LMFDB - Embedded newform 220.3.w.a.63.6

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			63.6
Character	$\chi$	$=$	220.63
Dual form			220.3.w.a.7.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.94429 + 0.468777i) q^{2} +(4.04592 + 2.06150i) q^{3} +(3.56050 - 1.82287i) q^{4} +(2.33189 - 4.42293i) q^{5} +(-8.83280 - 2.11151i) q^{6} +(3.03067 + 5.94803i) q^{7} +(-6.06810 + 5.21327i) 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} +(3.87209 - 24.4474i) q^{13} +(-8.68079 - 10.1440i) q^{14} +(18.5525 - 13.0876i) q^{15} +(9.35426 - 12.9807i) q^{16} +(2.85350 + 18.0163i) q^{17} +(-17.6853 - 15.0750i) q^{18} +(-10.7855 + 3.50442i) q^{19} +(0.240247 - 19.9986i) q^{20} +30.3129i q^{21} +(-10.3267 - 19.4257i) q^{22} +(20.8240 - 20.8240i) q^{23} +(-35.2982 + 8.58307i) q^{24} +(-14.1246 - 20.6276i) q^{25} +(3.93194 + 49.3479i) q^{26} +(1.86054 + 11.7470i) q^{27} +(21.6332 + 15.6534i) q^{28} +(-9.88305 + 30.4169i) q^{29} +(-29.9362 + 34.1430i) q^{30} +(8.80617 + 12.1207i) q^{31} +(-12.1023 + 29.6232i) q^{32} +(-10.8625 + 48.7538i) q^{33} +(-13.9936 - 33.6911i) q^{34} +(33.3749 + 0.465708i) q^{35} +(41.4520 + 21.0197i) q^{36} +(6.94136 + 13.6232i) q^{37} +(19.3273 - 11.8696i) q^{38} +(66.0644 - 90.9299i) q^{39} +(8.90776 + 38.9955i) q^{40} +(9.85319 - 3.20150i) q^{41} +(-14.2100 - 58.9370i) q^{42} +(-14.2190 - 14.2190i) q^{43} +(29.1844 + 32.9283i) q^{44} +(57.5020 - 8.28674i) q^{45} +(-30.7260 + 50.2496i) q^{46} +(-8.10427 + 15.9055i) q^{47} +(64.6062 - 33.2349i) q^{48} +(2.60743 - 3.58882i) q^{49} +(37.1319 + 33.4846i) q^{50} +(-25.5955 + 78.7748i) q^{51} +(-30.7780 - 94.1033i) 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} +(4.95673 - 63.7721i) q^{58} +(-24.7682 + 76.2288i) q^{59} +(42.1990 - 80.4172i) q^{60} +(-22.3830 + 30.8075i) q^{61} +(-22.8036 - 19.4379i) q^{62} +(-35.2140 + 69.1114i) q^{63} +(9.64368 - 63.2693i) q^{64} +(-99.0999 - 74.1347i) q^{65} +(-1.73484 - 99.8834i) q^{66} +(-15.3020 - 15.3020i) q^{67} +(43.0012 + 58.9453i) q^{68} +(127.181 - 41.3235i) q^{69} +(-65.1086 + 14.7399i) q^{70} +(12.2736 - 16.8932i) q^{71} +(-90.4481 - 21.4365i) q^{72} +(-36.2433 - 71.1314i) q^{73} +(-19.8822 - 23.2334i) q^{74} +(-14.6232 - 112.575i) q^{75} +(-32.0136 + 32.1380i) q^{76} +(-55.0486 + 48.5993i) q^{77} +(-85.8223 + 207.763i) q^{78} +(-58.2496 - 80.1738i) q^{79} +(-35.5995 - 71.6427i) q^{80} +(15.6260 - 48.0919i) q^{81} +(-17.6566 + 10.8436i) q^{82} +(-16.4491 - 103.856i) q^{83} +(55.2567 + 107.929i) q^{84} +(86.3386 + 29.3911i) q^{85} +(34.3112 + 20.9802i) q^{86} +(-102.690 + 102.690i) q^{87} +(-72.1788 - 50.3410i) q^{88} +69.0839i q^{89} +(-107.916 + 43.0674i) q^{90} +(157.149 - 51.0608i) q^{91} +(36.1842 - 112.103i) q^{92} +(10.6423 + 67.1931i) q^{93} +(8.30087 - 34.7240i) q^{94} +(-9.65079 + 55.8753i) q^{95} +(-110.033 + 94.9041i) q^{96} +(22.7249 - 143.479i) 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 $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.94429	+	0.468777i	−0.972143	+	0.234389i
$2$	−1.94429	+	0.468777i	−0.972143	+	0.234389i
$3$	4.04592	+	2.06150i	1.34864	+	0.687166i	0.971065	−	0.238814i	$-0.0767586\pi$
$3$	4.04592	+	2.06150i	1.34864	+	0.687166i	0.377573	+	0.925980i	$0.376759\pi$
$4$	3.56050	−	1.82287i	0.890124	−	0.455718i
$5$	2.33189	−	4.42293i	0.466378	−	0.884586i
$5$	2.33189	−	4.42293i	0.466378	−	0.884586i
$6$	−8.83280	−	2.11151i	−1.47213	−	0.351918i
$7$	3.03067	+	5.94803i	0.432953	+	0.849718i	0.999667	+	0.0258034i	$0.00821440\pi$
$7$	3.03067	+	5.94803i	0.432953	+	0.849718i	−0.566714	+	0.823914i	$0.691786\pi$
$8$	−6.06810	+	5.21327i	−0.758513	+	0.651658i
$9$	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
$13$	3.87209	−	24.4474i	0.297853	−	1.88057i	−0.153384	−	0.988167i	$-0.549017\pi$
$13$	3.87209	−	24.4474i	0.297853	−	1.88057i	0.451237	−	0.892404i	$-0.350983\pi$
$14$	−8.68079	−	10.1440i	−0.620056	−	0.724568i
$15$	18.5525	−	13.0876i	1.23683	−	0.872507i
$16$	9.35426	−	12.9807i	0.584641	−	0.811292i
$17$	2.85350	+	18.0163i	0.167853	+	1.05978i	0.917440	+	0.397874i	$0.130252\pi$
$17$	2.85350	+	18.0163i	0.167853	+	1.05978i	−0.749587	+	0.661906i	$0.769748\pi$
$18$	−17.6853	−	15.0750i	−0.982515	−	0.837500i
$19$	−10.7855	+	3.50442i	−0.567657	+	0.184443i	−0.578764	−	0.815495i	$-0.696465\pi$
$19$	−10.7855	+	3.50442i	−0.567657	+	0.184443i	0.0111065	+	0.999938i	$0.496465\pi$
$20$	0.240247	−	19.9986i	0.0120123	−	0.999928i
$21$			30.3129i			1.44347i
$22$	−10.3267	−	19.4257i	−0.469395	−	0.882988i
$23$	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	$0.0288483\pi$
$24$	−35.2982	+	8.58307i	−1.47076	+	0.357628i
$25$	−14.1246	−	20.6276i	−0.564983	−	0.825103i
$26$	3.93194	+	49.3479i	0.151228	+	1.89800i
$27$	1.86054	+	11.7470i	0.0689089	+	0.435073i
$28$	21.6332	+	15.6534i	0.772614	+	0.559050i
$29$	−9.88305	+	30.4169i	−0.340795	+	1.04886i	0.623002	+	0.782220i	$0.285913\pi$
$29$	−9.88305	+	30.4169i	−0.340795	+	1.04886i	−0.963797	+	0.266638i	$0.914087\pi$
$30$	−29.9362	+	34.1430i	−0.997872	+	1.13810i
$31$	8.80617	+	12.1207i	0.284070	+	0.390989i	0.927077	−	0.374872i	$-0.122313\pi$
$31$	8.80617	+	12.1207i	0.284070	+	0.390989i	−0.643007	+	0.765861i	$0.722313\pi$
$32$	−12.1023	+	29.6232i	−0.378197	+	0.925725i
$33$	−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
$36$	41.4520	+	21.0197i	1.15145	+	0.583879i
$37$	6.94136	+	13.6232i	0.187604	+	0.368194i	0.965582	−	0.260097i	$-0.0837545\pi$
$37$	6.94136	+	13.6232i	0.187604	+	0.368194i	−0.777978	+	0.628291i	$0.783755\pi$
$38$	19.3273	−	11.8696i	0.508613	−	0.312357i
$39$	66.0644	−	90.9299i	1.69396	−	2.33154i
$40$	8.90776	+	38.9955i	0.222694	+	0.974888i
$41$	9.85319	−	3.20150i	0.240322	−	0.0780853i	−0.186380	−	0.982478i	$-0.559675\pi$
$41$	9.85319	−	3.20150i	0.240322	−	0.0780853i	0.426702	+	0.904392i	$0.359675\pi$
$42$	−14.2100	−	58.9370i	−0.338334	−	1.40326i
$43$	−14.2190	−	14.2190i	−0.330673	−	0.330673i	0.522169	−	0.852842i	$-0.325123\pi$
$43$	−14.2190	−	14.2190i	−0.330673	−	0.330673i	−0.852842	+	0.522169i	$0.825123\pi$
$44$	29.1844	+	32.9283i	0.663282	+	0.748370i
$45$	57.5020	−	8.28674i	1.27782	−	0.184150i
$46$	−30.7260	+	50.2496i	−0.667956	+	1.09238i
$47$	−8.10427	+	15.9055i	−0.172431	+	0.338415i	−0.961008	−	0.276521i	$-0.910818\pi$
$47$	−8.10427	+	15.9055i	−0.172431	+	0.338415i	0.788577	+	0.614937i	$0.210818\pi$
$48$	64.6062	−	33.2349i	1.34596	−	0.692394i
$49$	2.60743	−	3.58882i	0.0532129	−	0.0732413i
$50$	37.1319	+	33.4846i	0.742639	+	0.669692i
$51$	−25.5955	+	78.7748i	−0.501872	+	1.54460i
$52$	−30.7780	−	94.1033i	−0.591885	−	1.80968i
$53$	−69.7703	−	11.0505i	−1.31642	−	0.208501i	−0.541576	−	0.840652i	$-0.682172\pi$
$53$	−69.7703	−	11.0505i	−1.31642	−	0.208501i	−0.774845	+	0.632151i	$0.782172\pi$
$54$	−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
$58$	4.95673	−	63.7721i	0.0854608	−	1.09952i
$59$	−24.7682	+	76.2288i	−0.419801	+	1.29201i	0.488085	+	0.872796i	$0.337696\pi$
$59$	−24.7682	+	76.2288i	−0.419801	+	1.29201i	−0.907886	+	0.419218i	$0.862304\pi$
$60$	42.1990	−	80.4172i	0.703316	−	1.34029i
$61$	−22.3830	+	30.8075i	−0.366934	+	0.505042i	−0.952064	−	0.305898i	$-0.901043\pi$
$61$	−22.3830	+	30.8075i	−0.366934	+	0.505042i	0.585130	+	0.810939i	$0.301043\pi$
$62$	−22.8036	−	19.4379i	−0.367800	−	0.313514i
$63$	−35.2140	+	69.1114i	−0.558952	+	1.09701i
$64$	9.64368	−	63.2693i	0.150683	−	0.988582i
$65$	−99.0999	−	74.1347i	−1.52461	−	1.14053i
$66$	−1.73484	−	99.8834i	−0.0262854	−	1.51338i
$67$	−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	$0.801631\pi$
$68$	43.0012	+	58.9453i	0.632371	+	0.866842i
$69$	127.181	−	41.3235i	1.84320	−	0.598891i
$70$	−65.1086	+	14.7399i	−0.930123	+	0.210570i
$71$	12.2736	−	16.8932i	0.172868	−	0.237932i	−0.713788	−	0.700362i	$-0.753022\pi$
$71$	12.2736	−	16.8932i	0.172868	−	0.237932i	0.886656	+	0.462429i	$0.153022\pi$
$72$	−90.4481	−	21.4365i	−1.25622	−	0.297728i
$73$	−36.2433	−	71.1314i	−0.496483	−	0.974403i	−0.994249	−	0.107092i	$-0.965846\pi$
$73$	−36.2433	−	71.1314i	−0.496483	−	0.974403i	0.497766	−	0.867311i	$-0.334154\pi$
$74$	−19.8822	−	23.2334i	−0.268679	−	0.313965i
$75$	−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
$78$	−85.8223	+	207.763i	−1.10029	+	2.66363i
$79$	−58.2496	−	80.1738i	−0.737337	−	1.01486i	−0.998767	−	0.0496354i	$-0.984194\pi$
$79$	−58.2496	−	80.1738i	−0.737337	−	1.01486i	0.261430	−	0.965222i	$-0.415806\pi$
$80$	−35.5995	−	71.6427i	−0.444993	−	0.895534i
$81$	15.6260	−	48.0919i	0.192914	−	0.593727i
$82$	−17.6566	+	10.8436i	−0.215325	+	0.132239i
$83$	−16.4491	−	103.856i	−0.198182	−	1.25127i	−0.863361	−	0.504587i	$-0.831645\pi$
$83$	−16.4491	−	103.856i	−0.198182	−	1.25127i	0.665179	−	0.746684i	$-0.268355\pi$
$84$	55.2567	+	107.929i	0.657817	+	1.28487i
$85$	86.3386	+	29.3911i	1.01575	+	0.345778i
$86$	34.3112	+	20.9802i	0.398968	+	0.243956i
$87$	−102.690	+	102.690i	−1.18035	+	1.18035i
$88$	−72.1788	−	50.3410i	−0.820214	−	0.572057i
$89$			69.0839i			0.776223i	0.921612	+	0.388112i	$0.126872\pi$
$89$			69.0839i			0.776223i	−0.921612	+	0.388112i	$0.873128\pi$
$90$	−107.916	+	43.0674i	−1.19906	+	0.478527i
$91$	157.149	−	51.0608i	1.72691	−	0.561107i
$92$	36.1842	−	112.103i	0.393306	−	1.21851i
$93$	10.6423	+	67.1931i	0.114434	+	0.722506i
$94$	8.30087	−	34.7240i	0.0883071	−	0.369404i
$95$	−9.65079	+	55.8753i	−0.101587	+	0.588161i
$96$	−110.033	+	94.9041i	−1.14618	+	0.988584i
$97$	22.7249	−	143.479i	0.234277	−	1.47917i	−0.537494	−	0.843268i	$-0.680629\pi$
$97$	22.7249	−	143.479i	0.234277	−	1.47917i	0.771771	−	0.635901i	$-0.219371\pi$
$98$	−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	−0.999408	−	0.0343985i	$-0.989048\pi$
$101$	−73.0522	−	100.548i	−0.723289	−	0.995522i	0.276119	−	0.961123i	$-0.410952\pi$
$102$	12.8371	−	165.159i	0.125854	−	1.61921i
$103$	−3.22225	−	6.32402i	−0.0312840	−	0.0613982i	0.874836	−	0.484420i	$-0.160969\pi$
$103$	−3.22225	−	6.32402i	−0.0312840	−	0.0613982i	−0.906119	+	0.423022i	$0.860969\pi$
$104$	103.955	+	168.536i	0.999564	+	1.62053i
$105$	134.072	+	70.6864i	1.27688	+	0.673204i
$106$	140.834	−	11.2213i	1.32862	−	0.105862i
$107$	0.785785	+	0.400378i	0.00734379	+	0.00374185i	0.457659	−	0.889128i	$-0.348688\pi$
$107$	0.785785	+	0.400378i	0.00734379	+	0.00374185i	−0.450315	+	0.892870i	$0.648688\pi$
$108$	28.0377	+	38.4336i	0.259608	+	0.355866i
$109$	187.495			1.72014			0.860068	−	0.510179i	$-0.170421\pi$
$109$	187.495			1.72014			0.860068	+	0.510179i	$0.170421\pi$
$110$	−109.999	+	0.375532i	−0.999994	+	0.00341392i
$111$			69.4279i			0.625477i
$112$	105.559	+	16.2993i	0.942491	+	0.145529i
$113$	−19.4858	+	38.2431i	−0.172441	+	0.338434i	−0.961011	−	0.276511i	$-0.910822\pi$
$113$	−19.4858	+	38.2431i	−0.172441	+	0.338434i	0.788570	+	0.614945i	$0.210822\pi$
$114$	102.666	−	8.18019i	0.900576	−	0.0717560i
$115$	−43.5437	−	140.662i	−0.378641	−	1.22315i
$116$	20.2576	+	126.315i	0.174635	+	1.08892i
$117$	256.254	−	130.568i	2.19020	−	1.11597i
$118$	12.4222	−	159.821i	0.105273	−	1.35442i
$119$	−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
$123$	46.4651	+	7.35934i	0.377765	+	0.0598321i
$124$	53.4488	+	27.1030i	0.431038	+	0.218573i
$125$	−124.171	+	14.3708i	−0.993369	+	0.114966i
$126$	36.0682	−	150.880i	0.286256	−	1.19746i
$127$	8.30422	−	1.31526i	0.0653876	−	0.0103564i	−0.123655	−	0.992325i	$-0.539462\pi$
$127$	8.30422	−	1.31526i	0.0653876	−	0.0103564i	0.189043	+	0.981969i	$0.439462\pi$
$128$	10.9091	+	127.534i	0.0852274	+	0.996362i
$129$	−28.2164	−	86.8411i	−0.218732	−	0.673187i
$130$	227.431	+	97.6832i	1.74947	+	0.751410i
$131$	−160.641			−1.22627			−0.613134	−	0.789979i	$-0.710091\pi$
$131$	−160.641			−1.22627			−0.613134	+	0.789979i	$0.710091\pi$
$132$	50.1961	+	193.389i	0.380273	+	1.46507i
$133$	−53.5316	−	53.5316i	−0.402493	−	0.402493i
$134$	36.9246	+	22.5782i	0.275557	+	0.168494i
$135$	56.2946	+	19.1636i	0.416997	+	0.141953i
$136$	−111.239	−	94.4484i	−0.817933	−	0.694474i
$137$	−77.5066	+	12.2758i	−0.565741	+	0.0896046i	−0.432752	−	0.901513i	$-0.642458\pi$
$137$	−77.5066	+	12.2758i	−0.565741	+	0.0896046i	−0.132989	+	0.991118i	$0.542458\pi$
$138$	−227.904	+	139.964i	−1.65148	+	1.01423i
$139$	−49.9473	−	16.2289i	−0.359333	−	0.116754i	0.123786	−	0.992309i	$-0.460496\pi$
$139$	−49.9473	−	16.2289i	−0.359333	−	0.116754i	−0.483119	+	0.875554i	$0.660496\pi$
$140$	119.680	−	59.1800i	0.854857	−	0.422715i
$141$	−65.5784	+	47.6455i	−0.465095	+	0.337911i
$142$	−15.9443	+	38.5988i	−0.112284	+	0.271822i
$143$	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
$146$	103.812	+	121.310i	0.711042	+	0.830889i
$147$	17.9478	−	9.14486i	0.122094	−	0.0622100i
$148$	49.5481	+	35.8521i	0.334784	+	0.242244i
$149$	−14.8092	−	10.7595i	−0.0993907	−	0.0722115i	0.536980	−	0.843595i	$-0.319565\pi$
$149$	−14.8092	−	10.7595i	−0.0993907	−	0.0722115i	−0.636371	+	0.771383i	$0.719565\pi$
$150$	81.2043	+	212.023i	0.541362	+	1.41349i
$151$	63.1157	+	194.250i	0.417984	+	1.28642i	0.909554	+	0.415586i	$0.136423\pi$
$151$	63.1157	+	194.250i	0.417984	+	1.28642i	−0.491570	+	0.870838i	$0.663577\pi$
$152$	47.1779	−	77.4928i	0.310381	−	0.509821i
$153$	−149.867	+	149.867i	−0.979524	+	0.979524i
$154$	84.2480	−	120.296i	0.547065	−	0.781146i
$155$	74.1438	−	10.6850i	0.478347	−	0.0689356i
$156$	69.4684	−	444.183i	0.445310	−	2.84732i
$157$	17.1413	+	8.73395i	0.109181	+	0.0556303i	0.507728	−	0.861518i	$-0.330486\pi$
$157$	17.1413	+	8.73395i	0.109181	+	0.0556303i	−0.398547	+	0.917148i	$0.630486\pi$
$158$	150.838	+	128.575i	0.954668	+	0.813763i
$159$	−259.504	−	188.541i	−1.63210	−	1.18579i
$160$	102.800	+	122.606i	0.642500	+	0.766286i
$161$	186.972	+	60.7509i	1.16132	+	0.377335i
$162$	−7.83704	+	100.830i	−0.0483768	+	0.622405i
$163$	−30.4629	+	192.335i	−0.186889	+	1.17997i	0.698671	+	0.715443i	$0.253775\pi$
$163$	−30.4629	+	192.335i	−0.186889	+	1.17997i	−0.885560	+	0.464526i	$0.846225\pi$
$164$	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	−0.617408	−	0.786643i	$-0.711817\pi$
$167$	35.5489	−	224.447i	0.212868	−	1.34400i	0.830276	−	0.557352i	$-0.188183\pi$
$168$	−158.029	−	183.942i	−0.940651	−	1.09489i
$169$	−421.955	−	137.101i	−2.49677	−	0.811251i
$170$	−181.645	−	16.6712i	−1.06850	−	0.0980658i
$171$	−106.603	−	77.4513i	−0.623407	−	0.452932i
$172$	−76.5459	−	24.7072i	−0.445034	−	0.143646i
$173$	69.3717	+	35.3466i	0.400992	+	0.204316i	0.642844	−	0.765998i	$-0.277755\pi$
$173$	69.3717	+	35.3466i	0.400992	+	0.204316i	−0.241851	+	0.970313i	$0.577755\pi$
$174$	151.521	−	247.798i	0.870807	−	1.42413i
$175$	79.8863	−	146.529i	0.456493	−	0.837307i
$176$	163.935	+	64.0415i	0.931449	+	0.363872i
$177$	−257.356	+	257.356i	−1.45399	+	1.45399i
$178$	−32.3849	−	134.319i	−0.181938	−	0.754600i
$179$	51.6714	+	159.028i	0.288667	+	0.888426i	0.985275	+	0.170975i	$0.0546916\pi$
$179$	51.6714	+	159.028i	0.288667	+	0.888426i	−0.696608	+	0.717452i	$0.745308\pi$
$180$	189.630	−	134.324i	1.05350	−	0.746243i
$181$	−244.342	−	177.525i	−1.34996	−	0.980802i	−0.999014	−	0.0444058i	$-0.985861\pi$
$181$	−244.342	−	177.525i	−1.34996	−	0.980802i	−0.350945	−	0.936396i	$-0.614139\pi$
$182$	−281.606	+	172.945i	−1.54729	+	0.950245i
$183$	−154.069	+	78.5022i	−0.841909	+	0.428974i
$184$	−17.8010	+	234.923i	−0.0967447	+	1.27676i
$185$	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
$188$	0.138548	+	71.4046i	0.000736956	+	0.379812i
$189$	−64.2327	+	46.6678i	−0.339855	+	0.246919i
$190$	−7.42919	−	113.162i	−0.0391010	−	0.595588i
$191$	123.363	+	40.0830i	0.645878	+	0.209859i	0.613596	−	0.789620i	$-0.289722\pi$
$191$	123.363	+	40.0830i	0.645878	+	0.209859i	0.0322823	+	0.999479i	$0.489722\pi$
$192$	169.447	−	236.102i	0.882536	−	1.22970i
$193$	67.9965	−	10.7696i	0.352314	−	0.0558010i	0.0222305	−	0.999753i	$-0.492923\pi$
$193$	67.9965	−	10.7696i	0.352314	−	0.0558010i	0.330083	+	0.943952i	$0.392923\pi$
$194$	23.0762	+	289.618i	0.118949	+	1.49288i
$195$	−248.121	−	504.237i	−1.27242	−	2.58583i
$196$	2.74178	−	17.5310i	0.0139887	−	0.0894439i
$197$	−67.2265	−	67.2265i	−0.341251	−	0.341251i	0.515586	−	0.856838i	$-0.327574\pi$
$197$	−67.2265	−	67.2265i	−0.341251	−	0.341251i	−0.856838	+	0.515586i	$0.827574\pi$
$198$	112.077	−	229.742i	0.566048	−	1.16032i
$199$	56.9753			0.286308			0.143154	−	0.989700i	$-0.454276\pi$
$199$	56.9753			0.286308			0.143154	+	0.989700i	$0.454276\pi$
$200$	193.246	+	51.5349i	0.966232	+	0.257675i
$201$	−30.3655	−	93.4554i	−0.151072	−	0.464952i
$202$	189.169	+	161.248i	0.936479	+	0.798259i
$203$	−210.873	+	33.3990i	−1.03878	+	0.164527i
$204$	52.4639	+	327.134i	0.257176	+	1.60360i
$205$	8.81658	−	51.0455i	0.0430077	−	0.249002i
$206$	9.22953	+	10.7852i	0.0448035	+	0.0523553i
$207$	337.968	+	53.5288i	1.63269	+	0.258593i
$208$	−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	$-0.929262\pi$
$211$	−225.181	+	163.604i	−1.06721	+	0.775373i	−0.0918009	+	0.995777i	$0.529262\pi$
$212$	−268.561	+	87.8371i	−1.26680	+	0.414326i
$213$	84.4833	−	43.0464i	0.396635	−	0.202096i
$214$	−1.71548	−	0.410090i	−0.00801626	−	0.00191631i
$215$	−96.0465	+	29.7324i	−0.446728	+	0.138290i
$216$	−72.5301	−	61.5824i	−0.335788	−	0.285104i
$217$	−45.4054	+	89.1131i	−0.209241	+	0.410659i
$218$	−364.544	+	87.8933i	−1.67222	+	0.403180i
$219$		−	362.507i		−	1.65528i
$220$	213.694	−	52.2953i	0.971337	−	0.237706i
$221$	451.500			2.04299
$222$	−32.5462	−	134.988i	−0.146605	−	0.608053i
$223$	174.457	+	88.8904i	0.782319	+	0.398612i	0.799062	−	0.601248i	$-0.205330\pi$
$223$	174.457	+	88.8904i	0.782319	+	0.398612i	−0.0167431	+	0.999860i	$0.505330\pi$
$224$	−212.878	+	17.7933i	−0.950347	+	0.0794342i
$225$	97.4368	−	273.651i	0.433052	−	1.21623i
$226$	19.9585	−	83.4900i	0.0883121	−	0.369425i
$227$	51.4767	+	101.029i	0.226770	+	0.445061i	0.976155	−	0.217073i	$-0.0696510\pi$
$227$	51.4767	+	101.029i	0.226770	+	0.445061i	−0.749386	+	0.662134i	$0.769651\pi$
$228$	−195.777	+	64.0319i	−0.858670	+	0.280842i
$229$	69.2755	+	95.3495i	0.302513	+	0.416373i	0.933028	−	0.359804i	$-0.117156\pi$
$229$	69.2755	+	95.3495i	0.302513	+	0.416373i	−0.630515	+	0.776177i	$0.717156\pi$
$230$	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
$233$	46.3997	−	292.956i	0.199140	−	1.25732i	−0.662213	−	0.749316i	$-0.730382\pi$
$233$	46.3997	−	292.956i	0.199140	−	1.25732i	0.861353	−	0.508007i	$-0.169618\pi$
$234$	−437.024	+	373.987i	−1.86762	+	1.59824i
$235$	51.4507	+	72.9345i	0.218939	+	0.310360i
$236$	50.7683	+	316.562i	0.215120	+	1.34136i
$237$	−70.3952	−	444.458i	−0.297026	−	1.87535i
$238$	157.986	−	185.341i	0.663805	−	0.778744i
$239$	163.096	−	52.9932i	0.682412	−	0.221729i	0.0527607	−	0.998607i	$-0.483198\pi$
$239$	163.096	−	52.9932i	0.682412	−	0.221729i	0.629651	+	0.776878i	$0.283198\pi$
$240$	3.65887	−	363.249i	0.0152453	−	1.51354i
$241$			132.086i			0.548074i	0.961719	+	0.274037i	$0.0883591\pi$
$241$			132.086i			0.548074i	−0.961719	+	0.274037i	$0.911641\pi$
$242$	178.608	−	163.289i	0.738049	−	0.674747i
$243$	238.052	−	238.052i	0.979638	−	0.979638i
$244$	−23.5363	+	150.491i	−0.0964601	+	0.616768i
$245$	−9.79286	−	19.9012i	−0.0399709	−	0.0812295i
$246$	−93.7913	+	7.47310i	−0.381265	+	0.0303784i
$247$	43.9116	+	277.247i	0.177780	+	1.12246i
$248$	−116.625	−	27.6404i	−0.470262	−	0.111453i
$249$	147.546	−	454.101i	0.592555	−	1.82370i
$250$	234.688	−	86.1495i	0.938750	−	0.344598i
$251$	15.5316	+	21.3775i	0.0618791	+	0.0851692i	0.838835	−	0.544386i	$-0.183237\pi$
$251$	15.5316	+	21.3775i	0.0618791	+	0.0851692i	−0.776956	+	0.629555i	$0.783237\pi$
$252$	0.602006	+	310.261i	0.00238891	+	1.23120i
$253$	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
$256$	−80.9956	−	242.849i	−0.316389	−	0.948630i
$257$	177.337	+	348.044i	0.690029	+	1.35426i	0.924142	+	0.382048i	$0.124781\pi$
$257$	177.337	+	348.044i	0.690029	+	1.35426i	−0.234114	+	0.972209i	$0.575219\pi$
$258$	95.5698	+	155.617i	0.370426	+	0.603165i
$259$	−59.9941	+	82.5748i	−0.231638	+	0.318822i
$260$	−487.983	−	83.3096i	−1.87686	−	0.320422i
$261$	−353.420	+	114.833i	−1.35410	+	0.439974i
$262$	312.332	−	75.3048i	1.19211	−	0.287423i
$263$	236.266	+	236.266i	0.898349	+	0.898349i	0.995290	−	0.0969412i	$-0.0309059\pi$
$263$	236.266	+	236.266i	0.898349	+	0.898349i	−0.0969412	+	0.995290i	$0.530906\pi$
$264$	−188.252	−	352.472i	−0.713075	−	1.33512i
$265$	−211.572	+	282.820i	−0.798386	+	1.06725i
$266$	129.175	+	78.9864i	0.485621	+	0.296941i
$267$	−142.416	+	279.507i	−0.533394	+	1.04684i
$268$	−82.3761	−	26.5890i	−0.307374	−	0.0992128i
$269$	−88.3574	+	121.614i	−0.328466	+	0.452095i	−0.941028	−	0.338327i	$-0.890139\pi$
$269$	−88.3574	+	121.614i	−0.328466	+	0.452095i	0.612562	+	0.790422i	$0.290139\pi$
$270$	−118.436	−	10.8700i	−0.438653	−	0.0402591i
$271$	−10.1507	+	31.2405i	−0.0374563	+	0.115279i	−0.968036	−	0.250810i	$-0.919303\pi$
$271$	−10.1507	+	31.2405i	−0.0374563	+	0.115279i	0.930580	+	0.366088i	$0.119303\pi$
$272$	260.555	+	131.489i	0.957924	+	0.483414i
$273$	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	0.0634762	−	0.997983i	$-0.479781\pi$
$277$	−51.1198	−	8.09659i	−0.184548	−	0.0292296i	−0.248024	+	0.968754i	$0.579781\pi$
$278$	104.720	+	8.13939i	0.376689	+	0.0292784i
$279$	−53.7932	+	165.558i	−0.192807	+	0.593400i
$280$	−204.950	+	171.166i	−0.731964	+	0.611308i
$281$	−24.6258	+	33.8946i	−0.0876365	+	0.120621i	−0.850584	−	0.525839i	$-0.823751\pi$
$281$	−24.6258	+	33.8946i	−0.0876365	+	0.120621i	0.762948	+	0.646460i	$0.223751\pi$
$282$	105.168	−	123.378i	0.372936	−	0.437511i
$283$	5.92958	−	11.6374i	0.0209526	−	0.0411217i	−0.880293	−	0.474430i	$-0.842654\pi$
$283$	5.92958	−	11.6374i	0.0209526	−	0.0411217i	0.901246	+	0.433309i	$0.142654\pi$
$284$	12.9060	−	82.5214i	0.0454437	−	0.290568i
$285$	−154.233	+	206.172i	−0.541169	+	0.723410i
$286$	−514.895	+	177.243i	−1.80033	+	0.619730i
$287$	48.9044	+	48.9044i	0.170398	+	0.170398i
$288$	−361.116	+	88.5512i	−1.25388	+	0.307469i
$289$	−41.5878	+	13.5127i	−0.143903	+	0.0467568i
$290$	−270.501	−	170.633i	−0.932761	−	0.588389i
$291$	387.725	−	533.658i	1.33239	−	1.83388i
$292$	−258.708	−	187.196i	−0.885985	−	0.641083i
$293$	−31.5886	−	61.9962i	−0.107811	−	0.211591i	0.830798	−	0.556574i	$-0.187885\pi$
$293$	−31.5886	−	61.9962i	−0.107811	−	0.211591i	−0.938609	+	0.344983i	$0.887885\pi$
$294$	−30.6088	+	26.1938i	−0.104111	+	0.0890944i
$295$	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
$298$	33.8372	+	13.9774i	0.113548	+	0.0469039i
$299$	−428.460	−	589.725i	−1.43298	−	1.97232i
$300$	−257.276	−	374.167i	−0.857587	−	1.24722i
$301$	41.4818	−	127.668i	0.137813	−	0.424145i
$302$	−213.775	−	348.090i	−0.707864	−	1.15262i
$303$	−88.2842	−	557.405i	−0.291367	−	1.83962i
$304$	−55.4006	+	172.784i	−0.182239	+	0.568369i
$305$	84.0648	+	170.838i	0.275622	+	0.560125i
$306$	221.130	−	361.639i	0.722648	−	1.18183i
$307$	13.7530	−	13.7530i	0.0447979	−	0.0447979i	−0.684353	−	0.729151i	$-0.739915\pi$
$307$	13.7530	−	13.7530i	0.0447979	−	0.0447979i	0.729151	+	0.684353i	$0.239915\pi$
$308$	−107.410	+	273.384i	−0.348734	+	0.887611i
$309$		−	32.2291i		−	0.104301i
$310$	−139.148	+	55.5317i	−0.448864	+	0.179134i
$311$	−313.415	+	101.835i	−1.00776	+	0.327442i	−0.765964	−	0.642884i	$-0.777738\pi$
$311$	−313.415	+	101.835i	−1.00776	+	0.327442i	−0.241800	+	0.970326i	$0.577738\pi$
$312$	73.1562	+	896.183i	0.234475	+	2.87238i
$313$	6.96579	+	43.9802i	0.0222549	+	0.140512i	0.996314	−	0.0857822i	$-0.0273389\pi$
$313$	6.96579	+	43.9802i	0.0222549	+	0.140512i	−0.974059	+	0.226294i	$0.927339\pi$
$314$	−37.4220	−	8.94583i	−0.119178	−	0.0284899i
$315$	223.559	+	316.909i	0.709712	+	1.00606i
$316$	−353.544	−	179.277i	−1.11881	−	0.567331i
$317$	−1.82444	+	11.5191i	−0.00575534	+	0.0363378i	−0.990399	−	0.138239i	$-0.955856\pi$
$317$	−1.82444	+	11.5191i	−0.00575534	+	0.0363378i	0.984644	+	0.174577i	$0.0558558\pi$
$318$	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
$322$	−392.006	−	30.4689i	−1.21741	−	0.0946239i
$323$	−93.9128	−	184.314i	−0.290752	−	0.570632i
$324$	−32.0292	−	199.715i	−0.0988554	−	0.616405i
$325$	−558.982	+	265.438i	−1.71995	+	0.816731i
$326$	−30.9337	−	388.234i	−0.0948887	−	1.19090i
$327$	758.589	+	386.520i	2.31984	+	1.18202i
$328$	−43.0999	+	70.7943i	−0.131402	+	0.215836i
$329$	−119.168			−0.362212
$330$	−445.822	−	225.244i	−1.35098	−	0.682558i
$331$			389.384i			1.17639i	0.808720	+	0.588194i	$0.200161\pi$
$331$			389.384i			1.17639i	−0.808720	+	0.588194i	$0.799839\pi$
$332$	−247.882	−	339.793i	−0.746634	−	1.02347i
$333$	−80.6532	+	158.291i	−0.242202	+	0.475348i
$334$	36.0984	+	453.054i	0.108079	+	1.35645i
$335$	−103.362	+	31.9970i	−0.308543	+	0.0955134i
$336$	393.482	+	283.555i	1.17108	+	0.843914i
$337$	376.907	−	192.044i	1.11842	−	0.569863i	0.205768	−	0.978601i	$-0.434031\pi$
$337$	376.907	−	192.044i	1.11842	−	0.569863i	0.912652	+	0.408738i	$0.134031\pi$
$338$	884.670	+	68.7615i	2.61737	+	0.203437i
$339$	−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
$343$	352.327	+	55.8031i	1.02719	+	0.162691i
$344$	160.409	+	12.1548i	0.466306	+	0.0353338i
$345$	113.800	−	658.873i	0.329856	−	1.90978i
$346$	−151.448	−	36.2041i	−0.437711	−	0.104636i
$347$	−60.5584	+	9.59150i	−0.174520	+	0.0276412i	−0.243083	−	0.970006i	$-0.578159\pi$
$347$	−60.5584	+	9.59150i	−0.174520	+	0.0276412i	0.0685629	+	0.997647i	$0.478159\pi$
$348$	−178.437	+	552.820i	−0.512750	+	1.58856i
$349$	12.3427	+	37.9869i	0.0353658	+	0.108845i	0.967181	−	0.254088i	$-0.0817754\pi$
$349$	12.3427	+	37.9869i	0.0353658	+	0.108845i	−0.931815	+	0.362933i	$0.881775\pi$
$350$	−86.6326	+	322.343i	−0.247522	+	0.920979i
$351$	294.388			0.838711
$352$	−348.758	−	47.6660i	−0.990789	−	0.135415i
$353$	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	$0.731427\pi$
$354$	379.731	−	621.016i	1.07269	−	1.75428i
$355$	−46.0966	−	93.6784i	−0.129850	−	0.263883i
$356$	125.931	+	245.973i	0.353739	+	0.690935i
$357$	−546.126	+	86.4978i	−1.52976	+	0.242291i
$358$	−175.013	−	284.974i	−0.488863	−	0.796017i
$359$	489.097	+	158.917i	1.36239	+	0.442667i	0.896840	−	0.442356i	$-0.145857\pi$
$359$	489.097	+	158.917i	1.36239	+	0.442667i	0.465548	+	0.885022i	$0.345857\pi$
$360$	−305.727	+	350.058i	−0.849242	+	0.972384i
$361$	−188.009	+	136.597i	−0.520802	+	0.378385i
$362$	558.291	+	230.618i	1.54224	+	0.637065i
$363$	−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
$366$	262.755	−	224.855i	0.717909	−	0.614358i
$367$	615.620	−	313.674i	1.67744	−	0.854697i	0.685485	−	0.728086i	$-0.259590\pi$
$367$	615.620	−	313.674i	1.67744	−	0.854697i	0.991952	−	0.126611i	$-0.0404100\pi$
$368$	−75.5162	−	465.102i	−0.205207	−	1.26386i
$369$	97.3879	+	70.7564i	0.263924	+	0.191752i
$370$	−149.123	+	33.7599i	−0.403035	+	0.0912430i
$371$	−145.722	−	448.486i	−0.392782	−	1.20886i
$372$	160.376	+	219.841i	0.431120	+	0.590970i
$373$	196.331	−	196.331i	0.526355	−	0.526355i	−0.393128	−	0.919484i	$-0.628607\pi$
$373$	196.331	−	196.331i	0.526355	−	0.526355i	0.919484	+	0.393128i	$0.128607\pi$
$374$	320.512	−	241.480i	0.856984	−	0.645668i
$375$	−532.011	−	197.836i	−1.41870	−	0.527562i
$376$	−33.7422	−	138.766i	−0.0897400	−	0.369059i
$377$	705.347	+	359.392i	1.87095	+	0.953294i
$378$	103.010	−	120.846i	0.272513	−	0.319699i
$379$	520.868	+	378.433i	1.37432	+	0.998503i	0.997386	+	0.0722642i	$0.0230225\pi$
$379$	520.868	+	378.433i	1.37432	+	0.998503i	0.376936	+	0.926239i	$0.376978\pi$
$380$	67.4921	+	216.536i	0.177611	+	0.569832i
$381$	36.3096	+	11.7977i	0.0953008	+	0.0309651i
$382$	−258.642	−	20.1031i	−0.677074	−	0.0526260i
$383$	60.8799	−	384.380i	0.158955	−	1.00360i	−0.771241	−	0.636543i	$-0.780364\pi$
$383$	60.8799	−	384.380i	0.158955	−	1.00360i	0.930197	−	0.367061i	$-0.119636\pi$
$384$	−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
$388$	−180.633	−	552.282i	−0.465549	−	1.42341i
$389$	−458.686	−	149.036i	−1.17914	−	0.383126i	−0.347093	−	0.937831i	$-0.612831\pi$
$389$	−458.686	−	149.036i	−1.17914	−	0.383126i	−0.832047	+	0.554704i	$0.812831\pi$
$390$	718.794	+	864.067i	1.84306	+	2.21556i
$391$	434.591	+	315.749i	1.11149	+	0.807542i
$392$	2.88733	+	35.3706i	0.00736564	+	0.0902311i
$393$	−649.940	−	331.161i	−1.65379	−	0.842649i
$394$	162.222	+	99.1933i	0.411730	+	0.251760i
$395$	−490.435	+	70.6776i	−1.24161	+	0.178931i
$396$	−110.213	+	499.224i	−0.278315	+	1.26067i
$397$	−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	$0.396221\pi$
$398$	−110.776	+	26.7087i	−0.278333	+	0.0671074i
$399$	−106.229	−	326.940i	−0.266238	−	0.819398i
$400$	−399.885	−	9.60917i	−0.999711	−	0.0240229i
$401$	295.201	+	214.476i	0.736163	+	0.534854i	0.891507	−	0.453007i	$-0.149649\pi$
$401$	295.201	+	214.476i	0.736163	+	0.534854i	−0.155344	+	0.987860i	$0.549649\pi$
$402$	102.849	+	167.469i	0.255843	+	0.416591i
$403$	330.417	−	168.356i	0.819893	−	0.417757i
$404$	−443.388	−	224.835i	−1.09749	−	0.556522i
$405$	−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
$408$	−255.358	−	611.449i	−0.625877	−	1.49865i
$409$	316.613	−	230.033i	0.774115	−	0.562427i	−0.129092	−	0.991633i	$-0.541206\pi$
$409$	316.613	−	230.033i	0.774115	−	0.562427i	0.903207	+	0.429205i	$0.141206\pi$
$410$	6.78702	+	103.380i	0.0165537	+	0.252146i
$411$	−338.892	−	110.113i	−0.824554	−	0.267914i
$412$	−23.0007	−	16.6429i	−0.0558269	−	0.0403954i
$413$	−528.475	+	83.7023i	−1.27960	+	0.202669i
$414$	−682.199	+	54.3562i	−1.64782	+	0.131295i
$415$	−497.703	−	169.427i	−1.19928	−	0.408257i
$416$	677.349	+	410.574i	1.62824	+	0.986957i
$417$	−168.627	−	168.627i	−0.404381	−	0.404381i
$418$	179.454	+	173.327i	0.429317	+	0.414658i
$419$	312.635			0.746145			0.373072	−	0.927802i	$-0.378304\pi$
$419$	312.635			0.746145			0.373072	+	0.927802i	$0.378304\pi$
$420$	606.215	+	7.28258i	1.44337	+	0.0173395i
$421$	32.3036	+	99.4203i	0.0767307	+	0.236153i	0.982064	−	0.188550i	$-0.0603787\pi$
$421$	32.3036	+	99.4203i	0.0767307	+	0.236153i	−0.905333	+	0.424703i	$0.860379\pi$
$422$	361.123	−	423.652i	0.855742	−	1.00392i
$423$	−204.863	+	32.4471i	−0.484310	+	0.0767071i
$424$	480.983	−	296.676i	1.13439	−	0.699707i
$425$	331.327	−	313.333i	0.779593	−	0.737253i
$426$	−144.081	+	123.298i	−0.338217	+	0.289433i
$427$	−251.079	−	39.7671i	−0.588008	−	0.0931313i
$428$	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	$-0.678371\pi$
$431$	47.3487	−	34.4008i	0.109858	−	0.0798164i	0.641358	+	0.767242i	$0.278371\pi$
$432$	169.888	+	85.7333i	0.393259	+	0.198457i
$433$	236.902	−	120.708i	0.547118	−	0.278770i	−0.158505	−	0.987358i	$-0.550667\pi$
$433$	236.902	−	120.708i	0.547118	−	0.278770i	0.705623	+	0.708588i	$0.250667\pi$
$434$	46.5069	−	194.546i	0.107159	−	0.448263i
$435$	214.729	+	693.655i	0.493631	+	1.59461i
$436$	667.575	−	341.780i	1.53114	−	0.783898i
$437$	−151.621	+	297.573i	−0.346958	+	0.680944i
$438$	169.935	+	704.818i	0.387980	+	1.60917i
$439$		−	132.823i		−	0.302557i	−0.988491	−	0.151279i	$-0.951661\pi$
$439$		−	132.823i		−	0.302557i	0.988491	−	0.151279i	$-0.0483391\pi$
$440$	−390.968	+	201.852i	−0.888563	+	0.458755i
$441$	51.5432			0.116878
$442$	−877.845	+	211.653i	−1.98607	+	0.478853i
$443$	−4.03740	−	2.05716i	−0.00911378	−	0.00464370i	0.449428	−	0.893317i	$-0.351628\pi$
$443$	−4.03740	−	2.05716i	−0.00911378	−	0.00464370i	−0.458541	+	0.888673i	$0.651628\pi$
$444$	126.558	+	247.198i	0.285041	+	0.556752i
$445$	305.553	+	161.096i	0.686636	+	0.362013i
$446$	−380.864	−	91.0467i	−0.853956	−	0.204141i
$447$	−37.7361	−	74.0613i	−0.0844208	−	0.165685i
$448$	405.554	−	134.387i	0.905254	−	0.299972i
$449$	132.107	+	181.830i	0.294225	+	0.404967i	0.930381	−	0.366594i	$-0.119476\pi$
$449$	132.107	+	181.830i	0.294225	+	0.404967i	−0.636155	+	0.771561i	$0.719476\pi$
$450$	−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
$453$	−145.085	+	916.032i	−0.320276	+	2.02215i
$454$	−147.445	−	172.298i	−0.324770	−	0.379510i
$455$	140.616	−	814.126i	0.309046	−	1.78929i
$456$	350.629	−	216.272i	0.768924	−	0.474281i
$457$	58.7670	+	371.040i	0.128593	+	0.811904i	0.964703	+	0.263342i	$0.0848246\pi$
$457$	58.7670	+	371.040i	0.128593	+	0.811904i	−0.836110	+	0.548562i	$0.815175\pi$
$458$	−179.389	−	152.912i	−0.391679	−	0.333869i
$459$	−206.328	+	67.0399i	−0.449516	+	0.146056i
$460$	−411.447	−	421.452i	−0.894449	−	0.916201i
$461$		−	886.126i		−	1.92218i	−0.276232	−	0.961091i	$-0.589086\pi$
$461$		−	886.126i		−	1.92218i	0.276232	−	0.961091i	$-0.410914\pi$
$462$	588.851	−	313.032i	1.27457	−	0.677559i
$463$	−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	$0.475244\pi$
$464$	302.383	+	412.816i	0.651688	+	0.889690i
$465$	322.007	+	109.617i	0.692488	+	0.235735i
$466$	47.1169	+	591.342i	0.101109	+	1.26897i
$467$	34.3556	+	216.913i	0.0735666	+	0.464481i	0.996779	+	0.0801922i	$0.0255534\pi$
$467$	34.3556	+	216.913i	0.0735666	+	0.464481i	−0.923213	+	0.384289i	$0.874447\pi$
$468$	674.382	−	932.005i	1.44099	−	1.99146i
$469$	44.6413	−	137.392i	0.0951839	−	0.292946i
$470$	−134.225	−	117.687i	−0.285585	−	0.250397i
$471$	51.3474	+	70.6737i	0.109018	+	0.150050i
$472$	−247.105	−	591.687i	−0.523528	−	1.25358i
$473$	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
$476$	−220.285	+	434.416i	−0.462784	+	0.912639i
$477$	−372.627	−	731.321i	−0.781188	−	1.53317i
$478$	−292.264	+	179.490i	−0.611431	+	0.375502i
$479$	−414.922	+	571.091i	−0.866226	+	1.19226i	0.113823	+	0.993501i	$0.463690\pi$
$479$	−414.922	+	571.091i	−0.866226	+	1.19226i	−0.980049	+	0.198756i	$0.936310\pi$
$480$	163.169	+	707.974i	0.339935	+	1.47495i
$481$	359.930	−	116.948i	0.748294	−	0.243136i
$482$	−61.9188	−	256.813i	−0.128462	−	0.532806i
$483$	631.236	+	631.236i	1.30691	+	1.30691i
$484$	−270.719	+	401.207i	−0.559336	+	0.828941i
$485$	−581.607	−	435.089i	−1.19919	−	0.897090i
$486$	−351.248	+	574.435i	−0.722732	+	1.18196i
$487$	157.422	−	308.957i	0.323248	−	0.634410i	−0.671007	−	0.741451i	$-0.734138\pi$
$487$	157.422	−	308.957i	0.323248	−	0.634410i	0.994255	+	0.107042i	$0.0341378\pi$
$488$	−24.7857	−	303.632i	−0.0507904	−	0.622196i
$489$	−519.748	+	715.372i	−1.06288	+	1.46293i
$490$	28.3694	+	34.1030i	0.0578967	+	0.0695980i
$491$	125.437	−	386.055i	0.255472	−	0.786263i	−0.738264	−	0.674512i	$-0.764354\pi$
$491$	125.437	−	386.055i	0.255472	−	0.786263i	0.993736	−	0.111751i	$-0.0356459\pi$
$492$	178.854	−	58.4971i	0.363524	−	0.118896i
$493$	−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
$498$	−74.0000	+	952.068i	−0.148594	+	1.91178i
$499$	−232.643	+	716.002i	−0.466219	+	1.43487i	0.391225	+	0.920295i	$0.372052\pi$
$499$	−232.643	+	716.002i	−0.466219	+	1.43487i	−0.857443	+	0.514578i	$0.827948\pi$
$500$	−415.915	+	277.515i	−0.831830	+	0.555031i
$501$	606.525	−	834.811i	1.21063	−	1.66629i
$502$	−40.2192	−	34.2830i	−0.0801180	−	0.0682929i
$503$	−394.361	+	773.978i	−0.784019	+	1.53872i	0.0574073	+	0.998351i	$0.481717\pi$
$503$	−394.361	+	773.978i	−0.784019	+	1.53872i	−0.841426	+	0.540372i	$0.818283\pi$
$504$	−146.614	−	602.955i	−0.290901	−	1.19634i
$505$	−615.065	+	88.6383i	−1.21795	+	0.175521i
$506$	−619.564	−	189.478i	−1.22443	−	0.374463i
$507$	−1424.56	−	1424.56i	−2.80978	−	2.80978i
$508$	27.1696	−	19.8205i	0.0534835	−	0.0390168i
$509$	820.967	−	266.748i	1.61290	−	0.524063i	0.642649	−	0.766161i	$-0.277835\pi$
$509$	820.967	−	266.748i	1.61290	−	0.524063i	0.970252	+	0.242097i	$0.0778353\pi$
$510$	−700.553	−	441.911i	−1.37363	−	0.866492i
$511$	313.250	−	431.152i	0.613014	−	0.843741i
$512$	271.321	+	434.199i	0.529923	+	0.848046i
$513$	−61.2331	−	120.177i	−0.119363	−	0.234263i
$514$	−507.950	−	593.566i	−0.988229	−	1.15480i
$515$	−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
$518$	77.9365	−	188.673i	0.150457	−	0.364234i
$519$	207.805	+	286.019i	0.400395	+	0.551097i
$520$	987.832	−	66.7775i	1.89968	−	0.128418i
$521$	−200.511	+	617.108i	−0.384857	+	1.18447i	0.551727	+	0.834025i	$0.313969\pi$
$521$	−200.511	+	617.108i	−0.384857	+	1.18447i	−0.936584	+	0.350444i	$0.886031\pi$
$522$	633.319	−	388.944i	1.21325	−	0.745104i
$523$	−45.6928	−	288.493i	−0.0873667	−	0.551612i	−0.992082	−	0.125594i	$-0.959916\pi$
$523$	−45.6928	−	288.493i	−0.0873667	−	0.551612i	0.904715	−	0.426017i	$-0.140084\pi$
$524$	−571.962	+	292.828i	−1.09153	+	0.558833i
$525$	625.282	−	428.157i	1.19101	−	0.815538i
$526$	−570.124	−	348.612i	−1.08389	−	0.662761i
$527$	−193.241	+	193.241i	−0.366680	+	0.366680i
$528$	531.246	+	597.058i	1.00615	+	1.13079i
$529$		−	338.276i		−	0.639463i
$530$	278.778	−	649.064i	0.525995	−	1.22465i
$531$	−885.719	+	287.787i	−1.66802	+	0.541973i
$532$	−288.180	−	93.0177i	−0.541693	−	0.174845i
$533$	−40.1159	−	253.282i	−0.0752643	−	0.475200i
$534$	145.871	−	610.204i	0.273167	−	1.14270i
$535$	3.60321	−	2.54183i	0.00673496	−	0.00475109i
$536$	172.627	+	13.0806i	0.322065	+	0.0244041i
$537$	−118.778	+	749.936i	−0.221188	+	1.39653i
$538$	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	0.978008	−	0.208567i	$-0.0668799\pi$
$541$	258.288	+	355.504i	0.477428	+	0.657123i	−0.500580	+	0.865690i	$0.666880\pi$
$542$	5.09094	−	65.4989i	0.00939289	−	0.120847i
$543$	−622.621	−	1221.96i	−1.14663	−	2.25039i
$544$	−568.233	−	133.509i	−1.04455	−	0.245421i
$545$	437.218	−	829.276i	0.802234	−	1.52161i
$546$	−1495.88	+	119.189i	−2.73971	+	0.218294i
$547$	−397.803	−	202.691i	−0.727244	−	0.370549i	0.0508421	−	0.998707i	$-0.483809\pi$
$547$	−397.803	−	202.691i	−0.727244	−	0.370549i	−0.778086	+	0.628157i	$0.783809\pi$
$548$	−253.585	+	184.993i	−0.462745	+	0.337578i
$549$	−442.462			−0.805942
$550$	−254.845	+	487.395i	−0.463355	+	0.886173i
$551$		−	362.695i		−	0.658249i
$552$	−556.314	+	913.782i	−1.00782	+	1.65540i
$553$	300.340	−	589.451i	0.543111	−	1.06591i
$554$	103.187	−	8.22174i	0.186258	−	0.0148407i
$555$	307.075	+	161.898i	0.553288	+	0.291709i
$556$	−207.420	+	33.2648i	−0.373058	+	0.0598289i
$557$	386.971	−	197.171i	0.694741	−	0.353988i	−0.0706972	−	0.997498i	$-0.522522\pi$
$557$	386.971	−	197.171i	0.694741	−	0.353988i	0.765438	+	0.643510i	$0.222522\pi$
$558$	26.9793	−	347.110i	0.0483501	−	0.622061i
$559$	−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
$563$	265.894	+	42.1135i	0.472280	+	0.0748019i	0.388038	−	0.921643i	$-0.373153\pi$
$563$	265.894	+	42.1135i	0.472280	+	0.0748019i	0.0842425	+	0.996445i	$0.473153\pi$
$564$	−146.640	+	289.183i	−0.260000	+	0.512735i
$565$	123.708	+	175.363i	0.218952	+	0.310377i
$566$	−6.07342	+	25.4062i	−0.0107304	+	0.0448872i
$567$	333.409	−	52.8068i	0.588023	−	0.0931338i
$568$	13.5912	+	166.495i	0.0239281	+	0.293125i
$569$	−9.37853	−	28.8642i	−0.0164825	−	0.0507279i	0.942477	−	0.334271i	$-0.108490\pi$
$569$	−9.37853	−	28.8642i	−0.0164825	−	0.0507279i	−0.958959	+	0.283543i	$0.908490\pi$
$570$	203.225	−	473.158i	0.356534	−	0.830102i
$571$	9.82448			0.0172057			0.00860287	−	0.999963i	$-0.497262\pi$
$571$	9.82448			0.0172057			0.00860287	+	0.999963i	$0.497262\pi$
$572$	918.016	−	585.982i	1.60492	−	1.02444i
$573$	416.484	+	416.484i	0.726849	+	0.726849i
$574$	−118.009	−	72.1588i	−0.205591	−	0.125712i
$575$	−723.678	−	135.418i	−1.25857	−	0.235510i
$576$	660.602	−	341.452i	1.14688	−	0.592798i
$577$	161.102	−	25.5160i	0.279206	−	0.0442219i	−0.0152610	−	0.999884i	$-0.504858\pi$
$577$	161.102	−	25.5160i	0.279206	−	0.0442219i	0.294467	+	0.955662i	$0.404858\pi$
$578$	74.5242	−	45.7680i	0.128935	−	0.0791834i
$579$	297.310	+	96.6018i	0.513488	+	0.166842i
$580$	605.920	+	204.954i	1.04469	+	0.353369i
$581$	567.883	−	412.591i	0.977424	−	0.710140i
$582$	−503.682	+	1219.34i	−0.865433	+	2.09509i
$583$	−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
$586$	90.4797	+	105.730i	0.154402	+	0.180427i
$587$	−494.198	+	251.807i	−0.841905	+	0.428972i	−0.821081	−	0.570811i	$-0.806629\pi$
$587$	−494.198	+	251.807i	−0.841905	+	0.428972i	−0.0208237	+	0.999783i	$0.506629\pi$
$588$	47.2332	−	65.2768i	0.0803285	−	0.111015i
$589$	−137.455	−	99.8667i	−0.233370	−	0.169553i
$590$	−677.911	−	427.628i	−1.14900	−	0.724794i
$591$	−133.406	−	410.580i	−0.225729	−	0.694721i
$592$	241.770	+	37.3314i	0.408395	+	0.0630597i
$593$	86.9546	−	86.9546i	0.146635	−	0.146635i	−0.629978	−	0.776613i	$-0.716936\pi$
$593$	86.9546	−	86.9546i	0.146635	−	0.146635i	0.776613	+	0.629978i	$0.216936\pi$
$594$	208.981	−	157.450i	0.351819	−	0.265067i
$595$	86.8447	+	602.619i	0.145958	+	1.01281i
$596$	−72.3414	−	11.3139i	−0.121378	−	0.0189831i
$597$	230.517	+	117.455i	0.386126	+	0.196741i
$598$	1109.50	+	945.741i	1.85535	+	1.58151i
$599$	−2.16024	−	1.56951i	−0.00360641	−	0.00262021i	0.585981	−	0.810325i	$-0.300709\pi$
$599$	−2.16024	−	1.56951i	−0.00360641	−	0.00262021i	−0.589587	+	0.807705i	$0.700709\pi$
$600$	675.619	+	606.883i	1.12603	+	1.01147i
$601$	274.011	+	89.0315i	0.455925	+	0.148139i	0.527971	−	0.849262i	$-0.322953\pi$
$601$	274.011	+	89.0315i	0.455925	+	0.148139i	−0.0720463	+	0.997401i	$0.522953\pi$
$602$	−20.8047	+	267.668i	−0.0345593	+	0.444632i
$603$	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	0.558538	+	0.829479i	$0.311363\pi$
$607$	−138.995	+	877.578i	−0.228986	+	1.44576i	−0.787524	+	0.616284i	$0.788637\pi$
$608$	26.7173	−	361.912i	0.0439430	−	0.595250i
$609$	−922.025	−	299.584i	−1.51400	−	0.491928i
$610$	−243.531	−	292.750i	−0.399231	−	0.479919i
$611$	357.468	+	259.716i	0.585055	+	0.425067i
$612$	−260.412	+	806.790i	−0.425510	+	1.31828i
$613$	−150.698	−	76.7845i	−0.245837	−	0.125260i	0.326731	−	0.945117i	$-0.394053\pi$
$613$	−150.698	−	76.7845i	−0.245837	−	0.125260i	−0.572568	+	0.819857i	$0.694053\pi$
$614$	−20.2926	+	33.1868i	−0.0330499	+	0.0540501i
$615$	140.901	−	188.350i	0.229108	−	0.306261i
$616$	80.6793	−	581.889i	0.130973	−	0.944624i
$617$	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	$0.158750\pi$
$618$	15.1083	+	62.6626i	0.0244470	+	0.101396i
$619$	−146.025	−	449.420i	−0.235905	−	0.726041i	−0.997000	−	0.0774008i	$-0.975338\pi$
$619$	−146.025	−	449.420i	−0.235905	−	0.726041i	0.761095	−	0.648641i	$-0.224662\pi$
$620$	244.511	−	173.199i	0.394373	−	0.279353i
$621$	283.363	+	205.875i	0.456301	+	0.331522i
$622$	561.630	−	344.917i	0.902942	−	0.554529i
$623$	−410.913	+	209.370i	−0.659571	+	0.336068i
$624$	−562.347	−	1708.14i	−0.901197	−	2.73741i
$625$	−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
$628$	76.9526	−	0.149313i	0.122536	−	0.000237759i
$629$	−225.632	+	163.931i	−0.358715	+	0.260622i
$630$	−583.223	−	511.362i	−0.925751	−	0.811686i
$631$	868.165	+	282.084i	1.37586	+	0.447042i	0.901305	−	0.433186i	$-0.142611\pi$
$631$	868.165	+	282.084i	1.37586	+	0.447042i	0.474550	+	0.880228i	$0.342611\pi$
$632$	771.432	+	182.831i	1.22062	+	0.289290i
$633$	−1248.33	+	197.717i	−1.97209	+	0.312348i
$634$	−1.85264	−	23.2516i	−0.00292215	−	0.0366745i
$635$	13.5472	−	39.7960i	0.0213342	−	0.0626709i
$636$	−1267.65	−	198.255i	−1.99316	−	0.311722i
$637$	−77.6412	−	77.6412i	−0.121886	−	0.121886i
$638$	692.930	−	122.120i	1.08610	−	0.191411i
$639$	242.622			0.379691
$640$	589.514	+	249.146i	0.921115	+	0.389290i
$641$	−127.066	−	391.068i	−0.198230	−	0.610090i	−0.999924	−	0.0123545i	$-0.996067\pi$
$641$	−127.066	−	391.068i	−0.198230	−	0.610090i	0.801693	−	0.597735i	$-0.203933\pi$
$642$	−6.09529	−	5.19565i	−0.00949421	−	0.00809291i
$643$	−973.141	+	154.130i	−1.51344	+	0.239705i	−0.857254	−	0.514894i	$-0.827831\pi$
$643$	−973.141	+	154.130i	−1.51344	+	0.239705i	−0.656186	+	0.754600i	$0.727831\pi$
$644$	776.455	−	124.523i	1.20568	−	0.193359i
$645$	−449.889	−	77.7049i	−0.697503	−	0.120473i
$646$	268.996	+	314.335i	0.416402	+	0.486587i
$647$	−887.815	−	140.616i	−1.37220	−	0.217336i	−0.573571	−	0.819156i	$-0.694442\pi$
$647$	−887.815	−	140.616i	−1.37220	−	0.217336i	−0.798632	+	0.601820i	$0.794442\pi$
$648$	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
$652$	242.139	+	740.338i	0.371380	+	1.13549i
$653$	−46.9707	+	23.9328i	−0.0719306	+	0.0366505i	−0.489586	−	0.871955i	$-0.662852\pi$
$653$	−46.9707	+	23.9328i	−0.0719306	+	0.0366505i	0.417655	+	0.908606i	$0.362852\pi$
$654$	−1656.11	−	395.897i	−2.53227	−	0.605347i
$655$	−374.597	+	710.503i	−0.571904	+	1.08474i
$656$	50.6118	−	157.849i	0.0771521	−	0.240623i
$657$	421.118	−	826.491i	0.640971	−	1.25798i
$658$	231.696	−	55.8632i	0.352122	−	0.0848984i
$659$		−	741.252i		−	1.12481i	−0.826861	−	0.562407i	$-0.809875\pi$
$659$		−	741.252i		−	1.12481i	0.826861	−	0.562407i	$-0.190125\pi$
$660$	972.395	+	228.947i	1.47333	+	0.346890i
$661$	−747.326			−1.13060			−0.565299	−	0.824886i	$-0.691239\pi$
$661$	−747.326			−1.13060			−0.565299	+	0.824886i	$0.691239\pi$
$662$	−182.534	−	757.074i	−0.275732	−	1.14362i
$663$	1826.73	+	930.766i	2.75525	+	1.40387i
$664$	641.241	+	544.452i	0.965725	+	0.819958i
$665$	−361.596	+	111.937i	−0.543754	+	0.168326i
$666$	82.6097	−	345.571i	0.124039	−	0.518875i
$667$	427.596	+	839.205i	0.641074	+	1.25818i
$668$	−282.567	−	863.945i	−0.423005	−	1.29333i
$669$	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
$673$	−168.295	+	1062.58i	−0.250068	+	1.57886i	0.468536	+	0.883444i	$0.344782\pi$
$673$	−168.295	+	1062.58i	−0.250068	+	1.57886i	−0.718604	+	0.695420i	$0.755218\pi$
$674$	−642.790	+	550.074i	−0.953694	+	0.816133i
$675$	216.032	−	204.300i	0.320048	−	0.302666i
$676$	−1752.29	+	281.021i	−2.59214	+	0.415712i
$677$	61.9243	+	390.975i	0.0914688	+	0.577511i	0.990271	+	0.139156i	$0.0444388\pi$
$677$	61.9243	+	390.975i	0.0914688	+	0.577511i	−0.898802	+	0.438355i	$0.855561\pi$
$678$	252.865	−	296.649i	0.372957	−	0.437536i
$679$	922.291	−	299.670i	1.35831	−	0.441341i
$680$	−677.135	+	271.758i	−0.995787	+	0.399644i
$681$			514.873i			0.756054i
$682$	144.514	−	296.233i	0.211897	−	0.434359i
$683$	−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	$0.440436\pi$
$684$	−520.742	−	81.4420i	−0.761319	−	0.119067i
$685$	−126.442	+	371.432i	−0.184586	+	0.542236i
$686$	−711.184	+	56.6657i	−1.03671	+	0.0826030i
$687$	83.7200	+	528.587i	0.121863	+	0.769414i
$688$	−317.579	+	51.5638i	−0.461598	+	0.0749473i
$689$	−540.314	+	1662.92i	−0.784200	+	2.41352i
$690$	87.6038	+	1334.38i	0.126962	+	1.93389i
$691$	−152.782	−	210.287i	−0.221103	−	0.304323i	0.684027	−	0.729457i	$-0.260227\pi$
$691$	−152.782	−	210.287i	−0.221103	−	0.304323i	−0.905130	+	0.425134i	$0.860227\pi$
$692$	311.430	−	0.604274i	0.450043	−	0.000873228i
$693$	−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
$696$	87.7831	−	1158.49i	0.126125	−	1.66449i
$697$	85.7950	+	168.382i	0.123092	+	0.241581i
$698$	−41.8051	−	68.0713i	−0.0598926	−	0.0975234i
$699$	791.658	−	1089.62i	1.13256	−	1.55883i
$700$	17.3317	−	667.337i	0.0247595	−	0.953339i
$701$	626.487	−	203.558i	0.893705	−	0.290382i	0.174069	−	0.984733i	$-0.444308\pi$
$701$	626.487	−	203.558i	0.893705	−	0.290382i	0.719636	+	0.694351i	$0.244308\pi$
$702$	−572.374	+	138.002i	−0.815347	+	0.196584i
$703$	−122.607	−	122.607i	−0.174406	−	0.174406i
$704$	700.429	−	70.8133i	0.994928	−	0.100587i
$705$	57.8109	+	401.153i	0.0820013	+	0.569011i
$706$	−70.2510	−	42.9562i	−0.0995056	−	0.0608444i
$707$	376.663	−	739.243i	0.532763	−	1.04561i
$708$	−447.187	+	1385.44i	−0.631620	+	1.95684i
$709$	305.162	−	420.020i	0.430412	−	0.592411i	−0.537636	−	0.843177i	$-0.680682\pi$
$709$	305.162	−	420.020i	0.430412	−	0.592411i	0.968048	+	0.250766i	$0.0806824\pi$
$710$	133.539	+	160.529i	0.188084	+	0.226097i
$711$	355.823	−	1095.11i	0.500454	−	1.54024i
$712$	−360.153	−	419.208i	−0.505832	−	0.588775i
$713$	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
$718$	−1025.44	−	79.7031i	−1.42819	−	0.111007i
$719$	363.969	−	1120.18i	0.506216	−	1.55797i	−0.292502	−	0.956265i	$-0.594488\pi$
$719$	363.969	−	1120.18i	0.506216	−	1.55797i	0.798717	−	0.601706i	$-0.205512\pi$
$720$	430.321	−	823.931i	0.597669	−	1.14435i
$721$	27.8498	−	38.3320i	0.0386267	−	0.0531651i
$722$	301.511	−	353.718i	0.417605	−	0.489914i
$723$	−272.295	+	534.408i	−0.376618	+	0.739154i
$724$	−1193.59	−	186.672i	−1.64860	−	0.257834i
$725$	767.020	−	225.763i	1.05796	−	0.311397i
$726$	1059.25	−	292.453i	1.45902	−	0.402828i
$727$	−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	$0.954698\pi$
$728$	−687.402	+	1129.10i	−0.944233	+	1.55096i
$729$	1021.06	−	331.761i	1.40062	−	0.455091i
$730$	778.623	−	176.272i	1.06661	−	0.241469i
$731$	215.599	−	296.746i	0.294937	−	0.405946i
$732$	−405.463	+	560.356i	−0.553912	+	0.765513i
$733$	−351.727	−	690.302i	−0.479845	−	0.941749i	−0.996342	−	0.0854600i	$-0.972764\pi$
$733$	−351.727	−	690.302i	−0.479845	−	0.941749i	0.516496	−	0.856289i	$-0.327236\pi$
$734$	−1049.90	+	898.460i	−1.43038	+	1.22406i
$735$	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
$738$	−222.519	−	91.9175i	−0.301516	−	0.124550i
$739$	401.252	+	552.275i	0.542966	+	0.747328i	0.989037	−	0.147669i	$-0.0471772\pi$
$739$	401.252	+	552.275i	0.542966	+	0.747328i	−0.446071	+	0.894997i	$0.647177\pi$
$740$	274.112	−	135.544i	0.370421	−	0.183168i
$741$	−393.881	+	1212.24i	−0.531553	+	1.63595i
$742$	493.565	+	803.674i	0.665182	+	1.08312i
$743$	158.762	+	1002.39i	0.213677	+	1.34911i	0.828300	+	0.560285i	$0.189308\pi$
$743$	158.762	+	1002.39i	0.213677	+	1.34911i	−0.614622	+	0.788822i	$0.710692\pi$
$744$	−414.874	−	352.253i	−0.557627	−	0.473458i
$745$	−82.1220	+	40.4100i	−0.110231	+	0.0542417i
$746$	−289.687	+	473.758i	−0.388321	+	0.635064i
$747$	863.916	−	863.916i	1.15651	−	1.15651i
$748$	−509.967	+	619.754i	−0.681774	+	0.828548i
$749$			5.88728i			0.00786019i
$750$	1127.12	+	135.254i	1.50283	+	0.180339i
$751$	486.255	−	157.994i	0.647477	−	0.210378i	0.0331758	−	0.999450i	$-0.489438\pi$
$751$	486.255	−	157.994i	0.647477	−	0.210378i	0.614301	+	0.789071i	$0.289438\pi$
$752$	130.655	+	253.983i	0.173743	+	0.337744i
$753$	18.7701	+	118.510i	0.0249271	+	0.157384i
$754$	−1539.87	−	368.110i	−2.04227	−	0.488210i
$755$	1006.33	+	173.814i	1.33289	+	0.230217i
$756$	−143.631	+	283.248i	−0.189988	+	0.374667i
$757$	175.399	−	1107.43i	0.231703	−	1.46292i	−0.547847	−	0.836578i	$-0.684552\pi$
$757$	175.399	−	1107.43i	0.231703	−	1.46292i	0.779551	−	0.626339i	$-0.215448\pi$
$758$	−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	0.760852	−	0.648925i	$-0.224781\pi$
$761$	−69.5768	−	95.7643i	−0.0914282	−	0.125840i	−0.852281	+	0.523085i	$0.824781\pi$
$762$	−76.1267	−	5.91700i	−0.0999039	−	0.00776509i
$763$	568.235	+	1115.22i	0.744738	+	1.46163i
$764$	512.299	−	82.1594i	0.670548	−	0.107538i
$765$	313.378	+	1012.33i	0.409644	+	1.32330i
$766$	61.8209	+	775.884i	0.0807061	+	1.01290i
$767$	1767.69	+	900.684i	2.30468	+	1.17430i
$768$	172.932	−	1149.52i	0.225171	−	1.49677i
$769$	−904.162			−1.17576			−0.587882	−	0.808947i	$-0.700038\pi$
$769$	−904.162			−1.17576			−0.587882	+	0.808947i	$0.700038\pi$
$770$	−335.605	−	653.141i	−0.435851	−	0.848235i
$771$			1773.74i			2.30057i
$772$	222.470	−	162.294i	0.288173	−	0.210226i
$773$	418.308	−	820.976i	0.541149	−	1.06206i	−0.444895	−	0.895582i	$-0.646759\pi$
$773$	418.308	−	820.976i	0.541149	−	1.06206i	0.986044	−	0.166482i	$-0.0532408\pi$
$774$	37.1153	+	465.817i	0.0479526	+	0.601831i
$775$	125.636	−	352.849i	0.162111	−	0.455289i
$776$	610.099	+	989.118i	0.786210	+	1.27464i
$777$	−412.959	+	210.413i	−0.531479	+	0.270802i
$778$	961.681	+	74.7473i	1.23609	+	0.0960762i
$779$	−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
$783$	−375.695	−	59.5042i	−0.479814	−	0.0759951i
$784$	−22.1947	−	67.4170i	−0.0283096	−	0.0859911i
$785$	78.6014	−	55.4483i	0.100129	−	0.0706348i
$786$	1418.91	+	339.195i	1.80523	+	0.431545i
$787$	−295.521	+	46.8059i	−0.375503	+	0.0594738i	−0.341333	−	0.939942i	$-0.610879\pi$
$787$	−295.521	+	46.8059i	−0.375503	+	0.0594738i	−0.0341693	+	0.999416i	$0.510879\pi$
$788$	−361.905	−	116.814i	−0.459270	−	0.148241i
$789$	468.850	+	1442.97i	0.594234	+	1.82886i
$790$	920.413	−	367.322i	1.16508	−	0.464964i
$791$	−286.526			−0.362233
$792$	−19.7402	−	1022.30i	−0.0249245	−	1.29078i
$793$	666.496	+	666.496i	0.840474	+	0.840474i
$794$	367.304	−	600.692i	0.462599	−	0.756540i
$795$	−1439.04	+	708.112i	−1.81011	+	0.890707i
$796$	202.860	−	103.859i	0.254850	−	0.130476i
$797$	536.361	−	84.9513i	0.672976	−	0.106589i	0.189411	−	0.981898i	$-0.439342\pi$
$797$	536.361	−	84.9513i	0.672976	−	0.106589i	0.483564	+	0.875309i	$0.339342\pi$
$798$	359.802	+	585.866i	0.450879	+	0.734168i
$799$	−309.684	−	100.622i	−0.387589	−	0.125935i
$800$	781.995	−	168.774i	0.977493	−	0.210967i
$801$	−649.398	+	471.815i	−0.810734	+	0.589033i
$802$	−674.498	−	278.620i	−0.841019	−	0.347406i
$803$	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
$806$	−563.504	+	482.224i	−0.699136	+	0.598293i
$807$	−608.193	+	309.890i	−0.753647	+	0.384002i
$808$	967.470	+	229.293i	1.19736	+	0.283778i
$809$	−400.547	−	291.015i	−0.495114	−	0.359721i	0.312034	−	0.950071i	$-0.398990\pi$
$809$	−400.547	−	291.015i	−0.495114	−	0.359721i	−0.807148	+	0.590350i	$0.798990\pi$
$810$	427.687	+	269.786i	0.528008	+	0.333069i
$811$	164.577	+	506.515i	0.202930	+	0.624556i	0.999792	+	0.0203937i	$0.00649198\pi$
$811$	164.577	+	506.515i	0.202930	+	0.624556i	−0.796862	+	0.604162i	$0.793508\pi$
$812$	−689.929	+	503.311i	−0.849667	+	0.619842i
$813$	−105.471	+	105.471i	−0.129731	+	0.129731i
$814$	192.959	−	275.524i	0.237051	−	0.338481i
$815$	779.647	+	583.239i	0.956623	+	0.715631i
$816$	783.122	+	1069.13i	0.959709	+	1.31020i
$817$	203.188	+	103.529i	0.248700	+	0.126719i
$818$	−507.752	+	595.670i	−0.620724	+	0.728203i
$819$	1553.24	+	1128.50i	1.89651	+	1.37790i
$820$	−61.6581	−	197.819i	−0.0751928	−	0.241242i
$821$	−628.739	−	204.290i	−0.765820	−	0.248830i	−0.100046	−	0.994983i	$-0.531899\pi$
$821$	−628.739	−	204.290i	−0.765820	−	0.248830i	−0.665775	+	0.746153i	$0.731899\pi$
$822$	710.521	+	55.2257i	0.864380	+	0.0671845i
$823$	183.754	−	1160.18i	0.223274	−	1.40969i	−0.580258	−	0.814433i	$-0.697048\pi$
$823$	183.754	−	1160.18i	0.223274	−	1.40969i	0.803532	−	0.595262i	$-0.202952\pi$
$824$	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	−0.381179	−	0.924501i	$-0.624482\pi$
$827$	220.834	−	1394.29i	0.267030	−	1.68596i	0.648209	−	0.761462i	$-0.275518\pi$
$828$	1300.91	−	425.483i	1.57115	−	0.513869i
$829$	346.209	+	112.490i	0.417622	+	0.135694i	0.510288	−	0.860004i	$-0.329539\pi$
$829$	346.209	+	112.490i	0.417622	+	0.135694i	−0.0926657	+	0.995697i	$0.529539\pi$
$830$	1047.10	+	96.1018i	1.26157	+	0.115785i
$831$	−190.136	−	138.142i	−0.228803	−	0.166235i
$832$	−1509.43	−	480.747i	−1.81422	−	0.577821i
$833$	72.0975	+	36.7355i	0.0865516	+	0.0441002i
$834$	406.907	+	248.810i	0.487898	+	0.298334i
$835$	−909.817	−	680.617i	−1.08960	−	0.815110i
$836$	−430.162	−	252.873i	−0.514548	−	0.302480i
$837$	−125.997	+	125.997i	−0.150534	+	0.150534i
$838$	−607.851	+	146.556i	−0.725359	+	0.174888i
$839$	206.240	+	634.743i	0.245817	+	0.756547i	0.995501	+	0.0947510i	$0.0302055\pi$
$839$	206.240	+	634.743i	0.245817	+	0.756547i	−0.749684	+	0.661796i	$0.769795\pi$
$840$	−1182.07	+	270.020i	−1.40723	+	0.321453i
$841$	−147.130	−	106.896i	−0.174946	−	0.127106i
$842$	−109.413	−	178.158i	−0.129945	−	0.211589i
$843$	−169.508	+	86.3685i	−0.201077	+	0.102454i
$844$	−503.528	+	992.987i	−0.596597	+	1.17653i
$845$	−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
$848$	−796.093	+	802.296i	−0.938789	+	0.946104i
$849$	47.9811	−	34.8603i	0.0565149	−	0.0410605i
$850$	−497.311	+	764.527i	−0.585072	+	0.899443i
$851$	428.236	+	139.142i	0.503215	+	0.163504i
$852$	222.334	−	307.269i	0.260956	−	0.360644i
$853$	1436.51	−	227.521i	1.68407	−	0.266731i	0.760272	−	0.649605i	$-0.225066\pi$
$853$	1436.51	−	227.521i	1.68407	−	0.266731i	0.923800	+	0.382875i	$0.125066\pi$
$854$	506.812	−	40.3817i	0.593457	−	0.0472854i
$855$	−591.147	+	290.887i	−0.691400	+	0.340219i
$856$	−6.85550	+	1.66698i	−0.00800876	+	0.00194740i
$857$	340.391	+	340.391i	0.397189	+	0.397189i	0.877240	−	0.480051i	$-0.159382\pi$
$857$	340.391	+	340.391i	0.397189	+	0.397189i	−0.480051	+	0.877240i	$0.659382\pi$
$858$	−2448.61	−	344.345i	−2.85386	−	0.401335i
$859$	1427.20			1.66147			0.830734	−	0.556670i	$-0.187921\pi$
$859$	1427.20			1.66147			0.830734	+	0.556670i	$0.187921\pi$
$860$	−287.775	+	280.943i	−0.334622	+	0.326677i
$861$	97.0468	+	298.679i	0.112714	+	0.346898i
$862$	−75.9331	+	89.0811i	−0.0880894	+	0.103342i
$863$	−1544.24	+	244.584i	−1.78939	+	0.283411i	−0.960961	−	0.276683i	$-0.910765\pi$
$863$	−1544.24	+	244.584i	−1.78939	+	0.283411i	−0.828428	+	0.560095i	$0.810765\pi$
$864$	−370.500	−	87.0506i	−0.428820	−	0.100753i
$865$	318.103	−	224.401i	0.367749	−	0.259424i
$866$	−404.020	+	345.744i	−0.466536	+	0.399243i
$867$	−196.117	−	31.0619i	−0.226202	−	0.0358269i
$868$	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
$872$	−1137.74	+	977.461i	−1.30475	+	1.12094i
$873$	1503.93	−	766.289i	1.72271	−	0.877766i
$874$	155.299	−	649.643i	0.177688	−	0.743298i
$875$	−461.800	−	695.020i	−0.527771	−	0.794309i
$876$	−660.805	−	1290.71i	−0.754344	−	1.47341i
$877$	−407.030	+	798.842i	−0.464117	+	0.910880i	0.533753	+	0.845640i	$0.320781\pi$
$877$	−407.030	+	798.842i	−0.464117	+	0.910880i	−0.997870	+	0.0652396i	$0.979219\pi$
$878$	62.2643	+	258.245i	0.0709160	+	0.294129i
$879$		−	315.951i		−	0.359444i
$880$	665.529	−	575.735i	0.756283	−	0.654244i
$881$	−1402.92			−1.59241			−0.796206	−	0.605025i	$-0.793163\pi$
$881$	−1402.92			−1.59241			−0.796206	+	0.605025i	$0.793163\pi$
$882$	−100.215	+	24.1623i	−0.113622	+	0.0273949i
$883$	217.848	+	110.999i	0.246713	+	0.125707i	0.572975	−	0.819573i	$-0.305789\pi$
$883$	217.848	+	110.999i	0.246713	+	0.125707i	−0.326262	+	0.945279i	$0.605789\pi$
$884$	1607.56	−	823.028i	1.81851	−	0.931027i
$885$	538.140	+	1738.39i	0.608068	+	1.96428i
$886$	8.81422	+	2.10706i	0.00994833	+	0.00237818i
$887$	−507.659	−	996.336i	−0.572332	−	1.12326i	−0.977875	−	0.209189i	$-0.932918\pi$
$887$	−507.659	−	996.336i	−0.572332	−	1.12326i	0.405543	−	0.914076i	$-0.367082\pi$
$888$	−361.946	−	421.296i	−0.407597	−	0.474432i
$889$	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
$893$	31.6689	−	199.950i	0.0354635	−	0.223908i
$894$	108.088	+	126.306i	0.120904	+	0.141282i
$895$	823.863	+	142.298i	0.920517	+	0.158992i
$896$	−725.515	+	451.402i	−0.809727	+	0.503797i
$897$	−517.798	−	3269.25i	−0.577255	−	3.64464i
$898$	−342.092	−	291.601i	−0.380949	−	0.324722i
$899$	−455.705	+	148.067i	−0.506902	+	0.164702i
$900$	−151.908	−	1151.95i	−0.168787	−	1.27994i
$901$		−	1288.53i		−	1.43011i
$902$	−163.942	−	158.345i	−0.181754	−	0.175548i
$903$	431.018	−	431.018i	0.477318	−	0.477318i
$904$	−81.1295	−	333.648i	−0.0897450	−	0.369079i
$905$	−1354.96	+	666.740i	−1.49719	+	0.736729i
$906$	−147.328	−	1849.04i	−0.162613	−	2.04088i
$907$	−138.930	−	877.167i	−0.153175	−	0.967109i	−0.937810	−	0.347150i	$-0.887149\pi$
$907$	−138.930	−	877.167i	−0.153175	−	0.967109i	0.784635	−	0.619958i	$-0.212851\pi$
$908$	367.445	+	265.877i	0.404675	+	0.292816i
$909$	446.245	−	1373.40i	0.490919	−	1.51089i
$910$	108.246	+	1648.81i	0.118952	+	1.81188i
$911$	−900.848	−	1239.91i	−0.988856	−	1.36104i	−0.931919	−	0.362666i	$-0.881867\pi$
$911$	−900.848	−	1239.91i	−0.988856	−	1.36104i	−0.0569372	−	0.998378i	$-0.518133\pi$
$912$	−580.340	+	584.862i	−0.636338	+	0.641296i
$913$	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
$916$	420.465	+	213.211i	0.459023	+	0.232763i
$917$	−486.850	−	955.497i	−0.530916	−	1.04198i
$918$	369.733	−	227.066i	0.402759	−	0.247349i
$919$	282.703	−	389.108i	0.307621	−	0.423403i	−0.627017	−	0.779006i	$-0.715724\pi$
$919$	282.703	−	389.108i	0.307621	−	0.423403i	0.934637	+	0.355602i	$0.115724\pi$
$920$	997.537	+	626.547i	1.08428	+	0.681029i
$921$	83.9950	−	27.2916i	0.0911998	−	0.0296326i
$922$	415.396	+	1722.88i	0.450538	+	1.86864i
$923$	−365.470	−	365.470i	−0.395959	−	0.395959i
$924$	−998.153	+	884.665i	−1.08025	+	0.957429i
$925$	182.969	−	335.605i	0.197805	−	0.362817i
$926$	628.018	−	1027.07i	0.678206	−	1.10915i
$927$	37.4400	−	73.4801i	0.0403883	−	0.0792666i
$928$	−781.438	−	660.882i	−0.842067	−	0.712158i
$929$	287.224	−	395.330i	0.309175	−	0.425543i	−0.625949	−	0.779864i	$-0.715288\pi$
$929$	287.224	−	395.330i	0.309175	−	0.425543i	0.935124	+	0.354321i	$0.115288\pi$
$930$	−677.459	−	62.1765i	−0.728451	−	0.0668565i
$931$	−15.5457	+	47.8447i	−0.0166978	+	0.0513907i
$932$	−368.816	−	1127.65i	−0.395726	−	1.20993i
$933$	−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	−0.694818	−	0.719186i	$-0.744515\pi$
$937$	−1478.46	−	234.166i	−1.57787	−	0.249910i	−0.883051	+	0.469276i	$0.844515\pi$
$938$	−22.3893	+	288.056i	−0.0238692	+	0.307095i
$939$	−62.4822	+	192.300i	−0.0665412	+	0.204793i
$940$	316.140	+	165.895i	0.336320	+	0.176484i
$941$	−481.598	+	662.863i	−0.511794	+	0.704425i	−0.984221	−	0.176946i	$-0.943378\pi$
$941$	−481.598	+	662.863i	−0.511794	+	0.704425i	0.472426	+	0.881370i	$0.343378\pi$
$942$	−132.964	−	113.339i	−0.141151	−	0.120318i
$943$	138.515	−	271.851i	0.146887	−	0.288283i
$944$	757.812	+	1034.57i	0.802767	+	1.09595i
$945$	56.6246	+	392.921i	0.0599202	+	0.415789i
$946$	−129.379	+	423.049i	−0.136764	+	0.447197i
$947$	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	$0.325700\pi$
$948$	−1060.83	−	1454.17i	−1.11902	−	1.53393i
$949$	−1879.32	+	610.627i	−1.98031	+	0.643443i
$950$	−517.830	−	231.022i	−0.545084	−	0.243181i
$951$	−31.1281	+	42.8442i	−0.0327320	+	0.0450517i
$952$	224.653	−	947.894i	0.235980	−	0.995687i
$953$	−212.877	−	417.794i	−0.223375	−	0.438398i	0.751935	−	0.659237i	$-0.229121\pi$
$953$	−212.877	−	417.794i	−0.223375	−	0.438398i	−0.975310	+	0.220839i	$0.929121\pi$
$954$	1067.32	+	1247.22i	1.11878	+	1.30736i
$955$	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
$958$	539.013	−	1304.87i	0.562644	−	1.36208i
$959$	−307.914	−	423.807i	−0.321078	−	0.441926i
$960$	−649.129	−	1300.01i	−0.676176	−	1.35418i
$961$	227.604	−	700.492i	0.236840	−	0.728920i
$962$	−644.983	+	396.107i	−0.670461	+	0.411754i
$963$	1.60299	+	10.1209i	0.00166458	+	0.0105098i
$964$	240.776	+	470.291i	0.249768	+	0.487854i
$965$	110.927	−	325.857i	0.114951	−	0.337676i
$966$	−1523.21	−	931.394i	−1.57682	−	0.964176i
$967$	−1024.95	+	1024.95i	−1.05993	+	1.05993i	−0.0618415	+	0.998086i	$0.519697\pi$
$967$	−1024.95	+	1024.95i	−1.05993	+	1.05993i	−0.998086	+	0.0618415i	$0.980303\pi$
$968$	338.278	−	906.969i	0.349460	−	0.936951i
$969$		−	939.321i		−	0.969372i
$970$	1334.77	+	573.293i	1.37605	+	0.591023i
$971$	478.302	−	155.410i	0.492587	−	0.160051i	−0.0521818	−	0.998638i	$-0.516618\pi$
$971$	478.302	−	155.410i	0.492587	−	0.160051i	0.544768	+	0.838586i	$0.316618\pi$
$972$	413.645	−	1281.52i	0.425560	−	1.31844i
$973$	−54.8441	−	346.272i	−0.0563660	−	0.355881i
$974$	−161.241	+	674.497i	−0.165545	+	0.692502i
$975$	−2808.79	−	78.4022i	−2.88081	−	0.0804125i
$976$	190.526	+	578.728i	0.195211	+	0.592959i
$977$	−172.132	+	1086.80i	−0.176184	+	1.11238i	0.728107	+	0.685463i	$0.240400\pi$
$977$	−172.132	+	1086.80i	−0.176184	+	1.11238i	−0.904291	+	0.426917i	$0.859600\pi$
$978$	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
$982$	−62.9114	+	809.403i	−0.0640645	+	0.824240i
$983$	538.862	+	1057.58i	0.548181	+	1.07587i	0.984387	+	0.176019i	$0.0563220\pi$
$983$	538.862	+	1057.58i	0.548181	+	1.07587i	−0.436206	+	0.899847i	$0.643678\pi$
$984$	−320.321	+	197.578i	−0.325529	+	0.200790i
$985$	−454.103	+	140.573i	−0.461018	+	0.142714i
$986$	1163.08	−	92.6717i	1.17959	−	0.0939875i
$987$	−482.143	−	245.664i	−0.488493	−	0.248900i
$988$	661.733	+	907.090i	0.669770	+	0.918108i
$989$	−592.190			−0.598777
$990$	−754.782	−	1031.44i	−0.762406	−	1.04186i
$991$		−	388.087i		−	0.391612i	−0.980643	−	0.195806i	$-0.937268\pi$
$991$		−	388.087i		−	0.391612i	0.980643	−	0.195806i	$-0.0627322\pi$
$992$	−465.628	+	114.179i	−0.469383	+	0.115100i
$993$	−802.714	+	1575.42i	−0.808373	+	1.58652i
$994$	−277.908	+	22.1432i	−0.279586	+	0.0222768i
$995$	132.860	−	251.998i	0.133528	−	0.253264i
$996$	−302.430	−	1885.78i	−0.303645	−	1.89335i
$997$	1455.78	−	741.756i	1.46016	−	0.743988i	0.469834	−	0.882755i	$-0.344314\pi$
$997$	1455.78	−	741.756i	1.46016	−	0.743988i	0.990325	+	0.138767i	$0.0443139\pi$
$998$	116.679	−	1501.17i	0.116913	−	1.50418i
$999$	−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.63.6	yes	544
4.3	odd	2	inner	220.3.w.a.63.13	yes	544
5.2	odd	4	inner	220.3.w.a.107.29	yes	544
11.7	odd	10	inner	220.3.w.a.183.45	yes	544
20.7	even	4	inner	220.3.w.a.107.45	yes	544
44.7	even	10	inner	220.3.w.a.183.29	yes	544
55.7	even	20	inner	220.3.w.a.7.13	yes	544
220.7	odd	20	inner	220.3.w.a.7.6	✓	544

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.w.a.7.6	✓	544	220.7	odd	20	inner
220.3.w.a.7.13	yes	544	55.7	even	20	inner
220.3.w.a.63.6	yes	544	1.1	even	1	trivial
220.3.w.a.63.13	yes	544	4.3	odd	2	inner
220.3.w.a.107.29	yes	544	5.2	odd	4	inner
220.3.w.a.107.45	yes	544	20.7	even	4	inner
220.3.w.a.183.29	yes	544	44.7	even	10	inner
220.3.w.a.183.45	yes	544	11.7	odd	10	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+(-1.94429 + 0.468777i) q^{2} +(4.04592 + 2.06150i) q^{3} +(3.56050 - 1.82287i) q^{4} +(2.33189 - 4.42293i) q^{5} +(-8.83280 - 2.11151i) q^{6} +(3.03067 + 5.94803i) q^{7} +(-6.06810 + 5.21327i) 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} +(3.87209 - 24.4474i) q^{13} +(-8.68079 - 10.1440i) q^{14} +(18.5525 - 13.0876i) q^{15} +(9.35426 - 12.9807i) q^{16} +(2.85350 + 18.0163i) q^{17} +(-17.6853 - 15.0750i) q^{18} +(-10.7855 + 3.50442i) q^{19} +(0.240247 - 19.9986i) q^{20} +30.3129i q^{21} +(-10.3267 - 19.4257i) q^{22} +(20.8240 - 20.8240i) q^{23} +(-35.2982 + 8.58307i) q^{24} +(-14.1246 - 20.6276i) q^{25} +(3.93194 + 49.3479i) q^{26} +(1.86054 + 11.7470i) q^{27} +(21.6332 + 15.6534i) q^{28} +(-9.88305 + 30.4169i) q^{29} +(-29.9362 + 34.1430i) q^{30} +(8.80617 + 12.1207i) q^{31} +(-12.1023 + 29.6232i) q^{32} +(-10.8625 + 48.7538i) q^{33} +(-13.9936 - 33.6911i) q^{34} +(33.3749 + 0.465708i) q^{35} +(41.4520 + 21.0197i) q^{36} +(6.94136 + 13.6232i) q^{37} +(19.3273 - 11.8696i) q^{38} +(66.0644 - 90.9299i) q^{39} +(8.90776 + 38.9955i) q^{40} +(9.85319 - 3.20150i) q^{41} +(-14.2100 - 58.9370i) q^{42} +(-14.2190 - 14.2190i) q^{43} +(29.1844 + 32.9283i) q^{44} +(57.5020 - 8.28674i) q^{45} +(-30.7260 + 50.2496i) q^{46} +(-8.10427 + 15.9055i) q^{47} +(64.6062 - 33.2349i) q^{48} +(2.60743 - 3.58882i) q^{49} +(37.1319 + 33.4846i) q^{50} +(-25.5955 + 78.7748i) q^{51} +(-30.7780 - 94.1033i) 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} +(4.95673 - 63.7721i) q^{58} +(-24.7682 + 76.2288i) q^{59} +(42.1990 - 80.4172i) q^{60} +(-22.3830 + 30.8075i) q^{61} +(-22.8036 - 19.4379i) q^{62} +(-35.2140 + 69.1114i) q^{63} +(9.64368 - 63.2693i) q^{64} +(-99.0999 - 74.1347i) q^{65} +(-1.73484 - 99.8834i) q^{66} +(-15.3020 - 15.3020i) q^{67} +(43.0012 + 58.9453i) q^{68} +(127.181 - 41.3235i) q^{69} +(-65.1086 + 14.7399i) q^{70} +(12.2736 - 16.8932i) q^{71} +(-90.4481 - 21.4365i) q^{72} +(-36.2433 - 71.1314i) q^{73} +(-19.8822 - 23.2334i) q^{74} +(-14.6232 - 112.575i) q^{75} +(-32.0136 + 32.1380i) q^{76} +(-55.0486 + 48.5993i) q^{77} +(-85.8223 + 207.763i) q^{78} +(-58.2496 - 80.1738i) q^{79} +(-35.5995 - 71.6427i) q^{80} +(15.6260 - 48.0919i) q^{81} +(-17.6566 + 10.8436i) q^{82} +(-16.4491 - 103.856i) q^{83} +(55.2567 + 107.929i) q^{84} +(86.3386 + 29.3911i) q^{85} +(34.3112 + 20.9802i) q^{86} +(-102.690 + 102.690i) q^{87} +(-72.1788 - 50.3410i) q^{88} +69.0839i q^{89} +(-107.916 + 43.0674i) q^{90} +(157.149 - 51.0608i) q^{91} +(36.1842 - 112.103i) q^{92} +(10.6423 + 67.1931i) q^{93} +(8.30087 - 34.7240i) q^{94} +(-9.65079 + 55.8753i) q^{95} +(-110.033 + 94.9041i) q^{96} +(22.7249 - 143.479i) 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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