LMFDB - Embedded newform 425.2.p.a.16.16

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			16.16
Character	$\chi$	$=$	425.16
Dual form			425.2.p.a.186.16

$q$-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} +(-3.55152 + 2.09445i) 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} +(3.90665 + 0.374157i) 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} +(-9.17844 - 0.869614i) 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	0.0789042	−	0.996882i	$-0.474858\pi$
$3$	1.26213	−	0.410091i	0.728692	−	0.236766i	0.649787	+	0.760116i	$0.274858\pi$
$4$	−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	$-0.842483\pi$
$7$		−	2.51296i		−	0.949808i	0.880038	−	0.474904i	$-0.157517\pi$
$8$	−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	−0.573709	−	0.819059i	$-0.694496\pi$
$11$	1.26877	−	1.74631i	0.382549	−	0.526533i	0.956257	+	0.292526i	$0.0944959\pi$
$12$	−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
$17$	−3.55152	+	2.09445i	−0.861370	+	0.507978i
$17$	−3.55152	+	2.09445i	−0.861370	+	0.507978i
$18$	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	−0.817371	−	0.576111i	$-0.804569\pi$
$23$	−0.0809312	+	0.111392i	−0.0168753	+	0.0232269i	0.800496	+	0.599338i	$0.204569\pi$
$24$			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	−0.639319	−	0.768942i	$-0.720784\pi$
$29$	−3.79420	+	1.23281i	−0.704566	+	0.228927i	−0.0652471	+	0.997869i	$0.520784\pi$
$30$	−1.66255	−	2.28340i	−0.303538	−	0.416890i
$31$	6.51159	+	2.11574i	1.16952	+	0.379999i	0.828462	−	0.560045i	$-0.189216\pi$
$31$	6.51159	+	2.11574i	1.16952	+	0.379999i	0.341054	+	0.940044i	$0.389216\pi$
$32$	5.30446			0.937705
$33$	0.885207	−	2.72439i	0.154095	−	0.474255i
$34$	3.90665	+	0.374157i	0.669986	+	0.0641674i
$35$	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	$-0.964685\pi$
$37$	−4.81775	−	6.63107i	−0.792033	−	1.09014i	0.201818	−	0.979423i	$-0.435315\pi$
$38$	−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	$-0.902535\pi$
$41$	−6.05430	−	8.33303i	−0.945523	−	1.30140i	0.00796516	−	0.999968i	$-0.497465\pi$
$42$	−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	−0.773182	−	0.634185i	$-0.781336\pi$
$61$	0.538047	−	0.740559i	0.0688899	−	0.0948188i	0.842072	+	0.539366i	$0.181336\pi$
$62$	−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	−0.223284	−	0.974753i	$-0.571678\pi$
$71$	1.42420	−	0.462751i	0.169022	−	0.0549185i	0.392305	+	0.919835i	$0.371678\pi$
$72$	−1.12742	−	3.46984i	−0.132868	−	0.408924i
$73$	−9.27222	+	12.7621i	−1.08523	+	1.49369i	−0.231604	+	0.972810i	$0.574397\pi$
$73$	−9.27222	+	12.7621i	−1.08523	+	1.49369i	−0.853628	+	0.520883i	$0.825603\pi$
$74$			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	0.163517	−	0.986541i	$-0.447716\pi$
$79$	7.78321	−	2.52892i	0.875679	−	0.284525i	0.712162	+	0.702015i	$0.247716\pi$
$80$	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
$85$	−9.17844	−	0.869614i	−0.995542	−	0.0943229i
$86$	−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	−0.216030	−	0.976387i	$-0.569311\pi$
$97$	1.80336	−	0.585948i	0.183104	−	0.0594940i	0.399134	+	0.916893i	$0.369311\pi$
$98$	−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	$0.498520\pi$
$102$	5.08415	−	1.12985i	0.503406	−	0.111872i
$103$	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	$0.202417\pi$
$107$			12.2869i			1.18782i	−0.804531	+	0.593910i	$0.797583\pi$
$108$	5.85290	+	1.90172i	0.563196	+	0.182993i
$109$	−0.509074	−	0.700680i	−0.0487604	−	0.0671130i	0.783941	−	0.620836i	$-0.213207\pi$
$109$	−0.509074	−	0.700680i	−0.0487604	−	0.0671130i	−0.832701	+	0.553723i	$0.813207\pi$
$110$	−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	0.995379	−	0.0960206i	$-0.0306115\pi$
$113$	6.34055	+	8.72702i	0.596469	+	0.820969i	−0.398910	+	0.916990i	$0.630611\pi$
$114$	−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
$119$	5.26325	+	8.92481i	0.482481	+	0.818136i
$120$	−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	0.425027	−	0.905181i	$-0.360265\pi$
$131$	2.71064	+	0.880740i	0.236830	+	0.0769506i	−0.188198	+	0.982131i	$0.560265\pi$
$132$	−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
$136$	−2.63417	−	11.8533i	−0.225878	−	1.01642i
$137$	−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	$0.410410\pi$
$139$	−8.50885	+	11.7114i	−0.721711	+	0.993350i	−0.999465	+	0.0326981i	$0.989590\pi$
$140$	−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
$153$	2.03439	−	4.68530i	0.164470	−	0.378784i
$154$	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	$-0.851398\pi$
$163$	−13.3428	−	18.3647i	−1.04509	−	1.43844i	−0.152094	−	0.988366i	$-0.548602\pi$
$164$	−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	−0.258875	−	0.965911i	$-0.583352\pi$
$167$	−13.3888	−	4.35029i	−1.03606	−	0.336636i	−0.777183	+	0.629275i	$0.783352\pi$
$168$	9.82126			0.757726
$169$	11.7590	−	36.1905i	0.904538	−	2.78388i
$170$	6.58136	+	5.80477i	0.504767	+	0.445206i
$171$	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	−0.625903	−	0.779901i	$-0.715270\pi$
$173$	4.06743	−	5.59833i	0.309241	−	0.425633i	0.935144	+	0.354267i	$0.115270\pi$
$174$	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	−0.178542	−	0.983932i	$-0.557138\pi$
$181$	−12.1261	−	3.94001i	−0.901327	−	0.292859i	−0.722785	+	0.691073i	$0.757138\pi$
$182$			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
$187$	−0.848506	+	8.85944i	−0.0620489	+	0.647866i
$188$	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	$0.0835278\pi$
$193$			7.20765i			0.518818i	−0.965768	+	0.259409i	$0.916472\pi$
$194$	−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	0.345256	−	0.938508i	$-0.387792\pi$
$197$	16.5090	−	5.36409i	1.17622	−	0.382176i	0.830960	+	0.556333i	$0.187792\pi$
$198$	1.49612	−	2.05923i	0.106324	−	0.146343i
$199$			4.36512i			0.309435i	0.987959	+	0.154718i	$0.0494467\pi$
$199$			4.36512i			0.309435i	−0.987959	+	0.154718i	$0.950553\pi$
$200$	−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
$204$	5.49080	+	2.38414i	0.384433	+	0.166923i
$205$	−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	−0.961135	−	0.276079i	$-0.910965\pi$
$211$	−5.83301	+	8.02845i	−0.401561	+	0.552702i	0.559574	+	0.828781i	$0.310965\pi$
$212$	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
$221$	−11.7334	+	27.0227i	−0.789275	+	1.81774i
$222$	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	$-0.435680\pi$
$227$	16.1269	−	22.1968i	1.07038	−	1.47326i	0.869688	−	0.493601i	$-0.164320\pi$
$228$	−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	0.412239	−	0.911076i	$-0.364747\pi$
$233$	3.20904	+	1.04268i	0.210231	+	0.0683082i	−0.202008	+	0.979384i	$0.564747\pi$
$234$	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
$238$	0.940240	−	9.81725i	0.0609467	−	0.636358i
$239$	−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	0.600161	−	0.799879i	$-0.295103\pi$
$241$	−5.37181	−	7.39367i	−0.346029	−	0.476268i	−0.946190	+	0.323611i	$0.895103\pi$
$242$	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
$255$	−11.9410	+	2.66643i	−0.747775	+	0.166978i
$256$	−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	−0.161126	−	0.986934i	$-0.551513\pi$
$269$	−14.2951	−	4.64475i	−0.871585	−	0.283195i	−0.710459	+	0.703739i	$0.751513\pi$
$270$	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	$0.795124\pi$
$272$	−1.01017	+	2.32648i	−0.0612506	+	0.141063i
$273$	−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	$0.422653\pi$
$277$	−12.5967	+	17.3378i	−0.756860	+	1.04173i	−0.997469	+	0.0711057i	$0.977347\pi$
$278$	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	0.801682	−	0.597750i	$-0.203939\pi$
$283$	18.4865	+	6.00663i	1.09891	+	0.357057i	0.297226	+	0.954807i	$0.403939\pi$
$284$	−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
$289$	8.22659	−	14.8769i	0.483917	−	0.875114i
$290$	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
$306$	−4.18790	+	2.46974i	−0.239406	+	0.141186i
$307$	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	−0.996506	−	0.0835169i	$-0.973385\pi$
$311$	−10.7423	+	14.7855i	−0.609140	+	0.838409i	0.387367	+	0.921926i	$0.373385\pi$
$312$	16.4139	+	22.5918i	0.929253	+	1.27901i
$313$	−2.28104	−	3.13959i	−0.128932	−	0.177460i	0.739670	−	0.672969i	$-0.234981\pi$
$313$	−2.28104	−	3.13959i	−0.128932	−	0.177460i	−0.868603	+	0.495509i	$0.834981\pi$
$314$	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	−0.266244	−	0.963906i	$-0.585783\pi$
$317$	−18.6628	−	6.06393i	−1.04821	−	0.340584i	−0.781966	+	0.623322i	$0.785783\pi$
$318$		−	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
$323$	5.37445	+	24.1842i	0.299042	+	1.34564i
$324$	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	$-0.933879\pi$
$337$	−16.0127	−	22.0396i	−0.872269	−	1.20058i	0.106233	−	0.994341i	$-0.466121\pi$
$338$	−29.3028	+	21.2897i	−1.59386	+	1.15801i
$339$	11.5815	+	8.41444i	0.629020	+	0.457010i
$340$	2.19812	+	9.84378i	0.119210	+	0.533854i
$341$	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	−0.578712	−	0.815532i	$-0.696445\pi$
$347$	−10.5721	+	3.43510i	−0.567542	+	0.184406i	0.0111697	+	0.999938i	$0.496445\pi$
$348$	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	0.830364	−	0.557221i	$-0.188132\pi$
$367$	22.5024	+	7.31148i	1.17462	+	0.381656i	0.344253	+	0.938877i	$0.388132\pi$
$368$			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	−0.0769327	−	0.997036i	$-0.524513\pi$
$379$	8.69964	−	2.82669i	0.446871	−	0.145197i	0.523803	+	0.851839i	$0.324513\pi$
$380$	−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
$391$	0.0541237	−	0.565118i	0.00273716	−	0.0285792i
$392$	−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	−0.506674	−	0.862138i	$-0.669125\pi$
$397$	−8.16581	+	2.65323i	−0.409830	+	0.133162i	0.0968439	+	0.995300i	$0.469125\pi$
$398$	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	$0.0614389\pi$
$401$			7.68237i			0.383639i	−0.981430	+	0.191820i	$0.938561\pi$
$402$	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
$408$	−8.18562	−	13.8802i	−0.405248	−	0.687173i
$409$	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	−0.380358	−	0.924839i	$-0.624199\pi$
$419$	−25.2119	−	8.19183i	−1.23168	−	0.400197i	−0.851323	+	0.524642i	$0.824199\pi$
$420$	−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
$425$	−15.4749	−	13.6209i	−0.750643	−	0.660708i
$426$	−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	0.948940	−	0.315458i	$-0.102158\pi$
$431$	31.7891	+	10.3289i	1.53123	+	0.497526i	0.582287	+	0.812983i	$0.302158\pi$
$432$			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	−0.913220	−	0.407467i	$-0.866412\pi$
$439$	−5.10179	+	7.02202i	−0.243495	+	0.335143i	0.669725	+	0.742610i	$0.266412\pi$
$440$	0.0144952	+	14.2146i	0.000691031	+	0.677652i
$441$	−0.686593	+	0.498839i	−0.0326949	+	0.0237542i
$442$	24.1539	−	14.2444i	1.14889	−	0.677535i
$443$	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	$-0.795951\pi$
$449$		−	25.3440i		−	1.19606i	0.801475	−	0.598028i	$-0.204049\pi$
$450$	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
$459$	2.21124	−	23.0881i	0.103212	−	1.07766i
$460$	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	−0.344309	−	0.938856i	$-0.611887\pi$
$479$	−1.55426	+	0.505008i	−0.0710158	+	0.0230744i	0.273294	+	0.961931i	$0.411887\pi$
$480$	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	$0.0190914\pi$
$487$	16.4793	+	22.6818i	0.746748	+	1.02781i	−0.251454	+	0.967869i	$0.580909\pi$
$488$	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	$-0.708434\pi$
$499$		−	35.4358i		−	1.58632i	0.609011	−	0.793161i	$-0.291566\pi$
$500$	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	−0.727393	−	0.686221i	$-0.759268\pi$
$503$	−20.4656	+	6.64968i	−0.912516	+	0.296494i	−0.185123	+	0.982715i	$0.559268\pi$
$504$	−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	$0.975496\pi$
$510$	10.6870	+	4.62742i	0.473229	+	0.204906i
$511$	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	−0.276949	−	0.960885i	$-0.589323\pi$
$521$	1.45602	−	0.473089i	0.0637893	−	0.0207264i	0.340738	+	0.940158i	$0.389323\pi$
$522$	−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
$527$	−27.5574	+	6.12407i	−1.20042	+	0.266769i
$528$	−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	0.974176	−	0.225791i	$-0.0724966\pi$
$541$	10.6621	+	14.6751i	0.458399	+	0.630932i	−0.515777	+	0.856723i	$0.672497\pi$
$542$	3.13328	−	9.64325i	0.134586	−	0.414213i
$543$	−16.9205			−0.726128
$544$	−18.8389	+	11.1099i	−0.807711	+	0.476333i
$545$	−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	−0.591446	−	0.806344i	$-0.701443\pi$
$547$	−13.9388	+	4.52898i	−0.595979	+	0.193645i	−0.00453268	+	0.999990i	$0.501443\pi$
$548$	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
$561$	2.56225	+	11.5297i	0.108178	+	0.486786i
$562$	−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	0.0248655	−	0.999691i	$-0.492084\pi$
$571$	15.1160	−	4.91149i	0.632586	−	0.205540i	0.607720	+	0.794151i	$0.292084\pi$
$572$	−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	$0.546064\pi$
$578$	−14.6582	+	6.85345i	−0.609701	+	0.285066i
$579$	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
$595$	−2.18530	+	23.0650i	−0.0895886	+	0.945574i
$596$	−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	$-0.827567\pi$
$601$		−	25.2805i		−	1.03121i	0.856826	−	0.515606i	$-0.172433\pi$
$602$	−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	$-0.773253\pi$
$607$		−	32.2066i		−	1.30722i	0.756830	−	0.653612i	$-0.226747\pi$
$608$	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
$612$	−5.56262	−	0.532756i	−0.224856	−	0.0215354i
$613$	−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	0.816353	−	0.577553i	$-0.195992\pi$
$617$	28.2504	+	9.17912i	1.13732	+	0.369537i	0.320966	+	0.947091i	$0.395992\pi$
$618$		−	16.9574i		−	0.682126i
$619$	−4.83208	−	1.57004i	−0.194218	−	0.0631051i	0.210293	−	0.977638i	$-0.432558\pi$
$619$	−4.83208	−	1.57004i	−0.194218	−	0.0631051i	−0.404511	+	0.914533i	$0.632558\pi$
$620$	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
$629$	30.9988	+	13.4598i	1.23600	+	0.536679i
$630$	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	0.805314	−	0.592849i	$-0.201997\pi$
$641$	−0.186719	−	0.256997i	−0.00737498	−	0.0101508i	−0.812689	+	0.582698i	$0.801997\pi$
$642$	4.79608	−	14.7608i	0.189286	−	0.582563i
$643$		−	26.5966i		−	1.04887i	−0.851452	−	0.524433i	$-0.824277\pi$
$643$		−	26.5966i		−	1.04887i	0.851452	−	0.524433i	$-0.175723\pi$
$644$	0.116972	−	0.360004i	0.00460936	−	0.0141861i
$645$	1.70536	+	0.552182i	0.0671483	+	0.0217421i
$646$	9.39188	−	21.6300i	0.369518	−	0.851021i
$647$	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	−0.780990	−	0.624543i	$-0.785285\pi$
$653$	−26.7224	+	8.68263i	−1.04573	+	0.339777i	−0.264737	+	0.964321i	$0.585285\pi$
$654$	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
$663$	−3.72734	+	38.9180i	−0.144758	+	1.51145i
$664$	−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	−0.793523	−	0.608540i	$-0.791756\pi$
$673$	0.789808	−	1.08708i	0.0304449	−	0.0419038i	0.823968	+	0.566636i	$0.191756\pi$
$674$			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	−0.892645	−	0.450761i	$-0.851153\pi$
$677$	−4.89429	+	6.73641i	−0.188103	+	0.258901i	0.704542	+	0.709663i	$0.251153\pi$
$678$	−4.21068	−	12.9591i	−0.161710	−	0.497693i
$679$	−1.47246	−	4.53177i	−0.0565079	−	0.173913i
$680$	10.7885	−	24.9161i	0.413721	−	0.955488i
$681$	11.2516	−	34.6288i	0.431162	−	1.32698i
$682$	−14.0672			−0.538662
$683$	30.2743	+	9.83670i	1.15841	+	0.376391i	0.824306	−	0.566144i	$-0.191566\pi$
$683$	30.2743	+	9.83670i	1.15841	+	0.376391i	0.334106	+	0.942535i	$0.391566\pi$
$684$	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	0.923716	−	0.383078i	$-0.125136\pi$
$691$	7.20110	+	9.91147i	0.273943	+	0.377050i	−0.649773	+	0.760128i	$0.725136\pi$
$692$	−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
$697$	38.9550	+	16.9145i	1.47553	+	0.640683i
$698$	−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	0.585485	−	0.810683i	$-0.300904\pi$
$709$	−9.75736	−	13.4299i	−0.366445	−	0.504369i	−0.951930	+	0.306314i	$0.900904\pi$
$710$	−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
$714$	−2.83926	−	12.7762i	−0.106257	−	0.478139i
$715$	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	0.802828	−	0.596211i	$-0.203328\pi$
$719$	29.5462	+	9.60013i	1.10189	+	0.358024i	0.299058	+	0.954235i	$0.403328\pi$
$720$	−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
$731$	−2.14534	+	1.26518i	−0.0793483	+	0.0467942i
$732$	−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	$-0.965778\pi$
$743$		−	5.84982i		−	0.214609i	0.994226	−	0.107305i	$-0.0342220\pi$
$744$	−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
$748$	9.50473	−	2.11224i	0.347527	−	0.0772310i
$749$	30.8765			1.12820
$750$	8.26610	−	11.4508i	0.301835	−	0.418124i
$751$			51.1108i			1.86506i	0.361092	+	0.932530i	$0.382404\pi$
$751$			51.1108i			1.86506i	−0.361092	+	0.932530i	$0.617596\pi$
$752$	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
$765$	9.83234	−	5.81197i	0.355489	−	0.210132i
$766$	−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

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} +(-3.55152 + 2.09445i) 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} +(3.90665 + 0.374157i) 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} +(-9.17844 - 0.869614i) 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

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