LMFDB - Embedded newform 220.3.w.a.183.45

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			183.45
Character	$\chi$	$=$	220.183
Dual form			220.3.w.a.107.45

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.04665 + 1.70427i) q^{2} +(-2.06150 - 4.04592i) q^{3} +(-1.80904 + 3.56754i) q^{4} +(-3.48586 - 3.58452i) q^{5} +(4.73765 - 7.74800i) q^{6} +(5.94803 + 3.03067i) q^{7} +(-7.97348 + 0.650882i) q^{8} +(-6.82960 + 9.40014i) q^{9} +(2.46049 - 9.69257i) q^{10} +(-2.74293 + 10.6525i) q^{11} +(18.1633 - 0.0352426i) q^{12} +(-24.4474 + 3.87209i) q^{13} +(1.06044 + 13.3091i) q^{14} +(-7.31657 + 21.4930i) q^{15} +(-9.45473 - 12.9077i) q^{16} +(-18.0163 - 2.85350i) q^{17} +(-23.1685 - 1.80079i) q^{18} +(-10.7855 - 3.50442i) q^{19} +(19.0940 - 5.95141i) q^{20} -30.3129i q^{21} +(-21.0256 + 6.47480i) q^{22} +(20.8240 - 20.8240i) q^{23} +(19.0707 + 30.9182i) q^{24} +(-0.697556 + 24.9903i) q^{25} +(-32.1870 - 37.6122i) q^{26} +(11.7470 + 1.86054i) q^{27} +(-21.5723 + 15.7372i) q^{28} +(9.88305 + 30.4169i) q^{29} +(-44.2876 + 10.0263i) q^{30} +(-8.80617 + 12.1207i) q^{31} +(12.1023 - 29.6232i) q^{32} +(48.7538 - 10.8625i) q^{33} +(-13.9936 - 33.6911i) q^{34} +(-9.87049 - 31.8853i) q^{35} +(-21.1804 - 41.3702i) q^{36} +(-13.6232 - 6.94136i) q^{37} +(-5.31618 - 22.0492i) q^{38} +(66.0644 + 90.9299i) q^{39} +(30.1275 + 26.3122i) q^{40} +(9.85319 + 3.20150i) q^{41} +(51.6613 - 31.7271i) 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} +(15.9055 - 8.10427i) q^{47} +(-32.7325 + 64.8622i) q^{48} +(-2.60743 - 3.58882i) q^{49} +(-43.3202 + 24.9673i) q^{50} +(25.5955 + 78.7748i) q^{51} +(30.4126 - 94.2220i) q^{52} +(-11.0505 - 69.7703i) q^{53} +(9.12414 + 21.9673i) q^{54} +(47.7456 - 27.3012i) q^{55} +(-49.3991 - 20.2935i) q^{56} +(8.05567 + 50.8615i) q^{57} +(-41.4944 + 48.6792i) q^{58} +(-24.7682 - 76.2288i) q^{59} +(-63.4411 - 64.9839i) q^{60} +(-22.3830 - 30.8075i) q^{61} +(-29.8738 - 2.32196i) q^{62} +(-69.1114 + 35.2140i) 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} +(42.7722 - 59.1117i) q^{68} +(-127.181 - 41.3235i) q^{69} +(44.0101 - 50.1947i) q^{70} +(-12.2736 - 16.8932i) q^{71} +(48.3373 - 79.3971i) q^{72} +(-71.1314 - 36.2433i) q^{73} +(-2.42880 - 30.4827i) q^{74} +(102.547 - 48.6951i) q^{75} +(32.0136 - 32.1380i) q^{76} +(-48.5993 + 55.0486i) q^{77} +(-85.8223 + 207.763i) q^{78} +(-58.2496 + 80.1738i) q^{79} +(-13.3100 + 78.8850i) q^{80} +(15.6260 + 48.0919i) q^{81} +(4.85665 + 20.1433i) q^{82} +(103.856 + 16.4491i) q^{83} +(108.143 + 54.8374i) q^{84} +(52.5738 + 74.5265i) q^{85} +(-9.35060 + 39.1152i) q^{86} +(102.690 - 102.690i) q^{87} +(14.9371 - 86.7230i) q^{88} +69.0839i q^{89} +(74.3073 + 89.3254i) q^{90} +(-157.149 - 51.0608i) q^{91} +(36.6190 + 111.962i) q^{92} +(67.1931 + 10.6423i) q^{93} +(30.4594 + 18.6249i) q^{94} +(25.0350 + 50.8767i) q^{95} +(-144.802 + 12.1032i) q^{96} +(143.479 - 22.7249i) q^{97} +(3.38724 - 8.20000i) 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 $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.04665	+	1.70427i	0.523326	+	0.852133i
$2$	1.04665	+	1.70427i	0.523326	+	0.852133i
$3$	−2.06150	−	4.04592i	−0.687166	−	1.34864i	−0.925980	−	0.377573i	$-0.876759\pi$
$3$	−2.06150	−	4.04592i	−0.687166	−	1.34864i	0.238814	−	0.971065i	$-0.423241\pi$
$4$	−1.80904	+	3.56754i	−0.452261	+	0.891886i
$5$	−3.48586	−	3.58452i	−0.697172	−	0.716904i
$5$	−3.48586	−	3.58452i	−0.697172	−	0.716904i
$6$	4.73765	−	7.74800i	0.789608	−	1.29133i
$7$	5.94803	+	3.03067i	0.849718	+	0.432953i	0.823914	−	0.566714i	$-0.191786\pi$
$7$	5.94803	+	3.03067i	0.849718	+	0.432953i	0.0258034	+	0.999667i	$0.491786\pi$
$8$	−7.97348	+	0.650882i	−0.996685	+	0.0813603i
$9$	−6.82960	+	9.40014i	−0.758845	+	1.04446i
$10$	2.46049	−	9.69257i	0.246049	−	0.969257i
$11$	−2.74293	+	10.6525i	−0.249357	+	0.968412i
$11$	−2.74293	+	10.6525i	−0.249357	+	0.968412i
$12$	18.1633	−	0.0352426i	1.51361	−	0.00293689i
$13$	−24.4474	+	3.87209i	−1.88057	+	0.297853i	−0.988167	−	0.153384i	$-0.950983\pi$
$13$	−24.4474	+	3.87209i	−1.88057	+	0.297853i	−0.892404	+	0.451237i	$0.850983\pi$
$14$	1.06044	+	13.3091i	0.0757457	+	0.950648i
$15$	−7.31657	+	21.4930i	−0.487772	+	1.43287i
$16$	−9.45473	−	12.9077i	−0.590920	−	0.806730i
$17$	−18.0163	−	2.85350i	−1.05978	−	0.167853i	−0.397874	−	0.917440i	$-0.630252\pi$
$17$	−18.0163	−	2.85350i	−1.05978	−	0.167853i	−0.661906	+	0.749587i	$0.730252\pi$
$18$	−23.1685	−	1.80079i	−1.28714	−	0.100044i
$19$	−10.7855	−	3.50442i	−0.567657	−	0.184443i	0.0111065	−	0.999938i	$-0.496465\pi$
$19$	−10.7855	−	3.50442i	−0.567657	−	0.184443i	−0.578764	+	0.815495i	$0.696465\pi$
$20$	19.0940	−	5.95141i	0.954700	−	0.297570i
$21$		−	30.3129i		−	1.44347i
$22$	−21.0256	+	6.47480i	−0.955710	+	0.294309i
$23$	20.8240	−	20.8240i	0.905390	−	0.905390i	−0.0905057	−	0.995896i	$-0.528848\pi$
$23$	20.8240	−	20.8240i	0.905390	−	0.905390i	0.995896	+	0.0905057i	$0.0288483\pi$
$24$	19.0707	+	30.9182i	0.794613	+	1.28826i
$25$	−0.697556	+	24.9903i	−0.0279022	+	0.999611i
$26$	−32.1870	−	37.6122i	−1.23796	−	1.44662i
$27$	11.7470	+	1.86054i	0.435073	+	0.0689089i
$28$	−21.5723	+	15.7372i	−0.770439	+	0.562044i
$29$	9.88305	+	30.4169i	0.340795	+	1.04886i	0.963797	+	0.266638i	$0.0859129\pi$
$29$	9.88305	+	30.4169i	0.340795	+	1.04886i	−0.623002	+	0.782220i	$0.714087\pi$
$30$	−44.2876	+	10.0263i	−1.47625	+	0.334209i
$31$	−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	$0.277687\pi$
$32$	12.1023	−	29.6232i	0.378197	−	0.925725i
$33$	48.7538	−	10.8625i	1.47739	−	0.329167i
$34$	−13.9936	−	33.6911i	−0.411577	−	0.990915i
$35$	−9.87049	−	31.8853i	−0.282014	−	0.911009i
$36$	−21.1804	−	41.3702i	−0.588343	−	1.14917i
$37$	−13.6232	−	6.94136i	−0.368194	−	0.187604i	0.260097	−	0.965582i	$-0.416245\pi$
$37$	−13.6232	−	6.94136i	−0.368194	−	0.187604i	−0.628291	+	0.777978i	$0.716245\pi$
$38$	−5.31618	−	22.0492i	−0.139900	−	0.580243i
$39$	66.0644	+	90.9299i	1.69396	+	2.33154i
$40$	30.1275	+	26.3122i	0.753188	+	0.657805i
$41$	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	$0.559675\pi$
$42$	51.6613	−	31.7271i	1.23003	−	0.755406i
$43$	14.2190	+	14.2190i	0.330673	+	0.330673i	0.852842	−	0.522169i	$-0.174877\pi$
$43$	14.2190	+	14.2190i	0.330673	+	0.330673i	−0.522169	+	0.852842i	$0.674877\pi$
$44$	−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
$47$	15.9055	−	8.10427i	0.338415	−	0.172431i	−0.276521	−	0.961008i	$-0.589182\pi$
$47$	15.9055	−	8.10427i	0.338415	−	0.172431i	0.614937	+	0.788577i	$0.289182\pi$
$48$	−32.7325	+	64.8622i	−0.681927	+	1.35130i
$49$	−2.60743	−	3.58882i	−0.0532129	−	0.0732413i
$50$	−43.3202	+	24.9673i	−0.866403	+	0.499345i
$51$	25.5955	+	78.7748i	0.501872	+	1.54460i
$52$	30.4126	−	94.2220i	0.584857	−	1.81196i
$53$	−11.0505	−	69.7703i	−0.208501	−	1.31642i	−0.840652	−	0.541576i	$-0.817828\pi$
$53$	−11.0505	−	69.7703i	−0.208501	−	1.31642i	0.632151	−	0.774845i	$-0.282172\pi$
$54$	9.12414	+	21.9673i	0.168966	+	0.406802i
$55$	47.7456	−	27.3012i	0.868103	−	0.496385i
$56$	−49.3991	−	20.2935i	−0.882126	−	0.362384i
$57$	8.05567	+	50.8615i	0.141328	+	0.892307i
$58$	−41.4944	+	48.6792i	−0.715420	+	0.839297i
$59$	−24.7682	−	76.2288i	−0.419801	−	1.29201i	−0.907886	−	0.419218i	$-0.862304\pi$
$59$	−24.7682	−	76.2288i	−0.419801	−	1.29201i	0.488085	−	0.872796i	$-0.337696\pi$
$60$	−63.4411	−	64.9839i	−1.05735	−	1.08307i
$61$	−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	$0.901043\pi$
$62$	−29.8738	−	2.32196i	−0.481836	−	0.0374510i
$63$	−69.1114	+	35.2140i	−1.09701	+	0.558952i
$64$	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	$-0.301631\pi$
$67$	−15.3020	−	15.3020i	−0.228388	−	0.228388i	−0.812019	+	0.583631i	$0.801631\pi$
$68$	42.7722	−	59.1117i	0.629002	−	0.869289i
$69$	−127.181	−	41.3235i	−1.84320	−	0.598891i
$70$	44.0101	−	50.1947i	0.628715	−	0.717067i
$71$	−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	$0.846978\pi$
$72$	48.3373	−	79.3971i	0.671351	−	1.10274i
$73$	−71.1314	−	36.2433i	−0.974403	−	0.496483i	−0.107092	−	0.994249i	$-0.534154\pi$
$73$	−71.1314	−	36.2433i	−0.974403	−	0.496483i	−0.867311	+	0.497766i	$0.834154\pi$
$74$	−2.42880	−	30.4827i	−0.0328216	−	0.411929i
$75$	102.547	−	48.6951i	1.36729	−	0.649268i
$76$	32.0136	−	32.1380i	0.421231	−	0.422869i
$77$	−48.5993	+	55.0486i	−0.631160	+	0.714917i
$78$	−85.8223	+	207.763i	−1.10029	+	2.66363i
$79$	−58.2496	+	80.1738i	−0.737337	+	1.01486i	0.261430	+	0.965222i	$0.415806\pi$
$79$	−58.2496	+	80.1738i	−0.737337	+	1.01486i	−0.998767	+	0.0496354i	$0.984194\pi$
$80$	−13.3100	+	78.8850i	−0.166375	+	0.986063i
$81$	15.6260	+	48.0919i	0.192914	+	0.593727i
$82$	4.85665	+	20.1433i	0.0592275	+	0.245650i
$83$	103.856	+	16.4491i	1.25127	+	0.198182i	0.746684	−	0.665179i	$-0.231645\pi$
$83$	103.856	+	16.4491i	1.25127	+	0.198182i	0.504587	+	0.863361i	$0.331645\pi$
$84$	108.143	+	54.8374i	1.28741	+	0.652826i
$85$	52.5738	+	74.5265i	0.618515	+	0.876783i
$86$	−9.35060	+	39.1152i	−0.108728	+	0.454828i
$87$	102.690	−	102.690i	1.18035	−	1.18035i
$88$	14.9371	−	86.7230i	0.169740	−	0.985489i
$89$			69.0839i			0.776223i	0.921612	+	0.388112i	$0.126872\pi$
$89$			69.0839i			0.776223i	−0.921612	+	0.388112i	$0.873128\pi$
$90$	74.3073	+	89.3254i	0.825637	+	0.992504i
$91$	−157.149	−	51.0608i	−1.72691	−	0.561107i
$92$	36.6190	+	111.962i	0.398032	+	1.21698i
$93$	67.1931	+	10.6423i	0.722506	+	0.114434i
$94$	30.4594	+	18.6249i	0.324036	+	0.198137i
$95$	25.0350	+	50.8767i	0.263527	+	0.535544i
$96$	−144.802	+	12.1032i	−1.50835	+	0.126075i
$97$	143.479	−	22.7249i	1.47917	−	0.234277i	0.635901	−	0.771771i	$-0.280629\pi$
$97$	143.479	−	22.7249i	1.47917	−	0.234277i	0.843268	+	0.537494i	$0.180629\pi$
$98$	3.38724	−	8.20000i	0.0345636	−	0.0836735i
$99$	−81.4022	−	98.5364i	−0.822244	−	0.995317i
$100$	−87.8919	−	47.6970i	−0.878919	−	0.476970i
$101$	−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	$0.989048\pi$
$102$	−107.464	+	126.071i	−1.05356	+	1.23599i
$103$	6.32402	+	3.22225i	0.0613982	+	0.0312840i	0.484420	−	0.874836i	$-0.339031\pi$
$103$	6.32402	+	3.22225i	0.0613982	+	0.0312840i	−0.423022	+	0.906119i	$0.639031\pi$
$104$	192.411	−	46.7864i	1.85010	−	0.449869i
$105$	−108.657	+	105.667i	−1.03483	+	1.00635i
$106$	107.341	−	91.8582i	1.01265	−	0.866587i
$107$	0.400378	+	0.785785i	0.00374185	+	0.00734379i	0.892870	−	0.450315i	$-0.148688\pi$
$107$	0.400378	+	0.785785i	0.00374185	+	0.00734379i	−0.889128	+	0.457659i	$0.848688\pi$
$108$	−27.8884	+	38.5421i	−0.258226	+	0.356871i
$109$	−187.495			−1.72014			−0.860068	−	0.510179i	$-0.829579\pi$
$109$	−187.495			−1.72014			−0.860068	+	0.510179i	$0.829579\pi$
$110$	96.5015	+	52.7965i	0.877286	+	0.479968i
$111$			69.4279i			0.625477i
$112$	−17.1180	−	105.429i	−0.152840	−	0.941334i
$113$	38.2431	−	19.4858i	0.338434	−	0.172441i	−0.276511	−	0.961011i	$-0.589178\pi$
$113$	38.2431	−	19.4858i	0.338434	−	0.172441i	0.614945	+	0.788570i	$0.289178\pi$
$114$	−78.2501	+	66.9633i	−0.686404	+	0.587397i
$115$	−147.233	−	2.05447i	−1.28029	−	0.0178650i
$116$	−126.392	−	19.7673i	−1.08959	−	0.170408i
$117$	130.568	−	256.254i	1.11597	−	2.19020i
$118$	103.990	−	121.997i	0.881275	−	1.03387i
$119$	−98.5132	−	71.5740i	−0.827842	−	0.601462i
$120$	44.3491	−	176.136i	0.369576	−	1.46780i
$121$	−105.953	−	58.4382i	−0.875642	−	0.482960i
$122$	29.0770	−	70.3913i	0.238336	−	0.576978i
$123$	−7.35934	−	46.4651i	−0.0598321	−	0.377765i
$124$	−27.3102	−	53.3432i	−0.220244	−	0.430187i
$125$	92.0097	−	84.6122i	0.736077	−	0.676897i
$126$	−132.349	−	80.9274i	−1.05039	−	0.642281i
$127$	−1.31526	+	8.30422i	−0.0103564	+	0.0653876i	−0.992325	−	0.123655i	$-0.960538\pi$
$127$	−1.31526	+	8.30422i	−0.0103564	+	0.0653876i	0.981969	+	0.189043i	$0.0605384\pi$
$128$	83.7884	+	96.7652i	0.654597	+	0.755978i
$129$	28.2164	−	86.8411i	0.218732	−	0.673187i
$130$	−22.6222	+	246.486i	−0.174017	+	1.89604i
$131$	160.641			1.22627			0.613134	−	0.789979i	$-0.289909\pi$
$131$	160.641			1.22627			0.613134	+	0.789979i	$0.289909\pi$
$132$	−49.4452	+	193.582i	−0.374585	+	1.46653i
$133$	−53.5316	−	53.5316i	−0.402493	−	0.402493i
$134$	10.0628	−	42.0944i	0.0750955	−	0.314138i
$135$	−34.2792	−	48.5929i	−0.253920	−	0.359947i
$136$	145.510	+	11.0258i	1.06992	+	0.0810722i
$137$	−12.2758	+	77.5066i	−0.0896046	+	0.565741i	0.901513	+	0.432752i	$0.142458\pi$
$137$	−12.2758	+	77.5066i	−0.0896046	+	0.565741i	−0.991118	+	0.132989i	$0.957542\pi$
$138$	−62.6875	−	260.001i	−0.454257	−	1.88406i
$139$	−49.9473	+	16.2289i	−0.359333	+	0.116754i	−0.483119	−	0.875554i	$-0.660496\pi$
$139$	−49.9473	+	16.2289i	−0.359333	+	0.116754i	0.123786	+	0.992309i	$0.460496\pi$
$140$	131.608	+	22.4685i	0.940060	+	0.160489i
$141$	−65.5784	−	47.6455i	−0.465095	−	0.337911i
$142$	15.9443	−	38.5988i	0.112284	−	0.271822i
$143$	25.8099	−	271.048i	0.180489	−	1.89544i
$144$	185.906	−	0.721436i	1.29101	−	0.00500998i
$145$	74.5790	−	141.455i	0.514338	−	0.975552i
$146$	−12.6816	−	159.161i	−0.0868604	−	1.09014i
$147$	−9.14486	+	17.9478i	−0.0622100	+	0.122094i
$148$	49.4086	−	36.0441i	0.333842	−	0.243541i
$149$	14.8092	−	10.7595i	0.0993907	−	0.0722115i	−0.536980	−	0.843595i	$-0.680435\pi$
$149$	14.8092	−	10.7595i	0.0993907	−	0.0722115i	0.636371	+	0.771383i	$0.280435\pi$
$150$	190.320	+	123.800i	1.26880	+	0.825332i
$151$	−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	$0.863577\pi$
$152$	88.2788	+	20.9223i	0.580782	+	0.137647i
$153$	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
$157$	−8.73395	−	17.1413i	−0.0556303	−	0.109181i	0.861518	−	0.507728i	$-0.169514\pi$
$157$	−8.73395	−	17.1413i	−0.0556303	−	0.109181i	−0.917148	+	0.398547i	$0.869514\pi$
$158$	−197.604	−	15.3589i	−1.25066	−	0.0972084i
$159$	−259.504	+	188.541i	−1.63210	+	1.18579i
$160$	−148.372	+	59.8813i	−0.927324	+	0.374258i
$161$	186.972	−	60.7509i	1.16132	−	0.377335i
$162$	−65.6064	+	76.9663i	−0.404978	+	0.475101i
$163$	−192.335	+	30.4629i	−1.17997	+	0.186889i	−0.715443	−	0.698671i	$-0.753775\pi$
$163$	−192.335	+	30.4629i	−1.17997	+	0.186889i	−0.464526	+	0.885560i	$0.653775\pi$
$164$	−29.2463	+	29.3600i	−0.178331	+	0.179025i
$165$	−208.886	−	136.894i	−1.26597	−	0.829658i
$166$	80.6669	+	194.214i	0.485945	+	1.16996i
$167$	−224.447	+	35.5489i	−1.34400	+	0.212868i	−0.786643	−	0.617408i	$-0.788183\pi$
$167$	−224.447	+	35.5489i	−1.34400	+	0.212868i	−0.557352	+	0.830276i	$0.688183\pi$
$168$	19.7301	+	241.700i	0.117441	+	1.43869i
$169$	421.955	−	137.101i	2.49677	−	0.811251i
$170$	−71.9866	+	167.603i	−0.423451	+	0.985899i
$171$	106.603	−	77.4513i	0.623407	−	0.452932i
$172$	−76.4495	+	25.0040i	−0.444474	+	0.145372i
$173$	35.3466	+	69.3717i	0.204316	+	0.400992i	0.970313	−	0.241851i	$-0.0777545\pi$
$173$	35.3466	+	69.3717i	0.204316	+	0.400992i	−0.765998	+	0.642844i	$0.777755\pi$
$174$	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
$178$	−117.737	+	72.3067i	−0.661445	+	0.406217i
$179$	51.6714	−	159.028i	0.288667	−	0.888426i	−0.696608	−	0.717452i	$-0.745308\pi$
$179$	51.6714	−	159.028i	0.288667	−	0.888426i	0.985275	−	0.170975i	$-0.0546916\pi$
$180$	−74.4603	+	220.132i	−0.413669	+	1.22296i
$181$	−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	$0.985861\pi$
$182$	−77.4589	−	321.266i	−0.425599	−	1.76520i
$183$	−78.5022	+	154.069i	−0.428974	+	0.841909i
$184$	−152.486	+	179.593i	−0.828726	+	0.976051i
$185$	22.6071	+	73.0292i	0.122201	+	0.394753i
$186$	52.1903	+	125.654i	0.280593	+	0.675557i
$187$	79.8142	−	184.092i	0.426814	−	0.984448i
$188$	0.138548	+	71.4046i	0.000736956	+	0.379812i
$189$	64.2327	+	46.6678i	0.339855	+	0.246919i
$190$	−60.5044	+	95.9165i	−0.318444	+	0.504824i
$191$	−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	$0.510278\pi$
$192$	−172.184	−	234.113i	−0.896792	−	1.21934i
$193$	−10.7696	+	67.9965i	−0.0558010	+	0.352314i	0.943952	+	0.330083i	$0.107077\pi$
$193$	−10.7696	+	67.9965i	−0.0558010	+	0.352314i	−0.999753	+	0.0222305i	$0.992923\pi$
$194$	188.902	+	220.742i	0.973722	+	1.13784i
$195$	95.6486	−	553.778i	0.490505	−	2.83989i
$196$	17.5202	−	2.80979i	0.0893890	−	0.0143357i
$197$	67.2265	+	67.2265i	0.341251	+	0.341251i	0.856838	−	0.515586i	$-0.172426\pi$
$197$	67.2265	+	67.2265i	0.341251	+	0.341251i	−0.515586	+	0.856838i	$0.672426\pi$
$198$	82.7326	−	241.864i	0.417841	−	1.22154i
$199$	56.9753			0.286308			0.143154	−	0.989700i	$-0.454276\pi$
$199$	56.9753			0.286308			0.143154	+	0.989700i	$0.454276\pi$
$200$	−10.7038	−	199.713i	−0.0535188	−	0.998567i
$201$	−30.3655	+	93.4554i	−0.151072	+	0.464952i
$202$	−247.820	−	19.2620i	−1.22683	−	0.0953563i
$203$	−33.3990	+	210.873i	−0.164527	+	1.03878i
$204$	−327.336	−	51.1940i	−1.60459	−	0.250951i
$205$	−22.8710	−	46.4789i	−0.111566	−	0.226726i
$206$	1.12747	+	14.1504i	0.00547317	+	0.0686911i
$207$	53.5288	+	337.968i	0.258593	+	1.63269i
$208$	281.123	+	278.950i	1.35155	+	1.34111i
$209$	66.9147	−	105.280i	0.320166	−	0.503734i
$210$	−293.810	−	74.5848i	−1.39910	−	0.355166i
$211$	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	$0.470738\pi$
$212$	268.899	+	86.7943i	1.26839	+	0.409407i
$213$	−43.0464	+	84.4833i	−0.202096	+	0.396635i
$214$	−0.920131	+	1.50479i	−0.00429968	+	0.00703174i
$215$	1.40283	−	100.533i	0.00652478	−	0.467597i
$216$	−94.8753	−	7.18907i	−0.439238	−	0.0332827i
$217$	−89.1131	+	45.4054i	−0.410659	+	0.209241i
$218$	−196.242	−	319.541i	−0.900192	−	1.46579i
$219$			362.507i			1.65528i
$220$	11.0241	+	219.724i	0.0501095	+	0.998744i
$221$	451.500			2.04299
$222$	−118.324	+	72.6668i	−0.532989	+	0.327328i
$223$	−88.8904	−	174.457i	−0.398612	−	0.782319i	0.601248	−	0.799062i	$-0.294670\pi$
$223$	−88.8904	−	174.457i	−0.398612	−	0.782319i	−0.999860	+	0.0167431i	$0.994670\pi$
$224$	161.763	−	139.521i	0.722156	−	0.622863i
$225$	−230.148	−	177.231i	−1.02288	−	0.787692i
$226$	73.2362	+	44.7815i	0.324054	+	0.198148i
$227$	101.029	+	51.4767i	0.445061	+	0.226770i	0.662134	−	0.749386i	$-0.269651\pi$
$227$	101.029	+	51.4767i	0.445061	+	0.226770i	−0.217073	+	0.976155i	$0.569651\pi$
$228$	−196.024	−	63.2717i	−0.859753	−	0.277508i
$229$	−69.2755	+	95.3495i	−0.302513	+	0.416373i	−0.933028	−	0.359804i	$-0.882844\pi$
$229$	−69.2755	+	95.3495i	−0.302513	+	0.416373i	0.630515	+	0.776177i	$0.282844\pi$
$230$	−150.601	−	253.075i	−0.654785	−	1.10033i
$231$	322.909	+	83.1461i	1.39788	+	0.359940i
$232$	−98.6001	−	236.096i	−0.425000	−	1.01765i
$233$	−292.956	+	46.3997i	−1.25732	+	0.199140i	−0.749316	−	0.662213i	$-0.769618\pi$
$233$	−292.956	+	46.3997i	−1.25732	+	0.199140i	−0.508007	+	0.861353i	$0.669618\pi$
$234$	573.384	−	45.6860i	2.45036	−	0.195240i
$235$	−84.4943	−	28.7633i	−0.359550	−	0.122397i
$236$	316.756	+	49.5394i	1.34219	+	0.209913i
$237$	444.458	+	70.3952i	1.87535	+	0.297026i
$238$	18.8722	−	242.806i	0.0792950	−	1.02019i
$239$	163.096	+	52.9932i	0.682412	+	0.221729i	0.629651	−	0.776878i	$-0.283198\pi$
$239$	163.096	+	52.9932i	0.682412	+	0.221729i	0.0527607	+	0.998607i	$0.483198\pi$
$240$	346.601	−	108.770i	1.44417	−	0.453209i
$241$		−	132.086i		−	0.548074i	−0.961719	−	0.274037i	$-0.911641\pi$
$241$		−	132.086i		−	0.548074i	0.961719	−	0.274037i	$-0.0883591\pi$
$242$	−11.3013	−	241.736i	−0.0466996	−	0.998909i
$243$	238.052	−	238.052i	0.979638	−	0.979638i
$244$	150.399	−	24.1201i	0.616389	−	0.0988528i
$245$	−3.77506	+	21.8565i	−0.0154084	+	0.0892103i
$246$	71.4862	−	61.1750i	0.290594	−	0.248679i
$247$	277.247	+	43.9116i	1.12246	+	0.177780i
$248$	62.3267	−	102.376i	0.251317	−	0.412805i
$249$	−147.546	−	454.101i	−0.592555	−	1.82370i
$250$	240.504	+	68.2495i	0.962015	+	0.272998i
$251$	−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	$0.216763\pi$
$252$	−0.602006	−	310.261i	−0.00238891	−	1.23120i
$253$	164.709	+	278.947i	0.651025	+	1.10256i
$254$	−15.5292	+	6.45007i	−0.0611387	+	0.0253940i
$255$	193.147	−	366.345i	0.757441	−	1.43665i
$256$	−77.2163	+	244.077i	−0.301626	+	0.953426i
$257$	−348.044	−	177.337i	−1.35426	−	0.690029i	−0.382048	−	0.924142i	$-0.624781\pi$
$257$	−348.044	−	177.337i	−1.35426	−	0.690029i	−0.972209	+	0.234114i	$0.924781\pi$
$258$	177.533	−	42.8041i	0.688112	−	0.165907i
$259$	−59.9941	−	82.5748i	−0.231638	−	0.318822i
$260$	−443.755	+	219.430i	−1.70675	+	0.843962i
$261$	−353.420	−	114.833i	−1.35410	−	0.439974i
$262$	168.135	+	273.775i	0.641737	+	1.04494i
$263$	−236.266	−	236.266i	−0.898349	−	0.898349i	0.0969412	−	0.995290i	$-0.469094\pi$
$263$	−236.266	−	236.266i	−0.898349	−	0.898349i	−0.995290	+	0.0969412i	$0.969094\pi$
$264$	−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
$267$	279.507	−	142.416i	1.04684	−	0.533394i
$268$	82.2723	−	26.9085i	0.306986	−	0.100405i
$269$	88.3574	+	121.614i	0.328466	+	0.452095i	0.941028	−	0.338327i	$-0.109861\pi$
$269$	88.3574	+	121.614i	0.328466	+	0.452095i	−0.612562	+	0.790422i	$0.709861\pi$
$270$	46.9368	−	109.281i	0.173840	−	0.404743i
$271$	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	$0.880697\pi$
$272$	133.507	+	259.527i	0.490834	+	0.954144i
$273$	117.374	+	741.073i	0.429943	+	2.71455i
$274$	−144.940	+	60.2010i	−0.528979	+	0.219712i
$275$	−264.296	−	75.9772i	−0.961077	−	0.276281i
$276$	377.499	−	378.966i	1.36775	−	1.37307i
$277$	8.09659	+	51.1198i	0.0292296	+	0.184548i	0.997983	−	0.0634762i	$-0.0202187\pi$
$277$	8.09659	+	51.1198i	0.0292296	+	0.184548i	−0.968754	+	0.248024i	$0.920219\pi$
$278$	−79.9357	−	68.1375i	−0.287538	−	0.245099i
$279$	−53.7932	−	165.558i	−0.192807	−	0.593400i
$280$	99.4557	+	247.812i	0.355199	+	0.885044i
$281$	−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	$0.823751\pi$
$282$	12.5629	−	161.631i	0.0445492	−	0.573160i
$283$	11.6374	−	5.92958i	0.0411217	−	0.0209526i	−0.433309	−	0.901246i	$-0.642654\pi$
$283$	11.6374	−	5.92958i	0.0411217	−	0.0209526i	0.474430	+	0.880293i	$0.342654\pi$
$284$	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
$288$	195.808	+	316.078i	0.679890	+	1.09749i
$289$	41.5878	+	13.5127i	0.143903	+	0.0467568i
$290$	319.135	−	20.9516i	1.10047	−	0.0722468i
$291$	−387.725	−	533.658i	−1.33239	−	1.83388i
$292$	257.979	−	188.199i	0.883491	−	0.644516i
$293$	−61.9962	−	31.5886i	−0.211591	−	0.107811i	0.344983	−	0.938609i	$-0.387885\pi$
$293$	−61.9962	−	31.5886i	−0.211591	−	0.107811i	−0.556574	+	0.830798i	$0.687885\pi$
$294$	−40.1593	+	3.19981i	−0.136596	+	0.0108837i
$295$	−186.905	+	354.505i	−0.633576	+	1.20171i
$296$	113.142	+	46.4797i	0.382237	+	0.157026i
$297$	−52.0406	+	120.032i	−0.175221	+	0.404147i
$298$	33.8372	+	13.9774i	0.113548	+	0.0469039i
$299$	−428.460	+	589.725i	−1.43298	+	1.97232i
$300$	−11.7892	+	453.931i	−0.0392974	+	1.51310i
$301$	41.4818	+	127.668i	0.137813	+	0.424145i
$302$	−397.114	+	95.7461i	−1.31495	+	0.317040i
$303$	557.405	+	88.2842i	1.83962	+	0.291367i
$304$	56.7399	+	172.349i	0.186644	+	0.566937i
$305$	−32.4062	+	187.623i	−0.106250	+	0.615157i
$306$	412.272	+	98.5548i	1.34729	+	0.322075i
$307$	−13.7530	+	13.7530i	−0.0447979	+	0.0447979i	−0.729151	−	0.684353i	$-0.760085\pi$
$307$	−13.7530	+	13.7530i	−0.0447979	+	0.0447979i	0.684353	+	0.729151i	$0.260085\pi$
$308$	−108.470	−	272.965i	−0.352175	−	0.886251i
$309$		−	32.2291i		−	0.104301i
$310$	95.8128	+	115.177i	0.309074	+	0.371540i
$311$	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	$0.422262\pi$
$312$	−585.948	−	682.027i	−1.87804	−	2.18599i
$313$	43.9802	+	6.96579i	0.140512	+	0.0222549i	0.226294	−	0.974059i	$-0.427339\pi$
$313$	43.9802	+	6.96579i	0.140512	+	0.0222549i	−0.0857822	+	0.996314i	$0.527339\pi$
$314$	20.0720	−	32.8260i	0.0639236	−	0.104541i
$315$	367.138	+	124.980i	1.16552	+	0.396762i
$316$	−180.647	−	352.846i	−0.571668	−	1.11660i
$317$	−11.5191	+	1.82444i	−0.0363378	+	0.00575534i	−0.174577	−	0.984644i	$-0.555856\pi$
$317$	−11.5191	+	1.82444i	−0.0363378	+	0.00575534i	0.138239	+	0.990399i	$0.455856\pi$
$318$	−592.934	−	244.928i	−1.86457	−	0.770213i
$319$	−351.125	+	21.8482i	−1.10071	+	0.0684895i
$320$	−257.347	−	190.190i	−0.804210	−	0.594345i
$321$	2.35384	−	3.23979i	0.00733285	−	0.0100928i
$322$	299.230	+	255.065i	0.929287	+	0.792128i
$323$	184.314	+	93.9128i	0.570632	+	0.290752i
$324$	−199.838	−	31.2539i	−0.616784	−	0.0964626i
$325$	−79.7111	−	613.648i	−0.245265	−	1.88815i
$326$	−253.224	−	295.906i	−0.776762	−	0.907687i
$327$	386.520	+	758.589i	1.18202	+	2.31984i
$328$	−80.6480	−	19.1138i	−0.245878	−	0.0582738i
$329$	119.168			0.362212
$330$	14.6727	−	499.277i	0.0444627	−	1.51296i
$331$			389.384i			1.17639i	0.808720	+	0.588194i	$0.200161\pi$
$331$			389.384i			1.17639i	−0.808720	+	0.588194i	$0.799839\pi$
$332$	−246.562	+	340.752i	−0.742657	+	1.02636i
$333$	158.291	−	80.6532i	0.475348	−	0.242202i
$334$	−295.503	−	345.310i	−0.884739	−	1.03386i
$335$	−1.50968	+	108.191i	−0.00450649	+	0.322957i
$336$	−391.270	+	286.600i	−1.16449	+	0.852978i
$337$	192.044	−	376.907i	0.569863	−	1.11842i	−0.408738	−	0.912652i	$-0.634031\pi$
$337$	192.044	−	376.907i	0.569863	−	1.11842i	0.978601	−	0.205768i	$-0.0659691\pi$
$338$	675.296	+	575.625i	1.99792	+	1.70303i
$339$	−157.676	−	114.558i	−0.465121	−	0.337930i
$340$	−360.985	+	52.7374i	−1.06172	+	0.155110i
$341$	−104.961	−	127.054i	−0.307803	−	0.372593i
$342$	243.573	+	100.615i	0.712203	+	0.294195i
$343$	−55.8031	−	352.327i	−0.162691	−	1.02719i
$344$	−122.629	−	104.120i	−0.356481	−	0.302674i
$345$	295.209	+	599.929i	0.855678	+	1.73893i
$346$	−81.2322	+	132.848i	−0.234775	+	0.383954i
$347$	9.59150	−	60.5584i	0.0276412	−	0.174520i	−0.970006	−	0.243083i	$-0.921841\pi$
$347$	9.59150	−	60.5584i	0.0276412	−	0.174520i	0.997647	+	0.0685629i	$0.0218414\pi$
$348$	180.581	+	552.123i	0.518911	+	1.58656i
$349$	−12.3427	+	37.9869i	−0.0353658	+	0.108845i	−0.967181	−	0.254088i	$-0.918225\pi$
$349$	−12.3427	+	37.9869i	−0.0353658	+	0.108845i	0.931815	+	0.362933i	$0.118225\pi$
$350$	−333.337	+	17.2168i	−0.952391	+	0.0491910i
$351$	−294.388			−0.838711
$352$	282.366	+	210.175i	0.802177	+	0.597087i
$353$	29.1128	+	29.1128i	0.0824725	+	0.0824725i	0.747140	−	0.664667i	$-0.231427\pi$
$353$	29.1128	+	29.1128i	0.0824725	+	0.0824725i	−0.664667	+	0.747140i	$0.731427\pi$
$354$	−707.964	−	169.241i	−1.99990	−	0.478082i
$355$	−17.7698	+	102.882i	−0.0500559	+	0.289809i
$356$	−246.460	−	124.976i	−0.692302	−	0.351055i
$357$	−86.4978	+	546.126i	−0.242291	+	1.52976i
$358$	325.108	−	78.3853i	0.908124	−	0.218953i
$359$	489.097	−	158.917i	1.36239	−	0.442667i	0.465548	−	0.885022i	$-0.345857\pi$
$359$	489.097	−	158.917i	1.36239	−	0.442667i	0.896840	+	0.442356i	$0.145857\pi$
$360$	−453.097	+	103.501i	−1.25860	+	0.287503i
$361$	−188.009	−	136.597i	−0.520802	−	0.378385i
$362$	−558.291	−	230.618i	−1.54224	−	0.637065i
$363$	−18.0148	+	549.146i	−0.0496276	+	1.51280i
$364$	466.451	−	468.264i	1.28146	−	1.28644i
$365$	118.040	+	381.311i	0.323396	+	1.04469i
$366$	−344.740	+	27.4681i	−0.941911	+	0.0750496i
$367$	−313.674	+	615.620i	−0.854697	+	1.67744i	−0.126611	+	0.991952i	$0.540410\pi$
$367$	−313.674	+	615.620i	−0.854697	+	1.67744i	−0.728086	+	0.685485i	$0.759590\pi$
$368$	−465.674	−	71.9042i	−1.26542	−	0.195392i
$369$	−97.3879	+	70.7564i	−0.263924	+	0.191752i
$370$	−100.799	+	114.965i	−0.272431	+	0.310715i
$371$	145.722	−	448.486i	0.392782	−	1.20886i
$372$	−159.522	+	220.462i	−0.428823	+	0.592639i
$373$	−196.331	+	196.331i	−0.526355	+	0.526355i	−0.919484	−	0.393128i	$-0.871393\pi$
$373$	−196.331	+	196.331i	−0.526355	+	0.526355i	0.393128	+	0.919484i	$0.371393\pi$
$374$	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
$377$	−359.392	−	705.347i	−0.953294	−	1.87095i
$378$	−12.3051	+	158.314i	−0.0325531	+	0.418821i
$379$	520.868	−	378.433i	1.37432	−	0.998503i	0.376936	−	0.926239i	$-0.376978\pi$
$379$	520.868	−	378.433i	1.37432	−	0.998503i	0.997386	−	0.0722642i	$-0.0230225\pi$
$380$	−226.794	−	2.72452i	−0.596827	−	0.00716980i
$381$	36.3096	−	11.7977i	0.0953008	−	0.0309651i
$382$	−197.430	−	168.290i	−0.516832	−	0.440550i
$383$	384.380	−	60.8799i	1.00360	−	0.158955i	0.367061	−	0.930197i	$-0.380364\pi$
$383$	384.380	−	60.8799i	1.00360	−	0.158955i	0.636543	+	0.771241i	$0.280364\pi$
$384$	218.774	−	538.482i	0.569725	−	1.40230i
$385$	366.733	−	17.6866i	0.952554	−	0.0459393i
$386$	−127.156	+	52.8144i	−0.329420	+	0.136825i
$387$	−230.770	+	36.5504i	−0.596305	+	0.0944454i
$388$	−178.488	+	552.979i	−0.460021	+	1.42520i
$389$	458.686	−	149.036i	1.17914	−	0.383126i	0.347093	−	0.937831i	$-0.387169\pi$
$389$	458.686	−	149.036i	1.17914	−	0.383126i	0.832047	+	0.554704i	$0.187169\pi$
$390$	1043.90	−	416.602i	2.67666	−	1.06821i
$391$	−434.591	+	315.749i	−1.11149	+	0.807542i
$392$	23.1262	+	26.9183i	0.0589954	+	0.0686691i
$393$	−331.161	−	649.940i	−0.842649	−	1.65379i
$394$	−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	−0.947321	−	0.320285i	$-0.896221\pi$
$397$	−248.934	+	248.934i	−0.627037	+	0.627037i	0.320285	+	0.947321i	$0.396221\pi$
$398$	59.6333	+	97.1011i	0.149832	+	0.243973i
$399$	−106.229	+	326.940i	−0.266238	+	0.819398i
$400$	329.162	−	227.272i	0.822904	−	0.568181i
$401$	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	$0.149649\pi$
$402$	−191.055	+	46.0643i	−0.475261	+	0.114588i
$403$	168.356	−	330.417i	0.417757	−	0.819893i
$404$	−226.554	−	442.512i	−0.560777	−	1.09533i
$405$	117.916	−	223.653i	0.291151	−	0.552231i
$406$	−394.340	+	163.789i	−0.971281	+	0.403422i
$407$	111.311	−	126.082i	0.273490	−	0.309783i
$408$	−255.358	−	611.449i	−0.625877	−	1.49865i
$409$	−316.613	−	230.033i	−0.774115	−	0.562427i	0.129092	−	0.991633i	$-0.458794\pi$
$409$	−316.613	−	230.033i	−0.774115	−	0.562427i	−0.903207	+	0.429205i	$0.858794\pi$
$410$	55.2745	−	87.6255i	0.134816	−	0.213721i
$411$	338.892	−	110.113i	0.824554	−	0.267914i
$412$	−22.9359	+	16.7320i	−0.0556697	+	0.0406117i
$413$	83.7023	−	528.475i	0.202669	−	1.27960i
$414$	−519.961	+	444.962i	−1.25594	+	1.07479i
$415$	−303.064	−	429.611i	−0.730274	−	1.03521i
$416$	−181.167	+	771.072i	−0.435497	+	1.85354i
$417$	168.627	+	168.627i	0.404381	+	0.404381i
$418$	249.462	+	3.84864i	0.596799	+	0.00920728i
$419$	312.635			0.746145			0.373072	−	0.927802i	$-0.378304\pi$
$419$	312.635			0.746145			0.373072	+	0.927802i	$0.378304\pi$
$420$	−180.405	−	578.795i	−0.429535	−	1.37808i
$421$	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	$0.0603787\pi$
$422$	−43.1381	+	555.005i	−0.102223	+	1.31518i
$423$	−32.4471	+	204.863i	−0.0767071	+	0.484310i
$424$	133.523	+	549.119i	0.314914	+	1.29509i
$425$	83.8770	−	448.241i	0.197358	−	1.05468i
$426$	−189.037	+	15.0620i	−0.443748	+	0.0353569i
$427$	−39.7671	−	251.079i	−0.0931313	−	0.588008i
$428$	−3.52762	+	0.00684471i	−0.00824211	+	1.59923e-5i
$429$	−1149.84	+	454.339i	−2.68029	+	1.05907i
$430$	172.804	−	102.833i	0.401870	−	0.239146i
$431$	−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	$0.721629\pi$
$432$	−87.0493	−	169.217i	−0.201503	−	0.391706i
$433$	−120.708	+	236.902i	−0.278770	+	0.547118i	−0.987358	−	0.158505i	$-0.949333\pi$
$433$	−120.708	+	236.902i	−0.278770	+	0.547118i	0.708588	+	0.705623i	$0.249333\pi$
$434$	−170.653	−	104.349i	−0.393210	−	0.240435i
$435$	−726.060	−	10.1313i	−1.66910	−	0.0232904i
$436$	339.186	−	668.896i	0.777951	−	1.53417i
$437$	−297.573	+	151.621i	−0.680944	+	0.346958i
$438$	−617.809	+	379.419i	−1.41052	+	0.866252i
$439$			132.823i			0.302557i	0.988491	+	0.151279i	$0.0483391\pi$
$439$			132.823i			0.302557i	−0.988491	+	0.151279i	$0.951661\pi$
$440$	−362.929	+	248.762i	−0.824839	+	0.565368i
$441$	51.5432			0.116878
$442$	472.563	+	769.476i	1.06915	+	1.74090i
$443$	2.05716	+	4.03740i	0.00464370	+	0.00911378i	0.893317	−	0.449428i	$-0.148372\pi$
$443$	2.05716	+	4.03740i	0.00464370	+	0.00911378i	−0.888673	+	0.458541i	$0.848372\pi$
$444$	−247.687	−	125.598i	−0.557854	−	0.282879i
$445$	247.632	−	240.817i	0.556477	−	0.541161i
$446$	204.284	−	334.089i	0.458036	−	0.749078i
$447$	−74.0613	−	37.7361i	−0.165685	−	0.0844208i
$448$	407.091	+	129.657i	0.908685	+	0.289413i
$449$	−132.107	+	181.830i	−0.294225	+	0.404967i	−0.930381	−	0.366594i	$-0.880524\pi$
$449$	−132.107	+	181.830i	−0.294225	+	0.404967i	0.636155	+	0.771561i	$0.280524\pi$
$450$	61.1636	−	577.732i	0.135919	−	1.28385i
$451$	−61.1306	+	96.1800i	−0.135545	+	0.213259i
$452$	0.333123	+	171.685i	0.000736998	+	0.379833i
$453$	916.032	−	145.085i	2.02215	−	0.320276i
$454$	18.0118	+	226.058i	0.0396737	+	0.497925i
$455$	364.771	+	741.294i	0.801694	+	1.62922i
$456$	−97.3366	−	400.300i	−0.213457	−	0.877851i
$457$	−371.040	−	58.7670i	−0.811904	−	0.128593i	−0.263342	−	0.964703i	$-0.584825\pi$
$457$	−371.040	−	58.7670i	−0.811904	−	0.128593i	−0.548562	+	0.836110i	$0.684825\pi$
$458$	−235.008	−	18.2661i	−0.513118	−	0.0398824i
$459$	−206.328	−	67.0399i	−0.449516	−	0.146056i
$460$	273.681	−	521.545i	0.594959	−	1.13379i
$461$			886.126i			1.92218i	0.276232	+	0.961091i	$0.410914\pi$
$461$			886.126i			1.92218i	−0.276232	+	0.961091i	$0.589086\pi$
$462$	196.270	+	637.348i	0.424828	+	1.37954i
$463$	−425.628	+	425.628i	−0.919284	+	0.919284i	−0.996977	−	0.0776934i	$-0.975244\pi$
$463$	−425.628	+	425.628i	−0.919284	+	0.919284i	0.0776934	+	0.996977i	$0.475244\pi$
$464$	299.170	−	415.151i	0.644763	−	0.894721i
$465$	−196.078	−	277.953i	−0.421673	−	0.597747i
$466$	−385.700	−	450.711i	−0.827683	−	0.967191i
$467$	216.913	+	34.3556i	0.464481	+	0.0735666i	0.384289	−	0.923213i	$-0.374447\pi$
$467$	216.913	+	34.3556i	0.464481	+	0.0735666i	0.0801922	+	0.996779i	$0.474447\pi$
$468$	677.994	+	929.381i	1.44871	+	1.98586i
$469$	−44.6413	−	137.392i	−0.0951839	−	0.292946i
$470$	−39.4158	−	174.106i	−0.0838633	−	0.370438i
$471$	−51.3474	+	70.6737i	−0.109018	+	0.150050i
$472$	247.105	+	591.687i	0.523528	+	1.25358i
$473$	−190.469	+	112.466i	−0.402684	+	0.237772i
$474$	345.220	+	831.153i	0.728313	+	1.75349i
$475$	95.0998	−	267.088i	0.200210	−	0.562290i
$476$	433.558	−	221.969i	0.910836	−	0.466322i
$477$	731.321	+	372.627i	1.53317	+	0.781188i
$478$	80.3905	+	333.425i	0.168181	+	0.697542i
$479$	−414.922	−	571.091i	−0.866226	−	1.19226i	−0.980049	−	0.198756i	$-0.936310\pi$
$479$	−414.922	−	571.091i	−0.866226	−	1.19226i	0.113823	−	0.993501i	$-0.463690\pi$
$480$	548.143	+	476.855i	1.14197	+	0.993448i
$481$	359.930	+	116.948i	0.748294	+	0.243136i
$482$	225.109	−	138.248i	0.467032	−	0.286821i
$483$	−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
$487$	−308.957	+	157.422i	−0.634410	+	0.323248i	−0.741451	−	0.671007i	$-0.765862\pi$
$487$	−308.957	+	157.422i	−0.634410	+	0.323248i	0.107042	+	0.994255i	$0.465862\pi$
$488$	198.522	+	231.074i	0.406808	+	0.473513i
$489$	519.748	+	715.372i	1.06288	+	1.46293i
$490$	−41.2005	+	16.4425i	−0.0840827	+	0.0335560i
$491$	−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	$-0.235646\pi$
$492$	179.080	+	57.8025i	0.363983	+	0.117485i
$493$	−91.2611	−	576.200i	−0.185114	−	1.16876i
$494$	215.344	+	518.462i	0.435918	+	1.04952i
$495$	−69.4491	+	635.272i	−0.140301	+	1.28338i
$496$	239.709	−	0.930229i	0.483285	−	0.00187546i
$497$	−21.8061	−	137.678i	−0.0438755	−	0.277019i
$498$	619.479	−	726.743i	1.24393	−	1.45932i
$499$	−232.643	−	716.002i	−0.466219	−	1.43487i	−0.857443	−	0.514578i	$-0.827948\pi$
$499$	−232.643	−	716.002i	−0.466219	−	1.43487i	0.391225	−	0.920295i	$-0.372052\pi$
$500$	135.408	+	481.316i	0.270816	+	0.962631i
$501$	606.525	+	834.811i	1.21063	+	1.66629i
$502$	−52.6891	−	4.09529i	−0.104958	−	0.00815796i
$503$	−773.978	+	394.361i	−1.53872	+	0.784019i	−0.998351	−	0.0574073i	$-0.981717\pi$
$503$	−773.978	+	394.361i	−1.53872	+	0.784019i	−0.540372	+	0.841426i	$0.681717\pi$
$504$	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
$508$	−27.2463	−	19.7149i	−0.0536345	−	0.0388090i
$509$	−820.967	−	266.748i	−1.61290	−	0.524063i	−0.642649	−	0.766161i	$-0.722165\pi$
$509$	−820.967	−	266.748i	−1.61290	−	0.524063i	−0.970252	+	0.242097i	$0.922165\pi$
$510$	826.508	−	54.2611i	1.62060	−	0.106394i
$511$	−313.250	−	431.152i	−0.613014	−	0.843741i
$512$	−496.791	+	123.866i	−0.970295	+	0.241927i
$513$	−120.177	−	61.2331i	−0.234263	−	0.119363i
$514$	−62.0508	−	778.770i	−0.120721	−	1.51512i
$515$	−10.4944	−	33.9009i	−0.0203775	−	0.0658269i
$516$	258.765	+	257.762i	0.501482	+	0.499539i
$517$	42.7033	+	191.663i	0.0825982	+	0.370722i
$518$	77.9365	−	188.673i	0.150457	−	0.364234i
$519$	207.805	−	286.019i	0.400395	−	0.551097i
$520$	−838.423	−	526.609i	−1.61235	−	1.01271i
$521$	−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	$-0.313969\pi$
$522$	−174.201	−	722.512i	−0.333719	−	1.38412i
$523$	288.493	+	45.6928i	0.551612	+	0.0873667i	0.426017	−	0.904715i	$-0.359916\pi$
$523$	288.493	+	45.6928i	0.551612	+	0.0873667i	0.125594	+	0.992082i	$0.459916\pi$
$524$	−290.607	+	573.094i	−0.554593	+	1.09369i
$525$	757.528	+	21.1450i	1.44291	+	0.0402761i
$526$	155.372	−	649.947i	0.295384	−	1.23564i
$527$	193.241	−	193.241i	0.366680	−	0.366680i
$528$	−601.163	−	526.596i	−1.13857	−	0.997341i
$529$		−	338.276i		−	0.639463i
$530$	−703.444	−	64.5613i	−1.32725	−	0.121814i
$531$	885.719	+	287.787i	1.66802	+	0.541973i
$532$	287.817	−	94.1353i	0.541010	−	0.176946i
$533$	−253.282	−	40.1159i	−0.475200	−	0.0752643i
$534$	535.262	+	327.295i	1.00236	+	0.612912i
$535$	1.42100	−	4.17430i	0.00265608	−	0.00780243i
$536$	131.970	+	112.050i	0.246212	+	0.209049i
$537$	−749.936	+	118.778i	−1.39653	+	0.221188i
$538$	−114.782	+	277.872i	−0.213350	+	0.516490i
$539$	45.3820	−	17.9319i	0.0841967	−	0.0332688i
$540$	235.370	−	34.3859i	0.435870	−	0.0636777i
$541$	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	$0.0668799\pi$
$542$	−42.6180	+	49.9974i	−0.0786309	+	0.0922461i
$543$	1221.96	+	622.621i	2.25039	+	1.14663i
$544$	−302.568	+	499.165i	−0.556191	+	0.917583i
$545$	653.581	+	672.079i	1.19923	+	1.23317i
$546$	−1140.14	+	975.682i	−2.08816	+	1.78696i
$547$	−202.691	−	397.803i	−0.370549	−	0.727244i	0.628157	−	0.778086i	$-0.283809\pi$
$547$	−202.691	−	397.803i	−0.370549	−	0.727244i	−0.998707	+	0.0508421i	$0.983809\pi$
$548$	−254.301	−	184.007i	−0.464052	−	0.335780i
$549$	442.462			0.805942
$550$	−147.141	−	529.953i	−0.267528	−	0.963550i
$551$		−	362.695i		−	0.658249i
$552$	1040.97	+	246.712i	1.88581	+	0.446943i
$553$	−589.451	+	300.340i	−1.06591	+	0.543111i
$554$	−78.6475	+	67.3034i	−0.141963	+	0.121486i
$555$	248.866	−	242.016i	0.448407	−	0.436065i
$556$	32.4597	−	207.548i	0.0583807	−	0.373288i
$557$	197.171	−	386.971i	0.353988	−	0.694741i	−0.643510	−	0.765438i	$-0.722522\pi$
$557$	197.171	−	386.971i	0.353988	−	0.694741i	0.997498	+	0.0706972i	$0.0225224\pi$
$558$	225.853	−	264.960i	0.404754	−	0.474839i
$559$	−402.674	−	292.560i	−0.720347	−	0.523363i
$560$	−318.243	+	428.872i	−0.568290	+	0.765843i
$561$	−909.357	+	56.5831i	−1.62096	+	0.100861i
$562$	31.9907	−	77.4448i	0.0569229	−	0.137802i
$563$	−42.1135	−	265.894i	−0.0748019	−	0.472280i	−0.996445	−	0.0842425i	$-0.973153\pi$
$563$	−42.1135	−	265.894i	−0.0748019	−	0.472280i	0.921643	−	0.388038i	$-0.126847\pi$
$564$	288.611	−	147.761i	0.511722	−	0.261988i
$565$	−203.157	−	69.1582i	−0.359571	−	0.122404i
$566$	22.2859	+	13.6271i	0.0393744	+	0.0240762i
$567$	−52.8068	+	333.409i	−0.0931338	+	0.588023i
$568$	108.859	+	126.709i	0.191653	+	0.223079i
$569$	9.37853	−	28.8642i	0.0164825	−	0.0507279i	−0.942477	−	0.334271i	$-0.891510\pi$
$569$	9.37853	−	28.8642i	0.0164825	−	0.0507279i	0.958959	+	0.283543i	$0.0915099\pi$
$570$	512.800	+	47.0643i	0.899649	+	0.0825689i
$571$	−9.82448			−0.0172057			−0.00860287	−	0.999963i	$-0.502738\pi$
$571$	−9.82448			−0.0172057			−0.00860287	+	0.999963i	$0.502738\pi$
$572$	920.283	+	582.415i	1.60889	+	1.01821i
$573$	416.484	+	416.484i	0.726849	+	0.726849i
$574$	−32.1602	+	134.532i	−0.0560283	+	0.234376i
$575$	505.871	+	534.923i	0.879775	+	0.930300i
$576$	−333.738	+	664.533i	−0.579407	+	1.15370i
$577$	25.5160	−	161.102i	0.0442219	−	0.279206i	−0.955662	−	0.294467i	$-0.904858\pi$
$577$	25.5160	−	161.102i	0.0442219	−	0.279206i	0.999884	+	0.0152610i	$0.00485791\pi$
$578$	20.4987	+	85.0198i	0.0354649	+	0.147093i
$579$	297.310	−	96.6018i	0.513488	−	0.166842i
$580$	369.730	+	521.962i	0.637466	+	0.899935i
$581$	567.883	+	412.591i	0.977424	+	0.710140i
$582$	503.682	−	1219.34i	0.865433	−	2.09509i
$583$	773.541	+	73.6587i	1.32683	+	0.126344i
$584$	590.755	+	242.687i	1.01157	+	0.415560i
$585$	−1373.69	+	425.242i	−2.34819	+	0.726910i
$586$	−11.0529	−	138.720i	−0.0188617	−	0.236724i
$587$	251.807	−	494.198i	0.428972	−	0.841905i	−0.570811	−	0.821081i	$-0.693371\pi$
$587$	251.807	−	494.198i	0.428972	−	0.841905i	0.999783	−	0.0208237i	$-0.00662888\pi$
$588$	−47.4861	−	65.0930i	−0.0807587	−	0.110702i
$589$	137.455	−	99.8667i	0.233370	−	0.169553i
$590$	−799.795	+	52.5075i	−1.35559	+	0.0889957i
$591$	133.406	−	410.580i	0.225729	−	0.694721i
$592$	39.2067	+	241.473i	0.0662275	+	0.407893i
$593$	−86.9546	+	86.9546i	−0.146635	+	0.146635i	−0.776613	−	0.629978i	$-0.783064\pi$
$593$	−86.9546	+	86.9546i	−0.146635	+	0.146635i	0.629978	+	0.776613i	$0.283064\pi$
$594$	−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
$597$	−117.455	−	230.517i	−0.196741	−	0.386126i
$598$	−1453.50	−	112.974i	−2.43060	−	0.188919i
$599$	−2.16024	+	1.56951i	−0.00360641	+	0.00262021i	−0.589587	−	0.807705i	$-0.700709\pi$
$599$	−2.16024	+	1.56951i	−0.00360641	+	0.00262021i	0.585981	+	0.810325i	$0.300709\pi$
$600$	−785.958	+	455.015i	−1.30993	+	0.758359i
$601$	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	$0.322953\pi$
$602$	−174.163	+	204.319i	−0.289307	+	0.339401i
$603$	248.347	−	39.3343i	0.411852	−	0.0652310i
$604$	−578.816	−	576.575i	−0.958305	−	0.954594i
$605$	159.864	+	583.497i	0.264237	+	0.964458i
$606$	432.948	+	1042.37i	0.714436	+	1.72008i
$607$	877.578	−	138.995i	1.44576	−	0.228986i	0.616284	−	0.787524i	$-0.288637\pi$
$607$	877.578	−	138.995i	1.44576	−	0.228986i	0.829479	+	0.558538i	$0.188637\pi$
$608$	−234.341	+	277.089i	−0.385430	+	0.455739i
$609$	922.025	−	299.584i	1.51400	−	0.491928i
$610$	−353.677	+	141.147i	−0.579799	+	0.231388i
$611$	−357.468	+	259.716i	−0.585055	+	0.425067i
$612$	263.541	+	805.773i	0.430623	+	1.31662i
$613$	−76.7845	−	150.698i	−0.125260	−	0.245837i	0.819857	−	0.572568i	$-0.194053\pi$
$613$	−76.7845	−	150.698i	−0.125260	−	0.245837i	−0.945117	+	0.326731i	$0.894053\pi$
$614$	−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	−0.478308	−	0.878192i	$-0.658750\pi$
$617$	246.729	−	246.729i	0.399884	−	0.399884i	0.878192	+	0.478308i	$0.158750\pi$
$618$	54.9270	−	33.7326i	0.0888786	−	0.0545835i
$619$	−146.025	+	449.420i	−0.235905	+	0.726041i	0.761095	+	0.648641i	$0.224662\pi$
$619$	−146.025	+	449.420i	−0.235905	+	0.726041i	−0.997000	+	0.0774008i	$0.975338\pi$
$620$	−96.0101	+	283.841i	−0.154855	+	0.457808i
$621$	283.363	−	205.875i	0.456301	−	0.331522i
$622$	154.483	+	640.727i	0.248364	+	1.03011i
$623$	−209.370	+	410.913i	−0.336068	+	0.659571i
$624$	549.073	−	1712.46i	0.879924	−	2.74432i
$625$	−624.027	−	34.8642i	−0.998443	−	0.0557828i
$626$	34.1604	+	82.2448i	0.0545694	+	0.131381i
$627$	−563.900	−	53.6961i	−0.899362	−	0.0856397i
$628$	76.9526	−	0.149313i	0.122536	−	0.000237759i
$629$	225.632	+	163.931i	0.358715	+	0.260622i
$630$	171.266	+	756.511i	0.271851	+	1.20081i
$631$	−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	$0.657389\pi$
$632$	412.269	−	677.177i	0.652324	−	1.07148i
$633$	197.717	−	1248.33i	0.312348	−	1.97209i
$634$	−15.1658	−	17.7220i	−0.0239208	−	0.0279527i
$635$	34.3515	−	24.2328i	0.0540968	−	0.0381619i
$636$	−203.173	−	1266.87i	−0.319455	−	1.99194i
$637$	77.6412	+	77.6412i	0.121886	+	0.121886i
$638$	−404.741	−	575.543i	−0.634390	−	0.902106i
$639$	242.622			0.379691
$640$	54.7819	−	637.651i	0.0855968	−	0.996330i
$641$	−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	$0.996067\pi$
$642$	7.98511	+	0.620648i	0.0124379	+	0.000966741i
$643$	−154.130	+	973.141i	−0.239705	+	1.51344i	0.514894	+	0.857254i	$0.327831\pi$
$643$	−154.130	+	973.141i	−0.239705	+	1.51344i	−0.754600	+	0.656186i	$0.772169\pi$
$644$	−121.509	+	776.932i	−0.188679	+	1.20642i
$645$	−409.642	+	201.574i	−0.635104	+	0.312517i
$646$	32.8603	+	412.414i	0.0508674	+	0.638412i
$647$	−140.616	−	887.815i	−0.217336	−	1.37220i	−0.819156	−	0.573571i	$-0.805558\pi$
$647$	−140.616	−	887.815i	−0.217336	−	1.37220i	0.601820	−	0.798632i	$-0.294442\pi$
$648$	−155.896	−	373.289i	−0.240580	−	0.576064i
$649$	879.967	−	54.7544i	1.35588	−	0.0843673i
$650$	962.390	−	778.125i	1.48060	−	1.19711i
$651$	367.413	+	266.941i	0.564382	+	0.410048i
$652$	239.265	−	741.272i	0.366970	−	1.13692i
$653$	23.9328	−	46.9707i	0.0366505	−	0.0719306i	−0.871955	−	0.489586i	$-0.837148\pi$
$653$	23.9328	−	46.9707i	0.0366505	−	0.0719306i	0.908606	+	0.417655i	$0.137148\pi$
$654$	−888.285	+	1452.71i	−1.35823	+	2.22127i
$655$	−559.972	−	575.821i	−0.854919	−	0.879116i
$656$	−51.8353	−	157.451i	−0.0790173	−	0.240017i
$657$	826.491	−	421.118i	1.25798	−	0.640971i
$658$	124.727	+	203.094i	0.189555	+	0.308653i
$659$			741.252i			1.12481i	0.826861	+	0.562407i	$0.190125\pi$
$659$			741.252i			1.12481i	−0.826861	+	0.562407i	$0.809875\pi$
$660$	866.257	−	497.562i	1.31251	−	0.753882i
$661$	−747.326			−1.13060			−0.565299	−	0.824886i	$-0.691239\pi$
$661$	−747.326			−1.13060			−0.565299	+	0.824886i	$0.691239\pi$
$662$	−663.614	+	407.549i	−1.00244	+	0.615633i
$663$	−930.766	−	1826.73i	−1.40387	−	2.75525i
$664$	−838.796	−	63.5588i	−1.26325	−	0.0957211i
$665$	−5.28137	+	378.489i	−0.00794191	+	0.569156i
$666$	303.130	+	185.354i	0.455150	+	0.278309i
$667$	839.205	+	427.596i	1.25818	+	0.641074i
$668$	279.212	−	865.035i	0.417982	−	1.29496i
$669$	−522.592	+	719.286i	−0.781154	+	1.07517i
$670$	−185.966	+	110.665i	−0.277561	+	0.165172i
$671$	389.573	−	153.933i	0.580586	−	0.229408i
$672$	−897.966	−	366.857i	−1.33626	−	0.545918i
$673$	1062.58	−	168.295i	1.57886	−	0.250068i	0.695420	−	0.718604i	$-0.255218\pi$
$673$	1062.58	−	168.295i	1.57886	−	0.250068i	0.883444	+	0.468536i	$0.155218\pi$
$674$	843.353	−	67.1967i	1.25127	−	0.0996983i
$675$	−54.6896	+	292.262i	−0.0810216	+	0.432981i
$676$	−274.219	+	1753.36i	−0.405650	+	2.59373i
$677$	−390.975	−	61.9243i	−0.577511	−	0.0914688i	−0.139156	−	0.990271i	$-0.544439\pi$
$677$	−390.975	−	61.9243i	−0.577511	−	0.0914688i	−0.438355	+	0.898802i	$0.644439\pi$
$678$	30.2061	−	388.625i	0.0445517	−	0.573193i
$679$	922.291	+	299.670i	1.35831	+	0.441341i
$680$	−467.704	−	560.016i	−0.687799	−	0.823553i
$681$		−	514.873i		−	0.756054i
$682$	106.676	−	311.863i	0.156417	−	0.457277i
$683$	−544.013	+	544.013i	−0.796506	+	0.796506i	−0.982543	−	0.186037i	$-0.940436\pi$
$683$	−544.013	+	544.013i	−0.796506	+	0.796506i	0.186037	+	0.982543i	$0.440436\pi$
$684$	83.4622	+	520.422i	0.122021	+	0.760851i
$685$	320.616	−	226.174i	0.468052	−	0.330181i
$686$	542.053	−	463.867i	0.790164	−	0.676191i
$687$	528.587	+	83.7200i	0.769414	+	0.121863i
$688$	49.0974	−	317.970i	0.0713625	−	0.462166i
$689$	540.314	+	1662.92i	0.784200	+	2.41352i
$690$	−713.458	+	1131.03i	−1.03400	+	1.63918i
$691$	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	$0.139773\pi$
$692$	−311.430	+	0.604274i	−0.450043	+	0.000873228i
$693$	−185.551	−	832.800i	−0.267750	−	1.20173i
$694$	113.247	−	47.0370i	0.163179	−	0.0677767i
$695$	232.282	+	122.466i	0.334219	+	0.176209i
$696$	−751.960	+	885.639i	−1.08040	+	1.27247i
$697$	−168.382	−	85.7950i	−0.241581	−	0.123092i
$698$	−77.6582	+	18.7238i	−0.111258	+	0.0268249i
$699$	791.658	+	1089.62i	1.13256	+	1.55883i
$700$	−378.230	−	550.075i	−0.540328	−	0.785821i
$701$	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	$0.444308\pi$
$702$	−308.121	−	501.715i	−0.438919	−	0.714693i
$703$	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
$707$	−739.243	+	376.663i	−1.04561	+	0.532763i
$708$	−452.560	−	1383.70i	−0.639209	−	1.95437i
$709$	−305.162	−	420.020i	−0.430412	−	0.592411i	0.537636	−	0.843177i	$-0.319318\pi$
$709$	−305.162	−	420.020i	−0.430412	−	0.592411i	−0.968048	+	0.250766i	$0.919318\pi$
$710$	−193.938	+	77.3974i	−0.273152	+	0.109010i
$711$	−355.823	−	1095.11i	−0.500454	−	1.54024i
$712$	−44.9654	−	550.839i	−0.0631537	−	0.773650i
$713$	69.0207	+	435.780i	0.0968033	+	0.611192i
$714$	−1021.28	+	424.188i	−1.43036	+	0.594100i
$715$	−1061.55	+	852.318i	−1.48468	+	1.19205i
$716$	473.864	+	472.029i	0.661822	+	0.659259i
$717$	−121.817	−	769.120i	−0.169898	−	1.07269i
$718$	782.752	+	667.221i	1.09018	+	0.929277i
$719$	363.969	+	1120.18i	0.506216	+	1.55797i	0.798717	+	0.601706i	$0.205512\pi$
$719$	363.969	+	1120.18i	0.506216	+	1.55797i	−0.292502	+	0.956265i	$0.594488\pi$
$720$	−650.628	−	663.869i	−0.903650	−	0.922040i
$721$	27.8498	+	38.3320i	0.0386267	+	0.0531651i
$722$	36.0170	−	463.387i	0.0498851	−	0.641810i
$723$	−534.408	+	272.295i	−0.739154	+	0.376618i
$724$	−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	$-0.454698\pi$
$727$	−616.533	−	616.533i	−0.848051	−	0.848051i	−0.989890	+	0.141839i	$0.954698\pi$
$728$	1286.26	+	304.847i	1.76684	+	0.418745i
$729$	−1021.06	−	331.761i	−1.40062	−	0.455091i
$730$	−526.309	+	600.270i	−0.720971	+	0.822288i
$731$	−215.599	−	296.746i	−0.294937	−	0.405946i
$732$	−407.635	−	558.778i	−0.556878	−	0.763358i
$733$	−690.302	−	351.727i	−0.941749	−	0.479845i	−0.0854600	−	0.996342i	$-0.527236\pi$
$733$	−690.302	−	351.727i	−0.941749	−	0.479845i	−0.856289	+	0.516496i	$0.827236\pi$
$734$	−1377.49	+	109.755i	−1.87668	+	0.149530i
$735$	96.2120	−	29.7836i	0.130901	−	0.0405219i
$736$	−364.854	−	868.891i	−0.495726	−	1.18056i
$737$	204.977	−	121.032i	0.278123	−	0.164223i
$738$	−222.519	−	91.9175i	−0.301516	−	0.124550i
$739$	401.252	−	552.275i	0.542966	−	0.747328i	−0.446071	−	0.894997i	$-0.647177\pi$
$739$	401.252	−	552.275i	0.542966	−	0.747328i	0.989037	+	0.147669i	$0.0471772\pi$
$740$	−301.432	−	51.4612i	−0.407341	−	0.0695422i
$741$	−393.881	−	1212.24i	−0.531553	−	1.63595i
$742$	916.860	−	221.059i	1.23566	−	0.297924i
$743$	−1002.39	−	158.762i	−1.34911	−	0.213677i	−0.560285	−	0.828300i	$-0.689308\pi$
$743$	−1002.39	−	158.762i	−1.34911	−	0.213677i	−0.788822	+	0.614622i	$0.789308\pi$
$744$	−542.689	−	41.1217i	−0.729421	−	0.0552711i
$745$	−90.1905	−	15.5777i	−0.121061	−	0.0209097i
$746$	−540.089	−	129.110i	−0.723980	−	0.173070i
$747$	−863.916	+	863.916i	−1.15651	+	1.15651i
$748$	512.368	+	617.771i	0.684984	+	0.825897i
$749$			5.88728i			0.00786019i
$750$	−219.666	−	1113.75i	−0.292888	−	1.48501i
$751$	−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	$0.710562\pi$
$752$	−254.990	−	128.680i	−0.339082	−	0.171117i
$753$	118.510	+	18.7701i	0.157384	+	0.0249271i
$754$	825.940	−	1350.75i	1.09541	−	1.79145i
$755$	916.305	−	450.889i	1.21365	−	0.597204i
$756$	−282.689	+	144.729i	−0.373927	+	0.191440i
$757$	1107.43	−	175.399i	1.46292	−	0.231703i	0.626339	−	0.779551i	$-0.284552\pi$
$757$	1107.43	−	175.399i	1.46292	−	0.231703i	0.836578	+	0.547847i	$0.184552\pi$
$758$	1190.12	+	491.610i	1.57008	+	0.648563i
$759$	789.047	−	1241.45i	1.03959	−	1.63564i
$760$	−232.731	−	389.369i	−0.306225	−	0.512328i
$761$	−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	$0.224781\pi$
$762$	58.1099	+	49.5331i	0.0762597	+	0.0650041i
$763$	−1115.22	−	568.235i	−1.46163	−	0.744738i
$764$	80.1707	−	512.614i	0.104936	−	0.670960i
$765$	−1059.62	−	14.7857i	−1.38512	−	0.0193277i
$766$	506.068	+	591.366i	0.660663	+	0.772019i
$767$	900.684	+	1767.69i	1.17430	+	2.30468i
$768$	1146.70	−	190.753i	1.49309	−	0.248377i
$769$	904.162			1.17576			0.587882	−	0.808947i	$-0.299962\pi$
$769$	904.162			1.17576			0.587882	+	0.808947i	$0.299962\pi$
$770$	413.984	+	606.499i	0.537642	+	0.787661i
$771$			1773.74i			2.30057i
$772$	−223.098	−	161.430i	−0.288987	−	0.209106i
$773$	−820.976	+	418.308i	−1.06206	+	0.541149i	−0.895582	−	0.444895i	$-0.853241\pi$
$773$	−820.976	+	418.308i	−1.06206	+	0.541149i	−0.166482	+	0.986044i	$0.553241\pi$
$774$	−303.827	−	355.038i	−0.392542	−	0.458705i
$775$	−296.756	−	228.523i	−0.382911	−	0.294869i
$776$	−1129.24	+	274.585i	−1.45520	+	0.353846i
$777$	−210.413	+	412.959i	−0.270802	+	0.531479i
$778$	734.081	+	625.734i	0.943549	+	0.804285i
$779$	−95.0521	−	69.0594i	−0.122018	−	0.0886513i
$780$	1802.60	+	1343.04i	2.31102	+	1.72184i
$781$	213.621	−	84.4083i	0.273522	−	0.108077i
$782$	−992.986	−	410.180i	−1.26980	−	0.524527i
$783$	59.5042	+	375.695i	0.0759951	+	0.479814i
$784$	−21.6708	+	67.5872i	−0.0276414	+	0.0862082i
$785$	−30.9981	+	91.0593i	−0.0394881	+	0.115999i
$786$	761.061	−	1244.65i	0.968270	−	1.58352i
$787$	46.8059	−	295.521i	0.0594738	−	0.375503i	−0.939942	−	0.341333i	$-0.889121\pi$
$787$	46.8059	−	295.521i	0.0594738	−	0.375503i	0.999416	−	0.0341693i	$-0.0108785\pi$
$788$	−361.449	+	118.218i	−0.458692	+	0.150023i
$789$	−468.850	+	1442.97i	−0.594234	+	1.82886i
$790$	633.767	+	761.856i	0.802237	+	0.964375i
$791$	286.526			0.362233
$792$	713.194	+	732.695i	0.900497	+	0.925119i
$793$	666.496	+	666.496i	0.840474	+	0.840474i
$794$	−684.796	−	163.702i	−0.862463	−	0.206174i
$795$	1580.42	+	272.971i	1.98795	+	0.343359i
$796$	−103.071	+	203.262i	−0.129486	+	0.255354i
$797$	84.9513	−	536.361i	0.106589	−	0.672976i	−0.875309	−	0.483564i	$-0.839342\pi$
$797$	84.9513	−	536.361i	0.106589	−	0.672976i	0.981898	−	0.189411i	$-0.0606580\pi$
$798$	−668.377	+	161.149i	−0.837565	+	0.201941i
$799$	−309.684	+	100.622i	−0.387589	+	0.125935i
$800$	731.850	+	323.104i	0.914812	+	0.403880i
$801$	−649.398	−	471.815i	−0.810734	−	0.589033i
$802$	674.498	+	278.620i	0.841019	+	0.347406i
$803$	581.191	−	658.317i	0.723774	−	0.819822i
$804$	−278.474	−	277.395i	−0.346360	−	0.345019i
$805$	−869.522	−	458.436i	−1.08015	−	0.569486i
$806$	739.328	−	58.9082i	0.917281	−	0.0730871i
$807$	309.890	−	608.193i	0.384002	−	0.753647i
$808$	517.035	−	849.263i	0.639895	−	1.05107i
$809$	400.547	−	291.015i	0.495114	−	0.359721i	−0.312034	−	0.950071i	$-0.601010\pi$
$809$	400.547	−	291.015i	0.495114	−	0.359721i	0.807148	+	0.590350i	$0.201010\pi$
$810$	504.582	−	33.1264i	0.622941	−	0.0408968i
$811$	−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	$0.993508\pi$
$812$	−691.877	−	500.630i	−0.852066	−	0.616540i
$813$	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
$817$	−103.529	−	203.188i	−0.126719	−	0.248700i
$818$	60.6537	−	780.357i	0.0741488	−	0.953981i
$819$	1553.24	−	1128.50i	1.89651	−	1.37790i
$820$	207.190	+	2.48902i	0.252671	+	0.00303539i
$821$	−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	$0.531899\pi$
$822$	542.362	+	462.312i	0.659808	+	0.562423i
$823$	1160.18	−	183.754i	1.40969	−	0.223274i	0.595262	−	0.803532i	$-0.297048\pi$
$823$	1160.18	−	183.754i	1.40969	−	0.223274i	0.814433	+	0.580258i	$0.197048\pi$
$824$	−52.5217	−	21.5763i	−0.0637400	−	0.0261849i
$825$	237.448	+	1225.95i	0.287816	+	1.48600i
$826$	988.269	−	410.478i	1.19645	−	0.496947i
$827$	−1394.29	+	220.834i	−1.68596	+	0.267030i	−0.924501	−	0.381179i	$-0.875518\pi$
$827$	−1394.29	+	220.834i	−1.68596	+	0.267030i	−0.761462	+	0.648209i	$0.775518\pi$
$828$	−1302.55	−	420.432i	−1.57313	−	0.507768i
$829$	−346.209	+	112.490i	−0.417622	+	0.135694i	−0.510288	−	0.860004i	$-0.670461\pi$
$829$	−346.209	+	112.490i	−0.417622	+	0.135694i	0.0926657	+	0.995697i	$0.470461\pi$
$830$	414.970	−	966.154i	0.499964	−	1.16404i
$831$	190.136	−	138.142i	0.228803	−	0.166235i
$832$	−1503.73	+	498.287i	−1.80737	+	0.598903i
$833$	36.7355	+	72.0975i	0.0441002	+	0.0865516i
$834$	−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
$838$	327.219	+	532.813i	0.390477	+	0.635815i
$839$	206.240	−	634.743i	0.245817	−	0.756547i	−0.749684	−	0.661796i	$-0.769795\pi$
$839$	206.240	−	634.743i	0.245817	−	0.756547i	0.995501	−	0.0947510i	$-0.0302055\pi$
$840$	797.600	−	913.254i	0.949524	−	1.08721i
$841$	−147.130	+	106.896i	−0.174946	+	0.127106i
$842$	203.249	−	49.0044i	0.241389	−	0.0582000i
$843$	−86.3685	+	169.508i	−0.102454	+	0.201077i
$844$	−991.026	+	507.377i	−1.17420	+	0.601158i
$845$	−1962.32	−	1034.59i	−2.32227	−	1.22436i
$846$	−383.102	+	159.122i	−0.452839	+	0.188087i
$847$	−453.103	−	668.700i	−0.534950	−	0.789492i
$848$	−796.093	+	802.296i	−0.938789	+	0.946104i
$849$	−47.9811	−	34.8603i	−0.0565149	−	0.0410605i
$850$	851.711	−	326.203i	1.00201	−	0.383768i
$851$	−428.236	+	139.142i	−0.503215	+	0.163504i
$852$	−223.525	−	306.404i	−0.262353	−	0.359629i
$853$	−227.521	+	1436.51i	−0.266731	+	1.68407i	0.382875	+	0.923800i	$0.374934\pi$
$853$	−227.521	+	1436.51i	−0.266731	+	1.68407i	−0.649605	+	0.760272i	$0.725066\pi$
$854$	386.284	−	330.566i	0.452323	−	0.387080i
$855$	−649.227	−	112.135i	−0.759330	−	0.131152i
$856$	−3.70386	−	6.00484i	−0.00432693	−	0.00701500i
$857$	−340.391	−	340.391i	−0.397189	−	0.397189i	0.480051	−	0.877240i	$-0.340618\pi$
$857$	−340.391	−	340.391i	−0.397189	−	0.397189i	−0.877240	+	0.480051i	$0.840618\pi$
$858$	−1977.80	−	1484.10i	−2.30513	−	1.72972i
$859$	1427.20			1.66147			0.830734	−	0.556670i	$-0.187921\pi$
$859$	1427.20			1.66147			0.830734	+	0.556670i	$0.187921\pi$
$860$	356.120	+	186.874i	0.414093	+	0.217295i
$861$	97.0468	−	298.679i	0.112714	−	0.346898i
$862$	9.07062	−	116.700i	0.0105228	−	0.135383i
$863$	−244.584	+	1544.24i	−0.283411	+	1.78939i	0.276683	+	0.960961i	$0.410765\pi$
$863$	−244.584	+	1544.24i	−0.283411	+	1.78939i	−0.560095	+	0.828428i	$0.689235\pi$
$864$	197.281	−	325.466i	0.228334	−	0.376697i
$865$	125.451	−	368.521i	0.145030	−	0.426036i
$866$	−530.083	+	42.2359i	−0.612105	+	0.0487712i
$867$	−31.0619	−	196.117i	−0.0358269	−	0.226202i
$868$	−0.776234	−	400.055i	−0.000894279	−	0.460893i
$869$	−694.279	−	840.417i	−0.798940	−	0.967108i
$870$	−742.665	−	1248.00i	−0.853638	−	1.43449i
$871$	433.344	+	314.843i	0.497525	+	0.361473i
$872$	1494.99	−	122.037i	1.71443	−	0.139951i
$873$	−766.289	+	1503.93i	−0.877766	+	1.72271i
$874$	−569.857	−	348.449i	−0.652010	−	0.398683i
$875$	803.707	−	224.424i	0.918523	−	0.256485i
$876$	−1293.26	−	655.791i	−1.47632	−	0.748620i
$877$	−798.842	+	407.030i	−0.910880	+	0.464117i	−0.845640	−	0.533753i	$-0.820781\pi$
$877$	−798.842	+	407.030i	−0.910880	+	0.464117i	−0.0652396	+	0.997870i	$0.520781\pi$
$878$	−226.365	+	139.019i	−0.257819	+	0.158336i
$879$			315.951i			0.359444i
$880$	−803.817	−	358.161i	−0.913428	−	0.407001i
$881$	−1402.92			−1.59241			−0.796206	−	0.605025i	$-0.793163\pi$
$881$	−1402.92			−1.59241			−0.796206	+	0.605025i	$0.793163\pi$
$882$	53.9477	+	87.8432i	0.0611652	+	0.0995955i
$883$	−110.999	−	217.848i	−0.125707	−	0.246713i	0.819573	−	0.572975i	$-0.194211\pi$
$883$	−110.999	−	217.848i	−0.125707	−	0.246713i	−0.945279	+	0.326262i	$0.894211\pi$
$884$	−816.783	+	1610.75i	−0.923963	+	1.82211i
$885$	1819.60	+	25.3904i	2.05605	+	0.0286898i
$886$	−4.72768	+	7.73170i	−0.00533598	+	0.00872652i
$887$	−996.336	−	507.659i	−1.12326	−	0.572332i	−0.209189	−	0.977875i	$-0.567082\pi$
$887$	−996.336	−	507.659i	−1.12326	−	0.572332i	−0.914076	+	0.405543i	$0.867082\pi$
$888$	−45.1894	−	553.582i	−0.0508889	−	0.623403i
$889$	−32.9906	+	45.4076i	−0.0371097	+	0.0510772i
$890$	669.600	+	169.980i	0.752360	+	0.190989i
$891$	−555.162	+	34.5439i	−0.623077	+	0.0387699i
$892$	783.190	−	1.51964i	0.878016	−	0.00170363i
$893$	−199.950	+	31.6689i	−0.223908	+	0.0354635i
$894$	−13.2040	−	165.717i	−0.0147695	−	0.185365i
$895$	−750.159	+	369.133i	−0.838167	+	0.412439i
$896$	205.112	+	829.497i	0.228920	+	0.925778i
$897$	3269.25	+	517.798i	3.64464	+	0.577255i
$898$	−448.157	−	34.8333i	−0.499061	−	0.0387898i
$899$	−455.705	−	148.067i	−0.506902	−	0.164702i
$900$	1048.63	−	500.445i	1.16514	−	0.556050i
$901$			1288.53i			1.43011i
$902$	−227.899	−	3.51597i	−0.252659	−	0.00389797i
$903$	431.018	−	431.018i	0.477318	−	0.477318i
$904$	−292.248	+	180.262i	−0.323283	+	0.199404i
$905$	1488.09	+	257.022i	1.64429	+	0.284002i
$906$	1206.03	+	1409.31i	1.33116	+	1.55553i
$907$	−877.167	−	138.930i	−0.967109	−	0.153175i	−0.347150	−	0.937810i	$-0.612851\pi$
$907$	−877.167	−	138.930i	−0.967109	−	0.153175i	−0.619958	+	0.784635i	$0.712851\pi$
$908$	−366.411	+	267.301i	−0.403536	+	0.294384i
$909$	−446.245	−	1373.40i	−0.490919	−	1.51089i
$910$	−881.574	+	1397.54i	−0.968763	+	1.53576i
$911$	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	$-0.118133\pi$
$912$	580.340	−	584.862i	0.636338	−	0.641296i
$913$	−460.093	+	1061.21i	−0.503935	+	1.16233i
$914$	−288.195	−	693.859i	−0.315312	−	0.759146i
$915$	825.912	−	255.671i	0.902636	−	0.279422i
$916$	−214.841	−	419.635i	−0.234543	−	0.458116i
$917$	955.497	+	486.850i	1.04198	+	0.530916i
$918$	−101.699	−	421.805i	−0.110783	−	0.459482i
$919$	282.703	+	389.108i	0.307621	+	0.423403i	0.934637	−	0.355602i	$-0.115724\pi$
$919$	282.703	+	389.108i	0.307621	+	0.423403i	−0.627017	+	0.779006i	$0.715724\pi$
$920$	1175.30	−	79.4503i	1.27750	−	0.0863590i
$921$	83.9950	+	27.2916i	0.0911998	+	0.0296326i
$922$	−1510.19	+	927.464i	−1.63795	+	1.00593i
$923$	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
$927$	−73.4801	+	37.4400i	−0.0792666	+	0.0403883i
$928$	1020.65	+	75.3474i	1.09984	+	0.0811933i
$929$	−287.224	−	395.330i	−0.309175	−	0.425543i	0.625949	−	0.779864i	$-0.284712\pi$
$929$	−287.224	−	395.330i	−0.309175	−	0.425543i	−0.935124	+	0.354321i	$0.884712\pi$
$930$	268.480	−	625.088i	0.288688	−	0.672138i
$931$	15.5457	+	47.8447i	0.0166978	+	0.0513907i
$932$	364.438	−	1129.07i	0.391027	−	1.21145i
$933$	−234.089	−	1477.98i	−0.250899	−	1.58412i
$934$	168.481	+	405.635i	0.180386	+	0.434299i
$935$	−938.102	+	355.623i	−1.00332	+	0.380345i
$936$	−874.289	+	2128.22i	−0.934070	+	2.27374i
$937$	234.166	+	1478.46i	0.249910	+	1.57787i	0.719186	+	0.694818i	$0.244515\pi$
$937$	234.166	+	1478.46i	0.249910	+	1.57787i	−0.469276	+	0.883051i	$0.655485\pi$
$938$	187.428	−	219.882i	0.199817	−	0.234415i
$939$	−62.4822	−	192.300i	−0.0665412	−	0.204793i
$940$	255.468	−	249.403i	0.271775	−	0.265322i
$941$	−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	$0.943378\pi$
$942$	−174.190	−	13.5390i	−0.184915	−	0.0143726i
$943$	271.851	−	138.515i	0.288283	−	0.146887i
$944$	−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	0.853787	+	0.520622i	$0.174300\pi$
$947$	1301.57	+	1301.57i	1.37441	+	1.37441i	0.520622	+	0.853787i	$0.325700\pi$
$948$	−1055.18	+	1458.27i	−1.11306	+	1.53826i
$949$	1879.32	+	610.627i	1.98031	+	0.643443i
$950$	554.725	−	117.472i	0.583921	−	0.123655i
$951$	31.1281	+	42.8442i	0.0327320	+	0.0450517i
$952$	832.079	+	506.573i	0.874032	+	0.532115i
$953$	−417.794	−	212.877i	−0.438398	−	0.223375i	0.220839	−	0.975310i	$-0.429121\pi$
$953$	−417.794	−	212.877i	−0.438398	−	0.223375i	−0.659237	+	0.751935i	$0.729121\pi$
$954$	130.383	+	1636.38i	0.136670	+	1.71528i
$955$	573.703	+	302.472i	0.600737	+	0.316725i
$956$	−484.104	+	485.986i	−0.506385	+	0.508354i
$957$	812.240	+	1375.58i	0.848735	+	1.43739i
$958$	539.013	−	1304.87i	0.562644	−	1.36208i
$959$	−307.914	+	423.807i	−0.321078	+	0.441926i
$960$	−238.973	+	1433.28i	−0.248930	+	1.49300i
$961$	227.604	+	700.492i	0.236840	+	0.728920i
$962$	177.410	+	735.819i	0.184418	+	0.764885i
$963$	−10.1209	−	1.60299i	−0.0105098	−	0.00166458i
$964$	471.222	+	238.949i	0.488820	+	0.247872i
$965$	281.276	−	198.423i	0.291478	−	0.205619i
$966$	415.110	−	1736.48i	0.429720	−	1.79760i
$967$	1024.95	−	1024.95i	1.05993	−	1.05993i	0.0618415	−	0.998086i	$-0.480303\pi$
$967$	1024.95	−	1024.95i	1.05993	−	1.05993i	0.998086	−	0.0618415i	$-0.0196973\pi$
$968$	882.848	+	396.993i	0.912033	+	0.410117i
$969$		−	939.321i		−	0.969372i
$970$	132.767	−	1446.60i	0.136874	−	1.49134i
$971$	−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	$0.683382\pi$
$972$	418.615	+	1279.91i	0.430673	+	1.31678i
$973$	−346.272	−	54.8441i	−0.355881	−	0.0563660i
$974$	−591.659	−	361.780i	−0.607453	−	0.371437i
$975$	−2318.45	+	1587.54i	−2.37789	+	1.62825i
$976$	−186.029	+	580.189i	−0.190603	+	0.594456i
$977$	−1086.80	+	172.132i	−1.11238	+	0.176184i	−0.685463	−	0.728107i	$-0.740400\pi$
$977$	−1086.80	+	172.132i	−1.11238	+	0.176184i	−0.426917	+	0.904291i	$0.640400\pi$
$978$	−675.189	+	1634.53i	−0.690377	+	1.67130i
$979$	−735.918	−	189.492i	−0.751703	−	0.193557i
$980$	−71.1449	−	53.0071i	−0.0725968	−	0.0540889i
$981$	1280.52	−	1762.48i	1.30532	−	1.79661i
$982$	526.652	−	617.843i	0.536305	−	0.629168i
$983$	−1057.58	−	538.862i	−1.07587	−	0.548181i	−0.176019	−	0.984387i	$-0.556322\pi$
$983$	−1057.58	−	538.862i	−1.07587	−	0.548181i	−0.899847	+	0.436206i	$0.856322\pi$
$984$	88.9229	+	365.698i	0.0903688	+	0.371644i
$985$	6.63249	−	475.317i	0.00673350	−	0.482555i
$986$	886.479	−	758.613i	0.899066	−	0.769385i
$987$	−245.664	−	482.143i	−0.248900	−	0.488493i
$988$	−658.208	+	909.651i	−0.666202	+	0.920700i
$989$	592.190			0.598777
$990$	−1155.36	+	546.548i	−1.16703	+	0.552069i
$991$		−	388.087i		−	0.391612i	−0.980643	−	0.195806i	$-0.937268\pi$
$991$		−	388.087i		−	0.391612i	0.980643	−	0.195806i	$-0.0627322\pi$
$992$	252.478	+	407.555i	0.254514	+	0.410842i
$993$	1575.42	−	802.714i	1.58652	−	0.808373i
$994$	211.817	−	181.265i	0.213096	−	0.182359i
$995$	−198.608	−	204.229i	−0.199606	−	0.205255i
$996$	1886.94	+	295.110i	1.89452	+	0.296295i
$997$	741.756	−	1455.78i	0.743988	−	1.46016i	−0.138767	−	0.990325i	$-0.544314\pi$
$997$	741.756	−	1455.78i	0.743988	−	1.46016i	0.882755	−	0.469834i	$-0.155686\pi$
$998$	976.761	−	1145.89i	0.978719	−	1.14819i
$999$	−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.183.45	yes	544
4.3	odd	2	inner	220.3.w.a.183.29	yes	544
5.2	odd	4	inner	220.3.w.a.7.13	yes	544
11.8	odd	10	inner	220.3.w.a.63.6	yes	544
20.7	even	4	inner	220.3.w.a.7.6	✓	544
44.19	even	10	inner	220.3.w.a.63.13	yes	544
55.52	even	20	inner	220.3.w.a.107.29	yes	544
220.107	odd	20	inner	220.3.w.a.107.45	yes	544

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.w.a.7.6	✓	544	20.7	even	4	inner
220.3.w.a.7.13	yes	544	5.2	odd	4	inner
220.3.w.a.63.6	yes	544	11.8	odd	10	inner
220.3.w.a.63.13	yes	544	44.19	even	10	inner
220.3.w.a.107.29	yes	544	55.52	even	20	inner
220.3.w.a.107.45	yes	544	220.107	odd	20	inner
220.3.w.a.183.29	yes	544	4.3	odd	2	inner
220.3.w.a.183.45	yes	544	1.1	even	1	trivial

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+(1.04665 + 1.70427i) q^{2} +(-2.06150 - 4.04592i) q^{3} +(-1.80904 + 3.56754i) q^{4} +(-3.48586 - 3.58452i) q^{5} +(4.73765 - 7.74800i) q^{6} +(5.94803 + 3.03067i) q^{7} +(-7.97348 + 0.650882i) q^{8} +(-6.82960 + 9.40014i) q^{9} +(2.46049 - 9.69257i) q^{10} +(-2.74293 + 10.6525i) q^{11} +(18.1633 - 0.0352426i) q^{12} +(-24.4474 + 3.87209i) q^{13} +(1.06044 + 13.3091i) q^{14} +(-7.31657 + 21.4930i) q^{15} +(-9.45473 - 12.9077i) q^{16} +(-18.0163 - 2.85350i) q^{17} +(-23.1685 - 1.80079i) q^{18} +(-10.7855 - 3.50442i) q^{19} +(19.0940 - 5.95141i) q^{20} -30.3129i q^{21} +(-21.0256 + 6.47480i) q^{22} +(20.8240 - 20.8240i) q^{23} +(19.0707 + 30.9182i) q^{24} +(-0.697556 + 24.9903i) q^{25} +(-32.1870 - 37.6122i) q^{26} +(11.7470 + 1.86054i) q^{27} +(-21.5723 + 15.7372i) q^{28} +(9.88305 + 30.4169i) q^{29} +(-44.2876 + 10.0263i) q^{30} +(-8.80617 + 12.1207i) q^{31} +(12.1023 - 29.6232i) q^{32} +(48.7538 - 10.8625i) q^{33} +(-13.9936 - 33.6911i) q^{34} +(-9.87049 - 31.8853i) q^{35} +(-21.1804 - 41.3702i) q^{36} +(-13.6232 - 6.94136i) q^{37} +(-5.31618 - 22.0492i) q^{38} +(66.0644 + 90.9299i) q^{39} +(30.1275 + 26.3122i) q^{40} +(9.85319 + 3.20150i) q^{41} +(51.6613 - 31.7271i) 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} +(15.9055 - 8.10427i) q^{47} +(-32.7325 + 64.8622i) q^{48} +(-2.60743 - 3.58882i) q^{49} +(-43.3202 + 24.9673i) q^{50} +(25.5955 + 78.7748i) q^{51} +(30.4126 - 94.2220i) q^{52} +(-11.0505 - 69.7703i) q^{53} +(9.12414 + 21.9673i) q^{54} +(47.7456 - 27.3012i) q^{55} +(-49.3991 - 20.2935i) q^{56} +(8.05567 + 50.8615i) q^{57} +(-41.4944 + 48.6792i) q^{58} +(-24.7682 - 76.2288i) q^{59} +(-63.4411 - 64.9839i) q^{60} +(-22.3830 - 30.8075i) q^{61} +(-29.8738 - 2.32196i) q^{62} +(-69.1114 + 35.2140i) 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} +(42.7722 - 59.1117i) q^{68} +(-127.181 - 41.3235i) q^{69} +(44.0101 - 50.1947i) q^{70} +(-12.2736 - 16.8932i) q^{71} +(48.3373 - 79.3971i) q^{72} +(-71.1314 - 36.2433i) q^{73} +(-2.42880 - 30.4827i) q^{74} +(102.547 - 48.6951i) q^{75} +(32.0136 - 32.1380i) q^{76} +(-48.5993 + 55.0486i) q^{77} +(-85.8223 + 207.763i) q^{78} +(-58.2496 + 80.1738i) q^{79} +(-13.3100 + 78.8850i) q^{80} +(15.6260 + 48.0919i) q^{81} +(4.85665 + 20.1433i) q^{82} +(103.856 + 16.4491i) q^{83} +(108.143 + 54.8374i) q^{84} +(52.5738 + 74.5265i) q^{85} +(-9.35060 + 39.1152i) q^{86} +(102.690 - 102.690i) q^{87} +(14.9371 - 86.7230i) q^{88} +69.0839i q^{89} +(74.3073 + 89.3254i) q^{90} +(-157.149 - 51.0608i) q^{91} +(36.6190 + 111.962i) q^{92} +(67.1931 + 10.6423i) q^{93} +(30.4594 + 18.6249i) q^{94} +(25.0350 + 50.8767i) q^{95} +(-144.802 + 12.1032i) q^{96} +(143.479 - 22.7249i) q^{97} +(3.38724 - 8.20000i) 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

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