LMFDB - Embedded newform 459.3.j.a.341.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [459,3,Mod(35,459)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(459, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("459.35"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 459 = 3^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	459.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$12.5068441341$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 153)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			341.14
Character	$\chi$	$=$	459.341
Dual form			459.3.j.a.35.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.700836 + 0.404628i) q^{2} +(-1.67255 + 2.89695i) q^{4} +(6.73682 + 3.88950i) q^{5} +(-1.30137 - 2.25403i) q^{7} -5.94407i q^{8} -6.29521 q^{10} +(15.0999 - 8.71794i) q^{11} +(11.9586 - 20.7129i) q^{13} +(1.82409 + 1.05314i) q^{14} +(-4.28507 - 7.42196i) q^{16} -4.12311i q^{17} +8.89419 q^{19} +(-22.5354 + 13.0108i) q^{20} +(-7.05505 + 12.2197i) q^{22} +(14.5631 + 8.40799i) q^{23} +(17.7565 + 30.7551i) q^{25} +19.3552i q^{26} +8.70641 q^{28} +(-28.3321 + 16.3576i) q^{29} +(16.5527 - 28.6701i) q^{31} +(26.5971 + 15.3559i) q^{32} +(1.66832 + 2.88962i) q^{34} -20.2467i q^{35} -45.9261 q^{37} +(-6.23337 + 3.59884i) q^{38} +(23.1195 - 40.0441i) q^{40} +(31.3907 + 18.1234i) q^{41} +(14.4282 + 24.9905i) q^{43} +58.3248i q^{44} -13.6084 q^{46} +(-55.0612 + 31.7896i) q^{47} +(21.1129 - 36.5686i) q^{49} +(-24.8888 - 14.3696i) q^{50} +(40.0028 + 69.2870i) q^{52} -48.8363i q^{53} +135.634 q^{55} +(-13.3981 + 7.73542i) q^{56} +(13.2375 - 22.9279i) q^{58} +(25.6105 + 14.7862i) q^{59} +(19.2375 + 33.3204i) q^{61} +26.7907i q^{62} +9.42690 q^{64} +(161.126 - 93.0262i) q^{65} +(-28.8502 + 49.9700i) q^{67} +(11.9444 + 6.89611i) q^{68} +(8.19238 + 14.1896i) q^{70} +16.3591i q^{71} -1.61860 q^{73} +(32.1867 - 18.5830i) q^{74} +(-14.8760 + 25.7660i) q^{76} +(-39.3011 - 22.6905i) q^{77} +(-8.91008 - 15.4327i) q^{79} -66.6672i q^{80} -29.3330 q^{82} +(42.2194 - 24.3754i) q^{83} +(16.0368 - 27.7766i) q^{85} +(-20.2237 - 11.6762i) q^{86} +(-51.8201 - 89.7550i) q^{88} +137.254i q^{89} -62.2502 q^{91} +(-48.7150 + 28.1256i) q^{92} +(25.7259 - 44.5586i) q^{94} +(59.9186 + 34.5940i) q^{95} +(-80.2196 - 138.945i) q^{97} +34.1715i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 64 q^{4} + 18 q^{5} + 2 q^{7} - 10 q^{13} - 72 q^{14} - 128 q^{16} - 28 q^{19} + 18 q^{20} - 144 q^{23} + 154 q^{25} + 32 q^{28} + 162 q^{29} + 62 q^{31} - 126 q^{32} + 128 q^{37} + 36 q^{38} + 144 q^{41}+ \cdots + 140 q^{97}+O(q^{100}) $ 64 * q + 64 * q^4 + 18 * q^5 + 2 * q^7 - 10 * q^13 - 72 * q^14 - 128 * q^16 - 28 * q^19 + 18 * q^20 - 144 * q^23 + 154 * q^25 + 32 * q^28 + 162 * q^29 + 62 * q^31 - 126 * q^32 + 128 * q^37 + 36 * q^38 + 144 * q^41 - 64 * q^43 - 48 * q^46 - 288 * q^47 - 246 * q^49 + 62 * q^52 - 84 * q^55 - 684 * q^56 + 138 * q^58 + 432 * q^59 + 110 * q^61 - 260 * q^64 - 148 * q^67 - 216 * q^70 - 196 * q^73 + 918 * q^74 - 112 * q^76 + 504 * q^77 + 86 * q^79 - 396 * q^82 + 594 * q^83 - 126 * q^86 + 24 * q^88 + 52 * q^91 + 36 * q^92 - 186 * q^94 + 144 * q^95 + 140 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/459\mathbb{Z}\right)^\times$.

$n$	$137$	$190$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.700836	+	0.404628i	−0.350418	+	0.202314i	−0.664869	−	0.746960i	$-0.731513\pi$
$2$	−0.700836	+	0.404628i	−0.350418	+	0.202314i	0.314451	+	0.949274i	$0.398180\pi$
$3$		0			0
$3$		0			0
$4$	−1.67255	+	2.89695i	−0.418138	+	0.724236i
$5$	6.73682	+	3.88950i	1.34736	+	0.777901i	0.987875	−	0.155249i	$-0.0496179\pi$
$5$	6.73682	+	3.88950i	1.34736	+	0.777901i	0.359488	+	0.933150i	$0.382951\pi$
$6$		0			0
$7$	−1.30137	−	2.25403i	−0.185910	−	0.322005i	0.757973	−	0.652286i	$-0.226190\pi$
$7$	−1.30137	−	2.25403i	−0.185910	−	0.322005i	−0.943883	+	0.330281i	$0.892856\pi$
$8$		−	5.94407i		−	0.743009i
$9$		0			0
$10$	−6.29521			−0.629521
$11$	15.0999	−	8.71794i	1.37272	−	0.792540i	0.381450	−	0.924390i	$-0.375425\pi$
$11$	15.0999	−	8.71794i	1.37272	−	0.792540i	0.991270	+	0.131849i	$0.0420915\pi$
$12$		0			0
$13$	11.9586	−	20.7129i	0.919894	−	1.59330i	0.120321	−	0.992735i	$-0.461608\pi$
$13$	11.9586	−	20.7129i	0.919894	−	1.59330i	0.799574	−	0.600568i	$-0.205059\pi$
$14$	1.82409	+	1.05314i	0.130292	+	0.0752242i
$15$		0			0
$16$	−4.28507	−	7.42196i	−0.267817	−	0.463872i
$17$		−	4.12311i		−	0.242536i
$17$		−	4.12311i		−	0.242536i
$18$		0			0
$19$	8.89419			0.468115			0.234058	−	0.972223i	$-0.424800\pi$
$19$	8.89419			0.468115			0.234058	+	0.972223i	$0.424800\pi$
$20$	−22.5354	+	13.0108i	−1.12677	+	0.650540i
$21$		0			0
$22$	−7.05505	+	12.2197i	−0.320684	+	0.555441i
$23$	14.5631	+	8.40799i	0.633177	+	0.365565i	0.781981	−	0.623302i	$-0.214209\pi$
$23$	14.5631	+	8.40799i	0.633177	+	0.365565i	−0.148804	+	0.988867i	$0.547542\pi$
$24$		0			0
$25$	17.7565	+	30.7551i	0.710260	+	1.23021i
$26$			19.3552i			0.744430i
$27$		0			0
$28$	8.70641			0.310943
$29$	−28.3321	+	16.3576i	−0.976969	+	0.564054i	−0.901354	−	0.433083i	$-0.857426\pi$
$29$	−28.3321	+	16.3576i	−0.976969	+	0.564054i	−0.0756157	+	0.997137i	$0.524092\pi$
$30$		0			0
$31$	16.5527	−	28.6701i	0.533957	−	0.924841i	−0.465256	−	0.885176i	$-0.654038\pi$
$31$	16.5527	−	28.6701i	0.533957	−	0.924841i	0.999213	−	0.0396646i	$-0.0126290\pi$
$32$	26.5971	+	15.3559i	0.831160	+	0.479871i
$33$		0			0
$34$	1.66832	+	2.88962i	0.0490684	+	0.0849889i
$35$		−	20.2467i		−	0.578477i
$36$		0			0
$37$	−45.9261			−1.24125			−0.620623	−	0.784109i	$-0.713120\pi$
$37$	−45.9261			−1.24125			−0.620623	+	0.784109i	$0.713120\pi$
$38$	−6.23337	+	3.59884i	−0.164036	+	0.0947063i
$39$		0			0
$40$	23.1195	−	40.0441i	0.577987	−	1.00110i
$41$	31.3907	+	18.1234i	0.765626	+	0.442035i	0.831312	−	0.555806i	$-0.187590\pi$
$41$	31.3907	+	18.1234i	0.765626	+	0.442035i	−0.0656858	+	0.997840i	$0.520924\pi$
$42$		0			0
$43$	14.4282	+	24.9905i	0.335541	+	0.581174i	0.983589	−	0.180426i	$-0.0577477\pi$
$43$	14.4282	+	24.9905i	0.335541	+	0.581174i	−0.648048	+	0.761600i	$0.724414\pi$
$44$			58.3248i			1.32556i
$45$		0			0
$46$	−13.6084			−0.295836
$47$	−55.0612	+	31.7896i	−1.17152	+	0.676375i	−0.954037	−	0.299690i	$-0.903117\pi$
$47$	−55.0612	+	31.7896i	−1.17152	+	0.676375i	−0.217479	+	0.976065i	$0.569783\pi$
$48$		0			0
$49$	21.1129	−	36.5686i	0.430875	−	0.746298i
$50$	−24.8888	−	14.3696i	−0.497776	−	0.287391i
$51$		0			0
$52$	40.0028	+	69.2870i	0.769285	+	1.33244i
$53$		−	48.8363i		−	0.921440i	−0.887545	−	0.460720i	$-0.847591\pi$
$53$		−	48.8363i		−	0.921440i	0.887545	−	0.460720i	$-0.152409\pi$
$54$		0			0
$55$	135.634			2.46607
$56$	−13.3981	+	7.73542i	−0.239252	+	0.138132i
$57$		0			0
$58$	13.2375	−	22.9279i	0.228232	−	0.395309i
$59$	25.6105	+	14.7862i	0.434076	+	0.250614i	0.701082	−	0.713081i	$-0.252701\pi$
$59$	25.6105	+	14.7862i	0.434076	+	0.250614i	−0.267005	+	0.963695i	$0.586034\pi$
$60$		0			0
$61$	19.2375	+	33.3204i	0.315369	+	0.546236i	0.979516	−	0.201367i	$-0.0645383\pi$
$61$	19.2375	+	33.3204i	0.315369	+	0.546236i	−0.664147	+	0.747602i	$0.731205\pi$
$62$			26.7907i			0.432108i
$63$		0			0
$64$	9.42690			0.147295
$65$	161.126	−	93.0262i	2.47886	−	1.43117i
$66$		0			0
$67$	−28.8502	+	49.9700i	−0.430600	+	0.745820i	−0.996925	−	0.0783614i	$-0.975031\pi$
$67$	−28.8502	+	49.9700i	−0.430600	+	0.745820i	0.566326	+	0.824182i	$0.308365\pi$
$68$	11.9444	+	6.89611i	0.175653	+	0.101413i
$69$		0			0
$70$	8.19238	+	14.1896i	0.117034	+	0.202709i
$71$			16.3591i			0.230410i	0.993342	+	0.115205i	$0.0367525\pi$
$71$			16.3591i			0.230410i	−0.993342	+	0.115205i	$0.963248\pi$
$72$		0			0
$73$	−1.61860			−0.0221726			−0.0110863	−	0.999939i	$-0.503529\pi$
$73$	−1.61860			−0.0221726			−0.0110863	+	0.999939i	$0.503529\pi$
$74$	32.1867	−	18.5830i	0.434955	−	0.251121i
$75$		0			0
$76$	−14.8760	+	25.7660i	−0.195737	+	0.339026i
$77$	−39.3011	−	22.6905i	−0.510403	−	0.294682i
$78$		0			0
$79$	−8.91008	−	15.4327i	−0.112786	−	0.195351i	0.804107	−	0.594485i	$-0.202644\pi$
$79$	−8.91008	−	15.4327i	−0.112786	−	0.195351i	−0.916892	+	0.399134i	$0.869311\pi$
$80$		−	66.6672i		−	0.833340i
$81$		0			0
$82$	−29.3330			−0.357719
$83$	42.2194	−	24.3754i	0.508667	−	0.293679i	−0.223618	−	0.974677i	$-0.571787\pi$
$83$	42.2194	−	24.3754i	0.508667	−	0.293679i	0.732286	+	0.680998i	$0.238454\pi$
$84$		0			0
$85$	16.0368	−	27.7766i	0.188669	−	0.326784i
$86$	−20.2237	−	11.6762i	−0.235159	−	0.135769i
$87$		0			0
$88$	−51.8201	−	89.7550i	−0.588864	−	1.01994i
$89$			137.254i			1.54218i	0.636728	+	0.771089i	$0.280288\pi$
$89$			137.254i			1.54218i	−0.636728	+	0.771089i	$0.719712\pi$
$90$		0			0
$91$	−62.2502			−0.684068
$92$	−48.7150	+	28.1256i	−0.529511	+	0.305713i
$93$		0			0
$94$	25.7259	−	44.5586i	0.273680	−	0.474028i
$95$	59.9186	+	34.5940i	0.630722	+	0.364147i
$96$		0			0
$97$	−80.2196	−	138.945i	−0.827007	−	1.43242i	−0.900376	−	0.435113i	$-0.856709\pi$
$97$	−80.2196	−	138.945i	−0.827007	−	1.43242i	0.0733693	−	0.997305i	$-0.476625\pi$
$98$			34.1715i			0.348689i
$99$		0			0
$100$	−118.795			−1.18795
$101$	68.9485	−	39.8074i	0.682658	−	0.394133i	−0.118198	−	0.992990i	$-0.537712\pi$
$101$	68.9485	−	39.8074i	0.682658	−	0.394133i	0.800856	+	0.598857i	$0.204378\pi$
$102$		0			0
$103$	−60.9085	+	105.497i	−0.591345	+	1.02424i	0.402706	+	0.915329i	$0.368070\pi$
$103$	−60.9085	+	105.497i	−0.591345	+	1.02424i	−0.994052	+	0.108911i	$0.965264\pi$
$104$	−123.119	−	71.0829i	−1.18384	−	0.683490i
$105$		0			0
$106$	19.7606	+	34.2263i	0.186420	+	0.322890i
$107$			36.7905i			0.343837i	0.985111	+	0.171918i	$0.0549966\pi$
$107$			36.7905i			0.343837i	−0.985111	+	0.171918i	$0.945003\pi$
$108$		0			0
$109$	−83.1756			−0.763078			−0.381539	−	0.924353i	$-0.624606\pi$
$109$	−83.1756			−0.763078			−0.381539	+	0.924353i	$0.624606\pi$
$110$	−95.0572	+	54.8813i	−0.864156	+	0.498921i
$111$		0			0
$112$	−11.1529	+	19.3174i	−0.0995794	+	0.172477i
$113$	−43.3330	−	25.0183i	−0.383478	−	0.221401i	0.295853	−	0.955234i	$-0.404396\pi$
$113$	−43.3330	−	25.0183i	−0.383478	−	0.221401i	−0.679330	+	0.733833i	$0.737730\pi$
$114$		0			0
$115$	65.4059	+	113.286i	0.568747	+	0.985098i
$116$		−	109.435i		−	0.943409i
$117$		0			0
$118$	−23.9317			−0.202811
$119$	−9.29362	+	5.36567i	−0.0780976	+	0.0450897i
$120$		0			0
$121$	91.5050	−	158.491i	0.756240	−	1.30985i
$122$	−26.9647	−	15.5681i	−0.221022	−	0.127607i
$123$		0			0
$124$	55.3704	+	95.9044i	0.446536	+	0.773422i
$125$			81.7806i			0.654245i
$126$		0			0
$127$	−133.526			−1.05139			−0.525694	−	0.850674i	$-0.676194\pi$
$127$	−133.526			−1.05139			−0.525694	+	0.850674i	$0.676194\pi$
$128$	−112.995	+	65.2378i	−0.882775	+	0.509671i
$129$		0			0
$130$	−75.2821	+	130.392i	−0.579093	+	1.00302i
$131$	114.524	+	66.1203i	0.874226	+	0.504735i	0.868750	−	0.495250i	$-0.164924\pi$
$131$	114.524	+	66.1203i	0.874226	+	0.504735i	0.00547589	+	0.999985i	$0.498257\pi$
$132$		0			0
$133$	−11.5746	−	20.0478i	−0.0870271	−	0.150735i
$134$		−	46.6944i		−	0.348465i
$135$		0			0
$136$	−24.5080			−0.180206
$137$	−74.6702	+	43.1108i	−0.545038	+	0.314678i	−0.747118	−	0.664691i	$-0.768563\pi$
$137$	−74.6702	+	43.1108i	−0.545038	+	0.314678i	0.202080	+	0.979369i	$0.435230\pi$
$138$		0			0
$139$	5.93501	−	10.2797i	0.0426979	−	0.0739550i	−0.843887	−	0.536522i	$-0.819738\pi$
$139$	5.93501	−	10.2797i	0.0426979	−	0.0739550i	0.886585	+	0.462567i	$0.153071\pi$
$140$	58.6535	+	33.8636i	0.418954	+	0.241883i
$141$		0			0
$142$	−6.61935	−	11.4651i	−0.0466152	−	0.0807398i
$143$		−	417.018i		−	2.91621i
$144$		0			0
$145$	−254.491			−1.75511
$146$	1.13437	−	0.654930i	0.00776967	−	0.00448582i
$147$		0			0
$148$	76.8137	−	133.045i	0.519012	−	0.898955i
$149$	−63.4767	−	36.6483i	−0.426018	−	0.245962i	0.271631	−	0.962402i	$-0.412437\pi$
$149$	−63.4767	−	36.6483i	−0.426018	−	0.245962i	−0.697649	+	0.716440i	$0.745770\pi$
$150$		0			0
$151$	94.7149	+	164.051i	0.627251	+	1.08643i	0.988101	+	0.153807i	$0.0491533\pi$
$151$	94.7149	+	164.051i	0.627251	+	1.08643i	−0.360850	+	0.932624i	$0.617513\pi$
$152$		−	52.8677i		−	0.347814i
$153$		0			0
$154$	36.7248			0.238473
$155$	223.025	−	128.763i	1.43887	−	0.830731i
$156$		0			0
$157$	22.6267	−	39.1906i	0.144119	−	0.249621i	−0.784925	−	0.619591i	$-0.787299\pi$
$157$	22.6267	−	39.1906i	0.144119	−	0.249621i	0.929044	+	0.369970i	$0.120632\pi$
$158$	12.4890	+	7.21054i	0.0790444	+	0.0456363i
$159$		0			0
$160$	119.453	+	206.899i	0.746584	+	1.29312i
$161$		−	43.7675i		−	0.271848i
$162$		0			0
$163$	280.866			1.72310			0.861552	−	0.507670i	$-0.169493\pi$
$163$	280.866			1.72310			0.861552	+	0.507670i	$0.169493\pi$
$164$	−105.005	+	60.6247i	−0.640275	+	0.369663i
$165$		0			0
$166$	−19.7259	+	34.1663i	−0.118831	+	0.205821i
$167$	−97.4945	−	56.2885i	−0.583800	−	0.337057i	0.178842	−	0.983878i	$-0.442765\pi$
$167$	−97.4945	−	56.2885i	−0.583800	−	0.337057i	−0.762642	+	0.646821i	$0.776098\pi$
$168$		0			0
$169$	−201.517	−	349.038i	−1.19241	−	2.06532i
$170$			25.9558i			0.152681i
$171$		0			0
$172$	−96.5280			−0.561209
$173$	−108.216	+	62.4783i	−0.625524	+	0.361146i	−0.779017	−	0.627003i	$-0.784281\pi$
$173$	−108.216	+	62.4783i	−0.625524	+	0.361146i	0.153493	+	0.988150i	$0.450948\pi$
$174$		0			0
$175$	46.2154	−	80.0475i	0.264088	−	0.457414i
$176$	−129.408	−	74.7140i	−0.735275	−	0.424511i
$177$		0			0
$178$	−55.5368	−	96.1925i	−0.312004	−	0.540407i
$179$			231.060i			1.29084i	0.763830	+	0.645418i	$0.223317\pi$
$179$			231.060i			1.29084i	−0.763830	+	0.645418i	$0.776683\pi$
$180$		0			0
$181$	−21.6045			−0.119362			−0.0596808	−	0.998218i	$-0.519008\pi$
$181$	−21.6045			−0.119362			−0.0596808	+	0.998218i	$0.519008\pi$
$182$	43.6272	−	25.1882i	0.239710	−	0.138397i
$183$		0			0
$184$	49.9777	−	86.5640i	0.271618	−	0.470456i
$185$	−309.396	−	178.630i	−1.67241	−	0.965566i
$186$		0			0
$187$	−35.9450	−	62.2586i	−0.192219	−	0.332933i
$188$		−	212.679i		−	1.13127i
$189$		0			0
$190$	−55.9908			−0.294689
$191$	−250.277	+	144.498i	−1.31035	+	0.756533i	−0.982154	−	0.188076i	$-0.939775\pi$
$191$	−250.277	+	144.498i	−1.31035	+	0.756533i	−0.328198	+	0.944609i	$0.606441\pi$
$192$		0			0
$193$	7.41936	−	12.8507i	0.0384423	−	0.0665840i	−0.846164	−	0.532922i	$-0.821094\pi$
$193$	7.41936	−	12.8507i	0.0384423	−	0.0665840i	0.884606	+	0.466338i	$0.154427\pi$
$194$	112.442	+	64.9183i	0.579596	+	0.334630i
$195$		0			0
$196$	70.6248	+	122.326i	0.360331	+	0.624111i
$197$		−	8.61853i		−	0.0437489i	−0.999761	−	0.0218745i	$-0.993037\pi$
$197$		−	8.61853i		−	0.0437489i	0.999761	−	0.0218745i	$-0.00696341\pi$
$198$		0			0
$199$	286.779			1.44110			0.720550	−	0.693403i	$-0.243889\pi$
$199$	286.779			1.44110			0.720550	+	0.693403i	$0.243889\pi$
$200$	182.811	−	105.546i	0.914054	−	0.527729i
$201$		0			0
$202$	−32.2144	+	55.7970i	−0.159477	+	0.276223i
$203$	73.7409	+	42.5744i	0.363256	+	0.209726i
$204$		0			0
$205$	140.982	+	244.188i	0.687718	+	1.19116i
$206$		−	98.5813i		−	0.478550i
$207$		0			0
$208$	−204.974			−0.985453
$209$	134.302	−	77.5390i	0.642591	−	0.371000i
$210$		0			0
$211$	−48.9118	+	84.7177i	−0.231809	+	0.401506i	−0.958341	−	0.285628i	$-0.907798\pi$
$211$	−48.9118	+	84.7177i	−0.231809	+	0.401506i	0.726531	+	0.687133i	$0.241131\pi$
$212$	141.476	+	81.6813i	0.667341	+	0.385289i
$213$		0			0
$214$	−14.8865	−	25.7842i	−0.0695630	−	0.120487i
$215$			224.475i			1.04407i
$216$		0			0
$217$	−86.1644			−0.397071
$218$	58.2925	−	33.6552i	0.267397	−	0.154382i
$219$		0			0
$220$	−226.855	+	392.924i	−1.03116	+	1.78602i
$221$	−85.4017	−	49.3067i	−0.386433	−	0.223107i
$222$		0			0
$223$	−118.031	−	204.435i	−0.529286	−	0.916750i	−0.999417	−	0.0341533i	$-0.989127\pi$
$223$	−118.031	−	204.435i	−0.529286	−	0.916750i	0.470131	−	0.882597i	$-0.344207\pi$
$224$		−	79.9344i		−	0.356850i
$225$		0			0
$226$	40.4924			0.179170
$227$	−185.599	+	107.156i	−0.817616	+	0.472051i	−0.849594	−	0.527438i	$-0.823153\pi$
$227$	−185.599	+	107.156i	−0.817616	+	0.472051i	0.0319778	+	0.999489i	$0.489819\pi$
$228$		0			0
$229$	141.310	−	244.755i	0.617072	−	1.06880i	−0.372945	−	0.927854i	$-0.621652\pi$
$229$	141.310	−	244.755i	0.617072	−	1.06880i	0.990017	−	0.140947i	$-0.0450147\pi$
$230$	−91.6776	−	52.9301i	−0.398598	−	0.230131i
$231$		0			0
$232$	97.2305	+	168.408i	0.419097	+	0.725897i
$233$		−	59.8313i		−	0.256786i	−0.991723	−	0.128393i	$-0.959018\pi$
$233$		−	59.8313i		−	0.256786i	0.991723	−	0.128393i	$-0.0409820\pi$
$234$		0			0
$235$	−494.583			−2.10461
$236$	−85.6698	+	49.4615i	−0.363008	+	0.209582i
$237$		0			0
$238$	4.34220	−	7.52092i	0.0182446	−	0.0316005i
$239$	69.7376	+	40.2630i	0.291789	+	0.168465i	0.638748	−	0.769416i	$-0.279452\pi$
$239$	69.7376	+	40.2630i	0.291789	+	0.168465i	−0.346959	+	0.937880i	$0.612786\pi$
$240$		0			0
$241$	−72.3297	−	125.279i	−0.300123	−	0.519829i	0.676040	−	0.736865i	$-0.263695\pi$
$241$	−72.3297	−	125.279i	−0.300123	−	0.519829i	−0.976164	+	0.217036i	$0.930361\pi$
$242$			148.102i			0.611992i
$243$		0			0
$244$	−128.703			−0.527472
$245$	284.467	−	164.237i	1.16109	−	0.670357i
$246$		0			0
$247$	106.362	−	184.225i	0.430617	−	0.745850i
$248$	−170.417	−	98.3903i	−0.687165	−	0.396735i
$249$		0			0
$250$	−33.0907	−	57.3148i	−0.132363	−	0.229259i
$251$		−	187.445i		−	0.746793i	−0.927672	−	0.373397i	$-0.878193\pi$
$251$		−	187.445i		−	0.746793i	0.927672	−	0.373397i	$-0.121807\pi$
$252$		0			0
$253$	293.202			1.15890
$254$	93.5801	−	54.0285i	0.368425	−	0.212711i
$255$		0			0
$256$	33.9403	−	58.7864i	0.132579	−	0.229634i
$257$	181.025	+	104.515i	0.704377	+	0.406672i	0.808975	−	0.587842i	$-0.200022\pi$
$257$	181.025	+	104.515i	0.704377	+	0.406672i	−0.104599	+	0.994515i	$0.533356\pi$
$258$		0			0
$259$	59.7667	+	103.519i	0.230759	+	0.399687i
$260$			622.365i			2.39371i
$261$		0			0
$262$	−107.016			−0.408460
$263$	−111.963	+	64.6421i	−0.425716	+	0.245787i	−0.697520	−	0.716565i	$-0.745713\pi$
$263$	−111.963	+	64.6421i	−0.425716	+	0.245787i	0.271804	+	0.962353i	$0.412380\pi$
$264$		0			0
$265$	189.949	−	329.002i	0.716789	−	1.24152i
$266$	16.2238	+	9.36682i	0.0609918	+	0.0352136i
$267$		0			0
$268$	−96.5068	−	167.155i	−0.360100	−	0.623712i
$269$			151.018i			0.561405i	0.959795	+	0.280702i	$0.0905674\pi$
$269$			151.018i			0.561405i	−0.959795	+	0.280702i	$0.909433\pi$
$270$		0			0
$271$	402.721			1.48605			0.743027	−	0.669261i	$-0.233389\pi$
$271$	402.721			1.48605			0.743027	+	0.669261i	$0.233389\pi$
$272$	−30.6015	+	17.6678i	−0.112506	+	0.0649551i
$273$		0			0
$274$	34.8877	−	60.4273i	0.127327	−	0.220538i
$275$	536.243	+	309.600i	1.94997	+	1.12582i
$276$		0			0
$277$	80.4259	+	139.302i	0.290346	+	0.502894i	0.973892	−	0.227014i	$-0.0728962\pi$
$277$	80.4259	+	139.302i	0.290346	+	0.502894i	−0.683545	+	0.729908i	$0.739563\pi$
$278$			9.60589i			0.0345536i
$279$		0			0
$280$	−120.348			−0.429813
$281$	−70.3081	+	40.5924i	−0.250207	+	0.144457i	−0.619859	−	0.784713i	$-0.712810\pi$
$281$	−70.3081	+	40.5924i	−0.250207	+	0.144457i	0.369652	+	0.929170i	$0.379477\pi$
$282$		0			0
$283$	−159.276	+	275.875i	−0.562814	+	0.974823i	0.434435	+	0.900703i	$0.356948\pi$
$283$	−159.276	+	275.875i	−0.562814	+	0.974823i	−0.997249	+	0.0741197i	$0.976385\pi$
$284$	−47.3914	−	27.3615i	−0.166871	−	0.0963431i
$285$		0			0
$286$	168.737	+	292.262i	0.589991	+	1.02189i
$287$		−	94.3409i		−	0.328714i
$288$		0			0
$289$	−17.0000			−0.0588235
$290$	178.357	−	102.974i	0.615023	−	0.355084i
$291$		0			0
$292$	2.70719	−	4.68899i	0.00927119	−	0.0160582i
$293$	387.823	+	223.910i	1.32363	+	0.764196i	0.984305	−	0.176474i	$-0.0564692\pi$
$293$	387.823	+	223.910i	1.32363	+	0.764196i	0.339322	+	0.940670i	$0.389803\pi$
$294$		0			0
$295$	115.022	+	199.224i	0.389906	+	0.675337i
$296$			272.988i			0.922256i
$297$		0			0
$298$	59.3157			0.199046
$299$	348.309	−	201.096i	1.16491	−	0.672562i
$300$		0			0
$301$	37.5529	−	65.0435i	0.124760	−	0.216091i
$302$	−132.759	−	76.6486i	−0.439600	−	0.253803i
$303$		0			0
$304$	−38.1122	−	66.0123i	−0.125369	−	0.217146i
$305$			299.298i			0.981304i
$306$		0			0
$307$	306.100			0.997068			0.498534	−	0.866870i	$-0.333872\pi$
$307$	306.100			0.997068			0.498534	+	0.866870i	$0.333872\pi$
$308$	131.466	−	75.9020i	0.426838	−	0.246435i
$309$		0			0
$310$	−104.203	+	180.484i	−0.336137	+	0.582207i
$311$	−204.646	−	118.153i	−0.658026	−	0.379912i	0.133498	−	0.991049i	$-0.457379\pi$
$311$	−204.646	−	118.153i	−0.658026	−	0.379912i	−0.791524	+	0.611137i	$0.790712\pi$
$312$		0			0
$313$	−96.4374	−	167.035i	−0.308107	−	0.533657i	0.669841	−	0.742504i	$-0.266362\pi$
$313$	−96.4374	−	167.035i	−0.308107	−	0.533657i	−0.977948	+	0.208848i	$0.933029\pi$
$314$			36.6216i			0.116629i
$315$		0			0
$316$	59.6103			0.188640
$317$	185.112	−	106.874i	0.583948	−	0.337143i	−0.178753	−	0.983894i	$-0.557206\pi$
$317$	185.112	−	106.874i	0.583948	−	0.337143i	0.762701	+	0.646751i	$0.223873\pi$
$318$		0			0
$319$	−285.208	+	493.995i	−0.894070	+	1.54857i
$320$	63.5073	+	36.6660i	0.198460	+	0.114581i
$321$		0			0
$322$	17.7096	+	30.6739i	0.0549987	+	0.0952605i
$323$		−	36.6717i		−	0.113535i
$324$		0			0
$325$	849.373			2.61345
$326$	−196.841	+	113.646i	−0.603807	+	0.348608i
$327$		0			0
$328$	107.727	−	186.588i	0.328436	−	0.568867i
$329$	143.310	+	82.7399i	0.435592	+	0.251489i
$330$		0			0
$331$	257.827	+	446.570i	0.778934	+	1.34915i	0.932557	+	0.361023i	$0.117573\pi$
$331$	257.827	+	446.570i	0.778934	+	1.34915i	−0.153623	+	0.988130i	$0.549094\pi$
$332$			163.076i			0.491194i
$333$		0			0
$334$	91.1036			0.272765
$335$	−388.717	+	224.426i	−1.16035	+	0.669928i
$336$		0			0
$337$	139.812	−	242.161i	0.414871	−	0.718578i	−0.580544	−	0.814229i	$-0.697160\pi$
$337$	139.812	−	242.161i	0.414871	−	0.718578i	0.995415	+	0.0956509i	$0.0304932\pi$
$338$	282.461	+	163.079i	0.835685	+	0.482483i
$339$		0			0
$340$	53.6449	+	92.9157i	0.157779	+	0.273281i
$341$		−	577.221i		−	1.69273i
$342$		0			0
$343$	−237.436			−0.692234
$344$	148.545	−	85.7626i	0.431817	−	0.249310i
$345$		0			0
$346$	50.5610	−	87.5742i	0.146130	−	0.253105i
$347$	−9.39562	−	5.42457i	−0.0270767	−	0.0156328i	0.486401	−	0.873736i	$-0.338310\pi$
$347$	−9.39562	−	5.42457i	−0.0270767	−	0.0156328i	−0.513477	+	0.858103i	$0.671643\pi$
$348$		0			0
$349$	−220.265	−	381.511i	−0.631133	−	1.09315i	−0.987320	−	0.158740i	$-0.949257\pi$
$349$	−220.265	−	381.511i	−0.631133	−	1.09315i	0.356187	−	0.934415i	$-0.384076\pi$
$350$			74.8002i			0.213715i
$351$		0			0
$352$	535.486			1.52127
$353$	104.849	−	60.5347i	0.297023	−	0.171486i	−0.344082	−	0.938940i	$-0.611810\pi$
$353$	104.849	−	60.5347i	0.297023	−	0.171486i	0.641105	+	0.767453i	$0.278476\pi$
$354$		0			0
$355$	−63.6288	+	110.208i	−0.179236	+	0.310446i
$356$	−397.617	−	229.564i	−1.11690	−	0.644843i
$357$		0			0
$358$	−93.4932	−	161.935i	−0.261154	−	0.452332i
$359$		−	447.022i		−	1.24519i	−0.782546	−	0.622593i	$-0.786079\pi$
$359$		−	447.022i		−	1.24519i	0.782546	−	0.622593i	$-0.213921\pi$
$360$		0			0
$361$	−281.893			−0.780868
$362$	15.1412	−	8.74177i	0.0418265	−	0.0241485i
$363$		0			0
$364$	104.117	−	180.335i	0.286035	−	0.495427i
$365$	−10.9042	−	6.29554i	−0.0298745	−	0.0172481i
$366$		0			0
$367$	−203.580	−	352.610i	−0.554713	−	0.960791i	−0.997926	−	0.0643744i	$-0.979495\pi$
$367$	−203.580	−	352.610i	−0.554713	−	0.960791i	0.443213	−	0.896416i	$-0.353839\pi$
$368$		−	144.115i		−	0.391618i
$369$		0			0
$370$	289.114			0.781390
$371$	−110.079	+	63.5540i	−0.296708	+	0.171305i
$372$		0			0
$373$	−311.242	+	539.088i	−0.834430	+	1.44528i	0.0600638	+	0.998195i	$0.480870\pi$
$373$	−311.242	+	539.088i	−0.834430	+	1.44528i	−0.894494	+	0.447081i	$0.852464\pi$
$374$	50.3831	+	29.0887i	0.134714	+	0.0777773i
$375$		0			0
$376$	188.960	+	327.288i	0.502552	+	0.870446i
$377$			782.455i			2.07548i
$378$		0			0
$379$	−572.862			−1.51151			−0.755755	−	0.654855i	$-0.772730\pi$
$379$	−572.862			−1.51151			−0.755755	+	0.654855i	$0.772730\pi$
$380$	−200.434	+	115.721i	−0.527457	+	0.304528i
$381$		0			0
$382$	116.936	−	202.539i	0.306114	−	0.530206i
$383$	68.2467	+	39.4023i	0.178190	+	0.102878i	0.586442	−	0.809991i	$-0.300528\pi$
$383$	68.2467	+	39.4023i	0.178190	+	0.102878i	−0.408252	+	0.912869i	$0.633862\pi$
$384$		0			0
$385$	−176.509	−	305.723i	−0.458466	−	0.794086i
$386$			12.0083i			0.0311097i
$387$		0			0
$388$	536.686			1.38321
$389$	2.14950	−	1.24102i	0.00552572	−	0.00319027i	−0.497235	−	0.867616i	$-0.665651\pi$
$389$	2.14950	−	1.24102i	0.00552572	−	0.00319027i	0.502760	+	0.864426i	$0.332318\pi$
$390$		0			0
$391$	34.6671	−	60.0451i	0.0886625	−	0.153568i
$392$	−217.366	−	125.497i	−0.554506	−	0.320144i
$393$		0			0
$394$	3.48730	+	6.04018i	0.00885102	+	0.0153304i
$395$		−	138.623i		−	0.350945i
$396$		0			0
$397$	242.224			0.610135			0.305067	−	0.952331i	$-0.401321\pi$
$397$	242.224			0.610135			0.305067	+	0.952331i	$0.401321\pi$
$398$	−200.985	+	116.039i	−0.504988	+	0.291555i
$399$		0			0
$400$	152.176	−	263.576i	0.380439	−	0.658940i
$401$	−469.035	−	270.798i	−1.16966	−	0.675306i	−0.216063	−	0.976379i	$-0.569322\pi$
$401$	−469.035	−	270.798i	−1.16966	−	0.675306i	−0.953601	+	0.301073i	$0.902655\pi$
$402$		0			0
$403$	−395.894	−	685.709i	−0.982368	−	1.70151i
$404$			266.320i			0.659208i
$405$		0			0
$406$	−68.9071			−0.169722
$407$	−693.480	+	400.381i	−1.70388	+	0.983737i
$408$		0			0
$409$	−212.264	+	367.652i	−0.518984	+	0.898906i	0.480773	+	0.876845i	$0.340356\pi$
$409$	−212.264	+	367.652i	−0.518984	+	0.898906i	−0.999757	+	0.0220608i	$0.992977\pi$
$410$	−197.611	−	114.091i	−0.481978	−	0.278270i
$411$		0			0
$412$	−203.745	−	352.897i	−0.494528	−	0.856547i
$413$		−	76.9692i		−	0.186366i
$414$		0			0
$415$	379.233			0.913813
$416$	636.130	−	367.270i	1.52916	−	0.882860i
$417$		0			0
$418$	−62.7489	+	108.684i	−0.150117	+	0.260010i
$419$	−107.238	−	61.9139i	−0.255938	−	0.147766i	0.366542	−	0.930401i	$-0.380542\pi$
$419$	−107.238	−	61.9139i	−0.255938	−	0.147766i	−0.622480	+	0.782635i	$0.713875\pi$
$420$		0			0
$421$	−206.378	−	357.457i	−0.490208	−	0.849065i	0.509728	−	0.860335i	$-0.329746\pi$
$421$	−206.378	−	357.457i	−0.490208	−	0.849065i	−0.999936	+	0.0112700i	$0.996413\pi$
$422$		−	79.1643i		−	0.187593i
$423$		0			0
$424$	−290.287			−0.684638
$425$	126.807	−	73.2119i	0.298369	−	0.172263i
$426$		0			0
$427$	50.0702	−	86.7241i	0.117260	−	0.203101i
$428$	−106.580	−	61.5341i	−0.249019	−	0.143771i
$429$		0			0
$430$	−90.8289	−	157.320i	−0.211230	−	0.365861i
$431$			360.015i			0.835303i	0.908607	+	0.417651i	$0.137147\pi$
$431$			360.015i			0.835303i	−0.908607	+	0.417651i	$0.862853\pi$
$432$		0			0
$433$	−299.670			−0.692078			−0.346039	−	0.938220i	$-0.612473\pi$
$433$	−299.670			−0.692078			−0.346039	+	0.938220i	$0.612473\pi$
$434$	60.3871	−	34.8645i	0.139141	−	0.0803330i
$435$		0			0
$436$	139.115	−	240.955i	0.319072	−	0.552649i
$437$	129.527	+	74.7823i	0.296400	+	0.171127i
$438$		0			0
$439$	219.286	+	379.815i	0.499513	+	0.865183i	1.00000		0.000561671i	$-0.000178786\pi$
$439$	219.286	+	379.815i	0.499513	+	0.865183i	−0.500486	+	0.865744i	$0.666845\pi$
$440$		−	806.218i		−	1.83231i
$441$		0			0
$442$	79.8035			0.180551
$443$	−271.723	+	156.879i	−0.613370	+	0.354130i	−0.774283	−	0.632839i	$-0.781889\pi$
$443$	−271.723	+	156.879i	−0.613370	+	0.354130i	0.160913	+	0.986969i	$0.448556\pi$
$444$		0			0
$445$	−533.849	+	924.654i	−1.19966	+	2.07787i
$446$	165.441	+	95.5171i	0.370943	+	0.214164i
$447$		0			0
$448$	−12.2679	−	21.2485i	−0.0273836	−	0.0474298i
$449$			575.345i			1.28139i	0.767795	+	0.640696i	$0.221354\pi$
$449$			575.345i			1.28139i	−0.767795	+	0.640696i	$0.778646\pi$
$450$		0			0
$451$	631.996			1.40132
$452$	144.953	−	83.6888i	0.320693	−	0.185152i
$453$		0			0
$454$	86.7163	−	150.197i	0.191005	−	0.330830i
$455$	−419.368	−	242.123i	−0.921689	−	0.532137i
$456$		0			0
$457$	−220.299	−	381.569i	−0.482054	−	0.834942i	0.517734	−	0.855542i	$-0.326776\pi$
$457$	−220.299	−	381.569i	−0.482054	−	0.834942i	−0.999788	+	0.0205996i	$0.993442\pi$
$458$			228.711i			0.499370i
$459$		0			0
$460$	−437.579			−0.951258
$461$	−93.3163	+	53.8762i	−0.202421	+	0.116868i	−0.597784	−	0.801657i	$-0.703952\pi$
$461$	−93.3163	+	53.8762i	−0.202421	+	0.116868i	0.395363	+	0.918525i	$0.370619\pi$
$462$		0			0
$463$	253.384	−	438.875i	0.547267	−	0.947894i	−0.451194	−	0.892426i	$-0.649002\pi$
$463$	253.384	−	438.875i	0.547267	−	0.947894i	0.998460	−	0.0554677i	$-0.0176650\pi$
$464$	242.810	+	140.187i	0.523298	+	0.302126i
$465$		0			0
$466$	24.2094	+	41.9319i	0.0519515	+	0.0899827i
$467$		−	182.287i		−	0.390337i	−0.980770	−	0.195169i	$-0.937475\pi$
$467$		−	182.287i		−	0.390337i	0.980770	−	0.195169i	$-0.0625254\pi$
$468$		0			0
$469$	150.179			0.320210
$470$	346.622	−	200.122i	0.737494	−	0.425792i
$471$		0			0
$472$	87.8904	−	152.231i	0.186208	−	0.322523i
$473$	435.731	+	251.569i	0.921207	+	0.531859i
$474$		0			0
$475$	157.930	+	273.542i	0.332483	+	0.575878i
$476$		−	35.8975i		−	0.0754148i
$477$		0			0
$478$	−65.1662			−0.136331
$479$	−21.7465	+	12.5553i	−0.0453998	+	0.0262116i	−0.522528	−	0.852622i	$-0.675011\pi$
$479$	−21.7465	+	12.5553i	−0.0453998	+	0.0262116i	0.477128	+	0.878834i	$0.341678\pi$
$480$		0			0
$481$	−549.213	+	951.264i	−1.14181	+	1.97768i
$482$	101.383	+	58.5333i	0.210337	+	0.121438i
$483$		0			0
$484$	306.094	+	530.170i	0.632425	+	1.09539i
$485$		−	1248.06i		−	2.57332i
$486$		0			0
$487$	−374.163			−0.768302			−0.384151	−	0.923270i	$-0.625506\pi$
$487$	−374.163			−0.768302			−0.384151	+	0.923270i	$0.625506\pi$
$488$	198.059	−	114.349i	0.405858	−	0.234322i
$489$		0			0
$490$	−132.910	+	230.207i	−0.271245	+	0.469810i
$491$	360.289	+	208.013i	0.733786	+	0.423652i	0.819806	−	0.572642i	$-0.194081\pi$
$491$	360.289	+	208.013i	0.733786	+	0.423652i	−0.0860194	+	0.996293i	$0.527415\pi$
$492$		0			0
$493$	67.4439	+	116.816i	0.136803	+	0.236950i
$494$			172.149i			0.348479i
$495$		0			0
$496$	−283.717			−0.572011
$497$	36.8740	−	21.2892i	0.0741931	−	0.0428354i
$498$		0			0
$499$	−175.883	+	304.638i	−0.352470	+	0.610496i	−0.986682	−	0.162663i	$-0.947992\pi$
$499$	−175.883	+	304.638i	−0.352470	+	0.610496i	0.634211	+	0.773160i	$0.281325\pi$
$500$	−236.914	−	136.782i	−0.473828	−	0.273565i
$501$		0			0
$502$	75.8456	+	131.368i	0.151087	+	0.261690i
$503$		−	262.131i		−	0.521134i	−0.965456	−	0.260567i	$-0.916090\pi$
$503$		−	262.131i		−	0.521134i	0.965456	−	0.260567i	$-0.0839095\pi$
$504$		0			0
$505$	619.325			1.22639
$506$	−205.486	+	118.638i	−0.406100	+	0.234462i
$507$		0			0
$508$	223.330	−	386.818i	0.439625	−	0.761453i
$509$	686.562	+	396.387i	1.34885	+	0.778756i	0.988086	−	0.153902i	$-0.0491842\pi$
$509$	686.562	+	396.387i	1.34885	+	0.778756i	0.360760	+	0.932659i	$0.382517\pi$
$510$		0			0
$511$	2.10639	+	3.64837i	0.00412209	+	0.00713967i
$512$		−	466.970i		−	0.912051i
$513$		0			0
$514$	−169.158			−0.329102
$515$	−820.660	+	473.808i	−1.59351	+	0.920016i
$516$		0			0
$517$	−554.280	+	960.041i	−1.07211	+	1.85695i
$518$	−83.7733	−	48.3665i	−0.161725	−	0.0933717i
$519$		0			0
$520$	−552.955	−	957.746i	−1.06337	−	1.84182i
$521$		−	113.473i		−	0.217798i	−0.994053	−	0.108899i	$-0.965267\pi$
$521$		−	113.473i		−	0.217798i	0.994053	−	0.108899i	$-0.0347326\pi$
$522$		0			0
$523$	145.974			0.279108			0.139554	−	0.990214i	$-0.455433\pi$
$523$	145.974			0.279108			0.139554	+	0.990214i	$0.455433\pi$
$524$	−383.094	+	221.179i	−0.731094	+	0.422098i
$525$		0			0
$526$	52.3120	−	90.6071i	0.0994525	−	0.172257i
$527$	−118.210	−	68.2484i	−0.224307	−	0.129504i
$528$		0			0
$529$	−123.111	−	213.235i	−0.232724	−	0.403091i
$530$			307.435i			0.580066i
$531$		0			0
$532$	77.4365			0.145557
$533$	750.779	−	433.462i	1.40859	−	0.813250i
$534$		0			0
$535$	−143.097	+	247.851i	−0.267471	+	0.463273i
$536$	297.025	+	171.487i	0.554151	+	0.319939i
$537$		0			0
$538$	−61.1061	−	105.839i	−0.113580	−	0.196726i
$539$		−	736.244i		−	1.36594i
$540$		0			0
$541$	−707.289			−1.30737			−0.653687	−	0.756765i	$-0.726779\pi$
$541$	−707.289			−1.30737			−0.653687	+	0.756765i	$0.726779\pi$
$542$	−282.241	+	162.952i	−0.520741	+	0.300650i
$543$		0			0
$544$	63.3138	−	109.663i	0.116386	−	0.201586i
$545$	−560.339	−	323.512i	−1.02814	−	0.593599i
$546$		0			0
$547$	395.340	+	684.749i	0.722742	+	1.25183i	0.959897	+	0.280354i	$0.0904517\pi$
$547$	395.340	+	684.749i	0.722742	+	1.25183i	−0.237155	+	0.971472i	$0.576215\pi$
$548$		−	288.421i		−	0.526315i
$549$		0			0
$550$	−501.092			−0.911076
$551$	−251.991	+	145.487i	−0.457334	+	0.264042i
$552$		0			0
$553$	−23.1906	+	40.1672i	−0.0419359	+	0.0726351i
$554$	−112.731	−	65.0851i	−0.203485	−	0.117482i
$555$		0			0
$556$	19.8532	+	34.3868i	0.0357073	+	0.0618468i
$557$		−	669.172i		−	1.20139i	−0.799480	−	0.600693i	$-0.794891\pi$
$557$		−	669.172i		−	1.20139i	0.799480	−	0.600693i	$-0.205109\pi$
$558$		0			0
$559$	690.168			1.23465
$560$	−150.270	+	86.7585i	−0.268339	+	0.154926i
$561$		0			0
$562$	32.8496	−	56.8973i	0.0584513	−	0.101241i
$563$	−407.216	−	235.106i	−0.723296	−	0.417595i	0.0926683	−	0.995697i	$-0.470460\pi$
$563$	−407.216	−	235.106i	−0.723296	−	0.417595i	−0.815965	+	0.578102i	$0.803794\pi$
$564$		0			0
$565$	−194.618	−	337.088i	−0.344456	−	0.596615i
$566$		−	257.791i		−	0.455461i
$567$		0			0
$568$	97.2397			0.171197
$569$	−740.263	+	427.391i	−1.30099	+	0.751126i	−0.980574	−	0.196151i	$-0.937156\pi$
$569$	−740.263	+	427.391i	−1.30099	+	0.751126i	−0.320415	+	0.947277i	$0.603822\pi$
$570$		0			0
$571$	−26.2338	+	45.4382i	−0.0459435	+	0.0795765i	−0.888083	−	0.459684i	$-0.847963\pi$
$571$	−26.2338	+	45.4382i	−0.0459435	+	0.0795765i	0.842139	+	0.539260i	$0.181296\pi$
$572$	1208.08	+	697.485i	2.11203	+	1.21938i
$573$		0			0
$574$	38.1730	+	66.1175i	0.0665034	+	0.115187i
$575$			597.186i			1.03858i
$576$		0			0
$577$	−116.156			−0.201310			−0.100655	−	0.994921i	$-0.532094\pi$
$577$	−116.156			−0.201310			−0.100655	+	0.994921i	$0.532094\pi$
$578$	11.9142	−	6.87868i	0.0206128	−	0.0119008i
$579$		0			0
$580$	425.650	−	737.247i	0.733879	−	1.27112i
$581$	−109.886	−	63.4426i	−0.189132	−	0.109196i
$582$		0			0
$583$	−425.752	−	737.425i	−0.730278	−	1.26488i
$584$			9.62106i			0.0164744i
$585$		0			0
$586$	−362.400			−0.618431
$587$	102.248	−	59.0327i	0.174187	−	0.100567i	−0.410372	−	0.911918i	$-0.634601\pi$
$587$	102.248	−	59.0327i	0.174187	−	0.100567i	0.584559	+	0.811352i	$0.301268\pi$
$588$		0			0
$589$	147.223	−	254.997i	0.249954	−	0.432932i
$590$	−161.223	−	93.0824i	−0.273260	−	0.157767i
$591$		0			0
$592$	196.796	+	340.861i	0.332426	+	0.575779i
$593$		−	826.854i		−	1.39436i	−0.716897	−	0.697179i	$-0.754438\pi$
$593$		−	826.854i		−	1.39436i	0.716897	−	0.697179i	$-0.245562\pi$
$594$		0			0
$595$	−83.4792			−0.140301
$596$	212.336	−	122.592i	0.356269	−	0.205692i
$597$		0			0
$598$	−162.738	+	281.871i	−0.272138	+	0.471356i
$599$	−398.877	−	230.292i	−0.665905	−	0.384460i	0.128618	−	0.991694i	$-0.458946\pi$
$599$	−398.877	−	230.292i	−0.665905	−	0.384460i	−0.794523	+	0.607234i	$0.792279\pi$
$600$		0			0
$601$	109.567	+	189.775i	0.182307	+	0.315765i	0.942666	−	0.333738i	$-0.108310\pi$
$601$	109.567	+	189.775i	0.182307	+	0.315765i	−0.760359	+	0.649503i	$0.774977\pi$
$602$			60.7798i			0.100963i
$603$		0			0
$604$	−633.663			−1.04911
$605$	1232.91	−	711.818i	2.03786	−	1.17656i
$606$		0			0
$607$	−317.333	+	549.637i	−0.522789	+	0.905498i	0.476859	+	0.878980i	$0.341775\pi$
$607$	−317.333	+	549.637i	−0.522789	+	0.905498i	−0.999648	+	0.0265179i	$0.991558\pi$
$608$	236.560	+	136.578i	0.389079	+	0.224635i
$609$		0			0
$610$	−121.104	−	209.759i	−0.198532	−	0.343867i
$611$			1520.64i			2.48877i
$612$		0			0
$613$	−536.095			−0.874543			−0.437272	−	0.899329i	$-0.644055\pi$
$613$	−536.095			−0.874543			−0.437272	+	0.899329i	$0.644055\pi$
$614$	−214.526	+	123.857i	−0.349391	+	0.201721i
$615$		0			0
$616$	−134.874	+	233.608i	−0.218951	+	0.379234i
$617$	9.53178	+	5.50317i	0.0154486	+	0.00891924i	0.507704	−	0.861531i	$-0.330494\pi$
$617$	9.53178	+	5.50317i	0.0154486	+	0.00891924i	−0.492256	+	0.870451i	$0.663828\pi$
$618$		0			0
$619$	−334.758	−	579.817i	−0.540804	−	0.936700i	−0.998858	−	0.0477756i	$-0.984787\pi$
$619$	−334.758	−	579.817i	−0.540804	−	0.936700i	0.458054	−	0.888924i	$-0.348547\pi$
$620$			861.454i			1.38944i
$621$		0			0
$622$	191.231			0.307446
$623$	309.375	−	178.618i	0.496589	−	0.286706i
$624$		0			0
$625$	125.826	−	217.937i	0.201322	−	0.348700i
$626$	135.174	+	78.0426i	0.215932	+	0.124669i
$627$		0			0
$628$	75.6886	+	131.096i	0.120523	+	0.208752i
$629$			189.358i			0.301046i
$630$		0			0
$631$	571.390			0.905530			0.452765	−	0.891630i	$-0.350438\pi$
$631$	571.390			0.905530			0.452765	+	0.891630i	$0.350438\pi$
$632$	−91.7331	+	52.9622i	−0.145147	+	0.0838009i
$633$		0			0
$634$	−86.4886	+	149.803i	−0.136417	+	0.236282i
$635$	−899.542	−	519.351i	−1.41660	−	0.817875i
$636$		0			0
$637$	−504.962	−	874.620i	−0.792719	−	1.37303i
$638$		−	461.613i		−	0.723532i
$639$		0			0
$640$	−1014.97			−1.58589
$641$	90.7482	−	52.3935i	0.141573	−	0.0817371i	−0.427541	−	0.903996i	$-0.640620\pi$
$641$	90.7482	−	52.3935i	0.141573	−	0.0817371i	0.569113	+	0.822259i	$0.307287\pi$
$642$		0			0
$643$	338.509	−	586.314i	0.526452	−	0.911842i	−0.473073	−	0.881023i	$-0.656855\pi$
$643$	338.509	−	586.314i	0.526452	−	0.911842i	0.999525	−	0.0308184i	$-0.00981135\pi$
$644$	126.792	+	73.2035i	0.196882	+	0.113670i
$645$		0			0
$646$	14.8384	+	25.7009i	0.0229697	+	0.0397846i
$647$			118.927i			0.183813i	0.995768	+	0.0919063i	$0.0292960\pi$
$647$			118.927i			0.183813i	−0.995768	+	0.0919063i	$0.970704\pi$
$648$		0			0
$649$	515.622			0.794487
$650$	−595.271	+	343.680i	−0.915802	+	0.528739i
$651$		0			0
$652$	−469.763	+	813.653i	−0.720495	+	1.24793i
$653$	−577.614	−	333.486i	−0.884555	−	0.510698i	−0.0123973	−	0.999923i	$-0.503946\pi$
$653$	−577.614	−	333.486i	−0.884555	−	0.510698i	−0.872158	+	0.489225i	$0.837280\pi$
$654$		0			0
$655$	514.350	+	890.880i	0.785267	+	1.36012i
$656$		−	310.640i		−	0.473537i
$657$		0			0
$658$	−133.916			−0.203519
$659$	459.361	−	265.212i	0.697057	−	0.402446i	−0.109193	−	0.994021i	$-0.534827\pi$
$659$	459.361	−	265.212i	0.697057	−	0.402446i	0.806250	+	0.591574i	$0.201493\pi$
$660$		0			0
$661$	40.9369	−	70.9047i	0.0619317	−	0.107269i	−0.833397	−	0.552675i	$-0.813607\pi$
$661$	40.9369	−	70.9047i	0.0619317	−	0.107269i	0.895329	+	0.445406i	$0.146941\pi$
$662$	−361.389	−	208.648i	−0.545905	−	0.315179i
$663$		0			0
$664$	−144.889	−	250.955i	−0.218206	−	0.377944i
$665$		−	180.078i		−	0.270794i
$666$		0			0
$667$	−550.137			−0.824793
$668$	326.129	−	188.291i	0.488218	−	0.281873i
$669$		0			0
$670$	181.618	−	314.571i	0.271072	−	0.469510i
$671$	580.970	+	335.423i	0.865827	+	0.499886i
$672$		0			0
$673$	469.151	+	812.594i	0.697104	+	1.20742i	0.969466	+	0.245225i	$0.0788618\pi$
$673$	469.151	+	812.594i	0.697104	+	1.20742i	−0.272362	+	0.962195i	$0.587805\pi$
$674$			226.287i			0.335737i
$675$		0			0
$676$	1348.19			1.99437
$677$	−1115.11	+	643.808i	−1.64713	+	0.950972i	−0.668929	+	0.743327i	$0.733247\pi$
$677$	−1115.11	+	643.808i	−1.64713	+	0.950972i	−0.978204	+	0.207646i	$0.933420\pi$
$678$		0			0
$679$	−208.790	+	361.636i	−0.307497	+	0.532600i
$680$	−165.106	−	95.3241i	−0.242803	−	0.140183i
$681$		0			0
$682$	233.560	+	404.537i	0.342463	+	0.593163i
$683$			37.8698i			0.0554463i	0.999616	+	0.0277231i	$0.00882568\pi$
$683$			37.8698i			0.0554463i	−0.999616	+	0.0277231i	$0.991174\pi$
$684$		0			0
$685$	−670.719			−0.979152
$686$	166.404	−	96.0734i	0.242572	−	0.140049i
$687$		0			0
$688$	123.652	−	214.172i	0.179727	−	0.311296i
$689$	−1011.54	−	584.015i	−1.46813	−	0.847628i
$690$		0			0
$691$	151.336	+	262.121i	0.219010	+	0.379336i	0.954506	−	0.298193i	$-0.0963840\pi$
$691$	151.336	+	262.121i	0.219010	+	0.379336i	−0.735496	+	0.677529i	$0.763051\pi$
$692$		−	417.993i		−	0.604036i
$693$		0			0
$694$	8.77973			0.0126509
$695$	79.9662	−	46.1685i	0.115059	−	0.0664295i
$696$		0			0
$697$	74.7248	−	129.427i	0.107209	−	0.185692i
$698$	308.740	+	178.251i	0.442321	+	0.255374i
$699$		0			0
$700$	154.595	+	267.767i	0.220851	+	0.382524i
$701$			864.985i			1.23393i	0.786990	+	0.616965i	$0.211638\pi$
$701$			864.985i			1.23393i	−0.786990	+	0.616965i	$0.788362\pi$
$702$		0			0
$703$	−408.475			−0.581046
$704$	142.345	−	82.1832i	0.202195	−	0.116737i
$705$		0			0
$706$	−48.9881	+	84.8499i	−0.0693882	+	0.120184i
$707$	−179.455	−	103.608i	−0.253825	−	0.146546i
$708$		0			0
$709$	556.871	+	964.529i	0.785432	+	1.36041i	0.928741	+	0.370729i	$0.120892\pi$
$709$	556.871	+	964.529i	0.785432	+	1.36041i	−0.143309	+	0.989678i	$0.545774\pi$
$710$		−	102.984i		−	0.145048i
$711$		0			0
$712$	815.846			1.14585
$713$	482.116	−	278.350i	0.676179	−	0.390392i
$714$		0			0
$715$	1621.99	−	2809.38i	2.26852	−	3.92920i
$716$	−669.367	−	386.459i	−0.934870	−	0.539747i
$717$		0			0
$718$	180.878	+	313.289i	0.251919	+	0.436336i
$719$			325.866i			0.453221i	0.973985	+	0.226610i	$0.0727644\pi$
$719$			325.866i			0.453221i	−0.973985	+	0.226610i	$0.927236\pi$
$720$		0			0
$721$	317.057			0.439747
$722$	197.561	−	114.062i	0.273630	−	0.157981i
$723$		0			0
$724$	36.1346	−	62.5869i	0.0499097	−	0.0864461i
$725$	−1006.16	−	580.906i	−1.38780	−	0.801249i
$726$		0			0
$727$	86.7563	+	150.266i	0.119335	+	0.206694i	0.919504	−	0.393080i	$-0.128591\pi$
$727$	86.7563	+	150.266i	0.119335	+	0.206694i	−0.800170	+	0.599774i	$0.795257\pi$
$728$			370.020i			0.508269i
$729$		0			0
$730$	10.1894			0.0139581
$731$	103.038	−	59.4892i	0.140955	−	0.0813806i
$732$		0			0
$733$	607.986	−	1053.06i	0.829449	−	1.43665i	−0.0690228	−	0.997615i	$-0.521988\pi$
$733$	607.986	−	1053.06i	0.829449	−	1.43665i	0.898471	−	0.439032i	$-0.144679\pi$
$734$	285.352	+	164.748i	0.388763	+	0.224452i
$735$		0			0
$736$	258.224	+	447.257i	0.350848	+	0.607686i
$737$			1006.06i			1.36507i
$738$		0			0
$739$	−555.714			−0.751981			−0.375991	−	0.926623i	$-0.622698\pi$
$739$	−555.714			−0.751981			−0.375991	+	0.926623i	$0.622698\pi$
$740$	1034.96	−	597.535i	1.39860	−	0.807480i
$741$		0			0
$742$	51.4315	−	89.0819i	0.0693146	−	0.120056i
$743$	−418.217	−	241.458i	−0.562877	−	0.324977i	0.191423	−	0.981508i	$-0.438690\pi$
$743$	−418.217	−	241.458i	−0.562877	−	0.324977i	−0.754299	+	0.656531i	$0.772023\pi$
$744$		0			0
$745$	−285.087	−	493.786i	−0.382668	−	0.662800i
$746$		−	503.750i		−	0.675268i
$747$		0			0
$748$	240.479			0.321497
$749$	82.9271	−	47.8780i	0.110717	−	0.0639226i
$750$		0			0
$751$	−44.9522	+	77.8596i	−0.0598565	+	0.103675i	−0.894401	−	0.447266i	$-0.852398\pi$
$751$	−44.9522	+	77.8596i	−0.0598565	+	0.103675i	0.834544	+	0.550941i	$0.185731\pi$
$752$	471.882	+	272.441i	0.627503	+	0.362289i
$753$		0			0
$754$	−316.603	−	548.373i	−0.419898	−	0.727285i
$755$			1473.58i			1.95176i
$756$		0			0
$757$	647.421			0.855246			0.427623	−	0.903957i	$-0.359351\pi$
$757$	647.421			0.855246			0.427623	+	0.903957i	$0.359351\pi$
$758$	401.483	−	231.796i	0.529661	−	0.305800i
$759$		0			0
$760$	205.629	−	356.160i	0.270565	−	0.468632i
$761$	889.297	+	513.436i	1.16859	+	0.674686i	0.953347	−	0.301875i	$-0.0976126\pi$
$761$	889.297	+	513.436i	1.16859	+	0.674686i	0.215242	+	0.976561i	$0.430946\pi$
$762$		0			0
$763$	108.242	+	187.480i	0.141864	+	0.245715i
$764$		−	966.720i		−	1.26534i
$765$		0			0
$766$	−63.7731			−0.0832547
$767$	612.533	−	353.646i	0.798608	−	0.461077i
$768$		0			0
$769$	−731.569	+	1267.12i	−0.951325	+	1.64774i	−0.208764	+	0.977966i	$0.566944\pi$
$769$	−731.569	+	1267.12i	−0.951325	+	1.64774i	−0.742562	+	0.669778i	$0.766389\pi$
$770$	247.408	+	142.841i	0.321310	+	0.185508i
$771$		0			0
$772$	24.8185	+	42.9870i	0.0321484	+	0.0556826i
$773$		−	808.771i		−	1.04628i	−0.852248	−	0.523138i	$-0.824761\pi$
$773$		−	808.771i		−	1.04628i	0.852248	−	0.523138i	$-0.175239\pi$
$774$		0			0
$775$	1175.67			1.51699
$776$	−825.896	+	476.831i	−1.06430	+	0.614473i
$777$		0			0
$778$	−1.00430	+	1.73950i	−0.00129087	+	0.00223586i
$779$	279.195	+	161.193i	0.358401	+	0.206923i
$780$		0			0
$781$	142.618	+	247.021i	0.182609	+	0.316288i
$782$			56.1091i			0.0717507i
$783$		0			0
$784$	−361.881			−0.461583
$785$	304.864	−	176.013i	0.388361	−	0.224221i
$786$		0			0
$787$	−610.354	+	1057.16i	−0.775546	+	1.34328i	0.158942	+	0.987288i	$0.449192\pi$
$787$	−610.354	+	1057.16i	−0.775546	+	1.34328i	−0.934487	+	0.355996i	$0.884142\pi$
$788$	24.9674	+	14.4149i	0.0316845	+	0.0182931i
$789$		0			0
$790$	56.0908	+	97.1522i	0.0710011	+	0.122977i
$791$			130.232i			0.164642i
$792$		0			0
$793$	920.217			1.16043
$794$	−169.759	+	98.0105i	−0.213802	+	0.123439i
$795$		0			0
$796$	−479.653	+	830.783i	−0.602579	+	1.04370i
$797$	39.7449	+	22.9467i	0.0498681	+	0.0287914i	0.524727	−	0.851271i	$-0.324167\pi$
$797$	39.7449	+	22.9467i	0.0498681	+	0.0287914i	−0.474859	+	0.880062i	$0.657501\pi$
$798$		0			0
$799$	131.072	+	227.023i	0.164045	+	0.284134i
$800$			1090.67i			1.36333i
$801$		0			0
$802$	438.289			0.546496
$803$	−24.4407	+	14.1108i	−0.0304367	+	0.0175726i
$804$		0			0
$805$	170.234	−	294.854i	0.211471	−	0.366278i
$806$	554.914	+	320.380i	0.688479	+	0.397494i
$807$		0			0
$808$	−236.618	−	409.835i	−0.292844	−	0.507221i
$809$			1333.69i			1.64856i	0.566181	+	0.824281i	$0.308420\pi$
$809$			1333.69i			1.64856i	−0.566181	+	0.824281i	$0.691580\pi$
$810$		0			0
$811$	123.988			0.152883			0.0764413	−	0.997074i	$-0.475644\pi$
$811$	123.988			0.152883			0.0764413	+	0.997074i	$0.475644\pi$
$812$	−246.671	+	142.416i	−0.303782	+	0.175389i
$813$		0			0
$814$	324.011	−	561.203i	0.398047	−	0.689438i
$815$	1892.14	+	1092.43i	2.32165	+	1.34040i
$816$		0			0
$817$	128.328	+	222.270i	0.157072	+	0.272056i
$818$		−	343.552i		−	0.419991i
$819$		0			0
$820$	−943.201			−1.15024
$821$	−55.9299	+	32.2911i	−0.0681241	+	0.0393315i	−0.533675	−	0.845690i	$-0.679189\pi$
$821$	−55.9299	+	32.2911i	−0.0681241	+	0.0393315i	0.465551	+	0.885021i	$0.345856\pi$
$822$		0			0
$823$	−319.130	+	552.749i	−0.387764	+	0.671627i	−0.992148	−	0.125066i	$-0.960086\pi$
$823$	−319.130	+	552.749i	−0.387764	+	0.671627i	0.604384	+	0.796693i	$0.293419\pi$
$824$	627.080	+	362.045i	0.761019	+	0.439375i
$825$		0			0
$826$	31.1439	+	53.9428i	0.0377045	+	0.0653061i
$827$			1439.50i			1.74063i	0.492499	+	0.870313i	$0.336084\pi$
$827$			1439.50i			1.74063i	−0.492499	+	0.870313i	$0.663916\pi$
$828$		0			0
$829$	459.699			0.554522			0.277261	−	0.960795i	$-0.410573\pi$
$829$	459.699			0.554522			0.277261	+	0.960795i	$0.410573\pi$
$830$	−265.780	+	153.448i	−0.320217	+	0.184877i
$831$		0			0
$832$	112.733	−	195.259i	0.135496	−	0.234686i
$833$	−150.776	−	87.0507i	−0.181004	−	0.104503i
$834$		0			0
$835$	−437.869	−	758.411i	−0.524394	−	0.908277i
$836$			518.752i			0.620517i
$837$		0			0
$838$	100.208			0.119581
$839$	−1048.31	+	605.242i	−1.24948	+	0.721385i	−0.971005	−	0.239059i	$-0.923161\pi$
$839$	−1048.31	+	605.242i	−1.24948	+	0.721385i	−0.278471	+	0.960445i	$0.589828\pi$
$840$		0			0
$841$	114.639	−	198.561i	0.136313	−	0.236101i
$842$	289.274	+	167.012i	0.343556	+	0.198352i
$843$		0			0
$844$	−163.615	−	283.390i	−0.193857	−	0.335770i
$845$		−	3135.21i		−	3.71031i
$846$		0			0
$847$	−476.326			−0.562369
$848$	−362.461	+	209.267i	−0.427431	+	0.246777i
$849$		0			0
$850$	−59.2472	+	102.619i	−0.0697026	+	0.120728i
$851$	−668.825	−	386.146i	−0.785928	−	0.453756i
$852$		0			0
$853$	−577.517	−	1000.29i	−0.677042	−	1.17267i	−0.975867	−	0.218364i	$-0.929928\pi$
$853$	−577.517	−	1000.29i	−0.677042	−	1.17267i	0.298825	−	0.954308i	$-0.403405\pi$
$854$			81.0392i			0.0948936i
$855$		0			0
$856$	218.686			0.255474
$857$	490.803	−	283.365i	0.572699	−	0.330648i	−0.185528	−	0.982639i	$-0.559399\pi$
$857$	490.803	−	283.365i	0.572699	−	0.330648i	0.758226	+	0.651991i	$0.226066\pi$
$858$		0			0
$859$	39.6787	−	68.7256i	0.0461918	−	0.0800065i	−0.842005	−	0.539470i	$-0.818625\pi$
$859$	39.6787	−	68.7256i	0.0461918	−	0.0800065i	0.888197	+	0.459463i	$0.151958\pi$
$860$	−650.292	−	375.446i	−0.756153	−	0.436565i
$861$		0			0
$862$	−145.672	−	252.312i	−0.168993	−	0.292705i
$863$			828.604i			0.960144i	0.877229	+	0.480072i	$0.159389\pi$
$863$			828.604i			0.960144i	−0.877229	+	0.480072i	$0.840611\pi$
$864$		0			0
$865$	−972.039			−1.12374
$866$	210.019	−	121.255i	0.242517	−	0.140017i
$867$		0			0
$868$	144.114	−	249.613i	0.166030	−	0.287573i
$869$	−269.083	−	155.355i	−0.309647	−	0.178775i
$870$		0			0
$871$	690.017	+	1195.14i	0.792212	+	1.37215i
$872$			494.401i			0.566974i
$873$		0			0
$874$	−121.036			−0.138485
$875$	184.336	−	106.427i	0.210670	−	0.121630i
$876$		0			0
$877$	661.272	−	1145.36i	0.754016	−	1.30599i	−0.191845	−	0.981425i	$-0.561447\pi$
$877$	661.272	−	1145.36i	0.754016	−	1.30599i	0.945862	−	0.324570i	$-0.105219\pi$
$878$	−307.368	−	177.459i	−0.350077	−	0.202117i
$879$		0			0
$880$	−581.201	−	1006.67i	−0.660455	−	1.14394i
$881$		−	807.386i		−	0.916443i	−0.888838	−	0.458221i	$-0.848487\pi$
$881$		−	807.386i		−	0.916443i	0.888838	−	0.458221i	$-0.151513\pi$
$882$		0			0
$883$	−1103.04			−1.24919			−0.624597	−	0.780947i	$-0.714737\pi$
$883$	−1103.04			−1.24919			−0.624597	+	0.780947i	$0.714737\pi$
$884$	285.677	−	164.936i	0.323165	−	0.186579i
$885$		0			0
$886$	126.956	−	219.894i	0.143291	−	0.248187i
$887$	1173.09	+	677.283i	1.32253	+	0.763566i	0.984132	−	0.177436i	$-0.0567802\pi$
$887$	1173.09	+	677.283i	1.32253	+	0.763566i	0.338402	+	0.941002i	$0.390114\pi$
$888$		0			0
$889$	173.767	+	300.973i	0.195463	+	0.338552i
$890$		−	864.042i		−	0.970833i
$891$		0			0
$892$	789.650			0.885258
$893$	−489.725	+	282.743i	−0.548404	+	0.316621i
$894$		0			0
$895$	−898.707	+	1556.61i	−1.00414	+	1.73923i
$896$	294.097	+	169.797i	0.328233	+	0.189505i
$897$		0			0
$898$	−232.801	−	403.223i	−0.259244	−	0.449023i
$899$			1083.04i			1.20472i
$900$		0			0
$901$	−201.357			−0.223482
$902$	−442.926	+	255.723i	−0.491048	+	0.283507i
$903$		0			0
$904$	−148.711	+	257.574i	−0.164503	+	0.284927i
$905$	−145.545	−	84.0307i	−0.160824	−	0.0928515i
$906$		0			0
$907$	2.58101	+	4.47044i	0.00284565	+	0.00492882i	0.867445	−	0.497534i	$-0.165761\pi$
$907$	2.58101	+	4.47044i	0.00284565	+	0.00492882i	−0.864599	+	0.502462i	$0.832428\pi$
$908$		−	716.893i		−	0.789529i
$909$		0			0
$910$	391.878			0.430636
$911$	−1259.49	+	727.164i	−1.38253	+	0.798205i	−0.992459	−	0.122580i	$-0.960883\pi$
$911$	−1259.49	+	727.164i	−1.38253	+	0.798205i	−0.390072	+	0.920784i	$0.627550\pi$
$912$		0			0
$913$	425.006	−	736.132i	0.465505	−	0.806279i
$914$	308.787	+	178.278i	0.337841	+	0.195053i
$915$		0			0
$916$	472.695	+	818.732i	0.516043	+	0.893812i
$917$		−	344.187i		−	0.375340i
$918$		0			0
$919$	285.223			0.310362			0.155181	−	0.987886i	$-0.450404\pi$
$919$	285.223			0.310362			0.155181	+	0.987886i	$0.450404\pi$
$920$	673.382	−	388.777i	0.731937	−	0.422584i
$921$		0			0
$922$	43.5996	−	75.5168i	0.0472881	−	0.0819054i
$923$	338.845	+	195.632i	0.367113	+	0.211953i
$924$		0			0
$925$	−815.486	−	1412.46i	−0.881606	−	1.52699i
$926$			410.106i			0.442879i
$927$		0			0
$928$	−1004.74			−1.08269
$929$	−748.901	+	432.378i	−0.806137	+	0.465423i	−0.845612	−	0.533797i	$-0.820765\pi$
$929$	−748.901	+	432.378i	−0.806137	+	0.465423i	0.0394759	+	0.999221i	$0.487431\pi$
$930$		0			0
$931$	187.782	−	325.248i	0.201699	−	0.349353i
$932$	173.328	+	100.071i	0.185974	+	0.107372i
$933$		0			0
$934$	73.7586	+	127.754i	0.0789707	+	0.136781i
$935$		−	559.233i		−	0.598110i
$936$		0			0
$937$	468.142			0.499618			0.249809	−	0.968295i	$-0.419632\pi$
$937$	468.142			0.499618			0.249809	+	0.968295i	$0.419632\pi$
$938$	−105.251	+	60.7665i	−0.112208	+	0.0647830i
$939$		0			0
$940$	827.216	−	1432.78i	0.880018	−	1.52424i
$941$	398.668	+	230.171i	0.423665	+	0.244603i	0.696644	−	0.717417i	$-0.254676\pi$
$941$	398.668	+	230.171i	0.423665	+	0.244603i	−0.272979	+	0.962020i	$0.588009\pi$
$942$		0			0
$943$	304.763	+	527.865i	0.323185	+	0.559772i
$944$		−	253.440i		−	0.268475i
$945$		0			0
$946$	−407.168			−0.430410
$947$	1377.75	−	795.443i	1.45486	−	0.839961i	0.456104	−	0.889926i	$-0.349244\pi$
$947$	1377.75	−	795.443i	1.45486	−	0.839961i	0.998751	+	0.0499655i	$0.0159111\pi$
$948$		0			0
$949$	−19.3562	+	33.5259i	−0.0203964	+	0.0353276i
$950$	−221.366	−	127.806i	−0.233017	−	0.134532i
$951$		0			0
$952$	31.8939	+	55.2419i	0.0335020	+	0.0580272i
$953$		−	1298.89i		−	1.36295i	−0.731843	−	0.681474i	$-0.761339\pi$
$953$		−	1298.89i		−	1.36295i	0.731843	−	0.681474i	$-0.238661\pi$
$954$		0			0
$955$	−2248.10			−2.35403
$956$	−233.280	+	134.684i	−0.244016	+	0.140883i
$957$		0			0
$958$	10.1605	−	17.5985i	0.0106059	−	0.0183700i
$959$	194.347	+	112.206i	0.202655	+	0.117003i
$960$		0			0
$961$	−67.4818	−	116.882i	−0.0702204	−	0.121625i
$962$		−	888.907i		−	0.924020i
$963$		0			0
$964$	483.901			0.501972
$965$	99.9658	−	57.7153i	0.103591	−	0.0598086i
$966$		0			0
$967$	424.725	−	735.645i	0.439219	−	0.760750i	−0.558410	−	0.829565i	$-0.688588\pi$
$967$	424.725	−	735.645i	0.439219	−	0.760750i	0.997629	+	0.0688148i	$0.0219218\pi$
$968$	−942.084	−	543.912i	−0.973227	−	0.561893i
$969$		0			0
$970$	505.000	+	874.685i	0.520618	+	0.901737i
$971$			620.233i			0.638757i	0.947627	+	0.319379i	$0.103474\pi$
$971$			620.233i			0.638757i	−0.947627	+	0.319379i	$0.896526\pi$
$972$		0			0
$973$	−30.8945			−0.0317518
$974$	262.227	−	151.397i	0.269227	−	0.155438i
$975$		0			0
$976$	164.868	−	285.560i	0.168922	−	0.292582i
$977$	−543.231	−	313.635i	−0.556020	−	0.321018i	0.195527	−	0.980698i	$-0.437358\pi$
$977$	−543.231	−	313.635i	−0.556020	−	0.321018i	−0.751546	+	0.659680i	$0.770692\pi$
$978$		0			0
$979$	1196.57	+	2072.52i	1.22224	+	2.11698i
$980$			1098.78i			1.12121i
$981$		0			0
$982$	−336.672			−0.342843
$983$	1397.22	−	806.683i	1.42138	−	0.820634i	0.424963	−	0.905211i	$-0.360287\pi$
$983$	1397.22	−	806.683i	1.42138	−	0.820634i	0.996417	+	0.0845766i	$0.0269538\pi$
$984$		0			0
$985$	33.5218	−	58.0615i	0.0340323	−	0.0589457i
$986$	−94.5343	−	54.5794i	−0.0958766	−	0.0553544i
$987$		0			0
$988$	355.793	+	616.251i	0.360114	+	0.623736i
$989$			485.251i			0.490648i
$990$		0			0
$991$	968.743			0.977541			0.488770	−	0.872412i	$-0.337446\pi$
$991$	968.743			0.977541			0.488770	+	0.872412i	$0.337446\pi$
$992$	880.507	−	508.361i	0.887608	−	0.512461i
$993$		0			0
$994$	−17.2284	+	29.8405i	−0.0173324	+	0.0300206i
$995$	1931.98	+	1115.43i	1.94169	+	1.12103i
$996$		0			0
$997$	886.595	+	1535.63i	0.889262	+	1.54025i	0.840749	+	0.541425i	$0.182115\pi$
$997$	886.595	+	1535.63i	0.889262	+	1.54025i	0.0485132	+	0.998823i	$0.484552\pi$
$998$		−	284.668i		−	0.285239i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	459.3.j.a.341.14		64
3.2	odd	2		153.3.j.a.86.19	✓	64
9.2	odd	6	inner	459.3.j.a.35.14		64
9.7	even	3		153.3.j.a.137.19	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.j.a.86.19	✓	64	3.2	odd	2
153.3.j.a.137.19	yes	64	9.7	even	3
459.3.j.a.35.14		64	9.2	odd	6	inner
459.3.j.a.341.14		64	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 459 = 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	459.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.700836 + 0.404628i) q^{2} +(-1.67255 + 2.89695i) q^{4} +(6.73682 + 3.88950i) q^{5} +(-1.30137 - 2.25403i) q^{7} -5.94407i q^{8} -6.29521 q^{10} +(15.0999 - 8.71794i) q^{11} +(11.9586 - 20.7129i) q^{13} +(1.82409 + 1.05314i) q^{14} +(-4.28507 - 7.42196i) q^{16} -4.12311i q^{17} +8.89419 q^{19} +(-22.5354 + 13.0108i) q^{20} +(-7.05505 + 12.2197i) q^{22} +(14.5631 + 8.40799i) q^{23} +(17.7565 + 30.7551i) q^{25} +19.3552i q^{26} +8.70641 q^{28} +(-28.3321 + 16.3576i) q^{29} +(16.5527 - 28.6701i) q^{31} +(26.5971 + 15.3559i) q^{32} +(1.66832 + 2.88962i) q^{34} -20.2467i q^{35} -45.9261 q^{37} +(-6.23337 + 3.59884i) q^{38} +(23.1195 - 40.0441i) q^{40} +(31.3907 + 18.1234i) q^{41} +(14.4282 + 24.9905i) q^{43} +58.3248i q^{44} -13.6084 q^{46} +(-55.0612 + 31.7896i) q^{47} +(21.1129 - 36.5686i) q^{49} +(-24.8888 - 14.3696i) q^{50} +(40.0028 + 69.2870i) q^{52} -48.8363i q^{53} +135.634 q^{55} +(-13.3981 + 7.73542i) q^{56} +(13.2375 - 22.9279i) q^{58} +(25.6105 + 14.7862i) q^{59} +(19.2375 + 33.3204i) q^{61} +26.7907i q^{62} +9.42690 q^{64} +(161.126 - 93.0262i) q^{65} +(-28.8502 + 49.9700i) q^{67} +(11.9444 + 6.89611i) q^{68} +(8.19238 + 14.1896i) q^{70} +16.3591i q^{71} -1.61860 q^{73} +(32.1867 - 18.5830i) q^{74} +(-14.8760 + 25.7660i) q^{76} +(-39.3011 - 22.6905i) q^{77} +(-8.91008 - 15.4327i) q^{79} -66.6672i q^{80} -29.3330 q^{82} +(42.2194 - 24.3754i) q^{83} +(16.0368 - 27.7766i) q^{85} +(-20.2237 - 11.6762i) q^{86} +(-51.8201 - 89.7550i) q^{88} +137.254i q^{89} -62.2502 q^{91} +(-48.7150 + 28.1256i) q^{92} +(25.7259 - 44.5586i) q^{94} +(59.9186 + 34.5940i) q^{95} +(-80.2196 - 138.945i) q^{97} +34.1715i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 64 q^{4} + 18 q^{5} + 2 q^{7} - 10 q^{13} - 72 q^{14} - 128 q^{16} - 28 q^{19} + 18 q^{20} - 144 q^{23} + 154 q^{25} + 32 q^{28} + 162 q^{29} + 62 q^{31} - 126 q^{32} + 128 q^{37} + 36 q^{38} + 144 q^{41}+ \cdots + 140 q^{97}+O(q^{100}) \) 64 * q + 64 * q^4 + 18 * q^5 + 2 * q^7 - 10 * q^13 - 72 * q^14 - 128 * q^16 - 28 * q^19 + 18 * q^20 - 144 * q^23 + 154 * q^25 + 32 * q^28 + 162 * q^29 + 62 * q^31 - 126 * q^32 + 128 * q^37 + 36 * q^38 + 144 * q^41 - 64 * q^43 - 48 * q^46 - 288 * q^47 - 246 * q^49 + 62 * q^52 - 84 * q^55 - 684 * q^56 + 138 * q^58 + 432 * q^59 + 110 * q^61 - 260 * q^64 - 148 * q^67 - 216 * q^70 - 196 * q^73 + 918 * q^74 - 112 * q^76 + 504 * q^77 + 86 * q^79 - 396 * q^82 + 594 * q^83 - 126 * q^86 + 24 * q^88 + 52 * q^91 + 36 * q^92 - 186 * q^94 + 144 * q^95 + 140 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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