LMFDB - Embedded newform 798.2.cj.b.241.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(241,798)] 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("798.241"); 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, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.cj (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			241.3
Character	$\chi$	$=$	798.241
Dual form			798.2.cj.b.649.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.342020 + 0.939693i) q^{2} +(-0.766044 + 0.642788i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.687355 - 0.819158i) q^{5} +(-0.342020 - 0.939693i) q^{6} +(-1.68696 + 2.03818i) q^{7} +(0.866025 - 0.500000i) q^{8} +(0.173648 - 0.984808i) q^{9} +(1.00485 - 0.365734i) q^{10} +4.33999 q^{11} +1.00000 q^{12} +(-4.42506 + 1.61059i) q^{13} +(-1.33828 - 2.28232i) q^{14} +(1.05309 + 0.185688i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-5.55669 + 0.979794i) q^{17} +(0.866025 + 0.500000i) q^{18} +(1.98224 - 3.88210i) q^{19} +1.06934i q^{20} +(-0.0178271 - 2.64569i) q^{21} +(-1.48436 + 4.07825i) q^{22} +(-5.14492 + 1.87260i) q^{23} +(-0.342020 + 0.939693i) q^{24} +(0.669678 - 3.79793i) q^{25} -4.70905i q^{26} +(0.500000 + 0.866025i) q^{27} +(2.60240 - 0.476976i) q^{28} +(4.27200 - 5.09117i) q^{29} +(-0.534668 + 0.926071i) q^{30} +(-3.12424 - 5.41135i) q^{31} +(-0.984808 - 0.173648i) q^{32} +(-3.32462 + 2.78969i) q^{33} +(0.979794 - 5.55669i) q^{34} +(2.82913 - 0.0190632i) q^{35} +(-0.766044 + 0.642788i) q^{36} +(8.67783 - 5.01015i) q^{37} +(2.97002 + 3.19045i) q^{38} +(2.35452 - 4.07816i) q^{39} +(-1.00485 - 0.365734i) q^{40} +(-5.27060 - 1.91834i) q^{41} +(2.49223 + 0.888128i) q^{42} +(-1.03850 - 5.88963i) q^{43} +(-3.32462 - 2.78969i) q^{44} +(-0.926071 + 0.534668i) q^{45} -5.47511i q^{46} +(8.42350 + 1.48529i) q^{47} +(-0.766044 - 0.642788i) q^{48} +(-1.30832 - 6.87665i) q^{49} +(3.33985 + 1.92826i) q^{50} +(3.62687 - 4.32233i) q^{51} +(4.42506 + 1.61059i) q^{52} +(-7.30024 + 8.70009i) q^{53} +(-0.984808 + 0.173648i) 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} +(-0.282071 - 1.59970i) q^{59} +(-0.687355 - 0.819158i) q^{60} +(-1.81067 - 4.97478i) q^{61} +(6.15355 - 1.08504i) q^{62} +(1.71427 + 2.01526i) q^{63} +(0.500000 - 0.866025i) q^{64} +(4.36092 + 2.51778i) q^{65} +(-1.48436 - 4.07825i) q^{66} +(-2.96160 - 8.13692i) q^{67} +(4.88647 + 2.82120i) q^{68} +(2.73755 - 4.74158i) q^{69} +(-0.949706 + 2.66503i) q^{70} +(-11.5265 + 2.03243i) q^{71} +(-0.342020 - 0.939693i) q^{72} +(2.11404 + 2.51942i) q^{73} +(1.74001 + 9.86806i) 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} +(7.04605 - 1.24241i) q^{79} +(0.687355 - 0.819158i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(3.60530 - 4.29663i) q^{82} +(-3.27774 - 1.89240i) q^{83} +(-1.68696 + 2.03818i) q^{84} +(4.62202 + 3.87834i) q^{85} +(5.88963 + 1.03850i) q^{86} +6.64606i q^{87} +(3.75854 - 2.16999i) q^{88} +(4.76380 + 3.99731i) q^{89} +(-0.185688 - 1.05309i) q^{90} +(4.18224 - 11.7360i) q^{91} +(5.14492 + 1.87260i) q^{92} +(5.87165 + 2.13711i) q^{93} +(-4.27672 + 7.40750i) q^{94} +(-4.54256 + 1.04461i) q^{95} +(0.866025 - 0.500000i) q^{96} +(-4.53730 + 3.80725i) q^{97} +(6.90941 + 1.12253i) q^{98} +(0.753631 - 4.27405i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 12 q^{7} - 12 q^{10} - 12 q^{11} + 84 q^{12} + 24 q^{13} + 6 q^{14} + 6 q^{19} - 6 q^{21} + 12 q^{22} - 42 q^{23} - 30 q^{25} + 42 q^{27} + 6 q^{28} + 6 q^{31} + 12 q^{33} - 30 q^{34} - 42 q^{35}+ \cdots + 6 q^{99}+O(q^{100}) $ 84 * q + 12 * q^7 - 12 * q^10 - 12 * q^11 + 84 * q^12 + 24 * q^13 + 6 * q^14 + 6 * q^19 - 6 * q^21 + 12 * q^22 - 42 * q^23 - 30 * q^25 + 42 * q^27 + 6 * q^28 + 6 * q^31 + 12 * q^33 - 30 * q^34 - 42 * q^35 - 18 * q^37 + 12 * q^38 + 12 * q^40 + 36 * q^41 + 18 * q^42 + 12 * q^43 + 12 * q^44 - 18 * q^45 + 18 * q^47 - 24 * q^49 + 18 * q^51 - 24 * q^52 + 60 * q^53 - 30 * q^55 - 18 * q^56 + 6 * q^57 + 48 * q^59 - 12 * q^62 - 6 * q^63 + 42 * q^64 + 108 * q^65 + 12 * q^66 + 42 * q^67 + 6 * q^69 + 18 * q^70 + 42 * q^71 - 48 * q^73 - 18 * q^74 - 48 * q^75 + 18 * q^76 - 96 * q^77 - 12 * q^78 - 60 * q^79 - 6 * q^82 + 54 * q^83 + 12 * q^84 - 24 * q^85 - 12 * q^86 - 24 * q^89 + 6 * q^90 + 24 * q^91 + 42 * q^92 - 36 * q^93 + 18 * q^94 - 12 * q^95 - 78 * q^97 + 24 * q^98 + 6 * q^99

Character values

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

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

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 $

$2$	−0.342020	+	0.939693i	−0.241845	+	0.664463i
$2$	−0.342020	+	0.939693i	−0.241845	+	0.664463i
$3$	−0.766044	+	0.642788i	−0.442276	+	0.371114i
$3$	−0.766044	+	0.642788i	−0.442276	+	0.371114i
$4$	−0.766044	−	0.642788i	−0.383022	−	0.321394i
$5$	−0.687355	−	0.819158i	−0.307395	−	0.366339i	0.590126	−	0.807311i	$-0.299078\pi$
$5$	−0.687355	−	0.819158i	−0.307395	−	0.366339i	−0.897521	+	0.440972i	$0.854634\pi$
$6$	−0.342020	−	0.939693i	−0.139629	−	0.383628i
$7$	−1.68696	+	2.03818i	−0.637611	+	0.770358i
$7$	−1.68696	+	2.03818i	−0.637611	+	0.770358i
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	0.173648	−	0.984808i	0.0578827	−	0.328269i
$10$	1.00485	−	0.365734i	0.317760	−	0.115655i
$11$	4.33999			1.30855			0.654277	−	0.756255i	$-0.272973\pi$
$11$	4.33999			1.30855			0.654277	+	0.756255i	$0.272973\pi$
$12$	1.00000			0.288675
$13$	−4.42506	+	1.61059i	−1.22729	+	0.446697i	−0.872669	−	0.488313i	$-0.837613\pi$
$13$	−4.42506	+	1.61059i	−1.22729	+	0.446697i	−0.354622	+	0.935010i	$0.615390\pi$
$14$	−1.33828	−	2.28232i	−0.357672	−	0.609976i
$15$	1.05309	+	0.185688i	0.271907	+	0.0479445i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−5.55669	+	0.979794i	−1.34769	+	0.237635i	−0.800481	−	0.599358i	$-0.795422\pi$
$17$	−5.55669	+	0.979794i	−1.34769	+	0.237635i	−0.547213	+	0.836993i	$0.684311\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	1.98224	−	3.88210i	0.454757	−	0.890615i
$19$	1.98224	−	3.88210i	0.454757	−	0.890615i
$20$			1.06934i			0.239111i
$21$	−0.0178271	−	2.64569i	−0.00389020	−	0.577337i
$22$	−1.48436	+	4.07825i	−0.316467	+	0.869486i
$23$	−5.14492	+	1.87260i	−1.07279	+	0.390463i	−0.817219	−	0.576327i	$-0.804485\pi$
$23$	−5.14492	+	1.87260i	−1.07279	+	0.390463i	−0.255570	+	0.966790i	$0.582263\pi$
$24$	−0.342020	+	0.939693i	−0.0698146	+	0.191814i
$25$	0.669678	−	3.79793i	0.133936	−	0.759587i
$26$		−	4.70905i		−	0.923520i
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$	2.60240	−	0.476976i	0.491808	−	0.0901399i
$29$	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	$0.0105414\pi$
$30$	−0.534668	+	0.926071i	−0.0976165	+	0.169077i
$31$	−3.12424	−	5.41135i	−0.561130	−	0.971906i	−0.997398	−	0.0720895i	$-0.977033\pi$
$31$	−3.12424	−	5.41135i	−0.561130	−	0.971906i	0.436268	−	0.899817i	$-0.356300\pi$
$32$	−0.984808	−	0.173648i	−0.174091	−	0.0306970i
$33$	−3.32462	+	2.78969i	−0.578742	+	0.485622i
$34$	0.979794	−	5.55669i	0.168033	−	0.952964i
$35$	2.82913	−	0.0190632i	0.478210	−	0.00322227i
$36$	−0.766044	+	0.642788i	−0.127674	+	0.107131i
$37$	8.67783	−	5.01015i	1.42663	−	0.823663i	0.429773	−	0.902937i	$-0.358594\pi$
$37$	8.67783	−	5.01015i	1.42663	−	0.823663i	0.996853	+	0.0792741i	$0.0252602\pi$
$38$	2.97002	+	3.19045i	0.481800	+	0.517560i
$39$	2.35452	−	4.07816i	0.377026	−	0.653028i
$40$	−1.00485	−	0.365734i	−0.158880	−	0.0578277i
$41$	−5.27060	−	1.91834i	−0.823130	−	0.299595i	−0.104094	−	0.994568i	$-0.533194\pi$
$41$	−5.27060	−	1.91834i	−0.823130	−	0.299595i	−0.719036	+	0.694973i	$0.755416\pi$
$42$	2.49223	+	0.888128i	0.384560	+	0.137041i
$43$	−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	$-0.206277\pi$
$44$	−3.32462	−	2.78969i	−0.501206	−	0.420561i
$45$	−0.926071	+	0.534668i	−0.138051	+	0.0797035i
$46$		−	5.47511i		−	0.807260i
$47$	8.42350	+	1.48529i	1.22869	+	0.216652i	0.750064	−	0.661365i	$-0.230023\pi$
$47$	8.42350	+	1.48529i	1.22869	+	0.216652i	0.478629	+	0.878017i	$0.341134\pi$
$48$	−0.766044	−	0.642788i	−0.110569	−	0.0927784i
$49$	−1.30832	−	6.87665i	−0.186903	−	0.982378i
$50$	3.33985	+	1.92826i	0.472326	+	0.272697i
$51$	3.62687	−	4.32233i	0.507863	−	0.605248i
$52$	4.42506	+	1.61059i	0.613645	+	0.223349i
$53$	−7.30024	+	8.70009i	−1.00277	+	1.19505i	−0.0220201	+	0.999758i	$0.507010\pi$
$53$	−7.30024	+	8.70009i	−1.00277	+	1.19505i	−0.980745	+	0.195292i	$0.937435\pi$
$54$	−0.984808	+	0.173648i	−0.134015	+	0.0236305i
$55$	−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
$59$	−0.282071	−	1.59970i	−0.0367225	−	0.208264i	0.960926	−	0.276807i	$-0.0892761\pi$
$59$	−0.282071	−	1.59970i	−0.0367225	−	0.208264i	−0.997648	+	0.0685429i	$0.978165\pi$
$60$	−0.687355	−	0.819158i	−0.0887372	−	0.105753i
$61$	−1.81067	−	4.97478i	−0.231833	−	0.636955i	0.768162	−	0.640256i	$-0.221172\pi$
$61$	−1.81067	−	4.97478i	−0.231833	−	0.636955i	−0.999995	+	0.00330077i	$0.998949\pi$
$62$	6.15355	−	1.08504i	0.781502	−	0.137800i
$63$	1.71427	+	2.01526i	0.215978	+	0.253899i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	4.36092	+	2.51778i	0.540905	+	0.312292i
$66$	−1.48436	−	4.07825i	−0.182712	−	0.501998i
$67$	−2.96160	−	8.13692i	−0.361816	−	0.994083i	−0.978387	−	0.206783i	$-0.933701\pi$
$67$	−2.96160	−	8.13692i	−0.361816	−	0.994083i	0.616570	−	0.787300i	$-0.288522\pi$
$68$	4.88647	+	2.82120i	0.592571	+	0.342121i
$69$	2.73755	−	4.74158i	0.329563	−	0.570819i
$70$	−0.949706	+	2.66503i	−0.113512	+	0.318532i
$71$	−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	$0.688829\pi$
$72$	−0.342020	−	0.939693i	−0.0403075	−	0.110744i
$73$	2.11404	+	2.51942i	0.247430	+	0.294876i	0.875437	−	0.483332i	$-0.160574\pi$
$73$	2.11404	+	2.51942i	0.247430	+	0.294876i	−0.628007	+	0.778208i	$0.716129\pi$
$74$	1.74001	+	9.86806i	0.202272	+	1.14714i
$75$	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
$79$	7.04605	−	1.24241i	0.792742	−	0.139782i	0.237409	−	0.971410i	$-0.423702\pi$
$79$	7.04605	−	1.24241i	0.792742	−	0.139782i	0.555333	+	0.831628i	$0.312591\pi$
$80$	0.687355	−	0.819158i	0.0768487	−	0.0915847i
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$	3.60530	−	4.29663i	0.398139	−	0.474484i
$83$	−3.27774	−	1.89240i	−0.359778	−	0.207718i	0.309205	−	0.950995i	$-0.399937\pi$
$83$	−3.27774	−	1.89240i	−0.359778	−	0.207718i	−0.668984	+	0.743277i	$0.733270\pi$
$84$	−1.68696	+	2.03818i	−0.184063	+	0.222383i
$85$	4.62202	+	3.87834i	0.501329	+	0.420665i
$86$	5.88963	+	1.03850i	0.635095	+	0.111984i
$87$			6.64606i			0.712532i
$88$	3.75854	−	2.16999i	0.400661	−	0.231322i
$89$	4.76380	+	3.99731i	0.504962	+	0.423714i	0.859352	−	0.511384i	$-0.170867\pi$
$89$	4.76380	+	3.99731i	0.504962	+	0.423714i	−0.354390	+	0.935098i	$0.615311\pi$
$90$	−0.185688	−	1.05309i	−0.0195732	−	0.111005i
$91$	4.18224	−	11.7360i	0.438417	−	1.23027i
$92$	5.14492	+	1.87260i	0.536395	+	0.195232i
$93$	5.87165	+	2.13711i	0.608862	+	0.221608i
$94$	−4.27672	+	7.40750i	−0.441110	+	0.764025i
$95$	−4.54256	+	1.04461i	−0.466057	+	0.107175i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	−4.53730	+	3.80725i	−0.460693	+	0.386568i	−0.843386	−	0.537308i	$-0.819441\pi$
$97$	−4.53730	+	3.80725i	−0.460693	+	0.386568i	0.382693	+	0.923876i	$0.374997\pi$
$98$	6.90941	+	1.12253i	0.697956	+	0.113393i
$99$	0.753631	−	4.27405i	0.0757427	−	0.429558i
$100$	−2.95427	+	2.47892i	−0.295427	+	0.247892i
$101$	−8.28612	−	1.46107i	−0.824500	−	0.145382i	−0.254548	−	0.967060i	$-0.581927\pi$
$101$	−8.28612	−	1.46107i	−0.824500	−	0.145382i	−0.569951	+	0.821679i	$0.693038\pi$
$102$	2.82120	+	4.88647i	0.279341	+	0.483832i
$103$	4.56695	−	7.91019i	0.449995	−	0.779414i	−0.548390	−	0.836223i	$-0.684759\pi$
$103$	4.56695	−	7.91019i	0.449995	−	0.779414i	0.998385	+	0.0568083i	$0.0180924\pi$
$104$	−3.02692	+	3.60734i	−0.296814	+	0.353729i
$105$	−2.15499	+	1.83313i	−0.210305	+	0.178896i
$106$	−5.67858	−	9.83559i	−0.551552	−	0.955317i
$107$		−	20.0159i		−	1.93501i	−0.252846	−	0.967507i	$-0.581367\pi$
$107$		−	20.0159i		−	1.93501i	0.252846	−	0.967507i	$-0.418633\pi$
$108$	0.173648	−	0.984808i	0.0167093	−	0.0947632i
$109$	−5.95327	+	16.3565i	−0.570220	+	1.56667i	0.233939	+	0.972251i	$0.424839\pi$
$109$	−5.95327	+	16.3565i	−0.570220	+	1.56667i	−0.804159	+	0.594415i	$0.797384\pi$
$110$	4.36102	−	1.58728i	0.415807	−	0.151341i
$111$	−3.42714	+	9.41599i	−0.325290	+	0.893727i
$112$	−2.30015	−	1.30741i	−0.217344	−	0.123538i
$113$			0.609169i			0.0573058i	0.999589	+	0.0286529i	$0.00912175\pi$
$113$			0.609169i			0.0573058i	−0.999589	+	0.0286529i	$0.990878\pi$
$114$	−4.32595	−	0.534940i	−0.405162	−	0.0501017i
$115$	5.07034	+	2.92736i	0.472812	+	0.272978i
$116$	−6.54509	+	1.15408i	−0.607696	+	0.107153i
$117$	0.817718	+	4.63751i	0.0755980	+	0.428738i
$118$	1.59970	+	0.282071i	0.147265	+	0.0259667i
$119$	7.37692	−	12.9784i	0.676241	−	1.18973i
$120$	1.00485	−	0.365734i	0.0917295	−	0.0333868i
$121$	7.83547			0.712316
$122$	5.29405			0.479300
$123$	5.27060	−	1.91834i	0.475234	−	0.172971i
$124$	−1.08504	+	6.15355i	−0.0974393	+	0.552606i
$125$	−8.20177	+	4.73530i	−0.733589	+	0.423538i
$126$	−2.48004	+	0.921632i	−0.220939	+	0.0821055i
$127$	−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	$-0.394648\pi$
$128$	0.642788	+	0.766044i	0.0568149	+	0.0677094i
$129$	4.58132	+	3.84418i	0.403362	+	0.338461i
$130$	−3.85746	+	3.23679i	−0.338321	+	0.283885i
$131$	3.07323	−	8.44362i	0.268509	−	0.737723i	−0.730016	−	0.683430i	$-0.760487\pi$
$131$	3.07323	−	8.44362i	0.268509	−	0.737723i	0.998525	−	0.0542926i	$-0.0172904\pi$
$132$	4.33999			0.377747
$133$	4.56844	+	10.5891i	0.396134	+	0.918193i
$134$	8.65913			0.748035
$135$	0.365734	−	1.00485i	0.0314774	−	0.0864834i
$136$	−4.32233	+	3.62687i	−0.370637	+	0.311001i
$137$	4.77818	+	4.00937i	0.408227	+	0.342544i	0.823663	−	0.567079i	$-0.191927\pi$
$137$	4.77818	+	4.00937i	0.408227	+	0.342544i	−0.415436	+	0.909622i	$0.636371\pi$
$138$	3.51933	+	4.19417i	0.299585	+	0.357032i
$139$	3.76077	+	10.3326i	0.318984	+	0.876402i	0.990757	+	0.135645i	$0.0433107\pi$
$139$	3.76077	+	10.3326i	0.318984	+	0.876402i	−0.671773	+	0.740757i	$0.734467\pi$
$140$	−2.17949	−	1.80393i	−0.184201	−	0.152460i
$141$	−7.40750	+	4.27672i	−0.623824	+	0.360165i
$142$	2.03243	−	11.5265i	0.170558	−	0.967283i
$143$	−19.2047	+	6.98993i	−1.60598	+	0.584528i
$144$	1.00000			0.0833333
$145$	−7.10686			−0.590193
$146$	−3.09052	+	1.12486i	−0.255774	+	0.0930940i
$147$	5.42246	+	4.42684i	0.447237	+	0.365120i
$148$	−9.86806	−	1.74001i	−0.811150	−	0.143028i
$149$	2.42597	+	13.7584i	0.198743	+	1.12713i	0.906986	+	0.421160i	$0.138377\pi$
$149$	2.42597	+	13.7584i	0.198743	+	1.12713i	−0.708243	+	0.705969i	$0.750512\pi$
$150$	−3.79793	+	0.669678i	−0.310100	+	0.0546790i
$151$	−20.0418	−	11.5711i	−1.63098	−	0.941646i	−0.983792	−	0.179316i	$-0.942612\pi$
$151$	−20.0418	−	11.5711i	−1.63098	−	0.941646i	−0.647188	−	0.762331i	$-0.724055\pi$
$152$	−0.224380	−	4.35312i	−0.0181996	−	0.353085i
$153$			5.64241i			0.456162i
$154$	−5.80813	−	9.90524i	−0.468033	−	0.798187i
$155$	−2.28528	+	6.27877i	−0.183558	+	0.504323i
$156$	−4.42506	+	1.61059i	−0.354288	+	0.128950i
$157$	−4.77384	+	13.1160i	−0.380994	+	1.04677i	0.589944	+	0.807444i	$0.299150\pi$
$157$	−4.77384	+	13.1160i	−0.380994	+	1.04677i	−0.970939	+	0.239329i	$0.923073\pi$
$158$	−1.24241	+	7.04605i	−0.0988407	+	0.560553i
$159$		−	11.3572i		−	0.900681i
$160$	0.534668	+	0.926071i	0.0422692	+	0.0732124i
$161$	4.86259	−	13.6452i	0.383226	−	1.07540i
$162$	0.642788	−	0.766044i	0.0505022	−	0.0601861i
$163$	−6.71941	+	11.6384i	−0.526305	+	0.911586i	0.473226	+	0.880941i	$0.343090\pi$
$163$	−6.71941	+	11.6384i	−0.526305	+	0.911586i	−0.999530	+	0.0306452i	$0.990244\pi$
$164$	2.80443	+	4.85741i	0.218989	+	0.379300i
$165$	4.57039	+	0.805884i	0.355805	+	0.0627380i
$166$	2.89933	−	2.43282i	0.225031	−	0.188824i
$167$	−3.68088	+	20.8753i	−0.284835	+	1.61538i	0.421038	+	0.907043i	$0.361666\pi$
$167$	−3.68088	+	20.8753i	−0.284835	+	1.61538i	−0.705873	+	0.708338i	$0.749445\pi$
$168$	−1.33828	−	2.28232i	−0.103251	−	0.176085i
$169$	7.02856	−	5.89766i	0.540659	−	0.453666i
$170$	−5.22527	+	3.01681i	−0.400760	+	0.231379i
$171$	−3.47891	−	2.62625i	−0.266039	−	0.200834i
$172$	−2.99024	+	5.17925i	−0.228004	+	0.394914i
$173$	−18.2151	−	6.62974i	−1.38487	−	0.504050i	−0.461217	−	0.887288i	$-0.652587\pi$
$173$	−18.2151	−	6.62974i	−1.38487	−	0.504050i	−0.923650	+	0.383237i	$0.874809\pi$
$174$	−6.24525	−	2.27309i	−0.473451	−	0.172322i
$175$	6.61114	+	7.77189i	0.499755	+	0.587499i
$176$	0.753631	+	4.27405i	0.0568070	+	0.322169i
$177$	1.24435	+	1.04413i	0.0935310	+	0.0784818i
$178$	−5.38556	+	3.10935i	−0.403664	+	0.233056i
$179$			9.08900i			0.679343i	0.940544	+	0.339672i	$0.110316\pi$
$179$			9.08900i			0.679343i	−0.940544	+	0.339672i	$0.889684\pi$
$180$	1.05309	+	0.185688i	0.0784927	+	0.0138404i
$181$	0.273711	+	0.229671i	0.0203448	+	0.0170713i	0.652903	−	0.757441i	$-0.273551\pi$
$181$	0.273711	+	0.229671i	0.0203448	+	0.0170713i	−0.632559	+	0.774513i	$0.717995\pi$
$182$	9.59787	+	7.94398i	0.711441	+	0.588847i
$183$	4.58478	+	2.64702i	0.338917	+	0.195674i
$184$	−3.51933	+	4.19417i	−0.259448	+	0.309199i
$185$	−10.0689	−	3.66476i	−0.740277	−	0.269439i
$186$	−4.01645	+	4.78662i	−0.294500	+	0.350972i
$187$	−24.1159	+	4.25229i	−1.76353	+	0.310958i
$188$	−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	0.993243	+	0.116056i	$0.0370253\pi$
$191$	8.25249	+	14.2937i	0.597129	+	1.03426i	−0.396114	+	0.918202i	$0.629641\pi$
$192$	0.173648	+	0.984808i	0.0125320	+	0.0710724i
$193$	−8.20031	−	9.77275i	−0.590271	−	0.703458i	0.385387	−	0.922755i	$-0.374068\pi$
$193$	−8.20031	−	9.77275i	−0.590271	−	0.703458i	−0.975658	+	0.219297i	$0.929624\pi$
$194$	−2.02580	−	5.56583i	−0.145444	−	0.399603i
$195$	−4.95905	+	0.874414i	−0.355125	+	0.0626181i
$196$	−3.41799	+	6.10879i	−0.244142	+	0.436342i
$197$	−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	$0.239781\pi$
$198$	3.75854	+	2.16999i	0.267108	+	0.154215i
$199$	−7.53816	−	20.7109i	−0.534366	−	1.46816i	−0.853825	−	0.520559i	$-0.825723\pi$
$199$	−7.53816	−	20.7109i	−0.534366	−	1.46816i	0.319459	−	0.947600i	$-0.396499\pi$
$200$	−1.31901	−	3.62395i	−0.0932680	−	0.256252i
$201$	7.49902	+	4.32956i	0.528940	+	0.305384i
$202$	4.20697	−	7.28669i	0.296002	−	0.512690i
$203$	3.17001	+	17.2957i	0.222491	+	1.21392i
$204$	−5.55669	+	0.979794i	−0.389046	+	0.0685993i
$205$	2.05135	+	5.63604i	0.143273	+	0.393638i
$206$	5.87116	+	6.99698i	0.409063	+	0.487502i
$207$	0.950742	+	5.39193i	0.0660812	+	0.374765i
$208$	−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	$0.732553\pi$
$212$	11.1846	−	1.97215i	0.768163	−	0.135448i
$213$	7.52339	−	8.96603i	0.515494	−	0.614342i
$214$	18.8088	+	6.84585i	1.28574	+	0.467973i
$215$	−4.11072	+	4.89896i	−0.280349	+	0.334107i
$216$	0.866025	+	0.500000i	0.0589256	+	0.0340207i
$217$	16.2997	+	2.76097i	1.10650	+	0.187427i
$218$	−13.3339	−	11.1885i	−0.903087	−	0.757780i
$219$	−3.23890	−	0.571106i	−0.218865	−	0.0385918i
$220$			4.64090i			0.312889i
$221$	23.0106	−	13.2852i	1.54786	−	0.893658i
$222$	−7.67599	−	6.44092i	−0.515179	−	0.432286i
$223$	−4.19519	−	23.7921i	−0.280930	−	1.59324i	−0.719470	−	0.694523i	$-0.755615\pi$
$223$	−4.19519	−	23.7921i	−0.280930	−	1.59324i	0.438540	−	0.898712i	$-0.355496\pi$
$224$	2.01526	−	1.71427i	0.134650	−	0.114540i
$225$	−3.62395	−	1.31901i	−0.241596	−	0.0879339i
$226$	−0.572432	−	0.208348i	−0.0380776	−	0.0138591i
$227$	2.51146	−	4.34998i	0.166692	−	0.288718i	−0.770563	−	0.637364i	$-0.780025\pi$
$227$	2.51146	−	4.34998i	0.166692	−	0.288718i	0.937255	+	0.348645i	$0.113358\pi$
$228$	1.98224	−	3.88210i	0.131277	−	0.257099i
$229$	−2.62312	+	1.51446i	−0.173341	+	0.100078i	−0.584160	−	0.811638i	$-0.698576\pi$
$229$	−2.62312	+	1.51446i	−0.173341	+	0.100078i	0.410819	+	0.911717i	$0.365243\pi$
$230$	−4.48498	+	3.76334i	−0.295731	+	0.248148i
$231$	−0.0773695	−	11.4823i	−0.00509054	−	0.755477i
$232$	1.15408	−	6.54509i	0.0757688	−	0.429706i
$233$	12.0289	−	10.0934i	0.788036	−	0.661241i	−0.157222	−	0.987563i	$-0.550254\pi$
$233$	12.0289	−	10.0934i	0.788036	−	0.661241i	0.945259	+	0.326322i	$0.105809\pi$
$234$	−4.63751	−	0.817718i	−0.303163	−	0.0534559i
$235$	−4.57325	−	7.92110i	−0.298326	−	0.516716i
$236$	−0.812191	+	1.40676i	−0.0528691	+	0.0915720i
$237$	−4.59898	+	5.48085i	−0.298736	+	0.356019i
$238$	9.67263	+	11.3709i	0.626984	+	0.737066i
$239$	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	$0.602758\pi$
$240$			1.06934i			0.0690253i
$241$	−0.668094	+	3.78895i	−0.0430357	+	0.244068i	−0.998735	−	0.0502759i	$-0.983990\pi$
$241$	−0.668094	+	3.78895i	−0.0430357	+	0.244068i	0.955700	+	0.294344i	$0.0951010\pi$
$242$	−2.67989	+	7.36293i	−0.172270	+	0.473307i
$243$	0.939693	−	0.342020i	0.0602813	−	0.0219406i
$244$	−1.81067	+	4.97478i	−0.115916	+	0.318477i
$245$	−4.73378	+	5.79843i	−0.302430	+	0.370448i
$246$			5.60886i			0.357608i
$247$	−2.51906	+	20.3711i	−0.160284	+	1.29618i
$248$	−5.41135	−	3.12424i	−0.343621	−	0.198390i
$249$	3.72730	−	0.657224i	0.236208	−	0.0416499i
$250$	−1.64455	−	9.32671i	−0.104011	−	0.589873i
$251$	2.78226	+	0.490588i	0.175615	+	0.0309656i	0.260764	−	0.965403i	$-0.416026\pi$
$251$	2.78226	+	0.490588i	0.175615	+	0.0309656i	−0.0851492	+	0.996368i	$0.527137\pi$
$252$	−0.0178271	−	2.64569i	−0.00112300	−	0.166663i
$253$	−22.3289	+	8.12704i	−1.40380	+	0.510943i
$254$	17.5251			1.09962
$255$	−6.03362			−0.377840
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	1.57291	−	8.92041i	0.0981154	−	0.556440i	−0.895633	−	0.444794i	$-0.853277\pi$
$257$	1.57291	−	8.92041i	0.0981154	−	0.556440i	0.993748	−	0.111646i	$-0.0356122\pi$
$258$	−5.17925	+	2.99024i	−0.322446	+	0.186164i
$259$	−4.42760	+	26.1389i	−0.275118	+	1.62419i
$260$	−1.72226	−	4.73187i	−0.106810	−	0.293458i
$261$	−4.27200	−	5.09117i	−0.264430	−	0.315136i
$262$	6.88330	+	5.77578i	0.425252	+	0.356829i
$263$	12.0345	−	10.0981i	0.742079	−	0.622678i	−0.191316	−	0.981528i	$-0.561276\pi$
$263$	12.0345	−	10.0981i	0.742079	−	0.622678i	0.933395	+	0.358850i	$0.116831\pi$
$264$	−1.48436	+	4.07825i	−0.0913562	+	0.250999i
$265$	12.1446			0.746038
$266$	−11.5130	+	0.671244i	−0.705908	+	0.0411566i
$267$	−6.21870			−0.380579
$268$	−2.96160	+	8.13692i	−0.180908	+	0.497041i
$269$	−5.90892	+	4.95817i	−0.360273	+	0.302305i	−0.804900	−	0.593411i	$-0.797781\pi$
$269$	−5.90892	+	4.95817i	−0.360273	+	0.302305i	0.444626	+	0.895716i	$0.353336\pi$
$270$	0.819158	+	0.687355i	0.0498524	+	0.0418311i
$271$	15.7329	+	18.7497i	0.955706	+	1.13897i	0.990213	+	0.139561i	$0.0445692\pi$
$271$	15.7329	+	18.7497i	0.955706	+	1.13897i	−0.0345078	+	0.999404i	$0.510986\pi$
$272$	−1.92982	−	5.30213i	−0.117012	−	0.321489i
$273$	4.34001	+	11.6786i	0.262669	+	0.706823i
$274$	−5.40181	+	3.11874i	−0.326335	+	0.188410i
$275$	2.90639	−	16.4830i	0.175262	−	0.993961i
$276$	−5.14492	+	1.87260i	−0.309688	+	0.112717i
$277$	16.2542			0.976619			0.488310	−	0.872670i	$-0.337614\pi$
$277$	16.2542			0.976619			0.488310	+	0.872670i	$0.337614\pi$
$278$	−10.9958			−0.659481
$279$	−5.87165	+	2.13711i	−0.351527	+	0.127945i
$280$	2.44057	−	1.43107i	0.145852	−	0.0855231i
$281$	−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	$0.591432\pi$
$282$	−1.48529	−	8.42350i	−0.0884477	−	0.501612i
$283$	−12.9686	+	2.28672i	−0.770906	+	0.135931i	−0.545248	−	0.838275i	$-0.683564\pi$
$283$	−12.9686	+	2.28672i	−0.770906	+	0.135931i	−0.225658	+	0.974207i	$0.572453\pi$
$284$	10.1362	+	5.85216i	0.601475	+	0.347262i
$285$	2.80834	−	3.72012i	0.166352	−	0.220361i
$286$		−	20.4372i		−	1.20848i
$287$	12.8012	−	7.50624i	0.755632	−	0.443080i
$288$	−0.342020	+	0.939693i	−0.0201537	+	0.0553719i
$289$	13.9420	−	5.07447i	0.820117	−	0.298498i
$290$	2.43069	−	6.67827i	0.142735	−	0.392161i
$291$	1.02852	−	5.83305i	0.0602931	−	0.341939i
$292$		−	3.28887i		−	0.192466i
$293$	7.32020	+	12.6790i	0.427650	+	0.740712i	0.996664	−	0.0816160i	$-0.0260081\pi$
$293$	7.32020	+	12.6790i	0.427650	+	0.740712i	−0.569013	+	0.822328i	$0.692675\pi$
$294$	−6.01446	+	3.58137i	−0.350771	+	0.208870i
$295$	−1.11653	+	1.33063i	−0.0650067	+	0.0774720i
$296$	5.01015	−	8.67783i	0.291209	−	0.504388i
$297$	2.16999	+	3.75854i	0.125916	+	0.218092i
$298$	−13.7584	−	2.42597i	−0.797000	−	0.140533i
$299$	19.7506	−	16.5727i	1.14221	−	0.958424i
$300$	0.669678	−	3.79793i	0.0386639	−	0.219274i
$301$	13.7560	+	7.81893i	0.792883	+	0.450675i
$302$	17.7280	−	14.8756i	1.02013	−	0.855993i
$303$	7.28669	−	4.20697i	0.418609	−	0.241684i
$304$	4.16734	+	1.27801i	0.239013	+	0.0732987i
$305$	−2.83056	+	4.90267i	−0.162077	+	0.280726i
$306$	−5.30213	−	1.92982i	−0.303102	−	0.110320i
$307$	−27.5530	−	10.0285i	−1.57253	−	0.572356i	−0.598971	−	0.800771i	$-0.704424\pi$
$307$	−27.5530	−	10.0285i	−1.57253	−	0.572356i	−0.973564	+	0.228415i	$0.926646\pi$
$308$	11.2944	−	2.07007i	0.643557	−	0.117953i
$309$	1.58609	+	8.99514i	0.0902293	+	0.511716i
$310$	−5.11850	−	4.29493i	−0.290711	−	0.243936i
$311$	−14.0904	+	8.13511i	−0.798994	+	0.461300i	−0.843119	−	0.537726i	$-0.819283\pi$
$311$	−14.0904	+	8.13511i	−0.798994	+	0.461300i	0.0441250	+	0.999026i	$0.485950\pi$
$312$		−	4.70905i		−	0.266597i
$313$	6.51012	+	1.14791i	0.367974	+	0.0648837i	0.354578	−	0.935027i	$-0.384625\pi$
$313$	6.51012	+	1.14791i	0.367974	+	0.0648837i	0.0133961	+	0.999910i	$0.495736\pi$
$314$	−10.6923	−	8.97189i	−0.603400	−	0.506313i
$315$	0.472500	−	2.78946i	0.0266224	−	0.157168i
$316$	−6.19619	−	3.57737i	−0.348563	−	0.201243i
$317$	−6.17577	+	7.35999i	−0.346866	+	0.413378i	−0.911067	−	0.412259i	$-0.864740\pi$
$317$	−6.17577	+	7.35999i	−0.346866	+	0.413378i	0.564201	+	0.825638i	$0.309184\pi$
$318$	10.6722	+	3.88438i	0.598469	+	0.217825i
$319$	18.5404	−	22.0956i	1.03806	−	1.23712i
$320$	−1.05309	+	0.185688i	−0.0588695	+	0.0103803i
$321$	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
$325$	3.15355	+	17.8846i	0.174927	+	0.992062i
$326$	−8.63830	−	10.2947i	−0.478431	−	0.570172i
$327$	−5.95327	−	16.3565i	−0.329217	−	0.904515i
$328$	−5.52364	+	0.973968i	−0.304992	+	0.0537784i
$329$	−17.2374	+	14.6629i	−0.950329	+	0.808394i
$330$	−2.32045	+	4.01914i	−0.127737	+	0.221246i
$331$	19.9051	+	11.4922i	1.09408	+	0.631670i	0.934661	−	0.355541i	$-0.115703\pi$
$331$	19.9051	+	11.4922i	1.09408	+	0.631670i	0.159423	+	0.987210i	$0.449037\pi$
$332$	1.29448	+	3.55655i	0.0710438	+	0.195191i
$333$	−3.42714	−	9.41599i	−0.187806	−	0.515993i
$334$	−18.3575	−	10.5987i	−1.00448	−	0.579934i
$335$	−4.62975	+	8.01897i	−0.252951	+	0.438123i
$336$	2.60240	−	0.476976i	0.141973	−	0.0260212i
$337$	−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	$0.540898\pi$
$338$	3.13808	+	8.62181i	0.170689	+	0.468964i
$339$	−0.391566	−	0.466651i	−0.0212670	−	0.0253450i
$340$	−1.04773	−	5.94196i	−0.0568210	−	0.322248i
$341$	−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
$345$	−5.76578	+	1.01666i	−0.310419	+	0.0547353i
$346$	12.4598	−	14.8491i	0.669845	−	0.798291i
$347$	−11.4268	−	4.15902i	−0.613423	−	0.223268i	0.0165774	−	0.999863i	$-0.494723\pi$
$347$	−11.4268	−	4.15902i	−0.613423	−	0.223268i	−0.630000	+	0.776595i	$0.716945\pi$
$348$	4.27200	−	5.09117i	0.229003	−	0.272916i
$349$	16.4221	+	9.48131i	0.879055	+	0.507523i	0.870347	−	0.492439i	$-0.163895\pi$
$349$	16.4221	+	9.48131i	0.879055	+	0.507523i	0.00870861	+	0.999962i	$0.497228\pi$
$350$	−9.56433	+	3.55429i	−0.511235	+	0.189985i
$351$	−3.60734	−	3.02692i	−0.192546	−	0.161565i
$352$	−4.27405	−	0.753631i	−0.227808	−	0.0401686i
$353$		−	14.8185i		−	0.788711i	−0.918958	−	0.394355i	$-0.870968\pi$
$353$		−	14.8185i		−	0.788711i	0.918958	−	0.394355i	$-0.129032\pi$
$354$	−1.40676	+	0.812191i	−0.0747682	+	0.0431674i
$355$	9.58769	+	8.04503i	0.508862	+	0.426986i
$356$	−1.07987	−	6.12423i	−0.0572328	−	0.324583i
$357$	2.69129	+	14.6838i	0.142438	+	0.777150i
$358$	−8.54086	−	3.10862i	−0.451399	−	0.164296i
$359$	−17.7310	−	6.45355i	−0.935805	−	0.340605i	−0.171297	−	0.985219i	$-0.554796\pi$
$359$	−17.7310	−	6.45355i	−0.935805	−	0.340605i	−0.764508	+	0.644614i	$0.777018\pi$
$360$	−0.534668	+	0.926071i	−0.0281795	+	0.0488083i
$361$	−11.1414	−	15.3905i	−0.586392	−	0.810028i
$362$	−0.309435	+	0.178652i	−0.0162635	+	0.00938975i
$363$	−6.00232	+	5.03654i	−0.315040	+	0.264350i
$364$	−10.7476	+	6.30205i	−0.563326	+	0.330317i
$365$	0.610704	−	3.46347i	0.0319657	−	0.181286i
$366$	−4.05547	+	3.40295i	−0.211983	+	0.177875i
$367$	27.7305	+	4.88963i	1.44752	+	0.255237i	0.841519	−	0.540227i	$-0.181662\pi$
$367$	27.7305	+	4.88963i	1.44752	+	0.255237i	0.606001	+	0.795464i	$0.292773\pi$
$368$	−2.73755	−	4.74158i	−0.142705	−	0.247172i
$369$	−2.80443	+	4.85741i	−0.145993	+	0.252867i
$370$	6.88750	−	8.20821i	0.358064	−	0.426724i
$371$	−5.41709	−	29.5559i	−0.281241	−	1.53447i
$372$	−3.12424	−	5.41135i	−0.161984	−	0.280565i
$373$		−	10.3780i		−	0.537355i	−0.963230	−	0.268677i	$-0.913413\pi$
$373$		−	10.3780i		−	0.537355i	0.963230	−	0.268677i	$-0.0865866\pi$
$374$	4.25229	−	24.1159i	0.219881	−	1.24701i
$375$	3.23913	−	8.89944i	0.167268	−	0.459565i
$376$	8.03761	−	2.92545i	0.414508	−	0.150869i
$377$	−10.7041	+	29.4092i	−0.551288	+	1.51465i
$378$	1.30741	−	2.30015i	0.0672458	−	0.118307i
$379$		−	6.71133i		−	0.344738i	−0.985032	−	0.172369i	$-0.944858\pi$
$379$		−	6.71133i		−	0.344738i	0.985032	−	0.172369i	$-0.0551421\pi$
$380$	4.15127	+	2.11968i	0.212956	+	0.108737i
$381$	15.1771	+	8.76253i	0.777549	+	0.448918i
$382$	−16.2542	+	2.86606i	−0.831639	+	0.146640i
$383$	−1.72909	−	9.80616i	−0.0883524	−	0.501071i	−0.996583	−	0.0826007i	$-0.973677\pi$
$383$	−1.72909	−	9.80616i	−0.0883524	−	0.501071i	0.908230	−	0.418471i	$-0.137434\pi$
$384$	−0.984808	−	0.173648i	−0.0502558	−	0.00886145i
$385$	12.2784	−	0.0827339i	0.625765	−	0.00421651i
$386$	11.9881	−	4.36329i	0.610176	−	0.222086i
$387$	−5.98048			−0.304005
$388$	5.92303			0.300696
$389$	5.52346	−	2.01038i	0.280051	−	0.101930i	−0.198176	−	0.980166i	$-0.563502\pi$
$389$	5.52346	−	2.01038i	0.280051	−	0.101930i	0.478227	+	0.878236i	$0.341280\pi$
$390$	0.874414	−	4.95905i	0.0442777	−	0.251111i
$391$	26.7539	−	15.4464i	1.35300	−	0.781157i
$392$	−4.57137	−	5.30119i	−0.230889	−	0.267751i
$393$	3.07323	+	8.44362i	0.155024	+	0.425924i
$394$	−4.10823	−	4.89600i	−0.206970	−	0.246657i
$395$	−5.86087	−	4.91785i	−0.294892	−	0.247444i
$396$	−3.32462	+	2.78969i	−0.167069	+	0.140187i
$397$	9.46167	−	25.9957i	0.474868	−	1.30469i	−0.438931	−	0.898521i	$-0.644643\pi$
$397$	9.46167	−	25.9957i	0.474868	−	1.30469i	0.913799	−	0.406167i	$-0.133135\pi$
$398$	22.0401			1.10477
$399$	−10.3062	−	5.17519i	−0.515954	−	0.259084i
$400$	3.85652			0.192826
$401$	7.51073	−	20.6356i	0.375068	−	1.03049i	−0.598306	−	0.801268i	$-0.704159\pi$
$401$	7.51073	−	20.6356i	0.375068	−	1.03049i	0.973374	−	0.229223i	$-0.0736185\pi$
$402$	−6.63328	+	5.56598i	−0.330838	+	0.277606i
$403$	22.5404	+	18.9136i	1.12282	+	0.942156i
$404$	5.40838	+	6.44546i	0.269077	+	0.320673i
$405$	0.365734	+	1.00485i	0.0181735	+	0.0499312i
$406$	−17.3369	−	2.93665i	−0.860414	−	0.145743i
$407$	37.6616	−	21.7440i	1.86682	−	1.07781i
$408$	0.979794	−	5.55669i	0.0485070	−	0.275097i
$409$	−14.3982	+	5.24052i	−0.711945	+	0.259127i	−0.672502	−	0.740095i	$-0.734781\pi$
$409$	−14.3982	+	5.24052i	−0.711945	+	0.259127i	−0.0394430	+	0.999222i	$0.512558\pi$
$410$	−5.99775			−0.296208
$411$	−6.23747			−0.307672
$412$	−8.58306	+	3.12398i	−0.422857	+	0.153907i
$413$	3.73632	+	2.12373i	0.183852	+	0.104502i
$414$	−5.39193	−	0.950742i	−0.264999	−	0.0467264i
$415$	0.702793	+	3.98574i	0.0344988	+	0.195652i
$416$	4.63751	−	0.817718i	0.227373	−	0.0400919i
$417$	−9.52260	−	5.49788i	−0.466324	−	0.269232i
$418$	12.8898	+	13.8465i	0.630462	+	0.677256i
$419$		−	29.1585i		−	1.42448i	−0.701934	−	0.712242i	$-0.747680\pi$
$419$		−	29.1585i		−	1.42448i	0.701934	−	0.712242i	$-0.252320\pi$
$420$	2.82913	−	0.0190632i	0.138047	−	0.000930188i
$421$	−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	$0.201810\pi$
$422$	−3.86561	+	1.40697i	−0.188175	+	0.0684901i
$423$	2.92545	−	8.03761i	0.142240	−	0.390802i
$424$	−1.97215	+	11.1846i	−0.0957761	+	0.543173i
$425$			21.7601i			1.05552i
$426$	5.85216	+	10.1362i	0.283538	+	0.491102i
$427$	13.1940	+	4.70179i	0.638502	+	0.227536i
$428$	−12.8660	+	15.3331i	−0.621901	+	0.741153i
$429$	10.2186	−	17.6991i	0.493359	−	0.854522i
$430$	−3.19757	−	5.53836i	−0.154201	−	0.267083i
$431$	19.6334	+	3.46189i	0.945706	+	0.166754i	0.625175	−	0.780484i	$-0.285028\pi$
$431$	19.6334	+	3.46189i	0.945706	+	0.166754i	0.320531	+	0.947238i	$0.396139\pi$
$432$	−0.766044	+	0.642788i	−0.0368563	+	0.0309261i
$433$	1.47022	−	8.33804i	0.0706543	−	0.400701i	−0.928886	−	0.370367i	$-0.879232\pi$
$433$	1.47022	−	8.33804i	0.0706543	−	0.400701i	0.999540	−	0.0303335i	$-0.00965695\pi$
$434$	−8.16931	+	14.3724i	−0.392139	+	0.689899i
$435$	5.44417	−	4.56820i	0.261028	−	0.219029i
$436$	15.0742	−	8.70310i	0.721924	−	0.416803i
$437$	−2.92885	+	23.6850i	−0.140106	+	1.13301i
$438$	1.64443	−	2.84824i	0.0785741	−	0.136094i
$439$	−10.6803	−	3.88730i	−0.509742	−	0.185531i	0.0743287	−	0.997234i	$-0.476319\pi$
$439$	−10.6803	−	3.88730i	−0.509742	−	0.185531i	−0.584070	+	0.811703i	$0.698541\pi$
$440$	−4.36102	−	1.58728i	−0.207903	−	0.0756707i
$441$	−6.99936	+	0.0943302i	−0.333303	+	0.00449191i
$442$	4.61390	+	26.1667i	0.219461	+	1.24462i
$443$	20.2825	+	17.0191i	0.963653	+	0.808601i	0.981543	−	0.191239i	$-0.0612506\pi$
$443$	20.2825	+	17.0191i	0.963653	+	0.808601i	−0.0178907	+	0.999840i	$0.505695\pi$
$444$	8.67783	−	5.01015i	0.411831	−	0.237771i
$445$		−	6.64988i		−	0.315235i
$446$	23.7921	+	4.19519i	1.12659	+	0.198648i
$447$	−10.7021	−	8.98013i	−0.506192	−	0.424746i
$448$	0.921632	+	2.48004i	0.0435430	+	0.117171i
$449$	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	$0.454285\pi$
$450$	2.47892	−	2.95427i	0.116858	−	0.139265i
$451$	−22.8743	−	8.32557i	−1.07711	−	0.392036i
$452$	0.391566	−	0.466651i	0.0184177	−	0.0219494i
$453$	22.7907	−	4.01862i	1.07080	−	0.188811i
$454$	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	0.625076	−	0.780564i	$-0.285068\pi$
$457$	−7.76968	−	13.4575i	−0.363450	−	0.629514i	−0.988526	+	0.151050i	$0.951735\pi$
$458$	−0.525966	−	2.98290i	−0.0245768	−	0.139382i
$459$	−3.62687	−	4.32233i	−0.169288	−	0.201749i
$460$	−2.00243	−	5.50164i	−0.0933639	−	0.256515i
$461$	−35.6786	+	6.29109i	−1.66172	+	0.293005i	−0.924082	−	0.382195i	$-0.875168\pi$
$461$	−35.6786	+	6.29109i	−1.66172	+	0.293005i	−0.737634	+	0.675200i	$0.764057\pi$
$462$	10.8163	+	3.85446i	0.503218	+	0.179326i
$463$	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	$-0.00456465\pi$
$464$	5.75565	+	3.32303i	0.267200	+	0.154268i
$465$	−2.28528	−	6.27877i	−0.105978	−	0.291171i
$466$	5.37059	+	14.7556i	0.248788	+	0.683539i
$467$	1.28322	+	0.740866i	0.0593802	+	0.0342832i	0.529396	−	0.848375i	$-0.322419\pi$
$467$	1.28322	+	0.740866i	0.0593802	+	0.0342832i	−0.470016	+	0.882658i	$0.655752\pi$
$468$	2.35452	−	4.07816i	0.108838	−	0.188513i
$469$	21.5806	+	7.69041i	0.996498	+	0.355110i
$470$	9.00754	−	1.58827i	0.415487	−	0.0732616i
$471$	−4.77384	−	13.1160i	−0.219967	−	0.604355i
$472$	−1.04413	−	1.24435i	−0.0480601	−	0.0572758i
$473$	−4.50708	−	25.5609i	−0.207236	−	1.17529i
$474$	−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
$478$	−20.1779	+	3.55790i	−0.922915	+	0.162735i
$479$	−7.77589	+	9.26694i	−0.355289	+	0.423417i	−0.913854	−	0.406044i	$-0.866908\pi$
$479$	−7.77589	+	9.26694i	−0.355289	+	0.423417i	0.558564	+	0.829461i	$0.311352\pi$
$480$	−1.00485	−	0.365734i	−0.0458648	−	0.0166934i
$481$	−30.3306	+	36.1466i	−1.38296	+	1.64814i
$482$	−3.33195	−	1.92370i	−0.151766	−	0.0876222i
$483$	5.04603	+	13.5785i	0.229602	+	0.617842i
$484$	−6.00232	−	5.03654i	−0.272833	−	0.228934i
$485$	6.23748	+	1.09984i	0.283229	+	0.0499410i
$486$			1.00000i			0.0453609i
$487$	−13.1535	+	7.59417i	−0.596041	+	0.344124i	−0.767483	−	0.641070i	$-0.778491\pi$
$487$	−13.1535	+	7.59417i	−0.596041	+	0.344124i	0.171441	+	0.985194i	$0.445158\pi$
$488$	−4.05547	−	3.40295i	−0.183583	−	0.154044i
$489$	−2.33363	−	13.2347i	−0.105530	−	0.598492i
$490$	−3.82969	−	6.43148i	−0.173008	−	0.290544i
$491$	−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	$0.792851\pi$
$492$	−5.27060	−	1.91834i	−0.237617	−	0.0864855i
$493$	−18.7499	+	32.4757i	−0.844452	+	1.46263i
$494$	−18.2810	−	9.33447i	−0.822501	−	0.419978i
$495$	−4.01914	+	2.32045i	−0.180647	+	0.104296i
$496$	4.78662	−	4.01645i	0.214925	−	0.180344i
$497$	15.3023	−	26.9217i	0.686402	−	1.20760i
$498$	−0.657224	+	3.72730i	−0.0294509	+	0.167024i
$499$	29.8633	−	25.0582i	1.33686	−	1.12176i	0.354443	−	0.935078i	$-0.384671\pi$
$499$	29.8633	−	25.0582i	1.33686	−	1.12176i	0.982420	−	0.186683i	$-0.0597739\pi$
$500$	9.32671	+	1.64455i	0.417103	+	0.0735466i
$501$	−10.5987	−	18.3575i	−0.473514	−	0.820151i
$502$	−1.41259	+	2.44668i	−0.0630470	+	0.109201i
$503$	16.7795	−	19.9970i	0.748161	−	0.891624i	−0.248877	−	0.968535i	$-0.580061\pi$
$503$	16.7795	−	19.9970i	0.748161	−	0.891624i	0.997038	+	0.0769113i	$0.0245058\pi$
$504$	2.49223	+	0.888128i	0.111013	+	0.0395604i
$505$	4.49866	+	7.79191i	0.200188	+	0.346736i
$506$		−	23.7619i		−	1.05634i
$507$	−1.59325	+	9.03574i	−0.0707585	+	0.401292i
$508$	−5.99392	+	16.4682i	−0.265937	+	0.730657i
$509$	−7.33639	+	2.67023i	−0.325180	+	0.118356i	−0.499451	−	0.866342i	$-0.666465\pi$
$509$	−7.33639	+	2.67023i	−0.325180	+	0.118356i	0.174272	+	0.984698i	$0.444243\pi$
$510$	2.06362	−	5.66975i	0.0913787	−	0.251061i
$511$	−8.70133	+	0.0586311i	−0.384924	+	0.00259369i
$512$		−	1.00000i		−	0.0441942i
$513$	4.35312	−	0.224380i	0.192195	−	0.00990662i
$514$	7.84448	+	4.52901i	0.346005	+	0.199766i
$515$	−9.61882	+	1.69606i	−0.423856	+	0.0747372i
$516$	−1.03850	−	5.88963i	−0.0457174	−	0.259276i
$517$	36.5579	+	6.44614i	1.60781	+	0.283501i
$518$	−23.0482	−	13.1006i	−1.01268	−	0.575607i
$519$	18.2151	−	6.62974i	0.799553	−	0.291013i
$520$	5.03555			0.220824
$521$	−12.9725			−0.568338			−0.284169	−	0.958774i	$-0.591718\pi$
$521$	−12.9725			−0.568338			−0.284169	+	0.958774i	$0.591718\pi$
$522$	6.24525	−	2.27309i	0.273347	−	0.0994902i
$523$	3.30278	−	18.7310i	0.144421	−	0.819050i	−0.823410	−	0.567447i	$-0.807931\pi$
$523$	3.30278	−	18.7310i	0.144421	−	0.819050i	0.967831	−	0.251603i	$-0.0809577\pi$
$524$	−7.78168	+	4.49276i	−0.339944	+	0.196267i
$525$	−10.0601	−	1.70406i	−0.439059	−	0.0743711i
$526$	5.37311	+	14.7625i	0.234279	+	0.643676i
$527$	22.6624	+	27.0080i	0.987191	+	1.17649i
$528$	−3.32462	−	2.78969i	−0.144686	−	0.121406i
$529$	5.34453	−	4.48459i	0.232371	−	0.194982i
$530$	−4.15370	+	11.4122i	−0.180425	+	0.495714i
$531$	−1.62438			−0.0704921
$532$	3.30692	−	11.0483i	0.143373	−	0.479003i
$533$	26.4124			1.14405
$534$	2.12692	−	5.84367i	0.0920409	−	0.252880i
$535$	−16.3962	+	13.7581i	−0.708870	+	0.594813i
$536$	−6.63328	−	5.56598i	−0.286514	−	0.240414i
$537$	−5.84229	−	6.96257i	−0.252114	−	0.300457i
$538$	−2.63819	−	7.24836i	−0.113740	−	0.312499i
$539$	−5.67811	−	29.8446i	−0.244573	−	1.28550i
$540$	−0.926071	+	0.534668i	−0.0398518	+	0.0230084i
$541$	−1.79398	+	10.1742i	−0.0771294	+	0.437422i	0.921650	+	0.388023i	$0.126842\pi$
$541$	−1.79398	+	10.1742i	−0.0771294	+	0.437422i	−0.998779	+	0.0493995i	$0.984269\pi$
$542$	−23.0000	+	8.37130i	−0.987933	+	0.359578i
$543$	−0.357305			−0.0153334
$544$	5.64241			0.241916
$545$	17.4906	−	6.36604i	0.749213	−	0.272691i
$546$	−12.4587	+	0.0839488i	−0.533183	+	0.00359268i
$547$	−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	$0.787113\pi$
$548$	−1.08313	−	6.14271i	−0.0462688	−	0.262404i
$549$	−5.21362	+	0.919301i	−0.222512	+	0.0392348i
$550$	14.4949	+	8.36862i	0.618064	+	0.356839i
$551$	−11.2963	−	26.6763i	−0.481239	−	1.13645i
$552$		−	5.47511i		−	0.233036i
$553$	−9.35416	+	16.4570i	−0.397779	+	0.699822i
$554$	−5.55926	+	15.2739i	−0.236190	+	0.648927i
$555$	10.0689	−	3.66476i	0.427399	−	0.155561i
$556$	3.76077	−	10.3326i	0.159492	−	0.438201i
$557$	3.47287	−	19.6956i	0.147150	−	0.834531i	−0.818465	−	0.574556i	$-0.805175\pi$
$557$	3.47287	−	19.6956i	0.147150	−	0.834531i	0.965615	−	0.259975i	$-0.0837142\pi$
$558$		−	6.24848i		−	0.264519i
$559$	14.0812	+	24.3893i	0.595571	+	1.03156i
$560$	0.510047	+	2.78284i	0.0215534	+	0.117596i
$561$	15.7406	−	18.7589i	0.664567	−	0.792000i
$562$	1.88537	−	3.26556i	0.0795296	−	0.137749i
$563$	−15.4460	−	26.7533i	−0.650973	−	1.12752i	−0.982887	−	0.184208i	$-0.941028\pi$
$563$	−15.4460	−	26.7533i	−0.650973	−	1.12752i	0.331915	−	0.943309i	$-0.392305\pi$
$564$	8.42350	+	1.48529i	0.354693	+	0.0625420i
$565$	0.499006	−	0.418716i	0.0209933	−	0.0176155i
$566$	2.28672	−	12.9686i	0.0961181	−	0.545113i
$567$	2.28232	−	1.33828i	0.0958485	−	0.0562027i
$568$	−8.96603	+	7.52339i	−0.376206	+	0.315674i
$569$	−4.69111	+	2.70841i	−0.196662	+	0.113543i	−0.595097	−	0.803654i	$-0.702887\pi$
$569$	−4.69111	+	2.70841i	−0.196662	+	0.113543i	0.398436	+	0.917196i	$0.369553\pi$
$570$	2.53526	+	3.91133i	0.106191	+	0.163828i
$571$	4.92524	−	8.53076i	0.206115	−	0.357001i	−0.744373	−	0.667765i	$-0.767251\pi$
$571$	4.92524	−	8.53076i	0.206115	−	0.357001i	0.950487	+	0.310763i	$0.100585\pi$
$572$	19.2047	+	6.98993i	0.802988	+	0.292264i
$573$	−15.5096	−	5.64503i	−0.647923	−	0.235825i
$574$	2.67529	+	14.5965i	0.111664	+	0.609246i
$575$	3.66656	+	20.7941i	0.152906	+	0.867173i
$576$	−0.766044	−	0.642788i	−0.0319185	−	0.0267828i
$577$	24.8894	−	14.3699i	1.03616	−	0.598226i	0.117415	−	0.993083i	$-0.462539\pi$
$577$	24.8894	−	14.3699i	1.03616	−	0.598226i	0.918743	+	0.394857i	$0.129206\pi$
$578$			14.8368i			0.617128i
$579$	12.5636	+	2.21530i	0.522126	+	0.0920648i
$580$	5.44417	+	4.56820i	0.226057	+	0.189684i
$581$	9.38646	−	3.48820i	0.389416	−	0.144715i
$582$	5.12950	+	2.96152i	0.212624	+	0.122759i
$583$	−31.6829	+	37.7583i	−1.31217	+	1.56379i
$584$	3.09052	+	1.12486i	0.127887	+	0.0465470i
$585$	3.23679	−	3.85746i	0.133825	−	0.159486i
$586$	−14.4180	+	2.54228i	−0.595601	+	0.105021i
$587$	20.0258	+	23.8658i	0.826554	+	0.985049i	1.00000		0.000205410i	$6.53839e-5\pi$
$587$	20.0258	+	23.8658i	0.826554	+	0.985049i	−0.173446	+	0.984843i	$0.555490\pi$
$588$	−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
$591$	−1.10983	−	6.29417i	−0.0456524	−	0.258908i
$592$	6.44092	+	7.67599i	0.264720	+	0.315481i
$593$	−0.582077	−	1.59924i	−0.0239031	−	0.0656731i	0.927167	−	0.374648i	$-0.122236\pi$
$593$	−0.582077	−	1.59924i	−0.0239031	−	0.0656731i	−0.951070	+	0.308975i	$0.900014\pi$
$594$	−4.27405	+	0.753631i	−0.175366	+	0.0309218i
$595$	−15.7019	+	2.87789i	−0.643716	+	0.117982i
$596$	6.98530	−	12.0989i	0.286129	−	0.495590i
$597$	19.0873	+	11.0201i	0.781191	+	0.451021i
$598$	8.81815	+	24.2277i	0.360601	+	0.990743i
$599$	0.0902097	+	0.247849i	0.00368587	+	0.0101268i	0.941522	−	0.336952i	$-0.109396\pi$
$599$	0.0902097	+	0.247849i	0.00368587	+	0.0101268i	−0.937836	+	0.347079i	$0.887174\pi$
$600$	3.33985	+	1.92826i	0.136349	+	0.0787209i
$601$	19.8478	−	34.3774i	0.809608	−	1.40228i	−0.103527	−	0.994627i	$-0.533013\pi$
$601$	19.8478	−	34.3774i	0.809608	−	1.40228i	0.913136	−	0.407656i	$-0.133654\pi$
$602$	−12.0522	+	10.2522i	−0.491212	+	0.417848i
$603$	−8.52757	+	1.50364i	−0.347270	+	0.0612330i
$604$	7.91513	+	21.7466i	0.322062	+	0.884858i
$605$	−5.38575	−	6.41849i	−0.218962	−	0.260949i
$606$	1.46107	+	8.28612i	0.0593518	+	0.336601i
$607$	7.02092	+	12.1606i	0.284970	+	0.493583i	0.972602	−	0.232477i	$-0.0746829\pi$
$607$	7.02092	+	12.1606i	0.284970	+	0.493583i	−0.687632	+	0.726060i	$0.741350\pi$
$608$	−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
$611$	−39.6667	+	6.99430i	−1.60474	+	0.282959i
$612$	3.62687	−	4.32233i	0.146607	−	0.174720i
$613$	0.215074	+	0.0782804i	0.00868674	+	0.00316172i	0.346360	−	0.938102i	$-0.387418\pi$
$613$	0.215074	+	0.0782804i	0.00868674	+	0.00316172i	−0.337673	+	0.941263i	$0.609640\pi$
$614$	18.8474	−	22.4614i	0.760619	−	0.906470i
$615$	−5.19420	−	2.99887i	−0.209450	−	0.120926i
$616$	−1.91768	+	11.3213i	−0.0772655	+	0.456146i
$617$	−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	$0.877639\pi$
$618$	−8.99514	−	1.58609i	−0.361838	−	0.0638017i
$619$			17.5556i			0.705621i	0.935695	+	0.352811i	$0.114774\pi$
$619$			17.5556i			0.705621i	−0.935695	+	0.352811i	$0.885226\pi$
$620$	5.78654	−	3.34086i	0.232393	−	0.134172i
$621$	−4.19417	−	3.51933i	−0.168306	−	0.141226i
$622$	−2.82529	−	16.0230i	−0.113284	−	0.642465i
$623$	−16.1836	+	2.96617i	−0.648381	+	0.118837i
$624$	4.42506	+	1.61059i	0.177144	+	0.0644752i
$625$	−8.60324	−	3.13132i	−0.344129	−	0.125253i
$626$	−3.30527	+	5.72490i	−0.132105	+	0.228813i
$627$	4.23966	+	18.4364i	0.169316	+	0.736277i
$628$	12.0878	−	6.97889i	0.482356	−	0.278488i
$629$	−43.3110	+	36.3423i	−1.72692	+	1.44906i
$630$	2.45963	+	1.39806i	0.0979940	+	0.0556999i
$631$	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	$-0.0536868\pi$
$632$	5.48085	−	4.59898i	0.218017	−	0.182938i
$633$	−4.05120	−	0.714336i	−0.161021	−	0.0283923i
$634$	−4.80390	−	8.32059i	−0.190787	−	0.330453i
$635$	−9.37008	+	16.2295i	−0.371840	+	0.644047i
$636$	−7.30024	+	8.70009i	−0.289473	+	0.344981i
$637$	16.8649	+	28.3224i	0.668210	+	1.12217i
$638$	14.4219	+	24.9795i	0.570968	+	0.988946i
$639$			11.7043i			0.463016i
$640$	0.185688	−	1.05309i	0.00733997	−	0.0416270i
$641$	−15.6724	+	43.0595i	−0.619022	+	1.70075i	0.0903464	+	0.995910i	$0.471203\pi$
$641$	−15.6724	+	43.0595i	−0.619022	+	1.70075i	−0.709368	+	0.704838i	$0.751020\pi$
$642$	−18.8088	+	6.84585i	−0.742325	+	0.270184i
$643$	−0.266212	+	0.731412i	−0.0104984	+	0.0288441i	−0.944831	−	0.327558i	$-0.893774\pi$
$643$	−0.266212	+	0.731412i	−0.0104984	+	0.0288441i	0.934333	+	0.356402i	$0.115997\pi$
$644$	−12.4960	+	7.32725i	−0.492410	+	0.288734i
$645$		−	6.39514i		−	0.251808i
$646$	−19.6294	−	14.8184i	−0.772310	−	0.583020i
$647$	19.1522	+	11.0575i	0.752952	+	0.434717i	0.826759	−	0.562556i	$-0.190182\pi$
$647$	19.1522	+	11.0575i	0.752952	+	0.434717i	−0.0738077	+	0.997272i	$0.523515\pi$
$648$	−0.984808	+	0.173648i	−0.0386869	+	0.00682154i
$649$	−1.22418	−	6.94269i	−0.0480534	−	0.272524i
$650$	−17.8846	−	3.15355i	−0.701494	−	0.123692i
$651$	−14.2611	+	8.36225i	−0.558935	+	0.327742i
$652$	12.6284	−	4.59635i	0.494565	−	0.180007i
$653$	−14.3097			−0.559982			−0.279991	−	0.960003i	$-0.590332\pi$
$653$	−14.3097			−0.559982			−0.279991	+	0.960003i	$0.590332\pi$
$654$	17.4062			0.680636
$655$	−9.02906	+	3.28631i	−0.352795	+	0.128407i
$656$	0.973968	−	5.52364i	0.0380270	−	0.215662i
$657$	2.84824	−	1.64443i	0.111121	−	0.0641555i
$658$	−7.88313	−	21.2129i	−0.307316	−	0.826964i
$659$	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	$0.652033\pi$
$660$	−2.98311	−	3.55513i	−0.116117	−	0.138383i
$661$	8.28685	+	6.95349i	0.322321	+	0.270460i	0.789562	−	0.613670i	$-0.210308\pi$
$661$	8.28685	+	6.95349i	0.322321	+	0.270460i	−0.467241	+	0.884130i	$0.654752\pi$
$662$	−17.6071	+	14.7741i	−0.684319	+	0.574212i
$663$	−9.08760	+	24.9680i	−0.352933	+	0.969676i
$664$	−3.78480			−0.146879
$665$	5.53401	−	11.0208i	0.214600	−	0.427367i
$666$	10.0203			0.388278
$667$	−12.4454	+	34.1934i	−0.481887	+	1.32397i
$668$	16.2381	−	13.6254i	0.628272	−	0.527183i
$669$	18.5070	+	15.5292i	0.715520	+	0.600393i
$670$	−5.95190	−	7.09320i	−0.229942	−	0.274034i
$671$	−7.85828	−	21.5905i	−0.303366	−	0.833490i
$672$	−0.441863	+	2.60859i	−0.0170452	+	0.100629i
$673$	−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	$0.622596\pi$
$674$	1.90247	−	10.7894i	0.0732804	−	0.415594i
$675$	3.62395	−	1.31901i	0.139486	−	0.0507687i
$676$	−9.17514			−0.352890
$677$	−32.5429			−1.25072			−0.625362	−	0.780335i	$-0.715049\pi$
$677$	−32.5429			−1.25072			−0.625362	+	0.780335i	$0.715049\pi$
$678$	0.572432	−	0.208348i	0.0219841	−	0.00800156i
$679$	−0.105591	−	15.6705i	−0.00405220	−	0.601379i
$680$	5.94196	+	1.04773i	0.227864	+	0.0401785i
$681$	0.872222	+	4.94662i	0.0334236	+	0.189555i
$682$	26.7063	−	4.70905i	1.02264	−	0.180319i
$683$	18.7725	+	10.8383i	0.718309	+	0.414716i	0.814130	−	0.580683i	$-0.197214\pi$
$683$	18.7725	+	10.8383i	0.718309	+	0.414716i	−0.0958209	+	0.995399i	$0.530548\pi$
$684$	0.976882	+	4.24802i	0.0373520	+	0.162427i
$685$		−	6.66995i		−	0.254846i
$686$	−13.9438	+	12.1889i	−0.532377	+	0.465375i
$687$	1.03595	−	2.84625i	0.0395240	−	0.108591i
$688$	5.61982	−	2.04545i	0.214253	−	0.0779819i
$689$	18.2917	−	50.2561i	0.696859	−	1.91460i
$690$	1.01666	−	5.76578i	0.0387037	−	0.219499i
$691$			16.0931i			0.612212i	0.951997	+	0.306106i	$0.0990262\pi$
$691$			16.0931i			0.612212i	−0.951997	+	0.306106i	$0.900974\pi$
$692$	9.69204	+	16.7871i	0.368436	+	0.638150i
$693$	7.43992	+	8.74619i	0.282619	+	0.332240i
$694$	7.81639	−	9.31521i	0.296706	−	0.353601i
$695$	5.87907	−	10.1829i	0.223006	−	0.386258i
$696$	3.32303	+	5.75565i	0.125959	+	0.218167i
$697$	31.1667	+	5.49552i	1.18052	+	0.208158i
$698$	−14.5262	+	12.1889i	−0.549825	+	0.461358i
$699$	−2.72672	+	15.4640i	−0.103134	+	0.584902i
$700$	−0.0687507	−	10.2032i	−0.00259853	−	0.385643i
$701$	−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
$703$	−2.24835	−	43.6195i	−0.0847982	−	1.64514i
$704$	2.16999	−	3.75854i	0.0817847	−	0.141655i
$705$	8.59490	+	3.12829i	0.323703	+	0.117818i
$706$	13.9249	+	5.06824i	0.524069	+	0.190746i
$707$	16.9563	−	14.4238i	0.637706	−	0.542463i
$708$	−0.282071	−	1.59970i	−0.0106009	−	0.0601205i
$709$	−5.04294	−	4.23153i	−0.189392	−	0.158919i	0.543162	−	0.839628i	$-0.317227\pi$
$709$	−5.04294	−	4.23153i	−0.189392	−	0.158919i	−0.732553	+	0.680710i	$0.761672\pi$
$710$	−10.8390	+	6.25792i	−0.406782	+	0.234856i
$711$		−	7.15474i		−	0.268324i
$712$	6.12423	+	1.07987i	0.229515	+	0.0404697i
$713$	26.2072	+	21.9905i	0.981469	+	0.823550i
$714$	−14.7187	−	2.49317i	−0.550835	−	0.0933046i
$715$	18.9263	+	10.9271i	0.707804	+	0.408651i
$716$	5.84229	−	6.96257i	0.218337	−	0.260204i
$717$	−19.2535	−	7.00770i	−0.719035	−	0.261707i
$718$	12.1287	−	14.4544i	0.452639	−	0.539434i
$719$	−5.35343	+	0.943955i	−0.199649	+	0.0352036i	−0.272578	−	0.962134i	$-0.587876\pi$
$719$	−5.35343	+	0.943955i	−0.199649	+	0.0352036i	0.0729291	+	0.997337i	$0.476765\pi$
$720$	−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
$724$	−0.0620453	−	0.351876i	−0.00230589	−	0.0130774i
$725$	−16.4751	−	19.6342i	−0.611869	−	0.729197i
$726$	−2.67989	−	7.36293i	−0.0994600	−	0.273264i
$727$	42.6461	−	7.51966i	1.58166	−	0.278889i	0.687345	−	0.726331i	$-0.258776\pi$
$727$	42.6461	−	7.51966i	1.58166	−	0.278889i	0.894313	+	0.447442i	$0.147665\pi$
$728$	−2.24610	−	12.2548i	−0.0832461	−	0.454194i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	3.04573	+	1.75845i	0.112727	+	0.0650832i
$731$	11.5412	+	31.7093i	0.426868	+	1.17281i
$732$	−1.81067	−	4.97478i	−0.0669243	−	0.183873i
$733$	−25.1223	−	14.5044i	−0.927912	−	0.535730i	−0.0417616	−	0.999128i	$-0.513297\pi$
$733$	−25.1223	−	14.5044i	−0.927912	−	0.535730i	−0.886151	+	0.463397i	$0.846630\pi$
$734$	−14.0791	+	24.3858i	−0.519671	+	0.900096i
$735$	−0.100871	−	7.48467i	−0.00372067	−	0.276076i
$736$	5.39193	−	0.950742i	0.198749	−	0.0350448i
$737$	−12.8533	−	35.3141i	−0.473457	−	1.30081i
$738$	−3.60530	−	4.29663i	−0.132713	−	0.158161i
$739$	−5.84075	−	33.1245i	−0.214855	−	1.21851i	−0.881157	−	0.472824i	$-0.843235\pi$
$739$	−5.84075	−	33.1245i	−0.214855	−	1.21851i	0.666302	−	0.745682i	$-0.267876\pi$
$740$	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	$0.780727\pi$
$744$	6.15355	−	1.08504i	0.225600	−	0.0397794i
$745$	9.60277	−	11.4441i	0.351818	−	0.419281i
$746$	9.75218	+	3.54950i	0.357053	+	0.129956i
$747$	−2.43282	+	2.89933i	−0.0890124	+	0.106081i
$748$	21.2072	+	12.2440i	0.775412	+	0.447684i
$749$	40.7960	+	33.7661i	1.49065	+	1.23379i
$750$	7.25489	+	6.08758i	0.264911	+	0.222287i
$751$	−45.0018	−	7.93504i	−1.64214	−	0.289554i	−0.725188	−	0.688551i	$-0.758247\pi$
$751$	−45.0018	−	7.93504i	−1.64214	−	0.289554i	−0.916952	+	0.398997i	$0.869358\pi$
$752$			8.55344i			0.311912i
$753$	−2.44668	+	1.41259i	−0.0891619	+	0.0514777i
$754$	−23.9746	−	20.1171i	−0.873103	−	0.732620i
$755$	4.29725	+	24.3709i	0.156393	+	0.886948i
$756$	1.71427	+	2.01526i	0.0623475	+	0.0732942i
$757$	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	$0.520825\pi$
$758$	6.30659	+	2.29541i	0.229066	+	0.0833731i
$759$	11.8809	−	20.5784i	0.431251	−	0.746948i
$760$	−3.41167	+	3.17594i	−0.123754	+	0.115204i
$761$	−8.34260	+	4.81660i	−0.302419	+	0.174602i	−0.643529	−	0.765422i	$-0.722530\pi$
$761$	−8.34260	+	4.81660i	−0.302419	+	0.174602i	0.341110	+	0.940023i	$0.389197\pi$
$762$	−13.4250	+	11.2649i	−0.486336	+	0.408084i
$763$	−23.2944	−	39.7266i	−0.843315	−	1.43820i
$764$	2.86606	−	16.2542i	0.103690	−	0.588057i
$765$	4.62202	−	3.87834i	0.167110	−	0.140222i
$766$	9.80616	+	1.72909i	0.354311	+	0.0624746i
$767$	3.82465	+	6.62448i	0.138100	+	0.239196i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	6.76484	−	8.06202i	0.243946	−	0.290724i	−0.630153	−	0.776471i	$-0.717008\pi$
$769$	6.76484	−	8.06202i	0.243946	−	0.290724i	0.874100	+	0.485747i	$0.161452\pi$
$770$	−4.12171	+	11.5662i	−0.148536	+	0.416817i
$771$	4.52901	+	7.84448i	0.163108	+	0.282512i
$772$			12.7574i			0.459150i
$773$	4.27152	−	24.2250i	0.153636	−	0.871313i	−0.806386	−	0.591389i	$-0.798580\pi$
$773$	4.27152	−	24.2250i	0.153636	−	0.871313i	0.960022	−	0.279924i	$-0.0903092\pi$
$774$	2.04545	−	5.61982i	0.0735220	−	0.202000i
$775$	−22.6442	+	8.24180i	−0.813402	+	0.296054i
$776$	−2.02580	+	5.56583i	−0.0727218	+	0.199802i
$777$	−13.4100	−	22.8695i	−0.481081	−	0.820440i
$778$			5.87795i			0.210735i
$779$	−17.8948	+	16.6584i	−0.641148	+	0.596849i
$780$	4.36092	+	2.51778i	0.156146	+	0.0901508i
$781$	−50.0248	+	8.82073i	−1.79003	+	0.315631i
$782$	5.36447	+	30.4234i	0.191833	+	1.08794i
$783$	6.54509	+	1.15408i	0.233902	+	0.0412433i
$784$	6.54499	−	2.48256i	0.233750	−	0.0886630i
$785$	14.0254	−	5.10484i	0.500589	−	0.182200i
$786$	−8.98551			−0.320503
$787$	10.9505			0.390343			0.195172	−	0.980769i	$-0.437474\pi$
$787$	10.9505			0.390343			0.195172	+	0.980769i	$0.437474\pi$
$788$	6.00583	−	2.18594i	0.213949	−	0.0778710i
$789$	−2.72800	+	15.4713i	−0.0971194	+	0.550791i
$790$	6.62580	−	3.82541i	0.235735	−	0.136102i
$791$	−1.24159	−	1.02764i	−0.0441460	−	0.0365388i
$792$	−1.48436	−	4.07825i	−0.0527445	−	0.144914i
$793$	16.0246	+	19.0974i	0.569052	+	0.678169i
$794$	21.1919	+	17.7821i	0.752073	+	0.631064i
$795$	−9.30331	+	7.80641i	−0.329954	+	0.276865i
$796$	−7.53816	+	20.7109i	−0.267183	+	0.734080i
$797$	−42.4569			−1.50390			−0.751950	−	0.659220i	$-0.770887\pi$
$797$	−42.4569			−1.50390			−0.751950	+	0.659220i	$0.770887\pi$
$798$	8.38801	−	7.91462i	0.296932	−	0.280175i
$799$	−48.2620			−1.70739
$800$	−1.31901	+	3.62395i	−0.0466340	+	0.128126i
$801$	4.76380	−	3.99731i	0.168321	−	0.141238i
$802$	16.8223	+	14.1156i	0.594015	+	0.498438i
$803$	9.17492	+	10.9342i	0.323776	+	0.385861i
$804$	−2.96160	−	8.13692i	−0.104447	−	0.286967i
$805$	−14.5199	+	5.39590i	−0.511761	+	0.190180i
$806$	−25.4823	+	14.7122i	−0.897575	+	0.518215i
$807$	1.33944	−	7.59636i	0.0471506	−	0.267405i
$808$	−7.90652	+	2.87774i	−0.278150	+	0.101238i
$809$	−45.0744			−1.58473			−0.792366	−	0.610047i	$-0.791151\pi$
$809$	−45.0744			−1.58473			−0.792366	+	0.610047i	$0.791151\pi$
$810$	−1.06934			−0.0375726
$811$	1.83714	−	0.668663i	0.0645106	−	0.0234799i	−0.309563	−	0.950879i	$-0.600183\pi$
$811$	1.83714	−	0.668663i	0.0645106	−	0.0234799i	0.374074	+	0.927399i	$0.377961\pi$
$812$	8.68910	−	15.2869i	0.304928	−	0.536466i
$813$	−24.1042	−	4.25022i	−0.845371	−	0.149062i
$814$	7.55160	+	42.8272i	0.264683	+	1.50109i
$815$	14.1523	−	2.49543i	0.495733	−	0.0874110i
$816$	4.88647	+	2.82120i	0.171061	+	0.0987619i
$817$	−24.9227	−	7.64310i	−0.871935	−	0.267398i
$818$		−	15.3222i		−	0.535730i
$819$	−10.8315	−	6.15664i	−0.378484	−	0.215130i
$820$	2.05135	−	5.63604i	0.0716363	−	0.196819i
$821$	−3.44589	+	1.25420i	−0.120262	+	0.0437719i	−0.401450	−	0.915881i	$-0.631494\pi$
$821$	−3.44589	+	1.25420i	−0.120262	+	0.0437719i	0.281188	+	0.959653i	$0.409272\pi$
$822$	2.13334	−	5.86131i	0.0744088	−	0.204437i
$823$	−7.86573	+	44.6088i	−0.274182	+	1.55496i	0.467366	+	0.884064i	$0.345203\pi$
$823$	−7.86573	+	44.6088i	−0.274182	+	1.55496i	−0.741548	+	0.670900i	$0.765908\pi$
$824$		−	9.13390i		−	0.318195i
$825$	8.36862	+	14.4949i	0.291358	+	0.504647i
$826$	−3.27355	+	2.78463i	−0.113901	+	0.0968898i
$827$	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	$0.0951953\pi$
$828$	2.73755	−	4.74158i	0.0951365	−	0.164781i
$829$	−3.60210	−	6.23901i	−0.125106	−	0.216690i	0.796668	−	0.604417i	$-0.206594\pi$
$829$	−3.60210	−	6.23901i	−0.125106	−	0.216690i	−0.921774	+	0.387727i	$0.873260\pi$
$830$	−3.98574	−	0.702793i	−0.138347	−	0.0243943i
$831$	−12.4514	+	10.4480i	−0.431935	+	0.362437i
$832$	−0.817718	+	4.63751i	−0.0283493	+	0.160777i
$833$	14.0076	+	36.9295i	0.485336	+	1.27953i
$834$	8.42323	−	7.06793i	0.291673	−	0.244743i
$835$	19.6303	−	11.3335i	0.679334	−	0.392214i
$836$	−17.4201	+	7.37669i	−0.602485	+	0.255128i
$837$	3.12424	−	5.41135i	0.107990	−	0.187043i
$838$	27.4000	+	9.97278i	0.946517	+	0.344504i
$839$	47.0759	+	17.1342i	1.62524	+	0.591539i	0.984371	−	0.176110i	$-0.0563514\pi$
$839$	47.0759	+	17.1342i	1.62524	+	0.591539i	0.640870	+	0.767649i	$0.278574\pi$
$840$	−0.949706	+	2.66503i	−0.0327680	+	0.0919524i
$841$	−2.63425	−	14.9396i	−0.0908364	−	0.515159i
$842$	−8.83660	−	7.41479i	−0.304529	−	0.255531i
$843$	3.26556	−	1.88537i	0.112472	−	0.0649356i
$844$		−	4.11369i		−	0.141599i
$845$	−9.66224	−	1.70371i	−0.332391	−	0.0586095i
$846$	6.55232	+	5.49805i	0.225273	+	0.189027i
$847$	−13.2181	+	15.9701i	−0.454181	+	0.548738i
$848$	−9.83559	−	5.67858i	−0.337756	−	0.195003i
$849$	8.46468	−	10.0878i	0.290507	−	0.346213i
$850$	−20.4478	−	7.44238i	−0.701353	−	0.255272i
$851$	−35.2647	+	42.0269i	−1.20886	+	1.44066i
$852$	−11.5265	+	2.03243i	−0.394891	+	0.0696300i
$853$	9.52893	+	11.3561i	0.326264	+	0.388827i	0.904096	−	0.427329i	$-0.140545\pi$
$853$	9.52893	+	11.3561i	0.326264	+	0.388827i	−0.577832	+	0.816156i	$0.696101\pi$
$854$	−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
$857$	−3.53629	−	20.0553i	−0.120797	−	0.685075i	−0.983716	−	0.179732i	$-0.942477\pi$
$857$	−3.53629	−	20.0553i	−0.120797	−	0.685075i	0.862918	−	0.505343i	$-0.168634\pi$
$858$	13.1368	+	15.6558i	0.448482	+	0.534480i
$859$	18.7845	+	51.6101i	0.640920	+	1.76091i	0.648816	+	0.760946i	$0.275265\pi$
$859$	18.7845	+	51.6101i	0.640920	+	1.76091i	−0.00789531	+	0.999969i	$0.502513\pi$
$860$	6.29799	−	1.11050i	0.214760	−	0.0378679i
$861$	−4.98138	+	13.9786i	−0.169765	+	0.476389i
$862$	−9.96812	+	17.2653i	−0.339516	+	0.588058i
$863$	−5.02105	−	2.89890i	−0.170918	−	0.0986798i	0.412100	−	0.911138i	$-0.364795\pi$
$863$	−5.02105	−	2.89890i	−0.170918	−	0.0986798i	−0.583019	+	0.812459i	$0.698129\pi$
$864$	−0.342020	−	0.939693i	−0.0116358	−	0.0319690i
$865$	7.08942	+	19.4780i	0.241047	+	0.662273i
$866$	7.33235	+	4.23333i	0.249163	+	0.143854i
$867$	−7.41838	+	12.8490i	−0.251941	+	0.436375i
$868$	−10.7116	−	12.5923i	−0.363576	−	0.427411i
$869$	30.5797	−	5.39203i	1.03735	−	0.182912i
$870$	2.43069	+	6.67827i	0.0824081	+	0.226414i
$871$	26.2105	+	31.2364i	0.888108	+	1.05841i
$872$	3.02255	+	17.1418i	0.102357	+	0.580493i
$873$	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
$877$	9.55468	−	1.68475i	0.322639	−	0.0568899i	−0.00998325	−	0.999950i	$-0.503178\pi$
$877$	9.55468	−	1.68475i	0.322639	−	0.0568899i	0.332622	+	0.943060i	$0.392067\pi$
$878$	7.30574	−	8.70664i	0.246557	−	0.293835i
$879$	−13.7575	−	5.00731i	−0.464028	−	0.168892i
$880$	2.98311	−	3.55513i	0.100561	−	0.119844i
$881$	−15.7293	−	9.08130i	−0.529933	−	0.305957i	0.211056	−	0.977474i	$-0.432310\pi$
$881$	−15.7293	−	9.08130i	−0.529933	−	0.305957i	−0.740989	+	0.671517i	$0.765643\pi$
$882$	2.30528	−	6.60951i	0.0776229	−	0.222554i
$883$	−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	$0.876180\pi$
$884$	−26.1667	−	4.61390i	−0.880081	−	0.155182i
$885$		−	1.73701i		−	0.0583889i
$886$	−22.9297	+	13.2385i	−0.770340	+	0.444756i
$887$	−1.24067	−	1.04105i	−0.0416577	−	0.0349550i	0.621721	−	0.783239i	$-0.286434\pi$
$887$	−1.24067	−	1.04105i	−0.0416577	−	0.0349550i	−0.663379	+	0.748284i	$0.730878\pi$
$888$	1.74001	+	9.86806i	0.0583908	+	0.331150i
$889$	43.6766	+	15.5645i	1.46486	+	0.522016i
$890$	6.24884	+	2.27439i	0.209462	+	0.0762378i
$891$	−4.07825	−	1.48436i	−0.136627	−	0.0497280i
$892$	−12.0796	+	20.9224i	−0.404453	+	0.700534i
$893$	22.4635	−	29.7567i	0.751711	−	0.995769i
$894$	12.0989	−	6.98530i	0.404648	−	0.233623i
$895$	7.44533	−	6.24737i	0.248870	−	0.208827i
$896$	−2.64569	+	0.0178271i	−0.0883863	+	0.000595563i
$897$	−4.47709	+	25.3908i	−0.149486	+	0.847776i
$898$	−20.0890	+	16.8567i	−0.670378	+	0.562514i
$899$	−40.8969	−	7.21122i	−1.36399	−	0.240508i
$900$	1.92826	+	3.33985i	0.0642754	+	0.111328i
$901$	32.0409	−	55.4964i	1.06744	−	1.84885i
$902$	15.6470	−	18.6473i	0.520987	−	0.620888i
$903$	−15.5636	+	2.85255i	−0.517925	+	0.0949268i
$904$	0.304585	+	0.527556i	0.0101303	+	0.0175463i
$905$		−	0.382078i		−	0.0127007i
$906$	−4.01862	+	22.7907i	−0.133510	+	0.757171i
$907$	−8.63183	+	23.7157i	−0.286615	+	0.787469i	0.709919	+	0.704283i	$0.248732\pi$
$907$	−8.63183	+	23.7157i	−0.286615	+	0.787469i	−0.996534	+	0.0831852i	$0.973491\pi$
$908$	−4.72001	+	1.71794i	−0.156639	+	0.0570119i
$909$	−2.87774	+	7.90652i	−0.0954486	+	0.262243i
$910$	−0.0897695	−	13.3225i	−0.00297583	−	0.441637i
$911$		−	24.1881i		−	0.801387i	−0.916212	−	0.400693i	$-0.868769\pi$
$911$		−	24.1881i		−	0.801387i	0.916212	−	0.400693i	$-0.131231\pi$
$912$	−4.01385	+	1.69970i	−0.132912	+	0.0562828i
$913$	−14.2253	−	8.21300i	−0.470790	−	0.271811i
$914$	15.3033	−	2.69838i	0.506187	−	0.0892545i
$915$	−0.983041	−	5.57511i	−0.0324983	−	0.184307i
$916$	2.98290	+	0.525966i	0.0985579	+	0.0173784i
$917$	12.0252	+	20.5078i	0.397106	+	0.677229i
$918$	5.30213	−	1.92982i	0.174996	−	0.0636934i
$919$	18.2099			0.600690			0.300345	−	0.953831i	$-0.402898\pi$
$919$	18.2099			0.600690			0.300345	+	0.953831i	$0.402898\pi$
$920$	5.85472			0.193025
$921$	27.5530	−	10.0285i	0.907903	−	0.330450i
$922$	6.29109	−	35.6786i	0.207186	−	1.17501i
$923$	47.7320	−	27.5581i	1.57112	−	0.907086i
$924$	−7.32139	+	8.84565i	−0.240856	+	0.291001i
$925$	−13.2168	−	36.3130i	−0.434567	−	1.19396i
$926$	14.1732	+	16.8910i	0.465762	+	0.555073i
$927$	−6.99698	−	5.87116i	−0.229811	−	0.192834i
$928$	−5.09117	+	4.27200i	−0.167126	+	0.140235i
$929$	15.6517	−	43.0027i	0.513516	−	1.41087i	−0.364032	−	0.931386i	$-0.618600\pi$
$929$	15.6517	−	43.0027i	0.513516	−	1.41087i	0.877549	−	0.479488i	$-0.159178\pi$
$930$	6.68172			0.219102
$931$	−29.2893	−	8.55213i	−0.959917	−	0.280285i
$932$	−15.7026			−0.514354
$933$	5.56474	−	15.2890i	0.182181	−	0.500539i
$934$	−1.13507	+	0.952439i	−0.0371407	+	0.0311648i
$935$	20.0595	+	16.8319i	0.656016	+	0.550463i
$936$	3.02692	+	3.60734i	0.0989379	+	0.117910i
$937$	15.0289	+	41.2916i	0.490973	+	1.34894i	0.899791	+	0.436322i	$0.143719\pi$
$937$	15.0289	+	41.2916i	0.490973	+	1.34894i	−0.408817	+	0.912616i	$0.634059\pi$
$938$	−14.6076	+	17.6488i	−0.476955	+	0.576255i
$939$	−5.72490	+	3.30527i	−0.186825	+	0.107864i
$940$	−1.58827	+	9.00754i	−0.0518038	+	0.293794i
$941$	−7.53421	+	2.74223i	−0.245608	+	0.0893941i	−0.461891	−	0.886937i	$-0.652829\pi$
$941$	−7.53421	+	2.74223i	−0.245608	+	0.0893941i	0.216283	+	0.976331i	$0.430607\pi$
$942$	13.9578			0.454769
$943$	30.7091			1.00003
$944$	1.52642	−	0.555571i	0.0496807	−	0.0180823i
$945$	1.43107	+	2.44057i	0.0465529	+	0.0793917i
$946$	25.5609	+	4.50708i	0.831056	+	0.146538i
$947$	1.38737	+	7.86817i	0.0450835	+	0.255681i	0.999017	−	0.0443382i	$-0.0141179\pi$
$947$	1.38737	+	7.86817i	0.0450835	+	0.255681i	−0.953933	+	0.300019i	$0.903007\pi$
$948$	7.04605	−	1.24241i	0.228845	−	0.0403515i
$949$	−13.4125	−	7.74372i	−0.435389	−	0.251372i
$950$	14.1061	−	9.14335i	0.457662	−	0.296649i
$951$		−	9.60779i		−	0.311554i
$952$	−0.100588	−	14.9281i	−0.00326007	−	0.483821i
$953$	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	$-0.0186662\pi$
$954$	−10.6722	+	3.88438i	−0.345526	+	0.125761i
$955$	6.03643	−	16.5850i	0.195334	−	0.536677i
$956$	3.55790	−	20.1779i	0.115071	−	0.652599i
$957$			28.8438i			0.932387i
$958$	−6.04857	−	10.4764i	−0.195420	−	0.338478i
$959$	−16.2324	+	2.97512i	−0.524172	+	0.0960717i
$960$	0.687355	−	0.819158i	0.0221843	−	0.0264382i
$961$	−4.02177	+	6.96591i	−0.129735	+	0.224707i
$962$	−23.5930	−	40.8643i	−0.760669	−	1.31752i
$963$	−19.7118	−	3.47573i	−0.635205	−	0.112004i
$964$	2.94728	−	2.47306i	0.0949255	−	0.0796520i
$965$	−2.36890	+	13.4347i	−0.0762576	+	0.432479i
$966$	−14.4854	+	0.0976055i	−0.466061	+	0.00314040i
$967$	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
$969$	−9.59041	−	22.6478i	−0.308089	−	0.727552i
$970$	−3.16685	+	5.48515i	−0.101682	+	0.176118i
$971$	20.5879	+	7.49339i	0.660698	+	0.240474i	0.650538	−	0.759474i	$-0.274544\pi$
$971$	20.5879	+	7.49339i	0.660698	+	0.240474i	0.0101602	+	0.999948i	$0.496766\pi$
$972$	−0.939693	−	0.342020i	−0.0301407	−	0.0109703i
$973$	−27.4040	−	9.76563i	−0.878531	−	0.313072i
$974$	−2.63743	−	14.9576i	−0.0845086	−	0.479272i
$975$	−13.9118	−	11.6734i	−0.445534	−	0.373847i
$976$	4.58478	−	2.64702i	0.146755	−	0.0847291i
$977$			11.1510i			0.356752i	0.983962	+	0.178376i	$0.0570844\pi$
$977$			11.1510i			0.356752i	−0.983962	+	0.178376i	$0.942916\pi$
$978$	13.2347	+	2.33363i	0.423197	+	0.0746211i
$979$	20.6748	+	17.3482i	0.660771	+	0.554452i
$980$	7.35344	−	1.39904i	0.234897	−	0.0446906i
$981$	15.0742	+	8.70310i	0.481282	+	0.277869i
$982$	15.3950	−	18.3471i	0.491274	−	0.585478i
$983$	0.0536687	+	0.0195338i	0.00171177	+	0.000623032i	0.342876	−	0.939381i	$-0.388599\pi$
$983$	0.0536687	+	0.0195338i	0.00171177	+	0.000623032i	−0.341164	+	0.940004i	$0.610821\pi$
$984$	3.60530	−	4.29663i	0.114933	−	0.136972i
$985$	6.73058	−	1.18678i	0.214454	−	0.0378141i
$986$	−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
$990$	−0.805884	−	4.57039i	−0.0256127	−	0.145257i
$991$	2.98907	+	3.56223i	0.0949509	+	0.113158i	0.811428	−	0.584453i	$-0.198691\pi$
$991$	2.98907	+	3.56223i	0.0949509	+	0.113158i	−0.716477	+	0.697611i	$0.754246\pi$
$992$	2.13711	+	5.87165i	0.0678532	+	0.186425i
$993$	−22.6353	+	3.99121i	−0.718308	+	0.126657i
$994$	20.0644	+	23.5872i	0.636404	+	0.748141i
$995$	−11.7841	+	20.4107i	−0.373582	+	0.647064i
$996$	−3.27774	−	1.89240i	−0.103859	−	0.0599630i
$997$	8.90490	+	24.4660i	0.282021	+	0.774847i	0.997121	+	0.0758245i	$0.0241589\pi$
$997$	8.90490	+	24.4660i	0.282021	+	0.774847i	−0.715100	+	0.699022i	$0.753619\pi$
$998$	13.3332	+	36.6327i	0.422056	+	1.15959i
$999$	8.67783	+	5.01015i	0.274554	+	0.158514i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.ca.b.355.12	✓	84	7.5	odd	6
798.2.ca.b.535.12	yes	84	19.3	odd	18
798.2.cj.b.241.3	yes	84	1.1	even	1	trivial
798.2.cj.b.649.3	yes	84	133.117	even	18	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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.cj (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.342020 + 0.939693i) q^{2} +(-0.766044 + 0.642788i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.687355 - 0.819158i) q^{5} +(-0.342020 - 0.939693i) q^{6} +(-1.68696 + 2.03818i) q^{7} +(0.866025 - 0.500000i) q^{8} +(0.173648 - 0.984808i) q^{9} +(1.00485 - 0.365734i) q^{10} +4.33999 q^{11} +1.00000 q^{12} +(-4.42506 + 1.61059i) q^{13} +(-1.33828 - 2.28232i) q^{14} +(1.05309 + 0.185688i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-5.55669 + 0.979794i) q^{17} +(0.866025 + 0.500000i) q^{18} +(1.98224 - 3.88210i) q^{19} +1.06934i q^{20} +(-0.0178271 - 2.64569i) q^{21} +(-1.48436 + 4.07825i) q^{22} +(-5.14492 + 1.87260i) q^{23} +(-0.342020 + 0.939693i) q^{24} +(0.669678 - 3.79793i) q^{25} -4.70905i q^{26} +(0.500000 + 0.866025i) q^{27} +(2.60240 - 0.476976i) q^{28} +(4.27200 - 5.09117i) q^{29} +(-0.534668 + 0.926071i) q^{30} +(-3.12424 - 5.41135i) q^{31} +(-0.984808 - 0.173648i) q^{32} +(-3.32462 + 2.78969i) q^{33} +(0.979794 - 5.55669i) q^{34} +(2.82913 - 0.0190632i) q^{35} +(-0.766044 + 0.642788i) q^{36} +(8.67783 - 5.01015i) q^{37} +(2.97002 + 3.19045i) q^{38} +(2.35452 - 4.07816i) q^{39} +(-1.00485 - 0.365734i) q^{40} +(-5.27060 - 1.91834i) q^{41} +(2.49223 + 0.888128i) q^{42} +(-1.03850 - 5.88963i) q^{43} +(-3.32462 - 2.78969i) q^{44} +(-0.926071 + 0.534668i) q^{45} -5.47511i q^{46} +(8.42350 + 1.48529i) q^{47} +(-0.766044 - 0.642788i) q^{48} +(-1.30832 - 6.87665i) q^{49} +(3.33985 + 1.92826i) q^{50} +(3.62687 - 4.32233i) q^{51} +(4.42506 + 1.61059i) q^{52} +(-7.30024 + 8.70009i) q^{53} +(-0.984808 + 0.173648i) 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} +(-0.282071 - 1.59970i) q^{59} +(-0.687355 - 0.819158i) q^{60} +(-1.81067 - 4.97478i) q^{61} +(6.15355 - 1.08504i) q^{62} +(1.71427 + 2.01526i) q^{63} +(0.500000 - 0.866025i) q^{64} +(4.36092 + 2.51778i) q^{65} +(-1.48436 - 4.07825i) q^{66} +(-2.96160 - 8.13692i) q^{67} +(4.88647 + 2.82120i) q^{68} +(2.73755 - 4.74158i) q^{69} +(-0.949706 + 2.66503i) q^{70} +(-11.5265 + 2.03243i) q^{71} +(-0.342020 - 0.939693i) q^{72} +(2.11404 + 2.51942i) q^{73} +(1.74001 + 9.86806i) 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} +(7.04605 - 1.24241i) q^{79} +(0.687355 - 0.819158i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(3.60530 - 4.29663i) q^{82} +(-3.27774 - 1.89240i) q^{83} +(-1.68696 + 2.03818i) q^{84} +(4.62202 + 3.87834i) q^{85} +(5.88963 + 1.03850i) q^{86} +6.64606i q^{87} +(3.75854 - 2.16999i) q^{88} +(4.76380 + 3.99731i) q^{89} +(-0.185688 - 1.05309i) q^{90} +(4.18224 - 11.7360i) q^{91} +(5.14492 + 1.87260i) q^{92} +(5.87165 + 2.13711i) q^{93} +(-4.27672 + 7.40750i) q^{94} +(-4.54256 + 1.04461i) q^{95} +(0.866025 - 0.500000i) q^{96} +(-4.53730 + 3.80725i) q^{97} +(6.90941 + 1.12253i) q^{98} +(0.753631 - 4.27405i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 12 q^{7} - 12 q^{10} - 12 q^{11} + 84 q^{12} + 24 q^{13} + 6 q^{14} + 6 q^{19} - 6 q^{21} + 12 q^{22} - 42 q^{23} - 30 q^{25} + 42 q^{27} + 6 q^{28} + 6 q^{31} + 12 q^{33} - 30 q^{34} - 42 q^{35}+ \cdots + 6 q^{99}+O(q^{100}) \) 84 * q + 12 * q^7 - 12 * q^10 - 12 * q^11 + 84 * q^12 + 24 * q^13 + 6 * q^14 + 6 * q^19 - 6 * q^21 + 12 * q^22 - 42 * q^23 - 30 * q^25 + 42 * q^27 + 6 * q^28 + 6 * q^31 + 12 * q^33 - 30 * q^34 - 42 * q^35 - 18 * q^37 + 12 * q^38 + 12 * q^40 + 36 * q^41 + 18 * q^42 + 12 * q^43 + 12 * q^44 - 18 * q^45 + 18 * q^47 - 24 * q^49 + 18 * q^51 - 24 * q^52 + 60 * q^53 - 30 * q^55 - 18 * q^56 + 6 * q^57 + 48 * q^59 - 12 * q^62 - 6 * q^63 + 42 * q^64 + 108 * q^65 + 12 * q^66 + 42 * q^67 + 6 * q^69 + 18 * q^70 + 42 * q^71 - 48 * q^73 - 18 * q^74 - 48 * q^75 + 18 * q^76 - 96 * q^77 - 12 * q^78 - 60 * q^79 - 6 * q^82 + 54 * q^83 + 12 * q^84 - 24 * q^85 - 12 * q^86 - 24 * q^89 + 6 * q^90 + 24 * q^91 + 42 * q^92 - 36 * q^93 + 18 * q^94 - 12 * q^95 - 78 * q^97 + 24 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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