LMFDB - Embedded newform 459.3.i.a.152.25

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [459,3,Mod(152,459)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("459.152"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(459, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 459 = 3^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	459.i (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:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 153)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			152.25
Character	$\chi$	$=$	459.152
Dual form			459.3.i.a.305.25

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.95399 - 1.12814i) q^{2} +(0.545389 - 0.944642i) q^{4} +(-0.723667 + 1.25343i) q^{5} +(9.69315 - 5.59634i) q^{7} +6.56401i q^{8} +3.26558i q^{10} +(-2.23569 - 3.87232i) q^{11} +(2.00404 - 3.47110i) q^{13} +(12.6269 - 21.8704i) q^{14} +(9.58666 + 16.6046i) q^{16} +(10.2467 + 13.5648i) q^{17} +10.9947 q^{19} +(0.789360 + 1.36721i) q^{20} +(-8.73702 - 5.04432i) q^{22} +(19.8891 - 34.4489i) q^{23} +(11.4526 + 19.8365i) q^{25} -9.04333i q^{26} -12.2087i q^{28} +(0.551179 + 0.954670i) q^{29} +(10.1684 + 5.87073i) q^{31} +(14.7261 + 8.50213i) q^{32} +(35.3250 + 14.9459i) q^{34} +16.1995i q^{35} -8.93275i q^{37} +(21.4835 - 12.4035i) q^{38} +(-8.22750 - 4.75015i) q^{40} +(-6.83609 + 11.8404i) q^{41} +(-39.5158 - 68.4434i) q^{43} -4.87727 q^{44} -89.7504i q^{46} +(46.1242 - 26.6298i) q^{47} +(38.1380 - 66.0570i) q^{49} +(44.7566 + 25.8402i) q^{50} +(-2.18596 - 3.78620i) q^{52} +72.6186i q^{53} +6.47156 q^{55} +(36.7344 + 63.6259i) q^{56} +(2.15400 + 1.24361i) q^{58} +(-36.9587 - 21.3381i) q^{59} +(-70.5042 + 40.7056i) q^{61} +26.4920 q^{62} -38.3270 q^{64} +(2.90051 + 5.02384i) q^{65} +(-32.0932 + 55.5871i) q^{67} +(18.4024 - 2.28137i) q^{68} +(18.2753 + 31.6538i) q^{70} -10.3563 q^{71} -56.3300i q^{73} +(-10.0774 - 17.4545i) q^{74} +(5.99637 - 10.3860i) q^{76} +(-43.3417 - 25.0233i) q^{77} +(-33.6356 + 19.4195i) q^{79} -27.7502 q^{80} +30.8482i q^{82} +(-110.509 + 63.8025i) q^{83} +(-24.4177 + 3.02711i) q^{85} +(-154.427 - 89.1585i) q^{86} +(25.4179 - 14.6751i) q^{88} +79.8410i q^{89} -44.8612i q^{91} +(-21.6946 - 37.5761i) q^{92} +(60.0842 - 104.069i) q^{94} +(-7.95647 + 13.7810i) q^{95} +(-140.476 + 81.1039i) q^{97} -172.100i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 6 q^{2} + 62 q^{4} - 2 q^{13} - 106 q^{16} - 32 q^{19} - 132 q^{25} - 27 q^{34} + 102 q^{38} + 58 q^{43} + 312 q^{47} + 152 q^{49} + 90 q^{50} + 70 q^{52} + 92 q^{55} + 258 q^{59} - 16 q^{64} + 82 q^{67}+ \cdots - 18 q^{94}+O(q^{100}) $ 68 * q + 6 * q^2 + 62 * q^4 - 2 * q^13 - 106 * q^16 - 32 * q^19 - 132 * q^25 - 27 * q^34 + 102 * q^38 + 58 * q^43 + 312 * q^47 + 152 * q^49 + 90 * q^50 + 70 * q^52 + 92 * q^55 + 258 * q^59 - 16 * q^64 + 82 * q^67 + 333 * q^68 + 204 * q^70 + 34 * q^76 + 60 * q^77 + 690 * q^83 - 44 * q^85 + 1248 * q^86 - 18 * q^94

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 $

$2$	1.95399	−	1.12814i	0.976996	−	0.564069i	0.0756340	−	0.997136i	$-0.475902\pi$
$2$	1.95399	−	1.12814i	0.976996	−	0.564069i	0.901362	+	0.433067i	$0.142569\pi$
$3$		0			0
$3$		0			0
$4$	0.545389	−	0.944642i	0.136347	−	0.236160i
$5$	−0.723667	+	1.25343i	−0.144733	+	0.250685i	−0.929273	−	0.369393i	$-0.879566\pi$
$5$	−0.723667	+	1.25343i	−0.144733	+	0.250685i	0.784540	+	0.620078i	$0.212899\pi$
$6$		0			0
$7$	9.69315	−	5.59634i	1.38474	−	0.799477i	0.392019	−	0.919957i	$-0.371777\pi$
$7$	9.69315	−	5.59634i	1.38474	−	0.799477i	0.992716	+	0.120480i	$0.0384433\pi$
$8$			6.56401i			0.820501i
$9$		0			0
$10$			3.26558i			0.326558i
$11$	−2.23569	−	3.87232i	−0.203244	−	0.352029i	0.746328	−	0.665579i	$-0.231815\pi$
$11$	−2.23569	−	3.87232i	−0.203244	−	0.352029i	−0.949572	+	0.313549i	$0.898482\pi$
$12$		0			0
$13$	2.00404	−	3.47110i	0.154157	−	0.267008i	−0.778595	−	0.627527i	$-0.784067\pi$
$13$	2.00404	−	3.47110i	0.154157	−	0.267008i	0.932752	+	0.360519i	$0.117401\pi$
$14$	12.6269	−	21.8704i	0.901920	−	1.56217i
$15$		0			0
$16$	9.58666	+	16.6046i	0.599166	+	1.03779i
$17$	10.2467	+	13.5648i	0.602748	+	0.797931i
$17$	10.2467	+	13.5648i	0.602748	+	0.797931i
$18$		0			0
$19$	10.9947			0.578667			0.289333	−	0.957228i	$-0.406566\pi$
$19$	10.9947			0.578667			0.289333	+	0.957228i	$0.406566\pi$
$20$	0.789360	+	1.36721i	0.0394680	+	0.0683605i
$21$		0			0
$22$	−8.73702	−	5.04432i	−0.397137	−	0.229287i
$23$	19.8891	−	34.4489i	0.864742	−	1.49778i	−0.00256093	−	0.999997i	$-0.500815\pi$
$23$	19.8891	−	34.4489i	0.864742	−	1.49778i	0.867303	−	0.497781i	$-0.165851\pi$
$24$		0			0
$25$	11.4526	+	19.8365i	0.458105	+	0.793460i
$26$		−	9.04333i		−	0.347820i
$27$		0			0
$28$		−	12.2087i		−	0.436026i
$29$	0.551179	+	0.954670i	0.0190062	+	0.0329197i	0.875372	−	0.483450i	$-0.160616\pi$
$29$	0.551179	+	0.954670i	0.0190062	+	0.0329197i	−0.856366	+	0.516370i	$0.827283\pi$
$30$		0			0
$31$	10.1684	+	5.87073i	0.328013	+	0.189378i	0.654959	−	0.755665i	$-0.272686\pi$
$31$	10.1684	+	5.87073i	0.328013	+	0.189378i	−0.326946	+	0.945043i	$0.606019\pi$
$32$	14.7261	+	8.50213i	0.460191	+	0.265691i
$33$		0			0
$34$	35.3250	+	14.9459i	1.03897	+	0.439584i
$35$			16.1995i			0.462844i
$36$		0			0
$37$		−	8.93275i		−	0.241426i	−0.992687	−	0.120713i	$-0.961482\pi$
$37$		−	8.93275i		−	0.241426i	0.992687	−	0.120713i	$-0.0385180\pi$
$38$	21.4835	−	12.4035i	0.565355	−	0.326408i
$39$		0			0
$40$	−8.22750	−	4.75015i	−0.205688	−	0.118754i
$41$	−6.83609	+	11.8404i	−0.166734	+	0.288791i	−0.937270	−	0.348605i	$-0.886655\pi$
$41$	−6.83609	+	11.8404i	−0.166734	+	0.288791i	0.770536	+	0.637397i	$0.219989\pi$
$42$		0			0
$43$	−39.5158	−	68.4434i	−0.918972	−	1.59171i	−0.800979	−	0.598692i	$-0.795687\pi$
$43$	−39.5158	−	68.4434i	−0.918972	−	1.59171i	−0.117993	−	0.993014i	$-0.537646\pi$
$44$	−4.87727			−0.110847
$45$		0			0
$46$		−	89.7504i		−	1.95110i
$47$	46.1242	−	26.6298i	0.981366	−	0.566592i	0.0786839	−	0.996900i	$-0.474928\pi$
$47$	46.1242	−	26.6298i	0.981366	−	0.566592i	0.902682	+	0.430308i	$0.141595\pi$
$48$		0			0
$49$	38.1380	−	66.0570i	0.778327	−	1.34810i
$50$	44.7566	+	25.8402i	0.895132	+	0.516805i
$51$		0			0
$52$	−2.18596	−	3.78620i	−0.0420378	−	0.0728115i
$53$			72.6186i			1.37016i	0.728467	+	0.685081i	$0.240233\pi$
$53$			72.6186i			1.37016i	−0.728467	+	0.685081i	$0.759767\pi$
$54$		0			0
$55$	6.47156			0.117665
$56$	36.7344	+	63.6259i	0.655972	+	1.13618i
$57$		0			0
$58$	2.15400	+	1.24361i	0.0371379	+	0.0214416i
$59$	−36.9587	−	21.3381i	−0.626418	−	0.361663i	0.152945	−	0.988235i	$-0.451124\pi$
$59$	−36.9587	−	21.3381i	−0.626418	−	0.361663i	−0.779364	+	0.626572i	$0.784457\pi$
$60$		0			0
$61$	−70.5042	+	40.7056i	−1.15581	+	0.667305i	−0.950295	−	0.311350i	$-0.899219\pi$
$61$	−70.5042	+	40.7056i	−1.15581	+	0.667305i	−0.205511	+	0.978655i	$0.565886\pi$
$62$	26.4920			0.427290
$63$		0			0
$64$	−38.3270			−0.598859
$65$	2.90051	+	5.02384i	0.0446233	+	0.0772898i
$66$		0			0
$67$	−32.0932	+	55.5871i	−0.479003	+	0.829658i	−0.999710	−	0.0240774i	$-0.992335\pi$
$67$	−32.0932	+	55.5871i	−0.479003	+	0.829658i	0.520707	+	0.853736i	$0.325669\pi$
$68$	18.4024	−	2.28137i	0.270623	−	0.0335496i
$69$		0			0
$70$	18.2753	+	31.6538i	0.261076	+	0.452197i
$71$	−10.3563			−0.145863			−0.0729315	−	0.997337i	$-0.523235\pi$
$71$	−10.3563			−0.145863			−0.0729315	+	0.997337i	$0.523235\pi$
$72$		0			0
$73$		−	56.3300i		−	0.771644i	−0.922573	−	0.385822i	$-0.873918\pi$
$73$		−	56.3300i		−	0.771644i	0.922573	−	0.385822i	$-0.126082\pi$
$74$	−10.0774	−	17.4545i	−0.136181	−	0.235872i
$75$		0			0
$76$	5.99637	−	10.3860i	0.0788996	−	0.136658i
$77$	−43.3417	−	25.0233i	−0.562879	−	0.324978i
$78$		0			0
$79$	−33.6356	+	19.4195i	−0.425767	+	0.245817i	−0.697542	−	0.716544i	$-0.745723\pi$
$79$	−33.6356	+	19.4195i	−0.425767	+	0.245817i	0.271774	+	0.962361i	$0.412390\pi$
$80$	−27.7502			−0.346877
$81$		0			0
$82$			30.8482i			0.376197i
$83$	−110.509	+	63.8025i	−1.33143	+	0.768704i	−0.985520	−	0.169561i	$-0.945765\pi$
$83$	−110.509	+	63.8025i	−1.33143	+	0.768704i	−0.345915	+	0.938266i	$0.612432\pi$
$84$		0			0
$85$	−24.4177	+	3.02711i	−0.287268	+	0.0356130i
$86$	−154.427	−	89.1585i	−1.79566	−	1.03673i
$87$		0			0
$88$	25.4179	−	14.6751i	0.288840	−	0.166762i
$89$			79.8410i			0.897090i	0.893760	+	0.448545i	$0.148058\pi$
$89$			79.8410i			0.897090i	−0.893760	+	0.448545i	$0.851942\pi$
$90$		0			0
$91$		−	44.8612i		−	0.492980i
$92$	−21.6946	−	37.5761i	−0.235810	−	0.408436i
$93$		0			0
$94$	60.0842	−	104.069i	0.639194	−	1.10712i
$95$	−7.95647	+	13.7810i	−0.0837523	+	0.145063i
$96$		0			0
$97$	−140.476	+	81.1039i	−1.44821	+	0.836123i	−0.998375	−	0.0569895i	$-0.981850\pi$
$97$	−140.476	+	81.1039i	−1.44821	+	0.836123i	−0.449833	+	0.893113i	$0.648517\pi$
$98$		−	172.100i		−	1.75612i
$99$		0			0
$100$	24.9845			0.249845
$101$	89.7223	−	51.8012i	0.888340	−	0.512883i	0.0149408	−	0.999888i	$-0.495244\pi$
$101$	89.7223	−	51.8012i	0.888340	−	0.512883i	0.873399	+	0.487005i	$0.161911\pi$
$102$		0			0
$103$	41.1871	−	71.3381i	0.399874	−	0.692603i	−0.593836	−	0.804586i	$-0.702387\pi$
$103$	41.1871	−	71.3381i	0.399874	−	0.692603i	0.993710	+	0.111984i	$0.0357204\pi$
$104$	22.7843	+	13.1545i	0.219080	+	0.126486i
$105$		0			0
$106$	81.9238	+	141.896i	0.772866	+	1.33864i
$107$	−71.6149			−0.669298			−0.334649	−	0.942343i	$-0.608618\pi$
$107$	−71.6149			−0.669298			−0.334649	+	0.942343i	$0.608618\pi$
$108$		0			0
$109$			159.142i			1.46001i	0.683440	+	0.730007i	$0.260483\pi$
$109$			159.142i			1.46001i	−0.683440	+	0.730007i	$0.739517\pi$
$110$	12.6454	−	7.30081i	0.114958	−	0.0663710i
$111$		0			0
$112$	185.850	+	107.300i	1.65937	+	0.958039i
$113$	9.13859	−	15.8285i	0.0808725	−	0.140075i	−0.822752	−	0.568400i	$-0.807563\pi$
$113$	9.13859	−	15.8285i	0.0808725	−	0.140075i	0.903625	+	0.428325i	$0.140896\pi$
$114$		0			0
$115$	28.7861	+	49.8590i	0.250314	+	0.433556i
$116$	1.20243			0.0103658
$117$		0			0
$118$	−96.2893			−0.816011
$119$	175.236	+	74.1417i	1.47257	+	0.623040i
$120$		0			0
$121$	50.5034	−	87.4745i	0.417384	−	0.722930i
$122$	−91.8431	+	159.077i	−0.752812	+	1.30391i
$123$		0			0
$124$	11.0915	−	6.40366i	0.0894474	−	0.0516425i
$125$	−69.3348			−0.554679
$126$		0			0
$127$	−168.975			−1.33051			−0.665257	−	0.746614i	$-0.731678\pi$
$127$	−168.975			−1.33051			−0.665257	+	0.746614i	$0.731678\pi$
$128$	−133.795	+	77.2466i	−1.04527	+	0.603489i
$129$		0			0
$130$	11.3352	+	6.54436i	0.0871935	+	0.0503412i
$131$	107.927	−	186.936i	0.823872	−	1.42699i	−0.0789058	−	0.996882i	$-0.525143\pi$
$131$	107.927	−	186.936i	0.823872	−	1.42699i	0.902778	−	0.430107i	$-0.141524\pi$
$132$		0			0
$133$	106.573	−	61.5299i	0.801300	−	0.462631i
$134$			144.822i			1.08076i
$135$		0			0
$136$	−89.0396	+	67.2596i	−0.654703	+	0.494556i
$137$	40.7215	−	23.5105i	0.297237	−	0.171610i	−0.343964	−	0.938983i	$-0.611770\pi$
$137$	40.7215	−	23.5105i	0.297237	−	0.171610i	0.641201	+	0.767373i	$0.278436\pi$
$138$		0			0
$139$	−7.66224	−	4.42380i	−0.0551240	−	0.0318259i	0.472185	−	0.881500i	$-0.343466\pi$
$139$	−7.66224	−	4.42380i	−0.0551240	−	0.0318259i	−0.527309	+	0.849674i	$0.676799\pi$
$140$	15.3028	+	8.83505i	0.109305	+	0.0631075i
$141$		0			0
$142$	−20.2361	+	11.6833i	−0.142508	+	0.0822768i
$143$	−17.9216			−0.125326
$144$		0			0
$145$	−1.59548			−0.0110033
$146$	−63.5480	−	110.068i	−0.435260	−	0.753893i
$147$		0			0
$148$	−8.43825	−	4.87182i	−0.0570152	−	0.0329177i
$149$	73.1705	+	42.2450i	0.491077	+	0.283523i	0.725021	−	0.688727i	$-0.241830\pi$
$149$	73.1705	+	42.2450i	0.491077	+	0.283523i	−0.233944	+	0.972250i	$0.575163\pi$
$150$		0			0
$151$	−54.8670	−	95.0324i	−0.363358	−	0.629354i	0.625154	−	0.780502i	$-0.285036\pi$
$151$	−54.8670	−	95.0324i	−0.363358	−	0.629354i	−0.988511	+	0.151148i	$0.951703\pi$
$152$			72.1691i			0.474796i
$153$		0			0
$154$	−112.919			−0.733240
$155$	−14.7171	+	8.49690i	−0.0949488	+	0.0548187i
$156$		0			0
$157$	−52.4868	+	90.9098i	−0.334311	+	0.579043i	−0.983352	−	0.181710i	$-0.941837\pi$
$157$	−52.4868	+	90.9098i	−0.334311	+	0.579043i	0.649041	+	0.760753i	$0.275170\pi$
$158$	−43.8158	+	75.8912i	−0.277315	+	0.480324i
$159$		0			0
$160$	−21.3136	+	12.3054i	−0.133210	+	0.0769088i
$161$		−	445.224i		−	2.76537i
$162$		0			0
$163$		−	143.888i		−	0.882746i	−0.897324	−	0.441373i	$-0.854492\pi$
$163$		−	143.888i		−	0.882746i	0.897324	−	0.441373i	$-0.145508\pi$
$164$	7.45665	+	12.9153i	0.0454674	+	0.0787518i
$165$		0			0
$166$	−143.956	+	249.339i	−0.867204	+	1.50204i
$167$	−52.8753	+	91.5827i	−0.316619	+	0.548400i	−0.979780	−	0.200077i	$-0.935881\pi$
$167$	−52.8753	+	91.5827i	−0.316619	+	0.548400i	0.663162	+	0.748476i	$0.269214\pi$
$168$		0			0
$169$	76.4676	+	132.446i	0.452471	+	0.783703i
$170$	−44.2971	+	33.4615i	−0.260571	+	0.196832i
$171$		0			0
$172$	−86.2060			−0.501197
$173$	−81.3590	−	140.918i	−0.470283	−	0.814555i	0.529139	−	0.848535i	$-0.322515\pi$
$173$	−81.3590	−	140.918i	−0.470283	−	0.814555i	−0.999422	+	0.0339804i	$0.989182\pi$
$174$		0			0
$175$	222.024	+	128.185i	1.26871	+	0.732488i
$176$	42.8655	−	74.2452i	0.243554	−	0.421848i
$177$		0			0
$178$	90.0716	+	156.009i	0.506020	+	0.876453i
$179$			146.892i			0.820628i	0.911944	+	0.410314i	$0.134581\pi$
$179$			146.892i			0.820628i	−0.911944	+	0.410314i	$0.865419\pi$
$180$		0			0
$181$			149.938i			0.828384i	0.910189	+	0.414192i	$0.135936\pi$
$181$			149.938i			0.828384i	−0.910189	+	0.414192i	$0.864064\pi$
$182$	−50.6096	−	87.6583i	−0.278075	−	0.481639i
$183$		0			0
$184$	226.123	+	130.552i	1.22893	+	0.709521i
$185$	11.1966	+	6.46433i	0.0605219	+	0.0349423i
$186$		0			0
$187$	29.6189	−	70.0053i	0.158390	−	0.374360i
$188$		−	58.0945i		−	0.309013i
$189$		0			0
$190$			35.9040i			0.188968i
$191$	17.2042	−	9.93284i	0.0900743	−	0.0520044i	−0.454286	−	0.890856i	$-0.650106\pi$
$191$	17.2042	−	9.93284i	0.0900743	−	0.0520044i	0.544361	+	0.838851i	$0.316772\pi$
$192$		0			0
$193$	−245.445	−	141.708i	−1.27174	−	0.734238i	−0.296423	−	0.955057i	$-0.595794\pi$
$193$	−245.445	−	141.708i	−1.27174	−	0.734238i	−0.975315	+	0.220818i	$0.929127\pi$
$194$	−182.993	+	316.953i	−0.943262	+	1.63378i
$195$		0			0
$196$	−41.6001	−	72.0536i	−0.212246	−	0.367620i
$197$	289.203			1.46804			0.734019	−	0.679129i	$-0.237642\pi$
$197$	289.203			1.46804			0.734019	+	0.679129i	$0.237642\pi$
$198$		0			0
$199$		−	211.138i		−	1.06100i	−0.847686	−	0.530498i	$-0.822005\pi$
$199$		−	211.138i		−	1.06100i	0.847686	−	0.530498i	$-0.177995\pi$
$200$	−130.207	+	75.1750i	−0.651035	+	0.375875i
$201$		0			0
$202$	116.878	−	202.438i	0.578603	−	1.00217i
$203$	10.6853	+	6.16917i	0.0526370	+	0.0303900i
$204$		0			0
$205$	−9.89409	−	17.1371i	−0.0482639	−	0.0835955i
$206$		−	185.859i		−	0.902227i
$207$		0			0
$208$	76.8482			0.369462
$209$	−24.5806	−	42.5749i	−0.117611	−	0.203708i
$210$		0			0
$211$	−152.186	−	87.8649i	−0.721263	−	0.416421i	0.0939545	−	0.995576i	$-0.470049\pi$
$211$	−152.186	−	87.8649i	−0.721263	−	0.416421i	−0.815217	+	0.579155i	$0.803382\pi$
$212$	68.5985	+	39.6054i	0.323578	+	0.186818i
$213$		0			0
$214$	−139.935	+	80.7915i	−0.653901	+	0.377530i
$215$	114.385			0.532024
$216$		0			0
$217$	131.418			0.605615
$218$	179.534	+	310.961i	0.823548	+	1.42643i
$219$		0			0
$220$	3.52952	−	6.11331i	0.0160433	−	0.0277878i
$221$	67.6197	−	8.38293i	0.305972	−	0.0379318i
$222$		0			0
$223$	−92.4137	−	160.065i	−0.414411	−	0.717781i	0.580955	−	0.813936i	$-0.302679\pi$
$223$	−92.4137	−	160.065i	−0.414411	−	0.717781i	−0.995366	+	0.0961542i	$0.969346\pi$
$224$	190.323			0.849657
$225$		0			0
$226$		−	41.2384i		−	0.182471i
$227$	−122.286	−	211.806i	−0.538706	−	0.933066i	−0.998974	−	0.0452858i	$-0.985580\pi$
$227$	−122.286	−	211.806i	−0.538706	−	0.933066i	0.460268	−	0.887780i	$-0.347753\pi$
$228$		0			0
$229$	−36.9808	+	64.0526i	−0.161488	+	0.279706i	−0.935403	−	0.353584i	$-0.884963\pi$
$229$	−36.9808	+	64.0526i	−0.161488	+	0.279706i	0.773914	+	0.633290i	$0.218296\pi$
$230$	112.496	+	64.9494i	0.489111	+	0.282389i
$231$		0			0
$232$	−6.26646	+	3.61794i	−0.0270106	+	0.0155946i
$233$	−420.854			−1.80624			−0.903120	−	0.429388i	$-0.858729\pi$
$233$	−420.854			−1.80624			−0.903120	+	0.429388i	$0.858729\pi$
$234$		0			0
$235$			77.0845i			0.328019i
$236$	−40.3137	+	23.2751i	−0.170821	+	0.0986235i
$237$		0			0
$238$	426.053	−	52.8185i	1.79014	−	0.221926i
$239$	218.231	+	125.996i	0.913100	+	0.527179i	0.881427	−	0.472320i	$-0.156583\pi$
$239$	218.231	+	125.996i	0.913100	+	0.527179i	0.0316729	+	0.999498i	$0.489917\pi$
$240$		0			0
$241$	−101.407	+	58.5474i	−0.420776	+	0.242935i	−0.695409	−	0.718614i	$-0.744777\pi$
$241$	−101.407	+	58.5474i	−0.420776	+	0.242935i	0.274633	+	0.961549i	$0.411444\pi$
$242$		−	227.899i		−	0.941732i
$243$		0			0
$244$			88.8016i			0.363941i
$245$	55.1984	+	95.6065i	0.225300	+	0.390231i
$246$		0			0
$247$	22.0338	−	38.1636i	0.0892055	−	0.154508i
$248$	−38.5355	+	66.7455i	−0.155385	+	0.269135i
$249$		0			0
$250$	−135.480	+	78.2192i	−0.541919	+	0.312877i
$251$			61.2200i			0.243905i	0.992536	+	0.121952i	$0.0389155\pi$
$251$			61.2200i			0.243905i	−0.992536	+	0.121952i	$0.961085\pi$
$252$		0			0
$253$	−177.863			−0.703015
$254$	−330.176	+	190.627i	−1.29991	+	0.750502i
$255$		0			0
$256$	−97.6357	+	169.110i	−0.381389	+	0.660586i
$257$	−72.9310	−	42.1067i	−0.283778	−	0.163839i	0.351355	−	0.936242i	$-0.385721\pi$
$257$	−72.9310	−	42.1067i	−0.283778	−	0.163839i	−0.635133	+	0.772403i	$0.719055\pi$
$258$		0			0
$259$	−49.9907	−	86.5864i	−0.193014	−	0.334311i
$260$	6.32763			0.0243371
$261$		0			0
$262$		−	487.027i		−	1.85888i
$263$	53.7891	−	31.0552i	0.204521	−	0.118081i	−0.394241	−	0.919007i	$-0.628993\pi$
$263$	53.7891	−	31.0552i	0.204521	−	0.118081i	0.598763	+	0.800926i	$0.295659\pi$
$264$		0			0
$265$	−91.0221	−	52.5517i	−0.343480	−	0.198308i
$266$	138.828	−	240.458i	0.521911	−	0.903977i
$267$		0			0
$268$	35.0066	+	60.6332i	0.130622	+	0.226243i
$269$	82.2459			0.305747			0.152873	−	0.988246i	$-0.451147\pi$
$269$	82.2459			0.305747			0.152873	+	0.988246i	$0.451147\pi$
$270$		0			0
$271$	531.432			1.96100			0.980501	−	0.196514i	$-0.0629621\pi$
$271$	531.432			1.96100			0.980501	+	0.196514i	$0.0629621\pi$
$272$	−127.006	+	300.184i	−0.466936	+	1.10362i
$273$		0			0
$274$	53.0463	−	91.8788i	0.193600	−	0.335324i
$275$	51.2089	−	88.6964i	0.186214	−	0.322532i
$276$		0			0
$277$	−14.6454	+	8.45551i	−0.0528714	+	0.0305253i	−0.526203	−	0.850359i	$-0.676385\pi$
$277$	−14.6454	+	8.45551i	−0.0528714	+	0.0305253i	0.473331	+	0.880884i	$0.343051\pi$
$278$	−19.9626			−0.0718079
$279$		0			0
$280$	−106.334			−0.379764
$281$	127.565	−	73.6499i	0.453969	−	0.262099i	−0.255536	−	0.966800i	$-0.582252\pi$
$281$	127.565	−	73.6499i	0.453969	−	0.262099i	0.709505	+	0.704700i	$0.248919\pi$
$282$		0			0
$283$	−144.610	−	83.4908i	−0.510990	−	0.295020i	0.222250	−	0.974990i	$-0.428660\pi$
$283$	−144.610	−	83.4908i	−0.510990	−	0.295020i	−0.733241	+	0.679969i	$0.761993\pi$
$284$	−5.64820	+	9.78297i	−0.0198880	+	0.0344471i
$285$		0			0
$286$	−35.0187	+	20.2181i	−0.122443	+	0.0706925i
$287$			153.028i			0.533199i
$288$		0			0
$289$	−79.0093	+	277.990i	−0.273389	+	0.961904i
$290$	−3.11755	+	1.79992i	−0.0107502	+	0.00620662i
$291$		0			0
$292$	−53.2116	−	30.7218i	−0.182232	−	0.105212i
$293$	−355.205	−	205.078i	−1.21230	−	0.699923i	−0.249043	−	0.968493i	$-0.580116\pi$
$293$	−355.205	−	205.078i	−1.21230	−	0.699923i	−0.963260	+	0.268569i	$0.913449\pi$
$294$		0			0
$295$	53.4915	−	30.8833i	0.181327	−	0.104689i
$296$	58.6346			0.198090
$297$		0			0
$298$	190.633			0.639707
$299$	−79.7170	−	138.074i	−0.266612	−	0.461786i
$300$		0			0
$301$	−766.065	−	442.288i	−2.54507	−	1.46939i
$302$	−214.419	−	123.795i	−0.709998	−	0.409917i
$303$		0			0
$304$	105.402	+	182.562i	0.346717	+	0.600532i
$305$		−	117.829i		−	0.386325i
$306$		0			0
$307$	392.680			1.27909			0.639544	−	0.768755i	$-0.279123\pi$
$307$	392.680			1.27909			0.639544	+	0.768755i	$0.279123\pi$
$308$	−47.2761	+	27.2949i	−0.153494	+	0.0886198i
$309$		0			0
$310$	−19.1714	+	33.2058i	−0.0618431	+	0.107115i
$311$	−165.116	+	285.990i	−0.530921	+	0.919582i	0.468428	+	0.883502i	$0.344821\pi$
$311$	−165.116	+	285.990i	−0.530921	+	0.919582i	−0.999349	+	0.0360804i	$0.988513\pi$
$312$		0			0
$313$	403.046	−	232.699i	1.28769	−	0.743447i	0.309446	−	0.950917i	$-0.399856\pi$
$313$	403.046	−	232.699i	1.28769	−	0.743447i	0.978241	+	0.207471i	$0.0665231\pi$
$314$			236.849i			0.754297i
$315$		0			0
$316$			42.3648i			0.134066i
$317$	−204.824	−	354.766i	−0.646132	−	1.11913i	−0.984039	−	0.177954i	$-0.943052\pi$
$317$	−204.824	−	354.766i	−0.646132	−	1.11913i	0.337906	−	0.941180i	$-0.390281\pi$
$318$		0			0
$319$	2.46453	−	4.26869i	0.00772579	−	0.0133815i
$320$	27.7360	−	48.0401i	0.0866749	−	0.150125i
$321$		0			0
$322$	−502.274	−	869.964i	−1.55986	−	2.70175i
$323$	112.659	+	149.141i	0.348790	+	0.461736i
$324$		0			0
$325$	91.8060			0.282480
$326$	−162.325	−	281.155i	−0.497929	−	0.862439i
$327$		0			0
$328$	−77.7208	−	44.8721i	−0.236954	−	0.136805i
$329$	298.059	−	516.254i	0.905955	−	1.56916i
$330$		0			0
$331$	291.899	+	505.583i	0.881869	+	1.52744i	0.849260	+	0.527974i	$0.177048\pi$
$331$	291.899	+	505.583i	0.881869	+	1.52744i	0.0326088	+	0.999468i	$0.489618\pi$
$332$			139.189i			0.419243i
$333$		0			0
$334$			238.603i			0.714379i
$335$	−46.4496	−	80.4530i	−0.138655	−	0.240158i
$336$		0			0
$337$	390.476	+	225.442i	1.15868	+	0.668966i	0.950988	−	0.309227i	$-0.100070\pi$
$337$	390.476	+	225.442i	1.15868	+	0.668966i	0.207695	+	0.978194i	$0.433404\pi$
$338$	298.834	+	172.532i	0.884125	+	0.510450i
$339$		0			0
$340$	−10.4576	+	24.7170i	−0.0307577	+	0.0726969i
$341$		−	52.5004i		−	0.153960i
$342$		0			0
$343$		−	305.293i		−	0.890066i
$344$	449.263	−	259.382i	1.30600	−	0.754017i
$345$		0			0
$346$	−317.950	−	183.568i	−0.918930	−	0.530544i
$347$	−195.751	+	339.050i	−0.564123	+	0.977090i	0.433008	+	0.901390i	$0.357452\pi$
$347$	−195.751	+	339.050i	−0.564123	+	0.977090i	−0.997131	+	0.0756995i	$0.975881\pi$
$348$		0			0
$349$	−55.9660	−	96.9360i	−0.160361	−	0.277754i	0.774637	−	0.632406i	$-0.217933\pi$
$349$	−55.9660	−	96.9360i	−0.160361	−	0.277754i	−0.934998	+	0.354652i	$0.884599\pi$
$350$	578.443			1.65270
$351$		0			0
$352$		−	76.0323i		−	0.216001i
$353$	342.065	−	197.491i	0.969021	−	0.559465i	0.0700835	−	0.997541i	$-0.477673\pi$
$353$	342.065	−	197.491i	0.969021	−	0.559465i	0.898938	+	0.438076i	$0.144340\pi$
$354$		0			0
$355$	7.49449	−	12.9808i	0.0211112	−	0.0365658i
$356$	75.4211	+	43.5444i	0.211857	+	0.122316i
$357$		0			0
$358$	165.715	+	287.026i	0.462891	+	0.801750i
$359$			389.704i			1.08553i	0.839885	+	0.542764i	$0.182622\pi$
$359$			389.704i			1.08553i	−0.839885	+	0.542764i	$0.817378\pi$
$360$		0			0
$361$	−240.117			−0.665145
$362$	169.150	+	292.977i	0.467266	+	0.809328i
$363$		0			0
$364$	−42.3777	−	24.4668i	−0.116422	−	0.0672164i
$365$	70.6055	+	40.7641i	0.193440	+	0.111683i
$366$		0			0
$367$	263.721	−	152.260i	0.718587	−	0.414876i	−0.0956456	−	0.995415i	$-0.530492\pi$
$367$	263.721	−	152.260i	0.718587	−	0.414876i	0.814232	+	0.580539i	$0.197158\pi$
$368$	762.679			2.07250
$369$		0			0
$370$	29.1706			0.0788395
$371$	406.398	+	703.903i	1.09541	+	1.89731i
$372$		0			0
$373$	157.657	−	273.069i	0.422672	−	0.732089i	−0.573528	−	0.819186i	$-0.694426\pi$
$373$	157.657	−	273.069i	0.422672	−	0.732089i	0.996200	+	0.0870970i	$0.0277590\pi$
$374$	−21.1005	−	170.204i	−0.0564184	−	0.455091i
$375$		0			0
$376$	174.798	+	302.760i	0.464889	+	0.805212i
$377$	4.41834			0.0117197
$378$		0			0
$379$			72.6723i			0.191747i	0.995394	+	0.0958737i	$0.0305645\pi$
$379$			72.6723i			0.191747i	−0.995394	+	0.0958737i	$0.969435\pi$
$380$	8.67875	+	15.0320i	0.0228388	+	0.0395580i
$381$		0			0
$382$	22.4112	−	38.8174i	0.0586681	−	0.101616i
$383$	332.076	+	191.724i	0.867039	+	0.500585i	0.866363	−	0.499414i	$-0.166451\pi$
$383$	332.076	+	191.724i	0.867039	+	0.500585i	0.000676091		1.00000i	$0.499785\pi$
$384$		0			0
$385$	62.7298	−	36.2171i	0.162935	−	0.0940703i
$386$	−639.465			−1.65664
$387$		0			0
$388$			176.933i			0.456012i
$389$	36.0560	−	20.8169i	0.0926890	−	0.0535140i	−0.452939	−	0.891541i	$-0.649624\pi$
$389$	36.0560	−	20.8169i	0.0926890	−	0.0535140i	0.545628	+	0.838027i	$0.316291\pi$
$390$		0			0
$391$	671.091	−	83.1963i	1.71635	−	0.212778i
$392$	433.599	+	250.338i	1.10612	+	0.638618i
$393$		0			0
$394$	565.101	−	326.261i	1.43427	−	0.828074i
$395$		−	56.2131i		−	0.142312i
$396$		0			0
$397$		−	222.169i		−	0.559618i	−0.960056	−	0.279809i	$-0.909729\pi$
$397$		−	222.169i		−	0.559618i	0.960056	−	0.279809i	$-0.0902712\pi$
$398$	−238.193	−	412.562i	−0.598475	−	1.03659i
$399$		0			0
$400$	−219.585	+	380.332i	−0.548961	+	0.950829i
$401$	126.387	−	218.909i	0.315179	−	0.545907i	−0.664296	−	0.747469i	$-0.731269\pi$
$401$	126.387	−	218.909i	0.315179	−	0.545907i	0.979476	+	0.201563i	$0.0646019\pi$
$402$		0			0
$403$	40.7558	−	23.5304i	0.101131	−	0.0583880i
$404$		−	113.007i		−	0.279721i
$405$		0			0
$406$	27.8387			0.0685682
$407$	−34.5905	+	19.9708i	−0.0849889	+	0.0490684i
$408$		0			0
$409$	−349.619	+	605.558i	−0.854815	+	1.48058i	0.0220017	+	0.999758i	$0.492996\pi$
$409$	−349.619	+	605.558i	−0.854815	+	1.48058i	−0.876817	+	0.480825i	$0.840337\pi$
$410$	−38.6659	−	22.3238i	−0.0943072	−	0.0544483i
$411$		0			0
$412$	−44.9259	−	77.8140i	−0.109044	−	0.188869i
$413$	−477.661			−1.15656
$414$		0			0
$415$		−	184.687i		−	0.445028i
$416$	59.0235	−	34.0772i	0.141883	−	0.0819164i
$417$		0			0
$418$	−96.0607	−	55.4606i	−0.229810	−	0.132681i
$419$	280.556	−	485.937i	0.669584	−	1.15975i	−0.308436	−	0.951245i	$-0.599806\pi$
$419$	280.556	−	485.937i	0.669584	−	1.15975i	0.978020	−	0.208509i	$-0.0668610\pi$
$420$		0			0
$421$	−371.879	−	644.113i	−0.883323	−	1.52996i	−0.847624	−	0.530597i	$-0.821968\pi$
$421$	−371.879	−	644.113i	−0.883323	−	1.52996i	−0.0356985	−	0.999363i	$-0.511366\pi$
$422$	−396.495			−0.939561
$423$		0			0
$424$	−476.669			−1.12422
$425$	−151.727	+	358.612i	−0.357005	+	0.843793i
$426$		0			0
$427$	−455.605	+	789.131i	−1.06699	+	1.84808i
$428$	−39.0580	+	67.6504i	−0.0912570	+	0.158062i
$429$		0			0
$430$	223.507	−	129.042i	0.519785	−	0.300098i
$431$	−269.585			−0.625488			−0.312744	−	0.949838i	$-0.601248\pi$
$431$	−269.585			−0.625488			−0.312744	+	0.949838i	$0.601248\pi$
$432$		0			0
$433$	337.140			0.778613			0.389307	−	0.921108i	$-0.372715\pi$
$433$	337.140			0.778613			0.389307	+	0.921108i	$0.372715\pi$
$434$	256.791	−	148.258i	0.591683	−	0.341608i
$435$		0			0
$436$	150.332	+	86.7940i	0.344797	+	0.199069i
$437$	218.674	−	378.754i	0.500397	−	0.866714i
$438$		0			0
$439$	536.529	−	309.765i	1.22216	−	0.705615i	0.256783	−	0.966469i	$-0.417337\pi$
$439$	536.529	−	309.765i	1.22216	−	0.705615i	0.965378	+	0.260854i	$0.0840041\pi$
$440$			42.4794i			0.0965440i
$441$		0			0
$442$	122.671	−	92.6645i	0.277537	−	0.209648i
$443$	−193.616	+	111.784i	−0.437056	+	0.252334i	−0.702348	−	0.711834i	$-0.747865\pi$
$443$	−193.616	+	111.784i	−0.437056	+	0.252334i	0.265292	+	0.964168i	$0.414532\pi$
$444$		0			0
$445$	−100.075	−	57.7782i	−0.224887	−	0.129839i
$446$	−361.151	−	208.511i	−0.809756	−	0.467513i
$447$		0			0
$448$	−371.509	+	214.491i	−0.829261	+	0.478774i
$449$	−115.549			−0.257349			−0.128674	−	0.991687i	$-0.541072\pi$
$449$	−115.549			−0.257349			−0.128674	+	0.991687i	$0.541072\pi$
$450$		0			0
$451$	61.1334			0.135551
$452$	−9.96817	−	17.2654i	−0.0220535	−	0.0381978i
$453$		0			0
$454$	−477.892	−	275.911i	−1.05263	−	0.607734i
$455$	56.2302	+	32.4645i	0.123583	+	0.0713506i
$456$		0			0
$457$	−4.91125	−	8.50653i	−0.0107467	−	0.0186138i	0.860602	−	0.509278i	$-0.170088\pi$
$457$	−4.91125	−	8.50653i	−0.0107467	−	0.0186138i	−0.871349	+	0.490664i	$0.836754\pi$
$458$			166.878i			0.364362i
$459$		0			0
$460$	62.7985			0.136518
$461$	308.892	−	178.339i	0.670049	−	0.386853i	−0.126046	−	0.992024i	$-0.540229\pi$
$461$	308.892	−	178.339i	0.670049	−	0.386853i	0.796095	+	0.605172i	$0.206896\pi$
$462$		0			0
$463$	−120.872	+	209.357i	−0.261063	+	0.452175i	−0.966525	−	0.256573i	$-0.917406\pi$
$463$	−120.872	+	209.357i	−0.261063	+	0.452175i	0.705461	+	0.708748i	$0.250740\pi$
$464$	−10.5679	+	18.3042i	−0.0227757	+	0.0394487i
$465$		0			0
$466$	−822.345	+	474.781i	−1.76469	+	1.01884i
$467$			229.157i			0.490701i	0.969435	+	0.245350i	$0.0789030\pi$
$467$			229.157i			0.490701i	−0.969435	+	0.245350i	$0.921097\pi$
$468$		0			0
$469$			718.418i			1.53181i
$470$	86.9619	+	150.622i	0.185025	+	0.320473i
$471$		0			0
$472$	140.063	−	242.597i	0.296745	−	0.513977i
$473$	−176.690	+	306.036i	−0.373552	+	0.647010i
$474$		0			0
$475$	125.918	+	218.096i	0.265090	+	0.459149i
$476$	165.609	−	125.099i	0.347919	−	0.262814i
$477$		0			0
$478$	568.562			1.18946
$479$	178.133	+	308.536i	0.371886	+	0.644125i	0.989856	−	0.142077i	$-0.0453780\pi$
$479$	178.133	+	308.536i	0.371886	+	0.644125i	−0.617970	+	0.786202i	$0.712045\pi$
$480$		0			0
$481$	−31.0065	−	17.9016i	−0.0644625	−	0.0372174i
$482$	−132.099	+	228.802i	−0.274065	+	0.474694i
$483$		0			0
$484$	−55.0880	−	95.4152i	−0.113818	−	0.197139i
$485$		−	234.769i		−	0.484059i
$486$		0			0
$487$			478.597i			0.982745i	0.870950	+	0.491373i	$0.163505\pi$
$487$			478.597i			0.982745i	−0.870950	+	0.491373i	$0.836495\pi$
$488$	−267.192	−	462.790i	−0.547524	−	0.948340i
$489$		0			0
$490$	215.715	+	124.543i	0.440234	+	0.254169i
$491$	−640.303	−	369.679i	−1.30408	−	0.752910i	−0.322978	−	0.946406i	$-0.604684\pi$
$491$	−640.303	−	369.679i	−1.30408	−	0.752910i	−0.981101	+	0.193496i	$0.938017\pi$
$492$		0			0
$493$	−7.30216	+	17.2589i	−0.0148117	+	0.0350079i
$494$		−	99.4284i		−	0.201272i
$495$		0			0
$496$			225.123i			0.453877i
$497$	−100.385	+	57.9573i	−0.201982	+	0.116614i
$498$		0			0
$499$	506.185	+	292.246i	1.01440	+	0.585663i	0.912476	−	0.409129i	$-0.134167\pi$
$499$	506.185	+	292.246i	1.01440	+	0.585663i	0.101922	+	0.994792i	$0.467501\pi$
$500$	−37.8144	+	65.4965i	−0.0756289	+	0.130993i
$501$		0			0
$502$	69.0646	+	119.623i	0.137579	+	0.238294i
$503$	234.299			0.465803			0.232901	−	0.972500i	$-0.425178\pi$
$503$	234.299			0.465803			0.232901	+	0.972500i	$0.425178\pi$
$504$		0			0
$505$			149.947i			0.296925i
$506$	−347.542	+	200.654i	−0.686843	+	0.396549i
$507$		0			0
$508$	−92.1573	+	159.621i	−0.181412	+	0.314215i
$509$	−585.148	−	337.835i	−1.14960	−	0.663723i	−0.200812	−	0.979630i	$-0.564358\pi$
$509$	−585.148	−	337.835i	−1.14960	−	0.663723i	−0.948790	+	0.315907i	$0.897691\pi$
$510$		0			0
$511$	−315.242	−	546.015i	−0.616912	−	1.06852i
$512$		−	177.387i		−	0.346459i
$513$		0			0
$514$	−190.009			−0.369667
$515$	59.6114	+	103.250i	0.115750	+	0.200485i
$516$		0			0
$517$	−206.239	−	119.072i	−0.398914	−	0.230313i
$518$	−195.363	−	112.793i	−0.377148	−	0.217747i
$519$		0			0
$520$	−32.9765	+	19.0390i	−0.0634163	+	0.0366134i
$521$	−492.195			−0.944712			−0.472356	−	0.881408i	$-0.656596\pi$
$521$	−492.195			−0.944712			−0.472356	+	0.881408i	$0.656596\pi$
$522$		0			0
$523$	514.256			0.983280			0.491640	−	0.870799i	$-0.336398\pi$
$523$	514.256			0.983280			0.491640	+	0.870799i	$0.336398\pi$
$524$	−117.725	−	203.905i	−0.224665	−	0.389132i
$525$		0			0
$526$	70.0690	−	121.363i	0.133211	−	0.230728i
$527$	24.5574	+	198.088i	0.0465984	+	0.375879i
$528$		0			0
$529$	−526.650	−	912.185i	−0.995558	−	1.72436i
$530$	−237.142			−0.447438
$531$		0			0
$532$		−	134.231i		−	0.252314i
$533$	27.3996	+	47.4575i	0.0514063	+	0.0890384i
$534$		0			0
$535$	51.8253	−	89.7640i	0.0968697	−	0.167783i
$536$	−364.874	−	210.660i	−0.680735	−	0.393023i
$537$		0			0
$538$	160.708	−	92.7847i	0.298713	−	0.172462i
$539$	−341.059			−0.632762
$540$		0			0
$541$			891.685i			1.64822i	0.566433	+	0.824108i	$0.308323\pi$
$541$			891.685i			1.64822i	−0.566433	+	0.824108i	$0.691677\pi$
$542$	1038.41	−	599.528i	1.91589	−	1.10614i
$543$		0			0
$544$	35.5645	+	286.876i	0.0653760	+	0.527346i
$545$	−199.472	−	115.165i	−0.366004	−	0.211313i
$546$		0			0
$547$	−884.620	+	510.735i	−1.61722	+	0.933703i	−0.629585	+	0.776931i	$0.716775\pi$
$547$	−884.620	+	510.735i	−1.61722	+	0.933703i	−0.987635	+	0.156771i	$0.949891\pi$
$548$		−	51.2896i		−	0.0935941i
$549$		0			0
$550$		−	231.083i		−	0.420150i
$551$	6.06003	+	10.4963i	0.0109982	+	0.0190495i
$552$		0			0
$553$	−217.357	+	376.473i	−0.393050	+	0.680783i
$554$	−19.0780	+	33.0440i	−0.0344367	+	0.0596462i
$555$		0			0
$556$	−8.35780	+	4.82538i	−0.0150320	+	0.00867874i
$557$			297.630i			0.534345i	0.963649	+	0.267173i	$0.0860894\pi$
$557$			297.630i			0.534345i	−0.963649	+	0.267173i	$0.913911\pi$
$558$		0			0
$559$	−316.765			−0.566664
$560$	−268.986	+	155.299i	−0.480333	+	0.277320i
$561$		0			0
$562$	166.174	−	287.823i	0.295684	−	0.512140i
$563$	−613.907	−	354.440i	−1.09042	−	0.629555i	−0.156733	−	0.987641i	$-0.550096\pi$
$563$	−613.907	−	354.440i	−1.09042	−	0.629555i	−0.933689	+	0.358086i	$0.883430\pi$
$564$		0			0
$565$	13.2266	+	22.9091i	0.0234099	+	0.0405471i
$566$	−376.756			−0.665647
$567$		0			0
$568$		−	67.9787i		−	0.119681i
$569$	−183.634	+	106.021i	−0.322731	+	0.186329i	−0.652609	−	0.757695i	$-0.726326\pi$
$569$	−183.634	+	106.021i	−0.322731	+	0.186329i	0.329878	+	0.944024i	$0.392992\pi$
$570$		0			0
$571$	622.489	+	359.394i	1.09017	+	0.629411i	0.933622	−	0.358259i	$-0.116629\pi$
$571$	622.489	+	359.394i	1.09017	+	0.629411i	0.156550	+	0.987670i	$0.449963\pi$
$572$	−9.77425	+	16.9295i	−0.0170879	+	0.0295970i
$573$		0			0
$574$	172.637	+	299.016i	0.300761	+	0.520934i
$575$	911.127			1.58457
$576$		0			0
$577$	744.493			1.29028			0.645142	−	0.764063i	$-0.276798\pi$
$577$	744.493			1.29028			0.645142	+	0.764063i	$0.276798\pi$
$578$	159.228	+	632.324i	0.275480	+	1.09399i
$579$		0			0
$580$	−0.870157	+	1.50716i	−0.00150027	+	0.00259854i
$581$	−714.120	+	1236.89i	−1.22912	+	2.12890i
$582$		0			0
$583$	281.203	−	162.352i	0.482337	−	0.278477i
$584$	369.750			0.633134
$585$		0			0
$586$	−925.423			−1.57922
$587$	−669.831	+	386.727i	−1.14111	+	0.658819i	−0.946705	−	0.322102i	$-0.895610\pi$
$587$	−669.831	+	386.727i	−1.14111	+	0.658819i	−0.194403	+	0.980922i	$0.562277\pi$
$588$		0			0
$589$	111.798	+	64.5467i	0.189810	+	0.109587i
$590$	69.6813	−	120.692i	0.118104	−	0.204562i
$591$		0			0
$592$	148.325	−	85.6352i	0.250548	−	0.144654i
$593$			74.9340i			0.126364i	0.998002	+	0.0631821i	$0.0201249\pi$
$593$			74.9340i			0.126364i	−0.998002	+	0.0631821i	$0.979875\pi$
$594$		0			0
$595$	−219.744	+	165.992i	−0.369318	+	0.278978i
$596$	79.8128	−	46.0799i	0.133914	−	0.0773153i
$597$		0			0
$598$	−311.533	−	179.863i	−0.520958	−	0.300775i
$599$	192.205	+	110.970i	0.320877	+	0.185259i	0.651783	−	0.758405i	$-0.274021\pi$
$599$	192.205	+	110.970i	0.320877	+	0.185259i	−0.330906	+	0.943664i	$0.607354\pi$
$600$		0			0
$601$	−802.239	+	463.173i	−1.33484	+	0.770671i	−0.986037	−	0.166525i	$-0.946745\pi$
$601$	−802.239	+	463.173i	−1.33484	+	0.770671i	−0.348804	+	0.937196i	$0.613412\pi$
$602$	−1995.85			−3.31536
$603$		0			0
$604$	−119.695			−0.198171
$605$	73.0953	+	126.605i	0.120819	+	0.209264i
$606$		0			0
$607$	−795.808	−	459.460i	−1.31105	−	0.756936i	−0.328781	−	0.944406i	$-0.606638\pi$
$607$	−795.808	−	459.460i	−1.31105	−	0.756936i	−0.982270	+	0.187470i	$0.939971\pi$
$608$	161.909	+	93.4781i	0.266297	+	0.153747i
$609$		0			0
$610$	−132.928	−	230.237i	−0.217914	−	0.377438i
$611$		−	213.469i		−	0.349376i
$612$		0			0
$613$	−27.9652			−0.0456202			−0.0228101	−	0.999740i	$-0.507261\pi$
$613$	−27.9652			−0.0456202			−0.0228101	+	0.999740i	$0.507261\pi$
$614$	767.293	−	442.997i	1.24966	−	0.721494i
$615$		0			0
$616$	164.253	−	284.495i	0.266645	−	0.461842i
$617$	−443.301	+	767.820i	−0.718478	+	1.24444i	0.243125	+	0.969995i	$0.421828\pi$
$617$	−443.301	+	767.820i	−0.718478	+	1.24444i	−0.961603	+	0.274445i	$0.911506\pi$
$618$		0			0
$619$	523.815	−	302.425i	0.846228	−	0.488570i	−0.0131486	−	0.999914i	$-0.504185\pi$
$619$	523.815	−	302.425i	0.846228	−	0.488570i	0.859376	+	0.511344i	$0.170852\pi$
$620$			18.5365i			0.0298975i
$621$		0			0
$622$			745.096i			1.19790i
$623$	446.817	+	773.910i	0.717203	+	1.24223i
$624$		0			0
$625$	−236.140	+	409.007i	−0.377824	+	0.654411i
$626$	525.032	−	909.383i	0.838710	−	1.45269i
$627$		0			0
$628$	57.2514	+	99.1624i	0.0911647	+	0.157902i
$629$	121.171	−	91.5314i	0.192641	−	0.145519i
$630$		0			0
$631$	−487.278			−0.772231			−0.386115	−	0.922450i	$-0.626183\pi$
$631$	−487.278			−0.772231			−0.386115	+	0.922450i	$0.626183\pi$
$632$	−127.470	−	220.784i	−0.201693	−	0.349342i
$633$		0			0
$634$	−800.449	−	462.139i	−1.26254	−	0.728926i
$635$	122.282	−	211.798i	0.192570	−	0.333541i
$636$		0			0
$637$	−152.860	−	264.762i	−0.239969	−	0.415639i
$638$		−	11.1213i		−	0.0174315i
$639$		0			0
$640$		−	223.603i		−	0.349380i
$641$	−67.1633	−	116.330i	−0.104779	−	0.181482i	0.808869	−	0.587989i	$-0.200080\pi$
$641$	−67.1633	−	116.330i	−0.104779	−	0.181482i	−0.913648	+	0.406507i	$0.866747\pi$
$642$		0			0
$643$	62.6386	+	36.1644i	0.0974162	+	0.0562433i	0.547917	−	0.836533i	$-0.315421\pi$
$643$	62.6386	+	36.1644i	0.0974162	+	0.0562433i	−0.450500	+	0.892776i	$0.648754\pi$
$644$	−420.577	−	242.820i	−0.653070	−	0.377050i
$645$		0			0
$646$	388.387	+	164.325i	0.601218	+	0.254373i
$647$		−	709.660i		−	1.09685i	−0.836201	−	0.548423i	$-0.815228\pi$
$647$		−	709.660i		−	1.09685i	0.836201	−	0.548423i	$-0.184772\pi$
$648$		0			0
$649$			190.821i			0.294023i
$650$	179.388	−	103.570i	0.275982	−	0.159338i
$651$		0			0
$652$	−135.922	−	78.4747i	−0.208470	−	0.120360i
$653$	−325.713	+	564.151i	−0.498794	+	0.863937i	−0.999999	−	0.00139158i	$-0.999557\pi$
$653$	−325.713	+	564.151i	−0.498794	+	0.863937i	0.501205	+	0.865329i	$0.332890\pi$
$654$		0			0
$655$	156.207	+	270.558i	0.238484	+	0.413066i
$656$	−262.141			−0.399605
$657$		0			0
$658$		−	1345.01i		−	2.04408i
$659$	−808.335	+	466.693i	−1.22661	+	0.708183i	−0.966319	−	0.257348i	$-0.917151\pi$
$659$	−808.335	+	466.693i	−1.22661	+	0.708183i	−0.260290	+	0.965531i	$0.583818\pi$
$660$		0			0
$661$	203.907	−	353.177i	0.308482	−	0.534307i	−0.669548	−	0.742769i	$-0.733512\pi$
$661$	203.907	−	353.177i	0.308482	−	0.534307i	0.978031	+	0.208461i	$0.0668456\pi$
$662$	1140.74	+	658.604i	1.72317	+	0.994870i
$663$		0			0
$664$	−418.800	−	725.382i	−0.630722	−	1.09244i
$665$			178.109i			0.267832i
$666$		0			0
$667$	43.8498			0.0657418
$668$	57.6752	+	99.8964i	0.0863402	+	0.149546i
$669$		0			0
$670$	−181.524	−	104.803i	−0.270932	−	0.156422i
$671$	315.250	+	182.010i	0.469822	+	0.271252i
$672$		0			0
$673$	613.622	−	354.275i	0.911771	−	0.526411i	0.0307704	−	0.999526i	$-0.490204\pi$
$673$	613.622	−	354.275i	0.911771	−	0.526411i	0.881001	+	0.473115i	$0.156871\pi$
$674$	1017.32			1.50937
$675$		0			0
$676$	166.818			0.246773
$677$	80.2456	+	138.990i	0.118531	+	0.205302i	0.919186	−	0.393824i	$-0.128848\pi$
$677$	80.2456	+	138.990i	0.118531	+	0.205302i	−0.800655	+	0.599126i	$0.795515\pi$
$678$		0			0
$679$	−907.771	+	1572.30i	−1.33692	+	2.31562i
$680$	−19.8700	−	160.278i	−0.0292205	−	0.235703i
$681$		0			0
$682$	−59.2277	−	102.585i	−0.0868442	−	0.150419i
$683$	247.116			0.361809			0.180905	−	0.983501i	$-0.442097\pi$
$683$	247.116			0.361809			0.180905	+	0.983501i	$0.442097\pi$
$684$		0			0
$685$			68.0552i			0.0993506i
$686$	−344.412	−	596.539i	−0.502058	−	0.869590i
$687$		0			0
$688$	757.649	−	1312.29i	1.10123	−	1.90739i
$689$	252.066	+	145.531i	0.365844	+	0.211220i
$690$		0			0
$691$	−251.002	+	144.916i	−0.363245	+	0.209719i	−0.670503	−	0.741907i	$-0.733922\pi$
$691$	−251.002	+	144.916i	−0.363245	+	0.209719i	0.307258	+	0.951626i	$0.400588\pi$
$692$	−177.489			−0.256487
$693$		0			0
$694$			883.335i			1.27282i
$695$	11.0898	−	6.40271i	0.0159566	−	0.00921253i
$696$		0			0
$697$	−230.661	+	28.5955i	−0.330934	+	0.0410265i
$698$	−218.714	−	126.275i	−0.313344	−	0.180909i
$699$		0			0
$700$	242.179	−	139.822i	0.345969	−	0.199746i
$701$			1016.86i			1.45059i	0.688438	+	0.725296i	$0.258297\pi$
$701$			1016.86i			1.45059i	−0.688438	+	0.725296i	$0.741703\pi$
$702$		0			0
$703$		−	98.2126i		−	0.139705i
$704$	85.6871	+	148.414i	0.121715	+	0.210816i
$705$		0			0
$706$	445.594	−	771.792i	0.631153	−	1.09319i
$707$	579.794	−	1004.23i	0.820077	−	1.42042i
$708$		0			0
$709$	228.924	−	132.169i	0.322883	−	0.186417i	−0.329794	−	0.944053i	$-0.606979\pi$
$709$	228.924	−	132.169i	0.322883	−	0.186417i	0.652677	+	0.757636i	$0.273646\pi$
$710$		−	33.8193i		−	0.0476328i
$711$		0			0
$712$	−524.077			−0.736063
$713$	404.480	−	233.527i	0.567293	−	0.327527i
$714$		0			0
$715$	12.9693	−	22.4634i	0.0181388	−	0.0314174i
$716$	138.761	+	80.1135i	0.193800	+	0.111890i
$717$		0			0
$718$	439.640	+	761.479i	0.612312	+	1.06056i
$719$	577.307			0.802931			0.401465	−	0.915874i	$-0.368501\pi$
$719$	577.307			0.802931			0.401465	+	0.915874i	$0.368501\pi$
$720$		0			0
$721$		−	921.987i		−	1.27876i
$722$	−469.187	+	270.885i	−0.649844	+	0.375187i
$723$		0			0
$724$	141.637	+	81.7743i	0.195632	+	0.112948i
$725$	−12.6249	+	21.8669i	−0.0174136	+	0.0301613i
$726$		0			0
$727$	72.8716	+	126.217i	0.100236	+	0.173614i	0.911782	−	0.410675i	$-0.134707\pi$
$727$	72.8716	+	126.217i	0.100236	+	0.173614i	−0.811546	+	0.584289i	$0.801374\pi$
$728$	294.469			0.404490
$729$		0			0
$730$	183.950			0.251987
$731$	523.515	−	1237.35i	0.716163	−	1.69268i
$732$		0			0
$733$	−231.832	+	401.544i	−0.316278	+	0.547809i	−0.979708	−	0.200429i	$-0.935766\pi$
$733$	−231.832	+	401.544i	−0.316278	+	0.547809i	0.663431	+	0.748238i	$0.269100\pi$
$734$	343.540	−	595.028i	0.468037	−	0.810665i
$735$		0			0
$736$	585.777	−	338.199i	0.795893	−	0.459509i
$737$	287.002			0.389419
$738$		0			0
$739$	−386.300			−0.522733			−0.261367	−	0.965240i	$-0.584173\pi$
$739$	−386.300			−0.522733			−0.261367	+	0.965240i	$0.584173\pi$
$740$	12.2130	−	7.05115i	0.0165040	−	0.00952858i
$741$		0			0
$742$	1588.20	+	916.947i	2.14043	+	1.23578i
$743$	−565.286	+	979.104i	−0.760815	+	1.31777i	0.181616	+	0.983370i	$0.441867\pi$
$743$	−565.286	+	979.104i	−0.760815	+	1.31777i	−0.942431	+	0.334401i	$0.891466\pi$
$744$		0			0
$745$	−105.902	+	61.1426i	−0.142150	+	0.0820706i
$746$		−	711.433i		−	0.953664i
$747$		0			0
$748$	−49.9761	−	66.1594i	−0.0668129	−	0.0884484i
$749$	−694.174	+	400.781i	−0.926800	+	0.535088i
$750$		0			0
$751$	240.217	+	138.690i	0.319863	+	0.184673i	0.651332	−	0.758793i	$-0.274211\pi$
$751$	240.217	+	138.690i	0.319863	+	0.184673i	−0.331468	+	0.943466i	$0.607544\pi$
$752$	884.354	+	510.582i	1.17600	+	0.678966i
$753$		0			0
$754$	8.63340	−	4.98450i	0.0114501	−	0.00661074i
$755$	158.822			0.210360
$756$		0			0
$757$	−353.193			−0.466569			−0.233284	−	0.972409i	$-0.574947\pi$
$757$	−353.193			−0.466569			−0.233284	+	0.972409i	$0.574947\pi$
$758$	81.9843	+	142.001i	0.108159	+	0.187336i
$759$		0			0
$760$	−90.4587	−	52.2263i	−0.119025	−	0.0687189i
$761$	991.541	+	572.466i	1.30294	+	0.752256i	0.980908	−	0.194472i	$-0.0622992\pi$
$761$	991.541	+	572.466i	1.30294	+	0.752256i	0.322037	+	0.946727i	$0.395633\pi$
$762$		0			0
$763$	890.610	+	1542.58i	1.16725	+	2.02173i
$764$		−	21.6690i		−	0.0283626i
$765$		0			0
$766$	865.165			1.12946
$767$	−148.133	+	85.5248i	−0.193133	+	0.111506i
$768$		0			0
$769$	450.918	−	781.014i	0.586370	−	1.01562i	−0.408333	−	0.912833i	$-0.633890\pi$
$769$	450.918	−	781.014i	0.586370	−	1.01562i	0.994703	−	0.102789i	$-0.0327768\pi$
$770$	81.7157	−	141.536i	0.106124	−	0.183813i
$771$		0			0
$772$	−267.727	+	154.572i	−0.346796	+	0.200223i
$773$		−	737.598i		−	0.954202i	−0.878849	−	0.477101i	$-0.841688\pi$
$773$		−	737.598i		−	0.954202i	0.878849	−	0.477101i	$-0.158312\pi$
$774$		0			0
$775$			268.941i			0.347020i
$776$	−532.367	−	922.086i	−0.686040	−	1.18826i
$777$		0			0
$778$	46.9688	−	81.3523i	0.0603712	−	0.104566i
$779$	−75.1605	+	130.182i	−0.0964833	+	0.167114i
$780$		0			0
$781$	23.1534	+	40.1028i	0.0296458	+	0.0513481i
$782$	1217.45	−	919.648i	1.55684	−	1.17602i
$783$		0			0
$784$	1462.47			1.86539
$785$	−75.9659	−	131.577i	−0.0967718	−	0.167614i
$786$		0			0
$787$	−409.850	−	236.627i	−0.520775	−	0.300670i	0.216476	−	0.976288i	$-0.430544\pi$
$787$	−409.850	−	236.627i	−0.520775	−	0.300670i	−0.737252	+	0.675618i	$0.763877\pi$
$788$	157.728	−	273.194i	0.200163	−	0.346692i
$789$		0			0
$790$	−63.4161	−	109.840i	−0.0802735	−	0.139038i
$791$		−	204.571i		−	0.258623i
$792$		0			0
$793$			326.303i			0.411479i
$794$	−250.637	−	434.115i	−0.315663	−	0.546745i
$795$		0			0
$796$	−199.450	−	115.152i	−0.250565	−	0.144664i
$797$	159.795	+	92.2578i	0.200496	+	0.115756i	0.596887	−	0.802325i	$-0.296404\pi$
$797$	159.795	+	92.2578i	0.200496	+	0.115756i	−0.396391	+	0.918082i	$0.629737\pi$
$798$		0			0
$799$	833.851	+	352.799i	1.04362	+	0.441550i
$800$			389.486i			0.486858i
$801$		0			0
$802$		−	570.328i		−	0.711132i
$803$	−218.128	+	125.936i	−0.271641	+	0.156832i
$804$		0			0
$805$	558.056	+	322.194i	0.693237	+	0.400241i
$806$	53.0910	−	91.9563i	0.0658697	−	0.114090i
$807$		0			0
$808$	340.023	+	588.938i	0.420821	+	0.728884i
$809$	609.972			0.753982			0.376991	−	0.926217i	$-0.376959\pi$
$809$	609.972			0.753982			0.376991	+	0.926217i	$0.376959\pi$
$810$		0			0
$811$		−	862.103i		−	1.06301i	−0.847054	−	0.531506i	$-0.821626\pi$
$811$		−	862.103i		−	1.06301i	0.847054	−	0.531506i	$-0.178374\pi$
$812$	11.6553	−	6.72920i	0.0143538	−	0.00828719i
$813$		0			0
$814$	−45.0597	+	78.0456i	−0.0553559	+	0.0958792i
$815$	180.353	+	104.127i	0.221292	+	0.127763i
$816$		0			0
$817$	−434.463	−	752.512i	−0.531779	−	0.921068i
$818$			1577.67i			1.92870i
$819$		0			0
$820$	−21.5845			−0.0263226
$821$	−777.577	−	1346.80i	−0.947110	−	1.64044i	−0.751471	−	0.659766i	$-0.770655\pi$
$821$	−777.577	−	1346.80i	−0.947110	−	1.64044i	−0.195639	−	0.980676i	$-0.562678\pi$
$822$		0			0
$823$	−511.055	−	295.058i	−0.620966	−	0.358515i	0.156279	−	0.987713i	$-0.450050\pi$
$823$	−511.055	−	295.058i	−0.620966	−	0.358515i	−0.777245	+	0.629198i	$0.783383\pi$
$824$	468.264	+	270.352i	0.568281	+	0.328097i
$825$		0			0
$826$	−933.346	+	538.867i	−1.12996	+	0.652382i
$827$	1114.88			1.34810			0.674048	−	0.738687i	$-0.264554\pi$
$827$	1114.88			1.34810			0.674048	+	0.738687i	$0.264554\pi$
$828$		0			0
$829$	−588.636			−0.710055			−0.355028	−	0.934856i	$-0.615529\pi$
$829$	−588.636			−0.710055			−0.355028	+	0.934856i	$0.615529\pi$
$830$	−208.352	−	360.876i	−0.251027	−	0.434791i
$831$		0			0
$832$	−76.8088	+	133.037i	−0.0923183	+	0.159900i
$833$	1286.84	−	159.532i	1.54483	−	0.191515i
$834$		0			0
$835$	−76.5282	−	132.551i	−0.0916505	−	0.158743i
$836$	−53.6240			−0.0641435
$837$		0			0
$838$		−	1266.02i		−	1.51077i
$839$	589.367	+	1020.81i	0.702463	+	1.21670i	0.967599	+	0.252491i	$0.0812497\pi$
$839$	589.367	+	1020.81i	0.702463	+	1.21670i	−0.265136	+	0.964211i	$0.585417\pi$
$840$		0			0
$841$	419.892	−	727.275i	0.499278	−	0.864774i
$842$	−1453.30	−	839.061i	−1.72601	−	0.996510i
$843$		0			0
$844$	−166.002	+	95.8411i	−0.196684	+	0.113556i
$845$	−221.348			−0.261951
$846$		0			0
$847$		−	1130.54i		−	1.33475i
$848$	−1205.80	+	696.170i	−1.42194	+	0.820955i
$849$		0			0
$850$	108.090	+	871.894i	0.127165	+	1.02576i
$851$	−307.723	−	177.664i	−0.361602	−	0.208771i
$852$		0			0
$853$	155.292	−	89.6579i	0.182054	−	0.105109i	−0.406203	−	0.913783i	$-0.633148\pi$
$853$	155.292	−	89.6579i	0.182054	−	0.105109i	0.588257	+	0.808674i	$0.299814\pi$
$854$			2055.94i			2.40742i
$855$		0			0
$856$		−	470.081i		−	0.549159i
$857$	−575.734	−	997.200i	−0.671801	−	1.16359i	−0.977393	−	0.211431i	$-0.932188\pi$
$857$	−575.734	−	997.200i	−0.671801	−	1.16359i	0.305592	−	0.952163i	$-0.401146\pi$
$858$		0			0
$859$	331.359	−	573.930i	0.385749	−	0.668138i	−0.606123	−	0.795371i	$-0.707276\pi$
$859$	331.359	−	573.930i	0.385749	−	0.668138i	0.991873	+	0.127233i	$0.0406096\pi$
$860$	62.3844	−	108.053i	0.0725400	−	0.125643i
$861$		0			0
$862$	−526.767	+	304.129i	−0.611099	+	0.352818i
$863$		−	791.536i		−	0.917191i	−0.888645	−	0.458595i	$-0.848353\pi$
$863$		−	791.536i		−	0.917191i	0.888645	−	0.458595i	$-0.151647\pi$
$864$		0			0
$865$	235.507			0.272263
$866$	658.768	−	380.340i	0.760702	−	0.439191i
$867$		0			0
$868$	71.6742	−	124.143i	0.0825739	−	0.143022i
$869$	150.397	+	86.8320i	0.173069	+	0.0999217i
$870$		0			0
$871$	128.632	+	222.798i	0.147683	+	0.255795i
$872$	−1044.61			−1.19794
$873$		0			0
$874$		−	986.776i		−	1.12903i
$875$	−672.072	+	388.021i	−0.768083	+	0.443453i
$876$		0			0
$877$	591.963	+	341.770i	0.674986	+	0.389704i	0.797963	−	0.602706i	$-0.205911\pi$
$877$	591.963	+	341.770i	0.674986	+	0.389704i	−0.122977	+	0.992410i	$0.539244\pi$
$878$	698.915	−	1210.56i	0.796031	−	1.37877i
$879$		0			0
$880$	62.0407	+	107.458i	0.0705008	+	0.122111i
$881$	972.438			1.10379			0.551895	−	0.833914i	$-0.313905\pi$
$881$	972.438			1.10379			0.551895	+	0.833914i	$0.313905\pi$
$882$		0			0
$883$	−257.671			−0.291814			−0.145907	−	0.989298i	$-0.546610\pi$
$883$	−257.671			−0.291814			−0.145907	+	0.989298i	$0.546610\pi$
$884$	28.9602	−	68.4484i	0.0327604	−	0.0774303i
$885$		0			0
$886$	−252.216	+	436.851i	−0.284668	+	0.493059i
$887$	525.785	−	910.687i	0.592768	−	1.02670i	−0.401090	−	0.916039i	$-0.631368\pi$
$887$	525.785	−	910.687i	0.592768	−	1.02670i	0.993858	−	0.110665i	$-0.0352982\pi$
$888$		0			0
$889$	−1637.90	+	945.644i	−1.84241	+	1.06372i
$890$	−260.727			−0.292952
$891$		0			0
$892$	−201.606			−0.226015
$893$	507.120	−	292.786i	0.567884	−	0.327868i
$894$		0			0
$895$	−184.119	−	106.301i	−0.205719	−	0.118772i
$896$	−864.597	+	1497.53i	−0.964952	+	1.67135i
$897$		0			0
$898$	−225.783	+	130.356i	−0.251428	+	0.145162i
$899$			12.9433i			0.0143974i
$900$		0			0
$901$	−985.059	+	744.103i	−1.09330	+	0.825863i
$902$	119.454	−	68.9668i	0.132432	−	0.0764599i
$903$		0			0
$904$	103.898	+	59.9858i	0.114932	+	0.0663559i
$905$	−187.936	−	108.505i	−0.207664	−	0.119895i
$906$		0			0
$907$	1220.24	−	704.504i	1.34535	−	0.776741i	0.357767	−	0.933811i	$-0.383538\pi$
$907$	1220.24	−	704.504i	1.34535	−	0.776741i	0.987587	+	0.157070i	$0.0502048\pi$
$908$	−266.774			−0.293804
$909$		0			0
$910$	146.498			0.160987
$911$	686.223	+	1188.57i	0.753263	+	1.30469i	0.946233	+	0.323486i	$0.104855\pi$
$911$	686.223	+	1188.57i	0.753263	+	1.30469i	−0.192970	+	0.981205i	$0.561812\pi$
$912$		0			0
$913$	494.127	+	285.284i	0.541213	+	0.312469i
$914$	−19.1931	−	11.0811i	−0.0209990	−	0.0121238i
$915$		0			0
$916$	40.3378	+	69.8672i	0.0440369	+	0.0762742i
$917$		−	2415.99i		−	2.63467i
$918$		0			0
$919$	849.649			0.924537			0.462268	−	0.886740i	$-0.347036\pi$
$919$	849.649			0.924537			0.462268	+	0.886740i	$0.347036\pi$
$920$	−327.275	+	188.952i	−0.355733	+	0.205383i
$921$		0			0
$922$	402.382	−	696.946i	0.436423	−	0.755907i
$923$	−20.7544	+	35.9477i	−0.0224858	+	0.0389466i
$924$		0			0
$925$	177.195	−	102.303i	0.191562	−	0.110598i
$926$			545.442i			0.589031i
$927$		0			0
$928$			18.7448i			0.0201991i
$929$	272.517	+	472.013i	0.293344	+	0.508087i	0.974598	−	0.223960i	$-0.0718985\pi$
$929$	272.517	+	472.013i	0.293344	+	0.508087i	−0.681254	+	0.732047i	$0.738565\pi$
$930$		0			0
$931$	419.315	−	726.275i	0.450392	−	0.780102i
$932$	−229.529	+	397.556i	−0.246276	+	0.426562i
$933$		0			0
$934$	258.521	+	447.771i	0.276789	+	0.479412i
$935$	66.3123	+	87.7857i	0.0709223	+	0.0938884i
$936$		0			0
$937$	1418.88			1.51428			0.757140	−	0.653253i	$-0.226596\pi$
$937$	1418.88			1.51428			0.757140	+	0.653253i	$0.226596\pi$
$938$	810.475	+	1403.78i	0.864046	+	1.49657i
$939$		0			0
$940$	72.8172	+	42.0410i	0.0774651	+	0.0447245i
$941$	−255.539	+	442.607i	−0.271561	+	0.470358i	−0.969262	−	0.246032i	$-0.920873\pi$
$941$	−255.539	+	442.607i	−0.271561	+	0.470358i	0.697701	+	0.716389i	$0.254207\pi$
$942$		0			0
$943$	271.927	+	470.991i	0.288363	+	0.499460i
$944$		−	818.244i		−	0.866784i
$945$		0			0
$946$			797.322i			0.842835i
$947$	−48.4833	−	83.9755i	−0.0511967	−	0.0886753i	0.839291	−	0.543682i	$-0.182970\pi$
$947$	−48.4833	−	83.9755i	−0.0511967	−	0.0886753i	−0.890488	+	0.455007i	$0.849637\pi$
$948$		0			0
$949$	−195.527	−	112.888i	−0.206035	−	0.118954i
$950$	492.084	+	284.105i	0.517983	+	0.299058i
$951$		0			0
$952$	−486.667	+	1150.25i	−0.511205	+	1.20825i
$953$			759.400i			0.796852i	0.917200	+	0.398426i	$0.130443\pi$
$953$			759.400i			0.796852i	−0.917200	+	0.398426i	$0.869557\pi$
$954$		0			0
$955$			28.7523i			0.0301071i
$956$	238.042	−	137.433i	0.248997	−	0.143759i
$957$		0			0
$958$	696.142	+	401.918i	0.726661	+	0.419538i
$959$	263.146	−	455.782i	0.274396	−	0.475268i
$960$		0			0
$961$	−411.569	−	712.858i	−0.428272	−	0.741788i
$962$	−80.7818			−0.0839728
$963$		0			0
$964$			127.725i			0.132494i
$965$	355.241	−	205.099i	0.368126	−	0.212538i
$966$		0			0
$967$	523.075	−	905.993i	0.540926	−	0.936911i	−0.457925	−	0.888991i	$-0.651407\pi$
$967$	523.075	−	905.993i	0.540926	−	0.936911i	0.998851	−	0.0479203i	$-0.0152593\pi$
$968$	574.183	+	331.505i	0.593164	+	0.342464i
$969$		0			0
$970$	−264.852	−	458.736i	−0.273043	−	0.472924i
$971$		−	29.9038i		−	0.0307969i	−0.999881	−	0.0153985i	$-0.995098\pi$
$971$		−	29.9038i		−	0.0307969i	0.999881	−	0.0153985i	$-0.00490168\pi$
$972$		0			0
$973$	−99.0283			−0.101776
$974$	539.923	+	935.174i	0.554336	+	0.960138i
$975$		0			0
$976$	−1351.80	−	780.462i	−1.38504	−	0.799653i
$977$	54.6776	+	31.5681i	0.0559648	+	0.0323113i	0.527721	−	0.849418i	$-0.323047\pi$
$977$	54.6776	+	31.5681i	0.0559648	+	0.0323113i	−0.471757	+	0.881729i	$0.656380\pi$
$978$		0			0
$979$	309.170	−	178.499i	0.315802	−	0.182328i
$980$	120.419			0.122876
$981$		0			0
$982$	−1668.20			−1.69877
$983$	−327.329	−	566.950i	−0.332990	−	0.576755i	0.650107	−	0.759843i	$-0.274724\pi$
$983$	−327.329	−	566.950i	−0.332990	−	0.576755i	−0.983097	+	0.183088i	$0.941391\pi$
$984$		0			0
$985$	−209.287	+	362.495i	−0.212474	+	0.368016i
$986$	5.20205	+	41.9616i	0.00527591	+	0.0425574i
$987$		0			0
$988$	−24.0339	−	41.6280i	−0.0243258	−	0.0421336i
$989$	−3143.73			−3.17870
$990$		0			0
$991$		−	173.917i		−	0.175496i	−0.996143	−	0.0877481i	$-0.972033\pi$
$991$		−	173.917i		−	0.175496i	0.996143	−	0.0877481i	$-0.0279671\pi$
$992$	99.8274	+	172.906i	0.100632	+	0.174301i
$993$		0			0
$994$	−130.768	+	226.496i	−0.131557	+	0.227863i
$995$	264.646	+	152.794i	0.265976	+	0.153561i
$996$		0			0
$997$	7.95246	−	4.59136i	0.00797639	−	0.00460517i	−0.496007	−	0.868319i	$-0.665201\pi$
$997$	7.95246	−	4.59136i	0.00797639	−	0.00460517i	0.503983	+	0.863714i	$0.331867\pi$
$998$	1318.77			1.32142
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	459.3.i.a.152.25		68
3.2	odd	2		153.3.i.a.50.10	yes	68
9.2	odd	6	inner	459.3.i.a.305.26		68
9.7	even	3		153.3.i.a.101.9	yes	68
17.16	even	2	inner	459.3.i.a.152.26		68
51.50	odd	2		153.3.i.a.50.9	✓	68
153.16	even	6		153.3.i.a.101.10	yes	68
153.101	odd	6	inner	459.3.i.a.305.25		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.i.a.50.9	✓	68	51.50	odd	2
153.3.i.a.50.10	yes	68	3.2	odd	2
153.3.i.a.101.9	yes	68	9.7	even	3
153.3.i.a.101.10	yes	68	153.16	even	6
459.3.i.a.152.25		68	1.1	even	1	trivial
459.3.i.a.152.26		68	17.16	even	2	inner
459.3.i.a.305.25		68	153.101	odd	6	inner
459.3.i.a.305.26		68	9.2	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(1.95399 - 1.12814i) q^{2} +(0.545389 - 0.944642i) q^{4} +(-0.723667 + 1.25343i) q^{5} +(9.69315 - 5.59634i) q^{7} +6.56401i q^{8} +3.26558i q^{10} +(-2.23569 - 3.87232i) q^{11} +(2.00404 - 3.47110i) q^{13} +(12.6269 - 21.8704i) q^{14} +(9.58666 + 16.6046i) q^{16} +(10.2467 + 13.5648i) q^{17} +10.9947 q^{19} +(0.789360 + 1.36721i) q^{20} +(-8.73702 - 5.04432i) q^{22} +(19.8891 - 34.4489i) q^{23} +(11.4526 + 19.8365i) q^{25} -9.04333i q^{26} -12.2087i q^{28} +(0.551179 + 0.954670i) q^{29} +(10.1684 + 5.87073i) q^{31} +(14.7261 + 8.50213i) q^{32} +(35.3250 + 14.9459i) q^{34} +16.1995i q^{35} -8.93275i q^{37} +(21.4835 - 12.4035i) q^{38} +(-8.22750 - 4.75015i) q^{40} +(-6.83609 + 11.8404i) q^{41} +(-39.5158 - 68.4434i) q^{43} -4.87727 q^{44} -89.7504i q^{46} +(46.1242 - 26.6298i) q^{47} +(38.1380 - 66.0570i) q^{49} +(44.7566 + 25.8402i) q^{50} +(-2.18596 - 3.78620i) q^{52} +72.6186i q^{53} +6.47156 q^{55} +(36.7344 + 63.6259i) q^{56} +(2.15400 + 1.24361i) q^{58} +(-36.9587 - 21.3381i) q^{59} +(-70.5042 + 40.7056i) q^{61} +26.4920 q^{62} -38.3270 q^{64} +(2.90051 + 5.02384i) q^{65} +(-32.0932 + 55.5871i) q^{67} +(18.4024 - 2.28137i) q^{68} +(18.2753 + 31.6538i) q^{70} -10.3563 q^{71} -56.3300i q^{73} +(-10.0774 - 17.4545i) q^{74} +(5.99637 - 10.3860i) q^{76} +(-43.3417 - 25.0233i) q^{77} +(-33.6356 + 19.4195i) q^{79} -27.7502 q^{80} +30.8482i q^{82} +(-110.509 + 63.8025i) q^{83} +(-24.4177 + 3.02711i) q^{85} +(-154.427 - 89.1585i) q^{86} +(25.4179 - 14.6751i) q^{88} +79.8410i q^{89} -44.8612i q^{91} +(-21.6946 - 37.5761i) q^{92} +(60.0842 - 104.069i) q^{94} +(-7.95647 + 13.7810i) q^{95} +(-140.476 + 81.1039i) q^{97} -172.100i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 6 q^{2} + 62 q^{4} - 2 q^{13} - 106 q^{16} - 32 q^{19} - 132 q^{25} - 27 q^{34} + 102 q^{38} + 58 q^{43} + 312 q^{47} + 152 q^{49} + 90 q^{50} + 70 q^{52} + 92 q^{55} + 258 q^{59} - 16 q^{64} + 82 q^{67}+ \cdots - 18 q^{94}+O(q^{100}) \) 68 * q + 6 * q^2 + 62 * q^4 - 2 * q^13 - 106 * q^16 - 32 * q^19 - 132 * q^25 - 27 * q^34 + 102 * q^38 + 58 * q^43 + 312 * q^47 + 152 * q^49 + 90 * q^50 + 70 * q^52 + 92 * q^55 + 258 * q^59 - 16 * q^64 + 82 * q^67 + 333 * q^68 + 204 * q^70 + 34 * q^76 + 60 * q^77 + 690 * q^83 - 44 * q^85 + 1248 * q^86 - 18 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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