LMFDB - Embedded newform 117.2.r.b.43.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,2,Mod(43,117)] 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("117.43"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(117, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.r (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [22] 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:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.2
Character	$\chi$	$=$	117.43
Dual form			117.2.r.b.49.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.00627 + 1.15832i) q^{2} +(1.71454 - 0.245682i) q^{3} +(1.68341 - 2.91575i) q^{4} +(1.09505 - 0.632228i) q^{5} +(-3.15524 + 2.47889i) q^{6} -4.17527i q^{7} +3.16642i q^{8} +(2.87928 - 0.842464i) q^{9} +(-1.46464 + 2.53684i) q^{10} +(-2.34999 + 1.35677i) q^{11} +(2.16992 - 5.41274i) q^{12} +(2.05335 + 2.96374i) q^{13} +(4.83630 + 8.37672i) q^{14} +(1.72218 - 1.35301i) q^{15} +(-0.300907 - 0.521186i) q^{16} +(1.05102 + 1.82043i) q^{17} +(-4.80077 + 5.02533i) q^{18} +(-2.74246 + 1.58336i) q^{19} -4.25719i q^{20} +(-1.02579 - 7.15866i) q^{21} +(3.14314 - 5.44409i) q^{22} +0.452373 q^{23} +(0.777933 + 5.42894i) q^{24} +(-1.70057 + 2.94548i) q^{25} +(-7.55253 - 3.56763i) q^{26} +(4.72966 - 2.15182i) q^{27} +(-12.1740 - 7.02869i) q^{28} +(-4.29209 - 7.43413i) q^{29} +(-1.88793 + 4.70934i) q^{30} +(-3.34195 + 1.92947i) q^{31} +(-4.27700 - 2.46932i) q^{32} +(-3.69582 + 2.90358i) q^{33} +(-4.21727 - 2.43484i) q^{34} +(-2.63973 - 4.57214i) q^{35} +(2.39059 - 9.81346i) q^{36} +(7.55106 + 4.35961i) q^{37} +(3.66807 - 6.35328i) q^{38} +(4.24868 + 4.57697i) q^{39} +(2.00190 + 3.46739i) q^{40} +2.51117i q^{41} +(10.3500 + 13.1740i) q^{42} -4.98614 q^{43} +9.13598i q^{44} +(2.62033 - 2.74290i) q^{45} +(-0.907582 + 0.523993i) q^{46} +(10.8108 + 6.24161i) q^{47} +(-0.643962 - 0.819665i) q^{48} -10.4329 q^{49} -7.87923i q^{50} +(2.24927 + 2.86297i) q^{51} +(12.0981 - 0.997861i) q^{52} -1.14568 q^{53} +(-6.99646 + 9.79559i) q^{54} +(-1.71558 + 2.97147i) q^{55} +13.2207 q^{56} +(-4.31304 + 3.38850i) q^{57} +(17.2222 + 9.94323i) q^{58} +(-5.47680 - 3.16203i) q^{59} +(-1.04592 - 7.29912i) q^{60} -5.09646 q^{61} +(4.46989 - 7.74208i) q^{62} +(-3.51752 - 12.0218i) q^{63} +12.6447 q^{64} +(4.12228 + 1.94726i) q^{65} +(4.05152 - 10.1063i) q^{66} -14.1824i q^{67} +7.07720 q^{68} +(0.775611 - 0.111140i) q^{69} +(10.5920 + 6.11529i) q^{70} +(-6.49685 + 3.75096i) q^{71} +(2.66759 + 9.11700i) q^{72} +7.95754i q^{73} -20.1993 q^{74} +(-2.19205 + 5.46794i) q^{75} +10.6617i q^{76} +(5.66488 + 9.81187i) q^{77} +(-13.8256 - 4.26131i) q^{78} +(-1.82489 + 3.16081i) q^{79} +(-0.659017 - 0.380484i) q^{80} +(7.58051 - 4.85138i) q^{81} +(-2.90873 - 5.03807i) q^{82} +(-1.96005 - 1.13164i) q^{83} +(-22.5997 - 9.06000i) q^{84} +(2.30185 + 1.32897i) q^{85} +(10.0035 - 5.77554i) q^{86} +(-9.18539 - 11.6916i) q^{87} +(-4.29610 - 7.44106i) q^{88} +(1.31792 + 0.760899i) q^{89} +(-2.07993 + 8.53818i) q^{90} +(12.3744 - 8.57329i) q^{91} +(0.761528 - 1.31901i) q^{92} +(-5.25585 + 4.12921i) q^{93} -28.9191 q^{94} +(-2.00209 + 3.46772i) q^{95} +(-7.93974 - 3.18297i) q^{96} +2.38580i q^{97} +(20.9312 - 12.0846i) q^{98} +(-5.62326 + 5.88630i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{3} + 10 q^{4} + 3 q^{5} - 6 q^{6} - 2 q^{9} - 7 q^{10} + 3 q^{11} - 11 q^{12} + 3 q^{13} - 9 q^{14} - 15 q^{15} - 12 q^{16} + 9 q^{17} - 30 q^{18} - 6 q^{19} + 12 q^{21} - 13 q^{22} - 12 q^{23}+ \cdots - 18 q^{99}+O(q^{100}) $ 22 * q + 2 * q^3 + 10 * q^4 + 3 * q^5 - 6 * q^6 - 2 * q^9 - 7 * q^10 + 3 * q^11 - 11 * q^12 + 3 * q^13 - 9 * q^14 - 15 * q^15 - 12 * q^16 + 9 * q^17 - 30 * q^18 - 6 * q^19 + 12 * q^21 - 13 * q^22 - 12 * q^23 + 45 * q^24 + 4 * q^25 - 12 * q^26 + 14 * q^27 + 3 * q^28 - 24 * q^29 - 39 * q^30 + 27 * q^31 - 18 * q^33 - 15 * q^34 - 27 * q^35 + 2 * q^36 + 6 * q^37 + 21 * q^38 + 13 * q^39 + 13 * q^40 + 27 * q^42 + 8 * q^43 + 27 * q^45 - 15 * q^46 + 6 * q^47 + 11 * q^48 - 14 * q^49 + 12 * q^51 - 7 * q^52 - 24 * q^53 - 33 * q^54 - 13 * q^55 + 18 * q^56 + 42 * q^57 + 15 * q^58 - 33 * q^59 - 6 * q^60 - 6 * q^61 - 3 * q^63 - 24 * q^64 + 3 * q^65 + 30 * q^66 + 138 * q^68 - 3 * q^69 + 24 * q^70 + 9 * q^71 - 6 * q^72 + 12 * q^74 + 22 * q^75 + 42 * q^77 - 42 * q^78 - 6 * q^79 + 105 * q^80 + 10 * q^81 - 16 * q^82 - 42 * q^83 - 18 * q^84 - 51 * q^85 - 45 * q^86 + 27 * q^87 - 11 * q^88 - 30 * q^89 + 30 * q^90 + 15 * q^91 - 3 * q^92 + 6 * q^93 - 88 * q^94 - 3 * q^95 + 9 * q^96 + 117 * q^98 - 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.00627	+	1.15832i	−1.41865	+	0.819055i	−0.996180	−	0.0873234i	$-0.972169\pi$
$2$	−2.00627	+	1.15832i	−1.41865	+	0.819055i	−0.422466	+	0.906379i	$0.638835\pi$
$3$	1.71454	−	0.245682i	0.989889	−	0.141845i
$3$	1.71454	−	0.245682i	0.989889	−	0.141845i
$4$	1.68341	−	2.91575i	0.841704	−	1.45787i
$5$	1.09505	−	0.632228i	0.489722	−	0.282741i	−0.234737	−	0.972059i	$-0.575423\pi$
$5$	1.09505	−	0.632228i	0.489722	−	0.282741i	0.724459	+	0.689318i	$0.242090\pi$
$6$	−3.15524	+	2.47889i	−1.28812	+	1.01200i
$7$		−	4.17527i		−	1.57811i	−0.614326	−	0.789053i	$-0.710572\pi$
$7$		−	4.17527i		−	1.57811i	0.614326	−	0.789053i	$-0.289428\pi$
$8$			3.16642i			1.11950i
$9$	2.87928	−	0.842464i	0.959760	−	0.280821i
$10$	−1.46464	+	2.53684i	−0.463161	+	0.802219i
$11$	−2.34999	+	1.35677i	−0.708550	+	0.409081i	−0.810524	−	0.585706i	$-0.800817\pi$
$11$	−2.34999	+	1.35677i	−0.708550	+	0.409081i	0.101974	+	0.994787i	$0.467484\pi$
$12$	2.16992	−	5.41274i	0.626401	−	1.56252i
$13$	2.05335	+	2.96374i	0.569496	+	0.821994i
$13$	2.05335	+	2.96374i	0.569496	+	0.821994i
$14$	4.83630	+	8.37672i	1.29256	+	2.23877i
$15$	1.72218	−	1.35301i	0.444665	−	0.349347i
$16$	−0.300907	−	0.521186i	−0.0752267	−	0.130296i
$17$	1.05102	+	1.82043i	0.254911	+	0.441518i	0.964871	−	0.262723i	$-0.0846206\pi$
$17$	1.05102	+	1.82043i	0.254911	+	0.441518i	−0.709961	+	0.704241i	$0.751287\pi$
$18$	−4.80077	+	5.02533i	−1.13155	+	1.18448i
$19$	−2.74246	+	1.58336i	−0.629163	+	0.363247i	−0.780428	−	0.625246i	$-0.784999\pi$
$19$	−2.74246	+	1.58336i	−0.629163	+	0.363247i	0.151265	+	0.988493i	$0.451665\pi$
$20$		−	4.25719i		−	0.951937i
$21$	−1.02579	−	7.15866i	−0.223846	−	1.56215i
$22$	3.14314	−	5.44409i	0.670121	−	1.16068i
$23$	0.452373			0.0943263			0.0471632	−	0.998887i	$-0.484982\pi$
$23$	0.452373			0.0943263			0.0471632	+	0.998887i	$0.484982\pi$
$24$	0.777933	+	5.42894i	0.158795	+	1.10818i
$25$	−1.70057	+	2.94548i	−0.340115	+	0.589096i
$26$	−7.55253	−	3.56763i	−1.48117	−	0.699669i
$27$	4.72966	−	2.15182i	0.910223	−	0.414119i
$28$	−12.1740	−	7.02869i	−2.30068	−	1.32830i
$29$	−4.29209	−	7.43413i	−0.797022	−	1.38048i	−0.921547	−	0.388266i	$-0.873074\pi$
$29$	−4.29209	−	7.43413i	−0.797022	−	1.38048i	0.124525	−	0.992216i	$-0.460259\pi$
$30$	−1.88793	+	4.70934i	−0.344688	+	0.859805i
$31$	−3.34195	+	1.92947i	−0.600231	+	0.346544i	−0.769133	−	0.639089i	$-0.779311\pi$
$31$	−3.34195	+	1.92947i	−0.600231	+	0.346544i	0.168901	+	0.985633i	$0.445978\pi$
$32$	−4.27700	−	2.46932i	−0.756073	−	0.436519i
$33$	−3.69582	+	2.90358i	−0.643359	+	0.505449i
$34$	−4.21727	−	2.43484i	−0.723256	−	0.417572i
$35$	−2.63973	−	4.57214i	−0.446195	−	0.772833i
$36$	2.39059	−	9.81346i	0.398432	−	1.63558i
$37$	7.55106	+	4.35961i	1.24139	+	0.716715i	0.969377	−	0.245579i	$-0.0789782\pi$
$37$	7.55106	+	4.35961i	1.24139	+	0.716715i	0.272010	+	0.962294i	$0.412311\pi$
$38$	3.66807	−	6.35328i	0.595039	−	1.03064i
$39$	4.24868	+	4.57697i	0.680334	+	0.732903i
$40$	2.00190	+	3.46739i	0.316528	+	0.548243i
$41$			2.51117i			0.392178i	0.980586	+	0.196089i	$0.0628242\pi$
$41$			2.51117i			0.392178i	−0.980586	+	0.196089i	$0.937176\pi$
$42$	10.3500	+	13.1740i	1.59704	+	2.03279i
$43$	−4.98614			−0.760379			−0.380189	−	0.924909i	$-0.624141\pi$
$43$	−4.98614			−0.760379			−0.380189	+	0.924909i	$0.624141\pi$
$44$			9.13598i			1.37730i
$45$	2.62033	−	2.74290i	0.390616	−	0.408888i
$46$	−0.907582	+	0.523993i	−0.133816	+	0.0772585i
$47$	10.8108	+	6.24161i	1.57692	+	0.910432i	0.995287	+	0.0969780i	$0.0309176\pi$
$47$	10.8108	+	6.24161i	1.57692	+	0.910432i	0.581629	+	0.813454i	$0.302416\pi$
$48$	−0.643962	−	0.819665i	−0.0929480	−	0.118309i
$49$	−10.4329			−1.49042
$50$		−	7.87923i		−	1.11429i
$51$	2.24927	+	2.86297i	0.314960	+	0.400896i
$52$	12.0981	−	0.997861i	1.67771	−	0.138378i
$53$	−1.14568			−0.157371			−0.0786857	−	0.996899i	$-0.525072\pi$
$53$	−1.14568			−0.157371			−0.0786857	+	0.996899i	$0.525072\pi$
$54$	−6.99646	+	9.79559i	−0.952098	+	1.33301i
$55$	−1.71558	+	2.97147i	−0.231328	+	0.400672i
$56$	13.2207			1.76668
$57$	−4.31304	+	3.38850i	−0.571277	+	0.448818i
$58$	17.2222	+	9.94323i	2.26138	+	1.30561i
$59$	−5.47680	−	3.16203i	−0.713019	−	0.411662i	0.0991588	−	0.995072i	$-0.468385\pi$
$59$	−5.47680	−	3.16203i	−0.713019	−	0.411662i	−0.812178	+	0.583410i	$0.801718\pi$
$60$	−1.04592	−	7.29912i	−0.135027	−	0.942312i
$61$	−5.09646			−0.652535			−0.326267	−	0.945278i	$-0.605791\pi$
$61$	−5.09646			−0.652535			−0.326267	+	0.945278i	$0.605791\pi$
$62$	4.46989	−	7.74208i	0.567677	−	0.983245i
$63$	−3.51752	−	12.0218i	−0.443165	−	1.51460i
$64$	12.6447			1.58059
$65$	4.12228	+	1.94726i	0.511306	+	0.241528i
$66$	4.05152	−	10.1063i	0.498708	−	1.24400i
$67$		−	14.1824i		−	1.73266i	−0.499476	−	0.866328i	$-0.666474\pi$
$67$		−	14.1824i		−	1.73266i	0.499476	−	0.866328i	$-0.333526\pi$
$68$	7.07720			0.858237
$69$	0.775611	−	0.111140i	0.0933726	−	0.0133797i
$70$	10.5920	+	6.11529i	1.26599	+	0.730917i
$71$	−6.49685	+	3.75096i	−0.771034	+	0.445157i	−0.833243	−	0.552906i	$-0.813519\pi$
$71$	−6.49685	+	3.75096i	−0.771034	+	0.445157i	0.0622094	+	0.998063i	$0.480185\pi$
$72$	2.66759	+	9.11700i	0.314379	+	1.07445i
$73$			7.95754i			0.931360i	0.884953	+	0.465680i	$0.154190\pi$
$73$			7.95754i			0.931360i	−0.884953	+	0.465680i	$0.845810\pi$
$74$	−20.1993			−2.34812
$75$	−2.19205	+	5.46794i	−0.253116	+	0.631383i
$76$			10.6617i			1.22299i
$77$	5.66488	+	9.81187i	0.645573	+	1.11817i
$78$	−13.8256	−	4.26131i	−1.56544	−	0.482498i
$79$	−1.82489	+	3.16081i	−0.205317	+	0.355619i	−0.950234	−	0.311538i	$-0.899156\pi$
$79$	−1.82489	+	3.16081i	−0.205317	+	0.355619i	0.744917	+	0.667157i	$0.232489\pi$
$80$	−0.659017	−	0.380484i	−0.0736804	−	0.0425394i
$81$	7.58051	−	4.85138i	0.842279	−	0.539042i
$82$	−2.90873	−	5.03807i	−0.321216	−	0.556362i
$83$	−1.96005	−	1.13164i	−0.215144	−	0.124213i	0.388556	−	0.921425i	$-0.372974\pi$
$83$	−1.96005	−	1.13164i	−0.215144	−	0.124213i	−0.603700	+	0.797212i	$0.706307\pi$
$84$	−22.5997	−	9.06000i	−2.46583	−	0.988527i
$85$	2.30185	+	1.32897i	0.249671	+	0.144147i
$86$	10.0035	−	5.77554i	1.07871	−	0.622792i
$87$	−9.18539	−	11.6916i	−0.984778	−	1.25347i
$88$	−4.29610	−	7.44106i	−0.457966	−	0.793220i
$89$	1.31792	+	0.760899i	0.139699	+	0.0806552i	0.568220	−	0.822876i	$-0.307632\pi$
$89$	1.31792	+	0.760899i	0.139699	+	0.0806552i	−0.428522	+	0.903532i	$0.640965\pi$
$90$	−2.07993	+	8.53818i	−0.219244	+	0.900003i
$91$	12.3744	−	8.57329i	1.29719	−	0.898725i
$92$	0.761528	−	1.31901i	0.0793948	−	0.137516i
$93$	−5.25585	+	4.12921i	−0.545007	+	0.428179i
$94$	−28.9191			−2.98278
$95$	−2.00209	+	3.46772i	−0.205410	+	0.355780i
$96$	−7.93974	−	3.18297i	−0.810346	−	0.324860i
$97$			2.38580i			0.242242i	0.992638	+	0.121121i	$0.0386489\pi$
$97$			2.38580i			0.242242i	−0.992638	+	0.121121i	$0.961351\pi$
$98$	20.9312	−	12.0846i	2.11437	−	1.22073i
$99$	−5.62326	+	5.88630i	−0.565159	+	0.591596i
$100$	5.72552	+	9.91689i	0.572552	+	0.991689i
$101$	5.59898	+	9.69772i	0.557119	+	0.964959i	0.997735	+	0.0672632i	$0.0214267\pi$
$101$	5.59898	+	9.69772i	0.557119	+	0.964959i	−0.440616	+	0.897696i	$0.645240\pi$
$102$	−7.82887	−	3.13852i	−0.775173	−	0.310760i
$103$	−1.45757	−	2.52458i	−0.143618	−	0.248754i	0.785238	−	0.619194i	$-0.212540\pi$
$103$	−1.45757	−	2.52458i	−0.143618	−	0.248754i	−0.928857	+	0.370440i	$0.879207\pi$
$104$	−9.38444	+	6.50176i	−0.920220	+	0.637550i
$105$	−5.64921	−	7.19057i	−0.551306	−	0.701728i
$106$	2.29854	−	1.32706i	0.223254	−	0.128896i
$107$	−1.33105	+	2.30545i	−0.128678	+	0.222876i	−0.923164	−	0.384405i	$-0.874407\pi$
$107$	−1.33105	+	2.30545i	−0.128678	+	0.222876i	0.794487	+	0.607281i	$0.207740\pi$
$108$	1.68776	−	17.4129i	0.162405	−	1.67556i
$109$		−	8.32143i		−	0.797049i	−0.917158	−	0.398524i	$-0.869522\pi$
$109$		−	8.32143i		−	0.797049i	0.917158	−	0.398524i	$-0.130478\pi$
$110$		−	7.94874i		−	0.757883i
$111$	14.0177	+	5.61955i	1.33050	+	0.533384i
$112$	−2.17609	+	1.25637i	−0.205622	+	0.118716i
$113$	−1.75803	+	3.04500i	−0.165382	+	0.286449i	−0.936791	−	0.349890i	$-0.886219\pi$
$113$	−1.75803	+	3.04500i	−0.165382	+	0.286449i	0.771409	+	0.636340i	$0.219552\pi$
$114$	4.72815	−	11.7941i	0.442832	−	1.10462i
$115$	0.495372	−	0.286003i	0.0461937	−	0.0266699i
$116$	−28.9014			−2.68343
$117$	8.40901	+	6.80357i	0.777413	+	0.628990i
$118$	14.6506			1.34870
$119$	7.60078	−	4.38831i	0.696762	−	0.402276i
$120$	4.28421	+	5.45314i	0.391093	+	0.497801i
$121$	−1.81835	+	3.14948i	−0.165305	+	0.286316i
$122$	10.2249	−	5.90333i	0.925715	−	0.534462i
$123$	0.616949	+	4.30549i	0.0556284	+	0.388213i
$124$			12.9924i			1.16675i
$125$			10.6229i			0.950140i
$126$	20.9821	+	20.0445i	1.86924	+	1.78571i
$127$	7.86992	−	13.6311i	0.698342	−	1.20956i	−0.270699	−	0.962664i	$-0.587255\pi$
$127$	7.86992	−	13.6311i	0.698342	−	1.20956i	0.969041	−	0.246900i	$-0.0794119\pi$
$128$	−16.8147	+	9.70794i	−1.48622	+	0.858069i
$129$	−8.54892	+	1.22501i	−0.752690	+	0.107856i
$130$	−10.5260	+	0.868186i	−0.923188	+	0.0761450i
$131$	−6.82094	−	11.8142i	−0.595949	−	1.03221i	−0.993412	−	0.114595i	$-0.963443\pi$
$131$	−6.82094	−	11.8142i	−0.595949	−	1.03221i	0.397464	−	0.917618i	$-0.369890\pi$
$132$	2.24455	+	15.6640i	0.195363	+	1.36338i
$133$	6.61095	+	11.4505i	0.573242	+	0.992885i
$134$	16.4277	+	28.4537i	1.41914	+	2.45802i
$135$	3.81877	−	5.34658i	0.328668	−	0.460161i
$136$	−5.76423	+	3.32798i	−0.494278	+	0.285372i
$137$		−	11.4539i		−	0.978569i	−0.872124	−	0.489285i	$-0.837258\pi$
$137$		−	11.4539i		−	0.978569i	0.872124	−	0.489285i	$-0.162742\pi$
$138$	−1.42735	+	1.12138i	−0.121504	+	0.0954584i
$139$	−2.42317	+	4.19706i	−0.205531	+	0.355990i	−0.950302	−	0.311330i	$-0.899225\pi$
$139$	−2.42317	+	4.19706i	−0.205531	+	0.355990i	0.744771	+	0.667320i	$0.232559\pi$
$140$	−17.7749			−1.50226
$141$	20.0690	+	8.04546i	1.69011	+	0.677550i
$142$	8.68961	−	15.0508i	0.729216	−	1.26304i
$143$	−8.84647	−	4.17885i	−0.739779	−	0.349453i
$144$	−1.30548	−	1.24714i	−0.108790	−	0.103928i
$145$	−9.40013	−	5.42717i	−0.780639	−	0.450702i
$146$	−9.21738	−	15.9650i	−0.762836	−	1.32127i
$147$	−17.8876	+	2.56318i	−1.47535	+	0.211408i
$148$	25.4230	−	14.6780i	2.08976	−	1.20652i
$149$	18.7955	+	10.8516i	1.53978	+	0.888994i	0.998851	+	0.0479284i	$0.0152619\pi$
$149$	18.7955	+	10.8516i	1.53978	+	0.888994i	0.540933	+	0.841066i	$0.318071\pi$
$150$	−1.93579	−	13.5092i	−0.158056	−	1.10303i
$151$	−2.34152	−	1.35188i	−0.190550	−	0.110014i	0.401690	−	0.915776i	$-0.368423\pi$
$151$	−2.34152	−	1.35188i	−0.190550	−	0.110014i	−0.592240	+	0.805762i	$0.701756\pi$
$152$	−5.01357	−	8.68376i	−0.406654	−	0.704346i
$153$	4.55983	+	4.35607i	0.368641	+	0.352167i
$154$	−22.7305	−	13.1235i	−1.83168	−	1.05752i
$155$	−2.43974	+	4.22575i	−0.195964	+	0.339420i
$156$	20.4976	−	4.68317i	1.64112	−	0.374954i
$157$	−7.83378	−	13.5685i	−0.625204	−	1.08288i	−0.988501	−	0.151212i	$-0.951682\pi$
$157$	−7.83378	−	13.5685i	−0.625204	−	1.08288i	0.363298	−	0.931673i	$-0.381651\pi$
$158$		−	8.45524i		−	0.672663i
$159$	−1.96431	+	0.281474i	−0.155780	+	0.0223223i
$160$	−6.24471			−0.493688
$161$		−	1.88878i		−	0.148857i
$162$	−9.58909	+	18.5138i	−0.753390	+	1.45458i
$163$	−5.73759	+	3.31260i	−0.449403	+	0.259463i	−0.707578	−	0.706635i	$-0.750212\pi$
$163$	−5.73759	+	3.31260i	−0.449403	+	0.259463i	0.258175	+	0.966098i	$0.416879\pi$
$164$	7.32193	+	4.22732i	0.571746	+	0.330098i
$165$	−2.21138	+	5.51618i	−0.172156	+	0.429434i
$166$	5.24319			0.406950
$167$		−	10.7941i		−	0.835270i	−0.908615	−	0.417635i	$-0.862859\pi$
$167$		−	10.7941i		−	0.835270i	0.908615	−	0.417635i	$-0.137141\pi$
$168$	22.6673	−	3.24808i	1.74882	−	0.250595i
$169$	−4.56752	+	12.1712i	−0.351348	+	0.936245i
$170$	−6.15751			−0.472259
$171$	−6.56238	+	6.86935i	−0.501838	+	0.525313i
$172$	−8.39370	+	14.5383i	−0.640013	+	1.10854i
$173$	4.87660			0.370761			0.185380	−	0.982667i	$-0.440648\pi$
$173$	4.87660			0.370761			0.185380	+	0.982667i	$0.440648\pi$
$174$	31.9710	+	12.8169i	2.42371	+	0.971644i
$175$	12.2982	+	7.10036i	0.929656	+	0.536737i
$176$	1.41426	+	0.816522i	0.106604	+	0.0615477i
$177$	−10.1670	−	4.07587i	−0.764202	−	0.306361i
$178$	−3.52546			−0.264244
$179$	6.61646	−	11.4601i	0.494538	−	0.856564i	−0.505442	−	0.862860i	$-0.668671\pi$
$179$	6.61646	−	11.4601i	0.494538	−	0.856564i	0.999980	+	0.00629588i	$0.00200406\pi$
$180$	−3.58653	−	12.2577i	−0.267324	−	0.913631i
$181$	−18.2227			−1.35448			−0.677242	−	0.735760i	$-0.736825\pi$
$181$	−18.2227			−1.35448			−0.677242	+	0.735760i	$0.736825\pi$
$182$	−14.8958	+	31.5339i	−1.10415	+	2.33745i
$183$	−8.73807	+	1.25211i	−0.645937	+	0.0925586i
$184$			1.43240i			0.105598i
$185$	11.0251			0.810579
$186$	5.76171	−	14.3723i	0.422469	−	1.05383i
$187$	−4.93980	−	2.85199i	−0.361234	−	0.208558i
$188$	36.3979	−	21.0143i	2.65459	−	1.53263i
$189$	−8.98445	−	19.7476i	−0.653523	−	1.43643i
$190$		−	9.27623i		−	0.672969i
$191$	15.3708			1.11219			0.556096	−	0.831118i	$-0.312299\pi$
$191$	15.3708			1.11219			0.556096	+	0.831118i	$0.312299\pi$
$192$	21.6798	−	3.10658i	1.56461	−	0.224198i
$193$		−	5.65364i		−	0.406958i	−0.979079	−	0.203479i	$-0.934775\pi$
$193$		−	5.65364i		−	0.406958i	0.979079	−	0.203479i	$-0.0652249\pi$
$194$	−2.76352	−	4.78656i	−0.198409	−	0.343655i
$195$	7.54622	+	2.32589i	0.540396	+	0.166560i
$196$	−17.5628	+	30.4197i	−1.25449	+	2.17284i
$197$	5.46126	+	3.15306i	0.389098	+	0.224646i	0.681769	−	0.731567i	$-0.261211\pi$
$197$	5.46126	+	3.15306i	0.389098	+	0.224646i	−0.292671	+	0.956213i	$0.594544\pi$
$198$	4.46355	−	18.3230i	0.317211	−	1.30216i
$199$	−0.849701	−	1.47173i	−0.0602337	−	0.104328i	0.834336	−	0.551256i	$-0.185851\pi$
$199$	−0.849701	−	1.47173i	−0.0602337	−	0.104328i	−0.894570	+	0.446928i	$0.852518\pi$
$200$	−9.32662	−	5.38473i	−0.659492	−	0.380758i
$201$	−3.48437	−	24.3163i	−0.245768	−	1.71514i
$202$	−22.4661	−	12.9708i	−1.58071	−	0.912623i
$203$	−31.0395	+	17.9207i	−2.17855	+	1.25778i
$204$	12.1341	−	1.73874i	0.849559	−	0.121736i
$205$	1.58763	+	2.74986i	0.110885	+	0.192058i
$206$	5.84854	+	3.37665i	0.407487	+	0.235263i
$207$	1.30251	−	0.381108i	0.0905306	−	0.0264888i
$208$	0.926794	−	1.96199i	0.0642616	−	0.136039i
$209$	4.29650	−	7.44176i	0.297195	−	0.514758i
$210$	19.6628	+	7.88263i	1.35686	+	0.543953i
$211$	4.56391			0.314193			0.157096	−	0.987583i	$-0.449787\pi$
$211$	4.56391			0.314193			0.157096	+	0.987583i	$0.449787\pi$
$212$	−1.92865	+	3.34052i	−0.132460	+	0.229428i
$213$	−10.2175	+	8.02732i	−0.700095	+	0.550023i
$214$		−	6.16713i		−	0.421577i
$215$	−5.46008	+	3.15238i	−0.372374	+	0.214990i
$216$	6.81357	+	14.9761i	0.463605	+	1.01899i
$217$	8.05608	+	13.9535i	0.546882	+	0.947228i
$218$	9.63888	+	16.6950i	0.652827	+	1.13073i
$219$	1.95503	+	13.6435i	0.132109	+	0.921943i
$220$	5.77603	+	10.0044i	0.389420	+	0.674495i
$221$	−3.23715	+	6.85293i	−0.217755	+	0.460978i
$222$	−34.6324	+	4.96261i	−2.32438	+	0.333068i
$223$	19.2946	−	11.1398i	1.29206	−	0.745974i	0.313045	−	0.949738i	$-0.398651\pi$
$223$	19.2946	−	11.1398i	1.29206	−	0.745974i	0.979020	+	0.203764i	$0.0653177\pi$
$224$	−10.3101	+	17.8576i	−0.688873	+	1.19316i
$225$	−2.41497	+	9.91354i	−0.160998	+	0.660903i
$226$		−	8.14545i		−	0.541827i
$227$		−	4.20189i		−	0.278889i	−0.990230	−	0.139445i	$-0.955468\pi$
$227$		−	4.20189i		−	0.278889i	0.990230	−	0.139445i	$-0.0445318\pi$
$228$	2.61940	+	18.2800i	0.173474	+	1.21062i
$229$	19.7986	−	11.4307i	1.30833	−	0.755365i	0.326513	−	0.945193i	$-0.394126\pi$
$229$	19.7986	−	11.4307i	1.30833	−	0.755365i	0.981817	+	0.189827i	$0.0607929\pi$
$230$	−0.662566	+	1.14760i	−0.0436883	+	0.0756704i
$231$	12.1233	+	15.4311i	0.797652	+	1.01529i
$232$	23.5395	−	13.5906i	1.54545	−	0.892264i
$233$	17.2872			1.13252			0.566260	−	0.824226i	$-0.308390\pi$
$233$	17.2872			1.13252			0.566260	+	0.824226i	$0.308390\pi$
$234$	−24.7514	−	3.90947i	−1.61805	−	0.255570i
$235$	15.7845			1.02967
$236$	−18.4394	+	10.6460i	−1.20030	+	0.692994i
$237$	−2.35229	+	5.86767i	−0.152798	+	0.381146i
$238$	−10.1661	+	17.6083i	−0.658972	+	1.14137i
$239$	−5.61354	+	3.24098i	−0.363110	+	0.209642i	−0.670444	−	0.741960i	$-0.733896\pi$
$239$	−5.61354	+	3.24098i	−0.363110	+	0.209642i	0.307334	+	0.951602i	$0.400563\pi$
$240$	−1.22339	−	0.490445i	−0.0789694	−	0.0316581i
$241$			0.183966i			0.0118503i	0.999982	+	0.00592515i	$0.00188605\pi$
$241$			0.183966i			0.0118503i	−0.999982	+	0.00592515i	$0.998114\pi$
$242$		−	8.42494i		−	0.541575i
$243$	11.8052	−	10.1803i	0.757302	−	0.653065i
$244$	−8.57941	+	14.8600i	−0.549241	+	0.951313i
$245$	−11.4246	+	6.59598i	−0.729889	+	0.421402i
$246$	−6.22490	−	7.92334i	−0.396885	−	0.505174i
$247$	−10.3239	−	4.87675i	−0.656893	−	0.310300i
$248$	−6.10952	−	10.5820i	−0.387955	−	0.671957i
$249$	−3.63861	−	1.45868i	−0.230587	−	0.0924404i
$250$	−12.3047	−	21.3124i	−0.778218	−	1.34791i
$251$	−11.8003	−	20.4387i	−0.744827	−	1.29008i	−0.950276	−	0.311410i	$-0.899199\pi$
$251$	−11.8003	−	20.4387i	−0.744827	−	1.29008i	0.205449	−	0.978668i	$-0.434135\pi$
$252$	−40.9739	−	9.98137i	−2.58111	−	0.628767i
$253$	−1.06307	+	0.613766i	−0.0668349	+	0.0385871i
$254$			36.4635i			2.28792i
$255$	4.27312	+	1.71305i	0.267593	+	0.107275i
$256$	9.84511	−	17.0522i	0.615319	−	1.06576i
$257$	−5.84983			−0.364902			−0.182451	−	0.983215i	$-0.558403\pi$
$257$	−5.84983			−0.364902			−0.182451	+	0.983215i	$0.558403\pi$
$258$	15.7325	−	12.3601i	0.979461	−	0.769504i
$259$	18.2026	−	31.5277i	1.13105	−	1.95904i
$260$	12.6172	−	8.74150i	0.782487	−	0.542125i
$261$	−18.6211	−	17.7890i	−1.15262	−	1.10111i
$262$	27.3693	+	15.8017i	1.69088	+	0.976230i
$263$	4.84907	+	8.39884i	0.299007	+	0.517895i	0.975909	−	0.218178i	$-0.0700114\pi$
$263$	4.84907	+	8.39884i	0.299007	+	0.517895i	−0.676902	+	0.736073i	$0.736678\pi$
$264$	−9.19396	−	11.7025i	−0.565849	−	0.720239i
$265$	−1.25458	+	0.724332i	−0.0770683	+	0.0444954i
$266$	−26.5267	−	15.3152i	−1.62646	−	0.939035i
$267$	2.44656	+	0.980802i	0.149727	+	0.0600241i
$268$	−41.3523	−	23.8748i	−2.52599	−	1.45838i
$269$	−10.4720	−	18.1380i	−0.638487	−	1.10589i	−0.985765	−	0.168130i	$-0.946227\pi$
$269$	−10.4720	−	18.1380i	−0.638487	−	1.10589i	0.347278	−	0.937762i	$-0.387106\pi$
$270$	−1.46844	+	15.1500i	−0.0893661	+	0.922002i
$271$	4.98580	+	2.87855i	0.302866	+	0.174860i	0.643730	−	0.765253i	$-0.277386\pi$
$271$	4.98580	+	2.87855i	0.302866	+	0.174860i	−0.340864	+	0.940113i	$0.610720\pi$
$272$	0.632520	−	1.09556i	0.0383522	−	0.0664279i
$273$	19.1101	−	17.7394i	1.15660	−	1.07364i
$274$	13.2672	+	22.9795i	0.801502	+	1.38824i
$275$		−	9.22915i		−	0.556539i
$276$	0.981613	−	2.44858i	0.0590861	−	0.147387i
$277$	−15.9997			−0.961330			−0.480665	−	0.876904i	$-0.659605\pi$
$277$	−15.9997			−0.961330			−0.480665	+	0.876904i	$0.659605\pi$
$278$		−	11.2272i		−	0.673364i
$279$	−7.99689	+	8.37096i	−0.478761	+	0.501156i
$280$	14.4773	−	8.35848i	0.865184	−	0.499514i
$281$	−16.2457	−	9.37948i	−0.969139	−	0.559533i	−0.0701653	−	0.997535i	$-0.522353\pi$
$281$	−16.2457	−	9.37948i	−0.969139	−	0.559533i	−0.898974	+	0.438003i	$0.855686\pi$
$282$	−49.5829	+	7.10492i	−2.95262	+	0.423092i
$283$	−4.52331			−0.268883			−0.134442	−	0.990922i	$-0.542924\pi$
$283$	−4.52331			−0.268883			−0.134442	+	0.990922i	$0.542924\pi$
$284$			25.2576i			1.49876i
$285$	−2.58070	+	6.43741i	−0.152867	+	0.381319i
$286$	22.5888	−	1.86314i	1.33571	−	0.110170i
$287$	10.4848			0.618899
$288$	−14.3950	−	3.50666i	−0.848233	−	0.206632i
$289$	6.29070	−	10.8958i	0.370041	−	0.640930i
$290$	25.1456			1.47660
$291$	0.586150	+	4.09055i	0.0343607	+	0.239792i
$292$	23.2022	+	13.3958i	1.35781	+	0.783929i
$293$	0.274290	+	0.158362i	0.0160242	+	0.00925159i	0.507991	−	0.861363i	$-0.330388\pi$
$293$	0.274290	+	0.158362i	0.0160242	+	0.00925159i	−0.491966	+	0.870614i	$0.663722\pi$
$294$	32.9184	−	25.8620i	1.91984	−	1.50830i
$295$	−7.99651			−0.465575
$296$	−13.8043	+	23.9098i	−0.802361	+	1.38973i
$297$	−8.19513	+	11.4738i	−0.475530	+	0.665779i
$298$	−50.2783			−2.91254
$299$	0.928879	+	1.34072i	0.0537185	+	0.0775356i
$300$	12.2530	+	15.5962i	0.707429	+	0.900448i
$301$			20.8185i			1.19996i
$302$	6.26361			0.360430
$303$	11.9822	+	15.2515i	0.688361	+	0.876178i
$304$	1.65045	+	0.952887i	0.0946597	+	0.0546518i
$305$	−5.58089	+	3.22213i	−0.319561	+	0.184498i
$306$	−14.1940	−	3.45770i	−0.811415	−	0.197663i
$307$			11.2849i			0.644066i	0.946728	+	0.322033i	$0.104366\pi$
$307$			11.2849i			0.644066i	−0.946728	+	0.322033i	$0.895634\pi$
$308$	38.1452			2.17353
$309$	−3.11930	−	3.97039i	−0.177451	−	0.225867i
$310$		−	11.3040i		−	0.642023i
$311$	15.9070	+	27.5517i	0.902004	+	1.56232i	0.824890	+	0.565294i	$0.191237\pi$
$311$	15.9070	+	27.5517i	0.902004	+	1.56232i	0.0771139	+	0.997022i	$0.475429\pi$
$312$	−14.4926	+	13.4531i	−0.820482	+	0.761632i
$313$	−0.0740804	+	0.128311i	−0.00418727	+	0.00725257i	−0.868111	−	0.496369i	$-0.834666\pi$
$313$	−0.0740804	+	0.128311i	−0.00418727	+	0.00725257i	0.863924	+	0.503622i	$0.168000\pi$
$314$	31.4333	+	18.1480i	1.77389	+	1.02415i
$315$	−11.4524	−	10.9406i	−0.645268	−	0.616433i
$316$	6.14408	+	10.6419i	0.345631	+	0.598651i
$317$	−17.0960	−	9.87036i	−0.960205	−	0.554375i	−0.0639691	−	0.997952i	$-0.520376\pi$
$317$	−17.0960	−	9.87036i	−0.960205	−	0.554375i	−0.896236	+	0.443577i	$0.853709\pi$
$318$	3.61490	−	2.84001i	0.202714	−	0.159260i
$319$	20.1728	+	11.6468i	1.12946	+	0.652094i
$320$	13.8466	−	7.99433i	0.774048	−	0.446897i
$321$	−1.71573	+	4.27980i	−0.0957627	+	0.238875i
$322$	2.18781	+	3.78940i	0.121922	+	0.211175i
$323$	−5.76477	−	3.32829i	−0.320761	−	0.185191i
$324$	−1.38430	−	30.2697i	−0.0769057	−	1.68165i
$325$	−12.2215	+	1.00804i	−0.677928	+	0.0559158i
$326$	7.67410	−	13.2919i	0.425029	−	0.736172i
$327$	−2.04443	−	14.2674i	−0.113057	−	0.788990i
$328$	−7.95140			−0.439043
$329$	26.0604	−	45.1380i	1.43676	−	2.48854i
$330$	−1.95287	−	13.6284i	−0.107502	−	0.750220i
$331$			17.0277i			0.935926i	0.883748	+	0.467963i	$0.155012\pi$
$331$			17.0277i			0.935926i	−0.883748	+	0.467963i	$0.844988\pi$
$332$	−6.59914	+	3.81001i	−0.362175	+	0.209102i
$333$	25.4144	+	6.19104i	1.39270	+	0.339267i
$334$	12.5030	+	21.6558i	0.684132	+	1.18495i
$335$	−8.96652	−	15.5305i	−0.489893	−	0.848520i
$336$	−3.42233	+	2.68872i	−0.186703	+	0.146682i
$337$	6.54226	+	11.3315i	0.356379	+	0.617267i	0.987353	−	0.158537i	$-0.0506777\pi$
$337$	6.54226	+	11.3315i	0.356379	+	0.617267i	−0.630974	+	0.775804i	$0.717344\pi$
$338$	−4.93445	−	29.7093i	−0.268398	−	1.61597i
$339$	−2.26611	+	5.65269i	−0.123078	+	0.307012i
$340$	7.74990	−	4.47441i	0.420298	−	0.242659i
$341$	5.23570	−	9.06850i	0.283529	−	0.491087i
$342$	5.20899	−	21.3831i	0.281670	−	1.15627i
$343$			14.3333i			0.773927i
$344$		−	15.7882i		−	0.851242i
$345$	0.779068	−	0.612067i	0.0419436	−	0.0329526i
$346$	−9.78377	+	5.64866i	−0.525978	+	0.303674i
$347$	−7.49603	+	12.9835i	−0.402408	+	0.696991i	−0.994016	−	0.109235i	$-0.965160\pi$
$347$	−7.49603	+	12.9835i	−0.402408	+	0.696991i	0.591608	+	0.806226i	$0.298493\pi$
$348$	−49.5525	+	7.10056i	−2.65629	+	0.380630i
$349$	1.80559	−	1.04246i	0.0966511	−	0.0558015i	−0.450895	−	0.892577i	$-0.648895\pi$
$349$	1.80559	−	1.04246i	0.0966511	−	0.0558015i	0.547546	+	0.836775i	$0.315562\pi$
$350$	−32.8980			−1.75847
$351$	16.0891	+	9.59903i	0.858772	+	0.512359i
$352$	13.4012			0.714287
$353$	−3.58076	+	2.06735i	−0.190584	+	0.110034i	−0.592256	−	0.805750i	$-0.701763\pi$
$353$	−3.58076	+	2.06735i	−0.190584	+	0.110034i	0.401672	+	0.915784i	$0.368429\pi$
$354$	25.1190	−	3.59939i	1.33506	−	0.191305i
$355$	−4.74292	+	8.21498i	−0.251728	+	0.436006i
$356$	4.43718	−	2.56181i	0.235170	−	0.135776i
$357$	11.9537	−	9.39130i	0.632656	−	0.497040i
$358$			30.6559i			1.62022i
$359$			20.5783i			1.08608i	0.839706	+	0.543042i	$0.182727\pi$
$359$			20.5783i			1.08608i	−0.839706	+	0.543042i	$0.817273\pi$
$360$	8.68518	+	8.29706i	0.457749	+	0.437294i
$361$	−4.48595	+	7.76990i	−0.236103	+	0.408942i
$362$	36.5597	−	21.1077i	1.92153	−	1.10940i
$363$	−2.34386	+	5.84664i	−0.123021	+	0.306869i
$364$	−4.16634	−	50.5131i	−0.218376	−	2.64760i
$365$	5.03099	+	8.71392i	0.263334	+	0.456108i
$366$	16.0806	−	12.6335i	0.840545	−	0.660366i
$367$	7.33819	+	12.7101i	0.383050	+	0.663463i	0.991497	−	0.130132i	$-0.0415402\pi$
$367$	7.33819	+	12.7101i	0.383050	+	0.663463i	−0.608446	+	0.793595i	$0.708207\pi$
$368$	−0.136122	−	0.235770i	−0.00709586	−	0.0122904i
$369$	2.11557	+	7.23035i	0.110132	+	0.376397i
$370$	−22.1192	+	12.7706i	−1.14993	+	0.663910i
$371$			4.78353i			0.248349i
$372$	3.19199	+	22.2759i	0.165497	+	1.15495i
$373$	14.8959	−	25.8004i	0.771279	−	1.33589i	−0.165583	−	0.986196i	$-0.552951\pi$
$373$	14.8959	−	25.8004i	0.771279	−	1.33589i	0.936862	−	0.349699i	$-0.113716\pi$
$374$	13.2141			0.683284
$375$	2.60986	+	18.2133i	0.134772	+	0.940533i
$376$	−19.7635	+	34.2315i	−1.01923	+	1.76535i
$377$	13.2197	−	27.9855i	0.680847	−	1.44133i
$378$	40.8993	+	29.2121i	2.10363	+	1.50251i
$379$	−11.5590	−	6.67356i	−0.593743	−	0.342798i	0.172833	−	0.984951i	$-0.444708\pi$
$379$	−11.5590	−	6.67356i	−0.593743	−	0.342798i	−0.766576	+	0.642153i	$0.778041\pi$
$380$	6.74066	+	11.6752i	0.345789	+	0.598924i
$381$	10.1443	−	25.3045i	0.519711	−	1.29639i
$382$	−30.8379	+	17.8043i	−1.57781	+	0.910946i
$383$	−2.55425	−	1.47470i	−0.130516	−	0.0753536i	0.433320	−	0.901240i	$-0.357342\pi$
$383$	−2.55425	−	1.47470i	−0.130516	−	0.0753536i	−0.563837	+	0.825886i	$0.690675\pi$
$384$	−26.4443	+	20.7757i	−1.34948	+	1.06021i
$385$	12.4067	+	7.16300i	0.632303	+	0.365060i
$386$	6.54872	+	11.3427i	0.333321	+	0.577329i
$387$	−14.3565	+	4.20064i	−0.729781	+	0.213530i
$388$	6.95640	+	4.01628i	0.353158	+	0.203896i
$389$	8.31532	−	14.4026i	0.421603	−	0.730238i	−0.574493	−	0.818509i	$-0.694801\pi$
$389$	8.31532	−	14.4026i	0.421603	−	0.730238i	0.996096	+	0.0882711i	$0.0281342\pi$
$390$	−17.8339	+	4.07458i	−0.903053	+	0.206324i
$391$	0.475455	+	0.823512i	0.0240448	+	0.0416468i
$392$		−	33.0349i		−	1.66852i
$393$	−14.5973	−	18.5801i	−0.736337	−	0.937244i
$394$	−14.6090			−0.735990
$395$			4.61500i			0.232206i
$396$	7.69673	+	26.3051i	0.386775	+	1.32188i
$397$	5.23157	−	3.02045i	0.262565	−	0.151592i	−0.362939	−	0.931813i	$-0.618227\pi$
$397$	5.23157	−	3.02045i	0.262565	−	0.151592i	0.625504	+	0.780221i	$0.284893\pi$
$398$	3.40946	+	1.96845i	0.170901	+	0.0986695i
$399$	14.1479	+	18.0081i	0.708282	+	0.901534i
$400$	2.04686			0.102343
$401$		−	14.3432i		−	0.716266i	−0.933671	−	0.358133i	$-0.883413\pi$
$401$		−	14.3432i		−	0.716266i	0.933671	−	0.358133i	$-0.116587\pi$
$402$	35.1566	+	44.7489i	1.75345	+	2.23187i
$403$	−12.5806	−	5.94278i	−0.626686	−	0.296031i
$404$	37.7015			1.87572
$405$	5.23387	−	10.1051i	0.260073	−	0.502128i
$406$	41.5157	−	71.9073i	2.06039	−	3.56870i
$407$	−23.6599			−1.17278
$408$	−9.06536	+	7.12211i	−0.448802	+	0.352597i
$409$	−5.33628	−	3.08090i	−0.263862	−	0.152341i	0.362233	−	0.932088i	$-0.382014\pi$
$409$	−5.33628	−	3.08090i	−0.263862	−	0.152341i	−0.626095	+	0.779747i	$0.715348\pi$
$410$	−6.37043	−	3.67797i	−0.314613	−	0.181642i
$411$	−2.81401	−	19.6381i	−0.138805	−	0.968675i
$412$	−9.81471			−0.483536
$413$	−13.2024	+	22.8672i	−0.649645	+	1.12522i
$414$	−2.17174	+	2.27333i	−0.106735	+	0.111728i
$415$	−2.86181			−0.140481
$416$	−1.46372	−	17.7463i	−0.0717649	−	0.870083i
$417$	−3.12348	+	7.79134i	−0.152957	+	0.381544i
$418$			19.9069i			0.973678i
$419$	−13.8846			−0.678306			−0.339153	−	0.940731i	$-0.610140\pi$
$419$	−13.8846			−0.678306			−0.339153	+	0.940731i	$0.610140\pi$
$420$	−30.4758	+	4.36699i	−1.48707	+	0.213087i
$421$	4.55207	+	2.62814i	0.221854	+	0.128088i	0.606808	−	0.794848i	$-0.292449\pi$
$421$	4.55207	+	2.62814i	0.221854	+	0.128088i	−0.384954	+	0.922936i	$0.625783\pi$
$422$	−9.15643	+	5.28647i	−0.445728	+	0.257341i
$423$	36.3856	+	8.86365i	1.76913	+	0.430966i
$424$		−	3.62770i		−	0.176177i
$425$	−7.14937			−0.346796
$426$	11.2009	−	27.9401i	0.542687	−	1.35370i
$427$			21.2791i			1.02977i
$428$	4.48141	+	7.76202i	0.216617	+	0.375191i
$429$	−16.1943	−	4.99138i	−0.781867	−	0.240986i
$430$	7.30292	−	12.6490i	0.352178	−	0.609990i
$431$	−29.8506	−	17.2343i	−1.43785	−	0.830145i	−0.440152	−	0.897923i	$-0.645076\pi$
$431$	−29.8506	−	17.2343i	−1.43785	−	0.830145i	−0.997700	+	0.0677785i	$0.978409\pi$
$432$	−2.54469	−	1.81753i	−0.122431	−	0.0874460i
$433$	7.36538	+	12.7572i	0.353957	+	0.613072i	0.986939	−	0.161095i	$-0.0515024\pi$
$433$	7.36538	+	12.7572i	0.353957	+	0.613072i	−0.632982	+	0.774167i	$0.718169\pi$
$434$	−32.3253	−	18.6630i	−1.55166	−	0.895854i
$435$	−17.4502	−	6.99564i	−0.836675	−	0.335415i
$436$	−24.2632	−	14.0084i	−1.16200	−	0.670879i
$437$	−1.24061	+	0.716269i	−0.0593466	+	0.0342638i
$438$	−19.7259	−	25.1080i	−0.942538	−	1.19971i
$439$	1.27254	+	2.20410i	0.0607349	+	0.105196i	0.894794	−	0.446479i	$-0.147322\pi$
$439$	1.27254	+	2.20410i	0.0607349	+	0.105196i	−0.834059	+	0.551675i	$0.813989\pi$
$440$	−9.40890	−	5.43223i	−0.448552	−	0.258971i
$441$	−30.0393	+	8.78935i	−1.43044	+	0.418540i
$442$	−1.44328	−	17.4985i	−0.0686500	−	0.832317i
$443$	−15.7844	+	27.3394i	−0.749941	+	1.29894i	0.197909	+	0.980220i	$0.436585\pi$
$443$	−15.7844	+	27.3394i	−0.749941	+	1.29894i	−0.947850	+	0.318716i	$0.896748\pi$
$444$	39.9826	−	31.4120i	1.89749	−	1.49075i
$445$	1.92425			0.0912181
$446$	−25.8068	+	44.6987i	−1.22199	+	2.11655i
$447$	34.8915	+	13.9877i	1.65031	+	0.661595i
$448$		−	52.7950i		−	2.49433i
$449$	−22.0161	+	12.7110i	−1.03900	+	0.599869i	−0.919551	−	0.392971i	$-0.871447\pi$
$449$	−22.0161	+	12.7110i	−1.03900	+	0.599869i	−0.119453	+	0.992840i	$0.538114\pi$
$450$	−6.63797	−	22.6865i	−0.312917	−	1.06945i
$451$	−3.40707	−	5.90122i	−0.160433	−	0.277878i
$452$	5.91897	+	10.2520i	0.278405	+	0.482211i
$453$	−4.34675	−	1.74257i	−0.204228	−	0.0818732i
$454$	4.86713	+	8.43012i	0.228426	+	0.395645i
$455$	8.13036	−	17.2117i	0.381157	−	0.806895i
$456$	−10.7294	−	13.6569i	−0.502451	−	0.639543i
$457$	19.6897	−	11.3678i	0.921044	−	0.531765i	0.0370761	−	0.999312i	$-0.488196\pi$
$457$	19.6897	−	11.3678i	0.921044	−	0.531765i	0.883968	+	0.467547i	$0.154862\pi$
$458$	−26.4809	+	45.8663i	−1.23737	+	2.14319i
$459$	8.88822	+	6.34837i	0.414866	+	0.296317i
$460$		−	1.92584i		−	0.0897927i
$461$		−	20.4265i		−	0.951359i	−0.879619	−	0.475679i	$-0.842202\pi$
$461$		−	20.4265i		−	0.951359i	0.879619	−	0.475679i	$-0.157798\pi$
$462$	−42.1966	−	16.9162i	−1.96316	−	0.787014i
$463$	−4.68063	+	2.70237i	−0.217528	+	0.125590i	−0.604805	−	0.796374i	$-0.706749\pi$
$463$	−4.68063	+	2.70237i	−0.217528	+	0.125590i	0.387277	+	0.921963i	$0.373416\pi$
$464$	−2.58304	+	4.47396i	−0.119915	+	0.207698i
$465$	−3.14483	+	7.84460i	−0.145838	+	0.363785i
$466$	−34.6827	+	20.0241i	−1.60665	+	0.927597i
$467$	10.0719			0.466072			0.233036	−	0.972468i	$-0.425134\pi$
$467$	10.0719			0.466072			0.233036	+	0.972468i	$0.425134\pi$
$468$	33.9933	−	13.0654i	1.57134	−	0.603947i
$469$	−59.2154			−2.73431
$470$	−31.6679	+	18.2835i	−1.46073	+	0.843354i
$471$	−16.7649	−	21.3391i	−0.772484	−	0.983254i
$472$	10.0123	−	17.3418i	0.460854	−	0.798223i
$473$	11.7174	−	6.76504i	0.538766	−	0.311057i
$474$	−2.07730	−	14.4968i	−0.0954137	−	0.665861i
$475$		−	10.7705i		−	0.494183i
$476$		−	29.5493i		−	1.35439i
$477$	−3.29874	+	0.965195i	−0.151039	+	0.0441932i
$478$	7.50818	−	13.0046i	0.343416	−	0.594814i
$479$	19.3968	−	11.1988i	0.886264	−	0.511685i	0.0135454	−	0.999908i	$-0.495688\pi$
$479$	19.3968	−	11.1988i	0.886264	−	0.511685i	0.872719	+	0.488223i	$0.162355\pi$
$480$	−10.7068	+	1.53421i	−0.488696	+	0.0700270i
$481$	2.58421	+	31.3312i	0.117830	+	1.42858i
$482$	−0.213092	−	0.369085i	−0.00970605	−	0.0168114i
$483$	−0.464040	−	3.23839i	−0.0211146	−	0.147352i
$484$	6.12206	+	10.6037i	0.278275	+	0.481987i
$485$	1.50837	+	2.61258i	0.0684917	+	0.118631i
$486$	−11.8923	+	34.0985i	−0.539448	+	1.54674i
$487$	−1.75362	+	1.01245i	−0.0794641	+	0.0458786i	−0.539206	−	0.842174i	$-0.681275\pi$
$487$	−1.75362	+	1.01245i	−0.0794641	+	0.0458786i	0.459741	+	0.888053i	$0.347942\pi$
$488$		−	16.1375i		−	0.730511i
$489$	−9.02347	+	7.08920i	−0.408055	+	0.320585i
$490$	15.2805	−	26.4666i	0.690303	−	1.19564i
$491$	3.05618			0.137924			0.0689618	−	0.997619i	$-0.478031\pi$
$491$	3.05618			0.137924			0.0689618	+	0.997619i	$0.478031\pi$
$492$	13.5923	+	5.44903i	0.612788	+	0.245661i
$493$	9.02218	−	15.6269i	0.406339	−	0.703799i
$494$	26.3613	−	2.17429i	1.18605	−	0.0978261i
$495$	−2.43627	+	10.0010i	−0.109502	+	0.449511i
$496$	2.01123	+	1.16118i	0.0903068	+	0.0521387i
$497$	15.6613	+	27.1261i	0.702504	+	1.21677i
$498$	8.98965	−	1.28816i	0.402836	−	0.0577238i
$499$	−17.6833	+	10.2094i	−0.791613	+	0.457038i	−0.840530	−	0.541765i	$-0.817756\pi$
$499$	−17.6833	+	10.2094i	−0.791613	+	0.457038i	0.0489173	+	0.998803i	$0.484423\pi$
$500$	30.9737	+	17.8827i	1.38518	+	0.799737i
$501$	−2.65191	−	18.5068i	−0.118479	−	0.826824i
$502$	47.3490	+	27.3370i	2.11329	+	1.22011i
$503$	1.22893	+	2.12856i	0.0547951	+	0.0949080i	0.892122	−	0.451795i	$-0.149216\pi$
$503$	1.22893	+	2.12856i	0.0547951	+	0.0949080i	−0.837327	+	0.546703i	$0.815883\pi$
$504$	38.0660	−	11.1379i	1.69559	−	0.496122i
$505$	12.2623	+	7.07967i	0.545667	+	0.315041i
$506$	1.42187	−	2.46276i	0.0632100	−	0.109483i
$507$	−4.84094	+	21.9901i	−0.214994	+	0.976615i
$508$	−26.4966	−	45.8934i	−1.17559	−	2.03619i
$509$			39.4938i			1.75053i	0.483643	+	0.875265i	$0.339313\pi$
$509$			39.4938i			1.75053i	−0.483643	+	0.875265i	$0.660687\pi$
$510$	−10.5573	+	1.51279i	−0.467484	+	0.0669875i
$511$	33.2249			1.46978
$512$			6.78333i			0.299784i
$513$	−9.56377	+	13.3900i	−0.422251	+	0.591184i
$514$	11.7363	−	6.77597i	0.517667	−	0.298875i
$515$	−3.19222	−	1.84303i	−0.140666	−	0.0812136i
$516$	−10.8195	+	26.9887i	−0.476302	+	1.18811i
$517$	−33.8737			−1.48976
$518$			84.3375i			3.70558i
$519$	8.36111	−	1.19809i	0.367012	−	0.0525905i
$520$	−6.16585	+	13.0529i	−0.270391	+	0.572406i
$521$	33.5976			1.47194			0.735970	−	0.677015i	$-0.236727\pi$
$521$	33.5976			1.47194			0.735970	+	0.677015i	$0.236727\pi$
$522$	57.9643	+	14.1203i	2.53703	+	0.618028i
$523$	3.09661	−	5.36349i	0.135405	−	0.234529i	−0.790347	−	0.612660i	$-0.790100\pi$
$523$	3.09661	−	5.36349i	0.135405	−	0.234529i	0.925752	+	0.378131i	$0.123433\pi$
$524$	−45.9297			−2.00645
$525$	22.8301	+	9.15239i	0.996389	+	0.399443i
$526$	−19.4571	−	11.2335i	−0.848369	−	0.489806i
$527$	−7.02493	−	4.05584i	−0.306011	−	0.176675i
$528$	2.62540	+	1.05250i	0.114256	+	0.0458042i
$529$	−22.7954			−0.991103
$530$	1.67802	−	2.90641i	0.0728884	−	0.126246i
$531$	−18.4332	−	4.49037i	−0.799931	−	0.194866i
$532$	44.5157			1.93000
$533$	−7.44245	+	5.15630i	−0.322368	+	0.223344i
$534$	−6.04453	+	0.866143i	−0.261572	+	0.0374817i
$535$			3.36612i			0.145530i
$536$	44.9074			1.93970
$537$	8.52864	−	21.2742i	0.368038	−	0.918051i
$538$	42.0192	+	24.2598i	1.81157	+	1.04591i
$539$	24.5173	−	14.1551i	1.05603	−	0.609701i
$540$	−9.16073	−	20.1351i	−0.394215	−	0.866475i
$541$		−	13.3436i		−	0.573685i	−0.957978	−	0.286843i	$-0.907394\pi$
$541$		−	13.3436i		−	0.573685i	0.957978	−	0.286843i	$-0.0926057\pi$
$542$	−13.3371			−0.572879
$543$	−31.2435	+	4.47700i	−1.34079	+	0.192127i
$544$		−	10.3813i		−	0.445093i
$545$	−5.26105	−	9.11240i	−0.225358	−	0.390332i
$546$	−17.7921	+	57.7256i	−0.761433	+	2.47043i
$547$	−2.28845	+	3.96371i	−0.0978471	+	0.169476i	−0.910793	−	0.412863i	$-0.864529\pi$
$547$	−2.28845	+	3.96371i	−0.0978471	+	0.169476i	0.812946	+	0.582339i	$0.197862\pi$
$548$	−33.3966	−	19.2815i	−1.42663	−	0.823665i
$549$	−14.6741	+	4.29358i	−0.626277	+	0.183246i
$550$	10.6903	+	18.5161i	0.455836	+	0.789531i
$551$	23.5418	+	13.5918i	1.00291	+	0.579032i
$552$	0.351916	+	2.45591i	0.0149785	+	0.104530i
$553$	13.1972	+	7.61943i	0.561204	+	0.324011i
$554$	32.0997	−	18.5328i	1.36379	−	0.787382i
$555$	18.9029	−	2.70867i	0.802384	−	0.114976i
$556$	8.15837	+	14.1307i	0.345992	+	0.599276i
$557$	−31.3528	−	18.1016i	−1.32846	−	0.766988i	−0.343400	−	0.939189i	$-0.611579\pi$
$557$	−31.3528	−	18.1016i	−1.32846	−	0.766988i	−0.985062	+	0.172201i	$0.944912\pi$
$558$	6.34765	−	26.0573i	0.268718	−	1.10310i
$559$	−10.2383	−	14.7776i	−0.433033	−	0.625026i
$560$	−1.58862	+	2.75158i	−0.0671316	+	0.116275i
$561$	−9.17015	−	3.67623i	−0.387164	−	0.155211i
$562$	43.4577			1.83315
$563$	−20.3321	+	35.2161i	−0.856894	+	1.48418i	0.0179832	+	0.999838i	$0.494275\pi$
$563$	−20.3321	+	35.2161i	−0.856894	+	1.48418i	−0.874877	+	0.484345i	$0.839058\pi$
$564$	57.2428	−	44.9722i	2.41035	−	1.89367i
$565$			4.44591i			0.187041i
$566$	9.07498	−	5.23944i	0.381450	−	0.220230i
$567$	−20.2558	−	31.6507i	−0.850665	−	1.32920i
$568$	−11.8771	−	20.5717i	−0.498352	−	0.863171i
$569$	8.50764	+	14.7357i	0.356659	+	0.617751i	0.987400	−	0.158242i	$-0.0505825\pi$
$569$	8.50764	+	14.7357i	0.356659	+	0.617751i	−0.630742	+	0.775993i	$0.717249\pi$
$570$	−2.27901	−	15.9045i	−0.0954571	−	0.666164i
$571$	−11.0113	−	19.0721i	−0.460809	−	0.798144i	0.538193	−	0.842822i	$-0.319107\pi$
$571$	−11.0113	−	19.0721i	−0.460809	−	0.798144i	−0.999001	+	0.0446778i	$0.985774\pi$
$572$	−27.0767	+	18.7594i	−1.13213	+	0.784368i
$573$	26.3538	−	3.77633i	1.10095	−	0.157759i
$574$	−21.0353	+	12.1448i	−0.877998	+	0.506912i
$575$	−0.769294	+	1.33246i	−0.0320818	+	0.0555673i
$576$	36.4076	−	10.6527i	1.51698	−	0.443862i
$577$		−	8.16526i		−	0.339924i	−0.985451	−	0.169962i	$-0.945635\pi$
$577$		−	8.16526i		−	0.339924i	0.985451	−	0.169962i	$-0.0543645\pi$
$578$			29.1466i			1.21234i
$579$	−1.38900	−	9.69338i	−0.0577249	−	0.402843i
$580$	−31.6485	+	18.2723i	−1.31413	+	0.758715i
$581$	−4.72490	+	8.18376i	−0.196022	+	0.339520i
$582$	−5.91414	−	7.52779i	−0.245149	−	0.312037i
$583$	2.69234	−	1.55443i	0.111505	−	0.0643777i
$584$	−25.1969			−1.04266
$585$	13.5097	+	2.13385i	0.558558	+	0.0882237i
$586$	−0.733734			−0.0303103
$587$	9.24313	−	5.33652i	0.381505	−	0.220262i	−0.296968	−	0.954887i	$-0.595975\pi$
$587$	9.24313	−	5.33652i	0.381505	−	0.220262i	0.678473	+	0.734626i	$0.262642\pi$
$588$	−22.6386	+	56.4707i	−0.933598	+	2.32881i
$589$	6.11010	−	10.5830i	0.251762	−	0.436065i
$590$	16.0431	−	9.26251i	0.660486	−	0.381332i
$591$	10.1382	+	4.06430i	0.417029	+	0.167183i
$592$		−	5.24734i		−	0.215664i
$593$			9.84678i			0.404359i	0.979348	+	0.202179i	$0.0648024\pi$
$593$			9.84678i			0.404359i	−0.979348	+	0.202179i	$0.935198\pi$
$594$	3.15128	−	32.5122i	0.129299	−	1.33399i
$595$	5.54883	−	9.61085i	0.227480	−	0.394007i
$596$	63.2808	−	36.5352i	2.59208	−	1.49654i
$597$	−1.81842	−	2.31457i	−0.0744230	−	0.0947291i
$598$	−3.41656	−	1.61390i	−0.139713	−	0.0659972i
$599$	6.98478	+	12.0980i	0.285391	+	0.494311i	0.972704	−	0.232050i	$-0.0745434\pi$
$599$	6.98478	+	12.0980i	0.285391	+	0.494311i	−0.687313	+	0.726361i	$0.741210\pi$
$600$	−17.3138	−	6.94093i	−0.706832	−	0.283362i
$601$	20.3592	+	35.2632i	0.830471	+	1.43842i	0.897665	+	0.440678i	$0.145262\pi$
$601$	20.3592	+	35.2632i	0.830471	+	1.43842i	−0.0671948	+	0.997740i	$0.521405\pi$
$602$	−24.1144	−	41.7674i	−0.982831	−	1.70231i
$603$	−11.9482	−	40.8351i	−0.486566	−	1.66293i
$604$	−7.88345	+	4.55151i	−0.320773	+	0.185198i
$605$			4.59846i			0.186954i
$606$	−41.7057	−	16.7194i	−1.69418	−	0.679180i
$607$	22.1684	−	38.3969i	0.899789	−	1.55848i	0.0720264	−	0.997403i	$-0.477053\pi$
$607$	22.1684	−	38.3969i	0.899789	−	1.55848i	0.827763	−	0.561078i	$-0.189613\pi$
$608$	15.6393			0.634257
$609$	−48.8156	+	38.3515i	−1.97811	+	1.55408i
$610$	7.46450	−	12.9289i	0.302229	−	0.523476i
$611$	3.69979	+	44.8566i	0.149678	+	1.81470i
$612$	20.3773	−	5.96229i	0.823702	−	0.241011i
$613$	7.43045	+	4.28997i	0.300113	+	0.173270i	0.642494	−	0.766291i	$-0.277900\pi$
$613$	7.43045	+	4.28997i	0.300113	+	0.173270i	−0.342381	+	0.939561i	$0.611233\pi$
$614$	−13.0716	−	22.6406i	−0.527526	−	0.913702i
$615$	3.39764	+	4.32468i	0.137006	+	0.174388i
$616$	−31.0685	+	17.9374i	−1.25178	+	0.722718i
$617$	−37.3259	−	21.5501i	−1.50268	−	0.867575i	−0.999995	−	0.00310830i	$-0.999011\pi$
$617$	−37.3259	−	21.5501i	−1.50268	−	0.867575i	−0.502689	−	0.864467i	$-0.667656\pi$
$618$	10.8571	+	4.35252i	0.436738	+	0.175084i
$619$	−40.7267	−	23.5136i	−1.63694	−	0.945090i	−0.981877	−	0.189520i	$-0.939307\pi$
$619$	−40.7267	−	23.5136i	−1.63694	−	0.945090i	−0.655067	−	0.755570i	$-0.727360\pi$
$620$	8.21414	+	14.2273i	0.329888	+	0.571382i
$621$	2.13957	−	0.973427i	0.0858580	−	0.0390623i
$622$	−63.8274	−	36.8508i	−2.55925	−	1.47758i
$623$	3.17696	−	5.50266i	0.127282	−	0.220459i
$624$	1.10700	−	3.59160i	0.0443154	−	0.143779i
$625$	−1.78678	−	3.09479i	−0.0714711	−	0.123792i
$626$		−	0.343235i		−	0.0137184i
$627$	5.53821	−	13.8148i	0.221175	−	0.551708i
$628$	−52.7498			−2.10495
$629$			18.3282i			0.730793i
$630$	35.6492	+	8.68427i	1.42030	+	0.345990i
$631$	24.6130	−	14.2103i	0.979828	−	0.565704i	0.0776098	−	0.996984i	$-0.475271\pi$
$631$	24.6130	−	14.2103i	0.979828	−	0.565704i	0.902218	+	0.431280i	$0.141938\pi$
$632$	−10.0084	−	5.77837i	−0.398114	−	0.229851i
$633$	7.82500	−	1.12127i	0.311016	−	0.0445666i
$634$	45.7321			1.81625
$635$		−	19.9023i		−	0.789800i
$636$	−2.48603	+	6.20128i	−0.0985777	+	0.245897i
$637$	−21.4224	−	30.9204i	−0.848786	−	1.22511i
$638$	−53.9627			−2.13640
$639$	−15.5462	+	16.2734i	−0.614998	+	0.643766i
$640$	−12.2753	+	21.2614i	−0.485223	+	0.840431i
$641$	16.7063			0.659860			0.329930	−	0.944005i	$-0.392975\pi$
$641$	16.7063			0.659860			0.329930	+	0.944005i	$0.392975\pi$
$642$	−1.51516	−	10.5738i	−0.0597984	−	0.417314i
$643$	17.2202	+	9.94208i	0.679098	+	0.392077i	0.799515	−	0.600646i	$-0.205090\pi$
$643$	17.2202	+	9.94208i	0.679098	+	0.392077i	−0.120417	+	0.992723i	$0.538423\pi$
$644$	−5.50721	−	3.17959i	−0.217014	−	0.125293i
$645$	−8.58702	+	6.74631i	−0.338114	+	0.265636i
$646$	15.4209			0.606728
$647$	4.08938	−	7.08301i	0.160770	−	0.278462i	−0.774375	−	0.632727i	$-0.781936\pi$
$647$	4.08938	−	7.08301i	0.160770	−	0.278462i	0.935145	+	0.354265i	$0.115269\pi$
$648$	15.3615	+	24.0031i	0.603456	+	0.942929i
$649$	17.1606			0.673613
$650$	23.3520	−	16.1788i	0.915941	−	0.634585i
$651$	17.2406	+	21.9446i	0.675712	+	0.860078i
$652$			22.3058i			0.873563i
$653$	−21.7572			−0.851426			−0.425713	−	0.904858i	$-0.639977\pi$
$653$	−21.7572			−0.851426			−0.425713	+	0.904858i	$0.639977\pi$
$654$	20.6279	+	26.2562i	0.806615	+	1.02670i
$655$	−14.9386	−	8.62479i	−0.583698	−	0.336998i
$656$	1.30878	−	0.755627i	0.0510994	−	0.0295023i
$657$	6.70394	+	22.9120i	0.261546	+	0.893882i
$658$			120.745i			4.70714i
$659$	37.4141			1.45745			0.728723	−	0.684809i	$-0.240114\pi$
$659$	37.4141			1.45745			0.728723	+	0.684809i	$0.240114\pi$
$660$	12.3611	+	15.7338i	0.481156	+	0.612438i
$661$		−	8.41108i		−	0.327153i	−0.986531	−	0.163576i	$-0.947697\pi$
$661$		−	8.41108i		−	0.327153i	0.986531	−	0.163576i	$-0.0523030\pi$
$662$	−19.7235	−	34.1621i	−0.766575	−	1.32775i
$663$	−3.86658	+	12.5449i	−0.150166	+	0.487204i
$664$	3.58324	−	6.20635i	0.139057	−	0.240853i
$665$	14.4787	+	8.35927i	0.561459	+	0.324158i
$666$	−58.1594	+	17.0172i	−2.25363	+	0.659401i
$667$	−1.94163	−	3.36300i	−0.0751801	−	0.130216i
$668$	−31.4728	−	18.1708i	−1.21772	−	0.703050i
$669$	30.3445	−	23.8399i	1.17319	−	0.921704i
$670$	35.9785	+	20.7722i	1.38997	+	0.802499i
$671$	11.9766	−	6.91472i	0.462353	−	0.266940i
$672$	−13.2898	+	33.1506i	−0.512664	+	1.27881i
$673$	−16.4682	−	28.5238i	−0.634803	−	1.09951i	−0.986557	−	0.163418i	$-0.947748\pi$
$673$	−16.4682	−	28.5238i	−0.634803	−	1.09951i	0.351754	−	0.936092i	$-0.385585\pi$
$674$	−26.2510	−	15.1560i	−1.01115	−	0.583789i
$675$	−1.70498	+	17.5905i	−0.0656245	+	0.677057i
$676$	27.7991	+	33.8068i	1.06920	+	1.30026i
$677$	−0.651673	+	1.12873i	−0.0250458	+	0.0433806i	−0.878277	−	0.478153i	$-0.841306\pi$
$677$	−0.651673	+	1.12873i	−0.0250458	+	0.0433806i	0.853231	+	0.521533i	$0.174640\pi$
$678$	−2.00119	−	13.9657i	−0.0768554	−	0.536349i
$679$	9.96138			0.382283
$680$	−4.20809	+	7.28862i	−0.161373	+	0.279506i
$681$	−1.03233	−	7.20430i	−0.0395590	−	0.276070i
$682$			24.2585i			0.928904i
$683$	−0.152548	+	0.0880738i	−0.00583710	+	0.00337005i	−0.502916	−	0.864335i	$-0.667739\pi$
$683$	−0.152548	+	0.0880738i	−0.00583710	+	0.00337005i	0.497079	+	0.867706i	$0.334406\pi$
$684$	8.98214	+	30.6982i	0.343441	+	1.17377i
$685$	−7.24145	−	12.5426i	−0.276682	−	0.479227i
$686$	−16.6026	−	28.7565i	−0.633889	−	1.09793i
$687$	31.1372	−	24.4626i	1.18796	−	0.933307i
$688$	1.50036	+	2.59870i	0.0572008	+	0.0990746i
$689$	−2.35248	−	3.39550i	−0.0896224	−	0.129358i
$690$	−0.854050	+	2.13038i	−0.0325131	+	0.0811022i
$691$	2.44577	−	1.41206i	0.0930414	−	0.0537175i	−0.452757	−	0.891634i	$-0.649560\pi$
$691$	2.44577	−	1.41206i	0.0930414	−	0.0537175i	0.545799	+	0.837916i	$0.316226\pi$
$692$	8.20930	−	14.2189i	0.312071	−	0.540523i
$693$	24.5769	+	23.4787i	0.933600	+	0.891880i
$694$		−	34.7312i		−	1.31838i
$695$			6.12799i			0.232448i
$696$	37.0205	−	29.0848i	1.40326	−	1.10246i
$697$	−4.57139	+	2.63929i	−0.173154	+	0.0999704i
$698$	−2.41500	+	4.18290i	−0.0914091	+	0.158325i
$699$	29.6395	−	4.24716i	1.12107	−	0.160642i
$700$	41.4057	−	23.9056i	1.56499	−	0.903547i
$701$	30.2245			1.14156			0.570782	−	0.821102i	$-0.306640\pi$
$701$	30.2245			1.14156			0.570782	+	0.821102i	$0.306640\pi$
$702$	−43.3978	−	0.621939i	−1.63794	−	0.0234736i
$703$	−27.6113			−1.04138
$704$	−29.7149	+	17.1559i	−1.11992	+	0.646589i
$705$	27.0631	−	3.87797i	1.01926	−	0.146053i
$706$	4.78931	−	8.29532i	0.180248	−	0.312199i
$707$	40.4906	−	23.3773i	1.52281	−	0.879193i
$708$	−28.9995	+	22.7832i	−1.08987	+	0.856244i
$709$			10.2338i			0.384340i	0.981362	+	0.192170i	$0.0615525\pi$
$709$			10.2338i			0.384340i	−0.981362	+	0.192170i	$0.938447\pi$
$710$		−	21.9753i		−	0.824718i
$711$	−2.59151	+	10.6383i	−0.0971894	+	0.398966i
$712$	−2.40932	+	4.17307i	−0.0902932	+	0.156392i
$713$	−1.51181	+	0.872842i	−0.0566176	+	0.0326882i
$714$	−13.1042	+	32.6877i	−0.490412	+	1.22330i
$715$	−12.3293	+	1.01693i	−0.461091	+	0.0380310i
$716$	−22.2764	−	38.5839i	−0.832508	−	1.44195i
$717$	−8.82838	+	6.93593i	−0.329702	+	0.259027i
$718$	−23.8363	−	41.2857i	−0.889562	−	1.54077i
$719$	−15.5196	−	26.8808i	−0.578785	−	1.00248i	−0.995619	−	0.0935023i	$-0.970194\pi$
$719$	−15.5196	−	26.8808i	−0.578785	−	1.00248i	0.416834	−	0.908983i	$-0.363140\pi$
$720$	−2.21804	−	0.540321i	−0.0826614	−	0.0201366i
$721$	−10.5408	+	6.08574i	−0.392560	+	0.226645i
$722$		−	20.7847i		−	0.773525i
$723$	0.0451972	+	0.315417i	0.00168090	+	0.0117305i
$724$	−30.6763	+	53.1328i	−1.14007	+	1.97467i
$725$	29.1961			1.08432
$726$	−2.06986	−	14.4449i	−0.0768197	−	0.536099i
$727$	−12.3666	+	21.4195i	−0.458650	+	0.794406i	−0.998890	−	0.0471055i	$-0.985000\pi$
$727$	−12.3666	+	21.4195i	−0.458650	+	0.794406i	0.540240	+	0.841511i	$0.318334\pi$
$728$	27.1466	+	39.1826i	1.00612	+	1.45220i
$729$	17.7393	−	20.3548i	0.657011	−	0.753881i
$730$	−20.1870	−	11.6550i	−0.747155	−	0.431370i
$731$	−5.24055	−	9.07689i	−0.193829	−	0.335721i
$732$	−11.0589	+	27.5858i	−0.408749	+	1.01960i
$733$	32.6554	−	18.8536i	1.20616	−	0.696375i	0.244239	−	0.969715i	$-0.421462\pi$
$733$	32.6554	−	18.8536i	1.20616	−	0.696375i	0.961917	+	0.273341i	$0.0881286\pi$
$734$	−29.4448	−	16.9999i	−1.08683	−	0.627479i
$735$	−17.9674	+	14.1159i	−0.662736	+	0.520672i
$736$	−1.93480	−	1.11706i	−0.0713176	−	0.0411752i
$737$	19.2422	+	33.3285i	0.708797	+	1.22767i
$738$	−12.6194	−	12.0555i	−0.464528	−	0.443770i
$739$	23.9351	+	13.8189i	0.880468	+	0.508338i	0.870813	−	0.491615i	$-0.163593\pi$
$739$	23.9351	+	13.8189i	0.880468	+	0.508338i	0.00965499	+	0.999953i	$0.496927\pi$
$740$	18.5597	−	32.1463i	0.682268	−	1.18172i
$741$	−18.8988	−	5.82497i	−0.694266	−	0.213986i
$742$	−5.54086	−	9.59705i	−0.203411	−	0.352319i
$743$		−	9.72719i		−	0.356856i	−0.983953	−	0.178428i	$-0.942899\pi$
$743$		−	9.72719i		−	0.356856i	0.983953	−	0.178428i	$-0.0571011\pi$
$744$	−13.0748	−	16.6422i	−0.479346	−	0.610134i
$745$	27.4427			1.00542
$746$			69.0167i			2.52688i
$747$	−6.59691	−	1.60703i	−0.241368	−	0.0587981i
$748$	−16.6314	+	9.60213i	−0.608104	+	0.351089i
$749$	9.62588	+	5.55751i	0.351722	+	0.203067i
$750$	−26.3329	−	33.5178i	−0.961543	−	1.22390i
$751$	−27.2580			−0.994658			−0.497329	−	0.867562i	$-0.665686\pi$
$751$	−27.2580			−0.994658			−0.497329	+	0.867562i	$0.665686\pi$
$752$		−	7.51257i		−	0.273955i
$753$	−25.2534	−	32.1438i	−0.920287	−	1.17138i
$754$	5.89397	+	71.4590i	0.214646	+	2.60238i
$755$	−3.41878			−0.124422
$756$	−72.7035	−	7.04688i	−2.64420	−	0.256292i
$757$	−16.3688	+	28.3517i	−0.594936	+	1.03046i	0.398620	+	0.917116i	$0.369489\pi$
$757$	−16.3688	+	28.3517i	−0.594936	+	1.03046i	−0.993556	+	0.113343i	$0.963844\pi$
$758$	30.9205			1.12308
$759$	−1.67189	+	1.31350i	−0.0606857	+	0.0476772i
$760$	−10.9802	−	6.33945i	−0.398295	−	0.229956i
$761$	40.3005	+	23.2675i	1.46089	+	0.843447i	0.999053	−	0.0435166i	$-0.0138562\pi$
$761$	40.3005	+	23.2675i	1.46089	+	0.843447i	0.461840	+	0.886963i	$0.347189\pi$
$762$	8.95844	+	62.5181i	0.324530	+	2.26479i
$763$	−34.7443			−1.25783
$764$	25.8753	−	44.8173i	0.936136	−	1.62143i
$765$	7.74728	+	1.88726i	0.280104	+	0.0682342i
$766$	6.83269			0.246875
$767$	−1.87433	−	22.7246i	−0.0676783	−	0.820537i
$768$	12.6904	−	31.6555i	0.457924	−	1.14227i
$769$			16.5704i			0.597544i	0.954325	+	0.298772i	$0.0965770\pi$
$769$			16.5704i			0.597544i	−0.954325	+	0.298772i	$0.903423\pi$
$770$	−33.1882			−1.19602
$771$	−10.0298	+	1.43720i	−0.361213	+	0.0517595i
$772$	−16.4846	−	9.51738i	−0.593293	−	0.342538i
$773$	2.28752	−	1.32070i	0.0822764	−	0.0475023i	−0.458297	−	0.888799i	$-0.651541\pi$
$773$	2.28752	−	1.32070i	0.0822764	−	0.0475023i	0.540574	+	0.841297i	$0.318207\pi$
$774$	23.9373	−	25.0570i	0.860407	−	0.900655i
$775$		−	13.1249i		−	0.471459i
$776$	−7.55445			−0.271189
$777$	23.4632	−	58.5276i	0.841736	−	2.09966i
$778$			38.5272i			1.38127i
$779$	−3.97608	−	6.88677i	−0.142458	−	0.246744i
$780$	19.4851	−	18.0875i	0.697677	−	0.647635i
$781$	10.1784	−	17.6294i	0.364211	−	0.630831i
$782$	−1.90778	−	1.10146i	−0.0682220	−	0.0393880i
$783$	−36.2971	−	25.9250i	−1.29715	−	0.926485i
$784$	3.13933	+	5.43748i	0.112119	+	0.194196i
$785$	−17.1568	−	9.90548i	−0.612352	−	0.353542i
$786$	50.8079	+	20.3684i	1.81226	+	0.726517i
$787$	6.17903	+	3.56746i	0.220259	+	0.127166i	0.606070	−	0.795411i	$-0.292745\pi$
$787$	6.17903	+	3.56746i	0.220259	+	0.127166i	−0.385811	+	0.922578i	$0.626078\pi$
$788$	18.3870	−	10.6158i	0.655011	−	0.378171i
$789$	10.3774	+	13.2088i	0.369444	+	0.470246i
$790$	−5.34564	−	9.25892i	−0.190189	−	0.329418i
$791$	12.7137	+	7.34026i	0.452047	+	0.260990i
$792$	−18.6385	−	17.8056i	−0.662290	−	0.632694i
$793$	−10.4648	−	15.1046i	−0.371616	−	0.536379i
$794$	−6.99729	+	12.1197i	−0.248324	+	0.430111i
$795$	−1.97307	+	1.55012i	−0.0699776	+	0.0549772i
$796$	−5.72157			−0.202796
$797$	14.4085	−	24.9563i	0.510376	−	0.883998i	−0.489551	−	0.871974i	$-0.662839\pi$
$797$	14.4085	−	24.9563i	0.510376	−	0.883998i	0.999928	−	0.0120233i	$-0.00382723\pi$
$798$	−49.2437	−	19.7413i	−1.74321	−	0.698836i
$799$			26.2403i			0.928316i
$800$	14.5467	−	8.39854i	0.514303	−	0.296933i
$801$	4.43568	+	1.08055i	0.156727	+	0.0381792i
$802$	16.6140	+	28.7763i	0.586662	+	1.01613i
$803$	−10.7966	−	18.7002i	−0.381002	−	0.659915i
$804$	−76.7657	−	30.7746i	−2.70732	−	1.08534i
$805$	−1.19414	−	2.06831i	−0.0420880	−	0.0728985i
$806$	32.1238	−	2.64958i	1.13151	−	0.0933276i
$807$	−22.4108	−	28.5255i	−0.788897	−	1.00414i
$808$	−30.7070	+	17.7287i	−1.08027	+	0.623694i
$809$	−3.89514	+	6.74657i	−0.136946	+	0.237197i	−0.926339	−	0.376691i	$-0.877062\pi$
$809$	−3.89514	+	6.74657i	−0.136946	+	0.237197i	0.789393	+	0.613888i	$0.210395\pi$
$810$	1.20441	+	26.3361i	0.0423186	+	0.925356i
$811$			43.2768i			1.51965i	0.650125	+	0.759827i	$0.274717\pi$
$811$			43.2768i			1.51965i	−0.650125	+	0.759827i	$0.725283\pi$
$812$			120.671i			4.23473i
$813$	9.25555	+	3.71046i	0.324606	+	0.130132i
$814$	47.4682	−	27.4058i	1.66376	−	0.960571i
$815$	−4.18864	+	7.25494i	−0.146722	+	0.254129i
$816$	0.815321	−	2.03377i	0.0285419	−	0.0711963i
$817$	13.6743	−	7.89484i	0.478402	−	0.276205i
$818$	14.2747			0.499103
$819$	28.4068	−	35.1099i	0.992613	−	1.22684i
$820$	10.6905			0.373329
$821$	−39.6462	+	22.8898i	−1.38366	+	0.798858i	−0.992591	−	0.121503i	$-0.961229\pi$
$821$	−39.6462	+	22.8898i	−1.38366	+	0.798858i	−0.391071	+	0.920360i	$0.627895\pi$
$822$	28.3928	+	36.1397i	0.990313	+	1.26052i
$823$	−9.61698	+	16.6571i	−0.335227	+	0.580630i	−0.983528	−	0.180754i	$-0.942146\pi$
$823$	−9.61698	+	16.6571i	−0.335227	+	0.580630i	0.648302	+	0.761384i	$0.275480\pi$
$824$	7.99387	−	4.61526i	0.278480	−	0.160780i
$825$	−2.26744	−	15.8237i	−0.0789421	−	0.550911i
$826$		−	61.1702i		−	2.12838i
$827$			34.1215i			1.18652i	0.805010	+	0.593261i	$0.202160\pi$
$827$			34.1215i			1.18652i	−0.805010	+	0.593261i	$0.797840\pi$
$828$	1.08144	−	4.43935i	0.0375826	−	0.154278i
$829$	21.0159	−	36.4006i	0.729913	−	1.26425i	−0.227007	−	0.973893i	$-0.572894\pi$
$829$	21.0159	−	36.4006i	0.729913	−	1.26425i	0.956920	−	0.290353i	$-0.0937727\pi$
$830$	5.74156	−	3.31489i	0.199293	−	0.115062i
$831$	−27.4321	+	3.93085i	−0.951610	+	0.136360i
$832$	25.9640	+	37.4756i	0.900138	+	1.29923i
$833$	−10.9652	−	18.9923i	−0.379923	−	0.658046i
$834$	−2.75833	−	19.2495i	−0.0955132	−	0.666556i
$835$	−6.82432	−	11.8201i	−0.236165	−	0.409050i
$836$	−14.4655	−	25.0550i	−0.500301	−	0.866547i
$837$	−11.6544	+	16.3170i	−0.402834	+	0.563999i
$838$	27.8562	−	16.0828i	0.962276	−	0.555570i
$839$			24.0777i			0.831254i	0.909535	+	0.415627i	$0.136438\pi$
$839$			24.0777i			0.831254i	−0.909535	+	0.415627i	$0.863562\pi$
$840$	22.7684	−	17.8877i	0.785583	−	0.617186i
$841$	−22.3442	+	38.7012i	−0.770488	+	1.33452i
$842$	−12.1769			−0.419643
$843$	−30.1583	−	12.0902i	−1.03871	−	0.416408i
$844$	7.68292	−	13.3072i	0.264457	−	0.458053i
$845$	2.69330	+	16.2158i	0.0926522	+	0.557840i
$846$	−83.2662	+	24.3633i	−2.86275	+	0.837627i
$847$	13.1499	+	7.59212i	0.451837	+	0.260868i
$848$	0.344743	+	0.597113i	0.0118385	+	0.0205049i
$849$	−7.75539	+	1.11130i	−0.266164	+	0.0381397i
$850$	14.3436	−	8.28126i	0.491980	−	0.284045i
$851$	3.41590	+	1.97217i	0.117095	+	0.0676051i
$852$	6.20534	+	43.3050i	0.212591	+	1.48361i
$853$	27.8602	+	16.0851i	0.953914	+	0.550742i	0.894295	−	0.447479i	$-0.147678\pi$
$853$	27.8602	+	16.0851i	0.953914	+	0.550742i	0.0596193	+	0.998221i	$0.481011\pi$
$854$	−24.6480	−	42.6916i	−0.843437	−	1.46088i
$855$	−2.84315	+	11.6712i	−0.0972336	+	0.399147i
$856$	−7.30001	−	4.21466i	−0.249509	−	0.144054i
$857$	7.08968	−	12.2797i	0.242179	−	0.419466i	−0.719156	−	0.694849i	$-0.755471\pi$
$857$	7.08968	−	12.2797i	0.242179	−	0.419466i	0.961335	+	0.275383i	$0.0888046\pi$
$858$	38.2717	−	8.74410i	1.30657	−	0.298519i
$859$	4.77386	+	8.26856i	0.162882	+	0.282120i	0.935901	−	0.352263i	$-0.114588\pi$
$859$	4.77386	+	8.26856i	0.162882	+	0.282120i	−0.773019	+	0.634383i	$0.781254\pi$
$860$			21.2269i			0.723833i
$861$	17.9766	−	2.57593i	0.612641	−	0.0877875i
$862$	79.8511			2.71974
$863$		−	27.1037i		−	0.922622i	−0.887238	−	0.461311i	$-0.847379\pi$
$863$		−	27.1037i		−	0.922622i	0.887238	−	0.461311i	$-0.152621\pi$
$864$	−25.5423	−	2.47571i	−0.868966	−	0.0842255i
$865$	5.34013	−	3.08313i	0.181570	−	0.104829i
$866$	−29.5538	−	17.0629i	−1.00428	−	0.579822i
$867$	8.10873	−	20.2268i	0.275387	−	0.686938i
$868$	54.2467			1.84125
$869$		−	9.90384i		−	0.335965i
$870$	43.1130	−	6.17783i	1.46167	−	0.209448i
$871$	42.0330	−	29.1214i	1.42423	−	0.986741i
$872$	26.3491			0.892294
$873$	2.00995	+	6.86940i	0.0680266	+	0.232494i
$874$	1.65934	−	2.87405i	0.0561279	−	0.0972163i
$875$	44.3535			1.49942
$876$	43.0721	+	17.2672i	1.45527	+	0.583405i
$877$	−34.3355	−	19.8236i	−1.15943	−	0.669395i	−0.208260	−	0.978074i	$-0.566780\pi$
$877$	−34.3355	−	19.8236i	−1.15943	−	0.669395i	−0.951166	+	0.308678i	$0.900113\pi$
$878$	−5.10610	−	2.94801i	−0.172322	−	0.0994904i
$879$	0.509188	+	0.204129i	0.0171745	+	0.00688509i
$880$	2.06491			0.0696083
$881$	−4.91250	+	8.50870i	−0.165506	+	0.286665i	−0.936835	−	0.349772i	$-0.886259\pi$
$881$	−4.91250	+	8.50870i	−0.165506	+	0.286665i	0.771329	+	0.636437i	$0.219592\pi$
$882$	50.0860	−	52.4288i	1.68648	−	1.76537i
$883$	−31.5744			−1.06256			−0.531282	−	0.847195i	$-0.678290\pi$
$883$	−31.5744			−1.06256			−0.531282	+	0.847195i	$0.678290\pi$
$884$	14.5320	+	20.9750i	0.488763	+	0.705466i
$885$	−13.7103	+	1.96460i	−0.460867	+	0.0660394i
$886$		−	73.1337i		−	2.45697i
$887$	15.1391			0.508322			0.254161	−	0.967162i	$-0.418201\pi$
$887$	15.1391			0.508322			0.254161	+	0.967162i	$0.418201\pi$
$888$	−17.7938	+	44.3858i	−0.597122	+	1.48949i
$889$	−56.9135	−	32.8591i	−1.90882	−	1.10206i
$890$	−3.86056	+	2.22889i	−0.129406	+	0.0747127i
$891$	−11.2319	+	21.6857i	−0.376284	+	0.726499i
$892$		−	75.0111i		−	2.51156i
$893$	−39.5308			−1.32285
$894$	−86.2040	+	12.3525i	−2.88309	+	0.413129i
$895$		−	16.7325i		−	0.559305i
$896$	40.5333	+	70.2058i	1.35412	+	2.34541i
$897$	1.92199	+	2.07050i	0.0641734	+	0.0691320i
$898$	29.4468	−	51.0033i	0.982652	−	1.70200i
$899$	28.6879	+	16.5630i	0.956795	+	0.552406i
$900$	24.8400	+	23.7300i	0.828000	+	0.790999i
$901$	−1.20414	−	2.08563i	−0.0401156	−	0.0694823i
$902$	13.6710	+	7.89296i	0.455195	+	0.262807i
$903$	5.11473	+	35.6941i	0.170208	+	1.18782i
$904$	−9.64174	−	5.56666i	−0.320679	−	0.185144i
$905$	−19.9548	+	11.5209i	−0.663321	+	0.382968i
$906$	10.7392	−	1.53886i	0.356786	−	0.0511252i
$907$	27.7852	+	48.1254i	0.922593	+	1.59798i	0.795388	+	0.606101i	$0.207267\pi$
$907$	27.7852	+	48.1254i	0.922593	+	1.59798i	0.127205	+	0.991876i	$0.459399\pi$
$908$	−12.2517	−	7.07350i	−0.406586	−	0.234742i
$909$	24.2910	+	23.2055i	0.805682	+	0.769678i
$910$	3.62492	+	43.9488i	0.120165	+	1.45689i
$911$	−17.3371	+	30.0288i	−0.574405	+	0.994899i	0.421701	+	0.906735i	$0.361433\pi$
$911$	−17.3371	+	30.0288i	−0.574405	+	0.994899i	−0.996106	+	0.0881637i	$0.971900\pi$
$912$	3.06386	+	1.22827i	0.101455	+	0.0406722i
$913$	6.14148			0.203253
$914$	−26.3352	+	45.6139i	−0.871090	+	1.50877i
$915$	−8.77702	+	6.89558i	−0.290159	+	0.227961i
$916$		−	76.9704i		−	2.54317i
$917$	−49.3276	+	28.4793i	−1.62894	+	0.940469i
$918$	−25.1856	−	2.44114i	−0.831248	−	0.0805697i
$919$	6.58230	+	11.4009i	0.217130	+	0.376080i	0.953929	−	0.300031i	$-0.0969971\pi$
$919$	6.58230	+	11.4009i	0.217130	+	0.376080i	−0.736799	+	0.676111i	$0.763664\pi$
$920$	0.905605	+	1.56855i	0.0298569	+	0.0517137i
$921$	2.77251	+	19.3485i	0.0913574	+	0.637554i
$922$	23.6604	+	40.9811i	0.779215	+	1.34964i
$923$	−24.4572	−	11.5530i	−0.805017	−	0.380270i
$924$	65.4014	−	9.37161i	2.15155	−	0.308303i
$925$	−25.6823	+	14.8277i	−0.844428	+	0.487531i
$926$	6.26040	−	10.8433i	0.205730	−	0.356334i
$927$	−6.32361	−	6.04102i	−0.207695	−	0.198413i
$928$			42.3943i			1.39166i
$929$			18.2960i			0.600271i	0.953897	+	0.300135i	$0.0970319\pi$
$929$			18.2960i			0.600271i	−0.953897	+	0.300135i	$0.902968\pi$
$930$	−2.77719	−	19.3811i	−0.0910676	−	0.635531i
$931$	28.6118	−	16.5190i	0.937714	−	0.541389i
$932$	29.1014	−	50.4051i	0.953247	−	1.65107i
$933$	34.0421	+	43.3304i	1.11449	+	1.41857i
$934$	−20.2069	+	11.6665i	−0.661191	+	0.381739i
$935$	−7.21244			−0.235872
$936$	−21.5429	+	26.6264i	−0.704153	+	0.870312i
$937$	50.7326			1.65736			0.828681	−	0.559722i	$-0.189092\pi$
$937$	50.7326			1.65736			0.828681	+	0.559722i	$0.189092\pi$
$938$	118.802	−	68.5903i	3.87902	−	2.23955i
$939$	−0.0954899	+	0.238194i	−0.00311619	+	0.00777318i
$940$	26.5717	−	46.0236i	0.866675	−	1.50112i
$941$	−24.2843	+	14.0206i	−0.791646	+	0.457057i	−0.840542	−	0.541747i	$-0.817763\pi$
$941$	−24.2843	+	14.0206i	−0.791646	+	0.457057i	0.0488955	+	0.998804i	$0.484430\pi$
$942$	58.3523	+	23.3929i	1.90122	+	0.762182i
$943$			1.13598i			0.0369927i
$944$			3.80591i			0.123872i
$945$	−22.3234	−	15.9444i	−0.726182	−	0.518672i
$946$	−15.6721	+	27.1450i	−0.509545	+	0.882558i
$947$	−38.3313	+	22.1306i	−1.24560	+	0.719148i	−0.970229	−	0.242189i	$-0.922134\pi$
$947$	−38.3313	+	22.1306i	−1.24560	+	0.719148i	−0.275372	+	0.961338i	$0.588801\pi$
$948$	13.1488	+	16.7364i	0.427052	+	0.543572i
$949$	−23.5841	+	16.3396i	−0.765572	+	0.530406i
$950$	12.4756	+	21.6085i	0.404764	+	0.701071i
$951$	−31.7367	−	12.7229i	−1.02913	−	0.412569i
$952$	13.8952	+	24.0672i	0.450347	+	0.780023i
$953$	5.98910	+	10.3734i	0.194006	+	0.336028i	0.946574	−	0.322486i	$-0.104519\pi$
$953$	5.98910	+	10.3734i	0.194006	+	0.336028i	−0.752568	+	0.658514i	$0.771185\pi$
$954$	5.50015	−	5.75743i	0.178074	−	0.186404i
$955$	16.8318	−	9.71785i	0.544665	−	0.314462i
$956$			21.8236i			0.705824i
$957$	37.4484	+	15.0127i	1.21054	+	0.485292i
$958$	−25.9435	+	44.9355i	−0.838196	+	1.45180i
$959$	−47.8230			−1.54428
$960$	21.7764	−	17.1085i	0.702832	−	0.552173i
$961$	−8.05427	+	13.9504i	−0.259815	+	0.450013i
$962$	−41.4761	−	59.8654i	−1.33724	−	1.93014i
$963$	−1.89021	+	7.75940i	−0.0609113	+	0.250043i
$964$	0.536399	+	0.309690i	0.0172762	+	0.00997444i
$965$	−3.57439	−	6.19103i	−0.115064	−	0.199296i
$966$	4.68208	+	5.95957i	0.150643	+	0.191746i
$967$	−7.75706	+	4.47854i	−0.249450	+	0.144020i	−0.619513	−	0.784987i	$-0.712670\pi$
$967$	−7.75706	+	4.47854i	−0.249450	+	0.144020i	0.370062	+	0.929007i	$0.379336\pi$
$968$	−9.97257	−	5.75766i	−0.320530	−	0.185058i
$969$	−10.7016	−	4.29018i	−0.343786	−	0.137821i
$970$	−6.05240	−	3.49436i	−0.194331	−	0.112197i
$971$	−8.19718	−	14.1979i	−0.263060	−	0.455633i	0.703994	−	0.710206i	$-0.251398\pi$
$971$	−8.19718	−	14.1979i	−0.263060	−	0.455633i	−0.967054	+	0.254573i	$0.918065\pi$
$972$	−9.81017	−	51.5584i	−0.314661	−	1.65374i
$973$	17.5239	+	10.1174i	0.561789	+	0.324349i
$974$	2.34549	−	4.06250i	0.0751542	−	0.130171i
$975$	−20.7066	+	4.73093i	−0.663142	+	0.151511i
$976$	1.53356	+	2.65620i	0.0490880	+	0.0850229i
$977$		−	37.3172i		−	1.19388i	−0.802285	−	0.596941i	$-0.796383\pi$
$977$		−	37.3172i		−	1.19388i	0.802285	−	0.596941i	$-0.203617\pi$
$978$	9.89194	−	24.6749i	0.316309	−	0.789016i
$979$	−4.12946			−0.131978
$980$			44.4149i			1.41878i
$981$	−7.01050	−	23.9597i	−0.223828	−	0.764976i
$982$	−6.13152	+	3.54003i	−0.195665	+	0.112967i
$983$	−44.4140	−	25.6424i	−1.41659	−	0.817866i	−0.420589	−	0.907251i	$-0.638176\pi$
$983$	−44.4140	−	25.6424i	−1.41659	−	0.817866i	−0.995997	+	0.0893852i	$0.971510\pi$
$984$	−13.6330	+	1.95352i	−0.434603	+	0.0622759i
$985$	7.97381			0.254067
$986$			41.8023i			1.33126i
$987$	33.5920	−	83.7934i	1.06924	−	2.66717i
$988$	−31.5987	+	21.8923i	−1.00529	+	0.696486i
$989$	−2.25559			−0.0717237
$990$	−6.69653	−	22.8867i	−0.212830	−	0.727386i
$991$	−28.1237	+	48.7116i	−0.893378	+	1.54738i	−0.0575787	+	0.998341i	$0.518338\pi$
$991$	−28.1237	+	48.7116i	−0.893378	+	1.54738i	−0.835799	+	0.549035i	$0.814995\pi$
$992$	19.0580			0.605092
$993$	4.18340	+	29.1946i	0.132756	+	0.926463i
$994$	−62.8414	−	36.2815i	−1.99321	−	1.15078i
$995$	−1.86093	−	1.07441i	−0.0589955	−	0.0340611i
$996$	−10.3784	+	8.15370i	−0.328853	+	0.258360i
$997$	−5.35303			−0.169532			−0.0847661	−	0.996401i	$-0.527014\pi$
$997$	−5.35303			−0.169532			−0.0847661	+	0.996401i	$0.527014\pi$
$998$	23.6516	−	40.9658i	0.748679	−	1.29675i
$999$	45.0950	+	4.37089i	1.42674	+	0.138289i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.r.b.43.2	yes	22
3.2	odd	2		351.2.r.b.316.10		22
9.4	even	3		117.2.l.b.4.2	✓	22
9.5	odd	6		351.2.l.b.199.10		22
13.10	even	6		117.2.l.b.88.10	yes	22
39.23	odd	6		351.2.l.b.127.2		22
117.23	odd	6		351.2.r.b.10.10		22
117.49	even	6	inner	117.2.r.b.49.2	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.l.b.4.2	✓	22	9.4	even	3
117.2.l.b.88.10	yes	22	13.10	even	6
117.2.r.b.43.2	yes	22	1.1	even	1	trivial
117.2.r.b.49.2	yes	22	117.49	even	6	inner
351.2.l.b.127.2		22	39.23	odd	6
351.2.l.b.199.10		22	9.5	odd	6
351.2.r.b.10.10		22	117.23	odd	6
351.2.r.b.316.10		22	3.2	odd	2

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00627 + 1.15832i) q^{2} +(1.71454 - 0.245682i) q^{3} +(1.68341 - 2.91575i) q^{4} +(1.09505 - 0.632228i) q^{5} +(-3.15524 + 2.47889i) q^{6} -4.17527i q^{7} +3.16642i q^{8} +(2.87928 - 0.842464i) q^{9} +(-1.46464 + 2.53684i) q^{10} +(-2.34999 + 1.35677i) q^{11} +(2.16992 - 5.41274i) q^{12} +(2.05335 + 2.96374i) q^{13} +(4.83630 + 8.37672i) q^{14} +(1.72218 - 1.35301i) q^{15} +(-0.300907 - 0.521186i) q^{16} +(1.05102 + 1.82043i) q^{17} +(-4.80077 + 5.02533i) q^{18} +(-2.74246 + 1.58336i) q^{19} -4.25719i q^{20} +(-1.02579 - 7.15866i) q^{21} +(3.14314 - 5.44409i) q^{22} +0.452373 q^{23} +(0.777933 + 5.42894i) q^{24} +(-1.70057 + 2.94548i) q^{25} +(-7.55253 - 3.56763i) q^{26} +(4.72966 - 2.15182i) q^{27} +(-12.1740 - 7.02869i) q^{28} +(-4.29209 - 7.43413i) q^{29} +(-1.88793 + 4.70934i) q^{30} +(-3.34195 + 1.92947i) q^{31} +(-4.27700 - 2.46932i) q^{32} +(-3.69582 + 2.90358i) q^{33} +(-4.21727 - 2.43484i) q^{34} +(-2.63973 - 4.57214i) q^{35} +(2.39059 - 9.81346i) q^{36} +(7.55106 + 4.35961i) q^{37} +(3.66807 - 6.35328i) q^{38} +(4.24868 + 4.57697i) q^{39} +(2.00190 + 3.46739i) q^{40} +2.51117i q^{41} +(10.3500 + 13.1740i) q^{42} -4.98614 q^{43} +9.13598i q^{44} +(2.62033 - 2.74290i) q^{45} +(-0.907582 + 0.523993i) q^{46} +(10.8108 + 6.24161i) q^{47} +(-0.643962 - 0.819665i) q^{48} -10.4329 q^{49} -7.87923i q^{50} +(2.24927 + 2.86297i) q^{51} +(12.0981 - 0.997861i) q^{52} -1.14568 q^{53} +(-6.99646 + 9.79559i) q^{54} +(-1.71558 + 2.97147i) q^{55} +13.2207 q^{56} +(-4.31304 + 3.38850i) q^{57} +(17.2222 + 9.94323i) q^{58} +(-5.47680 - 3.16203i) q^{59} +(-1.04592 - 7.29912i) q^{60} -5.09646 q^{61} +(4.46989 - 7.74208i) q^{62} +(-3.51752 - 12.0218i) q^{63} +12.6447 q^{64} +(4.12228 + 1.94726i) q^{65} +(4.05152 - 10.1063i) q^{66} -14.1824i q^{67} +7.07720 q^{68} +(0.775611 - 0.111140i) q^{69} +(10.5920 + 6.11529i) q^{70} +(-6.49685 + 3.75096i) q^{71} +(2.66759 + 9.11700i) q^{72} +7.95754i q^{73} -20.1993 q^{74} +(-2.19205 + 5.46794i) q^{75} +10.6617i q^{76} +(5.66488 + 9.81187i) q^{77} +(-13.8256 - 4.26131i) q^{78} +(-1.82489 + 3.16081i) q^{79} +(-0.659017 - 0.380484i) q^{80} +(7.58051 - 4.85138i) q^{81} +(-2.90873 - 5.03807i) q^{82} +(-1.96005 - 1.13164i) q^{83} +(-22.5997 - 9.06000i) q^{84} +(2.30185 + 1.32897i) q^{85} +(10.0035 - 5.77554i) q^{86} +(-9.18539 - 11.6916i) q^{87} +(-4.29610 - 7.44106i) q^{88} +(1.31792 + 0.760899i) q^{89} +(-2.07993 + 8.53818i) q^{90} +(12.3744 - 8.57329i) q^{91} +(0.761528 - 1.31901i) q^{92} +(-5.25585 + 4.12921i) q^{93} -28.9191 q^{94} +(-2.00209 + 3.46772i) q^{95} +(-7.93974 - 3.18297i) q^{96} +2.38580i q^{97} +(20.9312 - 12.0846i) q^{98} +(-5.62326 + 5.88630i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{3} + 10 q^{4} + 3 q^{5} - 6 q^{6} - 2 q^{9} - 7 q^{10} + 3 q^{11} - 11 q^{12} + 3 q^{13} - 9 q^{14} - 15 q^{15} - 12 q^{16} + 9 q^{17} - 30 q^{18} - 6 q^{19} + 12 q^{21} - 13 q^{22} - 12 q^{23}+ \cdots - 18 q^{99}+O(q^{100}) \) 22 * q + 2 * q^3 + 10 * q^4 + 3 * q^5 - 6 * q^6 - 2 * q^9 - 7 * q^10 + 3 * q^11 - 11 * q^12 + 3 * q^13 - 9 * q^14 - 15 * q^15 - 12 * q^16 + 9 * q^17 - 30 * q^18 - 6 * q^19 + 12 * q^21 - 13 * q^22 - 12 * q^23 + 45 * q^24 + 4 * q^25 - 12 * q^26 + 14 * q^27 + 3 * q^28 - 24 * q^29 - 39 * q^30 + 27 * q^31 - 18 * q^33 - 15 * q^34 - 27 * q^35 + 2 * q^36 + 6 * q^37 + 21 * q^38 + 13 * q^39 + 13 * q^40 + 27 * q^42 + 8 * q^43 + 27 * q^45 - 15 * q^46 + 6 * q^47 + 11 * q^48 - 14 * q^49 + 12 * q^51 - 7 * q^52 - 24 * q^53 - 33 * q^54 - 13 * q^55 + 18 * q^56 + 42 * q^57 + 15 * q^58 - 33 * q^59 - 6 * q^60 - 6 * q^61 - 3 * q^63 - 24 * q^64 + 3 * q^65 + 30 * q^66 + 138 * q^68 - 3 * q^69 + 24 * q^70 + 9 * q^71 - 6 * q^72 + 12 * q^74 + 22 * q^75 + 42 * q^77 - 42 * q^78 - 6 * q^79 + 105 * q^80 + 10 * q^81 - 16 * q^82 - 42 * q^83 - 18 * q^84 - 51 * q^85 - 45 * q^86 + 27 * q^87 - 11 * q^88 - 30 * q^89 + 30 * q^90 + 15 * q^91 - 3 * q^92 + 6 * q^93 - 88 * q^94 - 3 * q^95 + 9 * q^96 + 117 * q^98 - 18 * q^99

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