LMFDB - Embedded newform 640.2.bm.a.101.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [640,2,Mod(21,640)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("640.21"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(640, base_ring=CyclotomicField(32)) chi = DirichletCharacter(H, H._module([0, 13, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.bm (of order $32$, degree $16$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			101.12
Character	$\chi$	$=$	640.101
Dual form			640.2.bm.a.621.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.19364 + 0.758431i) q^{2} +(-1.32436 + 0.707885i) q^{3} +(0.849564 - 1.81059i) q^{4} +(0.634393 + 0.773010i) q^{5} +(1.04393 - 1.84940i) q^{6} +(2.75033 - 1.83771i) q^{7} +(0.359135 + 2.80553i) q^{8} +(-0.413883 + 0.619419i) q^{9} +(-1.34351 - 0.441554i) q^{10} +(-2.10074 + 0.637253i) q^{11} +(0.156563 + 2.99927i) q^{12} +(0.0473662 + 0.0388724i) q^{13} +(-1.88913 + 4.27950i) q^{14} +(-1.38737 - 0.574667i) q^{15} +(-2.55648 - 3.07643i) q^{16} +(5.58942 - 2.31521i) q^{17} +(0.0242409 - 1.05327i) q^{18} +(-0.326232 - 3.31229i) q^{19} +(1.93856 - 0.491906i) q^{20} +(-2.34154 + 4.38071i) q^{21} +(2.02422 - 2.35392i) q^{22} +(5.84516 - 1.16268i) q^{23} +(-2.46162 - 3.46131i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(-0.0860204 - 0.0104758i) q^{26} +(0.551222 - 5.59665i) q^{27} +(-0.990764 - 6.54097i) q^{28} +(-0.451849 + 1.48955i) q^{29} +(2.09187 - 0.366277i) q^{30} +(2.02974 + 2.02974i) q^{31} +(5.38478 + 1.73323i) q^{32} +(2.33104 - 2.33104i) q^{33} +(-4.91583 + 7.00272i) q^{34} +(3.16536 + 0.960201i) q^{35} +(0.769896 + 1.27561i) q^{36} +(-0.167854 - 0.0165321i) q^{37} +(2.90155 + 3.70627i) q^{38} +(-0.0902471 - 0.0179513i) q^{39} +(-1.94087 + 2.05743i) q^{40} +(1.59351 + 8.01110i) q^{41} +(-0.527509 - 7.00489i) q^{42} +(-1.24681 - 0.666436i) q^{43} +(-0.630909 + 4.34497i) q^{44} +(-0.741382 + 0.0730198i) q^{45} +(-6.09522 + 5.82097i) q^{46} +(3.14315 + 7.58822i) q^{47} +(5.56346 + 2.26460i) q^{48} +(1.50834 - 3.64145i) q^{49} +(-0.510990 - 1.31867i) q^{50} +(-5.76350 + 7.02284i) q^{51} +(0.110623 - 0.0527363i) q^{52} +(2.46646 + 8.13082i) q^{53} +(3.58671 + 7.09846i) q^{54} +(-1.82530 - 1.21963i) q^{55} +(6.14350 + 7.05615i) q^{56} +(2.77677 + 4.15573i) q^{57} +(-0.590373 - 2.12068i) q^{58} +(4.14048 - 3.39801i) q^{59} +(-2.21914 + 2.02374i) q^{60} +(4.86239 + 9.09689i) q^{61} +(-3.96220 - 0.883364i) q^{62} +2.46420i q^{63} +(-7.74204 + 2.01513i) q^{64} +0.0612750i q^{65} +(-1.01449 + 4.55035i) q^{66} +(-3.79490 - 7.09977i) q^{67} +(0.556661 - 12.0871i) q^{68} +(-6.91806 + 5.67750i) q^{69} +(-4.50655 + 1.25457i) q^{70} +(-0.364204 - 0.545070i) q^{71} +(-1.88644 - 0.938707i) q^{72} +(3.50343 + 2.34092i) q^{73} +(0.212896 - 0.107572i) q^{74} +(-0.435914 - 1.43701i) q^{75} +(-6.27436 - 2.22333i) q^{76} +(-4.60664 + 5.61321i) q^{77} +(0.121338 - 0.0470189i) q^{78} +(5.15974 - 12.4567i) q^{79} +(0.756293 - 3.92785i) q^{80} +(2.37651 + 5.73740i) q^{81} +(-7.97794 - 8.35382i) q^{82} +(14.9519 - 1.47263i) q^{83} +(5.94238 + 7.96125i) q^{84} +(5.33557 + 2.85192i) q^{85} +(1.99370 - 0.150137i) q^{86} +(-0.456017 - 2.29255i) q^{87} +(-2.54228 - 5.66484i) q^{88} +(-8.25366 - 1.64175i) q^{89} +(0.829564 - 0.649447i) q^{90} +(0.201709 + 0.0198666i) q^{91} +(2.86071 - 11.5710i) q^{92} +(-4.12492 - 1.25128i) q^{93} +(-9.50694 - 6.67376i) q^{94} +(2.35348 - 2.35348i) q^{95} +(-8.35832 + 1.51638i) q^{96} +(11.5228 + 11.5228i) q^{97} +(0.961375 + 5.49056i) q^{98} +(0.474734 - 1.56499i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) $ 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{9}{32}\right)$	$1$

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 $

$2$	−1.19364	+	0.758431i	−0.844033	+	0.536292i
$2$	−1.19364	+	0.758431i	−0.844033	+	0.536292i
$3$	−1.32436	+	0.707885i	−0.764620	+	0.408698i	−0.807111	−	0.590399i	$-0.798970\pi$
$3$	−1.32436	+	0.707885i	−0.764620	+	0.408698i	0.0424918	+	0.999097i	$0.486470\pi$
$4$	0.849564	−	1.81059i	0.424782	−	0.905296i
$5$	0.634393	+	0.773010i	0.283709	+	0.345701i
$5$	0.634393	+	0.773010i	0.283709	+	0.345701i
$6$	1.04393	−	1.84940i	0.426182	−	0.755014i
$7$	2.75033	−	1.83771i	1.03953	−	0.694589i	0.0861217	−	0.996285i	$-0.472553\pi$
$7$	2.75033	−	1.83771i	1.03953	−	0.694589i	0.953404	+	0.301696i	$0.0975526\pi$
$8$	0.359135	+	2.80553i	0.126973	+	0.991906i
$9$	−0.413883	+	0.619419i	−0.137961	+	0.206473i
$10$	−1.34351	−	0.441554i	−0.424856	−	0.139632i
$11$	−2.10074	+	0.637253i	−0.633397	+	0.192139i	−0.590625	−	0.806946i	$-0.701119\pi$
$11$	−2.10074	+	0.637253i	−0.633397	+	0.192139i	−0.0427720	+	0.999085i	$0.513619\pi$
$12$	0.156563	+	2.99927i	0.0451958	+	0.865814i
$13$	0.0473662	+	0.0388724i	0.0131370	+	0.0107813i	0.640939	−	0.767592i	$-0.278545\pi$
$13$	0.0473662	+	0.0388724i	0.0131370	+	0.0107813i	−0.627802	+	0.778373i	$0.716045\pi$
$14$	−1.88913	+	4.27950i	−0.504891	+	1.14375i
$15$	−1.38737	−	0.574667i	−0.358217	−	0.148378i
$16$	−2.55648	−	3.07643i	−0.639121	−	0.769106i
$17$	5.58942	−	2.31521i	1.35563	−	0.561521i	0.417778	−	0.908549i	$-0.362809\pi$
$17$	5.58942	−	2.31521i	1.35563	−	0.561521i	0.937855	+	0.347028i	$0.112809\pi$
$18$	0.0242409	−	1.05327i	0.00571363	−	0.248257i
$19$	−0.326232	−	3.31229i	−0.0748428	−	0.759892i	−0.957222	−	0.289354i	$-0.906560\pi$
$19$	−0.326232	−	3.31229i	−0.0748428	−	0.759892i	0.882379	−	0.470539i	$-0.155940\pi$
$20$	1.93856	−	0.491906i	0.433476	−	0.109993i
$21$	−2.34154	+	4.38071i	−0.510965	+	0.955948i
$22$	2.02422	−	2.35392i	0.431565	−	0.501858i
$23$	5.84516	−	1.16268i	1.21880	−	0.242435i	0.456539	−	0.889703i	$-0.349089\pi$
$23$	5.84516	−	1.16268i	1.21880	−	0.242435i	0.762262	+	0.647269i	$0.224089\pi$
$24$	−2.46162	−	3.46131i	−0.502476	−	0.706537i
$25$	−0.195090	+	0.980785i	−0.0390181	+	0.196157i
$26$	−0.0860204	−	0.0104758i	−0.0168700	−	0.00205447i
$27$	0.551222	−	5.59665i	0.106083	−	1.07708i
$28$	−0.990764	−	6.54097i	−0.187237	−	1.23613i
$29$	−0.451849	+	1.48955i	−0.0839063	+	0.276602i	−0.988847	−	0.148936i	$-0.952415\pi$
$29$	−0.451849	+	1.48955i	−0.0839063	+	0.276602i	0.904941	+	0.425538i	$0.139915\pi$
$30$	2.09187	−	0.366277i	0.381921	−	0.0668727i
$31$	2.02974	+	2.02974i	0.364552	+	0.364552i	0.865486	−	0.500934i	$-0.167010\pi$
$31$	2.02974	+	2.02974i	0.364552	+	0.364552i	−0.500934	+	0.865486i	$0.667010\pi$
$32$	5.38478	+	1.73323i	0.951904	+	0.306395i
$33$	2.33104	−	2.33104i	0.405781	−	0.405781i
$34$	−4.91583	+	7.00272i	−0.843059	+	1.20096i
$35$	3.16536	+	0.960201i	0.535043	+	0.162304i
$36$	0.769896	+	1.27561i	0.128316	+	0.212601i
$37$	−0.167854	−	0.0165321i	−0.0275950	−	0.00271787i	0.0842102	−	0.996448i	$-0.473163\pi$
$37$	−0.167854	−	0.0165321i	−0.0275950	−	0.00271787i	−0.111805	+	0.993730i	$0.535663\pi$
$38$	2.90155	+	3.70627i	0.470694	+	0.601236i
$39$	−0.0902471	−	0.0179513i	−0.0144511	−	0.00287450i
$40$	−1.94087	+	2.05743i	−0.306879	+	0.325308i
$41$	1.59351	+	8.01110i	0.248864	+	1.25112i	0.879821	+	0.475305i	$0.157662\pi$
$41$	1.59351	+	8.01110i	0.248864	+	1.25112i	−0.630957	+	0.775818i	$0.717338\pi$
$42$	−0.527509	−	7.00489i	−0.0813963	−	1.08088i
$43$	−1.24681	−	0.666436i	−0.190137	−	0.101631i	0.373581	−	0.927597i	$-0.378130\pi$
$43$	−1.24681	−	0.666436i	−0.190137	−	0.101631i	−0.563719	+	0.825967i	$0.690630\pi$
$44$	−0.630909	+	4.34497i	−0.0951131	+	0.655029i
$45$	−0.741382	+	0.0730198i	−0.110519	+	0.0108851i
$46$	−6.09522	+	5.82097i	−0.898692	+	0.858256i
$47$	3.14315	+	7.58822i	0.458475	+	1.10686i	0.969015	+	0.247002i	$0.0794455\pi$
$47$	3.14315	+	7.58822i	0.458475	+	1.10686i	−0.510540	+	0.859854i	$0.670555\pi$
$48$	5.56346	+	2.26460i	0.803016	+	0.326867i
$49$	1.50834	−	3.64145i	0.215477	−	0.520207i
$50$	−0.510990	−	1.31867i	−0.0722649	−	0.186488i
$51$	−5.76350	+	7.02284i	−0.807051	+	0.983394i
$52$	0.110623	−	0.0527363i	0.0153406	−	0.00731320i
$53$	2.46646	+	8.13082i	0.338794	+	1.11685i	0.946503	+	0.322694i	$0.104589\pi$
$53$	2.46646	+	8.13082i	0.338794	+	1.11685i	−0.607709	+	0.794159i	$0.707911\pi$
$54$	3.58671	+	7.09846i	0.488090	+	0.965978i
$55$	−1.82530	−	1.21963i	−0.246123	−	0.164454i
$56$	6.14350	+	7.05615i	0.820959	+	0.942918i
$57$	2.77677	+	4.15573i	0.367792	+	0.550440i
$58$	−0.590373	−	2.12068i	−0.0775198	−	0.278459i
$59$	4.14048	−	3.39801i	0.539045	−	0.442383i	−0.325061	−	0.945693i	$-0.605385\pi$
$59$	4.14048	−	3.39801i	0.539045	−	0.442383i	0.864106	+	0.503310i	$0.167885\pi$
$60$	−2.21914	+	2.02374i	−0.286490	+	0.261264i
$61$	4.86239	+	9.09689i	0.622565	+	1.16474i	0.973575	+	0.228366i	$0.0733384\pi$
$61$	4.86239	+	9.09689i	0.622565	+	1.16474i	−0.351010	+	0.936372i	$0.614162\pi$
$62$	−3.96220	−	0.883364i	−0.503200	−	0.112187i
$63$			2.46420i			0.310460i
$64$	−7.74204	+	2.01513i	−0.967756	+	0.251891i
$65$			0.0612750i			0.00760023i
$66$	−1.01449	+	4.55035i	−0.124875	+	0.560110i
$67$	−3.79490	−	7.09977i	−0.463621	−	0.867375i	−0.999730	−	0.0232258i	$-0.992606\pi$
$67$	−3.79490	−	7.09977i	−0.463621	−	0.867375i	0.536109	−	0.844149i	$-0.319894\pi$
$68$	0.556661	−	12.0871i	0.0675051	−	1.46577i
$69$	−6.91806	+	5.67750i	−0.832836	+	0.683491i
$70$	−4.50655	+	1.25457i	−0.538636	+	0.149950i
$71$	−0.364204	−	0.545070i	−0.0432231	−	0.0646879i	0.809229	−	0.587494i	$-0.199885\pi$
$71$	−0.364204	−	0.545070i	−0.0432231	−	0.0646879i	−0.852452	+	0.522806i	$0.824885\pi$
$72$	−1.88644	−	0.938707i	−0.222319	−	0.110628i
$73$	3.50343	+	2.34092i	0.410045	+	0.273983i	0.743438	−	0.668804i	$-0.233194\pi$
$73$	3.50343	+	2.34092i	0.410045	+	0.273983i	−0.333393	+	0.942788i	$0.608194\pi$
$74$	0.212896	−	0.107572i	0.0247486	−	0.0125050i
$75$	−0.435914	−	1.43701i	−0.0503350	−	0.165932i
$76$	−6.27436	−	2.22333i	−0.719719	−	0.255033i
$77$	−4.60664	+	5.61321i	−0.524976	+	0.639685i
$78$	0.121338	−	0.0470189i	0.0137388	−	0.00532384i
$79$	5.15974	−	12.4567i	0.580516	−	1.40149i	−0.311831	−	0.950138i	$-0.600942\pi$
$79$	5.15974	−	12.4567i	0.580516	−	1.40149i	0.892347	−	0.451351i	$-0.149058\pi$
$80$	0.756293	−	3.92785i	0.0845561	−	0.439147i
$81$	2.37651	+	5.73740i	0.264056	+	0.637488i
$82$	−7.97794	−	8.35382i	−0.881016	−	0.922525i
$83$	14.9519	−	1.47263i	1.64118	−	0.161642i	0.765136	−	0.643868i	$-0.222672\pi$
$83$	14.9519	−	1.47263i	1.64118	−	0.161642i	0.876047	+	0.482226i	$0.160172\pi$
$84$	5.94238	+	7.96125i	0.648367	+	0.868644i
$85$	5.33557	+	2.85192i	0.578724	+	0.309334i
$86$	1.99370	−	0.150137i	0.214986	−	0.0161897i
$87$	−0.456017	−	2.29255i	−0.0488902	−	0.245788i
$88$	−2.54228	−	5.66484i	−0.271008	−	0.603874i
$89$	−8.25366	−	1.64175i	−0.874886	−	0.174026i	−0.262832	−	0.964842i	$-0.584657\pi$
$89$	−8.25366	−	1.64175i	−0.874886	−	0.174026i	−0.612054	+	0.790816i	$0.709657\pi$
$90$	0.829564	−	0.649447i	0.0874438	−	0.0684577i
$91$	0.201709	+	0.0198666i	0.0211448	+	0.00208258i
$92$	2.86071	−	11.5710i	0.298249	−	1.20636i
$93$	−4.12492	−	1.25128i	−0.427735	−	0.129752i
$94$	−9.50694	−	6.67376i	−0.980566	−	0.688346i
$95$	2.35348	−	2.35348i	0.241462	−	0.241462i
$96$	−8.35832	+	1.51638i	−0.853068	+	0.154765i
$97$	11.5228	+	11.5228i	1.16997	+	1.16997i	0.982217	+	0.187749i	$0.0601191\pi$
$97$	11.5228	+	11.5228i	1.16997	+	1.16997i	0.187749	+	0.982217i	$0.439881\pi$
$98$	0.961375	+	5.49056i	0.0971135	+	0.554631i
$99$	0.474734	−	1.56499i	0.0477126	−	0.157287i
$100$	1.61006	+	1.18647i	0.161006	+	0.118647i
$101$	0.945311	−	9.59791i	0.0940620	−	0.955027i	−0.826109	−	0.563510i	$-0.809450\pi$
$101$	0.945311	−	9.59791i	0.0940620	−	0.955027i	0.920171	−	0.391517i	$-0.128050\pi$
$102$	1.55321	−	12.7540i	0.153791	−	1.26283i
$103$	1.41414	−	7.10934i	0.139339	−	0.700504i	−0.846444	−	0.532478i	$-0.821261\pi$
$103$	1.41414	−	7.10934i	0.139339	−	0.700504i	0.985783	−	0.168026i	$-0.0537392\pi$
$104$	−0.0920471	+	0.146848i	−0.00902596	+	0.0143996i
$105$	−4.87179	+	0.969058i	−0.475438	+	0.0945704i
$106$	−9.11073	−	7.83465i	−0.884913	−	0.760968i
$107$	−7.40187	+	13.8479i	−0.715565	+	1.33873i	0.216444	+	0.976295i	$0.430554\pi$
$107$	−7.40187	+	13.8479i	−0.715565	+	1.33873i	−0.932010	+	0.362434i	$0.881946\pi$
$108$	−9.66495	−	5.75275i	−0.930010	−	0.553558i
$109$	0.964519	+	9.79293i	0.0923842	+	0.937992i	0.923936	+	0.382546i	$0.124953\pi$
$109$	0.964519	+	9.79293i	0.0923842	+	0.937992i	−0.831552	+	0.555446i	$0.812547\pi$
$110$	3.10376	+	0.0714328i	0.295932	+	0.00681085i
$111$	0.234002	−	0.0969266i	0.0222104	−	0.00919987i
$112$	−12.6847	−	3.76310i	−1.19860	−	0.355580i
$113$	6.35821	+	2.63366i	0.598130	+	0.247754i	0.661144	−	0.750259i	$-0.270071\pi$
$113$	6.35821	+	2.63366i	0.598130	+	0.247754i	−0.0630137	+	0.998013i	$0.520071\pi$
$114$	−6.46631	−	2.85447i	−0.605626	−	0.267345i
$115$	4.60689	+	3.78078i	0.429595	+	0.352559i
$116$	2.31309	+	2.08358i	0.214765	+	0.193456i
$117$	−0.0436824	+	0.0132509i	−0.00403844	+	0.00122505i
$118$	−2.36510	+	7.19628i	−0.217725	+	0.662471i
$119$	11.1180	−	16.6393i	1.01919	−	1.52532i
$120$	1.11399	−	4.09869i	0.101693	−	0.374158i
$121$	−5.13914	+	3.43386i	−0.467195	+	0.312169i
$122$	−12.7033	−	7.17065i	−1.15011	−	0.649200i
$123$	−7.78131	−	9.48156i	−0.701617	−	0.854923i
$124$	5.39942	−	1.95063i	0.484882	−	0.175172i
$125$	−0.881921	+	0.471397i	−0.0788814	+	0.0421630i
$126$	−1.86893	−	2.94138i	−0.166497	−	0.262039i
$127$	0.863173			0.0765942			0.0382971	−	0.999266i	$-0.487807\pi$
$127$	0.863173			0.0765942			0.0382971	+	0.999266i	$0.487807\pi$
$128$	7.71289	−	8.27715i	0.681730	−	0.731604i
$129$	2.12299			0.186919
$130$	−0.0464729	−	0.0731404i	−0.00407594	−	0.00641484i
$131$	−17.1220	+	9.15188i	−1.49595	+	0.799603i	−0.997723	−	0.0674417i	$-0.978516\pi$
$131$	−17.1220	+	9.15188i	−1.49595	+	0.799603i	−0.498230	+	0.867045i	$0.666016\pi$
$132$	−2.24019	−	6.20092i	−0.194984	−	0.539721i
$133$	−6.98428	−	8.51037i	−0.605614	−	0.737943i
$134$	9.91445	+	5.59641i	0.856478	+	0.483456i
$135$	4.67596	−	3.12438i	0.402443	−	0.268904i
$136$	8.50276	+	14.8498i	0.729106	+	1.27336i
$137$	8.51529	−	12.7440i	0.727511	−	1.08880i	−0.264713	−	0.964327i	$-0.585277\pi$
$137$	8.51529	−	12.7440i	0.727511	−	1.08880i	0.992223	−	0.124469i	$-0.0397229\pi$
$138$	3.95169	−	12.0238i	0.336390	−	1.02353i
$139$	11.8288	−	3.58824i	1.00331	−	0.304350i	0.254454	−	0.967085i	$-0.418104\pi$
$139$	11.8288	−	3.58824i	1.00331	−	0.304350i	0.748854	+	0.662735i	$0.230604\pi$
$140$	4.42770	−	4.91542i	0.374209	−	0.415429i
$141$	−9.53425	−	7.82455i	−0.802928	−	0.658946i
$142$	0.848128	+	0.374395i	0.0711733	+	0.0314185i
$143$	−0.124276	−	0.0514767i	−0.0103925	−	0.00430470i
$144$	2.96368	−	0.310256i	0.246973	−	0.0258547i
$145$	−1.43809	+	0.595675i	−0.119427	+	0.0494681i
$146$	−5.95726	−	0.137106i	−0.493027	−	0.0113470i
$147$	0.580146	+	5.89032i	0.0478497	+	0.485826i
$148$	−0.172535	+	0.289869i	−0.0141823	+	0.0238271i
$149$	3.14839	−	5.89022i	0.257926	−	0.482546i	−0.719313	−	0.694686i	$-0.755543\pi$
$149$	3.14839	−	5.89022i	0.257926	−	0.482546i	0.977239	+	0.212140i	$0.0680434\pi$
$150$	1.61020	+	1.38467i	0.131472	+	0.113058i
$151$	−8.15779	+	1.62268i	−0.663871	+	0.132052i	−0.515513	−	0.856882i	$-0.672399\pi$
$151$	−8.15779	+	1.62268i	−0.663871	+	0.132052i	−0.148358	+	0.988934i	$0.547399\pi$
$152$	9.17559	−	2.10481i	0.744239	−	0.170723i
$153$	−0.879276	+	4.42042i	−0.0710852	+	0.357370i
$154$	1.24145	−	10.1940i	0.100039	−	0.821455i
$155$	−0.281356	+	2.85666i	−0.0225991	+	0.229452i
$156$	−0.109173	+	0.148150i	−0.00874084	+	0.0118615i
$157$	5.22167	−	17.2135i	0.416735	−	1.37379i	−0.457899	−	0.889004i	$-0.651398\pi$
$157$	5.22167	−	17.2135i	0.416735	−	1.37379i	0.874633	−	0.484785i	$-0.161102\pi$
$158$	3.28868	+	18.7822i	0.261633	+	1.49423i
$159$	−9.02216	−	9.02216i	−0.715504	−	0.715504i
$160$	2.07626	+	5.26205i	0.164143	+	0.416001i
$161$	13.9395	−	13.9395i	1.09858	−	1.09858i
$162$	−7.18812	−	5.04598i	−0.564752	−	0.396450i
$163$	−0.665245	−	0.201800i	−0.0521060	−	0.0158062i	0.264124	−	0.964489i	$-0.414917\pi$
$163$	−0.665245	−	0.201800i	−0.0521060	−	0.0158062i	−0.316230	+	0.948683i	$0.602417\pi$
$164$	15.8586	+	3.92075i	1.23835	+	0.306159i
$165$	3.28071	+	0.323122i	0.255403	+	0.0251550i
$166$	−16.7303	+	13.0978i	−1.29852	+	1.01658i
$167$	−18.1202	−	3.60434i	−1.40219	−	0.278912i	−0.564666	−	0.825320i	$-0.690995\pi$
$167$	−18.1202	−	3.60434i	−1.40219	−	0.278912i	−0.837519	+	0.546408i	$0.815995\pi$
$168$	−13.1311	−	4.99600i	−1.01309	−	0.385449i
$169$	−2.53544	−	12.7465i	−0.195034	−	0.980502i
$170$	−8.53175	+	0.642490i	−0.654355	+	0.0492767i
$171$	2.18672	+	1.16883i	0.167223	+	0.0893824i
$172$	−2.26589	+	1.69129i	−0.172773	+	0.128960i
$173$	−18.8161	+	1.85322i	−1.43056	+	0.140898i	−0.783429	−	0.621481i	$-0.786531\pi$
$173$	−18.8161	+	1.85322i	−1.43056	+	0.140898i	−0.647131	+	0.762379i	$0.724031\pi$
$174$	2.28307	+	2.39063i	0.173079	+	0.181233i
$175$	1.26584	+	3.05600i	0.0956883	+	0.231012i
$176$	7.33097	+	4.83365i	0.552593	+	0.364350i
$177$	−3.07809	+	7.43117i	−0.231364	+	0.558561i
$178$	11.0971	−	4.30017i	0.831761	−	0.322311i
$179$	−2.72647	+	3.32221i	−0.203786	+	0.248314i	−0.864868	−	0.502000i	$-0.832598\pi$
$179$	−2.72647	+	3.32221i	−0.203786	+	0.248314i	0.661082	+	0.750314i	$0.270098\pi$
$180$	−0.497642	+	1.40437i	−0.0370921	+	0.104676i
$181$	−0.569547	−	1.87754i	−0.0423341	−	0.139557i	0.933226	−	0.359290i	$-0.116981\pi$
$181$	−0.569547	−	1.87754i	−0.0423341	−	0.139557i	−0.975560	+	0.219734i	$0.929481\pi$
$182$	−0.255836	+	0.129269i	−0.0189638	+	0.00958204i
$183$	−12.8791	−	8.60555i	−0.952051	−	0.636140i
$184$	5.36112	+	15.9812i	0.395227	+	1.17815i
$185$	−0.0937057	−	0.140241i	−0.00688938	−	0.0103107i
$186$	5.87270	−	1.63489i	0.430607	−	0.119876i
$187$	−10.2665	+	8.42554i	−0.750764	+	0.616136i
$188$	16.4095	+	0.755726i	1.19678	+	0.0551170i
$189$	−8.76898	−	16.4056i	−0.637849	−	1.19333i
$190$	−1.02426	+	4.59416i	−0.0743075	+	0.333295i
$191$		−	2.24641i		−	0.162544i	−0.996692	−	0.0812721i	$-0.974102\pi$
$191$		−	2.24641i		−	0.162544i	0.996692	−	0.0812721i	$-0.0258983\pi$
$192$	8.82677	−	8.14923i	0.637018	−	0.588120i
$193$		−	19.6185i		−	1.41217i	−0.708128	−	0.706084i	$-0.750460\pi$
$193$		−	19.6185i		−	1.41217i	0.708128	−	0.706084i	$-0.249540\pi$
$194$	−22.4934	−	5.01486i	−1.61493	−	0.360046i
$195$	−0.0433757	−	0.0811502i	−0.00310620	−	0.00581128i
$196$	−5.31175	−	5.82463i	−0.379411	−	0.416045i
$197$	−0.849826	+	0.697434i	−0.0605476	+	0.0496901i	−0.664180	−	0.747572i	$-0.731219\pi$
$197$	−0.849826	+	0.697434i	−0.0605476	+	0.0496901i	0.603633	+	0.797262i	$0.293719\pi$
$198$	0.620274	+	2.22809i	0.0440809	+	0.158343i
$199$	−10.3996	−	15.5641i	−0.737209	−	1.10331i	−0.990712	−	0.135977i	$-0.956583\pi$
$199$	−10.3996	−	15.5641i	−0.737209	−	1.10331i	0.253503	−	0.967335i	$-0.418417\pi$
$200$	−2.82169	−	0.195099i	−0.199524	−	0.0137956i
$201$	10.0516	+	6.71629i	0.708988	+	0.473731i
$202$	6.15099	+	12.1734i	0.432782	+	0.856519i
$203$	1.49462	+	4.92711i	0.104902	+	0.345815i
$204$	7.81904	+	16.4017i	0.547442	+	1.14835i
$205$	−5.18175	+	6.31398i	−0.361909	+	0.440988i
$206$	3.70398	+	9.55853i	0.258068	+	0.665975i
$207$	−1.69903	+	4.10182i	−0.118091	+	0.285096i
$208$	−0.00150277	−	0.245095i	−0.000104198	−	0.0169943i
$209$	2.79610	+	6.75038i	0.193410	+	0.466934i
$210$	5.08021	−	4.85162i	0.350567	−	0.334794i
$211$	6.43352	−	0.633646i	0.442902	−	0.0436220i	0.125891	−	0.992044i	$-0.459821\pi$
$211$	6.43352	−	0.633646i	0.442902	−	0.0436220i	0.317010	+	0.948422i	$0.397321\pi$
$212$	16.8170	+	2.44190i	1.15500	+	0.167710i
$213$	0.868185	+	0.464054i	0.0594870	+	0.0317965i
$214$	−1.66752	−	22.1433i	−0.113989	−	1.51368i
$215$	−0.275808	−	1.38658i	−0.0188100	−	0.0945642i
$216$	15.8996	−	0.463478i	1.08183	−	0.0315357i
$217$	9.31251	+	1.85237i	0.632175	+	0.125747i
$218$	−8.57856	−	10.9577i	−0.581013	−	0.742151i
$219$	−6.29690	−	0.620190i	−0.425505	−	0.0419086i
$220$	−3.75895	+	2.26872i	−0.253429	+	0.152957i
$221$	0.354747	+	0.107611i	0.0238629	+	0.00723873i
$222$	−0.205802	+	0.293170i	−0.0138125	+	0.0196763i
$223$	−13.2371	+	13.2371i	−0.886420	+	0.886420i	−0.994177	−	0.107757i	$-0.965633\pi$
$223$	−13.2371	+	13.2371i	−0.886420	+	0.886420i	0.107757	+	0.994177i	$0.465633\pi$
$224$	17.9951	−	5.12871i	1.20235	−	0.342676i
$225$	−0.526773	−	0.526773i	−0.0351182	−	0.0351182i
$226$	−9.58688	+	1.67862i	−0.637710	+	0.111660i
$227$	3.32772	−	10.9700i	0.220869	−	0.728106i	−0.774552	−	0.632511i	$-0.782024\pi$
$227$	3.32772	−	10.9700i	0.220869	−	0.728106i	0.995420	−	0.0955955i	$-0.0304755\pi$
$228$	9.88338	−	1.49704i	0.654543	−	0.0991439i
$229$	1.08459	−	11.0120i	0.0716718	−	0.727696i	−0.890451	−	0.455079i	$-0.849611\pi$
$229$	1.08459	−	11.0120i	0.0716718	−	0.727696i	0.962123	−	0.272617i	$-0.0878892\pi$
$230$	−8.36644	−	1.01889i	−0.551667	−	0.0671833i
$231$	2.12734	−	10.6949i	0.139969	−	0.703672i
$232$	−4.34125	−	0.732731i	−0.285017	−	0.0481061i
$233$	−10.8763	+	2.16343i	−0.712530	+	0.141731i	−0.538029	−	0.842926i	$-0.680831\pi$
$233$	−10.8763	+	2.16343i	−0.712530	+	0.141731i	−0.174500	+	0.984657i	$0.555831\pi$
$234$	0.0420913	−	0.0489470i	0.00275159	−	0.00319976i
$235$	−3.87179	+	7.24360i	−0.252567	+	0.472520i
$236$	−2.63480	−	10.3835i	−0.171511	−	0.675911i
$237$	1.98457	+	20.1497i	0.128912	+	1.30886i
$238$	−0.651177	+	28.2937i	−0.0422095	+	1.83401i
$239$	11.9143	−	4.93505i	0.770670	−	0.319222i	0.0375265	−	0.999296i	$-0.488052\pi$
$239$	11.9143	−	4.93505i	0.770670	−	0.319222i	0.733144	+	0.680073i	$0.238052\pi$
$240$	1.77886	+	5.73726i	0.114825	+	0.370338i
$241$	3.29792	+	1.36604i	0.212438	+	0.0879947i	0.486365	−	0.873756i	$-0.338323\pi$
$241$	3.29792	+	1.36604i	0.212438	+	0.0879947i	−0.273927	+	0.961751i	$0.588323\pi$
$242$	3.52995	−	7.99649i	0.226913	−	0.514034i
$243$	5.83284	+	4.78689i	0.374177	+	0.307079i
$244$	20.6017	−	1.07541i	1.31889	−	0.0688464i
$245$	3.77176	−	1.14415i	0.240969	−	0.0730971i
$246$	16.4792	+	5.41599i	1.05068	+	0.345311i
$247$	0.113305	−	0.169572i	0.00720939	−	0.0107896i
$248$	−4.96555	+	6.42345i	−0.315313	+	0.407889i
$249$	−18.7592	+	12.5345i	−1.18882	+	0.794343i
$250$	0.695176	−	1.23156i	0.0439668	−	0.0778904i
$251$	8.37859	+	10.2093i	0.528852	+	0.644408i	0.967085	−	0.254454i	$-0.0818956\pi$
$251$	8.37859	+	10.2093i	0.528852	+	0.644408i	−0.438233	+	0.898861i	$0.644396\pi$
$252$	4.46166	+	2.09350i	0.281058	+	0.131878i
$253$	−11.5383	+	6.16733i	−0.725404	+	0.387737i
$254$	−1.03032	+	0.654658i	−0.0646480	+	0.0410769i
$255$	−9.08505			−0.568928
$256$	−2.92878	+	15.7297i	−0.183049	+	0.983104i
$257$	4.92891			0.307457			0.153728	−	0.988113i	$-0.450872\pi$
$257$	4.92891			0.307457			0.153728	+	0.988113i	$0.450872\pi$
$258$	−2.53409	+	1.61014i	−0.157766	+	0.100243i
$259$	−0.492034	+	0.262998i	−0.0305735	+	0.0163419i
$260$	0.110944	+	0.0520570i	0.00688045	+	0.00322844i
$261$	−0.735642	−	0.896382i	−0.0455351	−	0.0554847i
$262$	13.4964	−	23.9099i	0.833812	−	1.47716i
$263$	0.0383993	−	0.0256576i	0.00236780	−	0.00158211i	−0.554386	−	0.832260i	$-0.687047\pi$
$263$	0.0383993	−	0.0256576i	0.00236780	−	0.00158211i	0.556754	+	0.830678i	$0.312047\pi$
$264$	7.37696	+	5.70265i	0.454020	+	0.350974i
$265$	−4.72050	+	7.06473i	−0.289978	+	0.433983i
$266$	14.7913	+	4.86124i	0.906911	+	0.298062i
$267$	12.0930	−	3.66837i	0.740079	−	0.224500i
$268$	−16.0788	+	0.839319i	−0.982169	+	0.0512695i
$269$	−2.49297	−	2.04592i	−0.151999	−	0.124742i	0.555320	−	0.831636i	$-0.312596\pi$
$269$	−2.49297	−	2.04592i	−0.151999	−	0.124742i	−0.707319	+	0.706894i	$0.750096\pi$
$270$	−3.21180	+	7.27578i	−0.195464	+	0.442790i
$271$	−10.2816	−	4.25877i	−0.624561	−	0.258702i	0.0478791	−	0.998853i	$-0.484754\pi$
$271$	−10.2816	−	4.25877i	−0.624561	−	0.258702i	−0.672440	+	0.740151i	$0.734754\pi$
$272$	−21.4118	−	11.2766i	−1.29828	−	0.683746i
$273$	−0.281198	+	0.116476i	−0.0170189	+	0.00704946i
$274$	−0.498736	+	21.6701i	−0.0301297	+	1.30914i
$275$	−0.215174	−	2.18470i	−0.0129755	−	0.131742i
$276$	4.40231	+	17.3492i	0.264988	+	1.04430i
$277$	−11.7289	+	21.9433i	−0.704723	+	1.31844i	0.233481	+	0.972361i	$0.424988\pi$
$277$	−11.7289	+	21.9433i	−0.704723	+	1.31844i	−0.938204	+	0.346082i	$0.887512\pi$
$278$	−11.3980	+	13.2544i	−0.683604	+	0.794948i
$279$	−2.09733	+	0.417185i	−0.125564	+	0.0249762i
$280$	−1.55709	+	9.22536i	−0.0930538	+	0.551321i
$281$	−1.46882	+	7.38428i	−0.0876228	+	0.440509i	0.911923	+	0.410362i	$0.134598\pi$
$281$	−1.46882	+	7.38428i	−0.0876228	+	0.440509i	−0.999545	+	0.0301473i	$0.990402\pi$
$282$	17.3149	+	2.10865i	1.03109	+	0.125568i
$283$	−0.710543	+	7.21426i	−0.0422374	+	0.428843i	0.950692	+	0.310137i	$0.100375\pi$
$283$	−0.710543	+	7.21426i	−0.0422374	+	0.428843i	−0.992929	+	0.118707i	$0.962125\pi$
$284$	−1.29631	+	0.196353i	−0.0769221	+	0.0116514i
$285$	−1.45086	+	4.78284i	−0.0859415	+	0.283311i
$286$	0.187382	−	0.0328099i	0.0110802	−	0.00194009i
$287$	19.1047	+	19.1047i	1.12772	+	1.12772i
$288$	−3.30227	+	2.61808i	−0.194588	+	0.154272i
$289$	13.8606	−	13.8606i	0.815327	−	0.815327i
$290$	1.26478	−	1.80171i	0.0742705	−	0.105800i
$291$	−23.4172	−	7.10353i	−1.37274	−	0.416417i
$292$	7.21483	−	4.35452i	0.422216	−	0.254829i
$293$	24.2193	+	2.38539i	1.41491	+	0.139356i	0.776391	−	0.630252i	$-0.217048\pi$
$293$	24.2193	+	2.38539i	1.41491	+	0.139356i	0.638517	+	0.769608i	$0.279548\pi$
$294$	−5.15989	−	6.59094i	−0.300931	−	0.384391i
$295$	5.25339	+	1.04496i	0.305864	+	0.0608402i
$296$	−0.0139006	−	0.476857i	−0.000807954	−	0.0277167i
$297$	2.40851	+	12.1084i	0.139756	+	0.702600i
$298$	0.709279	+	9.41865i	0.0410874	+	0.545608i
$299$	0.322059	+	0.172144i	0.0186252	+	0.00995536i
$300$	−2.97218	−	0.431574i	−0.171599	−	0.0249169i
$301$	−4.65386	+	0.458365i	−0.268244	+	0.0264197i
$302$	8.50678	−	8.12403i	0.489510	−	0.467485i
$303$	5.54228	+	13.3803i	0.318396	+	0.768676i
$304$	−9.35601	+	9.47145i	−0.536604	+	0.543225i
$305$	−3.94733	+	9.52969i	−0.226023	+	0.545668i
$306$	−2.30304	−	5.94327i	−0.131656	−	0.339754i
$307$	−12.7503	+	15.5363i	−0.727697	+	0.886702i	−0.997083	−	0.0763308i	$-0.975679\pi$
$307$	−12.7503	+	15.5363i	−0.727697	+	0.886702i	0.269385	+	0.963032i	$0.413179\pi$
$308$	6.24959	+	13.1095i	0.356104	+	0.746984i
$309$	3.15977	+	10.4164i	0.179753	+	0.592567i
$310$	−1.83074	−	3.62322i	−0.103979	−	0.205785i
$311$	−13.7146	−	9.16379i	−0.777683	−	0.519631i	0.102233	−	0.994760i	$-0.467401\pi$
$311$	−13.7146	−	9.16379i	−0.777683	−	0.519631i	−0.879916	+	0.475130i	$0.842401\pi$
$312$	0.0179520	−	0.259638i	0.00101633	−	0.0146991i
$313$	−18.9862	−	28.4148i	−1.07316	−	1.60610i	−0.752106	−	0.659042i	$-0.770962\pi$
$313$	−18.9862	−	28.4148i	−1.07316	−	1.60610i	−0.321057	−	0.947060i	$-0.604038\pi$
$314$	6.82248	+	24.5071i	0.385015	+	1.38301i
$315$	−1.90485	+	1.56327i	−0.107326	+	0.0880805i
$316$	−18.1705	−	19.9249i	−1.02217	−	1.12087i
$317$	−14.8347	−	27.7537i	−0.833198	−	1.55880i	−0.829294	−	0.558812i	$-0.811257\pi$
$317$	−14.8347	−	27.7537i	−0.833198	−	1.55880i	−0.00390390	−	0.999992i	$-0.501243\pi$
$318$	17.6119	+	3.92654i	0.987628	+	0.220190i
$319$		−	3.41710i		−	0.191321i
$320$	−6.46922	−	4.70630i	−0.361640	−	0.263090i
$321$		−	23.5793i		−	1.31607i
$322$	−6.06660	+	27.2108i	−0.338078	+	1.51640i
$323$	−9.49211	−	17.7585i	−0.528155	−	0.988109i
$324$	12.4071	+	0.571399i	0.689282	+	0.0317444i
$325$	−0.0473662	+	0.0388724i	−0.00262740	+	0.00215626i
$326$	0.947116	−	0.263666i	0.0524559	−	0.0146031i
$327$	−8.20964	−	12.2866i	−0.453994	−	0.679450i
$328$	−21.9031	+	7.34770i	−1.20940	+	0.405709i
$329$	22.5896	+	15.0939i	1.24541	+	0.832154i
$330$	−4.16106	+	2.10250i	−0.229059	+	0.115739i
$331$	3.47926	+	11.4696i	0.191237	+	0.630426i	0.999154	+	0.0411284i	$0.0130953\pi$
$331$	3.47926	+	11.4696i	0.191237	+	0.630426i	−0.807916	+	0.589297i	$0.799405\pi$
$332$	10.0362	−	28.3229i	0.550811	−	1.55442i
$333$	0.0797121	−	0.0971294i	0.00436819	−	0.00532266i
$334$	24.3627	−	9.44066i	1.33307	−	0.516570i
$335$	3.08073	−	7.43755i	0.168318	−	0.406357i
$336$	19.4630	−	3.99564i	1.06179	−	0.217980i
$337$	−4.78910	−	11.5619i	−0.260879	−	0.629818i	0.738114	−	0.674676i	$-0.235716\pi$
$337$	−4.78910	−	11.5619i	−0.260879	−	0.629818i	−0.998993	+	0.0448579i	$0.985716\pi$
$338$	12.6938	+	13.2918i	0.690450	+	0.722980i
$339$	−10.2849	+	1.01297i	−0.558599	+	0.0550172i
$340$	9.69657	−	7.23765i	0.525871	−	0.392517i
$341$	−5.55741	−	2.97050i	−0.300951	−	0.160862i
$342$	−3.49664	+	0.263317i	−0.189076	+	0.0142385i
$343$	1.97372	+	9.92255i	0.106571	+	0.535767i
$344$	1.42193	−	3.73732i	0.0766656	−	0.201503i
$345$	−8.77754	−	1.74596i	−0.472567	−	0.0939994i
$346$	21.0541	−	16.4828i	1.13188	−	0.886120i
$347$	13.9189	+	1.37089i	0.747206	+	0.0735934i	0.464451	−	0.885599i	$-0.346252\pi$
$347$	13.9189	+	1.37089i	0.747206	+	0.0735934i	0.282755	+	0.959192i	$0.408752\pi$
$348$	−4.53830	−	1.12201i	−0.243278	−	0.0601460i
$349$	−8.73377	−	2.64936i	−0.467508	−	0.141817i	0.0477370	−	0.998860i	$-0.484799\pi$
$349$	−8.73377	−	2.64936i	−0.467508	−	0.141817i	−0.515245	+	0.857043i	$0.672299\pi$
$350$	−3.82872	−	2.68772i	−0.204654	−	0.143665i
$351$	0.243665	−	0.243665i	0.0130059	−	0.0130059i
$352$	−12.4165	−	0.209606i	−0.661804	−	0.0111721i
$353$	23.1103	+	23.1103i	1.23004	+	1.23004i	0.963949	+	0.266089i	$0.0857314\pi$
$353$	23.1103	+	23.1103i	1.23004	+	1.23004i	0.266089	+	0.963949i	$0.414269\pi$
$354$	−1.96189	−	11.2047i	−0.104273	−	0.595522i
$355$	0.190296	−	0.627323i	0.0100999	−	0.0332948i
$356$	−9.98455	+	13.5492i	−0.529180	+	0.718108i
$357$	−2.94556	+	29.9067i	−0.155895	+	1.58283i
$358$	0.734759	−	6.03338i	0.0388332	−	0.318874i
$359$	−0.130214	+	0.654630i	−0.00687243	+	0.0345501i	−0.984069	−	0.177785i	$-0.943107\pi$
$359$	−0.130214	+	0.654630i	−0.00687243	+	0.0345501i	0.977197	+	0.212335i	$0.0681068\pi$
$360$	−0.471115	−	2.05375i	−0.0248300	−	0.108242i
$361$	7.77006	−	1.54556i	0.408951	−	0.0813454i
$362$	2.10382	+	1.80915i	0.110575	+	0.0950870i
$363$	4.37529	−	8.18559i	0.229643	−	0.429632i
$364$	0.207335	−	0.348334i	0.0108673	−	0.0182577i
$365$	0.412999	+	4.19325i	0.0216173	+	0.219485i
$366$	21.8998	+	0.504022i	1.14472	+	0.0263456i
$367$	29.3813	−	12.1701i	1.53369	−	0.635275i	0.553414	−	0.832906i	$-0.313325\pi$
$367$	29.3813	−	12.1701i	1.53369	−	0.635275i	0.980276	+	0.197631i	$0.0633248\pi$
$368$	−18.5199	−	15.0098i	−0.965419	−	0.782442i
$369$	−5.62175	−	2.32861i	−0.292657	−	0.121222i
$370$	0.218214	+	0.0963277i	0.0113444	+	0.00500784i
$371$	21.7256	+	17.8298i	1.12794	+	0.925676i
$372$	−5.76995	+	6.40551i	−0.299158	+	0.332110i
$373$	7.26547	−	2.20396i	0.376192	−	0.114117i	−0.0965259	−	0.995330i	$-0.530773\pi$
$373$	7.26547	−	2.20396i	0.376192	−	0.114117i	0.472718	+	0.881214i	$0.343273\pi$
$374$	5.86439	−	17.8435i	0.303240	−	0.922668i
$375$	0.834286	−	1.24860i	0.0430824	−	0.0644773i
$376$	−20.1602	+	11.5434i	−1.03968	+	0.595305i
$377$	−0.0793048	+	0.0529897i	−0.00408440	+	0.00272911i
$378$	22.9096	+	12.9318i	1.17834	+	0.665138i
$379$	7.82370	+	9.53321i	0.401877	+	0.489688i	0.934148	−	0.356886i	$-0.116161\pi$
$379$	7.82370	+	9.53321i	0.401877	+	0.489688i	−0.532271	+	0.846574i	$0.678661\pi$
$380$	−2.26176	−	6.26061i	−0.116026	−	0.321163i
$381$	−1.14315	+	0.611028i	−0.0585655	+	0.0313039i
$382$	1.70374	+	2.68140i	0.0871711	+	0.137193i
$383$	−26.5201			−1.35512			−0.677558	−	0.735469i	$-0.736962\pi$
$383$	−26.5201			−1.35512			−0.677558	+	0.735469i	$0.736962\pi$
$384$	−4.35538	+	16.4218i	−0.222259	+	0.838020i
$385$	−7.26149			−0.370080
$386$	14.8793	+	23.4174i	0.757334	+	1.19192i
$387$	0.928838	−	0.496474i	0.0472155	−	0.0252372i
$388$	30.6525	−	11.0738i	1.55615	−	0.562185i
$389$	2.72418	+	3.31942i	0.138121	+	0.168301i	0.837477	−	0.546472i	$-0.184030\pi$
$389$	2.72418	+	3.31942i	0.138121	+	0.168301i	−0.699356	+	0.714774i	$0.746530\pi$
$390$	0.113322	+	0.0639668i	0.00573827	+	0.00323908i
$391$	29.9792	−	20.0315i	1.51611	−	1.01303i
$392$	10.7579	+	2.92393i	0.543357	+	0.147681i
$393$	16.1972	−	24.2408i	0.817039	−	1.22278i
$394$	0.485432	−	1.47702i	0.0244557	−	0.0744112i
$395$	12.9025	−	3.91392i	0.649193	−	0.196931i
$396$	−2.43024	−	2.18911i	−0.122124	−	0.110007i
$397$	−14.6926	−	12.0579i	−0.737400	−	0.605169i	0.188882	−	0.982000i	$-0.439514\pi$
$397$	−14.6926	−	12.0579i	−0.737400	−	0.605169i	−0.926282	+	0.376831i	$0.877014\pi$
$398$	24.2177	+	10.6906i	1.21393	+	0.535871i
$399$	15.2741	+	6.32672i	0.764660	+	0.316732i
$400$	3.51606	−	1.90718i	0.175803	−	0.0953590i
$401$	−6.98524	+	2.89338i	−0.348826	+	0.144489i	−0.550215	−	0.835023i	$-0.685454\pi$
$401$	−6.98524	+	2.89338i	−0.348826	+	0.144489i	0.201389	+	0.979511i	$0.435454\pi$
$402$	−17.0919	−	0.393369i	−0.852467	−	0.0196195i
$403$	0.0172401	+	0.175042i	0.000858791	+	0.00871946i
$404$	−16.5748	−	9.86560i	−0.824626	−	0.490832i
$405$	−2.92743	+	5.47683i	−0.145465	+	0.272146i
$406$	−5.52092	−	4.74764i	−0.273999	−	0.235621i
$407$	0.363152	−	0.0722355i	0.0180008	−	0.00358058i
$408$	−21.7727	−	13.6475i	−1.07791	−	0.675654i
$409$	−4.67316	+	23.4936i	−0.231073	+	1.16168i	0.674757	+	0.738040i	$0.264249\pi$
$409$	−4.67316	+	23.4936i	−0.231073	+	1.16168i	−0.905830	+	0.423642i	$0.860751\pi$
$410$	1.39643	−	11.4666i	0.0689650	−	0.566297i
$411$	−2.25600	+	22.9055i	−0.111280	+	1.12985i
$412$	−11.6707	−	8.60026i	−0.574975	−	0.423704i
$413$	5.14313	−	16.9546i	0.253077	−	0.834283i
$414$	−1.08292	−	6.18470i	−0.0532224	−	0.303961i
$415$	10.6237	+	10.6237i	0.521499	+	0.521499i
$416$	0.187682	+	0.291416i	0.00920186	+	0.0142879i
$417$	−13.1256	+	13.1256i	−0.642762	+	0.642762i
$418$	−8.45724	−	5.93689i	−0.413657	−	0.290383i
$419$	−24.1372	−	7.32194i	−1.17918	−	0.357700i	−0.360946	−	0.932587i	$-0.617546\pi$
$419$	−24.1372	−	7.32194i	−1.17918	−	0.357700i	−0.818233	+	0.574886i	$0.805046\pi$
$420$	−2.38432	+	9.64409i	−0.116343	+	0.470583i
$421$	2.32062	+	0.228561i	0.113100	+	0.0111394i	0.154409	−	0.988007i	$-0.450653\pi$
$421$	2.32062	+	0.228561i	0.113100	+	0.0111394i	−0.0413088	+	0.999146i	$0.513153\pi$
$422$	−7.19874	+	5.63573i	−0.350429	+	0.274343i
$423$	−6.00119	−	1.19371i	−0.291788	−	0.0580402i
$424$	−21.9255	+	9.83979i	−1.06480	+	0.477862i
$425$	1.18028	+	5.93369i	0.0572522	+	0.287826i
$426$	−1.38826	+	0.104544i	−0.0672612	+	0.00506516i
$427$	30.0906	+	16.0838i	1.45619	+	0.778348i
$428$	18.7846	+	25.1664i	0.907986	+	1.21647i
$429$	0.201025	−	0.0197993i	0.00970560	−	0.000955918i
$430$	1.38084	+	1.44590i	0.0665902	+	0.0697276i
$431$	−13.0295	−	31.4560i	−0.627610	−	1.51518i	−0.842584	−	0.538564i	$-0.818967\pi$
$431$	−13.0295	−	31.4560i	−0.627610	−	1.51518i	0.214975	−	0.976620i	$-0.431033\pi$
$432$	−18.6269	+	12.6120i	−0.896186	+	0.606793i
$433$	4.05248	−	9.78355i	0.194750	−	0.470167i	−0.796095	−	0.605171i	$-0.793105\pi$
$433$	4.05248	−	9.78355i	0.194750	−	0.470167i	0.990845	+	0.135004i	$0.0431047\pi$
$434$	−12.5207	+	4.85183i	−0.601013	+	0.232895i
$435$	1.48287	−	1.80689i	0.0710984	−	0.0866336i
$436$	18.5504	+	6.57336i	0.888404	+	0.314807i
$437$	−5.75800	−	18.9816i	−0.275443	−	0.908012i
$438$	7.98662	−	4.03548i	0.381615	−	0.192823i
$439$	−17.2828	−	11.5480i	−0.824863	−	0.551156i	0.0699742	−	0.997549i	$-0.477708\pi$
$439$	−17.2828	−	11.5480i	−0.824863	−	0.551156i	−0.894837	+	0.446393i	$0.852708\pi$
$440$	2.76618	−	5.55895i	0.131872	−	0.265013i
$441$	1.63131	+	2.44143i	0.0776814	+	0.116258i
$442$	−0.505057	+	0.140602i	−0.0240231	+	0.00668776i
$443$	26.7348	−	21.9407i	1.27021	−	1.04243i	0.273458	−	0.961884i	$-0.411832\pi$
$443$	26.7348	−	21.9407i	1.27021	−	1.04243i	0.996751	−	0.0805496i	$-0.0256676\pi$
$444$	0.0233047	−	0.506027i	0.00110599	−	0.0240150i
$445$	−3.96697	−	7.42168i	−0.188053	−	0.351821i
$446$	5.76092	−	25.8398i	0.272787	−	1.22355i
$447$			10.0295i			0.474378i
$448$	−17.5899	+	19.7699i	−0.831046	+	0.934040i
$449$			25.1762i			1.18814i	0.804415	+	0.594068i	$0.202479\pi$
$449$			25.1762i			1.18814i	−0.804415	+	0.594068i	$0.797521\pi$
$450$	1.02830	+	0.229257i	0.0484745	+	0.0108073i
$451$	−8.45264	−	15.8138i	−0.398019	−	0.744642i
$452$	10.1702	−	9.27467i	0.478365	−	0.436244i
$453$	9.65517	−	7.92380i	0.453640	−	0.372292i
$454$	4.34790	+	15.6181i	0.204057	+	0.732995i
$455$	0.112606	+	0.168526i	0.00527904	+	0.00790064i
$456$	−10.6618	+	9.28280i	−0.499285	+	0.434707i
$457$	19.3935	+	12.9584i	0.907192	+	0.606166i	0.919213	−	0.393761i	$-0.128826\pi$
$457$	19.3935	+	12.9584i	0.907192	+	0.606166i	−0.0120207	+	0.999928i	$0.503826\pi$
$458$	7.05727	+	13.9670i	0.329764	+	0.652636i
$459$	−9.87642	−	32.5582i	−0.460992	−	1.51969i
$460$	10.7593	−	5.12919i	0.501655	−	0.239150i
$461$	19.5536	−	23.8261i	0.910701	−	1.10969i	−0.0828788	−	0.996560i	$-0.526411\pi$
$461$	19.5536	−	23.8261i	0.910701	−	1.10969i	0.993580	−	0.113133i	$-0.0360886\pi$
$462$	5.57205	+	14.3793i	0.259235	+	0.668986i
$463$	−6.95733	+	16.7965i	−0.323334	+	0.780598i	0.675722	+	0.737157i	$0.263832\pi$
$463$	−6.95733	+	16.7965i	−0.323334	+	0.780598i	−0.999056	+	0.0434415i	$0.986168\pi$
$464$	5.73763	−	2.41792i	0.266363	−	0.112249i
$465$	−1.64957	−	3.98241i	−0.0764970	−	0.184680i
$466$	11.3416	−	10.8313i	0.525389	−	0.501750i
$467$	−39.6095	+	3.90120i	−1.83291	+	0.180526i	−0.954665	−	0.297683i	$-0.903786\pi$
$467$	−39.6095	+	3.90120i	−1.83291	+	0.180526i	−0.878246	+	0.478209i	$0.841286\pi$
$468$	−0.0131190	+	0.0903485i	−0.000606425	+	0.00417636i
$469$	−23.4845	−	12.5528i	−1.08442	−	0.579632i
$470$	−0.872248	−	11.5828i	−0.0402338	−	0.534273i
$471$	5.26984	+	26.4933i	0.242821	+	1.22074i
$472$	11.0202	+	10.3959i	0.507246	+	0.478511i
$473$	3.04392	+	0.605474i	0.139960	+	0.0278397i
$474$	−17.6510	−	22.5463i	−0.810737	−	1.03559i
$475$	3.31229	+	0.326232i	0.151978	+	0.0149686i
$476$	−20.6815	−	34.2664i	−0.947936	−	1.57060i
$477$	−6.05721	−	1.83743i	−0.277341	−	0.0841303i
$478$	−10.4785	+	14.9269i	−0.479275	+	0.682738i
$479$	−23.0995	+	23.0995i	−1.05544	+	1.05544i	−0.0570722	+	0.998370i	$0.518177\pi$
$479$	−23.0995	+	23.0995i	−1.05544	+	1.05544i	−0.998370	+	0.0570722i	$0.981823\pi$
$480$	−6.47464	−	5.49909i	−0.295526	−	0.250998i
$481$	−0.00730795	−	0.00730795i	−0.000333214	−	0.000333214i
$482$	−4.97259	+	0.870680i	−0.226495	+	0.0396584i
$483$	−8.59332	+	28.3284i	−0.391010	+	1.28899i
$484$	1.85130	+	12.2222i	0.0841499	+	0.555553i
$485$	−1.59726	+	16.2173i	−0.0725279	+	0.736388i
$486$	−10.5928	−	1.29002i	−0.480501	−	0.0585166i
$487$	1.79538	−	9.02596i	0.0813562	−	0.409005i	−0.918550	−	0.395305i	$-0.870639\pi$
$487$	1.79538	−	9.02596i	0.0813562	−	0.409005i	0.999906	−	0.0137004i	$-0.00436111\pi$
$488$	−23.7754	+	16.9086i	−1.07626	+	0.765417i
$489$	1.02387	−	0.203661i	0.0463012	−	0.00920988i
$490$	−3.63437	+	4.22633i	−0.164184	+	0.190926i
$491$	−16.7115	+	31.2651i	−0.754182	+	1.41097i	0.152128	+	0.988361i	$0.451387\pi$
$491$	−16.7115	+	31.2651i	−0.754182	+	1.41097i	−0.906310	+	0.422614i	$0.861113\pi$
$492$	−23.7779	+	6.03359i	−1.07199	+	0.272015i
$493$	0.923045	+	9.37183i	0.0415718	+	0.422086i
$494$	−0.00663618	+	0.288342i	−0.000298576	+	0.0129731i
$495$	1.51092	−	0.625844i	0.0679108	−	0.0281296i
$496$	1.05535	−	11.4333i	0.0473864	−	0.513372i
$497$	−2.00336	−	0.829820i	−0.0898631	−	0.0372225i
$498$	12.8852	−	29.1893i	0.577401	−	1.30800i
$499$	14.5857	+	11.9702i	0.652946	+	0.535859i	0.901511	−	0.432756i	$-0.142459\pi$
$499$	14.5857	+	11.9702i	0.652946	+	0.535859i	−0.248565	+	0.968615i	$0.579959\pi$
$500$	0.104259	+	1.99728i	0.00466259	+	0.0893211i
$501$	26.5492	−	8.05360i	1.18613	−	0.359808i
$502$	−17.7441	−	5.83171i	−0.791959	−	0.260282i
$503$	−3.92260	+	5.87058i	−0.174900	+	0.261756i	−0.908555	−	0.417766i	$-0.862813\pi$
$503$	−3.92260	+	5.87058i	−0.174900	+	0.261756i	0.733654	+	0.679523i	$0.237813\pi$
$504$	−6.91340	+	0.884980i	−0.307948	+	0.0394202i
$505$	8.01898	−	5.35811i	0.356840	−	0.238433i
$506$	9.09506	−	16.1126i	0.404325	−	0.716291i
$507$	12.3809	+	15.0862i	0.549856	+	0.670001i
$508$	0.733321	−	1.56285i	0.0325358	−	0.0693404i
$509$	−35.2552	+	18.8443i	−1.56266	+	0.835258i	−0.562695	+	0.826664i	$0.690236\pi$
$509$	−35.2552	+	18.8443i	−1.56266	+	0.835258i	−0.999963	+	0.00859401i	$0.997264\pi$
$510$	10.8443	−	6.89039i	0.480194	−	0.305111i
$511$	13.9375			0.616559
$512$	−8.43395	−	20.9969i	−0.372731	−	0.927939i
$513$	−18.7176			−0.826401
$514$	−5.88336	+	3.73824i	−0.259504	+	0.164887i
$515$	6.39271	−	3.41698i	0.281697	−	0.150570i
$516$	1.80362	−	3.84387i	0.0793997	−	0.169217i
$517$	−11.4386	−	13.9379i	−0.503067	−	0.612989i
$518$	0.387847	−	0.687099i	0.0170410	−	0.0301894i
$519$	23.6074	−	15.7740i	1.03625	−	0.692400i
$520$	−0.171909	+	0.0220060i	−0.00753871	+	0.000965026i
$521$	−20.0125	+	29.9509i	−0.876765	+	1.31217i	0.0723946	+	0.997376i	$0.476936\pi$
$521$	−20.0125	+	29.9509i	−0.876765	+	1.31217i	−0.949160	+	0.314795i	$0.898064\pi$
$522$	1.55794	+	0.512026i	0.0681891	+	0.0224108i
$523$	12.2961	−	3.72997i	0.537669	−	0.163100i	−0.00975988	−	0.999952i	$-0.503107\pi$
$523$	12.2961	−	3.72997i	0.537669	−	0.163100i	0.547429	+	0.836852i	$0.315607\pi$
$524$	2.02412	+	38.7760i	0.0884241	+	1.69394i
$525$	−3.83972	−	3.15118i	−0.167579	−	0.137529i
$526$	−0.0263755	+	0.0597492i	−0.00115003	+	0.00260519i
$527$	16.0443	+	6.64578i	0.698902	+	0.289495i
$528$	−13.1305	−	1.21200i	−0.571432	−	0.0527457i
$529$	11.5649	−	4.79033i	0.502821	−	0.208275i
$530$	0.276477	−	12.0129i	0.0120094	−	0.521809i
$531$	0.391116	+	3.97107i	0.0169730	+	0.172330i
$532$	−21.3424	+	5.41558i	−0.925310	+	0.234795i
$533$	−0.235933	+	0.441399i	−0.0102194	+	0.0191191i
$534$	−11.6525	+	13.5504i	−0.504253	+	0.586384i
$535$	−15.4003	+	3.06331i	−0.665812	+	0.132438i
$536$	18.5558	−	13.1965i	0.801487	−	0.570002i
$537$	1.25908	−	6.32984i	0.0543334	−	0.273153i
$538$	4.52740	+	0.551358i	0.195190	+	0.0237707i
$539$	−0.848104	+	8.61094i	−0.0365304	+	0.370900i
$540$	−1.68444	−	11.1206i	−0.0724870	−	0.478555i
$541$	6.65175	−	21.9279i	0.285981	−	0.942753i	−0.689799	−	0.724001i	$-0.742301\pi$
$541$	6.65175	−	21.9279i	0.285981	−	0.942753i	0.975780	−	0.218752i	$-0.0701987\pi$
$542$	15.5025	−	2.71442i	0.665890	−	0.116594i
$543$	2.08337	+	2.08337i	0.0894060	+	0.0894060i
$544$	34.1106	−	2.77915i	1.46248	−	0.119155i
$545$	−6.95815	+	6.95815i	−0.298054	+	0.298054i
$546$	0.247311	−	0.352301i	0.0105839	−	0.0150771i
$547$	23.1565	+	7.02446i	0.990102	+	0.300344i	0.743473	−	0.668766i	$-0.233177\pi$
$547$	23.1565	+	7.02446i	0.990102	+	0.300344i	0.246629	+	0.969110i	$0.420677\pi$
$548$	−15.8400	−	26.2446i	−0.676650	−	1.12111i
$549$	−7.64725	−	0.753189i	−0.326377	−	0.0321453i
$550$	1.91378	+	2.44455i	0.0816041	+	0.104236i
$551$	5.08123	+	1.01072i	0.216467	+	0.0430581i
$552$	−18.4129	−	17.3699i	−0.783707	−	0.739310i
$553$	−8.70085	−	43.7421i	−0.369998	−	1.86010i
$554$	−2.64233	−	35.0880i	−0.112262	−	1.49075i
$555$	0.223374	+	0.119396i	0.00948171	+	0.00506808i
$556$	3.55251	−	24.4656i	0.150660	−	1.03757i
$557$	22.4145	−	2.20764i	0.949735	−	0.0935407i	0.388729	−	0.921352i	$-0.372914\pi$
$557$	22.4145	−	2.20764i	0.949735	−	0.0935407i	0.561006	+	0.827812i	$0.310414\pi$
$558$	2.18706	−	2.08865i	0.0925855	−	0.0884197i
$559$	−0.0331509	−	0.0800333i	−0.00140213	−	0.00338505i
$560$	−5.13820	−	12.1927i	−0.217129	−	0.515237i
$561$	7.63229	−	18.4260i	0.322236	−	0.777945i
$562$	−3.84722	−	9.92819i	−0.162285	−	0.418796i
$563$	−18.3332	+	22.3391i	−0.772654	+	0.941482i	−0.999473	−	0.0324552i	$-0.989667\pi$
$563$	−18.3332	+	22.3391i	−0.772654	+	0.941482i	0.226819	+	0.973937i	$0.427167\pi$
$564$	−22.2670	+	10.6152i	−0.937611	+	0.446979i
$565$	1.99776	+	6.58574i	0.0840465	+	0.277064i
$566$	−4.62339	−	9.15014i	−0.194335	−	0.384609i
$567$	17.0798	+	11.4124i	0.717286	+	0.479275i
$568$	1.39841	−	1.21754i	0.0586762	−	0.0510869i
$569$	−16.3063	−	24.4041i	−0.683597	−	1.02307i	−0.997291	−	0.0735510i	$-0.976567\pi$
$569$	−16.3063	−	24.4041i	−0.683597	−	1.02307i	0.313695	−	0.949524i	$-0.398433\pi$
$570$	−1.89565	−	6.80938i	−0.0794001	−	0.285214i
$571$	−2.68586	+	2.20423i	−0.112400	+	0.0922442i	−0.688914	−	0.724843i	$-0.741912\pi$
$571$	−2.68586	+	2.20423i	−0.112400	+	0.0922442i	0.576515	+	0.817087i	$0.304412\pi$
$572$	−0.198783	+	0.181280i	−0.00831155	+	0.00757969i
$573$	1.59020	+	2.97505i	0.0664314	+	0.124284i
$574$	−37.2939	−	8.31459i	−1.55662	−	0.347044i
$575$			5.95968i			0.248536i
$576$	1.95609	−	5.62960i	0.0815037	−	0.234567i
$577$		−	27.1387i		−	1.12980i	−0.825160	−	0.564899i	$-0.808915\pi$
$577$		−	27.1387i		−	1.12980i	0.825160	−	0.564899i	$-0.191085\pi$
$578$	−6.03226	+	27.0568i	−0.250909	+	1.12542i
$579$	13.8876	+	25.9819i	0.577150	+	1.07977i
$580$	−0.143222	+	3.10985i	−0.00594696	+	0.129129i
$581$	38.4163	−	31.5275i	1.59378	−	1.30798i
$582$	33.3393	−	9.28127i	1.38196	−	0.384721i
$583$	−10.3628	−	15.5090i	−0.429182	−	0.642317i
$584$	−5.30932	+	10.6697i	−0.219701	+	0.441515i
$585$	−0.0379549	−	0.0253607i	−0.00156924	−	0.00104853i
$586$	−30.7184	+	15.5214i	−1.26896	+	0.641182i
$587$	−12.5687	−	41.4333i	−0.518764	−	1.71014i	−0.689026	−	0.724737i	$-0.741961\pi$
$587$	−12.5687	−	41.4333i	−0.518764	−	1.71014i	0.170262	−	0.985399i	$-0.445539\pi$
$588$	11.1578	+	3.95380i	0.460142	+	0.163052i
$589$	6.06092	−	7.38525i	0.249736	−	0.304304i
$590$	−7.06320	+	2.73702i	−0.290787	+	0.112681i
$591$	0.631772	−	1.52523i	0.0259876	−	0.0627397i
$592$	0.378255	+	0.558653i	0.0155462	+	0.0229605i
$593$	−4.48993	−	10.8396i	−0.184379	−	0.445131i	0.804481	−	0.593979i	$-0.202444\pi$
$593$	−4.48993	−	10.8396i	−0.184379	−	0.445131i	−0.988860	+	0.148848i	$0.952444\pi$
$594$	−12.0583	−	12.6264i	−0.494757	−	0.518067i
$595$	19.9156	−	1.96151i	0.816459	−	0.0804142i
$596$	−7.99003	−	10.7046i	−0.327284	−	0.438476i
$597$	24.7904	+	13.2508i	1.01461	+	0.542318i
$598$	−0.514983	+	0.0387812i	−0.0210592	+	0.00158588i
$599$	5.95829	+	29.9543i	0.243449	+	1.22390i	0.888182	+	0.459493i	$0.151969\pi$
$599$	5.95829	+	29.9543i	0.243449	+	1.22390i	−0.644732	+	0.764408i	$0.723031\pi$
$600$	3.87504	−	1.73905i	0.158198	−	0.0709965i
$601$	−9.50350	−	1.89036i	−0.387656	−	0.0771095i	−0.00258523	−	0.999997i	$-0.500823\pi$
$601$	−9.50350	−	1.89036i	−0.387656	−	0.0771095i	−0.385071	+	0.922887i	$0.625823\pi$
$602$	5.20741	−	4.07676i	0.212238	−	0.166156i
$603$	5.96838	+	0.587834i	0.243051	+	0.0239385i
$604$	−3.99254	+	16.1490i	−0.162454	+	0.657093i
$605$	−5.91465	−	1.79419i	−0.240465	−	0.0729442i
$606$	−16.7635	−	11.7678i	−0.680971	−	0.478034i
$607$	−14.3968	+	14.3968i	−0.584347	+	0.584347i	−0.936095	−	0.351748i	$-0.885587\pi$
$607$	−14.3968	+	14.3968i	−0.584347	+	0.584347i	0.351748	+	0.936095i	$0.385587\pi$
$608$	3.98429	−	18.4014i	0.161584	−	0.746276i
$609$	−5.46725	−	5.46725i	−0.221544	−	0.221544i
$610$	−2.51592	−	14.3688i	−0.101867	−	0.581776i
$611$	−0.146094	+	0.481607i	−0.00591033	+	0.0194837i
$612$	7.25657	+	5.34744i	0.293330	+	0.216157i
$613$	1.73357	−	17.6012i	0.0700182	−	0.710907i	−0.894531	−	0.447005i	$-0.852491\pi$
$613$	1.73357	−	17.6012i	0.0700182	−	0.710907i	0.964550	−	0.263902i	$-0.0850094\pi$
$614$	3.43609	−	28.2150i	0.138669	−	1.13866i
$615$	2.39293	−	12.0301i	0.0964922	−	0.485099i
$616$	−17.4025	−	10.9082i	−0.701165	−	0.439504i
$617$	8.61526	−	1.71368i	0.346837	−	0.0689902i	−0.0185979	−	0.999827i	$-0.505920\pi$
$617$	8.61526	−	1.71368i	0.346837	−	0.0689902i	0.365435	+	0.930837i	$0.380920\pi$
$618$	−11.6717	−	10.0370i	−0.469506	−	0.403745i
$619$	23.2865	−	43.5659i	0.935962	−	1.75106i	0.362008	−	0.932175i	$-0.382091\pi$
$619$	23.2865	−	43.5659i	0.935962	−	1.75106i	0.573954	−	0.818887i	$-0.305409\pi$
$620$	4.93321	+	2.93634i	0.198123	+	0.117926i
$621$	−3.28510	−	33.3542i	−0.131827	−	1.33846i
$622$	23.3204	+	0.536718i	0.935063	+	0.0215204i
$623$	−25.7173	+	10.6525i	−1.03034	+	0.426782i
$624$	0.175490	+	0.323531i	0.00702521	+	0.0129516i
$625$	−0.923880	−	0.382683i	−0.0369552	−	0.0153073i
$626$	44.2134	+	19.5174i	1.76712	+	0.780074i
$627$	−8.48153	−	6.96062i	−0.338720	−	0.277980i
$628$	−26.7305	−	24.0783i	−1.06666	−	0.960829i
$629$	−0.976480	+	0.296212i	−0.0389348	+	0.0118107i
$630$	1.08808	−	3.31069i	0.0433501	−	0.131901i
$631$	3.71588	−	5.56120i	0.147927	−	0.221388i	−0.750105	−	0.661319i	$-0.769997\pi$
$631$	3.71588	−	5.56120i	0.147927	−	0.221388i	0.898032	+	0.439931i	$0.144997\pi$
$632$	36.8007	+	10.0022i	1.46386	+	0.397865i
$633$	−8.07174	+	5.39337i	−0.320823	+	0.214367i
$634$	38.7566	+	21.8769i	1.53922	+	0.868844i
$635$	0.547591	+	0.667242i	0.0217305	+	0.0264787i
$636$	−24.0003	+	8.67055i	−0.951676	+	0.343810i
$637$	0.212996	−	0.113849i	0.00843923	−	0.00451086i
$638$	2.59163	+	4.07879i	0.102604	+	0.161481i
$639$	0.488365			0.0193194
$640$	11.2913	+	0.711178i	0.446329	+	0.0281118i
$641$	−9.94293			−0.392722			−0.196361	−	0.980532i	$-0.562912\pi$
$641$	−9.94293			−0.392722			−0.196361	+	0.980532i	$0.562912\pi$
$642$	17.8833	+	28.1452i	0.705797	+	1.11080i
$643$	−13.8420	+	7.39869i	−0.545874	+	0.291776i	−0.721191	−	0.692736i	$-0.756405\pi$
$643$	−13.8420	+	7.39869i	−0.545874	+	0.291776i	0.175317	+	0.984512i	$0.443905\pi$
$644$	−13.3962	−	37.0811i	−0.527884	−	1.46120i
$645$	1.34681	+	1.64109i	0.0530306	+	0.0646180i
$646$	24.7988	+	13.9982i	0.975695	+	0.550750i
$647$	−32.8826	+	21.9715i	−1.29275	+	0.863788i	−0.995840	−	0.0911174i	$-0.970956\pi$
$647$	−32.8826	+	21.9715i	−1.29275	+	0.863788i	−0.296910	+	0.954905i	$0.595956\pi$
$648$	−15.2430	+	8.72787i	−0.598801	+	0.342863i
$649$	−6.53270	+	9.77687i	−0.256431	+	0.383776i
$650$	0.0270562	−	0.0823238i	0.00106123	−	0.00322901i
$651$	−13.6444	+	4.13898i	−0.534766	+	0.162219i
$652$	−0.930545	+	1.03304i	−0.0364429	+	0.0404572i
$653$	22.7013	+	18.6305i	0.888372	+	0.729068i	0.963387	−	0.268115i	$-0.0864006\pi$
$653$	22.7013	+	18.6305i	0.888372	+	0.729068i	−0.0750154	+	0.997182i	$0.523901\pi$
$654$	19.1179	+	8.43935i	0.747569	+	0.330005i
$655$	−17.9366	−	7.42957i	−0.700839	−	0.290297i
$656$	20.5718	−	25.3825i	0.803193	−	0.991022i
$657$	−2.90002	+	1.20123i	−0.113140	+	0.0468643i
$658$	−38.4116	−	0.884041i	−1.49744	−	0.0344635i
$659$	−3.04891	−	30.9561i	−0.118769	−	1.20588i	−0.851127	−	0.524960i	$-0.824080\pi$
$659$	−3.04891	−	30.9561i	−0.118769	−	1.20588i	0.732358	−	0.680920i	$-0.238420\pi$
$660$	3.37221	−	5.66551i	0.131263	−	0.220530i
$661$	−16.4676	+	30.8087i	−0.640516	+	1.19832i	0.326883	+	0.945065i	$0.394002\pi$
$661$	−16.4676	+	30.8087i	−0.640516	+	1.19832i	−0.967399	+	0.253256i	$0.918498\pi$
$662$	−12.8519	−	11.0518i	−0.499503	−	0.429541i
$663$	−0.545990	+	0.108604i	−0.0212045	+	0.00421784i
$664$	9.50126	+	41.4192i	0.368720	+	1.60738i
$665$	2.14782	−	10.7978i	0.0832891	−	0.418722i
$666$	−0.0214817	+	0.176394i	−0.000832398	+	0.00683513i
$667$	−0.909273	+	9.23200i	−0.0352072	+	0.357465i
$668$	−21.9203	+	29.7462i	−0.848121	+	1.15092i
$669$	8.16033	−	26.9010i	0.315496	−	1.04005i
$670$	1.96358	+	11.2143i	0.0758596	+	0.433246i
$671$	−16.0117	−	16.0117i	−0.618123	−	0.618123i
$672$	−20.2015	+	19.5307i	−0.779288	+	0.753414i
$673$	31.7266	−	31.7266i	1.22297	−	1.22297i	0.256402	−	0.966570i	$-0.417463\pi$
$673$	31.7266	−	31.7266i	1.22297	−	1.22297i	0.966570	−	0.256402i	$-0.0825371\pi$
$674$	14.4854	+	10.1686i	0.557957	+	0.391679i
$675$	5.38157	+	1.63248i	0.207137	+	0.0628343i
$676$	−25.2328	−	6.23833i	−0.970491	−	0.239936i
$677$	−6.53080	−	0.643227i	−0.250999	−	0.0247212i	−0.0282648	−	0.999600i	$-0.508998\pi$
$677$	−6.53080	−	0.643227i	−0.250999	−	0.0247212i	−0.222734	+	0.974879i	$0.571498\pi$
$678$	11.5082	−	9.00951i	0.441970	−	0.346008i
$679$	52.8672	+	10.5159i	2.02886	+	0.403564i
$680$	−6.08498	+	15.9934i	−0.233348	+	0.613317i
$681$	3.35842	+	16.8839i	0.128695	+	0.646993i
$682$	8.88648	−	0.669203i	0.340281	−	0.0256251i
$683$	−13.2516	−	7.08311i	−0.507057	−	0.271028i	0.197970	−	0.980208i	$-0.436565\pi$
$683$	−13.2516	−	7.08311i	−0.507057	−	0.271028i	−0.705027	+	0.709180i	$0.749065\pi$
$684$	3.97402	−	2.96626i	0.151951	−	0.113418i
$685$	15.2533	−	1.50232i	0.582799	−	0.0574007i
$686$	−9.88149	−	10.3470i	−0.377277	−	0.395052i
$687$	6.35887	+	15.3517i	0.242606	+	0.585703i
$688$	1.13722	+	5.53946i	0.0433561	+	0.211190i
$689$	−0.199238	+	0.481003i	−0.00759037	+	0.0183248i
$690$	11.8014	−	4.57311i	0.449273	−	0.174095i
$691$	−0.617924	+	0.752942i	−0.0235069	+	0.0286433i	−0.784631	−	0.619963i	$-0.787148\pi$
$691$	−0.617924	+	0.752942i	−0.0235069	+	0.0286433i	0.761124	+	0.648606i	$0.224648\pi$
$692$	−12.6300	+	35.6427i	−0.480122	+	1.35493i
$693$	−1.57032	−	5.17665i	−0.0596515	−	0.196645i
$694$	−17.6539	+	8.92018i	−0.670134	+	0.338606i
$695$	10.2779	+	6.86746i	0.389862	+	0.260497i
$696$	6.26807	−	2.10271i	0.237591	−	0.0797030i
$697$	27.4542	+	41.0880i	1.03990	+	1.55632i
$698$	12.4344	−	3.46158i	0.470647	−	0.131023i
$699$	12.8727	−	10.5643i	0.486889	−	0.399580i
$700$	6.60858	+	0.304353i	0.249781	+	0.0115035i
$701$	−9.22073	−	17.2508i	−0.348262	−	0.651553i	0.645414	−	0.763833i	$-0.276685\pi$
$701$	−9.22073	−	17.2508i	−0.348262	−	0.651553i	−0.993677	+	0.112280i	$0.964185\pi$
$702$	−0.106046	+	0.475652i	−0.00400243	+	0.0179523i
$703$			0.561374i			0.0211726i
$704$	14.9799	−	9.16691i	0.564576	−	0.345491i
$705$		−	12.3339i		−	0.464522i
$706$	−45.1130	−	10.0579i	−1.69785	−	0.378532i
$707$	−15.0383	−	28.1346i	−0.565572	−	1.05811i
$708$	10.8398	+	11.8864i	0.407384	+	0.446719i
$709$	−26.9548	+	22.1212i	−1.01231	+	0.830780i	−0.985639	−	0.168864i	$-0.945990\pi$
$709$	−26.9548	+	22.1212i	−1.01231	+	0.830780i	−0.0266692	+	0.999644i	$0.508490\pi$
$710$	0.248636	+	0.893125i	0.00933113	+	0.0335184i
$711$	5.58040	+	8.35165i	0.209281	+	0.313212i
$712$	1.64183	−	23.7455i	0.0615300	−	0.889901i
$713$	14.2241	+	9.50422i	0.532696	+	0.355936i
$714$	−19.1663	−	37.9320i	−0.717280	−	1.41957i
$715$	−0.0390477	−	0.128723i	−0.00146030	−	0.00481397i
$716$	3.69886	+	7.75896i	0.138233	+	0.289966i
$717$	−12.2853	+	14.9697i	−0.458804	+	0.559055i
$718$	−0.341063	−	0.880153i	−0.0127284	−	0.0328470i
$719$	−1.21523	+	2.93383i	−0.0453206	+	0.109414i	−0.944919	−	0.327305i	$-0.893859\pi$
$719$	−1.21523	+	2.93383i	−0.0453206	+	0.109414i	0.899598	+	0.436719i	$0.143859\pi$
$720$	2.11997	+	2.09413i	0.0790066	+	0.0780437i
$721$	−9.17557	−	22.1518i	−0.341716	−	0.824976i
$722$	−8.10247	+	7.73791i	−0.301543	+	0.287975i
$723$	−5.33464	+	0.525416i	−0.198397	+	0.0195404i
$724$	−3.88333	−	0.563877i	−0.144323	−	0.0209563i
$725$	−1.37277	−	0.733764i	−0.0509836	−	0.0272513i
$726$	0.985679	+	13.0890i	0.0365820	+	0.485779i
$727$	−0.417003	−	2.09642i	−0.0154658	−	0.0777518i	0.972282	−	0.233813i	$-0.0751203\pi$
$727$	−0.417003	−	2.09642i	−0.0154658	−	0.0777518i	−0.987747	+	0.156061i	$0.950120\pi$
$728$	0.0167042	+	0.573036i	0.000619100	+	0.0212381i
$729$	−29.3857	−	5.84518i	−1.08836	−	0.216488i
$730$	−3.67326	−	4.69201i	−0.135954	−	0.173659i
$731$	−8.51190	−	0.838349i	−0.314824	−	0.0310075i
$732$	−26.5228	+	16.0079i	−0.980309	+	0.591667i
$733$	25.1455	+	7.62781i	0.928771	+	0.281740i	0.718198	−	0.695839i	$-0.244967\pi$
$733$	25.1455	+	7.62781i	0.928771	+	0.281740i	0.210573	+	0.977578i	$0.432467\pi$
$734$	−25.8405	+	36.8105i	−0.953792	+	1.35870i
$735$	−4.18524	+	4.18524i	−0.154375	+	0.154375i
$736$	33.4901	+	3.87028i	1.23446	+	0.142660i
$737$	12.4965	+	12.4965i	0.460313	+	0.460313i
$738$	8.47645	−	1.48419i	0.312022	−	0.0546338i
$739$	−2.76819	+	9.12550i	−0.101830	+	0.335687i	−0.993021	−	0.117941i	$-0.962371\pi$
$739$	−2.76819	+	9.12550i	−0.101830	+	0.335687i	0.891191	+	0.453628i	$0.149871\pi$
$740$	−0.333527	+	0.0505196i	−0.0122607	+	0.00185714i
$741$	−0.0300183	+	0.304781i	−0.00110275	+	0.0111964i
$742$	−39.4553	−	4.80496i	−1.44845	−	0.176396i
$743$	−3.27902	+	16.4848i	−0.120296	+	0.604768i	0.872860	+	0.487971i	$0.162263\pi$
$743$	−3.27902	+	16.4848i	−0.120296	+	0.604768i	−0.993156	+	0.116797i	$0.962737\pi$
$744$	2.02911	−	12.0220i	0.0743909	−	0.440748i
$745$	6.55052	−	1.30298i	0.239992	−	0.0477375i
$746$	−7.00082	+	8.14109i	−0.256318	+	0.298067i
$747$	−5.27615	+	9.87099i	−0.193044	+	0.361161i
$748$	6.53312	+	25.7465i	0.238875	+	0.941387i
$749$	5.09090	+	51.6888i	0.186017	+	1.88867i
$750$	−0.0488637	+	2.12313i	−0.00178425	+	0.0775257i
$751$	31.8770	−	13.2039i	1.16321	−	0.481816i	0.284265	−	0.958746i	$-0.408250\pi$
$751$	31.8770	−	13.2039i	1.16321	−	0.481816i	0.878941	+	0.476930i	$0.158250\pi$
$752$	15.3092	−	29.0688i	0.558269	−	1.06003i
$753$	−18.3233	−	7.58976i	−0.667738	−	0.276586i
$754$	0.0544724	−	0.123398i	0.00198377	−	0.00449389i
$755$	−6.42960	−	5.27663i	−0.233997	−	0.192036i
$756$	−37.1537	+	1.93943i	−1.35127	+	0.0705365i
$757$	−12.7114	+	3.85596i	−0.462004	+	0.140147i	−0.512702	−	0.858567i	$-0.671355\pi$
$757$	−12.7114	+	3.85596i	−0.462004	+	0.140147i	0.0506980	+	0.998714i	$0.483855\pi$
$758$	−16.5690	−	5.44550i	−0.601813	−	0.197789i
$759$	10.9150	−	16.3355i	0.396191	−	0.592942i
$760$	7.44798	+	5.75755i	0.270166	+	0.208848i
$761$	−34.7211	+	23.1999i	−1.25864	+	0.840995i	−0.992417	−	0.122917i	$-0.960775\pi$
$761$	−34.7211	+	23.1999i	−1.25864	+	0.840995i	−0.266221	+	0.963912i	$0.585775\pi$
$762$	0.901092	−	1.59635i	0.0326431	−	0.0578297i
$763$	20.6493	+	25.1613i	0.747555	+	0.910899i
$764$	−4.06732	−	1.90846i	−0.147151	−	0.0690458i
$765$	−3.97484	+	2.12459i	−0.143711	+	0.0768149i
$766$	31.6556	−	20.1137i	1.14376	−	0.726738i
$767$	0.328208			0.0118509
$768$	−7.25603	−	22.9050i	−0.261829	−	0.826512i
$769$	−11.4650			−0.413437			−0.206718	−	0.978400i	$-0.566278\pi$
$769$	−11.4650			−0.413437			−0.206718	+	0.978400i	$0.566278\pi$
$770$	8.66762	−	5.50734i	0.312359	−	0.198471i
$771$	−6.52765	+	3.48910i	−0.235088	+	0.125657i
$772$	−35.5210	−	16.6671i	−1.27843	−	0.599863i
$773$	13.5222	+	16.4768i	0.486359	+	0.592630i	0.957142	−	0.289619i	$-0.0935286\pi$
$773$	13.5222	+	16.4768i	0.486359	+	0.592630i	−0.470783	+	0.882249i	$0.656029\pi$
$774$	−0.732159	+	1.29707i	−0.0263169	+	0.0466223i
$775$	−2.38672	+	1.59475i	−0.0857335	+	0.0572853i
$776$	−28.1894	+	36.4659i	−1.01194	+	1.30905i
$777$	0.465458	−	0.696607i	0.0166982	−	0.0249906i
$778$	−5.76925	−	1.89610i	−0.206838	−	0.0679784i
$779$	26.0152	−	7.89164i	0.932093	−	0.282747i
$780$	−0.183780	+	0.00959339i	−0.00658039	+	0.000343498i
$781$	1.11245	+	0.912962i	0.0398065	+	0.0326683i
$782$	−20.5920	+	46.6476i	−0.736367	+	1.66811i
$783$	8.08741	+	3.34991i	0.289020	+	0.119716i
$784$	−15.0587	+	4.66902i	−0.537811	+	0.166751i
$785$	16.6188	−	6.88375i	0.593152	−	0.245691i
$786$	−0.948658	+	41.2192i	−0.0338375	+	1.47024i
$787$	2.37255	+	24.0889i	0.0845723	+	0.858677i	0.940095	+	0.340912i	$0.110736\pi$
$787$	2.37255	+	24.0889i	0.0845723	+	0.858677i	−0.855523	+	0.517765i	$0.826764\pi$
$788$	0.540787	+	2.13120i	0.0192647	+	0.0759209i
$789$	−0.0326919	+	0.0611622i	−0.00116386	+	0.00217743i
$790$	−12.4325	+	14.4575i	−0.442328	+	0.514373i
$791$	22.3271	−	4.44113i	0.793859	−	0.157908i
$792$	4.56112	+	0.769841i	0.162072	+	0.0273551i
$793$	−0.123305	+	0.619898i	−0.00437871	+	0.0220132i
$794$	26.6828	+	3.24949i	0.946937	+	0.115320i
$795$	1.25063	−	12.6978i	0.0443551	−	0.450345i
$796$	−37.0154	+	5.60674i	−1.31198	+	0.198726i
$797$	14.1467	−	46.6356i	0.501103	−	1.65192i	−0.232695	−	0.972550i	$-0.574754\pi$
$797$	14.1467	−	46.6356i	0.501103	−	1.65192i	0.733799	−	0.679367i	$-0.237746\pi$
$798$	−23.0302	+	4.03248i	−0.815259	+	0.142748i
$799$	35.1367	+	35.1367i	1.24305	+	1.24305i
$800$	−2.75045	+	4.94318i	−0.0972431	+	0.174768i
$801$	4.43298	−	4.43298i	0.156632	−	0.156632i
$802$	6.14345	−	8.75149i	0.216933	−	0.309026i
$803$	−8.85155	−	2.68509i	−0.312365	−	0.0947547i
$804$	20.7000	−	12.4935i	0.730032	−	0.440612i
$805$	19.6184	+	1.93225i	0.691459	+	0.0681028i
$806$	−0.153336	−	0.195862i	−0.00540102	−	0.00689894i
$807$	4.74986	+	0.944806i	0.167203	+	0.0332588i
$808$	27.2668	−	0.794837i	0.959241	−	0.0279623i
$809$	8.29363	+	41.6949i	0.291588	+	1.46591i	0.797495	+	0.603326i	$0.206158\pi$
$809$	8.29363	+	41.6949i	0.291588	+	1.46591i	−0.505907	+	0.862588i	$0.668842\pi$
$810$	−0.659500	−	8.75763i	−0.0231725	−	0.307712i
$811$	15.5586	+	8.31626i	0.546337	+	0.292023i	0.721382	−	0.692537i	$-0.243507\pi$
$811$	15.5586	+	8.31626i	0.546337	+	0.292023i	−0.175045	+	0.984560i	$0.556007\pi$
$812$	10.1908	+	1.47974i	0.357626	+	0.0519288i
$813$	16.6312	−	1.63803i	0.583282	−	0.0574483i
$814$	−0.378688	+	0.361650i	−0.0132730	+	0.0126758i
$815$	−0.266033	−	0.642262i	−0.00931875	−	0.0224974i
$816$	36.3395	−	0.222810i	1.27214	−	0.00779992i
$817$	−1.80068	+	4.34723i	−0.0629978	+	0.152090i
$818$	−12.2402	−	31.5872i	−0.427968	−	1.10442i
$819$	−0.0957896	+	0.116720i	−0.00334716	+	0.00407852i
$820$	7.02982	+	14.7462i	0.245492	+	0.514958i
$821$	−12.8717	−	42.4324i	−0.449226	−	1.48090i	−0.830805	−	0.556563i	$-0.812120\pi$
$821$	−12.8717	−	42.4324i	−0.449226	−	1.48090i	0.381579	−	0.924336i	$-0.375380\pi$
$822$	−14.6794	−	29.0520i	−0.512004	−	1.01331i
$823$	−6.86007	−	4.58375i	−0.239127	−	0.159780i	0.430233	−	0.902718i	$-0.358431\pi$
$823$	−6.86007	−	4.58375i	−0.239127	−	0.159780i	−0.669360	+	0.742938i	$0.733431\pi$
$824$	20.4534	+	1.41420i	0.712527	+	0.0492659i
$825$	1.83148	+	2.74101i	0.0637641	+	0.0954297i
$826$	6.71987	+	24.1385i	0.233814	+	0.839885i
$827$	−26.9340	+	22.1041i	−0.936586	+	0.768636i	−0.973025	−	0.230700i	$-0.925898\pi$
$827$	−26.9340	+	22.1041i	−0.936586	+	0.768636i	0.0364394	+	0.999336i	$0.488398\pi$
$828$	5.98328	+	6.56100i	0.207933	+	0.228011i
$829$	19.1166	+	35.7647i	0.663949	+	1.24216i	0.958109	+	0.286404i	$0.0924600\pi$
$829$	19.1166	+	35.7647i	0.663949	+	1.24216i	−0.294160	+	0.955756i	$0.595040\pi$
$830$	−20.7383	−	4.62357i	−0.719838	−	0.160486i
$831$		−	37.3635i		−	1.29613i
$832$	−0.445044	−	0.205503i	−0.0154291	−	0.00712454i
$833$		−	23.8457i		−	0.826205i
$834$	5.71239	−	25.6221i	0.197804	−	0.887220i
$835$	−8.70916	−	16.2937i	−0.301393	−	0.563867i
$836$	14.5976	+	0.672284i	0.504870	+	0.0232514i
$837$	12.4786	−	10.2409i	0.431322	−	0.353977i
$838$	34.3644	−	9.56664i	1.18710	−	0.330474i
$839$	6.72881	+	10.0704i	0.232304	+	0.347668i	0.929247	−	0.369459i	$-0.120457\pi$
$839$	6.72881	+	10.0704i	0.232304	+	0.347668i	−0.696943	+	0.717127i	$0.745457\pi$
$840$	−4.46835	−	13.3199i	−0.154173	−	0.459582i
$841$	22.0980	+	14.7654i	0.762001	+	0.509153i
$842$	−2.94333	+	1.48721i	−0.101434	+	0.0512526i
$843$	−3.28197	−	10.8192i	−0.113037	−	0.372633i
$844$	4.31841	−	12.1868i	0.148646	−	0.419487i
$845$	8.24473	−	10.0462i	0.283627	−	0.345601i
$846$	8.06862	−	3.12663i	0.277405	−	0.107496i
$847$	−7.82387	+	18.8885i	−0.268831	+	0.649017i
$848$	18.7084	−	28.3742i	0.642449	−	0.974373i
$849$	−4.16585	−	10.0573i	−0.142972	−	0.345164i
$850$	−5.90914	−	6.18754i	−0.202682	−	0.212231i
$851$	−1.00035	+	0.0985262i	−0.0342917	+	0.00337744i
$852$	1.57779	−	1.17768i	0.0540542	−	0.0403468i
$853$	27.3597	+	14.6241i	0.936780	+	0.500719i	0.867808	−	0.496899i	$-0.165528\pi$
$853$	27.3597	+	14.6241i	0.936780	+	0.500719i	0.0689716	+	0.997619i	$0.478028\pi$
$854$	−48.1159	+	3.62340i	−1.64649	+	0.123990i
$855$	0.483726	+	2.43185i	0.0165431	+	0.0831676i
$856$	−41.5091	−	15.7929i	−1.41875	−	0.539791i
$857$	−33.8088	−	6.72498i	−1.15489	−	0.229721i	−0.419749	−	0.907640i	$-0.637882\pi$
$857$	−33.8088	−	6.72498i	−1.15489	−	0.229721i	−0.735136	+	0.677919i	$0.762882\pi$
$858$	−0.224936	+	0.176097i	−0.00767919	+	0.00601186i
$859$	−6.23672	−	0.614263i	−0.212794	−	0.0209584i	−0.00894167	−	0.999960i	$-0.502846\pi$
$859$	−6.23672	−	0.614263i	−0.212794	−	0.0209584i	−0.203852	+	0.979002i	$0.565346\pi$
$860$	−2.74485	−	0.678614i	−0.0935987	−	0.0231405i
$861$	−38.8255	−	11.7776i	−1.32317	−	0.401379i
$862$	39.4098	+	27.6653i	1.34230	+	0.942283i
$863$	−21.9383	+	21.9383i	−0.746788	+	0.746788i	−0.973875	−	0.227087i	$-0.927080\pi$
$863$	−21.9383	+	21.9383i	−0.746788	+	0.746788i	0.227087	+	0.973875i	$0.427080\pi$
$864$	12.6685	−	29.1814i	0.430992	−	0.992770i
$865$	−13.3694	−	13.3694i	−0.454572	−	0.454572i
$866$	2.58294	+	14.7516i	0.0877719	+	0.501279i
$867$	−8.54468	+	28.1680i	−0.290193	+	0.956637i
$868$	11.2655	−	15.2874i	0.382375	−	0.518890i
$869$	−2.90120	+	29.4564i	−0.0984165	+	0.999239i
$870$	−0.399621	+	3.28144i	−0.0135484	+	0.111251i
$871$	0.0962351	−	0.483806i	0.00326080	−	0.0163932i
$872$	−27.1280	+	6.22297i	−0.918670	+	0.210736i
$873$	−11.9066	+	2.36836i	−0.402976	+	0.0801569i
$874$	21.2692	+	18.2902i	0.719442	+	0.618674i
$875$	−1.55928	+	2.91721i	−0.0527133	+	0.0986197i
$876$	−6.47253	+	10.8742i	−0.218686	+	0.367406i
$877$	−1.20168	−	12.2009i	−0.0405779	−	0.411994i	−0.993920	−	0.110103i	$-0.964882\pi$
$877$	−1.20168	−	12.2009i	−0.0405779	−	0.411994i	0.953342	−	0.301892i	$-0.0976180\pi$
$878$	29.3878	+	0.676359i	0.991791	+	0.0228260i
$879$	−33.7637	+	13.9854i	−1.13882	+	0.471715i
$880$	0.914260	+	8.73335i	0.0308197	+	0.294401i
$881$	44.5306	+	18.4452i	1.50027	+	0.621434i	0.973524	−	0.228586i	$-0.0734101\pi$
$881$	44.5306	+	18.4452i	1.50027	+	0.621434i	0.526751	+	0.850020i	$0.323410\pi$
$882$	−3.79886	−	1.67696i	−0.127914	−	0.0564660i
$883$	26.9431	+	22.1117i	0.906708	+	0.744116i	0.967190	−	0.254053i	$-0.0817638\pi$
$883$	26.9431	+	22.1117i	0.906708	+	0.744116i	−0.0604820	+	0.998169i	$0.519264\pi$
$884$	0.496221	−	0.550880i	0.0166897	−	0.0185281i
$885$	−7.69709	+	2.33489i	−0.258735	+	0.0784864i
$886$	−15.2713	+	46.4658i	−0.513049	+	1.56105i
$887$	−7.74323	+	11.5886i	−0.259992	+	0.389106i	−0.938384	−	0.345595i	$-0.887677\pi$
$887$	−7.74323	+	11.5886i	−0.259992	+	0.389106i	0.678392	+	0.734700i	$0.262677\pi$
$888$	0.355969	+	0.621690i	0.0119455	+	0.0208625i
$889$	2.37401	−	1.58626i	0.0796217	−	0.0532015i
$890$	10.3640	+	5.85016i	0.347401	+	0.196098i
$891$	−8.64860	−	10.5384i	−0.289739	−	0.353048i
$892$	12.7212	+	35.2127i	0.425937	+	1.17901i
$893$	24.1090	−	12.8865i	0.806778	−	0.431232i
$894$	−7.60667	−	11.9716i	−0.254405	−	0.400390i
$895$	−4.29776			−0.143658
$896$	6.00198	−	36.9389i	0.200512	−	1.23404i
$897$	−0.548381			−0.0183099
$898$	−19.0944	−	30.0513i	−0.637188	−	1.00283i
$899$	−3.94053	+	2.10626i	−0.131424	+	0.0702475i
$900$	−1.40130	+	0.506243i	−0.0467099	+	0.0168748i
$901$	32.6106	+	39.7362i	1.08642	+	1.32380i
$902$	22.0831	+	12.4652i	0.735287	+	0.415047i
$903$	5.83892	−	3.90144i	0.194307	−	0.129832i
$904$	−5.10536	+	18.7840i	−0.169802	+	0.624747i
$905$	1.09004	−	1.63137i	0.0362343	−	0.0542285i
$906$	−5.51517	+	16.7810i	−0.183229	+	0.557510i
$907$	45.2586	−	13.7291i	1.50279	−	0.455866i	0.571639	−	0.820505i	$-0.306308\pi$
$907$	45.2586	−	13.7291i	1.50279	−	0.455866i	0.931149	+	0.364640i	$0.118808\pi$
$908$	−17.0351	−	15.3449i	−0.565331	−	0.509238i
$909$	5.55388	+	4.55795i	0.184211	+	0.151178i
$910$	−0.262227	−	0.115756i	−0.00869273	−	0.00383729i
$911$	4.05263	+	1.67866i	0.134270	+	0.0556164i	0.448807	−	0.893629i	$-0.351849\pi$
$911$	4.05263	+	1.67866i	0.134270	+	0.0556164i	−0.314537	+	0.949245i	$0.601849\pi$
$912$	5.68603	−	19.1666i	0.188283	−	0.634669i
$913$	−30.4716	+	12.6218i	−1.00846	+	0.417719i
$914$	−32.9770	−	0.758963i	−1.09078	−	0.0251043i
$915$	−1.51824	−	15.4150i	−0.0501916	−	0.509604i
$916$	−19.0169	−	11.3192i	−0.628336	−	0.373996i
$917$	−30.2725	+	56.6359i	−0.999686	+	1.87028i
$918$	36.4821	+	31.3723i	1.20409	+	1.03544i
$919$	−49.9941	+	9.94445i	−1.64915	+	0.328037i	−0.930209	−	0.367029i	$-0.880375\pi$
$919$	−49.9941	+	9.94445i	−1.64915	+	0.328037i	−0.718945	+	0.695067i	$0.755375\pi$
$920$	−8.95261	+	14.2826i	−0.295159	+	0.470883i
$921$	5.88807	−	29.6013i	0.194019	−	0.975398i
$922$	−5.26951	+	43.2699i	−0.173542	+	1.42502i
$923$	0.00393724	−	0.0399754i	0.000129596	−	0.00131581i
$924$	−17.5567	−	12.9377i	−0.577575	−	0.425620i
$925$	0.0489611	−	0.161403i	0.00160983	−	0.00530690i
$926$	−4.43441	−	25.3256i	−0.145724	−	0.832252i
$927$	3.81838	+	3.81838i	0.125412	+	0.125412i
$928$	−5.01485	+	7.23773i	−0.164620	+	0.237590i
$929$	19.0466	−	19.0466i	0.624899	−	0.624899i	−0.321881	−	0.946780i	$-0.604315\pi$
$929$	19.0466	−	19.0466i	0.624899	−	0.624899i	0.946780	+	0.321881i	$0.104315\pi$
$930$	4.98939	+	3.50249i	0.163608	+	0.114851i
$931$	−12.5536	−	3.80810i	−0.411428	−	0.124805i
$932$	−5.32302	+	21.5305i	−0.174361	+	0.705255i
$933$	24.6500	+	2.42781i	0.807003	+	0.0794829i
$934$	44.3208	−	34.6978i	1.45022	−	1.13535i
$935$	−13.0261	−	2.59104i	−0.425998	−	0.0847362i
$936$	−0.0528637	−	0.117794i	−0.00172791	−	0.00385020i
$937$	−9.50600	−	47.7899i	−0.310548	−	1.56123i	−0.749060	−	0.662503i	$-0.769494\pi$
$937$	−9.50600	−	47.7899i	−0.310548	−	1.56123i	0.438512	−	0.898725i	$-0.355506\pi$
$938$	37.5525	−	2.82792i	1.22613	−	0.0923350i
$939$	45.2590	+	24.1914i	1.47697	+	0.789458i
$940$	9.82588	+	13.1641i	0.320485	+	0.429366i
$941$	−43.8772	+	4.32153i	−1.43036	+	0.140878i	−0.783338	−	0.621596i	$-0.786485\pi$
$941$	−43.8772	+	4.32153i	−1.43036	+	0.140878i	−0.647019	+	0.762474i	$0.723985\pi$
$942$	−26.3836	−	27.6267i	−0.859625	−	0.900125i
$943$	18.6286	+	44.9734i	0.606631	+	1.46454i
$944$	−21.0388	−	4.05094i	−0.684754	−	0.131847i
$945$	7.11872	−	17.1861i	0.231572	−	0.559065i
$946$	−4.09257	+	1.58589i	−0.133061	+	0.0515616i
$947$	−8.88346	+	10.8245i	−0.288674	+	0.351750i	−0.897074	−	0.441881i	$-0.854312\pi$
$947$	−8.88346	+	10.8245i	−0.288674	+	0.351750i	0.608400	+	0.793630i	$0.291812\pi$
$948$	38.1688	+	13.5252i	1.23967	+	0.439277i
$949$	0.0749470	+	0.247067i	0.00243288	+	0.00802014i
$950$	−4.20112	+	2.12274i	−0.136302	+	0.0688709i
$951$	39.2929	+	26.2547i	1.27416	+	0.851366i
$952$	50.6750	+	25.2163i	1.64239	+	0.817264i
$953$	0.730305	+	1.09298i	0.0236569	+	0.0354051i	0.843110	−	0.537742i	$-0.180722\pi$
$953$	0.730305	+	1.09298i	0.0236569	+	0.0354051i	−0.819453	+	0.573147i	$0.805722\pi$
$954$	8.62371	−	2.40074i	0.279203	−	0.0777268i
$955$	1.73649	−	1.42510i	0.0561916	−	0.0461153i
$956$	1.18657	−	25.7645i	0.0383763	−	0.833284i
$957$	2.41891	+	4.52547i	0.0781923	+	0.146288i
$958$	10.0531	−	45.0919i	0.324802	−	1.45685i
$959$		−	50.6989i		−	1.63715i
$960$	11.8991	+	1.65337i	0.384041	+	0.0533623i
$961$		−	22.7603i		−	0.734204i
$962$	0.0142657	+	0.00318050i	0.000459943	+	0.000102543i
$963$	−5.51416	−	10.3163i	−0.177691	−	0.332437i
$964$	5.27514	−	4.81065i	0.169901	−	0.154941i
$965$	15.1653	−	12.4458i	0.488188	−	0.400645i
$966$	−11.2278	−	40.3314i	−0.361248	−	1.29764i
$967$	−27.9841	−	41.8812i	−0.899908	−	1.34681i	−0.937672	−	0.347521i	$-0.887024\pi$
$967$	−27.9841	−	41.8812i	−0.899908	−	1.34681i	0.0377643	−	0.999287i	$-0.487976\pi$
$968$	−11.4795	−	13.1848i	−0.368964	−	0.423776i
$969$	25.1419	+	16.7993i	0.807675	+	0.539671i
$970$	−10.3931	−	20.5690i	−0.333703	−	0.660432i
$971$	−1.08557	−	3.57865i	−0.0348376	−	0.114844i	0.937797	−	0.347184i	$-0.112862\pi$
$971$	−1.08557	−	3.57865i	−0.0348376	−	0.114844i	−0.972635	+	0.232339i	$0.925362\pi$
$972$	13.6225	−	6.49412i	0.436941	−	0.208299i
$973$	25.9390	−	31.6068i	0.831567	−	1.01327i
$974$	4.70254	+	12.1354i	0.150679	+	0.388845i
$975$	0.0352127	−	0.0850110i	0.00112771	−	0.00272253i
$976$	15.5553	−	38.2148i	0.497913	−	1.22323i
$977$	17.9514	+	43.3385i	0.574316	+	1.38652i	0.897849	+	0.440305i	$0.145130\pi$
$977$	17.9514	+	43.3385i	0.574316	+	1.38652i	−0.323532	+	0.946217i	$0.604870\pi$
$978$	−1.06768	+	1.01964i	−0.0341405	+	0.0326044i
$979$	18.3850	−	1.81077i	0.587588	−	0.0578723i
$980$	1.13276	−	7.80115i	0.0361847	−	0.249199i
$981$	−6.46513	−	3.45568i	−0.206416	−	0.110331i
$982$	−3.76483	−	49.9939i	−0.120141	−	1.59537i
$983$	11.1207	+	55.9076i	0.354696	+	1.78318i	0.586018	+	0.810298i	$0.300695\pi$
$983$	11.1207	+	55.9076i	0.354696	+	1.78318i	−0.231322	+	0.972877i	$0.574305\pi$
$984$	23.8063	−	25.2359i	0.758917	−	0.804491i
$985$	−1.07825	−	0.214477i	−0.0343558	−	0.00683380i
$986$	−8.20967	−	10.4865i	−0.261449	−	0.333960i
$987$	−40.6016	−	3.99890i	−1.29236	−	0.127287i
$988$	−0.210767	−	0.349211i	−0.00670538	−	0.0111099i
$989$	−8.06268	−	2.44579i	−0.256378	−	0.0777715i
$990$	−1.32884	+	1.89296i	−0.0422333	+	0.0601623i
$991$	−26.0576	+	26.0576i	−0.827747	+	0.827747i	−0.987205	−	0.159457i	$-0.949026\pi$
$991$	−26.0576	+	26.0576i	−0.827747	+	0.827747i	0.159457	+	0.987205i	$0.449026\pi$
$992$	7.41169	+	14.4477i	0.235321	+	0.458715i
$993$	−12.7269	−	12.7269i	−0.403877	−	0.403877i
$994$	3.02066	−	0.528905i	0.0958095	−	0.0167758i
$995$	5.43378	−	17.9128i	0.172263	−	0.567873i
$996$	6.75773	+	44.6142i	0.214127	+	1.41365i
$997$	2.88976	−	29.3403i	0.0915197	−	0.929215i	−0.834315	−	0.551287i	$-0.814137\pi$
$997$	2.88976	−	29.3403i	0.0915197	−	0.929215i	0.925835	−	0.377928i	$-0.123363\pi$
$998$	−26.4887	−	3.22586i	−0.838485	−	0.102113i
$999$	−0.185049	+	0.930306i	−0.00585470	+	0.0294336i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.101.12	✓	1024
128.109	even	32	inner	640.2.bm.a.621.12	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.101.12	✓	1024	1.1	even	1	trivial
640.2.bm.a.621.12	yes	1024	128.109	even	32	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19364 + 0.758431i) q^{2} +(-1.32436 + 0.707885i) q^{3} +(0.849564 - 1.81059i) q^{4} +(0.634393 + 0.773010i) q^{5} +(1.04393 - 1.84940i) q^{6} +(2.75033 - 1.83771i) q^{7} +(0.359135 + 2.80553i) q^{8} +(-0.413883 + 0.619419i) q^{9} +(-1.34351 - 0.441554i) q^{10} +(-2.10074 + 0.637253i) q^{11} +(0.156563 + 2.99927i) q^{12} +(0.0473662 + 0.0388724i) q^{13} +(-1.88913 + 4.27950i) q^{14} +(-1.38737 - 0.574667i) q^{15} +(-2.55648 - 3.07643i) q^{16} +(5.58942 - 2.31521i) q^{17} +(0.0242409 - 1.05327i) q^{18} +(-0.326232 - 3.31229i) q^{19} +(1.93856 - 0.491906i) q^{20} +(-2.34154 + 4.38071i) q^{21} +(2.02422 - 2.35392i) q^{22} +(5.84516 - 1.16268i) q^{23} +(-2.46162 - 3.46131i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(-0.0860204 - 0.0104758i) q^{26} +(0.551222 - 5.59665i) q^{27} +(-0.990764 - 6.54097i) q^{28} +(-0.451849 + 1.48955i) q^{29} +(2.09187 - 0.366277i) q^{30} +(2.02974 + 2.02974i) q^{31} +(5.38478 + 1.73323i) q^{32} +(2.33104 - 2.33104i) q^{33} +(-4.91583 + 7.00272i) q^{34} +(3.16536 + 0.960201i) q^{35} +(0.769896 + 1.27561i) q^{36} +(-0.167854 - 0.0165321i) q^{37} +(2.90155 + 3.70627i) q^{38} +(-0.0902471 - 0.0179513i) q^{39} +(-1.94087 + 2.05743i) q^{40} +(1.59351 + 8.01110i) q^{41} +(-0.527509 - 7.00489i) q^{42} +(-1.24681 - 0.666436i) q^{43} +(-0.630909 + 4.34497i) q^{44} +(-0.741382 + 0.0730198i) q^{45} +(-6.09522 + 5.82097i) q^{46} +(3.14315 + 7.58822i) q^{47} +(5.56346 + 2.26460i) q^{48} +(1.50834 - 3.64145i) q^{49} +(-0.510990 - 1.31867i) q^{50} +(-5.76350 + 7.02284i) q^{51} +(0.110623 - 0.0527363i) q^{52} +(2.46646 + 8.13082i) q^{53} +(3.58671 + 7.09846i) q^{54} +(-1.82530 - 1.21963i) q^{55} +(6.14350 + 7.05615i) q^{56} +(2.77677 + 4.15573i) q^{57} +(-0.590373 - 2.12068i) q^{58} +(4.14048 - 3.39801i) q^{59} +(-2.21914 + 2.02374i) q^{60} +(4.86239 + 9.09689i) q^{61} +(-3.96220 - 0.883364i) q^{62} +2.46420i q^{63} +(-7.74204 + 2.01513i) q^{64} +0.0612750i q^{65} +(-1.01449 + 4.55035i) q^{66} +(-3.79490 - 7.09977i) q^{67} +(0.556661 - 12.0871i) q^{68} +(-6.91806 + 5.67750i) q^{69} +(-4.50655 + 1.25457i) q^{70} +(-0.364204 - 0.545070i) q^{71} +(-1.88644 - 0.938707i) q^{72} +(3.50343 + 2.34092i) q^{73} +(0.212896 - 0.107572i) q^{74} +(-0.435914 - 1.43701i) q^{75} +(-6.27436 - 2.22333i) q^{76} +(-4.60664 + 5.61321i) q^{77} +(0.121338 - 0.0470189i) q^{78} +(5.15974 - 12.4567i) q^{79} +(0.756293 - 3.92785i) q^{80} +(2.37651 + 5.73740i) q^{81} +(-7.97794 - 8.35382i) q^{82} +(14.9519 - 1.47263i) q^{83} +(5.94238 + 7.96125i) q^{84} +(5.33557 + 2.85192i) q^{85} +(1.99370 - 0.150137i) q^{86} +(-0.456017 - 2.29255i) q^{87} +(-2.54228 - 5.66484i) q^{88} +(-8.25366 - 1.64175i) q^{89} +(0.829564 - 0.649447i) q^{90} +(0.201709 + 0.0198666i) q^{91} +(2.86071 - 11.5710i) q^{92} +(-4.12492 - 1.25128i) q^{93} +(-9.50694 - 6.67376i) q^{94} +(2.35348 - 2.35348i) q^{95} +(-8.35832 + 1.51638i) q^{96} +(11.5228 + 11.5228i) q^{97} +(0.961375 + 5.49056i) q^{98} +(0.474734 - 1.56499i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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