LMFDB - Embedded newform 798.2.ca.b.355.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(325,798)] 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("798.325"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.ca (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [84] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$14$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			355.12
Character	$\chi$	$=$	798.355
Dual form			798.2.ca.b.535.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.984808 - 0.173648i) q^{2} +(0.173648 + 0.984808i) q^{3} +(0.939693 - 0.342020i) q^{4} +(0.365734 - 1.00485i) q^{5} +(0.342020 + 0.939693i) q^{6} +(-0.921632 + 2.48004i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(0.185688 - 1.05309i) q^{10} +(-2.16999 + 3.75854i) q^{11} +(0.500000 + 0.866025i) q^{12} +(4.42506 - 1.61059i) q^{13} +(-0.476976 + 2.60240i) q^{14} +(1.05309 + 0.185688i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-1.92982 + 5.30213i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(4.35312 - 0.224380i) q^{19} -1.06934i q^{20} +(-2.60240 - 0.476976i) q^{21} +(-1.48436 + 4.07825i) q^{22} +(4.19417 + 3.51933i) q^{23} +(0.642788 + 0.766044i) q^{24} +(2.95427 + 2.47892i) q^{25} +(4.07816 - 2.35452i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(-0.0178271 + 2.64569i) q^{28} +(4.27200 - 5.09117i) q^{29} +1.06934 q^{30} -6.24848 q^{31} +(0.642788 - 0.766044i) q^{32} +(-4.07825 - 1.48436i) q^{33} +(-0.979794 + 5.55669i) q^{34} +(2.15499 + 1.83313i) q^{35} +(-0.766044 + 0.642788i) q^{36} +(-8.67783 - 5.01015i) q^{37} +(4.24802 - 0.976882i) q^{38} +(2.35452 + 4.07816i) q^{39} +(-0.185688 - 1.05309i) q^{40} +(5.27060 + 1.91834i) q^{41} +(-2.64569 - 0.0178271i) q^{42} +(-1.03850 - 5.88963i) q^{43} +(-0.753631 + 4.27405i) q^{44} +1.06934i q^{45} +(4.74158 + 2.73755i) q^{46} +(2.92545 + 8.03761i) q^{47} +(0.766044 + 0.642788i) q^{48} +(-5.30119 - 4.57137i) q^{49} +(3.33985 + 1.92826i) q^{50} +(-5.55669 - 0.979794i) q^{51} +(3.60734 - 3.02692i) q^{52} +(-3.88438 - 10.6722i) q^{53} +(-0.642788 - 0.766044i) q^{54} +(2.98311 + 3.55513i) q^{55} +(0.441863 + 2.60859i) q^{56} +(0.976882 + 4.24802i) q^{57} +(3.32303 - 5.75565i) q^{58} +(-1.52642 - 0.555571i) q^{59} +(1.05309 - 0.185688i) q^{60} +(3.40295 - 4.05547i) q^{61} +(-6.15355 + 1.08504i) q^{62} +(0.0178271 - 2.64569i) q^{63} +(0.500000 - 0.866025i) q^{64} -5.03555i q^{65} +(-4.27405 - 0.753631i) q^{66} +(8.52757 + 1.50364i) q^{67} +5.64241i q^{68} +(-2.73755 + 4.74158i) q^{69} +(2.44057 + 1.43107i) q^{70} +(-11.5265 + 2.03243i) q^{71} +(-0.642788 + 0.766044i) q^{72} +(3.23890 - 0.571106i) q^{73} +(-9.41599 - 3.42714i) q^{74} +(-1.92826 + 3.33985i) q^{75} +(4.01385 - 1.69970i) q^{76} +(-7.32139 - 8.84565i) q^{77} +(3.02692 + 3.60734i) q^{78} +(-4.59898 - 5.48085i) q^{79} +(-0.365734 - 1.00485i) q^{80} +(0.766044 - 0.642788i) q^{81} +(5.52364 + 0.973968i) q^{82} +(3.27774 + 1.89240i) q^{83} +(-2.60859 + 0.441863i) q^{84} +(4.62202 + 3.87834i) q^{85} +(-2.04545 - 5.61982i) q^{86} +(5.75565 + 3.32303i) q^{87} +4.33999i q^{88} +(-1.07987 + 6.12423i) q^{89} +(0.185688 + 1.05309i) q^{90} +(-0.0839488 + 12.4587i) q^{91} +(5.14492 + 1.87260i) q^{92} +(-1.08504 - 6.15355i) q^{93} +(4.27672 + 7.40750i) q^{94} +(1.36662 - 4.45628i) q^{95} +(0.866025 + 0.500000i) q^{96} +(4.53730 - 3.80725i) q^{97} +(-6.01446 - 3.58137i) q^{98} +(0.753631 - 4.27405i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 6 q^{7} - 6 q^{10} + 6 q^{11} + 42 q^{12} - 24 q^{13} + 18 q^{17} - 6 q^{19} - 6 q^{21} + 12 q^{22} + 30 q^{23} + 24 q^{25} + 18 q^{26} - 42 q^{27} - 6 q^{28} + 12 q^{31} + 6 q^{33} + 30 q^{34} + 12 q^{35}+ \cdots + 6 q^{99}+O(q^{100}) $ 84 * q - 6 * q^7 - 6 * q^10 + 6 * q^11 + 42 * q^12 - 24 * q^13 + 18 * q^17 - 6 * q^19 - 6 * q^21 + 12 * q^22 + 30 * q^23 + 24 * q^25 + 18 * q^26 - 42 * q^27 - 6 * q^28 + 12 * q^31 + 6 * q^33 + 30 * q^34 + 12 * q^35 + 18 * q^37 + 24 * q^38 + 6 * q^40 - 36 * q^41 - 6 * q^42 + 12 * q^43 - 6 * q^44 + 18 * q^46 + 18 * q^47 + 12 * q^49 - 30 * q^52 - 12 * q^53 + 30 * q^55 + 18 * q^56 + 6 * q^57 + 6 * q^59 + 36 * q^61 + 12 * q^62 + 6 * q^63 + 42 * q^64 + 6 * q^66 - 12 * q^67 - 6 * q^69 - 18 * q^70 + 42 * q^71 - 6 * q^73 + 48 * q^75 - 18 * q^76 - 96 * q^77 - 12 * q^78 - 6 * q^79 - 12 * q^82 - 54 * q^83 + 6 * q^84 - 24 * q^85 - 30 * q^86 + 24 * q^89 - 6 * q^90 + 42 * q^91 + 42 * q^92 + 36 * q^93 - 18 * q^94 + 24 * q^95 + 78 * q^97 + 12 * q^98 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{18}\right)$	$1$

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 $

$2$	0.984808	−	0.173648i	0.696364	−	0.122788i
$2$	0.984808	−	0.173648i	0.696364	−	0.122788i
$3$	0.173648	+	0.984808i	0.100256	+	0.568579i
$3$	0.173648	+	0.984808i	0.100256	+	0.568579i
$4$	0.939693	−	0.342020i	0.469846	−	0.171010i
$5$	0.365734	−	1.00485i	0.163561	−	0.449381i	−0.830654	−	0.556789i	$-0.812033\pi$
$5$	0.365734	−	1.00485i	0.163561	−	0.449381i	0.994215	+	0.107408i	$0.0342553\pi$
$6$	0.342020	+	0.939693i	0.139629	+	0.383628i
$7$	−0.921632	+	2.48004i	−0.348344	+	0.937367i
$7$	−0.921632	+	2.48004i	−0.348344	+	0.937367i
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$	0.185688	−	1.05309i	0.0587197	−	0.333016i
$11$	−2.16999	+	3.75854i	−0.654277	+	1.13324i	0.327797	+	0.944748i	$0.393694\pi$
$11$	−2.16999	+	3.75854i	−0.654277	+	1.13324i	−0.982074	+	0.188494i	$0.939640\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	4.42506	−	1.61059i	1.22729	−	0.446697i	0.354622	−	0.935010i	$-0.384610\pi$
$13$	4.42506	−	1.61059i	1.22729	−	0.446697i	0.872669	+	0.488313i	$0.162387\pi$
$14$	−0.476976	+	2.60240i	−0.127477	+	0.695521i
$15$	1.05309	+	0.185688i	0.271907	+	0.0479445i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−1.92982	+	5.30213i	−0.468049	+	1.28595i	0.451251	+	0.892397i	$0.350978\pi$
$17$	−1.92982	+	5.30213i	−0.468049	+	1.28595i	−0.919300	+	0.393558i	$0.871244\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$	4.35312	−	0.224380i	0.998674	−	0.0514763i
$19$	4.35312	−	0.224380i	0.998674	−	0.0514763i
$20$		−	1.06934i		−	0.239111i
$21$	−2.60240	−	0.476976i	−0.567891	−	0.104085i
$22$	−1.48436	+	4.07825i	−0.316467	+	0.869486i
$23$	4.19417	+	3.51933i	0.874546	+	0.733831i	0.965050	−	0.262065i	$-0.0844035\pi$
$23$	4.19417	+	3.51933i	0.874546	+	0.733831i	−0.0905044	+	0.995896i	$0.528848\pi$
$24$	0.642788	+	0.766044i	0.131208	+	0.156368i
$25$	2.95427	+	2.47892i	0.590853	+	0.495785i
$26$	4.07816	−	2.35452i	0.799792	−	0.461760i
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$	−0.0178271	+	2.64569i	−0.00336901	+	0.499989i
$29$	4.27200	−	5.09117i	0.793291	−	0.945407i	−0.206161	−	0.978518i	$-0.566097\pi$
$29$	4.27200	−	5.09117i	0.793291	−	0.945407i	0.999452	+	0.0331108i	$0.0105414\pi$
$30$	1.06934			0.195233
$31$	−6.24848			−1.12226			−0.561130	−	0.827727i	$-0.689633\pi$
$31$	−6.24848			−1.12226			−0.561130	+	0.827727i	$0.689633\pi$
$32$	0.642788	−	0.766044i	0.113630	−	0.135419i
$33$	−4.07825	−	1.48436i	−0.709933	−	0.258394i
$34$	−0.979794	+	5.55669i	−0.168033	+	0.952964i
$35$	2.15499	+	1.83313i	0.364259	+	0.309856i
$36$	−0.766044	+	0.642788i	−0.127674	+	0.107131i
$37$	−8.67783	−	5.01015i	−1.42663	−	0.823663i	−0.429773	−	0.902937i	$-0.641406\pi$
$37$	−8.67783	−	5.01015i	−1.42663	−	0.823663i	−0.996853	+	0.0792741i	$0.974740\pi$
$38$	4.24802	−	0.976882i	0.689120	−	0.158471i
$39$	2.35452	+	4.07816i	0.377026	+	0.653028i
$40$	−0.185688	−	1.05309i	−0.0293599	−	0.166508i
$41$	5.27060	+	1.91834i	0.823130	+	0.299595i	0.719036	−	0.694973i	$-0.244584\pi$
$41$	5.27060	+	1.91834i	0.823130	+	0.299595i	0.104094	+	0.994568i	$0.466806\pi$
$42$	−2.64569	−	0.0178271i	−0.408239	−	0.00275079i
$43$	−1.03850	−	5.88963i	−0.158370	−	0.898160i	−0.955640	−	0.294537i	$-0.904835\pi$
$43$	−1.03850	−	5.88963i	−0.158370	−	0.898160i	0.797270	−	0.603623i	$-0.206277\pi$
$44$	−0.753631	+	4.27405i	−0.113614	+	0.644337i
$45$			1.06934i			0.159407i
$46$	4.74158	+	2.73755i	0.699108	+	0.403630i
$47$	2.92545	+	8.03761i	0.426721	+	1.17241i	0.947791	+	0.318892i	$0.103311\pi$
$47$	2.92545	+	8.03761i	0.426721	+	1.17241i	−0.521070	+	0.853514i	$0.674467\pi$
$48$	0.766044	+	0.642788i	0.110569	+	0.0927784i
$49$	−5.30119	−	4.57137i	−0.757313	−	0.653052i
$50$	3.33985	+	1.92826i	0.472326	+	0.272697i
$51$	−5.55669	−	0.979794i	−0.778092	−	0.137199i
$52$	3.60734	−	3.02692i	0.500248	−	0.419758i
$53$	−3.88438	−	10.6722i	−0.533560	−	1.46594i	−0.854805	−	0.518949i	$-0.826324\pi$
$53$	−3.88438	−	10.6722i	−0.533560	−	1.46594i	0.321245	−	0.946996i	$-0.395899\pi$
$54$	−0.642788	−	0.766044i	−0.0874723	−	0.104245i
$55$	2.98311	+	3.55513i	0.402243	+	0.479374i
$56$	0.441863	+	2.60859i	0.0590464	+	0.348588i
$57$	0.976882	+	4.24802i	0.129391	+	0.562664i
$58$	3.32303	−	5.75565i	0.436335	−	0.755754i
$59$	−1.52642	−	0.555571i	−0.198723	−	0.0723292i	0.240741	−	0.970589i	$-0.422609\pi$
$59$	−1.52642	−	0.555571i	−0.198723	−	0.0723292i	−0.439464	+	0.898260i	$0.644832\pi$
$60$	1.05309	−	0.185688i	0.135953	−	0.0239722i
$61$	3.40295	−	4.05547i	0.435703	−	0.519250i	−0.502856	−	0.864370i	$-0.667717\pi$
$61$	3.40295	−	4.05547i	0.435703	−	0.519250i	0.938559	+	0.345120i	$0.112162\pi$
$62$	−6.15355	+	1.08504i	−0.781502	+	0.137800i
$63$	0.0178271	−	2.64569i	0.00224601	−	0.333326i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$		−	5.03555i		−	0.624583i
$66$	−4.27405	−	0.753631i	−0.526099	−	0.0927655i
$67$	8.52757	+	1.50364i	1.04181	+	0.183699i	0.668273	−	0.743916i	$-0.267034\pi$
$67$	8.52757	+	1.50364i	1.04181	+	0.183699i	0.373536	+	0.927616i	$0.378145\pi$
$68$			5.64241i			0.684242i
$69$	−2.73755	+	4.74158i	−0.329563	+	0.570819i
$70$	2.44057	+	1.43107i	0.291704	+	0.171046i
$71$	−11.5265	+	2.03243i	−1.36794	+	0.241205i	−0.808907	−	0.587937i	$-0.799940\pi$
$71$	−11.5265	+	2.03243i	−1.36794	+	0.241205i	−0.559037	+	0.829142i	$0.688829\pi$
$72$	−0.642788	+	0.766044i	−0.0757532	+	0.0902792i
$73$	3.23890	−	0.571106i	0.379085	−	0.0668429i	0.0191408	−	0.999817i	$-0.493907\pi$
$73$	3.23890	−	0.571106i	0.379085	−	0.0668429i	0.359944	+	0.932974i	$0.382796\pi$
$74$	−9.41599	−	3.42714i	−1.09459	−	0.398397i
$75$	−1.92826	+	3.33985i	−0.222656	+	0.385652i
$76$	4.01385	−	1.69970i	0.460420	−	0.194969i
$77$	−7.32139	−	8.84565i	−0.834349	−	1.00806i
$78$	3.02692	+	3.60734i	0.342731	+	0.408451i
$79$	−4.59898	−	5.48085i	−0.517426	−	0.616644i	0.442544	−	0.896747i	$-0.354076\pi$
$79$	−4.59898	−	5.48085i	−0.517426	−	0.616644i	−0.959970	+	0.280103i	$0.909631\pi$
$80$	−0.365734	−	1.00485i	−0.0408903	−	0.112345i
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$	5.52364	+	0.973968i	0.609985	+	0.107557i
$83$	3.27774	+	1.89240i	0.359778	+	0.207718i	0.668984	−	0.743277i	$-0.266730\pi$
$83$	3.27774	+	1.89240i	0.359778	+	0.207718i	−0.309205	+	0.950995i	$0.600063\pi$
$84$	−2.60859	+	0.441863i	−0.284621	+	0.0482112i
$85$	4.62202	+	3.87834i	0.501329	+	0.420665i
$86$	−2.04545	−	5.61982i	−0.220566	−	0.606000i
$87$	5.75565	+	3.32303i	0.617071	+	0.356266i
$88$			4.33999i			0.462644i
$89$	−1.07987	+	6.12423i	−0.114466	+	0.649167i	0.872548	+	0.488529i	$0.162466\pi$
$89$	−1.07987	+	6.12423i	−0.114466	+	0.649167i	−0.987013	+	0.160638i	$0.948645\pi$
$90$	0.185688	+	1.05309i	0.0195732	+	0.111005i
$91$	−0.0839488	+	12.4587i	−0.00880023	+	1.30603i
$92$	5.14492	+	1.87260i	0.536395	+	0.195232i
$93$	−1.08504	−	6.15355i	−0.112513	−	0.638094i
$94$	4.27672	+	7.40750i	0.441110	+	0.764025i
$95$	1.36662	−	4.45628i	0.140212	−	0.457205i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	4.53730	−	3.80725i	0.460693	−	0.386568i	−0.382693	−	0.923876i	$-0.625003\pi$
$97$	4.53730	−	3.80725i	0.460693	−	0.386568i	0.843386	+	0.537308i	$0.180559\pi$
$98$	−6.01446	−	3.58137i	−0.607552	−	0.361773i
$99$	0.753631	−	4.27405i	0.0757427	−	0.429558i
$100$	3.62395	+	1.31901i	0.362395	+	0.131901i
$101$	−5.40838	+	6.44546i	−0.538154	+	0.641347i	−0.964773	−	0.263085i	$-0.915260\pi$
$101$	−5.40838	+	6.44546i	−0.538154	+	0.641347i	0.426619	+	0.904431i	$0.359705\pi$
$102$	−5.64241			−0.558682
$103$	9.13390			0.899990			0.449995	−	0.893031i	$-0.351426\pi$
$103$	9.13390			0.899990			0.449995	+	0.893031i	$0.351426\pi$
$104$	3.02692	−	3.60734i	0.296814	−	0.353729i
$105$	−1.43107	+	2.44057i	−0.139659	+	0.238175i
$106$	−5.67858	−	9.83559i	−0.551552	−	0.955317i
$107$	−17.3343	+	10.0080i	−1.67577	+	0.967507i	−0.711462	+	0.702724i	$0.751967\pi$
$107$	−17.3343	+	10.0080i	−1.67577	+	0.967507i	−0.964308	+	0.264782i	$0.914700\pi$
$108$	−0.766044	−	0.642788i	−0.0737127	−	0.0618523i
$109$	−11.1885	−	13.3339i	−1.07166	−	1.27716i	−0.958964	−	0.283529i	$-0.908495\pi$
$109$	−11.1885	−	13.3339i	−1.07166	−	1.27716i	−0.112699	−	0.993629i	$-0.535950\pi$
$110$	3.55513	+	2.98311i	0.338969	+	0.284429i
$111$	3.42714	−	9.41599i	0.325290	−	0.893727i
$112$	0.888128	+	2.49223i	0.0839202	+	0.235494i
$113$			0.609169i			0.0573058i	0.999589	+	0.0286529i	$0.00912175\pi$
$113$			0.609169i			0.0573058i	−0.999589	+	0.0286529i	$0.990878\pi$
$114$	1.69970	+	4.01385i	0.159192	+	0.375932i
$115$	5.07034	−	2.92736i	0.472812	−	0.272978i
$116$	2.27309	−	6.24525i	0.211051	−	0.579857i
$117$	−3.60734	+	3.02692i	−0.333499	+	0.279839i
$118$	−1.59970	−	0.282071i	−0.147265	−	0.0259667i
$119$	−11.3709	−	9.67263i	−1.04237	−	0.886689i
$120$	1.00485	−	0.365734i	0.0917295	−	0.0333868i
$121$	−3.91774	−	6.78572i	−0.356158	−	0.616883i
$122$	2.64702	−	4.58478i	0.239650	−	0.415086i
$123$	−0.973968	+	5.52364i	−0.0878197	+	0.498050i
$124$	−5.87165	+	2.13711i	−0.527290	+	0.191918i
$125$	8.20177	−	4.73530i	0.733589	−	0.423538i
$126$	−0.441863	−	2.60859i	−0.0393643	−	0.232392i
$127$	−5.99392	−	16.4682i	−0.531875	−	1.46131i	−0.856837	−	0.515587i	$-0.827574\pi$
$127$	−5.99392	−	16.4682i	−0.531875	−	1.46131i	0.324962	−	0.945727i	$-0.394648\pi$
$128$	0.342020	−	0.939693i	0.0302306	−	0.0830579i
$129$	5.61982	−	2.04545i	0.494797	−	0.180091i
$130$	−0.874414	−	4.95905i	−0.0766912	−	0.434937i
$131$	8.84900	−	1.56032i	0.773141	−	0.136326i	0.226860	−	0.973927i	$-0.427154\pi$
$131$	8.84900	−	1.56032i	0.773141	−	0.136326i	0.546281	+	0.837602i	$0.316043\pi$
$132$	−4.33999			−0.377747
$133$	−3.45550	+	11.0027i	−0.299630	+	0.954055i
$134$	8.65913			0.748035
$135$	−1.05309	+	0.185688i	−0.0906355	+	0.0159815i
$136$	0.979794	+	5.55669i	0.0840166	+	0.476482i
$137$	−5.86131	+	2.13334i	−0.500765	+	0.182264i	−0.580038	−	0.814589i	$-0.696962\pi$
$137$	−5.86131	+	2.13334i	−0.500765	+	0.182264i	0.0792730	+	0.996853i	$0.474740\pi$
$138$	−1.87260	+	5.14492i	−0.159406	+	0.437964i
$139$	−3.76077	−	10.3326i	−0.318984	−	0.876402i	−0.990757	−	0.135645i	$-0.956689\pi$
$139$	−3.76077	−	10.3326i	−0.318984	−	0.876402i	0.671773	−	0.740757i	$-0.265533\pi$
$140$	2.65199	+	0.985533i	0.224134	+	0.0832928i
$141$	−7.40750	+	4.27672i	−0.623824	+	0.360165i
$142$	−10.9985	+	4.00311i	−0.922970	+	0.335934i
$143$	−3.54888	+	20.1267i	−0.296772	+	1.68308i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−3.55343	−	6.15472i	−0.295096	−	0.511122i
$146$	3.09052	−	1.12486i	0.255774	−	0.0930940i
$147$	3.58137	−	6.01446i	0.295387	−	0.496064i
$148$	−9.86806	−	1.74001i	−0.811150	−	0.143028i
$149$	10.7021	−	8.98013i	0.876750	−	0.735681i	−0.0887579	−	0.996053i	$-0.528290\pi$
$149$	10.7021	−	8.98013i	0.876750	−	0.735681i	0.965508	+	0.260372i	$0.0838453\pi$
$150$	−1.31901	+	3.62395i	−0.107697	+	0.295894i
$151$	20.0418	−	11.5711i	1.63098	−	0.941646i	0.647188	−	0.762331i	$-0.275945\pi$
$151$	20.0418	−	11.5711i	1.63098	−	0.941646i	0.983792	−	0.179316i	$-0.0573884\pi$
$152$	3.65772	−	2.37088i	0.296680	−	0.192304i
$153$		−	5.64241i		−	0.456162i
$154$	−8.74619	−	7.43992i	−0.704788	−	0.599526i
$155$	−2.28528	+	6.27877i	−0.183558	+	0.504323i
$156$	3.60734	+	3.02692i	0.288818	+	0.242347i
$157$	8.97189	+	10.6923i	0.716035	+	0.853337i	0.994239	−	0.107185i	$-0.0341836\pi$
$157$	8.97189	+	10.6923i	0.716035	+	0.853337i	−0.278204	+	0.960522i	$0.589739\pi$
$158$	−5.48085	−	4.59898i	−0.436033	−	0.365875i
$159$	9.83559	−	5.67858i	0.780013	−	0.450341i
$160$	−0.534668	−	0.926071i	−0.0422692	−	0.0732124i
$161$	−12.5936	+	7.15819i	−0.992512	+	0.564145i
$162$	0.642788	−	0.766044i	0.0505022	−	0.0601861i
$163$	13.4388			1.05261			0.526305	−	0.850296i	$-0.323577\pi$
$163$	13.4388			1.05261			0.526305	+	0.850296i	$0.323577\pi$
$164$	5.60886			0.437978
$165$	−2.98311	+	3.55513i	−0.232235	+	0.276767i
$166$	3.55655	+	1.29448i	0.276042	+	0.100471i
$167$	3.68088	−	20.8753i	0.284835	−	1.61538i	−0.421038	−	0.907043i	$-0.638334\pi$
$167$	3.68088	−	20.8753i	0.284835	−	1.61538i	0.705873	−	0.708338i	$-0.250555\pi$
$168$	−2.49223	+	0.888128i	−0.192280	+	0.0685205i
$169$	7.02856	−	5.89766i	0.540659	−	0.453666i
$170$	5.22527	+	3.01681i	0.400760	+	0.231379i
$171$	−4.01385	+	1.69970i	−0.306947	+	0.129980i
$172$	−2.99024	−	5.17925i	−0.228004	−	0.394914i
$173$	−3.36601	−	19.0896i	−0.255913	−	1.45135i	−0.793718	−	0.608286i	$-0.791858\pi$
$173$	−3.36601	−	19.0896i	−0.255913	−	1.45135i	0.537805	−	0.843069i	$-0.319254\pi$
$174$	6.24525	+	2.27309i	0.473451	+	0.172322i
$175$	−8.87058	+	5.04204i	−0.670553	+	0.381143i
$176$	0.753631	+	4.27405i	0.0568070	+	0.322169i
$177$	0.282071	−	1.59970i	0.0212017	−	0.120241i
$178$			6.21870i			0.466112i
$179$	−7.87130	−	4.54450i	−0.588329	−	0.339672i	0.176108	−	0.984371i	$-0.443649\pi$
$179$	−7.87130	−	4.54450i	−0.588329	−	0.339672i	−0.764436	+	0.644699i	$0.776983\pi$
$180$	0.365734	+	1.00485i	0.0272602	+	0.0748968i
$181$	−0.273711	−	0.229671i	−0.0203448	−	0.0170713i	0.632559	−	0.774513i	$-0.282005\pi$
$181$	−0.273711	−	0.229671i	−0.0203448	−	0.0170713i	−0.652903	+	0.757441i	$0.726449\pi$
$182$	2.08075	+	12.2840i	0.154236	+	0.910550i
$183$	4.58478	+	2.64702i	0.338917	+	0.195674i
$184$	5.39193	+	0.950742i	0.397498	+	0.0700896i
$185$	−8.20821	+	6.88750i	−0.603479	+	0.506379i
$186$	−2.13711	−	5.87165i	−0.156700	−	0.430531i
$187$	−15.7406	−	18.7589i	−1.15106	−	1.37178i
$188$	5.49805	+	6.55232i	0.400986	+	0.477877i
$189$	2.60859	−	0.441863i	0.189747	−	0.0321408i
$190$	0.572030	−	4.62589i	0.0414994	−	0.335597i
$191$	8.25249	−	14.2937i	0.597129	−	1.03426i	−0.396114	−	0.918202i	$-0.629641\pi$
$191$	8.25249	−	14.2937i	0.597129	−	1.03426i	0.993243	−	0.116056i	$-0.0370253\pi$
$192$	0.939693	+	0.342020i	0.0678165	+	0.0246832i
$193$	12.5636	−	2.21530i	0.904348	−	0.159461i	0.297912	−	0.954593i	$-0.403710\pi$
$193$	12.5636	−	2.21530i	0.904348	−	0.159461i	0.606436	+	0.795132i	$0.292599\pi$
$194$	3.80725	−	4.53730i	0.273345	−	0.325759i
$195$	4.95905	−	0.874414i	0.355125	−	0.0626181i
$196$	−6.54499	−	2.48256i	−0.467499	−	0.177326i
$197$	−3.19564	+	5.53500i	−0.227680	+	0.394353i	−0.957120	−	0.289692i	$-0.906447\pi$
$197$	−3.19564	+	5.53500i	−0.227680	+	0.394353i	0.729440	+	0.684044i	$0.239781\pi$
$198$		−	4.33999i		−	0.308429i
$199$	−21.7053	−	3.82723i	−1.53865	−	0.271305i	−0.660916	−	0.750460i	$-0.729832\pi$
$199$	−21.7053	−	3.82723i	−1.53865	−	0.271305i	−0.877730	+	0.479155i	$0.840943\pi$
$200$	3.79793	+	0.669678i	0.268554	+	0.0473534i
$201$			8.65913i			0.610768i
$202$	−4.20697	+	7.28669i	−0.296002	+	0.512690i
$203$	8.68910	+	15.2869i	0.609855	+	1.07293i
$204$	−5.55669	+	0.979794i	−0.389046	+	0.0685993i
$205$	3.85528	−	4.59454i	0.269264	−	0.320897i
$206$	8.99514	−	1.58609i	0.626721	−	0.110508i
$207$	−5.14492	−	1.87260i	−0.357596	−	0.130154i
$208$	2.35452	−	4.07816i	0.163257	−	0.282769i
$209$	−8.60290	+	16.8483i	−0.595075	+	1.16542i
$210$	−0.985533	+	2.65199i	−0.0680083	+	0.183005i
$211$	2.64423	+	3.15127i	0.182036	+	0.216943i	0.849344	−	0.527840i	$-0.176998\pi$
$211$	2.64423	+	3.15127i	0.182036	+	0.216943i	−0.667308	+	0.744782i	$0.732553\pi$
$212$	−7.30024	−	8.70009i	−0.501383	−	0.597525i
$213$	−4.00311	−	10.9985i	−0.274289	−	0.753602i
$214$	−15.3331	+	12.8660i	−1.04815	+	0.879501i
$215$	−6.29799	−	1.11050i	−0.429519	−	0.0757358i
$216$	−0.866025	−	0.500000i	−0.0589256	−	0.0340207i
$217$	5.75880	−	15.4965i	0.390933	−	1.05197i
$218$	−13.3339	−	11.1885i	−0.903087	−	0.757780i
$219$	1.12486	+	3.09052i	0.0760109	+	0.208838i
$220$	4.01914	+	2.32045i	0.270970	+	0.156445i
$221$			26.5704i			1.78732i
$222$	1.74001	−	9.86806i	0.116782	−	0.662301i
$223$	4.19519	+	23.7921i	0.280930	+	1.59324i	0.719470	+	0.694523i	$0.244385\pi$
$223$	4.19519	+	23.7921i	0.280930	+	1.59324i	−0.438540	+	0.898712i	$0.644504\pi$
$224$	1.30741	+	2.30015i	0.0873548	+	0.153685i
$225$	−3.62395	−	1.31901i	−0.241596	−	0.0879339i
$226$	0.105781	+	0.599915i	0.00703646	+	0.0399057i
$227$	−2.51146	−	4.34998i	−0.166692	−	0.288718i	0.770563	−	0.637364i	$-0.219975\pi$
$227$	−2.51146	−	4.34998i	−0.166692	−	0.288718i	−0.937255	+	0.348645i	$0.886642\pi$
$228$	2.37088	+	3.65772i	0.157015	+	0.242239i
$229$	−2.62312	−	1.51446i	−0.173341	−	0.100078i	0.410819	−	0.911717i	$-0.365243\pi$
$229$	−2.62312	−	1.51446i	−0.173341	−	0.100078i	−0.584160	+	0.811638i	$0.698576\pi$
$230$	4.48498	−	3.76334i	0.295731	−	0.248148i
$231$	7.43992	−	8.74619i	0.489511	−	0.575457i
$232$	1.15408	−	6.54509i	0.0757688	−	0.429706i
$233$	−14.7556	−	5.37059i	−0.966670	−	0.351839i	−0.190026	−	0.981779i	$-0.560857\pi$
$233$	−14.7556	−	5.37059i	−0.966670	−	0.351839i	−0.776644	+	0.629940i	$0.783079\pi$
$234$	−3.02692	+	3.60734i	−0.197876	+	0.235819i
$235$	9.14650			0.596652
$236$	−1.62438			−0.105738
$237$	4.59898	−	5.48085i	0.298736	−	0.356019i
$238$	−12.8778	−	7.55114i	−0.834743	−	0.489468i
$239$	10.2446	+	17.7441i	0.662667	+	1.14777i	0.979912	+	0.199429i	$0.0639087\pi$
$239$	10.2446	+	17.7441i	0.662667	+	1.14777i	−0.317246	+	0.948343i	$0.602758\pi$
$240$	0.926071	−	0.534668i	0.0597777	−	0.0345126i
$241$	2.94728	+	2.47306i	0.189851	+	0.159304i	0.732759	−	0.680488i	$-0.238232\pi$
$241$	2.94728	+	2.47306i	0.189851	+	0.159304i	−0.542908	+	0.839792i	$0.682677\pi$
$242$	−5.03654	−	6.00232i	−0.323761	−	0.385844i
$243$	0.766044	+	0.642788i	0.0491418	+	0.0412348i
$244$	1.81067	−	4.97478i	0.115916	−	0.318477i
$245$	−6.53235	+	3.65498i	−0.417336	+	0.233508i
$246$			5.60886i			0.357608i
$247$	18.9014	−	8.00398i	1.20267	−	0.509281i
$248$	−5.41135	+	3.12424i	−0.343621	+	0.198390i
$249$	−1.29448	+	3.55655i	−0.0820343	+	0.225387i
$250$	7.25489	−	6.08758i	0.458840	−	0.385012i
$251$	−2.78226	−	0.490588i	−0.175615	−	0.0309656i	0.0851492	−	0.996368i	$-0.472863\pi$
$251$	−2.78226	−	0.490588i	−0.175615	−	0.0309656i	−0.260764	+	0.965403i	$0.583974\pi$
$252$	−0.888128	−	2.49223i	−0.0559468	−	0.156996i
$253$	−22.3289	+	8.12704i	−1.40380	+	0.510943i
$254$	−8.76253	−	15.1771i	−0.549810	−	0.952299i
$255$	−3.01681	+	5.22527i	−0.188920	+	0.327219i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	8.51176	−	3.09803i	0.530949	−	0.193250i	−0.0626130	−	0.998038i	$-0.519943\pi$
$257$	8.51176	−	3.09803i	0.530949	−	0.193250i	0.593562	+	0.804788i	$0.297721\pi$
$258$	5.17925	−	2.99024i	0.322446	−	0.186164i
$259$	20.4231	−	16.9038i	1.26903	−	1.05035i
$260$	−1.72226	−	4.73187i	−0.106810	−	0.293458i
$261$	−2.27309	+	6.24525i	−0.140700	+	0.386571i
$262$	8.44362	−	3.07323i	0.521649	−	0.189865i
$263$	2.72800	+	15.4713i	0.168216	+	0.953998i	0.945687	+	0.325080i	$0.105391\pi$
$263$	2.72800	+	15.4713i	0.168216	+	0.953998i	−0.777471	+	0.628919i	$0.783498\pi$
$264$	−4.27405	+	0.753631i	−0.263050	+	0.0463828i
$265$	−12.1446			−0.746038
$266$	−1.49241	+	11.4356i	−0.0915053	+	0.701161i
$267$	−6.21870			−0.380579
$268$	8.52757	−	1.50364i	0.520905	−	0.0918495i
$269$	1.33944	+	7.59636i	0.0816673	+	0.463158i	0.998026	+	0.0628003i	$0.0200031\pi$
$269$	1.33944	+	7.59636i	0.0816673	+	0.463158i	−0.916359	+	0.400358i	$0.868886\pi$
$270$	−1.00485	+	0.365734i	−0.0611530	+	0.0222579i
$271$	−8.37130	+	23.0000i	−0.508520	+	1.39715i	0.374243	+	0.927331i	$0.377903\pi$
$271$	−8.37130	+	23.0000i	−0.508520	+	1.39715i	−0.882764	+	0.469818i	$0.844320\pi$
$272$	1.92982	+	5.30213i	0.117012	+	0.321489i
$273$	−12.2840	+	2.08075i	−0.743461	+	0.125933i
$274$	−5.40181	+	3.11874i	−0.326335	+	0.188410i
$275$	−15.7279	+	5.72448i	−0.948426	+	0.345199i
$276$	−0.950742	+	5.39193i	−0.0572280	+	0.324556i
$277$	−8.12709	+	14.0765i	−0.488310	+	0.845777i	−0.999910	−	0.0134467i	$-0.995720\pi$
$277$	−8.12709	+	14.0765i	−0.488310	+	0.845777i	0.511600	+	0.859224i	$0.329053\pi$
$278$	−5.49788	−	9.52260i	−0.329741	−	0.571128i
$279$	5.87165	−	2.13711i	0.351527	−	0.127945i
$280$	2.78284	+	0.510047i	0.166306	+	0.0304811i
$281$	−3.71346	−	0.654782i	−0.221526	−	0.0390610i	0.0617833	−	0.998090i	$-0.480321\pi$
$281$	−3.71346	−	0.654782i	−0.221526	−	0.0390610i	−0.283309	+	0.959029i	$0.591432\pi$
$282$	−6.55232	+	5.49805i	−0.390185	+	0.327404i
$283$	−4.50396	+	12.3745i	−0.267733	+	0.735590i	0.730859	+	0.682529i	$0.239120\pi$
$283$	−4.50396	+	12.3745i	−0.267733	+	0.735590i	−0.998591	+	0.0530608i	$0.983102\pi$
$284$	−10.1362	+	5.85216i	−0.601475	+	0.347262i
$285$	4.62589	+	0.572030i	0.274014	+	0.0338842i
$286$			20.4372i			1.20848i
$287$	−9.61512	+	11.3033i	−0.567562	+	0.667212i
$288$	−0.342020	+	0.939693i	−0.0201537	+	0.0553719i
$289$	−11.3656	−	9.53688i	−0.668565	−	0.560993i
$290$	−4.56820	−	5.44417i	−0.268254	−	0.319693i
$291$	4.53730	+	3.80725i	0.265982	+	0.223185i
$292$	2.84824	−	1.64443i	0.166681	−	0.0962332i
$293$	−7.32020	−	12.6790i	−0.427650	−	0.740712i	0.569013	−	0.822328i	$-0.307325\pi$
$293$	−7.32020	−	12.6790i	−0.427650	−	0.740712i	−0.996664	+	0.0816160i	$0.973992\pi$
$294$	2.48256	−	6.54499i	0.144786	−	0.381711i
$295$	−1.11653	+	1.33063i	−0.0650067	+	0.0774720i
$296$	−10.0203			−0.582418
$297$	4.33999			0.251831
$298$	8.98013	−	10.7021i	0.520205	−	0.619956i
$299$	24.2277	+	8.81815i	1.40112	+	0.509967i
$300$	−0.669678	+	3.79793i	−0.0386639	+	0.219274i
$301$	15.5636	+	2.85255i	0.897072	+	0.164418i
$302$	17.7280	−	14.8756i	1.02013	−	0.855993i
$303$	−7.28669	−	4.20697i	−0.418609	−	0.241684i
$304$	3.19045	−	2.97002i	0.182985	−	0.170342i
$305$	−2.83056	−	4.90267i	−0.162077	−	0.280726i
$306$	−0.979794	−	5.55669i	−0.0560111	−	0.317655i
$307$	27.5530	+	10.0285i	1.57253	+	0.572356i	0.973564	−	0.228415i	$-0.0733542\pi$
$307$	27.5530	+	10.0285i	1.57253	+	0.572356i	0.598971	+	0.800771i	$0.295576\pi$
$308$	−9.90524	−	5.80813i	−0.564404	−	0.330949i
$309$	1.58609	+	8.99514i	0.0902293	+	0.511716i
$310$	−1.16027	+	6.58021i	−0.0658989	+	0.373731i
$311$			16.2702i			0.922599i	0.887244	+	0.461300i	$0.152617\pi$
$311$			16.2702i			0.922599i	−0.887244	+	0.461300i	$0.847383\pi$
$312$	4.07816	+	2.35452i	0.230880	+	0.133299i
$313$	2.26094	+	6.21188i	0.127796	+	0.351116i	0.987046	−	0.160440i	$-0.0512913\pi$
$313$	2.26094	+	6.21188i	0.127796	+	0.351116i	−0.859250	+	0.511556i	$0.829069\pi$
$314$	10.6923	+	8.97189i	0.603400	+	0.506313i
$315$	−2.65199	−	0.985533i	−0.149423	−	0.0555285i
$316$	−6.19619	−	3.57737i	−0.348563	−	0.201243i
$317$	9.46183	+	1.66838i	0.531429	+	0.0937053i	0.432923	−	0.901431i	$-0.357482\pi$
$317$	9.46183	+	1.66838i	0.531429	+	0.0937053i	0.0985066	+	0.995136i	$0.468593\pi$
$318$	8.70009	−	7.30024i	0.487877	−	0.409377i
$319$	9.86516	+	27.1043i	0.552343	+	1.51755i
$320$	−0.687355	−	0.819158i	−0.0384243	−	0.0457923i
$321$	−12.8660	−	15.3331i	−0.718110	−	0.855810i
$322$	−11.1592	+	9.23629i	−0.621880	+	0.514718i
$323$	−7.21103	+	23.5138i	−0.401233	+	1.30834i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	17.0653	+	6.21127i	0.946614	+	0.344539i
$326$	13.2347	−	2.33363i	0.733000	−	0.129248i
$327$	11.1885	−	13.3339i	0.618725	−	0.737368i
$328$	5.52364	−	0.973968i	0.304992	−	0.0537784i
$329$	−22.6298	−	0.152483i	−1.24762	−	0.00840668i
$330$	−2.32045	+	4.01914i	−0.127737	+	0.221246i
$331$		−	22.9844i		−	1.26334i	−0.775238	−	0.631670i	$-0.782370\pi$
$331$		−	22.9844i		−	1.26334i	0.775238	−	0.631670i	$-0.217630\pi$
$332$	3.72730	+	0.657224i	0.204562	+	0.0360699i
$333$	9.86806	+	1.74001i	0.540766	+	0.0953517i
$334$		−	21.1974i		−	1.15987i
$335$	4.62975	−	8.01897i	0.252951	−	0.438123i
$336$	−2.30015	+	1.30741i	−0.125483	+	0.0713249i
$337$	−10.7894	+	1.90247i	−0.587738	+	0.103634i	−0.459606	−	0.888123i	$-0.652009\pi$
$337$	−10.7894	+	1.90247i	−0.587738	+	0.103634i	−0.128132	+	0.991757i	$0.540898\pi$
$338$	5.89766	−	7.02856i	0.320791	−	0.382303i
$339$	−0.599915	+	0.105781i	−0.0325829	+	0.00574524i
$340$	5.66975	+	2.06362i	0.307485	+	0.111916i
$341$	13.5592	−	23.4852i	0.734270	−	1.27179i
$342$	−3.65772	+	2.37088i	−0.197787	+	0.128202i
$343$	16.2229	−	8.93404i	0.875955	−	0.482393i
$344$	−3.84418	−	4.58132i	−0.207264	−	0.247008i
$345$	3.76334	+	4.48498i	0.202612	+	0.241463i
$346$	−6.62974	−	18.2151i	−0.356417	−	0.979248i
$347$	9.31521	−	7.81639i	0.500067	−	0.419606i	−0.357551	−	0.933894i	$-0.616388\pi$
$347$	9.31521	−	7.81639i	0.500067	−	0.419606i	0.857618	+	0.514288i	$0.171944\pi$
$348$	6.54509	+	1.15408i	0.350854	+	0.0618649i
$349$	−16.4221	−	9.48131i	−0.879055	−	0.507523i	−0.00870861	−	0.999962i	$-0.502772\pi$
$349$	−16.4221	−	9.48131i	−0.879055	−	0.507523i	−0.870347	+	0.492439i	$0.836105\pi$
$350$	−7.86027	+	6.50580i	−0.420149	+	0.347750i
$351$	−3.60734	−	3.02692i	−0.192546	−	0.161565i
$352$	1.48436	+	4.07825i	0.0791168	+	0.217372i
$353$	−12.8332	−	7.40927i	−0.683044	−	0.394355i	0.117957	−	0.993019i	$-0.462365\pi$
$353$	−12.8332	−	7.40927i	−0.683044	−	0.394355i	−0.801001	+	0.598663i	$0.795699\pi$
$354$		−	1.62438i		−	0.0863349i
$355$	−2.17335	+	12.3257i	−0.115350	+	0.654180i
$356$	1.07987	+	6.12423i	0.0572328	+	0.324583i
$357$	7.55114	−	12.8778i	0.399649	−	0.681565i
$358$	−8.54086	−	3.10862i	−0.451399	−	0.164296i
$359$	3.27655	+	18.5822i	0.172930	+	0.980734i	0.940506	+	0.339776i	$0.110351\pi$
$359$	3.27655	+	18.5822i	0.172930	+	0.980734i	−0.767577	+	0.640957i	$0.778538\pi$
$360$	0.534668	+	0.926071i	0.0281795	+	0.0488083i
$361$	18.8993	−	1.95351i	0.994700	−	0.102816i
$362$	−0.309435	−	0.178652i	−0.0162635	−	0.00938975i
$363$	6.00232	−	5.03654i	0.315040	−	0.264350i
$364$	4.18224	+	11.7360i	0.219209	+	0.615136i
$365$	0.610704	−	3.46347i	0.0319657	−	0.181286i
$366$	4.97478	+	1.81067i	0.260036	+	0.0946453i
$367$	18.0998	−	21.5705i	0.944802	−	1.12597i	−0.0470908	−	0.998891i	$-0.514995\pi$
$367$	18.0998	−	21.5705i	0.944802	−	1.12597i	0.991892	−	0.127080i	$-0.0405605\pi$
$368$	5.47511			0.285410
$369$	−5.60886			−0.291985
$370$	−6.88750	+	8.20821i	−0.358064	+	0.426724i
$371$	30.0475	+	0.202466i	1.55999	+	0.0105115i
$372$	−3.12424	−	5.41135i	−0.161984	−	0.280565i
$373$	−8.98765	+	5.18902i	−0.465363	+	0.268677i	−0.714297	−	0.699843i	$-0.753253\pi$
$373$	−8.98765	+	5.18902i	−0.465363	+	0.268677i	0.248934	+	0.968521i	$0.419920\pi$
$374$	−18.7589	−	15.7406i	−0.969998	−	0.813925i
$375$	6.08758	+	7.25489i	0.314361	+	0.374641i
$376$	6.55232	+	5.49805i	0.337910	+	0.283540i
$377$	10.7041	−	29.4092i	0.551288	−	1.51465i
$378$	2.49223	−	0.888128i	0.128187	−	0.0456804i
$379$		−	6.71133i		−	0.344738i	−0.985032	−	0.172369i	$-0.944858\pi$
$379$		−	6.71133i		−	0.344738i	0.985032	−	0.172369i	$-0.0551421\pi$
$380$	−0.239937	−	4.65494i	−0.0123085	−	0.238794i
$381$	15.1771	−	8.76253i	0.777549	−	0.448918i
$382$	5.64503	−	15.5096i	0.288825	−	0.793540i
$383$	7.62784	−	6.40052i	0.389764	−	0.327051i	−0.426757	−	0.904366i	$-0.640344\pi$
$383$	7.62784	−	6.40052i	0.389764	−	0.327051i	0.816521	+	0.577315i	$0.195900\pi$
$384$	0.984808	+	0.173648i	0.0502558	+	0.00886145i
$385$	−11.5662	+	4.12171i	−0.589468	+	0.210062i
$386$	11.9881	−	4.36329i	0.610176	−	0.222086i
$387$	2.99024	+	5.17925i	0.152003	+	0.263276i
$388$	2.96152	−	5.12950i	0.150348	−	0.260411i
$389$	−1.02069	+	5.78865i	−0.0517513	+	0.293496i	−0.999688	−	0.0249615i	$-0.992054\pi$
$389$	−1.02069	+	5.78865i	−0.0517513	+	0.293496i	0.947937	+	0.318457i	$0.103165\pi$
$390$	4.73187	−	1.72226i	0.239608	−	0.0872100i
$391$	−26.7539	+	15.4464i	−1.35300	+	0.781157i
$392$	−6.87665	−	1.30832i	−0.347323	−	0.0660803i
$393$	3.07323	+	8.44362i	0.155024	+	0.425924i
$394$	−2.18594	+	6.00583i	−0.110126	+	0.302569i
$395$	−7.18942	+	2.61673i	−0.361739	+	0.131662i
$396$	−0.753631	−	4.27405i	−0.0378714	−	0.214779i
$397$	27.2438	−	4.80382i	1.36733	−	0.241097i	0.558676	−	0.829386i	$-0.311309\pi$
$397$	27.2438	−	4.80382i	1.36733	−	0.241097i	0.808651	+	0.588289i	$0.200198\pi$
$398$	−22.0401			−1.10477
$399$	−11.4356	−	1.49241i	−0.572496	−	0.0747137i
$400$	3.85652			0.192826
$401$	−21.6263	+	3.81330i	−1.07996	+	0.190427i	−0.685200	−	0.728355i	$-0.740285\pi$
$401$	−21.6263	+	3.81330i	−1.07996	+	0.190427i	−0.394765	+	0.918782i	$0.629174\pi$
$402$	1.50364	+	8.52757i	0.0749948	+	0.425317i
$403$	−27.6499	+	10.0637i	−1.37734	+	0.501311i
$404$	−2.87774	+	7.90652i	−0.143173	+	0.393364i
$405$	−0.365734	−	1.00485i	−0.0181735	−	0.0499312i
$406$	11.2116	+	13.5458i	0.556424	+	0.672268i
$407$	37.6616	−	21.7440i	1.86682	−	1.07781i
$408$	−5.30213	+	1.92982i	−0.262494	+	0.0955402i
$409$	−2.66068	+	15.0895i	−0.131562	+	0.746126i	0.845630	+	0.533770i	$0.179225\pi$
$409$	−2.66068	+	15.0895i	−0.131562	+	0.746126i	−0.977192	+	0.212357i	$0.931886\pi$
$410$	2.99887	−	5.19420i	0.148104	−	0.256523i
$411$	−3.11874	−	5.40181i	−0.153836	−	0.266452i
$412$	8.58306	−	3.12398i	0.422857	−	0.153907i
$413$	2.78463	−	3.27355i	0.137023	−	0.161081i
$414$	−5.39193	−	0.950742i	−0.264999	−	0.0467264i
$415$	3.10035	−	2.60151i	0.152190	−	0.127703i
$416$	1.61059	−	4.42506i	0.0789656	−	0.216956i
$417$	9.52260	−	5.49788i	0.466324	−	0.269232i
$418$	−5.54653	+	18.0862i	−0.271290	+	0.884624i
$419$			29.1585i			1.42448i	0.701934	+	0.712242i	$0.252320\pi$
$419$			29.1585i			1.42448i	−0.701934	+	0.712242i	$0.747680\pi$
$420$	−0.510047	+	2.78284i	−0.0248877	+	0.135789i
$421$	−3.94533	+	10.8397i	−0.192283	+	0.528294i	−0.997945	−	0.0640822i	$-0.979588\pi$
$421$	−3.94533	+	10.8397i	−0.192283	+	0.528294i	0.805661	+	0.592377i	$0.201810\pi$
$422$	3.15127	+	2.64423i	0.153402	+	0.128719i
$423$	−5.49805	−	6.55232i	−0.267324	−	0.318585i
$424$	−8.70009	−	7.30024i	−0.422514	−	0.354531i
$425$	−18.8448	+	10.8800i	−0.914106	+	0.527759i
$426$	−5.85216	−	10.1362i	−0.283538	−	0.491102i
$427$	6.92147	+	12.1771i	0.334954	+	0.589291i
$428$	−12.8660	+	15.3331i	−0.621901	+	0.741153i
$429$	−20.4372			−0.986717
$430$	−6.39514			−0.308401
$431$	−12.8148	+	15.2721i	−0.617266	+	0.735629i	−0.980598	−	0.196031i	$-0.937195\pi$
$431$	−12.8148	+	15.2721i	−0.617266	+	0.735629i	0.363332	+	0.931660i	$0.381639\pi$
$432$	−0.939693	−	0.342020i	−0.0452110	−	0.0164555i
$433$	−1.47022	+	8.33804i	−0.0706543	+	0.400701i	0.928886	+	0.370367i	$0.120768\pi$
$433$	−1.47022	+	8.33804i	−0.0706543	+	0.400701i	−0.999540	+	0.0303335i	$0.990343\pi$
$434$	2.98038	−	16.2611i	0.143063	−	0.780556i
$435$	5.44417	−	4.56820i	0.261028	−	0.219029i
$436$	−15.0742	−	8.70310i	−0.721924	−	0.416803i
$437$	19.0474	+	14.3790i	0.911161	+	0.687840i
$438$	1.64443	+	2.84824i	0.0785741	+	0.136094i
$439$	−1.97364	−	11.1930i	−0.0941965	−	0.534215i	−0.994991	−	0.0999683i	$-0.968126\pi$
$439$	−1.97364	−	11.1930i	−0.0941965	−	0.534215i	0.900794	−	0.434246i	$-0.142985\pi$
$440$	4.36102	+	1.58728i	0.207903	+	0.0756707i
$441$	6.54499	+	2.48256i	0.311666	+	0.118217i
$442$	4.61390	+	26.1667i	0.219461	+	1.24462i
$443$	4.59768	−	26.0747i	0.218442	−	1.23885i	−0.656390	−	0.754422i	$-0.727917\pi$
$443$	4.59768	−	26.0747i	0.218442	−	1.23885i	0.874832	−	0.484426i	$-0.160972\pi$
$444$		−	10.0203i		−	0.475542i
$445$	5.75896	+	3.32494i	0.273001	+	0.157617i
$446$	8.26290	+	22.7021i	0.391260	+	1.07498i
$447$	10.7021	+	8.98013i	0.506192	+	0.424746i
$448$	1.68696	+	2.03818i	0.0797014	+	0.0962948i
$449$	22.7109	+	13.1122i	1.07180	+	0.618801i	0.928671	−	0.370904i	$-0.120952\pi$
$449$	22.7109	+	13.1122i	1.07180	+	0.618801i	0.143124	+	0.989705i	$0.454285\pi$
$450$	−3.79793	−	0.669678i	−0.179036	−	0.0315689i
$451$	−18.6473	+	15.6470i	−0.878068	+	0.736787i
$452$	0.208348	+	0.572432i	0.00979987	+	0.0269249i
$453$	14.8756	+	17.7280i	0.698916	+	0.832935i
$454$	−3.22867	−	3.84778i	−0.151529	−	0.180585i
$455$	12.4884	+	4.64092i	0.585464	+	0.217570i
$456$	2.97002	+	3.19045i	0.139084	+	0.149407i
$457$	−7.76968	+	13.4575i	−0.363450	+	0.629514i	−0.988526	−	0.151050i	$-0.951735\pi$
$457$	−7.76968	+	13.4575i	−0.363450	+	0.629514i	0.625076	+	0.780564i	$0.285068\pi$
$458$	−2.84625	−	1.03595i	−0.132997	−	0.0484068i
$459$	5.55669	−	0.979794i	0.259364	−	0.0457328i
$460$	3.76334	−	4.48498i	0.175467	−	0.209113i
$461$	35.6786	−	6.29109i	1.66172	−	0.293005i	0.737634	−	0.675200i	$-0.235943\pi$
$461$	35.6786	−	6.29109i	1.66172	−	0.293005i	0.924082	+	0.382195i	$0.124832\pi$
$462$	5.80813	−	9.90524i	0.270219	−	0.460834i
$463$	11.0248	−	19.0956i	0.512367	−	0.887446i	−0.487530	−	0.873106i	$-0.662102\pi$
$463$	11.0248	−	19.0956i	0.512367	−	0.887446i	0.999897	−	0.0143398i	$-0.00456465\pi$
$464$		−	6.64606i		−	0.308535i
$465$	−6.58021	−	1.16027i	−0.305150	−	0.0538062i
$466$	−15.4640	−	2.72672i	−0.716356	−	0.126313i
$467$			1.48173i			0.0685664i	0.999412	+	0.0342832i	$0.0109148\pi$
$467$			1.48173i			0.0685664i	−0.999412	+	0.0342832i	$0.989085\pi$
$468$	−2.35452	+	4.07816i	−0.108838	+	0.188513i
$469$	−11.5884	+	19.7629i	−0.535101	+	0.912567i
$470$	9.00754	−	1.58827i	0.415487	−	0.0732616i
$471$	−8.97189	+	10.6923i	−0.413403	+	0.492674i
$472$	−1.59970	+	0.282071i	−0.0736323	+	0.0129834i
$473$	24.3899	+	8.87720i	1.12145	+	0.408174i
$474$	3.57737	−	6.19619i	0.164314	−	0.284600i
$475$	13.4165	+	10.1282i	0.615591	+	0.464713i
$476$	−13.9934	−	5.20022i	−0.641386	−	0.238352i
$477$	7.30024	+	8.70009i	0.334255	+	0.398350i
$478$	13.1702	+	15.6956i	0.602390	+	0.717900i
$479$	4.13746	+	11.3676i	0.189046	+	0.519398i	0.997617	−	0.0690002i	$-0.0219809\pi$
$479$	4.13746	+	11.3676i	0.189046	+	0.519398i	−0.808571	+	0.588398i	$0.799759\pi$
$480$	0.819158	−	0.687355i	0.0373893	−	0.0313733i
$481$	−46.4692	−	8.19377i	−2.11881	−	0.373604i
$482$	3.33195	+	1.92370i	0.151766	+	0.0876222i
$483$	−9.23629	−	11.1592i	−0.420266	−	0.507763i
$484$	−6.00232	−	5.03654i	−0.272833	−	0.228934i
$485$	−2.16625	−	5.95174i	−0.0983646	−	0.270254i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$		−	15.1883i		−	0.688249i	−0.938924	−	0.344124i	$-0.888176\pi$
$487$		−	15.1883i		−	0.688249i	0.938924	−	0.344124i	$-0.111824\pi$
$488$	0.919301	−	5.21362i	0.0416148	−	0.236009i
$489$	2.33363	+	13.2347i	0.105530	+	0.598492i
$490$	−5.79843	+	4.73378i	−0.261946	+	0.213850i
$491$	−22.5060	−	8.19151i	−1.01568	−	0.369678i	−0.220069	−	0.975484i	$-0.570628\pi$
$491$	−22.5060	−	8.19151i	−1.01568	−	0.369678i	−0.795612	+	0.605806i	$0.792851\pi$
$492$	0.973968	+	5.52364i	0.0439099	+	0.249025i
$493$	18.7499	+	32.4757i	0.844452	+	1.46263i
$494$	17.2244	−	11.1646i	0.774962	−	0.502318i
$495$	−4.01914	−	2.32045i	−0.180647	−	0.104296i
$496$	−4.78662	+	4.01645i	−0.214925	+	0.180344i
$497$	5.58268	−	30.4593i	0.250417	−	1.36629i
$498$	−0.657224	+	3.72730i	−0.0294509	+	0.167024i
$499$	−36.6327	−	13.3332i	−1.63991	−	0.596877i	−0.652883	−	0.757459i	$-0.726441\pi$
$499$	−36.6327	−	13.3332i	−1.63991	−	0.596877i	−0.987022	+	0.160582i	$0.948663\pi$
$500$	6.08758	−	7.25489i	0.272245	−	0.324449i
$501$	21.1974			0.947028
$502$	−2.82518			−0.126094
$503$	−16.7795	+	19.9970i	−0.748161	+	0.891624i	−0.997038	−	0.0769113i	$-0.975494\pi$
$503$	−16.7795	+	19.9970i	−0.748161	+	0.891624i	0.248877	+	0.968535i	$0.419939\pi$
$504$	−1.30741	−	2.30015i	−0.0582365	−	0.102457i
$505$	4.49866	+	7.79191i	0.200188	+	0.346736i
$506$	−20.5784	+	11.8809i	−0.914821	+	0.528172i
$507$	7.02856	+	5.89766i	0.312149	+	0.261924i
$508$	−11.2649	−	13.4250i	−0.499799	−	0.595637i
$509$	−5.98068	−	5.01839i	−0.265089	−	0.222436i	0.500548	−	0.865709i	$-0.333132\pi$
$509$	−5.98068	−	5.01839i	−0.265089	−	0.222436i	−0.765637	+	0.643273i	$0.777576\pi$
$510$	−2.06362	+	5.66975i	−0.0913787	+	0.251061i
$511$	−1.56871	+	8.55895i	−0.0693956	+	0.378626i
$512$		−	1.00000i		−	0.0441942i
$513$	−2.37088	−	3.65772i	−0.104677	−	0.161492i
$514$	7.84448	−	4.52901i	0.346005	−	0.199766i
$515$	3.34058	−	9.17817i	0.147204	−	0.404438i
$516$	4.58132	−	3.84418i	0.201681	−	0.169231i
$517$	−36.5579	−	6.44614i	−1.60781	−	0.283501i
$518$	17.1775	−	20.1935i	0.754737	−	0.887250i
$519$	18.2151	−	6.62974i	0.799553	−	0.291013i
$520$	−2.51778	−	4.36092i	−0.110412	−	0.191239i
$521$	−6.48627	+	11.2346i	−0.284169	+	0.492195i	−0.972407	−	0.233290i	$-0.925051\pi$
$521$	−6.48627	+	11.2346i	−0.284169	+	0.492195i	0.688239	+	0.725485i	$0.258384\pi$
$522$	−1.15408	+	6.54509i	−0.0505125	+	0.286471i
$523$	17.8729	−	6.50521i	0.781528	−	0.284453i	0.0797185	−	0.996817i	$-0.474598\pi$
$523$	17.8729	−	6.50521i	0.781528	−	0.284453i	0.701810	+	0.712364i	$0.252376\pi$
$524$	7.78168	−	4.49276i	0.339944	−	0.196267i
$525$	−6.50580	−	7.86027i	−0.283937	−	0.343050i
$526$	5.37311	+	14.7625i	0.234279	+	0.643676i
$527$	12.0584	−	33.1303i	0.525273	−	1.44318i
$528$	−4.07825	+	1.48436i	−0.177483	+	0.0645986i
$529$	1.21151	+	6.87080i	0.0526742	+	0.298730i
$530$	−11.9601	+	2.10889i	−0.519514	+	0.0916043i
$531$	1.62438			0.0704921
$532$	0.516036	+	11.5210i	0.0223730	+	0.499499i
$533$	26.4124			1.14405
$534$	−6.12423	+	1.07987i	−0.265021	+	0.0467304i
$535$	3.71672	+	21.0786i	0.160688	+	0.911306i
$536$	8.13692	−	2.96160i	0.351461	−	0.127921i
$537$	3.10862	−	8.54086i	0.134147	−	0.368565i
$538$	2.63819	+	7.24836i	0.113740	+	0.312499i
$539$	28.6852	−	10.0049i	1.23556	−	0.430941i
$540$	−0.926071	+	0.534668i	−0.0398518	+	0.0230084i
$541$	9.70810	−	3.53346i	0.417384	−	0.151915i	−0.124787	−	0.992184i	$-0.539825\pi$
$541$	9.70810	−	3.53346i	0.417384	−	0.151915i	0.542171	+	0.840268i	$0.317603\pi$
$542$	−4.25022	+	24.1042i	−0.182563	+	1.03536i
$543$	0.178652	−	0.309435i	0.00766670	−	0.0132791i
$544$	2.82120	+	4.88647i	0.120958	+	0.209506i
$545$	−17.4906	+	6.36604i	−0.749213	+	0.272691i
$546$	−11.7360	+	4.18224i	−0.502257	+	0.178983i
$547$	−30.6323	−	5.40130i	−1.30974	−	0.230943i	−0.525179	−	0.850992i	$-0.676002\pi$
$547$	−30.6323	−	5.40130i	−1.30974	−	0.230943i	−0.784563	+	0.620049i	$0.787113\pi$
$548$	−4.77818	+	4.00937i	−0.204114	+	0.171272i
$549$	−1.81067	+	4.97478i	−0.0772775	+	0.212318i
$550$	−14.4949	+	8.36862i	−0.618064	+	0.356839i
$551$	17.4542	−	23.1210i	0.743573	−	0.984990i
$552$			5.47511i			0.233036i
$553$	17.8313	−	6.35432i	0.758264	−	0.270213i
$554$	−5.55926	+	15.2739i	−0.236190	+	0.648927i
$555$	−8.20821	−	6.88750i	−0.348419	−	0.292358i
$556$	−7.06793	−	8.42323i	−0.299747	−	0.357225i
$557$	15.3205	+	12.8554i	0.649150	+	0.544701i	0.906813	−	0.421534i	$-0.138508\pi$
$557$	15.3205	+	12.8554i	0.649150	+	0.544701i	−0.257663	+	0.966235i	$0.582952\pi$
$558$	5.41135	−	3.12424i	0.229081	−	0.132260i
$559$	−14.0812	−	24.3893i	−0.595571	−	1.03156i
$560$	2.82913	+	0.0190632i	0.119553	+	0.000805567i
$561$	15.7406	−	18.7589i	0.664567	−	0.792000i
$562$	−3.77074			−0.159059
$563$	−30.8921			−1.30195			−0.650973	−	0.759101i	$-0.725639\pi$
$563$	−30.8921			−1.30195			−0.650973	+	0.759101i	$0.725639\pi$
$564$	−5.49805	+	6.55232i	−0.231510	+	0.275902i
$565$	0.612121	+	0.222794i	0.0257521	+	0.00937301i
$566$	−2.28672	+	12.9686i	−0.0961181	+	0.545113i
$567$	0.888128	+	2.49223i	0.0372979	+	0.104664i
$568$	−8.96603	+	7.52339i	−0.376206	+	0.315674i
$569$	4.69111	+	2.70841i	0.196662	+	0.113543i	0.595097	−	0.803654i	$-0.297113\pi$
$569$	4.69111	+	2.70841i	0.196662	+	0.113543i	−0.398436	+	0.917196i	$0.630447\pi$
$570$	4.65494	−	0.239937i	0.194974	−	0.0100499i
$571$	4.92524	+	8.53076i	0.206115	+	0.357001i	0.950487	−	0.310763i	$-0.100585\pi$
$571$	4.92524	+	8.53076i	0.206115	+	0.357001i	−0.744373	+	0.667765i	$0.767251\pi$
$572$	3.54888	+	20.1267i	0.148386	+	0.841540i
$573$	15.5096	+	5.64503i	0.647923	+	0.235825i
$574$	−7.50624	+	12.8012i	−0.313305	+	0.534312i
$575$	3.66656	+	20.7941i	0.152906	+	0.867173i
$576$	−0.173648	+	0.984808i	−0.00723534	+	0.0410337i
$577$		−	28.7398i		−	1.19645i	−0.801328	−	0.598226i	$-0.795873\pi$
$577$		−	28.7398i		−	1.19645i	0.801328	−	0.598226i	$-0.204127\pi$
$578$	−12.8490	−	7.41838i	−0.534448	−	0.308564i
$579$	4.36329	+	11.9881i	0.181332	+	0.498207i
$580$	−5.44417	−	4.56820i	−0.226057	−	0.189684i
$581$	−7.71410	+	6.38482i	−0.320035	+	0.264887i
$582$	5.12950	+	2.96152i	0.212624	+	0.122759i
$583$	48.5411	+	8.55910i	2.01037	+	0.354482i
$584$	2.51942	−	2.11404i	0.104254	−	0.0874797i
$585$	1.72226	+	4.73187i	0.0712067	+	0.195639i
$586$	−9.41066	−	11.2152i	−0.388751	−	0.463295i
$587$	−20.0258	−	23.8658i	−0.826554	−	0.985049i	−1.00000		0.000205410i	$-0.999935\pi$
$587$	−20.0258	−	23.8658i	−0.826554	−	0.985049i	0.173446	−	0.984843i	$-0.444510\pi$
$588$	1.30832	−	6.87665i	0.0539544	−	0.283588i
$589$	−27.2004	+	1.40203i	−1.12077	+	0.0577698i
$590$	−0.868504	+	1.50429i	−0.0357558	+	0.0619308i
$591$	−6.00583	−	2.18594i	−0.247047	−	0.0899177i
$592$	−9.86806	+	1.74001i	−0.405575	+	0.0715138i
$593$	1.09395	−	1.30372i	0.0449231	−	0.0535372i	−0.743115	−	0.669164i	$-0.766653\pi$
$593$	1.09395	−	1.30372i	0.0449231	−	0.0535372i	0.788038	+	0.615626i	$0.211097\pi$
$594$	4.27405	−	0.753631i	0.175366	−	0.0309218i
$595$	−13.8782	+	7.88840i	−0.568952	+	0.323393i
$596$	6.98530	−	12.0989i	0.286129	−	0.495590i
$597$		−	22.0401i		−	0.902042i
$598$	25.3908	+	4.47709i	1.03831	+	0.183082i
$599$	−0.259748	−	0.0458006i	−0.0106130	−	0.00187136i	0.168339	−	0.985729i	$-0.446160\pi$
$599$	−0.259748	−	0.0458006i	−0.0106130	−	0.00187136i	−0.178952	+	0.983858i	$0.557271\pi$
$600$			3.85652i			0.157442i
$601$	−19.8478	+	34.3774i	−0.809608	+	1.40228i	0.103527	+	0.994627i	$0.466987\pi$
$601$	−19.8478	+	34.3774i	−0.809608	+	1.40228i	−0.913136	+	0.407656i	$0.866346\pi$
$602$	15.8225	+	0.106615i	0.644878	+	0.00434530i
$603$	−8.52757	+	1.50364i	−0.347270	+	0.0612330i
$604$	14.8756	−	17.7280i	0.605279	−	0.721343i
$605$	−8.25145	+	1.45495i	−0.335469	+	0.0591523i
$606$	−7.90652	−	2.87774i	−0.321180	−	0.116900i
$607$	−7.02092	+	12.1606i	−0.284970	+	0.493583i	−0.972602	−	0.232477i	$-0.925317\pi$
$607$	−7.02092	+	12.1606i	−0.284970	+	0.493583i	0.687632	+	0.726060i	$0.258650\pi$
$608$	2.62625	−	3.47891i	0.106508	−	0.141089i
$609$	−13.5458	+	11.2116i	−0.548905	+	0.454319i
$610$	−3.63889	−	4.33666i	−0.147334	−	0.175586i
$611$	25.8906	+	30.8552i	1.04742	+	1.24827i
$612$	−1.92982	−	5.30213i	−0.0780082	−	0.214326i
$613$	−0.175330	+	0.147119i	−0.00708150	+	0.00594208i	−0.646321	−	0.763065i	$-0.723693\pi$
$613$	−0.175330	+	0.147119i	−0.00708150	+	0.00594208i	0.639240	+	0.769007i	$0.279249\pi$
$614$	28.8759	+	5.09160i	1.16534	+	0.205480i
$615$	5.19420	+	2.99887i	0.209450	+	0.120926i
$616$	−10.7633	−	3.99987i	−0.433667	−	0.161159i
$617$	−17.8517	−	14.9794i	−0.718682	−	0.603046i	0.208338	−	0.978057i	$-0.433195\pi$
$617$	−17.8517	−	14.9794i	−0.718682	−	0.603046i	−0.927020	+	0.375011i	$0.877639\pi$
$618$	3.12398	+	8.58306i	0.125665	+	0.345261i
$619$	15.2036	+	8.77782i	0.611086	+	0.352811i	0.773390	−	0.633930i	$-0.218559\pi$
$619$	15.2036	+	8.77782i	0.611086	+	0.352811i	−0.162304	+	0.986741i	$0.551893\pi$
$620$			6.68172i			0.268344i
$621$	0.950742	−	5.39193i	0.0381520	−	0.216371i
$622$	2.82529	+	16.0230i	0.113284	+	0.642465i
$623$	−14.1931	−	8.32239i	−0.568634	−	0.333430i
$624$	4.42506	+	1.61059i	0.177144	+	0.0644752i
$625$	1.58981	+	9.01628i	0.0635926	+	0.360651i
$626$	3.30527	+	5.72490i	0.132105	+	0.228813i
$627$	−18.0862	−	5.54653i	−0.722293	−	0.221507i
$628$	12.0878	+	6.97889i	0.482356	+	0.278488i
$629$	43.3110	−	36.3423i	1.72692	−	1.44906i
$630$	−2.78284	−	0.510047i	−0.110871	−	0.0203208i
$631$	2.93560	−	16.6486i	0.116864	−	0.662771i	−0.868946	−	0.494907i	$-0.835202\pi$
$631$	2.93560	−	16.6486i	0.116864	−	0.662771i	0.985810	−	0.167864i	$-0.0536868\pi$
$632$	−6.72326	−	2.44707i	−0.267437	−	0.0973391i
$633$	−2.64423	+	3.15127i	−0.105099	+	0.125252i
$634$	9.60779			0.381574
$635$	−18.7402			−0.743681
$636$	7.30024	−	8.70009i	0.289473	−	0.344981i
$637$	−30.8207	−	11.6905i	−1.22116	−	0.463195i
$638$	14.4219	+	24.9795i	0.570968	+	0.988946i
$639$	10.1362	−	5.85216i	0.400983	−	0.231508i
$640$	−0.819158	−	0.687355i	−0.0323801	−	0.0271701i
$641$	−29.4544	−	35.1024i	−1.16338	−	1.38646i	−0.907657	−	0.419713i	$-0.862131\pi$
$641$	−29.4544	−	35.1024i	−1.16338	−	1.38646i	−0.255724	−	0.966750i	$-0.582314\pi$
$642$	−15.3331	−	12.8660i	−0.605149	−	0.507780i
$643$	0.266212	−	0.731412i	0.0104984	−	0.0288441i	−0.934333	−	0.356402i	$-0.884003\pi$
$643$	0.266212	−	0.731412i	0.0104984	−	0.0288441i	0.944831	+	0.327558i	$0.106226\pi$
$644$	−9.38583	+	11.0338i	−0.369854	+	0.434791i
$645$		−	6.39514i		−	0.251808i
$646$	−3.01835	+	24.4088i	−0.118755	+	0.960350i
$647$	19.1522	−	11.0575i	0.752952	−	0.434717i	−0.0738077	−	0.997272i	$-0.523515\pi$
$647$	19.1522	−	11.0575i	0.752952	−	0.434717i	0.826759	+	0.562556i	$0.190182\pi$
$648$	0.342020	−	0.939693i	0.0134358	−	0.0369146i
$649$	5.40045	−	4.53152i	0.211986	−	0.177878i
$650$	17.8846	+	3.15355i	0.701494	+	0.123692i
$651$	16.2611	+	2.98038i	0.637321	+	0.116810i
$652$	12.6284	−	4.59635i	0.494565	−	0.180007i
$653$	7.15486	+	12.3926i	0.279991	+	0.484959i	0.971382	−	0.237522i	$-0.0763351\pi$
$653$	7.15486	+	12.3926i	0.279991	+	0.484959i	−0.691391	+	0.722481i	$0.743002\pi$
$654$	8.70310	−	15.0742i	0.340318	−	0.589448i
$655$	1.66850	−	9.46255i	0.0651938	−	0.369732i
$656$	5.27060	−	1.91834i	0.205782	−	0.0748987i
$657$	−2.84824	+	1.64443i	−0.111121	+	0.0641555i
$658$	−22.3125	+	3.77945i	−0.869830	+	0.147338i
$659$	11.8936	+	32.6774i	0.463309	+	1.27293i	0.922982	+	0.384844i	$0.125745\pi$
$659$	11.8936	+	32.6774i	0.463309	+	1.27293i	−0.459672	+	0.888089i	$0.652033\pi$
$660$	−1.58728	+	4.36102i	−0.0617848	+	0.169752i
$661$	10.1653	−	3.69988i	0.395385	−	0.143908i	−0.136673	−	0.990616i	$-0.543641\pi$
$661$	10.1653	−	3.69988i	0.395385	−	0.143908i	0.532058	+	0.846708i	$0.321419\pi$
$662$	−3.99121	−	22.6353i	−0.155123	−	0.879744i
$663$	−26.1667	+	4.61390i	−1.01623	+	0.179189i
$664$	3.78480			0.146879
$665$	9.79223	+	7.49631i	0.379727	+	0.290695i
$666$	10.0203			0.388278
$667$	35.8351	−	6.31869i	1.38754	−	0.244661i
$668$	−3.68088	−	20.8753i	−0.142418	−	0.807691i
$669$	−22.7021	+	8.26290i	−0.877715	+	0.319462i
$670$	3.16694	−	8.70109i	0.122350	−	0.336153i
$671$	7.85828	+	21.5905i	0.303366	+	0.833490i
$672$	−2.03818	+	1.68696i	−0.0786244	+	0.0650759i
$673$	−35.4404	+	20.4615i	−1.36613	+	0.788733i	−0.990431	−	0.138011i	$-0.955929\pi$
$673$	−35.4404	+	20.4615i	−1.36613	+	0.788733i	−0.375695	+	0.926743i	$0.622596\pi$
$674$	−10.2952	+	3.74713i	−0.396555	+	0.144334i
$675$	0.669678	−	3.79793i	0.0257759	−	0.146183i
$676$	4.58757	−	7.94590i	0.176445	−	0.305612i
$677$	−16.2714	−	28.1829i	−0.625362	−	1.08316i	−0.988471	−	0.151412i	$-0.951618\pi$
$677$	−16.2714	−	28.1829i	−0.625362	−	1.08316i	0.363109	−	0.931747i	$-0.381715\pi$
$678$	−0.572432	+	0.208348i	−0.0219841	+	0.00800156i
$679$	5.26041	+	14.7616i	0.201876	+	0.566497i
$680$	5.94196	+	1.04773i	0.227864	+	0.0401785i
$681$	3.84778	−	3.22867i	0.147447	−	0.123723i
$682$	9.27501	−	25.4829i	0.355159	−	0.975790i
$683$	−18.7725	+	10.8383i	−0.718309	+	0.414716i	−0.814130	−	0.580683i	$-0.802786\pi$
$683$	−18.7725	+	10.8383i	−0.718309	+	0.414716i	0.0958209	+	0.995399i	$0.469452\pi$
$684$	−3.19045	+	2.97002i	−0.121990	+	0.113561i
$685$			6.66995i			0.254846i
$686$	14.4251	−	11.6154i	0.550752	−	0.443478i
$687$	1.03595	−	2.84625i	0.0395240	−	0.108591i
$688$	−4.58132	−	3.84418i	−0.174661	−	0.146558i
$689$	−34.3772	−	40.9691i	−1.30967	−	1.56080i
$690$	4.48498	+	3.76334i	0.170740	+	0.143268i
$691$	−13.9371	+	8.04657i	−0.530191	+	0.306106i	−0.741094	−	0.671401i	$-0.765693\pi$
$691$	−13.9371	+	8.04657i	−0.530191	+	0.306106i	0.210903	+	0.977507i	$0.432359\pi$
$692$	−9.69204	−	16.7871i	−0.368436	−	0.638150i
$693$	9.90524	+	5.80813i	0.376269	+	0.220633i
$694$	7.81639	−	9.31521i	0.296706	−	0.353601i
$695$	−11.7581			−0.446012
$696$	6.64606			0.251918
$697$	−20.3426	+	24.2434i	−0.770530	+	0.918282i
$698$	−17.8190	−	6.48560i	−0.674460	−	0.245484i
$699$	2.72672	−	15.4640i	0.103134	−	0.584902i
$700$	−6.61114	+	7.77189i	−0.249877	+	0.293750i
$701$	−27.9209	+	23.4285i	−1.05456	+	0.884880i	−0.993566	−	0.113258i	$-0.963871\pi$
$701$	−27.9209	+	23.4285i	−1.05456	+	0.884880i	−0.0609938	+	0.998138i	$0.519427\pi$
$702$	−4.07816	−	2.35452i	−0.153920	−	0.0888658i
$703$	−38.8998	−	19.8626i	−1.46713	−	0.749133i
$704$	2.16999	+	3.75854i	0.0817847	+	0.141655i
$705$	1.58827	+	9.00754i	0.0598178	+	0.339244i
$706$	−13.9249	−	5.06824i	−0.524069	−	0.190746i
$707$	−11.0004	−	19.3533i	−0.413714	−	0.727857i
$708$	−0.282071	−	1.59970i	−0.0106009	−	0.0601205i
$709$	−1.14314	+	6.48308i	−0.0429316	+	0.243477i	−0.998720	−	0.0505776i	$-0.983894\pi$
$709$	−1.14314	+	6.48308i	−0.0429316	+	0.243477i	0.955789	+	0.294055i	$0.0950049\pi$
$710$			12.5158i			0.469711i
$711$	6.19619	+	3.57737i	0.232375	+	0.134162i
$712$	2.12692	+	5.84367i	0.0797098	+	0.219001i
$713$	−26.2072	−	21.9905i	−0.981469	−	0.823550i
$714$	5.20022	−	13.9934i	0.194613	−	0.523689i
$715$	18.9263	+	10.9271i	0.707804	+	0.408651i
$716$	−8.95091	−	1.57829i	−0.334511	−	0.0589834i
$717$	−15.6956	+	13.1702i	−0.586163	+	0.491849i
$718$	6.45355	+	17.7310i	0.240844	+	0.661714i
$719$	−3.49421	−	4.16423i	−0.130312	−	0.155300i	0.696943	−	0.717127i	$-0.254543\pi$
$719$	−3.49421	−	4.16423i	−0.130312	−	0.155300i	−0.827255	+	0.561827i	$0.810099\pi$
$720$	0.687355	+	0.819158i	0.0256162	+	0.0305282i
$721$	−8.41809	+	22.6524i	−0.313506	+	0.843621i
$722$	18.2730	−	5.20566i	0.680049	−	0.193735i
$723$	−1.92370	+	3.33195i	−0.0715432	+	0.123916i
$724$	−0.335756	−	0.122205i	−0.0124783	−	0.00454173i
$725$	25.2413	−	4.45072i	0.937437	−	0.165296i
$726$	5.03654	−	6.00232i	0.186924	−	0.222767i
$727$	−42.6461	+	7.51966i	−1.58166	+	0.278889i	−0.894313	−	0.447442i	$-0.852335\pi$
$727$	−42.6461	+	7.51966i	−1.58166	+	0.278889i	−0.687345	+	0.726331i	$0.741224\pi$
$728$	6.15664	+	10.8315i	0.228180	+	0.401443i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$		−	3.51690i		−	0.130166i
$731$	33.2317	+	5.85964i	1.22912	+	0.216727i
$732$	5.21362	+	0.919301i	0.192701	+	0.0339784i
$733$		−	29.0087i		−	1.07146i	−0.844389	−	0.535730i	$-0.820036\pi$
$733$		−	29.0087i		−	1.07146i	0.844389	−	0.535730i	$-0.179964\pi$
$734$	14.0791	−	24.3858i	0.519671	−	0.900096i
$735$	−4.73378	−	5.79843i	−0.174608	−	0.213878i
$736$	5.39193	−	0.950742i	0.198749	−	0.0350448i
$737$	−24.1563	+	28.7883i	−0.889808	+	1.06043i
$738$	−5.52364	+	0.973968i	−0.203328	+	0.0358522i
$739$	31.6071	+	11.5040i	1.16268	+	0.423183i	0.850056	−	0.526693i	$-0.176568\pi$
$739$	31.6071	+	11.5040i	1.16268	+	0.423183i	0.312629	+	0.949875i	$0.398790\pi$
$740$	−5.35753	+	9.27951i	−0.196947	+	0.341121i
$741$	11.1646	+	17.2244i	0.410141	+	0.632754i
$742$	29.6262	−	5.01831i	1.08761	−	0.184228i
$743$	−0.324722	−	0.386989i	−0.0119129	−	0.0141972i	0.760055	−	0.649859i	$-0.225172\pi$
$743$	−0.324722	−	0.386989i	−0.0119129	−	0.0141972i	−0.771968	+	0.635661i	$0.780727\pi$
$744$	−4.01645	−	4.78662i	−0.147250	−	0.175486i
$745$	−5.10953	−	14.0383i	−0.187199	−	0.514324i
$746$	−7.95005	+	6.67088i	−0.291072	+	0.244238i
$747$	−3.72730	−	0.657224i	−0.136375	−	0.0240466i
$748$	−21.2072	−	12.2440i	−0.775412	−	0.447684i
$749$	−8.84430	−	52.2134i	−0.323164	−	1.90784i
$750$	7.25489	+	6.08758i	0.264911	+	0.222287i
$751$	15.6290	+	42.9403i	0.570309	+	1.56691i	0.804018	+	0.594606i	$0.202692\pi$
$751$	15.6290	+	42.9403i	0.570309	+	1.56691i	−0.233708	+	0.972307i	$0.575086\pi$
$752$	7.40750	+	4.27672i	0.270124	+	0.155956i
$753$		−	2.82518i		−	0.102955i
$754$	5.43460	−	30.8211i	0.197916	−	1.12244i
$755$	−4.29725	−	24.3709i	−0.156393	−	0.886948i
$756$	2.30015	−	1.30741i	0.0836556	−	0.0475499i
$757$	14.4709	+	5.26699i	0.525955	+	0.191432i	0.591331	−	0.806429i	$-0.298603\pi$
$757$	14.4709	+	5.26699i	0.525955	+	0.191432i	−0.0653764	+	0.997861i	$0.520825\pi$
$758$	−1.16541	−	6.60937i	−0.0423296	−	0.240063i
$759$	−11.8809	−	20.5784i	−0.431251	−	0.746948i
$760$	−1.04461	−	4.54256i	−0.0378922	−	0.164776i
$761$	−8.34260	−	4.81660i	−0.302419	−	0.174602i	0.341110	−	0.940023i	$-0.389197\pi$
$761$	−8.34260	−	4.81660i	−0.302419	−	0.174602i	−0.643529	+	0.765422i	$0.722530\pi$
$762$	13.4250	−	11.2649i	0.486336	−	0.408084i
$763$	43.3803	−	15.4589i	1.57047	−	0.559651i
$764$	2.86606	−	16.2542i	0.103690	−	0.588057i
$765$	−5.66975	−	2.06362i	−0.204990	−	0.0746104i
$766$	6.40052	−	7.62784i	0.231260	−	0.275605i
$767$	−7.64929			−0.276200
$768$	1.00000			0.0360844
$769$	−6.76484	+	8.06202i	−0.243946	+	0.290724i	−0.874100	−	0.485747i	$-0.838548\pi$
$769$	−6.76484	+	8.06202i	−0.243946	+	0.290724i	0.630153	+	0.776471i	$0.282992\pi$
$770$	−10.6748	+	6.06754i	−0.384692	+	0.218659i
$771$	4.52901	+	7.84448i	0.163108	+	0.282512i
$772$	11.0483	−	6.37871i	0.397635	−	0.229575i
$773$	−18.8437	−	15.8118i	−0.677761	−	0.568709i	0.237590	−	0.971366i	$-0.423643\pi$
$773$	−18.8437	−	15.8118i	−0.677761	−	0.568709i	−0.915351	+	0.402656i	$0.868087\pi$
$774$	3.84418	+	4.58132i	0.138176	+	0.164672i
$775$	−18.4597	−	15.4895i	−0.663092	−	0.556400i
$776$	2.02580	−	5.56583i	0.0727218	−	0.199802i
$777$	20.1935	+	17.1775i	0.724437	+	0.616240i
$778$			5.87795i			0.210735i
$779$	23.3740	+	7.16815i	0.837460	+	0.256826i
$780$	4.36092	−	2.51778i	0.156146	−	0.0901508i
$781$	17.3734	−	47.7332i	0.621671	−	1.70803i
$782$	−23.6652	+	19.8575i	−0.846267	+	0.710103i
$783$	−6.54509	−	1.15408i	−0.233902	−	0.0412433i
$784$	−6.99936	−	0.0943302i	−0.249977	−	0.00336894i
$785$	14.0254	−	5.10484i	0.500589	−	0.182200i
$786$	4.49276	+	7.78168i	0.160251	+	0.277563i
$787$	5.47525	−	9.48341i	0.195172	−	0.338047i	−0.751785	−	0.659408i	$-0.770807\pi$
$787$	5.47525	−	9.48341i	0.195172	−	0.338047i	0.946957	+	0.321361i	$0.104140\pi$
$788$	−1.10983	+	6.29417i	−0.0395361	+	0.224221i
$789$	−14.7625	+	5.37311i	−0.525559	+	0.191288i
$790$	−6.62580	+	3.82541i	−0.235735	+	0.136102i
$791$	−1.51076	−	0.561430i	−0.0537166	−	0.0199621i
$792$	−1.48436	−	4.07825i	−0.0527445	−	0.144914i
$793$	8.52653	−	23.4265i	0.302786	−	0.831898i
$794$	25.9957	−	9.46167i	0.922554	−	0.335782i
$795$	−2.10889	−	11.9601i	−0.0747946	−	0.424181i
$796$	−21.7053	+	3.82723i	−0.769323	+	0.135652i
$797$	42.4569			1.50390			0.751950	−	0.659220i	$-0.229113\pi$
$797$	42.4569			1.50390			0.751950	+	0.659220i	$0.229113\pi$
$798$	−11.5210	+	0.516036i	−0.407839	+	0.0182675i
$799$	−48.2620			−1.70739
$800$	3.79793	−	0.669678i	0.134277	−	0.0236767i
$801$	−1.07987	−	6.12423i	−0.0381552	−	0.216389i
$802$	−20.6356	+	7.51073i	−0.728667	+	0.265213i
$803$	−4.88187	+	13.4128i	−0.172277	+	0.473328i
$804$	2.96160	+	8.13692i	0.104447	+	0.286967i
$805$	2.58699	+	15.2726i	0.0911793	+	0.538288i
$806$	−25.4823	+	14.7122i	−0.897575	+	0.518215i
$807$	−7.24836	+	2.63819i	−0.255154	+	0.0928686i
$808$	−1.46107	+	8.28612i	−0.0514001	+	0.291505i
$809$	22.5372	−	39.0356i	0.792366	−	1.37242i	−0.132133	−	0.991232i	$-0.542183\pi$
$809$	22.5372	−	39.0356i	0.792366	−	1.37242i	0.924499	−	0.381185i	$-0.124484\pi$
$810$	−0.534668	−	0.926071i	−0.0187863	−	0.0325388i
$811$	−1.83714	+	0.668663i	−0.0645106	+	0.0234799i	−0.374074	−	0.927399i	$-0.622039\pi$
$811$	−1.83714	+	0.668663i	−0.0645106	+	0.0234799i	0.309563	+	0.950879i	$0.399817\pi$
$812$	13.3935	+	11.3932i	0.470020	+	0.399822i
$813$	−24.1042	−	4.25022i	−0.845371	−	0.149062i
$814$	33.3137	−	27.9535i	1.16764	−	0.979769i
$815$	4.91503	−	13.5039i	0.172166	−	0.473023i
$816$	−4.88647	+	2.82120i	−0.171061	+	0.0987619i
$817$	−5.84223	−	25.4052i	−0.204394	−	0.888817i
$818$			15.3222i			0.535730i
$819$	−4.18224	−	11.7360i	−0.146139	−	0.410091i
$820$	2.05135	−	5.63604i	0.0716363	−	0.196819i
$821$	2.80911	+	2.35713i	0.0980387	+	0.0822643i	0.690490	−	0.723342i	$-0.257395\pi$
$821$	2.80911	+	2.35713i	0.0980387	+	0.0822643i	−0.592451	+	0.805607i	$0.701840\pi$
$822$	−4.00937	−	4.77818i	−0.139843	−	0.166658i
$823$	−34.6995	−	29.1163i	−1.20955	−	1.01493i	−0.999305	−	0.0372815i	$-0.988130\pi$
$823$	−34.6995	−	29.1163i	−1.20955	−	1.01493i	−0.210243	−	0.977649i	$-0.567425\pi$
$824$	7.91019	−	4.56695i	0.275565	−	0.159097i
$825$	−8.36862	−	14.4949i	−0.291358	−	0.504647i
$826$	2.17388	−	3.70736i	0.0756391	−	0.128996i
$827$	14.3650	−	17.1196i	0.499521	−	0.595306i	−0.456091	−	0.889933i	$-0.650751\pi$
$827$	14.3650	−	17.1196i	0.499521	−	0.595306i	0.955612	+	0.294627i	$0.0951953\pi$
$828$	−5.47511			−0.190273
$829$	−7.20419			−0.250212			−0.125106	−	0.992143i	$-0.539927\pi$
$829$	−7.20419			−0.250212			−0.125106	+	0.992143i	$0.539927\pi$
$830$	2.60151	−	3.10035i	0.0902996	−	0.107615i
$831$	−15.2739	−	5.55926i	−0.529847	−	0.192849i
$832$	0.817718	−	4.63751i	0.0283493	−	0.160777i
$833$	34.4683	−	19.2857i	1.19426	−	0.668210i
$834$	8.42323	−	7.06793i	0.291673	−	0.244743i
$835$	−19.6303	−	11.3335i	−0.679334	−	0.392214i
$836$	−2.32163	+	18.7746i	−0.0802953	+	0.649332i
$837$	3.12424	+	5.41135i	0.107990	+	0.187043i
$838$	5.06331	+	28.7155i	0.174909	+	0.991959i
$839$	−47.0759	−	17.1342i	−1.62524	−	0.591539i	−0.640870	−	0.767649i	$-0.721426\pi$
$839$	−47.0759	−	17.1342i	−1.62524	−	0.591539i	−0.984371	+	0.176110i	$0.943649\pi$
$840$	−0.0190632	+	2.82913i	−0.000657742	+	0.0976143i
$841$	−2.63425	−	14.9396i	−0.0908364	−	0.515159i
$842$	−2.00309	+	11.3601i	−0.0690312	+	0.391495i
$843$		−	3.77074i		−	0.129871i
$844$	3.56256	+	2.05685i	0.122629	+	0.0707996i
$845$	−3.35566	−	9.21960i	−0.115438	−	0.317164i
$846$	−6.55232	−	5.49805i	−0.225273	−	0.189027i
$847$	20.4396	−	3.46221i	0.702311	−	0.118963i
$848$	−9.83559	−	5.67858i	−0.337756	−	0.195003i
$849$	−12.9686	−	2.28672i	−0.445083	−	0.0784801i
$850$	−16.6692	+	13.9871i	−0.571748	+	0.479754i
$851$	−18.7640	−	51.5536i	−0.643220	−	1.76723i
$852$	−7.52339	−	8.96603i	−0.257747	−	0.307171i
$853$	−9.52893	−	11.3561i	−0.326264	−	0.388827i	0.577832	−	0.816156i	$-0.303899\pi$
$853$	−9.52893	−	11.3561i	−0.326264	−	0.388827i	−0.904096	+	0.427329i	$0.859455\pi$
$854$	8.93085	+	10.7902i	0.305607	+	0.369233i
$855$	0.239937	+	4.65494i	0.00820569	+	0.159196i
$856$	−10.0080	+	17.3343i	−0.342065	+	0.592474i
$857$	−19.1365	−	6.96512i	−0.653691	−	0.237924i	−0.00618091	−	0.999981i	$-0.501967\pi$
$857$	−19.1365	−	6.96512i	−0.653691	−	0.237924i	−0.647510	+	0.762057i	$0.724190\pi$
$858$	−20.1267	+	3.54888i	−0.687115	+	0.121157i
$859$	−35.3034	+	42.0730i	−1.20454	+	1.43551i	−0.334590	+	0.942364i	$0.608598\pi$
$859$	−35.3034	+	42.0730i	−1.20454	+	1.43551i	−0.869946	+	0.493147i	$0.835847\pi$
$860$	−6.29799	+	1.11050i	−0.214760	+	0.0378679i
$861$	−12.8012	−	7.50624i	−0.436264	−	0.255812i
$862$	−9.96812	+	17.2653i	−0.339516	+	0.588058i
$863$			5.79781i			0.197360i	0.995119	+	0.0986798i	$0.0314620\pi$
$863$			5.79781i			0.197360i	−0.995119	+	0.0986798i	$0.968538\pi$
$864$	−0.984808	−	0.173648i	−0.0335038	−	0.00590763i
$865$	−20.4132	−	3.59939i	−0.694069	−	0.122383i
$866$			8.46667i			0.287709i
$867$	7.41838	−	12.8490i	0.251941	−	0.436375i
$868$	0.111393	−	16.5316i	0.00378091	−	0.561118i
$869$	30.5797	−	5.39203i	1.03735	−	0.182912i
$870$	4.56820	−	5.44417i	0.154877	−	0.184575i
$871$	40.1568	−	7.08072i	1.36066	−	0.239921i
$872$	−16.3565	−	5.95327i	−0.553900	−	0.201603i
$873$	−2.96152	+	5.12950i	−0.100232	+	0.173607i
$874$	21.2549	+	10.8530i	0.718959	+	0.367108i
$875$	4.18471	+	24.7049i	0.141469	+	0.835179i
$876$	2.11404	+	2.51942i	0.0714269	+	0.0851233i
$877$	−6.23638	−	7.43222i	−0.210587	−	0.250968i	0.650403	−	0.759589i	$-0.274600\pi$
$877$	−6.23638	−	7.43222i	−0.210587	−	0.250968i	−0.860991	+	0.508621i	$0.830156\pi$
$878$	−3.88730	−	10.6803i	−0.131190	−	0.360442i
$879$	11.2152	−	9.41066i	0.378279	−	0.317414i
$880$	4.57039	+	0.805884i	0.154068	+	0.0271663i
$881$	15.7293	+	9.08130i	0.529933	+	0.305957i	0.740989	−	0.671517i	$-0.234357\pi$
$881$	15.7293	+	9.08130i	0.529933	+	0.305957i	−0.211056	+	0.977474i	$0.567690\pi$
$882$	6.87665	+	1.30832i	0.231549	+	0.0440536i
$883$	−21.1713	−	17.7649i	−0.712473	−	0.597836i	0.212819	−	0.977092i	$-0.431735\pi$
$883$	−21.1713	−	17.7649i	−0.712473	−	0.597836i	−0.925292	+	0.379256i	$0.876180\pi$
$884$	9.08760	+	24.9680i	0.305649	+	0.839764i
$885$	−1.50429	−	0.868504i	−0.0505663	−	0.0291944i
$886$		−	26.4770i		−	0.889512i
$887$	0.281238	−	1.59498i	0.00944304	−	0.0535541i	−0.979722	−	0.200361i	$-0.935788\pi$
$887$	0.281238	−	1.59498i	0.00944304	−	0.0535541i	0.989165	+	0.146807i	$0.0468996\pi$
$888$	−1.74001	−	9.86806i	−0.0583908	−	0.331150i
$889$	46.3659	+	0.312422i	1.55506	+	0.0104783i
$890$	6.24884	+	2.27439i	0.209462	+	0.0762378i
$891$	0.753631	+	4.27405i	0.0252476	+	0.143186i
$892$	12.0796	+	20.9224i	0.404453	+	0.700534i
$893$	14.5383	+	34.3323i	0.486506	+	1.14889i
$894$	12.0989	+	6.98530i	0.404648	+	0.233623i
$895$	−7.44533	+	6.24737i	−0.248870	+	0.208827i
$896$	2.01526	+	1.71427i	0.0673250	+	0.0572699i
$897$	−4.47709	+	25.3908i	−0.149486	+	0.847776i
$898$	24.6428	+	8.96925i	0.822341	+	0.299308i
$899$	−26.6935	+	31.8121i	−0.890279	+	1.06099i
$900$	−3.85652			−0.128551
$901$	64.0817			2.13487
$902$	−15.6470	+	18.6473i	−0.520987	+	0.620888i
$903$	−0.106615	+	15.8225i	−0.00354792	+	0.526540i
$904$	0.304585	+	0.527556i	0.0101303	+	0.0175463i
$905$	−0.330890	+	0.191039i	−0.0109991	+	0.00635036i
$906$	17.7280	+	14.8756i	0.588974	+	0.494208i
$907$	−16.2225	−	19.3333i	−0.538660	−	0.641950i	0.426227	−	0.904616i	$-0.359843\pi$
$907$	−16.2225	−	19.3333i	−0.538660	−	0.641950i	−0.964887	+	0.262666i	$0.915398\pi$
$908$	−3.84778	−	3.22867i	−0.127693	−	0.107147i
$909$	2.87774	−	7.90652i	0.0954486	−	0.262243i
$910$	13.1045	+	2.40184i	0.434411	+	0.0796201i
$911$		−	24.1881i		−	0.801387i	−0.916212	−	0.400693i	$-0.868769\pi$
$911$		−	24.1881i		−	0.801387i	0.916212	−	0.400693i	$-0.131231\pi$
$912$	3.47891	+	2.62625i	0.115198	+	0.0869637i
$913$	−14.2253	+	8.21300i	−0.470790	+	0.271811i
$914$	−5.31477	+	14.6022i	−0.175797	+	0.482998i
$915$	4.33666	−	3.63889i	0.143366	−	0.120298i
$916$	−2.98290	−	0.525966i	−0.0985579	−	0.0173784i
$917$	−4.28587	+	23.3839i	−0.141532	+	0.772205i
$918$	5.30213	−	1.92982i	0.174996	−	0.0636934i
$919$	−9.10497	−	15.7703i	−0.300345	−	0.520213i	0.675869	−	0.737022i	$-0.263769\pi$
$919$	−9.10497	−	15.7703i	−0.300345	−	0.520213i	−0.976214	+	0.216809i	$0.930435\pi$
$920$	2.92736	−	5.07034i	0.0965123	−	0.167164i
$921$	−5.09160	+	28.8759i	−0.167774	+	0.951492i
$922$	34.0441	−	12.3910i	1.12118	−	0.408077i
$923$	−47.7320	+	27.5581i	−1.57112	+	0.907086i
$924$	3.99987	−	10.7633i	0.131586	−	0.354088i
$925$	−13.2168	−	36.3130i	−0.434567	−	1.19396i
$926$	7.54143	−	20.7199i	0.247827	−	0.680898i
$927$	−8.58306	+	3.12398i	−0.281905	+	0.102605i
$928$	−1.15408	−	6.54509i	−0.0378844	−	0.214853i
$929$	45.0673	−	7.94659i	1.47861	−	0.260719i	0.624588	−	0.780954i	$-0.285267\pi$
$929$	45.0673	−	7.94659i	1.47861	−	0.260719i	0.854023	+	0.520235i	$0.174156\pi$
$930$	−6.68172			−0.219102
$931$	−24.1024	−	18.7102i	−0.789926	−	0.613203i
$932$	−15.7026			−0.514354
$933$	−16.0230	+	2.82529i	−0.524571	+	0.0924959i
$934$	0.257300	+	1.45922i	0.00841912	+	0.0477472i
$935$	−24.6066	+	8.95608i	−0.804723	+	0.292895i
$936$	−1.61059	+	4.42506i	−0.0526438	+	0.144638i
$937$	−15.0289	−	41.2916i	−0.490973	−	1.34894i	−0.899791	−	0.436322i	$-0.856281\pi$
$937$	−15.0289	−	41.2916i	−0.490973	−	1.34894i	0.408817	−	0.912616i	$-0.365941\pi$
$938$	−7.98053	+	21.4750i	−0.260573	+	0.701183i
$939$	−5.72490	+	3.30527i	−0.186825	+	0.107864i
$940$	8.59490	−	3.12829i	0.280335	−	0.102033i
$941$	−1.39227	+	7.89593i	−0.0453866	+	0.257400i	−0.999055	−	0.0434590i	$-0.986162\pi$
$941$	−1.39227	+	7.89593i	−0.0453866	+	0.257400i	0.953669	+	0.300859i	$0.0972733\pi$
$942$	−6.97889	+	12.0878i	−0.227385	+	0.393842i
$943$	15.3545	+	26.5948i	0.500013	+	0.866047i
$944$	−1.52642	+	0.555571i	−0.0496807	+	0.0180823i
$945$	0.510047	−	2.78284i	0.0165918	−	0.0905258i
$946$	25.5609	+	4.50708i	0.831056	+	0.146538i
$947$	6.12035	−	5.13558i	0.198885	−	0.166884i	−0.537906	−	0.843005i	$-0.680785\pi$
$947$	6.12035	−	5.13558i	0.198885	−	0.166884i	0.736791	+	0.676121i	$0.236340\pi$
$948$	2.44707	−	6.72326i	0.0794770	−	0.218361i
$949$	13.4125	−	7.74372i	0.435389	−	0.251372i
$950$	14.9714	+	7.64456i	0.485737	+	0.248022i
$951$			9.60779i			0.311554i
$952$	−14.6838	−	2.69129i	−0.475905	−	0.0872252i
$953$	8.37293	−	23.0044i	0.271226	−	0.745187i	−0.727055	−	0.686579i	$-0.759112\pi$
$953$	8.37293	−	23.0044i	0.271226	−	0.745187i	0.998281	−	0.0586080i	$-0.0186662\pi$
$954$	8.70009	+	7.30024i	0.281676	+	0.236354i
$955$	−11.3448	−	13.5202i	−0.367109	−	0.437503i
$956$	15.6956	+	13.1702i	0.507632	+	0.425954i
$957$	−24.9795	+	14.4219i	−0.807471	+	0.466194i
$958$	6.04857	+	10.4764i	0.195420	+	0.338478i
$959$	0.111196	−	16.5024i	0.00359071	−	0.532891i
$960$	0.687355	−	0.819158i	0.0221843	−	0.0264382i
$961$	8.04355			0.259469
$962$	−47.1860			−1.52134
$963$	12.8660	−	15.3331i	0.414601	−	0.494102i
$964$	3.61538	+	1.31589i	0.116443	+	0.0423819i
$965$	2.36890	−	13.4347i	0.0762576	−	0.432479i
$966$	−11.0338	−	9.38583i	−0.355005	−	0.301984i
$967$	36.0257	−	30.2291i	1.15851	−	0.972103i	0.158623	−	0.987339i	$-0.449294\pi$
$967$	36.0257	−	30.2291i	1.15851	−	0.972103i	0.999884	+	0.0152360i	$0.00484996\pi$
$968$	−6.78572	−	3.91774i	−0.218101	−	0.125921i
$969$	−24.4088	−	3.01835i	−0.784123	−	0.0969634i
$970$	−3.16685	−	5.48515i	−0.101682	−	0.176118i
$971$	3.80449	+	21.5764i	0.122092	+	0.692418i	0.982993	+	0.183645i	$0.0587897\pi$
$971$	3.80449	+	21.5764i	0.122092	+	0.692418i	−0.860901	+	0.508773i	$0.830099\pi$
$972$	0.939693	+	0.342020i	0.0301407	+	0.0109703i
$973$	29.0914	+	0.196023i	0.932626	+	0.00628420i
$974$	−2.63743	−	14.9576i	−0.0845086	−	0.479272i
$975$	−3.15355	+	17.8846i	−0.100994	+	0.572767i
$976$		−	5.29405i		−	0.169458i
$977$	−9.65706	−	5.57551i	−0.308957	−	0.178376i	0.337503	−	0.941325i	$-0.390418\pi$
$977$	−9.65706	−	5.57551i	−0.308957	−	0.178376i	−0.646460	+	0.762948i	$0.723751\pi$
$978$	4.59635	+	12.6284i	0.146975	+	0.403810i
$979$	−20.6748	−	17.3482i	−0.660771	−	0.554452i
$980$	−4.88832	+	5.66875i	−0.156152	+	0.181082i
$981$	15.0742	+	8.70310i	0.481282	+	0.277869i
$982$	−23.5865	−	4.15894i	−0.752676	−	0.132717i
$983$	0.0437512	−	0.0367116i	0.00139545	−	0.00117092i	−0.642090	−	0.766630i	$-0.721932\pi$
$983$	0.0437512	−	0.0367116i	0.00139545	−	0.00117092i	0.643485	+	0.765459i	$0.277488\pi$
$984$	1.91834	+	5.27060i	0.0611545	+	0.168021i
$985$	4.39307	+	5.23546i	0.139975	+	0.166816i
$986$	24.1044	+	28.7265i	0.767640	+	0.914837i
$987$	−3.77945	−	22.3125i	−0.120301	−	0.710213i
$988$	15.0240	−	13.9860i	0.477977	−	0.444952i
$989$	16.3719	−	28.3569i	0.520596	−	0.901699i
$990$	−4.36102	−	1.58728i	−0.138602	−	0.0504471i
$991$	−4.57952	+	0.807493i	−0.145473	+	0.0256509i	−0.245911	−	0.969293i	$-0.579087\pi$
$991$	−4.57952	+	0.807493i	−0.145473	+	0.0256509i	0.100437	+	0.994943i	$0.467976\pi$
$992$	−4.01645	+	4.78662i	−0.127522	+	0.151975i
$993$	22.6353	−	3.99121i	0.718308	−	0.126657i
$994$	0.208654	−	30.9660i	0.00661812	−	0.982182i
$995$	−11.7841	+	20.4107i	−0.373582	+	0.647064i
$996$			3.78480i			0.119926i
$997$	25.6406	+	4.52114i	0.812047	+	0.143186i	0.564227	−	0.825620i	$-0.309174\pi$
$997$	25.6406	+	4.52114i	0.812047	+	0.143186i	0.247821	+	0.968806i	$0.420286\pi$
$998$	−38.3915	−	6.76945i	−1.21526	−	0.214283i
$999$			10.0203i			0.317028i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.ca.b.355.12	✓	84
7.3	odd	6		798.2.cj.b.241.3	yes	84
19.3	odd	18		798.2.cj.b.649.3	yes	84
133.3	even	18	inner	798.2.ca.b.535.12	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.ca.b.355.12	✓	84	1.1	even	1	trivial
798.2.ca.b.535.12	yes	84	133.3	even	18	inner
798.2.cj.b.241.3	yes	84	7.3	odd	6
798.2.cj.b.649.3	yes	84	19.3	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.ca (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.984808 - 0.173648i) q^{2} +(0.173648 + 0.984808i) q^{3} +(0.939693 - 0.342020i) q^{4} +(0.365734 - 1.00485i) q^{5} +(0.342020 + 0.939693i) q^{6} +(-0.921632 + 2.48004i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(0.185688 - 1.05309i) q^{10} +(-2.16999 + 3.75854i) q^{11} +(0.500000 + 0.866025i) q^{12} +(4.42506 - 1.61059i) q^{13} +(-0.476976 + 2.60240i) q^{14} +(1.05309 + 0.185688i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-1.92982 + 5.30213i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(4.35312 - 0.224380i) q^{19} -1.06934i q^{20} +(-2.60240 - 0.476976i) q^{21} +(-1.48436 + 4.07825i) q^{22} +(4.19417 + 3.51933i) q^{23} +(0.642788 + 0.766044i) q^{24} +(2.95427 + 2.47892i) q^{25} +(4.07816 - 2.35452i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(-0.0178271 + 2.64569i) q^{28} +(4.27200 - 5.09117i) q^{29} +1.06934 q^{30} -6.24848 q^{31} +(0.642788 - 0.766044i) q^{32} +(-4.07825 - 1.48436i) q^{33} +(-0.979794 + 5.55669i) q^{34} +(2.15499 + 1.83313i) q^{35} +(-0.766044 + 0.642788i) q^{36} +(-8.67783 - 5.01015i) q^{37} +(4.24802 - 0.976882i) q^{38} +(2.35452 + 4.07816i) q^{39} +(-0.185688 - 1.05309i) q^{40} +(5.27060 + 1.91834i) q^{41} +(-2.64569 - 0.0178271i) q^{42} +(-1.03850 - 5.88963i) q^{43} +(-0.753631 + 4.27405i) q^{44} +1.06934i q^{45} +(4.74158 + 2.73755i) q^{46} +(2.92545 + 8.03761i) q^{47} +(0.766044 + 0.642788i) q^{48} +(-5.30119 - 4.57137i) q^{49} +(3.33985 + 1.92826i) q^{50} +(-5.55669 - 0.979794i) q^{51} +(3.60734 - 3.02692i) q^{52} +(-3.88438 - 10.6722i) q^{53} +(-0.642788 - 0.766044i) q^{54} +(2.98311 + 3.55513i) q^{55} +(0.441863 + 2.60859i) q^{56} +(0.976882 + 4.24802i) q^{57} +(3.32303 - 5.75565i) q^{58} +(-1.52642 - 0.555571i) q^{59} +(1.05309 - 0.185688i) q^{60} +(3.40295 - 4.05547i) q^{61} +(-6.15355 + 1.08504i) q^{62} +(0.0178271 - 2.64569i) q^{63} +(0.500000 - 0.866025i) q^{64} -5.03555i q^{65} +(-4.27405 - 0.753631i) q^{66} +(8.52757 + 1.50364i) q^{67} +5.64241i q^{68} +(-2.73755 + 4.74158i) q^{69} +(2.44057 + 1.43107i) q^{70} +(-11.5265 + 2.03243i) q^{71} +(-0.642788 + 0.766044i) q^{72} +(3.23890 - 0.571106i) q^{73} +(-9.41599 - 3.42714i) q^{74} +(-1.92826 + 3.33985i) q^{75} +(4.01385 - 1.69970i) q^{76} +(-7.32139 - 8.84565i) q^{77} +(3.02692 + 3.60734i) q^{78} +(-4.59898 - 5.48085i) q^{79} +(-0.365734 - 1.00485i) q^{80} +(0.766044 - 0.642788i) q^{81} +(5.52364 + 0.973968i) q^{82} +(3.27774 + 1.89240i) q^{83} +(-2.60859 + 0.441863i) q^{84} +(4.62202 + 3.87834i) q^{85} +(-2.04545 - 5.61982i) q^{86} +(5.75565 + 3.32303i) q^{87} +4.33999i q^{88} +(-1.07987 + 6.12423i) q^{89} +(0.185688 + 1.05309i) q^{90} +(-0.0839488 + 12.4587i) q^{91} +(5.14492 + 1.87260i) q^{92} +(-1.08504 - 6.15355i) q^{93} +(4.27672 + 7.40750i) q^{94} +(1.36662 - 4.45628i) q^{95} +(0.866025 + 0.500000i) q^{96} +(4.53730 - 3.80725i) q^{97} +(-6.01446 - 3.58137i) q^{98} +(0.753631 - 4.27405i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 6 q^{7} - 6 q^{10} + 6 q^{11} + 42 q^{12} - 24 q^{13} + 18 q^{17} - 6 q^{19} - 6 q^{21} + 12 q^{22} + 30 q^{23} + 24 q^{25} + 18 q^{26} - 42 q^{27} - 6 q^{28} + 12 q^{31} + 6 q^{33} + 30 q^{34} + 12 q^{35}+ \cdots + 6 q^{99}+O(q^{100}) \) 84 * q - 6 * q^7 - 6 * q^10 + 6 * q^11 + 42 * q^12 - 24 * q^13 + 18 * q^17 - 6 * q^19 - 6 * q^21 + 12 * q^22 + 30 * q^23 + 24 * q^25 + 18 * q^26 - 42 * q^27 - 6 * q^28 + 12 * q^31 + 6 * q^33 + 30 * q^34 + 12 * q^35 + 18 * q^37 + 24 * q^38 + 6 * q^40 - 36 * q^41 - 6 * q^42 + 12 * q^43 - 6 * q^44 + 18 * q^46 + 18 * q^47 + 12 * q^49 - 30 * q^52 - 12 * q^53 + 30 * q^55 + 18 * q^56 + 6 * q^57 + 6 * q^59 + 36 * q^61 + 12 * q^62 + 6 * q^63 + 42 * q^64 + 6 * q^66 - 12 * q^67 - 6 * q^69 - 18 * q^70 + 42 * q^71 - 6 * q^73 + 48 * q^75 - 18 * q^76 - 96 * q^77 - 12 * q^78 - 6 * q^79 - 12 * q^82 - 54 * q^83 + 6 * q^84 - 24 * q^85 - 30 * q^86 + 24 * q^89 - 6 * q^90 + 42 * q^91 + 42 * q^92 + 36 * q^93 - 18 * q^94 + 24 * q^95 + 78 * q^97 + 12 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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