LMFDB - Embedded newform 459.3.i.a.152.17

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)

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")

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);

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			152.17
Character	$\chi$	$=$	459.152
Dual form			459.3.i.a.305.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.129772 - 0.0749237i) q^{2} +(-1.98877 + 3.44466i) q^{4} +(1.38111 - 2.39215i) q^{5} +(2.73699 - 1.58020i) q^{7} +1.19542i q^{8} -0.413911i q^{10} +(6.09900 + 10.5638i) q^{11} +(-8.45595 + 14.6461i) q^{13} +(0.236789 - 0.410131i) q^{14} +(-7.86553 - 13.6235i) q^{16} +(-4.71123 - 16.3341i) q^{17} +9.05723 q^{19} +(5.49342 + 9.51489i) q^{20} +(1.58296 + 0.913920i) q^{22} +(-10.2096 + 17.6835i) q^{23} +(8.68508 + 15.0430i) q^{25} +2.53421i q^{26} +12.5706i q^{28} +(-1.08463 - 1.87864i) q^{29} +(38.1700 + 22.0374i) q^{31} +(-6.18249 - 3.56946i) q^{32} +(-1.83520 - 1.76673i) q^{34} -8.72972i q^{35} +62.4071i q^{37} +(1.17537 - 0.678602i) q^{38} +(2.85961 + 1.65100i) q^{40} +(-31.2890 + 54.1941i) q^{41} +(-14.0734 - 24.3759i) q^{43} -48.5181 q^{44} +3.05976i q^{46} +(-37.6889 + 21.7597i) q^{47} +(-19.5059 + 33.7853i) q^{49} +(2.25415 + 1.30144i) q^{50} +(-33.6339 - 58.2557i) q^{52} +66.8350i q^{53} +33.6935 q^{55} +(1.88900 + 3.27184i) q^{56} +(-0.281509 - 0.162529i) q^{58} +(-68.5161 - 39.5578i) q^{59} +(65.5511 - 37.8459i) q^{61} +6.60451 q^{62} +61.8545 q^{64} +(23.3572 + 40.4558i) q^{65} +(-10.6797 + 18.4979i) q^{67} +(65.6351 + 16.2563i) q^{68} +(-0.654064 - 1.13287i) q^{70} +80.2879 q^{71} -23.7538i q^{73} +(4.67578 + 8.09868i) q^{74} +(-18.0128 + 31.1990i) q^{76} +(33.3858 + 19.2753i) q^{77} +(6.49716 - 3.75114i) q^{79} -43.4526 q^{80} +9.37714i q^{82} +(12.4098 - 7.16481i) q^{83} +(-45.5805 - 11.2893i) q^{85} +(-3.65266 - 2.10887i) q^{86} +(-12.6281 + 7.29084i) q^{88} -115.581i q^{89} +53.4484i q^{91} +(-40.6091 - 70.3370i) q^{92} +(-3.26063 + 5.64758i) q^{94} +(12.5090 - 21.6663i) q^{95} +(9.98636 - 5.76563i) q^{97} +5.84583i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.129772	−	0.0749237i	0.0648859	−	0.0374619i	−0.467206	−	0.884148i	$-0.654739\pi$
$2$	0.129772	−	0.0749237i	0.0648859	−	0.0374619i	0.532092	+	0.846687i	$0.321406\pi$
$3$		0			0
$3$		0			0
$4$	−1.98877	+	3.44466i	−0.497193	+	0.861164i
$5$	1.38111	−	2.39215i	0.276222	−	0.478430i	−0.694221	−	0.719762i	$-0.744251\pi$
$5$	1.38111	−	2.39215i	0.276222	−	0.478430i	0.970443	+	0.241332i	$0.0775842\pi$
$6$		0			0
$7$	2.73699	−	1.58020i	0.390999	−	0.225743i	−0.291594	−	0.956542i	$-0.594186\pi$
$7$	2.73699	−	1.58020i	0.390999	−	0.225743i	0.682593	+	0.730799i	$0.260852\pi$
$8$			1.19542i			0.149427i
$9$		0			0
$10$		−	0.413911i		−	0.0413911i
$11$	6.09900	+	10.5638i	0.554455	+	0.960344i	0.997946	+	0.0640648i	$0.0204064\pi$
$11$	6.09900	+	10.5638i	0.554455	+	0.960344i	−0.443491	+	0.896279i	$0.646260\pi$
$12$		0			0
$13$	−8.45595	+	14.6461i	−0.650458	+	1.12663i	0.332554	+	0.943084i	$0.392090\pi$
$13$	−8.45595	+	14.6461i	−0.650458	+	1.12663i	−0.983012	+	0.183542i	$0.941244\pi$
$14$	0.236789	−	0.410131i	0.0169135	−	0.0292951i
$15$		0			0
$16$	−7.86553	−	13.6235i	−0.491595	−	0.851468i
$17$	−4.71123	−	16.3341i	−0.277131	−	0.960832i
$17$	−4.71123	−	16.3341i	−0.277131	−	0.960832i
$18$		0			0
$19$	9.05723			0.476696			0.238348	−	0.971180i	$-0.423394\pi$
$19$	9.05723			0.476696			0.238348	+	0.971180i	$0.423394\pi$
$20$	5.49342	+	9.51489i	0.274671	+	0.475745i
$21$		0			0
$22$	1.58296	+	0.913920i	0.0719525	+	0.0415418i
$23$	−10.2096	+	17.6835i	−0.443895	+	0.768849i	−0.997975	−	0.0636149i	$-0.979737\pi$
$23$	−10.2096	+	17.6835i	−0.443895	+	0.768849i	0.554079	+	0.832464i	$0.313070\pi$
$24$		0			0
$25$	8.68508	+	15.0430i	0.347403	+	0.601720i
$26$			2.53421i			0.0974695i
$27$		0			0
$28$			12.5706i			0.448952i
$29$	−1.08463	−	1.87864i	−0.0374011	−	0.0647807i	0.846719	−	0.532040i	$-0.178575\pi$
$29$	−1.08463	−	1.87864i	−0.0374011	−	0.0647807i	−0.884120	+	0.467260i	$0.845241\pi$
$30$		0			0
$31$	38.1700	+	22.0374i	1.23129	+	0.710885i	0.967299	−	0.253640i	$-0.0816278\pi$
$31$	38.1700	+	22.0374i	1.23129	+	0.710885i	0.263991	+	0.964525i	$0.414961\pi$
$32$	−6.18249	−	3.56946i	−0.193203	−	0.111546i
$33$		0			0
$34$	−1.83520	−	1.76673i	−0.0539765	−	0.0519626i
$35$		−	8.72972i		−	0.249421i
$36$		0			0
$37$			62.4071i			1.68668i	0.537381	+	0.843340i	$0.319414\pi$
$37$			62.4071i			1.68668i	−0.537381	+	0.843340i	$0.680586\pi$
$38$	1.17537	−	0.678602i	0.0309309	−	0.0178579i
$39$		0			0
$40$	2.85961	+	1.65100i	0.0714903	+	0.0412750i
$41$	−31.2890	+	54.1941i	−0.763145	+	1.32181i	0.178076	+	0.984017i	$0.443013\pi$
$41$	−31.2890	+	54.1941i	−0.763145	+	1.32181i	−0.941222	+	0.337790i	$0.890321\pi$
$42$		0			0
$43$	−14.0734	−	24.3759i	−0.327289	−	0.566881i	0.654684	−	0.755903i	$-0.272802\pi$
$43$	−14.0734	−	24.3759i	−0.327289	−	0.566881i	−0.981973	+	0.189022i	$0.939468\pi$
$44$	−48.5181			−1.10268
$45$		0			0
$46$			3.05976i			0.0665166i
$47$	−37.6889	+	21.7597i	−0.801891	+	0.462972i	−0.844132	−	0.536136i	$-0.819884\pi$
$47$	−37.6889	+	21.7597i	−0.801891	+	0.462972i	0.0422410	+	0.999107i	$0.486550\pi$
$48$		0			0
$49$	−19.5059	+	33.7853i	−0.398080	+	0.689495i
$50$	2.25415	+	1.30144i	0.0450831	+	0.0260287i
$51$		0			0
$52$	−33.6339	−	58.2557i	−0.646807	−	1.12030i
$53$			66.8350i			1.26104i	0.776174	+	0.630518i	$0.217158\pi$
$53$			66.8350i			1.26104i	−0.776174	+	0.630518i	$0.782842\pi$
$54$		0			0
$55$	33.6935			0.612610
$56$	1.88900	+	3.27184i	0.0337321	+	0.0584257i
$57$		0			0
$58$	−0.281509	−	0.162529i	−0.00485361	−	0.00280223i
$59$	−68.5161	−	39.5578i	−1.16129	−	0.670471i	−0.209678	−	0.977771i	$-0.567241\pi$
$59$	−68.5161	−	39.5578i	−1.16129	−	0.670471i	−0.951613	+	0.307299i	$0.900575\pi$
$60$		0			0
$61$	65.5511	−	37.8459i	1.07461	−	0.620425i	0.145171	−	0.989407i	$-0.453627\pi$
$61$	65.5511	−	37.8459i	1.07461	−	0.620425i	0.929437	+	0.368981i	$0.120293\pi$
$62$	6.60451			0.106524
$63$		0			0
$64$	61.8545			0.966476
$65$	23.3572	+	40.4558i	0.359341	+	0.622397i
$66$		0			0
$67$	−10.6797	+	18.4979i	−0.159399	+	0.276087i	−0.934652	−	0.355563i	$-0.884289\pi$
$67$	−10.6797	+	18.4979i	−0.159399	+	0.276087i	0.775253	+	0.631651i	$0.217622\pi$
$68$	65.6351	+	16.2563i	0.965222	+	0.239064i
$69$		0			0
$70$	−0.654064	−	1.13287i	−0.00934377	−	0.0161839i
$71$	80.2879			1.13082			0.565408	−	0.824811i	$-0.308719\pi$
$71$	80.2879			1.13082			0.565408	+	0.824811i	$0.308719\pi$
$72$		0			0
$73$		−	23.7538i		−	0.325394i	−0.986676	−	0.162697i	$-0.947981\pi$
$73$		−	23.7538i		−	0.325394i	0.986676	−	0.162697i	$-0.0520193\pi$
$74$	4.67578	+	8.09868i	0.0631862	+	0.109442i
$75$		0			0
$76$	−18.0128	+	31.1990i	−0.237010	+	0.410514i
$77$	33.3858	+	19.2753i	0.433582	+	0.250329i
$78$		0			0
$79$	6.49716	−	3.75114i	0.0822426	−	0.0474828i	−0.458315	−	0.888790i	$-0.651547\pi$
$79$	6.49716	−	3.75114i	0.0822426	−	0.0474828i	0.540557	+	0.841307i	$0.318213\pi$
$80$	−43.4526			−0.543157
$81$		0			0
$82$			9.37714i			0.114355i
$83$	12.4098	−	7.16481i	0.149516	−	0.0863230i	−0.423376	−	0.905954i	$-0.639155\pi$
$83$	12.4098	−	7.16481i	0.149516	−	0.0863230i	0.572892	+	0.819631i	$0.305822\pi$
$84$		0			0
$85$	−45.5805	−	11.2893i	−0.536241	−	0.132815i
$86$	−3.65266	−	2.10887i	−0.0424728	−	0.0245217i
$87$		0			0
$88$	−12.6281	+	7.29084i	−0.143501	+	0.0828504i
$89$		−	115.581i		−	1.29867i	−0.760504	−	0.649333i	$-0.775048\pi$
$89$		−	115.581i		−	1.29867i	0.760504	−	0.649333i	$-0.224952\pi$
$90$		0			0
$91$			53.4484i			0.587346i
$92$	−40.6091	−	70.3370i	−0.441403	−	0.764533i
$93$		0			0
$94$	−3.26063	+	5.64758i	−0.0346876	+	0.0600807i
$95$	12.5090	−	21.6663i	0.131674	−	0.228066i
$96$		0			0
$97$	9.98636	−	5.76563i	0.102952	−	0.0594395i	−0.447640	−	0.894214i	$-0.647735\pi$
$97$	9.98636	−	5.76563i	0.102952	−	0.0594395i	0.550592	+	0.834774i	$0.314402\pi$
$98$			5.84583i			0.0596513i
$99$		0			0
$100$	−69.0906			−0.690906
$101$	64.3415	−	37.1476i	0.637045	−	0.367798i	−0.146431	−	0.989221i	$-0.546778\pi$
$101$	64.3415	−	37.1476i	0.637045	−	0.367798i	0.783475	+	0.621423i	$0.213445\pi$
$102$		0			0
$103$	4.63237	−	8.02349i	0.0449744	−	0.0778980i	−0.842662	−	0.538443i	$-0.819013\pi$
$103$	4.63237	−	8.02349i	0.0449744	−	0.0778980i	0.887636	+	0.460545i	$0.152346\pi$
$104$	−17.5082	−	10.1084i	−0.168348	−	0.0971959i
$105$		0			0
$106$	5.00753	+	8.67329i	0.0472408	+	0.0818235i
$107$	45.5617			0.425811			0.212905	−	0.977073i	$-0.431707\pi$
$107$	45.5617			0.425811			0.212905	+	0.977073i	$0.431707\pi$
$108$		0			0
$109$		−	158.516i		−	1.45428i	−0.686490	−	0.727140i	$-0.740849\pi$
$109$		−	158.516i		−	1.45428i	0.686490	−	0.727140i	$-0.259151\pi$
$110$	4.37247	−	2.52445i	0.0397497	−	0.0229495i
$111$		0			0
$112$	−43.0557	−	24.8582i	−0.384426	−	0.221949i
$113$	27.6157	−	47.8318i	0.244387	−	0.423291i	−0.717572	−	0.696484i	$-0.754747\pi$
$113$	27.6157	−	47.8318i	0.244387	−	0.423291i	0.961959	+	0.273194i	$0.0880800\pi$
$114$		0			0
$115$	28.2011	+	48.8458i	0.245227	+	0.424746i
$116$	8.62835			0.0743824
$117$		0			0
$118$	−11.8553			−0.100468
$119$	−38.7058	−	37.2617i	−0.325259	−	0.313123i
$120$		0			0
$121$	−13.8956	+	24.0679i	−0.114840	+	0.198909i
$122$	5.67112	−	9.82267i	0.0464846	−	0.0805137i
$123$		0			0
$124$	−151.823	+	87.6550i	−1.22438	+	0.706895i
$125$	117.036			0.936285
$126$		0			0
$127$	164.891			1.29835			0.649176	−	0.760638i	$-0.275114\pi$
$127$	164.891			1.29835			0.649176	+	0.760638i	$0.275114\pi$
$128$	32.7569	−	18.9122i	0.255913	−	0.147752i
$129$		0			0
$130$	6.06221	+	3.50002i	0.0466324	+	0.0269232i
$131$	0.0321956	−	0.0557644i	0.000245768	−	0.000425682i	−0.865902	−	0.500213i	$-0.833255\pi$
$131$	0.0321956	−	0.0557644i	0.000245768	−	0.000425682i	0.866148	+	0.499787i	$0.166588\pi$
$132$		0			0
$133$	24.7896	−	14.3123i	0.186388	−	0.107611i
$134$			3.20066i			0.0238856i
$135$		0			0
$136$	19.5261	−	5.63188i	0.143574	−	0.0414109i
$137$	−62.9889	+	36.3666i	−0.459773	+	0.265450i	−0.711949	−	0.702231i	$-0.752187\pi$
$137$	−62.9889	+	36.3666i	−0.459773	+	0.265450i	0.252176	+	0.967681i	$0.418854\pi$
$138$		0			0
$139$	−21.6096	−	12.4763i	−0.155465	−	0.0897578i	0.420249	−	0.907409i	$-0.361943\pi$
$139$	−21.6096	−	12.4763i	−0.155465	−	0.0897578i	−0.575714	+	0.817651i	$0.695276\pi$
$140$	30.0709	+	17.3614i	0.214792	+	0.124010i
$141$		0			0
$142$	10.4191	−	6.01547i	0.0733740	−	0.0423625i
$143$	−206.291			−1.44260
$144$		0			0
$145$	−5.99198			−0.0413240
$146$	−1.77972	−	3.08257i	−0.0121899	−	0.0211135i
$147$		0			0
$148$	−214.971	−	124.114i	−1.45251	−	0.838606i
$149$	−18.2046	−	10.5104i	−0.122179	−	0.0705398i	0.437665	−	0.899138i	$-0.355806\pi$
$149$	−18.2046	−	10.5104i	−0.122179	−	0.0705398i	−0.559844	+	0.828598i	$0.689139\pi$
$150$		0			0
$151$	−121.688	−	210.770i	−0.805882	−	1.39583i	−0.915694	−	0.401877i	$-0.868358\pi$
$151$	−121.688	−	210.770i	−0.805882	−	1.39583i	0.109811	−	0.993952i	$-0.464975\pi$
$152$			10.8272i			0.0712313i
$153$		0			0
$154$	5.77671			0.0375111
$155$	105.434	−	60.8722i	0.680218	−	0.392724i
$156$		0			0
$157$	−22.7702	+	39.4391i	−0.145033	+	0.251205i	−0.929385	−	0.369111i	$-0.879662\pi$
$157$	−22.7702	+	39.4391i	−0.145033	+	0.251205i	0.784352	+	0.620316i	$0.212996\pi$
$158$	0.562099	−	0.973584i	0.00355759	−	0.00616192i
$159$		0			0
$160$	−17.0774	+	9.85963i	−0.106734	+	0.0616227i
$161$			64.5328i			0.400825i
$162$		0			0
$163$			157.251i			0.964732i	0.875970	+	0.482366i	$0.160222\pi$
$163$			157.251i			0.964732i	−0.875970	+	0.482366i	$0.839778\pi$
$164$	−124.453	−	215.559i	−0.758861	−	1.31439i
$165$		0			0
$166$	1.07363	−	1.85958i	0.00646764	−	0.0112023i
$167$	46.0342	−	79.7336i	0.275654	−	0.477447i	−0.694646	−	0.719352i	$-0.744439\pi$
$167$	46.0342	−	79.7336i	0.275654	−	0.477447i	0.970300	+	0.241905i	$0.0777722\pi$
$168$		0			0
$169$	−58.5063	−	101.336i	−0.346191	−	0.599621i
$170$	−6.76089	+	1.95003i	−0.0397699	+	0.0114708i
$171$		0			0
$172$	111.955			0.650903
$173$	22.7265	+	39.3635i	0.131367	+	0.227535i	0.924204	−	0.381900i	$-0.124730\pi$
$173$	22.7265	+	39.3635i	0.131367	+	0.227535i	−0.792837	+	0.609434i	$0.791397\pi$
$174$		0			0
$175$	47.5419	+	27.4483i	0.271668	+	0.156848i
$176$	95.9437	−	166.179i	0.545135	−	0.944201i
$177$		0			0
$178$	−8.65978	−	14.9992i	−0.0486505	−	0.0842651i
$179$			294.556i			1.64556i	0.568357	+	0.822782i	$0.307579\pi$
$179$			294.556i			1.64556i	−0.568357	+	0.822782i	$0.692421\pi$
$180$		0			0
$181$		−	279.929i		−	1.54657i	−0.634058	−	0.773285i	$-0.718612\pi$
$181$		−	279.929i		−	1.54657i	0.634058	−	0.773285i	$-0.281388\pi$
$182$	4.00456	+	6.93610i	0.0220031	+	0.0381104i
$183$		0			0
$184$	−21.1392	−	12.2047i	−0.114887	−	0.0663299i
$185$	149.287	+	86.1911i	0.806958	+	0.465898i
$186$		0			0
$187$	143.817	−	149.390i	0.769072	−	0.798879i
$188$		−	173.100i		−	0.920746i
$189$		0			0
$190$		−	3.74889i		−	0.0197310i
$191$	−247.642	+	142.976i	−1.29656	+	0.748567i	−0.979808	−	0.199942i	$-0.935925\pi$
$191$	−247.642	+	142.976i	−1.29656	+	0.748567i	−0.316749	+	0.948510i	$0.602591\pi$
$192$		0			0
$193$	121.814	+	70.3291i	0.631159	+	0.364400i	0.781201	−	0.624280i	$-0.214608\pi$
$193$	121.814	+	70.3291i	0.631159	+	0.364400i	−0.150042	+	0.988680i	$0.547941\pi$
$194$	0.863965	−	1.49643i	0.00445343	−	0.00771356i
$195$		0			0
$196$	−77.5857	−	134.382i	−0.395845	−	0.685624i
$197$	347.281			1.76285			0.881423	−	0.472327i	$-0.156586\pi$
$197$	347.281			1.76285			0.881423	+	0.472327i	$0.156586\pi$
$198$		0			0
$199$		−	55.1047i		−	0.276908i	−0.990369	−	0.138454i	$-0.955787\pi$
$199$		−	55.1047i		−	0.276908i	0.990369	−	0.138454i	$-0.0442133\pi$
$200$	−17.9826	+	10.3823i	−0.0899131	+	0.0519114i
$201$		0			0
$202$	5.56647	−	9.64141i	0.0275568	−	0.0477298i
$203$	−5.93726	−	3.42788i	−0.0292476	−	0.0168861i
$204$		0			0
$205$	86.4269	+	149.696i	0.421595	+	0.730223i
$206$		−	1.38830i		−	0.00673931i
$207$		0			0
$208$	266.042			1.27905
$209$	55.2401	+	95.6786i	0.264307	+	0.457792i
$210$		0			0
$211$	−285.929	−	165.081i	−1.35511	−	0.782374i	−0.366152	−	0.930555i	$-0.619325\pi$
$211$	−285.929	−	165.081i	−1.35511	−	0.782374i	−0.988960	+	0.148181i	$0.952658\pi$
$212$	−230.223	−	132.920i	−1.08596	−	0.626979i
$213$		0			0
$214$	5.91263	−	3.41366i	0.0276291	−	0.0159517i
$215$	−77.7477			−0.361617
$216$		0			0
$217$	139.294			0.641910
$218$	−11.8766	−	20.5710i	−0.0544800	−	0.0943622i
$219$		0			0
$220$	−67.0088	+	116.063i	−0.304585	+	0.527558i
$221$	279.070	+	69.1194i	1.26276	+	0.312757i
$222$		0			0
$223$	−1.03255	−	1.78843i	−0.00463026	−	0.00801984i	0.863701	−	0.504005i	$-0.168141\pi$
$223$	−1.03255	−	1.78843i	−0.00463026	−	0.00801984i	−0.868331	+	0.495985i	$0.834807\pi$
$224$	−22.5619			−0.100723
$225$		0			0
$226$		−	8.27629i		−	0.0366208i
$227$	99.7577	+	172.785i	0.439461	+	0.761169i	0.997648	−	0.0685463i	$-0.0218361\pi$
$227$	99.7577	+	172.785i	0.439461	+	0.761169i	−0.558187	+	0.829715i	$0.688503\pi$
$228$		0			0
$229$	69.4180	−	120.235i	0.303135	−	0.525046i	−0.673709	−	0.738997i	$-0.735300\pi$
$229$	69.4180	−	120.235i	0.303135	−	0.525046i	0.976844	+	0.213951i	$0.0686332\pi$
$230$	7.31941	+	4.22587i	0.0318235	+	0.0183733i
$231$		0			0
$232$	2.24575	−	1.29659i	0.00967997	−	0.00558873i
$233$	−325.344			−1.39633			−0.698164	−	0.715938i	$-0.745999\pi$
$233$	−325.344			−1.39633			−0.698164	+	0.715938i	$0.745999\pi$
$234$		0			0
$235$			120.210i			0.511532i
$236$	272.526	−	157.343i	1.15477	−	0.666708i
$237$		0			0
$238$	−7.81471	−	1.93553i	−0.0328349	−	0.00813247i
$239$	−147.606	−	85.2204i	−0.617598	−	0.356571i	0.158335	−	0.987385i	$-0.449387\pi$
$239$	−147.606	−	85.2204i	−0.617598	−	0.356571i	−0.775933	+	0.630815i	$0.782721\pi$
$240$		0			0
$241$	20.3122	−	11.7272i	0.0842829	−	0.0486607i	−0.457266	−	0.889330i	$-0.651171\pi$
$241$	20.3122	−	11.7272i	0.0842829	−	0.0486607i	0.541549	+	0.840669i	$0.317838\pi$
$242$			4.16445i			0.0172085i
$243$		0			0
$244$			301.068i			1.23389i
$245$	53.8796	+	93.3222i	0.219917	+	0.380907i
$246$		0			0
$247$	−76.5875	+	132.654i	−0.310071	+	0.537059i
$248$	−26.3439	+	45.6290i	−0.106225	+	0.183988i
$249$		0			0
$250$	15.1879	−	8.76875i	0.0607517	−	0.0350750i
$251$		−	335.935i		−	1.33839i	−0.743088	−	0.669194i	$-0.766640\pi$
$251$		−	335.935i		−	1.33839i	0.743088	−	0.669194i	$-0.233360\pi$
$252$		0			0
$253$	−249.073			−0.984479
$254$	21.3982	−	12.3542i	0.0842447	−	0.0486387i
$255$		0			0
$256$	−120.875	+	209.362i	−0.472168	+	0.817819i
$257$	46.1536	+	26.6468i	0.179586	+	0.103684i	0.587098	−	0.809516i	$-0.300270\pi$
$257$	46.1536	+	26.6468i	0.179586	+	0.103684i	−0.407512	+	0.913200i	$0.633604\pi$
$258$		0			0
$259$	98.6159	+	170.808i	0.380756	+	0.659489i
$260$	−185.809			−0.714648
$261$		0			0
$262$		−	0.00964885i		−	3.68277e-5i
$263$	−43.3604	+	25.0342i	−0.164869	+	0.0951869i	−0.580164	−	0.814500i	$-0.697012\pi$
$263$	−43.3604	+	25.0342i	−0.164869	+	0.0951869i	0.415295	+	0.909687i	$0.363678\pi$
$264$		0			0
$265$	159.879	+	92.3064i	0.603318	+	0.348326i
$266$	2.14466	−	3.71465i	0.00806261	−	0.0139649i
$267$		0			0
$268$	−42.4792	−	73.5761i	−0.158504	−	0.274538i
$269$	299.181			1.11220			0.556098	−	0.831117i	$-0.312298\pi$
$269$	299.181			1.11220			0.556098	+	0.831117i	$0.312298\pi$
$270$		0			0
$271$	−159.041			−0.586868			−0.293434	−	0.955979i	$-0.594798\pi$
$271$	−159.041			−0.586868			−0.293434	+	0.955979i	$0.594798\pi$
$272$	−185.472	+	192.660i	−0.681881	+	0.708309i
$273$		0			0
$274$	−5.44945	+	9.43873i	−0.0198885	+	0.0344479i
$275$	−105.941	+	183.494i	−0.385238	+	0.667253i
$276$		0			0
$277$	175.498	−	101.324i	0.633567	−	0.365790i	−0.148565	−	0.988903i	$-0.547465\pi$
$277$	175.498	−	101.324i	0.633567	−	0.365790i	0.782132	+	0.623112i	$0.214132\pi$
$278$	−3.73909			−0.0134500
$279$		0			0
$280$	10.4356			0.0372702
$281$	368.933	−	213.003i	1.31293	−	0.758019i	0.330348	−	0.943859i	$-0.392834\pi$
$281$	368.933	−	213.003i	1.31293	−	0.758019i	0.982580	+	0.185840i	$0.0595007\pi$
$282$		0			0
$283$	402.896	+	232.612i	1.42366	+	0.821950i	0.996609	−	0.0822775i	$-0.0262194\pi$
$283$	402.896	+	232.612i	1.42366	+	0.821950i	0.427050	+	0.904228i	$0.359553\pi$
$284$	−159.674	+	276.564i	−0.562234	+	0.973818i
$285$		0			0
$286$	−26.7708	+	15.4561i	−0.0936042	+	0.0540424i
$287$			197.771i			0.689099i
$288$		0			0
$289$	−244.609	+	153.908i	−0.846396	+	0.532553i
$290$	−0.777590	+	0.448942i	−0.00268135	+	0.00154808i
$291$		0			0
$292$	81.8236	+	47.2409i	0.280218	+	0.161784i
$293$	−302.277	−	174.519i	−1.03166	−	0.595630i	−0.114201	−	0.993458i	$-0.536431\pi$
$293$	−302.277	−	174.519i	−1.03166	−	0.595630i	−0.917460	+	0.397828i	$0.869764\pi$
$294$		0			0
$295$	−189.257	+	109.267i	−0.641548	+	0.370398i
$296$	−74.6024			−0.252035
$297$		0			0
$298$	−3.14992			−0.0105702
$299$	−172.664	−	299.062i	−0.577470	−	1.00021i
$300$		0			0
$301$	−77.0376	−	44.4777i	−0.255939	−	0.147766i
$302$	−31.5834	−	18.2347i	−0.104581	−	0.0603797i
$303$		0			0
$304$	−71.2399	−	123.391i	−0.234342	−	0.405892i
$305$		−	209.078i		−	0.685500i
$306$		0			0
$307$	171.450			0.558468			0.279234	−	0.960223i	$-0.409920\pi$
$307$	171.450			0.558468			0.279234	+	0.960223i	$0.409920\pi$
$308$	−132.794	+	76.6684i	−0.431148	+	0.248923i
$309$		0			0
$310$	9.12155	−	15.7990i	0.0294244	−	0.0509645i
$311$	−213.902	+	370.488i	−0.687786	+	1.19128i	0.284766	+	0.958597i	$0.408084\pi$
$311$	−213.902	+	370.488i	−0.687786	+	1.19128i	−0.972552	+	0.232684i	$0.925249\pi$
$312$		0			0
$313$	−303.815	+	175.407i	−0.970654	+	0.560407i	−0.899436	−	0.437053i	$-0.856022\pi$
$313$	−303.815	+	175.407i	−0.970654	+	0.560407i	−0.0712184	+	0.997461i	$0.522689\pi$
$314$			6.82412i			0.0217329i
$315$		0			0
$316$			29.8407i			0.0944324i
$317$	85.4313	+	147.971i	0.269499	+	0.466787i	0.968733	−	0.248107i	$-0.0798084\pi$
$317$	85.4313	+	147.971i	0.269499	+	0.466787i	−0.699233	+	0.714894i	$0.746475\pi$
$318$		0			0
$319$	13.2304	−	22.9156i	0.0414745	−	0.0718359i
$320$	85.4278	−	147.965i	0.266962	−	0.462391i
$321$		0			0
$322$	4.83504	+	8.37454i	0.0150157	+	0.0260079i
$323$	−42.6707	−	147.942i	−0.132108	−	0.458025i
$324$		0			0
$325$	−293.762			−0.903884
$326$	11.7819	+	20.4068i	0.0361407	+	0.0625975i
$327$		0			0
$328$	−64.7844	−	37.4033i	−0.197513	−	0.114034i
$329$	−68.7694	+	119.112i	−0.209025	+	0.362043i
$330$		0			0
$331$	277.160	+	480.056i	0.837343	+	1.45032i	0.892109	+	0.451821i	$0.149225\pi$
$331$	277.160	+	480.056i	0.837343	+	1.45032i	−0.0547661	+	0.998499i	$0.517441\pi$
$332$			56.9967i			0.171677i
$333$		0			0
$334$		−	13.7962i		−	0.0413061i
$335$	29.4998	+	51.0951i	0.0880590	+	0.152523i
$336$		0			0
$337$	475.857	+	274.736i	1.41204	+	0.815242i	0.995580	−	0.0939126i	$-0.0299374\pi$
$337$	475.857	+	274.736i	1.41204	+	0.815242i	0.416460	+	0.909154i	$0.363271\pi$
$338$	−15.1849	−	8.76702i	−0.0449258	−	0.0259379i
$339$		0			0
$340$	129.537	−	134.557i	0.380991	−	0.395757i
$341$			537.626i			1.57661i
$342$		0			0
$343$			278.153i			0.810942i
$344$	29.1393	−	16.8236i	0.0847072	−	0.0489057i
$345$		0			0
$346$	5.89852	+	3.40551i	0.0170477	+	0.00984252i
$347$	−255.193	+	442.007i	−0.735426	+	1.27380i	0.219110	+	0.975700i	$0.429685\pi$
$347$	−255.193	+	442.007i	−0.735426	+	1.27380i	−0.954536	+	0.298095i	$0.903649\pi$
$348$		0			0
$349$	69.4543	+	120.298i	0.199010	+	0.344695i	0.948208	−	0.317651i	$-0.102894\pi$
$349$	69.4543	+	120.298i	0.199010	+	0.344695i	−0.749198	+	0.662346i	$0.769561\pi$
$350$	8.22613			0.0235032
$351$		0			0
$352$		−	87.0806i		−	0.247388i
$353$	−257.287	+	148.545i	−0.728859	+	0.420807i	−0.818005	−	0.575212i	$-0.804920\pi$
$353$	−257.287	+	148.545i	−0.728859	+	0.420807i	0.0891457	+	0.996019i	$0.471586\pi$
$354$		0			0
$355$	110.886	−	192.061i	0.312356	−	0.541016i
$356$	398.138	+	229.865i	1.11836	+	0.645688i
$357$		0			0
$358$	22.0692	+	38.2250i	0.0616459	+	0.106774i
$359$		−	251.878i		−	0.701611i	−0.936448	−	0.350805i	$-0.885908\pi$
$359$		−	251.878i		−	0.701611i	0.936448	−	0.350805i	$-0.114092\pi$
$360$		0			0
$361$	−278.967			−0.772760
$362$	−20.9733	−	36.3269i	−0.0579374	−	0.100351i
$363$		0			0
$364$	−184.111	−	106.297i	−0.505801	−	0.292024i
$365$	−56.8226	−	32.8065i	−0.155678	−	0.0898810i
$366$		0			0
$367$	409.800	−	236.598i	1.11662	−	0.644681i	0.176084	−	0.984375i	$-0.443657\pi$
$367$	409.800	−	236.598i	1.11662	−	0.644681i	0.940536	+	0.339694i	$0.110324\pi$
$368$	321.215			0.872867
$369$		0			0
$370$	25.8310			0.0698136
$371$	105.613	+	182.927i	0.284670	+	0.493064i
$372$		0			0
$373$	171.228	−	296.575i	0.459055	−	0.795107i	−0.539856	−	0.841757i	$-0.681521\pi$
$373$	171.228	−	296.575i	0.459055	−	0.795107i	0.998911	+	0.0466504i	$0.0148547\pi$
$374$	7.47043	−	30.1619i	0.0199744	−	0.0806468i
$375$		0			0
$376$	−26.0119	−	45.0538i	−0.0691805	−	0.119824i
$377$	36.6864			0.0973115
$378$		0			0
$379$		−	144.860i		−	0.382216i	−0.981569	−	0.191108i	$-0.938792\pi$
$379$		−	144.860i		−	0.382216i	0.981569	−	0.191108i	$-0.0612081\pi$
$380$	49.7552	+	86.1786i	0.130935	+	0.226786i
$381$		0			0
$382$	−21.4246	+	37.1086i	−0.0560855	+	0.0971429i
$383$	−188.695	−	108.943i	−0.492677	−	0.284447i	0.233007	−	0.972475i	$-0.425143\pi$
$383$	−188.695	−	108.943i	−0.492677	−	0.284447i	−0.725684	+	0.688028i	$0.758477\pi$
$384$		0			0
$385$	92.2189	−	53.2426i	0.239530	−	0.138292i
$386$	21.0773			0.0546044
$387$		0			0
$388$			45.8661i			0.118212i
$389$	−65.1167	+	37.5951i	−0.167395	+	0.0966456i	−0.581357	−	0.813649i	$-0.697478\pi$
$389$	−65.1167	+	37.5951i	−0.167395	+	0.0966456i	0.413962	+	0.910294i	$0.364145\pi$
$390$		0			0
$391$	336.945	+	83.4537i	0.861752	+	0.213437i
$392$	−40.3874	−	23.3177i	−0.103029	−	0.0594839i
$393$		0			0
$394$	45.0672	−	26.0196i	0.114384	−	0.0660395i
$395$		−	20.7229i		−	0.0524631i
$396$		0			0
$397$		−	547.908i		−	1.38012i	−0.723752	−	0.690060i	$-0.757584\pi$
$397$		−	547.908i		−	1.38012i	0.723752	−	0.690060i	$-0.242416\pi$
$398$	−4.12865	−	7.15104i	−0.0103735	−	0.0179674i
$399$		0			0
$400$	136.625	−	236.642i	0.341563	−	0.591605i
$401$	352.711	−	610.913i	0.879577	−	1.52347i	0.0277720	−	0.999614i	$-0.491159\pi$
$401$	352.711	−	610.913i	0.879577	−	1.52347i	0.851805	−	0.523858i	$-0.175508\pi$
$402$		0			0
$403$	−645.527	+	372.695i	−1.60180	+	0.924802i
$404$			295.512i			0.731467i
$405$		0			0
$406$	−1.02732			−0.00253034
$407$	−659.255	+	380.621i	−1.61979	+	0.935187i
$408$		0			0
$409$	281.335	−	487.286i	0.687860	−	1.19141i	−0.284668	−	0.958626i	$-0.591883\pi$
$409$	281.335	−	487.286i	0.687860	−	1.19141i	0.972529	−	0.232783i	$-0.0747832\pi$
$410$	22.4315	+	12.9509i	0.0547111	+	0.0315875i
$411$		0			0
$412$	18.4255	+	31.9138i	0.0447220	+	0.0774607i
$413$	−250.037			−0.605417
$414$		0			0
$415$		−	39.5815i		−	0.0953772i
$416$	104.558	−	60.3664i	0.251340	−	0.145111i
$417$		0			0
$418$	14.3372	+	8.27759i	0.0342995	+	0.0198028i
$419$	300.580	−	520.620i	0.717375	−	1.24253i	−0.244662	−	0.969608i	$-0.578677\pi$
$419$	300.580	−	520.620i	0.717375	−	1.24253i	0.962036	−	0.272921i	$-0.0879897\pi$
$420$		0			0
$421$	167.946	+	290.891i	0.398921	+	0.690952i	0.993593	−	0.113017i	$-0.0360513\pi$
$421$	167.946	+	290.891i	0.398921	+	0.690952i	−0.594672	+	0.803969i	$0.702718\pi$
$422$	−49.4739			−0.117237
$423$		0			0
$424$	−79.8955			−0.188433
$425$	204.797	−	212.734i	0.481875	−	0.500551i
$426$		0			0
$427$	119.608	−	207.168i	0.280113	−	0.485171i
$428$	−90.6120	+	156.945i	−0.211710	+	0.366693i
$429$		0			0
$430$	−10.0895	+	5.82515i	−0.0234638	+	0.0135469i
$431$	−260.303			−0.603952			−0.301976	−	0.953316i	$-0.597646\pi$
$431$	−260.303			−0.603952			−0.301976	+	0.953316i	$0.597646\pi$
$432$		0			0
$433$	−11.2018			−0.0258703			−0.0129351	−	0.999916i	$-0.504118\pi$
$433$	−11.2018			−0.0258703			−0.0129351	+	0.999916i	$0.504118\pi$
$434$	18.0765	−	10.4365i	0.0416509	−	0.0240471i
$435$		0			0
$436$	546.035	+	315.253i	1.25237	+	0.723058i
$437$	−92.4706	+	160.164i	−0.211603	+	0.366508i
$438$		0			0
$439$	−214.805	+	124.018i	−0.489305	+	0.282500i	−0.724286	−	0.689500i	$-0.757830\pi$
$439$	−214.805	+	124.018i	−0.489305	+	0.282500i	0.234981	+	0.972000i	$0.424497\pi$
$440$			40.2778i			0.0915404i
$441$		0			0
$442$	41.3941	−	11.9392i	0.0936518	−	0.0270118i
$443$	713.529	−	411.956i	1.61067	−	0.929923i	0.621461	−	0.783445i	$-0.286540\pi$
$443$	713.529	−	411.956i	1.61067	−	0.929923i	0.989214	−	0.146478i	$-0.0467937\pi$
$444$		0			0
$445$	−276.488	−	159.630i	−0.621321	−	0.358720i
$446$	−0.267991	−	0.154725i	−0.000600877	−	0.000346916i
$447$		0			0
$448$	169.295	−	97.7425i	0.377891	−	0.218175i
$449$	−124.936			−0.278253			−0.139126	−	0.990275i	$-0.544429\pi$
$449$	−124.936			−0.278253			−0.139126	+	0.990275i	$0.544429\pi$
$450$		0			0
$451$	−763.325			−1.69252
$452$	109.843	+	190.253i	0.243015	+	0.420914i
$453$		0			0
$454$	25.8915	+	14.9484i	0.0570296	+	0.0329261i
$455$	127.857	+	73.8181i	0.281004	+	0.162238i
$456$		0			0
$457$	433.428	+	750.719i	0.948419	+	1.64271i	0.748756	+	0.662846i	$0.230651\pi$
$457$	433.428	+	750.719i	0.948419	+	1.64271i	0.199663	+	0.979865i	$0.436015\pi$
$458$		−	20.8042i		−	0.0454241i
$459$		0			0
$460$	−224.342			−0.487701
$461$	−251.349	+	145.116i	−0.545225	+	0.314786i	−0.747194	−	0.664606i	$-0.768599\pi$
$461$	−251.349	+	145.116i	−0.545225	+	0.314786i	0.201969	+	0.979392i	$0.435266\pi$
$462$		0			0
$463$	175.796	−	304.487i	0.379689	−	0.657640i	−0.611328	−	0.791377i	$-0.709364\pi$
$463$	175.796	−	304.487i	0.379689	−	0.657640i	0.991017	+	0.133737i	$0.0426978\pi$
$464$	−17.0624	+	29.5530i	−0.0367724	+	0.0636917i
$465$		0			0
$466$	−42.2205	+	24.3760i	−0.0906019	+	0.0523090i
$467$		−	394.357i		−	0.844447i	−0.906492	−	0.422224i	$-0.861250\pi$
$467$		−	394.357i		−	0.844447i	0.906492	−	0.422224i	$-0.138750\pi$
$468$		0			0
$469$			67.5046i			0.143933i
$470$	9.00658	+	15.5999i	0.0191629	+	0.0331912i
$471$		0			0
$472$	47.2880	−	81.9052i	0.100186	−	0.173528i
$473$	171.668	−	297.337i	0.362933	−	0.628619i
$474$		0			0
$475$	78.6628	+	136.248i	0.165606	+	0.286838i
$476$	205.331	−	59.2232i	0.431367	−	0.124419i
$477$		0			0
$478$	−25.5401			−0.0534312
$479$	−172.631	−	299.005i	−0.360398	−	0.624227i	0.627628	−	0.778513i	$-0.284026\pi$
$479$	−172.631	−	299.005i	−0.360398	−	0.624227i	−0.988026	+	0.154286i	$0.950692\pi$
$480$		0			0
$481$	−914.024	−	527.712i	−1.90026	−	1.09711i
$482$	1.75730	−	3.04373i	0.00364584	−	0.00631479i
$483$		0			0
$484$	−55.2705	−	95.7313i	−0.114195	−	0.197792i
$485$		−	31.8519i		−	0.0656739i
$486$		0			0
$487$			592.593i			1.21682i	0.793622	+	0.608412i	$0.208193\pi$
$487$			592.593i			1.21682i	−0.793622	+	0.608412i	$0.791807\pi$
$488$	45.2416	+	78.3608i	0.0927082	+	0.160575i
$489$		0			0
$490$	13.9841	+	8.07373i	0.0285390	+	0.0164770i
$491$	−107.710	−	62.1865i	−0.219369	−	0.126653i	0.386289	−	0.922378i	$-0.373757\pi$
$491$	−107.710	−	62.1865i	−0.219369	−	0.126653i	−0.605658	+	0.795725i	$0.707090\pi$
$492$		0			0
$493$	−25.5760	+	26.5673i	−0.0518783	+	0.0538890i
$494$			22.9529i			0.0464634i
$495$		0			0
$496$		−	693.344i		−	1.39787i
$497$	219.747	−	126.871i	0.442147	−	0.255274i
$498$		0			0
$499$	−272.670	−	157.426i	−0.546434	−	0.315484i	0.201249	−	0.979540i	$-0.435500\pi$
$499$	−272.670	−	157.426i	−0.546434	−	0.315484i	−0.747682	+	0.664056i	$0.768833\pi$
$500$	−232.757	+	403.147i	−0.465514	+	0.806295i
$501$		0			0
$502$	−25.1695	−	43.5949i	−0.0501385	−	0.0868425i
$503$	−158.607			−0.315323			−0.157661	−	0.987493i	$-0.550395\pi$
$503$	−158.607			−0.315323			−0.157661	+	0.987493i	$0.550395\pi$
$504$		0			0
$505$		−	205.220i		−	0.406375i
$506$	−32.3227	+	18.6615i	−0.0638788	+	0.0368804i
$507$		0			0
$508$	−327.930	+	567.992i	−0.645532	+	1.11809i
$509$	575.309	+	332.155i	1.13027	+	0.652563i	0.944003	−	0.329936i	$-0.107027\pi$
$509$	575.309	+	332.155i	1.13027	+	0.652563i	0.186269	+	0.982499i	$0.440360\pi$
$510$		0			0
$511$	−37.5357	−	65.0138i	−0.0734555	−	0.127229i
$512$			187.523i			0.366256i
$513$		0			0
$514$	7.98591			0.0155368
$515$	−12.7956	−	22.1626i	−0.0248458	−	0.0430343i
$516$		0			0
$517$	−459.729	−	265.425i	−0.889224	−	0.513394i
$518$	25.5951	+	14.7773i	0.0494114	+	0.0285277i
$519$		0			0
$520$	−48.3615	+	27.9215i	−0.0930029	+	0.0536953i
$521$	924.333			1.77415			0.887076	−	0.461624i	$-0.152733\pi$
$521$	924.333			1.77415			0.887076	+	0.461624i	$0.152733\pi$
$522$		0			0
$523$	−619.916			−1.18531			−0.592654	−	0.805457i	$-0.701920\pi$
$523$	−619.916			−1.18531			−0.592654	+	0.805457i	$0.701920\pi$
$524$	0.128059	+	0.221805i	0.000244388	+	0.000423293i
$525$		0			0
$526$	−3.75131	+	6.49745i	−0.00713176	+	0.0123526i
$527$	180.135	−	727.297i	0.341813	−	1.38007i
$528$		0			0
$529$	56.0286	+	97.0444i	0.105914	+	0.183449i
$530$	27.6638			0.0521958
$531$		0			0
$532$			113.855i			0.214014i
$533$	−529.156	−	916.525i	−0.992788	−	1.71956i
$534$		0			0
$535$	62.9257	−	108.991i	0.117618	−	0.203721i
$536$	−22.1126	−	12.7667i	−0.0412549	−	0.0238185i
$537$		0			0
$538$	38.8252	−	22.4157i	0.0721658	−	0.0416649i
$539$	−475.867			−0.882869
$540$		0			0
$541$		−	757.243i		−	1.39971i	−0.714285	−	0.699855i	$-0.753248\pi$
$541$		−	757.243i		−	1.39971i	0.714285	−	0.699855i	$-0.246752\pi$
$542$	−20.6390	+	11.9160i	−0.0380794	+	0.0219852i
$543$		0			0
$544$	−29.1769	+	117.802i	−0.0536341	+	0.216548i
$545$	−379.195	−	218.928i	−0.695771	−	0.401704i
$546$		0			0
$547$	−670.522	+	387.126i	−1.22582	+	0.707726i	−0.966152	−	0.257972i	$-0.916946\pi$
$547$	−670.522	+	387.126i	−1.22582	+	0.707726i	−0.259666	+	0.965699i	$0.583612\pi$
$548$		−	289.300i		−	0.527920i
$549$		0			0
$550$			31.7499i			0.0577270i
$551$	−9.82377	−	17.0153i	−0.0178290	−	0.0308807i
$552$		0			0
$553$	11.8551	−	20.5337i	0.0214378	−	0.0371314i
$554$	15.1831	−	26.2979i	0.0274064	−	0.0474692i
$555$		0			0
$556$	85.9533	−	49.6252i	0.154592	−	0.0892539i
$557$		−	375.595i		−	0.674318i	−0.941448	−	0.337159i	$-0.890534\pi$
$557$		−	375.595i		−	0.674318i	0.941448	−	0.337159i	$-0.109466\pi$
$558$		0			0
$559$	476.017			0.851550
$560$	−118.929	+	68.6639i	−0.212374	+	0.122614i
$561$		0			0
$562$	31.9180	−	55.2836i	0.0567936	−	0.0983695i
$563$	267.021	+	154.165i	0.474283	+	0.273827i	0.718031	−	0.696011i	$-0.245044\pi$
$563$	267.021	+	154.165i	0.474283	+	0.273827i	−0.243748	+	0.969839i	$0.578377\pi$
$564$		0			0
$565$	−76.2807	−	132.122i	−0.135010	−	0.233844i
$566$	69.7126			0.123167
$567$		0			0
$568$			95.9774i			0.168974i
$569$	−127.010	+	73.3291i	−0.223216	+	0.128874i	−0.607438	−	0.794367i	$-0.707803\pi$
$569$	−127.010	+	73.3291i	−0.223216	+	0.128874i	0.384223	+	0.923240i	$0.374469\pi$
$570$		0			0
$571$	431.255	+	248.985i	0.755262	+	0.436051i	0.827592	−	0.561330i	$-0.189710\pi$
$571$	431.255	+	248.985i	0.755262	+	0.436051i	−0.0723301	+	0.997381i	$0.523044\pi$
$572$	410.267	−	710.603i	0.717250	−	1.24231i
$573$		0			0
$574$	14.8178	+	25.6651i	0.0258149	+	0.0447128i
$575$	−354.684			−0.616842
$576$		0			0
$577$	442.364			0.766662			0.383331	−	0.923611i	$-0.374777\pi$
$577$	442.364			0.766662			0.383331	+	0.923611i	$0.374777\pi$
$578$	−20.2119	+	38.2999i	−0.0349687	+	0.0662628i
$579$		0			0
$580$	11.9167	−	20.6403i	0.0205460	−	0.0355868i
$581$	22.6437	−	39.2200i	0.0389736	−	0.0675043i
$582$		0			0
$583$	−706.030	+	407.626i	−1.21103	+	0.699188i
$584$	28.3956			0.0486226
$585$		0			0
$586$	−52.3026			−0.0892536
$587$	396.514	−	228.928i	0.675492	−	0.389996i	−0.122662	−	0.992448i	$-0.539143\pi$
$587$	396.514	−	228.928i	0.675492	−	0.389996i	0.798155	+	0.602453i	$0.205810\pi$
$588$		0			0
$589$	345.714	+	199.598i	0.586951	+	0.338877i
$590$	−16.3734	+	28.3596i	−0.0277516	+	0.0480672i
$591$		0			0
$592$	850.203	−	490.865i	1.43615	−	0.829164i
$593$			578.833i			0.976109i	0.872813	+	0.488055i	$0.162293\pi$
$593$			578.833i			0.976109i	−0.872813	+	0.488055i	$0.837707\pi$
$594$		0			0
$595$	−142.593	+	41.1278i	−0.239651	+	0.0691223i
$596$	72.4097	−	41.8057i	0.121493	−	0.0701439i
$597$		0			0
$598$	−44.8137	−	25.8732i	−0.0749393	−	0.0432662i
$599$	432.584	+	249.752i	0.722176	+	0.416949i	0.815553	−	0.578682i	$-0.196433\pi$
$599$	432.584	+	249.752i	0.722176	+	0.416949i	−0.0933770	+	0.995631i	$0.529766\pi$
$600$		0			0
$601$	720.962	−	416.247i	1.19960	−	0.692591i	0.239136	−	0.970986i	$-0.423136\pi$
$601$	720.962	−	416.247i	1.19960	−	0.692591i	0.960467	+	0.278395i	$0.0898023\pi$
$602$	−13.3297			−0.0221424
$603$		0			0
$604$	968.041			1.60272
$605$	38.3828	+	66.4809i	0.0634426	+	0.109886i
$606$		0			0
$607$	−945.923	−	546.129i	−1.55836	−	0.899718i	−0.997415	−	0.0718628i	$-0.977106\pi$
$607$	−945.923	−	546.129i	−1.55836	−	0.899718i	−0.560942	−	0.827855i	$-0.689561\pi$
$608$	−55.9962	−	32.3294i	−0.0920990	−	0.0531734i
$609$		0			0
$610$	−15.6649	−	27.1324i	−0.0256801	−	0.0444793i
$611$		−	735.995i		−	1.20458i
$612$		0			0
$613$	53.8085			0.0877790			0.0438895	−	0.999036i	$-0.486025\pi$
$613$	53.8085			0.0877790			0.0438895	+	0.999036i	$0.486025\pi$
$614$	22.2493	−	12.8456i	0.0362367	−	0.0209212i
$615$		0			0
$616$	−23.0420	+	39.9099i	−0.0374058	+	0.0647888i
$617$	−70.0923	+	121.403i	−0.113602	+	0.196764i	−0.917220	−	0.398381i	$-0.869572\pi$
$617$	−70.0923	+	121.403i	−0.113602	+	0.196764i	0.803618	+	0.595145i	$0.202905\pi$
$618$		0			0
$619$	−274.717	+	158.608i	−0.443807	+	0.256232i	−0.705211	−	0.708997i	$-0.749148\pi$
$619$	−274.717	+	158.608i	−0.443807	+	0.256232i	0.261404	+	0.965230i	$0.415815\pi$
$620$			484.244i			0.781039i
$621$		0			0
$622$			64.1052i			0.103063i
$623$	−182.642	−	316.345i	−0.293165	−	0.507776i
$624$		0			0
$625$	−55.4880	+	96.1080i	−0.0887807	+	0.153773i
$626$	−26.2844	+	45.5259i	−0.0419878	+	0.0727250i
$627$		0			0
$628$	−90.5695	−	156.871i	−0.144219	−	0.249795i
$629$	1019.37	−	294.015i	1.62062	−	0.467432i
$630$		0			0
$631$	−152.848			−0.242232			−0.121116	−	0.992638i	$-0.538647\pi$
$631$	−152.848			−0.242232			−0.121116	+	0.992638i	$0.538647\pi$
$632$	4.48417	+	7.76681i	0.00709520	+	0.0122893i
$633$		0			0
$634$	22.1731	+	12.8017i	0.0349734	+	0.0201919i
$635$	227.732	−	394.444i	0.358633	−	0.621171i
$636$		0			0
$637$	−329.882	−	571.373i	−0.517869	−	0.896975i
$638$		−	3.96507i		−	0.00621484i
$639$		0			0
$640$		−	104.479i		−	0.163249i
$641$	318.805	+	552.187i	0.497356	+	0.861447i	0.999995	−	0.00304989i	$-0.000970811\pi$
$641$	318.805	+	552.187i	0.497356	+	0.861447i	−0.502639	+	0.864496i	$0.667637\pi$
$642$		0			0
$643$	121.948	+	70.4067i	0.189655	+	0.109497i	0.591821	−	0.806069i	$-0.298409\pi$
$643$	121.948	+	70.4067i	0.189655	+	0.109497i	−0.402166	+	0.915567i	$0.631743\pi$
$644$	−222.293	−	128.341i	−0.345176	−	0.199288i
$645$		0			0
$646$	−16.6218	−	16.0017i	−0.0257304	−	0.0247704i
$647$			997.613i			1.54191i	0.636892	+	0.770953i	$0.280220\pi$
$647$			997.613i			1.54191i	−0.636892	+	0.770953i	$0.719780\pi$
$648$		0			0
$649$		−	965.053i		−	1.48698i
$650$	−38.1221	+	22.0098i	−0.0586493	+	0.0338612i
$651$		0			0
$652$	−541.677	−	312.737i	−0.830793	−	0.479658i
$653$	−327.153	+	566.646i	−0.501000	+	0.867758i	0.498999	+	0.866603i	$0.333701\pi$
$653$	−327.153	+	566.646i	−0.501000	+	0.867758i	−0.999999	+	0.00115542i	$0.999632\pi$
$654$		0			0
$655$	−0.0889312	−	0.154033i	−0.000135773	−	0.000235165i
$656$	984.416			1.50063
$657$		0			0
$658$			20.6098i			0.0313219i
$659$	63.6237	−	36.7332i	0.0965459	−	0.0557408i	−0.450950	−	0.892549i	$-0.648915\pi$
$659$	63.6237	−	36.7332i	0.0965459	−	0.0557408i	0.547496	+	0.836809i	$0.315581\pi$
$660$		0			0
$661$	559.494	−	969.071i	0.846435	−	1.46607i	−0.0379339	−	0.999280i	$-0.512078\pi$
$661$	559.494	−	969.071i	0.846435	−	1.46607i	0.884369	−	0.466788i	$-0.154589\pi$
$662$	71.9352	+	41.5318i	0.108663	+	0.0627368i
$663$		0			0
$664$	8.56492	+	14.8349i	0.0128990	+	0.0223417i
$665$		−	79.0671i		−	0.118898i
$666$		0			0
$667$	44.2946			0.0664087
$668$	183.103	+	317.144i	0.274107	+	0.474767i
$669$		0			0
$670$	7.65647	+	4.42047i	0.0114276	+	0.00659771i
$671$	799.592	+	461.645i	1.19164	+	0.687995i
$672$		0			0
$673$	505.859	−	292.058i	0.751648	−	0.433964i	−0.0746413	−	0.997210i	$-0.523781\pi$
$673$	505.859	−	292.058i	0.751648	−	0.433964i	0.826289	+	0.563246i	$0.190448\pi$
$674$	82.3371			0.122162
$675$		0			0
$676$	465.423			0.688496
$677$	−533.325	−	923.745i	−0.787776	−	1.36447i	−0.927326	−	0.374254i	$-0.877899\pi$
$677$	−533.325	−	923.745i	−0.787776	−	1.36447i	0.139550	−	0.990215i	$-0.455434\pi$
$678$		0			0
$679$	18.2217	−	31.5609i	0.0268361	−	0.0464815i
$680$	13.4953	−	54.4876i	0.0198461	−	0.0801288i
$681$		0			0
$682$	40.2809	+	69.7686i	0.0590629	+	0.102300i
$683$	−1096.38			−1.60524			−0.802621	−	0.596489i	$-0.796562\pi$
$683$	−1096.38			−1.60524			−0.802621	+	0.596489i	$0.796562\pi$
$684$		0			0
$685$			200.905i			0.293292i
$686$	20.8403	+	36.0964i	0.0303794	+	0.0526186i
$687$		0			0
$688$	−221.390	+	383.458i	−0.321787	+	0.557352i
$689$	−978.874	−	565.153i	−1.42072	−	0.820252i
$690$		0			0
$691$	450.025	−	259.822i	0.651267	−	0.376009i	−0.137675	−	0.990478i	$-0.543963\pi$
$691$	450.025	−	259.822i	0.651267	−	0.376009i	0.788941	+	0.614468i	$0.210629\pi$
$692$	−180.792			−0.261259
$693$		0			0
$694$			76.4800i			0.110202i
$695$	−59.6905	+	34.4623i	−0.0858857	+	0.0495861i
$696$		0			0
$697$	1032.62	+	255.758i	1.48153	+	0.366941i
$698$	18.0264	+	10.4076i	0.0258258	+	0.0149105i
$699$		0			0
$700$	−189.100	+	109.177i	−0.270143	+	0.155967i
$701$			926.951i			1.32233i	0.750242	+	0.661163i	$0.229937\pi$
$701$			926.951i			1.32233i	−0.750242	+	0.661163i	$0.770063\pi$
$702$		0			0
$703$			565.236i			0.804034i
$704$	377.250	+	653.417i	0.535867	+	0.928149i
$705$		0			0
$706$	−22.2591	+	38.5538i	−0.0315284	+	0.0546088i
$707$	117.401	−	203.345i	0.166056	−	0.287617i
$708$		0			0
$709$	−865.153	+	499.496i	−1.22024	+	0.704508i	−0.964970	−	0.262361i	$-0.915499\pi$
$709$	−865.153	+	499.496i	−1.22024	+	0.704508i	−0.255274	+	0.966869i	$0.582166\pi$
$710$		−	33.2321i		−	0.0468058i
$711$		0			0
$712$	138.168			0.194056
$713$	−779.400	+	449.987i	−1.09313	+	0.631117i
$714$		0			0
$715$	−284.911	+	493.480i	−0.398477	+	0.690182i
$716$	−1014.64	−	585.805i	−1.41710	−	0.818163i
$717$		0			0
$718$	−18.8717	−	32.6867i	−0.0262836	−	0.0455246i
$719$	−659.825			−0.917698			−0.458849	−	0.888514i	$-0.651738\pi$
$719$	−659.825			−0.917698			−0.458849	+	0.888514i	$0.651738\pi$
$720$		0			0
$721$		−	29.2803i		−	0.0406107i
$722$	−36.2020	+	20.9012i	−0.0501412	+	0.0289491i
$723$		0			0
$724$	964.260	+	556.716i	1.33185	+	0.768944i
$725$	18.8402	−	32.6322i	0.0259865	−	0.0450100i
$726$		0			0
$727$	−373.310	−	646.592i	−0.513494	−	0.889398i	−0.999877	−	0.0156524i	$-0.995017\pi$
$727$	−373.310	−	646.592i	−0.513494	−	0.889398i	0.486383	−	0.873746i	$-0.338316\pi$
$728$	−63.8931			−0.0877652
$729$		0			0
$730$	−9.83196			−0.0134684
$731$	−331.856	+	344.718i	−0.453975	+	0.471570i
$732$		0			0
$733$	−333.459	+	577.568i	−0.454924	+	0.787951i	−0.998684	−	0.0512897i	$-0.983667\pi$
$733$	−333.459	+	577.568i	−0.454924	+	0.787951i	0.543760	+	0.839241i	$0.317000\pi$
$734$	35.4536	−	61.4074i	0.0483019	−	0.0836613i
$735$		0			0
$736$	126.241	−	72.8854i	0.171523	−	0.0990291i
$737$	−260.543			−0.353518
$738$		0			0
$739$	−1026.55			−1.38911			−0.694554	−	0.719440i	$-0.744398\pi$
$739$	−1026.55			−1.38911			−0.694554	+	0.719440i	$0.744398\pi$
$740$	−593.797	+	342.829i	−0.802429	+	0.463282i
$741$		0			0
$742$	27.4111	+	15.8258i	0.0369422	+	0.0213286i
$743$	−609.448	+	1055.59i	−0.820253	+	1.42072i	0.0852417	+	0.996360i	$0.472834\pi$
$743$	−609.448	+	1055.59i	−0.820253	+	1.42072i	−0.905494	+	0.424359i	$0.860500\pi$
$744$		0			0
$745$	−50.2851	+	29.0321i	−0.0674968	+	0.0389693i
$746$		−	51.3161i		−	0.0687883i
$747$		0			0
$748$	228.580	+	792.502i	0.305588	+	1.05949i
$749$	124.702	−	71.9968i	0.166491	−	0.0961238i
$750$		0			0
$751$	84.1112	+	48.5616i	0.111999	+	0.0646626i	0.554953	−	0.831882i	$-0.312736\pi$
$751$	84.1112	+	48.5616i	0.111999	+	0.0646626i	−0.442954	+	0.896544i	$0.646070\pi$
$752$	592.886	+	342.303i	0.788412	+	0.455190i
$753$		0			0
$754$	4.76086	−	2.74868i	0.00631414	−	0.00364547i
$755$	−672.259			−0.890409
$756$		0			0
$757$	−183.164			−0.241960			−0.120980	−	0.992655i	$-0.538604\pi$
$757$	−183.164			−0.241960			−0.120980	+	0.992655i	$0.538604\pi$
$758$	−10.8535	−	18.7987i	−0.0143185	−	0.0248004i
$759$		0			0
$760$	25.9002	+	14.9535i	0.0340792	+	0.0196756i
$761$	926.306	+	534.803i	1.21722	+	0.702764i	0.964323	−	0.264729i	$-0.0852825\pi$
$761$	926.306	+	534.803i	1.21722	+	0.702764i	0.252899	+	0.967493i	$0.418616\pi$
$762$		0			0
$763$	−250.488	−	433.858i	−0.328293	−	0.568621i
$764$		−	1137.39i		−	1.48873i
$765$		0			0
$766$	−32.6498			−0.0426237
$767$	1158.74	−	668.998i	1.51074	−	0.872227i
$768$		0			0
$769$	−316.206	+	547.685i	−0.411192	+	0.712205i	−0.995020	−	0.0996721i	$-0.968221\pi$
$769$	−316.206	+	547.685i	−0.411192	+	0.712205i	0.583829	+	0.811877i	$0.301554\pi$
$770$	7.97827	−	13.8188i	0.0103614	−	0.0179465i
$771$		0			0
$772$	−484.519	+	279.737i	−0.627616	+	0.362354i
$773$			7.38633i			0.00955541i	0.999989	+	0.00477771i	$0.00152080\pi$
$773$			7.38633i			0.00955541i	−0.999989	+	0.00477771i	$0.998479\pi$
$774$		0			0
$775$			765.588i			0.987855i
$776$	6.89232	+	11.9379i	0.00888186	+	0.0153838i
$777$		0			0
$778$	−5.63353	+	9.75757i	−0.00724105	+	0.0125419i
$779$	−283.391	+	490.848i	−0.363789	+	0.630100i
$780$		0			0
$781$	489.676	+	848.144i	0.626986	+	1.08597i
$782$	49.9786	−	14.4153i	0.0639113	−	0.0184338i
$783$		0			0
$784$	613.697			0.782777
$785$	62.8963	+	108.940i	0.0801226	+	0.138776i
$786$		0			0
$787$	−363.589	−	209.918i	−0.461994	−	0.266732i	0.250888	−	0.968016i	$-0.419277\pi$
$787$	−363.589	−	209.918i	−0.461994	−	0.266732i	−0.712882	+	0.701284i	$0.752611\pi$
$788$	−690.663	+	1196.26i	−0.876475	+	1.51810i
$789$		0			0
$790$	−1.55264	−	2.68925i	−0.00196537	−	0.00340411i
$791$		−	174.554i		−	0.220675i
$792$		0			0
$793$			1280.09i			1.61424i
$794$	−41.0513	−	71.1029i	−0.0517019	−	0.0895503i
$795$		0			0
$796$	189.817	+	109.591i	0.238463	+	0.137677i
$797$	−1351.72	−	780.418i	−1.69601	−	0.979194i	−0.949470	−	0.313859i	$-0.898378\pi$
$797$	−1351.72	−	780.418i	−1.69601	−	0.979194i	−0.746545	−	0.665335i	$-0.768289\pi$
$798$		0			0
$799$	532.987	+	513.101i	0.667067	+	0.642178i
$800$		−	124.004i		−	0.155005i
$801$		0			0
$802$		−	105.706i		−	0.131802i
$803$	250.930	−	144.874i	0.312490	−	0.180416i
$804$		0			0
$805$	154.372	+	89.1269i	0.191767	+	0.110717i
$806$	−55.8475	+	96.7306i	−0.0692896	+	0.120013i
$807$		0			0
$808$	44.4068	+	76.9148i	0.0549589	+	0.0951916i
$809$	474.700			0.586774			0.293387	−	0.955994i	$-0.405218\pi$
$809$	474.700			0.586774			0.293387	+	0.955994i	$0.405218\pi$
$810$		0			0
$811$		−	291.146i		−	0.358997i	−0.983758	−	0.179498i	$-0.942553\pi$
$811$		−	291.146i		−	0.358997i	0.983758	−	0.179498i	$-0.0574475\pi$
$812$	23.6157	−	13.6345i	0.0290834	−	0.0167913i
$813$		0			0
$814$	−57.0351	+	98.7878i	−0.0700677	+	0.121361i
$815$	376.169	+	217.181i	0.461557	+	0.266480i
$816$		0			0
$817$	−127.466	−	220.778i	−0.156017	−	0.270230i
$818$		−	84.3147i		−	0.103074i
$819$		0			0
$820$	−687.534			−0.838456
$821$	−88.4256	−	153.158i	−0.107705	−	0.186550i	0.807135	−	0.590367i	$-0.201017\pi$
$821$	−88.4256	−	153.158i	−0.107705	−	0.186550i	−0.914840	+	0.403816i	$0.867683\pi$
$822$		0			0
$823$	−38.5079	−	22.2325i	−0.0467896	−	0.0270140i	0.476423	−	0.879216i	$-0.341933\pi$
$823$	−38.5079	−	22.2325i	−0.0467896	−	0.0270140i	−0.523212	+	0.852202i	$0.675267\pi$
$824$	9.59141	+	5.53760i	0.0116401	+	0.00672039i
$825$		0			0
$826$	−32.4478	+	18.7337i	−0.0392830	+	0.0226801i
$827$	900.292			1.08862			0.544312	−	0.838883i	$-0.316791\pi$
$827$	900.292			1.08862			0.544312	+	0.838883i	$0.316791\pi$
$828$		0			0
$829$	−537.393			−0.648242			−0.324121	−	0.946016i	$-0.605069\pi$
$829$	−537.393			−0.648242			−0.324121	+	0.946016i	$0.605069\pi$
$830$	−2.96560	−	5.13656i	−0.00357301	−	0.00618863i
$831$		0			0
$832$	−523.038	+	905.929i	−0.628652	+	1.08886i
$833$	643.750	+	159.442i	0.772809	+	0.191407i
$834$		0			0
$835$	−127.157	−	220.242i	−0.152283	−	0.263763i
$836$	−439.440			−0.525646
$837$		0			0
$838$		−	90.0823i		−	0.107497i
$839$	519.335	+	899.515i	0.618993	+	1.07213i	0.989670	+	0.143366i	$0.0457925\pi$
$839$	519.335	+	899.515i	0.618993	+	1.07213i	−0.370677	+	0.928762i	$0.620874\pi$
$840$		0			0
$841$	418.147	−	724.252i	0.497202	−	0.861180i
$842$	43.5893	+	25.1663i	0.0517687	+	0.0298887i
$843$		0			0
$844$	1137.29	−	656.617i	1.34750	−	0.777982i
$845$	−323.214			−0.382502
$846$		0			0
$847$			87.8316i			0.103697i
$848$	910.526	−	525.692i	1.07373	−	0.619920i
$849$		0			0
$850$	10.6380	−	42.9511i	0.0125153	−	0.0505307i
$851$	−1103.58	−	637.151i	−1.29680	−	0.748709i
$852$		0			0
$853$	197.058	−	113.771i	0.231017	−	0.133378i	−0.380024	−	0.924977i	$-0.624084\pi$
$853$	197.058	−	113.771i	0.231017	−	0.133378i	0.611041	+	0.791599i	$0.290751\pi$
$854$		−	35.8461i		−	0.0419743i
$855$		0			0
$856$			54.4652i			0.0636276i
$857$	467.534	+	809.793i	0.545547	+	0.944916i	0.998572	+	0.0534180i	$0.0170116\pi$
$857$	467.534	+	809.793i	0.545547	+	0.944916i	−0.453025	+	0.891498i	$0.649655\pi$
$858$		0			0
$859$	−264.570	+	458.248i	−0.307997	+	0.533467i	−0.977924	−	0.208960i	$-0.932992\pi$
$859$	−264.570	+	458.248i	−0.307997	+	0.533467i	0.669927	+	0.742427i	$0.266325\pi$
$860$	154.622	−	267.814i	0.179794	−	0.311412i
$861$		0			0
$862$	−33.7800	+	19.5029i	−0.0391880	+	0.0226252i
$863$		−	271.514i		−	0.314616i	−0.987550	−	0.157308i	$-0.949718\pi$
$863$		−	271.514i		−	0.314616i	0.987550	−	0.157308i	$-0.0502815\pi$
$864$		0			0
$865$	125.551			0.145146
$866$	−1.45368	+	0.839284i	−0.00167862	+	0.000969150i
$867$		0			0
$868$	−277.025	+	479.821i	−0.319153	+	0.552790i
$869$	79.2524	+	45.7564i	0.0911995	+	0.0526541i
$870$		0			0
$871$	−180.615	−	312.834i	−0.207365	−	0.359166i
$872$	189.493			0.217308
$873$		0			0
$874$			27.7130i			0.0317082i
$875$	320.325	−	184.940i	0.366086	−	0.211360i
$876$		0			0
$877$	−88.4609	−	51.0729i	−0.100868	−	0.0582359i	0.448718	−	0.893674i	$-0.351881\pi$
$877$	−88.4609	−	51.0729i	−0.100868	−	0.0582359i	−0.549585	+	0.835438i	$0.685214\pi$
$878$	−18.5837	+	32.1880i	−0.0211660	+	0.0366605i
$879$		0			0
$880$	−265.017	−	459.024i	−0.301156	−	0.521618i
$881$	1034.23			1.17392			0.586961	−	0.809615i	$-0.300324\pi$
$881$	1034.23			1.17392			0.586961	+	0.809615i	$0.300324\pi$
$882$		0			0
$883$	823.510			0.932628			0.466314	−	0.884619i	$-0.345582\pi$
$883$	823.510			0.932628			0.466314	+	0.884619i	$0.345582\pi$
$884$	−793.100	+	823.838i	−0.897172	+	0.931943i
$885$		0			0
$886$	61.7306	−	106.921i	0.0696733	−	0.120678i
$887$	−496.209	+	859.460i	−0.559424	+	0.968952i	0.438120	+	0.898916i	$0.355644\pi$
$887$	−496.209	+	859.460i	−0.559424	+	0.968952i	−0.997545	+	0.0700351i	$0.977689\pi$
$888$		0			0
$889$	451.304	−	260.561i	0.507654	−	0.293094i
$890$	−47.8404			−0.0537533
$891$		0			0
$892$	8.21401			0.00920853
$893$	−341.357	+	197.082i	−0.382259	+	0.220697i
$894$		0			0
$895$	704.622	+	406.814i	0.787288	+	0.454541i
$896$	59.7702	−	103.525i	0.0667078	−	0.115541i
$897$		0			0
$898$	−16.2131	+	9.36064i	−0.0180547	+	0.0104239i
$899$		−	95.6101i		−	0.106352i
$900$		0			0
$901$	1091.69	−	314.875i	1.21164	−	0.349473i
$902$	−99.0581	+	57.1912i	−0.109820	+	0.0634049i
$903$		0			0
$904$	57.1789	+	33.0123i	0.0632510	+	0.0365180i
$905$	−669.633	−	386.613i	−0.739926	−	0.427196i
$906$		0			0
$907$	−67.6442	+	39.0544i	−0.0745801	+	0.0430589i	−0.536826	−	0.843693i	$-0.680377\pi$
$907$	−67.6442	+	39.0544i	−0.0745801	+	0.0430589i	0.462246	+	0.886752i	$0.347044\pi$
$908$	−793.581			−0.873988
$909$		0			0
$910$	22.1229			0.0243109
$911$	−442.812	−	766.974i	−0.486073	−	0.841903i	0.513799	−	0.857911i	$-0.328238\pi$
$911$	−442.812	−	766.974i	−0.486073	−	0.841903i	−0.999872	+	0.0160076i	$0.994904\pi$
$912$		0			0
$913$	151.375	+	87.3963i	0.165799	+	0.0957244i
$914$	112.493	+	64.9480i	0.123078	+	0.0710591i
$915$		0			0
$916$	276.113	+	478.242i	0.301434	+	0.522098i
$917$		−	0.203502i		−	0.000221922i
$918$		0			0
$919$	−11.6428			−0.0126690			−0.00633450	−	0.999980i	$-0.502016\pi$
$919$	−11.6428			−0.0126690			−0.00633450	+	0.999980i	$0.502016\pi$
$920$	−58.3910	+	33.7120i	−0.0634684	+	0.0366435i
$921$		0			0
$922$	−21.7453	+	37.6640i	−0.0235849	+	0.0408503i
$923$	−678.911	+	1175.91i	−0.735548	+	1.27401i
$924$		0			0
$925$	−938.790	+	542.011i	−1.01491	+	0.585958i
$926$		−	52.6851i		−	0.0568954i
$927$		0			0
$928$			15.4862i			0.0166877i
$929$	207.366	+	359.168i	0.223214	+	0.386618i	0.955782	−	0.294076i	$-0.0950118\pi$
$929$	207.366	+	359.168i	0.223214	+	0.386618i	−0.732568	+	0.680694i	$0.761678\pi$
$930$		0			0
$931$	−176.670	+	306.001i	−0.189763	+	0.328680i
$932$	647.036	−	1120.70i	0.694244	−	1.20247i
$933$		0			0
$934$	−29.5467	−	51.1764i	−0.0316346	−	0.0547927i
$935$	−158.738	−	550.355i	−0.169773	−	0.588615i
$936$		0			0
$937$	434.596			0.463817			0.231908	−	0.972738i	$-0.425503\pi$
$937$	434.596			0.463817			0.231908	+	0.972738i	$0.425503\pi$
$938$	5.05770	+	8.76019i	0.00539200	+	0.00933922i
$939$		0			0
$940$	−414.082	−	239.070i	−0.440513	−	0.254330i
$941$	762.435	−	1320.58i	0.810239	−	1.40337i	−0.102458	−	0.994737i	$-0.532671\pi$
$941$	762.435	−	1320.58i	0.810239	−	1.40337i	0.912697	−	0.408637i	$-0.133996\pi$
$942$		0			0
$943$	−638.895	−	1106.60i	−0.677513	−	1.17349i
$944$			1244.57i			1.31840i
$945$		0			0
$946$		−	51.4479i		−	0.0543847i
$947$	−201.357	−	348.761i	−0.212626	−	0.368280i	0.739909	−	0.672707i	$-0.234868\pi$
$947$	−201.357	−	348.761i	−0.212626	−	0.368280i	−0.952536	+	0.304427i	$0.901535\pi$
$948$		0			0
$949$	347.901	+	200.861i	0.366598	+	0.211655i
$950$	20.4164	+	11.7874i	0.0214910	+	0.0124078i
$951$		0			0
$952$	44.5432	−	46.2695i	0.0467891	−	0.0486025i
$953$		−	671.106i		−	0.704203i	−0.935962	−	0.352102i	$-0.885467\pi$
$953$		−	671.106i		−	0.704203i	0.935962	−	0.352102i	$-0.114533\pi$
$954$		0			0
$955$			789.864i			0.827082i
$956$	587.110	−	338.968i	0.614132	−	0.354569i
$957$		0			0
$958$	−44.8051	−	25.8683i	−0.0467695	−	0.0270024i
$959$	−114.933	+	199.070i	−0.119847	+	0.207581i
$960$		0			0
$961$	490.798	+	850.087i	0.510716	+	0.884586i
$962$	−158.153			−0.164400
$963$		0			0
$964$			93.2912i			0.0967751i
$965$	336.476	−	194.264i	0.348680	−	0.201310i
$966$		0			0
$967$	−409.830	+	709.846i	−0.423816	+	0.734070i	−0.996309	−	0.0858390i	$-0.972643\pi$
$967$	−409.830	+	709.846i	−0.423816	+	0.734070i	0.572493	+	0.819909i	$0.305976\pi$
$968$	−28.7712	−	16.6110i	−0.0297223	−	0.0171602i
$969$		0			0
$970$	−2.38646	−	4.13347i	−0.00246027	−	0.00426131i
$971$			877.715i			0.903929i	0.892036	+	0.451965i	$0.149277\pi$
$971$			877.715i			0.903929i	−0.892036	+	0.451965i	$0.850723\pi$
$972$		0			0
$973$	−78.8605			−0.0810488
$974$	44.3993	+	76.9018i	0.0455845	+	0.0789546i
$975$		0			0
$976$	−1031.19	−	595.357i	−1.05654	−	0.609996i
$977$	966.293	+	557.890i	0.989041	+	0.571023i	0.904988	−	0.425438i	$-0.139880\pi$
$977$	966.293	+	557.890i	0.989041	+	0.571023i	0.0840537	+	0.996461i	$0.473213\pi$
$978$		0			0
$979$	1220.98	−	704.930i	1.24717	−	0.720051i
$980$	−428.617			−0.437365
$981$		0			0
$982$	−18.6370			−0.0189786
$983$	546.561	+	946.671i	0.556013	+	0.963043i	0.997824	+	0.0659348i	$0.0210029\pi$
$983$	546.561	+	946.671i	0.556013	+	0.963043i	−0.441811	+	0.897108i	$0.645664\pi$
$984$		0			0
$985$	479.633	−	830.748i	0.486937	−	0.843399i
$986$	−1.32852	+	5.36393i	−0.00134739	+	0.00544009i
$987$		0			0
$988$	−304.630	−	527.635i	−0.308330	−	0.534044i
$989$	574.735			0.581128
$990$		0			0
$991$		−	672.370i		−	0.678477i	−0.940700	−	0.339238i	$-0.889831\pi$
$991$		−	672.370i		−	0.678477i	0.940700	−	0.339238i	$-0.110169\pi$
$992$	−157.324	−	272.492i	−0.158592	−	0.274690i
$993$		0			0
$994$	19.0113	−	32.9286i	0.0191261	−	0.0331273i
$995$	−131.819	−	76.1056i	−0.132481	−	0.0764881i
$996$		0			0
$997$	264.679	−	152.813i	0.265476	−	0.153272i	−0.361354	−	0.932429i	$-0.617685\pi$
$997$	264.679	−	152.813i	0.265476	−	0.153272i	0.626830	+	0.779156i	$0.284352\pi$
$998$	−47.1799			−0.0472744
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	459.3.i.a.152.17		68
3.2	odd	2		153.3.i.a.50.18	yes	68
9.2	odd	6	inner	459.3.i.a.305.18		68
9.7	even	3		153.3.i.a.101.17	yes	68
17.16	even	2	inner	459.3.i.a.152.18		68
51.50	odd	2		153.3.i.a.50.17	✓	68
153.16	even	6		153.3.i.a.101.18	yes	68
153.101	odd	6	inner	459.3.i.a.305.17		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.i.a.50.17	✓	68	51.50	odd	2
153.3.i.a.50.18	yes	68	3.2	odd	2
153.3.i.a.101.17	yes	68	9.7	even	3
153.3.i.a.101.18	yes	68	153.16	even	6
459.3.i.a.152.17		68	1.1	even	1	trivial
459.3.i.a.152.18		68	17.16	even	2	inner
459.3.i.a.305.17		68	153.101	odd	6	inner
459.3.i.a.305.18		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)

\(f(q)\)	\(=\)	\(q+(0.129772 - 0.0749237i) q^{2} +(-1.98877 + 3.44466i) q^{4} +(1.38111 - 2.39215i) q^{5} +(2.73699 - 1.58020i) q^{7} +1.19542i q^{8} -0.413911i q^{10} +(6.09900 + 10.5638i) q^{11} +(-8.45595 + 14.6461i) q^{13} +(0.236789 - 0.410131i) q^{14} +(-7.86553 - 13.6235i) q^{16} +(-4.71123 - 16.3341i) q^{17} +9.05723 q^{19} +(5.49342 + 9.51489i) q^{20} +(1.58296 + 0.913920i) q^{22} +(-10.2096 + 17.6835i) q^{23} +(8.68508 + 15.0430i) q^{25} +2.53421i q^{26} +12.5706i q^{28} +(-1.08463 - 1.87864i) q^{29} +(38.1700 + 22.0374i) q^{31} +(-6.18249 - 3.56946i) q^{32} +(-1.83520 - 1.76673i) q^{34} -8.72972i q^{35} +62.4071i q^{37} +(1.17537 - 0.678602i) q^{38} +(2.85961 + 1.65100i) q^{40} +(-31.2890 + 54.1941i) q^{41} +(-14.0734 - 24.3759i) q^{43} -48.5181 q^{44} +3.05976i q^{46} +(-37.6889 + 21.7597i) q^{47} +(-19.5059 + 33.7853i) q^{49} +(2.25415 + 1.30144i) q^{50} +(-33.6339 - 58.2557i) q^{52} +66.8350i q^{53} +33.6935 q^{55} +(1.88900 + 3.27184i) q^{56} +(-0.281509 - 0.162529i) q^{58} +(-68.5161 - 39.5578i) q^{59} +(65.5511 - 37.8459i) q^{61} +6.60451 q^{62} +61.8545 q^{64} +(23.3572 + 40.4558i) q^{65} +(-10.6797 + 18.4979i) q^{67} +(65.6351 + 16.2563i) q^{68} +(-0.654064 - 1.13287i) q^{70} +80.2879 q^{71} -23.7538i q^{73} +(4.67578 + 8.09868i) q^{74} +(-18.0128 + 31.1990i) q^{76} +(33.3858 + 19.2753i) q^{77} +(6.49716 - 3.75114i) q^{79} -43.4526 q^{80} +9.37714i q^{82} +(12.4098 - 7.16481i) q^{83} +(-45.5805 - 11.2893i) q^{85} +(-3.65266 - 2.10887i) q^{86} +(-12.6281 + 7.29084i) q^{88} -115.581i q^{89} +53.4484i q^{91} +(-40.6091 - 70.3370i) q^{92} +(-3.26063 + 5.64758i) q^{94} +(12.5090 - 21.6663i) q^{95} +(9.98636 - 5.76563i) q^{97} +5.84583i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 6 q^{2} + 62 q^{4} - 2 q^{13} - 106 q^{16} - 32 q^{19} - 132 q^{25} - 27 q^{34} + 102 q^{38} + 58 q^{43} + 312 q^{47} + 152 q^{49} + 90 q^{50} + 70 q^{52} + 92 q^{55} + 258 q^{59} - 16 q^{64} + 82 q^{67}+ \cdots - 18 q^{94}+O(q^{100}) \) 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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