LMFDB - Embedded newform 87.2.k.a.8.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [87,2,Mod(2,87)] 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("87.2"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(87, base_ring=CyclotomicField(28)) chi = DirichletCharacter(H, H._module([14, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	87.k (of order $28$, degree $12$, 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:	$0.694698497585$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			8.2
Character	$\chi$	$=$	87.8
Dual form			87.2.k.a.11.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.576259 + 1.64685i) q^{2} +(0.598445 - 1.62538i) q^{3} +(-0.816387 - 0.651047i) q^{4} +(1.59790 - 0.769508i) q^{5} +(2.33190 + 1.92219i) q^{6} +(1.54710 + 1.94000i) q^{7} +(-1.41204 + 0.887242i) q^{8} +(-2.28373 - 1.94540i) q^{9} +(0.346463 + 3.07494i) q^{10} +(-1.02572 - 0.644501i) q^{11} +(-1.54676 + 0.937325i) q^{12} +(-1.08029 + 0.246570i) q^{13} +(-4.08643 + 1.42990i) q^{14} +(-0.294489 - 3.05770i) q^{15} +(-1.11217 - 4.87274i) q^{16} +(-2.39140 + 2.39140i) q^{17} +(4.51981 - 2.63991i) q^{18} +(0.482698 - 0.0543871i) q^{19} +(-1.80549 - 0.412091i) q^{20} +(4.07910 - 1.35364i) q^{21} +(1.65248 - 1.31781i) q^{22} +(3.99989 - 8.30586i) q^{23} +(0.597080 + 2.82606i) q^{24} +(-1.15631 + 1.44997i) q^{25} +(0.216464 - 1.92117i) q^{26} +(-4.52870 + 2.54771i) q^{27} -2.59103i q^{28} +(-5.27938 + 1.06215i) q^{29} +(5.20529 + 1.27705i) q^{30} +(-9.19909 - 3.21890i) q^{31} +(5.35125 + 0.602941i) q^{32} +(-1.66139 + 1.28148i) q^{33} +(-2.56022 - 5.31635i) q^{34} +(3.96496 + 1.90942i) q^{35} +(0.597858 + 3.07502i) q^{36} +(4.30274 + 6.84777i) q^{37} +(-0.188592 + 0.826274i) q^{38} +(-0.245726 + 1.90345i) q^{39} +(-1.57355 + 2.50430i) q^{40} +(6.28241 + 6.28241i) q^{41} +(-0.121364 + 7.49772i) q^{42} +(-1.18857 - 3.39673i) q^{43} +(0.417782 + 1.19395i) q^{44} +(-5.14617 - 1.35121i) q^{45} +(11.3736 + 11.3736i) q^{46} +(2.28637 - 3.63873i) q^{47} +(-8.58562 - 1.10836i) q^{48} +(0.187557 - 0.821739i) q^{49} +(-1.72155 - 2.73983i) q^{50} +(2.45581 + 5.31805i) q^{51} +(1.04247 + 0.502026i) q^{52} +(5.08537 + 10.5599i) q^{53} +(-1.58600 - 8.92625i) q^{54} +(-2.13494 - 0.240550i) q^{55} +(-3.90581 - 1.36670i) q^{56} +(0.200469 - 0.817117i) q^{57} +(1.29308 - 9.30643i) q^{58} +2.84288i q^{59} +(-1.75029 + 2.68800i) q^{60} +(0.299240 - 2.65582i) q^{61} +(10.6021 - 13.2946i) q^{62} +(0.240929 - 7.44017i) q^{63} +(0.260480 - 0.540893i) q^{64} +(-1.53646 + 1.22529i) q^{65} +(-1.15302 - 3.47454i) q^{66} +(11.9366 + 2.72445i) q^{67} +(3.50922 - 0.395394i) q^{68} +(-11.1065 - 11.4720i) q^{69} +(-5.42938 + 5.42938i) q^{70} +(-1.90444 - 8.34388i) q^{71} +(4.95075 + 0.720761i) q^{72} +(1.41405 - 0.494798i) q^{73} +(-13.7568 + 3.13989i) q^{74} +(1.66476 + 2.74717i) q^{75} +(-0.429477 - 0.269859i) q^{76} +(-0.336554 - 2.98700i) q^{77} +(-2.99310 - 1.50155i) q^{78} +(1.96273 - 1.23326i) q^{79} +(-5.52674 - 6.93032i) q^{80} +(1.43082 + 8.88554i) q^{81} +(-13.9665 + 6.72591i) q^{82} +(6.97313 + 5.56088i) q^{83} +(-4.21141 - 1.55059i) q^{84} +(-1.98101 + 5.66141i) q^{85} +6.27884 q^{86} +(-1.43302 + 9.21664i) q^{87} +2.02018 q^{88} +(3.09433 - 8.84308i) q^{89} +(5.19077 - 7.69634i) q^{90} +(-2.14967 - 1.71431i) q^{91} +(-8.67297 + 4.17668i) q^{92} +(-10.7371 + 13.0257i) q^{93} +(4.67492 + 5.86216i) q^{94} +(0.729452 - 0.458345i) q^{95} +(4.18244 - 8.33700i) q^{96} +(-0.582251 - 5.16762i) q^{97} +(1.24520 + 0.782413i) q^{98} +(1.08865 + 3.46730i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{3} - 28 q^{4} - 14 q^{6} - 20 q^{7} - 14 q^{9} - 4 q^{10} - 8 q^{12} - 28 q^{13} - 16 q^{15} - 48 q^{16} - 28 q^{18} - 20 q^{19} + 26 q^{21} - 28 q^{22} + 58 q^{24} - 20 q^{25} + 36 q^{27}+ \cdots + 82 q^{99}+O(q^{100}) $ 96 * q - 12 * q^3 - 28 * q^4 - 14 * q^6 - 20 * q^7 - 14 * q^9 - 4 * q^10 - 8 * q^12 - 28 * q^13 - 16 * q^15 - 48 * q^16 - 28 * q^18 - 20 * q^19 + 26 * q^21 - 28 * q^22 + 58 * q^24 - 20 * q^25 + 36 * q^27 + 96 * q^30 - 32 * q^31 + 28 * q^33 - 28 * q^34 + 22 * q^36 - 4 * q^37 - 40 * q^39 - 48 * q^40 - 14 * q^42 - 32 * q^43 + 42 * q^45 + 120 * q^46 - 20 * q^48 + 4 * q^49 - 14 * q^51 + 72 * q^52 - 30 * q^54 + 148 * q^55 + 112 * q^58 + 20 * q^60 + 12 * q^61 - 14 * q^63 + 224 * q^64 - 32 * q^66 + 28 * q^67 + 10 * q^69 + 52 * q^70 - 44 * q^72 + 16 * q^73 - 144 * q^75 - 100 * q^76 - 102 * q^78 - 60 * q^79 - 146 * q^81 - 108 * q^82 - 64 * q^84 - 104 * q^85 - 70 * q^87 - 312 * q^88 - 96 * q^90 - 112 * q^91 - 70 * q^93 + 56 * q^94 - 168 * q^96 + 32 * q^97 + 82 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{3}{28}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.576259	+	1.64685i	−0.407476	+	1.16450i	0.539162	+	0.842202i	$0.318741\pi$
$2$	−0.576259	+	1.64685i	−0.407476	+	1.16450i	−0.946638	+	0.322299i	$0.895545\pi$
$3$	0.598445	−	1.62538i	0.345512	−	0.938414i
$3$	0.598445	−	1.62538i	0.345512	−	0.938414i
$4$	−0.816387	−	0.651047i	−0.408194	−	0.325524i
$5$	1.59790	−	0.769508i	0.714602	−	0.344134i	−0.0410052	−	0.999159i	$-0.513056\pi$
$5$	1.59790	−	0.769508i	0.714602	−	0.344134i	0.755608	+	0.655025i	$0.227342\pi$
$6$	2.33190	+	1.92219i	0.951996	+	0.784731i
$7$	1.54710	+	1.94000i	0.584749	+	0.733252i	0.982915	−	0.184062i	$-0.0589246\pi$
$7$	1.54710	+	1.94000i	0.584749	+	0.733252i	−0.398166	+	0.917313i	$0.630353\pi$
$8$	−1.41204	+	0.887242i	−0.499231	+	0.313687i
$9$	−2.28373	−	1.94540i	−0.761243	−	0.648467i
$10$	0.346463	+	3.07494i	0.109561	+	0.972382i
$11$	−1.02572	−	0.644501i	−0.309265	−	0.194324i	0.368452	−	0.929647i	$-0.379888\pi$
$11$	−1.02572	−	0.644501i	−0.309265	−	0.194324i	−0.677717	+	0.735322i	$0.737031\pi$
$12$	−1.54676	+	0.937325i	−0.446512	+	0.270582i
$13$	−1.08029	+	0.246570i	−0.299620	+	0.0683863i	−0.369688	−	0.929156i	$-0.620535\pi$
$13$	−1.08029	+	0.246570i	−0.299620	+	0.0683863i	0.0700682	+	0.997542i	$0.477678\pi$
$14$	−4.08643	+	1.42990i	−1.09214	+	0.382158i
$15$	−0.294489	−	3.05770i	−0.0760367	−	0.789496i
$16$	−1.11217	−	4.87274i	−0.278042	−	1.21818i
$17$	−2.39140	+	2.39140i	−0.579999	+	0.579999i	−0.934903	−	0.354904i	$-0.884514\pi$
$17$	−2.39140	+	2.39140i	−0.579999	+	0.579999i	0.354904	+	0.934903i	$0.384514\pi$
$18$	4.51981	−	2.63991i	1.06533	−	0.622232i
$19$	0.482698	−	0.0543871i	0.110739	−	0.0124772i	−0.0564212	−	0.998407i	$-0.517969\pi$
$19$	0.482698	−	0.0543871i	0.110739	−	0.0124772i	0.167160	+	0.985930i	$0.446540\pi$
$20$	−1.80549	−	0.412091i	−0.403720	−	0.0921465i
$21$	4.07910	−	1.35364i	0.890132	−	0.295389i
$22$	1.65248	−	1.31781i	0.352309	−	0.280957i
$23$	3.99989	−	8.30586i	0.834035	−	1.73189i	0.168257	−	0.985743i	$-0.446186\pi$
$23$	3.99989	−	8.30586i	0.834035	−	1.73189i	0.665779	−	0.746149i	$-0.268099\pi$
$24$	0.597080	+	2.82606i	0.121878	+	0.576868i
$25$	−1.15631	+	1.44997i	−0.231262	+	0.289993i
$26$	0.216464	−	1.92117i	0.0424522	−	0.376773i
$27$	−4.52870	+	2.54771i	−0.871550	+	0.490307i
$28$		−	2.59103i		−	0.489658i
$29$	−5.27938	+	1.06215i	−0.980356	+	0.197236i
$29$	−5.27938	+	1.06215i	−0.980356	+	0.197236i
$30$	5.20529	+	1.27705i	0.950352	+	0.233156i
$31$	−9.19909	−	3.21890i	−1.65221	−	0.578132i	−0.666337	−	0.745651i	$-0.732139\pi$
$31$	−9.19909	−	3.21890i	−1.65221	−	0.578132i	−0.985869	+	0.167520i	$0.946424\pi$
$32$	5.35125	+	0.602941i	0.945977	+	0.106586i
$33$	−1.66139	+	1.28148i	−0.289212	+	0.223078i
$34$	−2.56022	−	5.31635i	−0.439074	−	0.911746i
$35$	3.96496	+	1.90942i	0.670200	+	0.322751i
$36$	0.597858	+	3.07502i	0.0996430	+	0.512503i
$37$	4.30274	+	6.84777i	0.707366	+	1.12577i	0.986221	+	0.165434i	$0.0529024\pi$
$37$	4.30274	+	6.84777i	0.707366	+	1.12577i	−0.278855	+	0.960333i	$0.589955\pi$
$38$	−0.188592	+	0.826274i	−0.0305936	+	0.134039i
$39$	−0.245726	+	1.90345i	−0.0393477	+	0.304796i
$40$	−1.57355	+	2.50430i	−0.248801	+	0.395964i
$41$	6.28241	+	6.28241i	0.981148	+	0.981148i	0.999826	−	0.0186776i	$-0.00594559\pi$
$41$	6.28241	+	6.28241i	0.981148	+	0.981148i	−0.0186776	+	0.999826i	$0.505946\pi$
$42$	−0.121364	+	7.49772i	−0.0187269	+	1.15692i
$43$	−1.18857	−	3.39673i	−0.181255	−	0.517997i	0.817026	−	0.576600i	$-0.195621\pi$
$43$	−1.18857	−	3.39673i	−0.181255	−	0.517997i	−0.998281	+	0.0586033i	$0.981335\pi$
$44$	0.417782	+	1.19395i	0.0629830	+	0.179995i
$45$	−5.14617	−	1.35121i	−0.767146	−	0.201427i
$46$	11.3736	+	11.3736i	1.67694	+	1.67694i
$47$	2.28637	−	3.63873i	0.333501	−	0.530764i	−0.637311	−	0.770607i	$-0.719953\pi$
$47$	2.28637	−	3.63873i	0.333501	−	0.530764i	0.970812	+	0.239843i	$0.0770960\pi$
$48$	−8.58562	−	1.10836i	−1.23923	−	0.159978i
$49$	0.187557	−	0.821739i	0.0267938	−	0.117391i
$50$	−1.72155	−	2.73983i	−0.243463	−	0.387470i
$51$	2.45581	+	5.31805i	0.343883	+	0.744676i
$52$	1.04247	+	0.502026i	0.144564	+	0.0696185i
$53$	5.08537	+	10.5599i	0.698530	+	1.45051i	0.883820	+	0.467828i	$0.154963\pi$
$53$	5.08537	+	10.5599i	0.698530	+	1.45051i	−0.185290	+	0.982684i	$0.559322\pi$
$54$	−1.58600	−	8.92625i	−0.215827	−	1.21471i
$55$	−2.13494	−	0.240550i	−0.287875	−	0.0324358i
$56$	−3.90581	−	1.36670i	−0.521936	−	0.182633i
$57$	0.200469	−	0.817117i	0.0265527	−	0.108230i
$58$	1.29308	−	9.30643i	0.169790	−	1.22199i
$59$			2.84288i			0.370111i	0.982728	+	0.185056i	$0.0592465\pi$
$59$			2.84288i			0.370111i	−0.982728	+	0.185056i	$0.940754\pi$
$60$	−1.75029	+	2.68800i	−0.225962	+	0.347019i
$61$	0.299240	−	2.65582i	0.0383137	−	0.340043i	−0.959902	−	0.280335i	$-0.909554\pi$
$61$	0.299240	−	2.65582i	0.0383137	−	0.340043i	0.998216	−	0.0597083i	$-0.0190170\pi$
$62$	10.6021	−	13.2946i	1.34647	−	1.68842i
$63$	0.240929	−	7.44017i	0.0303542	−	0.937373i
$64$	0.260480	−	0.540893i	0.0325600	−	0.0676116i
$65$	−1.53646	+	1.22529i	−0.190575	+	0.151978i
$66$	−1.15302	−	3.47454i	−0.141927	−	0.427686i
$67$	11.9366	+	2.72445i	1.45829	+	0.332844i	0.876857	−	0.480752i	$-0.159636\pi$
$67$	11.9366	+	2.72445i	1.45829	+	0.332844i	0.581430	+	0.813596i	$0.302493\pi$
$68$	3.50922	−	0.395394i	0.425555	−	0.0479486i
$69$	−11.1065	−	11.4720i	−1.33706	−	1.38106i
$70$	−5.42938	+	5.42938i	−0.648935	+	0.648935i
$71$	−1.90444	−	8.34388i	−0.226015	−	0.990236i	−0.952854	−	0.303428i	$-0.901869\pi$
$71$	−1.90444	−	8.34388i	−0.226015	−	0.990236i	0.726839	−	0.686808i	$-0.240988\pi$
$72$	4.95075	+	0.720761i	0.583451	+	0.0849425i
$73$	1.41405	−	0.494798i	0.165502	−	0.0579118i	−0.246256	−	0.969205i	$-0.579200\pi$
$73$	1.41405	−	0.494798i	0.165502	−	0.0579118i	0.411758	+	0.911293i	$0.364915\pi$
$74$	−13.7568	+	3.13989i	−1.59919	+	0.365005i
$75$	1.66476	+	2.74717i	0.192230	+	0.317215i
$76$	−0.429477	−	0.269859i	−0.0492644	−	0.0309549i
$77$	−0.336554	−	2.98700i	−0.0383539	−	0.340400i
$78$	−2.99310	−	1.50155i	−0.338902	−	0.170018i
$79$	1.96273	−	1.23326i	0.220824	−	0.138753i	−0.417077	−	0.908871i	$-0.636946\pi$
$79$	1.96273	−	1.23326i	0.220824	−	0.138753i	0.637901	+	0.770118i	$0.279803\pi$
$80$	−5.52674	−	6.93032i	−0.617909	−	0.774833i
$81$	1.43082	+	8.88554i	0.158980	+	0.987282i
$82$	−13.9665	+	6.72591i	−1.54234	+	0.742753i
$83$	6.97313	+	5.56088i	0.765400	+	0.610386i	0.926388	−	0.376570i	$-0.122897\pi$
$83$	6.97313	+	5.56088i	0.765400	+	0.610386i	−0.160988	+	0.986956i	$0.551468\pi$
$84$	−4.21141	−	1.55059i	−0.459502	−	0.169183i
$85$	−1.98101	+	5.66141i	−0.214871	+	0.614067i
$86$	6.27884			0.677065
$87$	−1.43302	+	9.21664i	−0.153636	+	0.988128i
$88$	2.02018			0.215352
$89$	3.09433	−	8.84308i	0.327998	−	0.937365i	−0.655301	−	0.755368i	$-0.727458\pi$
$89$	3.09433	−	8.84308i	0.327998	−	0.937365i	0.983299	−	0.181997i	$-0.0582561\pi$
$90$	5.19077	−	7.69634i	0.547155	−	0.811265i
$91$	−2.14967	−	1.71431i	−0.225347	−	0.179708i
$92$	−8.67297	+	4.17668i	−0.904220	+	0.435449i
$93$	−10.7371	+	13.0257i	−1.11338	+	1.35070i
$94$	4.67492	+	5.86216i	0.482181	+	0.604636i
$95$	0.729452	−	0.458345i	0.0748402	−	0.0470252i
$96$	4.18244	−	8.33700i	0.426868	−	0.850891i
$97$	−0.582251	−	5.16762i	−0.0591186	−	0.524692i	−0.988016	−	0.154354i	$-0.950670\pi$
$97$	−0.582251	−	5.16762i	−0.0591186	−	0.524692i	0.928897	−	0.370338i	$-0.120758\pi$
$98$	1.24520	+	0.782413i	0.125784	+	0.0790356i
$99$	1.08865	+	3.46730i	0.109413	+	0.348476i
$100$	1.88799	−	0.430922i	0.188799	−	0.0430922i
$101$	−11.4685	+	4.01299i	−1.14116	+	0.399308i	−0.833680	−	0.552248i	$-0.813770\pi$
$101$	−11.4685	+	4.01299i	−1.14116	+	0.399308i	−0.307476	+	0.951556i	$0.599484\pi$
$102$	−10.1732	+	0.979789i	−1.00730	+	0.0970136i
$103$	2.53000	+	11.0847i	0.249288	+	1.09220i	0.932269	+	0.361767i	$0.117826\pi$
$103$	2.53000	+	11.0847i	0.249288	+	1.09220i	−0.682980	+	0.730437i	$0.739317\pi$
$104$	1.30665	−	1.30665i	0.128127	−	0.128127i
$105$	5.47635	−	5.30188i	0.534437	−	0.517411i
$106$	−20.3211	+	2.28963i	−1.97376	+	0.222389i
$107$	1.16741	+	0.266455i	0.112858	+	0.0257592i	0.278577	−	0.960414i	$-0.410137\pi$
$107$	1.16741	+	0.266455i	0.112858	+	0.0257592i	−0.165719	+	0.986173i	$0.552994\pi$
$108$	5.35586	+	0.868480i	0.515368	+	0.0835696i
$109$	8.29478	−	6.61487i	0.794496	−	0.633589i	−0.139763	−	0.990185i	$-0.544634\pi$
$109$	8.29478	−	6.61487i	0.794496	−	0.633589i	0.934259	+	0.356596i	$0.116063\pi$
$110$	1.62643	−	3.37731i	0.155074	−	0.322014i
$111$	13.7052	−	2.89558i	1.30084	−	0.274836i
$112$	7.73248	−	9.69622i	0.730651	−	0.916207i
$113$	−0.516504	+	4.58410i	−0.0485886	+	0.431236i	0.945743	+	0.324915i	$0.105336\pi$
$113$	−0.516504	+	4.58410i	−0.0485886	+	0.431236i	−0.994332	+	0.106321i	$0.966093\pi$
$114$	1.23015	+	0.801013i	0.115214	+	0.0750217i
$115$		−	16.3499i		−	1.52463i
$116$	5.00153	+	2.57000i	0.464380	+	0.238618i
$117$	2.94678	+	1.53851i	0.272430	+	0.142235i
$118$	−4.68180	−	1.63823i	−0.430995	−	0.150812i
$119$	−8.33905	−	0.939585i	−0.764440	−	0.0861316i
$120$	3.12875	+	4.05631i	0.285615	+	0.370289i
$121$	−4.13601	−	8.58851i	−0.376001	−	0.780773i
$122$	4.20131	+	2.02325i	0.380369	+	0.183176i
$123$	13.9710	−	6.45164i	1.25972	−	0.581725i
$124$	5.41436	+	8.61691i	0.486224	+	0.773821i
$125$	−2.70515	+	11.8520i	−0.241956	+	1.06008i
$126$	12.1140	+	4.68424i	1.07920	+	0.417305i
$127$	1.38905	−	2.21065i	0.123258	−	0.196164i	−0.779395	−	0.626532i	$-0.784474\pi$
$127$	1.38905	−	2.21065i	0.123258	−	0.196164i	0.902653	+	0.430369i	$0.141616\pi$
$128$	8.35637	+	8.35637i	0.738605	+	0.738605i
$129$	−6.23228	−	0.100881i	−0.548722	−	0.00888206i
$130$	−1.13247	−	3.23641i	−0.0993242	−	0.283852i
$131$	−0.142233	−	0.406478i	−0.0124269	−	0.0355142i	0.937503	−	0.347978i	$-0.113132\pi$
$131$	−0.142233	−	0.406478i	−0.0124269	−	0.0355142i	−0.949930	+	0.312464i	$0.898846\pi$
$132$	2.19065	+	0.0354596i	0.190671	+	0.00308636i
$133$	0.852294	+	0.852294i	0.0739033	+	0.0739033i
$134$	−11.3653	+	18.0878i	−0.981815	+	1.56255i
$135$	−5.27593	+	7.55586i	−0.454080	+	0.650305i
$136$	1.25499	−	5.49849i	0.107615	−	0.471492i
$137$	−2.75997	−	4.39247i	−0.235800	−	0.375274i	0.707772	−	0.706441i	$-0.249701\pi$
$137$	−2.75997	−	4.39247i	−0.235800	−	0.375274i	−0.943572	+	0.331167i	$0.892558\pi$
$138$	25.2928	−	11.6799i	2.15307	−	0.994261i
$139$	−5.43195	−	2.61589i	−0.460732	−	0.221877i	0.189095	−	0.981959i	$-0.439445\pi$
$139$	−5.43195	−	2.61589i	−0.460732	−	0.221877i	−0.649827	+	0.760082i	$0.725159\pi$
$140$	−1.99382	−	4.14020i	−0.168508	−	0.349911i
$141$	−4.54606	−	5.89380i	−0.382848	−	0.496348i
$142$	14.8386	+	1.67191i	1.24523	+	0.140303i
$143$	1.26699	+	0.443339i	0.105951	+	0.0370739i
$144$	−6.93953	+	13.2916i	−0.578295	+	1.10763i
$145$	−7.61858	+	5.75973i	−0.632689	+	0.478320i
$146$			2.61387i			0.216325i
$147$	−1.22340	−	0.796617i	−0.100904	−	0.0657038i
$148$	0.945520	−	8.39172i	0.0777213	−	0.689795i
$149$	−2.74781	+	3.44564i	−0.225109	+	0.282278i	−0.881541	−	0.472107i	$-0.843493\pi$
$149$	−2.74781	+	3.44564i	−0.225109	+	0.282278i	0.656432	+	0.754385i	$0.272065\pi$
$150$	−5.48351	+	1.15853i	−0.447727	+	0.0945940i
$151$	−3.83234	+	7.95793i	−0.311871	+	0.647607i	−0.996707	−	0.0810904i	$-0.974160\pi$
$151$	−3.83234	+	7.95793i	−0.311871	+	0.647607i	0.684836	+	0.728698i	$0.259874\pi$
$152$	−0.633334	+	0.505067i	−0.0513701	+	0.0409663i
$153$	10.1135	−	0.809072i	0.817631	−	0.0654096i
$154$	5.11309	+	1.16703i	0.412025	+	0.0940420i
$155$	−17.1762	+	1.93529i	−1.37962	+	0.155446i
$156$	1.43984	−	1.39397i	0.115280	−	0.111607i
$157$	−7.17901	+	7.17901i	−0.572948	+	0.572948i	−0.932951	−	0.360003i	$-0.882776\pi$
$157$	−7.17901	+	7.17901i	−0.572948	+	0.572948i	0.360003	+	0.932951i	$0.382776\pi$
$158$	0.899964	+	3.94300i	0.0715973	+	0.313688i
$159$	20.2072	−	1.94616i	1.60253	−	0.154341i
$160$	9.01473	−	3.15439i	0.712677	−	0.249377i
$161$	22.3016	−	5.09020i	1.75761	−	0.401164i
$162$	−15.4577	−	2.76401i	−1.21447	−	0.217161i
$163$	−3.44823	−	2.16667i	−0.270086	−	0.169706i	0.390179	−	0.920739i	$-0.372413\pi$
$163$	−3.44823	−	2.16667i	−0.270086	−	0.169706i	−0.660265	+	0.751033i	$0.729556\pi$
$164$	−1.03874	−	9.21903i	−0.0811116	−	0.719885i
$165$	−1.66863	+	3.32614i	−0.129903	+	0.258939i
$166$	−13.1763	+	8.27920i	−1.02268	+	0.642591i
$167$	−12.6392	−	15.8490i	−0.978047	−	1.22643i	−0.974025	−	0.226440i	$-0.927291\pi$
$167$	−12.6392	−	15.8490i	−0.978047	−	1.22643i	−0.00402168	−	0.999992i	$-0.501280\pi$
$168$	−4.55883	+	5.53054i	−0.351721	+	0.426690i
$169$	−10.6064	+	5.10775i	−0.815874	+	0.392904i
$170$	−8.18194	−	6.52488i	−0.627526	−	0.500435i
$171$	−1.20816	−	0.814837i	−0.0923900	−	0.0623122i
$172$	−1.24110	+	3.54686i	−0.0946331	+	0.270446i
$173$	−3.30578			−0.251334			−0.125667	−	0.992072i	$-0.540107\pi$
$173$	−3.30578			−0.251334			−0.125667	+	0.992072i	$0.540107\pi$
$174$	−14.3527	−	7.67114i	−1.08807	−	0.581548i
$175$	−4.60186			−0.347868
$176$	−1.99971	+	5.71484i	−0.150734	+	0.430772i
$177$	4.62076	+	1.70130i	0.347317	+	0.127878i
$178$	12.7801	+	10.1918i	0.957910	+	0.763908i
$179$	4.99423	−	2.40509i	0.373286	−	0.179765i	−0.237829	−	0.971307i	$-0.576436\pi$
$179$	4.99423	−	2.40509i	0.373286	−	0.179765i	0.611115	+	0.791542i	$0.290721\pi$
$180$	3.32157	+	4.45351i	0.247575	+	0.331945i
$181$	−4.91454	−	6.16264i	−0.365295	−	0.458065i	0.564885	−	0.825170i	$-0.308921\pi$
$181$	−4.91454	−	6.16264i	−0.365295	−	0.458065i	−0.930180	+	0.367105i	$0.880349\pi$
$182$	4.06197	−	2.55231i	0.301094	−	0.189190i
$183$	−4.13765	−	2.07574i	−0.305864	−	0.153443i
$184$	1.72131	+	15.2771i	0.126897	+	1.12624i
$185$	12.1448	+	7.63106i	0.892901	+	0.561047i
$186$	−15.2641	−	25.1886i	−1.11922	−	1.84692i
$187$	3.99416	−	0.911640i	0.292082	−	0.0666657i
$188$	−4.23555	+	1.48208i	−0.308909	+	0.108092i
$189$	−11.9489	−	4.84413i	−0.869157	−	0.352359i
$190$	0.334474	+	1.46543i	0.0242653	+	0.106313i
$191$	6.59651	−	6.59651i	0.477307	−	0.477307i	−0.426963	−	0.904269i	$-0.640416\pi$
$191$	6.59651	−	6.59651i	0.477307	−	0.477307i	0.904269	+	0.426963i	$0.140416\pi$
$192$	−0.723274	−	0.747074i	−0.0521978	−	0.0539154i
$193$	11.7855	−	1.32791i	0.848338	−	0.0955847i	0.322917	−	0.946427i	$-0.395337\pi$
$193$	11.7855	−	1.32791i	0.848338	−	0.0955847i	0.525421	+	0.850843i	$0.323908\pi$
$194$	8.84584	+	2.01900i	0.635094	+	0.144956i
$195$	1.07207	+	3.23061i	0.0767728	+	0.231349i
$196$	−0.688110	+	0.548749i	−0.0491507	+	0.0391964i
$197$	1.76954	−	3.67449i	0.126075	−	0.261797i	−0.828372	−	0.560179i	$-0.810733\pi$
$197$	1.76954	−	3.67449i	0.126075	−	0.261797i	0.954447	+	0.298382i	$0.0964468\pi$
$198$	−6.33747	−	0.205221i	−0.450384	−	0.0145844i
$199$	6.84164	−	8.57915i	0.484991	−	0.608160i	−0.477779	−	0.878480i	$-0.658558\pi$
$199$	6.84164	−	8.57915i	0.484991	−	0.608160i	0.962770	+	0.270320i	$0.0871296\pi$
$200$	0.346281	−	3.07333i	0.0244858	−	0.217317i
$201$	11.5717	−	17.7711i	0.816202	−	1.25348i
$202$		−	21.1994i		−	1.49159i
$203$	−10.2283	−	8.59875i	−0.717886	−	0.603514i
$204$	1.45741	−	5.94044i	0.102039	−	0.415914i
$205$	14.8730	+	5.20430i	1.03878	+	0.363484i
$206$	−19.7127	−	2.22109i	−1.37345	−	0.154751i
$207$	−25.2929	+	11.1869i	−1.75798	+	0.777545i
$208$	2.40294	+	4.98976i	0.166614	+	0.345978i
$209$	−0.530165	−	0.255314i	−0.0366722	−	0.0176604i
$210$	5.57563	+	12.0740i	0.384755	+	0.833185i
$211$	13.1840	+	20.9822i	0.907622	+	1.44447i	0.895758	+	0.444542i	$0.146634\pi$
$211$	13.1840	+	20.9822i	0.907622	+	1.44447i	0.0118637	+	0.999930i	$0.496224\pi$
$212$	2.72335	−	11.9318i	0.187040	−	0.819478i
$213$	−14.7017	−	1.89792i	−1.00734	−	0.130043i
$214$	−1.11154	+	1.76901i	−0.0759836	+	0.120927i
$215$	−4.51303	−	4.51303i	−0.307786	−	0.307786i
$216$	4.13426	−	7.61552i	0.281301	−	0.518170i
$217$	−7.98724	−	22.8262i	−0.542209	−	1.54954i
$218$	6.11377	+	17.4722i	0.414077	+	1.18336i
$219$	0.0419965	−	2.59448i	0.00283786	−	0.175319i
$220$	1.58633	+	1.58633i	0.106950	+	0.106950i
$221$	1.99377	−	3.17306i	0.134115	−	0.213443i
$222$	−3.12914	+	24.2390i	−0.210014	+	1.62682i
$223$	−4.07939	+	17.8730i	−0.273176	+	1.19686i	0.633063	+	0.774100i	$0.281797\pi$
$223$	−4.07939	+	17.8730i	−0.273176	+	1.19686i	−0.906240	+	0.422764i	$0.861060\pi$
$224$	7.10922	+	11.3143i	0.475005	+	0.755965i
$225$	5.46146	−	1.06184i	0.364097	−	0.0707894i
$226$	−7.25170	−	3.49224i	−0.482376	−	0.232300i
$227$	−10.5337	−	21.8734i	−0.699145	−	1.45179i	−0.883259	−	0.468884i	$-0.844656\pi$
$227$	−10.5337	−	21.8734i	−0.699145	−	1.45179i	0.184115	−	0.982905i	$-0.441058\pi$
$228$	−0.695642	+	0.536569i	−0.0460700	+	0.0355352i
$229$	−6.13894	−	0.691693i	−0.405673	−	0.0457084i	−0.0932293	−	0.995645i	$-0.529719\pi$
$229$	−6.13894	−	0.691693i	−0.405673	−	0.0457084i	−0.312444	+	0.949936i	$0.601148\pi$
$230$	26.9259	+	9.42176i	1.77544	+	0.621253i
$231$	−5.05642	−	1.24053i	−0.332688	−	0.0816206i
$232$	6.51229	−	6.18388i	0.427553	−	0.405992i
$233$		−	13.5660i		−	0.888735i	−0.895845	−	0.444368i	$-0.853428\pi$
$233$		−	13.5660i		−	0.888735i	0.895845	−	0.444368i	$-0.146572\pi$
$234$	−4.23180	+	3.96633i	−0.276642	+	0.259287i
$235$	0.853352	−	7.57371i	0.0556666	−	0.494054i
$236$	1.85085	−	2.32089i	0.120480	−	0.151077i
$237$	−0.829938	−	3.92822i	−0.0539103	−	0.255165i
$238$	6.35281	−	13.1917i	0.411792	−	0.855094i
$239$	−13.4160	+	10.6989i	−0.867808	+	0.692053i	−0.952561	−	0.304349i	$-0.901561\pi$
$239$	−13.4160	+	10.6989i	−0.867808	+	0.692053i	0.0847532	+	0.996402i	$0.472990\pi$
$240$	−14.5719	+	4.83565i	−0.940609	+	0.312140i
$241$	15.9674	+	3.64445i	1.02855	+	0.234760i	0.703319	−	0.710875i	$-0.251701\pi$
$241$	15.9674	+	3.64445i	1.02855	+	0.234760i	0.325231	+	0.945634i	$0.394558\pi$
$242$	16.5274	−	1.86219i	1.06242	−	0.119706i
$243$	15.2987	+	2.99187i	0.981409	+	0.191929i
$244$	−1.97336	+	1.97336i	−0.126332	+	0.126332i
$245$	−0.332638	−	1.45738i	−0.0212515	−	0.0931088i
$246$	2.57399	+	26.7260i	0.164112	+	1.70399i
$247$	−0.508046	+	0.177773i	−0.0323262	+	0.0113114i
$248$	15.8454	−	3.61661i	1.00618	−	0.229655i
$249$	13.2116	−	8.00611i	0.837250	−	0.507366i
$250$	−17.9597	−	11.2848i	−1.13587	−	0.713714i
$251$	2.30792	+	20.4833i	0.145675	+	1.29290i	0.827535	+	0.561415i	$0.189743\pi$
$251$	2.30792	+	20.4833i	0.145675	+	1.29290i	−0.681860	+	0.731483i	$0.738829\pi$
$252$	−5.04059	+	5.91720i	−0.317527	+	0.372749i
$253$	−9.45589	+	5.94153i	−0.594487	+	0.373541i
$254$	2.84017	+	3.56146i	0.178208	+	0.223466i
$255$	8.01643	+	6.60795i	0.502008	+	0.413806i
$256$	−17.4954	+	8.42532i	−1.09346	+	0.526582i
$257$	11.3696	+	9.06698i	0.709218	+	0.565582i	0.910279	−	0.413996i	$-0.135867\pi$
$257$	11.3696	+	9.06698i	0.709218	+	0.565582i	−0.201061	+	0.979579i	$0.564439\pi$
$258$	3.75754	−	10.2055i	0.233934	−	0.635368i
$259$	−6.62792	+	18.9415i	−0.411839	+	1.17697i
$260$	2.05207			0.127264
$261$	14.1230	+	7.84485i	0.874190	+	0.485584i
$262$	0.751373			0.0464200
$263$	−3.08537	+	8.81747i	−0.190252	+	0.543709i	−0.999013	−	0.0444293i	$-0.985853\pi$
$263$	−3.08537	+	8.81747i	−0.190252	+	0.543709i	0.808761	+	0.588138i	$0.200139\pi$
$264$	1.20897	−	3.28356i	0.0744067	−	0.202089i
$265$	16.2518	+	12.9604i	0.998342	+	0.796151i
$266$	−1.89474	+	0.912461i	−0.116174	+	0.0559466i
$267$	−12.5216	−	10.3216i	−0.766309	−	0.631669i
$268$	−7.97114	−	9.99549i	−0.486915	−	0.610572i
$269$	4.66339	−	2.93020i	0.284332	−	0.178657i	−0.382313	−	0.924033i	$-0.624873\pi$
$269$	4.66339	−	2.93020i	0.284332	−	0.178657i	0.666645	+	0.745375i	$0.267730\pi$
$270$	−9.40309	−	13.0428i	−0.572254	−	0.793760i
$271$	−2.43068	−	21.5728i	−0.147653	−	1.31046i	−0.820914	−	0.571052i	$-0.806536\pi$
$271$	−2.43068	−	21.5728i	−0.147653	−	1.31046i	0.673261	−	0.739405i	$-0.264893\pi$
$272$	14.3123	+	8.99301i	0.867810	+	0.545281i
$273$	−4.07286	+	2.46812i	−0.246501	+	0.149377i
$274$	8.82421	−	2.01407i	0.533090	−	0.121674i
$275$	2.12055	−	0.742012i	0.127874	−	0.0447450i
$276$	1.59841	+	16.5964i	0.0962128	+	0.998986i
$277$	−5.43368	−	23.8065i	−0.326478	−	1.43040i	−0.825792	−	0.563974i	$-0.809272\pi$
$277$	−5.43368	−	23.8065i	−0.326478	−	1.43040i	0.499314	−	0.866421i	$-0.333585\pi$
$278$	7.43820	−	7.43820i	0.446113	−	0.446113i
$279$	14.7462	+	25.2470i	0.882829	+	1.51150i
$280$	−7.29279	+	0.821700i	−0.435827	+	0.0491060i
$281$	22.3808	+	5.10828i	1.33513	+	0.304734i	0.829737	−	0.558155i	$-0.188491\pi$
$281$	22.3808	+	5.10828i	1.33513	+	0.304734i	0.505392	+	0.862890i	$0.331348\pi$
$282$	12.3259	−	4.09035i	0.733999	−	0.243577i
$283$	−20.7543	+	16.5510i	−1.23372	+	0.983857i	−0.233784	+	0.972288i	$0.575111\pi$
$283$	−20.7543	+	16.5510i	−1.23372	+	0.983857i	−0.999933	+	0.0115684i	$0.996318\pi$
$284$	−3.87750	+	8.05171i	−0.230087	+	0.477781i
$285$	−0.308449	−	1.45993i	−0.0182709	−	0.0864789i
$286$	−1.46023	+	1.83107i	−0.0863452	+	0.108273i
$287$	−2.46837	+	21.9074i	−0.145703	+	1.29315i
$288$	−11.0478	−	11.7873i	−0.651000	−	0.694573i
$289$			5.56243i			0.327202i
$290$	−5.09516	−	15.8658i	−0.299198	−	0.931671i
$291$	−8.74780	−	2.14616i	−0.512805	−	0.125810i
$292$	−1.47655	−	0.516668i	−0.0864086	−	0.0302357i
$293$	−18.8457	−	2.12340i	−1.10098	−	0.124051i	−0.457275	−	0.889325i	$-0.651174\pi$
$293$	−18.8457	−	2.12340i	−1.10098	−	0.124051i	−0.643704	+	0.765275i	$0.722603\pi$
$294$	2.01690	−	1.55570i	0.117628	−	0.0907302i
$295$	2.18762	+	4.54263i	0.127368	+	0.264482i
$296$	−12.1513	−	5.85174i	−0.706278	−	0.340125i
$297$	6.28717	+	0.305522i	0.364819	+	0.0177282i
$298$	−4.09101	−	6.51081i	−0.236986	−	0.377161i
$299$	−2.27308	+	9.95903i	−0.131456	+	0.575946i
$300$	0.429447	−	3.32659i	0.0247941	−	0.192061i
$301$	4.75084	−	7.56091i	0.273834	−	0.435804i
$302$	−10.8971	−	10.8971i	−0.627059	−	0.627059i
$303$	−0.340607	+	21.0422i	−0.0195673	+	1.20884i
$304$	−0.801856	−	2.29157i	−0.0459896	−	0.131431i
$305$	−1.56552	−	4.47401i	−0.0896416	−	0.256181i
$306$	−4.49559	+	17.1217i	−0.256996	+	0.978784i
$307$	1.83383	+	1.83383i	0.104662	+	0.104662i	0.757499	−	0.652837i	$-0.226421\pi$
$307$	1.83383	+	1.83383i	0.104662	+	0.104662i	−0.652837	+	0.757499i	$0.726421\pi$
$308$	−1.66992	+	2.65766i	−0.0951525	+	0.151434i
$309$	19.5308	+	2.52134i	1.11107	+	0.143434i
$310$	6.71079	−	29.4019i	0.381147	−	1.66991i
$311$	−10.6017	−	16.8725i	−0.601166	−	0.956750i	−0.999224	−	0.0393897i	$-0.987459\pi$
$311$	−10.6017	−	16.8725i	−0.601166	−	0.956750i	0.398058	−	0.917360i	$-0.369684\pi$
$312$	−1.34184	−	2.90576i	−0.0759670	−	0.164506i
$313$	10.9283	+	5.26280i	0.617705	+	0.297471i	0.716446	−	0.697642i	$-0.245767\pi$
$313$	10.9283	+	5.26280i	0.617705	+	0.297471i	−0.0987415	+	0.995113i	$0.531482\pi$
$314$	−7.68581	−	15.9597i	−0.433735	−	0.900661i
$315$	−5.34029	−	12.0740i	−0.300891	−	0.680295i
$316$	−2.40526	−	0.271007i	−0.135306	−	0.0152454i
$317$	−19.6625	−	6.88021i	−1.10436	−	0.386431i	−0.284312	−	0.958732i	$-0.591765\pi$
$317$	−19.6625	−	6.88021i	−1.10436	−	0.386431i	−0.820044	+	0.572301i	$0.806051\pi$
$318$	−8.43951	+	34.3997i	−0.473264	+	1.92904i
$319$	6.09970	+	2.31310i	0.341518	+	0.129509i
$320$		−	1.06473i		−	0.0595204i
$321$	1.13172	−	1.73804i	0.0631667	−	0.0970077i
$322$	−4.46870	+	39.6608i	−0.249031	+	2.21021i
$323$	−1.02426	+	1.28439i	−0.0569915	+	0.0714651i
$324$	4.61680	−	8.18557i	0.256489	−	0.454754i
$325$	0.891636	−	1.85150i	0.0494590	−	0.102703i
$326$	5.55525	−	4.43016i	0.307677	−	0.245364i
$327$	−5.78771	−	17.4408i	−0.320061	−	0.964479i
$328$	−14.4450	−	3.29698i	−0.797593	−	0.182045i
$329$	10.5964	−	1.19393i	0.584198	−	0.0658233i
$330$	−4.51610	−	4.66470i	−0.248603	−	0.256783i
$331$	12.4740	−	12.4740i	0.685633	−	0.685633i	−0.275630	−	0.961264i	$-0.588887\pi$
$331$	12.4740	−	12.4740i	0.685633	−	0.685633i	0.961264	+	0.275630i	$0.0888866\pi$
$332$	−2.07237	−	9.07967i	−0.113736	−	0.498311i
$333$	3.49538	−	24.0090i	0.191546	−	1.31569i
$334$	33.3844	−	11.6817i	1.82671	−	0.639194i
$335$	21.1700	−	4.83190i	1.15664	−	0.263995i
$336$	−11.1326	−	18.3709i	−0.607333	−	1.00221i
$337$	8.26097	+	5.19071i	0.450004	+	0.282756i	0.737906	−	0.674904i	$-0.235815\pi$
$337$	8.26097	+	5.19071i	0.450004	+	0.282756i	−0.287902	+	0.957660i	$0.592958\pi$
$338$	−2.29971	−	20.4105i	−0.125088	−	1.11018i
$339$	7.14181	+	3.58285i	0.387890	+	0.194594i
$340$	5.30312	−	3.33217i	0.287602	−	0.180712i
$341$	7.36108	+	9.23050i	0.398625	+	0.499860i
$342$	2.03813	−	1.52010i	0.110209	−	0.0821975i
$343$	17.5337	−	8.44379i	0.946732	−	0.455922i
$344$	4.69203	+	3.74177i	0.252977	+	0.201743i
$345$	−26.5748	−	9.78450i	−1.43074	−	0.526780i
$346$	1.90499	−	5.44414i	0.102413	−	0.292679i
$347$	−13.9768			−0.750316			−0.375158	−	0.926961i	$-0.622412\pi$
$347$	−13.9768			−0.750316			−0.375158	+	0.926961i	$0.622412\pi$
$348$	7.17037	−	6.59139i	0.384372	−	0.353335i
$349$	−15.1394			−0.810391			−0.405196	−	0.914230i	$-0.632797\pi$
$349$	−15.1394			−0.810391			−0.405196	+	0.914230i	$0.632797\pi$
$350$	2.65186	−	7.57859i	0.141748	−	0.405093i
$351$	4.26414	−	3.86892i	0.227603	−	0.206508i
$352$	−5.10027	−	4.06733i	−0.271846	−	0.216790i
$353$	−15.0405	+	7.24310i	−0.800522	+	0.385511i	−0.788978	−	0.614422i	$-0.789389\pi$
$353$	−15.0405	+	7.24310i	−0.800522	+	0.385511i	−0.0115449	+	0.999933i	$0.503675\pi$
$354$	−5.46455	+	6.62932i	−0.290438	+	0.352344i
$355$	−9.46378	−	11.8672i	−0.502285	−	0.629846i
$356$	−8.28343	+	5.20483i	−0.439021	+	0.275855i
$357$	−6.51765	+	12.9918i	−0.344950	+	0.687601i
$358$	1.08287	+	9.61072i	0.0572314	+	0.507942i
$359$	4.93936	+	3.10361i	0.260690	+	0.163802i	0.656035	−	0.754730i	$-0.272232\pi$
$359$	4.93936	+	3.10361i	0.260690	+	0.163802i	−0.395346	+	0.918532i	$0.629375\pi$
$360$	8.46543	−	2.65794i	0.446167	−	0.140086i
$361$	−18.2936	+	4.17539i	−0.962821	+	0.219758i
$362$	12.9810	−	4.54225i	0.682266	−	0.238735i
$363$	−16.4348	+	1.58284i	−0.862602	+	0.0830776i
$364$	0.638870	+	2.79907i	0.0334859	+	0.146711i
$365$	1.87876	−	1.87876i	0.0983389	−	0.0983389i
$366$	5.80280	−	5.61793i	0.303317	−	0.293654i
$367$	2.23954	−	0.252336i	0.116903	−	0.0131718i	−0.0533190	−	0.998578i	$-0.516980\pi$
$367$	2.23954	−	0.252336i	0.116903	−	0.0131718i	0.170222	+	0.985406i	$0.445551\pi$
$368$	−44.9208	−	10.2529i	−2.34166	−	0.534469i
$369$	−2.12550	−	26.5691i	−0.110649	−	1.38313i
$370$	−19.5658	+	15.6032i	−1.01718	+	0.811170i
$371$	−12.6186	+	26.2028i	−0.655126	+	1.36038i
$372$	17.2460	−	3.64366i	0.894162	−	0.188915i
$373$	−19.9800	+	25.0542i	−1.03453	+	1.29726i	−0.0807529	+	0.996734i	$0.525732\pi$
$373$	−19.9800	+	25.0542i	−1.03453	+	1.29726i	−0.953775	+	0.300522i	$0.902839\pi$
$374$	−0.800330	+	7.10313i	−0.0413841	+	0.367294i
$375$	17.6452	+	11.4897i	0.911193	+	0.593325i
$376$			7.16659i			0.369589i
$377$	5.44139	−	2.44917i	0.280246	−	0.126139i
$378$	14.8632	−	16.8867i	0.764483	−	0.868556i
$379$	−9.87263	−	3.45458i	−0.507123	−	0.177450i	0.0645770	−	0.997913i	$-0.479430\pi$
$379$	−9.87263	−	3.45458i	−0.507123	−	0.177450i	−0.571700	+	0.820463i	$0.693716\pi$
$380$	−0.893920	−	0.100721i	−0.0458571	−	0.00516686i
$381$	−2.76189	−	3.58068i	−0.141496	−	0.183444i
$382$	7.06218	+	14.6648i	0.361333	+	0.750315i
$383$	−11.3746	−	5.47770i	−0.581213	−	0.279897i	0.120087	−	0.992763i	$-0.461683\pi$
$383$	−11.3746	−	5.47770i	−0.581213	−	0.279897i	−0.701300	+	0.712866i	$0.747397\pi$
$384$	18.5831	−	8.58146i	0.948315	−	0.437921i
$385$	−2.83630	−	4.51395i	−0.144551	−	0.230052i
$386$	−4.60462	+	20.1742i	−0.234369	+	1.02684i
$387$	−3.89364	+	10.0695i	−0.197925	+	0.511859i
$388$	−2.88902	+	4.59785i	−0.146668	+	0.233421i
$389$	5.76046	+	5.76046i	0.292067	+	0.292067i	0.837896	−	0.545829i	$-0.183785\pi$
$389$	5.76046	+	5.76046i	0.292067	+	0.292067i	−0.545829	+	0.837896i	$0.683785\pi$
$390$	−5.93813	−	0.0961195i	−0.300689	−	0.00486720i
$391$	10.2973	+	29.4280i	0.520756	+	1.48824i
$392$	0.464245	+	1.32673i	0.0234479	+	0.0670102i
$393$	−0.745801	−	0.0120721i	−0.0376207	−	0.000608959i
$394$	5.03164	+	5.03164i	0.253490	+	0.253490i
$395$	2.18723	−	3.48096i	0.110052	−	0.175146i
$396$	1.36862	−	3.53942i	0.0687756	−	0.177862i
$397$	−3.95989	+	17.3494i	−0.198741	+	0.870743i	0.772946	+	0.634472i	$0.218782\pi$
$397$	−3.95989	+	17.3494i	−0.198741	+	0.870743i	−0.971687	+	0.236271i	$0.924075\pi$
$398$	10.1860	+	16.2110i	0.510580	+	0.812583i
$399$	1.89535	−	0.875252i	0.0948863	−	0.0438174i
$400$	8.35131	+	4.02178i	0.417565	+	0.201089i
$401$	6.89266	+	14.3128i	0.344203	+	0.714745i	0.999162	−	0.0409190i	$-0.0130286\pi$
$401$	6.89266	+	14.3128i	0.344203	+	0.714745i	−0.654959	+	0.755664i	$0.727314\pi$
$402$	22.5981	+	29.2976i	1.12709	+	1.46123i
$403$	10.7314	+	1.20914i	0.534570	+	0.0602315i
$404$	11.9754	+	4.19036i	0.595797	+	0.208478i
$405$	9.12380	+	13.0972i	0.453365	+	0.650803i
$406$	20.0550	−	11.8894i	0.995314	−	0.590061i
$407$		−	9.79700i		−	0.485619i
$408$	−8.18610	−	5.33039i	−0.405272	−	0.263894i
$409$	1.02652	−	9.11057i	0.0507579	−	0.450489i	−0.942469	−	0.334295i	$-0.891502\pi$
$409$	1.02652	−	9.11057i	0.0507579	−	0.450489i	0.993227	−	0.116194i	$-0.0370695\pi$
$410$	−17.1414	+	21.4947i	−0.846555	+	1.06155i
$411$	−8.79113	+	1.85736i	−0.433635	+	0.0916166i
$412$	5.15117	−	10.6965i	0.253780	−	0.526980i
$413$	−5.51519	+	4.39822i	−0.271385	+	0.216422i
$414$	−3.84797	−	48.1003i	−0.189117	−	2.36400i
$415$	15.4215	+	3.51986i	0.757011	+	0.172783i
$416$	−5.92960	+	0.668105i	−0.290722	+	0.0327565i
$417$	−7.50254	+	7.26353i	−0.367401	+	0.355696i
$418$	0.725976	−	0.725976i	0.0355087	−	0.0355087i
$419$	3.95430	+	17.3249i	0.193180	+	0.846377i	0.974881	+	0.222724i	$0.0714950\pi$
$419$	3.95430	+	17.3249i	0.193180	+	0.846377i	−0.781701	+	0.623653i	$0.785648\pi$
$420$	−7.92260	+	0.763029i	−0.386583	+	0.0372320i
$421$	9.92465	−	3.47278i	0.483698	−	0.169253i	−0.0774043	−	0.997000i	$-0.524663\pi$
$421$	9.92465	−	3.47278i	0.483698	−	0.169253i	0.561102	+	0.827747i	$0.310378\pi$
$422$	−42.1519	+	9.62090i	−2.05192	+	0.468338i
$423$	−12.3002	+	3.86197i	−0.598058	+	0.187776i
$424$	−16.5499	−	10.3990i	−0.803735	−	0.505020i
$425$	−0.702250	−	6.23264i	−0.0340641	−	0.302327i
$426$	11.5976	−	23.1178i	0.561904	−	1.12006i
$427$	5.61526	−	3.52830i	0.271741	−	0.170746i
$428$	−0.779588	−	0.977572i	−0.0376828	−	0.0472527i
$429$	1.47882	−	1.79403i	0.0713981	−	0.0866165i
$430$	10.0330	−	4.83162i	0.483832	−	0.233001i
$431$	11.2015	+	8.93286i	0.539555	+	0.430281i	0.854973	−	0.518672i	$-0.173573\pi$
$431$	11.2015	+	8.93286i	0.539555	+	0.430281i	−0.315418	+	0.948953i	$0.602145\pi$
$432$	17.4510	+	19.2337i	0.839612	+	0.925381i
$433$	3.24108	−	9.26247i	0.155756	−	0.445126i	−0.839390	−	0.543529i	$-0.817088\pi$
$433$	3.24108	−	9.26247i	0.155756	−	0.445126i	0.995147	+	0.0984033i	$0.0313735\pi$
$434$	42.1941			2.02538
$435$	4.80246	+	15.8300i	0.230260	+	0.758990i
$436$	−11.0783			−0.530557
$437$	1.47901	−	4.22677i	0.0707507	−	0.202194i
$438$	4.24853	+	1.56426i	0.203003	+	0.0747430i
$439$	−30.2976	−	24.1616i	−1.44603	−	1.15317i	−0.960269	−	0.279075i	$-0.909972\pi$
$439$	−30.2976	−	24.1616i	−1.44603	−	1.15317i	−0.485758	−	0.874093i	$-0.661456\pi$
$440$	3.22804	−	1.55454i	0.153891	−	0.0741099i
$441$	−2.02694	+	1.51176i	−0.0965210	+	0.0719884i
$442$	4.07664	+	5.11195i	0.193906	+	0.243150i
$443$	16.3625	−	10.2813i	0.777408	−	0.488478i	−0.0839538	−	0.996470i	$-0.526755\pi$
$443$	16.3625	−	10.2813i	0.777408	−	0.488478i	0.861362	+	0.507992i	$0.169612\pi$
$444$	−13.0739	−	6.55881i	−0.620460	−	0.311268i
$445$	−1.86040	−	16.5115i	−0.0881912	−	0.782718i
$446$	−27.0834	−	17.0176i	−1.28244	−	0.805808i
$447$	3.95607	+	6.52826i	0.187116	+	0.308776i
$448$	1.45232	−	0.331483i	0.0686158	−	0.0156611i
$449$	0.404176	−	0.141427i	0.0190742	−	0.00667436i	−0.320725	−	0.947172i	$-0.603927\pi$
$449$	0.404176	−	0.141427i	0.0190742	−	0.00667436i	0.339799	+	0.940498i	$0.389641\pi$
$450$	−1.39852	+	9.60611i	−0.0659268	+	0.452837i
$451$	−2.39496	−	10.4930i	−0.112774	−	0.494096i
$452$	3.40613	−	3.40613i	0.160211	−	0.160211i
$453$	10.6412	+	10.9914i	0.499969	+	0.516421i
$454$	42.0924	−	4.74268i	1.97549	−	0.222585i
$455$	−4.75413	−	1.08510i	−0.222877	−	0.0508702i
$456$	0.441911	+	1.33166i	0.0206944	+	0.0623608i
$457$	−6.74257	+	5.37702i	−0.315404	+	0.251526i	−0.768376	−	0.639998i	$-0.778935\pi$
$457$	−6.74257	+	5.37702i	−0.315404	+	0.251526i	0.452972	+	0.891525i	$0.350364\pi$
$458$	4.67674	−	9.71134i	0.218530	−	0.453781i
$459$	4.73734	−	16.9225i	0.221120	−	0.789876i
$460$	−10.6445	+	13.3478i	−0.496305	+	0.622346i
$461$	3.41255	−	30.2872i	0.158938	−	1.41062i	−0.620534	−	0.784180i	$-0.713084\pi$
$461$	3.41255	−	30.2872i	0.158938	−	1.41062i	0.779472	−	0.626437i	$-0.215488\pi$
$462$	4.95677	−	7.61232i	0.230610	−	0.354157i
$463$		−	18.6575i		−	0.867086i	−0.901133	−	0.433543i	$-0.857263\pi$
$463$		−	18.6575i		−	0.867086i	0.901133	−	0.433543i	$-0.142737\pi$
$464$	11.0471	+	24.5437i	0.512851	+	1.13941i
$465$	−7.13342	+	29.0760i	−0.330804	+	1.34837i
$466$	22.3411	+	7.81750i	1.03493	+	0.362139i
$467$	18.2564	+	2.05701i	0.844807	+	0.0951869i	0.523749	−	0.851873i	$-0.324533\pi$
$467$	18.2564	+	2.05701i	0.844807	+	0.0951869i	0.321058	+	0.947060i	$0.395962\pi$
$468$	−1.40407	−	3.17451i	−0.0649031	−	0.146742i
$469$	13.1817	+	27.3720i	0.608673	+	1.26392i
$470$	11.9810	+	5.76976i	0.552644	+	0.266139i
$471$	7.37239	+	15.9649i	0.339702	+	0.735623i
$472$	−2.52232	−	4.01425i	−0.116099	−	0.184771i
$473$	−0.970062	+	4.25012i	−0.0446035	+	0.195421i
$474$	6.94746	+	0.896883i	0.319107	+	0.0411952i
$475$	−0.479289	+	0.762784i	−0.0219913	+	0.0349989i
$476$	6.19618	+	6.19618i	0.284001	+	0.284001i
$477$	8.92962	−	34.0090i	0.408859	−	1.55717i
$478$	−9.88842	−	28.2595i	−0.452286	−	1.29256i
$479$	−4.21591	−	12.0484i	−0.192630	−	0.550504i	0.806543	−	0.591176i	$-0.201336\pi$
$479$	−4.21591	−	12.0484i	−0.192630	−	0.550504i	−0.999173	+	0.0406714i	$0.987050\pi$
$480$	0.267732	−	16.5401i	0.0122202	−	0.754949i
$481$	−6.33668	−	6.33668i	−0.288928	−	0.288928i
$482$	−15.2032	+	24.1958i	−0.692488	+	1.10209i
$483$	5.07278	−	39.2949i	0.230819	−	1.78798i
$484$	−2.21494	+	9.70428i	−0.100679	+	0.441104i
$485$	−4.90690	−	7.80929i	−0.222811	−	0.354602i
$486$	−13.7432	+	23.4705i	−0.623402	+	1.06465i
$487$	−11.2965	−	5.44009i	−0.511892	−	0.246514i	0.160062	−	0.987107i	$-0.448831\pi$
$487$	−11.2965	−	5.44009i	−0.511892	−	0.246514i	−0.671954	+	0.740593i	$0.734545\pi$
$488$	1.93382	+	4.01562i	0.0875400	+	0.181779i
$489$	−5.58523	+	4.30806i	−0.252573	+	0.194817i
$490$	2.59178	+	0.292024i	0.117085	+	0.0131923i
$491$	−15.4772	−	5.41572i	−0.698477	−	0.244408i	−0.0423993	−	0.999101i	$-0.513500\pi$
$491$	−15.4772	−	5.41572i	−0.698477	−	0.244408i	−0.656078	+	0.754693i	$0.727786\pi$
$492$	−15.6061	−	3.82874i	−0.703576	−	0.172613i
$493$	10.0851	−	15.1651i	0.454209	−	0.683003i
$494$		−	0.939121i		−	0.0422530i
$495$	4.40766	+	4.70267i	0.198109	+	0.211369i
$496$	−5.45390	+	48.4047i	−0.244887	+	2.17343i
$497$	13.2408	−	16.6034i	0.593931	−	0.744765i
$498$	5.57159	+	26.3711i	0.249669	+	1.18172i
$499$	8.87570	−	18.4306i	0.397331	−	0.825066i	−0.602310	−	0.798262i	$-0.705753\pi$
$499$	8.87570	−	18.4306i	0.397331	−	0.825066i	0.999641	−	0.0268037i	$-0.00853291\pi$
$500$	9.92468	−	7.91467i	0.443845	−	0.353955i
$501$	−33.3245	+	11.0587i	−1.48883	+	0.494066i
$502$	−35.0630	−	8.00291i	−1.56494	−	0.357187i
$503$	0.689827	−	0.0777249i	0.0307579	−	0.00346558i	−0.0965721	−	0.995326i	$-0.530788\pi$
$503$	0.689827	−	0.0777249i	0.0307579	−	0.00346558i	0.127330	+	0.991860i	$0.459359\pi$
$504$	6.26103	+	10.7196i	0.278888	+	0.477487i
$505$	−15.2374	+	15.2374i	−0.678057	+	0.678057i
$506$	−4.33579	−	18.9963i	−0.192749	−	0.844490i
$507$	1.95472	+	20.2961i	0.0868124	+	0.901380i
$508$	−2.57324	+	0.900415i	−0.114169	+	0.0399495i
$509$	−14.3369	+	3.27230i	−0.635471	+	0.145042i	−0.528107	−	0.849178i	$-0.677098\pi$
$509$	−14.3369	+	3.27230i	−0.635471	+	0.145042i	−0.107364	+	0.994220i	$0.534241\pi$
$510$	−15.5019	+	9.39399i	−0.686434	+	0.415973i
$511$	3.14759	+	1.97776i	0.139241	+	0.0874910i
$512$	−1.14709	−	10.1807i	−0.0506945	−	0.449926i
$513$	−2.04744	+	1.47608i	−0.0903965	+	0.0651705i
$514$	−21.4838	+	13.4992i	−0.947611	+	0.595423i
$515$	12.5724	+	15.7653i	0.554007	+	0.694702i
$516$	5.02228	+	4.13987i	0.221093	+	0.182247i
$517$	−4.69033	+	2.25875i	−0.206281	+	0.0993395i
$518$	−27.3745	−	21.8304i	−1.20277	−	0.959174i
$519$	−1.97833	+	5.37316i	−0.0868390	+	0.235856i
$520$	1.08242	−	3.09337i	0.0474671	−	0.135653i
$521$	−10.8298			−0.474462			−0.237231	−	0.971453i	$-0.576240\pi$
$521$	−10.8298			−0.474462			−0.237231	+	0.971453i	$0.576240\pi$
$522$	−21.0578	+	18.7378i	−0.921675	+	0.820131i
$523$	5.85546			0.256041			0.128021	−	0.991771i	$-0.459138\pi$
$523$	5.85546			0.256041			0.128021	+	0.991771i	$0.459138\pi$
$524$	−0.148519	+	0.424444i	−0.00648810	+	0.0185419i
$525$	−2.75396	+	7.47978i	−0.120193	+	0.326444i
$526$	−12.7431	−	10.1623i	−0.555626	−	0.443097i
$527$	29.6964	−	14.3010i	1.29359	−	0.622962i
$528$	8.09208	+	6.67031i	0.352163	+	0.290288i
$529$	−38.6480	−	48.4630i	−1.68035	−	2.10709i
$530$	−30.7091	+	19.2958i	−1.33392	+	0.838157i
$531$	5.53054	−	6.49236i	0.240005	−	0.281744i
$532$	−0.140918	−	1.25069i	−0.00610959	−	0.0542241i
$533$	−8.33591	−	5.23780i	−0.361068	−	0.226874i
$534$	24.2138	−	14.6733i	1.04783	−	0.634977i
$535$	2.07045	−	0.472567i	0.0895134	−	0.0204308i
$536$	−19.2722	+	6.74362i	−0.832430	+	0.291280i
$537$	−0.920424	−	9.55685i	−0.0397192	−	0.412408i
$538$	2.13829	+	9.36846i	0.0921883	+	0.403903i
$539$	−0.721992	+	0.721992i	−0.0310984	+	0.0310984i
$540$	9.22642	−	2.73363i	0.397042	−	0.117637i
$541$	27.5408	−	3.10311i	1.18407	−	0.133413i	0.502112	−	0.864802i	$-0.332556\pi$
$541$	27.5408	−	3.10311i	1.18407	−	0.133413i	0.681960	+	0.731389i	$0.261128\pi$
$542$	36.9280	+	8.42857i	1.58619	+	0.362038i
$543$	−12.9577	+	4.30000i	−0.556069	+	0.184531i
$544$	−14.2388	+	11.3551i	−0.610486	+	0.486846i
$545$	8.16404	−	16.9528i	0.349709	−	0.726178i
$546$	−1.71761	−	8.12967i	−0.0735067	−	0.347918i
$547$	−18.6234	+	23.3530i	−0.796278	+	0.998502i	0.203533	+	0.979068i	$0.434758\pi$
$547$	−18.6234	+	23.3530i	−0.796278	+	0.998502i	−0.999811	+	0.0194334i	$0.993814\pi$
$548$	−0.606499	+	5.38283i	−0.0259084	+	0.229943i
$549$	−5.85003	+	5.48304i	−0.249673	+	0.234010i
$550$			3.91982i			0.167142i
$551$	−2.49058	+	0.799828i	−0.106102	+	0.0340738i
$552$	25.8612	+	6.34469i	1.10072	+	0.270048i
$553$	5.42907	+	1.89971i	0.230867	+	0.0807840i
$554$	42.3370	+	4.77024i	1.79873	+	0.202668i
$555$	19.6714	−	15.1731i	0.835002	−	0.644062i
$556$	2.73151	+	5.67204i	0.115842	+	0.240548i
$557$	20.5785	+	9.91006i	0.871937	+	0.419903i	0.815673	−	0.578513i	$-0.196367\pi$
$557$	20.5785	+	9.91006i	0.871937	+	0.419903i	0.0562642	+	0.998416i	$0.482081\pi$
$558$	−50.0757	+	9.73594i	−2.11987	+	0.412155i
$559$	2.12154	+	3.37641i	0.0897315	+	0.142807i
$560$	4.89441	−	21.4438i	0.206826	−	0.906166i
$561$	0.908519	−	7.03759i	0.0383577	−	0.297127i
$562$	−21.3097	+	33.9143i	−0.898897	+	1.43059i
$563$	−10.4785	−	10.4785i	−0.441617	−	0.441617i	0.450938	−	0.892555i	$-0.351089\pi$
$563$	−10.4785	−	10.4785i	−0.441617	−	0.441617i	−0.892555	+	0.450938i	$0.851089\pi$
$564$	−0.125793	+	7.77133i	−0.00529685	+	0.327232i
$565$	2.70218	+	7.72239i	0.113682	+	0.324883i
$566$	−15.2972	−	43.7170i	−0.642991	−	1.83756i
$567$	−15.0243	+	16.5226i	−0.630963	+	0.693885i
$568$	10.0922	+	10.0922i	0.423458	+	0.423458i
$569$	19.8489	−	31.5893i	0.832107	−	1.32429i	−0.111682	−	0.993744i	$-0.535624\pi$
$569$	19.8489	−	31.5893i	0.832107	−	1.32429i	0.943789	−	0.330547i	$-0.107233\pi$
$570$	2.58204	+	0.333329i	0.108150	+	0.0139616i
$571$	4.57150	−	20.0290i	0.191311	−	0.838189i	−0.784597	−	0.620007i	$-0.787130\pi$
$571$	4.57150	−	20.0290i	0.191311	−	0.838189i	0.975908	−	0.218183i	$-0.0700129\pi$
$572$	−0.745721	−	1.18681i	−0.0311801	−	0.0496229i
$573$	−6.77419	−	14.6695i	−0.282996	−	0.612826i
$574$	−34.6559	−	16.6894i	−1.44651	−	0.696602i
$575$	7.41810	+	15.4038i	0.309356	+	0.642385i
$576$	−1.64712	+	0.728513i	−0.0686300	+	0.0303547i
$577$	47.2544	+	5.32429i	1.96723	+	0.221653i	0.999535	−	0.0304845i	$-0.00970503\pi$
$577$	47.2544	+	5.32429i	1.96723	+	0.221653i	0.967691	+	0.252138i	$0.0811336\pi$
$578$	−9.16050	−	3.20540i	−0.381027	−	0.133327i
$579$	4.89461	−	19.9506i	0.203413	−	0.829118i
$580$	9.96957	+	0.257885i	0.413964	+	0.0107081i
$581$			22.1311i			0.918154i
$582$	8.57540	−	13.1696i	0.355462	−	0.545897i
$583$	1.58970	−	14.1090i	0.0658387	−	0.584334i
$584$	−1.55769	+	1.95328i	−0.0644576	+	0.0808273i
$585$	5.89255	+	0.190813i	0.243627	+	0.00788916i
$586$	14.3569	−	29.8125i	0.593080	−	1.23154i
$587$	14.0552	−	11.2086i	0.580119	−	0.462629i	−0.288934	−	0.957349i	$-0.593301\pi$
$587$	14.0552	−	11.2086i	0.580119	−	0.462629i	0.869053	+	0.494720i	$0.164729\pi$
$588$	0.480131	+	1.44684i	0.0198003	+	0.0596666i
$589$	−4.61545	−	1.05345i	−0.190176	−	0.0434065i
$590$	−8.74168	+	0.984951i	−0.359889	+	0.0405498i
$591$	−4.91348	−	5.07516i	−0.202114	−	0.208764i
$592$	28.5820	−	28.5820i	1.17471	−	1.17471i
$593$	7.33679	+	32.1446i	0.301286	+	1.32002i	0.868189	+	0.496234i	$0.165284\pi$
$593$	7.33679	+	32.1446i	0.301286	+	1.32002i	−0.566903	+	0.823785i	$0.691859\pi$
$594$	−4.12619	+	10.1780i	−0.169299	+	0.417608i
$595$	−14.0480	+	4.91560i	−0.575911	+	0.201520i
$596$	4.48655	−	1.02403i	0.183776	−	0.0419457i
$597$	−9.85004	−	16.2544i	−0.403135	−	0.665249i
$598$	−15.0912	−	9.48242i	−0.617124	−	0.387765i
$599$	0.0259349	+	0.230179i	0.00105967	+	0.00940485i	0.994231	−	0.107261i	$-0.0342080\pi$
$599$	0.0259349	+	0.230179i	0.00105967	+	0.00940485i	−0.993171	+	0.116666i	$0.962779\pi$
$600$	−4.78810	−	2.40206i	−0.195473	−	0.0980636i
$601$	5.17627	−	3.25247i	0.211144	−	0.132671i	−0.422308	−	0.906452i	$-0.638780\pi$
$601$	5.17627	−	3.25247i	0.211144	−	0.132671i	0.633453	+	0.773781i	$0.281637\pi$
$602$	9.71400	+	12.1810i	0.395913	+	0.496459i
$603$	−21.9598	−	29.4434i	−0.894271	−	1.19903i
$604$	8.30966	−	4.00172i	0.338115	−	0.162828i
$605$	−13.2178	−	10.5409i	−0.537382	−	0.428548i
$606$	−34.4571	−	12.6867i	−1.39973	−	0.515361i
$607$	−4.49999	+	12.8602i	−0.182649	+	0.521981i	−0.998408	−	0.0564117i	$-0.982034\pi$
$607$	−4.49999	+	12.8602i	−0.182649	+	0.521981i	0.815759	+	0.578393i	$0.196320\pi$
$608$	2.61583			0.106086
$609$	−20.0973	+	11.4790i	−0.814385	+	0.465153i
$610$	8.27018			0.334850
$611$	−1.57275	+	4.49465i	−0.0636266	+	0.181834i
$612$	−8.78330	−	5.92387i	−0.355044	−	0.239458i
$613$	21.5711	+	17.2023i	0.871247	+	0.694796i	0.953363	−	0.301826i	$-0.0975963\pi$
$613$	21.5711	+	17.2023i	0.871247	+	0.694796i	−0.0821159	+	0.996623i	$0.526168\pi$
$614$	−4.07681	+	1.96329i	−0.164527	+	0.0792319i
$615$	17.3597	−	21.0599i	0.700009	−	0.849215i
$616$	3.12542	+	3.91915i	0.125927	+	0.157907i
$617$	−12.3887	+	7.78436i	−0.498752	+	0.313387i	−0.757810	−	0.652475i	$-0.773731\pi$
$617$	−12.3887	+	7.78436i	−0.498752	+	0.313387i	0.259058	+	0.965862i	$0.416588\pi$
$618$	−15.4071	+	30.7115i	−0.619764	+	1.23540i
$619$	1.50822	+	13.3858i	0.0606205	+	0.538022i	0.986917	+	0.161227i	$0.0515451\pi$
$619$	1.50822	+	13.3858i	0.0606205	+	0.538022i	−0.926297	+	0.376794i	$0.877026\pi$
$620$	15.2824	+	9.60256i	0.613756	+	0.385648i
$621$	3.04662	+	47.8054i	0.122256	+	1.91836i
$622$	33.8958	−	7.73649i	1.35910	−	0.310205i
$623$	21.9428	−	7.67813i	0.879121	−	0.307618i
$624$	9.54829	−	0.919600i	0.382238	−	0.0368135i
$625$	2.73427	+	11.9796i	0.109371	+	0.479184i
$626$	−14.9646	+	14.9646i	−0.598105	+	0.598105i
$627$	−0.732256	+	0.708928i	−0.0292435	+	0.0283119i
$628$	10.5347	−	1.18698i	0.420381	−	0.0473656i
$629$	−26.6653	−	6.08619i	−1.06322	−	0.242672i
$630$	22.9616	−	1.83690i	0.914810	−	0.0731838i
$631$	−16.5679	+	13.2125i	−0.659558	+	0.525980i	−0.895089	−	0.445887i	$-0.852888\pi$
$631$	−16.5679	+	13.2125i	−0.659558	+	0.525980i	0.235531	+	0.971867i	$0.424317\pi$
$632$	−1.67724	+	3.48283i	−0.0667170	+	0.138539i
$633$	41.9939	−	8.87230i	1.66911	−	0.352642i
$634$	22.6614	−	28.4165i	0.899998	−	1.12856i
$635$	0.518440	−	4.60128i	0.0205737	−	0.182596i
$636$	−17.7639	−	11.5670i	−0.704385	−	0.458661i
$637$			0.933967i			0.0370051i
$638$	−7.32434	+	8.71237i	−0.289973	+	0.344926i
$639$	−11.8830	+	22.7600i	−0.470084	+	0.900373i
$640$	19.7829	+	6.92234i	0.781989	+	0.273630i
$641$	33.9080	+	3.82051i	1.33929	+	0.150901i	0.752367	−	0.658745i	$-0.228912\pi$
$641$	33.9080	+	3.82051i	1.33929	+	0.150901i	0.586919	+	0.809646i	$0.300341\pi$
$642$	2.21012	+	2.86534i	0.0872266	+	0.113086i
$643$	−8.94126	−	18.5667i	−0.352609	−	0.732200i	0.646931	−	0.762549i	$-0.276052\pi$
$643$	−8.94126	−	18.5667i	−0.352609	−	0.732200i	−0.999539	+	0.0303492i	$0.990338\pi$
$644$	−21.5207	−	10.3638i	−0.848036	−	0.408392i
$645$	−10.0362	+	4.63459i	−0.395174	+	0.182487i
$646$	−1.52495	−	2.42695i	−0.0599985	−	0.0954870i
$647$	8.36804	−	36.6628i	0.328982	−	1.44136i	−0.492093	−	0.870543i	$-0.663768\pi$
$647$	8.36804	−	36.6628i	0.328982	−	1.44136i	0.821075	−	0.570821i	$-0.193375\pi$
$648$	−9.90399	−	11.2772i	−0.389066	−	0.443011i
$649$	1.83224	−	2.91599i	0.0719216	−	0.114463i
$650$	2.53534	+	2.53534i	0.0994441	+	0.0994441i
$651$	−41.8812	−	0.677924i	−1.64145	−	0.0265699i
$652$	1.40449	+	4.01380i	0.0550040	+	0.157192i
$653$	12.3466	+	35.2847i	0.483161	+	1.38080i	0.885216	+	0.465180i	$0.154010\pi$
$653$	12.3466	+	35.2847i	0.483161	+	1.38080i	−0.402055	+	0.915616i	$0.631704\pi$
$654$	32.0577	+	0.518912i	1.25355	+	0.0202911i
$655$	−0.540062	−	0.540062i	−0.0211020	−	0.0211020i
$656$	23.6254	−	37.5996i	0.922418	−	1.46802i
$657$	−4.19189	−	1.62092i	−0.163541	−	0.0632379i
$658$	−4.14004	+	18.1387i	−0.161396	+	0.707121i
$659$	27.0994	+	43.1284i	1.05564	+	1.68005i	0.634140	+	0.773218i	$0.281354\pi$
$659$	27.0994	+	43.1284i	1.05564	+	1.68005i	0.421502	+	0.906827i	$0.361503\pi$
$660$	3.52772	−	1.62906i	0.137316	−	0.0634110i
$661$	7.29040	+	3.51087i	0.283564	+	0.136557i	0.570259	−	0.821465i	$-0.306843\pi$
$661$	7.29040	+	3.51087i	0.283564	+	0.136557i	−0.286696	+	0.958022i	$0.592557\pi$
$662$	13.3546	+	27.7311i	0.519041	+	1.07780i
$663$	−3.96428	−	5.13953i	−0.153960	−	0.199603i
$664$	−14.7802	−	1.66532i	−0.573581	−	0.0646271i
$665$	2.01773	+	0.706033i	0.0782441	+	0.0273788i
$666$	37.5251	+	19.5918i	1.45407	+	0.759166i
$667$	−12.2949	+	48.0983i	−0.476060	+	1.86237i
$668$			21.1676i			0.818999i
$669$	26.6091	+	17.3266i	1.02877	+	0.669884i
$670$	−4.24194	+	37.6482i	−0.163880	+	1.45448i
$671$	−2.01862	+	2.53126i	−0.0779278	+	0.0977184i
$672$	22.6444	−	4.78423i	0.873529	−	0.184556i
$673$	−4.56760	+	9.48471i	−0.176068	+	0.365609i	−0.970263	−	0.242055i	$-0.922179\pi$
$673$	−4.56760	+	9.48471i	−0.176068	+	0.365609i	0.794195	+	0.607663i	$0.207893\pi$
$674$	−13.3088	+	10.6134i	−0.512636	+	0.408813i
$675$	1.54249	−	9.51240i	0.0593703	−	0.366133i
$676$	11.9843	+	2.73533i	0.460934	+	0.105205i
$677$	−23.0750	+	2.59993i	−0.886846	+	0.0999235i	−0.543622	−	0.839330i	$-0.682947\pi$
$677$	−23.0750	+	2.59993i	−0.886846	+	0.0999235i	−0.343224	+	0.939254i	$0.611519\pi$
$678$	−10.0160	+	9.69687i	−0.384661	+	0.372406i
$679$	9.12439	−	9.12439i	0.350162	−	0.350162i
$680$	−2.22578	−	9.75177i	−0.0853546	−	0.373963i
$681$	−41.8565	+	4.03121i	−1.60394	+	0.154476i
$682$	−19.4432	+	6.80346i	−0.744517	+	0.260518i
$683$	−14.9652	+	3.41570i	−0.572627	+	0.130698i	−0.499022	−	0.866589i	$-0.666307\pi$
$683$	−14.9652	+	3.41570i	−0.572627	+	0.130698i	−0.0736044	+	0.997288i	$0.523450\pi$
$684$	0.455826	+	1.45179i	0.0174289	+	0.0555106i
$685$	−7.79020	−	4.89491i	−0.297648	−	0.187025i
$686$	3.80173	+	33.7413i	0.145151	+	1.28825i
$687$	−4.79808	+	9.56418i	−0.183058	+	0.364896i
$688$	−15.2295	+	9.56932i	−0.580619	+	0.364827i
$689$	−8.09745	−	10.1539i	−0.308488	−	0.386832i
$690$	31.4276	−	38.1264i	1.19643	−	1.45145i
$691$	14.5662	−	7.01469i	0.554123	−	0.266852i	−0.135798	−	0.990737i	$-0.543360\pi$
$691$	14.5662	−	7.01469i	0.554123	−	0.266852i	0.689921	+	0.723885i	$0.257645\pi$
$692$	2.69880	+	2.15222i	0.102593	+	0.0818152i
$693$	−5.04232	+	7.47623i	−0.191542	+	0.283998i
$694$	8.05427	−	23.0178i	0.305736	−	0.873744i
$695$	−10.6927			−0.405596
$696$	−6.15391	−	14.2857i	−0.233263	−	0.541497i
$697$	−30.0475			−1.13813
$698$	8.72419	−	24.9323i	0.330215	−	0.943701i
$699$	−22.0498	−	8.11847i	−0.834002	−	0.307069i
$700$	3.75690	+	2.99603i	0.141998	+	0.113239i
$701$	28.6080	−	13.7769i	1.08051	−	0.520346i	0.193029	−	0.981193i	$-0.438169\pi$
$701$	28.6080	−	13.7769i	1.08051	−	0.520346i	0.887479	+	0.460847i	$0.152454\pi$
$702$	3.91430	+	9.25192i	0.147736	+	0.349191i
$703$	2.44936	+	3.07140i	0.0923792	+	0.115840i
$704$	−0.615785	+	0.386923i	−0.0232083	+	0.0145827i
$705$	−11.7995	−	5.91947i	−0.444394	−	0.222940i
$706$	−3.26113	−	28.9433i	−0.122734	−	1.08930i
$707$	−25.5281	−	16.0404i	−0.960083	−	0.603260i
$708$	−2.66470	−	4.39726i	−0.100146	−	0.165259i
$709$	0.0799658	−	0.0182517i	0.00300318	−	0.000685456i	−0.221019	−	0.975269i	$-0.570938\pi$
$709$	0.0799658	−	0.0182517i	0.00300318	−	0.000685456i	0.224022	+	0.974584i	$0.428081\pi$
$710$	24.9971	−	8.74687i	0.938125	−	0.328264i
$711$	−6.88152	−	1.00186i	−0.258077	−	0.0375725i
$712$	3.47664	+	15.2322i	0.130293	+	0.570850i
$713$	−63.5311	+	63.5311i	−2.37926	+	2.37926i
$714$	−17.6398	−	18.2203i	−0.660153	−	0.681876i
$715$	2.36568	−	0.266548i	0.0884713	−	0.00996832i
$716$	−5.64306	−	1.28799i	−0.210891	−	0.0481345i
$717$	9.36105	+	28.2088i	0.349595	+	1.05348i
$718$	−7.95753	+	6.34592i	−0.296973	+	0.236828i
$719$	6.89173	−	14.3108i	0.257018	−	0.533704i	−0.732034	−	0.681268i	$-0.761429\pi$
$719$	6.89173	−	14.3108i	0.257018	−	0.533704i	0.989053	+	0.147564i	$0.0471432\pi$
$720$	−0.860675	+	26.5787i	−0.0320755	+	0.990529i
$721$	−17.5901	+	22.0573i	−0.655089	+	0.821456i
$722$	3.66558	−	32.5330i	0.136419	−	1.21075i
$723$	15.4792	−	23.7721i	0.575679	−	0.884094i
$724$			8.23069i			0.305891i
$725$	4.56451	−	8.88309i	0.169522	−	0.329910i
$726$	6.86397	−	27.9778i	0.254746	−	1.03835i
$727$	−4.29705	−	1.50360i	−0.159369	−	0.0557655i	0.249416	−	0.968397i	$-0.419761\pi$
$727$	−4.29705	−	1.50360i	−0.159369	−	0.0557655i	−0.408784	+	0.912631i	$0.634047\pi$
$728$	4.55642	+	0.513385i	0.168872	+	0.0190273i
$729$	14.0183	−	23.0757i	0.519197	−	0.854654i
$730$	2.01139	+	4.17670i	0.0744450	+	0.154587i
$731$	10.9653	+	5.28060i	0.405566	+	0.195310i
$732$	2.02652	+	4.38841i	0.0749022	+	0.162200i
$733$	−9.11220	−	14.5020i	−0.336567	−	0.535643i	0.634968	−	0.772538i	$-0.281013\pi$
$733$	−9.11220	−	14.5020i	−0.336567	−	0.535643i	−0.971535	+	0.236895i	$0.923870\pi$
$734$	−0.874997	+	3.83361i	−0.0322967	+	0.141501i
$735$	−2.56787	−	0.331500i	−0.0947173	−	0.0122275i
$736$	26.4124	−	42.0351i	0.973574	−	1.54943i
$737$	−10.4877	−	10.4877i	−0.386318	−	0.386318i
$738$	44.9803	+	11.8103i	1.65575	+	0.434743i
$739$	4.94780	+	14.1400i	0.182008	+	0.520148i	0.998350	−	0.0574202i	$-0.0182875\pi$
$739$	4.94780	+	14.1400i	0.182008	+	0.520148i	−0.816342	+	0.577568i	$0.804002\pi$
$740$	−4.94665	−	14.1367i	−0.181842	−	0.519676i
$741$	−0.0150887	+	0.932156i	−0.000554296	+	0.0342436i
$742$	−35.8806	−	35.8806i	−1.31722	−	1.31722i
$743$	5.32655	−	8.47716i	0.195412	−	0.310997i	−0.734617	−	0.678482i	$-0.762638\pi$
$743$	5.32655	−	8.47716i	0.195412	−	0.310997i	0.930029	+	0.367485i	$0.119781\pi$
$744$	3.60423	−	27.9192i	0.132137	−	1.02357i
$745$	−1.73927	+	7.62024i	−0.0637220	+	0.279184i
$746$	−29.7469	−	47.3419i	−1.08911	−	1.73331i
$747$	−5.10657	−	26.2651i	−0.186840	−	0.960989i
$748$	−3.85430	−	1.85613i	−0.140927	−	0.0678669i
$749$	1.28918	+	2.67702i	0.0471058	+	0.0978162i
$750$	−29.0900	+	22.4380i	−1.06222	+	0.819320i
$751$	−0.260316	−	0.0293306i	−0.00949907	−	0.00107029i	0.107214	−	0.994236i	$-0.465807\pi$
$751$	−0.260316	−	0.0293306i	−0.00949907	−	0.00107029i	−0.116713	+	0.993166i	$0.537236\pi$
$752$	−20.2734	−	7.09398i	−0.739295	−	0.258691i
$753$	34.6744	+	8.50691i	1.26361	+	0.310009i
$754$	0.897778	+	10.3725i	0.0326951	+	0.377745i
$755$			15.6650i			0.570107i
$756$	6.60119	+	11.7340i	0.240083	+	0.426762i
$757$	4.38898	−	38.9533i	0.159520	−	1.41578i	−0.617631	−	0.786468i	$-0.711907\pi$
$757$	4.38898	−	38.9533i	0.159520	−	1.41578i	0.777151	−	0.629314i	$-0.216664\pi$
$758$	11.3784	−	14.2680i	0.413281	−	0.518239i
$759$	3.99842	+	18.9251i	0.145134	+	0.686938i
$760$	−0.623351	+	1.29440i	−0.0226113	+	0.0469529i
$761$	−18.6302	+	14.8571i	−0.675344	+	0.538569i	−0.900011	−	0.435867i	$-0.856442\pi$
$761$	−18.6302	+	14.8571i	−0.675344	+	0.538569i	0.224667	+	0.974436i	$0.427871\pi$
$762$	7.48842	−	2.48502i	0.271277	−	0.0900228i
$763$	25.6657	+	5.85803i	0.929161	+	0.212075i
$764$	−9.67994	+	1.09067i	−0.350208	+	0.0394590i
$765$	15.5378	−	9.07526i	0.561771	−	0.328117i
$766$	15.5757	−	15.5757i	0.562771	−	0.562771i
$767$	−0.700969	−	3.07114i	−0.0253105	−	0.110893i
$768$	3.22435	+	33.4787i	0.116349	+	1.20806i
$769$	−2.11272	+	0.739272i	−0.0761865	+	0.0266588i	−0.368103	−	0.929785i	$-0.619993\pi$
$769$	−2.11272	+	0.739272i	−0.0761865	+	0.0266588i	0.291917	+	0.956444i	$0.405707\pi$
$770$	9.06825	−	2.06977i	0.326797	−	0.0745893i
$771$	21.5414	−	13.0539i	0.775794	−	0.470125i
$772$	−10.4860	−	6.58882i	−0.377401	−	0.237137i
$773$	−0.614691	−	5.45554i	−0.0221089	−	0.196222i	0.977803	−	0.209528i	$-0.0671929\pi$
$773$	−0.614691	−	5.45554i	−0.0221089	−	0.196222i	−0.999911	+	0.0133064i	$0.995764\pi$
$774$	−14.3392	−	12.2149i	−0.515411	−	0.439055i
$775$	15.3043	−	9.61632i	0.549746	−	0.345428i
$776$	5.40709	+	6.78027i	0.194103	+	0.243398i
$777$	26.8207	+	22.1084i	0.962189	+	0.793133i
$778$	−12.8062	+	6.16712i	−0.459123	+	0.221102i
$779$	3.37419	+	2.69083i	0.120893	+	0.0964090i
$780$	1.22805	−	3.33540i	0.0439713	−	0.119426i
$781$	−3.42422	+	9.78587i	−0.122528	+	0.350166i
$782$	−54.3974			−1.94525
$783$	21.2027	−	18.2605i	0.757722	−	0.652577i
$784$	−4.21271			−0.150454
$785$	−5.94703	+	16.9956i	−0.212259	+	0.606601i
$786$	0.449655	−	1.22127i	0.0160387	−	0.0435612i
$787$	−20.8008	−	16.5881i	−0.741469	−	0.591302i	0.178201	−	0.983994i	$-0.442972\pi$
$787$	−20.8008	−	16.5881i	−0.741469	−	0.591302i	−0.919670	+	0.392692i	$0.871544\pi$
$788$	−3.83690	+	1.84775i	−0.136684	+	0.0658235i
$789$	12.4853	+	10.2917i	0.444490	+	0.366393i
$790$	4.47222	+	5.60799i	0.159114	+	0.199523i
$791$	−9.69225	+	6.09005i	−0.344617	+	0.216537i
$792$	−4.61354	−	3.93006i	−0.163935	−	0.139649i
$793$	0.331580	+	2.94286i	0.0117748	+	0.104504i
$794$	−26.2900	−	16.5191i	−0.932998	−	0.586242i
$795$	30.7914	−	18.6593i	1.09206	−	0.661778i
$796$	−11.1709	+	2.54968i	−0.395941	+	0.0903709i
$797$	−3.37422	+	1.18069i	−0.119521	+	0.0418222i	−0.389377	−	0.921078i	$-0.627310\pi$
$797$	−3.37422	+	1.18069i	−0.119521	+	0.0418222i	0.269856	+	0.962901i	$0.413024\pi$
$798$	0.349197	+	3.62574i	0.0123614	+	0.128350i
$799$	3.23405	+	14.1693i	0.114412	+	0.501273i
$800$	−7.06194	+	7.06194i	−0.249677	+	0.249677i
$801$	−24.2699	+	14.1755i	−0.857536	+	0.500866i
$802$	−27.5430	+	3.10335i	−0.972576	+	0.109583i
$803$	−1.76932	−	0.403835i	−0.0624378	−	0.0142510i
$804$	−21.0168	+	6.97439i	−0.741204	+	0.245968i
$805$	31.7188	−	25.2949i	1.11794	−	0.891528i
$806$	−8.17534	+	16.9763i	−0.287964	+	0.597964i
$807$	−1.97191	−	9.33334i	−0.0694146	−	0.328549i
$808$	12.6334	−	15.8418i	0.444442	−	0.557313i
$809$	−0.733011	+	6.50565i	−0.0257713	+	0.228727i	0.974224	+	0.225584i	$0.0724289\pi$
$809$	−0.733011	+	6.50565i	−0.0257713	+	0.228727i	−0.999995	+	0.00314277i	$0.999000\pi$
$810$	−26.8268	+	7.47820i	−0.942597	+	0.262757i
$811$			30.0526i			1.05529i	0.849465	+	0.527645i	$0.176925\pi$
$811$			30.0526i			1.05529i	−0.849465	+	0.527645i	$0.823075\pi$
$812$	2.75206	+	13.6790i	0.0965784	+	0.480040i
$813$	−36.5187	−	8.95938i	−1.28077	−	0.314219i
$814$	16.1342	+	5.64561i	0.565504	+	0.197878i
$815$	−7.17719	−	0.808675i	−0.251406	−	0.0283266i
$816$	23.1822	−	17.8811i	0.811539	−	0.625964i
$817$	−0.758459	−	1.57496i	−0.0265351	−	0.0551007i
$818$	14.4122	+	6.94057i	0.503912	+	0.242671i
$819$	1.57425	+	8.09698i	0.0550087	+	0.282931i
$820$	−8.75391	−	13.9318i	−0.305700	−	0.486518i
$821$	7.11158	−	31.1579i	0.248196	−	1.08742i	−0.685140	−	0.728412i	$-0.740259\pi$
$821$	7.11158	−	31.1579i	0.248196	−	1.08742i	0.933336	−	0.359005i	$-0.116884\pi$
$822$	2.00717	−	15.5480i	0.0700083	−	0.542299i
$823$	−10.7333	+	17.0819i	−0.374139	+	0.595439i	−0.979726	−	0.200340i	$-0.935795\pi$
$823$	−10.7333	+	17.0819i	−0.374139	+	0.595439i	0.605587	+	0.795779i	$0.292938\pi$
$824$	−13.4072	−	13.4072i	−0.467063	−	0.467063i
$825$	0.0629790	−	3.89075i	0.00219265	−	0.135459i
$826$	−4.06504	−	11.6172i	−0.141441	−	0.404215i
$827$	8.59715	+	24.5693i	0.298952	+	0.854357i	0.991162	+	0.132660i	$0.0423518\pi$
$827$	8.59715	+	24.5693i	0.298952	+	0.854357i	−0.692209	+	0.721697i	$0.743363\pi$
$828$	27.9320	+	7.33401i	0.970705	+	0.254874i
$829$	3.76700	+	3.76700i	0.130833	+	0.130833i	0.769491	−	0.638658i	$-0.220510\pi$
$829$	3.76700	+	3.76700i	0.130833	+	0.130833i	−0.638658	+	0.769491i	$0.720510\pi$
$830$	−14.6835	+	23.3686i	−0.509670	+	0.811135i
$831$	−41.9464	−	5.41508i	−1.45511	−	0.187847i
$832$	−0.148027	+	0.648550i	−0.00513192	+	0.0224844i
$833$	1.51658	+	2.41363i	0.0525465	+	0.0836273i
$834$	−7.63855	−	16.5413i	−0.264502	−	0.572777i
$835$	−32.3920	−	15.5992i	−1.12097	−	0.539832i
$836$	0.266598	+	0.553597i	0.00922049	+	0.0191466i
$837$	49.8608	−	8.85918i	1.72344	−	0.306218i
$838$	−30.8103	−	3.47148i	−1.06432	−	0.119920i
$839$	−45.6449	−	15.9718i	−1.57584	−	0.551409i	−0.606063	−	0.795417i	$-0.707252\pi$
$839$	−45.6449	−	15.9718i	−1.57584	−	0.551409i	−0.969773	+	0.244008i	$0.921538\pi$
$840$	−3.02876	+	12.3453i	−0.104502	+	0.425953i
$841$	26.7437	−	11.2150i	0.922196	−	0.386724i
$842$			18.3457i			0.632233i
$843$	21.6966	−	33.3204i	0.747271	−	1.14761i
$844$	2.89715	−	25.7130i	0.0997242	−	0.885076i
$845$	−13.0174	+	16.3233i	−0.447813	+	0.561540i
$846$	0.728021	−	22.4822i	0.0250299	−	0.772953i
$847$	10.2629	−	21.3111i	0.352638	−	0.732260i
$848$	45.7997	−	36.5241i	1.57277	−	1.25424i
$849$	14.4814	+	43.6386i	0.497001	+	1.49767i
$850$	10.6689	+	2.43511i	0.365941	+	0.0835236i
$851$	74.0872	−	8.34762i	2.53968	−	0.286153i
$852$	10.7666	+	11.1209i	0.368859	+	0.380997i
$853$	−13.2989	+	13.2989i	−0.455345	+	0.455345i	−0.897124	−	0.441779i	$-0.854347\pi$
$853$	−13.2989	+	13.2989i	−0.455345	+	0.455345i	0.441779	+	0.897124i	$0.354347\pi$
$854$	2.57475	+	11.2807i	0.0881062	+	0.386018i
$855$	−2.55754	−	0.372342i	−0.0874659	−	0.0127338i
$856$	−1.88484	+	0.659535i	−0.0644226	+	0.0225424i
$857$	−21.8609	+	4.98961i	−0.746754	+	0.170442i	−0.578932	−	0.815375i	$-0.696531\pi$
$857$	−21.8609	+	4.98961i	−0.746754	+	0.170442i	−0.167822	+	0.985817i	$0.553673\pi$
$858$	2.10232	+	3.46922i	0.0717720	+	0.118437i
$859$	18.0755	+	11.3576i	0.616730	+	0.387517i	0.803860	−	0.594818i	$-0.202776\pi$
$859$	18.0755	+	11.3576i	0.616730	+	0.387517i	−0.187131	+	0.982335i	$0.559919\pi$
$860$	0.746184	+	6.62257i	0.0254447	+	0.225828i
$861$	34.1307	+	17.1224i	1.16317	+	0.583531i
$862$	−21.1660	+	13.2995i	−0.720918	+	0.452983i
$863$	23.5034	+	29.4724i	0.800066	+	1.00325i	0.999727	+	0.0233862i	$0.00744473\pi$
$863$	23.5034	+	29.4724i	0.800066	+	1.00325i	−0.199660	+	0.979865i	$0.563984\pi$
$864$	−25.7704	+	10.9029i	−0.876726	+	0.370924i
$865$	−5.28231	+	2.54383i	−0.179604	+	0.0864927i
$866$	13.3862	+	10.6752i	0.454882	+	0.362757i
$867$	9.04107	+	3.32881i	0.307051	+	0.113052i
$868$	−8.34026	+	23.8351i	−0.283087	+	0.809016i
$869$	−2.80804			−0.0952562
$870$	−28.8371	−	1.21323i	−0.977670	−	0.0411322i
$871$	−13.5668			−0.459694
$872$	−5.84355	+	16.6999i	−0.197888	+	0.565531i
$873$	−8.72339	+	12.9341i	−0.295242	+	0.437755i
$874$	6.10858	+	4.87143i	0.206626	+	0.164778i
$875$	−27.1781	+	13.0883i	−0.918787	+	0.442465i
$876$	−1.72342	+	2.09076i	−0.0582288	+	0.0706403i
$877$	16.0258	+	20.0958i	0.541154	+	0.678586i	0.974950	−	0.222425i	$-0.0713974\pi$
$877$	16.0258	+	20.0958i	0.541154	+	0.678586i	−0.433796	+	0.901011i	$0.642826\pi$
$878$	57.2498	−	35.9724i	1.93209	−	1.21401i
$879$	−14.7295	+	29.3607i	−0.496812	+	0.990313i
$880$	1.20228	+	10.6705i	0.0405289	+	0.359704i
$881$	−43.6456	−	27.4243i	−1.47046	−	0.923949i	−0.999118	−	0.0419974i	$-0.986628\pi$
$881$	−43.6456	−	27.4243i	−1.47046	−	0.923949i	−0.471339	−	0.881952i	$-0.656229\pi$
$882$	−1.32160	−	4.20924i	−0.0445005	−	0.141732i
$883$	−3.39773	+	0.775510i	−0.114343	+	0.0260980i	−0.279309	−	0.960201i	$-0.590106\pi$
$883$	−3.39773	+	0.775510i	−0.114343	+	0.0260980i	0.164967	+	0.986299i	$0.447248\pi$
$884$	−3.69350	+	1.29241i	−0.124226	+	0.0434685i
$885$	8.69268	−	0.837196i	0.292201	−	0.0281420i
$886$	7.50268	+	32.8714i	0.252057	+	1.10434i
$887$	21.7214	−	21.7214i	0.729332	−	0.729332i	−0.241155	−	0.970487i	$-0.577526\pi$
$887$	21.7214	−	21.7214i	0.729332	−	0.729332i	0.970487	+	0.241155i	$0.0775262\pi$
$888$	−16.7832	+	16.2485i	−0.563206	+	0.545264i
$889$	6.43766	−	0.725351i	0.215912	−	0.0243275i
$890$	28.2640	+	6.45108i	0.947412	+	0.216241i
$891$	4.25911	−	10.0362i	0.142686	−	0.336226i
$892$	14.9665	−	11.9354i	0.501116	−	0.399627i
$893$	0.905726	−	1.88076i	0.0303090	−	0.0629372i
$894$	−13.0308	+	2.75310i	−0.435815	+	0.0920773i
$895$	6.12954	−	7.68620i	0.204888	−	0.256921i
$896$	−3.28323	+	29.1395i	−0.109685	+	0.973483i
$897$	14.8269	+	9.65456i	0.495056	+	0.322356i
$898$			0.747116i			0.0249316i
$899$	51.9844	+	7.22298i	1.73378	+	0.240900i
$900$	−5.14997	−	2.68879i	−0.171666	−	0.0896265i
$901$	−37.4140	−	13.0917i	−1.24644	−	0.436149i
$902$	18.6605	+	2.10254i	0.621328	+	0.0700068i
$903$	−9.44625	−	12.2467i	−0.314352	−	0.407545i
$904$	−3.33788	−	6.93119i	−0.111016	−	0.230528i
$905$	−12.5951	−	6.06550i	−0.418676	−	0.201624i
$906$	−24.2333	+	11.1907i	−0.805098	+	0.371784i
$907$	8.72468	+	13.8852i	0.289698	+	0.461052i	0.959588	−	0.281408i	$-0.0908016\pi$
$907$	8.72468	+	13.8852i	0.289698	+	0.461052i	−0.669890	+	0.742460i	$0.733659\pi$
$908$	−5.64106	+	24.7151i	−0.187205	+	0.820199i
$909$	33.9978	+	13.1462i	1.12763	+	0.436032i
$910$	4.52661	−	7.20405i	0.150056	−	0.238812i
$911$	−11.4146	−	11.4146i	−0.378182	−	0.378182i	0.492264	−	0.870446i	$-0.336170\pi$
$911$	−11.4146	−	11.4146i	−0.378182	−	0.378182i	−0.870446	+	0.492264i	$0.836170\pi$
$912$	−4.20455	−	0.0680583i	−0.139227	−	0.00225364i
$913$	−3.56846	−	10.1981i	−0.118099	−	0.337507i
$914$	−4.96970	−	14.2026i	−0.164383	−	0.469779i
$915$	−8.20885	−	0.132875i	−0.271376	−	0.00439272i
$916$	4.56143	+	4.56143i	0.150714	+	0.150714i
$917$	0.568520	−	0.904795i	0.0187742	−	0.0298790i
$918$	25.1390	+	17.5535i	0.829710	+	0.579351i
$919$	0.854390	−	3.74333i	0.0281837	−	0.123481i	−0.958879	−	0.283815i	$-0.908400\pi$
$919$	0.854390	−	3.74333i	0.0281837	−	0.123481i	0.987063	+	0.160334i	$0.0512571\pi$
$920$	14.5063	+	23.0866i	0.478259	+	0.761144i
$921$	4.07812	−	1.88323i	0.134379	−	0.0620545i
$922$	47.9121	+	23.0733i	1.57790	+	0.759877i
$923$	4.11470	+	8.54427i	0.135437	+	0.281238i
$924$	3.32036	+	4.30472i	0.109232	+	0.141615i
$925$	−14.9043	−	1.67931i	−0.490051	−	0.0552155i
$926$	30.7261	+	10.7515i	1.00972	+	0.353317i
$927$	15.7863	−	30.2362i	0.518489	−	0.993087i
$928$	−28.8917	+	2.50068i	−0.948417	+	0.0820887i
$929$		−	40.7797i		−	1.33794i	−0.743290	−	0.668970i	$-0.766736\pi$
$929$		−	40.7797i		−	1.33794i	0.743290	−	0.668970i	$-0.233264\pi$
$930$	−43.7732	−	28.5030i	−1.43538	−	0.934650i
$931$	0.0458413	−	0.406853i	0.00150239	−	0.0133341i
$932$	−8.83208	+	11.0751i	−0.289304	+	0.362776i
$933$	−33.7687	+	7.13452i	−1.10554	+	0.233574i
$934$	−13.9080	+	28.8803i	−0.455084	+	0.944992i
$935$	5.68075	−	4.53024i	0.185780	−	0.148155i
$936$	−5.52599	+	0.442073i	−0.180623	+	0.0144496i
$937$	−31.6163	−	7.21621i	−1.03286	−	0.235743i	−0.327692	−	0.944785i	$-0.606271\pi$
$937$	−31.6163	−	7.21621i	−1.03286	−	0.235743i	−0.705167	+	0.709041i	$0.749128\pi$
$938$	−52.6737	+	5.93490i	−1.71986	+	0.193781i
$939$	15.0940	−	14.6132i	0.492576	−	0.476883i
$940$	−5.62751	+	5.62751i	−0.183549	+	0.183549i
$941$	−1.18385	−	5.18681i	−0.0385926	−	0.169085i	0.951959	−	0.306225i	$-0.0990661\pi$
$941$	−1.18385	−	5.18681i	−0.0385926	−	0.169085i	−0.990552	+	0.137140i	$0.956209\pi$
$942$	−30.5402	+	2.94134i	−0.995054	+	0.0958341i
$943$	77.3098	−	27.0519i	2.51755	−	0.880931i
$944$	13.8526	−	3.16176i	0.450863	−	0.102907i
$945$	−22.8208	+	1.45436i	−0.742360	+	0.0473103i
$946$	−6.44032	−	4.04672i	−0.209393	−	0.131570i
$947$	5.03475	+	44.6846i	0.163607	+	1.45205i	0.760293	+	0.649580i	$0.225055\pi$
$947$	5.03475	+	44.6846i	0.163607	+	1.45205i	−0.596686	+	0.802475i	$0.703516\pi$
$948$	−1.87990	+	3.74728i	−0.0610564	+	0.121706i
$949$	−1.40559	+	0.883191i	−0.0456274	+	0.0286696i
$950$	−0.979999	−	1.22888i	−0.0317954	−	0.0398701i
$951$	−22.9499	+	27.8416i	−0.744201	+	0.902827i
$952$	12.6087	−	6.07202i	0.408650	−	0.196795i
$953$	−27.9048	−	22.2534i	−0.903926	−	0.720857i	0.0567912	−	0.998386i	$-0.481913\pi$
$953$	−27.9048	−	22.2534i	−0.903926	−	0.720857i	−0.960717	+	0.277529i	$0.910485\pi$
$954$	50.8620	+	34.3037i	1.64672	+	1.11062i
$955$	5.46449	−	15.6166i	0.176827	−	0.505342i
$956$	17.9181			0.579513
$957$	7.41000	−	8.53008i	0.239531	−	0.275738i
$958$	22.2714			0.719555
$959$	4.25145	−	12.1499i	0.137286	−	0.392342i
$960$	−1.73060	−	0.637184i	−0.0558548	−	0.0205650i
$961$	50.0252	+	39.8937i	1.61371	+	1.28689i
$962$	14.0872	−	6.78402i	0.454188	−	0.218725i
$963$	−2.14770	−	2.87960i	−0.0692085	−	0.0927939i
$964$	−10.6629	−	13.3708i	−0.343428	−	0.430645i
$965$	17.8102	−	11.1909i	0.573330	−	0.360247i
$966$	61.7896	+	30.9981i	1.98805	+	0.997348i
$967$	−3.77346	−	33.4904i	−0.121346	−	1.07698i	−0.895834	−	0.444389i	$-0.853421\pi$
$967$	−3.77346	−	33.4904i	−0.121346	−	1.07698i	0.774487	−	0.632589i	$-0.218008\pi$
$968$	13.4603	+	8.45765i	0.432630	+	0.271839i
$969$	1.47465	+	2.43345i	0.0473726	+	0.0781737i
$970$	15.6884	−	3.58077i	0.503724	−	0.114972i
$971$	−16.1225	+	5.64150i	−0.517395	+	0.181044i	−0.576329	−	0.817218i	$-0.695515\pi$
$971$	−16.1225	+	5.64150i	−0.517395	+	0.181044i	0.0589345	+	0.998262i	$0.481230\pi$
$972$	−10.5418	−	12.4027i	−0.338128	−	0.397816i
$973$	−3.32894	−	14.5850i	−0.106721	−	0.467575i
$974$	15.4687	−	15.4687i	0.495650	−	0.495650i
$975$	−2.47580	−	2.55727i	−0.0792890	−	0.0818981i
$976$	−13.2739	+	1.49561i	−0.424888	+	0.0478734i
$977$	−20.1415	−	4.59718i	−0.644385	−	0.147077i	−0.112174	−	0.993689i	$-0.535782\pi$
$977$	−20.1415	−	4.59718i	−0.644385	−	0.147077i	−0.532211	+	0.846612i	$0.678639\pi$
$978$	−3.87619	−	11.6806i	−0.123947	−	0.373505i
$979$	−8.87328	+	7.07620i	−0.283591	+	0.226156i
$980$	−0.677264	+	1.40635i	−0.0216344	+	0.0449243i
$981$	−31.8116	−	1.03013i	−1.01567	−	0.0328895i
$982$	17.8378	−	22.3679i	0.569226	−	0.713787i
$983$	5.02289	−	44.5794i	0.160205	−	1.42186i	−0.614189	−	0.789159i	$-0.710517\pi$
$983$	5.02289	−	44.5794i	0.160205	−	1.42186i	0.774394	−	0.632703i	$-0.218055\pi$
$984$	−14.0034	+	21.5056i	−0.446412	+	0.685573i
$985$		−	7.23315i		−	0.230467i
$986$	19.1631	+	25.3477i	0.610278	+	0.807234i
$987$	4.40077	−	17.9377i	0.140078	−	0.570963i
$988$	0.530501	+	0.185630i	0.0168775	+	0.00590569i
$989$	−32.9670	−	3.71448i	−1.04829	−	0.118114i
$990$	−10.2846	+	4.54881i	−0.326865	+	0.144571i
$991$	10.6671	+	22.1505i	0.338852	+	0.703633i	0.998865	−	0.0476206i	$-0.0151638\pi$
$991$	10.6671	+	22.1505i	0.338852	+	0.703633i	−0.660014	+	0.751254i	$0.729450\pi$
$992$	−47.2858	−	22.7717i	−1.50133	−	0.723001i
$993$	−12.8100	−	27.7400i	−0.406513	−	0.880303i
$994$	19.7133	+	31.3735i	0.625267	+	0.995107i
$995$	4.33053	−	18.9733i	0.137287	−	0.601494i
$996$	−15.9981	−	2.06528i	−0.506920	−	0.0654409i
$997$	−27.1748	+	43.2484i	−0.860634	+	1.36969i	0.0676073	+	0.997712i	$0.478463\pi$
$997$	−27.1748	+	43.2484i	−0.860634	+	1.36969i	−0.928241	+	0.371979i	$0.878679\pi$
$998$	25.2378	+	25.2378i	0.798887	+	0.798887i
$999$	−36.9320	−	20.0494i	−1.16848	−	0.634335i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	87.2.k.a.8.2	✓	96
3.2	odd	2	inner	87.2.k.a.8.7	yes	96
29.11	odd	28	inner	87.2.k.a.11.7	yes	96
87.11	even	28	inner	87.2.k.a.11.2	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.k.a.8.2	✓	96	1.1	even	1	trivial
87.2.k.a.8.7	yes	96	3.2	odd	2	inner
87.2.k.a.11.2	yes	96	87.11	even	28	inner
87.2.k.a.11.7	yes	96	29.11	odd	28	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.k (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.576259 + 1.64685i) q^{2} +(0.598445 - 1.62538i) q^{3} +(-0.816387 - 0.651047i) q^{4} +(1.59790 - 0.769508i) q^{5} +(2.33190 + 1.92219i) q^{6} +(1.54710 + 1.94000i) q^{7} +(-1.41204 + 0.887242i) q^{8} +(-2.28373 - 1.94540i) q^{9} +(0.346463 + 3.07494i) q^{10} +(-1.02572 - 0.644501i) q^{11} +(-1.54676 + 0.937325i) q^{12} +(-1.08029 + 0.246570i) q^{13} +(-4.08643 + 1.42990i) q^{14} +(-0.294489 - 3.05770i) q^{15} +(-1.11217 - 4.87274i) q^{16} +(-2.39140 + 2.39140i) q^{17} +(4.51981 - 2.63991i) q^{18} +(0.482698 - 0.0543871i) q^{19} +(-1.80549 - 0.412091i) q^{20} +(4.07910 - 1.35364i) q^{21} +(1.65248 - 1.31781i) q^{22} +(3.99989 - 8.30586i) q^{23} +(0.597080 + 2.82606i) q^{24} +(-1.15631 + 1.44997i) q^{25} +(0.216464 - 1.92117i) q^{26} +(-4.52870 + 2.54771i) q^{27} -2.59103i q^{28} +(-5.27938 + 1.06215i) q^{29} +(5.20529 + 1.27705i) q^{30} +(-9.19909 - 3.21890i) q^{31} +(5.35125 + 0.602941i) q^{32} +(-1.66139 + 1.28148i) q^{33} +(-2.56022 - 5.31635i) q^{34} +(3.96496 + 1.90942i) q^{35} +(0.597858 + 3.07502i) q^{36} +(4.30274 + 6.84777i) q^{37} +(-0.188592 + 0.826274i) q^{38} +(-0.245726 + 1.90345i) q^{39} +(-1.57355 + 2.50430i) q^{40} +(6.28241 + 6.28241i) q^{41} +(-0.121364 + 7.49772i) q^{42} +(-1.18857 - 3.39673i) q^{43} +(0.417782 + 1.19395i) q^{44} +(-5.14617 - 1.35121i) q^{45} +(11.3736 + 11.3736i) q^{46} +(2.28637 - 3.63873i) q^{47} +(-8.58562 - 1.10836i) q^{48} +(0.187557 - 0.821739i) q^{49} +(-1.72155 - 2.73983i) q^{50} +(2.45581 + 5.31805i) q^{51} +(1.04247 + 0.502026i) q^{52} +(5.08537 + 10.5599i) q^{53} +(-1.58600 - 8.92625i) q^{54} +(-2.13494 - 0.240550i) q^{55} +(-3.90581 - 1.36670i) q^{56} +(0.200469 - 0.817117i) q^{57} +(1.29308 - 9.30643i) q^{58} +2.84288i q^{59} +(-1.75029 + 2.68800i) q^{60} +(0.299240 - 2.65582i) q^{61} +(10.6021 - 13.2946i) q^{62} +(0.240929 - 7.44017i) q^{63} +(0.260480 - 0.540893i) q^{64} +(-1.53646 + 1.22529i) q^{65} +(-1.15302 - 3.47454i) q^{66} +(11.9366 + 2.72445i) q^{67} +(3.50922 - 0.395394i) q^{68} +(-11.1065 - 11.4720i) q^{69} +(-5.42938 + 5.42938i) q^{70} +(-1.90444 - 8.34388i) q^{71} +(4.95075 + 0.720761i) q^{72} +(1.41405 - 0.494798i) q^{73} +(-13.7568 + 3.13989i) q^{74} +(1.66476 + 2.74717i) q^{75} +(-0.429477 - 0.269859i) q^{76} +(-0.336554 - 2.98700i) q^{77} +(-2.99310 - 1.50155i) q^{78} +(1.96273 - 1.23326i) q^{79} +(-5.52674 - 6.93032i) q^{80} +(1.43082 + 8.88554i) q^{81} +(-13.9665 + 6.72591i) q^{82} +(6.97313 + 5.56088i) q^{83} +(-4.21141 - 1.55059i) q^{84} +(-1.98101 + 5.66141i) q^{85} +6.27884 q^{86} +(-1.43302 + 9.21664i) q^{87} +2.02018 q^{88} +(3.09433 - 8.84308i) q^{89} +(5.19077 - 7.69634i) q^{90} +(-2.14967 - 1.71431i) q^{91} +(-8.67297 + 4.17668i) q^{92} +(-10.7371 + 13.0257i) q^{93} +(4.67492 + 5.86216i) q^{94} +(0.729452 - 0.458345i) q^{95} +(4.18244 - 8.33700i) q^{96} +(-0.582251 - 5.16762i) q^{97} +(1.24520 + 0.782413i) q^{98} +(1.08865 + 3.46730i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{3} - 28 q^{4} - 14 q^{6} - 20 q^{7} - 14 q^{9} - 4 q^{10} - 8 q^{12} - 28 q^{13} - 16 q^{15} - 48 q^{16} - 28 q^{18} - 20 q^{19} + 26 q^{21} - 28 q^{22} + 58 q^{24} - 20 q^{25} + 36 q^{27}+ \cdots + 82 q^{99}+O(q^{100}) \) 96 * q - 12 * q^3 - 28 * q^4 - 14 * q^6 - 20 * q^7 - 14 * q^9 - 4 * q^10 - 8 * q^12 - 28 * q^13 - 16 * q^15 - 48 * q^16 - 28 * q^18 - 20 * q^19 + 26 * q^21 - 28 * q^22 + 58 * q^24 - 20 * q^25 + 36 * q^27 + 96 * q^30 - 32 * q^31 + 28 * q^33 - 28 * q^34 + 22 * q^36 - 4 * q^37 - 40 * q^39 - 48 * q^40 - 14 * q^42 - 32 * q^43 + 42 * q^45 + 120 * q^46 - 20 * q^48 + 4 * q^49 - 14 * q^51 + 72 * q^52 - 30 * q^54 + 148 * q^55 + 112 * q^58 + 20 * q^60 + 12 * q^61 - 14 * q^63 + 224 * q^64 - 32 * q^66 + 28 * q^67 + 10 * q^69 + 52 * q^70 - 44 * q^72 + 16 * q^73 - 144 * q^75 - 100 * q^76 - 102 * q^78 - 60 * q^79 - 146 * q^81 - 108 * q^82 - 64 * q^84 - 104 * q^85 - 70 * q^87 - 312 * q^88 - 96 * q^90 - 112 * q^91 - 70 * q^93 + 56 * q^94 - 168 * q^96 + 32 * q^97 + 82 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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