0.907766	+	0.524099i	0.879712	−	0.475508i	$-0.157736\pi$
$577$	21.8053	+	12.5893i	0.907766	+	0.524099i	0.0280542	+	0.999606i	$0.491069\pi$
$578$	−0.813452	−	0.469647i	−0.0338352	−	0.0195347i
$579$		0			0
$580$	−18.7150			−0.777099
$581$	−17.6932	+	15.2186i	−0.734037	+	0.631375i
$582$		0			0
$583$	4.04613	−	21.6748i	0.167574	−	0.897679i
$584$	−6.94840	−	4.01166i	−0.287527	−	0.166004i
$585$		0			0
$586$	6.75880	−	3.90220i	0.279204	−	0.161198i
$587$			20.1219i			0.830520i	0.909703	+	0.415260i	$0.136309\pi$
$587$			20.1219i			0.830520i	−0.909703	+	0.415260i	$0.863691\pi$
$588$		0			0
$589$			58.1115i			2.39444i
$590$	−20.0278	+	11.5631i	−0.824532	+	0.476044i
$591$		0			0
$592$	−5.36015	+	9.28405i	−0.220301	+	0.381572i
$593$	23.0400	+	39.9065i	0.946140	+	1.63876i	0.753452	+	0.657503i	$0.228387\pi$
$593$	23.0400	+	39.9065i	0.946140	+	1.63876i	0.192688	+	0.981260i	$0.438279\pi$
$594$		0			0
$595$	−20.2004	−	23.4850i	−0.828136	−	0.962792i
$596$		−	13.7913i		−	0.564913i
$597$		0			0
$598$	1.65107	+	0.953243i	0.0675171	+	0.0389810i
$599$	−6.63371	+	11.4899i	−0.271046	+	0.469465i	−0.969130	−	0.246551i	$-0.920703\pi$
$599$	−6.63371	+	11.4899i	−0.271046	+	0.469465i	0.698084	+	0.716016i	$0.254036\pi$
$600$		0			0
$601$	−40.2620			−1.64232			−0.821160	−	0.570698i	$-0.806673\pi$
$601$	−40.2620			−1.64232			−0.821160	+	0.570698i	$0.806673\pi$
$602$	−3.61724	−	1.26673i	−0.147428	−	0.0516280i
$603$		0			0
$604$	−7.55104	+	4.35960i	−0.307248	+	0.177389i
$605$	11.5943	−	29.9728i	0.471377	−	1.21857i
$606$		0			0
$607$	−16.7092	−	28.9412i	−0.678205	−	1.17469i	−0.975521	−	0.219907i	$-0.929425\pi$
$607$	−16.7092	−	28.9412i	−0.678205	−	1.17469i	0.297316	−	0.954779i	$-0.403909\pi$
$608$		−	6.65419i		−	0.269863i
$609$		0			0
$610$	8.03475			0.325318
$611$	1.83061	−	1.05690i	0.0740585	−	0.0427577i
$612$		0			0
$613$	−40.2610	−	23.2447i	−1.62613	−	0.938845i	−0.985234	−	0.171216i	$-0.945231\pi$
$613$	−40.2610	−	23.2447i	−1.62613	−	0.938845i	−0.640894	−	0.767629i	$-0.721436\pi$
$614$	−21.8324	+	12.6049i	−0.881084	+	0.508694i
$615$		0			0
$616$	7.60899	+	4.37073i	0.306575	+	0.176102i
$617$	−41.6397			−1.67635			−0.838176	−	0.545399i	$-0.816378\pi$
$617$	−41.6397			−1.67635			−0.838176	+	0.545399i	$0.816378\pi$
$618$		0			0
$619$	−24.2001	−	13.9720i	−0.972686	−	0.561580i	−0.0726317	−	0.997359i	$-0.523140\pi$
$619$	−24.2001	−	13.9720i	−0.972686	−	0.561580i	−0.900054	+	0.435779i	$0.856473\pi$
$620$	−12.7571	+	22.0959i	−0.512337	+	0.887394i
$621$		0			0
$622$	11.3693			0.455867
$623$	7.01601	−	20.0348i	0.281090	−	0.802675i
$624$		0			0
$625$	15.0889	+	26.1347i	0.603555	+	1.04539i
$626$	1.83744	−	3.18253i	0.0734387	−	0.127200i
$627$		0			0
$628$	13.0804	−	7.55200i	0.521967	−	0.301358i
$629$	42.9625			1.71303
$630$		0			0
$631$	42.5667			1.69455			0.847277	−	0.531151i	$-0.178240\pi$
$631$	42.5667			1.69455			0.847277	+	0.531151i	$0.178240\pi$
$632$	−4.27905	−	7.41153i	−0.170211	−	0.294815i
$633$		0			0
$634$	21.2789	+	12.2854i	0.845093	+	0.487915i
$635$	17.2377	+	29.8566i	0.684058	+	1.18482i
$636$		0			0
$637$	−1.14102	+	7.54493i	−0.0452089	+	0.298941i
$638$	−16.1376	−	13.8189i	−0.638893	−	0.547094i
$639$		0			0
$640$	1.46078	−	2.53014i	0.0577423	−	0.100013i
$641$	13.2962	−	23.0297i	0.525168	−	0.909617i	−0.474403	−	0.880308i	$-0.657336\pi$
$641$	13.2962	−	23.0297i	0.525168	−	0.909617i	0.999570	−	0.0293092i	$-0.00933074\pi$
$642$		0			0
$643$			10.7136i			0.422502i	0.977432	+	0.211251i	$0.0677537\pi$
$643$			10.7136i			0.422502i	−0.977432	+	0.211251i	$0.932246\pi$
$644$	−3.50800	+	3.01738i	−0.138235	+	0.118901i
$645$		0			0
$646$	−23.0945	+	13.3336i	−0.908640	+	0.524603i
$647$	−29.0896	−	16.7949i	−1.14363	−	0.660275i	−0.196303	−	0.980543i	$-0.562894\pi$
$647$	−29.0896	−	16.7949i	−1.14363	−	0.660275i	−0.947327	+	0.320268i	$0.896227\pi$
$648$		0			0
$649$	−25.8076	−	4.81761i	−1.01304	−	0.189108i
$650$		−	3.85406i		−	0.151169i
$651$		0			0
$652$	−23.2196			−0.909348
$653$	10.0497	+	17.4067i	0.393277	+	0.681176i	0.992880	−	0.119122i	$-0.0380080\pi$
$653$	10.0497	+	17.4067i	0.393277	+	0.681176i	−0.599603	+	0.800298i	$0.704675\pi$
$654$		0			0
$655$	−47.9516	−	27.6849i	−1.87362	−	1.08174i
$656$	−2.31943	−	4.01738i	−0.0905587	−	0.156852i
$657$		0			0
$658$	0.952547	+	5.04114i	0.0371342	+	0.196524i
$659$			14.5906i			0.568371i	0.958769	+	0.284185i	$0.0917231\pi$
$659$			14.5906i			0.568371i	−0.958769	+	0.284185i	$0.908277\pi$
$660$		0			0
$661$	−19.8956	−	11.4868i	−0.773851	−	0.446783i	0.0603957	−	0.998175i	$-0.480764\pi$
$661$	−19.8956	−	11.4868i	−0.773851	−	0.446783i	−0.834247	+	0.551391i	$0.814097\pi$
$662$	14.1080	+	8.14527i	0.548324	+	0.316575i
$663$		0			0
$664$			8.82088i			0.342317i
$665$	50.5406	−	9.54989i	1.95988	−	0.370329i
$666$		0			0
$667$	9.70225	−	5.60160i	0.375673	−	0.216895i
$668$	−0.630108	+	1.09138i	−0.0243796	+	0.0422267i
$669$		0			0
$670$	−4.97517	−	8.61726i	−0.192208	−	0.332914i
$671$	6.92820	+	5.93273i	0.267460	+	0.229030i
$672$		0			0
$673$			9.22437i			0.355573i	0.984069	+	0.177787i	$0.0568937\pi$
$673$			9.22437i			0.355573i	−0.984069	+	0.177787i	$0.943106\pi$
$674$	−3.94591	−	6.83451i	−0.151991	−	0.263256i
$675$		0			0
$676$	−5.90584	+	10.2292i	−0.227148	+	0.393431i
$677$	0.577220	+	0.999774i	0.0221844	+	0.0384244i	0.876904	−	0.480665i	$-0.159605\pi$
$677$	0.577220	+	0.999774i	0.0221844	+	0.0384244i	−0.854720	+	0.519089i	$0.826271\pi$
$678$		0			0
$679$	22.2803	+	25.9031i	0.855040	+	0.994071i
$680$	−11.7084			−0.448996
$681$		0			0
$682$	−27.3154	+	9.63324i	−1.04596	+	0.368876i
$683$	10.2586	−	17.7683i	0.392533	−	0.679887i	−0.600250	−	0.799812i	$-0.704932\pi$
$683$	10.2586	−	17.7683i	0.392533	−	0.679887i	0.992783	+	0.119926i	$0.0382656\pi$
$684$		0			0
$685$		−	38.7177i		−	1.47933i
$686$	−16.3676	−	8.66605i	−0.624919	−	0.330871i
$687$		0			0
$688$	−1.25452	+	0.724298i	−0.0478282	+	0.0276136i
$689$	3.62355	−	6.27618i	0.138046	−	0.239103i
$690$		0			0
$691$	29.9000	−	17.2628i	1.13745	−	0.656708i	0.191653	−	0.981463i	$-0.438615\pi$
$691$	29.9000	−	17.2628i	1.13745	−	0.656708i	0.945798	+	0.324755i	$0.105282\pi$
$692$	−5.98689			−0.227587
$693$		0			0
$694$	−9.58860			−0.363978
$695$	−7.02371	+	4.05514i	−0.266424	+	0.153820i
$696$		0			0
$697$	−9.29532	+	16.1000i	−0.352085	+	0.609830i
$698$	11.5582	−	6.67314i	0.437485	−	0.252582i
$699$		0			0
$700$	8.82836	+	3.09162i	0.333681	+	0.116852i
$701$		−	26.5927i		−	1.00439i	−0.864754	−	0.502196i	$-0.832526\pi$
$701$		−	26.5927i		−	1.00439i	0.864754	−	0.502196i	$-0.167474\pi$
$702$		0			0
$703$	−35.6674	+	61.7778i	−1.34522	+	2.32999i
$704$	3.12781	−	1.10308i	0.117884	−	0.0415737i
$705$		0			0
$706$	16.6564			0.626872
$707$	4.47864	+	23.7022i	0.168437	+	0.891412i
$708$		0			0
$709$	−25.1514	−	43.5636i	−0.944582	−	1.63606i	−0.756586	−	0.653894i	$-0.773134\pi$
$709$	−25.1514	−	43.5636i	−0.944582	−	1.63606i	−0.187996	−	0.982170i	$-0.560199\pi$
$710$	19.1875	−	33.2336i	0.720092	−	1.24724i
$711$		0			0
$712$	−4.01166	−	6.94840i	−0.150343	−	0.260402i
$713$		−	15.2733i		−	0.571990i
$714$		0			0
$715$	6.87034	−	8.02314i	0.256936	−	0.300048i
$716$	−2.58708	−	4.48096i	−0.0966838	−	0.167461i
$717$		0			0
$718$	−1.72030	+	2.97964i	−0.0642009	+	0.111199i
$719$	9.75818	−	5.63389i	0.363919	−	0.210109i	−0.306880	−	0.951748i	$-0.599285\pi$
$719$	9.75818	−	5.63389i	0.363919	−	0.210109i	0.670798	+	0.741640i	$0.265952\pi$
$720$		0			0
$721$	−1.10200	+	3.14684i	−0.0410406	+	0.117195i
$722$		−	25.2782i		−	0.940758i
$723$		0			0
$724$	6.00000	+	3.46410i	0.222988	+	0.128742i
$725$	−19.6136	−	11.3239i	−0.728430	−	0.420559i
$726$		0			0
$727$			14.4011i			0.534106i	0.963682	+	0.267053i	$0.0860499\pi$
$727$			14.4011i			0.534106i	−0.963682	+	0.267053i	$0.913950\pi$
$728$	1.88075	+	2.18656i	0.0697052	+	0.0810394i
$729$		0			0
$730$	−11.7203	−	20.3001i	−0.433788	−	0.751342i
$731$	5.02760	+	2.90268i	0.185952	+	0.107360i
$732$		0			0
$733$	2.30680	+	3.99549i	0.0852034	+	0.147577i	0.905478	−	0.424393i	$-0.139513\pi$
$733$	2.30680	+	3.99549i	0.0852034	+	0.147577i	−0.820274	+	0.571970i	$0.806179\pi$
$734$	−36.0994			−1.33245
$735$		0			0
$736$			1.74890i			0.0644655i
$737$	2.07285	−	11.1041i	0.0763543	−	0.409024i
$738$		0			0
$739$	−43.4306	−	25.0747i	−1.59762	−	0.922387i	−0.991944	−	0.126675i	$-0.959569\pi$
$739$	−43.4306	−	25.0747i	−1.59762	−	0.922387i	−0.605676	−	0.795711i	$-0.707097\pi$
$740$	−27.1239	+	15.6600i	−0.997094	+	0.575672i
$741$		0			0
$742$	11.4699	+	13.3349i	0.421074	+	0.489541i
$743$		−	30.7639i		−	1.12862i	−0.825564	−	0.564308i	$-0.809143\pi$
$743$		−	30.7639i		−	1.12862i	0.825564	−	0.564308i	$-0.190857\pi$
$744$		0			0
$745$	20.1460	−	34.8939i	0.738093	−	1.27841i
$746$	−15.6094	+	27.0363i	−0.571502	+	0.989870i
$747$		0			0
$748$	−10.0959	−	8.64527i	−0.369142	−	0.316102i
$749$	13.4204	−	38.3229i	0.490370	−	1.40029i
$750$		0			0
$751$	−19.5044	−	33.7826i	−0.711726	−	1.23275i	−0.964209	−	0.265144i	$-0.914581\pi$
$751$	−19.5044	−	33.7826i	−0.711726	−	1.23275i	0.252483	−	0.967601i	$-0.418753\pi$
$752$	1.67930	+	0.969544i	0.0612377	+	0.0353556i
$753$		0			0
$754$	−3.49151	−	6.04748i	−0.127153	−	0.220236i
$755$	−25.4736			−0.927080
$756$		0			0
$757$	3.09695			0.112560			0.0562802	−	0.998415i	$-0.482076\pi$
$757$	3.09695			0.112560			0.0562802	+	0.998415i	$0.482076\pi$
$758$	−14.1080	+	8.14527i	−0.512427	+	0.295850i
$759$		0			0
$760$	9.72030	−	16.8360i	0.352592	−	0.610708i
$761$	−19.2290	−	33.3056i	−0.697051	−	1.20733i	−0.969484	−	0.245153i	$-0.921162\pi$
$761$	−19.2290	−	33.3056i	−0.697051	−	1.20733i	0.272434	−	0.962175i	$-0.412171\pi$
$762$		0			0
$763$	−22.1830	+	4.19159i	−0.803080	+	0.151746i
$764$	25.5326			0.923738
$765$		0			0
$766$	−2.67441	+	4.63221i	−0.0966303	+	0.167369i
$767$	−7.47286	−	4.31446i	−0.269829	−	0.155786i
$768$		0			0
$769$	9.12126			0.328921			0.164460	−	0.986384i	$-0.447412\pi$
$769$	9.12126			0.328921			0.164460	+	0.986384i	$0.447412\pi$
$770$	12.8672	+	22.1736i	0.463700	+	0.799082i
$771$		0			0
$772$	10.6629	−	6.15622i	0.383765	−	0.221567i
$773$	−18.0906	−	10.4446i	−0.650675	−	0.375667i	0.138040	−	0.990427i	$-0.455920\pi$
$773$	−18.0906	−	10.4446i	−0.650675	−	0.375667i	−0.788715	+	0.614759i	$0.789253\pi$
$774$		0			0
$775$	−26.7392	+	15.4379i	−0.960500	+	0.554545i
$776$	12.9139			0.463583
$777$		0			0
$778$			35.7764i			1.28265i
$779$	−15.4339	−	26.7324i	−0.552979	−	0.957787i
$780$		0			0
$781$	41.0841	−	14.4890i	1.47011	−	0.518457i
$782$	6.06986	−	3.50444i	0.217058	−	0.125318i
$783$		0			0
$784$	−6.51738	+	2.55417i	−0.232763	+	0.0912205i
$785$	44.1272			1.57497
$786$		0			0
$787$	21.5599	−	37.3428i	0.768527	−	1.33113i	−0.169835	−	0.985472i	$-0.554324\pi$
$787$	21.5599	−	37.3428i	0.768527	−	1.33113i	0.938362	−	0.345655i	$-0.112343\pi$
$788$	−0.0791369	−	0.0456897i	−0.00281913	−	0.00162763i
$789$		0			0
$790$		−	25.0030i		−	0.889565i
$791$	7.57447	−	6.51511i	0.269317	−	0.231651i
$792$		0			0
$793$	1.49898	+	2.59631i	0.0532303	+	0.0921976i
$794$	−5.81877	+	10.0784i	−0.206500	+	0.357669i
$795$		0			0
$796$	4.09342	−	2.36334i	0.145087	−	0.0837663i
$797$		−	9.58780i		−	0.339617i	−0.985477	−	0.169809i	$-0.945685\pi$
$797$		−	9.58780i		−	0.339617i	0.985477	−	0.169809i	$-0.0543150\pi$
$798$		0			0
$799$		−	7.77105i		−	0.274920i
$800$	3.06183	−	1.76775i	0.108252	−	0.0624993i
$801$		0			0
$802$	5.53823	+	3.19750i	0.195562	+	0.112908i
$803$	4.88312	−	26.1585i	0.172322	−	0.923112i
$804$		0			0
$805$	−13.2835	+	2.50998i	−0.468181	+	0.0884650i
$806$	−9.51996			−0.335326
$807$		0			0
$808$	7.89564	+	4.55855i	0.277768	+	0.160369i
$809$	−6.29068	−	3.63193i	−0.221169	−	0.127692i	0.385323	−	0.922782i	$-0.374090\pi$
$809$	−6.29068	−	3.63193i	−0.221169	−	0.127692i	−0.606491	+	0.795090i	$0.707423\pi$
$810$		0			0
$811$	30.8894			1.08467			0.542337	−	0.840161i	$-0.317540\pi$
$811$	30.8894			1.08467			0.542337	+	0.840161i	$0.317540\pi$
$812$	16.6536	−	3.14677i	0.584425	−	0.110430i
$813$		0			0
$814$	−34.9514	−	6.52454i	−1.22505	−	0.228685i
$815$	−58.7488	−	33.9186i	−2.05788	−	1.18812i
$816$		0			0
$817$	−8.34782	+	4.81962i	−0.292053	+	0.168617i
$818$		−	26.1286i		−	0.913564i
$819$		0			0
$820$		−	13.5527i		−	0.473281i
$821$	−46.0688	+	26.5978i	−1.60781	+	0.928270i	−0.617953	+	0.786215i	$0.712038\pi$
$821$	−46.0688	+	26.5978i	−1.60781	+	0.928270i	−0.989859	+	0.142055i	$0.954629\pi$
$822$		0			0
$823$	−5.37108	+	9.30299i	−0.187224	+	0.324282i	−0.944324	−	0.329018i	$-0.893282\pi$
$823$	−5.37108	+	9.30299i	−0.187224	+	0.324282i	0.757100	+	0.653300i	$0.226616\pi$
$824$	0.630108	+	1.09138i	0.0219509	+	0.0380200i
$825$		0			0
$826$	15.8775	−	13.6569i	0.552450	−	0.475184i
$827$			32.1624i			1.11840i	0.829034	+	0.559198i	$0.188891\pi$
$827$			32.1624i			1.11840i	−0.829034	+	0.559198i	$0.811109\pi$
$828$		0			0
$829$	7.38257	+	4.26233i	0.256407	+	0.148037i	0.622695	−	0.782465i	$-0.286038\pi$
$829$	7.38257	+	4.26233i	0.256407	+	0.148037i	−0.366287	+	0.930502i	$0.619371\pi$
$830$	−12.8854	+	22.3181i	−0.447257	+	0.774672i
$831$		0			0
$832$	1.09010			0.0377925
$833$	21.9241	+	17.5016i	0.759626	+	0.606395i
$834$		0			0
$835$	−3.18853	+	1.84090i	−0.110344	+	0.0637069i
$836$	20.8131	−	7.34007i	0.719835	−	0.253862i
$837$		0			0
$838$	6.55353	+	11.3511i	0.226388	+	0.392116i
$839$			12.2064i			0.421411i	0.977550	+	0.210705i	$0.0675761\pi$
$839$			12.2064i			0.421411i	−0.977550	+	0.210705i	$0.932424\pi$
$840$		0			0
$841$	−12.0348			−0.414992
$842$	1.42834	−	0.824651i	0.0492238	−	0.0284194i
$843$		0			0
$844$	−11.7121	−	6.76197i	−0.403146	−	0.232757i
$845$	−29.8852	+	17.2542i	−1.02808	+	0.593564i
$846$		0			0
$847$	−5.27755	+	28.6208i	−0.181339	+	0.983421i
$848$	6.64809			0.228296
$849$		0			0
$850$	−12.2705	−	7.08439i	−0.420876	−	0.242993i
$851$	9.37439	−	16.2369i	0.321350	−	0.556594i
$852$		0			0
$853$	−19.0638			−0.652731			−0.326366	−	0.945244i	$-0.605824\pi$
$853$	−19.0638			−0.652731			−0.326366	+	0.945244i	$0.605824\pi$
$854$	−7.14973	+	1.35097i	−0.244659	+	0.0462294i
$855$		0			0
$856$	−7.67359	−	13.2910i	−0.262278	−	0.454278i
$857$	−24.6052	+	42.6175i	−0.840498	+	1.45578i	0.0489767	+	0.998800i	$0.484404\pi$
$857$	−24.6052	+	42.6175i	−0.840498	+	1.45578i	−0.889474	+	0.456985i	$0.848929\pi$
$858$		0			0
$859$	−24.4358	+	14.1080i	−0.833739	+	0.481360i	−0.855131	−	0.518412i	$-0.826524\pi$
$859$	−24.4358	+	14.1080i	−0.833739	+	0.481360i	0.0213919	+	0.999771i	$0.493190\pi$
$860$	−4.23216			−0.144315
$861$		0			0
$862$	28.5116			0.971108
$863$	24.5811	+	42.5757i	0.836749	+	1.44929i	0.892598	+	0.450853i	$0.148880\pi$
$863$	24.5811	+	42.5757i	0.836749	+	1.44929i	−0.0558487	+	0.998439i	$0.517786\pi$
$864$		0			0
$865$	−15.1477	−	8.74552i	−0.515037	−	0.297357i
$866$	5.70322	+	9.87827i	0.193803	+	0.335677i
$867$		0			0
$868$	7.63666	−	21.8071i	0.259205	−	0.740180i
$869$	18.4618	−	21.5595i	0.626273	−	0.731357i
$870$		0			0
$871$	1.85636	−	3.21531i	0.0629003	−	0.108946i
$872$	−4.26638	+	7.38959i	−0.144478	+	0.250243i
$873$		0			0
$874$			11.6375i			0.393646i
$875$	−7.38190	−	8.58221i	−0.249554	−	0.290132i
$876$		0			0
$877$	−2.48413	+	1.43421i	−0.0838830	+	0.0484299i	−0.541355	−	0.840794i	$-0.682088\pi$
$877$	−2.48413	+	1.43421i	−0.0838830	+	0.0484299i	0.457472	+	0.889224i	$0.348755\pi$
$878$	11.1681	+	6.44793i	0.376907	+	0.217607i
$879$		0			0
$880$	9.52517	+	1.77811i	0.321093	+	0.0599399i
$881$		−	34.1857i		−	1.15175i	−0.817539	−	0.575874i	$-0.804662\pi$
$881$		−	34.1857i		−	1.15175i	0.817539	−	0.575874i	$-0.195338\pi$
$882$		0			0
$883$	−8.91891			−0.300145			−0.150073	−	0.988675i	$-0.547951\pi$
$883$	−8.91891			−0.300145			−0.150073	+	0.988675i	$0.547951\pi$
$884$	−2.18434	−	3.78339i	−0.0734673	−	0.127249i
$885$		0			0
$886$	−11.9174	−	6.88052i	−0.400373	−	0.231155i
$887$	14.9572	+	25.9066i	0.502213	+	0.869858i	0.999997	+	0.00255684i	$0.000813869\pi$
$887$	14.9572	+	25.9066i	0.502213	+	0.869858i	−0.497784	+	0.867301i	$0.665853\pi$
$888$		0			0
$889$	−20.3591	−	23.6695i	−0.682823	−	0.793851i
$890$		−	23.4406i		−	0.785730i
$891$		0			0
$892$	17.6565	+	10.1940i	0.591183	+	0.341320i
$893$	11.1744	+	6.45153i	0.373936	+	0.215892i
$894$		0			0
$895$		−	15.1166i		−	0.505293i
$896$	−0.874452	+	2.49706i	−0.0292134	+	0.0834211i
$897$		0			0
$898$	0.476277	−	0.274979i	0.0158936	−	0.00917615i
$899$	−27.9713	+	48.4478i	−0.932896	+	1.61582i
$900$		0			0
$901$	−13.3214	−	23.0733i	−0.443800	−	0.768684i
$902$	10.0071	−	11.6862i	0.333200	−	0.389109i
$903$		0			0
$904$		−	3.77623i		−	0.125595i
$905$	10.1206	+	17.5293i	0.336419	+	0.582695i
$906$		0			0
$907$	26.5493	−	45.9848i	0.881557	−	1.52690i	0.0319465	−	0.999490i	$-0.489829\pi$
$907$	26.5493	−	45.9848i	0.881557	−	1.52690i	0.849610	−	0.527411i	$-0.176837\pi$
$908$	6.92130	+	11.9880i	0.229691	+	0.397837i
$909$		0			0
$910$	1.56448	+	8.27967i	0.0518621	+	0.274469i
$911$	−33.6396			−1.11453			−0.557266	−	0.830334i	$-0.688149\pi$
$911$	−33.6396			−1.11453			−0.557266	+	0.830334i	$0.688149\pi$
$912$		0			0
$913$	−27.5901	+	9.73010i	−0.913099	+	0.322019i
$914$	−5.53371	+	9.58467i	−0.183039	+	0.317033i
$915$		0			0
$916$			26.4250i			0.873106i
$917$	47.3247	+	16.5727i	1.56280	+	0.547280i
$918$		0			0
$919$	−0.202342	+	0.116822i	−0.00667464	+	0.00385361i	−0.503334	−	0.864092i	$-0.667893\pi$
$919$	−0.202342	+	0.116822i	−0.00667464	+	0.00385361i	0.496659	+	0.867946i	$0.334560\pi$
$920$	−2.55476	+	4.42498i	−0.0842280	+	0.145887i
$921$		0			0
$922$	−4.89768	+	2.82768i	−0.161297	+	0.0931247i
$923$	14.3186			0.471302
$924$		0			0
$925$	−37.9016			−1.24620
$926$	10.7752	−	6.22104i	0.354094	−	0.204436i
$927$		0			0
$928$	3.20292	−	5.54762i	0.105141	−	0.182109i
$929$	−23.5789	+	13.6133i	−0.773597	+	0.446636i	−0.834156	−	0.551528i	$-0.814045\pi$
$929$	−23.5789	+	13.6133i	−0.773597	+	0.446636i	0.0605592	+	0.998165i	$0.480712\pi$
$930$		0			0
$931$	−43.3679	+	16.9959i	−1.42132	+	0.557020i
$932$		−	17.0551i		−	0.558660i
$933$		0			0
$934$	−14.5510	+	25.2031i	−0.476123	+	0.824670i
$935$	−12.9152	−	36.6216i	−0.422373	−	1.19766i
$936$		0			0
$937$	−18.3603			−0.599805			−0.299903	−	0.953970i	$-0.596954\pi$
$937$	−18.3603			−0.599805			−0.299903	+	0.953970i	$0.596954\pi$
$938$	5.87608	+	6.83153i	0.191861	+	0.223057i
$939$		0			0
$940$	2.83258	+	4.90617i	0.0923885	+	0.160022i
$941$	−11.4479	+	19.8283i	−0.373190	+	0.646384i	−0.990054	−	0.140685i	$-0.955069\pi$
$941$	−11.4479	+	19.8283i	−0.373190	+	0.646384i	0.616864	+	0.787070i	$0.288403\pi$
$942$		0			0
$943$	4.05647	+	7.02601i	0.132097	+	0.228798i
$944$		−	7.91569i		−	0.257634i
$945$		0			0
$946$	−3.64930	−	3.12495i	−0.118649	−	0.101601i
$947$	13.9066	+	24.0869i	0.451904	+	0.782720i	0.998504	−	0.0546731i	$-0.0174117\pi$
$947$	13.9066	+	24.0869i	0.451904	+	0.782720i	−0.546600	+	0.837394i	$0.684078\pi$
$948$		0			0
$949$	4.37312	−	7.57447i	0.141958	−	0.245878i
$950$	20.3740	−	11.7629i	0.661020	−	0.381640i
$951$		0			0
$952$	10.4187	−	1.96866i	0.337672	−	0.0638047i
$953$		−	54.6637i		−	1.77073i	−0.464897	−	0.885365i	$-0.653909\pi$
$953$		−	54.6637i		−	1.77073i	0.464897	−	0.885365i	$-0.346091\pi$
$954$		0			0
$955$	64.6012	+	37.2975i	2.09045	+	1.20692i
$956$	0.544657	+	0.314458i	0.0176155	+	0.0101703i
$957$		0			0
$958$			10.5656i			0.341358i
$959$	6.51004	+	34.4529i	0.210220	+	1.11254i
$960$		0			0
$961$	22.6333	+	39.2021i	0.730107	+	1.26458i
$962$	−10.1206	−	5.84311i	−0.326300	−	0.188390i
$963$		0			0
$964$	10.0989	+	17.4917i	0.325262	+	0.563371i
$965$	35.9715			1.15796
$966$		0			0
$967$		−	44.7015i		−	1.43750i	−0.695267	−	0.718751i	$-0.744714\pi$
$967$		−	44.7015i		−	1.43750i	0.695267	−	0.718751i	$-0.255286\pi$
$968$	6.90043	+	8.56645i	0.221788	+	0.275336i
$969$		0			0
$970$	32.6740	+	18.8644i	1.04910	+	0.605698i
$971$	−13.7915	+	7.96253i	−0.442590	+	0.255530i	−0.704696	−	0.709510i	$-0.748917\pi$
$971$	−13.7915	+	7.96253i	−0.442590	+	0.255530i	0.262105	+	0.965039i	$0.415583\pi$
$972$		0			0
$973$	5.56821	−	4.78944i	0.178509	−	0.153542i
$974$			29.3089i			0.939117i
$975$		0			0
$976$	−1.37508	+	2.38171i	−0.0440153	+	0.0762367i
$977$	24.8882	−	43.1077i	0.796245	−	1.37914i	−0.125800	−	0.992056i	$-0.540150\pi$
$977$	24.8882	−	43.1077i	0.796245	−	1.37914i	0.922045	−	0.387082i	$-0.126517\pi$
$978$		0			0
$979$	17.3081	−	20.2123i	0.553171	−	0.645989i
$980$	−20.2210	−	3.05802i	−0.645935	−	0.0976849i
$981$		0			0
$982$	0.0119561	+	0.0207086i	0.000381536	+	0.000660839i
$983$	−11.5461	−	6.66617i	−0.368265	−	0.212618i	0.304435	−	0.952533i	$-0.401532\pi$
$983$	−11.5461	−	6.66617i	−0.368265	−	0.212618i	−0.672700	+	0.739915i	$0.734866\pi$
$984$		0			0
$985$	−0.133485	−	0.231203i	−0.00425319	−	0.00736674i
$986$	−25.6719			−0.817560
$987$		0			0
$988$	7.25375			0.230773
$989$	2.19404	−	1.26673i	0.0697663	−	0.0402796i
$990$		0			0
$991$	6.93415	−	12.0103i	0.220271	−	0.381520i	−0.734620	−	0.678479i	$-0.762639\pi$
$991$	6.93415	−	12.0103i	0.220271	−	0.381520i	0.954890	+	0.296960i	$0.0959726\pi$
$992$	−4.36654	−	7.56307i	−0.138638	−	0.240128i
$993$		0			0
$994$	−11.4860	+	32.7992i	−0.364314	+	1.04033i
$995$	13.8092			0.437783
$996$		0			0
$997$	17.1237	−	29.6592i	0.542314	−	0.939316i	−0.456456	−	0.889746i	$-0.650882\pi$
$997$	17.1237	−	29.6592i	0.542314	−	0.939316i	0.998771	−	0.0495700i	$-0.0157851\pi$
$998$	15.8732	+	9.16441i	0.502458	+	0.290094i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.bk.d.703.8	yes	32
3.2	odd	2	inner	1386.2.bk.d.703.11	yes	32
7.5	odd	6	inner	1386.2.bk.d.901.12	yes	32
11.10	odd	2	inner	1386.2.bk.d.703.12	yes	32
21.5	even	6	inner	1386.2.bk.d.901.7	yes	32
33.32	even	2	inner	1386.2.bk.d.703.7	✓	32
77.54	even	6	inner	1386.2.bk.d.901.8	yes	32
231.131	odd	6	inner	1386.2.bk.d.901.11	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.bk.d.703.7	✓	32	33.32	even	2	inner
1386.2.bk.d.703.8	yes	32	1.1	even	1	trivial
1386.2.bk.d.703.11	yes	32	3.2	odd	2	inner
1386.2.bk.d.703.12	yes	32	11.10	odd	2	inner
1386.2.bk.d.901.7	yes	32	21.5	even	6	inner
1386.2.bk.d.901.8	yes	32	77.54	even	6	inner
1386.2.bk.d.901.11	yes	32	231.131	odd	6	inner
1386.2.bk.d.901.12	yes	32	7.5	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.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.53014 - 1.46078i) q^{5} +(-2.00583 + 1.72530i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.53014 - 1.46078i) q^{5} +(-2.00583 + 1.72530i) q^{7} +1.00000i q^{8} +(-1.46078 + 2.53014i) q^{10} +(-3.12781 + 1.10308i) q^{11} -1.09010 q^{13} +(0.874452 - 2.49706i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.00379 + 3.47067i) q^{17} +(-3.32709 - 5.76270i) q^{19} -2.92156i q^{20} +(2.15723 - 2.51920i) q^{22} +(0.874452 + 1.51460i) q^{23} +(1.76775 - 3.06183i) q^{25} +(0.944057 - 0.545052i) q^{26} +(0.491235 + 2.59975i) q^{28} -6.40584i q^{29} +(-7.56307 - 4.36654i) q^{31} +(0.866025 + 0.500000i) q^{32} -4.00758i q^{34} +(-2.55476 + 7.29532i) q^{35} +(-5.36015 - 9.28405i) q^{37} +(5.76270 + 3.32709i) q^{38} +(1.46078 + 2.53014i) q^{40} +4.63887 q^{41} -1.44860i q^{43} +(-0.608616 + 3.26030i) q^{44} +(-1.51460 - 0.874452i) q^{46} +(-1.67930 + 0.969544i) q^{47} +(1.04671 - 6.92130i) q^{49} +3.53550i q^{50} +(-0.545052 + 0.944057i) q^{52} +(-3.32405 + 5.75742i) q^{53} +(-6.30247 + 7.35998i) q^{55} +(-1.72530 - 2.00583i) q^{56} +(3.20292 + 5.54762i) q^{58} +(6.85519 + 3.95784i) q^{59} +(-1.37508 - 2.38171i) q^{61} +8.73308 q^{62} -1.00000 q^{64} +(-2.75812 + 1.59240i) q^{65} +(-1.70292 + 2.94954i) q^{67} +(2.00379 + 3.47067i) q^{68} +(-1.43517 - 7.59531i) q^{70} -13.1351 q^{71} +(-4.01166 + 6.94840i) q^{73} +(9.28405 + 5.36015i) q^{74} -6.65419 q^{76} +(4.37073 - 7.60899i) q^{77} +(-7.41153 + 4.27905i) q^{79} +(-2.53014 - 1.46078i) q^{80} +(-4.01738 + 2.31943i) q^{82} +8.82088 q^{83} +11.7084i q^{85} +(0.724298 + 1.25452i) q^{86} +(-1.10308 - 3.12781i) q^{88} +(-6.94840 + 4.01166i) q^{89} +(2.18656 - 1.88075i) q^{91} +1.74890 q^{92} +(0.969544 - 1.67930i) q^{94} +(-16.8360 - 9.72030i) q^{95} -12.9139i q^{97} +(2.55417 + 6.51738i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4}+O(q^{10}) \) 32 * q + 16 * q^4	\( 32 q + 16 q^{4} - 16 q^{16} + 20 q^{22} + 36 q^{25} + 12 q^{31} - 20 q^{37} - 44 q^{49} - 32 q^{64} + 48 q^{67} + 36 q^{70} + 72 q^{82} + 10 q^{88} + 144 q^{91}+O(q^{100}) \) 32 * q + 16 * q^4 - 16 * q^16 + 20 * q^22 + 36 * q^25 + 12 * q^31 - 20 * q^37 - 44 * q^49 - 32 * q^64 + 48 * q^67 + 36 * q^70 + 72 * q^82 + 10 * q^88 + 144 * q^91

Introduction

L-functions

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