LMFDB - Embedded newform 140.2.s.b.59.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,2,Mod(19,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5]))

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

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

chi := DirichletCharacter("140.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	140.s (of order $6$, degree $2$, 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:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			59.3
Character	$\chi$	$=$	140.59
Dual form			140.2.s.b.19.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36614 + 0.365598i) q^{2} +(-1.28100 - 0.739583i) q^{3} +(1.73268 - 0.998916i) q^{4} +(-1.26649 + 1.84283i) q^{5} +(2.02041 + 0.542044i) q^{6} +(0.664037 - 2.56107i) q^{7} +(-2.00188 + 1.99812i) q^{8} +(-0.406034 - 0.703271i) q^{9} +(1.05646 - 2.98058i) q^{10} +(-5.32875 - 3.07655i) q^{11} +(-2.95833 - 0.00185057i) q^{12} -3.33366 q^{13} +(0.0291534 + 3.74154i) q^{14} +(2.98529 - 1.42398i) q^{15} +(2.00433 - 3.46160i) q^{16} +(1.27594 - 2.21000i) q^{17} +(0.811813 + 0.812321i) q^{18} +(0.352781 + 0.611035i) q^{19} +(-0.353580 + 4.45814i) q^{20} +(-2.74475 + 2.78960i) q^{21} +(8.40459 + 2.25482i) q^{22} +(-0.983411 - 1.70332i) q^{23} +(4.04217 - 1.07903i) q^{24} +(-1.79203 - 4.66783i) q^{25} +(4.55424 - 1.21878i) q^{26} +5.63868i q^{27} +(-1.40773 - 5.10081i) q^{28} +5.17926 q^{29} +(-3.55771 + 3.03677i) q^{30} +(-3.40156 + 5.89167i) q^{31} +(-1.47264 + 5.46181i) q^{32} +(4.55073 + 7.88210i) q^{33} +(-0.935146 + 3.48565i) q^{34} +(3.87861 + 4.46726i) q^{35} +(-1.40603 - 0.812947i) q^{36} +(5.90431 - 3.40886i) q^{37} +(-0.705342 - 0.705783i) q^{38} +(4.27040 + 2.46552i) q^{39} +(-1.14685 - 6.21971i) q^{40} +2.53373i q^{41} +(2.72984 - 4.81446i) q^{42} -4.59892 q^{43} +(-12.3062 - 0.00769809i) q^{44} +(1.81024 + 0.142433i) q^{45} +(1.96621 + 1.96744i) q^{46} +(3.78388 - 2.18463i) q^{47} +(-5.12768 + 2.95192i) q^{48} +(-6.11811 - 3.40128i) q^{49} +(4.15471 + 5.72175i) q^{50} +(-3.26896 + 1.88733i) q^{51} +(-5.77615 + 3.33005i) q^{52} +(-4.80929 - 2.77664i) q^{53} +(-2.06149 - 7.70323i) q^{54} +(12.4183 - 5.92355i) q^{55} +(3.78800 + 6.45376i) q^{56} -1.04364i q^{57} +(-7.07560 + 1.89353i) q^{58} +(3.40156 - 5.89167i) q^{59} +(3.75010 - 5.44935i) q^{60} +(3.07800 - 1.77708i) q^{61} +(2.49302 - 9.29244i) q^{62} +(-2.07074 + 0.572881i) q^{63} +(0.0150131 - 7.99999i) q^{64} +(4.22203 - 6.14336i) q^{65} +(-9.09862 - 9.10431i) q^{66} +(-1.45061 + 2.51253i) q^{67} +(0.00319264 - 5.10377i) q^{68} +2.90926i q^{69} +(-6.93194 - 4.68489i) q^{70} -3.37084i q^{71} +(2.21805 + 0.596556i) q^{72} +(-1.27594 + 2.21000i) q^{73} +(-6.81984 + 6.81558i) q^{74} +(-1.15667 + 7.30482i) q^{75} +(1.22163 + 0.706327i) q^{76} +(-11.4177 + 11.6043i) q^{77} +(-6.73536 - 1.80699i) q^{78} +(5.38564 - 3.10940i) q^{79} +(3.84067 + 8.07770i) q^{80} +(2.95217 - 5.11331i) q^{81} +(-0.926327 - 3.46143i) q^{82} +4.70266i q^{83} +(-1.96918 + 7.57525i) q^{84} +(2.45668 + 5.15028i) q^{85} +(6.28277 - 1.68136i) q^{86} +(-6.63461 - 3.83049i) q^{87} +(16.8148 - 4.48861i) q^{88} +(-5.19692 + 3.00044i) q^{89} +(-2.52512 + 0.467238i) q^{90} +(-2.21367 + 8.53772i) q^{91} +(-3.40541 - 1.96895i) q^{92} +(8.71475 - 5.03147i) q^{93} +(-4.37062 + 4.36789i) q^{94} +(-1.57282 - 0.123752i) q^{95} +(5.92591 - 5.90740i) q^{96} -9.46331 q^{97} +(9.60170 + 2.40986i) q^{98} +4.99674i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 6 q^{4} - 6 q^{5} + 4 q^{9} - 12 q^{10} + 22 q^{14} + 18 q^{16} - 52 q^{21} - 48 q^{24} - 26 q^{25} - 18 q^{26} - 26 q^{30} - 28 q^{36} + 42 q^{40} - 26 q^{44} + 36 q^{45} - 22 q^{46} + 36 q^{50}+ \cdots + 60 q^{96}+O(q^{100}) $ 32 * q + 6 * q^4 - 6 * q^5 + 4 * q^9 - 12 * q^10 + 22 * q^14 + 18 * q^16 - 52 * q^21 - 48 * q^24 - 26 * q^25 - 18 * q^26 - 26 * q^30 - 28 * q^36 + 42 * q^40 - 26 * q^44 + 36 * q^45 - 22 * q^46 + 36 * q^50 + 48 * q^54 - 16 * q^56 + 4 * q^60 + 36 * q^61 + 36 * q^64 - 4 * q^65 - 24 * q^66 + 26 * q^70 + 14 * q^74 + 72 * q^80 + 72 * q^81 + 56 * q^84 + 20 * q^85 + 8 * q^86 - 108 * q^89 + 30 * q^94 + 60 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.36614	+	0.365598i	−0.966007	+	0.258517i
$2$	−1.36614	+	0.365598i	−0.966007	+	0.258517i
$3$	−1.28100	−	0.739583i	−0.739583	−	0.426999i	0.0823346	−	0.996605i	$-0.473762\pi$
$3$	−1.28100	−	0.739583i	−0.739583	−	0.426999i	−0.821918	+	0.569606i	$0.807096\pi$
$4$	1.73268	−	0.998916i	0.866338	−	0.499458i
$5$	−1.26649	+	1.84283i	−0.566390	+	0.824137i
$5$	−1.26649	+	1.84283i	−0.566390	+	0.824137i
$6$	2.02041	+	0.542044i	0.824829	+	0.221289i
$7$	0.664037	−	2.56107i	0.250982	−	0.967992i
$7$	0.664037	−	2.56107i	0.250982	−	0.967992i
$8$	−2.00188	+	1.99812i	−0.707770	+	0.706443i
$9$	−0.406034	−	0.703271i	−0.135345	−	0.234424i
$10$	1.05646	−	2.98058i	0.334083	−	0.942544i
$11$	−5.32875	−	3.07655i	−1.60668	−	0.927616i	−0.990107	−	0.140316i	$-0.955188\pi$
$11$	−5.32875	−	3.07655i	−1.60668	−	0.927616i	−0.616570	−	0.787300i	$-0.711478\pi$
$12$	−2.95833	−	0.00185057i	−0.853997	−	0.000534214i
$13$	−3.33366			−0.924591			−0.462295	−	0.886726i	$-0.652974\pi$
$13$	−3.33366			−0.924591			−0.462295	+	0.886726i	$0.652974\pi$
$14$	0.0291534	+	3.74154i	0.00779158	+	0.999970i
$15$	2.98529	−	1.42398i	0.770798	−	0.367671i
$16$	2.00433	−	3.46160i	0.501083	−	0.865399i
$17$	1.27594	−	2.21000i	0.309462	−	0.536004i	−0.668783	−	0.743458i	$-0.733184\pi$
$17$	1.27594	−	2.21000i	0.309462	−	0.536004i	0.978245	+	0.207454i	$0.0665178\pi$
$18$	0.811813	+	0.812321i	0.191346	+	0.191466i
$19$	0.352781	+	0.611035i	0.0809335	+	0.140181i	0.903651	−	0.428269i	$-0.140877\pi$
$19$	0.352781	+	0.611035i	0.0809335	+	0.140181i	−0.822718	+	0.568450i	$0.807543\pi$
$20$	−0.353580	+	4.45814i	−0.0790628	+	0.996870i
$21$	−2.74475	+	2.78960i	−0.598953	+	0.608741i
$22$	8.40459	+	2.25482i	1.79187	+	0.480730i
$23$	−0.983411	−	1.70332i	−0.205055	−	0.355166i	0.745095	−	0.666958i	$-0.232404\pi$
$23$	−0.983411	−	1.70332i	−0.205055	−	0.355166i	−0.950150	+	0.311792i	$0.899071\pi$
$24$	4.04217	−	1.07903i	0.825105	−	0.220257i
$25$	−1.79203	−	4.66783i	−0.358405	−	0.933566i
$26$	4.55424	−	1.21878i	0.893161	−	0.239022i
$27$			5.63868i			1.08516i
$28$	−1.40773	−	5.10081i	−0.266036	−	0.963963i
$29$	5.17926			0.961765			0.480882	−	0.876785i	$-0.340316\pi$
$29$	5.17926			0.961765			0.480882	+	0.876785i	$0.340316\pi$
$30$	−3.55771	+	3.03677i	−0.649547	+	0.554436i
$31$	−3.40156	+	5.89167i	−0.610937	+	1.05817i	0.380145	+	0.924927i	$0.375874\pi$
$31$	−3.40156	+	5.89167i	−0.610937	+	1.05817i	−0.991083	+	0.133248i	$0.957459\pi$
$32$	−1.47264	+	5.46181i	−0.260329	+	0.965520i
$33$	4.55073	+	7.88210i	0.792181	+	1.37210i
$34$	−0.935146	+	3.48565i	−0.160376	+	0.597784i
$35$	3.87861	+	4.46726i	0.655604	+	0.755105i
$36$	−1.40603	−	0.812947i	−0.234339	−	0.135491i
$37$	5.90431	−	3.40886i	0.970663	−	0.560412i	0.0712245	−	0.997460i	$-0.477309\pi$
$37$	5.90431	−	3.40886i	0.970663	−	0.560412i	0.899438	+	0.437048i	$0.143976\pi$
$38$	−0.705342	−	0.705783i	−0.114422	−	0.114493i
$39$	4.27040	+	2.46552i	0.683812	+	0.394799i
$40$	−1.14685	−	6.21971i	−0.181332	−	0.983422i
$41$			2.53373i			0.395702i	0.980232	+	0.197851i	$0.0633962\pi$
$41$			2.53373i			0.395702i	−0.980232	+	0.197851i	$0.936604\pi$
$42$	2.72984	−	4.81446i	0.421223	−	0.742888i
$43$	−4.59892			−0.701329			−0.350664	−	0.936501i	$-0.614044\pi$
$43$	−4.59892			−0.701329			−0.350664	+	0.936501i	$0.614044\pi$
$44$	−12.3062	−	0.00769809i	−1.85523	−	0.00116053i
$45$	1.81024	+	0.142433i	0.269855	+	0.0212326i
$46$	1.96621	+	1.96744i	0.289901	+	0.290083i
$47$	3.78388	−	2.18463i	0.551936	−	0.318660i	−0.197966	−	0.980209i	$-0.563434\pi$
$47$	3.78388	−	2.18463i	0.551936	−	0.318660i	0.749903	+	0.661548i	$0.230100\pi$
$48$	−5.12768	+	2.95192i	−0.740117	+	0.426073i
$49$	−6.11811	−	3.40128i	−0.874016	−	0.485898i
$50$	4.15471	+	5.72175i	0.587564	+	0.809177i
$51$	−3.26896	+	1.88733i	−0.457746	+	0.264280i
$52$	−5.77615	+	3.33005i	−0.801008	+	0.461794i
$53$	−4.80929	−	2.77664i	−0.660606	−	0.381401i	0.131902	−	0.991263i	$-0.457892\pi$
$53$	−4.80929	−	2.77664i	−0.660606	−	0.381401i	−0.792508	+	0.609861i	$0.791225\pi$
$54$	−2.06149	−	7.70323i	−0.280533	−	1.04828i
$55$	12.4183	−	5.92355i	1.67449	−	0.798731i
$56$	3.78800	+	6.45376i	0.506193	+	0.862420i
$57$		−	1.04364i		−	0.138234i
$58$	−7.07560	+	1.89353i	−0.929071	+	0.248632i
$59$	3.40156	−	5.89167i	0.442845	−	0.767030i	−0.555055	−	0.831814i	$-0.687303\pi$
$59$	3.40156	−	5.89167i	0.442845	−	0.767030i	0.997899	+	0.0647843i	$0.0206359\pi$
$60$	3.75010	−	5.44935i	0.484135	−	0.703508i
$61$	3.07800	−	1.77708i	0.394097	−	0.227532i	−0.289837	−	0.957076i	$-0.593601\pi$
$61$	3.07800	−	1.77708i	0.394097	−	0.227532i	0.683934	+	0.729544i	$0.260268\pi$
$62$	2.49302	−	9.29244i	0.316614	−	1.18014i
$63$	−2.07074	+	0.572881i	−0.260889	+	0.0721762i
$64$	0.0150131	−	7.99999i	0.00187664	−	0.999998i
$65$	4.22203	−	6.14336i	0.523679	−	0.761990i
$66$	−9.09862	−	9.10431i	−1.11996	−	1.12066i
$67$	−1.45061	+	2.51253i	−0.177220	+	0.306954i	−0.940927	−	0.338609i	$-0.890044\pi$
$67$	−1.45061	+	2.51253i	−0.177220	+	0.306954i	0.763707	+	0.645563i	$0.223377\pi$
$68$	0.00319264	−	5.10377i	0.000387165	−	0.618924i
$69$			2.90926i			0.350233i
$70$	−6.93194	−	4.68489i	−0.828526	−	0.559951i
$71$		−	3.37084i		−	0.400045i	−0.979791	−	0.200023i	$-0.935898\pi$
$71$		−	3.37084i		−	0.400045i	0.979791	−	0.200023i	$-0.0641016\pi$
$72$	2.21805	+	0.596556i	0.261400	+	0.0703048i
$73$	−1.27594	+	2.21000i	−0.149338	+	0.258661i	−0.930983	−	0.365063i	$-0.881048\pi$
$73$	−1.27594	+	2.21000i	−0.149338	+	0.258661i	0.781645	+	0.623724i	$0.214381\pi$
$74$	−6.81984	+	6.81558i	−0.792791	+	0.792295i
$75$	−1.15667	+	7.30482i	−0.133561	+	0.843488i
$76$	1.22163	+	0.706327i	0.140130	+	0.0810212i
$77$	−11.4177	+	11.6043i	−1.30117	+	1.32244i
$78$	−6.73536	−	1.80699i	−0.762629	−	0.204601i
$79$	5.38564	−	3.10940i	0.605932	−	0.349835i	−0.165440	−	0.986220i	$-0.552904\pi$
$79$	5.38564	−	3.10940i	0.605932	−	0.349835i	0.771372	+	0.636385i	$0.219571\pi$
$80$	3.84067	+	8.07770i	0.429400	+	0.903115i
$81$	2.95217	−	5.11331i	0.328019	−	0.568146i
$82$	−0.926327	−	3.46143i	−0.102296	−	0.382251i
$83$			4.70266i			0.516184i	0.966120	+	0.258092i	$0.0830937\pi$
$83$			4.70266i			0.516184i	−0.966120	+	0.258092i	$0.916906\pi$
$84$	−1.96918	+	7.57525i	−0.214855	+	0.826528i
$85$	2.45668	+	5.15028i	0.266465	+	0.558626i
$86$	6.28277	−	1.68136i	0.677488	−	0.181305i
$87$	−6.63461	−	3.83049i	−0.711305	−	0.410672i
$88$	16.8148	−	4.48861i	1.79247	−	0.478487i
$89$	−5.19692	+	3.00044i	−0.550873	+	0.318046i	−0.749474	−	0.662034i	$-0.769693\pi$
$89$	−5.19692	+	3.00044i	−0.550873	+	0.318046i	0.198601	+	0.980080i	$0.436360\pi$
$90$	−2.52512	+	0.467238i	−0.266171	+	0.0492512i
$91$	−2.21367	+	8.53772i	−0.232056	+	0.894996i
$92$	−3.40541	−	1.96895i	−0.355038	−	0.205278i
$93$	8.71475	−	5.03147i	0.903678	−	0.521739i
$94$	−4.37062	+	4.36789i	−0.450795	+	0.450513i
$95$	−1.57282	−	0.123752i	−0.161368	−	0.0126967i
$96$	5.92591	−	5.90740i	0.604811	−	0.602922i
$97$	−9.46331			−0.960853			−0.480427	−	0.877035i	$-0.659518\pi$
$97$	−9.46331			−0.960853			−0.480427	+	0.877035i	$0.659518\pi$
$98$	9.60170	+	2.40986i	0.969918	+	0.243433i
$99$			4.99674i			0.502191i
$100$	−7.76777	−	6.29775i	−0.776777	−	0.629775i
$101$	−7.67045	−	4.42854i	−0.763238	−	0.440656i	0.0672190	−	0.997738i	$-0.478587\pi$
$101$	−7.67045	−	4.42854i	−0.763238	−	0.440656i	−0.830457	+	0.557082i	$0.811921\pi$
$102$	3.77585	−	3.77349i	0.373865	−	0.373631i
$103$	7.34573	−	4.24106i	0.723796	−	0.417884i	−0.0923523	−	0.995726i	$-0.529439\pi$
$103$	7.34573	−	4.24106i	0.723796	−	0.417884i	0.816148	+	0.577843i	$0.196105\pi$
$104$	6.67357	−	6.66106i	0.654397	−	0.653171i
$105$	−1.66457	−	8.59109i	−0.162445	−	0.838405i
$106$	7.58530	+	2.03502i	0.736749	+	0.197658i
$107$	0.354428	+	0.613887i	0.0342638	+	0.0593467i	0.882649	−	0.470033i	$-0.155758\pi$
$107$	0.354428	+	0.613887i	0.0342638	+	0.0593467i	−0.848385	+	0.529380i	$0.822425\pi$
$108$	5.63257	+	9.77001i	0.541994	+	0.940119i
$109$	1.54614	−	2.67799i	0.148093	−	0.256505i	−0.782429	−	0.622739i	$-0.786020\pi$
$109$	1.54614	−	2.67799i	0.148093	−	0.256505i	0.930523	+	0.366234i	$0.119353\pi$
$110$	−14.7995	+	12.6325i	−1.41108	+	1.20446i
$111$	−10.0845			−0.957181
$112$	−7.53442	−	7.43185i	−0.711936	−	0.702244i
$113$		−	14.7206i		−	1.38479i	−0.721517	−	0.692397i	$-0.756555\pi$
$113$		−	14.7206i		−	1.38479i	0.721517	−	0.692397i	$-0.243445\pi$
$114$	0.381554	+	1.42576i	0.0357358	+	0.133535i
$115$	4.38440	+	0.344972i	0.408847	+	0.0321688i
$116$	8.97398	−	5.17365i	0.833213	−	0.480361i
$117$	1.35358	+	2.34447i	0.125138	+	0.216746i
$118$	−2.49302	+	9.29244i	−0.229501	+	0.855439i
$119$	−4.81268	−	4.73530i	−0.441178	−	0.434084i
$120$	−3.13088	+	8.81560i	−0.285809	+	0.804751i
$121$	13.4304	+	23.2621i	1.22094	+	2.11473i
$122$	−3.55528	+	3.55305i	−0.321880	+	0.321678i
$123$	1.87390	−	3.24570i	0.168964	−	0.292655i
$124$	−0.00851131	+	13.6062i	−0.000764338	+	1.22187i
$125$	10.8716	+	2.60935i	0.972384	+	0.233387i
$126$	2.61948	−	1.53970i	0.233362	−	0.137167i
$127$	4.48071			0.397599			0.198800	−	0.980040i	$-0.436296\pi$
$127$	4.48071			0.397599			0.198800	+	0.980040i	$0.436296\pi$
$128$	2.90427	+	10.9346i	0.256704	+	0.966490i
$129$	5.89120	+	3.40128i	0.518691	+	0.299466i
$130$	−3.52189	+	9.93625i	−0.308890	+	0.871467i
$131$	−8.09104	−	14.0141i	−0.706917	−	1.22442i	−0.965995	−	0.258560i	$-0.916752\pi$
$131$	−8.09104	−	14.0141i	−0.706917	−	1.22442i	0.259078	−	0.965856i	$-0.416581\pi$
$132$	15.7585	+	9.11132i	1.37160	+	0.793039i
$133$	1.79916	−	0.497746i	0.156007	−	0.0431600i
$134$	1.06316	−	3.96280i	0.0918429	−	0.342334i
$135$	−10.3911	−	7.14131i	−0.894325	−	0.614626i
$136$	1.86157	+	6.97364i	0.159628	+	0.597984i
$137$	9.27211	+	5.35325i	0.792170	+	0.457359i	0.840726	−	0.541461i	$-0.182129\pi$
$137$	9.27211	+	5.35325i	0.792170	+	0.457359i	−0.0485562	+	0.998820i	$0.515462\pi$
$138$	−1.06362	−	3.97445i	−0.0905413	−	0.338328i
$139$	−16.1633			−1.37095			−0.685475	−	0.728096i	$-0.740406\pi$
$139$	−16.1633			−1.37095			−0.685475	+	0.728096i	$0.740406\pi$
$140$	11.1828	+	3.86591i	0.945118	+	0.326729i
$141$	−6.46285			−0.544270
$142$	1.23237	+	4.60504i	0.103418	+	0.386446i
$143$	17.7642	+	10.2562i	1.48552	+	0.857665i
$144$	−3.24827	−	0.00406388i	−0.270689	−	0.000338657i
$145$	−6.55946	+	9.54449i	−0.544734	+	0.792626i
$146$	0.935146	−	3.48565i	0.0773932	−	0.288475i
$147$	5.32174	+	8.88188i	0.438930	+	0.732565i
$148$	6.82510	−	11.8044i	0.561019	−	0.970312i
$149$	−3.79441	−	6.57211i	−0.310850	−	0.538408i	0.667697	−	0.744434i	$-0.267280\pi$
$149$	−3.79441	−	6.57211i	−0.310850	−	0.538408i	−0.978547	+	0.206025i	$0.933947\pi$
$150$	−1.09045	−	10.4023i	−0.0890352	−	0.849343i
$151$	1.80399	+	1.04154i	0.146807	+	0.0847590i	0.571604	−	0.820530i	$-0.306321\pi$
$151$	1.80399	+	1.04154i	0.146807	+	0.0847590i	−0.424797	+	0.905288i	$0.639655\pi$
$152$	−1.92715	−	0.518316i	−0.156312	−	0.0420410i
$153$	−2.07230			−0.167536
$154$	11.3557	−	20.0274i	0.915069	−	1.61386i
$155$	−6.54930	−	13.7302i	−0.526053	−	1.10284i
$156$	9.86207	+	0.00616917i	0.789597	+	0.000493929i
$157$	6.52053	−	11.2939i	0.520395	−	0.901351i	−0.479324	−	0.877638i	$-0.659118\pi$
$157$	6.52053	−	11.2939i	0.520395	−	0.901351i	0.999719	−	0.0237128i	$-0.00754873\pi$
$158$	−6.22075	+	6.21686i	−0.494896	+	0.494587i
$159$	4.10712	+	7.11374i	0.325716	+	0.564156i
$160$	−8.20008	−	9.63113i	−0.648273	−	0.761408i
$161$	−5.01533	+	1.38751i	−0.395263	+	0.109351i
$162$	−2.16366	+	8.06481i	−0.169993	+	0.633631i
$163$	0.754695	+	1.30717i	0.0591123	+	0.102386i	0.894067	−	0.447933i	$-0.147840\pi$
$163$	0.754695	+	1.30717i	0.0591123	+	0.102386i	−0.834955	+	0.550318i	$0.814506\pi$
$164$	2.53098	+	4.39013i	0.197637	+	0.342812i
$165$	−20.2888	−	1.59636i	−1.57948	−	0.124276i
$166$	−1.71928	−	6.42449i	−0.133442	−	0.498637i
$167$		−	20.2522i		−	1.56716i	−0.621290	−	0.783581i	$-0.713391\pi$
$167$		−	20.2522i		−	1.56716i	0.621290	−	0.783581i	$-0.286609\pi$
$168$	−0.0793216	−	11.0688i	−0.00611979	−	0.853975i
$169$	−1.88672			−0.145132
$170$	−5.23910	−	6.13784i	−0.401821	−	0.470751i
$171$	0.286482	−	0.496201i	0.0219078	−	0.0379455i
$172$	−7.96844	+	4.59394i	−0.607588	+	0.350284i
$173$	4.86816	+	8.43190i	0.370119	+	0.641065i	0.989584	−	0.143960i	$-0.0459835\pi$
$173$	4.86816	+	8.43190i	0.370119	+	0.641065i	−0.619464	+	0.785025i	$0.712650\pi$
$174$	10.4642	+	2.80739i	0.793291	+	0.212828i
$175$	−13.1446	+	1.48988i	−0.993638	+	0.112625i
$176$	−21.3304	+	12.2795i	−1.60784	+	0.925605i
$177$	−8.71475	+	5.03147i	−0.655041	+	0.378188i
$178$	6.00276	−	5.99901i	0.449926	−	0.449645i
$179$	5.99116	+	3.45900i	0.447800	+	0.258538i	0.706901	−	0.707313i	$-0.250093\pi$
$179$	5.99116	+	3.45900i	0.447800	+	0.258538i	−0.259100	+	0.965850i	$0.583426\pi$
$180$	3.27884	−	1.56149i	0.244391	−	0.116387i
$181$		−	23.5933i		−	1.75367i	−0.480789	−	0.876836i	$-0.659650\pi$
$181$		−	23.5933i		−	1.75367i	0.480789	−	0.876836i	$-0.340350\pi$
$182$	−0.0971876	−	12.4730i	−0.00720403	−	0.924563i
$183$	−5.25720			−0.388623
$184$	5.37211	+	1.44486i	0.396037	+	0.106516i
$185$	−1.19580	+	15.1979i	−0.0879166	+	1.11737i
$186$	−10.0661	+	10.0598i	−0.738081	+	0.737619i
$187$	−13.5984	+	7.85102i	−0.994411	+	0.574123i
$188$	4.37399	−	7.56503i	0.319006	−	0.551737i
$189$	14.4410	+	3.74429i	1.05043	+	0.272357i
$190$	2.19394	−	0.405959i	0.159165	−	0.0294513i
$191$	9.40212	−	5.42832i	0.680313	−	0.392779i	−0.119660	−	0.992815i	$-0.538180\pi$
$191$	9.40212	−	5.42832i	0.680313	−	0.392779i	0.799973	+	0.600036i	$0.204847\pi$
$192$	−5.93589	+	10.2368i	−0.428386	+	0.738780i
$193$	−6.57523	−	3.79621i	−0.473295	−	0.273257i	0.244323	−	0.969694i	$-0.421434\pi$
$193$	−6.57523	−	3.79621i	−0.473295	−	0.273257i	−0.717618	+	0.696437i	$0.754768\pi$
$194$	12.9282	−	3.45977i	0.928191	−	0.248397i
$195$	−9.95193	+	4.74707i	−0.712672	+	0.339945i
$196$	−13.9983	+	0.218158i	−0.999879	+	0.0155827i
$197$		−	13.5289i		−	0.963896i	−0.876200	−	0.481948i	$-0.839929\pi$
$197$		−	13.5289i		−	0.963896i	0.876200	−	0.481948i	$-0.160071\pi$
$198$	−1.82680	−	6.82624i	−0.129825	−	0.485120i
$199$	2.27997	−	3.94903i	0.161623	−	0.279939i	−0.773828	−	0.633396i	$-0.781661\pi$
$199$	2.27997	−	3.94903i	0.161623	−	0.279939i	0.935451	+	0.353457i	$0.114994\pi$
$200$	12.9143	+	5.76373i	0.913180	+	0.407557i
$201$	3.71644	−	2.14569i	0.262138	−	0.151345i
$202$	12.0980	+	3.24570i	0.851210	+	0.228366i
$203$	3.43922	−	13.2644i	0.241386	−	0.930980i
$204$	−3.77876	+	6.53555i	−0.264566	+	0.457580i
$205$	−4.66923	−	3.20893i	−0.326113	−	0.224122i
$206$	−8.48477	+	8.47946i	−0.591162	+	0.590792i
$207$	−0.798596	+	1.38321i	−0.0555063	+	0.0961397i
$208$	−6.68176	+	11.5398i	−0.463297	+	0.800140i
$209$		−	4.34140i		−	0.300301i
$210$	5.41492	+	11.1281i	0.373665	+	0.767910i
$211$			10.6803i			0.735263i	0.929971	+	0.367632i	$0.119831\pi$
$211$			10.6803i			0.735263i	−0.929971	+	0.367632i	$0.880169\pi$
$212$	−11.1066	−	0.00694767i	−0.762803	−	0.000477168i
$213$	−2.49302	+	4.31803i	−0.170819	+	0.295867i
$214$	−0.708633	−	0.709077i	−0.0484412	−	0.0484715i
$215$	5.82447	−	8.47502i	0.397225	−	0.577991i
$216$	−11.2668	−	11.2879i	−0.766607	−	0.768047i
$217$	12.8302	+	12.6239i	0.870970	+	0.856965i
$218$	−1.13317	+	4.22377i	−0.0767482	+	0.286070i
$219$	3.26896	−	1.88733i	0.220896	−	0.127534i
$220$	15.5998	−	22.6685i	1.05174	−	1.52831i
$221$	−4.25356	+	7.36739i	−0.286126	+	0.495584i
$222$	13.7769	−	3.68688i	0.924643	−	0.247447i
$223$			10.9683i			0.734492i	0.930124	+	0.367246i	$0.119699\pi$
$223$			10.9683i			0.734492i	−0.930124	+	0.367246i	$0.880301\pi$
$224$	13.0101	+	7.39838i	0.869277	+	0.494325i
$225$	−2.55513	+	3.15558i	−0.170342	+	0.210372i
$226$	5.38181	+	20.1103i	0.357993	+	1.33772i
$227$	−9.75105	−	5.62977i	−0.647200	−	0.373661i	0.140183	−	0.990126i	$-0.455231\pi$
$227$	−9.75105	−	5.62977i	−0.647200	−	0.373661i	−0.787383	+	0.616465i	$0.788564\pi$
$228$	−1.04251	−	1.80830i	−0.0690421	−	0.119757i
$229$	−6.16780	+	3.56098i	−0.407580	+	0.235316i	−0.689749	−	0.724048i	$-0.742279\pi$
$229$	−6.16780	+	3.56098i	−0.407580	+	0.235316i	0.282169	+	0.959365i	$0.408946\pi$
$230$	−6.11582	+	1.13165i	−0.403265	+	0.0746187i
$231$	23.2084	−	6.42072i	1.52700	−	0.422452i
$232$	−10.3682	+	10.3488i	−0.680708	+	0.679432i
$233$	−4.87233	+	2.81304i	−0.319197	+	0.184289i	−0.651035	−	0.759048i	$-0.725665\pi$
$233$	−4.87233	+	2.81304i	−0.319197	+	0.184289i	0.331838	+	0.943337i	$0.392331\pi$
$234$	−2.70631	−	2.70800i	−0.176917	−	0.177028i
$235$	−0.766347	+	9.73984i	−0.0499910	+	0.635357i
$236$	0.00851131	−	13.6062i	0.000554039	−	0.885689i
$237$	−9.19865			−0.597516
$238$	8.30601	+	4.70957i	0.538399	+	0.305276i
$239$			18.9288i			1.22440i	0.790701	+	0.612202i	$0.209716\pi$
$239$			18.9288i			1.22440i	−0.790701	+	0.612202i	$0.790284\pi$
$240$	1.05426	−	13.1880i	0.0680519	−	0.851281i
$241$	−4.08233	−	2.35694i	−0.262966	−	0.151824i	0.362721	−	0.931898i	$-0.381848\pi$
$241$	−4.08233	−	2.35694i	−0.262966	−	0.151824i	−0.625687	+	0.780074i	$0.715181\pi$
$242$	−26.8523	−	26.8691i	−1.72613	−	1.72721i
$243$	7.08628	−	4.09127i	0.454585	−	0.262455i
$244$	3.55801	−	6.15377i	0.227779	−	0.393955i
$245$	14.0165	−	6.96694i	0.895480	−	0.445102i
$246$	−1.37339	+	5.11917i	−0.0875644	+	0.326386i
$247$	−1.17605	−	2.03698i	−0.0748304	−	0.129610i
$248$	−4.96278	−	18.5911i	−0.315137	−	1.18054i
$249$	3.47801	−	6.02408i	0.220410	−	0.381761i
$250$	−15.8061	+	0.409896i	−0.999664	+	0.0259241i
$251$	23.7582			1.49961			0.749803	−	0.661661i	$-0.230148\pi$
$251$	23.7582			1.49961			0.749803	+	0.661661i	$0.230148\pi$
$252$	−3.01567	+	3.06112i	−0.189969	+	0.192832i
$253$			12.1021i			0.760850i
$254$	−6.12128	+	1.63814i	−0.384083	+	0.102786i
$255$	0.662059	−	8.41440i	0.0414598	−	0.526930i
$256$	−7.96530	−	13.8764i	−0.497831	−	0.867274i
$257$	−7.61973	−	13.1978i	−0.475306	−	0.823254i	0.524294	−	0.851537i	$-0.324329\pi$
$257$	−7.61973	−	13.1978i	−0.475306	−	0.823254i	−0.999600	+	0.0282835i	$0.990996\pi$
$258$	−9.29170	−	2.49282i	−0.578476	−	0.155196i
$259$	−4.80962	−	17.3849i	−0.298855	−	1.08025i
$260$	1.17871	−	14.8619i	0.0731007	−	0.921696i
$261$	−2.10295	−	3.64242i	−0.130170	−	0.225460i
$262$	16.1770	+	16.1871i	0.999419	+	1.00004i
$263$	−8.46144	+	14.6556i	−0.521755	+	0.903705i	0.477925	+	0.878401i	$0.341389\pi$
$263$	−8.46144	+	14.6556i	−0.521755	+	0.903705i	−0.999680	+	0.0253049i	$0.991944\pi$
$264$	−24.8594	−	6.68606i	−1.52999	−	0.411499i
$265$	11.2078	−	5.34611i	0.688488	−	0.328409i
$266$	−2.27593	+	1.33776i	−0.139546	+	0.0820233i
$267$	8.87631			0.543221
$268$	−0.00362968	+	5.80243i	−0.000221718	+	0.354440i
$269$	−0.516112	−	0.297978i	−0.0314679	−	0.0181680i	0.484184	−	0.874966i	$-0.339117\pi$
$269$	−0.516112	−	0.297978i	−0.0314679	−	0.0181680i	−0.515651	+	0.856798i	$0.672450\pi$
$270$	16.8066	+	5.95706i	1.02282	+	0.362535i
$271$	7.12334	+	12.3380i	0.432712	+	0.749479i	0.997106	−	0.0760266i	$-0.0242234\pi$
$271$	7.12334	+	12.3380i	0.432712	+	0.749479i	−0.564394	+	0.825506i	$0.690890\pi$
$272$	−5.09271	−	8.84638i	−0.308791	−	0.536390i
$273$	9.15006	−	9.29958i	0.553787	−	0.562836i
$274$	−14.6241	−	3.92343i	−0.883476	−	0.237023i
$275$	−4.81158	+	30.3869i	−0.290149	+	1.83240i
$276$	2.90610	+	5.04080i	0.174927	+	0.303421i
$277$	20.0576	+	11.5802i	1.20514	+	0.695789i	0.961694	−	0.274124i	$-0.0883880\pi$
$277$	20.0576	+	11.5802i	1.20514	+	0.695789i	0.243448	+	0.969914i	$0.421721\pi$
$278$	22.0813	−	5.90926i	1.32435	−	0.354414i
$279$	5.52458			0.330748
$280$	−16.6906	−	1.19296i	−0.997455	−	0.0712932i
$281$	−6.58882			−0.393056			−0.196528	−	0.980498i	$-0.562967\pi$
$281$	−6.58882			−0.393056			−0.196528	+	0.980498i	$0.562967\pi$
$282$	8.82916	−	2.36281i	0.525769	−	0.140703i
$283$	−23.2154	−	13.4034i	−1.38001	−	0.796751i	−0.387852	−	0.921722i	$-0.626783\pi$
$283$	−23.2154	−	13.4034i	−1.38001	−	0.796751i	−0.992160	+	0.124971i	$0.960116\pi$
$284$	−3.36719	−	5.84058i	−0.199806	−	0.346574i
$285$	1.92326	+	1.32176i	0.113924	+	0.0782943i
$286$	−28.0180	−	7.51681i	−1.65674	−	0.444478i
$287$	6.48905	+	1.68249i	0.383036	+	0.0993143i
$288$	4.43907	−	1.18201i	0.261575	−	0.0696505i
$289$	5.24393	+	9.08276i	0.308467	+	0.534280i
$290$	5.47170	−	15.4372i	0.321309	−	0.906505i
$291$	12.1225	+	6.99890i	0.710631	+	0.410283i
$292$	−0.00319264	+	5.10377i	−0.000186835	+	0.298676i
$293$	14.2428			0.832071			0.416036	−	0.909348i	$-0.363419\pi$
$293$	14.2428			0.832071			0.416036	+	0.909348i	$0.363419\pi$
$294$	−10.5174	−	10.1883i	−0.613390	−	0.594192i
$295$	6.54930	+	13.7302i	0.381315	+	0.799403i
$296$	−5.00839	+	18.6216i	−0.291107	+	1.08236i
$297$	17.3477	−	30.0471i	1.00662	−	1.74351i
$298$	7.58644	+	7.59119i	0.439471	+	0.439746i
$299$	3.27836	+	5.67828i	0.189592	+	0.328384i
$300$	5.29277	+	13.8123i	0.305578	+	0.797454i
$301$	−3.05385	+	11.7781i	−0.176021	+	0.678880i
$302$	−2.84529	−	0.763347i	−0.163728	−	0.0439257i
$303$	6.55054	+	11.3459i	0.376319	+	0.651803i
$304$	2.82225	+	0.00353089i	0.161867	+	0.000202510i
$305$	−0.623384	+	7.92287i	−0.0356949	+	0.453662i
$306$	2.83106	−	0.757631i	0.161841	−	0.0433109i
$307$			26.0778i			1.48834i	0.667991	+	0.744169i	$0.267154\pi$
$307$			26.0778i			1.48834i	−0.667991	+	0.744169i	$0.732846\pi$
$308$	−8.19149	+	31.5119i	−0.466754	+	1.79556i
$309$	−12.5465			−0.713743
$310$	13.9670	+	16.3630i	0.793272	+	0.929353i
$311$	−1.47742	+	2.55897i	−0.0837770	+	0.145106i	−0.904869	−	0.425689i	$-0.860032\pi$
$311$	−1.47742	+	2.55897i	−0.0837770	+	0.145106i	0.821092	+	0.570795i	$0.193365\pi$
$312$	−13.4752	+	3.59713i	−0.762884	+	0.203647i
$313$	−11.7352	−	20.3259i	−0.663311	−	1.14889i	−0.979740	−	0.200272i	$-0.935818\pi$
$313$	−11.7352	−	20.3259i	−0.663311	−	1.14889i	0.316430	−	0.948616i	$-0.397516\pi$
$314$	−4.77893	+	17.8129i	−0.269691	+	1.00524i
$315$	1.56685	−	4.54157i	0.0882819	−	0.255888i
$316$	6.22554	−	10.7674i	0.350214	−	0.605713i
$317$	−11.5127	+	6.64685i	−0.646616	+	0.373324i	−0.787159	−	0.616751i	$-0.788449\pi$
$317$	−11.5127	+	6.64685i	−0.646616	+	0.373324i	0.140542	+	0.990075i	$0.455115\pi$
$318$	−8.21167	−	8.21680i	−0.460487	−	0.460775i
$319$	−27.5990	−	15.9343i	−1.54525	−	0.892148i
$320$	14.7236	+	10.1595i	0.823073	+	0.567935i
$321$		−	1.04851i		−	0.0585224i
$322$	6.34437	−	3.72913i	0.353558	−	0.207817i
$323$	1.80052			0.100183
$324$	0.00738687	−	11.8087i	0.000410382	−	0.656038i
$325$	5.97400	+	15.5610i	0.331378	+	0.863167i
$326$	−1.50892	−	1.50986i	−0.0835713	−	0.0836236i
$327$	−3.96119	+	2.28700i	−0.219054	+	0.126471i
$328$	−5.06270	−	5.07221i	−0.279541	−	0.280066i
$329$	−3.08233	−	11.1414i	−0.169934	−	0.614248i
$330$	28.3009	−	5.23670i	1.55792	−	0.288271i
$331$	26.5406	−	15.3232i	1.45880	−	0.842241i	0.459852	−	0.887996i	$-0.347902\pi$
$331$	26.5406	−	15.3232i	1.45880	−	0.842241i	0.998953	+	0.0457544i	$0.0145692\pi$
$332$	4.69756	+	8.14818i	0.257812	+	0.447189i
$333$	−4.79470	−	2.76822i	−0.262748	−	0.151698i
$334$	7.40416	+	27.6673i	0.405138	+	1.51389i
$335$	−2.79298	−	5.85530i	−0.152597	−	0.319909i
$336$	4.15509	+	15.0925i	0.226679	+	0.823364i
$337$			16.1059i			0.877346i	0.898647	+	0.438673i	$0.144551\pi$
$337$			16.1059i			0.877346i	−0.898647	+	0.438673i	$0.855449\pi$
$338$	2.57752	−	0.689781i	0.140199	−	0.0375191i
$339$	−10.8871	+	18.8570i	−0.591305	+	1.02417i
$340$	9.40133	+	6.46974i	0.509859	+	0.350871i
$341$	36.2520	−	20.9301i	1.96316	−	1.13343i
$342$	−0.209964	+	0.782618i	−0.0113536	+	0.0423191i
$343$	−12.7736	+	13.4103i	−0.689707	+	0.724088i
$344$	9.20647	−	9.18921i	0.496379	−	0.495449i
$345$	−5.36126	−	3.68453i	−0.288641	−	0.198369i
$346$	−9.73327	−	9.73936i	−0.523264	−	0.523591i
$347$	17.5378	−	30.3763i	0.941477	−	1.63069i	0.178820	−	0.983882i	$-0.442772\pi$
$347$	17.5378	−	30.3763i	0.941477	−	1.63069i	0.762657	−	0.646803i	$-0.223895\pi$
$348$	−15.3220	−	0.00958459i	−0.821344	−	0.000513788i
$349$			20.3154i			1.08746i	0.839261	+	0.543729i	$0.182988\pi$
$349$			20.3154i			1.08746i	−0.839261	+	0.543729i	$0.817012\pi$
$350$	17.4126	−	6.84103i	0.930745	−	0.365668i
$351$		−	18.7974i		−	1.00333i
$352$	24.6509	−	24.5739i	1.31390	−	1.30979i
$353$	−14.4826	+	25.0845i	−0.770829	+	1.33511i	0.166280	+	0.986079i	$0.446824\pi$
$353$	−14.4826	+	25.0845i	−0.770829	+	1.33511i	−0.937109	+	0.349036i	$0.886509\pi$
$354$	10.0661	−	10.0598i	0.535006	−	0.534671i
$355$	6.21188	+	4.26912i	0.329692	+	0.226582i
$356$	−6.00739	+	10.3901i	−0.318391	+	0.550673i
$357$	2.66288	+	9.62527i	0.140934	+	0.509423i
$358$	−9.44937	−	2.53512i	−0.499415	−	0.133985i
$359$	−8.85350	+	5.11157i	−0.467270	+	0.269778i	−0.715096	−	0.699026i	$-0.753617\pi$
$359$	−8.85350	+	5.11157i	−0.467270	+	0.269778i	0.247826	+	0.968804i	$0.420284\pi$
$360$	−3.90848	+	3.33195i	−0.205995	+	0.175609i
$361$	9.25109	−	16.0234i	0.486900	−	0.843335i
$362$	8.62565	+	32.2317i	0.453354	+	1.69406i
$363$		−	39.7314i		−	2.08536i
$364$	4.69289	+	17.0044i	0.245974	+	0.891271i
$365$	−2.45668	−	5.15028i	−0.128589	−	0.269578i
$366$	7.18207	−	1.92202i	0.375413	−	0.100466i
$367$	24.4416	+	14.1114i	1.27584	+	0.736608i	0.976081	−	0.217406i	$-0.0697597\pi$
$367$	24.4416	+	14.1114i	1.27584	+	0.736608i	0.299761	+	0.954014i	$0.403093\pi$
$368$	−7.86728	−	0.00984269i	−0.410111	−	0.000513086i
$369$	1.78190	−	1.02878i	0.0927620	−	0.0535561i
$370$	−3.92270	−	21.1996i	−0.203931	−	1.10212i
$371$	−10.3047	+	10.4731i	−0.534994	+	0.543737i
$372$	10.0738	−	17.4232i	0.522304	−	0.903351i
$373$	−11.1106	+	6.41470i	−0.575285	+	0.332141i	−0.759257	−	0.650791i	$-0.774438\pi$
$373$	−11.1106	+	6.41470i	−0.575285	+	0.332141i	0.183973	+	0.982931i	$0.441104\pi$
$374$	15.7069	−	15.6971i	0.812187	−	0.811679i
$375$	−11.9966	−	11.3830i	−0.619503	−	0.587816i
$376$	−3.20971	+	11.9340i	−0.165528	+	0.615450i
$377$	−17.2659			−0.889239
$378$	−21.0974	+	0.164387i	−1.08513	+	0.00845515i
$379$		−	18.2296i		−	0.936394i	−0.883624	−	0.468197i	$-0.844904\pi$
$379$		−	18.2296i		−	0.936394i	0.883624	−	0.468197i	$-0.155096\pi$
$380$	−2.84881	+	1.35670i	−0.146141	+	0.0695971i
$381$	−5.73977	−	3.31386i	−0.294058	−	0.169774i
$382$	−10.8600	+	10.8532i	−0.555647	+	0.555300i
$383$	−29.2023	+	16.8600i	−1.49217	+	0.861504i	−0.999960	−	0.00897238i	$-0.997144\pi$
$383$	−29.2023	+	16.8600i	−1.49217	+	0.861504i	−0.492210	+	0.870477i	$0.663811\pi$
$384$	4.36668	−	16.1551i	0.222836	−	0.824412i
$385$	−6.92436	−	35.7376i	−0.352898	−	1.82136i
$386$	10.3706	+	2.78226i	0.527848	+	0.141613i
$387$	1.86732	+	3.23429i	0.0949210	+	0.164408i
$388$	−16.3968	+	9.45305i	−0.832424	+	0.479906i
$389$	−17.3437	+	30.0401i	−0.879360	+	1.52310i	−0.0273150	+	0.999627i	$0.508696\pi$
$389$	−17.3437	+	30.0401i	−0.879360	+	1.52310i	−0.852045	+	0.523469i	$0.824638\pi$
$390$	11.8602	−	10.1236i	0.600565	−	0.512627i
$391$	−5.01911			−0.253827
$392$	19.0439	−	5.41579i	0.961861	−	0.273539i
$393$			23.9360i			1.20741i
$394$	4.94615	+	18.4824i	0.249184	+	0.931130i
$395$	−1.09075	+	13.8628i	−0.0548816	+	0.697515i
$396$	4.99132	+	8.65772i	0.250823	+	0.435067i
$397$	−14.2787	−	24.7314i	−0.716627	−	1.24124i	−0.962328	−	0.271890i	$-0.912351\pi$
$397$	−14.2787	−	24.7314i	−0.716627	−	1.24124i	0.245701	−	0.969346i	$-0.420982\pi$
$398$	−1.67100	+	6.22848i	−0.0837598	+	0.312205i
$399$	−2.67284	−	0.693018i	−0.133809	−	0.0346943i
$400$	−19.7500	−	3.15261i	−0.987498	−	0.157631i
$401$	−1.67926	−	2.90857i	−0.0838583	−	0.145247i	0.821046	−	0.570862i	$-0.193391\pi$
$401$	−1.67926	−	2.90857i	−0.0838583	−	0.145247i	−0.904904	+	0.425615i	$0.860058\pi$
$402$	−4.29272	+	4.29004i	−0.214102	+	0.213968i
$403$	11.3396	−	19.6408i	0.564867	−	0.978378i
$404$	−17.7141	−	0.0110810i	−0.881311	−	0.000551300i
$405$	5.68407	+	11.9163i	0.282444	+	0.592125i
$406$	0.150993	+	19.3784i	0.00749367	+	0.961736i
$407$	−41.9501			−2.07939
$408$	2.77292	−	10.3100i	0.137280	−	0.510420i
$409$	−6.05900	−	3.49816i	−0.299598	−	0.172973i	0.342664	−	0.939458i	$-0.388671\pi$
$409$	−6.05900	−	3.49816i	−0.299598	−	0.172973i	−0.642262	+	0.766485i	$0.722004\pi$
$410$	7.55200	+	2.67679i	0.372967	+	0.132197i
$411$	−7.91835	−	13.7150i	−0.390583	−	0.676510i
$412$	8.49130	−	14.6861i	0.418336	−	0.723534i
$413$	−12.8302	−	12.6239i	−0.631332	−	0.621181i
$414$	0.585295	−	2.18162i	0.0287657	−	0.107221i
$415$	−8.66618	−	5.95585i	−0.425406	−	0.292361i
$416$	4.90930	−	18.2078i	0.240698	−	0.892711i
$417$	20.7051	+	11.9541i	1.01393	+	0.585394i
$418$	1.58721	+	5.93096i	0.0776329	+	0.290093i
$419$	10.0657			0.491743			0.245871	−	0.969302i	$-0.420926\pi$
$419$	10.0657			0.491743			0.245871	+	0.969302i	$0.420926\pi$
$420$	−11.4659	−	13.2228i	−0.559481	−	0.645207i
$421$	−8.08361			−0.393971			−0.196985	−	0.980406i	$-0.563115\pi$
$421$	−8.08361			−0.393971			−0.196985	+	0.980406i	$0.563115\pi$
$422$	−3.90470	−	14.5908i	−0.190078	−	0.710269i
$423$	−3.07277	−	1.77406i	−0.149403	−	0.0862579i
$424$	15.1757	−	4.05105i	0.736996	−	0.196736i
$425$	−12.6024	−	1.99551i	−0.611308	−	0.0967966i
$426$	1.82715	−	6.81048i	0.0885255	−	0.329969i
$427$	−2.50732	−	9.06300i	−0.121338	−	0.438589i
$428$	1.22733	+	0.709623i	0.0593252	+	0.0343009i
$429$	−15.1706	−	26.2762i	−0.732443	−	1.26863i
$430$	−4.85859	+	13.7075i	−0.234302	+	0.661033i
$431$	−1.70089	−	0.982009i	−0.0819290	−	0.0473017i	0.458476	−	0.888707i	$-0.348396\pi$
$431$	−1.70089	−	0.982009i	−0.0819290	−	0.0473017i	−0.540405	+	0.841405i	$0.681729\pi$
$432$	19.5188	+	11.3018i	0.939101	+	0.543758i
$433$	32.6523			1.56917			0.784584	−	0.620022i	$-0.212877\pi$
$433$	32.6523			1.56917			0.784584	+	0.620022i	$0.212877\pi$
$434$	−22.1431	−	12.5553i	−1.06290	−	0.602674i
$435$	15.4616	−	7.37518i	0.741326	−	0.353613i
$436$	0.00386872	−	6.18455i	0.000185278	−	0.296186i
$437$	0.693858	−	1.20180i	0.0331917	−	0.0574898i
$438$	−3.77585	+	3.77349i	−0.180417	+	0.180304i
$439$	−12.2319	−	21.1863i	−0.583797	−	1.01117i	−0.995024	−	0.0996329i	$-0.968233\pi$
$439$	−12.2319	−	21.1863i	−0.583797	−	1.01117i	0.411228	−	0.911533i	$-0.365100\pi$
$440$	−13.0240	+	36.6716i	−0.620895	+	1.74825i
$441$	0.0921348	+	5.68372i	0.00438737	+	0.270654i
$442$	3.11746	−	11.6200i	0.148282	−	0.552706i
$443$	−18.7990	−	32.5609i	−0.893169	−	1.54701i	−0.836054	−	0.548647i	$-0.815143\pi$
$443$	−18.7990	−	32.5609i	−0.893169	−	1.54701i	−0.0571150	−	0.998368i	$-0.518190\pi$
$444$	−17.4732	+	10.0736i	−0.829242	+	0.478072i
$445$	1.05253	−	13.3770i	0.0498946	−	0.634133i
$446$	−4.00999	−	14.9842i	−0.189879	−	0.709525i
$447$			11.2251i			0.530930i
$448$	−20.4785	−	5.35074i	−0.967519	−	0.252798i
$449$	30.2759			1.42881			0.714404	−	0.699733i	$-0.246698\pi$
$449$	30.2759			1.42881			0.714404	+	0.699733i	$0.246698\pi$
$450$	2.33699	−	5.24511i	0.110167	−	0.247257i
$451$	7.79515	−	13.5016i	0.367059	−	0.635766i
$452$	−14.7046	−	25.5060i	−0.691646	−	1.19970i
$453$	−1.54060	−	2.66841i	−0.0723839	−	0.125373i
$454$	15.3795	+	4.12609i	0.721797	+	0.193647i
$455$	−12.9300	−	14.8923i	−0.606166	−	0.698163i
$456$	2.08533	+	2.08925i	0.0976544	+	0.0978379i
$457$	−23.0145	+	13.2874i	−1.07657	+	0.621559i	−0.929969	−	0.367637i	$-0.880167\pi$
$457$	−23.0145	+	13.2874i	−1.07657	+	0.621559i	−0.146602	+	0.989196i	$0.546834\pi$
$458$	7.12419	−	7.11974i	0.332892	−	0.332683i
$459$	12.4615	+	7.19464i	0.581652	+	0.335817i
$460$	7.94134	−	3.78192i	0.370267	−	0.176333i
$461$			26.3218i			1.22593i	0.790110	+	0.612965i	$0.210023\pi$
$461$			26.3218i			1.22593i	−0.790110	+	0.612965i	$0.789977\pi$
$462$	−29.3586	+	17.2566i	−1.36588	+	0.802848i
$463$	33.8611			1.57366			0.786830	−	0.617169i	$-0.211721\pi$
$463$	33.8611			1.57366			0.786830	+	0.617169i	$0.211721\pi$
$464$	10.3810	−	17.9285i	0.481924	−	0.832310i
$465$	−1.76499	+	22.4321i	−0.0818495	+	1.04026i
$466$	5.62784	−	5.62432i	0.260705	−	0.260542i
$467$	18.0343	−	10.4121i	0.834526	−	0.481814i	−0.0208739	−	0.999782i	$-0.506645\pi$
$467$	18.0343	−	10.4121i	0.834526	−	0.481814i	0.855400	+	0.517968i	$0.173312\pi$
$468$	4.68724	+	2.71009i	0.216668	+	0.125274i
$469$	5.47149	+	5.38351i	0.252650	+	0.248588i
$470$	−2.51393	−	13.5862i	−0.115959	−	0.626683i
$471$	−16.7056	+	9.64495i	−0.769751	+	0.444416i
$472$	4.96278	+	18.5911i	0.228430	+	0.855725i
$473$	24.5065	+	14.1488i	1.12681	+	0.650563i
$474$	12.5666	−	3.36301i	0.577205	−	0.154468i
$475$	2.22001	−	2.74171i	0.101861	−	0.125798i
$476$	−13.0690	−	3.39727i	−0.599016	−	0.155714i
$477$			4.50964i			0.206482i
$478$	−6.92035	−	25.8594i	−0.316529	−	1.18278i
$479$	−2.62335	+	4.54378i	−0.119864	+	0.207611i	−0.919714	−	0.392590i	$-0.871579\pi$
$479$	−2.62335	+	4.54378i	−0.119864	+	0.207611i	0.799850	+	0.600200i	$0.204913\pi$
$480$	3.38124	+	18.4021i	0.154332	+	0.839936i
$481$	−19.6830	+	11.3640i	−0.897466	+	0.518152i
$482$	6.43873	+	1.72741i	0.293276	+	0.0786814i
$483$	7.45080	+	1.93185i	0.339023	+	0.0879024i
$484$	46.5073	+	26.8898i	2.11397	+	1.22226i
$485$	11.9851	−	17.4392i	0.544218	−	0.791875i
$486$	−8.18510	+	8.17998i	−0.371283	+	0.371051i
$487$	5.99236	−	10.3791i	0.271540	−	0.470321i	−0.697716	−	0.716374i	$-0.745800\pi$
$487$	5.99236	−	10.3791i	0.271540	−	0.470321i	0.969256	+	0.246053i	$0.0791338\pi$
$488$	−2.61094	+	9.70771i	−0.118192	+	0.439447i
$489$		−	2.23264i		−	0.100963i
$490$	−16.6014	+	14.6422i	−0.749973	+	0.661468i
$491$			22.8018i			1.02903i	0.857481	+	0.514515i	$0.172028\pi$
$491$			22.8018i			1.02903i	−0.857481	+	0.514515i	$0.827972\pi$
$492$	0.00468885	−	7.49561i	0.000211390	−	0.337928i
$493$	6.60845	−	11.4462i	0.297630	−	0.515509i
$494$	2.35137	+	2.35284i	0.105793	+	0.105859i
$495$	−9.20812	−	6.32830i	−0.413874	−	0.284436i
$496$	13.5767	+	23.5837i	0.609613	+	1.05894i
$497$	−8.63295	−	2.23836i	−0.387241	−	0.100404i
$498$	−2.54905	+	9.50129i	−0.114226	+	0.425763i
$499$	−18.0567	+	10.4251i	−0.808330	+	0.466689i	−0.846376	−	0.532587i	$-0.821220\pi$
$499$	−18.0567	+	10.4251i	−0.808330	+	0.466689i	0.0380458	+	0.999276i	$0.487887\pi$
$500$	21.4435	−	6.33865i	0.958980	−	0.283473i
$501$	−14.9782	+	25.9430i	−0.669176	+	1.15905i
$502$	−32.4571	+	8.68597i	−1.44863	+	0.387674i
$503$			18.5545i			0.827305i	0.910435	+	0.413653i	$0.135747\pi$
$503$			18.5545i			0.827305i	−0.910435	+	0.413653i	$0.864253\pi$
$504$	3.00069	−	5.28444i	0.133661	−	0.235388i
$505$	17.8755	−	8.52663i	0.795451	−	0.379430i
$506$	−4.42449	−	16.5331i	−0.196693	−	0.734987i
$507$	2.41688	+	1.39538i	0.107337	+	0.0619712i
$508$	7.76362	−	4.47586i	0.344455	−	0.198584i
$509$	29.7157	−	17.1564i	1.31713	−	0.760443i	0.333860	−	0.942623i	$-0.391649\pi$
$509$	29.7157	−	17.1564i	1.31713	−	0.760443i	0.983265	+	0.182180i	$0.0583153\pi$
$510$	2.17183	+	11.7373i	0.0961700	+	0.519736i
$511$	4.81268	+	4.73530i	0.212900	+	0.209477i
$512$	15.9549	+	16.0450i	0.705114	+	0.709094i
$513$	−3.44543	+	1.98922i	−0.152119	+	0.0878262i
$514$	15.2347	+	15.2442i	0.671974	+	0.672394i
$515$	−1.48772	+	18.9081i	−0.0655570	+	0.833192i
$516$	13.6051	+	0.00851063i	0.598933	+	0.000374660i
$517$	−26.8845			−1.18238
$518$	12.9265	+	21.9919i	0.567958	+	0.966267i
$519$		−	14.4016i		−	0.632161i
$520$	3.82320	+	20.7344i	0.167658	+	0.909263i
$521$	−18.3115	−	10.5722i	−0.802242	−	0.463175i	0.0420126	−	0.999117i	$-0.486623\pi$
$521$	−18.3115	−	10.5722i	−0.802242	−	0.463175i	−0.844254	+	0.535943i	$0.819956\pi$
$522$	4.20459	+	4.20722i	0.184030	+	0.184145i
$523$	−3.44125	+	1.98681i	−0.150475	+	0.0868769i	−0.573347	−	0.819313i	$-0.694355\pi$
$523$	−3.44125	+	1.98681i	−0.150475	+	0.0868769i	0.422872	+	0.906189i	$0.361022\pi$
$524$	−28.0180	−	16.1996i	−1.22397	−	0.707683i
$525$	17.9401	+	7.81298i	0.782968	+	0.340987i
$526$	6.20143	−	23.1151i	0.270395	−	1.00787i
$527$	8.68039	+	15.0349i	0.378124	+	0.654929i
$528$	36.4058	+	0.0455470i	1.58436	+	0.00198218i
$529$	9.56580	−	16.5685i	0.415905	−	0.720368i
$530$	−13.3569	+	11.4011i	−0.580185	+	0.495231i
$531$	−5.52458			−0.239747
$532$	2.62015	−	2.65964i	0.113598	−	0.115310i
$533$		−	8.44659i		−	0.365863i
$534$	−12.1263	+	3.24516i	−0.524755	+	0.140432i
$535$	−1.58016	−	0.124330i	−0.0683165	−	0.00537525i
$536$	−2.11640	−	7.92826i	−0.0914145	−	0.342449i
$537$	−5.11643	−	8.86192i	−0.220790	−	0.382420i
$538$	0.814022	+	0.218389i	0.0350950	+	0.00941543i
$539$	22.1376	+	36.9473i	0.953535	+	1.59143i
$540$	−25.1380	−	1.99372i	−1.08177	−	0.0857962i
$541$	−14.6794	−	25.4255i	−0.631117	−	1.09313i	−0.987324	−	0.158719i	$-0.949263\pi$
$541$	−14.6794	−	25.4255i	−0.631117	−	1.09313i	0.356207	−	0.934407i	$-0.384070\pi$
$542$	−14.2422	−	14.2511i	−0.611756	−	0.612138i
$543$	−17.4492	+	30.2229i	−0.748816	+	1.29699i
$544$	10.1916	+	10.2235i	0.436960	+	0.438329i
$545$	2.97691	+	6.24090i	0.127517	+	0.267331i
$546$	−9.10035	+	16.0498i	−0.389459	+	0.686867i
$547$	−1.50735			−0.0644495			−0.0322248	−	0.999481i	$-0.510259\pi$
$547$	−1.50735			−0.0644495			−0.0322248	+	0.999481i	$0.510259\pi$
$548$	21.4130	+	0.0133948i	0.914718	+	0.000572198i
$549$	−2.49954	−	1.44311i	−0.106678	−	0.0615904i
$550$	−4.53612	−	43.2719i	−0.193421	−	1.84512i
$551$	1.82715	+	3.16471i	0.0778390	+	0.134821i
$552$	−5.81305	−	5.82397i	−0.247420	−	0.247885i
$553$	−4.38712	−	15.8577i	−0.186559	−	0.674340i
$554$	−31.6352	−	8.48722i	−1.34405	−	0.360588i
$555$	12.7719	−	18.5840i	0.542138	−	0.788849i
$556$	−28.0057	+	16.1458i	−1.18771	+	0.684733i
$557$	39.5927	+	22.8589i	1.67760	+	0.968562i	0.963186	+	0.268837i	$0.0866392\pi$
$557$	39.5927	+	22.8589i	1.67760	+	0.968562i	0.714412	+	0.699725i	$0.246694\pi$
$558$	−7.54735	+	2.01978i	−0.319505	+	0.0855040i
$559$	15.3312			0.648442
$560$	23.2379	−	4.47230i	0.981979	−	0.188989i
$561$	23.2259			0.980599
$562$	9.00124	−	2.40886i	0.379695	−	0.101612i
$563$	15.9077	+	9.18431i	0.670429	+	0.387072i	0.796239	−	0.604982i	$-0.206820\pi$
$563$	15.9077	+	9.18431i	0.670429	+	0.387072i	−0.125810	+	0.992054i	$0.540153\pi$
$564$	−11.1980	+	6.45585i	−0.471522	+	0.271840i
$565$	27.1274	+	18.6434i	1.14126	+	0.784333i
$566$	36.6158	+	9.82344i	1.53907	+	0.412910i
$567$	−11.1352	−	10.9561i	−0.467633	−	0.460114i
$568$	6.73536	+	6.74801i	0.282609	+	0.283140i
$569$	4.58078	+	7.93415i	0.192036	+	0.332617i	0.945925	−	0.324385i	$-0.105157\pi$
$569$	4.58078	+	7.93415i	0.192036	+	0.332617i	−0.753889	+	0.657002i	$0.771824\pi$
$570$	−3.11067	−	1.10257i	−0.130292	−	0.0461816i
$571$	−12.5753	−	7.26034i	−0.526259	−	0.303836i	0.213233	−	0.977001i	$-0.431601\pi$
$571$	−12.5753	−	7.26034i	−0.526259	−	0.303836i	−0.739492	+	0.673166i	$0.764934\pi$
$572$	41.0247	+	0.0256628i	1.71533	+	0.00107302i
$573$	−16.0588			−0.670864
$574$	−9.48006	+	0.0738669i	−0.395690	+	0.00308315i
$575$	−6.18850	+	7.64279i	−0.258078	+	0.318726i
$576$	−5.63225	+	3.23771i	−0.234677	+	0.134904i
$577$	7.87411	−	13.6384i	0.327804	−	0.567772i	−0.654272	−	0.756259i	$-0.727025\pi$
$577$	7.87411	−	13.6384i	0.327804	−	0.567772i	0.982076	+	0.188487i	$0.0603582\pi$
$578$	−10.4846	−	10.4911i	−0.436101	−	0.436374i
$579$	5.61523	+	9.72586i	0.233361	+	0.404193i
$580$	−1.83128	+	23.0899i	−0.0760398	+	0.958754i
$581$	12.0438	+	3.12274i	0.499661	+	0.129553i
$582$	−19.1198	−	5.12953i	−0.792539	−	0.212626i
$583$	17.0850	+	29.5921i	0.707588	+	1.22558i
$584$	−1.86157	−	6.97364i	−0.0770323	−	0.288571i
$585$	−6.03473	−	0.474823i	−0.249506	−	0.0196315i
$586$	−19.4576	+	5.20713i	−0.803787	+	0.215105i
$587$			21.3535i			0.881355i	0.897665	+	0.440678i	$0.145262\pi$
$587$			21.3535i			0.881355i	−0.897665	+	0.440678i	$0.854738\pi$
$588$	18.0931	+	10.0734i	0.746147	+	0.415422i
$589$	−4.80002			−0.197781
$590$	−13.9670	−	16.3630i	−0.575012	−	0.673652i
$591$	−10.0058	+	17.3305i	−0.411582	+	0.712881i
$592$	0.0341183	−	27.2708i	0.00140225	−	1.12082i
$593$	−9.12440	−	15.8039i	−0.374694	−	0.648990i	0.615587	−	0.788069i	$-0.288919\pi$
$593$	−9.12440	−	15.8039i	−0.374694	−	0.648990i	−0.990281	+	0.139079i	$0.955586\pi$
$594$	−12.7142	+	47.3908i	−0.521671	+	1.94447i
$595$	14.8215	−	2.87175i	0.607623	−	0.117730i
$596$	−13.1395	−	7.59704i	−0.538213	−	0.311187i
$597$	−5.84127	+	3.37246i	−0.239067	+	0.138025i
$598$	−6.55466	−	6.55877i	−0.268040	−	0.268208i
$599$	37.6528	+	21.7389i	1.53845	+	0.888226i	0.998930	+	0.0462544i	$0.0147285\pi$
$599$	37.6528	+	21.7389i	1.53845	+	0.888226i	0.539522	+	0.841971i	$0.318605\pi$
$600$	−12.2804	−	16.9345i	−0.501346	−	0.691349i
$601$		−	0.772217i		−	0.0314994i	−0.999876	−	0.0157497i	$-0.994987\pi$
$601$		−	0.772217i		−	0.0314994i	0.999876	−	0.0157497i	$-0.00501349\pi$
$602$	−0.134074	−	17.2071i	−0.00546446	−	0.701307i
$603$	2.35598			0.0959430
$604$	4.16614	+	0.00260611i	0.169518	+	0.000106041i
$605$	−59.8773	−	4.71124i	−2.43436	−	0.191539i
$606$	−13.0970	−	13.1052i	−0.532029	−	0.532361i
$607$	−4.78567	+	2.76301i	−0.194245	+	0.112147i	−0.593968	−	0.804489i	$-0.702439\pi$
$607$	−4.78567	+	2.76301i	−0.194245	+	0.112147i	0.399724	+	0.916636i	$0.369106\pi$
$608$	−3.85687	+	1.02698i	−0.156417	+	0.0416497i
$609$	−14.2158	+	14.4481i	−0.576052	+	0.585466i
$610$	−2.04495	−	11.0516i	−0.0827978	−	0.447468i
$611$	−12.6142	+	7.28280i	−0.510315	+	0.294630i
$612$	−3.59063	+	2.07006i	−0.145143	+	0.0836772i
$613$	−23.8912	−	13.7936i	−0.964955	−	0.557117i	−0.0672607	−	0.997735i	$-0.521426\pi$
$613$	−23.8912	−	13.7936i	−0.964955	−	0.557117i	−0.897695	+	0.440618i	$0.854759\pi$
$614$	−9.53399	−	35.6259i	−0.384761	−	1.43774i
$615$	3.60799	+	7.56391i	0.145488	+	0.305006i
$616$	−0.329966	−	46.0444i	−0.0132947	−	1.85518i
$617$		−	13.6354i		−	0.548941i	−0.961595	−	0.274471i	$-0.911497\pi$
$617$		−	13.6354i		−	0.548941i	0.961595	−	0.274471i	$-0.0885026\pi$
$618$	17.1402	−	4.58696i	0.689480	−	0.184515i
$619$	18.4295	−	31.9208i	0.740744	−	1.28301i	−0.211413	−	0.977397i	$-0.567807\pi$
$619$	18.4295	−	31.9208i	0.740744	−	1.28301i	0.952157	−	0.305609i	$-0.0988601\pi$
$620$	−25.0631	−	17.2478i	−1.00656	−	0.692687i
$621$	9.60447	−	5.54514i	0.385414	−	0.222519i
$622$	1.08281	−	4.03606i	0.0434168	−	0.161831i
$623$	4.23338	+	15.3021i	0.169607	+	0.613064i
$624$	17.0939	−	9.84069i	0.684305	−	0.393943i
$625$	−18.5773	+	16.7297i	−0.743091	+	0.669190i
$626$	23.4630	+	23.4777i	0.937769	+	0.938356i
$627$	−3.21083	+	5.56131i	−0.128228	+	0.222097i
$628$	0.0163156	−	26.0821i	0.000651062	−	1.04079i
$629$		−	17.3980i		−	0.693705i
$630$	−0.480144	+	6.77726i	−0.0191294	+	0.270012i
$631$		−	16.3105i		−	0.649312i	−0.945832	−	0.324656i	$-0.894751\pi$
$631$		−	16.3105i		−	0.649312i	0.945832	−	0.324656i	$-0.105249\pi$
$632$	−4.56842	+	16.9858i	−0.181722	+	0.675659i
$633$	7.89898	−	13.6814i	0.313956	−	0.543788i
$634$	13.2978	−	13.2895i	0.528125	−	0.527795i
$635$	−5.67476	+	8.25718i	−0.225196	+	0.327676i
$636$	14.2223	+	8.22313i	0.563952	+	0.326068i
$637$	20.3957	+	11.3387i	0.808107	+	0.449256i
$638$	43.5296	+	11.6783i	1.72335	+	0.462349i
$639$	−2.37062	+	1.36868i	−0.0937801	+	0.0541440i
$640$	−23.8288	−	8.49644i	−0.941915	−	0.335851i
$641$	10.7109	−	18.5519i	0.423057	−	0.732756i	−0.573180	−	0.819430i	$-0.694290\pi$
$641$	10.7109	−	18.5519i	0.423057	−	0.732756i	0.996237	+	0.0866736i	$0.0276237\pi$
$642$	0.383335	+	1.43242i	0.0151290	+	0.0565330i
$643$		−	38.3710i		−	1.51320i	−0.653876	−	0.756601i	$-0.726858\pi$
$643$		−	38.3710i		−	1.51320i	0.653876	−	0.756601i	$-0.273142\pi$
$644$	−7.30393	+	7.41401i	−0.287815	+	0.292153i
$645$	−13.7291	+	6.54878i	−0.540583	+	0.257858i
$646$	−2.45976	+	0.658265i	−0.0967778	+	0.0258991i
$647$	−31.0838	−	17.9463i	−1.22203	−	0.705540i	−0.256681	−	0.966496i	$-0.582629\pi$
$647$	−31.0838	−	17.9463i	−1.22203	−	0.705540i	−0.965351	+	0.260956i	$0.915962\pi$
$648$	4.30714	+	16.1350i	0.169201	+	0.633843i
$649$	−36.2520	+	20.9301i	−1.42302	+	0.821579i
$650$	−13.8504	−	19.0744i	−0.543257	−	0.748158i
$651$	−7.09899	−	25.6601i	−0.278231	−	1.00570i
$652$	2.61340	+	1.51103i	0.102349	+	0.0591763i
$653$	23.6657	−	13.6634i	0.926110	−	0.534690i	0.0405310	−	0.999178i	$-0.487095\pi$
$653$	23.6657	−	13.6634i	0.926110	−	0.534690i	0.885579	+	0.464488i	$0.153762\pi$
$654$	4.57542	−	4.57256i	0.178913	−	0.178801i
$655$	36.0727	+	2.83826i	1.40948	+	0.110900i
$656$	8.77075	+	5.07844i	0.342440	+	0.198280i
$657$	2.07230			0.0808483
$658$	8.28419	+	14.0939i	0.322951	+	0.549436i
$659$		−	22.7714i		−	0.887046i	−0.896263	−	0.443523i	$-0.853728\pi$
$659$		−	22.7714i		−	0.887046i	0.896263	−	0.443523i	$-0.146272\pi$
$660$	−36.7485	+	17.5008i	−1.43043	+	0.681219i
$661$	35.2100	+	20.3285i	1.36951	+	0.790686i	0.990865	−	0.134857i	$-0.0430573\pi$
$661$	35.2100	+	20.3285i	1.36951	+	0.790686i	0.378643	+	0.925543i	$0.376391\pi$
$662$	−30.6561	+	30.6369i	−1.19148	+	1.19074i
$663$	10.8976	−	6.29173i	0.423227	−	0.244350i
$664$	−9.39648	−	9.41413i	−0.364654	−	0.365339i
$665$	−1.36135	+	3.94593i	−0.0527909	+	0.153017i
$666$	7.56228	+	2.02884i	0.293033	+	0.0786161i
$667$	−5.09334	−	8.82193i	−0.197215	−	0.341587i
$668$	−20.2302	−	35.0905i	−0.782732	−	1.35769i
$669$	8.11198	−	14.0504i	0.313627	−	0.543218i
$670$	5.95629	+	6.97805i	0.230111	+	0.269586i
$671$	−21.8691			−0.844249
$672$	−11.1942	−	19.0994i	−0.431827	−	0.736774i
$673$			37.5436i			1.44720i	0.690220	+	0.723599i	$0.257514\pi$
$673$			37.5436i			1.44720i	−0.690220	+	0.723599i	$0.742486\pi$
$674$	−5.88830	−	22.0030i	−0.226809	−	0.847522i
$675$	26.3204	−	10.1047i	1.01307	−	0.388929i
$676$	−3.26907	+	1.88467i	−0.125734	+	0.0724874i
$677$	5.33668	+	9.24340i	0.205105	+	0.355253i	0.950166	−	0.311744i	$-0.100913\pi$
$677$	5.33668	+	9.24340i	0.205105	+	0.355253i	−0.745061	+	0.666996i	$0.767580\pi$
$678$	7.97919	−	29.7415i	0.306439	−	1.14222i
$679$	−6.28399	+	24.2361i	−0.241157	+	0.930098i
$680$	−15.2089	−	5.40146i	−0.583233	−	0.207137i
$681$	8.32736	+	14.4234i	0.319105	+	0.552707i
$682$	−41.8733	+	41.8472i	−1.60341	+	1.60241i
$683$	8.06776	−	13.9738i	0.308704	−	0.534691i	−0.669375	−	0.742925i	$-0.733438\pi$
$683$	8.06776	−	13.9738i	0.308704	−	0.534691i	0.978079	+	0.208233i	$0.0667714\pi$
$684$	0.000716830	−	1.14593i	2.74087e−5	−	0.0438157i
$685$	−21.6081	+	10.3071i	−0.825604	+	0.393813i
$686$	12.5477	−	22.9903i	0.479073	−	0.877775i
$687$	10.5346			0.401919
$688$	−9.21776	+	15.9196i	−0.351424	+	0.606929i
$689$	16.0325	+	9.25638i	0.610791	+	0.352640i
$690$	8.67129	+	3.07352i	0.330110	+	0.117007i
$691$	10.1615	+	17.6003i	0.386562	+	0.669546i	0.991985	−	0.126359i	$-0.0403291\pi$
$691$	10.1615	+	17.6003i	0.386562	+	0.669546i	−0.605422	+	0.795904i	$0.706996\pi$
$692$	16.8577	+	9.74686i	0.640834	+	0.370520i
$693$	12.7970	+	3.31802i	0.486117	+	0.126041i
$694$	−12.8535	+	47.9100i	−0.487913	+	1.81864i
$695$	20.4706	−	29.7861i	0.776493	−	1.12985i
$696$	20.9355	−	5.58859i	0.793557	−	0.211835i
$697$	5.59954	+	3.23290i	0.212098	+	0.122455i
$698$	−7.42727	−	27.7537i	−0.281126	−	1.05049i
$699$	8.32191			0.314764
$700$	−21.2870	+	15.7118i	−0.804575	+	0.593851i
$701$	5.55111			0.209663			0.104831	−	0.994490i	$-0.466570\pi$
$701$	5.55111			0.209663			0.104831	+	0.994490i	$0.466570\pi$
$702$	6.87231	+	25.6799i	0.259379	+	0.969227i
$703$	4.16586	+	2.40516i	0.157118	+	0.0907123i
$704$	−24.6924	+	42.5837i	−0.930629	+	1.60493i
$705$	8.18511	−	11.9099i	0.308269	−	0.448553i
$706$	10.6143	−	39.5638i	0.399476	−	1.48900i
$707$	−16.4352	+	16.7038i	−0.618110	+	0.628211i
$708$	−10.0738	+	17.4232i	−0.378598	+	0.654804i
$709$	−1.13330	−	1.96293i	−0.0425619	−	0.0737194i	0.843960	−	0.536407i	$-0.180219\pi$
$709$	−1.13330	−	1.96293i	−0.0425619	−	0.0737194i	−0.886522	+	0.462687i	$0.846885\pi$
$710$	−10.0471	−	3.56117i	−0.377060	−	0.133648i
$711$	−4.37351	−	2.52504i	−0.164019	−	0.0946966i
$712$	4.40834	−	16.3906i	0.165209	−	0.614264i
$713$	13.3805			0.501104
$714$	−7.15684	−	12.1759i	−0.267838	−	0.455672i
$715$	−41.3985	+	19.7471i	−1.54822	+	0.738499i
$716$	13.8360	+	0.00865504i	0.517075	+	0.000323454i
$717$	13.9995	−	24.2478i	0.522819	−	0.905549i
$718$	10.2263	−	10.2199i	0.381643	−	0.381405i
$719$	−2.78544	−	4.82453i	−0.103880	−	0.179925i	0.809400	−	0.587257i	$-0.199792\pi$
$719$	−2.78544	−	4.82453i	−0.103880	−	0.179925i	−0.913280	+	0.407333i	$0.866459\pi$
$720$	4.12137	−	5.98085i	0.153595	−	0.222893i
$721$	−5.98379	−	21.6291i	−0.222848	−	0.805510i
$722$	−6.78017	+	25.2723i	−0.252332	+	0.940539i
$723$	3.48630	+	6.03845i	0.129657	+	0.224572i
$724$	−23.5677	−	40.8795i	−0.875886	−	1.51927i
$725$	−9.28137	−	24.1759i	−0.344701	−	0.897871i
$726$	14.5257	+	54.2787i	0.539101	+	2.01447i
$727$		−	31.2822i		−	1.16019i	−0.814548	−	0.580097i	$-0.803015\pi$
$727$		−	31.2822i		−	1.16019i	0.814548	−	0.580097i	$-0.196985\pi$
$728$	−12.6279	−	21.5146i	−0.468021	−	0.797386i
$729$	−29.8164			−1.10431
$730$	5.23910	+	6.13784i	0.193908	+	0.227172i
$731$	−5.86796	+	10.1636i	−0.217034	+	0.375915i
$732$	−9.10902	+	5.25150i	−0.336679	+	0.194101i
$733$	10.5369	+	18.2504i	0.389187	+	0.674092i	0.992340	−	0.123533i	$-0.0394225\pi$
$733$	10.5369	+	18.2504i	0.389187	+	0.674092i	−0.603153	+	0.797626i	$0.706089\pi$
$734$	−38.5498	−	10.3423i	−1.42290	−	0.381741i
$735$	−23.1077	−	1.44173i	−0.852340	−	0.0531790i
$736$	10.7514	−	2.86282i	0.396302	−	0.105525i
$737$	15.4598	−	8.92574i	0.569471	−	0.328784i
$738$	−2.05820	+	2.05692i	−0.0757635	+	0.0757161i
$739$	−33.6932	−	19.4528i	−1.23943	−	0.715583i	−0.270449	−	0.962734i	$-0.587172\pi$
$739$	−33.6932	−	19.4528i	−1.23943	−	0.715583i	−0.968977	+	0.247152i	$0.920505\pi$
$740$	13.1095	+	27.5275i	0.481915	+	1.01193i
$741$			3.47915i			0.127810i
$742$	10.2487	−	18.0751i	0.376243	−	0.663558i
$743$	15.9696			0.585867			0.292934	−	0.956133i	$-0.405368\pi$
$743$	15.9696			0.585867			0.292934	+	0.956133i	$0.405368\pi$
$744$	−7.39237	+	27.4855i	−0.271017	+	1.00767i
$745$	16.9168	+	1.33104i	0.619785	+	0.0487657i
$746$	12.8334	−	12.8254i	0.469865	−	0.469571i
$747$	3.30724	−	1.90944i	0.121006	−	0.0698626i
$748$	−15.7190	+	27.1869i	−0.574745	+	0.994051i
$749$	1.80756	−	0.500069i	0.0660467	−	0.0182721i
$750$	20.5507	+	11.1648i	0.750404	+	0.407682i
$751$	−16.3642	+	9.44785i	−0.597137	+	0.344757i	−0.767914	−	0.640553i	$-0.778705\pi$
$751$	−16.3642	+	9.44785i	−0.597137	+	0.344757i	0.170778	+	0.985310i	$0.445372\pi$
$752$	0.0218653	−	17.4770i	0.000797346	−	0.637320i
$753$	−30.4342	−	17.5712i	−1.10908	−	0.640330i
$754$	23.5876	−	6.31238i	0.859011	−	0.229883i
$755$	−4.20410	+	2.00536i	−0.153003	+	0.0729824i
$756$	28.7619	−	7.93774i	1.04606	−	0.288693i
$757$		−	21.9755i		−	0.798714i	−0.916796	−	0.399357i	$-0.869233\pi$
$757$		−	21.9755i		−	0.798714i	0.916796	−	0.399357i	$-0.130767\pi$
$758$	6.66473	+	24.9042i	0.242074	+	0.904563i
$759$	8.95048	−	15.5027i	0.324882	−	0.562712i
$760$	3.39587	−	2.89496i	0.123181	−	0.105011i
$761$	−44.7044	+	25.8101i	−1.62053	+	0.935616i	−0.633757	+	0.773532i	$0.718488\pi$
$761$	−44.7044	+	25.8101i	−1.62053	+	0.935616i	−0.986777	+	0.162084i	$0.948179\pi$
$762$	9.05287	+	2.42875i	0.327951	+	0.0879842i
$763$	−5.83182	−	5.73805i	−0.211126	−	0.207731i
$764$	10.8684	−	18.7974i	0.393205	−	0.680068i
$765$	2.62455	−	3.81890i	0.0948906	−	0.138073i
$766$	33.7305	−	33.7094i	1.21873	−	1.21797i
$767$	−11.3396	+	19.6408i	−0.409450	+	0.709188i
$768$	−0.0592182	+	23.6666i	−0.00213685	+	0.853994i
$769$		−	16.7704i		−	0.604756i	−0.953188	−	0.302378i	$-0.902220\pi$
$769$		−	16.7704i		−	0.604756i	0.953188	−	0.302378i	$-0.0977805\pi$
$770$	22.5252	+	46.2911i	0.811754	+	1.66821i
$771$			22.5417i			0.811819i
$772$	−15.1848	−	0.00949881i	−0.546514	−	0.000341870i
$773$	−13.1290	+	22.7401i	−0.472217	+	0.817903i	−0.999495	−	0.0317896i	$-0.989879\pi$
$773$	−13.1290	+	22.7401i	−0.472217	+	0.817903i	0.527278	+	0.849693i	$0.323213\pi$
$774$	−3.73346	−	3.73580i	−0.134197	−	0.134281i
$775$	33.5970	+	5.31986i	1.20684	+	0.191095i
$776$	18.9444	−	18.9088i	0.680063	−	0.678788i
$777$	−6.69650	+	25.8271i	−0.240236	+	0.926543i
$778$	12.7113	−	47.3799i	0.455721	−	1.69865i
$779$	−1.54820	+	0.893852i	−0.0554699	+	0.0320256i
$780$	−12.5015	+	18.1663i	−0.447627	+	0.650457i
$781$	−10.3706	+	17.9624i	−0.371088	+	0.642744i
$782$	6.85681	−	1.83498i	0.245199	−	0.0656187i
$783$			29.2042i			1.04367i
$784$	−24.0366	+	14.3611i	−0.858450	+	0.512897i
$785$	12.5545	+	26.3198i	0.448091	+	0.939393i
$786$	−8.75095	−	32.6999i	−0.312136	−	1.16637i
$787$	−25.8693	−	14.9357i	−0.922141	−	0.532398i	−0.0378237	−	0.999284i	$-0.512043\pi$
$787$	−25.8693	−	14.9357i	−0.922141	−	0.532398i	−0.884318	+	0.466886i	$0.845376\pi$
$788$	−13.5143	−	23.4413i	−0.481426	−	0.835060i
$789$	21.6781	−	12.5159i	0.771762	−	0.445577i
$790$	−3.57811	−	19.3373i	−0.127303	−	0.687992i
$791$	−37.7003	−	9.77499i	−1.34047	−	0.347559i
$792$	−9.98409	−	10.0028i	−0.354769	−	0.355436i
$793$	−10.2610	+	5.92419i	−0.364378	+	0.210374i
$794$	28.5485	+	28.5663i	1.01315	+	1.01378i
$795$	−18.3110	−	1.44074i	−0.649424	−	0.0510978i
$796$	0.00570490	−	9.11988i	0.000202205	−	0.323246i
$797$	−17.1648			−0.608010			−0.304005	−	0.952670i	$-0.598324\pi$
$797$	−17.1648			−0.608010			−0.304005	+	0.952670i	$0.598324\pi$
$798$	3.90484	−	0.0304258i	0.138230	−	0.00107706i
$799$		−	11.1498i		−	0.394453i
$800$	28.1338	−	2.91364i	0.994680	−	0.103013i
$801$	4.22025	+	2.43656i	0.149115	+	0.0860917i
$802$	3.35747	+	3.35957i	0.118556	+	0.118631i
$803$	13.5984	−	7.85102i	0.479876	−	0.277056i
$804$	4.29603	−	7.43020i	0.151509	−	0.262043i
$805$	3.79490	−	10.9997i	0.133753	−	0.387687i
$806$	−8.31087	+	30.9778i	−0.292738	+	1.09115i
$807$	0.440758	+	0.763416i	0.0155154	+	0.0268735i
$808$	24.2040	−	6.46112i	0.851495	−	0.227301i
$809$	−13.6136	+	23.5795i	−0.478630	+	0.829011i	−0.999700	−	0.0245028i	$-0.992200\pi$
$809$	−13.6136	+	23.5795i	−0.478630	+	0.829011i	0.521070	+	0.853514i	$0.325533\pi$
$810$	−12.1218	−	14.2012i	−0.425917	−	0.498980i
$811$	−26.6882			−0.937148			−0.468574	−	0.883424i	$-0.655232\pi$
$811$	−26.6882			−0.937148			−0.468574	+	0.883424i	$0.655232\pi$
$812$	−7.29100	−	26.4184i	−0.255864	−	0.927106i
$813$		−	21.0732i		−	0.739069i
$814$	57.3097	−	15.3369i	2.00870	−	0.537557i
$815$	−3.36470	−	0.264740i	−0.117860	−	0.00927345i
$816$	−0.0188898	+	15.0987i	−0.000661275	+	0.528559i
$817$	−1.62241	−	2.81010i	−0.0567610	−	0.0983130i
$818$	9.55636	+	2.56382i	0.334130	+	0.0896420i
$819$	6.90315	−	1.90979i	0.241216	−	0.0667334i
$820$	−11.2957	−	0.895876i	−0.394463	−	0.0312853i
$821$	3.81521	+	6.60813i	0.133152	+	0.230625i	0.924890	−	0.380235i	$-0.124157\pi$
$821$	3.81521	+	6.60813i	0.133152	+	0.230625i	−0.791738	+	0.610861i	$0.790824\pi$
$822$	15.8317	+	15.8417i	0.552196	+	0.552541i
$823$	−2.70858	+	4.69139i	−0.0944150	+	0.163532i	−0.909364	−	0.416001i	$-0.863431\pi$
$823$	−2.70858	+	4.69139i	−0.0944150	+	0.163532i	0.814949	+	0.579532i	$0.196765\pi$
$824$	−6.23108	+	23.1677i	−0.217070	+	0.807086i
$825$	28.6373	−	35.3670i	0.997022	−	1.23132i
$826$	22.1431	+	12.5553i	0.770457	+	0.436855i
$827$	54.4560			1.89362			0.946810	−	0.321792i	$-0.104285\pi$
$827$	54.4560			1.89362			0.946810	+	0.321792i	$0.104285\pi$
$828$	−0.00199823	+	3.19438i	−6.94434e−5	+	0.111013i
$829$	1.41764	+	0.818472i	0.0492365	+	0.0284267i	0.524416	−	0.851462i	$-0.324284\pi$
$829$	1.41764	+	0.818472i	0.0492365	+	0.0284267i	−0.475180	+	0.879889i	$0.657617\pi$
$830$	14.0167	+	4.96818i	0.486526	+	0.172448i
$831$	−17.1291	−	29.6685i	−0.594202	−	1.02919i
$832$	−0.0500485	+	26.6692i	−0.00173512	+	0.924589i
$833$	−15.3232	+	9.18117i	−0.530917	+	0.318109i
$834$	−32.6564	−	8.76121i	−1.13080	−	0.303376i
$835$	37.3213	+	25.6491i	1.29156	+	0.887624i
$836$	−4.33669	−	7.52224i	−0.149988	−	0.260162i
$837$	−33.2212	−	19.1803i	−1.14829	−	0.662968i
$838$	−13.7512	+	3.68001i	−0.475027	+	0.127124i
$839$	−13.4985			−0.466021			−0.233011	−	0.972474i	$-0.574858\pi$
$839$	−13.4985			−0.466021			−0.233011	+	0.972474i	$0.574858\pi$
$840$	20.4983	+	13.8723i	0.707259	+	0.478639i
$841$	−2.17525			−0.0750086
$842$	11.0433	−	2.95535i	0.380579	−	0.101848i
$843$	8.44024	+	4.87298i	0.290697	+	0.167834i
$844$	10.6687	+	18.5055i	0.367233	+	0.636987i
$845$	2.38950	−	3.47690i	0.0822014	−	0.119609i
$846$	4.84643	+	1.30022i	0.166624	+	0.0447025i
$847$	68.4939	−	18.9491i	2.35348	−	0.651100i
$848$	−19.2510	+	11.0825i	−0.661083	+	0.380575i
$849$	19.8259	+	34.3394i	0.680423	+	1.17853i
$850$	17.9462	−	1.88127i	0.615551	−	0.0645272i
$851$	−11.6127	−	6.70461i	−0.398079	−	0.229831i
$852$	−0.00623798	+	9.97207i	−0.000213710	+	0.341637i
$853$	37.8821			1.29706			0.648530	−	0.761189i	$-0.275384\pi$
$853$	37.8821			1.29706			0.648530	+	0.761189i	$0.275384\pi$
$854$	6.73876	+	11.4646i	0.230596	+	0.392312i
$855$	0.551588	+	1.15637i	0.0188639	+	0.0395470i
$856$	−1.93614	−	0.520735i	−0.0661759	−	0.0177984i
$857$	−9.33854	+	16.1748i	−0.318998	+	0.552522i	−0.980279	−	0.197617i	$-0.936680\pi$
$857$	−9.33854	+	16.1748i	−0.318998	+	0.552522i	0.661281	+	0.750138i	$0.270013\pi$
$858$	30.3317	+	30.3507i	1.03551	+	1.03615i
$859$	−13.6369	−	23.6198i	−0.465285	−	0.805898i	0.533929	−	0.845529i	$-0.320715\pi$
$859$	−13.6369	−	23.6198i	−0.465285	−	0.805898i	−0.999214	+	0.0396315i	$0.987382\pi$
$860$	1.62608	−	20.5026i	0.0554490	−	0.699133i
$861$	−7.06810	−	6.95445i	−0.240880	−	0.237007i
$862$	2.68267	+	0.719720i	0.0913722	+	0.0245137i
$863$	−12.1098	−	20.9749i	−0.412224	−	0.713993i	0.582909	−	0.812538i	$-0.301915\pi$
$863$	−12.1098	−	20.9749i	−0.412224	−	0.713993i	−0.995133	+	0.0985450i	$0.968581\pi$
$864$	−30.7974	−	8.30378i	−1.04775	−	0.282500i
$865$	−21.7040	−	1.70771i	−0.737958	−	0.0580637i
$866$	−44.6076	+	11.9376i	−1.51583	+	0.405657i
$867$		−	15.5133i		−	0.526859i
$868$	34.8408	+	9.05683i	1.18257	+	0.307409i
$869$	−38.2650			−1.29805
$870$	−18.4263	+	15.7282i	−0.624711	+	0.533237i
$871$	4.83583	−	8.37591i	0.163856	−	0.283807i
$872$	2.25578	+	8.45038i	0.0763902	+	0.286166i
$873$	3.84242	+	6.65527i	0.130046	+	0.225247i
$874$	−0.508532	+	1.89550i	−0.0172014	+	0.0641161i
$875$	13.9018	−	26.1101i	0.469968	−	0.882683i
$876$	3.77876	−	6.53555i	0.127672	−	0.220816i
$877$	24.3570	−	14.0625i	0.822477	−	0.474857i	−0.0287932	−	0.999585i	$-0.509166\pi$
$877$	24.3570	−	14.0625i	0.822477	−	0.474857i	0.851270	+	0.524728i	$0.175833\pi$
$878$	24.4561	+	24.4715i	0.825355	+	0.825871i
$879$	−18.2449	−	10.5337i	−0.615386	−	0.355293i
$880$	4.38554	−	54.8600i	0.147837	−	1.84933i
$881$			12.3462i			0.415953i	0.978134	+	0.207976i	$0.0666877\pi$
$881$			12.3462i			0.415953i	−0.978134	+	0.207976i	$0.933312\pi$
$882$	−2.20383	−	7.73108i	−0.0742068	−	0.260319i
$883$	−33.0518			−1.11228			−0.556140	−	0.831088i	$-0.687718\pi$
$883$	−33.0518			−1.11228			−0.556140	+	0.831088i	$0.687718\pi$
$884$	−0.0106432	+	17.0142i	−0.000357969	+	0.572251i
$885$	1.76499	−	22.4321i	0.0593296	−	0.754046i
$886$	37.5863	+	37.6098i	1.26274	+	1.26353i
$887$	−26.2017	+	15.1276i	−0.879767	+	0.507934i	−0.870582	−	0.492024i	$-0.836257\pi$
$887$	−26.2017	+	15.1276i	−0.879767	+	0.507934i	−0.00918566	+	0.999958i	$0.502924\pi$
$888$	20.1880	−	20.1501i	0.677464	−	0.676194i
$889$	2.97536	−	11.4754i	0.0997903	−	0.384873i
$890$	3.45272	+	18.6597i	0.115736	+	0.625475i
$891$	−31.4627	+	18.1650i	−1.05404	+	0.608551i
$892$	10.9564	+	19.0045i	0.366848	+	0.636319i
$893$	2.66977	+	1.54139i	0.0893403	+	0.0515806i
$894$	−4.10388	−	15.3351i	−0.137254	−	0.512882i
$895$	−13.9621	+	6.65990i	−0.466700	+	0.222616i
$896$	29.9327	−	0.177055i	0.999983	−	0.00591499i
$897$		−	9.69847i		−	0.323823i
$898$	−41.3611	+	11.0688i	−1.38024	+	0.369371i
$899$	−17.6175	+	30.5145i	−0.587578	+	1.01771i
$900$	−1.27505	+	8.01995i	−0.0425017	+	0.267332i
$901$	−12.2728	+	7.08568i	−0.408865	+	0.236058i
$902$	−5.71311	+	21.2950i	−0.190226	+	0.709045i
$903$	12.6229	−	12.8292i	0.420063	−	0.426928i
$904$	29.4135	+	29.4687i	0.978278	+	0.980115i
$905$	43.4783	+	29.8805i	1.44527	+	0.993262i
$906$	3.08025	+	3.08217i	0.102334	+	0.102398i
$907$	−18.6808	+	32.3561i	−0.620287	+	1.07437i	0.369145	+	0.929372i	$0.379650\pi$
$907$	−18.6808	+	32.3561i	−0.620287	+	1.07437i	−0.989432	+	0.144997i	$0.953683\pi$
$908$	−22.5191	−	0.0140867i	−0.747322	−	0.000467484i
$909$			7.19254i			0.238561i
$910$	23.1087	+	15.6178i	0.766047	+	0.517726i
$911$			21.4157i			0.709535i	0.934955	+	0.354768i	$0.115440\pi$
$911$			21.4157i			0.709535i	−0.934955	+	0.354768i	$0.884560\pi$
$912$	−3.61267	−	2.09181i	−0.119628	−	0.0692667i
$913$	14.4680	−	25.0593i	0.478820	−	0.829340i
$914$	26.5831	−	26.5665i	0.879291	−	0.878742i
$915$	6.65817	−	9.68811i	0.220112	−	0.320279i
$916$	−7.12968	+	12.3311i	−0.235571	+	0.407433i
$917$	−41.2637	+	11.4158i	−1.36265	+	0.376983i
$918$	−19.6545	−	5.27299i	−0.648694	−	0.174035i
$919$	13.1132	−	7.57091i	0.432565	−	0.249741i	−0.267874	−	0.963454i	$-0.586321\pi$
$919$	13.1132	−	7.57091i	0.432565	−	0.249741i	0.700439	+	0.713713i	$0.252988\pi$
$920$	−9.46632	+	8.06997i	−0.312095	+	0.266059i
$921$	19.2867	−	33.4055i	0.635518	−	1.10075i
$922$	−9.62321	−	35.9593i	−0.316923	−	1.18426i
$923$			11.2372i			0.369878i
$924$	33.7989	−	34.3083i	1.11190	−	1.12866i
$925$	−26.4926	−	21.4516i	−0.871073	−	0.705323i
$926$	−46.2591	+	12.3796i	−1.52017	+	0.406818i
$927$	−5.96522	−	3.44402i	−0.195924	−	0.113117i
$928$	−7.62721	+	28.2881i	−0.250376	+	0.928603i
$929$	12.1825	−	7.03359i	0.399696	−	0.230765i	−0.286657	−	0.958033i	$-0.592544\pi$
$929$	12.1825	−	7.03359i	0.399696	−	0.230765i	0.686353	+	0.727269i	$0.259211\pi$
$930$	−5.78990	−	31.2906i	−0.189858	−	1.02606i
$931$	−0.0800511	−	4.93829i	−0.00262357	−	0.161846i
$932$	−5.63218	+	9.74114i	−0.184488	+	0.319082i
$933$	3.78515	−	2.18536i	0.123920	−	0.0715453i
$934$	−20.8307	+	20.8177i	−0.681601	+	0.681174i
$935$	2.75407	−	35.0026i	0.0900676	−	1.14471i
$936$	−7.39422	−	1.98871i	−0.241688	−	0.0650032i
$937$	−6.12130			−0.199974			−0.0999871	−	0.994989i	$-0.531880\pi$
$937$	−6.12130			−0.199974			−0.0999871	+	0.994989i	$0.531880\pi$
$938$	−9.44302	−	5.35426i	−0.308326	−	0.174823i
$939$			34.7165i			1.13293i
$940$	8.40146	+	17.6415i	0.274025	+	0.575403i
$941$	24.8876	+	14.3689i	0.811312	+	0.468411i	0.847411	−	0.530937i	$-0.178160\pi$
$941$	24.8876	+	14.3689i	0.811312	+	0.468411i	−0.0360991	+	0.999348i	$0.511493\pi$
$942$	19.2959	−	19.2839i	0.628696	−	0.628303i
$943$	4.31575	−	2.49170i	0.140540	−	0.0811409i
$944$	−13.5767	−	23.5837i	−0.441885	−	0.767583i
$945$	−25.1894	+	21.8702i	−0.819413	+	0.711439i
$946$	−38.6521	−	10.3697i	−1.25669	−	0.337149i
$947$	−5.72800	−	9.92118i	−0.186135	−	0.322395i	0.757823	−	0.652460i	$-0.226263\pi$
$947$	−5.72800	−	9.92118i	−0.186135	−	0.322395i	−0.943958	+	0.330065i	$0.892929\pi$
$948$	−15.9383	+	9.18868i	−0.517651	+	0.298434i
$949$	4.25356	−	7.36739i	0.138076	−	0.239155i
$950$	−2.03048	+	4.55720i	−0.0658776	+	0.147855i
$951$	19.6636			0.637635
$952$	19.0961	−	0.136847i	0.618908	−	0.00443524i
$953$		−	39.4042i		−	1.27643i	−0.769859	−	0.638214i	$-0.779674\pi$
$953$		−	39.4042i		−	1.27643i	0.769859	−	0.638214i	$-0.220326\pi$
$954$	−1.64872	−	6.16080i	−0.0533792	−	0.199463i
$955$	−1.90420	+	24.2014i	−0.0616186	+	0.783138i
$956$	18.9083	+	32.7975i	0.611539	+	1.06075i
$957$	23.5694	+	40.8235i	0.761892	+	1.31964i
$958$	1.92267	−	7.16653i	0.0621186	−	0.231540i
$959$	19.8671	−	20.1917i	0.641541	−	0.652024i
$960$	−11.3470	−	23.9036i	−0.366223	−	0.771486i
$961$	−7.64115	−	13.2349i	−0.246489	−	0.426931i
$962$	22.7350	−	22.7208i	0.733007	−	0.732548i
$963$	0.287819	−	0.498517i	0.00927484	−	0.0160645i
$964$	−9.42774	−	0.00589748i	−0.303647	−	0.000189945i
$965$	15.3232	−	7.30917i	0.493271	−	0.235290i
$966$	−10.8851	+	0.0848149i	−0.350223	+	0.00272887i
$967$	−6.27278			−0.201719			−0.100860	−	0.994901i	$-0.532159\pi$
$967$	−6.27278			−0.201719			−0.100860	+	0.994901i	$0.532159\pi$
$968$	−73.3663	−	19.7323i	−2.35808	−	0.634219i
$969$	−2.30645	−	1.33163i	−0.0740939	−	0.0427782i
$970$	−9.99763	+	28.2062i	−0.321005	+	0.905646i
$971$	14.2485	+	24.6792i	0.457257	+	0.791993i	0.998815	−	0.0486706i	$-0.0154984\pi$
$971$	14.2485	+	24.6792i	0.457257	+	0.791993i	−0.541557	+	0.840664i	$0.682165\pi$
$972$	8.19140	−	14.1674i	0.262739	−	0.454421i
$973$	−10.7330	+	41.3952i	−0.344084	+	1.32707i
$974$	−4.39184	+	16.3701i	−0.140723	+	0.524531i
$975$	3.85595	−	24.3518i	0.123489	−	0.779881i
$976$	0.0177863	−	14.2166i	0.000569326	−	0.455064i
$977$	23.7793	+	13.7290i	0.760766	+	0.439228i	0.829571	−	0.558402i	$-0.188585\pi$
$977$	23.7793	+	13.7290i	0.760766	+	0.439228i	−0.0688047	+	0.997630i	$0.521919\pi$
$978$	0.816249	+	3.05010i	0.0261008	+	0.0975314i
$979$	36.9241			1.18010
$980$	17.3266	−	26.0727i	0.553479	−	0.832863i
$981$	−2.51114			−0.0801744
$982$	−8.33629	−	31.1504i	−0.266022	−	0.994050i
$983$	−23.2784	−	13.4398i	−0.742465	−	0.428662i	0.0804998	−	0.996755i	$-0.474348\pi$
$983$	−23.2784	−	13.4398i	−0.742465	−	0.428662i	−0.822965	+	0.568092i	$0.807682\pi$
$984$	2.73398	+	10.2418i	0.0871560	+	0.326496i
$985$	24.9315	+	17.1342i	0.794383	+	0.545941i
$986$	−4.84337	+	18.0531i	−0.154244	+	0.574928i
$987$	−4.29157	+	16.5518i	−0.136602	+	0.526849i
$988$	−4.07249	−	2.35465i	−0.129563	−	0.0749115i
$989$	4.52263	+	7.83342i	0.143811	+	0.249088i
$990$	14.8932	+	5.27887i	0.473337	+	0.167773i
$991$	21.5616	+	12.4486i	0.684927	+	0.395443i	0.801709	−	0.597715i	$-0.203925\pi$
$991$	21.5616	+	12.4486i	0.684927	+	0.395443i	−0.116782	+	0.993158i	$0.537258\pi$
$992$	−27.1699	−	27.2550i	−0.862644	−	0.865346i
$993$	−45.3312			−1.43854
$994$	12.6122	−	0.0982716i	0.400033	−	0.00311699i
$995$	4.38982	+	9.20298i	0.139167	+	0.291754i
$996$	0.00870260	−	13.9120i	0.000275752	−	0.440819i
$997$	−6.77909	+	11.7417i	−0.214696	+	0.371864i	−0.953178	−	0.302408i	$-0.902209\pi$
$997$	−6.77909	+	11.7417i	−0.214696	+	0.371864i	0.738483	+	0.674273i	$0.235543\pi$
$998$	20.8566	−	20.8436i	0.660205	−	0.659792i
$999$	19.2214	+	33.2925i	0.608140	+	1.05333i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.s.b.59.3	yes	32
4.3	odd	2	inner	140.2.s.b.59.5	yes	32
5.2	odd	4		700.2.p.e.451.6		32
5.3	odd	4		700.2.p.e.451.11		32
5.4	even	2	inner	140.2.s.b.59.14	yes	32
7.2	even	3		980.2.s.e.19.12		32
7.3	odd	6		980.2.c.d.979.17		32
7.4	even	3		980.2.c.d.979.18		32
7.5	odd	6	inner	140.2.s.b.19.12	yes	32
7.6	odd	2		980.2.s.e.619.3		32
20.3	even	4		700.2.p.e.451.13		32
20.7	even	4		700.2.p.e.451.4		32
20.19	odd	2	inner	140.2.s.b.59.12	yes	32
28.3	even	6		980.2.c.d.979.14		32
28.11	odd	6		980.2.c.d.979.13		32
28.19	even	6	inner	140.2.s.b.19.14	yes	32
28.23	odd	6		980.2.s.e.19.14		32
28.27	even	2		980.2.s.e.619.5		32
35.4	even	6		980.2.c.d.979.15		32
35.9	even	6		980.2.s.e.19.5		32
35.12	even	12		700.2.p.e.551.4		32
35.19	odd	6	inner	140.2.s.b.19.5	yes	32
35.24	odd	6		980.2.c.d.979.16		32
35.33	even	12		700.2.p.e.551.13		32
35.34	odd	2		980.2.s.e.619.14		32
140.19	even	6	inner	140.2.s.b.19.3	✓	32
140.39	odd	6		980.2.c.d.979.20		32
140.47	odd	12		700.2.p.e.551.6		32
140.59	even	6		980.2.c.d.979.19		32
140.79	odd	6		980.2.s.e.19.3		32
140.103	odd	12		700.2.p.e.551.11		32
140.139	even	2		980.2.s.e.619.12		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.s.b.19.3	✓	32	140.19	even	6	inner
140.2.s.b.19.5	yes	32	35.19	odd	6	inner
140.2.s.b.19.12	yes	32	7.5	odd	6	inner
140.2.s.b.19.14	yes	32	28.19	even	6	inner
140.2.s.b.59.3	yes	32	1.1	even	1	trivial
140.2.s.b.59.5	yes	32	4.3	odd	2	inner
140.2.s.b.59.12	yes	32	20.19	odd	2	inner
140.2.s.b.59.14	yes	32	5.4	even	2	inner
700.2.p.e.451.4		32	20.7	even	4
700.2.p.e.451.6		32	5.2	odd	4
700.2.p.e.451.11		32	5.3	odd	4
700.2.p.e.451.13		32	20.3	even	4
700.2.p.e.551.4		32	35.12	even	12
700.2.p.e.551.6		32	140.47	odd	12
700.2.p.e.551.11		32	140.103	odd	12
700.2.p.e.551.13		32	35.33	even	12
980.2.c.d.979.13		32	28.11	odd	6
980.2.c.d.979.14		32	28.3	even	6
980.2.c.d.979.15		32	35.4	even	6
980.2.c.d.979.16		32	35.24	odd	6
980.2.c.d.979.17		32	7.3	odd	6
980.2.c.d.979.18		32	7.4	even	3
980.2.c.d.979.19		32	140.59	even	6
980.2.c.d.979.20		32	140.39	odd	6
980.2.s.e.19.3		32	140.79	odd	6
980.2.s.e.19.5		32	35.9	even	6
980.2.s.e.19.12		32	7.2	even	3
980.2.s.e.19.14		32	28.23	odd	6
980.2.s.e.619.3		32	7.6	odd	2
980.2.s.e.619.5		32	28.27	even	2
980.2.s.e.619.12		32	140.139	even	2
980.2.s.e.619.14		32	35.34	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36614 + 0.365598i) q^{2} +(-1.28100 - 0.739583i) q^{3} +(1.73268 - 0.998916i) q^{4} +(-1.26649 + 1.84283i) q^{5} +(2.02041 + 0.542044i) q^{6} +(0.664037 - 2.56107i) q^{7} +(-2.00188 + 1.99812i) q^{8} +(-0.406034 - 0.703271i) q^{9} +(1.05646 - 2.98058i) q^{10} +(-5.32875 - 3.07655i) q^{11} +(-2.95833 - 0.00185057i) q^{12} -3.33366 q^{13} +(0.0291534 + 3.74154i) q^{14} +(2.98529 - 1.42398i) q^{15} +(2.00433 - 3.46160i) q^{16} +(1.27594 - 2.21000i) q^{17} +(0.811813 + 0.812321i) q^{18} +(0.352781 + 0.611035i) q^{19} +(-0.353580 + 4.45814i) q^{20} +(-2.74475 + 2.78960i) q^{21} +(8.40459 + 2.25482i) q^{22} +(-0.983411 - 1.70332i) q^{23} +(4.04217 - 1.07903i) q^{24} +(-1.79203 - 4.66783i) q^{25} +(4.55424 - 1.21878i) q^{26} +5.63868i q^{27} +(-1.40773 - 5.10081i) q^{28} +5.17926 q^{29} +(-3.55771 + 3.03677i) q^{30} +(-3.40156 + 5.89167i) q^{31} +(-1.47264 + 5.46181i) q^{32} +(4.55073 + 7.88210i) q^{33} +(-0.935146 + 3.48565i) q^{34} +(3.87861 + 4.46726i) q^{35} +(-1.40603 - 0.812947i) q^{36} +(5.90431 - 3.40886i) q^{37} +(-0.705342 - 0.705783i) q^{38} +(4.27040 + 2.46552i) q^{39} +(-1.14685 - 6.21971i) q^{40} +2.53373i q^{41} +(2.72984 - 4.81446i) q^{42} -4.59892 q^{43} +(-12.3062 - 0.00769809i) q^{44} +(1.81024 + 0.142433i) q^{45} +(1.96621 + 1.96744i) q^{46} +(3.78388 - 2.18463i) q^{47} +(-5.12768 + 2.95192i) q^{48} +(-6.11811 - 3.40128i) q^{49} +(4.15471 + 5.72175i) q^{50} +(-3.26896 + 1.88733i) q^{51} +(-5.77615 + 3.33005i) q^{52} +(-4.80929 - 2.77664i) q^{53} +(-2.06149 - 7.70323i) q^{54} +(12.4183 - 5.92355i) q^{55} +(3.78800 + 6.45376i) q^{56} -1.04364i q^{57} +(-7.07560 + 1.89353i) q^{58} +(3.40156 - 5.89167i) q^{59} +(3.75010 - 5.44935i) q^{60} +(3.07800 - 1.77708i) q^{61} +(2.49302 - 9.29244i) q^{62} +(-2.07074 + 0.572881i) q^{63} +(0.0150131 - 7.99999i) q^{64} +(4.22203 - 6.14336i) q^{65} +(-9.09862 - 9.10431i) q^{66} +(-1.45061 + 2.51253i) q^{67} +(0.00319264 - 5.10377i) q^{68} +2.90926i q^{69} +(-6.93194 - 4.68489i) q^{70} -3.37084i q^{71} +(2.21805 + 0.596556i) q^{72} +(-1.27594 + 2.21000i) q^{73} +(-6.81984 + 6.81558i) q^{74} +(-1.15667 + 7.30482i) q^{75} +(1.22163 + 0.706327i) q^{76} +(-11.4177 + 11.6043i) q^{77} +(-6.73536 - 1.80699i) q^{78} +(5.38564 - 3.10940i) q^{79} +(3.84067 + 8.07770i) q^{80} +(2.95217 - 5.11331i) q^{81} +(-0.926327 - 3.46143i) q^{82} +4.70266i q^{83} +(-1.96918 + 7.57525i) q^{84} +(2.45668 + 5.15028i) q^{85} +(6.28277 - 1.68136i) q^{86} +(-6.63461 - 3.83049i) q^{87} +(16.8148 - 4.48861i) q^{88} +(-5.19692 + 3.00044i) q^{89} +(-2.52512 + 0.467238i) q^{90} +(-2.21367 + 8.53772i) q^{91} +(-3.40541 - 1.96895i) q^{92} +(8.71475 - 5.03147i) q^{93} +(-4.37062 + 4.36789i) q^{94} +(-1.57282 - 0.123752i) q^{95} +(5.92591 - 5.90740i) q^{96} -9.46331 q^{97} +(9.60170 + 2.40986i) q^{98} +4.99674i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 6 q^{4} - 6 q^{5} + 4 q^{9} - 12 q^{10} + 22 q^{14} + 18 q^{16} - 52 q^{21} - 48 q^{24} - 26 q^{25} - 18 q^{26} - 26 q^{30} - 28 q^{36} + 42 q^{40} - 26 q^{44} + 36 q^{45} - 22 q^{46} + 36 q^{50}+ \cdots + 60 q^{96}+O(q^{100}) \) 32 * q + 6 * q^4 - 6 * q^5 + 4 * q^9 - 12 * q^10 + 22 * q^14 + 18 * q^16 - 52 * q^21 - 48 * q^24 - 26 * q^25 - 18 * q^26 - 26 * q^30 - 28 * q^36 + 42 * q^40 - 26 * q^44 + 36 * q^45 - 22 * q^46 + 36 * q^50 + 48 * q^54 - 16 * q^56 + 4 * q^60 + 36 * q^61 + 36 * q^64 - 4 * q^65 - 24 * q^66 + 26 * q^70 + 14 * q^74 + 72 * q^80 + 72 * q^81 + 56 * q^84 + 20 * q^85 + 8 * q^86 - 108 * q^89 + 30 * q^94 + 60 * q^96

Introduction

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