LMFDB - Embedded newform 216.3.u.a.41.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(41,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 17]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("216.41");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.u (of order $18$, degree $6$, 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:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.5
Character	$\chi$	$=$	216.41
Dual form			216.3.u.a.137.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.11535 + 2.12727i) q^{3} +(1.88267 - 2.24368i) q^{5} +(4.85852 + 1.76836i) q^{7} +(-0.0505567 - 8.99986i) q^{9} +O(q^{10})$	\(q+(-2.11535 + 2.12727i) q^{3} +(1.88267 - 2.24368i) q^{5} +(4.85852 + 1.76836i) q^{7} +(-0.0505567 - 8.99986i) q^{9} +(5.52146 + 6.58021i) q^{11} +(-0.973431 + 5.52060i) q^{13} +(0.790397 + 8.75112i) q^{15} +(0.985037 + 0.568711i) q^{17} +(16.5025 + 28.5831i) q^{19} +(-14.0393 + 6.59468i) q^{21} +(2.55606 + 7.02272i) q^{23} +(2.85156 + 16.1720i) q^{25} +(19.2521 + 18.9303i) q^{27} +(15.0012 - 2.64512i) q^{29} +(-11.8151 + 4.30035i) q^{31} +(-25.6777 - 2.17385i) q^{33} +(13.1146 - 7.57172i) q^{35} +(3.41504 - 5.91502i) q^{37} +(-9.68466 - 13.7488i) q^{39} +(14.2631 + 2.51496i) q^{41} +(-16.8812 + 14.1650i) q^{43} +(-20.2880 - 16.8303i) q^{45} +(18.3705 - 50.4726i) q^{47} +(-17.0581 - 14.3134i) q^{49} +(-3.29350 + 0.892414i) q^{51} -67.6881i q^{53} +25.1589 q^{55} +(-95.7126 - 25.3582i) q^{57} +(60.8233 - 72.4864i) q^{59} +(73.9307 + 26.9086i) q^{61} +(15.6693 - 43.8154i) q^{63} +(10.5538 + 12.5775i) q^{65} +(-21.9759 + 124.632i) q^{67} +(-20.3462 - 9.41811i) q^{69} +(-79.6970 - 46.0131i) q^{71} +(-52.7493 - 91.3645i) q^{73} +(-40.4343 - 28.1434i) q^{75} +(15.1899 + 41.7340i) q^{77} +(10.6681 + 60.5017i) q^{79} +(-80.9949 + 0.910006i) q^{81} +(-94.2798 + 16.6241i) q^{83} +(3.13050 - 1.13941i) q^{85} +(-26.1060 + 37.5070i) q^{87} +(63.5663 - 36.7000i) q^{89} +(-14.4918 + 25.1006i) q^{91} +(15.8452 - 34.2307i) q^{93} +(95.1999 + 16.7863i) q^{95} +(28.1582 - 23.6276i) q^{97} +(58.9418 - 50.0250i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q+O(q^{10}) $ 108 * q	$ 108 q - 18 q^{11} - 24 q^{15} + 48 q^{21} + 72 q^{23} + 174 q^{27} + 108 q^{29} + 18 q^{33} - 144 q^{39} + 90 q^{41} - 90 q^{43} + 108 q^{45} - 72 q^{49} + 84 q^{51} - 18 q^{57} - 252 q^{59} + 144 q^{61} - 360 q^{63} - 216 q^{65} + 126 q^{67} - 120 q^{69} - 252 q^{75} - 504 q^{77} - 552 q^{81} - 180 q^{83} - 60 q^{87} - 486 q^{89} - 360 q^{93} - 1116 q^{95} + 270 q^{97} - 564 q^{99}+O(q^{100}) $ 108 * q - 18 * q^11 - 24 * q^15 + 48 * q^21 + 72 * q^23 + 174 * q^27 + 108 * q^29 + 18 * q^33 - 144 * q^39 + 90 * q^41 - 90 * q^43 + 108 * q^45 - 72 * q^49 + 84 * q^51 - 18 * q^57 - 252 * q^59 + 144 * q^61 - 360 * q^63 - 216 * q^65 + 126 * q^67 - 120 * q^69 - 252 * q^75 - 504 * q^77 - 552 * q^81 - 180 * q^83 - 60 * q^87 - 486 * q^89 - 360 * q^93 - 1116 * q^95 + 270 * q^97 - 564 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$1$	$e\left(\frac{17}{18}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.11535	+	2.12727i	−0.705118	+	0.709090i
$3$	−2.11535	+	2.12727i	−0.705118	+	0.709090i
$4$		0			0
$5$	1.88267	−	2.24368i	0.376534	−	0.448735i	−0.544183	−	0.838966i	$-0.683160\pi$
$5$	1.88267	−	2.24368i	0.376534	−	0.448735i	0.920717	+	0.390231i	$0.127605\pi$
$6$		0			0
$7$	4.85852	+	1.76836i	0.694074	+	0.252622i	0.664879	−	0.746951i	$-0.268483\pi$
$7$	4.85852	+	1.76836i	0.694074	+	0.252622i	0.0291955	+	0.999574i	$0.490705\pi$
$8$		0			0
$9$	−0.0505567	−	8.99986i	−0.00561741	−	0.999984i
$10$		0			0
$11$	5.52146	+	6.58021i	0.501950	+	0.598201i	0.956215	−	0.292666i	$-0.0945423\pi$
$11$	5.52146	+	6.58021i	0.501950	+	0.598201i	−0.454264	+	0.890867i	$0.650098\pi$
$12$		0			0
$13$	−0.973431	+	5.52060i	−0.0748793	+	0.424662i	0.924206	+	0.381895i	$0.124728\pi$
$13$	−0.973431	+	5.52060i	−0.0748793	+	0.424662i	−0.999085	+	0.0427669i	$0.986383\pi$
$14$		0			0
$15$	0.790397	+	8.75112i	0.0526931	+	0.583408i
$16$		0			0
$17$	0.985037	+	0.568711i	0.0579434	+	0.0334536i	0.528692	−	0.848814i	$-0.322683\pi$
$17$	0.985037	+	0.568711i	0.0579434	+	0.0334536i	−0.470748	+	0.882267i	$0.656016\pi$
$18$		0			0
$19$	16.5025	+	28.5831i	0.868551	+	1.50437i	0.863478	+	0.504387i	$0.168282\pi$
$19$	16.5025	+	28.5831i	0.868551	+	1.50437i	0.00507316	+	0.999987i	$0.498385\pi$
$20$		0			0
$21$	−14.0393	+	6.59468i	−0.668536	+	0.314033i
$22$		0			0
$23$	2.55606	+	7.02272i	0.111133	+	0.305336i	0.982775	−	0.184808i	$-0.0591664\pi$
$23$	2.55606	+	7.02272i	0.111133	+	0.305336i	−0.871641	+	0.490144i	$0.836944\pi$
$24$		0			0
$25$	2.85156	+	16.1720i	0.114062	+	0.646880i
$26$		0			0
$27$	19.2521	+	18.9303i	0.713040	+	0.701124i
$28$		0			0
$29$	15.0012	−	2.64512i	0.517283	−	0.0912110i	0.0910892	−	0.995843i	$-0.470965\pi$
$29$	15.0012	−	2.64512i	0.517283	−	0.0912110i	0.426194	+	0.904632i	$0.359854\pi$
$30$		0			0
$31$	−11.8151	+	4.30035i	−0.381133	+	0.138721i	−0.525480	−	0.850806i	$-0.676114\pi$
$31$	−11.8151	+	4.30035i	−0.381133	+	0.138721i	0.144347	+	0.989527i	$0.453892\pi$
$32$		0			0
$33$	−25.6777	−	2.17385i	−0.778113	−	0.0658744i
$34$		0			0
$35$	13.1146	−	7.57172i	0.374703	−	0.216335i
$36$		0			0
$37$	3.41504	−	5.91502i	0.0922984	−	0.159866i	−0.816179	−	0.577798i	$-0.803912\pi$
$37$	3.41504	−	5.91502i	0.0922984	−	0.159866i	0.908478	+	0.417933i	$0.137245\pi$
$38$		0			0
$39$	−9.68466	−	13.7488i	−0.248325	−	0.352533i
$40$		0			0
$41$	14.2631	+	2.51496i	0.347879	+	0.0613405i	0.344858	−	0.938655i	$-0.387927\pi$
$41$	14.2631	+	2.51496i	0.347879	+	0.0613405i	0.00302148	+	0.999995i	$0.499038\pi$
$42$		0			0
$43$	−16.8812	+	14.1650i	−0.392585	+	0.329418i	−0.817619	−	0.575759i	$-0.804707\pi$
$43$	−16.8812	+	14.1650i	−0.392585	+	0.329418i	0.425034	+	0.905177i	$0.360262\pi$
$44$		0			0
$45$	−20.2880	−	16.8303i	−0.450844	−	0.374007i
$46$		0			0
$47$	18.3705	−	50.4726i	0.390862	−	1.07389i	−0.575746	−	0.817628i	$-0.695288\pi$
$47$	18.3705	−	50.4726i	0.390862	−	1.07389i	0.966609	−	0.256257i	$-0.0824894\pi$
$48$		0			0
$49$	−17.0581	−	14.3134i	−0.348124	−	0.292110i
$50$		0			0
$51$	−3.29350	+	0.892414i	−0.0645785	+	0.0174983i
$52$		0			0
$53$		−	67.6881i		−	1.27713i	−0.769566	−	0.638567i	$-0.779528\pi$
$53$		−	67.6881i		−	1.27713i	0.769566	−	0.638567i	$-0.220472\pi$
$54$		0			0
$55$	25.1589			0.457435
$56$		0			0
$57$	−95.7126	−	25.3582i	−1.67917	−	0.444880i
$58$		0			0
$59$	60.8233	−	72.4864i	1.03090	−	1.22858i	0.0577724	−	0.998330i	$-0.481600\pi$
$59$	60.8233	−	72.4864i	1.03090	−	1.22858i	0.973131	−	0.230253i	$-0.0739553\pi$
$60$		0			0
$61$	73.9307	+	26.9086i	1.21198	+	0.441124i	0.867389	−	0.497630i	$-0.165796\pi$
$61$	73.9307	+	26.9086i	1.21198	+	0.441124i	0.344589	+	0.938754i	$0.388018\pi$
$62$		0			0
$63$	15.6693	−	43.8154i	0.248719	−	0.695482i
$64$		0			0
$65$	10.5538	+	12.5775i	0.162366	+	0.193501i
$66$		0			0
$67$	−21.9759	+	124.632i	−0.327998	+	1.86017i	0.159708	+	0.987164i	$0.448945\pi$
$67$	−21.9759	+	124.632i	−0.327998	+	1.86017i	−0.487707	+	0.873008i	$0.662166\pi$
$68$		0			0
$69$	−20.3462	−	9.41811i	−0.294872	−	0.136494i
$70$		0			0
$71$	−79.6970	−	46.0131i	−1.12249	−	0.648072i	−0.180457	−	0.983583i	$-0.557758\pi$
$71$	−79.6970	−	46.0131i	−1.12249	−	0.648072i	−0.942036	+	0.335511i	$0.891091\pi$
$72$		0			0
$73$	−52.7493	−	91.3645i	−0.722593	−	1.25157i	−0.959957	−	0.280147i	$-0.909617\pi$
$73$	−52.7493	−	91.3645i	−0.722593	−	1.25157i	0.237364	−	0.971421i	$-0.423717\pi$
$74$		0			0
$75$	−40.4343	−	28.1434i	−0.539123	−	0.375246i
$76$		0			0
$77$	15.1899	+	41.7340i	0.197272	+	0.542000i
$78$		0			0
$79$	10.6681	+	60.5017i	0.135039	+	0.765845i	0.974832	+	0.222939i	$0.0715650\pi$
$79$	10.6681	+	60.5017i	0.135039	+	0.765845i	−0.839793	+	0.542906i	$0.817324\pi$
$80$		0			0
$81$	−80.9949	+	0.910006i	−0.999937	+	0.0112346i
$82$		0			0
$83$	−94.2798	+	16.6241i	−1.13590	+	0.200290i	−0.709812	−	0.704391i	$-0.751220\pi$
$83$	−94.2798	+	16.6241i	−1.13590	+	0.200290i	−0.426089	+	0.904681i	$0.640109\pi$
$84$		0			0
$85$	3.13050	−	1.13941i	0.0368295	−	0.0134048i
$86$		0			0
$87$	−26.1060	+	37.5070i	−0.300069	+	0.431115i
$88$		0			0
$89$	63.5663	−	36.7000i	0.714228	−	0.412360i	−0.0983967	−	0.995147i	$-0.531371\pi$
$89$	63.5663	−	36.7000i	0.714228	−	0.412360i	0.812624	+	0.582788i	$0.198038\pi$
$90$		0			0
$91$	−14.4918	+	25.1006i	−0.159251	+	0.275831i
$92$		0			0
$93$	15.8452	−	34.2307i	0.170378	−	0.368072i
$94$		0			0
$95$	95.1999	+	16.7863i	1.00210	+	0.176698i
$96$		0			0
$97$	28.1582	−	23.6276i	0.290291	−	0.243583i	−0.485998	−	0.873960i	$-0.661544\pi$
$97$	28.1582	−	23.6276i	0.290291	−	0.243583i	0.776290	+	0.630377i	$0.217099\pi$
$98$		0			0
$99$	58.9418	−	50.0250i	0.595372	−	0.505303i
$100$		0			0
$101$	−46.9354	+	128.954i	−0.464707	+	1.27677i	0.457201	+	0.889363i	$0.348852\pi$
$101$	−46.9354	+	128.954i	−0.464707	+	1.27677i	−0.921908	+	0.387409i	$0.873370\pi$
$102$		0			0
$103$	−52.8351	−	44.3339i	−0.512962	−	0.430427i	0.349208	−	0.937045i	$-0.386451\pi$
$103$	−52.8351	−	44.3339i	−0.512962	−	0.430427i	−0.862170	+	0.506619i	$0.830895\pi$
$104$		0			0
$105$	−11.6349	+	43.9152i	−0.110809	+	0.418240i
$106$		0			0
$107$		−	109.975i		−	1.02781i	−0.857848	−	0.513904i	$-0.828199\pi$
$107$		−	109.975i		−	1.02781i	0.857848	−	0.513904i	$-0.171801\pi$
$108$		0			0
$109$	123.810			1.13587			0.567935	−	0.823074i	$-0.307743\pi$
$109$	123.810			1.13587			0.567935	+	0.823074i	$0.307743\pi$
$110$		0			0
$111$	5.35884	+	19.7771i	0.0482778	+	0.178172i
$112$		0			0
$113$	6.59695	−	7.86194i	0.0583801	−	0.0695747i	−0.736064	−	0.676912i	$-0.763318\pi$
$113$	6.59695	−	7.86194i	0.0583801	−	0.0695747i	0.794444	+	0.607337i	$0.207762\pi$
$114$		0			0
$115$	20.5689	+	7.48648i	0.178860	+	0.0650998i
$116$		0			0
$117$	49.7339	+	8.48164i	0.425076	+	0.0724927i
$118$		0			0
$119$	3.78014	+	4.50499i	0.0317659	+	0.0378571i
$120$		0			0
$121$	8.19868	−	46.4970i	0.0677577	−	0.384273i
$122$		0			0
$123$	−35.5214	+	25.0213i	−0.288792	+	0.203425i
$124$		0			0
$125$	105.066	+	60.6599i	0.840529	+	0.485279i
$126$		0			0
$127$	−67.8518	−	117.523i	−0.534267	−	0.925377i	−0.999198	−	0.0400303i	$-0.987255\pi$
$127$	−67.8518	−	117.523i	−0.534267	−	0.925377i	0.464932	−	0.885346i	$-0.346079\pi$
$128$		0			0
$129$	5.57690	−	65.8748i	0.0432318	−	0.510657i
$130$		0			0
$131$	−8.38253	−	23.0308i	−0.0639888	−	0.175808i	0.903578	−	0.428424i	$-0.140931\pi$
$131$	−8.38253	−	23.0308i	−0.0639888	−	0.175808i	−0.967566	+	0.252617i	$0.918709\pi$
$132$		0			0
$133$	29.6324	+	168.054i	0.222800	+	1.26356i
$134$		0			0
$135$	78.7188	−	7.55589i	0.583103	−	0.0559696i
$136$		0			0
$137$	−179.801	+	31.7037i	−1.31241	+	0.231414i	−0.785688	−	0.618622i	$-0.787691\pi$
$137$	−179.801	+	31.7037i	−1.31241	+	0.231414i	−0.526724	+	0.850036i	$0.676580\pi$
$138$		0			0
$139$	−139.327	+	50.7109i	−1.00235	+	0.364827i	−0.790491	−	0.612473i	$-0.790175\pi$
$139$	−139.327	+	50.7109i	−1.00235	+	0.364827i	−0.211861	+	0.977300i	$0.567953\pi$
$140$		0			0
$141$	68.5087	+	145.847i	0.485877	+	1.03437i
$142$		0			0
$143$	−41.7015	+	24.0764i	−0.291619	+	0.168366i
$144$		0			0
$145$	22.3075	−	38.6378i	0.153845	−	0.266467i
$146$		0			0
$147$	66.5323	−	6.00917i	0.452601	−	0.0408787i
$148$		0			0
$149$	177.076	+	31.2232i	1.18843	+	0.209552i	0.732690	−	0.680563i	$-0.238265\pi$
$149$	177.076	+	31.2232i	1.18843	+	0.209552i	0.455737	+	0.890115i	$0.349376\pi$
$150$		0			0
$151$	−20.6757	+	17.3489i	−0.136925	+	0.114894i	−0.708678	−	0.705532i	$-0.750708\pi$
$151$	−20.6757	+	17.3489i	−0.136925	+	0.114894i	0.571753	+	0.820426i	$0.306264\pi$
$152$		0			0
$153$	5.06852	−	8.89395i	0.0331276	−	0.0581304i
$154$		0			0
$155$	−12.5954	+	34.6055i	−0.0812604	+	0.223261i
$156$		0			0
$157$	−14.2031	−	11.9178i	−0.0904658	−	0.0759098i	0.596433	−	0.802663i	$-0.296584\pi$
$157$	−14.2031	−	11.9178i	−0.0904658	−	0.0759098i	−0.686899	+	0.726753i	$0.741029\pi$
$158$		0			0
$159$	143.991	+	143.184i	0.905603	+	0.900530i
$160$		0			0
$161$			38.6401i			0.240000i
$162$		0			0
$163$	98.3980			0.603668			0.301834	−	0.953360i	$-0.402401\pi$
$163$	98.3980			0.603668			0.301834	+	0.953360i	$0.402401\pi$
$164$		0			0
$165$	−53.2201	+	53.5199i	−0.322546	+	0.324363i
$166$		0			0
$167$	−43.8794	+	52.2934i	−0.262751	+	0.313134i	−0.881249	−	0.472652i	$-0.843297\pi$
$167$	−43.8794	+	52.2934i	−0.262751	+	0.313134i	0.618499	+	0.785786i	$0.287741\pi$
$168$		0			0
$169$	129.279	+	47.0535i	0.764962	+	0.278423i
$170$		0			0
$171$	256.410	−	149.965i	1.49947	−	0.876988i
$172$		0			0
$173$	180.478	+	215.085i	1.04322	+	1.24327i	0.969269	+	0.246005i	$0.0791179\pi$
$173$	180.478	+	215.085i	1.04322	+	1.24327i	0.0739559	+	0.997262i	$0.476438\pi$
$174$		0			0
$175$	−14.7435	+	83.6145i	−0.0842485	+	0.477797i
$176$		0			0
$177$	25.5353	+	282.722i	0.144267	+	1.59730i
$178$		0			0
$179$	−274.462	−	158.461i	−1.53331	−	0.885256i	−0.999206	−	0.0398352i	$-0.987317\pi$
$179$	−274.462	−	158.461i	−1.53331	−	0.885256i	−0.534101	−	0.845420i	$-0.679350\pi$
$180$		0			0
$181$	−116.010	−	200.935i	−0.640939	−	1.11014i	−0.985224	−	0.171274i	$-0.945212\pi$
$181$	−116.010	−	200.935i	−0.640939	−	1.11014i	0.344285	−	0.938865i	$-0.388122\pi$
$182$		0			0
$183$	−213.631	+	100.349i	−1.16738	+	0.548357i
$184$		0			0
$185$	−6.84201	−	18.7983i	−0.0369839	−	0.101612i
$186$		0			0
$187$	1.69660	+	9.62187i	0.00907270	+	0.0514538i
$188$		0			0
$189$	60.0610	+	126.018i	0.317783	+	0.666762i
$190$		0			0
$191$	−74.4294	+	13.1239i	−0.389683	+	0.0687116i	−0.365057	−	0.930985i	$-0.618950\pi$
$191$	−74.4294	+	13.1239i	−0.389683	+	0.0687116i	−0.0246256	+	0.999697i	$0.507839\pi$
$192$		0			0
$193$	−119.419	+	43.4651i	−0.618753	+	0.225208i	−0.632329	−	0.774700i	$-0.717901\pi$
$193$	−119.419	+	43.4651i	−0.618753	+	0.225208i	0.0135760	+	0.999908i	$0.495678\pi$
$194$		0			0
$195$	−49.0808	−	4.15514i	−0.251697	−	0.0213084i
$196$		0			0
$197$	−101.232	+	58.4461i	−0.513866	+	0.296681i	−0.734422	−	0.678694i	$-0.762546\pi$
$197$	−101.232	+	58.4461i	−0.513866	+	0.296681i	0.220555	+	0.975375i	$0.429213\pi$
$198$		0			0
$199$	146.951	−	254.526i	0.738447	−	1.27903i	−0.214748	−	0.976670i	$-0.568893\pi$
$199$	146.951	−	254.526i	0.738447	−	1.27903i	0.953194	−	0.302358i	$-0.0977738\pi$
$200$		0			0
$201$	−218.638	−	310.388i	−1.08775	−	1.54422i
$202$		0			0
$203$	77.5612	+	13.6761i	0.382075	+	0.0673701i
$204$		0			0
$205$	32.4954	−	27.2668i	0.158514	−	0.133009i
$206$		0			0
$207$	63.0743	−	23.3592i	0.304707	−	0.112847i
$208$		0			0
$209$	−96.9654	+	266.410i	−0.463949	+	1.27469i
$210$		0			0
$211$	−135.466	−	113.669i	−0.642017	−	0.538716i	0.262620	−	0.964899i	$-0.415413\pi$
$211$	−135.466	−	113.669i	−0.642017	−	0.538716i	−0.904637	+	0.426183i	$0.859858\pi$
$212$		0			0
$213$	266.470	−	72.2031i	1.25103	−	0.338982i
$214$		0			0
$215$			64.5439i			0.300204i
$216$		0			0
$217$	−65.0086			−0.299579
$218$		0			0
$219$	305.940	+	81.0562i	1.39699	+	0.370119i
$220$		0			0
$221$	−4.09850	+	4.88440i	−0.0185452	+	0.0221013i
$222$		0			0
$223$	−102.190	−	37.1940i	−0.458249	−	0.166789i	0.102573	−	0.994726i	$-0.467293\pi$
$223$	−102.190	−	37.1940i	−0.458249	−	0.166789i	−0.560822	+	0.827936i	$0.689515\pi$
$224$		0			0
$225$	145.401	−	26.4812i	0.646229	−	0.117694i
$226$		0			0
$227$	−141.428	−	168.547i	−0.623030	−	0.742498i	0.358558	−	0.933507i	$-0.383268\pi$
$227$	−141.428	−	168.547i	−0.623030	−	0.742498i	−0.981588	+	0.191009i	$0.938824\pi$
$228$		0			0
$229$	79.5032	−	450.885i	0.347176	−	1.96893i	0.147620	−	0.989044i	$-0.452839\pi$
$229$	79.5032	−	450.885i	0.347176	−	1.96893i	0.199556	−	0.979886i	$-0.436050\pi$
$230$		0			0
$231$	−120.912	−	55.9691i	−0.523427	−	0.242290i
$232$		0			0
$233$	−131.519	−	75.9324i	−0.564458	−	0.325890i	0.190475	−	0.981692i	$-0.438997\pi$
$233$	−131.519	−	75.9324i	−0.564458	−	0.325890i	−0.754933	+	0.655802i	$0.772331\pi$
$234$		0			0
$235$	−78.6586	−	136.241i	−0.334718	−	0.579748i
$236$		0			0
$237$	−151.270	−	105.289i	−0.638271	−	0.444256i
$238$		0			0
$239$	129.057	+	354.581i	0.539987	+	1.48360i	0.846841	+	0.531846i	$0.178501\pi$
$239$	129.057	+	354.581i	0.539987	+	1.48360i	−0.306854	+	0.951757i	$0.599276\pi$
$240$		0			0
$241$	−17.1243	−	97.1166i	−0.0710551	−	0.402973i	−0.999503	−	0.0315117i	$-0.989968\pi$
$241$	−17.1243	−	97.1166i	−0.0710551	−	0.402973i	0.928448	−	0.371462i	$-0.121143\pi$
$242$		0			0
$243$	169.397	−	174.223i	0.697107	−	0.716967i
$244$		0			0
$245$	−64.2293	+	11.3254i	−0.262160	+	0.0462260i
$246$		0			0
$247$	−173.860	+	63.2799i	−0.703887	+	0.256194i
$248$		0			0
$249$	164.071	−	235.725i	0.658921	−	0.946685i
$250$		0			0
$251$	−112.771	+	65.1085i	−0.449288	+	0.259396i	−0.707529	−	0.706684i	$-0.750190\pi$
$251$	−112.771	+	65.1085i	−0.449288	+	0.259396i	0.258242	+	0.966080i	$0.416857\pi$
$252$		0			0
$253$	−32.0978	+	55.5951i	−0.126869	+	0.219743i
$254$		0			0
$255$	−4.19829	+	9.06968i	−0.0164639	+	0.0355674i
$256$		0			0
$257$	−275.088	−	48.5053i	−1.07038	−	0.188737i	−0.389422	−	0.921060i	$-0.627325\pi$
$257$	−275.088	−	48.5053i	−1.07038	−	0.188737i	−0.680958	+	0.732323i	$0.738436\pi$
$258$		0			0
$259$	27.0519	−	22.6993i	0.104448	−	0.0876419i
$260$		0			0
$261$	−24.5641	−	134.875i	−0.0941154	−	0.516763i
$262$		0			0
$263$	19.8615	−	54.5691i	0.0755192	−	0.207487i	−0.896189	−	0.443673i	$-0.853675\pi$
$263$	19.8615	−	54.5691i	0.0755192	−	0.207487i	0.971708	+	0.236186i	$0.0758974\pi$
$264$		0			0
$265$	−151.870	−	127.434i	−0.573095	−	0.480884i
$266$		0			0
$267$	−56.3943	+	212.856i	−0.211215	+	0.797214i
$268$		0			0
$269$		−	443.455i		−	1.64853i	−0.566203	−	0.824266i	$-0.691588\pi$
$269$		−	443.455i		−	1.64853i	0.566203	−	0.824266i	$-0.308412\pi$
$270$		0			0
$271$	517.921			1.91115			0.955574	−	0.294753i	$-0.0952373\pi$
$271$	517.921			1.91115			0.955574	+	0.294753i	$0.0952373\pi$
$272$		0			0
$273$	−22.7404	−	83.9247i	−0.0832981	−	0.307416i
$274$		0			0
$275$	−90.6704	+	108.057i	−0.329711	+	0.392934i
$276$		0			0
$277$	96.3698	+	35.0757i	0.347905	+	0.126627i	0.510062	−	0.860138i	$-0.329623\pi$
$277$	96.3698	+	35.0757i	0.347905	+	0.126627i	−0.162156	+	0.986765i	$0.551845\pi$
$278$		0			0
$279$	39.2999	+	106.117i	0.140860	+	0.380348i
$280$		0			0
$281$	−148.666	−	177.173i	−0.529060	−	0.630509i	0.433638	−	0.901087i	$-0.357230\pi$
$281$	−148.666	−	177.173i	−0.529060	−	0.630509i	−0.962698	+	0.270578i	$0.912785\pi$
$282$		0			0
$283$	−35.7541	+	202.771i	−0.126339	+	0.716506i	0.854164	+	0.520004i	$0.174070\pi$
$283$	−35.7541	+	202.771i	−0.126339	+	0.716506i	−0.980503	+	0.196503i	$0.937042\pi$
$284$		0			0
$285$	−237.091	+	167.007i	−0.831897	+	0.585989i
$286$		0			0
$287$	64.8500	+	37.4411i	0.225958	+	0.130457i
$288$		0			0
$289$	−143.853	−	249.161i	−0.497762	−	0.862149i
$290$		0			0
$291$	−9.30241	+	109.881i	−0.0319671	+	0.377597i
$292$		0			0
$293$	−77.0978	−	211.825i	−0.263133	−	0.722951i	−0.998952	−	0.0457728i	$-0.985425\pi$
$293$	−77.0978	−	211.825i	−0.263133	−	0.722951i	0.735819	−	0.677178i	$-0.236797\pi$
$294$		0			0
$295$	−48.1259	−	272.936i	−0.163139	−	0.925206i
$296$		0			0
$297$	−18.2662	+	231.206i	−0.0615023	+	0.778471i
$298$		0			0
$299$	−41.2578	+	7.27487i	−0.137986	+	0.0243307i
$300$		0			0
$301$	−107.066	+	38.9689i	−0.355702	+	0.129465i
$302$		0			0
$303$	−175.035	−	372.628i	−0.577673	−	1.22979i
$304$		0			0
$305$	199.561	−	115.217i	0.654299	−	0.377759i
$306$		0			0
$307$	−198.513	+	343.834i	−0.646621	+	1.11998i	0.337303	+	0.941396i	$0.390485\pi$
$307$	−198.513	+	343.834i	−0.646621	+	1.11998i	−0.983925	+	0.178585i	$0.942848\pi$
$308$		0			0
$309$	206.075	−	18.6126i	0.666910	−	0.0602351i
$310$		0			0
$311$	523.952	+	92.3869i	1.68473	+	0.297064i	0.932322	−	0.361629i	$-0.117779\pi$
$311$	523.952	+	92.3869i	1.68473	+	0.297064i	0.752412	+	0.658693i	$0.228890\pi$
$312$		0			0
$313$	−14.5839	+	12.2373i	−0.0465938	+	0.0390969i	−0.665787	−	0.746142i	$-0.731904\pi$
$313$	−14.5839	+	12.2373i	−0.0465938	+	0.0390969i	0.619193	+	0.785239i	$0.287460\pi$
$314$		0			0
$315$	−68.8074	−	117.647i	−0.218436	−	0.373482i
$316$		0			0
$317$	−151.494	+	416.228i	−0.477901	+	1.31302i	0.433371	+	0.901215i	$0.357324\pi$
$317$	−151.494	+	416.228i	−0.477901	+	1.31302i	−0.911272	+	0.411805i	$0.864898\pi$
$318$		0			0
$319$	100.234	+	84.1063i	0.314213	+	0.263656i
$320$		0			0
$321$	233.948	+	232.637i	0.728808	+	0.724726i
$322$		0			0
$323$			37.5406i			0.116225i
$324$		0			0
$325$	−92.0550			−0.283246
$326$		0			0
$327$	−261.901	+	263.377i	−0.800922	+	0.805434i
$328$		0			0
$329$	178.507	−	212.737i	0.542575	−	0.646616i
$330$		0			0
$331$	226.716	+	82.5177i	0.684941	+	0.249298i	0.660968	−	0.750414i	$-0.270146\pi$
$331$	226.716	+	82.5177i	0.684941	+	0.249298i	0.0239735	+	0.999713i	$0.492368\pi$
$332$		0			0
$333$	−53.4070	−	30.4358i	−0.160381	−	0.0913989i
$334$		0			0
$335$	238.260	+	283.947i	0.711223	+	0.847602i
$336$		0			0
$337$	−40.3532	+	228.854i	−0.119742	+	0.679093i	0.864550	+	0.502547i	$0.167604\pi$
$337$	−40.3532	+	228.854i	−0.119742	+	0.679093i	−0.984292	+	0.176546i	$0.943508\pi$
$338$		0			0
$339$	2.76958	+	30.6643i	0.00816987	+	0.0904551i
$340$		0			0
$341$	−93.5340	−	54.0019i	−0.274293	−	0.158363i
$342$		0			0
$343$	−184.239	−	319.111i	−0.537139	−	0.930352i
$344$		0			0
$345$	−59.4364	+	27.9191i	−0.172279	+	0.0809250i
$346$		0			0
$347$	71.4998	+	196.444i	0.206051	+	0.566121i	0.999072	−	0.0430737i	$-0.0137150\pi$
$347$	71.4998	+	196.444i	0.206051	+	0.566121i	−0.793021	+	0.609195i	$0.791493\pi$
$348$		0			0
$349$	83.7765	+	475.120i	0.240047	+	1.36138i	0.831719	+	0.555197i	$0.187357\pi$
$349$	83.7765	+	475.120i	0.240047	+	1.36138i	−0.591671	+	0.806179i	$0.701532\pi$
$350$		0			0
$351$	−123.247	+	87.8557i	−0.351132	+	0.250301i
$352$		0			0
$353$	297.212	−	52.4064i	0.841959	−	0.148460i	0.263997	−	0.964524i	$-0.414959\pi$
$353$	297.212	−	52.4064i	0.841959	−	0.148460i	0.577962	+	0.816063i	$0.303848\pi$
$354$		0			0
$355$	−253.282	+	92.1870i	−0.713469	+	0.259682i
$356$		0			0
$357$	−17.5797	−	1.48828i	−0.0492428	−	0.00416885i
$358$		0			0
$359$	−10.0982	+	5.83021i	−0.0281287	+	0.0162401i	−0.513998	−	0.857791i	$-0.671836\pi$
$359$	−10.0982	+	5.83021i	−0.0281287	+	0.0162401i	0.485870	+	0.874031i	$0.338503\pi$
$360$		0			0
$361$	−364.163	+	630.748i	−1.00876	+	1.74723i
$362$		0			0
$363$	81.5686	+	115.798i	0.224707	+	0.319004i
$364$		0			0
$365$	−304.302	−	53.6566i	−0.833704	−	0.147004i
$366$		0			0
$367$	340.230	−	285.487i	0.927057	−	0.777894i	−0.0482294	−	0.998836i	$-0.515358\pi$
$367$	340.230	−	285.487i	0.927057	−	0.777894i	0.975287	+	0.220943i	$0.0709134\pi$
$368$		0			0
$369$	21.9132	−	128.493i	0.0593854	−	0.348218i
$370$		0			0
$371$	119.697	−	328.864i	0.322632	−	0.886425i
$372$		0			0
$373$	341.772	+	286.781i	0.916278	+	0.768849i	0.973303	−	0.229524i	$-0.0737170\pi$
$373$	341.772	+	286.781i	0.916278	+	0.768849i	−0.0570249	+	0.998373i	$0.518161\pi$
$374$		0			0
$375$	−351.292	+	95.1867i	−0.936779	+	0.253831i
$376$		0			0
$377$			85.3906i			0.226500i
$378$		0			0
$379$	755.304			1.99289			0.996443	−	0.0842684i	$-0.0268553\pi$
$379$	755.304			1.99289			0.996443	+	0.0842684i	$0.0268553\pi$
$380$		0			0
$381$	393.534	+	104.263i	1.03290	+	0.273657i
$382$		0			0
$383$	207.741	−	247.577i	0.542406	−	0.646414i	−0.423320	−	0.905980i	$-0.639135\pi$
$383$	207.741	−	247.577i	0.542406	−	0.646414i	0.965725	+	0.259567i	$0.0835797\pi$
$384$		0			0
$385$	122.235	+	44.4900i	0.317494	+	0.115558i
$386$		0			0
$387$	128.336	+	151.212i	0.331618	+	0.390729i
$388$		0			0
$389$	−226.139	−	269.502i	−0.581334	−	0.692807i	0.392582	−	0.919717i	$-0.371582\pi$
$389$	−226.139	−	269.502i	−0.581334	−	0.692807i	−0.973916	+	0.226910i	$0.927138\pi$
$390$		0			0
$391$	−1.47609	+	8.37130i	−0.00377516	+	0.0214100i
$392$		0			0
$393$	66.7248	+	30.8864i	0.169783	+	0.0785913i
$394$		0			0
$395$	155.831	+	89.9690i	0.394509	+	0.227770i
$396$		0			0
$397$	−131.739	−	228.179i	−0.331837	−	0.574759i	0.651035	−	0.759048i	$-0.274335\pi$
$397$	−131.739	−	228.179i	−0.331837	−	0.574759i	−0.982872	+	0.184289i	$0.941002\pi$
$398$		0			0
$399$	−420.179	−	292.457i	−1.05308	−	0.732975i
$400$		0			0
$401$	−16.7696	−	46.0740i	−0.0418194	−	0.114898i	0.917025	−	0.398829i	$-0.130583\pi$
$401$	−16.7696	−	46.0740i	−0.0418194	−	0.114898i	−0.958845	+	0.283931i	$0.908361\pi$
$402$		0			0
$403$	−12.2393	−	69.4127i	−0.0303706	−	0.172240i
$404$		0			0
$405$	−150.445	+	183.440i	−0.371469	+	0.452937i
$406$		0			0
$407$	57.7781	−	10.1878i	0.141961	−	0.0250316i
$408$		0			0
$409$	367.169	−	133.639i	0.897724	−	0.326745i	0.148384	−	0.988930i	$-0.452593\pi$
$409$	367.169	−	133.639i	0.897724	−	0.326745i	0.749340	+	0.662185i	$0.230371\pi$
$410$		0			0
$411$	312.899	−	449.549i	0.761312	−	1.09379i
$412$		0			0
$413$	423.693	−	244.619i	1.02589	−	0.592298i
$414$		0			0
$415$	−140.199	+	242.831i	−0.337828	+	0.585135i
$416$		0			0
$417$	186.850	−	403.658i	0.448082	−	0.968004i
$418$		0			0
$419$	−150.712	−	26.5747i	−0.359695	−	0.0634240i	−0.00911972	−	0.999958i	$-0.502903\pi$
$419$	−150.712	−	26.5747i	−0.359695	−	0.0634240i	−0.350576	+	0.936534i	$0.614014\pi$
$420$		0			0
$421$	−578.991	+	485.832i	−1.37528	+	1.15399i	−0.404353	+	0.914603i	$0.632503\pi$
$421$	−578.991	+	485.832i	−1.37528	+	1.15399i	−0.970923	+	0.239391i	$0.923052\pi$
$422$		0			0
$423$	−455.175	−	162.780i	−1.07606	−	0.384824i
$424$		0			0
$425$	−6.38831	+	17.5517i	−0.0150313	+	0.0412982i
$426$		0			0
$427$	311.610	+	261.472i	0.729765	+	0.612345i
$428$		0			0
$429$	36.9965	−	139.640i	0.0862389	−	0.325502i
$430$		0			0
$431$			441.038i			1.02329i	0.859197	+	0.511645i	$0.170964\pi$
$431$			441.038i			1.02329i	−0.859197	+	0.511645i	$0.829036\pi$
$432$		0			0
$433$	324.144			0.748601			0.374301	−	0.927307i	$-0.377883\pi$
$433$	324.144			0.748601			0.374301	+	0.927307i	$0.377883\pi$
$434$		0			0
$435$	35.0047	+	129.187i	0.0804705	+	0.296981i
$436$		0			0
$437$	−158.550	+	188.952i	−0.362814	+	0.432385i
$438$		0			0
$439$	−395.622	−	143.995i	−0.901189	−	0.328006i	−0.150460	−	0.988616i	$-0.548075\pi$
$439$	−395.622	−	143.995i	−0.901189	−	0.328006i	−0.750729	+	0.660610i	$0.770298\pi$
$440$		0			0
$441$	−127.956	+	154.244i	−0.290150	+	0.349759i
$442$		0			0
$443$	−42.3882	−	50.5163i	−0.0956845	−	0.114032i	0.716077	−	0.698021i	$-0.245936\pi$
$443$	−42.3882	−	50.5163i	−0.0956845	−	0.114032i	−0.811762	+	0.583989i	$0.801491\pi$
$444$		0			0
$445$	37.3313	−	211.716i	0.0838905	−	0.475767i
$446$		0			0
$447$	−440.998	+	310.639i	−0.986572	+	0.694943i
$448$		0			0
$449$	544.844	+	314.566i	1.21346	+	0.700593i	0.963512	−	0.267666i	$-0.0862524\pi$
$449$	544.844	+	314.566i	1.21346	+	0.700593i	0.249950	+	0.968259i	$0.419586\pi$
$450$		0			0
$451$	62.2038	+	107.740i	0.137924	+	0.238892i
$452$		0			0
$453$	6.83046	−	80.6819i	0.0150783	−	0.178106i
$454$		0			0
$455$	29.0343	+	79.7711i	0.0638116	+	0.175321i
$456$		0			0
$457$	74.3220	+	421.501i	0.162630	+	0.922322i	0.951474	+	0.307728i	$0.0995688\pi$
$457$	74.3220	+	421.501i	0.162630	+	0.922322i	−0.788844	+	0.614593i	$0.789320\pi$
$458$		0			0
$459$	8.19811	+	29.5960i	0.0178608	+	0.0644792i
$460$		0			0
$461$	816.328	−	143.941i	1.77078	−	0.312236i	0.809356	−	0.587318i	$-0.199816\pi$
$461$	816.328	−	143.941i	1.77078	−	0.312236i	0.961421	+	0.275083i	$0.0887052\pi$
$462$		0			0
$463$	599.606	−	218.239i	1.29504	−	0.471358i	0.399665	−	0.916661i	$-0.369126\pi$
$463$	599.606	−	218.239i	1.29504	−	0.471358i	0.895380	+	0.445304i	$0.146904\pi$
$464$		0			0
$465$	−46.9715	−	99.9966i	−0.101014	−	0.215046i
$466$		0			0
$467$	−494.230	+	285.344i	−1.05831	+	0.611015i	−0.924964	−	0.380055i	$-0.875905\pi$
$467$	−494.230	+	285.344i	−1.05831	+	0.611015i	−0.133345	+	0.991070i	$0.542572\pi$
$468$		0			0
$469$	−327.163	+	566.663i	−0.697576	+	1.20824i
$470$		0			0
$471$	55.3971	−	5.00344i	0.117616	−	0.0106230i
$472$		0			0
$473$	−186.417	−	32.8704i	−0.394117	−	0.0694934i
$474$		0			0
$475$	−415.188	+	348.384i	−0.874080	+	0.733440i
$476$		0			0
$477$	−609.183	+	3.42209i	−1.27711	+	0.00717418i
$478$		0			0
$479$	243.428	−	668.812i	0.508200	−	1.39627i	−0.374893	−	0.927068i	$-0.622321\pi$
$479$	243.428	−	668.812i	0.508200	−	1.39627i	0.883093	−	0.469199i	$-0.155457\pi$
$480$		0			0
$481$	29.3302	+	24.6110i	0.0609775	+	0.0511662i
$482$		0			0
$483$	−82.1978	−	81.7374i	−0.170182	−	0.169229i
$484$		0			0
$485$		−	107.661i		−	0.221981i
$486$		0			0
$487$	218.973			0.449636			0.224818	−	0.974401i	$-0.427821\pi$
$487$	218.973			0.449636			0.224818	+	0.974401i	$0.427821\pi$
$488$		0			0
$489$	−208.146	+	209.319i	−0.425657	+	0.428055i
$490$		0			0
$491$	118.919	−	141.722i	0.242198	−	0.288640i	−0.631228	−	0.775597i	$-0.717449\pi$
$491$	118.919	−	141.722i	0.242198	−	0.288640i	0.873426	+	0.486957i	$0.161893\pi$
$492$		0			0
$493$	16.2811	+	5.92582i	0.0330245	+	0.0120199i
$494$		0			0
$495$	−1.27195	−	226.427i	−0.00256960	−	0.457428i
$496$		0			0
$497$	−305.842	−	364.488i	−0.615376	−	0.733377i
$498$		0			0
$499$	−45.3528	+	257.209i	−0.0908874	+	0.515448i	0.905043	+	0.425321i	$0.139839\pi$
$499$	−45.3528	+	257.209i	−0.0908874	+	0.515448i	−0.995930	+	0.0901277i	$0.971272\pi$
$500$		0			0
$501$	−18.4218	−	203.962i	−0.0367700	−	0.407110i
$502$		0			0
$503$	112.328	+	64.8525i	0.223316	+	0.128931i	0.607485	−	0.794331i	$-0.292179\pi$
$503$	112.328	+	64.8525i	0.223316	+	0.128931i	−0.384169	+	0.923263i	$0.625512\pi$
$504$		0			0
$505$	200.967	+	348.086i	0.397955	+	0.689278i
$506$		0			0
$507$	−373.565	+	175.476i	−0.736816	+	0.346106i
$508$		0			0
$509$	−257.981	−	708.796i	−0.506838	−	1.39253i	−0.884481	−	0.466576i	$-0.845488\pi$
$509$	−257.981	−	708.796i	−0.506838	−	1.39253i	0.377643	−	0.925951i	$-0.376735\pi$
$510$		0			0
$511$	−94.7185	−	537.176i	−0.185359	−	1.05122i
$512$		0			0
$513$	−223.381	+	862.681i	−0.435441	+	1.68164i
$514$		0			0
$515$	−198.942	+	35.0789i	−0.386295	+	0.0681143i
$516$		0			0
$517$	433.553	−	157.800i	0.838593	−	0.305223i
$518$		0			0
$519$	−839.319	−	71.0560i	−1.61718	−	0.136909i
$520$		0			0
$521$	343.653	−	198.408i	0.659603	−	0.380822i	−0.132523	−	0.991180i	$-0.542308\pi$
$521$	343.653	−	198.408i	0.659603	−	0.380822i	0.792126	+	0.610358i	$0.208974\pi$
$522$		0			0
$523$	−71.8797	+	124.499i	−0.137437	+	0.238048i	−0.926526	−	0.376231i	$-0.877220\pi$
$523$	−71.8797	+	124.499i	−0.137437	+	0.238048i	0.789089	+	0.614279i	$0.210553\pi$
$524$		0			0
$525$	−146.683	−	208.238i	−0.279396	−	0.396643i
$526$		0			0
$527$	−14.0840	−	2.48339i	−0.0267249	−	0.00471231i
$528$		0			0
$529$	362.452	−	304.134i	0.685165	−	0.574922i
$530$		0			0
$531$	−655.442	−	543.736i	−1.23435	−	1.02399i
$532$		0			0
$533$	−27.7682	+	76.2925i	−0.0520979	+	0.143138i
$534$		0			0
$535$	−246.749	−	207.047i	−0.461214	−	0.387004i
$536$		0			0
$537$	917.673	−	248.654i	1.70889	−	0.463044i
$538$		0			0
$539$		−	191.276i		−	0.354873i
$540$		0			0
$541$	−511.807			−0.946038			−0.473019	−	0.881052i	$-0.656836\pi$
$541$	−511.807			−0.946038			−0.473019	+	0.881052i	$0.656836\pi$
$542$		0			0
$543$	672.845	+	178.264i	1.23913	+	0.328295i
$544$		0			0
$545$	233.093	−	277.789i	0.427693	−	0.509705i
$546$		0			0
$547$	−745.287	−	271.262i	−1.36250	−	0.495909i	−0.445673	−	0.895196i	$-0.647036\pi$
$547$	−745.287	−	271.262i	−1.36250	−	0.495909i	−0.916826	+	0.399286i	$0.869258\pi$
$548$		0			0
$549$	238.436	−	666.726i	0.434309	−	1.21444i
$550$		0			0
$551$	323.163	+	385.130i	0.586502	+	0.698966i
$552$		0			0
$553$	−55.1575	+	312.814i	−0.0997424	+	0.565667i
$554$		0			0
$555$	54.4623	+	25.2102i	0.0981303	+	0.0454238i
$556$		0			0
$557$	−290.915	−	167.960i	−0.522289	−	0.301543i	0.215582	−	0.976486i	$-0.430835\pi$
$557$	−290.915	−	167.960i	−0.522289	−	0.301543i	−0.737871	+	0.674942i	$0.764169\pi$
$558$		0			0
$559$	−61.7666	−	106.983i	−0.110495	−	0.191383i
$560$		0			0
$561$	−24.0572	−	16.7445i	−0.0428827	−	0.0298477i
$562$		0			0
$563$	−270.154	−	742.242i	−0.479847	−	1.31837i	−0.909623	−	0.415434i	$-0.863630\pi$
$563$	−270.154	−	742.242i	−0.479847	−	1.31837i	0.429776	−	0.902935i	$-0.358592\pi$
$564$		0			0
$565$	−5.21978	−	29.6029i	−0.00923855	−	0.0523944i
$566$		0			0
$567$	−395.124	−	138.807i	−0.696869	−	0.244809i
$568$		0			0
$569$	126.461	−	22.2984i	0.222251	−	0.0391888i	−0.0614138	−	0.998112i	$-0.519561\pi$
$569$	126.461	−	22.2984i	0.222251	−	0.0391888i	0.283664	+	0.958924i	$0.408450\pi$
$570$		0			0
$571$	240.668	−	87.5960i	0.421485	−	0.153408i	−0.122565	−	0.992460i	$-0.539112\pi$
$571$	240.668	−	87.5960i	0.421485	−	0.153408i	0.544051	+	0.839052i	$0.316890\pi$
$572$		0			0
$573$	129.526	−	186.093i	0.226050	−	0.324770i
$574$		0			0
$575$	−106.283	+	61.3623i	−0.184839	+	0.106717i
$576$		0			0
$577$	−216.309	+	374.658i	−0.374885	+	0.649320i	−0.990310	−	0.138875i	$-0.955651\pi$
$577$	−216.309	+	374.658i	−0.374885	+	0.649320i	0.615425	+	0.788196i	$0.288985\pi$
$578$		0			0
$579$	160.152	−	345.981i	0.276601	−	0.597549i
$580$		0			0
$581$	−487.458	−	85.9520i	−0.838998	−	0.147938i
$582$		0			0
$583$	445.402	−	373.737i	0.763983	−	0.641058i
$584$		0			0
$585$	112.662	−	95.6186i	0.192585	−	0.163451i
$586$		0			0
$587$	299.625	−	823.213i	0.510434	−	1.40241i	−0.370352	−	0.928892i	$-0.620763\pi$
$587$	299.625	−	823.213i	0.510434	−	1.40241i	0.880786	−	0.473515i	$-0.157015\pi$
$588$		0			0
$589$	−317.896	−	266.747i	−0.539722	−	0.452881i
$590$		0			0
$591$	89.8101	−	338.981i	0.151963	−	0.573573i
$592$		0			0
$593$			811.453i			1.36839i	0.729301	+	0.684193i	$0.239845\pi$
$593$			811.453i			1.36839i	−0.729301	+	0.684193i	$0.760155\pi$
$594$		0			0
$595$	17.2245			0.0289487
$596$		0			0
$597$	230.593	+	851.018i	0.386254	+	1.42549i
$598$		0			0
$599$	−415.664	+	495.369i	−0.693930	+	0.826994i	−0.991825	−	0.127605i	$-0.959271\pi$
$599$	−415.664	+	495.369i	−0.693930	+	0.826994i	0.297895	+	0.954599i	$0.403716\pi$
$600$		0			0
$601$	−189.910	−	69.1215i	−0.315990	−	0.115011i	0.179156	−	0.983821i	$-0.442663\pi$
$601$	−189.910	−	69.1215i	−0.315990	−	0.115011i	−0.495146	+	0.868810i	$0.664885\pi$
$602$		0			0
$603$	1122.78	+	191.479i	1.86199	+	0.317544i
$604$		0			0
$605$	−88.8889	−	105.934i	−0.146924	−	0.175097i
$606$		0			0
$607$	117.693	−	667.467i	0.193892	−	1.09962i	−0.720096	−	0.693875i	$-0.755902\pi$
$607$	117.693	−	667.467i	0.193892	−	1.09962i	0.913988	−	0.405742i	$-0.132987\pi$
$608$		0			0
$609$	−193.162	+	136.064i	−0.317179	+	0.223422i
$610$		0			0
$611$	260.757	+	150.548i	0.426771	+	0.246396i
$612$		0			0
$613$	−309.577	−	536.204i	−0.505020	−	0.874721i	−0.999983	−	0.00580667i	$-0.998152\pi$
$613$	−309.577	−	536.204i	−0.505020	−	0.874721i	0.494963	−	0.868914i	$-0.335182\pi$
$614$		0			0
$615$	−10.7352	+	126.805i	−0.0174557	+	0.206188i
$616$		0			0
$617$	−9.59799	−	26.3703i	−0.0155559	−	0.0427395i	0.931672	−	0.363301i	$-0.118350\pi$
$617$	−9.59799	−	26.3703i	−0.0155559	−	0.0427395i	−0.947228	+	0.320562i	$0.896128\pi$
$618$		0			0
$619$	−77.8850	−	441.708i	−0.125824	−	0.713583i	−0.980815	−	0.194940i	$-0.937549\pi$
$619$	−77.8850	−	441.708i	−0.125824	−	0.713583i	0.854991	−	0.518643i	$-0.173562\pi$
$620$		0			0
$621$	−83.7330	+	183.589i	−0.134836	+	0.295635i
$622$		0			0
$623$	373.737	−	65.8999i	0.599898	−	0.105778i
$624$		0			0
$625$	−51.8724	+	18.8800i	−0.0829959	+	0.0302080i
$626$		0			0
$627$	−361.610	−	769.823i	−0.576731	−	1.22779i
$628$		0			0
$629$	6.72788	−	3.88435i	0.0106962	−	0.00617543i
$630$		0			0
$631$	−402.008	+	696.299i	−0.637097	+	1.10348i	0.348970	+	0.937134i	$0.386532\pi$
$631$	−402.008	+	696.299i	−0.637097	+	1.10348i	−0.986067	+	0.166350i	$0.946802\pi$
$632$		0			0
$633$	528.362	−	47.7215i	0.834696	−	0.0753894i
$634$		0			0
$635$	−391.426	−	69.0189i	−0.616419	−	0.108691i
$636$		0			0
$637$	95.6235	−	80.2376i	0.150115	−	0.125962i
$638$		0			0
$639$	−410.082	+	719.588i	−0.641756	+	1.12612i
$640$		0			0
$641$	−41.6523	+	114.439i	−0.0649802	+	0.178532i	−0.967933	−	0.251208i	$-0.919172\pi$
$641$	−41.6523	+	114.439i	−0.0649802	+	0.178532i	0.902953	+	0.429739i	$0.141395\pi$
$642$		0			0
$643$	273.951	+	229.872i	0.426052	+	0.357500i	0.830460	−	0.557079i	$-0.188078\pi$
$643$	273.951	+	229.872i	0.426052	+	0.357500i	−0.404408	+	0.914579i	$0.632522\pi$
$644$		0			0
$645$	−137.302	−	136.533i	−0.212872	−	0.211679i
$646$		0			0
$647$			142.711i			0.220573i	0.993900	+	0.110287i	$0.0351769\pi$
$647$			142.711i			0.220573i	−0.993900	+	0.110287i	$0.964823\pi$
$648$		0			0
$649$	812.809			1.25240
$650$		0			0
$651$	137.516	−	138.291i	0.211238	−	0.212428i
$652$		0			0
$653$	−808.810	+	963.902i	−1.23861	+	1.47611i	−0.414130	+	0.910218i	$0.635914\pi$
$653$	−808.810	+	963.902i	−1.23861	+	1.47611i	−0.824477	+	0.565896i	$0.808530\pi$
$654$		0			0
$655$	−67.4552	−	24.5517i	−0.102985	−	0.0374835i
$656$		0			0
$657$	−819.600	+	479.355i	−1.24749	+	0.729612i
$658$		0			0
$659$	−51.7614	−	61.6869i	−0.0785454	−	0.0936068i	0.725341	−	0.688390i	$-0.241682\pi$
$659$	−51.7614	−	61.6869i	−0.0785454	−	0.0936068i	−0.803886	+	0.594783i	$0.797238\pi$
$660$		0			0
$661$	−38.8436	+	220.293i	−0.0587649	+	0.333272i	−0.999990	−	0.00450823i	$-0.998565\pi$
$661$	−38.8436	+	220.293i	−0.0587649	+	0.333272i	0.941225	+	0.337780i	$0.109676\pi$
$662$		0			0
$663$	−1.72066	−	19.0508i	−0.00259527	−	0.0287343i
$664$		0			0
$665$	432.847	+	249.904i	0.650897	+	0.375796i
$666$		0			0
$667$	56.9200	+	98.5883i	0.0853373	+	0.147809i
$668$		0			0
$669$	295.289	−	138.706i	0.441388	−	0.207334i
$670$		0			0
$671$	231.141	+	635.054i	0.344472	+	0.946429i
$672$		0			0
$673$	−195.214	−	1107.11i	−0.290065	−	1.64504i	−0.686610	−	0.727026i	$-0.740902\pi$
$673$	−195.214	−	1107.11i	−0.290065	−	1.64504i	0.396545	−	0.918015i	$-0.370209\pi$
$674$		0			0
$675$	−251.243	+	365.325i	−0.372212	+	0.541223i
$676$		0			0
$677$	−202.718	+	35.7446i	−0.299436	+	0.0527986i	−0.321348	−	0.946961i	$-0.604136\pi$
$677$	−202.718	+	35.7446i	−0.299436	+	0.0527986i	0.0219120	+	0.999760i	$0.493025\pi$
$678$		0			0
$679$	178.589	−	65.0012i	0.263018	−	0.0957307i
$680$		0			0
$681$	657.715	+	55.6816i	0.965808	+	0.0817644i
$682$		0			0
$683$	−68.6095	+	39.6117i	−0.100453	+	0.0579966i	−0.549385	−	0.835569i	$-0.685138\pi$
$683$	−68.6095	+	39.6117i	−0.100453	+	0.0579966i	0.448932	+	0.893566i	$0.351805\pi$
$684$		0			0
$685$	−267.372	+	463.102i	−0.390324	+	0.676061i
$686$		0			0
$687$	790.977	+	1122.91i	1.15135	+	1.63451i
$688$		0			0
$689$	373.679	+	65.8897i	0.542350	+	0.0956309i
$690$		0			0
$691$	−362.390	+	304.082i	−0.524443	+	0.440060i	−0.866177	−	0.499737i	$-0.833430\pi$
$691$	−362.390	+	304.082i	−0.524443	+	0.440060i	0.341734	+	0.939797i	$0.388986\pi$
$692$		0			0
$693$	374.832	−	138.817i	0.540883	−	0.200313i
$694$		0			0
$695$	−148.528	+	408.077i	−0.213709	+	0.587161i
$696$		0			0
$697$	12.6193	+	10.5889i	0.0181052	+	0.0151921i
$698$		0			0
$699$	439.737	−	119.152i	0.629095	−	0.170461i
$700$		0			0
$701$			659.567i			0.940895i	0.882428	+	0.470448i	$0.155908\pi$
$701$			659.567i			0.940895i	−0.882428	+	0.470448i	$0.844092\pi$
$702$		0			0
$703$	225.426			0.320663
$704$		0			0
$705$	456.212	+	120.869i	0.647109	+	0.171446i
$706$		0			0
$707$	−456.073	+	543.527i	−0.645082	+	0.768779i
$708$		0			0
$709$	−343.375	−	124.978i	−0.484309	−	0.176274i	0.0883141	−	0.996093i	$-0.471852\pi$
$709$	−343.375	−	124.978i	−0.484309	−	0.176274i	−0.572624	+	0.819818i	$0.694074\pi$
$710$		0			0
$711$	543.968	−	99.0701i	0.765074	−	0.139339i
$712$		0			0
$713$	−60.4004	−	71.9824i	−0.0847130	−	0.100957i
$714$		0			0
$715$	−24.4905	+	138.893i	−0.0342525	+	0.194255i
$716$		0			0
$717$	−1027.29	−	475.525i	−1.43276	−	0.663215i
$718$		0			0
$719$	391.257	+	225.893i	0.544169	+	0.314176i	0.746767	−	0.665086i	$-0.231605\pi$
$719$	391.257	+	225.893i	0.544169	+	0.314176i	−0.202598	+	0.979262i	$0.564938\pi$
$720$		0			0
$721$	−178.302	−	308.829i	−0.247299	−	0.428334i
$722$		0			0
$723$	242.817	+	169.008i	0.335847	+	0.233759i
$724$		0			0
$725$	85.5537	+	235.057i	0.118005	+	0.324216i
$726$		0			0
$727$	38.4206	+	217.894i	0.0528481	+	0.299717i	0.999763	−	0.0217676i	$-0.00692939\pi$
$727$	38.4206	+	217.894i	0.0528481	+	0.299717i	−0.946915	+	0.321484i	$0.895818\pi$
$728$		0			0
$729$	12.2848	+	728.896i	0.0168515	+	0.999858i
$730$		0			0
$731$	−24.6844	+	4.35252i	−0.0337679	+	0.00595420i
$732$		0			0
$733$	991.436	−	360.853i	1.35257	−	0.492296i	0.438823	−	0.898573i	$-0.355395\pi$
$733$	991.436	−	360.853i	1.35257	−	0.492296i	0.913750	+	0.406277i	$0.133173\pi$
$734$		0			0
$735$	111.776	−	160.590i	0.152076	−	0.218490i
$736$		0			0
$737$	−941.441	+	543.541i	−1.27740	+	0.737505i
$738$		0			0
$739$	−407.744	+	706.234i	−0.551751	+	0.955661i	0.446397	+	0.894835i	$0.352707\pi$
$739$	−407.744	+	706.234i	−0.551751	+	0.955661i	−0.998148	+	0.0608262i	$0.980626\pi$
$740$		0			0
$741$	233.162	−	503.707i	0.314659	−	0.679766i
$742$		0			0
$743$	−676.258	−	119.242i	−0.910172	−	0.160488i	−0.301091	−	0.953596i	$-0.597351\pi$
$743$	−676.258	−	119.242i	−0.910172	−	0.160488i	−0.609081	+	0.793108i	$0.708462\pi$
$744$		0			0
$745$	403.429	−	338.517i	0.541516	−	0.454386i
$746$		0			0
$747$	154.381	+	847.665i	0.206668	+	1.13476i
$748$		0			0
$749$	194.476	−	534.318i	0.259647	−	0.713375i
$750$		0			0
$751$	207.687	+	174.270i	0.276548	+	0.232051i	0.770503	−	0.637436i	$-0.220005\pi$
$751$	207.687	+	174.270i	0.276548	+	0.232051i	−0.493956	+	0.869487i	$0.664449\pi$
$752$		0			0
$753$	100.048	−	377.622i	0.132865	−	0.501490i
$754$		0			0
$755$			79.0518i			0.104704i
$756$		0			0
$757$	724.827			0.957499			0.478750	−	0.877951i	$-0.341090\pi$
$757$	724.827			0.957499			0.478750	+	0.877951i	$0.341090\pi$
$758$		0			0
$759$	−50.3675	−	185.884i	−0.0663603	−	0.244906i
$760$		0			0
$761$	98.1598	−	116.982i	0.128988	−	0.153722i	−0.697685	−	0.716405i	$-0.745786\pi$
$761$	98.1598	−	116.982i	0.128988	−	0.153722i	0.826673	+	0.562683i	$0.190231\pi$
$762$		0			0
$763$	601.532	+	218.940i	0.788378	+	0.286946i
$764$		0			0
$765$	−10.4128	−	28.1165i	−0.0136115	−	0.0367536i
$766$		0			0
$767$	340.961	+	406.342i	0.444539	+	0.529781i
$768$		0			0
$769$	75.3696	−	427.442i	0.0980099	−	0.555842i	−0.895773	−	0.444511i	$-0.853377\pi$
$769$	75.3696	−	427.442i	0.0980099	−	0.555842i	0.993783	−	0.111331i	$-0.0355114\pi$
$770$		0			0
$771$	685.091	−	482.579i	0.888575	−	0.625914i
$772$		0			0
$773$	−501.382	−	289.473i	−0.648619	−	0.374480i	0.139308	−	0.990249i	$-0.455512\pi$
$773$	−501.382	−	289.473i	−0.648619	−	0.374480i	−0.787927	+	0.615769i	$0.788845\pi$
$774$		0			0
$775$	−103.237	−	178.811i	−0.133209	−	0.230724i
$776$		0			0
$777$	−8.93693	+	105.564i	−0.0115018	+	0.135861i
$778$		0			0
$779$	163.490	+	449.185i	0.209872	+	0.576618i
$780$		0			0
$781$	−137.267	−	778.483i	−0.175759	−	0.996777i
$782$		0			0
$783$	338.878	+	233.054i	0.432794	+	0.297642i
$784$		0			0
$785$	−53.4796	+	9.42989i	−0.0681268	+	0.0120126i
$786$		0			0
$787$	−78.3658	+	28.5228i	−0.0995754	+	0.0362425i	−0.391327	−	0.920252i	$-0.627984\pi$
$787$	−78.3658	+	28.5228i	−0.0995754	+	0.0362425i	0.291752	+	0.956494i	$0.405762\pi$
$788$		0			0
$789$	74.0691	+	157.684i	0.0938772	+	0.199853i
$790$		0			0
$791$	45.9541	−	26.5316i	0.0580962	−	0.0335419i
$792$		0			0
$793$	−220.518	+	381.948i	−0.278081	+	0.481650i
$794$		0			0
$795$	592.346	−	53.5005i	0.745090	−	0.0672962i
$796$		0			0
$797$	24.7309	+	4.36073i	0.0310300	+	0.00547143i	0.189142	−	0.981950i	$-0.439429\pi$
$797$	24.7309	+	4.36073i	0.0310300	+	0.00547143i	−0.158112	+	0.987421i	$0.550541\pi$
$798$		0			0
$799$	46.8000	−	39.2699i	0.0585732	−	0.0491488i
$800$		0			0
$801$	−333.509	−	570.232i	−0.416365	−	0.711900i
$802$		0			0
$803$	309.945	−	851.566i	0.385984	−	1.06048i
$804$		0			0
$805$	86.6958	+	72.7464i	0.107697	+	0.0903682i
$806$		0			0
$807$	943.349	+	938.064i	1.16896	+	1.16241i
$808$		0			0
$809$		−	86.0087i		−	0.106315i	−0.998586	−	0.0531574i	$-0.983071\pi$
$809$		−	86.0087i		−	0.106315i	0.998586	−	0.0531574i	$-0.0169285\pi$
$810$		0			0
$811$	−636.808			−0.785214			−0.392607	−	0.919706i	$-0.628427\pi$
$811$	−636.808			−0.785214			−0.392607	+	0.919706i	$0.628427\pi$
$812$		0			0
$813$	−1095.59	+	1101.76i	−1.34758	+	1.35518i
$814$		0			0
$815$	185.251	−	220.773i	0.227302	−	0.270887i
$816$		0			0
$817$	−683.460	−	248.759i	−0.836549	−	0.304479i
$818$		0			0
$819$	226.634	+	129.155i	0.276721	+	0.157699i
$820$		0			0
$821$	362.517	+	432.031i	0.441555	+	0.526225i	0.940219	−	0.340570i	$-0.110620\pi$
$821$	362.517	+	432.031i	0.441555	+	0.526225i	−0.498664	+	0.866796i	$0.666176\pi$
$822$		0			0
$823$	19.3815	−	109.918i	0.0235499	−	0.133558i	−0.970766	−	0.240027i	$-0.922844\pi$
$823$	19.3815	−	109.918i	0.0235499	−	0.133558i	0.994316	+	0.106470i	$0.0339547\pi$
$824$		0			0
$825$	−38.0660	−	421.459i	−0.0461406	−	0.510859i
$826$		0			0
$827$	−732.643	−	422.992i	−0.885905	−	0.511477i	−0.0133039	−	0.999911i	$-0.504235\pi$
$827$	−732.643	−	422.992i	−0.885905	−	0.511477i	−0.872601	+	0.488434i	$0.837568\pi$
$828$		0			0
$829$	−792.472	−	1372.60i	−0.955937	−	1.65573i	−0.732209	−	0.681080i	$-0.761511\pi$
$829$	−792.472	−	1372.60i	−0.955937	−	1.65573i	−0.223728	−	0.974652i	$-0.571823\pi$
$830$		0			0
$831$	−278.472	+	130.807i	−0.335104	+	0.157409i
$832$		0			0
$833$	−8.66262	−	23.8003i	−0.0103993	−	0.0285718i
$834$		0			0
$835$	34.7192	+	196.902i	0.0415799	+	0.235811i
$836$		0			0
$837$	−308.873	−	140.874i	−0.369024	−	0.168308i
$838$		0			0
$839$	−1495.60	+	263.715i	−1.78260	+	0.314321i	−0.965154	−	0.261683i	$-0.915723\pi$
$839$	−1495.60	+	263.715i	−1.78260	+	0.314321i	−0.817447	+	0.576003i	$0.804612\pi$
$840$		0			0
$841$	−572.242	+	208.279i	−0.680430	+	0.247656i
$842$		0			0
$843$	691.376	+	58.5313i	0.820138	+	0.0694321i
$844$		0			0
$845$	348.962	−	201.473i	0.412972	−	0.238430i
$846$		0			0
$847$	122.057	−	211.408i	0.144105	−	0.249597i
$848$		0			0
$849$	−355.717	−	504.992i	−0.418983	−	0.594808i
$850$		0			0
$851$	50.2686	+	8.86372i	0.0590701	+	0.0104156i
$852$		0			0
$853$	−55.4944	+	46.5654i	−0.0650580	+	0.0545901i	−0.674737	−	0.738058i	$-0.735743\pi$
$853$	−55.4944	+	46.5654i	−0.0650580	+	0.0545901i	0.609679	+	0.792649i	$0.291298\pi$
$854$		0			0
$855$	146.261	−	857.635i	0.171066	−	1.00308i
$856$		0			0
$857$	−348.367	+	957.131i	−0.406496	+	1.11684i	0.552523	+	0.833498i	$0.313665\pi$
$857$	−348.367	+	957.131i	−0.406496	+	1.11684i	−0.959019	+	0.283342i	$0.908557\pi$
$858$		0			0
$859$	379.573	+	318.500i	0.441878	+	0.370780i	0.836412	−	0.548102i	$-0.184649\pi$
$859$	379.573	+	318.500i	0.441878	+	0.370780i	−0.394534	+	0.918881i	$0.629094\pi$
$860$		0			0
$861$	−216.828	+	58.7521i	−0.251833	+	0.0682371i
$862$		0			0
$863$			827.531i			0.958900i	0.877569	+	0.479450i	$0.159164\pi$
$863$			827.531i			0.958900i	−0.877569	+	0.479450i	$0.840836\pi$
$864$		0			0
$865$	822.361			0.950707
$866$		0			0
$867$	834.333	+	221.049i	0.962322	+	0.254959i
$868$		0			0
$869$	−339.211	+	404.256i	−0.390346	+	0.465197i
$870$		0			0
$871$	−666.649	−	242.640i	−0.765384	−	0.278577i
$872$		0			0
$873$	−214.068	−	252.226i	−0.245210	−	0.288918i
$874$		0			0
$875$	403.197	+	480.512i	0.460797	+	0.549156i
$876$		0			0
$877$	206.829	−	1172.98i	0.235837	−	1.33750i	−0.605008	−	0.796219i	$-0.706830\pi$
$877$	206.829	−	1172.98i	0.235837	−	1.33750i	0.840845	−	0.541276i	$-0.182059\pi$
$878$		0			0
$879$	613.697	+	284.076i	0.698177	+	0.323181i
$880$		0			0
$881$	1011.68	+	584.096i	1.14834	+	0.662993i	0.948481	−	0.316833i	$-0.102619\pi$
$881$	1011.68	+	584.096i	1.14834	+	0.662993i	0.199855	+	0.979825i	$0.435953\pi$
$882$		0			0
$883$	−387.243	−	670.725i	−0.438554	−	0.759598i	0.559024	−	0.829152i	$-0.311176\pi$
$883$	−387.243	−	670.725i	−0.438554	−	0.759598i	−0.997578	+	0.0695531i	$0.977843\pi$
$884$		0			0
$885$	682.411	+	474.979i	0.771086	+	0.536699i
$886$		0			0
$887$	−514.115	−	1412.52i	−0.579611	−	1.59247i	−0.788838	−	0.614601i	$-0.789317\pi$
$887$	−514.115	−	1412.52i	−0.579611	−	1.59247i	0.209227	−	0.977867i	$-0.432905\pi$
$888$		0			0
$889$	−121.837	−	690.973i	−0.137050	−	0.777248i
$890$		0			0
$891$	−453.198	−	527.939i	−0.508639	−	0.592524i
$892$		0			0
$893$	1745.82	−	307.836i	1.95501	−	0.344721i
$894$		0			0
$895$	−872.256	+	317.475i	−0.974588	+	0.354721i
$896$		0			0
$897$	71.7993	−	103.155i	0.0800438	−	0.115000i
$898$		0			0
$899$	−165.866	+	95.7630i	−0.184501	+	0.106522i
$900$		0			0
$901$	38.4950	−	66.6753i	0.0427247	−	0.0740014i
$902$		0			0
$903$	143.586	−	310.192i	0.159009	−	0.343513i
$904$		0			0
$905$	−669.242	−	118.005i	−0.739494	−	0.130393i
$906$		0			0
$907$	−417.913	+	350.670i	−0.460764	+	0.386627i	−0.843412	−	0.537268i	$-0.819457\pi$
$907$	−417.913	+	350.670i	−0.460764	+	0.386627i	0.382648	+	0.923894i	$0.375012\pi$
$908$		0			0
$909$	1162.94	+	415.893i	1.27936	+	0.457528i
$910$		0			0
$911$	284.602	−	781.938i	0.312406	−	0.858329i	−0.679763	−	0.733431i	$-0.737918\pi$
$911$	284.602	−	781.938i	0.312406	−	0.858329i	0.992170	−	0.124897i	$-0.0398602\pi$
$912$		0			0
$913$	−629.952	−	528.592i	−0.689980	−	0.578962i
$914$		0			0
$915$	−177.045	+	668.244i	−0.193492	+	0.730322i
$916$		0			0
$917$		−	126.719i		−	0.138189i
$918$		0			0
$919$	75.3946			0.0820398			0.0410199	−	0.999158i	$-0.486939\pi$
$919$	75.3946			0.0820398			0.0410199	+	0.999158i	$0.486939\pi$
$920$		0			0
$921$	−311.503	−	1149.62i	−0.338223	−	1.24823i
$922$		0			0
$923$	331.600	−	395.185i	0.359263	−	0.428153i
$924$		0			0
$925$	105.396	+	38.3610i	0.113942	+	0.0414713i
$926$		0			0
$927$	−396.328	+	477.750i	−0.427538	+	0.515372i
$928$		0			0
$929$	−791.162	−	942.870i	−0.851628	−	1.01493i	−0.999663	−	0.0259483i	$-0.991739\pi$
$929$	−791.162	−	942.870i	−0.851628	−	1.01493i	0.148036	−	0.988982i	$-0.452705\pi$
$930$		0			0
$931$	127.622	−	723.779i	0.137080	−	0.777421i
$932$		0			0
$933$	−1304.88	+	919.157i	−1.39858	+	0.985163i
$934$		0			0
$935$	24.7825	+	14.3082i	0.0265053	+	0.0153029i
$936$		0			0
$937$	790.426	+	1369.06i	0.843571	+	1.46111i	0.886857	+	0.462045i	$0.152884\pi$
$937$	790.426	+	1369.06i	0.843571	+	1.46111i	−0.0432859	+	0.999063i	$0.513783\pi$
$938$		0			0
$939$	4.81796	−	56.9101i	0.00513095	−	0.0606071i
$940$		0			0
$941$	455.549	+	1251.61i	0.484111	+	1.33009i	0.905939	+	0.423409i	$0.139167\pi$
$941$	455.549	+	1251.61i	0.484111	+	1.33009i	−0.421827	+	0.906676i	$0.638611\pi$
$942$		0			0
$943$	18.7954	+	106.594i	0.0199315	+	0.113037i
$944$		0			0
$945$	395.819	+	102.493i	0.418856	+	0.108458i
$946$		0			0
$947$	−1216.44	+	214.491i	−1.28452	+	0.226496i	−0.773899	−	0.633310i	$-0.781696\pi$
$947$	−1216.44	+	214.491i	−1.28452	+	0.226496i	−0.510622	+	0.859805i	$0.670585\pi$
$948$		0			0
$949$	555.735	−	202.271i	0.585600	−	0.213141i
$950$		0			0
$951$	−564.964	−	1202.74i	−0.594074	−	1.26471i
$952$		0			0
$953$	−1219.58	+	704.124i	−1.27973	+	0.738850i	−0.976798	−	0.214164i	$-0.931297\pi$
$953$	−1219.58	+	704.124i	−1.27973	+	0.738850i	−0.302927	+	0.953014i	$0.597964\pi$
$954$		0			0
$955$	−110.680	+	191.703i	−0.115895	+	0.200737i
$956$		0			0
$957$	−390.947	+	35.3102i	−0.408513	+	0.0368968i
$958$		0			0
$959$	−929.628	−	163.918i	−0.969372	−	0.170926i
$960$		0			0
$961$	−615.065	+	516.100i	−0.640026	+	0.537045i
$962$		0			0
$963$	−989.764	+	5.56000i	−1.02779	+	0.00577362i
$964$		0			0
$965$	−127.305	+	349.769i	−0.131923	+	0.362454i
$966$		0			0
$967$	−310.451	−	260.500i	−0.321046	−	0.269390i	0.467994	−	0.883732i	$-0.344977\pi$
$967$	−310.451	−	260.500i	−0.321046	−	0.269390i	−0.789040	+	0.614342i	$0.789421\pi$
$968$		0			0
$969$	−79.8589	−	79.4116i	−0.0824137	−	0.0819521i
$970$		0			0
$971$		−	912.433i		−	0.939683i	−0.882751	−	0.469842i	$-0.844311\pi$
$971$		−	912.433i		−	0.939683i	0.882751	−	0.469842i	$-0.155689\pi$
$972$		0			0
$973$	−766.598			−0.787871
$974$		0			0
$975$	194.729	−	195.826i	0.199722	−	0.200847i
$976$		0			0
$977$	1013.42	−	1207.75i	1.03728	−	1.23618i	0.0661057	−	0.997813i	$-0.478943\pi$
$977$	1013.42	−	1207.75i	1.03728	−	1.23618i	0.971174	−	0.238370i	$-0.0766130\pi$
$978$		0			0
$979$	592.472	+	215.642i	0.605181	+	0.220268i
$980$		0			0
$981$	−6.25941	−	1114.27i	−0.00638065	−	1.13585i
$982$		0			0
$983$	−275.489	−	328.315i	−0.280253	−	0.333992i	0.607494	−	0.794324i	$-0.292175\pi$
$983$	−275.489	−	328.315i	−0.280253	−	0.333992i	−0.887747	+	0.460332i	$0.847730\pi$
$984$		0			0
$985$	−59.4514	+	337.166i	−0.0603568	+	0.342300i
$986$		0			0
$987$	74.9423	+	829.746i	0.0759294	+	0.840675i
$988$		0			0
$989$	−142.626	−	82.3452i	−0.144212	−	0.0832611i
$990$		0			0
$991$	123.501	+	213.911i	0.124623	+	0.215853i	0.921586	−	0.388175i	$-0.126895\pi$
$991$	123.501	+	213.911i	0.124623	+	0.215853i	−0.796962	+	0.604029i	$0.793561\pi$
$992$		0			0
$993$	−655.121	+	307.731i	−0.659739	+	0.309900i
$994$		0			0
$995$	−294.415	−	808.899i	−0.295895	−	0.812964i
$996$		0			0
$997$	187.279	+	1062.11i	0.187842	+	1.06531i	0.922249	+	0.386597i	$0.126350\pi$
$997$	187.279	+	1062.11i	0.187842	+	1.06531i	−0.734406	+	0.678710i	$0.762539\pi$
$998$		0			0
$999$	177.720	−	49.2286i	0.177898	−	0.0492779i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.u.a.41.5	✓	108
4.3	odd	2		432.3.bc.d.257.14		108
27.2	odd	18	inner	216.3.u.a.137.5	yes	108
108.83	even	18		432.3.bc.d.353.14		108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.3.u.a.41.5	✓	108	1.1	even	1	trivial
216.3.u.a.137.5	yes	108	27.2	odd	18	inner
432.3.bc.d.257.14		108	4.3	odd	2
432.3.bc.d.353.14		108	108.83	even	18

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.u (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.11535 + 2.12727i) q^{3} +(1.88267 - 2.24368i) q^{5} +(4.85852 + 1.76836i) q^{7} +(-0.0505567 - 8.99986i) q^{9} +O(q^{10})\)	\(q+(-2.11535 + 2.12727i) q^{3} +(1.88267 - 2.24368i) q^{5} +(4.85852 + 1.76836i) q^{7} +(-0.0505567 - 8.99986i) q^{9} +(5.52146 + 6.58021i) q^{11} +(-0.973431 + 5.52060i) q^{13} +(0.790397 + 8.75112i) q^{15} +(0.985037 + 0.568711i) q^{17} +(16.5025 + 28.5831i) q^{19} +(-14.0393 + 6.59468i) q^{21} +(2.55606 + 7.02272i) q^{23} +(2.85156 + 16.1720i) q^{25} +(19.2521 + 18.9303i) q^{27} +(15.0012 - 2.64512i) q^{29} +(-11.8151 + 4.30035i) q^{31} +(-25.6777 - 2.17385i) q^{33} +(13.1146 - 7.57172i) q^{35} +(3.41504 - 5.91502i) q^{37} +(-9.68466 - 13.7488i) q^{39} +(14.2631 + 2.51496i) q^{41} +(-16.8812 + 14.1650i) q^{43} +(-20.2880 - 16.8303i) q^{45} +(18.3705 - 50.4726i) q^{47} +(-17.0581 - 14.3134i) q^{49} +(-3.29350 + 0.892414i) q^{51} -67.6881i q^{53} +25.1589 q^{55} +(-95.7126 - 25.3582i) q^{57} +(60.8233 - 72.4864i) q^{59} +(73.9307 + 26.9086i) q^{61} +(15.6693 - 43.8154i) q^{63} +(10.5538 + 12.5775i) q^{65} +(-21.9759 + 124.632i) q^{67} +(-20.3462 - 9.41811i) q^{69} +(-79.6970 - 46.0131i) q^{71} +(-52.7493 - 91.3645i) q^{73} +(-40.4343 - 28.1434i) q^{75} +(15.1899 + 41.7340i) q^{77} +(10.6681 + 60.5017i) q^{79} +(-80.9949 + 0.910006i) q^{81} +(-94.2798 + 16.6241i) q^{83} +(3.13050 - 1.13941i) q^{85} +(-26.1060 + 37.5070i) q^{87} +(63.5663 - 36.7000i) q^{89} +(-14.4918 + 25.1006i) q^{91} +(15.8452 - 34.2307i) q^{93} +(95.1999 + 16.7863i) q^{95} +(28.1582 - 23.6276i) q^{97} +(58.9418 - 50.0250i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q+O(q^{10}) \) 108 * q	\( 108 q - 18 q^{11} - 24 q^{15} + 48 q^{21} + 72 q^{23} + 174 q^{27} + 108 q^{29} + 18 q^{33} - 144 q^{39} + 90 q^{41} - 90 q^{43} + 108 q^{45} - 72 q^{49} + 84 q^{51} - 18 q^{57} - 252 q^{59} + 144 q^{61} - 360 q^{63} - 216 q^{65} + 126 q^{67} - 120 q^{69} - 252 q^{75} - 504 q^{77} - 552 q^{81} - 180 q^{83} - 60 q^{87} - 486 q^{89} - 360 q^{93} - 1116 q^{95} + 270 q^{97} - 564 q^{99}+O(q^{100}) \) 108 * q - 18 * q^11 - 24 * q^15 + 48 * q^21 + 72 * q^23 + 174 * q^27 + 108 * q^29 + 18 * q^33 - 144 * q^39 + 90 * q^41 - 90 * q^43 + 108 * q^45 - 72 * q^49 + 84 * q^51 - 18 * q^57 - 252 * q^59 + 144 * q^61 - 360 * q^63 - 216 * q^65 + 126 * q^67 - 120 * q^69 - 252 * q^75 - 504 * q^77 - 552 * q^81 - 180 * q^83 - 60 * q^87 - 486 * q^89 - 360 * q^93 - 1116 * q^95 + 270 * q^97 - 564 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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