LMFDB - Embedded newform 220.3.i.a.43.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,3,Mod(43,220)] 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("220.43"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 2])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.i (of order $4$, 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:	$5.99456581593$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.16
Character	$\chi$	$=$	220.43
Dual form			220.3.i.a.87.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.49067 + 1.33338i) q^{2} +(-3.87627 + 3.87627i) q^{3} +(0.444207 - 3.97526i) q^{4} +(3.64792 + 3.41945i) q^{5} +(0.609714 - 10.9468i) q^{6} +(5.44609 - 5.44609i) q^{7} +(4.63836 + 6.51810i) q^{8} -21.0509i q^{9} +(-9.99728 - 0.233225i) q^{10} +(7.73363 - 7.82247i) q^{11} +(13.6873 + 17.1310i) q^{12} +(14.7946 - 14.7946i) q^{13} +(-0.856637 + 15.3800i) q^{14} +(-27.3951 + 0.885606i) q^{15} +(-15.6054 - 3.53167i) q^{16} +(5.69580 + 5.69580i) q^{17} +(28.0688 + 31.3800i) q^{18} -21.1920i q^{19} +(15.2136 - 12.9825i) q^{20} +42.2210i q^{21} +(-1.09800 + 21.9726i) q^{22} +(-7.64133 + 7.64133i) q^{23} +(-43.2454 - 7.28640i) q^{24} +(1.61467 + 24.9478i) q^{25} +(-2.32710 + 41.7806i) q^{26} +(46.7126 + 46.7126i) q^{27} +(-19.2304 - 24.0688i) q^{28} -2.11660 q^{29} +(39.6562 - 37.8481i) q^{30} -23.3398i q^{31} +(27.9715 - 15.5433i) q^{32} +(0.344346 + 60.2996i) q^{33} +(-16.0852 - 0.895915i) q^{34} +(38.4895 - 1.24426i) q^{35} +(-83.6829 - 9.35096i) q^{36} +(7.12170 - 7.12170i) q^{37} +(28.2570 + 31.5904i) q^{38} +114.695i q^{39} +(-5.36799 + 39.6382i) q^{40} -13.4770i q^{41} +(-56.2965 - 62.9377i) q^{42} +(-18.4300 - 18.4300i) q^{43} +(-27.6610 - 34.2180i) q^{44} +(71.9827 - 76.7922i) q^{45} +(1.20194 - 21.5795i) q^{46} +(-25.7009 - 25.7009i) q^{47} +(74.1803 - 46.8009i) q^{48} -10.3197i q^{49} +(-35.6718 - 35.0360i) q^{50} -44.1569 q^{51} +(-52.2403 - 65.3840i) q^{52} +(-10.8004 - 10.8004i) q^{53} +(-131.919 - 7.34763i) q^{54} +(54.9602 - 2.09095i) q^{55} +(60.7590 + 10.2373i) q^{56} +(82.1460 + 82.1460i) q^{57} +(3.15516 - 2.82223i) q^{58} +84.0088 q^{59} +(-8.64855 + 109.296i) q^{60} -87.3519i q^{61} +(31.1207 + 34.7919i) q^{62} +(-114.645 - 114.645i) q^{63} +(-20.9713 + 60.4666i) q^{64} +(104.559 - 3.38009i) q^{65} +(-80.9155 - 89.4278i) q^{66} +(55.9563 + 55.9563i) q^{67} +(25.1724 - 20.1122i) q^{68} -59.2397i q^{69} +(-55.7162 + 53.1759i) q^{70} +24.0536i q^{71} +(137.212 - 97.6417i) q^{72} +(-69.0302 + 69.0302i) q^{73} +(-1.12020 + 20.1120i) q^{74} +(-102.963 - 90.4455i) q^{75} +(-84.2438 - 9.41364i) q^{76} +(-0.483800 - 84.7198i) q^{77} +(-152.932 - 170.973i) q^{78} +47.8344i q^{79} +(-44.8508 - 66.2451i) q^{80} -172.683 q^{81} +(17.9699 + 20.0898i) q^{82} +(11.0631 + 11.0631i) q^{83} +(167.839 + 18.7548i) q^{84} +(1.30131 + 40.2543i) q^{85} +(52.0472 + 2.89893i) q^{86} +(8.20451 - 8.20451i) q^{87} +(86.8590 + 14.1252i) q^{88} +90.4306i q^{89} +(-4.90960 + 210.452i) q^{90} -161.145i q^{91} +(26.9819 + 33.7706i) q^{92} +(90.4712 + 90.4712i) q^{93} +(72.5807 + 4.04261i) q^{94} +(72.4652 - 77.3069i) q^{95} +(-48.1752 + 168.675i) q^{96} +(-88.2136 + 88.2136i) q^{97} +(13.7601 + 15.3833i) q^{98} +(-164.670 - 162.800i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 8 q^{5} + 8 q^{12} + 16 q^{16} + 80 q^{20} - 96 q^{22} - 8 q^{25} - 160 q^{26} + 80 q^{33} - 104 q^{36} - 8 q^{37} - 16 q^{38} - 168 q^{42} + 192 q^{45} + 32 q^{48} + 136 q^{53} + 264 q^{56} - 248 q^{58}+ \cdots - 168 q^{97}+O(q^{100}) $ 136 * q - 8 * q^5 + 8 * q^12 + 16 * q^16 + 80 * q^20 - 96 * q^22 - 8 * q^25 - 160 * q^26 + 80 * q^33 - 104 * q^36 - 8 * q^37 - 16 * q^38 - 168 * q^42 + 192 * q^45 + 32 * q^48 + 136 * q^53 + 264 * q^56 - 248 * q^58 - 128 * q^60 + 328 * q^66 + 96 * q^70 - 152 * q^77 - 24 * q^78 - 624 * q^80 - 664 * q^81 - 200 * q^82 + 752 * q^86 - 296 * q^88 - 776 * q^92 + 592 * q^93 - 168 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.49067	+	1.33338i	−0.745336	+	0.666689i
$2$	−1.49067	+	1.33338i	−0.745336	+	0.666689i
$3$	−3.87627	+	3.87627i	−1.29209	+	1.29209i	−0.358598	+	0.933492i	$0.616745\pi$
$3$	−3.87627	+	3.87627i	−1.29209	+	1.29209i	−0.933492	+	0.358598i	$0.883255\pi$
$4$	0.444207	−	3.97526i	0.111052	−	0.993815i
$5$	3.64792	+	3.41945i	0.729584	+	0.683891i
$5$	3.64792	+	3.41945i	0.729584	+	0.683891i
$6$	0.609714	−	10.9468i	0.101619	−	1.82446i
$7$	5.44609	−	5.44609i	0.778012	−	0.778012i	−0.201480	−	0.979493i	$-0.564575\pi$
$7$	5.44609	−	5.44609i	0.778012	−	0.778012i	0.979493	+	0.201480i	$0.0645752\pi$
$8$	4.63836	+	6.51810i	0.579794	+	0.814763i
$9$		−	21.0509i		−	2.33899i
$10$	−9.99728	−	0.233225i	−0.999728	−	0.0233225i
$11$	7.73363	−	7.82247i	0.703057	−	0.711133i
$11$	7.73363	−	7.82247i	0.703057	−	0.711133i
$12$	13.6873	+	17.1310i	1.14061	+	1.42759i
$13$	14.7946	−	14.7946i	1.13804	−	1.13804i	0.149242	−	0.988801i	$-0.452317\pi$
$13$	14.7946	−	14.7946i	1.13804	−	1.13804i	0.988801	−	0.149242i	$-0.0476834\pi$
$14$	−0.856637	+	15.3800i	−0.0611884	+	1.09857i
$15$	−27.3951	+	0.885606i	−1.82634	+	0.0590404i
$16$	−15.6054	−	3.53167i	−0.975335	−	0.220729i
$17$	5.69580	+	5.69580i	0.335047	+	0.335047i	0.854499	−	0.519452i	$-0.173864\pi$
$17$	5.69580	+	5.69580i	0.335047	+	0.335047i	−0.519452	+	0.854499i	$0.673864\pi$
$18$	28.0688	+	31.3800i	1.55938	+	1.74334i
$19$		−	21.1920i		−	1.11537i	−0.830053	−	0.557685i	$-0.811690\pi$
$19$		−	21.1920i		−	1.11537i	0.830053	−	0.557685i	$-0.188310\pi$
$20$	15.2136	−	12.9825i	0.760682	−	0.649125i
$21$			42.2210i			2.01052i
$22$	−1.09800	+	21.9726i	−0.0499093	+	0.998754i
$23$	−7.64133	+	7.64133i	−0.332232	+	0.332232i	−0.853434	−	0.521202i	$-0.825484\pi$
$23$	−7.64133	+	7.64133i	−0.332232	+	0.332232i	0.521202	+	0.853434i	$0.325484\pi$
$24$	−43.2454	−	7.28640i	−1.80189	−	0.303600i
$25$	1.61467	+	24.9478i	0.0645869	+	0.997912i
$26$	−2.32710	+	41.7806i	−0.0895037	+	1.60694i
$27$	46.7126	+	46.7126i	1.73010	+	1.73010i
$28$	−19.2304	−	24.0688i	−0.686801	−	0.859600i
$29$	−2.11660			−0.0729862			−0.0364931	−	0.999334i	$-0.511619\pi$
$29$	−2.11660			−0.0729862			−0.0364931	+	0.999334i	$0.511619\pi$
$30$	39.6562	−	37.8481i	1.32187	−	1.26160i
$31$		−	23.3398i		−	0.752896i	−0.926438	−	0.376448i	$-0.877145\pi$
$31$		−	23.3398i		−	0.752896i	0.926438	−	0.376448i	$-0.122855\pi$
$32$	27.9715	−	15.5433i	0.874110	−	0.485728i
$33$	0.344346	+	60.2996i	0.0104347	+	1.82726i
$34$	−16.0852	−	0.895915i	−0.473095	−	0.0263505i
$35$	38.4895	−	1.24426i	1.09970	−	0.0355503i
$36$	−83.6829	−	9.35096i	−2.32452	−	0.259749i
$37$	7.12170	−	7.12170i	0.192478	−	0.192478i	−0.604288	−	0.796766i	$-0.706542\pi$
$37$	7.12170	−	7.12170i	0.192478	−	0.192478i	0.796766	+	0.604288i	$0.206542\pi$
$38$	28.2570	+	31.5904i	0.743605	+	0.831326i
$39$			114.695i			2.94091i
$40$	−5.36799	+	39.6382i	−0.134200	+	0.990954i
$41$		−	13.4770i		−	0.328707i	−0.986401	−	0.164354i	$-0.947446\pi$
$41$		−	13.4770i		−	0.328707i	0.986401	−	0.164354i	$-0.0525538\pi$
$42$	−56.2965	−	62.9377i	−1.34039	−	1.49852i
$43$	−18.4300	−	18.4300i	−0.428604	−	0.428604i	0.459548	−	0.888153i	$-0.348011\pi$
$43$	−18.4300	−	18.4300i	−0.428604	−	0.428604i	−0.888153	+	0.459548i	$0.848011\pi$
$44$	−27.6610	−	34.2180i	−0.628659	−	0.777681i
$45$	71.9827	−	76.7922i	1.59962	−	1.70649i
$46$	1.20194	−	21.5795i	0.0261291	−	0.469120i
$47$	−25.7009	−	25.7009i	−0.546829	−	0.546829i	0.378694	−	0.925522i	$-0.376373\pi$
$47$	−25.7009	−	25.7009i	−0.546829	−	0.546829i	−0.925522	+	0.378694i	$0.876373\pi$
$48$	74.1803	−	46.8009i	1.54542	−	0.975018i
$49$		−	10.3197i		−	0.210606i
$50$	−35.6718	−	35.0360i	−0.713436	−	0.700720i
$51$	−44.1569			−0.865821
$52$	−52.2403	−	65.3840i	−1.00462	−	1.25739i
$53$	−10.8004	−	10.8004i	−0.203782	−	0.203782i	0.597836	−	0.801618i	$-0.296027\pi$
$53$	−10.8004	−	10.8004i	−0.203782	−	0.203782i	−0.801618	+	0.597836i	$0.796027\pi$
$54$	−131.919	−	7.34763i	−2.44294	−	0.136067i
$55$	54.9602	−	2.09095i	0.999277	−	0.0380173i
$56$	60.7590	+	10.2373i	1.08498	+	0.182808i
$57$	82.1460	+	82.1460i	1.44116	+	1.44116i
$58$	3.15516	−	2.82223i	0.0543992	−	0.0486591i
$59$	84.0088			1.42388			0.711939	−	0.702242i	$-0.247817\pi$
$59$	84.0088			1.42388			0.711939	+	0.702242i	$0.247817\pi$
$60$	−8.64855	+	109.296i	−0.144142	+	1.82160i
$61$		−	87.3519i		−	1.43200i	−0.698101	−	0.715999i	$-0.745971\pi$
$61$		−	87.3519i		−	1.43200i	0.698101	−	0.715999i	$-0.254029\pi$
$62$	31.1207	+	34.7919i	0.501947	+	0.561160i
$63$	−114.645	−	114.645i	−1.81976	−	1.81976i
$64$	−20.9713	+	60.4666i	−0.327677	+	0.944790i
$65$	104.559	−	3.38009i	1.60860	−	0.0520014i
$66$	−80.9155	−	89.4278i	−1.22599	−	1.35497i
$67$	55.9563	+	55.9563i	0.835169	+	0.835169i	0.988218	−	0.153050i	$-0.0489095\pi$
$67$	55.9563	+	55.9563i	0.835169	+	0.835169i	−0.153050	+	0.988218i	$0.548909\pi$
$68$	25.1724	−	20.1122i	0.370182	−	0.295767i
$69$		−	59.2397i		−	0.858547i
$70$	−55.7162	+	53.1759i	−0.795946	+	0.759656i
$71$			24.0536i			0.338784i	0.985549	+	0.169392i	$0.0541804\pi$
$71$			24.0536i			0.338784i	−0.985549	+	0.169392i	$0.945820\pi$
$72$	137.212	−	97.6417i	1.90572	−	1.35613i
$73$	−69.0302	+	69.0302i	−0.945619	+	0.945619i	−0.998596	−	0.0529764i	$-0.983129\pi$
$73$	−69.0302	+	69.0302i	−0.945619	+	0.945619i	0.0529764	+	0.998596i	$0.483129\pi$
$74$	−1.12020	+	20.1120i	−0.0151379	+	0.271784i
$75$	−102.963	−	90.4455i	−1.37284	−	1.20594i
$76$	−84.2438	−	9.41364i	−1.10847	−	0.123864i
$77$	−0.483800	−	84.7198i	−0.00628312	−	1.10026i
$78$	−152.932	−	170.973i	−1.96067	−	2.19196i
$79$			47.8344i			0.605499i	0.953070	+	0.302749i	$0.0979045\pi$
$79$			47.8344i			0.605499i	−0.953070	+	0.302749i	$0.902095\pi$
$80$	−44.8508	−	66.2451i	−0.560634	−	0.828063i
$81$	−172.683			−2.13189
$82$	17.9699	+	20.0898i	0.219145	+	0.244997i
$83$	11.0631	+	11.0631i	0.133290	+	0.133290i	0.770604	−	0.637314i	$-0.219955\pi$
$83$	11.0631	+	11.0631i	0.133290	+	0.133290i	−0.637314	+	0.770604i	$0.719955\pi$
$84$	167.839	+	18.7548i	1.99809	+	0.223272i
$85$	1.30131	+	40.2543i	0.0153095	+	0.473580i
$86$	52.0472	+	2.89893i	0.605200	+	0.0337085i
$87$	8.20451	−	8.20451i	0.0943047	−	0.0943047i
$88$	86.8590	+	14.1252i	0.987034	+	0.160514i
$89$			90.4306i			1.01607i	0.861335	+	0.508037i	$0.169629\pi$
$89$			90.4306i			1.01607i	−0.861335	+	0.508037i	$0.830371\pi$
$90$	−4.90960	+	210.452i	−0.0545511	+	2.33836i
$91$		−	161.145i		−	1.77082i
$92$	26.9819	+	33.7706i	0.293282	+	0.367072i
$93$	90.4712	+	90.4712i	0.972809	+	0.972809i
$94$	72.5807	+	4.04261i	0.772136	+	0.0430065i
$95$	72.4652	−	77.3069i	0.762791	−	0.813757i
$96$	−48.1752	+	168.675i	−0.501825	+	1.75703i
$97$	−88.2136	+	88.2136i	−0.909418	+	0.909418i	−0.996225	−	0.0868070i	$-0.972334\pi$
$97$	−88.2136	+	88.2136i	−0.909418	+	0.909418i	0.0868070	+	0.996225i	$0.472334\pi$
$98$	13.7601	+	15.3833i	0.140409	+	0.156973i
$99$	−164.670	−	162.800i	−1.66333	−	1.64445i
$100$	99.8912	+	4.66323i	0.998912	+	0.0466323i
$101$		−	52.6106i		−	0.520897i	−0.965488	−	0.260449i	$-0.916130\pi$
$101$		−	52.6106i		−	0.520897i	0.965488	−	0.260449i	$-0.0838704\pi$
$102$	65.8234	−	58.8778i	0.645328	−	0.577234i
$103$	−53.2977	+	53.2977i	−0.517453	+	0.517453i	−0.916800	−	0.399347i	$-0.869237\pi$
$103$	−53.2977	+	53.2977i	−0.517453	+	0.517453i	0.399347	+	0.916800i	$0.369237\pi$
$104$	165.055	+	27.8100i	1.58707	+	0.267404i
$105$	−144.373	+	154.019i	−1.37498	+	1.46685i
$106$	30.5010	+	1.69885i	0.287745	+	0.0160269i
$107$	−47.1165	+	47.1165i	−0.440341	+	0.440341i	−0.892127	−	0.451786i	$-0.850787\pi$
$107$	−47.1165	+	47.1165i	−0.440341	+	0.440341i	0.451786	+	0.892127i	$0.350787\pi$
$108$	206.445	−	164.945i	1.91153	−	1.52727i
$109$	178.673			1.63920			0.819599	−	0.572938i	$-0.194196\pi$
$109$	178.673			1.63920			0.819599	+	0.572938i	$0.194196\pi$
$110$	−79.1397	+	76.3997i	−0.719451	+	0.694543i
$111$			55.2113i			0.497399i
$112$	−104.222	+	65.7544i	−0.930553	+	0.587092i
$113$	−22.6903	−	22.6903i	−0.200799	−	0.200799i	0.599543	−	0.800342i	$-0.295349\pi$
$113$	−22.6903	−	22.6903i	−0.200799	−	0.200799i	−0.800342	+	0.599543i	$0.795349\pi$
$114$	−231.985	−	12.9211i	−2.03495	−	0.113343i
$115$	−54.0042	+	1.74580i	−0.469601	+	0.0151809i
$116$	−0.940207	+	8.41403i	−0.00810524	+	0.0725347i
$117$	−311.439	−	311.439i	−2.66187	−	2.66187i
$118$	−125.230	+	112.015i	−1.06127	+	0.949283i
$119$	62.0396			0.521341
$120$	−132.840	−	174.456i	−1.10700	−	1.45380i
$121$	−1.38192	−	120.992i	−0.0114208	−	0.999935i
$122$	116.473	+	130.213i	0.954698	+	1.06732i
$123$	52.2405	+	52.2405i	0.424719	+	0.424719i
$124$	−92.7816	−	10.3677i	−0.748239	−	0.0836103i
$125$	−79.4176	+	96.5289i	−0.635341	+	0.772232i
$126$	323.764	+	18.0330i	2.56955	+	0.143119i
$127$	0.187577	−	0.187577i	0.00147699	−	0.00147699i	−0.706368	−	0.707845i	$-0.749668\pi$
$127$	0.187577	−	0.187577i	0.00147699	−	0.00147699i	0.707845	+	0.706368i	$0.249668\pi$
$128$	−49.3634	−	118.098i	−0.385652	−	0.922644i
$129$	142.879			1.10759
$130$	−151.356	+	144.455i	−1.16428	+	1.11119i
$131$	106.461			0.812681			0.406340	−	0.913722i	$-0.366805\pi$
$131$	106.461			0.812681			0.406340	+	0.913722i	$0.366805\pi$
$132$	239.860	+	25.4166i	1.81712	+	0.192550i
$133$	−115.414	−	115.414i	−0.867772	−	0.867772i
$134$	−158.023	−	8.80160i	−1.17928	−	0.0656836i
$135$	10.6724	+	330.136i	0.0790546	+	2.44545i
$136$	−10.7067	+	63.5449i	−0.0787254	+	0.467242i
$137$	63.3415	−	63.3415i	0.462347	−	0.462347i	−0.437077	−	0.899424i	$-0.643986\pi$
$137$	63.3415	−	63.3415i	0.462347	−	0.462347i	0.899424	+	0.437077i	$0.143986\pi$
$138$	78.9889	+	88.3070i	0.572384	+	0.639906i
$139$			224.103i			1.61225i	0.591746	+	0.806124i	$0.298439\pi$
$139$			224.103i			1.61225i	−0.591746	+	0.806124i	$0.701561\pi$
$140$	12.1510	−	153.559i	0.0867932	−	1.09685i
$141$	199.248			1.41310
$142$	−32.0726	−	35.8561i	−0.225863	−	0.252508i
$143$	−1.31427	−	230.146i	−0.00919067	−	1.60941i
$144$	−74.3450	+	328.507i	−0.516284	+	2.28130i
$145$	−7.72119	−	7.23761i	−0.0532496	−	0.0499146i
$146$	10.8580	−	194.945i	0.0743702	−	1.33524i
$147$	40.0020	+	40.0020i	0.272122	+	0.272122i
$148$	−25.1471	−	31.4741i	−0.169913	−	0.212663i
$149$	−160.633			−1.07807			−0.539037	−	0.842282i	$-0.681212\pi$
$149$	−160.633			−1.07807			−0.539037	+	0.842282i	$0.681212\pi$
$150$	274.083	−	2.46444i	1.82722	−	0.0164296i
$151$	190.101			1.25895			0.629474	−	0.777022i	$-0.283271\pi$
$151$	190.101			1.25895			0.629474	+	0.777022i	$0.283271\pi$
$152$	138.132	−	98.2962i	0.908762	−	0.646686i
$153$	119.902	−	119.902i	0.783672	−	0.783672i
$154$	113.685	+	125.644i	0.738213	+	0.815873i
$155$	79.8093	−	85.1417i	0.514898	−	0.549301i
$156$	455.944	+	50.9484i	2.92272	+	0.326592i
$157$	−60.5266	+	60.5266i	−0.385520	+	0.385520i	−0.873086	−	0.487566i	$-0.837885\pi$
$157$	−60.5266	+	60.5266i	−0.385520	+	0.385520i	0.487566	+	0.873086i	$0.337885\pi$
$158$	−63.7813	−	71.3054i	−0.403679	−	0.451300i
$159$	83.7309			0.526609
$160$	155.187	+	38.9467i	0.969922	+	0.243417i
$161$			83.2307i			0.516961i
$162$	257.414	−	230.252i	1.58898	−	1.42131i
$163$	−40.7392	+	40.7392i	−0.249934	+	0.249934i	−0.820943	−	0.571010i	$-0.806552\pi$
$163$	−40.7392	+	40.7392i	−0.249934	+	0.249934i	0.571010	+	0.820943i	$0.306552\pi$
$164$	−53.5745	−	5.98657i	−0.326674	−	0.0365035i
$165$	−204.936	+	221.146i	−1.24203	+	1.34028i
$166$	−31.2428	−	1.74016i	−0.188209	−	0.0104829i
$167$	100.104	−	100.104i	0.599423	−	0.599423i	−0.340736	−	0.940159i	$-0.610676\pi$
$167$	100.104	−	100.104i	0.599423	−	0.599423i	0.940159	+	0.340736i	$0.110676\pi$
$168$	−275.201	+	195.836i	−1.63810	+	1.16569i
$169$		−	268.758i		−	1.59028i
$170$	−55.6141	−	58.2709i	−0.327142	−	0.342770i
$171$	−446.112			−2.60884
$172$	−81.4507	+	65.0772i	−0.473551	+	0.378356i
$173$	−139.979	+	139.979i	−0.809126	+	0.809126i	−0.984502	−	0.175376i	$-0.943886\pi$
$173$	−139.979	+	139.979i	−0.809126	+	0.809126i	0.175376	+	0.984502i	$0.443886\pi$
$174$	−1.29052	+	23.1699i	−0.00741679	+	0.133161i
$175$	144.662	+	127.074i	0.826637	+	0.726138i
$176$	−148.312	+	94.7597i	−0.842685	+	0.538408i
$177$	−325.641	+	325.641i	−1.83978	+	1.83978i
$178$	−120.578	−	134.802i	−0.677405	−	0.757316i
$179$	106.678			0.595964			0.297982	−	0.954571i	$-0.403686\pi$
$179$	106.678			0.595964			0.297982	+	0.954571i	$0.403686\pi$
$180$	−273.293	−	320.261i	−1.51830	−	1.77923i
$181$	12.7141			0.0702438			0.0351219	−	0.999383i	$-0.488818\pi$
$181$	12.7141			0.0702438			0.0351219	+	0.999383i	$0.488818\pi$
$182$	214.867	+	240.214i	1.18059	+	1.31986i
$183$	338.600	+	338.600i	1.85027	+	1.85027i
$184$	−85.2502	−	14.3638i	−0.463316	−	0.0780639i
$185$	50.3318	−	1.62709i	0.272064	−	0.00879506i
$186$	−255.495	−	14.2306i	−1.37363	−	0.0765086i
$187$	88.6044	−	0.505983i	0.473820	−	0.00270579i
$188$	−113.584	+	90.7514i	−0.604172	+	0.482720i
$189$	508.802			2.69208
$190$	−4.94251	+	211.863i	−0.0260132	+	1.11507i
$191$		−	4.38351i		−	0.0229503i	−0.999934	−	0.0114751i	$-0.996347\pi$
$191$		−	4.38351i		−	0.0229503i	0.999934	−	0.0114751i	$-0.00365273\pi$
$192$	−153.094	−	315.675i	−0.797366	−	1.64414i
$193$	194.296	−	194.296i	1.00672	−	1.00672i	0.00673955	−	0.999977i	$-0.497855\pi$
$193$	194.296	−	194.296i	1.00672	−	1.00672i	0.999977	−	0.00673955i	$-0.00214528\pi$
$194$	13.8755	−	249.119i	0.0715231	−	1.28412i
$195$	−392.195	+	418.400i	−2.01126	+	2.14564i
$196$	−41.0235	−	4.58408i	−0.209304	−	0.0233882i
$197$	119.247	+	119.247i	0.605314	+	0.605314i	0.941718	−	0.336404i	$-0.109211\pi$
$197$	119.247	+	119.247i	0.605314	+	0.605314i	−0.336404	+	0.941718i	$0.609211\pi$
$198$	462.543	+	23.1140i	2.33608	+	0.116737i
$199$	−351.199			−1.76482			−0.882410	−	0.470482i	$-0.844080\pi$
$199$	−351.199			−1.76482			−0.882410	+	0.470482i	$0.844080\pi$
$200$	−155.123	+	126.241i	−0.775614	+	0.631207i
$201$	−433.803			−2.15823
$202$	70.1498	+	78.4252i	0.347276	+	0.388243i
$203$	−11.5272	+	11.5272i	−0.0567842	+	0.0567842i
$204$	−19.6148	+	175.535i	−0.0961509	+	0.860466i
$205$	46.0840	−	49.1630i	0.224800	−	0.239820i
$206$	8.38341	−	150.515i	0.0406962	−	0.730657i
$207$	160.857	+	160.857i	0.777088	+	0.777088i
$208$	−283.124	+	178.625i	−1.36117	+	0.858773i
$209$	−165.774	−	163.891i	−0.793177	−	0.784169i
$210$	9.84699	−	422.095i	0.0468904	−	2.00998i
$211$	−253.350			−1.20071			−0.600355	−	0.799734i	$-0.704974\pi$
$211$	−253.350			−1.20071			−0.600355	+	0.799734i	$0.704974\pi$
$212$	−47.7322	+	38.1369i	−0.225152	+	0.179891i
$213$	−93.2384	−	93.2384i	−0.437739	−	0.437739i
$214$	7.41114	−	133.059i	0.0346315	−	0.621772i
$215$	−4.21067	−	130.252i	−0.0195845	−	0.605822i
$216$	−87.8079	+	521.148i	−0.406518	+	2.41272i
$217$	−127.110	−	127.110i	−0.585762	−	0.585762i
$218$	−266.342	+	238.238i	−1.22175	+	1.09283i
$219$		−	535.159i		−	2.44365i
$220$	16.1016	−	219.410i	0.0731892	−	0.997318i
$221$	168.534			0.762595
$222$	−73.6175	−	82.3019i	−0.331610	−	0.370729i
$223$	77.2143	−	77.2143i	0.346252	−	0.346252i	−0.512459	−	0.858712i	$-0.671265\pi$
$223$	77.2143	−	77.2143i	0.346252	−	0.346252i	0.858712	+	0.512459i	$0.171265\pi$
$224$	67.6853	−	236.985i	0.302167	−	1.05797i
$225$	525.174	−	33.9904i	2.33411	−	0.151068i
$226$	64.0785	+	3.56905i	0.283533	+	0.0157922i
$227$	219.293	−	219.293i	0.966048	−	0.966048i	−0.0333944	−	0.999442i	$-0.510632\pi$
$227$	219.293	−	219.293i	0.966048	−	0.966048i	0.999442	+	0.0333944i	$0.0106317\pi$
$228$	363.042	−	290.062i	1.59229	−	1.27220i
$229$		−	257.724i		−	1.12543i	−0.826650	−	0.562717i	$-0.809756\pi$
$229$		−	257.724i		−	1.12543i	0.826650	−	0.562717i	$-0.190244\pi$
$230$	78.1747	−	74.6104i	0.339890	−	0.324393i
$231$	330.272	+	326.522i	1.42975	+	1.41351i
$232$	−9.81754	−	13.7962i	−0.0423170	−	0.0594664i
$233$	−153.796	+	153.796i	−0.660067	+	0.660067i	−0.955396	−	0.295328i	$-0.904571\pi$
$233$	−153.796	+	153.796i	−0.660067	+	0.660067i	0.295328	+	0.955396i	$0.404571\pi$
$234$	879.520	+	48.9876i	3.75863	+	0.209349i
$235$	−5.87186	−	181.638i	−0.0249866	−	0.772929i
$236$	37.3172	−	333.957i	0.158124	−	1.41507i
$237$	−185.419	−	185.419i	−0.782359	−	0.782359i
$238$	−92.4807	+	82.7222i	−0.388574	+	0.347572i
$239$		−	38.8269i		−	0.162456i	−0.996696	−	0.0812279i	$-0.974116\pi$
$239$		−	38.8269i		−	0.162456i	0.996696	−	0.0812279i	$-0.0258842\pi$
$240$	430.637	+	82.9301i	1.79432	+	0.345542i
$241$		−	0.772619i		−	0.00320589i	−0.999999	−	0.00160294i	$-0.999490\pi$
$241$		−	0.772619i		−	0.00320589i	0.999999	−	0.00160294i	$-0.000510233\pi$
$242$	163.388	+	178.517i	0.675158	+	0.737673i
$243$	248.953	−	248.953i	1.02450	−	1.02450i
$244$	−347.246	−	38.8023i	−1.42314	−	0.159026i
$245$	35.2878	−	37.6455i	0.144032	−	0.153655i
$246$	−147.530	−	8.21712i	−0.599714	−	0.0334029i
$247$	−313.527	−	313.527i	−1.26934	−	1.26934i
$248$	152.131	−	108.258i	0.613431	−	0.436525i
$249$	−85.7672			−0.344446
$250$	−10.3239	−	249.787i	−0.0412956	−	0.999147i
$251$		−	14.8441i		−	0.0591399i	−0.999563	−	0.0295699i	$-0.990586\pi$
$251$		−	14.8441i		−	0.0591399i	0.999563	−	0.0295699i	$-0.00941378\pi$
$252$	−506.670	+	404.818i	−2.01060	+	1.60642i
$253$	0.678814	+	118.869i	0.00268306	+	0.469839i
$254$	−0.0295048	+	0.529727i	−0.000116161	+	0.00208554i
$255$	−161.081	−	150.992i	−0.631690	−	0.592127i
$256$	231.055	+	110.226i	0.902557	+	0.430570i
$257$	−64.3743	+	64.3743i	−0.250484	+	0.250484i	−0.821169	−	0.570685i	$-0.806678\pi$
$257$	−64.3743	+	64.3743i	−0.250484	+	0.250484i	0.570685	+	0.821169i	$0.306678\pi$
$258$	−212.986	+	190.512i	−0.825527	+	0.738418i
$259$		−	77.5708i		−	0.299501i
$260$	33.0089	−	417.149i	0.126957	−	1.60442i
$261$			44.5564i			0.170714i
$262$	−158.699	+	141.953i	−0.605720	+	0.541805i
$263$	−67.4719	−	67.4719i	−0.256547	−	0.256547i	0.567101	−	0.823648i	$-0.308065\pi$
$263$	−67.4719	−	67.4719i	−0.256547	−	0.256547i	−0.823648	+	0.567101i	$0.808065\pi$
$264$	−391.442	+	281.936i	−1.48273	+	1.06794i
$265$	−2.46756	−	76.3308i	−0.00931156	−	0.288041i
$266$	325.934	+	18.1539i	1.22532	+	0.0682477i
$267$	−350.533	−	350.533i	−1.31286	−	1.31286i
$268$	247.297	−	197.585i	0.922750	−	0.737256i
$269$			261.542i			0.972275i	0.873882	+	0.486137i	$0.161595\pi$
$269$			261.542i			0.972275i	−0.873882	+	0.486137i	$0.838405\pi$
$270$	−456.105	−	477.894i	−1.68928	−	1.76998i
$271$	−383.025			−1.41338			−0.706689	−	0.707525i	$-0.749812\pi$
$271$	−383.025			−1.41338			−0.706689	+	0.707525i	$0.749812\pi$
$272$	−68.7693	−	109.001i	−0.252828	−	0.400738i
$273$	624.641	+	624.641i	2.28806	+	2.28806i
$274$	−9.96325	+	178.880i	−0.0363622	+	0.652845i
$275$	207.641	+	180.306i	0.755057	+	0.655659i
$276$	−235.493	−	26.3147i	−0.853236	−	0.0953430i
$277$	105.551	+	105.551i	0.381051	+	0.381051i	0.871481	−	0.490430i	$-0.163160\pi$
$277$	105.551	+	105.551i	0.381051	+	0.381051i	−0.490430	+	0.871481i	$0.663160\pi$
$278$	−298.813	−	334.063i	−1.07487	−	1.20167i
$279$	−491.324			−1.76102
$280$	186.638	+	245.107i	0.666566	+	0.875384i
$281$			198.947i			0.707998i	0.935246	+	0.353999i	$0.115178\pi$
$281$			198.947i			0.707998i	−0.935246	+	0.353999i	$0.884822\pi$
$282$	−297.013	+	265.672i	−1.05324	+	0.942100i
$283$	−169.428	−	169.428i	−0.598687	−	0.598687i	0.341276	−	0.939963i	$-0.389141\pi$
$283$	−169.428	−	169.428i	−0.598687	−	0.598687i	−0.939963	+	0.341276i	$0.889141\pi$
$284$	95.6195	+	10.6848i	0.336688	+	0.0376225i
$285$	18.7678	+	580.557i	0.0658519	+	2.03704i
$286$	308.830	+	341.319i	1.07983	+	1.19342i
$287$	−73.3969	−	73.3969i	−0.255738	−	0.255738i
$288$	−327.200	−	588.827i	−1.13611	−	2.04454i
$289$		−	224.116i		−	0.775487i
$290$	21.1602	+	0.493644i	0.0729663	+	0.00170222i
$291$		−	683.879i		−	2.35010i
$292$	243.749	+	305.077i	0.834758	+	1.04478i
$293$	−118.377	+	118.377i	−0.404016	+	0.404016i	−0.879646	−	0.475629i	$-0.842220\pi$
$293$	−118.377	+	118.377i	−0.404016	+	0.404016i	0.475629	+	0.879646i	$0.342220\pi$
$294$	−112.968	−	6.29208i	−0.384244	−	0.0214016i
$295$	306.457	+	287.264i	1.03884	+	0.973777i
$296$	79.4530	+	13.3870i	0.268422	+	0.0452263i
$297$	726.666	−	4.14969i	2.44669	−	0.0139720i
$298$	239.451	−	214.185i	0.803528	−	0.718740i
$299$			226.100i			0.756188i
$300$	−405.281	+	369.129i	−1.35094	+	1.23043i
$301$	−200.743			−0.666919
$302$	−283.378	+	253.477i	−0.938339	+	0.839326i
$303$	203.933	+	203.933i	0.673046	+	0.673046i
$304$	−74.8433	+	330.709i	−0.246195	+	1.08786i
$305$	298.696	−	318.653i	0.979331	−	1.04476i
$306$	−18.8599	+	338.609i	−0.0616335	+	1.10656i
$307$	195.242	−	195.242i	0.635966	−	0.635966i	−0.313592	−	0.949558i	$-0.601532\pi$
$307$	195.242	−	195.242i	0.635966	−	0.635966i	0.949558	+	0.313592i	$0.101532\pi$
$308$	−336.998	−	35.7099i	−1.09415	−	0.115941i
$309$		−	413.192i		−	1.33719i
$310$	−5.44342	+	233.334i	−0.0175594	+	0.752691i
$311$			522.926i			1.68144i	0.541474	+	0.840718i	$0.317867\pi$
$311$			522.926i			1.68144i	−0.541474	+	0.840718i	$0.682133\pi$
$312$	−747.596	+	531.998i	−2.39614	+	1.70512i
$313$	−242.759	−	242.759i	−0.775587	−	0.775587i	0.203490	−	0.979077i	$-0.434772\pi$
$313$	−242.759	−	242.759i	−0.775587	−	0.775587i	−0.979077	+	0.203490i	$0.934772\pi$
$314$	9.52047	−	170.930i	0.0303200	−	0.544363i
$315$	−26.1928	−	810.241i	−0.0831518	−	2.57219i
$316$	190.154	+	21.2484i	0.601753	+	0.0672416i
$317$	−33.9249	+	33.9249i	−0.107019	+	0.107019i	−0.758589	−	0.651570i	$-0.774111\pi$
$317$	−33.9249	+	33.9249i	−0.107019	+	0.107019i	0.651570	+	0.758589i	$0.274111\pi$
$318$	−124.815	+	111.645i	−0.392501	+	0.351085i
$319$	−16.3690	+	16.5570i	−0.0513135	+	0.0519029i
$320$	−283.264	+	148.867i	−0.885201	+	0.465209i
$321$		−	365.272i		−	1.13792i
$322$	−110.978	−	124.070i	−0.344652	−	0.385310i
$323$	120.706	−	120.706i	0.373701	−	0.373701i
$324$	−76.7070	+	686.461i	−0.236750	+	2.11871i
$325$	392.980	+	345.203i	1.20917	+	1.06216i
$326$	6.40803	−	115.049i	0.0196565	−	0.352912i
$327$	−692.583	+	692.583i	−2.11799	+	2.11799i
$328$	87.8444	−	62.5111i	0.267818	−	0.190583i
$329$	−279.939			−0.850879
$330$	10.6209	−	602.912i	0.0321844	−	1.82701i
$331$			423.596i			1.27975i	0.768480	+	0.639873i	$0.221013\pi$
$331$			423.596i			1.27975i	−0.768480	+	0.639873i	$0.778987\pi$
$332$	48.8930	−	39.0644i	0.147268	−	0.117664i
$333$	−149.918	−	149.918i	−0.450206	−	0.450206i
$334$	−15.7457	+	282.698i	−0.0471429	+	0.846400i
$335$	12.7843	+	395.464i	0.0381620	+	1.18049i
$336$	149.111	−	658.874i	0.443782	−	1.96093i
$337$	295.524	+	295.524i	0.876926	+	0.876926i	0.993215	−	0.116290i	$-0.0371001\pi$
$337$	295.524	+	295.524i	0.876926	+	0.876926i	−0.116290	+	0.993215i	$0.537100\pi$
$338$	358.356	+	400.630i	1.06022	+	1.18529i
$339$	175.907			0.518900
$340$	160.599	+	12.7082i	0.472351	+	0.0373770i
$341$	−182.575	−	180.501i	−0.535409	−	0.529329i
$342$	665.007	−	594.836i	1.94446	−	1.73929i
$343$	210.656	+	210.656i	0.614158	+	0.614158i
$344$	34.6437	−	205.613i	0.100708	−	0.597713i
$345$	202.567	−	216.102i	0.587152	−	0.626382i
$346$	22.0178	−	395.307i	0.0636354	−	1.14251i
$347$	−235.404	+	235.404i	−0.678398	+	0.678398i	−0.959638	−	0.281239i	$-0.909255\pi$
$347$	−235.404	+	235.404i	−0.678398	+	0.678398i	0.281239	+	0.959638i	$0.409255\pi$
$348$	−28.9706	−	36.2595i	−0.0832487	−	0.104194i
$349$	487.495			1.39683			0.698416	−	0.715692i	$-0.253888\pi$
$349$	487.495			1.39683			0.698416	+	0.715692i	$0.253888\pi$
$350$	−385.081	+	3.46249i	−1.10023	+	0.00989283i
$351$	1382.19			3.93785
$352$	94.7347	−	339.012i	0.269133	−	0.963103i
$353$	292.174	+	292.174i	0.827689	+	0.827689i	0.987197	−	0.159508i	$-0.0509907\pi$
$353$	292.174	+	292.174i	0.827689	+	0.827689i	−0.159508	+	0.987197i	$0.550991\pi$
$354$	51.2214	−	919.625i	0.144693	−	2.59781i
$355$	−82.2503	+	87.7458i	−0.231691	+	0.247171i
$356$	359.485	+	40.1698i	1.00979	+	0.112837i
$357$	−240.482	+	240.482i	−0.673620	+	0.673620i
$358$	−159.021	+	142.242i	−0.444194	+	0.397323i
$359$		−	183.518i		−	0.511193i	−0.966784	−	0.255596i	$-0.917728\pi$
$359$		−	183.518i		−	0.511193i	0.966784	−	0.255596i	$-0.0822718\pi$
$360$	834.420	+	113.001i	2.31783	+	0.313892i
$361$	−88.1024			−0.244051
$362$	−18.9526	+	16.9527i	−0.0523553	+	0.0468308i
$363$	474.355	+	463.641i	1.30676	+	1.27725i
$364$	−640.592	−	71.5816i	−1.75987	−	0.196653i
$365$	−487.862	+	15.7712i	−1.33661	+	0.0432089i
$366$	−956.222	−	53.2597i	−2.61263	−	0.145518i
$367$	309.683	+	309.683i	0.843822	+	0.843822i	0.989354	−	0.145532i	$-0.0464893\pi$
$367$	309.683	+	309.683i	0.843822	+	0.843822i	−0.145532	+	0.989354i	$0.546489\pi$
$368$	146.232	−	92.2591i	0.397371	−	0.250704i
$369$	−283.703			−0.768843
$370$	−72.8586	+	69.5367i	−0.196915	+	0.187937i
$371$	−117.640			−0.317090
$372$	399.834	−	319.459i	1.07482	−	0.858760i
$373$	195.281	−	195.281i	0.523542	−	0.523542i	−0.395097	−	0.918639i	$-0.629289\pi$
$373$	195.281	−	195.281i	0.523542	−	0.523542i	0.918639	+	0.395097i	$0.129289\pi$
$374$	−131.405	+	118.897i	−0.351351	+	0.317907i
$375$	−66.3280	−	682.016i	−0.176875	−	1.81871i
$376$	48.3112	−	286.731i	0.128487	−	0.762584i
$377$	−31.3142	+	31.3142i	−0.0830614	+	0.0830614i
$378$	−758.457	+	678.426i	−2.00650	+	1.79478i
$379$	683.030			1.80219			0.901095	−	0.433621i	$-0.142764\pi$
$379$	683.030			1.80219			0.901095	+	0.433621i	$0.142764\pi$
$380$	−275.125	−	322.408i	−0.724014	−	0.848442i
$381$			1.45420i			0.00381680i
$382$	5.84487	+	6.53437i	0.0153007	+	0.0171057i
$383$	−283.380	+	283.380i	−0.739895	+	0.739895i	−0.972557	−	0.232663i	$-0.925256\pi$
$383$	−283.380	+	283.380i	−0.739895	+	0.739895i	0.232663	+	0.972557i	$0.425256\pi$
$384$	649.127	+	266.436i	1.69044	+	0.693843i
$385$	287.931	−	310.706i	0.747872	−	0.807028i
$386$	−30.5617	+	548.703i	−0.0791753	+	1.42151i
$387$	−387.968	+	387.968i	−1.00250	+	1.00250i
$388$	311.487	+	389.857i	0.802801	+	1.00479i
$389$			699.754i			1.79885i	0.437072	+	0.899427i	$0.356016\pi$
$389$			699.754i			1.79885i	−0.437072	+	0.899427i	$0.643984\pi$
$390$	26.7498	−	1146.64i	0.0685893	−	2.94011i
$391$	−87.0469			−0.222626
$392$	67.2650	−	47.8665i	0.171594	−	0.122108i
$393$	−412.672	+	412.672i	−1.05006	+	1.05006i
$394$	−336.759	−	18.7568i	−0.854718	−	0.0476062i
$395$	−163.568	+	174.496i	−0.414095	+	0.441762i
$396$	−720.320	+	582.290i	−1.81899	+	1.47043i
$397$	482.013	−	482.013i	1.21414	−	1.21414i	0.244487	−	0.969653i	$-0.421380\pi$
$397$	482.013	−	482.013i	1.21414	−	1.21414i	0.969653	−	0.244487i	$-0.0786195\pi$
$398$	523.523	−	468.281i	1.31538	−	1.17659i
$399$	894.749			2.24248
$400$	62.9099	−	395.022i	0.157275	−	0.987555i
$401$	615.908			1.53593			0.767965	−	0.640492i	$-0.221270\pi$
$401$	615.908			1.53593			0.767965	+	0.640492i	$0.221270\pi$
$402$	646.659	−	578.424i	1.60860	−	1.43887i
$403$	−345.301	−	345.301i	−0.856828	−	0.856828i
$404$	−209.141	−	23.3700i	−0.517675	−	0.0578465i
$405$	−629.935	−	590.482i	−1.55540	−	1.45798i
$406$	1.81316	−	32.5533i	0.00446591	−	0.0801807i
$407$	−0.632653	−	110.786i	−0.00155443	−	0.272201i
$408$	−204.815	−	287.819i	−0.501998	−	0.705439i
$409$	−330.071			−0.807019			−0.403509	−	0.914976i	$-0.632210\pi$
$409$	−330.071			−0.807019			−0.403509	+	0.914976i	$0.632210\pi$
$410$	−3.14317	+	134.733i	−0.00766627	+	0.328618i
$411$			491.058i			1.19479i
$412$	188.197	+	235.547i	0.456789	+	0.571717i
$413$	457.519	−	457.519i	1.10779	−	1.10779i
$414$	−454.269	−	25.3019i	−1.09727	−	0.0611157i
$415$	2.52757	+	78.1871i	0.00609054	+	0.188403i
$416$	183.870	−	643.782i	0.441996	−	1.54755i
$417$	−868.682	−	868.682i	−2.08317	−	2.08317i
$418$	465.644	+	23.2690i	1.11398	+	0.0556674i
$419$	−429.690			−1.02551			−0.512757	−	0.858534i	$-0.671376\pi$
$419$	−429.690			−1.02551			−0.512757	+	0.858534i	$0.671376\pi$
$420$	548.134	+	642.335i	1.30508	+	1.52937i
$421$	261.974			0.622267			0.311134	−	0.950366i	$-0.399291\pi$
$421$	261.974			0.622267			0.311134	+	0.950366i	$0.399291\pi$
$422$	377.661	−	337.811i	0.894932	−	0.800500i
$423$	−541.029	+	541.029i	−1.27903	+	1.27903i
$424$	20.3021	−	120.495i	0.0478823	−	0.284186i
$425$	−132.901	+	151.294i	−0.312708	+	0.355987i
$426$	263.310	+	14.6659i	0.618098	+	0.0344269i
$427$	−475.726	−	475.726i	−1.11411	−	1.11411i
$428$	166.371	+	208.230i	0.388717	+	0.486518i
$429$	897.201	+	887.012i	2.09138	+	2.06763i
$430$	179.951	+	188.548i	0.418492	+	0.438484i
$431$	−425.806			−0.987949			−0.493974	−	0.869476i	$-0.664456\pi$
$431$	−425.806			−0.987949			−0.493974	+	0.869476i	$0.664456\pi$
$432$	−563.994	−	893.941i	−1.30554	−	2.06931i
$433$	−441.920	−	441.920i	−1.02060	−	1.02060i	−0.999783	−	0.0208168i	$-0.993373\pi$
$433$	−441.920	−	441.920i	−1.02060	−	1.02060i	−0.0208168	−	0.999783i	$-0.506627\pi$
$434$	358.966	+	19.9937i	0.827111	+	0.0460685i
$435$	57.9844	−	1.87447i	0.133297	−	0.00430913i
$436$	79.3675	−	710.270i	0.182036	−	1.62906i
$437$	161.935	+	161.935i	0.370561	+	0.370561i
$438$	713.570	+	797.747i	1.62915	+	1.82134i
$439$		−	39.1211i		−	0.0891140i	−0.999007	−	0.0445570i	$-0.985812\pi$
$439$		−	39.1211i		−	0.0891140i	0.999007	−	0.0445570i	$-0.0141876\pi$
$440$	268.554	+	348.538i	0.610350	+	0.792132i
$441$	−217.240			−0.492607
$442$	−251.228	+	224.719i	−0.568390	+	0.508414i
$443$	−441.330	+	441.330i	−0.996231	+	0.996231i	−0.999993	−	0.00376227i	$-0.998802\pi$
$443$	−441.330	+	441.330i	−0.996231	+	0.996231i	0.00376227	+	0.999993i	$0.498802\pi$
$444$	219.479	+	24.5252i	0.494322	+	0.0552370i
$445$	−309.223	+	329.884i	−0.694883	+	0.741312i
$446$	−12.1454	+	218.057i	−0.0272317	+	0.488917i
$447$	622.657	−	622.657i	1.39297	−	1.39297i
$448$	215.095	+	443.518i	0.480122	+	0.989995i
$449$		−	553.397i		−	1.23251i	−0.787547	−	0.616254i	$-0.788649\pi$
$449$		−	553.397i		−	1.23251i	0.787547	−	0.616254i	$-0.211351\pi$
$450$	−737.541	+	750.924i	−1.63898	+	1.66872i
$451$	−105.423	−	104.226i	−0.233755	−	0.231100i
$452$	−100.279	+	80.1205i	−0.221856	+	0.177258i
$453$	−736.883	+	736.883i	−1.62667	+	1.62667i
$454$	−34.4935	+	619.294i	−0.0759768	+	1.36408i
$455$	551.027	−	587.844i	1.21105	−	1.29196i
$456$	−154.414	+	916.459i	−0.338627	+	2.00978i
$457$	−154.432	−	154.432i	−0.337925	−	0.337925i	0.517661	−	0.855586i	$-0.326803\pi$
$457$	−154.432	−	154.432i	−0.337925	−	0.337925i	−0.855586	+	0.517661i	$0.826803\pi$
$458$	343.644	+	384.182i	0.750314	+	0.838826i
$459$			532.132i			1.15933i
$460$	−17.0490	+	215.456i	−0.0370630	+	0.468383i
$461$		−	471.965i		−	1.02379i	−0.859049	−	0.511893i	$-0.828944\pi$
$461$		−	471.965i		−	1.02379i	0.859049	−	0.511893i	$-0.171056\pi$
$462$	−927.704	−	46.3589i	−2.00802	−	0.100344i
$463$	−100.365	+	100.365i	−0.216771	+	0.216771i	−0.807136	−	0.590365i	$-0.798984\pi$
$463$	−100.365	+	100.365i	−0.216771	+	0.216771i	0.590365	+	0.807136i	$0.298984\pi$
$464$	33.0303	+	7.47513i	0.0711860	+	0.0161102i
$465$	20.6698	+	639.394i	0.0444513	+	1.37504i
$466$	24.1912	−	434.327i	0.0519124	−	0.932032i
$467$	−239.686	−	239.686i	−0.513247	−	0.513247i	0.402273	−	0.915520i	$-0.368220\pi$
$467$	−239.686	−	239.686i	−0.513247	−	0.513247i	−0.915520	+	0.402273i	$0.868220\pi$
$468$	−1376.39	+	1099.71i	−2.94101	+	2.34980i
$469$	609.486			1.29954
$470$	250.945	+	262.934i	0.533926	+	0.559433i
$471$		−	469.235i		−	0.996252i
$472$	389.663	+	547.578i	0.825556	+	1.16012i
$473$	−286.699	+	1.63722i	−0.606128	+	0.00346135i
$474$	523.633	+	29.1653i	1.10471	+	0.0615302i
$475$	528.695	−	34.2182i	1.11304	−	0.0720384i
$476$	27.5584	−	246.623i	0.0578958	−	0.518117i
$477$	−227.359	+	227.359i	−0.476645	+	0.476645i
$478$	51.7710	+	57.8782i	0.108307	+	0.121084i
$479$			400.843i			0.836833i	0.908255	+	0.418417i	$0.137415\pi$
$479$			400.843i			0.836833i	−0.908255	+	0.418417i	$0.862585\pi$
$480$	−752.516	+	450.581i	−1.56774	+	0.938710i
$481$		−	210.725i		−	0.438098i
$482$	1.03019	+	1.15172i	0.00213733	+	0.00238946i
$483$	−322.625	−	322.625i	−0.667960	−	0.667960i
$484$	−481.589	−	48.2520i	−0.995018	−	0.0996942i
$485$	−623.438	+	20.1540i	−1.28544	+	0.0415547i
$486$	−39.1588	+	703.056i	−0.0805738	+	1.44662i
$487$	24.4248	+	24.4248i	0.0501536	+	0.0501536i	0.731739	−	0.681585i	$-0.238709\pi$
$487$	24.4248	+	24.4248i	0.0501536	+	0.0501536i	−0.681585	+	0.731739i	$0.738709\pi$
$488$	569.369	−	405.169i	1.16674	−	0.830265i
$489$		−	315.832i		−	0.645873i
$490$	−2.40682	+	103.169i	−0.00491187	+	0.210549i
$491$	311.219			0.633846			0.316923	−	0.948451i	$-0.397350\pi$
$491$	311.219			0.633846			0.316923	+	0.948451i	$0.397350\pi$
$492$	230.875	−	184.464i	0.469258	−	0.374926i
$493$	−12.0557	−	12.0557i	−0.0244538	−	0.0244538i
$494$	885.415	+	49.3159i	1.79234	+	0.0998298i
$495$	−44.0165	−	1156.96i	−0.0889222	−	2.33730i
$496$	−82.4284	+	364.226i	−0.166186	+	0.734326i
$497$	130.998	+	130.998i	0.263578	+	0.263578i
$498$	127.851	−	114.360i	0.256728	−	0.229639i
$499$	−108.280			−0.216994			−0.108497	−	0.994097i	$-0.534604\pi$
$499$	−108.280			−0.216994			−0.108497	+	0.994097i	$0.534604\pi$
$500$	348.450	+	358.584i	0.696899	+	0.717169i
$501$			776.057i			1.54902i
$502$	19.7928	+	22.1277i	0.0394279	+	0.0440791i
$503$	22.0758	+	22.0758i	0.0438882	+	0.0438882i	0.728710	−	0.684822i	$-0.240120\pi$
$503$	22.0758	+	22.0758i	0.0438882	+	0.0438882i	−0.684822	+	0.728710i	$0.740120\pi$
$504$	215.504	−	1279.03i	0.427587	−	2.53777i
$505$	179.900	−	191.919i	0.356237	−	0.380038i
$506$	−159.510	−	176.290i	−0.315236	−	0.348399i
$507$	1041.78	+	1041.78i	2.05479	+	2.05479i
$508$	−0.662345	−	0.828991i	−0.00130383	−	0.00163187i
$509$			417.953i			0.821125i	0.911832	+	0.410562i	$0.134668\pi$
$509$			417.953i			0.821125i	−0.911832	+	0.410562i	$0.865332\pi$
$510$	441.449	+	10.2985i	0.865586	+	0.0201931i
$511$			751.889i			1.47141i
$512$	−491.400	+	143.772i	−0.959765	+	0.280805i
$513$	989.936	−	989.936i	1.92970	−	1.92970i
$514$	10.1257	−	181.796i	0.0196998	−	0.353689i
$515$	−376.675	+	12.1768i	−0.731407	+	0.0236444i
$516$	63.4679	−	567.982i	0.123000	−	1.10074i
$517$	−399.806	+	2.28313i	−0.773320	+	0.00441611i
$518$	103.431	+	115.633i	0.199674	+	0.223229i
$519$		−	1085.19i		−	2.09093i
$520$	507.012	+	665.846i	0.975023	+	1.28047i
$521$	253.019			0.485640			0.242820	−	0.970071i	$-0.421927\pi$
$521$	253.019			0.485640			0.242820	+	0.970071i	$0.421927\pi$
$522$	−59.4105	−	66.4190i	−0.113813	−	0.127239i
$523$	−605.834	−	605.834i	−1.15838	−	1.15838i	−0.984823	−	0.173559i	$-0.944473\pi$
$523$	−605.834	−	605.834i	−1.15838	−	1.15838i	−0.173559	−	0.984823i	$-0.555527\pi$
$524$	47.2907	−	423.211i	0.0902495	−	0.807654i
$525$	−1053.32	+	68.1731i	−2.00633	+	0.129854i
$526$	190.544	+	10.6129i	0.362251	+	0.0201767i
$527$	132.939	−	132.939i	0.252255	−	0.252255i
$528$	207.585	−	942.213i	0.393153	−	1.78450i
$529$			412.220i			0.779244i
$530$	105.456	+	110.494i	0.198974	+	0.208479i
$531$		−	1768.46i		−	3.33044i
$532$	−510.067	+	407.532i	−0.958772	+	0.766037i
$533$	−199.386	−	199.386i	−0.374083	−	0.374083i
$534$	989.923	+	55.1368i	1.85379	+	0.103252i
$535$	−332.990	+	10.7646i	−0.622411	+	0.0201208i
$536$	−105.184	+	624.274i	−0.196238	+	1.16469i
$537$	−413.511	+	413.511i	−0.770040	+	0.770040i
$538$	−348.734	−	389.873i	−0.648205	−	0.724671i
$539$	−80.7256	−	79.8089i	−0.149769	−	0.148068i
$540$	1317.12	+	104.223i	2.43910	+	0.193006i
$541$		−	391.623i		−	0.723887i	−0.932200	−	0.361944i	$-0.882113\pi$
$541$		−	391.623i		−	0.723887i	0.932200	−	0.361944i	$-0.117887\pi$
$542$	570.965	−	510.718i	1.05344	−	0.942283i
$543$	−49.2834	+	49.2834i	−0.0907613	+	0.0907613i
$544$	247.852	+	70.7888i	0.455609	+	0.130126i
$545$	651.784	+	610.962i	1.19593	+	1.12103i
$546$	−1764.02	−	98.2524i	−3.23080	−	0.179949i
$547$	−166.752	+	166.752i	−0.304847	+	0.304847i	−0.842907	−	0.538059i	$-0.819158\pi$
$547$	−166.752	+	166.752i	−0.304847	+	0.304847i	0.538059	+	0.842907i	$0.319158\pi$
$548$	−223.662	−	279.936i	−0.408143	−	0.510832i
$549$	−1838.84			−3.34943
$550$	−549.941	+	8.08574i	−0.999892	+	0.0147014i
$551$			44.8551i			0.0814066i
$552$	386.131	−	274.775i	0.699512	−	0.497781i
$553$	260.510	+	260.510i	0.471085	+	0.471085i
$554$	−298.082	−	16.6026i	−0.538053	−	0.0299685i
$555$	−188.792	+	201.406i	−0.340167	+	0.362895i
$556$	890.866	+	99.5478i	1.60228	+	0.179043i
$557$	355.499	+	355.499i	0.638238	+	0.638238i	0.950121	−	0.311883i	$-0.100960\pi$
$557$	355.499	+	355.499i	0.638238	+	0.638238i	−0.311883	+	0.950121i	$0.600960\pi$
$558$	732.403	−	655.120i	1.31255	−	1.17405i
$559$	−545.327			−0.975540
$560$	−605.037	−	116.515i	−1.08042	−	0.208063i
$561$	−341.493	+	345.416i	−0.608722	+	0.615714i
$562$	−265.272	−	296.565i	−0.472014	−	0.527696i
$563$	−608.314	−	608.314i	−1.08049	−	1.08049i	−0.996464	−	0.0840234i	$-0.973223\pi$
$563$	−608.314	−	608.314i	−1.08049	−	1.08049i	−0.0840234	−	0.996464i	$-0.526777\pi$
$564$	88.5071	−	792.060i	0.156927	−	1.40436i
$565$	−5.18401	−	160.361i	−0.00917525	−	0.283824i
$566$	478.474	+	26.6501i	0.845361	+	0.0470850i
$567$	−940.448	+	940.448i	−1.65864	+	1.65864i
$568$	−156.784	+	111.569i	−0.276028	+	0.196425i
$569$	−937.364			−1.64739			−0.823694	−	0.567035i	$-0.808091\pi$
$569$	−937.364			−1.64739			−0.823694	+	0.567035i	$0.808091\pi$
$570$	−802.078	−	840.396i	−1.40716	−	1.47438i
$571$	703.275			1.23166			0.615828	−	0.787881i	$-0.288822\pi$
$571$	703.275			1.23166			0.615828	+	0.787881i	$0.288822\pi$
$572$	−915.472	−	97.0076i	−1.60048	−	0.169594i
$573$	16.9917	+	16.9917i	0.0296538	+	0.0296538i
$574$	207.276	+	11.5449i	0.361109	+	0.0201131i
$575$	−202.973	−	178.296i	−0.352996	−	0.310080i
$576$	1272.88	+	441.466i	2.20986	+	0.766433i
$577$	−123.821	+	123.821i	−0.214594	+	0.214594i	−0.806216	−	0.591621i	$-0.798488\pi$
$577$	−123.821	+	123.821i	−0.214594	+	0.214594i	0.591621	+	0.806216i	$0.298488\pi$
$578$	298.831	+	334.083i	0.517009	+	0.577999i
$579$			1506.29i			2.60154i
$580$	−32.2012	+	27.4787i	−0.0555193	+	0.0473771i
$581$	120.501			0.207403
$582$	911.869	+	1019.44i	1.56679	+	1.75161i
$583$	−168.013	+	0.959452i	−0.288187	+	0.00164572i
$584$	−770.133	−	129.759i	−1.31872	−	0.222191i
$585$	−71.1541	−	2201.06i	−0.121631	−	3.76249i
$586$	18.6200	−	334.302i	0.0317747	−	0.570481i
$587$	−37.1908	−	37.1908i	−0.0633573	−	0.0633573i	0.674718	−	0.738075i	$-0.264265\pi$
$587$	−37.1908	−	37.1908i	−0.0633573	−	0.0633573i	−0.738075	+	0.674718i	$0.764265\pi$
$588$	176.787	−	141.249i	0.300659	−	0.240220i
$589$	−494.617			−0.839758
$590$	−839.859	−	19.5929i	−1.42349	−	0.0332084i
$591$	−924.465			−1.56424
$592$	−136.288	+	85.9852i	−0.230217	+	0.145245i
$593$	−113.671	+	113.671i	−0.191688	+	0.191688i	−0.796425	−	0.604737i	$-0.793278\pi$
$593$	−113.671	+	113.671i	−0.191688	+	0.191688i	0.604737	+	0.796425i	$0.293278\pi$
$594$	−1077.69	+	975.107i	−1.81429	+	1.64159i
$595$	226.316	+	212.142i	0.380362	+	0.356540i
$596$	−71.3543	+	638.558i	−0.119722	+	1.07141i
$597$	1361.34	−	1361.34i	2.28031	−	2.28031i
$598$	−301.477	−	337.041i	−0.504142	−	0.563614i
$599$	811.770			1.35521			0.677605	−	0.735426i	$-0.263018\pi$
$599$	811.770			1.35521			0.677605	+	0.735426i	$0.263018\pi$
$600$	111.952	−	1090.64i	0.186587	−	1.81774i
$601$			210.411i			0.350102i	0.984559	+	0.175051i	$0.0560091\pi$
$601$			210.411i			0.350102i	−0.984559	+	0.175051i	$0.943991\pi$
$602$	299.241	−	267.666i	0.497079	−	0.444628i
$603$	1177.93	−	1177.93i	1.95345	−	1.95345i
$604$	84.4441	−	755.701i	0.139808	−	1.25116i
$605$	408.686	−	446.095i	0.675514	−	0.737347i
$606$	−575.917	−	32.0774i	−0.950358	−	0.0529331i
$607$	14.5520	−	14.5520i	0.0239736	−	0.0239736i	−0.695018	−	0.718992i	$-0.744604\pi$
$607$	14.5520	−	14.5520i	0.0239736	−	0.0239736i	0.718992	+	0.695018i	$0.244604\pi$
$608$	−329.394	−	592.774i	−0.541766	−	0.974957i
$609$		−	89.3649i		−	0.146740i
$610$	−20.3726	+	873.282i	−0.0333978	+	1.43161i
$611$	−760.468			−1.24463
$612$	−423.380	−	529.902i	−0.691797	−	0.865853i
$613$	511.327	−	511.327i	0.834139	−	0.834139i	−0.153941	−	0.988080i	$-0.549197\pi$
$613$	511.327	−	511.327i	0.834139	−	0.834139i	0.988080	+	0.153941i	$0.0491966\pi$
$614$	−30.7104	+	551.372i	−0.0500169	+	0.898000i
$615$	11.9353	+	369.203i	0.0194070	+	0.600330i
$616$	549.969	−	396.114i	0.892806	−	0.643043i
$617$	−307.862	+	307.862i	−0.498965	+	0.498965i	−0.911116	−	0.412151i	$-0.864778\pi$
$617$	−307.862	+	307.862i	−0.498965	+	0.498965i	0.412151	+	0.911116i	$0.364778\pi$
$618$	550.942	+	615.934i	0.891491	+	0.996657i
$619$	−149.498			−0.241515			−0.120758	−	0.992682i	$-0.538532\pi$
$619$	−149.498			−0.241515			−0.120758	+	0.992682i	$0.538532\pi$
$620$	−303.008	−	355.083i	−0.488723	−	0.572714i
$621$	−713.894			−1.14959
$622$	−697.259	−	779.512i	−1.12099	−	1.25323i
$623$	492.493	+	492.493i	0.790518	+	0.790518i
$624$	405.066	−	1789.86i	0.649145	−	2.86837i
$625$	−619.786	+	80.5651i	−0.991657	+	0.128904i
$626$	685.563	+	38.1845i	1.09515	+	0.0609976i
$627$	1277.87	−	7.29740i	2.03807	−	0.0116386i
$628$	213.722	+	267.495i	0.340322	+	0.425948i
$629$	81.1276			0.128979
$630$	1119.40	+	1172.88i	1.77683	+	1.86171i
$631$		−	367.025i		−	0.581655i	−0.956775	−	0.290828i	$-0.906069\pi$
$631$		−	367.025i		−	0.581655i	0.956775	−	0.290828i	$-0.0939306\pi$
$632$	−311.789	+	221.873i	−0.493338	+	0.351065i
$633$	982.052	−	982.052i	1.55142	−	1.55142i
$634$	5.33619	−	95.8057i	0.00841671	−	0.151113i
$635$	1.32568	−	0.0428555i	0.00208768	−	6.74890e-5i
$636$	37.1938	−	332.852i	0.0584808	−	0.523352i
$637$	−152.676	−	152.676i	−0.239679	−	0.239679i
$638$	2.32404	−	46.5072i	0.00364269	−	0.0728952i
$639$	506.352			0.792413
$640$	223.758	−	599.610i	0.349622	−	0.936891i
$641$	−768.223			−1.19848			−0.599238	−	0.800571i	$-0.704530\pi$
$641$	−768.223			−1.19848			−0.599238	+	0.800571i	$0.704530\pi$
$642$	487.046	+	544.501i	0.758639	+	0.848133i
$643$	440.590	−	440.590i	0.685210	−	0.685210i	−0.275959	−	0.961169i	$-0.588996\pi$
$643$	440.590	−	440.590i	0.685210	−	0.685210i	0.961169	+	0.275959i	$0.0889955\pi$
$644$	330.864	+	36.9716i	0.513763	+	0.0574093i
$645$	521.212	+	488.569i	0.808081	+	0.757471i
$646$	−18.9863	+	340.878i	−0.0293905	+	0.527676i
$647$	−93.8740	−	93.8740i	−0.145091	−	0.145091i	0.630830	−	0.775921i	$-0.282715\pi$
$647$	−93.8740	−	93.8740i	−0.145091	−	0.145091i	−0.775921	+	0.630830i	$0.782715\pi$
$648$	−800.966	−	1125.57i	−1.23606	−	1.73699i
$649$	649.693	−	657.156i	1.00107	−	1.01257i
$650$	−1046.09	+	9.40602i	−1.60937	+	0.0144708i
$651$	985.428			1.51371
$652$	143.852	+	180.045i	0.220632	+	0.276143i
$653$	539.451	+	539.451i	0.826112	+	0.826112i	0.986977	−	0.160864i	$-0.0514281\pi$
$653$	539.451	+	539.451i	0.826112	+	0.826112i	−0.160864	+	0.986977i	$0.551428\pi$
$654$	108.939	−	1955.89i	0.166574	−	2.99066i
$655$	388.362	+	364.039i	0.592919	+	0.555785i
$656$	−47.5963	+	210.313i	−0.0725554	+	0.320600i
$657$	1453.15	+	1453.15i	2.21180	+	2.21180i
$658$	417.297	−	373.265i	0.634191	−	0.567271i
$659$			232.233i			0.352402i	0.984354	+	0.176201i	$0.0563809\pi$
$659$			232.233i			0.352402i	−0.984354	+	0.176201i	$0.943619\pi$
$660$	788.078	+	912.906i	1.19406	+	1.38319i
$661$	579.441			0.876613			0.438306	−	0.898826i	$-0.355578\pi$
$661$	579.441			0.876613			0.438306	+	0.898826i	$0.355578\pi$
$662$	−564.814	−	631.443i	−0.853193	−	0.953841i
$663$	−653.282	+	653.282i	−0.985342	+	0.985342i
$664$	−20.7958	+	123.425i	−0.0313190	+	0.185881i
$665$	−26.3684	−	815.672i	−0.0396517	−	1.22657i
$666$	423.377	+	23.5813i	0.635702	+	0.0354074i
$667$	16.1736	−	16.1736i	0.0242483	−	0.0242483i
$668$	−353.471	−	442.405i	−0.529148	−	0.662282i
$669$			598.607i			0.894778i
$670$	−546.360	−	572.461i	−0.815463	−	0.854420i
$671$	−683.307	−	675.547i	−1.01834	−	1.00678i
$672$	656.253	+	1180.99i	0.976567	+	1.75742i
$673$	−727.635	+	727.635i	−1.08118	+	1.08118i	−0.0847817	+	0.996400i	$0.527019\pi$
$673$	−727.635	+	727.635i	−1.08118	+	1.08118i	−0.996400	+	0.0847817i	$0.972981\pi$
$674$	−834.574	−	46.4842i	−1.23824	−	0.0689676i
$675$	−1089.95	+	1240.80i	−1.61474	+	1.83823i
$676$	−1068.38	−	119.384i	−1.58045	−	0.176603i
$677$	−464.202	−	464.202i	−0.685675	−	0.685675i	0.275598	−	0.961273i	$-0.411124\pi$
$677$	−464.202	−	464.202i	−0.685675	−	0.685675i	−0.961273	+	0.275598i	$0.911124\pi$
$678$	−262.220	+	234.551i	−0.386755	+	0.345945i
$679$			960.837i			1.41508i
$680$	−256.346	+	195.196i	−0.376979	+	0.287053i
$681$			1700.08i			2.49644i
$682$	512.835	+	25.6272i	0.751957	+	0.0375765i
$683$	−419.389	+	419.389i	−0.614040	+	0.614040i	−0.943996	−	0.329956i	$-0.892966\pi$
$683$	−419.389	+	419.389i	−0.614040	+	0.614040i	0.329956	+	0.943996i	$0.392966\pi$
$684$	−198.166	+	1773.41i	−0.289716	+	2.59271i
$685$	447.658	−	14.4716i	0.653516	−	0.0211264i
$686$	−594.904	−	33.1350i	−0.867206	−	0.0483017i
$687$	999.009	+	999.009i	1.45416	+	1.45416i
$688$	222.518	+	352.695i	0.323427	+	0.512638i
$689$	−319.576			−0.463825
$690$	−13.8162	+	592.236i	−0.0200235	+	0.858313i
$691$			1091.80i			1.58003i	0.613085	+	0.790017i	$0.289928\pi$
$691$			1091.80i			1.58003i	−0.613085	+	0.790017i	$0.710072\pi$
$692$	494.272	+	618.631i	0.714266	+	0.893976i
$693$	−1783.43	+	10.1844i	−2.57349	+	0.0146962i
$694$	37.0277	−	664.793i	0.0533541	−	0.957916i
$695$	−766.308	+	817.509i	−1.10260	+	1.17627i
$696$	91.5333	+	15.4224i	0.131513	+	0.0221586i
$697$	76.7622	−	76.7622i	0.110132	−	0.110132i
$698$	−726.695	+	650.015i	−1.04111	+	0.931253i
$699$		−	1192.31i		−	1.70573i
$700$	569.413	−	518.620i	0.813446	−	0.740885i
$701$		−	1231.26i		−	1.75643i	−0.478262	−	0.878217i	$-0.658733\pi$
$701$		−	1231.26i		−	1.75643i	0.478262	−	0.878217i	$-0.341267\pi$
$702$	−2060.39	+	1842.98i	−2.93502	+	2.62532i
$703$	−150.923	−	150.923i	−0.214685	−	0.214685i
$704$	310.813	+	631.673i	0.441496	+	0.897263i
$705$	726.840	+	681.318i	1.03098	+	0.966408i
$706$	−825.115	−	45.9573i	−1.16872	−	0.0650953i
$707$	−286.522	−	286.522i	−0.405264	−	0.405264i
$708$	1149.85	+	1439.16i	1.62409	+	2.03271i
$709$			172.519i			0.243327i	0.992571	+	0.121664i	$0.0388229\pi$
$709$			172.519i			0.243327i	−0.992571	+	0.121664i	$0.961177\pi$
$710$	5.60991	−	240.471i	0.00790128	−	0.338692i
$711$	1006.96			1.41626
$712$	−589.436	+	419.449i	−0.827859	+	0.589114i
$713$	178.347	+	178.347i	0.250136	+	0.250136i
$714$	37.8264	−	679.134i	0.0529782	−	0.951168i
$715$	782.178	−	844.047i	1.09395	−	1.18049i
$716$	47.3869	−	424.071i	0.0661828	−	0.592278i
$717$	150.504	+	150.504i	0.209907	+	0.209907i
$718$	244.699	+	273.566i	0.340807	+	0.381011i
$719$	−157.766			−0.219424			−0.109712	−	0.993963i	$-0.534993\pi$
$719$	−157.766			−0.219424			−0.109712	+	0.993963i	$0.534993\pi$
$720$	−1394.52	+	944.150i	−1.93683	+	1.31132i
$721$			580.528i			0.805170i
$722$	131.332	−	117.474i	0.181900	−	0.162706i
$723$	2.99488	+	2.99488i	0.00414229	+	0.00414229i
$724$	5.64770	−	50.5420i	0.00780069	−	0.0698093i
$725$	−3.41762	−	52.8045i	−0.00471396	−	0.0728338i
$726$	−1325.32	−	58.6431i	−1.82550	−	0.0807756i
$727$	−883.116	−	883.116i	−1.21474	−	1.21474i	−0.969450	−	0.245290i	$-0.921117\pi$
$727$	−883.116	−	883.116i	−1.21474	−	1.21474i	−0.245290	−	0.969450i	$-0.578883\pi$
$728$	1050.36	−	747.447i	1.44280	−	1.02671i
$729$			375.868i			0.515595i
$730$	706.214	−	674.015i	0.967416	−	0.923308i
$731$		−	209.947i		−	0.287205i
$732$	1496.43	−	1195.61i	2.04430	−	1.63335i
$733$	−125.612	+	125.612i	−0.171366	+	0.171366i	−0.787580	−	0.616213i	$-0.788666\pi$
$733$	−125.612	+	125.612i	−0.171366	+	0.171366i	0.616213	+	0.787580i	$0.288666\pi$
$734$	−874.559	−	48.7112i	−1.19150	−	0.0663641i
$735$	9.13920	+	282.709i	0.0124343	+	0.384638i
$736$	−94.9684	+	332.511i	−0.129033	+	0.451781i
$737$	870.462	−	4.97085i	1.18109	−	0.00674471i
$738$	422.909	−	378.284i	0.573047	−	0.512579i
$739$			47.4462i			0.0642033i	0.999485	+	0.0321016i	$0.0102200\pi$
$739$			47.4462i			0.0642033i	−0.999485	+	0.0321016i	$0.989780\pi$
$740$	15.8896	−	200.805i	0.0214724	−	0.271357i
$741$	2430.63			3.28020
$742$	175.363	−	156.859i	0.236339	−	0.211400i
$743$	735.075	+	735.075i	0.989334	+	0.989334i	0.999944	−	0.0106101i	$-0.00337736\pi$
$743$	735.075	+	735.075i	0.989334	+	0.989334i	−0.0106101	+	0.999944i	$0.503377\pi$
$744$	−170.063	+	1009.34i	−0.228579	+	1.35664i
$745$	−585.977	−	549.277i	−0.786546	−	0.737285i
$746$	−30.7166	+	551.484i	−0.0411751	+	0.739255i
$747$	232.889	−	232.889i	0.311765	−	0.311765i
$748$	37.3472	−	352.450i	0.0499294	−	0.471190i
$749$			513.201i			0.685181i
$750$	1008.26	+	928.223i	1.34435	+	1.23763i
$751$			1011.71i			1.34715i	0.739120	+	0.673573i	$0.235241\pi$
$751$			1011.71i			1.34715i	−0.739120	+	0.673573i	$0.764759\pi$
$752$	310.305	+	491.840i	0.412640	+	0.654042i
$753$	57.5398	+	57.5398i	0.0764140	+	0.0764140i
$754$	4.92553	−	88.4327i	0.00653254	−	0.117285i
$755$	693.474	+	650.042i	0.918509	+	0.860983i
$756$	226.013	−	2022.62i	0.298959	−	2.67542i
$757$	−788.218	+	788.218i	−1.04124	+	1.04124i	−0.0421273	+	0.999112i	$0.513414\pi$
$757$	−788.218	+	788.218i	−1.04124	+	1.04124i	−0.999112	+	0.0421273i	$0.986586\pi$
$758$	−1018.17	+	910.737i	−1.34324	+	1.20150i
$759$	−463.401	−	458.138i	−0.610541	−	0.603607i
$760$	840.014	+	113.759i	1.10528	+	0.149682i
$761$			1401.09i			1.84111i	0.390609	+	0.920557i	$0.372265\pi$
$761$			1401.09i			1.84111i	−0.390609	+	0.920557i	$0.627735\pi$
$762$	−1.93900	−	2.16774i	−0.00254462	−	0.00284480i
$763$	973.066	−	973.066i	1.27532	−	1.27532i
$764$	−17.4256	−	1.94718i	−0.0228083	−	0.00254867i
$765$	847.391	−	27.3938i	1.10770	−	0.0358089i
$766$	44.5740	−	800.279i	0.0581906	−	1.04475i
$767$	1242.87	−	1242.87i	1.62043	−	1.62043i
$768$	−1322.90	+	468.364i	−1.72252	+	0.609849i
$769$	−392.963			−0.511005			−0.255502	−	0.966808i	$-0.582241\pi$
$769$	−392.963			−0.511005			−0.255502	+	0.966808i	$0.582241\pi$
$770$	−14.9221	+	847.081i	−0.0193793	+	1.10010i
$771$		−	499.064i		−	0.647295i
$772$	−686.071	−	858.686i	−0.888692	−	1.11229i
$773$	−147.039	−	147.039i	−0.190219	−	0.190219i	0.605572	−	0.795791i	$-0.292944\pi$
$773$	−147.039	−	147.039i	−0.190219	−	0.190219i	−0.795791	+	0.605572i	$0.792944\pi$
$774$	61.0251	−	1095.64i	0.0788439	−	1.41556i
$775$	582.276	−	37.6861i	0.751324	−	0.0486272i
$776$	−984.151	−	165.819i	−1.26824	−	0.213684i
$777$	300.685	+	300.685i	0.386983	+	0.386983i
$778$	−933.036	−	1043.10i	−1.19928	−	1.34075i
$779$	−285.605			−0.366630
$780$	1489.03	+	1744.93i	1.90901	+	2.23710i
$781$	188.159	+	186.022i	0.240920	+	0.238184i
$782$	129.758	−	116.066i	0.165932	−	0.148423i
$783$	−98.8720	−	98.8720i	−0.126273	−	0.126273i
$784$	−36.4458	+	161.043i	−0.0464870	+	0.205412i
$785$	−427.764	+	13.8284i	−0.544922	+	0.0176158i
$786$	64.9109	−	1165.41i	0.0825839	−	1.48271i
$787$	69.9045	−	69.9045i	0.0888240	−	0.0888240i	−0.661299	−	0.750123i	$-0.729994\pi$
$787$	69.9045	−	69.9045i	0.0888240	−	0.0888240i	0.750123	+	0.661299i	$0.229994\pi$
$788$	527.007	−	421.067i	0.668791	−	0.534349i
$789$	523.078			0.662963
$790$	11.1562	−	478.214i	0.0141217	−	0.605334i
$791$	−247.146			−0.312448
$792$	297.349	−	1828.46i	0.375441	−	2.30866i
$793$	−1292.33	−	1292.33i	−1.62968	−	1.62968i
$794$	−75.8179	+	1361.23i	−0.0954885	+	1.71440i
$795$	305.444	+	286.314i	0.384206	+	0.360143i
$796$	−156.005	+	1396.11i	−0.195986	+	1.75390i
$797$	733.422	−	733.422i	0.920228	−	0.920228i	−0.0768168	−	0.997045i	$-0.524476\pi$
$797$	733.422	−	733.422i	0.920228	−	0.920228i	0.997045	+	0.0768168i	$0.0244757\pi$
$798$	−1333.78	+	1193.04i	−1.67140	+	1.49504i
$799$		−	292.775i		−	0.366426i
$800$	432.936	+	672.731i	0.541169	+	0.840914i
$801$	1903.65			2.37659
$802$	−918.116	+	821.238i	−1.14478	+	1.02399i
$803$	6.13226	+	1073.84i	0.00763669	+	1.33729i
$804$	−192.698	+	1724.48i	−0.239675	+	2.14488i
$805$	−284.604	+	303.619i	−0.353545	+	0.377167i
$806$	975.149	+	54.3139i	1.20986	+	0.0673870i
$807$	−1013.81	−	1013.81i	−1.25627	−	1.25627i
$808$	342.921	−	244.027i	0.424408	−	0.302013i
$809$	−641.096			−0.792455			−0.396227	−	0.918152i	$-0.629681\pi$
$809$	−641.096			−0.792455			−0.396227	+	0.918152i	$0.629681\pi$
$810$	1726.36	+	40.2741i	2.13131	+	0.0497210i
$811$	−1069.33			−1.31853			−0.659264	−	0.751911i	$-0.729132\pi$
$811$	−1069.33			−1.31853			−0.659264	+	0.751911i	$0.729132\pi$
$812$	40.7031	+	50.9440i	0.0501270	+	0.0627389i
$813$	1484.71	−	1484.71i	1.82621	−	1.82621i
$814$	148.663	+	164.302i	0.182632	+	0.201845i
$815$	−287.919	+	9.30762i	−0.353275	+	0.0114204i
$816$	689.084	+	155.948i	0.844466	+	0.191112i
$817$	−390.569	+	390.569i	−0.478053	+	0.478053i
$818$	492.027	−	440.109i	0.601500	−	0.538030i
$819$	−3392.25			−4.14194
$820$	−174.965	−	205.034i	−0.213372	−	0.250042i
$821$			20.6937i			0.0252055i	0.999921	+	0.0126028i	$0.00401169\pi$
$821$			20.6937i			0.0252055i	−0.999921	+	0.0126028i	$0.995988\pi$
$822$	−654.765	−	732.006i	−0.796552	−	0.890518i
$823$	−210.860	+	210.860i	−0.256209	+	0.256209i	−0.823510	−	0.567301i	$-0.807988\pi$
$823$	−210.860	+	210.860i	−0.256209	+	0.256209i	0.567301	+	0.823510i	$0.307988\pi$
$824$	−594.613	−	100.186i	−0.721618	−	0.121585i
$825$	−1503.79	+	105.955i	−1.82277	+	0.128430i
$826$	−71.9651	+	1292.06i	−0.0871248	+	1.56423i
$827$	127.688	−	127.688i	0.154399	−	0.154399i	−0.625680	−	0.780080i	$-0.715179\pi$
$827$	127.688	−	127.688i	0.154399	−	0.154399i	0.780080	+	0.625680i	$0.215179\pi$
$828$	710.902	−	567.995i	0.858578	−	0.685984i
$829$		−	1285.31i		−	1.55044i	−0.631693	−	0.775219i	$-0.717640\pi$
$829$		−	1285.31i		−	1.55044i	0.631693	−	0.775219i	$-0.282360\pi$
$830$	−108.021	−	113.181i	−0.130146	−	0.136363i
$831$	−818.289			−0.984704
$832$	584.315	+	1204.84i	0.702301	+	1.44812i
$833$	58.7790	−	58.7790i	0.0705630	−	0.0705630i
$834$	2453.20	+	136.639i	2.94149	+	0.163835i
$835$	707.470	−	22.8705i	0.847270	−	0.0273899i
$836$	−725.149	+	586.193i	−0.867403	+	0.701188i
$837$	1090.26	−	1090.26i	1.30258	−	1.30258i
$838$	640.527	−	572.939i	0.764352	−	0.683698i
$839$	723.511			0.862350			0.431175	−	0.902268i	$-0.358099\pi$
$839$	723.511			0.862350			0.431175	+	0.902268i	$0.358099\pi$
$840$	−1673.56	−	226.642i	−1.99234	−	0.269812i
$841$	−836.520			−0.994673
$842$	−390.518	+	349.311i	−0.463798	+	0.414859i
$843$	−771.174	−	771.174i	−0.914797	−	0.914797i
$844$	−112.540	+	1007.13i	−0.133341	+	1.19328i
$845$	919.005	−	980.407i	1.08758	−	1.16025i
$846$	85.1006	−	1527.89i	0.100592	−	1.80602i
$847$	−666.460	−	651.407i	−0.786847	−	0.769076i
$848$	130.401	+	206.689i	0.153775	+	0.243736i
$849$	1313.50			1.54711
$850$	−3.62125	−	402.737i	−0.00426030	−	0.473809i
$851$			108.839i			0.127895i
$852$	−412.064	+	329.230i	−0.483643	+	0.386420i
$853$	258.829	−	258.829i	0.303434	−	0.303434i	−0.538922	−	0.842356i	$-0.681168\pi$
$853$	258.829	−	258.829i	0.303434	−	0.303434i	0.842356	+	0.538922i	$0.181168\pi$
$854$	1343.47	+	74.8289i	1.57315	+	0.0876217i
$855$	−1627.38	−	1525.46i	−1.90337	−	1.78416i
$856$	−525.653	−	88.5670i	−0.614081	−	0.103466i
$857$	206.625	+	206.625i	0.241102	+	0.241102i	0.817306	−	0.576204i	$-0.195467\pi$
$857$	206.625	+	206.625i	0.241102	+	0.241102i	−0.576204	+	0.817306i	$0.695467\pi$
$858$	−2520.15	−	125.936i	−2.93724	−	0.146779i
$859$	−231.485			−0.269482			−0.134741	−	0.990881i	$-0.543020\pi$
$859$	−231.485			−0.269482			−0.134741	+	0.990881i	$0.543020\pi$
$860$	−519.654	−	41.1201i	−0.604249	−	0.0478141i
$861$	569.012			0.660874
$862$	634.737	−	567.760i	0.736354	−	0.658655i
$863$	638.441	−	638.441i	0.739793	−	0.739793i	−0.232745	−	0.972538i	$-0.574771\pi$
$863$	638.441	−	638.441i	0.739793	−	0.739793i	0.972538	+	0.232745i	$0.0747708\pi$
$864$	2032.69	+	580.556i	2.35265	+	0.671940i
$865$	−989.282	+	31.9807i	−1.14368	+	0.0369720i
$866$	1248.00	+	69.5114i	1.44111	+	0.0802672i
$867$	868.733	+	868.733i	1.00200	+	1.00200i
$868$	−561.760	+	448.833i	−0.647189	+	0.517089i
$869$	374.183	+	369.934i	0.430590	+	0.425700i
$870$	−83.9363	+	80.1093i	−0.0964785	+	0.0920796i
$871$	1655.70			1.90092
$872$	828.747	+	1164.61i	0.950398	+	1.33556i
$873$	1856.98	+	1856.98i	2.12712	+	2.12712i
$874$	−457.314	−	25.4715i	−0.523242	−	0.0291436i
$875$	93.1896	+	958.220i	0.106502	+	1.09511i
$876$	−2127.40	−	237.721i	−2.42854	−	0.271371i
$877$	−481.721	−	481.721i	−0.549282	−	0.549282i	0.376951	−	0.926233i	$-0.376973\pi$
$877$	−481.721	−	481.721i	−0.549282	−	0.549282i	−0.926233	+	0.376951i	$0.876973\pi$
$878$	52.1632	+	58.3167i	0.0594113	+	0.0664199i
$879$		−	917.721i		−	1.04405i
$880$	−865.059	−	161.471i	−0.983022	−	0.183490i
$881$	−878.141			−0.996755			−0.498377	−	0.866960i	$-0.666071\pi$
$881$	−878.141			−0.996755			−0.498377	+	0.866960i	$0.666071\pi$
$882$	323.833	−	289.662i	0.367158	−	0.328415i
$883$	792.572	−	792.572i	0.897591	−	0.897591i	−0.0976320	−	0.995223i	$-0.531127\pi$
$883$	792.572	−	792.572i	0.897591	−	0.897591i	0.995223	+	0.0976320i	$0.0311268\pi$
$884$	74.8637	−	669.965i	0.0846875	−	0.757878i
$885$	−2301.42	+	74.3987i	−2.60048	+	0.0840663i
$886$	69.4186	−	1246.34i	0.0783506	−	1.40670i
$887$	395.005	−	395.005i	0.445327	−	0.445327i	−0.448471	−	0.893798i	$-0.648031\pi$
$887$	395.005	−	395.005i	0.445327	−	0.445327i	0.893798	+	0.448471i	$0.148031\pi$
$888$	−359.873	+	256.090i	−0.405262	+	0.288389i
$889$		−	2.04312i		−	0.00229823i
$890$	21.0907	−	904.060i	0.0236974	−	1.01580i
$891$	−1335.47	+	1350.81i	−1.49884	+	1.51606i
$892$	−272.648	−	341.246i	−0.305659	−	0.382563i
$893$	−544.655	+	544.655i	−0.609916	+	0.609916i
$894$	−97.9403	+	1758.41i	−0.109553	+	1.96691i
$895$	389.152	+	364.779i	0.434806	+	0.407575i
$896$	−912.012	−	374.337i	−1.01787	−	0.417787i
$897$	−876.425	−	876.425i	−0.977063	−	0.977063i
$898$	737.887	+	824.933i	0.821700	+	0.918633i
$899$			49.4009i			0.0549510i
$900$	98.1653	−	2102.80i	0.109073	−	2.33645i
$901$		−	123.034i		−	0.136553i
$902$	296.124	+	14.7978i	0.328298	+	0.0164055i
$903$	778.132	−	778.132i	0.861719	−	0.861719i
$904$	42.6520	−	253.143i	0.0471814	−	0.280025i
$905$	46.3802	+	43.4754i	0.0512488	+	0.0480391i
$906$	115.907	−	2080.99i	0.127933	−	2.29690i
$907$	−948.453	−	948.453i	−1.04570	−	1.04570i	−0.998904	−	0.0467987i	$-0.985098\pi$
$907$	−948.453	−	948.453i	−1.04570	−	1.04570i	−0.0467987	−	0.998904i	$-0.514902\pi$
$908$	−774.335	−	969.157i	−0.852791	−	1.06735i
$909$	−1107.50			−1.21837
$910$	−37.5830	+	1611.01i	−0.0413000	+	1.77034i
$911$		−	190.484i		−	0.209093i	−0.994520	−	0.104546i	$-0.966661\pi$
$911$		−	190.484i		−	0.209093i	0.994520	−	0.104546i	$-0.0333391\pi$
$912$	−991.806	−	1572.03i	−1.08751	−	1.72372i
$913$	172.099	−	0.982785i	0.188498	−	0.00107644i
$914$	436.123	+	24.2912i	0.477159	+	0.0265768i
$915$	77.3594	+	2393.01i	0.0845458	+	2.61531i
$916$	−1024.52	−	114.483i	−1.11847	−	0.124981i
$917$	579.797	−	579.797i	0.632276	−	0.632276i
$918$	−709.532	−	793.234i	−0.772911	−	0.864089i
$919$		−	139.794i		−	0.152115i	−0.997103	−	0.0760576i	$-0.975767\pi$
$919$		−	139.794i		−	0.152115i	0.997103	−	0.0760576i	$-0.0242333\pi$
$920$	−261.870	−	343.907i	−0.284641	−	0.373812i
$921$			1513.62i			1.64345i
$922$	629.308	+	703.546i	0.682547	+	0.763065i
$923$	355.863	+	355.863i	0.385550	+	0.385550i
$924$	1444.72	−	1167.87i	1.56355	−	1.26393i
$925$	189.170	+	166.172i	0.204508	+	0.179645i
$926$	15.7868	−	283.436i	0.0170484	−	0.306086i
$927$	1121.97	+	1121.97i	1.21032	+	1.21032i
$928$	−59.2045	+	32.8989i	−0.0637980	+	0.0354514i
$929$			98.0946i			0.105592i	0.998605	+	0.0527958i	$0.0168133\pi$
$929$			98.0946i			0.105592i	−0.998605	+	0.0527958i	$0.983187\pi$
$930$	−883.366	−	925.566i	−0.949856	−	0.995233i
$931$	−218.696			−0.234904
$932$	543.061	+	679.695i	0.582683	+	0.729286i
$933$	−2027.00	−	2027.00i	−2.17257	−	2.17257i
$934$	676.886	+	37.7013i	0.724717	+	0.0403654i
$935$	324.952	+	301.133i	0.347542	+	0.322067i
$936$	585.427	−	3474.56i	0.625456	−	3.71213i
$937$	1026.90	+	1026.90i	1.09594	+	1.09594i	0.994880	+	0.101059i	$0.0322231\pi$
$937$	1026.90	+	1026.90i	1.09594	+	1.09594i	0.101059	+	0.994880i	$0.467777\pi$
$938$	−908.543	+	812.675i	−0.968596	+	0.866391i
$939$	1882.00			2.00426
$940$	−724.667	−	57.3427i	−0.770923	−	0.0610029i
$941$			1528.72i			1.62457i	0.583262	+	0.812284i	$0.301776\pi$
$941$			1528.72i			1.62457i	−0.583262	+	0.812284i	$0.698224\pi$
$942$	625.667	+	699.475i	0.664190	+	0.742542i
$943$	102.982	+	102.982i	0.109207	+	0.109207i
$944$	−1310.99	−	296.691i	−1.38876	−	0.314292i
$945$	1856.07	+	1739.83i	1.96410	+	1.84109i
$946$	425.191	−	384.718i	0.449462	−	0.406679i
$947$	118.985	+	118.985i	0.125644	+	0.125644i	0.767132	−	0.641489i	$-0.221683\pi$
$947$	118.985	+	118.985i	0.125644	+	0.125644i	−0.641489	+	0.767132i	$0.721683\pi$
$948$	−819.453	+	654.724i	−0.864402	+	0.690637i
$949$			2042.54i			2.15231i
$950$	−742.485	+	755.958i	−0.781563	+	0.795745i
$951$		−	263.004i		−	0.276556i
$952$	287.762	+	404.380i	0.302271	+	0.424769i
$953$	−204.792	+	204.792i	−0.214892	+	0.214892i	−0.806342	−	0.591450i	$-0.798556\pi$
$953$	−204.792	+	204.792i	−0.214892	+	0.214892i	0.591450	+	0.806342i	$0.298556\pi$
$954$	35.7623	−	642.075i	0.0374867	−	0.673034i
$955$	14.9892	−	15.9907i	0.0156955	−	0.0167442i
$956$	−154.347	−	17.2472i	−0.161451	−	0.0180410i
$957$	−0.728843	−	127.630i	−0.000761592	−	0.133365i
$958$	−534.475	−	597.526i	−0.557908	−	0.623722i
$959$		−	689.927i		−	0.719423i
$960$	520.961	−	1675.06i	0.542667	−	1.74485i
$961$	416.255			0.433148
$962$	280.976	+	314.122i	0.292075	+	0.326530i
$963$	991.846	+	991.846i	1.02995	+	1.02995i
$964$	−3.07136	−	0.343202i	−0.00318606	−	0.000356019i
$965$	1373.17	−	44.3906i	1.42297	−	0.0460006i
$966$	911.108	+	50.7470i	0.943176	+	0.0525331i
$967$	−327.566	+	327.566i	−0.338745	+	0.338745i	−0.855895	−	0.517150i	$-0.826993\pi$
$967$	−327.566	+	327.566i	−0.338745	+	0.338745i	0.517150	+	0.855895i	$0.326993\pi$
$968$	782.229	−	570.212i	0.808088	−	0.589062i
$969$			935.774i			0.965711i
$970$	902.469	−	861.322i	0.930381	−	0.887961i
$971$		−	702.038i		−	0.723005i	−0.932371	−	0.361503i	$-0.882264\pi$
$971$		−	702.038i		−	0.723005i	0.932371	−	0.361503i	$-0.117736\pi$
$972$	−879.066	−	1100.24i	−0.904389	−	1.13193i
$973$	1220.48	+	1220.48i	1.25435	+	1.25435i
$974$	−68.9769	−	3.84188i	−0.0708181	−	0.00394443i
$975$	−2861.40	+	185.196i	−2.93477	+	0.189944i
$976$	−308.498	+	1363.16i	−0.316084	+	1.39668i
$977$	96.8366	−	96.8366i	0.0991163	−	0.0991163i	−0.655810	−	0.754926i	$-0.727673\pi$
$977$	96.8366	−	96.8366i	0.0991163	−	0.0991163i	0.754926	+	0.655810i	$0.227673\pi$
$978$	421.123	+	470.802i	0.430597	+	0.481393i
$979$	707.390	+	699.357i	0.722564	+	0.714358i
$980$	−133.976	−	157.000i	−0.136710	−	0.160205i
$981$		−	3761.22i		−	3.83407i
$982$	−463.925	+	414.972i	−0.472429	+	0.422578i
$983$	−374.140	+	374.140i	−0.380611	+	0.380611i	−0.871322	−	0.490711i	$-0.836737\pi$
$983$	−374.140	+	374.140i	−0.380611	+	0.380611i	0.490711	+	0.871322i	$0.336737\pi$
$984$	−98.1988	+	582.818i	−0.0997955	+	0.592295i
$985$	27.2442	+	842.762i	0.0276590	+	0.855596i
$986$	34.0460	+	1.89629i	0.0345294	+	0.00192322i
$987$	1085.12	−	1085.12i	1.09941	−	1.09941i
$988$	−1385.62	+	1107.08i	−1.40245	+	1.12053i
$989$	281.659			0.284792
$990$	1608.28	+	1665.96i	1.62453	+	1.68279i
$991$		−	905.275i		−	0.913496i	−0.889596	−	0.456748i	$-0.849014\pi$
$991$		−	905.275i		−	0.913496i	0.889596	−	0.456748i	$-0.150986\pi$
$992$	−362.777	−	652.849i	−0.365702	−	0.658114i
$993$	−1641.97	−	1641.97i	−1.65355	−	1.65355i
$994$	−369.946	−	20.6053i	−0.372179	−	0.0207296i
$995$	−1281.15	−	1200.91i	−1.28758	−	1.20694i
$996$	−38.0983	+	340.947i	−0.0382513	+	0.342316i
$997$	−618.290	−	618.290i	−0.620150	−	0.620150i	0.325419	−	0.945570i	$-0.394495\pi$
$997$	−618.290	−	618.290i	−0.620150	−	0.620150i	−0.945570	+	0.325419i	$0.894495\pi$
$998$	161.410	−	144.378i	0.161734	−	0.144668i
$999$	665.347			0.666013

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.3.i.a.43.16	✓	136
4.3	odd	2	inner	220.3.i.a.43.50	yes	136
5.2	odd	4	inner	220.3.i.a.87.19	yes	136
11.10	odd	2	inner	220.3.i.a.43.53	yes	136
20.7	even	4	inner	220.3.i.a.87.53	yes	136
44.43	even	2	inner	220.3.i.a.43.19	yes	136
55.32	even	4	inner	220.3.i.a.87.50	yes	136
220.87	odd	4	inner	220.3.i.a.87.16	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.i.a.43.16	✓	136	1.1	even	1	trivial
220.3.i.a.43.19	yes	136	44.43	even	2	inner
220.3.i.a.43.50	yes	136	4.3	odd	2	inner
220.3.i.a.43.53	yes	136	11.10	odd	2	inner
220.3.i.a.87.16	yes	136	220.87	odd	4	inner
220.3.i.a.87.19	yes	136	5.2	odd	4	inner
220.3.i.a.87.50	yes	136	55.32	even	4	inner
220.3.i.a.87.53	yes	136	20.7	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.49067 + 1.33338i) q^{2} +(-3.87627 + 3.87627i) q^{3} +(0.444207 - 3.97526i) q^{4} +(3.64792 + 3.41945i) q^{5} +(0.609714 - 10.9468i) q^{6} +(5.44609 - 5.44609i) q^{7} +(4.63836 + 6.51810i) q^{8} -21.0509i q^{9} +(-9.99728 - 0.233225i) q^{10} +(7.73363 - 7.82247i) q^{11} +(13.6873 + 17.1310i) q^{12} +(14.7946 - 14.7946i) q^{13} +(-0.856637 + 15.3800i) q^{14} +(-27.3951 + 0.885606i) q^{15} +(-15.6054 - 3.53167i) q^{16} +(5.69580 + 5.69580i) q^{17} +(28.0688 + 31.3800i) q^{18} -21.1920i q^{19} +(15.2136 - 12.9825i) q^{20} +42.2210i q^{21} +(-1.09800 + 21.9726i) q^{22} +(-7.64133 + 7.64133i) q^{23} +(-43.2454 - 7.28640i) q^{24} +(1.61467 + 24.9478i) q^{25} +(-2.32710 + 41.7806i) q^{26} +(46.7126 + 46.7126i) q^{27} +(-19.2304 - 24.0688i) q^{28} -2.11660 q^{29} +(39.6562 - 37.8481i) q^{30} -23.3398i q^{31} +(27.9715 - 15.5433i) q^{32} +(0.344346 + 60.2996i) q^{33} +(-16.0852 - 0.895915i) q^{34} +(38.4895 - 1.24426i) q^{35} +(-83.6829 - 9.35096i) q^{36} +(7.12170 - 7.12170i) q^{37} +(28.2570 + 31.5904i) q^{38} +114.695i q^{39} +(-5.36799 + 39.6382i) q^{40} -13.4770i q^{41} +(-56.2965 - 62.9377i) q^{42} +(-18.4300 - 18.4300i) q^{43} +(-27.6610 - 34.2180i) q^{44} +(71.9827 - 76.7922i) q^{45} +(1.20194 - 21.5795i) q^{46} +(-25.7009 - 25.7009i) q^{47} +(74.1803 - 46.8009i) q^{48} -10.3197i q^{49} +(-35.6718 - 35.0360i) q^{50} -44.1569 q^{51} +(-52.2403 - 65.3840i) q^{52} +(-10.8004 - 10.8004i) q^{53} +(-131.919 - 7.34763i) q^{54} +(54.9602 - 2.09095i) q^{55} +(60.7590 + 10.2373i) q^{56} +(82.1460 + 82.1460i) q^{57} +(3.15516 - 2.82223i) q^{58} +84.0088 q^{59} +(-8.64855 + 109.296i) q^{60} -87.3519i q^{61} +(31.1207 + 34.7919i) q^{62} +(-114.645 - 114.645i) q^{63} +(-20.9713 + 60.4666i) q^{64} +(104.559 - 3.38009i) q^{65} +(-80.9155 - 89.4278i) q^{66} +(55.9563 + 55.9563i) q^{67} +(25.1724 - 20.1122i) q^{68} -59.2397i q^{69} +(-55.7162 + 53.1759i) q^{70} +24.0536i q^{71} +(137.212 - 97.6417i) q^{72} +(-69.0302 + 69.0302i) q^{73} +(-1.12020 + 20.1120i) q^{74} +(-102.963 - 90.4455i) q^{75} +(-84.2438 - 9.41364i) q^{76} +(-0.483800 - 84.7198i) q^{77} +(-152.932 - 170.973i) q^{78} +47.8344i q^{79} +(-44.8508 - 66.2451i) q^{80} -172.683 q^{81} +(17.9699 + 20.0898i) q^{82} +(11.0631 + 11.0631i) q^{83} +(167.839 + 18.7548i) q^{84} +(1.30131 + 40.2543i) q^{85} +(52.0472 + 2.89893i) q^{86} +(8.20451 - 8.20451i) q^{87} +(86.8590 + 14.1252i) q^{88} +90.4306i q^{89} +(-4.90960 + 210.452i) q^{90} -161.145i q^{91} +(26.9819 + 33.7706i) q^{92} +(90.4712 + 90.4712i) q^{93} +(72.5807 + 4.04261i) q^{94} +(72.4652 - 77.3069i) q^{95} +(-48.1752 + 168.675i) q^{96} +(-88.2136 + 88.2136i) q^{97} +(13.7601 + 15.3833i) q^{98} +(-164.670 - 162.800i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 8 q^{5} + 8 q^{12} + 16 q^{16} + 80 q^{20} - 96 q^{22} - 8 q^{25} - 160 q^{26} + 80 q^{33} - 104 q^{36} - 8 q^{37} - 16 q^{38} - 168 q^{42} + 192 q^{45} + 32 q^{48} + 136 q^{53} + 264 q^{56} - 248 q^{58}+ \cdots - 168 q^{97}+O(q^{100}) \) 136 * q - 8 * q^5 + 8 * q^12 + 16 * q^16 + 80 * q^20 - 96 * q^22 - 8 * q^25 - 160 * q^26 + 80 * q^33 - 104 * q^36 - 8 * q^37 - 16 * q^38 - 168 * q^42 + 192 * q^45 + 32 * q^48 + 136 * q^53 + 264 * q^56 - 248 * q^58 - 128 * q^60 + 328 * q^66 + 96 * q^70 - 152 * q^77 - 24 * q^78 - 624 * q^80 - 664 * q^81 - 200 * q^82 + 752 * q^86 - 296 * q^88 - 776 * q^92 + 592 * q^93 - 168 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more