LMFDB - Embedded newform 168.4.t.a.19.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [168,4,Mod(19,168)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(168, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 0, 5])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("168.19"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	168.t (of order $6$, degree $2$, 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:	$9.91232088096$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.3
Character	$\chi$	$=$	168.19
Dual form			168.4.t.a.115.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.80302 + 0.378234i) q^{2} +(2.59808 - 1.50000i) q^{3} +(7.71388 - 2.12040i) q^{4} +(-7.30307 + 12.6493i) q^{5} +(-6.71512 + 5.18721i) q^{6} +(-0.782311 + 18.5037i) q^{7} +(-20.8202 + 8.86116i) q^{8} +(4.50000 - 7.79423i) q^{9} +(15.6863 - 38.2185i) q^{10} +(-29.8704 - 51.7370i) q^{11} +(16.8607 - 17.0798i) q^{12} -3.68912 q^{13} +(-4.80590 - 52.1623i) q^{14} +43.8184i q^{15} +(55.0078 - 32.7129i) q^{16} +(-29.8369 + 17.2263i) q^{17} +(-9.66557 + 23.5495i) q^{18} +(1.17719 + 0.679649i) q^{19} +(-29.5135 + 113.061i) q^{20} +(25.7231 + 49.2476i) q^{21} +(103.296 + 133.722i) q^{22} +(-152.250 - 87.9014i) q^{23} +(-40.8007 + 54.2522i) q^{24} +(-44.1698 - 76.5043i) q^{25} +(10.3407 - 1.39535i) q^{26} -27.0000i q^{27} +(33.2006 + 144.394i) q^{28} +2.05927i q^{29} +(-16.5736 - 122.824i) q^{30} +(-53.5006 - 92.6658i) q^{31} +(-141.815 + 112.501i) q^{32} +(-155.211 - 89.6112i) q^{33} +(77.1180 - 59.5712i) q^{34} +(-228.346 - 145.030i) q^{35} +(18.1856 - 69.6655i) q^{36} +(-237.518 - 137.131i) q^{37} +(-3.55675 - 1.45982i) q^{38} +(-9.58462 + 5.53369i) q^{39} +(39.9638 - 328.074i) q^{40} +316.949i q^{41} +(-90.7295 - 128.313i) q^{42} -187.107 q^{43} +(-340.120 - 335.756i) q^{44} +(65.7277 + 113.844i) q^{45} +(460.007 + 188.804i) q^{46} +(-174.173 + 301.677i) q^{47} +(93.8452 - 167.502i) q^{48} +(-341.776 - 28.9513i) q^{49} +(152.745 + 197.737i) q^{50} +(-51.6790 + 89.5107i) q^{51} +(-28.4575 + 7.82240i) q^{52} +(-260.246 + 150.253i) q^{53} +(10.2123 + 75.6816i) q^{54} +872.583 q^{55} +(-147.677 - 392.183i) q^{56} +4.07790 q^{57} +(-0.778887 - 5.77219i) q^{58} +(711.540 - 410.808i) q^{59} +(92.9124 + 338.010i) q^{60} +(67.3551 - 116.662i) q^{61} +(185.013 + 239.509i) q^{62} +(140.702 + 89.3643i) q^{63} +(354.960 - 368.982i) q^{64} +(26.9419 - 46.6648i) q^{65} +(468.954 + 192.476i) q^{66} +(53.6072 + 92.8504i) q^{67} +(-193.632 + 196.148i) q^{68} -527.409 q^{69} +(694.914 + 320.154i) q^{70} +451.011i q^{71} +(-24.6249 + 202.152i) q^{72} +(-394.990 + 228.048i) q^{73} +(717.637 + 294.545i) q^{74} +(-229.513 - 132.509i) q^{75} +(10.5218 + 2.74663i) q^{76} +(980.696 - 512.239i) q^{77} +(24.7729 - 19.1363i) q^{78} +(1038.98 + 599.857i) q^{79} +(12.0692 + 934.716i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-119.881 - 888.415i) q^{82} +543.746i q^{83} +(302.849 + 325.347i) q^{84} -503.221i q^{85} +(524.466 - 70.7702i) q^{86} +(3.08891 + 5.35015i) q^{87} +(1080.36 + 812.488i) q^{88} +(-1088.45 - 628.419i) q^{89} +(-227.296 - 294.246i) q^{90} +(2.88604 - 68.2625i) q^{91} +(-1360.82 - 355.231i) q^{92} +(-277.997 - 160.502i) q^{93} +(374.108 - 911.486i) q^{94} +(-17.1942 + 9.92706i) q^{95} +(-199.695 + 505.009i) q^{96} +1031.36i q^{97} +(968.956 - 48.1199i) q^{98} -537.667 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 2 q^{2} - 10 q^{4} - 16 q^{8} + 432 q^{9} + 18 q^{10} + 40 q^{11} + 274 q^{14} - 26 q^{16} - 18 q^{18} + 4 q^{22} + 270 q^{24} - 1200 q^{25} + 750 q^{26} + 922 q^{28} + 168 q^{30} - 108 q^{32} + 456 q^{35}+ \cdots + 720 q^{99}+O(q^{100}) $ 96 * q + 2 * q^2 - 10 * q^4 - 16 * q^8 + 432 * q^9 + 18 * q^10 + 40 * q^11 + 274 * q^14 - 26 * q^16 - 18 * q^18 + 4 * q^22 + 270 * q^24 - 1200 * q^25 + 750 * q^26 + 922 * q^28 + 168 * q^30 - 108 * q^32 + 456 * q^35 - 180 * q^36 - 1494 * q^38 + 1170 * q^40 - 564 * q^42 - 1616 * q^43 + 264 * q^44 + 808 * q^46 - 360 * q^49 - 1036 * q^50 - 3564 * q^52 + 176 * q^56 - 336 * q^57 - 394 * q^58 + 4128 * q^59 + 822 * q^60 - 2644 * q^64 + 2052 * q^66 - 1440 * q^67 - 1392 * q^68 + 3234 * q^70 - 72 * q^72 - 648 * q^73 + 850 * q^74 + 1692 * q^78 - 1548 * q^80 - 3888 * q^81 + 4596 * q^82 + 3120 * q^84 - 2522 * q^86 - 1454 * q^88 - 104 * q^91 + 5600 * q^92 - 2052 * q^94 + 3870 * q^96 + 852 * q^98 + 720 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$-1$

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 $

$2$	−2.80302	+	0.378234i	−0.991018	+	0.133726i
$2$	−2.80302	+	0.378234i	−0.991018	+	0.133726i
$3$	2.59808	−	1.50000i	0.500000	−	0.288675i
$3$	2.59808	−	1.50000i	0.500000	−	0.288675i
$4$	7.71388	−	2.12040i	0.964235	−	0.265049i
$5$	−7.30307	+	12.6493i	−0.653207	+	1.13139i	0.329133	+	0.944283i	$0.393243\pi$
$5$	−7.30307	+	12.6493i	−0.653207	+	1.13139i	−0.982340	+	0.187104i	$0.940090\pi$
$6$	−6.71512	+	5.18721i	−0.456906	+	0.352945i
$7$	−0.782311	+	18.5037i	−0.0422408	+	0.999107i
$7$	−0.782311	+	18.5037i	−0.0422408	+	0.999107i
$8$	−20.8202	+	8.86116i	−0.920131	+	0.391612i
$9$	4.50000	−	7.79423i	0.166667	−	0.288675i
$10$	15.6863	−	38.2185i	0.496044	−	1.20858i
$11$	−29.8704	−	51.7370i	−0.818751	−	1.41812i	−0.906603	−	0.421985i	$-0.861333\pi$
$11$	−29.8704	−	51.7370i	−0.818751	−	1.41812i	0.0878515	−	0.996134i	$-0.472000\pi$
$12$	16.8607	−	17.0798i	0.405604	−	0.410875i
$13$	−3.68912			−0.0787061			−0.0393530	−	0.999225i	$-0.512530\pi$
$13$	−3.68912			−0.0787061			−0.0393530	+	0.999225i	$0.512530\pi$
$14$	−4.80590	−	52.1623i	−0.0917450	−	0.995783i
$15$			43.8184i			0.754258i
$16$	55.0078	−	32.7129i	0.859498	−	0.511140i
$17$	−29.8369	+	17.2263i	−0.425677	+	0.245765i	−0.697503	−	0.716582i	$-0.745706\pi$
$17$	−29.8369	+	17.2263i	−0.425677	+	0.245765i	0.271826	+	0.962346i	$0.412372\pi$
$18$	−9.66557	+	23.5495i	−0.126566	+	0.308370i
$19$	1.17719	+	0.679649i	0.0142140	+	0.00820643i	0.507090	−	0.861893i	$-0.330721\pi$
$19$	1.17719	+	0.679649i	0.0142140	+	0.00820643i	−0.492876	+	0.870099i	$0.664054\pi$
$20$	−29.5135	+	113.061i	−0.329971	+	1.26406i
$21$	25.7231	+	49.2476i	0.267297	+	0.511748i
$22$	103.296	+	133.722i	1.00104	+	1.29589i
$23$	−152.250	−	87.9014i	−1.38027	−	0.796901i	−0.388081	−	0.921625i	$-0.626862\pi$
$23$	−152.250	−	87.9014i	−1.38027	−	0.796901i	−0.992191	+	0.124725i	$0.960195\pi$
$24$	−40.8007	+	54.2522i	−0.347017	+	0.461425i
$25$	−44.1698	−	76.5043i	−0.353358	−	0.612034i
$26$	10.3407	−	1.39535i	0.0779992	−	0.0105250i
$27$		−	27.0000i		−	0.192450i
$28$	33.2006	+	144.394i	0.224083	+	0.974570i
$29$			2.05927i			0.0131861i	0.999978	+	0.00659306i	$0.00209865\pi$
$29$			2.05927i			0.0131861i	−0.999978	+	0.00659306i	$0.997901\pi$
$30$	−16.5736	−	122.824i	−0.100864	−	0.747484i
$31$	−53.5006	−	92.6658i	−0.309968	−	0.536880i	0.668387	−	0.743813i	$-0.266985\pi$
$31$	−53.5006	−	92.6658i	−0.309968	−	0.536880i	−0.978355	+	0.206934i	$0.933652\pi$
$32$	−141.815	+	112.501i	−0.783425	+	0.621486i
$33$	−155.211	−	89.6112i	−0.818751	−	0.472706i
$34$	77.1180	−	59.5712i	0.388989	−	0.300482i
$35$	−228.346	−	145.030i	−1.10279	−	0.700414i
$36$	18.1856	−	69.6655i	0.0841926	−	0.322526i
$37$	−237.518	−	137.131i	−1.05534	−	0.609303i	−0.131204	−	0.991355i	$-0.541884\pi$
$37$	−237.518	−	137.131i	−1.05534	−	0.609303i	−0.924141	+	0.382052i	$0.875218\pi$
$38$	−3.55675	−	1.45982i	−0.0151837	−	0.00623195i
$39$	−9.58462	+	5.53369i	−0.0393530	+	0.0227205i
$40$	39.9638	−	328.074i	0.157971	−	1.29683i
$41$			316.949i			1.20729i	0.797252	+	0.603647i	$0.206286\pi$
$41$			316.949i			1.20729i	−0.797252	+	0.603647i	$0.793714\pi$
$42$	−90.7295	−	128.313i	−0.333330	−	0.471407i
$43$	−187.107			−0.663572			−0.331786	−	0.943355i	$-0.607651\pi$
$43$	−187.107			−0.663572			−0.331786	+	0.943355i	$0.607651\pi$
$44$	−340.120	−	335.756i	−1.16534	−	1.15039i
$45$	65.7277	+	113.844i	0.217736	+	0.377129i
$46$	460.007	+	188.804i	1.47444	+	0.605165i
$47$	−174.173	+	301.677i	−0.540549	+	0.936258i	0.458324	+	0.888785i	$0.348450\pi$
$47$	−174.173	+	301.677i	−0.540549	+	0.936258i	−0.998873	+	0.0474729i	$0.984883\pi$
$48$	93.8452	−	167.502i	0.282196	−	0.503685i
$49$	−341.776	−	28.9513i	−0.996431	−	0.0844062i
$50$	152.745	+	197.737i	0.432029	+	0.559284i
$51$	−51.6790	+	89.5107i	−0.141892	+	0.245765i
$52$	−28.4575	+	7.82240i	−0.0758911	+	0.0208610i
$53$	−260.246	+	150.253i	−0.674482	+	0.389412i	−0.797773	−	0.602958i	$-0.793989\pi$
$53$	−260.246	+	150.253i	−0.674482	+	0.389412i	0.123291	+	0.992371i	$0.460655\pi$
$54$	10.2123	+	75.6816i	0.0257355	+	0.190722i
$55$	872.583			2.13926
$56$	−147.677	−	392.183i	−0.352395	−	0.935851i
$57$	4.07790			0.00947597
$58$	−0.778887	−	5.77219i	−0.00176332	−	0.0130677i
$59$	711.540	−	410.808i	1.57008	−	0.906485i	0.573921	−	0.818911i	$-0.305422\pi$
$59$	711.540	−	410.808i	1.57008	−	0.906485i	0.996158	−	0.0875743i	$-0.0279115\pi$
$60$	92.9124	+	338.010i	0.199916	+	0.727282i
$61$	67.3551	−	116.662i	0.141376	−	0.244870i	−0.786639	−	0.617413i	$-0.788181\pi$
$61$	67.3551	−	116.662i	0.141376	−	0.244870i	0.928015	+	0.372543i	$0.121514\pi$
$62$	185.013	+	239.509i	0.378978	+	0.490607i
$63$	140.702	+	89.3643i	0.281377	+	0.178712i
$64$	354.960	−	368.982i	0.693280	−	0.720668i
$65$	26.9419	−	46.6648i	0.0514113	−	0.0890470i
$66$	468.954	+	192.476i	0.874611	+	0.358972i
$67$	53.6072	+	92.8504i	0.0977487	+	0.169306i	0.910752	−	0.412953i	$-0.135503\pi$
$67$	53.6072	+	92.8504i	0.0977487	+	0.169306i	−0.813004	+	0.582258i	$0.802169\pi$
$68$	−193.632	+	196.148i	−0.345313	+	0.349801i
$69$	−527.409			−0.920182
$70$	694.914	+	320.154i	1.18654	+	0.546653i
$71$			451.011i			0.753875i	0.926239	+	0.376938i	$0.123023\pi$
$71$			451.011i			0.753875i	−0.926239	+	0.376938i	$0.876977\pi$
$72$	−24.6249	+	202.152i	−0.0403065	+	0.330887i
$73$	−394.990	+	228.048i	−0.633289	+	0.365629i	−0.782025	−	0.623248i	$-0.785813\pi$
$73$	−394.990	+	228.048i	−0.633289	+	0.365629i	0.148736	+	0.988877i	$0.452480\pi$
$74$	717.637	+	294.545i	1.12735	+	0.462704i
$75$	−229.513	−	132.509i	−0.353358	−	0.204011i
$76$	10.5218	+	2.74663i	0.0158807	+	0.00414553i
$77$	980.696	−	512.239i	1.45144	−	0.758118i
$78$	24.7729	−	19.1363i	0.0359613	−	0.0277789i
$79$	1038.98	+	599.857i	1.47968	+	0.854294i	0.999735	−	0.0230042i	$-0.00732311\pi$
$79$	1038.98	+	599.857i	1.47968	+	0.854294i	0.479945	+	0.877298i	$0.340656\pi$
$80$	12.0692	+	934.716i	0.0168673	+	1.30630i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	−119.881	−	888.415i	−0.161446	−	1.19645i
$83$			543.746i			0.719082i	0.933129	+	0.359541i	$0.117067\pi$
$83$			543.746i			0.719082i	−0.933129	+	0.359541i	$0.882933\pi$
$84$	302.849	+	325.347i	0.393376	+	0.422598i
$85$		−	503.221i		−	0.642141i
$86$	524.466	−	70.7702i	0.657612	−	0.0887366i
$87$	3.08891	+	5.35015i	0.00380651	+	0.00659306i
$88$	1080.36	+	812.488i	1.30871	+	0.984222i
$89$	−1088.45	−	628.419i	−1.29636	−	0.748453i	−0.316586	−	0.948564i	$-0.602536\pi$
$89$	−1088.45	−	628.419i	−1.29636	−	0.748453i	−0.979773	+	0.200111i	$0.935870\pi$
$90$	−227.296	−	294.246i	−0.266212	−	0.344625i
$91$	2.88604	−	68.2625i	0.00332461	−	0.0786358i
$92$	−1360.82	−	355.231i	−1.54212	−	0.402559i
$93$	−277.997	−	160.502i	−0.309968	−	0.178960i
$94$	374.108	−	911.486i	0.410492	−	1.00013i
$95$	−17.1942	+	9.92706i	−0.0185693	+	0.0107210i
$96$	−199.695	+	505.009i	−0.212305	+	0.536898i
$97$			1031.36i			1.07958i	0.841800	+	0.539790i	$0.181496\pi$
$97$			1031.36i			1.07958i	−0.841800	+	0.539790i	$0.818504\pi$
$98$	968.956	−	48.1199i	0.998769	−	0.0496005i
$99$	−537.667			−0.545834
$100$	−502.940	−	496.487i	−0.502940	−	0.496487i
$101$	−524.728	−	908.856i	−0.516954	−	0.895391i	−0.999806	−	0.0196891i	$-0.993732\pi$
$101$	−524.728	−	908.856i	−0.516954	−	0.895391i	0.482852	−	0.875702i	$-0.339601\pi$
$102$	111.002	−	270.447i	0.107753	−	0.262532i
$103$	−247.505	+	428.691i	−0.236771	+	0.410099i	−0.959786	−	0.280733i	$-0.909422\pi$
$103$	−247.505	+	428.691i	−0.236771	+	0.410099i	0.723015	+	0.690832i	$0.242756\pi$
$104$	76.8082	−	32.6899i	0.0724198	−	0.0308222i
$105$	−810.805	−	34.2796i	−0.753585	−	0.0318605i
$106$	672.645	−	519.597i	0.616350	−	0.476111i
$107$	975.400	−	1689.44i	0.881266	−	1.52640i	0.0313312	−	0.999509i	$-0.490025\pi$
$107$	975.400	−	1689.44i	0.881266	−	1.52640i	0.849935	−	0.526888i	$-0.176641\pi$
$108$	−57.2507	−	208.275i	−0.0510088	−	0.185567i
$109$	−113.918	+	65.7708i	−0.100105	+	0.0577954i	−0.549217	−	0.835680i	$-0.685074\pi$
$109$	−113.918	+	65.7708i	−0.100105	+	0.0577954i	0.449112	+	0.893476i	$0.351740\pi$
$110$	−2445.87	+	330.040i	−2.12004	+	0.286074i
$111$	−822.787			−0.703563
$112$	562.278	+	1043.44i	0.474378	+	0.880321i
$113$	1197.97			0.997303			0.498652	−	0.866803i	$-0.333829\pi$
$113$	1197.97			0.997303			0.498652	+	0.866803i	$0.333829\pi$
$114$	−11.4304	+	1.54240i	−0.00939086	+	0.00126718i
$115$	2223.78	−	1283.90i	1.80321	−	1.04108i
$116$	4.36647	+	15.8850i	0.00349497	+	0.0127145i
$117$	−16.6011	+	28.7539i	−0.0131177	+	0.0227205i
$118$	−1839.08	+	1420.63i	−1.43476	+	1.10830i
$119$	−295.410	−	565.570i	−0.227565	−	0.435679i
$120$	−388.282	−	912.308i	−0.295376	−	0.694016i
$121$	−1118.98	+	1938.13i	−0.840707	+	1.45615i
$122$	−144.672	+	352.484i	−0.107361	+	0.261577i
$123$	475.423	+	823.457i	0.348516	+	0.603647i
$124$	−609.186	−	601.370i	−0.441181	−	0.435521i
$125$	−535.468			−0.383150
$126$	−428.191	−	197.272i	−0.302748	−	0.139479i
$127$		−	1079.60i		−	0.754322i	−0.926148	−	0.377161i	$-0.876900\pi$
$127$		−	1079.60i		−	0.754322i	0.926148	−	0.377161i	$-0.123100\pi$
$128$	−855.398	+	1168.52i	−0.590682	+	0.806905i
$129$	−486.119	+	280.661i	−0.331786	+	0.191557i
$130$	−57.8687	+	140.993i	−0.0390417	+	0.0951223i
$131$	1600.22	+	923.885i	1.06726	+	0.616185i	0.927432	−	0.373991i	$-0.122011\pi$
$131$	1600.22	+	923.885i	1.06726	+	0.616185i	0.139831	+	0.990175i	$0.455344\pi$
$132$	−1387.29	−	362.141i	−0.914759	−	0.238790i
$133$	−13.4970	+	21.2507i	−0.00879952	+	0.0138546i
$134$	−185.381	−	239.986i	−0.119511	−	0.154714i
$135$	341.531	+	197.183i	0.217736	+	0.125710i
$136$	468.564	−	623.045i	0.295434	−	0.392836i
$137$	1295.60	+	2244.04i	0.807959	+	1.39943i	0.914275	+	0.405094i	$0.132761\pi$
$137$	1295.60	+	2244.04i	0.807959	+	1.39943i	−0.106316	+	0.994332i	$0.533905\pi$
$138$	1478.34	−	199.484i	0.911917	−	0.123052i
$139$		−	3020.36i		−	1.84305i	−0.388319	−	0.921525i	$-0.626944\pi$
$139$		−	3020.36i		−	1.84305i	0.388319	−	0.921525i	$-0.373056\pi$
$140$	−2068.95	−	634.559i	−1.24899	−	0.383071i
$141$			1045.04i			0.624172i
$142$	−170.587	−	1264.19i	−0.100813	−	0.747104i
$143$	110.196	+	190.864i	0.0644407	+	0.111615i
$144$	−7.43682	−	575.952i	−0.00430371	−	0.333306i
$145$	−26.0484	−	15.0390i	−0.0149186	−	0.00861327i
$146$	1020.91	−	788.621i	0.578707	−	0.447032i
$147$	−931.387	+	437.446i	−0.522582	+	0.245442i
$148$	−2122.96	−	554.181i	−1.17910	−	0.307793i
$149$	−592.829	−	342.270i	−0.325949	−	0.188187i	0.328092	−	0.944646i	$-0.393594\pi$
$149$	−592.829	−	342.270i	−0.325949	−	0.188187i	−0.654041	+	0.756459i	$0.726928\pi$
$150$	693.449	+	284.617i	0.377466	+	0.154926i
$151$	−2681.30	+	1548.05i	−1.44504	+	0.834294i	−0.998180	−	0.0603091i	$-0.980791\pi$
$151$	−2681.30	+	1548.05i	−1.44504	+	0.834294i	−0.446861	+	0.894604i	$0.647458\pi$
$152$	−30.5317	−	3.71917i	−0.0162924	−	0.00198464i
$153$			310.074i			0.163843i
$154$	−2555.17	+	1806.75i	−1.33702	+	0.945403i
$155$	1562.88			0.809892
$156$	−62.2010	+	63.0094i	−0.0319235	+	0.0323384i
$157$	−487.393	−	844.190i	−0.247759	−	0.429132i	0.715145	−	0.698977i	$-0.246361\pi$
$157$	−487.393	−	844.190i	−0.247759	−	0.429132i	−0.962904	+	0.269845i	$0.913028\pi$
$158$	−3139.18	−	1288.44i	−1.58063	−	0.648750i
$159$	−450.760	+	780.738i	−0.224827	+	0.389412i
$160$	−387.371	−	2615.46i	−0.191402	−	1.29232i
$161$	1745.61	−	2748.42i	0.854493	−	1.34538i
$162$	140.055	+	181.308i	0.0679243	+	0.0879316i
$163$	−1169.12	+	2024.97i	−0.561795	+	0.973057i	0.435545	+	0.900167i	$0.356556\pi$
$163$	−1169.12	+	2024.97i	−0.561795	+	0.973057i	−0.997340	+	0.0728901i	$0.976778\pi$
$164$	672.056	+	2444.90i	0.319993	+	1.16412i
$165$	2267.04	−	1308.87i	1.06963	−	0.617550i
$166$	−205.663	−	1524.13i	−0.0961598	−	0.712624i
$167$	4248.42			1.96858			0.984290	−	0.176558i	$-0.0564964\pi$
$167$	4248.42			1.96858			0.984290	+	0.176558i	$0.0564964\pi$
$168$	−971.950	−	797.406i	−0.446355	−	0.366198i
$169$	−2183.39			−0.993805
$170$	190.335	+	1410.54i	0.0858708	+	0.636374i
$171$	10.5947	−	6.11684i	0.00473799	−	0.00273548i
$172$	−1443.32	+	396.741i	−0.639839	+	0.175879i
$173$	−1110.85	+	1924.04i	−0.488185	+	0.845562i	−0.999908	−	0.0135890i	$-0.995674\pi$
$173$	−1110.85	+	1924.04i	−0.488185	+	0.845562i	0.511722	+	0.859151i	$0.329008\pi$
$174$	−10.6819	−	13.8283i	−0.00465398	−	0.00602482i
$175$	1450.17	−	757.455i	0.626414	−	0.327190i
$176$	−3335.58	−	1868.80i	−1.42857	−	0.800373i
$177$	1232.42	−	2134.62i	0.523360	−	0.906485i
$178$	3288.65	+	1349.78i	1.38480	+	0.568374i
$179$	1419.31	+	2458.31i	0.592647	+	1.02650i	0.993874	+	0.110517i	$0.0352506\pi$
$179$	1419.31	+	2458.31i	0.592647	+	1.02650i	−0.401227	+	0.915979i	$0.631416\pi$
$180$	748.409	+	738.808i	0.309906	+	0.305930i
$181$	−646.757			−0.265597			−0.132798	−	0.991143i	$-0.542396\pi$
$181$	−646.757			−0.265597			−0.132798	+	0.991143i	$0.542396\pi$
$182$	17.7295	+	192.433i	0.00722089	+	0.0783741i
$183$		−	404.131i		−	0.163247i
$184$	3948.78	+	481.013i	1.58211	+	0.192722i
$185$	3469.23	−	2002.96i	1.37872	−	0.796002i
$186$	839.941	+	344.743i	0.331115	+	0.135902i
$187$	1782.48	+	1029.12i	0.697048	+	0.402441i
$188$	−703.878	+	2696.42i	−0.273061	+	1.04605i
$189$	499.601	+	21.1224i	0.192278	+	0.00812925i
$190$	44.4409	−	34.3292i	0.0169689	−	0.0131079i
$191$	−2565.46	−	1481.17i	−0.971887	−	0.561119i	−0.0720758	−	0.997399i	$-0.522962\pi$
$191$	−2565.46	−	1481.17i	−0.971887	−	0.561119i	−0.899811	+	0.436280i	$0.856296\pi$
$192$	368.739	−	1491.08i	0.138601	−	0.560467i
$193$	1557.81	+	2698.21i	0.581004	+	1.00633i	0.995361	+	0.0962141i	$0.0306734\pi$
$193$	1557.81	+	2698.21i	0.581004	+	1.00633i	−0.414356	+	0.910115i	$0.635993\pi$
$194$	−390.097	−	2890.94i	−0.144368	−	1.06988i
$195$		−	161.652i		−	0.0593647i
$196$	−2697.81	+	501.373i	−0.983166	+	0.182716i
$197$		−	215.710i		−	0.0780137i	−0.999239	−	0.0390068i	$-0.987581\pi$
$197$		−	215.710i		−	0.0780137i	0.999239	−	0.0390068i	$-0.0124194\pi$
$198$	1507.09	−	203.364i	0.540932	−	0.0729921i
$199$	1208.29	+	2092.81i	0.430418	+	0.745506i	0.996909	−	0.0785620i	$-0.0250329\pi$
$199$	1208.29	+	2092.81i	0.430418	+	0.745506i	−0.566491	+	0.824068i	$0.691700\pi$
$200$	1597.54	+	1201.44i	0.564815	+	0.424772i
$201$	278.551	+	160.822i	0.0977487	+	0.0564353i
$202$	1814.58	+	2349.07i	0.632048	+	0.818219i
$203$	−38.1042	−	1.61099i	−0.0131744	−	0.000556992i
$204$	−208.848	+	800.055i	−0.0716778	+	0.274584i
$205$	−4009.18	−	2314.70i	−1.36592	−	0.788613i
$206$	531.616	−	1295.25i	0.179803	−	0.438078i
$207$	−1370.25	+	791.113i	−0.460091	+	0.265634i
$208$	−202.931	+	120.682i	−0.0676477	+	0.0402298i
$209$		−	81.2056i		−	0.0268761i
$210$	2285.67	−	210.587i	0.751077	−	0.0691994i
$211$	−4710.50			−1.53689			−0.768445	−	0.639915i	$-0.778969\pi$
$211$	−4710.50			−1.53689			−0.768445	+	0.639915i	$0.778969\pi$
$212$	−1688.91	+	1710.86i	−0.547146	+	0.554256i
$213$	676.516	+	1171.76i	0.217625	+	0.376938i
$214$	−2095.06	+	5104.47i	−0.669232	+	1.63054i
$215$	1366.46	−	2366.77i	0.433450	−	0.750757i
$216$	239.251	+	562.145i	0.0753657	+	0.177079i
$217$	1756.52	−	917.468i	0.549494	−	0.287013i
$218$	294.439	−	227.445i	0.0914768	−	0.0706629i
$219$	−684.143	+	1184.97i	−0.211096	+	0.365629i
$220$	6731.00	−	1850.22i	2.06274	−	0.567008i
$221$	110.072	−	63.5501i	0.0335034	−	0.0193432i
$222$	2306.29	−	311.206i	0.697244	−	0.0940845i
$223$	1574.47			0.472799			0.236399	−	0.971656i	$-0.424033\pi$
$223$	1574.47			0.472799			0.236399	+	0.971656i	$0.424033\pi$
$224$	−1970.74	−	2712.12i	−0.587839	−	0.808978i
$225$	−795.056			−0.235572
$226$	−3357.93	+	453.111i	−0.988346	+	0.133365i
$227$	−4128.15	+	2383.39i	−1.20703	+	0.696877i	−0.962108	−	0.272667i	$-0.912094\pi$
$227$	−4128.15	+	2383.39i	−1.20703	+	0.696877i	−0.244918	+	0.969544i	$0.578761\pi$
$228$	31.4564	−	8.64675i	0.00913706	−	0.00251160i
$229$	222.868	−	386.019i	0.0643124	−	0.111392i	−0.832076	−	0.554661i	$-0.812848\pi$
$229$	222.868	−	386.019i	0.0643124	−	0.111392i	0.896389	+	0.443269i	$0.146181\pi$
$230$	−5747.70	+	4439.91i	−1.64779	+	1.27287i
$231$	1779.56	−	2801.88i	0.506869	−	0.798053i
$232$	−18.2476	−	42.8744i	−0.00516384	−	0.0121330i
$233$	323.623	−	560.532i	0.0909926	−	0.157604i	−0.816936	−	0.576728i	$-0.804329\pi$
$233$	323.623	−	560.532i	0.0909926	−	0.157604i	0.907929	+	0.419124i	$0.137663\pi$
$234$	35.6575	−	86.8769i	0.00996154	−	0.0242706i
$235$	−2544.00	−	4406.34i	−0.706181	−	1.22314i
$236$	4617.66	−	4677.67i	1.27366	−	1.29021i
$237$	3599.14			0.986454
$238$	1041.96	+	1473.57i	0.283782	+	0.401334i
$239$		−	1481.31i		−	0.400912i	−0.979703	−	0.200456i	$-0.935758\pi$
$239$		−	1481.31i		−	0.400912i	0.979703	−	0.200456i	$-0.0642424\pi$
$240$	1433.43	+	2410.36i	0.385531	+	0.648283i
$241$	−2967.07	+	1713.04i	−0.793052	+	0.457869i	−0.841036	−	0.540979i	$-0.818054\pi$
$241$	−2967.07	+	1713.04i	−0.793052	+	0.457869i	0.0479838	+	0.998848i	$0.484720\pi$
$242$	2403.46	−	5855.87i	0.638432	−	1.55549i
$243$	−210.444	−	121.500i	−0.0555556	−	0.0320750i
$244$	272.199	−	1042.74i	0.0714169	−	0.273584i
$245$	2862.23	−	4111.79i	0.746372	−	1.07222i
$246$	−1644.08	−	2128.35i	−0.426109	−	0.551620i
$247$	−4.34279	−	2.50731i	−0.00111872	−	0.000645896i
$248$	1935.02	+	1455.24i	0.495459	+	0.372612i
$249$	815.618	+	1412.69i	0.207581	+	0.359541i
$250$	1500.93	−	202.532i	0.379709	−	0.0512370i
$251$			984.409i			0.247551i	0.992310	+	0.123776i	$0.0395003\pi$
$251$			984.409i			0.247551i	−0.992310	+	0.123776i	$0.960500\pi$
$252$	1274.84	+	391.002i	0.318681	+	0.0977412i
$253$			10502.6i			2.60985i
$254$	408.340	+	3026.14i	0.100872	+	0.747547i
$255$	−754.832	−	1307.41i	−0.185370	−	0.321071i
$256$	1955.73	−	3598.94i	0.477472	−	0.878647i
$257$	−4647.53	−	2683.25i	−1.12803	−	0.651271i	−0.184595	−	0.982815i	$-0.559097\pi$
$257$	−4647.53	−	2683.25i	−1.12803	−	0.651271i	−0.943440	+	0.331544i	$0.892431\pi$
$258$	1256.45	−	970.565i	0.303190	−	0.234204i
$259$	2723.25	−	4287.69i	0.653338	−	1.02867i
$260$	108.879	−	417.094i	0.0259707	−	0.0994888i
$261$	16.0505	+	9.26673i	0.00380651	+	0.00219769i
$262$	−4834.89	−	1984.42i	−1.14008	−	0.467930i
$263$	−5562.21	+	3211.34i	−1.30411	+	0.752927i	−0.981106	−	0.193471i	$-0.938025\pi$
$263$	−5562.21	+	3211.34i	−1.30411	+	0.752927i	−0.323002	+	0.946398i	$0.604692\pi$
$264$	4025.58	+	490.369i	0.938475	+	0.114319i
$265$		−	4389.24i		−	1.01747i
$266$	29.7946	−	64.6711i	0.00686776	−	0.0149069i
$267$	−3770.52			−0.864239
$268$	610.399	+	602.569i	0.139127	+	0.137342i
$269$	2724.40	+	4718.80i	0.617509	+	1.06956i	0.989939	+	0.141496i	$0.0451912\pi$
$269$	2724.40	+	4718.80i	0.617509	+	1.06956i	−0.372430	+	0.928060i	$0.621475\pi$
$270$	−1031.90	−	423.530i	−0.232591	−	0.0954638i
$271$	2644.96	−	4581.21i	0.592878	−	1.02689i	−0.400965	−	0.916093i	$-0.631325\pi$
$271$	2644.96	−	4581.21i	0.592878	−	1.02689i	0.993843	−	0.110801i	$-0.0353416\pi$
$272$	−1077.74	+	1923.64i	−0.240248	+	0.428815i
$273$	−94.8957	−	181.680i	−0.0210379	−	0.0402776i
$274$	−4480.36	−	5800.06i	−0.987842	−	1.27881i
$275$	−2638.74	+	4570.43i	−0.578625	+	1.00221i
$276$	−4068.37	+	1118.31i	−0.887271	+	0.243894i
$277$	−734.901	+	424.295i	−0.159408	+	0.0920341i	−0.577582	−	0.816333i	$-0.696004\pi$
$277$	−734.901	+	424.295i	−0.159408	+	0.0920341i	0.418174	+	0.908367i	$0.362670\pi$
$278$	1142.40	+	8466.15i	0.246463	+	1.82650i
$279$	−963.012			−0.206645
$280$	6039.33	+	996.135i	1.28900	+	0.212609i
$281$	2590.85			0.550026			0.275013	−	0.961441i	$-0.411318\pi$
$281$	2590.85			0.550026			0.275013	+	0.961441i	$0.411318\pi$
$282$	−395.269	−	2929.27i	−0.0834679	−	0.618566i
$283$	1757.27	−	1014.56i	0.369113	−	0.213108i	−0.303958	−	0.952686i	$-0.598308\pi$
$283$	1757.27	−	1014.56i	0.369113	−	0.213108i	0.673071	+	0.739578i	$0.264975\pi$
$284$	956.321	+	3479.04i	0.199814	+	0.726913i
$285$	−29.7812	+	51.5825i	−0.00618977	+	0.0107210i
$286$	−381.072	−	493.318i	−0.0787876	−	0.101995i
$287$	−5864.73	−	247.952i	−1.20622	−	0.0509971i
$288$	238.690	+	1611.59i	0.0488366	+	0.329736i
$289$	−1863.01	+	3226.82i	−0.379199	+	0.656792i
$290$	78.7024	+	32.3024i	0.0159364	+	0.00654090i
$291$	1547.05	+	2679.56i	0.311648	+	0.539790i
$292$	−2563.35	+	2596.67i	−0.513729	+	0.520405i
$293$	9290.50			1.85241			0.926206	−	0.377017i	$-0.123050\pi$
$293$	9290.50			1.85241			0.926206	+	0.377017i	$0.123050\pi$
$294$	2445.24	−	1578.45i	0.485066	−	0.313120i
$295$			12000.6i			2.36849i
$296$	6160.31	+	750.408i	1.20967	+	0.147353i
$297$	−1396.90	+	806.501i	−0.272917	+	0.157569i
$298$	1791.17	+	735.163i	0.348187	+	0.142909i
$299$	561.668	+	324.279i	0.108636	+	0.0627209i
$300$	−2051.41	−	535.503i	−0.394793	−	0.103058i
$301$	146.376	−	3462.18i	0.0280298	−	0.662979i
$302$	6930.22	−	5353.38i	1.32049	−	1.02004i
$303$	−2726.57	−	1574.18i	−0.516954	−	0.298464i
$304$	86.9879	−	1.12321i	0.0164115	−	0.000211909i
$305$	983.799	+	1703.99i	0.184696	+	0.319902i
$306$	−117.281	−	869.145i	−0.0219101	−	0.162372i
$307$		−	2214.01i		−	0.411598i	−0.978594	−	0.205799i	$-0.934021\pi$
$307$		−	2214.01i		−	0.411598i	0.978594	−	0.205799i	$-0.0659793\pi$
$308$	6478.82	−	6030.82i	1.19859	−	1.11571i
$309$			1485.03i			0.273399i
$310$	−4380.78	+	591.132i	−0.802618	+	0.108303i
$311$	−4427.78	−	7669.15i	−0.807320	−	1.39832i	−0.914713	−	0.404103i	$-0.867584\pi$
$311$	−4427.78	−	7669.15i	−0.807320	−	1.39832i	0.107393	−	0.994217i	$-0.465750\pi$
$312$	150.519	−	200.143i	0.0273123	−	0.0363169i
$313$	164.785	+	95.1386i	0.0297578	+	0.0171807i	0.514805	−	0.857307i	$-0.327864\pi$
$313$	164.785	+	95.1386i	0.0297578	+	0.0171807i	−0.485047	+	0.874488i	$0.661198\pi$
$314$	1685.48	+	2181.93i	0.302920	+	0.392146i
$315$	−2157.95	+	1127.15i	−0.385990	+	0.201611i
$316$	9286.53	+	2424.17i	1.65319	+	0.431552i
$317$	378.138	+	218.318i	0.0669980	+	0.0386813i	0.533125	−	0.846037i	$-0.321018\pi$
$317$	378.138	+	218.318i	0.0669980	+	0.0386813i	−0.466127	+	0.884718i	$0.654351\pi$
$318$	968.188	−	2358.92i	0.170734	−	0.415980i
$319$	106.541	−	61.5113i	0.0186995	−	0.0107962i
$320$	2075.07	+	7184.69i	0.362499	+	1.25511i
$321$		−	5852.40i		−	1.01760i
$322$	−3853.44	+	8364.14i	−0.666907	+	1.44756i
$323$	−46.8315			−0.00806741
$324$	−461.154	−	455.238i	−0.0790730	−	0.0780586i
$325$	162.948	+	282.234i	0.0278114	+	0.0481708i
$326$	2511.16	−	6118.25i	0.426626	−	1.03944i
$327$	−197.312	+	341.755i	−0.0333682	+	0.0577954i
$328$	−2808.53	−	6598.93i	−0.472791	−	1.11087i
$329$	−5445.90	−	3458.86i	−0.912589	−	0.579615i
$330$	−5859.50	+	4526.27i	−0.977438	+	0.755040i
$331$	−4927.37	+	8534.46i	−0.818226	+	1.41721i	0.0887622	+	0.996053i	$0.471709\pi$
$331$	−4927.37	+	8534.46i	−0.818226	+	1.41721i	−0.906988	+	0.421156i	$0.861624\pi$
$332$	1152.96	+	4194.39i	0.190592	+	0.693364i
$333$	−2137.66	+	1234.18i	−0.351781	+	0.203101i
$334$	−11908.4	+	1606.90i	−1.95090	+	0.263250i
$335$	−1565.99			−0.255401
$336$	3026.00	+	1867.52i	0.491316	+	0.303220i
$337$	2518.25			0.407057			0.203528	−	0.979069i	$-0.434759\pi$
$337$	2518.25			0.407057			0.203528	+	0.979069i	$0.434759\pi$
$338$	6120.09	−	825.832i	0.984879	−	0.132897i
$339$	3112.41	−	1796.95i	0.498652	−	0.287897i
$340$	−1067.03	−	3881.79i	−0.170199	−	0.619175i
$341$	−3196.17	+	5535.93i	−0.507573	+	0.879142i
$342$	−27.3836	+	21.1529i	−0.00432963	+	0.00334450i
$343$	803.082	−	6301.48i	0.126421	−	0.991977i
$344$	3895.61	−	1657.99i	0.610573	−	0.259863i
$345$	3851.70	−	6671.35i	0.601069	−	1.04108i
$346$	2385.99	−	5813.29i	0.370727	−	0.903250i
$347$	−5797.56	−	10041.7i	−0.896914	−	1.55350i	−0.831417	−	0.555648i	$-0.812470\pi$
$347$	−5797.56	−	10041.7i	−0.896914	−	1.55350i	−0.0654969	−	0.997853i	$-0.520863\pi$
$348$	35.1719	+	34.7207i	0.00541785	+	0.00534835i
$349$	−1813.09			−0.278088			−0.139044	−	0.990286i	$-0.544403\pi$
$349$	−1813.09			−0.278088			−0.139044	+	0.990286i	$0.544403\pi$
$350$	−3778.36	+	2671.67i	−0.577034	+	0.408019i
$351$			99.6063i			0.0151470i
$352$	10056.5	+	3976.65i	1.52277	+	0.602148i
$353$	2083.52	−	1202.92i	0.314149	−	0.181374i	−0.334633	−	0.942349i	$-0.608612\pi$
$353$	2083.52	−	1202.92i	0.314149	−	0.181374i	0.648782	+	0.760975i	$0.275279\pi$
$354$	−2647.13	+	6449.53i	−0.397438	+	0.968330i
$355$	−5704.97	−	3293.76i	−0.852925	−	0.492436i
$356$	−9728.70	−	2539.60i	−1.44837	−	0.378085i
$357$	−1615.85	−	1026.28i	−0.239552	−	0.152147i
$358$	−4908.16	−	6353.87i	−0.724593	−	0.938024i
$359$	6925.06	+	3998.18i	1.01808	+	0.587789i	0.913547	−	0.406733i	$-0.133332\pi$
$359$	6925.06	+	3998.18i	1.01808	+	0.587789i	0.104533	+	0.994521i	$0.466665\pi$
$360$	−2377.25	−	1787.82i	−0.348033	−	0.261740i
$361$	−3428.58	−	5938.47i	−0.499865	−	0.865792i
$362$	1812.87	−	244.625i	0.263211	−	0.0355172i
$363$			6713.89i			0.970765i
$364$	−122.481	−	532.689i	−0.0176367	−	0.0767046i
$365$		−	6661.79i		−	0.955326i
$366$	152.856	+	1132.79i	0.0218303	+	0.161781i
$367$	−617.136	−	1068.91i	−0.0877773	−	0.152035i	0.818794	−	0.574087i	$-0.194643\pi$
$367$	−617.136	−	1068.91i	−0.0877773	−	0.152035i	−0.906571	+	0.422053i	$0.861310\pi$
$368$	−11250.4	+	145.268i	−1.59367	+	0.0205778i
$369$	2470.37	+	1426.27i	0.348516	+	0.201216i
$370$	−8966.73	+	6926.52i	−1.25989	+	0.973223i
$371$	−2576.65	−	4933.07i	−0.360574	−	0.690329i
$372$	−2484.77	−	648.628i	−0.346315	−	0.0904027i
$373$	−11025.6	−	6365.63i	−1.53052	−	0.883646i	−0.999338	−	0.0363881i	$-0.988415\pi$
$373$	−11025.6	−	6365.63i	−1.53052	−	0.883646i	−0.531182	−	0.847258i	$-0.678252\pi$
$374$	−5385.58	−	2210.44i	−0.744604	−	0.305613i
$375$	−1391.19	+	803.202i	−0.191575	+	0.110606i
$376$	953.110	−	7824.35i	0.130726	−	1.07317i
$377$		−	7.59692i		−	0.00103783i
$378$	−1408.38	+	129.759i	−0.191638	+	0.0176563i
$379$	11102.4			1.50472			0.752362	−	0.658750i	$-0.228914\pi$
$379$	11102.4			1.50472			0.752362	+	0.658750i	$0.228914\pi$
$380$	−111.584	+	113.035i	−0.0150636	+	0.0152593i
$381$	−1619.40	−	2804.88i	−0.217754	−	0.377161i
$382$	7751.28	+	3181.41i	1.03819	+	0.426113i
$383$	1130.11	−	1957.40i	0.150772	−	0.261145i	−0.780739	−	0.624857i	$-0.785157\pi$
$383$	1130.11	−	1957.40i	0.150772	−	0.261145i	0.931512	+	0.363712i	$0.118491\pi$
$384$	−469.606	+	4319.01i	−0.0624075	+	0.573967i
$385$	−682.631	+	16146.0i	−0.0903639	+	2.13735i
$386$	−5387.14	−	6973.93i	−0.710358	−	0.919595i
$387$	−841.983	+	1458.36i	−0.110595	+	0.191557i
$388$	2186.90	+	7955.82i	0.286142	+	1.04097i
$389$	−6521.27	+	3765.06i	−0.849978	+	0.490735i	−0.860643	−	0.509208i	$-0.829938\pi$
$389$	−6521.27	+	3765.06i	−0.849978	+	0.490735i	0.0106655	+	0.999943i	$0.496605\pi$
$390$	61.1421	+	453.113i	0.00793859	+	0.0588315i
$391$	6056.88			0.783401
$392$	7372.38	−	2425.76i	0.949901	−	0.312550i
$393$	5543.31			0.711509
$394$	81.5888	+	604.640i	0.0104324	+	0.0773130i
$395$	−15175.5	+	8761.61i	−1.93308	+	1.11606i
$396$	−4147.50	+	1140.07i	−0.526312	+	0.144673i
$397$	−2213.94	+	3834.66i	−0.279885	+	0.484775i	−0.971356	−	0.237629i	$-0.923630\pi$
$397$	−2213.94	+	3834.66i	−0.279885	+	0.484775i	0.691471	+	0.722404i	$0.256963\pi$
$398$	−4178.43	−	5409.19i	−0.526245	−	0.681252i
$399$	−3.19018	+	75.4563i	−0.000400273	+	0.00946752i
$400$	−4932.36	−	2763.41i	−0.616545	−	0.345427i
$401$	3501.96	−	6065.57i	0.436108	−	0.755361i	−0.561277	−	0.827628i	$-0.689690\pi$
$401$	3501.96	−	6065.57i	0.436108	−	0.755361i	0.997385	+	0.0722664i	$0.0230232\pi$
$402$	−841.614	−	345.429i	−0.104418	−	0.0428569i
$403$	197.370	+	341.856i	0.0243963	+	0.0422557i
$404$	−5974.82	−	5898.17i	−0.735788	−	0.726349i
$405$	1183.10			0.145157
$406$	107.416	−	9.89666i	0.0131305	−	0.00120976i
$407$			16384.7i			1.99547i
$408$	282.798	−	2321.57i	0.0343151	−	0.281703i
$409$	7550.94	−	4359.54i	0.912885	−	0.527055i	0.0315269	−	0.999503i	$-0.489963\pi$
$409$	7550.94	−	4359.54i	0.912885	−	0.527055i	0.881358	+	0.472448i	$0.156630\pi$
$410$	12113.3	+	4971.75i	1.45911	+	0.598871i
$411$	6732.13	+	3886.79i	0.807959	+	0.466476i
$412$	−1000.23	+	3831.68i	−0.119606	+	0.458187i
$413$	7044.83	+	13487.5i	0.839355	+	1.60697i
$414$	3541.61	−	2735.78i	0.420436	−	0.324774i
$415$	−6878.00	−	3971.01i	−0.813561	−	0.469709i
$416$	523.174	−	415.030i	0.0616603	−	0.0489147i
$417$	−4530.55	−	7847.14i	−0.532043	−	0.921525i
$418$	30.7147	+	227.621i	0.00359403	+	0.0266347i
$419$			7052.74i			0.822312i	0.911565	+	0.411156i	$0.134875\pi$
$419$			7052.74i			0.822312i	−0.911565	+	0.411156i	$0.865125\pi$
$420$	−6327.13	+	1454.80i	−0.735077	+	0.169016i
$421$		−	6931.64i		−	0.802440i	−0.915982	−	0.401220i	$-0.868586\pi$
$421$		−	6931.64i		−	0.802440i	0.915982	−	0.401220i	$-0.131414\pi$
$422$	13203.6	−	1781.67i	1.52309	−	0.205522i
$423$	1567.56	+	2715.09i	0.180183	+	0.312086i
$424$	4086.95	−	5434.38i	0.468113	−	0.622446i
$425$	2635.78	+	1521.77i	0.300833	+	0.173686i
$426$	−2339.49	−	3028.59i	−0.266077	−	0.344450i
$427$	2106.00	+	1337.59i	0.238680	+	0.151593i
$428$	3941.83	−	15100.4i	0.445177	−	1.70538i
$429$	572.593	+	330.587i	0.0644407	+	0.0372048i
$430$	−2935.02	+	7150.96i	−0.329161	+	0.801977i
$431$	−2301.26	+	1328.63i	−0.257187	+	0.148487i	−0.623051	−	0.782181i	$-0.714107\pi$
$431$	−2301.26	+	1328.63i	−0.257187	+	0.148487i	0.365863	+	0.930669i	$0.380774\pi$
$432$	−883.249	−	1485.21i	−0.0983689	−	0.165410i
$433$			2301.97i			0.255487i	0.991807	+	0.127743i	$0.0407734\pi$
$433$			2301.97i			0.255487i	−0.991807	+	0.127743i	$0.959227\pi$
$434$	−4576.54	+	3236.06i	−0.506178	+	0.357916i
$435$	−90.2342			−0.00994574
$436$	−739.293	+	748.900i	−0.0812057	+	0.0822610i
$437$	−119.484	−	206.953i	−0.0130794	−	0.0226542i
$438$	1469.47	−	3580.26i	0.160306	−	0.390574i
$439$	5316.12	−	9207.78i	0.577960	−	1.00106i	−0.417753	−	0.908561i	$-0.637182\pi$
$439$	5316.12	−	9207.78i	0.577960	−	1.00106i	0.995713	−	0.0924954i	$-0.0294843\pi$
$440$	−18167.3	+	7732.10i	−1.96839	+	0.837758i
$441$	−1763.65	+	2533.60i	−0.190438	+	0.273577i
$442$	−284.498	+	219.765i	−0.0306158	+	0.0236497i
$443$	−821.461	+	1422.81i	−0.0881011	+	0.152596i	−0.906708	−	0.421758i	$-0.861413\pi$
$443$	−821.461	+	1422.81i	−0.0881011	+	0.152596i	0.818607	+	0.574354i	$0.194747\pi$
$444$	−6346.88	+	1744.63i	−0.678400	+	0.186479i
$445$	15898.1	−	9178.79i	1.69358	−	0.977789i
$446$	−4413.27	+	595.517i	−0.468552	+	0.0632254i
$447$	−2053.62			−0.217299
$448$	6549.85	+	6856.73i	0.690740	+	0.723103i
$449$	−6402.50			−0.672945			−0.336473	−	0.941693i	$-0.609234\pi$
$449$	−6402.50			−0.672945			−0.336473	+	0.941693i	$0.609234\pi$
$450$	2228.56	−	300.717i	0.233456	−	0.0315021i
$451$	16398.0	−	9467.38i	1.71209	−	0.988474i
$452$	9240.97	−	2540.16i	0.961634	−	0.264335i
$453$	−4644.15	+	8043.90i	−0.481680	+	0.834294i
$454$	10669.8	−	8242.10i	1.10299	−	0.852028i
$455$	842.396	+	535.033i	0.0867959	+	0.0551269i
$456$	−84.9025	+	36.1349i	−0.00871913	+	0.00371090i
$457$	−782.070	+	1354.59i	−0.0800519	+	0.138654i	−0.903272	−	0.429068i	$-0.858842\pi$
$457$	−782.070	+	1354.59i	−0.0800519	+	0.138654i	0.823220	+	0.567722i	$0.192175\pi$
$458$	−478.699	+	1166.32i	−0.0488387	+	0.118992i
$459$	465.111	+	805.597i	0.0472975	+	0.0819216i
$460$	14431.6	−	14619.2i	1.46278	−	1.48179i
$461$	12965.9			1.30994			0.654970	−	0.755655i	$-0.272681\pi$
$461$	12965.9			1.30994			0.654970	+	0.755655i	$0.272681\pi$
$462$	−3928.40	+	8526.83i	−0.395596	+	0.858667i
$463$		−	1919.05i		−	0.192626i	−0.995351	−	0.0963130i	$-0.969295\pi$
$463$		−	1919.05i		−	0.192626i	0.995351	−	0.0963130i	$-0.0307050\pi$
$464$	67.3649	+	113.276i	0.00673995	+	0.0113334i
$465$	4060.47	−	2344.31i	0.404946	−	0.233796i
$466$	−695.112	+	1693.59i	−0.0690996	+	0.168356i
$467$	3383.20	+	1953.29i	0.335237	+	0.193549i	0.658164	−	0.752875i	$-0.271333\pi$
$467$	3383.20	+	1953.29i	0.335237	+	0.193549i	−0.322927	+	0.946424i	$0.604667\pi$
$468$	−67.0890	+	257.005i	−0.00662647	+	0.0253847i
$469$	−1760.02	+	919.296i	−0.173284	+	0.0905099i
$470$	8797.52	+	11388.9i	0.863403	+	1.11772i
$471$	−2532.57	−	1462.18i	−0.247759	−	0.143044i
$472$	−11174.2	+	14858.2i	−1.08969	+	1.44895i
$473$	5588.97	+	9680.38i	0.543300	+	0.941024i
$474$	−10088.5	+	1361.32i	−0.977594	+	0.131914i
$475$		−	120.080i		−	0.0115992i
$476$	−3477.99	−	3736.36i	−0.334902	−	0.359781i
$477$			2704.56i			0.259608i
$478$	560.282	+	4152.15i	0.0536123	+	0.397312i
$479$	−9988.48	−	17300.6i	−0.952788	−	1.65028i	−0.739352	−	0.673320i	$-0.764868\pi$
$479$	−9988.48	−	17300.6i	−0.952788	−	1.65028i	−0.213436	−	0.976957i	$-0.568466\pi$
$480$	−4929.62	−	6214.12i	−0.468761	−	0.590905i
$481$	876.234	+	505.894i	0.0830620	+	0.0479559i
$482$	7668.83	−	5923.93i	0.724700	−	0.559808i
$483$	412.597	−	9759.03i	0.0388692	−	0.919360i
$484$	−4522.08	+	17323.2i	−0.424688	+	1.62690i
$485$	−13046.0	−	7532.13i	−1.22142	−	0.705189i
$486$	635.835	+	260.970i	0.0593458	+	0.0243577i
$487$	6372.05	−	3678.91i	0.592906	−	0.342314i	−0.173340	−	0.984862i	$-0.555456\pi$
$487$	6372.05	−	3678.91i	0.592906	−	0.342314i	0.766246	+	0.642548i	$0.222123\pi$
$488$	−368.580	+	3025.78i	−0.0341902	+	0.280677i
$489$			7014.72i			0.648705i
$490$	−6467.68	+	12608.0i	−0.596285	+	1.16239i
$491$	11334.2			1.04176			0.520882	−	0.853629i	$-0.325603\pi$
$491$	11334.2			1.04176			0.520882	+	0.853629i	$0.325603\pi$
$492$	5413.41	+	5343.96i	0.496047	+	0.489684i
$493$	−35.4738	−	61.4424i	−0.00324069	−	0.00561303i
$494$	13.1213	+	5.38546i	0.00119505	+	0.000490493i
$495$	3926.62	−	6801.11i	0.356543	−	0.617550i
$496$	−5974.33	−	3347.18i	−0.540837	−	0.303010i
$497$	−8345.38	−	352.830i	−0.753202	−	0.0318443i
$498$	−2820.52	−	3651.32i	−0.253797	−	0.328553i
$499$	3535.75	−	6124.10i	0.317198	−	0.549404i	−0.662704	−	0.748881i	$-0.730591\pi$
$499$	3535.75	−	6124.10i	0.317198	−	0.549404i	0.979902	+	0.199478i	$0.0639246\pi$
$500$	−4130.54	+	1135.40i	−0.369446	+	0.101554i
$501$	11037.7	−	6372.64i	0.984290	−	0.568280i
$502$	−372.337	−	2759.32i	−0.0331040	−	0.245328i
$503$	9193.47			0.814944			0.407472	−	0.913218i	$-0.366410\pi$
$503$	9193.47			0.814944			0.407472	+	0.913218i	$0.366410\pi$
$504$	−3721.31	−	613.798i	−0.328890	−	0.0542475i
$505$	15328.5			1.35071
$506$	−3972.44	−	29439.0i	−0.349005	−	2.58641i
$507$	−5672.61	+	3275.09i	−0.496903	+	0.286887i
$508$	−2289.17	−	8327.89i	−0.199933	−	0.727343i
$509$	1268.09	−	2196.40i	0.110427	−	0.191265i	−0.805516	−	0.592574i	$-0.798112\pi$
$509$	1268.09	−	2196.40i	0.110427	−	0.191265i	0.915942	+	0.401310i	$0.131445\pi$
$510$	2610.32	+	3379.19i	0.226641	+	0.293398i
$511$	−3910.72	−	7487.19i	−0.338552	−	0.648168i
$512$	−4120.71	+	10827.6i	−0.355686	+	0.934605i
$513$	18.3505	−	31.7841i	0.00157933	−	0.00273548i
$514$	14042.0	+	5763.37i	1.20499	+	0.494574i
$515$	−3615.09	−	6261.52i	−0.309320	−	0.535759i
$516$	−3154.75	+	3195.75i	−0.269148	+	0.272645i
$517$	20810.5			1.77030
$518$	−6011.59	+	13048.5i	−0.509911	+	1.10679i
$519$			6665.08i			0.563708i
$520$	−147.431	+	1210.31i	−0.0124333	+	0.102068i
$521$	−16234.3	+	9372.88i	−1.36514	+	0.788164i	−0.990303	−	0.138927i	$-0.955635\pi$
$521$	−16234.3	+	9372.88i	−1.36514	+	0.788164i	−0.374837	+	0.927091i	$0.622301\pi$
$522$	−48.4948	−	19.9040i	−0.00406620	−	0.00166892i
$523$	1445.82	+	834.745i	0.120882	+	0.0697913i	0.559222	−	0.829018i	$-0.311100\pi$
$523$	1445.82	+	834.745i	0.120882	+	0.0697913i	−0.438340	+	0.898809i	$0.644433\pi$
$524$	14302.9	+	3733.65i	1.19241	+	0.311269i
$525$	2631.47	−	4143.18i	0.218755	−	0.344425i
$526$	14376.4	−	11105.3i	1.19171	−	0.920558i
$527$	3192.59	+	1843.24i	0.263892	+	0.152358i
$528$	−11469.3	+	148.094i	−0.945334	+	0.0122064i
$529$	9369.82	+	16229.0i	0.770101	+	1.33385i
$530$	1660.16	+	12303.1i	0.136062	+	1.00833i
$531$		−	7394.54i		−	0.604324i
$532$	−59.0542	+	192.544i	−0.00481264	+	0.0156914i
$533$		−	1169.26i		−	0.0950214i
$534$	10568.8	−	1426.14i	0.856477	−	0.115571i
$535$	14246.8	+	24676.2i	1.15130	+	1.99411i
$536$	−1938.87	−	1458.14i	−0.156244	−	0.117504i
$537$	7374.93	+	4257.92i	0.592647	+	0.342165i
$538$	−9421.38	−	12196.5i	−0.754990	−	0.977373i
$539$	8711.13	+	18547.3i	0.696131	+	1.48217i
$540$	3052.63	+	796.865i	0.243268	+	0.0635030i
$541$	−11917.6	−	6880.64i	−0.947096	−	0.546806i	−0.0549180	−	0.998491i	$-0.517490\pi$
$541$	−11917.6	−	6880.64i	−0.947096	−	0.546806i	−0.892177	+	0.451685i	$0.850823\pi$
$542$	−5681.12	+	13841.6i	−0.450231	+	1.09695i
$543$	−1680.32	+	970.135i	−0.132798	+	0.0766712i
$544$	2293.35	−	5799.64i	0.180747	−	0.457091i
$545$		−	1921.32i		−	0.151009i
$546$	334.712	+	473.362i	0.0262351	+	0.0371026i
$547$	10496.8			0.820494			0.410247	−	0.911974i	$-0.365442\pi$
$547$	10496.8			0.820494			0.410247	+	0.911974i	$0.365442\pi$
$548$	14752.3	+	14563.1i	1.14998	+	1.13523i
$549$	−606.196	−	1049.96i	−0.0471253	−	0.0816235i
$550$	5667.75	−	13809.1i	0.439407	−	1.07058i
$551$	−1.39958	+	2.42415i	−0.000108211	+	0.000187427i
$552$	10980.7	−	4673.45i	0.846687	−	0.360354i
$553$	−11912.4	+	18755.8i	−0.916035	+	1.44227i
$554$	1899.46	−	1467.27i	0.145669	−	0.112524i
$555$	6008.87	−	10407.7i	0.459572	−	0.796002i
$556$	−6404.36	−	23298.7i	−0.488499	−	1.77713i
$557$	−8319.18	+	4803.08i	−0.632846	+	0.365374i	−0.781853	−	0.623462i	$-0.785725\pi$
$557$	−8319.18	+	4803.08i	−0.632846	+	0.365374i	0.149008	+	0.988836i	$0.452392\pi$
$558$	2699.34	−	364.243i	0.204789	−	0.0276338i
$559$	690.262			0.0522271
$560$	−17305.2	−	507.912i	−1.30585	−	0.0383271i
$561$	6174.69			0.464698
$562$	−7262.22	+	979.947i	−0.545086	+	0.0735526i
$563$	−3141.56	+	1813.78i	−0.235171	+	0.135776i	−0.612955	−	0.790118i	$-0.710019\pi$
$563$	−3141.56	+	1813.78i	−0.235171	+	0.135776i	0.377784	+	0.925894i	$0.376686\pi$
$564$	2215.90	+	8061.32i	0.165436	+	0.601849i
$565$	−8748.84	+	15153.4i	−0.651445	+	1.12834i
$566$	−4541.94	+	3508.50i	−0.337300	+	0.260554i
$567$	1329.68	−	694.523i	0.0984859	−	0.0514413i
$568$	−3996.48	−	9390.12i	−0.295226	−	0.693663i
$569$	2995.10	−	5187.66i	0.220670	−	0.382211i	−0.734342	−	0.678780i	$-0.762509\pi$
$569$	2995.10	−	5187.66i	0.220670	−	0.382211i	0.955012	+	0.296569i	$0.0958424\pi$
$570$	63.9671	−	155.851i	0.00470050	−	0.0114524i
$571$	−3174.42	−	5498.26i	−0.232654	−	0.402969i	0.725934	−	0.687764i	$-0.241408\pi$
$571$	−3174.42	−	5498.26i	−0.232654	−	0.402969i	−0.958588	+	0.284795i	$0.908074\pi$
$572$	1254.74	+	1238.65i	0.0917193	+	0.0905427i
$573$	−8887.02			−0.647924
$574$	16532.8	−	1523.22i	1.20220	−	0.110763i
$575$			15530.3i			1.12637i
$576$	−1278.61	−	4427.05i	−0.0924922	−	0.320244i
$577$	−628.970	+	363.136i	−0.0453802	+	0.0262003i	−0.522518	−	0.852628i	$-0.675007\pi$
$577$	−628.970	+	363.136i	−0.0453802	+	0.0262003i	0.477138	+	0.878828i	$0.341674\pi$
$578$	4001.56	−	9749.51i	0.287963	−	0.701602i
$579$	8094.63	+	4673.44i	0.581004	+	0.335443i
$580$	−232.823	−	60.7764i	−0.0166680	−	0.00435104i
$581$	−10061.3	−	425.378i	−0.718440	−	0.0303746i
$582$	−5349.91	−	6925.74i	−0.381032	−	0.493266i
$583$	15547.3	+	8976.24i	1.10447	+	0.637664i
$584$	6202.99	−	8248.06i	0.439523	−	0.584430i
$585$	−242.477	−	419.983i	−0.0171371	−	0.0296823i
$586$	−26041.5	+	3513.98i	−1.83577	+	0.247715i
$587$		−	16660.1i		−	1.17144i	−0.810512	−	0.585722i	$-0.800811\pi$
$587$		−	16660.1i		−	1.17144i	0.810512	−	0.585722i	$-0.199189\pi$
$588$	−6257.05	+	5349.32i	−0.438837	+	0.375174i
$589$		−	145.447i		−	0.0101749i
$590$	−4539.05	−	33638.1i	−0.316728	−	2.34722i
$591$	−323.565	−	560.431i	−0.0225206	−	0.0390068i
$592$	−17551.3	+	226.627i	−1.21851	+	0.0157336i
$593$	−10634.9	−	6140.07i	−0.736465	−	0.425198i	0.0843179	−	0.996439i	$-0.473129\pi$
$593$	−10634.9	−	6140.07i	−0.736465	−	0.425198i	−0.820782	+	0.571241i	$0.806462\pi$
$594$	3610.50	−	2788.99i	0.249395	−	0.192650i
$595$	9311.47	+	393.675i	0.641568	+	0.0271246i
$596$	−5298.76	−	1383.20i	−0.364170	−	0.0950637i
$597$	6278.44	+	3624.86i	0.430418	+	0.248502i
$598$	−1697.02	−	696.520i	−0.116047	−	0.0476302i
$599$	−8795.74	+	5078.22i	−0.599974	+	0.346395i	−0.769031	−	0.639211i	$-0.779261\pi$
$599$	−8795.74	+	5078.22i	−0.599974	+	0.346395i	0.169058	+	0.985606i	$0.445928\pi$
$600$	5952.68	+	725.116i	0.405029	+	0.0493379i
$601$		−	11938.9i		−	0.810316i	−0.914247	−	0.405158i	$-0.867217\pi$
$601$		−	11938.9i		−	0.810316i	0.914247	−	0.405158i	$-0.132783\pi$
$602$	899.218	+	9759.94i	0.0608794	+	0.660773i
$603$	964.930			0.0651658
$604$	−17400.7	+	17626.9i	−1.17223	+	1.18746i
$605$	−16344.0	−	28308.6i	−1.09831	−	1.90233i
$606$	8238.04	+	3381.20i	0.552224	+	0.226653i
$607$	−5904.55	+	10227.0i	−0.394824	+	0.683856i	−0.993079	−	0.117450i	$-0.962528\pi$
$607$	−5904.55	+	10227.0i	−0.394824	+	0.683856i	0.598254	+	0.801306i	$0.295861\pi$
$608$	−243.404	+	36.0501i	−0.0162358	+	0.00240465i
$609$	−101.414	+	52.9709i	−0.00674797	+	0.00352461i
$610$	−3402.12	−	4404.22i	−0.225816	−	0.292330i
$611$	642.547	−	1112.92i	0.0425445	−	0.0736892i
$612$	657.480	+	2391.88i	0.0434266	+	0.157983i
$613$	917.232	−	529.564i	0.0604350	−	0.0348922i	−0.469478	−	0.882944i	$-0.655558\pi$
$613$	917.232	−	529.564i	0.0604350	−	0.0348922i	0.529913	+	0.848052i	$0.322225\pi$
$614$	837.415	+	6205.94i	0.0550412	+	0.407901i
$615$	−13888.2			−0.910612
$616$	−15879.2	+	19355.0i	−1.03862	+	1.26597i
$617$	−17095.6			−1.11546			−0.557732	−	0.830021i	$-0.688328\pi$
$617$	−17095.6			−1.11546			−0.557732	+	0.830021i	$0.688328\pi$
$618$	−561.688	−	4162.57i	−0.0365605	−	0.270944i
$619$	−20388.9	+	11771.5i	−1.32391	+	0.764358i	−0.984349	−	0.176228i	$-0.943611\pi$
$619$	−20388.9	+	11771.5i	−1.32391	+	0.764358i	−0.339557	+	0.940585i	$0.610277\pi$
$620$	12055.8	−	3313.92i	0.780926	−	0.214661i
$621$	−2373.34	+	4110.74i	−0.153364	+	0.265634i
$622$	15311.9	+	19822.1i	0.987061	+	1.27780i
$623$	12479.6	−	19648.8i	0.802544	−	1.26359i
$624$	−346.206	+	617.937i	−0.0222105	+	0.0396431i
$625$	9431.78	−	16336.3i	0.603634	−	1.04553i
$626$	−497.880	−	204.348i	−0.0317880	−	0.0130470i
$627$	−121.808	−	210.978i	−0.00775847	−	0.0134381i
$628$	−5549.71	−	5478.51i	−0.352639	−	0.348115i
$629$	9449.08			0.598982
$630$	5622.46	−	3975.63i	0.355562	−	0.251417i
$631$		−	4861.23i		−	0.306692i	−0.988173	−	0.153346i	$-0.950995\pi$
$631$		−	4861.23i		−	0.306692i	0.988173	−	0.153346i	$-0.0490049\pi$
$632$	−26947.3	−	3282.53i	−1.69605	−	0.206602i
$633$	−12238.2	+	7065.75i	−0.768445	+	0.443662i
$634$	−1142.51	−	468.927i	−0.0715689	−	0.0293745i
$635$	13656.2	+	7884.39i	0.853430	+	0.492728i
$636$	−1821.63	+	6978.31i	−0.113573	+	0.435075i
$637$	1260.85	+	106.805i	0.0784252	+	0.00664328i
$638$	−275.371	+	212.715i	−0.0170878	+	0.0131998i
$639$	3515.28	+	2029.55i	0.217625	+	0.125646i
$640$	−8533.95	−	19354.0i	−0.527084	−	1.19537i
$641$	2933.33	+	5080.68i	0.180748	+	0.313066i	0.942136	−	0.335232i	$-0.108815\pi$
$641$	2933.33	+	5080.68i	0.180748	+	0.313066i	−0.761387	+	0.648297i	$0.775481\pi$
$642$	2213.57	+	16404.4i	0.136079	+	1.00846i
$643$		−	7634.50i		−	0.468235i	−0.972208	−	0.234118i	$-0.924780\pi$
$643$		−	7634.50i		−	0.468235i	0.972208	−	0.234118i	$-0.0752200\pi$
$644$	7637.69	−	24902.4i	0.467340	−	1.52374i
$645$		−	8198.75i		−	0.500504i
$646$	131.270	−	17.7132i	0.00799496	−	0.00107882i
$647$	6255.81	+	10835.4i	0.380126	+	0.658397i	0.991080	−	0.133269i	$-0.0425474\pi$
$647$	6255.81	+	10835.4i	0.380126	+	0.658397i	−0.610954	+	0.791666i	$0.709214\pi$
$648$	1464.81	+	1101.62i	0.0888012	+	0.0667834i
$649$	−42508.0	−	24542.0i	−2.57101	−	1.48437i
$650$	−563.497	−	729.475i	−0.0340033	−	0.0440190i
$651$	3187.36	−	5018.43i	0.191893	−	0.302132i
$652$	−4724.70	+	18099.4i	−0.283794	+	1.08716i
$653$	−15946.7	−	9206.83i	−0.955655	−	0.551748i	−0.0608221	−	0.998149i	$-0.519372\pi$
$653$	−15946.7	−	9206.83i	−0.955655	−	0.551748i	−0.894833	+	0.446401i	$0.852706\pi$
$654$	423.808	−	1032.58i	0.0253398	−	0.0617385i
$655$	−23373.0	+	13494.4i	−1.39429	+	0.804992i
$656$	10368.3	+	17434.7i	0.617096	+	1.03767i
$657$			4104.86i			0.243753i
$658$	16573.2	+	7635.45i	0.981902	+	0.452372i
$659$	−17590.5			−1.03980			−0.519900	−	0.854227i	$-0.674031\pi$
$659$	−17590.5			−1.03980			−0.519900	+	0.854227i	$0.674031\pi$
$660$	14712.3	−	14903.5i	0.867691	−	0.878967i
$661$	−11474.0	−	19873.5i	−0.675167	−	1.16942i	−0.976420	−	0.215880i	$-0.930738\pi$
$661$	−11474.0	−	19873.5i	−0.675167	−	1.16942i	0.301253	−	0.953544i	$-0.402595\pi$
$662$	10583.5	−	25786.0i	0.621360	−	1.51390i
$663$	190.650	−	330.216i	0.0111678	−	0.0193432i
$664$	−4818.22	−	11320.9i	−0.281601	−	0.661650i
$665$	−170.236	−	325.922i	−0.00992705	−	0.0190056i
$666$	5525.11	−	4267.97i	0.321462	−	0.248319i
$667$	181.013	−	313.524i	0.0105080	−	0.0182004i
$668$	32771.8	−	9008.34i	1.89817	−	0.521771i
$669$	4090.59	−	2361.70i	0.236399	−	0.136485i
$670$	4389.51	−	592.310i	0.253107	−	0.0341536i
$671$	−8047.70			−0.463007
$672$	−9188.32	−	4090.18i	−0.527451	−	0.234795i
$673$	−7222.11			−0.413658			−0.206829	−	0.978377i	$-0.566314\pi$
$673$	−7222.11			−0.413658			−0.206829	+	0.978377i	$0.566314\pi$
$674$	−7058.73	+	952.488i	−0.403401	+	0.0544339i
$675$	−2065.62	+	1192.58i	−0.117786	+	0.0680038i
$676$	−16842.4	+	4629.65i	−0.958262	+	0.263407i
$677$	−3598.04	+	6231.99i	−0.204260	+	0.353789i	−0.949897	−	0.312564i	$-0.898812\pi$
$677$	−3598.04	+	6231.99i	−0.204260	+	0.353789i	0.745637	+	0.666353i	$0.232145\pi$
$678$	−8044.49	+	6214.11i	−0.455674	+	0.351993i
$679$	−19084.1	−	806.847i	−1.07862	−	0.0456023i
$680$	4459.13	+	10477.2i	0.251470	+	0.590854i
$681$	−7150.17	+	12384.5i	−0.402342	+	0.696877i
$682$	6865.07	−	16726.2i	0.385450	−	0.939121i
$683$	−10062.8	−	17429.2i	−0.563751	−	0.976445i	−0.997165	−	0.0752497i	$-0.976025\pi$
$683$	−10062.8	−	17429.2i	−0.563751	−	0.976445i	0.433414	−	0.901195i	$-0.357309\pi$
$684$	68.7560	−	69.6495i	0.00384350	−	0.00389344i
$685$	−37847.4			−2.11106
$686$	132.373	+	17967.0i	0.00736739	+	0.999973i
$687$		−	1337.21i		−	0.0742616i
$688$	−10292.4	+	6120.83i	−0.570338	+	0.339178i
$689$	960.080	−	554.303i	0.0530858	−	0.0306491i
$690$	−8273.09	+	20156.8i	−0.456451	+	1.11211i
$691$	−11399.1	−	6581.29i	−0.627559	−	0.362322i	0.152247	−	0.988342i	$-0.451349\pi$
$691$	−11399.1	−	6581.29i	−0.627559	−	0.362322i	−0.779806	+	0.626021i	$0.784682\pi$
$692$	−4489.20	+	17197.3i	−0.246610	+	0.944714i
$693$	420.623	−	9948.85i	0.0230565	−	0.545347i
$694$	20048.8	+	25954.2i	1.09660	+	1.41961i
$695$	38205.5	+	22057.9i	2.08520	+	1.20389i
$696$	−111.720	−	84.0197i	−0.00608440	−	0.00457580i
$697$	−5459.87	−	9456.77i	−0.296711	−	0.513918i
$698$	5082.15	−	685.773i	0.275590	−	0.0371875i
$699$		−	1941.74i		−	0.105069i
$700$	9580.32	−	8917.85i	0.517289	−	0.481519i
$701$			18196.2i			0.980402i	0.871609	+	0.490201i	$0.163077\pi$
$701$			18196.2i			0.980402i	−0.871609	+	0.490201i	$0.836923\pi$
$702$	−37.6745	−	279.199i	−0.00202554	−	0.0150109i
$703$	−186.402	−	322.858i	−0.0100004	−	0.0173212i
$704$	−29692.8	−	7342.92i	−1.58962	−	0.393106i
$705$	−13219.0	−	7632.01i	−0.706181	−	0.407714i
$706$	−5385.17	+	4159.87i	−0.287073	+	0.221755i
$707$	17227.7	−	8998.42i	0.916429	−	0.478671i
$708$	4980.53	−	19079.4i	0.264378	−	1.01278i
$709$	16885.4	+	9748.77i	0.894419	+	0.516393i	0.875385	−	0.483426i	$-0.160608\pi$
$709$	16885.4	+	9748.77i	0.894419	+	0.516393i	0.0190336	+	0.999819i	$0.493941\pi$
$710$	17237.0	+	7074.69i	0.911115	+	0.373955i
$711$	9350.85	−	5398.72i	0.493227	−	0.284765i
$712$	28230.3	+	3438.83i	1.48592	+	0.181005i
$713$			18811.1i			0.988054i
$714$	4917.45	+	2265.52i	0.257746	+	0.118746i
$715$	−3219.07			−0.168372
$716$	16160.9	+	15953.6i	0.843523	+	0.832702i
$717$	−2221.97	−	3848.56i	−0.115733	−	0.200456i
$718$	−20923.3	−	8587.71i	−1.08754	−	0.446366i
$719$	7262.67	−	12579.3i	0.376707	−	0.652475i	−0.613874	−	0.789404i	$-0.710390\pi$
$719$	7262.67	−	12579.3i	0.376707	−	0.652475i	0.990581	+	0.136929i	$0.0437232\pi$
$720$	7339.70	+	4112.15i	0.379909	+	0.212848i
$721$	−7738.75	−	4915.13i	−0.399731	−	0.253882i
$722$	11856.5	+	15348.9i	0.611154	+	0.791171i
$723$	−5139.11	+	8901.20i	−0.264351	+	0.457869i
$724$	−4989.00	+	1371.38i	−0.256098	+	0.0703963i
$725$	157.543	−	90.9577i	0.00807036	−	0.00465942i
$726$	−2539.42	−	18819.2i	−0.129816	−	0.962046i
$727$	1.46093			7.45292e−5			3.72646e−5	−	1.00000i	$-0.499988\pi$
$727$	1.46093			7.45292e−5			3.72646e−5		1.00000i	$0.499988\pi$
$728$	544.798	+	1446.81i	0.0277356	+	0.0736572i
$729$	−729.000			−0.0370370
$730$	2519.71	+	18673.2i	0.127752	+	0.946746i
$731$	5582.70	−	3223.17i	0.282467	−	0.163083i
$732$	−856.917	−	3117.41i	−0.0432685	−	0.157408i
$733$	−2012.81	+	3486.29i	−0.101426	+	0.175674i	−0.912272	−	0.409584i	$-0.865674\pi$
$733$	−2012.81	+	3486.29i	−0.101426	+	0.175674i	0.810847	+	0.585259i	$0.199007\pi$
$734$	2134.15	+	2762.76i	0.107320	+	0.138931i
$735$	1268.60	−	14976.1i	0.0636641	−	0.751567i
$736$	31480.3	−	4662.49i	1.57660	−	0.233507i
$737$	3202.54	−	5546.96i	0.160064	−	0.277239i
$738$	−7463.97	−	3063.49i	−0.372293	−	0.152803i
$739$	4955.72	+	8583.56i	0.246684	+	0.427269i	0.962604	−	0.270914i	$-0.0873258\pi$
$739$	4955.72	+	8583.56i	0.246684	+	0.427269i	−0.715920	+	0.698182i	$0.753992\pi$
$740$	22514.1	−	22806.7i	1.11843	−	1.13296i
$741$	−15.0439			−0.000745817
$742$	9088.26	+	12852.9i	0.449651	+	0.635911i
$743$		−	5753.42i		−	0.284081i	−0.989861	−	0.142041i	$-0.954634\pi$
$743$		−	5753.42i		−	0.284081i	0.989861	−	0.142041i	$-0.0453664\pi$
$744$	7210.19	+	878.297i	0.355294	+	0.0432795i
$745$	8658.94	−	4999.24i	0.425824	−	0.245850i
$746$	33312.7	+	13672.8i	1.63494	+	0.671039i
$747$	4238.08	+	2446.86i	0.207581	+	0.119847i
$748$	15932.0	+	4158.91i	0.778784	+	0.203295i
$749$	30497.9	+	19370.2i	1.48781	+	0.944956i
$750$	3595.73	−	2777.59i	0.175063	−	0.135231i
$751$	−18819.5	−	10865.4i	−0.914426	−	0.527944i	−0.0325731	−	0.999469i	$-0.510370\pi$
$751$	−18819.5	−	10865.4i	−0.914426	−	0.527944i	−0.881852	+	0.471526i	$0.843704\pi$
$752$	287.843	+	22292.3i	0.0139582	+	1.08101i
$753$	1476.61	+	2557.57i	0.0714619	+	0.123776i
$754$	2.87341	+	21.2943i	0.000138784	+	0.00102851i
$755$		−	45222.1i		−	2.17987i
$756$	3898.65	−	896.415i	0.187556	−	0.0431247i
$757$			6876.55i			0.330162i	0.986280	+	0.165081i	$0.0527885\pi$
$757$			6876.55i			0.330162i	−0.986280	+	0.165081i	$0.947212\pi$
$758$	−31120.2	+	4199.29i	−1.49121	+	0.201220i
$759$	15753.9	+	27286.6i	0.753400	+	1.30493i
$760$	270.020	−	359.043i	0.0128877	−	0.0171367i
$761$	17277.0	+	9974.87i	0.822983	+	0.475150i	0.851444	−	0.524445i	$-0.175727\pi$
$761$	17277.0	+	9974.87i	0.822983	+	0.475150i	−0.0284609	+	0.999595i	$0.509061\pi$
$762$	5600.11	+	7249.63i	0.266234	+	0.344654i
$763$	−1127.89	−	2159.37i	−0.0535153	−	0.102457i
$764$	−22930.3	−	5985.78i	−1.08585	−	0.283453i
$765$	−3922.22	−	2264.50i	−0.185370	−	0.107024i
$766$	−2427.36	+	5914.09i	−0.114496	+	0.278962i
$767$	−2624.96	+	1515.52i	−0.123575	+	0.0713459i
$768$	−317.278	−	12283.9i	−0.0149073	−	0.577158i
$769$			22540.2i			1.05698i	0.848938	+	0.528492i	$0.177242\pi$
$769$			22540.2i			1.05698i	−0.848938	+	0.528492i	$0.822758\pi$
$770$	−4193.54	−	45515.9i	−0.196266	−	2.13023i
$771$	−16099.5			−0.752023
$772$	17738.1	+	17510.5i	0.826951	+	0.816342i
$773$	4451.60	+	7710.40i	0.207132	+	0.358763i	0.950810	−	0.309775i	$-0.100254\pi$
$773$	4451.60	+	7710.40i	0.207132	+	0.358763i	−0.743678	+	0.668538i	$0.766920\pi$
$774$	1808.50	−	4406.27i	0.0839859	−	0.204626i
$775$	−4726.22	+	8186.06i	−0.219059	+	0.379422i
$776$	−9139.09	−	21473.2i	−0.422776	−	0.993354i
$777$	643.675	−	15224.6i	0.0297191	−	0.702935i
$778$	16855.2	−	13020.1i	0.776720	−	0.599991i
$779$	−215.414	+	373.108i	−0.00990758	+	0.0171604i
$780$	−342.765	−	1246.96i	−0.0157346	−	0.0572415i
$781$	23334.0	−	13471.9i	1.06908	−	0.617236i
$782$	−16977.6	+	2290.92i	−0.776365	+	0.104761i
$783$	55.6004			0.00253767
$784$	−19747.4	+	9587.95i	−0.899574	+	0.436769i
$785$	14237.9			0.647352
$786$	−15538.0	+	2096.67i	−0.705118	+	0.0951471i
$787$	−16667.3	+	9622.88i	−0.754925	+	0.435856i	−0.827471	−	0.561509i	$-0.810221\pi$
$787$	−16667.3	+	9622.88i	−0.754925	+	0.435856i	0.0725459	+	0.997365i	$0.476888\pi$
$788$	−457.390	−	1663.96i	−0.0206775	−	0.0752235i
$789$	−9634.03	+	16686.6i	−0.434703	+	0.752927i
$790$	39223.5	−	30298.9i	1.76647	−	1.36454i
$791$	−937.182	+	22166.9i	−0.0421269	+	0.996413i
$792$	11194.3	−	4764.36i	0.502239	−	0.213755i
$793$	−248.481	+	430.382i	−0.0111272	+	0.0192728i
$794$	4755.33	−	11586.0i	0.212544	−	0.517849i
$795$	−6583.86	−	11403.6i	−0.293718	−	0.508734i
$796$	13758.2	+	13581.7i	0.612620	+	0.604761i
$797$	8439.84			0.375100			0.187550	−	0.982255i	$-0.439945\pi$
$797$	8439.84			0.375100			0.187550	+	0.982255i	$0.439945\pi$
$798$	−19.5979	−	212.712i	−0.000869373	−	0.00943601i
$799$		−	12001.5i		−	0.531392i
$800$	14870.7	+	5880.33i	0.657200	+	0.259876i
$801$	−9796.09	+	5655.77i	−0.432120	+	0.249484i
$802$	−7521.86	+	18326.5i	−0.331180	+	0.806896i
$803$	23597.0	+	13623.7i	1.03701	+	0.598719i
$804$	2489.72	+	649.920i	0.109211	+	0.0285086i
$805$	22017.3	+	42152.7i	0.963984	+	1.84557i
$806$	−682.535	−	883.577i	−0.0298279	−	0.0386138i
$807$	14156.4	+	8173.21i	0.617509	+	0.356519i
$808$	18978.4	+	14272.8i	0.826311	+	0.621431i
$809$	303.899	+	526.369i	0.0132071	+	0.0228754i	0.872553	−	0.488519i	$-0.162463\pi$
$809$	303.899	+	526.369i	0.0132071	+	0.0228754i	−0.859346	+	0.511394i	$0.829129\pi$
$810$	−3316.25	+	447.487i	−0.143853	+	0.0194112i
$811$			11135.6i			0.482151i	0.970506	+	0.241076i	$0.0775002\pi$
$811$			11135.6i			0.482151i	−0.970506	+	0.241076i	$0.922500\pi$
$812$	−297.347	+	68.3691i	−0.0128508	+	0.00295478i
$813$		−	15869.8i		−	0.684596i
$814$	−6197.23	−	45926.6i	−0.266846	−	1.97755i
$815$	−17076.3	−	29577.1i	−0.733936	−	1.27121i
$816$	85.4061	+	6614.37i	0.00366399	+	0.283761i
$817$	−220.260	−	127.167i	−0.00943198	−	0.00544556i
$818$	−19516.5	+	15075.9i	−0.834205	+	0.644397i
$819$	−519.067	−	329.676i	−0.0221461	−	0.0140657i
$820$	−35834.4	−	9354.27i	−1.52609	−	0.398372i
$821$	15564.9	+	8986.41i	0.661656	+	0.382007i	0.792908	−	0.609342i	$-0.208566\pi$
$821$	15564.9	+	8986.41i	0.661656	+	0.382007i	−0.131252	+	0.991349i	$0.541900\pi$
$822$	−20340.4	−	8348.46i	−0.863082	−	0.354241i
$823$	13440.2	−	7759.71i	0.569255	−	0.328659i	−0.187597	−	0.982246i	$-0.560070\pi$
$823$	13440.2	−	7759.71i	0.569255	−	0.328659i	0.756852	+	0.653587i	$0.226737\pi$
$824$	1354.39	−	11118.6i	0.0572603	−	0.470067i
$825$			15832.4i			0.668138i
$826$	−24848.3	−	35141.3i	−1.04671	−	1.48029i
$827$	−21438.2			−0.901426			−0.450713	−	0.892669i	$-0.648830\pi$
$827$	−21438.2			−0.901426			−0.450713	+	0.892669i	$0.648830\pi$
$828$	−8892.45	+	9008.01i	−0.373230	+	0.378080i
$829$	7490.88	+	12974.6i	0.313835	+	0.543578i	0.979189	−	0.202950i	$-0.0650529\pi$
$829$	7490.88	+	12974.6i	0.313835	+	0.543578i	−0.665354	+	0.746528i	$0.731720\pi$
$830$	20781.2	+	8529.35i	0.869066	+	0.356697i
$831$	−1272.89	+	2204.70i	−0.0531359	+	0.0920341i
$832$	−1309.49	+	1361.22i	−0.0545654	+	0.0567209i
$833$	10696.3	−	5023.73i	0.444902	−	0.208958i
$834$	15667.3	+	20282.1i	0.650496	+	0.842100i
$835$	−31026.6	+	53739.6i	−1.28589	+	2.22723i
$836$	−172.188	−	626.410i	−0.00712350	−	0.0259149i
$837$	−2501.98	+	1444.52i	−0.103323	+	0.0596533i
$838$	−2667.58	−	19769.0i	−0.109964	−	0.814927i
$839$	−12563.7			−0.516980			−0.258490	−	0.966014i	$-0.583225\pi$
$839$	−12563.7			−0.516980			−0.258490	+	0.966014i	$0.583225\pi$
$840$	17184.9	−	6470.96i	0.705873	−	0.265797i
$841$	24384.8			0.999826
$842$	2621.78	+	19429.5i	0.107307	+	0.795233i
$843$	6731.23	−	3886.28i	0.275013	−	0.158779i
$844$	−36336.2	+	9988.11i	−1.48192	+	0.407352i
$845$	15945.5	−	27618.3i	0.649160	−	1.12438i
$846$	−5420.85	−	7017.57i	−0.220299	−	0.285188i
$847$	−34987.3	−	22221.5i	−1.41934	−	0.901466i
$848$	−9400.36	+	16778.5i	−0.380672	+	0.679454i
$849$	3043.69	−	5271.82i	0.123038	−	0.213108i
$850$	−7963.73	−	3268.61i	−0.321357	−	0.131897i
$851$	24108.1	+	41756.4i	0.971109	+	1.68201i
$852$	7703.16	+	7604.34i	0.309749	+	0.305775i
$853$	19238.5			0.772231			0.386116	−	0.922450i	$-0.373817\pi$
$853$	19238.5			0.772231			0.386116	+	0.922450i	$0.373817\pi$
$854$	−6409.08	−	2952.73i	−0.256808	−	0.118314i
$855$			178.687i			0.00714733i
$856$	−5337.57	+	43817.7i	−0.213124	+	1.74960i
$857$	6425.02	−	3709.48i	0.256096	−	0.147857i	−0.366456	−	0.930435i	$-0.619429\pi$
$857$	6425.02	−	3709.48i	0.256096	−	0.147857i	0.622552	+	0.782578i	$0.286096\pi$
$858$	−1730.03	−	710.068i	−0.0688371	−	0.0282533i
$859$	6056.93	+	3496.97i	0.240582	+	0.138900i	0.615444	−	0.788181i	$-0.288977\pi$
$859$	6056.93	+	3496.97i	0.240582	+	0.138900i	−0.374862	+	0.927080i	$0.622310\pi$
$860$	5522.19	−	21154.4i	0.218960	−	0.838791i
$861$	−15609.0	+	8152.90i	−0.617830	+	0.322706i
$862$	5947.95	−	4594.60i	0.235021	−	0.181546i
$863$	2819.97	+	1628.11i	0.111232	+	0.0642196i	0.554584	−	0.832128i	$-0.312878\pi$
$863$	2819.97	+	1628.11i	0.111232	+	0.0642196i	−0.443352	+	0.896348i	$0.646211\pi$
$864$	3037.53	+	3829.01i	0.119605	+	0.150770i
$865$	−16225.2	−	28102.8i	−0.637772	−	1.10465i
$866$	−870.684	−	6452.48i	−0.0341652	−	0.253192i
$867$			11178.0i			0.437862i
$868$	11604.2	−	10801.7i	0.453769	−	0.422391i
$869$		−	71671.9i		−	2.79782i
$870$	252.929	−	34.1296i	0.00985641	−	0.00133000i
$871$	−197.764	−	342.537i	−0.00769342	−	0.0133254i
$872$	1789.00	−	2378.81i	0.0694759	−	0.0923815i
$873$	8038.69	+	4641.14i	0.311648	+	0.179930i
$874$	413.194	+	534.901i	0.0159914	+	0.0207017i
$875$	418.902	−	9908.16i	0.0161846	−	0.382808i
$876$	−2764.79	+	10591.4i	−0.106636	+	0.408503i
$877$	−18211.8	−	10514.6i	−0.701218	−	0.404848i	0.106583	−	0.994304i	$-0.466009\pi$
$877$	−18211.8	−	10514.6i	−0.701218	−	0.404848i	−0.807801	+	0.589455i	$0.799342\pi$
$878$	−11418.5	+	27820.4i	−0.438902	+	1.06935i
$879$	24137.4	−	13935.8i	0.926206	−	0.534745i
$880$	47998.9	−	28544.8i	1.83868	−	1.09346i
$881$			12959.5i			0.495593i	0.968812	+	0.247796i	$0.0797064\pi$
$881$			12959.5i			0.495593i	−0.968812	+	0.247796i	$0.920294\pi$
$882$	3985.25	−	7768.81i	0.152143	−	0.296587i
$883$	−31770.3			−1.21082			−0.605411	−	0.795913i	$-0.706991\pi$
$883$	−31770.3			−1.21082			−0.605411	+	0.795913i	$0.706991\pi$
$884$	714.331	−	723.614i	0.0271782	−	0.0275314i
$885$	18001.0	+	31178.6i	0.683724	+	1.18424i
$886$	1764.42	−	4298.88i	0.0669038	−	0.163006i
$887$	10095.1	−	17485.3i	0.382143	−	0.661891i	−0.609225	−	0.792997i	$-0.708520\pi$
$887$	10095.1	−	17485.3i	0.382143	−	0.661891i	0.991368	+	0.131106i	$0.0418528\pi$
$888$	17130.6	−	7290.85i	0.647370	−	0.275524i
$889$	19976.6	+	844.581i	0.753648	+	0.0318632i
$890$	−41091.1	+	31741.6i	−1.54761	+	1.19548i
$891$	−2419.50	+	4190.70i	−0.0909724	+	0.157569i
$892$	12145.3	−	3338.49i	0.455889	−	0.125315i
$893$	−410.069	+	236.754i	−0.0153667	+	0.00887196i
$894$	5756.34	−	776.748i	0.215348	−	0.0290585i
$895$	−41461.2			−1.54849
$896$	−20952.8	−	16742.2i	−0.781234	−	0.624239i
$897$	1945.68			0.0724239
$898$	17946.3	−	2421.64i	0.666901	−	0.0899902i
$899$	190.824	−	110.172i	0.00707936	−	0.00408727i
$900$	−6132.96	+	1685.83i	−0.227147	+	0.0624382i
$901$	5176.63	−	8966.18i	0.191408	−	0.331528i
$902$	−42383.1	+	32739.6i	−1.56453	+	1.20855i
$903$	−4812.98	−	9214.58i	−0.177371	−	0.339581i
$904$	−24941.9	+	10615.4i	−0.917649	+	0.390556i
$905$	4723.31	−	8181.02i	0.173490	−	0.300493i
$906$	9975.18	−	24303.8i	0.365787	−	0.891214i
$907$	−11196.6	−	19393.1i	−0.409897	−	0.709962i	0.584981	−	0.811047i	$-0.301102\pi$
$907$	−11196.6	−	19393.1i	−0.409897	−	0.709962i	−0.994878	+	0.101085i	$0.967769\pi$
$908$	−26790.3	+	27138.5i	−0.979150	+	0.991875i
$909$	−9445.10			−0.344636
$910$	−2563.62	−	1181.09i	−0.0933882	−	0.0430249i
$911$		−	37754.2i		−	1.37306i	−0.727104	−	0.686528i	$-0.759134\pi$
$911$		−	37754.2i		−	1.37306i	0.727104	−	0.686528i	$-0.240866\pi$
$912$	224.316	−	133.400i	0.00814458	−	0.00484355i
$913$	28131.8	−	16241.9i	1.01974	−	0.588750i
$914$	1679.81	−	4092.74i	0.0607913	−	0.148114i
$915$	5111.97	+	2951.40i	0.184696	+	0.106634i
$916$	900.665	−	3450.27i	0.0324878	−	0.124454i
$917$	−18347.2	+	28887.2i	−0.660717	+	1.04028i
$918$	−1608.42	−	2082.19i	−0.0578277	−	0.0748609i
$919$	37420.7	+	21604.8i	1.34319	+	0.775493i	0.987275	−	0.159024i	$-0.0508348\pi$
$919$	37420.7	+	21604.8i	1.34319	+	0.775493i	0.355918	+	0.934517i	$0.384168\pi$
$920$	−34922.7	+	46436.3i	−1.25149	+	1.66409i
$921$	−3321.02	−	5752.18i	−0.118818	−	0.205799i
$922$	−36343.7	+	4904.14i	−1.29817	+	0.175173i
$923$		−	1663.83i		−	0.0593345i
$924$	7786.25	−	25386.8i	0.277217	−	0.903856i
$925$			24228.2i			0.861209i
$926$	725.849	+	5379.14i	0.0257591	+	0.190896i
$927$	2227.54	+	3858.22i	0.0789235	+	0.136700i
$928$	−231.670	−	292.036i	−0.00819499	−	0.0103303i
$929$	10561.3	+	6097.59i	0.372988	+	0.215345i	0.674763	−	0.738034i	$-0.264246\pi$
$929$	10561.3	+	6097.59i	0.372988	+	0.215345i	−0.301775	+	0.953379i	$0.597579\pi$
$930$	−10494.9	+	8106.98i	−0.370044	+	0.285848i
$931$	−382.658	−	266.369i	−0.0134706	−	0.00937690i
$932$	1307.84	−	5010.08i	0.0459654	−	0.176085i
$933$	−23007.4	−	13283.4i	−0.807320	−	0.466107i
$934$	−10222.0	−	4195.48i	−0.358109	−	0.146981i
$935$	−26035.2	+	15031.4i	−0.910632	+	0.525754i
$936$	90.8441	−	745.765i	0.00317236	−	0.0260428i
$937$		−	30925.8i		−	1.07823i	−0.842232	−	0.539116i	$-0.818758\pi$
$937$		−	30925.8i		−	1.07823i	0.842232	−	0.539116i	$-0.181242\pi$
$938$	4585.66	−	3242.50i	0.159624	−	0.112869i
$939$	570.831			0.0198385
$940$	−28967.3	−	28595.7i	−1.00512	−	0.992222i
$941$	−10353.7	−	17933.2i	−0.358684	−	0.621259i	0.629057	−	0.777359i	$-0.283441\pi$
$941$	−10353.7	−	17933.2i	−0.358684	−	0.621259i	−0.987741	+	0.156100i	$0.950108\pi$
$942$	7651.89	+	3140.62i	0.264663	+	0.108627i
$943$	27860.2	−	48255.4i	0.962094	−	1.66640i
$944$	25701.6	−	45874.2i	0.886138	−	1.58165i
$945$	−3915.80	+	6165.34i	−0.134795	+	0.212231i
$946$	−19327.4	−	25020.4i	−0.664260	−	0.859918i
$947$	11086.5	−	19202.4i	0.380425	−	0.658916i	−0.610698	−	0.791864i	$-0.709111\pi$
$947$	11086.5	−	19202.4i	0.380425	−	0.658916i	0.991123	+	0.132948i	$0.0424443\pi$
$948$	27763.4	−	7631.61i	0.951173	−	0.261459i
$949$	1457.17	−	841.295i	0.0498437	−	0.0287772i
$950$	45.4182	+	336.587i	0.00155112	+	0.0114951i
$951$	1309.91			0.0446653
$952$	11162.1	+	9157.60i	0.380006	+	0.311764i
$953$	44804.6			1.52294			0.761471	−	0.648199i	$-0.224477\pi$
$953$	44804.6			1.52294			0.761471	+	0.648199i	$0.224477\pi$
$954$	−1022.95	−	7580.94i	−0.0347163	−	0.257277i
$955$	37471.5	−	21634.2i	1.26969	−	0.733053i
$956$	−3140.97	−	11426.7i	−0.106262	−	0.386574i
$957$	184.534	−	319.622i	0.00623316	−	0.0107962i
$958$	34541.6	+	44715.9i	1.16491	+	1.50804i
$959$	−42536.7	+	22217.9i	−1.43231	+	0.748125i
$960$	16168.2	+	15553.8i	0.543570	+	0.522912i
$961$	9170.86	−	15884.4i	0.307840	−	0.533195i
$962$	−2647.45	−	1086.61i	−0.0887289	−	0.0364176i
$963$	−8778.60	−	15205.0i	−0.293755	−	0.508799i
$964$	−19255.3	+	19505.5i	−0.643331	+	0.651691i
$965$	−45507.3			−1.51806
$966$	2534.67	+	27510.8i	0.0844221	+	0.916301i
$967$		−	9889.71i		−	0.328885i	−0.986387	−	0.164442i	$-0.947418\pi$
$967$		−	9889.71i		−	0.328885i	0.986387	−	0.164442i	$-0.0525825\pi$
$968$	6123.28	−	50267.7i	0.203316	−	1.66908i
$969$	−121.672	+	70.2473i	−0.00403371	+	0.00232886i
$970$	39417.2	+	16178.3i	1.30475	+	0.535519i
$971$	17583.8	+	10152.0i	0.581144	+	0.335524i	0.761588	−	0.648062i	$-0.224420\pi$
$971$	17583.8	+	10152.0i	0.581144	+	0.335524i	−0.180444	+	0.983585i	$0.557753\pi$
$972$	−1880.97	−	491.011i	−0.0620701	−	0.0162029i
$973$	55888.0	+	2362.86i	1.84140	+	0.0778519i
$974$	−16469.5	+	12722.2i	−0.541804	+	0.418527i
$975$	846.701	+	488.843i	0.0278114	+	0.0160569i
$976$	−111.313	−	8620.73i	−0.00365065	−	0.282728i
$977$	6912.50	+	11972.8i	0.226357	+	0.392061i	0.956726	−	0.290992i	$-0.0939852\pi$
$977$	6912.50	+	11972.8i	0.226357	+	0.392061i	−0.730369	+	0.683053i	$0.760652\pi$
$978$	−2653.20	−	19662.4i	−0.0867485	−	0.642878i
$979$			75084.6i			2.45119i
$980$	13360.3	−	37786.9i	0.435488	−	1.23169i
$981$			1183.87i			0.0385303i
$982$	−31770.1	+	4286.98i	−1.03241	+	0.139311i
$983$	3749.52	+	6494.36i	0.121659	+	0.210720i	0.920422	−	0.390926i	$-0.127845\pi$
$983$	3749.52	+	6494.36i	0.121659	+	0.210720i	−0.798763	+	0.601646i	$0.794512\pi$
$984$	−17195.2	−	12931.7i	−0.557076	−	0.418951i
$985$	2728.58	+	1575.35i	0.0882637	+	0.0509591i
$986$	122.673	+	158.807i	0.00396219	+	0.00512926i
$987$	−19337.1	−	817.546i	−0.623615	−	0.0263655i
$988$	−38.8162	−	10.1327i	−0.00124991	−	0.000326278i
$989$	28487.0	+	16447.0i	0.915910	+	0.528801i
$990$	−8434.01	+	20548.9i	−0.270758	+	0.659682i
$991$	−9141.90	+	5278.08i	−0.293039	+	0.169186i	−0.639312	−	0.768948i	$-0.720781\pi$
$991$	−9141.90	+	5278.08i	−0.293039	+	0.169186i	0.346272	+	0.938134i	$0.387447\pi$
$992$	18012.2	+	7122.55i	0.576500	+	0.227965i
$993$			29564.2i			0.944806i
$994$	23525.8	−	2167.51i	0.750696	−	0.0691643i
$995$	−35296.8			−1.12461
$996$	9287.05	+	9167.90i	0.295453	+	0.291663i
$997$	29838.4	+	51681.7i	0.947836	+	1.64170i	0.749971	+	0.661471i	$0.230068\pi$
$997$	29838.4	+	51681.7i	0.947836	+	1.64170i	0.197866	+	0.980229i	$0.436599\pi$
$998$	−7594.45	+	18503.3i	−0.240880	+	0.586887i
$999$	−3702.54	+	6412.99i	−0.117260	+	0.203101i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.4.t.a.19.3	✓	96
4.3	odd	2		672.4.bb.a.271.19		96
7.3	odd	6	inner	168.4.t.a.115.29	yes	96
8.3	odd	2	inner	168.4.t.a.19.29	yes	96
8.5	even	2		672.4.bb.a.271.20		96
28.3	even	6		672.4.bb.a.367.20		96
56.3	even	6	inner	168.4.t.a.115.3	yes	96
56.45	odd	6		672.4.bb.a.367.19		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.t.a.19.3	✓	96	1.1	even	1	trivial
168.4.t.a.19.29	yes	96	8.3	odd	2	inner
168.4.t.a.115.3	yes	96	56.3	even	6	inner
168.4.t.a.115.29	yes	96	7.3	odd	6	inner
672.4.bb.a.271.19		96	4.3	odd	2
672.4.bb.a.271.20		96	8.5	even	2
672.4.bb.a.367.19		96	56.45	odd	6
672.4.bb.a.367.20		96	28.3	even	6

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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	168.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.80302 + 0.378234i) q^{2} +(2.59808 - 1.50000i) q^{3} +(7.71388 - 2.12040i) q^{4} +(-7.30307 + 12.6493i) q^{5} +(-6.71512 + 5.18721i) q^{6} +(-0.782311 + 18.5037i) q^{7} +(-20.8202 + 8.86116i) q^{8} +(4.50000 - 7.79423i) q^{9} +(15.6863 - 38.2185i) q^{10} +(-29.8704 - 51.7370i) q^{11} +(16.8607 - 17.0798i) q^{12} -3.68912 q^{13} +(-4.80590 - 52.1623i) q^{14} +43.8184i q^{15} +(55.0078 - 32.7129i) q^{16} +(-29.8369 + 17.2263i) q^{17} +(-9.66557 + 23.5495i) q^{18} +(1.17719 + 0.679649i) q^{19} +(-29.5135 + 113.061i) q^{20} +(25.7231 + 49.2476i) q^{21} +(103.296 + 133.722i) q^{22} +(-152.250 - 87.9014i) q^{23} +(-40.8007 + 54.2522i) q^{24} +(-44.1698 - 76.5043i) q^{25} +(10.3407 - 1.39535i) q^{26} -27.0000i q^{27} +(33.2006 + 144.394i) q^{28} +2.05927i q^{29} +(-16.5736 - 122.824i) q^{30} +(-53.5006 - 92.6658i) q^{31} +(-141.815 + 112.501i) q^{32} +(-155.211 - 89.6112i) q^{33} +(77.1180 - 59.5712i) q^{34} +(-228.346 - 145.030i) q^{35} +(18.1856 - 69.6655i) q^{36} +(-237.518 - 137.131i) q^{37} +(-3.55675 - 1.45982i) q^{38} +(-9.58462 + 5.53369i) q^{39} +(39.9638 - 328.074i) q^{40} +316.949i q^{41} +(-90.7295 - 128.313i) q^{42} -187.107 q^{43} +(-340.120 - 335.756i) q^{44} +(65.7277 + 113.844i) q^{45} +(460.007 + 188.804i) q^{46} +(-174.173 + 301.677i) q^{47} +(93.8452 - 167.502i) q^{48} +(-341.776 - 28.9513i) q^{49} +(152.745 + 197.737i) q^{50} +(-51.6790 + 89.5107i) q^{51} +(-28.4575 + 7.82240i) q^{52} +(-260.246 + 150.253i) q^{53} +(10.2123 + 75.6816i) q^{54} +872.583 q^{55} +(-147.677 - 392.183i) q^{56} +4.07790 q^{57} +(-0.778887 - 5.77219i) q^{58} +(711.540 - 410.808i) q^{59} +(92.9124 + 338.010i) q^{60} +(67.3551 - 116.662i) q^{61} +(185.013 + 239.509i) q^{62} +(140.702 + 89.3643i) q^{63} +(354.960 - 368.982i) q^{64} +(26.9419 - 46.6648i) q^{65} +(468.954 + 192.476i) q^{66} +(53.6072 + 92.8504i) q^{67} +(-193.632 + 196.148i) q^{68} -527.409 q^{69} +(694.914 + 320.154i) q^{70} +451.011i q^{71} +(-24.6249 + 202.152i) q^{72} +(-394.990 + 228.048i) q^{73} +(717.637 + 294.545i) q^{74} +(-229.513 - 132.509i) q^{75} +(10.5218 + 2.74663i) q^{76} +(980.696 - 512.239i) q^{77} +(24.7729 - 19.1363i) q^{78} +(1038.98 + 599.857i) q^{79} +(12.0692 + 934.716i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-119.881 - 888.415i) q^{82} +543.746i q^{83} +(302.849 + 325.347i) q^{84} -503.221i q^{85} +(524.466 - 70.7702i) q^{86} +(3.08891 + 5.35015i) q^{87} +(1080.36 + 812.488i) q^{88} +(-1088.45 - 628.419i) q^{89} +(-227.296 - 294.246i) q^{90} +(2.88604 - 68.2625i) q^{91} +(-1360.82 - 355.231i) q^{92} +(-277.997 - 160.502i) q^{93} +(374.108 - 911.486i) q^{94} +(-17.1942 + 9.92706i) q^{95} +(-199.695 + 505.009i) q^{96} +1031.36i q^{97} +(968.956 - 48.1199i) q^{98} -537.667 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 2 q^{2} - 10 q^{4} - 16 q^{8} + 432 q^{9} + 18 q^{10} + 40 q^{11} + 274 q^{14} - 26 q^{16} - 18 q^{18} + 4 q^{22} + 270 q^{24} - 1200 q^{25} + 750 q^{26} + 922 q^{28} + 168 q^{30} - 108 q^{32} + 456 q^{35}+ \cdots + 720 q^{99}+O(q^{100}) \) 96 * q + 2 * q^2 - 10 * q^4 - 16 * q^8 + 432 * q^9 + 18 * q^10 + 40 * q^11 + 274 * q^14 - 26 * q^16 - 18 * q^18 + 4 * q^22 + 270 * q^24 - 1200 * q^25 + 750 * q^26 + 922 * q^28 + 168 * q^30 - 108 * q^32 + 456 * q^35 - 180 * q^36 - 1494 * q^38 + 1170 * q^40 - 564 * q^42 - 1616 * q^43 + 264 * q^44 + 808 * q^46 - 360 * q^49 - 1036 * q^50 - 3564 * q^52 + 176 * q^56 - 336 * q^57 - 394 * q^58 + 4128 * q^59 + 822 * q^60 - 2644 * q^64 + 2052 * q^66 - 1440 * q^67 - 1392 * q^68 + 3234 * q^70 - 72 * q^72 - 648 * q^73 + 850 * q^74 + 1692 * q^78 - 1548 * q^80 - 3888 * q^81 + 4596 * q^82 + 3120 * q^84 - 2522 * q^86 - 1454 * q^88 - 104 * q^91 + 5600 * q^92 - 2052 * q^94 + 3870 * q^96 + 852 * q^98 + 720 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more