LMFDB - Embedded newform 156.3.l.c.47.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [156,3,Mod(47,156)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("156.47"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(156, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	156.l (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,0,0,0,-36,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.25069212402$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.10
Character	$\chi$	$=$	156.47
Dual form			156.3.l.c.83.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.63658 - 1.14961i) q^{2} +(2.64742 + 1.41109i) q^{3} +(1.35681 + 3.76285i) q^{4} +(3.10286 - 3.10286i) q^{5} +(-2.71053 - 5.35285i) q^{6} +(-7.50740 - 7.50740i) q^{7} +(2.10527 - 7.71802i) q^{8} +(5.01767 + 7.47148i) q^{9} +(-8.64517 + 1.51102i) q^{10} +(8.95288 - 8.95288i) q^{11} +(-1.71767 + 11.8764i) q^{12} +(11.6170 + 5.83481i) q^{13} +(3.65593 + 20.9170i) q^{14} +(12.5930 - 3.83617i) q^{15} +(-12.3181 + 10.2109i) q^{16} +10.5509 q^{17} +(0.377438 - 17.9960i) q^{18} +(5.32408 - 5.32408i) q^{19} +(15.8856 + 7.46564i) q^{20} +(-9.28165 - 30.4688i) q^{21} +(-24.9444 + 4.35984i) q^{22} -13.8259i q^{23} +(16.4643 - 17.4621i) q^{24} +5.74446i q^{25} +(-12.3045 - 22.9042i) q^{26} +(2.74096 + 26.8605i) q^{27} +(18.0632 - 38.4354i) q^{28} -40.6250i q^{29} +(-25.0196 - 8.19878i) q^{30} +(-32.5642 + 32.5642i) q^{31} +(31.8982 - 2.55003i) q^{32} +(36.3353 - 11.0687i) q^{33} +(-17.2674 - 12.1294i) q^{34} -46.5889 q^{35} +(-21.3061 + 29.0181i) q^{36} +(18.5545 - 18.5545i) q^{37} +(-14.8339 + 2.59270i) q^{38} +(22.5217 + 31.8398i) q^{39} +(-17.4156 - 30.4804i) q^{40} +(-31.6904 + 31.6904i) q^{41} +(-19.8370 + 60.5350i) q^{42} +56.9036 q^{43} +(45.8357 + 21.5410i) q^{44} +(38.7521 + 7.61385i) q^{45} +(-15.8944 + 22.6273i) q^{46} +(-41.9868 + 41.9868i) q^{47} +(-47.0198 + 9.65068i) q^{48} +63.7221i q^{49} +(6.60387 - 9.40129i) q^{50} +(27.9326 + 14.8882i) q^{51} +(-6.19349 + 51.6298i) q^{52} -1.52710i q^{53} +(26.3932 - 47.1105i) q^{54} -55.5591i q^{55} +(-73.7474 + 42.1371i) q^{56} +(21.6078 - 6.58233i) q^{57} +(-46.7028 + 66.4862i) q^{58} +(-29.4245 + 29.4245i) q^{59} +(31.5212 + 42.1807i) q^{60} -91.3759 q^{61} +(90.7301 - 15.8580i) q^{62} +(18.4218 - 93.7610i) q^{63} +(-55.1356 - 32.4971i) q^{64} +(54.1506 - 17.9414i) q^{65} +(-72.1905 - 23.6564i) q^{66} +(-24.1047 + 24.1047i) q^{67} +(14.3155 + 39.7014i) q^{68} +(19.5096 - 36.6030i) q^{69} +(76.2466 + 53.5589i) q^{70} +(-31.2001 - 31.2001i) q^{71} +(68.2286 - 22.9969i) q^{72} +(-17.5775 + 17.5775i) q^{73} +(-51.6965 + 9.03562i) q^{74} +(-8.10593 + 15.2080i) q^{75} +(27.2575 + 12.8100i) q^{76} -134.426 q^{77} +(-0.255338 - 77.9996i) q^{78} +102.844i q^{79} +(-6.53836 + 69.9047i) q^{80} +(-30.6461 + 74.9788i) q^{81} +(88.2956 - 15.4325i) q^{82} +(38.2900 + 38.2900i) q^{83} +(102.056 - 76.2658i) q^{84} +(32.7379 - 32.7379i) q^{85} +(-93.1274 - 65.4167i) q^{86} +(57.3254 - 107.551i) q^{87} +(-50.2502 - 87.9468i) q^{88} +(0.515880 + 0.515880i) q^{89} +(-54.6681 - 57.0104i) q^{90} +(-43.4093 - 131.018i) q^{91} +(52.0249 - 18.7591i) q^{92} +(-132.162 + 40.2602i) q^{93} +(116.983 - 20.4466i) q^{94} -33.0398i q^{95} +(88.0463 + 38.2602i) q^{96} +(-61.1704 - 61.1704i) q^{97} +(73.2554 - 104.287i) q^{98} +(111.814 + 21.9687i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 36 q^{6} - 64 q^{9} - 8 q^{13} + 80 q^{16} + 48 q^{18} + 8 q^{21} + 124 q^{24} - 8 q^{28} + 24 q^{33} + 64 q^{34} - 128 q^{37} - 136 q^{40} - 140 q^{42} - 160 q^{45} + 88 q^{46} - 108 q^{48} - 320 q^{52}+ \cdots + 336 q^{97}+O(q^{100}) $ 96 * q - 36 * q^6 - 64 * q^9 - 8 * q^13 + 80 * q^16 + 48 * q^18 + 8 * q^21 + 124 * q^24 - 8 * q^28 + 24 * q^33 + 64 * q^34 - 128 * q^37 - 136 * q^40 - 140 * q^42 - 160 * q^45 + 88 * q^46 - 108 * q^48 - 320 * q^52 - 216 * q^54 + 136 * q^57 + 280 * q^58 + 80 * q^60 - 464 * q^61 - 240 * q^66 - 120 * q^70 - 32 * q^72 + 288 * q^73 + 88 * q^76 - 296 * q^78 - 144 * q^81 + 204 * q^84 + 848 * q^85 - 392 * q^93 + 1384 * q^94 - 204 * q^96 + 336 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.63658	−	1.14961i	−0.818292	−	0.574803i
$2$	−1.63658	−	1.14961i	−0.818292	−	0.574803i
$3$	2.64742	+	1.41109i	0.882473	+	0.470362i
$3$	2.64742	+	1.41109i	0.882473	+	0.470362i
$4$	1.35681	+	3.76285i	0.339202	+	0.940714i
$5$	3.10286	−	3.10286i	0.620573	−	0.620573i	−0.325105	−	0.945678i	$-0.605400\pi$
$5$	3.10286	−	3.10286i	0.620573	−	0.620573i	0.945678	+	0.325105i	$0.105400\pi$
$6$	−2.71053	−	5.35285i	−0.451755	−	0.892142i
$7$	−7.50740	−	7.50740i	−1.07249	−	1.07249i	−0.997159	−	0.0753268i	$-0.976000\pi$
$7$	−7.50740	−	7.50740i	−1.07249	−	1.07249i	−0.0753268	−	0.997159i	$-0.524000\pi$
$8$	2.10527	−	7.71802i	0.263159	−	0.964752i
$9$	5.01767	+	7.47148i	0.557518	+	0.830165i
$10$	−8.64517	+	1.51102i	−0.864517	+	0.151102i
$11$	8.95288	−	8.95288i	0.813898	−	0.813898i	−0.171318	−	0.985216i	$-0.554802\pi$
$11$	8.95288	−	8.95288i	0.813898	−	0.813898i	0.985216	+	0.171318i	$0.0548025\pi$
$12$	−1.71767	+	11.8764i	−0.143140	+	0.989703i
$13$	11.6170	+	5.83481i	0.893616	+	0.448832i
$13$	11.6170	+	5.83481i	0.893616	+	0.448832i
$14$	3.65593	+	20.9170i	0.261138	+	1.49407i
$15$	12.5930	−	3.83617i	0.839533	−	0.255745i
$16$	−12.3181	+	10.2109i	−0.769884	+	0.638184i
$17$	10.5509			0.620640			0.310320	−	0.950632i	$-0.399564\pi$
$17$	10.5509			0.620640			0.310320	+	0.950632i	$0.399564\pi$
$18$	0.377438	−	17.9960i	0.0209688	−	0.999780i
$19$	5.32408	−	5.32408i	0.280215	−	0.280215i	−0.552980	−	0.833195i	$-0.686509\pi$
$19$	5.32408	−	5.32408i	0.280215	−	0.280215i	0.833195	+	0.552980i	$0.186509\pi$
$20$	15.8856	+	7.46564i	0.794281	+	0.373282i
$21$	−9.28165	−	30.4688i	−0.441983	−	1.45090i
$22$	−24.9444	+	4.35984i	−1.13384	+	0.198174i
$23$		−	13.8259i		−	0.601127i	−0.953762	−	0.300563i	$-0.902825\pi$
$23$		−	13.8259i		−	0.601127i	0.953762	−	0.300563i	$-0.0971747\pi$
$24$	16.4643	−	17.4621i	0.686014	−	0.727588i
$25$			5.74446i			0.229778i
$26$	−12.3045	−	22.9042i	−0.473249	−	0.880929i
$27$	2.74096	+	26.8605i	0.101517	+	0.994834i
$28$	18.0632	−	38.4354i	0.645113	−	1.37269i
$29$		−	40.6250i		−	1.40086i	−0.713720	−	0.700431i	$-0.752991\pi$
$29$		−	40.6250i		−	1.40086i	0.713720	−	0.700431i	$-0.247009\pi$
$30$	−25.0196	−	8.19878i	−0.833986	−	0.273293i
$31$	−32.5642	+	32.5642i	−1.05046	+	1.05046i	−0.0518016	+	0.998657i	$0.516496\pi$
$31$	−32.5642	+	32.5642i	−1.05046	+	1.05046i	−0.998657	+	0.0518016i	$0.983504\pi$
$32$	31.8982	−	2.55003i	0.996820	−	0.0796885i
$33$	36.3353	−	11.0687i	1.10107	−	0.335416i
$34$	−17.2674	−	12.1294i	−0.507864	−	0.356746i
$35$	−46.5889			−1.33111
$36$	−21.3061	+	29.0181i	−0.591836	+	0.806059i
$37$	18.5545	−	18.5545i	0.501474	−	0.501474i	−0.410422	−	0.911896i	$-0.634618\pi$
$37$	18.5545	−	18.5545i	0.501474	−	0.501474i	0.911896	+	0.410422i	$0.134618\pi$
$38$	−14.8339	+	2.59270i	−0.390365	+	0.0682289i
$39$	22.5217	+	31.8398i	0.577479	+	0.816405i
$40$	−17.4156	−	30.4804i	−0.435390	−	0.762009i
$41$	−31.6904	+	31.6904i	−0.772937	+	0.772937i	−0.978619	−	0.205682i	$-0.934059\pi$
$41$	−31.6904	+	31.6904i	−0.772937	+	0.772937i	0.205682	+	0.978619i	$0.434059\pi$
$42$	−19.8370	+	60.5350i	−0.472310	+	1.44131i
$43$	56.9036			1.32334			0.661669	−	0.749796i	$-0.269848\pi$
$43$	56.9036			1.32334			0.661669	+	0.749796i	$0.269848\pi$
$44$	45.8357	+	21.5410i	1.04172	+	0.489569i
$45$	38.7521	+	7.61385i	0.861159	+	0.169197i
$46$	−15.8944	+	22.6273i	−0.345530	+	0.491897i
$47$	−41.9868	+	41.9868i	−0.893337	+	0.893337i	−0.994836	−	0.101499i	$-0.967636\pi$
$47$	−41.9868	+	41.9868i	−0.893337	+	0.893337i	0.101499	+	0.994836i	$0.467636\pi$
$48$	−47.0198	+	9.65068i	−0.979580	+	0.201056i
$49$			63.7221i			1.30045i
$50$	6.60387	−	9.40129i	0.132077	−	0.188026i
$51$	27.9326	+	14.8882i	0.547698	+	0.291926i
$52$	−6.19349	+	51.6298i	−0.119106	+	0.992882i
$53$		−	1.52710i		−	0.0288132i	−0.999896	−	0.0144066i	$-0.995414\pi$
$53$		−	1.52710i		−	0.0288132i	0.999896	−	0.0144066i	$-0.00458592\pi$
$54$	26.3932	−	47.1105i	0.488763	−	0.872416i
$55$		−	55.5591i		−	1.01017i
$56$	−73.7474	+	42.1371i	−1.31692	+	0.752449i
$57$	21.6078	−	6.58233i	0.379084	−	0.115479i
$58$	−46.7028	+	66.4862i	−0.805221	+	1.14631i
$59$	−29.4245	+	29.4245i	−0.498720	+	0.498720i	−0.911039	−	0.412319i	$-0.864719\pi$
$59$	−29.4245	+	29.4245i	−0.498720	+	0.498720i	0.412319	+	0.911039i	$0.364719\pi$
$60$	31.5212	+	42.1807i	0.525354	+	0.703011i
$61$	−91.3759			−1.49797			−0.748983	−	0.662589i	$-0.769458\pi$
$61$	−91.3759			−1.49797			−0.748983	+	0.662589i	$0.769458\pi$
$62$	90.7301	−	15.8580i	1.46339	−	0.255774i
$63$	18.4218	−	93.7610i	0.292409	−	1.48827i
$64$	−55.1356	−	32.4971i	−0.861494	−	0.507767i
$65$	54.1506	−	17.9414i	0.833087	−	0.276021i
$66$	−72.1905	−	23.6564i	−1.09380	−	0.358431i
$67$	−24.1047	+	24.1047i	−0.359772	+	0.359772i	−0.863729	−	0.503957i	$-0.831877\pi$
$67$	−24.1047	+	24.1047i	−0.359772	+	0.359772i	0.503957	+	0.863729i	$0.331877\pi$
$68$	14.3155	+	39.7014i	0.210522	+	0.583844i
$69$	19.5096	−	36.6030i	0.282747	−	0.530478i
$70$	76.2466	+	53.5589i	1.08924	+	0.765127i
$71$	−31.2001	−	31.2001i	−0.439438	−	0.439438i	0.452385	−	0.891823i	$-0.350573\pi$
$71$	−31.2001	−	31.2001i	−0.439438	−	0.439438i	−0.891823	+	0.452385i	$0.850573\pi$
$72$	68.2286	−	22.9969i	0.947619	−	0.319402i
$73$	−17.5775	+	17.5775i	−0.240788	+	0.240788i	−0.817176	−	0.576388i	$-0.804462\pi$
$73$	−17.5775	+	17.5775i	−0.240788	+	0.240788i	0.576388	+	0.817176i	$0.304462\pi$
$74$	−51.6965	+	9.03562i	−0.698601	+	0.122103i
$75$	−8.10593	+	15.2080i	−0.108079	+	0.202773i
$76$	27.2575	+	12.8100i	0.358651	+	0.168552i
$77$	−134.426			−1.74579
$78$	−0.255338	−	77.9996i	−0.00327357	−	0.999995i
$79$			102.844i			1.30183i	0.759151	+	0.650914i	$0.225614\pi$
$79$			102.844i			1.30183i	−0.759151	+	0.650914i	$0.774386\pi$
$80$	−6.53836	+	69.9047i	−0.0817295	+	0.873809i
$81$	−30.6461	+	74.9788i	−0.378346	+	0.925664i
$82$	88.2956	−	15.4325i	1.07678	−	0.188201i
$83$	38.2900	+	38.2900i	0.461326	+	0.461326i	0.899090	−	0.437764i	$-0.144230\pi$
$83$	38.2900	+	38.2900i	0.461326	+	0.461326i	−0.437764	+	0.899090i	$0.644230\pi$
$84$	102.056	−	76.2658i	1.21496	−	0.907927i
$85$	32.7379	−	32.7379i	0.385152	−	0.385152i
$86$	−93.1274	−	65.4167i	−1.08288	−	0.760660i
$87$	57.3254	−	107.551i	0.658913	−	1.23622i
$88$	−50.2502	−	87.9468i	−0.571025	−	0.999395i
$89$	0.515880	+	0.515880i	0.00579640	+	0.00579640i	0.709999	−	0.704203i	$-0.248695\pi$
$89$	0.515880	+	0.515880i	0.00579640	+	0.00579640i	−0.704203	+	0.709999i	$0.748695\pi$
$90$	−54.6681	−	57.0104i	−0.607424	−	0.633449i
$91$	−43.4093	−	131.018i	−0.477025	−	1.43976i
$92$	52.0249	−	18.7591i	0.565488	−	0.203903i
$93$	−132.162	+	40.2602i	−1.42110	+	0.432906i
$94$	116.983	−	20.4466i	1.24450	−	0.217517i
$95$		−	33.0398i		−	0.347787i
$96$	88.0463	+	38.2602i	0.917149	+	0.398544i
$97$	−61.1704	−	61.1704i	−0.630623	−	0.630623i	0.317602	−	0.948224i	$-0.397123\pi$
$97$	−61.1704	−	61.1704i	−0.630623	−	0.630623i	−0.948224	+	0.317602i	$0.897123\pi$
$98$	73.2554	−	104.287i	0.747504	−	1.06415i
$99$	111.814	+	21.9687i	1.12943	+	0.221906i
$100$	−21.6156	+	7.79413i	−0.216156	+	0.0779413i
$101$	154.942			1.53408			0.767040	−	0.641599i	$-0.221729\pi$
$101$	154.942			1.53408			0.767040	+	0.641599i	$0.221729\pi$
$102$	−28.5984	−	56.4773i	−0.280377	−	0.553699i
$103$	98.4770			0.956088			0.478044	−	0.878336i	$-0.341346\pi$
$103$	98.4770			0.956088			0.478044	+	0.878336i	$0.341346\pi$
$104$	69.4902	−	77.3764i	0.668175	−	0.744004i
$105$	−123.340	−	65.7410i	−1.17467	−	0.626105i
$106$	−1.75556	+	2.49922i	−0.0165619	+	0.0235776i
$107$	−21.3914			−0.199920			−0.0999600	−	0.994991i	$-0.531871\pi$
$107$	−21.3914			−0.199920			−0.0999600	+	0.994991i	$0.531871\pi$
$108$	−97.3532	+	46.7584i	−0.901419	+	0.432948i
$109$	38.8509	+	38.8509i	0.356430	+	0.356430i	0.862495	−	0.506065i	$-0.168900\pi$
$109$	38.8509	+	38.8509i	0.356430	+	0.356430i	−0.506065	+	0.862495i	$0.668900\pi$
$110$	−63.8712	+	90.9272i	−0.580647	+	0.826610i
$111$	75.3038	−	22.9396i	0.678412	−	0.206663i
$112$	169.135	+	15.8196i	1.51013	+	0.141246i
$113$			56.7285i			0.502022i	0.967984	+	0.251011i	$0.0807630\pi$
$113$			56.7285i			0.502022i	−0.967984	+	0.251011i	$0.919237\pi$
$114$	−42.9301	−	14.0679i	−0.376579	−	0.123403i
$115$	−42.8999	−	42.8999i	−0.373043	−	0.373043i
$116$	152.866	−	55.1204i	1.31781	−	0.475175i
$117$	14.6956	+	116.073i	0.125603	+	0.992081i
$118$	81.9822	−	14.3290i	0.694764	−	0.121432i
$119$	−79.2097	−	79.2097i	−0.665627	−	0.665627i
$120$	−3.09595	−	105.269i	−0.0257996	−	0.877243i
$121$		−	39.3081i		−	0.324860i
$122$	149.544	+	105.046i	1.22577	+	0.861036i
$123$	−128.616	+	39.1799i	−1.04566	+	0.318536i
$124$	−166.718	−	78.3510i	−1.34450	−	0.631863i
$125$	95.3959	+	95.3959i	0.763167	+	0.763167i
$126$	−137.937	+	132.270i	−1.09474	+	1.04976i
$127$	−103.517			−0.815098			−0.407549	−	0.913183i	$-0.633616\pi$
$127$	−103.517			−0.815098			−0.407549	+	0.913183i	$0.633616\pi$
$128$	52.8752	+	116.568i	0.413087	+	0.910691i
$129$	150.648	+	80.2959i	1.16781	+	0.622449i
$130$	−109.248	−	32.8894i	−0.840366	−	0.252995i
$131$	−243.602			−1.85956			−0.929779	−	0.368119i	$-0.880002\pi$
$131$	−243.602			−1.85956			−0.929779	+	0.368119i	$0.880002\pi$
$132$	90.9501	+	121.706i	0.689016	+	0.922018i
$133$	−79.9399			−0.601052
$134$	67.1604	−	11.7384i	0.501197	−	0.0876003i
$135$	91.8494	+	74.8397i	0.680366	+	0.554368i
$136$	22.2125	−	81.4319i	0.163327	−	0.598764i
$137$	−86.7590	−	86.7590i	−0.633278	−	0.633278i	0.315611	−	0.948889i	$-0.397791\pi$
$137$	−86.7590	−	86.7590i	−0.633278	−	0.633278i	−0.948889	+	0.315611i	$0.897791\pi$
$138$	−74.0081	+	37.4755i	−0.536291	+	0.271562i
$139$			39.1343i			0.281542i	0.990042	+	0.140771i	$0.0449581\pi$
$139$			39.1343i			0.281542i	−0.990042	+	0.140771i	$0.955042\pi$
$140$	−63.2122	−	175.307i	−0.451516	−	1.25219i
$141$	−170.404	+	51.9097i	−1.20854	+	0.368154i
$142$	15.1937	+	86.9295i	0.106998	+	0.612179i
$143$	156.244	−	51.7673i	1.09262	−	0.362009i
$144$	−138.099	−	40.7997i	−0.959022	−	0.283331i
$145$	−126.054	−	126.054i	−0.869338	−	0.869338i
$146$	48.9743	−	8.55984i	0.335441	−	0.0586290i
$147$	−89.9175	+	168.699i	−0.611683	+	1.14761i
$148$	94.9930	+	44.6431i	0.641845	+	0.301643i
$149$	11.4387	−	11.4387i	0.0767695	−	0.0767695i	−0.667679	−	0.744449i	$-0.732712\pi$
$149$	11.4387	−	11.4387i	0.0767695	−	0.0767695i	0.744449	+	0.667679i	$0.232712\pi$
$150$	30.7493	−	15.5705i	0.204995	−	0.103803i
$151$	−30.7068	−	30.7068i	−0.203356	−	0.203356i	0.598080	−	0.801436i	$-0.295930\pi$
$151$	−30.7068	−	30.7068i	−0.203356	−	0.203356i	−0.801436	+	0.598080i	$0.795930\pi$
$152$	−29.8827	−	52.3000i	−0.196597	−	0.344079i
$153$	52.9408	+	78.8307i	0.346018	+	0.515233i
$154$	219.999	+	154.537i	1.42856	+	1.00348i
$155$			202.085i			1.30377i
$156$	−89.2510	+	127.946i	−0.572122	+	0.820169i
$157$	204.657			1.30355			0.651774	−	0.758413i	$-0.274025\pi$
$157$	204.657			1.30355			0.651774	+	0.758413i	$0.274025\pi$
$158$	118.231	−	168.313i	0.748295	−	1.06527i
$159$	2.15487	−	4.04287i	0.0135526	−	0.0254269i
$160$	91.0635	−	106.888i	0.569147	−	0.668052i
$161$	−103.797	+	103.797i	−0.644700	+	0.644700i
$162$	136.351	−	87.4781i	0.841672	−	0.539988i
$163$	176.937	+	176.937i	1.08551	+	1.08551i	0.995985	+	0.0895203i	$0.0285334\pi$
$163$	176.937	+	176.937i	1.08551	+	1.08551i	0.0895203	+	0.995985i	$0.471467\pi$
$164$	−162.244	−	76.2487i	−0.989295	−	0.464931i
$165$	78.3988	−	147.088i	0.475144	−	0.891445i
$166$	−18.6463	−	106.683i	−0.112327	−	0.642671i
$167$	96.6155	−	96.6155i	0.578536	−	0.578536i	−0.355964	−	0.934500i	$-0.615847\pi$
$167$	96.6155	−	96.6155i	0.578536	−	0.578536i	0.934500	+	0.355964i	$0.115847\pi$
$168$	−254.699	+	7.49068i	−1.51607	+	0.0445874i
$169$	100.910	+	135.566i	0.597100	+	0.802167i
$170$	−91.2141	+	15.9426i	−0.536554	+	0.0937800i
$171$	66.4932	+	13.0643i	0.388849	+	0.0763994i
$172$	77.2072	+	214.120i	0.448879	+	1.24488i
$173$	−204.889			−1.18433			−0.592165	−	0.805817i	$-0.701727\pi$
$173$	−204.889			−1.18433			−0.592165	+	0.805817i	$0.701727\pi$
$174$	−217.460	+	110.115i	−1.24977	+	0.632846i
$175$	43.1260	−	43.1260i	0.246434	−	0.246434i
$176$	−18.8655	+	201.700i	−0.107190	+	1.14602i
$177$	−119.419	+	36.3784i	−0.674686	+	0.205528i
$178$	−0.251221	−	1.43734i	−0.00141135	−	0.00807494i
$179$		−	226.341i		−	1.26447i	−0.774776	−	0.632236i	$-0.782137\pi$
$179$		−	226.341i		−	1.26447i	0.774776	−	0.632236i	$-0.217863\pi$
$180$	23.9294	+	156.149i	0.132941	+	0.867495i
$181$		−	121.536i		−	0.671468i	−0.941957	−	0.335734i	$-0.891016\pi$
$181$		−	121.536i		−	0.671468i	0.941957	−	0.335734i	$-0.108984\pi$
$182$	−79.5761	+	264.325i	−0.437231	+	1.45234i
$183$	−241.911	−	128.939i	−1.32192	−	0.704587i
$184$	−106.709	−	29.1073i	−0.579938	−	0.158192i
$185$		−	115.145i		−	0.622403i
$186$	262.578	+	86.0453i	1.41171	+	0.462609i
$187$	94.4607	−	94.4607i	0.505138	−	0.505138i
$188$	−214.958	−	101.022i	−1.14340	−	0.537352i
$189$	181.075	−	222.230i	0.958069	−	1.17582i
$190$	−37.9828	+	54.0723i	−0.199909	+	0.284591i
$191$	110.508			0.578575			0.289287	−	0.957242i	$-0.406582\pi$
$191$	110.508			0.578575			0.289287	+	0.957242i	$0.406582\pi$
$192$	−100.111	−	163.835i	−0.521411	−	0.853305i
$193$	217.768	−	217.768i	1.12833	−	1.12833i	0.137886	−	0.990448i	$-0.455969\pi$
$193$	217.768	−	217.768i	1.12833	−	1.12833i	0.990448	−	0.137886i	$-0.0440306\pi$
$194$	29.7885	+	170.432i	0.153549	+	0.878517i
$195$	168.676	+	28.9129i	0.865007	+	0.148271i
$196$	−239.777	+	86.4587i	−1.22335	+	0.441116i
$197$	199.164	−	199.164i	1.01099	−	1.01099i	0.0110466	−	0.999939i	$-0.496484\pi$
$197$	199.164	−	199.164i	1.01099	−	1.01099i	0.999939	−	0.0110466i	$-0.00351630\pi$
$198$	−157.737	−	164.496i	−0.796653	−	0.830786i
$199$	−99.9625			−0.502324			−0.251162	−	0.967945i	$-0.580813\pi$
$199$	−99.9625			−0.502324			−0.251162	+	0.967945i	$0.580813\pi$
$200$	44.3359	+	12.0937i	0.221679	+	0.0604683i
$201$	−97.8293	+	29.8015i	−0.486713	+	0.148266i
$202$	−253.576	−	178.123i	−1.25532	−	0.881795i
$203$	−304.988	+	304.988i	−1.50241	+	1.50241i
$204$	−18.1230	+	125.307i	−0.0888381	+	0.614249i
$205$			196.662i			0.959328i
$206$	−161.166	−	113.210i	−0.782358	−	0.549562i
$207$	103.300	−	69.3738i	0.499034	−	0.335139i
$208$	−202.679	+	46.7466i	−0.974418	+	0.224743i
$209$		−	95.3316i		−	0.456132i
$210$	126.280	+	249.384i	0.601336	+	1.18754i
$211$			186.585i			0.884288i	0.896944	+	0.442144i	$0.145782\pi$
$211$			186.585i			0.884288i	−0.896944	+	0.442144i	$0.854218\pi$
$212$	5.74625	−	2.07198i	0.0271049	−	0.00977348i
$213$	−38.5737	−	126.626i	−0.181097	−	0.594488i
$214$	35.0089	+	24.5917i	0.163593	+	0.114915i
$215$	176.564	−	176.564i	0.821228	−	0.821228i
$216$	213.080	+	35.3940i	0.986483	+	0.163861i
$217$	488.945			2.25320
$218$	−18.9195	−	108.246i	−0.0867865	−	0.496541i
$219$	−71.3385	+	21.7317i	−0.325747	+	0.0992314i
$220$	209.061	−	75.3831i	0.950277	−	0.342650i
$221$	122.570	+	61.5624i	0.554614	+	0.278563i
$222$	−149.612	−	49.0272i	−0.673930	−	0.220843i
$223$	73.2786	−	73.2786i	0.328604	−	0.328604i	−0.523452	−	0.852055i	$-0.675356\pi$
$223$	73.2786	−	73.2786i	0.328604	−	0.328604i	0.852055	+	0.523452i	$0.175356\pi$
$224$	−258.617	−	220.329i	−1.15454	−	0.983610i
$225$	−42.9196	+	28.8238i	−0.190754	+	0.128106i
$226$	65.2154	−	92.8408i	0.288564	−	0.410800i
$227$	160.573	+	160.573i	0.707371	+	0.707371i	0.965982	−	0.258611i	$-0.0832647\pi$
$227$	160.573	+	160.573i	0.707371	+	0.707371i	−0.258611	+	0.965982i	$0.583265\pi$
$228$	54.0860	+	72.3760i	0.237219	+	0.317439i
$229$	−243.232	+	243.232i	−1.06215	+	1.06215i	−0.0642103	+	0.997936i	$0.520453\pi$
$229$	−243.232	+	243.232i	−1.06215	+	1.06215i	−0.997936	+	0.0642103i	$0.979547\pi$
$230$	20.8912	+	119.527i	0.0908315	+	0.519684i
$231$	−355.881	−	189.686i	−1.54061	−	0.821153i
$232$	−313.545	−	85.5268i	−1.35149	−	0.368650i
$233$	−17.1781			−0.0737259			−0.0368630	−	0.999320i	$-0.511737\pi$
$233$	−17.1781			−0.0737259			−0.0368630	+	0.999320i	$0.511737\pi$
$234$	109.388	−	206.858i	0.467471	−	0.884008i
$235$			260.559i			1.10876i
$236$	−150.643	−	70.7966i	−0.638319	−	0.299986i
$237$	−145.122	+	272.272i	−0.612331	+	1.14883i
$238$	38.5732	+	220.693i	0.162072	+	0.927282i
$239$	85.5184	+	85.5184i	0.357818	+	0.357818i	0.863008	−	0.505190i	$-0.168578\pi$
$239$	85.5184	+	85.5184i	0.357818	+	0.357818i	−0.505190	+	0.863008i	$0.668578\pi$
$240$	−115.951	+	175.841i	−0.483131	+	0.732671i
$241$	84.5939	−	84.5939i	0.351012	−	0.351012i	−0.509474	−	0.860486i	$-0.670160\pi$
$241$	84.5939	−	84.5939i	0.351012	−	0.351012i	0.860486	+	0.509474i	$0.170160\pi$
$242$	−45.1888	+	64.3309i	−0.186731	+	0.265830i
$243$	−186.935	+	155.256i	−0.769278	+	0.638914i
$244$	−123.980	−	343.834i	−0.508113	−	1.40916i
$245$	197.721	+	197.721i	0.807025	+	0.807025i
$246$	255.532	+	83.7365i	1.03875	+	0.340392i
$247$	92.9148	−	30.7849i	0.376173	−	0.124635i
$248$	182.775	+	319.888i	0.736995	+	1.28987i
$249$	47.3392	+	155.400i	0.190117	+	0.624098i
$250$	−46.4555	−	265.791i	−0.185822	−	1.06316i
$251$		−	5.28263i		−	0.0210463i	−0.999945	−	0.0105232i	$-0.996650\pi$
$251$		−	5.28263i		−	0.0210463i	0.999945	−	0.0105232i	$-0.00334969\pi$
$252$	377.804	−	57.8973i	1.49922	−	0.229751i
$253$	−123.782	−	123.782i	−0.489256	−	0.489256i
$254$	169.415	+	119.004i	0.666987	+	0.468521i
$255$	132.867	−	40.4750i	0.521048	−	0.158725i
$256$	47.4733	−	251.560i	0.185443	−	0.982655i
$257$	−14.0684			−0.0547409			−0.0273705	−	0.999625i	$-0.508713\pi$
$257$	−14.0684			−0.0547409			−0.0273705	+	0.999625i	$0.508713\pi$
$258$	−154.239	−	304.596i	−0.597824	−	1.18061i
$259$	−278.593			−1.07565
$260$	140.983	+	179.418i	0.542242	+	0.690069i
$261$	303.529	−	203.843i	1.16295	−	0.781007i
$262$	398.675	+	280.046i	1.52166	+	1.06888i
$263$	87.7912			0.333807			0.166903	−	0.985973i	$-0.446623\pi$
$263$	87.7912			0.333807			0.166903	+	0.985973i	$0.446623\pi$
$264$	−8.93294	−	303.739i	−0.0338369	−	1.15053i
$265$	−4.73838	−	4.73838i	−0.0178807	−	0.0178807i
$266$	130.828	+	91.8995i	0.491836	+	0.345487i
$267$	0.637799	+	2.09370i	0.00238876	+	0.00784158i
$268$	−123.408	−	57.9971i	−0.460478	−	0.216407i
$269$		−	283.264i		−	1.05303i	−0.850167	−	0.526513i	$-0.823499\pi$
$269$		−	283.264i		−	1.05303i	0.850167	−	0.526513i	$-0.176501\pi$
$270$	−64.2829	−	228.072i	−0.238085	−	0.844711i
$271$	−239.818	−	239.818i	−0.884939	−	0.884939i	0.109093	−	0.994032i	$-0.465205\pi$
$271$	−239.818	−	239.818i	−0.884939	−	0.884939i	−0.994032	+	0.109093i	$0.965205\pi$
$272$	−129.967	+	107.734i	−0.477821	+	0.396082i
$273$	69.9549	−	408.114i	0.256245	−	1.49492i
$274$	42.2496	+	241.727i	0.154196	+	0.882216i
$275$	51.4295	+	51.4295i	0.187016	+	0.187016i
$276$	164.202	+	23.7484i	0.594937	+	0.0860450i
$277$			529.071i			1.91000i	0.296598	+	0.955002i	$0.404148\pi$
$277$			529.071i			1.91000i	−0.296598	+	0.955002i	$0.595852\pi$
$278$	44.9890	−	64.0465i	0.161831	−	0.230383i
$279$	−406.699	−	79.9066i	−1.45770	−	0.286404i
$280$	−98.0824	+	359.574i	−0.350294	+	1.28419i
$281$	−76.5718	−	76.5718i	−0.272498	−	0.272498i	0.557607	−	0.830105i	$-0.311720\pi$
$281$	−76.5718	−	76.5718i	−0.272498	−	0.272498i	−0.830105	+	0.557607i	$0.811720\pi$
$282$	338.556	+	110.943i	1.20055	+	0.393415i
$283$	276.154			0.975810			0.487905	−	0.872897i	$-0.337761\pi$
$283$	276.154			0.975810			0.487905	+	0.872897i	$0.337761\pi$
$284$	75.0689	−	159.734i	0.264327	−	0.562444i
$285$	46.6220	−	87.4702i	0.163586	−	0.306913i
$286$	−315.218	−	94.8977i	−1.10216	−	0.331810i
$287$	475.826			1.65793
$288$	179.107	+	225.532i	0.621900	+	0.783097i
$289$	−177.679			−0.614806
$290$	61.3853	+	351.210i	0.211673	+	1.21107i
$291$	−75.6270	−	248.261i	−0.259887	−	0.853129i
$292$	−89.9910	−	42.2923i	−0.308188	−	0.144837i
$293$	−172.341	−	172.341i	−0.588195	−	0.588195i	0.348947	−	0.937142i	$-0.386539\pi$
$293$	−172.341	−	172.341i	−0.588195	−	0.588195i	−0.937142	+	0.348947i	$0.886539\pi$
$294$	341.095	−	172.721i	1.16019	−	0.587485i
$295$			182.600i			0.618984i
$296$	−104.142	−	182.267i	−0.351831	−	0.615766i
$297$	265.018	+	215.939i	0.892318	+	0.727069i
$298$	−31.8703	+	5.57035i	−0.106947	+	0.0186925i
$299$	80.6716	−	160.616i	0.269805	−	0.537177i
$300$	−68.2237	−	9.86711i	−0.227412	−	0.0328904i
$301$	−427.198	−	427.198i	−1.41926	−	1.41926i
$302$	14.9535	+	85.5548i	0.0495148	+	0.283294i
$303$	410.197	+	218.637i	1.35379	+	0.721574i
$304$	−11.2189	+	119.947i	−0.0369043	+	0.394561i
$305$	−283.527	+	283.527i	−0.929597	+	0.929597i
$306$	3.98230	−	189.874i	0.0130141	−	0.620503i
$307$	−24.6801	−	24.6801i	−0.0803911	−	0.0803911i	0.665768	−	0.746159i	$-0.268104\pi$
$307$	−24.6801	−	24.6801i	−0.0803911	−	0.0803911i	−0.746159	+	0.665768i	$0.768104\pi$
$308$	−182.390	−	505.824i	−0.592175	−	1.64229i
$309$	260.710	+	138.960i	0.843722	+	0.449708i
$310$	232.318	−	330.729i	0.749413	−	1.06687i
$311$		−	201.749i		−	0.648711i	−0.945935	−	0.324355i	$-0.894853\pi$
$311$		−	201.749i		−	0.648711i	0.945935	−	0.324355i	$-0.105147\pi$
$312$	293.155	−	106.791i	0.939598	−	0.342280i
$313$	−103.265			−0.329919			−0.164959	−	0.986300i	$-0.552749\pi$
$313$	−103.265			−0.329919			−0.164959	+	0.986300i	$0.552749\pi$
$314$	−334.938	−	235.275i	−1.06668	−	0.749284i
$315$	−233.768	−	348.088i	−0.742119	−	1.10504i
$316$	−386.989	+	139.540i	−1.22465	+	0.441583i
$317$	−328.742	+	328.742i	−1.03704	+	1.03704i	−0.0377544	+	0.999287i	$0.512020\pi$
$317$	−328.742	+	328.742i	−1.03704	+	1.03704i	−0.999287	+	0.0377544i	$0.987980\pi$
$318$	−8.17433	+	4.13924i	−0.0257054	+	0.0130165i
$319$	−363.711	−	363.711i	−1.14016	−	1.14016i
$320$	−271.913	+	70.2444i	−0.849727	+	0.219514i
$321$	−56.6321	−	30.1852i	−0.176424	−	0.0940348i
$322$	289.197	−	50.5465i	0.898128	−	0.156977i
$323$	56.1737	−	56.1737i	0.173912	−	0.173912i
$324$	−323.715	−	13.5848i	−0.999121	−	0.0419283i
$325$	−33.5178	+	66.7335i	−0.103132	+	0.205334i
$326$	−86.1643	−	492.981i	−0.264308	−	1.51221i
$327$	48.0327	+	157.677i	0.146889	+	0.482192i
$328$	177.870	+	311.304i	0.542288	+	0.949099i
$329$	630.424			1.91618
$330$	−297.400	+	150.595i	−0.901212	+	0.456347i
$331$	233.012	−	233.012i	0.703964	−	0.703964i	−0.261295	−	0.965259i	$-0.584150\pi$
$331$	233.012	−	233.012i	0.703964	−	0.703964i	0.965259	+	0.261295i	$0.0841496\pi$
$332$	−92.1276	+	196.032i	−0.277493	+	0.590458i
$333$	231.730	+	45.5294i	0.695887	+	0.136725i
$334$	−269.189	+	47.0494i	−0.805955	+	0.140867i
$335$			149.588i			0.446530i
$336$	425.448	+	280.545i	1.26621	+	0.834956i
$337$		−	571.366i		−	1.69545i	−0.530438	−	0.847724i	$-0.677972\pi$
$337$		−	571.366i		−	1.69545i	0.530438	−	0.847724i	$-0.322028\pi$
$338$	−9.29973	−	337.872i	−0.0275140	−	0.999621i
$339$	−80.0488	+	150.184i	−0.236132	+	0.443021i
$340$	167.607	+	78.7690i	0.492962	+	0.231674i
$341$			583.087i			1.70993i
$342$	−93.8028	−	97.8218i	−0.274277	−	0.286029i
$343$	110.525	−	110.525i	0.322230	−	0.322230i
$344$	119.798	−	439.183i	0.348249	−	1.27669i
$345$	−53.0386	−	174.110i	−0.153735	−	0.504666i
$346$	335.318	+	235.542i	0.969127	+	0.680757i
$347$	66.7122			0.192254			0.0961270	−	0.995369i	$-0.469354\pi$
$347$	66.7122			0.192254			0.0961270	+	0.995369i	$0.469354\pi$
$348$	482.480	+	69.7805i	1.38644	+	0.200519i
$349$	−380.088	+	380.088i	−1.08908	+	1.08908i	−0.0934534	+	0.995624i	$0.529791\pi$
$349$	−380.088	+	380.088i	−1.08908	+	1.08908i	−0.995624	+	0.0934534i	$0.970209\pi$
$350$	−120.157	+	21.0013i	−0.343306	+	0.0600038i
$351$	−124.884	+	328.032i	−0.355796	+	0.934564i
$352$	262.751	−	308.411i	0.746451	−	0.876168i
$353$	−321.141	+	321.141i	−0.909747	+	0.909747i	−0.996251	−	0.0865046i	$-0.972430\pi$
$353$	−321.141	+	321.141i	−0.909747	+	0.909747i	0.0865046	+	0.996251i	$0.472430\pi$
$354$	237.261	+	77.7491i	0.670228	+	0.219630i
$355$	−193.620			−0.545407
$356$	−1.24123	+	2.64113i	−0.00348660	+	0.00741890i
$357$	−97.9295	−	321.473i	−0.274312	−	0.900485i
$358$	−260.203	+	370.425i	−0.726823	+	1.03471i
$359$	−124.499	+	124.499i	−0.346794	+	0.346794i	−0.858914	−	0.512120i	$-0.828860\pi$
$359$	−124.499	+	124.499i	−0.346794	+	0.346794i	0.512120	+	0.858914i	$0.328860\pi$
$360$	140.348	−	283.060i	0.389855	−	0.786279i
$361$			304.308i			0.842960i
$362$	−139.718	+	198.903i	−0.385962	+	0.549457i
$363$	55.4671	−	104.065i	0.152802	−	0.286680i
$364$	434.103	−	341.109i	1.19259	−	0.937112i
$365$			109.081i			0.298853i
$366$	247.677	+	489.122i	0.676713	+	1.33640i
$367$			8.88159i			0.0242005i	0.999927	+	0.0121003i	$0.00385172\pi$
$367$			8.88159i			0.0242005i	−0.999927	+	0.0121003i	$0.996148\pi$
$368$	141.176	+	170.310i	0.383629	+	0.462798i
$369$	−395.787	−	77.7625i	−1.07259	−	0.210738i
$370$	−132.371	+	188.444i	−0.357759	+	0.509307i
$371$	−11.4645	+	11.4645i	−0.0309017	+	0.0309017i
$372$	−330.812	−	442.682i	−0.889280	−	1.19000i
$373$	306.101			0.820647			0.410324	−	0.911940i	$-0.365416\pi$
$373$	306.101			0.820647			0.410324	+	0.911940i	$0.365416\pi$
$374$	−263.186	+	46.0001i	−0.703705	+	0.122995i
$375$	117.941	+	387.165i	0.314510	+	1.03244i
$376$	235.661	+	412.449i	0.626759	+	1.09694i
$377$	237.039	−	471.941i	0.628752	−	1.25183i
$378$	−551.822	+	155.533i	−1.45985	+	0.411462i
$379$	192.411	−	192.411i	0.507681	−	0.507681i	−0.406133	−	0.913814i	$-0.633123\pi$
$379$	192.411	−	192.411i	0.507681	−	0.507681i	0.913814	+	0.406133i	$0.133123\pi$
$380$	124.324	−	44.8286i	0.327168	−	0.117970i
$381$	−274.054	−	146.072i	−0.719302	−	0.383391i
$382$	−180.855	−	127.040i	−0.473443	−	0.332567i
$383$	107.120	+	107.120i	0.279686	+	0.279686i	0.832983	−	0.553298i	$-0.186631\pi$
$383$	107.120	+	107.120i	0.279686	+	0.279686i	−0.553298	+	0.832983i	$0.686631\pi$
$384$	−24.5055	+	383.217i	−0.0638164	+	0.997962i
$385$	−417.105	+	417.105i	−1.08339	+	1.08339i
$386$	−606.744	+	106.048i	−1.57188	+	0.274736i
$387$	285.523	+	425.154i	0.737786	+	1.09859i
$388$	147.179	−	313.172i	0.379327	−	0.807144i
$389$	−173.833			−0.446871			−0.223436	−	0.974719i	$-0.571727\pi$
$389$	−173.833			−0.446871			−0.223436	+	0.974719i	$0.571727\pi$
$390$	−242.814	−	241.230i	−0.622601	−	0.618538i
$391$		−	145.876i		−	0.373083i
$392$	491.808	+	134.152i	1.25461	+	0.342226i
$393$	−644.917	−	343.744i	−1.64101	−	0.874666i
$394$	−554.909	+	96.9882i	−1.40840	+	0.246163i
$395$	319.112	+	319.112i	0.807879	+	0.807879i
$396$	69.0449	+	450.546i	0.174356	+	1.13774i
$397$	−55.4458	+	55.4458i	−0.139662	+	0.139662i	−0.773481	−	0.633819i	$-0.781486\pi$
$397$	−55.4458	+	55.4458i	−0.139662	+	0.139662i	0.633819	+	0.773481i	$0.281486\pi$
$398$	163.597	+	114.918i	0.411048	+	0.288738i
$399$	−211.635	−	112.802i	−0.530413	−	0.282712i
$400$	−58.6564	−	70.7611i	−0.146641	−	0.176903i
$401$	−240.104	−	240.104i	−0.598762	−	0.598762i	0.341221	−	0.939983i	$-0.389160\pi$
$401$	−240.104	−	240.104i	−0.598762	−	0.598762i	−0.939983	+	0.341221i	$0.889160\pi$
$402$	194.366	+	63.6926i	0.483497	+	0.158439i
$403$	−568.305	+	188.293i	−1.41019	+	0.467228i
$404$	210.227	+	583.025i	0.520363	+	1.44313i
$405$	137.559	+	327.740i	0.339651	+	0.809234i
$406$	849.755	−	148.522i	2.09299	−	0.365818i
$407$		−	332.233i		−	0.816298i
$408$	173.713	−	184.241i	0.425768	−	0.451570i
$409$	135.442	+	135.442i	0.331154	+	0.331154i	0.853025	−	0.521871i	$-0.174766\pi$
$409$	135.442	+	135.442i	0.331154	+	0.331154i	−0.521871	+	0.853025i	$0.674766\pi$
$410$	226.084	−	321.854i	0.551425	−	0.785010i
$411$	−107.263	−	352.112i	−0.260981	−	0.856720i
$412$	133.614	+	370.555i	0.324307	+	0.899405i
$413$	441.803			1.06974
$414$	−248.812	−	5.21843i	−0.600994	−	0.0126049i
$415$	237.618			0.572573
$416$	385.441	+	156.496i	0.926541	+	0.376193i
$417$	−55.2219	+	103.605i	−0.132427	+	0.248453i
$418$	−109.594	+	156.018i	−0.262186	+	0.373249i
$419$	−728.814			−1.73941			−0.869706	−	0.493570i	$-0.835692\pi$
$419$	−728.814			−1.73941			−0.869706	+	0.493570i	$0.835692\pi$
$420$	80.0245	−	553.310i	0.190535	−	1.31740i
$421$	−210.705	−	210.705i	−0.500487	−	0.500487i	0.411102	−	0.911589i	$-0.365144\pi$
$421$	−210.705	−	210.705i	−0.500487	−	0.500487i	−0.911589	+	0.411102i	$0.865144\pi$
$422$	214.499	−	305.361i	0.508292	−	0.723605i
$423$	−524.380	−	103.028i	−1.23967	−	0.243565i
$424$	−11.7862	−	3.21496i	−0.0277976	−	0.00758245i
$425$			60.6091i			0.142610i
$426$	−82.4409	+	251.578i	−0.193523	+	0.590560i
$427$	685.996	+	685.996i	1.60655	+	1.60655i
$428$	−29.0241	−	80.4929i	−0.0678133	−	0.188067i
$429$	486.692	+	83.4241i	1.13448	+	0.194462i
$430$	−491.941	+	85.9825i	−1.14405	+	0.199959i
$431$	18.9012	+	18.9012i	0.0438544	+	0.0438544i	0.728694	−	0.684840i	$-0.240128\pi$
$431$	18.9012	+	18.9012i	0.0438544	+	0.0438544i	−0.684840	+	0.728694i	$0.740128\pi$
$432$	−308.035	−	302.884i	−0.713043	−	0.701120i
$433$			191.361i			0.441943i	0.975280	+	0.220971i	$0.0709227\pi$
$433$			191.361i			0.441943i	−0.975280	+	0.220971i	$0.929077\pi$
$434$	−800.200	−	562.095i	−1.84378	−	1.29515i
$435$	−155.845	−	511.591i	−0.358264	−	1.17607i
$436$	−93.4771	+	198.904i	−0.214397	+	0.456201i
$437$	−73.6102	−	73.6102i	−0.168444	−	0.168444i
$438$	141.734	+	46.4456i	0.323594	+	0.106040i
$439$	−343.541			−0.782552			−0.391276	−	0.920273i	$-0.627966\pi$
$439$	−343.541			−0.782552			−0.391276	+	0.920273i	$0.627966\pi$
$440$	−428.807	−	116.967i	−0.974560	−	0.265835i
$441$	−476.099	+	319.736i	−1.07959	+	0.725026i
$442$	−129.823	−	241.659i	−0.293717	−	0.546740i
$443$	281.590			0.635644			0.317822	−	0.948150i	$-0.397049\pi$
$443$	281.590			0.635644			0.317822	+	0.948150i	$0.397049\pi$
$444$	188.491	+	252.232i	0.424530	+	0.568091i
$445$	3.20141			0.00719418
$446$	−204.168	+	35.6849i	−0.457776	+	0.0800111i
$447$	46.4239	−	14.1420i	0.103857	−	0.0316376i
$448$	169.957	+	657.894i	0.379368	+	1.46851i
$449$	168.238	+	168.238i	0.374695	+	0.374695i	0.869184	−	0.494489i	$-0.164645\pi$
$449$	168.238	+	168.238i	0.374695	+	0.374695i	−0.494489	+	0.869184i	$0.664645\pi$
$450$	103.378	+	2.16818i	0.229728	+	0.00481817i
$451$			567.441i			1.25818i
$452$	−213.461	+	76.9696i	−0.472259	+	0.170287i
$453$	−37.9638	−	124.624i	−0.0838052	−	0.275107i
$454$	−78.1953	−	447.387i	−0.172236	−	0.985435i
$455$	−541.224	−	271.837i	−1.18950	−	0.597445i
$456$	−5.31222	−	180.627i	−0.0116496	−	0.396112i
$457$	−499.399	−	499.399i	−1.09278	−	1.09278i	−0.995231	−	0.0975464i	$-0.968901\pi$
$457$	−499.399	−	499.399i	−1.09278	−	1.09278i	−0.0975464	−	0.995231i	$-0.531099\pi$
$458$	677.689	−	118.448i	1.47967	−	0.258620i
$459$	28.9195	+	283.402i	0.0630055	+	0.617433i
$460$	103.219	−	219.633i	0.224390	−	0.477463i
$461$	509.071	−	509.071i	1.10427	−	1.10427i	0.110386	−	0.993889i	$-0.464791\pi$
$461$	509.071	−	509.071i	1.10427	−	1.10427i	0.993889	−	0.110386i	$-0.0352087\pi$
$462$	364.365	+	719.561i	0.788668	+	1.55749i
$463$	−41.1500	−	41.1500i	−0.0888770	−	0.0888770i	0.661271	−	0.750148i	$-0.270018\pi$
$463$	−41.1500	−	41.1500i	−0.0888770	−	0.0888770i	−0.750148	+	0.661271i	$0.770018\pi$
$464$	414.820	+	500.425i	0.894008	+	1.07850i
$465$	−285.159	+	535.003i	−0.613246	+	1.15054i
$466$	28.1135	+	19.7481i	0.0603293	+	0.0423779i
$467$		−	189.828i		−	0.406483i	−0.979129	−	0.203242i	$-0.934852\pi$
$467$		−	189.828i		−	0.406483i	0.979129	−	0.203242i	$-0.0651477\pi$
$468$	−416.828	+	212.787i	−0.890659	+	0.454673i
$469$	361.928			0.771701
$470$	299.540	−	426.426i	0.637320	−	0.907290i
$471$	541.813	+	288.789i	1.15035	+	0.613140i
$472$	165.152	+	289.045i	0.349898	+	0.612384i
$473$	509.451	−	509.451i	1.07706	−	1.07706i
$474$	550.511	−	278.763i	1.16142	−	0.588107i
$475$	30.5839	+	30.5839i	0.0643872	+	0.0643872i
$476$	190.582	−	405.527i	0.400383	−	0.851947i
$477$	11.4097	−	7.66247i	0.0239197	−	0.0160639i
$478$	−41.6454	−	238.270i	−0.0871243	−	0.498474i
$479$	−19.6478	+	19.6478i	−0.0410183	+	0.0410183i	−0.727318	−	0.686300i	$-0.759234\pi$
$479$	−19.6478	+	19.6478i	−0.0410183	+	0.0410183i	0.686300	+	0.727318i	$0.259234\pi$
$480$	391.912	−	154.480i	0.816483	−	0.321833i
$481$	323.811	−	107.286i	0.673203	−	0.223048i
$482$	−235.695	+	41.1952i	−0.488993	+	0.0854673i
$483$	−421.260	+	128.327i	−0.872173	+	0.265688i
$484$	147.911	−	53.3335i	0.305600	−	0.110193i
$485$	−379.607			−0.782695
$486$	484.417	−	39.1883i	0.996744	−	0.0806343i
$487$	−44.1216	+	44.1216i	−0.0905988	+	0.0905988i	−0.750954	−	0.660355i	$-0.770406\pi$
$487$	−44.1216	+	44.1216i	−0.0905988	+	0.0905988i	0.660355	+	0.750954i	$0.270406\pi$
$488$	−192.371	+	705.241i	−0.394204	+	1.44517i
$489$	218.753	+	718.102i	0.447349	+	1.46851i
$490$	−96.2855	−	550.889i	−0.196501	−	1.12426i
$491$			12.3013i			0.0250535i	0.999922	+	0.0125268i	$0.00398750\pi$
$491$			12.3013i			0.0250535i	−0.999922	+	0.0125268i	$0.996013\pi$
$492$	−321.935	−	430.803i	−0.654340	−	0.875616i
$493$		−	428.630i		−	0.869431i
$494$	−187.453	−	56.4335i	−0.379460	−	0.114238i
$495$	415.109	−	278.777i	0.838604	−	0.563186i
$496$	68.6194	−	733.642i	0.138346	−	1.47912i
$497$			468.464i			0.942583i
$498$	101.175	−	308.747i	0.203162	−	0.619974i
$499$	126.349	−	126.349i	0.253205	−	0.253205i	−0.569078	−	0.822283i	$-0.692700\pi$
$499$	126.349	−	126.349i	0.253205	−	0.253205i	0.822283	+	0.569078i	$0.192700\pi$
$500$	−229.527	+	488.395i	−0.459054	+	0.976790i
$501$	392.115	−	119.449i	0.782664	−	0.238421i
$502$	−6.07295	+	8.64547i	−0.0120975	+	0.0172220i
$503$	301.791			0.599982			0.299991	−	0.953942i	$-0.403016\pi$
$503$	301.791			0.599982			0.299991	+	0.953942i	$0.403016\pi$
$504$	−684.867	−	339.572i	−1.35886	−	0.673754i
$505$	480.764	−	480.764i	0.952009	−	0.952009i
$506$	60.2788	+	344.879i	0.119128	+	0.681580i
$507$	75.8554	+	501.293i	0.149616	+	0.988744i
$508$	−140.453	−	389.521i	−0.276483	−	0.766773i
$509$	−284.202	+	284.202i	−0.558353	+	0.558353i	−0.928838	−	0.370485i	$-0.879191\pi$
$509$	−284.202	+	284.202i	−0.558353	+	0.558353i	0.370485	+	0.928838i	$0.379191\pi$
$510$	−263.979	−	86.5043i	−0.517605	−	0.169616i
$511$	263.923			0.516483
$512$	−366.889	+	357.123i	−0.716580	+	0.697505i
$513$	157.600	+	128.414i	0.307213	+	0.250320i
$514$	23.0241	+	16.1731i	0.0447940	+	0.0314653i
$515$	305.561	−	305.561i	0.593322	−	0.593322i
$516$	−97.7418	+	675.811i	−0.189422	+	1.30971i
$517$			751.806i			1.45417i
$518$	455.940	+	320.272i	0.880194	+	0.618286i
$519$	−542.428	−	289.116i	−1.04514	−	0.557064i
$520$	−24.4700	−	455.707i	−0.0470577	−	0.876360i
$521$			10.0392i			0.0192691i	0.999954	+	0.00963453i	$0.00306681\pi$
$521$			10.0392i			0.0192691i	−0.999954	+	0.00963453i	$0.996933\pi$
$522$	−731.090	−	15.3334i	−1.40055	−	0.0293744i
$523$		−	215.956i		−	0.412917i	−0.978455	−	0.206459i	$-0.933806\pi$
$523$		−	215.956i		−	0.412917i	0.978455	−	0.206459i	$-0.0661938\pi$
$524$	−330.521	−	916.639i	−0.630766	−	1.74931i
$525$	175.027	−	53.3180i	0.333385	−	0.101558i
$526$	−143.678	−	100.925i	−0.273151	−	0.191873i
$527$	−343.581	+	343.581i	−0.651957	+	0.651957i
$528$	−334.561	+	507.364i	−0.633639	+	0.960917i
$529$	337.844			0.638647
$530$	2.30748	+	13.2020i	0.00435373	+	0.0249095i
$531$	−367.487	−	72.2022i	−0.692065	−	0.135974i
$532$	−108.463	−	300.802i	−0.203878	−	0.565418i
$533$	−553.056	+	183.240i	−1.03763	+	0.343791i
$534$	1.36312	−	4.15973i	0.00255266	−	0.00778976i
$535$	−66.3747	+	66.3747i	−0.124065	+	0.124065i
$536$	135.294	+	236.788i	0.252414	+	0.441769i
$537$	319.386	−	599.219i	0.594760	−	1.11586i
$538$	−325.642	+	463.585i	−0.605283	+	0.861682i
$539$	570.496	+	570.496i	1.05843	+	1.05843i
$540$	−156.989	+	447.159i	−0.290720	+	0.828072i
$541$	444.062	−	444.062i	0.820818	−	0.820818i	−0.165408	−	0.986225i	$-0.552894\pi$
$541$	444.062	−	444.062i	0.820818	−	0.820818i	0.986225	+	0.165408i	$0.0528940\pi$
$542$	116.786	+	668.180i	0.215472	+	1.23280i
$543$	171.498	−	321.756i	0.315833	−	0.592553i
$544$	336.554	−	26.9051i	0.618666	−	0.0494579i
$545$	241.098			0.442382
$546$	−583.657	+	587.491i	−1.06897	+	1.07599i
$547$		−	944.412i		−	1.72653i	−0.504752	−	0.863265i	$-0.668416\pi$
$547$		−	944.412i		−	1.72653i	0.504752	−	0.863265i	$-0.331584\pi$
$548$	208.746	−	444.177i	0.380924	−	0.810542i
$549$	−458.494	−	682.714i	−0.835144	−	1.24356i
$550$	−25.0449	−	143.292i	−0.0455362	−	0.260531i
$551$	−216.291	−	216.291i	−0.392542	−	0.392542i
$552$	−241.430	−	227.635i	−0.437373	−	0.412381i
$553$	772.094	−	772.094i	1.39619	−	1.39619i
$554$	608.224	−	865.869i	1.09788	−	1.56294i
$555$	162.479	−	304.836i	0.292755	−	0.549254i
$556$	−147.257	+	53.0977i	−0.264850	+	0.0954995i
$557$	−521.219	−	521.219i	−0.935762	−	0.935762i	0.0622958	−	0.998058i	$-0.480158\pi$
$557$	−521.219	−	521.219i	−0.935762	−	0.935762i	−0.998058	+	0.0622958i	$0.980158\pi$
$558$	573.736	+	598.318i	1.02820	+	1.07225i
$559$	661.049	+	332.022i	1.18256	+	0.593956i
$560$	573.889	−	475.717i	1.02480	−	0.849494i
$561$	383.370	−	116.785i	0.683368	−	0.208173i
$562$	37.2887	+	213.344i	0.0663499	+	0.379615i
$563$		−	829.523i		−	1.47340i	−0.676221	−	0.736699i	$-0.736383\pi$
$563$		−	829.523i		−	1.47340i	0.676221	−	0.736699i	$-0.263617\pi$
$564$	−426.534	−	570.773i	−0.756266	−	1.01201i
$565$	176.021	+	176.021i	0.311541	+	0.311541i
$566$	−451.949	−	317.469i	−0.798497	−	0.560899i
$567$	792.968	−	332.824i	1.39853	−	0.586991i
$568$	−306.488	+	175.118i	−0.539591	+	0.308307i
$569$	171.340			0.301125			0.150563	−	0.988600i	$-0.451892\pi$
$569$	171.340			0.301125			0.150563	+	0.988600i	$0.451892\pi$
$570$	−176.857	+	89.5552i	−0.310276	+	0.157114i
$571$	−387.748			−0.679069			−0.339535	−	0.940594i	$-0.610270\pi$
$571$	−387.748			−0.679069			−0.339535	+	0.940594i	$0.610270\pi$
$572$	406.786	+	517.685i	0.711165	+	0.905044i
$573$	292.560	+	155.936i	0.510577	+	0.272140i
$574$	−778.728	−	547.012i	−1.35667	−	0.952983i
$575$	79.4224			0.138126
$576$	−33.8509	−	575.004i	−0.0587689	−	0.998272i
$577$	300.732	+	300.732i	0.521200	+	0.521200i	0.917934	−	0.396734i	$-0.129856\pi$
$577$	300.732	+	300.732i	0.521200	+	0.521200i	−0.396734	+	0.917934i	$0.629856\pi$
$578$	290.786	+	204.261i	0.503091	+	0.353393i
$579$	883.815	−	269.234i	1.52645	−	0.464999i
$580$	303.292	−	645.354i	0.522917	−	1.11268i
$581$		−	574.917i		−	0.989530i
$582$	−161.632	+	493.240i	−0.277718	+	0.847492i
$583$	−13.6719	−	13.6719i	−0.0234510	−	0.0234510i
$584$	98.6582	+	172.669i	0.168935	+	0.295666i
$585$	405.759	+	314.562i	0.693604	+	0.537712i
$586$	83.9260	+	480.175i	0.143218	+	0.819411i
$587$	48.2499	+	48.2499i	0.0821974	+	0.0821974i	0.747010	−	0.664813i	$-0.231489\pi$
$587$	48.2499	+	48.2499i	0.0821974	+	0.0821974i	−0.664813	+	0.747010i	$0.731489\pi$
$588$	−756.791	−	109.454i	−1.28706	−	0.186146i
$589$			346.749i			0.588708i
$590$	209.919	−	298.841i	0.355794	−	0.506510i
$591$	808.309	−	246.233i	1.36770	−	0.416638i
$592$	−39.0982	+	418.017i	−0.0660442	+	0.706110i
$593$	−99.9109	−	99.9109i	−0.168484	−	0.168484i	0.617829	−	0.786313i	$-0.288012\pi$
$593$	−99.9109	−	99.9109i	−0.168484	−	0.168484i	−0.786313	+	0.617829i	$0.788012\pi$
$594$	−185.479	−	658.070i	−0.312254	−	1.10786i
$595$	−491.554			−0.826141
$596$	58.5621	+	27.5219i	0.0982585	+	0.0461777i
$597$	−264.643	−	141.056i	−0.443288	−	0.236274i
$598$	−316.671	+	170.120i	−0.529550	+	0.284482i
$599$	−922.144			−1.53947			−0.769736	−	0.638362i	$-0.779612\pi$
$599$	−922.144			−1.53947			−0.769736	+	0.638362i	$0.779612\pi$
$600$	100.310	+	94.5788i	0.167184	+	0.157631i
$601$	473.733			0.788242			0.394121	−	0.919059i	$-0.371049\pi$
$601$	473.733			0.788242			0.394121	+	0.919059i	$0.371049\pi$
$602$	208.035	+	1190.25i	0.345573	+	1.97717i
$603$	−301.048	−	59.1486i	−0.499250	−	0.0980905i
$604$	73.8819	−	157.208i	0.122321	−	0.260278i
$605$	−121.968	−	121.968i	−0.201599	−	0.201599i
$606$	−419.975	−	829.382i	−0.693028	−	1.36862i
$607$		−	633.569i		−	1.04377i	−0.853015	−	0.521886i	$-0.825229\pi$
$607$		−	633.569i		−	1.04377i	0.853015	−	0.521886i	$-0.174771\pi$
$608$	156.252	−	183.405i	0.256993	−	0.301653i
$609$	−1237.80	+	377.067i	−2.03251	+	0.619158i
$610$	789.961	−	138.071i	1.29502	−	0.226346i
$611$	−732.747	+	242.776i	−1.19926	+	0.397343i
$612$	−224.798	+	306.167i	−0.367317	+	0.500272i
$613$	−433.178	−	433.178i	−0.706652	−	0.706652i	0.259177	−	0.965830i	$-0.416549\pi$
$613$	−433.178	−	433.178i	−0.706652	−	0.706652i	−0.965830	+	0.259177i	$0.916549\pi$
$614$	12.0186	+	68.7634i	0.0195743	+	0.111992i
$615$	−277.508	+	520.648i	−0.451232	+	0.846582i
$616$	−283.003	+	1037.50i	−0.459420	+	1.68425i
$617$	−740.860	+	740.860i	−1.20075	+	1.20075i	−0.226806	+	0.973940i	$0.572828\pi$
$617$	−740.860	+	740.860i	−1.20075	+	1.20075i	−0.973940	+	0.226806i	$0.927172\pi$
$618$	−266.925	−	527.133i	−0.431917	−	0.852966i
$619$	−283.799	−	283.799i	−0.458480	−	0.458480i	0.439676	−	0.898156i	$-0.355093\pi$
$619$	−283.799	−	283.799i	−0.458480	−	0.458480i	−0.898156	+	0.439676i	$0.855093\pi$
$620$	−760.416	+	274.190i	−1.22648	+	0.442242i
$621$	371.371	−	37.8963i	0.598021	−	0.0610246i
$622$	−231.932	+	330.179i	−0.372881	+	0.530834i
$623$		−	7.74583i		−	0.0124331i
$624$	−602.540	−	162.240i	−0.965609	−	0.260000i
$625$	448.390			0.717423
$626$	169.001	+	118.714i	0.269970	+	0.189638i
$627$	134.521	−	252.383i	0.214547	−	0.402524i
$628$	277.680	+	770.094i	0.442166	+	1.22626i
$629$	195.767	−	195.767i	0.311235	−	0.311235i
$630$	−17.5844	+	838.416i	−0.0279118	+	1.33082i
$631$	818.322	+	818.322i	1.29687	+	1.29687i	0.930452	+	0.366414i	$0.119415\pi$
$631$	818.322	+	818.322i	1.29687	+	1.29687i	0.366414	+	0.930452i	$0.380585\pi$
$632$	793.755	+	216.516i	1.25594	+	0.342588i
$633$	−263.287	+	493.968i	−0.415936	+	0.780360i
$634$	915.938	−	160.090i	1.44470	−	0.252507i
$635$	−321.200	+	321.200i	−0.505828	+	0.505828i
$636$	18.1365	+	2.62306i	0.0285165	+	0.00412430i
$637$	−371.807	+	740.261i	−0.583684	+	1.16210i
$638$	177.119	+	1013.37i	0.277615	+	1.58835i
$639$	76.5593	−	389.663i	0.119811	−	0.609801i
$640$	525.761	+	197.632i	0.821501	+	0.308800i
$641$	962.325			1.50129			0.750643	−	0.660707i	$-0.229744\pi$
$641$	962.325			1.50129			0.750643	+	0.660707i	$0.229744\pi$
$642$	57.9821	+	114.505i	0.0903148	+	0.178357i
$643$	−491.770	+	491.770i	−0.764806	+	0.764806i	−0.977187	−	0.212381i	$-0.931878\pi$
$643$	−491.770	+	491.770i	−0.764806	+	0.764806i	0.212381	+	0.977187i	$0.431878\pi$
$644$	−531.404	−	249.740i	−0.825161	−	0.387794i
$645$	716.587	−	218.292i	1.11099	−	0.338437i
$646$	−156.511	+	27.3552i	−0.242276	+	0.0423456i
$647$			1220.24i			1.88599i	0.332800	+	0.942997i	$0.392007\pi$
$647$			1220.24i			1.88599i	−0.332800	+	0.942997i	$0.607993\pi$
$648$	514.169	+	394.378i	0.793471	+	0.608608i
$649$			526.868i			0.811814i
$650$	131.572	−	70.6825i	0.202418	−	0.108742i
$651$	1294.44	+	689.945i	1.98839	+	1.05982i
$652$	−425.719	+	905.860i	−0.652944	+	1.38936i
$653$		−	257.945i		−	0.395015i	−0.980301	−	0.197507i	$-0.936715\pi$
$653$		−	257.945i		−	0.395015i	0.980301	−	0.197507i	$-0.0632846\pi$
$654$	102.657	−	313.270i	0.156968	−	0.479006i
$655$	−755.864	+	755.864i	−1.15399	+	1.15399i
$656$	66.7781	−	713.957i	0.101796	−	1.08835i
$657$	−219.528	−	43.1320i	−0.334137	−	0.0656499i
$658$	−1031.74	−	724.740i	−1.56800	−	1.10143i
$659$	167.489			0.254156			0.127078	−	0.991893i	$-0.459440\pi$
$659$	167.489			0.254156			0.127078	+	0.991893i	$0.459440\pi$
$660$	659.844	+	95.4325i	0.999764	+	0.144595i
$661$	87.0778	−	87.0778i	0.131736	−	0.131736i	−0.638164	−	0.769900i	$-0.720306\pi$
$661$	87.0778	−	87.0778i	0.131736	−	0.131736i	0.769900	+	0.638164i	$0.220306\pi$
$662$	−649.216	+	113.471i	−0.980688	+	0.171407i
$663$	237.624	+	335.938i	0.358407	+	0.506694i
$664$	376.134	−	214.912i	0.566467	−	0.323663i
$665$	−248.043	+	248.043i	−0.372997	+	0.372997i
$666$	−326.905	−	340.912i	−0.490849	−	0.511879i
$667$	−561.678			−0.842096
$668$	494.639	+	232.461i	0.740477	+	0.347996i
$669$	297.402	−	90.5968i	0.444547	−	0.135421i
$670$	171.967	−	244.812i	0.256667	−	0.365392i
$671$	−818.078	+	818.078i	−1.21919	+	1.21919i
$672$	−373.765	−	948.234i	−0.556197	−	1.41106i
$673$		−	632.512i		−	0.939840i	−0.882709	−	0.469920i	$-0.844283\pi$
$673$		−	632.512i		−	0.939840i	0.882709	−	0.469920i	$-0.155717\pi$
$674$	−656.846	+	935.088i	−0.974549	+	1.38737i
$675$	−154.299	+	15.7453i	−0.228591	+	0.0233264i
$676$	−373.200	+	563.647i	−0.552071	+	0.833797i
$677$		−	689.930i		−	1.01910i	−0.860442	−	0.509549i	$-0.829812\pi$
$677$		−	689.930i		−	1.01910i	0.860442	−	0.509549i	$-0.170188\pi$
$678$	303.659	−	153.764i	0.447875	−	0.226791i
$679$			918.461i			1.35267i
$680$	−183.750	−	321.594i	−0.270220	−	0.472933i
$681$	198.522	+	651.687i	0.291515	+	0.956956i
$682$	670.321	−	954.271i	0.982875	−	1.39922i
$683$	178.495	−	178.495i	0.261339	−	0.261339i	−0.564259	−	0.825598i	$-0.690838\pi$
$683$	178.495	−	178.495i	0.261339	−	0.261339i	0.825598	+	0.564259i	$0.190838\pi$
$684$	41.0594	+	267.930i	0.0600284	+	0.391710i
$685$	−538.403			−0.785990
$686$	−307.943	+	53.8229i	−0.448897	+	0.0784591i
$687$	−987.157	+	300.715i	−1.43691	+	0.437722i
$688$	−700.946	+	581.039i	−1.01882	+	0.844534i
$689$	8.91033	−	17.7403i	0.0129323	−	0.0257479i
$690$	−113.356	+	345.919i	−0.164284	+	0.501331i
$691$	639.614	−	639.614i	0.925635	−	0.925635i	−0.0717849	−	0.997420i	$-0.522870\pi$
$691$	639.614	−	639.614i	0.925635	−	0.925635i	0.997420	+	0.0717849i	$0.0228695\pi$
$692$	−277.995	−	770.968i	−0.401727	−	1.11412i
$693$	−674.503	−	1004.36i	−0.973309	−	1.44929i
$694$	−109.180	−	76.6928i	−0.157320	−	0.110508i
$695$	121.428	+	121.428i	0.174717	+	0.174717i
$696$	−709.399	−	668.864i	−1.01925	−	0.961012i
$697$	−334.362	+	334.362i	−0.479716	+	0.479716i
$698$	1059.00	−	185.094i	1.51719	−	0.265177i
$699$	−45.4778	−	24.2399i	−0.0650612	−	0.0346779i
$700$	220.790	+	103.763i	0.315415	+	0.148233i
$701$	282.058			0.402365			0.201183	−	0.979554i	$-0.435522\pi$
$701$	282.058			0.402365			0.201183	+	0.979554i	$0.435522\pi$
$702$	581.491	−	393.284i	0.828335	−	0.560233i
$703$		−	197.572i		−	0.281041i
$704$	−784.565	+	202.680i	−1.11444	+	0.287898i
$705$	−367.671	+	689.809i	−0.521520	+	0.978452i
$706$	894.759	−	156.388i	1.26736	−	0.221513i
$707$	−1163.21	−	1163.21i	−1.64528	−	1.64528i
$708$	−298.916	−	399.999i	−0.422198	−	0.564971i
$709$	−329.957	+	329.957i	−0.465383	+	0.465383i	−0.900415	−	0.435032i	$-0.856737\pi$
$709$	−329.957	+	329.957i	−0.465383	+	0.465383i	0.435032	+	0.900415i	$0.356737\pi$
$710$	316.874	+	222.586i	0.446302	+	0.313502i
$711$	−768.400	+	516.039i	−1.08073	+	0.725793i
$712$	5.06764	−	2.89550i	0.00711747	−	0.00406671i
$713$	450.230	+	450.230i	0.631459	+	0.631459i
$714$	−209.298	+	638.698i	−0.293134	+	0.894535i
$715$	324.177	−	645.431i	0.453395	−	0.902701i
$716$	851.687	−	307.101i	1.18951	−	0.428912i
$717$	105.729	+	347.077i	0.147461	+	0.484068i
$718$	346.878	−	60.6281i	0.483117	−	0.0844403i
$719$		−	467.890i		−	0.650751i	−0.945585	−	0.325375i	$-0.894509\pi$
$719$		−	467.890i		−	0.650751i	0.945585	−	0.325375i	$-0.105491\pi$
$720$	−555.099	+	301.907i	−0.770971	+	0.419316i
$721$	−739.306	−	739.306i	−1.02539	−	1.02539i
$722$	349.835	−	498.026i	0.484536	−	0.689787i
$723$	343.325	−	104.586i	0.474862	−	0.144656i
$724$	457.321	−	164.901i	0.631659	−	0.227763i
$725$	233.369			0.321888
$726$	−210.410	+	106.546i	−0.289821	+	0.146757i
$727$	722.849			0.994290			0.497145	−	0.867668i	$-0.334382\pi$
$727$	722.849			0.994290			0.497145	+	0.867668i	$0.334382\pi$
$728$	−1102.59	+	59.2054i	−1.51454	+	0.0813261i
$729$	−713.974	+	147.247i	−0.979389	+	0.201985i
$730$	125.401	−	178.521i	0.171782	−	0.244549i
$731$	600.383			0.821317
$732$	156.954	−	1085.22i	0.214418	−	1.48254i
$733$	−326.050	−	326.050i	−0.444815	−	0.444815i	0.448811	−	0.893627i	$-0.351848\pi$
$733$	−326.050	−	326.050i	−0.444815	−	0.444815i	−0.893627	+	0.448811i	$0.851848\pi$
$734$	10.2103	−	14.5355i	0.0139105	−	0.0198031i
$735$	244.449	+	802.453i	0.332584	+	1.09177i
$736$	−35.2565	−	441.022i	−0.0479029	−	0.599215i
$737$			431.614i			0.585636i
$738$	558.341	+	582.264i	0.756560	+	0.788975i
$739$	406.384	+	406.384i	0.549911	+	0.549911i	0.926415	−	0.376504i	$-0.122874\pi$
$739$	406.384	+	406.384i	0.549911	+	0.549911i	−0.376504	+	0.926415i	$0.622874\pi$
$740$	433.272	−	156.229i	0.585503	−	0.211120i
$741$	289.425	+	49.6104i	0.390587	+	0.0669506i
$742$	31.9424	−	5.58296i	0.0430490	−	0.00752420i
$743$	−743.337	−	743.337i	−1.00045	−	1.00045i	−1.00000		0.000454295i	$-0.999855\pi$
$743$	−743.337	−	743.337i	−1.00045	−	1.00045i	−0.000454295	−	1.00000i	$-0.500145\pi$
$744$	32.4917	+	1104.79i	0.0436716	+	1.48493i
$745$		−	70.9852i		−	0.0952822i
$746$	−500.960	−	351.896i	−0.671529	−	0.471711i
$747$	−93.9566	+	478.210i	−0.125779	+	0.640174i
$748$	483.607	+	227.277i	0.646533	+	0.303846i
$749$	160.594	+	160.594i	0.214411	+	0.214411i
$750$	252.067	−	769.214i	0.336089	−	1.02562i
$751$	761.694			1.01424			0.507120	−	0.861876i	$-0.330710\pi$
$751$	761.694			1.01424			0.507120	+	0.861876i	$0.330710\pi$
$752$	88.4747	−	945.925i	0.117653	−	1.25788i
$753$	7.45425	−	13.9853i	0.00989941	−	0.0185728i
$754$	−930.482	+	499.869i	−1.23406	+	0.662956i
$755$	−190.558			−0.252394
$756$	1081.90	+	379.836i	1.43109	+	0.502428i
$757$	24.4538			0.0323036			0.0161518	−	0.999870i	$-0.494858\pi$
$757$	24.4538			0.0323036			0.0161518	+	0.999870i	$0.494858\pi$
$758$	−536.093	+	93.6995i	−0.707247	+	0.123614i
$759$	−153.035	−	502.369i	−0.201628	−	0.661883i
$760$	−255.002	−	69.5578i	−0.335528	−	0.0915234i
$761$	−855.917	−	855.917i	−1.12473	−	1.12473i	−0.991021	−	0.133706i	$-0.957312\pi$
$761$	−855.917	−	855.917i	−1.12473	−	1.12473i	−0.133706	−	0.991021i	$-0.542688\pi$
$762$	280.587	+	554.113i	0.368224	+	0.727183i
$763$		−	583.339i		−	0.764533i
$764$	149.938	+	415.825i	0.196254	+	0.544273i
$765$	408.869	+	80.3328i	0.534469	+	0.105010i
$766$	−52.1647	−	298.456i	−0.0681001	−	0.389629i
$767$	−513.511	+	170.138i	−0.669506	+	0.221823i
$768$	480.654	−	598.995i	0.625852	−	0.779942i
$769$	220.319	+	220.319i	0.286501	+	0.286501i	0.835695	−	0.549194i	$-0.185065\pi$
$769$	220.319	+	220.319i	0.286501	+	0.286501i	−0.549194	+	0.835695i	$0.685065\pi$
$770$	1162.13	−	203.120i	1.50926	−	0.263792i
$771$	−37.2450	−	19.8518i	−0.0483074	−	0.0257481i
$772$	1114.90	+	523.961i	1.44417	+	0.678706i
$773$	−812.134	+	812.134i	−1.05063	+	1.05063i	−0.0519779	+	0.998648i	$0.516553\pi$
$773$	−812.134	+	812.134i	−1.05063	+	1.05063i	−0.998648	+	0.0519779i	$0.983447\pi$
$774$	21.4776	−	1024.04i	0.0277488	−	1.32305i
$775$	−187.064	−	187.064i	−0.241373	−	0.241373i
$776$	−600.895	+	343.334i	−0.774349	+	0.442441i
$777$	−737.552	−	393.119i	−0.949231	−	0.505944i
$778$	284.492	+	199.840i	0.365671	+	0.256863i
$779$			337.445i			0.433177i
$780$	120.066	+	673.934i	0.153931	+	0.864018i
$781$	−558.662			−0.715316
$782$	−167.699	+	238.737i	−0.214449	+	0.305291i
$783$	1091.21	−	111.352i	1.39363	−	0.142211i
$784$	−650.663	−	784.938i	−0.829927	−	1.00120i
$785$	635.023	−	635.023i	0.808946	−	0.808946i
$786$	660.290	+	1303.97i	0.840063	+	1.65899i
$787$	−862.612	−	862.612i	−1.09608	−	1.09608i	−0.994865	−	0.101211i	$-0.967728\pi$
$787$	−862.612	−	862.612i	−1.09608	−	1.09608i	−0.101211	−	0.994865i	$-0.532272\pi$
$788$	1019.65	+	479.198i	1.29398	+	0.608119i
$789$	232.420	+	123.881i	0.294576	+	0.157010i
$790$	−155.400	−	889.108i	−0.196709	−	1.12545i
$791$	425.883	−	425.883i	0.538411	−	0.538411i
$792$	404.954	−	816.731i	0.511305	−	1.03123i
$793$	−1061.52	−	533.161i	−1.33861	−	0.672335i
$794$	154.483	−	27.0008i	0.194563	−	0.0340061i
$795$	−5.85821	−	19.2307i	−0.00736882	−	0.0241896i
$796$	−135.630	−	376.144i	−0.170389	−	0.472543i
$797$	−94.0730			−0.118034			−0.0590169	−	0.998257i	$-0.518797\pi$
$797$	−94.0730			−0.118034			−0.0590169	+	0.998257i	$0.518797\pi$
$798$	216.679	+	427.907i	0.271528	+	0.536224i
$799$	−442.998	+	442.998i	−0.554440	+	0.554440i
$800$	14.6486	+	183.238i	0.0183107	+	0.229048i
$801$	−1.26587	+	6.44290i	−0.00158037	+	0.00804357i
$802$	116.925	+	668.975i	0.145792	+	0.834133i
$803$			314.739i			0.391954i
$804$	−244.874	−	327.682i	−0.304570	−	0.407565i
$805$			644.134i			0.800166i
$806$	1146.54	+	345.171i	1.42251	+	0.428251i
$807$	399.710	−	749.919i	0.495304	−	0.929267i
$808$	326.196	−	1195.85i	0.403707	−	1.48001i
$809$		−	278.849i		−	0.344684i	−0.985037	−	0.172342i	$-0.944867\pi$
$809$		−	278.849i		−	0.344684i	0.985037	−	0.172342i	$-0.0551334\pi$
$810$	151.646	−	694.511i	0.187217	−	0.857421i
$811$	153.941	−	153.941i	0.189816	−	0.189816i	−0.605801	−	0.795617i	$-0.707147\pi$
$811$	153.941	−	153.941i	0.189816	−	0.189816i	0.795617	+	0.605801i	$0.207147\pi$
$812$	−1561.44	−	733.816i	−1.92295	−	0.903714i
$813$	−296.495	−	973.305i	−0.364693	−	1.19718i
$814$	−381.938	+	543.727i	−0.469211	+	0.667970i
$815$	1098.03			1.34727
$816$	−496.100	+	101.823i	−0.607966	+	0.124783i
$817$	302.959	−	302.959i	0.370819	−	0.370819i
$818$	−65.9570	−	377.367i	−0.0806320	−	0.461329i
$819$	761.084	−	981.735i	0.929284	−	1.19870i
$820$	−740.011	+	266.833i	−0.902453	+	0.325406i
$821$	−220.394	+	220.394i	−0.268446	+	0.268446i	−0.828474	−	0.560028i	$-0.810791\pi$
$821$	−220.394	+	220.394i	−0.268446	+	0.268446i	0.560028	+	0.828474i	$0.310791\pi$
$822$	−229.246	+	699.571i	−0.278888	+	0.851060i
$823$	−336.446			−0.408805			−0.204402	−	0.978887i	$-0.565525\pi$
$823$	−336.446			−0.408805			−0.204402	+	0.978887i	$0.565525\pi$
$824$	207.321	−	760.048i	0.251603	−	0.922388i
$825$	63.5839	+	208.727i	0.0770714	+	0.253002i
$826$	−723.047	−	507.899i	−0.875359	−	0.614890i
$827$	760.113	−	760.113i	0.919121	−	0.919121i	−0.0778447	−	0.996965i	$-0.524804\pi$
$827$	760.113	−	760.113i	0.919121	−	0.919121i	0.996965	+	0.0778447i	$0.0248038\pi$
$828$	401.202	+	294.576i	0.484543	+	0.355768i
$829$			1192.06i			1.43795i	0.695035	+	0.718976i	$0.255389\pi$
$829$			1192.06i			1.43795i	−0.695035	+	0.718976i	$0.744611\pi$
$830$	−388.881	−	273.167i	−0.468531	−	0.329117i
$831$	−746.566	+	1400.67i	−0.898394	+	1.68553i
$832$	−450.897	−	699.225i	−0.541944	−	0.840415i
$833$			672.324i			0.807112i
$834$	209.480	−	106.075i	0.251175	−	0.127188i
$835$		−	599.569i		−	0.718047i
$836$	358.719	−	129.347i	0.429090	−	0.154721i
$837$	−963.949	−	785.435i	−1.15167	−	0.938393i
$838$	1192.76	+	837.849i	1.42335	+	0.999820i
$839$	−39.3907	+	39.3907i	−0.0469496	+	0.0469496i	−0.730192	−	0.683242i	$-0.760569\pi$
$839$	−39.3907	+	39.3907i	−0.0469496	+	0.0469496i	0.683242	+	0.730192i	$0.260569\pi$
$840$	−767.055	+	813.541i	−0.913161	+	0.968501i
$841$	−809.392			−0.962416
$842$	102.608	+	587.064i	0.121863	+	0.697226i
$843$	−94.6683	−	310.767i	−0.112299	−	0.368645i
$844$	−702.091	+	253.160i	−0.831861	+	0.299952i
$845$	733.753	+	107.534i	0.868347	+	0.127259i
$846$	739.749	+	771.444i	0.874408	+	0.911873i
$847$	−295.101	+	295.101i	−0.348408	+	0.348408i
$848$	15.5931	+	18.8110i	0.0183881	+	0.0221828i
$849$	731.096	+	389.678i	0.861126	+	0.458984i
$850$	69.6766	−	99.1918i	0.0819725	−	0.116696i
$851$	−256.534	−	256.534i	−0.301450	−	0.301450i
$852$	424.138	−	316.954i	0.497814	−	0.372012i
$853$	−535.536	+	535.536i	−0.627827	+	0.627827i	−0.947521	−	0.319694i	$-0.896420\pi$
$853$	−535.536	+	535.536i	−0.627827	+	0.627827i	0.319694	+	0.947521i	$0.396420\pi$
$854$	−334.064	−	1911.31i	−0.391175	−	2.23807i
$855$	246.856	−	165.783i	0.288721	−	0.193898i
$856$	−45.0348	+	165.100i	−0.0526108	+	0.192873i
$857$	796.605			0.929527			0.464764	−	0.885435i	$-0.346139\pi$
$857$	796.605			0.929527			0.464764	+	0.885435i	$0.346139\pi$
$858$	−700.607	−	696.035i	−0.816558	−	0.811229i
$859$			673.316i			0.783837i	0.920000	+	0.391919i	$0.128188\pi$
$859$			673.316i			0.783837i	−0.920000	+	0.391919i	$0.871812\pi$
$860$	903.948	+	424.821i	1.05110	+	0.493978i
$861$	1259.71	+	671.431i	1.46308	+	0.779827i
$862$	−9.20445	−	52.6624i	−0.0106780	−	0.0610933i
$863$	864.784	+	864.784i	1.00207	+	1.00207i	0.999998	+	0.00206905i	$0.000658599\pi$
$863$	864.784	+	864.784i	1.00207	+	1.00207i	0.00206905	+	0.999998i	$0.499341\pi$
$864$	155.927	+	849.813i	0.180471	+	0.983580i
$865$	−635.743	+	635.743i	−0.734963	+	0.734963i
$866$	219.990	−	313.178i	0.254030	−	0.361638i
$867$	−470.391	−	250.721i	−0.542550	−	0.289182i
$868$	663.405	+	1839.83i	0.764292	+	2.11962i
$869$	920.754	+	920.754i	1.05956	+	1.05956i
$870$	−333.076	+	1016.42i	−0.382846	+	1.16830i
$871$	−420.672	+	139.378i	−0.482976	+	0.160021i
$872$	381.644	−	218.060i	0.437665	−	0.250069i
$873$	150.101	−	763.966i	0.171937	−	0.875104i
$874$	35.8464	+	205.092i	0.0410142	+	0.234659i
$875$		−	1432.35i		−	1.63697i
$876$	−178.566	−	238.951i	−0.203842	−	0.272775i
$877$	−538.632	−	538.632i	−0.614176	−	0.614176i	0.329856	−	0.944031i	$-0.393000\pi$
$877$	−538.632	−	538.632i	−0.614176	−	0.614176i	−0.944031	+	0.329856i	$0.893000\pi$
$878$	562.233	+	394.937i	0.640356	+	0.449814i
$879$	−213.071	−	699.448i	−0.242402	−	0.795731i
$880$	567.311	+	684.386i	0.644672	+	0.777711i
$881$	−1705.76			−1.93616			−0.968082	−	0.250634i	$-0.919361\pi$
$881$	−1705.76			−1.93616			−0.968082	+	0.250634i	$0.919361\pi$
$882$	1146.75	+	24.0512i	1.30017	+	0.0272689i
$883$	224.488			0.254233			0.127117	−	0.991888i	$-0.459428\pi$
$883$	224.488			0.254233			0.127117	+	0.991888i	$0.459428\pi$
$884$	−65.3467	+	544.740i	−0.0739216	+	0.616222i
$885$	−257.665	+	483.420i	−0.291147	+	0.546237i
$886$	−460.846	−	323.718i	−0.520142	−	0.365370i
$887$	−1033.75			−1.16545			−0.582724	−	0.812670i	$-0.698013\pi$
$887$	−1033.75			−1.16545			−0.582724	+	0.812670i	$0.698013\pi$
$888$	−18.5132	−	629.490i	−0.0208482	−	0.708885i
$889$	777.147	+	777.147i	0.874181	+	0.874181i
$890$	−5.23937	−	3.68036i	−0.00588693	−	0.00413524i
$891$	396.906	+	945.646i	0.445461	+	1.06133i
$892$	375.162	+	176.312i	0.420585	+	0.197659i
$893$			447.082i			0.500652i
$894$	−92.2343	−	30.2247i	−0.103170	−	0.0338083i
$895$	−702.304	−	702.304i	−0.784697	−	0.784697i
$896$	478.171	−	1272.08i	0.533673	−	1.41973i
$897$	440.215	−	311.383i	0.490763	−	0.347138i
$898$	−81.9278	−	468.743i	−0.0912337	−	0.521985i
$899$	1322.92	+	1322.92i	1.47155	+	1.47155i
$900$	−166.693	−	122.392i	−0.185215	−	0.135991i
$901$		−	16.1122i		−	0.0178826i
$902$	652.334	−	928.665i	0.723209	−	1.02956i
$903$	−528.159	−	1733.79i	−0.584893	−	1.92003i
$904$	437.831	+	119.429i	0.484327	+	0.132112i
$905$	−377.109	−	377.109i	−0.416695	−	0.416695i
$906$	−81.1373	+	247.600i	−0.0895555	+	0.273289i
$907$	638.599			0.704079			0.352039	−	0.935985i	$-0.385488\pi$
$907$	638.599			0.704079			0.352039	+	0.935985i	$0.385488\pi$
$908$	−386.346	+	822.080i	−0.425492	+	0.905375i
$909$	777.448	+	1157.65i	0.855278	+	1.27354i
$910$	573.251	+	1067.08i	0.629947	+	1.17261i
$911$	−529.454			−0.581178			−0.290589	−	0.956848i	$-0.593851\pi$
$911$	−529.454			−0.581178			−0.290589	+	0.956848i	$0.593851\pi$
$912$	−198.956	+	301.718i	−0.218154	+	0.330831i
$913$	685.612			0.750944
$914$	243.196	+	1391.42i	0.266078	+	1.52234i
$915$	−1150.70	+	350.534i	−1.25759	+	0.383097i
$916$	−1245.26	−	585.226i	−1.35946	−	0.638893i
$917$	1828.82	+	1828.82i	1.99435	+	1.99435i
$918$	278.472	−	497.057i	0.303346	−	0.541456i
$919$		−	888.214i		−	0.966501i	−0.875482	−	0.483250i	$-0.839456\pi$
$919$		−	888.214i		−	0.966501i	0.875482	−	0.483250i	$-0.160544\pi$
$920$	−421.419	+	240.786i	−0.458064	+	0.261724i
$921$	−30.5128	−	100.164i	−0.0331301	−	0.108756i
$922$	−1418.37	+	247.905i	−1.53836	+	0.268878i
$923$	−180.405	−	544.499i	−0.195455	−	0.589923i
$924$	230.900	−	1596.50i	0.249891	−	1.72781i
$925$	106.586	+	106.586i	0.115228	+	0.115228i
$926$	20.0391	+	114.652i	0.0216405	+	0.123814i
$927$	494.125	+	735.769i	0.533037	+	0.793710i
$928$	−103.595	−	1295.87i	−0.111633	−	1.39641i
$929$	809.963	−	809.963i	0.871865	−	0.871865i	−0.120810	−	0.992676i	$-0.538549\pi$
$929$	809.963	−	809.963i	0.871865	−	0.871865i	0.992676	+	0.120810i	$0.0385493\pi$
$930$	1081.73	−	547.756i	1.16315	−	0.588985i
$931$	339.261	+	339.261i	0.364405	+	0.364405i
$932$	−23.3074	−	64.6388i	−0.0250080	−	0.0693550i
$933$	284.685	−	534.114i	0.305129	−	0.572470i
$934$	−218.227	+	310.669i	−0.233648	+	0.332622i
$935$		−	586.198i		−	0.626949i
$936$	926.795	+	130.945i	0.990166	+	0.139899i
$937$	866.894			0.925180			0.462590	−	0.886572i	$-0.346920\pi$
$937$	866.894			0.925180			0.462590	+	0.886572i	$0.346920\pi$
$938$	−592.325	−	416.075i	−0.631477	−	0.443577i
$939$	−273.385	−	145.715i	−0.291144	−	0.155181i
$940$	−980.445	+	353.528i	−1.04303	+	0.376094i
$941$	−1106.16	+	1106.16i	−1.17552	+	1.17552i	−0.194642	+	0.980874i	$0.562354\pi$
$941$	−1106.16	+	1106.16i	−1.17552	+	1.17552i	−0.980874	+	0.194642i	$0.937646\pi$
$942$	−554.728	−	1095.50i	−0.588884	−	1.16295i
$943$	438.149	+	438.149i	0.464633	+	0.464633i
$944$	62.0033	−	662.907i	0.0656814	−	0.702231i
$945$	−127.698	−	1251.40i	−0.135130	−	1.32423i
$946$	−1419.43	+	248.090i	−1.50045	+	0.262252i
$947$	1088.12	−	1088.12i	1.14902	−	1.14902i	0.162276	−	0.986745i	$-0.448117\pi$
$947$	1088.12	−	1088.12i	1.14902	−	1.14902i	0.986745	−	0.162276i	$-0.0518835\pi$
$948$	−1221.42	−	176.653i	−1.28842	−	0.186343i
$949$	−306.760	+	101.637i	−0.323245	+	0.107099i
$950$	−14.8937	−	85.2127i	−0.0156775	−	0.0896975i
$951$	−1334.20	+	406.435i	−1.40295	+	0.427376i
$952$	−778.100	+	444.584i	−0.817332	+	0.467000i
$953$	−1839.51			−1.93023			−0.965116	−	0.261822i	$-0.915677\pi$
$953$	−1839.51			−1.93023			−0.965116	+	0.261822i	$0.915677\pi$
$954$	−27.4817	−	0.576385i	−0.0288068	−	0.000604177i
$955$	342.891	−	342.891i	0.359048	−	0.359048i
$956$	−205.761	+	437.825i	−0.215231	+	0.457976i
$957$	−449.668	−	1476.12i	−0.469872	−	1.54245i
$958$	54.7424	−	9.56799i	0.0571424	−	0.00998747i
$959$			1302.67i			1.35836i
$960$	−818.988	−	197.726i	−0.853112	−	0.205964i
$961$		−	1159.86i		−	1.20693i
$962$	−653.280	−	196.672i	−0.679085	−	0.204441i
$963$	−107.335	−	159.826i	−0.111459	−	0.165966i
$964$	433.092	+	203.537i	0.449266	+	0.211138i
$965$		−	1351.41i		−	1.40043i
$966$	836.952	+	274.265i	0.866410	+	0.283918i
$967$	−874.943	+	874.943i	−0.904801	+	0.904801i	−0.995847	−	0.0910455i	$-0.970979\pi$
$967$	−874.943	+	874.943i	−0.904801	+	0.904801i	0.0910455	+	0.995847i	$0.470979\pi$
$968$	−303.380	−	82.7543i	−0.313410	−	0.0854899i
$969$	227.981	−	69.4494i	0.235275	−	0.0716712i
$970$	621.258	+	436.399i	0.640473	+	0.449896i
$971$	717.583			0.739015			0.369507	−	0.929228i	$-0.379526\pi$
$971$	717.583			0.739015			0.369507	+	0.929228i	$0.379526\pi$
$972$	−837.840	−	492.755i	−0.861976	−	0.506949i
$973$	293.797	−	293.797i	0.301949	−	0.301949i
$974$	122.931	−	21.4862i	0.126213	−	0.0220597i
$975$	−182.903	+	129.375i	−0.187592	+	0.132692i
$976$	1125.58	−	933.035i	1.15326	−	0.955978i
$977$	1232.22	−	1232.22i	1.26122	−	1.26122i	0.310724	−	0.950500i	$-0.399429\pi$
$977$	1232.22	−	1232.22i	1.26122	−	1.26122i	0.950500	−	0.310724i	$-0.100571\pi$
$978$	467.526	−	1426.71i	0.478043	−	1.45881i
$979$	9.23721			0.00943536
$980$	−475.726	+	1012.27i	−0.485435	+	1.03292i
$981$	−95.3329	+	485.215i	−0.0971793	+	0.494612i
$982$	14.1416	−	20.1321i	0.0144009	−	0.0205011i
$983$	−743.295	+	743.295i	−0.756149	+	0.756149i	−0.975619	−	0.219470i	$-0.929567\pi$
$983$	−743.295	+	743.295i	−0.756149	+	0.756149i	0.219470	+	0.975619i	$0.429567\pi$
$984$	31.6199	+	1075.14i	0.0321340	+	1.09263i
$985$		−	1235.96i		−	1.25478i
$986$	−492.756	+	701.488i	−0.499752	+	0.711448i
$987$	1669.00	+	889.583i	1.69098	+	0.901300i
$988$	241.907	+	307.856i	0.244845	+	0.311595i
$989$		−	786.744i		−	0.795494i
$990$	−999.845	−	20.9701i	−1.00994	−	0.0211820i
$991$		−	1572.92i		−	1.58721i	−0.608434	−	0.793604i	$-0.708202\pi$
$991$		−	1572.92i		−	1.58721i	0.608434	−	0.793604i	$-0.291798\pi$
$992$	−955.702	+	1121.78i	−0.963409	+	1.13083i
$993$	945.681	−	288.080i	0.952347	−	0.290111i
$994$	538.549	−	766.680i	0.541800	−	0.771307i
$995$	−310.170	+	310.170i	−0.311729	+	0.311729i
$996$	−520.519	+	388.979i	−0.522609	+	0.390541i
$997$	866.961			0.869570			0.434785	−	0.900534i	$-0.356824\pi$
$997$	866.961			0.869570			0.434785	+	0.900534i	$0.356824\pi$
$998$	−352.033	+	61.5292i	−0.352739	+	0.0616525i
$999$	549.242	+	447.527i	0.549792	+	0.447975i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.3.l.c.47.10	✓	96
3.2	odd	2	inner	156.3.l.c.47.39	yes	96
4.3	odd	2	inner	156.3.l.c.47.34	yes	96
12.11	even	2	inner	156.3.l.c.47.15	yes	96
13.5	odd	4	inner	156.3.l.c.83.15	yes	96
39.5	even	4	inner	156.3.l.c.83.34	yes	96
52.31	even	4	inner	156.3.l.c.83.39	yes	96
156.83	odd	4	inner	156.3.l.c.83.10	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.3.l.c.47.10	✓	96	1.1	even	1	trivial
156.3.l.c.47.15	yes	96	12.11	even	2	inner
156.3.l.c.47.34	yes	96	4.3	odd	2	inner
156.3.l.c.47.39	yes	96	3.2	odd	2	inner
156.3.l.c.83.10	yes	96	156.83	odd	4	inner
156.3.l.c.83.15	yes	96	13.5	odd	4	inner
156.3.l.c.83.34	yes	96	39.5	even	4	inner
156.3.l.c.83.39	yes	96	52.31	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	156.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.63658 - 1.14961i) q^{2} +(2.64742 + 1.41109i) q^{3} +(1.35681 + 3.76285i) q^{4} +(3.10286 - 3.10286i) q^{5} +(-2.71053 - 5.35285i) q^{6} +(-7.50740 - 7.50740i) q^{7} +(2.10527 - 7.71802i) q^{8} +(5.01767 + 7.47148i) q^{9} +(-8.64517 + 1.51102i) q^{10} +(8.95288 - 8.95288i) q^{11} +(-1.71767 + 11.8764i) q^{12} +(11.6170 + 5.83481i) q^{13} +(3.65593 + 20.9170i) q^{14} +(12.5930 - 3.83617i) q^{15} +(-12.3181 + 10.2109i) q^{16} +10.5509 q^{17} +(0.377438 - 17.9960i) q^{18} +(5.32408 - 5.32408i) q^{19} +(15.8856 + 7.46564i) q^{20} +(-9.28165 - 30.4688i) q^{21} +(-24.9444 + 4.35984i) q^{22} -13.8259i q^{23} +(16.4643 - 17.4621i) q^{24} +5.74446i q^{25} +(-12.3045 - 22.9042i) q^{26} +(2.74096 + 26.8605i) q^{27} +(18.0632 - 38.4354i) q^{28} -40.6250i q^{29} +(-25.0196 - 8.19878i) q^{30} +(-32.5642 + 32.5642i) q^{31} +(31.8982 - 2.55003i) q^{32} +(36.3353 - 11.0687i) q^{33} +(-17.2674 - 12.1294i) q^{34} -46.5889 q^{35} +(-21.3061 + 29.0181i) q^{36} +(18.5545 - 18.5545i) q^{37} +(-14.8339 + 2.59270i) q^{38} +(22.5217 + 31.8398i) q^{39} +(-17.4156 - 30.4804i) q^{40} +(-31.6904 + 31.6904i) q^{41} +(-19.8370 + 60.5350i) q^{42} +56.9036 q^{43} +(45.8357 + 21.5410i) q^{44} +(38.7521 + 7.61385i) q^{45} +(-15.8944 + 22.6273i) q^{46} +(-41.9868 + 41.9868i) q^{47} +(-47.0198 + 9.65068i) q^{48} +63.7221i q^{49} +(6.60387 - 9.40129i) q^{50} +(27.9326 + 14.8882i) q^{51} +(-6.19349 + 51.6298i) q^{52} -1.52710i q^{53} +(26.3932 - 47.1105i) q^{54} -55.5591i q^{55} +(-73.7474 + 42.1371i) q^{56} +(21.6078 - 6.58233i) q^{57} +(-46.7028 + 66.4862i) q^{58} +(-29.4245 + 29.4245i) q^{59} +(31.5212 + 42.1807i) q^{60} -91.3759 q^{61} +(90.7301 - 15.8580i) q^{62} +(18.4218 - 93.7610i) q^{63} +(-55.1356 - 32.4971i) q^{64} +(54.1506 - 17.9414i) q^{65} +(-72.1905 - 23.6564i) q^{66} +(-24.1047 + 24.1047i) q^{67} +(14.3155 + 39.7014i) q^{68} +(19.5096 - 36.6030i) q^{69} +(76.2466 + 53.5589i) q^{70} +(-31.2001 - 31.2001i) q^{71} +(68.2286 - 22.9969i) q^{72} +(-17.5775 + 17.5775i) q^{73} +(-51.6965 + 9.03562i) q^{74} +(-8.10593 + 15.2080i) q^{75} +(27.2575 + 12.8100i) q^{76} -134.426 q^{77} +(-0.255338 - 77.9996i) q^{78} +102.844i q^{79} +(-6.53836 + 69.9047i) q^{80} +(-30.6461 + 74.9788i) q^{81} +(88.2956 - 15.4325i) q^{82} +(38.2900 + 38.2900i) q^{83} +(102.056 - 76.2658i) q^{84} +(32.7379 - 32.7379i) q^{85} +(-93.1274 - 65.4167i) q^{86} +(57.3254 - 107.551i) q^{87} +(-50.2502 - 87.9468i) q^{88} +(0.515880 + 0.515880i) q^{89} +(-54.6681 - 57.0104i) q^{90} +(-43.4093 - 131.018i) q^{91} +(52.0249 - 18.7591i) q^{92} +(-132.162 + 40.2602i) q^{93} +(116.983 - 20.4466i) q^{94} -33.0398i q^{95} +(88.0463 + 38.2602i) q^{96} +(-61.1704 - 61.1704i) q^{97} +(73.2554 - 104.287i) q^{98} +(111.814 + 21.9687i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 36 q^{6} - 64 q^{9} - 8 q^{13} + 80 q^{16} + 48 q^{18} + 8 q^{21} + 124 q^{24} - 8 q^{28} + 24 q^{33} + 64 q^{34} - 128 q^{37} - 136 q^{40} - 140 q^{42} - 160 q^{45} + 88 q^{46} - 108 q^{48} - 320 q^{52}+ \cdots + 336 q^{97}+O(q^{100}) \) 96 * q - 36 * q^6 - 64 * q^9 - 8 * q^13 + 80 * q^16 + 48 * q^18 + 8 * q^21 + 124 * q^24 - 8 * q^28 + 24 * q^33 + 64 * q^34 - 128 * q^37 - 136 * q^40 - 140 * q^42 - 160 * q^45 + 88 * q^46 - 108 * q^48 - 320 * q^52 - 216 * q^54 + 136 * q^57 + 280 * q^58 + 80 * q^60 - 464 * q^61 - 240 * q^66 - 120 * q^70 - 32 * q^72 + 288 * q^73 + 88 * q^76 - 296 * q^78 - 144 * q^81 + 204 * q^84 + 848 * q^85 - 392 * q^93 + 1384 * q^94 - 204 * q^96 + 336 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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