LMFDB - Embedded newform 425.2.p.a.16.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(16,425)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([2, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("425.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.p (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$42$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			16.15
Character	$\chi$	$=$	425.16
Dual form			425.2.p.a.186.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.770053 - 0.559477i) q^{2} +(-1.26213 + 0.410091i) q^{3} +(-0.338066 - 1.04046i) q^{4} +(-1.81036 - 1.31248i) q^{5} +(1.20134 + 0.390341i) q^{6} +2.51296i q^{7} +(-0.910052 + 2.80085i) q^{8} +(-1.00225 + 0.728178i) q^{9} +(0.659768 + 2.02353i) q^{10} +(-1.26877 + 1.74631i) q^{11} +(0.853366 + 1.17456i) q^{12} +(5.78053 - 4.19980i) q^{13} +(1.40594 - 1.93511i) q^{14} +(2.82314 + 0.914113i) q^{15} +(0.497666 - 0.361576i) q^{16} +(1.64216 + 3.78197i) q^{17} +1.17919 q^{18} +(1.85677 - 5.71454i) q^{19} +(-0.753565 + 2.32731i) q^{20} +(-1.03054 - 3.17168i) q^{21} +(1.95404 - 0.634907i) q^{22} +(0.0809312 - 0.111392i) q^{23} -3.90825i q^{24} +(1.55478 + 4.75212i) q^{25} -6.80101 q^{26} +(3.30647 - 4.55097i) q^{27} +(2.61463 - 0.849544i) q^{28} +(3.79420 - 1.23281i) q^{29} +(-1.66255 - 2.28340i) q^{30} +(-6.51159 - 2.11574i) q^{31} +5.30446 q^{32} +(0.885207 - 2.72439i) q^{33} +(0.851378 - 3.83107i) q^{34} +(3.29821 - 4.54935i) q^{35} +(1.09647 + 0.796629i) q^{36} +(4.81775 + 6.63107i) q^{37} +(-4.62696 + 3.36168i) q^{38} +(-5.57349 + 7.67125i) q^{39} +(5.32359 - 3.87611i) q^{40} +(6.05430 + 8.33303i) q^{41} +(-0.980909 + 3.01893i) q^{42} +0.604063 q^{43} +(2.24589 + 0.729735i) q^{44} +(2.77015 - 0.00282484i) q^{45} +(-0.124643 + 0.0404989i) q^{46} +(1.05231 + 3.23867i) q^{47} +(-0.479841 + 0.660444i) q^{48} +0.685051 q^{49} +(1.46144 - 4.52925i) q^{50} +(-3.62357 - 4.09991i) q^{51} +(-6.32392 - 4.59460i) q^{52} +(3.27429 + 10.0772i) q^{53} +(-5.09232 + 1.65460i) q^{54} +(4.58893 - 1.49621i) q^{55} +(-7.03842 - 2.28692i) q^{56} +7.97394i q^{57} +(-3.61147 - 1.17344i) q^{58} +(1.08994 - 0.791889i) q^{59} +(-0.00331049 - 3.24640i) q^{60} +(-0.538047 + 0.740559i) q^{61} +(3.83056 + 5.27232i) q^{62} +(-1.82988 - 2.51861i) q^{63} +(-5.08005 - 3.69087i) q^{64} +(-15.9770 + 0.0162924i) q^{65} +(-2.20589 + 1.60267i) q^{66} +(-2.57036 + 7.91075i) q^{67} +(3.37983 - 2.98715i) q^{68} +(-0.0564648 + 0.173781i) q^{69} +(-5.08505 + 1.65797i) q^{70} +(-1.42420 + 0.462751i) q^{71} +(-1.12742 - 3.46984i) q^{72} +(9.27222 - 12.7621i) q^{73} -7.80170i q^{74} +(-3.91114 - 5.36020i) q^{75} -6.57345 q^{76} +(-4.38841 - 3.18836i) q^{77} +(8.58377 - 2.78904i) q^{78} +(-7.78321 + 2.52892i) q^{79} +(-1.37551 + 0.00140267i) q^{80} +(-1.15841 + 3.56522i) q^{81} -9.80411i q^{82} +(-1.25500 + 3.86248i) q^{83} +(-2.95161 + 2.14447i) q^{84} +(1.99089 - 9.00202i) q^{85} +(-0.465161 - 0.337959i) q^{86} +(-4.28322 + 3.11194i) q^{87} +(-3.73652 - 5.14288i) q^{88} +(2.16798 + 1.57513i) q^{89} +(-2.13475 - 1.54766i) q^{90} +(10.5539 + 14.5262i) q^{91} +(-0.143259 - 0.0465477i) q^{92} +9.08613 q^{93} +(1.00163 - 3.08269i) q^{94} +(-10.8616 + 7.90838i) q^{95} +(-6.69492 + 2.17531i) q^{96} +(-1.80336 + 0.585948i) q^{97} +(-0.527526 - 0.383270i) q^{98} -2.67413i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 8 q^{2} - 44 q^{4} - 4 q^{8} + 28 q^{9} - 18 q^{13} - 10 q^{15} - 28 q^{16} + 2 q^{17} - 60 q^{18} - 8 q^{19} + 32 q^{21} + 6 q^{25} + 52 q^{26} - 54 q^{30} + 44 q^{32} - 24 q^{33} + 26 q^{35} + 34 q^{36}+ \cdots - 36 q^{98}+O(q^{100}) $ 168 * q - 8 * q^2 - 44 * q^4 - 4 * q^8 + 28 * q^9 - 18 * q^13 - 10 * q^15 - 28 * q^16 + 2 * q^17 - 60 * q^18 - 8 * q^19 + 32 * q^21 + 6 * q^25 + 52 * q^26 - 54 * q^30 + 44 * q^32 - 24 * q^33 + 26 * q^35 + 34 * q^36 - 18 * q^38 + 80 * q^42 - 8 * q^43 - 40 * q^47 - 84 * q^49 - 82 * q^50 - 36 * q^51 - 30 * q^52 - 42 * q^53 - 18 * q^55 - 18 * q^59 + 28 * q^60 - 16 * q^64 - 140 * q^66 - 62 * q^67 + 144 * q^68 + 44 * q^69 + 4 * q^70 - 6 * q^72 + 72 * q^76 + 48 * q^77 - 28 * q^81 - 14 * q^83 + 24 * q^84 + 62 * q^85 + 82 * q^86 + 48 * q^87 + 90 * q^89 - 224 * q^93 + 26 * q^94 - 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$-1$

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 $

$2$	−0.770053	−	0.559477i	−0.544510	−	0.395610i	0.281247	−	0.959635i	$-0.409252\pi$
$2$	−0.770053	−	0.559477i	−0.544510	−	0.395610i	−0.825757	+	0.564026i	$0.809252\pi$
$3$	−1.26213	+	0.410091i	−0.728692	+	0.236766i	−0.649787	−	0.760116i	$-0.725142\pi$
$3$	−1.26213	+	0.410091i	−0.728692	+	0.236766i	−0.0789042	+	0.996882i	$0.525142\pi$
$4$	−0.338066	−	1.04046i	−0.169033	−	0.520230i
$5$	−1.81036	−	1.31248i	−0.809616	−	0.586960i
$5$	−1.81036	−	1.31248i	−0.809616	−	0.586960i
$6$	1.20134	+	0.390341i	0.490447	+	0.159356i
$7$			2.51296i			0.949808i	0.880038	+	0.474904i	$0.157517\pi$
$7$			2.51296i			0.949808i	−0.880038	+	0.474904i	$0.842483\pi$
$8$	−0.910052	+	2.80085i	−0.321752	+	0.990251i
$9$	−1.00225	+	0.728178i	−0.334084	+	0.242726i
$10$	0.659768	+	2.02353i	0.208637	+	0.639898i
$11$	−1.26877	+	1.74631i	−0.382549	+	0.526533i	−0.956257	−	0.292526i	$-0.905504\pi$
$11$	−1.26877	+	1.74631i	−0.382549	+	0.526533i	0.573709	+	0.819059i	$0.305504\pi$
$12$	0.853366	+	1.17456i	0.246346	+	0.339066i
$13$	5.78053	−	4.19980i	1.60323	−	1.16482i	0.722291	−	0.691589i	$-0.243089\pi$
$13$	5.78053	−	4.19980i	1.60323	−	1.16482i	0.880941	−	0.473227i	$-0.156911\pi$
$14$	1.40594	−	1.93511i	0.375753	−	0.517180i
$15$	2.82314	+	0.914113i	0.728933	+	0.236023i
$16$	0.497666	−	0.361576i	0.124417	−	0.0903939i
$17$	1.64216	+	3.78197i	0.398281	+	0.917263i
$17$	1.64216	+	3.78197i	0.398281	+	0.917263i
$18$	1.17919			0.277937
$19$	1.85677	−	5.71454i	0.425971	−	1.31101i	−0.476090	−	0.879397i	$-0.657946\pi$
$19$	1.85677	−	5.71454i	0.425971	−	1.31101i	0.902061	−	0.431608i	$-0.142054\pi$
$20$	−0.753565	+	2.32731i	−0.168502	+	0.520402i
$21$	−1.03054	−	3.17168i	−0.224883	−	0.692117i
$22$	1.95404	−	0.634907i	0.416603	−	0.135363i
$23$	0.0809312	−	0.111392i	0.0168753	−	0.0232269i	−0.800496	−	0.599338i	$-0.795431\pi$
$23$	0.0809312	−	0.111392i	0.0168753	−	0.0232269i	0.817371	+	0.576111i	$0.195431\pi$
$24$		−	3.90825i		−	0.797768i
$25$	1.55478	+	4.75212i	0.310956	+	0.950424i
$26$	−6.80101			−1.33379
$27$	3.30647	−	4.55097i	0.636331	−	0.875834i
$28$	2.61463	−	0.849544i	0.494118	−	0.160549i
$29$	3.79420	−	1.23281i	0.704566	−	0.228927i	0.0652471	−	0.997869i	$-0.479216\pi$
$29$	3.79420	−	1.23281i	0.704566	−	0.228927i	0.639319	+	0.768942i	$0.279216\pi$
$30$	−1.66255	−	2.28340i	−0.303538	−	0.416890i
$31$	−6.51159	−	2.11574i	−1.16952	−	0.379999i	−0.341054	−	0.940044i	$-0.610784\pi$
$31$	−6.51159	−	2.11574i	−1.16952	−	0.379999i	−0.828462	+	0.560045i	$0.810784\pi$
$32$	5.30446			0.937705
$33$	0.885207	−	2.72439i	0.154095	−	0.474255i
$34$	0.851378	−	3.83107i	0.146010	−	0.657023i
$35$	3.29821	−	4.54935i	0.557499	−	0.768980i
$36$	1.09647	+	0.796629i	0.182744	+	0.132772i
$37$	4.81775	+	6.63107i	0.792033	+	1.09014i	0.993852	+	0.110718i	$0.0353149\pi$
$37$	4.81775	+	6.63107i	0.792033	+	1.09014i	−0.201818	+	0.979423i	$0.564685\pi$
$38$	−4.62696	+	3.36168i	−0.750592	+	0.545337i
$39$	−5.57349	+	7.67125i	−0.892472	+	1.22838i
$40$	5.32359	−	3.87611i	0.841733	−	0.612868i
$41$	6.05430	+	8.33303i	0.945523	+	1.30140i	0.953488	+	0.301432i	$0.0974646\pi$
$41$	6.05430	+	8.33303i	0.945523	+	1.30140i	−0.00796516	+	0.999968i	$0.502535\pi$
$42$	−0.980909	+	3.01893i	−0.151358	+	0.465831i
$43$	0.604063			0.0921187			0.0460593	−	0.998939i	$-0.485334\pi$
$43$	0.604063			0.0921187			0.0460593	+	0.998939i	$0.485334\pi$
$44$	2.24589	+	0.729735i	0.338581	+	0.110012i
$45$	2.77015	−	0.00282484i	0.412950	−	0.000421103i
$46$	−0.124643	+	0.0404989i	−0.0183776	+	0.00597123i
$47$	1.05231	+	3.23867i	0.153495	+	0.472408i	0.998005	−	0.0631307i	$-0.0201085\pi$
$47$	1.05231	+	3.23867i	0.153495	+	0.472408i	−0.844511	+	0.535539i	$0.820108\pi$
$48$	−0.479841	+	0.660444i	−0.0692591	+	0.0953269i
$49$	0.685051			0.0978644
$50$	1.46144	−	4.52925i	0.206678	−	0.640533i
$51$	−3.62357	−	4.09991i	−0.507401	−	0.574103i
$52$	−6.32392	−	4.59460i	−0.876971	−	0.637156i
$53$	3.27429	+	10.0772i	0.449758	+	1.38421i	0.877180	+	0.480162i	$0.159422\pi$
$53$	3.27429	+	10.0772i	0.449758	+	1.38421i	−0.427422	+	0.904052i	$0.640578\pi$
$54$	−5.09232	+	1.65460i	−0.692977	+	0.225162i
$55$	4.58893	−	1.49621i	0.618771	−	0.201749i
$56$	−7.03842	−	2.28692i	−0.940549	−	0.305603i
$57$			7.97394i			1.05617i
$58$	−3.61147	−	1.17344i	−0.474209	−	0.154080i
$59$	1.08994	−	0.791889i	0.141898	−	0.103095i	−0.514571	−	0.857448i	$-0.672049\pi$
$59$	1.08994	−	0.791889i	0.141898	−	0.103095i	0.656470	+	0.754352i	$0.272049\pi$
$60$	−0.00331049	−	3.24640i	−0.000427382	−	0.419108i
$61$	−0.538047	+	0.740559i	−0.0688899	+	0.0948188i	−0.842072	−	0.539366i	$-0.818664\pi$
$61$	−0.538047	+	0.740559i	−0.0688899	+	0.0948188i	0.773182	+	0.634185i	$0.218664\pi$
$62$	3.83056	+	5.27232i	0.486482	+	0.669585i
$63$	−1.82988	−	2.51861i	−0.230543	−	0.317315i
$64$	−5.08005	−	3.69087i	−0.635006	−	0.461359i
$65$	−15.9770	+	0.0162924i	−1.98170	+	0.00202083i
$66$	−2.20589	+	1.60267i	−0.271526	+	0.197275i
$67$	−2.57036	+	7.91075i	−0.314019	+	0.966452i	0.662137	+	0.749383i	$0.269650\pi$
$67$	−2.57036	+	7.91075i	−0.314019	+	0.966452i	−0.976156	+	0.217069i	$0.930350\pi$
$68$	3.37983	−	2.98715i	0.409865	−	0.362245i
$69$	−0.0564648	+	0.173781i	−0.00679756	+	0.0209207i
$70$	−5.08505	+	1.65797i	−0.607780	+	0.198165i
$71$	−1.42420	+	0.462751i	−0.169022	+	0.0549185i	−0.392305	−	0.919835i	$-0.628322\pi$
$71$	−1.42420	+	0.462751i	−0.169022	+	0.0549185i	0.223284	+	0.974753i	$0.428322\pi$
$72$	−1.12742	−	3.46984i	−0.132868	−	0.408924i
$73$	9.27222	−	12.7621i	1.08523	−	1.49369i	0.231604	−	0.972810i	$-0.425603\pi$
$73$	9.27222	−	12.7621i	1.08523	−	1.49369i	0.853628	−	0.520883i	$-0.174397\pi$
$74$		−	7.80170i		−	0.906929i
$75$	−3.91114	−	5.36020i	−0.451619	−	0.618942i
$76$	−6.57345			−0.754027
$77$	−4.38841	−	3.18836i	−0.500105	−	0.363348i
$78$	8.58377	−	2.78904i	0.971920	−	0.315796i
$79$	−7.78321	+	2.52892i	−0.875679	+	0.284525i	−0.712162	−	0.702015i	$-0.752284\pi$
$79$	−7.78321	+	2.52892i	−0.875679	+	0.284525i	−0.163517	+	0.986541i	$0.552284\pi$
$80$	−1.37551	+	0.00140267i	−0.153787	+	0.000156823i
$81$	−1.15841	+	3.56522i	−0.128712	+	0.396136i
$82$		−	9.80411i		−	1.08268i
$83$	−1.25500	+	3.86248i	−0.137754	+	0.423963i	−0.996008	−	0.0892619i	$-0.971549\pi$
$83$	−1.25500	+	3.86248i	−0.137754	+	0.423963i	0.858254	+	0.513225i	$0.171549\pi$
$84$	−2.95161	+	2.14447i	−0.322047	+	0.233981i
$85$	1.99089	−	9.00202i	0.215942	−	0.976406i
$86$	−0.465161	−	0.337959i	−0.0501595	−	0.0364430i
$87$	−4.28322	+	3.11194i	−0.459209	+	0.333635i
$88$	−3.73652	−	5.14288i	−0.398314	−	0.548232i
$89$	2.16798	+	1.57513i	0.229806	+	0.166964i	0.696729	−	0.717334i	$-0.254638\pi$
$89$	2.16798	+	1.57513i	0.229806	+	0.166964i	−0.466924	+	0.884297i	$0.654638\pi$
$90$	−2.13475	−	1.54766i	−0.225022	−	0.163138i
$91$	10.5539	+	14.5262i	1.10635	+	1.52276i
$92$	−0.143259	−	0.0465477i	−0.0149358	−	0.00485294i
$93$	9.08613			0.942188
$94$	1.00163	−	3.08269i	0.103310	−	0.317955i
$95$	−10.8616	+	7.90838i	−1.11438	+	0.811382i
$96$	−6.69492	+	2.17531i	−0.683298	+	0.222017i
$97$	−1.80336	+	0.585948i	−0.183104	+	0.0594940i	−0.399134	−	0.916893i	$-0.630689\pi$
$97$	−1.80336	+	0.585948i	−0.183104	+	0.0594940i	0.216030	+	0.976387i	$0.430689\pi$
$98$	−0.527526	−	0.383270i	−0.0532882	−	0.0387161i
$99$		−	2.67413i		−	0.268761i
$100$	4.41877	−	3.22421i	0.441877	−	0.322421i
$101$	0.0934667			0.00930028			0.00465014	−	0.999989i	$-0.498520\pi$
$101$	0.0934667			0.00930028			0.00465014	+	0.999989i	$0.498520\pi$
$102$	0.496537	+	5.18445i	0.0491645	+	0.513337i
$103$	4.14839	+	12.7674i	0.408753	+	1.25801i	0.917720	+	0.397227i	$0.130027\pi$
$103$	4.14839	+	12.7674i	0.408753	+	1.25801i	−0.508967	+	0.860786i	$0.669973\pi$
$104$	6.50245	+	20.0125i	0.637617	+	1.96238i
$105$	−2.29713	+	7.09444i	−0.224177	+	0.692346i
$106$	3.11660	−	9.59189i	0.302710	−	0.931647i
$107$		−	12.2869i		−	1.18782i	−0.804531	−	0.593910i	$-0.797583\pi$
$107$		−	12.2869i		−	1.18782i	0.804531	−	0.593910i	$-0.202417\pi$
$108$	−5.85290	−	1.90172i	−0.563196	−	0.182993i
$109$	0.509074	+	0.700680i	0.0487604	+	0.0671130i	0.832701	−	0.553723i	$-0.186793\pi$
$109$	0.509074	+	0.700680i	0.0487604	+	0.0671130i	−0.783941	+	0.620836i	$0.786793\pi$
$110$	−4.37082	−	1.41524i	−0.416741	−	0.134938i
$111$	−8.79998	−	6.39356i	−0.835257	−	0.606850i
$112$	0.908624	+	1.25061i	0.0858569	+	0.118172i
$113$	−6.34055	−	8.72702i	−0.596469	−	0.820969i	0.398910	−	0.916990i	$-0.369389\pi$
$113$	−6.34055	−	8.72702i	−0.596469	−	0.820969i	−0.995379	+	0.0960206i	$0.969389\pi$
$114$	4.46123	−	6.14036i	0.417833	−	0.575097i
$115$	−0.292715	+	0.0954389i	−0.0272958	+	0.00889972i
$116$	−2.56538	−	3.53094i	−0.238190	−	0.327840i
$117$	−2.73534	+	8.41852i	−0.252882	+	0.778292i
$118$	−1.28236			−0.118051
$119$	−9.50393	+	4.12667i	−0.871224	+	0.378291i
$120$	−5.12951	+	7.07532i	−0.468258	+	0.645886i
$121$	1.95936	+	6.03028i	0.178123	+	0.548207i
$122$	0.828650	−	0.269245i	0.0750225	−	0.0243763i
$123$	−11.0586	−	8.03456i	−0.997122	−	0.724452i
$124$			7.49031i			0.672649i
$125$	3.42237	−	10.6437i	0.306106	−	0.951997i
$126$			2.96324i			0.263987i
$127$	8.98177	+	6.52563i	0.797003	+	0.579056i	0.910033	−	0.414535i	$-0.136056\pi$
$127$	8.98177	+	6.52563i	0.797003	+	0.579056i	−0.113031	+	0.993592i	$0.536056\pi$
$128$	−1.43138	−	4.40534i	−0.126518	−	0.389381i
$129$	−0.762406	+	0.247721i	−0.0671261	+	0.0218106i
$130$	12.3123	+	8.92621i	1.07986	+	0.782880i
$131$	−2.71064	−	0.880740i	−0.236830	−	0.0769506i	0.188198	−	0.982131i	$-0.439735\pi$
$131$	−2.71064	−	0.880740i	−0.236830	−	0.0769506i	−0.425027	+	0.905181i	$0.639735\pi$
$132$	−3.13387			−0.272769
$133$	14.3604	+	4.66597i	1.24520	+	0.404591i
$134$	6.40519	−	4.65364i	0.553324	−	0.402014i
$135$	−11.9590	+	3.89919i	−1.02926	+	0.335589i
$136$	−12.0872	+	1.15764i	−1.03647	+	0.0992670i
$137$	−5.95202	+	4.32439i	−0.508515	+	0.369458i	−0.812260	−	0.583295i	$-0.801763\pi$
$137$	−5.95202	+	4.32439i	−0.508515	+	0.369458i	0.303745	+	0.952753i	$0.401763\pi$
$138$	0.140707	−	0.102230i	0.0119778	−	0.00870238i
$139$	8.50885	−	11.7114i	0.721711	−	0.993350i	−0.277754	−	0.960652i	$-0.589590\pi$
$139$	8.50885	−	11.7114i	0.721711	−	0.993350i	0.999465	−	0.0326981i	$-0.0104100\pi$
$140$	−5.84842	−	1.89368i	−0.494282	−	0.160045i
$141$	−2.65630	−	3.65608i	−0.223701	−	0.307898i
$142$	1.35561	+	0.440464i	0.113760	+	0.0369629i
$143$			15.4232i			1.28975i
$144$	−0.235495	+	0.724779i	−0.0196246	+	0.0603983i
$145$	−8.48690	−	2.74800i	−0.704799	−	0.228209i
$146$	−14.2802	+	4.63992i	−1.18184	+	0.384003i
$147$	−0.864624	+	0.280933i	−0.0713130	+	0.0231710i
$148$	5.27064	−	7.25441i	0.433244	−	0.596309i
$149$	6.61368			0.541814			0.270907	−	0.962606i	$-0.412676\pi$
$149$	6.61368			0.541814			0.270907	+	0.962606i	$0.412676\pi$
$150$	0.0128811	+	6.31583i	0.00105173	+	0.515685i
$151$	14.4165			1.17320			0.586599	−	0.809877i	$-0.300466\pi$
$151$	14.4165			1.17320			0.586599	+	0.809877i	$0.300466\pi$
$152$	14.3158	+	10.4011i	1.16117	+	0.843637i
$153$	−4.39980	−	2.59471i	−0.355703	−	0.209770i
$154$	1.59549	+	4.91042i	0.128568	+	0.395693i
$155$	9.01142	+	12.3766i	0.723815	+	0.994112i
$156$	9.86583	+	3.20560i	0.789898	+	0.256654i
$157$	−16.6332			−1.32747			−0.663736	−	0.747967i	$-0.731030\pi$
$157$	−16.6332			−1.32747			−0.663736	+	0.747967i	$0.731030\pi$
$158$	7.40835	+	2.40712i	0.589377	+	0.191500i
$159$	−8.26517	−	11.3760i	−0.655470	−	0.902178i
$160$	−9.60296	−	6.96201i	−0.759181	−	0.550395i
$161$	0.279924	+	0.203377i	0.0220611	+	0.0160283i
$162$	2.88670	−	2.09731i	0.226800	−	0.164780i
$163$	13.3428	+	18.3647i	1.04509	+	1.43844i	0.892992	+	0.450072i	$0.148602\pi$
$163$	13.3428	+	18.3647i	1.04509	+	1.43844i	0.152094	+	0.988366i	$0.451398\pi$
$164$	6.62342	−	9.11636i	0.517203	−	0.711868i
$165$	−5.17825	+	3.77029i	−0.403126	+	0.293517i
$166$	3.12738	−	2.27218i	0.242732	−	0.176355i
$167$	13.3888	+	4.35029i	1.03606	+	0.336636i	0.777183	−	0.629275i	$-0.216648\pi$
$167$	13.3888	+	4.35029i	1.03606	+	0.336636i	0.258875	+	0.965911i	$0.416648\pi$
$168$	9.82126			0.757726
$169$	11.7590	−	36.1905i	0.904538	−	2.78388i
$170$	−6.56951	+	5.81818i	−0.503858	+	0.446234i
$171$	2.30026	+	7.07946i	0.175905	+	0.541380i
$172$	−0.204213	−	0.628503i	−0.0155711	−	0.0479229i
$173$	−4.06743	+	5.59833i	−0.309241	+	0.425633i	−0.935144	−	0.354267i	$-0.884730\pi$
$173$	−4.06743	+	5.59833i	−0.309241	+	0.425633i	0.625903	+	0.779901i	$0.284730\pi$
$174$	5.03936			0.382033
$175$	−11.9419	+	3.90709i	−0.902721	+	0.295349i
$176$			1.32784i			0.100089i
$177$	−1.05090	+	1.44644i	−0.0789907	+	0.108721i
$178$	−0.788213	−	2.42587i	−0.0590790	−	0.181827i
$179$	−4.02072	−	12.3745i	−0.300523	−	0.924913i	−0.981310	−	0.192433i	$-0.938362\pi$
$179$	−4.02072	−	12.3745i	−0.300523	−	0.924913i	0.680788	−	0.732481i	$-0.261638\pi$
$180$	−0.939433	−	2.88128i	−0.0700212	−	0.214758i
$181$	12.1261	+	3.94001i	0.901327	+	0.292859i	0.722785	−	0.691073i	$-0.242862\pi$
$181$	12.1261	+	3.94001i	0.901327	+	0.292859i	0.178542	+	0.983932i	$0.442862\pi$
$182$		−	17.0906i		−	1.26684i
$183$	0.375390	−	1.15533i	0.0277496	−	0.0854045i
$184$	0.238342	+	0.328049i	0.0175708	+	0.0241841i
$185$	−0.0186896	−	18.3278i	−0.00137409	−	1.34749i
$186$	−6.99681	−	5.08348i	−0.513031	−	0.372739i
$187$	−8.68803	−	1.93074i	−0.635331	−	0.141190i
$188$	3.01395	−	2.18977i	0.219815	−	0.159705i
$189$	11.4364	+	8.30902i	0.831875	+	0.604392i
$190$	12.7886	−	0.0130411i	0.927782	−	0.000946099i
$191$	5.62584	−	4.08741i	0.407071	−	0.295755i	−0.365344	−	0.930873i	$-0.619049\pi$
$191$	5.62584	−	4.08741i	0.407071	−	0.295755i	0.772415	+	0.635118i	$0.219049\pi$
$192$	7.92528	+	2.57508i	0.571958	+	0.185840i
$193$		−	7.20765i		−	0.518818i	−0.965768	−	0.259409i	$-0.916472\pi$
$193$		−	7.20765i		−	0.518818i	0.965768	−	0.259409i	$-0.0835278\pi$
$194$	1.71651	+	0.557728i	0.123238	+	0.0400425i
$195$	20.1584	−	6.57259i	1.44357	−	0.470673i
$196$	−0.231592	−	0.712768i	−0.0165423	−	0.0509120i
$197$	−16.5090	+	5.36409i	−1.17622	+	0.382176i	−0.830960	−	0.556333i	$-0.812208\pi$
$197$	−16.5090	+	5.36409i	−1.17622	+	0.382176i	−0.345256	+	0.938508i	$0.612208\pi$
$198$	−1.49612	+	2.05923i	−0.106324	+	0.146343i
$199$		−	4.36512i		−	0.309435i	−0.987959	−	0.154718i	$-0.950553\pi$
$199$		−	4.36512i		−	0.309435i	0.987959	−	0.154718i	$-0.0494467\pi$
$200$	−14.7249	+	0.0300313i	−1.04121	+	0.00212353i
$201$		−	11.0385i		−	0.778594i
$202$	−0.0719744	−	0.0522924i	−0.00506410	−	0.00367928i
$203$	3.09800	+	9.53467i	0.217437	+	0.669202i
$204$	−3.04079	+	5.15622i	−0.212898	+	0.361007i
$205$	−0.0234866	−	23.0319i	−0.00164038	−	1.60862i
$206$	3.94860	−	12.1525i	0.275112	−	0.846707i
$207$			0.170575i			0.0118558i
$208$	1.35823	−	4.18020i	0.0941763	−	0.289845i
$209$	7.62356	+	10.4929i	0.527333	+	0.725811i
$210$	5.73808	−	4.17791i	0.395965	−	0.288303i
$211$	5.83301	−	8.02845i	0.401561	−	0.552702i	−0.559574	−	0.828781i	$-0.689035\pi$
$211$	5.83301	−	8.02845i	0.401561	−	0.552702i	0.961135	+	0.276079i	$0.0890351\pi$
$212$	9.37802	−	6.81353i	0.644085	−	0.467955i
$213$	1.60776	−	1.16811i	0.110162	−	0.0800373i
$214$	−6.87424	+	9.46158i	−0.469913	+	0.646780i
$215$	−1.09357	−	0.792822i	−0.0745808	−	0.0540700i
$216$	9.73753	+	13.4026i	0.662555	+	0.911929i
$217$	5.31677	−	16.3633i	0.360926	−	1.11082i
$218$		−	0.824376i		−	0.0558338i
$219$	−6.46913	+	19.9099i	−0.437143	+	1.34539i
$220$	−3.10811	−	4.26878i	−0.209548	−	0.287801i
$221$	25.3761	+	14.9651i	1.70698	+	1.00666i
$222$	3.19941	+	9.84676i	0.214730	+	0.660871i
$223$	−4.11054	−	2.98648i	−0.275262	−	0.199990i	0.441586	−	0.897219i	$-0.354416\pi$
$223$	−4.11054	−	2.98648i	−0.275262	−	0.199990i	−0.716848	+	0.697229i	$0.754416\pi$
$224$			13.3299i			0.890640i
$225$	−5.01867	−	3.63066i	−0.334578	−	0.242044i
$226$			10.2677i			0.682995i
$227$	−16.1269	+	22.1968i	−1.07038	+	1.47326i	−0.200694	+	0.979654i	$0.564320\pi$
$227$	−16.1269	+	22.1968i	−1.07038	+	1.47326i	−0.869688	+	0.493601i	$0.835680\pi$
$228$	8.29656	−	2.69572i	0.549453	−	0.178528i
$229$	2.05713	+	6.33120i	0.135939	+	0.418378i	0.995735	−	0.0922603i	$-0.0294092\pi$
$229$	2.05713	+	6.33120i	0.135939	+	0.418378i	−0.859796	+	0.510638i	$0.829409\pi$
$230$	0.278802	+	0.0902740i	0.0183836	+	0.00595249i
$231$	6.84627	+	2.22449i	0.450451	+	0.146360i
$232$			11.7489i			0.771355i
$233$	−3.20904	−	1.04268i	−0.210231	−	0.0683082i	0.202008	−	0.979384i	$-0.435253\pi$
$233$	−3.20904	−	1.04268i	−0.210231	−	0.0683082i	−0.412239	+	0.911076i	$0.635253\pi$
$234$	6.81632	−	4.95235i	0.445597	−	0.323745i
$235$	2.34564	−	7.24428i	0.153013	−	0.472565i
$236$	−1.19240	−	0.866330i	−0.0776187	−	0.0563933i
$237$	8.78634	−	6.38365i	0.570734	−	0.414663i
$238$	9.62731	+	2.13948i	0.624046	+	0.138682i
$239$	−23.6467	−	17.1804i	−1.52958	−	1.11131i	−0.956471	−	0.291826i	$-0.905737\pi$
$239$	−23.6467	−	17.1804i	−1.52958	−	1.11131i	−0.573109	−	0.819479i	$-0.694263\pi$
$240$	1.73550	−	0.565857i	0.112026	−	0.0365259i
$241$	5.37181	+	7.39367i	0.346029	+	0.476268i	0.946190	−	0.323611i	$-0.104897\pi$
$241$	5.37181	+	7.39367i	0.346029	+	0.476268i	−0.600161	+	0.799879i	$0.704897\pi$
$242$	1.86499	−	5.73985i	0.119886	−	0.368972i
$243$			11.9011i			0.763455i
$244$	0.952416	+	0.309459i	0.0609722	+	0.0198111i
$245$	−1.24019	−	0.899118i	−0.0792326	−	0.0574425i
$246$	4.02058	+	12.3741i	0.256343	+	0.788942i
$247$	−13.2668	−	40.8311i	−0.844149	−	2.59802i
$248$	11.8518	−	16.3126i	0.752589	−	1.03585i
$249$		−	5.38962i		−	0.341553i
$250$	−8.59028	+	6.28145i	−0.543297	+	0.397274i
$251$	−9.36721			−0.591253			−0.295627	−	0.955304i	$-0.595528\pi$
$251$	−9.36721			−0.591253			−0.295627	+	0.955304i	$0.595528\pi$
$252$	−2.00189	+	2.75537i	−0.126108	+	0.173572i
$253$	0.0918426	+	0.282662i	0.00577409	+	0.0177708i
$254$	−3.26550	−	10.0502i	−0.204896	−	0.630604i
$255$	1.17889	+	12.1782i	0.0738249	+	0.762627i
$256$	−5.24326	+	16.1371i	−0.327704	+	1.00857i
$257$	12.4725			0.778010			0.389005	−	0.921236i	$-0.372819\pi$
$257$	12.4725			0.778010			0.389005	+	0.921236i	$0.372819\pi$
$258$	0.725688	+	0.235790i	0.0451793	+	0.0146797i
$259$	−16.6636	+	12.1068i	−1.03542	+	0.752280i
$260$	5.41823	+	16.6179i	0.336024	+	1.03060i
$261$	−2.90504	+	3.99844i	−0.179817	+	0.247497i
$262$	1.59458	+	2.19476i	0.0985137	+	0.135592i
$263$	−10.3401	+	7.51250i	−0.637596	+	0.463241i	−0.859023	−	0.511936i	$-0.828928\pi$
$263$	−10.3401	+	7.51250i	−0.637596	+	0.463241i	0.221427	+	0.975177i	$0.428928\pi$
$264$	6.82502	+	4.95867i	0.420051	+	0.305185i
$265$	7.29855	−	22.5408i	0.448347	−	1.38467i
$266$	−8.44776	−	11.6273i	−0.517966	−	0.712918i
$267$	−3.38222	−	1.09895i	−0.206989	−	0.0672547i
$268$	9.09976			0.555856
$269$	14.2951	+	4.64475i	0.871585	+	0.283195i	0.710459	−	0.703739i	$-0.248487\pi$
$269$	14.2951	+	4.64475i	0.871585	+	0.283195i	0.161126	+	0.986934i	$0.448487\pi$
$270$	11.3905	+	3.68817i	0.693206	+	0.224455i
$271$	3.29182	+	10.1312i	0.199964	+	0.615426i	0.999883	+	0.0153173i	$0.00487585\pi$
$271$	3.29182	+	10.1312i	0.199964	+	0.615426i	−0.799919	+	0.600108i	$0.795124\pi$
$272$	2.18471	+	1.28840i	0.132468	+	0.0781205i
$273$	−19.2775	−	14.0059i	−1.16673	−	0.847678i
$274$	7.00277			0.423053
$275$	−10.2713	−	3.31422i	−0.619386	−	0.199855i
$276$	0.199901			0.0120326
$277$	12.5967	−	17.3378i	0.756860	−	1.04173i	−0.240609	−	0.970622i	$-0.577347\pi$
$277$	12.5967	−	17.3378i	0.756860	−	1.04173i	0.997469	−	0.0711057i	$-0.0226528\pi$
$278$	−13.1045	+	4.25792i	−0.785958	+	0.255373i
$279$	8.06689	−	2.62109i	0.482952	−	0.156921i
$280$	9.74051	+	13.3779i	0.582107	+	0.799485i
$281$	5.72674	−	17.6251i	0.341629	−	1.05143i	−0.621735	−	0.783228i	$-0.713572\pi$
$281$	5.72674	−	17.6251i	0.341629	−	1.05143i	0.963364	−	0.268198i	$-0.0864281\pi$
$282$			4.30152i			0.256152i
$283$	−18.4865	−	6.00663i	−1.09891	−	0.357057i	−0.297226	−	0.954807i	$-0.596061\pi$
$283$	−18.4865	−	6.00663i	−1.09891	−	0.357057i	−0.801682	+	0.597750i	$0.796061\pi$
$284$	0.962947	+	1.32538i	0.0571404	+	0.0786470i
$285$	10.4657	−	14.4357i	0.619932	−	0.855095i
$286$	8.62892	−	11.8767i	0.510239	−	0.702284i
$287$	−20.9405	+	15.2142i	−1.23608	+	0.898065i
$288$	−5.31640	+	3.86259i	−0.313272	+	0.227605i
$289$	−11.6067	+	12.4212i	−0.682744	+	0.730658i
$290$	4.99793	+	6.86433i	0.293489	+	0.403087i
$291$	2.03579	−	1.47909i	0.119340	−	0.0867056i
$292$	−16.4131	−	5.33294i	−0.960503	−	0.312086i
$293$	−5.47783			−0.320018			−0.160009	−	0.987116i	$-0.551152\pi$
$293$	−5.47783			−0.320018			−0.160009	+	0.987116i	$0.551152\pi$
$294$	0.822983	+	0.267403i	0.0479973	+	0.0155953i
$295$	−3.01252	+	0.00307200i	−0.175396	+	0.000178859i
$296$	−22.9571	+	7.45920i	−1.33435	+	0.433557i
$297$	3.75226	+	11.5483i	0.217728	+	0.670099i
$298$	−5.09289	−	3.70020i	−0.295023	−	0.214347i
$299$		−	0.983802i		−	0.0568947i
$300$	−4.25485	+	5.88148i	−0.245654	+	0.339567i
$301$			1.51798i			0.0874951i
$302$	−11.1015	−	8.06570i	−0.638819	−	0.464129i
$303$	−0.117967	+	0.0383299i	−0.00677704	+	0.00220199i
$304$	−1.14219	−	3.51529i	−0.0655090	−	0.201616i
$305$	1.94603	−	0.634497i	0.111429	−	0.0363312i
$306$	1.93641	+	4.45965i	0.110697	+	0.254941i
$307$	21.8747			1.24846			0.624228	−	0.781243i	$-0.285414\pi$
$307$	21.8747			1.24846			0.624228	+	0.781243i	$0.285414\pi$
$308$	−1.83379	+	5.64384i	−0.104490	+	0.321587i
$309$	−10.4716	−	14.4130i	−0.595710	−	0.819924i
$310$	−0.0148600	−	14.5723i	−0.000843992	−	0.827652i
$311$	10.7423	−	14.7855i	0.609140	−	0.838409i	−0.387367	−	0.921926i	$-0.626615\pi$
$311$	10.7423	−	14.7855i	0.609140	−	0.838409i	0.996506	+	0.0835169i	$0.0266153\pi$
$312$	−16.4139	−	22.5918i	−0.929253	−	1.27901i
$313$	2.28104	+	3.13959i	0.128932	+	0.177460i	0.868603	−	0.495509i	$-0.165019\pi$
$313$	2.28104	+	3.13959i	0.128932	+	0.177460i	−0.739670	+	0.672969i	$0.765019\pi$
$314$	12.8084	+	9.30588i	0.722822	+	0.525161i
$315$	0.00709870	+	6.96127i	0.000399967	+	0.392223i
$316$	5.26247	+	7.24317i	0.296037	+	0.407460i
$317$	18.6628	+	6.06393i	1.04821	+	0.340584i	0.781966	−	0.623322i	$-0.214217\pi$
$317$	18.6628	+	6.06393i	1.04821	+	0.340584i	0.266244	+	0.963906i	$0.414217\pi$
$318$			13.3843i			0.750555i
$319$	−2.66110	+	8.19002i	−0.148993	+	0.458553i
$320$	4.35250	+	13.3493i	0.243312	+	0.746247i
$321$	5.03875	+	15.5077i	0.281236	+	0.865555i
$322$	−0.101772	−	0.313222i	−0.00567153	−	0.0174552i
$323$	24.6613	−	2.36192i	1.37219	−	0.131421i
$324$	4.10109			0.227838
$325$	28.9454	+	20.9400i	1.60560	+	1.16154i
$326$		−	21.6068i		−	1.19669i
$327$	−0.929861	−	0.675583i	−0.0514214	−	0.0373599i
$328$	−28.8493	+	9.37371i	−1.59294	+	0.517577i
$329$	−8.13863	+	2.64440i	−0.448697	+	0.145791i
$330$	6.09692	−	0.00621729i	0.335624	−	0.000342250i
$331$	−7.42569	+	22.8539i	−0.408153	+	1.25616i	0.510081	+	0.860126i	$0.329615\pi$
$331$	−7.42569	+	22.8539i	−0.408153	+	1.25616i	−0.918234	+	0.396038i	$0.870385\pi$
$332$	4.44303			0.243843
$333$	−9.65719	−	3.13781i	−0.529211	−	0.171951i
$334$	−7.87622	−	10.8407i	−0.430968	−	0.593176i
$335$	15.0360	−	10.9477i	0.821503	−	0.598138i
$336$	−1.65967	−	1.20582i	−0.0905423	−	0.0657828i
$337$	16.0127	+	22.0396i	0.872269	+	1.20058i	0.978503	+	0.206234i	$0.0661209\pi$
$337$	16.0127	+	22.0396i	0.872269	+	1.20058i	−0.106233	+	0.994341i	$0.533879\pi$
$338$	−29.3028	+	21.2897i	−1.59386	+	1.15801i
$339$	11.5815	+	8.41444i	0.629020	+	0.457010i
$340$	−10.0393	+	0.971837i	−0.544457	+	0.0527053i
$341$	11.9565	−	8.68688i	0.647479	−	0.470421i
$342$	2.18947	−	6.73850i	0.118393	−	0.364376i
$343$			19.3122i			1.04276i
$344$	−0.549729	+	1.69189i	−0.0296394	+	0.0912206i
$345$	0.330306	−	0.240496i	0.0177831	−	0.0129479i
$346$	6.26427	−	2.03539i	0.336769	−	0.109423i
$347$	10.5721	−	3.43510i	0.567542	−	0.184406i	−0.0111697	−	0.999938i	$-0.503555\pi$
$347$	10.5721	−	3.43510i	0.567542	−	0.184406i	0.578712	+	0.815532i	$0.303555\pi$
$348$	4.68585	+	3.40447i	0.251188	+	0.182499i
$349$	3.06179			0.163894			0.0819468	−	0.996637i	$-0.473886\pi$
$349$	3.06179			0.163894			0.0819468	+	0.996637i	$0.473886\pi$
$350$	11.3818	+	3.67253i	0.608383	+	0.196305i
$351$		−	40.1936i		−	2.14537i
$352$	−6.73014	+	9.26325i	−0.358718	+	0.493733i
$353$	−2.10618	−	6.48216i	−0.112101	−	0.345011i	0.879231	−	0.476397i	$-0.158057\pi$
$353$	−2.10618	−	6.48216i	−0.112101	−	0.345011i	−0.991331	+	0.131386i	$0.958057\pi$
$354$	1.61850	−	0.525883i	0.0860224	−	0.0279504i
$355$	3.18567	+	1.03150i	0.169078	+	0.0547461i
$356$	0.905939	−	2.78819i	0.0480147	−	0.147774i
$357$	10.3029	−	9.10587i	0.545287	−	0.481934i
$358$	−3.82707	+	11.7785i	−0.202267	+	0.622514i
$359$	−6.69565	+	4.86468i	−0.353383	+	0.256748i	−0.750287	−	0.661112i	$-0.770085\pi$
$359$	−6.69565	+	4.86468i	−0.353383	+	0.256748i	0.396904	+	0.917860i	$0.370085\pi$
$360$	−2.51307	+	7.76136i	−0.132451	+	0.409060i
$361$	−13.8370	−	10.0532i	−0.728266	−	0.529116i
$362$	−7.13341	−	9.81830i	−0.374924	−	0.516038i
$363$	−4.94593	−	6.80749i	−0.259594	−	0.357301i
$364$	11.5460	−	15.8917i	0.605176	−	0.832954i
$365$	−33.5361	+	10.9344i	−1.75536	+	0.572330i
$366$	−0.935450	+	0.679645i	−0.0488968	+	0.0355256i
$367$	−22.5024	−	7.31148i	−1.17462	−	0.381656i	−0.344253	−	0.938877i	$-0.611868\pi$
$367$	−22.5024	−	7.31148i	−1.17462	−	0.381656i	−0.830364	+	0.557221i	$0.811868\pi$
$368$		−	0.0846989i		−	0.00441524i
$369$	−12.1359	−	3.94318i	−0.631767	−	0.205274i
$370$	−10.2396	+	14.1238i	−0.532331	+	0.734264i
$371$	−25.3236	+	8.22815i	−1.31474	+	0.427184i
$372$	−3.07171	−	9.45375i	−0.159261	−	0.490154i
$373$	−23.6563	−	17.1873i	−1.22488	−	0.889926i	−0.228383	−	0.973571i	$-0.573344\pi$
$373$	−23.6563	−	17.1873i	−1.22488	−	0.889926i	−0.996496	+	0.0836450i	$0.973344\pi$
$374$	5.61004	+	6.34752i	0.290088	+	0.328222i
$375$	0.0453904	+	14.8372i	0.00234395	+	0.766188i
$376$	−10.0287			−0.517190
$377$	16.7550	−	23.0612i	0.862924	−	1.18771i
$378$	−4.15793	−	12.7968i	−0.213861	−	0.658195i
$379$	−8.69964	+	2.82669i	−0.446871	+	0.145197i	−0.523803	−	0.851839i	$-0.675487\pi$
$379$	−8.69964	+	2.82669i	−0.446871	+	0.145197i	0.0769327	+	0.997036i	$0.475487\pi$
$380$	11.9003	+	8.62754i	0.610472	+	0.442584i
$381$	−14.0123	−	4.55286i	−0.717870	−	0.233250i
$382$	−6.61901			−0.338658
$383$	3.38835	−	10.4283i	0.173136	−	0.532859i	−0.826407	−	0.563073i	$-0.809619\pi$
$383$	3.38835	−	10.4283i	0.173136	−	0.532859i	0.999543	+	0.0302140i	$0.00961888\pi$
$384$	3.61319	+	4.97312i	0.184385	+	0.253784i
$385$	3.75991	+	11.5318i	0.191623	+	0.587714i
$386$	−4.03251	+	5.55028i	−0.205249	+	0.282502i
$387$	−0.605422	+	0.439865i	−0.0307754	+	0.0223596i
$388$	1.21931	+	1.67824i	0.0619011	+	0.0851995i
$389$	−19.8244	−	14.4033i	−1.00514	−	0.730274i	−0.0419526	−	0.999120i	$-0.513358\pi$
$389$	−19.8244	−	14.4033i	−1.00514	−	0.730274i	−0.963183	+	0.268846i	$0.913358\pi$
$390$	−19.2002	−	6.21690i	−0.972242	−	0.314805i
$391$	0.554184	+	0.123156i	0.0280263	+	0.00622828i
$392$	−0.623432	+	1.91873i	−0.0314881	+	0.0969104i
$393$	3.78237			0.190795
$394$	15.7139	+	5.10575i	0.791654	+	0.257224i
$395$	17.4095	+	5.63708i	0.875969	+	0.283632i
$396$	−2.78233	+	0.904033i	−0.139817	+	0.0454294i
$397$	8.16581	−	2.65323i	0.409830	−	0.133162i	−0.0968439	−	0.995300i	$-0.530875\pi$
$397$	8.16581	−	2.65323i	0.409830	−	0.133162i	0.506674	+	0.862138i	$0.330875\pi$
$398$	−2.44218	+	3.36137i	−0.122415	+	0.168490i
$399$	−20.0382			−1.00316
$400$	2.49201	+	1.80280i	0.124601	+	0.0901400i
$401$		−	7.68237i		−	0.383639i	−0.981430	−	0.191820i	$-0.938561\pi$
$401$		−	7.68237i		−	0.383639i	0.981430	−	0.191820i	$-0.0614389\pi$
$402$	−6.17577	+	8.50022i	−0.308020	+	0.423952i
$403$	−46.5262	+	15.1173i	−2.31763	+	0.753045i
$404$	−0.0315979	−	0.0972483i	−0.00157205	−	0.00483828i
$405$	6.77643	−	4.93393i	0.336724	−	0.245169i
$406$	2.94880	−	9.07546i	0.146346	−	0.450408i
$407$	−17.6925			−0.876986
$408$	14.7809	−	6.41795i	0.731763	−	0.317736i
$409$	6.88829	−	5.00463i	0.340604	−	0.247463i	−0.404313	−	0.914621i	$-0.632489\pi$
$409$	6.88829	−	5.00463i	0.340604	−	0.247463i	0.744917	+	0.667158i	$0.232489\pi$
$410$	−12.8677	+	17.7489i	−0.635492	+	0.876558i
$411$	5.73883	−	7.89882i	0.283076	−	0.389620i
$412$	11.8816	−	8.63246i	0.585363	−	0.425291i
$413$	1.98998	+	2.73898i	0.0979207	+	0.134776i
$414$	0.0954329	−	0.131352i	0.00469027	−	0.00645561i
$415$	7.34143	−	5.34531i	0.360377	−	0.262391i
$416$	30.6626	−	22.2777i	1.50336	−	1.09225i
$417$	−5.93653	+	18.2708i	−0.290713	+	0.894723i
$418$		−	12.3453i		−	0.603829i
$419$	25.2119	+	8.19183i	1.23168	+	0.400197i	0.851323	−	0.524642i	$-0.175801\pi$
$419$	25.2119	+	8.19183i	1.23168	+	0.400197i	0.380358	+	0.924839i	$0.375801\pi$
$420$	8.15805	−	0.00831911i	0.398072	−	0.000405931i
$421$	−0.250519	−	0.771019i	−0.0122096	−	0.0375772i	0.944766	−	0.327745i	$-0.106289\pi$
$421$	−0.250519	−	0.771019i	−0.0122096	−	0.0375772i	−0.956976	+	0.290168i	$0.906289\pi$
$422$	−8.98347	+	2.91890i	−0.437308	+	0.142090i
$423$	−3.41300	−	2.47969i	−0.165946	−	0.120567i
$424$	−31.2046			−1.51543
$425$	−15.4192	+	13.6839i	−0.747941	+	0.663765i
$426$	−1.89159			−0.0916477
$427$	−1.86099	−	1.35209i	−0.0900597	−	0.0654322i
$428$	−12.7840	+	4.15378i	−0.617939	+	0.200781i
$429$	−6.32492	−	19.4661i	−0.305370	−	0.939833i
$430$	0.398541	+	1.22234i	0.0192194	+	0.0589465i
$431$	−31.7891	−	10.3289i	−1.53123	−	0.497526i	−0.582287	−	0.812983i	$-0.697842\pi$
$431$	−31.7891	−	10.3289i	−1.53123	−	0.497526i	−0.948940	+	0.315458i	$0.897842\pi$
$432$		−	3.46040i		−	0.166489i
$433$	−4.17734	+	12.8565i	−0.200750	+	0.617845i	0.799111	+	0.601183i	$0.205304\pi$
$433$	−4.17734	+	12.8565i	−0.200750	+	0.617845i	−0.999861	+	0.0166618i	$0.994696\pi$
$434$	−13.2491	+	9.62604i	−0.635977	+	0.462065i
$435$	11.8385	−	0.0120722i	0.567613	−	0.000578819i
$436$	0.556929	−	0.766547i	0.0266720	−	0.0367109i
$437$	−0.486285	−	0.669314i	−0.0232622	−	0.0320176i
$438$	16.1207	−	11.7124i	0.770278	−	0.559639i
$439$	5.10179	−	7.02202i	0.243495	−	0.335143i	−0.669725	−	0.742610i	$-0.733588\pi$
$439$	5.10179	−	7.02202i	0.243495	−	0.335143i	0.913220	+	0.407467i	$0.133588\pi$
$440$	0.0144952	+	14.2146i	0.000691031	+	0.677652i
$441$	−0.686593	+	0.498839i	−0.0326949	+	0.0237542i
$442$	−11.1683	−	25.7212i	−0.531223	−	1.22344i
$443$	13.4653			0.639754			0.319877	−	0.947459i	$-0.396358\pi$
$443$	13.4653			0.639754			0.319877	+	0.947459i	$0.396358\pi$
$444$	−3.67727	+	11.3175i	−0.174515	+	0.537103i
$445$	−1.85749	−	5.69698i	−0.0880534	−	0.270063i
$446$	1.49447	+	4.59950i	0.0707652	+	0.217793i
$447$	−8.34733	+	2.71221i	−0.394815	+	0.128283i
$448$	9.27500	−	12.7659i	0.438203	−	0.603134i
$449$			25.3440i			1.19606i	0.801475	+	0.598028i	$0.204049\pi$
$449$			25.3440i			1.19606i	−0.801475	+	0.598028i	$0.795951\pi$
$450$	1.83337	+	5.60363i	0.0864261	+	0.264158i
$451$	−22.2336			−1.04694
$452$	−6.93659	+	9.54740i	−0.326270	+	0.449072i
$453$	−18.1955	+	5.91208i	−0.854900	+	0.277774i
$454$	24.8372	−	8.07010i	1.16567	−	0.378749i
$455$	−0.0409421	−	40.1495i	−0.00191940	−	1.88224i
$456$	−22.3338	−	7.25670i	−1.04588	−	0.339826i
$457$	27.3059			1.27731			0.638657	−	0.769491i	$-0.279490\pi$
$457$	27.3059			1.27731			0.638657	+	0.769491i	$0.279490\pi$
$458$	1.95806	−	6.02628i	0.0914941	−	0.281590i
$459$	22.6414	+	5.03159i	1.05681	+	0.234855i
$460$	0.198257	+	0.272293i	0.00924378	+	0.0126957i
$461$	−5.21679	−	3.79022i	−0.242970	−	0.176528i	0.459635	−	0.888108i	$-0.347980\pi$
$461$	−5.21679	−	3.79022i	−0.242970	−	0.176528i	−0.702605	+	0.711580i	$0.747980\pi$
$462$	−4.02744	−	5.54330i	−0.187374	−	0.257898i
$463$	−9.37210	+	6.80923i	−0.435558	+	0.316452i	−0.783868	−	0.620928i	$-0.786756\pi$
$463$	−9.37210	+	6.80923i	−0.435558	+	0.316452i	0.348309	+	0.937380i	$0.386756\pi$
$464$	1.44249	−	1.98542i	0.0669660	−	0.0921708i
$465$	−16.4491	−	11.9254i	−0.762810	−	0.553026i
$466$	1.88778	+	2.59830i	0.0874496	+	0.120364i
$467$	1.12674	−	3.46775i	0.0521394	−	0.160469i	−0.921596	−	0.388150i	$-0.873114\pi$
$467$	1.12674	−	3.46775i	0.0521394	−	0.160469i	0.973736	+	0.227681i	$0.0731144\pi$
$468$	9.68385			0.447636
$469$	−19.8794	−	6.45920i	−0.917944	−	0.298258i
$470$	−5.85928	+	4.26615i	−0.270268	+	0.196783i
$471$	20.9933	−	6.82112i	0.967318	−	0.314301i
$472$	1.22606	+	3.77343i	0.0564340	+	0.173686i
$473$	−0.766417	+	1.05488i	−0.0352399	+	0.0485035i
$474$	−10.3375			−0.474815
$475$	30.0430	−	0.0612724i	1.37847	−	0.00281137i
$476$	7.50658	+	8.49337i	0.344064	+	0.389293i
$477$	−10.6197	−	7.71565i	−0.486242	−	0.353275i
$478$	8.59724	+	26.4596i	0.393229	+	1.21023i
$479$	1.55426	−	0.505008i	0.0710158	−	0.0230744i	−0.273294	−	0.961931i	$-0.588113\pi$
$479$	1.55426	−	0.505008i	0.0710158	−	0.0230744i	0.344309	+	0.938856i	$0.388113\pi$
$480$	14.9753	+	4.84888i	0.683524	+	0.221320i
$481$	55.6984	+	18.0975i	2.53963	+	0.825175i
$482$		−	8.69892i		−	0.396225i
$483$	−0.436704	−	0.141894i	−0.0198707	−	0.00645638i
$484$	5.61187	−	4.07726i	0.255085	−	0.185330i
$485$	4.03377	+	1.30611i	0.183164	+	0.0593072i
$486$	6.65838	−	9.16447i	0.302030	−	0.415709i
$487$	−16.4793	−	22.6818i	−0.746748	−	1.02781i	−0.998202	−	0.0599414i	$-0.980909\pi$
$487$	−16.4793	−	22.6818i	−0.746748	−	1.02781i	0.251454	−	0.967869i	$-0.419091\pi$
$488$	−1.58454	−	2.18094i	−0.0717290	−	0.0987265i
$489$	−24.3715	−	17.7070i	−1.10212	−	0.800737i
$490$	0.451975	+	1.38622i	0.0204181	+	0.0626232i
$491$	27.6052	−	20.0564i	1.24581	−	0.905131i	0.247835	−	0.968802i	$-0.420281\pi$
$491$	27.6052	−	20.0564i	1.24581	−	0.905131i	0.997971	+	0.0636709i	$0.0202808\pi$
$492$	−4.62109	+	14.2222i	−0.208335	+	0.641189i
$493$	10.8931	+	12.3251i	0.490602	+	0.555095i
$494$	−12.6279	+	38.8646i	−0.568156	+	1.74860i
$495$	−3.50975	+	4.84114i	−0.157752	+	0.217593i
$496$	−4.00560	+	1.30150i	−0.179857	+	0.0584390i
$497$	−1.16287	−	3.57896i	−0.0521620	−	0.160538i
$498$	−3.01537	+	4.15030i	−0.135122	+	0.185979i
$499$			35.4358i			1.58632i	0.609011	+	0.793161i	$0.291566\pi$
$499$			35.4358i			1.58632i	−0.609011	+	0.793161i	$0.708434\pi$
$500$	−12.2313	+	0.0374183i	−0.546999	+	0.00167340i
$501$	−18.6825			−0.834671
$502$	7.21326	+	5.24074i	0.321943	+	0.233906i
$503$	20.4656	−	6.64968i	0.912516	−	0.296494i	0.185123	−	0.982715i	$-0.440732\pi$
$503$	20.4656	−	6.64968i	0.912516	−	0.296494i	0.727393	+	0.686221i	$0.240732\pi$
$504$	8.71955	−	2.83315i	0.388400	−	0.126199i
$505$	−0.169208	−	0.122673i	−0.00752966	−	0.00545889i
$506$	0.0874193	−	0.269049i	0.00388626	−	0.0119607i
$507$			50.4994i			2.24276i
$508$	3.75323	−	11.5513i	0.166523	−	0.512504i
$509$	−31.0954	+	22.5922i	−1.37828	+	1.00138i	−0.381243	+	0.924475i	$0.624504\pi$
$509$	−31.0954	+	22.5922i	−1.37828	+	1.00138i	−0.997038	+	0.0769047i	$0.975496\pi$
$510$	5.90560	−	10.0374i	0.261504	−	0.444464i
$511$	32.0707	+	23.3007i	1.41872	+	1.03076i
$512$	5.57110	−	4.04764i	0.246210	−	0.178882i
$513$	−19.8673	−	27.3450i	−0.877164	−	1.20731i
$514$	−9.60446	−	6.97805i	−0.423634	−	0.307788i
$515$	9.24697	−	28.5583i	0.407470	−	1.25843i
$516$	0.515487	+	0.709507i	0.0226930	+	0.0312343i
$517$	−6.99086	−	2.27147i	−0.307458	−	0.0998991i
$518$	19.6053			0.861408
$519$	2.83780	−	8.73385i	0.124566	−	0.383373i
$520$	14.4943	−	44.7640i	0.635616	−	1.96303i
$521$	−1.45602	+	0.473089i	−0.0637893	+	0.0207264i	−0.340738	−	0.940158i	$-0.610677\pi$
$521$	−1.45602	+	0.473089i	−0.0637893	+	0.0207264i	0.276949	+	0.960885i	$0.410677\pi$
$522$	4.47407	−	1.45371i	0.195825	−	0.0636273i
$523$	−16.4387	−	11.9434i	−0.718813	−	0.522248i	0.167192	−	0.985924i	$-0.446530\pi$
$523$	−16.4387	−	11.9434i	−0.718813	−	0.522248i	−0.886005	+	0.463676i	$0.846530\pi$
$524$			3.11806i			0.136213i
$525$	13.4699	−	9.82852i	0.587877	−	0.428952i
$526$	12.1655			0.530440
$527$	−2.69136	−	28.1010i	−0.117237	−	1.22410i
$528$	−0.544534	−	1.67590i	−0.0236978	−	0.0729344i
$529$	7.10153	+	21.8563i	0.308762	+	0.950273i
$530$	−18.2313	+	13.2743i	−0.791919	+	0.576597i
$531$	−0.515759	+	1.58734i	−0.0223820	+	0.0688848i
$532$		−	16.5188i		−	0.716181i
$533$	69.9942	+	22.7425i	3.03178	+	0.985086i
$534$	1.98966	+	2.73853i	0.0861008	+	0.118508i
$535$	−16.1264	+	22.2437i	−0.697203	+	0.961678i
$536$	−19.8177	−	14.3984i	−0.855994	−	0.621916i
$537$	10.1493	+	13.9694i	0.437977	+	0.602823i
$538$	−8.40933	−	11.5745i	−0.362552	−	0.499010i
$539$	−0.869173	+	1.19631i	−0.0374379	+	0.0515289i
$540$	8.09986	+	11.1246i	0.348562	+	0.478728i
$541$	−10.6621	−	14.6751i	−0.458399	−	0.630932i	0.515777	−	0.856723i	$-0.327503\pi$
$541$	−10.6621	−	14.6751i	−0.458399	−	0.630932i	−0.974176	+	0.225791i	$0.927503\pi$
$542$	3.13328	−	9.64325i	0.134586	−	0.414213i
$543$	−16.9205			−0.726128
$544$	8.71075	+	20.0613i	0.373470	+	0.860122i
$545$	−0.00197487	−	1.93663i	−8.45939e−5	−	0.0829562i
$546$	7.00872	+	21.5706i	0.299946	+	0.923138i
$547$	13.9388	−	4.52898i	0.595979	−	0.193645i	0.00453268	−	0.999990i	$-0.498557\pi$
$547$	13.9388	−	4.52898i	0.595979	−	0.193645i	0.591446	+	0.806344i	$0.298557\pi$
$548$	6.51153	+	4.73090i	0.278159	+	0.202094i
$549$		−	1.13402i		−	0.0483988i
$550$	6.05526	+	8.29871i	0.258197	+	0.353858i
$551$		−	23.9712i		−	1.02121i
$552$	−0.435349	−	0.316299i	−0.0185297	−	0.0134626i
$553$	−6.35506	−	19.5589i	−0.270245	−	0.831727i
$554$	−19.4002	+	6.30350i	−0.824235	+	0.267810i
$555$	7.53966	+	23.1244i	0.320041	+	0.981577i
$556$	−15.0618	−	4.89388i	−0.638763	−	0.207547i
$557$	−8.39783			−0.355827			−0.177914	−	0.984046i	$-0.556935\pi$
$557$	−8.39783			−0.355827			−0.177914	+	0.984046i	$0.556935\pi$
$558$	−7.67837	−	2.49485i	−0.325051	−	0.105616i
$559$	3.49180	−	2.53694i	0.147688	−	0.107301i
$560$	−0.00352485	−	3.45661i	−0.000148952	−	0.146068i
$561$	11.7572	−	1.12604i	0.496390	−	0.0475414i
$562$	−14.2707	+	10.3683i	−0.601975	+	0.437360i
$563$	26.4200	−	19.1953i	1.11347	−	0.808984i	0.130265	−	0.991479i	$-0.458417\pi$
$563$	26.4200	−	19.1953i	1.11347	−	0.808984i	0.983207	+	0.182495i	$0.0584173\pi$
$564$	−2.90600	+	3.99977i	−0.122365	+	0.168421i
$565$	0.0245971	+	24.1209i	0.00103481	+	1.01477i
$566$	10.8750	+	14.9682i	0.457111	+	0.629160i
$567$	−8.95925	−	2.91104i	−0.376253	−	0.122252i
$568$		−	4.41011i		−	0.185044i
$569$	12.2628	−	37.7411i	0.514085	−	1.58219i	−0.270856	−	0.962620i	$-0.587307\pi$
$569$	12.2628	−	37.7411i	0.514085	−	1.58219i	0.784941	−	0.619571i	$-0.212693\pi$
$570$	−16.1355	+	5.26095i	−0.675843	+	0.220357i
$571$	−15.1160	+	4.91149i	−0.632586	+	0.205540i	−0.607720	−	0.794151i	$-0.707916\pi$
$571$	−15.1160	+	4.91149i	−0.632586	+	0.205540i	−0.0248655	+	0.999691i	$0.507916\pi$
$572$	16.0472	−	5.21406i	0.670968	−	0.218011i
$573$	−5.42433	+	7.46595i	−0.226605	+	0.311895i
$574$	24.6373			1.02834
$575$	0.655180	+	0.211404i	0.0273229	+	0.00881618i
$576$	7.77910			0.324129
$577$	18.0719	+	13.1300i	0.752343	+	0.546609i	0.896552	−	0.442938i	$-0.146064\pi$
$577$	18.0719	+	13.1300i	0.752343	+	0.546609i	−0.144210	+	0.989547i	$0.546064\pi$
$578$	15.8871	−	3.07132i	0.660816	−	0.127750i
$579$	2.95579	+	9.09700i	0.122839	+	0.378058i
$580$	0.00995195	+	9.75928i	0.000413232	+	0.405232i
$581$	−9.70625	−	3.15375i	−0.402683	−	0.130840i
$582$	−2.39518			−0.0992834
$583$	−21.7523	−	7.06776i	−0.900889	−	0.292717i
$584$	27.3066	+	37.5843i	1.12996	+	1.55525i
$585$	16.0011	−	11.6504i	0.661564	−	0.481686i
$586$	4.21822	+	3.06472i	0.174253	+	0.126602i
$587$	28.1511	−	20.4530i	1.16192	−	0.844184i	0.171900	−	0.985114i	$-0.445009\pi$
$587$	28.1511	−	20.4530i	1.16192	−	0.844184i	0.990020	+	0.140930i	$0.0450093\pi$
$588$	0.584600	+	0.804632i	0.0241085	+	0.0331825i
$589$	−24.1810	+	33.2823i	−0.996361	+	1.37137i
$590$	2.32152	+	1.68307i	0.0955756	+	0.0692909i
$591$	18.6367	−	13.5404i	0.766613	−	0.556977i
$592$	4.79526	+	1.55808i	0.197084	+	0.0640365i
$593$	−30.1187			−1.23683			−0.618414	−	0.785852i	$-0.712225\pi$
$593$	−30.1187			−1.23683			−0.618414	+	0.785852i	$0.712225\pi$
$594$	3.57155	−	10.9921i	0.146542	−	0.451011i
$595$	22.6217	+	5.00301i	0.927399	+	0.205103i
$596$	−2.23586	−	6.88127i	−0.0915844	−	0.281868i
$597$	1.79010	+	5.50935i	0.0732638	+	0.225483i
$598$	−0.550414	+	0.757580i	−0.0225081	+	0.0309798i
$599$	7.17687			0.293239			0.146619	−	0.989193i	$-0.453161\pi$
$599$	7.17687			0.293239			0.146619	+	0.989193i	$0.453161\pi$
$600$	18.5725	−	6.07647i	0.758218	−	0.248071i
$601$			25.2805i			1.03121i	0.856826	+	0.515606i	$0.172433\pi$
$601$			25.2805i			1.03121i	−0.856826	+	0.515606i	$0.827567\pi$
$602$	0.849276	−	1.16893i	0.0346139	−	0.0476420i
$603$	−3.18429	−	9.80023i	−0.129674	−	0.399096i
$604$	−4.87373	−	14.9998i	−0.198309	−	0.610333i
$605$	4.36750	−	13.4886i	0.177564	−	0.548389i
$606$	0.112286	+	0.0364838i	0.00456130	+	0.00148205i
$607$			32.2066i			1.30722i	0.756830	+	0.653612i	$0.226747\pi$
$607$			32.2066i			1.30722i	−0.756830	+	0.653612i	$0.773253\pi$
$608$	9.84914	−	30.3125i	0.399435	−	1.22934i
$609$	−7.82017	−	10.7635i	−0.316889	−	0.436160i
$610$	−1.85353	−	0.600160i	−0.0750473	−	0.0242998i
$611$	19.6847	+	14.3017i	0.796356	+	0.578587i
$612$	−1.21226	+	5.45500i	−0.0490028	+	0.220505i
$613$	−3.37497	+	2.45206i	−0.136314	+	0.0990379i	−0.653853	−	0.756622i	$-0.726848\pi$
$613$	−3.37497	+	2.45206i	−0.136314	+	0.0990379i	0.517539	+	0.855660i	$0.326848\pi$
$614$	−16.8447	−	12.2384i	−0.679796	−	0.493901i
$615$	9.47483	+	29.0597i	0.382062	+	1.17180i
$616$	12.9238	−	9.38971i	0.520716	−	0.378322i
$617$	−28.2504	−	9.17912i	−1.13732	−	0.369537i	−0.320966	−	0.947091i	$-0.604008\pi$
$617$	−28.2504	−	9.17912i	−1.13732	−	0.369537i	−0.816353	+	0.577553i	$0.804008\pi$
$618$			16.9574i			0.682126i
$619$	4.83208	+	1.57004i	0.194218	+	0.0631051i	0.404511	−	0.914533i	$-0.367442\pi$
$619$	4.83208	+	1.57004i	0.194218	+	0.0631051i	−0.210293	+	0.977638i	$0.567442\pi$
$620$	9.83089	−	13.5601i	0.394818	−	0.544588i
$621$	−0.239346	−	0.736631i	−0.00960462	−	0.0295600i
$622$	−16.5443	+	5.37556i	−0.663365	+	0.215540i
$623$	−3.95823	+	5.44804i	−0.158583	+	0.218271i
$624$			5.83296i			0.233505i
$625$	−20.1653	+	14.7770i	−0.806613	+	0.591080i
$626$		−	3.69384i		−	0.147636i
$627$	−13.9250	−	10.1171i	−0.556111	−	0.404038i
$628$	5.62311	+	17.3061i	0.224386	+	0.690590i
$629$	−17.1670	+	29.1099i	−0.684494	+	1.16069i
$630$	3.88920	−	5.36452i	0.154950	−	0.213728i
$631$	−5.09044	+	15.6668i	−0.202647	+	0.623684i	0.797155	+	0.603775i	$0.206338\pi$
$631$	−5.09044	+	15.6668i	−0.202647	+	0.623684i	−0.999802	+	0.0199089i	$0.993662\pi$
$632$		−	24.1011i		−	0.958689i
$633$	−4.06963	+	12.5250i	−0.161753	+	0.497825i
$634$	−10.9788	−	15.1110i	−0.436023	−	0.600133i
$635$	−7.69542	−	23.6021i	−0.305383	−	0.936622i
$636$	−9.04212	+	12.4454i	−0.358543	+	0.493493i
$637$	3.95996	−	2.87708i	0.156899	−	0.113994i
$638$	6.63131	−	4.81793i	0.262536	−	0.190744i
$639$	1.09044	−	1.50087i	0.0431372	−	0.0593733i
$640$	−3.19062	+	9.85391i	−0.126120	+	0.389510i
$641$	0.186719	+	0.256997i	0.00737498	+	0.0101508i	0.812689	−	0.582698i	$-0.198003\pi$
$641$	0.186719	+	0.256997i	0.00737498	+	0.0101508i	−0.805314	+	0.592849i	$0.798003\pi$
$642$	4.79608	−	14.7608i	0.189286	−	0.582563i
$643$			26.5966i			1.04887i	0.851452	+	0.524433i	$0.175723\pi$
$643$			26.5966i			1.04887i	−0.851452	+	0.524433i	$0.824277\pi$
$644$	0.116972	−	0.360004i	0.00460936	−	0.0141861i
$645$	1.70536	+	0.552182i	0.0671483	+	0.0217421i
$646$	−20.3120	−	11.9786i	−0.799164	−	0.471293i
$647$	10.8971	+	33.5377i	0.428407	+	1.31850i	0.899694	+	0.436522i	$0.143790\pi$
$647$	10.8971	+	33.5377i	0.428407	+	1.31850i	−0.471286	+	0.881980i	$0.656210\pi$
$648$	−8.93145	−	6.48908i	−0.350861	−	0.254915i
$649$			2.90811i			0.114153i
$650$	−10.5741	−	32.3192i	−0.414749	−	1.26766i
$651$			22.8330i			0.894898i
$652$	14.5970	−	20.0911i	0.571664	−	0.786828i
$653$	26.7224	−	8.68263i	1.04573	−	0.339777i	0.264737	−	0.964321i	$-0.414715\pi$
$653$	26.7224	−	8.68263i	1.04573	−	0.339777i	0.780990	+	0.624543i	$0.214715\pi$
$654$	0.338069	+	1.04047i	0.0132196	+	0.0406856i
$655$	3.75127	+	5.15212i	0.146574	+	0.201310i
$656$	6.02604	+	1.95798i	0.235277	+	0.0764462i
$657$			19.5427i			0.762433i
$658$	7.74666	+	2.51704i	0.301996	+	0.0981246i
$659$	−17.2435	+	12.5282i	−0.671713	+	0.488028i	−0.870598	−	0.491995i	$-0.836268\pi$
$659$	−17.2435	+	12.5282i	−0.671713	+	0.488028i	0.198885	+	0.980023i	$0.436268\pi$
$660$	5.67342	+	4.11315i	0.220838	+	0.160104i
$661$	−10.1931	−	7.40570i	−0.396465	−	0.288048i	0.371635	−	0.928379i	$-0.378797\pi$
$661$	−10.1931	−	7.40570i	−0.396465	−	0.288048i	−0.768099	+	0.640331i	$0.778797\pi$
$662$	18.5044	−	13.4442i	0.719194	−	0.522525i
$663$	−38.1650	−	8.48140i	−1.48221	−	0.329390i
$664$	−9.67614	−	7.03012i	−0.375507	−	0.272822i
$665$	−19.8734	−	27.2948i	−0.770658	−	1.05845i
$666$	5.68102	+	7.81926i	0.220135	+	0.302990i
$667$	0.169744	−	0.522418i	0.00657251	−	0.0202281i
$668$		−	15.4012i		−	0.595890i
$669$	6.41277	+	2.08364i	0.247932	+	0.0805580i
$670$	−17.7035	+	0.0180530i	−0.683946	+	0.000697449i
$671$	−0.610588	−	1.87920i	−0.0235715	−	0.0725456i
$672$	−5.46647	−	16.8241i	−0.210873	−	0.649002i
$673$	−0.789808	+	1.08708i	−0.0304449	+	0.0419038i	−0.823968	−	0.566636i	$-0.808244\pi$
$673$	−0.789808	+	1.08708i	−0.0304449	+	0.0419038i	0.793523	+	0.608540i	$0.208244\pi$
$674$		−	25.9305i		−	0.998804i
$675$	26.7676	+	8.63700i	1.03029	+	0.332438i
$676$	−41.6300			−1.60116
$677$	4.89429	−	6.73641i	0.188103	−	0.258901i	−0.704542	−	0.709663i	$-0.748847\pi$
$677$	4.89429	−	6.73641i	0.188103	−	0.258901i	0.892645	+	0.450761i	$0.148847\pi$
$678$	−4.21068	−	12.9591i	−0.161710	−	0.497693i
$679$	−1.47246	−	4.53177i	−0.0565079	−	0.173913i
$680$	23.4015	+	13.7685i	0.897408	+	0.527998i
$681$	11.2516	−	34.6288i	0.431162	−	1.32698i
$682$	−14.0672			−0.538662
$683$	−30.2743	−	9.83670i	−1.15841	−	0.376391i	−0.334106	−	0.942535i	$-0.608434\pi$
$683$	−30.2743	−	9.83670i	−1.15841	−	0.376391i	−0.824306	+	0.566144i	$0.808434\pi$
$684$	6.58825	−	4.78664i	0.251908	−	0.183022i
$685$	16.4510	−	0.0167757i	0.628559	−	0.000640968i
$686$	10.8047	−	14.8714i	0.412526	−	0.567794i
$687$	−5.19274	−	7.14720i	−0.198115	−	0.272683i
$688$	0.300621	−	0.218414i	0.0114611	−	0.00832697i
$689$	61.2495	+	44.5004i	2.33342	+	1.69533i
$690$	−0.388905		0.000396583i	−0.0148054		1.50976e-5i
$691$	−7.20110	−	9.91147i	−0.273943	−	0.377050i	0.649773	−	0.760128i	$-0.274864\pi$
$691$	−7.20110	−	9.91147i	−0.273943	−	0.377050i	−0.923716	+	0.383078i	$0.874864\pi$
$692$	7.19990	+	2.33939i	0.273699	+	0.0889302i
$693$	6.71998			0.255271
$694$	−10.0630	−	3.26966i	−0.381985	−	0.124115i
$695$	−30.7751	+	10.0341i	−1.16737	+	0.380617i
$696$	−4.81813	−	14.8287i	−0.182631	−	0.562080i
$697$	−21.5732	+	36.5813i	−0.817143	+	1.38562i
$698$	−2.35774	−	1.71300i	−0.0892417	−	0.0648379i
$699$	4.47782			0.169367
$700$	8.10231	+	11.1042i	0.306239	+	0.419698i
$701$	17.0752			0.644922			0.322461	−	0.946583i	$-0.395490\pi$
$701$	17.0752			0.644922			0.322461	+	0.946583i	$0.395490\pi$
$702$	−22.4874	+	30.9512i	−0.848731	+	1.16818i
$703$	46.8389	−	15.2189i	1.76656	−	0.573991i
$704$	12.8908	−	4.18849i	0.485842	−	0.157860i
$705$	0.0103047	+	10.1052i	0.000388096	+	0.380582i
$706$	−2.00475	+	6.16997i	−0.0754496	+	0.232210i
$707$			0.234878i			0.00883349i
$708$	1.86024	+	0.604428i	0.0699121	+	0.0227158i
$709$	9.75736	+	13.4299i	0.366445	+	0.504369i	0.951930	−	0.306314i	$-0.0990959\pi$
$709$	9.75736	+	13.4299i	0.366445	+	0.504369i	−0.585485	+	0.810683i	$0.699096\pi$
$710$	−1.87604	−	2.57661i	−0.0704064	−	0.0966985i
$711$	5.95923	−	8.20217i	0.223488	−	0.307605i
$712$	−6.38469	+	4.63875i	−0.239276	+	0.173844i
$713$	−0.762668	+	0.554111i	−0.0285622	+	0.0207516i
$714$	−13.0283	+	1.24778i	−0.487572	+	0.0466969i
$715$	20.2427	−	27.9215i	0.757034	−	1.04420i
$716$	−11.5159	+	8.36679i	−0.430369	+	0.312682i
$717$	36.8908	+	11.9865i	1.37771	+	0.447646i
$718$	7.87769			0.293993
$719$	−29.5462	−	9.60013i	−1.10189	−	0.358024i	−0.299058	−	0.954235i	$-0.596672\pi$
$719$	−29.5462	−	9.60013i	−1.10189	−	0.358024i	−0.802828	+	0.596211i	$0.796672\pi$
$720$	1.37759	−	1.00303i	0.0513397	−	0.0373805i
$721$	−32.0840	+	10.4247i	−1.19487	+	0.388237i
$722$	5.03073	+	15.4830i	0.187225	+	0.576218i
$723$	−9.81201	−	7.12884i	−0.364913	−	0.265125i
$724$		−	13.9487i		−	0.518400i
$725$	11.7576	+	16.1138i	0.436667	+	0.598450i
$726$			8.00926i			0.297252i
$727$	−0.493264	−	0.358377i	−0.0182941	−	0.0132915i	0.578601	−	0.815611i	$-0.303599\pi$
$727$	−0.493264	−	0.358377i	−0.0182941	−	0.0132915i	−0.596895	+	0.802320i	$0.703599\pi$
$728$	−50.2905	+	16.3404i	−1.86389	+	0.605614i
$729$	−8.35577	−	25.7164i	−0.309473	−	0.952459i
$730$	31.9421	+	10.3426i	1.18223	+	0.382797i
$731$	0.991965	+	2.28455i	0.0366891	+	0.0844971i
$732$	−1.32898			−0.0491205
$733$	14.3364	−	44.1230i	0.529528	−	1.62972i	−0.225657	−	0.974207i	$-0.572453\pi$
$733$	14.3364	−	44.1230i	0.529528	−	1.62972i	0.755185	−	0.655512i	$-0.227547\pi$
$734$	13.2375	+	18.2198i	0.488604	+	0.672505i
$735$	1.93400	+	0.626214i	0.0713366	+	0.0230983i
$736$	0.429296	−	0.590876i	0.0158241	−	0.0217800i
$737$	−10.5534	−	14.5256i	−0.388741	−	0.535056i
$738$	7.13914	+	9.82618i	0.262795	+	0.361707i
$739$	36.7857	+	26.7263i	1.35318	+	0.983144i	0.998846	+	0.0480263i	$0.0152931\pi$
$739$	36.7857	+	26.7263i	1.35318	+	0.983144i	0.354336	+	0.935118i	$0.384707\pi$
$740$	−19.0630	+	6.21545i	−0.700770	+	0.228484i
$741$	33.4890	+	46.0936i	1.23025	+	1.69329i
$742$	24.1040	+	7.83187i	0.884886	+	0.287517i
$743$			5.84982i			0.214609i	0.994226	+	0.107305i	$0.0342220\pi$
$743$			5.84982i			0.214609i	−0.994226	+	0.107305i	$0.965778\pi$
$744$	−8.26885	+	25.4489i	−0.303151	+	0.933003i
$745$	−11.9731	−	8.68034i	−0.438661	−	0.318023i
$746$	8.60073	+	26.4703i	0.314895	+	0.969148i
$747$	−1.55475	−	4.78504i	−0.0568855	−	0.175075i
$748$	0.928268	+	9.69225i	0.0339409	+	0.354384i
$749$	30.8765			1.12820
$750$	8.26610	−	11.4508i	0.301835	−	0.418124i
$751$		−	51.1108i		−	1.86506i	−0.361092	−	0.932530i	$-0.617596\pi$
$751$		−	51.1108i		−	1.86506i	0.361092	−	0.932530i	$-0.382404\pi$
$752$	1.69472	+	1.23129i	0.0618001	+	0.0449004i
$753$	11.8227	−	3.84141i	0.430841	−	0.139989i
$754$	−25.8044	+	8.38437i	−0.939742	+	0.305341i
$755$	−26.0990	−	18.9214i	−0.949840	−	0.688621i
$756$	4.77895	−	14.7081i	0.173809	−	0.534928i
$757$	−21.7284			−0.789732			−0.394866	−	0.918739i	$-0.629209\pi$
$757$	−21.7284			−0.789732			−0.394866	+	0.918739i	$0.629209\pi$
$758$	8.28065	+	2.69055i	0.300767	+	0.0977251i
$759$	−0.231835	−	0.319093i	−0.00841507	−	0.0115823i
$760$	−12.2655	−	37.6189i	−0.444918	−	1.36458i
$761$	−9.22137	−	6.69972i	−0.334274	−	0.242865i	0.407968	−	0.912996i	$-0.366238\pi$
$761$	−9.22137	−	6.69972i	−0.334274	−	0.242865i	−0.742242	+	0.670132i	$0.766238\pi$
$762$	8.24298	+	11.3455i	0.298612	+	0.411004i
$763$	−1.76078	+	1.27928i	−0.0637445	+	0.0463131i
$764$	−6.15469	−	4.47164i	−0.222669	−	0.161778i
$765$	4.55970	+	10.4720i	0.164856	+	0.378616i
$766$	−8.44358	+	6.13462i	−0.305079	+	0.221653i
$767$	2.97467	−	9.15508i	0.107409	−	0.330571i
$768$		−	22.5173i		−	0.812524i
$769$	4.75330	−	14.6292i	0.171408	−	0.527541i	−0.828043	−	0.560665i	$-0.810546\pi$
$769$	4.75330	−	14.6292i	0.171408	−	0.527541i	0.999451	+	0.0331238i	$0.0105456\pi$
$770$	3.55643	−	10.9837i	0.128165	−	0.395824i
$771$	−15.7419	+	5.11484i	−0.566930	+	0.184207i

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.p (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.770053 - 0.559477i) q^{2} +(-1.26213 + 0.410091i) q^{3} +(-0.338066 - 1.04046i) q^{4} +(-1.81036 - 1.31248i) q^{5} +(1.20134 + 0.390341i) q^{6} +2.51296i q^{7} +(-0.910052 + 2.80085i) q^{8} +(-1.00225 + 0.728178i) q^{9} +(0.659768 + 2.02353i) q^{10} +(-1.26877 + 1.74631i) q^{11} +(0.853366 + 1.17456i) q^{12} +(5.78053 - 4.19980i) q^{13} +(1.40594 - 1.93511i) q^{14} +(2.82314 + 0.914113i) q^{15} +(0.497666 - 0.361576i) q^{16} +(1.64216 + 3.78197i) q^{17} +1.17919 q^{18} +(1.85677 - 5.71454i) q^{19} +(-0.753565 + 2.32731i) q^{20} +(-1.03054 - 3.17168i) q^{21} +(1.95404 - 0.634907i) q^{22} +(0.0809312 - 0.111392i) q^{23} -3.90825i q^{24} +(1.55478 + 4.75212i) q^{25} -6.80101 q^{26} +(3.30647 - 4.55097i) q^{27} +(2.61463 - 0.849544i) q^{28} +(3.79420 - 1.23281i) q^{29} +(-1.66255 - 2.28340i) q^{30} +(-6.51159 - 2.11574i) q^{31} +5.30446 q^{32} +(0.885207 - 2.72439i) q^{33} +(0.851378 - 3.83107i) q^{34} +(3.29821 - 4.54935i) q^{35} +(1.09647 + 0.796629i) q^{36} +(4.81775 + 6.63107i) q^{37} +(-4.62696 + 3.36168i) q^{38} +(-5.57349 + 7.67125i) q^{39} +(5.32359 - 3.87611i) q^{40} +(6.05430 + 8.33303i) q^{41} +(-0.980909 + 3.01893i) q^{42} +0.604063 q^{43} +(2.24589 + 0.729735i) q^{44} +(2.77015 - 0.00282484i) q^{45} +(-0.124643 + 0.0404989i) q^{46} +(1.05231 + 3.23867i) q^{47} +(-0.479841 + 0.660444i) q^{48} +0.685051 q^{49} +(1.46144 - 4.52925i) q^{50} +(-3.62357 - 4.09991i) q^{51} +(-6.32392 - 4.59460i) q^{52} +(3.27429 + 10.0772i) q^{53} +(-5.09232 + 1.65460i) q^{54} +(4.58893 - 1.49621i) q^{55} +(-7.03842 - 2.28692i) q^{56} +7.97394i q^{57} +(-3.61147 - 1.17344i) q^{58} +(1.08994 - 0.791889i) q^{59} +(-0.00331049 - 3.24640i) q^{60} +(-0.538047 + 0.740559i) q^{61} +(3.83056 + 5.27232i) q^{62} +(-1.82988 - 2.51861i) q^{63} +(-5.08005 - 3.69087i) q^{64} +(-15.9770 + 0.0162924i) q^{65} +(-2.20589 + 1.60267i) q^{66} +(-2.57036 + 7.91075i) q^{67} +(3.37983 - 2.98715i) q^{68} +(-0.0564648 + 0.173781i) q^{69} +(-5.08505 + 1.65797i) q^{70} +(-1.42420 + 0.462751i) q^{71} +(-1.12742 - 3.46984i) q^{72} +(9.27222 - 12.7621i) q^{73} -7.80170i q^{74} +(-3.91114 - 5.36020i) q^{75} -6.57345 q^{76} +(-4.38841 - 3.18836i) q^{77} +(8.58377 - 2.78904i) q^{78} +(-7.78321 + 2.52892i) q^{79} +(-1.37551 + 0.00140267i) q^{80} +(-1.15841 + 3.56522i) q^{81} -9.80411i q^{82} +(-1.25500 + 3.86248i) q^{83} +(-2.95161 + 2.14447i) q^{84} +(1.99089 - 9.00202i) q^{85} +(-0.465161 - 0.337959i) q^{86} +(-4.28322 + 3.11194i) q^{87} +(-3.73652 - 5.14288i) q^{88} +(2.16798 + 1.57513i) q^{89} +(-2.13475 - 1.54766i) q^{90} +(10.5539 + 14.5262i) q^{91} +(-0.143259 - 0.0465477i) q^{92} +9.08613 q^{93} +(1.00163 - 3.08269i) q^{94} +(-10.8616 + 7.90838i) q^{95} +(-6.69492 + 2.17531i) q^{96} +(-1.80336 + 0.585948i) q^{97} +(-0.527526 - 0.383270i) q^{98} -2.67413i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 8 q^{2} - 44 q^{4} - 4 q^{8} + 28 q^{9} - 18 q^{13} - 10 q^{15} - 28 q^{16} + 2 q^{17} - 60 q^{18} - 8 q^{19} + 32 q^{21} + 6 q^{25} + 52 q^{26} - 54 q^{30} + 44 q^{32} - 24 q^{33} + 26 q^{35} + 34 q^{36}+ \cdots - 36 q^{98}+O(q^{100}) \) 168 * q - 8 * q^2 - 44 * q^4 - 4 * q^8 + 28 * q^9 - 18 * q^13 - 10 * q^15 - 28 * q^16 + 2 * q^17 - 60 * q^18 - 8 * q^19 + 32 * q^21 + 6 * q^25 + 52 * q^26 - 54 * q^30 + 44 * q^32 - 24 * q^33 + 26 * q^35 + 34 * q^36 - 18 * q^38 + 80 * q^42 - 8 * q^43 - 40 * q^47 - 84 * q^49 - 82 * q^50 - 36 * q^51 - 30 * q^52 - 42 * q^53 - 18 * q^55 - 18 * q^59 + 28 * q^60 - 16 * q^64 - 140 * q^66 - 62 * q^67 + 144 * q^68 + 44 * q^69 + 4 * q^70 - 6 * q^72 + 72 * q^76 + 48 * q^77 - 28 * q^81 - 14 * q^83 + 24 * q^84 + 62 * q^85 + 82 * q^86 + 48 * q^87 + 90 * q^89 - 224 * q^93 + 26 * q^94 - 36 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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