LMFDB - Embedded newform 156.3.l.c.47.39

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			47.39
Character	$\chi$	$=$	156.47
Dual form			156.3.l.c.83.39

$q$-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} +(-5.95492 - 0.734131i) 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} +(-8.90176 - 8.04728i) q^{12} +(11.6170 + 5.83481i) q^{13} +(-3.65593 - 20.9170i) q^{14} +(3.83617 - 12.5930i) q^{15} +(-12.3181 + 10.2109i) q^{16} -10.5509 q^{17} +(16.8011 - 6.45936i) q^{18} +(5.32408 - 5.32408i) q^{19} +(-15.8856 - 7.46564i) q^{20} +(30.4688 + 9.28165i) q^{21} +(-24.9444 + 4.35984i) q^{22} +13.8259i q^{23} +(-5.31725 - 23.4036i) 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} +(20.7552 - 16.1994i) q^{30} +(-32.5642 + 32.5642i) q^{31} +(-31.8982 + 2.55003i) q^{32} +(11.0687 - 36.3353i) q^{33} +(-17.2674 - 12.1294i) q^{34} +46.5889 q^{35} +(34.9221 + 8.74338i) q^{36} +(18.5545 - 18.5545i) q^{37} +(14.8339 - 2.59270i) q^{38} +(-38.9885 + 0.945419i) q^{39} +(-17.4156 - 30.4804i) q^{40} +(31.6904 - 31.6904i) q^{41} +(39.1945 + 50.2174i) q^{42} +56.9036 q^{43} +(-45.8357 - 21.5410i) q^{44} +(7.61385 + 38.7521i) q^{45} +(-15.8944 + 22.6273i) q^{46} +(41.9868 - 41.9868i) q^{47} +(18.2028 - 44.4146i) 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} +(-35.3648 + 40.8084i) q^{54} -55.5591i q^{55} +(73.7474 - 42.1371i) q^{56} +(-6.58233 + 21.6078i) q^{57} +(-46.7028 + 66.4862i) q^{58} +(29.4245 - 29.4245i) q^{59} +(52.5906 - 2.65132i) q^{60} -91.3759 q^{61} +(-90.7301 + 15.8580i) q^{62} +(-93.7610 + 18.4218i) q^{63} +(-55.1356 - 32.4971i) q^{64} +(-54.1506 + 17.9414i) q^{65} +(59.8862 - 46.7411i) 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} +(47.1015 + 54.4560i) 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} +(-64.8948 - 43.2742i) 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} +(6.41488 + 127.243i) 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} +(-32.0890 + 72.1740i) q^{90} +(-43.4093 - 131.018i) q^{91} +(-52.0249 + 18.7591i) q^{92} +(40.2602 - 132.162i) q^{93} +(116.983 - 20.4466i) q^{94} +33.0398i q^{95} +(80.8497 - 51.7622i) q^{96} +(-61.1704 - 61.1704i) q^{97} +(-73.2554 + 104.287i) q^{98} +(21.9687 + 111.814i) 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	−0.945678	−	0.325105i	$-0.894600\pi$
$5$	−3.10286	+	3.10286i	−0.620573	+	0.620573i	0.325105	+	0.945678i	$0.394600\pi$
$6$	−5.95492	−	0.734131i	−0.992486	−	0.122355i
$7$	−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	−0.985216	−	0.171318i	$-0.945198\pi$
$11$	−8.95288	+	8.95288i	−0.813898	+	0.813898i	0.171318	+	0.985216i	$0.445198\pi$
$12$	−8.90176	−	8.04728i	−0.741813	−	0.670607i
$13$	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
$15$	3.83617	−	12.5930i	0.255745	−	0.839533i
$16$	−12.3181	+	10.2109i	−0.769884	+	0.638184i
$17$	−10.5509			−0.620640			−0.310320	−	0.950632i	$-0.600436\pi$
$17$	−10.5509			−0.620640			−0.310320	+	0.950632i	$0.600436\pi$
$18$	16.8011	−	6.45936i	0.933394	−	0.358853i
$19$	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
$21$	30.4688	+	9.28165i	1.45090	+	0.441983i
$22$	−24.9444	+	4.35984i	−1.13384	+	0.198174i
$23$			13.8259i			0.601127i	0.953762	+	0.300563i	$0.0971747\pi$
$23$			13.8259i			0.601127i	−0.953762	+	0.300563i	$0.902825\pi$
$24$	−5.31725	−	23.4036i	−0.221552	−	0.975149i
$25$			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	$0.247009\pi$
$29$			40.6250i			1.40086i	−0.713720	+	0.700431i	$0.752991\pi$
$30$	20.7552	−	16.1994i	0.691841	−	0.539980i
$31$	−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
$33$	11.0687	−	36.3353i	0.335416	−	1.10107i
$34$	−17.2674	−	12.1294i	−0.507864	−	0.356746i
$35$	46.5889			1.33111
$36$	34.9221	+	8.74338i	0.970058	+	0.242872i
$37$	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
$39$	−38.9885	+	0.945419i	−0.999706	+	0.0242415i
$40$	−17.4156	−	30.4804i	−0.435390	−	0.762009i
$41$	31.6904	−	31.6904i	0.772937	−	0.772937i	−0.205682	−	0.978619i	$-0.565941\pi$
$41$	31.6904	−	31.6904i	0.772937	−	0.772937i	0.978619	+	0.205682i	$0.0659411\pi$
$42$	39.1945	+	50.2174i	0.933203	+	1.19565i
$43$	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
$45$	7.61385	+	38.7521i	0.169197	+	0.861159i
$46$	−15.8944	+	22.6273i	−0.345530	+	0.491897i
$47$	41.9868	−	41.9868i	0.893337	−	0.893337i	−0.101499	−	0.994836i	$-0.532364\pi$
$47$	41.9868	−	41.9868i	0.893337	−	0.893337i	0.994836	+	0.101499i	$0.0323638\pi$
$48$	18.2028	−	44.4146i	0.379224	−	0.925305i
$49$			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	$0.00458592\pi$
$53$			1.52710i			0.0288132i	−0.999896	+	0.0144066i	$0.995414\pi$
$54$	−35.3648	+	40.8084i	−0.654904	+	0.755712i
$55$		−	55.5591i		−	1.01017i
$56$	73.7474	−	42.1371i	1.31692	−	0.752449i
$57$	−6.58233	+	21.6078i	−0.115479	+	0.379084i
$58$	−46.7028	+	66.4862i	−0.805221	+	1.14631i
$59$	29.4245	−	29.4245i	0.498720	−	0.498720i	−0.412319	−	0.911039i	$-0.635281\pi$
$59$	29.4245	−	29.4245i	0.498720	−	0.498720i	0.911039	+	0.412319i	$0.135281\pi$
$60$	52.5906	−	2.65132i	0.876510	−	0.0441887i
$61$	−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
$63$	−93.7610	+	18.4218i	−1.48827	+	0.292409i
$64$	−55.1356	−	32.4971i	−0.861494	−	0.507767i
$65$	−54.1506	+	17.9414i	−0.833087	+	0.276021i
$66$	59.8862	−	46.7411i	0.907367	−	0.708198i
$67$	−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	0.891823	−	0.452385i	$-0.149427\pi$
$71$	31.2001	+	31.2001i	0.439438	+	0.439438i	−0.452385	+	0.891823i	$0.649427\pi$
$72$	47.1015	+	54.4560i	0.654187	+	0.756333i
$73$	−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
$78$	−64.8948	−	43.2742i	−0.831985	−	0.554798i
$79$			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	0.437764	−	0.899090i	$-0.355770\pi$
$83$	−38.2900	−	38.2900i	−0.461326	−	0.461326i	−0.899090	+	0.437764i	$0.855770\pi$
$84$	6.41488	+	127.243i	0.0763677	+	1.51480i
$85$	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	0.704203	−	0.709999i	$-0.251305\pi$
$89$	−0.515880	−	0.515880i	−0.00579640	−	0.00579640i	−0.709999	+	0.704203i	$0.751305\pi$
$90$	−32.0890	+	72.1740i	−0.356545	+	0.801934i
$91$	−43.4093	−	131.018i	−0.477025	−	1.43976i
$92$	−52.0249	+	18.7591i	−0.565488	+	0.203903i
$93$	40.2602	−	132.162i	0.432906	−	1.42110i
$94$	116.983	−	20.4466i	1.24450	−	0.217517i
$95$			33.0398i			0.347787i
$96$	80.8497	−	51.7622i	0.842184	−	0.539190i
$97$	−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
$99$	21.9687	+	111.814i	0.221906	+	1.12943i
$100$	−21.6156	+	7.79413i	−0.216156	+	0.0779413i
$101$	−154.942			−1.53408			−0.767040	−	0.641599i	$-0.778271\pi$
$101$	−154.942			−1.53408			−0.767040	+	0.641599i	$0.778271\pi$
$102$	62.8296	+	7.74573i	0.615977	+	0.0759385i
$103$	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	$-0.468129\pi$
$107$	21.3914			0.199920			0.0999600	+	0.994991i	$0.468129\pi$
$108$	−104.791	+	26.1307i	−0.970288	+	0.241951i
$109$	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
$111$	−22.9396	+	75.3038i	−0.206663	+	0.678412i
$112$	169.135	+	15.8196i	1.51013	+	0.141246i
$113$		−	56.7285i		−	0.502022i	−0.967984	−	0.251011i	$-0.919237\pi$
$113$		−	56.7285i		−	0.502022i	0.967984	−	0.251011i	$-0.0807630\pi$
$114$	−35.6130	+	27.7959i	−0.312395	+	0.243823i
$115$	−42.8999	−	42.8999i	−0.373043	−	0.373043i
$116$	−152.866	+	55.1204i	−1.31781	+	0.475175i
$117$	101.885	−	57.5191i	0.870812	−	0.491617i
$118$	81.9822	−	14.3290i	0.694764	−	0.121432i
$119$	79.2097	+	79.2097i	0.665627	+	0.665627i
$120$	89.1168	+	56.1194i	0.742640	+	0.467661i
$121$		−	39.3081i		−	0.324860i
$122$	−149.544	−	105.046i	−1.22577	−	0.861036i
$123$	−39.1799	+	128.616i	−0.318536	+	1.04566i
$124$	−166.718	−	78.3510i	−1.34450	−	0.631863i
$125$	−95.3959	−	95.3959i	−0.763167	−	0.763167i
$126$	−174.625	−	77.6396i	−1.38592	−	0.616187i
$127$	−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	$-0.119998\pi$
$131$	243.602			1.85956			0.929779	+	0.368119i	$0.119998\pi$
$132$	151.743	−	7.65001i	1.14957	−	0.0579546i
$133$	−79.9399			−0.601052
$134$	−67.1604	+	11.7384i	−0.501197	+	0.0876003i
$135$	−74.8397	−	91.8494i	−0.554368	−	0.680366i
$136$	22.2125	−	81.4319i	0.163327	−	0.598764i
$137$	86.7590	+	86.7590i	0.633278	+	0.633278i	0.948889	−	0.315611i	$-0.102209\pi$
$137$	86.7590	+	86.7590i	0.633278	+	0.633278i	−0.315611	+	0.948889i	$0.602209\pi$
$138$	10.1500	−	82.3322i	0.0735510	−	0.596610i
$139$			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
$141$	−51.9097	+	170.404i	−0.368154	+	1.20854i
$142$	15.1937	+	86.9295i	0.106998	+	0.612179i
$143$	−156.244	+	51.7673i	−1.09262	+	0.362009i
$144$	14.4825	+	143.270i	0.100573	+	0.994930i
$145$	−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	−0.744449	−	0.667679i	$-0.767288\pi$
$149$	−11.4387	+	11.4387i	−0.0767695	+	0.0767695i	0.667679	+	0.744449i	$0.267288\pi$
$150$	4.21719	−	34.2078i	0.0281146	−	0.228052i
$151$	−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
$156$	−56.4574	−	145.425i	−0.361907	−	0.932214i
$157$	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
$162$	36.0413	−	157.940i	0.222477	−	0.974938i
$163$	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	−0.934500	−	0.355964i	$-0.884153\pi$
$167$	−96.6155	+	96.6155i	−0.578536	+	0.578536i	0.355964	+	0.934500i	$0.384153\pi$
$168$	−135.781	+	215.619i	−0.808221	+	1.28344i
$169$	100.910	+	135.566i	0.597100	+	0.802167i
$170$	91.2141	−	15.9426i	0.536554	−	0.0937800i
$171$	−13.0643	−	66.4932i	−0.0763994	−	0.388849i
$172$	77.2072	+	214.120i	0.448879	+	1.24488i
$173$	204.889			1.18433			0.592165	−	0.805817i	$-0.298273\pi$
$173$	204.889			1.18433			0.592165	+	0.805817i	$0.298273\pi$
$174$	29.8241	−	241.919i	0.171403	−	1.39034i
$175$	43.1260	−	43.1260i	0.246434	−	0.246434i
$176$	18.8655	−	201.700i	0.107190	−	1.14602i
$177$	−36.3784	+	119.419i	−0.205528	+	0.674686i
$178$	−0.251221	−	1.43734i	−0.00141135	−	0.00807494i
$179$			226.341i			1.26447i	0.774776	+	0.632236i	$0.217863\pi$
$179$			226.341i			1.26447i	−0.774776	+	0.632236i	$0.782137\pi$
$180$	−135.488	+	81.2290i	−0.752712	+	0.451272i
$181$		−	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
$186$	217.824	−	170.011i	1.17110	−	0.914037i
$187$	94.4607	−	94.4607i	0.505138	−	0.505138i
$188$	214.958	+	101.022i	1.14340	+	0.537352i
$189$	222.230	−	181.075i	1.17582	−	0.958069i
$190$	−37.9828	+	54.0723i	−0.199909	+	0.284591i
$191$	−110.508			−0.578575			−0.289287	−	0.957242i	$-0.593418\pi$
$191$	−110.508			−0.578575			−0.289287	+	0.957242i	$0.593418\pi$
$192$	191.823	+	8.23225i	0.999080	+	0.0428763i
$193$	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
$195$	118.043	−	123.910i	0.605347	−	0.635434i
$196$	−239.777	+	86.4587i	−1.22335	+	0.441116i
$197$	−199.164	+	199.164i	−1.01099	+	1.01099i	−0.0110466	+	0.999939i	$0.503516\pi$
$197$	−199.164	+	199.164i	−1.01099	+	1.01099i	−0.999939	+	0.0110466i	$0.996484\pi$
$198$	−92.5883	+	208.248i	−0.467618	+	1.05176i
$199$	−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
$201$	29.8015	−	97.8293i	0.148266	−	0.486713i
$202$	−253.576	−	178.123i	−1.25532	−	0.881795i
$203$	304.988	−	304.988i	1.50241	−	1.50241i
$204$	93.9213	+	84.9059i	0.460399	+	0.416205i
$205$			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
$210$	−277.433	−	34.2024i	−1.32111	−	0.162868i
$211$			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
$213$	−126.626	−	38.5737i	−0.594488	−	0.181097i
$214$	35.0089	+	24.5917i	0.163593	+	0.114915i
$215$	−176.564	+	176.564i	−0.821228	+	0.821228i
$216$	−201.539	−	77.7035i	−0.933053	−	0.359739i
$217$	488.945			2.25320
$218$	18.9195	+	108.246i	0.0867865	+	0.496541i
$219$	21.7317	−	71.3385i	0.0992314	−	0.325747i
$220$	209.061	−	75.3831i	0.950277	−	0.342650i
$221$	−122.570	−	61.5624i	−0.554614	−	0.278563i
$222$	−124.112	+	96.8693i	−0.559064	+	0.436348i
$223$	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	0.258611	−	0.965982i	$-0.416735\pi$
$227$	−160.573	−	160.573i	−0.707371	−	0.707371i	−0.965982	+	0.258611i	$0.916735\pi$
$228$	−90.2380	+	4.54929i	−0.395781	+	0.0199530i
$229$	−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	$-0.488263\pi$
$233$	17.1781			0.0737259			0.0368630	+	0.999320i	$0.488263\pi$
$234$	232.868	+	22.9928i	0.995161	+	0.0982598i
$235$			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	0.505190	−	0.863008i	$-0.331422\pi$
$239$	−85.5184	−	85.5184i	−0.357818	−	0.357818i	−0.863008	+	0.505190i	$0.831422\pi$
$240$	81.3318	+	194.293i	0.338883	+	0.809556i
$241$	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
$246$	−211.979	+	165.449i	−0.861703	+	0.672557i
$247$	92.9148	−	30.7849i	0.376173	−	0.124635i
$248$	−182.775	−	319.888i	−0.736995	−	1.28987i
$249$	155.400	+	47.3392i	0.624098	+	0.190117i
$250$	−46.4555	−	265.791i	−0.185822	−	1.06316i
$251$			5.28263i			0.0210463i	0.999945	+	0.0105232i	$0.00334969\pi$
$251$			5.28263i			0.0210463i	−0.999945	+	0.0105232i	$0.996650\pi$
$252$	−196.534	−	327.814i	−0.779897	−	1.30085i
$253$	−123.782	−	123.782i	−0.489256	−	0.489256i
$254$	−169.415	−	119.004i	−0.666987	−	0.468521i
$255$	−40.4750	+	132.867i	−0.158725	+	0.521048i
$256$	47.4733	−	251.560i	0.185443	−	0.982655i
$257$	14.0684			0.0547409			0.0273705	−	0.999625i	$-0.491287\pi$
$257$	14.0684			0.0547409			0.0273705	+	0.999625i	$0.491287\pi$
$258$	−338.856	−	41.7747i	−1.31340	−	0.161917i
$259$	−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	$-0.553377\pi$
$263$	−87.7912			−0.333807			−0.166903	+	0.985973i	$0.553377\pi$
$264$	257.134	+	161.925i	0.973992	+	0.613351i
$265$	−4.73838	−	4.73838i	−0.0178807	−	0.0178807i
$266$	−130.828	−	91.8995i	−0.491836	−	0.345487i
$267$	2.09370	+	0.637799i	0.00784158	+	0.00238876i
$268$	−123.408	−	57.9971i	−0.460478	−	0.216407i
$269$			283.264i			1.05303i	0.850167	+	0.526513i	$0.176501\pi$
$269$			283.264i			1.05303i	−0.850167	+	0.526513i	$0.823499\pi$
$270$	−16.8907	−	236.355i	−0.0625583	−	0.875390i
$271$	−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
$273$	299.800	+	285.605i	1.09817	+	1.04617i
$274$	42.2496	+	241.727i	0.154196	+	0.882216i
$275$	−51.4295	−	51.4295i	−0.187016	−	0.187016i
$276$	111.261	−	123.075i	0.403120	−	0.445924i
$277$			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
$279$	79.9066	+	406.699i	0.286404	+	1.45770i
$280$	−98.0824	+	359.574i	−0.350294	+	1.28419i
$281$	76.5718	+	76.5718i	0.272498	+	0.272498i	0.830105	−	0.557607i	$-0.188280\pi$
$281$	76.5718	+	76.5718i	0.272498	+	0.272498i	−0.557607	+	0.830105i	$0.688280\pi$
$282$	−280.852	+	219.204i	−0.995929	+	0.777320i
$283$	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
$288$	−141.002	+	251.122i	−0.489591	+	0.871952i
$289$	−177.679			−0.614806
$290$	−61.3853	−	351.210i	−0.211673	−	1.21107i
$291$	248.261	+	75.6270i	0.853129	+	0.259887i
$292$	−89.9910	−	42.2923i	−0.308188	−	0.144837i
$293$	172.341	+	172.341i	0.588195	+	0.588195i	0.937142	−	0.348947i	$-0.113461\pi$
$293$	172.341	+	172.341i	0.588195	+	0.588195i	−0.348947	+	0.937142i	$0.613461\pi$
$294$	46.7804	−	379.460i	0.159117	−	1.29068i
$295$			182.600i			0.618984i
$296$	104.142	+	182.267i	0.351831	+	0.615766i
$297$	−215.939	−	265.018i	−0.727069	−	0.892318i
$298$	−31.8703	+	5.57035i	−0.106947	+	0.0186925i
$299$	−80.6716	+	160.616i	−0.269805	+	0.537177i
$300$	46.2273	−	51.1358i	0.154091	−	0.170453i
$301$	−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
$306$	−177.266	+	68.1519i	−0.579302	+	0.222719i
$307$	−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	$0.105147\pi$
$311$			201.749i			0.648711i	−0.945935	+	0.324355i	$0.894853\pi$
$312$	74.7848	−	302.905i	0.239695	−	0.970848i
$313$	−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	$-0.487980\pi$
$317$	328.742	−	328.742i	1.03704	−	1.03704i	0.999287	−	0.0377544i	$-0.0120204\pi$
$318$	1.12109	−	9.09374i	0.00352544	−	0.0285967i
$319$	−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
$324$	240.553	−	217.048i	0.742449	−	0.669903i
$325$	−33.5178	+	66.7335i	−0.103132	+	0.205334i
$326$	86.1643	+	492.981i	0.264308	+	1.51221i
$327$	−157.677	−	48.0327i	−0.482192	−	0.146889i
$328$	177.870	+	311.304i	0.542288	+	0.949099i
$329$	−630.424			−1.91618
$330$	−40.7877	+	330.850i	−0.123599	+	1.00258i
$331$	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
$333$	−45.5294	−	231.730i	−0.136725	−	0.695887i
$334$	−269.189	+	47.0494i	−0.805955	+	0.140867i
$335$		−	149.588i		−	0.446530i
$336$	−470.094	+	196.783i	−1.39909	+	0.585663i
$337$		−	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
$342$	55.0602	−	123.840i	0.160995	−	0.362106i
$343$	110.525	−	110.525i	0.322230	−	0.322230i
$344$	−119.798	+	439.183i	−0.348249	+	1.27669i
$345$	174.110	+	53.0386i	0.504666	+	0.153735i
$346$	335.318	+	235.542i	0.969127	+	0.680757i
$347$	−66.7122			−0.192254			−0.0961270	−	0.995369i	$-0.530646\pi$
$347$	−66.7122			−0.192254			−0.0961270	+	0.995369i	$0.530646\pi$
$348$	326.921	−	361.634i	0.939428	−	1.03918i
$349$	−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
$351$	−188.568	+	296.046i	−0.537230	+	0.843436i
$352$	262.751	−	308.411i	0.746451	−	0.876168i
$353$	321.141	−	321.141i	0.909747	−	0.909747i	−0.0865046	−	0.996251i	$-0.527570\pi$
$353$	321.141	−	321.141i	0.909747	−	0.909747i	0.996251	+	0.0865046i	$0.0275697\pi$
$354$	−196.822	+	153.619i	−0.555994	+	0.433952i
$355$	−193.620			−0.545407
$356$	1.24123	−	2.64113i	0.00348660	−	0.00741890i
$357$	−321.473	−	97.9295i	−0.900485	−	0.274312i
$358$	−260.203	+	370.425i	−0.726823	+	1.03471i
$359$	124.499	−	124.499i	0.346794	−	0.346794i	−0.512120	−	0.858914i	$-0.671140\pi$
$359$	124.499	−	124.499i	0.346794	−	0.346794i	0.858914	+	0.512120i	$0.171140\pi$
$360$	−315.119	−	22.8200i	−0.875330	−	0.0633888i
$361$			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
$366$	544.136	+	67.0819i	1.48671	+	0.183284i
$367$			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
$369$	−77.7625	−	395.787i	−0.210738	−	1.07259i
$370$	−132.371	+	188.444i	−0.357759	+	0.509307i
$371$	11.4645	−	11.4645i	0.0309017	−	0.0309017i
$372$	551.932	−	27.8253i	1.48369	−	0.0747992i
$373$	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
$375$	387.165	+	117.941i	1.03244	+	0.314510i
$376$	235.661	+	412.449i	0.626759	+	1.09694i
$377$	−237.039	+	471.941i	−0.628752	+	1.25183i
$378$	571.863	−	40.8672i	1.51287	−	0.108114i
$379$	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	0.553298	−	0.832983i	$-0.313369\pi$
$383$	−107.120	−	107.120i	−0.279686	−	0.279686i	−0.832983	+	0.553298i	$0.813369\pi$
$384$	304.471	+	233.994i	0.792894	+	0.609360i
$385$	−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	$-0.428273\pi$
$389$	173.833			0.446871			0.223436	+	0.974719i	$0.428273\pi$
$390$	335.634	−	67.0858i	0.860600	−	0.172015i
$391$		−	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
$396$	−390.932	+	234.375i	−0.987201	+	0.591856i
$397$	−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	0.939983	−	0.341221i	$-0.110840\pi$
$401$	240.104	+	240.104i	0.598762	+	0.598762i	−0.341221	+	0.939983i	$0.610840\pi$
$402$	161.238	−	125.846i	0.401089	−	0.313049i
$403$	−568.305	+	188.293i	−1.41019	+	0.467228i
$404$	−210.227	−	583.025i	−0.520363	−	1.44313i
$405$	327.740	+	137.559i	0.809234	+	0.339651i
$406$	849.755	−	148.522i	2.09299	−	0.365818i
$407$			332.233i			0.816298i
$408$	56.1017	+	246.928i	0.137504	+	0.605216i
$409$	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
$411$	−352.112	−	107.263i	−0.856720	−	0.260981i
$412$	133.614	+	370.555i	0.324307	+	0.899405i
$413$	−441.803			−1.06974
$414$	89.3065	+	232.290i	0.215716	+	0.561088i
$415$	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	$-0.164308\pi$
$419$	728.814			1.73941			0.869706	+	0.493570i	$0.164308\pi$
$420$	−414.723	−	374.914i	−0.987436	−	0.892652i
$421$	−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
$423$	−103.028	−	524.380i	−0.243565	−	1.23967i
$424$	−11.7862	−	3.21496i	−0.0277976	−	0.00758245i
$425$		−	60.6091i		−	0.142610i
$426$	−162.889	−	208.699i	−0.382369	−	0.489904i
$427$	685.996	+	685.996i	1.60655	+	1.60655i
$428$	29.0241	+	80.4929i	0.0678133	+	0.188067i
$429$	340.595	−	357.524i	0.793929	−	0.833389i
$430$	−491.941	+	85.9825i	−1.14405	+	0.199959i
$431$	−18.9012	−	18.9012i	−0.0438544	−	0.0438544i	0.684840	−	0.728694i	$-0.259872\pi$
$431$	−18.9012	−	18.9012i	−0.0438544	−	0.0438544i	−0.728694	+	0.684840i	$0.759872\pi$
$432$	−240.508	−	358.859i	−0.556731	−	0.830693i
$433$			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
$435$	511.591	+	155.845i	1.17607	+	0.358264i
$436$	−93.4771	+	198.904i	−0.214397	+	0.456201i
$437$	73.6102	+	73.6102i	0.168444	+	0.168444i
$438$	117.577	−	91.7685i	0.268440	−	0.209517i
$439$	−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	$-0.602951\pi$
$443$	−281.590			−0.635644			−0.317822	+	0.948150i	$0.602951\pi$
$444$	−314.482	+	15.8544i	−0.708292	+	0.0357081i
$445$	3.20141			0.00719418
$446$	204.168	−	35.6849i	0.457776	−	0.0800111i
$447$	14.1420	−	46.4239i	0.0316376	−	0.103857i
$448$	169.957	+	657.894i	0.379368	+	1.46851i
$449$	−168.238	−	168.238i	−0.374695	−	0.374695i	0.494489	−	0.869184i	$-0.335355\pi$
$449$	−168.238	−	168.238i	−0.374695	−	0.374695i	−0.869184	+	0.494489i	$0.835355\pi$
$450$	37.1055	+	96.5132i	0.0824567	+	0.214474i
$451$			567.441i			1.25818i
$452$	213.461	−	76.9696i	0.472259	−	0.170287i
$453$	124.624	+	37.9638i	0.275107	+	0.0838052i
$454$	−78.1953	−	447.387i	−0.172236	−	0.985435i
$455$	541.224	+	271.837i	1.18950	+	0.597445i
$456$	−152.912	−	96.2929i	−0.335333	−	0.211169i
$457$	−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	$0.535209\pi$
$461$	−509.071	+	509.071i	−1.10427	+	1.10427i	−0.993889	+	0.110386i	$0.964791\pi$
$462$	−800.494	−	98.6861i	−1.73267	−	0.213606i
$463$	−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	$0.0651477\pi$
$467$			189.828i			0.406483i	−0.979129	+	0.203242i	$0.934852\pi$
$468$	354.675	+	305.336i	0.757852	+	0.652427i
$469$	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
$474$	75.5013	−	612.430i	0.159285	−	1.29205i
$475$	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	−0.686300	−	0.727318i	$-0.740766\pi$
$479$	19.6478	−	19.6478i	0.0410183	−	0.0410183i	0.727318	+	0.686300i	$0.240766\pi$
$480$	−90.2546	+	411.477i	−0.188030	+	0.857243i
$481$	323.811	−	107.286i	0.673203	−	0.223048i
$482$	235.695	−	41.1952i	0.488993	−	0.0854673i
$483$	−128.327	+	421.260i	−0.265688	+	0.872173i
$484$	147.911	−	53.3335i	0.305600	−	0.110193i
$485$	379.607			0.782695
$486$	127.450	+	468.991i	0.262244	+	0.965002i
$487$	−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
$489$	−718.102	−	218.753i	−1.46851	−	0.447349i
$490$	−96.2855	−	550.889i	−0.196501	−	1.12426i
$491$		−	12.3013i		−	0.0250535i	−0.999922	−	0.0125268i	$-0.996013\pi$
$491$		−	12.3013i		−	0.0250535i	0.999922	−	0.0125268i	$-0.00398750\pi$
$492$	−537.122	+	27.0787i	−1.09171	+	0.0550380i
$493$		−	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
$498$	199.904	+	256.124i	0.401414	+	0.514305i
$499$	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
$501$	119.449	−	392.115i	0.238421	−	0.782664i
$502$	−6.07295	+	8.64547i	−0.0120975	+	0.0172220i
$503$	−301.791			−0.599982			−0.299991	−	0.953942i	$-0.596984\pi$
$503$	−301.791			−0.599982			−0.299991	+	0.953942i	$0.596984\pi$
$504$	55.2131	−	762.432i	0.109550	−	1.51276i
$505$	480.764	−	480.764i	0.952009	−	0.952009i
$506$	−60.2788	−	344.879i	−0.119128	−	0.681580i
$507$	−458.447	−	216.508i	−0.904234	−	0.427037i
$508$	−140.453	−	389.521i	−0.276483	−	0.766773i
$509$	284.202	−	284.202i	0.558353	−	0.558353i	−0.370485	−	0.928838i	$-0.620809\pi$
$509$	284.202	−	284.202i	0.558353	−	0.558353i	0.928838	+	0.370485i	$0.120809\pi$
$510$	−218.986	+	170.918i	−0.429384	+	0.335133i
$511$	263.923			0.516483
$512$	366.889	−	357.123i	0.716580	−	0.697505i
$513$	128.414	+	157.600i	0.250320	+	0.307213i
$514$	23.0241	+	16.1731i	0.0447940	+	0.0314653i
$515$	−305.561	+	305.561i	−0.593322	+	0.593322i
$516$	−506.542	−	457.919i	−0.981670	−	0.887440i
$517$			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	$-0.996933\pi$
$521$		−	10.0392i		−	0.0192691i	0.999954	−	0.00963453i	$-0.00306681\pi$
$522$	262.411	+	682.545i	0.502704	+	1.30756i
$523$		−	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
$525$	−53.3180	+	175.027i	−0.101558	+	0.333385i
$526$	−143.678	−	100.925i	−0.273151	−	0.191873i
$527$	343.581	−	343.581i	0.651957	−	0.651957i
$528$	234.672	+	560.606i	0.444454	+	1.06175i
$529$	337.844			0.638647
$530$	−2.30748	−	13.2020i	−0.00435373	−	0.0249095i
$531$	−72.2022	−	367.487i	−0.135974	−	0.692065i
$532$	−108.463	−	300.802i	−0.203878	−	0.565418i
$533$	553.056	−	183.240i	1.03763	−	0.343791i
$534$	2.69330	+	3.45074i	0.00504363	+	0.00646207i
$535$	−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
$540$	244.073	−	406.233i	0.451986	−	0.752283i
$541$	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
$546$	162.315	+	812.069i	0.297279	+	1.48731i
$547$		−	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
$552$	323.576	−	73.5159i	0.586188	−	0.133181i
$553$	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	0.998058	−	0.0622958i	$-0.0198422\pi$
$557$	521.219	+	521.219i	0.935762	+	0.935762i	−0.0622958	+	0.998058i	$0.519842\pi$
$558$	−336.771	+	757.459i	−0.603532	+	1.35745i
$559$	661.049	+	332.022i	1.18256	+	0.593956i
$560$	−573.889	+	475.717i	−1.02480	+	0.849494i
$561$	−116.785	+	383.370i	−0.208173	+	0.683368i
$562$	37.2887	+	213.344i	0.0663499	+	0.379615i
$563$			829.523i			1.47340i	0.676221	+	0.736699i	$0.263617\pi$
$563$			829.523i			1.47340i	−0.676221	+	0.736699i	$0.736383\pi$
$564$	−711.636	+	35.8767i	−1.26177	+	0.0636112i
$565$	176.021	+	176.021i	0.311541	+	0.311541i
$566$	451.949	+	317.469i	0.798497	+	0.560899i
$567$	−332.824	+	792.968i	−0.586991	+	1.39853i
$568$	−306.488	+	175.118i	−0.539591	+	0.308307i
$569$	−171.340			−0.301125			−0.150563	−	0.988600i	$-0.548108\pi$
$569$	−171.340			−0.301125			−0.150563	+	0.988600i	$0.548108\pi$
$570$	24.2555	−	196.749i	0.0425536	−	0.345174i
$571$	−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
$576$	−519.454	+	248.885i	−0.901829	+	0.432093i
$577$	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
$579$	−269.234	+	883.815i	−0.464999	+	1.52645i
$580$	303.292	−	645.354i	0.522917	−	1.11268i
$581$			574.917i			0.989530i
$582$	319.358	+	409.172i	0.548725	+	0.703044i
$583$	−13.6719	−	13.6719i	−0.0234510	−	0.0234510i
$584$	−98.6582	−	172.669i	−0.168935	−	0.295666i
$585$	−137.661	+	494.609i	−0.235318	+	0.845486i
$586$	83.9260	+	480.175i	0.143218	+	0.819411i
$587$	−48.2499	−	48.2499i	−0.0821974	−	0.0821974i	0.664813	−	0.747010i	$-0.268511\pi$
$587$	−48.2499	−	48.2499i	−0.0821974	−	0.0821974i	−0.747010	+	0.664813i	$0.768511\pi$
$588$	512.790	−	567.239i	0.872091	−	0.964692i
$589$			346.749i			0.588708i
$590$	−209.919	+	298.841i	−0.355794	+	0.506510i
$591$	246.233	−	808.309i	0.416638	−	1.36770i
$592$	−39.0982	+	418.017i	−0.0660442	+	0.706110i
$593$	99.9109	+	99.9109i	0.168484	+	0.168484i	0.786313	−	0.617829i	$-0.211988\pi$
$593$	99.9109	+	99.9109i	0.168484	+	0.168484i	−0.617829	+	0.786313i	$0.711988\pi$
$594$	−48.7358	−	681.970i	−0.0820469	−	1.14810i
$595$	−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	$-0.220388\pi$
$599$	922.144			1.53947			0.769736	+	0.638362i	$0.220388\pi$
$600$	134.441	−	30.5448i	0.224068	−	0.0509079i
$601$	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
$603$	59.1486	+	301.048i	0.0980905	+	0.499250i
$604$	73.8819	−	157.208i	0.122321	−	0.260278i
$605$	121.968	+	121.968i	0.201599	+	0.201599i
$606$	922.668	+	113.748i	1.52255	+	0.187703i
$607$		−	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
$609$	−377.067	+	1237.80i	−0.619158	+	2.03251i
$610$	789.961	−	138.071i	1.29502	−	0.226346i
$611$	732.747	−	242.776i	1.19926	−	0.397343i
$612$	−368.459	−	92.2503i	−0.602057	−	0.150736i
$613$	−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	$-0.427172\pi$
$617$	740.860	−	740.860i	1.20075	−	1.20075i	0.973940	−	0.226806i	$-0.0728285\pi$
$618$	−586.423	−	72.2950i	−0.948904	−	0.116982i
$619$	−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
$624$	470.613	−	409.756i	0.754187	−	0.656660i
$625$	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
$630$	782.744	−	300.934i	1.24245	−	0.477673i
$631$	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
$636$	12.2890	−	13.5939i	0.0193223	−	0.0213740i
$637$	−371.807	+	740.261i	−0.583684	+	1.16210i
$638$	−177.119	−	1013.37i	−0.277615	−	1.58835i
$639$	389.663	−	76.5593i	0.609801	−	0.119811i
$640$	525.761	+	197.632i	0.821501	+	0.308800i
$641$	−962.325			−1.50129			−0.750643	−	0.660707i	$-0.770256\pi$
$641$	−962.325			−1.50129			−0.750643	+	0.660707i	$0.770256\pi$
$642$	−127.384	−	15.7041i	−0.198418	−	0.0244612i
$643$	−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
$645$	218.292	−	716.587i	0.338437	−	1.11099i
$646$	−156.511	+	27.3552i	−0.242276	+	0.0423456i
$647$		−	1220.24i		−	1.88599i	−0.332800	−	0.942997i	$-0.607993\pi$
$647$		−	1220.24i		−	1.88599i	0.332800	−	0.942997i	$-0.392007\pi$
$648$	643.206	−	78.6759i	0.992602	−	0.121413i
$649$			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	$0.0632846\pi$
$653$			257.945i			0.395015i	−0.980301	+	0.197507i	$0.936715\pi$
$654$	−202.832	−	259.876i	−0.310141	−	0.397363i
$655$	−755.864	+	755.864i	−1.15399	+	1.15399i
$656$	−66.7781	+	713.957i	−0.101796	+	1.08835i
$657$	43.1320	+	219.528i	0.0656499	+	0.334137i
$658$	−1031.74	−	724.740i	−1.56800	−	1.10143i
$659$	−167.489			−0.254156			−0.127078	−	0.991893i	$-0.540560\pi$
$659$	−167.489			−0.254156			−0.127078	+	0.991893i	$0.540560\pi$
$660$	−447.100	+	494.574i	−0.677424	+	0.749354i
$661$	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
$663$	411.363	−	9.97500i	0.620457	−	0.0150453i
$664$	376.134	−	214.912i	0.566467	−	0.323663i
$665$	248.043	−	248.043i	0.372997	−	0.372997i
$666$	191.886	−	431.587i	0.288118	−	0.648029i
$667$	−561.678			−0.842096
$668$	−494.639	−	232.461i	−0.740477	−	0.347996i
$669$	−90.5968	+	297.402i	−0.135421	+	0.444547i
$670$	171.967	−	244.812i	0.256667	−	0.365392i
$671$	818.078	−	818.078i	1.21919	−	1.21919i
$672$	−995.571	−	218.372i	−1.48150	−	0.324958i
$673$		−	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	$0.170188\pi$
$677$			689.930i			1.01910i	−0.860442	+	0.509549i	$0.829812\pi$
$678$	−41.6461	+	337.813i	−0.0614250	+	0.498250i
$679$			918.461i			1.35267i
$680$	183.750	+	321.594i	0.270220	+	0.472933i
$681$	651.687	+	198.522i	0.956956	+	0.291515i
$682$	670.321	−	954.271i	0.982875	−	1.39922i
$683$	−178.495	+	178.495i	−0.261339	+	0.261339i	−0.825598	−	0.564259i	$-0.809162\pi$
$683$	−178.495	+	178.495i	−0.261339	+	0.261339i	0.564259	+	0.825598i	$0.309162\pi$
$684$	232.478	−	139.378i	0.339881	−	0.203768i
$685$	−538.403			−0.785990
$686$	307.943	−	53.8229i	0.448897	−	0.0784591i
$687$	300.715	−	987.157i	0.437722	−	1.43691i
$688$	−700.946	+	581.039i	−1.01882	+	0.844534i
$689$	−8.91033	+	17.7403i	−0.0129323	+	0.0257479i
$690$	223.971	+	286.960i	0.324596	+	0.415884i
$691$	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
$696$	950.770	−	216.014i	1.36605	−	0.310364i
$697$	−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	$-0.564478\pi$
$701$	−282.058			−0.402365			−0.201183	+	0.979554i	$0.564478\pi$
$702$	−648.943	+	267.725i	−0.924421	+	0.381374i
$703$		−	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
$708$	−498.717	+	25.1425i	−0.704402	+	0.0355120i
$709$	−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
$714$	−413.537	−	529.837i	−0.579183	−	0.742069i
$715$	324.177	−	645.431i	0.453395	−	0.902701i
$716$	−851.687	+	307.101i	−1.18951	+	0.428912i
$717$	347.077	+	105.729i	0.484068	+	0.147461i
$718$	346.878	−	60.6281i	0.483117	−	0.0844403i
$719$			467.890i			0.650751i	0.945585	+	0.325375i	$0.105491\pi$
$719$			467.890i			0.650751i	−0.945585	+	0.325375i	$0.894509\pi$
$720$	−489.484	−	399.610i	−0.679839	−	0.555014i
$721$	−739.306	−	739.306i	−1.02539	−	1.02539i
$722$	−349.835	+	498.026i	−0.484536	+	0.689787i
$723$	−104.586	+	343.325i	−0.144656	+	0.474862i
$724$	457.321	−	164.901i	0.631659	−	0.227763i
$725$	−233.369			−0.321888
$726$	−28.8573	+	234.076i	−0.0397483	+	0.322419i
$727$	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
$732$	813.406	+	735.328i	1.11121	+	1.00455i
$733$	−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
$735$	802.453	+	244.449i	1.09177	+	0.332584i
$736$	−35.2565	−	441.022i	−0.0479029	−	0.599215i
$737$		−	431.614i		−	0.585636i
$738$	327.734	−	737.134i	0.444084	−	0.998826i
$739$	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
$741$	−202.544	+	212.611i	−0.273339	+	0.286925i
$742$	31.9424	−	5.58296i	0.0430490	−	0.00752420i
$743$	743.337	+	743.337i	1.00045	+	1.00045i	1.00000		0.000454295i	$0.000144606\pi$
$743$	743.337	+	743.337i	1.00045	+	1.00045i	0.000454295		1.00000i	$0.499855\pi$
$744$	935.271	+	588.967i	1.25709	+	0.791622i
$745$		−	70.9852i		−	0.0952822i
$746$	500.960	+	351.896i	0.671529	+	0.471711i
$747$	−478.210	+	93.9566i	−0.640174	+	0.125779i
$748$	483.607	+	227.277i	0.646533	+	0.303846i
$749$	−160.594	−	160.594i	−0.214411	−	0.214411i
$750$	498.042	+	638.108i	0.664056	+	0.850811i
$751$	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
$756$	982.883	+	590.535i	1.30011	+	0.781131i
$757$	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
$759$	502.369	+	153.035i	0.661883	+	0.201628i
$760$	−255.002	−	69.5578i	−0.335528	−	0.0915234i
$761$	855.917	+	855.917i	1.12473	+	1.12473i	0.991021	+	0.133706i	$0.0426878\pi$
$761$	855.917	+	855.917i	1.12473	+	1.12473i	0.133706	+	0.991021i	$0.457312\pi$
$762$	616.438	+	75.9953i	0.808973	+	0.0997314i
$763$		−	583.339i		−	0.764533i
$764$	−149.938	−	415.825i	−0.196254	−	0.544273i
$765$	−80.3328	−	408.869i	−0.105010	−	0.534469i
$766$	−52.1647	−	298.456i	−0.0681001	−	0.389629i
$767$	513.511	−	170.138i	0.669506	−	0.221823i
$768$	229.291	+	732.973i	0.298556	+	0.954392i
$769$	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	$-0.483447\pi$
$773$	812.134	−	812.134i	1.05063	−	1.05063i	0.998648	−	0.0519779i	$-0.0165525\pi$
$774$	956.042	−	367.560i	1.23520	−	0.474884i
$775$	−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
$780$	626.415	+	276.056i	0.803097	+	0.353918i
$781$	−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
$786$	−1450.63	−	178.836i	−1.84558	−	0.227526i
$787$	−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
$792$	−909.231	−	65.8438i	−1.14802	−	0.0831361i
$793$	−1061.52	−	533.161i	−1.33861	−	0.672335i
$794$	−154.483	+	27.0008i	−0.194563	+	0.0340061i
$795$	19.2307	+	5.85821i	0.0241896	+	0.00736882i
$796$	−135.630	−	376.144i	−0.170389	−	0.472543i
$797$	94.0730			0.118034			0.0590169	−	0.998257i	$-0.481203\pi$
$797$	94.0730			0.118034			0.0590169	+	0.998257i	$0.481203\pi$
$798$	476.036	+	58.6864i	0.596536	+	0.0735418i
$799$	−442.998	+	442.998i	−0.554440	+	0.554440i
$800$	−14.6486	−	183.238i	−0.0183107	−	0.229048i
$801$	−6.44290	+	1.26587i	−0.00804357	+	0.00158037i
$802$	116.925	+	668.975i	0.145792	+	0.834133i
$803$		−	314.739i		−	0.391954i
$804$	408.552	−	20.5969i	0.508150	−	0.0256180i
$805$			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	$0.0551334\pi$
$809$			278.849i			0.344684i	−0.985037	+	0.172342i	$0.944867\pi$
$810$	378.235	+	601.898i	0.466957	+	0.743083i
$811$	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
$813$	973.305	+	296.495i	1.19718	+	0.364693i
$814$	−381.938	+	543.727i	−0.469211	+	0.667970i
$815$	−1098.03			−1.34727
$816$	−192.055	+	468.613i	−0.235362	+	0.574281i
$817$	302.959	−	302.959i	0.370819	−	0.370819i
$818$	65.9570	+	377.367i	0.0806320	+	0.461329i
$819$	−1196.71	−	333.072i	−1.46118	−	0.406681i
$820$	−740.011	+	266.833i	−0.902453	+	0.325406i
$821$	220.394	−	220.394i	0.268446	−	0.268446i	−0.560028	−	0.828474i	$-0.689209\pi$
$821$	220.394	−	220.394i	0.268446	−	0.268446i	0.828474	+	0.560028i	$0.189209\pi$
$822$	−452.950	−	580.335i	−0.551035	−	0.706004i
$823$	−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
$825$	208.727	+	63.5839i	0.253002	+	0.0770714i
$826$	−723.047	−	507.899i	−0.875359	−	0.614890i
$827$	−760.113	+	760.113i	−0.919121	+	0.919121i	−0.996965	−	0.0778447i	$-0.975196\pi$
$827$	−760.113	+	760.113i	−0.919121	+	0.919121i	0.0778447	+	0.996965i	$0.475196\pi$
$828$	−120.885	+	482.830i	−0.145997	+	0.583128i
$829$			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
$834$	28.7297	−	233.041i	0.0344481	−	0.279426i
$835$		−	599.569i		−	0.718047i
$836$	−358.719	+	129.347i	−0.429090	+	0.154721i
$837$	−785.435	−	963.949i	−0.938393	−	1.15167i
$838$	1192.76	+	837.849i	1.42335	+	0.999820i
$839$	39.3907	−	39.3907i	0.0469496	−	0.0469496i	−0.683242	−	0.730192i	$-0.739431\pi$
$839$	39.3907	−	39.3907i	0.0469496	−	0.0469496i	0.730192	+	0.683242i	$0.239431\pi$
$840$	−247.725	−	1090.35i	−0.294911	−	1.29803i
$841$	−809.392			−0.962416
$842$	−102.608	−	587.064i	−0.121863	−	0.697226i
$843$	−310.767	−	94.6683i	−0.368645	−	0.112299i
$844$	−702.091	+	253.160i	−0.831861	+	0.299952i
$845$	−733.753	−	107.534i	−0.868347	−	0.127259i
$846$	434.217	−	976.633i	0.513259	−	1.15441i
$847$	−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
$852$	−26.6597	−	528.812i	−0.0312908	−	0.620671i
$853$	−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	$-0.653861\pi$
$857$	−796.605			−0.929527			−0.464764	+	0.885435i	$0.653861\pi$
$858$	968.425	−	193.567i	1.12870	−	0.225602i
$859$			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	$-0.999341\pi$
$863$	−864.784	−	864.784i	−1.00207	−	1.00207i	−0.00206905	−	0.999998i	$-0.500659\pi$
$864$	18.9366	−	863.792i	0.0219174	−	0.999760i
$865$	−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
$870$	658.101	+	843.181i	0.756438	+	0.969174i
$871$	−420.672	+	139.378i	−0.482976	+	0.160021i
$872$	−381.644	+	218.060i	−0.437665	+	0.250069i
$873$	−763.966	+	150.101i	−0.875104	+	0.171937i
$874$	35.8464	+	205.092i	0.0410142	+	0.234659i
$875$			1432.35i			1.63697i
$876$	297.922	−	15.0196i	0.340094	−	0.0171456i
$877$	−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
$879$	−699.448	−	213.071i	−0.795731	−	0.242402i
$880$	567.311	+	684.386i	0.644672	+	0.777711i
$881$	1705.76			1.93616			0.968082	−	0.250634i	$-0.0806389\pi$
$881$	1705.76			1.93616			0.968082	+	0.250634i	$0.0806389\pi$
$882$	411.604	+	1070.60i	0.466671	+	1.21383i
$883$	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	$-0.301987\pi$
$887$	1033.75			1.16545			0.582724	+	0.812670i	$0.301987\pi$
$888$	−532.902	−	335.583i	−0.600115	−	0.377909i
$889$	777.147	+	777.147i	0.874181	+	0.874181i
$890$	5.23937	+	3.68036i	0.00588693	+	0.00413524i
$891$	945.646	+	396.906i	1.06133	+	0.445461i
$892$	375.162	+	176.312i	0.420585	+	0.197659i
$893$		−	447.082i		−	0.500652i
$894$	76.5137	−	59.7188i	0.0855858	−	0.0667995i
$895$	−702.304	−	702.304i	−0.784697	−	0.784697i
$896$	−478.171	+	1272.08i	−0.533673	+	1.41973i
$897$	−13.0713	−	539.052i	−0.0145722	−	0.600950i
$898$	−81.9278	−	468.743i	−0.0912337	−	0.521985i
$899$	−1322.92	−	1322.92i	−1.47155	−	1.47155i
$900$	−50.2260	+	200.609i	−0.0558067	+	0.222898i
$901$		−	16.1122i		−	0.0178826i
$902$	−652.334	+	928.665i	−0.723209	+	1.02956i
$903$	1733.79	+	528.159i	1.92003	+	0.584893i
$904$	437.831	+	119.429i	0.484327	+	0.132112i
$905$	377.109	+	377.109i	0.416695	+	0.416695i
$906$	160.313	+	205.399i	0.176946	+	0.226710i
$907$	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	$-0.406149\pi$
$911$	529.454			0.581178			0.290589	+	0.956848i	$0.406149\pi$
$912$	−139.554	−	333.380i	−0.153020	−	0.365548i
$913$	685.612			0.750944
$914$	−243.196	−	1391.42i	−0.266078	−	1.52234i
$915$	−350.534	+	1150.70i	−0.383097	+	1.25759i
$916$	−1245.26	−	585.226i	−1.35946	−	0.638893i
$917$	−1828.82	−	1828.82i	−1.99435	−	1.99435i
$918$	373.130	−	430.565i	0.406460	−	0.469025i
$919$		−	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
$921$	100.164	+	30.5128i	0.108756	+	0.0331301i
$922$	−1418.37	+	247.905i	−1.53836	+	0.268878i
$923$	180.405	+	544.499i	0.195455	+	0.589923i
$924$	−1196.62	−	1081.76i	−1.29505	−	1.17074i
$925$	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	−0.992676	−	0.120810i	$-0.961451\pi$
$929$	−809.963	+	809.963i	−0.871865	+	0.871865i	0.120810	+	0.992676i	$0.461451\pi$
$930$	−148.357	+	1203.40i	−0.159523	+	1.29398i
$931$	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
$936$	229.438	+	907.444i	0.245126	+	0.969491i
$937$	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	$-0.437646\pi$
$941$	1106.16	−	1106.16i	1.17552	−	1.17552i	0.980874	−	0.194642i	$-0.0623545\pi$
$942$	−1218.72	−	150.245i	−1.29375	−	0.159496i
$943$	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	$0.551883\pi$
$947$	−1088.12	+	1088.12i	−1.14902	+	1.14902i	−0.986745	+	0.162276i	$0.948117\pi$
$948$	827.618	−	915.496i	0.873015	−	0.965713i
$949$	−306.760	+	101.637i	−0.323245	+	0.107099i
$950$	14.8937	+	85.2127i	0.0156775	+	0.0896975i
$951$	−406.435	+	1334.20i	−0.427376	+	1.40295i
$952$	−778.100	+	444.584i	−0.817332	+	0.467000i
$953$	1839.51			1.93023			0.965116	−	0.261822i	$-0.0843232\pi$
$953$	1839.51			1.93023			0.965116	+	0.261822i	$0.0843232\pi$
$954$	9.86407	+	25.6569i	0.0103397	+	0.0268940i
$955$	342.891	−	342.891i	0.359048	−	0.359048i
$956$	205.761	−	437.825i	0.215231	−	0.457976i
$957$	1476.12	+	449.668i	1.54245	+	0.469872i
$958$	54.7424	−	9.56799i	0.0571424	−	0.00998747i
$959$		−	1302.67i		−	1.35836i
$960$	−620.746	+	569.659i	−0.646610	+	0.593394i
$961$		−	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
$966$	−694.301	+	541.900i	−0.718738	+	0.560973i
$967$	−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
$969$	69.4494	−	227.981i	0.0716712	−	0.235275i
$970$	621.258	+	436.399i	0.640473	+	0.449896i
$971$	−717.583			−0.739015			−0.369507	−	0.929228i	$-0.620474\pi$
$971$	−717.583			−0.739015			−0.369507	+	0.929228i	$0.620474\pi$
$972$	−330.572	+	914.060i	−0.340094	+	0.940391i
$973$	293.797	−	293.797i	0.301949	−	0.301949i
$974$	−122.931	+	21.4862i	−0.126213	+	0.0220597i
$975$	−5.43092	−	223.968i	−0.00557018	−	0.229711i
$976$	1125.58	−	933.035i	1.15326	−	0.955978i
$977$	−1232.22	+	1232.22i	−1.26122	+	1.26122i	−0.310724	+	0.950500i	$0.600571\pi$
$977$	−1232.22	+	1232.22i	−1.26122	+	1.26122i	−0.950500	+	0.310724i	$0.899429\pi$
$978$	−923.752	−	1183.54i	−0.944532	−	1.21017i
$979$	9.23721			0.00943536
$980$	475.726	−	1012.27i	0.485435	−	1.03292i
$981$	485.215	−	95.3329i	0.494612	−	0.0971793i
$982$	14.1416	−	20.1321i	0.0144009	−	0.0205011i
$983$	743.295	−	743.295i	0.756149	−	0.756149i	−0.219470	−	0.975619i	$-0.570433\pi$
$983$	743.295	−	743.295i	0.756149	−	0.756149i	0.975619	+	0.219470i	$0.0704328\pi$
$984$	−910.175	−	573.163i	−0.924975	−	0.582483i
$985$		−	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
$990$	−358.876	−	933.454i	−0.362501	−	0.942883i
$991$		−	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
$993$	−288.080	+	945.681i	−0.290111	+	0.952347i
$994$	538.549	−	766.680i	0.541800	−	0.771307i
$995$	310.170	−	310.170i	0.311729	−	0.311729i
$996$	32.7179	+	648.979i	0.0328493	+	0.651586i
$997$	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
$999$	447.527	+	549.242i	0.447975	+	0.549792i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.3.l.c.47.10	✓	96	3.2	odd	2	inner
156.3.l.c.47.15	yes	96	4.3	odd	2	inner
156.3.l.c.47.34	yes	96	12.11	even	2	inner
156.3.l.c.47.39	yes	96	1.1	even	1	trivial
156.3.l.c.83.10	yes	96	52.31	even	4	inner
156.3.l.c.83.15	yes	96	39.5	even	4	inner
156.3.l.c.83.34	yes	96	13.5	odd	4	inner
156.3.l.c.83.39	yes	96	156.83	odd	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} +(-5.95492 - 0.734131i) 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} +(-8.90176 - 8.04728i) q^{12} +(11.6170 + 5.83481i) q^{13} +(-3.65593 - 20.9170i) q^{14} +(3.83617 - 12.5930i) q^{15} +(-12.3181 + 10.2109i) q^{16} -10.5509 q^{17} +(16.8011 - 6.45936i) q^{18} +(5.32408 - 5.32408i) q^{19} +(-15.8856 - 7.46564i) q^{20} +(30.4688 + 9.28165i) q^{21} +(-24.9444 + 4.35984i) q^{22} +13.8259i q^{23} +(-5.31725 - 23.4036i) 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} +(20.7552 - 16.1994i) q^{30} +(-32.5642 + 32.5642i) q^{31} +(-31.8982 + 2.55003i) q^{32} +(11.0687 - 36.3353i) q^{33} +(-17.2674 - 12.1294i) q^{34} +46.5889 q^{35} +(34.9221 + 8.74338i) q^{36} +(18.5545 - 18.5545i) q^{37} +(14.8339 - 2.59270i) q^{38} +(-38.9885 + 0.945419i) q^{39} +(-17.4156 - 30.4804i) q^{40} +(31.6904 - 31.6904i) q^{41} +(39.1945 + 50.2174i) q^{42} +56.9036 q^{43} +(-45.8357 - 21.5410i) q^{44} +(7.61385 + 38.7521i) q^{45} +(-15.8944 + 22.6273i) q^{46} +(41.9868 - 41.9868i) q^{47} +(18.2028 - 44.4146i) 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} +(-35.3648 + 40.8084i) q^{54} -55.5591i q^{55} +(73.7474 - 42.1371i) q^{56} +(-6.58233 + 21.6078i) q^{57} +(-46.7028 + 66.4862i) q^{58} +(29.4245 - 29.4245i) q^{59} +(52.5906 - 2.65132i) q^{60} -91.3759 q^{61} +(-90.7301 + 15.8580i) q^{62} +(-93.7610 + 18.4218i) q^{63} +(-55.1356 - 32.4971i) q^{64} +(-54.1506 + 17.9414i) q^{65} +(59.8862 - 46.7411i) 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} +(47.1015 + 54.4560i) 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} +(-64.8948 - 43.2742i) 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} +(6.41488 + 127.243i) 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} +(-32.0890 + 72.1740i) q^{90} +(-43.4093 - 131.018i) q^{91} +(-52.0249 + 18.7591i) q^{92} +(40.2602 - 132.162i) q^{93} +(116.983 - 20.4466i) q^{94} +33.0398i q^{95} +(80.8497 - 51.7622i) q^{96} +(-61.1704 - 61.1704i) q^{97} +(-73.2554 + 104.287i) q^{98} +(21.9687 + 111.814i) 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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