LMFDB - Embedded newform 153.3.i.a.50.27

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [153,3,Mod(50,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

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

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.50"); S:= CuspForms(chi, 3); N := Newforms(S);

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

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.16894804471$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			50.27
Character	$\chi$	$=$	153.50
Dual form			153.3.i.a.101.27

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.91245 - 1.10416i) q^{2} +(-1.04331 + 2.81274i) q^{3} +(0.438319 - 0.759190i) q^{4} +(-1.77620 + 3.07647i) q^{5} +(1.11042 + 6.53121i) q^{6} +(-3.82505 + 2.20839i) q^{7} +6.89736i q^{8} +(-6.82301 - 5.86911i) q^{9} +7.84480i q^{10} +(0.708179 + 1.22660i) q^{11} +(1.67810 + 2.02495i) q^{12} +(-1.55468 + 2.69278i) q^{13} +(-4.87682 + 8.44690i) q^{14} +(-6.80018 - 8.20569i) q^{15} +(9.36903 + 16.2276i) q^{16} +(16.9994 - 0.139826i) q^{17} +(-19.5291 - 3.69074i) q^{18} +21.5252 q^{19} +(1.55708 + 2.69694i) q^{20} +(-2.22093 - 13.0629i) q^{21} +(2.70872 + 1.56388i) q^{22} +(-0.883809 + 1.53080i) q^{23} +(-19.4005 - 7.19607i) q^{24} +(6.19024 + 10.7218i) q^{25} +6.86643i q^{26} +(23.6268 - 13.0681i) q^{27} +3.87192i q^{28} +(-17.1717 - 29.7423i) q^{29} +(-22.0654 - 8.18455i) q^{30} +(5.35110 + 3.08946i) q^{31} +(11.9425 + 6.89502i) q^{32} +(-4.18896 + 0.712198i) q^{33} +(32.3562 - 19.0374i) q^{34} -15.6902i q^{35} +(-7.44643 + 2.60742i) q^{36} -7.71265i q^{37} +(41.1659 - 23.7671i) q^{38} +(-5.95209 - 7.18231i) q^{39} +(-21.2195 - 12.2511i) q^{40} +(-9.30986 + 16.1252i) q^{41} +(-18.6709 - 22.5299i) q^{42} +(22.6064 + 39.1554i) q^{43} +1.24163 q^{44} +(30.1752 - 10.5661i) q^{45} +3.90345i q^{46} +(27.3169 - 15.7714i) q^{47} +(-55.4189 + 9.42221i) q^{48} +(-14.7460 + 25.5408i) q^{49} +(23.6771 + 13.6700i) q^{50} +(-17.3424 + 47.9608i) q^{51} +(1.36289 + 2.36059i) q^{52} -55.4075i q^{53} +(30.7560 - 51.0797i) q^{54} -5.03146 q^{55} +(-15.2321 - 26.3827i) q^{56} +(-22.4574 + 60.5447i) q^{57} +(-65.6802 - 37.9205i) q^{58} +(-49.6000 - 28.6366i) q^{59} +(-9.21032 + 1.56592i) q^{60} +(-13.7839 + 7.95816i) q^{61} +13.6450 q^{62} +(39.0597 + 7.38175i) q^{63} -44.4995 q^{64} +(-5.52284 - 9.56584i) q^{65} +(-7.22481 + 5.98731i) q^{66} +(-52.9793 + 91.7628i) q^{67} +(7.34501 - 12.9671i) q^{68} +(-3.38366 - 4.08302i) q^{69} +(-17.3244 - 30.0067i) q^{70} +100.875 q^{71} +(40.4814 - 47.0608i) q^{72} +44.3391i q^{73} +(-8.51597 - 14.7501i) q^{74} +(-36.6160 + 6.22537i) q^{75} +(9.43489 - 16.3417i) q^{76} +(-5.41764 - 3.12787i) q^{77} +(-19.3135 - 7.16381i) q^{78} +(68.3530 - 39.4636i) q^{79} -66.5650 q^{80} +(12.1070 + 80.0901i) q^{81} +41.1181i q^{82} +(73.2711 - 42.3031i) q^{83} +(-10.8907 - 4.03961i) q^{84} +(-29.7642 + 52.5465i) q^{85} +(86.4674 + 49.9220i) q^{86} +(101.573 - 17.2692i) q^{87} +(-8.46031 + 4.88456i) q^{88} -150.514i q^{89} +(46.0420 - 53.5252i) q^{90} -13.7334i q^{91} +(0.774780 + 1.34196i) q^{92} +(-14.2727 + 11.8280i) q^{93} +(34.8282 - 60.3242i) q^{94} +(-38.2330 + 66.2215i) q^{95} +(-31.8536 + 26.3976i) q^{96} +(96.3476 - 55.6263i) q^{97} +65.1275i q^{98} +(2.36715 - 12.5255i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 6 q^{2} + 62 q^{4} - 8 q^{9} - 2 q^{13} - 106 q^{16} - 2 q^{18} - 32 q^{19} - 28 q^{21} - 132 q^{25} + 180 q^{30} - 98 q^{33} - 27 q^{34} + 158 q^{36} - 102 q^{38} + 110 q^{42} + 58 q^{43} - 312 q^{47}+ \cdots - 18 q^{94}+O(q^{100}) $ 68 * q - 6 * q^2 + 62 * q^4 - 8 * q^9 - 2 * q^13 - 106 * q^16 - 2 * q^18 - 32 * q^19 - 28 * q^21 - 132 * q^25 + 180 * q^30 - 98 * q^33 - 27 * q^34 + 158 * q^36 - 102 * q^38 + 110 * q^42 + 58 * q^43 - 312 * q^47 + 152 * q^49 - 90 * q^50 - 17 * q^51 + 70 * q^52 + 92 * q^55 - 258 * q^59 - 126 * q^60 - 16 * q^64 + 400 * q^66 + 82 * q^67 - 333 * q^68 + 404 * q^69 + 204 * q^70 + 474 * q^72 + 34 * q^76 - 60 * q^77 - 88 * q^81 - 690 * q^83 - 200 * q^84 - 44 * q^85 - 1248 * q^86 + 114 * q^87 + 50 * q^93 - 18 * q^94

Character values

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

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

Coefficient data

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

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

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

$2$	1.91245	−	1.10416i	0.956227	−	0.552078i	0.0612170	−	0.998124i	$-0.480502\pi$
$2$	1.91245	−	1.10416i	0.956227	−	0.552078i	0.895010	+	0.446047i	$0.147168\pi$
$3$	−1.04331	+	2.81274i	−0.347770	+	0.937580i
$3$	−1.04331	+	2.81274i	−0.347770	+	0.937580i
$4$	0.438319	−	0.759190i	0.109580	−	0.189798i
$5$	−1.77620	+	3.07647i	−0.355240	+	0.615293i	−0.987159	−	0.159741i	$-0.948934\pi$
$5$	−1.77620	+	3.07647i	−0.355240	+	0.615293i	0.631919	+	0.775034i	$0.282267\pi$
$6$	1.11042	+	6.53121i	0.185070	+	1.08853i
$7$	−3.82505	+	2.20839i	−0.546436	+	0.315485i	−0.747683	−	0.664056i	$-0.768834\pi$
$7$	−3.82505	+	2.20839i	−0.546436	+	0.315485i	0.201248	+	0.979540i	$0.435500\pi$
$8$			6.89736i			0.862169i
$9$	−6.82301	−	5.86911i	−0.758113	−	0.652124i
$10$			7.84480i			0.784480i
$11$	0.708179	+	1.22660i	0.0643799	+	0.111509i	0.896419	−	0.443208i	$-0.146160\pi$
$11$	0.708179	+	1.22660i	0.0643799	+	0.111509i	−0.832039	+	0.554717i	$0.812826\pi$
$12$	1.67810	+	2.02495i	0.139842	+	0.168746i
$13$	−1.55468	+	2.69278i	−0.119591	+	0.207137i	−0.919606	−	0.392843i	$-0.871492\pi$
$13$	−1.55468	+	2.69278i	−0.119591	+	0.207137i	0.800015	+	0.599980i	$0.204825\pi$
$14$	−4.87682	+	8.44690i	−0.348344	+	0.603350i
$15$	−6.80018	−	8.20569i	−0.453345	−	0.547046i
$16$	9.36903	+	16.2276i	0.585564	+	1.01423i
$17$	16.9994	−	0.139826i	0.999966	−	0.00822508i
$17$	16.9994	−	0.139826i	0.999966	−	0.00822508i
$18$	−19.5291	−	3.69074i	−1.08495	−	0.205041i
$19$	21.5252			1.13290			0.566452	−	0.824095i	$-0.308316\pi$
$19$	21.5252			1.13290			0.566452	+	0.824095i	$0.308316\pi$
$20$	1.55708	+	2.69694i	0.0778541	+	0.134847i
$21$	−2.22093	−	13.0629i	−0.105758	−	0.622043i
$22$	2.70872	+	1.56388i	0.123124	+	0.0710854i
$23$	−0.883809	+	1.53080i	−0.0384265	+	0.0665566i	−0.884599	−	0.466352i	$-0.845568\pi$
$23$	−0.883809	+	1.53080i	−0.0384265	+	0.0665566i	0.846173	+	0.532909i	$0.178901\pi$
$24$	−19.4005	−	7.19607i	−0.808353	−	0.299836i
$25$	6.19024	+	10.7218i	0.247610	+	0.428872i
$26$			6.86643i			0.264093i
$27$	23.6268	−	13.0681i	0.875067	−	0.484002i
$28$			3.87192i			0.138283i
$29$	−17.1717	−	29.7423i	−0.592128	−	1.02560i	−0.993945	−	0.109876i	$-0.964955\pi$
$29$	−17.1717	−	29.7423i	−0.592128	−	1.02560i	0.401817	−	0.915720i	$-0.368379\pi$
$30$	−22.0654	−	8.18455i	−0.735512	−	0.272818i
$31$	5.35110	+	3.08946i	0.172616	+	0.0996600i	0.583819	−	0.811884i	$-0.301558\pi$
$31$	5.35110	+	3.08946i	0.172616	+	0.0996600i	−0.411203	+	0.911544i	$0.634891\pi$
$32$	11.9425	+	6.89502i	0.373204	+	0.215469i
$33$	−4.18896	+	0.712198i	−0.126938	+	0.0215818i
$34$	32.3562	−	19.0374i	0.951653	−	0.559924i
$35$		−	15.6902i		−	0.448291i
$36$	−7.44643	+	2.60742i	−0.206845	+	0.0724284i
$37$		−	7.71265i		−	0.208450i	−0.994554	−	0.104225i	$-0.966764\pi$
$37$		−	7.71265i		−	0.208450i	0.994554	−	0.104225i	$-0.0332362\pi$
$38$	41.1659	−	23.7671i	1.08331	−	0.625451i
$39$	−5.95209	−	7.18231i	−0.152618	−	0.184162i
$40$	−21.2195	−	12.2511i	−0.530487	−	0.306277i
$41$	−9.30986	+	16.1252i	−0.227070	+	0.393296i	−0.956938	−	0.290291i	$-0.906248\pi$
$41$	−9.30986	+	16.1252i	−0.227070	+	0.393296i	0.729869	+	0.683587i	$0.239581\pi$
$42$	−18.6709	−	22.5299i	−0.444545	−	0.536427i
$43$	22.6064	+	39.1554i	0.525730	+	0.910591i	0.999551	+	0.0299700i	$0.00954118\pi$
$43$	22.6064	+	39.1554i	0.525730	+	0.910591i	−0.473821	+	0.880621i	$0.657125\pi$
$44$	1.24163			0.0282189
$45$	30.1752	−	10.5661i	0.670559	−	0.234801i
$46$			3.90345i			0.0848576i
$47$	27.3169	−	15.7714i	0.581211	−	0.335562i	−0.180404	−	0.983593i	$-0.557740\pi$
$47$	27.3169	−	15.7714i	0.581211	−	0.335562i	0.761614	+	0.648030i	$0.224407\pi$
$48$	−55.4189	+	9.42221i	−1.15456	+	0.196296i
$49$	−14.7460	+	25.5408i	−0.300939	+	0.521241i
$50$	23.6771	+	13.6700i	0.473542	+	0.273399i
$51$	−17.3424	+	47.9608i	−0.340046	+	0.940409i
$52$	1.36289	+	2.36059i	0.0262094	+	0.0453961i
$53$		−	55.4075i		−	1.04542i	−0.852509	−	0.522712i	$-0.824920\pi$
$53$		−	55.4075i		−	1.04542i	0.852509	−	0.522712i	$-0.175080\pi$
$54$	30.7560	−	51.0797i	0.569555	−	0.945921i
$55$	−5.03146			−0.0914811
$56$	−15.2321	−	26.3827i	−0.272001	−	0.471120i
$57$	−22.4574	+	60.5447i	−0.393990	+	1.06219i
$58$	−65.6802	−	37.9205i	−1.13242	−	0.653802i
$59$	−49.6000	−	28.6366i	−0.840677	−	0.485365i	0.0168170	−	0.999859i	$-0.494647\pi$
$59$	−49.6000	−	28.6366i	−0.840677	−	0.485365i	−0.857494	+	0.514493i	$0.827980\pi$
$60$	−9.21032	+	1.56592i	−0.153505	+	0.0260987i
$61$	−13.7839	+	7.95816i	−0.225966	+	0.130462i	−0.608710	−	0.793393i	$-0.708313\pi$
$61$	−13.7839	+	7.95816i	−0.225966	+	0.130462i	0.382744	+	0.923855i	$0.374979\pi$
$62$	13.6450			0.220080
$63$	39.0597	+	7.38175i	0.619995	+	0.117171i
$64$	−44.4995			−0.695305
$65$	−5.52284	−	9.56584i	−0.0849667	−	0.147167i
$66$	−7.22481	+	5.98731i	−0.109467	+	0.0907168i
$67$	−52.9793	+	91.7628i	−0.790736	+	1.36959i	0.134776	+	0.990876i	$0.456969\pi$
$67$	−52.9793	+	91.7628i	−0.790736	+	1.36959i	−0.925512	+	0.378719i	$0.876365\pi$
$68$	7.34501	−	12.9671i	0.108015	−	0.190692i
$69$	−3.38366	−	4.08302i	−0.0490386	−	0.0591743i
$70$	−17.3244	−	30.0067i	−0.247491	−	0.428668i
$71$	100.875			1.42078			0.710388	−	0.703810i	$-0.248519\pi$
$71$	100.875			1.42078			0.710388	+	0.703810i	$0.248519\pi$
$72$	40.4814	−	47.0608i	0.562241	−	0.653622i
$73$			44.3391i			0.607385i	0.952770	+	0.303692i	$0.0982195\pi$
$73$			44.3391i			0.607385i	−0.952770	+	0.303692i	$0.901780\pi$
$74$	−8.51597	−	14.7501i	−0.115081	−	0.199326i
$75$	−36.6160	+	6.22537i	−0.488213	+	0.0830050i
$76$	9.43489	−	16.3417i	0.124143	−	0.215022i
$77$	−5.41764	−	3.12787i	−0.0703589	−	0.0406217i
$78$	−19.3135	−	7.16381i	−0.247609	−	0.0918437i
$79$	68.3530	−	39.4636i	0.865228	−	0.499540i	−0.000531310	−	1.00000i	$-0.500169\pi$
$79$	68.3530	−	39.4636i	0.865228	−	0.499540i	0.865760	+	0.500460i	$0.166836\pi$
$80$	−66.5650			−0.832063
$81$	12.1070	+	80.0901i	0.149469	+	0.988766i
$82$			41.1181i			0.501441i
$83$	73.2711	−	42.3031i	0.882784	−	0.509675i	0.0112086	−	0.999937i	$-0.496432\pi$
$83$	73.2711	−	42.3031i	0.882784	−	0.509675i	0.871575	+	0.490262i	$0.163099\pi$
$84$	−10.8907	−	4.03961i	−0.129651	−	0.0480906i
$85$	−29.7642	+	52.5465i	−0.350167	+	0.618194i
$86$	86.4674	+	49.9220i	1.00543	+	0.580488i
$87$	101.573	−	17.2692i	1.16750	−	0.198496i
$88$	−8.46031	+	4.88456i	−0.0961398	+	0.0555064i
$89$		−	150.514i		−	1.69117i	−0.533840	−	0.845585i	$-0.679252\pi$
$89$		−	150.514i		−	1.69117i	0.533840	−	0.845585i	$-0.320748\pi$
$90$	46.0420	−	53.5252i	0.511578	−	0.594724i
$91$		−	13.7334i		−	0.150916i
$92$	0.774780	+	1.34196i	0.00842152	+	0.0145865i
$93$	−14.2727	+	11.8280i	−0.153470	+	0.127183i
$94$	34.8282	−	60.3242i	0.370513	−	0.641747i
$95$	−38.2330	+	66.2215i	−0.402452	+	0.697068i
$96$	−31.8536	+	26.3976i	−0.331809	+	0.274975i
$97$	96.3476	−	55.6263i	0.993274	−	0.573467i	0.0870227	−	0.996206i	$-0.472265\pi$
$97$	96.3476	−	55.6263i	0.993274	−	0.573467i	0.906251	+	0.422739i	$0.138931\pi$
$98$			65.1275i			0.664566i
$99$	2.36715	−	12.5255i	0.0239106	−	0.126520i
$100$	10.8532			0.108532
$101$	−81.4139	+	47.0043i	−0.806078	+	0.465389i	−0.845592	−	0.533830i	$-0.820752\pi$
$101$	−81.4139	+	47.0043i	−0.806078	+	0.465389i	0.0395141	+	0.999219i	$0.487419\pi$
$102$	19.7898	+	110.872i	0.194017	+	1.08698i
$103$	17.7283	−	30.7063i	0.172120	−	0.298120i	−0.767041	−	0.641598i	$-0.778272\pi$
$103$	17.7283	−	30.7063i	0.172120	−	0.298120i	0.939161	+	0.343478i	$0.111605\pi$
$104$	−18.5731	−	10.7232i	−0.178587	−	0.103107i
$105$	44.1324	+	16.3697i	0.420308	+	0.155902i
$106$	−61.1785	−	105.964i	−0.577156	−	0.999663i
$107$	148.903			1.39161			0.695807	−	0.718229i	$-0.255047\pi$
$107$	148.903			1.39161			0.695807	+	0.718229i	$0.255047\pi$
$108$	0.434921	−	23.6652i	0.00402704	−	0.219122i
$109$			203.589i			1.86779i	0.357544	+	0.933896i	$0.383614\pi$
$109$			203.589i			1.86779i	−0.357544	+	0.933896i	$0.616386\pi$
$110$	−9.62244	+	5.55552i	−0.0874767	+	0.0505047i
$111$	21.6937	+	8.04668i	0.195439	+	0.0724926i
$112$	−71.6740	−	41.3810i	−0.639946	−	0.369473i
$113$	−62.6190	+	108.459i	−0.554150	+	0.959816i	0.443819	+	0.896116i	$0.353623\pi$
$113$	−62.6190	+	108.459i	−0.554150	+	0.959816i	−0.997969	+	0.0636997i	$0.979710\pi$
$114$	23.9020	+	140.585i	0.209667	+	1.23321i
$115$	−3.13964	−	5.43802i	−0.0273012	−	0.0472871i
$116$	−30.1067			−0.259541
$117$	26.4118	−	9.24831i	0.225742	−	0.0790454i
$118$	−126.477			−1.07184
$119$	−64.7148	+	38.0763i	−0.543822	+	0.319969i
$120$	56.5976	−	46.9032i	0.471646	−	0.390860i
$121$	59.4970	−	103.052i	0.491710	−	0.851668i
$122$	−17.5741	+	30.4392i	−0.144050	+	0.249502i
$123$	−35.6428	−	43.0097i	−0.289779	−	0.349673i
$124$	4.69098	−	2.70834i	0.0378305	−	0.0218414i
$125$	−132.790			−1.06232
$126$	82.8504	−	29.0107i	0.657543	−	0.230244i
$127$	76.3604			0.601263			0.300631	−	0.953740i	$-0.402803\pi$
$127$	76.3604			0.601263			0.300631	+	0.953740i	$0.402803\pi$
$128$	−132.873	+	76.7145i	−1.03807	+	0.599332i
$129$	−133.720	+	22.7347i	−1.03659	+	0.176238i
$130$	−21.1243	−	12.1961i	−0.162495	−	0.0938165i
$131$	−7.14440	+	12.3745i	−0.0545374	+	0.0944615i	−0.892005	−	0.452025i	$-0.850702\pi$
$131$	−7.14440	+	12.3745i	−0.0545374	+	0.0944615i	0.837468	+	0.546487i	$0.184035\pi$
$132$	−1.29541	+	3.49239i	−0.00981368	+	0.0264575i
$133$	−82.3349	+	47.5361i	−0.619059	+	0.357414i
$134$			233.990i			1.74619i
$135$	−1.76243	+	95.8985i	−0.0130550	+	0.710359i
$136$	0.964432	+	117.251i	0.00709141	+	0.862140i
$137$	−81.9500	+	47.3139i	−0.598175	+	0.345357i	−0.768323	−	0.640062i	$-0.778909\pi$
$137$	−81.9500	+	47.3139i	−0.598175	+	0.345357i	0.170148	+	0.985419i	$0.445575\pi$
$138$	−10.9794	−	4.07250i	−0.0795608	−	0.0295109i
$139$	−72.1283	−	41.6433i	−0.518909	−	0.299592i	0.217579	−	0.976043i	$-0.430184\pi$
$139$	−72.1283	−	41.6433i	−0.518909	−	0.299592i	−0.736488	+	0.676451i	$0.763517\pi$
$140$	−11.9118	−	6.87730i	−0.0850845	−	0.0491236i
$141$	15.8609	+	93.2898i	0.112489	+	0.661630i
$142$	192.919	−	111.382i	1.35858	−	0.784379i
$143$	−4.40396			−0.0307969
$144$	31.3168	−	165.709i	0.217478	−	1.15076i
$145$	122.002			0.841390
$146$	48.9573	+	84.7964i	0.335324	+	0.580798i
$147$	−56.4551	−	68.1236i	−0.384048	−	0.463426i
$148$	−5.85537	−	3.38060i	−0.0395633	−	0.0228419i
$149$	−175.664	−	101.420i	−1.17895	−	0.680668i	−0.223180	−	0.974777i	$-0.571644\pi$
$149$	−175.664	−	101.420i	−1.17895	−	0.680668i	−0.955772	+	0.294109i	$0.904977\pi$
$150$	−63.1526	+	52.3355i	−0.421017	+	0.348903i
$151$	12.4662	+	21.5922i	0.0825579	+	0.142994i	0.904348	−	0.426796i	$-0.140358\pi$
$151$	12.4662	+	21.5922i	0.0825579	+	0.142994i	−0.821790	+	0.569790i	$0.807024\pi$
$152$			148.467i			0.976755i
$153$	−116.808	−	98.8175i	−0.763451	−	0.645866i
$154$	−13.8146			−0.0897054
$155$	−19.0092	+	10.9750i	−0.122640	+	0.0708064i
$156$	−8.06165	+	1.37063i	−0.0516773	+	0.00878606i
$157$	127.288	−	220.468i	0.810748	−	1.40426i	−0.101592	−	0.994826i	$-0.532394\pi$
$157$	127.288	−	220.468i	0.810748	−	1.40426i	0.912341	−	0.409431i	$-0.134273\pi$
$158$	87.1480	−	150.945i	0.551570	−	0.955347i
$159$	155.847	+	57.8072i	0.980169	+	0.363567i
$160$	−42.4246	+	24.4938i	−0.265154	+	0.153086i
$161$		−	7.80719i		−	0.0484919i
$162$	111.586	+	139.801i	0.688803	+	0.862966i
$163$		−	80.6427i		−	0.494740i	−0.968921	−	0.247370i	$-0.920434\pi$
$163$		−	80.6427i		−	0.494740i	0.968921	−	0.247370i	$-0.0795664\pi$
$164$	8.16137	+	14.1359i	0.0497645	+	0.0861946i
$165$	5.24937	−	14.1522i	0.0318144	−	0.0857709i
$166$	93.4183	−	161.805i	0.562761	−	0.974731i
$167$	130.070	−	225.288i	0.778862	−	1.34903i	−0.153736	−	0.988112i	$-0.549131\pi$
$167$	130.070	−	225.288i	0.778862	−	1.34903i	0.932598	−	0.360917i	$-0.117536\pi$
$168$	90.0995	−	15.3185i	0.536307	−	0.0911817i
$169$	79.6659	+	137.985i	0.471396	+	0.816482i
$170$	1.09691	+	133.357i	0.00645241	+	0.784453i
$171$	−146.867	−	126.334i	−0.858869	−	0.738794i
$172$	39.6352			0.230437
$173$	−65.8536	−	114.062i	−0.380657	−	0.659317i	0.610500	−	0.792017i	$-0.290969\pi$
$173$	−65.8536	−	114.062i	−0.380657	−	0.659317i	−0.991156	+	0.132700i	$0.957635\pi$
$174$	175.185	−	145.179i	1.00681	−	0.834360i
$175$	−47.3559	−	27.3410i	−0.270605	−	0.156234i
$176$	−13.2699	+	22.9841i	−0.0753971	+	0.130592i
$177$	132.295	−	109.635i	0.747431	−	0.619407i
$178$	−166.191	−	287.851i	−0.933658	−	1.61714i
$179$			115.487i			0.645179i	0.946539	+	0.322589i	$0.104553\pi$
$179$			115.487i			0.645179i	−0.946539	+	0.322589i	$0.895447\pi$
$180$	5.20468	−	27.5400i	0.0289149	−	0.153000i
$181$		−	199.995i		−	1.10495i	−0.833530	−	0.552474i	$-0.813684\pi$
$181$		−	199.995i		−	1.10495i	0.833530	−	0.552474i	$-0.186316\pi$
$182$	−15.1638	−	26.2644i	−0.0833175	−	0.144310i
$183$	−8.00333	−	47.0734i	−0.0437340	−	0.257232i
$184$	−10.5585	−	6.09595i	−0.0573831	−	0.0331301i
$185$	23.7277	+	13.6992i	0.128258	+	0.0740498i
$186$	−14.2359	+	38.3798i	−0.0765373	+	0.206343i
$187$	12.2101	+	20.7525i	0.0652949	+	0.110976i
$188$		−	27.6516i		−	0.147083i
$189$	−61.5142	+	102.163i	−0.325472	+	0.540546i
$190$			168.861i			0.888740i
$191$	53.6891	−	30.9974i	0.281095	−	0.162290i	−0.352824	−	0.935690i	$-0.614779\pi$
$191$	53.6891	−	30.9974i	0.281095	−	0.162290i	0.633919	+	0.773399i	$0.281445\pi$
$192$	46.4268	−	125.166i	0.241806	−	0.651904i
$193$	−143.537	−	82.8710i	−0.743714	−	0.429384i	0.0797040	−	0.996819i	$-0.474602\pi$
$193$	−143.537	−	82.8710i	−0.743714	−	0.429384i	−0.823418	+	0.567435i	$0.807936\pi$
$194$	122.840	−	212.765i	0.633197	−	1.09673i
$195$	32.6682	−	5.55419i	0.167529	−	0.0284830i
$196$	12.9269	+	22.3900i	0.0659535	+	0.114235i
$197$	−33.9096			−0.172130			−0.0860649	−	0.996290i	$-0.527429\pi$
$197$	−33.9096			−0.172130			−0.0860649	+	0.996290i	$0.527429\pi$
$198$	−9.30303	−	26.5681i	−0.0469850	−	0.134182i
$199$		−	216.086i		−	1.08586i	−0.839778	−	0.542929i	$-0.817315\pi$
$199$		−	216.086i		−	1.08586i	0.839778	−	0.542929i	$-0.182685\pi$
$200$	−73.9521	+	42.6963i	−0.369761	+	0.213481i
$201$	−202.831	−	244.754i	−1.00911	−	1.21768i
$202$	−103.800	+	179.787i	−0.513862	+	0.890035i
$203$	131.365	+	75.8438i	0.647120	+	0.373615i
$204$	28.8099	+	34.1883i	0.141225	+	0.167590i
$205$	−33.0723	−	57.2829i	−0.161328	−	0.279429i
$206$		−	78.2993i		−	0.380094i
$207$	15.0147	−	5.25751i	0.0725348	−	0.0253986i
$208$	−58.2633			−0.280112
$209$	15.2437	+	26.4028i	0.0729362	+	0.126329i
$210$	102.476	−	17.4227i	0.487980	−	0.0829654i
$211$	68.8378	+	39.7435i	0.326245	+	0.188358i	0.654173	−	0.756345i	$-0.273017\pi$
$211$	68.8378	+	39.7435i	0.326245	+	0.188358i	−0.327927	+	0.944703i	$0.606350\pi$
$212$	−42.0648	−	24.2862i	−0.198419	−	0.114557i
$213$	−105.244	+	283.735i	−0.494103	+	1.33209i
$214$	284.769	−	164.412i	1.33070	−	0.768279i
$215$	−160.614			−0.747041
$216$	90.1351	+	162.962i	0.417292	+	0.754456i
$217$	−27.2910			−0.125765
$218$	224.794	+	389.355i	1.03117	+	1.78603i
$219$	−124.714	−	46.2594i	−0.569472	−	0.211230i
$220$	−2.20538	+	3.81984i	−0.0100245	+	0.0173629i
$221$	−26.0521	+	45.9932i	−0.117883	+	0.208114i
$222$	50.3730	−	8.56431i	0.226905	−	0.0385780i
$223$	−5.57705	−	9.65974i	−0.0250092	−	0.0433172i	0.853250	−	0.521502i	$-0.174628\pi$
$223$	−5.57705	−	9.65974i	−0.0250092	−	0.0433172i	−0.878259	+	0.478185i	$0.841295\pi$
$224$	−60.9076			−0.271909
$225$	20.6914	−	109.486i	0.0919619	−	0.486606i
$226$			276.564i			1.22374i
$227$	9.08769	+	15.7403i	0.0400339	+	0.0693407i	0.885348	−	0.464929i	$-0.153920\pi$
$227$	9.08769	+	15.7403i	0.0400339	+	0.0693407i	−0.845314	+	0.534270i	$0.820587\pi$
$228$	36.1215	+	43.5873i	0.158427	+	0.191173i
$229$	−29.0162	+	50.2575i	−0.126708	+	0.219465i	−0.922399	−	0.386237i	$-0.873775\pi$
$229$	−29.0162	+	50.2575i	−0.126708	+	0.219465i	0.795691	+	0.605703i	$0.207108\pi$
$230$	−12.0088	−	6.93330i	−0.0522123	−	0.0301448i
$231$	14.4502	−	11.9751i	0.0625548	−	0.0518401i
$232$	205.143	−	118.439i	0.884238	−	0.510515i
$233$	−393.043			−1.68688			−0.843439	−	0.537224i	$-0.819473\pi$
$233$	−393.043			−1.68688			−0.843439	+	0.537224i	$0.819473\pi$
$234$	40.2999	−	46.8497i	0.172222	−	0.200213i
$235$			112.053i			0.476820i
$236$	−43.4812	+	25.1039i	−0.184242	+	0.106372i
$237$	39.6876	+	233.432i	0.167458	+	0.984946i
$238$	−81.7220	+	144.274i	−0.343370	+	0.606195i
$239$	−134.761	−	77.8044i	−0.563854	−	0.325541i	0.190837	−	0.981622i	$-0.438880\pi$
$239$	−134.761	−	77.8044i	−0.563854	−	0.325541i	−0.754691	+	0.656080i	$0.772213\pi$
$240$	69.4479	−	187.230i	0.289366	−	0.780125i
$241$	−118.785	+	68.5806i	−0.492884	+	0.284567i	−0.725770	−	0.687937i	$-0.758516\pi$
$241$	−118.785	+	68.5806i	−0.492884	+	0.284567i	0.232886	+	0.972504i	$0.425183\pi$
$242$		−	262.776i		−	1.08585i
$243$	−237.904	−	49.5048i	−0.979028	−	0.203723i
$244$			13.9528i			0.0571838i
$245$	−52.3836	−	90.7311i	−0.213811	−	0.370331i
$246$	−115.655	−	42.8989i	−0.470141	−	0.174386i
$247$	−33.4647	+	57.9626i	−0.135485	+	0.234667i
$248$	−21.3091	+	36.9085i	−0.0859238	+	0.148824i
$249$	42.5432	+	250.228i	0.170856	+	1.00493i
$250$	−253.955	+	146.621i	−1.01582	+	0.586484i
$251$		−	234.999i		−	0.936250i	−0.883662	−	0.468125i	$-0.844930\pi$
$251$		−	234.999i		−	0.936250i	0.883662	−	0.468125i	$-0.155070\pi$
$252$	22.7247	−	26.4182i	0.0901775	−	0.104834i
$253$	−2.50358			−0.00989557
$254$	146.036	−	84.3137i	0.574944	−	0.331944i
$255$	−116.746	−	138.541i	−0.457829	−	0.543299i
$256$	−80.4103	+	139.275i	−0.314103	+	0.544042i
$257$	82.7205	+	47.7587i	0.321870	+	0.185832i	0.652226	−	0.758025i	$-0.273835\pi$
$257$	82.7205	+	47.7587i	0.321870	+	0.185832i	−0.330356	+	0.943856i	$0.607169\pi$
$258$	−230.630	+	191.126i	−0.893913	+	0.740799i
$259$	17.0326	+	29.5013i	0.0657628	+	0.113905i
$260$	−9.68305			−0.0372425
$261$	−57.3980	+	303.715i	−0.219916	+	1.16366i
$262$			31.5541i			0.120436i
$263$	313.310	−	180.890i	1.19129	−	0.687793i	0.232693	−	0.972550i	$-0.425246\pi$
$263$	313.310	−	180.890i	1.19129	−	0.687793i	0.958600	+	0.284757i	$0.0919130\pi$
$264$	−4.91229	−	28.8927i	−0.0186071	−	0.109442i
$265$	170.459	+	98.4147i	0.643243	+	0.371376i
$266$	−104.974	+	181.821i	−0.394641	+	0.683537i
$267$	423.357	+	157.033i	1.58561	+	0.588138i
$268$	46.4436	+	80.4427i	0.173297	+	0.300159i
$269$	420.642			1.56373			0.781863	−	0.623450i	$-0.214270\pi$
$269$	420.642			1.56373			0.781863	+	0.623450i	$0.214270\pi$
$270$	102.516	+	185.347i	0.379690	+	0.686472i
$271$	−100.068			−0.369253			−0.184627	−	0.982809i	$-0.559108\pi$
$271$	−100.068			−0.369253			−0.184627	+	0.982809i	$0.559108\pi$
$272$	161.537	+	274.550i	0.593887	+	1.00938i
$273$	38.6284	+	14.3281i	0.141496	+	0.0524841i
$274$	−104.484	+	180.971i	−0.381328	+	0.660479i
$275$	−8.76759	+	15.1859i	−0.0318821	+	0.0552215i
$276$	−4.58292	+	0.779178i	−0.0166048	+	0.00282311i
$277$	−473.610	+	273.439i	−1.70978	+	0.987143i	−0.774972	+	0.631996i	$0.782236\pi$
$277$	−473.610	+	273.439i	−1.70978	+	0.987143i	−0.934810	+	0.355147i	$0.884431\pi$
$278$	−183.923			−0.661592
$279$	−18.3783	−	52.4857i	−0.0658719	−	0.188121i
$280$	108.221			0.386503
$281$	133.786	−	77.2417i	0.476109	−	0.274881i	−0.242685	−	0.970105i	$-0.578028\pi$
$281$	133.786	−	77.2417i	0.476109	−	0.274881i	0.718793	+	0.695224i	$0.244695\pi$
$282$	133.340	+	160.899i	0.472836	+	0.570566i
$283$	276.014	+	159.357i	0.975314	+	0.563098i	0.900852	−	0.434126i	$-0.142943\pi$
$283$	276.014	+	159.357i	0.975314	+	0.563098i	0.0744622	+	0.997224i	$0.476276\pi$
$284$	44.2154	−	76.5834i	0.155688	−	0.269660i
$285$	−146.375	−	176.629i	−0.513596	−	0.619751i
$286$	−8.42237	+	4.86266i	−0.0294489	+	0.0170023i
$287$		−	82.2393i		−	0.286548i
$288$	−41.0163	−	117.137i	−0.142418	−	0.406725i
$289$	288.961	−	4.75393i	0.999865	−	0.0164496i
$290$	233.322	−	134.709i	0.804559	−	0.464513i
$291$	55.9420	+	329.036i	0.192241	+	1.13071i
$292$	33.6618	+	19.4347i	0.115280	+	0.0665570i
$293$	87.7848	+	50.6826i	0.299607	+	0.172978i	0.642266	−	0.766482i	$-0.277994\pi$
$293$	87.7848	+	50.6826i	0.299607	+	0.172978i	−0.342659	+	0.939460i	$0.611328\pi$
$294$	−183.187	−	67.9481i	−0.623084	−	0.231116i
$295$	176.199	−	101.728i	0.597284	−	0.344842i
$296$	53.1969			0.179719
$297$	32.7613	+	19.7261i	0.110307	+	0.0664180i
$298$	−447.932			−1.50313
$299$	−2.74808	−	4.75981i	−0.00919090	−	0.0159191i
$300$	−11.3232	+	30.5272i	−0.0377441	+	0.101757i
$301$	−172.941	−	99.8476i	−0.574555	−	0.331720i
$302$	47.6822	+	27.5293i	0.157888	+	0.0911567i
$303$	−47.2711	−	278.036i	−0.156010	−	0.917611i
$304$	201.670	+	349.303i	0.663388	+	1.14902i
$305$		−	56.5411i		−	0.185381i
$306$	−332.500	−	60.0097i	−1.08660	−	0.196110i
$307$	−114.755			−0.373794			−0.186897	−	0.982380i	$-0.559843\pi$
$307$	−114.755			−0.373794			−0.186897	+	0.982380i	$0.559843\pi$
$308$	−4.74930	+	2.74201i	−0.0154198	+	0.00890263i
$309$	67.8729	+	81.9013i	0.219653	+	0.265053i
$310$	−24.2362	+	41.9783i	−0.0781813	+	0.135414i
$311$	−49.0382	+	84.9367i	−0.157679	+	0.273108i	−0.934031	−	0.357191i	$-0.883735\pi$
$311$	−49.0382	+	84.9367i	−0.157679	+	0.273108i	0.776352	+	0.630299i	$0.217068\pi$
$312$	49.5390	−	41.0537i	0.158779	−	0.131582i
$313$	−276.012	+	159.356i	−0.881829	+	0.509124i	−0.871261	−	0.490820i	$-0.836697\pi$
$313$	−276.012	+	159.356i	−0.881829	+	0.509124i	−0.0105678	+	0.999944i	$0.503364\pi$
$314$		−	562.181i		−	1.79038i
$315$	−92.0874	+	107.054i	−0.292341	+	0.339855i
$316$		−	69.1906i		−	0.218958i
$317$	84.7398	+	146.774i	0.267318	+	0.463008i	0.968168	−	0.250300i	$-0.0805293\pi$
$317$	84.7398	+	146.774i	0.267318	+	0.463008i	−0.700850	+	0.713308i	$0.747196\pi$
$318$	361.878	−	61.5258i	1.13798	−	0.193477i
$319$	24.3213	−	42.1257i	0.0762423	−	0.132055i
$320$	79.0400	−	136.901i	0.247000	−	0.427817i
$321$	−155.351	+	418.824i	−0.483961	+	1.30475i
$322$	−8.62035	−	14.9309i	−0.0267713	−	0.0463692i
$323$	365.916	−	3.00979i	1.13287	−	0.00931822i
$324$	66.1103	+	25.9134i	0.204044	+	0.0799798i
$325$	−38.4953			−0.118447
$326$	−89.0421	−	154.225i	−0.273135	−	0.473084i
$327$	−572.644	−	212.407i	−1.75120	−	0.649561i
$328$	−111.221	−	64.2134i	−0.339088	−	0.195773i
$329$	−69.6590	+	120.653i	−0.211729	+	0.366726i
$330$	−5.58705	−	32.8615i	−0.0169305	−	0.0995804i
$331$	−148.453	−	257.128i	−0.448498	−	0.776821i	0.549790	−	0.835303i	$-0.314708\pi$
$331$	−148.453	−	257.128i	−0.448498	−	0.776821i	−0.998289	+	0.0584812i	$0.981374\pi$
$332$		−	74.1689i		−	0.223400i
$333$	−45.2664	+	52.6235i	−0.135935	+	0.158029i
$334$		−	574.470i		−	1.71997i
$335$	−188.204	−	325.978i	−0.561802	−	0.973069i
$336$	191.172	−	158.427i	0.568965	−	0.471509i
$337$	454.800	+	262.579i	1.34955	+	0.779166i	0.988186	−	0.153257i	$-0.0489763\pi$
$337$	454.800	+	262.579i	1.34955	+	0.779166i	0.361368	+	0.932423i	$0.382310\pi$
$338$	304.715	+	175.927i	0.901523	+	0.520495i
$339$	−239.737	−	289.287i	−0.707188	−	0.853355i
$340$	26.8466	+	45.6288i	0.0789606	+	0.134202i
$341$			8.75156i			0.0256644i
$342$	−420.368	−	79.4438i	−1.22914	−	0.232292i
$343$		−	346.682i		−	1.01074i
$344$	−270.069	+	155.924i	−0.785084	+	0.453269i
$345$	18.5713	−	3.15746i	0.0538300	−	0.00915206i
$346$	−251.884	−	145.425i	−0.727988	−	0.420304i
$347$	209.954	−	363.652i	0.605056	−	1.04799i	−0.386987	−	0.922085i	$-0.626484\pi$
$347$	209.954	−	363.652i	0.605056	−	1.04799i	0.992043	−	0.125902i	$-0.0401825\pi$
$348$	31.4106	−	84.6824i	0.0902604	−	0.243340i
$349$	274.372	+	475.226i	0.786166	+	1.36168i	0.928300	+	0.371831i	$0.121270\pi$
$349$	274.372	+	475.226i	0.786166	+	1.36168i	−0.142135	+	0.989847i	$0.545397\pi$
$350$	−120.755			−0.345013
$351$	−1.54263	+	83.9385i	−0.00439495	+	0.239141i
$352$			19.5316i			0.0554875i
$353$	400.248	−	231.083i	1.13385	−	0.654627i	0.188947	−	0.981987i	$-0.439492\pi$
$353$	400.248	−	231.083i	1.13385	−	0.654627i	0.944900	+	0.327360i	$0.106159\pi$
$354$	131.954	−	355.746i	0.372753	−	1.00493i
$355$	−179.174	+	310.339i	−0.504716	+	0.874194i
$356$	−114.269	−	65.9732i	−0.320980	−	0.185318i
$357$	−39.5810	−	221.751i	−0.110871	−	0.621152i
$358$	127.516	+	220.864i	0.356189	+	0.616937i
$359$			377.149i			1.05055i	0.850931	+	0.525277i	$0.176038\pi$
$359$			377.149i			1.05055i	−0.850931	+	0.525277i	$0.823962\pi$
$360$	72.8779	+	208.129i	0.202439	+	0.578135i
$361$	102.333			0.283472
$362$	−220.826	−	382.482i	−0.610017	−	1.05658i
$363$	227.784	+	274.864i	0.627504	+	0.757202i
$364$	−10.4262	−	6.01959i	−0.0286435	−	0.0165373i
$365$	−136.408	−	78.7550i	−0.373720	−	0.215767i
$366$	−67.2824	−	81.1888i	−0.183832	−	0.221827i
$367$	481.665	−	278.090i	1.31244	−	0.757737i	0.329940	−	0.944002i	$-0.392972\pi$
$367$	481.665	−	278.090i	1.31244	−	0.757737i	0.982500	+	0.186265i	$0.0596383\pi$
$368$	−33.1217			−0.0900047
$369$	158.162	−	55.3815i	0.428622	−	0.150085i
$370$	60.5042			0.163525
$371$	122.362	+	211.936i	0.329816	+	0.571257i
$372$	2.72371	+	16.0201i	0.00732180	+	0.0430649i
$373$	182.405	−	315.935i	0.489022	−	0.847010i	−0.510899	−	0.859641i	$-0.670687\pi$
$373$	182.405	−	315.935i	0.489022	−	0.847010i	0.999920	+	0.0126306i	$0.00402055\pi$
$374$	46.2653	+	26.2063i	0.123704	+	0.0700703i
$375$	138.541	−	373.505i	0.369443	−	0.996012i
$376$	108.781	+	188.414i	0.289311	+	0.501102i
$377$	106.786			0.283252
$378$	−4.83901	+	263.304i	−0.0128016	+	0.696571i
$379$			555.368i			1.46535i	0.680579	+	0.732675i	$0.261728\pi$
$379$			555.368i			1.46535i	−0.680579	+	0.732675i	$0.738272\pi$
$380$	33.5165	+	58.0522i	0.0882012	+	0.152769i
$381$	−79.6675	+	214.782i	−0.209101	+	0.563732i
$382$	68.4520	−	118.562i	0.179194	−	0.310373i
$383$	446.221	+	257.626i	1.16507	+	0.672652i	0.952513	−	0.304498i	$-0.0984886\pi$
$383$	446.221	+	257.626i	1.16507	+	0.672652i	0.212554	+	0.977149i	$0.431822\pi$
$384$	−77.1499	−	453.775i	−0.200911	−	1.18171i
$385$	19.2456	−	11.1114i	0.0499885	−	0.0288609i
$386$	−366.010			−0.948213
$387$	75.5639	−	399.838i	0.195256	−	1.03317i
$388$		−	97.5282i		−	0.251361i
$389$	−560.338	+	323.511i	−1.44046	+	0.831649i	−0.997880	−	0.0650808i	$-0.979269\pi$
$389$	−560.338	+	323.511i	−1.44046	+	0.831649i	−0.442578	+	0.896730i	$0.645936\pi$
$390$	56.3438	−	46.6929i	0.144471	−	0.119725i
$391$	−14.8102	+	26.1463i	−0.0378778	+	0.0668704i
$392$	−176.164	−	101.708i	−0.449398	−	0.259460i
$393$	−27.3523	−	33.0057i	−0.0695988	−	0.0839840i
$394$	−64.8505	+	37.4414i	−0.164595	+	0.0950291i
$395$			280.381i			0.709825i
$396$	−8.47167	−	7.28728i	−0.0213931	−	0.0184022i
$397$		−	687.340i		−	1.73134i	−0.500619	−	0.865668i	$-0.666894\pi$
$397$		−	687.340i		−	1.73134i	0.500619	−	0.865668i	$-0.333106\pi$
$398$	−238.592	−	413.254i	−0.599479	−	1.03833i
$399$	−47.8059	−	281.181i	−0.119814	−	0.704715i
$400$	−115.993	+	200.906i	−0.289983	+	0.502265i
$401$	−120.496	+	208.705i	−0.300489	+	0.520462i	−0.976247	−	0.216662i	$-0.930483\pi$
$401$	−120.496	+	208.705i	−0.300489	+	0.520462i	0.675758	+	0.737124i	$0.263817\pi$
$402$	−658.152	−	244.123i	−1.63719	−	0.607272i
$403$	−16.6385	+	9.60624i	−0.0412866	+	0.0238368i
$404$			82.4115i			0.203989i
$405$	−267.899	−	105.009i	−0.661479	−	0.259282i
$406$	334.973			0.825058
$407$	9.46035	−	5.46194i	0.0232441	−	0.0134200i
$408$	−330.803	−	119.616i	−0.810792	−	0.293177i
$409$	288.068	−	498.948i	0.704322	−	1.21992i	−0.262614	−	0.964901i	$-0.584585\pi$
$409$	288.068	−	498.948i	0.704322	−	1.21992i	0.966936	−	0.255020i	$-0.0820820\pi$
$410$	−126.499	−	73.0340i	−0.308533	−	0.178132i
$411$	−47.5824	−	279.867i	−0.115772	−	0.680942i
$412$	−15.5413	−	26.9183i	−0.0377216	−	0.0653357i
$413$	252.963			0.612501
$414$	22.9098	−	26.6333i	0.0553377	−	0.0643316i
$415$			300.555i			0.724228i
$416$	−37.1336	+	21.4391i	−0.0892634	+	0.0515362i
$417$	192.384	−	159.431i	0.461352	−	0.382329i
$418$	58.3056	+	33.6628i	0.139487	+	0.0805329i
$419$	−398.013	+	689.378i	−0.949911	+	1.64529i	−0.204304	+	0.978908i	$0.565493\pi$
$419$	−398.013	+	689.378i	−0.949911	+	1.64529i	−0.745607	+	0.666386i	$0.767840\pi$
$420$	31.7718	−	26.3297i	0.0756471	−	0.0626898i
$421$	−52.6204	−	91.1413i	−0.124989	−	0.216488i	0.796740	−	0.604323i	$-0.206556\pi$
$421$	−52.6204	−	91.1413i	−0.124989	−	0.216488i	−0.921729	+	0.387835i	$0.873223\pi$
$422$	175.532			0.415953
$423$	−278.948	−	52.7174i	−0.659451	−	0.124627i
$424$	382.165			0.901333
$425$	106.730	+	181.399i	0.251129	+	0.426821i
$426$	112.014	+	658.836i	0.262944	+	1.54656i
$427$	35.1495	−	60.8807i	0.0823173	−	0.142578i
$428$	65.2668	−	113.045i	0.152493	−	0.264125i
$429$	4.59469	−	12.3872i	0.0107102	−	0.0288746i
$430$	−307.166	+	177.343i	−0.714340	+	0.412425i
$431$	−251.529			−0.583594			−0.291797	−	0.956480i	$-0.594253\pi$
$431$	−251.529			−0.583594			−0.291797	+	0.956480i	$0.594253\pi$
$432$	433.424	+	260.972i	1.00330	+	0.604102i
$433$	247.092			0.570651			0.285325	−	0.958431i	$-0.407898\pi$
$433$	247.092			0.570651			0.285325	+	0.958431i	$0.407898\pi$
$434$	−52.1927	+	30.1335i	−0.120260	+	0.0694320i
$435$	−127.285	+	343.159i	−0.292610	+	0.788870i
$436$	154.563	+	89.2370i	0.354502	+	0.204672i
$437$	−19.0241	+	32.9508i	−0.0435335	+	0.0754023i
$438$	−289.588	+	49.2351i	−0.661160	+	0.112409i
$439$	−536.953	+	310.010i	−1.22313	+	0.706173i	−0.965583	−	0.260094i	$-0.916247\pi$
$439$	−536.953	+	310.010i	−1.22313	+	0.706173i	−0.257544	+	0.966267i	$0.582913\pi$
$440$		−	34.7038i		−	0.0788722i
$441$	250.514	−	87.7194i	0.568059	−	0.198910i
$442$	0.960108	+	116.725i	0.00217219	+	0.264085i
$443$	321.142	−	185.411i	0.724925	−	0.418536i	−0.0916378	−	0.995792i	$-0.529210\pi$
$443$	321.142	−	185.411i	0.724925	−	0.418536i	0.816563	+	0.577257i	$0.195877\pi$
$444$	15.6177	−	12.9426i	0.0351750	−	0.0291501i
$445$	463.052	+	267.343i	1.04057	+	0.600771i
$446$	−21.3317	−	12.3159i	−0.0478289	−	0.0276140i
$447$	468.539	−	388.285i	1.04818	−	0.868646i
$448$	170.213	−	98.2725i	0.379940	−	0.219358i
$449$	454.217			1.01162			0.505810	−	0.862645i	$-0.331194\pi$
$449$	454.217			1.01162			0.505810	+	0.862645i	$0.331194\pi$
$450$	−81.3185	−	232.234i	−0.180708	−	0.516075i
$451$	−26.3722			−0.0584749
$452$	54.8941	+	95.0794i	0.121447	+	0.210353i
$453$	−73.7393	+	12.5370i	−0.162780	+	0.0276755i
$454$	34.7596	+	20.0685i	0.0765629	+	0.0442036i
$455$	42.2503	+	24.3932i	0.0928577	+	0.0536114i
$456$	−417.599	−	154.897i	−0.915786	−	0.339686i
$457$	−412.915	−	715.190i	−0.903534	−	1.56497i	−0.822873	−	0.568226i	$-0.807630\pi$
$457$	−412.915	−	715.190i	−0.903534	−	1.56497i	−0.0806614	−	0.996742i	$-0.525703\pi$
$458$			128.154i			0.279811i
$459$	399.815	−	225.453i	0.871056	−	0.491184i
$460$	−5.50465			−0.0119666
$461$	−373.424	+	215.597i	−0.810031	+	0.467672i	−0.846967	−	0.531646i	$-0.821574\pi$
$461$	−373.424	+	215.597i	−0.810031	+	0.467672i	0.0369358	+	0.999318i	$0.488240\pi$
$462$	14.4129	−	38.8570i	0.0311968	−	0.0841060i
$463$	−257.345	+	445.734i	−0.555821	+	0.962709i	0.442019	+	0.897006i	$0.354263\pi$
$463$	−257.345	+	445.734i	−0.555821	+	0.962709i	−0.997839	+	0.0657036i	$0.979071\pi$
$464$	321.765	−	557.313i	0.693458	−	1.20110i
$465$	−11.0373	−	64.9184i	−0.0237361	−	0.139609i
$466$	−751.676	+	433.980i	−1.61304	+	0.931288i
$467$			453.857i			0.971858i	0.873998	+	0.485929i	$0.161519\pi$
$467$			453.857i			0.971858i	−0.873998	+	0.485929i	$0.838481\pi$
$468$	4.55558	−	24.1053i	0.00973415	−	0.0515071i
$469$		−	467.996i		−	0.997860i
$470$	123.724	+	214.296i	0.263242	+	0.455948i
$471$	487.320	+	588.043i	1.03465	+	1.24850i
$472$	197.517	−	342.109i	0.418467	−	0.724806i
$473$	−32.0187	+	55.4581i	−0.0676929	+	0.117248i
$474$	333.646	+	402.607i	0.703895	+	0.849381i
$475$	133.246	+	230.789i	0.280518	+	0.485871i
$476$	0.541396	+	65.8204i	0.00113739	+	0.138278i
$477$	−325.193	+	378.046i	−0.681746	+	0.792550i
$478$	−343.632			−0.718896
$479$	−233.447	−	404.343i	−0.487364	−	0.844139i	0.512530	−	0.858669i	$-0.328708\pi$
$479$	−233.447	−	404.343i	−0.487364	−	0.844139i	−0.999894	+	0.0145299i	$0.995375\pi$
$480$	−24.6329	−	144.884i	−0.0513185	−	0.301841i
$481$	20.7685	+	11.9907i	0.0431778	+	0.0249287i
$482$	−151.447	+	262.315i	−0.314206	+	0.544221i
$483$	21.9596	+	8.14531i	0.0454650	+	0.0168640i
$484$	−52.1573	−	90.3390i	−0.107763	−	0.186651i
$485$			395.213i			0.814873i
$486$	−509.641	+	168.007i	−1.04864	+	0.345694i
$487$		−	610.782i		−	1.25417i	−0.778950	−	0.627086i	$-0.784248\pi$
$487$		−	610.782i		−	1.25417i	0.778950	−	0.627086i	$-0.215752\pi$
$488$	−54.8902	−	95.0727i	−0.112480	−	0.194821i
$489$	226.827	+	84.1352i	0.463859	+	0.172056i
$490$	−200.363	−	115.679i	−0.408903	−	0.236080i
$491$	−157.490	−	90.9272i	−0.320755	−	0.185188i	0.330974	−	0.943640i	$-0.392623\pi$
$491$	−157.490	−	90.9272i	−0.320755	−	0.185188i	−0.651729	+	0.758452i	$0.725956\pi$
$492$	−48.2755	+	8.20770i	−0.0981209	+	0.0166823i
$493$	−296.068	−	503.201i	−0.600544	−	1.02069i
$494$			147.801i			0.299193i
$495$	34.3297	+	29.5302i	0.0693530	+	0.0596570i
$496$			115.781i			0.233429i
$497$	−385.852	+	222.772i	−0.776363	+	0.448233i
$498$	357.652	+	431.574i	0.718177	+	0.866615i
$499$	633.250	+	365.607i	1.26904	+	0.732679i	0.974806	−	0.223055i	$-0.0716029\pi$
$499$	633.250	+	365.607i	1.26904	+	0.732679i	0.294232	+	0.955734i	$0.404936\pi$
$500$	−58.2045	+	100.813i	−0.116409	+	0.201626i
$501$	497.973	+	600.898i	0.993958	+	1.19940i
$502$	−259.475	−	449.424i	−0.516883	−	0.895267i
$503$	489.996			0.974147			0.487073	−	0.873361i	$-0.338064\pi$
$503$	489.996			0.974147			0.487073	+	0.873361i	$0.338064\pi$
$504$	−50.9146	+	269.408i	−0.101021	+	0.534541i
$505$		−	333.956i		−	0.661299i
$506$	−4.78798	+	2.76434i	−0.00946241	+	0.00546312i
$507$	−471.233	+	80.1181i	−0.929454	+	0.158024i
$508$	33.4702	−	57.9721i	0.0658862	−	0.114118i
$509$	−501.158	−	289.344i	−0.984593	−	0.568455i	−0.0809394	−	0.996719i	$-0.525792\pi$
$509$	−501.158	−	289.344i	−0.984593	−	0.568455i	−0.903654	+	0.428264i	$0.859125\pi$
$510$	−376.243	−	136.047i	−0.737732	−	0.266759i
$511$	−97.9181	−	169.599i	−0.191621	−	0.331897i
$512$		−	258.574i		−	0.505027i
$513$	508.571	−	281.292i	0.991367	−	0.548328i
$514$	210.932			0.410374
$515$	62.9780	+	109.081i	0.122287	+	0.211808i
$516$	−41.3518	+	111.484i	−0.0801391	+	0.216053i
$517$	38.6905	+	22.3380i	0.0748365	+	0.0432069i
$518$	65.1480	+	37.6132i	0.125768	+	0.0726124i
$519$	389.532	−	66.2274i	0.750543	−	0.127606i
$520$	65.9790	−	38.0930i	0.126883	−	0.0732557i
$521$	−353.079			−0.677695			−0.338848	−	0.940841i	$-0.610037\pi$
$521$	−353.079			−0.677695			−0.338848	+	0.940841i	$0.610037\pi$
$522$	225.577	+	644.217i	0.432140	+	1.23413i
$523$	−584.015			−1.11666			−0.558332	−	0.829618i	$-0.688559\pi$
$523$	−584.015			−1.11666			−0.558332	+	0.829618i	$0.688559\pi$
$524$	6.26305	+	10.8479i	0.0119524	+	0.0207021i
$525$	126.310	−	104.675i	0.240590	−	0.199381i
$526$	399.460	−	691.886i	0.759430	−	1.31537i
$527$	91.3977	+	51.7708i	0.173430	+	0.0982369i
$528$	−50.8038	−	61.3043i	−0.0962193	−	0.116107i
$529$	262.938	+	455.422i	0.497047	+	0.860910i
$530$	434.661			0.820115
$531$	170.350	+	486.495i	0.320810	+	0.916187i
$532$			83.3438i			0.156661i
$533$	−28.9477	−	50.1389i	−0.0543109	−	0.0940692i
$534$	983.040	−	167.134i	1.84090	−	0.312986i
$535$	−264.481	+	458.094i	−0.494356	+	0.856250i
$536$	−632.921	−	365.417i	−1.18082	−	0.681748i
$537$	−324.835	−	120.489i	−0.604907	−	0.224374i
$538$	804.459	−	464.454i	1.49528	−	0.863298i
$539$	−41.7712			−0.0774976
$540$	72.0327	+	43.3721i	0.133394	+	0.0803188i
$541$			203.117i			0.375448i	0.982222	+	0.187724i	$0.0601110\pi$
$541$			203.117i			0.375448i	−0.982222	+	0.187724i	$0.939889\pi$
$542$	−191.375	+	110.490i	−0.353090	+	0.203856i
$543$	562.535	+	208.657i	1.03598	+	0.384267i
$544$	203.980	+	115.541i	0.374963	+	0.212392i
$545$	−626.336	−	361.615i	−1.14924	−	0.663514i
$546$	89.6955	−	15.2498i	0.164278	−	0.0279301i
$547$	−632.756	+	365.322i	−1.15677	+	0.667864i	−0.950529	−	0.310636i	$-0.899458\pi$
$547$	−632.756	+	365.322i	−1.15677	+	0.667864i	−0.206246	+	0.978500i	$0.566125\pi$
$548$			82.9542i			0.151376i
$549$	140.755	+	26.6009i	0.256385	+	0.0484533i
$550$			38.7231i			0.0704057i
$551$	−369.624	−	640.208i	−0.670824	−	1.16190i
$552$	28.1621	−	23.3383i	0.0510183	−	0.0422796i
$553$	−174.302	+	301.901i	−0.315194	+	0.545933i
$554$	−603.838	+	1045.88i	−1.08996	+	1.88787i
$555$	−63.2876	+	52.4474i	−0.114032	+	0.0944998i
$556$	−63.2304	+	36.5061i	−0.113724	+	0.0656584i
$557$		−	274.409i		−	0.492654i	−0.969187	−	0.246327i	$-0.920776\pi$
$557$		−	274.409i		−	0.492654i	0.969187	−	0.246327i	$-0.0792238\pi$
$558$	−93.0999	−	80.0839i	−0.166846	−	0.143520i
$559$	−140.583			−0.251490
$560$	254.614	−	147.002i	0.454669	−	0.262503i
$561$	−71.1103	+	12.6927i	−0.126756	+	0.0226251i
$562$	170.574	−	295.442i	0.303512	−	0.525698i
$563$	838.226	+	483.950i	1.48886	+	0.859592i	0.999919	−	0.0127273i	$-0.00405134\pi$
$563$	838.226	+	483.950i	1.48886	+	0.859592i	0.488937	+	0.872319i	$0.337385\pi$
$564$	77.7769	+	28.8492i	0.137902	+	0.0511511i
$565$	−222.447	−	385.290i	−0.393712	−	0.681930i
$566$	703.819			1.24350
$567$	−223.180	−	279.611i	−0.393616	−	0.493142i
$568$			695.771i			1.22495i
$569$	−350.531	+	202.379i	−0.616048	+	0.355675i	−0.775329	−	0.631558i	$-0.782416\pi$
$569$	−350.531	+	202.379i	−0.616048	+	0.355675i	0.159281	+	0.987233i	$0.449082\pi$
$570$	−474.961	−	176.174i	−0.833265	−	0.309077i
$571$	−539.740	−	311.619i	−0.945253	−	0.545742i	−0.0536499	−	0.998560i	$-0.517086\pi$
$571$	−539.740	−	311.619i	−0.945253	−	0.545742i	−0.891603	+	0.452818i	$0.850419\pi$
$572$	−1.93034	+	3.34345i	−0.00337472	+	0.00584518i
$573$	31.1734	+	183.353i	0.0544038	+	0.319989i
$574$	−90.8050	−	157.279i	−0.158197	−	0.274005i
$575$	−21.8840			−0.0380591
$576$	303.621	+	261.173i	0.527120	+	0.453425i
$577$	−116.940			−0.202669			−0.101335	−	0.994852i	$-0.532311\pi$
$577$	−116.940			−0.202669			−0.101335	+	0.994852i	$0.532311\pi$
$578$	547.375	−	328.149i	0.947016	−	0.567733i
$579$	382.848	−	317.272i	0.661223	−	0.547965i
$580$	53.4755	−	92.6224i	0.0921992	−	0.159694i
$581$	−186.844	+	323.623i	−0.321590	+	0.557010i
$582$	470.294	+	567.498i	0.808065	+	0.975082i
$583$	67.9629	−	39.2384i	0.116574	−	0.0673043i
$584$	−305.822			−0.523669
$585$	−18.4606	+	97.6820i	−0.0315565	+	0.166978i
$586$	223.846			0.381989
$587$	164.072	−	94.7270i	0.279509	−	0.161375i	−0.353692	−	0.935362i	$-0.615074\pi$
$587$	164.072	−	94.7270i	0.279509	−	0.161375i	0.633201	+	0.773987i	$0.281741\pi$
$588$	−76.4641	+	13.0003i	−0.130041	+	0.0221093i
$589$	115.183	+	66.5012i	0.195558	+	0.112905i
$590$	224.648	−	389.102i	0.380759	−	0.659494i
$591$	35.3782	−	95.3788i	0.0598615	−	0.161386i
$592$	125.158	−	72.2601i	0.211416	−	0.122061i
$593$		−	436.488i		−	0.736068i	−0.929812	−	0.368034i	$-0.880031\pi$
$593$		−	436.488i		−	0.736068i	0.929812	−	0.368034i	$-0.119969\pi$
$594$	84.4352	+	1.55175i	0.142147	+	0.00261238i
$595$	−2.19390	−	266.724i	−0.00368723	−	0.448276i
$596$	−153.994	+	88.9082i	−0.258378	+	0.149175i
$597$	607.794	+	225.444i	1.01808	+	0.377629i
$598$	−10.5111	−	6.06861i	−0.0175772	−	0.0101482i
$599$	205.367	+	118.569i	0.342850	+	0.197944i	0.661531	−	0.749917i	$-0.269907\pi$
$599$	205.367	+	118.569i	0.342850	+	0.197944i	−0.318682	+	0.947862i	$0.603240\pi$
$600$	−42.9386	−	252.554i	−0.0715644	−	0.420923i
$601$	−167.618	+	96.7745i	−0.278899	+	0.161022i	−0.632925	−	0.774213i	$-0.718146\pi$
$601$	−167.618	+	96.7745i	−0.278899	+	0.161022i	0.354026	+	0.935236i	$0.384812\pi$
$602$	−440.989			−0.732540
$603$	900.045	−	315.158i	1.49261	−	0.522649i
$604$	21.8567			0.0361867
$605$	211.357	+	366.081i	0.349350	+	0.605092i
$606$	−397.399	−	479.536i	−0.655774	−	0.791314i
$607$	−127.850	−	73.8140i	−0.210625	−	0.121605i	0.390977	−	0.920401i	$-0.372137\pi$
$607$	−127.850	−	73.8140i	−0.210625	−	0.121605i	−0.601602	+	0.798796i	$0.705471\pi$
$608$	257.065	+	148.416i	0.422804	+	0.244106i
$609$	−350.383	+	290.368i	−0.575342	+	0.476795i
$610$	−62.4301	−	108.132i	−0.102344	−	0.177266i
$611$			98.0780i			0.160520i
$612$	−126.220	+	45.3659i	−0.206242	+	0.0741273i
$613$	−980.994			−1.60032			−0.800158	−	0.599789i	$-0.795251\pi$
$613$	−980.994			−1.60032			−0.800158	+	0.599789i	$0.795251\pi$
$614$	−219.463	+	126.707i	−0.357432	+	0.206363i
$615$	195.627	−	33.2600i	0.318092	−	0.0540814i
$616$	21.5741	−	37.3674i	0.0350228	−	0.0606613i
$617$	378.719	−	655.961i	0.613808	−	1.06315i	−0.376785	−	0.926301i	$-0.622970\pi$
$617$	378.719	−	655.961i	0.613808	−	1.06315i	0.990592	−	0.136845i	$-0.0436963\pi$
$618$	220.235	+	81.6903i	0.356368	+	0.132185i
$619$	−842.718	+	486.544i	−1.36142	+	0.786016i	−0.989813	−	0.142375i	$-0.954526\pi$
$619$	−842.718	+	486.544i	−1.36142	+	0.786016i	−0.371606	+	0.928390i	$0.621193\pi$
$620$			19.2422i			0.0310358i
$621$	−0.876957	+	47.7176i	−0.00141217	+	0.0768400i
$622$			216.583i			0.348205i
$623$	332.394	+	575.724i	0.533539	+	0.924116i
$624$	60.7867	−	163.880i	0.0974145	−	0.262628i
$625$	81.1059	−	140.480i	0.129769	−	0.224767i
$626$	−351.907	+	609.521i	−0.562152	+	0.973676i
$627$	−90.1681	+	15.3302i	−0.143809	+	0.0244501i
$628$	−111.585	−	193.271i	−0.177683	−	0.307756i
$629$	−1.07843	−	131.111i	−0.00171452	−	0.208443i
$630$	−57.9083	+	306.415i	−0.0919180	+	0.486373i
$631$	−850.171			−1.34734			−0.673669	−	0.739033i	$-0.735283\pi$
$631$	−850.171			−1.34734			−0.673669	+	0.739033i	$0.735283\pi$
$632$	272.195	+	471.455i	0.430688	+	0.745973i
$633$	−183.607	+	152.158i	−0.290059	+	0.240376i
$634$	324.122	+	187.132i	0.511233	+	0.295161i
$635$	−135.631	+	234.920i	−0.213592	+	0.369953i
$636$	112.197	−	92.9795i	0.176411	−	0.146194i
$637$	−45.8506	−	79.4156i	−0.0719790	−	0.124671i
$638$		−	107.418i		−	0.168367i
$639$	−688.272	−	592.047i	−1.07711	−	0.926522i
$640$		−	545.041i		−	0.851626i
$641$	−472.888	−	819.066i	−0.737735	−	1.27779i	−0.953513	−	0.301351i	$-0.902562\pi$
$641$	−472.888	−	819.066i	−0.737735	−	1.27779i	0.215779	−	0.976442i	$-0.430771\pi$
$642$	165.345	+	972.514i	0.257547	+	1.51482i
$643$	670.084	+	386.873i	1.04212	+	0.601669i	0.920433	−	0.390900i	$-0.127836\pi$
$643$	670.084	+	386.873i	1.04212	+	0.601669i	0.121688	+	0.992568i	$0.461169\pi$
$644$	−5.92714	−	3.42204i	−0.00920364	−	0.00531372i
$645$	167.570	−	451.765i	0.259798	−	0.700411i
$646$	696.473	−	409.784i	1.07813	−	0.634340i
$647$			329.359i			0.509056i	0.967065	+	0.254528i	$0.0819200\pi$
$647$			329.359i			0.509056i	−0.967065	+	0.254528i	$0.918080\pi$
$648$	−552.410	+	83.5064i	−0.852484	+	0.128868i
$649$		−	81.1192i		−	0.124991i
$650$	−73.6205	+	42.5048i	−0.113262	+	0.0653921i
$651$	28.4729	−	76.7624i	0.0437372	−	0.117915i
$652$	−61.2231	−	35.3472i	−0.0939005	−	0.0542135i
$653$	469.925	−	813.934i	0.719640	−	1.24645i	−0.241503	−	0.970400i	$-0.577640\pi$
$653$	469.925	−	813.934i	0.719640	−	1.24645i	0.961143	−	0.276052i	$-0.0890263\pi$
$654$	−1329.68	+	226.070i	−2.03316	+	0.345673i
$655$	−25.3797	−	43.9590i	−0.0387477	−	0.0671130i
$656$	−348.897			−0.531856
$657$	260.231	−	302.526i	0.396090	−	0.460466i
$658$			307.657i			0.467565i
$659$	−257.584	+	148.716i	−0.390871	+	0.225669i	−0.682537	−	0.730851i	$-0.739124\pi$
$659$	−257.584	+	148.716i	−0.390871	+	0.225669i	0.291667	+	0.956520i	$0.405790\pi$
$660$	−8.44331	−	10.1884i	−0.0127929	−	0.0154370i
$661$	165.831	−	287.228i	0.250879	−	0.434535i	−0.712889	−	0.701277i	$-0.752614\pi$
$661$	165.831	−	287.228i	0.250879	−	0.434535i	0.963768	+	0.266742i	$0.0859471\pi$
$662$	−567.818	−	327.830i	−0.857732	−	0.495212i
$663$	−102.186	−	121.263i	−0.154127	−	0.182900i
$664$	291.779	+	505.377i	0.439427	+	0.761109i
$665$		−	337.734i		−	0.507870i
$666$	−28.4654	+	150.621i	−0.0427408	+	0.226158i
$667$	60.7061			0.0910136
$668$	−114.024	−	197.496i	−0.170695	−	0.295652i
$669$	32.9889	−	5.60871i	0.0493108	−	0.00838372i
$670$	−719.861	−	415.612i	−1.07442	−	0.620316i
$671$	−19.5230	−	11.2716i	−0.0290953	−	0.0167982i
$672$	63.5455	−	171.317i	0.0945617	−	0.254936i
$673$	505.629	−	291.925i	0.751307	−	0.433767i	−0.0748591	−	0.997194i	$-0.523851\pi$
$673$	505.629	−	291.925i	0.751307	−	0.433767i	0.826166	+	0.563427i	$0.190517\pi$
$674$	1159.71			1.72064
$675$	286.369	+	172.428i	0.424250	+	0.255448i
$676$	139.676			0.206622
$677$	−66.8519	−	115.791i	−0.0987473	−	0.171035i	0.812419	−	0.583074i	$-0.198150\pi$
$677$	−66.8519	−	115.791i	−0.0987473	−	0.171035i	−0.911166	+	0.412039i	$0.864817\pi$
$678$	−777.903	−	288.542i	−1.14735	−	0.425578i
$679$	−245.689	+	425.547i	−0.361840	+	0.626726i
$680$	−362.432	−	205.294i	−0.532988	−	0.301903i
$681$	−53.7548	+	9.13928i	−0.0789350	+	0.0134204i
$682$	9.66308	+	16.7370i	0.0141687	+	0.0245410i
$683$	−867.670			−1.27038			−0.635190	−	0.772356i	$-0.719078\pi$
$683$	−867.670			−1.27038			−0.635190	+	0.772356i	$0.719078\pi$
$684$	−160.286	+	56.1252i	−0.234336	+	0.0820544i
$685$		−	336.155i		−	0.490738i
$686$	−382.791	−	663.014i	−0.558005	−	0.966493i
$687$	−111.088	−	134.049i	−0.161701	−	0.195122i
$688$	−423.600	+	733.697i	−0.615698	+	1.06642i
$689$	149.200	+	86.1409i	0.216546	+	0.125023i
$690$	32.0305	−	26.5442i	0.0464210	−	0.0384698i
$691$	157.602	−	90.9914i	0.228078	−	0.131681i	−0.381607	−	0.924325i	$-0.624629\pi$
$691$	157.602	−	90.9914i	0.228078	−	0.131681i	0.609685	+	0.792644i	$0.291296\pi$
$692$	−115.459			−0.166849
$693$	18.6068	+	53.1382i	0.0268496	+	0.0766786i
$694$		−	927.289i		−	1.33615i
$695$	256.228	−	147.933i	0.368674	−	0.212854i
$696$	119.112	+	700.583i	0.171138	+	1.00659i
$697$	−156.008	+	275.420i	−0.223827	+	0.395151i
$698$	1049.45	+	605.898i	1.50351	+	0.868049i
$699$	410.065	−	1105.53i	0.586645	−	1.58158i
$700$	−41.5140	+	23.9681i	−0.0593057	+	0.0342402i
$701$		−	637.468i		−	0.909369i	−0.890653	−	0.454684i	$-0.849752\pi$
$701$		−	637.468i		−	0.909369i	0.890653	−	0.454684i	$-0.150248\pi$
$702$	89.7310	+	162.232i	0.127822	+	0.231099i
$703$		−	166.016i		−	0.236154i
$704$	−31.5136	−	54.5832i	−0.0447637	−	0.0775330i
$705$	−315.175	−	116.906i	−0.447057	−	0.165824i
$706$	510.304	−	883.872i	0.722810	−	1.25194i
$707$	207.608	−	359.588i	0.293646	−	0.508611i
$708$	−25.2464	−	148.492i	−0.0356587	−	0.209735i
$709$	−675.791	+	390.168i	−0.953160	+	0.550307i	−0.894061	−	0.447945i	$-0.852156\pi$
$709$	−675.791	+	390.168i	−0.953160	+	0.550307i	−0.0590992	+	0.998252i	$0.518823\pi$
$710$			791.345i			1.11457i
$711$	−697.990	−	131.911i	−0.981702	−	0.185528i
$712$	1038.15			1.45808
$713$	−9.45871	+	5.46099i	−0.0132661	+	0.00765917i
$714$	−320.545	−	380.385i	−0.448942	−	0.532753i
$715$	7.82231	−	13.5486i	0.0109403	−	0.0189491i
$716$	87.6766	+	50.6201i	0.122453	+	0.0706985i
$717$	359.441	−	297.874i	0.501312	−	0.415445i
$718$	416.431	+	721.279i	0.579987	+	1.00457i
$719$	−942.607			−1.31100			−0.655498	−	0.755197i	$-0.727541\pi$
$719$	−942.607			−1.31100			−0.655498	+	0.755197i	$0.727541\pi$
$720$	454.174	+	390.678i	0.630797	+	0.542608i
$721$			156.604i			0.217204i
$722$	195.708	−	112.992i	0.271063	−	0.156498i
$723$	−68.9699	−	405.662i	−0.0953941	−	0.561082i
$724$	−151.835	−	87.6617i	−0.209716	−	0.121080i
$725$	212.594	−	368.224i	0.293233	−	0.507895i
$726$	739.119	+	274.156i	1.01807	+	0.377626i
$727$	498.869	+	864.067i	0.686202	+	1.18854i	0.973057	+	0.230563i	$0.0740569\pi$
$727$	498.869	+	864.067i	0.686202	+	1.18854i	−0.286855	+	0.957974i	$0.592610\pi$
$728$	94.7240			0.130115
$729$	387.451	−	617.513i	0.531483	−	0.847069i
$730$	−347.831			−0.476481
$731$	389.771	+	662.459i	0.533202	+	0.906236i
$732$	−39.2457	−	14.5571i	−0.0536143	−	0.0198868i
$733$	416.123	−	720.746i	0.567698	−	0.983283i	−0.429095	−	0.903260i	$-0.641167\pi$
$733$	416.123	−	720.746i	0.567698	−	0.983283i	0.996793	−	0.0800230i	$-0.0254994\pi$
$734$	614.108	−	1063.67i	0.836660	−	1.44914i
$735$	309.855	−	52.6810i	0.421572	−	0.0716748i
$736$	−21.1098	+	12.1878i	−0.0286818	+	0.0165595i
$737$	−150.075			−0.203630
$738$	241.327	−	280.550i	0.327001	−	0.380149i
$739$	587.105			0.794458			0.397229	−	0.917719i	$-0.369972\pi$
$739$	587.105			0.794458			0.397229	+	0.917719i	$0.369972\pi$
$740$	20.8006	−	12.0092i	0.0281089	−	0.0162287i
$741$	−128.120	−	154.601i	−0.172901	−	0.208638i
$742$	468.022	+	270.212i	0.630757	+	0.364168i
$743$	271.448	−	470.162i	0.365341	−	0.632789i	−0.623490	−	0.781831i	$-0.714286\pi$
$743$	271.448	−	470.162i	0.365341	−	0.632789i	0.988831	+	0.149042i	$0.0476191\pi$
$744$	−81.5819	−	98.4439i	−0.109653	−	0.132317i
$745$	624.028	−	360.283i	0.837621	−	0.483601i
$746$		−	805.614i		−	1.07991i
$747$	−748.211	−	141.402i	−1.00162	−	0.189293i
$748$	21.1070	−	0.173613i	0.0282179	−	0.000232103i
$749$	−569.560	+	328.836i	−0.760427	+	0.439033i
$750$	−147.453	−	867.281i	−0.196604	−	1.15637i
$751$	−324.334	−	187.254i	−0.431869	−	0.249340i	0.268273	−	0.963343i	$-0.413547\pi$
$751$	−324.334	−	187.254i	−0.431869	−	0.249340i	−0.700143	+	0.714003i	$0.746880\pi$
$752$	511.866	+	295.526i	0.680673	+	0.392986i
$753$	660.990	+	245.176i	0.877809	+	0.325599i
$754$	204.223	−	117.908i	0.270853	−	0.156377i
$755$	−88.5700			−0.117311
$756$	50.5985	+	91.4811i	0.0669292	+	0.121007i
$757$	1006.50			1.32959			0.664795	−	0.747026i	$-0.268519\pi$
$757$	1006.50			1.32959			0.664795	+	0.747026i	$0.268519\pi$
$758$	613.212	+	1062.11i	0.808987	+	1.40121i
$759$	2.61201	−	7.04192i	0.00344138	−	0.00927789i
$760$	−456.753	−	263.707i	−0.600991	−	0.346982i
$761$	2.45474	+	1.41725i	0.00322568	+	0.00186235i	0.501612	−	0.865093i	$-0.332741\pi$
$761$	2.45474	+	1.41725i	0.00322568	+	0.00186235i	−0.498386	+	0.866955i	$0.666074\pi$
$762$	84.7923	+	498.726i	0.111276	+	0.654496i
$763$	−449.605	−	778.739i	−0.589260	−	1.02063i
$764$		−	54.3470i		−	0.0711348i
$765$	511.483	−	183.836i	0.668605	−	0.240309i
$766$	1137.83			1.48542
$767$	154.224	−	89.0413i	0.201074	−	0.116090i
$768$	−307.851	−	371.480i	−0.400848	−	0.483698i
$769$	−121.604	+	210.625i	−0.158133	+	0.273895i	−0.934195	−	0.356762i	$-0.883881\pi$
$769$	−121.604	+	210.625i	−0.158133	+	0.273895i	0.776062	+	0.630656i	$0.217214\pi$
$770$	24.5375	−	42.5002i	0.0318669	−	0.0551951i
$771$	−220.636	+	182.844i	−0.286169	+	0.237152i
$772$	−125.830	+	72.6478i	−0.162992	+	0.0941034i
$773$			1414.57i			1.82997i	0.403485	+	0.914986i	$0.367799\pi$
$773$			1414.57i			1.82997i	−0.403485	+	0.914986i	$0.632201\pi$
$774$	−296.970	−	848.105i	−0.383683	−	1.09574i
$775$			76.4980i			0.0987071i
$776$	383.674	+	664.544i	0.494426	+	0.856371i
$777$	−100.750	+	17.1293i	−0.129665	+	0.0220454i
$778$	−714.414	+	1237.40i	−0.918270	+	1.59049i
$779$	−200.396	+	347.097i	−0.257248	+	0.445567i
$780$	10.1024	−	27.2359i	0.0129518	−	0.0349178i
$781$	71.4376	+	123.734i	0.0914694	+	0.158430i
$782$	0.545805	+	66.3564i	0.000697960	+	0.0848548i
$783$	−794.387	−	478.314i	−1.01454	−	0.610873i
$784$	−552.623			−0.704876
$785$	452.176	+	783.191i	0.576020	+	0.997696i
$786$	−88.7535	−	32.9207i	−0.112918	−	0.0418838i
$787$	−940.172	−	542.809i	−1.19463	−	0.689719i	−0.235276	−	0.971929i	$-0.575599\pi$
$787$	−940.172	−	542.809i	−1.19463	−	0.689719i	−0.959353	+	0.282210i	$0.908933\pi$
$788$	−14.8632	+	25.7438i	−0.0188619	+	0.0326698i
$789$	181.916	+	1069.98i	0.230566	+	1.35613i
$790$	309.584	+	536.216i	0.391879	+	0.678754i
$791$		−	553.149i		−	0.699304i
$792$	86.3928	+	16.3271i	0.109082	+	0.0206150i
$793$		−	49.4895i		−	0.0624080i
$794$	−758.930	−	1314.51i	−0.955832	−	1.65555i
$795$	−454.657	+	376.781i	−0.571895	+	0.473938i
$796$	−164.050	−	94.7145i	−0.206093	−	0.118988i
$797$	−326.560	−	188.539i	−0.409736	−	0.236561i	0.280940	−	0.959725i	$-0.409354\pi$
$797$	−326.560	−	188.539i	−0.409736	−	0.236561i	−0.690676	+	0.723164i	$0.742687\pi$
$798$	−401.894	−	484.961i	−0.503627	−	0.607721i
$799$	462.166	−	271.925i	0.578431	−	0.340331i
$800$			170.727i			0.213409i
$801$	−883.385	+	1026.96i	−1.10285	+	1.28210i
$802$			532.186i			0.663573i
$803$	−54.3864	+	31.4000i	−0.0677290	+	0.0391034i
$804$	−274.720	+	46.7073i	−0.341691	+	0.0580936i
$805$	24.0186	+	13.8671i	0.0298367	+	0.0172262i
$806$	−21.2136	+	36.7430i	−0.0263196	+	0.0455868i
$807$	−438.860	+	1183.16i	−0.543816	+	1.46612i
$808$	−324.206	−	561.540i	−0.401244	−	0.694976i
$809$	335.596			0.414828			0.207414	−	0.978253i	$-0.433495\pi$
$809$	335.596			0.414828			0.207414	+	0.978253i	$0.433495\pi$
$810$	−628.290	+	94.9771i	−0.775667	+	0.117256i
$811$			1601.45i			1.97466i	0.158674	+	0.987331i	$0.449278\pi$
$811$			1601.45i			1.97466i	−0.158674	+	0.987331i	$0.550722\pi$
$812$	115.160	−	66.4875i	0.141822	−	0.0818812i
$813$	104.401	−	281.464i	0.128415	−	0.346204i
$814$	12.0617	−	20.8914i	0.0148178	−	0.0256651i
$815$	248.094	+	143.237i	0.304410	+	0.175751i
$816$	−940.772	+	167.921i	−1.15291	+	0.205786i
$817$	486.607	+	842.828i	0.595602	+	1.03161i
$818$		−	1272.29i		−	1.55536i
$819$	−80.6027	+	93.7030i	−0.0984160	+	0.114411i
$820$	−57.9849			−0.0707133
$821$	89.3883	+	154.825i	0.108877	+	0.188581i	0.915316	−	0.402737i	$-0.131941\pi$
$821$	89.3883	+	154.825i	0.108877	+	0.188581i	−0.806438	+	0.591318i	$0.798608\pi$
$822$	−400.016	−	482.694i	−0.486637	−	0.587219i
$823$	−447.254	−	258.222i	−0.543444	−	0.313758i	0.203030	−	0.979173i	$-0.434921\pi$
$823$	−447.254	−	258.222i	−0.543444	−	0.313758i	−0.746474	+	0.665415i	$0.768255\pi$
$824$	211.793	+	122.279i	0.257030	+	0.148396i
$825$	−33.5667	−	40.5045i	−0.0406869	−	0.0490964i
$826$	483.780	−	279.311i	0.585690	−	0.338148i
$827$	−602.569			−0.728620			−0.364310	−	0.931278i	$-0.618695\pi$
$827$	−602.569			−0.728620			−0.364310	+	0.931278i	$0.618695\pi$
$828$	2.58977	−	13.7035i	0.00312774	−	0.0165501i
$829$	667.735			0.805471			0.402735	−	0.915316i	$-0.368060\pi$
$829$	667.735			0.805471			0.402735	+	0.915316i	$0.368060\pi$
$830$	331.859	+	574.797i	0.399830	+	0.692526i
$831$	−274.991	−	1617.42i	−0.330915	−	1.94636i
$832$	69.1825	−	119.828i	0.0831521	−	0.144024i
$833$	−247.102	+	436.241i	−0.296641	+	0.523699i
$834$	191.888	−	517.327i	0.230082	−	0.620296i
$835$	462.060	+	800.312i	0.553365	+	0.958457i
$836$	26.7263			0.0319693
$837$	166.803	+	3.06551i	0.199286	+	0.00366250i
$838$			1757.87i			2.09770i
$839$	607.384	+	1052.02i	0.723938	+	1.25390i	0.959409	+	0.282017i	$0.0910034\pi$
$839$	607.384	+	1052.02i	0.723938	+	1.25390i	−0.235471	+	0.971881i	$0.575663\pi$
$840$	−112.908	+	304.397i	−0.134414	+	0.362377i
$841$	−169.236	+	293.125i	−0.201232	+	0.348543i
$842$	−201.268	−	116.202i	−0.239036	−	0.138007i
$843$	77.6801	+	456.894i	0.0921472	+	0.541985i
$844$	60.3458	−	34.8407i	0.0714997	−	0.0412804i
$845$	−566.010			−0.669834
$846$	−591.683	+	207.182i	−0.699389	+	0.244896i
$847$			525.571i			0.620509i
$848$	899.133	−	519.115i	1.06030	−	0.612163i
$849$	−736.197	+	610.097i	−0.867134	+	0.718607i
$850$	404.408	+	229.071i	0.475774	+	0.269495i
$851$	11.8065	+	6.81651i	0.0138737	+	0.00801001i
$852$	169.279	+	204.267i	0.198684	+	0.239750i
$853$	131.958	−	76.1857i	0.154698	−	0.0893150i	−0.420653	−	0.907222i	$-0.638199\pi$
$853$	131.958	−	76.1857i	0.154698	−	0.0893150i	0.575351	+	0.817907i	$0.304866\pi$
$854$		−	155.242i		−	0.181782i
$855$	649.525	−	227.436i	0.759679	−	0.266007i
$856$			1027.03i			1.19981i
$857$	−291.231	−	504.426i	−0.339826	−	0.588596i	0.644574	−	0.764542i	$-0.277035\pi$
$857$	−291.231	−	504.426i	−0.339826	−	0.588596i	−0.984400	+	0.175946i	$0.943701\pi$
$858$	−4.89026	−	28.7632i	−0.00569960	−	0.0335235i
$859$	−219.907	+	380.890i	−0.256004	+	0.443412i	−0.965168	−	0.261632i	$-0.915739\pi$
$859$	−219.907	+	380.890i	−0.256004	+	0.443412i	0.709164	+	0.705044i	$0.249073\pi$
$860$	−70.4000	+	121.936i	−0.0818605	+	0.141787i
$861$	231.318	+	85.8010i	0.268662	+	0.0996528i
$862$	−481.037	+	277.727i	−0.558048	+	0.322189i
$863$			1284.95i			1.48893i	0.667659	+	0.744467i	$0.267297\pi$
$863$			1284.95i			1.48893i	−0.667659	+	0.744467i	$0.732703\pi$
$864$	372.268	+	6.84156i	0.430866	+	0.00791847i
$865$	467.876			0.540897
$866$	472.552	−	272.828i	0.545672	−	0.315044i
$867$	−288.104	+	817.732i	−0.332300	+	0.943174i
$868$	−11.9621	+	20.7190i	−0.0137813	+	0.0238699i
$869$	96.8123	+	55.8946i	0.111407	+	0.0643206i
$870$	135.473	+	796.817i	0.155716	+	0.915882i
$871$	−164.732	−	285.324i	−0.189129	−	0.327582i
$872$	−1404.23			−1.61035
$873$	−983.858	−	185.936i	−1.12699	−	0.212985i
$874$			84.0225i			0.0961356i
$875$	507.929	−	293.253i	0.580491	−	0.335146i
$876$	−89.7843	+	74.4056i	−0.102493	+	0.0849379i
$877$	1065.73	+	615.297i	1.21519	+	0.701593i	0.963886	−	0.266315i	$-0.0858060\pi$
$877$	1065.73	+	615.297i	1.21519	+	0.701593i	0.251308	+	0.967907i	$0.419139\pi$
$878$	−684.598	+	1185.76i	−0.779725	+	1.35052i
$879$	−234.144	+	194.038i	−0.266375	+	0.220749i
$880$	−47.1399	−	81.6487i	−0.0535681	−	0.0927826i
$881$	−168.980			−0.191804			−0.0959022	−	0.995391i	$-0.530574\pi$
$881$	−168.980			−0.191804			−0.0959022	+	0.995391i	$0.530574\pi$
$882$	382.241	−	444.366i	0.433380	−	0.503816i
$883$	−1721.94			−1.95011			−0.975053	−	0.221971i	$-0.928751\pi$
$883$	−1721.94			−1.95011			−0.975053	+	0.221971i	$0.928751\pi$
$884$	23.4984	+	39.9382i	0.0265819	+	0.0451789i
$885$	102.306	+	601.735i	0.115600	+	0.679927i
$886$	409.446	−	709.181i	0.462128	−	0.800430i
$887$	−47.2929	+	81.9137i	−0.0533178	+	0.0923492i	−0.891452	−	0.453114i	$-0.850313\pi$
$887$	−47.2929	+	81.9137i	−0.0533178	+	0.0923492i	0.838135	+	0.545463i	$0.183646\pi$
$888$	−55.5008	+	149.629i	−0.0625009	+	0.168501i
$889$	−292.082	+	168.634i	−0.328551	+	0.189689i
$890$	1180.75			1.32669
$891$	−89.6647	+	71.5686i	−0.100634	+	0.0803239i
$892$	−9.77810			−0.0109620
$893$	588.001	−	339.483i	0.658456	−	0.380160i
$894$	467.331	−	1259.92i	0.522742	−	1.40930i
$895$	−355.292	−	205.128i	−0.396974	−	0.229193i
$896$	338.831	−	586.873i	0.378160	−	0.654993i
$897$	16.2552	−	2.76368i	0.0181218	−	0.00308102i
$898$	868.669	−	501.526i	0.967338	−	0.558493i
$899$		−	212.205i		−	0.236046i
$900$	−74.0515	−	63.6986i	−0.0822794	−	0.0707762i
$901$	−7.74743	−	941.896i	−0.00859870	−	1.04539i
$902$	−50.4356	+	29.1190i	−0.0559153	+	0.0322827i
$903$	461.276	−	382.267i	0.510827	−	0.423330i
$904$	−748.082	−	431.905i	−0.827524	−	0.477771i
$905$	615.279	+	355.232i	0.679866	+	0.392521i
$906$	−127.180	+	105.396i	−0.140375	+	0.116331i
$907$	336.689	−	194.387i	0.371212	−	0.214319i	−0.302776	−	0.953062i	$-0.597913\pi$
$907$	336.689	−	194.387i	0.371212	−	0.214319i	0.673988	+	0.738743i	$0.264580\pi$
$908$	15.9332			0.0175476
$909$	831.362	+	157.116i	0.914589	+	0.172845i
$910$	107.736			0.118391
$911$	10.7455	+	18.6118i	0.0117953	+	0.0204301i	0.871863	−	0.489750i	$-0.162912\pi$
$911$	10.7455	+	18.6118i	0.0117953	+	0.0204301i	−0.860067	+	0.510180i	$0.829579\pi$
$912$	−1192.90	+	202.815i	−1.30801	+	0.222385i
$913$	103.778	+	59.9162i	0.113667	+	0.0656257i
$914$	−1579.36	−	911.845i	−1.72797	−	0.997642i
$915$	159.035	+	58.9898i	0.173809	+	0.0644697i
$916$	25.4367	+	44.0576i	0.0277693	+	0.0480978i
$917$		−	63.1106i		−	0.0688229i
$918$	515.692	−	872.626i	0.561756	−	0.950573i
$919$	−987.516			−1.07456			−0.537278	−	0.843406i	$-0.680547\pi$
$919$	−987.516			−1.07456			−0.537278	+	0.843406i	$0.680547\pi$
$920$	37.5079	−	21.6552i	0.0407695	−	0.0235383i
$921$	119.725	−	322.775i	0.129994	−	0.350462i
$922$	−476.104	+	824.637i	−0.516382	+	0.894400i
$923$	−156.828	+	271.635i	−0.169912	+	0.294296i
$924$	−2.75757	−	16.2193i	−0.00298439	−	0.0175534i
$925$	82.6936	−	47.7432i	0.0893985	−	0.0516142i
$926$			1136.60i			1.22742i
$927$	−301.180	+	105.460i	−0.324897	+	0.113765i
$928$		−	473.597i		−	0.510342i
$929$	360.372	+	624.183i	0.387914	+	0.671887i	0.992169	−	0.124904i	$-0.0398623\pi$
$929$	360.372	+	624.183i	0.387914	+	0.671887i	−0.604254	+	0.796791i	$0.706529\pi$
$930$	−92.7883	−	111.966i	−0.0997723	−	0.120394i
$931$	−317.410	+	549.771i	−0.340935	+	0.590516i
$932$	−172.278	+	298.394i	−0.184848	+	0.320165i
$933$	−187.743	−	226.547i	−0.201225	−	0.242816i
$934$	501.129	+	867.981i	0.536541	+	0.929316i
$935$	−85.5320	+	0.703531i	−0.0914780	+	0.000752439i
$936$	63.7889	+	182.172i	0.0681505	+	0.194628i
$937$	726.411			0.775251			0.387626	−	0.921817i	$-0.373295\pi$
$937$	726.411			0.775251			0.387626	+	0.921817i	$0.373295\pi$
$938$	−516.741	−	895.021i	−0.550896	−	0.954181i
$939$	−160.260	−	942.609i	−0.170671	−	1.00384i
$940$	85.0693	+	49.1148i	0.0904993	+	0.0522498i
$941$	699.817	−	1212.12i	0.743695	−	1.28812i	−0.207108	−	0.978318i	$-0.566405\pi$
$941$	699.817	−	1212.12i	0.743695	−	1.28812i	0.950802	−	0.309799i	$-0.100262\pi$
$942$	1581.27	+	586.528i	1.67863	+	0.622641i
$943$	−16.4563	−	28.5031i	−0.0174510	−	0.0302260i
$944$		−	1073.19i		−	1.13685i
$945$	−205.040	−	370.709i	−0.216974	−	0.392284i
$946$			141.415i			0.149487i
$947$	777.033	+	1345.86i	0.820520	+	1.42118i	0.905295	+	0.424783i	$0.139650\pi$
$947$	777.033	+	1345.86i	0.820520	+	1.42118i	−0.0847748	+	0.996400i	$0.527017\pi$
$948$	194.615	+	72.1872i	0.205290	+	0.0761468i
$949$	−119.396	−	68.9331i	−0.125812	−	0.0726376i
$950$	509.653	+	294.249i	0.536477	+	0.309735i
$951$	−501.246	+	85.2208i	−0.527072	+	0.0896117i
$952$	−262.625	−	446.361i	−0.275867	−	0.468867i
$953$		−	770.289i		−	0.808278i	−0.914698	−	0.404139i	$-0.867571\pi$
$953$		−	770.289i		−	0.808278i	0.914698	−	0.404139i	$-0.132429\pi$
$954$	−204.495	+	1082.06i	−0.214355	+	1.13423i
$955$			220.230i			0.230608i
$956$	−118.137	+	68.2062i	−0.123574	+	0.0713454i
$957$	93.1140	+	112.360i	0.0972978	+	0.117408i
$958$	−892.914	−	515.524i	−0.932061	−	0.538126i
$959$	208.975	−	361.956i	0.217910	−	0.377430i
$960$	302.605	+	365.149i	0.315213	+	0.380364i
$961$	−461.410	−	799.186i	−0.480136	−	0.831620i
$962$	52.9584			0.0550503
$963$	−1015.96	−	873.926i	−1.05500	−	0.907504i
$964$			120.241i			0.124731i
$965$	509.900	−	294.391i	0.528394	−	0.305068i
$966$	50.9904	−	8.66928i	0.0527851	−	0.00897441i
$967$	−65.1526	+	112.848i	−0.0673760	+	0.116699i	−0.897745	−	0.440515i	$-0.854796\pi$
$967$	−65.1526	+	112.848i	−0.0673760	+	0.116699i	0.830369	+	0.557213i	$0.188129\pi$
$968$	710.785	+	410.372i	0.734282	+	0.423938i
$969$	−373.297	+	1032.37i	−0.385240	+	1.06539i
$970$	436.377	+	755.827i	0.449873	+	0.779203i
$971$		−	643.927i		−	0.663158i	−0.943427	−	0.331579i	$-0.892419\pi$
$971$		−	643.927i		−	0.663158i	0.943427	−	0.331579i	$-0.107581\pi$
$972$	−141.861	+	158.915i	−0.145948	+	0.163493i
$973$	367.859			0.378067
$974$	−674.398	−	1168.09i	−0.692400	−	1.19927i
$975$	40.1625	−	108.277i	0.0411923	−	0.111054i
$976$	−258.284	−	149.120i	−0.264635	−	0.152787i
$977$	−417.532	−	241.062i	−0.427362	−	0.246737i	0.270860	−	0.962619i	$-0.412692\pi$
$977$	−417.532	−	241.062i	−0.427362	−	0.246737i	−0.698222	+	0.715881i	$0.746025\pi$
$978$	526.694	−	89.5475i	0.538542	−	0.0915618i
$979$	184.621	−	106.591i	0.188581	−	0.108877i
$980$	−91.8429			−0.0937173
$981$	1194.89	−	1389.09i	1.21803	−	1.41600i
$982$	−401.591			−0.408952
$983$	−806.156	−	1396.30i	−0.820097	−	1.42045i	−0.905609	−	0.424113i	$-0.860586\pi$
$983$	−806.156	−	1396.30i	−0.820097	−	1.42045i	0.0855119	−	0.996337i	$-0.472747\pi$
$984$	296.653	−	245.841i	0.301477	−	0.249839i
$985$	60.2301	−	104.322i	0.0611474	−	0.105910i
$986$	−1121.83	−	635.443i	−1.13776	−	0.644465i
$987$	−266.689	−	321.811i	−0.270202	−	0.326050i
$988$	29.3364	+	50.8122i	0.0296928	+	0.0514294i
$989$	−79.9190			−0.0808079
$990$	98.2600	+	18.5698i	0.0992525	+	0.0187574i
$991$		−	1219.44i		−	1.23051i	−0.788327	−	0.615257i	$-0.789052\pi$
$991$		−	1219.44i		−	1.23051i	0.788327	−	0.615257i	$-0.210948\pi$
$992$	42.6038	+	73.7919i	0.0429473	+	0.0743870i
$993$	878.116	−	149.295i	0.884306	−	0.150348i
$994$	−491.950	+	852.082i	−0.494919	+	0.857225i
$995$	664.781	+	383.811i	0.668122	+	0.385740i
$996$	208.618	+	77.3811i	0.209456	+	0.0776918i
$997$	563.615	−	325.403i	0.565311	−	0.326383i	−0.189963	−	0.981791i	$-0.560837\pi$
$997$	563.615	−	325.403i	0.565311	−	0.326383i	0.755274	+	0.655409i	$0.227504\pi$
$998$	1614.75			1.61798
$999$	−100.789	−	182.225i	−0.100890	−	0.182408i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.3.i.a.50.27	✓	68
3.2	odd	2		459.3.i.a.152.7		68
9.2	odd	6	inner	153.3.i.a.101.28	yes	68
9.7	even	3		459.3.i.a.305.8		68
17.16	even	2	inner	153.3.i.a.50.28	yes	68
51.50	odd	2		459.3.i.a.152.8		68
153.16	even	6		459.3.i.a.305.7		68
153.101	odd	6	inner	153.3.i.a.101.27	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.i.a.50.27	✓	68	1.1	even	1	trivial
153.3.i.a.50.28	yes	68	17.16	even	2	inner
153.3.i.a.101.27	yes	68	153.101	odd	6	inner
153.3.i.a.101.28	yes	68	9.2	odd	6	inner
459.3.i.a.152.7		68	3.2	odd	2
459.3.i.a.152.8		68	51.50	odd	2
459.3.i.a.305.7		68	153.16	even	6
459.3.i.a.305.8		68	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.91245 - 1.10416i) q^{2} +(-1.04331 + 2.81274i) q^{3} +(0.438319 - 0.759190i) q^{4} +(-1.77620 + 3.07647i) q^{5} +(1.11042 + 6.53121i) q^{6} +(-3.82505 + 2.20839i) q^{7} +6.89736i q^{8} +(-6.82301 - 5.86911i) q^{9} +7.84480i q^{10} +(0.708179 + 1.22660i) q^{11} +(1.67810 + 2.02495i) q^{12} +(-1.55468 + 2.69278i) q^{13} +(-4.87682 + 8.44690i) q^{14} +(-6.80018 - 8.20569i) q^{15} +(9.36903 + 16.2276i) q^{16} +(16.9994 - 0.139826i) q^{17} +(-19.5291 - 3.69074i) q^{18} +21.5252 q^{19} +(1.55708 + 2.69694i) q^{20} +(-2.22093 - 13.0629i) q^{21} +(2.70872 + 1.56388i) q^{22} +(-0.883809 + 1.53080i) q^{23} +(-19.4005 - 7.19607i) q^{24} +(6.19024 + 10.7218i) q^{25} +6.86643i q^{26} +(23.6268 - 13.0681i) q^{27} +3.87192i q^{28} +(-17.1717 - 29.7423i) q^{29} +(-22.0654 - 8.18455i) q^{30} +(5.35110 + 3.08946i) q^{31} +(11.9425 + 6.89502i) q^{32} +(-4.18896 + 0.712198i) q^{33} +(32.3562 - 19.0374i) q^{34} -15.6902i q^{35} +(-7.44643 + 2.60742i) q^{36} -7.71265i q^{37} +(41.1659 - 23.7671i) q^{38} +(-5.95209 - 7.18231i) q^{39} +(-21.2195 - 12.2511i) q^{40} +(-9.30986 + 16.1252i) q^{41} +(-18.6709 - 22.5299i) q^{42} +(22.6064 + 39.1554i) q^{43} +1.24163 q^{44} +(30.1752 - 10.5661i) q^{45} +3.90345i q^{46} +(27.3169 - 15.7714i) q^{47} +(-55.4189 + 9.42221i) q^{48} +(-14.7460 + 25.5408i) q^{49} +(23.6771 + 13.6700i) q^{50} +(-17.3424 + 47.9608i) q^{51} +(1.36289 + 2.36059i) q^{52} -55.4075i q^{53} +(30.7560 - 51.0797i) q^{54} -5.03146 q^{55} +(-15.2321 - 26.3827i) q^{56} +(-22.4574 + 60.5447i) q^{57} +(-65.6802 - 37.9205i) q^{58} +(-49.6000 - 28.6366i) q^{59} +(-9.21032 + 1.56592i) q^{60} +(-13.7839 + 7.95816i) q^{61} +13.6450 q^{62} +(39.0597 + 7.38175i) q^{63} -44.4995 q^{64} +(-5.52284 - 9.56584i) q^{65} +(-7.22481 + 5.98731i) q^{66} +(-52.9793 + 91.7628i) q^{67} +(7.34501 - 12.9671i) q^{68} +(-3.38366 - 4.08302i) q^{69} +(-17.3244 - 30.0067i) q^{70} +100.875 q^{71} +(40.4814 - 47.0608i) q^{72} +44.3391i q^{73} +(-8.51597 - 14.7501i) q^{74} +(-36.6160 + 6.22537i) q^{75} +(9.43489 - 16.3417i) q^{76} +(-5.41764 - 3.12787i) q^{77} +(-19.3135 - 7.16381i) q^{78} +(68.3530 - 39.4636i) q^{79} -66.5650 q^{80} +(12.1070 + 80.0901i) q^{81} +41.1181i q^{82} +(73.2711 - 42.3031i) q^{83} +(-10.8907 - 4.03961i) q^{84} +(-29.7642 + 52.5465i) q^{85} +(86.4674 + 49.9220i) q^{86} +(101.573 - 17.2692i) q^{87} +(-8.46031 + 4.88456i) q^{88} -150.514i q^{89} +(46.0420 - 53.5252i) q^{90} -13.7334i q^{91} +(0.774780 + 1.34196i) q^{92} +(-14.2727 + 11.8280i) q^{93} +(34.8282 - 60.3242i) q^{94} +(-38.2330 + 66.2215i) q^{95} +(-31.8536 + 26.3976i) q^{96} +(96.3476 - 55.6263i) q^{97} +65.1275i q^{98} +(2.36715 - 12.5255i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 6 q^{2} + 62 q^{4} - 8 q^{9} - 2 q^{13} - 106 q^{16} - 2 q^{18} - 32 q^{19} - 28 q^{21} - 132 q^{25} + 180 q^{30} - 98 q^{33} - 27 q^{34} + 158 q^{36} - 102 q^{38} + 110 q^{42} + 58 q^{43} - 312 q^{47}+ \cdots - 18 q^{94}+O(q^{100}) \) 68 * q - 6 * q^2 + 62 * q^4 - 8 * q^9 - 2 * q^13 - 106 * q^16 - 2 * q^18 - 32 * q^19 - 28 * q^21 - 132 * q^25 + 180 * q^30 - 98 * q^33 - 27 * q^34 + 158 * q^36 - 102 * q^38 + 110 * q^42 + 58 * q^43 - 312 * q^47 + 152 * q^49 - 90 * q^50 - 17 * q^51 + 70 * q^52 + 92 * q^55 - 258 * q^59 - 126 * q^60 - 16 * q^64 + 400 * q^66 + 82 * q^67 - 333 * q^68 + 404 * q^69 + 204 * q^70 + 474 * q^72 + 34 * q^76 - 60 * q^77 - 88 * q^81 - 690 * q^83 - 200 * q^84 - 44 * q^85 - 1248 * q^86 + 114 * q^87 + 50 * q^93 - 18 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more