LMFDB - Embedded newform 153.3.j.a.86.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [153,3,Mod(86,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.86"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	153.j (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:	$4.16894804471$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			86.19
Character	$\chi$	$=$	153.86
Dual form			153.3.j.a.137.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.700836 - 0.404628i) q^{2} +(0.807723 - 2.88922i) q^{3} +(-1.67255 + 2.89695i) q^{4} +(-6.73682 - 3.88950i) q^{5} +(-0.602977 - 2.35170i) q^{6} +(-1.30137 - 2.25403i) q^{7} +5.94407i q^{8} +(-7.69517 - 4.66738i) q^{9} -6.29521 q^{10} +(-15.0999 + 8.71794i) q^{11} +(7.01895 + 7.17230i) q^{12} +(11.9586 - 20.7129i) q^{13} +(-1.82409 - 1.05314i) q^{14} +(-16.6791 + 16.3225i) q^{15} +(-4.28507 - 7.42196i) q^{16} +4.12311i q^{17} +(-7.28161 - 0.157387i) q^{18} +8.89419 q^{19} +(22.5354 - 13.0108i) q^{20} +(-7.56354 + 1.93930i) q^{21} +(-7.05505 + 12.2197i) q^{22} +(-14.5631 - 8.40799i) q^{23} +(17.1737 + 4.80116i) q^{24} +(17.7565 + 30.7551i) q^{25} -19.3552i q^{26} +(-19.7006 + 18.4631i) q^{27} +8.70641 q^{28} +(28.3321 - 16.3576i) q^{29} +(-5.08479 + 18.1882i) q^{30} +(16.5527 - 28.6701i) q^{31} +(-26.5971 - 15.3559i) q^{32} +(12.9915 + 50.6686i) q^{33} +(1.66832 + 2.88962i) q^{34} +20.2467i q^{35} +(26.3917 - 14.4860i) q^{36} -45.9261 q^{37} +(6.23337 - 3.59884i) q^{38} +(-50.1850 - 51.2814i) q^{39} +(23.1195 - 40.0441i) q^{40} +(-31.3907 - 18.1234i) q^{41} +(-4.51611 + 4.41955i) q^{42} +(14.4282 + 24.9905i) q^{43} -58.3248i q^{44} +(33.6872 + 61.3737i) q^{45} -13.6084 q^{46} +(55.0612 - 31.7896i) q^{47} +(-24.9048 + 6.38562i) q^{48} +(21.1129 - 36.5686i) q^{49} +(24.8888 + 14.3696i) q^{50} +(11.9126 + 3.33033i) q^{51} +(40.0028 + 69.2870i) q^{52} +48.8363i q^{53} +(-6.33625 + 20.9110i) q^{54} +135.634 q^{55} +(13.3981 - 7.73542i) q^{56} +(7.18404 - 25.6973i) q^{57} +(13.2375 - 22.9279i) q^{58} +(-25.6105 - 14.7862i) q^{59} +(-19.3887 - 75.6187i) q^{60} +(19.2375 + 33.3204i) q^{61} -26.7907i q^{62} +(-0.506188 + 23.4191i) q^{63} +9.42690 q^{64} +(-161.126 + 93.0262i) q^{65} +(29.6069 + 30.2537i) q^{66} +(-28.8502 + 49.9700i) q^{67} +(-11.9444 - 6.89611i) q^{68} +(-36.0555 + 35.2846i) q^{69} +(8.19238 + 14.1896i) q^{70} -16.3591i q^{71} +(27.7432 - 45.7406i) q^{72} -1.61860 q^{73} +(-32.1867 + 18.5830i) q^{74} +(103.201 - 26.4607i) q^{75} +(-14.8760 + 25.7660i) q^{76} +(39.3011 + 22.6905i) q^{77} +(-55.9213 - 15.6336i) q^{78} +(-8.91008 - 15.4327i) q^{79} +66.6672i q^{80} +(37.4312 + 71.8325i) q^{81} -29.3330 q^{82} +(-42.2194 + 24.3754i) q^{83} +(7.03237 - 25.1547i) q^{84} +(16.0368 - 27.7766i) q^{85} +(20.2237 + 11.6762i) q^{86} +(-24.3760 - 95.0700i) q^{87} +(-51.8201 - 89.7550i) q^{88} -137.254i q^{89} +(48.4427 + 29.3821i) q^{90} -62.2502 q^{91} +(48.7150 - 28.1256i) q^{92} +(-69.4641 - 70.9818i) q^{93} +(25.7259 - 44.5586i) q^{94} +(-59.9186 - 34.5940i) q^{95} +(-65.8496 + 64.4417i) q^{96} +(-80.2196 - 138.945i) q^{97} -34.1715i q^{98} +(156.886 + 3.39099i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 2 q^{3} + 64 q^{4} - 18 q^{5} - 22 q^{6} + 2 q^{7} - 6 q^{9} - 44 q^{12} - 10 q^{13} + 72 q^{14} - 36 q^{15} - 128 q^{16} - 38 q^{18} - 28 q^{19} - 18 q^{20} + 88 q^{21} + 144 q^{23} - 42 q^{24}+ \cdots + 58 q^{99}+O(q^{100}) $ 64 * q - 2 * q^3 + 64 * q^4 - 18 * q^5 - 22 * q^6 + 2 * q^7 - 6 * q^9 - 44 * q^12 - 10 * q^13 + 72 * q^14 - 36 * q^15 - 128 * q^16 - 38 * q^18 - 28 * q^19 - 18 * q^20 + 88 * q^21 + 144 * q^23 - 42 * q^24 + 154 * q^25 - 164 * q^27 + 32 * q^28 - 162 * q^29 - 220 * q^30 + 62 * q^31 + 126 * q^32 - 40 * q^33 + 12 * q^36 + 128 * q^37 - 36 * q^38 - 126 * q^39 - 144 * q^41 + 114 * q^42 - 64 * q^43 - 72 * q^45 - 48 * q^46 + 288 * q^47 - 10 * q^48 - 246 * q^49 + 62 * q^52 + 374 * q^54 - 84 * q^55 + 684 * q^56 + 232 * q^57 + 138 * q^58 - 432 * q^59 - 86 * q^60 + 110 * q^61 + 304 * q^63 - 260 * q^64 + 328 * q^66 - 148 * q^67 + 36 * q^69 - 216 * q^70 - 96 * q^72 - 196 * q^73 - 918 * q^74 + 314 * q^75 - 112 * q^76 - 504 * q^77 + 276 * q^78 + 86 * q^79 + 234 * q^81 - 396 * q^82 - 594 * q^83 + 592 * q^84 + 126 * q^86 + 462 * q^87 + 24 * q^88 - 338 * q^90 + 52 * q^91 - 36 * q^92 - 1006 * q^93 - 186 * q^94 - 144 * q^95 + 18 * q^96 + 140 * q^97 + 58 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.700836	−	0.404628i	0.350418	−	0.202314i	−0.314451	−	0.949274i	$-0.601820\pi$
$2$	0.700836	−	0.404628i	0.350418	−	0.202314i	0.664869	+	0.746960i	$0.268487\pi$
$3$	0.807723	−	2.88922i	0.269241	−	0.963073i
$3$	0.807723	−	2.88922i	0.269241	−	0.963073i
$4$	−1.67255	+	2.89695i	−0.418138	+	0.724236i
$5$	−6.73682	−	3.88950i	−1.34736	−	0.777901i	−0.359488	−	0.933150i	$-0.617049\pi$
$5$	−6.73682	−	3.88950i	−1.34736	−	0.777901i	−0.987875	+	0.155249i	$0.950382\pi$
$6$	−0.602977	−	2.35170i	−0.100496	−	0.391950i
$7$	−1.30137	−	2.25403i	−0.185910	−	0.322005i	0.757973	−	0.652286i	$-0.226190\pi$
$7$	−1.30137	−	2.25403i	−0.185910	−	0.322005i	−0.943883	+	0.330281i	$0.892856\pi$
$8$			5.94407i			0.743009i
$9$	−7.69517	−	4.66738i	−0.855019	−	0.518597i
$10$	−6.29521			−0.629521
$11$	−15.0999	+	8.71794i	−1.37272	+	0.792540i	−0.991270	−	0.131849i	$-0.957908\pi$
$11$	−15.0999	+	8.71794i	−1.37272	+	0.792540i	−0.381450	+	0.924390i	$0.624575\pi$
$12$	7.01895	+	7.17230i	0.584912	+	0.597691i
$13$	11.9586	−	20.7129i	0.919894	−	1.59330i	0.120321	−	0.992735i	$-0.461608\pi$
$13$	11.9586	−	20.7129i	0.919894	−	1.59330i	0.799574	−	0.600568i	$-0.205059\pi$
$14$	−1.82409	−	1.05314i	−0.130292	−	0.0752242i
$15$	−16.6791	+	16.3225i	−1.11194	+	1.08817i
$16$	−4.28507	−	7.42196i	−0.267817	−	0.463872i
$17$			4.12311i			0.242536i
$17$			4.12311i			0.242536i
$18$	−7.28161	−	0.157387i	−0.404534	−	0.00874371i
$19$	8.89419			0.468115			0.234058	−	0.972223i	$-0.424800\pi$
$19$	8.89419			0.468115			0.234058	+	0.972223i	$0.424800\pi$
$20$	22.5354	−	13.0108i	1.12677	−	0.650540i
$21$	−7.56354	+	1.93930i	−0.360169	+	0.0923475i
$22$	−7.05505	+	12.2197i	−0.320684	+	0.555441i
$23$	−14.5631	−	8.40799i	−0.633177	−	0.365565i	0.148804	−	0.988867i	$-0.452458\pi$
$23$	−14.5631	−	8.40799i	−0.633177	−	0.365565i	−0.781981	+	0.623302i	$0.785791\pi$
$24$	17.1737	+	4.80116i	0.715572	+	0.200048i
$25$	17.7565	+	30.7551i	0.710260	+	1.23021i
$26$		−	19.3552i		−	0.744430i
$27$	−19.7006	+	18.4631i	−0.729653	+	0.683817i
$28$	8.70641			0.310943
$29$	28.3321	−	16.3576i	0.976969	−	0.564054i	0.0756157	−	0.997137i	$-0.475908\pi$
$29$	28.3321	−	16.3576i	0.976969	−	0.564054i	0.901354	+	0.433083i	$0.142574\pi$
$30$	−5.08479	+	18.1882i	−0.169493	+	0.606275i
$31$	16.5527	−	28.6701i	0.533957	−	0.924841i	−0.465256	−	0.885176i	$-0.654038\pi$
$31$	16.5527	−	28.6701i	0.533957	−	0.924841i	0.999213	−	0.0396646i	$-0.0126290\pi$
$32$	−26.5971	−	15.3559i	−0.831160	−	0.479871i
$33$	12.9915	+	50.6686i	0.393681	+	1.53541i
$34$	1.66832	+	2.88962i	0.0490684	+	0.0849889i
$35$			20.2467i			0.578477i
$36$	26.3917	−	14.4860i	0.733103	−	0.402390i
$37$	−45.9261			−1.24125			−0.620623	−	0.784109i	$-0.713120\pi$
$37$	−45.9261			−1.24125			−0.620623	+	0.784109i	$0.713120\pi$
$38$	6.23337	−	3.59884i	0.164036	−	0.0947063i
$39$	−50.1850	−	51.2814i	−1.28679	−	1.31491i
$40$	23.1195	−	40.0441i	0.577987	−	1.00110i
$41$	−31.3907	−	18.1234i	−0.765626	−	0.442035i	0.0656858	−	0.997840i	$-0.479076\pi$
$41$	−31.3907	−	18.1234i	−0.765626	−	0.442035i	−0.831312	+	0.555806i	$0.812410\pi$
$42$	−4.51611	+	4.41955i	−0.107526	+	0.105227i
$43$	14.4282	+	24.9905i	0.335541	+	0.581174i	0.983589	−	0.180426i	$-0.0577477\pi$
$43$	14.4282	+	24.9905i	0.335541	+	0.581174i	−0.648048	+	0.761600i	$0.724414\pi$
$44$		−	58.3248i		−	1.32556i
$45$	33.6872	+	61.3737i	0.748604	+	1.36386i
$46$	−13.6084			−0.295836
$47$	55.0612	−	31.7896i	1.17152	−	0.676375i	0.217479	−	0.976065i	$-0.430217\pi$
$47$	55.0612	−	31.7896i	1.17152	−	0.676375i	0.954037	+	0.299690i	$0.0968833\pi$
$48$	−24.9048	+	6.38562i	−0.518850	+	0.133034i
$49$	21.1129	−	36.5686i	0.430875	−	0.746298i
$50$	24.8888	+	14.3696i	0.497776	+	0.287391i
$51$	11.9126	+	3.33033i	0.233579	+	0.0653005i
$52$	40.0028	+	69.2870i	0.769285	+	1.33244i
$53$			48.8363i			0.921440i	0.887545	+	0.460720i	$0.152409\pi$
$53$			48.8363i			0.921440i	−0.887545	+	0.460720i	$0.847591\pi$
$54$	−6.33625	+	20.9110i	−0.117338	+	0.387241i
$55$	135.634			2.46607
$56$	13.3981	−	7.73542i	0.239252	−	0.138132i
$57$	7.18404	−	25.6973i	0.126036	−	0.450829i
$58$	13.2375	−	22.9279i	0.228232	−	0.395309i
$59$	−25.6105	−	14.7862i	−0.434076	−	0.250614i	0.267005	−	0.963695i	$-0.413966\pi$
$59$	−25.6105	−	14.7862i	−0.434076	−	0.250614i	−0.701082	+	0.713081i	$0.747299\pi$
$60$	−19.3887	−	75.6187i	−0.323145	−	1.26031i
$61$	19.2375	+	33.3204i	0.315369	+	0.546236i	0.979516	−	0.201367i	$-0.0645383\pi$
$61$	19.2375	+	33.3204i	0.315369	+	0.546236i	−0.664147	+	0.747602i	$0.731205\pi$
$62$		−	26.7907i		−	0.432108i
$63$	−0.506188	+	23.4191i	−0.00803473	+	0.371732i
$64$	9.42690			0.147295
$65$	−161.126	+	93.0262i	−2.47886	+	1.43117i
$66$	29.6069	+	30.2537i	0.448589	+	0.458390i
$67$	−28.8502	+	49.9700i	−0.430600	+	0.745820i	−0.996925	−	0.0783614i	$-0.975031\pi$
$67$	−28.8502	+	49.9700i	−0.430600	+	0.745820i	0.566326	+	0.824182i	$0.308365\pi$
$68$	−11.9444	−	6.89611i	−0.175653	−	0.101413i
$69$	−36.0555	+	35.2846i	−0.522543	+	0.511371i
$70$	8.19238	+	14.1896i	0.117034	+	0.202709i
$71$		−	16.3591i		−	0.230410i	−0.993342	−	0.115205i	$-0.963248\pi$
$71$		−	16.3591i		−	0.230410i	0.993342	−	0.115205i	$-0.0367525\pi$
$72$	27.7432	−	45.7406i	0.385323	−	0.635286i
$73$	−1.61860			−0.0221726			−0.0110863	−	0.999939i	$-0.503529\pi$
$73$	−1.61860			−0.0221726			−0.0110863	+	0.999939i	$0.503529\pi$
$74$	−32.1867	+	18.5830i	−0.434955	+	0.251121i
$75$	103.201	−	26.4607i	1.37601	−	0.352810i
$76$	−14.8760	+	25.7660i	−0.195737	+	0.339026i
$77$	39.3011	+	22.6905i	0.510403	+	0.294682i
$78$	−55.9213	−	15.6336i	−0.716940	−	0.200431i
$79$	−8.91008	−	15.4327i	−0.112786	−	0.195351i	0.804107	−	0.594485i	$-0.202644\pi$
$79$	−8.91008	−	15.4327i	−0.112786	−	0.195351i	−0.916892	+	0.399134i	$0.869311\pi$
$80$			66.6672i			0.833340i
$81$	37.4312	+	71.8325i	0.462113	+	0.886821i
$82$	−29.3330			−0.357719
$83$	−42.2194	+	24.3754i	−0.508667	+	0.293679i	−0.732286	−	0.680998i	$-0.761546\pi$
$83$	−42.2194	+	24.3754i	−0.508667	+	0.293679i	0.223618	+	0.974677i	$0.428213\pi$
$84$	7.03237	−	25.1547i	0.0837187	−	0.299461i
$85$	16.0368	−	27.7766i	0.188669	−	0.326784i
$86$	20.2237	+	11.6762i	0.235159	+	0.135769i
$87$	−24.3760	−	95.0700i	−0.280184	−	1.09276i
$88$	−51.8201	−	89.7550i	−0.588864	−	1.01994i
$89$		−	137.254i		−	1.54218i	−0.636728	−	0.771089i	$-0.719712\pi$
$89$		−	137.254i		−	1.54218i	0.636728	−	0.771089i	$-0.280288\pi$
$90$	48.4427	+	29.3821i	0.538252	+	0.326468i
$91$	−62.2502			−0.684068
$92$	48.7150	−	28.1256i	0.529511	−	0.305713i
$93$	−69.4641	−	70.9818i	−0.746926	−	0.763245i
$94$	25.7259	−	44.5586i	0.273680	−	0.474028i
$95$	−59.9186	−	34.5940i	−0.630722	−	0.364147i
$96$	−65.8496	+	64.4417i	−0.685933	+	0.671267i
$97$	−80.2196	−	138.945i	−0.827007	−	1.43242i	−0.900376	−	0.435113i	$-0.856709\pi$
$97$	−80.2196	−	138.945i	−0.827007	−	1.43242i	0.0733693	−	0.997305i	$-0.476625\pi$
$98$		−	34.1715i		−	0.348689i
$99$	156.886	+	3.39099i	1.58471	+	0.0342524i
$100$	−118.795			−1.18795
$101$	−68.9485	+	39.8074i	−0.682658	+	0.394133i	−0.800856	−	0.598857i	$-0.795622\pi$
$101$	−68.9485	+	39.8074i	−0.682658	+	0.394133i	0.118198	+	0.992990i	$0.462288\pi$
$102$	9.69630	−	2.48614i	0.0950617	−	0.0243739i
$103$	−60.9085	+	105.497i	−0.591345	+	1.02424i	0.402706	+	0.915329i	$0.368070\pi$
$103$	−60.9085	+	105.497i	−0.591345	+	1.02424i	−0.994052	+	0.108911i	$0.965264\pi$
$104$	123.119	+	71.0829i	1.18384	+	0.683490i
$105$	58.4971	+	16.3537i	0.557115	+	0.155750i
$106$	19.7606	+	34.2263i	0.186420	+	0.322890i
$107$		−	36.7905i		−	0.343837i	−0.985111	−	0.171918i	$-0.945003\pi$
$107$		−	36.7905i		−	0.343837i	0.985111	−	0.171918i	$-0.0549966\pi$
$108$	−20.5362	−	87.9521i	−0.190150	−	0.814371i
$109$	−83.1756			−0.763078			−0.381539	−	0.924353i	$-0.624606\pi$
$109$	−83.1756			−0.763078			−0.381539	+	0.924353i	$0.624606\pi$
$110$	95.0572	−	54.8813i	0.864156	−	0.498921i
$111$	−37.0955	+	132.690i	−0.334194	+	1.19541i
$112$	−11.1529	+	19.3174i	−0.0995794	+	0.172477i
$113$	43.3330	+	25.0183i	0.383478	+	0.221401i	0.679330	−	0.733833i	$-0.262270\pi$
$113$	43.3330	+	25.0183i	0.383478	+	0.221401i	−0.295853	+	0.955234i	$0.595604\pi$
$114$	−5.36300	−	20.9164i	−0.0470438	−	0.183478i
$115$	65.4059	+	113.286i	0.568747	+	0.985098i
$116$			109.435i			0.943409i
$117$	−188.699	+	103.574i	−1.61281	+	0.885249i
$118$	−23.9317			−0.202811
$119$	9.29362	−	5.36567i	0.0780976	−	0.0450897i
$120$	−97.0221	−	99.1418i	−0.808518	−	0.826182i
$121$	91.5050	−	158.491i	0.756240	−	1.30985i
$122$	26.9647	+	15.5681i	0.221022	+	0.127607i
$123$	−77.7175	+	76.0558i	−0.631850	+	0.618340i
$124$	55.3704	+	95.9044i	0.446536	+	0.773422i
$125$		−	81.7806i		−	0.654245i
$126$	9.12128	+	16.6178i	0.0723911	+	0.131887i
$127$	−133.526			−1.05139			−0.525694	−	0.850674i	$-0.676194\pi$
$127$	−133.526			−1.05139			−0.525694	+	0.850674i	$0.676194\pi$
$128$	112.995	−	65.2378i	0.882775	−	0.509671i
$129$	83.8569	−	21.5010i	0.650054	−	0.166674i
$130$	−75.2821	+	130.392i	−0.579093	+	1.00302i
$131$	−114.524	−	66.1203i	−0.874226	−	0.504735i	−0.00547589	−	0.999985i	$-0.501743\pi$
$131$	−114.524	−	66.1203i	−0.874226	−	0.504735i	−0.868750	+	0.495250i	$0.835076\pi$
$132$	−168.513	−	47.1103i	−1.27662	−	0.356896i
$133$	−11.5746	−	20.0478i	−0.0870271	−	0.150735i
$134$			46.6944i			0.348465i
$135$	204.532	−	47.7567i	1.51505	−	0.353753i
$136$	−24.5080			−0.180206
$137$	74.6702	−	43.1108i	0.545038	−	0.314678i	−0.202080	−	0.979369i	$-0.564770\pi$
$137$	74.6702	−	43.1108i	0.545038	−	0.314678i	0.747118	+	0.664691i	$0.231437\pi$
$138$	−10.9919	+	39.3178i	−0.0796511	+	0.284911i
$139$	5.93501	−	10.2797i	0.0426979	−	0.0739550i	−0.843887	−	0.536522i	$-0.819738\pi$
$139$	5.93501	−	10.2797i	0.0426979	−	0.0739550i	0.886585	+	0.462567i	$0.153071\pi$
$140$	−58.6535	−	33.8636i	−0.418954	−	0.241883i
$141$	−47.3729	−	184.761i	−0.335978	−	1.31036i
$142$	−6.61935	−	11.4651i	−0.0466152	−	0.0807398i
$143$			417.018i			2.91621i
$144$	−1.66675	+	77.1132i	−0.0115746	+	0.535509i
$145$	−254.491			−1.75511
$146$	−1.13437	+	0.654930i	−0.00776967	+	0.00448582i
$147$	−88.6013	−	90.5370i	−0.602730	−	0.615898i
$148$	76.8137	−	133.045i	0.519012	−	0.898955i
$149$	63.4767	+	36.6483i	0.426018	+	0.245962i	0.697649	−	0.716440i	$-0.254230\pi$
$149$	63.4767	+	36.6483i	0.426018	+	0.245962i	−0.271631	+	0.962402i	$0.587563\pi$
$150$	61.6200	−	60.3026i	0.410800	−	0.402017i
$151$	94.7149	+	164.051i	0.627251	+	1.08643i	0.988101	+	0.153807i	$0.0491533\pi$
$151$	94.7149	+	164.051i	0.627251	+	1.08643i	−0.360850	+	0.932624i	$0.617513\pi$
$152$			52.8677i			0.347814i
$153$	19.2441	−	31.7280i	0.125778	−	0.207372i
$154$	36.7248			0.238473
$155$	−223.025	+	128.763i	−1.43887	+	0.830731i
$156$	232.496	−	59.6123i	1.49036	−	0.382130i
$157$	22.6267	−	39.1906i	0.144119	−	0.249621i	−0.784925	−	0.619591i	$-0.787299\pi$
$157$	22.6267	−	39.1906i	0.144119	−	0.249621i	0.929044	+	0.369970i	$0.120632\pi$
$158$	−12.4890	−	7.21054i	−0.0790444	−	0.0456363i
$159$	141.099	+	39.4462i	0.887414	+	0.248090i
$160$	119.453	+	206.899i	0.746584	+	1.29312i
$161$			43.7675i			0.271848i
$162$	55.2986	+	35.1971i	0.341349	+	0.217266i
$163$	280.866			1.72310			0.861552	−	0.507670i	$-0.169493\pi$
$163$	280.866			1.72310			0.861552	+	0.507670i	$0.169493\pi$
$164$	105.005	−	60.6247i	0.640275	−	0.369663i
$165$	109.555	−	391.876i	0.663967	−	2.37501i
$166$	−19.7259	+	34.1663i	−0.118831	+	0.205821i
$167$	97.4945	+	56.2885i	0.583800	+	0.337057i	0.762642	−	0.646821i	$-0.223902\pi$
$167$	97.4945	+	56.2885i	0.583800	+	0.337057i	−0.178842	+	0.983878i	$0.557235\pi$
$168$	−11.5273	−	44.9582i	−0.0686150	−	0.267608i
$169$	−201.517	−	349.038i	−1.19241	−	2.06532i
$170$		−	25.9558i		−	0.152681i
$171$	−68.4423	−	41.5125i	−0.400247	−	0.242763i
$172$	−96.5280			−0.561209
$173$	108.216	−	62.4783i	0.625524	−	0.361146i	−0.153493	−	0.988150i	$-0.549052\pi$
$173$	108.216	−	62.4783i	0.625524	−	0.361146i	0.779017	+	0.627003i	$0.215719\pi$
$174$	−55.5516	−	56.7653i	−0.319262	−	0.326237i
$175$	46.2154	−	80.0475i	0.264088	−	0.457414i
$176$	129.408	+	74.7140i	0.735275	+	0.424511i
$177$	−63.4068	+	62.0511i	−0.358231	+	0.350571i
$178$	−55.5368	−	96.1925i	−0.312004	−	0.540407i
$179$		−	231.060i		−	1.29084i	−0.763830	−	0.645418i	$-0.776683\pi$
$179$		−	231.060i		−	1.29084i	0.763830	−	0.645418i	$-0.223317\pi$
$180$	−234.140	−	5.06076i	−1.30078	−	0.0281154i
$181$	−21.6045			−0.119362			−0.0596808	−	0.998218i	$-0.519008\pi$
$181$	−21.6045			−0.119362			−0.0596808	+	0.998218i	$0.519008\pi$
$182$	−43.6272	+	25.1882i	−0.239710	+	0.138397i
$183$	111.808	−	28.6678i	0.610975	−	0.156655i
$184$	49.9777	−	86.5640i	0.271618	−	0.470456i
$185$	309.396	+	178.630i	1.67241	+	0.965566i
$186$	−77.4042	−	21.6395i	−0.416152	−	0.116341i
$187$	−35.9450	−	62.2586i	−0.192219	−	0.332933i
$188$			212.679i			1.13127i
$189$	67.2541	+	20.3787i	0.355842	+	0.107824i
$190$	−55.9908			−0.294689
$191$	250.277	−	144.498i	1.31035	−	0.756533i	0.328198	−	0.944609i	$-0.393559\pi$
$191$	250.277	−	144.498i	1.31035	−	0.756533i	0.982154	+	0.188076i	$0.0602252\pi$
$192$	7.61433	−	27.2364i	0.0396579	−	0.141856i
$193$	7.41936	−	12.8507i	0.0384423	−	0.0665840i	−0.846164	−	0.532922i	$-0.821094\pi$
$193$	7.41936	−	12.8507i	0.0384423	−	0.0665840i	0.884606	+	0.466338i	$0.154427\pi$
$194$	−112.442	−	64.9183i	−0.579596	−	0.334630i
$195$	138.628	+	540.668i	0.710912	+	2.77266i
$196$	70.6248	+	122.326i	0.360331	+	0.624111i
$197$			8.61853i			0.0437489i	0.999761	+	0.0218745i	$0.00696341\pi$
$197$			8.61853i			0.0437489i	−0.999761	+	0.0218745i	$0.993037\pi$
$198$	111.324	−	61.1041i	0.562241	−	0.308606i
$199$	286.779			1.44110			0.720550	−	0.693403i	$-0.243889\pi$
$199$	286.779			1.44110			0.720550	+	0.693403i	$0.243889\pi$
$200$	−182.811	+	105.546i	−0.914054	+	0.527729i
$201$	121.071	+	123.716i	0.602344	+	0.615504i
$202$	−32.2144	+	55.7970i	−0.159477	+	0.276223i
$203$	−73.7409	−	42.5744i	−0.363256	−	0.209726i
$204$	−29.5721	+	28.9399i	−0.144961	+	0.141862i
$205$	140.982	+	244.188i	0.687718	+	1.19116i
$206$			98.5813i			0.478550i
$207$	72.8220	+	132.672i	0.351797	+	0.640929i
$208$	−204.974			−0.985453
$209$	−134.302	+	77.5390i	−0.642591	+	0.371000i
$210$	47.6141	−	12.2083i	0.226734	−	0.0581347i
$211$	−48.9118	+	84.7177i	−0.231809	+	0.401506i	−0.958341	−	0.285628i	$-0.907798\pi$
$211$	−48.9118	+	84.7177i	−0.231809	+	0.401506i	0.726531	+	0.687133i	$0.241131\pi$
$212$	−141.476	−	81.6813i	−0.667341	−	0.385289i
$213$	−47.2650	−	13.2136i	−0.221902	−	0.0620358i
$214$	−14.8865	−	25.7842i	−0.0695630	−	0.120487i
$215$		−	224.475i		−	1.04407i
$216$	−109.746	−	117.102i	−0.508083	−	0.542139i
$217$	−86.1644			−0.397071
$218$	−58.2925	+	33.6552i	−0.267397	+	0.154382i
$219$	−1.30738	+	4.67648i	−0.00596976	+	0.0213538i
$220$	−226.855	+	392.924i	−1.03116	+	1.78602i
$221$	85.4017	+	49.3067i	0.386433	+	0.223107i
$222$	27.6924	+	108.004i	0.124740	+	0.486505i
$223$	−118.031	−	204.435i	−0.529286	−	0.916750i	−0.999417	−	0.0341533i	$-0.989127\pi$
$223$	−118.031	−	204.435i	−0.529286	−	0.916750i	0.470131	−	0.882597i	$-0.344207\pi$
$224$			79.9344i			0.356850i
$225$	6.90668	−	319.542i	0.0306963	−	1.42019i
$226$	40.4924			0.179170
$227$	185.599	−	107.156i	0.817616	−	0.472051i	−0.0319778	−	0.999489i	$-0.510181\pi$
$227$	185.599	−	107.156i	0.817616	−	0.472051i	0.849594	+	0.527438i	$0.176847\pi$
$228$	62.4279	+	63.7918i	0.273806	+	0.279789i
$229$	141.310	−	244.755i	0.617072	−	1.06880i	−0.372945	−	0.927854i	$-0.621652\pi$
$229$	141.310	−	244.755i	0.617072	−	1.06880i	0.990017	−	0.140947i	$-0.0450147\pi$
$230$	91.6776	+	52.9301i	0.398598	+	0.230131i
$231$	97.3021	−	95.2217i	0.421221	−	0.412215i
$232$	97.2305	+	168.408i	0.419097	+	0.725897i
$233$			59.8313i			0.256786i	0.991723	+	0.128393i	$0.0409820\pi$
$233$			59.8313i			0.256786i	−0.991723	+	0.128393i	$0.959018\pi$
$234$	−90.3379	+	148.941i	−0.386059	+	0.636502i
$235$	−494.583			−2.10461
$236$	85.6698	−	49.4615i	0.363008	−	0.209582i
$237$	−51.7854	+	13.2778i	−0.218504	+	0.0560245i
$238$	4.34220	−	7.52092i	0.0182446	−	0.0316005i
$239$	−69.7376	−	40.2630i	−0.291789	−	0.168465i	0.346959	−	0.937880i	$-0.387214\pi$
$239$	−69.7376	−	40.2630i	−0.291789	−	0.168465i	−0.638748	+	0.769416i	$0.720548\pi$
$240$	192.616	+	53.8486i	0.802567	+	0.224369i
$241$	−72.3297	−	125.279i	−0.300123	−	0.519829i	0.676040	−	0.736865i	$-0.263695\pi$
$241$	−72.3297	−	125.279i	−0.300123	−	0.519829i	−0.976164	+	0.217036i	$0.930361\pi$
$242$		−	148.102i		−	0.611992i
$243$	237.774	−	50.1261i	0.978493	−	0.206280i
$244$	−128.703			−0.527472
$245$	−284.467	+	164.237i	−1.16109	+	0.670357i
$246$	−23.6929	+	84.7494i	−0.0963127	+	0.344510i
$247$	106.362	−	184.225i	0.430617	−	0.745850i
$248$	170.417	+	98.3903i	0.687165	+	0.396735i
$249$	36.3242	+	141.670i	0.145880	+	0.568954i
$250$	−33.0907	−	57.3148i	−0.132363	−	0.229259i
$251$			187.445i			0.746793i	0.927672	+	0.373397i	$0.121807\pi$
$251$			187.445i			0.746793i	−0.927672	+	0.373397i	$0.878193\pi$
$252$	−66.9973	−	40.6361i	−0.265862	−	0.161254i
$253$	293.202			1.15890
$254$	−93.5801	+	54.0285i	−0.368425	+	0.212711i
$255$	−67.2994	−	68.7697i	−0.263919	−	0.269685i
$256$	33.9403	−	58.7864i	0.132579	−	0.229634i
$257$	−181.025	−	104.515i	−0.704377	−	0.406672i	0.104599	−	0.994515i	$-0.466644\pi$
$257$	−181.025	−	104.515i	−0.704377	−	0.406672i	−0.808975	+	0.587842i	$0.799978\pi$
$258$	50.0701	−	48.9996i	0.194070	−	0.189921i
$259$	59.7667	+	103.519i	0.230759	+	0.399687i
$260$		−	622.365i		−	2.39371i
$261$	−294.367	−	6.36254i	−1.12784	−	0.0243775i
$262$	−107.016			−0.408460
$263$	111.963	−	64.6421i	0.425716	−	0.245787i	−0.271804	−	0.962353i	$-0.587620\pi$
$263$	111.963	−	64.6421i	0.425716	−	0.245787i	0.697520	+	0.716565i	$0.254287\pi$
$264$	−301.178	+	77.2223i	−1.14083	+	0.292509i
$265$	189.949	−	329.002i	0.716789	−	1.24152i
$266$	−16.2238	−	9.36682i	−0.0609918	−	0.0352136i
$267$	−396.556	−	110.863i	−1.48523	−	0.415217i
$268$	−96.5068	−	167.155i	−0.360100	−	0.623712i
$269$		−	151.018i		−	0.561405i	−0.959795	−	0.280702i	$-0.909433\pi$
$269$		−	151.018i		−	0.561405i	0.959795	−	0.280702i	$-0.0905674\pi$
$270$	124.020	−	116.229i	0.459332	−	0.430478i
$271$	402.721			1.48605			0.743027	−	0.669261i	$-0.233389\pi$
$271$	402.721			1.48605			0.743027	+	0.669261i	$0.233389\pi$
$272$	30.6015	−	17.6678i	0.112506	−	0.0649551i
$273$	−50.2809	+	179.854i	−0.184179	+	0.658808i
$274$	34.8877	−	60.4273i	0.127327	−	0.220538i
$275$	−536.243	−	309.600i	−1.94997	−	1.12582i
$276$	−41.9128	−	163.466i	−0.151858	−	0.592268i
$277$	80.4259	+	139.302i	0.290346	+	0.502894i	0.973892	−	0.227014i	$-0.0728962\pi$
$277$	80.4259	+	139.302i	0.290346	+	0.502894i	−0.683545	+	0.729908i	$0.739563\pi$
$278$		−	9.60589i		−	0.0345536i
$279$	−261.190	+	143.363i	−0.936163	+	0.513847i
$280$	−120.348			−0.429813
$281$	70.3081	−	40.5924i	0.250207	−	0.144457i	−0.369652	−	0.929170i	$-0.620523\pi$
$281$	70.3081	−	40.5924i	0.250207	−	0.144457i	0.619859	+	0.784713i	$0.287190\pi$
$282$	−107.960	−	110.319i	−0.382838	−	0.391202i
$283$	−159.276	+	275.875i	−0.562814	+	0.974823i	0.434435	+	0.900703i	$0.356948\pi$
$283$	−159.276	+	275.875i	−0.562814	+	0.974823i	−0.997249	+	0.0741197i	$0.976385\pi$
$284$	47.3914	+	27.3615i	0.166871	+	0.0963431i
$285$	−148.347	+	145.175i	−0.520517	+	0.509388i
$286$	168.737	+	292.262i	0.589991	+	1.02189i
$287$			94.3409i			0.328714i
$288$	132.998	+	242.305i	0.461798	+	0.841336i
$289$	−17.0000			−0.0588235
$290$	−178.357	+	102.974i	−0.615023	+	0.355084i
$291$	−466.236	+	119.543i	−1.60219	+	0.410802i
$292$	2.70719	−	4.68899i	0.00927119	−	0.0160582i
$293$	−387.823	−	223.910i	−1.32363	−	0.764196i	−0.339322	−	0.940670i	$-0.610197\pi$
$293$	−387.823	−	223.910i	−1.32363	−	0.764196i	−0.984305	+	0.176474i	$0.943531\pi$
$294$	−98.7289	−	27.6011i	−0.335812	−	0.0938813i
$295$	115.022	+	199.224i	0.389906	+	0.675337i
$296$		−	272.988i		−	0.922256i
$297$	136.518	−	450.540i	0.459656	−	1.51697i
$298$	59.3157			0.199046
$299$	−348.309	+	201.096i	−1.16491	+	0.672562i
$300$	−95.9532	+	343.224i	−0.319844	+	1.14408i
$301$	37.5529	−	65.0435i	0.124760	−	0.216091i
$302$	132.759	+	76.6486i	0.439600	+	0.253803i
$303$	59.3211	+	231.361i	0.195779	+	0.763566i
$304$	−38.1122	−	66.0123i	−0.125369	−	0.217146i
$305$		−	299.298i		−	0.981304i
$306$	0.648922	−	30.0228i	0.00212066	−	0.0981138i
$307$	306.100			0.997068			0.498534	−	0.866870i	$-0.333872\pi$
$307$	306.100			0.997068			0.498534	+	0.866870i	$0.333872\pi$
$308$	−131.466	+	75.9020i	−0.426838	+	0.246435i
$309$	255.606	+	261.190i	0.827203	+	0.845276i
$310$	−104.203	+	180.484i	−0.336137	+	0.582207i
$311$	204.646	+	118.153i	0.658026	+	0.379912i	0.791524	−	0.611137i	$-0.209288\pi$
$311$	204.646	+	118.153i	0.658026	+	0.379912i	−0.133498	+	0.991049i	$0.542621\pi$
$312$	304.820	−	298.303i	0.976988	−	0.956099i
$313$	−96.4374	−	167.035i	−0.308107	−	0.533657i	0.669841	−	0.742504i	$-0.266362\pi$
$313$	−96.4374	−	167.035i	−0.308107	−	0.533657i	−0.977948	+	0.208848i	$0.933029\pi$
$314$		−	36.6216i		−	0.116629i
$315$	94.4989	−	155.802i	0.299997	−	0.494608i
$316$	59.6103			0.188640
$317$	−185.112	+	106.874i	−0.583948	+	0.337143i	−0.762701	−	0.646751i	$-0.776127\pi$
$317$	−185.112	+	106.874i	−0.583948	+	0.337143i	0.178753	+	0.983894i	$0.442794\pi$
$318$	114.848	−	29.4472i	0.361158	−	0.0926013i
$319$	−285.208	+	493.995i	−0.894070	+	1.54857i
$320$	−63.5073	−	36.6660i	−0.198460	−	0.114581i
$321$	−106.296	−	29.7166i	−0.331140	−	0.0925750i
$322$	17.7096	+	30.6739i	0.0549987	+	0.0952605i
$323$			36.6717i			0.113535i
$324$	−270.700	−	11.7075i	−0.835495	−	0.0361341i
$325$	849.373			2.61345
$326$	196.841	−	113.646i	0.603807	−	0.348608i
$327$	−67.1828	+	240.312i	−0.205452	+	0.734900i
$328$	107.727	−	186.588i	0.328436	−	0.568867i
$329$	−143.310	−	82.7399i	−0.435592	−	0.251489i
$330$	−81.7842	−	318.970i	−0.247831	−	0.966575i
$331$	257.827	+	446.570i	0.778934	+	1.34915i	0.932557	+	0.361023i	$0.117573\pi$
$331$	257.827	+	446.570i	0.778934	+	1.34915i	−0.153623	+	0.988130i	$0.549094\pi$
$332$		−	163.076i		−	0.491194i
$333$	353.409	+	214.354i	1.06129	+	0.643707i
$334$	91.1036			0.272765
$335$	388.717	−	224.426i	1.16035	−	0.669928i
$336$	46.8037	+	47.8262i	0.139297	+	0.142340i
$337$	139.812	−	242.161i	0.414871	−	0.718578i	−0.580544	−	0.814229i	$-0.697160\pi$
$337$	139.812	−	242.161i	0.414871	−	0.718578i	0.995415	+	0.0956509i	$0.0304932\pi$
$338$	−282.461	−	163.079i	−0.835685	−	0.482483i
$339$	107.284	−	104.991i	0.316473	−	0.309707i
$340$	53.6449	+	92.9157i	0.157779	+	0.273281i
$341$			577.221i			1.69273i
$342$	−64.7640	−	1.39983i	−0.189368	−	0.00409306i
$343$	−237.436			−0.692234
$344$	−148.545	+	85.7626i	−0.431817	+	0.249310i
$345$	380.139	−	97.4679i	1.10185	−	0.282516i
$346$	50.5610	−	87.5742i	0.146130	−	0.253105i
$347$	9.39562	+	5.42457i	0.0270767	+	0.0156328i	0.513477	−	0.858103i	$-0.328357\pi$
$347$	9.39562	+	5.42457i	0.0270767	+	0.0156328i	−0.486401	+	0.873736i	$0.661690\pi$
$348$	316.183	+	88.3935i	0.908572	+	0.254004i
$349$	−220.265	−	381.511i	−0.631133	−	1.09315i	−0.987320	−	0.158740i	$-0.949257\pi$
$349$	−220.265	−	381.511i	−0.631133	−	1.09315i	0.356187	−	0.934415i	$-0.384076\pi$
$350$		−	74.8002i		−	0.213715i
$351$	146.832	+	628.851i	0.418325	+	1.79160i
$352$	535.486			1.52127
$353$	−104.849	+	60.5347i	−0.297023	+	0.171486i	−0.641105	−	0.767453i	$-0.721524\pi$
$353$	−104.849	+	60.5347i	−0.297023	+	0.171486i	0.344082	+	0.938940i	$0.388190\pi$
$354$	−19.3302	+	69.1439i	−0.0546050	+	0.195322i
$355$	−63.6288	+	110.208i	−0.179236	+	0.310446i
$356$	397.617	+	229.564i	1.11690	+	0.644843i
$357$	−7.99593	−	31.1853i	−0.0223976	−	0.0873537i
$358$	−93.4932	−	161.935i	−0.261154	−	0.452332i
$359$			447.022i			1.24519i	0.782546	+	0.622593i	$0.213921\pi$
$359$			447.022i			1.24519i	−0.782546	+	0.622593i	$0.786079\pi$
$360$	−364.809	+	200.239i	−1.01336	+	0.556219i
$361$	−281.893			−0.780868
$362$	−15.1412	+	8.74177i	−0.0418265	+	0.0241485i
$363$	−384.005	−	392.395i	−1.05787	−	1.08098i
$364$	104.117	−	180.335i	0.286035	−	0.495427i
$365$	10.9042	+	6.29554i	0.0298745	+	0.0172481i
$366$	66.7596	−	65.3323i	0.182403	−	0.178503i
$367$	−203.580	−	352.610i	−0.554713	−	0.960791i	−0.997926	−	0.0643744i	$-0.979495\pi$
$367$	−203.580	−	352.610i	−0.554713	−	0.960791i	0.443213	−	0.896416i	$-0.353839\pi$
$368$			144.115i			0.391618i
$369$	156.968	+	285.975i	0.425387	+	0.775000i
$370$	289.114			0.781390
$371$	110.079	−	63.5540i	0.296708	−	0.171305i
$372$	321.813	−	82.5130i	0.865088	−	0.221809i
$373$	−311.242	+	539.088i	−0.834430	+	1.44528i	0.0600638	+	0.998195i	$0.480870\pi$
$373$	−311.242	+	539.088i	−0.834430	+	1.44528i	−0.894494	+	0.447081i	$0.852464\pi$
$374$	−50.3831	−	29.0887i	−0.134714	−	0.0777773i
$375$	−236.282	−	66.0561i	−0.630085	−	0.176150i
$376$	188.960	+	327.288i	0.502552	+	0.870446i
$377$		−	782.455i		−	2.07548i
$378$	55.3799	−	12.9308i	0.146508	−	0.0342085i
$379$	−572.862			−1.51151			−0.755755	−	0.654855i	$-0.772730\pi$
$379$	−572.862			−1.51151			−0.755755	+	0.654855i	$0.772730\pi$
$380$	200.434	−	115.721i	0.527457	−	0.304528i
$381$	−107.852	+	385.786i	−0.283077	+	1.01256i
$382$	116.936	−	202.539i	0.306114	−	0.530206i
$383$	−68.2467	−	39.4023i	−0.178190	−	0.102878i	0.408252	−	0.912869i	$-0.366138\pi$
$383$	−68.2467	−	39.4023i	−0.178190	−	0.102878i	−0.586442	+	0.809991i	$0.699472\pi$
$384$	−97.2175	−	379.162i	−0.253171	−	0.987401i
$385$	−176.509	−	305.723i	−0.458466	−	0.794086i
$386$		−	12.0083i		−	0.0311097i
$387$	5.61210	−	259.648i	0.0145016	−	0.670925i
$388$	536.686			1.38321
$389$	−2.14950	+	1.24102i	−0.00552572	+	0.00319027i	−0.502760	−	0.864426i	$-0.667682\pi$
$389$	−2.14950	+	1.24102i	−0.00552572	+	0.00319027i	0.497235	+	0.867616i	$0.334349\pi$
$390$	315.925	+	322.827i	0.810064	+	0.827762i
$391$	34.6671	−	60.0451i	0.0886625	−	0.153568i
$392$	217.366	+	125.497i	0.554506	+	0.320144i
$393$	−283.539	+	277.477i	−0.721474	+	0.706048i
$394$	3.48730	+	6.04018i	0.00885102	+	0.0153304i
$395$			138.623i			0.350945i
$396$	−272.224	+	448.819i	−0.687434	+	1.13338i
$397$	242.224			0.610135			0.305067	−	0.952331i	$-0.401321\pi$
$397$	242.224			0.610135			0.305067	+	0.952331i	$0.401321\pi$
$398$	200.985	−	116.039i	0.504988	−	0.291555i
$399$	−67.2716	+	17.2485i	−0.168600	+	0.0432293i
$400$	152.176	−	263.576i	0.380439	−	0.658940i
$401$	469.035	+	270.798i	1.16966	+	0.675306i	0.953601	−	0.301073i	$-0.0973449\pi$
$401$	469.035	+	270.798i	1.16966	+	0.675306i	0.216063	+	0.976379i	$0.430678\pi$
$402$	134.910	+	37.7161i	0.335598	+	0.0938212i
$403$	−395.894	−	685.709i	−0.982368	−	1.70151i
$404$		−	266.320i		−	0.659208i
$405$	27.2256	−	629.511i	0.0672237	−	1.55435i
$406$	−68.9071			−0.169722
$407$	693.480	−	400.381i	1.70388	−	0.983737i
$408$	−19.7957	+	70.8091i	−0.0485189	+	0.173552i
$409$	−212.264	+	367.652i	−0.518984	+	0.898906i	0.480773	+	0.876845i	$0.340356\pi$
$409$	−212.264	+	367.652i	−0.518984	+	0.898906i	−0.999757	+	0.0220608i	$0.992977\pi$
$410$	197.611	+	114.091i	0.481978	+	0.278270i
$411$	−64.2438	−	250.560i	−0.156311	−	0.609635i
$412$	−203.745	−	352.897i	−0.494528	−	0.856547i
$413$			76.9692i			0.186366i
$414$	104.719	+	63.5157i	0.252945	+	0.153420i
$415$	379.233			0.913813
$416$	−636.130	+	367.270i	−1.52916	+	0.882860i
$417$	−24.9066	−	25.4507i	−0.0597280	−	0.0610329i
$418$	−62.7489	+	108.684i	−0.150117	+	0.260010i
$419$	107.238	+	61.9139i	0.255938	+	0.147766i	0.622480	−	0.782635i	$-0.286125\pi$
$419$	107.238	+	61.9139i	0.255938	+	0.147766i	−0.366542	+	0.930401i	$0.619458\pi$
$420$	−145.215	+	142.110i	−0.345751	+	0.338358i
$421$	−206.378	−	357.457i	−0.490208	−	0.849065i	0.509728	−	0.860335i	$-0.329746\pi$
$421$	−206.378	−	357.457i	−0.490208	−	0.849065i	−0.999936	+	0.0112700i	$0.996413\pi$
$422$			79.1643i			0.187593i
$423$	−572.079	−	12.3651i	−1.35243	−	0.0292319i
$424$	−290.287			−0.684638
$425$	−126.807	+	73.2119i	−0.298369	+	0.172263i
$426$	−38.4717	+	9.86417i	−0.0903091	+	0.0231553i
$427$	50.0702	−	86.7241i	0.117260	−	0.203101i
$428$	106.580	+	61.5341i	0.249019	+	0.143771i
$429$	1204.86	+	336.835i	2.80852	+	0.785164i
$430$	−90.8289	−	157.320i	−0.211230	−	0.365861i
$431$		−	360.015i		−	0.835303i	−0.908607	−	0.417651i	$-0.862853\pi$
$431$		−	360.015i		−	0.835303i	0.908607	−	0.417651i	$-0.137147\pi$
$432$	221.451	+	67.1017i	0.512617	+	0.155328i
$433$	−299.670			−0.692078			−0.346039	−	0.938220i	$-0.612473\pi$
$433$	−299.670			−0.692078			−0.346039	+	0.938220i	$0.612473\pi$
$434$	−60.3871	+	34.8645i	−0.139141	+	0.0803330i
$435$	−205.558	+	735.280i	−0.472548	+	1.69030i
$436$	139.115	−	240.955i	0.319072	−	0.552649i
$437$	−129.527	−	74.7823i	−0.296400	−	0.171127i
$438$	0.975978	+	3.80645i	0.00222826	+	0.00869053i
$439$	219.286	+	379.815i	0.499513	+	0.865183i	1.00000		0.000561671i	$-0.000178786\pi$
$439$	219.286	+	379.815i	0.499513	+	0.865183i	−0.500486	+	0.865744i	$0.666845\pi$
$440$			806.218i			1.83231i
$441$	−333.147	+	182.860i	−0.755435	+	0.414648i
$442$	79.8035			0.180551
$443$	271.723	−	156.879i	0.613370	−	0.354130i	−0.160913	−	0.986969i	$-0.551444\pi$
$443$	271.723	−	156.879i	0.613370	−	0.354130i	0.774283	+	0.632839i	$0.218111\pi$
$444$	−322.353	−	329.395i	−0.726020	−	0.741882i
$445$	−533.849	+	924.654i	−1.19966	+	2.07787i
$446$	−165.441	−	95.5171i	−0.370943	−	0.214164i
$447$	157.157	−	153.796i	0.351581	−	0.344064i
$448$	−12.2679	−	21.2485i	−0.0273836	−	0.0474298i
$449$		−	575.345i		−	1.28139i	−0.767795	−	0.640696i	$-0.778646\pi$
$449$		−	575.345i		−	1.28139i	0.767795	−	0.640696i	$-0.221354\pi$
$450$	−124.455	−	226.741i	−0.276567	−	0.503870i
$451$	631.996			1.40132
$452$	−144.953	+	83.6888i	−0.320693	+	0.185152i
$453$	550.483	−	141.144i	1.21519	−	0.311577i
$454$	86.7163	−	150.197i	0.191005	−	0.330830i
$455$	419.368	+	242.123i	0.921689	+	0.532137i
$456$	152.746	+	42.7025i	0.334970	+	0.0936458i
$457$	−220.299	−	381.569i	−0.482054	−	0.834942i	0.517734	−	0.855542i	$-0.326776\pi$
$457$	−220.299	−	381.569i	−0.482054	−	0.834942i	−0.999788	+	0.0205996i	$0.993442\pi$
$458$		−	228.711i		−	0.499370i
$459$	−76.1252	−	81.2278i	−0.165850	−	0.176967i
$460$	−437.579			−0.951258
$461$	93.3163	−	53.8762i	0.202421	−	0.116868i	−0.395363	−	0.918525i	$-0.629381\pi$
$461$	93.3163	−	53.8762i	0.202421	−	0.116868i	0.597784	+	0.801657i	$0.296048\pi$
$462$	29.6635	−	106.106i	0.0642067	−	0.229667i
$463$	253.384	−	438.875i	0.547267	−	0.947894i	−0.451194	−	0.892426i	$-0.649002\pi$
$463$	253.384	−	438.875i	0.547267	−	0.947894i	0.998460	−	0.0554677i	$-0.0176650\pi$
$464$	−242.810	−	140.187i	−0.523298	−	0.302126i
$465$	191.883	+	748.372i	0.412652	+	1.60940i
$466$	24.2094	+	41.9319i	0.0519515	+	0.0899827i
$467$			182.287i			0.390337i	0.980770	+	0.195169i	$0.0625254\pi$
$467$			182.287i			0.390337i	−0.980770	+	0.195169i	$0.937475\pi$
$468$	15.5598	−	719.883i	0.0332474	−	1.53821i
$469$	150.179			0.320210
$470$	−346.622	+	200.122i	−0.737494	+	0.425792i
$471$	−94.9540	−	97.0285i	−0.201601	−	0.206005i
$472$	87.8904	−	152.231i	0.186208	−	0.322523i
$473$	−435.731	−	251.569i	−0.921207	−	0.531859i
$474$	−30.9205	+	30.2594i	−0.0652331	+	0.0638384i
$475$	157.930	+	273.542i	0.332483	+	0.575878i
$476$			35.8975i			0.0754148i
$477$	227.938	−	375.804i	0.477857	−	0.787849i
$478$	−65.1662			−0.136331
$479$	21.7465	−	12.5553i	0.0453998	−	0.0262116i	−0.477128	−	0.878834i	$-0.658322\pi$
$479$	21.7465	−	12.5553i	0.0453998	−	0.0262116i	0.522528	+	0.852622i	$0.324989\pi$
$480$	694.263	−	178.010i	1.44638	−	0.370853i
$481$	−549.213	+	951.264i	−1.14181	+	1.97768i
$482$	−101.383	−	58.5333i	−0.210337	−	0.121438i
$483$	126.454	+	35.3520i	0.261809	+	0.0731926i
$484$	306.094	+	530.170i	0.632425	+	1.09539i
$485$			1248.06i			2.57332i
$486$	146.358	−	131.340i	0.301148	−	0.270247i
$487$	−374.163			−0.768302			−0.384151	−	0.923270i	$-0.625506\pi$
$487$	−374.163			−0.768302			−0.384151	+	0.923270i	$0.625506\pi$
$488$	−198.059	+	114.349i	−0.405858	+	0.234322i
$489$	226.862	−	811.483i	0.463930	−	1.65947i
$490$	−132.910	+	230.207i	−0.271245	+	0.469810i
$491$	−360.289	−	208.013i	−0.733786	−	0.423652i	0.0860194	−	0.996293i	$-0.472585\pi$
$491$	−360.289	−	208.013i	−0.733786	−	0.423652i	−0.819806	+	0.572642i	$0.805919\pi$
$492$	−90.3430	−	352.351i	−0.183624	−	0.716160i
$493$	67.4439	+	116.816i	0.136803	+	0.236950i
$494$		−	172.149i		−	0.348479i
$495$	−1043.73	−	633.054i	−2.10854	−	1.27890i
$496$	−283.717			−0.572011
$497$	−36.8740	+	21.2892i	−0.0741931	+	0.0428354i
$498$	82.7808	+	84.5894i	0.166227	+	0.169858i
$499$	−175.883	+	304.638i	−0.352470	+	0.610496i	−0.986682	−	0.162663i	$-0.947992\pi$
$499$	−175.883	+	304.638i	−0.352470	+	0.610496i	0.634211	+	0.773160i	$0.281325\pi$
$500$	236.914	+	136.782i	0.473828	+	0.273565i
$501$	241.378	−	236.218i	0.481793	−	0.471492i
$502$	75.8456	+	131.368i	0.151087	+	0.261690i
$503$			262.131i			0.521134i	0.965456	+	0.260567i	$0.0839095\pi$
$503$			262.131i			0.521134i	−0.965456	+	0.260567i	$0.916090\pi$
$504$	−139.205	−	3.00882i	−0.276200	−	0.00596988i
$505$	619.325			1.22639
$506$	205.486	−	118.638i	0.406100	−	0.234462i
$507$	−1171.22	+	300.301i	−2.31009	+	0.592310i
$508$	223.330	−	386.818i	0.439625	−	0.761453i
$509$	−686.562	−	396.387i	−1.34885	−	0.778756i	−0.360760	−	0.932659i	$-0.617483\pi$
$509$	−686.562	−	396.387i	−1.34885	−	0.778756i	−0.988086	+	0.153902i	$0.950816\pi$
$510$	−74.9920	−	20.9651i	−0.147043	−	0.0411081i
$511$	2.10639	+	3.64837i	0.00412209	+	0.00713967i
$512$			466.970i			0.912051i
$513$	−175.221	+	164.214i	−0.341562	+	0.320105i
$514$	−169.158			−0.329102
$515$	820.660	−	473.808i	1.59351	−	0.920016i
$516$	−77.9679	+	278.890i	−0.151101	+	0.540485i
$517$	−554.280	+	960.041i	−1.07211	+	1.85695i
$518$	83.7733	+	48.3665i	0.161725	+	0.0933717i
$519$	−93.1053	−	363.124i	−0.179394	−	0.699660i
$520$	−552.955	−	957.746i	−1.06337	−	1.84182i
$521$			113.473i			0.217798i	0.994053	+	0.108899i	$0.0347326\pi$
$521$			113.473i			0.217798i	−0.994053	+	0.108899i	$0.965267\pi$
$522$	−208.878	+	114.650i	−0.400149	+	0.219636i
$523$	145.974			0.279108			0.139554	−	0.990214i	$-0.455433\pi$
$523$	145.974			0.279108			0.139554	+	0.990214i	$0.455433\pi$
$524$	383.094	−	221.179i	0.731094	−	0.422098i
$525$	−193.945	−	198.183i	−0.369420	−	0.377491i
$526$	52.3120	−	90.6071i	0.0994525	−	0.172257i
$527$	118.210	+	68.2484i	0.224307	+	0.129504i
$528$	320.391	−	313.541i	0.606801	−	0.593828i
$529$	−123.111	−	213.235i	−0.232724	−	0.403091i
$530$		−	307.435i		−	0.580066i
$531$	128.064	+	233.316i	0.241175	+	0.439390i
$532$	77.4365			0.145557
$533$	−750.779	+	433.462i	−1.40859	+	0.813250i
$534$	−322.779	+	82.7609i	−0.604456	+	0.154983i
$535$	−143.097	+	247.851i	−0.267471	+	0.463273i
$536$	−297.025	−	171.487i	−0.554151	−	0.319939i
$537$	−667.581	−	186.632i	−1.24317	−	0.347546i
$538$	−61.1061	−	105.839i	−0.113580	−	0.196726i
$539$			736.244i			1.36594i
$540$	−203.742	+	672.393i	−0.377299	+	1.24517i
$541$	−707.289			−1.30737			−0.653687	−	0.756765i	$-0.726779\pi$
$541$	−707.289			−1.30737			−0.653687	+	0.756765i	$0.726779\pi$
$542$	282.241	−	162.952i	0.520741	−	0.300650i
$543$	−17.4504	+	62.4200i	−0.0321371	+	0.114954i
$544$	63.3138	−	109.663i	0.116386	−	0.201586i
$545$	560.339	+	323.512i	1.02814	+	0.593599i
$546$	37.5355	+	146.394i	0.0687463	+	0.268120i
$547$	395.340	+	684.749i	0.722742	+	1.25183i	0.959897	+	0.280354i	$0.0904517\pi$
$547$	395.340	+	684.749i	0.722742	+	1.25183i	−0.237155	+	0.971472i	$0.576215\pi$
$548$			288.421i			0.526315i
$549$	7.48275	−	346.195i	0.0136298	−	0.630591i
$550$	−501.092			−0.911076
$551$	251.991	−	145.487i	0.457334	−	0.264042i
$552$	−209.734	−	214.316i	−0.379953	−	0.388254i
$553$	−23.1906	+	40.1672i	−0.0419359	+	0.0726351i
$554$	112.731	+	65.0851i	0.203485	+	0.117482i
$555$	766.006	−	749.628i	1.38019	−	1.35068i
$556$	19.8532	+	34.3868i	0.0357073	+	0.0618468i
$557$			669.172i			1.20139i	0.799480	+	0.600693i	$0.205109\pi$
$557$			669.172i			1.20139i	−0.799480	+	0.600693i	$0.794891\pi$
$558$	−125.042	+	206.159i	−0.224090	+	0.369460i
$559$	690.168			1.23465
$560$	150.270	−	86.7585i	0.268339	−	0.154926i
$561$	−208.912	+	53.5653i	−0.372392	+	0.0954818i
$562$	32.8496	−	56.8973i	0.0584513	−	0.101241i
$563$	407.216	+	235.106i	0.723296	+	0.417595i	0.815965	−	0.578102i	$-0.196206\pi$
$563$	407.216	+	235.106i	0.723296	+	0.417595i	−0.0926683	+	0.995697i	$0.529540\pi$
$564$	614.477	+	171.786i	1.08950	+	0.304585i
$565$	−194.618	−	337.088i	−0.344456	−	0.596615i
$566$			257.791i			0.455461i
$567$	113.201	−	177.852i	0.199649	−	0.313671i
$568$	97.2397			0.171197
$569$	740.263	−	427.391i	1.30099	−	0.751126i	0.320415	−	0.947277i	$-0.396178\pi$
$569$	740.263	−	427.391i	1.30099	−	0.751126i	0.980574	+	0.196151i	$0.0628443\pi$
$570$	−45.2251	+	161.770i	−0.0793422	+	0.283807i
$571$	−26.2338	+	45.4382i	−0.0459435	+	0.0795765i	−0.888083	−	0.459684i	$-0.847963\pi$
$571$	−26.2338	+	45.4382i	−0.0459435	+	0.0795765i	0.842139	+	0.539260i	$0.181296\pi$
$572$	−1208.08	−	697.485i	−2.11203	−	1.21938i
$573$	−215.331	−	839.820i	−0.375795	−	1.46565i
$574$	38.1730	+	66.1175i	0.0665034	+	0.115187i
$575$		−	597.186i		−	1.03858i
$576$	−72.5416	−	43.9989i	−0.125940	−	0.0763870i
$577$	−116.156			−0.201310			−0.100655	−	0.994921i	$-0.532094\pi$
$577$	−116.156			−0.201310			−0.100655	+	0.994921i	$0.532094\pi$
$578$	−11.9142	+	6.87868i	−0.0206128	+	0.0119008i
$579$	−31.1357	−	31.8160i	−0.0537750	−	0.0549499i
$580$	425.650	−	737.247i	0.733879	−	1.27112i
$581$	109.886	+	63.4426i	0.189132	+	0.109196i
$582$	−278.385	+	272.433i	−0.478324	+	0.468097i
$583$	−425.752	−	737.425i	−0.730278	−	1.26488i
$584$		−	9.62106i		−	0.0164744i
$585$	1674.08	+	36.1841i	2.86168	+	0.0618531i
$586$	−362.400			−0.618431
$587$	−102.248	+	59.0327i	−0.174187	+	0.100567i	−0.584559	−	0.811352i	$-0.698732\pi$
$587$	−102.248	+	59.0327i	−0.174187	+	0.100567i	0.410372	+	0.911918i	$0.365399\pi$
$588$	410.471	−	105.245i	0.698080	−	0.178988i
$589$	147.223	−	254.997i	0.249954	−	0.432932i
$590$	161.223	+	93.0824i	0.273260	+	0.157767i
$591$	24.9008	+	6.96139i	0.0421334	+	0.0117790i
$592$	196.796	+	340.861i	0.332426	+	0.575779i
$593$			826.854i			1.39436i	0.716897	+	0.697179i	$0.245562\pi$
$593$			826.854i			1.39436i	−0.716897	+	0.697179i	$0.754438\pi$
$594$	−86.6243	−	370.994i	−0.145832	−	0.624569i
$595$	−83.4792			−0.140301
$596$	−212.336	+	122.592i	−0.356269	+	0.205692i
$597$	231.638	−	828.567i	0.388003	−	1.38788i
$598$	−162.738	+	281.871i	−0.272138	+	0.471356i
$599$	398.877	+	230.292i	0.665905	+	0.384460i	0.794523	−	0.607234i	$-0.207721\pi$
$599$	398.877	+	230.292i	0.665905	+	0.384460i	−0.128618	+	0.991694i	$0.541054\pi$
$600$	157.285	+	613.432i	0.262141	+	1.02239i
$601$	109.567	+	189.775i	0.182307	+	0.315765i	0.942666	−	0.333738i	$-0.108310\pi$
$601$	109.567	+	189.775i	0.182307	+	0.315765i	−0.760359	+	0.649503i	$0.774977\pi$
$602$		−	60.7798i		−	0.100963i
$603$	455.235	−	249.873i	0.754951	−	0.414382i
$604$	−633.663			−1.04911
$605$	−1232.91	+	711.818i	−2.03786	+	1.17656i
$606$	135.189	+	138.143i	0.223085	+	0.227959i
$607$	−317.333	+	549.637i	−0.522789	+	0.905498i	0.476859	+	0.878980i	$0.341775\pi$
$607$	−317.333	+	549.637i	−0.522789	+	0.905498i	−0.999648	+	0.0265179i	$0.991558\pi$
$608$	−236.560	−	136.578i	−0.389079	−	0.224635i
$609$	−182.569	+	178.665i	−0.299785	+	0.293375i
$610$	−121.104	−	209.759i	−0.198532	−	0.343867i
$611$		−	1520.64i		−	2.48877i
$612$	59.7275	+	108.816i	0.0975940	+	0.177804i
$613$	−536.095			−0.874543			−0.437272	−	0.899329i	$-0.644055\pi$
$613$	−536.095			−0.874543			−0.437272	+	0.899329i	$0.644055\pi$
$614$	214.526	−	123.857i	0.349391	−	0.201721i
$615$	819.388	−	210.092i	1.33234	−	0.341613i
$616$	−134.874	+	233.608i	−0.218951	+	0.379234i
$617$	−9.53178	−	5.50317i	−0.0154486	−	0.00891924i	0.492256	−	0.870451i	$-0.336172\pi$
$617$	−9.53178	−	5.50317i	−0.0154486	−	0.00891924i	−0.507704	+	0.861531i	$0.669506\pi$
$618$	284.823	+	79.6263i	0.460878	+	0.128845i
$619$	−334.758	−	579.817i	−0.540804	−	0.936700i	−0.998858	−	0.0477756i	$-0.984787\pi$
$619$	−334.758	−	579.817i	−0.540804	−	0.936700i	0.458054	−	0.888924i	$-0.348547\pi$
$620$		−	861.454i		−	1.38944i
$621$	442.139	−	103.236i	0.711979	−	0.166242i
$622$	191.231			0.307446
$623$	−309.375	+	178.618i	−0.496589	+	0.286706i
$624$	−165.562	+	592.215i	−0.265324	+	0.949063i
$625$	125.826	−	217.937i	0.201322	−	0.348700i
$626$	−135.174	−	78.0426i	−0.215932	−	0.124669i
$627$	115.549	+	450.657i	0.184288	+	0.718751i
$628$	75.6886	+	131.096i	0.120523	+	0.208752i
$629$		−	189.358i		−	0.301046i
$630$	3.18656	−	147.428i	0.00505803	−	0.234013i
$631$	571.390			0.905530			0.452765	−	0.891630i	$-0.350438\pi$
$631$	571.390			0.905530			0.452765	+	0.891630i	$0.350438\pi$
$632$	91.7331	−	52.9622i	0.145147	−	0.0838009i
$633$	205.261	+	209.745i	0.324267	+	0.331351i
$634$	−86.4886	+	149.803i	−0.136417	+	0.236282i
$635$	899.542	+	519.351i	1.41660	+	0.817875i
$636$	−350.269	+	342.780i	−0.550737	+	0.538962i
$637$	−504.962	−	874.620i	−0.792719	−	1.37303i
$638$			461.613i			0.723532i
$639$	−76.3541	+	125.886i	−0.119490	+	0.197005i
$640$	−1014.97			−1.58589
$641$	−90.7482	+	52.3935i	−0.141573	+	0.0817371i	−0.569113	−	0.822259i	$-0.692713\pi$
$641$	−90.7482	+	52.3935i	−0.141573	+	0.0817371i	0.427541	+	0.903996i	$0.359380\pi$
$642$	−86.5202	+	22.1839i	−0.134767	+	0.0345543i
$643$	338.509	−	586.314i	0.526452	−	0.911842i	−0.473073	−	0.881023i	$-0.656855\pi$
$643$	338.509	−	586.314i	0.526452	−	0.911842i	0.999525	−	0.0308184i	$-0.00981135\pi$
$644$	−126.792	−	73.2035i	−0.196882	−	0.113670i
$645$	−648.557	−	181.314i	−1.00552	−	0.281106i
$646$	14.8384	+	25.7009i	0.0229697	+	0.0397846i
$647$		−	118.927i		−	0.183813i	−0.995768	−	0.0919063i	$-0.970704\pi$
$647$		−	118.927i		−	0.183813i	0.995768	−	0.0919063i	$-0.0292960\pi$
$648$	−426.977	+	222.494i	−0.658916	+	0.343354i
$649$	515.622			0.794487
$650$	595.271	−	343.680i	0.915802	−	0.528739i
$651$	−69.5970	+	248.948i	−0.106908	+	0.382408i
$652$	−469.763	+	813.653i	−0.720495	+	1.24793i
$653$	577.614	+	333.486i	0.884555	+	0.510698i	0.872158	−	0.489225i	$-0.162720\pi$
$653$	577.614	+	333.486i	0.884555	+	0.510698i	0.0123973	+	0.999923i	$0.496054\pi$
$654$	50.1530	+	195.604i	0.0766865	+	0.299088i
$655$	514.350	+	890.880i	0.785267	+	1.36012i
$656$			310.640i			0.473537i
$657$	12.4554	+	7.55460i	0.0189580	+	0.0114986i
$658$	−133.916			−0.203519
$659$	−459.361	+	265.212i	−0.697057	+	0.402446i	−0.806250	−	0.591574i	$-0.798507\pi$
$659$	−459.361	+	265.212i	−0.697057	+	0.402446i	0.109193	+	0.994021i	$0.465173\pi$
$660$	952.007	+	972.807i	1.44244	+	1.47395i
$661$	40.9369	−	70.9047i	0.0619317	−	0.107269i	−0.833397	−	0.552675i	$-0.813607\pi$
$661$	40.9369	−	70.9047i	0.0619317	−	0.107269i	0.895329	+	0.445406i	$0.146941\pi$
$662$	361.389	+	208.648i	0.545905	+	0.315179i
$663$	211.439	−	206.918i	0.318912	−	0.312093i
$664$	−144.889	−	250.955i	−0.218206	−	0.377944i
$665$			180.078i			0.270794i
$666$	334.416	+	7.22815i	0.502125	+	0.0108531i
$667$	−550.137			−0.824793
$668$	−326.129	+	188.291i	−0.488218	+	0.281873i
$669$	−685.994	+	175.890i	−1.02540	+	0.262914i
$670$	181.618	−	314.571i	0.271072	−	0.469510i
$671$	−580.970	−	335.423i	−0.865827	−	0.499886i
$672$	230.948	+	64.5649i	0.343673	+	0.0960787i
$673$	469.151	+	812.594i	0.697104	+	1.20742i	0.969466	+	0.245225i	$0.0788618\pi$
$673$	469.151	+	812.594i	0.697104	+	1.20742i	−0.272362	+	0.962195i	$0.587805\pi$
$674$		−	226.287i		−	0.335737i
$675$	−917.649	−	278.057i	−1.35948	−	0.411936i
$676$	1348.19			1.99437
$677$	1115.11	−	643.808i	1.64713	−	0.950972i	0.668929	−	0.743327i	$-0.266753\pi$
$677$	1115.11	−	643.808i	1.64713	−	0.950972i	0.978204	−	0.207646i	$-0.0665801\pi$
$678$	32.7067	−	116.991i	0.0482399	−	0.172554i
$679$	−208.790	+	361.636i	−0.307497	+	0.532600i
$680$	165.106	+	95.3241i	0.242803	+	0.140183i
$681$	−159.683	−	622.787i	−0.234483	−	0.914519i
$682$	233.560	+	404.537i	0.342463	+	0.593163i
$683$		−	37.8698i		−	0.0554463i	−0.999616	−	0.0277231i	$-0.991174\pi$
$683$		−	37.8698i		−	0.0554463i	0.999616	−	0.0277231i	$-0.00882568\pi$
$684$	234.733	−	128.842i	0.343177	−	0.188365i
$685$	−670.719			−0.979152
$686$	−166.404	+	96.0734i	−0.242572	+	0.140049i
$687$	−593.013	−	605.969i	−0.863192	−	0.882051i
$688$	123.652	−	214.172i	0.179727	−	0.311296i
$689$	1011.54	+	584.015i	1.46813	+	0.847628i
$690$	226.977	−	222.124i	0.328952	−	0.321919i
$691$	151.336	+	262.121i	0.219010	+	0.379336i	0.954506	−	0.298193i	$-0.0963840\pi$
$691$	151.336	+	262.121i	0.219010	+	0.379336i	−0.735496	+	0.677529i	$0.763051\pi$
$692$			417.993i			0.604036i
$693$	−196.523	−	358.040i	−0.283583	−	0.516652i
$694$	8.77973			0.0126509
$695$	−79.9662	+	46.1685i	−0.115059	+	0.0664295i
$696$	565.103	−	144.893i	0.811930	−	0.208180i
$697$	74.7248	−	129.427i	0.107209	−	0.185692i
$698$	−308.740	−	178.251i	−0.442321	−	0.255374i
$699$	172.866	+	48.3271i	0.247304	+	0.0691375i
$700$	154.595	+	267.767i	0.220851	+	0.382524i
$701$		−	864.985i		−	1.23393i	−0.786990	−	0.616965i	$-0.788362\pi$
$701$		−	864.985i		−	1.23393i	0.786990	−	0.616965i	$-0.211638\pi$
$702$	357.356	+	381.309i	0.509054	+	0.543176i
$703$	−408.475			−0.581046
$704$	−142.345	+	82.1832i	−0.202195	+	0.116737i
$705$	−399.486	+	1428.96i	−0.566647	+	2.02689i
$706$	−48.9881	+	84.8499i	−0.0693882	+	0.120184i
$707$	179.455	+	103.608i	0.253825	+	0.146546i
$708$	−73.7075	−	287.470i	−0.104107	−	0.406031i
$709$	556.871	+	964.529i	0.785432	+	1.36041i	0.928741	+	0.370729i	$0.120892\pi$
$709$	556.871	+	964.529i	0.785432	+	1.36041i	−0.143309	+	0.989678i	$0.545774\pi$
$710$			102.984i			0.145048i
$711$	−3.46572	+	160.344i	−0.00487443	+	0.225519i
$712$	815.846			1.14585
$713$	−482.116	+	278.350i	−0.676179	+	0.390392i
$714$	−18.2223	−	18.6204i	−0.0255214	−	0.0260790i
$715$	1621.99	−	2809.38i	2.26852	−	3.92920i
$716$	669.367	+	386.459i	0.934870	+	0.539747i
$717$	−172.657	+	168.966i	−0.240805	+	0.235657i
$718$	180.878	+	313.289i	0.251919	+	0.436336i
$719$		−	325.866i		−	0.453221i	−0.973985	−	0.226610i	$-0.927236\pi$
$719$		−	325.866i		−	0.453221i	0.973985	−	0.226610i	$-0.0727644\pi$
$720$	311.161	−	513.015i	0.432168	−	0.712521i
$721$	317.057			0.439747
$722$	−197.561	+	114.062i	−0.273630	+	0.157981i
$723$	−420.380	+	107.786i	−0.581439	+	0.149081i
$724$	36.1346	−	62.5869i	0.0499097	−	0.0864461i
$725$	1006.16	+	580.906i	1.38780	+	0.801249i
$726$	−427.899	−	119.625i	−0.589392	−	0.164773i
$727$	86.7563	+	150.266i	0.119335	+	0.206694i	0.919504	−	0.393080i	$-0.128591\pi$
$727$	86.7563	+	150.266i	0.119335	+	0.206694i	−0.800170	+	0.599774i	$0.795257\pi$
$728$		−	370.020i		−	0.508269i
$729$	47.2300	−	727.468i	0.0647874	−	0.997899i
$730$	10.1894			0.0139581
$731$	−103.038	+	59.4892i	−0.140955	+	0.0813806i
$732$	−103.956	+	371.851i	−0.142017	+	0.507994i
$733$	607.986	−	1053.06i	0.829449	−	1.43665i	−0.0690228	−	0.997615i	$-0.521988\pi$
$733$	607.986	−	1053.06i	0.829449	−	1.43665i	0.898471	−	0.439032i	$-0.144679\pi$
$734$	−285.352	−	164.748i	−0.388763	−	0.224452i
$735$	244.747	+	954.547i	0.332989	+	1.29870i
$736$	258.224	+	447.257i	0.350848	+	0.607686i
$737$		−	1006.06i		−	1.36507i
$738$	225.722	+	136.908i	0.305857	+	0.185512i
$739$	−555.714			−0.751981			−0.375991	−	0.926623i	$-0.622698\pi$
$739$	−555.714			−0.751981			−0.375991	+	0.926623i	$0.622698\pi$
$740$	−1034.96	+	597.535i	−1.39860	+	0.807480i
$741$	−446.355	−	456.107i	−0.602368	−	0.615528i
$742$	51.4315	−	89.0819i	0.0693146	−	0.120056i
$743$	418.217	+	241.458i	0.562877	+	0.324977i	0.754299	−	0.656531i	$-0.227977\pi$
$743$	418.217	+	241.458i	0.562877	+	0.324977i	−0.191423	+	0.981508i	$0.561310\pi$
$744$	421.921	−	412.900i	0.567098	−	0.554973i
$745$	−285.087	−	493.786i	−0.382668	−	0.662800i
$746$			503.750i			0.675268i
$747$	438.654	+	9.48120i	0.587221	+	0.0126924i
$748$	240.479			0.321497
$749$	−82.9271	+	47.8780i	−0.110717	+	0.0639226i
$750$	−192.323	+	49.3119i	−0.256431	+	0.0657491i
$751$	−44.9522	+	77.8596i	−0.0598565	+	0.103675i	−0.894401	−	0.447266i	$-0.852398\pi$
$751$	−44.9522	+	77.8596i	−0.0598565	+	0.103675i	0.834544	+	0.550941i	$0.185731\pi$
$752$	−471.882	−	272.441i	−0.627503	−	0.362289i
$753$	541.570	+	151.404i	0.719216	+	0.201067i
$754$	−316.603	−	548.373i	−0.419898	−	0.727285i
$755$		−	1473.58i		−	1.95176i
$756$	−171.522	+	160.747i	−0.226881	+	0.212629i
$757$	647.421			0.855246			0.427623	−	0.903957i	$-0.359351\pi$
$757$	647.421			0.855246			0.427623	+	0.903957i	$0.359351\pi$
$758$	−401.483	+	231.796i	−0.529661	+	0.305800i
$759$	236.826	−	847.124i	0.312023	−	1.11610i
$760$	205.629	−	356.160i	0.270565	−	0.468632i
$761$	−889.297	−	513.436i	−1.16859	−	0.674686i	−0.215242	−	0.976561i	$-0.569054\pi$
$761$	−889.297	−	513.436i	−1.16859	−	0.674686i	−0.953347	+	0.301875i	$0.902387\pi$
$762$	80.5133	+	314.013i	0.105660	+	0.412091i
$763$	108.242	+	187.480i	0.141864	+	0.245715i
$764$			966.720i			1.26534i
$765$	−253.050	+	138.896i	−0.330784	+	0.181563i
$766$	−63.7731			−0.0832547
$767$	−612.533	+	353.646i	−0.798608	+	0.461077i
$768$	−142.432	−	145.544i	−0.185459	−	0.189511i
$769$	−731.569	+	1267.12i	−0.951325	+	1.64774i	−0.208764	+	0.977966i	$0.566944\pi$
$769$	−731.569	+	1267.12i	−0.951325	+	1.64774i	−0.742562	+	0.669778i	$0.766389\pi$
$770$	−247.408	−	142.841i	−0.321310	−	0.185508i
$771$	−448.184	+	438.601i	−0.581302	+	0.568873i
$772$	24.8185	+	42.9870i	0.0321484	+	0.0556826i
$773$			808.771i			1.04628i	0.852248	+	0.523138i	$0.175239\pi$
$773$			808.771i			1.04628i	−0.852248	+	0.523138i	$0.824761\pi$
$774$	−101.128	−	184.242i	−0.130656	−	0.238038i
$775$	1175.67			1.51699
$776$	825.896	−	476.831i	1.06430	−	0.614473i
$777$	347.364	−	89.0644i	0.447057	−	0.114626i
$778$	−1.00430	+	1.73950i	−0.00129087	+	0.00223586i
$779$	−279.195	−	161.193i	−0.358401	−	0.206923i
$780$	−1798.15	−	502.698i	−2.30532	−	0.644485i
$781$	142.618	+	247.021i	0.182609	+	0.316288i
$782$		−	56.1091i		−	0.0717507i
$783$	−256.150	+	845.352i	−0.327139	+	1.07963i
$784$	−361.881			−0.461583
$785$	−304.864	+	176.013i	−0.388361	+	0.224221i
$786$	−86.4397	+	309.194i	−0.109974	+	0.393377i
$787$	−610.354	+	1057.16i	−0.775546	+	1.34328i	0.158942	+	0.987288i	$0.449192\pi$
$787$	−610.354	+	1057.16i	−0.775546	+	1.34328i	−0.934487	+	0.355996i	$0.884142\pi$
$788$	−24.9674	−	14.4149i	−0.0316845	−	0.0182931i
$789$	−96.3297	−	375.700i	−0.122091	−	0.476172i
$790$	56.0908	+	97.1522i	0.0710011	+	0.122977i
$791$		−	130.232i		−	0.164642i
$792$	−20.1563	+	932.543i	−0.0254498	+	1.17745i
$793$	920.217			1.16043
$794$	169.759	−	98.0105i	0.213802	−	0.123439i
$795$	−797.131	−	814.547i	−1.00268	−	1.02459i
$796$	−479.653	+	830.783i	−0.602579	+	1.04370i
$797$	−39.7449	−	22.9467i	−0.0498681	−	0.0287914i	0.474859	−	0.880062i	$-0.342499\pi$
$797$	−39.7449	−	22.9467i	−0.0498681	−	0.0287914i	−0.524727	+	0.851271i	$0.675833\pi$
$798$	−40.1671	+	39.3083i	−0.0503348	+	0.0492586i
$799$	131.072	+	227.023i	0.164045	+	0.284134i
$800$		−	1090.67i		−	1.36333i
$801$	−640.615	+	1056.19i	−0.799769	+	1.31859i
$802$	438.289			0.546496
$803$	24.4407	−	14.1108i	0.0304367	−	0.0175726i
$804$	−560.897	+	143.815i	−0.697633	+	0.178874i
$805$	170.234	−	294.854i	0.211471	−	0.366278i
$806$	−554.914	−	320.380i	−0.688479	−	0.397494i
$807$	−436.324	−	121.981i	−0.540674	−	0.151153i
$808$	−236.618	−	409.835i	−0.292844	−	0.507221i
$809$		−	1333.69i		−	1.64856i	−0.566181	−	0.824281i	$-0.691580\pi$
$809$		−	1333.69i		−	1.64856i	0.566181	−	0.824281i	$-0.308420\pi$
$810$	−235.637	−	452.201i	−0.290910	−	0.558273i
$811$	123.988			0.152883			0.0764413	−	0.997074i	$-0.475644\pi$
$811$	123.988			0.152883			0.0764413	+	0.997074i	$0.475644\pi$
$812$	246.671	−	142.416i	0.303782	−	0.175389i
$813$	325.287	−	1163.55i	0.400107	−	1.43118i
$814$	324.011	−	561.203i	0.398047	−	0.689438i
$815$	−1892.14	−	1092.43i	−2.32165	−	1.34040i
$816$	−26.3286	−	102.685i	−0.0322654	−	0.125840i
$817$	128.328	+	222.270i	0.157072	+	0.272056i
$818$			343.552i			0.419991i
$819$	479.026	+	290.545i	0.584891	+	0.354756i
$820$	−943.201			−1.15024
$821$	55.9299	−	32.2911i	0.0681241	−	0.0393315i	−0.465551	−	0.885021i	$-0.654144\pi$
$821$	55.9299	−	32.2911i	0.0681241	−	0.0393315i	0.533675	+	0.845690i	$0.320811\pi$
$822$	−146.408	−	149.607i	−0.178112	−	0.182003i
$823$	−319.130	+	552.749i	−0.387764	+	0.671627i	−0.992148	−	0.125066i	$-0.960086\pi$
$823$	−319.130	+	552.749i	−0.387764	+	0.671627i	0.604384	+	0.796693i	$0.293419\pi$
$824$	−627.080	−	362.045i	−0.761019	−	0.439375i
$825$	−1327.64	+	1299.25i	−1.60926	+	1.57485i
$826$	31.1439	+	53.9428i	0.0377045	+	0.0653061i
$827$		−	1439.50i		−	1.74063i	−0.492499	−	0.870313i	$-0.663916\pi$
$827$		−	1439.50i		−	1.74063i	0.492499	−	0.870313i	$-0.336084\pi$
$828$	−506.143	−	10.9399i	−0.611284	−	0.0132125i
$829$	459.699			0.554522			0.277261	−	0.960795i	$-0.410573\pi$
$829$	459.699			0.554522			0.277261	+	0.960795i	$0.410573\pi$
$830$	265.780	−	153.448i	0.320217	−	0.184877i
$831$	467.435	−	119.851i	0.562497	−	0.144225i
$832$	112.733	−	195.259i	0.135496	−	0.234686i
$833$	150.776	+	87.0507i	0.181004	+	0.104503i
$834$	−27.7535	−	7.75890i	−0.0332776	−	0.00930324i
$835$	−437.869	−	758.411i	−0.524394	−	0.908277i
$836$		−	518.752i		−	0.620517i
$837$	203.239	+	870.432i	0.242819	+	1.03994i
$838$	100.208			0.119581
$839$	1048.31	−	605.242i	1.24948	−	0.721385i	0.278471	−	0.960445i	$-0.410172\pi$
$839$	1048.31	−	605.242i	1.24948	−	0.721385i	0.971005	+	0.239059i	$0.0768390\pi$
$840$	−97.2077	+	347.711i	−0.115723	+	0.413942i
$841$	114.639	−	198.561i	0.136313	−	0.236101i
$842$	−289.274	−	167.012i	−0.343556	−	0.198352i
$843$	−60.4908	−	235.923i	−0.0717566	−	0.279861i
$844$	−163.615	−	283.390i	−0.193857	−	0.335770i
$845$			3135.21i			3.71031i
$846$	−405.937	+	222.814i	−0.479831	+	0.263373i
$847$	−476.326			−0.562369
$848$	362.461	−	209.267i	0.427431	−	0.246777i
$849$	668.412	+	683.015i	0.787293	+	0.804493i
$850$	−59.2472	+	102.619i	−0.0697026	+	0.120728i
$851$	668.825	+	386.146i	0.785928	+	0.453756i
$852$	117.332	−	114.824i	0.137714	−	0.134770i
$853$	−577.517	−	1000.29i	−0.677042	−	1.17267i	−0.975867	−	0.218364i	$-0.929928\pi$
$853$	−577.517	−	1000.29i	−0.677042	−	1.17267i	0.298825	−	0.954308i	$-0.403405\pi$
$854$		−	81.0392i		−	0.0948936i
$855$	299.620	+	545.869i	0.350433	+	0.638443i
$856$	218.686			0.255474
$857$	−490.803	+	283.365i	−0.572699	+	0.330648i	−0.758226	−	0.651991i	$-0.773934\pi$
$857$	−490.803	+	283.365i	−0.572699	+	0.330648i	0.185528	+	0.982639i	$0.440601\pi$
$858$	980.701	−	251.453i	1.14301	−	0.293068i
$859$	39.6787	−	68.7256i	0.0461918	−	0.0800065i	−0.842005	−	0.539470i	$-0.818625\pi$
$859$	39.6787	−	68.7256i	0.0461918	−	0.0800065i	0.888197	+	0.459463i	$0.151958\pi$
$860$	650.292	+	375.446i	0.756153	+	0.436565i
$861$	272.571	+	76.2013i	0.316575	+	0.0885032i
$862$	−145.672	−	252.312i	−0.168993	−	0.292705i
$863$		−	828.604i		−	0.960144i	−0.877229	−	0.480072i	$-0.840611\pi$
$863$		−	828.604i		−	0.960144i	0.877229	−	0.480072i	$-0.159389\pi$
$864$	807.497	−	188.545i	0.934603	−	0.218223i
$865$	−972.039			−1.12374
$866$	−210.019	+	121.255i	−0.242517	+	0.140017i
$867$	−13.7313	+	49.1167i	−0.0158377	+	0.0566513i
$868$	144.114	−	249.613i	0.166030	−	0.287573i
$869$	269.083	+	155.355i	0.309647	+	0.178775i
$870$	153.452	+	598.486i	0.176382	+	0.687915i
$871$	690.017	+	1195.14i	0.792212	+	1.37215i
$872$		−	494.401i		−	0.566974i
$873$	−31.2027	+	1443.62i	−0.0357420	+	1.65363i
$874$	−121.036			−0.138485
$875$	−184.336	+	106.427i	−0.210670	+	0.121630i
$876$	−11.3609	−	11.6091i	−0.0129690	−	0.0132524i
$877$	661.272	−	1145.36i	0.754016	−	1.30599i	−0.191845	−	0.981425i	$-0.561447\pi$
$877$	661.272	−	1145.36i	0.754016	−	1.30599i	0.945862	−	0.324570i	$-0.105219\pi$
$878$	307.368	+	177.459i	0.350077	+	0.202117i
$879$	−960.177	+	939.648i	−1.09235	+	1.06900i
$880$	−581.201	−	1006.67i	−0.660455	−	1.14394i
$881$			807.386i			0.916443i	0.888838	+	0.458221i	$0.151513\pi$
$881$			807.386i			0.916443i	−0.888838	+	0.458221i	$0.848487\pi$
$882$	−159.491	+	262.955i	−0.180829	+	0.298135i
$883$	−1103.04			−1.24919			−0.624597	−	0.780947i	$-0.714737\pi$
$883$	−1103.04			−1.24919			−0.624597	+	0.780947i	$0.714737\pi$
$884$	−285.677	+	164.936i	−0.323165	+	0.186579i
$885$	668.509	−	171.406i	0.755377	−	0.193679i
$886$	126.956	−	219.894i	0.143291	−	0.248187i
$887$	−1173.09	−	677.283i	−1.32253	−	0.763566i	−0.338402	−	0.941002i	$-0.609886\pi$
$887$	−1173.09	−	677.283i	−1.32253	−	0.763566i	−0.984132	+	0.177436i	$0.943220\pi$
$888$	−788.722	−	220.499i	−0.888200	−	0.248309i
$889$	173.767	+	300.973i	0.195463	+	0.338552i
$890$			864.042i			0.970833i
$891$	−1191.44	−	758.342i	−1.33719	−	0.851113i
$892$	789.650			0.885258
$893$	489.725	−	282.743i	0.548404	−	0.316621i
$894$	47.9107	−	171.376i	0.0535914	−	0.191696i
$895$	−898.707	+	1556.61i	−1.00414	+	1.73923i
$896$	−294.097	−	169.797i	−0.328233	−	0.189505i
$897$	299.674	+	1168.77i	0.334084	+	1.30298i
$898$	−232.801	−	403.223i	−0.259244	−	0.449023i
$899$		−	1083.04i		−	1.20472i
$900$	914.145	+	554.459i	1.01572	+	0.616066i
$901$	−201.357			−0.223482
$902$	442.926	−	255.723i	0.491048	−	0.283507i
$903$	−157.593	−	161.036i	−0.174521	−	0.178334i
$904$	−148.711	+	257.574i	−0.164503	+	0.284927i
$905$	145.545	+	84.0307i	0.160824	+	0.0928515i
$906$	328.687	−	321.660i	0.362790	−	0.355033i
$907$	2.58101	+	4.47044i	0.00284565	+	0.00492882i	0.867445	−	0.497534i	$-0.165761\pi$
$907$	2.58101	+	4.47044i	0.00284565	+	0.00492882i	−0.864599	+	0.502462i	$0.832428\pi$
$908$			716.893i			0.789529i
$909$	716.366	+	15.4837i	0.788082	+	0.0170338i
$910$	391.878			0.430636
$911$	1259.49	−	727.164i	1.38253	−	0.798205i	0.390072	−	0.920784i	$-0.372450\pi$
$911$	1259.49	−	727.164i	1.38253	−	0.798205i	0.992459	+	0.122580i	$0.0391167\pi$
$912$	−221.508	+	56.7949i	−0.242882	+	0.0622751i
$913$	425.006	−	736.132i	0.465505	−	0.806279i
$914$	−308.787	−	178.278i	−0.337841	−	0.195053i
$915$	−864.737	−	241.750i	−0.945067	−	0.264207i
$916$	472.695	+	818.732i	0.516043	+	0.893812i
$917$			344.187i			0.375340i
$918$	−86.2184	−	26.1250i	−0.0939198	−	0.0284586i
$919$	285.223			0.310362			0.155181	−	0.987886i	$-0.450404\pi$
$919$	285.223			0.310362			0.155181	+	0.987886i	$0.450404\pi$
$920$	−673.382	+	388.777i	−0.731937	+	0.422584i
$921$	247.244	−	884.390i	0.268452	−	0.960249i
$922$	43.5996	−	75.5168i	0.0472881	−	0.0819054i
$923$	−338.845	−	195.632i	−0.367113	−	0.211953i
$924$	113.109	+	441.142i	0.122413	+	0.477427i
$925$	−815.486	−	1412.46i	−0.881606	−	1.52699i
$926$		−	410.106i		−	0.442879i
$927$	961.094	−	527.532i	1.03678	−	0.569074i
$928$	−1004.74			−1.08269
$929$	748.901	−	432.378i	0.806137	−	0.465423i	−0.0394759	−	0.999221i	$-0.512569\pi$
$929$	748.901	−	432.378i	0.806137	−	0.465423i	0.845612	+	0.533797i	$0.179235\pi$
$930$	437.291	+	446.845i	0.470206	+	0.480479i
$931$	187.782	−	325.248i	0.201699	−	0.349353i
$932$	−173.328	−	100.071i	−0.185974	−	0.107372i
$933$	506.666	−	495.833i	0.543050	−	0.531439i
$934$	73.7586	+	127.754i	0.0789707	+	0.136781i
$935$			559.233i			0.598110i
$936$	−615.652	−	1121.64i	−0.657748	−	1.19833i
$937$	468.142			0.499618			0.249809	−	0.968295i	$-0.419632\pi$
$937$	468.142			0.499618			0.249809	+	0.968295i	$0.419632\pi$
$938$	105.251	−	60.7665i	0.112208	−	0.0647830i
$939$	−560.494	+	143.711i	−0.596905	+	0.153047i
$940$	827.216	−	1432.78i	0.880018	−	1.52424i
$941$	−398.668	−	230.171i	−0.423665	−	0.244603i	0.272979	−	0.962020i	$-0.411991\pi$
$941$	−398.668	−	230.171i	−0.423665	−	0.244603i	−0.696644	+	0.717417i	$0.745324\pi$
$942$	−105.808	−	29.5801i	−0.112322	−	0.0314014i
$943$	304.763	+	527.865i	0.323185	+	0.559772i
$944$			253.440i			0.268475i
$945$	−373.816	−	398.873i	−0.395573	−	0.422087i
$946$	−407.168			−0.430410
$947$	−1377.75	+	795.443i	−1.45486	+	0.839961i	−0.998751	−	0.0499655i	$-0.984089\pi$
$947$	−1377.75	+	795.443i	−1.45486	+	0.839961i	−0.456104	+	0.889926i	$0.650756\pi$
$948$	48.1486	−	172.227i	0.0507897	−	0.181674i
$949$	−19.3562	+	33.5259i	−0.0203964	+	0.0353276i
$950$	221.366	+	127.806i	0.233017	+	0.134532i
$951$	159.264	+	621.153i	0.167470	+	0.653157i
$952$	31.8939	+	55.2419i	0.0335020	+	0.0580272i
$953$			1298.89i			1.36295i	0.731843	+	0.681474i	$0.238661\pi$
$953$			1298.89i			1.36295i	−0.731843	+	0.681474i	$0.761339\pi$
$954$	7.68619	−	355.607i	0.00805680	−	0.372754i
$955$	−2248.10			−2.35403
$956$	233.280	−	134.684i	0.244016	−	0.140883i
$957$	1196.89	+	1223.04i	1.25067	+	1.27799i
$958$	10.1605	−	17.5985i	0.0106059	−	0.0183700i
$959$	−194.347	−	112.206i	−0.202655	−	0.117003i
$960$	−157.232	+	153.871i	−0.163784	+	0.160282i
$961$	−67.4818	−	116.882i	−0.0702204	−	0.121625i
$962$			888.907i			0.924020i
$963$	−171.715	+	283.109i	−0.178313	+	0.293987i
$964$	483.901			0.501972
$965$	−99.9658	+	57.7153i	−0.103591	+	0.0598086i
$966$	102.928	−	26.3908i	0.106551	−	0.0273197i
$967$	424.725	−	735.645i	0.439219	−	0.760750i	−0.558410	−	0.829565i	$-0.688588\pi$
$967$	424.725	−	735.645i	0.439219	−	0.760750i	0.997629	+	0.0688148i	$0.0219218\pi$
$968$	942.084	+	543.912i	0.973227	+	0.561893i
$969$	105.953	+	29.6206i	0.109342	+	0.0305682i
$970$	505.000	+	874.685i	0.520618	+	0.901737i
$971$		−	620.233i		−	0.638757i	−0.947627	−	0.319379i	$-0.896526\pi$
$971$		−	620.233i		−	0.638757i	0.947627	−	0.319379i	$-0.103474\pi$
$972$	−252.476	+	772.656i	−0.259749	+	0.794914i
$973$	−30.8945			−0.0317518
$974$	−262.227	+	151.397i	−0.269227	+	0.155438i
$975$	686.058	−	2454.02i	0.703649	−	2.51695i
$976$	164.868	−	285.560i	0.168922	−	0.292582i
$977$	543.231	+	313.635i	0.556020	+	0.321018i	0.751546	−	0.659680i	$-0.229308\pi$
$977$	543.231	+	313.635i	0.556020	+	0.321018i	−0.195527	+	0.980698i	$0.562642\pi$
$978$	−169.356	−	660.511i	−0.173165	−	0.675369i
$979$	1196.57	+	2072.52i	1.22224	+	2.11698i
$980$		−	1098.78i		−	1.12121i
$981$	640.050	+	388.212i	0.652446	+	0.395731i
$982$	−336.672			−0.342843
$983$	−1397.22	+	806.683i	−1.42138	+	0.820634i	−0.996417	−	0.0845766i	$-0.973046\pi$
$983$	−1397.22	+	806.683i	−1.42138	+	0.820634i	−0.424963	+	0.905211i	$0.639713\pi$
$984$	−452.081	−	461.958i	−0.459432	−	0.469470i
$985$	33.5218	−	58.0615i	0.0340323	−	0.0589457i
$986$	94.5343	+	54.5794i	0.0958766	+	0.0553544i
$987$	−354.808	+	347.222i	−0.359481	+	0.351795i
$988$	355.793	+	616.251i	0.360114	+	0.623736i
$989$		−	485.251i		−	0.490648i
$990$	−987.632	−	21.3470i	−0.997609	−	0.0215626i
$991$	968.743			0.977541			0.488770	−	0.872412i	$-0.337446\pi$
$991$	968.743			0.977541			0.488770	+	0.872412i	$0.337446\pi$
$992$	−880.507	+	508.361i	−0.887608	+	0.512461i
$993$	1498.49	−	384.214i	1.50905	−	0.386923i
$994$	−17.2284	+	29.8405i	−0.0173324	+	0.0300206i
$995$	−1931.98	−	1115.43i	−1.94169	−	1.12103i
$996$	−471.163	−	131.721i	−0.473055	−	0.132250i
$997$	886.595	+	1535.63i	0.889262	+	1.54025i	0.840749	+	0.541425i	$0.182115\pi$
$997$	886.595	+	1535.63i	0.889262	+	1.54025i	0.0485132	+	0.998823i	$0.484552\pi$
$998$			284.668i			0.285239i
$999$	904.773	−	847.936i	0.905678	−	0.848785i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.3.j.a.86.19	✓	64
3.2	odd	2		459.3.j.a.341.14		64
9.2	odd	6	inner	153.3.j.a.137.19	yes	64
9.7	even	3		459.3.j.a.35.14		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.j.a.86.19	✓	64	1.1	even	1	trivial
153.3.j.a.137.19	yes	64	9.2	odd	6	inner
459.3.j.a.35.14		64	9.7	even	3
459.3.j.a.341.14		64	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	153.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.700836 - 0.404628i) q^{2} +(0.807723 - 2.88922i) q^{3} +(-1.67255 + 2.89695i) q^{4} +(-6.73682 - 3.88950i) q^{5} +(-0.602977 - 2.35170i) q^{6} +(-1.30137 - 2.25403i) q^{7} +5.94407i q^{8} +(-7.69517 - 4.66738i) q^{9} -6.29521 q^{10} +(-15.0999 + 8.71794i) q^{11} +(7.01895 + 7.17230i) q^{12} +(11.9586 - 20.7129i) q^{13} +(-1.82409 - 1.05314i) q^{14} +(-16.6791 + 16.3225i) q^{15} +(-4.28507 - 7.42196i) q^{16} +4.12311i q^{17} +(-7.28161 - 0.157387i) q^{18} +8.89419 q^{19} +(22.5354 - 13.0108i) q^{20} +(-7.56354 + 1.93930i) q^{21} +(-7.05505 + 12.2197i) q^{22} +(-14.5631 - 8.40799i) q^{23} +(17.1737 + 4.80116i) q^{24} +(17.7565 + 30.7551i) q^{25} -19.3552i q^{26} +(-19.7006 + 18.4631i) q^{27} +8.70641 q^{28} +(28.3321 - 16.3576i) q^{29} +(-5.08479 + 18.1882i) q^{30} +(16.5527 - 28.6701i) q^{31} +(-26.5971 - 15.3559i) q^{32} +(12.9915 + 50.6686i) q^{33} +(1.66832 + 2.88962i) q^{34} +20.2467i q^{35} +(26.3917 - 14.4860i) q^{36} -45.9261 q^{37} +(6.23337 - 3.59884i) q^{38} +(-50.1850 - 51.2814i) q^{39} +(23.1195 - 40.0441i) q^{40} +(-31.3907 - 18.1234i) q^{41} +(-4.51611 + 4.41955i) q^{42} +(14.4282 + 24.9905i) q^{43} -58.3248i q^{44} +(33.6872 + 61.3737i) q^{45} -13.6084 q^{46} +(55.0612 - 31.7896i) q^{47} +(-24.9048 + 6.38562i) q^{48} +(21.1129 - 36.5686i) q^{49} +(24.8888 + 14.3696i) q^{50} +(11.9126 + 3.33033i) q^{51} +(40.0028 + 69.2870i) q^{52} +48.8363i q^{53} +(-6.33625 + 20.9110i) q^{54} +135.634 q^{55} +(13.3981 - 7.73542i) q^{56} +(7.18404 - 25.6973i) q^{57} +(13.2375 - 22.9279i) q^{58} +(-25.6105 - 14.7862i) q^{59} +(-19.3887 - 75.6187i) q^{60} +(19.2375 + 33.3204i) q^{61} -26.7907i q^{62} +(-0.506188 + 23.4191i) q^{63} +9.42690 q^{64} +(-161.126 + 93.0262i) q^{65} +(29.6069 + 30.2537i) q^{66} +(-28.8502 + 49.9700i) q^{67} +(-11.9444 - 6.89611i) q^{68} +(-36.0555 + 35.2846i) q^{69} +(8.19238 + 14.1896i) q^{70} -16.3591i q^{71} +(27.7432 - 45.7406i) q^{72} -1.61860 q^{73} +(-32.1867 + 18.5830i) q^{74} +(103.201 - 26.4607i) q^{75} +(-14.8760 + 25.7660i) q^{76} +(39.3011 + 22.6905i) q^{77} +(-55.9213 - 15.6336i) q^{78} +(-8.91008 - 15.4327i) q^{79} +66.6672i q^{80} +(37.4312 + 71.8325i) q^{81} -29.3330 q^{82} +(-42.2194 + 24.3754i) q^{83} +(7.03237 - 25.1547i) q^{84} +(16.0368 - 27.7766i) q^{85} +(20.2237 + 11.6762i) q^{86} +(-24.3760 - 95.0700i) q^{87} +(-51.8201 - 89.7550i) q^{88} -137.254i q^{89} +(48.4427 + 29.3821i) q^{90} -62.2502 q^{91} +(48.7150 - 28.1256i) q^{92} +(-69.4641 - 70.9818i) q^{93} +(25.7259 - 44.5586i) q^{94} +(-59.9186 - 34.5940i) q^{95} +(-65.8496 + 64.4417i) q^{96} +(-80.2196 - 138.945i) q^{97} -34.1715i q^{98} +(156.886 + 3.39099i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 2 q^{3} + 64 q^{4} - 18 q^{5} - 22 q^{6} + 2 q^{7} - 6 q^{9} - 44 q^{12} - 10 q^{13} + 72 q^{14} - 36 q^{15} - 128 q^{16} - 38 q^{18} - 28 q^{19} - 18 q^{20} + 88 q^{21} + 144 q^{23} - 42 q^{24}+ \cdots + 58 q^{99}+O(q^{100}) \) 64 * q - 2 * q^3 + 64 * q^4 - 18 * q^5 - 22 * q^6 + 2 * q^7 - 6 * q^9 - 44 * q^12 - 10 * q^13 + 72 * q^14 - 36 * q^15 - 128 * q^16 - 38 * q^18 - 28 * q^19 - 18 * q^20 + 88 * q^21 + 144 * q^23 - 42 * q^24 + 154 * q^25 - 164 * q^27 + 32 * q^28 - 162 * q^29 - 220 * q^30 + 62 * q^31 + 126 * q^32 - 40 * q^33 + 12 * q^36 + 128 * q^37 - 36 * q^38 - 126 * q^39 - 144 * q^41 + 114 * q^42 - 64 * q^43 - 72 * q^45 - 48 * q^46 + 288 * q^47 - 10 * q^48 - 246 * q^49 + 62 * q^52 + 374 * q^54 - 84 * q^55 + 684 * q^56 + 232 * q^57 + 138 * q^58 - 432 * q^59 - 86 * q^60 + 110 * q^61 + 304 * q^63 - 260 * q^64 + 328 * q^66 - 148 * q^67 + 36 * q^69 - 216 * q^70 - 96 * q^72 - 196 * q^73 - 918 * q^74 + 314 * q^75 - 112 * q^76 - 504 * q^77 + 276 * q^78 + 86 * q^79 + 234 * q^81 - 396 * q^82 - 594 * q^83 + 592 * q^84 + 126 * q^86 + 462 * q^87 + 24 * q^88 - 338 * q^90 + 52 * q^91 - 36 * q^92 - 1006 * q^93 - 186 * q^94 - 144 * q^95 + 18 * q^96 + 140 * q^97 + 58 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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