LMFDB - Embedded newform 220.3.w.a.7.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,3,Mod(7,220)] 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("220.7"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 5, 14])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.w (of order $20$, degree $8$, 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:	$544$
Relative dimension:	$68$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			7.13
Character	$\chi$	$=$	220.7
Dual form			220.3.w.a.63.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.70427 + 1.04665i) q^{2} +(-4.04592 + 2.06150i) q^{3} +(1.80904 - 3.56754i) q^{4} +(2.33189 + 4.42293i) q^{5} +(4.73765 - 7.74800i) q^{6} +(-3.03067 + 5.94803i) q^{7} +(0.650882 + 7.97348i) q^{8} +(6.82960 - 9.40014i) q^{9} +(-8.60342 - 5.09717i) q^{10} +(-2.74293 + 10.6525i) q^{11} +(0.0352426 + 18.1633i) q^{12} +(3.87209 + 24.4474i) q^{13} +(-1.06044 - 13.3091i) q^{14} +(-18.5525 - 13.0876i) q^{15} +(-9.45473 - 12.9077i) q^{16} +(2.85350 - 18.0163i) q^{17} +(-1.80079 + 23.1685i) q^{18} +(10.7855 + 3.50442i) q^{19} +(19.9975 - 0.317852i) q^{20} -30.3129i q^{21} +(-6.47480 - 21.0256i) q^{22} +(-20.8240 - 20.8240i) q^{23} +(-19.0707 - 30.9182i) q^{24} +(-14.1246 + 20.6276i) q^{25} +(-32.1870 - 37.6122i) q^{26} +(-1.86054 + 11.7470i) q^{27} +(15.7372 + 21.5723i) q^{28} +(-9.88305 - 30.4169i) q^{29} +(45.3165 + 2.88678i) q^{30} +(-8.80617 + 12.1207i) q^{31} +(29.6232 + 12.1023i) q^{32} +(-10.8625 - 48.7538i) q^{33} +(13.9936 + 33.6911i) q^{34} +(-33.3749 + 0.465708i) q^{35} +(-21.1804 - 41.3702i) q^{36} +(6.94136 - 13.6232i) q^{37} +(-22.0492 + 5.31618i) q^{38} +(-66.0644 - 90.9299i) q^{39} +(-33.7483 + 21.4721i) q^{40} +(9.85319 + 3.20150i) q^{41} +(31.7271 + 51.6613i) q^{42} +(14.2190 - 14.2190i) q^{43} +(33.0413 + 29.0564i) q^{44} +(57.5020 + 8.28674i) q^{45} +(57.2850 + 13.6942i) q^{46} +(8.10427 + 15.9055i) q^{47} +(64.8622 + 32.7325i) q^{48} +(2.60743 + 3.58882i) q^{49} +(2.48217 - 49.9384i) q^{50} +(25.5955 + 78.7748i) q^{51} +(94.2220 + 30.4126i) q^{52} +(-69.7703 + 11.0505i) q^{53} +(-9.12414 - 21.9673i) q^{54} +(-53.5116 + 12.7088i) q^{55} +(-49.3991 - 20.2935i) q^{56} +(-50.8615 + 8.05567i) q^{57} +(48.6792 + 41.4944i) q^{58} +(24.7682 + 76.2288i) q^{59} +(-80.2529 + 42.5107i) q^{60} +(-22.3830 - 30.8075i) q^{61} +(2.32196 - 29.8738i) q^{62} +(35.2140 + 69.1114i) q^{63} +(-63.1527 + 10.3796i) q^{64} +(-99.0999 + 74.1347i) q^{65} +(69.5408 + 71.7201i) q^{66} +(15.3020 - 15.3020i) q^{67} +(-59.1117 - 42.7722i) q^{68} +(127.181 + 41.3235i) q^{69} +(56.3922 - 35.7255i) q^{70} +(-12.2736 - 16.8932i) q^{71} +(79.3971 + 48.3373i) q^{72} +(-36.2433 + 71.1314i) q^{73} +(2.42880 + 30.4827i) q^{74} +(14.6232 - 112.575i) q^{75} +(32.0136 - 32.1380i) q^{76} +(-55.0486 - 48.5993i) q^{77} +(207.763 + 85.8223i) q^{78} +(58.2496 - 80.1738i) q^{79} +(35.0423 - 71.9169i) q^{80} +(15.6260 + 48.0919i) q^{81} +(-20.1433 + 4.85665i) q^{82} +(16.4491 - 103.856i) q^{83} +(-108.143 - 54.8374i) q^{84} +(86.3386 - 29.3911i) q^{85} +(-9.35060 + 39.1152i) q^{86} +(102.690 + 102.690i) q^{87} +(-86.7230 - 14.9371i) q^{88} -69.0839i q^{89} +(-106.672 + 46.0617i) q^{90} +(-157.149 - 51.0608i) q^{91} +(-111.962 + 36.6190i) q^{92} +(10.6423 - 67.1931i) q^{93} +(-30.4594 - 18.6249i) q^{94} +(9.65079 + 55.8753i) q^{95} +(-144.802 + 12.1032i) q^{96} +(22.7249 + 143.479i) q^{97} +(-8.20000 - 3.38724i) q^{98} +(81.4022 + 98.5364i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 544 q - 10 q^{2} - 12 q^{5} - 20 q^{6} - 10 q^{8} - 28 q^{12} - 20 q^{13} - 36 q^{16} - 20 q^{17} - 10 q^{18} - 40 q^{20} + 86 q^{22} - 12 q^{25} + 140 q^{26} - 10 q^{28} - 370 q^{30} - 100 q^{33} - 476 q^{36}+ \cdots + 148 q^{97}+O(q^{100}) $ 544 * q - 10 * q^2 - 12 * q^5 - 20 * q^6 - 10 * q^8 - 28 * q^12 - 20 * q^13 - 36 * q^16 - 20 * q^17 - 10 * q^18 - 40 * q^20 + 86 * q^22 - 12 * q^25 + 140 * q^26 - 10 * q^28 - 370 * q^30 - 100 * q^33 - 476 * q^36 - 12 * q^37 + 6 * q^38 - 10 * q^40 + 40 * q^41 + 198 * q^42 - 232 * q^45 + 340 * q^46 - 42 * q^48 - 10 * q^50 + 510 * q^52 - 156 * q^53 + 216 * q^56 - 20 * q^57 + 238 * q^58 + 118 * q^60 - 40 * q^61 + 440 * q^62 - 348 * q^66 - 10 * q^68 - 106 * q^70 - 1060 * q^72 - 580 * q^73 + 132 * q^77 - 1076 * q^78 + 614 * q^80 + 624 * q^81 - 490 * q^82 - 20 * q^85 - 772 * q^86 + 446 * q^88 - 820 * q^90 - 244 * q^92 - 132 * q^93 - 1840 * q^96 + 148 * q^97

Character values

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

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.70427	+	1.04665i	−0.852133	+	0.523326i
$2$	−1.70427	+	1.04665i	−0.852133	+	0.523326i
$3$	−4.04592	+	2.06150i	−1.34864	+	0.687166i	−0.971065	−	0.238814i	$-0.923241\pi$
$3$	−4.04592	+	2.06150i	−1.34864	+	0.687166i	−0.377573	+	0.925980i	$0.623241\pi$
$4$	1.80904	−	3.56754i	0.452261	−	0.891886i
$5$	2.33189	+	4.42293i	0.466378	+	0.884586i
$5$	2.33189	+	4.42293i	0.466378	+	0.884586i
$6$	4.73765	−	7.74800i	0.789608	−	1.29133i
$7$	−3.03067	+	5.94803i	−0.432953	+	0.849718i	0.566714	+	0.823914i	$0.308214\pi$
$7$	−3.03067	+	5.94803i	−0.432953	+	0.849718i	−0.999667	+	0.0258034i	$0.991786\pi$
$8$	0.650882	+	7.97348i	0.0813603	+	0.996685i
$9$	6.82960	−	9.40014i	0.758845	−	1.04446i
$10$	−8.60342	−	5.09717i	−0.860342	−	0.509717i
$11$	−2.74293	+	10.6525i	−0.249357	+	0.968412i
$11$	−2.74293	+	10.6525i	−0.249357	+	0.968412i
$12$	0.0352426	+	18.1633i	0.00293689	+	1.51361i
$13$	3.87209	+	24.4474i	0.297853	+	1.88057i	0.451237	+	0.892404i	$0.350983\pi$
$13$	3.87209	+	24.4474i	0.297853	+	1.88057i	−0.153384	+	0.988167i	$0.549017\pi$
$14$	−1.06044	−	13.3091i	−0.0757457	−	0.950648i
$15$	−18.5525	−	13.0876i	−1.23683	−	0.872507i
$16$	−9.45473	−	12.9077i	−0.590920	−	0.806730i
$17$	2.85350	−	18.0163i	0.167853	−	1.05978i	−0.749587	−	0.661906i	$-0.769748\pi$
$17$	2.85350	−	18.0163i	0.167853	−	1.05978i	0.917440	−	0.397874i	$-0.130252\pi$
$18$	−1.80079	+	23.1685i	−0.100044	+	1.28714i
$19$	10.7855	+	3.50442i	0.567657	+	0.184443i	0.578764	−	0.815495i	$-0.303535\pi$
$19$	10.7855	+	3.50442i	0.567657	+	0.184443i	−0.0111065	+	0.999938i	$0.503535\pi$
$20$	19.9975	−	0.317852i	0.999874	−	0.0158926i
$21$		−	30.3129i		−	1.44347i
$22$	−6.47480	−	21.0256i	−0.294309	−	0.955710i
$23$	−20.8240	−	20.8240i	−0.905390	−	0.905390i	0.0905057	−	0.995896i	$-0.471152\pi$
$23$	−20.8240	−	20.8240i	−0.905390	−	0.905390i	−0.995896	+	0.0905057i	$0.971152\pi$
$24$	−19.0707	−	30.9182i	−0.794613	−	1.28826i
$25$	−14.1246	+	20.6276i	−0.564983	+	0.825103i
$26$	−32.1870	−	37.6122i	−1.23796	−	1.44662i
$27$	−1.86054	+	11.7470i	−0.0689089	+	0.435073i
$28$	15.7372	+	21.5723i	0.562044	+	0.770439i
$29$	−9.88305	−	30.4169i	−0.340795	−	1.04886i	−0.963797	−	0.266638i	$-0.914087\pi$
$29$	−9.88305	−	30.4169i	−0.340795	−	1.04886i	0.623002	−	0.782220i	$-0.285913\pi$
$30$	45.3165	+	2.88678i	1.51055	+	0.0962262i
$31$	−8.80617	+	12.1207i	−0.284070	+	0.390989i	−0.927077	−	0.374872i	$-0.877687\pi$
$31$	−8.80617	+	12.1207i	−0.284070	+	0.390989i	0.643007	+	0.765861i	$0.277687\pi$
$32$	29.6232	+	12.1023i	0.925725	+	0.378197i
$33$	−10.8625	−	48.7538i	−0.329167	−	1.47739i
$34$	13.9936	+	33.6911i	0.411577	+	0.990915i
$35$	−33.3749	+	0.465708i	−0.953568	+	0.0133059i
$36$	−21.1804	−	41.3702i	−0.588343	−	1.14917i
$37$	6.94136	−	13.6232i	0.187604	−	0.368194i	−0.777978	−	0.628291i	$-0.783755\pi$
$37$	6.94136	−	13.6232i	0.187604	−	0.368194i	0.965582	+	0.260097i	$0.0837545\pi$
$38$	−22.0492	+	5.31618i	−0.580243	+	0.139900i
$39$	−66.0644	−	90.9299i	−1.69396	−	2.33154i
$40$	−33.7483	+	21.4721i	−0.843708	+	0.536802i
$41$	9.85319	+	3.20150i	0.240322	+	0.0780853i	0.426702	−	0.904392i	$-0.359675\pi$
$41$	9.85319	+	3.20150i	0.240322	+	0.0780853i	−0.186380	+	0.982478i	$0.559675\pi$
$42$	31.7271	+	51.6613i	0.755406	+	1.23003i
$43$	14.2190	−	14.2190i	0.330673	−	0.330673i	−0.522169	−	0.852842i	$-0.674877\pi$
$43$	14.2190	−	14.2190i	0.330673	−	0.330673i	0.852842	+	0.522169i	$0.174877\pi$
$44$	33.0413	+	29.0564i	0.750938	+	0.660373i
$45$	57.5020	+	8.28674i	1.27782	+	0.184150i
$46$	57.2850	+	13.6942i	1.24533	+	0.297699i
$47$	8.10427	+	15.9055i	0.172431	+	0.338415i	0.961008	−	0.276521i	$-0.0891816\pi$
$47$	8.10427	+	15.9055i	0.172431	+	0.338415i	−0.788577	+	0.614937i	$0.789182\pi$
$48$	64.8622	+	32.7325i	1.35130	+	0.681927i
$49$	2.60743	+	3.58882i	0.0532129	+	0.0732413i
$50$	2.48217	−	49.9384i	0.0496434	−	0.998767i
$51$	25.5955	+	78.7748i	0.501872	+	1.54460i
$52$	94.2220	+	30.4126i	1.81196	+	0.584857i
$53$	−69.7703	+	11.0505i	−1.31642	+	0.208501i	−0.774845	−	0.632151i	$-0.782172\pi$
$53$	−69.7703	+	11.0505i	−1.31642	+	0.208501i	−0.541576	+	0.840652i	$0.682172\pi$
$54$	−9.12414	−	21.9673i	−0.168966	−	0.406802i
$55$	−53.5116	+	12.7088i	−0.972938	+	0.231068i
$56$	−49.3991	−	20.2935i	−0.882126	−	0.362384i
$57$	−50.8615	+	8.05567i	−0.892307	+	0.141328i
$58$	48.6792	+	41.4944i	0.839297	+	0.715420i
$59$	24.7682	+	76.2288i	0.419801	+	1.29201i	0.907886	+	0.419218i	$0.137696\pi$
$59$	24.7682	+	76.2288i	0.419801	+	1.29201i	−0.488085	+	0.872796i	$0.662304\pi$
$60$	−80.2529	+	42.5107i	−1.33755	+	0.708512i
$61$	−22.3830	−	30.8075i	−0.366934	−	0.505042i	0.585130	−	0.810939i	$-0.301043\pi$
$61$	−22.3830	−	30.8075i	−0.366934	−	0.505042i	−0.952064	+	0.305898i	$0.901043\pi$
$62$	2.32196	−	29.8738i	0.0374510	−	0.481836i
$63$	35.2140	+	69.1114i	0.558952	+	1.09701i
$64$	−63.1527	+	10.3796i	−0.986761	+	0.162181i
$65$	−99.0999	+	74.1347i	−1.52461	+	1.14053i
$66$	69.5408	+	71.7201i	1.05365	+	1.08667i
$67$	15.3020	−	15.3020i	0.228388	−	0.228388i	−0.583631	−	0.812019i	$-0.698369\pi$
$67$	15.3020	−	15.3020i	0.228388	−	0.228388i	0.812019	+	0.583631i	$0.198369\pi$
$68$	−59.1117	−	42.7722i	−0.869289	−	0.629002i
$69$	127.181	+	41.3235i	1.84320	+	0.598891i
$70$	56.3922	−	35.7255i	0.805603	−	0.510365i
$71$	−12.2736	−	16.8932i	−0.172868	−	0.237932i	0.713788	−	0.700362i	$-0.246978\pi$
$71$	−12.2736	−	16.8932i	−0.172868	−	0.237932i	−0.886656	+	0.462429i	$0.846978\pi$
$72$	79.3971	+	48.3373i	1.10274	+	0.671351i
$73$	−36.2433	+	71.1314i	−0.496483	+	0.974403i	0.497766	+	0.867311i	$0.334154\pi$
$73$	−36.2433	+	71.1314i	−0.496483	+	0.974403i	−0.994249	+	0.107092i	$0.965846\pi$
$74$	2.42880	+	30.4827i	0.0328216	+	0.411929i
$75$	14.6232	−	112.575i	0.194976	−	1.50100i
$76$	32.0136	−	32.1380i	0.421231	−	0.422869i
$77$	−55.0486	−	48.5993i	−0.714917	−	0.631160i
$78$	207.763	+	85.8223i	2.66363	+	1.10029i
$79$	58.2496	−	80.1738i	0.737337	−	1.01486i	−0.261430	−	0.965222i	$-0.584194\pi$
$79$	58.2496	−	80.1738i	0.737337	−	1.01486i	0.998767	−	0.0496354i	$-0.0158059\pi$
$80$	35.0423	−	71.9169i	0.438029	−	0.898961i
$81$	15.6260	+	48.0919i	0.192914	+	0.593727i
$82$	−20.1433	+	4.85665i	−0.245650	+	0.0592275i
$83$	16.4491	−	103.856i	0.198182	−	1.25127i	−0.665179	−	0.746684i	$-0.731645\pi$
$83$	16.4491	−	103.856i	0.198182	−	1.25127i	0.863361	−	0.504587i	$-0.168355\pi$
$84$	−108.143	−	54.8374i	−1.28741	−	0.652826i
$85$	86.3386	−	29.3911i	1.01575	−	0.345778i
$86$	−9.35060	+	39.1152i	−0.108728	+	0.454828i
$87$	102.690	+	102.690i	1.18035	+	1.18035i
$88$	−86.7230	−	14.9371i	−0.985489	−	0.169740i
$89$		−	69.0839i		−	0.776223i	−0.921612	−	0.388112i	$-0.873128\pi$
$89$		−	69.0839i		−	0.776223i	0.921612	−	0.388112i	$-0.126872\pi$
$90$	−106.672	+	46.0617i	−1.18524	+	0.511797i
$91$	−157.149	−	51.0608i	−1.72691	−	0.561107i
$92$	−111.962	+	36.6190i	−1.21698	+	0.398032i
$93$	10.6423	−	67.1931i	0.114434	−	0.722506i
$94$	−30.4594	−	18.6249i	−0.324036	−	0.198137i
$95$	9.65079	+	55.8753i	0.101587	+	0.588161i
$96$	−144.802	+	12.1032i	−1.50835	+	0.126075i
$97$	22.7249	+	143.479i	0.234277	+	1.47917i	0.771771	+	0.635901i	$0.219371\pi$
$97$	22.7249	+	143.479i	0.234277	+	1.47917i	−0.537494	+	0.843268i	$0.680629\pi$
$98$	−8.20000	−	3.38724i	−0.0836735	−	0.0345636i
$99$	81.4022	+	98.5364i	0.822244	+	0.995317i
$100$	48.0377	+	87.7062i	0.480377	+	0.877062i
$101$	−73.0522	+	100.548i	−0.723289	+	0.995522i	0.276119	+	0.961123i	$0.410952\pi$
$101$	−73.0522	+	100.548i	−0.723289	+	0.995522i	−0.999408	+	0.0343985i	$0.989048\pi$
$102$	−126.071	−	107.464i	−1.23599	−	1.05356i
$103$	3.22225	−	6.32402i	0.0312840	−	0.0613982i	−0.874836	−	0.484420i	$-0.839031\pi$
$103$	3.22225	−	6.32402i	0.0312840	−	0.0613982i	0.906119	+	0.423022i	$0.139031\pi$
$104$	−192.411	+	46.7864i	−1.85010	+	0.449869i
$105$	134.072	−	70.6864i	1.27688	−	0.673204i
$106$	107.341	−	91.8582i	1.01265	−	0.866587i
$107$	−0.785785	+	0.400378i	−0.00734379	+	0.00374185i	−0.457659	−	0.889128i	$-0.651312\pi$
$107$	−0.785785	+	0.400378i	−0.00734379	+	0.00374185i	0.450315	+	0.892870i	$0.351312\pi$
$108$	38.5421	+	27.8884i	0.356871	+	0.258226i
$109$	187.495			1.72014			0.860068	−	0.510179i	$-0.170421\pi$
$109$	187.495			1.72014			0.860068	+	0.510179i	$0.170421\pi$
$110$	77.8963	−	77.6670i	0.708148	−	0.706064i
$111$			69.4279i			0.625477i
$112$	105.429	−	17.1180i	0.941334	−	0.152840i
$113$	−19.4858	−	38.2431i	−0.172441	−	0.338434i	0.788570	−	0.614945i	$-0.210822\pi$
$113$	−19.4858	−	38.2431i	−0.172441	−	0.338434i	−0.961011	+	0.276511i	$0.910822\pi$
$114$	78.2501	−	66.9633i	0.686404	−	0.587397i
$115$	43.5437	−	140.662i	0.378641	−	1.22315i
$116$	−126.392	−	19.7673i	−1.08959	−	0.170408i
$117$	256.254	+	130.568i	2.19020	+	1.11597i
$118$	−121.997	−	103.990i	−1.03387	−	0.881275i
$119$	98.5132	+	71.5740i	0.827842	+	0.601462i
$120$	92.2783	−	156.446i	0.768986	−	1.30372i
$121$	−105.953	−	58.4382i	−0.875642	−	0.482960i
$122$	70.3913	+	29.0770i	0.576978	+	0.238336i
$123$	−46.4651	+	7.35934i	−0.377765	+	0.0598321i
$124$	27.3102	+	53.3432i	0.220244	+	0.430187i
$125$	−124.171	−	14.3708i	−0.993369	−	0.114966i
$126$	−132.349	−	80.9274i	−1.05039	−	0.642281i
$127$	−8.30422	−	1.31526i	−0.0653876	−	0.0103564i	0.123655	−	0.992325i	$-0.460538\pi$
$127$	−8.30422	−	1.31526i	−0.0653876	−	0.0103564i	−0.189043	+	0.981969i	$0.560538\pi$
$128$	96.7652	−	83.7884i	0.755978	−	0.654597i
$129$	−28.2164	+	86.8411i	−0.218732	+	0.673187i
$130$	91.2994	−	230.068i	0.702303	−	1.76975i
$131$	160.641			1.22627			0.613134	−	0.789979i	$-0.289909\pi$
$131$	160.641			1.22627			0.613134	+	0.789979i	$0.289909\pi$
$132$	−193.582	−	49.4452i	−1.46653	−	0.374585i
$133$	−53.5316	+	53.5316i	−0.402493	+	0.402493i
$134$	−10.0628	+	42.0944i	−0.0750955	+	0.314138i
$135$	−56.2946	+	19.1636i	−0.416997	+	0.141953i
$136$	145.510	+	11.0258i	1.06992	+	0.0810722i
$137$	−77.5066	−	12.2758i	−0.565741	−	0.0896046i	−0.132989	−	0.991118i	$-0.542458\pi$
$137$	−77.5066	−	12.2758i	−0.565741	−	0.0896046i	−0.432752	+	0.901513i	$0.642458\pi$
$138$	−260.001	+	62.6875i	−1.88406	+	0.454257i
$139$	49.9473	−	16.2289i	0.359333	−	0.116754i	−0.123786	−	0.992309i	$-0.539504\pi$
$139$	49.9473	−	16.2289i	0.359333	−	0.116754i	0.483119	+	0.875554i	$0.339504\pi$
$140$	−58.7152	+	119.909i	−0.419394	+	0.856491i
$141$	−65.5784	−	47.6455i	−0.465095	−	0.337911i
$142$	38.5988	+	15.9443i	0.271822	+	0.112284i
$143$	−271.048	−	25.8099i	−1.89544	−	0.180489i
$144$	−185.906	+	0.721436i	−1.29101	+	0.00500998i
$145$	111.486	−	114.641i	0.768866	−	0.790627i
$146$	−12.6816	−	159.161i	−0.0868604	−	1.09014i
$147$	−17.9478	−	9.14486i	−0.122094	−	0.0622100i
$148$	−36.0441	−	49.4086i	−0.243541	−	0.333842i
$149$	−14.8092	+	10.7595i	−0.0993907	+	0.0722115i	−0.636371	−	0.771383i	$-0.719565\pi$
$149$	−14.8092	+	10.7595i	−0.0993907	+	0.0722115i	0.536980	+	0.843595i	$0.319565\pi$
$150$	92.9051	+	207.163i	0.619368	+	1.38109i
$151$	−63.1157	+	194.250i	−0.417984	+	1.28642i	0.491570	+	0.870838i	$0.336423\pi$
$151$	−63.1157	+	194.250i	−0.417984	+	1.28642i	−0.909554	+	0.415586i	$0.863577\pi$
$152$	−20.9223	+	88.2788i	−0.137647	+	0.580782i
$153$	−149.867	−	149.867i	−0.979524	−	0.979524i
$154$	144.684	+	25.2094i	0.939506	+	0.163698i
$155$	−74.1438	−	10.6850i	−0.478347	−	0.0689356i
$156$	−443.910	+	71.1916i	−2.84558	+	0.456356i
$157$	17.1413	−	8.73395i	0.109181	−	0.0556303i	−0.398547	−	0.917148i	$-0.630486\pi$
$157$	17.1413	−	8.73395i	0.109181	−	0.0556303i	0.507728	+	0.861518i	$0.330486\pi$
$158$	−15.3589	+	197.604i	−0.0972084	+	1.25066i
$159$	259.504	−	188.541i	1.63210	−	1.18579i
$160$	15.5504	+	159.243i	0.0971899	+	0.995266i
$161$	186.972	−	60.7509i	1.16132	−	0.377335i
$162$	−76.9663	−	65.6064i	−0.475101	−	0.404978i
$163$	30.4629	+	192.335i	0.186889	+	1.17997i	0.885560	+	0.464526i	$0.153775\pi$
$163$	30.4629	+	192.335i	0.186889	+	1.17997i	−0.698671	+	0.715443i	$0.746225\pi$
$164$	29.2463	−	29.3600i	0.178331	−	0.179025i
$165$	190.304	−	161.733i	1.15336	−	0.980197i
$166$	80.6669	+	194.214i	0.485945	+	1.16996i
$167$	−35.5489	−	224.447i	−0.212868	−	1.34400i	−0.830276	−	0.557352i	$-0.811817\pi$
$167$	−35.5489	−	224.447i	−0.212868	−	1.34400i	0.617408	−	0.786643i	$-0.288183\pi$
$168$	241.700	−	19.7301i	1.43869	−	0.117441i
$169$	−421.955	+	137.101i	−2.49677	+	0.811251i
$170$	−116.382	+	140.457i	−0.684598	+	0.826216i
$171$	106.603	−	77.4513i	0.623407	−	0.452932i
$172$	−25.0040	−	76.4495i	−0.145372	−	0.444474i
$173$	69.3717	−	35.3466i	0.400992	−	0.204316i	−0.241851	−	0.970313i	$-0.577755\pi$
$173$	69.3717	−	35.3466i	0.400992	−	0.204316i	0.642844	+	0.765998i	$0.277755\pi$
$174$	−282.493	−	67.5307i	−1.62352	−	0.388107i
$175$	−79.8863	−	146.529i	−0.456493	−	0.837307i
$176$	163.433	−	65.3119i	0.928597	−	0.371090i
$177$	−257.356	−	257.356i	−1.45399	−	1.45399i
$178$	72.3067	+	117.737i	0.406217	+	0.661445i
$179$	−51.6714	+	159.028i	−0.288667	+	0.888426i	0.696608	+	0.717452i	$0.254692\pi$
$179$	−51.6714	+	159.028i	−0.288667	+	0.888426i	−0.985275	+	0.170975i	$0.945308\pi$
$180$	133.587	−	190.150i	0.742150	−	1.05639i
$181$	−244.342	+	177.525i	−1.34996	+	0.980802i	−0.350945	+	0.936396i	$0.614139\pi$
$181$	−244.342	+	177.525i	−1.34996	+	0.980802i	−0.999014	+	0.0444058i	$0.985861\pi$
$182$	321.266	−	77.4589i	1.76520	−	0.425599i
$183$	154.069	+	78.5022i	0.841909	+	0.428974i
$184$	152.486	−	179.593i	0.828726	−	0.976051i
$185$	76.4409	−	1.06664i	0.413194	−	0.00576564i
$186$	52.1903	+	125.654i	0.280593	+	0.675557i
$187$	184.092	+	79.8142i	0.984448	+	0.426814i
$188$	71.4046	−	0.138548i	0.379812	−	0.000736956i
$189$	−64.2327	−	46.6678i	−0.339855	−	0.246919i
$190$	−74.9295	−	85.1254i	−0.394366	−	0.448028i
$191$	−123.363	+	40.0830i	−0.645878	+	0.209859i	−0.613596	−	0.789620i	$-0.710278\pi$
$191$	−123.363	+	40.0830i	−0.645878	+	0.209859i	−0.0322823	+	0.999479i	$0.510278\pi$
$192$	234.113	−	172.184i	1.21934	−	0.896792i
$193$	67.9965	+	10.7696i	0.352314	+	0.0558010i	0.330083	−	0.943952i	$-0.392923\pi$
$193$	67.9965	+	10.7696i	0.352314	+	0.0558010i	0.0222305	+	0.999753i	$0.492923\pi$
$194$	−188.902	−	220.742i	−0.973722	−	1.13784i
$195$	248.121	−	504.237i	1.27242	−	2.58583i
$196$	17.5202	−	2.80979i	0.0893890	−	0.0143357i
$197$	−67.2265	+	67.2265i	−0.341251	+	0.341251i	−0.856838	−	0.515586i	$-0.827574\pi$
$197$	−67.2265	+	67.2265i	−0.341251	+	0.341251i	0.515586	+	0.856838i	$0.327574\pi$
$198$	−241.864	−	82.7326i	−1.22154	−	0.417841i
$199$	−56.9753			−0.286308			−0.143154	−	0.989700i	$-0.545724\pi$
$199$	−56.9753			−0.286308			−0.143154	+	0.989700i	$0.545724\pi$
$200$	−173.667	−	99.1959i	−0.868334	−	0.495979i
$201$	−30.3655	+	93.4554i	−0.151072	+	0.464952i
$202$	19.2620	−	247.820i	0.0953563	−	1.22683i
$203$	210.873	+	33.3990i	1.03878	+	0.164527i
$204$	327.336	+	51.1940i	1.60459	+	0.250951i
$205$	8.81658	+	51.0455i	0.0430077	+	0.249002i
$206$	1.12747	+	14.1504i	0.00547317	+	0.0686911i
$207$	−337.968	+	53.5288i	−1.63269	+	0.258593i
$208$	278.950	−	281.123i	1.34111	−	1.35155i
$209$	−66.9147	+	105.280i	−0.320166	+	0.503734i
$210$	−154.510	+	260.795i	−0.735762	+	1.24188i
$211$	225.181	+	163.604i	1.06721	+	0.775373i	0.975409	−	0.220404i	$-0.0707377\pi$
$211$	225.181	+	163.604i	1.06721	+	0.775373i	0.0918009	+	0.995777i	$0.470738\pi$
$212$	−86.7943	+	268.899i	−0.409407	+	1.26839i
$213$	84.4833	+	43.0464i	0.396635	+	0.202096i
$214$	0.920131	−	1.50479i	0.00429968	−	0.00703174i
$215$	96.0465	+	29.7324i	0.446728	+	0.138290i
$216$	−94.8753	−	7.18907i	−0.439238	−	0.0332827i
$217$	−45.4054	−	89.1131i	−0.209241	−	0.410659i
$218$	−319.541	+	196.242i	−1.46579	+	0.900192i
$219$		−	362.507i		−	1.65528i
$220$	−51.4657	+	213.895i	−0.233935	+	0.972252i
$221$	451.500			2.04299
$222$	−72.6668	−	118.324i	−0.327328	−	0.532989i
$223$	−174.457	+	88.8904i	−0.782319	+	0.398612i	−0.799062	−	0.601248i	$-0.794670\pi$
$223$	−174.457	+	88.8904i	−0.782319	+	0.398612i	0.0167431	+	0.999860i	$0.494670\pi$
$224$	−161.763	+	139.521i	−0.722156	+	0.622863i
$225$	97.4368	+	273.651i	0.433052	+	1.21623i
$226$	73.2362	+	44.7815i	0.324054	+	0.198148i
$227$	−51.4767	+	101.029i	−0.226770	+	0.445061i	−0.976155	−	0.217073i	$-0.930349\pi$
$227$	−51.4767	+	101.029i	−0.226770	+	0.445061i	0.749386	+	0.662134i	$0.230349\pi$
$228$	−63.2717	+	196.024i	−0.277508	+	0.859753i
$229$	69.2755	−	95.3495i	0.302513	−	0.416373i	−0.630515	−	0.776177i	$-0.717156\pi$
$229$	69.2755	−	95.3495i	0.302513	−	0.416373i	0.933028	+	0.359804i	$0.117156\pi$
$230$	73.0141	+	285.301i	0.317453	+	1.24044i
$231$	322.909	+	83.1461i	1.39788	+	0.359940i
$232$	236.096	−	98.6001i	1.01765	−	0.425000i
$233$	46.3997	+	292.956i	0.199140	+	1.25732i	0.861353	+	0.508007i	$0.169618\pi$
$233$	46.3997	+	292.956i	0.199140	+	1.25732i	−0.662213	+	0.749316i	$0.730382\pi$
$234$	−573.384	+	45.6860i	−2.45036	+	0.195240i
$235$	−51.4507	+	72.9345i	−0.218939	+	0.310360i
$236$	316.756	+	49.5394i	1.34219	+	0.209913i
$237$	−70.3952	+	444.458i	−0.297026	+	1.87535i
$238$	−242.806	−	18.8722i	−1.02019	−	0.0792950i
$239$	−163.096	−	52.9932i	−0.682412	−	0.221729i	−0.0527607	−	0.998607i	$-0.516802\pi$
$239$	−163.096	−	52.9932i	−0.682412	−	0.221729i	−0.629651	+	0.776878i	$0.716802\pi$
$240$	6.47800	+	363.209i	0.0269917	+	1.51337i
$241$		−	132.086i		−	0.548074i	−0.961719	−	0.274037i	$-0.911641\pi$
$241$		−	132.086i		−	0.548074i	0.961719	−	0.274037i	$-0.0883591\pi$
$242$	241.736	−	11.3013i	0.998909	−	0.0466996i
$243$	−238.052	−	238.052i	−0.979638	−	0.979638i
$244$	−150.399	+	24.1201i	−0.616389	+	0.0988528i
$245$	−9.79286	+	19.9012i	−0.0399709	+	0.0812295i
$246$	71.4862	−	61.1750i	0.290594	−	0.248679i
$247$	−43.9116	+	277.247i	−0.177780	+	1.12246i
$248$	−102.376	−	62.3267i	−0.412805	−	0.251317i
$249$	147.546	+	454.101i	0.592555	+	1.82370i
$250$	226.662	−	105.472i	0.906647	−	0.421889i
$251$	−15.5316	+	21.3775i	−0.0618791	+	0.0851692i	−0.838835	−	0.544386i	$-0.816763\pi$
$251$	−15.5316	+	21.3775i	−0.0618791	+	0.0851692i	0.776956	+	0.629555i	$0.216763\pi$
$252$	310.261	−	0.602006i	1.23120	−	0.00238891i
$253$	278.947	−	164.709i	1.10256	−	0.651025i
$254$	15.5292	−	6.45007i	0.0611387	−	0.0253940i
$255$	−288.729	+	296.901i	−1.13227	+	1.16432i
$256$	−77.2163	+	244.077i	−0.301626	+	0.953426i
$257$	177.337	−	348.044i	0.690029	−	1.35426i	−0.234114	−	0.972209i	$-0.575219\pi$
$257$	177.337	−	348.044i	0.690029	−	1.35426i	0.924142	−	0.382048i	$-0.124781\pi$
$258$	−42.8041	−	177.533i	−0.165907	−	0.688112i
$259$	59.9941	+	82.5748i	0.231638	+	0.318822i
$260$	85.2027	+	487.656i	0.327703	+	1.87560i
$261$	−353.420	−	114.833i	−1.35410	−	0.439974i
$262$	−273.775	+	168.135i	−1.04494	+	0.641737i
$263$	−236.266	+	236.266i	−0.898349	+	0.898349i	−0.995290	−	0.0969412i	$-0.969094\pi$
$263$	−236.266	+	236.266i	−0.898349	+	0.898349i	0.0969412	+	0.995290i	$0.469094\pi$
$264$	381.667	−	118.345i	1.44571	−	0.448276i
$265$	−211.572	−	282.820i	−0.798386	−	1.06725i
$266$	35.2032	−	147.261i	0.132343	−	0.553613i
$267$	142.416	+	279.507i	0.533394	+	1.04684i
$268$	−26.9085	−	82.2723i	−0.100405	−	0.306986i
$269$	−88.3574	−	121.614i	−0.328466	−	0.452095i	0.612562	−	0.790422i	$-0.290139\pi$
$269$	−88.3574	−	121.614i	−0.328466	−	0.452095i	−0.941028	+	0.338327i	$0.890139\pi$
$270$	75.8834	−	91.5808i	0.281049	−	0.339188i
$271$	10.1507	+	31.2405i	0.0374563	+	0.115279i	0.968036	−	0.250810i	$-0.0806968\pi$
$271$	10.1507	+	31.2405i	0.0374563	+	0.115279i	−0.930580	+	0.366088i	$0.880697\pi$
$272$	−259.527	+	133.507i	−0.954144	+	0.490834i
$273$	741.073	−	117.374i	2.71455	−	0.429943i
$274$	144.940	−	60.2010i	0.528979	−	0.219712i
$275$	−180.993	−	207.042i	−0.658156	−	0.752881i
$276$	377.499	−	378.966i	1.36775	−	1.37307i
$277$	−51.1198	+	8.09659i	−0.184548	+	0.0292296i	−0.248024	−	0.968754i	$-0.579781\pi$
$277$	−51.1198	+	8.09659i	−0.184548	+	0.0292296i	0.0634762	+	0.997983i	$0.479781\pi$
$278$	−68.1375	+	79.9357i	−0.245099	+	0.287538i
$279$	53.7932	+	165.558i	0.192807	+	0.593400i
$280$	−25.4364	−	265.811i	−0.0908444	−	0.949324i
$281$	−24.6258	−	33.8946i	−0.0876365	−	0.120621i	0.762948	−	0.646460i	$-0.223751\pi$
$281$	−24.6258	−	33.8946i	−0.0876365	−	0.120621i	−0.850584	+	0.525839i	$0.823751\pi$
$282$	161.631	+	12.5629i	0.573160	+	0.0445492i
$283$	−5.92958	−	11.6374i	−0.0209526	−	0.0411217i	0.880293	−	0.474430i	$-0.157346\pi$
$283$	−5.92958	−	11.6374i	−0.0209526	−	0.0411217i	−0.901246	+	0.433309i	$0.857346\pi$
$284$	−82.4707	+	13.2262i	−0.290390	+	0.0465710i
$285$	−154.233	−	206.172i	−0.541169	−	0.723410i
$286$	488.951	−	239.705i	1.70962	−	0.838131i
$287$	−48.9044	+	48.9044i	−0.170398	+	0.170398i
$288$	316.078	−	195.808i	1.09749	−	0.679890i
$289$	−41.5878	−	13.5127i	−0.143903	−	0.0467568i
$290$	−70.0120	+	312.065i	−0.241421	+	1.07609i
$291$	−387.725	−	533.658i	−1.33239	−	1.83388i
$292$	188.199	+	257.979i	0.644516	+	0.883491i
$293$	−31.5886	+	61.9962i	−0.107811	+	0.211591i	−0.938609	−	0.344983i	$-0.887885\pi$
$293$	−31.5886	+	61.9962i	−0.107811	+	0.211591i	0.830798	+	0.556574i	$0.187885\pi$
$294$	40.1593	−	3.19981i	0.136596	−	0.0108837i
$295$	−279.398	+	287.305i	−0.947111	+	0.973916i
$296$	113.142	+	46.4797i	0.382237	+	0.157026i
$297$	−120.032	−	52.0406i	−0.404147	−	0.175221i
$298$	13.9774	−	33.8372i	0.0469039	−	0.113548i
$299$	428.460	−	589.725i	1.43298	−	1.97232i
$300$	−375.163	−	255.822i	−1.25054	−	0.852741i
$301$	41.4818	+	127.668i	0.137813	+	0.424145i
$302$	−95.7461	−	397.114i	−0.317040	−	1.31495i
$303$	88.2842	−	557.405i	0.291367	−	1.83962i
$304$	−56.7399	−	172.349i	−0.186644	−	0.566937i
$305$	84.0648	−	170.838i	0.275622	−	0.560125i
$306$	412.272	+	98.5548i	1.34729	+	0.322075i
$307$	−13.7530	−	13.7530i	−0.0447979	−	0.0447979i	0.684353	−	0.729151i	$-0.260085\pi$
$307$	−13.7530	−	13.7530i	−0.0447979	−	0.0447979i	−0.729151	+	0.684353i	$0.760085\pi$
$308$	−272.965	+	108.470i	−0.886251	+	0.352175i
$309$			32.2291i			0.104301i
$310$	137.544	−	59.3926i	0.443691	−	0.191589i
$311$	313.415	+	101.835i	1.00776	+	0.327442i	0.765964	−	0.642884i	$-0.222262\pi$
$311$	313.415	+	101.835i	1.00776	+	0.327442i	0.241800	+	0.970326i	$0.422262\pi$
$312$	682.027	−	585.948i	2.18599	−	1.87804i
$313$	6.96579	−	43.9802i	0.0222549	−	0.140512i	−0.974059	−	0.226294i	$-0.927339\pi$
$313$	6.96579	−	43.9802i	0.0222549	−	0.140512i	0.996314	+	0.0857822i	$0.0273389\pi$
$314$	−20.0720	+	32.8260i	−0.0639236	+	0.104541i
$315$	−223.559	+	316.909i	−0.709712	+	1.00606i
$316$	−180.647	−	352.846i	−0.571668	−	1.11660i
$317$	−1.82444	−	11.5191i	−0.00575534	−	0.0363378i	0.984644	−	0.174577i	$-0.0558558\pi$
$317$	−1.82444	−	11.5191i	−0.00575534	−	0.0363378i	−0.990399	+	0.138239i	$0.955856\pi$
$318$	−244.928	+	592.934i	−0.770213	+	1.86457i
$319$	351.125	−	21.8482i	1.10071	−	0.0684895i
$320$	−193.173	−	255.116i	−0.603667	−	0.797237i
$321$	2.35384	−	3.23979i	0.00733285	−	0.0100928i
$322$	−255.065	+	299.230i	−0.792128	+	0.929287i
$323$	93.9128	−	184.314i	0.290752	−	0.570632i
$324$	199.838	+	31.2539i	0.616784	+	0.0964626i
$325$	−558.982	−	265.438i	−1.71995	−	0.816731i
$326$	−253.224	−	295.906i	−0.776762	−	0.907687i
$327$	−758.589	+	386.520i	−2.31984	+	1.18202i
$328$	−19.1138	+	80.6480i	−0.0582738	+	0.245878i
$329$	−119.168			−0.362212
$330$	−155.051	+	474.817i	−0.469853	+	1.43884i
$331$			389.384i			1.17639i	0.808720	+	0.588194i	$0.200161\pi$
$331$			389.384i			1.17639i	−0.808720	+	0.588194i	$0.799839\pi$
$332$	−340.752	−	246.562i	−1.02636	−	0.742657i
$333$	−80.6532	−	158.291i	−0.242202	−	0.475348i
$334$	295.503	+	345.310i	0.884739	+	1.03386i
$335$	103.362	+	31.9970i	0.308543	+	0.0955134i
$336$	−391.270	+	286.600i	−1.16449	+	0.852978i
$337$	376.907	+	192.044i	1.11842	+	0.569863i	0.912652	−	0.408738i	$-0.134031\pi$
$337$	376.907	+	192.044i	1.11842	+	0.569863i	0.205768	+	0.978601i	$0.434031\pi$
$338$	575.625	−	675.296i	1.70303	−	1.99792i
$339$	157.676	+	114.558i	0.465121	+	0.337930i
$340$	51.3362	−	361.187i	0.150989	−	1.06231i
$341$	−104.961	−	127.054i	−0.307803	−	0.372593i
$342$	−100.615	+	243.573i	−0.294195	+	0.712203i
$343$	−352.327	+	55.8031i	−1.02719	+	0.162691i
$344$	122.629	+	104.120i	0.356481	+	0.302674i
$345$	113.800	+	658.873i	0.329856	+	1.90978i
$346$	−81.2322	+	132.848i	−0.234775	+	0.383954i
$347$	60.5584	+	9.59150i	0.174520	+	0.0276412i	0.243083	−	0.970006i	$-0.421841\pi$
$347$	60.5584	+	9.59150i	0.174520	+	0.0276412i	−0.0685629	+	0.997647i	$0.521841\pi$
$348$	552.123	−	180.581i	1.58656	−	0.518911i
$349$	12.3427	−	37.9869i	0.0353658	−	0.108845i	−0.931815	−	0.362933i	$-0.881775\pi$
$349$	12.3427	−	37.9869i	0.0353658	−	0.108845i	0.967181	+	0.254088i	$0.0817754\pi$
$350$	289.512	+	166.111i	0.827177	+	0.474602i
$351$	−294.388			−0.838711
$352$	−210.175	+	282.366i	−0.597087	+	0.802177i
$353$	29.1128	−	29.1128i	0.0824725	−	0.0824725i	−0.664667	−	0.747140i	$-0.731427\pi$
$353$	29.1128	−	29.1128i	0.0824725	−	0.0824725i	0.747140	+	0.664667i	$0.231427\pi$
$354$	707.964	+	169.241i	1.99990	+	0.478082i
$355$	46.0966	−	93.6784i	0.129850	−	0.263883i
$356$	−246.460	−	124.976i	−0.692302	−	0.351055i
$357$	−546.126	−	86.4978i	−1.52976	−	0.242291i
$358$	−78.3853	−	325.108i	−0.218953	−	0.908124i
$359$	−489.097	+	158.917i	−1.36239	+	0.442667i	−0.896840	−	0.442356i	$-0.854143\pi$
$359$	−489.097	+	158.917i	−1.36239	+	0.442667i	−0.465548	+	0.885022i	$0.654143\pi$
$360$	−28.6471	+	463.885i	−0.0795752	+	1.28857i
$361$	−188.009	−	136.597i	−0.520802	−	0.378385i
$362$	230.618	−	558.291i	0.637065	−	1.54224i
$363$	549.146	+	18.0148i	1.51280	+	0.0496276i
$364$	−466.451	+	468.264i	−1.28146	+	1.28644i
$365$	−399.124	+	5.56932i	−1.09349	+	0.0152584i
$366$	−344.740	+	27.4681i	−0.941911	+	0.0750496i
$367$	−615.620	−	313.674i	−1.67744	−	0.854697i	−0.991952	−	0.126611i	$-0.959590\pi$
$367$	−615.620	−	313.674i	−1.67744	−	0.854697i	−0.685485	−	0.728086i	$-0.740410\pi$
$368$	−71.9042	+	465.674i	−0.195392	+	1.26542i
$369$	97.3879	−	70.7564i	0.263924	−	0.191752i
$370$	−129.159	+	81.8248i	−0.349079	+	0.221148i
$371$	145.722	−	448.486i	0.392782	−	1.20886i
$372$	−220.462	−	159.522i	−0.592639	−	0.428823i
$373$	196.331	+	196.331i	0.526355	+	0.526355i	0.919484	−	0.393128i	$-0.128607\pi$
$373$	196.331	+	196.331i	0.526355	+	0.526355i	−0.393128	+	0.919484i	$0.628607\pi$
$374$	−397.279	+	56.6552i	−1.06224	+	0.151485i
$375$	532.011	−	197.836i	1.41870	−	0.527562i
$376$	−121.547	+	74.9718i	−0.323264	+	0.199393i
$377$	705.347	−	359.392i	1.87095	−	0.953294i
$378$	158.314	+	12.3051i	0.418821	+	0.0325531i
$379$	−520.868	+	378.433i	−1.37432	+	0.998503i	−0.376936	+	0.926239i	$0.623022\pi$
$379$	−520.868	+	378.433i	−1.37432	+	0.998503i	−0.997386	+	0.0722642i	$0.976978\pi$
$380$	216.796	+	66.6513i	0.570517	+	0.175398i
$381$	36.3096	−	11.7977i	0.0953008	−	0.0309651i
$382$	168.290	−	197.430i	0.440550	−	0.516832i
$383$	−60.8799	−	384.380i	−0.158955	−	1.00360i	−0.930197	−	0.367061i	$-0.880364\pi$
$383$	−60.8799	−	384.380i	−0.158955	−	1.00360i	0.771241	−	0.636543i	$-0.219636\pi$
$384$	−218.774	+	538.482i	−0.569725	+	1.40230i
$385$	86.5839	−	356.804i	0.224893	−	0.926764i
$386$	−127.156	+	52.8144i	−0.329420	+	0.136825i
$387$	−36.5504	−	230.770i	−0.0944454	−	0.596305i
$388$	552.979	+	178.488i	1.42520	+	0.460021i
$389$	−458.686	+	149.036i	−1.17914	+	0.383126i	−0.832047	−	0.554704i	$-0.812831\pi$
$389$	−458.686	+	149.036i	−1.17914	+	0.383126i	−0.347093	+	0.937831i	$0.612831\pi$
$390$	104.895	+	1119.05i	0.268962	+	2.86936i
$391$	−434.591	+	315.749i	−1.11149	+	0.807542i
$392$	−26.9183	+	23.1262i	−0.0686691	+	0.0589954i
$393$	−649.940	+	331.161i	−1.65379	+	0.842649i
$394$	44.2091	−	184.935i	0.112206	−	0.469377i
$395$	490.435	+	70.6776i	1.24161	+	0.178931i
$396$	498.793	−	112.149i	1.25958	−	0.283205i
$397$	−248.934	−	248.934i	−0.627037	−	0.627037i	0.320285	−	0.947321i	$-0.396221\pi$
$397$	−248.934	−	248.934i	−0.627037	−	0.627037i	−0.947321	+	0.320285i	$0.896221\pi$
$398$	97.1011	−	59.6333i	0.243973	−	0.149832i
$399$	106.229	−	326.940i	0.266238	−	0.819398i
$400$	399.798	−	12.7125i	0.999495	−	0.0317811i
$401$	295.201	−	214.476i	0.736163	−	0.534854i	−0.155344	−	0.987860i	$-0.549649\pi$
$401$	295.201	−	214.476i	0.736163	−	0.534854i	0.891507	+	0.453007i	$0.149649\pi$
$402$	−46.0643	−	191.055i	−0.114588	−	0.475261i
$403$	−330.417	−	168.356i	−0.819893	−	0.417757i
$404$	226.554	+	442.512i	0.560777	+	1.09533i
$405$	−176.269	+	181.258i	−0.435232	+	0.447550i
$406$	−394.340	+	163.789i	−0.971281	+	0.403422i
$407$	126.082	+	111.311i	0.309783	+	0.273490i
$408$	−611.449	+	255.358i	−1.49865	+	0.625877i
$409$	316.613	+	230.033i	0.774115	+	0.562427i	0.903207	−	0.429205i	$-0.141206\pi$
$409$	316.613	+	230.033i	0.774115	+	0.562427i	−0.129092	+	0.991633i	$0.541206\pi$
$410$	−68.4526	−	77.7672i	−0.166958	−	0.189676i
$411$	338.892	−	110.113i	0.824554	−	0.267914i
$412$	−16.7320	−	22.9359i	−0.0406117	−	0.0556697i
$413$	−528.475	−	83.7023i	−1.27960	−	0.202669i
$414$	519.961	−	444.962i	1.25594	−	1.07479i
$415$	497.703	−	169.427i	1.19928	−	0.408257i
$416$	−181.167	+	771.072i	−0.435497	+	1.85354i
$417$	−168.627	+	168.627i	−0.404381	+	0.404381i
$418$	3.84864	−	249.462i	0.00920728	−	0.596799i
$419$	−312.635			−0.746145			−0.373072	−	0.927802i	$-0.621696\pi$
$419$	−312.635			−0.746145			−0.373072	+	0.927802i	$0.621696\pi$
$420$	−9.63501	−	606.182i	−0.0229405	−	1.44329i
$421$	32.3036	−	99.4203i	0.0767307	−	0.236153i	−0.905333	−	0.424703i	$-0.860379\pi$
$421$	32.3036	−	99.4203i	0.0767307	−	0.236153i	0.982064	+	0.188550i	$0.0603787\pi$
$422$	−555.005	−	43.1381i	−1.31518	−	0.102223i
$423$	204.863	+	32.4471i	0.484310	+	0.0767071i
$424$	−133.523	−	549.119i	−0.314914	−	1.29509i
$425$	331.327	+	313.333i	0.779593	+	0.737253i
$426$	−189.037	+	15.0620i	−0.443748	+	0.0353569i
$427$	251.079	−	39.7671i	0.588008	−	0.0931313i
$428$	0.00684471	+	3.52762i	1.59923e−5	+	0.00824211i
$429$	1149.84	−	454.339i	2.68029	−	1.05907i
$430$	−194.808	+	49.8553i	−0.453042	+	0.115943i
$431$	−47.3487	−	34.4008i	−0.109858	−	0.0798164i	0.531500	−	0.847058i	$-0.321629\pi$
$431$	−47.3487	−	34.4008i	−0.109858	−	0.0798164i	−0.641358	+	0.767242i	$0.721629\pi$
$432$	169.217	−	87.0493i	0.391706	−	0.201503i
$433$	236.902	+	120.708i	0.547118	+	0.278770i	0.705623	−	0.708588i	$-0.250667\pi$
$433$	236.902	+	120.708i	0.547118	+	0.278770i	−0.158505	+	0.987358i	$0.550667\pi$
$434$	170.653	+	104.349i	0.393210	+	0.240435i
$435$	−214.729	+	693.655i	−0.493631	+	1.59461i
$436$	339.186	−	668.896i	0.777951	−	1.53417i
$437$	−151.621	−	297.573i	−0.346958	−	0.680944i
$438$	379.419	+	617.809i	0.866252	+	1.41052i
$439$		−	132.823i		−	0.302557i	−0.988491	−	0.151279i	$-0.951661\pi$
$439$		−	132.823i		−	0.302557i	0.988491	−	0.151279i	$-0.0483391\pi$
$440$	−136.163	−	418.401i	−0.309461	−	0.950912i
$441$	51.5432			0.116878
$442$	−769.476	+	472.563i	−1.74090	+	1.06915i
$443$	4.03740	−	2.05716i	0.00911378	−	0.00464370i	−0.449428	−	0.893317i	$-0.648372\pi$
$443$	4.03740	−	2.05716i	0.00911378	−	0.00464370i	0.458541	+	0.888673i	$0.348372\pi$
$444$	247.687	+	125.598i	0.557854	+	0.282879i
$445$	305.553	−	161.096i	0.686636	−	0.362013i
$446$	204.284	−	334.089i	0.458036	−	0.749078i
$447$	37.7361	−	74.0613i	0.0844208	−	0.165685i
$448$	129.657	−	407.091i	0.289413	−	0.908685i
$449$	132.107	−	181.830i	0.294225	−	0.404967i	−0.636155	−	0.771561i	$-0.719476\pi$
$449$	132.107	−	181.830i	0.294225	−	0.404967i	0.930381	+	0.366594i	$0.119476\pi$
$450$	−452.475	−	364.392i	−1.00550	−	0.809759i
$451$	−61.1306	+	96.1800i	−0.135545	+	0.213259i
$452$	−171.685	+	0.333123i	−0.379833	+	0.000736998i
$453$	−145.085	−	916.032i	−0.320276	−	2.02215i
$454$	−18.0118	−	226.058i	−0.0396737	−	0.497925i
$455$	−140.616	−	814.126i	−0.309046	−	1.78929i
$456$	−97.3366	−	400.300i	−0.213457	−	0.877851i
$457$	58.7670	−	371.040i	0.128593	−	0.811904i	−0.836110	−	0.548562i	$-0.815175\pi$
$457$	58.7670	−	371.040i	0.128593	−	0.811904i	0.964703	−	0.263342i	$-0.0848246\pi$
$458$	−18.2661	+	235.008i	−0.0398824	+	0.513118i
$459$	206.328	+	67.0399i	0.449516	+	0.146056i
$460$	−423.046	−	409.808i	−0.919665	−	0.890887i
$461$			886.126i			1.92218i	0.276232	+	0.961091i	$0.410914\pi$
$461$			886.126i			1.92218i	−0.276232	+	0.961091i	$0.589086\pi$
$462$	−637.348	+	196.270i	−1.37954	+	0.424828i
$463$	425.628	+	425.628i	0.919284	+	0.919284i	0.996977	−	0.0776934i	$-0.0247555\pi$
$463$	425.628	+	425.628i	0.919284	+	0.919284i	−0.0776934	+	0.996977i	$0.524756\pi$
$464$	−299.170	+	415.151i	−0.644763	+	0.894721i
$465$	322.007	−	109.617i	0.692488	−	0.235735i
$466$	−385.700	−	450.711i	−0.827683	−	0.967191i
$467$	−34.3556	+	216.913i	−0.0735666	+	0.464481i	0.923213	+	0.384289i	$0.125553\pi$
$467$	−34.3556	+	216.913i	−0.0735666	+	0.464481i	−0.996779	+	0.0801922i	$0.974447\pi$
$468$	929.381	−	677.994i	1.98586	−	1.44871i
$469$	44.6413	+	137.392i	0.0951839	+	0.292946i
$470$	11.3487	−	178.151i	0.0241461	−	0.379044i
$471$	−51.3474	+	70.6737i	−0.109018	+	0.150050i
$472$	−591.687	+	247.105i	−1.25358	+	0.523528i
$473$	112.466	+	190.469i	0.237772	+	0.402684i
$474$	−345.220	−	831.153i	−0.728313	−	1.75349i
$475$	−224.628	+	172.980i	−0.472901	+	0.364168i
$476$	433.558	−	221.969i	0.910836	−	0.466322i
$477$	−372.627	+	731.321i	−0.781188	+	1.53317i
$478$	333.425	−	80.3905i	0.697542	−	0.168181i
$479$	414.922	+	571.091i	0.866226	+	1.19226i	0.980049	+	0.198756i	$0.0636902\pi$
$479$	414.922	+	571.091i	0.866226	+	1.19226i	−0.113823	+	0.993501i	$0.536310\pi$
$480$	−391.194	−	612.225i	−0.814987	−	1.27547i
$481$	359.930	+	116.948i	0.748294	+	0.243136i
$482$	138.248	+	225.109i	0.286821	+	0.467032i
$483$	−631.236	+	631.236i	−1.30691	+	1.30691i
$484$	−400.154	+	272.274i	−0.826764	+	0.562549i
$485$	−581.607	+	435.089i	−1.19919	+	0.897090i
$486$	654.862	+	156.547i	1.34745	+	0.322112i
$487$	−157.422	−	308.957i	−0.323248	−	0.634410i	0.671007	−	0.741451i	$-0.265862\pi$
$487$	−157.422	−	308.957i	−0.323248	−	0.634410i	−0.994255	+	0.107042i	$0.965862\pi$
$488$	231.074	−	198.522i	0.473513	−	0.406808i
$489$	−519.748	−	715.372i	−1.06288	−	1.46293i
$490$	−4.14001	−	44.1667i	−0.00844900	−	0.0901361i
$491$	−125.437	−	386.055i	−0.255472	−	0.786263i	−0.993736	−	0.111751i	$-0.964354\pi$
$491$	−125.437	−	386.055i	−0.255472	−	0.786263i	0.738264	−	0.674512i	$-0.235646\pi$
$492$	−57.8025	+	179.080i	−0.117485	+	0.363983i
$493$	−576.200	+	91.2611i	−1.16876	+	0.185114i
$494$	−215.344	−	518.462i	−0.435918	−	1.04952i
$495$	−245.998	+	589.812i	−0.496967	+	1.19154i
$496$	239.709	−	0.930229i	0.483285	−	0.00187546i
$497$	137.678	−	21.8061i	0.277019	−	0.0438755i
$498$	−726.743	−	619.479i	−1.45932	−	1.24393i
$499$	232.643	+	716.002i	0.466219	+	1.43487i	0.857443	+	0.514578i	$0.172052\pi$
$499$	232.643	+	716.002i	0.466219	+	1.43487i	−0.391225	+	0.920295i	$0.627948\pi$
$500$	−275.899	+	416.989i	−0.551799	+	0.833977i
$501$	606.525	+	834.811i	1.21063	+	1.66629i
$502$	4.09529	−	52.6891i	0.00815796	−	0.104958i
$503$	394.361	+	773.978i	0.784019	+	1.53872i	0.841426	+	0.540372i	$0.181717\pi$
$503$	394.361	+	773.978i	0.784019	+	1.53872i	−0.0574073	+	0.998351i	$0.518283\pi$
$504$	−528.138	+	325.761i	−1.04789	+	0.646352i
$505$	−615.065	−	88.6383i	−1.21795	−	0.175521i
$506$	−303.006	+	572.668i	−0.598826	+	1.13176i
$507$	1424.56	−	1424.56i	2.80978	−	2.80978i
$508$	−19.7149	+	27.2463i	−0.0388090	+	0.0536345i
$509$	820.967	+	266.748i	1.61290	+	0.524063i	0.970252	−	0.242097i	$-0.0778353\pi$
$509$	820.967	+	266.748i	1.61290	+	0.524063i	0.642649	+	0.766161i	$0.277835\pi$
$510$	181.320	−	808.197i	0.355529	−	1.58470i
$511$	−313.250	−	431.152i	−0.613014	−	0.843741i
$512$	−123.866	−	496.791i	−0.241927	−	0.970295i
$513$	−61.2331	+	120.177i	−0.119363	+	0.234263i
$514$	62.0508	+	778.770i	0.120721	+	1.51512i
$515$	35.4846	−	0.495146i	0.0689021	−	0.000961449i
$516$	258.765	+	257.762i	0.501482	+	0.499539i
$517$	−191.663	+	42.7033i	−0.370722	+	0.0825982i
$518$	−188.673	−	77.9365i	−0.364234	−	0.150457i
$519$	−207.805	+	286.019i	−0.400395	+	0.551097i
$520$	−655.613	−	741.918i	−1.26080	−	1.42676i
$521$	−200.511	−	617.108i	−0.384857	−	1.18447i	−0.936584	−	0.350444i	$-0.886031\pi$
$521$	−200.511	−	617.108i	−0.384857	−	1.18447i	0.551727	−	0.834025i	$-0.313969\pi$
$522$	722.512	−	174.201i	1.38412	−	0.333719i
$523$	45.6928	−	288.493i	0.0873667	−	0.551612i	−0.904715	−	0.426017i	$-0.859916\pi$
$523$	45.6928	−	288.493i	0.0873667	−	0.551612i	0.992082	−	0.125594i	$-0.0400838\pi$
$524$	290.607	−	573.094i	0.554593	−	1.09369i
$525$	625.282	+	428.157i	1.19101	+	0.815538i
$526$	155.372	−	649.947i	0.295384	−	1.23564i
$527$	193.241	+	193.241i	0.366680	+	0.366680i
$528$	−526.596	+	601.163i	−0.997341	+	1.13857i
$529$			338.276i			0.639463i
$530$	656.590	+	260.559i	1.23885	+	0.491620i
$531$	885.719	+	287.787i	1.66802	+	0.541973i
$532$	94.1353	+	287.817i	0.176946	+	0.541010i
$533$	−40.1159	+	253.282i	−0.0752643	+	0.475200i
$534$	−535.262	−	327.295i	−1.00236	−	0.612912i
$535$	−3.60321	−	2.54183i	−0.00673496	−	0.00475109i
$536$	131.970	+	112.050i	0.246212	+	0.209049i
$537$	−118.778	−	749.936i	−0.221188	−	1.39653i
$538$	277.872	+	114.782i	0.516490	+	0.213350i
$539$	−45.3820	+	17.9319i	−0.0841967	+	0.0332688i
$540$	−33.4723	+	235.501i	−0.0619857	+	0.436114i
$541$	258.288	−	355.504i	0.477428	−	0.657123i	−0.500580	−	0.865690i	$-0.666880\pi$
$541$	258.288	−	355.504i	0.477428	−	0.657123i	0.978008	+	0.208567i	$0.0668799\pi$
$542$	−49.9974	−	42.6180i	−0.0922461	−	0.0786309i
$543$	622.621	−	1221.96i	1.14663	−	2.25039i
$544$	302.568	−	499.165i	0.556191	−	0.917583i
$545$	437.218	+	829.276i	0.802234	+	1.52161i
$546$	−1140.14	+	975.682i	−2.08816	+	1.78696i
$547$	397.803	−	202.691i	0.727244	−	0.370549i	−0.0508421	−	0.998707i	$-0.516191\pi$
$547$	397.803	−	202.691i	0.727244	−	0.370549i	0.778086	+	0.628157i	$0.216191\pi$
$548$	−184.007	+	254.301i	−0.335780	+	0.464052i
$549$	−442.462			−0.805942
$550$	525.161	+	163.419i	0.954839	+	0.297125i
$551$		−	362.695i		−	0.658249i
$552$	−246.712	+	1040.97i	−0.446943	+	1.88581i
$553$	300.340	+	589.451i	0.543111	+	1.06591i
$554$	78.6475	−	67.3034i	0.141963	−	0.121486i
$555$	−307.075	+	161.898i	−0.553288	+	0.291709i
$556$	32.4597	−	207.548i	0.0583807	−	0.373288i
$557$	386.971	+	197.171i	0.694741	+	0.353988i	0.765438	−	0.643510i	$-0.222522\pi$
$557$	386.971	+	197.171i	0.694741	+	0.353988i	−0.0706972	+	0.997498i	$0.522522\pi$
$558$	−264.960	−	225.853i	−0.474839	−	0.404754i
$559$	402.674	+	292.560i	0.720347	+	0.523363i
$560$	321.561	+	426.389i	0.574217	+	0.761409i
$561$	−909.357	+	56.5831i	−1.62096	+	0.100861i
$562$	77.4448	+	31.9907i	0.137802	+	0.0569229i
$563$	−265.894	+	42.1135i	−0.472280	+	0.0748019i	−0.388038	−	0.921643i	$-0.626847\pi$
$563$	−265.894	+	42.1135i	−0.472280	+	0.0748019i	−0.0842425	+	0.996445i	$0.526847\pi$
$564$	−288.611	+	147.761i	−0.511722	+	0.261988i
$565$	123.708	−	175.363i	0.218952	−	0.310377i
$566$	22.2859	+	13.6271i	0.0393744	+	0.0240762i
$567$	−333.409	−	52.8068i	−0.588023	−	0.0931338i
$568$	126.709	−	108.859i	0.223079	−	0.191653i
$569$	−9.37853	+	28.8642i	−0.0164825	+	0.0507279i	−0.958959	−	0.283543i	$-0.908490\pi$
$569$	−9.37853	+	28.8642i	−0.0164825	+	0.0507279i	0.942477	+	0.334271i	$0.108490\pi$
$570$	478.644	+	189.943i	0.839727	+	0.333234i
$571$	−9.82448			−0.0172057			−0.00860287	−	0.999963i	$-0.502738\pi$
$571$	−9.82448			−0.0172057			−0.00860287	+	0.999963i	$0.502738\pi$
$572$	−582.415	+	920.283i	−1.01821	+	1.60889i
$573$	416.484	−	416.484i	0.726849	−	0.726849i
$574$	32.1602	−	134.532i	0.0560283	−	0.234376i
$575$	723.678	−	135.418i	1.25857	−	0.235510i
$576$	−333.738	+	664.533i	−0.579407	+	1.15370i
$577$	161.102	+	25.5160i	0.279206	+	0.0442219i	0.294467	−	0.955662i	$-0.404858\pi$
$577$	161.102	+	25.5160i	0.279206	+	0.0442219i	−0.0152610	+	0.999884i	$0.504858\pi$
$578$	85.0198	−	20.4987i	0.147093	−	0.0354649i
$579$	−297.310	+	96.6018i	−0.513488	+	0.166842i
$580$	−207.304	−	605.120i	−0.357421	−	1.04331i
$581$	567.883	+	412.591i	0.977424	+	0.710140i
$582$	1219.34	+	503.682i	2.09509	+	0.865433i
$583$	73.6587	−	773.541i	0.126344	−	1.32683i
$584$	−590.755	−	242.687i	−1.01157	−	0.415560i
$585$	20.0637	+	1437.86i	0.0342969	+	2.45788i
$586$	−11.0529	−	138.720i	−0.0188617	−	0.236724i
$587$	494.198	+	251.807i	0.841905	+	0.428972i	0.821081	−	0.570811i	$-0.193371\pi$
$587$	494.198	+	251.807i	0.841905	+	0.428972i	0.0208237	+	0.999783i	$0.493371\pi$
$588$	−65.0930	+	47.4861i	−0.110702	+	0.0807587i
$589$	−137.455	+	99.8667i	−0.233370	+	0.169553i
$590$	175.459	−	782.076i	0.297389	−	1.32555i
$591$	133.406	−	410.580i	0.225729	−	0.694721i
$592$	−241.473	+	39.2067i	−0.407893	+	0.0662275i
$593$	86.9546	+	86.9546i	0.146635	+	0.146635i	0.776613	−	0.629978i	$-0.216936\pi$
$593$	86.9546	+	86.9546i	0.146635	+	0.146635i	−0.629978	+	0.776613i	$0.716936\pi$
$594$	259.034	−	36.9404i	0.436085	−	0.0621893i
$595$	−86.8447	+	602.619i	−0.145958	+	1.01281i
$596$	11.5946	+	72.2969i	0.0194539	+	0.121304i
$597$	230.517	−	117.455i	0.386126	−	0.196741i
$598$	−112.974	+	1453.50i	−0.188919	+	2.43060i
$599$	2.16024	−	1.56951i	0.00360641	−	0.00262021i	−0.585981	−	0.810325i	$-0.699291\pi$
$599$	2.16024	−	1.56951i	0.00360641	−	0.00262021i	0.589587	+	0.807705i	$0.299291\pi$
$600$	907.134	+	43.3245i	1.51189	+	0.0722074i
$601$	274.011	−	89.0315i	0.455925	−	0.148139i	−0.0720463	−	0.997401i	$-0.522953\pi$
$601$	274.011	−	89.0315i	0.455925	−	0.148139i	0.527971	+	0.849262i	$0.322953\pi$
$602$	−204.319	−	174.163i	−0.339401	−	0.289307i
$603$	−39.3343	−	248.347i	−0.0652310	−	0.411852i
$604$	578.816	+	576.575i	0.958305	+	0.954594i
$605$	11.3978	−	604.893i	0.0188394	−	0.999823i
$606$	432.948	+	1042.37i	0.714436	+	1.72008i
$607$	138.995	+	877.578i	0.228986	+	1.44576i	0.787524	+	0.616284i	$0.211363\pi$
$607$	138.995	+	877.578i	0.228986	+	1.44576i	−0.558538	+	0.829479i	$0.688637\pi$
$608$	277.089	+	234.341i	0.455739	+	0.385430i
$609$	−922.025	+	299.584i	−1.51400	+	0.491928i
$610$	35.5391	+	379.140i	0.0582608	+	0.621541i
$611$	−357.468	+	259.716i	−0.585055	+	0.425067i
$612$	−805.773	+	263.541i	−1.31662	+	0.430623i
$613$	−150.698	+	76.7845i	−0.245837	+	0.125260i	−0.572568	−	0.819857i	$-0.694053\pi$
$613$	−150.698	+	76.7845i	−0.245837	+	0.125260i	0.326731	+	0.945117i	$0.394053\pi$
$614$	37.8332	+	9.04415i	0.0616177	+	0.0147299i
$615$	−140.901	−	188.350i	−0.229108	−	0.306261i
$616$	351.675	−	470.561i	0.570901	−	0.763898i
$617$	246.729	+	246.729i	0.399884	+	0.399884i	0.878192	−	0.478308i	$-0.158750\pi$
$617$	246.729	+	246.729i	0.399884	+	0.399884i	−0.478308	+	0.878192i	$0.658750\pi$
$618$	−33.7326	−	54.9270i	−0.0545835	−	0.0888786i
$619$	146.025	−	449.420i	0.235905	−	0.726041i	−0.761095	−	0.648641i	$-0.775338\pi$
$619$	146.025	−	449.420i	0.235905	−	0.726041i	0.997000	−	0.0774008i	$-0.0246621\pi$
$620$	−172.249	+	245.182i	−0.277820	+	0.395454i
$621$	283.363	−	205.875i	0.456301	−	0.331522i
$622$	−640.727	+	154.483i	−1.03011	+	0.248364i
$623$	410.913	+	209.370i	0.659571	+	0.336068i
$624$	−549.073	+	1712.46i	−0.879924	+	2.74432i
$625$	−225.993	−	582.711i	−0.361588	−	0.932338i
$626$	34.1604	+	82.2448i	0.0545694	+	0.131381i
$627$	53.6961	−	563.900i	0.0856397	−	0.899362i
$628$	−0.149313	−	76.9526i	−0.000237759	−	0.122536i
$629$	−225.632	−	163.931i	−0.358715	−	0.260622i
$630$	49.3114	−	774.086i	0.0782720	−	1.22871i
$631$	−868.165	+	282.084i	−1.37586	+	0.447042i	−0.901305	−	0.433186i	$-0.857389\pi$
$631$	−868.165	+	282.084i	−1.37586	+	0.447042i	−0.474550	+	0.880228i	$0.657389\pi$
$632$	677.177	+	412.269i	1.07148	+	0.652324i
$633$	−1248.33	−	197.717i	−1.97209	−	0.312348i
$634$	15.1658	+	17.7220i	0.0239208	+	0.0279527i
$635$	−13.5472	−	39.7960i	−0.0213342	−	0.0626709i
$636$	−203.173	−	1266.87i	−0.319455	−	1.99194i
$637$	−77.6412	+	77.6412i	−0.121886	+	0.121886i
$638$	−575.543	+	404.741i	−0.902106	+	0.634390i
$639$	−242.622			−0.379691
$640$	596.236	+	232.600i	0.931619	+	0.363437i
$641$	−127.066	+	391.068i	−0.198230	+	0.610090i	0.801693	+	0.597735i	$0.203933\pi$
$641$	−127.066	+	391.068i	−0.198230	+	0.610090i	−0.999924	+	0.0123545i	$0.996067\pi$
$642$	−0.620648	+	7.98511i	−0.000966741	+	0.0124379i
$643$	973.141	+	154.130i	1.51344	+	0.239705i	0.857254	−	0.514894i	$-0.172169\pi$
$643$	973.141	+	154.130i	1.51344	+	0.239705i	0.656186	+	0.754600i	$0.272169\pi$
$644$	121.509	−	776.932i	0.188679	−	1.20642i
$645$	−449.889	+	77.7049i	−0.697503	+	0.120473i
$646$	32.8603	+	412.414i	0.0508674	+	0.638412i
$647$	887.815	−	140.616i	1.37220	−	0.217336i	0.573571	−	0.819156i	$-0.305558\pi$
$647$	887.815	−	140.616i	1.37220	−	0.217336i	0.798632	+	0.601820i	$0.205558\pi$
$648$	−373.289	+	155.896i	−0.576064	+	0.240580i
$649$	−879.967	+	54.7544i	−1.35588	+	0.0843673i
$650$	1230.47	−	132.683i	1.89304	−	0.204128i
$651$	367.413	+	266.941i	0.564382	+	0.410048i
$652$	741.272	+	239.265i	1.13692	+	0.366970i
$653$	−46.9707	−	23.9328i	−0.0719306	−	0.0366505i	0.417655	−	0.908606i	$-0.362852\pi$
$653$	−46.9707	−	23.9328i	−0.0719306	−	0.0366505i	−0.489586	+	0.871955i	$0.662852\pi$
$654$	888.285	−	1452.71i	1.35823	−	2.22127i
$655$	374.597	+	710.503i	0.571904	+	1.08474i
$656$	−51.8353	−	157.451i	−0.0790173	−	0.240017i
$657$	421.118	+	826.491i	0.640971	+	1.25798i
$658$	203.094	−	124.727i	0.308653	−	0.189555i
$659$		−	741.252i		−	1.12481i	−0.826861	−	0.562407i	$-0.809875\pi$
$659$		−	741.252i		−	1.12481i	0.826861	−	0.562407i	$-0.190125\pi$
$660$	−232.719	−	971.500i	−0.352605	−	1.47197i
$661$	−747.326			−1.13060			−0.565299	−	0.824886i	$-0.691239\pi$
$661$	−747.326			−1.13060			−0.565299	+	0.824886i	$0.691239\pi$
$662$	−407.549	−	663.614i	−0.615633	−	1.00244i
$663$	−1826.73	+	930.766i	−2.75525	+	1.40387i
$664$	838.796	+	63.5588i	1.26325	+	0.0957211i
$665$	−361.596	−	111.937i	−0.543754	−	0.168326i
$666$	303.130	+	185.354i	0.455150	+	0.278309i
$667$	−427.596	+	839.205i	−0.641074	+	1.25818i
$668$	−865.035	−	279.212i	−1.29496	−	0.417982i
$669$	522.592	−	719.286i	0.781154	−	1.07517i
$670$	−209.646	+	53.6526i	−0.312904	+	0.0800785i
$671$	389.573	−	153.933i	0.580586	−	0.229408i
$672$	366.857	−	897.966i	0.545918	−	1.33626i
$673$	−168.295	−	1062.58i	−0.250068	−	1.57886i	−0.718604	−	0.695420i	$-0.755218\pi$
$673$	−168.295	−	1062.58i	−0.250068	−	1.57886i	0.468536	−	0.883444i	$-0.344782\pi$
$674$	−843.353	+	67.1967i	−1.25127	+	0.0996983i
$675$	−216.032	−	204.300i	−0.320048	−	0.302666i
$676$	−274.219	+	1753.36i	−0.405650	+	2.59373i
$677$	61.9243	−	390.975i	0.0914688	−	0.577511i	−0.898802	−	0.438355i	$-0.855561\pi$
$677$	61.9243	−	390.975i	0.0914688	−	0.577511i	0.990271	−	0.139156i	$-0.0444388\pi$
$678$	−388.625	−	30.2061i	−0.573193	−	0.0445517i
$679$	−922.291	−	299.670i	−1.35831	−	0.441341i
$680$	290.546	+	669.289i	0.427273	+	0.984249i
$681$		−	514.873i		−	0.756054i
$682$	311.863	+	106.676i	0.457277	+	0.156417i
$683$	544.013	+	544.013i	0.796506	+	0.796506i	0.982543	−	0.186037i	$-0.0595645\pi$
$683$	544.013	+	544.013i	0.796506	+	0.796506i	−0.186037	+	0.982543i	$0.559564\pi$
$684$	−83.4622	−	520.422i	−0.122021	−	0.760851i
$685$	−126.442	−	371.432i	−0.184586	−	0.542236i
$686$	542.053	−	463.867i	0.790164	−	0.676191i
$687$	−83.7200	+	528.587i	−0.121863	+	0.769414i
$688$	−317.970	−	49.0974i	−0.462166	−	0.0713625i
$689$	−540.314	−	1662.92i	−0.784200	−	2.41352i
$690$	−883.556	−	1003.78i	−1.28052	−	1.45476i
$691$	152.782	−	210.287i	0.221103	−	0.304323i	−0.684027	−	0.729457i	$-0.739773\pi$
$691$	152.782	−	210.287i	0.221103	−	0.304323i	0.905130	+	0.425134i	$0.139773\pi$
$692$	−0.604274	−	311.430i	−0.000873228	−	0.450043i
$693$	−832.800	+	185.551i	−1.20173	+	0.267750i
$694$	−113.247	+	47.0370i	−0.163179	+	0.0677767i
$695$	188.251	+	183.069i	0.270864	+	0.263409i
$696$	−751.960	+	885.639i	−1.08040	+	1.27247i
$697$	85.7950	−	168.382i	0.123092	−	0.241581i
$698$	18.7238	+	77.6582i	0.0268249	+	0.111258i
$699$	−791.658	−	1089.62i	−1.13256	−	1.55883i
$700$	−667.265	+	19.9212i	−0.953236	+	0.0284589i
$701$	626.487	+	203.558i	0.893705	+	0.290382i	0.719636	−	0.694351i	$-0.244308\pi$
$701$	626.487	+	203.558i	0.893705	+	0.290382i	0.174069	+	0.984733i	$0.444308\pi$
$702$	501.715	−	308.121i	0.714693	−	0.438919i
$703$	122.607	−	122.607i	0.174406	−	0.174406i
$704$	62.6544	−	701.206i	0.0889977	−	0.996032i
$705$	57.8109	−	401.153i	0.0820013	−	0.569011i
$706$	−19.1450	+	80.0868i	−0.0271176	+	0.113437i
$707$	−376.663	−	739.243i	−0.532763	−	1.04561i
$708$	−1383.70	+	452.560i	−1.95437	+	0.639209i
$709$	305.162	+	420.020i	0.430412	+	0.592411i	0.968048	−	0.250766i	$-0.0806824\pi$
$709$	305.162	+	420.020i	0.430412	+	0.592411i	−0.537636	+	0.843177i	$0.680682\pi$
$710$	19.4877	+	207.900i	0.0274475	+	0.292817i
$711$	−355.823	−	1095.11i	−0.500454	−	1.54024i
$712$	550.839	−	44.9654i	0.773650	−	0.0631537i
$713$	435.780	−	69.0207i	0.611192	−	0.0968033i
$714$	1021.28	−	424.188i	1.43036	−	0.594100i
$715$	−517.898	−	1259.01i	−0.724333	−	1.76085i
$716$	473.864	+	472.029i	0.661822	+	0.659259i
$717$	769.120	−	121.817i	1.07269	−	0.169898i
$718$	667.221	−	782.752i	0.929277	−	1.09018i
$719$	−363.969	−	1120.18i	−0.506216	−	1.55797i	−0.798717	−	0.601706i	$-0.794488\pi$
$719$	−363.969	−	1120.18i	−0.506216	−	1.55797i	0.292502	−	0.956265i	$-0.405512\pi$
$720$	−436.703	−	820.566i	−0.606532	−	1.13968i
$721$	27.8498	+	38.3320i	0.0386267	+	0.0531651i
$722$	463.387	+	36.0170i	0.641810	+	0.0498851i
$723$	272.295	+	534.408i	0.376618	+	0.739154i
$724$	191.303	+	1192.85i	0.264230	+	1.64759i
$725$	767.020	+	225.763i	1.05796	+	0.311397i
$726$	−954.746	+	544.062i	−1.31508	+	0.749397i
$727$	616.533	−	616.533i	0.848051	−	0.848051i	−0.141839	−	0.989890i	$-0.545302\pi$
$727$	616.533	−	616.533i	0.848051	−	0.848051i	0.989890	+	0.141839i	$0.0453015\pi$
$728$	304.847	−	1286.26i	0.418745	−	1.76684i
$729$	1021.06	+	331.761i	1.40062	+	0.455091i
$730$	674.385	−	427.236i	0.923815	−	0.585254i
$731$	−215.599	−	296.746i	−0.294937	−	0.405946i
$732$	558.778	−	407.635i	0.763358	−	0.556878i
$733$	−351.727	+	690.302i	−0.479845	+	0.941749i	0.516496	+	0.856289i	$0.327236\pi$
$733$	−351.727	+	690.302i	−0.479845	+	0.941749i	−0.996342	+	0.0854600i	$0.972764\pi$
$734$	1377.49	−	109.755i	1.87668	−	0.149530i
$735$	−1.40524	−	100.707i	−0.00191190	−	0.137016i
$736$	−364.854	−	868.891i	−0.495726	−	1.18056i
$737$	121.032	+	204.977i	0.164223	+	0.278123i
$738$	−91.9175	+	222.519i	−0.124550	+	0.301516i
$739$	−401.252	+	552.275i	−0.542966	+	0.747328i	−0.989037	−	0.147669i	$-0.952823\pi$
$739$	−401.252	+	552.275i	−0.542966	+	0.747328i	0.446071	+	0.894997i	$0.352823\pi$
$740$	134.480	−	274.636i	0.181729	−	0.371129i
$741$	−393.881	−	1212.24i	−0.531553	−	1.63595i
$742$	221.059	+	916.860i	0.297924	+	1.23566i
$743$	−158.762	+	1002.39i	−0.213677	+	1.34911i	0.614622	+	0.788822i	$0.289308\pi$
$743$	−158.762	+	1002.39i	−0.213677	+	1.34911i	−0.828300	+	0.560285i	$0.810692\pi$
$744$	542.689	+	41.1217i	0.729421	+	0.0552711i
$745$	−82.1220	−	40.4100i	−0.110231	−	0.0542417i
$746$	−540.089	−	129.110i	−0.723980	−	0.173070i
$747$	−863.916	−	863.916i	−1.15651	−	1.15651i
$748$	617.771	−	512.368i	0.825897	−	0.684984i
$749$		−	5.88728i		−	0.00786019i
$750$	−699.624	+	893.995i	−0.932832	+	1.19199i
$751$	−486.255	−	157.994i	−0.647477	−	0.210378i	−0.0331758	−	0.999450i	$-0.510562\pi$
$751$	−486.255	−	157.994i	−0.647477	−	0.210378i	−0.614301	+	0.789071i	$0.710562\pi$
$752$	128.680	−	254.990i	0.171117	−	0.339082i
$753$	18.7701	−	118.510i	0.0249271	−	0.157384i
$754$	−825.940	+	1350.75i	−1.09541	+	1.79145i
$755$	−1006.33	+	173.814i	−1.33289	+	0.230217i
$756$	−282.689	+	144.729i	−0.373927	+	0.191440i
$757$	175.399	+	1107.43i	0.231703	+	1.46292i	0.779551	+	0.626339i	$0.215448\pi$
$757$	175.399	+	1107.43i	0.231703	+	1.46292i	−0.547847	+	0.836578i	$0.684552\pi$
$758$	491.610	−	1190.12i	0.648563	−	1.57008i
$759$	−789.047	+	1241.45i	−1.03959	+	1.63564i
$760$	−439.239	+	113.319i	−0.577946	+	0.149103i
$761$	−69.5768	+	95.7643i	−0.0914282	+	0.125840i	−0.852281	−	0.523085i	$-0.824781\pi$
$761$	−69.5768	+	95.7643i	−0.0914282	+	0.125840i	0.760852	+	0.648925i	$0.224781\pi$
$762$	−49.5331	+	58.1099i	−0.0650041	+	0.0762597i
$763$	−568.235	+	1115.22i	−0.744738	+	1.46163i
$764$	−80.1707	+	512.614i	−0.104936	+	0.670960i
$765$	313.378	−	1012.33i	0.409644	−	1.32330i
$766$	506.068	+	591.366i	0.660663	+	0.772019i
$767$	−1767.69	+	900.684i	−2.30468	+	1.17430i
$768$	−190.753	−	1146.70i	−0.248377	−	1.49309i
$769$	−904.162			−1.17576			−0.587882	−	0.808947i	$-0.700038\pi$
$769$	−904.162			−1.17576			−0.587882	+	0.808947i	$0.700038\pi$
$770$	225.888	+	698.712i	0.293361	+	0.907419i
$771$			1773.74i			2.30057i
$772$	161.430	−	223.098i	0.209106	−	0.288987i
$773$	418.308	+	820.976i	0.541149	+	1.06206i	0.986044	+	0.166482i	$0.0532408\pi$
$773$	418.308	+	820.976i	0.541149	+	1.06206i	−0.444895	+	0.895582i	$0.646759\pi$
$774$	303.827	+	355.038i	0.392542	+	0.458705i
$775$	−125.636	−	352.849i	−0.162111	−	0.455289i
$776$	−1129.24	+	274.585i	−1.45520	+	0.353846i
$777$	−412.959	−	210.413i	−0.531479	−	0.270802i
$778$	625.734	−	734.081i	0.804285	−	0.943549i
$779$	95.0521	+	69.0594i	0.122018	+	0.0886513i
$780$	−1350.02	−	1797.37i	−1.73080	−	2.30432i
$781$	213.621	−	84.4083i	0.273522	−	0.108077i
$782$	410.180	−	992.986i	0.524527	−	1.26980i
$783$	375.695	−	59.5042i	0.479814	−	0.0759951i
$784$	21.6708	−	67.5872i	0.0276414	−	0.0862082i
$785$	78.6014	+	55.4483i	0.100129	+	0.0706348i
$786$	761.061	−	1244.65i	0.968270	−	1.58352i
$787$	295.521	+	46.8059i	0.375503	+	0.0594738i	0.341333	−	0.939942i	$-0.389121\pi$
$787$	295.521	+	46.8059i	0.375503	+	0.0594738i	0.0341693	+	0.999416i	$0.489121\pi$
$788$	118.218	+	361.449i	0.150023	+	0.458692i
$789$	468.850	−	1442.97i	0.594234	−	1.82886i
$790$	−909.806	+	392.860i	−1.15165	+	0.497292i
$791$	286.526			0.362233
$792$	−732.695	+	713.194i	−0.925119	+	0.900497i
$793$	666.496	−	666.496i	0.840474	−	0.840474i
$794$	684.796	+	163.702i	0.862463	+	0.206174i
$795$	1439.04	+	708.112i	1.81011	+	0.890707i
$796$	−103.071	+	203.262i	−0.129486	+	0.255354i
$797$	536.361	+	84.9513i	0.672976	+	0.106589i	0.483564	−	0.875309i	$-0.339342\pi$
$797$	536.361	+	84.9513i	0.672976	+	0.106589i	0.189411	+	0.981898i	$0.439342\pi$
$798$	161.149	+	668.377i	0.201941	+	0.837565i
$799$	309.684	−	100.622i	0.387589	−	0.125935i
$800$	−668.056	+	440.114i	−0.835071	+	0.550143i
$801$	−649.398	−	471.815i	−0.810734	−	0.589033i
$802$	−278.620	+	674.498i	−0.347406	+	0.841019i
$803$	−658.317	−	581.191i	−0.819822	−	0.723774i
$804$	278.474	+	277.395i	0.346360	+	0.345019i
$805$	704.696	+	685.300i	0.875398	+	0.851304i
$806$	739.328	−	58.9082i	0.917281	−	0.0730871i
$807$	608.193	+	309.890i	0.753647	+	0.384002i
$808$	−849.263	−	517.035i	−1.05107	−	0.639895i
$809$	−400.547	+	291.015i	−0.495114	+	0.359721i	−0.807148	−	0.590350i	$-0.798990\pi$
$809$	−400.547	+	291.015i	−0.495114	+	0.359721i	0.312034	+	0.950071i	$0.398990\pi$
$810$	110.695	−	493.404i	0.136661	−	0.609140i
$811$	−164.577	+	506.515i	−0.202930	+	0.624556i	0.796862	+	0.604162i	$0.206492\pi$
$811$	−164.577	+	506.515i	−0.202930	+	0.624556i	−0.999792	+	0.0203937i	$0.993508\pi$
$812$	500.630	−	691.877i	0.616540	−	0.852066i
$813$	−105.471	−	105.471i	−0.129731	−	0.129731i
$814$	−331.380	−	57.7390i	−0.407101	−	0.0709324i
$815$	−779.647	+	583.239i	−0.956623	+	0.715631i
$816$	774.801	−	1075.17i	0.949511	−	1.31761i
$817$	203.188	−	103.529i	0.248700	−	0.126719i
$818$	−780.357	−	60.6537i	−0.953981	−	0.0741488i
$819$	−1553.24	+	1128.50i	−1.89651	+	1.37790i
$820$	198.057	+	60.8900i	0.241532	+	0.0742561i
$821$	−628.739	+	204.290i	−0.765820	+	0.248830i	−0.665775	−	0.746153i	$-0.731899\pi$
$821$	−628.739	+	204.290i	−0.765820	+	0.248830i	−0.100046	+	0.994983i	$0.531899\pi$
$822$	−462.312	+	542.362i	−0.562423	+	0.659808i
$823$	−183.754	−	1160.18i	−0.223274	−	1.40969i	−0.803532	−	0.595262i	$-0.797048\pi$
$823$	−183.754	−	1160.18i	−0.223274	−	1.40969i	0.580258	−	0.814433i	$-0.302952\pi$
$824$	52.5217	+	21.5763i	0.0637400	+	0.0261849i
$825$	1159.10	+	464.559i	1.40497	+	0.563102i
$826$	988.269	−	410.478i	1.19645	−	0.496947i
$827$	−220.834	−	1394.29i	−0.267030	−	1.68596i	−0.648209	−	0.761462i	$-0.724482\pi$
$827$	−220.834	−	1394.29i	−0.267030	−	1.68596i	0.381179	−	0.924501i	$-0.375518\pi$
$828$	−420.432	+	1302.55i	−0.507768	+	1.57313i
$829$	346.209	−	112.490i	0.417622	−	0.135694i	−0.0926657	−	0.995697i	$-0.529539\pi$
$829$	346.209	−	112.490i	0.417622	−	0.135694i	0.510288	+	0.860004i	$0.329539\pi$
$830$	−670.888	+	809.669i	−0.808298	+	0.975505i
$831$	190.136	−	138.142i	0.228803	−	0.166235i
$832$	−498.287	−	1503.73i	−0.598903	−	1.80737i
$833$	72.0975	−	36.7355i	0.0865516	−	0.0441002i
$834$	110.892	−	463.879i	0.132963	−	0.556209i
$835$	909.817	−	680.617i	1.08960	−	0.815110i
$836$	254.541	+	429.178i	0.304474	+	0.513370i
$837$	−125.997	−	125.997i	−0.150534	−	0.150534i
$838$	532.813	−	327.219i	0.635815	−	0.390477i
$839$	−206.240	+	634.743i	−0.245817	+	0.756547i	0.749684	+	0.661796i	$0.230205\pi$
$839$	−206.240	+	634.743i	−0.245817	+	0.756547i	−0.995501	+	0.0947510i	$0.969795\pi$
$840$	650.882	+	1023.01i	0.774859	+	1.21787i
$841$	−147.130	+	106.896i	−0.174946	+	0.127106i
$842$	49.0044	+	203.249i	0.0582000	+	0.241389i
$843$	169.508	+	86.3685i	0.201077	+	0.102454i
$844$	991.026	−	507.377i	1.17420	−	0.601158i
$845$	−1590.34	−	1546.57i	−1.88206	−	1.83026i
$846$	−383.102	+	159.122i	−0.452839	+	0.188087i
$847$	668.700	−	453.103i	0.789492	−	0.534950i
$848$	802.296	+	796.093i	0.946104	+	0.938789i
$849$	47.9811	+	34.8603i	0.0565149	+	0.0410605i
$850$	−892.619	−	187.218i	−1.05014	−	0.220257i
$851$	−428.236	+	139.142i	−0.503215	+	0.163504i
$852$	306.404	−	223.525i	0.359629	−	0.262353i
$853$	1436.51	+	227.521i	1.68407	+	0.266731i	0.923800	−	0.382875i	$-0.125066\pi$
$853$	1436.51	+	227.521i	1.68407	+	0.266731i	0.760272	+	0.649605i	$0.225066\pi$
$854$	−386.284	+	330.566i	−0.452323	+	0.387080i
$855$	591.147	+	290.887i	0.691400	+	0.340219i
$856$	−3.70386	−	6.00484i	−0.00432693	−	0.00701500i
$857$	340.391	−	340.391i	0.397189	−	0.397189i	−0.480051	−	0.877240i	$-0.659382\pi$
$857$	340.391	−	340.391i	0.397189	−	0.397189i	0.877240	+	0.480051i	$0.159382\pi$
$858$	−1484.10	+	1977.80i	−1.72972	+	2.30513i
$859$	−1427.20			−1.66147			−0.830734	−	0.556670i	$-0.812079\pi$
$859$	−1427.20			−1.66147			−0.830734	+	0.556670i	$0.812079\pi$
$860$	279.824	−	288.863i	0.325376	−	0.335887i
$861$	97.0468	−	298.679i	0.112714	−	0.346898i
$862$	116.700	+	9.07062i	0.135383	+	0.0105228i
$863$	1544.24	+	244.584i	1.78939	+	0.283411i	0.960961	−	0.276683i	$-0.0892353\pi$
$863$	1544.24	+	244.584i	1.78939	+	0.283411i	0.828428	+	0.560095i	$0.189235\pi$
$864$	−197.281	+	325.466i	−0.228334	+	0.376697i
$865$	318.103	+	224.401i	0.367749	+	0.259424i
$866$	−530.083	+	42.2359i	−0.612105	+	0.0487712i
$867$	196.117	−	31.0619i	0.226202	−	0.0358269i
$868$	−400.055	+	0.776234i	−0.460893	+	0.000894279i
$869$	694.279	+	840.417i	0.798940	+	0.967108i
$870$	−360.058	−	1406.92i	−0.413860	−	1.61715i
$871$	433.344	+	314.843i	0.497525	+	0.361473i
$872$	122.037	+	1494.99i	0.139951	+	1.71443i
$873$	1503.93	+	766.289i	1.72271	+	0.877766i
$874$	569.857	+	348.449i	0.652010	+	0.398683i
$875$	461.800	−	695.020i	0.527771	−	0.794309i
$876$	−1293.26	−	655.791i	−1.47632	−	0.748620i
$877$	−407.030	−	798.842i	−0.464117	−	0.910880i	−0.997870	−	0.0652396i	$-0.979219\pi$
$877$	−407.030	−	798.842i	−0.464117	−	0.910880i	0.533753	−	0.845640i	$-0.320781\pi$
$878$	139.019	+	226.365i	0.158336	+	0.257819i
$879$		−	315.951i		−	0.359444i
$880$	669.978	+	570.552i	0.761338	+	0.648355i
$881$	−1402.92			−1.59241			−0.796206	−	0.605025i	$-0.793163\pi$
$881$	−1402.92			−1.59241			−0.796206	+	0.605025i	$0.793163\pi$
$882$	−87.8432	+	53.9477i	−0.0995955	+	0.0611652i
$883$	−217.848	+	110.999i	−0.246713	+	0.125707i	−0.572975	−	0.819573i	$-0.694211\pi$
$883$	−217.848	+	110.999i	−0.246713	+	0.125707i	0.326262	+	0.945279i	$0.394211\pi$
$884$	816.783	−	1610.75i	0.923963	−	1.82211i
$885$	538.140	−	1738.39i	0.608068	−	1.96428i
$886$	−4.72768	+	7.73170i	−0.00533598	+	0.00872652i
$887$	507.659	−	996.336i	0.572332	−	1.12326i	−0.405543	−	0.914076i	$-0.632918\pi$
$887$	507.659	−	996.336i	0.572332	−	1.12326i	0.977875	−	0.209189i	$-0.0670824\pi$
$888$	−553.582	+	45.1894i	−0.623403	+	0.0508889i
$889$	32.9906	−	45.4076i	0.0371097	−	0.0510772i
$890$	−352.132	+	594.358i	−0.395654	+	0.667817i
$891$	−555.162	+	34.5439i	−0.623077	+	0.0387699i
$892$	1.51964	+	783.190i	0.00170363	+	0.878016i
$893$	31.6689	+	199.950i	0.0354635	+	0.223908i
$894$	13.2040	+	165.717i	0.0147695	+	0.185365i
$895$	−823.863	+	142.298i	−0.920517	+	0.158992i
$896$	205.112	+	829.497i	0.228920	+	0.925778i
$897$	−517.798	+	3269.25i	−0.577255	+	3.64464i
$898$	−34.8333	+	448.157i	−0.0387898	+	0.499061i
$899$	455.705	+	148.067i	0.506902	+	0.164702i
$900$	1152.53	+	147.437i	1.28059	+	0.163819i
$901$			1288.53i			1.43011i
$902$	3.51597	−	227.899i	0.00389797	−	0.252659i
$903$	−431.018	−	431.018i	−0.477318	−	0.477318i
$904$	292.248	−	180.262i	0.323283	−	0.199404i
$905$	−1354.96	−	666.740i	−1.49719	−	0.736729i
$906$	1206.03	+	1409.31i	1.33116	+	1.55553i
$907$	138.930	−	877.167i	0.153175	−	0.967109i	−0.784635	−	0.619958i	$-0.787149\pi$
$907$	138.930	−	877.167i	0.153175	−	0.967109i	0.937810	−	0.347150i	$-0.112851\pi$
$908$	267.301	+	366.411i	0.294384	+	0.403536i
$909$	446.245	+	1373.40i	0.490919	+	1.51089i
$910$	1091.75	+	1240.31i	1.19973	+	1.36298i
$911$	900.848	−	1239.91i	0.988856	−	1.36104i	0.0569372	−	0.998378i	$-0.481867\pi$
$911$	900.848	−	1239.91i	0.988856	−	1.36104i	0.931919	−	0.362666i	$-0.118133\pi$
$912$	584.862	+	580.340i	0.641296	+	0.636338i
$913$	1061.21	+	460.093i	1.16233	+	0.503935i
$914$	288.195	+	693.859i	0.315312	+	0.759146i
$915$	12.0630	+	864.496i	0.0131836	+	0.944804i
$916$	−214.841	−	419.635i	−0.234543	−	0.458116i
$917$	−486.850	+	955.497i	−0.530916	+	1.04198i
$918$	−421.805	+	101.699i	−0.459482	+	0.110783i
$919$	−282.703	−	389.108i	−0.307621	−	0.423403i	0.627017	−	0.779006i	$-0.284276\pi$
$919$	−282.703	−	389.108i	−0.307621	−	0.423403i	−0.934637	+	0.355602i	$0.884276\pi$
$920$	1149.91	+	255.640i	1.24990	+	0.277870i
$921$	83.9950	+	27.2916i	0.0911998	+	0.0296326i
$922$	−927.464	−	1510.19i	−1.00593	−	1.63795i
$923$	365.470	−	365.470i	0.395959	−	0.395959i
$924$	880.784	−	1001.58i	0.953230	−	1.08396i
$925$	182.969	+	335.605i	0.197805	+	0.362817i
$926$	−1170.87	−	279.900i	−1.26444	−	0.302267i
$927$	−37.4400	−	73.4801i	−0.0403883	−	0.0792666i
$928$	75.3474	−	1020.65i	0.0811933	−	1.09984i
$929$	287.224	+	395.330i	0.309175	+	0.425543i	0.935124	−	0.354321i	$-0.115288\pi$
$929$	287.224	+	395.330i	0.309175	+	0.425543i	−0.625949	+	0.779864i	$0.715288\pi$
$930$	−434.055	+	523.845i	−0.466726	+	0.563274i
$931$	15.5457	+	47.8447i	0.0166978	+	0.0513907i
$932$	1129.07	+	364.438i	1.21145	+	0.391027i
$933$	−1477.98	+	234.089i	−1.58412	+	0.250899i
$934$	−168.481	−	405.635i	−0.180386	−	0.434299i
$935$	76.2694	+	1000.34i	0.0815715	+	1.06989i
$936$	−874.289	+	2128.22i	−0.934070	+	2.27374i
$937$	−1478.46	+	234.166i	−1.57787	+	0.249910i	−0.883051	−	0.469276i	$-0.844515\pi$
$937$	−1478.46	+	234.166i	−1.57787	+	0.249910i	−0.694818	+	0.719186i	$0.744515\pi$
$938$	−219.882	−	187.428i	−0.234415	−	0.199817i
$939$	62.4822	+	192.300i	0.0665412	+	0.204793i
$940$	167.121	+	315.494i	0.177788	+	0.335632i
$941$	−481.598	−	662.863i	−0.511794	−	0.704425i	0.472426	−	0.881370i	$-0.343378\pi$
$941$	−481.598	−	662.863i	−0.511794	−	0.704425i	−0.984221	+	0.176946i	$0.943378\pi$
$942$	13.5390	−	174.190i	0.0143726	−	0.184915i
$943$	−138.515	−	271.851i	−0.146887	−	0.288283i
$944$	749.760	−	1040.42i	0.794237	−	1.10214i
$945$	56.6246	−	392.921i	0.0599202	−	0.415789i
$946$	−391.027	−	206.898i	−0.413348	−	0.218708i
$947$	−1301.57	+	1301.57i	−1.37441	+	1.37441i	−0.520622	+	0.853787i	$0.674300\pi$
$947$	−1301.57	+	1301.57i	−1.37441	+	1.37441i	−0.853787	+	0.520622i	$0.825700\pi$
$948$	1458.27	+	1055.18i	1.53826	+	1.11306i
$949$	−1879.32	−	610.627i	−1.98031	−	0.643443i
$950$	201.776	−	529.911i	0.212396	−	0.557801i
$951$	31.1281	+	42.8442i	0.0327320	+	0.0450517i
$952$	−506.573	+	832.079i	−0.532115	+	0.874032i
$953$	−212.877	+	417.794i	−0.223375	+	0.438398i	−0.975310	−	0.220839i	$-0.929121\pi$
$953$	−212.877	+	417.794i	−0.223375	+	0.438398i	0.751935	+	0.659237i	$0.229121\pi$
$954$	−130.383	−	1636.38i	−0.136670	−	1.71528i
$955$	−464.952	−	452.155i	−0.486861	−	0.473461i
$956$	−484.104	+	485.986i	−0.506385	+	0.508354i
$957$	−1375.58	+	812.240i	−1.43739	+	0.848735i
$958$	−1304.87	−	539.013i	−1.36208	−	0.562644i
$959$	307.914	−	423.807i	0.321078	−	0.441926i
$960$	1307.48	+	633.951i	1.36196	+	0.660365i
$961$	227.604	+	700.492i	0.236840	+	0.728920i
$962$	−735.819	+	177.410i	−0.764885	+	0.184418i
$963$	−1.60299	+	10.1209i	−0.00166458	+	0.0105098i
$964$	−471.222	−	238.949i	−0.488820	−	0.247872i
$965$	110.927	+	325.857i	0.114951	+	0.337676i
$966$	415.110	−	1736.48i	0.429720	−	1.79760i
$967$	1024.95	+	1024.95i	1.05993	+	1.05993i	0.998086	+	0.0618415i	$0.0196973\pi$
$967$	1024.95	+	1024.95i	1.05993	+	1.05993i	0.0618415	+	0.998086i	$0.480303\pi$
$968$	396.993	−	882.848i	0.410117	−	0.912033i
$969$			939.321i			0.969372i
$970$	535.827	−	1350.25i	0.552398	−	1.39201i
$971$	−478.302	−	155.410i	−0.492587	−	0.160051i	0.0521818	−	0.998638i	$-0.483382\pi$
$971$	−478.302	−	155.410i	−0.492587	−	0.160051i	−0.544768	+	0.838586i	$0.683382\pi$
$972$	−1279.91	+	418.615i	−1.31678	+	0.430673i
$973$	−54.8441	+	346.272i	−0.0563660	+	0.355881i
$974$	591.659	+	361.780i	0.607453	+	0.371437i
$975$	2808.79	−	78.4022i	2.88081	−	0.0804125i
$976$	−186.029	+	580.189i	−0.190603	+	0.594456i
$977$	−172.132	−	1086.80i	−0.176184	−	1.11238i	−0.904291	−	0.426917i	$-0.859600\pi$
$977$	−172.132	−	1086.80i	−0.176184	−	1.11238i	0.728107	−	0.685463i	$-0.240400\pi$
$978$	1634.53	+	675.189i	1.67130	+	0.690377i
$979$	735.918	+	189.492i	0.751703	+	0.193557i
$980$	53.2828	+	70.9386i	0.0543702	+	0.0723864i
$981$	1280.52	−	1762.48i	1.30532	−	1.79661i
$982$	617.843	+	526.652i	0.629168	+	0.536305i
$983$	−538.862	+	1057.58i	−0.548181	+	1.07587i	0.436206	+	0.899847i	$0.356322\pi$
$983$	−538.862	+	1057.58i	−0.548181	+	1.07587i	−0.984387	+	0.176019i	$0.943678\pi$
$984$	−88.9229	−	365.698i	−0.0903688	−	0.371644i
$985$	−454.103	−	140.573i	−0.461018	−	0.142714i
$986$	886.479	−	758.613i	0.899066	−	0.769385i
$987$	482.143	−	245.664i	0.488493	−	0.248900i
$988$	909.651	+	658.208i	0.920700	+	0.666202i
$989$	−592.190			−0.598777
$990$	−198.080	−	1262.67i	−0.200081	−	1.27542i
$991$		−	388.087i		−	0.391612i	−0.980643	−	0.195806i	$-0.937268\pi$
$991$		−	388.087i		−	0.391612i	0.980643	−	0.195806i	$-0.0627322\pi$
$992$	−407.555	+	252.478i	−0.410842	+	0.254514i
$993$	−802.714	−	1575.42i	−0.808373	−	1.58652i
$994$	−211.817	+	181.265i	−0.213096	+	0.182359i
$995$	−132.860	−	251.998i	−0.133528	−	0.253264i
$996$	1886.94	+	295.110i	1.89452	+	0.296295i
$997$	1455.78	+	741.756i	1.46016	+	0.743988i	0.990325	−	0.138767i	$-0.0443139\pi$
$997$	1455.78	+	741.756i	1.46016	+	0.743988i	0.469834	+	0.882755i	$0.344314\pi$
$998$	−1145.89	−	976.761i	−1.14819	−	0.978719i
$999$	147.117	+	106.887i	0.147264	+	0.106994i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.3.w.a.7.13	yes	544
4.3	odd	2	inner	220.3.w.a.7.6	✓	544
5.3	odd	4	inner	220.3.w.a.183.45	yes	544
11.8	odd	10	inner	220.3.w.a.107.29	yes	544
20.3	even	4	inner	220.3.w.a.183.29	yes	544
44.19	even	10	inner	220.3.w.a.107.45	yes	544
55.8	even	20	inner	220.3.w.a.63.6	yes	544
220.63	odd	20	inner	220.3.w.a.63.13	yes	544

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.w.a.7.6	✓	544	4.3	odd	2	inner
220.3.w.a.7.13	yes	544	1.1	even	1	trivial
220.3.w.a.63.6	yes	544	55.8	even	20	inner
220.3.w.a.63.13	yes	544	220.63	odd	20	inner
220.3.w.a.107.29	yes	544	11.8	odd	10	inner
220.3.w.a.107.45	yes	544	44.19	even	10	inner
220.3.w.a.183.29	yes	544	20.3	even	4	inner
220.3.w.a.183.45	yes	544	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.70427 + 1.04665i) q^{2} +(-4.04592 + 2.06150i) q^{3} +(1.80904 - 3.56754i) q^{4} +(2.33189 + 4.42293i) q^{5} +(4.73765 - 7.74800i) q^{6} +(-3.03067 + 5.94803i) q^{7} +(0.650882 + 7.97348i) q^{8} +(6.82960 - 9.40014i) q^{9} +(-8.60342 - 5.09717i) q^{10} +(-2.74293 + 10.6525i) q^{11} +(0.0352426 + 18.1633i) q^{12} +(3.87209 + 24.4474i) q^{13} +(-1.06044 - 13.3091i) q^{14} +(-18.5525 - 13.0876i) q^{15} +(-9.45473 - 12.9077i) q^{16} +(2.85350 - 18.0163i) q^{17} +(-1.80079 + 23.1685i) q^{18} +(10.7855 + 3.50442i) q^{19} +(19.9975 - 0.317852i) q^{20} -30.3129i q^{21} +(-6.47480 - 21.0256i) q^{22} +(-20.8240 - 20.8240i) q^{23} +(-19.0707 - 30.9182i) q^{24} +(-14.1246 + 20.6276i) q^{25} +(-32.1870 - 37.6122i) q^{26} +(-1.86054 + 11.7470i) q^{27} +(15.7372 + 21.5723i) q^{28} +(-9.88305 - 30.4169i) q^{29} +(45.3165 + 2.88678i) q^{30} +(-8.80617 + 12.1207i) q^{31} +(29.6232 + 12.1023i) q^{32} +(-10.8625 - 48.7538i) q^{33} +(13.9936 + 33.6911i) q^{34} +(-33.3749 + 0.465708i) q^{35} +(-21.1804 - 41.3702i) q^{36} +(6.94136 - 13.6232i) q^{37} +(-22.0492 + 5.31618i) q^{38} +(-66.0644 - 90.9299i) q^{39} +(-33.7483 + 21.4721i) q^{40} +(9.85319 + 3.20150i) q^{41} +(31.7271 + 51.6613i) q^{42} +(14.2190 - 14.2190i) q^{43} +(33.0413 + 29.0564i) q^{44} +(57.5020 + 8.28674i) q^{45} +(57.2850 + 13.6942i) q^{46} +(8.10427 + 15.9055i) q^{47} +(64.8622 + 32.7325i) q^{48} +(2.60743 + 3.58882i) q^{49} +(2.48217 - 49.9384i) q^{50} +(25.5955 + 78.7748i) q^{51} +(94.2220 + 30.4126i) q^{52} +(-69.7703 + 11.0505i) q^{53} +(-9.12414 - 21.9673i) q^{54} +(-53.5116 + 12.7088i) q^{55} +(-49.3991 - 20.2935i) q^{56} +(-50.8615 + 8.05567i) q^{57} +(48.6792 + 41.4944i) q^{58} +(24.7682 + 76.2288i) q^{59} +(-80.2529 + 42.5107i) q^{60} +(-22.3830 - 30.8075i) q^{61} +(2.32196 - 29.8738i) q^{62} +(35.2140 + 69.1114i) q^{63} +(-63.1527 + 10.3796i) q^{64} +(-99.0999 + 74.1347i) q^{65} +(69.5408 + 71.7201i) q^{66} +(15.3020 - 15.3020i) q^{67} +(-59.1117 - 42.7722i) q^{68} +(127.181 + 41.3235i) q^{69} +(56.3922 - 35.7255i) q^{70} +(-12.2736 - 16.8932i) q^{71} +(79.3971 + 48.3373i) q^{72} +(-36.2433 + 71.1314i) q^{73} +(2.42880 + 30.4827i) q^{74} +(14.6232 - 112.575i) q^{75} +(32.0136 - 32.1380i) q^{76} +(-55.0486 - 48.5993i) q^{77} +(207.763 + 85.8223i) q^{78} +(58.2496 - 80.1738i) q^{79} +(35.0423 - 71.9169i) q^{80} +(15.6260 + 48.0919i) q^{81} +(-20.1433 + 4.85665i) q^{82} +(16.4491 - 103.856i) q^{83} +(-108.143 - 54.8374i) q^{84} +(86.3386 - 29.3911i) q^{85} +(-9.35060 + 39.1152i) q^{86} +(102.690 + 102.690i) q^{87} +(-86.7230 - 14.9371i) q^{88} -69.0839i q^{89} +(-106.672 + 46.0617i) q^{90} +(-157.149 - 51.0608i) q^{91} +(-111.962 + 36.6190i) q^{92} +(10.6423 - 67.1931i) q^{93} +(-30.4594 - 18.6249i) q^{94} +(9.65079 + 55.8753i) q^{95} +(-144.802 + 12.1032i) q^{96} +(22.7249 + 143.479i) q^{97} +(-8.20000 - 3.38724i) q^{98} +(81.4022 + 98.5364i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 544 q - 10 q^{2} - 12 q^{5} - 20 q^{6} - 10 q^{8} - 28 q^{12} - 20 q^{13} - 36 q^{16} - 20 q^{17} - 10 q^{18} - 40 q^{20} + 86 q^{22} - 12 q^{25} + 140 q^{26} - 10 q^{28} - 370 q^{30} - 100 q^{33} - 476 q^{36}+ \cdots + 148 q^{97}+O(q^{100}) \) 544 * q - 10 * q^2 - 12 * q^5 - 20 * q^6 - 10 * q^8 - 28 * q^12 - 20 * q^13 - 36 * q^16 - 20 * q^17 - 10 * q^18 - 40 * q^20 + 86 * q^22 - 12 * q^25 + 140 * q^26 - 10 * q^28 - 370 * q^30 - 100 * q^33 - 476 * q^36 - 12 * q^37 + 6 * q^38 - 10 * q^40 + 40 * q^41 + 198 * q^42 - 232 * q^45 + 340 * q^46 - 42 * q^48 - 10 * q^50 + 510 * q^52 - 156 * q^53 + 216 * q^56 - 20 * q^57 + 238 * q^58 + 118 * q^60 - 40 * q^61 + 440 * q^62 - 348 * q^66 - 10 * q^68 - 106 * q^70 - 1060 * q^72 - 580 * q^73 + 132 * q^77 - 1076 * q^78 + 614 * q^80 + 624 * q^81 - 490 * q^82 - 20 * q^85 - 772 * q^86 + 446 * q^88 - 820 * q^90 - 244 * q^92 - 132 * q^93 - 1840 * q^96 + 148 * q^97

Introduction

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