LMFDB - Embedded newform 133.2.g.a.102.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [133,2,Mod(30,133)] 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("133.30"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(133, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 133 = 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	133.g (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.06201034688$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			102.1
Character	$\chi$	$=$	133.102
Dual form			133.2.g.a.30.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.16102 + 2.01095i) q^{2} -1.27672 q^{3} +(-1.69596 - 2.93748i) q^{4} +(2.05173 - 3.55370i) q^{5} +(1.48231 - 2.56743i) q^{6} +(-0.208777 - 2.63750i) q^{7} +3.23209 q^{8} -1.36998 q^{9} +(4.76422 + 8.25187i) q^{10} +(-1.36662 + 2.36705i) q^{11} +(2.16526 + 3.75035i) q^{12} +(2.05362 - 3.55698i) q^{13} +(5.54629 + 2.64236i) q^{14} +(-2.61949 + 4.53709i) q^{15} +(-0.360622 + 0.624615i) q^{16} +1.24576 q^{17} +(1.59058 - 2.75497i) q^{18} +(-4.34562 - 0.339963i) q^{19} -13.9186 q^{20} +(0.266550 + 3.36736i) q^{21} +(-3.17335 - 5.49640i) q^{22} +5.63122 q^{23} -4.12648 q^{24} +(-5.91920 - 10.2524i) q^{25} +(4.76861 + 8.25948i) q^{26} +5.57925 q^{27} +(-7.39354 + 5.08636i) q^{28} +(0.386810 - 0.669975i) q^{29} +(-6.08259 - 10.5353i) q^{30} +(-1.21874 + 2.11091i) q^{31} +(2.39471 + 4.14775i) q^{32} +(1.74479 - 3.02206i) q^{33} +(-1.44636 + 2.50516i) q^{34} +(-9.80125 - 4.66951i) q^{35} +(2.32343 + 4.02429i) q^{36} +(-1.32075 - 2.28760i) q^{37} +(5.72902 - 8.34414i) q^{38} +(-2.62191 + 4.54127i) q^{39} +(6.63138 - 11.4859i) q^{40} +(2.41205 + 4.17779i) q^{41} +(-7.08107 - 3.37356i) q^{42} +(-0.250810 - 0.434416i) q^{43} +9.27088 q^{44} +(-2.81083 + 4.86851i) q^{45} +(-6.53798 + 11.3241i) q^{46} +0.00235232 q^{47} +(0.460414 - 0.797460i) q^{48} +(-6.91282 + 1.10130i) q^{49} +27.4894 q^{50} -1.59049 q^{51} -13.9314 q^{52} +(0.280212 + 0.485342i) q^{53} +(-6.47765 + 11.2196i) q^{54} +(5.60785 + 9.71309i) q^{55} +(-0.674784 - 8.52464i) q^{56} +(5.54815 + 0.434039i) q^{57} +(0.898192 + 1.55571i) q^{58} -2.61944 q^{59} +17.7702 q^{60} +11.7346 q^{61} +(-2.82997 - 4.90165i) q^{62} +(0.286020 + 3.61333i) q^{63} -12.5637 q^{64} +(-8.42696 - 14.5959i) q^{65} +(4.05148 + 7.01737i) q^{66} +(-4.70077 - 8.14198i) q^{67} +(-2.11275 - 3.65940i) q^{68} -7.18950 q^{69} +(20.7697 - 14.2884i) q^{70} +(5.28155 + 9.14791i) q^{71} -4.42790 q^{72} +11.2118 q^{73} +6.13367 q^{74} +(7.55718 + 13.0894i) q^{75} +(6.37135 + 13.3417i) q^{76} +(6.52841 + 3.11027i) q^{77} +(-6.08819 - 10.5451i) q^{78} +(-0.675335 + 1.16971i) q^{79} +(1.47980 + 2.56308i) q^{80} -3.01321 q^{81} -11.2018 q^{82} +6.83039 q^{83} +(9.43949 - 6.49387i) q^{84} +(2.55596 - 4.42706i) q^{85} +1.16479 q^{86} +(-0.493849 + 0.855372i) q^{87} +(-4.41702 + 7.65051i) q^{88} -7.59704 q^{89} +(-6.52689 - 11.3049i) q^{90} +(-9.81028 - 4.67382i) q^{91} +(-9.55030 - 16.5416i) q^{92} +(1.55599 - 2.69505i) q^{93} +(-0.00273110 + 0.00473040i) q^{94} +(-10.1242 + 14.7455i) q^{95} +(-3.05737 - 5.29553i) q^{96} +(1.72833 + 2.99355i) q^{97} +(5.81130 - 15.1800i) q^{98} +(1.87224 - 3.24281i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} - 6 q^{3} - 11 q^{4} - 6 q^{6} - 2 q^{7} - 18 q^{8} + 18 q^{9} + 16 q^{10} - q^{11} - 2 q^{12} + 6 q^{13} - q^{14} - 9 q^{15} - 9 q^{16} - 16 q^{17} + 5 q^{18} - 4 q^{19} - 21 q^{21} - 2 q^{22}+ \cdots + 43 q^{99}+O(q^{100}) $ 24 * q + q^2 - 6 * q^3 - 11 * q^4 - 6 * q^6 - 2 * q^7 - 18 * q^8 + 18 * q^9 + 16 * q^10 - q^11 - 2 * q^12 + 6 * q^13 - q^14 - 9 * q^15 - 9 * q^16 - 16 * q^17 + 5 * q^18 - 4 * q^19 - 21 * q^21 - 2 * q^22 + 18 * q^23 + 16 * q^24 - 14 * q^25 + q^26 - 18 * q^27 - 14 * q^28 - 2 * q^29 - 9 * q^30 + 11 * q^31 + 24 * q^32 + 3 * q^33 + 6 * q^34 + 38 * q^35 - 7 * q^36 - 14 * q^37 + 12 * q^38 - 10 * q^39 + 42 * q^40 + 20 * q^41 - 36 * q^42 + 2 * q^43 - 4 * q^44 - 12 * q^45 - 6 * q^46 + 39 * q^48 + 18 * q^49 + 22 * q^50 - 42 * q^51 - 22 * q^52 + 7 * q^53 - 43 * q^54 + 9 * q^55 - 21 * q^56 + 21 * q^57 + 35 * q^58 - 84 * q^59 + 12 * q^60 - 12 * q^61 - 19 * q^62 + 9 * q^63 - 2 * q^64 - 27 * q^65 + 3 * q^66 - 14 * q^67 + 51 * q^68 - 34 * q^69 + 33 * q^70 + q^71 - 36 * q^72 + 42 * q^73 + 50 * q^74 + 31 * q^75 - 70 * q^76 - 20 * q^77 + 57 * q^78 - 5 * q^79 + 13 * q^80 - 56 * q^81 + 24 * q^82 + 10 * q^83 + 129 * q^84 - 27 * q^85 - 36 * q^86 + 53 * q^87 - 36 * q^88 + 2 * q^89 + 27 * q^90 - 9 * q^91 - 72 * q^92 + 34 * q^93 + 12 * q^94 - 11 * q^95 - 94 * q^96 + 31 * q^97 - 26 * q^98 + 43 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/133\mathbb{Z}\right)^\times$.

$n$	$78$	$115$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.16102	+	2.01095i	−0.820968	+	1.42196i	0.0839936	+	0.996466i	$0.473232\pi$
$2$	−1.16102	+	2.01095i	−0.820968	+	1.42196i	−0.904962	+	0.425493i	$0.860101\pi$
$3$	−1.27672			−0.737116			−0.368558	−	0.929605i	$-0.620148\pi$
$3$	−1.27672			−0.737116			−0.368558	+	0.929605i	$0.620148\pi$
$4$	−1.69596	−	2.93748i	−0.847978	−	1.46874i
$5$	2.05173	−	3.55370i	0.917562	−	1.58926i	0.114456	−	0.993428i	$-0.463488\pi$
$5$	2.05173	−	3.55370i	0.917562	−	1.58926i	0.803106	−	0.595836i	$-0.203179\pi$
$6$	1.48231	−	2.56743i	0.605149	−	1.04815i
$7$	−0.208777	−	2.63750i	−0.0789101	−	0.996882i
$7$	−0.208777	−	2.63750i	−0.0789101	−	0.996882i
$8$	3.23209			1.14272
$9$	−1.36998			−0.456660
$10$	4.76422	+	8.25187i	1.50658	+	2.60947i
$11$	−1.36662	+	2.36705i	−0.412050	+	0.713692i	−0.995114	−	0.0987348i	$-0.968520\pi$
$11$	−1.36662	+	2.36705i	−0.412050	+	0.713692i	0.583064	+	0.812426i	$0.301854\pi$
$12$	2.16526	+	3.75035i	0.625058	+	1.08263i
$13$	2.05362	−	3.55698i	0.569572	−	0.986528i	−0.427036	−	0.904235i	$-0.640442\pi$
$13$	2.05362	−	3.55698i	0.569572	−	0.986528i	0.996608	−	0.0822936i	$-0.0262245\pi$
$14$	5.54629	+	2.64236i	1.48231	+	0.706201i
$15$	−2.61949	+	4.53709i	−0.676350	+	1.17147i
$16$	−0.360622	+	0.624615i	−0.0901554	+	0.156154i
$17$	1.24576			0.302141			0.151071	−	0.988523i	$-0.451728\pi$
$17$	1.24576			0.302141			0.151071	+	0.988523i	$0.451728\pi$
$18$	1.59058	−	2.75497i	0.374904	−	0.649352i
$19$	−4.34562	−	0.339963i	−0.996954	−	0.0779930i
$19$	−4.34562	−	0.339963i	−0.996954	−	0.0779930i
$20$	−13.9186			−3.11229
$21$	0.266550	+	3.36736i	0.0581659	+	0.734817i
$22$	−3.17335	−	5.49640i	−0.676560	−	1.17184i
$23$	5.63122			1.17419			0.587095	−	0.809518i	$-0.300272\pi$
$23$	5.63122			1.17419			0.587095	+	0.809518i	$0.300272\pi$
$24$	−4.12648			−0.842314
$25$	−5.91920	−	10.2524i	−1.18384	−	2.05047i
$26$	4.76861	+	8.25948i	0.935202	+	1.61982i
$27$	5.57925			1.07373
$28$	−7.39354	+	5.08636i	−1.39725	+	0.961232i
$29$	0.386810	−	0.669975i	0.0718288	−	0.124411i	−0.827874	−	0.560914i	$-0.810450\pi$
$29$	0.386810	−	0.669975i	0.0718288	−	0.124411i	0.899703	+	0.436503i	$0.143783\pi$
$30$	−6.08259	−	10.5353i	−1.11052	−	1.92348i
$31$	−1.21874	+	2.11091i	−0.218892	+	0.379131i	−0.954469	−	0.298309i	$-0.903577\pi$
$31$	−1.21874	+	2.11091i	−0.218892	+	0.379131i	0.735578	+	0.677440i	$0.236911\pi$
$32$	2.39471	+	4.14775i	0.423328	+	0.733226i
$33$	1.74479	−	3.02206i	0.303729	−	0.526073i
$34$	−1.44636	+	2.50516i	−0.248048	+	0.429632i
$35$	−9.80125	−	4.66951i	−1.65671	−	0.789292i
$36$	2.32343	+	4.02429i	0.387238	+	0.670716i
$37$	−1.32075	−	2.28760i	−0.217129	−	0.376079i	0.736800	−	0.676111i	$-0.236336\pi$
$37$	−1.32075	−	2.28760i	−0.217129	−	0.376079i	−0.953929	+	0.300032i	$0.903003\pi$
$38$	5.72902	−	8.34414i	0.929370	−	1.35360i
$39$	−2.62191	+	4.54127i	−0.419841	+	0.727186i
$40$	6.63138	−	11.4859i	1.04851	−	1.81608i
$41$	2.41205	+	4.17779i	0.376699	+	0.652461i	0.990580	−	0.136937i	$-0.0437259\pi$
$41$	2.41205	+	4.17779i	0.376699	+	0.652461i	−0.613881	+	0.789398i	$0.710393\pi$
$42$	−7.08107	−	3.37356i	−1.09263	−	0.520552i
$43$	−0.250810	−	0.434416i	−0.0382482	−	0.0662478i	0.846268	−	0.532758i	$-0.178844\pi$
$43$	−0.250810	−	0.434416i	−0.0382482	−	0.0662478i	−0.884516	+	0.466510i	$0.845511\pi$
$44$	9.27088			1.39764
$45$	−2.81083	+	4.86851i	−0.419014	+	0.725754i
$46$	−6.53798	+	11.3241i	−0.963973	+	1.66965i
$47$	0.00235232			0.000343121			0.000171560	−	1.00000i	$-0.499945\pi$
$47$	0.00235232			0.000343121			0.000171560		1.00000i	$0.499945\pi$
$48$	0.460414	−	0.797460i	0.0664550	−	0.115103i
$49$	−6.91282	+	1.10130i	−0.987546	+	0.157328i
$50$	27.4894			3.88758
$51$	−1.59049			−0.222713
$52$	−13.9314			−1.93194
$53$	0.280212	+	0.485342i	0.0384901	+	0.0666668i	0.884629	−	0.466296i	$-0.154412\pi$
$53$	0.280212	+	0.485342i	0.0384901	+	0.0666668i	−0.846139	+	0.532963i	$0.821079\pi$
$54$	−6.47765	+	11.2196i	−0.881496	+	1.52680i
$55$	5.60785	+	9.71309i	0.756163	+	1.30971i
$56$	−0.674784	−	8.52464i	−0.0901719	−	1.13915i
$57$	5.54815	+	0.434039i	0.734870	+	0.0574898i
$58$	0.898192	+	1.55571i	0.117938	+	0.204275i
$59$	−2.61944			−0.341022			−0.170511	−	0.985356i	$-0.554542\pi$
$59$	−2.61944			−0.341022			−0.170511	+	0.985356i	$0.554542\pi$
$60$	17.7702			2.29412
$61$	11.7346			1.50246			0.751232	−	0.660038i	$-0.229460\pi$
$61$	11.7346			1.50246			0.751232	+	0.660038i	$0.229460\pi$
$62$	−2.82997	−	4.90165i	−0.359406	−	0.622510i
$63$	0.286020	+	3.61333i	0.0360351	+	0.455236i
$64$	−12.5637			−1.57047
$65$	−8.42696	−	14.5959i	−1.04524	−	1.81040i
$66$	4.05148	+	7.01737i	0.498703	+	0.863779i
$67$	−4.70077	−	8.14198i	−0.574291	−	0.994701i	−0.996118	−	0.0880249i	$-0.971944\pi$
$67$	−4.70077	−	8.14198i	−0.574291	−	0.994701i	0.421827	−	0.906676i	$-0.361389\pi$
$68$	−2.11275	−	3.65940i	−0.256209	−	0.443767i
$69$	−7.18950			−0.865514
$70$	20.7697	−	14.2884i	2.48245	−	1.70779i
$71$	5.28155	+	9.14791i	0.626804	+	1.08566i	0.988189	+	0.153240i	$0.0489708\pi$
$71$	5.28155	+	9.14791i	0.626804	+	1.08566i	−0.361385	+	0.932417i	$0.617696\pi$
$72$	−4.42790			−0.521833
$73$	11.2118			1.31225			0.656123	−	0.754654i	$-0.272195\pi$
$73$	11.2118			1.31225			0.656123	+	0.754654i	$0.272195\pi$
$74$	6.13367			0.713025
$75$	7.55718	+	13.0894i	0.872627	+	1.51144i
$76$	6.37135	+	13.3417i	0.730844	+	1.53040i
$77$	6.52841	+	3.11027i	0.743981	+	0.354448i
$78$	−6.08819	−	10.5451i	−0.689352	−	1.19399i
$79$	−0.675335	+	1.16971i	−0.0759811	+	0.131603i	−0.901512	−	0.432753i	$-0.857542\pi$
$79$	−0.675335	+	1.16971i	−0.0759811	+	0.131603i	0.825531	+	0.564356i	$0.190876\pi$
$80$	1.47980	+	2.56308i	0.165446	+	0.286562i
$81$	−3.01321			−0.334801
$82$	−11.2018			−1.23703
$83$	6.83039			0.749732			0.374866	−	0.927079i	$-0.377689\pi$
$83$	6.83039			0.749732			0.374866	+	0.927079i	$0.377689\pi$
$84$	9.43949	−	6.49387i	1.02993	−	0.708540i
$85$	2.55596	−	4.42706i	0.277233	−	0.480182i
$86$	1.16479			0.125602
$87$	−0.493849	+	0.855372i	−0.0529462	+	0.0917055i
$88$	−4.41702	+	7.65051i	−0.470856	+	0.815547i
$89$	−7.59704			−0.805284			−0.402642	−	0.915358i	$-0.631908\pi$
$89$	−7.59704			−0.805284			−0.402642	+	0.915358i	$0.631908\pi$
$90$	−6.52689	−	11.3049i	−0.687995	−	1.19164i
$91$	−9.81028	−	4.67382i	−1.02840	−	0.489949i
$92$	−9.55030	−	16.5416i	−0.995687	−	1.72458i
$93$	1.55599	−	2.69505i	0.161348	−	0.279464i
$94$	−0.00273110	+	0.00473040i	−0.000281691	+	0.000487904i
$95$	−10.1242	+	14.7455i	−1.03872	+	1.51286i
$96$	−3.05737	−	5.29553i	−0.312042	−	0.540473i
$97$	1.72833	+	2.99355i	0.175485	+	0.303949i	0.940329	−	0.340267i	$-0.110517\pi$
$97$	1.72833	+	2.99355i	0.175485	+	0.303949i	−0.764844	+	0.644215i	$0.777184\pi$
$98$	5.81130	−	15.1800i	0.587030	−	1.53341i
$99$	1.87224	−	3.24281i	0.188167	−	0.325915i
$100$	−20.0774	+	34.7751i	−2.00774	+	3.47751i
$101$	−0.370914	−	0.642442i	−0.0369073	−	0.0639253i	0.846982	−	0.531622i	$-0.178417\pi$
$101$	−0.370914	−	0.642442i	−0.0369073	−	0.0639253i	−0.883889	+	0.467697i	$0.845084\pi$
$102$	1.84660	−	3.19840i	0.182840	−	0.316689i
$103$	−1.57050	−	2.72019i	−0.154746	−	0.268029i	0.778220	−	0.627991i	$-0.216123\pi$
$103$	−1.57050	−	2.72019i	−0.154746	−	0.268029i	−0.932967	+	0.359963i	$0.882789\pi$
$104$	6.63749	−	11.4965i	0.650859	−	1.12732i
$105$	12.5135	+	5.96167i	1.22119	+	0.581799i
$106$	−1.30133			−0.126397
$107$	5.92261	+	10.2583i	0.572561	+	0.991704i	0.996302	+	0.0859210i	$0.0273833\pi$
$107$	5.92261	+	10.2583i	0.572561	+	0.991704i	−0.423741	+	0.905783i	$0.639283\pi$
$108$	−9.46216	−	16.3889i	−0.910497	−	1.57703i
$109$	17.3988			1.66650			0.833252	−	0.552893i	$-0.186476\pi$
$109$	17.3988			1.66650			0.833252	+	0.552893i	$0.186476\pi$
$110$	−26.0434			−2.48314
$111$	1.68623	+	2.92063i	0.160049	+	0.277214i
$112$	1.72271	+	0.820735i	0.162781	+	0.0775522i
$113$	−18.4796			−1.73842			−0.869208	−	0.494447i	$-0.835371\pi$
$113$	−18.4796			−1.73842			−0.869208	+	0.494447i	$0.835371\pi$
$114$	−7.31437	+	10.6531i	−0.685054	+	0.997758i
$115$	11.5537	−	20.0117i	1.07739	−	1.86610i
$116$	−2.62405			−0.243637
$117$	−2.81342	+	4.87299i	−0.260101	+	0.450508i
$118$	3.04123	−	5.26757i	0.279968	−	0.484919i
$119$	−0.260085	−	3.28569i	−0.0238420	−	0.301199i
$120$	−8.46642	+	14.6643i	−0.772875	+	1.33866i
$121$	1.76473	+	3.05659i	0.160430	+	0.277872i
$122$	−13.6242	+	23.5978i	−1.23348	+	2.13644i
$123$	−3.07951	−	5.33388i	−0.277670	−	0.480939i
$124$	8.26770			0.742461
$125$	−28.0611			−2.50986
$126$	−7.59831	−	3.61999i	−0.676911	−	0.322494i
$127$	0.828285	−	1.43463i	0.0734984	−	0.127303i	−0.826934	−	0.562299i	$-0.809917\pi$
$127$	0.828285	−	1.43463i	0.0734984	−	0.127303i	0.900432	+	0.434996i	$0.143250\pi$
$128$	9.79740	−	16.9696i	0.865976	−	1.49991i
$129$	0.320215	+	0.554628i	0.0281933	+	0.0488323i
$130$	39.1356			3.43242
$131$	3.25292	−	5.63423i	0.284209	−	0.492265i	−0.688208	−	0.725514i	$-0.741602\pi$
$131$	3.25292	−	5.63423i	0.284209	−	0.492265i	0.972417	+	0.233249i	$0.0749356\pi$
$132$	−11.8363			−1.03022
$133$	0.0106100	+	11.5326i	0.000920008	+	1.00000i
$134$	21.8309			1.88590
$135$	11.4471	−	19.8270i	0.985212	−	1.70644i
$136$	4.02641			0.345261
$137$	2.82208	+	4.88798i	0.241106	+	0.417608i	0.961030	−	0.276445i	$-0.0891564\pi$
$137$	2.82208	+	4.88798i	0.241106	+	0.417608i	−0.719923	+	0.694053i	$0.755823\pi$
$138$	8.34718	−	14.4577i	0.710559	−	1.23073i
$139$	1.64060	−	2.84160i	0.139154	−	0.241021i	−0.788023	−	0.615646i	$-0.788895\pi$
$139$	1.64060	−	2.84160i	0.139154	−	0.241021i	0.927176	+	0.374625i	$0.122228\pi$
$140$	2.90587	+	36.7103i	0.245591	+	3.10259i
$141$	−0.00300326			−0.000252920
$142$	−24.5280			−2.05835
$143$	5.61302	+	9.72204i	0.469385	+	0.812998i
$144$	0.494045	−	0.855711i	0.0411704	−	0.0713092i
$145$	−1.58726	−	2.74922i	−0.131815	−	0.228310i
$146$	−13.0172	+	22.5465i	−1.07731	+	1.86596i
$147$	8.82576	−	1.40605i	0.727936	−	0.115969i
$148$	−4.47985	+	7.75933i	−0.368242	+	0.637813i
$149$	3.03506	−	5.25687i	0.248642	−	0.430660i	−0.714508	−	0.699628i	$-0.753349\pi$
$149$	3.03506	−	5.25687i	0.248642	−	0.430660i	0.963149	+	0.268968i	$0.0866825\pi$
$150$	−35.0963			−2.86560
$151$	−1.71726	+	2.97438i	−0.139748	+	0.242051i	−0.927401	−	0.374068i	$-0.877963\pi$
$151$	−1.71726	+	2.97438i	−0.139748	+	0.242051i	0.787653	+	0.616119i	$0.211296\pi$
$152$	−14.0454	−	1.09879i	−1.13923	−	0.0891238i
$153$	−1.70667			−0.137976
$154$	−13.8342	+	9.51723i	−1.11479	+	0.766920i
$155$	5.00104	+	8.66206i	0.401693	+	0.695753i
$156$	17.7865			1.42406
$157$	9.78495			0.780924			0.390462	−	0.920619i	$-0.372315\pi$
$157$	9.78495			0.780924			0.390462	+	0.920619i	$0.372315\pi$
$158$	−1.56816	−	2.71613i	−0.124756	−	0.216084i
$159$	−0.357753	−	0.619646i	−0.0283717	−	0.0491412i
$160$	19.6532			1.55372
$161$	−1.17567	−	14.8523i	−0.0926555	−	1.17053i
$162$	3.49841	−	6.05942i	0.274861	−	0.476073i
$163$	11.3656	+	19.6859i	0.890226	+	1.54192i	0.839604	+	0.543199i	$0.182787\pi$
$163$	11.3656	+	19.6859i	0.890226	+	1.54192i	0.0506219	+	0.998718i	$0.483880\pi$
$164$	8.18145	−	14.1707i	0.638864	−	1.10655i
$165$	−7.15967	−	12.4009i	−0.557380	−	0.965410i
$166$	−7.93024	+	13.7356i	−0.615506	+	1.06609i
$167$	10.3011	−	17.8420i	0.797123	−	1.38066i	−0.124359	−	0.992237i	$-0.539687\pi$
$167$	10.3011	−	17.8420i	0.797123	−	1.38066i	0.921482	−	0.388421i	$-0.126979\pi$
$168$	0.861512	+	10.8836i	0.0664671	+	0.839687i
$169$	−1.93473	−	3.35105i	−0.148826	−	0.257773i
$170$	5.93507	+	10.2798i	0.455199	+	0.788428i
$171$	5.95342	+	0.465743i	0.455269	+	0.0356163i
$172$	−0.850726	+	1.47350i	−0.0648672	+	0.112353i
$173$	2.53869	−	4.39714i	0.193013	−	0.334308i	−0.753234	−	0.657752i	$-0.771507\pi$
$173$	2.53869	−	4.39714i	0.193013	−	0.334308i	0.946247	+	0.323444i	$0.104841\pi$
$174$	−1.14674	−	1.98621i	−0.0869343	−	0.150575i
$175$	−25.8048	+	17.7524i	−1.95066	+	1.34195i
$176$	−0.985662	−	1.70722i	−0.0742971	−	0.128686i
$177$	3.34430			0.251373
$178$	8.82034	−	15.2773i	0.661113	−	1.14508i
$179$	−3.00370	+	5.20257i	−0.224507	+	0.388858i	−0.956172	−	0.292807i	$-0.905411\pi$
$179$	−3.00370	+	5.20257i	−0.224507	+	0.388858i	0.731664	+	0.681665i	$0.238744\pi$
$180$	19.0682			1.42126
$181$	6.03333	−	10.4500i	0.448454	−	0.776745i	−0.549832	−	0.835275i	$-0.685308\pi$
$181$	6.03333	−	10.4500i	0.448454	−	0.776745i	0.998286	+	0.0585307i	$0.0186415\pi$
$182$	20.7888	−	14.3016i	1.54097	−	1.06011i
$183$	−14.9818			−1.10749
$184$	18.2006			1.34177
$185$	−10.8393			−0.796918
$186$	3.61308	+	6.25804i	0.264924	+	0.458862i
$187$	−1.70247	+	2.94877i	−0.124497	+	0.215636i
$188$	−0.00398943	−	0.00690989i	−0.000290959	−	0.000503956i
$189$	−1.16482	−	14.7153i	−0.0847280	−	1.07038i
$190$	−17.8982	−	37.4792i	−1.29847	−	2.71903i
$191$	−12.9481	−	22.4268i	−0.936892	−	1.62274i	−0.771226	−	0.636562i	$-0.780356\pi$
$191$	−12.9481	−	22.4268i	−0.936892	−	1.62274i	−0.165666	−	0.986182i	$-0.552977\pi$
$192$	16.0404			1.15762
$193$	−13.9514			−1.00424			−0.502121	−	0.864797i	$-0.667447\pi$
$193$	−13.9514			−1.00424			−0.502121	+	0.864797i	$0.667447\pi$
$194$	−8.02651			−0.576270
$195$	10.7589	+	18.6349i	0.770460	+	1.33448i
$196$	14.9589	+	18.4385i	1.06849	+	1.31704i
$197$	3.51738			0.250603			0.125301	−	0.992119i	$-0.460010\pi$
$197$	3.51738			0.250603			0.125301	+	0.992119i	$0.460010\pi$
$198$	4.34743	+	7.52996i	0.308958	+	0.535131i
$199$	−1.17611	−	2.03708i	−0.0833721	−	0.144405i	0.821324	−	0.570462i	$-0.193236\pi$
$199$	−1.17611	−	2.03708i	−0.0833721	−	0.144405i	−0.904696	+	0.426057i	$0.859902\pi$
$200$	−19.1314	−	33.1365i	−1.35279	−	2.34311i
$201$	6.00158	+	10.3950i	0.423319	+	0.733210i
$202$	1.72256			0.121199
$203$	−1.84782	−	0.880337i	−0.129691	−	0.0617876i
$204$	2.69740	+	4.67203i	0.188856	+	0.327108i
$205$	19.7955			1.38258
$206$	7.29358			0.508168
$207$	−7.71466			−0.536206
$208$	1.48116	+	2.56545i	0.102700	+	0.177882i
$209$	6.74350	−	9.82169i	0.466458	−	0.679381i
$210$	−26.5171	+	18.2424i	−1.82985	+	1.25884i
$211$	−4.49929	−	7.79300i	−0.309744	−	0.536492i	0.668562	−	0.743656i	$-0.266910\pi$
$211$	−4.49929	−	7.79300i	−0.309744	−	0.536492i	−0.978306	+	0.207164i	$0.933577\pi$
$212$	0.950455	−	1.64624i	0.0652775	−	0.113064i
$213$	−6.74307	−	11.6793i	−0.462027	−	0.800255i
$214$	−27.5052			−1.88022
$215$	−2.05838			−0.140380
$216$	18.0326			1.22697
$217$	5.82198	+	2.77371i	0.395222	+	0.188292i
$218$	−20.2005	+	34.9882i	−1.36815	+	2.36970i
$219$	−14.3144			−0.967278
$220$	19.0213	−	32.9459i	1.28242	−	2.22122i
$221$	2.55832	−	4.43114i	0.172091	−	0.298071i
$222$	−7.83100			−0.525582
$223$	−0.416897	−	0.722088i	−0.0279175	−	0.0483546i	0.851729	−	0.523982i	$-0.175554\pi$
$223$	−0.416897	−	0.722088i	−0.0279175	−	0.0483546i	−0.879647	+	0.475628i	$0.842221\pi$
$224$	10.4397	−	7.18200i	0.697535	−	0.479867i
$225$	8.10919	+	14.0455i	0.540613	+	0.936369i
$226$	21.4553	−	37.1616i	1.42718	−	2.47196i
$227$	−0.864020	+	1.49653i	−0.0573470	+	0.0993279i	−0.893274	−	0.449513i	$-0.851597\pi$
$227$	−0.864020	+	1.49653i	−0.0573470	+	0.0993279i	0.835927	+	0.548841i	$0.184931\pi$
$228$	−8.13444	−	17.0337i	−0.538716	−	1.12808i
$229$	7.16700	+	12.4136i	0.473608	+	0.820314i	0.999544	−	0.0302108i	$-0.00961786\pi$
$229$	7.16700	+	12.4136i	0.473608	+	0.820314i	−0.525935	+	0.850525i	$0.676285\pi$
$230$	26.8284	+	46.4681i	1.76901	+	3.06401i
$231$	−8.33496	−	3.97094i	−0.548400	−	0.261269i
$232$	1.25020	−	2.16542i	0.0820799	−	0.142167i
$233$	−7.39894	+	12.8153i	−0.484721	+	0.839561i	−0.999846	−	0.0175537i	$-0.994412\pi$
$233$	−7.39894	+	12.8153i	−0.484721	+	0.839561i	0.515125	+	0.857115i	$0.327746\pi$
$234$	−6.53291	−	11.3153i	−0.427070	−	0.739706i
$235$	0.00482632	−	0.00835944i	0.000314835	−	0.000545310i
$236$	4.44246	+	7.69456i	0.289179	+	0.500873i
$237$	0.862214	−	1.49340i	0.0560068	−	0.0970067i
$238$	6.90934	+	3.29175i	0.447866	+	0.213372i
$239$	0.919825			0.0594985			0.0297493	−	0.999557i	$-0.490529\pi$
$239$	0.919825			0.0594985			0.0297493	+	0.999557i	$0.490529\pi$
$240$	−1.88929	−	3.27235i	−0.121953	−	0.211229i
$241$	10.7320	+	18.5883i	0.691307	+	1.19738i	0.971410	+	0.237409i	$0.0762982\pi$
$241$	10.7320	+	18.5883i	0.691307	+	1.19738i	−0.280103	+	0.959970i	$0.590369\pi$
$242$	−8.19556			−0.526830
$243$	−12.8907			−0.826940
$244$	−19.9014	−	34.4702i	−1.27406	−	2.20673i
$245$	−10.2696	+	26.8257i	−0.656099	+	1.71383i
$246$	14.3016			0.911835
$247$	−10.1335	+	14.7591i	−0.644780	+	0.939101i
$248$	−3.93907	+	6.82266i	−0.250131	+	0.433240i
$249$	−8.72050			−0.552639
$250$	32.5797	−	56.4296i	2.06052	−	3.56892i
$251$	1.53888	−	2.66541i	0.0971331	−	0.168239i	−0.813364	−	0.581755i	$-0.802366\pi$
$251$	1.53888	−	2.66541i	0.0971331	−	0.168239i	0.910497	+	0.413516i	$0.135699\pi$
$252$	10.1290	−	6.96822i	0.638067	−	0.438957i
$253$	−7.69571	+	13.3294i	−0.483825	+	0.838009i
$254$	1.92332	+	3.33129i	0.120680	+	0.209024i
$255$	−3.26326	+	5.65212i	−0.204353	+	0.353950i
$256$	10.1863	+	17.6432i	0.636644	+	1.10270i
$257$	23.8147			1.48552			0.742759	−	0.669559i	$-0.233517\pi$
$257$	23.8147			1.48552			0.742759	+	0.669559i	$0.233517\pi$
$258$	−1.48711			−0.0925833
$259$	−5.75780	+	3.96107i	−0.357773	+	0.246129i
$260$	−28.5835	+	49.5081i	−1.77267	+	3.07036i
$261$	−0.529923	+	0.917853i	−0.0328014	+	0.0568137i
$262$	7.55345	+	13.0830i	0.466654	+	0.808268i
$263$	−30.3468			−1.87126			−0.935631	−	0.352980i	$-0.885168\pi$
$263$	−30.3468			−1.87126			−0.935631	+	0.352980i	$0.885168\pi$
$264$	5.63931	−	9.76757i	0.347075	−	0.601152i
$265$	2.29968			0.141268
$266$	−23.2038	−	13.3682i	−1.42271	−	0.819660i
$267$	9.69930			0.593588
$268$	−15.9446	+	27.6169i	−0.973972	+	1.68697i
$269$	2.18323			0.133114			0.0665568	−	0.997783i	$-0.478799\pi$
$269$	2.18323			0.133114			0.0665568	+	0.997783i	$0.478799\pi$
$270$	26.5808	+	46.0393i	1.61765	+	2.80186i
$271$	−6.36764	+	11.0291i	−0.386806	+	0.669968i	−0.992018	−	0.126096i	$-0.959755\pi$
$271$	−6.36764	+	11.0291i	−0.386806	+	0.669968i	0.605212	+	0.796065i	$0.293089\pi$
$272$	−0.449248	+	0.778120i	−0.0272397	+	0.0471805i
$273$	12.5250	+	5.96717i	0.758048	+	0.361149i
$274$	−13.1060			−0.791762
$275$	32.3571			1.95121
$276$	12.1931	+	21.1190i	0.733937	+	1.27122i
$277$	14.8786	−	25.7705i	0.893967	−	1.54840i	0.0588902	−	0.998264i	$-0.481244\pi$
$277$	14.8786	−	25.7705i	0.893967	−	1.54840i	0.835077	−	0.550133i	$-0.185423\pi$
$278$	3.80955	+	6.59833i	0.228481	+	0.395741i
$279$	1.66965	−	2.89191i	0.0999591	−	0.173134i
$280$	−31.6785	−	15.0923i	−1.89315	−	0.901936i
$281$	−9.66027	+	16.7321i	−0.576283	+	0.998152i	0.419618	+	0.907701i	$0.362164\pi$
$281$	−9.66027	+	16.7321i	−0.576283	+	0.998152i	−0.995901	+	0.0904508i	$0.971169\pi$
$282$	0.00348685	−	0.00603941i	0.000207639	−	0.000359642i
$283$	0.799733			0.0475392			0.0237696	−	0.999717i	$-0.492433\pi$
$283$	0.799733			0.0475392			0.0237696	+	0.999717i	$0.492433\pi$
$284$	17.9145	−	31.0289i	1.06303	−	1.84123i
$285$	12.9258	−	18.8259i	0.765656	−	1.11515i
$286$	−26.0674			−1.54140
$287$	10.5153	−	7.23400i	0.620701	−	0.427010i
$288$	−3.28070	−	5.68234i	−0.193317	−	0.334835i
$289$	−15.4481			−0.908711
$290$	7.37140			0.432863
$291$	−2.20659	−	3.82193i	−0.129353	−	0.224045i
$292$	−19.0148	−	32.9346i	−1.11276	−	1.92735i
$293$	14.7714			0.862952			0.431476	−	0.902124i	$-0.357993\pi$
$293$	14.7714			0.862952			0.431476	+	0.902124i	$0.357993\pi$
$294$	−7.41942	+	19.3806i	−0.432709	+	1.13030i
$295$	−5.37439	+	9.30871i	−0.312909	+	0.541974i
$296$	−4.26877	−	7.39372i	−0.248117	−	0.429751i
$297$	−7.62469	+	13.2063i	−0.442429	+	0.766310i
$298$	7.04755	+	12.2067i	0.408254	+	0.707116i
$299$	11.5644	−	20.0301i	0.668786	−	1.15837i
$300$	25.6333	−	44.3981i	1.47994	−	2.56333i
$301$	−1.09341	+	0.752208i	−0.0630230	+	0.0433565i
$302$	−3.98756	−	6.90665i	−0.229458	−	0.397433i
$303$	0.473554	+	0.820219i	0.0272050	+	0.0471204i
$304$	1.77947	−	2.59174i	0.102060	−	0.148647i
$305$	24.0763	−	41.7014i	1.37860	−	2.38781i
$306$	1.98148	−	3.43203i	0.113274	−	0.196196i
$307$	−13.4804	−	23.3487i	−0.769366	−	1.33258i	−0.937907	−	0.346887i	$-0.887239\pi$
$307$	−13.4804	−	23.3487i	−0.769366	−	1.33258i	0.168540	−	0.985695i	$-0.446095\pi$
$308$	−1.93554	−	24.4520i	−0.110288	−	1.39328i
$309$	2.00510	+	3.47293i	0.114066	+	0.197568i
$310$	−23.2253			−1.31911
$311$	0.346289	−	0.599789i	0.0196362	−	0.0340109i	−0.856040	−	0.516909i	$-0.827083\pi$
$311$	0.346289	−	0.599789i	0.0196362	−	0.0340109i	0.875677	+	0.482898i	$0.160416\pi$
$312$	−8.47423	+	14.6778i	−0.479759	+	0.830966i
$313$	−20.8647			−1.17934			−0.589671	−	0.807644i	$-0.700742\pi$
$313$	−20.8647			−1.17934			−0.589671	+	0.807644i	$0.700742\pi$
$314$	−11.3606	+	19.6771i	−0.641114	+	1.11044i
$315$	13.4275	+	6.39714i	0.756555	+	0.360438i
$316$	4.58135			0.257721
$317$	−27.6716			−1.55419			−0.777095	−	0.629383i	$-0.783308\pi$
$317$	−27.6716			−1.55419			−0.777095	+	0.629383i	$0.783308\pi$
$318$	1.66144			0.0931689
$319$	1.05724	+	1.83120i	0.0591941	+	0.102527i
$320$	−25.7774	+	44.6478i	−1.44100	+	2.49589i
$321$	−7.56153	−	13.0970i	−0.422044	−	0.731001i
$322$	31.2323	+	14.8797i	1.74051	+	0.829214i
$323$	−5.41360	−	0.423513i	−0.301221	−	0.0235649i
$324$	5.11027	+	8.85125i	0.283904	+	0.491736i
$325$	−48.6232			−2.69713
$326$	−52.7832			−2.92339
$327$	−22.2135			−1.22841
$328$	7.79595	+	13.5030i	0.430459	+	0.745578i
$329$	−0.000491109	−	0.00620424i	−2.70757e−5	−	0.000342051i
$330$	33.2502			1.83036
$331$	−9.99545	−	17.3126i	−0.549399	−	0.951588i	−0.998316	−	0.0580140i	$-0.981523\pi$
$331$	−9.99545	−	17.3126i	−0.549399	−	0.951588i	0.448916	−	0.893574i	$-0.351810\pi$
$332$	−11.5840	−	20.0641i	−0.635756	−	1.10116i
$333$	1.80940	+	3.13397i	0.0991543	+	0.171740i
$334$	23.9197	+	41.4301i	1.30883	+	2.26695i
$335$	−38.5789			−2.10779
$336$	−2.19943	−	1.04785i	−0.119988	−	0.0571649i
$337$	−5.27398	−	9.13481i	−0.287292	−	0.497605i	0.685870	−	0.727724i	$-0.259422\pi$
$337$	−5.27398	−	9.13481i	−0.287292	−	0.497605i	−0.973162	+	0.230119i	$0.926088\pi$
$338$	8.98508			0.488724
$339$	23.5933			1.28141
$340$	−17.3392			−0.940351
$341$	−3.33109	−	5.76962i	−0.180389	−	0.312442i
$342$	−7.84865	+	11.4313i	−0.424407	+	0.618134i
$343$	4.34791	+	18.0027i	0.234765	+	0.972052i
$344$	−0.810640	−	1.40407i	−0.0437068	−	0.0757024i
$345$	−14.7509	+	25.5493i	−0.794163	+	1.37553i
$346$	5.89496	+	10.2104i	0.316915	+	0.548913i
$347$	20.9480			1.12455			0.562273	−	0.826952i	$-0.309927\pi$
$347$	20.9480			1.12455			0.562273	+	0.826952i	$0.309927\pi$
$348$	3.35018			0.179589
$349$	−36.5559			−1.95679			−0.978397	−	0.206737i	$-0.933716\pi$
$349$	−36.5559			−1.95679			−0.978397	+	0.206737i	$0.933716\pi$
$350$	−5.73913	−	72.5032i	−0.306770	−	3.87546i
$351$	11.4577	−	19.8453i	0.611565	−	1.05926i
$352$	−13.0906			−0.697730
$353$	1.47688	−	2.55803i	0.0786063	−	0.136150i	−0.824043	−	0.566528i	$-0.808286\pi$
$353$	1.47688	−	2.55803i	0.0786063	−	0.136150i	0.902649	+	0.430378i	$0.141620\pi$
$354$	−3.88281	+	6.72522i	−0.206369	+	0.357442i
$355$	43.3453			2.30053
$356$	12.8842	+	22.3162i	0.682863	+	1.18275i
$357$	0.332057	+	4.19492i	0.0175743	+	0.222018i
$358$	−6.97475	−	12.0806i	−0.368627	−	0.638480i
$359$	1.69428	−	2.93457i	0.0894204	−	0.154881i	−0.817846	−	0.575437i	$-0.804832\pi$
$359$	1.69428	−	2.93457i	0.0894204	−	0.154881i	0.907266	+	0.420557i	$0.138165\pi$
$360$	−9.08486	+	15.7354i	−0.478814	+	0.829330i
$361$	18.7688	+	2.95470i	0.987834	+	0.155511i
$362$	14.0097	+	24.2655i	0.736333	+	1.27537i
$363$	−2.25306	−	3.90242i	−0.118255	−	0.204824i
$364$	2.90855	+	36.7441i	0.152450	+	1.92592i
$365$	23.0037	−	39.8436i	1.20407	−	2.08551i
$366$	17.3943	−	30.1278i	0.909214	−	1.57481i
$367$	−15.3907	−	26.6575i	−0.803389	−	1.39151i	−0.917373	−	0.398028i	$-0.869695\pi$
$367$	−15.3907	−	26.6575i	−0.803389	−	1.39151i	0.113984	−	0.993483i	$-0.463639\pi$
$368$	−2.03074	+	3.51734i	−0.105860	+	0.183354i
$369$	−3.30446	−	5.72349i	−0.172023	−	0.297953i
$370$	12.5847	−	21.7973i	0.654245	−	1.13319i
$371$	1.22159	−	0.840388i	0.0634217	−	0.0436308i
$372$	−10.5556			−0.547280
$373$	10.2759	+	17.7984i	0.532065	+	0.921564i	0.999299	+	0.0374302i	$0.0119172\pi$
$373$	10.2759	+	17.7984i	0.532065	+	0.921564i	−0.467234	+	0.884134i	$0.654749\pi$
$374$	−3.95323	−	6.84719i	−0.204417	−	0.354060i
$375$	35.8263			1.85006
$376$	0.00760290			0.000392090
$377$	−1.58872	−	2.75175i	−0.0818234	−	0.141722i
$378$	30.9441	+	14.7424i	1.59159	+	0.758268i
$379$	10.4019			0.534310			0.267155	−	0.963654i	$-0.413916\pi$
$379$	10.4019			0.534310			0.267155	+	0.963654i	$0.413916\pi$
$380$	60.4849	+	4.73181i	3.10281	+	0.242737i
$381$	−1.05749	+	1.83163i	−0.0541769	+	0.0938371i
$382$	60.1322			3.07663
$383$	−9.33701	+	16.1722i	−0.477099	+	0.826359i	−0.999656	−	0.0262453i	$-0.991645\pi$
$383$	−9.33701	+	16.1722i	−0.477099	+	0.826359i	0.522557	+	0.852604i	$0.324978\pi$
$384$	−12.5086	+	21.6654i	−0.638324	+	1.10561i
$385$	24.4475	−	16.8186i	1.24596	−	0.857155i
$386$	16.1979	−	28.0556i	0.824451	−	1.42799i
$387$	0.343605	+	0.595141i	0.0174664	+	0.0302527i
$388$	5.86233	−	10.1538i	0.297615	−	0.515484i
$389$	10.5975	+	18.3555i	0.537317	+	0.930660i	0.999047	+	0.0436396i	$0.0138953\pi$
$389$	10.5975	+	18.3555i	0.537317	+	0.930660i	−0.461731	+	0.887020i	$0.652771\pi$
$390$	−49.9653			−2.53009
$391$	7.01514			0.354771
$392$	−22.3429	+	3.55949i	−1.12848	+	0.179781i
$393$	−4.15308	+	7.19335i	−0.209495	+	0.362856i
$394$	−4.08376	+	7.07328i	−0.205737	+	0.356347i
$395$	2.77121	+	4.79988i	0.139435	+	0.241508i
$396$	−12.7009			−0.638246
$397$	4.16973	−	7.22219i	0.209273	−	0.362471i	−0.742213	−	0.670164i	$-0.766224\pi$
$397$	4.16973	−	7.22219i	0.209273	−	0.362471i	0.951486	+	0.307693i	$0.0995570\pi$
$398$	5.46197			0.273784
$399$	−0.0135461	−	14.7239i	−0.000678152	−	0.737115i
$400$	8.53837			0.426919
$401$	−14.9040	+	25.8145i	−0.744270	+	1.28911i	0.206265	+	0.978496i	$0.433869\pi$
$401$	−14.9040	+	25.8145i	−0.744270	+	1.28911i	−0.950535	+	0.310618i	$0.899464\pi$
$402$	−27.8719			−1.39013
$403$	5.00565	+	8.67004i	0.249349	+	0.431886i
$404$	−1.25811	+	2.17911i	−0.0625932	+	0.108415i
$405$	−6.18230	+	10.7080i	−0.307201	+	0.532087i
$406$	3.91568	−	2.69378i	0.194332	−	0.133690i
$407$	7.21981			0.357872
$408$	−5.14060			−0.254498
$409$	13.9784	+	24.2113i	0.691188	+	1.19717i	0.971449	+	0.237249i	$0.0762456\pi$
$409$	13.9784	+	24.2113i	0.691188	+	1.19717i	−0.280261	+	0.959924i	$0.590421\pi$
$410$	−22.9831	+	39.8078i	−1.13505	+	1.96597i
$411$	−3.60301	−	6.24059i	−0.177723	−	0.307826i
$412$	−5.32701	+	9.22666i	−0.262443	+	0.454565i
$413$	0.546878	+	6.90878i	0.0269101	+	0.339959i
$414$	8.95691	−	15.5138i	0.440208	−	0.762463i
$415$	14.0141	−	24.2732i	0.687926	−	1.19152i
$416$	19.6713			0.964465
$417$	−2.09459	+	3.62793i	−0.102572	+	0.177660i
$418$	11.9216	+	24.9641i	0.583104	+	1.22103i
$419$	0.0133163			0.000650542			0.000325271	−	1.00000i	$-0.499896\pi$
$419$	0.0133163			0.000650542			0.000325271		1.00000i	$0.499896\pi$
$420$	−3.70999	−	46.8688i	−0.181029	−	2.28696i
$421$	6.48588	+	11.2339i	0.316103	+	0.547506i	0.979671	−	0.200610i	$-0.0642923\pi$
$421$	6.48588	+	11.2339i	0.316103	+	0.547506i	−0.663569	+	0.748115i	$0.730959\pi$
$422$	20.8951			1.01716
$423$	−0.00322263			−0.000156690
$424$	0.905670	+	1.56867i	0.0439832	+	0.0761812i
$425$	−7.37390	−	12.7720i	−0.357687	−	0.619532i
$426$	31.3155			1.51724
$427$	−2.44991	−	30.9501i	−0.118560	−	1.49778i
$428$	20.0890	−	34.7951i	0.971038	−	1.68189i
$429$	−7.16627	−	12.4123i	−0.345991	−	0.599274i
$430$	2.38983	−	4.13931i	0.115248	−	0.199615i
$431$	−3.23034	−	5.59510i	−0.155600	−	0.269507i	0.777677	−	0.628663i	$-0.216398\pi$
$431$	−3.23034	−	5.59510i	−0.155600	−	0.269507i	−0.933277	+	0.359157i	$0.883064\pi$
$432$	−2.01200	+	3.48488i	−0.0968024	+	0.167667i
$433$	7.41115	−	12.8365i	0.356157	−	0.616882i	−0.631158	−	0.775654i	$-0.717420\pi$
$433$	7.41115	−	12.8365i	0.356157	−	0.616882i	0.987315	+	0.158772i	$0.0507535\pi$
$434$	−12.3373	+	8.48739i	−0.592208	+	0.407408i
$435$	2.02649	+	3.50998i	0.0971628	+	0.168291i
$436$	−29.5076	−	51.1087i	−1.41316	−	2.44766i
$437$	−24.4711	−	1.91441i	−1.17061	−	0.0915785i
$438$	16.6194	−	28.7856i	0.794104	−	1.37543i
$439$	15.2513	−	26.4160i	0.727903	−	1.26077i	−0.229865	−	0.973223i	$-0.573828\pi$
$439$	15.2513	−	26.4160i	0.727903	−	1.26077i	0.957768	−	0.287543i	$-0.0928383\pi$
$440$	18.1251	+	31.3936i	0.864079	+	1.49663i
$441$	9.47044	−	1.50876i	0.450973	−	0.0718455i
$442$	5.94054	+	10.2893i	0.282563	+	0.489413i
$443$	0.862725			0.0409893			0.0204947	−	0.999790i	$-0.493476\pi$
$443$	0.862725			0.0409893			0.0204947	+	0.999790i	$0.493476\pi$
$444$	5.71953	−	9.90651i	0.271437	−	0.470142i
$445$	−15.5871	+	26.9976i	−0.738898	+	1.27981i
$446$	1.93611			0.0916776
$447$	−3.87492	+	6.71157i	−0.183278	+	0.317446i
$448$	2.62301	+	33.1369i	0.123926	+	1.56557i
$449$	−34.5578			−1.63088			−0.815441	−	0.578840i	$-0.803506\pi$
$449$	−34.5578			−1.63088			−0.815441	+	0.578840i	$0.803506\pi$
$450$	−37.6599			−1.77530
$451$	−13.1854			−0.620875
$452$	31.3406	+	54.2835i	1.47414	+	2.55328i
$453$	2.19246	−	3.79745i	0.103011	−	0.178420i
$454$	−2.00630	−	3.47501i	−0.0941601	−	0.163090i
$455$	−36.7374	+	25.2734i	−1.72228	+	1.18484i
$456$	17.9321	+	1.40285i	0.839748	+	0.0656945i
$457$	19.1330	+	33.1393i	0.895002	+	1.55019i	0.833802	+	0.552063i	$0.186159\pi$
$457$	19.1330	+	33.1393i	0.895002	+	1.55019i	0.0611997	+	0.998126i	$0.480507\pi$
$458$	−33.2842			−1.55527
$459$	6.95041			0.324417
$460$	−78.3786			−3.65442
$461$	15.8674	+	27.4831i	0.739016	+	1.28001i	0.952939	+	0.303163i	$0.0980427\pi$
$461$	15.8674	+	27.4831i	0.739016	+	1.28001i	−0.213922	+	0.976851i	$0.568624\pi$
$462$	17.6625	−	12.1509i	0.821733	−	0.565309i
$463$	16.7589			0.778854			0.389427	−	0.921057i	$-0.372673\pi$
$463$	16.7589			0.778854			0.389427	+	0.921057i	$0.372673\pi$
$464$	0.278984	+	0.483215i	0.0129515	+	0.0224327i
$465$	−6.38494	−	11.0590i	−0.296095	−	0.512851i
$466$	−17.1807	−	29.7579i	−0.795881	−	1.37851i
$467$	5.58248	+	9.66914i	0.258326	+	0.447434i	0.965794	−	0.259312i	$-0.0834957\pi$
$467$	5.58248	+	9.66914i	0.258326	+	0.447434i	−0.707467	+	0.706746i	$0.750162\pi$
$468$	19.0858			0.882240
$469$	−20.4931	+	14.0982i	−0.946282	+	0.650992i
$470$	0.0112070	+	0.0194110i	0.000516939	+	0.000895364i
$471$	−12.4927			−0.575631
$472$	−8.46626			−0.389691
$473$	1.37104			0.0630406
$474$	2.00210	+	3.46775i	0.0919597	+	0.159279i
$475$	22.2372	+	46.5652i	1.02031	+	2.13656i
$476$	−9.21057	+	6.33639i	−0.422166	+	0.290428i
$477$	−0.383885	−	0.664909i	−0.0175769	−	0.0304441i
$478$	−1.06794	+	1.84973i	−0.0488464	+	0.0846045i
$479$	3.75261	+	6.49972i	0.171461	+	0.296980i	0.938931	−	0.344106i	$-0.111818\pi$
$479$	3.75261	+	6.49972i	0.171461	+	0.296980i	−0.767470	+	0.641085i	$0.778484\pi$
$480$	−25.0916			−1.14527
$481$	−10.8493			−0.494683
$482$	−49.8403			−2.27017
$483$	1.50100	+	18.9623i	0.0682978	+	0.862815i
$484$	5.98579	−	10.3677i	0.272082	−	0.471259i
$485$	14.1842			0.644073
$486$	14.9664	−	25.9226i	0.678892	−	1.17587i
$487$	10.7276	−	18.5807i	0.486114	−	0.841974i	−0.513759	−	0.857935i	$-0.671747\pi$
$487$	10.7276	−	18.5807i	0.486114	−	0.841974i	0.999873	+	0.0159609i	$0.00508073\pi$
$488$	37.9273			1.71689
$489$	−14.5108	−	25.1334i	−0.656200	−	1.13657i
$490$	−42.0220	−	51.7969i	−1.89836	−	2.33995i
$491$	7.56085	+	13.0958i	0.341217	+	0.591004i	0.984659	−	0.174490i	$-0.0558277\pi$
$491$	7.56085	+	13.0958i	0.341217	+	0.591004i	−0.643442	+	0.765495i	$0.722494\pi$
$492$	−10.4454	+	18.0920i	−0.470917	+	0.815652i
$493$	0.481872	−	0.834628i	0.0217024	−	0.0375897i
$494$	−17.9147	−	37.5137i	−0.806019	−	1.68782i
$495$	−7.68265	−	13.3067i	−0.345310	−	0.598094i
$496$	−0.879006	−	1.52248i	−0.0394685	−	0.0683615i
$497$	23.0250	−	15.8400i	1.03281	−	0.710519i
$498$	10.1247	−	17.5365i	0.453699	−	0.785831i
$499$	9.78205	−	16.9430i	0.437905	−	0.758474i	−0.559623	−	0.828747i	$-0.689054\pi$
$499$	9.78205	−	16.9430i	0.437905	−	0.758474i	0.997528	+	0.0702739i	$0.0223873\pi$
$500$	47.5905	+	82.4291i	2.12831	+	3.68634i
$501$	−13.1516	+	22.7793i	−0.587572	+	1.01771i
$502$	3.57335	+	6.18922i	0.159486	+	0.276239i
$503$	−8.82783	+	15.2903i	−0.393614	+	0.681759i	−0.992923	−	0.118759i	$-0.962109\pi$
$503$	−8.82783	+	15.2903i	−0.393614	+	0.681759i	0.599310	+	0.800517i	$0.295442\pi$
$504$	0.924442	+	11.6786i	0.0411779	+	0.520206i
$505$	−3.04406			−0.135459
$506$	−17.8698	−	30.9514i	−0.794410	−	1.37596i
$507$	2.47011	+	4.27836i	0.109702	+	0.190009i
$508$	−5.61894			−0.249300
$509$	−23.3409			−1.03457			−0.517285	−	0.855813i	$-0.673057\pi$
$509$	−23.3409			−1.03457			−0.517285	+	0.855813i	$0.673057\pi$
$510$	−7.57744	−	13.1245i	−0.335535	−	0.581163i
$511$	−2.34077	−	29.5712i	−0.103550	−	1.30815i
$512$	−8.11658			−0.358705
$513$	−24.2453	−	1.89674i	−1.07046	−	0.0837432i
$514$	−27.6494	+	47.8902i	−1.21956	+	2.11235i
$515$	−12.8890			−0.567958
$516$	1.08614	−	1.88125i	0.0478147	−	0.0828174i
$517$	−0.00321471	+	0.00556805i	−0.000141383	+	0.000244882i
$518$	−1.28057	−	16.1776i	−0.0562649	−	0.710802i
$519$	−3.24120	+	5.61392i	−0.142273	+	0.246424i
$520$	−27.2367	−	47.1753i	−1.19441	−	2.06878i
$521$	−0.898463	+	1.55618i	−0.0393624	+	0.0681777i	−0.885035	−	0.465524i	$-0.845866\pi$
$521$	−0.898463	+	1.55618i	−0.0393624	+	0.0681777i	0.845673	+	0.533701i	$0.179199\pi$
$522$	−1.23051	−	2.13130i	−0.0538578	−	0.0932844i
$523$	−4.49941			−0.196745			−0.0983726	−	0.995150i	$-0.531364\pi$
$523$	−4.49941			−0.196745			−0.0983726	+	0.995150i	$0.531364\pi$
$524$	−22.0673			−0.964013
$525$	32.9456	−	22.6648i	1.43786	−	0.989174i
$526$	35.2333	−	61.0259i	1.53625	−	2.66086i
$527$	−1.51825	+	2.62969i	−0.0661362	+	0.114551i
$528$	1.25842	+	2.17964i	0.0547656	+	0.0948567i
$529$	8.71060			0.378722
$530$	−2.66999	+	4.62455i	−0.115977	+	0.200878i
$531$	3.58858			0.155731
$532$	33.8587	−	19.5899i	1.46796	−	0.849329i
$533$	19.8137			0.858228
$534$	−11.2611	+	19.5048i	−0.487317	+	0.844057i
$535$	48.6064			2.10144
$536$	−15.1933	−	26.3156i	−0.656251	−	1.13666i
$537$	3.83489	−	6.64223i	0.165488	−	0.286633i
$538$	−2.53478	+	4.39036i	−0.109282	+	0.189282i
$539$	6.84035	−	17.8680i	0.294635	−	0.769631i
$540$	−77.6553			−3.34175
$541$	16.4262			0.706217			0.353108	−	0.935582i	$-0.385125\pi$
$541$	16.4262			0.706217			0.353108	+	0.935582i	$0.385125\pi$
$542$	−14.7860	−	25.6101i	−0.635112	−	1.10005i
$543$	−7.70288	+	13.3418i	−0.330562	+	0.572551i
$544$	2.98323	+	5.16710i	0.127905	+	0.221538i
$545$	35.6977	−	61.8302i	1.52912	−	2.64852i
$546$	−26.5415	+	18.2592i	−1.13587	+	0.781421i
$547$	−9.02089	+	15.6246i	−0.385705	+	0.668061i	−0.991867	−	0.127280i	$-0.959375\pi$
$547$	−9.02089	+	15.6246i	−0.385705	+	0.668061i	0.606162	+	0.795342i	$0.292709\pi$
$548$	9.57223	−	16.5796i	0.408906	−	0.708245i
$549$	−16.0762			−0.686116
$550$	−37.5674	+	65.0686i	−1.60188	+	2.77453i
$551$	−1.90870	+	2.77996i	−0.0813132	+	0.118430i
$552$	−23.2371			−0.989036
$553$	3.22612	+	1.53699i	0.137188	+	0.0653593i
$554$	34.5488	+	59.8403i	1.46784	+	2.54237i
$555$	13.8387			0.587421
$556$	−11.1295			−0.471997
$557$	15.7465	+	27.2738i	0.667202	+	1.15563i	0.978683	+	0.205376i	$0.0658416\pi$
$557$	15.7465	+	27.2738i	0.667202	+	1.15563i	−0.311481	+	0.950252i	$0.600825\pi$
$558$	3.87700	+	6.71516i	0.164127	+	0.284276i
$559$	−2.06028			−0.0871404
$560$	6.45119	−	4.43808i	0.272613	−	0.187543i
$561$	2.17359	−	3.76476i	0.0917689	−	0.158948i
$562$	−22.4316	−	38.8527i	−0.946220	−	1.63890i
$563$	12.5429	−	21.7250i	0.528621	−	0.915598i	−0.470822	−	0.882228i	$-0.656043\pi$
$563$	12.5429	−	21.7250i	0.528621	−	0.915598i	0.999443	−	0.0333699i	$-0.0106240\pi$
$564$	0.00509339	+	0.00882201i	0.000214470	+	0.000371474i
$565$	−37.9152	+	65.6710i	−1.59510	+	2.76280i
$566$	−0.928509	+	1.60823i	−0.0390282	+	0.0675987i
$567$	0.629087	+	7.94734i	0.0264192	+	0.333757i
$568$	17.0704	+	29.5668i	0.716259	+	1.24060i
$569$	16.9539	+	29.3649i	0.710743	+	1.23104i	0.964579	+	0.263795i	$0.0849743\pi$
$569$	16.9539	+	29.3649i	0.710743	+	1.23104i	−0.253836	+	0.967247i	$0.581692\pi$
$570$	22.8510	+	47.8505i	0.957122	+	2.00424i
$571$	−4.44622	+	7.70108i	−0.186069	+	0.322280i	−0.943936	−	0.330128i	$-0.892908\pi$
$571$	−4.44622	+	7.70108i	−0.186069	+	0.322280i	0.757868	+	0.652408i	$0.226241\pi$
$572$	19.0389	−	32.9763i	0.796056	−	1.37881i
$573$	16.5311	+	28.6327i	0.690598	+	1.19615i
$574$	2.33867	+	29.5447i	0.0976142	+	1.23317i
$575$	−33.3323	−	57.7333i	−1.39005	−	2.40764i
$576$	17.2121			0.717170
$577$	5.26658	−	9.12198i	0.219251	−	0.379753i	−0.735328	−	0.677711i	$-0.762972\pi$
$577$	5.26658	−	9.12198i	0.219251	−	0.379753i	0.954579	+	0.297958i	$0.0963054\pi$
$578$	17.9356	−	31.0654i	0.746023	−	1.29215i
$579$	17.8120			0.740243
$580$	−5.38385	+	9.32510i	−0.223552	+	0.387204i
$581$	−1.42602	−	18.0151i	−0.0591615	−	0.747394i
$582$	10.2476			0.424778
$583$	−1.53177			−0.0634394
$584$	36.2377			1.49953
$585$	11.5448	+	19.9961i	0.477318	+	0.826739i
$586$	−17.1499	+	29.7045i	−0.708456	+	1.22708i
$587$	11.9909	+	20.7689i	0.494918	+	0.857223i	0.999983	−	0.00585866i	$-0.00186488\pi$
$587$	11.9909	+	20.7689i	0.494918	+	0.857223i	−0.505065	+	0.863081i	$0.668532\pi$
$588$	−19.0983	−	23.5409i	−0.787602	−	0.970810i
$589$	6.01380	−	8.75891i	0.247794	−	0.360905i
$590$	−12.4796	−	21.6153i	−0.513777	−	0.889887i
$591$	−4.49071			−0.184723
$592$	1.90516			0.0783015
$593$	−15.2823			−0.627571			−0.313785	−	0.949494i	$-0.601597\pi$
$593$	−15.2823			−0.627571			−0.313785	+	0.949494i	$0.601597\pi$
$594$	−17.7049	−	30.6658i	−0.726441	−	1.25823i
$595$	−12.2100	−	5.81709i	−0.500561	−	0.238478i
$596$	−20.5893			−0.843370
$597$	1.50156	+	2.60079i	0.0614549	+	0.106443i
$598$	26.8531	+	46.5109i	1.09810	+	1.90197i
$599$	−12.2653	−	21.2442i	−0.501148	−	0.868013i	−0.999999	−	0.00132562i	$-0.999578\pi$
$599$	−12.2653	−	21.2442i	−0.501148	−	0.868013i	0.498852	−	0.866687i	$-0.333755\pi$
$600$	24.4255	+	42.3061i	0.997165	+	1.72714i
$601$	3.34332			0.136377			0.0681885	−	0.997672i	$-0.478278\pi$
$601$	3.34332			0.136377			0.0681885	+	0.997672i	$0.478278\pi$
$602$	−0.243180	−	3.07213i	−0.00991128	−	0.125211i
$603$	6.43997	+	11.1544i	0.262256	+	0.454241i
$604$	11.6496			0.474014
$605$	14.4830			0.588816
$606$	−2.19923			−0.0893376
$607$	11.2313	+	19.4532i	0.455865	+	0.789582i	0.998738	−	0.0502335i	$-0.0159966\pi$
$607$	11.2313	+	19.4532i	0.455865	+	0.789582i	−0.542872	+	0.839815i	$0.682663\pi$
$608$	−8.99640	−	18.8387i	−0.364852	−	0.764009i
$609$	2.35915	+	1.12395i	0.0955975	+	0.0455446i
$610$	55.9063	+	96.8326i	2.26358	+	3.92064i
$611$	0.00483077	−	0.00836714i	0.000195432	−	0.000338498i
$612$	2.89443	+	5.01330i	0.117000	+	0.202651i
$613$	1.13031			0.0456529			0.0228264	−	0.999739i	$-0.492733\pi$
$613$	1.13031			0.0456529			0.0228264	+	0.999739i	$0.492733\pi$
$614$	62.6043			2.52650
$615$	−25.2733			−1.01912
$616$	21.1004	+	10.0527i	0.850159	+	0.405033i
$617$	−1.70395	+	2.95133i	−0.0685986	+	0.118816i	−0.898285	−	0.439414i	$-0.855186\pi$
$617$	−1.70395	+	2.95133i	−0.0685986	+	0.118816i	0.829686	+	0.558230i	$0.188519\pi$
$618$	−9.31187			−0.374578
$619$	−22.6808	+	39.2844i	−0.911620	+	1.57897i	−0.0998435	+	0.995003i	$0.531834\pi$
$619$	−22.6808	+	39.2844i	−0.911620	+	1.57897i	−0.811776	+	0.583969i	$0.801499\pi$
$620$	16.9631	−	29.3809i	0.681254	−	1.17997i
$621$	31.4180			1.26076
$622$	0.804099	+	1.39274i	0.0322414	+	0.0558438i
$623$	1.58608	+	20.0372i	0.0635451	+	0.802773i
$624$	−1.89103	−	3.27536i	−0.0757019	−	0.131119i
$625$	−27.9779	+	48.4591i	−1.11912	+	1.93837i
$626$	24.2244	−	41.9579i	0.968202	−	1.67697i
$627$	−8.60958	+	12.5396i	−0.343833	+	0.500782i
$628$	−16.5948	−	28.7431i	−0.662206	−	1.14697i
$629$	−1.64533	−	2.84980i	−0.0656037	−	0.113629i
$630$	−28.4540	+	19.5749i	−1.13364	+	0.779882i
$631$	−17.0210	+	29.4812i	−0.677595	+	1.17363i	0.298108	+	0.954532i	$0.403644\pi$
$631$	−17.0210	+	29.4812i	−0.677595	+	1.17363i	−0.975703	+	0.219097i	$0.929689\pi$
$632$	−2.18274	+	3.78062i	−0.0868248	+	0.150385i
$633$	5.74434	+	9.94949i	0.228317	+	0.395457i
$634$	32.1274	−	55.6462i	1.27594	−	2.20999i
$635$	−3.39884	−	5.88696i	−0.134879	−	0.233617i
$636$	−1.21347	+	2.10179i	−0.0481171	+	0.0833412i
$637$	−10.2790	+	26.8504i	−0.407271	+	1.06385i
$638$	−4.90993			−0.194386
$639$	−7.23562	−	12.5325i	−0.286237	−	0.495776i
$640$	−40.2033	−	69.6341i	−1.58917	−	2.75253i
$641$	−4.64100			−0.183309			−0.0916543	−	0.995791i	$-0.529215\pi$
$641$	−4.64100			−0.183309			−0.0916543	+	0.995791i	$0.529215\pi$
$642$	35.1165			1.38594
$643$	−21.7272	−	37.6326i	−0.856836	−	1.48408i	−0.874931	−	0.484248i	$-0.839093\pi$
$643$	−21.7272	−	37.6326i	−0.856836	−	1.48408i	0.0180946	−	0.999836i	$-0.494240\pi$
$644$	−41.6346	+	28.6424i	−1.64063	+	1.12867i
$645$	2.62798			0.103477
$646$	7.13699	−	10.3948i	0.280801	−	0.408977i
$647$	−13.7260	+	23.7742i	−0.539626	+	0.934660i	0.459298	+	0.888282i	$0.348101\pi$
$647$	−13.7260	+	23.7742i	−0.539626	+	0.934660i	−0.998924	+	0.0463776i	$0.985232\pi$
$648$	−9.73896			−0.382582
$649$	3.57977	−	6.20034i	0.140518	−	0.243385i
$650$	56.4528	−	97.7791i	2.21426	−	3.83521i
$651$	−7.43305	−	3.54126i	−0.291324	−	0.138793i
$652$	38.5513	−	66.7728i	1.50978	−	2.61502i
$653$	4.70438	+	8.14823i	0.184097	+	0.318865i	0.943272	−	0.332022i	$-0.107731\pi$
$653$	4.70438	+	8.14823i	0.184097	+	0.318865i	−0.759175	+	0.650887i	$0.774397\pi$
$654$	25.7904	−	44.6702i	1.00848	−	1.74674i
$655$	−13.3483	−	23.1199i	−0.521559	−	0.903368i
$656$	−3.47935			−0.135846
$657$	−15.3600			−0.599251
$658$	0.0130466	+	0.00621568i	0.000508611	+	0.000242312i
$659$	0.938918	−	1.62625i	0.0365751	−	0.0633499i	−0.847158	−	0.531340i	$-0.821689\pi$
$659$	0.938918	−	1.62625i	0.0365751	−	0.0633499i	0.883733	+	0.467991i	$0.155022\pi$
$660$	−24.2850	+	42.0628i	−0.945291	+	1.63729i
$661$	−7.71974	−	13.3710i	−0.300263	−	0.520071i	0.675932	−	0.736964i	$-0.263741\pi$
$661$	−7.71974	−	13.3710i	−0.300263	−	0.520071i	−0.976195	+	0.216893i	$0.930408\pi$
$662$	46.4198			1.80416
$663$	−3.26626	+	5.65733i	−0.126851	+	0.219713i
$664$	22.0764			0.856731
$665$	41.0051	+	23.6240i	1.59011	+	0.916100i
$666$	−8.40302			−0.325610
$667$	2.17821	−	3.77277i	0.0843407	−	0.146082i
$668$	−69.8809			−2.70377
$669$	0.532262	+	0.921905i	0.0205784	+	0.0356429i
$670$	44.7910	−	77.5804i	1.73043	−	2.99719i
$671$	−16.0367	+	27.7764i	−0.619090	+	1.07230i
$672$	−13.3287	+	9.16941i	−0.514164	+	0.353718i
$673$	−39.6783			−1.52949			−0.764744	−	0.644334i	$-0.777134\pi$
$673$	−39.6783			−1.52949			−0.764744	+	0.644334i	$0.777134\pi$
$674$	24.4929			0.943431
$675$	−33.0247	−	57.2005i	−1.27112	−	2.20165i
$676$	−6.56244	+	11.3665i	−0.252402	+	0.437172i
$677$	−14.3418	−	24.8407i	−0.551199	−	0.954705i	−0.998188	−	0.0601657i	$-0.980837\pi$
$677$	−14.3418	−	24.8407i	−0.551199	−	0.954705i	0.446989	−	0.894539i	$-0.352496\pi$
$678$	−27.3924	+	47.4451i	−1.05200	+	1.82212i
$679$	7.53465	−	5.18344i	0.289153	−	0.198922i
$680$	8.26110	−	14.3086i	0.316799	−	0.548712i
$681$	1.10311	−	1.91065i	0.0422714	−	0.0732162i
$682$	15.4699			0.592373
$683$	15.6283	−	27.0689i	0.597999	−	1.03576i	−0.395118	−	0.918631i	$-0.629296\pi$
$683$	15.6283	−	27.0689i	0.597999	−	1.03576i	0.993116	−	0.117133i	$-0.0373705\pi$
$684$	−8.72862	−	18.2779i	−0.333747	−	0.698875i
$685$	23.1606			0.884920
$686$	−41.2505	−	12.1581i	−1.57495	−	0.464198i
$687$	−9.15026	−	15.8487i	−0.349104	−	0.604666i
$688$	0.361790			0.0137931
$689$	2.30180			0.0876916
$690$	−34.2524	−	59.3268i	−1.30396	−	2.25853i
$691$	6.22071	+	10.7746i	0.236647	+	0.409884i	0.959750	−	0.280856i	$-0.0906182\pi$
$691$	6.22071	+	10.7746i	0.236647	+	0.409884i	−0.723103	+	0.690740i	$0.757285\pi$
$692$	−17.2220			−0.654683
$693$	−8.94379	−	4.26100i	−0.339747	−	0.161862i
$694$	−24.3211	+	42.1254i	−0.923217	+	1.59906i
$695$	−6.73213	−	11.6604i	−0.255364	−	0.442304i
$696$	−1.59616	+	2.76464i	−0.0605024	+	0.104793i
$697$	3.00483	+	5.20452i	0.113816	+	0.197135i
$698$	42.4423	−	73.5122i	1.60647	−	2.78248i
$699$	9.44640	−	16.3616i	0.357295	−	0.618854i
$700$	95.9111	+	45.6940i	3.62510	+	1.72707i
$701$	−6.21021	−	10.7564i	−0.234556	−	0.406264i	0.724587	−	0.689183i	$-0.242030\pi$
$701$	−6.21021	−	10.7564i	−0.234556	−	0.406264i	−0.959144	+	0.282919i	$0.908697\pi$
$702$	26.6053	+	46.0817i	1.00415	+	1.73924i
$703$	4.96176	+	10.3900i	0.187136	+	0.391868i
$704$	17.1698	−	29.7390i	0.647111	−	1.12083i
$705$	−0.00616187	+	0.0106727i	−0.000232070	+	0.000401956i
$706$	3.42938	+	5.93987i	0.129067	+	0.223550i
$707$	−1.61700	+	1.11241i	−0.0608136	+	0.0418366i
$708$	−5.67178	−	9.82381i	−0.213159	−	0.369201i
$709$	5.04388			0.189427			0.0947134	−	0.995505i	$-0.469807\pi$
$709$	5.04388			0.189427			0.0947134	+	0.995505i	$0.469807\pi$
$710$	−50.3249	+	87.1653i	−1.88866	+	3.27126i
$711$	0.925196	−	1.60249i	0.0346975	−	0.0600979i
$712$	−24.5543			−0.920211
$713$	−6.86297	+	11.8870i	−0.257020	+	0.445172i
$714$	−8.82131	−	4.20265i	−0.330129	−	0.157280i
$715$	46.0657			1.72276
$716$	20.3766			0.761509
$717$	−1.17436			−0.0438573
$718$	3.93419	+	6.81422i	0.146823	+	0.254304i
$719$	−6.33536	+	10.9732i	−0.236269	+	0.409230i	−0.959641	−	0.281229i	$-0.909258\pi$
$719$	−6.33536	+	10.9732i	−0.236269	+	0.409230i	0.723372	+	0.690459i	$0.242591\pi$
$720$	−2.02729	−	3.51138i	−0.0755528	−	0.130861i
$721$	−6.84663	+	4.71012i	−0.254982	+	0.175414i
$722$	−27.7329	+	34.3128i	−1.03211	+	1.27699i
$723$	−13.7017	−	23.7321i	−0.509573	−	0.882607i
$724$	−40.9290			−1.52112
$725$	−9.15843			−0.340136
$726$	10.4634			0.388335
$727$	7.19598	+	12.4638i	0.266884	+	0.462257i	0.968056	−	0.250736i	$-0.0806726\pi$
$727$	7.19598	+	12.4638i	0.266884	+	0.462257i	−0.701171	+	0.712993i	$0.747339\pi$
$728$	−31.7077	−	15.1062i	−1.17517	−	0.559873i
$729$	25.4975			0.944352
$730$	53.4157	+	92.5187i	1.97700	+	3.42427i
$731$	−0.312449	−	0.541178i	−0.0115563	−	0.0200162i
$732$	25.4086	+	44.0089i	0.939127	+	1.62662i
$733$	−12.8916	−	22.3288i	−0.476160	−	0.824734i	0.523467	−	0.852046i	$-0.324639\pi$
$733$	−12.8916	−	22.3288i	−0.476160	−	0.824734i	−0.999627	+	0.0273122i	$0.991305\pi$
$734$	71.4760			2.63823
$735$	13.1114	−	34.2489i	0.483621	−	1.26329i
$736$	13.4851	+	23.3569i	0.497068	+	0.860947i
$737$	25.6966			0.946546
$738$	15.3462			0.564903
$739$	−4.27879			−0.157398			−0.0786989	−	0.996898i	$-0.525077\pi$
$739$	−4.27879			−0.157398			−0.0786989	+	0.996898i	$0.525077\pi$
$740$	18.3829	+	31.8401i	0.675769	+	1.17047i
$741$	12.9377	−	18.8433i	0.475277	−	0.692226i
$742$	0.271688	+	3.43227i	0.00997397	+	0.126002i
$743$	−2.88947	−	5.00471i	−0.106004	−	0.183605i	0.808144	−	0.588985i	$-0.200472\pi$
$743$	−2.88947	−	5.00471i	−0.106004	−	0.183605i	−0.914148	+	0.405380i	$0.867139\pi$
$744$	5.02909	−	8.71064i	0.184375	−	0.319348i
$745$	−12.4542	−	21.5714i	−0.456288	−	0.790314i
$746$	−47.7222			−1.74723
$747$	−9.35750			−0.342373
$748$	11.5493			0.422284
$749$	25.8197	−	17.7626i	0.943431	−	0.649031i
$750$	−41.5952	+	72.0450i	−1.51884	+	2.63071i
$751$	−7.72901			−0.282036			−0.141018	−	0.990007i	$-0.545037\pi$
$751$	−7.72901			−0.282036			−0.141018	+	0.990007i	$0.545037\pi$
$752$	−0.000848297		0.00146929i	−3.09342e−5		5.35796e-5i
$753$	−1.96472	+	3.40299i	−0.0715983	+	0.124012i
$754$	7.37819			0.268698
$755$	7.04670	+	12.2052i	0.256456	+	0.444194i
$756$	−41.2504	+	28.3781i	−1.50026	+	1.03210i
$757$	−14.7409	−	25.5319i	−0.535766	−	0.927974i	−0.999126	−	0.0418040i	$-0.986690\pi$
$757$	−14.7409	−	25.5319i	−0.535766	−	0.927974i	0.463360	−	0.886170i	$-0.346644\pi$
$758$	−12.0769	+	20.9178i	−0.438652	+	0.759767i
$759$	9.82528	−	17.0179i	0.356635	−	0.617710i
$760$	−32.7222	+	47.6589i	−1.18696	+	1.72877i
$761$	−13.7486	−	23.8133i	−0.498386	−	0.863231i	0.501612	−	0.865093i	$-0.332741\pi$
$761$	−13.7486	−	23.8133i	−0.498386	−	0.863231i	−0.999998	+	0.00186216i	$0.999407\pi$
$762$	−2.45554	−	4.25313i	−0.0889550	−	0.154075i
$763$	−3.63247	−	45.8894i	−0.131504	−	1.66131i
$764$	−43.9188	+	76.0696i	−1.58893	+	2.75210i
$765$	−3.50162	+	6.06499i	−0.126601	+	0.219280i
$766$	−21.6810	−	37.5526i	−0.783366	−	1.35683i
$767$	−5.37934	+	9.31729i	−0.194237	+	0.336428i
$768$	−13.0051	−	22.5254i	−0.469280	−	0.812817i
$769$	−11.2332	+	19.4565i	−0.405080	+	0.701620i	−0.994331	−	0.106331i	$-0.966090\pi$
$769$	−11.2332	+	19.4565i	−0.405080	+	0.701620i	0.589250	+	0.807950i	$0.299423\pi$
$770$	5.43726	+	68.6896i	0.195945	+	2.47540i
$771$	−30.4047			−1.09500
$772$	23.6609	+	40.9819i	0.851575	+	1.47497i
$773$	5.32926	+	9.23055i	0.191680	+	0.332000i	0.945807	−	0.324729i	$-0.105273\pi$
$773$	5.32926	+	9.23055i	0.191680	+	0.332000i	−0.754127	+	0.656729i	$0.771940\pi$
$774$	−1.59574			−0.0573575
$775$	28.8558			1.03653
$776$	5.58610	+	9.67541i	0.200529	+	0.347327i
$777$	7.35112	−	5.05718i	0.263720	−	0.181425i
$778$	−49.2160			−1.76448
$779$	−9.06155	−	18.9751i	−0.324664	−	0.679853i
$780$	36.4932	−	63.2081i	1.30667	−	2.26321i
$781$	−28.8714			−1.03310
$782$	−8.14475	+	14.1071i	−0.291256	+	0.504470i
$783$	2.15811	−	3.73796i	0.0771246	−	0.133584i
$784$	1.80503	−	4.71501i	0.0644653	−	0.168393i
$785$	20.0761	−	34.7728i	0.716546	−	1.24109i
$786$	−9.64366	−	16.7033i	−0.343978	−	0.595787i
$787$	12.7835	−	22.1417i	0.455683	−	0.789266i	−0.543044	−	0.839704i	$-0.682728\pi$
$787$	12.7835	−	22.1417i	0.455683	−	0.789266i	0.998727	+	0.0504383i	$0.0160618\pi$
$788$	−5.96532	−	10.3322i	−0.212506	−	0.368071i
$789$	38.7444			1.37934
$790$	−12.8698			−0.457886
$791$	3.85811	+	48.7400i	0.137179	+	1.73299i
$792$	6.05124	−	10.4810i	0.215021	−	0.372428i
$793$	24.0985	−	41.7398i	0.855762	−	1.48222i
$794$	9.68232	+	16.7703i	0.343613	+	0.595155i
$795$	−2.93605			−0.104131
$796$	−3.98926	+	6.90960i	−0.141395	+	0.244904i
$797$	−34.8093			−1.23301			−0.616505	−	0.787351i	$-0.711452\pi$
$797$	−34.8093			−1.23301			−0.616505	+	0.787351i	$0.711452\pi$
$798$	29.6247	+	17.0675i	1.04870	+	0.604184i
$799$	0.00293042			0.000103671
$800$	28.3495	−	49.1028i	1.00231	−	1.73605i
$801$	10.4078			0.367741
$802$	−34.6078	−	59.9425i	−1.22204	−	2.11664i
$803$	−15.3223	+	26.5390i	−0.540711	+	0.936539i
$804$	20.3568	−	35.2591i	0.717930	−	1.24349i
$805$	−55.1930	−	26.2950i	−1.94530	−	0.926778i
$806$	−23.2467			−0.818832
$807$	−2.78737			−0.0981201
$808$	−1.19883	−	2.07643i	−0.0421746	−	0.0730485i
$809$	10.3393	−	17.9082i	0.363510	−	0.629617i	−0.625026	−	0.780604i	$-0.714912\pi$
$809$	10.3393	−	17.9082i	0.363510	−	0.629617i	0.988536	+	0.150987i	$0.0482450\pi$
$810$	−14.3556	−	24.8646i	−0.504404	−	0.873654i
$811$	−17.3069	+	29.9765i	−0.607729	+	1.05262i	0.383885	+	0.923381i	$0.374586\pi$
$811$	−17.3069	+	29.9765i	−0.607729	+	1.05262i	−0.991614	+	0.129237i	$0.958747\pi$
$812$	0.547841	+	6.92094i	0.0192254	+	0.242877i
$813$	8.12970	−	14.0811i	0.285121	−	0.493844i
$814$	−8.38237	+	14.5187i	−0.293802	+	0.508880i
$815$	93.2770			3.26735
$816$	0.573565	−	0.993443i	0.0200788	−	0.0347775i
$817$	0.942240	+	1.97307i	0.0329648	+	0.0690291i
$818$	−64.9171			−2.26977
$819$	13.4399	+	6.40304i	0.469628	+	0.223740i
$820$	−33.5723	−	58.1489i	−1.17240	−	2.03065i
$821$	−2.07772			−0.0725131			−0.0362565	−	0.999343i	$-0.511543\pi$
$821$	−2.07772			−0.0725131			−0.0362565	+	0.999343i	$0.511543\pi$
$822$	16.7327			0.583620
$823$	14.4407	+	25.0120i	0.503370	+	0.871862i	0.999992	+	0.00389542i	$0.00123995\pi$
$823$	14.4407	+	25.0120i	0.503370	+	0.871862i	−0.496623	+	0.867967i	$0.665427\pi$
$824$	−5.07601	−	8.79191i	−0.176831	−	0.306281i
$825$	−41.3110			−1.43826
$826$	−14.5282	−	6.92151i	−0.505500	−	0.240830i
$827$	15.7368	−	27.2569i	0.547222	−	0.947816i	−0.451241	−	0.892402i	$-0.649019\pi$
$827$	15.7368	−	27.2569i	0.547222	−	0.947816i	0.998463	−	0.0554145i	$-0.0176480\pi$
$828$	13.0837	+	22.6617i	0.454691	+	0.787548i
$829$	−19.6132	+	33.9711i	−0.681195	+	1.17986i	0.293422	+	0.955983i	$0.405206\pi$
$829$	−19.6132	+	33.9711i	−0.681195	+	1.17986i	−0.974617	+	0.223881i	$0.928127\pi$
$830$	32.5415	+	56.3635i	1.12953	+	1.95640i
$831$	−18.9958	+	32.9017i	−0.658958	+	1.14135i
$832$	−25.8012	+	44.6890i	−0.894495	+	1.54931i
$833$	−8.61172	+	1.37195i	−0.298378	+	0.0475353i
$834$	−4.86373	−	8.42423i	−0.168417	−	0.291707i
$835$	−42.2702	−	73.2141i	−1.46282	−	2.53368i
$836$	−40.2877	−	3.15176i	−1.39338	−	0.109006i
$837$	−6.79964	+	11.7773i	−0.235030	+	0.407084i
$838$	−0.0154605	+	0.0267784i	−0.000534074	+	0.000925044i
$839$	13.7322	+	23.7849i	0.474088	+	0.821144i	0.999560	−	0.0296665i	$-0.00944452\pi$
$839$	13.7322	+	23.7849i	0.474088	+	0.821144i	−0.525472	+	0.850811i	$0.676111\pi$
$840$	40.4446	+	19.2686i	1.39547	+	0.664831i
$841$	14.2008	+	24.5964i	0.489681	+	0.848153i
$842$	−30.1211			−1.03804
$843$	12.3335	−	21.3622i	0.424787	−	0.735753i
$844$	−15.2612	+	26.4332i	−0.525312	+	0.909867i
$845$	−15.8782			−0.546227
$846$	0.00374155	−	0.00648056i	0.000128637	−	0.000222806i
$847$	7.69334	−	5.29261i	0.264346	−	0.181856i
$848$	−0.404202			−0.0138804
$849$	−1.02104			−0.0350419
$850$	34.2451			1.17460
$851$	−7.43741	−	12.8820i	−0.254951	−	0.441588i
$852$	−22.8719	+	39.6153i	−0.783578	+	1.35720i
$853$	−13.1850	−	22.8371i	−0.451445	−	0.781926i	0.547031	−	0.837112i	$-0.315758\pi$
$853$	−13.1850	−	22.8371i	−0.451445	−	0.781926i	−0.998476	+	0.0551863i	$0.982425\pi$
$854$	65.0836	+	31.0071i	2.22711	+	1.06104i
$855$	13.8699	−	20.2011i	0.474342	−	0.690863i
$856$	19.1424	+	33.1556i	0.654274	+	1.13324i
$857$	33.9340			1.15916			0.579582	−	0.814914i	$-0.303216\pi$
$857$	33.9340			1.15916			0.579582	+	0.814914i	$0.303216\pi$
$858$	33.2809			1.13619
$859$	25.8010			0.880319			0.440160	−	0.897920i	$-0.354922\pi$
$859$	25.8010			0.880319			0.440160	+	0.897920i	$0.354922\pi$
$860$	3.49092	+	6.04645i	0.119039	+	0.206182i
$861$	−13.4252	+	9.23581i	−0.457529	+	0.314756i
$862$	15.0020			0.510970
$863$	5.07089	+	8.78303i	0.172615	+	0.298978i	0.939333	−	0.343006i	$-0.111445\pi$
$863$	5.07089	+	8.78303i	0.172615	+	0.298978i	−0.766718	+	0.641984i	$0.778112\pi$
$864$	13.3607	+	23.1414i	0.454539	+	0.787285i
$865$	−10.4174	−	18.0435i	−0.354203	−	0.613497i
$866$	17.2090	+	29.8069i	0.584787	+	1.01288i
$867$	19.7229			0.669825
$868$	−1.72610	−	21.8061i	−0.0585877	−	0.740146i
$869$	−1.84585	−	3.19710i	−0.0626160	−	0.108454i
$870$	−9.41122			−0.319070
$871$	−38.6145			−1.30840
$872$	56.2345			1.90434
$873$	−2.36777	−	4.10110i	−0.0801370	−	0.138801i
$874$	32.2614	−	46.9876i	1.09126	−	1.58938i
$875$	5.85851	+	74.0113i	0.198054	+	2.50204i
$876$	24.2766	+	42.0483i	0.820230	+	1.42068i
$877$	−3.29069	+	5.69964i	−0.111119	+	0.192463i	−0.916222	−	0.400672i	$-0.868777\pi$
$877$	−3.29069	+	5.69964i	−0.111119	+	0.192463i	0.805103	+	0.593135i	$0.202110\pi$
$878$	35.4142	+	61.3392i	1.19517	+	2.07010i
$879$	−18.8589			−0.636095
$880$	−8.08926			−0.272689
$881$	49.1651			1.65641			0.828207	−	0.560422i	$-0.189361\pi$
$881$	49.1651			1.65641			0.828207	+	0.560422i	$0.189361\pi$
$882$	−7.96137	+	20.7963i	−0.268073	+	0.700248i
$883$	7.69059	−	13.3205i	0.258809	−	0.448270i	−0.707114	−	0.707099i	$-0.750003\pi$
$883$	7.69059	−	13.3205i	0.258809	−	0.448270i	0.965923	+	0.258829i	$0.0833367\pi$
$884$	−17.3552			−0.583718
$885$	6.86160	−	11.8846i	0.230650	−	0.399498i
$886$	−1.00165	+	1.73490i	−0.0336509	+	0.0582851i
$887$	−55.0027			−1.84681			−0.923404	−	0.383829i	$-0.874605\pi$
$887$	−55.0027			−1.84681			−0.923404	+	0.383829i	$0.874605\pi$
$888$	5.45003	+	9.43973i	0.182891	+	0.316777i
$889$	−3.95677	−	1.88509i	−0.132706	−	0.0632238i
$890$	−36.1940	−	62.6898i	−1.21322	−	2.10137i
$891$	4.11790	−	7.13241i	0.137955	−	0.238945i
$892$	−1.41408	+	2.44926i	−0.0473469	+	0.0820072i
$893$	−0.0102223		0.000799702i	−0.000342076		2.67610e-5i
$894$	−8.99776	−	15.5846i	−0.300930	−	0.521226i
$895$	12.3256	+	21.3485i	0.411999	+	0.713603i
$896$	−46.8028	−	22.2978i	−1.56357	−	0.744917i
$897$	−14.7645	+	25.5729i	−0.492973	+	0.853854i
$898$	40.1224	−	69.4941i	1.33890	−	2.31905i
$899$	0.942840	+	1.63305i	0.0314455	+	0.0544651i
$900$	27.5057	−	47.6412i	0.916856	−	1.58804i
$901$	0.349077	+	0.604619i	0.0116294	+	0.0201428i
$902$	15.3085	−	26.5152i	0.509718	−	0.882858i
$903$	1.39598	−	0.960360i	0.0464553	−	0.0319588i
$904$	−59.7277			−1.98651
$905$	−24.7575	−	42.8813i	−0.822968	−	1.42542i
$906$	5.09100	+	8.81787i	0.169137	+	0.292954i
$907$	−17.8601			−0.593036			−0.296518	−	0.955027i	$-0.595825\pi$
$907$	−17.8601			−0.593036			−0.296518	+	0.955027i	$0.595825\pi$
$908$	5.86136			0.194516
$909$	0.508145	+	0.880133i	0.0168541	+	0.0291922i
$910$	−8.17061	−	103.220i	−0.270853	−	3.42172i
$911$	−27.0225			−0.895296			−0.447648	−	0.894210i	$-0.647738\pi$
$911$	−27.0225			−0.895296			−0.447648	+	0.894210i	$0.647738\pi$
$912$	−2.27189	+	3.30894i	−0.0752298	+	0.109570i
$913$	−9.33451	+	16.1678i	−0.308927	+	0.535078i
$914$	−88.8553			−2.93907
$915$	−30.7387	+	53.2410i	−1.01619	+	1.76009i
$916$	24.3098	−	42.1058i	0.803219	−	1.39122i
$917$	−15.5394	−	7.40330i	−0.513157	−	0.244478i
$918$	−8.06959	+	13.9769i	−0.266336	+	0.461308i
$919$	−5.44332	−	9.42811i	−0.179559	−	0.311005i	0.762171	−	0.647376i	$-0.224134\pi$
$919$	−5.44332	−	9.42811i	−0.179559	−	0.311005i	−0.941729	+	0.336371i	$0.890800\pi$
$920$	37.3427	−	64.6795i	1.23115	−	2.13242i
$921$	17.2107	+	29.8098i	0.567112	+	0.982267i
$922$	−73.6896			−2.42684
$923$	43.3852			1.42804
$924$	2.47115	+	31.2183i	0.0812948	+	1.02701i
$925$	−15.6355	+	27.0815i	−0.514093	+	0.890435i
$926$	−19.4575	+	33.7015i	−0.639415	+	1.10750i
$927$	2.15156	+	3.72661i	0.0706666	+	0.122398i
$928$	3.70519			0.121629
$929$	−4.61764	+	7.99798i	−0.151500	+	0.262405i	−0.931779	−	0.363026i	$-0.881744\pi$
$929$	−4.61764	+	7.99798i	−0.151500	+	0.262405i	0.780279	+	0.625431i	$0.215077\pi$
$930$	29.6523			0.972337
$931$	30.4149	−	2.43571i	0.996809	−	0.0798272i
$932$	50.1931			1.64413
$933$	−0.442114	+	0.765764i	−0.0144742	+	0.0250700i
$934$	−25.9256			−0.848311
$935$	6.98604	+	12.1002i	0.228468	+	0.395718i
$936$	−9.09323	+	15.7499i	−0.297222	+	0.514803i
$937$	23.2852	−	40.3311i	0.760694	−	1.31756i	−0.181799	−	0.983336i	$-0.558192\pi$
$937$	23.2852	−	40.3311i	0.760694	−	1.31756i	0.942493	−	0.334225i	$-0.108475\pi$
$938$	−4.55777	−	57.5789i	−0.148817	−	1.88002i
$939$	26.6384			0.869311
$940$	−0.0327409			−0.00106789
$941$	−13.8905	−	24.0591i	−0.452819	−	0.784305i	0.545741	−	0.837954i	$-0.316248\pi$
$941$	−13.8905	−	24.0591i	−0.452819	−	0.784305i	−0.998560	+	0.0536485i	$0.982915\pi$
$942$	14.5043	−	25.1221i	0.472575	−	0.818524i
$943$	13.5828	+	23.5260i	0.442316	+	0.766113i
$944$	0.944627	−	1.63614i	0.0307450	−	0.0532519i
$945$	−54.6836	−	26.0524i	−1.77886	−	0.847484i
$946$	−1.59182	+	2.75710i	−0.0517544	+	0.0896412i
$947$	−24.8062	+	42.9656i	−0.806093	+	1.39619i	0.109458	+	0.993991i	$0.465088\pi$
$947$	−24.8062	+	42.9656i	−0.806093	+	1.39619i	−0.915551	+	0.402202i	$0.868245\pi$
$948$	−5.84911			−0.189970
$949$	23.0249	−	39.8803i	0.747420	−	1.29457i
$950$	−119.458	−	9.34538i	−3.87574	−	0.303204i
$951$	35.3289			1.14562
$952$	−0.840619	−	10.6196i	−0.0272446	−	0.344185i
$953$	10.7175	+	18.5633i	0.347175	+	0.601324i	0.985746	−	0.168238i	$-0.0538078\pi$
$953$	10.7175	+	18.5633i	0.347175	+	0.601324i	−0.638572	+	0.769562i	$0.720474\pi$
$954$	1.78280			0.0577203
$955$	−106.264			−3.43862
$956$	−1.55998	−	2.70197i	−0.0504534	−	0.0873879i
$957$	−1.34980	−	2.33793i	−0.0436329	−	0.0755745i
$958$	−17.4275			−0.563057
$959$	12.3029	−	8.46372i	0.397280	−	0.273308i
$960$	32.9106	−	57.0028i	1.06218	−	1.83976i
$961$	12.5294	+	21.7015i	0.404173	+	0.700048i
$962$	12.5963	−	21.8173i	0.406119	−	0.703419i
$963$	−8.11387	−	14.0536i	−0.261466	−	0.452872i
$964$	36.4019	−	63.0500i	1.17243	−	2.03070i
$965$	−28.6245	+	49.5790i	−0.921454	+	1.59601i
$966$	−39.8750	−	18.9973i	−1.28296	−	0.611227i
$967$	21.1757	+	36.6774i	0.680965	+	1.17947i	0.974687	+	0.223575i	$0.0717728\pi$
$967$	21.1757	+	36.6774i	0.680965	+	1.17947i	−0.293721	+	0.955891i	$0.594894\pi$
$968$	5.70375	+	9.87918i	0.183325	+	0.317529i
$969$	6.91166	+	0.540708i	0.222035	+	0.0173700i
$970$	−16.4682	+	28.5238i	−0.528764	+	0.915845i
$971$	6.82503	−	11.8213i	0.219026	−	0.379364i	−0.735485	−	0.677541i	$-0.763045\pi$
$971$	6.82503	−	11.8213i	0.219026	−	0.379364i	0.954510	+	0.298178i	$0.0963788\pi$
$972$	21.8621	+	37.8663i	0.701227	+	1.21456i
$973$	−7.83723	−	3.73382i	−0.251250	−	0.119701i
$974$	24.9100	+	43.1454i	0.798168	+	1.38247i
$975$	62.0783			1.98810
$976$	−4.23176	+	7.32962i	−0.135455	+	0.234615i
$977$	−21.1687	+	36.6653i	−0.677246	+	1.17303i	0.298560	+	0.954391i	$0.403494\pi$
$977$	−21.1687	+	36.6653i	−0.677246	+	1.17303i	−0.975807	+	0.218635i	$0.929840\pi$
$978$	67.3894			2.15488
$979$	10.3822	−	17.9825i	0.331817	−	0.574724i
$980$	96.2167	−	15.3285i	3.07353	−	0.489651i
$981$	−23.8361			−0.761027
$982$	−35.1133			−1.12051
$983$	−3.00613			−0.0958806			−0.0479403	−	0.998850i	$-0.515266\pi$
$983$	−3.00613			−0.0958806			−0.0479403	+	0.998850i	$0.515266\pi$
$984$	−9.95326	−	17.2396i	−0.317298	−	0.549577i
$985$	7.21671	−	12.4997i	0.229944	−	0.398274i
$986$	1.11893	+	1.93805i	0.0356340	+	0.0617200i
$987$	0.000627010		0.00792109i	1.99579e−5		0.000252131i
$988$	60.5407	+	4.73617i	1.92605	+	0.150678i
$989$	−1.41237	−	2.44629i	−0.0449106	−	0.0777875i
$990$	35.6790			1.13395
$991$	49.5570			1.57423			0.787115	−	0.616806i	$-0.211574\pi$
$991$	49.5570			1.57423			0.787115	+	0.616806i	$0.211574\pi$
$992$	−11.6741			−0.370652
$993$	12.7614	+	22.1034i	0.404971	+	0.701430i
$994$	5.12088	+	64.6927i	0.162424	+	2.05193i
$995$	−9.65224			−0.305996
$996$	14.7896	+	25.6163i	0.468626	+	0.811684i
$997$	−2.88409	−	4.99539i	−0.0913400	−	0.158206i	0.816735	−	0.577013i	$-0.195782\pi$
$997$	−2.88409	−	4.99539i	−0.0913400	−	0.158206i	−0.908075	+	0.418807i	$0.862448\pi$
$998$	22.7144	+	39.3425i	0.719012	+	1.24537i
$999$	−7.36877	−	12.7631i	−0.233138	−	0.403806i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	133.2.g.a.102.1	yes	24
7.2	even	3		133.2.h.a.121.12	yes	24
7.3	odd	6		931.2.e.e.197.1		24
7.4	even	3		931.2.e.f.197.1		24
7.5	odd	6		931.2.h.h.520.12		24
7.6	odd	2		931.2.g.h.900.1		24
19.11	even	3		133.2.h.a.11.12	yes	24
133.11	even	3		931.2.e.f.638.1		24
133.30	even	3	inner	133.2.g.a.30.1	✓	24
133.68	odd	6		931.2.g.h.30.1		24
133.87	odd	6		931.2.e.e.638.1		24
133.125	odd	6		931.2.h.h.410.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.g.a.30.1	✓	24	133.30	even	3	inner
133.2.g.a.102.1	yes	24	1.1	even	1	trivial
133.2.h.a.11.12	yes	24	19.11	even	3
133.2.h.a.121.12	yes	24	7.2	even	3
931.2.e.e.197.1		24	7.3	odd	6
931.2.e.e.638.1		24	133.87	odd	6
931.2.e.f.197.1		24	7.4	even	3
931.2.e.f.638.1		24	133.11	even	3
931.2.g.h.30.1		24	133.68	odd	6
931.2.g.h.900.1		24	7.6	odd	2
931.2.h.h.410.12		24	133.125	odd	6
931.2.h.h.520.12		24	7.5	odd	6

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:	\( N \)	\(=\)	\( 133 = 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	133.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16102 + 2.01095i) q^{2} -1.27672 q^{3} +(-1.69596 - 2.93748i) q^{4} +(2.05173 - 3.55370i) q^{5} +(1.48231 - 2.56743i) q^{6} +(-0.208777 - 2.63750i) q^{7} +3.23209 q^{8} -1.36998 q^{9} +(4.76422 + 8.25187i) q^{10} +(-1.36662 + 2.36705i) q^{11} +(2.16526 + 3.75035i) q^{12} +(2.05362 - 3.55698i) q^{13} +(5.54629 + 2.64236i) q^{14} +(-2.61949 + 4.53709i) q^{15} +(-0.360622 + 0.624615i) q^{16} +1.24576 q^{17} +(1.59058 - 2.75497i) q^{18} +(-4.34562 - 0.339963i) q^{19} -13.9186 q^{20} +(0.266550 + 3.36736i) q^{21} +(-3.17335 - 5.49640i) q^{22} +5.63122 q^{23} -4.12648 q^{24} +(-5.91920 - 10.2524i) q^{25} +(4.76861 + 8.25948i) q^{26} +5.57925 q^{27} +(-7.39354 + 5.08636i) q^{28} +(0.386810 - 0.669975i) q^{29} +(-6.08259 - 10.5353i) q^{30} +(-1.21874 + 2.11091i) q^{31} +(2.39471 + 4.14775i) q^{32} +(1.74479 - 3.02206i) q^{33} +(-1.44636 + 2.50516i) q^{34} +(-9.80125 - 4.66951i) q^{35} +(2.32343 + 4.02429i) q^{36} +(-1.32075 - 2.28760i) q^{37} +(5.72902 - 8.34414i) q^{38} +(-2.62191 + 4.54127i) q^{39} +(6.63138 - 11.4859i) q^{40} +(2.41205 + 4.17779i) q^{41} +(-7.08107 - 3.37356i) q^{42} +(-0.250810 - 0.434416i) q^{43} +9.27088 q^{44} +(-2.81083 + 4.86851i) q^{45} +(-6.53798 + 11.3241i) q^{46} +0.00235232 q^{47} +(0.460414 - 0.797460i) q^{48} +(-6.91282 + 1.10130i) q^{49} +27.4894 q^{50} -1.59049 q^{51} -13.9314 q^{52} +(0.280212 + 0.485342i) q^{53} +(-6.47765 + 11.2196i) q^{54} +(5.60785 + 9.71309i) q^{55} +(-0.674784 - 8.52464i) q^{56} +(5.54815 + 0.434039i) q^{57} +(0.898192 + 1.55571i) q^{58} -2.61944 q^{59} +17.7702 q^{60} +11.7346 q^{61} +(-2.82997 - 4.90165i) q^{62} +(0.286020 + 3.61333i) q^{63} -12.5637 q^{64} +(-8.42696 - 14.5959i) q^{65} +(4.05148 + 7.01737i) q^{66} +(-4.70077 - 8.14198i) q^{67} +(-2.11275 - 3.65940i) q^{68} -7.18950 q^{69} +(20.7697 - 14.2884i) q^{70} +(5.28155 + 9.14791i) q^{71} -4.42790 q^{72} +11.2118 q^{73} +6.13367 q^{74} +(7.55718 + 13.0894i) q^{75} +(6.37135 + 13.3417i) q^{76} +(6.52841 + 3.11027i) q^{77} +(-6.08819 - 10.5451i) q^{78} +(-0.675335 + 1.16971i) q^{79} +(1.47980 + 2.56308i) q^{80} -3.01321 q^{81} -11.2018 q^{82} +6.83039 q^{83} +(9.43949 - 6.49387i) q^{84} +(2.55596 - 4.42706i) q^{85} +1.16479 q^{86} +(-0.493849 + 0.855372i) q^{87} +(-4.41702 + 7.65051i) q^{88} -7.59704 q^{89} +(-6.52689 - 11.3049i) q^{90} +(-9.81028 - 4.67382i) q^{91} +(-9.55030 - 16.5416i) q^{92} +(1.55599 - 2.69505i) q^{93} +(-0.00273110 + 0.00473040i) q^{94} +(-10.1242 + 14.7455i) q^{95} +(-3.05737 - 5.29553i) q^{96} +(1.72833 + 2.99355i) q^{97} +(5.81130 - 15.1800i) q^{98} +(1.87224 - 3.24281i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} - 6 q^{3} - 11 q^{4} - 6 q^{6} - 2 q^{7} - 18 q^{8} + 18 q^{9} + 16 q^{10} - q^{11} - 2 q^{12} + 6 q^{13} - q^{14} - 9 q^{15} - 9 q^{16} - 16 q^{17} + 5 q^{18} - 4 q^{19} - 21 q^{21} - 2 q^{22}+ \cdots + 43 q^{99}+O(q^{100}) \) 24 * q + q^2 - 6 * q^3 - 11 * q^4 - 6 * q^6 - 2 * q^7 - 18 * q^8 + 18 * q^9 + 16 * q^10 - q^11 - 2 * q^12 + 6 * q^13 - q^14 - 9 * q^15 - 9 * q^16 - 16 * q^17 + 5 * q^18 - 4 * q^19 - 21 * q^21 - 2 * q^22 + 18 * q^23 + 16 * q^24 - 14 * q^25 + q^26 - 18 * q^27 - 14 * q^28 - 2 * q^29 - 9 * q^30 + 11 * q^31 + 24 * q^32 + 3 * q^33 + 6 * q^34 + 38 * q^35 - 7 * q^36 - 14 * q^37 + 12 * q^38 - 10 * q^39 + 42 * q^40 + 20 * q^41 - 36 * q^42 + 2 * q^43 - 4 * q^44 - 12 * q^45 - 6 * q^46 + 39 * q^48 + 18 * q^49 + 22 * q^50 - 42 * q^51 - 22 * q^52 + 7 * q^53 - 43 * q^54 + 9 * q^55 - 21 * q^56 + 21 * q^57 + 35 * q^58 - 84 * q^59 + 12 * q^60 - 12 * q^61 - 19 * q^62 + 9 * q^63 - 2 * q^64 - 27 * q^65 + 3 * q^66 - 14 * q^67 + 51 * q^68 - 34 * q^69 + 33 * q^70 + q^71 - 36 * q^72 + 42 * q^73 + 50 * q^74 + 31 * q^75 - 70 * q^76 - 20 * q^77 + 57 * q^78 - 5 * q^79 + 13 * q^80 - 56 * q^81 + 24 * q^82 + 10 * q^83 + 129 * q^84 - 27 * q^85 - 36 * q^86 + 53 * q^87 - 36 * q^88 + 2 * q^89 + 27 * q^90 - 9 * q^91 - 72 * q^92 + 34 * q^93 + 12 * q^94 - 11 * q^95 - 94 * q^96 + 31 * q^97 - 26 * q^98 + 43 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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